id	sid	tid	token	lemma	pos
ejde-515	1	1	electronic	electronic	ADJ
ejde-515	1	2	journal	journal	NOUN
ejde-515	1	3	of	of	ADP
ejde-515	1	4	differential	differential	ADJ
ejde-515	1	5	equations	equation	NOUN
ejde-515	1	6	,	,	PUNCT
ejde-515	1	7	vol	vol	NOUN
ejde-515	1	8	.	.	PUNCT
ejde-515	1	9	2020	2020	NUM
ejde-515	1	10	(	(	PUNCT
ejde-515	1	11	2020	2020	NUM
ejde-515	1	12	)	)	PUNCT
ejde-515	1	13	,	,	PUNCT
ejde-515	1	14	no	no	INTJ
ejde-515	1	15	.	.	NOUN
ejde-515	1	16	92	92	NUM
ejde-515	1	17	,	,	PUNCT
ejde-515	1	18	pp	pp	ADJ
ejde-515	1	19	.	.	PUNCT
ejde-515	2	1	1–16	1–16	PROPN
ejde-515	2	2	.	.	PUNCT
ejde-515	3	1	issn	issn	PROPN
ejde-515	3	2	:	:	PUNCT
ejde-515	3	3	1072	1072	NUM
ejde-515	3	4	-	-	SYM
ejde-515	3	5	6691	6691	NUM
ejde-515	3	6	.	.	PUNCT
ejde-515	4	1	url	url	PROPN
ejde-515	4	2	:	:	PUNCT
ejde-515	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-515	4	4	or	or	CCONJ
ejde-515	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-515	4	6	asymptotic	asymptotic	ADJ
ejde-515	4	7	behavior	behavior	NOUN
ejde-515	4	8	for	for	ADP
ejde-515	4	9	a	a	DET
ejde-515	4	10	non	non	ADJ
ejde-515	4	11	-	-	ADJ
ejde-515	4	12	autonomous	autonomous	ADJ
ejde-515	4	13	model	model	NOUN
ejde-515	4	14	of	of	ADP
ejde-515	4	15	neural	neural	ADJ
ejde-515	4	16	fields	field	NOUN
ejde-515	4	17	with	with	ADP
ejde-515	4	18	variable	variable	ADJ
ejde-515	4	19	external	external	ADJ
ejde-515	4	20	stimuli	stimuli	VERB
ejde-515	4	21	severino	severino	PROPN
ejde-515	4	22	horácio	horácio	PROPN
ejde-515	4	23	da	da	PROPN
ejde-515	4	24	silva	silva	PROPN
ejde-515	4	25	abstract	abstract	NOUN
ejde-515	4	26	.	.	PUNCT
ejde-515	5	1	in	in	ADP
ejde-515	5	2	this	this	DET
ejde-515	5	3	work	work	NOUN
ejde-515	5	4	we	we	PRON
ejde-515	5	5	consider	consider	VERB
ejde-515	5	6	the	the	DET
ejde-515	5	7	class	class	NOUN
ejde-515	5	8	of	of	ADP
ejde-515	5	9	nonlocal	nonlocal	ADJ
ejde-515	5	10	non	non	ADJ
ejde-515	5	11	-	-	ADJ
ejde-515	5	12	autonomous	autonomous	ADJ
ejde-515	5	13	evolution	evolution	NOUN
ejde-515	5	14	problems	problem	NOUN
ejde-515	5	15	in	in	ADP
ejde-515	5	16	a	a	DET
ejde-515	5	17	bounded	bounded	ADJ
ejde-515	5	18	smooth	smooth	ADJ
ejde-515	5	19	domain	domain	NOUN
ejde-515	5	20	ω	ω	PROPN
ejde-515	5	21	in	in	ADP
ejde-515	5	22	rn	rn	PROPN
ejde-515	5	23	∂tu(t	∂tu(t	PROPN
ejde-515	5	24	,	,	PUNCT
ejde-515	5	25	x	x	X
ejde-515	5	26	)	)	PUNCT
ejde-515	5	27	=	=	SYM
ejde-515	5	28	−a(t)u(t	−a(t)u(t	NOUN
ejde-515	5	29	,	,	PUNCT
ejde-515	5	30	x	x	X
ejde-515	5	31	)	)	PUNCT
ejde-515	5	32	+	+	NUM
ejde-515	5	33	b(t	b(t	NOUN
ejde-515	5	34	)	)	PUNCT
ejde-515	5	35	∫	∫	PROPN
ejde-515	5	36	rn	rn	PROPN
ejde-515	5	37	j(x	j(x	PROPN
ejde-515	5	38	,	,	PUNCT
ejde-515	5	39	y)f(t	y)f(t	NOUN
ejde-515	5	40	,	,	PUNCT
ejde-515	5	41	u(t	u(t	NOUN
ejde-515	5	42	,	,	PUNCT
ejde-515	5	43	y	y	NOUN
ejde-515	5	44	)	)	PUNCT
ejde-515	5	45	)	)	PUNCT
ejde-515	6	1	dy	dy	NOUN
ejde-515	6	2	−	−	PROPN
ejde-515	6	3	h+	h+	X
ejde-515	6	4	s(t	s(t	PROPN
ejde-515	6	5	,	,	PUNCT
ejde-515	6	6	x	x	NOUN
ejde-515	6	7	)	)	PUNCT
ejde-515	6	8	,	,	PUNCT
ejde-515	6	9	t	t	PROPN
ejde-515	6	10	≥	≥	PROPN
ejde-515	6	11	τ	τ	X
ejde-515	6	12	u(τ	u(τ	PROPN
ejde-515	6	13	,	,	PUNCT
ejde-515	6	14	x	x	X
ejde-515	6	15	)	)	PUNCT
ejde-515	6	16	=	=	SYM
ejde-515	6	17	uτ	uτ	PROPN
ejde-515	6	18	(	(	PUNCT
ejde-515	6	19	x	x	NOUN
ejde-515	6	20	)	)	PUNCT
ejde-515	6	21	,	,	PUNCT
ejde-515	6	22	with	with	ADP
ejde-515	6	23	u(t	u(t	NOUN
ejde-515	6	24	,	,	PUNCT
ejde-515	6	25	x	x	NOUN
ejde-515	6	26	)	)	PUNCT
ejde-515	6	27	=	=	SYM
ejde-515	6	28	0	0	NUM
ejde-515	7	1	for	for	ADP
ejde-515	7	2	t	t	PROPN
ejde-515	7	3	≥	≥	PROPN
ejde-515	7	4	τ	τ	PROPN
ejde-515	7	5	and	and	CCONJ
ejde-515	7	6	x	x	PROPN
ejde-515	7	7	∈	∈	PROPN
ejde-515	7	8	rn\ω	rn\ω	NOUN
ejde-515	7	9	.	.	PUNCT
ejde-515	8	1	under	under	ADP
ejde-515	8	2	appropriate	appropriate	ADJ
ejde-515	8	3	assumptions	assumption	NOUN
ejde-515	8	4	we	we	PRON
ejde-515	8	5	study	study	VERB
ejde-515	8	6	the	the	DET
ejde-515	8	7	asymptotic	asymptotic	ADJ
ejde-515	8	8	behavior	behavior	NOUN
ejde-515	8	9	of	of	ADP
ejde-515	8	10	the	the	DET
ejde-515	8	11	evolution	evolution	NOUN
ejde-515	8	12	process	process	NOUN
ejde-515	8	13	,	,	PUNCT
ejde-515	8	14	generated	generate	VERB
ejde-515	8	15	by	by	ADP
ejde-515	8	16	this	this	DET
ejde-515	8	17	problem	problem	NOUN
ejde-515	8	18	in	in	ADP
ejde-515	8	19	a	a	DET
ejde-515	8	20	suitable	suitable	ADJ
ejde-515	8	21	banach	banach	NOUN
ejde-515	8	22	space	space	NOUN
ejde-515	8	23	.	.	PUNCT
ejde-515	9	1	we	we	PRON
ejde-515	9	2	prove	prove	VERB
ejde-515	9	3	results	result	NOUN
ejde-515	9	4	on	on	ADP
ejde-515	9	5	existence	existence	NOUN
ejde-515	9	6	,	,	PUNCT
ejde-515	9	7	uniqueness	uniqueness	NOUN
ejde-515	9	8	and	and	CCONJ
ejde-515	9	9	smoothness	smoothness	NOUN
ejde-515	9	10	of	of	ADP
ejde-515	9	11	the	the	DET
ejde-515	9	12	solutions	solution	NOUN
ejde-515	9	13	and	and	CCONJ
ejde-515	9	14	on	on	ADP
ejde-515	9	15	the	the	DET
ejde-515	9	16	existence	existence	NOUN
ejde-515	9	17	of	of	ADP
ejde-515	9	18	pullback	pullback	NOUN
ejde-515	9	19	attractor	attractor	NOUN
ejde-515	9	20	for	for	ADP
ejde-515	9	21	the	the	DET
ejde-515	9	22	evolution	evolution	NOUN
ejde-515	9	23	process	process	NOUN
ejde-515	9	24	.	.	PUNCT
ejde-515	10	1	we	we	PRON
ejde-515	10	2	also	also	ADV
ejde-515	10	3	prove	prove	VERB
ejde-515	10	4	a	a	DET
ejde-515	10	5	continuous	continuous	ADJ
ejde-515	10	6	dependence	dependence	NOUN
ejde-515	10	7	of	of	ADP
ejde-515	10	8	the	the	DET
ejde-515	10	9	evolution	evolution	NOUN
ejde-515	10	10	process	process	NOUN
ejde-515	10	11	with	with	ADP
ejde-515	10	12	respect	respect	NOUN
ejde-515	10	13	to	to	ADP
ejde-515	10	14	the	the	DET
ejde-515	10	15	external	external	ADJ
ejde-515	10	16	stimuli	stimulus	NOUN
ejde-515	10	17	function	function	NOUN
ejde-515	10	18	present	present	ADJ
ejde-515	10	19	in	in	ADP
ejde-515	10	20	the	the	DET
ejde-515	10	21	model	model	NOUN
ejde-515	10	22	.	.	PUNCT
ejde-515	11	1	furthermore	furthermore	ADV
ejde-515	11	2	,	,	PUNCT
ejde-515	11	3	using	use	VERB
ejde-515	11	4	the	the	DET
ejde-515	11	5	continuous	continuous	ADJ
ejde-515	11	6	dependence	dependence	NOUN
ejde-515	11	7	of	of	ADP
ejde-515	11	8	the	the	DET
ejde-515	11	9	evolution	evolution	NOUN
ejde-515	11	10	process	process	NOUN
ejde-515	11	11	,	,	PUNCT
ejde-515	11	12	we	we	PRON
ejde-515	11	13	prove	prove	VERB
ejde-515	11	14	the	the	DET
ejde-515	11	15	upper	upper	ADJ
ejde-515	11	16	semicontinuity	semicontinuity	NOUN
ejde-515	11	17	of	of	ADP
ejde-515	11	18	pullback	pullback	NOUN
ejde-515	11	19	attractors	attractor	NOUN
ejde-515	11	20	with	with	ADP
ejde-515	11	21	respect	respect	NOUN
ejde-515	11	22	to	to	ADP
ejde-515	11	23	the	the	DET
ejde-515	11	24	external	external	ADJ
ejde-515	11	25	stimuli	stimulus	NOUN
ejde-515	11	26	function	function	NOUN
ejde-515	11	27	.	.	PUNCT
ejde-515	12	1	we	we	PRON
ejde-515	12	2	finish	finish	VERB
ejde-515	12	3	this	this	DET
ejde-515	12	4	article	article	NOUN
ejde-515	12	5	with	with	ADP
ejde-515	12	6	a	a	DET
ejde-515	12	7	small	small	ADJ
ejde-515	12	8	discussion	discussion	NOUN
ejde-515	12	9	about	about	ADP
ejde-515	12	10	the	the	DET
ejde-515	12	11	model	model	NOUN
ejde-515	12	12	and	and	CCONJ
ejde-515	12	13	about	about	ADP
ejde-515	12	14	a	a	DET
ejde-515	12	15	biological	biological	ADJ
ejde-515	12	16	interpretation	interpretation	NOUN
ejde-515	12	17	of	of	ADP
ejde-515	12	18	the	the	DET
ejde-515	12	19	result	result	NOUN
ejde-515	12	20	on	on	ADP
ejde-515	12	21	the	the	DET
ejde-515	12	22	continuous	continuous	ADJ
ejde-515	12	23	dependence	dependence	NOUN
ejde-515	12	24	of	of	ADP
ejde-515	12	25	neuronal	neuronal	ADJ
ejde-515	12	26	activity	activity	NOUN
ejde-515	12	27	with	with	ADP
ejde-515	12	28	respect	respect	NOUN
ejde-515	12	29	to	to	ADP
ejde-515	12	30	the	the	DET
ejde-515	12	31	external	external	ADJ
ejde-515	12	32	stimuli	stimulus	NOUN
ejde-515	12	33	function	function	NOUN
ejde-515	12	34	.	.	PUNCT
ejde-515	13	1	1	1	X
ejde-515	13	2	.	.	X
ejde-515	13	3	introduction	introduction	NOUN
ejde-515	13	4	neural	neural	ADJ
ejde-515	13	5	field	field	NOUN
ejde-515	13	6	equations	equation	NOUN
ejde-515	13	7	describe	describe	VERB
ejde-515	13	8	the	the	DET
ejde-515	13	9	spatio	spatio	PROPN
ejde-515	13	10	-	-	PUNCT
ejde-515	13	11	temporal	temporal	ADJ
ejde-515	13	12	evolution	evolution	NOUN
ejde-515	13	13	of	of	ADP
ejde-515	13	14	variables	variable	NOUN
ejde-515	13	15	such	such	ADJ
ejde-515	13	16	as	as	ADP
ejde-515	13	17	synaptic	synaptic	ADJ
ejde-515	13	18	or	or	CCONJ
ejde-515	13	19	firing	firing	NOUN
ejde-515	13	20	rate	rate	NOUN
ejde-515	13	21	activity	activity	NOUN
ejde-515	13	22	in	in	ADP
ejde-515	13	23	populations	population	NOUN
ejde-515	13	24	of	of	ADP
ejde-515	13	25	neurons	neuron	NOUN
ejde-515	13	26	.	.	PUNCT
ejde-515	14	1	the	the	DET
ejde-515	14	2	neural	neural	ADJ
ejde-515	14	3	field	field	NOUN
ejde-515	14	4	model	model	NOUN
ejde-515	14	5	has	have	AUX
ejde-515	14	6	already	already	ADV
ejde-515	14	7	been	be	AUX
ejde-515	14	8	well	well	ADV
ejde-515	14	9	analyzed	analyze	VERB
ejde-515	14	10	in	in	ADP
ejde-515	14	11	the	the	DET
ejde-515	14	12	literature	literature	NOUN
ejde-515	14	13	(	(	PUNCT
ejde-515	14	14	see	see	VERB
ejde-515	14	15	[	[	X
ejde-515	14	16	1	1	NUM
ejde-515	14	17	,	,	PUNCT
ejde-515	14	18	4	4	NUM
ejde-515	14	19	,	,	PUNCT
ejde-515	14	20	5	5	NUM
ejde-515	14	21	,	,	PUNCT
ejde-515	14	22	7	7	NUM
ejde-515	14	23	,	,	PUNCT
ejde-515	14	24	11	11	NUM
ejde-515	14	25	,	,	PUNCT
ejde-515	14	26	13	13	NUM
ejde-515	14	27	,	,	PUNCT
ejde-515	14	28	14	14	NUM
ejde-515	14	29	,	,	PUNCT
ejde-515	14	30	15	15	NUM
ejde-515	14	31	,	,	PUNCT
ejde-515	14	32	16	16	NUM
ejde-515	14	33	,	,	PUNCT
ejde-515	14	34	21	21	NUM
ejde-515	14	35	,	,	PUNCT
ejde-515	14	36	25	25	NUM
ejde-515	14	37	,	,	PUNCT
ejde-515	14	38	26	26	NUM
ejde-515	14	39	,	,	PUNCT
ejde-515	14	40	28	28	NUM
ejde-515	14	41	,	,	PUNCT
ejde-515	14	42	33	33	NUM
ejde-515	14	43	,	,	PUNCT
ejde-515	14	44	32	32	NUM
ejde-515	14	45	]	]	PUNCT
ejde-515	14	46	)	)	PUNCT
ejde-515	14	47	.	.	PUNCT
ejde-515	15	1	although	although	SCONJ
ejde-515	15	2	this	this	DET
ejde-515	15	3	model	model	NOUN
ejde-515	15	4	has	have	AUX
ejde-515	15	5	been	be	AUX
ejde-515	15	6	used	use	VERB
ejde-515	15	7	to	to	ADP
ejde-515	15	8	working	work	VERB
ejde-515	15	9	memory	memory	NOUN
ejde-515	15	10	model	model	NOUN
ejde-515	15	11	,	,	PUNCT
ejde-515	15	12	it	it	PRON
ejde-515	15	13	arises	arise	VERB
ejde-515	15	14	also	also	ADV
ejde-515	15	15	in	in	ADP
ejde-515	15	16	cognitive	cognitive	ADJ
ejde-515	15	17	development	development	NOUN
ejde-515	15	18	of	of	ADP
ejde-515	15	19	infants	infant	NOUN
ejde-515	15	20	,	,	PUNCT
ejde-515	15	21	(	(	PUNCT
ejde-515	15	22	see	see	VERB
ejde-515	15	23	[	[	X
ejde-515	15	24	29	29	NUM
ejde-515	15	25	,	,	PUNCT
ejde-515	15	26	31	31	NUM
ejde-515	15	27	]	]	PUNCT
ejde-515	15	28	)	)	PUNCT
ejde-515	15	29	,	,	PUNCT
ejde-515	15	30	and	and	CCONJ
ejde-515	15	31	in	in	ADP
ejde-515	15	32	timing	time	VERB
ejde-515	15	33	sensory	sensory	ADJ
ejde-515	15	34	integration	integration	NOUN
ejde-515	15	35	for	for	ADP
ejde-515	15	36	robot	robot	NOUN
ejde-515	15	37	simulation	simulation	NOUN
ejde-515	15	38	of	of	ADP
ejde-515	15	39	autistic	autistic	ADJ
ejde-515	15	40	behavior	behavior	NOUN
ejde-515	15	41	(	(	PUNCT
ejde-515	15	42	see	see	VERB
ejde-515	15	43	[	[	X
ejde-515	15	44	3	3	NUM
ejde-515	15	45	]	]	NUM
ejde-515	15	46	)	)	PUNCT
ejde-515	15	47	.	.	PUNCT
ejde-515	16	1	as	as	SCONJ
ejde-515	16	2	in	in	ADP
ejde-515	16	3	[	[	X
ejde-515	16	4	1	1	NUM
ejde-515	16	5	]	]	PUNCT
ejde-515	16	6	,	,	PUNCT
ejde-515	16	7	we	we	PRON
ejde-515	16	8	will	will	AUX
ejde-515	16	9	denote	denote	VERB
ejde-515	16	10	by	by	ADP
ejde-515	16	11	u(t	u(t	NOUN
ejde-515	16	12	,	,	PUNCT
ejde-515	16	13	x	x	X
ejde-515	16	14	)	)	PUNCT
ejde-515	16	15	the	the	DET
ejde-515	16	16	membrane	membrane	NOUN
ejde-515	16	17	potential	potential	NOUN
ejde-515	16	18	of	of	ADP
ejde-515	16	19	a	a	DET
ejde-515	16	20	neuron	neuron	NOUN
ejde-515	16	21	located	locate	VERB
ejde-515	16	22	at	at	ADP
ejde-515	16	23	position	position	NOUN
ejde-515	16	24	x	x	ADP
ejde-515	16	25	,	,	PUNCT
ejde-515	16	26	and	and	CCONJ
ejde-515	16	27	time	time	NOUN
ejde-515	16	28	t	t	PROPN
ejde-515	16	29	,	,	PUNCT
ejde-515	16	30	which	which	PRON
ejde-515	16	31	we	we	PRON
ejde-515	16	32	are	be	AUX
ejde-515	16	33	assuming	assume	VERB
ejde-515	16	34	as	as	ADP
ejde-515	16	35	a	a	DET
ejde-515	16	36	differentiable	differentiable	ADJ
ejde-515	16	37	function	function	NOUN
ejde-515	16	38	of	of	ADP
ejde-515	16	39	t	t	PROPN
ejde-515	16	40	,	,	PUNCT
ejde-515	16	41	and	and	CCONJ
ejde-515	16	42	j(x	j(x	PROPN
ejde-515	16	43	,	,	PUNCT
ejde-515	16	44	y	y	PROPN
ejde-515	16	45	)	)	PUNCT
ejde-515	16	46	will	will	AUX
ejde-515	16	47	denote	denote	VERB
ejde-515	16	48	the	the	DET
ejde-515	16	49	average	average	ADJ
ejde-515	16	50	intensity	intensity	NOUN
ejde-515	16	51	of	of	ADP
ejde-515	16	52	connections	connection	NOUN
ejde-515	16	53	from	from	ADP
ejde-515	16	54	neurons	neuron	NOUN
ejde-515	16	55	located	locate	VERB
ejde-515	16	56	at	at	ADP
ejde-515	16	57	place	place	NOUN
ejde-515	16	58	y	y	PROPN
ejde-515	16	59	to	to	ADP
ejde-515	16	60	those	those	PRON
ejde-515	16	61	at	at	ADP
ejde-515	16	62	place	place	NOUN
ejde-515	16	63	x.	x.	NOUN
ejde-515	17	1	we	we	PRON
ejde-515	17	2	also	also	ADV
ejde-515	17	3	assume	assume	VERB
ejde-515	17	4	that	that	SCONJ
ejde-515	17	5	the	the	DET
ejde-515	17	6	pulse	pulse	NOUN
ejde-515	17	7	emission	emission	NOUN
ejde-515	17	8	rate	rate	NOUN
ejde-515	17	9	of	of	ADP
ejde-515	17	10	neurons	neuron	NOUN
ejde-515	17	11	at	at	ADP
ejde-515	17	12	position	position	NOUN
ejde-515	17	13	x	x	ADP
ejde-515	17	14	,	,	PUNCT
ejde-515	17	15	and	and	CCONJ
ejde-515	17	16	time	time	NOUN
ejde-515	17	17	t	t	PROPN
ejde-515	17	18	,	,	PUNCT
ejde-515	17	19	depends	depend	VERB
ejde-515	17	20	on	on	ADP
ejde-515	17	21	t	t	PROPN
ejde-515	17	22	and	and	CCONJ
ejde-515	17	23	u(x	u(x	PROPN
ejde-515	17	24	,	,	PUNCT
ejde-515	17	25	t	t	PROPN
ejde-515	17	26	)	)	PUNCT
ejde-515	17	27	,	,	PUNCT
ejde-515	17	28	that	that	ADV
ejde-515	17	29	is	is	ADV
ejde-515	17	30	,	,	PUNCT
ejde-515	17	31	it	it	PRON
ejde-515	17	32	is	be	AUX
ejde-515	17	33	given	give	VERB
ejde-515	17	34	by	by	ADP
ejde-515	17	35	f(t	f(t	NOUN
ejde-515	17	36	,	,	PUNCT
ejde-515	17	37	u(t	u(t	NOUN
ejde-515	17	38	,	,	PUNCT
ejde-515	17	39	x	x	NOUN
ejde-515	17	40	)	)	PUNCT
ejde-515	17	41	)	)	PUNCT
ejde-515	17	42	.	.	PUNCT
ejde-515	18	1	the	the	DET
ejde-515	18	2	activity	activity	NOUN
ejde-515	18	3	f(t	f(t	NOUN
ejde-515	18	4	,	,	PUNCT
ejde-515	18	5	u(t	u(t	NOUN
ejde-515	18	6	,	,	PUNCT
ejde-515	18	7	y	y	NOUN
ejde-515	18	8	)	)	PUNCT
ejde-515	18	9	)	)	PUNCT
ejde-515	18	10	of	of	ADP
ejde-515	18	11	neurons	neuron	NOUN
ejde-515	18	12	at	at	ADP
ejde-515	18	13	y	y	PROPN
ejde-515	18	14	causes	cause	VERB
ejde-515	18	15	an	an	DET
ejde-515	18	16	increase	increase	NOUN
ejde-515	18	17	in	in	ADP
ejde-515	18	18	the	the	DET
ejde-515	18	19	potential	potential	ADJ
ejde-515	18	20	u(t	u(t	NOUN
ejde-515	18	21	,	,	PUNCT
ejde-515	18	22	x	x	NOUN
ejde-515	18	23	)	)	PUNCT
ejde-515	18	24	at	at	ADP
ejde-515	18	25	x	x	NOUN
ejde-515	18	26	,	,	PUNCT
ejde-515	18	27	through	through	ADP
ejde-515	18	28	the	the	DET
ejde-515	18	29	connections	connection	NOUN
ejde-515	18	30	j(x	j(x	PROPN
ejde-515	18	31	,	,	PUNCT
ejde-515	18	32	y	y	PROPN
ejde-515	18	33	)	)	PUNCT
ejde-515	18	34	,	,	PUNCT
ejde-515	18	35	such	such	ADJ
ejde-515	18	36	that	that	SCONJ
ejde-515	18	37	the	the	DET
ejde-515	18	38	rate	rate	NOUN
ejde-515	18	39	of	of	ADP
ejde-515	18	40	emission	emission	NOUN
ejde-515	18	41	of	of	ADP
ejde-515	18	42	pulses	pulse	NOUN
ejde-515	18	43	is	be	AUX
ejde-515	18	44	proportional	proportional	ADJ
ejde-515	18	45	to	to	ADP
ejde-515	18	46	j(x	j(x	PROPN
ejde-515	18	47	,	,	PUNCT
ejde-515	18	48	y)f(t	y)f(t	NOUN
ejde-515	18	49	,	,	PUNCT
ejde-515	18	50	u(t	u(t	NOUN
ejde-515	18	51	,	,	PUNCT
ejde-515	18	52	x	x	NOUN
ejde-515	18	53	)	)	PUNCT
ejde-515	18	54	)	)	PUNCT
ejde-515	18	55	.	.	PUNCT
ejde-515	19	1	we	we	PRON
ejde-515	19	2	also	also	ADV
ejde-515	19	3	assume	assume	VERB
ejde-515	19	4	that	that	SCONJ
ejde-515	19	5	the	the	DET
ejde-515	19	6	potential	potential	ADJ
ejde-515	19	7	u(t	u(t	NOUN
ejde-515	19	8	,	,	PUNCT
ejde-515	19	9	x	x	X
ejde-515	19	10	)	)	PUNCT
ejde-515	19	11	decays	decay	NOUN
ejde-515	19	12	,	,	PUNCT
ejde-515	19	13	with	with	ADP
ejde-515	19	14	2010	2010	NUM
ejde-515	19	15	mathematics	mathematic	NOUN
ejde-515	19	16	subject	subject	NOUN
ejde-515	19	17	classification	classification	NOUN
ejde-515	19	18	.	.	PUNCT
ejde-515	20	1	35b40	35b40	NUM
ejde-515	20	2	,	,	PUNCT
ejde-515	20	3	35b41	35b41	NUM
ejde-515	20	4	,	,	PUNCT
ejde-515	20	5	37b55	37b55	NUM
ejde-515	20	6	.	.	PUNCT
ejde-515	21	1	key	key	ADJ
ejde-515	21	2	words	word	NOUN
ejde-515	21	3	and	and	CCONJ
ejde-515	21	4	phrases	phrase	NOUN
ejde-515	21	5	.	.	PUNCT
ejde-515	22	1	nonlocal	nonlocal	ADJ
ejde-515	22	2	evolution	evolution	NOUN
ejde-515	22	3	equation	equation	NOUN
ejde-515	22	4	;	;	PUNCT
ejde-515	22	5	neural	neural	ADJ
ejde-515	22	6	fields	field	NOUN
ejde-515	22	7	;	;	PUNCT
ejde-515	22	8	pullback	pullback	NOUN
ejde-515	22	9	attractors	attractor	NOUN
ejde-515	22	10	;	;	PUNCT
ejde-515	22	11	continuous	continuous	ADJ
ejde-515	22	12	dependence	dependence	NOUN
ejde-515	22	13	.	.	PUNCT
ejde-515	23	1	c	c	X
ejde-515	23	2	©	©	PROPN
ejde-515	23	3	2020	2020	NUM
ejde-515	23	4	texas	texas	PROPN
ejde-515	23	5	state	state	PROPN
ejde-515	23	6	university	university	PROPN
ejde-515	23	7	.	.	PUNCT
ejde-515	24	1	submitted	submit	VERB
ejde-515	24	2	july	july	PROPN
ejde-515	24	3	1	1	NUM
ejde-515	24	4	,	,	PUNCT
ejde-515	24	5	2019	2019	NUM
ejde-515	24	6	.	.	PUNCT
ejde-515	25	1	published	publish	VERB
ejde-515	25	2	september	september	PROPN
ejde-515	25	3	7	7	NUM
ejde-515	25	4	,	,	PUNCT
ejde-515	25	5	2020	2020	NUM
ejde-515	25	6	.	.	PUNCT
ejde-515	26	1	1	1	NUM
ejde-515	26	2	2	2	NUM
ejde-515	26	3	s.	s.	PROPN
ejde-515	26	4	h.	h.	PROPN
ejde-515	26	5	da	da	PROPN
ejde-515	26	6	silva	silva	PROPN
ejde-515	26	7	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	26	8	speed	speed	NOUN
ejde-515	26	9	0	0	NUM
ejde-515	26	10	<	<	X
ejde-515	26	11	α(t	α(t	PROPN
ejde-515	26	12	)	)	PUNCT
ejde-515	26	13	<	<	X
ejde-515	27	1	α0	α0	VERB
ejde-515	27	2	,	,	PUNCT
ejde-515	27	3	to	to	ADP
ejde-515	27	4	a	a	DET
ejde-515	27	5	constant	constant	ADJ
ejde-515	27	6	−h	−h	NOUN
ejde-515	27	7	(	(	PUNCT
ejde-515	27	8	which	which	PRON
ejde-515	27	9	we	we	PRON
ejde-515	27	10	call	call	VERB
ejde-515	27	11	the	the	DET
ejde-515	27	12	threshold	threshold	NOUN
ejde-515	27	13	of	of	ADP
ejde-515	27	14	the	the	DET
ejde-515	27	15	field	field	NOUN
ejde-515	27	16	)	)	PUNCT
ejde-515	27	17	,	,	PUNCT
ejde-515	27	18	and	and	CCONJ
ejde-515	27	19	that	that	SCONJ
ejde-515	27	20	it	it	PRON
ejde-515	27	21	increases	increase	VERB
ejde-515	27	22	proportionally	proportionally	ADV
ejde-515	27	23	to	to	ADP
ejde-515	27	24	the	the	DET
ejde-515	27	25	sum	sum	NOUN
ejde-515	27	26	of	of	ADP
ejde-515	27	27	all	all	DET
ejde-515	27	28	the	the	DET
ejde-515	27	29	stimuli	stimulus	NOUN
ejde-515	27	30	arriving	arrive	VERB
ejde-515	27	31	with	with	ADP
ejde-515	27	32	speed	speed	NOUN
ejde-515	27	33	b(t	b(t	NOUN
ejde-515	27	34	)	)	PUNCT
ejde-515	27	35	at	at	ADP
ejde-515	27	36	the	the	DET
ejde-515	27	37	neurons	neuron	NOUN
ejde-515	27	38	.	.	PUNCT
ejde-515	28	1	then	then	ADV
ejde-515	28	2	,	,	PUNCT
ejde-515	28	3	denoting	denote	VERB
ejde-515	28	4	by	by	ADP
ejde-515	28	5	s(x	s(x	PROPN
ejde-515	28	6	,	,	PUNCT
ejde-515	28	7	t	t	PROPN
ejde-515	28	8	)	)	PUNCT
ejde-515	28	9	the	the	DET
ejde-515	28	10	intensity	intensity	NOUN
ejde-515	28	11	of	of	ADP
ejde-515	28	12	the	the	DET
ejde-515	28	13	sum	sum	NOUN
ejde-515	28	14	of	of	ADP
ejde-515	28	15	applied	apply	VERB
ejde-515	28	16	external	external	ADJ
ejde-515	28	17	stimuli	stimulus	NOUN
ejde-515	28	18	at	at	ADP
ejde-515	28	19	x	x	PUNCT
ejde-515	28	20	at	at	ADP
ejde-515	28	21	time	time	NOUN
ejde-515	28	22	t	t	PROPN
ejde-515	28	23	,	,	PUNCT
ejde-515	28	24	and	and	CCONJ
ejde-515	28	25	writing	write	VERB
ejde-515	28	26	a(t	a(t	NOUN
ejde-515	28	27	)	)	PUNCT
ejde-515	28	28	=	=	SYM
ejde-515	28	29	1	1	NUM
ejde-515	28	30	/	/	SYM
ejde-515	28	31	α(t	α(t	PROPN
ejde-515	28	32	)	)	PUNCT
ejde-515	28	33	we	we	PRON
ejde-515	28	34	have	have	VERB
ejde-515	28	35	the	the	DET
ejde-515	28	36	following	follow	VERB
ejde-515	28	37	non	non	ADJ
ejde-515	28	38	-	-	ADJ
ejde-515	28	39	autonomous	autonomous	ADJ
ejde-515	28	40	evolution	evolution	NOUN
ejde-515	28	41	equation	equation	NOUN
ejde-515	28	42	∂tu(t	∂tu(t	PROPN
ejde-515	28	43	,	,	PUNCT
ejde-515	28	44	x	x	X
ejde-515	28	45	)	)	PUNCT
ejde-515	28	46	=	=	SYM
ejde-515	28	47	−a(t)u(t	−a(t)u(t	NOUN
ejde-515	28	48	,	,	PUNCT
ejde-515	28	49	x	x	X
ejde-515	28	50	)	)	PUNCT
ejde-515	28	51	+	+	NUM
ejde-515	28	52	b(t	b(t	NOUN
ejde-515	28	53	)	)	PUNCT
ejde-515	28	54	∫	∫	PROPN
ejde-515	28	55	rn	rn	PROPN
ejde-515	28	56	j(x	j(x	PROPN
ejde-515	28	57	,	,	PUNCT
ejde-515	28	58	y)f(t	y)f(t	NOUN
ejde-515	28	59	,	,	PUNCT
ejde-515	28	60	u(t	u(t	NOUN
ejde-515	28	61	,	,	PUNCT
ejde-515	28	62	y	y	NOUN
ejde-515	28	63	)	)	PUNCT
ejde-515	28	64	)	)	PUNCT
ejde-515	29	1	dy	dy	NOUN
ejde-515	29	2	−	−	PROPN
ejde-515	29	3	h+	h+	X
ejde-515	29	4	s(t	s(t	PROPN
ejde-515	29	5	,	,	PUNCT
ejde-515	29	6	x	x	NOUN
ejde-515	29	7	)	)	PUNCT
ejde-515	29	8	.	.	PUNCT
ejde-515	30	1	(	(	PUNCT
ejde-515	30	2	1.1	1.1	NUM
ejde-515	30	3	)	)	PUNCT
ejde-515	30	4	here	here	ADV
ejde-515	30	5	we	we	PRON
ejde-515	30	6	consider	consider	VERB
ejde-515	30	7	that	that	SCONJ
ejde-515	30	8	the	the	DET
ejde-515	30	9	rate	rate	NOUN
ejde-515	30	10	of	of	ADP
ejde-515	30	11	the	the	DET
ejde-515	30	12	intensity	intensity	NOUN
ejde-515	30	13	of	of	ADP
ejde-515	30	14	neuronal	neuronal	ADJ
ejde-515	30	15	potential	potential	ADJ
ejde-515	30	16	varies	varie	NOUN
ejde-515	30	17	explicitly	explicitly	ADV
ejde-515	30	18	accordingly	accordingly	ADV
ejde-515	30	19	to	to	ADP
ejde-515	30	20	time	time	NOUN
ejde-515	30	21	.	.	PUNCT
ejde-515	31	1	thus	thus	ADV
ejde-515	31	2	,	,	PUNCT
ejde-515	31	3	we	we	PRON
ejde-515	31	4	expect	expect	VERB
ejde-515	31	5	to	to	PART
ejde-515	31	6	have	have	VERB
ejde-515	31	7	a	a	DET
ejde-515	31	8	more	more	ADV
ejde-515	31	9	realistic	realistic	ADJ
ejde-515	31	10	model	model	NOUN
ejde-515	31	11	in	in	ADP
ejde-515	31	12	(	(	PUNCT
ejde-515	31	13	1.1	1.1	NUM
ejde-515	31	14	)	)	PUNCT
ejde-515	31	15	,	,	PUNCT
ejde-515	31	16	when	when	SCONJ
ejde-515	31	17	compared	compare	VERB
ejde-515	31	18	to	to	ADP
ejde-515	31	19	what	what	PRON
ejde-515	31	20	happens	happen	VERB
ejde-515	31	21	in	in	ADP
ejde-515	31	22	the	the	DET
ejde-515	31	23	brain	brain	NOUN
ejde-515	31	24	,	,	PUNCT
ejde-515	31	25	since	since	SCONJ
ejde-515	31	26	the	the	DET
ejde-515	31	27	potential	potential	ADJ
ejde-515	31	28	action	action	NOUN
ejde-515	31	29	of	of	ADP
ejde-515	31	30	the	the	DET
ejde-515	31	31	electric	electric	ADJ
ejde-515	31	32	impulses	impulse	NOUN
ejde-515	31	33	of	of	ADP
ejde-515	31	34	the	the	DET
ejde-515	31	35	neuronal	neuronal	ADJ
ejde-515	31	36	membrane	membrane	NOUN
ejde-515	31	37	is	be	AUX
ejde-515	31	38	a	a	DET
ejde-515	31	39	consequence	consequence	NOUN
ejde-515	31	40	of	of	ADP
ejde-515	31	41	the	the	DET
ejde-515	31	42	inversion	inversion	NOUN
ejde-515	31	43	of	of	ADP
ejde-515	31	44	the	the	DET
ejde-515	31	45	polarity	polarity	NOUN
ejde-515	31	46	inside	inside	ADP
ejde-515	31	47	the	the	DET
ejde-515	31	48	membrane	membrane	NOUN
ejde-515	31	49	,	,	PUNCT
ejde-515	31	50	which	which	PRON
ejde-515	31	51	is	be	AUX
ejde-515	31	52	not	not	PART
ejde-515	31	53	necessarily	necessarily	ADV
ejde-515	31	54	constant	constant	ADJ
ejde-515	31	55	.	.	PUNCT
ejde-515	32	1	note	note	VERB
ejde-515	32	2	that	that	SCONJ
ejde-515	32	3	,	,	PUNCT
ejde-515	32	4	when	when	SCONJ
ejde-515	32	5	a(t	a(t	VERB
ejde-515	32	6	)	)	PUNCT
ejde-515	32	7	=	=	SYM
ejde-515	32	8	b(t	b(t	NOUN
ejde-515	32	9	)	)	PUNCT
ejde-515	32	10	=	=	SYM
ejde-515	33	1	1	1	NUM
ejde-515	33	2	/	/	SYM
ejde-515	33	3	λ	λ	NOUN
ejde-515	33	4	,	,	PUNCT
ejde-515	33	5	for	for	ADP
ejde-515	33	6	any	any	DET
ejde-515	33	7	t	t	NOUN
ejde-515	33	8	∈	∈	PROPN
ejde-515	33	9	r	r	NOUN
ejde-515	33	10	,	,	PUNCT
ejde-515	33	11	for	for	ADP
ejde-515	33	12	some	some	DET
ejde-515	33	13	constant	constant	ADJ
ejde-515	33	14	λ	λ	X
ejde-515	33	15	>	>	X
ejde-515	33	16	0	0	NUM
ejde-515	33	17	,	,	PUNCT
ejde-515	33	18	and	and	CCONJ
ejde-515	33	19	f(t	f(t	NOUN
ejde-515	33	20	,	,	PUNCT
ejde-515	33	21	x	x	NOUN
ejde-515	33	22	)	)	PUNCT
ejde-515	33	23	=	=	SYM
ejde-515	33	24	f(x	f(x	PROPN
ejde-515	33	25	)	)	PUNCT
ejde-515	33	26	,	,	PUNCT
ejde-515	33	27	equation	equation	NOUN
ejde-515	33	28	(	(	PUNCT
ejde-515	33	29	1.1	1.1	NUM
ejde-515	33	30	)	)	PUNCT
ejde-515	33	31	becomes	become	VERB
ejde-515	33	32	λ∂tu(t	λ∂tu(t	NOUN
ejde-515	33	33	,	,	PUNCT
ejde-515	33	34	x	x	X
ejde-515	33	35	)	)	PUNCT
ejde-515	33	36	=	=	SYM
ejde-515	33	37	−u(t	−u(t	ADJ
ejde-515	33	38	,	,	PUNCT
ejde-515	33	39	x	x	PRON
ejde-515	33	40	)	)	PUNCT
ejde-515	34	1	+	+	CCONJ
ejde-515	34	2	∫	∫	PROPN
ejde-515	34	3	rn	rn	PROPN
ejde-515	34	4	j(x	j(x	PROPN
ejde-515	34	5	,	,	PUNCT
ejde-515	34	6	y)f(u(t	y)f(u(t	NOUN
ejde-515	34	7	,	,	PUNCT
ejde-515	34	8	y	y	NOUN
ejde-515	34	9	)	)	PUNCT
ejde-515	34	10	)	)	PUNCT
ejde-515	35	1	dy	dy	NOUN
ejde-515	36	1	−	−	PROPN
ejde-515	36	2	λh+	λh+	NOUN
ejde-515	36	3	λs(t	λs(t	ADP
ejde-515	36	4	,	,	PUNCT
ejde-515	36	5	x	x	NOUN
ejde-515	36	6	)	)	PUNCT
ejde-515	36	7	.	.	PUNCT
ejde-515	37	1	in	in	ADP
ejde-515	37	2	particular	particular	ADJ
ejde-515	37	3	,	,	PUNCT
ejde-515	37	4	if	if	SCONJ
ejde-515	37	5	a(t	a(t	VERB
ejde-515	37	6	)	)	PUNCT
ejde-515	37	7	=	=	SYM
ejde-515	37	8	b(t	b(t	NOUN
ejde-515	37	9	)	)	PUNCT
ejde-515	37	10	=	=	SYM
ejde-515	37	11	1	1	NUM
ejde-515	37	12	,	,	PUNCT
ejde-515	37	13	for	for	ADP
ejde-515	37	14	all	all	DET
ejde-515	37	15	t	t	NOUN
ejde-515	37	16	∈	∈	NOUN
ejde-515	37	17	r	r	NOUN
ejde-515	37	18	and	and	CCONJ
ejde-515	37	19	s(t	s(t	PROPN
ejde-515	37	20	,	,	PUNCT
ejde-515	37	21	x	x	X
ejde-515	37	22	)	)	PUNCT
ejde-515	37	23	=	=	SYM
ejde-515	37	24	h	h	NOUN
ejde-515	37	25	,	,	PUNCT
ejde-515	37	26	equation	equation	NOUN
ejde-515	37	27	(	(	PUNCT
ejde-515	37	28	1.1	1.1	NUM
ejde-515	37	29	)	)	PUNCT
ejde-515	37	30	becomes	become	VERB
ejde-515	37	31	∂tu(t	∂tu(t	ADJ
ejde-515	37	32	,	,	PUNCT
ejde-515	37	33	x	x	NOUN
ejde-515	37	34	)	)	PUNCT
ejde-515	37	35	=	=	SYM
ejde-515	37	36	−u(t	−u(t	ADJ
ejde-515	37	37	,	,	PUNCT
ejde-515	37	38	x	x	PRON
ejde-515	37	39	)	)	PUNCT
ejde-515	38	1	+	+	CCONJ
ejde-515	38	2	∫	∫	PROPN
ejde-515	38	3	rn	rn	PROPN
ejde-515	38	4	j(x	j(x	PROPN
ejde-515	38	5	,	,	PUNCT
ejde-515	38	6	y)f(t	y)f(t	NOUN
ejde-515	38	7	,	,	PUNCT
ejde-515	38	8	u(t	u(t	NOUN
ejde-515	38	9	,	,	PUNCT
ejde-515	38	10	y	y	NOUN
ejde-515	38	11	)	)	PUNCT
ejde-515	38	12	)	)	PUNCT
ejde-515	39	1	dy	dy	NOUN
ejde-515	39	2	.	.	PUNCT
ejde-515	40	1	therefore	therefore	ADV
ejde-515	40	2	,	,	PUNCT
ejde-515	40	3	equation	equation	NOUN
ejde-515	40	4	(	(	PUNCT
ejde-515	40	5	1.1	1.1	NUM
ejde-515	40	6	)	)	PUNCT
ejde-515	40	7	generalizes	generalize	VERB
ejde-515	40	8	the	the	DET
ejde-515	40	9	models	model	NOUN
ejde-515	40	10	studied	study	VERB
ejde-515	40	11	in	in	ADP
ejde-515	40	12	[	[	X
ejde-515	40	13	1	1	NUM
ejde-515	40	14	,	,	PUNCT
ejde-515	40	15	2	2	NUM
ejde-515	40	16	,	,	PUNCT
ejde-515	40	17	5	5	NUM
ejde-515	40	18	,	,	PUNCT
ejde-515	40	19	11	11	NUM
ejde-515	40	20	,	,	PUNCT
ejde-515	40	21	13	13	NUM
ejde-515	40	22	,	,	PUNCT
ejde-515	40	23	14	14	NUM
ejde-515	40	24	,	,	PUNCT
ejde-515	40	25	15	15	NUM
ejde-515	40	26	,	,	PUNCT
ejde-515	40	27	16	16	NUM
ejde-515	40	28	,	,	PUNCT
ejde-515	40	29	18	18	NUM
ejde-515	40	30	,	,	PUNCT
ejde-515	40	31	25	25	NUM
ejde-515	40	32	,	,	PUNCT
ejde-515	40	33	26	26	NUM
ejde-515	40	34	,	,	PUNCT
ejde-515	40	35	28	28	NUM
ejde-515	40	36	,	,	PUNCT
ejde-515	40	37	31	31	NUM
ejde-515	40	38	,	,	PUNCT
ejde-515	40	39	33	33	NUM
ejde-515	40	40	]	]	PUNCT
ejde-515	40	41	.	.	PUNCT
ejde-515	41	1	below	below	ADP
ejde-515	41	2	we	we	PRON
ejde-515	41	3	introduce	introduce	VERB
ejde-515	41	4	the	the	DET
ejde-515	41	5	notation	notation	NOUN
ejde-515	41	6	,	,	PUNCT
ejde-515	41	7	terminology	terminology	NOUN
ejde-515	41	8	and	and	CCONJ
ejde-515	41	9	some	some	DET
ejde-515	41	10	additional	additional	ADJ
ejde-515	41	11	hypotheses	hypothesis	NOUN
ejde-515	41	12	,	,	PUNCT
ejde-515	41	13	which	which	PRON
ejde-515	41	14	are	be	AUX
ejde-515	41	15	already	already	ADV
ejde-515	41	16	well	well	ADV
ejde-515	41	17	known	know	VERB
ejde-515	41	18	in	in	ADP
ejde-515	41	19	the	the	DET
ejde-515	41	20	literature	literature	NOUN
ejde-515	41	21	,	,	PUNCT
ejde-515	41	22	(	(	PUNCT
ejde-515	41	23	see	see	VERB
ejde-515	41	24	,	,	PUNCT
ejde-515	41	25	for	for	ADP
ejde-515	41	26	example	example	NOUN
ejde-515	41	27	[	[	X
ejde-515	41	28	1	1	NUM
ejde-515	41	29	,	,	PUNCT
ejde-515	41	30	2	2	NUM
ejde-515	41	31	,	,	PUNCT
ejde-515	41	32	5	5	NUM
ejde-515	41	33	,	,	PUNCT
ejde-515	41	34	11	11	NUM
ejde-515	41	35	,	,	PUNCT
ejde-515	41	36	17	17	NUM
ejde-515	41	37	,	,	PUNCT
ejde-515	41	38	21	21	NUM
ejde-515	41	39	]	]	PUNCT
ejde-515	41	40	)	)	PUNCT
ejde-515	41	41	.	.	PUNCT
ejde-515	42	1	let	let	VERB
ejde-515	42	2	ω	ω	PROPN
ejde-515	42	3	⊂	⊂	PROPN
ejde-515	42	4	rn	rn	AUX
ejde-515	42	5	be	be	AUX
ejde-515	42	6	a	a	DET
ejde-515	42	7	bounded	bounded	ADJ
ejde-515	42	8	smooth	smooth	ADJ
ejde-515	42	9	domain	domain	NOUN
ejde-515	42	10	modelling	model	VERB
ejde-515	42	11	the	the	DET
ejde-515	42	12	geometric	geometric	ADJ
ejde-515	42	13	configuration	configuration	NOUN
ejde-515	42	14	of	of	ADP
ejde-515	42	15	the	the	DET
ejde-515	42	16	network	network	NOUN
ejde-515	42	17	,	,	PUNCT
ejde-515	42	18	u	u	NOUN
ejde-515	42	19	:	:	PUNCT
ejde-515	42	20	r	r	NOUN
ejde-515	42	21	×	×	PROPN
ejde-515	42	22	rn	rn	PROPN
ejde-515	42	23	→	→	SYM
ejde-515	42	24	r	r	NOUN
ejde-515	42	25	be	be	AUX
ejde-515	42	26	a	a	DET
ejde-515	42	27	function	function	NOUN
ejde-515	42	28	modelling	model	VERB
ejde-515	42	29	the	the	DET
ejde-515	42	30	mean	mean	ADJ
ejde-515	42	31	membrane	membrane	NOUN
ejde-515	42	32	potential	potential	NOUN
ejde-515	42	33	,	,	PUNCT
ejde-515	42	34	u(t	u(t	NOUN
ejde-515	42	35	,	,	PUNCT
ejde-515	42	36	x	x	X
ejde-515	42	37	)	)	PUNCT
ejde-515	42	38	be	be	VERB
ejde-515	42	39	the	the	DET
ejde-515	42	40	potential	potential	NOUN
ejde-515	42	41	of	of	ADP
ejde-515	42	42	a	a	DET
ejde-515	42	43	patch	patch	NOUN
ejde-515	42	44	of	of	ADP
ejde-515	42	45	tissue	tissue	NOUN
ejde-515	42	46	located	locate	VERB
ejde-515	42	47	at	at	ADP
ejde-515	42	48	position	position	NOUN
ejde-515	42	49	x	x	X
ejde-515	42	50	∈	∈	PROPN
ejde-515	42	51	ω	ω	NOUN
ejde-515	42	52	at	at	ADP
ejde-515	42	53	time	time	NOUN
ejde-515	42	54	t	t	PROPN
ejde-515	42	55	∈	∈	PROPN
ejde-515	42	56	r	r	NOUN
ejde-515	42	57	and	and	CCONJ
ejde-515	42	58	f	f	NOUN
ejde-515	42	59	:	:	PUNCT
ejde-515	42	60	r	r	NOUN
ejde-515	42	61	×	×	NOUN
ejde-515	42	62	r	r	NOUN
ejde-515	42	63	→	→	SYM
ejde-515	42	64	r	r	NOUN
ejde-515	42	65	be	be	AUX
ejde-515	42	66	a	a	DET
ejde-515	42	67	time	time	NOUN
ejde-515	42	68	dependent	dependent	ADJ
ejde-515	42	69	transfer	transfer	NOUN
ejde-515	42	70	function	function	NOUN
ejde-515	42	71	.	.	PUNCT
ejde-515	43	1	we	we	PRON
ejde-515	43	2	say	say	VERB
ejde-515	43	3	that	that	SCONJ
ejde-515	43	4	a	a	DET
ejde-515	43	5	neuron	neuron	NOUN
ejde-515	43	6	at	at	ADP
ejde-515	43	7	a	a	DET
ejde-515	43	8	point	point	NOUN
ejde-515	43	9	x	x	PUNCT
ejde-515	43	10	is	be	AUX
ejde-515	43	11	active	active	ADJ
ejde-515	43	12	at	at	ADP
ejde-515	43	13	time	time	NOUN
ejde-515	43	14	t	t	PROPN
ejde-515	43	15	if	if	SCONJ
ejde-515	43	16	f(t	f(t	NOUN
ejde-515	43	17	,	,	PUNCT
ejde-515	43	18	u(t	u(t	NOUN
ejde-515	43	19	,	,	PUNCT
ejde-515	43	20	x	x	NOUN
ejde-515	43	21	)	)	PUNCT
ejde-515	43	22	)	)	PUNCT
ejde-515	43	23	>	>	X
ejde-515	44	1	0	0	X
ejde-515	44	2	.	.	PUNCT
ejde-515	45	1	in	in	ADP
ejde-515	45	2	what	what	PRON
ejde-515	45	3	follows	follow	VERB
ejde-515	45	4	,	,	PUNCT
ejde-515	45	5	b	b	X
ejde-515	45	6	:	:	PUNCT
ejde-515	45	7	r→	r→	PROPN
ejde-515	45	8	r	r	NOUN
ejde-515	45	9	is	be	AUX
ejde-515	45	10	a	a	DET
ejde-515	45	11	continuous	continuous	ADJ
ejde-515	45	12	function	function	NOUN
ejde-515	45	13	such	such	ADJ
ejde-515	45	14	that	that	SCONJ
ejde-515	45	15	0	0	NUM
ejde-515	45	16	<	<	X
ejde-515	45	17	b(t	b(t	PROPN
ejde-515	45	18	)	)	PUNCT
ejde-515	45	19	≤	≤	NOUN
ejde-515	45	20	b0	b0	ADP
ejde-515	45	21	<	<	NOUN
ejde-515	45	22	∞	∞	PROPN
ejde-515	45	23	,	,	PUNCT
ejde-515	45	24	and	and	CCONJ
ejde-515	45	25	it	it	PRON
ejde-515	45	26	denotes	denote	VERB
ejde-515	45	27	the	the	DET
ejde-515	45	28	increasing	increase	VERB
ejde-515	45	29	speed	speed	NOUN
ejde-515	45	30	of	of	ADP
ejde-515	45	31	the	the	DET
ejde-515	45	32	potential	potential	ADJ
ejde-515	45	33	function	function	NOUN
ejde-515	45	34	u(t	u(t	NOUN
ejde-515	45	35	,	,	PUNCT
ejde-515	45	36	x	x	NOUN
ejde-515	45	37	)	)	PUNCT
ejde-515	45	38	.	.	PUNCT
ejde-515	46	1	since	since	SCONJ
ejde-515	46	2	the	the	DET
ejde-515	46	3	decreasing	decrease	VERB
ejde-515	46	4	speed	speed	NOUN
ejde-515	46	5	of	of	ADP
ejde-515	46	6	the	the	DET
ejde-515	46	7	potential	potential	ADJ
ejde-515	46	8	function	function	NOUN
ejde-515	46	9	u(t	u(t	NOUN
ejde-515	46	10	,	,	PUNCT
ejde-515	46	11	x	x	X
ejde-515	46	12	)	)	PUNCT
ejde-515	46	13	satisfies	satisfie	NOUN
ejde-515	46	14	0	0	NUM
ejde-515	46	15	<	<	X
ejde-515	46	16	α(t	α(t	PROPN
ejde-515	46	17	)	)	PUNCT
ejde-515	46	18	<	<	X
ejde-515	47	1	α0	α0	PROPN
ejde-515	47	2	,	,	PUNCT
ejde-515	47	3	we	we	PRON
ejde-515	47	4	can	can	AUX
ejde-515	47	5	assume	assume	VERB
ejde-515	47	6	that	that	SCONJ
ejde-515	47	7	there	there	PRON
ejde-515	47	8	exist	exist	VERB
ejde-515	47	9	positive	positive	ADJ
ejde-515	47	10	constants	constant	NOUN
ejde-515	47	11	a−	a−	PROPN
ejde-515	47	12	and	and	CCONJ
ejde-515	47	13	a0	a0	NOUN
ejde-515	47	14	such	such	ADJ
ejde-515	47	15	that	that	SCONJ
ejde-515	47	16	0	0	NUM
ejde-515	47	17	<	<	X
ejde-515	47	18	a−	a−	PROPN
ejde-515	47	19	≤	≤	NOUN
ejde-515	47	20	a(t	a(t	NOUN
ejde-515	47	21	)	)	PUNCT
ejde-515	47	22	≤	≤	NOUN
ejde-515	48	1	a0	a0	PROPN
ejde-515	48	2	<	<	X
ejde-515	48	3	∞.	∞.	PROPN
ejde-515	48	4	let	let	VERB
ejde-515	48	5	us	we	PRON
ejde-515	48	6	also	also	ADV
ejde-515	48	7	denote	denote	VERB
ejde-515	48	8	the	the	DET
ejde-515	48	9	integrable	integrable	ADJ
ejde-515	48	10	function	function	NOUN
ejde-515	48	11	j	j	PROPN
ejde-515	48	12	:	:	PUNCT
ejde-515	48	13	rn	rn	PROPN
ejde-515	48	14	×	×	PROPN
ejde-515	48	15	rn	rn	PROPN
ejde-515	48	16	→	→	SYM
ejde-515	48	17	r	r	NOUN
ejde-515	48	18	as	as	ADP
ejde-515	48	19	the	the	DET
ejde-515	48	20	connection	connection	NOUN
ejde-515	48	21	between	between	ADP
ejde-515	48	22	locations	location	NOUN
ejde-515	48	23	,	,	PUNCT
ejde-515	48	24	that	that	ADV
ejde-515	48	25	is	is	ADV
ejde-515	48	26	,	,	PUNCT
ejde-515	48	27	j(x	j(x	PROPN
ejde-515	48	28	,	,	PUNCT
ejde-515	48	29	y	y	PROPN
ejde-515	48	30	)	)	PUNCT
ejde-515	48	31	is	be	AUX
ejde-515	48	32	the	the	DET
ejde-515	48	33	strength	strength	NOUN
ejde-515	48	34	of	of	ADP
ejde-515	48	35	the	the	DET
ejde-515	48	36	connections	connection	NOUN
ejde-515	48	37	of	of	ADP
ejde-515	48	38	neuronal	neuronal	ADJ
ejde-515	48	39	activity	activity	NOUN
ejde-515	48	40	at	at	ADP
ejde-515	48	41	location	location	NOUN
ejde-515	48	42	y	y	PROPN
ejde-515	48	43	on	on	ADP
ejde-515	48	44	the	the	DET
ejde-515	48	45	activity	activity	NOUN
ejde-515	48	46	of	of	ADP
ejde-515	48	47	the	the	DET
ejde-515	48	48	neuron	neuron	NOUN
ejde-515	48	49	at	at	ADP
ejde-515	48	50	location	location	NOUN
ejde-515	48	51	x.	x.	NOUN
ejde-515	49	1	the	the	DET
ejde-515	49	2	strength	strength	NOUN
ejde-515	49	3	of	of	ADP
ejde-515	49	4	the	the	DET
ejde-515	49	5	connection	connection	NOUN
ejde-515	49	6	is	be	AUX
ejde-515	49	7	assumed	assume	VERB
ejde-515	49	8	to	to	PART
ejde-515	49	9	be	be	AUX
ejde-515	49	10	symmetric	symmetric	ADJ
ejde-515	49	11	,	,	PUNCT
ejde-515	49	12	that	that	PRON
ejde-515	49	13	is	be	AUX
ejde-515	49	14	j(x	j(x	PROPN
ejde-515	49	15	,	,	PUNCT
ejde-515	49	16	y	y	NOUN
ejde-515	49	17	)	)	PUNCT
ejde-515	50	1	=	=	SYM
ejde-515	50	2	j(y	j(y	PROPN
ejde-515	50	3	,	,	PUNCT
ejde-515	50	4	x	x	NOUN
ejde-515	50	5	)	)	PUNCT
ejde-515	50	6	,	,	PUNCT
ejde-515	50	7	for	for	ADP
ejde-515	50	8	any	any	DET
ejde-515	50	9	x	x	NOUN
ejde-515	50	10	,	,	PUNCT
ejde-515	50	11	y	y	PROPN
ejde-515	50	12	∈	∈	PROPN
ejde-515	50	13	rn	rn	PROPN
ejde-515	50	14	and	and	CCONJ
ejde-515	50	15	that	that	SCONJ
ejde-515	50	16	∫	∫	PROPN
ejde-515	50	17	rn	rn	PROPN
ejde-515	50	18	j(x	j(x	PROPN
ejde-515	50	19	,	,	PUNCT
ejde-515	50	20	y)dy	y)dy	PROPN
ejde-515	50	21	=	=	SYM
ejde-515	50	22	∫	∫	PROPN
ejde-515	50	23	rn	rn	PROPN
ejde-515	50	24	j(x	j(x	PROPN
ejde-515	50	25	,	,	PUNCT
ejde-515	50	26	y)dx	y)dx	PROPN
ejde-515	50	27	=	=	SYM
ejde-515	50	28	1	1	NUM
ejde-515	50	29	.	.	X
ejde-515	50	30	ejde-2020/92	ejde-2020/92	VERB
ejde-515	50	31	non	non	ADJ
ejde-515	50	32	-	-	ADJ
ejde-515	50	33	autonomous	autonomous	ADJ
ejde-515	50	34	model	model	NOUN
ejde-515	50	35	for	for	ADP
ejde-515	50	36	neural	neural	ADJ
ejde-515	50	37	fields	field	NOUN
ejde-515	50	38	3	3	NUM
ejde-515	50	39	under	under	ADP
ejde-515	50	40	the	the	DET
ejde-515	50	41	above	above	ADJ
ejde-515	50	42	conditions	condition	NOUN
ejde-515	50	43	,	,	PUNCT
ejde-515	50	44	we	we	PRON
ejde-515	50	45	study	study	VERB
ejde-515	50	46	the	the	DET
ejde-515	50	47	following	follow	VERB
ejde-515	50	48	non	non	ADJ
ejde-515	50	49	-	-	ADJ
ejde-515	50	50	autonomous	autonomous	ADJ
ejde-515	50	51	model	model	NOUN
ejde-515	50	52	for	for	ADP
ejde-515	50	53	neural	neural	ADJ
ejde-515	50	54	fields	field	NOUN
ejde-515	50	55	∂tu(t	∂tu(t	PROPN
ejde-515	50	56	,	,	PUNCT
ejde-515	50	57	x	x	X
ejde-515	50	58	)	)	PUNCT
ejde-515	50	59	=	=	SYM
ejde-515	50	60	−a(t)u(t	−a(t)u(t	NOUN
ejde-515	50	61	,	,	PUNCT
ejde-515	50	62	x	x	X
ejde-515	50	63	)	)	PUNCT
ejde-515	51	1	+	+	NUM
ejde-515	51	2	b(t)kf(t	b(t)kf(t	NOUN
ejde-515	51	3	,	,	PUNCT
ejde-515	51	4	u(t	u(t	NOUN
ejde-515	51	5	,	,	PUNCT
ejde-515	51	6	y	y	NOUN
ejde-515	51	7	)	)	PUNCT
ejde-515	51	8	)	)	PUNCT
ejde-515	52	1	dy	dy	NOUN
ejde-515	52	2	−	−	PROPN
ejde-515	52	3	h+	h+	X
ejde-515	52	4	s(t	s(t	PROPN
ejde-515	52	5	,	,	PUNCT
ejde-515	52	6	x	x	NOUN
ejde-515	52	7	)	)	PUNCT
ejde-515	52	8	,	,	PUNCT
ejde-515	52	9	t	t	X
ejde-515	52	10	>	>	X
ejde-515	52	11	τ	τ	PROPN
ejde-515	52	12	,	,	PUNCT
ejde-515	52	13	x	x	PROPN
ejde-515	52	14	∈	∈	PROPN
ejde-515	52	15	ω	ω	PROPN
ejde-515	52	16	,	,	PUNCT
ejde-515	52	17	u(τ	u(τ	PROPN
ejde-515	52	18	,	,	PUNCT
ejde-515	52	19	x	x	NOUN
ejde-515	52	20	)	)	PUNCT
ejde-515	53	1	=	=	SYM
ejde-515	53	2	uτ	uτ	PROPN
ejde-515	53	3	(	(	PUNCT
ejde-515	53	4	x	x	NOUN
ejde-515	53	5	)	)	PUNCT
ejde-515	53	6	,	,	PUNCT
ejde-515	53	7	x	x	PUNCT
ejde-515	53	8	∈	∈	PROPN
ejde-515	53	9	ω	ω	NOUN
ejde-515	53	10	,	,	PUNCT
ejde-515	53	11	u(t	u(t	NOUN
ejde-515	53	12	,	,	PUNCT
ejde-515	53	13	x	x	NOUN
ejde-515	53	14	)	)	PUNCT
ejde-515	53	15	=	=	SYM
ejde-515	53	16	0	0	NUM
ejde-515	53	17	,	,	PUNCT
ejde-515	53	18	t	t	X
ejde-515	53	19	>	>	X
ejde-515	53	20	τ	τ	PROPN
ejde-515	53	21	,	,	PUNCT
ejde-515	53	22	x	x	PROPN
ejde-515	53	23	∈	∈	PROPN
ejde-515	53	24	rn\ω	rn\ω	NOUN
ejde-515	53	25	,	,	PUNCT
ejde-515	53	26	(	(	PUNCT
ejde-515	53	27	1.2	1.2	NUM
ejde-515	53	28	)	)	PUNCT
ejde-515	53	29	where	where	SCONJ
ejde-515	53	30	the	the	DET
ejde-515	53	31	integral	integral	ADJ
ejde-515	53	32	operator	operator	NOUN
ejde-515	53	33	,	,	PUNCT
ejde-515	53	34	with	with	ADP
ejde-515	53	35	symmetric	symmetric	ADJ
ejde-515	53	36	kernel	kernel	NOUN
ejde-515	53	37	,	,	PUNCT
ejde-515	53	38	k	k	PROPN
ejde-515	53	39	is	be	AUX
ejde-515	53	40	given	give	VERB
ejde-515	53	41	,	,	PUNCT
ejde-515	53	42	for	for	ADP
ejde-515	53	43	all	all	DET
ejde-515	53	44	v	v	NOUN
ejde-515	53	45	∈	∈	NOUN
ejde-515	53	46	l1(rn	l1(rn	PROPN
ejde-515	53	47	)	)	PUNCT
ejde-515	53	48	,	,	PUNCT
ejde-515	53	49	by	by	ADP
ejde-515	53	50	kv(x	kv(x	PRON
ejde-515	53	51	)	)	PUNCT
ejde-515	53	52	:	:	PUNCT
ejde-515	54	1	=	=	SYM
ejde-515	54	2	∫	∫	PROPN
ejde-515	54	3	rn	rn	PROPN
ejde-515	54	4	j(x	j(x	PROPN
ejde-515	54	5	,	,	PUNCT
ejde-515	54	6	y)v(y	y)v(y	NUM
ejde-515	54	7	)	)	PUNCT
ejde-515	54	8	dy	dy	NOUN
ejde-515	54	9	.	.	PUNCT
ejde-515	55	1	also	also	ADV
ejde-515	55	2	we	we	PRON
ejde-515	55	3	will	will	AUX
ejde-515	55	4	assume	assume	VERB
ejde-515	55	5	that	that	SCONJ
ejde-515	55	6	f	f	X
ejde-515	55	7	:	:	PUNCT
ejde-515	55	8	r	r	NOUN
ejde-515	55	9	×	×	NOUN
ejde-515	55	10	r	r	NOUN
ejde-515	55	11	→	→	SYM
ejde-515	55	12	r	r	NOUN
ejde-515	55	13	satisfies	satisfy	VERB
ejde-515	55	14	some	some	DET
ejde-515	55	15	growth	growth	NOUN
ejde-515	55	16	conditions	condition	NOUN
ejde-515	55	17	,	,	PUNCT
ejde-515	55	18	as	as	SCONJ
ejde-515	55	19	presented	present	VERB
ejde-515	55	20	along	along	ADP
ejde-515	55	21	the	the	DET
ejde-515	55	22	section	section	NOUN
ejde-515	55	23	2	2	NUM
ejde-515	55	24	,	,	PUNCT
ejde-515	55	25	and	and	CCONJ
ejde-515	55	26	that	that	PRON
ejde-515	55	27	s	s	VERB
ejde-515	55	28	:	:	PUNCT
ejde-515	55	29	r×	r×	PROPN
ejde-515	55	30	rn	rn	PROPN
ejde-515	55	31	→	→	SYM
ejde-515	55	32	r	r	NOUN
ejde-515	55	33	is	be	AUX
ejde-515	55	34	continuous	continuous	ADJ
ejde-515	55	35	at	at	ADP
ejde-515	55	36	variable	variable	ADJ
ejde-515	55	37	t	t	PROPN
ejde-515	55	38	and	and	CCONJ
ejde-515	55	39	s(t	s(t	PROPN
ejde-515	55	40	,	,	PUNCT
ejde-515	55	41	·	·	PUNCT
ejde-515	55	42	)	)	PUNCT
ejde-515	55	43	∈	∈	PROPN
ejde-515	55	44	lp(ω	lp(ω	PROPN
ejde-515	55	45	)	)	PUNCT
ejde-515	55	46	,	,	PUNCT
ejde-515	55	47	for	for	ADP
ejde-515	55	48	all	all	DET
ejde-515	55	49	t	t	PROPN
ejde-515	55	50	∈	∈	PROPN
ejde-515	55	51	r.	r.	NOUN
ejde-515	55	52	we	we	PRON
ejde-515	55	53	aim	aim	VERB
ejde-515	55	54	to	to	PART
ejde-515	55	55	study	study	VERB
ejde-515	55	56	the	the	DET
ejde-515	55	57	asymptotic	asymptotic	ADJ
ejde-515	55	58	behavior	behavior	NOUN
ejde-515	55	59	of	of	ADP
ejde-515	55	60	the	the	DET
ejde-515	55	61	evolution	evolution	NOUN
ejde-515	55	62	process	process	NOUN
ejde-515	55	63	associated	associate	VERB
ejde-515	55	64	to	to	ADP
ejde-515	55	65	the	the	DET
ejde-515	55	66	cauchy	cauchy	ADJ
ejde-515	55	67	problem	problem	NOUN
ejde-515	55	68	(	(	PUNCT
ejde-515	55	69	1.2	1.2	NUM
ejde-515	55	70	)	)	PUNCT
ejde-515	55	71	under	under	ADP
ejde-515	55	72	an	an	DET
ejde-515	55	73	appropriate	appropriate	ADJ
ejde-515	55	74	banach	banach	NOUN
ejde-515	55	75	space	space	NOUN
ejde-515	55	76	,	,	PUNCT
ejde-515	55	77	as	as	ADV
ejde-515	55	78	well	well	ADV
ejde-515	55	79	as	as	ADP
ejde-515	55	80	obtain	obtain	VERB
ejde-515	55	81	some	some	DET
ejde-515	55	82	biological	biological	ADJ
ejde-515	55	83	conclusion	conclusion	NOUN
ejde-515	55	84	.	.	PUNCT
ejde-515	56	1	then	then	ADV
ejde-515	56	2	,	,	PUNCT
ejde-515	56	3	using	use	VERB
ejde-515	56	4	the	the	DET
ejde-515	56	5	same	same	ADJ
ejde-515	56	6	techniques	technique	NOUN
ejde-515	56	7	employed	employ	VERB
ejde-515	56	8	in	in	ADP
ejde-515	56	9	[	[	X
ejde-515	56	10	5	5	NUM
ejde-515	56	11	,	,	PUNCT
ejde-515	56	12	17	17	NUM
ejde-515	56	13	]	]	PUNCT
ejde-515	56	14	,	,	PUNCT
ejde-515	56	15	we	we	PRON
ejde-515	56	16	prove	prove	VERB
ejde-515	56	17	results	result	NOUN
ejde-515	56	18	on	on	ADP
ejde-515	56	19	existence	existence	NOUN
ejde-515	56	20	,	,	PUNCT
ejde-515	56	21	uniqueness	uniqueness	NOUN
ejde-515	56	22	and	and	CCONJ
ejde-515	56	23	smoothness	smoothness	NOUN
ejde-515	56	24	of	of	ADP
ejde-515	56	25	the	the	DET
ejde-515	56	26	solutions	solution	NOUN
ejde-515	56	27	,	,	PUNCT
ejde-515	56	28	and	and	CCONJ
ejde-515	56	29	we	we	PRON
ejde-515	56	30	also	also	ADV
ejde-515	56	31	prove	prove	VERB
ejde-515	56	32	the	the	DET
ejde-515	56	33	existence	existence	NOUN
ejde-515	56	34	of	of	ADP
ejde-515	56	35	pullback	pullback	NOUN
ejde-515	56	36	attractors	attractor	NOUN
ejde-515	56	37	for	for	ADP
ejde-515	56	38	the	the	DET
ejde-515	56	39	evolution	evolution	NOUN
ejde-515	56	40	process	process	NOUN
ejde-515	56	41	associated	associate	VERB
ejde-515	56	42	to	to	ADP
ejde-515	56	43	(	(	PUNCT
ejde-515	56	44	1.2	1.2	NUM
ejde-515	56	45	)	)	PUNCT
ejde-515	56	46	,	,	PUNCT
ejde-515	56	47	which	which	PRON
ejde-515	56	48	is	be	AUX
ejde-515	56	49	a	a	DET
ejde-515	56	50	more	more	ADV
ejde-515	56	51	general	general	ADJ
ejde-515	56	52	model	model	NOUN
ejde-515	56	53	than	than	ADP
ejde-515	56	54	the	the	DET
ejde-515	56	55	models	model	NOUN
ejde-515	56	56	analyzed	analyze	VERB
ejde-515	56	57	in	in	ADP
ejde-515	56	58	previous	previous	ADJ
ejde-515	56	59	published	publish	VERB
ejde-515	56	60	works	work	NOUN
ejde-515	56	61	on	on	ADP
ejde-515	56	62	the	the	DET
ejde-515	56	63	subject	subject	NOUN
ejde-515	56	64	.	.	PUNCT
ejde-515	57	1	in	in	ADP
ejde-515	57	2	addition	addition	NOUN
ejde-515	57	3	,	,	PUNCT
ejde-515	57	4	we	we	PRON
ejde-515	57	5	prove	prove	VERB
ejde-515	57	6	a	a	DET
ejde-515	57	7	continuous	continuous	ADJ
ejde-515	57	8	dependence	dependence	NOUN
ejde-515	57	9	of	of	ADP
ejde-515	57	10	the	the	DET
ejde-515	57	11	solutions	solution	NOUN
ejde-515	57	12	with	with	ADP
ejde-515	57	13	respect	respect	NOUN
ejde-515	57	14	to	to	ADP
ejde-515	57	15	the	the	DET
ejde-515	57	16	external	external	ADJ
ejde-515	57	17	stimuli	stimulus	NOUN
ejde-515	57	18	function	function	NOUN
ejde-515	57	19	s	s	PART
ejde-515	57	20	,	,	PUNCT
ejde-515	57	21	concluding	conclude	VERB
ejde-515	57	22	mathematically	mathematically	ADV
ejde-515	57	23	that	that	SCONJ
ejde-515	57	24	the	the	DET
ejde-515	57	25	neuronal	neuronal	ADJ
ejde-515	57	26	activity	activity	NOUN
ejde-515	57	27	depends	depend	VERB
ejde-515	57	28	continuously	continuously	ADV
ejde-515	57	29	on	on	ADP
ejde-515	57	30	the	the	DET
ejde-515	57	31	sum	sum	NOUN
ejde-515	57	32	of	of	ADP
ejde-515	57	33	external	external	ADJ
ejde-515	57	34	stimuli	stimulus	NOUN
ejde-515	57	35	involved	involve	VERB
ejde-515	57	36	in	in	ADP
ejde-515	57	37	the	the	DET
ejde-515	57	38	neuronal	neuronal	ADJ
ejde-515	57	39	system	system	NOUN
ejde-515	57	40	.	.	PUNCT
ejde-515	58	1	this	this	PRON
ejde-515	58	2	suggests	suggest	VERB
ejde-515	58	3	the	the	DET
ejde-515	58	4	need	need	NOUN
ejde-515	58	5	for	for	ADP
ejde-515	58	6	intensive	intensive	ADJ
ejde-515	58	7	therapies	therapy	NOUN
ejde-515	58	8	to	to	PART
ejde-515	58	9	stimulate	stimulate	VERB
ejde-515	58	10	people	people	NOUN
ejde-515	58	11	with	with	ADP
ejde-515	58	12	poor	poor	ADJ
ejde-515	58	13	neuronal	neuronal	ADJ
ejde-515	58	14	activity	activity	NOUN
ejde-515	58	15	as	as	ADP
ejde-515	58	16	,	,	PUNCT
ejde-515	58	17	in	in	ADP
ejde-515	58	18	some	some	DET
ejde-515	58	19	cases	case	NOUN
ejde-515	58	20	,	,	PUNCT
ejde-515	58	21	people	people	NOUN
ejde-515	58	22	with	with	ADP
ejde-515	58	23	autism	autism	NOUN
ejde-515	58	24	or	or	CCONJ
ejde-515	58	25	other	other	ADJ
ejde-515	58	26	neurological	neurological	ADJ
ejde-515	58	27	disorders	disorder	NOUN
ejde-515	58	28	.	.	PUNCT
ejde-515	59	1	furthermore	furthermore	ADV
ejde-515	59	2	,	,	PUNCT
ejde-515	59	3	using	use	VERB
ejde-515	59	4	the	the	DET
ejde-515	59	5	result	result	NOUN
ejde-515	59	6	of	of	ADP
ejde-515	59	7	continuous	continuous	ADJ
ejde-515	59	8	dependence	dependence	NOUN
ejde-515	59	9	of	of	ADP
ejde-515	59	10	the	the	DET
ejde-515	59	11	evolution	evolution	NOUN
ejde-515	59	12	process	process	NOUN
ejde-515	59	13	,	,	PUNCT
ejde-515	59	14	we	we	PRON
ejde-515	59	15	also	also	ADV
ejde-515	59	16	prove	prove	VERB
ejde-515	59	17	the	the	DET
ejde-515	59	18	upper	upper	ADJ
ejde-515	59	19	semicontinuity	semicontinuity	NOUN
ejde-515	59	20	of	of	ADP
ejde-515	59	21	pullback	pullback	NOUN
ejde-515	59	22	attractors	attractor	NOUN
ejde-515	59	23	with	with	ADP
ejde-515	59	24	respect	respect	NOUN
ejde-515	59	25	to	to	AUX
ejde-515	59	26	function	function	VERB
ejde-515	59	27	s.	s.	PROPN
ejde-515	59	28	this	this	DET
ejde-515	59	29	article	article	NOUN
ejde-515	59	30	is	be	AUX
ejde-515	59	31	organized	organize	VERB
ejde-515	59	32	as	as	SCONJ
ejde-515	59	33	follows	follow	VERB
ejde-515	59	34	.	.	PUNCT
ejde-515	60	1	in	in	ADP
ejde-515	60	2	section	section	NOUN
ejde-515	60	3	2	2	NUM
ejde-515	60	4	,	,	PUNCT
ejde-515	60	5	under	under	ADP
ejde-515	60	6	the	the	DET
ejde-515	60	7	growth	growth	NOUN
ejde-515	60	8	conditions	condition	NOUN
ejde-515	60	9	(	(	PUNCT
ejde-515	60	10	2.7	2.7	NUM
ejde-515	60	11	)	)	PUNCT
ejde-515	60	12	,	,	PUNCT
ejde-515	60	13	(	(	PUNCT
ejde-515	60	14	2.9	2.9	NUM
ejde-515	60	15	)	)	PUNCT
ejde-515	60	16	,	,	PUNCT
ejde-515	60	17	(	(	PUNCT
ejde-515	60	18	2.11	2.11	NUM
ejde-515	60	19	)	)	PUNCT
ejde-515	60	20	and	and	CCONJ
ejde-515	60	21	(	(	PUNCT
ejde-515	60	22	2.14	2.14	NUM
ejde-515	60	23	)	)	PUNCT
ejde-515	60	24	,	,	PUNCT
ejde-515	60	25	on	on	ADP
ejde-515	60	26	the	the	DET
ejde-515	60	27	function	function	NOUN
ejde-515	60	28	f	f	NOUN
ejde-515	60	29	,	,	PUNCT
ejde-515	60	30	we	we	PRON
ejde-515	60	31	prove	prove	VERB
ejde-515	60	32	that	that	SCONJ
ejde-515	60	33	(	(	PUNCT
ejde-515	60	34	1.2	1.2	NUM
ejde-515	60	35	)	)	PUNCT
ejde-515	60	36	generates	generate	VERB
ejde-515	60	37	a	a	DET
ejde-515	60	38	c1	c1	PROPN
ejde-515	60	39	evolution	evolution	NOUN
ejde-515	60	40	process	process	NOUN
ejde-515	60	41	in	in	ADP
ejde-515	60	42	the	the	DET
ejde-515	60	43	phase	phase	NOUN
ejde-515	60	44	space	space	NOUN
ejde-515	60	45	xp	xp	NOUN
ejde-515	61	1	=	=	PRON
ejde-515	61	2	{	{	PUNCT
ejde-515	61	3	u	u	NOUN
ejde-515	61	4	∈	∈	PROPN
ejde-515	61	5	lp(rn	lp(rn	PROPN
ejde-515	61	6	)	)	PUNCT
ejde-515	61	7	:	:	PUNCT
ejde-515	61	8	u(x	u(x	PROPN
ejde-515	61	9	)	)	PUNCT
ejde-515	61	10	=	=	SYM
ejde-515	61	11	0	0	NUM
ejde-515	61	12	for	for	ADP
ejde-515	61	13	x	x	PROPN
ejde-515	61	14	∈	∈	PROPN
ejde-515	61	15	rn\ω	rn\ω	NOUN
ejde-515	61	16	}	}	PUNCT
ejde-515	61	17	(	(	PUNCT
ejde-515	61	18	1.3	1.3	NUM
ejde-515	61	19	)	)	PUNCT
ejde-515	61	20	with	with	ADP
ejde-515	61	21	the	the	DET
ejde-515	61	22	induced	induced	ADJ
ejde-515	61	23	norm	norm	NOUN
ejde-515	61	24	,	,	PUNCT
ejde-515	61	25	satisfying	satisfy	VERB
ejde-515	61	26	the	the	DET
ejde-515	61	27	“	"	PUNCT
ejde-515	61	28	variation	variation	NOUN
ejde-515	61	29	of	of	ADP
ejde-515	61	30	constants	constant	NOUN
ejde-515	61	31	formula	formula	NOUN
ejde-515	61	32	”	"	PUNCT
ejde-515	61	33	u(t	u(t	NOUN
ejde-515	61	34	,	,	PUNCT
ejde-515	61	35	x	x	NOUN
ejde-515	61	36	)	)	PUNCT
ejde-515	61	37	=	=	SYM
ejde-515	62	1			PRON
ejde-515	62	2	e−(a(t)−a(τ))uτ	e−(a(t)−a(τ))uτ	VERB
ejde-515	62	3	(	(	PUNCT
ejde-515	62	4	x	x	NOUN
ejde-515	62	5	)	)	PUNCT
ejde-515	63	1	+	+	CCONJ
ejde-515	63	2	∫	∫	PROPN
ejde-515	63	3	t	t	PROPN
ejde-515	63	4	τ	τ	PROPN
ejde-515	63	5	e−(a(t)−a(s))b(s)kf(s	e−(a(t)−a(s))b(s)kf(	NOUN
ejde-515	63	6	,	,	PUNCT
ejde-515	63	7	u(s	u(s	ADJ
ejde-515	63	8	,	,	PUNCT
ejde-515	63	9	·	·	PUNCT
ejde-515	63	10	)	)	PUNCT
ejde-515	63	11	)	)	PUNCT
ejde-515	63	12	(	(	PUNCT
ejde-515	63	13	x	x	X
ejde-515	63	14	)	)	PUNCT
ejde-515	63	15	ds	ds	PROPN
ejde-515	64	1	+	+	NUM
ejde-515	64	2	∫	∫	PROPN
ejde-515	64	3	t	t	PROPN
ejde-515	64	4	τ	τ	PROPN
ejde-515	64	5	e−(a(t)−a(s))[s(s	e−(a(t)−a(s))[s(s	PROPN
ejde-515	64	6	,	,	PUNCT
ejde-515	64	7	x)−	x)−	PROPN
ejde-515	64	8	h]ds	h]ds	PROPN
ejde-515	64	9	,	,	PUNCT
ejde-515	64	10	x	x	X
ejde-515	64	11	∈	∈	PROPN
ejde-515	64	12	ω	ω	PROPN
ejde-515	64	13	,	,	PUNCT
ejde-515	64	14	0	0	NUM
ejde-515	64	15	,	,	PUNCT
ejde-515	64	16	x	x	SYM
ejde-515	64	17	∈	∈	PROPN
ejde-515	64	18	rn\ω	rn\ω	NOUN
ejde-515	64	19	,	,	PUNCT
ejde-515	64	20	where	where	SCONJ
ejde-515	64	21	a(ξ	a(ξ	PROPN
ejde-515	64	22	)	)	PUNCT
ejde-515	64	23	=	=	SYM
ejde-515	65	1	∫	∫	PROPN
ejde-515	65	2	ξ	ξ	SYM
ejde-515	65	3	0	0	PUNCT
ejde-515	65	4	a(η)dη	a(η)dη	PROPN
ejde-515	65	5	,	,	PUNCT
ejde-515	65	6	for	for	ADP
ejde-515	65	7	any	any	DET
ejde-515	65	8	ξ	ξ	PROPN
ejde-515	65	9	≥	≥	NOUN
ejde-515	65	10	τ	τ	X
ejde-515	65	11	.	.	PUNCT
ejde-515	66	1	in	in	ADP
ejde-515	66	2	section	section	NOUN
ejde-515	66	3	3	3	NUM
ejde-515	66	4	,	,	PUNCT
ejde-515	66	5	we	we	PRON
ejde-515	66	6	prove	prove	VERB
ejde-515	66	7	existence	existence	NOUN
ejde-515	66	8	of	of	ADP
ejde-515	66	9	a	a	DET
ejde-515	66	10	pullback	pullback	NOUN
ejde-515	66	11	attractor	attractor	NOUN
ejde-515	66	12	in	in	ADP
ejde-515	66	13	the	the	DET
ejde-515	66	14	phase	phase	NOUN
ejde-515	66	15	space	space	NOUN
ejde-515	66	16	xp	xp	NOUN
ejde-515	66	17	.	.	PUNCT
ejde-515	67	1	section	section	NOUN
ejde-515	67	2	4	4	NUM
ejde-515	67	3	is	be	AUX
ejde-515	67	4	dedicated	dedicate	VERB
ejde-515	67	5	to	to	ADP
ejde-515	67	6	continuity	continuity	NOUN
ejde-515	67	7	with	with	ADP
ejde-515	67	8	respect	respect	NOUN
ejde-515	67	9	to	to	ADP
ejde-515	67	10	the	the	DET
ejde-515	67	11	external	external	ADJ
ejde-515	67	12	stimuli	stimulus	NOUN
ejde-515	67	13	function	function	VERB
ejde-515	67	14	s.	s.	PROPN
ejde-515	67	15	in	in	ADP
ejde-515	67	16	subsection	subsection	NOUN
ejde-515	67	17	4.1	4.1	NUM
ejde-515	67	18	we	we	PRON
ejde-515	67	19	study	study	VERB
ejde-515	67	20	the	the	DET
ejde-515	67	21	continuity	continuity	NOUN
ejde-515	67	22	of	of	ADP
ejde-515	67	23	the	the	DET
ejde-515	67	24	process	process	NOUN
ejde-515	67	25	with	with	ADP
ejde-515	67	26	respect	respect	NOUN
ejde-515	67	27	to	to	ADP
ejde-515	67	28	the	the	DET
ejde-515	67	29	function	function	NOUN
ejde-515	67	30	s	s	NOUN
ejde-515	67	31	,	,	PUNCT
ejde-515	67	32	and	and	CCONJ
ejde-515	67	33	in	in	ADP
ejde-515	67	34	subsection	subsection	NOUN
ejde-515	67	35	4.2	4.2	NUM
ejde-515	67	36	we	we	PRON
ejde-515	67	37	use	use	VERB
ejde-515	67	38	this	this	DET
ejde-515	67	39	result	result	NOUN
ejde-515	67	40	to	to	PART
ejde-515	67	41	prove	prove	VERB
ejde-515	67	42	an	an	DET
ejde-515	67	43	upper	upper	ADJ
ejde-515	67	44	semicontinuity	semicontinuity	NOUN
ejde-515	67	45	of	of	ADP
ejde-515	67	46	the	the	DET
ejde-515	67	47	pullback	pullback	NOUN
ejde-515	67	48	attractors	attractor	NOUN
ejde-515	67	49	.	.	PUNCT
ejde-515	68	1	finally	finally	ADV
ejde-515	68	2	,	,	PUNCT
ejde-515	68	3	in	in	ADP
ejde-515	68	4	section	section	NOUN
ejde-515	68	5	5	5	NUM
ejde-515	68	6	,	,	PUNCT
ejde-515	68	7	we	we	PRON
ejde-515	68	8	conclude	conclude	AUX
ejde-515	68	9	presenting	present	VERB
ejde-515	68	10	a	a	DET
ejde-515	68	11	brief	brief	ADJ
ejde-515	68	12	discussion	discussion	NOUN
ejde-515	68	13	about	about	ADP
ejde-515	68	14	the	the	DET
ejde-515	68	15	model	model	NOUN
ejde-515	68	16	and	and	CCONJ
ejde-515	68	17	about	about	ADP
ejde-515	68	18	a	a	DET
ejde-515	68	19	biological	biological	ADJ
ejde-515	68	20	interpretation	interpretation	NOUN
ejde-515	68	21	of	of	ADP
ejde-515	68	22	the	the	DET
ejde-515	68	23	result	result	NOUN
ejde-515	68	24	on	on	ADP
ejde-515	68	25	the	the	DET
ejde-515	68	26	continuous	continuous	ADJ
ejde-515	68	27	dependence	dependence	NOUN
ejde-515	68	28	of	of	ADP
ejde-515	68	29	neuronal	neuronal	ADJ
ejde-515	68	30	activity	activity	NOUN
ejde-515	68	31	with	with	ADP
ejde-515	68	32	respect	respect	NOUN
ejde-515	68	33	to	to	ADP
ejde-515	68	34	the	the	DET
ejde-515	68	35	external	external	ADJ
ejde-515	68	36	stimuli	stimulus	NOUN
ejde-515	68	37	function	function	NOUN
ejde-515	68	38	.	.	PUNCT
ejde-515	69	1	4	4	NUM
ejde-515	69	2	s.	s.	PROPN
ejde-515	69	3	h.	h.	PROPN
ejde-515	69	4	da	da	PROPN
ejde-515	69	5	silva	silva	PROPN
ejde-515	69	6	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	69	7	2	2	NUM
ejde-515	69	8	.	.	PUNCT
ejde-515	69	9	flow	flow	NOUN
ejde-515	69	10	generated	generate	VERB
ejde-515	69	11	by	by	ADP
ejde-515	69	12	the	the	DET
ejde-515	69	13	model	model	NOUN
ejde-515	69	14	problem	problem	NOUN
ejde-515	69	15	in	in	ADP
ejde-515	69	16	this	this	DET
ejde-515	69	17	section	section	NOUN
ejde-515	69	18	we	we	PRON
ejde-515	69	19	show	show	VERB
ejde-515	69	20	the	the	DET
ejde-515	69	21	existence	existence	NOUN
ejde-515	69	22	of	of	ADP
ejde-515	69	23	global	global	ADJ
ejde-515	69	24	solution	solution	NOUN
ejde-515	69	25	for	for	ADP
ejde-515	69	26	problem	problem	NOUN
ejde-515	69	27	(	(	PUNCT
ejde-515	69	28	1.2	1.2	NUM
ejde-515	69	29	)	)	PUNCT
ejde-515	69	30	and	and	CCONJ
ejde-515	69	31	that	that	SCONJ
ejde-515	69	32	it	it	PRON
ejde-515	69	33	generates	generate	VERB
ejde-515	69	34	a	a	DET
ejde-515	69	35	c1	c1	PROPN
ejde-515	69	36	evolution	evolution	NOUN
ejde-515	69	37	process	process	NOUN
ejde-515	69	38	in	in	ADP
ejde-515	69	39	an	an	DET
ejde-515	69	40	appropriate	appropriate	ADJ
ejde-515	69	41	banach	banach	NOUN
ejde-515	69	42	space	space	NOUN
ejde-515	69	43	.	.	PUNCT
ejde-515	70	1	for	for	ADP
ejde-515	70	2	more	more	ADJ
ejde-515	70	3	details	detail	NOUN
ejde-515	70	4	on	on	ADP
ejde-515	70	5	the	the	DET
ejde-515	70	6	process	process	NOUN
ejde-515	70	7	evolution	evolution	NOUN
ejde-515	70	8	(	(	PUNCT
ejde-515	70	9	or	or	CCONJ
ejde-515	70	10	infinite	infinite	ADV
ejde-515	70	11	-	-	PUNCT
ejde-515	70	12	dimensional	dimensional	ADJ
ejde-515	70	13	non	non	ADJ
ejde-515	70	14	-	-	ADJ
ejde-515	70	15	autonomous	autonomous	ADJ
ejde-515	70	16	dynamical	dynamical	ADJ
ejde-515	70	17	systems	system	NOUN
ejde-515	70	18	)	)	PUNCT
ejde-515	70	19	see	see	VERB
ejde-515	70	20	,	,	PUNCT
ejde-515	70	21	for	for	ADP
ejde-515	70	22	example	example	NOUN
ejde-515	70	23	[	[	X
ejde-515	70	24	8	8	NUM
ejde-515	70	25	,	,	PUNCT
ejde-515	70	26	10	10	NUM
ejde-515	70	27	,	,	PUNCT
ejde-515	70	28	23	23	NUM
ejde-515	70	29	,	,	PUNCT
ejde-515	70	30	22	22	NUM
ejde-515	70	31	]	]	PUNCT
ejde-515	70	32	and	and	CCONJ
ejde-515	70	33	for	for	ADP
ejde-515	70	34	finite	finite	ADJ
ejde-515	70	35	-	-	ADJ
ejde-515	70	36	dimensional	dimensional	ADJ
ejde-515	70	37	non	non	ADJ
ejde-515	70	38	-	-	ADJ
ejde-515	70	39	autonomous	autonomous	ADJ
ejde-515	70	40	dynamical	dynamical	ADJ
ejde-515	70	41	systems	system	NOUN
ejde-515	70	42	,	,	PUNCT
ejde-515	70	43	see	see	VERB
ejde-515	70	44	[	[	X
ejde-515	70	45	9	9	NUM
ejde-515	70	46	]	]	PUNCT
ejde-515	70	47	.	.	PUNCT
ejde-515	71	1	see	see	VERB
ejde-515	71	2	also	also	ADV
ejde-515	71	3	[	[	X
ejde-515	71	4	5	5	NUM
ejde-515	71	5	,	,	PUNCT
ejde-515	71	6	30	30	NUM
ejde-515	71	7	]	]	PUNCT
ejde-515	71	8	for	for	ADP
ejde-515	71	9	related	related	ADJ
ejde-515	71	10	works	work	NOUN
ejde-515	71	11	.	.	PUNCT
ejde-515	72	1	2.1	2.1	NUM
ejde-515	72	2	.	.	PUNCT
ejde-515	73	1	well	well	INTJ
ejde-515	73	2	posedness	posedness	NOUN
ejde-515	73	3	.	.	PUNCT
ejde-515	74	1	in	in	ADP
ejde-515	74	2	this	this	DET
ejde-515	74	3	subsection	subsection	NOUN
ejde-515	74	4	,	,	PUNCT
ejde-515	74	5	under	under	ADP
ejde-515	74	6	suitable	suitable	ADJ
ejde-515	74	7	growth	growth	NOUN
ejde-515	74	8	condition	condition	NOUN
ejde-515	74	9	on	on	ADP
ejde-515	74	10	the	the	DET
ejde-515	74	11	nonlinearity	nonlinearity	NOUN
ejde-515	74	12	f	f	NOUN
ejde-515	74	13	,	,	PUNCT
ejde-515	74	14	we	we	PRON
ejde-515	74	15	show	show	VERB
ejde-515	74	16	the	the	DET
ejde-515	74	17	well	well	ADJ
ejde-515	74	18	posedness	posedness	NOUN
ejde-515	74	19	of	of	ADP
ejde-515	74	20	problem	problem	NOUN
ejde-515	74	21	(	(	PUNCT
ejde-515	74	22	1.2	1.2	NUM
ejde-515	74	23	)	)	PUNCT
ejde-515	74	24	in	in	ADP
ejde-515	74	25	the	the	DET
ejde-515	74	26	phase	phase	NOUN
ejde-515	74	27	space	space	NOUN
ejde-515	74	28	xp	xp	NOUN
ejde-515	74	29	,	,	PUNCT
ejde-515	74	30	for	for	ADP
ejde-515	74	31	1	1	NUM
ejde-515	74	32	≤	≤	NOUN
ejde-515	74	33	p	p	NOUN
ejde-515	74	34	≤	≤	NUM
ejde-515	74	35	∞	∞	PROPN
ejde-515	74	36	,	,	PUNCT
ejde-515	74	37	given	give	VERB
ejde-515	74	38	by	by	ADP
ejde-515	74	39	xp	xp	NOUN
ejde-515	75	1	=	=	SYM
ejde-515	76	1	{	{	PUNCT
ejde-515	76	2	u	u	NOUN
ejde-515	76	3	∈	∈	PROPN
ejde-515	76	4	lp(rn	lp(rn	PROPN
ejde-515	76	5	)	)	PUNCT
ejde-515	76	6	:	:	PUNCT
ejde-515	76	7	u(x	u(x	PROPN
ejde-515	76	8	)	)	PUNCT
ejde-515	76	9	=	=	SYM
ejde-515	76	10	0	0	NUM
ejde-515	76	11	,	,	PUNCT
ejde-515	76	12	for	for	ADP
ejde-515	76	13	x	x	PROPN
ejde-515	76	14	∈	∈	PROPN
ejde-515	76	15	rn\ω	rn\ω	NOUN
ejde-515	76	16	}	}	PUNCT
ejde-515	76	17	with	with	ADP
ejde-515	76	18	the	the	DET
ejde-515	76	19	induced	induced	ADJ
ejde-515	76	20	norm	norm	NOUN
ejde-515	76	21	.	.	PUNCT
ejde-515	77	1	it	it	PRON
ejde-515	77	2	is	be	AUX
ejde-515	77	3	easy	easy	ADJ
ejde-515	77	4	to	to	PART
ejde-515	77	5	see	see	VERB
ejde-515	77	6	that	that	SCONJ
ejde-515	77	7	the	the	DET
ejde-515	77	8	banach	banach	NOUN
ejde-515	77	9	space	space	NOUN
ejde-515	77	10	xp	xp	INTJ
ejde-515	77	11	is	be	AUX
ejde-515	77	12	canonically	canonically	ADV
ejde-515	77	13	isometric	isometric	ADJ
ejde-515	77	14	to	to	ADP
ejde-515	77	15	lp(ω	lp(ω	NUM
ejde-515	77	16	)	)	PUNCT
ejde-515	77	17	,	,	PUNCT
ejde-515	77	18	then	then	ADV
ejde-515	77	19	we	we	PRON
ejde-515	77	20	usually	usually	ADV
ejde-515	77	21	identify	identify	VERB
ejde-515	77	22	the	the	DET
ejde-515	77	23	two	two	NUM
ejde-515	77	24	spaces	space	NOUN
ejde-515	77	25	,	,	PUNCT
ejde-515	77	26	without	without	ADP
ejde-515	77	27	further	further	ADJ
ejde-515	77	28	comment	comment	NOUN
ejde-515	77	29	.	.	PUNCT
ejde-515	78	1	for	for	ADP
ejde-515	78	2	simplicity	simplicity	NOUN
ejde-515	78	3	,	,	PUNCT
ejde-515	78	4	we	we	PRON
ejde-515	78	5	use	use	VERB
ejde-515	78	6	the	the	DET
ejde-515	78	7	same	same	ADJ
ejde-515	78	8	notation	notation	NOUN
ejde-515	78	9	for	for	ADP
ejde-515	78	10	a	a	DET
ejde-515	78	11	function	function	NOUN
ejde-515	78	12	defined	define	VERB
ejde-515	78	13	on	on	ADP
ejde-515	78	14	the	the	DET
ejde-515	78	15	whole	whole	ADJ
ejde-515	78	16	rn	rn	PROPN
ejde-515	78	17	and	and	CCONJ
ejde-515	78	18	also	also	ADV
ejde-515	78	19	for	for	ADP
ejde-515	78	20	its	its	PRON
ejde-515	78	21	restriction	restriction	NOUN
ejde-515	78	22	on	on	ADP
ejde-515	78	23	ω	ω	NUM
ejde-515	78	24	wherever	wherever	SCONJ
ejde-515	78	25	we	we	PRON
ejde-515	78	26	believe	believe	VERB
ejde-515	78	27	the	the	DET
ejde-515	78	28	intention	intention	NOUN
ejde-515	78	29	is	be	AUX
ejde-515	78	30	clear	clear	ADJ
ejde-515	78	31	in	in	ADP
ejde-515	78	32	the	the	DET
ejde-515	78	33	context	context	NOUN
ejde-515	78	34	.	.	PUNCT
ejde-515	79	1	to	to	PART
ejde-515	79	2	obtain	obtain	VERB
ejde-515	79	3	well	well	ADJ
ejde-515	79	4	posedness	posedness	NOUN
ejde-515	79	5	of	of	ADP
ejde-515	79	6	(	(	PUNCT
ejde-515	79	7	1.2	1.2	NUM
ejde-515	79	8	)	)	PUNCT
ejde-515	79	9	in	in	ADP
ejde-515	79	10	xp	xp	PROPN
ejde-515	79	11	,	,	PUNCT
ejde-515	79	12	we	we	PRON
ejde-515	79	13	consider	consider	VERB
ejde-515	79	14	the	the	DET
ejde-515	79	15	cauchy	cauchy	ADJ
ejde-515	79	16	problem	problem	NOUN
ejde-515	79	17	du	du	PROPN
ejde-515	79	18	dt	dt	PROPN
ejde-515	79	19	=	=	SYM
ejde-515	79	20	f	f	PROPN
ejde-515	79	21	(	(	PUNCT
ejde-515	79	22	t	t	PROPN
ejde-515	79	23	,	,	PUNCT
ejde-515	79	24	u	u	NOUN
ejde-515	79	25	)	)	PUNCT
ejde-515	79	26	,	,	PUNCT
ejde-515	79	27	t	t	PROPN
ejde-515	79	28	>	>	X
ejde-515	79	29	τ	τ	PROPN
ejde-515	79	30	,	,	PUNCT
ejde-515	79	31	u(τ	u(τ	ADJ
ejde-515	79	32	)	)	PUNCT
ejde-515	79	33	=	=	SYM
ejde-515	79	34	uτ	uτ	NOUN
ejde-515	79	35	,	,	PUNCT
ejde-515	79	36	(	(	PUNCT
ejde-515	79	37	2.1	2.1	NUM
ejde-515	79	38	)	)	PUNCT
ejde-515	79	39	where	where	SCONJ
ejde-515	79	40	the	the	DET
ejde-515	79	41	map	map	NOUN
ejde-515	79	42	f	f	X
ejde-515	79	43	:	:	PUNCT
ejde-515	79	44	r×xp	r×xp	NUM
ejde-515	79	45	→	→	SYM
ejde-515	79	46	xp	xp	X
ejde-515	79	47	is	be	AUX
ejde-515	79	48	defined	define	VERB
ejde-515	79	49	by	by	ADP
ejde-515	79	50	f	f	PROPN
ejde-515	79	51	(	(	PUNCT
ejde-515	79	52	t	t	PROPN
ejde-515	79	53	,	,	PUNCT
ejde-515	79	54	u)(x	u)(x	PROPN
ejde-515	79	55	)	)	PUNCT
ejde-515	79	56	=	=	PRON
ejde-515	79	57	{	{	PUNCT
ejde-515	79	58	−a(t)u(x	−a(t)u(x	NOUN
ejde-515	79	59	)	)	PUNCT
ejde-515	80	1	+	+	CCONJ
ejde-515	80	2	b(t)kf(t	b(t)kf(t	NOUN
ejde-515	80	3	,	,	PUNCT
ejde-515	80	4	u)(x)−	u)(x)−	PROPN
ejde-515	80	5	h+	h+	PROPN
ejde-515	80	6	s(t	s(t	PROPN
ejde-515	80	7	,	,	PUNCT
ejde-515	80	8	x	x	NOUN
ejde-515	80	9	)	)	PUNCT
ejde-515	80	10	,	,	PUNCT
ejde-515	80	11	if	if	SCONJ
ejde-515	80	12	t	t	PROPN
ejde-515	80	13	∈	∈	PROPN
ejde-515	80	14	r	r	PROPN
ejde-515	80	15	,	,	PUNCT
ejde-515	80	16	x	x	SYM
ejde-515	80	17	∈	∈	PROPN
ejde-515	80	18	ω	ω	PROPN
ejde-515	80	19	,	,	PUNCT
ejde-515	80	20	0	0	NUM
ejde-515	80	21	,	,	PUNCT
ejde-515	80	22	if	if	SCONJ
ejde-515	80	23	t	t	PROPN
ejde-515	80	24	∈	∈	PROPN
ejde-515	80	25	r	r	PROPN
ejde-515	80	26	,	,	PUNCT
ejde-515	80	27	x	x	SYM
ejde-515	80	28	∈	∈	PROPN
ejde-515	80	29	rn\ω	rn\ω	NOUN
ejde-515	80	30	,	,	PUNCT
ejde-515	80	31	(	(	PUNCT
ejde-515	80	32	2.2	2.2	NUM
ejde-515	80	33	)	)	PUNCT
ejde-515	80	34	where	where	SCONJ
ejde-515	80	35	kf(t	kf(t	NOUN
ejde-515	80	36	,	,	PUNCT
ejde-515	80	37	u)(x	u)(x	PROPN
ejde-515	80	38	)	)	PUNCT
ejde-515	80	39	:	:	PUNCT
ejde-515	81	1	=	=	SYM
ejde-515	81	2	∫	∫	PROPN
ejde-515	81	3	rn	rn	PROPN
ejde-515	81	4	j(x	j(x	PROPN
ejde-515	81	5	,	,	PUNCT
ejde-515	81	6	y)f(t	y)f(t	NOUN
ejde-515	81	7	,	,	PUNCT
ejde-515	81	8	u(y))dy	u(y))dy	NOUN
ejde-515	81	9	.	.	PUNCT
ejde-515	82	1	(	(	PUNCT
ejde-515	82	2	2.3	2.3	NUM
ejde-515	82	3	)	)	PUNCT
ejde-515	82	4	the	the	DET
ejde-515	82	5	map	map	NOUN
ejde-515	82	6	k	k	NOUN
ejde-515	82	7	is	be	AUX
ejde-515	82	8	well	well	ADV
ejde-515	82	9	defined	define	VERB
ejde-515	82	10	as	as	ADP
ejde-515	82	11	a	a	DET
ejde-515	82	12	bounded	bounded	ADJ
ejde-515	82	13	linear	linear	ADJ
ejde-515	82	14	operator	operator	NOUN
ejde-515	82	15	in	in	ADP
ejde-515	82	16	various	various	ADJ
ejde-515	82	17	function	function	NOUN
ejde-515	82	18	spaces	space	NOUN
ejde-515	82	19	,	,	PUNCT
ejde-515	82	20	depending	depend	VERB
ejde-515	82	21	on	on	ADP
ejde-515	82	22	the	the	DET
ejde-515	82	23	properties	property	NOUN
ejde-515	82	24	assumed	assume	VERB
ejde-515	82	25	for	for	ADP
ejde-515	82	26	j	j	PROPN
ejde-515	82	27	;	;	PUNCT
ejde-515	82	28	for	for	ADP
ejde-515	82	29	example	example	NOUN
ejde-515	82	30	,	,	PUNCT
ejde-515	82	31	with	with	SCONJ
ejde-515	82	32	j	j	PROPN
ejde-515	82	33	satisfying	satisfy	VERB
ejde-515	82	34	the	the	DET
ejde-515	82	35	hypotheses	hypothesis	NOUN
ejde-515	82	36	stated	state	VERB
ejde-515	82	37	in	in	ADP
ejde-515	82	38	the	the	DET
ejde-515	82	39	introduction	introduction	NOUN
ejde-515	82	40	,	,	PUNCT
ejde-515	82	41	k	k	PROPN
ejde-515	82	42	is	be	AUX
ejde-515	82	43	well	well	ADV
ejde-515	82	44	defined	define	VERB
ejde-515	82	45	in	in	ADP
ejde-515	82	46	xp	xp	INTJ
ejde-515	82	47	as	as	SCONJ
ejde-515	82	48	shown	show	VERB
ejde-515	82	49	in	in	ADP
ejde-515	82	50	the	the	DET
ejde-515	82	51	lemma	lemma	PROPN
ejde-515	82	52	below	below	ADV
ejde-515	82	53	,	,	PUNCT
ejde-515	82	54	which	which	PRON
ejde-515	82	55	was	be	AUX
ejde-515	82	56	proved	prove	VERB
ejde-515	82	57	in	in	ADP
ejde-515	82	58	[	[	X
ejde-515	82	59	17	17	NUM
ejde-515	82	60	]	]	PUNCT
ejde-515	82	61	.	.	PUNCT
ejde-515	83	1	lemma	lemma	PROPN
ejde-515	83	2	2.1	2.1	NUM
ejde-515	83	3	.	.	PUNCT
ejde-515	84	1	let	let	VERB
ejde-515	84	2	k	k	X
ejde-515	84	3	be	be	AUX
ejde-515	84	4	defined	define	VERB
ejde-515	84	5	by	by	ADP
ejde-515	84	6	(	(	PUNCT
ejde-515	84	7	2.3	2.3	NUM
ejde-515	84	8	)	)	PUNCT
ejde-515	84	9	and	and	CCONJ
ejde-515	84	10	‖j‖r	‖j‖r	NOUN
ejde-515	84	11	:	:	PUNCT
ejde-515	84	12	=	=	SYM
ejde-515	84	13	supx∈ω	supx∈ω	NOUN
ejde-515	84	14	‖j(x	‖j(x	ADP
ejde-515	84	15	,	,	PUNCT
ejde-515	84	16	·	·	PUNCT
ejde-515	84	17	)	)	PUNCT
ejde-515	84	18	‖lr(ω	‖lr(ω	NUM
ejde-515	84	19	)	)	PUNCT
ejde-515	84	20	,	,	PUNCT
ejde-515	84	21	1	1	NUM
ejde-515	84	22	≤	≤	NOUN
ejde-515	84	23	r	r	NOUN
ejde-515	84	24	≤	≤	PUNCT
ejde-515	84	25	∞.	∞.	PROPN
ejde-515	84	26	if	if	SCONJ
ejde-515	84	27	u	u	PROPN
ejde-515	84	28	∈	∈	PROPN
ejde-515	84	29	lp(ω	lp(ω	PUNCT
ejde-515	84	30	)	)	PUNCT
ejde-515	84	31	with	with	ADP
ejde-515	84	32	1	1	NUM
ejde-515	84	33	≤	≤	NOUN
ejde-515	84	34	p	p	NOUN
ejde-515	84	35	≤	≤	NUM
ejde-515	84	36	∞	∞	PROPN
ejde-515	84	37	,	,	PUNCT
ejde-515	84	38	then	then	ADV
ejde-515	84	39	ku	ku	PROPN
ejde-515	84	40	∈	∈	PROPN
ejde-515	84	41	l∞(ω	l∞(ω	PROPN
ejde-515	84	42	)	)	PUNCT
ejde-515	84	43	,	,	PUNCT
ejde-515	84	44	and	and	CCONJ
ejde-515	84	45	|ku(x)|	|ku(x)|	ADJ
ejde-515	84	46	≤	≤	NOUN
ejde-515	84	47	‖j‖q‖u‖lp(ω	‖j‖q‖u‖lp(ω	PUNCT
ejde-515	84	48	)	)	PUNCT
ejde-515	84	49	for	for	ADP
ejde-515	84	50	all	all	DET
ejde-515	84	51	x	x	SYM
ejde-515	84	52	∈	∈	PROPN
ejde-515	84	53	ω	ω	PROPN
ejde-515	84	54	,	,	PUNCT
ejde-515	84	55	(	(	PUNCT
ejde-515	84	56	2.4	2.4	NUM
ejde-515	84	57	)	)	PUNCT
ejde-515	84	58	where	where	SCONJ
ejde-515	84	59	1	1	NUM
ejde-515	84	60	≤	≤	NOUN
ejde-515	84	61	q	q	PUNCT
ejde-515	84	62	≤	≤	NUM
ejde-515	84	63	∞	∞	NUM
ejde-515	84	64	is	be	AUX
ejde-515	84	65	the	the	DET
ejde-515	84	66	conjugate	conjugate	ADJ
ejde-515	84	67	exponent	exponent	NOUN
ejde-515	84	68	of	of	ADP
ejde-515	84	69	p.	p.	PROPN
ejde-515	84	70	moreover	moreover	ADV
ejde-515	84	71	,	,	PUNCT
ejde-515	84	72	‖ku‖lp(ω	‖ku‖lp(ω	PROPN
ejde-515	84	73	)	)	PUNCT
ejde-515	84	74	≤	≤	NUM
ejde-515	84	75	‖j‖1‖u‖lp(ω	‖j‖1‖u‖lp(ω	NUM
ejde-515	84	76	)	)	PUNCT
ejde-515	84	77	≤	≤	NUM
ejde-515	84	78	‖u‖lp(ω	‖u‖lp(ω	NUM
ejde-515	84	79	)	)	PUNCT
ejde-515	84	80	.	.	PUNCT
ejde-515	85	1	(	(	PUNCT
ejde-515	85	2	2.5	2.5	NUM
ejde-515	85	3	)	)	PUNCT
ejde-515	85	4	if	if	SCONJ
ejde-515	85	5	u	u	PROPN
ejde-515	85	6	∈	∈	PROPN
ejde-515	85	7	l1(ω	l1(ω	PROPN
ejde-515	85	8	)	)	PUNCT
ejde-515	85	9	,	,	PUNCT
ejde-515	85	10	then	then	ADV
ejde-515	85	11	ku	ku	PROPN
ejde-515	85	12	∈	∈	PROPN
ejde-515	85	13	lp(ω	lp(ω	PROPN
ejde-515	85	14	)	)	PUNCT
ejde-515	85	15	,	,	PUNCT
ejde-515	85	16	1	1	NUM
ejde-515	85	17	≤	≤	NOUN
ejde-515	85	18	p	p	NOUN
ejde-515	85	19	≤	≤	NUM
ejde-515	85	20	∞	∞	PROPN
ejde-515	85	21	,	,	PUNCT
ejde-515	85	22	and	and	CCONJ
ejde-515	85	23	‖ku‖lp(ω	‖ku‖lp(ω	PROPN
ejde-515	85	24	)	)	PUNCT
ejde-515	85	25	≤	≤	NUM
ejde-515	85	26	‖j‖p‖u‖l1(ω	‖j‖p‖u‖l1(ω	PROPN
ejde-515	85	27	)	)	PUNCT
ejde-515	85	28	.	.	PUNCT
ejde-515	86	1	(	(	PUNCT
ejde-515	86	2	2.6	2.6	NUM
ejde-515	86	3	)	)	PUNCT
ejde-515	86	4	the	the	DET
ejde-515	86	5	following	follow	VERB
ejde-515	86	6	definition	definition	NOUN
ejde-515	86	7	is	be	AUX
ejde-515	86	8	well	well	ADV
ejde-515	86	9	known	know	VERB
ejde-515	86	10	in	in	ADP
ejde-515	86	11	the	the	DET
ejde-515	86	12	theory	theory	NOUN
ejde-515	86	13	of	of	ADP
ejde-515	86	14	odes	ode	NOUN
ejde-515	86	15	in	in	ADP
ejde-515	86	16	banach	banach	NOUN
ejde-515	86	17	spaces	space	NOUN
ejde-515	86	18	and	and	CCONJ
ejde-515	86	19	it	it	PRON
ejde-515	86	20	can	can	AUX
ejde-515	86	21	be	be	AUX
ejde-515	86	22	found	find	VERB
ejde-515	86	23	in	in	ADP
ejde-515	86	24	[	[	X
ejde-515	86	25	5	5	NUM
ejde-515	86	26	]	]	PUNCT
ejde-515	86	27	.	.	PUNCT
ejde-515	87	1	definition	definition	NOUN
ejde-515	87	2	2.2	2.2	NUM
ejde-515	87	3	.	.	PUNCT
ejde-515	88	1	if	if	SCONJ
ejde-515	88	2	e	e	PROPN
ejde-515	88	3	is	be	AUX
ejde-515	88	4	a	a	DET
ejde-515	88	5	normed	normed	ADJ
ejde-515	88	6	space	space	NOUN
ejde-515	88	7	,	,	PUNCT
ejde-515	88	8	and	and	CCONJ
ejde-515	88	9	i	i	PRON
ejde-515	88	10	⊂	⊂	PROPN
ejde-515	88	11	r	r	NOUN
ejde-515	88	12	is	be	AUX
ejde-515	88	13	an	an	DET
ejde-515	88	14	interval	interval	NOUN
ejde-515	88	15	,	,	PUNCT
ejde-515	88	16	we	we	PRON
ejde-515	88	17	say	say	VERB
ejde-515	88	18	that	that	SCONJ
ejde-515	88	19	a	a	DET
ejde-515	88	20	function	function	NOUN
ejde-515	88	21	f	f	NOUN
ejde-515	88	22	:	:	PUNCT
ejde-515	88	23	i	i	PRON
ejde-515	88	24	×e	×e	AUX
ejde-515	88	25	→	→	SYM
ejde-515	88	26	e	e	X
ejde-515	88	27	is	be	AUX
ejde-515	88	28	locally	locally	ADV
ejde-515	88	29	lipschitz	lipschitz	VERB
ejde-515	88	30	continuous	continuous	ADJ
ejde-515	88	31	(	(	PUNCT
ejde-515	88	32	or	or	CCONJ
ejde-515	88	33	simply	simply	ADV
ejde-515	88	34	locally	locally	ADV
ejde-515	88	35	lipschitz	lipschitz	NOUN
ejde-515	88	36	)	)	PUNCT
ejde-515	88	37	with	with	ADP
ejde-515	88	38	respect	respect	NOUN
ejde-515	88	39	to	to	ADP
ejde-515	88	40	the	the	DET
ejde-515	88	41	second	second	ADJ
ejde-515	88	42	variable	variable	NOUN
ejde-515	88	43	if	if	SCONJ
ejde-515	88	44	,	,	PUNCT
ejde-515	88	45	for	for	ADP
ejde-515	88	46	any	any	DET
ejde-515	88	47	(	(	PUNCT
ejde-515	88	48	t0	t0	PROPN
ejde-515	88	49	,	,	PUNCT
ejde-515	88	50	x0	x0	PROPN
ejde-515	88	51	)	)	PUNCT
ejde-515	88	52	∈	∈	PROPN
ejde-515	88	53	i×e	i×e	PROPN
ejde-515	88	54	,	,	PUNCT
ejde-515	88	55	there	there	PRON
ejde-515	88	56	exists	exist	VERB
ejde-515	88	57	a	a	DET
ejde-515	88	58	constant	constant	ADJ
ejde-515	88	59	ejde-2020/92	ejde-2020/92	ADJ
ejde-515	88	60	non	non	ADJ
ejde-515	88	61	-	-	ADJ
ejde-515	88	62	autonomous	autonomous	ADJ
ejde-515	88	63	model	model	NOUN
ejde-515	88	64	for	for	ADP
ejde-515	88	65	neural	neural	ADJ
ejde-515	88	66	fields	field	NOUN
ejde-515	88	67	5	5	NUM
ejde-515	88	68	c	c	NOUN
ejde-515	88	69	and	and	CCONJ
ejde-515	88	70	a	a	DET
ejde-515	88	71	rectangle	rectangle	NOUN
ejde-515	88	72	r	r	NOUN
ejde-515	88	73	=	=	SYM
ejde-515	88	74	{	{	PUNCT
ejde-515	88	75	(	(	PUNCT
ejde-515	88	76	t	t	PROPN
ejde-515	88	77	,	,	PUNCT
ejde-515	88	78	x	x	X
ejde-515	88	79	)	)	PUNCT
ejde-515	88	80	∈	∈	NOUN
ejde-515	89	1	i	i	PRON
ejde-515	89	2	×	×	NOUN
ejde-515	89	3	e	e	NOUN
ejde-515	89	4	:	:	PUNCT
ejde-515	89	5	|t	|t	PROPN
ejde-515	89	6	−	−	PROPN
ejde-515	90	1	t0|	t0|	X
ejde-515	90	2	<	<	X
ejde-515	90	3	b1	b1	PROPN
ejde-515	90	4	,	,	PUNCT
ejde-515	90	5	‖x	‖x	NOUN
ejde-515	90	6	−	−	PROPN
ejde-515	91	1	x0‖	x0‖	PROPN
ejde-515	91	2	<	<	X
ejde-515	91	3	b2	b2	PROPN
ejde-515	91	4	}	}	PUNCT
ejde-515	91	5	such	such	ADJ
ejde-515	91	6	that	that	SCONJ
ejde-515	91	7	,	,	PUNCT
ejde-515	91	8	if	if	SCONJ
ejde-515	91	9	(	(	PUNCT
ejde-515	91	10	t	t	PROPN
ejde-515	91	11	,	,	PUNCT
ejde-515	91	12	x	x	NOUN
ejde-515	91	13	)	)	PUNCT
ejde-515	91	14	and	and	CCONJ
ejde-515	91	15	(	(	PUNCT
ejde-515	91	16	t	t	PROPN
ejde-515	91	17	,	,	PUNCT
ejde-515	91	18	y	y	NOUN
ejde-515	91	19	)	)	PUNCT
ejde-515	91	20	belong	belong	VERB
ejde-515	91	21	to	to	ADP
ejde-515	91	22	r	r	NOUN
ejde-515	91	23	,	,	PUNCT
ejde-515	91	24	then	then	ADV
ejde-515	91	25	‖f	‖f	PRON
ejde-515	91	26	(	(	PUNCT
ejde-515	91	27	t	t	PROPN
ejde-515	91	28	,	,	PUNCT
ejde-515	91	29	x)−	x)−	PROPN
ejde-515	91	30	f	f	PROPN
ejde-515	91	31	(	(	PUNCT
ejde-515	91	32	t	t	PROPN
ejde-515	91	33	,	,	PUNCT
ejde-515	91	34	y)‖	y)‖	ADJ
ejde-515	91	35	≤	≤	PUNCT
ejde-515	91	36	c‖x−	c‖x−	ADV
ejde-515	91	37	y‖.	y‖.	NUM
ejde-515	91	38	we	we	PRON
ejde-515	91	39	say	say	VERB
ejde-515	91	40	that	that	SCONJ
ejde-515	91	41	f	f	PROPN
ejde-515	91	42	is	be	AUX
ejde-515	91	43	lipschitz	lipschitz	ADJ
ejde-515	91	44	continuous	continuous	ADJ
ejde-515	91	45	on	on	ADP
ejde-515	91	46	bounded	bounded	ADJ
ejde-515	91	47	sets	set	NOUN
ejde-515	91	48	with	with	ADP
ejde-515	91	49	respect	respect	NOUN
ejde-515	91	50	to	to	ADP
ejde-515	91	51	the	the	DET
ejde-515	91	52	second	second	ADJ
ejde-515	91	53	variable	variable	NOUN
ejde-515	91	54	if	if	SCONJ
ejde-515	91	55	the	the	DET
ejde-515	91	56	rectangle	rectangle	NOUN
ejde-515	91	57	r	r	NOUN
ejde-515	91	58	in	in	ADP
ejde-515	91	59	the	the	DET
ejde-515	91	60	previous	previous	ADJ
ejde-515	91	61	definition	definition	NOUN
ejde-515	91	62	can	can	AUX
ejde-515	91	63	be	be	AUX
ejde-515	91	64	chosen	choose	VERB
ejde-515	91	65	as	as	ADP
ejde-515	91	66	any	any	DET
ejde-515	91	67	bounded	bounded	ADJ
ejde-515	91	68	rectangle	rectangle	NOUN
ejde-515	91	69	in	in	ADP
ejde-515	91	70	r×	r×	PROPN
ejde-515	91	71	e.	e.	PROPN
ejde-515	91	72	remark	remark	PROPN
ejde-515	91	73	2.3	2.3	NUM
ejde-515	91	74	.	.	PUNCT
ejde-515	92	1	if	if	SCONJ
ejde-515	92	2	the	the	DET
ejde-515	92	3	normed	normed	ADJ
ejde-515	92	4	space	space	NOUN
ejde-515	92	5	e	e	NOUN
ejde-515	92	6	is	be	AUX
ejde-515	92	7	locally	locally	ADV
ejde-515	92	8	compact	compact	ADJ
ejde-515	92	9	the	the	DET
ejde-515	92	10	definitions	definition	NOUN
ejde-515	92	11	of	of	ADP
ejde-515	92	12	locally	locally	ADV
ejde-515	92	13	lipschitz	lipschitz	ADJ
ejde-515	92	14	continuous	continuous	ADJ
ejde-515	92	15	and	and	CCONJ
ejde-515	92	16	lipschitz	lipschitz	VERB
ejde-515	92	17	continuous	continuous	ADJ
ejde-515	92	18	on	on	ADP
ejde-515	92	19	bounded	bounded	ADJ
ejde-515	92	20	sets	set	NOUN
ejde-515	92	21	are	be	AUX
ejde-515	92	22	equivalent	equivalent	ADJ
ejde-515	92	23	.	.	PUNCT
ejde-515	93	1	now	now	ADV
ejde-515	93	2	,	,	PUNCT
ejde-515	93	3	proceeding	proceed	VERB
ejde-515	93	4	as	as	ADP
ejde-515	93	5	in	in	ADP
ejde-515	93	6	[	[	X
ejde-515	93	7	5	5	NUM
ejde-515	93	8	,	,	PUNCT
ejde-515	93	9	17	17	NUM
ejde-515	93	10	]	]	PUNCT
ejde-515	93	11	,	,	PUNCT
ejde-515	93	12	we	we	PRON
ejde-515	93	13	prove	prove	VERB
ejde-515	93	14	that	that	SCONJ
ejde-515	93	15	the	the	DET
ejde-515	93	16	map	map	NOUN
ejde-515	93	17	f	f	PROPN
ejde-515	93	18	,	,	PUNCT
ejde-515	93	19	given	give	VERB
ejde-515	93	20	in	in	ADP
ejde-515	93	21	(	(	PUNCT
ejde-515	93	22	2.2	2.2	NUM
ejde-515	93	23	)	)	PUNCT
ejde-515	93	24	,	,	PUNCT
ejde-515	93	25	is	be	AUX
ejde-515	93	26	well	well	ADV
ejde-515	93	27	defined	define	VERB
ejde-515	93	28	under	under	ADP
ejde-515	93	29	appropriate	appropriate	ADJ
ejde-515	93	30	growth	growth	NOUN
ejde-515	93	31	conditions	condition	NOUN
ejde-515	93	32	on	on	ADP
ejde-515	93	33	f	f	PROPN
ejde-515	93	34	and	and	CCONJ
ejde-515	93	35	it	it	PRON
ejde-515	93	36	is	be	AUX
ejde-515	93	37	locally	locally	ADV
ejde-515	93	38	lipschitz	lipschitz	VERB
ejde-515	93	39	continuous	continuous	ADJ
ejde-515	93	40	(	(	PUNCT
ejde-515	93	41	see	see	VERB
ejde-515	93	42	proposition	proposition	NOUN
ejde-515	93	43	2.5	2.5	NUM
ejde-515	93	44	below	below	ADV
ejde-515	93	45	,	,	PUNCT
ejde-515	93	46	which	which	PRON
ejde-515	93	47	generalizes	generalize	VERB
ejde-515	93	48	[	[	X
ejde-515	93	49	5	5	NUM
ejde-515	93	50	,	,	PUNCT
ejde-515	93	51	proposition	proposition	NOUN
ejde-515	93	52	3.3	3.3	NUM
ejde-515	93	53	]	]	PUNCT
ejde-515	93	54	and	and	CCONJ
ejde-515	93	55	[	[	X
ejde-515	93	56	17	17	NUM
ejde-515	93	57	,	,	PUNCT
ejde-515	93	58	proposition	proposition	NOUN
ejde-515	93	59	2.4	2.4	NUM
ejde-515	93	60	]	]	PUNCT
ejde-515	93	61	)	)	PUNCT
ejde-515	93	62	.	.	PUNCT
ejde-515	94	1	lemma	lemma	PROPN
ejde-515	94	2	2.4	2.4	NUM
ejde-515	94	3	.	.	PUNCT
ejde-515	95	1	let	let	VERB
ejde-515	95	2	us	we	PRON
ejde-515	95	3	assume	assume	VERB
ejde-515	95	4	the	the	DET
ejde-515	95	5	same	same	ADJ
ejde-515	95	6	hypotheses	hypothesis	NOUN
ejde-515	95	7	stated	state	VERB
ejde-515	95	8	in	in	ADP
ejde-515	95	9	lemma	lemma	PROPN
ejde-515	95	10	2.1	2.1	NUM
ejde-515	95	11	hold	hold	NOUN
ejde-515	95	12	,	,	PUNCT
ejde-515	95	13	and	and	CCONJ
ejde-515	95	14	that	that	SCONJ
ejde-515	95	15	the	the	DET
ejde-515	95	16	function	function	NOUN
ejde-515	95	17	f	f	PROPN
ejde-515	95	18	satisfies	satisfy	VERB
ejde-515	95	19	the	the	DET
ejde-515	95	20	growth	growth	NOUN
ejde-515	95	21	condition	condition	NOUN
ejde-515	95	22	|f(t	|f(t	PROPN
ejde-515	95	23	,	,	PUNCT
ejde-515	95	24	x)|	x)|	ADJ
ejde-515	95	25	≤	≤	NOUN
ejde-515	95	26	c1(t)(1	c1(t)(1	X
ejde-515	95	27	+	+	CCONJ
ejde-515	95	28	|x|p	|x|p	PROPN
ejde-515	95	29	)	)	PUNCT
ejde-515	95	30	,	,	PUNCT
ejde-515	95	31	for	for	ADP
ejde-515	95	32	any	any	DET
ejde-515	95	33	(	(	PUNCT
ejde-515	95	34	t	t	PROPN
ejde-515	95	35	,	,	PUNCT
ejde-515	95	36	x	x	NOUN
ejde-515	95	37	)	)	PUNCT
ejde-515	95	38	∈	∈	PROPN
ejde-515	95	39	r×	r×	PROPN
ejde-515	95	40	rn	rn	PROPN
ejde-515	95	41	,	,	PUNCT
ejde-515	95	42	(	(	PUNCT
ejde-515	95	43	2.7	2.7	NUM
ejde-515	95	44	)	)	PUNCT
ejde-515	95	45	with	with	ADP
ejde-515	95	46	1	1	NUM
ejde-515	95	47	≤	≤	NOUN
ejde-515	95	48	p	p	NOUN
ejde-515	95	49	<	<	X
ejde-515	95	50	∞	∞	PROPN
ejde-515	95	51	and	and	CCONJ
ejde-515	95	52	c1	c1	PROPN
ejde-515	95	53	:	:	PUNCT
ejde-515	95	54	r	r	NOUN
ejde-515	95	55	→	→	SYM
ejde-515	95	56	r	r	NOUN
ejde-515	95	57	is	be	AUX
ejde-515	95	58	a	a	DET
ejde-515	95	59	locally	locally	ADV
ejde-515	95	60	bounded	bound	VERB
ejde-515	95	61	function	function	NOUN
ejde-515	95	62	.	.	PUNCT
ejde-515	96	1	then	then	ADV
ejde-515	96	2	the	the	DET
ejde-515	96	3	function	function	NOUN
ejde-515	96	4	f	f	NOUN
ejde-515	96	5	given	give	VERB
ejde-515	96	6	by	by	ADP
ejde-515	96	7	(	(	PUNCT
ejde-515	96	8	2.2	2.2	NUM
ejde-515	96	9	)	)	PUNCT
ejde-515	96	10	is	be	AUX
ejde-515	96	11	well	well	ADV
ejde-515	96	12	defined	define	VERB
ejde-515	96	13	on	on	ADP
ejde-515	96	14	r×xp	r×xp	NOUN
ejde-515	96	15	.	.	PUNCT
ejde-515	97	1	if	if	SCONJ
ejde-515	97	2	,	,	PUNCT
ejde-515	97	3	for	for	ADP
ejde-515	97	4	any	any	DET
ejde-515	97	5	t	t	NOUN
ejde-515	97	6	∈	∈	PROPN
ejde-515	97	7	r	r	NOUN
ejde-515	97	8	,	,	PUNCT
ejde-515	97	9	the	the	DET
ejde-515	97	10	function	function	NOUN
ejde-515	97	11	f(t	f(t	NOUN
ejde-515	97	12	,	,	PUNCT
ejde-515	97	13	·	·	PUNCT
ejde-515	97	14	)	)	PUNCT
ejde-515	97	15	is	be	AUX
ejde-515	97	16	locally	locally	ADV
ejde-515	97	17	bounded	bound	VERB
ejde-515	97	18	,	,	PUNCT
ejde-515	97	19	then	then	ADV
ejde-515	97	20	f	f	PROPN
ejde-515	97	21	is	be	AUX
ejde-515	97	22	well	well	ADV
ejde-515	97	23	defined	define	VERB
ejde-515	97	24	on	on	ADP
ejde-515	97	25	r×	r×	NOUN
ejde-515	97	26	l∞(ω	l∞(ω	NOUN
ejde-515	97	27	)	)	PUNCT
ejde-515	97	28	.	.	PUNCT
ejde-515	98	1	proof	proof	NOUN
ejde-515	98	2	.	.	PUNCT
ejde-515	99	1	suppose	suppose	VERB
ejde-515	99	2	1	1	NUM
ejde-515	99	3	≤	≤	NOUN
ejde-515	99	4	p	p	X
ejde-515	99	5	<	<	X
ejde-515	99	6	∞.	∞.	PROPN
ejde-515	99	7	given	give	VERB
ejde-515	99	8	u	u	PRON
ejde-515	99	9	∈	∈	PROPN
ejde-515	99	10	lp(ω	lp(ω	PROPN
ejde-515	99	11	)	)	PUNCT
ejde-515	99	12	,	,	PUNCT
ejde-515	99	13	denoting	denote	VERB
ejde-515	99	14	the	the	DET
ejde-515	99	15	function	function	NOUN
ejde-515	99	16	f(t	f(t	NOUN
ejde-515	99	17	,	,	PUNCT
ejde-515	99	18	u)(x	u)(x	NOUN
ejde-515	99	19	)	)	PUNCT
ejde-515	99	20	=	=	SYM
ejde-515	100	1	f(t	f(t	NOUN
ejde-515	100	2	,	,	PUNCT
ejde-515	100	3	u(x	u(x	NOUN
ejde-515	100	4	)	)	PUNCT
ejde-515	100	5	)	)	PUNCT
ejde-515	100	6	by	by	ADP
ejde-515	100	7	f(t	f(t	PROPN
ejde-515	100	8	,	,	PUNCT
ejde-515	100	9	u	u	NOUN
ejde-515	100	10	)	)	PUNCT
ejde-515	100	11	and	and	CCONJ
ejde-515	100	12	using	use	VERB
ejde-515	100	13	(	(	PUNCT
ejde-515	100	14	2.7	2.7	NUM
ejde-515	100	15	)	)	PUNCT
ejde-515	100	16	,	,	PUNCT
ejde-515	100	17	it	it	PRON
ejde-515	100	18	easy	easy	ADJ
ejde-515	100	19	to	to	PART
ejde-515	100	20	see	see	VERB
ejde-515	100	21	that	that	PRON
ejde-515	100	22	,	,	PUNCT
ejde-515	100	23	for	for	ADP
ejde-515	100	24	each	each	DET
ejde-515	100	25	t	t	NOUN
ejde-515	100	26	∈	∈	PROPN
ejde-515	100	27	r	r	NOUN
ejde-515	100	28	‖f(t	‖f(t	NOUN
ejde-515	100	29	,	,	PUNCT
ejde-515	100	30	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	100	31	)	)	PUNCT
ejde-515	100	32	≤	≤	PUNCT
ejde-515	100	33	c1(t)(|ω|+	c1(t)(|ω|+	PROPN
ejde-515	100	34	‖u‖plp(ω	‖u‖plp(ω	PROPN
ejde-515	100	35	)	)	PUNCT
ejde-515	100	36	)	)	PUNCT
ejde-515	100	37	.	.	PUNCT
ejde-515	101	1	(	(	PUNCT
ejde-515	101	2	2.8	2.8	NUM
ejde-515	101	3	)	)	PUNCT
ejde-515	101	4	thus	thus	ADV
ejde-515	101	5	,	,	PUNCT
ejde-515	101	6	using	use	VERB
ejde-515	101	7	(	(	PUNCT
ejde-515	101	8	2.6	2.6	NUM
ejde-515	101	9	)	)	PUNCT
ejde-515	101	10	and	and	CCONJ
ejde-515	101	11	(	(	PUNCT
ejde-515	101	12	2.8	2.8	NUM
ejde-515	101	13	)	)	PUNCT
ejde-515	101	14	,	,	PUNCT
ejde-515	101	15	it	it	PRON
ejde-515	101	16	follows	follow	VERB
ejde-515	101	17	that	that	SCONJ
ejde-515	101	18	‖f	‖f	ADP
ejde-515	101	19	(	(	PUNCT
ejde-515	101	20	t	t	PROPN
ejde-515	101	21	,	,	PUNCT
ejde-515	101	22	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	101	23	)	)	PUNCT
ejde-515	101	24	≤	≤	PROPN
ejde-515	101	25	a0‖u‖lp(ω	a0‖u‖lp(ω	PROPN
ejde-515	101	26	)	)	PUNCT
ejde-515	102	1	+	+	CCONJ
ejde-515	102	2	b0‖kf(t	b0‖kf(t	NOUN
ejde-515	102	3	,	,	PUNCT
ejde-515	102	4	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	102	5	)	)	PUNCT
ejde-515	102	6	+	+	CCONJ
ejde-515	102	7	‖s(t	‖s(t	ADJ
ejde-515	102	8	,	,	PUNCT
ejde-515	102	9	·	·	PUNCT
ejde-515	102	10	)	)	PUNCT
ejde-515	102	11	‖lp(ω	‖lp(ω	PUNCT
ejde-515	102	12	)	)	PUNCT
ejde-515	103	1	+	+	CCONJ
ejde-515	103	2	‖h‖lp(ω	‖h‖lp(ω	X
ejde-515	103	3	)	)	PUNCT
ejde-515	103	4	≤	≤	NOUN
ejde-515	103	5	a0‖u‖lp(ω	a0‖u‖lp(ω	PROPN
ejde-515	103	6	)	)	PUNCT
ejde-515	104	1	+	+	NUM
ejde-515	104	2	b0‖j‖p‖f(t	b0‖j‖p‖f(t	NOUN
ejde-515	104	3	,	,	PUNCT
ejde-515	104	4	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	104	5	)	)	PUNCT
ejde-515	104	6	+	+	CCONJ
ejde-515	104	7	‖s(t	‖s(t	PROPN
ejde-515	104	8	,	,	PUNCT
ejde-515	104	9	·	·	PUNCT
ejde-515	104	10	)	)	PUNCT
ejde-515	104	11	‖lp(ω	‖lp(ω	PUNCT
ejde-515	104	12	)	)	PUNCT
ejde-515	105	1	+	+	CCONJ
ejde-515	105	2	h|ω|1	h|ω|1	NOUN
ejde-515	105	3	/	/	SYM
ejde-515	105	4	p	p	NOUN
ejde-515	105	5	≤	≤	PROPN
ejde-515	105	6	a0‖u‖lp(ω	a0‖u‖lp(ω	PROPN
ejde-515	105	7	)	)	PUNCT
ejde-515	106	1	+	+	NUM
ejde-515	106	2	b0‖j‖p(c1(t)|ω|+	b0‖j‖p(c1(t)|ω|+	NUM
ejde-515	106	3	c1(t)‖u‖plp(ω	c1(t)‖u‖plp(ω	NUM
ejde-515	106	4	)	)	PUNCT
ejde-515	106	5	)	)	PUNCT
ejde-515	107	1	+	+	CCONJ
ejde-515	107	2	‖s(t	‖s(t	ADP
ejde-515	107	3	,	,	PUNCT
ejde-515	107	4	·	·	PUNCT
ejde-515	107	5	)	)	PUNCT
ejde-515	107	6	‖lp(ω	‖lp(ω	PUNCT
ejde-515	107	7	)	)	PUNCT
ejde-515	107	8	+	+	CCONJ
ejde-515	107	9	h|ω|1	h|ω|1	NOUN
ejde-515	107	10	/	/	SYM
ejde-515	107	11	p	p	NOUN
ejde-515	107	12	≤	≤	PROPN
ejde-515	107	13	a0‖u‖lp(ω	a0‖u‖lp(ω	PROPN
ejde-515	107	14	)	)	PUNCT
ejde-515	108	1	+	+	CCONJ
ejde-515	108	2	b0c1(t)‖j‖p|ω|+	b0c1(t)‖j‖p|ω|+	X
ejde-515	108	3	b0c1(t)‖j‖p‖u‖plp(ω	b0c1(t)‖j‖p‖u‖plp(ω	PROPN
ejde-515	108	4	)	)	PUNCT
ejde-515	108	5	+	+	CCONJ
ejde-515	108	6	‖s(t	‖s(t	ADJ
ejde-515	108	7	,	,	PUNCT
ejde-515	108	8	·	·	PUNCT
ejde-515	108	9	)	)	PUNCT
ejde-515	108	10	‖lp(ω	‖lp(ω	PUNCT
ejde-515	108	11	)	)	PUNCT
ejde-515	109	1	+	+	CCONJ
ejde-515	109	2	h|ω|1	h|ω|1	NOUN
ejde-515	109	3	/	/	SYM
ejde-515	109	4	p.	p.	NOUN
ejde-515	109	5	since	since	SCONJ
ejde-515	109	6	s(t	s(t	PROPN
ejde-515	109	7	,	,	PUNCT
ejde-515	109	8	·	·	PUNCT
ejde-515	109	9	)	)	PUNCT
ejde-515	109	10	∈	∈	PROPN
ejde-515	109	11	lp(ω	lp(ω	PROPN
ejde-515	109	12	)	)	PUNCT
ejde-515	109	13	,	,	PUNCT
ejde-515	109	14	it	it	PRON
ejde-515	109	15	follows	follow	VERB
ejde-515	109	16	immediately	immediately	ADV
ejde-515	109	17	that	that	SCONJ
ejde-515	109	18	f	f	PROPN
ejde-515	109	19	is	be	AUX
ejde-515	109	20	well	well	ADV
ejde-515	109	21	defined	define	VERB
ejde-515	109	22	in	in	ADP
ejde-515	109	23	the	the	DET
ejde-515	109	24	space	space	NOUN
ejde-515	109	25	lp(ω	lp(ω	PUNCT
ejde-515	109	26	)	)	PUNCT
ejde-515	109	27	for	for	ADP
ejde-515	109	28	1	1	NUM
ejde-515	109	29	≤	≤	NOUN
ejde-515	109	30	p	p	NOUN
ejde-515	109	31	<	<	X
ejde-515	109	32	∞.	∞.	PROPN
ejde-515	109	33	if	if	SCONJ
ejde-515	109	34	p	p	PROPN
ejde-515	110	1	=	=	NOUN
ejde-515	110	2	∞	∞	NOUN
ejde-515	110	3	the	the	DET
ejde-515	110	4	result	result	NOUN
ejde-515	110	5	easily	easily	ADV
ejde-515	110	6	follows	follow	VERB
ejde-515	110	7	from	from	ADP
ejde-515	110	8	(	(	PUNCT
ejde-515	110	9	2.4	2.4	NUM
ejde-515	110	10	)	)	PUNCT
ejde-515	110	11	.	.	PUNCT
ejde-515	111	1	�	�	PROPN
ejde-515	111	2	proposition	proposition	NOUN
ejde-515	111	3	2.5	2.5	NUM
ejde-515	111	4	.	.	PUNCT
ejde-515	112	1	under	under	ADP
ejde-515	112	2	the	the	DET
ejde-515	112	3	hypotheses	hypothesis	NOUN
ejde-515	112	4	of	of	ADP
ejde-515	112	5	lemma	lemma	PROPN
ejde-515	112	6	2.4	2.4	NUM
ejde-515	112	7	,	,	PUNCT
ejde-515	112	8	if	if	SCONJ
ejde-515	112	9	a	a	PRON
ejde-515	112	10	and	and	CCONJ
ejde-515	112	11	b	b	NOUN
ejde-515	112	12	are	be	AUX
ejde-515	112	13	continuous	continuous	ADJ
ejde-515	112	14	functions	function	NOUN
ejde-515	112	15	and	and	CCONJ
ejde-515	112	16	f	f	PROPN
ejde-515	112	17	and	and	CCONJ
ejde-515	112	18	s	s	VERB
ejde-515	112	19	are	be	AUX
ejde-515	112	20	continuous	continuous	ADJ
ejde-515	112	21	functions	function	NOUN
ejde-515	112	22	with	with	ADP
ejde-515	112	23	respect	respect	NOUN
ejde-515	112	24	to	to	ADP
ejde-515	112	25	the	the	DET
ejde-515	112	26	first	first	ADJ
ejde-515	112	27	variable	variable	NOUN
ejde-515	112	28	,	,	PUNCT
ejde-515	112	29	then	then	ADV
ejde-515	112	30	f	f	PROPN
ejde-515	112	31	is	be	AUX
ejde-515	112	32	also	also	ADV
ejde-515	112	33	continuous	continuous	ADJ
ejde-515	112	34	on	on	ADP
ejde-515	112	35	the	the	DET
ejde-515	112	36	first	first	ADJ
ejde-515	112	37	variable	variable	NOUN
ejde-515	112	38	.	.	PUNCT
ejde-515	113	1	moreover	moreover	ADV
ejde-515	113	2	if	if	SCONJ
ejde-515	113	3	|f(t	|f(t	NOUN
ejde-515	113	4	,	,	PUNCT
ejde-515	113	5	x)−	x)−	PROPN
ejde-515	113	6	f(t	f(t	PROPN
ejde-515	113	7	,	,	PUNCT
ejde-515	113	8	y)|	y)|	PROPN
ejde-515	113	9	≤	≤	NOUN
ejde-515	113	10	c2(t)(1	c2(t)(1	ADP
ejde-515	113	11	+	+	NOUN
ejde-515	113	12	|x|p−1	|x|p−1	NUM
ejde-515	113	13	+	+	NUM
ejde-515	113	14	|y|p−1)|x−	|y|p−1)|x−	PROPN
ejde-515	113	15	y|	y|	NOUN
ejde-515	113	16	,	,	PUNCT
ejde-515	113	17	(	(	PUNCT
ejde-515	113	18	2.9	2.9	NUM
ejde-515	113	19	)	)	PUNCT
ejde-515	113	20	for	for	ADP
ejde-515	113	21	any	any	DET
ejde-515	113	22	(	(	PUNCT
ejde-515	113	23	x	x	NOUN
ejde-515	113	24	,	,	PUNCT
ejde-515	113	25	y	y	NOUN
ejde-515	113	26	)	)	PUNCT
ejde-515	113	27	∈	∈	PROPN
ejde-515	113	28	rn×rn	rn×rn	PROPN
ejde-515	113	29	,	,	PUNCT
ejde-515	113	30	t	t	PROPN
ejde-515	113	31	∈	∈	PROPN
ejde-515	113	32	r	r	NOUN
ejde-515	113	33	,	,	PUNCT
ejde-515	113	34	and	and	CCONJ
ejde-515	113	35	for	for	ADP
ejde-515	113	36	some	some	DET
ejde-515	113	37	strictly	strictly	ADV
ejde-515	113	38	positive	positive	ADJ
ejde-515	113	39	function	function	NOUN
ejde-515	113	40	c2	c2	NOUN
ejde-515	113	41	:	:	PUNCT
ejde-515	113	42	r→	r→	PROPN
ejde-515	113	43	r	r	PROPN
ejde-515	113	44	,	,	PUNCT
ejde-515	113	45	then	then	ADV
ejde-515	113	46	,	,	PUNCT
ejde-515	113	47	for	for	ADP
ejde-515	113	48	any	any	DET
ejde-515	113	49	1	1	NUM
ejde-515	113	50	≤	≤	NOUN
ejde-515	113	51	p	p	NOUN
ejde-515	113	52	<	<	X
ejde-515	113	53	∞	∞	PROPN
ejde-515	113	54	,	,	PUNCT
ejde-515	113	55	the	the	DET
ejde-515	113	56	function	function	NOUN
ejde-515	113	57	f	f	PROPN
ejde-515	113	58	is	be	AUX
ejde-515	113	59	locally	locally	ADV
ejde-515	113	60	lipschitz	lipschitz	VERB
ejde-515	113	61	continuous	continuous	ADJ
ejde-515	113	62	on	on	ADP
ejde-515	113	63	bounded	bounded	ADJ
ejde-515	113	64	sets	set	NOUN
ejde-515	113	65	with	with	ADP
ejde-515	113	66	respect	respect	NOUN
ejde-515	113	67	to	to	ADP
ejde-515	113	68	the	the	DET
ejde-515	113	69	second	second	ADJ
ejde-515	113	70	variable	variable	NOUN
ejde-515	113	71	.	.	PUNCT
ejde-515	114	1	if	if	SCONJ
ejde-515	114	2	p	p	PROPN
ejde-515	114	3	=	=	NOUN
ejde-515	114	4	∞	∞	PROPN
ejde-515	114	5	,	,	PUNCT
ejde-515	114	6	this	this	PRON
ejde-515	114	7	is	be	AUX
ejde-515	114	8	true	true	ADJ
ejde-515	114	9	if	if	SCONJ
ejde-515	114	10	f	f	PROPN
ejde-515	114	11	is	be	AUX
ejde-515	114	12	locally	locally	ADV
ejde-515	114	13	lipschitz	lipschitz	VERB
ejde-515	114	14	fuction	fuction	NOUN
ejde-515	114	15	with	with	ADP
ejde-515	114	16	respect	respect	NOUN
ejde-515	114	17	to	to	ADP
ejde-515	114	18	the	the	DET
ejde-515	114	19	second	second	ADJ
ejde-515	114	20	variable	variable	NOUN
ejde-515	114	21	.	.	PUNCT
ejde-515	115	1	6	6	NUM
ejde-515	115	2	s.	s.	PROPN
ejde-515	115	3	h.	h.	PROPN
ejde-515	115	4	da	da	PROPN
ejde-515	115	5	silva	silva	PROPN
ejde-515	115	6	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	115	7	proof	proof	NOUN
ejde-515	115	8	.	.	PUNCT
ejde-515	115	9	suppose	suppose	VERB
ejde-515	115	10	that	that	SCONJ
ejde-515	115	11	f(t	f(t	PROPN
ejde-515	115	12	,	,	PUNCT
ejde-515	115	13	x	x	X
ejde-515	115	14	)	)	PUNCT
ejde-515	115	15	is	be	AUX
ejde-515	115	16	continuous	continuous	ADJ
ejde-515	115	17	at	at	ADP
ejde-515	115	18	t.	t.	PROPN
ejde-515	115	19	then	then	ADV
ejde-515	115	20	for	for	SCONJ
ejde-515	115	21	any	any	DET
ejde-515	115	22	(	(	PUNCT
ejde-515	115	23	t	t	PROPN
ejde-515	115	24	,	,	PUNCT
ejde-515	115	25	u	u	NOUN
ejde-515	115	26	)	)	PUNCT
ejde-515	115	27	∈	∈	PROPN
ejde-515	115	28	r	r	NOUN
ejde-515	115	29	×	×	NOUN
ejde-515	115	30	xp	xp	INTJ
ejde-515	115	31	,	,	PUNCT
ejde-515	115	32	we	we	PRON
ejde-515	115	33	obtain	obtain	VERB
ejde-515	115	34	‖f(t	‖f(t	NOUN
ejde-515	115	35	,	,	PUNCT
ejde-515	115	36	u)−	u)−	PROPN
ejde-515	115	37	f(t+	f(t+	PROPN
ejde-515	115	38	ξ	ξ	NOUN
ejde-515	115	39	,	,	PUNCT
ejde-515	115	40	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	115	41	)	)	PUNCT
ejde-515	115	42	≤	≤	NUM
ejde-515	115	43	∫	∫	PROPN
ejde-515	115	44	ω	ω	PROPN
ejde-515	115	45	|f(t	|f(t	PROPN
ejde-515	115	46	,	,	PUNCT
ejde-515	115	47	u(x))−	u(x))−	ADP
ejde-515	115	48	f(t+	f(t+	PROPN
ejde-515	115	49	ξ	ξ	X
ejde-515	115	50	,	,	PUNCT
ejde-515	115	51	u(x))|	u(x))|	PROPN
ejde-515	115	52	dx	dx	PROPN
ejde-515	115	53	(	(	PUNCT
ejde-515	115	54	2.10	2.10	NUM
ejde-515	115	55	)	)	PUNCT
ejde-515	115	56	for	for	ADP
ejde-515	115	57	a	a	DET
ejde-515	115	58	small	small	ADJ
ejde-515	115	59	ξ	ξ	PROPN
ejde-515	115	60	∈	∈	PROPN
ejde-515	115	61	r.	r.	PROPN
ejde-515	115	62	from	from	ADP
ejde-515	115	63	(	(	PUNCT
ejde-515	115	64	2.7	2.7	NUM
ejde-515	115	65	)	)	PUNCT
ejde-515	115	66	,	,	PUNCT
ejde-515	115	67	it	it	PRON
ejde-515	115	68	follows	follow	VERB
ejde-515	115	69	that	that	SCONJ
ejde-515	115	70	the	the	DET
ejde-515	115	71	integrand	integrand	NOUN
ejde-515	115	72	in	in	ADP
ejde-515	115	73	(	(	PUNCT
ejde-515	115	74	2.10	2.10	NUM
ejde-515	115	75	)	)	PUNCT
ejde-515	115	76	is	be	AUX
ejde-515	115	77	bounded	bound	VERB
ejde-515	115	78	by	by	ADP
ejde-515	115	79	2c(1	2c(1	X
ejde-515	115	80	+	+	CCONJ
ejde-515	115	81	|u(x)|p	|u(x)|p	NOUN
ejde-515	115	82	)	)	PUNCT
ejde-515	115	83	,	,	PUNCT
ejde-515	115	84	where	where	SCONJ
ejde-515	115	85	c	c	PROPN
ejde-515	115	86	is	be	AUX
ejde-515	115	87	a	a	DET
ejde-515	115	88	bound	bind	VERB
ejde-515	115	89	for	for	ADP
ejde-515	115	90	c(t	c(t	PROPN
ejde-515	115	91	)	)	PUNCT
ejde-515	115	92	in	in	ADP
ejde-515	115	93	a	a	DET
ejde-515	115	94	neighborhood	neighborhood	NOUN
ejde-515	115	95	of	of	ADP
ejde-515	115	96	t	t	PROPN
ejde-515	115	97	,	,	PUNCT
ejde-515	115	98	and	and	CCONJ
ejde-515	115	99	it	it	PRON
ejde-515	115	100	goes	go	VERB
ejde-515	115	101	to	to	ADP
ejde-515	115	102	0	0	NUM
ejde-515	115	103	as	as	ADP
ejde-515	115	104	ξ	ξ	PROPN
ejde-515	115	105	→	→	SYM
ejde-515	115	106	0	0	NUM
ejde-515	115	107	.	.	PUNCT
ejde-515	116	1	hence	hence	ADV
ejde-515	116	2	,	,	PUNCT
ejde-515	116	3	using	use	VERB
ejde-515	116	4	lebesgue	lebesgue	NOUN
ejde-515	116	5	dominated	dominate	VERB
ejde-515	116	6	convergence	convergence	NOUN
ejde-515	116	7	theorem	theorem	VERB
ejde-515	116	8	,	,	PUNCT
ejde-515	116	9	it	it	PRON
ejde-515	116	10	follows	follow	VERB
ejde-515	116	11	that	that	SCONJ
ejde-515	116	12	‖f(t	‖f(t	VERB
ejde-515	116	13	,	,	PUNCT
ejde-515	117	1	u)−	u)−	PROPN
ejde-515	117	2	f(t+	f(t+	PROPN
ejde-515	117	3	ξ	ξ	NOUN
ejde-515	117	4	,	,	PUNCT
ejde-515	117	5	u)‖l1(ω	u)‖l1(ω	ADJ
ejde-515	117	6	)	)	PUNCT
ejde-515	117	7	→	→	SYM
ejde-515	117	8	0	0	NUM
ejde-515	117	9	as	as	ADP
ejde-515	117	10	ξ	ξ	X
ejde-515	117	11	→	→	SYM
ejde-515	117	12	0	0	NUM
ejde-515	117	13	.	.	PUNCT
ejde-515	118	1	thus	thus	ADV
ejde-515	118	2	,	,	PUNCT
ejde-515	118	3	using	use	VERB
ejde-515	118	4	(	(	PUNCT
ejde-515	118	5	2.5	2.5	NUM
ejde-515	118	6	)	)	PUNCT
ejde-515	118	7	and	and	CCONJ
ejde-515	118	8	(	(	PUNCT
ejde-515	118	9	2.8	2.8	NUM
ejde-515	118	10	)	)	PUNCT
ejde-515	118	11	,	,	PUNCT
ejde-515	118	12	we	we	PRON
ejde-515	118	13	obtain	obtain	VERB
ejde-515	118	14	‖f	‖f	ADP
ejde-515	118	15	(	(	PUNCT
ejde-515	118	16	t+	t+	X
ejde-515	118	17	ξ	ξ	NOUN
ejde-515	118	18	,	,	PUNCT
ejde-515	118	19	u)−	u)−	PROPN
ejde-515	118	20	f	f	PROPN
ejde-515	118	21	(	(	PUNCT
ejde-515	118	22	t	t	PROPN
ejde-515	118	23	,	,	PUNCT
ejde-515	118	24	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	118	25	)	)	PUNCT
ejde-515	118	26	≤	≤	NUM
ejde-515	119	1	|a(t)−	|a(t)−	PROPN
ejde-515	119	2	a(t+	a(t+	PROPN
ejde-515	119	3	ξ)|‖u‖lp(ω	ξ)|‖u‖lp(ω	PROPN
ejde-515	119	4	)	)	PUNCT
ejde-515	120	1	+	+	CCONJ
ejde-515	120	2	|b(t+	|b(t+	ADJ
ejde-515	120	3	ξ)−	ξ)−	PROPN
ejde-515	120	4	b(t)|‖k(f(t+	b(t)|‖k(f(t+	NOUN
ejde-515	120	5	ξ	ξ	PROPN
ejde-515	120	6	,	,	PUNCT
ejde-515	120	7	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	120	8	)	)	PUNCT
ejde-515	121	1	+	+	CCONJ
ejde-515	121	2	|b(t)|‖k(f(t+	|b(t)|‖k(f(t+	PROPN
ejde-515	121	3	ξ	ξ	X
ejde-515	121	4	,	,	PUNCT
ejde-515	121	5	u)−	u)−	PROPN
ejde-515	121	6	f(t	f(t	NOUN
ejde-515	121	7	,	,	PUNCT
ejde-515	121	8	u))‖lp(ω	u))‖lp(ω	PUNCT
ejde-515	121	9	)	)	PUNCT
ejde-515	122	1	+	+	CCONJ
ejde-515	122	2	‖s(t+	‖s(t+	PROPN
ejde-515	122	3	ξ	ξ	PROPN
ejde-515	122	4	,	,	PUNCT
ejde-515	122	5	·	·	PUNCT
ejde-515	122	6	)	)	PUNCT
ejde-515	122	7	−	−	PROPN
ejde-515	122	8	s(t	s(t	PROPN
ejde-515	122	9	,	,	PUNCT
ejde-515	122	10	·	·	PUNCT
ejde-515	122	11	)	)	PUNCT
ejde-515	122	12	‖lp(ω	‖lp(ω	PUNCT
ejde-515	122	13	)	)	PUNCT
ejde-515	122	14	≤	≤	PUNCT
ejde-515	123	1	|a(t)−	|a(t)−	PROPN
ejde-515	123	2	a(t+	a(t+	PROPN
ejde-515	123	3	ξ)|‖u‖lp(ω	ξ)|‖u‖lp(ω	PROPN
ejde-515	123	4	)	)	PUNCT
ejde-515	124	1	+	+	CCONJ
ejde-515	124	2	|b(t+	|b(t+	ADJ
ejde-515	124	3	ξ)−	ξ)−	PROPN
ejde-515	124	4	b(t)|‖j‖pc1(t)(|ω|+	b(t)|‖j‖pc1(t)(|ω|+	NOUN
ejde-515	124	5	‖u‖plp(ω	‖u‖plp(ω	PROPN
ejde-515	124	6	)	)	PUNCT
ejde-515	124	7	)	)	PUNCT
ejde-515	125	1	+	+	CCONJ
ejde-515	125	2	|b(t)|‖j‖p‖f(t+	|b(t)|‖j‖p‖f(t+	PROPN
ejde-515	125	3	ξ	ξ	PROPN
ejde-515	125	4	,	,	PUNCT
ejde-515	125	5	u)−	u)−	PROPN
ejde-515	125	6	f(t	f(t	NOUN
ejde-515	125	7	,	,	PUNCT
ejde-515	125	8	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	125	9	)	)	PUNCT
ejde-515	125	10	+	+	CCONJ
ejde-515	125	11	‖s(t+	‖s(t+	PROPN
ejde-515	125	12	ξ	ξ	PROPN
ejde-515	125	13	,	,	PUNCT
ejde-515	125	14	·	·	PUNCT
ejde-515	125	15	)	)	PUNCT
ejde-515	125	16	−	−	PROPN
ejde-515	125	17	s(t	s(t	PROPN
ejde-515	125	18	,	,	PUNCT
ejde-515	125	19	·	·	PUNCT
ejde-515	125	20	)	)	PUNCT
ejde-515	125	21	‖lp(ω	‖lp(ω	PUNCT
ejde-515	125	22	)	)	PUNCT
ejde-515	125	23	which	which	PRON
ejde-515	125	24	approaches	approach	VERB
ejde-515	125	25	0	0	NUM
ejde-515	125	26	as	as	ADP
ejde-515	125	27	ξ	ξ	PROPN
ejde-515	125	28	→	→	SYM
ejde-515	125	29	0	0	NUM
ejde-515	125	30	,	,	PUNCT
ejde-515	125	31	proving	prove	VERB
ejde-515	125	32	the	the	DET
ejde-515	125	33	continuity	continuity	NOUN
ejde-515	125	34	of	of	ADP
ejde-515	125	35	f	f	PROPN
ejde-515	125	36	in	in	ADP
ejde-515	125	37	t.	t.	PROPN
ejde-515	125	38	now	now	ADV
ejde-515	125	39	assume	assume	VERB
ejde-515	125	40	that	that	SCONJ
ejde-515	125	41	|f(t	|f(t	NOUN
ejde-515	125	42	,	,	PUNCT
ejde-515	125	43	x)−	x)−	PROPN
ejde-515	125	44	f(t	f(t	PROPN
ejde-515	125	45	,	,	PUNCT
ejde-515	125	46	y)|	y)|	PROPN
ejde-515	125	47	≤	≤	NOUN
ejde-515	125	48	c2(t)(1	c2(t)(1	ADP
ejde-515	125	49	+	+	NOUN
ejde-515	125	50	|x|p−1	|x|p−1	NUM
ejde-515	125	51	+	+	NUM
ejde-515	125	52	|y|p−1)|x−	|y|p−1)|x−	PROPN
ejde-515	125	53	y|	y|	NOUN
ejde-515	125	54	,	,	PUNCT
ejde-515	125	55	for	for	ADP
ejde-515	125	56	some	some	DET
ejde-515	125	57	1	1	NUM
ejde-515	125	58	<	<	X
ejde-515	125	59	p	p	X
ejde-515	125	60	<	<	X
ejde-515	125	61	∞	∞	PROPN
ejde-515	125	62	,	,	PUNCT
ejde-515	125	63	where	where	SCONJ
ejde-515	125	64	c2	c2	PROPN
ejde-515	125	65	:	:	PUNCT
ejde-515	125	66	r→	r→	PROPN
ejde-515	125	67	r	r	NOUN
ejde-515	125	68	is	be	AUX
ejde-515	125	69	a	a	DET
ejde-515	125	70	strictly	strictly	ADV
ejde-515	125	71	positive	positive	ADJ
ejde-515	125	72	function	function	NOUN
ejde-515	125	73	.	.	PUNCT
ejde-515	126	1	then	then	ADV
ejde-515	126	2	,	,	PUNCT
ejde-515	126	3	for	for	ADP
ejde-515	126	4	u	u	NOUN
ejde-515	126	5	and	and	CCONJ
ejde-515	126	6	v	v	ADP
ejde-515	126	7	belonging	belong	VERB
ejde-515	126	8	to	to	ADP
ejde-515	126	9	lp(ω	lp(ω	NUM
ejde-515	126	10	)	)	PUNCT
ejde-515	126	11	,	,	PUNCT
ejde-515	126	12	using	use	VERB
ejde-515	126	13	hölder	hölder	NOUN
ejde-515	126	14	inequality	inequality	NOUN
ejde-515	126	15	,	,	PUNCT
ejde-515	126	16	see	see	VERB
ejde-515	126	17	[	[	X
ejde-515	126	18	6	6	NUM
ejde-515	126	19	]	]	PUNCT
ejde-515	126	20	,	,	PUNCT
ejde-515	126	21	we	we	PRON
ejde-515	126	22	obtain	obtain	VERB
ejde-515	126	23	‖f(t	‖f(t	NOUN
ejde-515	126	24	,	,	PUNCT
ejde-515	126	25	u)−	u)−	PROPN
ejde-515	126	26	f(t	f(t	NOUN
ejde-515	126	27	,	,	PUNCT
ejde-515	126	28	v)‖l1(ω	v)‖l1(ω	NOUN
ejde-515	126	29	)	)	PUNCT
ejde-515	126	30	≤	≤	NUM
ejde-515	126	31	∫	∫	PROPN
ejde-515	126	32	ω	ω	PROPN
ejde-515	126	33	c2(t)(1	c2(t)(1	PART
ejde-515	126	34	+	+	X
ejde-515	126	35	|u(x)|p−1	|u(x)|p−1	NOUN
ejde-515	126	36	+	+	CCONJ
ejde-515	126	37	|v(x)|p−1)|u−	|v(x)|p−1)|u−	PROPN
ejde-515	126	38	v|	v|	NOUN
ejde-515	126	39	dx	dx	PROPN
ejde-515	126	40	≤	≤	PROPN
ejde-515	126	41	c2(t	c2(t	PROPN
ejde-515	126	42	)	)	PUNCT
ejde-515	126	43	[	[	PUNCT
ejde-515	126	44	∫	∫	PROPN
ejde-515	126	45	ω	ω	PROPN
ejde-515	126	46	(	(	PUNCT
ejde-515	126	47	1	1	NUM
ejde-515	126	48	+	+	X
ejde-515	126	49	|u(x)|p−1	|u(x)|p−1	NOUN
ejde-515	126	50	+	+	CCONJ
ejde-515	126	51	|v(x)|p−1)qdx	|v(x)|p−1)qdx	NOUN
ejde-515	126	52	]	]	SYM
ejde-515	126	53	1	1	NUM
ejde-515	126	54	/	/	SYM
ejde-515	126	55	q	q	NOUN
ejde-515	126	56	[	[	PUNCT
ejde-515	126	57	∫	∫	PROPN
ejde-515	126	58	ω	ω	PROPN
ejde-515	126	59	|u(x)−	|u(x)−	PROPN
ejde-515	126	60	v(x)|pdx	v(x)|pdx	X
ejde-515	126	61	]	]	X
ejde-515	126	62	1	1	NUM
ejde-515	126	63	/	/	SYM
ejde-515	126	64	p	p	NOUN
ejde-515	126	65	≤	≤	NUM
ejde-515	126	66	c2(t	c2(t	NOUN
ejde-515	126	67	)	)	PUNCT
ejde-515	126	68	[	[	PUNCT
ejde-515	126	69	‖1‖lq(ω	‖1‖lq(ω	NOUN
ejde-515	126	70	)	)	PUNCT
ejde-515	127	1	+	+	CCONJ
ejde-515	127	2	‖up−1‖lq(ω	‖up−1‖lq(ω	NUM
ejde-515	127	3	)	)	PUNCT
ejde-515	127	4	+	+	ADJ
ejde-515	127	5	‖vp−1‖lq(ω	‖vp−1‖lq(ω	NUM
ejde-515	127	6	)	)	PUNCT
ejde-515	127	7	]	]	PUNCT
ejde-515	128	1	‖u−	‖u−	PROPN
ejde-515	128	2	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	128	3	)	)	PUNCT
ejde-515	128	4	≤	≤	NOUN
ejde-515	128	5	c2(t	c2(t	NOUN
ejde-515	128	6	)	)	PUNCT
ejde-515	128	7	[	[	PUNCT
ejde-515	128	8	|ω|1	|ω|1	PROPN
ejde-515	128	9	/	/	SYM
ejde-515	128	10	q	q	NOUN
ejde-515	128	11	+	+	NUM
ejde-515	128	12	‖u‖p	‖u‖p	NOUN
ejde-515	128	13	/	/	SYM
ejde-515	128	14	qlp(ω	qlp(ω	NOUN
ejde-515	128	15	)	)	PUNCT
ejde-515	128	16	+	+	CCONJ
ejde-515	128	17	‖v‖p	‖v‖p	NOUN
ejde-515	128	18	/	/	SYM
ejde-515	128	19	qlp(ω	qlp(ω	NOUN
ejde-515	128	20	)	)	PUNCT
ejde-515	128	21	]	]	PUNCT
ejde-515	129	1	‖u−	‖u−	PROPN
ejde-515	129	2	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	129	3	)	)	PUNCT
ejde-515	129	4	,	,	PUNCT
ejde-515	129	5	where	where	SCONJ
ejde-515	129	6	q	q	NOUN
ejde-515	129	7	is	be	AUX
ejde-515	129	8	the	the	DET
ejde-515	129	9	conjugate	conjugate	ADJ
ejde-515	129	10	exponent	exponent	NOUN
ejde-515	129	11	of	of	ADP
ejde-515	129	12	p.	p.	NOUN
ejde-515	129	13	using	use	VERB
ejde-515	129	14	(	(	PUNCT
ejde-515	129	15	2.6	2.6	NUM
ejde-515	129	16	)	)	PUNCT
ejde-515	129	17	once	once	ADV
ejde-515	129	18	again	again	ADV
ejde-515	129	19	and	and	CCONJ
ejde-515	129	20	the	the	DET
ejde-515	129	21	hypotheses	hypothesis	NOUN
ejde-515	129	22	on	on	ADP
ejde-515	129	23	f	f	PROPN
ejde-515	129	24	,	,	PUNCT
ejde-515	129	25	it	it	PRON
ejde-515	129	26	follows	follow	VERB
ejde-515	129	27	that	that	SCONJ
ejde-515	130	1	‖f	‖f	ADP
ejde-515	130	2	(	(	PUNCT
ejde-515	130	3	t	t	PROPN
ejde-515	130	4	,	,	PUNCT
ejde-515	130	5	u)−	u)−	PROPN
ejde-515	130	6	f	f	PROPN
ejde-515	130	7	(	(	PUNCT
ejde-515	130	8	t	t	PROPN
ejde-515	130	9	,	,	PUNCT
ejde-515	130	10	v)‖lp(ω	v)‖lp(ω	NOUN
ejde-515	130	11	)	)	PUNCT
ejde-515	130	12	≤	≤	NOUN
ejde-515	131	1	a0‖u−	a0‖u−	PUNCT
ejde-515	131	2	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	131	3	)	)	PUNCT
ejde-515	132	1	+	+	CCONJ
ejde-515	132	2	b0‖k(f(t	b0‖k(f(t	NOUN
ejde-515	132	3	,	,	PUNCT
ejde-515	132	4	u)−	u)−	PROPN
ejde-515	132	5	f(t	f(t	NOUN
ejde-515	132	6	,	,	PUNCT
ejde-515	132	7	v))‖lp(ω	v))‖lp(ω	NOUN
ejde-515	132	8	)	)	PUNCT
ejde-515	132	9	≤	≤	NOUN
ejde-515	132	10	a0‖u−	a0‖u−	PUNCT
ejde-515	132	11	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	132	12	)	)	PUNCT
ejde-515	132	13	+	+	NUM
ejde-515	132	14	b0‖j‖p‖f(t	b0‖j‖p‖f(t	NOUN
ejde-515	132	15	,	,	PUNCT
ejde-515	132	16	u)−	u)−	PROPN
ejde-515	132	17	f(t	f(t	NOUN
ejde-515	132	18	,	,	PUNCT
ejde-515	132	19	v)‖l1(ω	v)‖l1(ω	NOUN
ejde-515	132	20	)	)	PUNCT
ejde-515	132	21	≤	≤	NOUN
ejde-515	132	22	(	(	PUNCT
ejde-515	132	23	a0	a0	PROPN
ejde-515	132	24	+	+	CCONJ
ejde-515	132	25	b0c2(t)‖j‖p	b0c2(t)‖j‖p	NOUN
ejde-515	132	26	[	[	PUNCT
ejde-515	132	27	|ω|1	|ω|1	PROPN
ejde-515	132	28	/	/	SYM
ejde-515	132	29	q	q	NOUN
ejde-515	132	30	+	+	NUM
ejde-515	132	31	‖u‖p	‖u‖p	NOUN
ejde-515	132	32	/	/	SYM
ejde-515	132	33	qlp(ω	qlp(ω	NOUN
ejde-515	132	34	)	)	PUNCT
ejde-515	133	1	+	+	CCONJ
ejde-515	133	2	‖v‖p	‖v‖p	NOUN
ejde-515	133	3	/	/	SYM
ejde-515	133	4	qlp(ω	qlp(ω	NOUN
ejde-515	133	5	)	)	PUNCT
ejde-515	133	6	]	]	PUNCT
ejde-515	133	7	)	)	PUNCT
ejde-515	134	1	‖u−	‖u−	PROPN
ejde-515	134	2	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	134	3	)	)	PUNCT
ejde-515	134	4	,	,	PUNCT
ejde-515	134	5	showing	show	VERB
ejde-515	134	6	that	that	SCONJ
ejde-515	134	7	f	f	PROPN
ejde-515	134	8	is	be	AUX
ejde-515	134	9	lipschitz	lipschitz	NOUN
ejde-515	134	10	on	on	ADP
ejde-515	134	11	bounded	bounded	ADJ
ejde-515	134	12	sets	set	NOUN
ejde-515	134	13	of	of	ADP
ejde-515	134	14	lp(ω	lp(ω	PROPN
ejde-515	134	15	)	)	PUNCT
ejde-515	134	16	as	as	SCONJ
ejde-515	134	17	claimed	claim	VERB
ejde-515	134	18	.	.	PUNCT
ejde-515	135	1	if	if	SCONJ
ejde-515	135	2	p	p	NOUN
ejde-515	135	3	=	=	NOUN
ejde-515	135	4	1	1	NUM
ejde-515	135	5	,	,	PUNCT
ejde-515	135	6	the	the	DET
ejde-515	135	7	proof	proof	NOUN
ejde-515	135	8	is	be	AUX
ejde-515	135	9	similar	similar	ADJ
ejde-515	135	10	.	.	PUNCT
ejde-515	136	1	suppose	suppose	VERB
ejde-515	136	2	finally	finally	ADV
ejde-515	136	3	that	that	DET
ejde-515	136	4	‖u‖l∞(ω	‖u‖l∞(ω	NOUN
ejde-515	136	5	)	)	PUNCT
ejde-515	136	6	≤	≤	NOUN
ejde-515	136	7	r	r	NOUN
ejde-515	136	8	,	,	PUNCT
ejde-515	136	9	‖v‖l∞(ω	‖v‖l∞(ω	NOUN
ejde-515	136	10	)	)	PUNCT
ejde-515	136	11	≤	≤	NOUN
ejde-515	136	12	r	r	NOUN
ejde-515	136	13	and	and	CCONJ
ejde-515	136	14	let	let	VERB
ejde-515	136	15	m	m	PRON
ejde-515	136	16	be	be	AUX
ejde-515	136	17	the	the	DET
ejde-515	136	18	lipschitz	lipschitz	NOUN
ejde-515	136	19	constant	constant	ADJ
ejde-515	136	20	of	of	ADP
ejde-515	136	21	f	f	PROPN
ejde-515	136	22	in	in	ADP
ejde-515	136	23	the	the	DET
ejde-515	136	24	interval	interval	NOUN
ejde-515	136	25	[	[	X
ejde-515	136	26	−r	−r	ADJ
ejde-515	136	27	,	,	PUNCT
ejde-515	136	28	r	r	X
ejde-515	136	29	]	]	X
ejde-515	136	30	⊂	⊂	PROPN
ejde-515	136	31	r.	r.	PROPN
ejde-515	136	32	then	then	ADV
ejde-515	136	33	|f(t	|f(t	PROPN
ejde-515	136	34	,	,	PUNCT
ejde-515	136	35	u(x))−	u(x))−	ADJ
ejde-515	136	36	f(t	f(t	NOUN
ejde-515	136	37	,	,	PUNCT
ejde-515	136	38	v(x))|	v(x))|	PROPN
ejde-515	136	39	≤m	≤m	PROPN
ejde-515	136	40	|u(x)−	|u(x)−	PROPN
ejde-515	136	41	v(x)|	v(x)|	NOUN
ejde-515	136	42	,	,	PUNCT
ejde-515	136	43	for	for	ADP
ejde-515	136	44	any	any	DET
ejde-515	136	45	x	x	SYM
ejde-515	136	46	∈	∈	PROPN
ejde-515	136	47	ω	ω	PROPN
ejde-515	136	48	,	,	PUNCT
ejde-515	136	49	and	and	CCONJ
ejde-515	136	50	this	this	PRON
ejde-515	136	51	allows	allow	VERB
ejde-515	136	52	us	we	PRON
ejde-515	136	53	to	to	PART
ejde-515	136	54	conclude	conclude	VERB
ejde-515	136	55	that	that	SCONJ
ejde-515	136	56	‖f(t	‖f(t	VERB
ejde-515	136	57	,	,	PUNCT
ejde-515	136	58	u)−	u)−	PROPN
ejde-515	136	59	f(t	f(t	PROPN
ejde-515	136	60	,	,	PUNCT
ejde-515	136	61	v)‖l∞(ω	v)‖l∞(ω	NOUN
ejde-515	136	62	)	)	PUNCT
ejde-515	136	63	≤m‖u−	≤m‖u−	PROPN
ejde-515	136	64	v‖l∞(ω	v‖l∞(ω	NOUN
ejde-515	136	65	)	)	PUNCT
ejde-515	136	66	.	.	PUNCT
ejde-515	137	1	thus	thus	ADV
ejde-515	137	2	,	,	PUNCT
ejde-515	137	3	by	by	ADP
ejde-515	137	4	(	(	PUNCT
ejde-515	137	5	2.5	2.5	NUM
ejde-515	137	6	)	)	PUNCT
ejde-515	137	7	we	we	PRON
ejde-515	137	8	have	have	VERB
ejde-515	137	9	that	that	PRON
ejde-515	137	10	‖f	‖f	ADP
ejde-515	137	11	(	(	PUNCT
ejde-515	137	12	t	t	PROPN
ejde-515	137	13	,	,	PUNCT
ejde-515	137	14	u)−	u)−	PROPN
ejde-515	137	15	f	f	PROPN
ejde-515	137	16	(	(	PUNCT
ejde-515	137	17	t	t	PROPN
ejde-515	137	18	,	,	PUNCT
ejde-515	137	19	v)‖l∞(ω	v)‖l∞(ω	NOUN
ejde-515	137	20	)	)	PUNCT
ejde-515	137	21	≤	≤	NOUN
ejde-515	137	22	a0‖u−	a0‖u−	NOUN
ejde-515	137	23	v‖l∞(ω	v‖l∞(ω	NOUN
ejde-515	137	24	)	)	PUNCT
ejde-515	137	25	+	+	CCONJ
ejde-515	137	26	b0‖k(f(t	b0‖k(f(t	NOUN
ejde-515	137	27	,	,	PUNCT
ejde-515	137	28	u)−	u)−	PROPN
ejde-515	137	29	f(t	f(t	NOUN
ejde-515	137	30	,	,	PUNCT
ejde-515	137	31	v))‖l∞(ω	v))‖l∞(ω	NOUN
ejde-515	137	32	)	)	PUNCT
ejde-515	137	33	ejde-2020/92	ejde-2020/92	VERB
ejde-515	137	34	non	non	ADJ
ejde-515	137	35	-	-	ADJ
ejde-515	137	36	autonomous	autonomous	ADJ
ejde-515	137	37	model	model	NOUN
ejde-515	137	38	for	for	ADP
ejde-515	137	39	neural	neural	ADJ
ejde-515	137	40	fields	field	NOUN
ejde-515	137	41	7	7	NUM
ejde-515	137	42	≤	≤	NOUN
ejde-515	137	43	(	(	PUNCT
ejde-515	137	44	a0	a0	NOUN
ejde-515	137	45	+	+	CCONJ
ejde-515	137	46	b0m‖j‖1	b0m‖j‖1	PROPN
ejde-515	137	47	)	)	PUNCT
ejde-515	137	48	‖u−	‖u−	PROPN
ejde-515	137	49	v‖l∞(ω	v‖l∞(ω	NOUN
ejde-515	137	50	)	)	PUNCT
ejde-515	137	51	.	.	PUNCT
ejde-515	138	1	this	this	PRON
ejde-515	138	2	completes	complete	VERB
ejde-515	138	3	the	the	DET
ejde-515	138	4	proof	proof	NOUN
ejde-515	138	5	.	.	PUNCT
ejde-515	139	1	�	�	PROPN
ejde-515	139	2	using	use	VERB
ejde-515	139	3	proposition	proposition	NOUN
ejde-515	139	4	2.5	2.5	NUM
ejde-515	139	5	and	and	CCONJ
ejde-515	139	6	well	well	ADV
ejde-515	139	7	known	know	VERB
ejde-515	139	8	results	result	NOUN
ejde-515	139	9	of	of	ADP
ejde-515	139	10	odes	ode	NOUN
ejde-515	139	11	in	in	ADP
ejde-515	139	12	banach	banach	NOUN
ejde-515	139	13	spaces	space	NOUN
ejde-515	139	14	[	[	X
ejde-515	139	15	12	12	NUM
ejde-515	139	16	]	]	PUNCT
ejde-515	139	17	it	it	PRON
ejde-515	139	18	follows	follow	VERB
ejde-515	139	19	that	that	SCONJ
ejde-515	139	20	the	the	DET
ejde-515	139	21	initial	initial	ADJ
ejde-515	139	22	value	value	NOUN
ejde-515	139	23	problem	problem	NOUN
ejde-515	139	24	(	(	PUNCT
ejde-515	139	25	2.1	2.1	NUM
ejde-515	139	26	)	)	PUNCT
ejde-515	139	27	has	have	VERB
ejde-515	139	28	a	a	DET
ejde-515	139	29	unique	unique	ADJ
ejde-515	139	30	local	local	ADJ
ejde-515	139	31	solution	solution	NOUN
ejde-515	139	32	for	for	ADP
ejde-515	139	33	any	any	DET
ejde-515	139	34	initial	initial	ADJ
ejde-515	139	35	condition	condition	NOUN
ejde-515	139	36	in	in	ADP
ejde-515	139	37	xp	xp	PROPN
ejde-515	139	38	.	.	PUNCT
ejde-515	140	1	for	for	ADP
ejde-515	140	2	the	the	DET
ejde-515	140	3	existence	existence	NOUN
ejde-515	140	4	of	of	ADP
ejde-515	140	5	a	a	DET
ejde-515	140	6	global	global	ADJ
ejde-515	140	7	solution	solution	NOUN
ejde-515	140	8	,	,	PUNCT
ejde-515	140	9	we	we	PRON
ejde-515	140	10	use	use	VERB
ejde-515	140	11	[	[	PUNCT
ejde-515	140	12	24	24	NUM
ejde-515	140	13	,	,	PUNCT
ejde-515	140	14	theorem	theorem	VERB
ejde-515	140	15	5.6.1	5.6.1	NUM
ejde-515	140	16	]	]	PUNCT
ejde-515	140	17	.	.	PUNCT
ejde-515	141	1	proposition	proposition	NOUN
ejde-515	141	2	2.6	2.6	NUM
ejde-515	141	3	.	.	PUNCT
ejde-515	142	1	under	under	ADP
ejde-515	142	2	same	same	ADJ
ejde-515	142	3	hypotheses	hypothesis	NOUN
ejde-515	142	4	in	in	ADP
ejde-515	142	5	proposition	proposition	NOUN
ejde-515	142	6	2.5	2.5	NUM
ejde-515	142	7	,	,	PUNCT
ejde-515	142	8	if	if	SCONJ
ejde-515	142	9	there	there	PRON
ejde-515	142	10	exists	exist	VERB
ejde-515	142	11	a	a	DET
ejde-515	142	12	constant	constant	ADJ
ejde-515	142	13	k1	k1	NOUN
ejde-515	142	14	∈	∈	PROPN
ejde-515	142	15	r	r	NOUN
ejde-515	142	16	,	,	PUNCT
ejde-515	142	17	independent	independent	ADJ
ejde-515	142	18	of	of	ADP
ejde-515	142	19	t	t	PROPN
ejde-515	142	20	,	,	PUNCT
ejde-515	142	21	such	such	ADJ
ejde-515	142	22	that	that	SCONJ
ejde-515	142	23	f	f	PROPN
ejde-515	142	24	satisfies	satisfy	VERB
ejde-515	142	25	the	the	DET
ejde-515	142	26	dissipative	dissipative	ADJ
ejde-515	142	27	condition	condition	NOUN
ejde-515	142	28	lim	lim	PROPN
ejde-515	142	29	sup	sup	NOUN
ejde-515	142	30	|x|→∞	|x|→∞	NOUN
ejde-515	142	31	|f(t	|f(t	NOUN
ejde-515	142	32	,	,	PUNCT
ejde-515	142	33	x)|	x)|	PROPN
ejde-515	142	34	|x|	|x|	PROPN
ejde-515	142	35	<	<	X
ejde-515	142	36	k1	k1	PROPN
ejde-515	142	37	.	.	PUNCT
ejde-515	143	1	(	(	PUNCT
ejde-515	143	2	2.11	2.11	NUM
ejde-515	143	3	)	)	PUNCT
ejde-515	143	4	then	then	ADV
ejde-515	143	5	problem	problem	NOUN
ejde-515	143	6	(	(	PUNCT
ejde-515	143	7	2.1	2.1	NUM
ejde-515	143	8	)	)	PUNCT
ejde-515	143	9	has	have	VERB
ejde-515	143	10	a	a	DET
ejde-515	143	11	unique	unique	ADJ
ejde-515	143	12	globally	globally	ADV
ejde-515	143	13	defined	define	VERB
ejde-515	143	14	solution	solution	NOUN
ejde-515	143	15	for	for	ADP
ejde-515	143	16	any	any	DET
ejde-515	143	17	initial	initial	ADJ
ejde-515	143	18	condition	condition	NOUN
ejde-515	143	19	in	in	ADP
ejde-515	143	20	xp	xp	PROPN
ejde-515	143	21	,	,	PUNCT
ejde-515	143	22	which	which	PRON
ejde-515	143	23	is	be	AUX
ejde-515	143	24	given	give	VERB
ejde-515	143	25	for	for	ADP
ejde-515	143	26	t	t	PROPN
ejde-515	143	27	≥	≥	PROPN
ejde-515	143	28	τ	τ	PROPN
ejde-515	143	29	,	,	PUNCT
ejde-515	143	30	by	by	ADP
ejde-515	143	31	the	the	DET
ejde-515	143	32	“	"	PUNCT
ejde-515	143	33	variation	variation	NOUN
ejde-515	143	34	of	of	ADP
ejde-515	143	35	constants	constant	NOUN
ejde-515	143	36	formula	formula	NOUN
ejde-515	143	37	”	"	PUNCT
ejde-515	143	38	u(t	u(t	NOUN
ejde-515	143	39	,	,	PUNCT
ejde-515	143	40	x	x	NOUN
ejde-515	143	41	)	)	PUNCT
ejde-515	143	42	=	=	SYM
ejde-515	144	1			PRON
ejde-515	144	2	e−(a(t)−a(τ))uτ	e−(a(t)−a(τ))uτ	VERB
ejde-515	144	3	(	(	PUNCT
ejde-515	144	4	x	x	NOUN
ejde-515	144	5	)	)	PUNCT
ejde-515	145	1	+	+	CCONJ
ejde-515	145	2	∫	∫	PROPN
ejde-515	145	3	t	t	PROPN
ejde-515	145	4	τ	τ	PROPN
ejde-515	145	5	e−(a(t)−a(s))b(s)kf(s	e−(a(t)−a(s))b(s)kf(	NOUN
ejde-515	145	6	,	,	PUNCT
ejde-515	145	7	u(s	u(s	ADJ
ejde-515	145	8	,	,	PUNCT
ejde-515	145	9	·	·	PUNCT
ejde-515	145	10	)	)	PUNCT
ejde-515	145	11	)	)	PUNCT
ejde-515	145	12	(	(	PUNCT
ejde-515	145	13	x	x	X
ejde-515	145	14	)	)	PUNCT
ejde-515	145	15	ds	ds	PROPN
ejde-515	146	1	+	+	CCONJ
ejde-515	146	2	∫	∫	PROPN
ejde-515	146	3	t	t	PROPN
ejde-515	146	4	τ	τ	PROPN
ejde-515	146	5	e−(a(t)−a(s))[−h+	e−(a(t)−a(s))[−h+	PROPN
ejde-515	146	6	s(s	s(s	PROPN
ejde-515	146	7	,	,	PUNCT
ejde-515	146	8	x)]ds	x)]ds	PRON
ejde-515	146	9	,	,	PUNCT
ejde-515	146	10	x	x	PROPN
ejde-515	146	11	∈	∈	PROPN
ejde-515	146	12	ω	ω	PROPN
ejde-515	146	13	,	,	PUNCT
ejde-515	146	14	0	0	NUM
ejde-515	146	15	,	,	PUNCT
ejde-515	146	16	x	x	SYM
ejde-515	146	17	∈	∈	NOUN
ejde-515	146	18	ωc	ωc	X
ejde-515	146	19	,	,	PUNCT
ejde-515	146	20	(	(	PUNCT
ejde-515	146	21	2.12	2.12	NUM
ejde-515	146	22	)	)	PUNCT
ejde-515	146	23	where	where	SCONJ
ejde-515	146	24	a(ξ	a(ξ	PROPN
ejde-515	146	25	)	)	PUNCT
ejde-515	146	26	=	=	SYM
ejde-515	147	1	∫	∫	PROPN
ejde-515	147	2	ξ	ξ	SYM
ejde-515	147	3	0	0	PUNCT
ejde-515	147	4	a(η)dη	a(η)dη	PROPN
ejde-515	147	5	,	,	PUNCT
ejde-515	147	6	for	for	ADP
ejde-515	147	7	any	any	DET
ejde-515	147	8	ξ	ξ	PROPN
ejde-515	147	9	≥	≥	NOUN
ejde-515	147	10	τ	τ	X
ejde-515	147	11	,	,	PUNCT
ejde-515	147	12	and	and	CCONJ
ejde-515	147	13	ωc	ωc	ADP
ejde-515	147	14	=	=	SYM
ejde-515	147	15	rn\ω	rn\ω	NOUN
ejde-515	147	16	.	.	PUNCT
ejde-515	148	1	proof	proof	NOUN
ejde-515	148	2	.	.	PUNCT
ejde-515	149	1	the	the	DET
ejde-515	149	2	existence	existence	NOUN
ejde-515	149	3	and	and	CCONJ
ejde-515	149	4	uniqueness	uniqueness	NOUN
ejde-515	149	5	of	of	ADP
ejde-515	149	6	local	local	ADJ
ejde-515	149	7	solutions	solution	NOUN
ejde-515	149	8	for	for	ADP
ejde-515	149	9	(	(	PUNCT
ejde-515	149	10	2.1	2.1	NUM
ejde-515	149	11	)	)	PUNCT
ejde-515	149	12	,	,	PUNCT
ejde-515	149	13	in	in	ADP
ejde-515	149	14	xp	xp	PROPN
ejde-515	149	15	,	,	PUNCT
ejde-515	149	16	follow	follow	VERB
ejde-515	149	17	from	from	ADP
ejde-515	149	18	proposition	proposition	NOUN
ejde-515	149	19	2.5	2.5	NUM
ejde-515	149	20	and	and	CCONJ
ejde-515	149	21	the	the	DET
ejde-515	149	22	well	well	ADV
ejde-515	149	23	-	-	PUNCT
ejde-515	149	24	known	know	VERB
ejde-515	149	25	results	result	NOUN
ejde-515	149	26	in	in	ADP
ejde-515	149	27	[	[	X
ejde-515	149	28	12	12	NUM
ejde-515	149	29	]	]	PUNCT
ejde-515	149	30	.	.	PUNCT
ejde-515	150	1	the	the	DET
ejde-515	150	2	variation	variation	NOUN
ejde-515	150	3	of	of	ADP
ejde-515	150	4	constants	constant	NOUN
ejde-515	150	5	formula	formula	NOUN
ejde-515	150	6	(	(	PUNCT
ejde-515	150	7	2.12	2.12	NUM
ejde-515	150	8	)	)	PUNCT
ejde-515	150	9	can	can	AUX
ejde-515	150	10	be	be	AUX
ejde-515	150	11	easily	easily	ADV
ejde-515	150	12	verified	verify	VERB
ejde-515	150	13	by	by	ADP
ejde-515	150	14	direct	direct	ADJ
ejde-515	150	15	derivation	derivation	NOUN
ejde-515	150	16	.	.	PUNCT
ejde-515	151	1	now	now	ADV
ejde-515	151	2	,	,	PUNCT
ejde-515	151	3	using	use	VERB
ejde-515	151	4	condition	condition	NOUN
ejde-515	151	5	(	(	PUNCT
ejde-515	151	6	2.11	2.11	NUM
ejde-515	151	7	)	)	PUNCT
ejde-515	151	8	,	,	PUNCT
ejde-515	151	9	it	it	PRON
ejde-515	151	10	follows	follow	VERB
ejde-515	151	11	that	that	SCONJ
ejde-515	151	12	|f(t	|f(t	NOUN
ejde-515	151	13	,	,	PUNCT
ejde-515	151	14	x)|	x)|	PROPN
ejde-515	151	15	≤	≤	NUM
ejde-515	151	16	k2(t	k2(t	PROPN
ejde-515	151	17	)	)	PUNCT
ejde-515	151	18	+	+	CCONJ
ejde-515	152	1	k1|x|	k1|x|	PROPN
ejde-515	152	2	,	,	PUNCT
ejde-515	152	3	for	for	ADP
ejde-515	152	4	any	any	DET
ejde-515	152	5	(	(	PUNCT
ejde-515	152	6	t	t	PROPN
ejde-515	152	7	,	,	PUNCT
ejde-515	152	8	x	x	NOUN
ejde-515	152	9	)	)	PUNCT
ejde-515	152	10	∈	∈	PROPN
ejde-515	152	11	r×	r×	PROPN
ejde-515	152	12	rn	rn	PROPN
ejde-515	152	13	,	,	PUNCT
ejde-515	152	14	(	(	PUNCT
ejde-515	152	15	2.13	2.13	NUM
ejde-515	152	16	)	)	PUNCT
ejde-515	152	17	for	for	ADP
ejde-515	152	18	some	some	DET
ejde-515	152	19	continuous	continuous	ADJ
ejde-515	152	20	and	and	CCONJ
ejde-515	152	21	strictly	strictly	ADV
ejde-515	152	22	positive	positive	ADJ
ejde-515	152	23	function	function	NOUN
ejde-515	152	24	k2	k2	NOUN
ejde-515	152	25	:	:	PUNCT
ejde-515	152	26	r→	r→	PROPN
ejde-515	152	27	r.	r.	PROPN
ejde-515	152	28	if	if	SCONJ
ejde-515	152	29	1	1	NUM
ejde-515	152	30	≤	≤	NOUN
ejde-515	152	31	p	p	NOUN
ejde-515	152	32	<	<	X
ejde-515	152	33	∞	∞	PROPN
ejde-515	152	34	,	,	PUNCT
ejde-515	152	35	using	use	VERB
ejde-515	152	36	(	(	PUNCT
ejde-515	152	37	2.5	2.5	NUM
ejde-515	152	38	)	)	PUNCT
ejde-515	152	39	and	and	CCONJ
ejde-515	152	40	(	(	PUNCT
ejde-515	152	41	2.13	2.13	NUM
ejde-515	152	42	)	)	PUNCT
ejde-515	152	43	,	,	PUNCT
ejde-515	152	44	we	we	PRON
ejde-515	152	45	obtain	obtain	VERB
ejde-515	152	46	the	the	DET
ejde-515	152	47	estimate	estimate	NOUN
ejde-515	152	48	‖kf(t	‖kf(t	NOUN
ejde-515	152	49	,	,	PUNCT
ejde-515	152	50	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	152	51	)	)	PUNCT
ejde-515	152	52	≤	≤	NOUN
ejde-515	152	53	‖f(t	‖f(t	NOUN
ejde-515	152	54	,	,	PUNCT
ejde-515	152	55	u)‖lp(ω	u)‖lp(ω	ADJ
ejde-515	152	56	)	)	PUNCT
ejde-515	152	57	≤	≤	NUM
ejde-515	152	58	k2(t)|ω|1	k2(t)|ω|1	PROPN
ejde-515	152	59	/	/	SYM
ejde-515	152	60	p	p	PROPN
ejde-515	153	1	+	+	CCONJ
ejde-515	153	2	k1‖u‖lp(ω	k1‖u‖lp(ω	PROPN
ejde-515	153	3	)	)	PUNCT
ejde-515	153	4	.	.	PUNCT
ejde-515	154	1	for	for	ADP
ejde-515	154	2	p	p	NOUN
ejde-515	154	3	=	=	SYM
ejde-515	154	4	∞	∞	PROPN
ejde-515	154	5	,	,	PUNCT
ejde-515	154	6	using	use	VERB
ejde-515	154	7	the	the	DET
ejde-515	154	8	same	same	ADJ
ejde-515	154	9	arguments	argument	NOUN
ejde-515	154	10	(	(	PUNCT
ejde-515	154	11	or	or	CCONJ
ejde-515	154	12	passing	pass	VERB
ejde-515	154	13	to	to	ADP
ejde-515	154	14	the	the	DET
ejde-515	154	15	limit	limit	NOUN
ejde-515	154	16	p	p	X
ejde-515	154	17	→	→	SYM
ejde-515	154	18	∞	∞	PROPN
ejde-515	154	19	in	in	ADP
ejde-515	154	20	the	the	DET
ejde-515	154	21	previous	previous	ADJ
ejde-515	154	22	inequality	inequality	NOUN
ejde-515	154	23	)	)	PUNCT
ejde-515	154	24	,	,	PUNCT
ejde-515	154	25	we	we	PRON
ejde-515	154	26	have	have	VERB
ejde-515	154	27	‖kf(t	‖kf(t	PROPN
ejde-515	154	28	,	,	PUNCT
ejde-515	154	29	u)‖l∞(ω	u)‖l∞(ω	NOUN
ejde-515	154	30	)	)	PUNCT
ejde-515	154	31	≤	≤	NOUN
ejde-515	154	32	k2(t	k2(t	PROPN
ejde-515	154	33	)	)	PUNCT
ejde-515	155	1	+	+	NUM
ejde-515	155	2	k1‖u‖l∞(ω	k1‖u‖l∞(ω	NOUN
ejde-515	155	3	)	)	PUNCT
ejde-515	155	4	.	.	PUNCT
ejde-515	156	1	now	now	ADV
ejde-515	156	2	defining	define	VERB
ejde-515	156	3	the	the	DET
ejde-515	156	4	function	function	NOUN
ejde-515	156	5	g	g	NOUN
ejde-515	156	6	:	:	PUNCT
ejde-515	157	1	[	[	X
ejde-515	157	2	t0,∞)×	t0,∞)×	NOUN
ejde-515	157	3	r+	r+	PUNCT
ejde-515	157	4	→	→	PUNCT
ejde-515	157	5	r+	r+	NOUN
ejde-515	157	6	by	by	ADP
ejde-515	157	7	g(t	g(t	PROPN
ejde-515	157	8	,	,	PUNCT
ejde-515	157	9	r	r	NOUN
ejde-515	157	10	)	)	PUNCT
ejde-515	157	11	=	=	SYM
ejde-515	157	12	b0|ω|1	b0|ω|1	PROPN
ejde-515	157	13	/	/	SYM
ejde-515	157	14	pk2(t	pk2(t	PROPN
ejde-515	157	15	)	)	PUNCT
ejde-515	158	1	+	+	CCONJ
ejde-515	158	2	‖s‖p	‖s‖p	NOUN
ejde-515	158	3	+	+	CCONJ
ejde-515	158	4	h|ω|1	h|ω|1	NOUN
ejde-515	158	5	/	/	SYM
ejde-515	158	6	p	p	NOUN
ejde-515	158	7	+	+	CCONJ
ejde-515	158	8	(	(	PUNCT
ejde-515	158	9	k1	k1	NOUN
ejde-515	158	10	+	+	CCONJ
ejde-515	158	11	a0)r	a0)r	ADV
ejde-515	158	12	,	,	PUNCT
ejde-515	158	13	it	it	PRON
ejde-515	158	14	follows	follow	VERB
ejde-515	158	15	that	that	DET
ejde-515	158	16	problem	problem	NOUN
ejde-515	158	17	(	(	PUNCT
ejde-515	158	18	2.1	2.1	NUM
ejde-515	158	19	)	)	PUNCT
ejde-515	158	20	satisfies	satisfy	VERB
ejde-515	158	21	the	the	DET
ejde-515	158	22	hypothesis	hypothesis	NOUN
ejde-515	158	23	of	of	ADP
ejde-515	158	24	[	[	X
ejde-515	158	25	24	24	NUM
ejde-515	158	26	,	,	PUNCT
ejde-515	158	27	theorem	theorem	VERB
ejde-515	158	28	5.6.1	5.6.1	NUM
ejde-515	158	29	]	]	PUNCT
ejde-515	158	30	and	and	CCONJ
ejde-515	158	31	the	the	DET
ejde-515	158	32	existence	existence	NOUN
ejde-515	158	33	of	of	ADP
ejde-515	158	34	a	a	DET
ejde-515	158	35	global	global	ADJ
ejde-515	158	36	solution	solution	NOUN
ejde-515	158	37	follows	follow	VERB
ejde-515	158	38	immediately	immediately	ADV
ejde-515	158	39	.	.	PUNCT
ejde-515	159	1	�	�	PROPN
ejde-515	159	2	2.2	2.2	NUM
ejde-515	159	3	.	.	PUNCT
ejde-515	160	1	smoothness	smoothness	NOUN
ejde-515	160	2	of	of	ADP
ejde-515	160	3	the	the	DET
ejde-515	160	4	evolution	evolution	NOUN
ejde-515	160	5	process	process	NOUN
ejde-515	160	6	.	.	PUNCT
ejde-515	161	1	in	in	ADP
ejde-515	161	2	this	this	DET
ejde-515	161	3	subsection	subsection	NOUN
ejde-515	161	4	we	we	PRON
ejde-515	161	5	show	show	VERB
ejde-515	161	6	that	that	DET
ejde-515	161	7	problem	problem	NOUN
ejde-515	161	8	(	(	PUNCT
ejde-515	161	9	1.2	1.2	NUM
ejde-515	161	10	)	)	PUNCT
ejde-515	161	11	generates	generate	VERB
ejde-515	161	12	a	a	DET
ejde-515	161	13	c1	c1	NOUN
ejde-515	161	14	flow	flow	NOUN
ejde-515	161	15	in	in	ADP
ejde-515	161	16	the	the	DET
ejde-515	161	17	phase	phase	NOUN
ejde-515	161	18	space	space	NOUN
ejde-515	161	19	xp	xp	NOUN
ejde-515	161	20	.	.	PUNCT
ejde-515	162	1	proposition	proposition	NOUN
ejde-515	162	2	2.7	2.7	NUM
ejde-515	162	3	.	.	PUNCT
ejde-515	163	1	assume	assume	VERB
ejde-515	163	2	the	the	DET
ejde-515	163	3	same	same	ADJ
ejde-515	163	4	hypotheses	hypothesis	NOUN
ejde-515	163	5	of	of	ADP
ejde-515	163	6	proposition	proposition	NOUN
ejde-515	163	7	2.6	2.6	NUM
ejde-515	163	8	hold	hold	NOUN
ejde-515	163	9	and	and	CCONJ
ejde-515	163	10	that	that	SCONJ
ejde-515	163	11	the	the	DET
ejde-515	163	12	function	function	NOUN
ejde-515	163	13	f	f	PROPN
ejde-515	163	14	is	be	AUX
ejde-515	163	15	continuously	continuously	ADV
ejde-515	163	16	differentiable	differentiable	ADJ
ejde-515	163	17	with	with	ADP
ejde-515	163	18	respect	respect	NOUN
ejde-515	163	19	to	to	ADP
ejde-515	163	20	the	the	DET
ejde-515	163	21	second	second	ADJ
ejde-515	163	22	variable	variable	NOUN
ejde-515	163	23	and	and	CCONJ
ejde-515	163	24	∂2f	∂2f	VERB
ejde-515	163	25	satisfies	satisfie	NOUN
ejde-515	163	26	the	the	DET
ejde-515	163	27	growth	growth	NOUN
ejde-515	163	28	condition	condition	NOUN
ejde-515	163	29	|∂2f(t	|∂2f(t	PROPN
ejde-515	163	30	,	,	PUNCT
ejde-515	163	31	x)|	x)|	PROPN
ejde-515	163	32	≤	≤	NOUN
ejde-515	163	33	c1(t)(1	c1(t)(1	X
ejde-515	163	34	+	+	CCONJ
ejde-515	163	35	|x|p−1	|x|p−1	NUM
ejde-515	163	36	)	)	PUNCT
ejde-515	163	37	,	,	PUNCT
ejde-515	163	38	for	for	ADP
ejde-515	163	39	any	any	DET
ejde-515	163	40	(	(	PUNCT
ejde-515	163	41	t	t	PROPN
ejde-515	163	42	,	,	PUNCT
ejde-515	163	43	x	x	NOUN
ejde-515	163	44	)	)	PUNCT
ejde-515	163	45	∈	∈	PROPN
ejde-515	163	46	r×	r×	PROPN
ejde-515	163	47	rn	rn	PROPN
ejde-515	163	48	,	,	PUNCT
ejde-515	163	49	(	(	PUNCT
ejde-515	163	50	2.14	2.14	NUM
ejde-515	163	51	)	)	PUNCT
ejde-515	163	52	8	8	NUM
ejde-515	163	53	s.	s.	PROPN
ejde-515	163	54	h.	h.	PROPN
ejde-515	163	55	da	da	PROPN
ejde-515	163	56	silva	silva	PROPN
ejde-515	163	57	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	163	58	for	for	ADP
ejde-515	163	59	1	1	NUM
ejde-515	163	60	≤	≤	NOUN
ejde-515	163	61	p	p	NOUN
ejde-515	163	62	<	<	X
ejde-515	163	63	∞.	∞.	PROPN
ejde-515	163	64	then	then	ADV
ejde-515	163	65	f	f	PROPN
ejde-515	163	66	(	(	PUNCT
ejde-515	163	67	t	t	PROPN
ejde-515	163	68	,	,	PUNCT
ejde-515	163	69	·	·	PUNCT
ejde-515	163	70	)	)	PUNCT
ejde-515	163	71	is	be	AUX
ejde-515	163	72	continuously	continuously	ADV
ejde-515	163	73	frechét	frechét	ADJ
ejde-515	163	74	differentiable	differentiable	NOUN
ejde-515	163	75	on	on	ADP
ejde-515	163	76	xp	xp	INTJ
ejde-515	163	77	with	with	ADP
ejde-515	163	78	derivative	derivative	ADJ
ejde-515	163	79	df	df	NOUN
ejde-515	163	80	(	(	PUNCT
ejde-515	163	81	t	t	PROPN
ejde-515	163	82	,	,	PUNCT
ejde-515	163	83	u)v(x	u)v(x	NOUN
ejde-515	163	84	)	)	PUNCT
ejde-515	164	1	=	=	NOUN
ejde-515	164	2	{	{	PUNCT
ejde-515	164	3	−a(t)v(x	−a(t)v(x	PROPN
ejde-515	164	4	)	)	PUNCT
ejde-515	164	5	+	+	NUM
ejde-515	164	6	b(t)k(∂2f(t	b(t)k(∂2f(t	NOUN
ejde-515	164	7	,	,	PUNCT
ejde-515	164	8	u)v)(x	u)v)(x	PROPN
ejde-515	164	9	)	)	PUNCT
ejde-515	164	10	,	,	PUNCT
ejde-515	164	11	x	x	PUNCT
ejde-515	164	12	∈	∈	PROPN
ejde-515	164	13	ω	ω	PROPN
ejde-515	164	14	,	,	PUNCT
ejde-515	164	15	0	0	NUM
ejde-515	164	16	,	,	PUNCT
ejde-515	164	17	x	x	SYM
ejde-515	164	18	∈	∈	PROPN
ejde-515	164	19	rn\ω	rn\ω	NOUN
ejde-515	164	20	.	.	PUNCT
ejde-515	165	1	proof	proof	NOUN
ejde-515	165	2	.	.	PUNCT
ejde-515	166	1	using	use	VERB
ejde-515	166	2	that	that	SCONJ
ejde-515	166	3	f	f	PROPN
ejde-515	166	4	is	be	AUX
ejde-515	166	5	continuously	continuously	ADV
ejde-515	166	6	differentiable	differentiable	ADJ
ejde-515	166	7	in	in	ADP
ejde-515	166	8	the	the	DET
ejde-515	166	9	second	second	ADJ
ejde-515	166	10	variable	variable	NOUN
ejde-515	166	11	,	,	PUNCT
ejde-515	166	12	by	by	ADP
ejde-515	166	13	a	a	DET
ejde-515	166	14	simple	simple	ADJ
ejde-515	166	15	computation	computation	NOUN
ejde-515	166	16	,	,	PUNCT
ejde-515	166	17	it	it	PRON
ejde-515	166	18	follows	follow	VERB
ejde-515	166	19	that	that	SCONJ
ejde-515	166	20	the	the	DET
ejde-515	166	21	gateaux	gateaux	PROPN
ejde-515	166	22	’s	’s	PART
ejde-515	166	23	derivative	derivative	NOUN
ejde-515	166	24	of	of	ADP
ejde-515	166	25	f	f	PROPN
ejde-515	166	26	(	(	PUNCT
ejde-515	166	27	t	t	PROPN
ejde-515	166	28	,	,	PUNCT
ejde-515	166	29	·	·	PUNCT
ejde-515	166	30	)	)	PUNCT
ejde-515	166	31	is	be	AUX
ejde-515	166	32	df	df	PROPN
ejde-515	166	33	(	(	PUNCT
ejde-515	166	34	t	t	PROPN
ejde-515	166	35	,	,	PUNCT
ejde-515	166	36	u)v(x	u)v(x	NOUN
ejde-515	166	37	)	)	PUNCT
ejde-515	166	38	:	:	PUNCT
ejde-515	167	1	=	=	X
ejde-515	167	2	{	{	PUNCT
ejde-515	167	3	−a(t)v(x	−a(t)v(x	PROPN
ejde-515	167	4	)	)	PUNCT
ejde-515	167	5	+	+	NUM
ejde-515	167	6	b(t)k(∂2f(t	b(t)k(∂2f(t	NOUN
ejde-515	167	7	,	,	PUNCT
ejde-515	167	8	u)v)(x	u)v)(x	PROPN
ejde-515	167	9	)	)	PUNCT
ejde-515	167	10	,	,	PUNCT
ejde-515	167	11	x	x	PUNCT
ejde-515	167	12	∈	∈	PROPN
ejde-515	167	13	ω	ω	PROPN
ejde-515	167	14	,	,	PUNCT
ejde-515	167	15	0	0	NUM
ejde-515	167	16	,	,	PUNCT
ejde-515	167	17	x	x	SYM
ejde-515	167	18	∈	∈	PROPN
ejde-515	167	19	rn\ω	rn\ω	NOUN
ejde-515	167	20	,	,	PUNCT
ejde-515	167	21	where	where	SCONJ
ejde-515	167	22	(	(	PUNCT
ejde-515	167	23	∂2f(t	∂2f(t	NOUN
ejde-515	167	24	,	,	PUNCT
ejde-515	167	25	u)v)(x	u)v)(x	PROPN
ejde-515	167	26	)	)	PUNCT
ejde-515	167	27	:	:	PUNCT
ejde-515	167	28	=	=	SYM
ejde-515	167	29	∂2f(t	∂2f(t	NOUN
ejde-515	167	30	,	,	PUNCT
ejde-515	167	31	u(x	u(x	NOUN
ejde-515	167	32	)	)	PUNCT
ejde-515	167	33	)	)	PUNCT
ejde-515	167	34	·	·	PUNCT
ejde-515	168	1	v(x	v(x	NOUN
ejde-515	168	2	)	)	PUNCT
ejde-515	168	3	.	.	PUNCT
ejde-515	169	1	note	note	VERB
ejde-515	169	2	that	that	SCONJ
ejde-515	169	3	the	the	DET
ejde-515	169	4	operator	operator	NOUN
ejde-515	169	5	d2f	d2f	PROPN
ejde-515	169	6	(	(	PUNCT
ejde-515	169	7	t	t	PROPN
ejde-515	169	8	,	,	PUNCT
ejde-515	169	9	u	u	NOUN
ejde-515	169	10	)	)	PUNCT
ejde-515	169	11	is	be	AUX
ejde-515	169	12	a	a	DET
ejde-515	169	13	linear	linear	ADJ
ejde-515	169	14	operator	operator	NOUN
ejde-515	169	15	on	on	ADP
ejde-515	169	16	xp	xp	PROPN
ejde-515	169	17	.	.	PUNCT
ejde-515	170	1	let	let	VERB
ejde-515	170	2	u	u	PRON
ejde-515	170	3	∈	∈	PROPN
ejde-515	170	4	lp(ω	lp(ω	PROPN
ejde-515	170	5	)	)	PUNCT
ejde-515	170	6	,	,	PUNCT
ejde-515	170	7	with	with	ADP
ejde-515	170	8	1	1	NUM
ejde-515	170	9	≤	≤	NOUN
ejde-515	170	10	p	p	NOUN
ejde-515	170	11	<	<	X
ejde-515	170	12	∞.	∞.	PROPN
ejde-515	170	13	then	then	ADV
ejde-515	170	14	,	,	PUNCT
ejde-515	170	15	if	if	SCONJ
ejde-515	170	16	q	q	NOUN
ejde-515	170	17	is	be	AUX
ejde-515	170	18	the	the	DET
ejde-515	170	19	conjugate	conjugate	ADJ
ejde-515	170	20	exponent	exponent	NOUN
ejde-515	170	21	of	of	ADP
ejde-515	170	22	p	p	X
ejde-515	170	23	,	,	PUNCT
ejde-515	170	24	it	it	PRON
ejde-515	170	25	is	be	AUX
ejde-515	170	26	easy	easy	ADJ
ejde-515	170	27	to	to	PART
ejde-515	170	28	see	see	VERB
ejde-515	170	29	that	that	SCONJ
ejde-515	170	30	‖∂2f(t	‖∂2f(t	NOUN
ejde-515	170	31	,	,	PUNCT
ejde-515	170	32	u)‖lq(ω	u)‖lq(ω	NOUN
ejde-515	170	33	)	)	PUNCT
ejde-515	170	34	≤	≤	NOUN
ejde-515	170	35	c1(t	c1(t	NOUN
ejde-515	170	36	)	)	PUNCT
ejde-515	170	37	(	(	PUNCT
ejde-515	170	38	|ω|1	|ω|1	PROPN
ejde-515	170	39	/	/	SYM
ejde-515	170	40	q	q	PROPN
ejde-515	171	1	+	+	CCONJ
ejde-515	171	2	‖u‖p−1	‖u‖p−1	ADJ
ejde-515	171	3	lp(ω	lp(ω	PUNCT
ejde-515	171	4	)	)	PUNCT
ejde-515	171	5	)	)	PUNCT
ejde-515	171	6	.	.	PUNCT
ejde-515	172	1	(	(	PUNCT
ejde-515	172	2	2.15	2.15	NUM
ejde-515	172	3	)	)	PUNCT
ejde-515	172	4	from	from	ADP
ejde-515	172	5	this	this	DET
ejde-515	172	6	estimate	estimate	NOUN
ejde-515	172	7	and	and	CCONJ
ejde-515	172	8	hölder	hölder	NOUN
ejde-515	172	9	’s	’s	PART
ejde-515	172	10	inequality	inequality	NOUN
ejde-515	172	11	,	,	PUNCT
ejde-515	172	12	it	it	PRON
ejde-515	172	13	follows	follow	VERB
ejde-515	172	14	that	that	SCONJ
ejde-515	172	15	‖∂2f(t	‖∂2f(t	NOUN
ejde-515	172	16	,	,	PUNCT
ejde-515	172	17	u	u	NOUN
ejde-515	172	18	)	)	PUNCT
ejde-515	172	19	·	·	PUNCT
ejde-515	172	20	v‖l1(ω	v‖l1(ω	X
ejde-515	172	21	)	)	PUNCT
ejde-515	172	22	≤	≤	NOUN
ejde-515	172	23	c1(t)(|ω|1	c1(t)(|ω|1	PROPN
ejde-515	172	24	/	/	SYM
ejde-515	172	25	q	q	PROPN
ejde-515	172	26	+	+	CCONJ
ejde-515	172	27	‖u‖p−1	‖u‖p−1	ADJ
ejde-515	172	28	lp(ω))‖v‖lp(ω	lp(ω))‖v‖lp(ω	PROPN
ejde-515	172	29	)	)	PUNCT
ejde-515	172	30	.	.	PUNCT
ejde-515	173	1	hence	hence	ADV
ejde-515	173	2	,	,	PUNCT
ejde-515	173	3	by	by	ADP
ejde-515	173	4	estimate	estimate	NOUN
ejde-515	173	5	(	(	PUNCT
ejde-515	173	6	2.6	2.6	NUM
ejde-515	173	7	)	)	PUNCT
ejde-515	173	8	,	,	PUNCT
ejde-515	173	9	we	we	PRON
ejde-515	173	10	conclude	conclude	VERB
ejde-515	173	11	that	that	SCONJ
ejde-515	173	12	‖df	‖df	NUM
ejde-515	173	13	(	(	PUNCT
ejde-515	173	14	t	t	PROPN
ejde-515	173	15	,	,	PUNCT
ejde-515	173	16	u	u	NOUN
ejde-515	173	17	)	)	PUNCT
ejde-515	173	18	·	·	PUNCT
ejde-515	173	19	v‖lp(ω	v‖lp(ω	PROPN
ejde-515	173	20	)	)	PUNCT
ejde-515	173	21	≤	≤	NOUN
ejde-515	173	22	‖a0v‖lp(ω	‖a0v‖lp(ω	PROPN
ejde-515	173	23	)	)	PUNCT
ejde-515	174	1	+	+	NUM
ejde-515	174	2	b0‖k(∂2f(t	b0‖k(∂2f(t	NOUN
ejde-515	174	3	,	,	PUNCT
ejde-515	174	4	u)v)‖lp(ω	u)v)‖lp(ω	PROPN
ejde-515	174	5	)	)	PUNCT
ejde-515	174	6	≤	≤	NOUN
ejde-515	174	7	‖a0v‖lp(ω	‖a0v‖lp(ω	PROPN
ejde-515	174	8	)	)	PUNCT
ejde-515	175	1	+	+	CCONJ
ejde-515	175	2	b0c1(t)‖j‖p‖∂2f(t	b0c1(t)‖j‖p‖∂2f(t	PROPN
ejde-515	175	3	,	,	PUNCT
ejde-515	175	4	u)v‖l1(ω	u)v‖l1(ω	SYM
ejde-515	175	5	)	)	PUNCT
ejde-515	175	6	≤	≤	NOUN
ejde-515	175	7	‖a0v‖lp(ω	‖a0v‖lp(ω	PROPN
ejde-515	175	8	)	)	PUNCT
ejde-515	176	1	+	+	NUM
ejde-515	176	2	b0c1(t)‖j‖p	b0c1(t)‖j‖p	NOUN
ejde-515	176	3	(	(	PUNCT
ejde-515	176	4	|ω|1	|ω|1	PROPN
ejde-515	176	5	/	/	SYM
ejde-515	176	6	q	q	PROPN
ejde-515	176	7	+	+	CCONJ
ejde-515	176	8	‖u‖p−1	‖u‖p−1	ADJ
ejde-515	176	9	lp(ω	lp(ω	X
ejde-515	176	10	)	)	PUNCT
ejde-515	176	11	)	)	PUNCT
ejde-515	176	12	‖v‖lp(ω	‖v‖lp(ω	PROPN
ejde-515	176	13	)	)	PUNCT
ejde-515	176	14	=	=	PUNCT
ejde-515	177	1	[	[	X
ejde-515	177	2	a0	a0	PROPN
ejde-515	177	3	+	+	CCONJ
ejde-515	177	4	b0c1(t)‖j‖p	b0c1(t)‖j‖p	NOUN
ejde-515	177	5	(	(	PUNCT
ejde-515	177	6	|ω|1	|ω|1	PROPN
ejde-515	177	7	/	/	SYM
ejde-515	177	8	q	q	PROPN
ejde-515	177	9	+	+	CCONJ
ejde-515	177	10	‖u‖p−1	‖u‖p−1	ADJ
ejde-515	177	11	lp(ω	lp(ω	PUNCT
ejde-515	177	12	)	)	PUNCT
ejde-515	177	13	)	)	PUNCT
ejde-515	178	1	]	]	X
ejde-515	178	2	‖v‖lp(ω	‖v‖lp(ω	PROPN
ejde-515	178	3	)	)	PUNCT
ejde-515	178	4	,	,	PUNCT
ejde-515	178	5	that	that	ADV
ejde-515	178	6	is	is	ADV
ejde-515	178	7	,	,	PUNCT
ejde-515	178	8	df	df	PROPN
ejde-515	178	9	(	(	PUNCT
ejde-515	178	10	t	t	PROPN
ejde-515	178	11	,	,	PUNCT
ejde-515	178	12	u	u	NOUN
ejde-515	178	13	)	)	PUNCT
ejde-515	178	14	is	be	AUX
ejde-515	178	15	a	a	DET
ejde-515	178	16	bounded	bounded	ADJ
ejde-515	178	17	operator	operator	NOUN
ejde-515	178	18	.	.	PUNCT
ejde-515	179	1	in	in	ADP
ejde-515	179	2	the	the	DET
ejde-515	179	3	case	case	NOUN
ejde-515	179	4	p	p	X
ejde-515	179	5	=	=	NOUN
ejde-515	179	6	∞	∞	PROPN
ejde-515	179	7	,	,	PUNCT
ejde-515	179	8	it	it	PRON
ejde-515	179	9	follows	follow	VERB
ejde-515	179	10	that	that	SCONJ
ejde-515	179	11	for	for	ADP
ejde-515	179	12	each	each	DET
ejde-515	179	13	u	u	NOUN
ejde-515	179	14	∈	∈	PROPN
ejde-515	179	15	l∞(ω	l∞(ω	NOUN
ejde-515	179	16	)	)	PUNCT
ejde-515	179	17	,	,	PUNCT
ejde-515	179	18	|∂2f(t	|∂2f(t	PROPN
ejde-515	179	19	,	,	PUNCT
ejde-515	179	20	u)|	u)|	PROPN
ejde-515	179	21	is	be	AUX
ejde-515	179	22	bounded	bound	VERB
ejde-515	179	23	by	by	ADP
ejde-515	179	24	c2(t	c2(t	PROPN
ejde-515	179	25	)	)	PUNCT
ejde-515	179	26	.	.	PUNCT
ejde-515	180	1	hence	hence	ADV
ejde-515	180	2	‖∂2f(t	‖∂2f(t	VERB
ejde-515	180	3	,	,	PUNCT
ejde-515	180	4	u)v‖l∞(ω	u)v‖l∞(ω	NOUN
ejde-515	180	5	)	)	PUNCT
ejde-515	180	6	≤	≤	NOUN
ejde-515	180	7	c2(t)‖v‖l∞(ω	c2(t)‖v‖l∞(ω	NOUN
ejde-515	180	8	)	)	PUNCT
ejde-515	180	9	.	.	PUNCT
ejde-515	181	1	thus	thus	ADV
ejde-515	181	2	‖df	‖df	NUM
ejde-515	181	3	(	(	PUNCT
ejde-515	181	4	t	t	PROPN
ejde-515	181	5	,	,	PUNCT
ejde-515	181	6	u	u	NOUN
ejde-515	181	7	)	)	PUNCT
ejde-515	181	8	·	·	PUNCT
ejde-515	181	9	v‖l∞(ω	v‖l∞(ω	X
ejde-515	181	10	)	)	PUNCT
ejde-515	181	11	≤	≤	NOUN
ejde-515	181	12	a0‖v‖l∞	a0‖v‖l∞	NOUN
ejde-515	181	13	+	+	NUM
ejde-515	181	14	b0‖k(∂2f(t	b0‖k(∂2f(t	NOUN
ejde-515	181	15	,	,	PUNCT
ejde-515	181	16	u)v)‖l∞(ω	u)v)‖l∞(ω	NOUN
ejde-515	181	17	)	)	PUNCT
ejde-515	181	18	≤	≤	NOUN
ejde-515	181	19	a0‖v‖l∞	a0‖v‖l∞	NOUN
ejde-515	182	1	+	+	X
ejde-515	182	2	b0‖j‖1‖∂2f(t	b0‖j‖1‖∂2f(t	X
ejde-515	182	3	,	,	PUNCT
ejde-515	182	4	u)v‖l∞(ω	u)v‖l∞(ω	NOUN
ejde-515	182	5	)	)	PUNCT
ejde-515	182	6	≤	≤	NOUN
ejde-515	182	7	a0‖v‖l∞	a0‖v‖l∞	NOUN
ejde-515	182	8	+	+	NUM
ejde-515	182	9	b0c2(t)‖j‖1‖v‖l∞(ω	b0c2(t)‖j‖1‖v‖l∞(ω	NOUN
ejde-515	182	10	)	)	PUNCT
ejde-515	182	11	=	=	SYM
ejde-515	182	12	(	(	PUNCT
ejde-515	182	13	a0	a0	NOUN
ejde-515	182	14	+	+	CCONJ
ejde-515	182	15	b0c2(t)‖j‖1)‖v‖l∞(ω	b0c2(t)‖j‖1)‖v‖l∞(ω	NOUN
ejde-515	182	16	)	)	PUNCT
ejde-515	182	17	,	,	PUNCT
ejde-515	182	18	which	which	PRON
ejde-515	182	19	results	result	VERB
ejde-515	182	20	,	,	PUNCT
ejde-515	182	21	also	also	ADV
ejde-515	182	22	in	in	ADP
ejde-515	182	23	this	this	DET
ejde-515	182	24	case	case	NOUN
ejde-515	182	25	,	,	PUNCT
ejde-515	182	26	in	in	ADP
ejde-515	182	27	the	the	DET
ejde-515	182	28	boundedness	boundedness	NOUN
ejde-515	182	29	of	of	ADP
ejde-515	182	30	df	df	PROPN
ejde-515	182	31	(	(	PUNCT
ejde-515	182	32	t	t	PROPN
ejde-515	182	33	,	,	PUNCT
ejde-515	182	34	u	u	NOUN
ejde-515	182	35	)	)	PUNCT
ejde-515	182	36	.	.	PUNCT
ejde-515	183	1	now	now	ADV
ejde-515	183	2	,	,	PUNCT
ejde-515	183	3	suppose	suppose	VERB
ejde-515	183	4	that	that	SCONJ
ejde-515	183	5	u1	u1	NOUN
ejde-515	183	6	,	,	PUNCT
ejde-515	183	7	u2	u2	PROPN
ejde-515	183	8	and	and	CCONJ
ejde-515	183	9	v	v	NOUN
ejde-515	183	10	belong	belong	VERB
ejde-515	183	11	to	to	ADP
ejde-515	183	12	lp(ω	lp(ω	PROPN
ejde-515	183	13	)	)	PUNCT
ejde-515	183	14	,	,	PUNCT
ejde-515	183	15	1	1	NUM
ejde-515	183	16	≤	≤	NOUN
ejde-515	183	17	p	p	NOUN
ejde-515	183	18	<	<	X
ejde-515	183	19	∞.	∞.	PROPN
ejde-515	183	20	using	use	VERB
ejde-515	183	21	(	(	PUNCT
ejde-515	183	22	2.6	2.6	NUM
ejde-515	183	23	)	)	PUNCT
ejde-515	183	24	and	and	CCONJ
ejde-515	183	25	hölder	hölder	PROPN
ejde-515	183	26	’s	’s	PART
ejde-515	183	27	inequality	inequality	NOUN
ejde-515	183	28	it	it	PRON
ejde-515	183	29	follows	follow	VERB
ejde-515	183	30	that	that	SCONJ
ejde-515	183	31	‖(df	‖(df	PROPN
ejde-515	183	32	(	(	PUNCT
ejde-515	183	33	t	t	PROPN
ejde-515	183	34	,	,	PUNCT
ejde-515	183	35	u1)−df	u1)−df	PROPN
ejde-515	183	36	(	(	PUNCT
ejde-515	183	37	t	t	PROPN
ejde-515	183	38	,	,	PUNCT
ejde-515	183	39	u2))v‖lp(ω	u2))v‖lp(ω	NUM
ejde-515	183	40	)	)	PUNCT
ejde-515	183	41	≤	≤	NUM
ejde-515	183	42	b0‖k[(∂2f(t	b0‖k[(∂2f(t	NOUN
ejde-515	183	43	,	,	PUNCT
ejde-515	183	44	u1)−	u1)−	PROPN
ejde-515	183	45	∂2f(t	∂2f(t	NOUN
ejde-515	183	46	,	,	PUNCT
ejde-515	183	47	u2))v]‖lp(ω	u2))v]‖lp(ω	PROPN
ejde-515	183	48	)	)	PUNCT
ejde-515	183	49	≤	≤	NUM
ejde-515	183	50	b0‖j‖p‖(∂2f(t	b0‖j‖p‖(∂2f(t	PROPN
ejde-515	183	51	,	,	PUNCT
ejde-515	183	52	u1)−	u1)−	PROPN
ejde-515	183	53	∂2f(t	∂2f(t	NOUN
ejde-515	183	54	,	,	PUNCT
ejde-515	183	55	u2))v‖l1(ω	u2))v‖l1(ω	PROPN
ejde-515	183	56	)	)	PUNCT
ejde-515	183	57	≤	≤	NOUN
ejde-515	183	58	b0‖j‖p‖∂2f(t	b0‖j‖p‖∂2f(t	PUNCT
ejde-515	183	59	,	,	PUNCT
ejde-515	183	60	u1)−	u1)−	PROPN
ejde-515	183	61	∂2f(t	∂2f(t	NOUN
ejde-515	183	62	,	,	PUNCT
ejde-515	183	63	u2)‖lq(ω)‖v‖lp(ω	u2)‖lq(ω)‖v‖lp(ω	NUM
ejde-515	183	64	)	)	PUNCT
ejde-515	183	65	=	=	PUNCT
ejde-515	183	66	b0‖j‖p‖∂2f(t	b0‖j‖p‖∂2f(t	NOUN
ejde-515	183	67	,	,	PUNCT
ejde-515	183	68	u1)−	u1)−	PROPN
ejde-515	183	69	∂2f(t	∂2f(t	NOUN
ejde-515	183	70	,	,	PUNCT
ejde-515	183	71	u2)‖lq(ω)‖v‖lp(ω	u2)‖lq(ω)‖v‖lp(ω	PROPN
ejde-515	183	72	)	)	PUNCT
ejde-515	183	73	.	.	PUNCT
ejde-515	184	1	then	then	ADV
ejde-515	184	2	to	to	PART
ejde-515	184	3	prove	prove	VERB
ejde-515	184	4	continuity	continuity	NOUN
ejde-515	184	5	of	of	ADP
ejde-515	184	6	the	the	DET
ejde-515	184	7	derivative	derivative	NOUN
ejde-515	184	8	,	,	PUNCT
ejde-515	184	9	df	df	PROPN
ejde-515	184	10	(	(	PUNCT
ejde-515	184	11	t	t	PROPN
ejde-515	184	12	,	,	PUNCT
ejde-515	184	13	·	·	PUNCT
ejde-515	184	14	)	)	PUNCT
ejde-515	184	15	,	,	PUNCT
ejde-515	184	16	it	it	PRON
ejde-515	184	17	is	be	AUX
ejde-515	184	18	sufficient	sufficient	ADJ
ejde-515	184	19	to	to	PART
ejde-515	184	20	show	show	VERB
ejde-515	184	21	that	that	SCONJ
ejde-515	184	22	‖∂2f(t	‖∂2f(t	NOUN
ejde-515	184	23	,	,	PUNCT
ejde-515	184	24	u1)−	u1)−	PROPN
ejde-515	184	25	∂2f(t	∂2f(t	NOUN
ejde-515	184	26	,	,	PUNCT
ejde-515	184	27	u2)‖lq(ω	u2)‖lq(ω	ADJ
ejde-515	184	28	)	)	PUNCT
ejde-515	184	29	→	→	SYM
ejde-515	184	30	0	0	NUM
ejde-515	184	31	ejde-2020/92	ejde-2020/92	ADJ
ejde-515	184	32	non	non	ADJ
ejde-515	184	33	-	-	ADJ
ejde-515	184	34	autonomous	autonomous	ADJ
ejde-515	184	35	model	model	NOUN
ejde-515	184	36	for	for	ADP
ejde-515	184	37	neural	neural	ADJ
ejde-515	184	38	fields	field	NOUN
ejde-515	184	39	9	9	NUM
ejde-515	184	40	as	as	ADP
ejde-515	184	41	‖u1	‖u1	PROPN
ejde-515	184	42	−	−	PROPN
ejde-515	184	43	u2‖lp(ω	u2‖lp(ω	PROPN
ejde-515	184	44	)	)	PUNCT
ejde-515	184	45	→	→	SYM
ejde-515	184	46	0	0	X
ejde-515	184	47	.	.	PUNCT
ejde-515	185	1	on	on	ADP
ejde-515	185	2	the	the	DET
ejde-515	185	3	other	other	ADJ
ejde-515	185	4	hand	hand	NOUN
ejde-515	185	5	,	,	PUNCT
ejde-515	185	6	by	by	ADP
ejde-515	185	7	(	(	PUNCT
ejde-515	185	8	2.14	2.14	NUM
ejde-515	185	9	)	)	PUNCT
ejde-515	185	10	,	,	PUNCT
ejde-515	185	11	it	it	PRON
ejde-515	185	12	follows	follow	VERB
ejde-515	185	13	that	that	SCONJ
ejde-515	186	1	|∂2f(t	|∂2f(t	PROPN
ejde-515	186	2	,	,	PUNCT
ejde-515	186	3	u1)(x)−	u1)(x)−	NOUN
ejde-515	186	4	∂2f(t	∂2f(t	PROPN
ejde-515	186	5	,	,	PUNCT
ejde-515	186	6	u2)(x)|q	u2)(x)|q	NOUN
ejde-515	186	7	≤	≤	PUNCT
ejde-515	187	1	[	[	PUNCT
ejde-515	187	2	c1(t)(2	c1(t)(2	NOUN
ejde-515	187	3	+	+	NOUN
ejde-515	187	4	|u1(x)|p−1	|u1(x)|p−1	NUM
ejde-515	187	5	+	+	PUNCT
ejde-515	187	6	|u2(x)|p−1)]q	|u2(x)|p−1)]q	PROPN
ejde-515	187	7	.	.	PUNCT
ejde-515	188	1	a	a	DET
ejde-515	188	2	simple	simple	ADJ
ejde-515	188	3	computation	computation	NOUN
ejde-515	188	4	shows	show	VERB
ejde-515	188	5	that	that	SCONJ
ejde-515	188	6	the	the	DET
ejde-515	188	7	right	right	ADJ
ejde-515	188	8	-	-	PUNCT
ejde-515	188	9	hand	hand	NOUN
ejde-515	188	10	-	-	PUNCT
ejde-515	188	11	side	side	NOUN
ejde-515	188	12	of	of	ADP
ejde-515	188	13	this	this	DET
ejde-515	188	14	inequality	inequality	NOUN
ejde-515	188	15	is	be	AUX
ejde-515	188	16	integrable	integrable	ADJ
ejde-515	188	17	.	.	PUNCT
ejde-515	189	1	then	then	ADV
ejde-515	189	2	the	the	DET
ejde-515	189	3	result	result	NOUN
ejde-515	189	4	follows	follow	VERB
ejde-515	189	5	from	from	ADP
ejde-515	189	6	lebesgue	lebesgue	PROPN
ejde-515	189	7	convergence	convergence	NOUN
ejde-515	189	8	theorem	theorem	VERB
ejde-515	189	9	.	.	PUNCT
ejde-515	190	1	in	in	ADP
ejde-515	190	2	the	the	DET
ejde-515	190	3	case	case	NOUN
ejde-515	190	4	p	p	X
ejde-515	190	5	=	=	SYM
ejde-515	190	6	∞	∞	PROPN
ejde-515	190	7	,	,	PUNCT
ejde-515	190	8	the	the	DET
ejde-515	190	9	continuity	continuity	NOUN
ejde-515	190	10	of	of	ADP
ejde-515	190	11	df	df	PROPN
ejde-515	190	12	follows	follow	VERB
ejde-515	190	13	from	from	ADP
ejde-515	190	14	(	(	PUNCT
ejde-515	190	15	2.5	2.5	NUM
ejde-515	190	16	)	)	PUNCT
ejde-515	190	17	and	and	CCONJ
ejde-515	190	18	from	from	ADP
ejde-515	190	19	the	the	DET
ejde-515	190	20	continuity	continuity	NOUN
ejde-515	190	21	of	of	ADP
ejde-515	190	22	∂2f(t	∂2f(t	PROPN
ejde-515	190	23	,	,	PUNCT
ejde-515	190	24	u	u	NOUN
ejde-515	190	25	)	)	PUNCT
ejde-515	190	26	.	.	PUNCT
ejde-515	191	1	therefore	therefore	ADV
ejde-515	191	2	,	,	PUNCT
ejde-515	191	3	it	it	PRON
ejde-515	191	4	follows	follow	VERB
ejde-515	191	5	from	from	ADP
ejde-515	191	6	[	[	X
ejde-515	191	7	27	27	NUM
ejde-515	191	8	,	,	PUNCT
ejde-515	191	9	proposition	proposition	NOUN
ejde-515	191	10	2.8	2.8	NUM
ejde-515	191	11	]	]	PUNCT
ejde-515	191	12	that	that	SCONJ
ejde-515	191	13	f	f	PROPN
ejde-515	191	14	(	(	PUNCT
ejde-515	191	15	t	t	PROPN
ejde-515	191	16	,	,	PUNCT
ejde-515	191	17	·	·	PUNCT
ejde-515	191	18	)	)	PUNCT
ejde-515	191	19	is	be	AUX
ejde-515	191	20	fréchet	fréchet	VERB
ejde-515	191	21	differentiable	differentiable	ADJ
ejde-515	191	22	with	with	ADP
ejde-515	191	23	continuous	continuous	ADJ
ejde-515	191	24	derivative	derivative	NOUN
ejde-515	191	25	in	in	ADP
ejde-515	191	26	xp	xp	PROPN
ejde-515	191	27	.	.	PUNCT
ejde-515	192	1	�	�	PROPN
ejde-515	192	2	thanks	thank	NOUN
ejde-515	192	3	to	to	ADP
ejde-515	192	4	proposition	proposition	VERB
ejde-515	192	5	2.7	2.7	NUM
ejde-515	192	6	and	and	CCONJ
ejde-515	192	7	well	well	ADV
ejde-515	192	8	known	know	VERB
ejde-515	192	9	results	result	NOUN
ejde-515	192	10	in	in	ADP
ejde-515	192	11	[	[	X
ejde-515	192	12	12	12	NUM
ejde-515	192	13	,	,	PUNCT
ejde-515	192	14	20	20	NUM
ejde-515	192	15	]	]	PUNCT
ejde-515	192	16	,	,	PUNCT
ejde-515	192	17	we	we	PRON
ejde-515	192	18	have	have	VERB
ejde-515	192	19	the	the	DET
ejde-515	192	20	following	follow	VERB
ejde-515	192	21	result	result	NOUN
ejde-515	192	22	.	.	PUNCT
ejde-515	193	1	corollary	corollary	ADJ
ejde-515	193	2	2.8	2.8	NUM
ejde-515	193	3	.	.	PUNCT
ejde-515	194	1	assume	assume	VERB
ejde-515	194	2	the	the	DET
ejde-515	194	3	hypotheses	hypothesis	NOUN
ejde-515	194	4	of	of	ADP
ejde-515	194	5	proposition	proposition	NOUN
ejde-515	194	6	2.7	2.7	NUM
ejde-515	194	7	hold	hold	NOUN
ejde-515	194	8	.	.	PUNCT
ejde-515	195	1	then	then	ADV
ejde-515	195	2	,	,	PUNCT
ejde-515	195	3	for	for	ADP
ejde-515	195	4	each	each	DET
ejde-515	195	5	t	t	NOUN
ejde-515	195	6	∈	∈	PROPN
ejde-515	195	7	r	r	NOUN
ejde-515	195	8	and	and	CCONJ
ejde-515	195	9	uτ	uτ	PROPN
ejde-515	195	10	∈	∈	PROPN
ejde-515	195	11	xp	xp	NOUN
ejde-515	195	12	,	,	PUNCT
ejde-515	195	13	the	the	DET
ejde-515	195	14	unique	unique	ADJ
ejde-515	195	15	solution	solution	NOUN
ejde-515	195	16	of	of	ADP
ejde-515	195	17	(	(	PUNCT
ejde-515	195	18	2.1	2.1	NUM
ejde-515	195	19	)	)	PUNCT
ejde-515	195	20	with	with	ADP
ejde-515	195	21	initial	initial	ADJ
ejde-515	195	22	condition	condition	NOUN
ejde-515	195	23	uτ	uτ	NOUN
ejde-515	195	24	exists	exist	VERB
ejde-515	195	25	for	for	ADP
ejde-515	195	26	all	all	DET
ejde-515	195	27	t	t	PROPN
ejde-515	195	28	≥	≥	PROPN
ejde-515	195	29	τ	τ	X
ejde-515	195	30	,	,	PUNCT
ejde-515	195	31	and	and	CCONJ
ejde-515	195	32	the	the	DET
ejde-515	195	33	solution	solution	NOUN
ejde-515	195	34	(	(	PUNCT
ejde-515	195	35	t	t	PROPN
ejde-515	195	36	,	,	PUNCT
ejde-515	195	37	τ	τ	PROPN
ejde-515	195	38	,	,	PUNCT
ejde-515	195	39	x	x	NOUN
ejde-515	195	40	)	)	PUNCT
ejde-515	195	41	7→	7→	NUM
ejde-515	195	42	u(t	u(t	NOUN
ejde-515	195	43	,	,	PUNCT
ejde-515	195	44	x	x	NOUN
ejde-515	195	45	)	)	PUNCT
ejde-515	195	46	=	=	SYM
ejde-515	195	47	u(t	u(t	NOUN
ejde-515	195	48	;	;	PUNCT
ejde-515	195	49	τ	τ	X
ejde-515	195	50	,	,	PUNCT
ejde-515	195	51	x	x	NOUN
ejde-515	195	52	,	,	PUNCT
ejde-515	195	53	uτ	uτ	PROPN
ejde-515	195	54	)	)	PUNCT
ejde-515	195	55	(	(	PUNCT
ejde-515	195	56	defined	define	VERB
ejde-515	195	57	by	by	ADP
ejde-515	195	58	(	(	PUNCT
ejde-515	195	59	2.12	2.12	NUM
ejde-515	195	60	)	)	PUNCT
ejde-515	195	61	)	)	PUNCT
ejde-515	195	62	gives	give	VERB
ejde-515	195	63	rise	rise	NOUN
ejde-515	195	64	to	to	ADP
ejde-515	195	65	a	a	DET
ejde-515	195	66	family	family	NOUN
ejde-515	195	67	of	of	ADP
ejde-515	195	68	nonlinear	nonlinear	PROPN
ejde-515	195	69	c1	c1	PROPN
ejde-515	195	70	process	process	NOUN
ejde-515	195	71	on	on	ADP
ejde-515	195	72	xp	xp	PROPN
ejde-515	195	73	,	,	PUNCT
ejde-515	195	74	given	give	VERB
ejde-515	195	75	by	by	ADP
ejde-515	195	76	t	t	PROPN
ejde-515	195	77	(	(	PUNCT
ejde-515	195	78	t	t	PROPN
ejde-515	195	79	,	,	PUNCT
ejde-515	195	80	τ)uτ	τ)uτ	PROPN
ejde-515	195	81	(	(	PUNCT
ejde-515	195	82	x	x	NOUN
ejde-515	195	83	)	)	PUNCT
ejde-515	195	84	:	:	PUNCT
ejde-515	195	85	=	=	SYM
ejde-515	195	86	u(t	u(t	NOUN
ejde-515	195	87	,	,	PUNCT
ejde-515	195	88	x	x	NOUN
ejde-515	195	89	)	)	PUNCT
ejde-515	195	90	,	,	PUNCT
ejde-515	195	91	t	t	PROPN
ejde-515	195	92	≥	≥	PROPN
ejde-515	195	93	τ	τ	PROPN
ejde-515	195	94	∈	∈	PROPN
ejde-515	195	95	r.	r.	PROPN
ejde-515	195	96	3	3	PROPN
ejde-515	195	97	.	.	PUNCT
ejde-515	195	98	existence	existence	NOUN
ejde-515	195	99	of	of	ADP
ejde-515	195	100	a	a	DET
ejde-515	195	101	pullback	pullback	NOUN
ejde-515	195	102	attractor	attractor	NOUN
ejde-515	195	103	in	in	ADP
ejde-515	195	104	this	this	DET
ejde-515	195	105	section	section	NOUN
ejde-515	195	106	we	we	PRON
ejde-515	195	107	prove	prove	VERB
ejde-515	195	108	the	the	DET
ejde-515	195	109	existence	existence	NOUN
ejde-515	195	110	of	of	ADP
ejde-515	195	111	a	a	DET
ejde-515	195	112	pullback	pullback	NOUN
ejde-515	195	113	attractor	attractor	NOUN
ejde-515	195	114	{	{	PUNCT
ejde-515	195	115	a(t	a(t	PROPN
ejde-515	195	116	)	)	PUNCT
ejde-515	195	117	;	;	PUNCT
ejde-515	196	1	t	t	PROPN
ejde-515	196	2	∈	∈	PROPN
ejde-515	196	3	r	r	X
ejde-515	196	4	}	}	PUNCT
ejde-515	196	5	in	in	ADP
ejde-515	196	6	xp	xp	INTJ
ejde-515	196	7	for	for	ADP
ejde-515	196	8	the	the	DET
ejde-515	196	9	evolution	evolution	NOUN
ejde-515	196	10	process	process	NOUN
ejde-515	196	11	{	{	PUNCT
ejde-515	196	12	t	t	PROPN
ejde-515	196	13	(	(	PUNCT
ejde-515	196	14	t	t	PROPN
ejde-515	196	15	,	,	PUNCT
ejde-515	196	16	τ	τ	PROPN
ejde-515	196	17	)	)	PUNCT
ejde-515	196	18	;	;	PUNCT
ejde-515	196	19	t	t	PROPN
ejde-515	196	20	≥	≥	PROPN
ejde-515	196	21	τ	τ	PROPN
ejde-515	196	22	,	,	PUNCT
ejde-515	196	23	τ	τ	PROPN
ejde-515	196	24	∈	∈	PROPN
ejde-515	196	25	r	r	NOUN
ejde-515	196	26	}	}	PUNCT
ejde-515	196	27	for	for	ADP
ejde-515	196	28	1	1	NUM
ejde-515	196	29	≤	≤	NOUN
ejde-515	196	30	p	p	NOUN
ejde-515	196	31	<	<	X
ejde-515	196	32	∞	∞	PROPN
ejde-515	196	33	,	,	PUNCT
ejde-515	196	34	generalizing	generalize	VERB
ejde-515	196	35	,	,	PUNCT
ejde-515	196	36	among	among	ADP
ejde-515	196	37	others	other	NOUN
ejde-515	196	38	,	,	PUNCT
ejde-515	196	39	[	[	X
ejde-515	196	40	17	17	NUM
ejde-515	196	41	,	,	PUNCT
ejde-515	196	42	theorem	theorem	VERB
ejde-515	196	43	3.2	3.2	NUM
ejde-515	196	44	]	]	PUNCT
ejde-515	196	45	and	and	CCONJ
ejde-515	196	46	[	[	X
ejde-515	196	47	5	5	NUM
ejde-515	196	48	,	,	PUNCT
ejde-515	196	49	theorem	theorem	VERB
ejde-515	196	50	4.2	4.2	NUM
ejde-515	196	51	]	]	PUNCT
ejde-515	196	52	.	.	PUNCT
ejde-515	197	1	lemma	lemma	PROPN
ejde-515	197	2	3.1	3.1	NUM
ejde-515	197	3	.	.	PUNCT
ejde-515	197	4	assume	assume	VERB
ejde-515	197	5	that	that	SCONJ
ejde-515	197	6	the	the	DET
ejde-515	197	7	hypotheses	hypothesis	NOUN
ejde-515	197	8	of	of	ADP
ejde-515	197	9	proposition	proposition	NOUN
ejde-515	197	10	2.7	2.7	NUM
ejde-515	197	11	hold	hold	VERB
ejde-515	197	12	with	with	ADP
ejde-515	197	13	the	the	DET
ejde-515	197	14	constant	constant	ADJ
ejde-515	197	15	k1	k1	NOUN
ejde-515	197	16	in	in	ADP
ejde-515	197	17	(	(	PUNCT
ejde-515	197	18	2.11	2.11	NUM
ejde-515	197	19	)	)	PUNCT
ejde-515	197	20	satisfying	satisfy	VERB
ejde-515	198	1	k1b0	k1b0	AUX
ejde-515	198	2	<	<	X
ejde-515	198	3	a−.	a−.	VERB
ejde-515	198	4	let	let	VERB
ejde-515	198	5	rδ(t	rδ(t	NOUN
ejde-515	198	6	)	)	PUNCT
ejde-515	198	7	=	=	SYM
ejde-515	198	8	1	1	NUM
ejde-515	198	9	a−	a−	PROPN
ejde-515	198	10	−	−	NOUN
ejde-515	198	11	k1b0	k1b0	X
ejde-515	198	12	(	(	PUNCT
ejde-515	198	13	1	1	NUM
ejde-515	198	14	+	+	NUM
ejde-515	198	15	δ)[b0k2(t)|ω|1	δ)[b0k2(t)|ω|1	NOUN
ejde-515	198	16	/	/	SYM
ejde-515	198	17	p	p	X
ejde-515	198	18	+	+	NOUN
ejde-515	198	19	‖s(t	‖s(t	ADJ
ejde-515	198	20	,	,	PUNCT
ejde-515	198	21	·	·	PUNCT
ejde-515	198	22	)	)	PUNCT
ejde-515	198	23	‖lp(ω	‖lp(ω	PUNCT
ejde-515	198	24	)	)	PUNCT
ejde-515	198	25	]	]	PUNCT
ejde-515	198	26	,	,	PUNCT
ejde-515	198	27	(	(	PUNCT
ejde-515	198	28	3.1	3.1	NUM
ejde-515	198	29	)	)	PUNCT
ejde-515	198	30	where	where	SCONJ
ejde-515	198	31	k2	k2	PROPN
ejde-515	198	32	is	be	AUX
ejde-515	198	33	derived	derive	VERB
ejde-515	198	34	from	from	ADP
ejde-515	198	35	(	(	PUNCT
ejde-515	198	36	2.13	2.13	NUM
ejde-515	198	37	)	)	PUNCT
ejde-515	198	38	and	and	CCONJ
ejde-515	198	39	δ	δ	PROPN
ejde-515	198	40	is	be	AUX
ejde-515	198	41	any	any	DET
ejde-515	198	42	positive	positive	ADJ
ejde-515	198	43	constant	constant	NOUN
ejde-515	198	44	.	.	PUNCT
ejde-515	199	1	then	then	ADV
ejde-515	199	2	the	the	DET
ejde-515	199	3	ball	ball	NOUN
ejde-515	199	4	,	,	PUNCT
ejde-515	199	5	centered	center	VERB
ejde-515	199	6	at	at	ADP
ejde-515	199	7	the	the	DET
ejde-515	199	8	origin	origin	NOUN
ejde-515	199	9	with	with	ADP
ejde-515	199	10	radius	radius	NOUN
ejde-515	199	11	rδ(t	rδ(t	NOUN
ejde-515	199	12	)	)	PUNCT
ejde-515	199	13	,	,	PUNCT
ejde-515	199	14	in	in	ADP
ejde-515	199	15	the	the	DET
ejde-515	199	16	space	space	NOUN
ejde-515	199	17	lp(ω	lp(ω	PROPN
ejde-515	199	18	)	)	PUNCT
ejde-515	199	19	,	,	PUNCT
ejde-515	199	20	1	1	NUM
ejde-515	199	21	≤	≤	NOUN
ejde-515	199	22	p	p	X
ejde-515	199	23	<	<	X
ejde-515	199	24	∞	∞	PROPN
ejde-515	199	25	,	,	PUNCT
ejde-515	199	26	which	which	PRON
ejde-515	199	27	we	we	PRON
ejde-515	199	28	denote	denote	VERB
ejde-515	199	29	by	by	ADP
ejde-515	199	30	b(0	b(0	NOUN
ejde-515	199	31	,	,	PUNCT
ejde-515	199	32	rδ(t	rδ(t	NOUN
ejde-515	199	33	)	)	PUNCT
ejde-515	199	34	)	)	PUNCT
ejde-515	199	35	,	,	PUNCT
ejde-515	199	36	pullback	pullback	NOUN
ejde-515	199	37	absorbs	absorb	VERB
ejde-515	199	38	bounded	bound	VERB
ejde-515	199	39	subsets	subset	NOUN
ejde-515	199	40	of	of	ADP
ejde-515	199	41	xp	xp	INTJ
ejde-515	199	42	at	at	ADP
ejde-515	199	43	time	time	NOUN
ejde-515	199	44	t	t	PROPN
ejde-515	199	45	∈	∈	PROPN
ejde-515	199	46	r	r	NOUN
ejde-515	199	47	with	with	ADP
ejde-515	199	48	respect	respect	NOUN
ejde-515	199	49	to	to	ADP
ejde-515	199	50	the	the	DET
ejde-515	199	51	process	process	NOUN
ejde-515	199	52	t	t	NOUN
ejde-515	199	53	(	(	PUNCT
ejde-515	199	54	·	·	PUNCT
ejde-515	199	55	,	,	PUNCT
ejde-515	199	56	·	·	PUNCT
ejde-515	199	57	)	)	PUNCT
ejde-515	199	58	generated	generate	VERB
ejde-515	199	59	by	by	ADP
ejde-515	199	60	(	(	PUNCT
ejde-515	199	61	2.1	2.1	NUM
ejde-515	199	62	)	)	PUNCT
ejde-515	199	63	.	.	PUNCT
ejde-515	200	1	proof	proof	NOUN
ejde-515	200	2	.	.	PUNCT
ejde-515	201	1	if	if	SCONJ
ejde-515	201	2	u(t	u(t	NOUN
ejde-515	201	3	,	,	PUNCT
ejde-515	201	4	x	x	X
ejde-515	201	5	)	)	PUNCT
ejde-515	201	6	is	be	AUX
ejde-515	201	7	the	the	DET
ejde-515	201	8	solution	solution	NOUN
ejde-515	201	9	of	of	ADP
ejde-515	201	10	(	(	PUNCT
ejde-515	201	11	2.1	2.1	NUM
ejde-515	201	12	)	)	PUNCT
ejde-515	201	13	with	with	ADP
ejde-515	201	14	initial	initial	ADJ
ejde-515	201	15	condition	condition	NOUN
ejde-515	201	16	uτ	uτ	PROPN
ejde-515	201	17	∈	∈	PROPN
ejde-515	201	18	xp	xp	INTJ
ejde-515	201	19	,	,	PUNCT
ejde-515	201	20	for	for	ADP
ejde-515	201	21	1	1	NUM
ejde-515	201	22	≤	≤	NOUN
ejde-515	201	23	p	p	NOUN
ejde-515	201	24	<	<	X
ejde-515	201	25	∞	∞	PROPN
ejde-515	201	26	,	,	PUNCT
ejde-515	201	27	then	then	ADV
ejde-515	202	1	d	d	X
ejde-515	202	2	dt	dt	X
ejde-515	202	3	∫	∫	PROPN
ejde-515	202	4	ω	ω	PROPN
ejde-515	202	5	|u(t	|u(t	PROPN
ejde-515	202	6	,	,	PUNCT
ejde-515	202	7	x)|pdx	x)|pdx	PROPN
ejde-515	202	8	=	=	SYM
ejde-515	202	9	∫	∫	PROPN
ejde-515	202	10	ω	ω	NUM
ejde-515	202	11	p|u(t	p|u(t	PROPN
ejde-515	202	12	,	,	PUNCT
ejde-515	202	13	x)|p−1sgn(u(t	x)|p−1sgn(u(t	NUM
ejde-515	202	14	,	,	PUNCT
ejde-515	202	15	x))ut(t	x))ut(t	NUM
ejde-515	202	16	,	,	PUNCT
ejde-515	202	17	x)dx	x)dx	PROPN
ejde-515	202	18	=	=	SYM
ejde-515	202	19	−pa(t	−pa(t	PROPN
ejde-515	202	20	)	)	PUNCT
ejde-515	202	21	∫	∫	PROPN
ejde-515	203	1	ω	ω	PROPN
ejde-515	203	2	|u(t	|u(t	PROPN
ejde-515	203	3	,	,	PUNCT
ejde-515	203	4	x)|pdx+	x)|pdx+	X
ejde-515	203	5	pb(t	pb(t	X
ejde-515	203	6	)	)	PUNCT
ejde-515	203	7	∫	∫	PROPN
ejde-515	204	1	ω	ω	PROPN
ejde-515	204	2	|u(t	|u(t	PROPN
ejde-515	204	3	,	,	PUNCT
ejde-515	204	4	x)|p−1sgn(u(t	x)|p−1sgn(u(t	NUM
ejde-515	204	5	,	,	PUNCT
ejde-515	204	6	x))kf(t	x))kf(t	NUM
ejde-515	204	7	,	,	PUNCT
ejde-515	204	8	u(t	u(t	NOUN
ejde-515	204	9	,	,	PUNCT
ejde-515	204	10	x))dx	x))dx	VERB
ejde-515	204	11	+	+	CCONJ
ejde-515	204	12	p	p	X
ejde-515	204	13	∫	∫	PROPN
ejde-515	204	14	ω	ω	PROPN
ejde-515	204	15	|u(t	|u(t	PROPN
ejde-515	204	16	,	,	PUNCT
ejde-515	204	17	x)|p−1sgn(u(t	x)|p−1sgn(u(t	PROPN
ejde-515	204	18	,	,	PUNCT
ejde-515	204	19	x))s(t	x))s(t	PROPN
ejde-515	204	20	,	,	PUNCT
ejde-515	204	21	x)dx−	x)dx−	PROPN
ejde-515	204	22	ph	ph	PROPN
ejde-515	204	23	∫	∫	PROPN
ejde-515	204	24	ω	ω	PROPN
ejde-515	204	25	|u(t	|u(t	PROPN
ejde-515	204	26	,	,	PUNCT
ejde-515	204	27	x)|p−1dx	x)|p−1dx	NUM
ejde-515	204	28	.	.	PUNCT
ejde-515	205	1	(	(	PUNCT
ejde-515	205	2	3.2	3.2	NUM
ejde-515	205	3	)	)	PUNCT
ejde-515	205	4	10	10	NUM
ejde-515	205	5	s.	s.	PROPN
ejde-515	205	6	h.	h.	PROPN
ejde-515	205	7	da	da	PROPN
ejde-515	205	8	silva	silva	PROPN
ejde-515	205	9	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	205	10	thus	thus	ADV
ejde-515	205	11	,	,	PUNCT
ejde-515	205	12	if	if	SCONJ
ejde-515	205	13	q	q	ADJ
ejde-515	205	14	is	be	AUX
ejde-515	205	15	the	the	DET
ejde-515	205	16	conjugate	conjugate	ADJ
ejde-515	205	17	exponent	exponent	NOUN
ejde-515	205	18	of	of	ADP
ejde-515	205	19	p	p	X
ejde-515	205	20	,	,	PUNCT
ejde-515	205	21	by	by	ADP
ejde-515	205	22	hölder	hölder	PROPN
ejde-515	205	23	’s	’s	PART
ejde-515	205	24	inequality	inequality	NOUN
ejde-515	205	25	,	,	PUNCT
ejde-515	205	26	estimate	estimate	NOUN
ejde-515	205	27	(	(	PUNCT
ejde-515	205	28	2.5	2.5	NUM
ejde-515	205	29	)	)	PUNCT
ejde-515	205	30	,	,	PUNCT
ejde-515	205	31	and	and	CCONJ
ejde-515	205	32	condition	condition	NOUN
ejde-515	205	33	(	(	PUNCT
ejde-515	205	34	2.11	2.11	NUM
ejde-515	205	35	)	)	PUNCT
ejde-515	205	36	,	,	PUNCT
ejde-515	205	37	we	we	PRON
ejde-515	205	38	have∫	have∫	VERB
ejde-515	205	39	ω	ω	PROPN
ejde-515	205	40	|u(t	|u(t	PROPN
ejde-515	205	41	,	,	PUNCT
ejde-515	205	42	x)|p−1sgn(u(t	x)|p−1sgn(u(t	NUM
ejde-515	205	43	,	,	PUNCT
ejde-515	205	44	x))kf(t	x))kf(t	NUM
ejde-515	205	45	,	,	PUNCT
ejde-515	205	46	u(t	u(t	NOUN
ejde-515	205	47	,	,	PUNCT
ejde-515	205	48	x	x	NOUN
ejde-515	205	49	)	)	PUNCT
ejde-515	205	50	)	)	PUNCT
ejde-515	206	1	dx	dx	PROPN
ejde-515	206	2	≤	≤	NUM
ejde-515	206	3	(	(	PUNCT
ejde-515	206	4	∫	∫	PROPN
ejde-515	206	5	ω	ω	PROPN
ejde-515	206	6	|u(t	|u(t	PROPN
ejde-515	206	7	,	,	PUNCT
ejde-515	206	8	x)|q(p−1)dx	x)|q(p−1)dx	ADJ
ejde-515	206	9	)	)	PUNCT
ejde-515	206	10	1	1	X
ejde-515	206	11	/	/	SYM
ejde-515	206	12	q(∫	q(∫	ADJ
ejde-515	206	13	ω	ω	NUM
ejde-515	207	1	|kf(t	|kf(t	X
ejde-515	207	2	,	,	PUNCT
ejde-515	207	3	u(t	u(t	NOUN
ejde-515	207	4	,	,	PUNCT
ejde-515	207	5	x))|pdx	x))|pdx	PROPN
ejde-515	207	6	)	)	PUNCT
ejde-515	207	7	1	1	X
ejde-515	207	8	/	/	SYM
ejde-515	207	9	p	p	NOUN
ejde-515	207	10	≤	≤	NOUN
ejde-515	207	11	(	(	PUNCT
ejde-515	207	12	∫	∫	PROPN
ejde-515	207	13	ω	ω	PROPN
ejde-515	207	14	|u(t	|u(t	PROPN
ejde-515	207	15	,	,	PUNCT
ejde-515	207	16	x)|pdx	x)|pdx	PROPN
ejde-515	207	17	)	)	PUNCT
ejde-515	207	18	1	1	X
ejde-515	207	19	/	/	SYM
ejde-515	207	20	q	q	NOUN
ejde-515	207	21	‖j‖1‖f(t	‖j‖1‖f(t	NOUN
ejde-515	207	22	,	,	PUNCT
ejde-515	207	23	u(t	u(t	NOUN
ejde-515	207	24	,	,	PUNCT
ejde-515	207	25	·	·	PUNCT
ejde-515	207	26	)	)	PUNCT
ejde-515	207	27	)	)	PUNCT
ejde-515	207	28	‖lp(ω	‖lp(ω	X
ejde-515	207	29	)	)	PUNCT
ejde-515	207	30	≤	≤	NOUN
ejde-515	207	31	‖u(t	‖u(t	PUNCT
ejde-515	207	32	,	,	PUNCT
ejde-515	207	33	·	·	PUNCT
ejde-515	207	34	)	)	PUNCT
ejde-515	207	35	‖p−1	‖p−1	X
ejde-515	207	36	lp(ω	lp(ω	X
ejde-515	207	37	)	)	PUNCT
ejde-515	207	38	(	(	PUNCT
ejde-515	207	39	k1‖u(t	k1‖u(t	PROPN
ejde-515	207	40	,	,	PUNCT
ejde-515	207	41	·	·	PUNCT
ejde-515	207	42	)	)	PUNCT
ejde-515	207	43	‖lp(ω	‖lp(ω	PUNCT
ejde-515	207	44	)	)	PUNCT
ejde-515	208	1	+	+	NUM
ejde-515	208	2	k2(t)|ω|1	k2(t)|ω|1	PROPN
ejde-515	208	3	/	/	SYM
ejde-515	208	4	p	p	NOUN
ejde-515	208	5	)	)	PUNCT
ejde-515	208	6	,	,	PUNCT
ejde-515	208	7	(	(	PUNCT
ejde-515	208	8	3.3	3.3	NUM
ejde-515	208	9	)	)	PUNCT
ejde-515	208	10	and	and	CCONJ
ejde-515	208	11	∫	∫	PROPN
ejde-515	208	12	ω	ω	PROPN
ejde-515	208	13	|u(t	|u(t	PROPN
ejde-515	208	14	,	,	PUNCT
ejde-515	208	15	x)|p−1sgn(u(t	x)|p−1sgn(u(t	PROPN
ejde-515	208	16	,	,	PUNCT
ejde-515	208	17	x))s(t	x))s(t	PROPN
ejde-515	208	18	,	,	PUNCT
ejde-515	208	19	x	x	X
ejde-515	208	20	)	)	PUNCT
ejde-515	208	21	dx	dx	PROPN
ejde-515	208	22	≤	≤	NUM
ejde-515	208	23	(	(	PUNCT
ejde-515	208	24	∫	∫	PROPN
ejde-515	208	25	ω	ω	PROPN
ejde-515	208	26	|u(t	|u(t	PROPN
ejde-515	208	27	,	,	PUNCT
ejde-515	208	28	x)|q(p−1)dx	x)|q(p−1)dx	ADJ
ejde-515	208	29	)	)	PUNCT
ejde-515	208	30	1	1	X
ejde-515	208	31	/	/	SYM
ejde-515	208	32	q(∫	q(∫	PROPN
ejde-515	208	33	ω	ω	X
ejde-515	209	1	|s(t	|s(t	PROPN
ejde-515	209	2	,	,	PUNCT
ejde-515	209	3	x)|pdx	x)|pdx	PROPN
ejde-515	209	4	)	)	PUNCT
ejde-515	209	5	1	1	X
ejde-515	209	6	/	/	SYM
ejde-515	209	7	p	p	NOUN
ejde-515	209	8	≤	≤	NOUN
ejde-515	209	9	(	(	PUNCT
ejde-515	209	10	∫	∫	PROPN
ejde-515	209	11	ω	ω	PROPN
ejde-515	209	12	|u(t	|u(t	PROPN
ejde-515	209	13	,	,	PUNCT
ejde-515	209	14	x)|pdx	x)|pdx	PROPN
ejde-515	209	15	)	)	PUNCT
ejde-515	209	16	1	1	X
ejde-515	209	17	/	/	SYM
ejde-515	209	18	q	q	NOUN
ejde-515	209	19	‖s(t	‖s(t	NOUN
ejde-515	209	20	,	,	PUNCT
ejde-515	209	21	·	·	PUNCT
ejde-515	209	22	)	)	PUNCT
ejde-515	209	23	‖lp(ω	‖lp(ω	X
ejde-515	209	24	)	)	PUNCT
ejde-515	209	25	≤	≤	NOUN
ejde-515	209	26	‖u(t	‖u(t	PUNCT
ejde-515	209	27	,	,	PUNCT
ejde-515	209	28	·	·	PUNCT
ejde-515	209	29	)	)	PUNCT
ejde-515	209	30	‖p−1	‖p−1	PUNCT
ejde-515	209	31	lp(ω)‖s(t	lp(ω)‖s(t	PROPN
ejde-515	209	32	,	,	PUNCT
ejde-515	209	33	·	·	PUNCT
ejde-515	209	34	)	)	PUNCT
ejde-515	209	35	‖lp(ω	‖lp(ω	PUNCT
ejde-515	209	36	)	)	PUNCT
ejde-515	209	37	.	.	PUNCT
ejde-515	210	1	(	(	PUNCT
ejde-515	210	2	3.4	3.4	NUM
ejde-515	210	3	)	)	PUNCT
ejde-515	210	4	hence	hence	ADV
ejde-515	210	5	,	,	PUNCT
ejde-515	210	6	using	use	VERB
ejde-515	210	7	(	(	PUNCT
ejde-515	210	8	3.3	3.3	NUM
ejde-515	210	9	)	)	PUNCT
ejde-515	210	10	and	and	CCONJ
ejde-515	210	11	(	(	PUNCT
ejde-515	210	12	3.4	3.4	NUM
ejde-515	210	13	)	)	PUNCT
ejde-515	210	14	in	in	ADP
ejde-515	210	15	(	(	PUNCT
ejde-515	210	16	3.2	3.2	NUM
ejde-515	210	17	)	)	PUNCT
ejde-515	210	18	,	,	PUNCT
ejde-515	210	19	we	we	PRON
ejde-515	210	20	obtain	obtain	VERB
ejde-515	210	21	d	d	X
ejde-515	210	22	dt	dt	NOUN
ejde-515	210	23	‖u(t	‖u(t	NOUN
ejde-515	210	24	,	,	PUNCT
ejde-515	210	25	·	·	PUNCT
ejde-515	210	26	)	)	PUNCT
ejde-515	210	27	‖plp(ω	‖plp(ω	NUM
ejde-515	210	28	)	)	PUNCT
ejde-515	210	29	≤	≤	NUM
ejde-515	210	30	−pa(t)‖u(t	−pa(t)‖u(t	PROPN
ejde-515	210	31	,	,	PUNCT
ejde-515	210	32	·	·	PUNCT
ejde-515	210	33	)	)	PUNCT
ejde-515	210	34	‖plp(ω	‖plp(ω	NUM
ejde-515	210	35	)	)	PUNCT
ejde-515	211	1	+	+	CCONJ
ejde-515	211	2	pb(t)‖u(t	pb(t)‖u(t	PROPN
ejde-515	211	3	,	,	PUNCT
ejde-515	211	4	·	·	PUNCT
ejde-515	211	5	)	)	PUNCT
ejde-515	211	6	‖p−1	‖p−1	X
ejde-515	211	7	lp(ω	lp(ω	X
ejde-515	211	8	)	)	PUNCT
ejde-515	211	9	(	(	PUNCT
ejde-515	211	10	k1‖u(t	k1‖u(t	PROPN
ejde-515	211	11	,	,	PUNCT
ejde-515	211	12	·	·	PUNCT
ejde-515	211	13	)	)	PUNCT
ejde-515	211	14	‖lp(ω	‖lp(ω	PUNCT
ejde-515	211	15	)	)	PUNCT
ejde-515	212	1	+	+	NUM
ejde-515	212	2	k2(t)|ω|1	k2(t)|ω|1	PROPN
ejde-515	212	3	/	/	SYM
ejde-515	212	4	p	p	NOUN
ejde-515	212	5	)	)	PUNCT
ejde-515	212	6	+	+	NUM
ejde-515	212	7	p‖u(t	p‖u(t	NOUN
ejde-515	212	8	,	,	PUNCT
ejde-515	212	9	·	·	PUNCT
ejde-515	212	10	)	)	PUNCT
ejde-515	212	11	‖p−1	‖p−1	PUNCT
ejde-515	212	12	lp(ω)‖s(t	lp(ω)‖s(t	PROPN
ejde-515	212	13	,	,	PUNCT
ejde-515	212	14	·	·	PUNCT
ejde-515	212	15	)	)	PUNCT
ejde-515	212	16	‖lp(ω	‖lp(ω	PUNCT
ejde-515	212	17	)	)	PUNCT
ejde-515	213	1	−	−	ADP
ejde-515	213	2	ph|ω|1	ph|ω|1	PROPN
ejde-515	213	3	/	/	SYM
ejde-515	213	4	p‖u(t	p‖u(t	NOUN
ejde-515	213	5	,	,	PUNCT
ejde-515	213	6	·	·	PUNCT
ejde-515	213	7	)	)	PUNCT
ejde-515	213	8	‖p−1	‖p−1	NUM
ejde-515	213	9	lp(ω	lp(ω	PROPN
ejde-515	213	10	)	)	PUNCT
ejde-515	213	11	.	.	PUNCT
ejde-515	214	1	thus	thus	ADV
ejde-515	214	2	d	d	X
ejde-515	214	3	dt	dt	X
ejde-515	214	4	‖u(t	‖u(t	NOUN
ejde-515	214	5	,	,	PUNCT
ejde-515	214	6	·	·	PUNCT
ejde-515	214	7	)	)	PUNCT
ejde-515	214	8	‖plp(ω	‖plp(ω	NUM
ejde-515	214	9	)	)	PUNCT
ejde-515	214	10	≤	≤	NOUN
ejde-515	214	11	−a−p‖u(t	−a−p‖u(t	PROPN
ejde-515	214	12	,	,	PUNCT
ejde-515	214	13	·	·	PUNCT
ejde-515	214	14	)	)	PUNCT
ejde-515	214	15	‖plp(ω	‖plp(ω	NUM
ejde-515	214	16	)	)	PUNCT
ejde-515	215	1	+	+	CCONJ
ejde-515	215	2	pb0‖u(t	pb0‖u(t	NUM
ejde-515	215	3	,	,	PUNCT
ejde-515	215	4	·	·	PUNCT
ejde-515	215	5	)	)	PUNCT
ejde-515	215	6	‖p−1	‖p−1	X
ejde-515	215	7	lp(ω	lp(ω	X
ejde-515	215	8	)	)	PUNCT
ejde-515	215	9	(	(	PUNCT
ejde-515	215	10	k1‖u(t	k1‖u(t	PROPN
ejde-515	215	11	,	,	PUNCT
ejde-515	215	12	·	·	PUNCT
ejde-515	215	13	)	)	PUNCT
ejde-515	215	14	‖lp(ω	‖lp(ω	PUNCT
ejde-515	215	15	)	)	PUNCT
ejde-515	216	1	+	+	NUM
ejde-515	216	2	k2(t)|ω|1	k2(t)|ω|1	PROPN
ejde-515	216	3	/	/	SYM
ejde-515	216	4	p	p	NOUN
ejde-515	216	5	)	)	PUNCT
ejde-515	217	1	+	+	CCONJ
ejde-515	217	2	p‖s(t	p‖s(t	PROPN
ejde-515	217	3	,	,	PUNCT
ejde-515	217	4	·	·	PUNCT
ejde-515	217	5	)	)	PUNCT
ejde-515	217	6	‖lp(ω)‖u(t	‖lp(ω)‖u(t	PROPN
ejde-515	217	7	,	,	PUNCT
ejde-515	217	8	·	·	PUNCT
ejde-515	217	9	)	)	PUNCT
ejde-515	217	10	‖p−1	‖p−1	NUM
ejde-515	217	11	lp(ω	lp(ω	X
ejde-515	217	12	)	)	PUNCT
ejde-515	217	13	=	=	SYM
ejde-515	217	14	−a−p‖u(t	−a−p‖u(t	PROPN
ejde-515	217	15	,	,	PUNCT
ejde-515	217	16	·	·	PUNCT
ejde-515	217	17	)	)	PUNCT
ejde-515	217	18	‖plp(ω	‖plp(ω	NUM
ejde-515	217	19	)	)	PUNCT
ejde-515	218	1	+	+	CCONJ
ejde-515	218	2	pb0k1‖u(t	pb0k1‖u(t	ADJ
ejde-515	218	3	,	,	PUNCT
ejde-515	218	4	·	·	PUNCT
ejde-515	218	5	)	)	PUNCT
ejde-515	218	6	‖plp(ω	‖plp(ω	NUM
ejde-515	218	7	)	)	PUNCT
ejde-515	219	1	+	+	CCONJ
ejde-515	219	2	pb0|ω|1	pb0|ω|1	NOUN
ejde-515	219	3	/	/	SYM
ejde-515	219	4	pk2(t)‖u(t	pk2(t)‖u(t	PROPN
ejde-515	219	5	,	,	PUNCT
ejde-515	219	6	·	·	PUNCT
ejde-515	219	7	)	)	PUNCT
ejde-515	219	8	‖p−1	‖p−1	X
ejde-515	219	9	lp(ω	lp(ω	X
ejde-515	219	10	)	)	PUNCT
ejde-515	219	11	+	+	CCONJ
ejde-515	219	12	p‖s(t	p‖s(t	PROPN
ejde-515	219	13	,	,	PUNCT
ejde-515	219	14	·	·	PUNCT
ejde-515	219	15	)	)	PUNCT
ejde-515	219	16	‖lp(ω)‖u(t	‖lp(ω)‖u(t	PROPN
ejde-515	219	17	,	,	PUNCT
ejde-515	219	18	·	·	PUNCT
ejde-515	219	19	)	)	PUNCT
ejde-515	219	20	‖p−1	‖p−1	NUM
ejde-515	219	21	lp(ω	lp(ω	X
ejde-515	219	22	)	)	PUNCT
ejde-515	219	23	=	=	SYM
ejde-515	219	24	p‖u(t	p‖u(t	NOUN
ejde-515	219	25	,	,	PUNCT
ejde-515	219	26	·	·	PUNCT
ejde-515	219	27	)	)	PUNCT
ejde-515	219	28	‖plp(ω	‖plp(ω	NUM
ejde-515	219	29	)	)	PUNCT
ejde-515	220	1	[	[	PUNCT
ejde-515	220	2	−	−	NOUN
ejde-515	220	3	a−	a−	NOUN
ejde-515	220	4	+	+	CCONJ
ejde-515	220	5	k1b0	k1b0	X
ejde-515	220	6	+	+	CCONJ
ejde-515	220	7	(	(	PUNCT
ejde-515	220	8	b0k2(t)|ω|1	b0k2(t)|ω|1	NOUN
ejde-515	220	9	/	/	SYM
ejde-515	220	10	p	p	X
ejde-515	220	11	+	+	NOUN
ejde-515	220	12	‖s(t	‖s(t	ADJ
ejde-515	220	13	,	,	PUNCT
ejde-515	220	14	·	·	PUNCT
ejde-515	220	15	)	)	PUNCT
ejde-515	220	16	‖lp(ω	‖lp(ω	PUNCT
ejde-515	220	17	)	)	PUNCT
ejde-515	220	18	)	)	PUNCT
ejde-515	221	1	‖u(t	‖u(t	X
ejde-515	221	2	,	,	PUNCT
ejde-515	221	3	·	·	PUNCT
ejde-515	221	4	)	)	PUNCT
ejde-515	221	5	‖plp(ω	‖plp(ω	NUM
ejde-515	221	6	)	)	PUNCT
ejde-515	221	7	]	]	PUNCT
ejde-515	221	8	.	.	PUNCT
ejde-515	222	1	writing	write	VERB
ejde-515	222	2	ε	ε	PROPN
ejde-515	222	3	=	=	SYM
ejde-515	222	4	a−	a−	PROPN
ejde-515	222	5	−	−	PROPN
ejde-515	223	1	k1b0	k1b0	X
ejde-515	223	2	>	>	X
ejde-515	223	3	0	0	NUM
ejde-515	223	4	,	,	PUNCT
ejde-515	223	5	since	since	SCONJ
ejde-515	223	6	‖u(t	‖u(t	NUM
ejde-515	223	7	,	,	PUNCT
ejde-515	223	8	·	·	PUNCT
ejde-515	223	9	)	)	PUNCT
ejde-515	223	10	‖lp(ω	‖lp(ω	PUNCT
ejde-515	223	11	)	)	PUNCT
ejde-515	223	12	≥	≥	NOUN
ejde-515	223	13	1	1	NUM
ejde-515	223	14	ε	ε	PROPN
ejde-515	223	15	(	(	PUNCT
ejde-515	223	16	1	1	NUM
ejde-515	223	17	+	+	NUM
ejde-515	223	18	δ	δ	NOUN
ejde-515	223	19	)	)	PUNCT
ejde-515	223	20	(	(	PUNCT
ejde-515	223	21	b0k2(t)|ω|1	b0k2(t)|ω|1	PROPN
ejde-515	223	22	/	/	SYM
ejde-515	223	23	p	p	X
ejde-515	223	24	+	+	NOUN
ejde-515	223	25	‖s(t	‖s(t	ADJ
ejde-515	223	26	,	,	PUNCT
ejde-515	223	27	·	·	PUNCT
ejde-515	223	28	)	)	PUNCT
ejde-515	223	29	‖lp(ω	‖lp(ω	PUNCT
ejde-515	223	30	)	)	PUNCT
ejde-515	223	31	)	)	PUNCT
ejde-515	223	32	,	,	PUNCT
ejde-515	223	33	we	we	PRON
ejde-515	223	34	obtain	obtain	VERB
ejde-515	223	35	d	d	X
ejde-515	223	36	dt	dt	NOUN
ejde-515	223	37	‖u(t	‖u(t	NOUN
ejde-515	223	38	,	,	PUNCT
ejde-515	223	39	·	·	PUNCT
ejde-515	223	40	)	)	PUNCT
ejde-515	223	41	‖plp(ω	‖plp(ω	NUM
ejde-515	223	42	)	)	PUNCT
ejde-515	223	43	≤	≤	NUM
ejde-515	223	44	p‖u(t	p‖u(t	NOUN
ejde-515	223	45	,	,	PUNCT
ejde-515	223	46	·	·	PUNCT
ejde-515	223	47	)	)	PUNCT
ejde-515	223	48	‖plp(ω	‖plp(ω	NUM
ejde-515	223	49	)	)	PUNCT
ejde-515	224	1	(	(	PUNCT
ejde-515	224	2	−	−	PROPN
ejde-515	224	3	ε+	ε+	X
ejde-515	224	4	ε	ε	PROPN
ejde-515	224	5	1	1	NUM
ejde-515	224	6	+	+	NUM
ejde-515	224	7	δ	δ	NOUN
ejde-515	224	8	)	)	PUNCT
ejde-515	225	1	=	=	PUNCT
ejde-515	226	1	−	−	PROPN
ejde-515	227	1	δp	δp	PRON
ejde-515	227	2	(	(	PUNCT
ejde-515	227	3	1	1	NUM
ejde-515	227	4	+	+	CCONJ
ejde-515	227	5	δ	δ	PROPN
ejde-515	227	6	)	)	PUNCT
ejde-515	227	7	ε‖u(t	ε‖u(t	PROPN
ejde-515	227	8	,	,	PUNCT
ejde-515	227	9	·	·	PUNCT
ejde-515	227	10	)	)	PUNCT
ejde-515	227	11	‖plp(ω	‖plp(ω	NUM
ejde-515	227	12	)	)	PUNCT
ejde-515	227	13	.	.	PUNCT
ejde-515	228	1	ejde-2020/92	ejde-2020/92	ADJ
ejde-515	228	2	non	non	ADJ
ejde-515	228	3	-	-	ADJ
ejde-515	228	4	autonomous	autonomous	ADJ
ejde-515	228	5	model	model	NOUN
ejde-515	228	6	for	for	ADP
ejde-515	228	7	neural	neural	ADJ
ejde-515	228	8	fields	field	NOUN
ejde-515	228	9	11	11	NUM
ejde-515	228	10	therefore	therefore	ADV
ejde-515	228	11	,	,	PUNCT
ejde-515	228	12	‖u(t	‖u(t	X
ejde-515	228	13	,	,	PUNCT
ejde-515	228	14	·	·	PUNCT
ejde-515	228	15	)	)	PUNCT
ejde-515	228	16	‖plp(ω	‖plp(ω	NUM
ejde-515	228	17	)	)	PUNCT
ejde-515	228	18	≤	≤	NUM
ejde-515	229	1	e	e	X
ejde-515	229	2	−	−	PUNCT
ejde-515	229	3	δp	δp	ADP
ejde-515	229	4	(	(	PUNCT
ejde-515	229	5	1+δ	1+δ	NUM
ejde-515	229	6	)	)	PUNCT
ejde-515	229	7	ε(t−τ)‖uτ‖plp(ω	ε(t−τ)‖uτ‖plp(ω	NOUN
ejde-515	229	8	)	)	PUNCT
ejde-515	229	9	=	=	SYM
ejde-515	230	1	e−	e−	PROPN
ejde-515	230	2	δp	δp	ADV
ejde-515	230	3	(	(	PUNCT
ejde-515	230	4	1+δ	1+δ	NUM
ejde-515	230	5	)	)	PUNCT
ejde-515	230	6	(	(	PUNCT
ejde-515	230	7	a−−k1b0)(t−τ)‖uτ‖plp(ω	a−−k1b0)(t−τ)‖uτ‖plp(ω	PROPN
ejde-515	230	8	)	)	PUNCT
ejde-515	230	9	.	.	PUNCT
ejde-515	231	1	(	(	PUNCT
ejde-515	231	2	3.5	3.5	NUM
ejde-515	231	3	)	)	PUNCT
ejde-515	231	4	thus	thus	ADV
ejde-515	231	5	,	,	PUNCT
ejde-515	231	6	the	the	DET
ejde-515	231	7	result	result	NOUN
ejde-515	231	8	follows	follow	VERB
ejde-515	231	9	immediately	immediately	ADV
ejde-515	231	10	.	.	PUNCT
ejde-515	232	1	�	�	PROPN
ejde-515	232	2	theorem	theorem	VERB
ejde-515	232	3	3.2	3.2	NUM
ejde-515	232	4	.	.	PUNCT
ejde-515	233	1	in	in	ADP
ejde-515	233	2	addition	addition	NOUN
ejde-515	233	3	to	to	ADP
ejde-515	233	4	the	the	DET
ejde-515	233	5	conditions	condition	NOUN
ejde-515	233	6	of	of	ADP
ejde-515	233	7	lemma	lemma	PROPN
ejde-515	233	8	3.1	3.1	NUM
ejde-515	233	9	,	,	PUNCT
ejde-515	233	10	suppose	suppose	VERB
ejde-515	233	11	that	that	SCONJ
ejde-515	233	12	c1(t	c1(t	PROPN
ejde-515	233	13	)	)	PUNCT
ejde-515	233	14	and	and	CCONJ
ejde-515	233	15	k2(t	k2(t	PROPN
ejde-515	233	16	)	)	PUNCT
ejde-515	233	17	are	be	AUX
ejde-515	233	18	non	non	ADJ
ejde-515	233	19	-	-	ADJ
ejde-515	233	20	decreasing	decrease	VERB
ejde-515	233	21	functions	function	NOUN
ejde-515	233	22	and	and	CCONJ
ejde-515	233	23	‖jx‖lp(ω	‖jx‖lp(ω	NOUN
ejde-515	233	24	)	)	PUNCT
ejde-515	234	1	=	=	SYM
ejde-515	234	2	sup	sup	NOUN
ejde-515	234	3	x∈ω	x∈ω	NOUN
ejde-515	234	4	‖∂xj(x	‖∂xj(x	NUM
ejde-515	234	5	,	,	PUNCT
ejde-515	234	6	·	·	PUNCT
ejde-515	234	7	)	)	PUNCT
ejde-515	234	8	‖lq(ω	‖lq(ω	NUM
ejde-515	234	9	)	)	PUNCT
ejde-515	234	10	<	<	X
ejde-515	234	11	∞	∞	PROPN
ejde-515	234	12	,	,	PUNCT
ejde-515	234	13	‖∂xs‖p	‖∂xs‖p	ADJ
ejde-515	234	14	=	=	SYM
ejde-515	234	15	sup	sup	NOUN
ejde-515	234	16	t∈r+	t∈r+	NOUN
ejde-515	234	17	‖∂xs(t	‖∂xs(t	NOUN
ejde-515	234	18	,	,	PUNCT
ejde-515	234	19	·	·	PUNCT
ejde-515	234	20	)	)	PUNCT
ejde-515	234	21	‖lp(ω	‖lp(ω	PUNCT
ejde-515	234	22	)	)	PUNCT
ejde-515	235	1	<	<	X
ejde-515	235	2	∞.	∞.	PROPN
ejde-515	235	3	then	then	ADV
ejde-515	235	4	there	there	PRON
ejde-515	235	5	exists	exist	VERB
ejde-515	235	6	a	a	DET
ejde-515	235	7	pullback	pullback	NOUN
ejde-515	235	8	attractor	attractor	NOUN
ejde-515	235	9	{	{	PUNCT
ejde-515	235	10	a(t	a(t	PROPN
ejde-515	235	11	)	)	PUNCT
ejde-515	235	12	;	;	PUNCT
ejde-515	235	13	t	t	PROPN
ejde-515	235	14	∈	∈	PROPN
ejde-515	235	15	r	r	X
ejde-515	235	16	}	}	PUNCT
ejde-515	235	17	for	for	ADP
ejde-515	235	18	the	the	DET
ejde-515	235	19	process	process	NOUN
ejde-515	235	20	{	{	PUNCT
ejde-515	235	21	t	t	PROPN
ejde-515	235	22	(	(	PUNCT
ejde-515	235	23	t	t	PROPN
ejde-515	235	24	,	,	PUNCT
ejde-515	235	25	τ	τ	PROPN
ejde-515	235	26	)	)	PUNCT
ejde-515	235	27	;	;	PUNCT
ejde-515	235	28	t	t	PROPN
ejde-515	235	29	≥	≥	PROPN
ejde-515	235	30	τ	τ	PROPN
ejde-515	235	31	,	,	PUNCT
ejde-515	235	32	τ	τ	PROPN
ejde-515	235	33	∈	∈	PROPN
ejde-515	235	34	r	r	PROPN
ejde-515	235	35	}	}	PUNCT
ejde-515	235	36	generated	generate	VERB
ejde-515	235	37	by	by	ADP
ejde-515	235	38	(	(	PUNCT
ejde-515	235	39	2.1	2.1	NUM
ejde-515	235	40	)	)	PUNCT
ejde-515	235	41	in	in	ADP
ejde-515	235	42	xp	xp	PROPN
ejde-515	235	43	=	=	PUNCT
ejde-515	235	44	lp(ω	lp(ω	X
ejde-515	235	45	)	)	PUNCT
ejde-515	235	46	and	and	CCONJ
ejde-515	235	47	the	the	DET
ejde-515	235	48	“	"	PUNCT
ejde-515	235	49	section	section	NOUN
ejde-515	235	50	”	"	PUNCT
ejde-515	235	51	a(t	a(t	NOUN
ejde-515	235	52	)	)	PUNCT
ejde-515	235	53	of	of	ADP
ejde-515	235	54	the	the	DET
ejde-515	235	55	pullback	pullback	NOUN
ejde-515	235	56	attractor	attractor	NOUN
ejde-515	235	57	a	a	PRON
ejde-515	235	58	(	(	PUNCT
ejde-515	235	59	·	·	PUNCT
ejde-515	235	60	)	)	PUNCT
ejde-515	235	61	of	of	ADP
ejde-515	235	62	t	t	PROPN
ejde-515	235	63	(	(	PUNCT
ejde-515	235	64	·	·	PUNCT
ejde-515	235	65	,	,	PUNCT
ejde-515	235	66	·	·	PUNCT
ejde-515	235	67	)	)	PUNCT
ejde-515	235	68	is	be	AUX
ejde-515	235	69	contained	contain	VERB
ejde-515	235	70	in	in	ADP
ejde-515	235	71	the	the	DET
ejde-515	235	72	ball	ball	NOUN
ejde-515	235	73	centered	center	VERB
ejde-515	235	74	at	at	ADP
ejde-515	235	75	the	the	DET
ejde-515	235	76	origin	origin	NOUN
ejde-515	235	77	with	with	ADP
ejde-515	235	78	radius	radius	NOUN
ejde-515	235	79	rδ(t	rδ(t	NOUN
ejde-515	235	80	)	)	PUNCT
ejde-515	235	81	defined	define	VERB
ejde-515	235	82	in	in	ADP
ejde-515	235	83	(	(	PUNCT
ejde-515	235	84	3.1	3.1	NUM
ejde-515	235	85	)	)	PUNCT
ejde-515	235	86	,	,	PUNCT
ejde-515	235	87	in	in	ADP
ejde-515	235	88	lp(ω	lp(ω	PROPN
ejde-515	235	89	)	)	PUNCT
ejde-515	235	90	,	,	PUNCT
ejde-515	235	91	for	for	ADP
ejde-515	235	92	any	any	DET
ejde-515	235	93	δ	δ	PROPN
ejde-515	235	94	>	>	X
ejde-515	235	95	0	0	PROPN
ejde-515	235	96	,	,	PUNCT
ejde-515	235	97	t	t	PROPN
ejde-515	235	98	∈	∈	PROPN
ejde-515	235	99	r	r	NOUN
ejde-515	235	100	and	and	CCONJ
ejde-515	235	101	1	1	NUM
ejde-515	235	102	≤	≤	NOUN
ejde-515	236	1	p	p	NOUN
ejde-515	236	2	<	<	X
ejde-515	236	3	∞.	∞.	PROPN
ejde-515	236	4	proof	proof	NOUN
ejde-515	236	5	.	.	PUNCT
ejde-515	237	1	from	from	ADP
ejde-515	237	2	theorem	theorem	NOUN
ejde-515	237	3	2.6	2.6	NUM
ejde-515	237	4	it	it	PRON
ejde-515	237	5	follows	follow	VERB
ejde-515	237	6	that	that	SCONJ
ejde-515	237	7	,	,	PUNCT
ejde-515	237	8	for	for	ADP
ejde-515	237	9	each	each	DET
ejde-515	237	10	initial	initial	ADJ
ejde-515	237	11	value	value	NOUN
ejde-515	237	12	u(τ	u(τ	ADJ
ejde-515	237	13	,	,	PUNCT
ejde-515	237	14	·	·	PUNCT
ejde-515	237	15	)	)	PUNCT
ejde-515	237	16	∈	∈	PROPN
ejde-515	238	1	xp	xp	NOUN
ejde-515	238	2	and	and	CCONJ
ejde-515	238	3	initial	initial	ADJ
ejde-515	238	4	time	time	NOUN
ejde-515	238	5	τ	τ	X
ejde-515	238	6	∈	∈	PROPN
ejde-515	238	7	r	r	NOUN
ejde-515	238	8	,	,	PUNCT
ejde-515	238	9	the	the	DET
ejde-515	238	10	process	process	NOUN
ejde-515	238	11	generated	generate	VERB
ejde-515	238	12	by	by	ADP
ejde-515	238	13	(	(	PUNCT
ejde-515	238	14	2.1	2.1	NUM
ejde-515	238	15	)	)	PUNCT
ejde-515	238	16	has	have	VERB
ejde-515	238	17	a	a	DET
ejde-515	238	18	unique	unique	ADJ
ejde-515	238	19	solution	solution	NOUN
ejde-515	238	20	,	,	PUNCT
ejde-515	238	21	which	which	PRON
ejde-515	238	22	we	we	PRON
ejde-515	238	23	can	can	AUX
ejde-515	238	24	to	to	PART
ejde-515	238	25	write	write	VERB
ejde-515	238	26	,	,	PUNCT
ejde-515	238	27	for	for	ADP
ejde-515	238	28	x	x	PROPN
ejde-515	238	29	∈	∈	PROPN
ejde-515	238	30	ω	ω	PROPN
ejde-515	238	31	,	,	PUNCT
ejde-515	238	32	as	as	ADP
ejde-515	238	33	t	t	PROPN
ejde-515	238	34	(	(	PUNCT
ejde-515	238	35	t	t	PROPN
ejde-515	238	36	,	,	PUNCT
ejde-515	238	37	τ)u(τ	τ)u(τ	PROPN
ejde-515	238	38	,	,	PUNCT
ejde-515	238	39	x	x	NOUN
ejde-515	238	40	)	)	PUNCT
ejde-515	238	41	=	=	SYM
ejde-515	238	42	t1(t	t1(t	PROPN
ejde-515	238	43	,	,	PUNCT
ejde-515	238	44	τ)u(τ	τ)u(τ	PROPN
ejde-515	238	45	,	,	PUNCT
ejde-515	238	46	x	x	NOUN
ejde-515	238	47	)	)	PUNCT
ejde-515	239	1	+	+	CCONJ
ejde-515	239	2	t2(t	t2(t	NOUN
ejde-515	239	3	,	,	PUNCT
ejde-515	239	4	τ)u(τ	τ)u(τ	NUM
ejde-515	239	5	,	,	PUNCT
ejde-515	239	6	x	x	NOUN
ejde-515	239	7	)	)	PUNCT
ejde-515	239	8	,	,	PUNCT
ejde-515	239	9	where	where	SCONJ
ejde-515	239	10	t1(t	t1(t	ADV
ejde-515	239	11	,	,	PUNCT
ejde-515	239	12	τ)u(τ	τ)u(τ	PROPN
ejde-515	239	13	,	,	PUNCT
ejde-515	239	14	x	x	NOUN
ejde-515	239	15	)	)	PUNCT
ejde-515	239	16	:	:	PUNCT
ejde-515	239	17	=	=	SYM
ejde-515	239	18	e−(a(t)−a(τ))u(τ	e−(a(t)−a(τ))u(τ	ADJ
ejde-515	239	19	,	,	PUNCT
ejde-515	239	20	x	x	NOUN
ejde-515	239	21	)	)	PUNCT
ejde-515	239	22	,	,	PUNCT
ejde-515	239	23	t2(t	t2(t	NOUN
ejde-515	239	24	,	,	PUNCT
ejde-515	239	25	τ)u(τ	τ)u(τ	NUM
ejde-515	239	26	,	,	PUNCT
ejde-515	239	27	x	x	NOUN
ejde-515	239	28	)	)	PUNCT
ejde-515	239	29	:	:	PUNCT
ejde-515	240	1	=	=	SYM
ejde-515	240	2	∫	∫	PROPN
ejde-515	240	3	t	t	PROPN
ejde-515	240	4	τ	τ	X
ejde-515	240	5	e−(a(t)−a(s))b(s)[kf(s	e−(a(t)−a(s))b(s)[kf(	VERB
ejde-515	240	6	,	,	PUNCT
ejde-515	240	7	u(s	u(s	ADJ
ejde-515	240	8	,	,	PUNCT
ejde-515	240	9	x	x	NOUN
ejde-515	240	10	)	)	PUNCT
ejde-515	240	11	)	)	PUNCT
ejde-515	241	1	+	+	CCONJ
ejde-515	241	2	s(s	s(s	PROPN
ejde-515	241	3	,	,	PUNCT
ejde-515	241	4	x)−	x)−	PROPN
ejde-515	241	5	h]ds	h]ds	PROPN
ejde-515	241	6	.	.	PUNCT
ejde-515	242	1	now	now	ADV
ejde-515	242	2	,	,	PUNCT
ejde-515	242	3	we	we	PRON
ejde-515	242	4	use	use	VERB
ejde-515	242	5	[	[	X
ejde-515	242	6	8	8	NUM
ejde-515	242	7	,	,	PUNCT
ejde-515	242	8	theorem	theorem	VERB
ejde-515	242	9	2.37	2.37	NUM
ejde-515	242	10	]	]	PUNCT
ejde-515	242	11	to	to	PART
ejde-515	242	12	prove	prove	VERB
ejde-515	242	13	that	that	SCONJ
ejde-515	242	14	t	t	PROPN
ejde-515	242	15	(	(	PUNCT
ejde-515	242	16	·	·	PUNCT
ejde-515	242	17	,	,	PUNCT
ejde-515	242	18	·	·	PUNCT
ejde-515	242	19	)	)	PUNCT
ejde-515	242	20	is	be	AUX
ejde-515	242	21	pullback	pullback	NOUN
ejde-515	242	22	asymptotically	asymptotically	ADV
ejde-515	242	23	compact	compact	ADJ
ejde-515	242	24	.	.	PUNCT
ejde-515	243	1	for	for	ADP
ejde-515	243	2	this	this	PRON
ejde-515	243	3	,	,	PUNCT
ejde-515	243	4	let	let	VERB
ejde-515	243	5	u	u	PRON
ejde-515	243	6	∈	∈	PROPN
ejde-515	243	7	b	b	AUX
ejde-515	243	8	be	be	AUX
ejde-515	243	9	a	a	DET
ejde-515	243	10	bounded	bounded	ADJ
ejde-515	243	11	subset	subset	NOUN
ejde-515	243	12	of	of	ADP
ejde-515	243	13	xp	xp	PROPN
ejde-515	243	14	.	.	PUNCT
ejde-515	244	1	without	without	ADP
ejde-515	244	2	loss	loss	NOUN
ejde-515	244	3	of	of	ADP
ejde-515	244	4	generality	generality	NOUN
ejde-515	244	5	,	,	PUNCT
ejde-515	244	6	we	we	PRON
ejde-515	244	7	suppose	suppose	VERB
ejde-515	244	8	that	that	SCONJ
ejde-515	244	9	b	b	NOUN
ejde-515	244	10	is	be	AUX
ejde-515	244	11	contained	contain	VERB
ejde-515	244	12	in	in	ADP
ejde-515	244	13	the	the	DET
ejde-515	244	14	ball	ball	NOUN
ejde-515	244	15	centered	center	VERB
ejde-515	244	16	at	at	ADP
ejde-515	244	17	the	the	DET
ejde-515	244	18	origin	origin	NOUN
ejde-515	244	19	of	of	ADP
ejde-515	244	20	radius	radius	NOUN
ejde-515	244	21	r	r	NOUN
ejde-515	244	22	>	>	X
ejde-515	244	23	0	0	NUM
ejde-515	244	24	.	.	PUNCT
ejde-515	245	1	then	then	ADV
ejde-515	245	2	,	,	PUNCT
ejde-515	245	3	for	for	ADP
ejde-515	245	4	t	t	PROPN
ejde-515	245	5	≥	≥	PROPN
ejde-515	245	6	τ	τ	PROPN
ejde-515	245	7	,	,	PUNCT
ejde-515	245	8	we	we	PRON
ejde-515	245	9	have	have	VERB
ejde-515	245	10	‖t1(t	‖t1(t	VERB
ejde-515	245	11	,	,	PUNCT
ejde-515	245	12	τ)u‖lp(ω	τ)u‖lp(ω	PROPN
ejde-515	245	13	)	)	PUNCT
ejde-515	245	14	≤	≤	NOUN
ejde-515	245	15	re−(a(t)−a(τ	re−(a(t)−a(τ	NOUN
ejde-515	245	16	)	)	PUNCT
ejde-515	245	17	)	)	PUNCT
ejde-515	245	18	≤	≤	NUM
ejde-515	245	19	re−a−tea0τ	re−a−tea0τ	NOUN
ejde-515	245	20	=	=	SYM
ejde-515	245	21	σ(t	σ(t	PROPN
ejde-515	245	22	,	,	PUNCT
ejde-515	245	23	τ)→	τ)→	PROPN
ejde-515	245	24	0	0	NUM
ejde-515	245	25	,	,	PUNCT
ejde-515	245	26	t→∞.	t→∞.	PUNCT
ejde-515	245	27	using	use	VERB
ejde-515	245	28	(	(	PUNCT
ejde-515	245	29	3.5	3.5	NUM
ejde-515	245	30	)	)	PUNCT
ejde-515	245	31	,	,	PUNCT
ejde-515	245	32	it	it	PRON
ejde-515	245	33	follows	follow	VERB
ejde-515	245	34	that	that	SCONJ
ejde-515	245	35	‖u(t	‖u(t	PUNCT
ejde-515	245	36	,	,	PUNCT
ejde-515	245	37	·	·	PUNCT
ejde-515	245	38	)	)	PUNCT
ejde-515	245	39	‖lp(ω	‖lp(ω	SYM
ejde-515	245	40	)	)	PUNCT
ejde-515	245	41	≤m	≤m	NOUN
ejde-515	245	42	,	,	PUNCT
ejde-515	245	43	for	for	ADP
ejde-515	245	44	t	t	PROPN
ejde-515	245	45	≥	≥	PROPN
ejde-515	245	46	τ	τ	PROPN
ejde-515	245	47	,	,	PUNCT
ejde-515	245	48	where	where	SCONJ
ejde-515	245	49	m	m	VERB
ejde-515	245	50	is	be	AUX
ejde-515	245	51	given	give	VERB
ejde-515	245	52	in	in	ADP
ejde-515	245	53	(	(	PUNCT
ejde-515	245	54	3.6	3.6	NUM
ejde-515	245	55	)	)	PUNCT
ejde-515	245	56	below	below	ADP
ejde-515	245	57	m	m	PROPN
ejde-515	245	58	=	=	SYM
ejde-515	245	59	m(t	m(t	NOUN
ejde-515	245	60	)	)	PUNCT
ejde-515	246	1	=	=	SYM
ejde-515	246	2	max	max	X
ejde-515	246	3	{	{	PUNCT
ejde-515	246	4	r	r	NOUN
ejde-515	246	5	,	,	PUNCT
ejde-515	246	6	2[b0k2(t)|ω|1	2[b0k2(t)|ω|1	NOUN
ejde-515	246	7	/	/	SYM
ejde-515	246	8	p	p	X
ejde-515	246	9	+	+	NOUN
ejde-515	246	10	‖s(t	‖s(t	ADJ
ejde-515	246	11	,	,	PUNCT
ejde-515	246	12	·	·	PUNCT
ejde-515	246	13	)	)	PUNCT
ejde-515	246	14	‖lp(ω	‖lp(ω	PUNCT
ejde-515	246	15	)	)	PUNCT
ejde-515	246	16	]	]	PUNCT
ejde-515	247	1	a−	a−	PROPN
ejde-515	247	2	−	−	PROPN
ejde-515	247	3	k1b0	k1b0	X
ejde-515	247	4	}	}	PUNCT
ejde-515	247	5	>	>	X
ejde-515	247	6	0	0	X
ejde-515	247	7	.	.	PUNCT
ejde-515	248	1	(	(	PUNCT
ejde-515	248	2	3.6	3.6	NUM
ejde-515	248	3	)	)	PUNCT
ejde-515	248	4	then	then	ADV
ejde-515	248	5	,	,	PUNCT
ejde-515	248	6	using	use	VERB
ejde-515	248	7	(	(	PUNCT
ejde-515	248	8	2.8	2.8	NUM
ejde-515	248	9	)	)	PUNCT
ejde-515	248	10	,	,	PUNCT
ejde-515	248	11	we	we	PRON
ejde-515	248	12	have	have	AUX
ejde-515	248	13	‖f(t	‖f(t	X
ejde-515	248	14	,	,	PUNCT
ejde-515	248	15	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	248	16	)	)	PUNCT
ejde-515	248	17	≤	≤	PUNCT
ejde-515	248	18	c1(t)(|ω|+	c1(t)(|ω|+	PROPN
ejde-515	248	19	‖u‖plp(ω	‖u‖plp(ω	PROPN
ejde-515	248	20	)	)	PUNCT
ejde-515	248	21	)	)	PUNCT
ejde-515	249	1	≤	≤	PROPN
ejde-515	249	2	c1(t)(|ω|+m(t)p	c1(t)(|ω|+m(t)p	PROPN
ejde-515	249	3	)	)	PUNCT
ejde-515	249	4	.	.	PUNCT
ejde-515	250	1	since	since	SCONJ
ejde-515	250	2	∂x(t2(t	∂x(t2(t	NOUN
ejde-515	250	3	,	,	PUNCT
ejde-515	250	4	τ)u(τ	τ)u(τ	PROPN
ejde-515	250	5	,	,	PUNCT
ejde-515	250	6	x	x	NOUN
ejde-515	250	7	)	)	PUNCT
ejde-515	250	8	)	)	PUNCT
ejde-515	251	1	=	=	SYM
ejde-515	252	1	∫	∫	PROPN
ejde-515	252	2	t	t	PROPN
ejde-515	252	3	τ	τ	PROPN
ejde-515	252	4	e−(a(t)−a(s))[b(s	e−(a(t)−a(s))[b(s	PROPN
ejde-515	252	5	)	)	PUNCT
ejde-515	252	6	∂	∂	NUM
ejde-515	252	7	∂x	∂x	PROPN
ejde-515	252	8	kf(t	kf(t	NOUN
ejde-515	252	9	,	,	PUNCT
ejde-515	252	10	u)(t	u)(t	NOUN
ejde-515	252	11	,	,	PUNCT
ejde-515	252	12	x	x	PRON
ejde-515	252	13	)	)	PUNCT
ejde-515	253	1	+	+	NUM
ejde-515	253	2	∂s	∂s	PROPN
ejde-515	253	3	∂x	∂x	PROPN
ejde-515	253	4	(	(	PUNCT
ejde-515	253	5	s	s	PROPN
ejde-515	253	6	,	,	PUNCT
ejde-515	253	7	x)]ds	x)]ds	X
ejde-515	253	8	.	.	PUNCT
ejde-515	254	1	proceeding	proceed	VERB
ejde-515	254	2	as	as	ADP
ejde-515	254	3	in	in	ADP
ejde-515	254	4	(	(	PUNCT
ejde-515	254	5	2.6	2.6	NUM
ejde-515	254	6	)	)	PUNCT
ejde-515	254	7	(	(	PUNCT
ejde-515	254	8	with	with	ADP
ejde-515	254	9	jx	jx	PROPN
ejde-515	254	10	replacing	replace	VERB
ejde-515	254	11	j	j	PROPN
ejde-515	254	12	)	)	PUNCT
ejde-515	254	13	and	and	CCONJ
ejde-515	254	14	using	use	VERB
ejde-515	254	15	(	(	PUNCT
ejde-515	254	16	2.8	2.8	NUM
ejde-515	254	17	)	)	PUNCT
ejde-515	254	18	,	,	PUNCT
ejde-515	254	19	it	it	PRON
ejde-515	254	20	follows	follow	VERB
ejde-515	254	21	that	that	SCONJ
ejde-515	254	22	‖∂x(kf(t	‖∂x(kf(t	NUM
ejde-515	254	23	,	,	PUNCT
ejde-515	254	24	u))‖lp(ω	u))‖lp(ω	SYM
ejde-515	254	25	)	)	PUNCT
ejde-515	254	26	≤	≤	NOUN
ejde-515	255	1	‖jx‖lp(ω)b0‖f(t	‖jx‖lp(ω)b0‖f(t	PROPN
ejde-515	255	2	,	,	PUNCT
ejde-515	255	3	u)‖l1(ω	u)‖l1(ω	NOUN
ejde-515	255	4	)	)	PUNCT
ejde-515	255	5	≤	≤	NOUN
ejde-515	255	6	c1(t)‖jx‖lp(ω)(|ω|+m(t)p	c1(t)‖jx‖lp(ω)(|ω|+m(t)p	NOUN
ejde-515	255	7	)	)	PUNCT
ejde-515	255	8	.	.	PUNCT
ejde-515	256	1	thus	thus	ADV
ejde-515	256	2	,	,	PUNCT
ejde-515	256	3	since	since	SCONJ
ejde-515	256	4	c1	c1	PROPN
ejde-515	256	5	and	and	CCONJ
ejde-515	256	6	k2	k2	PROPN
ejde-515	256	7	are	be	AUX
ejde-515	256	8	non	non	ADJ
ejde-515	256	9	-	-	ADJ
ejde-515	256	10	decreasing	decrease	VERB
ejde-515	256	11	,	,	PUNCT
ejde-515	256	12	we	we	PRON
ejde-515	256	13	obtain	obtain	VERB
ejde-515	256	14	‖∂x(t2(t	‖∂x(t2(t	NUM
ejde-515	256	15	,	,	PUNCT
ejde-515	256	16	τ)u)‖lp(ω	τ)u)‖lp(ω	PROPN
ejde-515	256	17	)	)	PUNCT
ejde-515	256	18	≤	≤	NUM
ejde-515	256	19	∫	∫	PROPN
ejde-515	256	20	t	t	PROPN
ejde-515	256	21	τ	τ	PROPN
ejde-515	256	22	e−(a(t)−a(s	e−(a(t)−a(s	PROPN
ejde-515	256	23	)	)	PUNCT
ejde-515	256	24	)	)	PUNCT
ejde-515	256	25	(	(	PUNCT
ejde-515	256	26	b(s)‖∂xkf(s	b(s)‖∂xkf(s	VERB
ejde-515	256	27	,	,	PUNCT
ejde-515	256	28	u(s	u(s	ADJ
ejde-515	256	29	,	,	PUNCT
ejde-515	256	30	·	·	PUNCT
ejde-515	256	31	)	)	PUNCT
ejde-515	256	32	)	)	PUNCT
ejde-515	256	33	‖lp(ω	‖lp(ω	PUNCT
ejde-515	256	34	)	)	PUNCT
ejde-515	256	35	+	+	NUM
ejde-515	256	36	‖∂xs(s	‖∂xs(s	NUM
ejde-515	256	37	,	,	PUNCT
ejde-515	256	38	·	·	PUNCT
ejde-515	256	39	)	)	PUNCT
ejde-515	256	40	‖lp(ω	‖lp(ω	PUNCT
ejde-515	256	41	)	)	PUNCT
ejde-515	256	42	)	)	PUNCT
ejde-515	257	1	ds	ds	PROPN
ejde-515	257	2	12	12	NUM
ejde-515	257	3	s.	s.	PROPN
ejde-515	257	4	h.	h.	PROPN
ejde-515	257	5	da	da	PROPN
ejde-515	257	6	silva	silva	PROPN
ejde-515	257	7	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	257	8	≤	≤	NUM
ejde-515	257	9	∫	∫	PROPN
ejde-515	257	10	t	t	PROPN
ejde-515	257	11	τ	τ	PROPN
ejde-515	257	12	e−(a(t)−a(s	e−(a(t)−a(s	PROPN
ejde-515	257	13	)	)	PUNCT
ejde-515	257	14	)	)	PUNCT
ejde-515	257	15	(	(	PUNCT
ejde-515	257	16	b0c1(s)‖jx‖lp(ω)|ω|1	b0c1(s)‖jx‖lp(ω)|ω|1	NOUN
ejde-515	257	17	/	/	SYM
ejde-515	257	18	p	p	NOUN
ejde-515	258	1	+	+	PROPN
ejde-515	258	2	m(s)p	m(s)p	PROPN
ejde-515	258	3	+	+	CCONJ
ejde-515	258	4	‖∂xs‖p	‖∂xs‖p	ADJ
ejde-515	258	5	)	)	PUNCT
ejde-515	258	6	ds	ds	PROPN
ejde-515	258	7	≤	≤	NUM
ejde-515	258	8	∫	∫	PROPN
ejde-515	258	9	t	t	PROPN
ejde-515	258	10	τ	τ	PROPN
ejde-515	258	11	e−(a(t)−a(s	e−(a(t)−a(s	PROPN
ejde-515	258	12	)	)	PUNCT
ejde-515	258	13	)	)	PUNCT
ejde-515	258	14	(	(	PUNCT
ejde-515	258	15	b0c1(t)‖jx‖lp(ω)|ω|1	b0c1(t)‖jx‖lp(ω)|ω|1	NOUN
ejde-515	258	16	/	/	SYM
ejde-515	258	17	p	p	X
ejde-515	258	18	+	+	PROPN
ejde-515	258	19	m(t)p	m(t)p	PROPN
ejde-515	258	20	+	+	NUM
ejde-515	258	21	‖∂xs‖p	‖∂xs‖p	ADJ
ejde-515	258	22	)	)	PUNCT
ejde-515	258	23	ds	ds	PROPN
ejde-515	258	24	≤	≤	NUM
ejde-515	258	25	c1(t)‖jx‖p	c1(t)‖jx‖p	PROPN
ejde-515	258	26	1	1	NUM
ejde-515	258	27	a0	a0	PROPN
ejde-515	259	1	[	[	X
ejde-515	259	2	e(a0−a−)t	e(a0−a−)t	NOUN
ejde-515	259	3	−	−	NOUN
ejde-515	259	4	e−a−tea0τ	e−a−tea0τ	NOUN
ejde-515	259	5	]	]	PUNCT
ejde-515	259	6	(	(	PUNCT
ejde-515	259	7	|ω|1	|ω|1	PROPN
ejde-515	259	8	/	/	SYM
ejde-515	259	9	p	p	X
ejde-515	259	10	+	+	NOUN
ejde-515	259	11	m(t)p	m(t)p	PROPN
ejde-515	259	12	)	)	PUNCT
ejde-515	260	1	+	+	CCONJ
ejde-515	260	2	c1(t	c1(t	NUM
ejde-515	260	3	)	)	PUNCT
ejde-515	260	4	1	1	NUM
ejde-515	260	5	a0	a0	PROPN
ejde-515	260	6	[	[	X
ejde-515	260	7	e(a0−a−)t	e(a0−a−)t	NOUN
ejde-515	260	8	−	−	NOUN
ejde-515	260	9	e−a−tea0τ	e−a−tea0τ	NOUN
ejde-515	260	10	]	]	PUNCT
ejde-515	260	11	‖∂xs‖p	‖∂xs‖p	PRON
ejde-515	260	12	≤	≤	PUNCT
ejde-515	260	13	c1(t)‖jx‖p	c1(t)‖jx‖p	PROPN
ejde-515	260	14	1	1	NUM
ejde-515	260	15	a0	a0	PROPN
ejde-515	260	16	e(a0−a−)t(|ω|+m(t)p	e(a0−a−)t(|ω|+m(t)p	PROPN
ejde-515	260	17	)	)	PUNCT
ejde-515	260	18	+	+	CCONJ
ejde-515	260	19	c1(t	c1(t	NUM
ejde-515	260	20	)	)	PUNCT
ejde-515	260	21	1	1	NUM
ejde-515	260	22	a0	a0	NOUN
ejde-515	260	23	e(a0−a−)t‖∂xs‖p	e(a0−a−)t‖∂xs‖p	ADV
ejde-515	260	24	=	=	SYM
ejde-515	260	25	c1(t)‖jx‖p(|ω|+m(t)p	c1(t)‖jx‖p(|ω|+m(t)p	PROPN
ejde-515	260	26	)	)	PUNCT
ejde-515	260	27	+	+	NUM
ejde-515	260	28	‖∂xs‖p	‖∂xs‖p	PROPN
ejde-515	260	29	a0	a0	PROPN
ejde-515	260	30	e(a0−a−)t	e(a0−a−)t	PROPN
ejde-515	260	31	.	.	PUNCT
ejde-515	261	1	hence	hence	ADV
ejde-515	261	2	,	,	PUNCT
ejde-515	261	3	for	for	ADP
ejde-515	261	4	any	any	DET
ejde-515	261	5	u	u	PROPN
ejde-515	261	6	∈	∈	PROPN
ejde-515	261	7	b	b	PROPN
ejde-515	261	8	and	and	CCONJ
ejde-515	261	9	t	t	PROPN
ejde-515	261	10	>	>	X
ejde-515	261	11	τ	τ	PROPN
ejde-515	261	12	,	,	PUNCT
ejde-515	261	13	the	the	DET
ejde-515	261	14	value	value	NOUN
ejde-515	261	15	of	of	ADP
ejde-515	261	16	‖	‖	PROPN
ejde-515	261	17	∂∂xt2(t	∂∂xt2(t	PROPN
ejde-515	261	18	,	,	PUNCT
ejde-515	261	19	τ)u‖lp(ω	τ)u‖lp(ω	PROPN
ejde-515	261	20	)	)	PUNCT
ejde-515	261	21	is	be	AUX
ejde-515	261	22	bounded	bound	VERB
ejde-515	261	23	by	by	ADP
ejde-515	261	24	a	a	DET
ejde-515	261	25	constant	constant	ADJ
ejde-515	261	26	(	(	PUNCT
ejde-515	261	27	independent	independent	ADJ
ejde-515	261	28	of	of	ADP
ejde-515	261	29	u	u	PROPN
ejde-515	261	30	∈	∈	PROPN
ejde-515	261	31	b	b	PROPN
ejde-515	261	32	)	)	PUNCT
ejde-515	261	33	.	.	PUNCT
ejde-515	262	1	then	then	ADV
ejde-515	262	2	t2(t	t2(t	NOUN
ejde-515	262	3	,	,	PUNCT
ejde-515	262	4	τ)u	τ)u	PUNCT
ejde-515	262	5	belongs	belong	VERB
ejde-515	262	6	to	to	ADP
ejde-515	262	7	a	a	DET
ejde-515	262	8	ball	ball	NOUN
ejde-515	262	9	in	in	ADP
ejde-515	262	10	the	the	DET
ejde-515	262	11	space	space	NOUN
ejde-515	262	12	w	w	PROPN
ejde-515	262	13	1,p(ω	1,p(ω	NUM
ejde-515	262	14	)	)	PUNCT
ejde-515	262	15	for	for	ADP
ejde-515	262	16	all	all	DET
ejde-515	262	17	u	u	PROPN
ejde-515	262	18	∈	∈	PROPN
ejde-515	262	19	b.	b.	NOUN
ejde-515	262	20	hence	hence	ADV
ejde-515	262	21	,	,	PUNCT
ejde-515	262	22	by	by	ADP
ejde-515	262	23	the	the	DET
ejde-515	262	24	sobolev	sobolev	NOUN
ejde-515	262	25	embedding	embed	VERB
ejde-515	262	26	theorem	theorem	VERB
ejde-515	262	27	,	,	PUNCT
ejde-515	262	28	it	it	PRON
ejde-515	262	29	follows	follow	VERB
ejde-515	262	30	that	that	SCONJ
ejde-515	262	31	t2(t	t2(t	PROPN
ejde-515	262	32	,	,	PUNCT
ejde-515	262	33	τ	τ	X
ejde-515	262	34	)	)	PUNCT
ejde-515	262	35	is	be	AUX
ejde-515	262	36	a	a	DET
ejde-515	262	37	compact	compact	ADJ
ejde-515	262	38	operator	operator	NOUN
ejde-515	262	39	,	,	PUNCT
ejde-515	262	40	for	for	ADP
ejde-515	262	41	any	any	DET
ejde-515	262	42	t	t	NOUN
ejde-515	263	1	>	>	X
ejde-515	263	2	τ	τ	PROPN
ejde-515	263	3	.	.	PUNCT
ejde-515	264	1	therefore	therefore	ADV
ejde-515	264	2	,	,	PUNCT
ejde-515	264	3	using	use	VERB
ejde-515	264	4	lemma	lemma	PROPN
ejde-515	264	5	3.1	3.1	NUM
ejde-515	264	6	and	and	CCONJ
ejde-515	264	7	[	[	X
ejde-515	264	8	8	8	NUM
ejde-515	264	9	]	]	PUNCT
ejde-515	264	10	,	,	PUNCT
ejde-515	264	11	there	there	PRON
ejde-515	264	12	exists	exist	VERB
ejde-515	264	13	the	the	DET
ejde-515	264	14	pullback	pullback	NOUN
ejde-515	264	15	attractor	attractor	NOUN
ejde-515	264	16	{	{	PUNCT
ejde-515	264	17	a(t	a(t	PROPN
ejde-515	264	18	)	)	PUNCT
ejde-515	264	19	;	;	PUNCT
ejde-515	264	20	t	t	PROPN
ejde-515	264	21	∈	∈	PROPN
ejde-515	264	22	r	r	X
ejde-515	264	23	}	}	PUNCT
ejde-515	264	24	and	and	CCONJ
ejde-515	264	25	each	each	DET
ejde-515	264	26	“	"	PUNCT
ejde-515	264	27	section	section	NOUN
ejde-515	264	28	”	"	PUNCT
ejde-515	264	29	a(t	a(t	NOUN
ejde-515	264	30	)	)	PUNCT
ejde-515	264	31	of	of	ADP
ejde-515	264	32	the	the	DET
ejde-515	264	33	pullback	pullback	NOUN
ejde-515	264	34	attractor	attractor	NOUN
ejde-515	264	35	a	a	PRON
ejde-515	264	36	(	(	PUNCT
ejde-515	264	37	·	·	PUNCT
ejde-515	264	38	)	)	PUNCT
ejde-515	264	39	is	be	AUX
ejde-515	264	40	the	the	DET
ejde-515	264	41	pullback	pullback	NOUN
ejde-515	264	42	ω	ω	ADJ
ejde-515	264	43	-	-	PUNCT
ejde-515	264	44	limit	limit	NOUN
ejde-515	264	45	set	set	NOUN
ejde-515	264	46	of	of	ADP
ejde-515	264	47	any	any	DET
ejde-515	264	48	bounded	bounded	ADJ
ejde-515	264	49	subset	subset	NOUN
ejde-515	264	50	of	of	ADP
ejde-515	264	51	xp	xp	ADV
ejde-515	264	52	containing	contain	VERB
ejde-515	264	53	the	the	DET
ejde-515	264	54	ball	ball	NOUN
ejde-515	264	55	centered	center	VERB
ejde-515	264	56	at	at	ADP
ejde-515	264	57	the	the	DET
ejde-515	264	58	origin	origin	NOUN
ejde-515	264	59	with	with	ADP
ejde-515	264	60	radius	radius	PROPN
ejde-515	264	61	rδ	rδ	PROPN
ejde-515	264	62	,	,	PUNCT
ejde-515	264	63	given	give	VERB
ejde-515	264	64	in	in	ADP
ejde-515	264	65	(	(	PUNCT
ejde-515	264	66	3.1	3.1	NUM
ejde-515	264	67	)	)	PUNCT
ejde-515	264	68	,	,	PUNCT
ejde-515	264	69	for	for	ADP
ejde-515	264	70	any	any	DET
ejde-515	264	71	δ	δ	PROPN
ejde-515	264	72	>	>	X
ejde-515	264	73	0	0	PROPN
ejde-515	264	74	.	.	PUNCT
ejde-515	265	1	since	since	SCONJ
ejde-515	265	2	the	the	DET
ejde-515	265	3	ball	ball	NOUN
ejde-515	265	4	centered	center	VERB
ejde-515	265	5	at	at	ADP
ejde-515	265	6	the	the	DET
ejde-515	265	7	origin	origin	NOUN
ejde-515	265	8	with	with	ADP
ejde-515	265	9	radius	radius	NOUN
ejde-515	265	10	rδ	rδ	NOUN
ejde-515	265	11	pullback	pullback	NOUN
ejde-515	265	12	absorbs	absorb	VERB
ejde-515	265	13	bounded	bound	VERB
ejde-515	265	14	subsets	subset	NOUN
ejde-515	265	15	of	of	ADP
ejde-515	265	16	xp	xp	PROPN
ejde-515	265	17	,	,	PUNCT
ejde-515	265	18	it	it	PRON
ejde-515	265	19	also	also	ADV
ejde-515	265	20	follows	follow	VERB
ejde-515	265	21	that	that	SCONJ
ejde-515	265	22	the	the	DET
ejde-515	265	23	set	set	NOUN
ejde-515	265	24	a(t	a(t	NOUN
ejde-515	265	25	)	)	PUNCT
ejde-515	265	26	is	be	AUX
ejde-515	265	27	contained	contain	VERB
ejde-515	265	28	in	in	ADP
ejde-515	265	29	the	the	DET
ejde-515	265	30	ball	ball	NOUN
ejde-515	265	31	centered	center	VERB
ejde-515	265	32	at	at	ADP
ejde-515	265	33	the	the	DET
ejde-515	265	34	origin	origin	NOUN
ejde-515	265	35	of	of	ADP
ejde-515	265	36	xp	xp	PROPN
ejde-515	265	37	and	and	CCONJ
ejde-515	265	38	of	of	ADP
ejde-515	265	39	radius	radius	NOUN
ejde-515	265	40	r(t	r(t	NOUN
ejde-515	265	41	)	)	PUNCT
ejde-515	266	1	=	=	SYM
ejde-515	266	2	1	1	NUM
ejde-515	266	3	a−	a−	PROPN
ejde-515	266	4	−	−	NOUN
ejde-515	266	5	k1b0	k1b0	X
ejde-515	266	6	[	[	X
ejde-515	266	7	b0k2(t)|ω|1	b0k2(t)|ω|1	NOUN
ejde-515	266	8	/	/	SYM
ejde-515	266	9	p	p	NOUN
ejde-515	266	10	+	+	X
ejde-515	266	11	‖s‖p	‖s‖p	NOUN
ejde-515	266	12	]	]	PUNCT
ejde-515	266	13	for	for	ADP
ejde-515	266	14	any	any	DET
ejde-515	266	15	t	t	NOUN
ejde-515	266	16	∈	∈	NOUN
ejde-515	266	17	r	r	NOUN
ejde-515	266	18	and	and	CCONJ
ejde-515	266	19	1	1	NUM
ejde-515	266	20	≤	≤	NOUN
ejde-515	267	1	p	p	NOUN
ejde-515	267	2	<	<	X
ejde-515	267	3	∞.	∞.	PROPN
ejde-515	267	4	�	�	PROPN
ejde-515	267	5	4	4	NUM
ejde-515	267	6	.	.	PUNCT
ejde-515	267	7	continuity	continuity	NOUN
ejde-515	267	8	with	with	ADP
ejde-515	267	9	respect	respect	NOUN
ejde-515	267	10	to	to	ADP
ejde-515	267	11	parameter	parameter	NOUN
ejde-515	267	12	s	s	PRON
ejde-515	267	13	a	a	DET
ejde-515	267	14	natural	natural	ADJ
ejde-515	267	15	question	question	NOUN
ejde-515	267	16	to	to	PART
ejde-515	267	17	examine	examine	VERB
ejde-515	267	18	at	at	ADP
ejde-515	267	19	this	this	DET
ejde-515	267	20	point	point	NOUN
ejde-515	267	21	is	be	AUX
ejde-515	267	22	the	the	DET
ejde-515	267	23	depedence	depedence	NOUN
ejde-515	267	24	of	of	ADP
ejde-515	267	25	the	the	DET
ejde-515	267	26	process	process	NOUN
ejde-515	267	27	with	with	ADP
ejde-515	267	28	respect	respect	NOUN
ejde-515	267	29	to	to	ADP
ejde-515	267	30	parameters	parameter	NOUN
ejde-515	267	31	that	that	PRON
ejde-515	267	32	arise	arise	VERB
ejde-515	267	33	in	in	ADP
ejde-515	267	34	the	the	DET
ejde-515	267	35	equation	equation	NOUN
ejde-515	267	36	.	.	PUNCT
ejde-515	268	1	in	in	ADP
ejde-515	268	2	this	this	DET
ejde-515	268	3	section	section	NOUN
ejde-515	268	4	we	we	PRON
ejde-515	268	5	prove	prove	VERB
ejde-515	268	6	the	the	DET
ejde-515	268	7	continuity	continuity	NOUN
ejde-515	268	8	of	of	ADP
ejde-515	268	9	the	the	DET
ejde-515	268	10	process	process	NOUN
ejde-515	268	11	with	with	ADP
ejde-515	268	12	respect	respect	NOUN
ejde-515	268	13	to	to	ADP
ejde-515	268	14	a	a	DET
ejde-515	268	15	external	external	ADJ
ejde-515	268	16	stimuli	stimulus	NOUN
ejde-515	268	17	function	function	NOUN
ejde-515	268	18	and	and	CCONJ
ejde-515	268	19	we	we	PRON
ejde-515	268	20	use	use	VERB
ejde-515	268	21	this	this	DET
ejde-515	268	22	result	result	NOUN
ejde-515	268	23	to	to	PART
ejde-515	268	24	prove	prove	VERB
ejde-515	268	25	the	the	DET
ejde-515	268	26	upper	upper	ADJ
ejde-515	268	27	semicontinuity	semicontinuity	NOUN
ejde-515	268	28	of	of	ADP
ejde-515	268	29	the	the	DET
ejde-515	268	30	pullback	pullback	NOUN
ejde-515	268	31	attractors	attractor	NOUN
ejde-515	268	32	.	.	PUNCT
ejde-515	269	1	4.1	4.1	NUM
ejde-515	269	2	.	.	PUNCT
ejde-515	269	3	continuity	continuity	NOUN
ejde-515	269	4	of	of	ADP
ejde-515	269	5	the	the	DET
ejde-515	269	6	process	process	NOUN
ejde-515	269	7	with	with	ADP
ejde-515	269	8	respect	respect	NOUN
ejde-515	269	9	to	to	ADP
ejde-515	269	10	external	external	ADJ
ejde-515	269	11	stimuli	stimulus	NOUN
ejde-515	269	12	.	.	PUNCT
ejde-515	270	1	from	from	ADP
ejde-515	270	2	now	now	ADV
ejde-515	270	3	on	on	ADV
ejde-515	270	4	we	we	PRON
ejde-515	270	5	denote	denote	VERB
ejde-515	270	6	by	by	ADP
ejde-515	270	7	ts(t	ts(t	PROPN
ejde-515	270	8	,	,	PUNCT
ejde-515	270	9	τ	τ	PROPN
ejde-515	270	10	)	)	PUNCT
ejde-515	270	11	the	the	DET
ejde-515	270	12	family	family	NOUN
ejde-515	270	13	of	of	ADP
ejde-515	270	14	processes	process	NOUN
ejde-515	270	15	associated	associate	VERB
ejde-515	270	16	with	with	ADP
ejde-515	270	17	the	the	DET
ejde-515	270	18	family	family	NOUN
ejde-515	270	19	of	of	ADP
ejde-515	270	20	problems	problem	NOUN
ejde-515	270	21	∂tus(t	∂tus(t	VERB
ejde-515	270	22	,	,	PUNCT
ejde-515	270	23	x	x	X
ejde-515	270	24	)	)	PUNCT
ejde-515	271	1	=	=	SYM
ejde-515	271	2	−a(t)us(t	−a(t)us(t	PROPN
ejde-515	271	3	,	,	PUNCT
ejde-515	271	4	x	x	PRON
ejde-515	271	5	)	)	PUNCT
ejde-515	271	6	+	+	NUM
ejde-515	271	7	b(t)kf(t	b(t)kf(t	NOUN
ejde-515	271	8	,	,	PUNCT
ejde-515	271	9	us(t	us(t	NOUN
ejde-515	271	10	,	,	PUNCT
ejde-515	271	11	x	x	NOUN
ejde-515	271	12	)	)	PUNCT
ejde-515	271	13	)	)	PUNCT
ejde-515	272	1	+	+	CCONJ
ejde-515	273	1	s(t	s(t	PROPN
ejde-515	273	2	,	,	PUNCT
ejde-515	273	3	x	x	NOUN
ejde-515	273	4	)	)	PUNCT
ejde-515	273	5	,	,	PUNCT
ejde-515	273	6	t	t	PROPN
ejde-515	273	7	≥	≥	PROPN
ejde-515	273	8	τ	τ	PROPN
ejde-515	273	9	,	,	PUNCT
ejde-515	273	10	x	x	PROPN
ejde-515	273	11	∈	∈	PROPN
ejde-515	273	12	ω	ω	NOUN
ejde-515	273	13	,	,	PUNCT
ejde-515	273	14	us(τ	us(τ	NOUN
ejde-515	273	15	,	,	PUNCT
ejde-515	273	16	x	x	X
ejde-515	273	17	)	)	PUNCT
ejde-515	273	18	=	=	SYM
ejde-515	273	19	uτ	uτ	PROPN
ejde-515	273	20	(	(	PUNCT
ejde-515	273	21	x	x	NOUN
ejde-515	273	22	)	)	PUNCT
ejde-515	273	23	,	,	PUNCT
ejde-515	273	24	x	x	PUNCT
ejde-515	273	25	∈	∈	PROPN
ejde-515	273	26	ω	ω	PROPN
ejde-515	273	27	,	,	PUNCT
ejde-515	273	28	us(t	us(t	NOUN
ejde-515	273	29	,	,	PUNCT
ejde-515	273	30	x	x	X
ejde-515	273	31	)	)	PUNCT
ejde-515	273	32	=	=	SYM
ejde-515	273	33	0	0	NUM
ejde-515	273	34	,	,	PUNCT
ejde-515	273	35	t	t	PROPN
ejde-515	273	36	≥	≥	PROPN
ejde-515	273	37	τ	τ	PROPN
ejde-515	273	38	,	,	PUNCT
ejde-515	273	39	x	x	PROPN
ejde-515	273	40	∈	∈	PROPN
ejde-515	273	41	rn\ω	rn\ω	NOUN
ejde-515	273	42	.	.	PUNCT
ejde-515	274	1	(	(	PUNCT
ejde-515	274	2	4.1	4.1	NUM
ejde-515	274	3	)	)	PUNCT
ejde-515	274	4	in	in	ADP
ejde-515	274	5	this	this	DET
ejde-515	274	6	subsection	subsection	NOUN
ejde-515	274	7	we	we	PRON
ejde-515	274	8	prove	prove	VERB
ejde-515	274	9	the	the	DET
ejde-515	274	10	continuous	continuous	ADJ
ejde-515	274	11	dependence	dependence	NOUN
ejde-515	274	12	of	of	ADP
ejde-515	274	13	the	the	DET
ejde-515	274	14	process	process	NOUN
ejde-515	274	15	with	with	ADP
ejde-515	274	16	respect	respect	NOUN
ejde-515	274	17	to	to	ADP
ejde-515	274	18	the	the	DET
ejde-515	274	19	stimuli	stimulus	NOUN
ejde-515	274	20	function	function	NOUN
ejde-515	274	21	s	s	VERB
ejde-515	274	22	at	at	ADP
ejde-515	274	23	s0	s0	PROPN
ejde-515	274	24	∈	∈	PROPN
ejde-515	274	25	σ	σ	PROPN
ejde-515	274	26	,	,	PUNCT
ejde-515	274	27	where	where	SCONJ
ejde-515	274	28	σ	σ	NOUN
ejde-515	274	29	=	=	PUNCT
ejde-515	274	30	{	{	PUNCT
ejde-515	274	31	s	s	X
ejde-515	274	32	:	:	PUNCT
ejde-515	274	33	r×	r×	PROPN
ejde-515	274	34	rn	rn	PROPN
ejde-515	274	35	→	→	SYM
ejde-515	274	36	r	r	NOUN
ejde-515	274	37	,	,	PUNCT
ejde-515	274	38	‖s‖p	‖s‖p	NOUN
ejde-515	274	39	=	=	SYM
ejde-515	274	40	sup	sup	NUM
ejde-515	274	41	t∈r+	t∈r+	NOUN
ejde-515	274	42	‖s(t	‖s(t	NOUN
ejde-515	274	43	,	,	PUNCT
ejde-515	274	44	·	·	PUNCT
ejde-515	274	45	)	)	PUNCT
ejde-515	274	46	‖lp(ω	‖lp(ω	PUNCT
ejde-515	274	47	)	)	PUNCT
ejde-515	275	1	<	<	X
ejde-515	275	2	∞	∞	NUM
ejde-515	275	3	}	}	PUNCT
ejde-515	275	4	.	.	PUNCT
ejde-515	276	1	more	more	ADV
ejde-515	276	2	precisely	precisely	ADV
ejde-515	276	3	we	we	PRON
ejde-515	276	4	have	have	VERB
ejde-515	276	5	the	the	DET
ejde-515	276	6	following	follow	VERB
ejde-515	276	7	result	result	NOUN
ejde-515	276	8	.	.	PUNCT
ejde-515	277	1	ejde-2020/92	ejde-2020/92	ADJ
ejde-515	277	2	non	non	ADJ
ejde-515	277	3	-	-	ADJ
ejde-515	277	4	autonomous	autonomous	ADJ
ejde-515	277	5	model	model	NOUN
ejde-515	277	6	for	for	ADP
ejde-515	277	7	neural	neural	ADJ
ejde-515	277	8	fields	field	NOUN
ejde-515	277	9	13	13	NUM
ejde-515	277	10	theorem	theorem	VERB
ejde-515	277	11	4.1	4.1	NUM
ejde-515	277	12	.	.	PUNCT
ejde-515	278	1	in	in	ADP
ejde-515	278	2	addition	addition	NOUN
ejde-515	278	3	to	to	ADP
ejde-515	278	4	the	the	DET
ejde-515	278	5	hypotheses	hypothesis	NOUN
ejde-515	278	6	of	of	ADP
ejde-515	278	7	theorem	theorem	NOUN
ejde-515	278	8	3.2	3.2	NUM
ejde-515	278	9	,	,	PUNCT
ejde-515	278	10	suppose	suppose	VERB
ejde-515	278	11	that	that	SCONJ
ejde-515	278	12	the	the	DET
ejde-515	278	13	function	function	NOUN
ejde-515	278	14	c2	c2	PROPN
ejde-515	278	15	given	give	VERB
ejde-515	278	16	in	in	ADP
ejde-515	278	17	(	(	PUNCT
ejde-515	278	18	2.9	2.9	NUM
ejde-515	278	19	)	)	PUNCT
ejde-515	278	20	is	be	AUX
ejde-515	278	21	non	non	ADJ
ejde-515	278	22	-	-	ADJ
ejde-515	278	23	decreasing	decrease	VERB
ejde-515	278	24	.	.	PUNCT
ejde-515	279	1	then	then	ADV
ejde-515	279	2	,	,	PUNCT
ejde-515	279	3	if	if	SCONJ
ejde-515	279	4	ts	ts	X
ejde-515	279	5	(	(	PUNCT
ejde-515	279	6	·	·	PUNCT
ejde-515	279	7	,	,	PUNCT
ejde-515	279	8	·	·	PUNCT
ejde-515	279	9	)	)	PUNCT
ejde-515	279	10	denotes	denote	VERB
ejde-515	279	11	the	the	DET
ejde-515	279	12	process	process	NOUN
ejde-515	279	13	generated	generate	VERB
ejde-515	279	14	by	by	ADP
ejde-515	279	15	the	the	DET
ejde-515	279	16	problem	problem	NOUN
ejde-515	279	17	(	(	PUNCT
ejde-515	279	18	4.1	4.1	NUM
ejde-515	279	19	)	)	PUNCT
ejde-515	279	20	,	,	PUNCT
ejde-515	279	21	for	for	ADP
ejde-515	279	22	s	s	PROPN
ejde-515	279	23	∈	∈	PROPN
ejde-515	279	24	σ	σ	PROPN
ejde-515	279	25	,	,	PUNCT
ejde-515	279	26	we	we	PRON
ejde-515	279	27	have	have	VERB
ejde-515	279	28	that	that	PRON
ejde-515	279	29	ts(t	ts(t	PROPN
ejde-515	279	30	,	,	PUNCT
ejde-515	279	31	τ)uτ	τ)uτ	PROPN
ejde-515	279	32	converges	converge	VERB
ejde-515	279	33	uniformly	uniformly	ADV
ejde-515	279	34	to	to	PART
ejde-515	279	35	ts0	ts0	PROPN
ejde-515	279	36	(	(	PUNCT
ejde-515	279	37	t	t	PROPN
ejde-515	279	38	,	,	PUNCT
ejde-515	279	39	τ)uτ	τ)uτ	PROPN
ejde-515	279	40	in	in	ADP
ejde-515	279	41	xp	xp	PROPN
ejde-515	279	42	,	,	PUNCT
ejde-515	279	43	as	as	ADP
ejde-515	279	44	‖s	‖s	ADJ
ejde-515	279	45	−	−	PROPN
ejde-515	279	46	s0‖p	s0‖p	PROPN
ejde-515	279	47	→	→	SYM
ejde-515	279	48	0	0	NUM
ejde-515	279	49	,	,	PUNCT
ejde-515	279	50	for	for	ADP
ejde-515	279	51	t	t	PROPN
ejde-515	279	52	∈	∈	PROPN
ejde-515	280	1	[	[	X
ejde-515	280	2	τ	τ	X
ejde-515	280	3	,	,	PUNCT
ejde-515	280	4	l	l	NOUN
ejde-515	280	5	]	]	PUNCT
ejde-515	280	6	,	,	PUNCT
ejde-515	280	7	and	and	CCONJ
ejde-515	280	8	any	any	DET
ejde-515	280	9	l	l	NOUN
ejde-515	280	10	>	>	X
ejde-515	280	11	τ	τ	PROPN
ejde-515	280	12	.	.	PUNCT
ejde-515	281	1	proof	proof	NOUN
ejde-515	281	2	.	.	PUNCT
ejde-515	282	1	let	let	VERB
ejde-515	282	2	l	l	PROPN
ejde-515	282	3	>	>	X
ejde-515	282	4	τ	τ	PROPN
ejde-515	282	5	and	and	CCONJ
ejde-515	282	6	us(t	us(t	NOUN
ejde-515	282	7	,	,	PUNCT
ejde-515	282	8	x	x	X
ejde-515	282	9	)	)	PUNCT
ejde-515	282	10	=	=	SYM
ejde-515	282	11	ts(t	ts(t	PROPN
ejde-515	282	12	,	,	PUNCT
ejde-515	282	13	τ)uτ	τ)uτ	PROPN
ejde-515	282	14	(	(	PUNCT
ejde-515	282	15	x	x	X
ejde-515	282	16	)	)	PUNCT
ejde-515	282	17	be	be	VERB
ejde-515	282	18	the	the	DET
ejde-515	282	19	solution	solution	NOUN
ejde-515	282	20	of	of	ADP
ejde-515	282	21	(	(	PUNCT
ejde-515	282	22	4.1	4.1	NUM
ejde-515	282	23	)	)	PUNCT
ejde-515	282	24	for	for	ADP
ejde-515	282	25	t	t	PROPN
ejde-515	282	26	∈	∈	PROPN
ejde-515	282	27	[	[	X
ejde-515	282	28	τ	τ	X
ejde-515	282	29	,	,	PUNCT
ejde-515	282	30	l	l	NOUN
ejde-515	282	31	]	]	X
ejde-515	282	32	,	,	PUNCT
ejde-515	282	33	given	give	VERB
ejde-515	282	34	by	by	ADP
ejde-515	282	35	(	(	PUNCT
ejde-515	282	36	2.12	2.12	NUM
ejde-515	282	37	)	)	PUNCT
ejde-515	282	38	.	.	PUNCT
ejde-515	283	1	then	then	ADV
ejde-515	283	2	,	,	PUNCT
ejde-515	283	3	for	for	ADP
ejde-515	283	4	x	x	PROPN
ejde-515	283	5	∈	∈	PROPN
ejde-515	283	6	ω	ω	PROPN
ejde-515	283	7	,	,	PUNCT
ejde-515	283	8	and	and	CCONJ
ejde-515	283	9	us(t	us(t	NOUN
ejde-515	283	10	,	,	PUNCT
ejde-515	283	11	x)−	x)−	PROPN
ejde-515	283	12	us0	us0	PROPN
ejde-515	283	13	(	(	PUNCT
ejde-515	283	14	t	t	PROPN
ejde-515	283	15	,	,	PUNCT
ejde-515	283	16	x	x	NOUN
ejde-515	283	17	)	)	PUNCT
ejde-515	283	18	=	=	SYM
ejde-515	284	1	∫	∫	PROPN
ejde-515	284	2	t	t	PROPN
ejde-515	284	3	τ	τ	PROPN
ejde-515	284	4	e−(a(t)−a(s))b(s)[k(f(s	e−(a(t)−a(s))b(s)[k(f(s	PROPN
ejde-515	284	5	,	,	PUNCT
ejde-515	284	6	us(s	us(s	X
ejde-515	284	7	,	,	PUNCT
ejde-515	284	8	x))−	x))−	PROPN
ejde-515	284	9	f(s	f(	NOUN
ejde-515	284	10	,	,	PUNCT
ejde-515	284	11	us0	us0	PROPN
ejde-515	284	12	(	(	PUNCT
ejde-515	284	13	s	s	PROPN
ejde-515	284	14	,	,	PUNCT
ejde-515	284	15	x)))]ds	x)))]ds	PUNCT
ejde-515	284	16	+	+	CCONJ
ejde-515	284	17	∫	∫	PROPN
ejde-515	284	18	t	t	PROPN
ejde-515	284	19	τ	τ	PROPN
ejde-515	284	20	e−(a(t)−a(s))[s(s	e−(a(t)−a(s))[s(s	PROPN
ejde-515	284	21	,	,	PUNCT
ejde-515	284	22	x)−	x)−	PROPN
ejde-515	284	23	s0(s	s0(s	PROPN
ejde-515	284	24	,	,	PUNCT
ejde-515	284	25	x)]ds	x)]ds	PUNCT
ejde-515	284	26	thus	thus	ADV
ejde-515	284	27	,	,	PUNCT
ejde-515	284	28	for	for	ADP
ejde-515	284	29	x	x	PROPN
ejde-515	284	30	∈	∈	PROPN
ejde-515	284	31	ω	ω	PROPN
ejde-515	284	32	,	,	PUNCT
ejde-515	284	33	using	use	VERB
ejde-515	284	34	(	(	PUNCT
ejde-515	284	35	2.6	2.6	NUM
ejde-515	284	36	)	)	PUNCT
ejde-515	284	37	,	,	PUNCT
ejde-515	284	38	we	we	PRON
ejde-515	284	39	obtain	obtain	VERB
ejde-515	284	40	‖us(t	‖us(t	PROPN
ejde-515	284	41	,	,	PUNCT
ejde-515	284	42	·	·	PUNCT
ejde-515	284	43	)	)	PUNCT
ejde-515	284	44	−	−	PROPN
ejde-515	285	1	us0	us0	PROPN
ejde-515	285	2	(	(	PUNCT
ejde-515	285	3	t	t	PROPN
ejde-515	285	4	,	,	PUNCT
ejde-515	285	5	·	·	PUNCT
ejde-515	285	6	)	)	PUNCT
ejde-515	285	7	‖lp(ω	‖lp(ω	PUNCT
ejde-515	285	8	)	)	PUNCT
ejde-515	285	9	≤	≤	NUM
ejde-515	286	1	∫	∫	PROPN
ejde-515	286	2	t	t	PROPN
ejde-515	286	3	τ	τ	PROPN
ejde-515	286	4	e−(a(t)−a(s))b0‖j‖p‖f(s	e−(a(t)−a(s))b0‖j‖p‖f(s	PROPN
ejde-515	286	5	,	,	PUNCT
ejde-515	286	6	us(s	us(s	X
ejde-515	286	7	,	,	PUNCT
ejde-515	286	8	·	·	PUNCT
ejde-515	286	9	)	)	PUNCT
ejde-515	286	10	)	)	PUNCT
ejde-515	287	1	−	−	PROPN
ejde-515	288	1	f(s	f(s	PROPN
ejde-515	288	2	,	,	PUNCT
ejde-515	288	3	us0	us0	PROPN
ejde-515	288	4	(	(	PUNCT
ejde-515	288	5	s	s	PROPN
ejde-515	288	6	,	,	PUNCT
ejde-515	288	7	·	·	PUNCT
ejde-515	288	8	)	)	PUNCT
ejde-515	288	9	)	)	PUNCT
ejde-515	288	10	‖l1(ω)ds	‖l1(ω)ds	PROPN
ejde-515	289	1	+	+	CCONJ
ejde-515	290	1	∫	∫	PROPN
ejde-515	290	2	t	t	PROPN
ejde-515	290	3	τ	τ	X
ejde-515	290	4	e−(a(t)−a(s))‖s(s	e−(a(t)−a(s))‖s(s	X
ejde-515	290	5	,	,	PUNCT
ejde-515	290	6	·	·	PUNCT
ejde-515	290	7	)	)	PUNCT
ejde-515	290	8	−	−	PROPN
ejde-515	290	9	s0(s	s0(s	PROPN
ejde-515	290	10	,	,	PUNCT
ejde-515	290	11	·	·	PUNCT
ejde-515	290	12	)	)	PUNCT
ejde-515	290	13	‖lp(ω)ds	‖lp(ω)ds	NUM
ejde-515	290	14	.	.	PUNCT
ejde-515	291	1	by	by	ADP
ejde-515	291	2	(	(	PUNCT
ejde-515	291	3	2.9	2.9	NUM
ejde-515	291	4	)	)	PUNCT
ejde-515	291	5	it	it	PRON
ejde-515	291	6	follows	follow	VERB
ejde-515	291	7	that	that	SCONJ
ejde-515	291	8	‖us(t	‖us(t	PROPN
ejde-515	291	9	,	,	PUNCT
ejde-515	291	10	·	·	PUNCT
ejde-515	291	11	)	)	PUNCT
ejde-515	291	12	−	−	PROPN
ejde-515	292	1	us0(t	us0(t	PROPN
ejde-515	292	2	,	,	PUNCT
ejde-515	292	3	·	·	PUNCT
ejde-515	292	4	)	)	PUNCT
ejde-515	292	5	‖lp(ω	‖lp(ω	PUNCT
ejde-515	292	6	)	)	PUNCT
ejde-515	292	7	≤	≤	NUM
ejde-515	292	8	∫	∫	PROPN
ejde-515	292	9	t	t	PROPN
ejde-515	292	10	τ	τ	PROPN
ejde-515	292	11	e−(a(t)−a(s))b0‖j‖pc2(s	e−(a(t)−a(s))b0‖j‖pc2(s	PROPN
ejde-515	292	12	)	)	PUNCT
ejde-515	292	13	[	[	PUNCT
ejde-515	292	14	|ω|1	|ω|1	PROPN
ejde-515	292	15	/	/	SYM
ejde-515	292	16	q	q	NOUN
ejde-515	293	1	+	+	NUM
ejde-515	293	2	‖us(s	‖us(	NOUN
ejde-515	293	3	,	,	PUNCT
ejde-515	293	4	·	·	PUNCT
ejde-515	293	5	)	)	PUNCT
ejde-515	293	6	‖p	‖p	PROPN
ejde-515	293	7	/	/	SYM
ejde-515	293	8	qlp(ω	qlp(ω	PROPN
ejde-515	293	9	)	)	PUNCT
ejde-515	294	1	+	+	CCONJ
ejde-515	294	2	‖us0	‖us0	PROPN
ejde-515	294	3	(	(	PUNCT
ejde-515	294	4	s	s	PROPN
ejde-515	294	5	,	,	PUNCT
ejde-515	294	6	·	·	PUNCT
ejde-515	294	7	)	)	PUNCT
ejde-515	294	8	‖p	‖p	PROPN
ejde-515	294	9	/	/	SYM
ejde-515	294	10	qlp(ω	qlp(ω	NOUN
ejde-515	294	11	)	)	PUNCT
ejde-515	294	12	]	]	PUNCT
ejde-515	294	13	‖us(s	‖us(s	X
ejde-515	294	14	,	,	PUNCT
ejde-515	294	15	·	·	PUNCT
ejde-515	294	16	)	)	PUNCT
ejde-515	294	17	−	−	PROPN
ejde-515	295	1	us0	us0	PROPN
ejde-515	295	2	(	(	PUNCT
ejde-515	295	3	s	s	PROPN
ejde-515	295	4	,	,	PUNCT
ejde-515	295	5	·	·	PUNCT
ejde-515	295	6	)	)	PUNCT
ejde-515	295	7	‖lp(ω)ds	‖lp(ω)ds	PUNCT
ejde-515	296	1	+	+	CCONJ
ejde-515	296	2	∫	∫	PROPN
ejde-515	296	3	t	t	PROPN
ejde-515	296	4	τ	τ	PROPN
ejde-515	296	5	e−(a(t)−a(s	e−(a(t)−a(s	PROPN
ejde-515	296	6	)	)	PUNCT
ejde-515	296	7	)	)	PUNCT
ejde-515	297	1	sup	sup	PROPN
ejde-515	297	2	s∈r	s∈r	NOUN
ejde-515	297	3	‖s(s	‖s(s	PROPN
ejde-515	297	4	,	,	PUNCT
ejde-515	297	5	·	·	PUNCT
ejde-515	297	6	)	)	PUNCT
ejde-515	297	7	−	−	PROPN
ejde-515	298	1	s0(s	s0(s	PROPN
ejde-515	298	2	,	,	PUNCT
ejde-515	298	3	·	·	PUNCT
ejde-515	298	4	)	)	PUNCT
ejde-515	298	5	‖lp(ω)ds	‖lp(ω)ds	PUNCT
ejde-515	298	6	.	.	PUNCT
ejde-515	299	1	let	let	VERB
ejde-515	299	2	b	b	PROPN
ejde-515	299	3	⊂	⊂	PROPN
ejde-515	299	4	xp	xp	PROPN
ejde-515	299	5	be	be	AUX
ejde-515	299	6	a	a	DET
ejde-515	299	7	bounded	bounded	ADJ
ejde-515	299	8	subset	subset	NOUN
ejde-515	299	9	(	(	PUNCT
ejde-515	299	10	for	for	ADP
ejde-515	299	11	example	example	NOUN
ejde-515	299	12	a	a	DET
ejde-515	299	13	ball	ball	NOUN
ejde-515	299	14	of	of	ADP
ejde-515	299	15	radius	radius	PROPN
ejde-515	299	16	ρ	ρ	PROPN
ejde-515	299	17	)	)	PUNCT
ejde-515	300	1	such	such	ADJ
ejde-515	300	2	that	that	DET
ejde-515	300	3	us(t	us(t	NOUN
ejde-515	300	4	,	,	PUNCT
ejde-515	300	5	·	·	PUNCT
ejde-515	300	6	)	)	PUNCT
ejde-515	300	7	∈	∈	PROPN
ejde-515	300	8	b	b	PROPN
ejde-515	300	9	for	for	ADP
ejde-515	300	10	all	all	DET
ejde-515	300	11	s	s	PART
ejde-515	300	12	∈	∈	PROPN
ejde-515	300	13	σ	σ	NOUN
ejde-515	300	14	and	and	CCONJ
ejde-515	300	15	t	t	PROPN
ejde-515	300	16	∈	∈	PROPN
ejde-515	301	1	[	[	X
ejde-515	301	2	τ	τ	X
ejde-515	301	3	,	,	PUNCT
ejde-515	301	4	l	l	NOUN
ejde-515	301	5	]	]	PUNCT
ejde-515	301	6	.	.	PUNCT
ejde-515	302	1	then	then	ADV
ejde-515	302	2	ea(t)‖us(t	ea(t)‖us(t	PROPN
ejde-515	302	3	,	,	PUNCT
ejde-515	302	4	·	·	PUNCT
ejde-515	302	5	)	)	PUNCT
ejde-515	302	6	−	−	PROPN
ejde-515	303	1	us0	us0	PROPN
ejde-515	303	2	(	(	PUNCT
ejde-515	303	3	t	t	PROPN
ejde-515	303	4	,	,	PUNCT
ejde-515	303	5	·	·	PUNCT
ejde-515	303	6	)	)	PUNCT
ejde-515	303	7	‖lp(ω	‖lp(ω	PUNCT
ejde-515	303	8	)	)	PUNCT
ejde-515	303	9	≤	≤	NUM
ejde-515	303	10	∫	∫	PROPN
ejde-515	303	11	t	t	PROPN
ejde-515	303	12	τ	τ	PROPN
ejde-515	303	13	b0‖j‖pc2(s	b0‖j‖pc2(s	PROPN
ejde-515	303	14	)	)	PUNCT
ejde-515	303	15	[	[	PUNCT
ejde-515	303	16	|ω|1	|ω|1	PROPN
ejde-515	303	17	/	/	SYM
ejde-515	303	18	q	q	NOUN
ejde-515	303	19	+	+	NOUN
ejde-515	303	20	2ρp	2ρp	ADJ
ejde-515	303	21	/	/	SYM
ejde-515	303	22	q	q	NOUN
ejde-515	303	23	]	]	X
ejde-515	303	24	ea(s)‖us(s	ea(s)‖us(s	NOUN
ejde-515	303	25	,	,	PUNCT
ejde-515	303	26	·	·	PUNCT
ejde-515	303	27	)	)	PUNCT
ejde-515	303	28	−	−	PROPN
ejde-515	303	29	us0	us0	PROPN
ejde-515	303	30	(	(	PUNCT
ejde-515	303	31	s	s	PROPN
ejde-515	303	32	,	,	PUNCT
ejde-515	303	33	·	·	PUNCT
ejde-515	303	34	)	)	PUNCT
ejde-515	303	35	‖lp(ω)ds	‖lp(ω)ds	PUNCT
ejde-515	304	1	+	+	CCONJ
ejde-515	304	2	∫	∫	PROPN
ejde-515	304	3	t	t	PROPN
ejde-515	304	4	τ	τ	PROPN
ejde-515	304	5	ea(s)‖s	ea(s)‖s	ADV
ejde-515	304	6	−	−	PROPN
ejde-515	304	7	s0‖pds	s0‖pds	PROPN
ejde-515	304	8	.	.	PUNCT
ejde-515	304	9	using	use	VERB
ejde-515	304	10	the	the	DET
ejde-515	304	11	gronwall	gronwall	ADJ
ejde-515	304	12	generalized	generalized	ADJ
ejde-515	304	13	inequality	inequality	NOUN
ejde-515	304	14	[	[	X
ejde-515	304	15	19	19	NUM
ejde-515	304	16	]	]	PUNCT
ejde-515	304	17	,	,	PUNCT
ejde-515	304	18	we	we	PRON
ejde-515	304	19	obtain	obtain	VERB
ejde-515	304	20	ea(t)‖us(t	ea(t)‖us(t	NOUN
ejde-515	304	21	,	,	PUNCT
ejde-515	304	22	·	·	PUNCT
ejde-515	304	23	)	)	PUNCT
ejde-515	304	24	−us0(t	−us0(t	PROPN
ejde-515	304	25	,	,	PUNCT
ejde-515	304	26	·	·	PUNCT
ejde-515	304	27	)	)	PUNCT
ejde-515	304	28	‖lp(ω	‖lp(ω	SYM
ejde-515	304	29	)	)	PUNCT
ejde-515	304	30	≤	≤	NOUN
ejde-515	304	31	(	(	PUNCT
ejde-515	304	32	∫	∫	PROPN
ejde-515	304	33	t	t	PROPN
ejde-515	304	34	τ	τ	PROPN
ejde-515	304	35	ea(s)‖s−s0‖pds	ea(s)‖s−s0‖pds	PROPN
ejde-515	304	36	)	)	PUNCT
ejde-515	305	1	e	e	PROPN
ejde-515	305	2	∫	∫	PROPN
ejde-515	305	3	t	t	PROPN
ejde-515	305	4	τ	τ	PROPN
ejde-515	305	5	b0‖j‖pc2(s)[|ω|1	b0‖j‖pc2(s)[|ω|1	PROPN
ejde-515	305	6	/	/	SYM
ejde-515	305	7	q+2ρp	q+2ρp	PROPN
ejde-515	305	8	/	/	SYM
ejde-515	305	9	q	q	NOUN
ejde-515	305	10	]	]	X
ejde-515	305	11	ds	ds	X
ejde-515	305	12	.	.	NOUN
ejde-515	305	13	hence	hence	ADV
ejde-515	305	14	,	,	PUNCT
ejde-515	305	15	for	for	ADP
ejde-515	305	16	t	t	PROPN
ejde-515	305	17	∈	∈	PROPN
ejde-515	306	1	[	[	X
ejde-515	306	2	τ	τ	X
ejde-515	306	3	,	,	PUNCT
ejde-515	306	4	l	l	NOUN
ejde-515	306	5	]	]	X
ejde-515	306	6	,	,	PUNCT
ejde-515	306	7	it	it	PRON
ejde-515	306	8	follows	follow	VERB
ejde-515	306	9	that	that	SCONJ
ejde-515	306	10	‖us(t	‖us(t	PROPN
ejde-515	306	11	,	,	PUNCT
ejde-515	306	12	·	·	PUNCT
ejde-515	306	13	)	)	PUNCT
ejde-515	306	14	−	−	PROPN
ejde-515	307	1	us0(t	us0(t	PROPN
ejde-515	307	2	,	,	PUNCT
ejde-515	307	3	·	·	PUNCT
ejde-515	307	4	)	)	PUNCT
ejde-515	307	5	‖lp(ω	‖lp(ω	SYM
ejde-515	307	6	)	)	PUNCT
ejde-515	307	7	≤	≤	NOUN
ejde-515	307	8	(	(	PUNCT
ejde-515	307	9	∫	∫	PROPN
ejde-515	307	10	t	t	PROPN
ejde-515	307	11	τ	τ	PROPN
ejde-515	307	12	e−(a(t)−a(s))‖s	e−(a(t)−a(s))‖s	PROPN
ejde-515	307	13	−	−	PROPN
ejde-515	307	14	s0‖pds	s0‖pds	PROPN
ejde-515	307	15	)	)	PUNCT
ejde-515	307	16	e	e	PROPN
ejde-515	307	17	∫	∫	PROPN
ejde-515	307	18	t	t	PROPN
ejde-515	307	19	τ	τ	PROPN
ejde-515	307	20	b0‖j‖pc2(s)[|ω|1	b0‖j‖pc2(s)[|ω|1	PROPN
ejde-515	307	21	/	/	SYM
ejde-515	307	22	q+2ρp	q+2ρp	PROPN
ejde-515	307	23	/	/	SYM
ejde-515	307	24	q]ds	q]ds	PROPN
ejde-515	307	25	≤	≤	PROPN
ejde-515	307	26	e(a0−a−)t	e(a0−a−)t	PUNCT
ejde-515	308	1	a0	a0	PROPN
ejde-515	308	2	e	e	PROPN
ejde-515	308	3	∫	∫	PROPN
ejde-515	308	4	t	t	PROPN
ejde-515	308	5	τ	τ	PROPN
ejde-515	308	6	b0‖j‖pc2(s)[|ω|1	b0‖j‖pc2(s)[|ω|1	PROPN
ejde-515	308	7	/	/	SYM
ejde-515	308	8	q+2ρp	q+2ρp	PROPN
ejde-515	308	9	/	/	SYM
ejde-515	308	10	q]ds‖s	q]ds‖s	ADJ
ejde-515	308	11	−	−	PROPN
ejde-515	308	12	s0‖p	s0‖p	PROPN
ejde-515	308	13	.	.	PUNCT
ejde-515	309	1	the	the	DET
ejde-515	309	2	result	result	NOUN
ejde-515	309	3	follows	follow	VERB
ejde-515	309	4	.	.	PUNCT
ejde-515	310	1	�	�	PROPN
ejde-515	310	2	14	14	NUM
ejde-515	310	3	s.	s.	PROPN
ejde-515	310	4	h.	h.	PROPN
ejde-515	310	5	da	da	PROPN
ejde-515	310	6	silva	silva	PROPN
ejde-515	310	7	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	310	8	4.2	4.2	NUM
ejde-515	310	9	.	.	PUNCT
ejde-515	311	1	upper	upper	ADJ
ejde-515	311	2	semicontinuity	semicontinuity	NOUN
ejde-515	311	3	of	of	ADP
ejde-515	311	4	the	the	DET
ejde-515	311	5	pullback	pullback	NOUN
ejde-515	311	6	attractors	attractor	NOUN
ejde-515	311	7	.	.	PUNCT
ejde-515	312	1	in	in	ADP
ejde-515	312	2	this	this	DET
ejde-515	312	3	subsection	subsection	NOUN
ejde-515	312	4	{	{	PUNCT
ejde-515	312	5	as(t	as(t	ADJ
ejde-515	312	6	)	)	PUNCT
ejde-515	312	7	;	;	PUNCT
ejde-515	312	8	t	t	PROPN
ejde-515	312	9	∈	∈	PROPN
ejde-515	312	10	r	r	NOUN
ejde-515	312	11	}	}	PUNCT
ejde-515	312	12	denotes	denote	VERB
ejde-515	312	13	the	the	DET
ejde-515	312	14	pullback	pullback	NOUN
ejde-515	312	15	attractor	attractor	NOUN
ejde-515	312	16	for	for	ADP
ejde-515	312	17	the	the	DET
ejde-515	312	18	process	process	NOUN
ejde-515	312	19	ts	ts	NOUN
ejde-515	312	20	(	(	PUNCT
ejde-515	312	21	·	·	PUNCT
ejde-515	312	22	,	,	PUNCT
ejde-515	312	23	·	·	PUNCT
ejde-515	312	24	)	)	PUNCT
ejde-515	312	25	in	in	ADP
ejde-515	312	26	xp	xp	PROPN
ejde-515	312	27	,	,	PUNCT
ejde-515	312	28	for	for	ADP
ejde-515	312	29	1	1	NUM
ejde-515	312	30	≤	≤	NOUN
ejde-515	312	31	p	p	NOUN
ejde-515	312	32	<	<	X
ejde-515	312	33	∞.	∞.	PROPN
ejde-515	312	34	using	use	VERB
ejde-515	312	35	theorem	theorem	NOUN
ejde-515	312	36	4.1	4.1	NUM
ejde-515	312	37	,	,	PUNCT
ejde-515	312	38	we	we	PRON
ejde-515	312	39	prove	prove	VERB
ejde-515	312	40	that	that	SCONJ
ejde-515	312	41	the	the	DET
ejde-515	312	42	family	family	NOUN
ejde-515	312	43	of	of	ADP
ejde-515	312	44	pullback	pullback	NOUN
ejde-515	312	45	attractors	attractor	NOUN
ejde-515	312	46	{	{	PUNCT
ejde-515	312	47	as(t	as(t	ADJ
ejde-515	312	48	)	)	PUNCT
ejde-515	312	49	;	;	PUNCT
ejde-515	312	50	t	t	PROPN
ejde-515	312	51	∈	∈	PROPN
ejde-515	312	52	r}s∈σ	r}s∈σ	NOUN
ejde-515	312	53	is	be	AUX
ejde-515	312	54	upper	upper	ADJ
ejde-515	312	55	-	-	PUNCT
ejde-515	312	56	semicontinuous	semicontinuous	ADJ
ejde-515	312	57	at	at	ADP
ejde-515	312	58	s0	s0	PROPN
ejde-515	312	59	∈	∈	PROPN
ejde-515	312	60	σ	σ	PROPN
ejde-515	312	61	,	,	PUNCT
ejde-515	312	62	i.e.	i.e.	X
ejde-515	312	63	,	,	PUNCT
ejde-515	312	64	we	we	PRON
ejde-515	312	65	show	show	VERB
ejde-515	312	66	that	that	SCONJ
ejde-515	312	67	lim	lim	PROPN
ejde-515	312	68	t→∞	t→∞	X
ejde-515	312	69	disth(as(t),as0(t	disth(as(t),as0(t	PROPN
ejde-515	312	70	)	)	PUNCT
ejde-515	312	71	)	)	PUNCT
ejde-515	313	1	=	=	SYM
ejde-515	313	2	0	0	NUM
ejde-515	313	3	,	,	PUNCT
ejde-515	313	4	where	where	SCONJ
ejde-515	313	5	disth	disth	PROPN
ejde-515	313	6	(	(	PUNCT
ejde-515	313	7	·	·	PUNCT
ejde-515	313	8	,	,	PUNCT
ejde-515	313	9	·	·	PUNCT
ejde-515	313	10	)	)	PUNCT
ejde-515	313	11	denotes	denote	VERB
ejde-515	313	12	the	the	DET
ejde-515	313	13	hausdorff	hausdorff	NOUN
ejde-515	313	14	semi	semi	NOUN
ejde-515	313	15	-	-	NOUN
ejde-515	313	16	distance	distance	NOUN
ejde-515	313	17	.	.	PUNCT
ejde-515	314	1	theorem	theorem	VERB
ejde-515	314	2	4.2	4.2	NUM
ejde-515	314	3	.	.	PUNCT
ejde-515	315	1	under	under	ADP
ejde-515	315	2	the	the	DET
ejde-515	315	3	hypotheses	hypothesis	NOUN
ejde-515	315	4	of	of	ADP
ejde-515	315	5	theorem	theorem	NOUN
ejde-515	315	6	4.1	4.1	NUM
ejde-515	315	7	the	the	DET
ejde-515	315	8	family	family	NOUN
ejde-515	315	9	of	of	ADP
ejde-515	315	10	pullback	pullback	NOUN
ejde-515	315	11	attractors	attractor	NOUN
ejde-515	315	12	{	{	PUNCT
ejde-515	315	13	as(t	as(t	ADJ
ejde-515	315	14	)	)	PUNCT
ejde-515	315	15	;	;	PUNCT
ejde-515	315	16	t	t	PROPN
ejde-515	315	17	∈	∈	PROPN
ejde-515	315	18	r}s∈σ	r}s∈σ	PRON
ejde-515	315	19	is	be	AUX
ejde-515	315	20	upper	upper	ADJ
ejde-515	315	21	semicontinuous	semicontinuous	NOUN
ejde-515	315	22	at	at	ADP
ejde-515	315	23	s0	s0	PROPN
ejde-515	315	24	∈	∈	PROPN
ejde-515	315	25	σ	σ	PROPN
ejde-515	315	26	.	.	PUNCT
ejde-515	315	27	proof	proof	NOUN
ejde-515	315	28	.	.	PUNCT
ejde-515	316	1	note	note	VERB
ejde-515	316	2	that	that	SCONJ
ejde-515	316	3	,	,	PUNCT
ejde-515	316	4	from	from	ADP
ejde-515	316	5	theorem	theorem	ADJ
ejde-515	316	6	3.2	3.2	NUM
ejde-515	316	7	,	,	PUNCT
ejde-515	316	8	it	it	PRON
ejde-515	316	9	follows	follow	VERB
ejde-515	316	10	that	that	SCONJ
ejde-515	316	11	∪s∈σas(t	∪s∈σas(t	NOUN
ejde-515	316	12	)	)	PUNCT
ejde-515	317	1	⊂	⊂	PROPN
ejde-515	317	2	b(0	b(0	NOUN
ejde-515	317	3	,	,	PUNCT
ejde-515	317	4	r	r	NOUN
ejde-515	317	5	)	)	PUNCT
ejde-515	317	6	,	,	PUNCT
ejde-515	317	7	where	where	SCONJ
ejde-515	317	8	r	r	NOUN
ejde-515	317	9	=	=	SYM
ejde-515	317	10	r(t	r(t	NOUN
ejde-515	317	11	)	)	PUNCT
ejde-515	317	12	=	=	SYM
ejde-515	317	13	1	1	NUM
ejde-515	317	14	a−−k1b0	a−−k1b0	VERB
ejde-515	317	15	[	[	X
ejde-515	317	16	b0k2(t)|ω|1	b0k2(t)|ω|1	NOUN
ejde-515	317	17	/	/	SYM
ejde-515	317	18	p	p	NOUN
ejde-515	317	19	+	+	X
ejde-515	317	20	p‖s‖p	p‖s‖p	ADV
ejde-515	317	21	]	]	PUNCT
ejde-515	317	22	.	.	PUNCT
ejde-515	318	1	let	let	VERB
ejde-515	318	2	us	we	PRON
ejde-515	318	3	fix	fix	VERB
ejde-515	318	4	ε	ε	PROPN
ejde-515	318	5	>	>	PUNCT
ejde-515	318	6	0	0	PUNCT
ejde-515	319	1	and	and	CCONJ
ejde-515	319	2	t	t	PROPN
ejde-515	319	3	∈	∈	PROPN
ejde-515	319	4	r.	r.	PROPN
ejde-515	319	5	thus	thus	ADV
ejde-515	319	6	choose	choose	VERB
ejde-515	319	7	τ	τ	PROPN
ejde-515	319	8	∈	∈	PROPN
ejde-515	319	9	r	r	PROPN
ejde-515	319	10	,	,	PUNCT
ejde-515	319	11	τ	τ	PROPN
ejde-515	319	12	≤	≤	PROPN
ejde-515	319	13	t	t	PROPN
ejde-515	319	14	,	,	PUNCT
ejde-515	319	15	such	such	ADJ
ejde-515	319	16	that	that	SCONJ
ejde-515	319	17	disth(ts0	disth(ts0	PROPN
ejde-515	319	18	(	(	PUNCT
ejde-515	319	19	t	t	PROPN
ejde-515	319	20	,	,	PUNCT
ejde-515	319	21	τ)b(0	τ)b(0	PROPN
ejde-515	319	22	,	,	PUNCT
ejde-515	319	23	r),as0	r),as0	NUM
ejde-515	319	24	(	(	PUNCT
ejde-515	319	25	t	t	PROPN
ejde-515	319	26	)	)	PUNCT
ejde-515	319	27	)	)	PUNCT
ejde-515	320	1	<	<	X
ejde-515	320	2	ε	ε	PROPN
ejde-515	320	3	2	2	NUM
ejde-515	320	4	.	.	PUNCT
ejde-515	321	1	now	now	ADV
ejde-515	321	2	,	,	PUNCT
ejde-515	321	3	by	by	ADP
ejde-515	321	4	theorem	theorem	NOUN
ejde-515	321	5	4.1	4.1	NUM
ejde-515	321	6	,	,	PUNCT
ejde-515	321	7	it	it	PRON
ejde-515	321	8	follows	follow	VERB
ejde-515	321	9	that	that	SCONJ
ejde-515	321	10	there	there	PRON
ejde-515	321	11	exists	exist	VERB
ejde-515	321	12	δ	δ	PROPN
ejde-515	321	13	>	>	X
ejde-515	321	14	0	0	NUM
ejde-515	321	15	such	such	ADJ
ejde-515	321	16	that	that	SCONJ
ejde-515	321	17	,	,	PUNCT
ejde-515	321	18	for	for	ADP
ejde-515	321	19	‖s−s0‖p	‖s−s0‖p	ADJ
ejde-515	321	20	<	<	X
ejde-515	321	21	δ	δ	PROPN
ejde-515	321	22	,	,	PUNCT
ejde-515	321	23	we	we	PRON
ejde-515	321	24	have	have	VERB
ejde-515	321	25	sup	sup	NOUN
ejde-515	321	26	as∈as(τ	as∈as(τ	NUM
ejde-515	321	27	)	)	PUNCT
ejde-515	321	28	dist(ts(t	dist(ts(t	NOUN
ejde-515	321	29	,	,	PUNCT
ejde-515	321	30	τ)as	τ)as	PROPN
ejde-515	321	31	,	,	PUNCT
ejde-515	321	32	ts0	ts0	PROPN
ejde-515	321	33	(	(	PUNCT
ejde-515	321	34	t	t	PROPN
ejde-515	321	35	,	,	PUNCT
ejde-515	321	36	τ)as	τ)as	PROPN
ejde-515	321	37	)	)	PUNCT
ejde-515	321	38	<	<	X
ejde-515	321	39	ε	ε	PROPN
ejde-515	321	40	2	2	NUM
ejde-515	321	41	.	.	PUNCT
ejde-515	322	1	then	then	ADV
ejde-515	322	2	,	,	PUNCT
ejde-515	322	3	for	for	ADP
ejde-515	322	4	‖s−s0‖p	‖s−s0‖p	ADJ
ejde-515	322	5	<	<	X
ejde-515	322	6	δ	δ	PROPN
ejde-515	322	7	,	,	PUNCT
ejde-515	322	8	using	use	VERB
ejde-515	322	9	the	the	DET
ejde-515	322	10	invariance	invariance	NOUN
ejde-515	322	11	of	of	ADP
ejde-515	322	12	the	the	DET
ejde-515	322	13	pullback	pullback	NOUN
ejde-515	322	14	attractors	attractor	NOUN
ejde-515	322	15	,	,	PUNCT
ejde-515	322	16	we	we	PRON
ejde-515	322	17	obtain	obtain	VERB
ejde-515	322	18	disth(as(t),as0	disth(as(t),as0	PROPN
ejde-515	322	19	(	(	PUNCT
ejde-515	322	20	t	t	NOUN
ejde-515	322	21	)	)	PUNCT
ejde-515	322	22	)	)	PUNCT
ejde-515	322	23	≤	≤	NUM
ejde-515	322	24	disth(ts(t	disth(ts(t	VERB
ejde-515	322	25	,	,	PUNCT
ejde-515	322	26	τ)as(τ	τ)as(τ	NOUN
ejde-515	322	27	)	)	PUNCT
ejde-515	322	28	,	,	PUNCT
ejde-515	322	29	ts0(t	ts0(t	PROPN
ejde-515	322	30	,	,	PUNCT
ejde-515	322	31	τ)as(τ	τ)as(τ	NOUN
ejde-515	322	32	)	)	PUNCT
ejde-515	322	33	)	)	PUNCT
ejde-515	323	1	+	+	CCONJ
ejde-515	323	2	disth(ts0(t	disth(ts0(t	PROPN
ejde-515	323	3	,	,	PUNCT
ejde-515	323	4	τ)as(τ	τ)as(τ	NOUN
ejde-515	323	5	)	)	PUNCT
ejde-515	323	6	,	,	PUNCT
ejde-515	323	7	ts0(t	ts0(t	PROPN
ejde-515	323	8	,	,	PUNCT
ejde-515	323	9	τ)as0(τ	τ)as0(τ	PROPN
ejde-515	323	10	)	)	PUNCT
ejde-515	323	11	)	)	PUNCT
ejde-515	324	1	=	=	SYM
ejde-515	324	2	sup	sup	NOUN
ejde-515	324	3	as∈as(τ	as∈as(τ	NUM
ejde-515	324	4	)	)	PUNCT
ejde-515	324	5	disth(ts(t	disth(ts(t	NOUN
ejde-515	324	6	,	,	PUNCT
ejde-515	324	7	τ)as	τ)as	PROPN
ejde-515	324	8	,	,	PUNCT
ejde-515	324	9	ts0	ts0	PROPN
ejde-515	324	10	(	(	PUNCT
ejde-515	324	11	t	t	PROPN
ejde-515	324	12	,	,	PUNCT
ejde-515	324	13	τ)as	τ)as	PROPN
ejde-515	324	14	)	)	PUNCT
ejde-515	324	15	+	+	CCONJ
ejde-515	324	16	disth(ts0	disth(ts0	PROPN
ejde-515	324	17	(	(	PUNCT
ejde-515	324	18	t	t	PROPN
ejde-515	324	19	,	,	PUNCT
ejde-515	324	20	τ)as(τ),as0	τ)as(τ),as0	PROPN
ejde-515	324	21	(	(	PUNCT
ejde-515	324	22	t	t	PROPN
ejde-515	324	23	)	)	PUNCT
ejde-515	324	24	)	)	PUNCT
ejde-515	324	25	<	<	X
ejde-515	324	26	ε	ε	PROPN
ejde-515	324	27	2	2	NUM
ejde-515	324	28	+	+	CCONJ
ejde-515	324	29	ε	ε	PROPN
ejde-515	324	30	2	2	NUM
ejde-515	324	31	=	=	SYM
ejde-515	324	32	ε	ε	PROPN
ejde-515	324	33	.	.	PUNCT
ejde-515	324	34	�	�	PROPN
ejde-515	324	35	5	5	NUM
ejde-515	324	36	.	.	PUNCT
ejde-515	324	37	discussions	discussion	NOUN
ejde-515	324	38	and	and	CCONJ
ejde-515	324	39	biological	biological	ADJ
ejde-515	324	40	interpretation	interpretation	NOUN
ejde-515	324	41	as	as	SCONJ
ejde-515	324	42	we	we	PRON
ejde-515	324	43	saw	see	VERB
ejde-515	324	44	in	in	ADP
ejde-515	324	45	the	the	DET
ejde-515	324	46	introduction	introduction	NOUN
ejde-515	324	47	,	,	PUNCT
ejde-515	324	48	equation	equation	NOUN
ejde-515	324	49	(	(	PUNCT
ejde-515	324	50	1.1	1.1	NUM
ejde-515	324	51	)	)	PUNCT
ejde-515	324	52	generalizes	generalize	VERB
ejde-515	324	53	the	the	DET
ejde-515	324	54	model	model	NOUN
ejde-515	324	55	studied	study	VERB
ejde-515	324	56	in	in	ADP
ejde-515	324	57	[	[	X
ejde-515	324	58	1	1	NUM
ejde-515	324	59	]	]	PUNCT
ejde-515	324	60	,	,	PUNCT
ejde-515	324	61	which	which	PRON
ejde-515	324	62	is	be	AUX
ejde-515	324	63	already	already	ADV
ejde-515	324	64	well	well	ADV
ejde-515	324	65	known	know	VERB
ejde-515	324	66	in	in	ADP
ejde-515	324	67	the	the	DET
ejde-515	324	68	literature	literature	NOUN
ejde-515	324	69	,	,	PUNCT
ejde-515	324	70	because	because	SCONJ
ejde-515	324	71	we	we	PRON
ejde-515	324	72	consider	consider	VERB
ejde-515	324	73	that	that	SCONJ
ejde-515	324	74	the	the	DET
ejde-515	324	75	rate	rate	NOUN
ejde-515	324	76	in	in	ADP
ejde-515	324	77	the	the	DET
ejde-515	324	78	intensity	intensity	NOUN
ejde-515	324	79	of	of	ADP
ejde-515	324	80	neuronal	neuronal	ADJ
ejde-515	324	81	potential	potential	NOUN
ejde-515	324	82	is	be	AUX
ejde-515	324	83	explicitly	explicitly	ADV
ejde-515	324	84	time	time	NOUN
ejde-515	324	85	dependent	dependent	ADJ
ejde-515	324	86	,	,	PUNCT
ejde-515	324	87	while	while	SCONJ
ejde-515	324	88	in	in	ADP
ejde-515	324	89	[	[	PUNCT
ejde-515	324	90	1	1	X
ejde-515	324	91	]	]	PUNCT
ejde-515	324	92	this	this	DET
ejde-515	324	93	rate	rate	NOUN
ejde-515	324	94	was	be	AUX
ejde-515	324	95	considered	consider	VERB
ejde-515	324	96	constant	constant	ADJ
ejde-515	324	97	.	.	PUNCT
ejde-515	325	1	we	we	PRON
ejde-515	325	2	expect	expect	VERB
ejde-515	325	3	to	to	PART
ejde-515	325	4	have	have	VERB
ejde-515	325	5	a	a	DET
ejde-515	325	6	more	more	ADV
ejde-515	325	7	realistic	realistic	ADJ
ejde-515	325	8	model	model	NOUN
ejde-515	325	9	when	when	SCONJ
ejde-515	325	10	compared	compare	VERB
ejde-515	325	11	to	to	ADP
ejde-515	325	12	what	what	PRON
ejde-515	325	13	happens	happen	VERB
ejde-515	325	14	in	in	ADP
ejde-515	325	15	the	the	DET
ejde-515	325	16	brain	brain	NOUN
ejde-515	325	17	,	,	PUNCT
ejde-515	325	18	since	since	SCONJ
ejde-515	325	19	this	this	DET
ejde-515	325	20	behavior	behavior	NOUN
ejde-515	325	21	is	be	AUX
ejde-515	325	22	due	due	ADJ
ejde-515	325	23	to	to	ADP
ejde-515	325	24	variations	variation	NOUN
ejde-515	325	25	of	of	ADP
ejde-515	325	26	polarity	polarity	NOUN
ejde-515	325	27	inside	inside	ADP
ejde-515	325	28	the	the	DET
ejde-515	325	29	membrane	membrane	NOUN
ejde-515	325	30	,	,	PUNCT
ejde-515	325	31	which	which	PRON
ejde-515	325	32	is	be	AUX
ejde-515	325	33	not	not	PART
ejde-515	325	34	necessarily	necessarily	ADV
ejde-515	325	35	constant	constant	ADJ
ejde-515	325	36	.	.	PUNCT
ejde-515	326	1	furthermore	furthermore	ADV
ejde-515	326	2	,	,	PUNCT
ejde-515	326	3	in	in	ADP
ejde-515	326	4	proposition	proposition	NOUN
ejde-515	326	5	2.6	2.6	NUM
ejde-515	326	6	and	and	CCONJ
ejde-515	326	7	corollary	corollary	ADJ
ejde-515	326	8	2.8	2.8	NUM
ejde-515	326	9	,	,	PUNCT
ejde-515	326	10	we	we	PRON
ejde-515	326	11	are	be	AUX
ejde-515	326	12	not	not	PART
ejde-515	326	13	considering	consider	VERB
ejde-515	326	14	that	that	SCONJ
ejde-515	326	15	the	the	DET
ejde-515	326	16	synaptic	synaptic	ADJ
ejde-515	326	17	connectivity	connectivity	NOUN
ejde-515	326	18	function	function	NOUN
ejde-515	326	19	j(x	j(x	PROPN
ejde-515	326	20	,	,	PUNCT
ejde-515	326	21	y	y	NOUN
ejde-515	326	22	)	)	PUNCT
ejde-515	326	23	is	be	AUX
ejde-515	326	24	smooth	smooth	ADJ
ejde-515	326	25	,	,	PUNCT
ejde-515	326	26	as	as	SCONJ
ejde-515	326	27	occurs	occur	VERB
ejde-515	326	28	for	for	ADP
ejde-515	326	29	example	example	NOUN
ejde-515	326	30	in	in	ADP
ejde-515	326	31	[	[	X
ejde-515	326	32	1	1	NUM
ejde-515	326	33	,	,	PUNCT
ejde-515	326	34	2	2	NUM
ejde-515	326	35	,	,	PUNCT
ejde-515	326	36	5	5	NUM
ejde-515	326	37	,	,	PUNCT
ejde-515	326	38	13	13	NUM
ejde-515	326	39	]	]	PUNCT
ejde-515	326	40	.	.	PUNCT
ejde-515	327	1	for	for	ADP
ejde-515	327	2	these	these	DET
ejde-515	327	3	results	result	NOUN
ejde-515	327	4	,	,	PUNCT
ejde-515	327	5	we	we	PRON
ejde-515	327	6	assume	assume	VERB
ejde-515	327	7	j	j	PROPN
ejde-515	327	8	∈	∈	PROPN
ejde-515	327	9	l1(rn	l1(rn	PROPN
ejde-515	327	10	)	)	PUNCT
ejde-515	327	11	,	,	PUNCT
ejde-515	327	12	leaving	leave	VERB
ejde-515	327	13	the	the	DET
ejde-515	327	14	model	model	NOUN
ejde-515	327	15	closer	close	ADV
ejde-515	327	16	to	to	ADP
ejde-515	327	17	real	real	ADJ
ejde-515	327	18	situation	situation	NOUN
ejde-515	327	19	of	of	ADP
ejde-515	327	20	mild	mild	ADJ
ejde-515	327	21	autism	autism	NOUN
ejde-515	327	22	,	,	PUNCT
ejde-515	327	23	where	where	SCONJ
ejde-515	327	24	simple	simple	ADJ
ejde-515	327	25	breaks	break	NOUN
ejde-515	327	26	in	in	ADP
ejde-515	327	27	the	the	DET
ejde-515	327	28	synaptic	synaptic	ADJ
ejde-515	327	29	connections	connection	NOUN
ejde-515	327	30	occurs	occur	VERB
ejde-515	327	31	.	.	PUNCT
ejde-515	328	1	thus	thus	ADV
ejde-515	328	2	,	,	PUNCT
ejde-515	328	3	we	we	PRON
ejde-515	328	4	hope	hope	VERB
ejde-515	328	5	that	that	SCONJ
ejde-515	328	6	the	the	DET
ejde-515	328	7	results	result	NOUN
ejde-515	328	8	on	on	ADP
ejde-515	328	9	global	global	ADJ
ejde-515	328	10	existence	existence	NOUN
ejde-515	328	11	and	and	CCONJ
ejde-515	328	12	smoothness	smoothness	NOUN
ejde-515	328	13	of	of	ADP
ejde-515	328	14	solutions	solution	NOUN
ejde-515	328	15	,	,	PUNCT
ejde-515	328	16	given	give	VERB
ejde-515	328	17	in	in	ADP
ejde-515	328	18	proposition	proposition	NOUN
ejde-515	328	19	2.6	2.6	NUM
ejde-515	328	20	and	and	CCONJ
ejde-515	328	21	corollary	corollary	ADJ
ejde-515	328	22	2.8	2.8	NUM
ejde-515	328	23	contribute	contribute	NOUN
ejde-515	328	24	to	to	ADP
ejde-515	328	25	future	future	ADJ
ejde-515	328	26	research	research	NOUN
ejde-515	328	27	.	.	PUNCT
ejde-515	329	1	in	in	ADP
ejde-515	329	2	theorem	theorem	NOUN
ejde-515	329	3	4.1	4.1	NUM
ejde-515	329	4	we	we	PRON
ejde-515	329	5	show	show	VERB
ejde-515	329	6	that	that	SCONJ
ejde-515	329	7	the	the	DET
ejde-515	329	8	neuronal	neuronal	ADJ
ejde-515	329	9	activity	activity	NOUN
ejde-515	329	10	depends	depend	VERB
ejde-515	329	11	continuously	continuously	ADV
ejde-515	329	12	on	on	ADP
ejde-515	329	13	the	the	DET
ejde-515	329	14	sum	sum	NOUN
ejde-515	329	15	of	of	ADP
ejde-515	329	16	the	the	DET
ejde-515	329	17	external	external	ADJ
ejde-515	329	18	stimuli	stimulus	NOUN
ejde-515	329	19	involved	involve	VERB
ejde-515	329	20	in	in	ADP
ejde-515	329	21	the	the	DET
ejde-515	329	22	process	process	NOUN
ejde-515	329	23	.	.	PUNCT
ejde-515	330	1	this	this	PRON
ejde-515	330	2	reinforces	reinforce	VERB
ejde-515	330	3	the	the	DET
ejde-515	330	4	importance	importance	NOUN
ejde-515	330	5	of	of	ADP
ejde-515	330	6	appropriate	appropriate	ADJ
ejde-515	330	7	continuous	continuous	ADJ
ejde-515	330	8	stimulation	stimulation	NOUN
ejde-515	330	9	for	for	ADP
ejde-515	330	10	a	a	DET
ejde-515	330	11	good	good	ADJ
ejde-515	330	12	neural	neural	ADJ
ejde-515	330	13	activity	activity	NOUN
ejde-515	330	14	,	,	PUNCT
ejde-515	330	15	especially	especially	ADV
ejde-515	330	16	in	in	ADP
ejde-515	330	17	individuals	individual	NOUN
ejde-515	330	18	suffering	suffer	VERB
ejde-515	330	19	from	from	ADP
ejde-515	330	20	neurological	neurological	ADJ
ejde-515	330	21	disorder	disorder	NOUN
ejde-515	330	22	,	,	PUNCT
ejde-515	330	23	as	as	SCONJ
ejde-515	330	24	occurs	occur	VERB
ejde-515	330	25	in	in	ADP
ejde-515	330	26	cases	case	NOUN
ejde-515	330	27	of	of	ADP
ejde-515	330	28	cerebral	cerebral	ADJ
ejde-515	330	29	paralysis	paralysis	NOUN
ejde-515	330	30	and	and	CCONJ
ejde-515	330	31	in	in	ADP
ejde-515	330	32	some	some	DET
ejde-515	330	33	cases	case	NOUN
ejde-515	330	34	of	of	ADP
ejde-515	330	35	autism	autism	NOUN
ejde-515	330	36	.	.	PUNCT
ejde-515	331	1	ejde-2020/92	ejde-2020/92	ADJ
ejde-515	331	2	non	non	ADJ
ejde-515	331	3	-	-	ADJ
ejde-515	331	4	autonomous	autonomous	ADJ
ejde-515	331	5	model	model	NOUN
ejde-515	331	6	for	for	ADP
ejde-515	331	7	neural	neural	ADJ
ejde-515	331	8	fields	field	NOUN
ejde-515	331	9	15	15	NUM
ejde-515	331	10	finally	finally	ADV
ejde-515	331	11	,	,	PUNCT
ejde-515	331	12	we	we	PRON
ejde-515	331	13	expect	expect	VERB
ejde-515	331	14	that	that	SCONJ
ejde-515	331	15	the	the	DET
ejde-515	331	16	mathematical	mathematical	ADJ
ejde-515	331	17	results	result	NOUN
ejde-515	331	18	presented	present	VERB
ejde-515	331	19	in	in	ADP
ejde-515	331	20	theorem	theorem	ADJ
ejde-515	331	21	3.2	3.2	NUM
ejde-515	331	22	and	and	CCONJ
ejde-515	331	23	theorem	theorem	VERB
ejde-515	331	24	4.2	4.2	NUM
ejde-515	331	25	will	will	AUX
ejde-515	331	26	contribute	contribute	VERB
ejde-515	331	27	to	to	ADP
ejde-515	331	28	other	other	ADJ
ejde-515	331	29	mathematical	mathematical	ADJ
ejde-515	331	30	properties	property	NOUN
ejde-515	331	31	associated	associate	VERB
ejde-515	331	32	with	with	ADP
ejde-515	331	33	the	the	DET
ejde-515	331	34	dynamics	dynamic	NOUN
ejde-515	331	35	of	of	ADP
ejde-515	331	36	this	this	DET
ejde-515	331	37	model	model	NOUN
ejde-515	331	38	and	and	CCONJ
ejde-515	331	39	that	that	SCONJ
ejde-515	331	40	other	other	ADJ
ejde-515	331	41	biological	biological	ADJ
ejde-515	331	42	conclusions	conclusion	NOUN
ejde-515	331	43	may	may	AUX
ejde-515	331	44	be	be	AUX
ejde-515	331	45	possible	possible	ADJ
ejde-515	331	46	.	.	PUNCT
ejde-515	332	1	acknowledgments	acknowledgment	NOUN
ejde-515	332	2	.	.	PUNCT
ejde-515	333	1	the	the	DET
ejde-515	333	2	author	author	NOUN
ejde-515	333	3	wants	want	VERB
ejde-515	333	4	to	to	PART
ejde-515	333	5	thank	thank	VERB
ejde-515	333	6	the	the	DET
ejde-515	333	7	anonymous	anonymous	ADJ
ejde-515	333	8	referee	referee	NOUN
ejde-515	333	9	for	for	ADP
ejde-515	333	10	his	his	PRON
ejde-515	333	11	/	/	SYM
ejde-515	333	12	her	her	PRON
ejde-515	333	13	reading	reading	NOUN
ejde-515	333	14	of	of	ADP
ejde-515	333	15	the	the	DET
ejde-515	333	16	original	original	ADJ
ejde-515	333	17	manuscript	manuscript	NOUN
ejde-515	333	18	.	.	PUNCT
ejde-515	334	1	he	he	PRON
ejde-515	334	2	also	also	ADV
ejde-515	334	3	thanks	thank	NOUN
ejde-515	334	4	prof	prof	PROPN
ejde-515	334	5	.	.	PROPN
ejde-515	334	6	flank	flank	PROPN
ejde-515	334	7	bezerra	bezerra	PROPN
ejde-515	334	8	(	(	PUNCT
ejde-515	334	9	ufpb	ufpb	ADJ
ejde-515	334	10	)	)	PUNCT
ejde-515	334	11	for	for	ADP
ejde-515	334	12	critical	critical	ADJ
ejde-515	334	13	reading	reading	NOUN
ejde-515	334	14	of	of	ADP
ejde-515	334	15	this	this	DET
ejde-515	334	16	work	work	NOUN
ejde-515	334	17	and	and	CCONJ
ejde-515	334	18	professors	professor	NOUN
ejde-515	334	19	daniel	daniel	PROPN
ejde-515	334	20	cordeiro	cordeiro	PROPN
ejde-515	334	21	(	(	PUNCT
ejde-515	334	22	ufcg	ufcg	NOUN
ejde-515	334	23	)	)	PUNCT
ejde-515	334	24	and	and	CCONJ
ejde-515	334	25	adriano	adriano	PROPN
ejde-515	334	26	batista	batista	PROPN
ejde-515	334	27	(	(	PUNCT
ejde-515	334	28	ufcg	ufcg	NOUN
ejde-515	334	29	)	)	PUNCT
ejde-515	334	30	for	for	ADP
ejde-515	334	31	reviewing	review	VERB
ejde-515	334	32	the	the	DET
ejde-515	334	33	english	english	PROPN
ejde-515	334	34	used	use	VERB
ejde-515	334	35	in	in	ADP
ejde-515	334	36	this	this	DET
ejde-515	334	37	paper	paper	NOUN
ejde-515	334	38	.	.	PUNCT
ejde-515	335	1	finally	finally	ADV
ejde-515	335	2	,	,	PUNCT
ejde-515	335	3	the	the	DET
ejde-515	335	4	author	author	NOUN
ejde-515	335	5	dedicates	dedicate	VERB
ejde-515	335	6	this	this	DET
ejde-515	335	7	work	work	NOUN
ejde-515	335	8	to	to	ADP
ejde-515	335	9	his	his	PRON
ejde-515	335	10	hildren	hildren	NOUN
ejde-515	335	11	arthur	arthur	PROPN
ejde-515	335	12	and	and	CCONJ
ejde-515	335	13	luana	luana	PROPN
ejde-515	335	14	.	.	PUNCT
ejde-515	336	1	references	reference	NOUN
ejde-515	336	2	[	[	X
ejde-515	336	3	1	1	NUM
ejde-515	336	4	]	]	X
ejde-515	336	5	amari	amari	PROPN
ejde-515	336	6	,	,	PUNCT
ejde-515	336	7	s.	s.	PROPN
ejde-515	336	8	;	;	PUNCT
ejde-515	336	9	dynamics	dynamic	NOUN
ejde-515	336	10	of	of	ADP
ejde-515	336	11	pattern	pattern	NOUN
ejde-515	336	12	formation	formation	NOUN
ejde-515	336	13	in	in	ADP
ejde-515	336	14	lateral	lateral	ADJ
ejde-515	336	15	-	-	PUNCT
ejde-515	336	16	inhibition	inhibition	NOUN
ejde-515	336	17	type	type	NOUN
ejde-515	336	18	neural	neural	ADJ
ejde-515	336	19	fields	field	NOUN
ejde-515	336	20	,	,	PUNCT
ejde-515	336	21	biol	biol	NOUN
ejde-515	336	22	.	.	PUNCT
ejde-515	337	1	cybernetics	cybernetic	NOUN
ejde-515	337	2	,	,	PUNCT
ejde-515	337	3	27	27	NUM
ejde-515	337	4	(	(	PUNCT
ejde-515	337	5	1977	1977	NUM
ejde-515	337	6	)	)	PUNCT
ejde-515	337	7	,	,	PUNCT
ejde-515	337	8	77–87	77–87	NUM
ejde-515	337	9	.	.	PUNCT
ejde-515	338	1	[	[	X
ejde-515	338	2	2	2	NUM
ejde-515	338	3	]	]	X
ejde-515	338	4	amari	amari	PROPN
ejde-515	338	5	,	,	PUNCT
ejde-515	338	6	s.	s.	PROPN
ejde-515	338	7	;	;	PUNCT
ejde-515	338	8	dynamics	dynamic	NOUN
ejde-515	338	9	stability	stability	NOUN
ejde-515	338	10	of	of	ADP
ejde-515	338	11	formation	formation	NOUN
ejde-515	338	12	of	of	ADP
ejde-515	338	13	cortical	cortical	ADJ
ejde-515	338	14	maps	map	NOUN
ejde-515	338	15	,	,	PUNCT
ejde-515	338	16	in	in	ADP
ejde-515	338	17	:	:	PUNCT
ejde-515	338	18	m.	m.	NOUN
ejde-515	338	19	a.	a.	NOUN
ejde-515	338	20	arbib	arbib	PROPN
ejde-515	338	21	and	and	CCONJ
ejde-515	338	22	s.	s.	PROPN
ejde-515	338	23	i.	i.	PROPN
ejde-515	338	24	amari	amari	PROPN
ejde-515	338	25	(	(	PUNCT
ejde-515	338	26	eds	ed	NOUN
ejde-515	338	27	)	)	PUNCT
ejde-515	338	28	,	,	PUNCT
ejde-515	338	29	dynamic	dynamic	ADJ
ejde-515	338	30	interactions	interaction	NOUN
ejde-515	338	31	in	in	ADP
ejde-515	338	32	neural	neural	ADJ
ejde-515	338	33	networks	network	NOUN
ejde-515	338	34	:	:	PUNCT
ejde-515	338	35	models	model	NOUN
ejde-515	338	36	and	and	CCONJ
ejde-515	338	37	data	datum	NOUN
ejde-515	338	38	,	,	PUNCT
ejde-515	338	39	springer	springer	NOUN
ejde-515	338	40	-	-	PUNCT
ejde-515	338	41	verlag	verlag	PROPN
ejde-515	338	42	,	,	PUNCT
ejde-515	338	43	new	new	PROPN
ejde-515	338	44	york	york	PROPN
ejde-515	338	45	,	,	PUNCT
ejde-515	338	46	(	(	PUNCT
ejde-515	338	47	1989	1989	NUM
ejde-515	338	48	)	)	PUNCT
ejde-515	338	49	15–34	15–34	NUM
ejde-515	338	50	.	.	PUNCT
ejde-515	339	1	[	[	X
ejde-515	339	2	3	3	NUM
ejde-515	339	3	]	]	X
ejde-515	339	4	barakova	barakova	NOUN
ejde-515	339	5	,	,	PUNCT
ejde-515	339	6	e.	e.	PROPN
ejde-515	339	7	i.	i.	PROPN
ejde-515	339	8	b.	b.	PROPN
ejde-515	339	9	;	;	PUNCT
ejde-515	339	10	timing	time	VERB
ejde-515	339	11	sensory	sensory	ADJ
ejde-515	339	12	integration	integration	NOUN
ejde-515	339	13	for	for	ADP
ejde-515	339	14	robot	robot	NOUN
ejde-515	339	15	simulation	simulation	NOUN
ejde-515	339	16	of	of	ADP
ejde-515	339	17	autistic	autistic	ADJ
ejde-515	339	18	behavior	behavior	NOUN
ejde-515	339	19	,	,	PUNCT
ejde-515	339	20	robotics	robotic	NOUN
ejde-515	339	21	and	and	CCONJ
ejde-515	339	22	automation	automation	NOUN
ejde-515	339	23	magazine	magazine	NOUN
ejde-515	339	24	,	,	PUNCT
ejde-515	339	25	16	16	NUM
ejde-515	339	26	(	(	PUNCT
ejde-515	339	27	2012	2012	NUM
ejde-515	339	28	)	)	PUNCT
ejde-515	339	29	,	,	PUNCT
ejde-515	339	30	1	1	NUM
ejde-515	339	31	-	-	SYM
ejde-515	339	32	8	8	NUM
ejde-515	339	33	,	,	PUNCT
ejde-515	339	34	[	[	X
ejde-515	339	35	4	4	NUM
ejde-515	339	36	]	]	PUNCT
ejde-515	339	37	beurle	beurle	NOUN
ejde-515	339	38	,	,	PUNCT
ejde-515	339	39	r.	r.	PROPN
ejde-515	339	40	l.	l.	PROPN
ejde-515	339	41	;	;	PUNCT
ejde-515	339	42	properties	property	NOUN
ejde-515	339	43	of	of	ADP
ejde-515	339	44	a	a	DET
ejde-515	339	45	mass	mass	NOUN
ejde-515	339	46	of	of	ADP
ejde-515	339	47	cells	cell	NOUN
ejde-515	339	48	capable	capable	ADJ
ejde-515	339	49	of	of	ADP
ejde-515	339	50	regenerating	regenerate	VERB
ejde-515	339	51	pulses	pulse	NOUN
ejde-515	339	52	,	,	PUNCT
ejde-515	339	53	philosophical	philosophical	ADJ
ejde-515	339	54	transactions	transaction	NOUN
ejde-515	339	55	of	of	ADP
ejde-515	339	56	the	the	DET
ejde-515	339	57	royal	royal	ADJ
ejde-515	339	58	society	society	PROPN
ejde-515	339	59	london	london	PROPN
ejde-515	339	60	b	b	PROPN
ejde-515	339	61	,	,	PUNCT
ejde-515	339	62	240	240	NUM
ejde-515	339	63	(	(	PUNCT
ejde-515	339	64	1956	1956	NUM
ejde-515	339	65	)	)	PUNCT
ejde-515	339	66	,	,	PUNCT
ejde-515	339	67	55–94	55–94	NUM
ejde-515	339	68	.	.	PUNCT
ejde-515	340	1	[	[	X
ejde-515	340	2	5	5	NUM
ejde-515	340	3	]	]	X
ejde-515	340	4	bezerra	bezerra	PROPN
ejde-515	340	5	,	,	PUNCT
ejde-515	340	6	f.	f.	PROPN
ejde-515	340	7	d.	d.	PROPN
ejde-515	340	8	;	;	PUNCT
ejde-515	340	9	pereira	pereira	PROPN
ejde-515	340	10	,	,	PUNCT
ejde-515	340	11	a.	a.	PROPN
ejde-515	340	12	l.	l.	PROPN
ejde-515	340	13	;	;	PUNCT
ejde-515	340	14	da	da	PROPN
ejde-515	340	15	silva	silva	PROPN
ejde-515	340	16	,	,	PUNCT
ejde-515	340	17	s.	s.	PROPN
ejde-515	340	18	h.	h.	PROPN
ejde-515	340	19	;	;	PUNCT
ejde-515	340	20	existence	existence	NOUN
ejde-515	340	21	,	,	PUNCT
ejde-515	340	22	regularity	regularity	NOUN
ejde-515	340	23	and	and	CCONJ
ejde-515	340	24	upper	upper	ADJ
ejde-515	340	25	semicontinuity	semicontinuity	NOUN
ejde-515	340	26	of	of	ADP
ejde-515	340	27	pullback	pullback	NOUN
ejde-515	340	28	attractors	attractor	NOUN
ejde-515	340	29	for	for	ADP
ejde-515	340	30	the	the	DET
ejde-515	340	31	evolution	evolution	NOUN
ejde-515	340	32	process	process	NOUN
ejde-515	340	33	associated	associate	VERB
ejde-515	340	34	to	to	ADP
ejde-515	340	35	a	a	DET
ejde-515	340	36	neural	neural	ADJ
ejde-515	340	37	field	field	NOUN
ejde-515	340	38	model	model	NOUN
ejde-515	340	39	,	,	PUNCT
ejde-515	340	40	electronic	electronic	ADJ
ejde-515	340	41	journal	journal	NOUN
ejde-515	340	42	of	of	ADP
ejde-515	340	43	qualitative	qualitative	ADJ
ejde-515	340	44	theory	theory	NOUN
ejde-515	340	45	of	of	ADP
ejde-515	340	46	differential	differential	ADJ
ejde-515	340	47	equations	equation	NOUN
ejde-515	340	48	,	,	PUNCT
ejde-515	340	49	2017	2017	NUM
ejde-515	340	50	(	(	PUNCT
ejde-515	340	51	2017	2017	NUM
ejde-515	340	52	)	)	PUNCT
ejde-515	340	53	,	,	PUNCT
ejde-515	340	54	1	1	NUM
ejde-515	340	55	-	-	SYM
ejde-515	340	56	18	18	NUM
ejde-515	340	57	.	.	PUNCT
ejde-515	341	1	[	[	X
ejde-515	341	2	6	6	NUM
ejde-515	341	3	]	]	X
ejde-515	341	4	brezis	brezis	PROPN
ejde-515	341	5	h.	h.	PROPN
ejde-515	341	6	;	;	PUNCT
ejde-515	341	7	functional	functional	ADJ
ejde-515	341	8	analysis	analysis	NOUN
ejde-515	341	9	,	,	PUNCT
ejde-515	341	10	sobolev	sobolev	NOUN
ejde-515	341	11	spaces	space	NOUN
ejde-515	341	12	and	and	CCONJ
ejde-515	341	13	partial	partial	ADJ
ejde-515	341	14	differential	differential	NOUN
ejde-515	341	15	equations	equation	NOUN
ejde-515	341	16	,	,	PUNCT
ejde-515	341	17	springer	springer	NOUN
ejde-515	341	18	,	,	PUNCT
ejde-515	341	19	new	new	PROPN
ejde-515	341	20	york	york	PROPN
ejde-515	341	21	,	,	PUNCT
ejde-515	341	22	2011	2011	NUM
ejde-515	341	23	.	.	PUNCT
ejde-515	342	1	[	[	X
ejde-515	342	2	7	7	NUM
ejde-515	342	3	]	]	X
ejde-515	342	4	carroll	carroll	PROPN
ejde-515	342	5	,	,	PUNCT
ejde-515	342	6	s.	s.	PROPN
ejde-515	342	7	r.	r.	PROPN
ejde-515	342	8	;	;	PUNCT
ejde-515	342	9	bressloff	bressloff	NOUN
ejde-515	342	10	,	,	PUNCT
ejde-515	342	11	p.	p.	NOUN
ejde-515	342	12	;	;	PUNCT
ejde-515	342	13	symmetric	symmetric	ADJ
ejde-515	342	14	bifurcations	bifurcation	NOUN
ejde-515	342	15	in	in	ADP
ejde-515	342	16	a	a	DET
ejde-515	342	17	neural	neural	ADJ
ejde-515	342	18	field	field	NOUN
ejde-515	342	19	model	model	NOUN
ejde-515	342	20	for	for	ADP
ejde-515	342	21	encoding	encode	VERB
ejde-515	342	22	the	the	DET
ejde-515	342	23	direction	direction	NOUN
ejde-515	342	24	of	of	ADP
ejde-515	342	25	spatial	spatial	ADJ
ejde-515	342	26	contrast	contrast	NOUN
ejde-515	342	27	gradients	gradient	NOUN
ejde-515	342	28	,	,	PUNCT
ejde-515	342	29	journal	journal	NOUN
ejde-515	342	30	on	on	ADP
ejde-515	342	31	applied	apply	VERB
ejde-515	342	32	dynamical	dynamical	ADJ
ejde-515	342	33	systems	system	NOUN
ejde-515	342	34	,	,	PUNCT
ejde-515	342	35	17	17	NUM
ejde-515	342	36	no	no	NOUN
ejde-515	342	37	.	.	NOUN
ejde-515	342	38	1	1	NUM
ejde-515	342	39	(	(	PUNCT
ejde-515	342	40	2018	2018	NUM
ejde-515	342	41	)	)	PUNCT
ejde-515	342	42	,	,	PUNCT
ejde-515	342	43	1–51	1–51	PROPN
ejde-515	342	44	.	.	PUNCT
ejde-515	343	1	[	[	X
ejde-515	343	2	8	8	NUM
ejde-515	343	3	]	]	X
ejde-515	343	4	carvalho	carvalho	NOUN
ejde-515	343	5	,	,	PUNCT
ejde-515	343	6	a.	a.	NOUN
ejde-515	343	7	n.	n.	NOUN
ejde-515	343	8	;	;	PUNCT
ejde-515	343	9	langa	langa	PROPN
ejde-515	343	10	,	,	PUNCT
ejde-515	343	11	j.	j.	PROPN
ejde-515	343	12	a.	a.	PROPN
ejde-515	343	13	;	;	PUNCT
ejde-515	343	14	robinson	robinson	PROPN
ejde-515	343	15	,	,	PUNCT
ejde-515	343	16	j.	j.	PROPN
ejde-515	343	17	c.	c.	PROPN
ejde-515	343	18	;	;	PUNCT
ejde-515	343	19	attractors	attractor	NOUN
ejde-515	343	20	for	for	ADP
ejde-515	343	21	infinite	infinite	ADJ
ejde-515	343	22	-	-	PUNCT
ejde-515	343	23	dimensional	dimensional	ADJ
ejde-515	343	24	nonautonomous	nonautonomous	ADJ
ejde-515	343	25	dynamical	dynamical	ADJ
ejde-515	343	26	systems	system	NOUN
ejde-515	343	27	.	.	PUNCT
ejde-515	344	1	applied	apply	VERB
ejde-515	344	2	mathematical	mathematical	ADJ
ejde-515	344	3	sciences	science	NOUN
ejde-515	344	4	182	182	NUM
ejde-515	344	5	.	.	PUNCT
ejde-515	344	6	springer	springer	NOUN
ejde-515	344	7	-	-	PUNCT
ejde-515	344	8	verlag	verlag	PROPN
ejde-515	344	9	,	,	PUNCT
ejde-515	344	10	new	new	PROPN
ejde-515	344	11	york	york	PROPN
ejde-515	344	12	,	,	PUNCT
ejde-515	344	13	2012	2012	NUM
ejde-515	344	14	.	.	PUNCT
ejde-515	345	1	[	[	X
ejde-515	345	2	9	9	NUM
ejde-515	345	3	]	]	SYM
ejde-515	345	4	castillo	castillo	PROPN
ejde-515	345	5	,	,	PUNCT
ejde-515	345	6	s.	s.	PROPN
ejde-515	345	7	;	;	PUNCT
ejde-515	345	8	pinto	pinto	NOUN
ejde-515	345	9	,	,	PUNCT
ejde-515	345	10	m.	m.	NOUN
ejde-515	345	11	;	;	PUNCT
ejde-515	345	12	torres	torre	NOUN
ejde-515	345	13	,	,	PUNCT
ejde-515	345	14	r.	r.	PROPN
ejde-515	345	15	;	;	PUNCT
ejde-515	345	16	asymptotic	asymptotic	ADJ
ejde-515	345	17	formulae	formulae	NOUN
ejde-515	345	18	for	for	ADP
ejde-515	345	19	solutions	solution	NOUN
ejde-515	345	20	to	to	ADP
ejde-515	345	21	impulsive	impulsive	ADJ
ejde-515	345	22	differential	differential	ADJ
ejde-515	345	23	equations	equation	NOUN
ejde-515	345	24	with	with	ADP
ejde-515	345	25	piecewise	piecewise	NOUN
ejde-515	345	26	constant	constant	ADJ
ejde-515	345	27	argument	argument	NOUN
ejde-515	345	28	of	of	ADP
ejde-515	345	29	generalized	generalized	ADJ
ejde-515	345	30	type	type	NOUN
ejde-515	345	31	,	,	PUNCT
ejde-515	345	32	electron	electron	NOUN
ejde-515	345	33	.	.	PUNCT
ejde-515	346	1	j.	j.	PROPN
ejde-515	346	2	differential	differential	PROPN
ejde-515	346	3	equations	equations	PROPN
ejde-515	346	4	,	,	PUNCT
ejde-515	346	5	2019	2019	NUM
ejde-515	346	6	no	no	NOUN
ejde-515	346	7	.	.	PROPN
ejde-515	346	8	40	40	NUM
ejde-515	346	9	(	(	PUNCT
ejde-515	346	10	2019	2019	NUM
ejde-515	346	11	)	)	PUNCT
ejde-515	346	12	,	,	PUNCT
ejde-515	346	13	1	1	NUM
ejde-515	346	14	-	-	SYM
ejde-515	346	15	22	22	NUM
ejde-515	346	16	.	.	PUNCT
ejde-515	347	1	[	[	X
ejde-515	347	2	10	10	NUM
ejde-515	347	3	]	]	X
ejde-515	347	4	chepyzhov	chepyzhov	NOUN
ejde-515	347	5	,	,	PUNCT
ejde-515	347	6	v.	v.	PROPN
ejde-515	347	7	v.	v.	ADP
ejde-515	347	8	;	;	PUNCT
ejde-515	347	9	vishik	vishik	NOUN
ejde-515	347	10	,	,	PUNCT
ejde-515	347	11	m.	m.	NOUN
ejde-515	347	12	i.	i.	NOUN
ejde-515	347	13	;	;	PUNCT
ejde-515	347	14	attractors	attractor	NOUN
ejde-515	347	15	for	for	ADP
ejde-515	347	16	equations	equation	NOUN
ejde-515	347	17	of	of	ADP
ejde-515	347	18	mathematical	mathematical	ADJ
ejde-515	347	19	physics	physics	NOUN
ejde-515	347	20	,	,	PUNCT
ejde-515	347	21	in	in	ADP
ejde-515	347	22	:	:	PUNCT
ejde-515	347	23	colloquium	colloquium	NOUN
ejde-515	347	24	publications	publication	NOUN
ejde-515	347	25	,	,	PUNCT
ejde-515	347	26	49	49	NUM
ejde-515	347	27	,	,	PUNCT
ejde-515	347	28	america	america	PROPN
ejde-515	347	29	mathematical	mathematical	PROPN
ejde-515	347	30	society	society	NOUN
ejde-515	347	31	,	,	PUNCT
ejde-515	347	32	2002	2002	NUM
ejde-515	347	33	.	.	PUNCT
ejde-515	348	1	[	[	X
ejde-515	348	2	11	11	NUM
ejde-515	348	3	]	]	PUNCT
ejde-515	348	4	coombes	coombe	NOUN
ejde-515	348	5	,	,	PUNCT
ejde-515	348	6	s.	s.	PROPN
ejde-515	348	7	;	;	PUNCT
ejde-515	348	8	lord	lord	PROPN
ejde-515	348	9	,	,	PUNCT
ejde-515	348	10	g.	g.	PROPN
ejde-515	348	11	j.	j.	PROPN
ejde-515	348	12	;	;	PUNCT
ejde-515	348	13	owen	owen	PROPN
ejde-515	348	14	,	,	PUNCT
ejde-515	348	15	m.	m.	PROPN
ejde-515	348	16	r.	r.	PROPN
ejde-515	348	17	;	;	PUNCT
ejde-515	348	18	waves	wave	NOUN
ejde-515	348	19	and	and	CCONJ
ejde-515	348	20	bumps	bump	NOUN
ejde-515	348	21	in	in	ADP
ejde-515	348	22	neuronal	neuronal	ADJ
ejde-515	348	23	networks	network	NOUN
ejde-515	348	24	with	with	ADP
ejde-515	348	25	axodendritic	axodendritic	ADJ
ejde-515	348	26	synaptic	synaptic	ADJ
ejde-515	348	27	interactions	interaction	NOUN
ejde-515	348	28	.	.	PUNCT
ejde-515	349	1	physica	physica	PROPN
ejde-515	349	2	d	d	PROPN
ejde-515	349	3	,	,	PUNCT
ejde-515	349	4	178	178	NUM
ejde-515	349	5	(	(	PUNCT
ejde-515	349	6	2003	2003	NUM
ejde-515	349	7	)	)	PUNCT
ejde-515	349	8	,	,	PUNCT
ejde-515	349	9	219–241	219–241	NUM
ejde-515	349	10	.	.	PUNCT
ejde-515	350	1	[	[	X
ejde-515	350	2	12	12	NUM
ejde-515	350	3	]	]	X
ejde-515	350	4	daleckii	daleckii	PROPN
ejde-515	350	5	,	,	PUNCT
ejde-515	350	6	j.	j.	PROPN
ejde-515	350	7	l.	l.	PROPN
ejde-515	350	8	;	;	PUNCT
ejde-515	350	9	krein	krein	PROPN
ejde-515	350	10	,	,	PUNCT
ejde-515	350	11	m.	m.	NOUN
ejde-515	350	12	g.	g.	PROPN
ejde-515	350	13	;	;	PUNCT
ejde-515	350	14	stability	stability	NOUN
ejde-515	350	15	of	of	ADP
ejde-515	350	16	solutions	solution	NOUN
ejde-515	350	17	of	of	ADP
ejde-515	350	18	differential	differential	ADJ
ejde-515	350	19	equations	equation	NOUN
ejde-515	350	20	in	in	ADP
ejde-515	350	21	banach	banach	NOUN
ejde-515	350	22	spaces	space	NOUN
ejde-515	350	23	.	.	PUNCT
ejde-515	351	1	american	american	PROPN
ejde-515	351	2	mathematical	mathematical	PROPN
ejde-515	351	3	society	society	NOUN
ejde-515	351	4	,	,	PUNCT
ejde-515	351	5	providence	providence	NOUN
ejde-515	351	6	,	,	PUNCT
ejde-515	351	7	rhode	rhode	NOUN
ejde-515	351	8	island	island	NOUN
ejde-515	351	9	,	,	PUNCT
ejde-515	351	10	1974	1974	NUM
ejde-515	351	11	.	.	PUNCT
ejde-515	352	1	[	[	X
ejde-515	352	2	13	13	NUM
ejde-515	352	3	]	]	SYM
ejde-515	352	4	da	da	PROPN
ejde-515	352	5	silva	silva	PROPN
ejde-515	352	6	,	,	PUNCT
ejde-515	352	7	s.	s.	PROPN
ejde-515	352	8	h.	h.	PROPN
ejde-515	352	9	;	;	PUNCT
ejde-515	352	10	pereira	pereira	PROPN
ejde-515	352	11	,	,	PUNCT
ejde-515	352	12	a.	a.	PROPN
ejde-515	352	13	l.	l.	PROPN
ejde-515	352	14	;	;	PUNCT
ejde-515	352	15	global	global	ADJ
ejde-515	352	16	attractors	attractor	NOUN
ejde-515	352	17	for	for	ADP
ejde-515	352	18	neural	neural	ADJ
ejde-515	352	19	fields	field	NOUN
ejde-515	352	20	in	in	ADP
ejde-515	352	21	a	a	DET
ejde-515	352	22	weighted	weighted	ADJ
ejde-515	352	23	space	space	NOUN
ejde-515	352	24	.	.	PUNCT
ejde-515	353	1	matemática	matemática	PROPN
ejde-515	353	2	contemporanea	contemporanea	PROPN
ejde-515	353	3	,	,	PUNCT
ejde-515	353	4	36	36	NUM
ejde-515	353	5	(	(	PUNCT
ejde-515	353	6	2009	2009	NUM
ejde-515	353	7	)	)	PUNCT
ejde-515	353	8	,	,	PUNCT
ejde-515	353	9	139–153	139–153	NUM
ejde-515	353	10	.	.	PUNCT
ejde-515	354	1	[	[	X
ejde-515	354	2	14	14	NUM
ejde-515	354	3	]	]	SYM
ejde-515	354	4	da	da	PROPN
ejde-515	354	5	silva	silva	PROPN
ejde-515	354	6	,	,	PUNCT
ejde-515	354	7	s.	s.	PROPN
ejde-515	354	8	h.	h.	PROPN
ejde-515	354	9	;	;	PUNCT
ejde-515	354	10	existence	existence	NOUN
ejde-515	354	11	and	and	CCONJ
ejde-515	354	12	upper	upper	ADJ
ejde-515	354	13	semicontinuity	semicontinuity	NOUN
ejde-515	354	14	of	of	ADP
ejde-515	354	15	global	global	ADJ
ejde-515	354	16	attractors	attractor	NOUN
ejde-515	354	17	for	for	ADP
ejde-515	354	18	neural	neural	ADJ
ejde-515	354	19	fields	field	NOUN
ejde-515	354	20	in	in	ADP
ejde-515	354	21	an	an	DET
ejde-515	354	22	unbounded	unbounded	ADJ
ejde-515	354	23	domain	domain	NOUN
ejde-515	354	24	.	.	PUNCT
ejde-515	355	1	electronic	electronic	ADJ
ejde-515	355	2	journal	journal	NOUN
ejde-515	355	3	of	of	ADP
ejde-515	355	4	differential	differential	ADJ
ejde-515	355	5	equations	equation	NOUN
ejde-515	355	6	,	,	PUNCT
ejde-515	355	7	2010	2010	NUM
ejde-515	355	8	no	no	NOUN
ejde-515	355	9	.	.	PROPN
ejde-515	356	1	138	138	NUM
ejde-515	356	2	(	(	PUNCT
ejde-515	356	3	2010	2010	NUM
ejde-515	356	4	)	)	PUNCT
ejde-515	356	5	,	,	PUNCT
ejde-515	356	6	1–12	1–12	NOUN
ejde-515	356	7	.	.	PUNCT
ejde-515	357	1	[	[	X
ejde-515	357	2	15	15	NUM
ejde-515	357	3	]	]	X
ejde-515	357	4	da	da	PROPN
ejde-515	357	5	silva	silva	PROPN
ejde-515	357	6	,	,	PUNCT
ejde-515	357	7	s.	s.	PROPN
ejde-515	357	8	h.	h.	PROPN
ejde-515	357	9	;	;	PUNCT
ejde-515	357	10	existence	existence	NOUN
ejde-515	357	11	and	and	CCONJ
ejde-515	357	12	upper	upper	ADJ
ejde-515	357	13	semicontinuity	semicontinuity	NOUN
ejde-515	357	14	of	of	ADP
ejde-515	357	15	global	global	ADJ
ejde-515	357	16	attractors	attractor	NOUN
ejde-515	357	17	for	for	ADP
ejde-515	357	18	neural	neural	ADJ
ejde-515	357	19	network	network	NOUN
ejde-515	357	20	in	in	ADP
ejde-515	357	21	a	a	DET
ejde-515	357	22	bounded	bounded	ADJ
ejde-515	357	23	domain	domain	NOUN
ejde-515	357	24	.	.	PUNCT
ejde-515	358	1	differential	differential	ADJ
ejde-515	358	2	equations	equation	NOUN
ejde-515	358	3	and	and	CCONJ
ejde-515	358	4	dynamical	dynamical	ADJ
ejde-515	358	5	systems	system	NOUN
ejde-515	358	6	,	,	PUNCT
ejde-515	358	7	19	19	NUM
ejde-515	358	8	no	no	NOUN
ejde-515	358	9	.	.	NOUN
ejde-515	359	1	1	1	NUM
ejde-515	359	2	-	-	SYM
ejde-515	359	3	2	2	NUM
ejde-515	359	4	(	(	PUNCT
ejde-515	359	5	2011	2011	NUM
ejde-515	359	6	)	)	PUNCT
ejde-515	359	7	,	,	PUNCT
ejde-515	359	8	87–96	87–96	NUM
ejde-515	359	9	.	.	PUNCT
ejde-515	360	1	[	[	X
ejde-515	360	2	16	16	NUM
ejde-515	360	3	]	]	X
ejde-515	360	4	da	da	PROPN
ejde-515	360	5	silva	silva	PROPN
ejde-515	360	6	,	,	PUNCT
ejde-515	360	7	s.	s.	PROPN
ejde-515	360	8	h.	h.	PROPN
ejde-515	360	9	;	;	PUNCT
ejde-515	360	10	properties	property	NOUN
ejde-515	360	11	of	of	ADP
ejde-515	360	12	an	an	DET
ejde-515	360	13	equation	equation	NOUN
ejde-515	360	14	for	for	ADP
ejde-515	360	15	neural	neural	ADJ
ejde-515	360	16	fields	field	NOUN
ejde-515	360	17	ina	ina	PROPN
ejde-515	360	18	bounded	bound	VERB
ejde-515	360	19	domain	domain	NOUN
ejde-515	360	20	.	.	PUNCT
ejde-515	361	1	electronic	electronic	ADJ
ejde-515	361	2	journal	journal	NOUN
ejde-515	361	3	of	of	ADP
ejde-515	361	4	differential	differential	ADJ
ejde-515	361	5	equations	equation	NOUN
ejde-515	361	6	,	,	PUNCT
ejde-515	361	7	2012	2012	NUM
ejde-515	361	8	no	no	NOUN
ejde-515	361	9	.	.	PROPN
ejde-515	361	10	42	42	NUM
ejde-515	361	11	(	(	PUNCT
ejde-515	361	12	2012	2012	NUM
ejde-515	361	13	)	)	PUNCT
ejde-515	361	14	,	,	PUNCT
ejde-515	361	15	1–9	1–9	NOUN
ejde-515	361	16	.	.	PUNCT
ejde-515	362	1	[	[	X
ejde-515	362	2	17	17	NUM
ejde-515	362	3	]	]	X
ejde-515	362	4	da	da	PROPN
ejde-515	362	5	silva	silva	PROPN
ejde-515	362	6	,	,	PUNCT
ejde-515	362	7	s.	s.	PROPN
ejde-515	362	8	h.	h.	PROPN
ejde-515	362	9	;	;	PUNCT
ejde-515	362	10	pereira	pereira	PROPN
ejde-515	362	11	,	,	PUNCT
ejde-515	362	12	a.	a.	PROPN
ejde-515	362	13	l.	l.	PROPN
ejde-515	362	14	;	;	PUNCT
ejde-515	362	15	asymptotic	asymptotic	ADJ
ejde-515	362	16	behavior	behavior	NOUN
ejde-515	362	17	for	for	ADP
ejde-515	362	18	a	a	DET
ejde-515	362	19	nonlocal	nonlocal	ADJ
ejde-515	362	20	model	model	NOUN
ejde-515	362	21	of	of	ADP
ejde-515	362	22	neural	neural	ADJ
ejde-515	362	23	fields	field	NOUN
ejde-515	362	24	.	.	PUNCT
ejde-515	363	1	são	são	PROPN
ejde-515	363	2	paulo	paulo	PROPN
ejde-515	363	3	journal	journal	PROPN
ejde-515	363	4	of	of	ADP
ejde-515	363	5	math	math	NOUN
ejde-515	363	6	.	.	PUNCT
ejde-515	364	1	sci	sci	PROPN
ejde-515	364	2	.	.	PROPN
ejde-515	364	3	,	,	PUNCT
ejde-515	364	4	9	9	NUM
ejde-515	364	5	(	(	PUNCT
ejde-515	364	6	2015	2015	NUM
ejde-515	364	7	)	)	PUNCT
ejde-515	364	8	,	,	PUNCT
ejde-515	364	9	181–194	181–194	NUM
ejde-515	364	10	.	.	PUNCT
ejde-515	365	1	[	[	X
ejde-515	365	2	18	18	NUM
ejde-515	365	3	]	]	PUNCT
ejde-515	365	4	ermentrout	ermentrout	NOUN
ejde-515	365	5	,	,	PUNCT
ejde-515	365	6	g.	g.	PROPN
ejde-515	365	7	b.	b.	PROPN
ejde-515	365	8	;	;	PUNCT
ejde-515	365	9	jalics	jalic	NOUN
ejde-515	365	10	,	,	PUNCT
ejde-515	365	11	j.	j.	PROPN
ejde-515	365	12	z.	z.	PROPN
ejde-515	365	13	rubin	rubin	PROPN
ejde-515	365	14	,	,	PUNCT
ejde-515	365	15	j.	j.	PROPN
ejde-515	365	16	e.	e.	PROPN
ejde-515	365	17	;	;	PUNCT
ejde-515	365	18	stimulus	stimulus	ADJ
ejde-515	365	19	-	-	PUNCT
ejde-515	365	20	driven	drive	VERB
ejde-515	365	21	travelling	travel	VERB
ejde-515	365	22	solutions	solution	NOUN
ejde-515	365	23	in	in	ADP
ejde-515	365	24	continuum	continuum	ADJ
ejde-515	365	25	neuronal	neuronal	ADJ
ejde-515	365	26	models	model	NOUN
ejde-515	365	27	with	with	ADP
ejde-515	365	28	general	general	ADJ
ejde-515	365	29	smooth	smooth	ADJ
ejde-515	365	30	firing	firing	NOUN
ejde-515	365	31	rate	rate	NOUN
ejde-515	365	32	functions	function	NOUN
ejde-515	365	33	.	.	PUNCT
ejde-515	366	1	siam	siam	PROPN
ejde-515	366	2	,	,	PUNCT
ejde-515	366	3	j.	j.	PROPN
ejde-515	366	4	appl	appl	PROPN
ejde-515	366	5	.	.	PROPN
ejde-515	366	6	math	math	PROPN
ejde-515	366	7	.	.	PUNCT
ejde-515	367	1	,	,	PUNCT
ejde-515	367	2	70	70	NUM
ejde-515	367	3	(	(	PUNCT
ejde-515	367	4	2010	2010	NUM
ejde-515	367	5	)	)	PUNCT
ejde-515	367	6	,	,	PUNCT
ejde-515	367	7	3039–3064	3039–3064	NUM
ejde-515	367	8	.	.	PUNCT
ejde-515	368	1	[	[	X
ejde-515	368	2	19	19	NUM
ejde-515	368	3	]	]	X
ejde-515	368	4	hale	hale	PROPN
ejde-515	368	5	,	,	PUNCT
ejde-515	368	6	j.	j.	PROPN
ejde-515	368	7	k.	k.	PROPN
ejde-515	368	8	;	;	PUNCT
ejde-515	368	9	ordinary	ordinary	ADJ
ejde-515	368	10	differential	differential	ADJ
ejde-515	368	11	equations	equation	NOUN
ejde-515	368	12	.	.	PUNCT
ejde-515	369	1	pure	pure	ADJ
ejde-515	369	2	and	and	CCONJ
ejde-515	369	3	applied	applied	ADJ
ejde-515	369	4	mathematics	mathematic	NOUN
ejde-515	369	5	.	.	PUNCT
ejde-515	370	1	a	a	DET
ejde-515	370	2	series	series	NOUN
ejde-515	370	3	of	of	ADP
ejde-515	370	4	texts	text	NOUN
ejde-515	370	5	and	and	CCONJ
ejde-515	370	6	monographslecture	monographslecture	NOUN
ejde-515	370	7	,	,	PUNCT
ejde-515	370	8	v.	v.	ADP
ejde-515	370	9	xxi	xxi	PROPN
ejde-515	370	10	,	,	PUNCT
ejde-515	370	11	krieger	krieger	PROPN
ejde-515	370	12	publishing	publishing	PROPN
ejde-515	370	13	company	company	PROPN
ejde-515	370	14	,	,	PUNCT
ejde-515	370	15	florida	florida	PROPN
ejde-515	370	16	,	,	PUNCT
ejde-515	370	17	1981	1981	NUM
ejde-515	370	18	.	.	PUNCT
ejde-515	371	1	16	16	NUM
ejde-515	371	2	s.	s.	PROPN
ejde-515	371	3	h.	h.	PROPN
ejde-515	371	4	da	da	PROPN
ejde-515	371	5	silva	silva	PROPN
ejde-515	371	6	ejde-2020/92	ejde-2020/92	PROPN
ejde-515	371	7	[	[	X
ejde-515	371	8	20	20	NUM
ejde-515	371	9	]	]	X
ejde-515	371	10	henry	henry	PROPN
ejde-515	371	11	,	,	PUNCT
ejde-515	371	12	d.	d.	PROPN
ejde-515	371	13	;	;	PUNCT
ejde-515	371	14	geometric	geometric	ADJ
ejde-515	371	15	theory	theory	NOUN
ejde-515	371	16	of	of	ADP
ejde-515	371	17	semilinear	semilinear	PROPN
ejde-515	371	18	parabolic	parabolic	PROPN
ejde-515	371	19	equations	equation	NOUN
ejde-515	371	20	.	.	PUNCT
ejde-515	372	1	lecture	lecture	NOUN
ejde-515	372	2	notes	note	NOUN
ejde-515	372	3	in	in	ADP
ejde-515	372	4	mathematics	mathematics	PROPN
ejde-515	372	5	n.	n.	PROPN
ejde-515	372	6	840	840	NUM
ejde-515	372	7	,	,	PUNCT
ejde-515	372	8	springer	springer	NOUN
ejde-515	372	9	-	-	PUNCT
ejde-515	372	10	verlag	verlag	PROPN
ejde-515	372	11	,	,	PUNCT
ejde-515	372	12	1981	1981	NUM
ejde-515	372	13	.	.	PUNCT
ejde-515	373	1	[	[	X
ejde-515	373	2	21	21	NUM
ejde-515	373	3	]	]	X
ejde-515	373	4	kishimoto	kishimoto	PROPN
ejde-515	373	5	,	,	PUNCT
ejde-515	373	6	k.	k.	PROPN
ejde-515	373	7	;	;	PUNCT
ejde-515	373	8	amari	amari	PROPN
ejde-515	373	9	,	,	PUNCT
ejde-515	373	10	s.	s.	PROPN
ejde-515	373	11	;	;	PUNCT
ejde-515	373	12	existence	existence	NOUN
ejde-515	373	13	and	and	CCONJ
ejde-515	373	14	stability	stability	NOUN
ejde-515	373	15	of	of	ADP
ejde-515	373	16	local	local	ADJ
ejde-515	373	17	excitations	excitation	NOUN
ejde-515	373	18	in	in	ADP
ejde-515	373	19	homogeneous	homogeneous	ADJ
ejde-515	373	20	neural	neural	ADJ
ejde-515	373	21	fields	field	NOUN
ejde-515	373	22	,	,	PUNCT
ejde-515	373	23	journal	journal	NOUN
ejde-515	373	24	mathematical	mathematical	ADJ
ejde-515	373	25	biology	biology	NOUN
ejde-515	373	26	,	,	PUNCT
ejde-515	373	27	7	7	NUM
ejde-515	373	28	(	(	PUNCT
ejde-515	373	29	1979	1979	NUM
ejde-515	373	30	)	)	PUNCT
ejde-515	373	31	,	,	PUNCT
ejde-515	373	32	303–318	303–318	NUM
ejde-515	373	33	.	.	PUNCT
ejde-515	374	1	[	[	X
ejde-515	374	2	22	22	NUM
ejde-515	374	3	]	]	X
ejde-515	374	4	kloeden	kloeden	PROPN
ejde-515	374	5	,	,	PUNCT
ejde-515	374	6	p.	p.	PROPN
ejde-515	374	7	e.	e.	PROPN
ejde-515	374	8	;	;	PUNCT
ejde-515	374	9	schmalfuß	schmalfuß	VERB
ejde-515	374	10	,	,	PUNCT
ejde-515	374	11	b.	b.	PROPN
ejde-515	374	12	;	;	PUNCT
ejde-515	374	13	asymptotic	asymptotic	ADJ
ejde-515	374	14	behaviour	behaviour	NOUN
ejde-515	374	15	of	of	ADP
ejde-515	374	16	non	non	ADJ
ejde-515	374	17	-	-	ADJ
ejde-515	374	18	autonomous	autonomous	ADJ
ejde-515	374	19	difference	difference	NOUN
ejde-515	374	20	inclusions	inclusion	NOUN
ejde-515	374	21	,	,	PUNCT
ejde-515	374	22	systems	system	NOUN
ejde-515	374	23	control	control	VERB
ejde-515	374	24	lett	lett	PROPN
ejde-515	374	25	.	.	PROPN
ejde-515	374	26	,	,	PUNCT
ejde-515	374	27	33	33	NUM
ejde-515	374	28	,	,	PUNCT
ejde-515	374	29	(	(	PUNCT
ejde-515	374	30	1998	1998	NUM
ejde-515	374	31	)	)	PUNCT
ejde-515	374	32	275–280	275–280	NUM
ejde-515	374	33	.	.	PUNCT
ejde-515	375	1	[	[	X
ejde-515	375	2	23	23	NUM
ejde-515	375	3	]	]	X
ejde-515	375	4	kloeden	kloeden	PROPN
ejde-515	375	5	,	,	PUNCT
ejde-515	375	6	p.	p.	PROPN
ejde-515	375	7	e.	e.	PROPN
ejde-515	375	8	;	;	PUNCT
ejde-515	375	9	pullback	pullback	NOUN
ejde-515	375	10	attractors	attractor	NOUN
ejde-515	375	11	in	in	ADP
ejde-515	375	12	nonautonomous	nonautonomous	ADJ
ejde-515	375	13	difference	difference	NOUN
ejde-515	375	14	equations	equation	NOUN
ejde-515	375	15	.	.	PUNCT
ejde-515	376	1	j.	j.	PROPN
ejde-515	376	2	differ	differ	VERB
ejde-515	376	3	.	.	PUNCT
ejde-515	377	1	equations	equation	NOUN
ejde-515	377	2	appl	appl	PROPN
ejde-515	377	3	.	.	PROPN
ejde-515	377	4	,	,	PUNCT
ejde-515	377	5	6	6	NUM
ejde-515	377	6	no	no	NOUN
ejde-515	377	7	.	.	NOUN
ejde-515	377	8	1	1	NUM
ejde-515	377	9	(	(	PUNCT
ejde-515	377	10	2000	2000	NUM
ejde-515	377	11	)	)	PUNCT
ejde-515	377	12	,	,	PUNCT
ejde-515	377	13	33–52	33–52	NUM
ejde-515	377	14	.	.	PUNCT
ejde-515	378	1	[	[	X
ejde-515	378	2	24	24	NUM
ejde-515	378	3	]	]	X
ejde-515	378	4	ladas	ladas	PROPN
ejde-515	378	5	,	,	PUNCT
ejde-515	378	6	g.	g.	PROPN
ejde-515	378	7	e.	e.	PROPN
ejde-515	378	8	;	;	PUNCT
ejde-515	378	9	lakshmikantham	lakshmikantham	PROPN
ejde-515	378	10	,	,	PUNCT
ejde-515	378	11	v.	v.	ADV
ejde-515	378	12	;	;	PUNCT
ejde-515	378	13	differential	differential	ADJ
ejde-515	378	14	equations	equation	NOUN
ejde-515	378	15	in	in	ADP
ejde-515	378	16	abstract	abstract	ADJ
ejde-515	378	17	spaces	space	NOUN
ejde-515	378	18	,	,	PUNCT
ejde-515	378	19	academic	academic	ADJ
ejde-515	378	20	press	press	NOUN
ejde-515	378	21	,	,	PUNCT
ejde-515	378	22	new	new	PROPN
ejde-515	378	23	york	york	PROPN
ejde-515	378	24	,	,	PUNCT
ejde-515	378	25	1972	1972	NUM
ejde-515	378	26	.	.	PUNCT
ejde-515	379	1	[	[	X
ejde-515	379	2	25	25	NUM
ejde-515	379	3	]	]	X
ejde-515	379	4	laing	laing	PROPN
ejde-515	379	5	,	,	PUNCT
ejde-515	379	6	c.	c.	PROPN
ejde-515	379	7	r.	r.	PROPN
ejde-515	379	8	;	;	PUNCT
ejde-515	379	9	troy	troy	PROPN
ejde-515	379	10	,	,	PUNCT
ejde-515	379	11	w.	w.	PROPN
ejde-515	379	12	c.	c.	PROPN
ejde-515	379	13	;	;	PUNCT
ejde-515	379	14	gutkin	gutkin	PROPN
ejde-515	379	15	,	,	PUNCT
ejde-515	379	16	b.	b.	PROPN
ejde-515	379	17	;	;	PUNCT
ejde-515	379	18	ermentrout	ermentrout	PROPN
ejde-515	379	19	,	,	PUNCT
ejde-515	379	20	g.	g.	PROPN
ejde-515	379	21	b.	b.	PROPN
ejde-515	379	22	;	;	PUNCT
ejde-515	379	23	multiple	multiple	ADJ
ejde-515	379	24	bumps	bump	NOUN
ejde-515	379	25	in	in	ADP
ejde-515	379	26	a	a	DET
ejde-515	379	27	neuronal	neuronal	ADJ
ejde-515	379	28	model	model	NOUN
ejde-515	379	29	of	of	ADP
ejde-515	379	30	working	work	VERB
ejde-515	379	31	memory	memory	NOUN
ejde-515	379	32	.	.	PUNCT
ejde-515	380	1	siam	siam	PROPN
ejde-515	380	2	journal	journal	PROPN
ejde-515	380	3	on	on	ADP
ejde-515	380	4	applied	apply	VERB
ejde-515	380	5	mathematics	mathematic	NOUN
ejde-515	380	6	,	,	PUNCT
ejde-515	380	7	63	63	NUM
ejde-515	380	8	no	no	NOUN
ejde-515	380	9	.	.	NOUN
ejde-515	380	10	1	1	NUM
ejde-515	380	11	(	(	PUNCT
ejde-515	380	12	2002	2002	NUM
ejde-515	380	13	)	)	PUNCT
ejde-515	380	14	,	,	PUNCT
ejde-515	380	15	206–225	206–225	NUM
ejde-515	380	16	.	.	PUNCT
ejde-515	381	1	[	[	X
ejde-515	381	2	26	26	NUM
ejde-515	381	3	]	]	X
ejde-515	381	4	pinto	pinto	NOUN
ejde-515	381	5	,	,	PUNCT
ejde-515	381	6	d.	d.	PROPN
ejde-515	381	7	j.	j.	PROPN
ejde-515	381	8	;	;	PUNCT
ejde-515	381	9	ermentrout	ermentrout	PROPN
ejde-515	381	10	,	,	PUNCT
ejde-515	381	11	g.	g.	PROPN
ejde-515	381	12	b.	b.	PROPN
ejde-515	381	13	;	;	PUNCT
ejde-515	381	14	spatially	spatially	ADV
ejde-515	381	15	structured	structure	VERB
ejde-515	381	16	activity	activity	NOUN
ejde-515	381	17	in	in	ADP
ejde-515	381	18	synaptically	synaptically	ADV
ejde-515	381	19	coupled	couple	VERB
ejde-515	381	20	neuronal	neuronal	ADJ
ejde-515	381	21	networks	network	NOUN
ejde-515	381	22	:	:	PUNCT
ejde-515	381	23	i	i	PRON
ejde-515	381	24	traveling	travel	VERB
ejde-515	381	25	fronts	front	NOUN
ejde-515	381	26	and	and	CCONJ
ejde-515	381	27	pulses	pulse	NOUN
ejde-515	381	28	.	.	PUNCT
ejde-515	382	1	siam	siam	PROPN
ejde-515	382	2	journal	journal	PROPN
ejde-515	382	3	on	on	ADP
ejde-515	382	4	applied	apply	VERB
ejde-515	382	5	mathematics	mathematic	NOUN
ejde-515	382	6	,	,	PUNCT
ejde-515	382	7	62	62	NUM
ejde-515	382	8	(	(	PUNCT
ejde-515	382	9	2001	2001	NUM
ejde-515	382	10	)	)	PUNCT
ejde-515	382	11	,	,	PUNCT
ejde-515	382	12	206–225	206–225	NUM
ejde-515	382	13	.	.	PUNCT
ejde-515	383	1	[	[	X
ejde-515	383	2	27	27	NUM
ejde-515	383	3	]	]	X
ejde-515	383	4	rall	rall	PROPN
ejde-515	383	5	,	,	PUNCT
ejde-515	383	6	l.	l.	PROPN
ejde-515	383	7	b.	b.	PROPN
ejde-515	383	8	;	;	PUNCT
ejde-515	383	9	nonlinear	nonlinear	ADJ
ejde-515	383	10	functional	functional	ADJ
ejde-515	383	11	analysis	analysis	NOUN
ejde-515	383	12	and	and	CCONJ
ejde-515	383	13	applications	application	NOUN
ejde-515	383	14	.	.	PUNCT
ejde-515	384	1	academic	academic	ADJ
ejde-515	384	2	press	press	NOUN
ejde-515	384	3	,	,	PUNCT
ejde-515	384	4	new	new	ADJ
ejde-515	384	5	yorklondon	yorklondon	NOUN
ejde-515	384	6	,	,	PUNCT
ejde-515	384	7	1971	1971	NUM
ejde-515	384	8	.	.	PUNCT
ejde-515	385	1	[	[	X
ejde-515	385	2	28	28	NUM
ejde-515	385	3	]	]	X
ejde-515	385	4	rukatmatakul	rukatmatakul	NOUN
ejde-515	385	5	,	,	PUNCT
ejde-515	385	6	s.	s.	PROPN
ejde-515	385	7	;	;	PUNCT
ejde-515	385	8	yimprayoon	yimprayoon	ADV
ejde-515	385	9	,	,	PUNCT
ejde-515	385	10	p.	p.	NOUN
ejde-515	385	11	;	;	PUNCT
ejde-515	385	12	traveling	travel	VERB
ejde-515	385	13	wave	wave	NOUN
ejde-515	385	14	front	front	ADJ
ejde-515	385	15	solutions	solution	NOUN
ejde-515	385	16	in	in	ADP
ejde-515	385	17	lateral	lateral	ADJ
ejde-515	385	18	-	-	PUNCT
ejde-515	385	19	excitatory	excitatory	NOUN
ejde-515	385	20	neuronal	neuronal	ADJ
ejde-515	385	21	networks	network	NOUN
ejde-515	385	22	.	.	PUNCT
ejde-515	386	1	songklanakarin	songklanakarin	PROPN
ejde-515	386	2	j.	j.	PROPN
ejde-515	386	3	sci	sci	PROPN
ejde-515	386	4	.	.	PUNCT
ejde-515	386	5	tecnol	tecnol	PROPN
ejde-515	386	6	.	.	PROPN
ejde-515	386	7	,	,	PUNCT
ejde-515	386	8	30	30	NUM
ejde-515	386	9	no	no	NOUN
ejde-515	386	10	.	.	NOUN
ejde-515	386	11	3	3	NUM
ejde-515	386	12	(	(	PUNCT
ejde-515	386	13	2008	2008	NUM
ejde-515	386	14	)	)	PUNCT
ejde-515	386	15	,	,	PUNCT
ejde-515	386	16	313–321	313–321	NUM
ejde-515	386	17	.	.	PUNCT
ejde-515	387	1	[	[	X
ejde-515	387	2	29	29	NUM
ejde-515	387	3	]	]	PUNCT
ejde-515	387	4	sandamirskaya	sandamirskaya	NOUN
ejde-515	387	5	,	,	PUNCT
ejde-515	387	6	y.	y.	PROPN
ejde-515	387	7	;	;	PUNCT
ejde-515	387	8	dynamic	dynamic	ADJ
ejde-515	387	9	neural	neural	ADJ
ejde-515	387	10	fields	field	NOUN
ejde-515	387	11	as	as	ADP
ejde-515	387	12	a	a	DET
ejde-515	387	13	step	step	NOUN
ejde-515	387	14	toward	toward	ADP
ejde-515	387	15	cognitive	cognitive	ADJ
ejde-515	387	16	neuromorphic	neuromorphic	ADJ
ejde-515	387	17	architectures	architecture	NOUN
ejde-515	387	18	.	.	PUNCT
ejde-515	388	1	frontiers	frontier	NOUN
ejde-515	388	2	in	in	ADP
ejde-515	388	3	neuroscience	neuroscience	NOUN
ejde-515	388	4	,	,	PUNCT
ejde-515	388	5	30	30	NUM
ejde-515	388	6	no	no	NOUN
ejde-515	388	7	.	.	NOUN
ejde-515	388	8	3	3	NUM
ejde-515	388	9	,	,	PUNCT
ejde-515	388	10	(	(	PUNCT
ejde-515	388	11	2008	2008	NUM
ejde-515	388	12	)	)	PUNCT
ejde-515	388	13	,	,	PUNCT
ejde-515	388	14	313–321	313–321	NUM
ejde-515	388	15	.	.	PUNCT
ejde-515	389	1	[	[	X
ejde-515	389	2	30	30	NUM
ejde-515	389	3	]	]	X
ejde-515	389	4	sell	sell	NOUN
ejde-515	389	5	,	,	PUNCT
ejde-515	389	6	g.	g.	PROPN
ejde-515	389	7	r.	r.	PROPN
ejde-515	389	8	;	;	PUNCT
ejde-515	389	9	non	non	ADJ
ejde-515	389	10	-	-	ADJ
ejde-515	389	11	autonomous	autonomous	ADJ
ejde-515	389	12	differential	differential	ADJ
ejde-515	389	13	equations	equation	NOUN
ejde-515	389	14	and	and	CCONJ
ejde-515	389	15	dynamical	dynamical	ADJ
ejde-515	389	16	systems	system	NOUN
ejde-515	389	17	,	,	PUNCT
ejde-515	389	18	trans	trans	PROPN
ejde-515	389	19	.	.	PROPN
ejde-515	390	1	amer	amer	PROPN
ejde-515	390	2	.	.	PUNCT
ejde-515	390	3	math	math	PROPN
ejde-515	390	4	.	.	PUNCT
ejde-515	391	1	soc	soc	PROPN
ejde-515	391	2	.	.	PUNCT
ejde-515	391	3	,	,	PUNCT
ejde-515	391	4	127	127	NUM
ejde-515	391	5	(	(	PUNCT
ejde-515	391	6	1967	1967	NUM
ejde-515	391	7	)	)	PUNCT
ejde-515	391	8	,	,	PUNCT
ejde-515	391	9	241–283	241–283	NUM
ejde-515	391	10	.	.	PUNCT
ejde-515	392	1	[	[	X
ejde-515	392	2	31	31	NUM
ejde-515	392	3	]	]	PUNCT
ejde-515	392	4	thelen	thelen	PROPN
ejde-515	392	5	,	,	PUNCT
ejde-515	392	6	e.	e.	PROPN
ejde-515	392	7	;	;	PUNCT
ejde-515	392	8	schoner	schoner	NOUN
ejde-515	392	9	,	,	PUNCT
ejde-515	392	10	g.	g.	PROPN
ejde-515	392	11	;	;	PUNCT
ejde-515	392	12	scheier	scheier	PROPN
ejde-515	392	13	,	,	PUNCT
ejde-515	392	14	c.	c.	PROPN
ejde-515	392	15	;	;	PUNCT
ejde-515	392	16	smith	smith	PROPN
ejde-515	392	17	,	,	PUNCT
ejde-515	392	18	l.	l.	PROPN
ejde-515	392	19	b.	b.	PROPN
ejde-515	392	20	;	;	PUNCT
ejde-515	392	21	the	the	DET
ejde-515	392	22	dynamics	dynamic	NOUN
ejde-515	392	23	of	of	ADP
ejde-515	392	24	embodiment	embodiment	NOUN
ejde-515	392	25	:	:	PUNCT
ejde-515	392	26	a	a	DET
ejde-515	392	27	field	field	NOUN
ejde-515	392	28	theory	theory	NOUN
ejde-515	392	29	of	of	ADP
ejde-515	392	30	infant	infant	PROPN
ejde-515	392	31	perseverative	perseverative	NOUN
ejde-515	392	32	reaching	reach	VERB
ejde-515	392	33	,	,	PUNCT
ejde-515	392	34	behavioral	behavioral	ADJ
ejde-515	392	35	and	and	CCONJ
ejde-515	392	36	brain	brain	NOUN
ejde-515	392	37	sciences	science	NOUN
ejde-515	392	38	,	,	PUNCT
ejde-515	392	39	24	24	NUM
ejde-515	392	40	(	(	PUNCT
ejde-515	392	41	2001	2001	NUM
ejde-515	392	42	)	)	PUNCT
ejde-515	392	43	,	,	PUNCT
ejde-515	392	44	1–34	1–34	NOUN
ejde-515	392	45	.	.	PUNCT
ejde-515	393	1	[	[	X
ejde-515	393	2	32	32	NUM
ejde-515	393	3	]	]	SYM
ejde-515	393	4	wilson	wilson	PROPN
ejde-515	393	5	,	,	PUNCT
ejde-515	393	6	h.	h.	PROPN
ejde-515	393	7	r.	r.	PROPN
ejde-515	393	8	;	;	PUNCT
ejde-515	393	9	cowan	cowan	PROPN
ejde-515	393	10	,	,	PUNCT
ejde-515	393	11	j.	j.	PROPN
ejde-515	393	12	d.	d.	PROPN
ejde-515	393	13	;	;	PUNCT
ejde-515	393	14	excitatory	excitatory	NOUN
ejde-515	393	15	and	and	CCONJ
ejde-515	393	16	inhibitory	inhibitory	ADJ
ejde-515	393	17	interactions	interaction	NOUN
ejde-515	393	18	in	in	ADP
ejde-515	393	19	localized	localized	ADJ
ejde-515	393	20	populations	population	NOUN
ejde-515	393	21	of	of	ADP
ejde-515	393	22	model	model	NOUN
ejde-515	393	23	neurons	neuron	NOUN
ejde-515	393	24	.	.	PUNCT
ejde-515	394	1	biophys	biophy	NOUN
ejde-515	394	2	.	.	PUNCT
ejde-515	395	1	j.	j.	PROPN
ejde-515	395	2	,	,	PUNCT
ejde-515	395	3	12	12	NUM
ejde-515	395	4	(	(	PUNCT
ejde-515	395	5	1972	1972	NUM
ejde-515	395	6	)	)	PUNCT
ejde-515	395	7	,	,	PUNCT
ejde-515	395	8	1–24	1–24	PROPN
ejde-515	395	9	.	.	PUNCT
ejde-515	396	1	[	[	X
ejde-515	396	2	33	33	NUM
ejde-515	396	3	]	]	X
ejde-515	396	4	zhang	zhang	PROPN
ejde-515	396	5	,	,	PUNCT
ejde-515	396	6	l.	l.	PROPN
ejde-515	396	7	;	;	PUNCT
ejde-515	396	8	existence	existence	NOUN
ejde-515	396	9	,	,	PUNCT
ejde-515	396	10	uniqueness	uniqueness	NOUN
ejde-515	396	11	and	and	CCONJ
ejde-515	396	12	exponential	exponential	ADJ
ejde-515	396	13	stability	stability	NOUN
ejde-515	396	14	of	of	ADP
ejde-515	396	15	traveling	travel	VERB
ejde-515	396	16	wave	wave	NOUN
ejde-515	396	17	solutions	solution	NOUN
ejde-515	396	18	of	of	ADP
ejde-515	396	19	some	some	DET
ejde-515	396	20	integral	integral	ADJ
ejde-515	396	21	differential	differential	ADJ
ejde-515	396	22	equations	equation	NOUN
ejde-515	396	23	arising	arise	VERB
ejde-515	396	24	from	from	ADP
ejde-515	396	25	neuronal	neuronal	ADJ
ejde-515	396	26	networks	network	NOUN
ejde-515	396	27	,	,	PUNCT
ejde-515	396	28	journal	journal	NOUN
ejde-515	396	29	of	of	ADP
ejde-515	396	30	differential	differential	ADJ
ejde-515	396	31	equations	equation	NOUN
ejde-515	396	32	,	,	PUNCT
ejde-515	396	33	197	197	NUM
ejde-515	396	34	(	(	PUNCT
ejde-515	396	35	2004	2004	NUM
ejde-515	396	36	)	)	PUNCT
ejde-515	396	37	,	,	PUNCT
ejde-515	396	38	162–196	162–196	NUM
ejde-515	396	39	.	.	PUNCT
ejde-515	396	40	severino	severino	PROPN
ejde-515	396	41	horácio	horácio	PROPN
ejde-515	396	42	da	da	PROPN
ejde-515	396	43	silva	silva	PROPN
ejde-515	396	44	universidade	universidade	PROPN
ejde-515	396	45	federal	federal	PROPN
ejde-515	396	46	de	de	PROPN
ejde-515	396	47	campina	campina	PROPN
ejde-515	396	48	grande	grande	PROPN
ejde-515	396	49	,	,	PUNCT
ejde-515	396	50	unidade	unidade	ADJ
ejde-515	396	51	acadêmica	acadêmica	PROPN
ejde-515	396	52	de	de	PROPN
ejde-515	396	53	matemática	matemática	PROPN
ejde-515	396	54	,	,	PUNCT
ejde-515	396	55	58429900	58429900	NUM
ejde-515	396	56	,	,	PUNCT
ejde-515	396	57	campina	campina	PROPN
ejde-515	396	58	grande	grande	PROPN
ejde-515	396	59	,	,	PUNCT
ejde-515	396	60	pb	pb	PROPN
ejde-515	396	61	,	,	PUNCT
ejde-515	396	62	brazil	brazil	PROPN
ejde-515	396	63	email	email	NOUN
ejde-515	396	64	address	address	NOUN
ejde-515	396	65	:	:	PUNCT
ejde-515	396	66	horacio@mat.ufcg.edu.br	horacio@mat.ufcg.edu.br	PROPN
ejde-515	396	67	,	,	PUNCT
ejde-515	396	68	horaciousp@gmail.com	horaciousp@gmail.com	NOUN
ejde-515	396	69	1	1	NUM
ejde-515	396	70	.	.	PUNCT
ejde-515	396	71	introduction	introduction	NOUN
ejde-515	396	72	2	2	NUM
ejde-515	396	73	.	.	PUNCT
ejde-515	396	74	flow	flow	NOUN
ejde-515	396	75	generated	generate	VERB
ejde-515	396	76	by	by	ADP
ejde-515	396	77	the	the	DET
ejde-515	396	78	model	model	NOUN
ejde-515	396	79	problem	problem	NOUN
ejde-515	396	80	2.1	2.1	NUM
ejde-515	396	81	.	.	PUNCT
ejde-515	397	1	well	well	INTJ
ejde-515	397	2	posedness	posedness	NOUN
ejde-515	397	3	2.2	2.2	NUM
ejde-515	397	4	.	.	PUNCT
ejde-515	398	1	smoothness	smoothness	NOUN
ejde-515	398	2	of	of	ADP
ejde-515	398	3	the	the	DET
ejde-515	398	4	evolution	evolution	NOUN
ejde-515	398	5	process	process	NOUN
ejde-515	398	6	3	3	NUM
ejde-515	398	7	.	.	PUNCT
ejde-515	398	8	existence	existence	NOUN
ejde-515	398	9	of	of	ADP
ejde-515	398	10	a	a	DET
ejde-515	398	11	pullback	pullback	NOUN
ejde-515	398	12	attractor	attractor	NOUN
ejde-515	398	13	4	4	NUM
ejde-515	398	14	.	.	PUNCT
ejde-515	399	1	continuity	continuity	NOUN
ejde-515	399	2	with	with	ADP
ejde-515	399	3	respect	respect	NOUN
ejde-515	399	4	to	to	ADP
ejde-515	399	5	parameter	parameter	NOUN
ejde-515	399	6	s	s	PART
ejde-515	399	7	4.1	4.1	NUM
ejde-515	399	8	.	.	PUNCT
ejde-515	400	1	continuity	continuity	NOUN
ejde-515	400	2	of	of	ADP
ejde-515	400	3	the	the	DET
ejde-515	400	4	process	process	NOUN
ejde-515	400	5	with	with	ADP
ejde-515	400	6	respect	respect	NOUN
ejde-515	400	7	to	to	ADP
ejde-515	400	8	external	external	ADJ
ejde-515	400	9	stimuli	stimulus	NOUN
ejde-515	400	10	4.2	4.2	NUM
ejde-515	400	11	.	.	PUNCT
ejde-515	401	1	upper	upper	ADJ
ejde-515	401	2	semicontinuity	semicontinuity	NOUN
ejde-515	401	3	of	of	ADP
ejde-515	401	4	the	the	DET
ejde-515	401	5	pullback	pullback	NOUN
ejde-515	401	6	attractors	attractor	NOUN
ejde-515	401	7	5	5	NUM
ejde-515	401	8	.	.	PUNCT
ejde-515	401	9	discussions	discussion	NOUN
ejde-515	401	10	and	and	CCONJ
ejde-515	401	11	biological	biological	ADJ
ejde-515	401	12	interpretation	interpretation	NOUN
ejde-515	401	13	acknowledgments	acknowledgment	NOUN
ejde-515	401	14	references	reference	NOUN