id	sid	tid	token	lemma	pos
ejpam-5017	1	1	european	european	PROPN
ejpam-5017	1	2	journal	journal	PROPN
ejpam-5017	1	3	of	of	ADP
ejpam-5017	1	4	pure	pure	ADJ
ejpam-5017	1	5	and	and	CCONJ
ejpam-5017	1	6	applied	apply	VERB
ejpam-5017	1	7	mathematics	mathematic	NOUN
ejpam-5017	1	8	vol	vol	NOUN
ejpam-5017	1	9	.	.	PROPN
ejpam-5017	2	1	17	17	NUM
ejpam-5017	2	2	,	,	PUNCT
ejpam-5017	2	3	no	no	INTJ
ejpam-5017	2	4	.	.	NOUN
ejpam-5017	2	5	2	2	NUM
ejpam-5017	2	6	,	,	PUNCT
ejpam-5017	2	7	2024	2024	NUM
ejpam-5017	2	8	,	,	PUNCT
ejpam-5017	2	9	1321	1321	NUM
ejpam-5017	2	10	-	-	SYM
ejpam-5017	2	11	1334	1334	NUM
ejpam-5017	2	12	issn	issn	PROPN
ejpam-5017	2	13	1307	1307	NUM
ejpam-5017	2	14	-	-	SYM
ejpam-5017	2	15	5543	5543	NUM
ejpam-5017	2	16	–	–	PUNCT
ejpam-5017	3	1	ejpam.com	ejpam.com	X
ejpam-5017	3	2	published	publish	VERB
ejpam-5017	3	3	by	by	ADP
ejpam-5017	3	4	new	new	PROPN
ejpam-5017	3	5	york	york	PROPN
ejpam-5017	3	6	business	business	PROPN
ejpam-5017	3	7	global	global	ADJ
ejpam-5017	3	8	asymptotic	asymptotic	ADJ
ejpam-5017	3	9	behavior	behavior	NOUN
ejpam-5017	3	10	of	of	ADP
ejpam-5017	3	11	global	global	ADJ
ejpam-5017	3	12	solutions	solution	NOUN
ejpam-5017	3	13	of	of	ADP
ejpam-5017	3	14	an	an	DET
ejpam-5017	3	15	anomalous	anomalous	ADJ
ejpam-5017	3	16	gray	gray	ADJ
ejpam-5017	3	17	-	-	PUNCT
ejpam-5017	3	18	scott	scott	NOUN
ejpam-5017	3	19	model	model	NOUN
ejpam-5017	3	20	maroua	maroua	PROPN
ejpam-5017	3	21	mebarki	mebarki	PROPN
ejpam-5017	3	22	department	department	NOUN
ejpam-5017	3	23	of	of	ADP
ejpam-5017	3	24	mathematics	mathematics	PROPN
ejpam-5017	3	25	and	and	CCONJ
ejpam-5017	3	26	computer	computer	NOUN
ejpam-5017	3	27	science	science	NOUN
ejpam-5017	3	28	,	,	PUNCT
ejpam-5017	3	29	faculty	faculty	NOUN
ejpam-5017	3	30	of	of	ADP
ejpam-5017	3	31	technology	technology	NOUN
ejpam-5017	3	32	and	and	CCONJ
ejpam-5017	3	33	sciences/	sciences/	NUM
ejpam-5017	3	34	amine	amine	ADJ
ejpam-5017	3	35	elokkal	elokkal	NOUN
ejpam-5017	3	36	el	el	PROPN
ejpam-5017	3	37	hadj	hadj	PROPN
ejpam-5017	3	38	moussa	moussa	PROPN
ejpam-5017	3	39	ag	ag	PROPN
ejpam-5017	3	40	akhamouk	akhamouk	PROPN
ejpam-5017	3	41	,	,	PUNCT
ejpam-5017	3	42	p.o.box	p.o.box	PROPN
ejpam-5017	3	43	10034	10034	NUM
ejpam-5017	3	44	,	,	PUNCT
ejpam-5017	3	45	tamanrasset	tamanrasset	NOUN
ejpam-5017	3	46	11000	11000	NUM
ejpam-5017	3	47	,	,	PUNCT
ejpam-5017	3	48	algeria	algeria	PROPN
ejpam-5017	3	49	abstract	abstract	NOUN
ejpam-5017	3	50	.	.	PUNCT
ejpam-5017	4	1	the	the	DET
ejpam-5017	4	2	object	object	NOUN
ejpam-5017	4	3	of	of	ADP
ejpam-5017	4	4	this	this	DET
ejpam-5017	4	5	paper	paper	NOUN
ejpam-5017	4	6	is	be	AUX
ejpam-5017	4	7	to	to	PART
ejpam-5017	4	8	prove	prove	VERB
ejpam-5017	4	9	that	that	DET
ejpam-5017	4	10	existence	existence	NOUN
ejpam-5017	4	11	global	global	ADJ
ejpam-5017	4	12	and	and	CCONJ
ejpam-5017	4	13	asymptotic	asymptotic	ADJ
ejpam-5017	4	14	behavior	behavior	NOUN
ejpam-5017	4	15	of	of	ADP
ejpam-5017	4	16	solutions	solution	NOUN
ejpam-5017	4	17	for	for	ADP
ejpam-5017	4	18	anomalous	anomalous	ADJ
ejpam-5017	4	19	coupled	couple	VERB
ejpam-5017	4	20	reaction	reaction	NOUN
ejpam-5017	4	21	diffusion	diffusion	NOUN
ejpam-5017	4	22	system	system	NOUN
ejpam-5017	4	23	(	(	PUNCT
ejpam-5017	4	24	gray	gray	ADJ
ejpam-5017	4	25	-	-	PUNCT
ejpam-5017	4	26	scott	scott	PROPN
ejpam-5017	4	27	model	model	NOUN
ejpam-5017	4	28	)	)	PUNCT
ejpam-5017	4	29	with	with	ADP
ejpam-5017	4	30	homogeneous	homogeneous	ADJ
ejpam-5017	4	31	neumann	neumann	PROPN
ejpam-5017	4	32	boundary	boundary	ADJ
ejpam-5017	4	33	conditions	condition	NOUN
ejpam-5017	4	34	.	.	PUNCT
ejpam-5017	5	1	the	the	DET
ejpam-5017	5	2	existence	existence	NOUN
ejpam-5017	5	3	and	and	CCONJ
ejpam-5017	5	4	uniqueness	uniqueness	NOUN
ejpam-5017	5	5	of	of	ADP
ejpam-5017	5	6	the	the	DET
ejpam-5017	5	7	local	local	ADJ
ejpam-5017	5	8	solution	solution	NOUN
ejpam-5017	5	9	are	be	AUX
ejpam-5017	5	10	given	give	VERB
ejpam-5017	5	11	by	by	ADP
ejpam-5017	5	12	the	the	DET
ejpam-5017	5	13	banach	banach	ADV
ejpam-5017	5	14	fixed	fix	VERB
ejpam-5017	5	15	point	point	NOUN
ejpam-5017	5	16	theorem	theorem	VERB
ejpam-5017	5	17	.	.	PUNCT
ejpam-5017	6	1	further	far	ADV
ejpam-5017	6	2	,	,	PUNCT
ejpam-5017	6	3	the	the	DET
ejpam-5017	6	4	asymptotic	asymptotic	ADJ
ejpam-5017	6	5	behavior	behavior	NOUN
ejpam-5017	6	6	is	be	AUX
ejpam-5017	6	7	investigated	investigate	VERB
ejpam-5017	6	8	by	by	ADP
ejpam-5017	6	9	technique	technique	NOUN
ejpam-5017	6	10	semi	semi	ADJ
ejpam-5017	6	11	group	group	NOUN
ejpam-5017	6	12	estimates	estimate	NOUN
ejpam-5017	6	13	and	and	CCONJ
ejpam-5017	6	14	the	the	DET
ejpam-5017	6	15	sobolev	sobolev	NOUN
ejpam-5017	6	16	embedding	embed	VERB
ejpam-5017	6	17	theorem	theorem	NOUN
ejpam-5017	6	18	.	.	PUNCT
ejpam-5017	7	1	2020	2020	NUM
ejpam-5017	7	2	mathematics	mathematics	PROPN
ejpam-5017	7	3	subject	subject	NOUN
ejpam-5017	7	4	classifications	classification	NOUN
ejpam-5017	7	5	:	:	PUNCT
ejpam-5017	7	6	35k51	35k51	NUM
ejpam-5017	7	7	,	,	PUNCT
ejpam-5017	7	8	35a01	35a01	NUM
ejpam-5017	7	9	,	,	PUNCT
ejpam-5017	7	10	35b40	35b40	NUM
ejpam-5017	7	11	key	key	ADJ
ejpam-5017	7	12	words	word	NOUN
ejpam-5017	7	13	and	and	CCONJ
ejpam-5017	7	14	phrases	phrase	NOUN
ejpam-5017	7	15	:	:	PUNCT
ejpam-5017	7	16	parabolic	parabolic	ADJ
ejpam-5017	7	17	system	system	NOUN
ejpam-5017	7	18	,	,	PUNCT
ejpam-5017	7	19	fractional	fractional	PROPN
ejpam-5017	7	20	laplacian	laplacian	PROPN
ejpam-5017	7	21	,	,	PUNCT
ejpam-5017	7	22	local	local	ADJ
ejpam-5017	7	23	and	and	CCONJ
ejpam-5017	7	24	global	global	ADJ
ejpam-5017	7	25	existence	existence	NOUN
ejpam-5017	7	26	,	,	PUNCT
ejpam-5017	7	27	asymptotic	asymptotic	ADJ
ejpam-5017	7	28	behavior	behavior	NOUN
ejpam-5017	7	29	1	1	NUM
ejpam-5017	7	30	.	.	X
ejpam-5017	7	31	introduction	introduction	NOUN
ejpam-5017	7	32	the	the	DET
ejpam-5017	7	33	gray	gray	ADJ
ejpam-5017	7	34	-	-	PUNCT
ejpam-5017	7	35	scott	scott	NOUN
ejpam-5017	7	36	system	system	NOUN
ejpam-5017	7	37	is	be	AUX
ejpam-5017	7	38	a	a	DET
ejpam-5017	7	39	reaction	reaction	NOUN
ejpam-5017	7	40	-	-	PUNCT
ejpam-5017	7	41	diffusion	diffusion	NOUN
ejpam-5017	7	42	system	system	NOUN
ejpam-5017	7	43	.	.	PUNCT
ejpam-5017	8	1	this	this	PRON
ejpam-5017	8	2	means	mean	VERB
ejpam-5017	8	3	that	that	SCONJ
ejpam-5017	8	4	it	it	PRON
ejpam-5017	8	5	models	model	VERB
ejpam-5017	8	6	a	a	DET
ejpam-5017	8	7	process	process	NOUN
ejpam-5017	8	8	that	that	PRON
ejpam-5017	8	9	consists	consist	VERB
ejpam-5017	8	10	of	of	ADP
ejpam-5017	8	11	a	a	DET
ejpam-5017	8	12	reaction	reaction	NOUN
ejpam-5017	8	13	and	and	CCONJ
ejpam-5017	8	14	diffusion	diffusion	NOUN
ejpam-5017	8	15	.	.	PUNCT
ejpam-5017	9	1	in	in	ADP
ejpam-5017	9	2	the	the	DET
ejpam-5017	9	3	case	case	NOUN
ejpam-5017	9	4	of	of	ADP
ejpam-5017	9	5	the	the	DET
ejpam-5017	9	6	gray	gray	ADJ
ejpam-5017	9	7	-	-	PUNCT
ejpam-5017	9	8	scott	scott	PROPN
ejpam-5017	9	9	model	model	NOUN
ejpam-5017	9	10	that	that	SCONJ
ejpam-5017	9	11	reaction	reaction	NOUN
ejpam-5017	9	12	is	be	AUX
ejpam-5017	9	13	a	a	DET
ejpam-5017	9	14	chemical	chemical	ADJ
ejpam-5017	9	15	reaction	reaction	NOUN
ejpam-5017	9	16	between	between	ADP
ejpam-5017	9	17	two	two	NUM
ejpam-5017	9	18	substances	substance	NOUN
ejpam-5017	9	19	w	w	NOUN
ejpam-5017	9	20	and	and	CCONJ
ejpam-5017	9	21	z	z	NOUN
ejpam-5017	9	22	,	,	PUNCT
ejpam-5017	9	23	both	both	PRON
ejpam-5017	9	24	of	of	ADP
ejpam-5017	9	25	which	which	PRON
ejpam-5017	9	26	diffuse	diffuse	VERB
ejpam-5017	9	27	over	over	ADP
ejpam-5017	9	28	time	time	NOUN
ejpam-5017	9	29	.	.	PUNCT
ejpam-5017	10	1	during	during	ADP
ejpam-5017	10	2	the	the	DET
ejpam-5017	10	3	reaction	reaction	NOUN
ejpam-5017	10	4	w	w	NOUN
ejpam-5017	10	5	gets	get	AUX
ejpam-5017	10	6	used	use	VERB
ejpam-5017	10	7	up	up	ADP
ejpam-5017	10	8	,	,	PUNCT
ejpam-5017	10	9	while	while	SCONJ
ejpam-5017	10	10	z	z	NOUN
ejpam-5017	10	11	is	be	AUX
ejpam-5017	10	12	produced	produce	VERB
ejpam-5017	10	13	.	.	PUNCT
ejpam-5017	11	1	the	the	DET
ejpam-5017	11	2	system	system	NOUN
ejpam-5017	11	3	is	be	AUX
ejpam-5017	11	4	characterised	characterise	VERB
ejpam-5017	11	5	by	by	ADP
ejpam-5017	11	6	two	two	NUM
ejpam-5017	11	7	parameters	parameter	NOUN
ejpam-5017	11	8	:	:	PUNCT
ejpam-5017	11	9	f	f	PROPN
ejpam-5017	11	10	is	be	AUX
ejpam-5017	11	11	the	the	DET
ejpam-5017	11	12	rate	rate	NOUN
ejpam-5017	11	13	at	at	ADP
ejpam-5017	11	14	which	which	PRON
ejpam-5017	11	15	is	be	AUX
ejpam-5017	11	16	replenished	replenish	VERB
ejpam-5017	11	17	,	,	PUNCT
ejpam-5017	11	18	and	and	CCONJ
ejpam-5017	11	19	k	k	PROPN
ejpam-5017	11	20	controls	control	VERB
ejpam-5017	11	21	the	the	DET
ejpam-5017	11	22	rate	rate	NOUN
ejpam-5017	11	23	at	at	ADP
ejpam-5017	11	24	which	which	PRON
ejpam-5017	11	25	z	z	NOUN
ejpam-5017	11	26	is	be	AUX
ejpam-5017	11	27	removed	remove	VERB
ejpam-5017	11	28	from	from	ADP
ejpam-5017	11	29	the	the	DET
ejpam-5017	11	30	system	system	NOUN
ejpam-5017	11	31	.	.	PUNCT
ejpam-5017	12	1	varying	vary	VERB
ejpam-5017	12	2	these	these	DET
ejpam-5017	12	3	parameters	parameter	NOUN
ejpam-5017	12	4	leads	lead	VERB
ejpam-5017	12	5	to	to	ADP
ejpam-5017	12	6	a	a	DET
ejpam-5017	12	7	wide	wide	ADJ
ejpam-5017	12	8	range	range	NOUN
ejpam-5017	12	9	of	of	ADP
ejpam-5017	12	10	interesting	interesting	ADJ
ejpam-5017	12	11	patterns	pattern	NOUN
ejpam-5017	12	12	,	,	PUNCT
ejpam-5017	12	13	some	some	PRON
ejpam-5017	12	14	of	of	ADP
ejpam-5017	12	15	which	which	PRON
ejpam-5017	12	16	look	look	VERB
ejpam-5017	12	17	quite	quite	ADV
ejpam-5017	12	18	familiar	familiar	ADJ
ejpam-5017	12	19	.	.	PUNCT
ejpam-5017	13	1	the	the	DET
ejpam-5017	13	2	gray	gray	ADJ
ejpam-5017	13	3	-	-	PUNCT
ejpam-5017	13	4	scott	scott	NOUN
ejpam-5017	13	5	system	system	NOUN
ejpam-5017	13	6	models	model	VERB
ejpam-5017	13	7	the	the	DET
ejpam-5017	13	8	chemical	chemical	NOUN
ejpam-5017	13	9	reaction	reaction	NOUN
ejpam-5017	13	10	w	w	PROPN
ejpam-5017	14	1	+	+	PUNCT
ejpam-5017	14	2	2z	2z	NUM
ejpam-5017	14	3	→	→	SYM
ejpam-5017	14	4	3z	3z	NUM
ejpam-5017	14	5	.	.	PUNCT
ejpam-5017	15	1	this	this	DET
ejpam-5017	15	2	reaction	reaction	NOUN
ejpam-5017	15	3	consumesw	consumesw	NOUN
ejpam-5017	15	4	and	and	CCONJ
ejpam-5017	15	5	produces	produce	VERB
ejpam-5017	15	6	z.	z.	PROPN
ejpam-5017	15	7	consequently	consequently	ADV
ejpam-5017	15	8	,	,	PUNCT
ejpam-5017	15	9	the	the	DET
ejpam-5017	15	10	amount	amount	NOUN
ejpam-5017	15	11	of	of	ADP
ejpam-5017	15	12	both	both	DET
ejpam-5017	15	13	substances	substance	NOUN
ejpam-5017	15	14	needs	need	VERB
ejpam-5017	15	15	to	to	PART
ejpam-5017	15	16	be	be	AUX
ejpam-5017	15	17	controlled	control	VERB
ejpam-5017	15	18	to	to	PART
ejpam-5017	15	19	maintain	maintain	VERB
ejpam-5017	15	20	the	the	DET
ejpam-5017	15	21	reaction	reaction	NOUN
ejpam-5017	15	22	.	.	PUNCT
ejpam-5017	16	1	this	this	PRON
ejpam-5017	16	2	is	be	AUX
ejpam-5017	16	3	done	do	VERB
ejpam-5017	16	4	by	by	ADP
ejpam-5017	16	5	adding	add	VERB
ejpam-5017	16	6	w	w	NOUN
ejpam-5017	16	7	at	at	ADP
ejpam-5017	16	8	the	the	DET
ejpam-5017	16	9	”	"	PUNCT
ejpam-5017	16	10	feed	feed	NOUN
ejpam-5017	16	11	rate	rate	NOUN
ejpam-5017	16	12	”	"	PUNCT
ejpam-5017	16	13	f	f	PROPN
ejpam-5017	16	14	and	and	CCONJ
ejpam-5017	16	15	removing	remove	VERB
ejpam-5017	16	16	z	z	NOUN
ejpam-5017	16	17	at	at	ADP
ejpam-5017	16	18	the	the	DET
ejpam-5017	16	19	”	"	PUNCT
ejpam-5017	16	20	kill	kill	NOUN
ejpam-5017	16	21	rate	rate	NOUN
ejpam-5017	16	22	”	"	PUNCT
ejpam-5017	16	23	k	k	PROPN
ejpam-5017	16	24	the	the	DET
ejpam-5017	16	25	removal	removal	NOUN
ejpam-5017	16	26	of	of	ADP
ejpam-5017	16	27	z	z	PROPN
ejpam-5017	16	28	can	can	AUX
ejpam-5017	16	29	also	also	ADV
ejpam-5017	16	30	be	be	AUX
ejpam-5017	16	31	described	describe	VERB
ejpam-5017	16	32	by	by	ADP
ejpam-5017	16	33	another	another	DET
ejpam-5017	16	34	chemical	chemical	NOUN
ejpam-5017	16	35	reaction	reaction	NOUN
ejpam-5017	16	36	:	:	PUNCT
ejpam-5017	17	1	z	z	NOUN
ejpam-5017	17	2	→	→	SYM
ejpam-5017	17	3	p.	p.	NOUN
ejpam-5017	17	4	for	for	ADP
ejpam-5017	17	5	this	this	DET
ejpam-5017	17	6	reaction	reaction	NOUN
ejpam-5017	17	7	p	p	NOUN
ejpam-5017	17	8	is	be	AUX
ejpam-5017	17	9	an	an	DET
ejpam-5017	17	10	inert	inert	ADJ
ejpam-5017	17	11	product	product	NOUN
ejpam-5017	17	12	,	,	PUNCT
ejpam-5017	17	13	meaning	mean	VERB
ejpam-5017	17	14	it	it	PRON
ejpam-5017	17	15	does	do	AUX
ejpam-5017	17	16	n’t	not	PART
ejpam-5017	17	17	react	react	VERB
ejpam-5017	17	18	.	.	PUNCT
ejpam-5017	18	1	in	in	ADP
ejpam-5017	18	2	this	this	DET
ejpam-5017	18	3	case	case	NOUN
ejpam-5017	18	4	the	the	DET
ejpam-5017	18	5	parameter	parameter	NOUN
ejpam-5017	18	6	k	k	PROPN
ejpam-5017	18	7	controls	control	VERB
ejpam-5017	18	8	the	the	DET
ejpam-5017	18	9	rate	rate	NOUN
ejpam-5017	18	10	of	of	ADP
ejpam-5017	18	11	the	the	DET
ejpam-5017	18	12	second	second	ADJ
ejpam-5017	18	13	reaction	reaction	NOUN
ejpam-5017	18	14	.	.	PUNCT
ejpam-5017	19	1	both	both	DET
ejpam-5017	19	2	substances	substance	VERB
ejpam-5017	19	3	diffuse	diffuse	VERB
ejpam-5017	19	4	over	over	ADP
ejpam-5017	19	5	time	time	NOUN
ejpam-5017	19	6	at	at	ADP
ejpam-5017	19	7	the	the	DET
ejpam-5017	19	8	diffusion	diffusion	NOUN
ejpam-5017	19	9	rates	rate	NOUN
ejpam-5017	19	10	d1	d1	PROPN
ejpam-5017	19	11	and	and	CCONJ
ejpam-5017	19	12	d2	d2	PROPN
ejpam-5017	19	13	.	.	PUNCT
ejpam-5017	20	1	the	the	DET
ejpam-5017	20	2	gray	gray	ADJ
ejpam-5017	20	3	-	-	PUNCT
ejpam-5017	20	4	scott	scott	NOUN
ejpam-5017	20	5	system	system	NOUN
ejpam-5017	20	6	is	be	AUX
ejpam-5017	20	7	defined	define	VERB
ejpam-5017	20	8	by	by	ADP
ejpam-5017	20	9	two	two	NUM
ejpam-5017	20	10	equations	equation	NOUN
ejpam-5017	20	11	that	that	PRON
ejpam-5017	20	12	describe	describe	VERB
ejpam-5017	20	13	the	the	DET
ejpam-5017	20	14	behavior	behavior	NOUN
ejpam-5017	20	15	of	of	ADP
ejpam-5017	20	16	two	two	NUM
ejpam-5017	20	17	reacting	react	VERB
ejpam-5017	20	18	substances	substance	NOUN
ejpam-5017	20	19	:	:	PUNCT
ejpam-5017	20	20	doi	doi	NOUN
ejpam-5017	20	21	:	:	PUNCT
ejpam-5017	20	22	https://doi.org/10.29020/nybg.ejpam.v17i2.5017	https://doi.org/10.29020/nybg.ejpam.v17i2.5017	DET
ejpam-5017	20	23	email	email	NOUN
ejpam-5017	20	24	address	address	NOUN
ejpam-5017	20	25	:	:	PUNCT
ejpam-5017	20	26	maroua.mebarki@univ-tam.dz	maroua.mebarki@univ-tam.dz	PROPN
ejpam-5017	20	27	(	(	PUNCT
ejpam-5017	20	28	m.	m.	NOUN
ejpam-5017	20	29	mebarki	mebarki	PROPN
ejpam-5017	20	30	)	)	PUNCT
ejpam-5017	20	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5017	20	32	1321	1321	NUM
ejpam-5017	20	33	©	©	PROPN
ejpam-5017	20	34	2024	2024	NUM
ejpam-5017	20	35	ejpam	ejpam	NOUN
ejpam-5017	20	36	all	all	DET
ejpam-5017	20	37	rights	right	NOUN
ejpam-5017	20	38	reserved	reserve	VERB
ejpam-5017	20	39	.	.	PUNCT
ejpam-5017	21	1	m.	m.	NOUN
ejpam-5017	21	2	mebarki	mebarki	PROPN
ejpam-5017	21	3	/	/	SYM
ejpam-5017	21	4	eur	eur	PROPN
ejpam-5017	21	5	.	.	PUNCT
ejpam-5017	22	1	j.	j.	PROPN
ejpam-5017	22	2	pure	pure	PROPN
ejpam-5017	22	3	appl	appl	PROPN
ejpam-5017	22	4	.	.	PROPN
ejpam-5017	22	5	math	math	PROPN
ejpam-5017	22	6	,	,	PUNCT
ejpam-5017	22	7	17	17	NUM
ejpam-5017	22	8	(	(	PUNCT
ejpam-5017	22	9	2	2	NUM
ejpam-5017	22	10	)	)	PUNCT
ejpam-5017	22	11	(	(	PUNCT
ejpam-5017	22	12	2024	2024	NUM
ejpam-5017	22	13	)	)	PUNCT
ejpam-5017	22	14	,	,	PUNCT
ejpam-5017	22	15	1321	1321	NUM
ejpam-5017	22	16	-	-	SYM
ejpam-5017	22	17	1334	1334	NUM
ejpam-5017	22	18	1322	1322	NUM
ejpam-5017	22	19			PUNCT
ejpam-5017	22	20	∂w	∂w	PROPN
ejpam-5017	22	21	∂t	∂t	PROPN
ejpam-5017	22	22	=	=	PUNCT
ejpam-5017	22	23	−d1(−∆)w	−d1(−∆)w	PROPN
ejpam-5017	23	1	−	−	PROPN
ejpam-5017	23	2	w2z	w2z	NOUN
ejpam-5017	23	3	+	+	CCONJ
ejpam-5017	23	4	f(1−	f(1−	PROPN
ejpam-5017	23	5	w	w	NOUN
ejpam-5017	23	6	)	)	PUNCT
ejpam-5017	24	1	∂z	∂z	PROPN
ejpam-5017	25	1	∂t	∂t	PROPN
ejpam-5017	25	2	=	=	SYM
ejpam-5017	25	3	−d2(−∆)z	−d2(−∆)z	PROPN
ejpam-5017	25	4	+	+	NUM
ejpam-5017	25	5	w2z	w2z	PROPN
ejpam-5017	25	6	−	−	PROPN
ejpam-5017	25	7	(	(	PUNCT
ejpam-5017	25	8	f	f	PROPN
ejpam-5017	26	1	+	+	CCONJ
ejpam-5017	26	2	k)z	k)z	X
ejpam-5017	26	3	the	the	DET
ejpam-5017	26	4	variables	variable	NOUN
ejpam-5017	26	5	in	in	ADP
ejpam-5017	26	6	these	these	DET
ejpam-5017	26	7	equations	equation	NOUN
ejpam-5017	26	8	w	w	PROPN
ejpam-5017	26	9	and	and	CCONJ
ejpam-5017	26	10	z	z	NOUN
ejpam-5017	26	11	are	be	AUX
ejpam-5017	26	12	the	the	DET
ejpam-5017	26	13	concentrations	concentration	NOUN
ejpam-5017	26	14	of	of	ADP
ejpam-5017	26	15	the	the	DET
ejpam-5017	26	16	two	two	NUM
ejpam-5017	26	17	reacting	react	VERB
ejpam-5017	26	18	substances	substance	NOUN
ejpam-5017	26	19	w	w	VERB
ejpam-5017	26	20	and	and	CCONJ
ejpam-5017	26	21	z.	z.	PROPN
ejpam-5017	26	22	on	on	ADP
ejpam-5017	26	23	the	the	DET
ejpam-5017	26	24	left	left	ADJ
ejpam-5017	26	25	-	-	PUNCT
ejpam-5017	26	26	hand	hand	NOUN
ejpam-5017	26	27	side	side	NOUN
ejpam-5017	26	28	of	of	ADP
ejpam-5017	26	29	each	each	DET
ejpam-5017	26	30	equation	equation	NOUN
ejpam-5017	26	31	is	be	AUX
ejpam-5017	26	32	the	the	DET
ejpam-5017	26	33	time	time	NOUN
ejpam-5017	26	34	derivative	derivative	NOUN
ejpam-5017	26	35	of	of	ADP
ejpam-5017	26	36	one	one	NUM
ejpam-5017	26	37	of	of	ADP
ejpam-5017	26	38	these	these	DET
ejpam-5017	26	39	concentrations	concentration	NOUN
ejpam-5017	26	40	,	,	PUNCT
ejpam-5017	26	41	describing	describe	VERB
ejpam-5017	26	42	the	the	DET
ejpam-5017	26	43	rate	rate	NOUN
ejpam-5017	26	44	at	at	ADP
ejpam-5017	26	45	which	which	PRON
ejpam-5017	26	46	it	it	PRON
ejpam-5017	26	47	changes	change	VERB
ejpam-5017	26	48	.	.	PUNCT
ejpam-5017	27	1	the	the	DET
ejpam-5017	27	2	right	right	ADJ
ejpam-5017	27	3	-	-	PUNCT
ejpam-5017	27	4	hand	hand	NOUN
ejpam-5017	27	5	sides	side	NOUN
ejpam-5017	27	6	of	of	ADP
ejpam-5017	27	7	the	the	DET
ejpam-5017	27	8	equations	equation	NOUN
ejpam-5017	27	9	both	both	PRON
ejpam-5017	27	10	contain	contain	VERB
ejpam-5017	27	11	three	three	NUM
ejpam-5017	27	12	separate	separate	ADJ
ejpam-5017	27	13	terms	term	NOUN
ejpam-5017	27	14	.	.	PUNCT
ejpam-5017	28	1	the	the	DET
ejpam-5017	28	2	first	first	ADJ
ejpam-5017	28	3	describes	describe	VERB
ejpam-5017	28	4	the	the	DET
ejpam-5017	28	5	reaction	reaction	NOUN
ejpam-5017	28	6	between	between	ADP
ejpam-5017	28	7	the	the	DET
ejpam-5017	28	8	two	two	NUM
ejpam-5017	28	9	substances	substance	NOUN
ejpam-5017	28	10	.	.	PUNCT
ejpam-5017	29	1	since	since	SCONJ
ejpam-5017	29	2	one	one	NUM
ejpam-5017	29	3	w	w	NOUN
ejpam-5017	29	4	and	and	CCONJ
ejpam-5017	29	5	two	two	NUM
ejpam-5017	29	6	z	z	NOUN
ejpam-5017	29	7	react	react	VERB
ejpam-5017	29	8	,	,	PUNCT
ejpam-5017	29	9	the	the	DET
ejpam-5017	29	10	corresponding	corresponding	ADJ
ejpam-5017	29	11	term	term	NOUN
ejpam-5017	29	12	includes	include	VERB
ejpam-5017	29	13	w	w	NOUN
ejpam-5017	29	14	to	to	ADP
ejpam-5017	29	15	the	the	DET
ejpam-5017	29	16	power	power	NOUN
ejpam-5017	29	17	of	of	ADP
ejpam-5017	29	18	one	one	NUM
ejpam-5017	29	19	and	and	CCONJ
ejpam-5017	29	20	z	z	NOUN
ejpam-5017	29	21	to	to	ADP
ejpam-5017	29	22	the	the	DET
ejpam-5017	29	23	power	power	NOUN
ejpam-5017	29	24	of	of	ADP
ejpam-5017	29	25	two	two	NUM
ejpam-5017	29	26	:	:	PUNCT
ejpam-5017	29	27	w2z	w2z	PROPN
ejpam-5017	29	28	as	as	SCONJ
ejpam-5017	29	29	w	w	PROPN
ejpam-5017	29	30	gets	get	AUX
ejpam-5017	29	31	consumed	consume	VERB
ejpam-5017	29	32	by	by	ADP
ejpam-5017	29	33	the	the	DET
ejpam-5017	29	34	reaction	reaction	NOUN
ejpam-5017	29	35	,	,	PUNCT
ejpam-5017	29	36	the	the	DET
ejpam-5017	29	37	term	term	NOUN
ejpam-5017	29	38	has	have	VERB
ejpam-5017	29	39	a	a	DET
ejpam-5017	29	40	negative	negative	ADJ
ejpam-5017	29	41	sign	sign	NOUN
ejpam-5017	29	42	in	in	ADP
ejpam-5017	29	43	the	the	DET
ejpam-5017	29	44	first	first	ADJ
ejpam-5017	29	45	equation	equation	NOUN
ejpam-5017	29	46	.	.	PUNCT
ejpam-5017	30	1	in	in	ADP
ejpam-5017	30	2	the	the	DET
ejpam-5017	30	3	second	second	ADJ
ejpam-5017	30	4	equation	equation	NOUN
ejpam-5017	30	5	it	it	PRON
ejpam-5017	30	6	has	have	VERB
ejpam-5017	30	7	a	a	DET
ejpam-5017	30	8	positive	positive	ADJ
ejpam-5017	30	9	sign	sign	NOUN
ejpam-5017	30	10	,	,	PUNCT
ejpam-5017	30	11	as	as	SCONJ
ejpam-5017	30	12	is	be	AUX
ejpam-5017	30	13	produced	produce	VERB
ejpam-5017	30	14	in	in	ADP
ejpam-5017	30	15	the	the	DET
ejpam-5017	30	16	reaction	reaction	NOUN
ejpam-5017	30	17	.	.	PUNCT
ejpam-5017	31	1	the	the	DET
ejpam-5017	31	2	second	second	ADJ
ejpam-5017	31	3	term	term	NOUN
ejpam-5017	31	4	of	of	ADP
ejpam-5017	31	5	the	the	DET
ejpam-5017	31	6	first	first	ADJ
ejpam-5017	31	7	equation	equation	NOUN
ejpam-5017	31	8	describes	describe	VERB
ejpam-5017	31	9	the	the	DET
ejpam-5017	31	10	rate	rate	NOUN
ejpam-5017	31	11	at	at	ADP
ejpam-5017	31	12	which	which	PRON
ejpam-5017	31	13	w	w	NOUN
ejpam-5017	31	14	is	be	AUX
ejpam-5017	31	15	replenished	replenish	VERB
ejpam-5017	31	16	externally	externally	ADV
ejpam-5017	31	17	.	.	PUNCT
ejpam-5017	32	1	this	this	PRON
ejpam-5017	32	2	is	be	AUX
ejpam-5017	32	3	necessary	necessary	ADJ
ejpam-5017	32	4	,	,	PUNCT
ejpam-5017	32	5	as	as	SCONJ
ejpam-5017	32	6	w	w	PROPN
ejpam-5017	32	7	would	would	AUX
ejpam-5017	32	8	otherwise	otherwise	ADV
ejpam-5017	32	9	simply	simply	ADV
ejpam-5017	32	10	be	be	AUX
ejpam-5017	32	11	used	use	VERB
ejpam-5017	32	12	up	up	ADP
ejpam-5017	32	13	.	.	PUNCT
ejpam-5017	33	1	the	the	DET
ejpam-5017	33	2	feed	feed	NOUN
ejpam-5017	33	3	rate	rate	NOUN
ejpam-5017	33	4	is	be	AUX
ejpam-5017	33	5	given	give	VERB
ejpam-5017	33	6	by	by	ADP
ejpam-5017	33	7	the	the	DET
ejpam-5017	33	8	parameter	parameter	NOUN
ejpam-5017	33	9	f	f	PROPN
ejpam-5017	33	10	.	.	PUNCT
ejpam-5017	34	1	f	f	PROPN
ejpam-5017	34	2	is	be	AUX
ejpam-5017	34	3	multiplied	multiply	VERB
ejpam-5017	34	4	by	by	ADP
ejpam-5017	34	5	1	1	NUM
ejpam-5017	34	6	−	−	NOUN
ejpam-5017	34	7	w	w	NOUN
ejpam-5017	34	8	to	to	PART
ejpam-5017	34	9	ensure	ensure	VERB
ejpam-5017	34	10	that	that	SCONJ
ejpam-5017	34	11	w	w	NOUN
ejpam-5017	34	12	is	be	AUX
ejpam-5017	34	13	replenished	replenish	VERB
ejpam-5017	34	14	at	at	ADP
ejpam-5017	34	15	a	a	DET
ejpam-5017	34	16	rate	rate	NOUN
ejpam-5017	34	17	dependent	dependent	ADJ
ejpam-5017	34	18	on	on	ADP
ejpam-5017	34	19	the	the	DET
ejpam-5017	34	20	current	current	ADJ
ejpam-5017	34	21	concentration	concentration	NOUN
ejpam-5017	34	22	,	,	PUNCT
ejpam-5017	34	23	which	which	PRON
ejpam-5017	34	24	never	never	ADV
ejpam-5017	34	25	exceeds	exceed	VERB
ejpam-5017	34	26	z	z	NOUN
ejpam-5017	34	27	does	do	AUX
ejpam-5017	34	28	not	not	PART
ejpam-5017	34	29	need	need	VERB
ejpam-5017	34	30	to	to	PART
ejpam-5017	34	31	replenished	replenished	VERB
ejpam-5017	34	32	,	,	PUNCT
ejpam-5017	34	33	since	since	SCONJ
ejpam-5017	34	34	it	it	PRON
ejpam-5017	34	35	is	be	AUX
ejpam-5017	34	36	produced	produce	VERB
ejpam-5017	34	37	in	in	ADP
ejpam-5017	34	38	the	the	DET
ejpam-5017	34	39	reaction	reaction	NOUN
ejpam-5017	34	40	.	.	PUNCT
ejpam-5017	35	1	booth	booth	NOUN
ejpam-5017	35	2	,	,	PUNCT
ejpam-5017	35	3	it	it	PRON
ejpam-5017	35	4	needs	need	VERB
ejpam-5017	35	5	to	to	PART
ejpam-5017	35	6	be	be	AUX
ejpam-5017	35	7	removed	remove	VERB
ejpam-5017	35	8	in	in	ADP
ejpam-5017	35	9	order	order	NOUN
ejpam-5017	35	10	maintain	maintain	VERB
ejpam-5017	35	11	the	the	DET
ejpam-5017	35	12	reaction	reaction	NOUN
ejpam-5017	35	13	.	.	PUNCT
ejpam-5017	36	1	the	the	DET
ejpam-5017	36	2	rate	rate	NOUN
ejpam-5017	36	3	of	of	ADP
ejpam-5017	36	4	removal	removal	NOUN
ejpam-5017	36	5	,	,	PUNCT
ejpam-5017	36	6	the	the	DET
ejpam-5017	36	7	kill	kill	NOUN
ejpam-5017	36	8	rate	rate	NOUN
ejpam-5017	36	9	,	,	PUNCT
ejpam-5017	36	10	is	be	AUX
ejpam-5017	36	11	controlled	control	VERB
ejpam-5017	36	12	by	by	ADP
ejpam-5017	36	13	the	the	DET
ejpam-5017	36	14	parameter	parameter	PROPN
ejpam-5017	36	15	k.	k.	PROPN
ejpam-5017	36	16	to	to	PART
ejpam-5017	36	17	remove	remove	VERB
ejpam-5017	36	18	z	z	NOUN
ejpam-5017	36	19	faster	fast	ADV
ejpam-5017	36	20	than	than	SCONJ
ejpam-5017	36	21	w	w	PROPN
ejpam-5017	36	22	is	be	AUX
ejpam-5017	36	23	added	add	VERB
ejpam-5017	36	24	,	,	PUNCT
ejpam-5017	36	25	k	k	PROPN
ejpam-5017	36	26	is	be	AUX
ejpam-5017	36	27	added	add	VERB
ejpam-5017	36	28	to	to	ADP
ejpam-5017	36	29	f	f	PROPN
ejpam-5017	36	30	and	and	CCONJ
ejpam-5017	36	31	multiplied	multiply	VERB
ejpam-5017	36	32	by	by	ADP
ejpam-5017	36	33	z	z	PROPN
ejpam-5017	36	34	,	,	PUNCT
ejpam-5017	36	35	since	since	SCONJ
ejpam-5017	36	36	the	the	DET
ejpam-5017	36	37	removal	removal	NOUN
ejpam-5017	36	38	of	of	ADP
ejpam-5017	36	39	z	z	PROPN
ejpam-5017	36	40	is	be	AUX
ejpam-5017	36	41	also	also	ADV
ejpam-5017	36	42	supposed	suppose	VERB
ejpam-5017	36	43	to	to	PART
ejpam-5017	36	44	be	be	AUX
ejpam-5017	36	45	dependent	dependent	ADJ
ejpam-5017	36	46	on	on	ADP
ejpam-5017	36	47	its	its	PRON
ejpam-5017	36	48	concentration	concentration	NOUN
ejpam-5017	36	49	.	.	PUNCT
ejpam-5017	37	1	the	the	DET
ejpam-5017	37	2	last	last	ADJ
ejpam-5017	37	3	term	term	NOUN
ejpam-5017	37	4	in	in	ADP
ejpam-5017	37	5	both	both	DET
ejpam-5017	37	6	equations	equation	NOUN
ejpam-5017	37	7	describe	describe	VERB
ejpam-5017	37	8	the	the	DET
ejpam-5017	37	9	diffusion	diffusion	NOUN
ejpam-5017	37	10	of	of	ADP
ejpam-5017	37	11	and	and	CCONJ
ejpam-5017	37	12	,	,	PUNCT
ejpam-5017	37	13	respectively	respectively	ADV
ejpam-5017	37	14	.	.	PUNCT
ejpam-5017	38	1	in	in	ADP
ejpam-5017	38	2	this	this	DET
ejpam-5017	38	3	current	current	ADJ
ejpam-5017	38	4	manuscript	manuscript	NOUN
ejpam-5017	38	5	,	,	PUNCT
ejpam-5017	38	6	we	we	PRON
ejpam-5017	38	7	are	be	AUX
ejpam-5017	38	8	interested	interested	ADJ
ejpam-5017	38	9	in	in	ADP
ejpam-5017	38	10	the	the	DET
ejpam-5017	38	11	fractional	fractional	ADJ
ejpam-5017	38	12	gray	gray	ADJ
ejpam-5017	38	13	scott	scott	PROPN
ejpam-5017	38	14	model	model	NOUN
ejpam-5017	38	15	which	which	PRON
ejpam-5017	38	16	arises	arise	VERB
ejpam-5017	38	17	in	in	ADP
ejpam-5017	38	18	the	the	DET
ejpam-5017	38	19	modelling	modelling	NOUN
ejpam-5017	38	20	of	of	ADP
ejpam-5017	38	21	autocatalytic	autocatalytic	ADJ
ejpam-5017	38	22	reactions	reaction	NOUN
ejpam-5017	38	23	.	.	PUNCT
ejpam-5017	39	1	we	we	PRON
ejpam-5017	39	2	study	study	VERB
ejpam-5017	39	3	the	the	DET
ejpam-5017	39	4	global	global	ADJ
ejpam-5017	39	5	existence	existence	NOUN
ejpam-5017	39	6	and	and	CCONJ
ejpam-5017	39	7	asymptotic	asymptotic	ADJ
ejpam-5017	39	8	behavior	behavior	NOUN
ejpam-5017	39	9	of	of	ADP
ejpam-5017	39	10	solutions	solution	NOUN
ejpam-5017	39	11	to	to	ADP
ejpam-5017	39	12	the	the	DET
ejpam-5017	39	13	system:	system:	NOUN
ejpam-5017	39	14	∂w	∂w	PROPN
ejpam-5017	39	15	∂t	∂t	PROPN
ejpam-5017	39	16	=	=	SYM
ejpam-5017	39	17	−d1(−∆)δw	−d1(−∆)δw	PROPN
ejpam-5017	39	18	−	−	PROPN
ejpam-5017	39	19	w2z	w2z	PROPN
ejpam-5017	39	20	+	+	CCONJ
ejpam-5017	39	21	f(1−	f(1−	PROPN
ejpam-5017	39	22	w	w	NOUN
ejpam-5017	39	23	)	)	PUNCT
ejpam-5017	39	24	in	in	ADP
ejpam-5017	39	25	ω×	ω×	NOUN
ejpam-5017	39	26	r+	r+	NOUN
ejpam-5017	39	27	,	,	PUNCT
ejpam-5017	39	28	∂z	∂z	PROPN
ejpam-5017	39	29	∂t	∂t	PROPN
ejpam-5017	39	30	=	=	PUNCT
ejpam-5017	39	31	−d2(−∆)ϵz	−d2(−∆)ϵz	PROPN
ejpam-5017	39	32	+	+	CCONJ
ejpam-5017	39	33	w2z	w2z	PROPN
ejpam-5017	39	34	−	−	PROPN
ejpam-5017	39	35	(	(	PUNCT
ejpam-5017	39	36	f	f	PROPN
ejpam-5017	39	37	+	+	CCONJ
ejpam-5017	39	38	k)z	k)z	PROPN
ejpam-5017	39	39	in	in	ADP
ejpam-5017	39	40	ω×	ω×	NOUN
ejpam-5017	39	41	r+	r+	X
ejpam-5017	39	42	,	,	PUNCT
ejpam-5017	39	43	(	(	PUNCT
ejpam-5017	39	44	1	1	X
ejpam-5017	39	45	)	)	PUNCT
ejpam-5017	39	46	subjected	subject	VERB
ejpam-5017	39	47	with	with	ADP
ejpam-5017	39	48	the	the	DET
ejpam-5017	39	49	boundary	boundary	ADJ
ejpam-5017	39	50	and	and	CCONJ
ejpam-5017	39	51	initial	initial	ADJ
ejpam-5017	40	1	conditions	conditions	PUNCT
ejpam-5017	40	2	∂w	∂w	PROPN
ejpam-5017	40	3	∂η	∂η	PROPN
ejpam-5017	40	4	=	=	SYM
ejpam-5017	40	5	∂z	∂z	PROPN
ejpam-5017	40	6	∂η	∂η	PROPN
ejpam-5017	40	7	=	=	NOUN
ejpam-5017	40	8	0	0	NUM
ejpam-5017	40	9	in	in	ADP
ejpam-5017	40	10	∂ω×	∂ω×	PROPN
ejpam-5017	40	11	r+	r+	X
ejpam-5017	40	12	,	,	PUNCT
ejpam-5017	40	13	w	w	PROPN
ejpam-5017	40	14	(	(	PUNCT
ejpam-5017	40	15	.	.	NUM
ejpam-5017	40	16	,	,	PUNCT
ejpam-5017	40	17	0	0	NUM
ejpam-5017	40	18	)	)	PUNCT
ejpam-5017	40	19	=	=	NOUN
ejpam-5017	40	20	w0	w0	PROPN
ejpam-5017	40	21	(	(	PUNCT
ejpam-5017	40	22	.	.	PUNCT
ejpam-5017	40	23	)	)	PUNCT
ejpam-5017	40	24	,	,	PUNCT
ejpam-5017	40	25	z	z	NOUN
ejpam-5017	40	26	(	(	PUNCT
ejpam-5017	40	27	.	.	NUM
ejpam-5017	40	28	,	,	PUNCT
ejpam-5017	40	29	0	0	X
ejpam-5017	40	30	)	)	PUNCT
ejpam-5017	40	31	=	=	SYM
ejpam-5017	40	32	z0	z0	PROPN
ejpam-5017	40	33	(	(	PUNCT
ejpam-5017	40	34	.	.	PUNCT
ejpam-5017	40	35	)	)	PUNCT
ejpam-5017	41	1	in	in	ADP
ejpam-5017	41	2	ω	ω	NUM
ejpam-5017	41	3	,	,	PUNCT
ejpam-5017	41	4	here	here	ADV
ejpam-5017	41	5	ω	ω	PROPN
ejpam-5017	41	6	is	be	AUX
ejpam-5017	41	7	an	an	DET
ejpam-5017	41	8	open	open	ADJ
ejpam-5017	41	9	bounded	bounded	ADJ
ejpam-5017	41	10	domain	domain	NOUN
ejpam-5017	41	11	of	of	ADP
ejpam-5017	41	12	class	class	NOUN
ejpam-5017	41	13	c1	c1	PROPN
ejpam-5017	41	14	in	in	ADP
ejpam-5017	41	15	rn	rn	PROPN
ejpam-5017	41	16	,	,	PUNCT
ejpam-5017	41	17	w	w	PROPN
ejpam-5017	41	18	(	(	PUNCT
ejpam-5017	41	19	t	t	PROPN
ejpam-5017	41	20	,	,	PUNCT
ejpam-5017	41	21	x	x	NOUN
ejpam-5017	41	22	)	)	PUNCT
ejpam-5017	41	23	and	and	CCONJ
ejpam-5017	41	24	z(t	z(t	PROPN
ejpam-5017	41	25	,	,	PUNCT
ejpam-5017	41	26	x	x	NOUN
ejpam-5017	41	27	)	)	PUNCT
ejpam-5017	41	28	,	,	PUNCT
ejpam-5017	41	29	t	t	PROPN
ejpam-5017	41	30	≥	≥	NUM
ejpam-5017	41	31	0	0	NUM
ejpam-5017	41	32	,	,	PUNCT
ejpam-5017	41	33	x	x	SYM
ejpam-5017	41	34	∈	∈	NOUN
ejpam-5017	41	35	ω	ω	NOUN
ejpam-5017	41	36	are	be	AUX
ejpam-5017	41	37	real	real	ADV
ejpam-5017	41	38	valued	value	VERB
ejpam-5017	41	39	functions	function	NOUN
ejpam-5017	41	40	.	.	PUNCT
ejpam-5017	42	1	w0	w0	PROPN
ejpam-5017	42	2	(	(	PUNCT
ejpam-5017	42	3	.	.	PUNCT
ejpam-5017	42	4	)	)	PUNCT
ejpam-5017	42	5	and	and	CCONJ
ejpam-5017	42	6	z0	z0	PROPN
ejpam-5017	42	7	(	(	PUNCT
ejpam-5017	42	8	.	.	PUNCT
ejpam-5017	42	9	)	)	PUNCT
ejpam-5017	42	10	are	be	AUX
ejpam-5017	42	11	non	non	ADJ
ejpam-5017	42	12	negatives	negative	NOUN
ejpam-5017	42	13	,	,	PUNCT
ejpam-5017	42	14	the	the	DET
ejpam-5017	42	15	constants	constant	NOUN
ejpam-5017	42	16	d1	d1	PROPN
ejpam-5017	42	17	,	,	PUNCT
ejpam-5017	42	18	d2	d2	PROPN
ejpam-5017	42	19	,	,	PUNCT
ejpam-5017	42	20	k	k	PROPN
ejpam-5017	42	21	are	be	AUX
ejpam-5017	42	22	positive	positive	ADJ
ejpam-5017	42	23	and	and	CCONJ
ejpam-5017	42	24	0	0	NUM
ejpam-5017	42	25	<	<	X
ejpam-5017	42	26	ϵ	ϵ	X
ejpam-5017	42	27	<	<	X
ejpam-5017	42	28	1	1	NUM
ejpam-5017	42	29	,	,	PUNCT
ejpam-5017	42	30	0	0	NUM
ejpam-5017	42	31	<	<	X
ejpam-5017	42	32	δ	δ	X
ejpam-5017	42	33	<	<	X
ejpam-5017	42	34	1	1	NUM
ejpam-5017	42	35	and	and	CCONJ
ejpam-5017	42	36	f	f	PROPN
ejpam-5017	42	37	≥	≥	NUM
ejpam-5017	42	38	0	0	NUM
ejpam-5017	42	39	.	.	PUNCT
ejpam-5017	43	1	the	the	DET
ejpam-5017	43	2	system	system	NOUN
ejpam-5017	43	3	,	,	PUNCT
ejpam-5017	43	4	obtained	obtain	VERB
ejpam-5017	43	5	by	by	ADP
ejpam-5017	43	6	replacing	replace	VERB
ejpam-5017	43	7	the	the	DET
ejpam-5017	43	8	fractional	fractional	ADJ
ejpam-5017	43	9	laplacian	laplacian	NOUN
ejpam-5017	43	10	by	by	ADP
ejpam-5017	43	11	the	the	DET
ejpam-5017	43	12	classical	classical	ADJ
ejpam-5017	43	13	one	one	NOUN
ejpam-5017	43	14	,	,	PUNCT
ejpam-5017	43	15	is	be	AUX
ejpam-5017	43	16	known	know	VERB
ejpam-5017	43	17	as	as	ADP
ejpam-5017	43	18	the	the	DET
ejpam-5017	43	19	chemical	chemical	NOUN
ejpam-5017	43	20	diffusion	diffusion	NOUN
ejpam-5017	43	21	gray	gray	PROPN
ejpam-5017	43	22	scott	scott	PROPN
ejpam-5017	43	23	.	.	PUNCT
ejpam-5017	44	1	this	this	DET
ejpam-5017	44	2	model	model	NOUN
ejpam-5017	44	3	was	be	AUX
ejpam-5017	44	4	proposed	propose	VERB
ejpam-5017	44	5	by	by	ADP
ejpam-5017	44	6	gray	gray	ADJ
ejpam-5017	44	7	and	and	CCONJ
ejpam-5017	44	8	scott	scott	PROPN
ejpam-5017	44	9	in	in	ADP
ejpam-5017	44	10	1983	1983	NUM
ejpam-5017	44	11	.	.	PUNCT
ejpam-5017	45	1	later	later	ADV
ejpam-5017	45	2	on	on	ADV
ejpam-5017	45	3	,	,	PUNCT
ejpam-5017	45	4	the	the	DET
ejpam-5017	45	5	gray	gray	ADJ
ejpam-5017	45	6	scott	scott	PROPN
ejpam-5017	45	7	model	model	NOUN
ejpam-5017	45	8	has	have	AUX
ejpam-5017	45	9	attracted	attract	VERB
ejpam-5017	45	10	significant	significant	ADJ
ejpam-5017	45	11	attention	attention	NOUN
ejpam-5017	45	12	.	.	PUNCT
ejpam-5017	46	1	it	it	PRON
ejpam-5017	46	2	has	have	AUX
ejpam-5017	46	3	been	be	AUX
ejpam-5017	46	4	subject	subject	ADJ
ejpam-5017	46	5	of	of	ADP
ejpam-5017	46	6	a	a	DET
ejpam-5017	46	7	number	number	NOUN
ejpam-5017	46	8	of	of	ADP
ejpam-5017	46	9	papers	paper	NOUN
ejpam-5017	46	10	,	,	PUNCT
ejpam-5017	46	11	for	for	ADP
ejpam-5017	46	12	example	example	NOUN
ejpam-5017	46	13	kirane	kirane	NOUN
ejpam-5017	47	1	[	[	X
ejpam-5017	47	2	1	1	NUM
ejpam-5017	47	3	]	]	PUNCT
ejpam-5017	47	4	,	,	PUNCT
ejpam-5017	47	5	hollis	hollis	PROPN
ejpam-5017	48	1	[	[	X
ejpam-5017	48	2	4	4	NUM
ejpam-5017	48	3	]	]	PUNCT
ejpam-5017	48	4	,	,	PUNCT
ejpam-5017	48	5	roth[9	roth[9	X
ejpam-5017	48	6	]	]	PUNCT
ejpam-5017	48	7	,	,	PUNCT
ejpam-5017	48	8	kouachi	kouachi	PROPN
ejpam-5017	48	9	[	[	X
ejpam-5017	48	10	10	10	NUM
ejpam-5017	48	11	]	]	PUNCT
ejpam-5017	48	12	,	,	PUNCT
ejpam-5017	48	13	lin[6	lin[6	PROPN
ejpam-5017	48	14	]	]	PUNCT
ejpam-5017	48	15	,	,	PUNCT
ejpam-5017	48	16	...	...	PUNCT
ejpam-5017	48	17	,	,	PUNCT
ejpam-5017	48	18	etc	etc	X
ejpam-5017	48	19	.	.	X
ejpam-5017	48	20	m.	m.	NOUN
ejpam-5017	48	21	mebarki	mebarki	PROPN
ejpam-5017	48	22	/	/	SYM
ejpam-5017	48	23	eur	eur	PROPN
ejpam-5017	48	24	.	.	PUNCT
ejpam-5017	49	1	j.	j.	PROPN
ejpam-5017	49	2	pure	pure	PROPN
ejpam-5017	49	3	appl	appl	PROPN
ejpam-5017	49	4	.	.	PROPN
ejpam-5017	49	5	math	math	PROPN
ejpam-5017	49	6	,	,	PUNCT
ejpam-5017	49	7	17	17	NUM
ejpam-5017	49	8	(	(	PUNCT
ejpam-5017	49	9	2	2	NUM
ejpam-5017	49	10	)	)	PUNCT
ejpam-5017	49	11	(	(	PUNCT
ejpam-5017	49	12	2024	2024	NUM
ejpam-5017	49	13	)	)	PUNCT
ejpam-5017	49	14	,	,	PUNCT
ejpam-5017	49	15	1321	1321	NUM
ejpam-5017	49	16	-	-	SYM
ejpam-5017	49	17	1334	1334	NUM
ejpam-5017	49	18	1323	1323	NUM
ejpam-5017	49	19	our	our	PRON
ejpam-5017	49	20	paper	paper	NOUN
ejpam-5017	49	21	is	be	AUX
ejpam-5017	49	22	organized	organize	VERB
ejpam-5017	49	23	as	as	SCONJ
ejpam-5017	49	24	follows	follow	VERB
ejpam-5017	49	25	.	.	PUNCT
ejpam-5017	50	1	in	in	ADP
ejpam-5017	50	2	section	section	NOUN
ejpam-5017	50	3	2	2	NUM
ejpam-5017	50	4	,	,	PUNCT
ejpam-5017	50	5	we	we	PRON
ejpam-5017	50	6	present	present	VERB
ejpam-5017	50	7	some	some	DET
ejpam-5017	50	8	preliminaries	preliminary	NOUN
ejpam-5017	50	9	and	and	CCONJ
ejpam-5017	50	10	definitions	definition	NOUN
ejpam-5017	50	11	which	which	PRON
ejpam-5017	50	12	used	use	VERB
ejpam-5017	50	13	in	in	ADP
ejpam-5017	50	14	the	the	DET
ejpam-5017	50	15	following	follow	VERB
ejpam-5017	50	16	sections	section	NOUN
ejpam-5017	50	17	.	.	PUNCT
ejpam-5017	51	1	in	in	ADP
ejpam-5017	51	2	section	section	NOUN
ejpam-5017	51	3	3	3	NUM
ejpam-5017	51	4	,	,	PUNCT
ejpam-5017	51	5	the	the	DET
ejpam-5017	51	6	definition	definition	NOUN
ejpam-5017	51	7	of	of	ADP
ejpam-5017	51	8	mild	mild	ADJ
ejpam-5017	51	9	solution	solution	NOUN
ejpam-5017	51	10	of	of	ADP
ejpam-5017	51	11	the	the	DET
ejpam-5017	51	12	system	system	NOUN
ejpam-5017	51	13	(	(	PUNCT
ejpam-5017	51	14	1	1	NUM
ejpam-5017	51	15	)	)	PUNCT
ejpam-5017	51	16	and	and	CCONJ
ejpam-5017	51	17	the	the	DET
ejpam-5017	51	18	theorem	theorem	NOUN
ejpam-5017	51	19	of	of	ADP
ejpam-5017	51	20	local	local	ADJ
ejpam-5017	51	21	existence	existence	NOUN
ejpam-5017	51	22	are	be	AUX
ejpam-5017	51	23	obtained	obtain	VERB
ejpam-5017	51	24	.	.	PUNCT
ejpam-5017	52	1	the	the	DET
ejpam-5017	52	2	main	main	ADJ
ejpam-5017	52	3	results	result	NOUN
ejpam-5017	52	4	of	of	ADP
ejpam-5017	52	5	global	global	ADJ
ejpam-5017	52	6	existence	existence	NOUN
ejpam-5017	52	7	and	and	CCONJ
ejpam-5017	52	8	large	large	ADJ
ejpam-5017	52	9	time	time	NOUN
ejpam-5017	52	10	behavior	behavior	NOUN
ejpam-5017	52	11	for	for	ADP
ejpam-5017	52	12	the	the	DET
ejpam-5017	52	13	solution	solution	NOUN
ejpam-5017	52	14	are	be	AUX
ejpam-5017	52	15	presented	present	VERB
ejpam-5017	52	16	in	in	ADP
ejpam-5017	52	17	section	section	NOUN
ejpam-5017	52	18	4	4	NUM
ejpam-5017	52	19	.	.	NOUN
ejpam-5017	52	20	2	2	NUM
ejpam-5017	52	21	.	.	NOUN
ejpam-5017	52	22	notations	notation	NOUN
ejpam-5017	52	23	and	and	CCONJ
ejpam-5017	52	24	preliminary	preliminary	ADJ
ejpam-5017	52	25	in	in	ADP
ejpam-5017	52	26	this	this	DET
ejpam-5017	52	27	section	section	NOUN
ejpam-5017	52	28	,	,	PUNCT
ejpam-5017	52	29	we	we	PRON
ejpam-5017	52	30	introduce	introduce	VERB
ejpam-5017	52	31	some	some	DET
ejpam-5017	52	32	notations	notation	NOUN
ejpam-5017	52	33	,	,	PUNCT
ejpam-5017	52	34	definitions	definition	NOUN
ejpam-5017	52	35	and	and	CCONJ
ejpam-5017	52	36	lemmas	lemma	NOUN
ejpam-5017	52	37	which	which	PRON
ejpam-5017	52	38	will	will	AUX
ejpam-5017	52	39	be	be	AUX
ejpam-5017	52	40	used	use	VERB
ejpam-5017	52	41	in	in	ADP
ejpam-5017	52	42	the	the	DET
ejpam-5017	52	43	sequel	sequel	NOUN
ejpam-5017	52	44	.	.	PUNCT
ejpam-5017	53	1	where	where	SCONJ
ejpam-5017	53	2	ω	ω	NOUN
ejpam-5017	53	3	is	be	AUX
ejpam-5017	53	4	an	an	DET
ejpam-5017	53	5	open	open	ADJ
ejpam-5017	53	6	bounded	bounded	ADJ
ejpam-5017	53	7	domain	domain	NOUN
ejpam-5017	53	8	of	of	ADP
ejpam-5017	53	9	class	class	NOUN
ejpam-5017	53	10	c1	c1	PROPN
ejpam-5017	53	11	in	in	ADP
ejpam-5017	53	12	rn	rn	PROPN
ejpam-5017	53	13	,	,	PUNCT
ejpam-5017	53	14	we	we	PRON
ejpam-5017	53	15	denote(−∆n	denote(−∆n	VERB
ejpam-5017	53	16	)	)	PUNCT
ejpam-5017	53	17	δ	δ	PROPN
ejpam-5017	53	18	the	the	DET
ejpam-5017	53	19	fractional	fractional	ADJ
ejpam-5017	53	20	power	power	NOUN
ejpam-5017	53	21	of	of	ADP
ejpam-5017	53	22	the	the	DET
ejpam-5017	53	23	laplacian	laplacian	NOUN
ejpam-5017	53	24	in	in	ADP
ejpam-5017	53	25	ω	ω	PROPN
ejpam-5017	53	26	with	with	ADP
ejpam-5017	53	27	homogenous	homogenous	ADJ
ejpam-5017	53	28	neumann	neumann	PROPN
ejpam-5017	53	29	boundary	boundary	ADJ
ejpam-5017	53	30	condition	condition	NOUN
ejpam-5017	53	31	.	.	PUNCT
ejpam-5017	54	1	let	let	VERB
ejpam-5017	54	2	αm{m	αm{m	NOUN
ejpam-5017	54	3	=	=	SYM
ejpam-5017	54	4	0	0	NUM
ejpam-5017	54	5	,	,	PUNCT
ejpam-5017	54	6	1	1	NUM
ejpam-5017	54	7	,	,	PUNCT
ejpam-5017	54	8	...	...	PUNCT
ejpam-5017	54	9	,	,	PUNCT
ejpam-5017	54	10	+	+	NOUN
ejpam-5017	54	11	∞	∞	NOUN
ejpam-5017	54	12	}	}	PUNCT
ejpam-5017	54	13	be	be	VERB
ejpam-5017	54	14	the	the	DET
ejpam-5017	54	15	eigenvalues	eigenvalue	NOUN
ejpam-5017	54	16	of	of	ADP
ejpam-5017	54	17	the	the	DET
ejpam-5017	54	18	laplacian	laplacian	ADJ
ejpam-5017	54	19	operator	operator	NOUN
ejpam-5017	54	20	in	in	ADP
ejpam-5017	54	21	l2	l2	NOUN
ejpam-5017	54	22	(	(	PUNCT
ejpam-5017	54	23	ω	ω	NOUN
ejpam-5017	54	24	)	)	PUNCT
ejpam-5017	54	25	with	with	ADP
ejpam-5017	54	26	homogenous	homogenous	ADJ
ejpam-5017	54	27	neumann	neumann	PROPN
ejpam-5017	54	28	boundary	boundary	ADJ
ejpam-5017	54	29	condition	condition	NOUN
ejpam-5017	54	30	and	and	CCONJ
ejpam-5017	54	31	let	let	VERB
ejpam-5017	54	32	ψm	ψm	PRON
ejpam-5017	54	33	be	be	AUX
ejpam-5017	54	34	the	the	DET
ejpam-5017	54	35	corresponding	correspond	VERB
ejpam-5017	54	36	eigenfunction	eigenfunction	NOUN
ejpam-5017	54	37	i.e.	i.e.	X
ejpam-5017	54	38			PUNCT
ejpam-5017	54	39	(	(	PUNCT
ejpam-5017	54	40	−∆n	−∆n	NUM
ejpam-5017	54	41	)	)	PUNCT
ejpam-5017	54	42	δψm	δψm	PROPN
ejpam-5017	54	43	=	=	PUNCT
ejpam-5017	54	44	αδ	αδ	PART
ejpam-5017	54	45	mψm	mψm	NOUN
ejpam-5017	54	46	in	in	ADP
ejpam-5017	54	47	ω	ω	PROPN
ejpam-5017	54	48	,	,	PUNCT
ejpam-5017	54	49	∂ψm	∂ψm	PROPN
ejpam-5017	54	50	∂t	∂t	PROPN
ejpam-5017	54	51	=	=	NOUN
ejpam-5017	54	52	0	0	PROPN
ejpam-5017	54	53	in	in	ADP
ejpam-5017	54	54	∂ω	∂ω	PROPN
ejpam-5017	54	55	,	,	PUNCT
ejpam-5017	54	56	and	and	CCONJ
ejpam-5017	54	57	d((−∆n	d((−∆n	PROPN
ejpam-5017	54	58	)	)	PUNCT
ejpam-5017	54	59	δ	δ	PROPN
ejpam-5017	54	60	)	)	PUNCT
ejpam-5017	55	1	=	=	PRON
ejpam-5017	55	2	{	{	PUNCT
ejpam-5017	55	3	w	w	NOUN
ejpam-5017	55	4	∈	∈	NOUN
ejpam-5017	55	5	l2	l2	NOUN
ejpam-5017	55	6	(	(	PUNCT
ejpam-5017	55	7	ω	ω	NOUN
ejpam-5017	55	8	)	)	PUNCT
ejpam-5017	55	9	;	;	PUNCT
ejpam-5017	56	1	∂w	∂w	PROPN
ejpam-5017	56	2	∂η	∂η	PROPN
ejpam-5017	57	1	=	=	PROPN
ejpam-5017	57	2	,	,	PUNCT
ejpam-5017	57	3	0	0	NUM
ejpam-5017	57	4	∥∥∥(−∆n	∥∥∥(−∆n	NOUN
ejpam-5017	57	5	)	)	PUNCT
ejpam-5017	57	6	δw	δw	ADP
ejpam-5017	57	7	∥∥∥	∥∥∥	PROPN
ejpam-5017	57	8	l2(ω	l2(ω	NUM
ejpam-5017	57	9	)	)	PUNCT
ejpam-5017	57	10	≺	≺	NOUN
ejpam-5017	57	11	+	+	NOUN
ejpam-5017	57	12	∞	∞	NOUN
ejpam-5017	57	13	}	}	PUNCT
ejpam-5017	57	14	∥∥∥(−∆n	∥∥∥(−∆n	PUNCT
ejpam-5017	57	15	)	)	PUNCT
ejpam-5017	57	16	δw	δw	ADP
ejpam-5017	57	17	∥∥∥	∥∥∥	PROPN
ejpam-5017	57	18	l2(ω	l2(ω	NUM
ejpam-5017	57	19	)	)	PUNCT
ejpam-5017	57	20	=	=	PUNCT
ejpam-5017	58	1	+	+	ADP
ejpam-5017	58	2	∞∑	∞∑	PROPN
ejpam-5017	58	3	m=1	m=1	PROPN
ejpam-5017	58	4	∣∣∣αδ	∣∣∣αδ	PROPN
ejpam-5017	58	5	m	m	VERB
ejpam-5017	58	6	⟨w	⟨w	X
ejpam-5017	58	7	,	,	PUNCT
ejpam-5017	58	8	ψm⟩	ψm⟩	NOUN
ejpam-5017	58	9	∣∣∣2	∣∣∣2	NOUN
ejpam-5017	58	10	so	so	ADV
ejpam-5017	58	11	for	for	ADP
ejpam-5017	58	12	w	w	PROPN
ejpam-5017	58	13	∈	∈	PROPN
ejpam-5017	58	14	d((−∆n	d((−∆n	PROPN
ejpam-5017	58	15	)	)	PUNCT
ejpam-5017	58	16	δ	δ	PROPN
ejpam-5017	58	17	)	)	PUNCT
ejpam-5017	58	18	we	we	PRON
ejpam-5017	58	19	get	get	VERB
ejpam-5017	58	20	(	(	PUNCT
ejpam-5017	58	21	−∆n	−∆n	NUM
ejpam-5017	58	22	)	)	PUNCT
ejpam-5017	58	23	δw	δw	ADP
ejpam-5017	59	1	=	=	PUNCT
ejpam-5017	60	1	+	+	ADP
ejpam-5017	60	2	∞∑	∞∑	PROPN
ejpam-5017	60	3	m=1	m=1	PROPN
ejpam-5017	60	4	αδ	αδ	ADP
ejpam-5017	60	5	m	m	PRON
ejpam-5017	60	6	⟨w	⟨w	X
ejpam-5017	60	7	,	,	PUNCT
ejpam-5017	60	8	ψm⟩ψm	ψm⟩ψm	VERB
ejpam-5017	60	9	we	we	PRON
ejpam-5017	60	10	obtain	obtain	VERB
ejpam-5017	60	11	the	the	DET
ejpam-5017	60	12	following	follow	VERB
ejpam-5017	60	13	integration	integration	NOUN
ejpam-5017	60	14	by	by	ADP
ejpam-5017	60	15	parts	part	NOUN
ejpam-5017	60	16	formula∫	formula∫	PROPN
ejpam-5017	60	17	ω	ω	PROPN
ejpam-5017	60	18	w(x)(−∆n	w(x)(−∆n	NOUN
ejpam-5017	60	19	)	)	PUNCT
ejpam-5017	60	20	δz(x)dx	δz(x)dx	VERB
ejpam-5017	60	21	=	=	SYM
ejpam-5017	60	22	∫	∫	PROPN
ejpam-5017	60	23	ω	ω	PROPN
ejpam-5017	60	24	z(x)(−∆n	z(x)(−∆n	NOUN
ejpam-5017	60	25	)	)	PUNCT
ejpam-5017	60	26	δw(x)dx	δw(x)dx	NOUN
ejpam-5017	60	27	,	,	PUNCT
ejpam-5017	60	28	for	for	ADP
ejpam-5017	60	29	w	w	PROPN
ejpam-5017	60	30	,	,	PUNCT
ejpam-5017	60	31	z	z	NOUN
ejpam-5017	60	32	∈	∈	PROPN
ejpam-5017	60	33	d((−∆n	d((−∆n	NOUN
ejpam-5017	60	34	)	)	PUNCT
ejpam-5017	60	35	δ	δ	PROPN
ejpam-5017	60	36	)	)	PUNCT
ejpam-5017	60	37	(	(	PUNCT
ejpam-5017	60	38	2	2	X
ejpam-5017	60	39	)	)	PUNCT
ejpam-5017	60	40	we	we	PRON
ejpam-5017	60	41	will	will	AUX
ejpam-5017	60	42	employ	employ	VERB
ejpam-5017	60	43	the	the	DET
ejpam-5017	60	44	following	follow	VERB
ejpam-5017	60	45	important	important	ADJ
ejpam-5017	60	46	inequalities	inequality	NOUN
ejpam-5017	60	47	of	of	ADP
ejpam-5017	60	48	strook	strook	NOUN
ejpam-5017	60	49	and	and	CCONJ
ejpam-5017	60	50	varopoulos	varopoulo	NOUN
ejpam-5017	60	51	see	see	VERB
ejpam-5017	60	52	(	(	PUNCT
ejpam-5017	60	53	[	[	X
ejpam-5017	60	54	8	8	NUM
ejpam-5017	60	55	]	]	PUNCT
ejpam-5017	60	56	,	,	PUNCT
ejpam-5017	60	57	theorem1	theorem1	PROPN
ejpam-5017	60	58	)	)	PUNCT
ejpam-5017	61	1	∫	∫	PROPN
ejpam-5017	61	2	ω	ω	NUM
ejpam-5017	61	3	w(x)(−∆n	w(x)(−∆n	NOUN
ejpam-5017	61	4	)	)	PUNCT
ejpam-5017	61	5	δw(x)dx	δw(x)dx	VERB
ejpam-5017	61	6	≥	≥	NOUN
ejpam-5017	61	7	0	0	NUM
ejpam-5017	61	8	,	,	PUNCT
ejpam-5017	61	9	for	for	ADP
ejpam-5017	61	10	w	w	PROPN
ejpam-5017	61	11	∈	∈	PROPN
ejpam-5017	61	12	d((−∆n	d((−∆n	PROPN
ejpam-5017	61	13	)	)	PUNCT
ejpam-5017	61	14	δ	δ	PROPN
ejpam-5017	61	15	)	)	PUNCT
ejpam-5017	61	16	(	(	PUNCT
ejpam-5017	61	17	3	3	X
ejpam-5017	61	18	)	)	PUNCT
ejpam-5017	61	19	∫	∫	PROPN
ejpam-5017	62	1	ω	ω	PROPN
ejpam-5017	62	2	wp−1(x)(−∆n	wp−1(x)(−∆n	PROPN
ejpam-5017	62	3	)	)	PUNCT
ejpam-5017	62	4	δw(x)dx	δw(x)dx	ADJ
ejpam-5017	62	5	≥	≥	NOUN
ejpam-5017	62	6	4(p−	4(p−	NUM
ejpam-5017	62	7	1	1	NUM
ejpam-5017	62	8	)	)	PUNCT
ejpam-5017	62	9	p2	p2	PROPN
ejpam-5017	63	1	∫	∫	PROPN
ejpam-5017	63	2	ω	ω	PROPN
ejpam-5017	63	3	∣∣∣(−∆n	∣∣∣(−∆n	PROPN
ejpam-5017	63	4	)	)	PUNCT
ejpam-5017	63	5	δ	δ	PROPN
ejpam-5017	63	6	2w(x	2w(x	PROPN
ejpam-5017	63	7	)	)	PUNCT
ejpam-5017	64	1	p	p	NOUN
ejpam-5017	64	2	2	2	NUM
ejpam-5017	64	3	∣∣∣2	∣∣∣2	NOUN
ejpam-5017	64	4	dx	dx	PROPN
ejpam-5017	64	5	≥	≥	PROPN
ejpam-5017	64	6	0	0	NUM
ejpam-5017	64	7	,	,	PUNCT
ejpam-5017	64	8	p	p	NOUN
ejpam-5017	64	9	≻	≻	PROPN
ejpam-5017	64	10	1	1	NUM
ejpam-5017	64	11	(	(	PUNCT
ejpam-5017	64	12	4	4	NUM
ejpam-5017	64	13	)	)	PUNCT
ejpam-5017	64	14	for	for	ADP
ejpam-5017	64	15	all	all	DET
ejpam-5017	64	16	w	w	PROPN
ejpam-5017	64	17	∈	∈	ADP
ejpam-5017	64	18	lp	lp	PROPN
ejpam-5017	64	19	(	(	PUNCT
ejpam-5017	64	20	ω	ω	NOUN
ejpam-5017	64	21	)	)	PUNCT
ejpam-5017	64	22	such	such	ADJ
ejpam-5017	64	23	that	that	SCONJ
ejpam-5017	64	24	(	(	PUNCT
ejpam-5017	64	25	−∆n	−∆n	NUM
ejpam-5017	64	26	)	)	PUNCT
ejpam-5017	64	27	δ	δ	PROPN
ejpam-5017	64	28	2w	2w	NUM
ejpam-5017	64	29	∈	∈	PROPN
ejpam-5017	64	30	lp	lp	PROPN
ejpam-5017	64	31	(	(	PUNCT
ejpam-5017	64	32	ω	ω	NOUN
ejpam-5017	64	33	)	)	PUNCT
ejpam-5017	64	34	m.	m.	NOUN
ejpam-5017	64	35	mebarki	mebarki	PROPN
ejpam-5017	64	36	/	/	SYM
ejpam-5017	64	37	eur	eur	PROPN
ejpam-5017	64	38	.	.	PUNCT
ejpam-5017	65	1	j.	j.	PROPN
ejpam-5017	65	2	pure	pure	PROPN
ejpam-5017	65	3	appl	appl	PROPN
ejpam-5017	65	4	.	.	PROPN
ejpam-5017	65	5	math	math	PROPN
ejpam-5017	65	6	,	,	PUNCT
ejpam-5017	65	7	17	17	NUM
ejpam-5017	65	8	(	(	PUNCT
ejpam-5017	65	9	2	2	NUM
ejpam-5017	65	10	)	)	PUNCT
ejpam-5017	65	11	(	(	PUNCT
ejpam-5017	65	12	2024	2024	NUM
ejpam-5017	65	13	)	)	PUNCT
ejpam-5017	65	14	,	,	PUNCT
ejpam-5017	65	15	1321	1321	NUM
ejpam-5017	65	16	-	-	SYM
ejpam-5017	65	17	1334	1334	NUM
ejpam-5017	65	18	1324	1324	NUM
ejpam-5017	65	19	definition	definition	NOUN
ejpam-5017	65	20	1	1	NUM
ejpam-5017	65	21	.	.	PUNCT
ejpam-5017	66	1	for	for	ADP
ejpam-5017	66	2	p	p	PROPN
ejpam-5017	66	3	∈	∈	PROPN
ejpam-5017	66	4	(	(	PUNCT
ejpam-5017	66	5	1,+∞	1,+∞	NUM
ejpam-5017	66	6	)	)	PUNCT
ejpam-5017	66	7	,	,	PUNCT
ejpam-5017	66	8	we	we	PRON
ejpam-5017	66	9	denote	denote	VERB
ejpam-5017	66	10	sp	sp	ADP
ejpam-5017	66	11	(	(	PUNCT
ejpam-5017	66	12	resp	resp	NOUN
ejpam-5017	66	13	.	.	PUNCT
ejpam-5017	67	1	tp	tp	X
ejpam-5017	67	2	)	)	PUNCT
ejpam-5017	67	3	the	the	DET
ejpam-5017	67	4	realisation	realisation	NOUN
ejpam-5017	67	5	of	of	ADP
ejpam-5017	67	6	(	(	PUNCT
ejpam-5017	67	7	−∆)δ	−∆)δ	X
ejpam-5017	67	8	(	(	PUNCT
ejpam-5017	67	9	resp	resp	NOUN
ejpam-5017	67	10	.	.	PUNCT
ejpam-5017	68	1	(	(	PUNCT
ejpam-5017	68	2	−∆)ϵ	−∆)ϵ	X
ejpam-5017	68	3	)	)	PUNCT
ejpam-5017	68	4	with	with	ADP
ejpam-5017	68	5	a	a	DET
ejpam-5017	68	6	homogeneous	homogeneous	ADJ
ejpam-5017	68	7	neumann	neumann	PROPN
ejpam-5017	68	8	boundary	boundary	ADJ
ejpam-5017	68	9	condition	condition	NOUN
ejpam-5017	68	10	in	in	ADP
ejpam-5017	68	11	lp	lp	PROPN
ejpam-5017	68	12	(	(	PUNCT
ejpam-5017	68	13	ω	ω	NOUN
ejpam-5017	68	14	)	)	PUNCT
ejpam-5017	68	15	.	.	PUNCT
ejpam-5017	69	1	it	it	PRON
ejpam-5017	69	2	is	be	AUX
ejpam-5017	69	3	well	well	ADV
ejpam-5017	69	4	known	know	VERB
ejpam-5017	69	5	that−sp	that−sp	NOUN
ejpam-5017	69	6	(	(	PUNCT
ejpam-5017	69	7	resp	resp	NOUN
ejpam-5017	69	8	.	.	PUNCT
ejpam-5017	70	1	−	−	PROPN
ejpam-5017	70	2	tp	tp	X
ejpam-5017	70	3	)	)	PUNCT
ejpam-5017	70	4	is	be	AUX
ejpam-5017	70	5	a	a	DET
ejpam-5017	70	6	sectorial	sectorial	ADJ
ejpam-5017	70	7	operator	operator	NOUN
ejpam-5017	70	8	(	(	PUNCT
ejpam-5017	70	9	see	see	VERB
ejpam-5017	70	10	[	[	X
ejpam-5017	70	11	4	4	NUM
ejpam-5017	70	12	]	]	NUM
ejpam-5017	70	13	)	)	PUNCT
ejpam-5017	70	14	;	;	PUNCT
ejpam-5017	70	15	hence−sp	hence−sp	PROPN
ejpam-5017	70	16	(	(	PUNCT
ejpam-5017	70	17	resp	resp	NOUN
ejpam-5017	70	18	.	.	PUNCT
ejpam-5017	71	1	−	−	PROPN
ejpam-5017	71	2	tp	tp	NOUN
ejpam-5017	71	3	)	)	PUNCT
ejpam-5017	71	4	generates	generate	VERB
ejpam-5017	71	5	an	an	DET
ejpam-5017	71	6	analytic	analytic	ADJ
ejpam-5017	71	7	semigroup	semigroup	NOUN
ejpam-5017	71	8	{	{	PUNCT
ejpam-5017	71	9	e−tsp}t≥0	e−tsp}t≥0	PROPN
ejpam-5017	71	10	(	(	PUNCT
ejpam-5017	71	11	resp	resp	NOUN
ejpam-5017	71	12	.	.	PUNCT
ejpam-5017	72	1	{	{	PUNCT
ejpam-5017	72	2	e−ttp}t≥0	e−ttp}t≥0	PROPN
ejpam-5017	72	3	)	)	PUNCT
ejpam-5017	72	4	lemma	lemma	PROPN
ejpam-5017	72	5	1	1	NUM
ejpam-5017	72	6	.	.	PUNCT
ejpam-5017	73	1	for	for	ADP
ejpam-5017	73	2	λ	λ	PROPN
ejpam-5017	73	3	∈	∈	PROPN
ejpam-5017	74	1	[	[	X
ejpam-5017	74	2	0	0	NUM
ejpam-5017	74	3	,	,	PUNCT
ejpam-5017	74	4	1	1	NUM
ejpam-5017	74	5	]	]	PUNCT
ejpam-5017	74	6	and	and	CCONJ
ejpam-5017	74	7	µ	µ	PRON
ejpam-5017	74	8	∈	∈	NOUN
ejpam-5017	74	9	r	r	NOUN
ejpam-5017	74	10	,	,	PUNCT
ejpam-5017	74	11	there	there	PRON
ejpam-5017	74	12	exists	exist	VERB
ejpam-5017	74	13	a	a	DET
ejpam-5017	74	14	constant	constant	ADJ
ejpam-5017	74	15	m	m	NOUN
ejpam-5017	74	16	(	(	PUNCT
ejpam-5017	74	17	λ	λ	PROPN
ejpam-5017	74	18	,	,	PUNCT
ejpam-5017	74	19	µ	µ	NOUN
ejpam-5017	74	20	)	)	PUNCT
ejpam-5017	74	21	such	such	ADJ
ejpam-5017	74	22	that	that	SCONJ
ejpam-5017	74	23	,	,	PUNCT
ejpam-5017	74	24	for	for	ADP
ejpam-5017	74	25	all	all	DET
ejpam-5017	74	26	t	t	PROPN
ejpam-5017	74	27	≻	≻	PROPN
ejpam-5017	74	28	0	0	NUM
ejpam-5017	74	29	,	,	PUNCT
ejpam-5017	74	30	∫	∫	PROPN
ejpam-5017	74	31	t	t	PROPN
ejpam-5017	74	32	0	0	NUM
ejpam-5017	74	33	c(s)−λeµsds	c(s)−λeµsds	NOUN
ejpam-5017	75	1	≤	≤	NUM
ejpam-5017	76	1			PUNCT
ejpam-5017	76	2	m	m	PROPN
ejpam-5017	76	3	(	(	PUNCT
ejpam-5017	76	4	λ	λ	PROPN
ejpam-5017	76	5	,	,	PUNCT
ejpam-5017	76	6	µ	µ	NOUN
ejpam-5017	76	7	)	)	PUNCT
ejpam-5017	76	8	eµt	eµt	NOUN
ejpam-5017	76	9	,	,	PUNCT
ejpam-5017	76	10	if	if	SCONJ
ejpam-5017	76	11	µ	µ	PROPN
ejpam-5017	76	12	≻	≻	NOUN
ejpam-5017	76	13	0	0	NUM
ejpam-5017	76	14	,	,	PUNCT
ejpam-5017	76	15	m	m	VERB
ejpam-5017	76	16	(	(	PUNCT
ejpam-5017	76	17	λ	λ	PROPN
ejpam-5017	76	18	,	,	PUNCT
ejpam-5017	76	19	µ	µ	NOUN
ejpam-5017	76	20	)	)	PUNCT
ejpam-5017	76	21	(	(	PUNCT
ejpam-5017	76	22	t+	t+	NOUN
ejpam-5017	76	23	1	1	NUM
ejpam-5017	76	24	)	)	PUNCT
ejpam-5017	76	25	,	,	PUNCT
ejpam-5017	76	26	if	if	SCONJ
ejpam-5017	76	27	µ	µ	X
ejpam-5017	76	28	=	=	SYM
ejpam-5017	76	29	0	0	NUM
ejpam-5017	76	30	,	,	PUNCT
ejpam-5017	76	31	m	m	VERB
ejpam-5017	76	32	(	(	PUNCT
ejpam-5017	76	33	λ	λ	PROPN
ejpam-5017	76	34	,	,	PUNCT
ejpam-5017	76	35	µ	µ	NOUN
ejpam-5017	76	36	)	)	PUNCT
ejpam-5017	76	37	,	,	PUNCT
ejpam-5017	76	38	if	if	SCONJ
ejpam-5017	76	39	µ	µ	PRON
ejpam-5017	76	40	≺	≺	NOUN
ejpam-5017	76	41	0	0	NUM
ejpam-5017	76	42	,	,	PUNCT
ejpam-5017	76	43	here	here	ADV
ejpam-5017	76	44	c(t	c(t	PROPN
ejpam-5017	76	45	)	)	PUNCT
ejpam-5017	76	46	=	=	PUNCT
ejpam-5017	76	47	min{t	min{t	PROPN
ejpam-5017	76	48	,	,	PUNCT
ejpam-5017	76	49	1	1	NUM
ejpam-5017	76	50	}	}	PUNCT
ejpam-5017	76	51	.	.	PUNCT
ejpam-5017	77	1	proof	proof	NOUN
ejpam-5017	77	2	.	.	PUNCT
ejpam-5017	78	1	see	see	VERB
ejpam-5017	78	2	[	[	X
ejpam-5017	78	3	5	5	X
ejpam-5017	78	4	]	]	X
ejpam-5017	78	5	lemma	lemma	PROPN
ejpam-5017	78	6	2	2	X
ejpam-5017	78	7	.	.	PUNCT
ejpam-5017	78	8	let	let	VERB
ejpam-5017	78	9	p	p	PRON
ejpam-5017	78	10	,	,	PUNCT
ejpam-5017	78	11	q	q	ADJ
ejpam-5017	78	12	,	,	PUNCT
ejpam-5017	78	13	r	r	NOUN
ejpam-5017	78	14	∈	∈	PROPN
ejpam-5017	79	1	[	[	X
ejpam-5017	79	2	0	0	NUM
ejpam-5017	79	3	,	,	PUNCT
ejpam-5017	79	4	1	1	NUM
ejpam-5017	79	5	]	]	PUNCT
ejpam-5017	79	6	,	,	PUNCT
ejpam-5017	79	7	r	r	NOUN
ejpam-5017	79	8	≤	≤	PUNCT
ejpam-5017	79	9	p	p	NOUN
ejpam-5017	79	10	≤	≤	ADJ
ejpam-5017	79	11	q	q	PUNCT
ejpam-5017	79	12	and	and	CCONJ
ejpam-5017	79	13	λ	λ	X
ejpam-5017	79	14	∈	∈	PROPN
ejpam-5017	80	1	[	[	X
ejpam-5017	80	2	0	0	NUM
ejpam-5017	80	3	,	,	PUNCT
ejpam-5017	80	4	1	1	NUM
ejpam-5017	80	5	]	]	PUNCT
ejpam-5017	80	6	be	be	AUX
ejpam-5017	80	7	such	such	ADJ
ejpam-5017	80	8	that	that	SCONJ
ejpam-5017	80	9	1	1	NUM
ejpam-5017	80	10	p	p	NOUN
ejpam-5017	80	11	=	=	PUNCT
ejpam-5017	80	12	λ	λ	X
ejpam-5017	80	13	r	r	NOUN
ejpam-5017	80	14	+	+	NUM
ejpam-5017	80	15	1−λ	1−λ	NUM
ejpam-5017	80	16	q	q	NOUN
ejpam-5017	80	17	,	,	PUNCT
ejpam-5017	80	18	we	we	PRON
ejpam-5017	80	19	gain∥∥e−tspw	gain∥∥e−tspw	VERB
ejpam-5017	80	20	∥∥	∥∥	X
ejpam-5017	80	21	p	p	NOUN
ejpam-5017	80	22	≤	≤	NUM
ejpam-5017	80	23	e−αδ	e−αδ	NOUN
ejpam-5017	80	24	1λtc(t	1λtc(t	NUM
ejpam-5017	80	25	)	)	PUNCT
ejpam-5017	81	1	−n	−n	SYM
ejpam-5017	81	2	2δ	2δ	NUM
ejpam-5017	81	3	(	(	PUNCT
ejpam-5017	81	4	1	1	NUM
ejpam-5017	81	5	r	r	NOUN
ejpam-5017	81	6	−	−	NOUN
ejpam-5017	81	7	1	1	NUM
ejpam-5017	81	8	p	p	NOUN
ejpam-5017	81	9	)	)	PUNCT
ejpam-5017	81	10	∥w∥r	∥w∥r	NOUN
ejpam-5017	81	11	proof	proof	NOUN
ejpam-5017	81	12	.	.	PUNCT
ejpam-5017	82	1	see	see	VERB
ejpam-5017	82	2	[	[	X
ejpam-5017	82	3	3	3	X
ejpam-5017	82	4	]	]	PUNCT
ejpam-5017	82	5	by	by	ADP
ejpam-5017	82	6	the	the	DET
ejpam-5017	82	7	interpolation	interpolation	NOUN
ejpam-5017	82	8	inequality	inequality	NOUN
ejpam-5017	82	9	,	,	PUNCT
ejpam-5017	82	10	we	we	PRON
ejpam-5017	82	11	obtain∥∥e−tspw	obtain∥∥e−tspw	X
ejpam-5017	82	12	∥∥	∥∥	X
ejpam-5017	83	1	p	p	PROPN
ejpam-5017	83	2	≤	≤	PUNCT
ejpam-5017	83	3	∥∥e−tspw	∥∥e−tspw	PROPN
ejpam-5017	83	4	∥∥λ	∥∥λ	NOUN
ejpam-5017	83	5	r	r	NOUN
ejpam-5017	83	6	∥∥e−tspw	∥∥e−tspw	PROPN
ejpam-5017	83	7	∥∥1−λ	∥∥1−λ	PROPN
ejpam-5017	83	8	q	q	X
ejpam-5017	83	9	(	(	PUNCT
ejpam-5017	83	10	5	5	NUM
ejpam-5017	83	11	)	)	PUNCT
ejpam-5017	83	12	practising	practise	VERB
ejpam-5017	83	13	the	the	DET
ejpam-5017	83	14	following	following	NOUN
ejpam-5017	83	15	inequalities∥∥e−tspw	inequalities∥∥e−tspw	PROPN
ejpam-5017	83	16	∥∥	∥∥	X
ejpam-5017	83	17	r	r	NOUN
ejpam-5017	83	18	≤	≤	NUM
ejpam-5017	83	19	e−αδ	e−αδ	NOUN
ejpam-5017	83	20	1	1	NUM
ejpam-5017	83	21	t	t	NOUN
ejpam-5017	83	22	∥w∥r	∥w∥r	NOUN
ejpam-5017	83	23	(	(	PUNCT
ejpam-5017	83	24	6	6	NUM
ejpam-5017	83	25	)	)	PUNCT
ejpam-5017	83	26	and	and	CCONJ
ejpam-5017	83	27	∥∥e−tspw	∥∥e−tspw	X
ejpam-5017	83	28	∥∥	∥∥	PROPN
ejpam-5017	83	29	q	q	PROPN
ejpam-5017	83	30	≤	≤	PROPN
ejpam-5017	83	31	t	t	NOUN
ejpam-5017	83	32	−n	−n	ADJ
ejpam-5017	83	33	2δ	2δ	NUM
ejpam-5017	83	34	(	(	PUNCT
ejpam-5017	83	35	1r−	1r−	PROPN
ejpam-5017	83	36	1	1	NUM
ejpam-5017	83	37	q	q	NOUN
ejpam-5017	83	38	)	)	PUNCT
ejpam-5017	83	39	∥w∥r	∥w∥r	NOUN
ejpam-5017	83	40	,	,	PUNCT
ejpam-5017	83	41	(	(	PUNCT
ejpam-5017	83	42	7	7	X
ejpam-5017	83	43	)	)	PUNCT
ejpam-5017	83	44	we	we	PRON
ejpam-5017	83	45	get	get	VERB
ejpam-5017	83	46	∥∥e−tspw	∥∥e−tspw	PROPN
ejpam-5017	83	47	∥∥	∥∥	PROPN
ejpam-5017	83	48	p	p	NOUN
ejpam-5017	83	49	≤	≤	NUM
ejpam-5017	83	50	e−αδ	e−αδ	NOUN
ejpam-5017	83	51	1λtt	1λtt	NUM
ejpam-5017	83	52	−n	−n	NUM
ejpam-5017	83	53	2δ	2δ	NUM
ejpam-5017	83	54	(	(	PUNCT
ejpam-5017	83	55	1−λ	1−λ	NUM
ejpam-5017	83	56	)	)	PUNCT
ejpam-5017	83	57	(	(	PUNCT
ejpam-5017	83	58	1r−	1r−	PROPN
ejpam-5017	83	59	1	1	NUM
ejpam-5017	83	60	q	q	NOUN
ejpam-5017	83	61	)	)	PUNCT
ejpam-5017	83	62	∥w∥r	∥w∥r	NOUN
ejpam-5017	83	63	,	,	PUNCT
ejpam-5017	83	64	(	(	PUNCT
ejpam-5017	83	65	8)	8)	NUM
ejpam-5017	83	66	here	here	ADV
ejpam-5017	83	67	(	(	PUNCT
ejpam-5017	83	68	1−	1−	NUM
ejpam-5017	83	69	λ)(1r	λ)(1r	PROPN
ejpam-5017	83	70	−	−	PROPN
ejpam-5017	83	71	1	1	NUM
ejpam-5017	83	72	q	q	NOUN
ejpam-5017	83	73	)	)	PUNCT
ejpam-5017	83	74	=	=	SYM
ejpam-5017	84	1	(	(	PUNCT
ejpam-5017	84	2	1r	1r	NUM
ejpam-5017	84	3	−	−	PROPN
ejpam-5017	84	4	1	1	NUM
ejpam-5017	84	5	p	p	NOUN
ejpam-5017	84	6	)	)	PUNCT
ejpam-5017	84	7	.	.	PUNCT
ejpam-5017	85	1	consequently	consequently	ADV
ejpam-5017	85	2	,	,	PUNCT
ejpam-5017	85	3	we	we	PRON
ejpam-5017	85	4	gain∥∥e−tspw	gain∥∥e−tspw	VERB
ejpam-5017	85	5	∥∥	∥∥	X
ejpam-5017	85	6	p	p	NOUN
ejpam-5017	85	7	≤	≤	NUM
ejpam-5017	85	8	e−αδ	e−αδ	NOUN
ejpam-5017	85	9	1λtt	1λtt	NUM
ejpam-5017	85	10	−n	−n	NUM
ejpam-5017	85	11	2δ	2δ	NUM
ejpam-5017	85	12	(	(	PUNCT
ejpam-5017	85	13	1r−	1r−	PROPN
ejpam-5017	85	14	1	1	NUM
ejpam-5017	85	15	p	p	NOUN
ejpam-5017	85	16	)	)	PUNCT
ejpam-5017	85	17	∥w∥r	∥w∥r	NOUN
ejpam-5017	85	18	(	(	PUNCT
ejpam-5017	85	19	9	9	NUM
ejpam-5017	85	20	)	)	PUNCT
ejpam-5017	85	21	≤	≤	NUM
ejpam-5017	85	22	e−αδ	e−αδ	NOUN
ejpam-5017	85	23	1λtc(t	1λtc(t	NUM
ejpam-5017	85	24	)	)	PUNCT
ejpam-5017	86	1	−n	−n	SYM
ejpam-5017	86	2	2δ	2δ	NUM
ejpam-5017	86	3	(	(	PUNCT
ejpam-5017	86	4	1	1	NUM
ejpam-5017	86	5	r	r	NOUN
ejpam-5017	86	6	−	−	NOUN
ejpam-5017	86	7	1	1	NUM
ejpam-5017	86	8	p	p	NOUN
ejpam-5017	86	9	)	)	PUNCT
ejpam-5017	86	10	∥w∥	∥w∥	PROPN
ejpam-5017	86	11	r	r	NOUN
ejpam-5017	86	12	where	where	SCONJ
ejpam-5017	86	13	c(t	c(t	NOUN
ejpam-5017	86	14	)	)	PUNCT
ejpam-5017	86	15	=	=	PUNCT
ejpam-5017	86	16	min{t	min{t	PROPN
ejpam-5017	86	17	,	,	PUNCT
ejpam-5017	86	18	1	1	NUM
ejpam-5017	86	19	}	}	PUNCT
ejpam-5017	86	20	.	.	PUNCT
ejpam-5017	87	1	remark	remark	NOUN
ejpam-5017	87	2	:	:	PUNCT
ejpam-5017	87	3	an	an	DET
ejpam-5017	87	4	main	main	ADJ
ejpam-5017	87	5	result	result	NOUN
ejpam-5017	87	6	in	in	ADP
ejpam-5017	87	7	[	[	X
ejpam-5017	87	8	8	8	NUM
ejpam-5017	87	9	]	]	PUNCT
ejpam-5017	87	10	comes	come	VERB
ejpam-5017	87	11	in	in	ADP
ejpam-5017	87	12	our	our	PRON
ejpam-5017	87	13	case	case	NOUN
ejpam-5017	87	14	∀ξ	∀ξ	X
ejpam-5017	87	15	≻	≻	NUM
ejpam-5017	87	16	0,∃m(ξ	0,∃m(ξ	NOUN
ejpam-5017	87	17	)	)	PUNCT
ejpam-5017	87	18	∈	∈	PROPN
ejpam-5017	87	19	r+	r+	NOUN
ejpam-5017	87	20	such	such	ADJ
ejpam-5017	87	21	that∥∥e−ttpz	that∥∥e−ttpz	NOUN
ejpam-5017	87	22	∥∥	∥∥	X
ejpam-5017	87	23	∞	∞	NUM
ejpam-5017	87	24	≤	≤	PUNCT
ejpam-5017	88	1	m(ξ)t	m(ξ)t	PROPN
ejpam-5017	88	2	−n	−n	NOUN
ejpam-5017	88	3	(	(	PUNCT
ejpam-5017	88	4	n+ξ)ϵ	n+ξ)ϵ	NOUN
ejpam-5017	88	5	)	)	PUNCT
ejpam-5017	88	6	∥z∥n	∥z∥n	VERB
ejpam-5017	88	7	2	2	NUM
ejpam-5017	89	1	+	+	ADJ
ejpam-5017	89	2	ξ′	ξ′	NOUN
ejpam-5017	89	3	,	,	PUNCT
ejpam-5017	89	4	for	for	ADP
ejpam-5017	89	5	all	all	DET
ejpam-5017	89	6	z	z	NOUN
ejpam-5017	89	7	∈	∈	PROPN
ejpam-5017	89	8	l∞	l∞	NOUN
ejpam-5017	89	9	(	(	PUNCT
ejpam-5017	89	10	ω	ω	NOUN
ejpam-5017	89	11	)	)	PUNCT
ejpam-5017	89	12	,	,	PUNCT
ejpam-5017	89	13	t	t	PROPN
ejpam-5017	89	14	≻	≻	PROPN
ejpam-5017	89	15	0	0	NUM
ejpam-5017	89	16	.	.	PUNCT
ejpam-5017	90	1	(	(	PUNCT
ejpam-5017	90	2	10	10	NUM
ejpam-5017	90	3	)	)	PUNCT
ejpam-5017	90	4	the	the	DET
ejpam-5017	90	5	relation	relation	NOUN
ejpam-5017	90	6	(	(	PUNCT
ejpam-5017	90	7	10	10	NUM
ejpam-5017	90	8	)	)	PUNCT
ejpam-5017	90	9	with	with	ADP
ejpam-5017	90	10	ϵ	ϵ	PROPN
ejpam-5017	90	11	=	=	SYM
ejpam-5017	90	12	1	1	NUM
ejpam-5017	90	13	injected	inject	VERB
ejpam-5017	90	14	with	with	ADP
ejpam-5017	90	15	a	a	DET
ejpam-5017	90	16	successive	successive	ADJ
ejpam-5017	90	17	iterations	iteration	NOUN
ejpam-5017	90	18	method	method	NOUN
ejpam-5017	90	19	have	have	AUX
ejpam-5017	90	20	been	be	AUX
ejpam-5017	90	21	used	use	VERB
ejpam-5017	90	22	in	in	ADP
ejpam-5017	90	23	(	(	PUNCT
ejpam-5017	90	24	[	[	X
ejpam-5017	90	25	8	8	NUM
ejpam-5017	90	26	]	]	PUNCT
ejpam-5017	90	27	proposition	proposition	NOUN
ejpam-5017	90	28	3.3	3.3	NUM
ejpam-5017	90	29	)	)	PUNCT
ejpam-5017	90	30	to	to	PART
ejpam-5017	90	31	prove	prove	VERB
ejpam-5017	90	32	that	that	SCONJ
ejpam-5017	90	33	the	the	DET
ejpam-5017	90	34	solutions	solution	NOUN
ejpam-5017	90	35	are	be	AUX
ejpam-5017	90	36	bounded	bound	VERB
ejpam-5017	90	37	in	in	ADP
ejpam-5017	90	38	c	c	PROPN
ejpam-5017	90	39	(	(	PUNCT
ejpam-5017	90	40	ω	ω	PROPN
ejpam-5017	90	41	)	)	PUNCT
ejpam-5017	90	42	.	.	PUNCT
ejpam-5017	91	1	m.	m.	NOUN
ejpam-5017	91	2	mebarki	mebarki	PROPN
ejpam-5017	91	3	/	/	SYM
ejpam-5017	91	4	eur	eur	PROPN
ejpam-5017	91	5	.	.	PUNCT
ejpam-5017	92	1	j.	j.	PROPN
ejpam-5017	92	2	pure	pure	PROPN
ejpam-5017	92	3	appl	appl	PROPN
ejpam-5017	92	4	.	.	PROPN
ejpam-5017	92	5	math	math	PROPN
ejpam-5017	92	6	,	,	PUNCT
ejpam-5017	92	7	17	17	NUM
ejpam-5017	92	8	(	(	PUNCT
ejpam-5017	92	9	2	2	NUM
ejpam-5017	92	10	)	)	PUNCT
ejpam-5017	92	11	(	(	PUNCT
ejpam-5017	92	12	2024	2024	NUM
ejpam-5017	92	13	)	)	PUNCT
ejpam-5017	92	14	,	,	PUNCT
ejpam-5017	92	15	1321	1321	NUM
ejpam-5017	92	16	-	-	SYM
ejpam-5017	92	17	1334	1334	NUM
ejpam-5017	92	18	1325	1325	NUM
ejpam-5017	92	19	3	3	NUM
ejpam-5017	92	20	.	.	PUNCT
ejpam-5017	92	21	local	local	ADJ
ejpam-5017	92	22	existence	existence	NOUN
ejpam-5017	92	23	in	in	ADP
ejpam-5017	92	24	this	this	DET
ejpam-5017	92	25	section	section	NOUN
ejpam-5017	92	26	,	,	PUNCT
ejpam-5017	92	27	we	we	PRON
ejpam-5017	92	28	investigate	investigate	VERB
ejpam-5017	92	29	the	the	DET
ejpam-5017	92	30	local	local	ADJ
ejpam-5017	92	31	existence	existence	NOUN
ejpam-5017	92	32	of	of	ADP
ejpam-5017	92	33	mild	mild	ADJ
ejpam-5017	92	34	solutions	solution	NOUN
ejpam-5017	92	35	to	to	ADP
ejpam-5017	92	36	the	the	DET
ejpam-5017	92	37	problem	problem	NOUN
ejpam-5017	92	38	(	(	PUNCT
ejpam-5017	92	39	1)-(2	1)-(2	NUM
ejpam-5017	92	40	)	)	PUNCT
ejpam-5017	92	41	lemma	lemma	PROPN
ejpam-5017	92	42	3	3	NUM
ejpam-5017	92	43	(	(	PUNCT
ejpam-5017	92	44	definition	definition	NOUN
ejpam-5017	92	45	)	)	PUNCT
ejpam-5017	92	46	.	.	PUNCT
ejpam-5017	93	1	(	(	PUNCT
ejpam-5017	93	2	mild	mild	ADJ
ejpam-5017	93	3	solution	solution	NOUN
ejpam-5017	93	4	)	)	PUNCT
ejpam-5017	93	5	let	let	VERB
ejpam-5017	93	6	w0	w0	PROPN
ejpam-5017	93	7	,	,	PUNCT
ejpam-5017	93	8	z0	z0	PROPN
ejpam-5017	93	9	∈	∈	PROPN
ejpam-5017	93	10	l∞	l∞	PROPN
ejpam-5017	93	11	(	(	PUNCT
ejpam-5017	93	12	ω	ω	NOUN
ejpam-5017	93	13	)	)	PUNCT
ejpam-5017	93	14	and	and	CCONJ
ejpam-5017	93	15	t	t	PROPN
ejpam-5017	93	16	≻	≻	PROPN
ejpam-5017	93	17	0	0	X
ejpam-5017	93	18	.	.	PUNCT
ejpam-5017	94	1	we	we	PRON
ejpam-5017	94	2	say	say	VERB
ejpam-5017	94	3	that	that	SCONJ
ejpam-5017	94	4	(	(	PUNCT
ejpam-5017	94	5	w	w	PROPN
ejpam-5017	94	6	,	,	PUNCT
ejpam-5017	94	7	z	z	NOUN
ejpam-5017	94	8	)	)	PUNCT
ejpam-5017	94	9	∈c	∈c	PROPN
ejpam-5017	94	10	(	(	PUNCT
ejpam-5017	94	11	[	[	X
ejpam-5017	94	12	0	0	NUM
ejpam-5017	94	13	,	,	PUNCT
ejpam-5017	94	14	t	t	X
ejpam-5017	94	15	]	]	PUNCT
ejpam-5017	94	16	;	;	PUNCT
ejpam-5017	94	17	l∞	l∞	X
ejpam-5017	94	18	(	(	PUNCT
ejpam-5017	94	19	ω)×	ω)×	PROPN
ejpam-5017	94	20	l∞	l∞	PROPN
ejpam-5017	94	21	(	(	PUNCT
ejpam-5017	94	22	ω	ω	NOUN
ejpam-5017	94	23	)	)	PUNCT
ejpam-5017	94	24	)	)	PUNCT
ejpam-5017	94	25	is	be	AUX
ejpam-5017	94	26	a	a	DET
ejpam-5017	94	27	mild	mild	ADJ
ejpam-5017	94	28	solution	solution	NOUN
ejpam-5017	94	29	of	of	ADP
ejpam-5017	94	30	(	(	PUNCT
ejpam-5017	94	31	1)-(2	1)-(2	NUM
ejpam-5017	94	32	)	)	PUNCT
ejpam-5017	94	33	if	if	SCONJ
ejpam-5017	94	34	w	w	NOUN
ejpam-5017	94	35	,	,	PUNCT
ejpam-5017	94	36	z	z	NOUN
ejpam-5017	94	37	satisfy	satisfy	VERB
ejpam-5017	94	38	the	the	DET
ejpam-5017	94	39	followings	following	NOUN
ejpam-5017	94	40	integral	integral	ADJ
ejpam-5017	94	41	equations	equation	NOUN
ejpam-5017	94	42	for	for	ADP
ejpam-5017	94	43	t	t	PROPN
ejpam-5017	94	44	∈	∈	PROPN
ejpam-5017	95	1	[	[	X
ejpam-5017	95	2	0	0	NUM
ejpam-5017	95	3	,	,	PUNCT
ejpam-5017	95	4	t	t	X
ejpam-5017	95	5	]	]	PUNCT
ejpam-5017	95	6	:	:	PUNCT
ejpam-5017	95	7	{	{	PUNCT
ejpam-5017	95	8	w(t	w(t	NOUN
ejpam-5017	95	9	)	)	PUNCT
ejpam-5017	95	10	=	=	SYM
ejpam-5017	95	11	e−d1tspw0	e−d1tspw0	NOUN
ejpam-5017	95	12	+	+	CCONJ
ejpam-5017	95	13	∫	∫	PROPN
ejpam-5017	95	14	t	t	NOUN
ejpam-5017	95	15	0	0	NUM
ejpam-5017	95	16	e	e	NOUN
ejpam-5017	95	17	−d1(t−s)sp(−w2z	−d1(t−s)sp(−w2z	NOUN
ejpam-5017	95	18	+	+	CCONJ
ejpam-5017	95	19	f(1−	f(1−	PROPN
ejpam-5017	95	20	w))ds	w))ds	PROPN
ejpam-5017	95	21	,	,	PUNCT
ejpam-5017	95	22	z(t	z(t	PROPN
ejpam-5017	95	23	)	)	PUNCT
ejpam-5017	95	24	=	=	SYM
ejpam-5017	96	1	e−d2ttpz0	e−d2ttpz0	ADJ
ejpam-5017	96	2	+	+	NUM
ejpam-5017	96	3	∫	∫	PROPN
ejpam-5017	96	4	t	t	NOUN
ejpam-5017	96	5	0	0	PUNCT
ejpam-5017	97	1	e	e	X
ejpam-5017	97	2	−d2(t−s)tp(w2z	−d2(t−s)tp(w2z	NOUN
ejpam-5017	97	3	−	−	PROPN
ejpam-5017	98	1	(	(	PUNCT
ejpam-5017	98	2	f	f	PROPN
ejpam-5017	98	3	+	+	CCONJ
ejpam-5017	98	4	k)z)ds	k)z)ds	PROPN
ejpam-5017	98	5	.	.	PROPN
ejpam-5017	99	1	(	(	PUNCT
ejpam-5017	99	2	11	11	NUM
ejpam-5017	99	3	)	)	PUNCT
ejpam-5017	99	4	theorem	theorem	NOUN
ejpam-5017	99	5	1	1	NUM
ejpam-5017	99	6	.	.	PUNCT
ejpam-5017	99	7	local	local	ADJ
ejpam-5017	99	8	existence	existence	NOUN
ejpam-5017	99	9	let	let	VERB
ejpam-5017	99	10	w0	w0	PROPN
ejpam-5017	99	11	,	,	PUNCT
ejpam-5017	100	1	z0	z0	PROPN
ejpam-5017	100	2	∈	∈	PROPN
ejpam-5017	100	3	c	c	PROPN
ejpam-5017	100	4	(	(	PUNCT
ejpam-5017	100	5	ω	ω	PROPN
ejpam-5017	100	6	)	)	PUNCT
ejpam-5017	100	7	,	,	PUNCT
ejpam-5017	100	8	then	then	ADV
ejpam-5017	100	9	there	there	PRON
ejpam-5017	100	10	exist	exist	VERB
ejpam-5017	100	11	a	a	DET
ejpam-5017	100	12	maximal	maximal	ADJ
ejpam-5017	100	13	time	time	NOUN
ejpam-5017	100	14	tmax	tmax	ADP
ejpam-5017	100	15	≻	≻	PROPN
ejpam-5017	100	16	0	0	NUM
ejpam-5017	100	17	and	and	CCONJ
ejpam-5017	100	18	a	a	DET
ejpam-5017	100	19	unique	unique	ADJ
ejpam-5017	100	20	mild	mild	ADJ
ejpam-5017	100	21	solution	solution	NOUN
ejpam-5017	100	22	(	(	PUNCT
ejpam-5017	100	23	w	w	PROPN
ejpam-5017	100	24	,	,	PUNCT
ejpam-5017	100	25	z	z	NOUN
ejpam-5017	100	26	)	)	PUNCT
ejpam-5017	100	27	∈c	∈c	PROPN
ejpam-5017	100	28	(	(	PUNCT
ejpam-5017	100	29	[	[	X
ejpam-5017	100	30	0	0	NUM
ejpam-5017	100	31	,	,	PUNCT
ejpam-5017	100	32	tmax);c	tmax);c	PROPN
ejpam-5017	100	33	(	(	PUNCT
ejpam-5017	100	34	ω	ω	NOUN
ejpam-5017	100	35	)	)	PUNCT
ejpam-5017	100	36	×	×	PROPN
ejpam-5017	100	37	c	c	PROPN
ejpam-5017	100	38	(	(	PUNCT
ejpam-5017	100	39	ω	ω	NOUN
ejpam-5017	100	40	)	)	PUNCT
ejpam-5017	100	41	)	)	PUNCT
ejpam-5017	100	42	to	to	ADP
ejpam-5017	100	43	the	the	DET
ejpam-5017	100	44	system	system	NOUN
ejpam-5017	100	45	(	(	PUNCT
ejpam-5017	100	46	1)-(2	1)-(2	NUM
ejpam-5017	100	47	)	)	PUNCT
ejpam-5017	100	48	,	,	PUNCT
ejpam-5017	100	49	with	with	ADP
ejpam-5017	100	50	the	the	DET
ejpam-5017	100	51	alternative	alternative	NOUN
ejpam-5017	100	52	:	:	PUNCT
ejpam-5017	100	53	-either	-either	ADJ
ejpam-5017	100	54	tmax	tmax	NOUN
ejpam-5017	100	55	=	=	PUNCT
ejpam-5017	100	56	+	+	NUM
ejpam-5017	100	57	∞	∞	NOUN
ejpam-5017	100	58	;	;	PUNCT
ejpam-5017	100	59	-or	-or	X
ejpam-5017	100	60	tmax	tmax	VERB
ejpam-5017	100	61	≺	≺	NOUN
ejpam-5017	100	62	+	+	NOUN
ejpam-5017	100	63	∞	∞	PROPN
ejpam-5017	100	64	and	and	CCONJ
ejpam-5017	100	65	limt→tmax(∥w(t)∥∞	limt→tmax(∥w(t)∥∞	PROPN
ejpam-5017	100	66	+	+	CCONJ
ejpam-5017	100	67	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	100	68	)	)	PUNCT
ejpam-5017	100	69	=	=	PUNCT
ejpam-5017	101	1	+	+	ADP
ejpam-5017	101	2	∞.	∞.	PROPN
ejpam-5017	101	3	proof	proof	NOUN
ejpam-5017	101	4	.	.	PUNCT
ejpam-5017	102	1	∀t	∀t	PROPN
ejpam-5017	102	2	≻	≻	PROPN
ejpam-5017	102	3	0	0	NUM
ejpam-5017	102	4	,	,	PUNCT
ejpam-5017	102	5	we	we	PRON
ejpam-5017	102	6	define	define	VERB
ejpam-5017	102	7	the	the	DET
ejpam-5017	102	8	banach	banach	NOUN
ejpam-5017	102	9	space	space	NOUN
ejpam-5017	102	10	:	:	PUNCT
ejpam-5017	102	11	bt	bt	X
ejpam-5017	102	12	:	:	PUNCT
ejpam-5017	103	1	=	=	SYM
ejpam-5017	103	2	{	{	PUNCT
ejpam-5017	103	3	(	(	PUNCT
ejpam-5017	103	4	w	w	PROPN
ejpam-5017	103	5	,	,	PUNCT
ejpam-5017	103	6	z	z	NOUN
ejpam-5017	103	7	)	)	PUNCT
ejpam-5017	103	8	∈	∈	PROPN
ejpam-5017	103	9	c	c	NOUN
ejpam-5017	103	10	(	(	PUNCT
ejpam-5017	103	11	[	[	X
ejpam-5017	103	12	0	0	NUM
ejpam-5017	103	13	,	,	PUNCT
ejpam-5017	103	14	t	t	X
ejpam-5017	103	15	]	]	PUNCT
ejpam-5017	103	16	;	;	PUNCT
ejpam-5017	103	17	c	c	X
ejpam-5017	103	18	(	(	PUNCT
ejpam-5017	103	19	ω	ω	PROPN
ejpam-5017	103	20	)	)	PUNCT
ejpam-5017	103	21	×	×	PROPN
ejpam-5017	103	22	c	c	PROPN
ejpam-5017	103	23	(	(	PUNCT
ejpam-5017	103	24	ω	ω	NOUN
ejpam-5017	103	25	)	)	PUNCT
ejpam-5017	103	26	)	)	PUNCT
ejpam-5017	103	27	;	;	PUNCT
ejpam-5017	103	28	∥(w	∥(w	NOUN
ejpam-5017	103	29	,	,	PUNCT
ejpam-5017	103	30	z)∥	z)∥	NUM
ejpam-5017	103	31	≤	≤	NOUN
ejpam-5017	103	32	2	2	NUM
ejpam-5017	103	33	∥(w0	∥(w0	NOUN
ejpam-5017	103	34	,	,	PUNCT
ejpam-5017	103	35	z0)∥	z0)∥	PUNCT
ejpam-5017	103	36	=	=	PUNCT
ejpam-5017	103	37	l	l	NOUN
ejpam-5017	103	38	}	}	PUNCT
ejpam-5017	103	39	,	,	PUNCT
ejpam-5017	103	40	where	where	SCONJ
ejpam-5017	103	41	∥.∥∞	∥.∥∞	ADV
ejpam-5017	103	42	:	:	PUNCT
ejpam-5017	103	43	=	=	SYM
ejpam-5017	103	44	∥.∥l∞(ω	∥.∥l∞(ω	NOUN
ejpam-5017	103	45	)	)	PUNCT
ejpam-5017	103	46	and∥.∥	and∥.∥	PROPN
ejpam-5017	103	47	is	be	AUX
ejpam-5017	103	48	the	the	DET
ejpam-5017	103	49	norm	norm	NOUN
ejpam-5017	103	50	of	of	ADP
ejpam-5017	103	51	bt	bt	NOUN
ejpam-5017	103	52	defined	define	VERB
ejpam-5017	103	53	by	by	ADP
ejpam-5017	103	54	:	:	PUNCT
ejpam-5017	103	55	∥(w	∥(w	NOUN
ejpam-5017	103	56	,	,	PUNCT
ejpam-5017	103	57	z)∥	z)∥	NUM
ejpam-5017	103	58	:	:	PUNCT
ejpam-5017	103	59	=	=	SYM
ejpam-5017	103	60	∥w∥l∞([0,t	∥w∥l∞([0,t	NOUN
ejpam-5017	103	61	]	]	X
ejpam-5017	103	62	;	;	PUNCT
ejpam-5017	103	63	l∞(ω	l∞(ω	X
ejpam-5017	103	64	)	)	PUNCT
ejpam-5017	103	65	)	)	PUNCT
ejpam-5017	104	1	+	+	CCONJ
ejpam-5017	104	2	∥z∥l∞([0,t	∥z∥l∞([0,t	NOUN
ejpam-5017	104	3	]	]	X
ejpam-5017	104	4	;	;	PUNCT
ejpam-5017	104	5	l∞(ω	l∞(ω	X
ejpam-5017	104	6	)	)	PUNCT
ejpam-5017	104	7	)	)	PUNCT
ejpam-5017	104	8	.	.	PUNCT
ejpam-5017	105	1	next	next	ADV
ejpam-5017	105	2	,	,	PUNCT
ejpam-5017	105	3	∀	∀	X
ejpam-5017	105	4	(	(	PUNCT
ejpam-5017	105	5	w	w	PROPN
ejpam-5017	105	6	,	,	PUNCT
ejpam-5017	105	7	z	z	NOUN
ejpam-5017	105	8	)	)	PUNCT
ejpam-5017	105	9	∈	∈	PROPN
ejpam-5017	105	10	bt	bt	NOUN
ejpam-5017	105	11	,	,	PUNCT
ejpam-5017	105	12	,	,	PUNCT
ejpam-5017	105	13	we	we	PRON
ejpam-5017	105	14	define	define	VERB
ejpam-5017	105	15	φ	φ	PROPN
ejpam-5017	105	16	(	(	PUNCT
ejpam-5017	105	17	w	w	PROPN
ejpam-5017	105	18	,	,	PUNCT
ejpam-5017	105	19	z	z	NOUN
ejpam-5017	105	20	)	)	PUNCT
ejpam-5017	105	21	;	;	PUNCT
ejpam-5017	106	1	=	=	SYM
ejpam-5017	106	2	(	(	PUNCT
ejpam-5017	106	3	φ1	φ1	PROPN
ejpam-5017	106	4	(	(	PUNCT
ejpam-5017	106	5	w	w	PROPN
ejpam-5017	106	6	,	,	PUNCT
ejpam-5017	106	7	z	z	NOUN
ejpam-5017	106	8	)	)	PUNCT
ejpam-5017	106	9	,	,	PUNCT
ejpam-5017	106	10	φ2	φ2	PROPN
ejpam-5017	106	11	(	(	PUNCT
ejpam-5017	106	12	w	w	PROPN
ejpam-5017	106	13	,	,	PUNCT
ejpam-5017	106	14	z	z	NOUN
ejpam-5017	106	15	)	)	PUNCT
ejpam-5017	106	16	)	)	PUNCT
ejpam-5017	106	17	where	where	SCONJ
ejpam-5017	106	18	for	for	ADP
ejpam-5017	106	19	t	t	PROPN
ejpam-5017	106	20	∈	∈	PROPN
ejpam-5017	107	1	[	[	X
ejpam-5017	107	2	0	0	NUM
ejpam-5017	107	3	,	,	PUNCT
ejpam-5017	107	4	t	t	X
ejpam-5017	107	5	]	]	PUNCT
ejpam-5017	107	6	φ1	φ1	PROPN
ejpam-5017	107	7	(	(	PUNCT
ejpam-5017	107	8	w	w	PROPN
ejpam-5017	107	9	,	,	PUNCT
ejpam-5017	107	10	z	z	NOUN
ejpam-5017	107	11	)	)	PUNCT
ejpam-5017	107	12	=	=	NOUN
ejpam-5017	107	13	e−d1tspw0	e−d1tspw0	NOUN
ejpam-5017	107	14	+	+	CCONJ
ejpam-5017	108	1	∫	∫	PROPN
ejpam-5017	108	2	t	t	PROPN
ejpam-5017	108	3	0	0	NUM
ejpam-5017	108	4	e−d1(t−s)sp(−w2z	e−d1(t−s)sp(−w2z	PRON
ejpam-5017	109	1	+	+	CCONJ
ejpam-5017	109	2	f(1−	f(1−	ADJ
ejpam-5017	109	3	w))ds	w))ds	NOUN
ejpam-5017	109	4	and	and	CCONJ
ejpam-5017	109	5	φ2	φ2	PROPN
ejpam-5017	109	6	(	(	PUNCT
ejpam-5017	109	7	w	w	PROPN
ejpam-5017	109	8	,	,	PUNCT
ejpam-5017	109	9	z	z	NOUN
ejpam-5017	109	10	)	)	PUNCT
ejpam-5017	109	11	=	=	PUNCT
ejpam-5017	110	1	e−d2ttpz0	e−d2ttpz0	ADJ
ejpam-5017	110	2	+	+	NUM
ejpam-5017	110	3	∫	∫	PROPN
ejpam-5017	110	4	t	t	PROPN
ejpam-5017	110	5	0	0	NUM
ejpam-5017	110	6	e−d2(t−s)tp(w2z	e−d2(t−s)tp(w2z	PROPN
ejpam-5017	110	7	−	−	PROPN
ejpam-5017	110	8	(	(	PUNCT
ejpam-5017	110	9	f	f	PROPN
ejpam-5017	110	10	+	+	CCONJ
ejpam-5017	110	11	k)z)ds	k)z)ds	PROPN
ejpam-5017	110	12	.	.	PUNCT
ejpam-5017	111	1	we	we	PRON
ejpam-5017	111	2	will	will	AUX
ejpam-5017	111	3	show	show	VERB
ejpam-5017	111	4	the	the	DET
ejpam-5017	111	5	local	local	ADJ
ejpam-5017	111	6	existence	existence	NOUN
ejpam-5017	111	7	by	by	ADP
ejpam-5017	111	8	the	the	DET
ejpam-5017	111	9	banach	banach	ADV
ejpam-5017	111	10	fixed	fix	VERB
ejpam-5017	111	11	point	point	NOUN
ejpam-5017	111	12	theorem	theorem	VERB
ejpam-5017	111	13	.	.	PROPN
ejpam-5017	112	1	•	•	NUM
ejpam-5017	112	2	φ	φ	PROPN
ejpam-5017	112	3	:	:	PUNCT
ejpam-5017	112	4	bt	bt	PROPN
ejpam-5017	112	5	→	→	SYM
ejpam-5017	112	6	bt	bt	PROPN
ejpam-5017	112	7	:	:	PUNCT
ejpam-5017	112	8	let	let	VERB
ejpam-5017	112	9	(	(	PUNCT
ejpam-5017	112	10	w	w	PROPN
ejpam-5017	112	11	,	,	PUNCT
ejpam-5017	112	12	z	z	NOUN
ejpam-5017	112	13	)	)	PUNCT
ejpam-5017	112	14	∈	∈	PROPN
ejpam-5017	112	15	bt	bt	NOUN
ejpam-5017	112	16	.	.	PUNCT
ejpam-5017	113	1	practising	practise	VERB
ejpam-5017	113	2	the	the	DET
ejpam-5017	113	3	estimate	estimate	NOUN
ejpam-5017	113	4	(	(	PUNCT
ejpam-5017	113	5	8)	8)	NUM
ejpam-5017	113	6	(	(	PUNCT
ejpam-5017	113	7	with	with	ADP
ejpam-5017	113	8	r	r	NOUN
ejpam-5017	113	9	=	=	SYM
ejpam-5017	113	10	p	p	NOUN
ejpam-5017	113	11	=	=	PUNCT
ejpam-5017	114	1	+	+	NOUN
ejpam-5017	114	2	∞),we	∞),we	PROPN
ejpam-5017	114	3	attain	attain	VERB
ejpam-5017	114	4	∥φ1	∥φ1	X
ejpam-5017	114	5	(	(	PUNCT
ejpam-5017	114	6	w	w	PROPN
ejpam-5017	114	7	,	,	PUNCT
ejpam-5017	114	8	z)∥∞	z)∥∞	PROPN
ejpam-5017	114	9	≤	≤	NUM
ejpam-5017	114	10	∥w0∥∞	∥w0∥∞	PROPN
ejpam-5017	115	1	+	+	NUM
ejpam-5017	115	2	∫	∫	PROPN
ejpam-5017	115	3	t	t	PROPN
ejpam-5017	115	4	0	0	NUM
ejpam-5017	115	5	∥∥−w2z(s	∥∥−w2z(s	NOUN
ejpam-5017	115	6	)	)	PUNCT
ejpam-5017	115	7	∥∥	∥∥	PROPN
ejpam-5017	116	1	∞	∞	NUM
ejpam-5017	116	2	ds+	ds+	PROPN
ejpam-5017	116	3	f	f	PROPN
ejpam-5017	116	4	∫	∫	PROPN
ejpam-5017	116	5	t	t	PROPN
ejpam-5017	116	6	0	0	NUM
ejpam-5017	116	7	∥(1−	∥(1−	NUM
ejpam-5017	116	8	w)(s)∥∞	w)(s)∥∞	X
ejpam-5017	116	9	ds	ds	VERB
ejpam-5017	116	10	≤	≤	NUM
ejpam-5017	116	11	∥w0∥∞	∥w0∥∞	PROPN
ejpam-5017	117	1	+	+	CCONJ
ejpam-5017	117	2	tl3	tl3	NOUN
ejpam-5017	117	3	+	+	CCONJ
ejpam-5017	117	4	ft	ft	PROPN
ejpam-5017	117	5	+	+	NUM
ejpam-5017	117	6	ftl	ftl	NOUN
ejpam-5017	117	7	.	.	PUNCT
ejpam-5017	118	1	similarly	similarly	ADV
ejpam-5017	118	2	,	,	PUNCT
ejpam-5017	118	3	we	we	PRON
ejpam-5017	118	4	obtain	obtain	VERB
ejpam-5017	118	5	∥φ2	∥φ2	PUNCT
ejpam-5017	118	6	(	(	PUNCT
ejpam-5017	118	7	w	w	PROPN
ejpam-5017	118	8	,	,	PUNCT
ejpam-5017	118	9	z)∥∞	z)∥∞	PROPN
ejpam-5017	118	10	≤	≤	NUM
ejpam-5017	118	11	∥z0∥∞	∥z0∥∞	PROPN
ejpam-5017	119	1	+	+	CCONJ
ejpam-5017	119	2	tl3	tl3	NOUN
ejpam-5017	119	3	+	+	CCONJ
ejpam-5017	119	4	(	(	PUNCT
ejpam-5017	119	5	f	f	PROPN
ejpam-5017	119	6	+	+	PROPN
ejpam-5017	119	7	k)tl	k)tl	PROPN
ejpam-5017	119	8	.	.	PUNCT
ejpam-5017	119	9	m.	m.	NOUN
ejpam-5017	119	10	mebarki	mebarki	PROPN
ejpam-5017	119	11	/	/	SYM
ejpam-5017	119	12	eur	eur	PROPN
ejpam-5017	119	13	.	.	PUNCT
ejpam-5017	120	1	j.	j.	PROPN
ejpam-5017	120	2	pure	pure	PROPN
ejpam-5017	120	3	appl	appl	PROPN
ejpam-5017	120	4	.	.	PROPN
ejpam-5017	120	5	math	math	PROPN
ejpam-5017	120	6	,	,	PUNCT
ejpam-5017	120	7	17	17	NUM
ejpam-5017	120	8	(	(	PUNCT
ejpam-5017	120	9	2	2	NUM
ejpam-5017	120	10	)	)	PUNCT
ejpam-5017	120	11	(	(	PUNCT
ejpam-5017	120	12	2024	2024	NUM
ejpam-5017	120	13	)	)	PUNCT
ejpam-5017	120	14	,	,	PUNCT
ejpam-5017	120	15	1321	1321	NUM
ejpam-5017	120	16	-	-	SYM
ejpam-5017	120	17	1334	1334	NUM
ejpam-5017	120	18	1326	1326	NUM
ejpam-5017	120	19	therefore	therefore	ADV
ejpam-5017	120	20	we	we	PRON
ejpam-5017	120	21	get	get	VERB
ejpam-5017	120	22	,	,	PUNCT
ejpam-5017	120	23	∥φ	∥φ	PROPN
ejpam-5017	120	24	(	(	PUNCT
ejpam-5017	120	25	w	w	PROPN
ejpam-5017	120	26	,	,	PUNCT
ejpam-5017	120	27	z)∥∞	z)∥∞	X
ejpam-5017	120	28	≤	≤	NUM
ejpam-5017	120	29	(	(	PUNCT
ejpam-5017	120	30	∥w0∥∞	∥w0∥∞	PROPN
ejpam-5017	120	31	+	+	CCONJ
ejpam-5017	120	32	∥z0∥∞	∥z0∥∞	PROPN
ejpam-5017	120	33	)	)	PUNCT
ejpam-5017	120	34	+	+	NUM
ejpam-5017	121	1	2tl3	2tl3	NUM
ejpam-5017	121	2	+	+	CCONJ
ejpam-5017	121	3	(	(	PUNCT
ejpam-5017	121	4	2f	2f	NOUN
ejpam-5017	121	5	+	+	X
ejpam-5017	121	6	k)tl+	k)tl+	X
ejpam-5017	121	7	ft	ft	VERB
ejpam-5017	121	8	≤	≤	NOUN
ejpam-5017	121	9	2(∥w0∥∞	2(∥w0∥∞	NUM
ejpam-5017	121	10	+	+	CCONJ
ejpam-5017	121	11	∥z0∥∞	∥z0∥∞	NOUN
ejpam-5017	121	12	)	)	PUNCT
ejpam-5017	121	13	by	by	ADP
ejpam-5017	121	14	choosing	choose	VERB
ejpam-5017	121	15	t	t	PROPN
ejpam-5017	121	16	such	such	ADJ
ejpam-5017	121	17	that	that	SCONJ
ejpam-5017	121	18	t	t	PROPN
ejpam-5017	121	19	≤	≤	NOUN
ejpam-5017	121	20	1	1	NUM
ejpam-5017	121	21	2(6l2+(2f+k	2(6l2+(2f+k	NUM
ejpam-5017	121	22	)	)	PUNCT
ejpam-5017	121	23	)	)	PUNCT
ejpam-5017	121	24	.	.	PUNCT
ejpam-5017	122	1	hence	hence	ADV
ejpam-5017	122	2	φ	φ	PROPN
ejpam-5017	122	3	(	(	PUNCT
ejpam-5017	122	4	w	w	PROPN
ejpam-5017	122	5	,	,	PUNCT
ejpam-5017	122	6	z	z	NOUN
ejpam-5017	122	7	)	)	PUNCT
ejpam-5017	122	8	∈	∈	PROPN
ejpam-5017	122	9	bt	bt	NOUN
ejpam-5017	122	10	for	for	ADP
ejpam-5017	122	11	t	t	PROPN
ejpam-5017	122	12	≤	≤	NUM
ejpam-5017	122	13	1	1	NUM
ejpam-5017	122	14	2(6l2+(2f+k	2(6l2+(2f+k	NUM
ejpam-5017	122	15	)	)	PUNCT
ejpam-5017	122	16	)	)	PUNCT
ejpam-5017	122	17	.	.	PUNCT
ejpam-5017	123	1	•	•	NUM
ejpam-5017	123	2	φ	φ	PROPN
ejpam-5017	123	3	(	(	PUNCT
ejpam-5017	123	4	w	w	PROPN
ejpam-5017	123	5	,	,	PUNCT
ejpam-5017	123	6	z	z	NOUN
ejpam-5017	123	7	)	)	PUNCT
ejpam-5017	123	8	is	be	AUX
ejpam-5017	123	9	contraction	contraction	NOUN
ejpam-5017	123	10	map	map	NOUN
ejpam-5017	123	11	:	:	PUNCT
ejpam-5017	123	12	for	for	ADP
ejpam-5017	123	13	(	(	PUNCT
ejpam-5017	123	14	w	w	PROPN
ejpam-5017	123	15	,	,	PUNCT
ejpam-5017	123	16	z	z	NOUN
ejpam-5017	123	17	)	)	PUNCT
ejpam-5017	123	18	,	,	PUNCT
ejpam-5017	123	19	(	(	PUNCT
ejpam-5017	123	20	w′′	w′′	PROPN
ejpam-5017	123	21	,	,	PUNCT
ejpam-5017	123	22	z	z	NOUN
ejpam-5017	123	23	”	"	PUNCT
ejpam-5017	123	24	)	)	PUNCT
ejpam-5017	123	25	∈	∈	PROPN
ejpam-5017	123	26	bt	bt	NOUN
ejpam-5017	123	27	,	,	PUNCT
ejpam-5017	123	28	we	we	PRON
ejpam-5017	123	29	obtain	obtain	VERB
ejpam-5017	123	30	∥φ1	∥φ1	ADJ
ejpam-5017	123	31	(	(	PUNCT
ejpam-5017	123	32	w	w	PROPN
ejpam-5017	123	33	,	,	PUNCT
ejpam-5017	123	34	z)−	z)−	PROPN
ejpam-5017	123	35	φ1	φ1	NOUN
ejpam-5017	123	36	(	(	PUNCT
ejpam-5017	123	37	w	w	PROPN
ejpam-5017	123	38	”	"	PUNCT
ejpam-5017	123	39	,	,	PUNCT
ejpam-5017	123	40	z”)∥∞	z”)∥∞	PROPN
ejpam-5017	123	41	≤	≤	X
ejpam-5017	124	1	∫	∫	PROPN
ejpam-5017	124	2	t	t	PROPN
ejpam-5017	124	3	0	0	NUM
ejpam-5017	124	4	∥∥−w2z(s	∥∥−w2z(s	NOUN
ejpam-5017	124	5	)	)	PUNCT
ejpam-5017	125	1	+	+	CCONJ
ejpam-5017	125	2	w”2z”(s	w”2z”(s	PROPN
ejpam-5017	125	3	)	)	PUNCT
ejpam-5017	125	4	∥∥	∥∥	PROPN
ejpam-5017	125	5	∞	∞	PROPN
ejpam-5017	125	6	ds+	ds+	PROPN
ejpam-5017	125	7	f	f	PROPN
ejpam-5017	125	8	∫	∫	PROPN
ejpam-5017	125	9	t	t	PROPN
ejpam-5017	125	10	0	0	NUM
ejpam-5017	125	11	∥(w	∥(w	VERB
ejpam-5017	125	12	−	−	PROPN
ejpam-5017	125	13	w”)(s)∥∞	w”)(s)∥∞	PROPN
ejpam-5017	125	14	ds	ds	PROPN
ejpam-5017	125	15	≤	≤	NUM
ejpam-5017	125	16	∫	∫	PROPN
ejpam-5017	126	1	t	t	NOUN
ejpam-5017	126	2	0	0	NUM
ejpam-5017	126	3	∥∥w2	∥∥w2	PROPN
ejpam-5017	126	4	∥∥	∥∥	X
ejpam-5017	126	5	∥z	∥z	PROPN
ejpam-5017	126	6	−	−	PROPN
ejpam-5017	126	7	z”∥+	z”∥+	NOUN
ejpam-5017	126	8	∥z”∥	∥z”∥	PROPN
ejpam-5017	126	9	(	(	PUNCT
ejpam-5017	126	10	∥w∥+	∥w∥+	NOUN
ejpam-5017	126	11	∥w”∥)(∥w	∥w”∥)(∥w	VERB
ejpam-5017	126	12	−	−	PROPN
ejpam-5017	126	13	w”∥	w”∥	NOUN
ejpam-5017	126	14	ds+	ds+	PROPN
ejpam-5017	127	1	f	f	PROPN
ejpam-5017	127	2	∫	∫	PROPN
ejpam-5017	127	3	t	t	PROPN
ejpam-5017	127	4	0	0	NUM
ejpam-5017	128	1	∥w	∥w	PROPN
ejpam-5017	128	2	−	−	PROPN
ejpam-5017	128	3	w”∥	w”∥	NOUN
ejpam-5017	128	4	ds	ds	ADJ
ejpam-5017	128	5	≤	≤	NOUN
ejpam-5017	128	6	3tl2	3tl2	NUM
ejpam-5017	129	1	+	+	CCONJ
ejpam-5017	129	2	ft	ft	PRON
ejpam-5017	129	3	∥(w	∥(w	NOUN
ejpam-5017	129	4	,	,	PUNCT
ejpam-5017	129	5	z)−	z)−	PROPN
ejpam-5017	129	6	(	(	PUNCT
ejpam-5017	129	7	w	w	NOUN
ejpam-5017	129	8	”	"	PUNCT
ejpam-5017	129	9	,	,	PUNCT
ejpam-5017	129	10	z”)∥	z”)∥	NOUN
ejpam-5017	129	11	by	by	ADP
ejpam-5017	129	12	the	the	DET
ejpam-5017	129	13	same	same	ADJ
ejpam-5017	129	14	way	way	NOUN
ejpam-5017	129	15	,	,	PUNCT
ejpam-5017	129	16	∥φ1	∥φ1	X
ejpam-5017	129	17	(	(	PUNCT
ejpam-5017	129	18	w	w	PROPN
ejpam-5017	129	19	,	,	PUNCT
ejpam-5017	129	20	z)−	z)−	PROPN
ejpam-5017	129	21	φ1	φ1	NOUN
ejpam-5017	129	22	(	(	PUNCT
ejpam-5017	129	23	w	w	PROPN
ejpam-5017	129	24	”	"	PUNCT
ejpam-5017	129	25	,	,	PUNCT
ejpam-5017	129	26	z”)∥∞	z”)∥∞	X
ejpam-5017	129	27	≤	≤	PROPN
ejpam-5017	129	28	3tl2	3tl2	NUM
ejpam-5017	130	1	+	+	CCONJ
ejpam-5017	130	2	(	(	PUNCT
ejpam-5017	130	3	f	f	X
ejpam-5017	130	4	+	+	CCONJ
ejpam-5017	130	5	k)t	k)t	X
ejpam-5017	130	6	∥(w	∥(w	NOUN
ejpam-5017	130	7	,	,	PUNCT
ejpam-5017	130	8	z)−	z)−	PROPN
ejpam-5017	130	9	(	(	PUNCT
ejpam-5017	130	10	w	w	NOUN
ejpam-5017	130	11	”	"	PUNCT
ejpam-5017	130	12	,	,	PUNCT
ejpam-5017	130	13	z”)∥	z”)∥	NOUN
ejpam-5017	130	14	so	so	ADV
ejpam-5017	130	15	∥φ	∥φ	PROPN
ejpam-5017	130	16	(	(	PUNCT
ejpam-5017	130	17	w	w	PROPN
ejpam-5017	130	18	,	,	PUNCT
ejpam-5017	130	19	z)−	z)−	PROPN
ejpam-5017	130	20	φ	φ	X
ejpam-5017	130	21	(	(	PUNCT
ejpam-5017	130	22	w	w	NOUN
ejpam-5017	130	23	”	"	PUNCT
ejpam-5017	130	24	,	,	PUNCT
ejpam-5017	130	25	z”)∥	z”)∥	NOUN
ejpam-5017	130	26	≤	≤	NUM
ejpam-5017	130	27	6tl2	6tl2	PUNCT
ejpam-5017	131	1	+	+	CCONJ
ejpam-5017	131	2	2	2	NUM
ejpam-5017	131	3	ft	ft	NOUN
ejpam-5017	131	4	+	+	NUM
ejpam-5017	131	5	kt	kt	PRON
ejpam-5017	131	6	≤	≤	PROPN
ejpam-5017	131	7	1/2	1/2	NUM
ejpam-5017	131	8	|∥(w	|∥(w	PROPN
ejpam-5017	131	9	,	,	PUNCT
ejpam-5017	131	10	z)−	z)−	PROPN
ejpam-5017	131	11	(	(	PUNCT
ejpam-5017	131	12	w	w	NOUN
ejpam-5017	131	13	”	"	PUNCT
ejpam-5017	131	14	,	,	PUNCT
ejpam-5017	131	15	z”)∥|	z”)∥|	NOUN
ejpam-5017	131	16	.	.	PUNCT
ejpam-5017	132	1	for	for	ADP
ejpam-5017	132	2	t	t	PROPN
ejpam-5017	132	3	≤	≤	NUM
ejpam-5017	132	4	1	1	NUM
ejpam-5017	132	5	2(6l2+(2f+k	2(6l2+(2f+k	NUM
ejpam-5017	132	6	)	)	PUNCT
ejpam-5017	132	7	)	)	PUNCT
ejpam-5017	132	8	.	.	PUNCT
ejpam-5017	133	1	consequently	consequently	ADV
ejpam-5017	133	2	,	,	PUNCT
ejpam-5017	133	3	in	in	ADP
ejpam-5017	133	4	view	view	NOUN
ejpam-5017	133	5	of	of	ADP
ejpam-5017	133	6	the	the	DET
ejpam-5017	133	7	banach	banach	ADV
ejpam-5017	133	8	fixed	fix	VERB
ejpam-5017	133	9	point	point	NOUN
ejpam-5017	133	10	theorem	theorem	VERB
ejpam-5017	133	11	ç	ç	NOUN
ejpam-5017	133	12	,	,	PUNCT
ejpam-5017	133	13	φ	φ	PROPN
ejpam-5017	133	14	admits	admit	VERB
ejpam-5017	133	15	a	a	DET
ejpam-5017	133	16	fixed	fixed	ADJ
ejpam-5017	133	17	point	point	NOUN
ejpam-5017	133	18	on	on	ADP
ejpam-5017	133	19	b.	b.	PROPN
ejpam-5017	133	20	thus	thus	ADV
ejpam-5017	133	21	the	the	DET
ejpam-5017	133	22	system	system	NOUN
ejpam-5017	133	23	(	(	PUNCT
ejpam-5017	133	24	1)-(2	1)-(2	NUM
ejpam-5017	133	25	)	)	PUNCT
ejpam-5017	133	26	has	have	VERB
ejpam-5017	133	27	a	a	DET
ejpam-5017	133	28	mild	mild	ADJ
ejpam-5017	133	29	solution	solution	NOUN
ejpam-5017	133	30	.	.	PUNCT
ejpam-5017	134	1	the	the	DET
ejpam-5017	134	2	solution	solution	NOUN
ejpam-5017	134	3	can	can	AUX
ejpam-5017	134	4	be	be	AUX
ejpam-5017	134	5	extended	extend	VERB
ejpam-5017	134	6	on	on	ADP
ejpam-5017	134	7	a	a	DET
ejpam-5017	134	8	maximal	maximal	ADJ
ejpam-5017	134	9	interval	interval	NOUN
ejpam-5017	134	10	[	[	X
ejpam-5017	134	11	0	0	NUM
ejpam-5017	134	12	,	,	PUNCT
ejpam-5017	134	13	tmax	tmax	NUM
ejpam-5017	134	14	)	)	PUNCT
ejpam-5017	134	15	where	where	SCONJ
ejpam-5017	134	16	tmax	tmax	ADV
ejpam-5017	134	17	:	:	PUNCT
ejpam-5017	134	18	=	=	SYM
ejpam-5017	134	19	sup	sup	INTJ
ejpam-5017	134	20	{	{	PUNCT
ejpam-5017	134	21	t	t	PROPN
ejpam-5017	134	22	≻	≻	PROPN
ejpam-5017	134	23	0	0	NUM
ejpam-5017	134	24	;	;	PUNCT
ejpam-5017	134	25	(	(	PUNCT
ejpam-5017	134	26	w	w	PROPN
ejpam-5017	134	27	,	,	PUNCT
ejpam-5017	134	28	z	z	NOUN
ejpam-5017	134	29	)	)	PUNCT
ejpam-5017	134	30	}	}	PUNCT
ejpam-5017	134	31	.	.	PUNCT
ejpam-5017	135	1	is	be	AUX
ejpam-5017	135	2	a	a	DET
ejpam-5017	135	3	solution	solution	NOUN
ejpam-5017	135	4	to	to	ADP
ejpam-5017	135	5	(	(	PUNCT
ejpam-5017	135	6	1)-(2	1)-(2	NUM
ejpam-5017	135	7	)	)	PUNCT
ejpam-5017	135	8	4	4	NUM
ejpam-5017	135	9	.	.	X
ejpam-5017	135	10	global	global	ADJ
ejpam-5017	135	11	existence	existence	NOUN
ejpam-5017	135	12	and	and	CCONJ
ejpam-5017	135	13	asymptotic	asymptotic	ADJ
ejpam-5017	135	14	behavior	behavior	NOUN
ejpam-5017	135	15	in	in	ADP
ejpam-5017	135	16	this	this	DET
ejpam-5017	135	17	section	section	NOUN
ejpam-5017	135	18	,	,	PUNCT
ejpam-5017	135	19	we	we	PRON
ejpam-5017	135	20	state	state	VERB
ejpam-5017	135	21	and	and	CCONJ
ejpam-5017	135	22	prove	prove	VERB
ejpam-5017	135	23	the	the	DET
ejpam-5017	135	24	main	main	ADJ
ejpam-5017	135	25	result	result	NOUN
ejpam-5017	135	26	using	use	VERB
ejpam-5017	135	27	the	the	DET
ejpam-5017	135	28	ideas	idea	NOUN
ejpam-5017	135	29	of	of	ADP
ejpam-5017	135	30	[	[	X
ejpam-5017	135	31	2	2	NUM
ejpam-5017	135	32	]	]	PUNCT
ejpam-5017	135	33	or	or	CCONJ
ejpam-5017	135	34	[	[	X
ejpam-5017	135	35	1	1	NUM
ejpam-5017	135	36	]	]	PUNCT
ejpam-5017	135	37	.	.	PUNCT
ejpam-5017	136	1	theorem	theorem	NOUN
ejpam-5017	136	2	2	2	NUM
ejpam-5017	136	3	.	.	PUNCT
ejpam-5017	137	1	let	let	VERB
ejpam-5017	137	2	(	(	PUNCT
ejpam-5017	137	3	w0	w0	VERB
ejpam-5017	137	4	,	,	PUNCT
ejpam-5017	137	5	z0	z0	PROPN
ejpam-5017	137	6	)	)	PUNCT
ejpam-5017	137	7	∈	∈	PROPN
ejpam-5017	137	8	c	c	PROPN
ejpam-5017	137	9	(	(	PUNCT
ejpam-5017	137	10	ω	ω	PROPN
ejpam-5017	137	11	)	)	PUNCT
ejpam-5017	137	12	×c	×c	X
ejpam-5017	137	13	(	(	PUNCT
ejpam-5017	137	14	ω	ω	NOUN
ejpam-5017	137	15	)	)	PUNCT
ejpam-5017	137	16	be	be	AUX
ejpam-5017	137	17	such	such	ADJ
ejpam-5017	137	18	that	that	SCONJ
ejpam-5017	137	19	w0	w0	PROPN
ejpam-5017	137	20	≥	≥	NOUN
ejpam-5017	137	21	0	0	NUM
ejpam-5017	137	22	,	,	PUNCT
ejpam-5017	137	23	z0	z0	PROPN
ejpam-5017	137	24	≥	≥	NUM
ejpam-5017	137	25	0.then	0.then	PUNCT
ejpam-5017	138	1	there	there	PRON
ejpam-5017	138	2	exists	exist	VERB
ejpam-5017	138	3	a	a	DET
ejpam-5017	138	4	unique	unique	ADJ
ejpam-5017	138	5	global	global	ADJ
ejpam-5017	138	6	solution	solution	NOUN
ejpam-5017	138	7	(	(	PUNCT
ejpam-5017	138	8	w	w	PROPN
ejpam-5017	138	9	,	,	PUNCT
ejpam-5017	138	10	z	z	NOUN
ejpam-5017	138	11	)	)	PUNCT
ejpam-5017	138	12	of	of	ADP
ejpam-5017	138	13	(	(	PUNCT
ejpam-5017	138	14	1)-(2	1)-(2	NUM
ejpam-5017	138	15	)	)	PUNCT
ejpam-5017	138	16	which	which	PRON
ejpam-5017	138	17	satisfy	satisfy	VERB
ejpam-5017	138	18	:	:	PUNCT
ejpam-5017	138	19	m.	m.	NOUN
ejpam-5017	138	20	mebarki	mebarki	PROPN
ejpam-5017	138	21	/	/	SYM
ejpam-5017	138	22	eur	eur	PROPN
ejpam-5017	138	23	.	.	PUNCT
ejpam-5017	139	1	j.	j.	PROPN
ejpam-5017	139	2	pure	pure	PROPN
ejpam-5017	139	3	appl	appl	PROPN
ejpam-5017	139	4	.	.	PROPN
ejpam-5017	139	5	math	math	PROPN
ejpam-5017	139	6	,	,	PUNCT
ejpam-5017	139	7	17	17	NUM
ejpam-5017	139	8	(	(	PUNCT
ejpam-5017	139	9	2	2	NUM
ejpam-5017	139	10	)	)	PUNCT
ejpam-5017	139	11	(	(	PUNCT
ejpam-5017	139	12	2024	2024	NUM
ejpam-5017	139	13	)	)	PUNCT
ejpam-5017	139	14	,	,	PUNCT
ejpam-5017	139	15	1321	1321	NUM
ejpam-5017	139	16	-	-	SYM
ejpam-5017	139	17	1334	1334	NUM
ejpam-5017	139	18	1327	1327	NUM
ejpam-5017	139	19	·	·	PUNCT
ejpam-5017	139	20	w(x	w(x	PROPN
ejpam-5017	139	21	,	,	PUNCT
ejpam-5017	139	22	t	t	PROPN
ejpam-5017	139	23	)	)	PUNCT
ejpam-5017	139	24	≥	≥	NOUN
ejpam-5017	139	25	0	0	NUM
ejpam-5017	139	26	,	,	PUNCT
ejpam-5017	139	27	z(x	z(x	NUM
ejpam-5017	139	28	,	,	PUNCT
ejpam-5017	139	29	t	t	PROPN
ejpam-5017	139	30	)	)	PUNCT
ejpam-5017	139	31	≥	≥	NOUN
ejpam-5017	139	32	0	0	NUM
ejpam-5017	139	33	;	;	PUNCT
ejpam-5017	139	34	x	x	X
ejpam-5017	139	35	∈	∈	PROPN
ejpam-5017	139	36	ω	ω	PROPN
ejpam-5017	139	37	,	,	PUNCT
ejpam-5017	139	38	t	t	PROPN
ejpam-5017	139	39	≥	≥	PROPN
ejpam-5017	139	40	0	0	NUM
ejpam-5017	139	41	.	.	PUNCT
ejpam-5017	139	42	·	·	PUNCT
ejpam-5017	139	43	w	w	X
ejpam-5017	139	44	∈	∈	PROPN
ejpam-5017	139	45	c	c	X
ejpam-5017	139	46	(	(	PUNCT
ejpam-5017	139	47	r+	r+	X
ejpam-5017	139	48	,	,	PUNCT
ejpam-5017	139	49	c	c	PROPN
ejpam-5017	139	50	(	(	PUNCT
ejpam-5017	139	51	ω	ω	NOUN
ejpam-5017	139	52	)	)	PUNCT
ejpam-5017	139	53	)	)	PUNCT
ejpam-5017	139	54	,	,	PUNCT
ejpam-5017	139	55	z	z	NOUN
ejpam-5017	139	56	∈	∈	PROPN
ejpam-5017	139	57	c	c	X
ejpam-5017	139	58	(	(	PUNCT
ejpam-5017	139	59	r+	r+	X
ejpam-5017	139	60	,	,	PUNCT
ejpam-5017	139	61	c	c	PROPN
ejpam-5017	139	62	(	(	PUNCT
ejpam-5017	139	63	ω	ω	NOUN
ejpam-5017	139	64	)	)	PUNCT
ejpam-5017	139	65	)	)	PUNCT
ejpam-5017	139	66	.	.	PUNCT
ejpam-5017	140	1	·	·	PUNCT
ejpam-5017	141	1	limt→+∞	limt→+∞	X
ejpam-5017	141	2	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	141	3	=	=	SYM
ejpam-5017	141	4	0	0	NUM
ejpam-5017	141	5	;	;	PUNCT
ejpam-5017	141	6	∃w∞	∃w∞	X
ejpam-5017	141	7	≥	≥	NOUN
ejpam-5017	141	8	0.such	0.such	PUNCT
ejpam-5017	141	9	that	that	SCONJ
ejpam-5017	141	10	limt→+∞	limt→+∞	ADP
ejpam-5017	141	11	∥w(x	∥w(x	ADJ
ejpam-5017	141	12	,	,	PUNCT
ejpam-5017	141	13	t)−	t)−	PROPN
ejpam-5017	141	14	w∞∥∞	w∞∥∞	VERB
ejpam-5017	141	15	=	=	SYM
ejpam-5017	141	16	0	0	X
ejpam-5017	141	17	.	.	PUNCT
ejpam-5017	142	1	proof	proof	NOUN
ejpam-5017	142	2	.	.	PUNCT
ejpam-5017	142	3	.	.	PUNCT
ejpam-5017	143	1	·	·	PUNCT
ejpam-5017	143	2	step1	step1	PROPN
ejpam-5017	143	3	.	.	PUNCT
ejpam-5017	144	1	we	we	PRON
ejpam-5017	144	2	define	define	VERB
ejpam-5017	144	3	w+	w+	NOUN
ejpam-5017	144	4	=	=	SYM
ejpam-5017	144	5	max(0	max(0	NOUN
ejpam-5017	144	6	,	,	PUNCT
ejpam-5017	144	7	w	w	PROPN
ejpam-5017	144	8	)	)	PUNCT
ejpam-5017	144	9	and	and	CCONJ
ejpam-5017	144	10	w−	w−	NOUN
ejpam-5017	144	11	=	=	SYM
ejpam-5017	144	12	max(0,−w	max(0,−w	NUM
ejpam-5017	144	13	)	)	PUNCT
ejpam-5017	144	14	.	.	PUNCT
ejpam-5017	145	1	we	we	PRON
ejpam-5017	145	2	write	write	VERB
ejpam-5017	145	3	w	w	PROPN
ejpam-5017	145	4	=	=	PUNCT
ejpam-5017	145	5	w+	w+	PUNCT
ejpam-5017	145	6	−	−	PROPN
ejpam-5017	145	7	w−	w−	NOUN
ejpam-5017	145	8	,	,	PUNCT
ejpam-5017	145	9	multiply	multiply	VERB
ejpam-5017	145	10	the	the	DET
ejpam-5017	145	11	first	first	ADJ
ejpam-5017	145	12	equation	equation	NOUN
ejpam-5017	145	13	of	of	ADP
ejpam-5017	145	14	system	system	NOUN
ejpam-5017	145	15	(	(	PUNCT
ejpam-5017	145	16	1	1	NUM
ejpam-5017	145	17	)	)	PUNCT
ejpam-5017	145	18	by	by	ADP
ejpam-5017	145	19	(	(	PUNCT
ejpam-5017	145	20	−w−	−w−	NOUN
ejpam-5017	145	21	)	)	PUNCT
ejpam-5017	145	22	and	and	CCONJ
ejpam-5017	145	23	integrate	integrate	VERB
ejpam-5017	145	24	over	over	ADP
ejpam-5017	145	25	ω	ω	NOUN
ejpam-5017	145	26	;	;	PUNCT
ejpam-5017	145	27	we	we	PRON
ejpam-5017	145	28	get∫	get∫	PROPN
ejpam-5017	145	29	ω	ω	NUM
ejpam-5017	145	30	∂w−	∂w−	PROPN
ejpam-5017	145	31	∂t	∂t	PROPN
ejpam-5017	145	32	w−dx	w−dx	NOUN
ejpam-5017	145	33	=	=	PROPN
ejpam-5017	145	34	−d1	−d1	PROPN
ejpam-5017	145	35	∫	∫	PROPN
ejpam-5017	145	36	ω	ω	PROPN
ejpam-5017	145	37	−spw	−spw	PUNCT
ejpam-5017	145	38	−w−dx−	−w−dx−	PROPN
ejpam-5017	145	39	∫	∫	PROPN
ejpam-5017	145	40	ω	ω	PROPN
ejpam-5017	145	41	(	(	PUNCT
ejpam-5017	145	42	w−2z)w−dx+	w−2z)w−dx+	PROPN
ejpam-5017	145	43	∫	∫	PROPN
ejpam-5017	145	44	ω	ω	NUM
ejpam-5017	145	45	f(1−	f(1−	PROPN
ejpam-5017	145	46	w−)w−dx	w−)w−dx	PROPN
ejpam-5017	145	47	.	.	PUNCT
ejpam-5017	146	1	by	by	ADP
ejpam-5017	146	2	estimate	estimate	NOUN
ejpam-5017	146	3	(	(	PUNCT
ejpam-5017	146	4	4	4	NUM
ejpam-5017	146	5	)	)	PUNCT
ejpam-5017	146	6	,	,	PUNCT
ejpam-5017	146	7	we	we	PRON
ejpam-5017	146	8	have	have	VERB
ejpam-5017	146	9	d	d	NOUN
ejpam-5017	146	10	dt	dt	X
ejpam-5017	146	11	∫	∫	PROPN
ejpam-5017	146	12	ω	ω	PROPN
ejpam-5017	146	13	(	(	PUNCT
ejpam-5017	146	14	w−)2dx	w−)2dx	VERB
ejpam-5017	146	15	≤	≤	ADV
ejpam-5017	146	16	2	2	NUM
ejpam-5017	146	17	[	[	PUNCT
ejpam-5017	146	18	∫	∫	PROPN
ejpam-5017	146	19	ω	ω	PROPN
ejpam-5017	146	20	(	(	PUNCT
ejpam-5017	146	21	w−2)(zw−)dx+	w−2)(zw−)dx+	PROPN
ejpam-5017	146	22	∫	∫	PROPN
ejpam-5017	146	23	ω	ω	PROPN
ejpam-5017	146	24	fw−dx+	fw−dx+	PROPN
ejpam-5017	146	25	∫	∫	PROPN
ejpam-5017	146	26	ω	ω	SYM
ejpam-5017	146	27	f(w−)2dx	f(w−)2dx	PROPN
ejpam-5017	146	28	.	.	PUNCT
ejpam-5017	147	1	since	since	SCONJ
ejpam-5017	147	2	(	(	PUNCT
ejpam-5017	147	3	w	w	PROPN
ejpam-5017	147	4	,	,	PUNCT
ejpam-5017	147	5	z	z	NOUN
ejpam-5017	147	6	)	)	PUNCT
ejpam-5017	147	7	is	be	AUX
ejpam-5017	147	8	a	a	DET
ejpam-5017	147	9	local	local	ADJ
ejpam-5017	147	10	solution	solution	NOUN
ejpam-5017	147	11	on	on	ADP
ejpam-5017	147	12	[	[	X
ejpam-5017	147	13	0	0	NUM
ejpam-5017	147	14	,	,	PUNCT
ejpam-5017	147	15	tmax	tmax	NUM
ejpam-5017	147	16	)	)	PUNCT
ejpam-5017	147	17	,	,	PUNCT
ejpam-5017	147	18	then	then	ADV
ejpam-5017	147	19	w	w	PROPN
ejpam-5017	147	20	and	and	CCONJ
ejpam-5017	147	21	z	z	PROPN
ejpam-5017	147	22	are	be	AUX
ejpam-5017	147	23	bounded	bound	VERB
ejpam-5017	147	24	on	on	ADP
ejpam-5017	147	25	[	[	X
ejpam-5017	147	26	0	0	NUM
ejpam-5017	147	27	,	,	PUNCT
ejpam-5017	147	28	t	t	X
ejpam-5017	147	29	]	]	PUNCT
ejpam-5017	147	30	for	for	ADP
ejpam-5017	147	31	t	t	NOUN
ejpam-5017	147	32	≺	≺	NOUN
ejpam-5017	147	33	tmax	tmax	ADV
ejpam-5017	147	34	;	;	PUNCT
ejpam-5017	147	35	furthermore	furthermore	ADV
ejpam-5017	147	36	,	,	PUNCT
ejpam-5017	147	37	there	there	PRON
ejpam-5017	147	38	exist	exist	VERB
ejpam-5017	147	39	continuous	continuous	ADJ
ejpam-5017	147	40	functions	function	NOUN
ejpam-5017	147	41	m(t	m(t	NOUN
ejpam-5017	147	42	)	)	PUNCT
ejpam-5017	147	43	and	and	CCONJ
ejpam-5017	147	44	h(t	h(t	NOUN
ejpam-5017	147	45	)	)	PUNCT
ejpam-5017	147	46	such	such	ADJ
ejpam-5017	147	47	that	that	SCONJ
ejpam-5017	147	48	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	147	49	≤	≤	NUM
ejpam-5017	147	50	m(t	m(t	NOUN
ejpam-5017	147	51	)	)	PUNCT
ejpam-5017	147	52	and	and	CCONJ
ejpam-5017	147	53	∥w(t)∥∞	∥w(t)∥∞	PROPN
ejpam-5017	147	54	≤	≤	NUM
ejpam-5017	147	55	h(t	h(t	PROPN
ejpam-5017	147	56	)	)	PUNCT
ejpam-5017	147	57	.	.	PUNCT
ejpam-5017	148	1	it	it	PRON
ejpam-5017	148	2	holds	hold	VERB
ejpam-5017	148	3	that	that	SCONJ
ejpam-5017	149	1	d	d	NOUN
ejpam-5017	149	2	dt	dt	X
ejpam-5017	149	3	∫	∫	PROPN
ejpam-5017	149	4	ω	ω	PROPN
ejpam-5017	149	5	(	(	PUNCT
ejpam-5017	149	6	w−)2dx	w−)2dx	VERB
ejpam-5017	149	7	≤	≤	NUM
ejpam-5017	149	8	2[(m(t)h(t	2[(m(t)h(t	NUM
ejpam-5017	149	9	)	)	PUNCT
ejpam-5017	150	1	+	+	NUM
ejpam-5017	150	2	f	f	X
ejpam-5017	150	3	)	)	PUNCT
ejpam-5017	150	4	∫	∫	PROPN
ejpam-5017	150	5	ω	ω	PROPN
ejpam-5017	150	6	(	(	PUNCT
ejpam-5017	150	7	w−2)dx+	w−2)dx+	ADV
ejpam-5017	150	8	fh(t	fh(t	X
ejpam-5017	150	9	)	)	PUNCT
ejpam-5017	150	10	]	]	PUNCT
ejpam-5017	150	11	.	.	PUNCT
ejpam-5017	151	1	(	(	PUNCT
ejpam-5017	151	2	12	12	NUM
ejpam-5017	151	3	)	)	PUNCT
ejpam-5017	151	4	as	as	ADP
ejpam-5017	151	5	∫	∫	PROPN
ejpam-5017	151	6	ω(w	ω(w	PROPN
ejpam-5017	151	7	−2)(0)dx	−2)(0)dx	PROPN
ejpam-5017	151	8	=	=	SYM
ejpam-5017	151	9	0	0	NUM
ejpam-5017	151	10	and	and	CCONJ
ejpam-5017	151	11	f	f	PROPN
ejpam-5017	151	12	≥	≥	NUM
ejpam-5017	151	13	0	0	NUM
ejpam-5017	151	14	,	,	PUNCT
ejpam-5017	151	15	gronwall	gronwall	PROPN
ejpam-5017	151	16	’s	’s	PART
ejpam-5017	151	17	inequality	inequality	NOUN
ejpam-5017	151	18	[	[	X
ejpam-5017	151	19	3	3	X
ejpam-5017	151	20	]	]	PUNCT
ejpam-5017	151	21	allows	allow	VERB
ejpam-5017	151	22	us	we	PRON
ejpam-5017	151	23	to	to	PART
ejpam-5017	151	24	attain∫	attain∫	ADP
ejpam-5017	151	25	ω(w	ω(w	PROPN
ejpam-5017	151	26	−2)dx	−2)dx	PROPN
ejpam-5017	151	27	=	=	SYM
ejpam-5017	151	28	0	0	NUM
ejpam-5017	151	29	;	;	PUNCT
ejpam-5017	151	30	consequently	consequently	ADV
ejpam-5017	151	31	,	,	PUNCT
ejpam-5017	151	32	w(x	w(x	PROPN
ejpam-5017	151	33	,	,	PUNCT
ejpam-5017	151	34	t	t	PROPN
ejpam-5017	151	35	)	)	PUNCT
ejpam-5017	151	36	≥	≥	NOUN
ejpam-5017	151	37	0	0	NUM
ejpam-5017	151	38	.	.	PUNCT
ejpam-5017	152	1	by	by	ADP
ejpam-5017	152	2	same	same	ADJ
ejpam-5017	152	3	manner	manner	NOUN
ejpam-5017	152	4	,	,	PUNCT
ejpam-5017	152	5	we	we	PRON
ejpam-5017	152	6	gain∫	gain∫	VERB
ejpam-5017	152	7	ω	ω	NOUN
ejpam-5017	152	8	∂z−	∂z−	PROPN
ejpam-5017	152	9	∂t	∂t	PROPN
ejpam-5017	152	10	z−dx	z−dx	X
ejpam-5017	152	11	=	=	PUNCT
ejpam-5017	153	1	−d2	−d2	PROPN
ejpam-5017	153	2	∫	∫	PROPN
ejpam-5017	153	3	ω	ω	PROPN
ejpam-5017	153	4	−tpz	−tpz	NOUN
ejpam-5017	153	5	−z−dx+	−z−dx+	PROPN
ejpam-5017	153	6	∫	∫	PROPN
ejpam-5017	154	1	ω	ω	NUM
ejpam-5017	154	2	w2(z−)2dx−	w2(z−)2dx−	NOUN
ejpam-5017	154	3	∫	∫	PROPN
ejpam-5017	154	4	ω	ω	INTJ
ejpam-5017	154	5	(	(	PUNCT
ejpam-5017	154	6	f	f	PROPN
ejpam-5017	154	7	+	+	CCONJ
ejpam-5017	154	8	k)(z−)2dx	k)(z−)2dx	X
ejpam-5017	154	9	.	.	PUNCT
ejpam-5017	155	1	employing	employ	VERB
ejpam-5017	155	2	inequality	inequality	NOUN
ejpam-5017	155	3	(	(	PUNCT
ejpam-5017	155	4	4	4	NUM
ejpam-5017	155	5	)	)	PUNCT
ejpam-5017	155	6	,	,	PUNCT
ejpam-5017	155	7	we	we	PRON
ejpam-5017	155	8	obtain	obtain	VERB
ejpam-5017	155	9	d	d	PRON
ejpam-5017	155	10	dt	dt	X
ejpam-5017	156	1	∫	∫	PROPN
ejpam-5017	156	2	ω	ω	PROPN
ejpam-5017	156	3	(	(	PUNCT
ejpam-5017	156	4	w−)2dx	w−)2dx	VERB
ejpam-5017	156	5	≤	≤	ADV
ejpam-5017	156	6	2	2	NUM
ejpam-5017	156	7	[	[	PUNCT
ejpam-5017	156	8	∫	∫	PROPN
ejpam-5017	156	9	ω	ω	PROPN
ejpam-5017	156	10	(	(	PUNCT
ejpam-5017	156	11	w2	w2	NOUN
ejpam-5017	156	12	−	−	PROPN
ejpam-5017	156	13	(	(	PUNCT
ejpam-5017	156	14	f	f	PROPN
ejpam-5017	156	15	+	+	CCONJ
ejpam-5017	156	16	k))(z−)2dx	k))(z−)2dx	PROPN
ejpam-5017	156	17	.	.	PUNCT
ejpam-5017	157	1	it	it	PRON
ejpam-5017	157	2	follows	follow	VERB
ejpam-5017	157	3	that	that	SCONJ
ejpam-5017	157	4	2[h2(t)−	2[h2(t)−	PROPN
ejpam-5017	157	5	(	(	PUNCT
ejpam-5017	157	6	f	f	X
ejpam-5017	157	7	+	+	CCONJ
ejpam-5017	157	8	k	k	NOUN
ejpam-5017	157	9	)	)	PUNCT
ejpam-5017	157	10	]	]	PUNCT
ejpam-5017	158	1	∫	∫	PROPN
ejpam-5017	158	2	ω	ω	PROPN
ejpam-5017	158	3	(	(	PUNCT
ejpam-5017	158	4	z−)2dx	z−)2dx	NUM
ejpam-5017	158	5	.	.	PUNCT
ejpam-5017	159	1	by	by	ADP
ejpam-5017	159	2	integration	integration	NOUN
ejpam-5017	159	3	we	we	PRON
ejpam-5017	159	4	have	have	VERB
ejpam-5017	159	5	z−	z−	NOUN
ejpam-5017	159	6	=	=	SYM
ejpam-5017	159	7	0	0	NUM
ejpam-5017	159	8	which	which	PRON
ejpam-5017	159	9	gives	give	VERB
ejpam-5017	159	10	z(x	z(x	PROPN
ejpam-5017	159	11	,	,	PUNCT
ejpam-5017	159	12	t	t	PROPN
ejpam-5017	159	13	)	)	PUNCT
ejpam-5017	159	14	≥	≥	NOUN
ejpam-5017	159	15	0	0	NUM
ejpam-5017	159	16	.	.	PUNCT
ejpam-5017	159	17	·	·	PUNCT
ejpam-5017	159	18	step	step	NOUN
ejpam-5017	159	19	2	2	NUM
ejpam-5017	159	20	.	.	PUNCT
ejpam-5017	160	1	we	we	PRON
ejpam-5017	160	2	will	will	AUX
ejpam-5017	160	3	derive	derive	VERB
ejpam-5017	160	4	a	a	DET
ejpam-5017	160	5	uniform	uniform	NOUN
ejpam-5017	160	6	bound	bind	VERB
ejpam-5017	160	7	of	of	ADP
ejpam-5017	160	8	∥w(t)∥∞	∥w(t)∥∞	PRON
ejpam-5017	160	9	.	.	PUNCT
ejpam-5017	161	1	multiplying	multiply	VERB
ejpam-5017	161	2	the	the	DET
ejpam-5017	161	3	first	first	ADJ
ejpam-5017	161	4	equation	equation	NOUN
ejpam-5017	161	5	of	of	ADP
ejpam-5017	161	6	(	(	PUNCT
ejpam-5017	161	7	1	1	NUM
ejpam-5017	161	8	)	)	PUNCT
ejpam-5017	161	9	by	by	ADP
ejpam-5017	161	10	wp−1	wp−1	ADJ
ejpam-5017	161	11	and	and	CCONJ
ejpam-5017	161	12	integrating	integrate	VERB
ejpam-5017	161	13	over	over	ADP
ejpam-5017	161	14	ω	ω	PROPN
ejpam-5017	161	15	,	,	PUNCT
ejpam-5017	161	16	we	we	PRON
ejpam-5017	161	17	get	get	VERB
ejpam-5017	161	18	d	d	DET
ejpam-5017	161	19	dt	dt	X
ejpam-5017	161	20	∫	∫	PROPN
ejpam-5017	161	21	ωwpdx	ωwpdx	PROPN
ejpam-5017	161	22	≤	≤	NUM
ejpam-5017	161	23	0	0	NUM
ejpam-5017	162	1	thanks	thank	NOUN
ejpam-5017	162	2	to	to	ADP
ejpam-5017	162	3	relation	relation	NOUN
ejpam-5017	162	4	(	(	PUNCT
ejpam-5017	162	5	5	5	NUM
ejpam-5017	162	6	)	)	PUNCT
ejpam-5017	162	7	and	and	CCONJ
ejpam-5017	162	8	f	f	X
ejpam-5017	162	9	=	=	SYM
ejpam-5017	162	10	0	0	PROPN
ejpam-5017	162	11	.	.	PUNCT
ejpam-5017	163	1	hence	hence	ADV
ejpam-5017	163	2	,	,	PUNCT
ejpam-5017	163	3	we	we	PRON
ejpam-5017	163	4	get	get	VERB
ejpam-5017	163	5	∥w(t)∥∞	∥w(t)∥∞	PROPN
ejpam-5017	163	6	≤	≤	NUM
ejpam-5017	163	7	∥w0∥∞	∥w0∥∞	PROPN
ejpam-5017	163	8	,	,	PUNCT
ejpam-5017	163	9	∀t	∀t	PROPN
ejpam-5017	163	10	∈	∈	PROPN
ejpam-5017	164	1	[	[	X
ejpam-5017	164	2	0	0	NUM
ejpam-5017	164	3	,	,	PUNCT
ejpam-5017	164	4	tmax	tmax	NUM
ejpam-5017	164	5	)	)	PUNCT
ejpam-5017	164	6	.	.	PUNCT
ejpam-5017	165	1	(	(	PUNCT
ejpam-5017	165	2	13	13	NUM
ejpam-5017	165	3	)	)	PUNCT
ejpam-5017	165	4	m.	m.	NOUN
ejpam-5017	165	5	mebarki	mebarki	NOUN
ejpam-5017	165	6	/	/	SYM
ejpam-5017	165	7	eur	eur	PROPN
ejpam-5017	165	8	.	.	PUNCT
ejpam-5017	166	1	j.	j.	PROPN
ejpam-5017	166	2	pure	pure	PROPN
ejpam-5017	166	3	appl	appl	PROPN
ejpam-5017	166	4	.	.	PROPN
ejpam-5017	166	5	math	math	PROPN
ejpam-5017	166	6	,	,	PUNCT
ejpam-5017	166	7	17	17	NUM
ejpam-5017	166	8	(	(	PUNCT
ejpam-5017	166	9	2	2	NUM
ejpam-5017	166	10	)	)	PUNCT
ejpam-5017	166	11	(	(	PUNCT
ejpam-5017	166	12	2024	2024	NUM
ejpam-5017	166	13	)	)	PUNCT
ejpam-5017	166	14	,	,	PUNCT
ejpam-5017	166	15	1321	1321	NUM
ejpam-5017	166	16	-	-	SYM
ejpam-5017	166	17	1334	1334	NUM
ejpam-5017	166	18	1328	1328	NUM
ejpam-5017	166	19	now	now	ADV
ejpam-5017	166	20	,	,	PUNCT
ejpam-5017	166	21	we	we	PRON
ejpam-5017	166	22	integrate	integrate	VERB
ejpam-5017	166	23	the	the	DET
ejpam-5017	166	24	first	first	ADJ
ejpam-5017	166	25	equation	equation	NOUN
ejpam-5017	166	26	of	of	ADP
ejpam-5017	166	27	(	(	PUNCT
ejpam-5017	166	28	1	1	NUM
ejpam-5017	166	29	)	)	PUNCT
ejpam-5017	166	30	over	over	ADP
ejpam-5017	166	31	ω	ω	NOUN
ejpam-5017	166	32	and	and	CCONJ
ejpam-5017	166	33	practise	practise	VERB
ejpam-5017	166	34	the	the	DET
ejpam-5017	166	35	integration	integration	NOUN
ejpam-5017	166	36	by	by	ADP
ejpam-5017	166	37	parts	part	NOUN
ejpam-5017	166	38	formula	formula	NOUN
ejpam-5017	166	39	(	(	PUNCT
ejpam-5017	166	40	3	3	X
ejpam-5017	166	41	)	)	PUNCT
ejpam-5017	166	42	which	which	PRON
ejpam-5017	166	43	haven	haven	NOUN
ejpam-5017	166	44	∫	∫	PROPN
ejpam-5017	166	45	ω	ω	PROPN
ejpam-5017	166	46	(	(	PUNCT
ejpam-5017	166	47	−∆n	−∆n	NUM
ejpam-5017	166	48	)	)	PUNCT
ejpam-5017	166	49	δw(x)dx	δw(x)dx	ADJ
ejpam-5017	166	50	=	=	SYM
ejpam-5017	166	51	0	0	NUM
ejpam-5017	166	52	and	and	CCONJ
ejpam-5017	166	53	f	f	PROPN
ejpam-5017	166	54	=	=	SYM
ejpam-5017	166	55	0	0	NUM
ejpam-5017	166	56	;	;	PUNCT
ejpam-5017	166	57	we	we	PRON
ejpam-5017	166	58	attain	attain	VERB
ejpam-5017	166	59	∫	∫	PROPN
ejpam-5017	166	60	ω	ω	PROPN
ejpam-5017	166	61	∂w	∂w	PROPN
ejpam-5017	166	62	∂t	∂t	PROPN
ejpam-5017	166	63	dx	dx	PROPN
ejpam-5017	167	1	=	=	SYM
ejpam-5017	168	1	−	−	PROPN
ejpam-5017	168	2	∫	∫	PROPN
ejpam-5017	168	3	ω	ω	NUM
ejpam-5017	168	4	w2zdx	w2zdx	PROPN
ejpam-5017	168	5	≤	≤	NOUN
ejpam-5017	168	6	0	0	PUNCT
ejpam-5017	169	1	therefore	therefore	ADV
ejpam-5017	169	2	,	,	PUNCT
ejpam-5017	169	3	the	the	DET
ejpam-5017	169	4	function	function	NOUN
ejpam-5017	169	5	t	t	PROPN
ejpam-5017	169	6	7→	7→	NUM
ejpam-5017	169	7	∫	∫	NOUN
ejpam-5017	169	8	ωw(x	ωw(x	NUM
ejpam-5017	169	9	,	,	PUNCT
ejpam-5017	169	10	t)dx	t)dx	PROPN
ejpam-5017	169	11	is	be	AUX
ejpam-5017	169	12	nonincreasing	nonincrease	VERB
ejpam-5017	169	13	.	.	PUNCT
ejpam-5017	170	1	since	since	SCONJ
ejpam-5017	170	2	w	w	PROPN
ejpam-5017	170	3	≥	≥	NOUN
ejpam-5017	170	4	0	0	NUM
ejpam-5017	170	5	.	.	PUNCT
ejpam-5017	171	1	then	then	ADV
ejpam-5017	171	2	it	it	PRON
ejpam-5017	171	3	admits	admit	VERB
ejpam-5017	171	4	a	a	DET
ejpam-5017	171	5	limit	limit	NOUN
ejpam-5017	171	6	as	as	ADP
ejpam-5017	171	7	t	t	PROPN
ejpam-5017	171	8	→	→	PUNCT
ejpam-5017	171	9	+	+	NUM
ejpam-5017	171	10	∞	∞	NUM
ejpam-5017	171	11	:	:	PUNCT
ejpam-5017	172	1	lim	lim	PROPN
ejpam-5017	172	2	t→+∞	t→+∞	VERB
ejpam-5017	172	3	1	1	NUM
ejpam-5017	172	4	|ω|	|ω|	NUM
ejpam-5017	172	5	∫	∫	PROPN
ejpam-5017	172	6	ω	ω	PROPN
ejpam-5017	172	7	w(x	w(x	PROPN
ejpam-5017	172	8	,	,	PUNCT
ejpam-5017	172	9	t)dx	t)dx	PROPN
ejpam-5017	172	10	=	=	SYM
ejpam-5017	172	11	w∞	w∞	X
ejpam-5017	172	12	≥	≥	NOUN
ejpam-5017	172	13	0	0	NUM
ejpam-5017	172	14	.	.	PUNCT
ejpam-5017	173	1	we	we	PRON
ejpam-5017	173	2	add	add	VERB
ejpam-5017	173	3	the	the	DET
ejpam-5017	173	4	equations	equation	NOUN
ejpam-5017	173	5	of	of	ADP
ejpam-5017	173	6	system(1	system(1	NOUN
ejpam-5017	173	7	)	)	PUNCT
ejpam-5017	173	8	and	and	CCONJ
ejpam-5017	173	9	we	we	PRON
ejpam-5017	173	10	integrate	integrate	VERB
ejpam-5017	173	11	over	over	ADP
ejpam-5017	173	12	ω	ω	PROPN
ejpam-5017	173	13	and	and	CCONJ
ejpam-5017	173	14	putting	put	VERB
ejpam-5017	173	15	f	f	NOUN
ejpam-5017	173	16	=	=	SYM
ejpam-5017	173	17	0	0	PROPN
ejpam-5017	173	18	to	to	PART
ejpam-5017	173	19	obtain	obtain	VERB
ejpam-5017	173	20	d	d	PRON
ejpam-5017	173	21	dt	dt	X
ejpam-5017	173	22	∫	∫	PROPN
ejpam-5017	173	23	ω	ω	PROPN
ejpam-5017	173	24	(	(	PUNCT
ejpam-5017	173	25	w	w	PROPN
ejpam-5017	173	26	+	+	X
ejpam-5017	173	27	z)dx	z)dx	PROPN
ejpam-5017	173	28	=	=	SYM
ejpam-5017	173	29	−k	−k	PROPN
ejpam-5017	173	30	∫	∫	PROPN
ejpam-5017	173	31	ω	ω	PROPN
ejpam-5017	173	32	zdx	zdx	PROPN
ejpam-5017	173	33	≤	≤	ADV
ejpam-5017	173	34	0	0	NUM
ejpam-5017	173	35	.	.	PUNCT
ejpam-5017	174	1	(	(	PUNCT
ejpam-5017	174	2	14	14	NUM
ejpam-5017	174	3	)	)	PUNCT
ejpam-5017	174	4	we	we	PRON
ejpam-5017	174	5	observe	observe	VERB
ejpam-5017	174	6	that	that	SCONJ
ejpam-5017	174	7	the	the	DET
ejpam-5017	174	8	function	function	NOUN
ejpam-5017	174	9	t	t	PROPN
ejpam-5017	174	10	7→	7→	NUM
ejpam-5017	174	11	∫	∫	NOUN
ejpam-5017	174	12	ω(w	ω(w	PROPN
ejpam-5017	174	13	+	+	CCONJ
ejpam-5017	175	1	z)dx	z)dx	NOUN
ejpam-5017	175	2	≥	≥	NOUN
ejpam-5017	175	3	0	0	NUM
ejpam-5017	175	4	is	be	AUX
ejpam-5017	175	5	nonincreasing	nonincrease	VERB
ejpam-5017	175	6	.	.	PUNCT
ejpam-5017	176	1	accordingly	accordingly	ADV
ejpam-5017	176	2	admits	admit	VERB
ejpam-5017	176	3	a	a	DET
ejpam-5017	176	4	limit	limit	NOUN
ejpam-5017	176	5	;	;	PUNCT
ejpam-5017	176	6	also	also	ADV
ejpam-5017	176	7	we	we	PRON
ejpam-5017	176	8	obtain	obtain	VERB
ejpam-5017	176	9	lim	lim	PROPN
ejpam-5017	176	10	t→+∞	t→+∞	PROPN
ejpam-5017	176	11	∫	∫	PROPN
ejpam-5017	176	12	ω	ω	PROPN
ejpam-5017	176	13	z(x	z(x	PROPN
ejpam-5017	176	14	,	,	PUNCT
ejpam-5017	176	15	t)dx	t)dx	PROPN
ejpam-5017	176	16	=	=	SYM
ejpam-5017	176	17	l	l	NOUN
ejpam-5017	176	18	≥	≥	NOUN
ejpam-5017	176	19	0	0	NUM
ejpam-5017	176	20	.	.	PUNCT
ejpam-5017	177	1	thence	thence	NOUN
ejpam-5017	177	2	,	,	PUNCT
ejpam-5017	177	3	z	z	PROPN
ejpam-5017	177	4	∈	∈	PROPN
ejpam-5017	177	5	l∞	l∞	NOUN
ejpam-5017	177	6	(	(	PUNCT
ejpam-5017	177	7	r+;l1	r+;l1	NOUN
ejpam-5017	177	8	(	(	PUNCT
ejpam-5017	177	9	ω	ω	NOUN
ejpam-5017	177	10	)	)	PUNCT
ejpam-5017	177	11	)	)	PUNCT
ejpam-5017	177	12	.	.	PUNCT
ejpam-5017	178	1	thanks	thank	NOUN
ejpam-5017	178	2	to	to	PART
ejpam-5017	178	3	estimate	estimate	VERB
ejpam-5017	178	4	(	(	PUNCT
ejpam-5017	178	5	11	11	NUM
ejpam-5017	178	6	)	)	PUNCT
ejpam-5017	178	7	we	we	PRON
ejpam-5017	178	8	can	can	AUX
ejpam-5017	178	9	proceed	proceed	VERB
ejpam-5017	178	10	analogously	analogously	ADV
ejpam-5017	178	11	to	to	ADP
ejpam-5017	178	12	the	the	DET
ejpam-5017	178	13	proof	proof	NOUN
ejpam-5017	178	14	of	of	ADP
ejpam-5017	178	15	of	of	ADP
ejpam-5017	178	16	(	(	PUNCT
ejpam-5017	178	17	[	[	X
ejpam-5017	178	18	8],proposition	8],proposition	NOUN
ejpam-5017	178	19	3.3	3.3	NUM
ejpam-5017	178	20	)	)	PUNCT
ejpam-5017	178	21	.	.	PUNCT
ejpam-5017	179	1	consequently	consequently	ADV
ejpam-5017	179	2	,	,	PUNCT
ejpam-5017	179	3	we	we	PRON
ejpam-5017	179	4	get	get	VERB
ejpam-5017	179	5	z	z	NOUN
ejpam-5017	179	6	∈	∈	PROPN
ejpam-5017	179	7	c	c	X
ejpam-5017	179	8	(	(	PUNCT
ejpam-5017	179	9	r+	r+	X
ejpam-5017	179	10	,	,	PUNCT
ejpam-5017	179	11	c	c	PROPN
ejpam-5017	179	12	(	(	PUNCT
ejpam-5017	179	13	ω	ω	NOUN
ejpam-5017	179	14	)	)	PUNCT
ejpam-5017	179	15	)	)	PUNCT
ejpam-5017	179	16	.	.	PUNCT
ejpam-5017	180	1	·	·	PUNCT
ejpam-5017	180	2	step	step	NOUN
ejpam-5017	180	3	3	3	NUM
ejpam-5017	180	4	.	.	PUNCT
ejpam-5017	181	1	integrating	integrate	VERB
ejpam-5017	181	2	the	the	DET
ejpam-5017	181	3	equation	equation	NOUN
ejpam-5017	181	4	(	(	PUNCT
ejpam-5017	181	5	15	15	NUM
ejpam-5017	181	6	)	)	PUNCT
ejpam-5017	181	7	over	over	ADP
ejpam-5017	181	8	[	[	X
ejpam-5017	181	9	0	0	NUM
ejpam-5017	181	10	,	,	PUNCT
ejpam-5017	181	11	t	t	X
ejpam-5017	181	12	]	]	PUNCT
ejpam-5017	181	13	,	,	PUNCT
ejpam-5017	181	14	we	we	PRON
ejpam-5017	181	15	have	have	VERB
ejpam-5017	181	16	−k	−k	PROPN
ejpam-5017	181	17	∫	∫	PROPN
ejpam-5017	182	1	t	t	PROPN
ejpam-5017	182	2	0	0	NUM
ejpam-5017	182	3	∫	∫	PROPN
ejpam-5017	182	4	ω	ω	NUM
ejpam-5017	182	5	z(x	z(x	PROPN
ejpam-5017	182	6	,	,	PUNCT
ejpam-5017	182	7	s)dxds	s)dxds	X
ejpam-5017	182	8	=	=	SYM
ejpam-5017	182	9	∫	∫	PROPN
ejpam-5017	182	10	ω	ω	PROPN
ejpam-5017	182	11	(	(	PUNCT
ejpam-5017	182	12	w0	w0	PROPN
ejpam-5017	182	13	+	+	CCONJ
ejpam-5017	182	14	z0)dx−	z0)dx−	PROPN
ejpam-5017	182	15	∫	∫	PROPN
ejpam-5017	182	16	ω	ω	PROPN
ejpam-5017	182	17	(	(	PUNCT
ejpam-5017	182	18	w	w	PROPN
ejpam-5017	182	19	+	+	NOUN
ejpam-5017	182	20	z)(x	z)(x	NUM
ejpam-5017	182	21	,	,	PUNCT
ejpam-5017	182	22	t)dx	t)dx	PROPN
ejpam-5017	182	23	≤	≤	NUM
ejpam-5017	182	24	∫	∫	PROPN
ejpam-5017	182	25	ω	ω	PROPN
ejpam-5017	182	26	(	(	PUNCT
ejpam-5017	182	27	w0	w0	PROPN
ejpam-5017	182	28	+	+	CCONJ
ejpam-5017	182	29	z0)dx	z0)dx	NOUN
ejpam-5017	182	30	.	.	PUNCT
ejpam-5017	183	1	also	also	ADV
ejpam-5017	183	2	,	,	PUNCT
ejpam-5017	183	3	∫	∫	PROPN
ejpam-5017	183	4	t	t	PROPN
ejpam-5017	183	5	0	0	NUM
ejpam-5017	183	6	∫	∫	PROPN
ejpam-5017	183	7	ω	ω	PROPN
ejpam-5017	183	8	z(x	z(x	PROPN
ejpam-5017	183	9	,	,	PUNCT
ejpam-5017	183	10	s)dxds	s)dxds	NOUN
ejpam-5017	183	11	is	be	AUX
ejpam-5017	183	12	finite	finite	ADJ
ejpam-5017	183	13	.	.	PUNCT
ejpam-5017	184	1	moreover	moreover	ADV
ejpam-5017	184	2	,	,	PUNCT
ejpam-5017	184	3	z(x	z(x	PROPN
ejpam-5017	184	4	,	,	PUNCT
ejpam-5017	184	5	t	t	PROPN
ejpam-5017	184	6	)	)	PUNCT
ejpam-5017	184	7	is	be	AUX
ejpam-5017	184	8	uniformly	uniformly	ADV
ejpam-5017	184	9	continuous	continuous	ADJ
ejpam-5017	184	10	in	in	ADP
ejpam-5017	184	11	t.	t.	NOUN
ejpam-5017	184	12	in	in	ADP
ejpam-5017	184	13	fact	fact	NOUN
ejpam-5017	184	14	,	,	PUNCT
ejpam-5017	184	15	let	let	VERB
ejpam-5017	184	16	h	h	PRON
ejpam-5017	184	17	≻	≻	PROPN
ejpam-5017	184	18	0	0	NUM
ejpam-5017	184	19	and	and	CCONJ
ejpam-5017	184	20	0	0	NUM
ejpam-5017	184	21	≤	≤	NOUN
ejpam-5017	184	22	t	t	NOUN
ejpam-5017	184	23	≺	≺	NOUN
ejpam-5017	184	24	t+	t+	PUNCT
ejpam-5017	184	25	h	h	NOUN
ejpam-5017	184	26	≺	≺	NOUN
ejpam-5017	184	27	tmax	tmax	NUM
ejpam-5017	184	28	,	,	PUNCT
ejpam-5017	184	29	it	it	PRON
ejpam-5017	184	30	follows	follow	VERB
ejpam-5017	184	31	that	that	SCONJ
ejpam-5017	184	32	,	,	PUNCT
ejpam-5017	184	33	∥z(t+	∥z(t+	PROPN
ejpam-5017	184	34	h)−	h)−	PROPN
ejpam-5017	184	35	z(t)∥∞	z(t)∥∞	PROPN
ejpam-5017	184	36	≤	≤	NUM
ejpam-5017	184	37	∥∥∥(e−d2htp	∥∥∥(e−d2htp	VERB
ejpam-5017	184	38	−	−	PROPN
ejpam-5017	184	39	i)e−d2ttpz0	i)e−d2ttpz0	NUM
ejpam-5017	184	40	∥∥∥	∥∥∥	PROPN
ejpam-5017	184	41	∞	∞	PROPN
ejpam-5017	184	42	+	+	CCONJ
ejpam-5017	184	43	∫	∫	PROPN
ejpam-5017	184	44	t	t	PROPN
ejpam-5017	184	45	0	0	NUM
ejpam-5017	184	46	∥∥∥(e−d2htp	∥∥∥(e−d2htp	VERB
ejpam-5017	184	47	−	−	PROPN
ejpam-5017	184	48	i)e−d2(t−h)tpw2z(s	i)e−d2(t−h)tpw2z(s	PROPN
ejpam-5017	184	49	)	)	PUNCT
ejpam-5017	185	1	∥∥∥	∥∥∥	PROPN
ejpam-5017	185	2	∞	∞	NUM
ejpam-5017	185	3	ds	ds	PROPN
ejpam-5017	185	4	−(f	−(f	PROPN
ejpam-5017	185	5	+	+	CCONJ
ejpam-5017	185	6	k	k	X
ejpam-5017	185	7	)	)	PUNCT
ejpam-5017	185	8	∫	∫	PROPN
ejpam-5017	186	1	t	t	PROPN
ejpam-5017	186	2	0	0	NUM
ejpam-5017	186	3	∥∥∥(e−d2htp	∥∥∥(e−d2htp	VERB
ejpam-5017	186	4	−	−	PROPN
ejpam-5017	186	5	i)e−d2(t−h)tpz(s	i)e−d2(t−h)tpz(s	NOUN
ejpam-5017	186	6	)	)	PUNCT
ejpam-5017	186	7	∥∥∥	∥∥∥	PROPN
ejpam-5017	186	8	∞	∞	NUM
ejpam-5017	186	9	ds+	ds+	PROPN
ejpam-5017	186	10	∫	∫	PROPN
ejpam-5017	186	11	t+h	t+h	PROPN
ejpam-5017	186	12	t	t	PROPN
ejpam-5017	186	13	∥∥∥e−d2(t+h−s)tpw2z(s	∥∥∥e−d2(t+h−s)tpw2z(s	NUM
ejpam-5017	186	14	)	)	PUNCT
ejpam-5017	186	15	∥∥∥	∥∥∥	PROPN
ejpam-5017	186	16	∞	∞	NUM
ejpam-5017	186	17	ds	ds	PROPN
ejpam-5017	186	18	−(f	−(f	PROPN
ejpam-5017	186	19	+	+	CCONJ
ejpam-5017	186	20	k	k	X
ejpam-5017	186	21	)	)	PUNCT
ejpam-5017	186	22	∫	∫	PROPN
ejpam-5017	186	23	t+h	t+h	PROPN
ejpam-5017	186	24	t	t	PROPN
ejpam-5017	186	25	∥∥∥e−d2(t+h−s)tpz(s	∥∥∥e−d2(t+h−s)tpz(s	PROPN
ejpam-5017	186	26	)	)	PUNCT
ejpam-5017	186	27	∥∥∥	∥∥∥	PROPN
ejpam-5017	186	28	∞	∞	NUM
ejpam-5017	186	29	ds	ds	PROPN
ejpam-5017	186	30	=	=	SYM
ejpam-5017	186	31	a1	a1	PROPN
ejpam-5017	186	32	+	+	PROPN
ejpam-5017	186	33	a2	a2	PROPN
ejpam-5017	186	34	+	+	NOUN
ejpam-5017	186	35	a3	a3	NOUN
ejpam-5017	186	36	+	+	ADJ
ejpam-5017	186	37	a4	a4	NOUN
ejpam-5017	186	38	+	+	NOUN
ejpam-5017	186	39	a5	a5	NOUN
ejpam-5017	186	40	.	.	PUNCT
ejpam-5017	187	1	m.	m.	NOUN
ejpam-5017	187	2	mebarki	mebarki	PROPN
ejpam-5017	187	3	/	/	SYM
ejpam-5017	187	4	eur	eur	PROPN
ejpam-5017	187	5	.	.	PUNCT
ejpam-5017	188	1	j.	j.	PROPN
ejpam-5017	188	2	pure	pure	PROPN
ejpam-5017	188	3	appl	appl	PROPN
ejpam-5017	188	4	.	.	PROPN
ejpam-5017	188	5	math	math	PROPN
ejpam-5017	188	6	,	,	PUNCT
ejpam-5017	188	7	17	17	NUM
ejpam-5017	188	8	(	(	PUNCT
ejpam-5017	188	9	2	2	NUM
ejpam-5017	188	10	)	)	PUNCT
ejpam-5017	188	11	(	(	PUNCT
ejpam-5017	188	12	2024	2024	NUM
ejpam-5017	188	13	)	)	PUNCT
ejpam-5017	188	14	,	,	PUNCT
ejpam-5017	188	15	1321	1321	NUM
ejpam-5017	188	16	-	-	SYM
ejpam-5017	188	17	1334	1334	NUM
ejpam-5017	188	18	1329	1329	NUM
ejpam-5017	188	19	employing	employ	VERB
ejpam-5017	188	20	(	(	PUNCT
ejpam-5017	188	21	[	[	NOUN
ejpam-5017	188	22	6],lemma2.1	6],lemma2.1	NUM
ejpam-5017	188	23	)	)	PUNCT
ejpam-5017	189	1	,	,	PUNCT
ejpam-5017	189	2	we	we	PRON
ejpam-5017	189	3	get	get	VERB
ejpam-5017	189	4	that	that	PRON
ejpam-5017	189	5	for	for	ADP
ejpam-5017	189	6	every	every	DET
ejpam-5017	189	7	θ	θ	PROPN
ejpam-5017	189	8	∈	∈	PROPN
ejpam-5017	189	9	(	(	PUNCT
ejpam-5017	189	10	0.1	0.1	NUM
ejpam-5017	189	11	)	)	PUNCT
ejpam-5017	189	12	a1	a1	NOUN
ejpam-5017	189	13	≤	≤	ADJ
ejpam-5017	189	14	m2	m2	PROPN
ejpam-5017	189	15	(	(	PUNCT
ejpam-5017	189	16	θ)h	θ)h	ADJ
ejpam-5017	189	17	θ	θ	X
ejpam-5017	189	18	∥∥∥t	∥∥∥t	NOUN
ejpam-5017	189	19	θ	θ	PROPN
ejpam-5017	189	20	p	p	NOUN
ejpam-5017	189	21	e	e	X
ejpam-5017	189	22	−d2ttpz0	−d2ttpz0	PROPN
ejpam-5017	189	23	∥∥∥	∥∥∥	PROPN
ejpam-5017	189	24	∞	∞	NUM
ejpam-5017	189	25	≤	≤	PROPN
ejpam-5017	189	26	m2	m2	PROPN
ejpam-5017	189	27	(	(	PUNCT
ejpam-5017	189	28	θ)m1	θ)m1	PROPN
ejpam-5017	189	29	(	(	PUNCT
ejpam-5017	189	30	θ)h	θ)h	ADJ
ejpam-5017	189	31	θt−θe−d2αϵ	θt−θe−d2αϵ	ADJ
ejpam-5017	189	32	1	1	NUM
ejpam-5017	189	33	t	t	NOUN
ejpam-5017	189	34	∥z0∥∞	∥z0∥∞	PROPN
ejpam-5017	189	35	we	we	PRON
ejpam-5017	189	36	also	also	ADV
ejpam-5017	189	37	find	find	VERB
ejpam-5017	189	38	a2	a2	PROPN
ejpam-5017	189	39	≤	≤	PROPN
ejpam-5017	189	40	m2	m2	PROPN
ejpam-5017	189	41	(	(	PUNCT
ejpam-5017	189	42	θ)m1	θ)m1	PROPN
ejpam-5017	189	43	(	(	PUNCT
ejpam-5017	189	44	θ)h	θ)h	ADJ
ejpam-5017	189	45	θ	θ	PROPN
ejpam-5017	189	46	∫	∫	PROPN
ejpam-5017	189	47	t	t	PROPN
ejpam-5017	189	48	0	0	NUM
ejpam-5017	189	49	(	(	PUNCT
ejpam-5017	189	50	t−	t−	PROPN
ejpam-5017	189	51	s)−θe−d2αϵ	s)−θe−d2αϵ	PROPN
ejpam-5017	189	52	1(t−s	1(t−s	X
ejpam-5017	189	53	)	)	PUNCT
ejpam-5017	189	54	∥∥w2z(s	∥∥w2z(s	PROPN
ejpam-5017	189	55	)	)	PUNCT
ejpam-5017	189	56	∥∥	∥∥	PROPN
ejpam-5017	190	1	∞	∞	NUM
ejpam-5017	190	2	ds	ds	AUX
ejpam-5017	190	3	.	.	NOUN
ejpam-5017	190	4	using	use	VERB
ejpam-5017	190	5	lemma	lemma	PROPN
ejpam-5017	190	6	1	1	NUM
ejpam-5017	190	7	,	,	PUNCT
ejpam-5017	190	8	we	we	PRON
ejpam-5017	190	9	can	can	AUX
ejpam-5017	190	10	observe	observe	VERB
ejpam-5017	190	11	that∫	that∫	NOUN
ejpam-5017	190	12	t	t	NOUN
ejpam-5017	190	13	0	0	NUM
ejpam-5017	191	1	(	(	PUNCT
ejpam-5017	191	2	t−	t−	PROPN
ejpam-5017	191	3	s)−θe−d2αϵ	s)−θe−d2αϵ	PROPN
ejpam-5017	191	4	1(t−s	1(t−s	NUM
ejpam-5017	191	5	)	)	PUNCT
ejpam-5017	191	6	≤	≤	NOUN
ejpam-5017	191	7	m3	m3	PROPN
ejpam-5017	191	8	(	(	PUNCT
ejpam-5017	191	9	θ,−d2α	θ,−d2α	NOUN
ejpam-5017	191	10	ϵ	ϵ	PROPN
ejpam-5017	191	11	1	1	NUM
ejpam-5017	191	12	)	)	PUNCT
ejpam-5017	191	13	.	.	PUNCT
ejpam-5017	192	1	as	as	SCONJ
ejpam-5017	192	2	z	z	PROPN
ejpam-5017	192	3	∈	∈	PROPN
ejpam-5017	192	4	c	c	X
ejpam-5017	192	5	(	(	PUNCT
ejpam-5017	192	6	r+	r+	X
ejpam-5017	192	7	,	,	PUNCT
ejpam-5017	192	8	c	c	PROPN
ejpam-5017	192	9	(	(	PUNCT
ejpam-5017	192	10	ω	ω	NOUN
ejpam-5017	192	11	)	)	PUNCT
ejpam-5017	192	12	)	)	PUNCT
ejpam-5017	192	13	we	we	PRON
ejpam-5017	192	14	obtain	obtain	VERB
ejpam-5017	192	15	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	192	16	≤	≤	NUM
ejpam-5017	192	17	c,∀t	c,∀t	PROPN
ejpam-5017	192	18	≻	≻	NUM
ejpam-5017	192	19	0	0	NUM
ejpam-5017	192	20	,	,	PUNCT
ejpam-5017	192	21	here	here	ADV
ejpam-5017	192	22	c	c	NOUN
ejpam-5017	192	23	is	be	AUX
ejpam-5017	192	24	positive	positive	ADJ
ejpam-5017	192	25	constant	constant	ADJ
ejpam-5017	192	26	.	.	PUNCT
ejpam-5017	193	1	so	so	ADV
ejpam-5017	193	2	,	,	PUNCT
ejpam-5017	193	3	we	we	PRON
ejpam-5017	193	4	have	have	VERB
ejpam-5017	193	5	a2	a2	PROPN
ejpam-5017	193	6	≤	≤	PROPN
ejpam-5017	193	7	m2	m2	PROPN
ejpam-5017	193	8	(	(	PUNCT
ejpam-5017	193	9	θ)m1	θ)m1	PROPN
ejpam-5017	193	10	(	(	PUNCT
ejpam-5017	193	11	θ)m3	θ)m3	PROPN
ejpam-5017	193	12	(	(	PUNCT
ejpam-5017	193	13	θ,−d2α	θ,−d2α	NOUN
ejpam-5017	193	14	ϵ	ϵ	PROPN
ejpam-5017	193	15	1)chθ	1)chθ	NUM
ejpam-5017	193	16	∥w0∥2	∥w0∥2	NOUN
ejpam-5017	193	17	.	.	PUNCT
ejpam-5017	194	1	similarly	similarly	ADV
ejpam-5017	194	2	,	,	PUNCT
ejpam-5017	194	3	it	it	PRON
ejpam-5017	194	4	follows	follow	VERB
ejpam-5017	194	5	that	that	DET
ejpam-5017	194	6	a3	a3	VERB
ejpam-5017	194	7	≤	≤	ADJ
ejpam-5017	194	8	m2	m2	PROPN
ejpam-5017	194	9	(	(	PUNCT
ejpam-5017	194	10	θ)m1	θ)m1	PROPN
ejpam-5017	194	11	(	(	PUNCT
ejpam-5017	194	12	θ)m3	θ)m3	PROPN
ejpam-5017	194	13	(	(	PUNCT
ejpam-5017	194	14	θ,−d2α	θ,−d2α	NOUN
ejpam-5017	194	15	ϵ	ϵ	NOUN
ejpam-5017	194	16	1)chθ	1)chθ	NUM
ejpam-5017	194	17	.	.	PUNCT
ejpam-5017	195	1	using	use	VERB
ejpam-5017	195	2	the	the	DET
ejpam-5017	195	3	relation	relation	NOUN
ejpam-5017	195	4	see([7	see([7	NOUN
ejpam-5017	195	5	]	]	PUNCT
ejpam-5017	195	6	)	)	PUNCT
ejpam-5017	195	7	∥∥∥e−d2ttpw	∥∥∥e−d2ttpw	NOUN
ejpam-5017	195	8	∥∥∥	∥∥∥	PROPN
ejpam-5017	195	9	∞	∞	NUM
ejpam-5017	195	10	≤	≤	NUM
ejpam-5017	195	11	r	r	NOUN
ejpam-5017	195	12	∥w∥∞	∥w∥∞	PUNCT
ejpam-5017	195	13	,	,	PUNCT
ejpam-5017	195	14	we	we	PRON
ejpam-5017	195	15	obtain	obtain	VERB
ejpam-5017	195	16	a4	a4	NOUN
ejpam-5017	195	17	=	=	SYM
ejpam-5017	195	18	∫	∫	PROPN
ejpam-5017	195	19	h	h	NOUN
ejpam-5017	195	20	0	0	NUM
ejpam-5017	195	21	∥∥∥e−d2τtpw2z(t−	∥∥∥e−d2τtpw2z(t−	NOUN
ejpam-5017	196	1	h−	h−	PROPN
ejpam-5017	196	2	τ	τ	PROPN
ejpam-5017	196	3	)	)	PUNCT
ejpam-5017	196	4	∥∥∥	∥∥∥	PROPN
ejpam-5017	196	5	∞	∞	NUM
ejpam-5017	196	6	dτ	dτ	PROPN
ejpam-5017	196	7	≤	≤	PROPN
ejpam-5017	196	8	mrh	mrh	PROPN
ejpam-5017	196	9	∥w∥2∞	∥w∥2∞	NOUN
ejpam-5017	196	10	.	.	PUNCT
ejpam-5017	197	1	therefore	therefore	ADV
ejpam-5017	197	2	,	,	PUNCT
ejpam-5017	197	3	∀t	∀t	PROPN
ejpam-5017	197	4	⪰	⪰	NOUN
ejpam-5017	197	5	β	β	X
ejpam-5017	197	6	≻	≻	PROPN
ejpam-5017	197	7	0	0	PUNCT
ejpam-5017	197	8	∥z(t+	∥z(t+	PROPN
ejpam-5017	198	1	h)−	h)−	PROPN
ejpam-5017	198	2	z(t)∥∞	z(t)∥∞	PROPN
ejpam-5017	198	3	≤	≤	NUM
ejpam-5017	198	4	m	m	PROPN
ejpam-5017	198	5	(	(	PUNCT
ejpam-5017	198	6	θ	θ	PROPN
ejpam-5017	198	7	,	,	PUNCT
ejpam-5017	198	8	ϵ	ϵ	X
ejpam-5017	198	9	,	,	PUNCT
ejpam-5017	198	10	β)hθ	β)hθ	PROPN
ejpam-5017	198	11	.	.	PUNCT
ejpam-5017	199	1	consequently	consequently	ADV
ejpam-5017	199	2	,	,	PUNCT
ejpam-5017	199	3	limt→+∞	limt→+∞	PROPN
ejpam-5017	199	4	∫	∫	PROPN
ejpam-5017	199	5	ω	ω	PROPN
ejpam-5017	199	6	z(x	z(x	PROPN
ejpam-5017	199	7	,	,	PUNCT
ejpam-5017	199	8	t)dx	t)dx	PROPN
ejpam-5017	199	9	=	=	SYM
ejpam-5017	199	10	0	0	X
ejpam-5017	199	11	.	.	PUNCT
ejpam-5017	200	1	then	then	ADV
ejpam-5017	200	2	,	,	PUNCT
ejpam-5017	200	3	for	for	ADP
ejpam-5017	200	4	θ	θ	PROPN
ejpam-5017	200	5	∈	∈	PROPN
ejpam-5017	200	6	(	(	PUNCT
ejpam-5017	200	7	0.1	0.1	NUM
ejpam-5017	200	8	)	)	PUNCT
ejpam-5017	200	9	,	,	PUNCT
ejpam-5017	200	10	applying	apply	VERB
ejpam-5017	200	11	t	t	NOUN
ejpam-5017	200	12	θ	θ	PROPN
ejpam-5017	200	13	p	p	NOUN
ejpam-5017	200	14	to	to	ADP
ejpam-5017	200	15	both	both	DET
ejpam-5017	200	16	sides	side	NOUN
ejpam-5017	200	17	of	of	ADP
ejpam-5017	200	18	the	the	DET
ejpam-5017	200	19	second	second	ADJ
ejpam-5017	200	20	equation	equation	NOUN
ejpam-5017	200	21	of	of	ADP
ejpam-5017	200	22	(	(	PUNCT
ejpam-5017	200	23	12	12	NUM
ejpam-5017	200	24	)	)	PUNCT
ejpam-5017	200	25	and	and	CCONJ
ejpam-5017	200	26	estimate	estimate	VERB
ejpam-5017	200	27	,	,	PUNCT
ejpam-5017	200	28	we	we	PRON
ejpam-5017	200	29	have∥∥∥t	have∥∥∥t	VERB
ejpam-5017	200	30	θ	θ	X
ejpam-5017	200	31	p	p	X
ejpam-5017	200	32	z(t	z(t	NOUN
ejpam-5017	200	33	)	)	PUNCT
ejpam-5017	200	34	∥∥∥	∥∥∥	PROPN
ejpam-5017	200	35	p	p	NOUN
ejpam-5017	200	36	≤	≤	ADJ
ejpam-5017	200	37	∥∥∥t	∥∥∥t	NOUN
ejpam-5017	200	38	θ	θ	PROPN
ejpam-5017	200	39	p	p	X
ejpam-5017	200	40	e	e	X
ejpam-5017	200	41	−d2ttpz0	−d2ttpz0	PROPN
ejpam-5017	200	42	∥∥∥	∥∥∥	PROPN
ejpam-5017	200	43	p	p	NOUN
ejpam-5017	201	1	+	+	NUM
ejpam-5017	201	2	∫	∫	PROPN
ejpam-5017	201	3	t	t	PROPN
ejpam-5017	201	4	0	0	NUM
ejpam-5017	201	5	∥∥∥t	∥∥∥t	PROPN
ejpam-5017	201	6	θ	θ	PROPN
ejpam-5017	201	7	p	p	X
ejpam-5017	201	8	e	e	PROPN
ejpam-5017	201	9	−d2(t−s)tpw2z(s	−d2(t−s)tpw2z(s	PROPN
ejpam-5017	201	10	)	)	PUNCT
ejpam-5017	201	11	∥∥∥	∥∥∥	PROPN
ejpam-5017	201	12	p	p	NOUN
ejpam-5017	201	13	ds	ds	AUX
ejpam-5017	201	14	.	.	NOUN
ejpam-5017	201	15	using	use	VERB
ejpam-5017	201	16	(	(	PUNCT
ejpam-5017	201	17	[	[	X
ejpam-5017	201	18	3],theorem1.4.3	3],theorem1.4.3	NUM
ejpam-5017	201	19	)	)	PUNCT
ejpam-5017	201	20	,	,	PUNCT
ejpam-5017	201	21	we	we	PRON
ejpam-5017	201	22	obtain∥∥∥t	obtain∥∥∥t	VERB
ejpam-5017	201	23	θ	θ	PROPN
ejpam-5017	201	24	p	p	PROPN
ejpam-5017	201	25	z(t	z(t	NOUN
ejpam-5017	201	26	)	)	PUNCT
ejpam-5017	202	1	∥∥∥	∥∥∥	PROPN
ejpam-5017	202	2	p	p	NOUN
ejpam-5017	203	1	≤	≤	NUM
ejpam-5017	203	2	rc(t)−θe−d2αϵ	rc(t)−θe−d2αϵ	VERB
ejpam-5017	203	3	1	1	NUM
ejpam-5017	203	4	t	t	NOUN
ejpam-5017	203	5	∥z0∥p	∥z0∥p	NOUN
ejpam-5017	203	6	+	+	ADP
ejpam-5017	203	7	r	r	NOUN
ejpam-5017	203	8	|ω|	|ω|	ADP
ejpam-5017	203	9	1	1	NUM
ejpam-5017	203	10	p	p	NOUN
ejpam-5017	203	11	∥w0∥2∞	∥w0∥2∞	PROPN
ejpam-5017	203	12	∥z0∥∞	∥z0∥∞	PROPN
ejpam-5017	204	1	∫	∫	PROPN
ejpam-5017	204	2	t	t	PROPN
ejpam-5017	204	3	0	0	NUM
ejpam-5017	204	4	c(t−	c(t−	PROPN
ejpam-5017	204	5	s)−θe−d2αϵ	s)−θe−d2αϵ	PROPN
ejpam-5017	204	6	1(t−s)ds	1(t−s)ds	NUM
ejpam-5017	204	7	.	.	PUNCT
ejpam-5017	204	8	m.	m.	NOUN
ejpam-5017	204	9	mebarki	mebarki	PROPN
ejpam-5017	204	10	/	/	SYM
ejpam-5017	204	11	eur	eur	PROPN
ejpam-5017	204	12	.	.	PUNCT
ejpam-5017	205	1	j.	j.	PROPN
ejpam-5017	205	2	pure	pure	PROPN
ejpam-5017	205	3	appl	appl	PROPN
ejpam-5017	205	4	.	.	PROPN
ejpam-5017	205	5	math	math	PROPN
ejpam-5017	205	6	,	,	PUNCT
ejpam-5017	205	7	17	17	NUM
ejpam-5017	205	8	(	(	PUNCT
ejpam-5017	205	9	2	2	NUM
ejpam-5017	205	10	)	)	PUNCT
ejpam-5017	205	11	(	(	PUNCT
ejpam-5017	205	12	2024	2024	NUM
ejpam-5017	205	13	)	)	PUNCT
ejpam-5017	205	14	,	,	PUNCT
ejpam-5017	205	15	1321	1321	NUM
ejpam-5017	205	16	-	-	SYM
ejpam-5017	205	17	1334	1334	NUM
ejpam-5017	205	18	1330	1330	NUM
ejpam-5017	205	19	thus	thus	ADV
ejpam-5017	205	20	by	by	ADP
ejpam-5017	205	21	lemma	lemma	PROPN
ejpam-5017	205	22	(	(	PUNCT
ejpam-5017	205	23	1	1	NUM
ejpam-5017	205	24	)	)	PUNCT
ejpam-5017	205	25	and	and	CCONJ
ejpam-5017	205	26	∀t	∀t	PROPN
ejpam-5017	205	27	≥	≥	NUM
ejpam-5017	205	28	β	β	NOUN
ejpam-5017	205	29	,	,	PUNCT
ejpam-5017	205	30	we	we	PRON
ejpam-5017	205	31	get	get	AUX
ejpam-5017	205	32	∥∥t	∥∥t	VERB
ejpam-5017	205	33	θ	θ	PROPN
ejpam-5017	205	34	p	p	NOUN
ejpam-5017	205	35	z(t	z(t	NOUN
ejpam-5017	205	36	)	)	PUNCT
ejpam-5017	205	37	∥∥	∥∥	X
ejpam-5017	205	38	p	p	NOUN
ejpam-5017	205	39	≤	≤	ADJ
ejpam-5017	205	40	r	r	NOUN
ejpam-5017	205	41	(	(	PUNCT
ejpam-5017	205	42	θ	θ	PROPN
ejpam-5017	205	43	,	,	PUNCT
ejpam-5017	205	44	p	p	X
ejpam-5017	205	45	,	,	PUNCT
ejpam-5017	205	46	β	β	NOUN
ejpam-5017	205	47	)	)	PUNCT
ejpam-5017	205	48	.	.	PUNCT
ejpam-5017	206	1	tereupon	tereupon	ADV
ejpam-5017	206	2	{	{	PUNCT
ejpam-5017	206	3	z(t)}t≥β	z(t)}t≥β	NUM
ejpam-5017	206	4	is	be	AUX
ejpam-5017	206	5	uniformly	uniformly	ADV
ejpam-5017	206	6	bounded	bound	VERB
ejpam-5017	206	7	in	in	ADP
ejpam-5017	206	8	d(t	d(t	PROPN
ejpam-5017	206	9	θ	θ	PROPN
ejpam-5017	206	10	p	p	NOUN
ejpam-5017	206	11	)	)	PUNCT
ejpam-5017	206	12	;	;	PUNCT
ejpam-5017	206	13	so	so	ADV
ejpam-5017	206	14	by	by	ADP
ejpam-5017	206	15	sobolev	sobolev	PROPN
ejpam-5017	206	16	’s	’s	PART
ejpam-5017	206	17	imbeding	imbeding	NOUN
ejpam-5017	206	18	theorem	theorem	NOUN
ejpam-5017	206	19	,	,	PUNCT
ejpam-5017	206	20	the	the	DET
ejpam-5017	206	21	compactness	compactness	NOUN
ejpam-5017	206	22	of	of	ADP
ejpam-5017	206	23	{	{	PUNCT
ejpam-5017	206	24	z(t)}t≥β	z(t)}t≥β	NUM
ejpam-5017	206	25	in	in	ADP
ejpam-5017	206	26	c	c	PROPN
ejpam-5017	206	27	(	(	PUNCT
ejpam-5017	206	28	ω	ω	PROPN
ejpam-5017	206	29	)	)	PUNCT
ejpam-5017	206	30	is	be	AUX
ejpam-5017	206	31	assured	assure	VERB
ejpam-5017	206	32	.	.	PUNCT
ejpam-5017	207	1	therefore	therefore	ADV
ejpam-5017	207	2	,	,	PUNCT
ejpam-5017	207	3	there	there	PRON
ejpam-5017	207	4	exists	exist	VERB
ejpam-5017	207	5	a	a	DET
ejpam-5017	207	6	sequence	sequence	NOUN
ejpam-5017	207	7	{	{	PUNCT
ejpam-5017	207	8	tj}j≥0	tj}j≥0	NOUN
ejpam-5017	207	9	,	,	PUNCT
ejpam-5017	207	10	tj	tj	X
ejpam-5017	207	11	→	→	SYM
ejpam-5017	207	12	+	+	PROPN
ejpam-5017	207	13	∞	∞	NUM
ejpam-5017	207	14	such	such	ADJ
ejpam-5017	207	15	that	that	SCONJ
ejpam-5017	207	16	z(tj	z(tj	NUM
ejpam-5017	207	17	)	)	PUNCT
ejpam-5017	207	18	→	→	SYM
ejpam-5017	207	19	z∗	z∗	NOUN
ejpam-5017	207	20	in	in	ADP
ejpam-5017	207	21	c	c	PROPN
ejpam-5017	207	22	(	(	PUNCT
ejpam-5017	207	23	ω	ω	PROPN
ejpam-5017	207	24	)	)	PUNCT
ejpam-5017	207	25	as	as	SCONJ
ejpam-5017	207	26	j	j	PROPN
ejpam-5017	207	27	→	→	SYM
ejpam-5017	207	28	+	+	PROPN
ejpam-5017	207	29	∞.	∞.	PROPN
ejpam-5017	207	30	away	away	ADV
ejpam-5017	207	31	we	we	PRON
ejpam-5017	207	32	find	find	VERB
ejpam-5017	207	33	limt→+∞	limt→+∞	ADV
ejpam-5017	207	34	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	207	35	=	=	SYM
ejpam-5017	207	36	0	0	X
ejpam-5017	207	37	.	.	PUNCT
ejpam-5017	208	1	similarly	similarly	ADV
ejpam-5017	208	2	,	,	PUNCT
ejpam-5017	208	3	we	we	PRON
ejpam-5017	208	4	can	can	AUX
ejpam-5017	208	5	prove	prove	VERB
ejpam-5017	208	6	that	that	SCONJ
ejpam-5017	208	7	{	{	PUNCT
ejpam-5017	208	8	w(t)}t≥β	w(t)}t≥β	PROPN
ejpam-5017	208	9	is	be	AUX
ejpam-5017	208	10	precompact	precompact	ADJ
ejpam-5017	208	11	in	in	ADP
ejpam-5017	208	12	c	c	PROPN
ejpam-5017	208	13	(	(	PUNCT
ejpam-5017	208	14	ω	ω	PROPN
ejpam-5017	208	15	)	)	PUNCT
ejpam-5017	208	16	;	;	PUNCT
ejpam-5017	208	17	so	so	CCONJ
ejpam-5017	208	18	,	,	PUNCT
ejpam-5017	208	19	there	there	PRON
ejpam-5017	208	20	exists	exist	VERB
ejpam-5017	208	21	a	a	DET
ejpam-5017	208	22	sequence	sequence	NOUN
ejpam-5017	208	23	{	{	PUNCT
ejpam-5017	208	24	τj}j≥0	τj}j≥0	NUM
ejpam-5017	208	25	,	,	PUNCT
ejpam-5017	208	26	τj	τj	ADP
ejpam-5017	208	27	→	→	SYM
ejpam-5017	208	28	+	+	NUM
ejpam-5017	208	29	∞	∞	NUM
ejpam-5017	208	30	such	such	ADJ
ejpam-5017	208	31	that	that	DET
ejpam-5017	208	32	w(τj	w(τj	NOUN
ejpam-5017	208	33	)	)	PUNCT
ejpam-5017	208	34	→	→	SYM
ejpam-5017	208	35	w∗	w∗	NOUN
ejpam-5017	208	36	in	in	ADP
ejpam-5017	208	37	c	c	PROPN
ejpam-5017	208	38	(	(	PUNCT
ejpam-5017	208	39	ω	ω	NOUN
ejpam-5017	208	40	)	)	PUNCT
ejpam-5017	208	41	as	as	ADP
ejpam-5017	208	42	j	j	PROPN
ejpam-5017	208	43	→	→	SYM
ejpam-5017	208	44	+	+	PROPN
ejpam-5017	208	45	∞.	∞.	PROPN
ejpam-5017	208	46	we	we	PRON
ejpam-5017	208	47	have	have	AUX
ejpam-5017	208	48	(	(	PUNCT
ejpam-5017	208	49	w	w	NOUN
ejpam-5017	208	50	+	+	CCONJ
ejpam-5017	208	51	z)(t	z)(t	NUM
ejpam-5017	208	52	)	)	PUNCT
ejpam-5017	208	53	→	→	SYM
ejpam-5017	208	54	w∗	w∗	NOUN
ejpam-5017	208	55	in	in	ADP
ejpam-5017	208	56	c	c	PROPN
ejpam-5017	208	57	(	(	PUNCT
ejpam-5017	208	58	ω	ω	PROPN
ejpam-5017	208	59	)	)	PUNCT
ejpam-5017	208	60	,	,	PUNCT
ejpam-5017	208	61	then	then	ADV
ejpam-5017	208	62	(	(	PUNCT
ejpam-5017	208	63	w	w	NOUN
ejpam-5017	208	64	+	+	CCONJ
ejpam-5017	208	65	z)(t	z)(t	NUM
ejpam-5017	208	66	)	)	PUNCT
ejpam-5017	208	67	→	→	SYM
ejpam-5017	208	68	w∗	w∗	NOUN
ejpam-5017	208	69	in	in	ADP
ejpam-5017	208	70	l1(ω	l1(ω	PROPN
ejpam-5017	208	71	)	)	PUNCT
ejpam-5017	208	72	as	as	ADP
ejpam-5017	208	73	t	t	PROPN
ejpam-5017	208	74	→	→	PUNCT
ejpam-5017	208	75	+	+	PROPN
ejpam-5017	208	76	∞.	∞.	PROPN
ejpam-5017	208	77	using	use	VERB
ejpam-5017	208	78	the	the	DET
ejpam-5017	208	79	fact	fact	NOUN
ejpam-5017	208	80	that	that	SCONJ
ejpam-5017	208	81	limt→+∞	limt→+∞	PROPN
ejpam-5017	208	82	∫	∫	PROPN
ejpam-5017	208	83	ω	ω	PROPN
ejpam-5017	208	84	z(x	z(x	PROPN
ejpam-5017	208	85	,	,	PUNCT
ejpam-5017	208	86	t)dx	t)dx	PROPN
ejpam-5017	208	87	=	=	SYM
ejpam-5017	208	88	0	0	NUM
ejpam-5017	209	1	and	and	CCONJ
ejpam-5017	209	2	limt→+∞	limt→+∞	ADP
ejpam-5017	209	3	1	1	NUM
ejpam-5017	209	4	|ω|	|ω|	NUM
ejpam-5017	209	5	∫	∫	PROPN
ejpam-5017	209	6	ωw(x	ωw(x	NUM
ejpam-5017	209	7	,	,	PUNCT
ejpam-5017	209	8	t)dx	t)dx	PROPN
ejpam-5017	209	9	=	=	SYM
ejpam-5017	209	10	w∞	w∞	PROPN
ejpam-5017	209	11	,	,	PUNCT
ejpam-5017	209	12	we	we	PRON
ejpam-5017	209	13	gain	gain	VERB
ejpam-5017	209	14	(	(	PUNCT
ejpam-5017	209	15	w	w	NOUN
ejpam-5017	209	16	+	+	CCONJ
ejpam-5017	209	17	z)(t	z)(t	NUM
ejpam-5017	209	18	)	)	PUNCT
ejpam-5017	209	19	→	→	SYM
ejpam-5017	209	20	w∞	w∞	PROPN
ejpam-5017	209	21	in	in	ADP
ejpam-5017	209	22	l1(ω	l1(ω	PROPN
ejpam-5017	209	23	)	)	PUNCT
ejpam-5017	209	24	as	as	ADP
ejpam-5017	209	25	t	t	PROPN
ejpam-5017	209	26	→	→	PUNCT
ejpam-5017	209	27	+	+	PROPN
ejpam-5017	209	28	∞.	∞.	PROPN
ejpam-5017	209	29	by	by	ADP
ejpam-5017	209	30	uniqueness	uniqueness	NOUN
ejpam-5017	209	31	of	of	ADP
ejpam-5017	209	32	the	the	DET
ejpam-5017	209	33	limit	limit	NOUN
ejpam-5017	209	34	,	,	PUNCT
ejpam-5017	209	35	w∗	w∗	NOUN
ejpam-5017	209	36	=	=	SYM
ejpam-5017	209	37	w∞.	w∞.	NOUN
ejpam-5017	209	38	theorem	theorem	ADJ
ejpam-5017	209	39	3	3	X
ejpam-5017	209	40	.	.	PUNCT
ejpam-5017	210	1	let	let	VERB
ejpam-5017	210	2	(	(	PUNCT
ejpam-5017	210	3	w	w	PROPN
ejpam-5017	210	4	,	,	PUNCT
ejpam-5017	210	5	z	z	NOUN
ejpam-5017	210	6	)	)	PUNCT
ejpam-5017	210	7	be	be	AUX
ejpam-5017	210	8	the	the	DET
ejpam-5017	210	9	solution	solution	NOUN
ejpam-5017	210	10	of	of	ADP
ejpam-5017	210	11	(	(	PUNCT
ejpam-5017	210	12	1)-(2	1)-(2	NUM
ejpam-5017	210	13	)	)	PUNCT
ejpam-5017	210	14	.	.	PUNCT
ejpam-5017	211	1	therefore	therefore	ADV
ejpam-5017	211	2	assume	assume	VERB
ejpam-5017	211	3	that	that	SCONJ
ejpam-5017	211	4	k	k	PROPN
ejpam-5017	211	5	−	−	PROPN
ejpam-5017	211	6	w∞	w∞	PROPN
ejpam-5017	211	7	≻	≻	PROPN
ejpam-5017	211	8	0	0	NUM
ejpam-5017	211	9	.	.	PUNCT
ejpam-5017	212	1	then	then	ADV
ejpam-5017	212	2	there	there	PRON
ejpam-5017	212	3	exist	exist	VERB
ejpam-5017	212	4	positive	positive	ADJ
ejpam-5017	212	5	constants	constant	NOUN
ejpam-5017	212	6	t	t	PROPN
ejpam-5017	212	7	and	and	CCONJ
ejpam-5017	212	8	r	r	PRON
ejpam-5017	212	9	such	such	ADJ
ejpam-5017	212	10	that	that	PRON
ejpam-5017	212	11	∥w(t)−	∥w(t)−	PROPN
ejpam-5017	212	12	w∞∥∞	w∞∥∞	VERB
ejpam-5017	212	13	≤	≤	NOUN
ejpam-5017	212	14	{	{	PUNCT
ejpam-5017	212	15	r	r	NOUN
ejpam-5017	212	16	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	212	17	)	)	PUNCT
ejpam-5017	213	1	if	if	SCONJ
ejpam-5017	213	2	2d1α	2d1α	NUM
ejpam-5017	213	3	δ	δ	PROPN
ejpam-5017	213	4	1λ	1λ	PROPN
ejpam-5017	213	5	̸=	̸=	PROPN
ejpam-5017	213	6	h(w∞	h(w∞	PROPN
ejpam-5017	213	7	)	)	PUNCT
ejpam-5017	213	8	r(t−	r(t−	NOUN
ejpam-5017	213	9	t	t	NOUN
ejpam-5017	213	10	+	+	CCONJ
ejpam-5017	213	11	1	1	X
ejpam-5017	213	12	)	)	PUNCT
ejpam-5017	213	13	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	213	14	)	)	PUNCT
ejpam-5017	214	1	if	if	SCONJ
ejpam-5017	214	2	2d1α	2d1α	NUM
ejpam-5017	214	3	δ	δ	PROPN
ejpam-5017	214	4	1λ	1λ	NUM
ejpam-5017	214	5	=	=	SYM
ejpam-5017	214	6	h(w∞	h(w∞	PROPN
ejpam-5017	214	7	)	)	PUNCT
ejpam-5017	214	8	,	,	PUNCT
ejpam-5017	214	9	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	214	10	≤	≤	NUM
ejpam-5017	214	11	r	r	NOUN
ejpam-5017	214	12	exp(−h(w∞)(t−	exp(−h(w∞)(t−	PROPN
ejpam-5017	214	13	t	t	NOUN
ejpam-5017	214	14	)	)	PUNCT
ejpam-5017	214	15	,	,	PUNCT
ejpam-5017	214	16	t	t	PROPN
ejpam-5017	214	17	≥	≥	PROPN
ejpam-5017	214	18	t	t	PROPN
ejpam-5017	214	19	where	where	SCONJ
ejpam-5017	214	20	κ	κ	PROPN
ejpam-5017	214	21	=	=	SYM
ejpam-5017	214	22	min	min	PROPN
ejpam-5017	214	23	{	{	PUNCT
ejpam-5017	214	24	h(w∞	h(w∞	PROPN
ejpam-5017	214	25	)	)	PUNCT
ejpam-5017	214	26	,	,	PUNCT
ejpam-5017	215	1	2d1α	2d1α	NOUN
ejpam-5017	215	2	δ	δ	PROPN
ejpam-5017	215	3	1λ	1λ	NUM
ejpam-5017	215	4	}	}	PUNCT
ejpam-5017	215	5	,	,	PUNCT
ejpam-5017	215	6	h(w∞	h(w∞	PROPN
ejpam-5017	215	7	)	)	PUNCT
ejpam-5017	215	8	=	=	SYM
ejpam-5017	215	9	(	(	PUNCT
ejpam-5017	215	10	w0	w0	PROPN
ejpam-5017	215	11	+	+	CCONJ
ejpam-5017	215	12	ε)2	ε)2	PROPN
ejpam-5017	215	13	−	−	PROPN
ejpam-5017	215	14	k	k	PROPN
ejpam-5017	215	15	≻	≻	PROPN
ejpam-5017	215	16	0	0	X
ejpam-5017	215	17	.	.	PUNCT
ejpam-5017	216	1	proof	proof	NOUN
ejpam-5017	216	2	.	.	PUNCT
ejpam-5017	217	1	[	[	X
ejpam-5017	217	2	proof	proof	NOUN
ejpam-5017	217	3	of	of	ADP
ejpam-5017	217	4	theorem	theorem	NOUN
ejpam-5017	217	5	]	]	X
ejpam-5017	217	6	for	for	ADP
ejpam-5017	217	7	ε	ε	PROPN
ejpam-5017	217	8	≻	≻	PROPN
ejpam-5017	217	9	0	0	NUM
ejpam-5017	217	10	,	,	PUNCT
ejpam-5017	217	11	there	there	PRON
ejpam-5017	217	12	exists	exist	VERB
ejpam-5017	217	13	a	a	DET
ejpam-5017	217	14	constant	constant	ADJ
ejpam-5017	217	15	t	t	NOUN
ejpam-5017	217	16	≻	≻	PROPN
ejpam-5017	217	17	0	0	NUM
ejpam-5017	217	18	such	such	ADJ
ejpam-5017	217	19	that	that	SCONJ
ejpam-5017	217	20	fort	fort	PROPN
ejpam-5017	217	21	≥	≥	PROPN
ejpam-5017	217	22	t	t	PROPN
ejpam-5017	217	23	w∞	w∞	PROPN
ejpam-5017	217	24	−	−	PROPN
ejpam-5017	217	25	ε	ε	PROPN
ejpam-5017	217	26	≺	≺	PROPN
ejpam-5017	217	27	w(t	w(t	PROPN
ejpam-5017	217	28	)	)	PUNCT
ejpam-5017	217	29	≺	≺	NOUN
ejpam-5017	217	30	w∞	w∞	PROPN
ejpam-5017	217	31	+	+	CCONJ
ejpam-5017	217	32	ε	ε	PROPN
ejpam-5017	217	33	.	.	PUNCT
ejpam-5017	218	1	putting	put	VERB
ejpam-5017	218	2	0	0	NUM
ejpam-5017	218	3	≺	≺	NOUN
ejpam-5017	218	4	ε	ε	PROPN
ejpam-5017	218	5	≺	≺	NOUN
ejpam-5017	218	6	k	k	X
ejpam-5017	218	7	−	−	PROPN
ejpam-5017	219	1	w∞.	w∞.	NOUN
ejpam-5017	219	2	we	we	PRON
ejpam-5017	219	3	multiply	multiply	VERB
ejpam-5017	219	4	the	the	DET
ejpam-5017	219	5	second	second	ADJ
ejpam-5017	219	6	equation	equation	NOUN
ejpam-5017	219	7	of	of	ADP
ejpam-5017	219	8	(	(	PUNCT
ejpam-5017	219	9	1	1	NUM
ejpam-5017	219	10	)	)	PUNCT
ejpam-5017	219	11	by	by	ADP
ejpam-5017	219	12	zp−1	zp−1	PROPN
ejpam-5017	219	13	and	and	CCONJ
ejpam-5017	219	14	integrate	integrate	VERB
ejpam-5017	219	15	over	over	ADP
ejpam-5017	219	16	ω	ω	NUM
ejpam-5017	219	17	;	;	PUNCT
ejpam-5017	219	18	it	it	PRON
ejpam-5017	219	19	follows	follow	VERB
ejpam-5017	219	20	that	that	SCONJ
ejpam-5017	220	1	d	d	PROPN
ejpam-5017	220	2	dt	dt	X
ejpam-5017	220	3	∫	∫	PROPN
ejpam-5017	220	4	ω	ω	NUM
ejpam-5017	220	5	zpdx	zpdx	PROPN
ejpam-5017	220	6	≤	≤	PROPN
ejpam-5017	220	7	p	p	PRON
ejpam-5017	220	8	∫	∫	PROPN
ejpam-5017	220	9	ω	ω	PROPN
ejpam-5017	220	10	(	(	PUNCT
ejpam-5017	220	11	w2	w2	NOUN
ejpam-5017	220	12	−	−	PROPN
ejpam-5017	220	13	(	(	PUNCT
ejpam-5017	220	14	f	f	PROPN
ejpam-5017	220	15	+	+	CCONJ
ejpam-5017	220	16	k))zpdx,∀t	k))zpdx,∀t	PROPN
ejpam-5017	220	17	≥	≥	NUM
ejpam-5017	220	18	t	t	PROPN
ejpam-5017	220	19	,	,	PUNCT
ejpam-5017	220	20	in	in	ADP
ejpam-5017	220	21	the	the	DET
ejpam-5017	220	22	light	light	NOUN
ejpam-5017	220	23	of	of	ADP
ejpam-5017	220	24	relation	relation	NOUN
ejpam-5017	220	25	(	(	PUNCT
ejpam-5017	220	26	5	5	NUM
ejpam-5017	220	27	)	)	PUNCT
ejpam-5017	220	28	.	.	PUNCT
ejpam-5017	221	1	so	so	ADV
ejpam-5017	221	2	d	d	ADV
ejpam-5017	221	3	dt	dt	X
ejpam-5017	221	4	∥z(t)∥pp	∥z(t)∥pp	PROPN
ejpam-5017	221	5	≤	≤	PROPN
ejpam-5017	221	6	p((w∞	p((w∞	VERB
ejpam-5017	221	7	+	+	CCONJ
ejpam-5017	221	8	ε)2	ε)2	PROPN
ejpam-5017	221	9	−	−	PROPN
ejpam-5017	222	1	(	(	PUNCT
ejpam-5017	222	2	f	f	PROPN
ejpam-5017	222	3	+	+	CCONJ
ejpam-5017	222	4	k	k	NOUN
ejpam-5017	222	5	)	)	PUNCT
ejpam-5017	222	6	)	)	PUNCT
ejpam-5017	223	1	∥z(t)∥pp	∥z(t)∥pp	PROPN
ejpam-5017	223	2	,	,	PUNCT
ejpam-5017	223	3	∀t	∀t	PROPN
ejpam-5017	223	4	≥	≥	NOUN
ejpam-5017	223	5	t.	t.	PROPN
ejpam-5017	223	6	thus	thus	ADV
ejpam-5017	223	7	,	,	PUNCT
ejpam-5017	223	8	for	for	ADP
ejpam-5017	223	9	1	1	NUM
ejpam-5017	223	10	≤	≤	NOUN
ejpam-5017	223	11	p	p	NOUN
ejpam-5017	223	12	≤	≤	NOUN
ejpam-5017	224	1	+	+	PROPN
ejpam-5017	224	2	∞	∞	PROPN
ejpam-5017	224	3	,	,	PUNCT
ejpam-5017	224	4	we	we	PRON
ejpam-5017	224	5	have	have	VERB
ejpam-5017	224	6	∥z(t)∥p	∥z(t)∥p	NUM
ejpam-5017	224	7	≤	≤	NUM
ejpam-5017	224	8	∥z(t	∥z(t	NOUN
ejpam-5017	224	9	)	)	PUNCT
ejpam-5017	224	10	∥p	∥p	PROPN
ejpam-5017	224	11	exp((w∞	exp((w∞	NOUN
ejpam-5017	224	12	+	+	CCONJ
ejpam-5017	224	13	ε)2	ε)2	NOUN
ejpam-5017	225	1	−	−	PROPN
ejpam-5017	226	1	(	(	PUNCT
ejpam-5017	226	2	f	f	PROPN
ejpam-5017	226	3	+	+	CCONJ
ejpam-5017	226	4	k))(t−	k))(t−	PROPN
ejpam-5017	226	5	t	t	PROPN
ejpam-5017	226	6	)	)	PUNCT
ejpam-5017	226	7	,	,	PUNCT
ejpam-5017	226	8	t	t	PROPN
ejpam-5017	226	9	≥	≥	PROPN
ejpam-5017	226	10	t.	t.	PROPN
ejpam-5017	226	11	(	(	PUNCT
ejpam-5017	226	12	15	15	NUM
ejpam-5017	226	13	)	)	PUNCT
ejpam-5017	226	14	which	which	PRON
ejpam-5017	226	15	implies	imply	VERB
ejpam-5017	226	16	∥z(t)∥∞	∥z(t)∥∞	PROPN
ejpam-5017	226	17	≤	≤	PROPN
ejpam-5017	226	18	∥z(t	∥z(t	X
ejpam-5017	226	19	)	)	PUNCT
ejpam-5017	226	20	∥∞	∥∞	ADJ
ejpam-5017	226	21	exp((w∞	exp((w∞	NOUN
ejpam-5017	226	22	+	+	NUM
ejpam-5017	226	23	ε)2	ε)2	PROPN
ejpam-5017	226	24	−	−	PROPN
ejpam-5017	226	25	(	(	PUNCT
ejpam-5017	226	26	f	f	PROPN
ejpam-5017	226	27	+	+	CCONJ
ejpam-5017	226	28	k))(t−	k))(t−	PROPN
ejpam-5017	226	29	t	t	PROPN
ejpam-5017	226	30	)	)	PUNCT
ejpam-5017	226	31	,	,	PUNCT
ejpam-5017	226	32	t	t	PROPN
ejpam-5017	226	33	≥	≥	NOUN
ejpam-5017	226	34	t.	t.	PROPN
ejpam-5017	226	35	(	(	PUNCT
ejpam-5017	226	36	16	16	NUM
ejpam-5017	226	37	)	)	PUNCT
ejpam-5017	226	38	for	for	ADP
ejpam-5017	226	39	the	the	DET
ejpam-5017	226	40	rate	rate	NOUN
ejpam-5017	226	41	of	of	ADP
ejpam-5017	226	42	convergence	convergence	NOUN
ejpam-5017	226	43	of	of	ADP
ejpam-5017	226	44	∥w(t)−	∥w(t)−	PROPN
ejpam-5017	226	45	w∞∥∞	w∞∥∞	VERB
ejpam-5017	226	46	to	to	ADP
ejpam-5017	226	47	zero	zero	NUM
ejpam-5017	226	48	,	,	PUNCT
ejpam-5017	226	49	we	we	PRON
ejpam-5017	226	50	define	define	VERB
ejpam-5017	226	51	as	as	ADP
ejpam-5017	226	52	in	in	ADP
ejpam-5017	226	53	[	[	X
ejpam-5017	226	54	14	14	NUM
ejpam-5017	226	55	]	]	SYM
ejpam-5017	226	56	two	two	NUM
ejpam-5017	226	57	bounded	bound	VERB
ejpam-5017	226	58	linear	linear	PROPN
ejpam-5017	226	59	operators	operator	NOUN
ejpam-5017	226	60	i	i	PRON
ejpam-5017	226	61	and	and	CCONJ
ejpam-5017	226	62	g	g	PROPN
ejpam-5017	226	63	by	by	ADP
ejpam-5017	226	64	m.	m.	NOUN
ejpam-5017	226	65	mebarki	mebarki	PROPN
ejpam-5017	226	66	/	/	SYM
ejpam-5017	226	67	eur	eur	PROPN
ejpam-5017	226	68	.	.	PUNCT
ejpam-5017	227	1	j.	j.	PROPN
ejpam-5017	227	2	pure	pure	PROPN
ejpam-5017	227	3	appl	appl	PROPN
ejpam-5017	227	4	.	.	PROPN
ejpam-5017	227	5	math	math	PROPN
ejpam-5017	227	6	,	,	PUNCT
ejpam-5017	227	7	17	17	NUM
ejpam-5017	227	8	(	(	PUNCT
ejpam-5017	227	9	2	2	NUM
ejpam-5017	227	10	)	)	PUNCT
ejpam-5017	227	11	(	(	PUNCT
ejpam-5017	227	12	2024	2024	NUM
ejpam-5017	227	13	)	)	PUNCT
ejpam-5017	227	14	,	,	PUNCT
ejpam-5017	227	15	1321	1321	NUM
ejpam-5017	227	16	-	-	SYM
ejpam-5017	227	17	1334	1334	NUM
ejpam-5017	227	18	1331	1331	NUM
ejpam-5017	227	19	iu	iu	ADP
ejpam-5017	227	20	:	:	PUNCT
ejpam-5017	227	21	=	=	SYM
ejpam-5017	227	22	⟨u⟩	⟨u⟩	PROPN
ejpam-5017	227	23	,	,	PUNCT
ejpam-5017	227	24	gu	gu	NOUN
ejpam-5017	227	25	:	:	PUNCT
ejpam-5017	228	1	=	=	PROPN
ejpam-5017	228	2	u−	u−	PROPN
ejpam-5017	228	3	⟨u⟩	⟨u⟩	PROPN
ejpam-5017	228	4	,	,	PUNCT
ejpam-5017	228	5	here	here	ADV
ejpam-5017	228	6	⟨u⟩	⟨u⟩	VERB
ejpam-5017	228	7	:	:	PUNCT
ejpam-5017	229	1	=	=	SYM
ejpam-5017	229	2	1	1	NUM
ejpam-5017	229	3	|ω|	|ω|	NUM
ejpam-5017	229	4	∫	∫	PROPN
ejpam-5017	229	5	ω	ω	PROPN
ejpam-5017	229	6	u(x	u(x	PROPN
ejpam-5017	229	7	,	,	PUNCT
ejpam-5017	229	8	t)dx	t)dx	PROPN
ejpam-5017	229	9	.	.	PUNCT
ejpam-5017	230	1	adding	add	VERB
ejpam-5017	230	2	the	the	DET
ejpam-5017	230	3	two	two	NUM
ejpam-5017	230	4	equations	equation	NOUN
ejpam-5017	230	5	of	of	ADP
ejpam-5017	230	6	problem	problem	NOUN
ejpam-5017	230	7	(	(	PUNCT
ejpam-5017	230	8	1	1	NUM
ejpam-5017	230	9	)	)	PUNCT
ejpam-5017	230	10	and	and	CCONJ
ejpam-5017	230	11	integrating	integrate	VERB
ejpam-5017	230	12	over	over	ADP
ejpam-5017	230	13	ω	ω	PROPN
ejpam-5017	230	14	,	,	PUNCT
ejpam-5017	230	15	we	we	PRON
ejpam-5017	230	16	obtain	obtain	VERB
ejpam-5017	230	17	if	if	SCONJ
ejpam-5017	230	18	f	f	PROPN
ejpam-5017	230	19	=	=	SYM
ejpam-5017	230	20	0	0	NUM
ejpam-5017	231	1	⟨w(t)⟩	⟨w(t)⟩	NOUN
ejpam-5017	231	2	=	=	PUNCT
ejpam-5017	231	3	−⟨z(t)⟩+	−⟨z(t)⟩+	PROPN
ejpam-5017	231	4	⟨w0⟩+	⟨w0⟩+	NOUN
ejpam-5017	231	5	⟨z0⟩	⟨z0⟩	VERB
ejpam-5017	231	6	−	−	PROPN
ejpam-5017	232	1	k	k	PROPN
ejpam-5017	232	2	∫	∫	PROPN
ejpam-5017	232	3	t	t	PROPN
ejpam-5017	232	4	0	0	NUM
ejpam-5017	232	5	⟨z(s)⟩	⟨z(s)⟩	NOUN
ejpam-5017	232	6	ds	ds	PROPN
ejpam-5017	232	7	,	,	PUNCT
ejpam-5017	232	8	as	as	ADP
ejpam-5017	232	9	t	t	PROPN
ejpam-5017	232	10	→	→	SYM
ejpam-5017	232	11	∞.	∞.	PROPN
ejpam-5017	232	12	it	it	PRON
ejpam-5017	232	13	holds	hold	VERB
ejpam-5017	232	14	that	that	SCONJ
ejpam-5017	232	15	w∞	w∞	PROPN
ejpam-5017	232	16	=	=	SYM
ejpam-5017	232	17	⟨w0⟩+	⟨w0⟩+	ADJ
ejpam-5017	232	18	⟨z0⟩	⟨z0⟩	X
ejpam-5017	232	19	−	−	PROPN
ejpam-5017	233	1	k	k	PROPN
ejpam-5017	233	2	∫	∫	PROPN
ejpam-5017	233	3	t	t	PROPN
ejpam-5017	233	4	0	0	NUM
ejpam-5017	233	5	⟨z(s)⟩	⟨z(s)⟩	NOUN
ejpam-5017	233	6	ds	ds	PROPN
ejpam-5017	233	7	.	.	PROPN
ejpam-5017	233	8	hence	hence	PROPN
ejpam-5017	233	9	|⟨w(t)−	|⟨w(t)−	PROPN
ejpam-5017	233	10	w∞⟩|	w∞⟩|	PROPN
ejpam-5017	233	11	≤≺	≤≺	PROPN
ejpam-5017	233	12	⟨z(t)⟩+	⟨z(t)⟩+	PROPN
ejpam-5017	233	13	k	k	PROPN
ejpam-5017	233	14	∫	∫	PROPN
ejpam-5017	233	15	t	t	PROPN
ejpam-5017	233	16	0	0	NUM
ejpam-5017	233	17	⟨z(s)⟩	⟨z(s)⟩	NOUN
ejpam-5017	233	18	ds	ds	PROPN
ejpam-5017	233	19	.	.	NOUN
ejpam-5017	233	20	using	use	VERB
ejpam-5017	233	21	inequality	inequality	NOUN
ejpam-5017	233	22	(	(	PUNCT
ejpam-5017	233	23	16	16	NUM
ejpam-5017	233	24	)	)	PUNCT
ejpam-5017	233	25	we	we	PRON
ejpam-5017	233	26	get∫	get∫	VERB
ejpam-5017	233	27	∞	∞	PROPN
ejpam-5017	233	28	t	t	PROPN
ejpam-5017	233	29	⟨z(s)⟩	⟨z(s)⟩	NOUN
ejpam-5017	233	30	ds	ds	PROPN
ejpam-5017	233	31	≤	≤	NUM
ejpam-5017	233	32	⟨z(t	⟨z(t	PROPN
ejpam-5017	233	33	)	)	PUNCT
ejpam-5017	234	1	⟩	⟩	NOUN
ejpam-5017	234	2	∫	∫	PROPN
ejpam-5017	235	1	∞	∞	PROPN
ejpam-5017	235	2	t	t	PROPN
ejpam-5017	235	3	exp((w∞	exp((w∞	PROPN
ejpam-5017	235	4	+	+	CCONJ
ejpam-5017	235	5	ε)2	ε)2	PROPN
ejpam-5017	235	6	−	−	NOUN
ejpam-5017	235	7	(	(	PUNCT
ejpam-5017	235	8	k))(s−	k))(s−	PROPN
ejpam-5017	235	9	t	t	NOUN
ejpam-5017	235	10	)	)	PUNCT
ejpam-5017	235	11	ds	ds	PROPN
ejpam-5017	235	12	≤	≤	PROPN
ejpam-5017	235	13	r1	r1	PROPN
ejpam-5017	235	14	⟨z(t	⟨z(t	PROPN
ejpam-5017	235	15	)	)	PUNCT
ejpam-5017	236	1	⟩	⟩	PROPN
ejpam-5017	236	2	exp((w∞	exp((w∞	PROPN
ejpam-5017	236	3	+	+	CCONJ
ejpam-5017	236	4	ε)2	ε)2	PROPN
ejpam-5017	236	5	−	−	PROPN
ejpam-5017	236	6	(	(	PUNCT
ejpam-5017	236	7	k))(t−	k))(t−	PROPN
ejpam-5017	236	8	t	t	PROPN
ejpam-5017	236	9	)	)	PUNCT
ejpam-5017	236	10	,	,	PUNCT
ejpam-5017	236	11	t	t	PROPN
ejpam-5017	236	12	≥	≥	PROPN
ejpam-5017	236	13	t	t	PROPN
ejpam-5017	236	14	,	,	PUNCT
ejpam-5017	236	15	where	where	SCONJ
ejpam-5017	236	16	r1	r1	PROPN
ejpam-5017	236	17	=	=	SYM
ejpam-5017	236	18	1	1	NUM
ejpam-5017	236	19	k−(w∞+ε)2	k−(w∞+ε)2	PROPN
ejpam-5017	236	20	.out	.out	PUNCT
ejpam-5017	237	1	|⟨iw(t)−	|⟨iw(t)−	PROPN
ejpam-5017	237	2	w∞⟩|	w∞⟩|	PUNCT
ejpam-5017	237	3	≤	≤	NUM
ejpam-5017	237	4	r2	r2	PROPN
ejpam-5017	237	5	⟨z(t	⟨z(t	PROPN
ejpam-5017	237	6	)	)	PUNCT
ejpam-5017	237	7	⟩	⟩	PROPN
ejpam-5017	237	8	exp((w∞	exp((w∞	PROPN
ejpam-5017	237	9	+	+	CCONJ
ejpam-5017	237	10	ε)2	ε)2	PROPN
ejpam-5017	237	11	−	−	PROPN
ejpam-5017	237	12	(	(	PUNCT
ejpam-5017	237	13	k))(t−	k))(t−	PROPN
ejpam-5017	237	14	t	t	PROPN
ejpam-5017	237	15	)	)	PUNCT
ejpam-5017	237	16	,	,	PUNCT
ejpam-5017	237	17	t	t	PROPN
ejpam-5017	237	18	≥	≥	PROPN
ejpam-5017	237	19	t	t	PROPN
ejpam-5017	237	20	,	,	PUNCT
ejpam-5017	237	21	(	(	PUNCT
ejpam-5017	237	22	17	17	NUM
ejpam-5017	237	23	)	)	PUNCT
ejpam-5017	237	24	where	where	SCONJ
ejpam-5017	237	25	r2	r2	PROPN
ejpam-5017	237	26	=	=	SYM
ejpam-5017	237	27	max	max	PROPN
ejpam-5017	237	28	{	{	PUNCT
ejpam-5017	237	29	1	1	PROPN
ejpam-5017	237	30	,	,	PUNCT
ejpam-5017	237	31	kr1	kr1	PROPN
ejpam-5017	237	32	}	}	PUNCT
ejpam-5017	237	33	.	.	PUNCT
ejpam-5017	238	1	accordingly	accordingly	ADV
ejpam-5017	238	2	w(t	w(t	PROPN
ejpam-5017	238	3	)	)	PUNCT
ejpam-5017	238	4	satisfies	satisfy	VERB
ejpam-5017	238	5	the	the	DET
ejpam-5017	238	6	integral	integral	ADJ
ejpam-5017	238	7	equation	equation	NOUN
ejpam-5017	238	8	for	for	ADP
ejpam-5017	238	9	t	t	PROPN
ejpam-5017	238	10	≥	≥	PROPN
ejpam-5017	238	11	t	t	PROPN
ejpam-5017	238	12	,	,	PUNCT
ejpam-5017	238	13	w(t	w(t	PROPN
ejpam-5017	238	14	)	)	PUNCT
ejpam-5017	239	1	=	=	PUNCT
ejpam-5017	239	2	e−d1tspw0	e−d1tspw0	NOUN
ejpam-5017	239	3	+	+	CCONJ
ejpam-5017	240	1	∫	∫	PROPN
ejpam-5017	240	2	t	t	PROPN
ejpam-5017	240	3	0	0	NUM
ejpam-5017	240	4	e−d1(t−s)sp(−w2z	e−d1(t−s)sp(−w2z	DET
ejpam-5017	241	1	+	+	CCONJ
ejpam-5017	241	2	f(1−	f(1−	ADJ
ejpam-5017	241	3	w))(s)ds	w))(s)ds	NUM
ejpam-5017	241	4	,	,	PUNCT
ejpam-5017	241	5	as	as	ADP
ejpam-5017	241	6	f	f	PROPN
ejpam-5017	241	7	=	=	SYM
ejpam-5017	241	8	0	0	PROPN
ejpam-5017	241	9	,	,	PUNCT
ejpam-5017	241	10	we	we	PRON
ejpam-5017	241	11	get	get	VERB
ejpam-5017	241	12	w(t	w(t	PROPN
ejpam-5017	241	13	)	)	PUNCT
ejpam-5017	242	1	=	=	PUNCT
ejpam-5017	242	2	e−d1tspw0	e−d1tspw0	NOUN
ejpam-5017	242	3	−	−	PROPN
ejpam-5017	243	1	∫	∫	PROPN
ejpam-5017	243	2	t	t	NOUN
ejpam-5017	243	3	0	0	NUM
ejpam-5017	243	4	e−d1(t−s)sp(w2z)(s)ds	e−d1(t−s)sp(w2z)(s)ds	PROPN
ejpam-5017	243	5	,	,	PUNCT
ejpam-5017	243	6	=	=	SYM
ejpam-5017	243	7	e−d1(t−t	e−d1(t−t	ADJ
ejpam-5017	243	8	)	)	PUNCT
ejpam-5017	243	9	spw(t	spw(t	PROPN
ejpam-5017	243	10	)	)	PUNCT
ejpam-5017	243	11	−	−	PROPN
ejpam-5017	244	1	∫	∫	PROPN
ejpam-5017	244	2	t	t	PROPN
ejpam-5017	244	3	t	t	PROPN
ejpam-5017	244	4	e−d1(t−s)sp(−w2z)(s)ds	e−d1(t−s)sp(−w2z)(s)ds	PROPN
ejpam-5017	244	5	,	,	PUNCT
ejpam-5017	244	6	thus	thus	ADV
ejpam-5017	244	7	we	we	PRON
ejpam-5017	244	8	have	have	AUX
ejpam-5017	244	9	gw(t	gw(t	VERB
ejpam-5017	244	10	)	)	PUNCT
ejpam-5017	244	11	=	=	SYM
ejpam-5017	244	12	e−d1(t−t	e−d1(t−t	ADJ
ejpam-5017	244	13	)	)	PUNCT
ejpam-5017	244	14	spgw(t	spgw(t	NOUN
ejpam-5017	244	15	)	)	PUNCT
ejpam-5017	244	16	−	−	PROPN
ejpam-5017	245	1	∫	∫	PROPN
ejpam-5017	245	2	t	t	PROPN
ejpam-5017	245	3	t	t	PROPN
ejpam-5017	245	4	e−d1(t−s)spg(w2z)(s)ds	e−d1(t−s)spg(w2z)(s)ds	PROPN
ejpam-5017	245	5	.	.	PUNCT
ejpam-5017	246	1	using	use	VERB
ejpam-5017	246	2	lemma	lemma	PROPN
ejpam-5017	246	3	2	2	NUM
ejpam-5017	246	4	,	,	PUNCT
ejpam-5017	246	5	we	we	PRON
ejpam-5017	246	6	get	get	VERB
ejpam-5017	246	7	the	the	DET
ejpam-5017	246	8	estimate∥∥∥e−d1(t−t	estimate∥∥∥e−d1(t−t	NOUN
ejpam-5017	246	9	)	)	PUNCT
ejpam-5017	246	10	spgw(t	spgw(t	NOUN
ejpam-5017	246	11	)	)	PUNCT
ejpam-5017	246	12	∥∥∥	∥∥∥	PROPN
ejpam-5017	246	13	p	p	PROPN
ejpam-5017	246	14	≤	≤	PROPN
ejpam-5017	246	15	re−d1αδ	re−d1αδ	PROPN
ejpam-5017	246	16	1(t−t	1(t−t	NUM
ejpam-5017	246	17	)	)	PUNCT
ejpam-5017	246	18	∥w(t	∥w(t	ADV
ejpam-5017	246	19	)	)	PUNCT
ejpam-5017	247	1	∥p	∥p	ADJ
ejpam-5017	247	2	(	(	PUNCT
ejpam-5017	247	3	18	18	NUM
ejpam-5017	247	4	)	)	PUNCT
ejpam-5017	247	5	now	now	ADV
ejpam-5017	247	6	,	,	PUNCT
ejpam-5017	247	7	to	to	PART
ejpam-5017	247	8	calculate	calculate	VERB
ejpam-5017	247	9	a(t	a(t	NOUN
ejpam-5017	247	10	)	)	PUNCT
ejpam-5017	247	11	=	=	SYM
ejpam-5017	248	1	∫	∫	PROPN
ejpam-5017	248	2	t	t	PROPN
ejpam-5017	248	3	t	t	PROPN
ejpam-5017	248	4	∥∥e−d1(t−s)spg(w2z)(s)ds	∥∥e−d1(t−s)spg(w2z)(s)ds	PROPN
ejpam-5017	248	5	∥∥	∥∥	PROPN
ejpam-5017	248	6	p	p	NOUN
ejpam-5017	248	7	.	.	PUNCT
ejpam-5017	249	1	m.	m.	NOUN
ejpam-5017	249	2	mebarki	mebarki	PROPN
ejpam-5017	249	3	/	/	SYM
ejpam-5017	249	4	eur	eur	PROPN
ejpam-5017	249	5	.	.	PUNCT
ejpam-5017	250	1	j.	j.	PROPN
ejpam-5017	250	2	pure	pure	PROPN
ejpam-5017	250	3	appl	appl	PROPN
ejpam-5017	250	4	.	.	PROPN
ejpam-5017	250	5	math	math	PROPN
ejpam-5017	250	6	,	,	PUNCT
ejpam-5017	250	7	17	17	NUM
ejpam-5017	250	8	(	(	PUNCT
ejpam-5017	250	9	2	2	NUM
ejpam-5017	250	10	)	)	PUNCT
ejpam-5017	250	11	(	(	PUNCT
ejpam-5017	250	12	2024	2024	NUM
ejpam-5017	250	13	)	)	PUNCT
ejpam-5017	250	14	,	,	PUNCT
ejpam-5017	250	15	1321	1321	NUM
ejpam-5017	250	16	-	-	SYM
ejpam-5017	250	17	1334	1334	NUM
ejpam-5017	250	18	1332	1332	NUM
ejpam-5017	250	19	∫	∫	PROPN
ejpam-5017	250	20	t	t	PROPN
ejpam-5017	250	21	t	t	PROPN
ejpam-5017	250	22	∥∥∥e−d1(t−s)spg(w2z)(s)ds	∥∥∥e−d1(t−s)spg(w2z)(s)ds	PROPN
ejpam-5017	251	1	∥∥∥	∥∥∥	PROPN
ejpam-5017	251	2	p	p	NOUN
ejpam-5017	251	3	≤	≤	NUM
ejpam-5017	251	4	r	r	NOUN
ejpam-5017	251	5	∫	∫	PROPN
ejpam-5017	251	6	t	t	PROPN
ejpam-5017	251	7	t	t	PROPN
ejpam-5017	251	8	c(t−	c(t−	PROPN
ejpam-5017	251	9	s	s	X
ejpam-5017	251	10	)	)	PUNCT
ejpam-5017	251	11	−n	−n	NUM
ejpam-5017	251	12	2δ	2δ	NUM
ejpam-5017	251	13	(	(	PUNCT
ejpam-5017	251	14	1	1	NUM
ejpam-5017	251	15	q	q	NOUN
ejpam-5017	251	16	−	−	PROPN
ejpam-5017	251	17	1	1	NUM
ejpam-5017	251	18	p	p	NOUN
ejpam-5017	251	19	)	)	PUNCT
ejpam-5017	251	20	e−2d1αδ	e−2d1αδ	VERB
ejpam-5017	251	21	1λ(t−s	1λ(t−s	NUM
ejpam-5017	251	22	)	)	PUNCT
ejpam-5017	251	23	∥z(s)∥q	∥z(s)∥q	NOUN
ejpam-5017	251	24	using	use	VERB
ejpam-5017	251	25	the	the	DET
ejpam-5017	251	26	estimate	estimate	NOUN
ejpam-5017	251	27	(	(	PUNCT
ejpam-5017	251	28	16	16	NUM
ejpam-5017	251	29	)	)	PUNCT
ejpam-5017	251	30	,	,	PUNCT
ejpam-5017	251	31	we	we	PRON
ejpam-5017	251	32	find	find	VERB
ejpam-5017	251	33	a(t	a(t	NOUN
ejpam-5017	251	34	)	)	PUNCT
ejpam-5017	251	35	≤	≤	NOUN
ejpam-5017	251	36	r	r	NOUN
ejpam-5017	251	37	∥z(t	∥z(t	PROPN
ejpam-5017	251	38	)	)	PUNCT
ejpam-5017	251	39	∥q	∥q	ADJ
ejpam-5017	251	40	∫	∫	PROPN
ejpam-5017	251	41	t	t	PROPN
ejpam-5017	251	42	t	t	PROPN
ejpam-5017	251	43	c(t−	c(t−	PROPN
ejpam-5017	251	44	s	s	X
ejpam-5017	251	45	)	)	PUNCT
ejpam-5017	251	46	−n	−n	NUM
ejpam-5017	251	47	2δ	2δ	NUM
ejpam-5017	251	48	(	(	PUNCT
ejpam-5017	251	49	1	1	NUM
ejpam-5017	251	50	q	q	NOUN
ejpam-5017	251	51	−	−	PROPN
ejpam-5017	251	52	1	1	NUM
ejpam-5017	251	53	p	p	NOUN
ejpam-5017	251	54	)	)	PUNCT
ejpam-5017	251	55	e−2d1αδ	e−2d1αδ	VERB
ejpam-5017	251	56	1λ(t−s)e((w∞+ε)2−(k))(s−t	1λ(t−s)e((w∞+ε)2−(k))(s−t	NUM
ejpam-5017	251	57	)	)	PUNCT
ejpam-5017	251	58	ds	ds	ADJ
ejpam-5017	251	59	≤	≤	NOUN
ejpam-5017	251	60	r	r	NOUN
ejpam-5017	251	61	∥z(t	∥z(t	PROPN
ejpam-5017	251	62	)	)	PUNCT
ejpam-5017	251	63	∥q	∥q	ADJ
ejpam-5017	251	64	∫	∫	PROPN
ejpam-5017	251	65	t−t	t−t	PROPN
ejpam-5017	251	66	0	0	NUM
ejpam-5017	252	1	c(t−	c(t−	PROPN
ejpam-5017	252	2	t	t	NOUN
ejpam-5017	252	3	−	−	PROPN
ejpam-5017	252	4	τ	τ	X
ejpam-5017	252	5	)	)	PUNCT
ejpam-5017	252	6	−n	−n	SYM
ejpam-5017	252	7	2δ	2δ	NUM
ejpam-5017	252	8	(	(	PUNCT
ejpam-5017	252	9	1	1	NUM
ejpam-5017	252	10	q	q	NOUN
ejpam-5017	252	11	−	−	PROPN
ejpam-5017	252	12	1	1	NUM
ejpam-5017	252	13	p	p	NOUN
ejpam-5017	252	14	)	)	PUNCT
ejpam-5017	252	15	e−2d1αδ	e−2d1αδ	VERB
ejpam-5017	252	16	1λ(t−t−τ)e(w∞+ε)2−(k))(τ)dτ	1λ(t−t−τ)e(w∞+ε)2−(k))(τ)dτ	PROPN
ejpam-5017	252	17	r	r	PROPN
ejpam-5017	252	18	∥z(t	∥z(t	PROPN
ejpam-5017	252	19	)	)	PUNCT
ejpam-5017	252	20	∥q	∥q	ADJ
ejpam-5017	252	21	e	e	X
ejpam-5017	252	22	(	(	PUNCT
ejpam-5017	252	23	w∞+ε)2−(k))(t−t	w∞+ε)2−(k))(t−t	PROPN
ejpam-5017	252	24	)	)	PUNCT
ejpam-5017	252	25	×	×	NOUN
ejpam-5017	252	26	∫	∫	PROPN
ejpam-5017	252	27	t−t	t−t	PROPN
ejpam-5017	252	28	0	0	NUM
ejpam-5017	253	1	c(t−	c(t−	PROPN
ejpam-5017	253	2	t	t	NOUN
ejpam-5017	253	3	−	−	PROPN
ejpam-5017	253	4	τ	τ	X
ejpam-5017	253	5	)	)	PUNCT
ejpam-5017	253	6	−n	−n	SYM
ejpam-5017	253	7	2δ	2δ	NUM
ejpam-5017	253	8	(	(	PUNCT
ejpam-5017	253	9	1	1	NUM
ejpam-5017	253	10	q	q	NOUN
ejpam-5017	253	11	−	−	PROPN
ejpam-5017	253	12	1	1	NUM
ejpam-5017	253	13	p	p	NOUN
ejpam-5017	253	14	)	)	PUNCT
ejpam-5017	253	15	e(((w0+ε)2−k)−2d1αδ	e(((w0+ε)2−k)−2d1αδ	NOUN
ejpam-5017	253	16	1λ)(t−t−τ)dτ	1λ)(t−t−τ)dτ	NUM
ejpam-5017	253	17	we	we	PRON
ejpam-5017	253	18	note	note	VERB
ejpam-5017	253	19	aε(t	aε(t	PUNCT
ejpam-5017	253	20	)	)	PUNCT
ejpam-5017	254	1	=	=	SYM
ejpam-5017	254	2	∫	∫	PROPN
ejpam-5017	254	3	t−t	t−t	PROPN
ejpam-5017	254	4	0	0	NUM
ejpam-5017	255	1	c(t−	c(t−	PROPN
ejpam-5017	255	2	t	t	NOUN
ejpam-5017	255	3	−	−	PROPN
ejpam-5017	255	4	τ	τ	X
ejpam-5017	255	5	)	)	PUNCT
ejpam-5017	255	6	−n	−n	SYM
ejpam-5017	255	7	2δ	2δ	NUM
ejpam-5017	255	8	(	(	PUNCT
ejpam-5017	255	9	1	1	NUM
ejpam-5017	255	10	q	q	NOUN
ejpam-5017	255	11	−	−	PROPN
ejpam-5017	255	12	1	1	NUM
ejpam-5017	255	13	p	p	NOUN
ejpam-5017	255	14	)	)	PUNCT
ejpam-5017	255	15	e(((w0+ε)2−k)−2d1αδ	e(((w0+ε)2−k)−2d1αδ	PROPN
ejpam-5017	255	16	1λ)(t−t−τ)dτ	1λ)(t−t−τ)dτ	NUM
ejpam-5017	255	17	.	.	PUNCT
ejpam-5017	256	1	if	if	SCONJ
ejpam-5017	256	2	we	we	PRON
ejpam-5017	256	3	choose	choose	VERB
ejpam-5017	256	4	p	p	NOUN
ejpam-5017	256	5	and	and	CCONJ
ejpam-5017	256	6	q	q	NOUN
ejpam-5017	256	7	satisfying	satisfy	VERB
ejpam-5017	256	8	0	0	NUM
ejpam-5017	256	9	≤	≤	NUM
ejpam-5017	256	10	−n	−n	NOUN
ejpam-5017	256	11	2δ	2δ	NUM
ejpam-5017	256	12	(	(	PUNCT
ejpam-5017	256	13	1	1	NUM
ejpam-5017	256	14	q	q	NOUN
ejpam-5017	256	15	−	−	PROPN
ejpam-5017	256	16	1	1	NUM
ejpam-5017	256	17	p	p	NOUN
ejpam-5017	256	18	)	)	PUNCT
ejpam-5017	256	19	≺	≺	NOUN
ejpam-5017	256	20	1	1	NUM
ejpam-5017	256	21	and	and	CCONJ
ejpam-5017	256	22	use	use	VERB
ejpam-5017	256	23	lemma	lemma	PROPN
ejpam-5017	256	24	1	1	NUM
ejpam-5017	256	25	,	,	PUNCT
ejpam-5017	256	26	we	we	PRON
ejpam-5017	256	27	obtain	obtain	VERB
ejpam-5017	256	28	◦	◦	NOUN
ejpam-5017	256	29	when	when	SCONJ
ejpam-5017	256	30	2d1α	2d1α	PROPN
ejpam-5017	256	31	δ	δ	PROPN
ejpam-5017	256	32	1λ	1λ	PROPN
ejpam-5017	256	33	≺	≺	NOUN
ejpam-5017	256	34	(	(	PUNCT
ejpam-5017	256	35	w0	w0	PROPN
ejpam-5017	256	36	+	+	CCONJ
ejpam-5017	256	37	ε)2	ε)2	PROPN
ejpam-5017	256	38	−	−	PROPN
ejpam-5017	256	39	k	k	NOUN
ejpam-5017	256	40	=	=	SYM
ejpam-5017	256	41	h(w∞	h(w∞	PROPN
ejpam-5017	256	42	)	)	PUNCT
ejpam-5017	256	43	,	,	PUNCT
ejpam-5017	256	44	we	we	PRON
ejpam-5017	256	45	choose	choose	VERB
ejpam-5017	256	46	ε	ε	PROPN
ejpam-5017	256	47	such	such	ADJ
ejpam-5017	256	48	that	that	SCONJ
ejpam-5017	256	49	0	0	NUM
ejpam-5017	256	50	≺	≺	NOUN
ejpam-5017	256	51	ε	ε	PROPN
ejpam-5017	256	52	≺	≺	NOUN
ejpam-5017	256	53	h(w∞	h(w∞	PROPN
ejpam-5017	256	54	)	)	PUNCT
ejpam-5017	256	55	−	−	PROPN
ejpam-5017	256	56	2d1α	2d1α	ADJ
ejpam-5017	256	57	δ	δ	PROPN
ejpam-5017	256	58	1λ	1λ	NUM
ejpam-5017	256	59	,	,	PUNCT
ejpam-5017	256	60	so	so	ADV
ejpam-5017	256	61	aε(t	aε(t	NOUN
ejpam-5017	256	62	)	)	PUNCT
ejpam-5017	256	63	≤	≤	NOUN
ejpam-5017	257	1	r	r	NOUN
ejpam-5017	257	2	(	(	PUNCT
ejpam-5017	257	3	n	n	DET
ejpam-5017	257	4	2δ	2δ	NUM
ejpam-5017	257	5	(	(	PUNCT
ejpam-5017	257	6	1	1	NUM
ejpam-5017	257	7	q	q	NOUN
ejpam-5017	257	8	−	−	PROPN
ejpam-5017	257	9	1	1	NUM
ejpam-5017	257	10	p	p	NOUN
ejpam-5017	257	11	)	)	PUNCT
ejpam-5017	257	12	,	,	PUNCT
ejpam-5017	257	13	h(w∞)−	h(w∞)−	NUM
ejpam-5017	257	14	2d1α	2d1α	ADJ
ejpam-5017	257	15	δ	δ	PROPN
ejpam-5017	257	16	1λ−	1λ−	PROPN
ejpam-5017	257	17	ε)e(h(w∞)−2d1αδ	ε)e(h(w∞)−2d1αδ	PROPN
ejpam-5017	257	18	1λ−ε)(t−t	1λ−ε)(t−t	NUM
ejpam-5017	257	19	)	)	PUNCT
ejpam-5017	257	20	.	.	PUNCT
ejpam-5017	258	1	◦	◦	VERB
ejpam-5017	258	2	when	when	SCONJ
ejpam-5017	258	3	2d1α	2d1α	PROPN
ejpam-5017	258	4	δ	δ	PROPN
ejpam-5017	258	5	1λ	1λ	NUM
ejpam-5017	258	6	≥	≥	NOUN
ejpam-5017	258	7	(	(	PUNCT
ejpam-5017	258	8	w0	w0	PROPN
ejpam-5017	258	9	+	+	CCONJ
ejpam-5017	258	10	ε)2	ε)2	PROPN
ejpam-5017	258	11	−	−	PROPN
ejpam-5017	258	12	k	k	NOUN
ejpam-5017	258	13	=	=	SYM
ejpam-5017	258	14	h(w∞	h(w∞	PROPN
ejpam-5017	258	15	)	)	PUNCT
ejpam-5017	258	16	,	,	PUNCT
ejpam-5017	258	17	aε(t	aε(t	NOUN
ejpam-5017	258	18	)	)	PUNCT
ejpam-5017	258	19	≤	≤	NOUN
ejpam-5017	259	1	r	r	NOUN
ejpam-5017	259	2	(	(	PUNCT
ejpam-5017	259	3	n	n	DET
ejpam-5017	259	4	2δ	2δ	NUM
ejpam-5017	259	5	(	(	PUNCT
ejpam-5017	259	6	1	1	NUM
ejpam-5017	259	7	q	q	NOUN
ejpam-5017	259	8	−	−	PROPN
ejpam-5017	259	9	1	1	NUM
ejpam-5017	259	10	p	p	NOUN
ejpam-5017	259	11	)	)	PUNCT
ejpam-5017	259	12	,	,	PUNCT
ejpam-5017	259	13	h(w∞)−	h(w∞)−	NUM
ejpam-5017	259	14	2d1α	2d1α	ADJ
ejpam-5017	259	15	δ	δ	PROPN
ejpam-5017	259	16	1λ−	1λ−	PROPN
ejpam-5017	259	17	ε	ε	PROPN
ejpam-5017	259	18	)	)	PUNCT
ejpam-5017	259	19	.	.	PUNCT
ejpam-5017	260	1	hence	hence	ADV
ejpam-5017	260	2	a(t	a(t	NOUN
ejpam-5017	260	3	)	)	PUNCT
ejpam-5017	260	4	≤	≤	NUM
ejpam-5017	260	5	r	r	NOUN
ejpam-5017	260	6	∥z(t	∥z(t	PROPN
ejpam-5017	260	7	)	)	PUNCT
ejpam-5017	260	8	∥q	∥q	ADJ
ejpam-5017	260	9	e	e	NOUN
ejpam-5017	260	10	−µ(t−t	−µ(t−t	PROPN
ejpam-5017	260	11	)	)	PUNCT
ejpam-5017	260	12	(	(	PUNCT
ejpam-5017	260	13	19	19	NUM
ejpam-5017	260	14	)	)	PUNCT
ejpam-5017	260	15	where	where	SCONJ
ejpam-5017	260	16	µ	µ	X
ejpam-5017	260	17	=	=	SYM
ejpam-5017	260	18	{	{	PUNCT
ejpam-5017	260	19	2d1α	2d1α	NUM
ejpam-5017	260	20	δ	δ	PROPN
ejpam-5017	260	21	1λ	1λ	NUM
ejpam-5017	260	22	if	if	SCONJ
ejpam-5017	260	23	2d1α	2d1α	PROPN
ejpam-5017	260	24	δ	δ	PROPN
ejpam-5017	260	25	1λ	1λ	PROPN
ejpam-5017	260	26	≺	≺	NOUN
ejpam-5017	260	27	h(w∞	h(w∞	PROPN
ejpam-5017	260	28	)	)	PUNCT
ejpam-5017	260	29	(	(	PUNCT
ejpam-5017	260	30	w0	w0	PROPN
ejpam-5017	260	31	+	+	CCONJ
ejpam-5017	260	32	ε)2	ε)2	PROPN
ejpam-5017	260	33	−	−	PROPN
ejpam-5017	260	34	k	k	NOUN
ejpam-5017	260	35	if	if	SCONJ
ejpam-5017	260	36	2d1α	2d1α	PROPN
ejpam-5017	260	37	δ	δ	PROPN
ejpam-5017	260	38	1λ	1λ	NUM
ejpam-5017	260	39	≥	≥	PROPN
ejpam-5017	260	40	h(w∞	h(w∞	PROPN
ejpam-5017	260	41	)	)	PUNCT
ejpam-5017	260	42	combining	combine	VERB
ejpam-5017	260	43	relation	relation	NOUN
ejpam-5017	260	44	(	(	PUNCT
ejpam-5017	260	45	19	19	NUM
ejpam-5017	260	46	)	)	PUNCT
ejpam-5017	260	47	and	and	CCONJ
ejpam-5017	260	48	(	(	PUNCT
ejpam-5017	260	49	20	20	NUM
ejpam-5017	260	50	)	)	PUNCT
ejpam-5017	260	51	,	,	PUNCT
ejpam-5017	260	52	we	we	PRON
ejpam-5017	260	53	obtain	obtain	VERB
ejpam-5017	260	54	∥gw(t	∥gw(t	NOUN
ejpam-5017	260	55	)	)	PUNCT
ejpam-5017	260	56	∥p	∥p	ADJ
ejpam-5017	260	57	≤	≤	NUM
ejpam-5017	260	58	r	r	NOUN
ejpam-5017	260	59	∥(w	∥(w	NOUN
ejpam-5017	260	60	,	,	PUNCT
ejpam-5017	260	61	z)(t	z)(t	NUM
ejpam-5017	260	62	)	)	PUNCT
ejpam-5017	260	63	∥p	∥p	ADJ
ejpam-5017	260	64	e	e	NOUN
ejpam-5017	260	65	−µ(t−t	−µ(t−t	PROPN
ejpam-5017	260	66	)	)	PUNCT
ejpam-5017	260	67	;	;	PUNCT
ejpam-5017	261	1	t	t	PROPN
ejpam-5017	261	2	≥	≥	NOUN
ejpam-5017	261	3	t.	t.	PROPN
ejpam-5017	261	4	(	(	PUNCT
ejpam-5017	261	5	20	20	NUM
ejpam-5017	261	6	)	)	PUNCT
ejpam-5017	261	7	so	so	ADV
ejpam-5017	261	8	,	,	PUNCT
ejpam-5017	261	9	we	we	PRON
ejpam-5017	261	10	get	get	VERB
ejpam-5017	261	11	from	from	ADP
ejpam-5017	261	12	(	(	PUNCT
ejpam-5017	261	13	18	18	NUM
ejpam-5017	261	14	)	)	PUNCT
ejpam-5017	261	15	and	and	CCONJ
ejpam-5017	261	16	(	(	PUNCT
ejpam-5017	261	17	21	21	NUM
ejpam-5017	261	18	)	)	PUNCT
ejpam-5017	261	19	∥w(t)−	∥w(t)−	PUNCT
ejpam-5017	261	20	w∞∥p	w∞∥p	VERB
ejpam-5017	261	21	≤	≤	NUM
ejpam-5017	261	22	r	r	NOUN
ejpam-5017	261	23	∥(w	∥(w	NOUN
ejpam-5017	261	24	,	,	PUNCT
ejpam-5017	261	25	z)(t	z)(t	NUM
ejpam-5017	261	26	)	)	PUNCT
ejpam-5017	262	1	∥∞	∥∞	ADJ
ejpam-5017	262	2	e−µ(t−t	e−µ(t−t	PROPN
ejpam-5017	262	3	)	)	PUNCT
ejpam-5017	262	4	;	;	PUNCT
ejpam-5017	262	5	t	t	PROPN
ejpam-5017	262	6	≥	≥	NOUN
ejpam-5017	262	7	t.	t.	ADV
ejpam-5017	263	1	now	now	ADV
ejpam-5017	263	2	,	,	PUNCT
ejpam-5017	263	3	we	we	PRON
ejpam-5017	263	4	have	have	VERB
ejpam-5017	263	5	w∞	w∞	PROPN
ejpam-5017	263	6	−re−µ(t−t	−re−µ(t−t	NUM
ejpam-5017	263	7	)	)	PUNCT
ejpam-5017	263	8	≺	≺	NOUN
ejpam-5017	263	9	w(t	w(t	PROPN
ejpam-5017	263	10	)	)	PUNCT
ejpam-5017	263	11	≺	≺	NOUN
ejpam-5017	263	12	w∞	w∞	PROPN
ejpam-5017	264	1	+	+	NOUN
ejpam-5017	264	2	re−µ(t−t	re−µ(t−t	ADJ
ejpam-5017	264	3	)	)	PUNCT
ejpam-5017	264	4	;	;	PUNCT
ejpam-5017	264	5	t	t	PROPN
ejpam-5017	264	6	≥	≥	NOUN
ejpam-5017	264	7	t.	t.	PROPN
ejpam-5017	264	8	therefore	therefore	ADV
ejpam-5017	264	9	,	,	PUNCT
ejpam-5017	264	10	we	we	PRON
ejpam-5017	264	11	can	can	AUX
ejpam-5017	264	12	assert	assert	VERB
ejpam-5017	264	13	that	that	PRON
ejpam-5017	264	14	∀1	∀1	VERB
ejpam-5017	264	15	≤	≤	NOUN
ejpam-5017	264	16	p	p	NOUN
ejpam-5017	264	17	≤	≤	NOUN
ejpam-5017	265	1	+	+	PROPN
ejpam-5017	265	2	∞	∞	PROPN
ejpam-5017	265	3	,	,	PUNCT
ejpam-5017	265	4	∥z(t)∥p	∥z(t)∥p	NUM
ejpam-5017	265	5	≤	≤	NUM
ejpam-5017	265	6	r	r	NOUN
ejpam-5017	265	7	∥z(t	∥z(t	PROPN
ejpam-5017	265	8	)	)	PUNCT
ejpam-5017	265	9	∥p	∥p	ADJ
ejpam-5017	265	10	e−h(w∞)(t−t	e−h(w∞)(t−t	PRON
ejpam-5017	265	11	)	)	PUNCT
ejpam-5017	265	12	,	,	PUNCT
ejpam-5017	265	13	t	t	PROPN
ejpam-5017	265	14	≥	≥	NOUN
ejpam-5017	265	15	t.	t.	PROPN
ejpam-5017	265	16	references	reference	NOUN
ejpam-5017	265	17	1333	1333	NUM
ejpam-5017	265	18	hence	hence	ADV
ejpam-5017	265	19	,	,	PUNCT
ejpam-5017	265	20	gw(t)−	gw(t)−	PROPN
ejpam-5017	265	21	w∞	w∞	PROPN
ejpam-5017	265	22	can	can	AUX
ejpam-5017	265	23	be	be	AUX
ejpam-5017	265	24	estimated	estimate	VERB
ejpam-5017	265	25	as	as	SCONJ
ejpam-5017	265	26	|gw(t)−	|gw(t)−	PROPN
ejpam-5017	265	27	w∞|	w∞|	VERB
ejpam-5017	265	28	≤	≤	ADJ
ejpam-5017	265	29	r	r	NOUN
ejpam-5017	265	30	|gw(t	|gw(t	X
ejpam-5017	265	31	)	)	PUNCT
ejpam-5017	265	32	|	|	ADV
ejpam-5017	265	33	e−h(w∞)(t−t	e−h(w∞)(t−t	PRON
ejpam-5017	265	34	)	)	PUNCT
ejpam-5017	265	35	;	;	PUNCT
ejpam-5017	265	36	t	t	PROPN
ejpam-5017	265	37	≥	≥	NOUN
ejpam-5017	265	38	t.	t.	PROPN
ejpam-5017	265	39	and	and	CCONJ
ejpam-5017	265	40	∥gw(t)∥∞	∥gw(t)∥∞	PROPN
ejpam-5017	265	41	≤	≤	NUM
ejpam-5017	265	42	{	{	PUNCT
ejpam-5017	265	43	r	r	NOUN
ejpam-5017	265	44	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	265	45	)	)	PUNCT
ejpam-5017	266	1	if	if	SCONJ
ejpam-5017	266	2	2d1α	2d1α	NUM
ejpam-5017	266	3	δ	δ	PROPN
ejpam-5017	266	4	1λ	1λ	PROPN
ejpam-5017	266	5	̸=	̸=	PROPN
ejpam-5017	266	6	h(w∞	h(w∞	PROPN
ejpam-5017	266	7	)	)	PUNCT
ejpam-5017	266	8	r(t−	r(t−	NOUN
ejpam-5017	266	9	t	t	NOUN
ejpam-5017	266	10	+	+	CCONJ
ejpam-5017	266	11	1	1	X
ejpam-5017	266	12	)	)	PUNCT
ejpam-5017	266	13	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	266	14	)	)	PUNCT
ejpam-5017	267	1	if	if	SCONJ
ejpam-5017	267	2	2d1α	2d1α	NUM
ejpam-5017	267	3	δ	δ	PROPN
ejpam-5017	267	4	1λ	1λ	NUM
ejpam-5017	267	5	=	=	SYM
ejpam-5017	267	6	h(w∞	h(w∞	PROPN
ejpam-5017	267	7	)	)	PUNCT
ejpam-5017	267	8	,	,	PUNCT
ejpam-5017	267	9	where	where	SCONJ
ejpam-5017	267	10	κ	κ	PROPN
ejpam-5017	267	11	=	=	SYM
ejpam-5017	267	12	min	min	PROPN
ejpam-5017	267	13	{	{	PUNCT
ejpam-5017	267	14	h(w∞	h(w∞	PROPN
ejpam-5017	267	15	)	)	PUNCT
ejpam-5017	267	16	,	,	PUNCT
ejpam-5017	267	17	2d1α	2d1α	NOUN
ejpam-5017	267	18	δ	δ	PROPN
ejpam-5017	267	19	1λ	1λ	NUM
ejpam-5017	267	20	}	}	PUNCT
ejpam-5017	267	21	.	.	PUNCT
ejpam-5017	268	1	accordingly	accordingly	ADV
ejpam-5017	268	2	∥w(t)−	∥w(t)−	PROPN
ejpam-5017	268	3	w∞∥∞	w∞∥∞	VERB
ejpam-5017	268	4	≤	≤	NOUN
ejpam-5017	268	5	{	{	PUNCT
ejpam-5017	268	6	r	r	NOUN
ejpam-5017	268	7	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	268	8	)	)	PUNCT
ejpam-5017	269	1	if	if	SCONJ
ejpam-5017	269	2	2d1α	2d1α	NUM
ejpam-5017	269	3	δ	δ	PROPN
ejpam-5017	269	4	1λ	1λ	PROPN
ejpam-5017	269	5	̸=	̸=	PROPN
ejpam-5017	269	6	h(w∞	h(w∞	PROPN
ejpam-5017	269	7	)	)	PUNCT
ejpam-5017	269	8	r(t−	r(t−	NOUN
ejpam-5017	269	9	t	t	NOUN
ejpam-5017	269	10	+	+	CCONJ
ejpam-5017	269	11	1	1	X
ejpam-5017	269	12	)	)	PUNCT
ejpam-5017	269	13	exp−κ(t−t	exp−κ(t−t	PROPN
ejpam-5017	269	14	)	)	PUNCT
ejpam-5017	270	1	if	if	SCONJ
ejpam-5017	270	2	2d1α	2d1α	NUM
ejpam-5017	270	3	δ	δ	PROPN
ejpam-5017	270	4	1λ	1λ	NUM
ejpam-5017	270	5	=	=	SYM
ejpam-5017	270	6	h(w∞	h(w∞	PROPN
ejpam-5017	270	7	)	)	PUNCT
ejpam-5017	270	8	.	.	PUNCT
ejpam-5017	271	1	5	5	X
ejpam-5017	271	2	.	.	X
ejpam-5017	271	3	conclusion	conclusion	NOUN
ejpam-5017	271	4	in	in	ADP
ejpam-5017	271	5	this	this	DET
ejpam-5017	271	6	paper	paper	NOUN
ejpam-5017	271	7	,	,	PUNCT
ejpam-5017	271	8	we	we	PRON
ejpam-5017	271	9	considered	consider	VERB
ejpam-5017	271	10	a	a	DET
ejpam-5017	271	11	gray	gray	ADJ
ejpam-5017	271	12	scott	scott	NOUN
ejpam-5017	271	13	system	system	NOUN
ejpam-5017	271	14	with	with	ADP
ejpam-5017	271	15	anomalous	anomalous	ADJ
ejpam-5017	271	16	diffusion	diffusion	NOUN
ejpam-5017	271	17	described	describe	VERB
ejpam-5017	271	18	by	by	ADP
ejpam-5017	271	19	a	a	DET
ejpam-5017	271	20	fractional	fractional	ADJ
ejpam-5017	271	21	laplacian	laplacian	ADJ
ejpam-5017	271	22	power	power	NOUN
ejpam-5017	271	23	which	which	PRON
ejpam-5017	271	24	accounts	account	VERB
ejpam-5017	271	25	for	for	ADP
ejpam-5017	271	26	a	a	DET
ejpam-5017	271	27	sub	sub	ADJ
ejpam-5017	271	28	-	-	ADJ
ejpam-5017	271	29	diffusive	diffusive	ADJ
ejpam-5017	271	30	situation	situation	NOUN
ejpam-5017	271	31	.	.	PUNCT
ejpam-5017	272	1	in	in	ADP
ejpam-5017	272	2	addition	addition	NOUN
ejpam-5017	272	3	to	to	ADP
ejpam-5017	272	4	the	the	DET
ejpam-5017	272	5	global	global	ADJ
ejpam-5017	272	6	existence	existence	NOUN
ejpam-5017	272	7	of	of	ADP
ejpam-5017	272	8	bounded	bounded	ADJ
ejpam-5017	272	9	solutions	solution	NOUN
ejpam-5017	272	10	,	,	PUNCT
ejpam-5017	272	11	we	we	PRON
ejpam-5017	272	12	showed	show	VERB
ejpam-5017	272	13	the	the	DET
ejpam-5017	272	14	convergence	convergence	NOUN
ejpam-5017	272	15	of	of	ADP
ejpam-5017	272	16	the	the	DET
ejpam-5017	272	17	solution	solution	NOUN
ejpam-5017	272	18	(	(	PUNCT
ejpam-5017	272	19	w∞	w∞	PROPN
ejpam-5017	272	20	,	,	PUNCT
ejpam-5017	272	21	0	0	NUM
ejpam-5017	272	22	)	)	PUNCT
ejpam-5017	272	23	.	.	PUNCT
ejpam-5017	273	1	(	(	PUNCT
ejpam-5017	273	2	w∞	w∞	PROPN
ejpam-5017	273	3	):	):	PUNCT
ejpam-5017	273	4	the	the	DET
ejpam-5017	273	5	final	final	ADJ
ejpam-5017	273	6	state	state	NOUN
ejpam-5017	273	7	of	of	ADP
ejpam-5017	273	8	susceptible	susceptible	ADJ
ejpam-5017	273	9	individuals	individual	NOUN
ejpam-5017	273	10	and	and	CCONJ
ejpam-5017	273	11	0	0	NUM
ejpam-5017	273	12	:	:	PUNCT
ejpam-5017	273	13	the	the	DET
ejpam-5017	273	14	final	final	ADJ
ejpam-5017	273	15	state	state	NOUN
ejpam-5017	273	16	of	of	ADP
ejpam-5017	273	17	infected	infected	ADJ
ejpam-5017	273	18	individuals	individual	NOUN
ejpam-5017	273	19	.	.	PUNCT
ejpam-5017	274	1	the	the	DET
ejpam-5017	274	2	exponent	exponent	NOUN
ejpam-5017	274	3	of	of	ADP
ejpam-5017	274	4	the	the	DET
ejpam-5017	274	5	fractional	fractional	ADJ
ejpam-5017	274	6	laplacian	laplacian	ADJ
ejpam-5017	274	7	influences	influence	VERB
ejpam-5017	274	8	the	the	DET
ejpam-5017	274	9	asymptotic	asymptotic	ADJ
ejpam-5017	274	10	behavior	behavior	NOUN
ejpam-5017	274	11	in	in	ADP
ejpam-5017	274	12	time	time	NOUN
ejpam-5017	274	13	from	from	ADP
ejpam-5017	274	14	w	w	PROPN
ejpam-5017	274	15	to	to	PART
ejpam-5017	274	16	w∞.	w∞.	NOUN
ejpam-5017	274	17	acknowledgements	acknowledgement	NOUN
ejpam-5017	274	18	the	the	DET
ejpam-5017	274	19	authors	author	NOUN
ejpam-5017	274	20	would	would	AUX
ejpam-5017	274	21	like	like	VERB
ejpam-5017	274	22	to	to	PART
ejpam-5017	274	23	thank	thank	VERB
ejpam-5017	274	24	the	the	DET
ejpam-5017	274	25	anonymous	anonymous	ADJ
ejpam-5017	274	26	referee	referee	NOUN
ejpam-5017	274	27	for	for	ADP
ejpam-5017	274	28	his	his	PRON
ejpam-5017	274	29	/	/	SYM
ejpam-5017	274	30	her	her	PRON
ejpam-5017	274	31	comments	comment	NOUN
ejpam-5017	274	32	that	that	PRON
ejpam-5017	274	33	helped	help	VERB
ejpam-5017	274	34	us	we	PRON
ejpam-5017	274	35	improve	improve	VERB
ejpam-5017	274	36	this	this	DET
ejpam-5017	274	37	article	article	NOUN
ejpam-5017	274	38	.	.	PUNCT
ejpam-5017	275	1	references	reference	NOUN
ejpam-5017	275	2	[	[	X
ejpam-5017	275	3	1	1	NUM
ejpam-5017	275	4	]	]	PUNCT
ejpam-5017	275	5	d.hnaien	d.hnaien	NOUN
ejpam-5017	275	6	,	,	PUNCT
ejpam-5017	275	7	f.kellil	f.kellil	NOUN
ejpam-5017	275	8	,	,	PUNCT
ejpam-5017	275	9	and	and	CCONJ
ejpam-5017	275	10	r.lassoued	r.lassoue	VERB
ejpam-5017	275	11	.	.	PUNCT
ejpam-5017	276	1	asymptotic	asymptotic	ADJ
ejpam-5017	276	2	behavior	behavior	NOUN
ejpam-5017	276	3	of	of	ADP
ejpam-5017	276	4	global	global	ADJ
ejpam-5017	276	5	solutions	solution	NOUN
ejpam-5017	276	6	of	of	ADP
ejpam-5017	276	7	an	an	DET
ejpam-5017	276	8	anomalous	anomalous	ADJ
ejpam-5017	276	9	diffusion	diffusion	NOUN
ejpam-5017	276	10	system	system	NOUN
ejpam-5017	276	11	.	.	PUNCT
ejpam-5017	277	1	mathematical	mathematical	ADJ
ejpam-5017	277	2	analysis	analysis	NOUN
ejpam-5017	277	3	and	and	CCONJ
ejpam-5017	277	4	applications	application	NOUN
ejpam-5017	277	5	,	,	PUNCT
ejpam-5017	277	6	421:1519	421:1519	NUM
ejpam-5017	277	7	–	–	PUNCT
ejpam-5017	277	8	1530	1530	NUM
ejpam-5017	277	9	,	,	PUNCT
ejpam-5017	277	10	2015	2015	NUM
ejpam-5017	277	11	.	.	PUNCT
ejpam-5017	278	1	[	[	X
ejpam-5017	278	2	2	2	NUM
ejpam-5017	278	3	]	]	PUNCT
ejpam-5017	278	4	a.	a.	NOUN
ejpam-5017	278	5	haraux	haraux	PROPN
ejpam-5017	278	6	and	and	CCONJ
ejpam-5017	278	7	m.	m.	PROPN
ejpam-5017	278	8	kirane	kirane	PROPN
ejpam-5017	278	9	.	.	PUNCT
ejpam-5017	279	1	estimations	estimation	NOUN
ejpam-5017	279	2	c1	c1	PROPN
ejpam-5017	279	3	pour	pour	PROPN
ejpam-5017	279	4	des	des	PROPN
ejpam-5017	279	5	problèmes	problèmes	PROPN
ejpam-5017	279	6	paraboliques	parabolique	NOUN
ejpam-5017	279	7	semilinéaires	semilinéaire	VERB
ejpam-5017	279	8	.	.	PUNCT
ejpam-5017	280	1	ann	ann	PROPN
ejpam-5017	280	2	.	.	PUNCT
ejpam-5017	280	3	fac	fac	PROPN
ejpam-5017	280	4	.	.	PUNCT
ejpam-5017	281	1	sci	sci	PROPN
ejpam-5017	281	2	.	.	PROPN
ejpam-5017	281	3	toulouse	toulouse	PROPN
ejpam-5017	281	4	math	math	NOUN
ejpam-5017	281	5	,	,	PUNCT
ejpam-5017	281	6	5:265–280	5:265–280	NUM
ejpam-5017	281	7	,	,	PUNCT
ejpam-5017	281	8	1983	1983	NUM
ejpam-5017	281	9	.	.	PUNCT
ejpam-5017	282	1	[	[	X
ejpam-5017	282	2	3	3	X
ejpam-5017	282	3	]	]	X
ejpam-5017	282	4	d.	d.	PROPN
ejpam-5017	282	5	henry	henry	PROPN
ejpam-5017	282	6	.	.	PUNCT
ejpam-5017	283	1	geometric	geometric	ADJ
ejpam-5017	283	2	theory	theory	NOUN
ejpam-5017	283	3	of	of	ADP
ejpam-5017	283	4	semilinear	semilinear	PROPN
ejpam-5017	283	5	parabolic	parabolic	PROPN
ejpam-5017	283	6	equations	equation	NOUN
ejpam-5017	283	7	.	.	PUNCT
ejpam-5017	284	1	lecture	lecture	NOUN
ejpam-5017	284	2	notes	note	NOUN
ejpam-5017	284	3	in	in	ADP
ejpam-5017	284	4	mathematics	mathematic	NOUN
ejpam-5017	284	5	.	.	PUNCT
ejpam-5017	285	1	springer	springer	NOUN
ejpam-5017	285	2	-	-	PUNCT
ejpam-5017	285	3	verlag	verlag	PROPN
ejpam-5017	285	4	,	,	PUNCT
ejpam-5017	285	5	1981	1981	NUM
ejpam-5017	285	6	.	.	PUNCT
ejpam-5017	286	1	[	[	X
ejpam-5017	286	2	4	4	X
ejpam-5017	286	3	]	]	PUNCT
ejpam-5017	286	4	s.	s.	PROPN
ejpam-5017	286	5	l.	l.	PROPN
ejpam-5017	286	6	hollis	hollis	PROPN
ejpam-5017	286	7	,	,	PUNCT
ejpam-5017	286	8	r.	r.	PROPN
ejpam-5017	286	9	h.	h.	PROPN
ejpam-5017	286	10	martin	martin	PROPN
ejpam-5017	286	11	,	,	PUNCT
ejpam-5017	286	12	and	and	CCONJ
ejpam-5017	286	13	m.	m.	NOUN
ejpam-5017	286	14	pierre	pierre	PROPN
ejpam-5017	286	15	.	.	PUNCT
ejpam-5017	287	1	global	global	ADJ
ejpam-5017	287	2	existence	existence	NOUN
ejpam-5017	287	3	and	and	CCONJ
ejpam-5017	287	4	boundedness	boundedness	NOUN
ejpam-5017	287	5	in	in	ADP
ejpam-5017	287	6	reaction	reaction	NOUN
ejpam-5017	287	7	diffusion	diffusion	NOUN
ejpam-5017	287	8	systems	system	NOUN
ejpam-5017	287	9	.	.	PUNCT
ejpam-5017	288	1	siam	siam	PROPN
ejpam-5017	288	2	j.	j.	PROPN
ejpam-5017	288	3	math	math	PROPN
ejpam-5017	288	4	.	.	PUNCT
ejpam-5017	289	1	anal	anal	PROPN
ejpam-5017	289	2	,	,	PUNCT
ejpam-5017	289	3	18:744–761	18:744–761	PROPN
ejpam-5017	289	4	,	,	PUNCT
ejpam-5017	289	5	1987	1987	NUM
ejpam-5017	289	6	.	.	PUNCT
ejpam-5017	290	1	[	[	X
ejpam-5017	290	2	5	5	X
ejpam-5017	290	3	]	]	PUNCT
ejpam-5017	290	4	h.	h.	PROPN
ejpam-5017	290	5	hoshino	hoshino	PROPN
ejpam-5017	290	6	and	and	CCONJ
ejpam-5017	290	7	y.	y.	PROPN
ejpam-5017	290	8	yamada	yamada	PROPN
ejpam-5017	290	9	.	.	PUNCT
ejpam-5017	291	1	asymptotic	asymptotic	ADJ
ejpam-5017	291	2	behavior	behavior	NOUN
ejpam-5017	291	3	of	of	ADP
ejpam-5017	291	4	global	global	ADJ
ejpam-5017	291	5	solutions	solution	NOUN
ejpam-5017	291	6	for	for	ADP
ejpam-5017	291	7	some	some	DET
ejpam-5017	291	8	reaction	reaction	NOUN
ejpam-5017	291	9	-	-	PUNCT
ejpam-5017	291	10	diffusion	diffusion	NOUN
ejpam-5017	291	11	systems	system	NOUN
ejpam-5017	291	12	.	.	PUNCT
ejpam-5017	292	1	nonlinear	nonlinear	ADJ
ejpam-5017	292	2	anal	anal	PROPN
ejpam-5017	292	3	,	,	PUNCT
ejpam-5017	292	4	23:639–650	23:639–650	PROPN
ejpam-5017	292	5	,	,	PUNCT
ejpam-5017	292	6	1994	1994	NUM
ejpam-5017	292	7	.	.	PUNCT
ejpam-5017	293	1	references	reference	NOUN
ejpam-5017	293	2	1334	1334	NUM
ejpam-5017	293	3	[	[	X
ejpam-5017	293	4	6	6	NUM
ejpam-5017	293	5	]	]	PUNCT
ejpam-5017	293	6	m.	m.	NOUN
ejpam-5017	293	7	ilic	ilic	NOUN
ejpam-5017	293	8	,	,	PUNCT
ejpam-5017	293	9	f.	f.	PROPN
ejpam-5017	293	10	liu	liu	PROPN
ejpam-5017	293	11	,	,	PUNCT
ejpam-5017	293	12	i.	i.	PROPN
ejpam-5017	293	13	turner	turner	PROPN
ejpam-5017	293	14	,	,	PUNCT
ejpam-5017	293	15	and	and	CCONJ
ejpam-5017	293	16	v.	v.	ADP
ejpam-5017	293	17	anh	anh	PROPN
ejpam-5017	293	18	.	.	PUNCT
ejpam-5017	294	1	numerical	numerical	ADJ
ejpam-5017	294	2	approximation	approximation	NOUN
ejpam-5017	294	3	of	of	ADP
ejpam-5017	294	4	a	a	DET
ejpam-5017	294	5	fractional	fractional	ADJ
ejpam-5017	294	6	-	-	PUNCT
ejpam-5017	294	7	inspace	inspace	NOUN
ejpam-5017	294	8	diffusion	diffusion	NOUN
ejpam-5017	294	9	equation	equation	NOUN
ejpam-5017	294	10	(	(	PUNCT
ejpam-5017	294	11	ii)with	ii)with	ADP
ejpam-5017	294	12	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5017	294	13	boundary	boundary	ADJ
ejpam-5017	294	14	conditions	condition	NOUN
ejpam-5017	294	15	.	.	PUNCT
ejpam-5017	295	1	fract	fract	PROPN
ejpam-5017	295	2	.	.	PUNCT
ejpam-5017	296	1	calc	calc	PROPN
ejpam-5017	296	2	.	.	PUNCT
ejpam-5017	297	1	appl	appl	PROPN
ejpam-5017	297	2	.	.	PUNCT
ejpam-5017	298	1	anal	anal	PROPN
ejpam-5017	298	2	,	,	PUNCT
ejpam-5017	298	3	9:333–349	9:333–349	NUM
ejpam-5017	298	4	,	,	PUNCT
ejpam-5017	298	5	2006	2006	NUM
ejpam-5017	298	6	.	.	PUNCT
ejpam-5017	299	1	[	[	X
ejpam-5017	299	2	7	7	X
ejpam-5017	299	3	]	]	X
ejpam-5017	299	4	g.	g.	PROPN
ejpam-5017	299	5	karch	karch	PROPN
ejpam-5017	299	6	.	.	PUNCT
ejpam-5017	300	1	nonlinear	nonlinear	ADJ
ejpam-5017	300	2	evolution	evolution	NOUN
ejpam-5017	300	3	equations	equation	NOUN
ejpam-5017	300	4	with	with	ADP
ejpam-5017	300	5	anomalous	anomalous	ADJ
ejpam-5017	300	6	diffusion	diffusion	NOUN
ejpam-5017	300	7	.	.	PUNCT
ejpam-5017	301	1	qualitative	qualitative	ADJ
ejpam-5017	301	2	properties	property	NOUN
ejpam-5017	301	3	of	of	ADP
ejpam-5017	301	4	solutions	solution	NOUN
ejpam-5017	301	5	to	to	ADP
ejpam-5017	301	6	partial	partial	ADJ
ejpam-5017	301	7	differential	differential	ADJ
ejpam-5017	301	8	equations	equation	NOUN
ejpam-5017	301	9	.	.	PUNCT
ejpam-5017	302	1	jindrich	jindrich	PROPN
ejpam-5017	302	2	necās	necās	PROPN
ejpam-5017	302	3	cent	cent	NOUN
ejpam-5017	302	4	.	.	PUNCT
ejpam-5017	303	1	math	math	NOUN
ejpam-5017	303	2	.	.	PUNCT
ejpam-5017	304	1	model.lect	model.lect	PROPN
ejpam-5017	304	2	.	.	PUNCT
ejpam-5017	305	1	notes	note	NOUN
ejpam-5017	305	2	,	,	PUNCT
ejpam-5017	305	3	5	5	NUM
ejpam-5017	305	4	,	,	PUNCT
ejpam-5017	305	5	matfyzpress	matfyzpress	NOUN
ejpam-5017	305	6	,	,	PUNCT
ejpam-5017	305	7	prague	prague	NOUN
ejpam-5017	305	8	,	,	PUNCT
ejpam-5017	305	9	pages	page	VERB
ejpam-5017	305	10	25–68	25–68	NUM
ejpam-5017	305	11	,	,	PUNCT
ejpam-5017	305	12	2009	2009	NUM
ejpam-5017	305	13	.	.	PUNCT
ejpam-5017	306	1	[	[	X
ejpam-5017	306	2	8	8	NUM
ejpam-5017	306	3	]	]	X
ejpam-5017	306	4	v.a	v.a	PROPN
ejpam-5017	306	5	.	.	PROPN
ejpam-5017	306	6	liskevich	liskevich	PROPN
ejpam-5017	306	7	and	and	CCONJ
ejpam-5017	306	8	yu.a	yu.a	PROPN
ejpam-5017	306	9	.	.	PUNCT
ejpam-5017	307	1	semenov	semenov	PROPN
ejpam-5017	307	2	.	.	PUNCT
ejpam-5017	308	1	some	some	DET
ejpam-5017	308	2	inequalities	inequality	NOUN
ejpam-5017	308	3	for	for	ADP
ejpam-5017	308	4	submarkovian	submarkovian	ADJ
ejpam-5017	308	5	generators	generator	NOUN
ejpam-5017	308	6	and	and	CCONJ
ejpam-5017	308	7	their	their	PRON
ejpam-5017	308	8	applications	application	NOUN
ejpam-5017	308	9	to	to	ADP
ejpam-5017	308	10	the	the	DET
ejpam-5017	308	11	perturbation	perturbation	NOUN
ejpam-5017	308	12	theory	theory	NOUN
ejpam-5017	308	13	.	.	PUNCT
ejpam-5017	309	1	proc	proc	PROPN
ejpam-5017	309	2	.	.	PUNCT
ejpam-5017	310	1	amer	amer	PROPN
ejpam-5017	310	2	.	.	PUNCT
ejpam-5017	310	3	math	math	PROPN
ejpam-5017	310	4	.	.	PUNCT
ejpam-5017	311	1	soc	soc	PROPN
ejpam-5017	311	2	.	.	PUNCT
ejpam-5017	311	3	,	,	PUNCT
ejpam-5017	311	4	119:1171	119:1171	NUM
ejpam-5017	311	5	–	–	PUNCT
ejpam-5017	311	6	1177	1177	NUM
ejpam-5017	311	7	,	,	PUNCT
ejpam-5017	311	8	1993	1993	NUM
ejpam-5017	311	9	.	.	PUNCT
ejpam-5017	312	1	[	[	X
ejpam-5017	312	2	9	9	NUM
ejpam-5017	312	3	]	]	X
ejpam-5017	312	4	f.	f.	PROPN
ejpam-5017	312	5	rothe	rothe	PROPN
ejpam-5017	312	6	.	.	PUNCT
ejpam-5017	313	1	global	global	ADJ
ejpam-5017	313	2	solutions	solution	NOUN
ejpam-5017	313	3	of	of	ADP
ejpam-5017	313	4	reaction	reaction	NOUN
ejpam-5017	313	5	systems	system	NOUN
ejpam-5017	313	6	.	.	PUNCT
ejpam-5017	314	1	lecture	lecture	NOUN
ejpam-5017	314	2	notes	note	NOUN
ejpam-5017	314	3	in	in	ADP
ejpam-5017	314	4	math	math	NOUN
ejpam-5017	314	5	.	.	PUNCT
ejpam-5017	314	6	,	,	PUNCT
ejpam-5017	314	7	1072	1072	NUM
ejpam-5017	314	8	,	,	PUNCT
ejpam-5017	314	9	springer	springer	NOUN
ejpam-5017	314	10	,	,	PUNCT
ejpam-5017	314	11	berlin	berlin	PROPN
ejpam-5017	314	12	,	,	PUNCT
ejpam-5017	314	13	1984	1984	NUM
ejpam-5017	314	14	.	.	PUNCT
ejpam-5017	315	1	[	[	X
ejpam-5017	315	2	10	10	NUM
ejpam-5017	315	3	]	]	PUNCT
ejpam-5017	315	4	s.kouachi	s.kouachi	ADJ
ejpam-5017	315	5	and	and	CCONJ
ejpam-5017	315	6	a.	a.	PROPN
ejpam-5017	315	7	youkana	youkana	PROPN
ejpam-5017	315	8	.	.	PUNCT
ejpam-5017	316	1	global	global	ADJ
ejpam-5017	316	2	existence	existence	NOUN
ejpam-5017	316	3	and	and	CCONJ
ejpam-5017	316	4	asymptotics	asymptotic	NOUN
ejpam-5017	316	5	for	for	ADP
ejpam-5017	316	6	a	a	DET
ejpam-5017	316	7	class	class	NOUN
ejpam-5017	316	8	of	of	ADP
ejpam-5017	316	9	reaction	reaction	NOUN
ejpam-5017	316	10	diffusion	diffusion	NOUN
ejpam-5017	316	11	systems	system	NOUN
ejpam-5017	316	12	.	.	PUNCT
ejpam-5017	317	1	bull	bull	NOUN
ejpam-5017	317	2	.	.	PUNCT
ejpam-5017	318	1	polish	polish	PROPN
ejpam-5017	318	2	acad	acad	PROPN
ejpam-5017	318	3	.	.	PUNCT
ejpam-5017	319	1	sci.math	sci.math	PROPN
ejpam-5017	319	2	,	,	PUNCT
ejpam-5017	319	3	2001	2001	NUM
ejpam-5017	319	4	.	.	PUNCT