id	sid	tid	token	lemma	pos
ejpam-3479	1	1	european	european	PROPN
ejpam-3479	1	2	journal	journal	PROPN
ejpam-3479	1	3	of	of	ADP
ejpam-3479	1	4	pure	pure	ADJ
ejpam-3479	1	5	and	and	CCONJ
ejpam-3479	1	6	applied	apply	VERB
ejpam-3479	1	7	mathematics	mathematic	NOUN
ejpam-3479	1	8	vol	vol	NOUN
ejpam-3479	1	9	.	.	PROPN
ejpam-3479	2	1	12	12	NUM
ejpam-3479	2	2	,	,	PUNCT
ejpam-3479	2	3	no	no	INTJ
ejpam-3479	2	4	.	.	NOUN
ejpam-3479	2	5	3	3	NUM
ejpam-3479	2	6	,	,	PUNCT
ejpam-3479	2	7	2019	2019	NUM
ejpam-3479	2	8	,	,	PUNCT
ejpam-3479	2	9	1277	1277	NUM
ejpam-3479	2	10	-	-	SYM
ejpam-3479	2	11	1296	1296	NUM
ejpam-3479	2	12	issn	issn	PROPN
ejpam-3479	2	13	1307	1307	NUM
ejpam-3479	2	14	-	-	SYM
ejpam-3479	2	15	5543	5543	NUM
ejpam-3479	2	16	–	–	PUNCT
ejpam-3479	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3479	2	18	published	publish	VERB
ejpam-3479	2	19	by	by	ADP
ejpam-3479	2	20	new	new	PROPN
ejpam-3479	2	21	york	york	PROPN
ejpam-3479	2	22	business	business	PROPN
ejpam-3479	2	23	global	global	ADJ
ejpam-3479	2	24	boundary	boundary	ADJ
ejpam-3479	2	25	sentinel	sentinel	NOUN
ejpam-3479	2	26	with	with	ADP
ejpam-3479	2	27	given	give	VERB
ejpam-3479	2	28	sensitivity	sensitivity	NOUN
ejpam-3479	2	29	in	in	ADP
ejpam-3479	2	30	population	population	NOUN
ejpam-3479	2	31	dynamics	dynamic	NOUN
ejpam-3479	2	32	problem	problem	NOUN
ejpam-3479	2	33	and	and	CCONJ
ejpam-3479	2	34	parameters	parameter	NOUN
ejpam-3479	2	35	identification	identification	NOUN
ejpam-3479	2	36	mifiamba	mifiamba	NOUN
ejpam-3479	2	37	soma1	soma1	PROPN
ejpam-3479	2	38	,	,	PUNCT
ejpam-3479	2	39	somdouda	somdouda	NOUN
ejpam-3479	2	40	sawadogo2,∗	sawadogo2,∗	PROPN
ejpam-3479	2	41	1	1	NUM
ejpam-3479	2	42	département	département	PROPN
ejpam-3479	2	43	de	de	X
ejpam-3479	2	44	mathématiques	mathématiques	X
ejpam-3479	2	45	et	et	PROPN
ejpam-3479	2	46	informatique	informatique	PROPN
ejpam-3479	2	47	,	,	PUNCT
ejpam-3479	2	48	université	université	ADJ
ejpam-3479	2	49	joseph	joseph	PROPN
ejpam-3479	2	50	ki	ki	PROPN
ejpam-3479	2	51	-	-	PUNCT
ejpam-3479	2	52	zerbo	zerbo	PROPN
ejpam-3479	2	53	,	,	PUNCT
ejpam-3479	2	54	ouagadougou	ouagadougou	PROPN
ejpam-3479	2	55	,	,	PUNCT
ejpam-3479	2	56	burkina	burkina	PROPN
ejpam-3479	2	57	faso	faso	PROPN
ejpam-3479	2	58	.	.	PUNCT
ejpam-3479	3	1	2	2	NUM
ejpam-3479	3	2	département	département	PROPN
ejpam-3479	3	3	de	de	X
ejpam-3479	3	4	mathématiques	mathématiques	PROPN
ejpam-3479	3	5	,	,	PUNCT
ejpam-3479	3	6	institut	institut	PROPN
ejpam-3479	3	7	des	des	PROPN
ejpam-3479	3	8	sciences	sciences	PROPN
ejpam-3479	3	9	,	,	PUNCT
ejpam-3479	3	10	ouagadougou	ouagadougou	PROPN
ejpam-3479	3	11	,	,	PUNCT
ejpam-3479	3	12	burkina	burkina	PROPN
ejpam-3479	3	13	faso	faso	PROPN
ejpam-3479	3	14	.	.	PUNCT
ejpam-3479	4	1	abstract	abstract	ADJ
ejpam-3479	4	2	.	.	PUNCT
ejpam-3479	5	1	the	the	DET
ejpam-3479	5	2	notion	notion	NOUN
ejpam-3479	5	3	of	of	ADP
ejpam-3479	5	4	sentinels	sentinel	NOUN
ejpam-3479	5	5	with	with	ADP
ejpam-3479	5	6	given	give	VERB
ejpam-3479	5	7	sensitivity	sensitivity	NOUN
ejpam-3479	5	8	was	be	AUX
ejpam-3479	5	9	introduced	introduce	VERB
ejpam-3479	5	10	by	by	ADP
ejpam-3479	5	11	j.l.lions	j.l.lion	NOUN
ejpam-3479	5	12	[	[	X
ejpam-3479	5	13	11	11	NUM
ejpam-3479	5	14	]	]	PUNCT
ejpam-3479	5	15	in	in	ADP
ejpam-3479	5	16	order	order	NOUN
ejpam-3479	5	17	to	to	PART
ejpam-3479	5	18	identify	identify	VERB
ejpam-3479	5	19	parameters	parameter	NOUN
ejpam-3479	5	20	in	in	ADP
ejpam-3479	5	21	the	the	DET
ejpam-3479	5	22	problem	problem	NOUN
ejpam-3479	5	23	of	of	ADP
ejpam-3479	5	24	pollution	pollution	NOUN
ejpam-3479	5	25	ruled	rule	VERB
ejpam-3479	5	26	by	by	ADP
ejpam-3479	5	27	a	a	DET
ejpam-3479	5	28	parabolic	parabolic	ADJ
ejpam-3479	5	29	equation	equation	NOUN
ejpam-3479	5	30	.	.	PUNCT
ejpam-3479	6	1	he	he	PRON
ejpam-3479	6	2	proves	prove	VERB
ejpam-3479	6	3	that	that	SCONJ
ejpam-3479	6	4	the	the	DET
ejpam-3479	6	5	existence	existence	NOUN
ejpam-3479	6	6	of	of	ADP
ejpam-3479	6	7	such	such	ADJ
ejpam-3479	6	8	sentinels	sentinel	NOUN
ejpam-3479	6	9	is	be	AUX
ejpam-3479	6	10	reduced	reduce	VERB
ejpam-3479	6	11	to	to	ADP
ejpam-3479	6	12	the	the	DET
ejpam-3479	6	13	solution	solution	NOUN
ejpam-3479	6	14	of	of	ADP
ejpam-3479	6	15	exact	exact	ADJ
ejpam-3479	6	16	controllability	controllability	NOUN
ejpam-3479	6	17	problem	problem	NOUN
ejpam-3479	6	18	with	with	ADP
ejpam-3479	6	19	constraints	constraint	NOUN
ejpam-3479	6	20	on	on	ADP
ejpam-3479	6	21	the	the	DET
ejpam-3479	6	22	state	state	NOUN
ejpam-3479	6	23	.	.	PUNCT
ejpam-3479	7	1	in	in	ADP
ejpam-3479	7	2	population	population	NOUN
ejpam-3479	7	3	dynamics	dynamic	NOUN
ejpam-3479	7	4	model	model	NOUN
ejpam-3479	7	5	,	,	PUNCT
ejpam-3479	7	6	we	we	PRON
ejpam-3479	7	7	reconsider	reconsider	VERB
ejpam-3479	7	8	this	this	DET
ejpam-3479	7	9	notion	notion	NOUN
ejpam-3479	7	10	of	of	ADP
ejpam-3479	7	11	sentinels	sentinel	NOUN
ejpam-3479	7	12	in	in	ADP
ejpam-3479	7	13	a	a	DET
ejpam-3479	7	14	more	more	ADV
ejpam-3479	7	15	general	general	ADJ
ejpam-3479	7	16	framework	framework	NOUN
ejpam-3479	7	17	.	.	PUNCT
ejpam-3479	8	1	we	we	PRON
ejpam-3479	8	2	prove	prove	VERB
ejpam-3479	8	3	the	the	DET
ejpam-3479	8	4	existence	existence	NOUN
ejpam-3479	8	5	of	of	ADP
ejpam-3479	8	6	the	the	DET
ejpam-3479	8	7	boundary	boundary	ADJ
ejpam-3479	8	8	sentinels	sentinel	NOUN
ejpam-3479	8	9	by	by	ADP
ejpam-3479	8	10	solving	solve	VERB
ejpam-3479	8	11	a	a	DET
ejpam-3479	8	12	boundary	boundary	ADJ
ejpam-3479	8	13	null	null	ADJ
ejpam-3479	8	14	-	-	PUNCT
ejpam-3479	8	15	controllability	controllability	NOUN
ejpam-3479	8	16	problem	problem	NOUN
ejpam-3479	8	17	with	with	ADP
ejpam-3479	8	18	constraint	constraint	NOUN
ejpam-3479	8	19	on	on	ADP
ejpam-3479	8	20	the	the	DET
ejpam-3479	8	21	control	control	NOUN
ejpam-3479	8	22	.	.	PUNCT
ejpam-3479	9	1	our	our	PRON
ejpam-3479	9	2	results	result	NOUN
ejpam-3479	9	3	use	use	VERB
ejpam-3479	9	4	carleman	carleman	ADJ
ejpam-3479	9	5	inequality	inequality	NOUN
ejpam-3479	9	6	which	which	PRON
ejpam-3479	9	7	is	be	AUX
ejpam-3479	9	8	adapted	adapt	VERB
ejpam-3479	9	9	to	to	ADP
ejpam-3479	9	10	the	the	DET
ejpam-3479	9	11	constraint	constraint	NOUN
ejpam-3479	9	12	.	.	PUNCT
ejpam-3479	10	1	2010	2010	NUM
ejpam-3479	10	2	mathematics	mathematic	NOUN
ejpam-3479	10	3	subject	subject	NOUN
ejpam-3479	10	4	classifications	classification	NOUN
ejpam-3479	10	5	:	:	PUNCT
ejpam-3479	10	6	49j20	49j20	NUM
ejpam-3479	10	7	,	,	PUNCT
ejpam-3479	10	8	93b05	93b05	NUM
ejpam-3479	10	9	,	,	PUNCT
ejpam-3479	10	10	92d25	92d25	NUM
ejpam-3479	10	11	,	,	PUNCT
ejpam-3479	10	12	35q92	35q92	NUM
ejpam-3479	10	13	,	,	PUNCT
ejpam-3479	10	14	35q93	35q93	NUM
ejpam-3479	10	15	key	key	ADJ
ejpam-3479	10	16	words	word	NOUN
ejpam-3479	10	17	and	and	CCONJ
ejpam-3479	10	18	phrases	phrase	NOUN
ejpam-3479	10	19	:	:	PUNCT
ejpam-3479	10	20	population	population	NOUN
ejpam-3479	10	21	dynamics	dynamic	NOUN
ejpam-3479	10	22	,	,	PUNCT
ejpam-3479	10	23	optimal	optimal	ADJ
ejpam-3479	10	24	control	control	NOUN
ejpam-3479	10	25	,	,	PUNCT
ejpam-3479	10	26	controllability	controllability	NOUN
ejpam-3479	10	27	,	,	PUNCT
ejpam-3479	10	28	sentinels	sentinel	NOUN
ejpam-3479	10	29	,	,	PUNCT
ejpam-3479	10	30	carleman	carleman	ADJ
ejpam-3479	10	31	inequality	inequality	NOUN
ejpam-3479	10	32	1	1	NUM
ejpam-3479	10	33	.	.	PUNCT
ejpam-3479	10	34	introduction	introduction	NOUN
ejpam-3479	10	35	the	the	DET
ejpam-3479	10	36	notion	notion	NOUN
ejpam-3479	10	37	of	of	ADP
ejpam-3479	10	38	sentinel	sentinel	NOUN
ejpam-3479	10	39	was	be	AUX
ejpam-3479	10	40	introduced	introduce	VERB
ejpam-3479	10	41	by	by	ADP
ejpam-3479	10	42	j.l.lions	j.l.lion	NOUN
ejpam-3479	10	43	to	to	PART
ejpam-3479	10	44	study	study	VERB
ejpam-3479	10	45	systems	system	NOUN
ejpam-3479	10	46	with	with	ADP
ejpam-3479	10	47	incomplete	incomplete	ADJ
ejpam-3479	10	48	data	datum	NOUN
ejpam-3479	11	1	[	[	X
ejpam-3479	11	2	11	11	NUM
ejpam-3479	11	3	]	]	PUNCT
ejpam-3479	11	4	.	.	PUNCT
ejpam-3479	12	1	the	the	DET
ejpam-3479	12	2	notion	notion	NOUN
ejpam-3479	12	3	permits	permit	VERB
ejpam-3479	12	4	us	we	PRON
ejpam-3479	12	5	to	to	PART
ejpam-3479	12	6	distinguish	distinguish	VERB
ejpam-3479	12	7	and	and	CCONJ
ejpam-3479	12	8	to	to	PART
ejpam-3479	12	9	analyse	analyse	VERB
ejpam-3479	12	10	two	two	NUM
ejpam-3479	12	11	types	type	NOUN
ejpam-3479	12	12	of	of	ADP
ejpam-3479	12	13	incomplete	incomplete	ADJ
ejpam-3479	12	14	data	datum	NOUN
ejpam-3479	12	15	:	:	PUNCT
ejpam-3479	12	16	the	the	DET
ejpam-3479	12	17	so	so	ADV
ejpam-3479	12	18	-	-	PUNCT
ejpam-3479	12	19	called	call	VERB
ejpam-3479	12	20	pollution	pollution	NOUN
ejpam-3479	12	21	terms	term	NOUN
ejpam-3479	12	22	at	at	ADP
ejpam-3479	12	23	which	which	PRON
ejpam-3479	12	24	we	we	PRON
ejpam-3479	12	25	look	look	VERB
ejpam-3479	12	26	for	for	ADP
ejpam-3479	12	27	information	information	NOUN
ejpam-3479	12	28	,	,	PUNCT
ejpam-3479	12	29	independently	independently	ADV
ejpam-3479	12	30	of	of	ADP
ejpam-3479	12	31	the	the	DET
ejpam-3479	12	32	other	other	ADJ
ejpam-3479	12	33	type	type	NOUN
ejpam-3479	12	34	of	of	ADP
ejpam-3479	12	35	incomplete	incomplete	ADJ
ejpam-3479	12	36	data	datum	NOUN
ejpam-3479	12	37	which	which	PRON
ejpam-3479	12	38	is	be	AUX
ejpam-3479	12	39	the	the	DET
ejpam-3479	12	40	missing	missing	ADJ
ejpam-3479	12	41	terms	term	NOUN
ejpam-3479	12	42	and	and	CCONJ
ejpam-3479	12	43	that	that	SCONJ
ejpam-3479	12	44	we	we	PRON
ejpam-3479	12	45	do	do	AUX
ejpam-3479	12	46	not	not	PART
ejpam-3479	12	47	want	want	VERB
ejpam-3479	12	48	to	to	PART
ejpam-3479	12	49	identify	identify	VERB
ejpam-3479	12	50	.	.	PUNCT
ejpam-3479	13	1	typically	typically	ADV
ejpam-3479	13	2	,	,	PUNCT
ejpam-3479	13	3	the	the	DET
ejpam-3479	13	4	lions	lion	NOUN
ejpam-3479	13	5	’s	’s	PART
ejpam-3479	13	6	sentinel	sentinel	NOUN
ejpam-3479	13	7	is	be	AUX
ejpam-3479	13	8	a	a	DET
ejpam-3479	13	9	functional	functional	ADJ
ejpam-3479	13	10	defined	define	VERB
ejpam-3479	13	11	on	on	ADP
ejpam-3479	13	12	an	an	DET
ejpam-3479	13	13	open	open	ADJ
ejpam-3479	13	14	set	set	NOUN
ejpam-3479	13	15	o	o	NOUN
ejpam-3479	13	16	where	where	SCONJ
ejpam-3479	13	17	we	we	PRON
ejpam-3479	13	18	consider	consider	VERB
ejpam-3479	13	19	three	three	NUM
ejpam-3479	13	20	functions	function	NOUN
ejpam-3479	13	21	:	:	PUNCT
ejpam-3479	13	22	the	the	DET
ejpam-3479	13	23	”	"	PUNCT
ejpam-3479	13	24	observation	observation	NOUN
ejpam-3479	13	25	”	"	PUNCT
ejpam-3479	13	26	yobs	yob	NOUN
ejpam-3479	13	27	corresponding	correspond	VERB
ejpam-3479	13	28	to	to	ADP
ejpam-3479	13	29	measurements	measurement	NOUN
ejpam-3479	13	30	,	,	PUNCT
ejpam-3479	13	31	a	a	DET
ejpam-3479	13	32	given	give	VERB
ejpam-3479	13	33	”	"	PUNCT
ejpam-3479	13	34	mean	mean	ADJ
ejpam-3479	13	35	”	"	PUNCT
ejpam-3479	13	36	function	function	NOUN
ejpam-3479	13	37	h0	h0	PROPN
ejpam-3479	13	38	,	,	PUNCT
ejpam-3479	13	39	and	and	CCONJ
ejpam-3479	13	40	a	a	DET
ejpam-3479	13	41	control	control	NOUN
ejpam-3479	13	42	function	function	NOUN
ejpam-3479	13	43	w	w	NOUN
ejpam-3479	13	44	to	to	PART
ejpam-3479	13	45	be	be	AUX
ejpam-3479	13	46	determined	determine	VERB
ejpam-3479	13	47	.	.	PUNCT
ejpam-3479	14	1	let	let	VERB
ejpam-3479	14	2	us	we	PRON
ejpam-3479	14	3	remind	remind	VERB
ejpam-3479	14	4	that	that	SCONJ
ejpam-3479	14	5	lions	lion	NOUN
ejpam-3479	14	6	’s	’s	PART
ejpam-3479	14	7	sentinel	sentinel	ADJ
ejpam-3479	14	8	theory	theory	NOUN
ejpam-3479	14	9	[	[	X
ejpam-3479	14	10	11	11	NUM
ejpam-3479	14	11	]	]	PUNCT
ejpam-3479	14	12	relies	rely	VERB
ejpam-3479	14	13	on	on	ADP
ejpam-3479	14	14	the	the	DET
ejpam-3479	14	15	following	follow	VERB
ejpam-3479	14	16	three	three	NUM
ejpam-3479	14	17	features	feature	NOUN
ejpam-3479	14	18	:	:	PUNCT
ejpam-3479	14	19	the	the	DET
ejpam-3479	14	20	state	state	NOUN
ejpam-3479	14	21	equation	equation	NOUN
ejpam-3479	14	22	y	y	PROPN
ejpam-3479	14	23	which	which	PRON
ejpam-3479	14	24	is	be	AUX
ejpam-3479	14	25	governed	govern	VERB
ejpam-3479	14	26	by	by	ADP
ejpam-3479	14	27	a	a	DET
ejpam-3479	14	28	partial	partial	ADJ
ejpam-3479	14	29	differential	differential	NOUN
ejpam-3479	14	30	equation	equation	NOUN
ejpam-3479	14	31	,	,	PUNCT
ejpam-3479	14	32	the	the	DET
ejpam-3479	14	33	observation	observation	NOUN
ejpam-3479	14	34	system	system	NOUN
ejpam-3479	14	35	and	and	CCONJ
ejpam-3479	14	36	some	some	DET
ejpam-3479	14	37	particular	particular	ADJ
ejpam-3479	14	38	evaluation	evaluation	NOUN
ejpam-3479	14	39	function	function	NOUN
ejpam-3479	14	40	:	:	PUNCT
ejpam-3479	14	41	the	the	DET
ejpam-3479	14	42	sentinel	sentinel	NOUN
ejpam-3479	14	43	itself	itself	PRON
ejpam-3479	14	44	.	.	PUNCT
ejpam-3479	15	1	more	more	ADV
ejpam-3479	15	2	precisely	precisely	ADV
ejpam-3479	15	3	,	,	PUNCT
ejpam-3479	15	4	we	we	PRON
ejpam-3479	15	5	consider	consider	VERB
ejpam-3479	15	6	a	a	DET
ejpam-3479	15	7	linear	linear	ADJ
ejpam-3479	15	8	model	model	NOUN
ejpam-3479	15	9	(	(	PUNCT
ejpam-3479	15	10	1	1	X
ejpam-3479	15	11	)	)	PUNCT
ejpam-3479	15	12	describing	describe	VERB
ejpam-3479	15	13	the	the	DET
ejpam-3479	15	14	dynamics	dynamic	NOUN
ejpam-3479	15	15	of	of	ADP
ejpam-3479	15	16	population	population	NOUN
ejpam-3479	15	17	with	with	ADP
ejpam-3479	15	18	age	age	NOUN
ejpam-3479	15	19	dependence	dependence	NOUN
ejpam-3479	15	20	,	,	PUNCT
ejpam-3479	15	21	spatial	spatial	ADJ
ejpam-3479	15	22	structure	structure	NOUN
ejpam-3479	15	23	with	with	ADP
ejpam-3479	15	24	incomplete	incomplete	ADJ
ejpam-3479	15	25	data	datum	NOUN
ejpam-3479	15	26	.	.	PUNCT
ejpam-3479	16	1	∗corresponding	∗corresponde	VERB
ejpam-3479	16	2	author	author	NOUN
ejpam-3479	16	3	.	.	PUNCT
ejpam-3479	17	1	doi	doi	PROPN
ejpam-3479	17	2	:	:	PUNCT
ejpam-3479	17	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3479	https://doi.org/10.29020/nybg.ejpam.v12i3.3479	PROPN
ejpam-3479	17	4	email	email	NOUN
ejpam-3479	17	5	addresses	address	VERB
ejpam-3479	17	6	:	:	PUNCT
ejpam-3479	17	7	mifiambasoma@yahoo.fr	mifiambasoma@yahoo.fr	PROPN
ejpam-3479	17	8	(	(	PUNCT
ejpam-3479	17	9	m.	m.	NOUN
ejpam-3479	17	10	soma	soma	PROPN
ejpam-3479	17	11	)	)	PUNCT
ejpam-3479	17	12	,	,	PUNCT
ejpam-3479	17	13	sawasom@yahoo.fr	sawasom@yahoo.fr	PROPN
ejpam-3479	17	14	(	(	PUNCT
ejpam-3479	17	15	s.	s.	PROPN
ejpam-3479	17	16	sawadogo	sawadogo	PROPN
ejpam-3479	17	17	)	)	PUNCT
ejpam-3479	17	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3479	18	1	1277	1277	NUM
ejpam-3479	19	1	c	c	NOUN
ejpam-3479	19	2	©	©	PROPN
ejpam-3479	19	3	2019	2019	NUM
ejpam-3479	19	4	ejpam	ejpam	NOUN
ejpam-3479	19	5	all	all	DET
ejpam-3479	19	6	rights	right	NOUN
ejpam-3479	19	7	reserved	reserve	VERB
ejpam-3479	19	8	.	.	PUNCT
ejpam-3479	20	1	m.soma	m.soma	ADV
ejpam-3479	20	2	,	,	PUNCT
ejpam-3479	20	3	s.	s.	PROPN
ejpam-3479	20	4	sawadogo	sawadogo	PROPN
ejpam-3479	20	5	/	/	SYM
ejpam-3479	20	6	eur	eur	PROPN
ejpam-3479	20	7	.	.	PUNCT
ejpam-3479	21	1	j.	j.	PROPN
ejpam-3479	21	2	pure	pure	PROPN
ejpam-3479	21	3	appl	appl	PROPN
ejpam-3479	21	4	.	.	PROPN
ejpam-3479	21	5	math	math	PROPN
ejpam-3479	21	6	,	,	PUNCT
ejpam-3479	21	7	12	12	NUM
ejpam-3479	21	8	(	(	PUNCT
ejpam-3479	21	9	3	3	NUM
ejpam-3479	21	10	)	)	PUNCT
ejpam-3479	21	11	(	(	PUNCT
ejpam-3479	21	12	2019	2019	NUM
ejpam-3479	21	13	)	)	PUNCT
ejpam-3479	21	14	,	,	PUNCT
ejpam-3479	21	15	1277	1277	NUM
ejpam-3479	21	16	-	-	SYM
ejpam-3479	21	17	1296	1296	NUM
ejpam-3479	21	18	1278	1278	NUM
ejpam-3479	21	19	let	let	VERB
ejpam-3479	21	20	ω	ω	NUM
ejpam-3479	21	21	be	be	AUX
ejpam-3479	21	22	an	an	DET
ejpam-3479	21	23	open	open	ADJ
ejpam-3479	21	24	and	and	CCONJ
ejpam-3479	21	25	bounded	bounded	ADJ
ejpam-3479	21	26	domain	domain	NOUN
ejpam-3479	21	27	of	of	ADP
ejpam-3479	21	28	rn	rn	PROPN
ejpam-3479	21	29	,	,	PUNCT
ejpam-3479	21	30	n	n	PROPN
ejpam-3479	21	31	∈	∈	PROPN
ejpam-3479	21	32	{	{	PUNCT
ejpam-3479	21	33	1	1	NUM
ejpam-3479	21	34	,	,	PUNCT
ejpam-3479	21	35	2	2	NUM
ejpam-3479	21	36	,	,	PUNCT
ejpam-3479	21	37	3	3	NUM
ejpam-3479	21	38	}	}	PUNCT
ejpam-3479	21	39	,	,	PUNCT
ejpam-3479	21	40	with	with	ADP
ejpam-3479	21	41	boundary	boundary	ADJ
ejpam-3479	21	42	γ	γ	NOUN
ejpam-3479	21	43	of	of	ADP
ejpam-3479	21	44	c∞.	c∞.	PROPN
ejpam-3479	21	45	for	for	ADP
ejpam-3479	21	46	the	the	DET
ejpam-3479	21	47	time	time	NOUN
ejpam-3479	21	48	t	t	PROPN
ejpam-3479	21	49	>	>	X
ejpam-3479	21	50	0	0	PUNCT
ejpam-3479	22	1	and	and	CCONJ
ejpam-3479	22	2	the	the	DET
ejpam-3479	22	3	life	life	NOUN
ejpam-3479	22	4	expectancy	expectancy	NOUN
ejpam-3479	22	5	of	of	ADP
ejpam-3479	22	6	an	an	DET
ejpam-3479	22	7	individual	individual	NOUN
ejpam-3479	22	8	a	a	DET
ejpam-3479	22	9	>	>	X
ejpam-3479	22	10	0	0	NUM
ejpam-3479	22	11	,	,	PUNCT
ejpam-3479	22	12	we	we	PRON
ejpam-3479	22	13	set	set	VERB
ejpam-3479	22	14	u	u	PRON
ejpam-3479	22	15	=	=	SYM
ejpam-3479	22	16	(	(	PUNCT
ejpam-3479	22	17	0	0	NUM
ejpam-3479	22	18	,	,	PUNCT
ejpam-3479	22	19	t	t	NOUN
ejpam-3479	22	20	)	)	PUNCT
ejpam-3479	22	21	×	×	NOUN
ejpam-3479	22	22	(	(	PUNCT
ejpam-3479	22	23	0	0	NUM
ejpam-3479	22	24	,	,	PUNCT
ejpam-3479	22	25	a	a	PRON
ejpam-3479	22	26	)	)	PUNCT
ejpam-3479	22	27	,	,	PUNCT
ejpam-3479	22	28	q	q	NOUN
ejpam-3479	22	29	=	=	PUNCT
ejpam-3479	22	30	u	u	NOUN
ejpam-3479	22	31	×	×	PROPN
ejpam-3479	22	32	ω	ω	PROPN
ejpam-3479	22	33	,	,	PUNCT
ejpam-3479	22	34	qa	qa	X
ejpam-3479	22	35	=	=	SYM
ejpam-3479	22	36	(	(	PUNCT
ejpam-3479	22	37	0	0	NUM
ejpam-3479	22	38	,	,	PUNCT
ejpam-3479	22	39	a	a	PRON
ejpam-3479	22	40	)	)	PUNCT
ejpam-3479	22	41	×	×	PROPN
ejpam-3479	22	42	ω	ω	PROPN
ejpam-3479	22	43	,	,	PUNCT
ejpam-3479	22	44	qt	qt	NOUN
ejpam-3479	22	45	=	=	SYM
ejpam-3479	22	46	(	(	PUNCT
ejpam-3479	22	47	0	0	NUM
ejpam-3479	22	48	,	,	PUNCT
ejpam-3479	22	49	t	t	PROPN
ejpam-3479	22	50	)	)	PUNCT
ejpam-3479	22	51	×	×	PROPN
ejpam-3479	22	52	ω	ω	PROPN
ejpam-3479	22	53	,	,	PUNCT
ejpam-3479	22	54	σ	σ	PROPN
ejpam-3479	22	55	=	=	PUNCT
ejpam-3479	22	56	u	u	PROPN
ejpam-3479	22	57	×	×	PROPN
ejpam-3479	22	58	γ	γ	X
ejpam-3479	22	59	,	,	PUNCT
ejpam-3479	22	60	σ1	σ1	PROPN
ejpam-3479	22	61	=	=	SYM
ejpam-3479	22	62	u	u	PROPN
ejpam-3479	22	63	×	×	NOUN
ejpam-3479	22	64	γ1	γ1	NOUN
ejpam-3479	22	65	,	,	PUNCT
ejpam-3479	22	66	where	where	SCONJ
ejpam-3479	22	67	γ1	γ1	PROPN
ejpam-3479	22	68	is	be	AUX
ejpam-3479	22	69	a	a	DET
ejpam-3479	22	70	non	non	ADJ
ejpam-3479	22	71	-	-	ADJ
ejpam-3479	22	72	empty	empty	ADJ
ejpam-3479	22	73	open	open	ADJ
ejpam-3479	22	74	subset	subset	NOUN
ejpam-3479	22	75	of	of	ADP
ejpam-3479	22	76	γ	γ	PROPN
ejpam-3479	22	77	.	.	PROPN
ejpam-3479	22	78	then	then	ADV
ejpam-3479	22	79	consider	consider	VERB
ejpam-3479	22	80	the	the	DET
ejpam-3479	22	81	following	follow	VERB
ejpam-3479	22	82	two	two	NUM
ejpam-3479	22	83	stroke	stroke	NOUN
ejpam-3479	22	84	problem:	problem:	PROPN
ejpam-3479	22	85	∂y	∂y	PROPN
ejpam-3479	22	86	∂t	∂t	PROPN
ejpam-3479	22	87	+	+	CCONJ
ejpam-3479	22	88	∂y	∂y	PROPN
ejpam-3479	22	89	∂a	∂a	PROPN
ejpam-3479	22	90	−∆y	−∆y	NOUN
ejpam-3479	22	91	+	+	CCONJ
ejpam-3479	22	92	µy	µy	VERB
ejpam-3479	22	93	=	=	SYM
ejpam-3479	22	94	0	0	NUM
ejpam-3479	22	95	in	in	ADP
ejpam-3479	22	96	q	q	PROPN
ejpam-3479	22	97	y(0	y(0	PROPN
ejpam-3479	22	98	,	,	PUNCT
ejpam-3479	22	99	a	a	DET
ejpam-3479	22	100	,	,	PUNCT
ejpam-3479	22	101	x	x	NOUN
ejpam-3479	22	102	)	)	PUNCT
ejpam-3479	23	1	=	=	SYM
ejpam-3479	23	2	y0	y0	NOUN
ejpam-3479	23	3	+	+	CCONJ
ejpam-3479	23	4	τ	τ	PROPN
ejpam-3479	23	5	ŷ0	ŷ0	NOUN
ejpam-3479	23	6	in	in	ADP
ejpam-3479	23	7	qa	qa	PROPN
ejpam-3479	23	8	y(t	y(t	PROPN
ejpam-3479	23	9	,	,	PUNCT
ejpam-3479	23	10	0	0	NUM
ejpam-3479	23	11	,	,	PUNCT
ejpam-3479	23	12	x	x	NOUN
ejpam-3479	23	13	)	)	PUNCT
ejpam-3479	23	14	=	=	SYM
ejpam-3479	24	1	∫	∫	PROPN
ejpam-3479	24	2	a	a	DET
ejpam-3479	24	3	0	0	NUM
ejpam-3479	24	4	β(t	β(t	PROPN
ejpam-3479	24	5	,	,	PUNCT
ejpam-3479	24	6	a	a	PRON
ejpam-3479	24	7	,	,	PUNCT
ejpam-3479	24	8	x)y(t	x)y(t	PROPN
ejpam-3479	24	9	,	,	PUNCT
ejpam-3479	24	10	a	a	PRON
ejpam-3479	24	11	,	,	PUNCT
ejpam-3479	24	12	x)da	x)da	PROPN
ejpam-3479	24	13	in	in	ADP
ejpam-3479	24	14	qt	qt	NOUN
ejpam-3479	24	15	y	y	NOUN
ejpam-3479	24	16	=	=	PUNCT
ejpam-3479	25	1			PROPN
ejpam-3479	25	2	ξ	ξ	PROPN
ejpam-3479	25	3	+	+	CCONJ
ejpam-3479	25	4	m∑	m∑	INTJ
ejpam-3479	25	5	i=1	i=1	PROPN
ejpam-3479	25	6	λiξ̂i	λiξ̂i	PROPN
ejpam-3479	25	7	on	on	ADP
ejpam-3479	25	8	σ1	σ1	PROPN
ejpam-3479	25	9	0	0	NUM
ejpam-3479	25	10	on	on	ADP
ejpam-3479	25	11	σ	σ	PROPN
ejpam-3479	25	12	\	\	PROPN
ejpam-3479	25	13	σ1	σ1	PROPN
ejpam-3479	25	14	(	(	PUNCT
ejpam-3479	25	15	1	1	NUM
ejpam-3479	25	16	)	)	PUNCT
ejpam-3479	25	17	where	where	SCONJ
ejpam-3479	25	18	:	:	PUNCT
ejpam-3479	25	19	y(t	y(t	PROPN
ejpam-3479	25	20	,	,	PUNCT
ejpam-3479	25	21	a	a	PRON
ejpam-3479	25	22	,	,	PUNCT
ejpam-3479	25	23	x	x	X
ejpam-3479	25	24	)	)	PUNCT
ejpam-3479	25	25	is	be	AUX
ejpam-3479	25	26	the	the	DET
ejpam-3479	25	27	distribution	distribution	NOUN
ejpam-3479	25	28	of	of	ADP
ejpam-3479	25	29	a	a	DET
ejpam-3479	25	30	-	-	PUNCT
ejpam-3479	25	31	year	year	NOUN
ejpam-3479	25	32	old	old	ADJ
ejpam-3479	25	33	individuals	individual	NOUN
ejpam-3479	25	34	at	at	ADP
ejpam-3479	25	35	time	time	NOUN
ejpam-3479	25	36	t	t	NOUN
ejpam-3479	25	37	at	at	ADP
ejpam-3479	25	38	the	the	DET
ejpam-3479	25	39	point	point	NOUN
ejpam-3479	25	40	x	x	X
ejpam-3479	25	41	∈	∈	PROPN
ejpam-3479	25	42	ω	ω	PROPN
ejpam-3479	25	43	.	.	PUNCT
ejpam-3479	26	1	β(t	β(t	PROPN
ejpam-3479	26	2	,	,	PUNCT
ejpam-3479	26	3	a	a	PRON
ejpam-3479	26	4	,	,	PUNCT
ejpam-3479	26	5	x	x	NOUN
ejpam-3479	26	6	)	)	PUNCT
ejpam-3479	26	7	≥	≥	NOUN
ejpam-3479	26	8	0	0	NUM
ejpam-3479	26	9	and	and	CCONJ
ejpam-3479	26	10	µ(t	µ(t	ADJ
ejpam-3479	26	11	,	,	PUNCT
ejpam-3479	26	12	a	a	DET
ejpam-3479	26	13	,	,	PUNCT
ejpam-3479	26	14	x	x	NOUN
ejpam-3479	26	15	)	)	PUNCT
ejpam-3479	26	16	≥	≥	X
ejpam-3479	26	17	0	0	NUM
ejpam-3479	26	18	are	be	AUX
ejpam-3479	26	19	respectively	respectively	ADV
ejpam-3479	26	20	the	the	DET
ejpam-3479	26	21	natural	natural	ADJ
ejpam-3479	26	22	fertility	fertility	NOUN
ejpam-3479	26	23	and	and	CCONJ
ejpam-3479	26	24	the	the	DET
ejpam-3479	26	25	natural	natural	ADJ
ejpam-3479	26	26	death	death	NOUN
ejpam-3479	26	27	rate	rate	NOUN
ejpam-3479	26	28	of	of	ADP
ejpam-3479	26	29	age	age	NOUN
ejpam-3479	26	30	a	a	DET
ejpam-3479	26	31	at	at	ADP
ejpam-3479	26	32	time	time	NOUN
ejpam-3479	26	33	t	t	NOUN
ejpam-3479	26	34	and	and	CCONJ
ejpam-3479	26	35	position	position	NOUN
ejpam-3479	26	36	x	x	X
ejpam-3479	26	37	∈	∈	PROPN
ejpam-3479	26	38	ω	ω	PROPN
ejpam-3479	26	39	.	.	PUNCT
ejpam-3479	27	1	thus	thus	ADV
ejpam-3479	27	2	,	,	PUNCT
ejpam-3479	27	3	the	the	DET
ejpam-3479	27	4	formula	formula	NOUN
ejpam-3479	27	5	∫	∫	PROPN
ejpam-3479	27	6	a	a	DET
ejpam-3479	27	7	0	0	NUM
ejpam-3479	27	8	β(t	β(t	PROPN
ejpam-3479	27	9	,	,	PUNCT
ejpam-3479	27	10	a	a	PRON
ejpam-3479	27	11	,	,	PUNCT
ejpam-3479	27	12	x)y(t	x)y(t	PROPN
ejpam-3479	27	13	,	,	PUNCT
ejpam-3479	27	14	a	a	PRON
ejpam-3479	27	15	,	,	PUNCT
ejpam-3479	27	16	x)da	x)da	PROPN
ejpam-3479	27	17	denotes	denote	VERB
ejpam-3479	27	18	the	the	DET
ejpam-3479	27	19	distribution	distribution	NOUN
ejpam-3479	27	20	of	of	ADP
ejpam-3479	27	21	newborn	newborn	ADJ
ejpam-3479	27	22	individuals	individual	NOUN
ejpam-3479	27	23	at	at	ADP
ejpam-3479	27	24	time	time	NOUN
ejpam-3479	27	25	t	t	PROPN
ejpam-3479	27	26	and	and	CCONJ
ejpam-3479	27	27	location	location	NOUN
ejpam-3479	27	28	x.	x.	NOUN
ejpam-3479	28	1	the	the	DET
ejpam-3479	28	2	boundary	boundary	ADJ
ejpam-3479	28	3	condition	condition	NOUN
ejpam-3479	28	4	is	be	AUX
ejpam-3479	28	5	unknown	unknown	ADJ
ejpam-3479	28	6	on	on	ADP
ejpam-3479	28	7	a	a	DET
ejpam-3479	28	8	part	part	NOUN
ejpam-3479	28	9	σ1	σ1	NOUN
ejpam-3479	28	10	of	of	ADP
ejpam-3479	28	11	the	the	DET
ejpam-3479	28	12	boundary	boundary	NOUN
ejpam-3479	28	13	and	and	CCONJ
ejpam-3479	28	14	represents	represent	VERB
ejpam-3479	28	15	a	a	DET
ejpam-3479	28	16	pollution	pollution	NOUN
ejpam-3479	28	17	with	with	ADP
ejpam-3479	28	18	a	a	DET
ejpam-3479	28	19	structure	structure	NOUN
ejpam-3479	28	20	of	of	ADP
ejpam-3479	28	21	the	the	DET
ejpam-3479	28	22	form	form	NOUN
ejpam-3479	28	23	ξ	ξ	PROPN
ejpam-3479	28	24	+	+	NUM
ejpam-3479	28	25	m∑	m∑	INTJ
ejpam-3479	28	26	i=1	i=1	PROPN
ejpam-3479	28	27	λiξ̂i	λiξ̂i	PROPN
ejpam-3479	28	28	.	.	PUNCT
ejpam-3479	29	1	in	in	ADP
ejpam-3479	29	2	this	this	DET
ejpam-3479	29	3	structure	structure	NOUN
ejpam-3479	29	4	,	,	PUNCT
ejpam-3479	29	5	the	the	DET
ejpam-3479	29	6	functions	function	NOUN
ejpam-3479	29	7	ξ	ξ	PROPN
ejpam-3479	29	8	and	and	CCONJ
ejpam-3479	29	9	ξ̂i	ξ̂i	NUM
ejpam-3479	29	10	,	,	PUNCT
ejpam-3479	29	11	i	i	PRON
ejpam-3479	29	12	=	=	NOUN
ejpam-3479	29	13	1	1	NUM
ejpam-3479	29	14	,	,	PUNCT
ejpam-3479	29	15	.	.	PUNCT
ejpam-3479	29	16	.	.	PUNCT
ejpam-3479	30	1	.m	.m	PROPN
ejpam-3479	30	2	are	be	AUX
ejpam-3479	30	3	known	know	VERB
ejpam-3479	30	4	whereas	whereas	SCONJ
ejpam-3479	30	5	the	the	DET
ejpam-3479	30	6	real	real	ADJ
ejpam-3479	30	7	λi	λi	NOUN
ejpam-3479	30	8	,	,	PUNCT
ejpam-3479	30	9	i	i	NOUN
ejpam-3479	30	10	=	=	NOUN
ejpam-3479	30	11	1	1	NUM
ejpam-3479	30	12	,	,	PUNCT
ejpam-3479	30	13	.	.	PUNCT
ejpam-3479	30	14	.	.	PUNCT
ejpam-3479	31	1	.m	.m	PROPN
ejpam-3479	31	2	are	be	AUX
ejpam-3479	31	3	unknown	unknown	ADJ
ejpam-3479	31	4	.	.	PUNCT
ejpam-3479	32	1	the	the	DET
ejpam-3479	32	2	initial	initial	ADJ
ejpam-3479	32	3	distribution	distribution	NOUN
ejpam-3479	32	4	of	of	ADP
ejpam-3479	32	5	individuals	individual	NOUN
ejpam-3479	32	6	is	be	AUX
ejpam-3479	32	7	unknown	unknown	ADJ
ejpam-3479	32	8	and	and	CCONJ
ejpam-3479	32	9	its	its	PRON
ejpam-3479	32	10	structure	structure	NOUN
ejpam-3479	32	11	is	be	AUX
ejpam-3479	32	12	of	of	ADP
ejpam-3479	32	13	the	the	DET
ejpam-3479	32	14	form	form	NOUN
ejpam-3479	32	15	y0+τ	y0+τ	PROPN
ejpam-3479	32	16	ŷ0	ŷ0	PROPN
ejpam-3479	32	17	where	where	SCONJ
ejpam-3479	32	18	the	the	DET
ejpam-3479	32	19	function	function	NOUN
ejpam-3479	32	20	y0	y0	PROPN
ejpam-3479	32	21	is	be	AUX
ejpam-3479	32	22	known	know	VERB
ejpam-3479	32	23	and	and	CCONJ
ejpam-3479	32	24	the	the	DET
ejpam-3479	32	25	term	term	NOUN
ejpam-3479	32	26	τ	τ	PROPN
ejpam-3479	32	27	ŷ0	ŷ0	PROPN
ejpam-3479	32	28	is	be	AUX
ejpam-3479	32	29	unknown	unknown	ADJ
ejpam-3479	32	30	.	.	PUNCT
ejpam-3479	33	1	system	system	NOUN
ejpam-3479	33	2	(	(	PUNCT
ejpam-3479	33	3	1	1	X
ejpam-3479	33	4	)	)	PUNCT
ejpam-3479	33	5	is	be	AUX
ejpam-3479	33	6	a	a	DET
ejpam-3479	33	7	system	system	NOUN
ejpam-3479	33	8	with	with	ADP
ejpam-3479	33	9	incomplete	incomplete	ADJ
ejpam-3479	33	10	data	datum	NOUN
ejpam-3479	33	11	because	because	SCONJ
ejpam-3479	33	12	the	the	DET
ejpam-3479	33	13	information	information	NOUN
ejpam-3479	33	14	on	on	ADP
ejpam-3479	33	15	the	the	DET
ejpam-3479	33	16	boundary	boundary	ADJ
ejpam-3479	33	17	condition	condition	NOUN
ejpam-3479	33	18	as	as	ADV
ejpam-3479	33	19	well	well	ADV
ejpam-3479	33	20	as	as	ADP
ejpam-3479	33	21	on	on	ADP
ejpam-3479	33	22	the	the	DET
ejpam-3479	33	23	initial	initial	ADJ
ejpam-3479	33	24	condition	condition	NOUN
ejpam-3479	33	25	are	be	AUX
ejpam-3479	33	26	partially	partially	ADV
ejpam-3479	33	27	or	or	CCONJ
ejpam-3479	33	28	completely	completely	ADV
ejpam-3479	33	29	unknown	unknown	ADJ
ejpam-3479	33	30	.	.	PUNCT
ejpam-3479	34	1	here	here	ADV
ejpam-3479	34	2	,	,	PUNCT
ejpam-3479	34	3	the	the	DET
ejpam-3479	34	4	pollution	pollution	NOUN
ejpam-3479	34	5	is	be	AUX
ejpam-3479	34	6	isolated	isolate	VERB
ejpam-3479	34	7	on	on	ADP
ejpam-3479	34	8	the	the	DET
ejpam-3479	34	9	boundary	boundary	ADJ
ejpam-3479	34	10	γ\γ1	γ\γ1	NOUN
ejpam-3479	34	11	.	.	PUNCT
ejpam-3479	35	1	the	the	DET
ejpam-3479	35	2	missing	missing	ADJ
ejpam-3479	35	3	term	term	NOUN
ejpam-3479	35	4	is	be	AUX
ejpam-3479	35	5	located	locate	VERB
ejpam-3479	35	6	in	in	ADP
ejpam-3479	35	7	the	the	DET
ejpam-3479	35	8	initial	initial	ADJ
ejpam-3479	35	9	conditions	condition	NOUN
ejpam-3479	35	10	.	.	PUNCT
ejpam-3479	36	1	in	in	ADP
ejpam-3479	36	2	what	what	PRON
ejpam-3479	36	3	follows	follow	VERB
ejpam-3479	36	4	,	,	PUNCT
ejpam-3479	36	5	we	we	PRON
ejpam-3479	36	6	assume	assume	VERB
ejpam-3479	36	7	as	as	ADP
ejpam-3479	36	8	in	in	ADP
ejpam-3479	36	9	[	[	X
ejpam-3479	36	10	8	8	NUM
ejpam-3479	36	11	]	]	PUNCT
ejpam-3479	36	12	that	that	PRON
ejpam-3479	36	13	:	:	PUNCT
ejpam-3479	36	14	(	(	PUNCT
ejpam-3479	36	15	h1	h1	PROPN
ejpam-3479	36	16	)	)	PUNCT
ejpam-3479	36	17	:	:	PUNCT
ejpam-3479	37	1			NUM
ejpam-3479	37	2	β	β	X
ejpam-3479	37	3	∈	∈	PROPN
ejpam-3479	37	4	l∞(q	l∞(q	NOUN
ejpam-3479	37	5	)	)	PUNCT
ejpam-3479	37	6	,	,	PUNCT
ejpam-3479	37	7	β(t	β(t	PROPN
ejpam-3479	37	8	,	,	PUNCT
ejpam-3479	37	9	a	a	PRON
ejpam-3479	37	10	,	,	PUNCT
ejpam-3479	37	11	x	x	NOUN
ejpam-3479	37	12	)	)	PUNCT
ejpam-3479	37	13	≥	≥	NOUN
ejpam-3479	37	14	0	0	NUM
ejpam-3479	38	1	a.e	a.e	PROPN
ejpam-3479	38	2	.	.	PROPN
ejpam-3479	39	1	in	in	ADP
ejpam-3479	39	2	q	q	NOUN
ejpam-3479	39	3	;	;	PUNCT
ejpam-3479	39	4	sup	sup	NUM
ejpam-3479	39	5	(	(	PUNCT
ejpam-3479	39	6	t	t	PROPN
ejpam-3479	39	7	,	,	PUNCT
ejpam-3479	39	8	x)∈]0,t	x)∈]0,t	PROPN
ejpam-3479	40	1	[	[	X
ejpam-3479	40	2	×ω	×ω	X
ejpam-3479	40	3	∫	∫	X
ejpam-3479	40	4	]	]	X
ejpam-3479	40	5	0,a	0,a	PROPN
ejpam-3479	40	6	[	[	PUNCT
ejpam-3479	40	7	(	(	PUNCT
ejpam-3479	40	8	‖β2(t	‖β2(t	PROPN
ejpam-3479	40	9	,	,	PUNCT
ejpam-3479	40	10	a	a	PRON
ejpam-3479	40	11	,	,	PUNCT
ejpam-3479	40	12	x)‖+	x)‖+	PROPN
ejpam-3479	40	13	‖∇β‖2(t	‖∇β‖2(t	PROPN
ejpam-3479	40	14	,	,	PUNCT
ejpam-3479	40	15	a	a	PRON
ejpam-3479	40	16	,	,	PUNCT
ejpam-3479	40	17	x)da	x)da	PROPN
ejpam-3479	40	18	)	)	PUNCT
ejpam-3479	40	19	;	;	PUNCT
ejpam-3479	40	20	∃	∃	PROPN
ejpam-3479	40	21	δ	δ	PROPN
ejpam-3479	40	22	∈	∈	PROPN
ejpam-3479	40	23	(	(	PUNCT
ejpam-3479	40	24	0	0	NUM
ejpam-3479	40	25	,	,	PUNCT
ejpam-3479	40	26	a	a	PRON
ejpam-3479	40	27	)	)	PUNCT
ejpam-3479	40	28	s.t	s.t	PROPN
ejpam-3479	40	29	.	.	PUNCT
ejpam-3479	40	30	β(a	β(a	PROPN
ejpam-3479	40	31	,	,	PUNCT
ejpam-3479	40	32	.	.	PUNCT
ejpam-3479	40	33	,	,	PUNCT
ejpam-3479	40	34	)	)	PUNCT
ejpam-3479	41	1	=	=	SYM
ejpam-3479	41	2	0	0	NUM
ejpam-3479	41	3	for	for	ADP
ejpam-3479	41	4	a	a	DET
ejpam-3479	41	5	∈	∈	PROPN
ejpam-3479	41	6	(	(	PUNCT
ejpam-3479	41	7	δ	δ	PROPN
ejpam-3479	41	8	,	,	PUNCT
ejpam-3479	41	9	a	a	PRON
ejpam-3479	41	10	)	)	PUNCT
ejpam-3479	41	11	;	;	PUNCT
ejpam-3479	41	12	(	(	PUNCT
ejpam-3479	41	13	h2	h2	NOUN
ejpam-3479	41	14	)	)	PUNCT
ejpam-3479	41	15	:	:	PUNCT
ejpam-3479	41	16	µ	µ	X
ejpam-3479	41	17	∈	∈	PROPN
ejpam-3479	41	18	c([0	c([0	NOUN
ejpam-3479	41	19	,	,	PUNCT
ejpam-3479	41	20	t	t	X
ejpam-3479	41	21	]	]	X
ejpam-3479	41	22	×	×	NOUN
ejpam-3479	42	1	[	[	X
ejpam-3479	42	2	0	0	NUM
ejpam-3479	42	3	,	,	PUNCT
ejpam-3479	42	4	a]×	a]×	PROPN
ejpam-3479	42	5	ω̄	ω̄	NOUN
ejpam-3479	42	6	)	)	PUNCT
ejpam-3479	42	7	,	,	PUNCT
ejpam-3479	42	8	µ(t	µ(t	ADJ
ejpam-3479	42	9	,	,	PUNCT
ejpam-3479	42	10	a	a	DET
ejpam-3479	42	11	,	,	PUNCT
ejpam-3479	42	12	x	x	NOUN
ejpam-3479	42	13	)	)	PUNCT
ejpam-3479	42	14	≥	≥	NOUN
ejpam-3479	42	15	0	0	NUM
ejpam-3479	43	1	a.e	a.e	NOUN
ejpam-3479	43	2	in	in	ADP
ejpam-3479	43	3	q	q	NOUN
ejpam-3479	43	4	m.soma	m.soma	ADV
ejpam-3479	43	5	,	,	PUNCT
ejpam-3479	43	6	s.	s.	PROPN
ejpam-3479	43	7	sawadogo	sawadogo	PROPN
ejpam-3479	43	8	/	/	SYM
ejpam-3479	43	9	eur	eur	PROPN
ejpam-3479	43	10	.	.	PUNCT
ejpam-3479	44	1	j.	j.	PROPN
ejpam-3479	44	2	pure	pure	PROPN
ejpam-3479	44	3	appl	appl	PROPN
ejpam-3479	44	4	.	.	PROPN
ejpam-3479	44	5	math	math	PROPN
ejpam-3479	44	6	,	,	PUNCT
ejpam-3479	44	7	12	12	NUM
ejpam-3479	44	8	(	(	PUNCT
ejpam-3479	44	9	3	3	NUM
ejpam-3479	44	10	)	)	PUNCT
ejpam-3479	44	11	(	(	PUNCT
ejpam-3479	44	12	2019	2019	NUM
ejpam-3479	44	13	)	)	PUNCT
ejpam-3479	44	14	,	,	PUNCT
ejpam-3479	44	15	1277	1277	NUM
ejpam-3479	44	16	-	-	SYM
ejpam-3479	44	17	1296	1296	NUM
ejpam-3479	44	18	1279	1279	NUM
ejpam-3479	44	19	(	(	PUNCT
ejpam-3479	44	20	h3	h3	NOUN
ejpam-3479	44	21	)	)	PUNCT
ejpam-3479	44	22	:	:	PUNCT
ejpam-3479	45	1			NUM
ejpam-3479	45	2	∀t	∀t	PROPN
ejpam-3479	45	3	,	,	PUNCT
ejpam-3479	45	4	0	0	NUM
ejpam-3479	45	5	<	<	X
ejpam-3479	45	6	t	t	X
ejpam-3479	45	7	<	<	X
ejpam-3479	45	8	a	a	PRON
ejpam-3479	45	9	,	,	PUNCT
ejpam-3479	45	10	∀x	∀x	X
ejpam-3479	45	11	∈	∈	PROPN
ejpam-3479	45	12	ω	ω	NOUN
ejpam-3479	45	13	,	,	PUNCT
ejpam-3479	45	14	lim	lim	PROPN
ejpam-3479	45	15	∫	∫	PROPN
ejpam-3479	45	16	a	a	DET
ejpam-3479	45	17	0	0	NUM
ejpam-3479	45	18	µ(ι	µ(ι	NOUN
ejpam-3479	45	19	,	,	PUNCT
ejpam-3479	45	20	a−	a−	PROPN
ejpam-3479	45	21	t+	t+	NOUN
ejpam-3479	45	22	ι	ι	PROPN
ejpam-3479	45	23	,	,	PUNCT
ejpam-3479	45	24	x)dι	x)dι	PROPN
ejpam-3479	45	25	=	=	PUNCT
ejpam-3479	46	1	+	+	PROPN
ejpam-3479	46	2	∞	∞	NUM
ejpam-3479	46	3	a−→a	a−→a	INTJ
ejpam-3479	46	4	;	;	PUNCT
ejpam-3479	46	5	∀t	∀t	PROPN
ejpam-3479	46	6	,	,	PUNCT
ejpam-3479	46	7	a	a	DET
ejpam-3479	46	8	<	<	X
ejpam-3479	46	9	t	t	X
ejpam-3479	46	10	<	<	X
ejpam-3479	46	11	t	t	PROPN
ejpam-3479	46	12	,	,	PUNCT
ejpam-3479	46	13	∀x	∀x	X
ejpam-3479	46	14	∈	∈	PROPN
ejpam-3479	46	15	ω	ω	PROPN
ejpam-3479	46	16	,	,	PUNCT
ejpam-3479	46	17	lim	lim	PROPN
ejpam-3479	46	18	∫	∫	PROPN
ejpam-3479	46	19	a	a	DET
ejpam-3479	46	20	0	0	NUM
ejpam-3479	46	21	µ(t−	µ(t−	NOUN
ejpam-3479	46	22	a+	a+	PUNCT
ejpam-3479	46	23	α	α	PROPN
ejpam-3479	46	24	,	,	PUNCT
ejpam-3479	46	25	α	α	NOUN
ejpam-3479	46	26	,	,	PUNCT
ejpam-3479	46	27	x)dα	x)dα	PROPN
ejpam-3479	46	28	=	=	PUNCT
ejpam-3479	47	1	+	+	NUM
ejpam-3479	47	2	∞	∞	NUM
ejpam-3479	47	3	a−→a	a−→a	INTJ
ejpam-3479	47	4	;	;	PUNCT
ejpam-3479	47	5	∇µ	∇µ	PROPN
ejpam-3479	47	6	∈	∈	PROPN
ejpam-3479	48	1	[	[	X
ejpam-3479	48	2	l∞(q)]n	l∞(q)]n	NOUN
ejpam-3479	48	3	.	.	PUNCT
ejpam-3479	49	1	we	we	PRON
ejpam-3479	49	2	also	also	ADV
ejpam-3479	49	3	assume	assume	VERB
ejpam-3479	49	4	that	that	SCONJ
ejpam-3479	49	5	:	:	PUNCT
ejpam-3479	49	6	y0	y0	NOUN
ejpam-3479	49	7	and	and	CCONJ
ejpam-3479	49	8	ŷ0	ŷ0	PROPN
ejpam-3479	49	9	belong	belong	VERB
ejpam-3479	49	10	to	to	ADP
ejpam-3479	49	11	l2(qa	l2(qa	PROPN
ejpam-3479	49	12	)	)	PUNCT
ejpam-3479	49	13	,	,	PUNCT
ejpam-3479	49	14	ξ	ξ	PROPN
ejpam-3479	49	15	and	and	CCONJ
ejpam-3479	49	16	ξ̂i	ξ̂i	PRON
ejpam-3479	49	17	belong	belong	VERB
ejpam-3479	49	18	to	to	ADP
ejpam-3479	49	19	l2(σ	l2(σ	NOUN
ejpam-3479	49	20	)	)	PUNCT
ejpam-3479	49	21	,	,	PUNCT
ejpam-3479	49	22	the	the	DET
ejpam-3479	49	23	reals	real	NOUN
ejpam-3479	49	24	τ	τ	X
ejpam-3479	49	25	,	,	PUNCT
ejpam-3479	49	26	λi	λi	ADP
ejpam-3479	49	27	1	1	NUM
ejpam-3479	49	28	≤	≤	NUM
ejpam-3479	50	1	i	i	PRON
ejpam-3479	50	2	≤	≤	NOUN
ejpam-3479	50	3	m	m	VERB
ejpam-3479	50	4	are	be	AUX
ejpam-3479	50	5	sufficiently	sufficiently	ADV
ejpam-3479	50	6	small	small	ADJ
ejpam-3479	50	7	and	and	CCONJ
ejpam-3479	50	8	‖ŷ0‖l2(qa	‖ŷ0‖l2(qa	NOUN
ejpam-3479	50	9	)	)	PUNCT
ejpam-3479	50	10	≤	≤	NUM
ejpam-3479	50	11	1	1	NUM
ejpam-3479	50	12	,	,	PUNCT
ejpam-3479	50	13	and	and	CCONJ
ejpam-3479	50	14	we	we	PRON
ejpam-3479	50	15	set	set	VERB
ejpam-3479	50	16	λ	λ	X
ejpam-3479	50	17	=	=	SYM
ejpam-3479	50	18	(	(	PUNCT
ejpam-3479	50	19	λ1	λ1	ADJ
ejpam-3479	50	20	,	,	PUNCT
ejpam-3479	50	21	.	.	PUNCT
ejpam-3479	50	22	.	.	PUNCT
ejpam-3479	50	23	.	.	PUNCT
ejpam-3479	51	1	,	,	PUNCT
ejpam-3479	51	2	λm	λm	X
ejpam-3479	51	3	)	)	PUNCT
ejpam-3479	51	4	.	.	PUNCT
ejpam-3479	52	1	under	under	ADP
ejpam-3479	52	2	the	the	DET
ejpam-3479	52	3	above	above	ADJ
ejpam-3479	52	4	assumptions	assumption	NOUN
ejpam-3479	52	5	on	on	ADP
ejpam-3479	52	6	the	the	DET
ejpam-3479	52	7	data	datum	NOUN
ejpam-3479	52	8	,	,	PUNCT
ejpam-3479	52	9	one	one	PRON
ejpam-3479	52	10	can	can	AUX
ejpam-3479	52	11	prove	prove	VERB
ejpam-3479	52	12	as	as	ADP
ejpam-3479	52	13	in	in	ADP
ejpam-3479	52	14	[	[	X
ejpam-3479	52	15	17	17	NUM
ejpam-3479	52	16	]	]	PUNCT
ejpam-3479	52	17	that	that	DET
ejpam-3479	52	18	problem	problem	NOUN
ejpam-3479	52	19	(	(	PUNCT
ejpam-3479	52	20	1	1	X
ejpam-3479	52	21	)	)	PUNCT
ejpam-3479	52	22	has	have	VERB
ejpam-3479	52	23	a	a	DET
ejpam-3479	52	24	unique	unique	ADJ
ejpam-3479	52	25	solution	solution	NOUN
ejpam-3479	52	26	in	in	ADP
ejpam-3479	52	27	l2(q	l2(q	PROPN
ejpam-3479	52	28	)	)	PUNCT
ejpam-3479	52	29	.	.	PUNCT
ejpam-3479	53	1	for	for	ADP
ejpam-3479	53	2	the	the	DET
ejpam-3479	53	3	sake	sake	NOUN
ejpam-3479	53	4	of	of	ADP
ejpam-3479	53	5	simplicity	simplicity	NOUN
ejpam-3479	53	6	,	,	PUNCT
ejpam-3479	53	7	we	we	PRON
ejpam-3479	53	8	denote	denote	VERB
ejpam-3479	53	9	y(t	y(t	PROPN
ejpam-3479	53	10	,	,	PUNCT
ejpam-3479	53	11	a	a	PRON
ejpam-3479	53	12	,	,	PUNCT
ejpam-3479	53	13	x;λ	x;λ	NUM
ejpam-3479	53	14	,	,	PUNCT
ejpam-3479	53	15	τ	τ	PROPN
ejpam-3479	53	16	)	)	PUNCT
ejpam-3479	53	17	(	(	PUNCT
ejpam-3479	53	18	2	2	X
ejpam-3479	53	19	)	)	PUNCT
ejpam-3479	53	20	the	the	DET
ejpam-3479	53	21	unique	unique	ADJ
ejpam-3479	53	22	solution	solution	NOUN
ejpam-3479	53	23	of	of	ADP
ejpam-3479	53	24	(	(	PUNCT
ejpam-3479	53	25	1	1	NUM
ejpam-3479	53	26	)	)	PUNCT
ejpam-3479	53	27	.	.	PUNCT
ejpam-3479	54	1	therefore	therefore	ADV
ejpam-3479	54	2	,	,	PUNCT
ejpam-3479	54	3	the	the	DET
ejpam-3479	54	4	map	map	NOUN
ejpam-3479	54	5	(	(	PUNCT
ejpam-3479	54	6	λ	λ	NOUN
ejpam-3479	54	7	,	,	PUNCT
ejpam-3479	54	8	τ	τ	NOUN
ejpam-3479	54	9	)	)	PUNCT
ejpam-3479	54	10	7→	7→	NUM
ejpam-3479	54	11	y(λ	y(λ	PROPN
ejpam-3479	54	12	,	,	PUNCT
ejpam-3479	54	13	τ	τ	X
ejpam-3479	54	14	)	)	PUNCT
ejpam-3479	54	15	is	be	AUX
ejpam-3479	54	16	in	in	ADP
ejpam-3479	54	17	c1(r×	c1(r×	VERB
ejpam-3479	54	18	r;l2(q	r;l2(q	PROPN
ejpam-3479	54	19	)	)	PUNCT
ejpam-3479	54	20	)	)	PUNCT
ejpam-3479	54	21	.	.	PUNCT
ejpam-3479	55	1	(	(	PUNCT
ejpam-3479	55	2	3	3	X
ejpam-3479	55	3	)	)	PUNCT
ejpam-3479	55	4	for	for	ADP
ejpam-3479	55	5	more	more	ADJ
ejpam-3479	55	6	literature	literature	NOUN
ejpam-3479	55	7	on	on	ADP
ejpam-3479	55	8	the	the	DET
ejpam-3479	55	9	model	model	NOUN
ejpam-3479	55	10	describing	describe	VERB
ejpam-3479	55	11	the	the	DET
ejpam-3479	55	12	dynamics	dynamic	NOUN
ejpam-3479	55	13	of	of	ADP
ejpam-3479	55	14	population	population	NOUN
ejpam-3479	55	15	with	with	ADP
ejpam-3479	55	16	age	age	NOUN
ejpam-3479	55	17	dependence	dependence	NOUN
ejpam-3479	55	18	and	and	CCONJ
ejpam-3479	55	19	spatial	spatial	ADJ
ejpam-3479	55	20	structure	structure	NOUN
ejpam-3479	55	21	as	as	ADV
ejpam-3479	55	22	well	well	ADV
ejpam-3479	55	23	as	as	ADP
ejpam-3479	55	24	for	for	ADP
ejpam-3479	55	25	some	some	DET
ejpam-3479	55	26	existence	existence	NOUN
ejpam-3479	55	27	results	result	VERB
ejpam-3479	55	28	on	on	ADP
ejpam-3479	55	29	such	such	ADJ
ejpam-3479	55	30	problem	problem	NOUN
ejpam-3479	55	31	,	,	PUNCT
ejpam-3479	55	32	we	we	PRON
ejpam-3479	55	33	refer	refer	VERB
ejpam-3479	55	34	for	for	ADP
ejpam-3479	55	35	instance	instance	NOUN
ejpam-3479	55	36	to	to	ADP
ejpam-3479	55	37	[	[	X
ejpam-3479	55	38	1	1	NUM
ejpam-3479	55	39	,	,	PUNCT
ejpam-3479	55	40	3	3	NUM
ejpam-3479	55	41	,	,	PUNCT
ejpam-3479	55	42	8	8	NUM
ejpam-3479	55	43	,	,	PUNCT
ejpam-3479	55	44	17	17	NUM
ejpam-3479	55	45	]	]	PUNCT
ejpam-3479	55	46	and	and	CCONJ
ejpam-3479	55	47	the	the	DET
ejpam-3479	55	48	reference	reference	NOUN
ejpam-3479	55	49	therein	therein	ADV
ejpam-3479	55	50	.	.	PUNCT
ejpam-3479	56	1	recently	recently	ADV
ejpam-3479	56	2	s.	s.	PROPN
ejpam-3479	56	3	sawadogo	sawadogo	PROPN
ejpam-3479	56	4	[	[	X
ejpam-3479	56	5	16	16	NUM
ejpam-3479	56	6	]	]	PUNCT
ejpam-3479	56	7	use	use	VERB
ejpam-3479	56	8	the	the	DET
ejpam-3479	56	9	sentinel	sentinel	ADJ
ejpam-3479	56	10	method	method	NOUN
ejpam-3479	56	11	to	to	PART
ejpam-3479	56	12	control	control	VERB
ejpam-3479	56	13	the	the	DET
ejpam-3479	56	14	migration	migration	NOUN
ejpam-3479	56	15	of	of	ADP
ejpam-3479	56	16	a	a	DET
ejpam-3479	56	17	single	single	ADJ
ejpam-3479	56	18	species	specie	NOUN
ejpam-3479	56	19	population	population	NOUN
ejpam-3479	56	20	subjected	subject	VERB
ejpam-3479	56	21	to	to	ADP
ejpam-3479	56	22	a	a	DET
ejpam-3479	56	23	migratory	migratory	ADJ
ejpam-3479	56	24	phenomenon	phenomenon	NOUN
ejpam-3479	56	25	.	.	PUNCT
ejpam-3479	57	1	for	for	ADP
ejpam-3479	57	2	the	the	DET
ejpam-3479	57	3	model	model	NOUN
ejpam-3479	57	4	(	(	PUNCT
ejpam-3479	57	5	1	1	NUM
ejpam-3479	57	6	)	)	PUNCT
ejpam-3479	57	7	,	,	PUNCT
ejpam-3479	57	8	we	we	PRON
ejpam-3479	57	9	are	be	AUX
ejpam-3479	57	10	interested	interested	ADJ
ejpam-3479	57	11	in	in	ADP
ejpam-3479	57	12	identifying	identify	VERB
ejpam-3479	57	13	the	the	DET
ejpam-3479	57	14	parameters	parameter	NOUN
ejpam-3479	57	15	λi	λi	VERB
ejpam-3479	57	16	without	without	ADP
ejpam-3479	57	17	any	any	DET
ejpam-3479	57	18	attempt	attempt	NOUN
ejpam-3479	57	19	at	at	ADP
ejpam-3479	57	20	computing	compute	VERB
ejpam-3479	57	21	τ	τ	PROPN
ejpam-3479	57	22	ŷ0	ŷ0	PROPN
ejpam-3479	57	23	.	.	PUNCT
ejpam-3479	58	1	to	to	PART
ejpam-3479	58	2	identify	identify	VERB
ejpam-3479	58	3	these	these	DET
ejpam-3479	58	4	parameters	parameter	NOUN
ejpam-3479	58	5	,	,	PUNCT
ejpam-3479	58	6	we	we	PRON
ejpam-3479	58	7	use	use	VERB
ejpam-3479	58	8	the	the	DET
ejpam-3479	58	9	theory	theory	NOUN
ejpam-3479	58	10	of	of	ADP
ejpam-3479	58	11	sentinel	sentinel	NOUN
ejpam-3479	58	12	in	in	ADP
ejpam-3479	58	13	a	a	DET
ejpam-3479	58	14	general	general	ADJ
ejpam-3479	58	15	framework	framework	NOUN
ejpam-3479	58	16	.	.	PUNCT
ejpam-3479	59	1	more	more	ADV
ejpam-3479	59	2	precisely	precisely	ADV
ejpam-3479	59	3	,	,	PUNCT
ejpam-3479	59	4	let	let	VERB
ejpam-3479	59	5	o	o	NOUN
ejpam-3479	59	6	be	be	AUX
ejpam-3479	59	7	a	a	DET
ejpam-3479	59	8	nonempty	nonempty	ADJ
ejpam-3479	59	9	open	open	ADJ
ejpam-3479	59	10	subset	subset	NOUN
ejpam-3479	59	11	of	of	ADP
ejpam-3479	59	12	γ\γ1	γ\γ1	NOUN
ejpam-3479	59	13	and	and	CCONJ
ejpam-3479	59	14	let	let	VERB
ejpam-3479	59	15	y	y	PROPN
ejpam-3479	59	16	=	=	SYM
ejpam-3479	59	17	y(t	y(t	PROPN
ejpam-3479	59	18	,	,	PUNCT
ejpam-3479	59	19	a	a	PRON
ejpam-3479	59	20	,	,	PUNCT
ejpam-3479	59	21	x;λ	x;λ	NUM
ejpam-3479	59	22	,	,	PUNCT
ejpam-3479	59	23	τ	τ	X
ejpam-3479	59	24	)	)	PUNCT
ejpam-3479	59	25	=	=	SYM
ejpam-3479	59	26	y(λ	y(λ	PROPN
ejpam-3479	59	27	,	,	PUNCT
ejpam-3479	59	28	τ	τ	X
ejpam-3479	59	29	)	)	PUNCT
ejpam-3479	59	30	be	be	VERB
ejpam-3479	59	31	the	the	DET
ejpam-3479	59	32	solution	solution	NOUN
ejpam-3479	59	33	of	of	ADP
ejpam-3479	59	34	(	(	PUNCT
ejpam-3479	59	35	1	1	NUM
ejpam-3479	59	36	)	)	PUNCT
ejpam-3479	59	37	.	.	PUNCT
ejpam-3479	60	1	then	then	ADV
ejpam-3479	60	2	for	for	ADP
ejpam-3479	60	3	any	any	DET
ejpam-3479	60	4	non	non	ADJ
ejpam-3479	60	5	-	-	ADJ
ejpam-3479	60	6	empty	empty	ADJ
ejpam-3479	60	7	open	open	ADJ
ejpam-3479	60	8	subset	subset	NOUN
ejpam-3479	60	9	γ	γ	NOUN
ejpam-3479	60	10	of	of	ADP
ejpam-3479	60	11	γ\γ1	γ\γ1	NOUN
ejpam-3479	60	12	such	such	ADJ
ejpam-3479	60	13	that	that	SCONJ
ejpam-3479	60	14	o	o	PROPN
ejpam-3479	60	15	∩	∩	NOUN
ejpam-3479	60	16	γ	γ	X
ejpam-3479	60	17	6=	6=	NOUN
ejpam-3479	60	18	∅	∅	NOUN
ejpam-3479	60	19	,	,	PUNCT
ejpam-3479	60	20	we	we	PRON
ejpam-3479	60	21	look	look	VERB
ejpam-3479	60	22	for	for	ADP
ejpam-3479	60	23	a	a	DET
ejpam-3479	60	24	function	function	NOUN
ejpam-3479	60	25	s(λ	s(λ	PROPN
ejpam-3479	60	26	,	,	PUNCT
ejpam-3479	60	27	τ	τ	NOUN
ejpam-3479	60	28	)	)	PUNCT
ejpam-3479	60	29	solution	solution	NOUN
ejpam-3479	60	30	to	to	ADP
ejpam-3479	60	31	the	the	DET
ejpam-3479	60	32	following	following	ADJ
ejpam-3479	60	33	problem	problem	NOUN
ejpam-3479	60	34	:	:	PUNCT
ejpam-3479	60	35	given	give	VERB
ejpam-3479	60	36	h0	h0	PROPN
ejpam-3479	60	37	∈	∈	PROPN
ejpam-3479	60	38	l2(u	l2(u	X
ejpam-3479	60	39	×o	×o	PROPN
ejpam-3479	60	40	)	)	PUNCT
ejpam-3479	60	41	,	,	PUNCT
ejpam-3479	60	42	find	find	VERB
ejpam-3479	60	43	w	w	ADP
ejpam-3479	60	44	∈	∈	PROPN
ejpam-3479	61	1	l2(u	l2(u	X
ejpam-3479	61	2	×	×	PROPN
ejpam-3479	61	3	γ	γ	NOUN
ejpam-3479	61	4	)	)	PUNCT
ejpam-3479	61	5	such	such	ADJ
ejpam-3479	61	6	that	that	SCONJ
ejpam-3479	61	7	i	i	PRON
ejpam-3479	61	8	)	)	PUNCT
ejpam-3479	61	9	the	the	DET
ejpam-3479	61	10	function	function	NOUN
ejpam-3479	61	11	s	s	AUX
ejpam-3479	61	12	defined	define	VERB
ejpam-3479	61	13	by	by	ADP
ejpam-3479	61	14	s(λ	s(λ	PROPN
ejpam-3479	61	15	,	,	PUNCT
ejpam-3479	61	16	τ	τ	X
ejpam-3479	61	17	)	)	PUNCT
ejpam-3479	61	18	=	=	SYM
ejpam-3479	62	1	∫	∫	PUNCT
ejpam-3479	62	2	u	u	NOUN
ejpam-3479	62	3	∫	∫	PROPN
ejpam-3479	62	4	o	o	PROPN
ejpam-3479	62	5	h0	h0	PROPN
ejpam-3479	62	6	∂y	∂y	PROPN
ejpam-3479	62	7	∂ν	∂ν	PROPN
ejpam-3479	62	8	(	(	PUNCT
ejpam-3479	62	9	λ	λ	PROPN
ejpam-3479	62	10	,	,	PUNCT
ejpam-3479	62	11	τ)dtdadγ	τ)dtdadγ	PUNCT
ejpam-3479	63	1	+	+	CCONJ
ejpam-3479	63	2	∫	∫	X
ejpam-3479	63	3	u	u	X
ejpam-3479	63	4	∫	∫	PROPN
ejpam-3479	63	5	γ	γ	X
ejpam-3479	63	6	w	w	PROPN
ejpam-3479	63	7	∂y	∂y	PROPN
ejpam-3479	63	8	∂ν	∂ν	PROPN
ejpam-3479	63	9	(	(	PUNCT
ejpam-3479	63	10	λ	λ	PROPN
ejpam-3479	63	11	,	,	PUNCT
ejpam-3479	63	12	τ)dtdadγ	τ)dtdadγ	PUNCT
ejpam-3479	63	13	,	,	PUNCT
ejpam-3479	63	14	(	(	PUNCT
ejpam-3479	63	15	4	4	X
ejpam-3479	63	16	)	)	PUNCT
ejpam-3479	63	17	satisfies	satisfie	NOUN
ejpam-3479	63	18	:	:	PUNCT
ejpam-3479	63	19	m.soma	m.soma	ADV
ejpam-3479	63	20	,	,	PUNCT
ejpam-3479	63	21	s.	s.	PROPN
ejpam-3479	63	22	sawadogo	sawadogo	PROPN
ejpam-3479	63	23	/	/	SYM
ejpam-3479	63	24	eur	eur	PROPN
ejpam-3479	63	25	.	.	PUNCT
ejpam-3479	64	1	j.	j.	PROPN
ejpam-3479	64	2	pure	pure	PROPN
ejpam-3479	64	3	appl	appl	PROPN
ejpam-3479	64	4	.	.	PROPN
ejpam-3479	64	5	math	math	PROPN
ejpam-3479	64	6	,	,	PUNCT
ejpam-3479	64	7	12	12	NUM
ejpam-3479	64	8	(	(	PUNCT
ejpam-3479	64	9	3	3	NUM
ejpam-3479	64	10	)	)	PUNCT
ejpam-3479	64	11	(	(	PUNCT
ejpam-3479	64	12	2019	2019	NUM
ejpam-3479	64	13	)	)	PUNCT
ejpam-3479	64	14	,	,	PUNCT
ejpam-3479	64	15	1277	1277	NUM
ejpam-3479	64	16	-	-	SYM
ejpam-3479	64	17	1296	1296	NUM
ejpam-3479	64	18	1280	1280	NUM
ejpam-3479	64	19	s	s	NOUN
ejpam-3479	64	20	is	be	AUX
ejpam-3479	64	21	stationary	stationary	ADJ
ejpam-3479	64	22	to	to	ADP
ejpam-3479	64	23	the	the	DET
ejpam-3479	64	24	first	first	ADJ
ejpam-3479	64	25	order	order	NOUN
ejpam-3479	64	26	with	with	ADP
ejpam-3479	64	27	respect	respect	NOUN
ejpam-3479	64	28	to	to	ADP
ejpam-3479	64	29	missing	miss	VERB
ejpam-3479	64	30	term	term	NOUN
ejpam-3479	64	31	τ	τ	PROPN
ejpam-3479	64	32	ŷ0	ŷ0	PROPN
ejpam-3479	64	33	∂s	∂s	PROPN
ejpam-3479	64	34	∂τ	∂τ	PROPN
ejpam-3479	64	35	(	(	PUNCT
ejpam-3479	64	36	0	0	NUM
ejpam-3479	64	37	,	,	PUNCT
ejpam-3479	64	38	0	0	NUM
ejpam-3479	64	39	)	)	PUNCT
ejpam-3479	64	40	=	=	SYM
ejpam-3479	64	41	0	0	NUM
ejpam-3479	64	42	∀	∀	NOUN
ejpam-3479	64	43	ŷ0	ŷ0	NOUN
ejpam-3479	64	44	(	(	PUNCT
ejpam-3479	64	45	5	5	NUM
ejpam-3479	64	46	)	)	PUNCT
ejpam-3479	64	47	s	s	VERB
ejpam-3479	64	48	is	be	AUX
ejpam-3479	64	49	sensitive	sensitive	ADJ
ejpam-3479	64	50	to	to	ADP
ejpam-3479	64	51	the	the	DET
ejpam-3479	64	52	first	first	ADJ
ejpam-3479	64	53	order	order	NOUN
ejpam-3479	64	54	with	with	ADP
ejpam-3479	64	55	respect	respect	NOUN
ejpam-3479	64	56	to	to	ADP
ejpam-3479	64	57	pollution	pollution	NOUN
ejpam-3479	64	58	terms	term	NOUN
ejpam-3479	65	1	λiξ̂i	λiξ̂i	ADP
ejpam-3479	65	2	:	:	PUNCT
ejpam-3479	65	3	∂s	∂s	PROPN
ejpam-3479	65	4	∂λi	∂λi	PROPN
ejpam-3479	65	5	(	(	PUNCT
ejpam-3479	65	6	0	0	NUM
ejpam-3479	65	7	,	,	PUNCT
ejpam-3479	65	8	0	0	NUM
ejpam-3479	65	9	)	)	PUNCT
ejpam-3479	65	10	=	=	SYM
ejpam-3479	65	11	ci	ci	NOUN
ejpam-3479	65	12	1	1	NUM
ejpam-3479	65	13	≤	≤	PUNCT
ejpam-3479	65	14	i	i	PROPN
ejpam-3479	65	15	≤m	≤m	PROPN
ejpam-3479	65	16	,	,	PUNCT
ejpam-3479	65	17	(	(	PUNCT
ejpam-3479	65	18	6	6	NUM
ejpam-3479	65	19	)	)	PUNCT
ejpam-3479	65	20	where	where	SCONJ
ejpam-3479	65	21	ci	ci	NOUN
ejpam-3479	65	22	,	,	PUNCT
ejpam-3479	65	23	1	1	NUM
ejpam-3479	65	24	≤	≤	NUM
ejpam-3479	65	25	i	i	NUM
ejpam-3479	65	26	≤m	≤m	PROPN
ejpam-3479	65	27	,	,	PUNCT
ejpam-3479	65	28	are	be	AUX
ejpam-3479	65	29	given	give	VERB
ejpam-3479	65	30	constants	constant	NOUN
ejpam-3479	65	31	not	not	PART
ejpam-3479	65	32	all	all	ADV
ejpam-3479	65	33	identically	identically	ADV
ejpam-3479	65	34	zero	zero	NUM
ejpam-3479	65	35	.	.	PUNCT
ejpam-3479	65	36	ii	ii	PROPN
ejpam-3479	65	37	)	)	PUNCT
ejpam-3479	65	38	the	the	DET
ejpam-3479	65	39	control	control	NOUN
ejpam-3479	65	40	w	w	PROPN
ejpam-3479	65	41	is	be	AUX
ejpam-3479	65	42	of	of	ADP
ejpam-3479	65	43	minimal	minimal	ADJ
ejpam-3479	65	44	norm	norm	NOUN
ejpam-3479	65	45	in	in	ADP
ejpam-3479	65	46	l2(u	l2(u	PROPN
ejpam-3479	65	47	×	×	PROPN
ejpam-3479	65	48	γ	γ	PROPN
ejpam-3479	65	49	)	)	PUNCT
ejpam-3479	65	50	among	among	ADP
ejpam-3479	65	51	”	"	PUNCT
ejpam-3479	65	52	the	the	DET
ejpam-3479	65	53	admissible	admissible	ADJ
ejpam-3479	65	54	controls	control	NOUN
ejpam-3479	65	55	”	"	PUNCT
ejpam-3479	65	56	,	,	PUNCT
ejpam-3479	65	57	i.e.	i.e.	X
ejpam-3479	65	58	‖w‖2l2(u×γ	‖w‖2l2(u×γ	NOUN
ejpam-3479	65	59	)	)	PUNCT
ejpam-3479	66	1	=	=	SYM
ejpam-3479	66	2	min	min	PROPN
ejpam-3479	66	3	w̄∈e	w̄∈e	PROPN
ejpam-3479	66	4	‖w̃‖2l2(u×γ	‖w̃‖2l2(u×γ	NUM
ejpam-3479	66	5	)	)	PUNCT
ejpam-3479	66	6	,	,	PUNCT
ejpam-3479	66	7	(	(	PUNCT
ejpam-3479	66	8	7	7	X
ejpam-3479	66	9	)	)	PUNCT
ejpam-3479	66	10	where	where	SCONJ
ejpam-3479	66	11	e	e	NOUN
ejpam-3479	66	12	=	=	PRON
ejpam-3479	66	13	{	{	PUNCT
ejpam-3479	66	14	w̃	w̃	PROPN
ejpam-3479	66	15	∈	∈	PROPN
ejpam-3479	67	1	l2(u	l2(u	PROPN
ejpam-3479	67	2	×	×	PROPN
ejpam-3479	67	3	γ	γ	NOUN
ejpam-3479	67	4	)	)	PUNCT
ejpam-3479	67	5	,	,	PUNCT
ejpam-3479	67	6	such	such	ADJ
ejpam-3479	67	7	that	that	SCONJ
ejpam-3479	67	8	(	(	PUNCT
ejpam-3479	67	9	w̃	w̃	PROPN
ejpam-3479	67	10	,	,	PUNCT
ejpam-3479	67	11	s(w̃	s(w̃	NOUN
ejpam-3479	67	12	)	)	PUNCT
ejpam-3479	67	13	)	)	PUNCT
ejpam-3479	67	14	satisfies	satisfie	NOUN
ejpam-3479	67	15	(	(	PUNCT
ejpam-3479	67	16	4)−	4)−	NOUN
ejpam-3479	67	17	(	(	PUNCT
ejpam-3479	67	18	7	7	NUM
ejpam-3479	67	19	)	)	PUNCT
ejpam-3479	67	20	}	}	PUNCT
ejpam-3479	67	21	.	.	PUNCT
ejpam-3479	68	1	(	(	PUNCT
ejpam-3479	68	2	8)	8)	NUM
ejpam-3479	68	3	remark	remark	NOUN
ejpam-3479	68	4	1	1	NUM
ejpam-3479	68	5	.	.	PUNCT
ejpam-3479	68	6	j.l.lions	j.l.lion	NOUN
ejpam-3479	68	7	refers	refer	VERB
ejpam-3479	68	8	to	to	ADP
ejpam-3479	68	9	the	the	DET
ejpam-3479	68	10	function	function	NOUN
ejpam-3479	68	11	s	s	NOUN
ejpam-3479	68	12	as	as	ADP
ejpam-3479	68	13	a	a	DET
ejpam-3479	68	14	sentinel	sentinel	NOUN
ejpam-3479	68	15	with	with	ADP
ejpam-3479	68	16	given	give	VERB
ejpam-3479	68	17	sensitivity	sensitivity	NOUN
ejpam-3479	68	18	ci	ci	NOUN
ejpam-3479	68	19	.	.	PUNCT
ejpam-3479	69	1	in	in	ADP
ejpam-3479	69	2	(	(	PUNCT
ejpam-3479	69	3	6	6	NUM
ejpam-3479	69	4	)	)	PUNCT
ejpam-3479	69	5	,	,	PUNCT
ejpam-3479	69	6	the	the	DET
ejpam-3479	69	7	ci	ci	NOUN
ejpam-3479	69	8	are	be	AUX
ejpam-3479	69	9	chosen	choose	VERB
ejpam-3479	69	10	according	accord	VERB
ejpam-3479	69	11	to	to	ADP
ejpam-3479	69	12	the	the	DET
ejpam-3479	69	13	importance	importance	NOUN
ejpam-3479	69	14	which	which	PRON
ejpam-3479	69	15	is	be	AUX
ejpam-3479	69	16	conferred	confer	VERB
ejpam-3479	69	17	to	to	ADP
ejpam-3479	69	18	the	the	DET
ejpam-3479	69	19	component	component	NOUN
ejpam-3479	69	20	ξi	ξi	NOUN
ejpam-3479	69	21	of	of	ADP
ejpam-3479	69	22	the	the	DET
ejpam-3479	69	23	pollution	pollution	NOUN
ejpam-3479	69	24	.	.	PUNCT
ejpam-3479	70	1	remark	remark	PROPN
ejpam-3479	70	2	2	2	NUM
ejpam-3479	70	3	.	.	PUNCT
ejpam-3479	70	4	notice	notice	VERB
ejpam-3479	70	5	that	that	SCONJ
ejpam-3479	70	6	for	for	ADP
ejpam-3479	70	7	the	the	DET
ejpam-3479	70	8	j.l.lions	j.l.lion	NOUN
ejpam-3479	70	9	’s	’s	PART
ejpam-3479	70	10	sentinels	sentinel	NOUN
ejpam-3479	70	11	defined	define	VERB
ejpam-3479	70	12	by	by	ADP
ejpam-3479	70	13	(	(	PUNCT
ejpam-3479	70	14	4)-(7	4)-(7	NOUN
ejpam-3479	70	15	)	)	PUNCT
ejpam-3479	70	16	,	,	PUNCT
ejpam-3479	70	17	the	the	DET
ejpam-3479	70	18	observatory	observatory	NOUN
ejpam-3479	70	19	o	o	X
ejpam-3479	70	20	⊂	⊂	X
ejpam-3479	70	21	(	(	PUNCT
ejpam-3479	70	22	γ	γ	PROPN
ejpam-3479	70	23	\	\	PROPN
ejpam-3479	70	24	γ1	γ1	PROPN
ejpam-3479	70	25	)	)	PUNCT
ejpam-3479	70	26	is	be	AUX
ejpam-3479	70	27	also	also	ADV
ejpam-3479	70	28	the	the	DET
ejpam-3479	70	29	support	support	NOUN
ejpam-3479	70	30	of	of	ADP
ejpam-3479	70	31	the	the	DET
ejpam-3479	70	32	control	control	NOUN
ejpam-3479	70	33	function	function	VERB
ejpam-3479	70	34	w.	w.	NOUN
ejpam-3479	70	35	for	for	ADP
ejpam-3479	70	36	more	more	ADJ
ejpam-3479	70	37	information	information	NOUN
ejpam-3479	70	38	on	on	ADP
ejpam-3479	70	39	the	the	DET
ejpam-3479	70	40	theory	theory	NOUN
ejpam-3479	70	41	of	of	ADP
ejpam-3479	70	42	sentinel	sentinel	NOUN
ejpam-3479	70	43	,	,	PUNCT
ejpam-3479	70	44	we	we	PRON
ejpam-3479	70	45	refer	refer	VERB
ejpam-3479	70	46	to	to	ADP
ejpam-3479	70	47	[	[	X
ejpam-3479	70	48	9–11	9–11	NOUN
ejpam-3479	70	49	,	,	PUNCT
ejpam-3479	70	50	14	14	NUM
ejpam-3479	70	51	,	,	PUNCT
ejpam-3479	70	52	15	15	NUM
ejpam-3479	70	53	,	,	PUNCT
ejpam-3479	70	54	20	20	NUM
ejpam-3479	70	55	]	]	PUNCT
ejpam-3479	70	56	and	and	CCONJ
ejpam-3479	70	57	the	the	DET
ejpam-3479	70	58	reference	reference	NOUN
ejpam-3479	70	59	therein	therein	ADV
ejpam-3479	70	60	.	.	PUNCT
ejpam-3479	71	1	we	we	PRON
ejpam-3479	71	2	set	set	VERB
ejpam-3479	71	3	y0	y0	PROPN
ejpam-3479	71	4	=	=	SYM
ejpam-3479	71	5	y(0	y(0	PROPN
ejpam-3479	71	6	,	,	PUNCT
ejpam-3479	71	7	0	0	NUM
ejpam-3479	71	8	)	)	PUNCT
ejpam-3479	71	9	∈	∈	PROPN
ejpam-3479	71	10	l2(q	l2(q	PROPN
ejpam-3479	71	11	)	)	PUNCT
ejpam-3479	71	12	,	,	PUNCT
ejpam-3479	71	13	the	the	DET
ejpam-3479	71	14	solution	solution	NOUN
ejpam-3479	71	15	of	of	ADP
ejpam-3479	71	16	(	(	PUNCT
ejpam-3479	71	17	1	1	NUM
ejpam-3479	71	18	)	)	PUNCT
ejpam-3479	71	19	when	when	SCONJ
ejpam-3479	71	20	λ	λ	X
ejpam-3479	71	21	=	=	SYM
ejpam-3479	71	22	0	0	NUM
ejpam-3479	71	23	and	and	CCONJ
ejpam-3479	71	24	τ	τ	X
ejpam-3479	71	25	=	=	SYM
ejpam-3479	71	26	0	0	PUNCT
ejpam-3479	71	27	and	and	CCONJ
ejpam-3479	71	28	we	we	PRON
ejpam-3479	71	29	denote	denote	VERB
ejpam-3479	71	30	respectively	respectively	ADV
ejpam-3479	71	31	by	by	ADP
ejpam-3479	71	32	yτ	yτ	PRON
ejpam-3479	71	33	and	and	CCONJ
ejpam-3479	71	34	yλi	yλi	NOUN
ejpam-3479	71	35	,	,	PUNCT
ejpam-3479	71	36	the	the	DET
ejpam-3479	71	37	derivatives	derivative	NOUN
ejpam-3479	71	38	of	of	ADP
ejpam-3479	71	39	y	y	PROPN
ejpam-3479	71	40	at	at	ADP
ejpam-3479	71	41	(	(	PUNCT
ejpam-3479	71	42	0	0	NUM
ejpam-3479	71	43	,	,	PUNCT
ejpam-3479	71	44	0	0	NUM
ejpam-3479	71	45	)	)	PUNCT
ejpam-3479	71	46	with	with	ADP
ejpam-3479	71	47	respect	respect	NOUN
ejpam-3479	71	48	to	to	ADP
ejpam-3479	71	49	τ	τ	PROPN
ejpam-3479	71	50	and	and	CCONJ
ejpam-3479	71	51	λi	λi	CCONJ
ejpam-3479	71	52	,	,	PUNCT
ejpam-3479	71	53	i.e.	i.e.	X
ejpam-3479	71	54	:	:	PUNCT
ejpam-3479	71	55	yτ	yτ	PROPN
ejpam-3479	71	56	=	=	PROPN
ejpam-3479	71	57	lim	lim	PROPN
ejpam-3479	71	58	τ→0	τ→0	PUNCT
ejpam-3479	71	59	y(0	y(0	PROPN
ejpam-3479	71	60	,	,	PUNCT
ejpam-3479	71	61	τ)−	τ)−	PROPN
ejpam-3479	71	62	y(0	y(0	PROPN
ejpam-3479	71	63	,	,	PUNCT
ejpam-3479	71	64	0	0	NUM
ejpam-3479	71	65	)	)	PUNCT
ejpam-3479	71	66	τ	τ	PROPN
ejpam-3479	71	67	and	and	CCONJ
ejpam-3479	71	68	yλi	yλi	NOUN
ejpam-3479	71	69	=	=	PROPN
ejpam-3479	71	70	lim	lim	PROPN
ejpam-3479	71	71	λi→0	λi→0	PROPN
ejpam-3479	71	72	y(λi	y(λi	PROPN
ejpam-3479	71	73	,	,	PUNCT
ejpam-3479	71	74	0)−	0)−	PUNCT
ejpam-3479	71	75	y(0	y(0	PROPN
ejpam-3479	71	76	,	,	PUNCT
ejpam-3479	71	77	0	0	NUM
ejpam-3479	71	78	)	)	PUNCT
ejpam-3479	71	79	λ	λ	NOUN
ejpam-3479	71	80	.	.	PUNCT
ejpam-3479	72	1	then	then	ADV
ejpam-3479	72	2	yτ	yτ	PROPN
ejpam-3479	72	3	and	and	CCONJ
ejpam-3479	72	4	yλi	yλi	PROPN
ejpam-3479	72	5	are	be	AUX
ejpam-3479	72	6	respectively	respectively	ADV
ejpam-3479	72	7	solutions	solution	NOUN
ejpam-3479	72	8	of	of	NOUN
ejpam-3479	72	9	∂yτ	∂yτ	NOUN
ejpam-3479	72	10	∂t	∂t	PROPN
ejpam-3479	72	11	+	+	CCONJ
ejpam-3479	72	12	∂yτ	∂yτ	NOUN
ejpam-3479	72	13	∂a	∂a	VERB
ejpam-3479	72	14	−4yτ	−4yτ	NOUN
ejpam-3479	72	15	+	+	CCONJ
ejpam-3479	72	16	µyτ	µyτ	ADJ
ejpam-3479	72	17	=	=	NOUN
ejpam-3479	72	18	0	0	NUM
ejpam-3479	72	19	in	in	ADP
ejpam-3479	72	20	q	q	PROPN
ejpam-3479	72	21	,	,	PUNCT
ejpam-3479	72	22	yτ	yτ	PROPN
ejpam-3479	72	23	(	(	PUNCT
ejpam-3479	72	24	0	0	NUM
ejpam-3479	72	25	,	,	PUNCT
ejpam-3479	72	26	a	a	PRON
ejpam-3479	72	27	,	,	PUNCT
ejpam-3479	72	28	x	x	NOUN
ejpam-3479	72	29	)	)	PUNCT
ejpam-3479	72	30	=	=	SYM
ejpam-3479	72	31	ŷ0	ŷ0	PROPN
ejpam-3479	72	32	in	in	ADP
ejpam-3479	72	33	qa	qa	PROPN
ejpam-3479	72	34	,	,	PUNCT
ejpam-3479	72	35	yτ	yτ	PROPN
ejpam-3479	72	36	(	(	PUNCT
ejpam-3479	72	37	t	t	PROPN
ejpam-3479	72	38	,	,	PUNCT
ejpam-3479	72	39	0	0	NUM
ejpam-3479	72	40	,	,	PUNCT
ejpam-3479	72	41	x	x	NOUN
ejpam-3479	72	42	)	)	PUNCT
ejpam-3479	73	1	=	=	SYM
ejpam-3479	73	2	∫	∫	PROPN
ejpam-3479	73	3	a	a	DET
ejpam-3479	73	4	0	0	NUM
ejpam-3479	73	5	β(t	β(t	PROPN
ejpam-3479	73	6	,	,	PUNCT
ejpam-3479	73	7	a	a	PRON
ejpam-3479	73	8	,	,	PUNCT
ejpam-3479	73	9	x)yτ	x)yτ	PROPN
ejpam-3479	73	10	(	(	PUNCT
ejpam-3479	73	11	t	t	PROPN
ejpam-3479	73	12	,	,	PUNCT
ejpam-3479	73	13	a	a	PRON
ejpam-3479	73	14	,	,	PUNCT
ejpam-3479	74	1	x)da	x)da	PROPN
ejpam-3479	74	2	in	in	ADP
ejpam-3479	74	3	qt	qt	NOUN
ejpam-3479	74	4	,	,	PUNCT
ejpam-3479	74	5	yτ	yτ	PROPN
ejpam-3479	74	6	=	=	NOUN
ejpam-3479	74	7	0	0	NUM
ejpam-3479	75	1	on	on	ADP
ejpam-3479	75	2	σ	σ	PROPN
ejpam-3479	75	3	,	,	PUNCT
ejpam-3479	75	4	(	(	PUNCT
ejpam-3479	75	5	9	9	NUM
ejpam-3479	75	6	)	)	PUNCT
ejpam-3479	75	7	and	and	CCONJ
ejpam-3479	75	8	m.soma	m.soma	ADV
ejpam-3479	75	9	,	,	PUNCT
ejpam-3479	75	10	s.	s.	PROPN
ejpam-3479	75	11	sawadogo	sawadogo	PROPN
ejpam-3479	75	12	/	/	SYM
ejpam-3479	75	13	eur	eur	PROPN
ejpam-3479	75	14	.	.	PUNCT
ejpam-3479	76	1	j.	j.	PROPN
ejpam-3479	76	2	pure	pure	PROPN
ejpam-3479	76	3	appl	appl	PROPN
ejpam-3479	76	4	.	.	PROPN
ejpam-3479	76	5	math	math	PROPN
ejpam-3479	76	6	,	,	PUNCT
ejpam-3479	76	7	12	12	NUM
ejpam-3479	76	8	(	(	PUNCT
ejpam-3479	76	9	3	3	NUM
ejpam-3479	76	10	)	)	PUNCT
ejpam-3479	76	11	(	(	PUNCT
ejpam-3479	76	12	2019	2019	NUM
ejpam-3479	76	13	)	)	PUNCT
ejpam-3479	76	14	,	,	PUNCT
ejpam-3479	76	15	1277	1277	NUM
ejpam-3479	76	16	-	-	SYM
ejpam-3479	76	17	1296	1296	NUM
ejpam-3479	76	18	1281	1281	NUM
ejpam-3479	76	19			NUM
ejpam-3479	76	20	∂yλi	∂yλi	SCONJ
ejpam-3479	76	21	∂t	∂t	PROPN
ejpam-3479	76	22	+	+	CCONJ
ejpam-3479	76	23	∂yλi	∂yλi	ADV
ejpam-3479	76	24	∂a	∂a	NOUN
ejpam-3479	76	25	−4yλi	−4yλi	ADV
ejpam-3479	76	26	+	+	NUM
ejpam-3479	76	27	µyλi	µyλi	ADJ
ejpam-3479	76	28	=	=	SYM
ejpam-3479	76	29	0	0	NUM
ejpam-3479	76	30	in	in	ADP
ejpam-3479	76	31	q	q	NOUN
ejpam-3479	76	32	,	,	PUNCT
ejpam-3479	76	33	yλi(0	yλi(0	PROPN
ejpam-3479	76	34	,	,	PUNCT
ejpam-3479	76	35	a	a	DET
ejpam-3479	76	36	,	,	PUNCT
ejpam-3479	76	37	x	x	NOUN
ejpam-3479	76	38	)	)	PUNCT
ejpam-3479	76	39	=	=	SYM
ejpam-3479	76	40	0	0	NUM
ejpam-3479	77	1	in	in	ADP
ejpam-3479	77	2	qa	qa	PROPN
ejpam-3479	77	3	,	,	PUNCT
ejpam-3479	77	4	yλi(t	yλi(t	PROPN
ejpam-3479	77	5	,	,	PUNCT
ejpam-3479	77	6	0	0	NUM
ejpam-3479	77	7	,	,	PUNCT
ejpam-3479	77	8	x	x	X
ejpam-3479	77	9	)	)	PUNCT
ejpam-3479	77	10	=	=	SYM
ejpam-3479	77	11	∫	∫	PROPN
ejpam-3479	77	12	a	a	DET
ejpam-3479	77	13	0	0	NUM
ejpam-3479	77	14	βyλi(t	βyλi(t	NOUN
ejpam-3479	77	15	,	,	PUNCT
ejpam-3479	77	16	a	a	PRON
ejpam-3479	77	17	,	,	PUNCT
ejpam-3479	77	18	x)da	x)da	PROPN
ejpam-3479	77	19	in	in	ADP
ejpam-3479	77	20	qt	qt	NOUN
ejpam-3479	77	21	,	,	PUNCT
ejpam-3479	77	22	yλi	yλi	NOUN
ejpam-3479	77	23	=	=	SYM
ejpam-3479	77	24	ξ̂iχς1	ξ̂iχς1	ADJ
ejpam-3479	77	25	on	on	ADP
ejpam-3479	77	26	σ	σ	PROPN
ejpam-3479	77	27	,	,	PUNCT
ejpam-3479	77	28	(	(	PUNCT
ejpam-3479	77	29	10	10	NUM
ejpam-3479	77	30	)	)	PUNCT
ejpam-3479	77	31	where	where	SCONJ
ejpam-3479	77	32	χx	χx	PROPN
ejpam-3479	77	33	denote	denote	VERB
ejpam-3479	77	34	now	now	ADV
ejpam-3479	77	35	and	and	CCONJ
ejpam-3479	77	36	in	in	ADP
ejpam-3479	77	37	the	the	DET
ejpam-3479	77	38	sequel	sequel	NOUN
ejpam-3479	77	39	,	,	PUNCT
ejpam-3479	77	40	the	the	DET
ejpam-3479	77	41	characteristic	characteristic	ADJ
ejpam-3479	77	42	function	function	NOUN
ejpam-3479	77	43	of	of	ADP
ejpam-3479	77	44	the	the	DET
ejpam-3479	77	45	set	set	NOUN
ejpam-3479	77	46	x.	x.	NOUN
ejpam-3479	77	47	under	under	ADP
ejpam-3479	77	48	the	the	DET
ejpam-3479	77	49	assumptions	assumption	NOUN
ejpam-3479	77	50	(	(	PUNCT
ejpam-3479	77	51	h1)−(h4	h1)−(h4	NOUN
ejpam-3479	77	52	)	)	PUNCT
ejpam-3479	77	53	,	,	PUNCT
ejpam-3479	77	54	the	the	DET
ejpam-3479	77	55	systems	system	NOUN
ejpam-3479	77	56	(	(	PUNCT
ejpam-3479	77	57	9	9	NUM
ejpam-3479	77	58	)	)	PUNCT
ejpam-3479	77	59	and	and	CCONJ
ejpam-3479	77	60	(	(	PUNCT
ejpam-3479	77	61	10	10	NUM
ejpam-3479	77	62	)	)	PUNCT
ejpam-3479	77	63	have	have	VERB
ejpam-3479	77	64	respectively	respectively	ADV
ejpam-3479	77	65	a	a	DET
ejpam-3479	77	66	unique	unique	ADJ
ejpam-3479	77	67	solution	solution	NOUN
ejpam-3479	77	68	yτ	yτ	PROPN
ejpam-3479	77	69	∈	∈	PROPN
ejpam-3479	77	70	l2(q	l2(q	PROPN
ejpam-3479	77	71	)	)	PUNCT
ejpam-3479	77	72	and	and	CCONJ
ejpam-3479	77	73	yλi	yλi	NOUN
ejpam-3479	77	74	∈	∈	PROPN
ejpam-3479	77	75	l2(q	l2(q	PROPN
ejpam-3479	77	76	)	)	PUNCT
ejpam-3479	77	77	(	(	PUNCT
ejpam-3479	77	78	see	see	VERB
ejpam-3479	77	79	[	[	X
ejpam-3479	77	80	8	8	NUM
ejpam-3479	77	81	,	,	PUNCT
ejpam-3479	77	82	17	17	NUM
ejpam-3479	77	83	]	]	PUNCT
ejpam-3479	77	84	)	)	PUNCT
ejpam-3479	77	85	.	.	PUNCT
ejpam-3479	78	1	from	from	ADP
ejpam-3479	78	2	now	now	ADV
ejpam-3479	78	3	on	on	ADV
ejpam-3479	78	4	,	,	PUNCT
ejpam-3479	78	5	we	we	PRON
ejpam-3479	78	6	make	make	VERB
ejpam-3479	78	7	the	the	DET
ejpam-3479	78	8	following	follow	VERB
ejpam-3479	78	9	assumptions	assumption	NOUN
ejpam-3479	78	10	:	:	PUNCT
ejpam-3479	78	11	the	the	DET
ejpam-3479	78	12	functions	function	NOUN
ejpam-3479	78	13	ξ̂i.χς1	ξ̂i.χς1	PROPN
ejpam-3479	78	14	,	,	PUNCT
ejpam-3479	78	15	1	1	NUM
ejpam-3479	78	16	≤	≤	NUM
ejpam-3479	78	17	i	i	PRON
ejpam-3479	78	18	≤m	≤m	PROPN
ejpam-3479	78	19	are	be	AUX
ejpam-3479	78	20	linearly	linearly	ADV
ejpam-3479	78	21	independent	independent	ADJ
ejpam-3479	78	22	(	(	PUNCT
ejpam-3479	78	23	11	11	NUM
ejpam-3479	78	24	)	)	PUNCT
ejpam-3479	78	25	any	any	DET
ejpam-3479	78	26	function	function	NOUN
ejpam-3479	78	27	ρ	ρ	NOUN
ejpam-3479	78	28	such	such	ADJ
ejpam-3479	78	29	that	that	NUM
ejpam-3479	79	1	∂ρ	∂ρ	PROPN
ejpam-3479	79	2	∂t	∂t	PROPN
ejpam-3479	79	3	+	+	CCONJ
ejpam-3479	79	4	∂ρ	∂ρ	PROPN
ejpam-3479	80	1	∂a	∂a	PROPN
ejpam-3479	80	2	−∆ρ+	−∆ρ+	PROPN
ejpam-3479	80	3	µρ	µρ	ADP
ejpam-3479	80	4	=	=	PUNCT
ejpam-3479	80	5	0	0	NUM
ejpam-3479	80	6	in	in	ADP
ejpam-3479	80	7	q	q	PROPN
ejpam-3479	80	8	,	,	PUNCT
ejpam-3479	80	9	ρ	ρ	PROPN
ejpam-3479	80	10	=	=	SYM
ejpam-3479	80	11	0	0	NUM
ejpam-3479	80	12	in	in	ADP
ejpam-3479	80	13	u	u	PROPN
ejpam-3479	80	14	×	×	PROPN
ejpam-3479	80	15	γ	γ	X
ejpam-3479	80	16	,	,	PUNCT
ejpam-3479	80	17	∂ρ	∂ρ	NOUN
ejpam-3479	80	18	∂ν	∂ν	NOUN
ejpam-3479	81	1	=	=	PUNCT
ejpam-3479	81	2	0	0	PROPN
ejpam-3479	81	3	on	on	ADP
ejpam-3479	81	4	u	u	PROPN
ejpam-3479	81	5	×	×	PROPN
ejpam-3479	81	6	γ	γ	X
ejpam-3479	81	7	,	,	PUNCT
ejpam-3479	81	8	(	(	PUNCT
ejpam-3479	81	9	12	12	NUM
ejpam-3479	81	10	)	)	PUNCT
ejpam-3479	81	11	is	be	AUX
ejpam-3479	81	12	identically	identically	ADV
ejpam-3479	81	13	zero	zero	NUM
ejpam-3479	81	14	.	.	PUNCT
ejpam-3479	82	1	and	and	CCONJ
ejpam-3479	82	2	we	we	PRON
ejpam-3479	82	3	set	set	VERB
ejpam-3479	82	4	y	y	NOUN
ejpam-3479	82	5	=	=	PUNCT
ejpam-3479	82	6	span{∂yλ1	span{∂yλ1	VERB
ejpam-3479	82	7	∂ν	∂ν	PROPN
ejpam-3479	82	8	χγ	χγ	VERB
ejpam-3479	82	9	,	,	PUNCT
ejpam-3479	82	10	...	...	PUNCT
ejpam-3479	82	11	,	,	PUNCT
ejpam-3479	82	12	∂yλm	∂yλm	PUNCT
ejpam-3479	82	13	∂ν	∂ν	PROPN
ejpam-3479	82	14	χγ	χγ	PROPN
ejpam-3479	82	15	}	}	PUNCT
ejpam-3479	82	16	.	.	PUNCT
ejpam-3479	83	1	(	(	PUNCT
ejpam-3479	83	2	13	13	NUM
ejpam-3479	83	3	)	)	PUNCT
ejpam-3479	83	4	the	the	DET
ejpam-3479	83	5	vector	vector	NOUN
ejpam-3479	83	6	subspace	subspace	NOUN
ejpam-3479	83	7	of	of	ADP
ejpam-3479	83	8	l2(u	l2(u	PROPN
ejpam-3479	83	9	×	×	PROPN
ejpam-3479	83	10	γ	γ	PROPN
ejpam-3479	83	11	)	)	PUNCT
ejpam-3479	83	12	generated	generate	VERB
ejpam-3479	83	13	by	by	ADP
ejpam-3479	83	14	m	m	PROPN
ejpam-3479	83	15	functions	function	NOUN
ejpam-3479	83	16	{	{	PUNCT
ejpam-3479	83	17	∂yλi∂ν	∂yλi∂ν	NOUN
ejpam-3479	83	18	χγ	χγ	PROPN
ejpam-3479	83	19	}	}	PUNCT
ejpam-3479	83	20	m	m	VERB
ejpam-3479	83	21	i=1	i=1	X
ejpam-3479	83	22	.	.	PUNCT
ejpam-3479	84	1	yθ	yθ	NOUN
ejpam-3479	85	1	=	=	SYM
ejpam-3479	85	2	1	1	NUM
ejpam-3479	85	3	θ	θ	NOUN
ejpam-3479	85	4	y	y	NOUN
ejpam-3479	85	5	the	the	DET
ejpam-3479	85	6	vector	vector	NOUN
ejpam-3479	85	7	subspace	subspace	NOUN
ejpam-3479	85	8	of	of	ADP
ejpam-3479	85	9	l2(u	l2(u	PROPN
ejpam-3479	85	10	×	×	PROPN
ejpam-3479	85	11	γ	γ	PROPN
ejpam-3479	85	12	)	)	PUNCT
ejpam-3479	85	13	generated	generate	VERB
ejpam-3479	85	14	by	by	ADP
ejpam-3479	85	15	m	m	PROPN
ejpam-3479	85	16	functions	function	NOUN
ejpam-3479	85	17	{	{	PUNCT
ejpam-3479	85	18	1	1	NUM
ejpam-3479	85	19	θ	θ	NOUN
ejpam-3479	85	20	∂yλi	∂yλi	SCONJ
ejpam-3479	85	21	∂ν	∂ν	PROPN
ejpam-3479	85	22	χγ	χγ	VERB
ejpam-3479	85	23	}	}	PUNCT
ejpam-3479	85	24	m	m	VERB
ejpam-3479	85	25	i=1	i=1	ADP
ejpam-3479	85	26	,	,	PUNCT
ejpam-3479	85	27	where	where	SCONJ
ejpam-3479	85	28	θ	θ	PROPN
ejpam-3479	85	29	is	be	AUX
ejpam-3479	85	30	the	the	DET
ejpam-3479	85	31	positive	positive	ADJ
ejpam-3479	85	32	function	function	NOUN
ejpam-3479	85	33	precisely	precisely	ADV
ejpam-3479	85	34	defined	define	VERB
ejpam-3479	85	35	later	later	ADV
ejpam-3479	85	36	on	on	ADV
ejpam-3479	85	37	by	by	ADP
ejpam-3479	85	38	(	(	PUNCT
ejpam-3479	85	39	31	31	NUM
ejpam-3479	85	40	)	)	PUNCT
ejpam-3479	85	41	.	.	PUNCT
ejpam-3479	86	1	remark	remark	NOUN
ejpam-3479	86	2	3	3	NUM
ejpam-3479	86	3	.	.	PUNCT
ejpam-3479	87	1	we	we	PRON
ejpam-3479	87	2	will	will	AUX
ejpam-3479	87	3	prove	prove	VERB
ejpam-3479	87	4	in	in	ADP
ejpam-3479	87	5	lemma	lemma	PROPN
ejpam-3479	87	6	1	1	NUM
ejpam-3479	87	7	that	that	SCONJ
ejpam-3479	87	8	the	the	DET
ejpam-3479	87	9	function	function	NOUN
ejpam-3479	87	10	{	{	PUNCT
ejpam-3479	87	11	∂yλi∂ν	∂yλi∂ν	NOUN
ejpam-3479	87	12	χγ	χγ	NOUN
ejpam-3479	87	13	}	}	PUNCT
ejpam-3479	87	14	m	m	VERB
ejpam-3479	87	15	i=1	i=1	PROPN
ejpam-3479	87	16	and	and	CCONJ
ejpam-3479	87	17	{	{	PUNCT
ejpam-3479	87	18	1	1	NUM
ejpam-3479	87	19	θ	θ	NOUN
ejpam-3479	87	20	∂yλi	∂yλi	SCONJ
ejpam-3479	87	21	∂ν	∂ν	PROPN
ejpam-3479	87	22	χγ	χγ	VERB
ejpam-3479	87	23	}	}	PUNCT
ejpam-3479	87	24	m	m	VERB
ejpam-3479	87	25	i=1	i=1	PROPN
ejpam-3479	87	26	are	be	AUX
ejpam-3479	87	27	linearly	linearly	ADV
ejpam-3479	87	28	independent	independent	ADJ
ejpam-3479	87	29	.	.	PUNCT
ejpam-3479	88	1	we	we	PRON
ejpam-3479	88	2	now	now	ADV
ejpam-3479	88	3	consider	consider	VERB
ejpam-3479	88	4	the	the	DET
ejpam-3479	88	5	following	follow	VERB
ejpam-3479	88	6	boundary	boundary	ADJ
ejpam-3479	88	7	null	null	ADJ
ejpam-3479	88	8	-	-	PUNCT
ejpam-3479	88	9	controllability	controllability	NOUN
ejpam-3479	88	10	problem	problem	NOUN
ejpam-3479	88	11	:	:	PUNCT
ejpam-3479	88	12	given	give	VERB
ejpam-3479	88	13	h0	h0	PROPN
ejpam-3479	88	14	∈	∈	PROPN
ejpam-3479	88	15	l2(u	l2(u	X
ejpam-3479	88	16	×o	×o	PROPN
ejpam-3479	88	17	)	)	PUNCT
ejpam-3479	88	18	,	,	PUNCT
ejpam-3479	88	19	w0	w0	PROPN
ejpam-3479	88	20	∈	∈	PROPN
ejpam-3479	88	21	yθ	yθ	NOUN
ejpam-3479	88	22	,	,	PUNCT
ejpam-3479	88	23	find	find	VERB
ejpam-3479	88	24	v	v	ADP
ejpam-3479	88	25	∈	∈	PROPN
ejpam-3479	89	1	l2(u	l2(u	X
ejpam-3479	89	2	×	×	PROPN
ejpam-3479	89	3	γ	γ	NOUN
ejpam-3479	89	4	)	)	PUNCT
ejpam-3479	89	5	such	such	ADJ
ejpam-3479	89	6	that	that	DET
ejpam-3479	89	7	v	v	NUM
ejpam-3479	89	8	∈	∈	PROPN
ejpam-3479	89	9	y	y	PROPN
ejpam-3479	89	10	⊥	⊥	PROPN
ejpam-3479	89	11	,	,	PUNCT
ejpam-3479	89	12	(	(	PUNCT
ejpam-3479	89	13	14	14	NUM
ejpam-3479	89	14	)	)	PUNCT
ejpam-3479	89	15	and	and	CCONJ
ejpam-3479	89	16	if	if	SCONJ
ejpam-3479	89	17	q	q	X
ejpam-3479	89	18	=	=	SYM
ejpam-3479	89	19	q(t	q(t	PROPN
ejpam-3479	89	20	,	,	PUNCT
ejpam-3479	89	21	a	a	PRON
ejpam-3479	89	22	,	,	PUNCT
ejpam-3479	89	23	x	x	NOUN
ejpam-3479	89	24	;	;	PUNCT
ejpam-3479	89	25	v	v	X
ejpam-3479	89	26	)	)	PUNCT
ejpam-3479	89	27	is	be	AUX
ejpam-3479	89	28	solution	solution	NOUN
ejpam-3479	89	29	of	of	ADP
ejpam-3479	89	30	m.soma	m.soma	ADJ
ejpam-3479	89	31	,	,	PUNCT
ejpam-3479	89	32	s.	s.	PROPN
ejpam-3479	89	33	sawadogo	sawadogo	PROPN
ejpam-3479	89	34	/	/	SYM
ejpam-3479	89	35	eur	eur	PROPN
ejpam-3479	89	36	.	.	PUNCT
ejpam-3479	90	1	j.	j.	PROPN
ejpam-3479	90	2	pure	pure	PROPN
ejpam-3479	90	3	appl	appl	PROPN
ejpam-3479	90	4	.	.	PROPN
ejpam-3479	90	5	math	math	PROPN
ejpam-3479	90	6	,	,	PUNCT
ejpam-3479	90	7	12	12	NUM
ejpam-3479	90	8	(	(	PUNCT
ejpam-3479	90	9	3	3	NUM
ejpam-3479	90	10	)	)	PUNCT
ejpam-3479	90	11	(	(	PUNCT
ejpam-3479	90	12	2019	2019	NUM
ejpam-3479	90	13	)	)	PUNCT
ejpam-3479	90	14	,	,	PUNCT
ejpam-3479	90	15	1277	1277	NUM
ejpam-3479	90	16	-	-	SYM
ejpam-3479	90	17	1296	1296	NUM
ejpam-3479	90	18	1282	1282	NUM
ejpam-3479	90	19			NOUN
ejpam-3479	90	20	−∂q	−∂q	NOUN
ejpam-3479	91	1	∂t	∂t	PROPN
ejpam-3479	91	2	−	−	PROPN
ejpam-3479	91	3	∂q	∂q	PROPN
ejpam-3479	91	4	∂a	∂a	PROPN
ejpam-3479	91	5	−4q	−4q	PROPN
ejpam-3479	91	6	+	+	NUM
ejpam-3479	91	7	µq	µq	PROPN
ejpam-3479	91	8	=	=	SYM
ejpam-3479	91	9	βq(t	βq(t	X
ejpam-3479	91	10	,	,	PUNCT
ejpam-3479	91	11	0	0	NUM
ejpam-3479	91	12	,	,	PUNCT
ejpam-3479	91	13	x	x	NOUN
ejpam-3479	91	14	)	)	PUNCT
ejpam-3479	91	15	in	in	ADP
ejpam-3479	91	16	q	q	NOUN
ejpam-3479	91	17	,	,	PUNCT
ejpam-3479	91	18	q	q	X
ejpam-3479	91	19	=	=	PUNCT
ejpam-3479	91	20	h0χo	h0χo	X
ejpam-3479	91	21	+	+	CCONJ
ejpam-3479	91	22	(	(	PUNCT
ejpam-3479	91	23	w0	w0	PROPN
ejpam-3479	91	24	−	−	PROPN
ejpam-3479	91	25	v)χγ	v)χγ	PROPN
ejpam-3479	91	26	on	on	ADP
ejpam-3479	91	27	σ	σ	PROPN
ejpam-3479	91	28	,	,	PUNCT
ejpam-3479	91	29	q(t	q(t	PROPN
ejpam-3479	91	30	,	,	PUNCT
ejpam-3479	91	31	a	a	PRON
ejpam-3479	91	32	,	,	PUNCT
ejpam-3479	91	33	x	x	NOUN
ejpam-3479	91	34	)	)	PUNCT
ejpam-3479	91	35	=	=	SYM
ejpam-3479	91	36	0	0	NUM
ejpam-3479	92	1	in	in	ADP
ejpam-3479	92	2	qa	qa	PROPN
ejpam-3479	92	3	,	,	PUNCT
ejpam-3479	92	4	q(t	q(t	PROPN
ejpam-3479	92	5	,	,	PUNCT
ejpam-3479	92	6	a	a	PRON
ejpam-3479	92	7	,	,	PUNCT
ejpam-3479	92	8	x	x	NOUN
ejpam-3479	92	9	)	)	PUNCT
ejpam-3479	92	10	=	=	SYM
ejpam-3479	92	11	0	0	NUM
ejpam-3479	93	1	in	in	ADP
ejpam-3479	93	2	qt	qt	NOUN
ejpam-3479	93	3	,	,	PUNCT
ejpam-3479	93	4	(	(	PUNCT
ejpam-3479	93	5	15	15	NUM
ejpam-3479	93	6	)	)	PUNCT
ejpam-3479	93	7	q	q	NOUN
ejpam-3479	93	8	satisfy	satisfy	NOUN
ejpam-3479	93	9	q(0	q(0	PROPN
ejpam-3479	93	10	,	,	PUNCT
ejpam-3479	93	11	a	a	PRON
ejpam-3479	93	12	,	,	PUNCT
ejpam-3479	93	13	x	x	NOUN
ejpam-3479	93	14	;	;	PUNCT
ejpam-3479	93	15	v	v	X
ejpam-3479	93	16	)	)	PUNCT
ejpam-3479	93	17	=	=	SYM
ejpam-3479	93	18	0	0	NUM
ejpam-3479	94	1	in	in	ADP
ejpam-3479	94	2	qa	qa	PROPN
ejpam-3479	94	3	.	.	PUNCT
ejpam-3479	95	1	(	(	PUNCT
ejpam-3479	95	2	16	16	NUM
ejpam-3479	95	3	)	)	PUNCT
ejpam-3479	95	4	remark	remark	NOUN
ejpam-3479	95	5	4	4	NUM
ejpam-3479	95	6	.	.	PUNCT
ejpam-3479	96	1	let	let	VERB
ejpam-3479	96	2	us	we	PRON
ejpam-3479	96	3	notice	notice	VERB
ejpam-3479	96	4	that	that	SCONJ
ejpam-3479	96	5	if	if	SCONJ
ejpam-3479	96	6	v	v	NOUN
ejpam-3479	96	7	exists	exist	VERB
ejpam-3479	96	8	,	,	PUNCT
ejpam-3479	96	9	the	the	DET
ejpam-3479	96	10	set	set	NOUN
ejpam-3479	96	11	e	e	NOUN
ejpam-3479	96	12	=	=	NOUN
ejpam-3479	96	13	{	{	PUNCT
ejpam-3479	96	14	v	v	NUM
ejpam-3479	96	15	∈	∈	NOUN
ejpam-3479	96	16	y	y	NOUN
ejpam-3479	96	17	⊥such	⊥such	PROPN
ejpam-3479	96	18	that	that	SCONJ
ejpam-3479	96	19	(	(	PUNCT
ejpam-3479	96	20	v	v	NOUN
ejpam-3479	96	21	,	,	PUNCT
ejpam-3479	96	22	q	q	NOUN
ejpam-3479	96	23	=	=	SYM
ejpam-3479	96	24	q(t	q(t	PROPN
ejpam-3479	96	25	,	,	PUNCT
ejpam-3479	96	26	a	a	PRON
ejpam-3479	96	27	,	,	PUNCT
ejpam-3479	96	28	x	x	NOUN
ejpam-3479	96	29	;	;	PUNCT
ejpam-3479	96	30	v	v	NOUN
ejpam-3479	96	31	)	)	PUNCT
ejpam-3479	96	32	)	)	PUNCT
ejpam-3479	96	33	satisfies	satisfie	NOUN
ejpam-3479	96	34	(	(	PUNCT
ejpam-3479	96	35	15)−	15)−	NUM
ejpam-3479	96	36	(	(	PUNCT
ejpam-3479	96	37	16	16	NUM
ejpam-3479	96	38	)	)	PUNCT
ejpam-3479	96	39	}	}	PUNCT
ejpam-3479	96	40	(	(	PUNCT
ejpam-3479	96	41	17	17	NUM
ejpam-3479	96	42	)	)	PUNCT
ejpam-3479	96	43	is	be	AUX
ejpam-3479	96	44	a	a	DET
ejpam-3479	96	45	non	non	ADJ
ejpam-3479	96	46	-	-	ADJ
ejpam-3479	96	47	empty	empty	ADJ
ejpam-3479	96	48	closed	closed	ADJ
ejpam-3479	96	49	,	,	PUNCT
ejpam-3479	96	50	and	and	CCONJ
ejpam-3479	96	51	convex	convex	NOUN
ejpam-3479	96	52	set	set	VERB
ejpam-3479	96	53	in	in	ADP
ejpam-3479	96	54	l2(u×γ	l2(u×γ	PROPN
ejpam-3479	96	55	)	)	PUNCT
ejpam-3479	96	56	.	.	PUNCT
ejpam-3479	97	1	therefore	therefore	ADV
ejpam-3479	97	2	there	there	PRON
ejpam-3479	97	3	exists	exist	VERB
ejpam-3479	97	4	v	v	ADP
ejpam-3479	97	5	∈	∈	PROPN
ejpam-3479	97	6	e	e	NOUN
ejpam-3479	97	7	of	of	ADP
ejpam-3479	97	8	minimal	minimal	ADJ
ejpam-3479	97	9	norm	norm	NOUN
ejpam-3479	97	10	.	.	PUNCT
ejpam-3479	98	1	the	the	DET
ejpam-3479	98	2	problem	problem	NOUN
ejpam-3479	98	3	(	(	PUNCT
ejpam-3479	98	4	14	14	NUM
ejpam-3479	98	5	)	)	PUNCT
ejpam-3479	98	6	−	−	PROPN
ejpam-3479	98	7	(	(	PUNCT
ejpam-3479	98	8	16	16	NUM
ejpam-3479	98	9	)	)	PUNCT
ejpam-3479	98	10	is	be	AUX
ejpam-3479	98	11	a	a	DET
ejpam-3479	98	12	null	null	ADJ
ejpam-3479	98	13	boundary	boundary	ADJ
ejpam-3479	98	14	controllability	controllability	NOUN
ejpam-3479	98	15	problem	problem	NOUN
ejpam-3479	98	16	with	with	ADP
ejpam-3479	98	17	constraint	constraint	NOUN
ejpam-3479	98	18	on	on	ADP
ejpam-3479	98	19	the	the	DET
ejpam-3479	98	20	control	control	NOUN
ejpam-3479	98	21	.	.	PUNCT
ejpam-3479	99	1	when	when	SCONJ
ejpam-3479	99	2	y	y	PROPN
ejpam-3479	99	3	⊥	⊥	PROPN
ejpam-3479	99	4	=	=	PUNCT
ejpam-3479	100	1	l2(u	l2(u	PROPN
ejpam-3479	100	2	×	×	PROPN
ejpam-3479	100	3	γ	γ	NOUN
ejpam-3479	100	4	)	)	PUNCT
ejpam-3479	100	5	,	,	PUNCT
ejpam-3479	100	6	this	this	DET
ejpam-3479	100	7	problem	problem	NOUN
ejpam-3479	100	8	becomes	become	VERB
ejpam-3479	100	9	a	a	DET
ejpam-3479	100	10	null	null	ADJ
ejpam-3479	100	11	controllability	controllability	NOUN
ejpam-3479	100	12	problem	problem	NOUN
ejpam-3479	100	13	without	without	ADP
ejpam-3479	100	14	constraint	constraint	NOUN
ejpam-3479	100	15	on	on	ADP
ejpam-3479	100	16	the	the	DET
ejpam-3479	100	17	control	control	NOUN
ejpam-3479	100	18	.	.	PUNCT
ejpam-3479	101	1	this	this	DET
ejpam-3479	101	2	kind	kind	NOUN
ejpam-3479	101	3	of	of	ADP
ejpam-3479	101	4	problem	problem	NOUN
ejpam-3479	101	5	has	have	AUX
ejpam-3479	101	6	been	be	AUX
ejpam-3479	101	7	studied	study	VERB
ejpam-3479	101	8	by	by	ADP
ejpam-3479	101	9	many	many	ADJ
ejpam-3479	101	10	authors	author	NOUN
ejpam-3479	101	11	with	with	ADP
ejpam-3479	101	12	various	various	ADJ
ejpam-3479	101	13	methods	method	NOUN
ejpam-3479	101	14	[	[	X
ejpam-3479	101	15	2	2	NUM
ejpam-3479	101	16	,	,	PUNCT
ejpam-3479	101	17	5	5	NUM
ejpam-3479	101	18	]	]	PUNCT
ejpam-3479	101	19	.	.	PUNCT
ejpam-3479	102	1	in	in	ADP
ejpam-3479	102	2	this	this	DET
ejpam-3479	102	3	paper	paper	NOUN
ejpam-3479	102	4	we	we	PRON
ejpam-3479	102	5	solve	solve	VERB
ejpam-3479	102	6	the	the	DET
ejpam-3479	102	7	boundary	boundary	ADJ
ejpam-3479	102	8	null	null	ADJ
ejpam-3479	102	9	controllability	controllability	NOUN
ejpam-3479	102	10	problem	problem	NOUN
ejpam-3479	102	11	with	with	ADP
ejpam-3479	102	12	constraint	constraint	NOUN
ejpam-3479	102	13	on	on	ADP
ejpam-3479	102	14	the	the	DET
ejpam-3479	102	15	control	control	NOUN
ejpam-3479	102	16	(	(	PUNCT
ejpam-3479	102	17	14)−	14)−	NUM
ejpam-3479	102	18	(	(	PUNCT
ejpam-3479	102	19	16	16	NUM
ejpam-3479	102	20	)	)	PUNCT
ejpam-3479	102	21	,	,	PUNCT
ejpam-3479	102	22	this	this	PRON
ejpam-3479	102	23	allows	allow	VERB
ejpam-3479	102	24	us	we	PRON
ejpam-3479	102	25	to	to	PART
ejpam-3479	102	26	prove	prove	VERB
ejpam-3479	102	27	the	the	DET
ejpam-3479	102	28	existence	existence	NOUN
ejpam-3479	102	29	of	of	ADP
ejpam-3479	102	30	the	the	DET
ejpam-3479	102	31	sentinel	sentinel	NOUN
ejpam-3479	102	32	with	with	ADP
ejpam-3479	102	33	given	give	VERB
ejpam-3479	102	34	sensitivity	sensitivity	NOUN
ejpam-3479	102	35	(	(	PUNCT
ejpam-3479	102	36	4	4	NUM
ejpam-3479	102	37	)	)	PUNCT
ejpam-3479	102	38	−	−	PROPN
ejpam-3479	102	39	(	(	PUNCT
ejpam-3479	102	40	7	7	NUM
ejpam-3479	102	41	)	)	PUNCT
ejpam-3479	102	42	.	.	PUNCT
ejpam-3479	103	1	more	more	ADV
ejpam-3479	103	2	precisely	precisely	ADV
ejpam-3479	103	3	,	,	PUNCT
ejpam-3479	103	4	we	we	PRON
ejpam-3479	103	5	have	have	VERB
ejpam-3479	103	6	the	the	DET
ejpam-3479	103	7	following	follow	VERB
ejpam-3479	103	8	results	result	NOUN
ejpam-3479	103	9	:	:	PUNCT
ejpam-3479	103	10	theorem	theorem	NOUN
ejpam-3479	103	11	1	1	NUM
ejpam-3479	103	12	.	.	PUNCT
ejpam-3479	104	1	let	let	VERB
ejpam-3479	104	2	ω	ω	PRON
ejpam-3479	104	3	be	be	AUX
ejpam-3479	104	4	a	a	DET
ejpam-3479	104	5	bounded	bounded	ADJ
ejpam-3479	104	6	open	open	ADJ
ejpam-3479	104	7	subset	subset	NOUN
ejpam-3479	104	8	of	of	ADP
ejpam-3479	104	9	rn	rn	PROPN
ejpam-3479	104	10	with	with	ADP
ejpam-3479	104	11	boundary	boundary	ADJ
ejpam-3479	104	12	γ	γ	NOUN
ejpam-3479	104	13	of	of	ADP
ejpam-3479	104	14	class	class	NOUN
ejpam-3479	104	15	c∞.	c∞.	PROPN
ejpam-3479	104	16	let	let	VERB
ejpam-3479	104	17	γ1	γ1	PROPN
ejpam-3479	104	18	be	be	AUX
ejpam-3479	104	19	a	a	DET
ejpam-3479	104	20	non	non	ADJ
ejpam-3479	104	21	-	-	ADJ
ejpam-3479	104	22	empty	empty	ADJ
ejpam-3479	104	23	open	open	ADJ
ejpam-3479	104	24	subset	subset	NOUN
ejpam-3479	104	25	of	of	ADP
ejpam-3479	104	26	γ	γ	PROPN
ejpam-3479	104	27	.	.	PUNCT
ejpam-3479	105	1	let	let	VERB
ejpam-3479	105	2	also	also	ADV
ejpam-3479	105	3	o	o	NOUN
ejpam-3479	105	4	and	and	CCONJ
ejpam-3479	105	5	γ	γ	X
ejpam-3479	105	6	be	be	AUX
ejpam-3479	105	7	two	two	NUM
ejpam-3479	105	8	non	non	ADJ
ejpam-3479	105	9	empty	empty	ADJ
ejpam-3479	105	10	subsets	subset	NOUN
ejpam-3479	105	11	of	of	ADP
ejpam-3479	105	12	γ\γ1	γ\γ1	PROPN
ejpam-3479	105	13	,	,	PUNCT
ejpam-3479	105	14	such	such	ADJ
ejpam-3479	105	15	that	that	SCONJ
ejpam-3479	105	16	o	o	NOUN
ejpam-3479	105	17	∩	∩	NOUN
ejpam-3479	105	18	γ	γ	X
ejpam-3479	105	19	6=	6=	PROPN
ejpam-3479	105	20	0	0	NUM
ejpam-3479	105	21	.	.	PUNCT
ejpam-3479	106	1	assume	assume	VERB
ejpam-3479	106	2	that	that	SCONJ
ejpam-3479	106	3	the	the	DET
ejpam-3479	106	4	assumptions	assumption	NOUN
ejpam-3479	106	5	of	of	ADP
ejpam-3479	106	6	the	the	DET
ejpam-3479	106	7	data	datum	NOUN
ejpam-3479	106	8	of	of	ADP
ejpam-3479	106	9	the	the	DET
ejpam-3479	106	10	system	system	NOUN
ejpam-3479	106	11	(	(	PUNCT
ejpam-3479	106	12	1	1	X
ejpam-3479	106	13	)	)	PUNCT
ejpam-3479	106	14	are	be	AUX
ejpam-3479	106	15	satisfied	satisfied	ADJ
ejpam-3479	106	16	.	.	PUNCT
ejpam-3479	107	1	assume	assume	VERB
ejpam-3479	107	2	also	also	ADV
ejpam-3479	107	3	that	that	SCONJ
ejpam-3479	107	4	(	(	PUNCT
ejpam-3479	107	5	11	11	NUM
ejpam-3479	107	6	)	)	PUNCT
ejpam-3479	107	7	and	and	CCONJ
ejpam-3479	107	8	(	(	PUNCT
ejpam-3479	107	9	12	12	NUM
ejpam-3479	107	10	)	)	PUNCT
ejpam-3479	107	11	holds	hold	VERB
ejpam-3479	107	12	.	.	PUNCT
ejpam-3479	108	1	then	then	ADV
ejpam-3479	108	2	the	the	DET
ejpam-3479	108	3	existence	existence	NOUN
ejpam-3479	108	4	of	of	ADP
ejpam-3479	108	5	sentinel	sentinel	NOUN
ejpam-3479	108	6	(	(	PUNCT
ejpam-3479	108	7	4)−	4)−	NOUN
ejpam-3479	108	8	(	(	PUNCT
ejpam-3479	108	9	7	7	NUM
ejpam-3479	108	10	)	)	PUNCT
ejpam-3479	108	11	holds	hold	VERB
ejpam-3479	108	12	if	if	SCONJ
ejpam-3479	108	13	and	and	CCONJ
ejpam-3479	108	14	only	only	ADV
ejpam-3479	108	15	if	if	SCONJ
ejpam-3479	108	16	,	,	PUNCT
ejpam-3479	108	17	the	the	DET
ejpam-3479	108	18	boundary	boundary	ADJ
ejpam-3479	108	19	null	null	ADJ
ejpam-3479	108	20	-	-	PUNCT
ejpam-3479	108	21	controllability	controllability	NOUN
ejpam-3479	108	22	problem	problem	NOUN
ejpam-3479	108	23	with	with	ADP
ejpam-3479	108	24	constraints	constraint	NOUN
ejpam-3479	108	25	on	on	ADP
ejpam-3479	108	26	the	the	DET
ejpam-3479	108	27	control	control	NOUN
ejpam-3479	108	28	(	(	PUNCT
ejpam-3479	108	29	14)−(16	14)−(16	NUM
ejpam-3479	108	30	)	)	PUNCT
ejpam-3479	108	31	has	have	VERB
ejpam-3479	108	32	a	a	DET
ejpam-3479	108	33	solution	solution	NOUN
ejpam-3479	108	34	.	.	PUNCT
ejpam-3479	109	1	to	to	PART
ejpam-3479	109	2	prove	prove	VERB
ejpam-3479	109	3	the	the	DET
ejpam-3479	109	4	boundary	boundary	ADJ
ejpam-3479	109	5	null	null	ADJ
ejpam-3479	109	6	-	-	PUNCT
ejpam-3479	109	7	controllability	controllability	NOUN
ejpam-3479	109	8	problem	problem	NOUN
ejpam-3479	109	9	with	with	ADP
ejpam-3479	109	10	constraints	constraint	NOUN
ejpam-3479	109	11	on	on	ADP
ejpam-3479	109	12	the	the	DET
ejpam-3479	109	13	control	control	NOUN
ejpam-3479	109	14	(	(	PUNCT
ejpam-3479	109	15	14)−	14)−	NUM
ejpam-3479	109	16	(	(	PUNCT
ejpam-3479	109	17	16	16	NUM
ejpam-3479	109	18	)	)	PUNCT
ejpam-3479	109	19	,	,	PUNCT
ejpam-3479	109	20	we	we	PRON
ejpam-3479	109	21	use	use	VERB
ejpam-3479	109	22	an	an	DET
ejpam-3479	109	23	inequality	inequality	NOUN
ejpam-3479	109	24	of	of	ADP
ejpam-3479	109	25	carleman	carleman	NOUN
ejpam-3479	109	26	adapted	adapt	VERB
ejpam-3479	109	27	to	to	ADP
ejpam-3479	109	28	the	the	DET
ejpam-3479	109	29	constraint	constraint	NOUN
ejpam-3479	109	30	that	that	PRON
ejpam-3479	109	31	we	we	PRON
ejpam-3479	109	32	establish	establish	VERB
ejpam-3479	109	33	by	by	ADP
ejpam-3479	109	34	means	mean	NOUN
ejpam-3479	109	35	of	of	ADP
ejpam-3479	109	36	a	a	DET
ejpam-3479	109	37	global	global	ADJ
ejpam-3479	109	38	carleman	carleman	NOUN
ejpam-3479	109	39	inequality	inequality	NOUN
ejpam-3479	109	40	.	.	PUNCT
ejpam-3479	110	1	more	more	ADV
ejpam-3479	110	2	precisely	precisely	ADV
ejpam-3479	110	3	we	we	PRON
ejpam-3479	110	4	prove	prove	VERB
ejpam-3479	110	5	the	the	DET
ejpam-3479	110	6	following	follow	VERB
ejpam-3479	110	7	results	result	NOUN
ejpam-3479	110	8	.	.	PUNCT
ejpam-3479	111	1	theorem	theorem	NOUN
ejpam-3479	111	2	2	2	NUM
ejpam-3479	111	3	.	.	X
ejpam-3479	111	4	assume	assume	VERB
ejpam-3479	111	5	that	that	SCONJ
ejpam-3479	111	6	the	the	DET
ejpam-3479	111	7	hypotheses	hypothesis	NOUN
ejpam-3479	111	8	of	of	ADP
ejpam-3479	111	9	theorem	theorem	NOUN
ejpam-3479	111	10	1	1	NUM
ejpam-3479	111	11	are	be	AUX
ejpam-3479	111	12	satisfied	satisfied	ADJ
ejpam-3479	111	13	.	.	PUNCT
ejpam-3479	112	1	then	then	ADV
ejpam-3479	112	2	there	there	PRON
ejpam-3479	112	3	exists	exist	VERB
ejpam-3479	112	4	a	a	DET
ejpam-3479	112	5	positive	positive	ADJ
ejpam-3479	112	6	real	real	ADJ
ejpam-3479	112	7	weight	weight	NOUN
ejpam-3479	112	8	function	function	NOUN
ejpam-3479	112	9	θ	θ	PROPN
ejpam-3479	112	10	(	(	PUNCT
ejpam-3479	112	11	a	a	DET
ejpam-3479	112	12	precise	precise	ADJ
ejpam-3479	112	13	definition	definition	NOUN
ejpam-3479	112	14	of	of	ADP
ejpam-3479	112	15	θ	θ	PROPN
ejpam-3479	112	16	will	will	AUX
ejpam-3479	112	17	be	be	AUX
ejpam-3479	112	18	given	give	VERB
ejpam-3479	112	19	later	later	ADV
ejpam-3479	112	20	on	on	ADV
ejpam-3479	112	21	(	(	PUNCT
ejpam-3479	112	22	31	31	NUM
ejpam-3479	112	23	)	)	PUNCT
ejpam-3479	112	24	)	)	PUNCT
ejpam-3479	112	25	such	such	ADJ
ejpam-3479	112	26	that	that	SCONJ
ejpam-3479	112	27	,	,	PUNCT
ejpam-3479	112	28	for	for	ADP
ejpam-3479	112	29	any	any	DET
ejpam-3479	112	30	function	function	NOUN
ejpam-3479	112	31	h0	h0	NOUN
ejpam-3479	112	32	∈	∈	PROPN
ejpam-3479	112	33	l2(u	l2(u	X
ejpam-3479	112	34	×o	×o	NOUN
ejpam-3479	112	35	)	)	PUNCT
ejpam-3479	112	36	with	with	ADP
ejpam-3479	112	37	θh0	θh0	NOUN
ejpam-3479	112	38	∈	∈	PROPN
ejpam-3479	112	39	l2(u	l2(u	X
ejpam-3479	112	40	×o	×o	PROPN
ejpam-3479	112	41	)	)	PUNCT
ejpam-3479	112	42	there	there	PRON
ejpam-3479	112	43	exists	exist	VERB
ejpam-3479	112	44	a	a	DET
ejpam-3479	112	45	unique	unique	ADJ
ejpam-3479	112	46	control	control	NOUN
ejpam-3479	112	47	v̂	v̂	ADP
ejpam-3479	112	48	∈	∈	NOUN
ejpam-3479	113	1	l2(u	l2(u	X
ejpam-3479	113	2	×	×	PROPN
ejpam-3479	113	3	γ	γ	NOUN
ejpam-3479	113	4	)	)	PUNCT
ejpam-3479	113	5	such	such	ADJ
ejpam-3479	113	6	that	that	SCONJ
ejpam-3479	113	7	(	(	PUNCT
ejpam-3479	113	8	v̂	v̂	NOUN
ejpam-3479	113	9	,	,	PUNCT
ejpam-3479	113	10	q̂	q̂	NUM
ejpam-3479	113	11	)	)	PUNCT
ejpam-3479	113	12	with	with	ADP
ejpam-3479	113	13	q̂	q̂	X
ejpam-3479	113	14	=	=	SYM
ejpam-3479	113	15	q(v̂	q(v̂	NOUN
ejpam-3479	113	16	)	)	PUNCT
ejpam-3479	113	17	is	be	AUX
ejpam-3479	113	18	solution	solution	NOUN
ejpam-3479	113	19	of	of	ADP
ejpam-3479	113	20	null	null	ADJ
ejpam-3479	113	21	boundary	boundary	ADJ
ejpam-3479	113	22	controllability	controllability	NOUN
ejpam-3479	113	23	problem	problem	NOUN
ejpam-3479	113	24	with	with	ADP
ejpam-3479	113	25	constraint	constraint	NOUN
ejpam-3479	113	26	on	on	ADP
ejpam-3479	113	27	the	the	DET
ejpam-3479	113	28	control	control	NOUN
ejpam-3479	113	29	(	(	PUNCT
ejpam-3479	113	30	14)−	14)−	NUM
ejpam-3479	113	31	(	(	PUNCT
ejpam-3479	113	32	16	16	NUM
ejpam-3479	113	33	)	)	PUNCT
ejpam-3479	113	34	and	and	CCONJ
ejpam-3479	113	35	provides	provide	VERB
ejpam-3479	113	36	a	a	DET
ejpam-3479	113	37	control	control	NOUN
ejpam-3479	113	38	ŵ	ŵ	X
ejpam-3479	114	1	=	=	SYM
ejpam-3479	114	2	w0χγ	w0χγ	PUNCT
ejpam-3479	114	3	−	−	PROPN
ejpam-3479	114	4	v̂	v̂	NOUN
ejpam-3479	114	5	of	of	ADP
ejpam-3479	114	6	the	the	DET
ejpam-3479	114	7	sentinel	sentinel	ADJ
ejpam-3479	114	8	problem	problem	NOUN
ejpam-3479	114	9	satisfying	satisfying	ADJ
ejpam-3479	114	10	(	(	PUNCT
ejpam-3479	114	11	7	7	NUM
ejpam-3479	114	12	)	)	PUNCT
ejpam-3479	114	13	.	.	PUNCT
ejpam-3479	115	1	moreover	moreover	ADV
ejpam-3479	115	2	,	,	PUNCT
ejpam-3479	115	3	the	the	DET
ejpam-3479	115	4	control	control	NOUN
ejpam-3479	115	5	ŵ	ŵ	PROPN
ejpam-3479	115	6	is	be	AUX
ejpam-3479	115	7	given	give	VERB
ejpam-3479	115	8	by	by	ADP
ejpam-3479	115	9	ŵ	ŵ	X
ejpam-3479	115	10	=	=	SYM
ejpam-3479	115	11	p	p	X
ejpam-3479	115	12	(	(	PUNCT
ejpam-3479	115	13	w0	w0	PROPN
ejpam-3479	115	14	)	)	PUNCT
ejpam-3479	115	15	+	+	CCONJ
ejpam-3479	116	1	(	(	PUNCT
ejpam-3479	116	2	i	i	PRON
ejpam-3479	116	3	−	−	PROPN
ejpam-3479	116	4	p	p	NOUN
ejpam-3479	116	5	)	)	PUNCT
ejpam-3479	116	6	(	(	PUNCT
ejpam-3479	116	7	∂ρ̂	∂ρ̂	VERB
ejpam-3479	116	8	∂ν	∂ν	PRON
ejpam-3479	116	9	χγ	χγ	PROPN
ejpam-3479	116	10	)	)	PUNCT
ejpam-3479	116	11	,	,	PUNCT
ejpam-3479	116	12	(	(	PUNCT
ejpam-3479	116	13	18	18	NUM
ejpam-3479	116	14	)	)	PUNCT
ejpam-3479	116	15	m.soma	m.soma	NOUN
ejpam-3479	116	16	,	,	PUNCT
ejpam-3479	116	17	s.	s.	PROPN
ejpam-3479	116	18	sawadogo	sawadogo	PROPN
ejpam-3479	116	19	/	/	SYM
ejpam-3479	116	20	eur	eur	PROPN
ejpam-3479	116	21	.	.	PUNCT
ejpam-3479	117	1	j.	j.	PROPN
ejpam-3479	117	2	pure	pure	PROPN
ejpam-3479	117	3	appl	appl	PROPN
ejpam-3479	117	4	.	.	PROPN
ejpam-3479	117	5	math	math	PROPN
ejpam-3479	117	6	,	,	PUNCT
ejpam-3479	117	7	12	12	NUM
ejpam-3479	117	8	(	(	PUNCT
ejpam-3479	117	9	3	3	NUM
ejpam-3479	117	10	)	)	PUNCT
ejpam-3479	117	11	(	(	PUNCT
ejpam-3479	117	12	2019	2019	NUM
ejpam-3479	117	13	)	)	PUNCT
ejpam-3479	117	14	,	,	PUNCT
ejpam-3479	117	15	1277	1277	NUM
ejpam-3479	117	16	-	-	SYM
ejpam-3479	117	17	1296	1296	NUM
ejpam-3479	117	18	1283	1283	NUM
ejpam-3479	117	19	where	where	SCONJ
ejpam-3479	117	20	p	p	NOUN
ejpam-3479	117	21	is	be	AUX
ejpam-3479	117	22	the	the	DET
ejpam-3479	117	23	orthogonal	orthogonal	ADJ
ejpam-3479	117	24	projection	projection	NOUN
ejpam-3479	117	25	operator	operator	NOUN
ejpam-3479	117	26	from	from	ADP
ejpam-3479	117	27	l2(u	l2(u	PROPN
ejpam-3479	117	28	×	×	PROPN
ejpam-3479	117	29	γ	γ	NOUN
ejpam-3479	117	30	)	)	PUNCT
ejpam-3479	117	31	into	into	ADP
ejpam-3479	117	32	y	y	PROPN
ejpam-3479	117	33	,	,	PUNCT
ejpam-3479	117	34	w0	w0	PROPN
ejpam-3479	117	35	∈	∈	PROPN
ejpam-3479	117	36	yθ	yθ	NOUN
ejpam-3479	117	37	depends	depend	VERB
ejpam-3479	117	38	on	on	ADP
ejpam-3479	117	39	h0	h0	PROPN
ejpam-3479	117	40	and	and	CCONJ
ejpam-3479	117	41	ci	ci	PROPN
ejpam-3479	117	42	,	,	PUNCT
ejpam-3479	117	43	i	i	PRON
ejpam-3479	117	44	∈	∈	PROPN
ejpam-3479	117	45	{	{	PUNCT
ejpam-3479	117	46	1	1	NUM
ejpam-3479	117	47	,	,	PUNCT
ejpam-3479	117	48	.	.	PUNCT
ejpam-3479	117	49	.	.	PUNCT
ejpam-3479	117	50	.	.	PUNCT
ejpam-3479	118	1	,	,	PUNCT
ejpam-3479	118	2	m	m	VERB
ejpam-3479	118	3	}	}	PUNCT
ejpam-3479	118	4	,	,	PUNCT
ejpam-3479	118	5	and	and	CCONJ
ejpam-3479	118	6	will	will	AUX
ejpam-3479	118	7	be	be	AUX
ejpam-3479	118	8	precisely	precisely	ADV
ejpam-3479	118	9	determined	determined	ADJ
ejpam-3479	118	10	in	in	ADP
ejpam-3479	118	11	(	(	PUNCT
ejpam-3479	118	12	27	27	NUM
ejpam-3479	118	13	)	)	PUNCT
ejpam-3479	118	14	and	and	CCONJ
ejpam-3479	118	15	ρ̂	ρ̂	NUM
ejpam-3479	118	16	satisfies	satisfies	NOUN
ejpam-3479	118	17	∂ρ̂	∂ρ̂	VERB
ejpam-3479	119	1	∂t	∂t	PROPN
ejpam-3479	119	2	+	+	NUM
ejpam-3479	119	3	∂ρ̂	∂ρ̂	NOUN
ejpam-3479	119	4	∂a	∂a	VERB
ejpam-3479	119	5	−4ρ̂+	−4ρ̂+	NOUN
ejpam-3479	119	6	µρ̂	µρ̂	PROPN
ejpam-3479	120	1	=	=	NOUN
ejpam-3479	120	2	0	0	NUM
ejpam-3479	120	3	in	in	ADP
ejpam-3479	120	4	q	q	NOUN
ejpam-3479	120	5	,	,	PUNCT
ejpam-3479	120	6	ρ̂	ρ̂	NUM
ejpam-3479	120	7	=	=	SYM
ejpam-3479	120	8	0	0	NUM
ejpam-3479	121	1	on	on	ADP
ejpam-3479	121	2	σ	σ	PROPN
ejpam-3479	121	3	ρ̂(t	ρ̂(t	PROPN
ejpam-3479	121	4	,	,	PUNCT
ejpam-3479	121	5	0	0	NUM
ejpam-3479	121	6	,	,	PUNCT
ejpam-3479	121	7	x	x	NOUN
ejpam-3479	121	8	)	)	PUNCT
ejpam-3479	121	9	=	=	SYM
ejpam-3479	121	10	∫	∫	PROPN
ejpam-3479	121	11	a	a	DET
ejpam-3479	121	12	0	0	NUM
ejpam-3479	121	13	β(t	β(t	PROPN
ejpam-3479	121	14	,	,	PUNCT
ejpam-3479	121	15	a	a	PRON
ejpam-3479	121	16	,	,	PUNCT
ejpam-3479	121	17	x)ρ̂(t	x)ρ̂(t	PROPN
ejpam-3479	121	18	,	,	PUNCT
ejpam-3479	121	19	a	a	PRON
ejpam-3479	121	20	,	,	PUNCT
ejpam-3479	121	21	x)da	x)da	PROPN
ejpam-3479	121	22	in	in	ADP
ejpam-3479	121	23	qt	qt	NOUN
ejpam-3479	121	24	,	,	PUNCT
ejpam-3479	121	25	ρ̂(0	ρ̂(0	PROPN
ejpam-3479	121	26	,	,	PUNCT
ejpam-3479	121	27	.	.	PUNCT
ejpam-3479	121	28	,	,	PUNCT
ejpam-3479	121	29	.	.	PUNCT
ejpam-3479	121	30	)	)	PUNCT
ejpam-3479	122	1	=	=	PUNCT
ejpam-3479	122	2	0	0	NUM
ejpam-3479	123	1	in	in	ADP
ejpam-3479	123	2	qa	qa	PROPN
ejpam-3479	123	3	,	,	PUNCT
ejpam-3479	123	4	(	(	PUNCT
ejpam-3479	123	5	19	19	NUM
ejpam-3479	123	6	)	)	PUNCT
ejpam-3479	123	7	the	the	DET
ejpam-3479	123	8	rest	rest	NOUN
ejpam-3479	123	9	of	of	ADP
ejpam-3479	123	10	the	the	DET
ejpam-3479	123	11	paper	paper	NOUN
ejpam-3479	123	12	is	be	AUX
ejpam-3479	123	13	organized	organize	VERB
ejpam-3479	123	14	as	as	SCONJ
ejpam-3479	123	15	follows	follow	VERB
ejpam-3479	123	16	:	:	PUNCT
ejpam-3479	123	17	section	section	NOUN
ejpam-3479	123	18	2	2	NUM
ejpam-3479	123	19	is	be	AUX
ejpam-3479	123	20	devoted	devote	VERB
ejpam-3479	123	21	to	to	ADP
ejpam-3479	123	22	the	the	DET
ejpam-3479	123	23	equivalence	equivalence	NOUN
ejpam-3479	123	24	between	between	ADP
ejpam-3479	123	25	the	the	DET
ejpam-3479	123	26	sentinel	sentinel	ADJ
ejpam-3479	123	27	problem	problem	NOUN
ejpam-3479	123	28	and	and	CCONJ
ejpam-3479	123	29	the	the	DET
ejpam-3479	123	30	null	null	ADJ
ejpam-3479	123	31	boundary	boundary	ADJ
ejpam-3479	123	32	controllability	controllability	NOUN
ejpam-3479	123	33	problem	problem	NOUN
ejpam-3479	123	34	with	with	ADP
ejpam-3479	123	35	constraint	constraint	NOUN
ejpam-3479	123	36	on	on	ADP
ejpam-3479	123	37	the	the	DET
ejpam-3479	123	38	control	control	NOUN
ejpam-3479	123	39	.	.	PUNCT
ejpam-3479	124	1	in	in	ADP
ejpam-3479	124	2	this	this	DET
ejpam-3479	124	3	section	section	NOUN
ejpam-3479	124	4	we	we	PRON
ejpam-3479	124	5	give	give	VERB
ejpam-3479	124	6	the	the	DET
ejpam-3479	124	7	proof	proof	NOUN
ejpam-3479	124	8	of	of	ADP
ejpam-3479	124	9	theorem	theorem	NOUN
ejpam-3479	124	10	1	1	NUM
ejpam-3479	124	11	.	.	PUNCT
ejpam-3479	125	1	in	in	ADP
ejpam-3479	125	2	section	section	NOUN
ejpam-3479	125	3	3	3	NUM
ejpam-3479	125	4	,	,	PUNCT
ejpam-3479	125	5	we	we	PRON
ejpam-3479	125	6	establish	establish	VERB
ejpam-3479	125	7	carleman	carleman	ADJ
ejpam-3479	125	8	inequalities	inequality	NOUN
ejpam-3479	125	9	necessary	necessary	ADJ
ejpam-3479	125	10	to	to	PART
ejpam-3479	125	11	solve	solve	VERB
ejpam-3479	125	12	the	the	DET
ejpam-3479	125	13	boundary	boundary	ADJ
ejpam-3479	125	14	null	null	ADJ
ejpam-3479	125	15	-	-	PUNCT
ejpam-3479	125	16	controllability	controllability	NOUN
ejpam-3479	125	17	problem	problem	NOUN
ejpam-3479	125	18	with	with	ADP
ejpam-3479	125	19	constraint	constraint	NOUN
ejpam-3479	125	20	on	on	ADP
ejpam-3479	125	21	the	the	DET
ejpam-3479	125	22	control	control	NOUN
ejpam-3479	125	23	(	(	PUNCT
ejpam-3479	125	24	14	14	NUM
ejpam-3479	125	25	)	)	PUNCT
ejpam-3479	125	26	−	−	PROPN
ejpam-3479	126	1	(	(	PUNCT
ejpam-3479	126	2	16	16	NUM
ejpam-3479	126	3	)	)	PUNCT
ejpam-3479	126	4	.	.	PUNCT
ejpam-3479	127	1	in	in	ADP
ejpam-3479	127	2	subsection	subsection	NOUN
ejpam-3479	127	3	3.2	3.2	NUM
ejpam-3479	127	4	we	we	PRON
ejpam-3479	127	5	give	give	VERB
ejpam-3479	127	6	the	the	DET
ejpam-3479	127	7	proof	proof	NOUN
ejpam-3479	127	8	of	of	ADP
ejpam-3479	127	9	theorem	theorem	NOUN
ejpam-3479	127	10	2	2	NUM
ejpam-3479	127	11	.	.	PUNCT
ejpam-3479	128	1	in	in	ADP
ejpam-3479	128	2	section	section	NOUN
ejpam-3479	128	3	4	4	NUM
ejpam-3479	128	4	,	,	PUNCT
ejpam-3479	128	5	we	we	PRON
ejpam-3479	128	6	formulate	formulate	VERB
ejpam-3479	128	7	the	the	DET
ejpam-3479	128	8	sentinel	sentinel	NOUN
ejpam-3479	128	9	and	and	CCONJ
ejpam-3479	128	10	we	we	PRON
ejpam-3479	128	11	identify	identify	VERB
ejpam-3479	128	12	the	the	DET
ejpam-3479	128	13	parameters	parameter	NOUN
ejpam-3479	128	14	.	.	PUNCT
ejpam-3479	129	1	2	2	X
ejpam-3479	129	2	.	.	X
ejpam-3479	129	3	equivalence	equivalence	NOUN
ejpam-3479	129	4	between	between	ADP
ejpam-3479	129	5	the	the	DET
ejpam-3479	129	6	sentinel	sentinel	ADJ
ejpam-3479	129	7	problem	problem	NOUN
ejpam-3479	129	8	and	and	CCONJ
ejpam-3479	129	9	the	the	DET
ejpam-3479	129	10	null	null	ADJ
ejpam-3479	129	11	boundary	boundary	ADJ
ejpam-3479	129	12	controllability	controllability	NOUN
ejpam-3479	129	13	problem	problem	NOUN
ejpam-3479	129	14	with	with	ADP
ejpam-3479	129	15	constraint	constraint	NOUN
ejpam-3479	129	16	on	on	ADP
ejpam-3479	129	17	the	the	DET
ejpam-3479	129	18	control	control	NOUN
ejpam-3479	129	19	in	in	ADP
ejpam-3479	129	20	this	this	DET
ejpam-3479	129	21	subsection	subsection	NOUN
ejpam-3479	129	22	we	we	PRON
ejpam-3479	129	23	prove	prove	VERB
ejpam-3479	129	24	theorem	theorem	ADJ
ejpam-3479	129	25	1	1	NUM
ejpam-3479	129	26	.	.	PUNCT
ejpam-3479	130	1	but	but	CCONJ
ejpam-3479	130	2	before	before	ADP
ejpam-3479	130	3	going	go	VERB
ejpam-3479	130	4	further	far	ADV
ejpam-3479	130	5	,	,	PUNCT
ejpam-3479	130	6	we	we	PRON
ejpam-3479	130	7	need	need	VERB
ejpam-3479	130	8	the	the	DET
ejpam-3479	130	9	following	follow	VERB
ejpam-3479	130	10	result	result	NOUN
ejpam-3479	130	11	:	:	PUNCT
ejpam-3479	131	1	lemma	lemma	PROPN
ejpam-3479	131	2	1	1	X
ejpam-3479	131	3	.	.	X
ejpam-3479	131	4	assume	assume	VERB
ejpam-3479	131	5	that	that	SCONJ
ejpam-3479	131	6	(	(	PUNCT
ejpam-3479	131	7	11	11	NUM
ejpam-3479	131	8	)	)	PUNCT
ejpam-3479	131	9	and	and	CCONJ
ejpam-3479	131	10	(	(	PUNCT
ejpam-3479	131	11	12	12	NUM
ejpam-3479	131	12	)	)	PUNCT
ejpam-3479	131	13	holds	hold	VERB
ejpam-3479	131	14	.	.	PUNCT
ejpam-3479	132	1	then	then	ADV
ejpam-3479	132	2	the	the	DET
ejpam-3479	132	3	functions	function	NOUN
ejpam-3479	132	4	∂yλi	∂yλi	SCONJ
ejpam-3479	132	5	∂ν	∂ν	PROPN
ejpam-3479	132	6	χγ	χγ	VERB
ejpam-3479	132	7	,	,	PUNCT
ejpam-3479	132	8	1	1	NUM
ejpam-3479	132	9	≤	≤	NUM
ejpam-3479	133	1	i	i	PRON
ejpam-3479	133	2	≤	≤	NOUN
ejpam-3479	133	3	m	m	VERB
ejpam-3479	133	4	are	be	AUX
ejpam-3479	133	5	linearly	linearly	ADV
ejpam-3479	133	6	independent	independent	ADJ
ejpam-3479	133	7	.	.	PUNCT
ejpam-3479	134	1	moreover	moreover	ADV
ejpam-3479	134	2	the	the	DET
ejpam-3479	134	3	functions	function	NOUN
ejpam-3479	134	4	1	1	NUM
ejpam-3479	134	5	θ	θ	NOUN
ejpam-3479	134	6	∂yλi	∂yλi	SCONJ
ejpam-3479	134	7	∂ν	∂ν	PROPN
ejpam-3479	134	8	χγ	χγ	VERB
ejpam-3479	134	9	,	,	PUNCT
ejpam-3479	134	10	1	1	NUM
ejpam-3479	134	11	≤	≤	NUM
ejpam-3479	134	12	i	i	PRON
ejpam-3479	134	13	≤	≤	NOUN
ejpam-3479	134	14	m	m	VERB
ejpam-3479	134	15	,	,	PUNCT
ejpam-3479	134	16	are	be	AUX
ejpam-3479	134	17	also	also	ADV
ejpam-3479	134	18	linearly	linearly	ADV
ejpam-3479	134	19	independent	independent	ADJ
ejpam-3479	134	20	.	.	PUNCT
ejpam-3479	135	1	proof	proof	NOUN
ejpam-3479	135	2	.	.	PUNCT
ejpam-3479	136	1	let	let	VERB
ejpam-3479	136	2	αi	αi	PRON
ejpam-3479	136	3	∈	∈	PROPN
ejpam-3479	136	4	r	r	NOUN
ejpam-3479	136	5	,	,	PUNCT
ejpam-3479	136	6	1	1	NUM
ejpam-3479	136	7	≤	≤	NUM
ejpam-3479	136	8	i	i	PRON
ejpam-3479	136	9	≤	≤	NOUN
ejpam-3479	136	10	m	m	AUX
ejpam-3479	136	11	be	be	VERB
ejpam-3479	136	12	such	such	ADJ
ejpam-3479	136	13	that	that	SCONJ
ejpam-3479	136	14	m∑	m∑	VERB
ejpam-3479	136	15	i	i	PRON
ejpam-3479	136	16	αi	αi	VERB
ejpam-3479	136	17	∂yλi	∂yλi	SCONJ
ejpam-3479	136	18	∂ν	∂ν	X
ejpam-3479	136	19	χγ	χγ	NOUN
ejpam-3479	136	20	=	=	NOUN
ejpam-3479	136	21	0	0	PROPN
ejpam-3479	136	22	.	.	PUNCT
ejpam-3479	137	1	set	set	VERB
ejpam-3479	137	2	k	k	NOUN
ejpam-3479	138	1	=	=	PUNCT
ejpam-3479	138	2	m∑	m∑	ADV
ejpam-3479	138	3	i	i	PRON
ejpam-3479	138	4	αiyλi	αiyλi	ADV
ejpam-3479	138	5	,	,	PUNCT
ejpam-3479	138	6	using	use	VERB
ejpam-3479	138	7	(	(	PUNCT
ejpam-3479	138	8	10	10	NUM
ejpam-3479	138	9	)	)	PUNCT
ejpam-3479	139	1	k	k	X
ejpam-3479	139	2	is	be	AUX
ejpam-3479	139	3	solution	solution	NOUN
ejpam-3479	139	4	of	of	PROPN
ejpam-3479	139	5	∂k	∂k	PROPN
ejpam-3479	139	6	∂t	∂t	PROPN
ejpam-3479	140	1	+	+	CCONJ
ejpam-3479	141	1	∂k	∂k	PROPN
ejpam-3479	141	2	∂a	∂a	NOUN
ejpam-3479	141	3	−∆k	−∆k	PUNCT
ejpam-3479	142	1	+	+	CCONJ
ejpam-3479	142	2	µk	µk	X
ejpam-3479	142	3	=	=	NOUN
ejpam-3479	142	4	0	0	NUM
ejpam-3479	142	5	in	in	ADP
ejpam-3479	142	6	q	q	PROPN
ejpam-3479	142	7	,	,	PUNCT
ejpam-3479	142	8	k(0	k(0	PROPN
ejpam-3479	142	9	,	,	PUNCT
ejpam-3479	142	10	a	a	PRON
ejpam-3479	142	11	,	,	PUNCT
ejpam-3479	142	12	x	x	NOUN
ejpam-3479	142	13	)	)	PUNCT
ejpam-3479	142	14	=	=	SYM
ejpam-3479	142	15	0	0	NUM
ejpam-3479	143	1	in	in	ADP
ejpam-3479	143	2	qa	qa	PROPN
ejpam-3479	143	3	,	,	PUNCT
ejpam-3479	143	4	k(t	k(t	PROPN
ejpam-3479	143	5	,	,	PUNCT
ejpam-3479	143	6	0	0	NUM
ejpam-3479	143	7	,	,	PUNCT
ejpam-3479	143	8	x	x	NOUN
ejpam-3479	143	9	)	)	PUNCT
ejpam-3479	143	10	=	=	SYM
ejpam-3479	143	11	∫	∫	PROPN
ejpam-3479	143	12	a	a	DET
ejpam-3479	143	13	0	0	NUM
ejpam-3479	143	14	βk(t	βk(t	NUM
ejpam-3479	143	15	,	,	PUNCT
ejpam-3479	143	16	a	a	DET
ejpam-3479	143	17	,	,	PUNCT
ejpam-3479	143	18	x)da	x)da	PROPN
ejpam-3479	143	19	in	in	ADP
ejpam-3479	143	20	qt	qt	NOUN
ejpam-3479	143	21	,	,	PUNCT
ejpam-3479	143	22	k	k	PROPN
ejpam-3479	143	23	=	=	PUNCT
ejpam-3479	143	24	m∑	m∑	PROPN
ejpam-3479	143	25	i=1	i=1	PROPN
ejpam-3479	143	26	αiξ̂i.χς1	αiξ̂i.χς1	PROPN
ejpam-3479	143	27	on	on	ADP
ejpam-3479	143	28	σ	σ	NOUN
ejpam-3479	143	29	,	,	PUNCT
ejpam-3479	143	30	∂k	∂k	PROPN
ejpam-3479	143	31	∂ν	∂ν	PROPN
ejpam-3479	143	32	=	=	SYM
ejpam-3479	143	33	0	0	NUM
ejpam-3479	143	34	on	on	ADP
ejpam-3479	143	35	u	u	PROPN
ejpam-3479	143	36	×	×	PROPN
ejpam-3479	143	37	γ	γ	X
ejpam-3479	143	38	.	.	PROPN
ejpam-3479	144	1	(	(	PUNCT
ejpam-3479	144	2	20	20	NUM
ejpam-3479	144	3	)	)	PUNCT
ejpam-3479	144	4	assumption	assumption	NOUN
ejpam-3479	144	5	(	(	PUNCT
ejpam-3479	144	6	12	12	NUM
ejpam-3479	144	7	)	)	PUNCT
ejpam-3479	144	8	allows	allow	VERB
ejpam-3479	144	9	us	we	PRON
ejpam-3479	144	10	to	to	PART
ejpam-3479	144	11	say	say	VERB
ejpam-3479	144	12	that	that	SCONJ
ejpam-3479	144	13	k	k	PROPN
ejpam-3479	144	14	=	=	SYM
ejpam-3479	144	15	0	0	NUM
ejpam-3479	144	16	inq	inq	PROPN
ejpam-3479	144	17	.	.	PUNCT
ejpam-3479	145	1	therefore	therefore	ADV
ejpam-3479	145	2	,	,	PUNCT
ejpam-3479	145	3	we	we	PRON
ejpam-3479	145	4	deduce	deduce	VERB
ejpam-3479	145	5	that	that	SCONJ
ejpam-3479	145	6	m∑	m∑	VERB
ejpam-3479	145	7	i=1	i=1	PROPN
ejpam-3479	145	8	αiξ̂i.χς1	αiξ̂i.χς1	NUM
ejpam-3479	145	9	=	=	SYM
ejpam-3479	145	10	0	0	NUM
ejpam-3479	145	11	on	on	ADP
ejpam-3479	145	12	σ	σ	PROPN
ejpam-3479	145	13	.	.	PUNCT
ejpam-3479	146	1	then	then	ADV
ejpam-3479	146	2	it	it	PRON
ejpam-3479	146	3	follows	follow	VERB
ejpam-3479	146	4	from	from	ADP
ejpam-3479	146	5	(	(	PUNCT
ejpam-3479	146	6	11	11	NUM
ejpam-3479	146	7	)	)	PUNCT
ejpam-3479	146	8	that	that	PRON
ejpam-3479	146	9	αi	αi	VERB
ejpam-3479	146	10	=	=	SYM
ejpam-3479	146	11	0	0	NUM
ejpam-3479	146	12	for	for	ADP
ejpam-3479	146	13	1	1	NUM
ejpam-3479	146	14	≤	≤	NUM
ejpam-3479	146	15	i	i	PROPN
ejpam-3479	146	16	≤m	≤m	PROPN
ejpam-3479	146	17	.	.	PUNCT
ejpam-3479	147	1	the	the	DET
ejpam-3479	147	2	second	second	ADJ
ejpam-3479	147	3	assertion	assertion	NOUN
ejpam-3479	147	4	of	of	ADP
ejpam-3479	147	5	the	the	DET
ejpam-3479	147	6	lemma	lemma	PROPN
ejpam-3479	147	7	follows	follow	VERB
ejpam-3479	147	8	immediately	immediately	ADV
ejpam-3479	147	9	.	.	PUNCT
ejpam-3479	148	1	m.soma	m.soma	ADV
ejpam-3479	148	2	,	,	PUNCT
ejpam-3479	148	3	s.	s.	PROPN
ejpam-3479	148	4	sawadogo	sawadogo	PROPN
ejpam-3479	148	5	/	/	SYM
ejpam-3479	148	6	eur	eur	PROPN
ejpam-3479	148	7	.	.	PUNCT
ejpam-3479	149	1	j.	j.	PROPN
ejpam-3479	149	2	pure	pure	PROPN
ejpam-3479	149	3	appl	appl	PROPN
ejpam-3479	149	4	.	.	PROPN
ejpam-3479	149	5	math	math	PROPN
ejpam-3479	149	6	,	,	PUNCT
ejpam-3479	149	7	12	12	NUM
ejpam-3479	149	8	(	(	PUNCT
ejpam-3479	149	9	3	3	NUM
ejpam-3479	149	10	)	)	PUNCT
ejpam-3479	149	11	(	(	PUNCT
ejpam-3479	149	12	2019	2019	NUM
ejpam-3479	149	13	)	)	PUNCT
ejpam-3479	149	14	,	,	PUNCT
ejpam-3479	149	15	1277	1277	NUM
ejpam-3479	149	16	-	-	SYM
ejpam-3479	149	17	1296	1296	NUM
ejpam-3479	149	18	1284	1284	NUM
ejpam-3479	149	19	now	now	ADV
ejpam-3479	149	20	,	,	PUNCT
ejpam-3479	149	21	let	let	VERB
ejpam-3479	149	22	us	we	PRON
ejpam-3479	149	23	prove	prove	VERB
ejpam-3479	149	24	theorem	theorem	VERB
ejpam-3479	149	25	1	1	NUM
ejpam-3479	149	26	.	.	PUNCT
ejpam-3479	149	27	to	to	ADP
ejpam-3479	149	28	this	this	DET
ejpam-3479	149	29	end	end	NOUN
ejpam-3479	149	30	,	,	PUNCT
ejpam-3479	149	31	we	we	PRON
ejpam-3479	149	32	interpret	interpret	VERB
ejpam-3479	149	33	(	(	PUNCT
ejpam-3479	149	34	5	5	NUM
ejpam-3479	149	35	)	)	PUNCT
ejpam-3479	149	36	and	and	CCONJ
ejpam-3479	149	37	(	(	PUNCT
ejpam-3479	149	38	6	6	NUM
ejpam-3479	149	39	)	)	PUNCT
ejpam-3479	149	40	.	.	PUNCT
ejpam-3479	150	1	actually	actually	ADV
ejpam-3479	150	2	,	,	PUNCT
ejpam-3479	150	3	in	in	ADP
ejpam-3479	150	4	view	view	NOUN
ejpam-3479	150	5	of	of	ADP
ejpam-3479	150	6	(	(	PUNCT
ejpam-3479	150	7	4	4	NUM
ejpam-3479	150	8	)	)	PUNCT
ejpam-3479	150	9	,	,	PUNCT
ejpam-3479	150	10	the	the	DET
ejpam-3479	150	11	stationary	stationary	ADJ
ejpam-3479	150	12	condition	condition	NOUN
ejpam-3479	150	13	(	(	PUNCT
ejpam-3479	150	14	5	5	NUM
ejpam-3479	150	15	)	)	PUNCT
ejpam-3479	150	16	and	and	CCONJ
ejpam-3479	150	17	respectively	respectively	ADV
ejpam-3479	150	18	the	the	DET
ejpam-3479	150	19	sensitivity	sensitivity	NOUN
ejpam-3479	150	20	conditions	condition	NOUN
ejpam-3479	150	21	(	(	PUNCT
ejpam-3479	150	22	6	6	X
ejpam-3479	150	23	)	)	PUNCT
ejpam-3479	150	24	hold	hold	VERB
ejpam-3479	150	25	if	if	SCONJ
ejpam-3479	150	26	and	and	CCONJ
ejpam-3479	150	27	only	only	ADV
ejpam-3479	150	28	if∫	if∫	PROPN
ejpam-3479	150	29	u	u	NOUN
ejpam-3479	150	30	∫	∫	PROPN
ejpam-3479	150	31	o	o	PROPN
ejpam-3479	150	32	h0	h0	PROPN
ejpam-3479	150	33	∂yτ	∂yτ	PROPN
ejpam-3479	150	34	∂ν	∂ν	PROPN
ejpam-3479	150	35	dtdadγ	dtdadγ	PROPN
ejpam-3479	151	1	+	+	CCONJ
ejpam-3479	151	2	∫	∫	PROPN
ejpam-3479	151	3	u	u	X
ejpam-3479	151	4	∫	∫	PROPN
ejpam-3479	151	5	γ	γ	PROPN
ejpam-3479	151	6	w	w	PROPN
ejpam-3479	151	7	∂yτ	∂yτ	NOUN
ejpam-3479	151	8	∂ν	∂ν	NOUN
ejpam-3479	151	9	dtdadγ	dtdadγ	NOUN
ejpam-3479	151	10	=	=	SYM
ejpam-3479	151	11	0.∀ŷ0	0.∀ŷ0	NUM
ejpam-3479	151	12	,	,	PUNCT
ejpam-3479	151	13	‖ŷ0‖l2(qa	‖ŷ0‖l2(qa	NOUN
ejpam-3479	151	14	)	)	PUNCT
ejpam-3479	151	15	≤	≤	NUM
ejpam-3479	151	16	1	1	NUM
ejpam-3479	151	17	(	(	PUNCT
ejpam-3479	151	18	21	21	NUM
ejpam-3479	151	19	)	)	PUNCT
ejpam-3479	151	20	and	and	CCONJ
ejpam-3479	151	21	∫	∫	PROPN
ejpam-3479	151	22	u	u	X
ejpam-3479	151	23	∫	∫	PROPN
ejpam-3479	151	24	o	o	PROPN
ejpam-3479	151	25	h0	h0	PROPN
ejpam-3479	152	1	∂yλi	∂yλi	SCONJ
ejpam-3479	152	2	∂ν	∂ν	PROPN
ejpam-3479	152	3	dtdadγ	dtdadγ	VERB
ejpam-3479	152	4	+	+	CCONJ
ejpam-3479	152	5	∫	∫	PROPN
ejpam-3479	152	6	u	u	X
ejpam-3479	152	7	∫	∫	PROPN
ejpam-3479	152	8	γ	γ	X
ejpam-3479	152	9	w	w	PROPN
ejpam-3479	152	10	∂yλi	∂yλi	SCONJ
ejpam-3479	152	11	∂ν	∂ν	PROPN
ejpam-3479	152	12	dtdadγ	dtdadγ	PROPN
ejpam-3479	152	13	=	=	SYM
ejpam-3479	152	14	ci	ci	PROPN
ejpam-3479	152	15	,	,	PUNCT
ejpam-3479	152	16	1	1	NUM
ejpam-3479	152	17	≤	≤	NUM
ejpam-3479	152	18	i	i	PROPN
ejpam-3479	152	19	≤m	≤m	PROPN
ejpam-3479	152	20	.	.	PUNCT
ejpam-3479	153	1	(	(	PUNCT
ejpam-3479	153	2	22	22	NUM
ejpam-3479	153	3	)	)	PUNCT
ejpam-3479	153	4	therefore	therefore	ADV
ejpam-3479	153	5	,	,	PUNCT
ejpam-3479	153	6	in	in	ADP
ejpam-3479	153	7	order	order	NOUN
ejpam-3479	153	8	to	to	PART
ejpam-3479	153	9	transform	transform	VERB
ejpam-3479	153	10	equation	equation	NOUN
ejpam-3479	153	11	(	(	PUNCT
ejpam-3479	153	12	21	21	NUM
ejpam-3479	153	13	)	)	PUNCT
ejpam-3479	153	14	,	,	PUNCT
ejpam-3479	153	15	we	we	PRON
ejpam-3479	153	16	consider	consider	VERB
ejpam-3479	153	17	the	the	DET
ejpam-3479	153	18	following	follow	VERB
ejpam-3479	153	19	adjoint	adjoint	PROPN
ejpam-3479	153	20	equation	equation	PROPN
ejpam-3479	153	21	−∂q	−∂q	PROPN
ejpam-3479	153	22	∂t	∂t	PROPN
ejpam-3479	153	23	−	−	PROPN
ejpam-3479	153	24	∂q	∂q	PROPN
ejpam-3479	153	25	∂a	∂a	PROPN
ejpam-3479	153	26	−4q	−4q	PROPN
ejpam-3479	153	27	+	+	NUM
ejpam-3479	153	28	µq	µq	PROPN
ejpam-3479	153	29	=	=	SYM
ejpam-3479	153	30	βq(t	βq(t	X
ejpam-3479	153	31	,	,	PUNCT
ejpam-3479	153	32	0	0	NUM
ejpam-3479	153	33	,	,	PUNCT
ejpam-3479	153	34	x	x	NOUN
ejpam-3479	153	35	)	)	PUNCT
ejpam-3479	153	36	in	in	ADP
ejpam-3479	153	37	q	q	NOUN
ejpam-3479	153	38	,	,	PUNCT
ejpam-3479	153	39	q	q	X
ejpam-3479	153	40	=	=	PUNCT
ejpam-3479	153	41	h0χo	h0χo	X
ejpam-3479	153	42	+	+	CCONJ
ejpam-3479	153	43	wχγ	wχγ	VERB
ejpam-3479	153	44	on	on	ADP
ejpam-3479	153	45	σ	σ	PROPN
ejpam-3479	153	46	,	,	PUNCT
ejpam-3479	153	47	q(t	q(t	PROPN
ejpam-3479	153	48	,	,	PUNCT
ejpam-3479	153	49	a	a	PRON
ejpam-3479	153	50	,	,	PUNCT
ejpam-3479	153	51	x	x	NOUN
ejpam-3479	153	52	)	)	PUNCT
ejpam-3479	153	53	=	=	SYM
ejpam-3479	153	54	0	0	NUM
ejpam-3479	154	1	in	in	ADP
ejpam-3479	154	2	qa	qa	PROPN
ejpam-3479	154	3	,	,	PUNCT
ejpam-3479	154	4	q(t	q(t	PROPN
ejpam-3479	154	5	,	,	PUNCT
ejpam-3479	154	6	a	a	PRON
ejpam-3479	154	7	,	,	PUNCT
ejpam-3479	154	8	x	x	NOUN
ejpam-3479	154	9	)	)	PUNCT
ejpam-3479	154	10	=	=	SYM
ejpam-3479	154	11	0	0	NUM
ejpam-3479	155	1	in	in	ADP
ejpam-3479	155	2	qt	qt	NOUN
ejpam-3479	155	3	,	,	PUNCT
ejpam-3479	155	4	(	(	PUNCT
ejpam-3479	155	5	23	23	NUM
ejpam-3479	155	6	)	)	PUNCT
ejpam-3479	155	7	since	since	SCONJ
ejpam-3479	155	8	h0χo	h0χo	VERB
ejpam-3479	155	9	+	+	CCONJ
ejpam-3479	155	10	wχγ	wχγ	VERB
ejpam-3479	155	11	∈	∈	PROPN
ejpam-3479	155	12	l2(σ	l2(σ	NOUN
ejpam-3479	155	13	)	)	PUNCT
ejpam-3479	155	14	,	,	PUNCT
ejpam-3479	155	15	the	the	DET
ejpam-3479	155	16	assumptions	assumption	NOUN
ejpam-3479	155	17	(	(	PUNCT
ejpam-3479	155	18	h1	h1	PROPN
ejpam-3479	155	19	)	)	PUNCT
ejpam-3479	155	20	−	−	PROPN
ejpam-3479	155	21	(	(	PUNCT
ejpam-3479	155	22	h2	h2	NOUN
ejpam-3479	155	23	)	)	PUNCT
ejpam-3479	155	24	ensure	ensure	VERB
ejpam-3479	155	25	that	that	SCONJ
ejpam-3479	155	26	that	that	PRON
ejpam-3479	155	27	(	(	PUNCT
ejpam-3479	155	28	23	23	NUM
ejpam-3479	155	29	)	)	PUNCT
ejpam-3479	155	30	has	have	VERB
ejpam-3479	155	31	a	a	DET
ejpam-3479	155	32	unique	unique	ADJ
ejpam-3479	155	33	solution	solution	NOUN
ejpam-3479	155	34	q	q	PROPN
ejpam-3479	155	35	∈	∈	PROPN
ejpam-3479	155	36	l2(q	l2(q	PROPN
ejpam-3479	155	37	)	)	PUNCT
ejpam-3479	155	38	.	.	PUNCT
ejpam-3479	156	1	now	now	ADV
ejpam-3479	156	2	multiplying	multiply	VERB
ejpam-3479	156	3	both	both	DET
ejpam-3479	156	4	sides	side	NOUN
ejpam-3479	156	5	of	of	ADP
ejpam-3479	156	6	the	the	DET
ejpam-3479	156	7	differential	differential	ADJ
ejpam-3479	156	8	equation	equation	NOUN
ejpam-3479	156	9	in	in	ADP
ejpam-3479	156	10	(	(	PUNCT
ejpam-3479	156	11	23	23	NUM
ejpam-3479	156	12	)	)	PUNCT
ejpam-3479	156	13	by	by	ADP
ejpam-3479	156	14	yτ	yτ	NOUN
ejpam-3479	156	15	solution	solution	NOUN
ejpam-3479	156	16	of	of	ADP
ejpam-3479	156	17	(	(	PUNCT
ejpam-3479	156	18	9	9	NUM
ejpam-3479	156	19	)	)	PUNCT
ejpam-3479	156	20	and	and	CCONJ
ejpam-3479	156	21	integrating	integrate	VERB
ejpam-3479	156	22	by	by	ADP
ejpam-3479	156	23	parts	part	NOUN
ejpam-3479	156	24	in	in	ADP
ejpam-3479	156	25	q	q	NOUN
ejpam-3479	156	26	,	,	PUNCT
ejpam-3479	156	27	we	we	PRON
ejpam-3479	156	28	get∫	get∫	VERB
ejpam-3479	156	29	u	u	NOUN
ejpam-3479	156	30	∫	∫	PROPN
ejpam-3479	156	31	o	o	PROPN
ejpam-3479	156	32	h0	h0	PROPN
ejpam-3479	156	33	∂yτ	∂yτ	NOUN
ejpam-3479	156	34	∂ν	∂ν	ADP
ejpam-3479	156	35	dtdadγ+	dtdadγ+	NOUN
ejpam-3479	156	36	∫	∫	X
ejpam-3479	156	37	u	u	X
ejpam-3479	156	38	∫	∫	PROPN
ejpam-3479	156	39	γ	γ	PROPN
ejpam-3479	156	40	w	w	PROPN
ejpam-3479	156	41	∂yτ	∂yτ	NOUN
ejpam-3479	156	42	∂ν	∂ν	X
ejpam-3479	156	43	dtdadγ	dtdadγ	PROPN
ejpam-3479	156	44	=	=	PUNCT
ejpam-3479	156	45	∫	∫	PROPN
ejpam-3479	156	46	a	a	DET
ejpam-3479	156	47	0	0	NUM
ejpam-3479	156	48	∫	∫	PROPN
ejpam-3479	156	49	γ	γ	PROPN
ejpam-3479	156	50	q(0	q(0	PROPN
ejpam-3479	156	51	,	,	PUNCT
ejpam-3479	156	52	a	a	PRON
ejpam-3479	156	53	,	,	PUNCT
ejpam-3479	156	54	x)ŷ0dadx	x)ŷ0dadx	X
ejpam-3479	156	55	∀	∀	X
ejpam-3479	156	56	ŷ0	ŷ0	PROPN
ejpam-3479	156	57	∈	∈	PROPN
ejpam-3479	156	58	l2(qa	l2(qa	PROPN
ejpam-3479	156	59	)	)	PUNCT
ejpam-3479	156	60	(	(	PUNCT
ejpam-3479	156	61	24	24	NUM
ejpam-3479	156	62	)	)	PUNCT
ejpam-3479	156	63	thus	thus	ADV
ejpam-3479	156	64	,	,	PUNCT
ejpam-3479	156	65	the	the	DET
ejpam-3479	156	66	condition	condition	NOUN
ejpam-3479	156	67	(	(	PUNCT
ejpam-3479	156	68	5	5	NUM
ejpam-3479	156	69	)	)	PUNCT
ejpam-3479	156	70	or	or	CCONJ
ejpam-3479	156	71	(	(	PUNCT
ejpam-3479	156	72	21	21	NUM
ejpam-3479	156	73	)	)	PUNCT
ejpam-3479	156	74	holds	hold	VERB
ejpam-3479	156	75	if	if	SCONJ
ejpam-3479	156	76	and	and	CCONJ
ejpam-3479	156	77	only	only	ADV
ejpam-3479	156	78	if	if	SCONJ
ejpam-3479	156	79	q(0	q(0	PROPN
ejpam-3479	156	80	,	,	PUNCT
ejpam-3479	156	81	a	a	PRON
ejpam-3479	156	82	,	,	PUNCT
ejpam-3479	156	83	x	x	NOUN
ejpam-3479	156	84	;	;	PUNCT
ejpam-3479	156	85	v	v	X
ejpam-3479	156	86	)	)	PUNCT
ejpam-3479	156	87	=	=	SYM
ejpam-3479	156	88	0	0	NUM
ejpam-3479	156	89	in	in	ADP
ejpam-3479	156	90	qa	qa	PROPN
ejpam-3479	156	91	.	.	PUNCT
ejpam-3479	157	1	(	(	PUNCT
ejpam-3479	157	2	25	25	NUM
ejpam-3479	157	3	)	)	PUNCT
ejpam-3479	157	4	then	then	ADV
ejpam-3479	157	5	,	,	PUNCT
ejpam-3479	157	6	multiplying	multiply	VERB
ejpam-3479	157	7	both	both	DET
ejpam-3479	157	8	sides	side	NOUN
ejpam-3479	157	9	of	of	ADP
ejpam-3479	157	10	the	the	DET
ejpam-3479	157	11	differential	differential	ADJ
ejpam-3479	157	12	equation	equation	NOUN
ejpam-3479	157	13	in	in	ADP
ejpam-3479	157	14	(	(	PUNCT
ejpam-3479	157	15	23	23	NUM
ejpam-3479	157	16	)	)	PUNCT
ejpam-3479	157	17	by	by	ADP
ejpam-3479	157	18	yλi	yλi	NOUN
ejpam-3479	157	19	solution	solution	NOUN
ejpam-3479	157	20	of	of	ADP
ejpam-3479	157	21	(	(	PUNCT
ejpam-3479	157	22	10	10	NUM
ejpam-3479	157	23	)	)	PUNCT
ejpam-3479	157	24	and	and	CCONJ
ejpam-3479	157	25	integrating	integrate	VERB
ejpam-3479	157	26	by	by	ADP
ejpam-3479	157	27	parts	part	NOUN
ejpam-3479	157	28	in	in	ADP
ejpam-3479	157	29	q	q	NOUN
ejpam-3479	157	30	,	,	PUNCT
ejpam-3479	157	31	we	we	PRON
ejpam-3479	157	32	have	have	VERB
ejpam-3479	157	33	∫	∫	PROPN
ejpam-3479	157	34	u	u	PROPN
ejpam-3479	157	35	∫	∫	PROPN
ejpam-3479	157	36	o	o	PROPN
ejpam-3479	157	37	h0	h0	PROPN
ejpam-3479	158	1	∂yλi	∂yλi	SCONJ
ejpam-3479	158	2	∂ν	∂ν	PROPN
ejpam-3479	158	3	dtdadγ	dtdadγ	VERB
ejpam-3479	158	4	+	+	CCONJ
ejpam-3479	158	5	∫	∫	PROPN
ejpam-3479	158	6	u	u	X
ejpam-3479	158	7	∫	∫	PROPN
ejpam-3479	158	8	γ	γ	X
ejpam-3479	158	9	w	w	PROPN
ejpam-3479	158	10	∂yλi	∂yλi	SCONJ
ejpam-3479	158	11	∂ν	∂ν	X
ejpam-3479	158	12	dtdadγ	dtdadγ	PROPN
ejpam-3479	158	13	=	=	PUNCT
ejpam-3479	158	14	∫	∫	PROPN
ejpam-3479	159	1	σ1	σ1	PROPN
ejpam-3479	159	2	∂q	∂q	PROPN
ejpam-3479	159	3	∂ν	∂ν	PROPN
ejpam-3479	160	1	ξ̂i.χγ1dtda	ξ̂i.χγ1dtda	PROPN
ejpam-3479	160	2	,	,	PUNCT
ejpam-3479	160	3	1	1	NUM
ejpam-3479	160	4	≤	≤	NUM
ejpam-3479	160	5	i	i	PROPN
ejpam-3479	160	6	≤m	≤m	PROPN
ejpam-3479	160	7	.	.	PUNCT
ejpam-3479	161	1	thus	thus	ADV
ejpam-3479	161	2	,	,	PUNCT
ejpam-3479	161	3	the	the	DET
ejpam-3479	161	4	condition	condition	NOUN
ejpam-3479	161	5	the	the	DET
ejpam-3479	161	6	condition	condition	NOUN
ejpam-3479	161	7	(	(	PUNCT
ejpam-3479	161	8	6	6	NUM
ejpam-3479	161	9	)	)	PUNCT
ejpam-3479	161	10	or	or	CCONJ
ejpam-3479	161	11	(	(	PUNCT
ejpam-3479	161	12	22	22	NUM
ejpam-3479	161	13	)	)	PUNCT
ejpam-3479	161	14	is	be	AUX
ejpam-3479	161	15	equivalent	equivalent	ADJ
ejpam-3479	161	16	to∫	to∫	NOUN
ejpam-3479	161	17	σ1	σ1	PROPN
ejpam-3479	162	1	∂q	∂q	PROPN
ejpam-3479	163	1	∂ν	∂ν	PRON
ejpam-3479	164	1	ξ̂i.χγ1dtda	ξ̂i.χγ1dtda	PROPN
ejpam-3479	165	1	=	=	SYM
ejpam-3479	165	2	ci	ci	PROPN
ejpam-3479	165	3	,	,	PUNCT
ejpam-3479	165	4	1	1	NUM
ejpam-3479	165	5	≤	≤	NUM
ejpam-3479	165	6	i	i	PROPN
ejpam-3479	165	7	≤m	≤m	PROPN
ejpam-3479	165	8	.	.	PUNCT
ejpam-3479	166	1	(	(	PUNCT
ejpam-3479	166	2	26	26	NUM
ejpam-3479	166	3	)	)	PUNCT
ejpam-3479	166	4	now	now	ADV
ejpam-3479	166	5	,	,	PUNCT
ejpam-3479	166	6	consider	consider	VERB
ejpam-3479	166	7	the	the	DET
ejpam-3479	166	8	matrix(∫	matrix(∫	ADJ
ejpam-3479	166	9	t	t	PROPN
ejpam-3479	166	10	0	0	NUM
ejpam-3479	166	11	∫	∫	PROPN
ejpam-3479	166	12	a	a	DET
ejpam-3479	166	13	0	0	NUM
ejpam-3479	166	14	∫	∫	NOUN
ejpam-3479	166	15	γ	γ	PROPN
ejpam-3479	166	16	1	1	NUM
ejpam-3479	166	17	θ	θ	NUM
ejpam-3479	166	18	∂yλj	∂yλj	X
ejpam-3479	167	1	∂ν	∂ν	PROPN
ejpam-3479	167	2	∂yλi	∂yλi	ADP
ejpam-3479	167	3	∂ν	∂ν	X
ejpam-3479	167	4	dtdadγ	dtdadγ	PROPN
ejpam-3479	167	5	)	)	PUNCT
ejpam-3479	168	1	1≤i	1≤i	INTJ
ejpam-3479	168	2	,	,	PUNCT
ejpam-3479	168	3	j≤m	j≤m	NOUN
ejpam-3479	168	4	.	.	PUNCT
ejpam-3479	169	1	m.soma	m.soma	ADV
ejpam-3479	169	2	,	,	PUNCT
ejpam-3479	169	3	s.	s.	PROPN
ejpam-3479	169	4	sawadogo	sawadogo	PROPN
ejpam-3479	169	5	/	/	SYM
ejpam-3479	169	6	eur	eur	PROPN
ejpam-3479	169	7	.	.	PUNCT
ejpam-3479	170	1	j.	j.	PROPN
ejpam-3479	170	2	pure	pure	PROPN
ejpam-3479	170	3	appl	appl	PROPN
ejpam-3479	170	4	.	.	PROPN
ejpam-3479	170	5	math	math	PROPN
ejpam-3479	170	6	,	,	PUNCT
ejpam-3479	170	7	12	12	NUM
ejpam-3479	170	8	(	(	PUNCT
ejpam-3479	170	9	3	3	NUM
ejpam-3479	170	10	)	)	PUNCT
ejpam-3479	170	11	(	(	PUNCT
ejpam-3479	170	12	2019	2019	NUM
ejpam-3479	170	13	)	)	PUNCT
ejpam-3479	170	14	,	,	PUNCT
ejpam-3479	170	15	1277	1277	NUM
ejpam-3479	170	16	-	-	SYM
ejpam-3479	170	17	1296	1296	NUM
ejpam-3479	170	18	1285	1285	NUM
ejpam-3479	170	19	since	since	SCONJ
ejpam-3479	170	20	this	this	DET
ejpam-3479	170	21	matrix	matrix	NOUN
ejpam-3479	170	22	is	be	AUX
ejpam-3479	170	23	symmetric	symmetric	ADJ
ejpam-3479	170	24	positive	positive	ADJ
ejpam-3479	170	25	definite	definite	ADJ
ejpam-3479	170	26	therefore	therefore	ADV
ejpam-3479	171	1	,	,	PUNCT
ejpam-3479	171	2	there	there	PRON
ejpam-3479	171	3	exists	exist	VERB
ejpam-3479	171	4	a	a	DET
ejpam-3479	171	5	unique	unique	ADJ
ejpam-3479	171	6	w0	w0	PROPN
ejpam-3479	171	7	∈	∈	PROPN
ejpam-3479	171	8	yθ	yθ	NOUN
ejpam-3479	171	9	such	such	ADJ
ejpam-3479	171	10	that	that	DET
ejpam-3479	171	11	ci	ci	PROPN
ejpam-3479	171	12	−	−	NOUN
ejpam-3479	171	13	∫	∫	PROPN
ejpam-3479	171	14	u	u	NOUN
ejpam-3479	171	15	∫	∫	PROPN
ejpam-3479	171	16	o	o	PROPN
ejpam-3479	171	17	h0	h0	PROPN
ejpam-3479	171	18	∂yλi	∂yλi	SCONJ
ejpam-3479	171	19	∂ν	∂ν	X
ejpam-3479	171	20	dtdadγ	dtdadγ	PROPN
ejpam-3479	171	21	=	=	SYM
ejpam-3479	171	22	∫	∫	PROPN
ejpam-3479	171	23	u	u	NOUN
ejpam-3479	171	24	∫	∫	PROPN
ejpam-3479	171	25	γ	γ	PROPN
ejpam-3479	171	26	w0	w0	PROPN
ejpam-3479	171	27	∂yλi	∂yλi	SCONJ
ejpam-3479	171	28	∂ν	∂ν	PROPN
ejpam-3479	171	29	dtdadγ	dtdadγ	VERB
ejpam-3479	171	30	.	.	PUNCT
ejpam-3479	172	1	1	1	NUM
ejpam-3479	172	2	≤	≤	NUM
ejpam-3479	172	3	i	i	PRON
ejpam-3479	172	4	≤m	≤m	PROPN
ejpam-3479	172	5	(	(	PUNCT
ejpam-3479	172	6	27	27	NUM
ejpam-3479	172	7	)	)	PUNCT
ejpam-3479	172	8	consequently	consequently	ADV
ejpam-3479	172	9	,	,	PUNCT
ejpam-3479	172	10	combining	combine	VERB
ejpam-3479	172	11	(	(	PUNCT
ejpam-3479	172	12	27	27	NUM
ejpam-3479	172	13	)	)	PUNCT
ejpam-3479	172	14	with	with	ADP
ejpam-3479	172	15	(	(	PUNCT
ejpam-3479	172	16	22	22	NUM
ejpam-3479	172	17	)	)	PUNCT
ejpam-3479	172	18	,	,	PUNCT
ejpam-3479	172	19	we	we	PRON
ejpam-3479	172	20	observe	observe	VERB
ejpam-3479	172	21	that	that	SCONJ
ejpam-3479	172	22	condition	condition	NOUN
ejpam-3479	172	23	(	(	PUNCT
ejpam-3479	172	24	6	6	NUM
ejpam-3479	172	25	)	)	PUNCT
ejpam-3479	172	26	(	(	PUNCT
ejpam-3479	172	27	or	or	CCONJ
ejpam-3479	172	28	the	the	DET
ejpam-3479	172	29	constraints	constraint	NOUN
ejpam-3479	172	30	(	(	PUNCT
ejpam-3479	172	31	26	26	NUM
ejpam-3479	172	32	)	)	PUNCT
ejpam-3479	172	33	)	)	PUNCT
ejpam-3479	172	34	holds	hold	VERB
ejpam-3479	172	35	if	if	SCONJ
ejpam-3479	172	36	and	and	CCONJ
ejpam-3479	172	37	only	only	ADV
ejpam-3479	172	38	if	if	SCONJ
ejpam-3479	172	39	w	w	PROPN
ejpam-3479	172	40	−	−	PROPN
ejpam-3479	172	41	w0	w0	NOUN
ejpam-3479	172	42	=	=	PUNCT
ejpam-3479	172	43	−v	−v	PROPN
ejpam-3479	172	44	∈	∈	PROPN
ejpam-3479	172	45	y	y	PROPN
ejpam-3479	172	46	⊥	⊥	PROPN
ejpam-3479	172	47	,	,	PUNCT
ejpam-3479	172	48	where	where	SCONJ
ejpam-3479	172	49	y	y	PROPN
ejpam-3479	172	50	is	be	AUX
ejpam-3479	172	51	given	give	VERB
ejpam-3479	172	52	by	by	ADP
ejpam-3479	172	53	(	(	PUNCT
ejpam-3479	172	54	13	13	NUM
ejpam-3479	172	55	)	)	PUNCT
ejpam-3479	172	56	.	.	PUNCT
ejpam-3479	173	1	replacing	replace	VERB
ejpam-3479	173	2	w	w	NOUN
ejpam-3479	173	3	by	by	ADP
ejpam-3479	173	4	w0	w0	PROPN
ejpam-3479	173	5	−	−	PROPN
ejpam-3479	173	6	υ	υ	NOUN
ejpam-3479	173	7	in	in	ADP
ejpam-3479	173	8	the	the	DET
ejpam-3479	173	9	second	second	ADJ
ejpam-3479	173	10	expression	expression	NOUN
ejpam-3479	173	11	of	of	ADP
ejpam-3479	173	12	(	(	PUNCT
ejpam-3479	173	13	23	23	NUM
ejpam-3479	173	14	)	)	PUNCT
ejpam-3479	173	15	,	,	PUNCT
ejpam-3479	173	16	we	we	PRON
ejpam-3479	173	17	obtain	obtain	VERB
ejpam-3479	173	18	(	(	PUNCT
ejpam-3479	173	19	15	15	NUM
ejpam-3479	173	20	)	)	PUNCT
ejpam-3479	173	21	.	.	PUNCT
ejpam-3479	174	1	we	we	PRON
ejpam-3479	174	2	just	just	ADV
ejpam-3479	174	3	have	have	AUX
ejpam-3479	174	4	proved	prove	VERB
ejpam-3479	174	5	that	that	SCONJ
ejpam-3479	174	6	the	the	DET
ejpam-3479	174	7	sentinel	sentinel	ADJ
ejpam-3479	174	8	problem	problem	NOUN
ejpam-3479	174	9	(	(	PUNCT
ejpam-3479	174	10	4	4	NUM
ejpam-3479	174	11	)	)	PUNCT
ejpam-3479	174	12	−	−	PROPN
ejpam-3479	174	13	(	(	PUNCT
ejpam-3479	174	14	7	7	X
ejpam-3479	174	15	)	)	PUNCT
ejpam-3479	174	16	hold	hold	VERB
ejpam-3479	174	17	if	if	SCONJ
ejpam-3479	174	18	and	and	CCONJ
ejpam-3479	174	19	only	only	ADV
ejpam-3479	174	20	if	if	SCONJ
ejpam-3479	174	21	null	null	ADJ
ejpam-3479	174	22	controllability	controllability	NOUN
ejpam-3479	174	23	problem	problem	NOUN
ejpam-3479	174	24	with	with	ADP
ejpam-3479	174	25	constraint	constraint	NOUN
ejpam-3479	174	26	on	on	ADP
ejpam-3479	174	27	the	the	DET
ejpam-3479	174	28	control	control	NOUN
ejpam-3479	174	29	(	(	PUNCT
ejpam-3479	174	30	14)−	14)−	NUM
ejpam-3479	174	31	(	(	PUNCT
ejpam-3479	174	32	16	16	NUM
ejpam-3479	174	33	)	)	PUNCT
ejpam-3479	174	34	has	have	VERB
ejpam-3479	174	35	a	a	DET
ejpam-3479	174	36	solution	solution	NOUN
ejpam-3479	174	37	.	.	PUNCT
ejpam-3479	175	1	remark	remark	NOUN
ejpam-3479	175	2	5	5	NUM
ejpam-3479	175	3	.	.	PUNCT
ejpam-3479	176	1	if	if	SCONJ
ejpam-3479	176	2	e	e	PROPN
ejpam-3479	176	3	is	be	AUX
ejpam-3479	176	4	the	the	DET
ejpam-3479	176	5	set	set	NOUN
ejpam-3479	176	6	of	of	ADP
ejpam-3479	176	7	admissible	admissible	ADJ
ejpam-3479	176	8	control	control	NOUN
ejpam-3479	176	9	v	v	ADP
ejpam-3479	176	10	∈	∈	PROPN
ejpam-3479	177	1	l2(u	l2(u	X
ejpam-3479	177	2	×	×	PROPN
ejpam-3479	177	3	γ	γ	NOUN
ejpam-3479	177	4	)	)	PUNCT
ejpam-3479	178	1	such	such	ADJ
ejpam-3479	178	2	that	that	SCONJ
ejpam-3479	178	3	(	(	PUNCT
ejpam-3479	178	4	14	14	NUM
ejpam-3479	178	5	)	)	PUNCT
ejpam-3479	178	6	−	−	PROPN
ejpam-3479	179	1	(	(	PUNCT
ejpam-3479	179	2	16	16	NUM
ejpam-3479	179	3	)	)	PUNCT
ejpam-3479	179	4	is	be	AUX
ejpam-3479	179	5	satisfied	satisfied	ADJ
ejpam-3479	179	6	,	,	PUNCT
ejpam-3479	179	7	then	then	ADV
ejpam-3479	179	8	e	e	PROPN
ejpam-3479	179	9	is	be	AUX
ejpam-3479	179	10	a	a	DET
ejpam-3479	179	11	closed	closed	ADJ
ejpam-3479	179	12	convex	convex	NOUN
ejpam-3479	179	13	subset	subset	NOUN
ejpam-3479	179	14	of	of	ADP
ejpam-3479	179	15	l2(u	l2(u	PROPN
ejpam-3479	179	16	×	×	PROPN
ejpam-3479	179	17	γ	γ	NOUN
ejpam-3479	179	18	)	)	PUNCT
ejpam-3479	179	19	.	.	PUNCT
ejpam-3479	180	1	since	since	SCONJ
ejpam-3479	180	2	w0	w0	PROPN
ejpam-3479	180	3	−	−	PROPN
ejpam-3479	180	4	e	e	PROPN
ejpam-3479	180	5	is	be	AUX
ejpam-3479	180	6	also	also	ADV
ejpam-3479	180	7	a	a	DET
ejpam-3479	180	8	closed	closed	ADJ
ejpam-3479	180	9	convex	convex	NOUN
ejpam-3479	180	10	subset	subset	NOUN
ejpam-3479	180	11	of	of	ADP
ejpam-3479	180	12	l2(u	l2(u	PROPN
ejpam-3479	180	13	×	×	PROPN
ejpam-3479	180	14	γ	γ	PROPN
ejpam-3479	180	15	)	)	PUNCT
ejpam-3479	180	16	,	,	PUNCT
ejpam-3479	180	17	we	we	PRON
ejpam-3479	180	18	can	can	AUX
ejpam-3479	180	19	obtain	obtain	VERB
ejpam-3479	180	20	w	w	NOUN
ejpam-3479	180	21	to	to	PART
ejpam-3479	180	22	be	be	AUX
ejpam-3479	180	23	of	of	ADP
ejpam-3479	180	24	minimum	minimum	ADJ
ejpam-3479	180	25	norm	norm	NOUN
ejpam-3479	180	26	in	in	ADP
ejpam-3479	180	27	l2(u	l2(u	PROPN
ejpam-3479	180	28	×	×	PROPN
ejpam-3479	180	29	γ	γ	NOUN
ejpam-3479	180	30	)	)	PUNCT
ejpam-3479	180	31	by	by	ADP
ejpam-3479	180	32	minimizing	minimize	VERB
ejpam-3479	180	33	the	the	DET
ejpam-3479	180	34	norm	norm	NOUN
ejpam-3479	180	35	of	of	ADP
ejpam-3479	180	36	w0	w0	PROPN
ejpam-3479	180	37	−	−	PROPN
ejpam-3479	180	38	v	v	NOUN
ejpam-3479	180	39	when	when	SCONJ
ejpam-3479	180	40	v	v	X
ejpam-3479	180	41	∈	∈	PROPN
ejpam-3479	180	42	e.	e.	PROPN
ejpam-3479	180	43	then	then	ADV
ejpam-3479	180	44	the	the	DET
ejpam-3479	180	45	pair	pair	NOUN
ejpam-3479	180	46	(	(	PUNCT
ejpam-3479	180	47	v	v	NOUN
ejpam-3479	180	48	,	,	PUNCT
ejpam-3479	180	49	q(v	q(v	NOUN
ejpam-3479	180	50	)	)	PUNCT
ejpam-3479	180	51	)	)	PUNCT
ejpam-3479	181	1	satisfying	satisfy	VERB
ejpam-3479	181	2	(	(	PUNCT
ejpam-3479	181	3	14)−	14)−	NUM
ejpam-3479	181	4	(	(	PUNCT
ejpam-3479	181	5	16	16	NUM
ejpam-3479	181	6	)	)	PUNCT
ejpam-3479	181	7	necessarily	necessarily	ADV
ejpam-3479	181	8	provides	provide	VERB
ejpam-3479	181	9	a	a	DET
ejpam-3479	181	10	control	control	NOUN
ejpam-3479	181	11	w	w	ADP
ejpam-3479	181	12	satisfying	satisfy	VERB
ejpam-3479	181	13	(	(	PUNCT
ejpam-3479	181	14	7	7	NUM
ejpam-3479	181	15	)	)	SYM
ejpam-3479	181	16	3	3	NUM
ejpam-3479	181	17	.	.	X
ejpam-3479	181	18	study	study	NOUN
ejpam-3479	181	19	of	of	ADP
ejpam-3479	181	20	the	the	DET
ejpam-3479	181	21	boundary	boundary	ADJ
ejpam-3479	181	22	null	null	ADJ
ejpam-3479	181	23	-	-	PUNCT
ejpam-3479	181	24	controllability	controllability	NOUN
ejpam-3479	181	25	problem	problem	NOUN
ejpam-3479	181	26	with	with	ADP
ejpam-3479	181	27	constraint	constraint	NOUN
ejpam-3479	181	28	on	on	ADP
ejpam-3479	181	29	the	the	DET
ejpam-3479	181	30	control	control	NOUN
ejpam-3479	181	31	in	in	ADP
ejpam-3479	181	32	this	this	DET
ejpam-3479	181	33	section	section	NOUN
ejpam-3479	181	34	,	,	PUNCT
ejpam-3479	181	35	we	we	PRON
ejpam-3479	181	36	prove	prove	VERB
ejpam-3479	181	37	existence	existence	NOUN
ejpam-3479	181	38	of	of	ADP
ejpam-3479	181	39	the	the	DET
ejpam-3479	181	40	solution	solution	NOUN
ejpam-3479	181	41	of	of	ADP
ejpam-3479	181	42	the	the	DET
ejpam-3479	181	43	boundary	boundary	ADJ
ejpam-3479	181	44	null	null	ADJ
ejpam-3479	181	45	controllability	controllability	NOUN
ejpam-3479	181	46	problem	problem	NOUN
ejpam-3479	181	47	(	(	PUNCT
ejpam-3479	181	48	14)−(16	14)−(16	NUM
ejpam-3479	181	49	)	)	PUNCT
ejpam-3479	181	50	and	and	CCONJ
ejpam-3479	181	51	of	of	ADP
ejpam-3479	181	52	course	course	NOUN
ejpam-3479	181	53	uniqueness	uniqueness	NOUN
ejpam-3479	181	54	if	if	SCONJ
ejpam-3479	181	55	we	we	PRON
ejpam-3479	181	56	want	want	VERB
ejpam-3479	181	57	the	the	DET
ejpam-3479	181	58	control	control	NOUN
ejpam-3479	181	59	to	to	PART
ejpam-3479	181	60	be	be	AUX
ejpam-3479	181	61	of	of	ADP
ejpam-3479	181	62	minimal	minimal	ADJ
ejpam-3479	181	63	norm	norm	NOUN
ejpam-3479	181	64	among	among	ADP
ejpam-3479	181	65	admissible	admissible	ADJ
ejpam-3479	181	66	controls	control	NOUN
ejpam-3479	181	67	.	.	PUNCT
ejpam-3479	182	1	the	the	DET
ejpam-3479	182	2	main	main	ADJ
ejpam-3479	182	3	tool	tool	NOUN
ejpam-3479	182	4	we	we	PRON
ejpam-3479	182	5	use	use	VERB
ejpam-3479	182	6	is	be	AUX
ejpam-3479	182	7	an	an	DET
ejpam-3479	182	8	observability	observability	NOUN
ejpam-3479	182	9	inequality	inequality	NOUN
ejpam-3479	182	10	adapted	adapt	VERB
ejpam-3479	182	11	to	to	ADP
ejpam-3479	182	12	the	the	DET
ejpam-3479	182	13	constraint	constraint	NOUN
ejpam-3479	182	14	(	(	PUNCT
ejpam-3479	182	15	14	14	NUM
ejpam-3479	182	16	)	)	PUNCT
ejpam-3479	182	17	which	which	PRON
ejpam-3479	182	18	itself	itself	PRON
ejpam-3479	182	19	is	be	AUX
ejpam-3479	182	20	a	a	DET
ejpam-3479	182	21	consequence	consequence	NOUN
ejpam-3479	182	22	of	of	ADP
ejpam-3479	182	23	a	a	DET
ejpam-3479	182	24	global	global	ADJ
ejpam-3479	182	25	carleman	carleman	NOUN
ejpam-3479	182	26	inequality	inequality	NOUN
ejpam-3479	182	27	.	.	PUNCT
ejpam-3479	183	1	3.1	3.1	NUM
ejpam-3479	183	2	.	.	PUNCT
ejpam-3479	184	1	an	an	DET
ejpam-3479	184	2	adapted	adapt	VERB
ejpam-3479	184	3	carleman	carleman	ADJ
ejpam-3479	184	4	inequality	inequality	NOUN
ejpam-3479	184	5	the	the	DET
ejpam-3479	184	6	observability	observability	NOUN
ejpam-3479	184	7	inequality	inequality	NOUN
ejpam-3479	184	8	we	we	PRON
ejpam-3479	184	9	are	be	AUX
ejpam-3479	184	10	looking	look	VERB
ejpam-3479	184	11	for	for	ADP
ejpam-3479	184	12	is	be	AUX
ejpam-3479	184	13	a	a	DET
ejpam-3479	184	14	consequence	consequence	NOUN
ejpam-3479	184	15	of	of	ADP
ejpam-3479	184	16	the	the	DET
ejpam-3479	184	17	global	global	ADJ
ejpam-3479	184	18	carleman	carleman	NOUN
ejpam-3479	184	19	’s	’s	PART
ejpam-3479	184	20	inequality	inequality	NOUN
ejpam-3479	184	21	.	.	PUNCT
ejpam-3479	185	1	we	we	PRON
ejpam-3479	185	2	consider	consider	VERB
ejpam-3479	185	3	an	an	DET
ejpam-3479	185	4	auxiliary	auxiliary	ADJ
ejpam-3479	185	5	function	function	NOUN
ejpam-3479	185	6	an	an	DET
ejpam-3479	185	7	auxillary	auxillary	PROPN
ejpam-3479	185	8	function	function	NOUN
ejpam-3479	185	9	ψ	ψ	X
ejpam-3479	185	10	∈	∈	PROPN
ejpam-3479	185	11	c2(ω	c2(ω	NUM
ejpam-3479	185	12	)	)	PUNCT
ejpam-3479	185	13	which	which	PRON
ejpam-3479	185	14	satisfies	satisfy	VERB
ejpam-3479	185	15	the	the	DET
ejpam-3479	185	16	following	follow	VERB
ejpam-3479	185	17	conditions	condition	NOUN
ejpam-3479	185	18	:	:	PUNCT
ejpam-3479	185	19	ψ(x	ψ(x	NUM
ejpam-3479	185	20	)	)	PUNCT
ejpam-3479	185	21	>	>	X
ejpam-3479	185	22	0	0	NUM
ejpam-3479	185	23	,	,	PUNCT
ejpam-3479	185	24	∀x	∀x	VERB
ejpam-3479	185	25	∈	∈	PROPN
ejpam-3479	185	26	ω	ω	NOUN
ejpam-3479	185	27	,	,	PUNCT
ejpam-3479	185	28	∇ψ	∇ψ	PROPN
ejpam-3479	185	29	>	>	X
ejpam-3479	185	30	α,∀x	α,∀x	NUM
ejpam-3479	185	31	∈	∈	PROPN
ejpam-3479	185	32	ω	ω	PROPN
ejpam-3479	185	33	,	,	PUNCT
ejpam-3479	185	34	ψ(x	ψ(x	PROPN
ejpam-3479	185	35	)	)	PUNCT
ejpam-3479	185	36	=	=	SYM
ejpam-3479	185	37	0	0	NUM
ejpam-3479	185	38	,	,	PUNCT
ejpam-3479	185	39	∀x	∀x	VERB
ejpam-3479	185	40	∈	∈	PROPN
ejpam-3479	185	41	γ	γ	X
ejpam-3479	185	42	\	\	PROPN
ejpam-3479	185	43	γ	γ	X
ejpam-3479	185	44	,	,	PUNCT
ejpam-3479	185	45	∂ψ	∂ψ	VERB
ejpam-3479	185	46	∂ν	∂ν	ADP
ejpam-3479	185	47	<	<	X
ejpam-3479	185	48	0	0	PROPN
ejpam-3479	185	49	,	,	PUNCT
ejpam-3479	185	50	∀x	∀x	VERB
ejpam-3479	185	51	∈	∈	PROPN
ejpam-3479	185	52	γ	γ	X
ejpam-3479	185	53	\	\	PROPN
ejpam-3479	185	54	γ	γ	PROPN
ejpam-3479	185	55	.	.	PUNCT
ejpam-3479	186	1	(	(	PUNCT
ejpam-3479	186	2	28	28	NUM
ejpam-3479	186	3	)	)	PUNCT
ejpam-3479	186	4	such	such	DET
ejpam-3479	186	5	a	a	DET
ejpam-3479	186	6	function	function	NOUN
ejpam-3479	186	7	exists	exist	VERB
ejpam-3479	186	8	according	accord	VERB
ejpam-3479	186	9	to	to	ADP
ejpam-3479	186	10	a.	a.	NOUN
ejpam-3479	186	11	fursikov	fursikov	NOUN
ejpam-3479	186	12	and	and	CCONJ
ejpam-3479	186	13	o.	o.	PROPN
ejpam-3479	186	14	yu	yu	PROPN
ejpam-3479	187	1	.	.	PUNCT
ejpam-3479	187	2	imanuvilov	imanuvilov	PROPN
ejpam-3479	188	1	[	[	X
ejpam-3479	188	2	7	7	NUM
ejpam-3479	188	3	]	]	PUNCT
ejpam-3479	188	4	.	.	PUNCT
ejpam-3479	189	1	for	for	ADP
ejpam-3479	189	2	any	any	DET
ejpam-3479	189	3	positive	positive	ADJ
ejpam-3479	189	4	parameter	parameter	NOUN
ejpam-3479	189	5	value	value	NOUN
ejpam-3479	189	6	λ	λ	INTJ
ejpam-3479	189	7	we	we	PRON
ejpam-3479	189	8	define	define	VERB
ejpam-3479	189	9	the	the	DET
ejpam-3479	189	10	following	follow	VERB
ejpam-3479	189	11	weight	weight	NOUN
ejpam-3479	189	12	functions	function	NOUN
ejpam-3479	189	13	:	:	PUNCT
ejpam-3479	189	14	ϕ	ϕ	X
ejpam-3479	189	15	(	(	PUNCT
ejpam-3479	189	16	t	t	PROPN
ejpam-3479	189	17	,	,	PUNCT
ejpam-3479	189	18	a	a	PRON
ejpam-3479	189	19	,	,	PUNCT
ejpam-3479	189	20	x	x	NOUN
ejpam-3479	189	21	)	)	PUNCT
ejpam-3479	189	22	=	=	SYM
ejpam-3479	189	23	eλ(m|ψ|∞+ψ(x	eλ(m|ψ|∞+ψ(x	NOUN
ejpam-3479	189	24	)	)	PUNCT
ejpam-3479	189	25	)	)	PUNCT
ejpam-3479	189	26	at	at	ADP
ejpam-3479	189	27	(	(	PUNCT
ejpam-3479	189	28	a−	a−	PROPN
ejpam-3479	189	29	a	a	NOUN
ejpam-3479	189	30	)	)	PUNCT
ejpam-3479	189	31	(	(	PUNCT
ejpam-3479	189	32	t	t	PROPN
ejpam-3479	189	33	−	−	PROPN
ejpam-3479	189	34	t	t	PROPN
ejpam-3479	189	35	)	)	PUNCT
ejpam-3479	189	36	,	,	PUNCT
ejpam-3479	189	37	(	(	PUNCT
ejpam-3479	189	38	29	29	NUM
ejpam-3479	189	39	)	)	PUNCT
ejpam-3479	189	40	m.soma	m.soma	NOUN
ejpam-3479	189	41	,	,	PUNCT
ejpam-3479	189	42	s.	s.	PROPN
ejpam-3479	189	43	sawadogo	sawadogo	PROPN
ejpam-3479	189	44	/	/	SYM
ejpam-3479	189	45	eur	eur	PROPN
ejpam-3479	189	46	.	.	PUNCT
ejpam-3479	190	1	j.	j.	PROPN
ejpam-3479	190	2	pure	pure	PROPN
ejpam-3479	190	3	appl	appl	PROPN
ejpam-3479	190	4	.	.	PROPN
ejpam-3479	190	5	math	math	PROPN
ejpam-3479	190	6	,	,	PUNCT
ejpam-3479	190	7	12	12	NUM
ejpam-3479	190	8	(	(	PUNCT
ejpam-3479	190	9	3	3	NUM
ejpam-3479	190	10	)	)	PUNCT
ejpam-3479	190	11	(	(	PUNCT
ejpam-3479	190	12	2019	2019	NUM
ejpam-3479	190	13	)	)	PUNCT
ejpam-3479	190	14	,	,	PUNCT
ejpam-3479	190	15	1277	1277	NUM
ejpam-3479	190	16	-	-	SYM
ejpam-3479	190	17	1296	1296	NUM
ejpam-3479	190	18	1286	1286	NUM
ejpam-3479	190	19	η(t	η(t	NOUN
ejpam-3479	190	20	,	,	PUNCT
ejpam-3479	190	21	a	a	PRON
ejpam-3479	190	22	,	,	PUNCT
ejpam-3479	190	23	x	x	NOUN
ejpam-3479	190	24	)	)	PUNCT
ejpam-3479	190	25	=	=	SYM
ejpam-3479	190	26	e2λm|ψ|∞	e2λm|ψ|∞	NOUN
ejpam-3479	190	27	−	−	PROPN
ejpam-3479	190	28	eλ(m|ψ|∞+ψ(x	eλ(m|ψ|∞+ψ(x	NOUN
ejpam-3479	190	29	)	)	PUNCT
ejpam-3479	190	30	)	)	PUNCT
ejpam-3479	191	1	at	at	ADP
ejpam-3479	191	2	(	(	PUNCT
ejpam-3479	191	3	a−	a−	PROPN
ejpam-3479	191	4	a	a	NOUN
ejpam-3479	191	5	)	)	PUNCT
ejpam-3479	191	6	(	(	PUNCT
ejpam-3479	191	7	t	t	PROPN
ejpam-3479	191	8	−	−	PROPN
ejpam-3479	191	9	t	t	PROPN
ejpam-3479	191	10	)	)	PUNCT
ejpam-3479	191	11	,	,	PUNCT
ejpam-3479	191	12	(	(	PUNCT
ejpam-3479	191	13	30	30	NUM
ejpam-3479	191	14	)	)	PUNCT
ejpam-3479	191	15	with	with	ADP
ejpam-3479	191	16	m	m	PROPN
ejpam-3479	191	17	≥	≥	NOUN
ejpam-3479	191	18	1	1	NUM
ejpam-3479	191	19	.	.	PUNCT
ejpam-3479	192	1	since	since	SCONJ
ejpam-3479	192	2	ϕ	ϕ	NOUN
ejpam-3479	192	3	does	do	AUX
ejpam-3479	192	4	not	not	PART
ejpam-3479	192	5	vanish	vanish	VERB
ejpam-3479	192	6	in	in	ADP
ejpam-3479	192	7	q	q	NOUN
ejpam-3479	192	8	,	,	PUNCT
ejpam-3479	192	9	for	for	SCONJ
ejpam-3479	192	10	all	all	PRON
ejpam-3479	192	11	s	s	PROPN
ejpam-3479	192	12	>	>	X
ejpam-3479	192	13	0	0	PUNCT
ejpam-3479	193	1	and	and	CCONJ
ejpam-3479	193	2	λ	λ	X
ejpam-3479	193	3	>	>	X
ejpam-3479	193	4	0	0	NUM
ejpam-3479	193	5	,	,	PUNCT
ejpam-3479	193	6	we	we	PRON
ejpam-3479	193	7	set	set	VERB
ejpam-3479	193	8	1	1	NUM
ejpam-3479	193	9	θ2	θ2	PROPN
ejpam-3479	193	10	=	=	SYM
ejpam-3479	193	11	min	min	PROPN
ejpam-3479	193	12	[	[	PUNCT
ejpam-3479	193	13	e−2sη	e−2sη	NOUN
ejpam-3479	193	14	(	(	PUNCT
ejpam-3479	193	15	ϕ−1	ϕ−1	PROPN
ejpam-3479	193	16	,	,	PUNCT
ejpam-3479	193	17	ϕ	ϕ	NOUN
ejpam-3479	193	18	,	,	PUNCT
ejpam-3479	193	19	ϕ3	ϕ3	PROPN
ejpam-3479	193	20	,	,	PUNCT
ejpam-3479	193	21	ϕ	ϕ	NOUN
ejpam-3479	193	22	,	,	PUNCT
ejpam-3479	193	23	|∂ψ	|∂ψ	NOUN
ejpam-3479	193	24	∂ν	∂ν	PROPN
ejpam-3479	193	25	|	|	ADV
ejpam-3479	193	26	)	)	PUNCT
ejpam-3479	193	27	]	]	PUNCT
ejpam-3479	193	28	(	(	PUNCT
ejpam-3479	193	29	31	31	NUM
ejpam-3479	193	30	)	)	PUNCT
ejpam-3479	193	31	and	and	CCONJ
ejpam-3479	193	32	we	we	PRON
ejpam-3479	193	33	adopt	adopt	VERB
ejpam-3479	193	34	the	the	DET
ejpam-3479	193	35	following	follow	VERB
ejpam-3479	193	36	notations	notation	NOUN
ejpam-3479	193	37	:	:	PUNCT
ejpam-3479	194	1			X
ejpam-3479	194	2	l	l	NOUN
ejpam-3479	194	3	=	=	SYM
ejpam-3479	194	4	∂	∂	NOUN
ejpam-3479	194	5	∂t	∂t	PROPN
ejpam-3479	194	6	+	+	CCONJ
ejpam-3479	194	7	∂	∂	NUM
ejpam-3479	195	1	∂a	∂a	NOUN
ejpam-3479	195	2	−∆	−∆	NOUN
ejpam-3479	196	1	+	+	CCONJ
ejpam-3479	196	2	µi	µi	PROPN
ejpam-3479	196	3	l∗	l∗	NOUN
ejpam-3479	196	4	=	=	SYM
ejpam-3479	196	5	−	−	PROPN
ejpam-3479	196	6	∂	∂	NOUN
ejpam-3479	196	7	∂t	∂t	PROPN
ejpam-3479	196	8	−	−	PROPN
ejpam-3479	196	9	∂	∂	NOUN
ejpam-3479	197	1	∂a	∂a	NOUN
ejpam-3479	197	2	−∆	−∆	NOUN
ejpam-3479	197	3	+	+	CCONJ
ejpam-3479	197	4	µi	µi	PROPN
ejpam-3479	197	5	v	v	NOUN
ejpam-3479	197	6	=	=	PUNCT
ejpam-3479	197	7	{	{	PUNCT
ejpam-3479	197	8	ρ	ρ	PROPN
ejpam-3479	197	9	∈	∈	PROPN
ejpam-3479	197	10	c∞	c∞	PROPN
ejpam-3479	197	11	(	(	PUNCT
ejpam-3479	197	12	q	q	PROPN
ejpam-3479	197	13	)	)	PUNCT
ejpam-3479	197	14	,	,	PUNCT
ejpam-3479	197	15	ρ	ρ	PROPN
ejpam-3479	197	16	=	=	SYM
ejpam-3479	197	17	0	0	NUM
ejpam-3479	197	18	on	on	ADP
ejpam-3479	197	19	σ	σ	PROPN
ejpam-3479	197	20	}	}	PUNCT
ejpam-3479	197	21	(	(	PUNCT
ejpam-3479	197	22	32	32	NUM
ejpam-3479	197	23	)	)	PUNCT
ejpam-3479	197	24	using	use	VERB
ejpam-3479	197	25	the	the	DET
ejpam-3479	197	26	notations	notation	NOUN
ejpam-3479	197	27	given	give	VERB
ejpam-3479	197	28	by	by	ADP
ejpam-3479	197	29	(	(	PUNCT
ejpam-3479	197	30	32	32	NUM
ejpam-3479	197	31	)	)	PUNCT
ejpam-3479	197	32	and	and	CCONJ
ejpam-3479	197	33	the	the	DET
ejpam-3479	197	34	definition	definition	NOUN
ejpam-3479	197	35	of	of	ADP
ejpam-3479	197	36	θ	θ	PROPN
ejpam-3479	197	37	given	give	VERB
ejpam-3479	197	38	by	by	ADP
ejpam-3479	197	39	(	(	PUNCT
ejpam-3479	197	40	31	31	NUM
ejpam-3479	197	41	)	)	PUNCT
ejpam-3479	197	42	,	,	PUNCT
ejpam-3479	197	43	we	we	PRON
ejpam-3479	197	44	have	have	VERB
ejpam-3479	197	45	the	the	DET
ejpam-3479	197	46	following	follow	VERB
ejpam-3479	197	47	boundary	boundary	ADJ
ejpam-3479	197	48	carleman	carleman	ADJ
ejpam-3479	197	49	inequality	inequality	NOUN
ejpam-3479	197	50	:	:	PUNCT
ejpam-3479	197	51	proposition	proposition	NOUN
ejpam-3479	197	52	1	1	NUM
ejpam-3479	197	53	.	.	PUNCT
ejpam-3479	198	1	[	[	X
ejpam-3479	198	2	global	global	ADJ
ejpam-3479	198	3	carleman	carleman	ADJ
ejpam-3479	198	4	inequality	inequality	PROPN
ejpam-3479	198	5	]	]	PUNCT
ejpam-3479	198	6	let	let	VERB
ejpam-3479	198	7	ψ,ϕ	ψ,ϕ	NOUN
ejpam-3479	198	8	and	and	CCONJ
ejpam-3479	198	9	η	η	PROPN
ejpam-3479	198	10	be	be	AUX
ejpam-3479	198	11	defined	define	VERB
ejpam-3479	198	12	respectively	respectively	ADV
ejpam-3479	198	13	by	by	ADP
ejpam-3479	198	14	(	(	PUNCT
ejpam-3479	198	15	28	28	NUM
ejpam-3479	198	16	)	)	PUNCT
ejpam-3479	198	17	−	−	PROPN
ejpam-3479	198	18	(	(	PUNCT
ejpam-3479	198	19	30	30	NUM
ejpam-3479	198	20	)	)	PUNCT
ejpam-3479	198	21	.	.	PUNCT
ejpam-3479	199	1	then	then	ADV
ejpam-3479	199	2	,	,	PUNCT
ejpam-3479	199	3	there	there	PRON
ejpam-3479	199	4	exists	exist	VERB
ejpam-3479	199	5	numbers	number	NOUN
ejpam-3479	199	6	λ0	λ0	NOUN
ejpam-3479	199	7	=	=	NOUN
ejpam-3479	199	8	λ0	λ0	NOUN
ejpam-3479	199	9	(	(	PUNCT
ejpam-3479	199	10	γ	γ	X
ejpam-3479	199	11	,	,	PUNCT
ejpam-3479	199	12	µ	µ	NOUN
ejpam-3479	199	13	)	)	PUNCT
ejpam-3479	199	14	>	>	X
ejpam-3479	199	15	1	1	NUM
ejpam-3479	199	16	,	,	PUNCT
ejpam-3479	199	17	s0	s0	PROPN
ejpam-3479	199	18	=	=	SYM
ejpam-3479	199	19	s0	s0	PROPN
ejpam-3479	199	20	(	(	PUNCT
ejpam-3479	199	21	γ	γ	X
ejpam-3479	199	22	,	,	PUNCT
ejpam-3479	199	23	µ	µ	NOUN
ejpam-3479	199	24	,	,	PUNCT
ejpam-3479	199	25	t	t	PROPN
ejpam-3479	199	26	)	)	PUNCT
ejpam-3479	199	27	>	>	X
ejpam-3479	200	1	1	1	NUM
ejpam-3479	200	2	,	,	PUNCT
ejpam-3479	200	3	c0	c0	NOUN
ejpam-3479	200	4	=	=	SYM
ejpam-3479	200	5	c0	c0	PROPN
ejpam-3479	200	6	(	(	PUNCT
ejpam-3479	200	7	γ	γ	X
ejpam-3479	200	8	,	,	PUNCT
ejpam-3479	200	9	µ	µ	NOUN
ejpam-3479	200	10	)	)	PUNCT
ejpam-3479	200	11	>	>	X
ejpam-3479	200	12	0	0	PUNCT
ejpam-3479	200	13	and	and	CCONJ
ejpam-3479	200	14	c1	c1	PROPN
ejpam-3479	200	15	=	=	PROPN
ejpam-3479	200	16	c1	c1	PROPN
ejpam-3479	200	17	(	(	PUNCT
ejpam-3479	200	18	γ	γ	X
ejpam-3479	200	19	,	,	PUNCT
ejpam-3479	200	20	µ	µ	NOUN
ejpam-3479	200	21	)	)	PUNCT
ejpam-3479	200	22	>	>	X
ejpam-3479	200	23	0	0	NUM
ejpam-3479	200	24	such	such	ADJ
ejpam-3479	200	25	that	that	PRON
ejpam-3479	200	26	for	for	ADP
ejpam-3479	200	27	any	any	DET
ejpam-3479	200	28	λ	λ	PROPN
ejpam-3479	200	29	≥	≥	NOUN
ejpam-3479	200	30	λ0	λ0	NOUN
ejpam-3479	200	31	,	,	PUNCT
ejpam-3479	200	32	for	for	ADP
ejpam-3479	200	33	any	any	DET
ejpam-3479	200	34	s	s	PART
ejpam-3479	200	35	≥	≥	NOUN
ejpam-3479	200	36	s0	s0	NOUN
ejpam-3479	200	37	,	,	PUNCT
ejpam-3479	200	38	for	for	ADP
ejpam-3479	200	39	any	any	DET
ejpam-3479	200	40	ρ	ρ	PROPN
ejpam-3479	200	41	∈	∈	PROPN
ejpam-3479	200	42	ν	ν	NOUN
ejpam-3479	200	43	,	,	PUNCT
ejpam-3479	200	44	the	the	DET
ejpam-3479	200	45	following	follow	VERB
ejpam-3479	200	46	estimate	estimate	NOUN
ejpam-3479	200	47	holds	hold	VERB
ejpam-3479	200	48	:	:	PUNCT
ejpam-3479	200	49	∫	∫	PROPN
ejpam-3479	200	50	q	q	PROPN
ejpam-3479	200	51	e−2sη	e−2sη	NOUN
ejpam-3479	200	52	sϕ	sϕ	NOUN
ejpam-3479	200	53	(	(	PUNCT
ejpam-3479	200	54	|ρt	|ρt	PROPN
ejpam-3479	200	55	+	+	NUM
ejpam-3479	200	56	ρa|2	ρa|2	PROPN
ejpam-3479	200	57	+	+	CCONJ
ejpam-3479	200	58	|∆ρ|2	|∆ρ|2	NOUN
ejpam-3479	200	59	)	)	PUNCT
ejpam-3479	201	1	dadtdx+	dadtdx+	VERB
ejpam-3479	201	2	∫	∫	PROPN
ejpam-3479	201	3	q	q	X
ejpam-3479	201	4	e−2sη	e−2sη	NOUN
ejpam-3479	201	5	(	(	PUNCT
ejpam-3479	201	6	sλ2ϕ|∇ρ|2	sλ2ϕ|∇ρ|2	NOUN
ejpam-3479	201	7	+	+	CCONJ
ejpam-3479	201	8	s3λ4ϕ3|ρ|2	s3λ4ϕ3|ρ|2	NOUN
ejpam-3479	201	9	)	)	PUNCT
ejpam-3479	201	10	dtdadx	dtdadx	VERB
ejpam-3479	202	1	+	+	PROPN
ejpam-3479	203	1	c0	c0	PROPN
ejpam-3479	203	2	∫	∫	PROPN
ejpam-3479	203	3	t	t	PROPN
ejpam-3479	203	4	0	0	NUM
ejpam-3479	203	5	∫	∫	PROPN
ejpam-3479	203	6	a	a	DET
ejpam-3479	203	7	0	0	NUM
ejpam-3479	203	8	∫	∫	NOUN
ejpam-3479	203	9	γ\γ	γ\γ	PUNCT
ejpam-3479	203	10	se−2sηϕ(−∂ψ	se−2sηϕ(−∂ψ	NOUN
ejpam-3479	203	11	∂ν	∂ν	NOUN
ejpam-3479	203	12	)	)	PUNCT
ejpam-3479	204	1	|∂ρ	|∂ρ	PRON
ejpam-3479	204	2	∂ν	∂ν	PROPN
ejpam-3479	204	3	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	204	4	≤	≤	PROPN
ejpam-3479	204	5	c1	c1	PROPN
ejpam-3479	205	1	[	[	X
ejpam-3479	205	2	∫	∫	X
ejpam-3479	205	3	q	q	X
ejpam-3479	205	4	e−2η|lρ|2dtdadx+	e−2η|lρ|2dtdadx+	NOUN
ejpam-3479	205	5	∫	∫	PROPN
ejpam-3479	205	6	t	t	PROPN
ejpam-3479	205	7	0	0	NUM
ejpam-3479	205	8	∫	∫	PROPN
ejpam-3479	205	9	a	a	DET
ejpam-3479	205	10	0	0	NUM
ejpam-3479	205	11	∫	∫	NOUN
ejpam-3479	205	12	γ	γ	X
ejpam-3479	205	13	se−2ηϕ|∂ρ	se−2ηϕ|∂ρ	VERB
ejpam-3479	205	14	∂ν	∂ν	PROPN
ejpam-3479	205	15	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	205	16	]	]	PUNCT
ejpam-3479	205	17	.	.	PUNCT
ejpam-3479	206	1	(	(	PUNCT
ejpam-3479	206	2	33	33	NUM
ejpam-3479	206	3	)	)	PUNCT
ejpam-3479	206	4	proof	proof	NOUN
ejpam-3479	206	5	.	.	PUNCT
ejpam-3479	207	1	see	see	VERB
ejpam-3479	207	2	[	[	X
ejpam-3479	207	3	18	18	NUM
ejpam-3479	207	4	]	]	PUNCT
ejpam-3479	207	5	as	as	SCONJ
ejpam-3479	207	6	ψ	ψ	PRON
ejpam-3479	207	7	belong	belong	VERB
ejpam-3479	207	8	to	to	ADP
ejpam-3479	207	9	c2(ω	c2(ω	NUM
ejpam-3479	207	10	)	)	PUNCT
ejpam-3479	207	11	and	and	CCONJ
ejpam-3479	207	12	ϕe−2sη	ϕe−2sη	NUM
ejpam-3479	207	13	is	be	AUX
ejpam-3479	207	14	bounded	bound	VERB
ejpam-3479	207	15	,	,	PUNCT
ejpam-3479	207	16	then	then	ADV
ejpam-3479	207	17	1	1	NUM
ejpam-3479	207	18	θ	θ	NOUN
ejpam-3479	207	19	is	be	AUX
ejpam-3479	207	20	also	also	ADV
ejpam-3479	207	21	bounded	bound	VERB
ejpam-3479	207	22	in	in	ADP
ejpam-3479	207	23	q.	q.	PROPN
ejpam-3479	207	24	hence	hence	ADV
ejpam-3479	207	25	,	,	PUNCT
ejpam-3479	207	26	from	from	ADP
ejpam-3479	207	27	proposition	proposition	NOUN
ejpam-3479	207	28	1	1	NUM
ejpam-3479	207	29	,	,	PUNCT
ejpam-3479	207	30	we	we	PRON
ejpam-3479	207	31	have	have	VERB
ejpam-3479	207	32	this	this	DET
ejpam-3479	207	33	other	other	ADJ
ejpam-3479	207	34	inequality	inequality	NOUN
ejpam-3479	207	35	:	:	PUNCT
ejpam-3479	207	36	proposition	proposition	NOUN
ejpam-3479	207	37	2	2	NUM
ejpam-3479	207	38	.	.	PUNCT
ejpam-3479	208	1	let	let	VERB
ejpam-3479	208	2	θ	θ	PROPN
ejpam-3479	208	3	be	be	AUX
ejpam-3479	208	4	defined	define	VERB
ejpam-3479	208	5	by	by	ADP
ejpam-3479	208	6	(	(	PUNCT
ejpam-3479	208	7	31	31	NUM
ejpam-3479	208	8	)	)	PUNCT
ejpam-3479	208	9	.	.	PUNCT
ejpam-3479	209	1	then	then	ADV
ejpam-3479	209	2	,	,	PUNCT
ejpam-3479	209	3	there	there	PRON
ejpam-3479	209	4	exists	exist	VERB
ejpam-3479	209	5	numbers	number	NOUN
ejpam-3479	209	6	λ0	λ0	NOUN
ejpam-3479	209	7	=	=	SYM
ejpam-3479	209	8	λ0(ω	λ0(ω	PROPN
ejpam-3479	209	9	,	,	PUNCT
ejpam-3479	209	10	γ	γ	X
ejpam-3479	209	11	,	,	PUNCT
ejpam-3479	209	12	µ	µ	NOUN
ejpam-3479	209	13	)	)	PUNCT
ejpam-3479	209	14	>	>	X
ejpam-3479	209	15	1	1	NUM
ejpam-3479	209	16	,	,	PUNCT
ejpam-3479	209	17	s0	s0	PROPN
ejpam-3479	209	18	=	=	SYM
ejpam-3479	209	19	s0(ω	s0(ω	PROPN
ejpam-3479	209	20	,	,	PUNCT
ejpam-3479	209	21	γ	γ	PROPN
ejpam-3479	209	22	,	,	PUNCT
ejpam-3479	209	23	µ	µ	NOUN
ejpam-3479	209	24	,	,	PUNCT
ejpam-3479	209	25	t	t	PROPN
ejpam-3479	209	26	)	)	PUNCT
ejpam-3479	209	27	>	>	X
ejpam-3479	209	28	1	1	NUM
ejpam-3479	209	29	,	,	PUNCT
ejpam-3479	209	30	c0	c0	NOUN
ejpam-3479	209	31	=	=	SYM
ejpam-3479	209	32	c0(ω	c0(ω	PROPN
ejpam-3479	209	33	,	,	PUNCT
ejpam-3479	209	34	γ	γ	X
ejpam-3479	209	35	,	,	PUNCT
ejpam-3479	209	36	µ	µ	NOUN
ejpam-3479	209	37	)	)	PUNCT
ejpam-3479	209	38	>	>	X
ejpam-3479	209	39	0	0	NUM
ejpam-3479	209	40	,	,	PUNCT
ejpam-3479	209	41	and	and	CCONJ
ejpam-3479	209	42	c1	c1	PROPN
ejpam-3479	209	43	=	=	SYM
ejpam-3479	209	44	c1(ω	c1(ω	PROPN
ejpam-3479	209	45	,	,	PUNCT
ejpam-3479	209	46	γ	γ	PROPN
ejpam-3479	209	47	,	,	PUNCT
ejpam-3479	209	48	µ	µ	NOUN
ejpam-3479	209	49	)	)	PUNCT
ejpam-3479	209	50	>	>	X
ejpam-3479	209	51	0	0	NUM
ejpam-3479	209	52	such	such	ADJ
ejpam-3479	209	53	that	that	SCONJ
ejpam-3479	209	54	,	,	PUNCT
ejpam-3479	209	55	for	for	ADP
ejpam-3479	209	56	any	any	DET
ejpam-3479	209	57	λ	λ	PROPN
ejpam-3479	209	58	≥	≥	NOUN
ejpam-3479	209	59	λ0	λ0	NOUN
ejpam-3479	209	60	,	,	PUNCT
ejpam-3479	209	61	for	for	ADP
ejpam-3479	209	62	any	any	DET
ejpam-3479	209	63	s	s	PART
ejpam-3479	209	64	≥	≥	NOUN
ejpam-3479	209	65	s0	s0	NOUN
ejpam-3479	209	66	,	,	PUNCT
ejpam-3479	209	67	and	and	CCONJ
ejpam-3479	209	68	for	for	ADP
ejpam-3479	209	69	any	any	DET
ejpam-3479	209	70	ρ	ρ	PROPN
ejpam-3479	209	71	∈	∈	PROPN
ejpam-3479	209	72	v	v	NOUN
ejpam-3479	209	73	,	,	PUNCT
ejpam-3479	209	74	∫	∫	PROPN
ejpam-3479	209	75	u	u	PROPN
ejpam-3479	209	76	∫	∫	PROPN
ejpam-3479	209	77	ω	ω	PROPN
ejpam-3479	209	78	1	1	NUM
ejpam-3479	209	79	θ2	θ2	PROPN
ejpam-3479	209	80	(	(	PUNCT
ejpam-3479	209	81	|∂ρ	|∂ρ	PRON
ejpam-3479	209	82	∂ν	∂ν	ADP
ejpam-3479	209	83	|2	|2	NUM
ejpam-3479	209	84	+	+	X
ejpam-3479	209	85	|∆ρ|2	|∆ρ|2	X
ejpam-3479	209	86	+	+	PUNCT
ejpam-3479	209	87	|∇ρ|2	|∇ρ|2	NOUN
ejpam-3479	210	1	+	+	CCONJ
ejpam-3479	210	2	|ρ|2	|ρ|2	PROPN
ejpam-3479	210	3	)	)	PUNCT
ejpam-3479	210	4	dtdadγ+c0	dtdadγ+c0	PROPN
ejpam-3479	210	5	∫	∫	X
ejpam-3479	210	6	u	u	PROPN
ejpam-3479	210	7	∫	∫	PROPN
ejpam-3479	210	8	γ	γ	PROPN
ejpam-3479	210	9	1	1	NUM
ejpam-3479	210	10	θ2	θ2	ADV
ejpam-3479	210	11	|∂ρ	|∂ρ	PRON
ejpam-3479	210	12	∂ν	∂ν	PROPN
ejpam-3479	210	13	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	210	14	≤	≤	PROPN
ejpam-3479	210	15	c1	c1	PROPN
ejpam-3479	210	16	[	[	X
ejpam-3479	210	17	∫	∫	X
ejpam-3479	210	18	q	q	PROPN
ejpam-3479	210	19	|lρ|2dtdadx+	|lρ|2dtdadx+	NUM
ejpam-3479	210	20	∫	∫	PROPN
ejpam-3479	210	21	u	u	NOUN
ejpam-3479	210	22	∫	∫	PROPN
ejpam-3479	210	23	γ	γ	X
ejpam-3479	210	24	|∂ρ	|∂ρ	PRON
ejpam-3479	210	25	∂ν	∂ν	PROPN
ejpam-3479	210	26	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	210	27	]	]	PUNCT
ejpam-3479	210	28	.	.	PUNCT
ejpam-3479	211	1	(	(	PUNCT
ejpam-3479	211	2	34	34	NUM
ejpam-3479	211	3	)	)	PUNCT
ejpam-3479	211	4	m.soma	m.soma	NOUN
ejpam-3479	211	5	,	,	PUNCT
ejpam-3479	211	6	s.	s.	PROPN
ejpam-3479	211	7	sawadogo	sawadogo	PROPN
ejpam-3479	211	8	/	/	SYM
ejpam-3479	211	9	eur	eur	PROPN
ejpam-3479	211	10	.	.	PUNCT
ejpam-3479	212	1	j.	j.	PROPN
ejpam-3479	212	2	pure	pure	PROPN
ejpam-3479	212	3	appl	appl	PROPN
ejpam-3479	212	4	.	.	PROPN
ejpam-3479	212	5	math	math	PROPN
ejpam-3479	212	6	,	,	PUNCT
ejpam-3479	212	7	12	12	NUM
ejpam-3479	212	8	(	(	PUNCT
ejpam-3479	212	9	3	3	NUM
ejpam-3479	212	10	)	)	PUNCT
ejpam-3479	212	11	(	(	PUNCT
ejpam-3479	212	12	2019	2019	NUM
ejpam-3479	212	13	)	)	PUNCT
ejpam-3479	212	14	,	,	PUNCT
ejpam-3479	212	15	1277	1277	NUM
ejpam-3479	212	16	-	-	SYM
ejpam-3479	212	17	1296	1296	NUM
ejpam-3479	212	18	1287	1287	NUM
ejpam-3479	212	19	lemma	lemma	PROPN
ejpam-3479	212	20	2	2	NUM
ejpam-3479	212	21	.	.	PUNCT
ejpam-3479	213	1	under	under	ADP
ejpam-3479	213	2	the	the	DET
ejpam-3479	213	3	assumptions	assumption	NOUN
ejpam-3479	213	4	of	of	ADP
ejpam-3479	213	5	lemma	lemma	PROPN
ejpam-3479	213	6	1	1	NUM
ejpam-3479	213	7	.	.	PUNCT
ejpam-3479	214	1	let	let	VERB
ejpam-3479	214	2	y	y	PRON
ejpam-3479	214	3	be	be	AUX
ejpam-3479	214	4	the	the	DET
ejpam-3479	214	5	real	real	ADJ
ejpam-3479	214	6	vector	vector	NOUN
ejpam-3479	214	7	subspace	subspace	NOUN
ejpam-3479	214	8	of	of	ADP
ejpam-3479	214	9	l2(u	l2(u	PROPN
ejpam-3479	214	10	×	×	PROPN
ejpam-3479	214	11	γ	γ	NOUN
ejpam-3479	214	12	)	)	PUNCT
ejpam-3479	214	13	of	of	ADP
ejpam-3479	214	14	finite	finite	ADJ
ejpam-3479	214	15	dimension	dimension	NOUN
ejpam-3479	214	16	defined	define	VERB
ejpam-3479	214	17	in	in	ADP
ejpam-3479	214	18	(	(	PUNCT
ejpam-3479	214	19	13	13	NUM
ejpam-3479	214	20	)	)	PUNCT
ejpam-3479	214	21	.	.	PUNCT
ejpam-3479	215	1	then	then	ADV
ejpam-3479	215	2	any	any	DET
ejpam-3479	215	3	function	function	NOUN
ejpam-3479	215	4	ρ	ρ	NUM
ejpam-3479	215	5	such	such	ADJ
ejpam-3479	215	6	that	that	PROPN
ejpam-3479	215	7	∂ρ	∂ρ	PROPN
ejpam-3479	216	1	∂t	∂t	PROPN
ejpam-3479	216	2	+	+	CCONJ
ejpam-3479	216	3	∂ρ	∂ρ	PROPN
ejpam-3479	217	1	∂a	∂a	PROPN
ejpam-3479	217	2	−∆ρ+	−∆ρ+	PROPN
ejpam-3479	217	3	µρ	µρ	ADP
ejpam-3479	217	4	=	=	PUNCT
ejpam-3479	217	5	0	0	NUM
ejpam-3479	217	6	in	in	ADP
ejpam-3479	217	7	q	q	NOUN
ejpam-3479	217	8	,	,	PUNCT
ejpam-3479	217	9	ρ(0	ρ(0	PROPN
ejpam-3479	217	10	,	,	PUNCT
ejpam-3479	217	11	.	.	PUNCT
ejpam-3479	217	12	,	,	PUNCT
ejpam-3479	217	13	.	.	PUNCT
ejpam-3479	217	14	)	)	PUNCT
ejpam-3479	218	1	=	=	PUNCT
ejpam-3479	218	2	0	0	NUM
ejpam-3479	219	1	in	in	ADP
ejpam-3479	219	2	qa	qa	PROPN
ejpam-3479	219	3	,	,	PUNCT
ejpam-3479	219	4	ρ	ρ	PROPN
ejpam-3479	219	5	=	=	SYM
ejpam-3479	219	6	0	0	NUM
ejpam-3479	219	7	on	on	ADP
ejpam-3479	219	8	σ	σ	PROPN
ejpam-3479	219	9	\	\	PROPN
ejpam-3479	219	10	σ1	σ1	PROPN
ejpam-3479	219	11	,	,	PUNCT
ejpam-3479	219	12	∂ρ	∂ρ	PROPN
ejpam-3479	219	13	∂ν	∂ν	PROPN
ejpam-3479	219	14	|γ	|γ	ADP
ejpam-3479	219	15	∈	∈	PROPN
ejpam-3479	219	16	y	y	PROPN
ejpam-3479	219	17	,	,	PUNCT
ejpam-3479	219	18	(	(	PUNCT
ejpam-3479	219	19	35	35	NUM
ejpam-3479	219	20	)	)	PUNCT
ejpam-3479	219	21	is	be	AUX
ejpam-3479	219	22	identically	identically	ADV
ejpam-3479	219	23	zero	zero	NUM
ejpam-3479	219	24	.	.	PUNCT
ejpam-3479	220	1	proof	proof	NOUN
ejpam-3479	220	2	.	.	PUNCT
ejpam-3479	221	1	for	for	ADP
ejpam-3479	221	2	any	any	DET
ejpam-3479	221	3	ρ	ρ	PROPN
ejpam-3479	221	4	verifying	verifying	NOUN
ejpam-3479	221	5	(	(	PUNCT
ejpam-3479	221	6	35	35	NUM
ejpam-3479	221	7	)	)	PUNCT
ejpam-3479	221	8	there	there	PRON
ejpam-3479	221	9	exists	exist	VERB
ejpam-3479	221	10	αi	αi	PART
ejpam-3479	221	11	∈	∈	PROPN
ejpam-3479	221	12	r	r	NOUN
ejpam-3479	221	13	,	,	PUNCT
ejpam-3479	221	14	1≤	1≤	NUM
ejpam-3479	221	15	i	i	PRON
ejpam-3479	221	16	≤	≤	ADV
ejpam-3479	221	17	m	m	VERB
ejpam-3479	221	18	,	,	PUNCT
ejpam-3479	221	19	such	such	ADJ
ejpam-3479	221	20	that	that	PRON
ejpam-3479	221	21	∂ρ	∂ρ	NOUN
ejpam-3479	221	22	∂ν	∂ν	PROPN
ejpam-3479	221	23	=	=	PUNCT
ejpam-3479	221	24	m∑	m∑	INTJ
ejpam-3479	221	25	i=1	i=1	PROPN
ejpam-3479	221	26	αi	αi	PROPN
ejpam-3479	222	1	∂yi	∂yi	PROPN
ejpam-3479	222	2	∂ν	∂ν	PROPN
ejpam-3479	222	3	.	.	PUNCT
ejpam-3479	223	1	we	we	PRON
ejpam-3479	223	2	set	set	VERB
ejpam-3479	223	3	z	z	NOUN
ejpam-3479	223	4	=	=	PUNCT
ejpam-3479	224	1	ρ−	ρ−	NOUN
ejpam-3479	224	2	m∑	m∑	CCONJ
ejpam-3479	224	3	i=1	i=1	PROPN
ejpam-3479	224	4	αiyi	αiyi	PROPN
ejpam-3479	224	5	.	.	PUNCT
ejpam-3479	225	1	using	use	VERB
ejpam-3479	225	2	(	(	PUNCT
ejpam-3479	225	3	10	10	NUM
ejpam-3479	225	4	)	)	PUNCT
ejpam-3479	225	5	,	,	PUNCT
ejpam-3479	225	6	we	we	PRON
ejpam-3479	225	7	have	have	PROPN
ejpam-3479	225	8	∂z	∂z	PROPN
ejpam-3479	226	1	∂t	∂t	PROPN
ejpam-3479	226	2	+	+	CCONJ
ejpam-3479	226	3	∂z	∂z	PROPN
ejpam-3479	226	4	∂a	∂a	PROPN
ejpam-3479	226	5	−∆z	−∆z	X
ejpam-3479	226	6	+	+	NUM
ejpam-3479	226	7	µz	µz	NOUN
ejpam-3479	226	8	=	=	SYM
ejpam-3479	226	9	0	0	NUM
ejpam-3479	226	10	in	in	ADP
ejpam-3479	226	11	q	q	NOUN
ejpam-3479	226	12	,	,	PUNCT
ejpam-3479	226	13	z(0	z(0	ADV
ejpam-3479	226	14	,	,	PUNCT
ejpam-3479	226	15	.	.	PUNCT
ejpam-3479	226	16	,	,	PUNCT
ejpam-3479	226	17	.	.	PUNCT
ejpam-3479	226	18	)	)	PUNCT
ejpam-3479	227	1	=	=	PUNCT
ejpam-3479	227	2	0	0	NUM
ejpam-3479	228	1	in	in	ADP
ejpam-3479	228	2	qa	qa	PROPN
ejpam-3479	228	3	,	,	PUNCT
ejpam-3479	228	4	z	z	PROPN
ejpam-3479	228	5	=	=	SYM
ejpam-3479	228	6	0	0	NUM
ejpam-3479	228	7	on	on	ADP
ejpam-3479	228	8	σ	σ	PROPN
ejpam-3479	228	9	\	\	PROPN
ejpam-3479	228	10	σ1	σ1	PROPN
ejpam-3479	228	11	,	,	PUNCT
ejpam-3479	228	12	∂z	∂z	PROPN
ejpam-3479	228	13	∂ν	∂ν	X
ejpam-3479	228	14	=	=	PUNCT
ejpam-3479	228	15	0	0	PROPN
ejpam-3479	229	1	on	on	ADP
ejpam-3479	229	2	u	u	PROPN
ejpam-3479	229	3	×	×	PROPN
ejpam-3479	229	4	γ	γ	X
ejpam-3479	229	5	.	.	PROPN
ejpam-3479	229	6	(	(	PUNCT
ejpam-3479	229	7	36	36	NUM
ejpam-3479	229	8	)	)	PUNCT
ejpam-3479	229	9	as	as	ADP
ejpam-3479	229	10	γ	γ	PROPN
ejpam-3479	229	11	⊂	⊂	PROPN
ejpam-3479	229	12	γ	γ	PROPN
ejpam-3479	229	13	\	\	PROPN
ejpam-3479	229	14	γ1	γ1	PROPN
ejpam-3479	229	15	,	,	PUNCT
ejpam-3479	229	16	we	we	PRON
ejpam-3479	229	17	have	have	VERB
ejpam-3479	229	18	z	z	NOUN
ejpam-3479	229	19	=	=	SYM
ejpam-3479	229	20	0	0	NUM
ejpam-3479	229	21	and	and	CCONJ
ejpam-3479	229	22	∂z	∂z	PROPN
ejpam-3479	229	23	∂ν	∂ν	X
ejpam-3479	230	1	=	=	PUNCT
ejpam-3479	230	2	0	0	PROPN
ejpam-3479	231	1	in	in	ADP
ejpam-3479	231	2	u	u	PROPN
ejpam-3479	231	3	×	×	PROPN
ejpam-3479	231	4	γ	γ	X
ejpam-3479	231	5	.	.	PROPN
ejpam-3479	232	1	then	then	ADV
ejpam-3479	232	2	it	it	PRON
ejpam-3479	232	3	follows	follow	VERB
ejpam-3479	232	4	from	from	ADP
ejpam-3479	232	5	(	(	PUNCT
ejpam-3479	232	6	12	12	NUM
ejpam-3479	232	7	)	)	PUNCT
ejpam-3479	233	1	that	that	SCONJ
ejpam-3479	233	2	z	z	VERB
ejpam-3479	233	3	=	=	PUNCT
ejpam-3479	233	4	0	0	NUM
ejpam-3479	233	5	in	in	ADP
ejpam-3479	233	6	q.	q.	PROPN
ejpam-3479	233	7	consequently	consequently	ADV
ejpam-3479	233	8	,	,	PUNCT
ejpam-3479	233	9	we	we	PRON
ejpam-3479	233	10	deduce	deduce	VERB
ejpam-3479	233	11	on	on	ADP
ejpam-3479	233	12	the	the	DET
ejpam-3479	233	13	one	one	NUM
ejpam-3479	233	14	hand	hand	NOUN
ejpam-3479	233	15	that	that	PRON
ejpam-3479	233	16	ρ	ρ	NOUN
ejpam-3479	233	17	=	=	PUNCT
ejpam-3479	233	18	m∑	m∑	PROPN
ejpam-3479	233	19	i=1	i=1	PROPN
ejpam-3479	233	20	αiyi	αiyi	PROPN
ejpam-3479	233	21	and	and	CCONJ
ejpam-3479	233	22	on	on	ADP
ejpam-3479	233	23	the	the	DET
ejpam-3479	233	24	other	other	ADJ
ejpam-3479	233	25	hand	hand	NOUN
ejpam-3479	233	26	that	that	PRON
ejpam-3479	233	27	m∑	m∑	VERB
ejpam-3479	233	28	i=1	i=1	PROPN
ejpam-3479	233	29	αiξ̂i	αiξ̂i	PROPN
ejpam-3479	233	30	=	=	NOUN
ejpam-3479	233	31	0	0	NUM
ejpam-3479	233	32	on	on	ADP
ejpam-3479	233	33	σ1	σ1	PROPN
ejpam-3479	233	34	.	.	PUNCT
ejpam-3479	234	1	hence	hence	ADV
ejpam-3479	234	2	,	,	PUNCT
ejpam-3479	234	3	it	it	PRON
ejpam-3479	234	4	follows	follow	VERB
ejpam-3479	234	5	from	from	ADP
ejpam-3479	234	6	assumption	assumption	NOUN
ejpam-3479	234	7	(	(	PUNCT
ejpam-3479	234	8	11	11	NUM
ejpam-3479	234	9	)	)	PUNCT
ejpam-3479	234	10	that	that	PRON
ejpam-3479	234	11	αi	αi	VERB
ejpam-3479	234	12	=	=	SYM
ejpam-3479	234	13	0	0	NUM
ejpam-3479	234	14	for	for	ADP
ejpam-3479	234	15	1	1	NUM
ejpam-3479	234	16	≤	≤	NUM
ejpam-3479	234	17	i	i	PROPN
ejpam-3479	234	18	≤m	≤m	PROPN
ejpam-3479	234	19	.thus	.thus	PROPN
ejpam-3479	234	20	,	,	PUNCT
ejpam-3479	234	21	ρ	ρ	PROPN
ejpam-3479	234	22	=	=	SYM
ejpam-3479	234	23	0	0	NUM
ejpam-3479	234	24	in	in	ADP
ejpam-3479	234	25	q.	q.	NOUN
ejpam-3479	234	26	proposition	proposition	NOUN
ejpam-3479	234	27	3	3	NUM
ejpam-3479	234	28	(	(	PUNCT
ejpam-3479	234	29	adapted	adapt	VERB
ejpam-3479	234	30	carleman	carleman	ADJ
ejpam-3479	234	31	inequality	inequality	NOUN
ejpam-3479	234	32	)	)	PUNCT
ejpam-3479	234	33	.	.	PUNCT
ejpam-3479	235	1	under	under	ADP
ejpam-3479	235	2	the	the	DET
ejpam-3479	235	3	assumption	assumption	NOUN
ejpam-3479	235	4	of	of	ADP
ejpam-3479	235	5	lemma1	lemma1	PROPN
ejpam-3479	235	6	.	.	PUNCT
ejpam-3479	236	1	let	let	VERB
ejpam-3479	236	2	y	y	PRON
ejpam-3479	236	3	be	be	AUX
ejpam-3479	236	4	the	the	DET
ejpam-3479	236	5	real	real	ADJ
ejpam-3479	236	6	vector	vector	NOUN
ejpam-3479	236	7	subspace	subspace	NOUN
ejpam-3479	236	8	of	of	ADP
ejpam-3479	236	9	l2(u	l2(u	PROPN
ejpam-3479	236	10	×	×	PROPN
ejpam-3479	236	11	γ	γ	NOUN
ejpam-3479	236	12	)	)	PUNCT
ejpam-3479	236	13	of	of	ADP
ejpam-3479	236	14	finite	finite	ADJ
ejpam-3479	236	15	dimension	dimension	NOUN
ejpam-3479	236	16	defined	define	VERB
ejpam-3479	236	17	in	in	ADP
ejpam-3479	236	18	(	(	PUNCT
ejpam-3479	236	19	13	13	NUM
ejpam-3479	236	20	)	)	PUNCT
ejpam-3479	236	21	and	and	CCONJ
ejpam-3479	236	22	p	p	NOUN
ejpam-3479	236	23	be	be	AUX
ejpam-3479	236	24	the	the	DET
ejpam-3479	236	25	orthogonal	orthogonal	ADJ
ejpam-3479	236	26	projection	projection	NOUN
ejpam-3479	236	27	operator	operator	NOUN
ejpam-3479	236	28	from	from	ADP
ejpam-3479	236	29	l2(u	l2(u	PROPN
ejpam-3479	236	30	×	×	PROPN
ejpam-3479	236	31	γ	γ	NOUN
ejpam-3479	236	32	)	)	PUNCT
ejpam-3479	236	33	into	into	ADP
ejpam-3479	236	34	y	y	PROPN
ejpam-3479	236	35	.	.	PUNCT
ejpam-3479	237	1	let	let	VERB
ejpam-3479	237	2	also	also	ADV
ejpam-3479	237	3	θ	θ	PROPN
ejpam-3479	237	4	be	be	AUX
ejpam-3479	237	5	the	the	DET
ejpam-3479	237	6	function	function	NOUN
ejpam-3479	237	7	defined	define	VERB
ejpam-3479	237	8	by	by	ADP
ejpam-3479	237	9	(	(	PUNCT
ejpam-3479	237	10	31	31	NUM
ejpam-3479	237	11	)	)	PUNCT
ejpam-3479	237	12	.	.	PUNCT
ejpam-3479	238	1	then	then	ADV
ejpam-3479	238	2	,	,	PUNCT
ejpam-3479	238	3	there	there	PRON
ejpam-3479	238	4	exists	exist	VERB
ejpam-3479	238	5	numbers	number	NOUN
ejpam-3479	238	6	λ0	λ0	NOUN
ejpam-3479	238	7	=	=	SYM
ejpam-3479	238	8	λ0(ω	λ0(ω	PROPN
ejpam-3479	238	9	,	,	PUNCT
ejpam-3479	238	10	γ	γ	X
ejpam-3479	238	11	,	,	PUNCT
ejpam-3479	238	12	µ	µ	NOUN
ejpam-3479	238	13	)	)	PUNCT
ejpam-3479	238	14	>	>	X
ejpam-3479	238	15	1	1	NUM
ejpam-3479	238	16	,	,	PUNCT
ejpam-3479	238	17	s0	s0	PROPN
ejpam-3479	238	18	=	=	SYM
ejpam-3479	238	19	s0(ω	s0(ω	PROPN
ejpam-3479	238	20	,	,	PUNCT
ejpam-3479	238	21	γ	γ	PROPN
ejpam-3479	238	22	,	,	PUNCT
ejpam-3479	238	23	µ	µ	NOUN
ejpam-3479	238	24	,	,	PUNCT
ejpam-3479	238	25	t	t	PROPN
ejpam-3479	238	26	)	)	PUNCT
ejpam-3479	238	27	>	>	X
ejpam-3479	238	28	1	1	NUM
ejpam-3479	238	29	,	,	PUNCT
ejpam-3479	238	30	c0	c0	NOUN
ejpam-3479	238	31	=	=	SYM
ejpam-3479	238	32	c0(ω	c0(ω	PROPN
ejpam-3479	238	33	,	,	PUNCT
ejpam-3479	238	34	γ	γ	X
ejpam-3479	238	35	,	,	PUNCT
ejpam-3479	238	36	µ	µ	NOUN
ejpam-3479	238	37	)	)	PUNCT
ejpam-3479	238	38	>	>	X
ejpam-3479	238	39	0	0	PUNCT
ejpam-3479	238	40	and	and	CCONJ
ejpam-3479	238	41	c1	c1	PROPN
ejpam-3479	238	42	=	=	SYM
ejpam-3479	239	1	c1(ω	c1(ω	PROPN
ejpam-3479	239	2	,	,	PUNCT
ejpam-3479	239	3	γ	γ	PROPN
ejpam-3479	239	4	,	,	PUNCT
ejpam-3479	239	5	µ	µ	NOUN
ejpam-3479	239	6	)	)	PUNCT
ejpam-3479	239	7	>	>	X
ejpam-3479	239	8	0	0	NUM
ejpam-3479	240	1	such	such	ADJ
ejpam-3479	240	2	that	that	SCONJ
ejpam-3479	240	3	,	,	PUNCT
ejpam-3479	240	4	for	for	ADP
ejpam-3479	240	5	any	any	DET
ejpam-3479	240	6	λ	λ	PROPN
ejpam-3479	240	7	≥	≥	NOUN
ejpam-3479	240	8	λ0	λ0	NOUN
ejpam-3479	240	9	,	,	PUNCT
ejpam-3479	240	10	for	for	ADP
ejpam-3479	240	11	any	any	DET
ejpam-3479	240	12	s	s	PART
ejpam-3479	240	13	≥	≥	NOUN
ejpam-3479	240	14	s0	s0	NOUN
ejpam-3479	240	15	,	,	PUNCT
ejpam-3479	240	16	and	and	CCONJ
ejpam-3479	240	17	for	for	ADP
ejpam-3479	240	18	any	any	DET
ejpam-3479	240	19	ρ	ρ	PROPN
ejpam-3479	240	20	∈	∈	PROPN
ejpam-3479	240	21	v	v	NOUN
ejpam-3479	240	22	,	,	PUNCT
ejpam-3479	240	23	∫	∫	PROPN
ejpam-3479	240	24	u	u	PROPN
ejpam-3479	240	25	∫	∫	PROPN
ejpam-3479	240	26	ω	ω	PROPN
ejpam-3479	240	27	1	1	NUM
ejpam-3479	240	28	θ2	θ2	ADP
ejpam-3479	240	29	|∂ρ	|∂ρ	PRON
ejpam-3479	240	30	∂ν	∂ν	PROPN
ejpam-3479	240	31	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	240	32	≤	≤	PROPN
ejpam-3479	240	33	c1	c1	PROPN
ejpam-3479	241	1	[	[	X
ejpam-3479	241	2	∫	∫	X
ejpam-3479	241	3	q	q	PROPN
ejpam-3479	241	4	|lρ|2dtdadx+	|lρ|2dtdadx+	NUM
ejpam-3479	241	5	∫	∫	PROPN
ejpam-3479	241	6	u	u	NOUN
ejpam-3479	241	7	∫	∫	PROPN
ejpam-3479	241	8	γ	γ	PROPN
ejpam-3479	241	9	|p	|p	PROPN
ejpam-3479	241	10	∂ρ	∂ρ	PROPN
ejpam-3479	241	11	∂ν	∂ν	PROPN
ejpam-3479	241	12	−	−	PROPN
ejpam-3479	241	13	∂ρ	∂ρ	PROPN
ejpam-3479	241	14	∂ν	∂ν	PROPN
ejpam-3479	241	15	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	241	16	]	]	PUNCT
ejpam-3479	241	17	.	.	PUNCT
ejpam-3479	242	1	(	(	PUNCT
ejpam-3479	242	2	37	37	NUM
ejpam-3479	242	3	)	)	PUNCT
ejpam-3479	242	4	proof	proof	NOUN
ejpam-3479	242	5	.	.	PUNCT
ejpam-3479	243	1	as	as	ADP
ejpam-3479	243	2	in	in	ADP
ejpam-3479	243	3	[	[	X
ejpam-3479	243	4	9	9	NUM
ejpam-3479	243	5	]	]	PUNCT
ejpam-3479	243	6	,	,	PUNCT
ejpam-3479	243	7	we	we	PRON
ejpam-3479	243	8	use	use	VERB
ejpam-3479	243	9	a	a	DET
ejpam-3479	243	10	well	well	ADV
ejpam-3479	243	11	known	know	VERB
ejpam-3479	243	12	compactness	compactness	NOUN
ejpam-3479	243	13	-	-	PUNCT
ejpam-3479	243	14	uniqueness	uniqueness	NOUN
ejpam-3479	243	15	argument	argument	NOUN
ejpam-3479	243	16	and	and	CCONJ
ejpam-3479	243	17	the	the	DET
ejpam-3479	243	18	inequality	inequality	NOUN
ejpam-3479	243	19	(	(	PUNCT
ejpam-3479	243	20	34	34	NUM
ejpam-3479	243	21	)	)	PUNCT
ejpam-3479	243	22	.	.	PUNCT
ejpam-3479	244	1	indeed	indeed	ADV
ejpam-3479	244	2	,	,	PUNCT
ejpam-3479	244	3	suppose	suppose	VERB
ejpam-3479	244	4	that	that	SCONJ
ejpam-3479	244	5	(	(	PUNCT
ejpam-3479	244	6	37	37	NUM
ejpam-3479	244	7	)	)	PUNCT
ejpam-3479	244	8	does	do	AUX
ejpam-3479	244	9	not	not	PART
ejpam-3479	244	10	hold	hold	VERB
ejpam-3479	244	11	.	.	PUNCT
ejpam-3479	245	1	then	then	ADV
ejpam-3479	245	2	for	for	ADP
ejpam-3479	245	3	any	any	DET
ejpam-3479	245	4	j	j	PROPN
ejpam-3479	245	5	∈	∈	PROPN
ejpam-3479	245	6	n	n	CCONJ
ejpam-3479	245	7	,	,	PUNCT
ejpam-3479	245	8	there	there	PRON
ejpam-3479	245	9	exists	exist	VERB
ejpam-3479	245	10	ρj	ρj	PRON
ejpam-3479	245	11	∈	∈	PROPN
ejpam-3479	245	12	v	v	ADP
ejpam-3479	245	13	such	such	ADJ
ejpam-3479	245	14	that	that	DET
ejpam-3479	245	15	∫	∫	PROPN
ejpam-3479	245	16	u	u	PROPN
ejpam-3479	245	17	∫	∫	PROPN
ejpam-3479	245	18	ω	ω	PROPN
ejpam-3479	245	19	|lρj	|lρj	NOUN
ejpam-3479	245	20	|2dtdadx	|2dtdadx	VERB
ejpam-3479	245	21	≤	≤	NUM
ejpam-3479	245	22	1	1	NUM
ejpam-3479	245	23	j	j	PROPN
ejpam-3479	245	24	,	,	PUNCT
ejpam-3479	245	25	(	(	PUNCT
ejpam-3479	245	26	38	38	NUM
ejpam-3479	245	27	)	)	PUNCT
ejpam-3479	245	28	m.soma	m.soma	NOUN
ejpam-3479	245	29	,	,	PUNCT
ejpam-3479	245	30	s.	s.	PROPN
ejpam-3479	245	31	sawadogo	sawadogo	PROPN
ejpam-3479	245	32	/	/	SYM
ejpam-3479	245	33	eur	eur	PROPN
ejpam-3479	245	34	.	.	PUNCT
ejpam-3479	246	1	j.	j.	PROPN
ejpam-3479	246	2	pure	pure	PROPN
ejpam-3479	246	3	appl	appl	PROPN
ejpam-3479	246	4	.	.	PROPN
ejpam-3479	246	5	math	math	PROPN
ejpam-3479	246	6	,	,	PUNCT
ejpam-3479	246	7	12	12	NUM
ejpam-3479	246	8	(	(	PUNCT
ejpam-3479	246	9	3	3	NUM
ejpam-3479	246	10	)	)	PUNCT
ejpam-3479	246	11	(	(	PUNCT
ejpam-3479	246	12	2019	2019	NUM
ejpam-3479	246	13	)	)	PUNCT
ejpam-3479	246	14	,	,	PUNCT
ejpam-3479	246	15	1277	1277	NUM
ejpam-3479	246	16	-	-	SYM
ejpam-3479	246	17	1296	1296	NUM
ejpam-3479	246	18	1288	1288	NUM
ejpam-3479	246	19	∫	∫	PROPN
ejpam-3479	246	20	u	u	NOUN
ejpam-3479	246	21	∫	∫	PROPN
ejpam-3479	246	22	γ	γ	PROPN
ejpam-3479	246	23	|p	|p	PROPN
ejpam-3479	246	24	∂ρj	∂ρj	PROPN
ejpam-3479	246	25	∂ν	∂ν	PROPN
ejpam-3479	246	26	−	−	PROPN
ejpam-3479	246	27	∂ρj	∂ρj	PROPN
ejpam-3479	246	28	∂ν	∂ν	PROPN
ejpam-3479	246	29	χγ	χγ	PROPN
ejpam-3479	246	30	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	246	31	≤	≤	ADV
ejpam-3479	246	32	1	1	NUM
ejpam-3479	246	33	j	j	PROPN
ejpam-3479	246	34	,	,	PUNCT
ejpam-3479	246	35	(	(	PUNCT
ejpam-3479	246	36	39	39	NUM
ejpam-3479	246	37	)	)	PUNCT
ejpam-3479	246	38	∫	∫	PROPN
ejpam-3479	247	1	u	u	NOUN
ejpam-3479	247	2	∫	∫	PROPN
ejpam-3479	247	3	γ	γ	PROPN
ejpam-3479	247	4	1	1	NUM
ejpam-3479	247	5	θ2	θ2	NOUN
ejpam-3479	247	6	|∂ρj	|∂ρj	X
ejpam-3479	248	1	∂ν	∂ν	PROPN
ejpam-3479	248	2	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	248	3	=	=	VERB
ejpam-3479	248	4	1	1	X
ejpam-3479	248	5	.	.	PUNCT
ejpam-3479	248	6	(	(	PUNCT
ejpam-3479	248	7	40	40	NUM
ejpam-3479	248	8	)	)	PUNCT
ejpam-3479	248	9	in	in	ADP
ejpam-3479	248	10	what	what	PRON
ejpam-3479	248	11	follows	follow	VERB
ejpam-3479	248	12	,	,	PUNCT
ejpam-3479	248	13	we	we	PRON
ejpam-3479	248	14	prove	prove	VERB
ejpam-3479	248	15	in	in	ADP
ejpam-3479	248	16	three	three	NUM
ejpam-3479	248	17	steps	step	NOUN
ejpam-3479	248	18	that	that	PRON
ejpam-3479	248	19	(	(	PUNCT
ejpam-3479	248	20	38)−	38)−	NUM
ejpam-3479	248	21	(	(	PUNCT
ejpam-3479	248	22	40	40	NUM
ejpam-3479	248	23	)	)	PUNCT
ejpam-3479	248	24	yields	yield	NOUN
ejpam-3479	248	25	contradiction	contradiction	NOUN
ejpam-3479	248	26	.	.	PUNCT
ejpam-3479	249	1	step	step	NOUN
ejpam-3479	249	2	1	1	NUM
ejpam-3479	249	3	.	.	PUNCT
ejpam-3479	250	1	we	we	PRON
ejpam-3479	250	2	have∫	have∫	VERB
ejpam-3479	250	3	u	u	NOUN
ejpam-3479	250	4	∫	∫	PROPN
ejpam-3479	250	5	γ	γ	PROPN
ejpam-3479	250	6	1	1	NUM
ejpam-3479	250	7	θ2	θ2	PROPN
ejpam-3479	250	8	|p	|p	ADJ
ejpam-3479	250	9	∂ρj	∂ρj	PROPN
ejpam-3479	250	10	∂ν	∂ν	PROPN
ejpam-3479	250	11	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	250	12	≤	≤	ADV
ejpam-3479	250	13	2	2	NUM
ejpam-3479	250	14	∫	∫	NOUN
ejpam-3479	250	15	u	u	NOUN
ejpam-3479	250	16	∫	∫	PROPN
ejpam-3479	250	17	γ	γ	PROPN
ejpam-3479	250	18	1	1	NUM
ejpam-3479	250	19	θ2	θ2	PROPN
ejpam-3479	250	20	|p	|p	ADJ
ejpam-3479	250	21	∂ρj	∂ρj	PROPN
ejpam-3479	250	22	∂ν	∂ν	PROPN
ejpam-3479	250	23	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	250	24	+	+	CCONJ
ejpam-3479	250	25	2	2	NUM
ejpam-3479	250	26	∫	∫	NOUN
ejpam-3479	250	27	u	u	NOUN
ejpam-3479	250	28	∫	∫	PROPN
ejpam-3479	250	29	γ	γ	PROPN
ejpam-3479	250	30	1	1	NUM
ejpam-3479	250	31	θ2	θ2	PROPN
ejpam-3479	250	32	|p	|p	NOUN
ejpam-3479	250	33	∂ρj	∂ρj	PROPN
ejpam-3479	250	34	∂ν	∂ν	PROPN
ejpam-3479	250	35	−	−	PROPN
ejpam-3479	250	36	∂ρj	∂ρj	PROPN
ejpam-3479	250	37	∂ν	∂ν	PROPN
ejpam-3479	250	38	χγ	χγ	PROPN
ejpam-3479	250	39	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	250	40	.	.	PUNCT
ejpam-3479	251	1	(	(	PUNCT
ejpam-3479	251	2	41	41	NUM
ejpam-3479	251	3	)	)	PUNCT
ejpam-3479	251	4	since	since	SCONJ
ejpam-3479	251	5	1	1	NUM
ejpam-3479	251	6	θ2	θ2	PROPN
ejpam-3479	251	7	is	be	AUX
ejpam-3479	251	8	bounded	bound	VERB
ejpam-3479	251	9	,	,	PUNCT
ejpam-3479	251	10	using	use	VERB
ejpam-3479	251	11	(	(	PUNCT
ejpam-3479	251	12	38	38	NUM
ejpam-3479	251	13	)	)	PUNCT
ejpam-3479	251	14	and	and	CCONJ
ejpam-3479	251	15	(	(	PUNCT
ejpam-3479	251	16	39	39	NUM
ejpam-3479	251	17	)	)	PUNCT
ejpam-3479	251	18	,	,	PUNCT
ejpam-3479	251	19	it	it	PRON
ejpam-3479	251	20	follows	follow	VERB
ejpam-3479	251	21	that	that	SCONJ
ejpam-3479	251	22	there	there	PRON
ejpam-3479	251	23	exists	exist	VERB
ejpam-3479	251	24	a	a	DET
ejpam-3479	251	25	positive	positive	ADJ
ejpam-3479	251	26	constant	constant	ADJ
ejpam-3479	251	27	c	c	NOUN
ejpam-3479	252	1	such	such	ADJ
ejpam-3479	252	2	that	that	SCONJ
ejpam-3479	252	3	∀j	∀j	PROPN
ejpam-3479	252	4	∈	∈	PROPN
ejpam-3479	252	5	n	n	CCONJ
ejpam-3479	252	6	,	,	PUNCT
ejpam-3479	252	7	∫	∫	PROPN
ejpam-3479	252	8	u	u	NOUN
ejpam-3479	252	9	∫	∫	PROPN
ejpam-3479	252	10	γ	γ	PROPN
ejpam-3479	252	11	|p	|p	PROPN
ejpam-3479	252	12	∂ρj	∂ρj	PROPN
ejpam-3479	252	13	∂ν	∂ν	PROPN
ejpam-3479	252	14	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	252	15	≤	≤	PROPN
ejpam-3479	252	16	c.	c.	NOUN
ejpam-3479	252	17	(	(	PUNCT
ejpam-3479	252	18	42	42	NUM
ejpam-3479	252	19	)	)	PUNCT
ejpam-3479	252	20	as	as	ADP
ejpam-3479	252	21	∂ρ	∂ρ	PROPN
ejpam-3479	252	22	∂νχγ	∂νχγ	PUNCT
ejpam-3479	252	23	=	=	PUNCT
ejpam-3479	252	24	p	p	X
ejpam-3479	252	25	∂ρ	∂ρ	PROPN
ejpam-3479	252	26	∂νχγ	∂νχγ	VERB
ejpam-3479	252	27	+	+	CCONJ
ejpam-3479	252	28	(	(	PUNCT
ejpam-3479	252	29	∂ρ∂νχγ	∂ρ∂νχγ	ADP
ejpam-3479	252	30	−	−	PROPN
ejpam-3479	252	31	p	p	PROPN
ejpam-3479	252	32	∂ρ	∂ρ	PROPN
ejpam-3479	252	33	∂νχγ	∂νχγ	NUM
ejpam-3479	252	34	)	)	PUNCT
ejpam-3479	252	35	,	,	PUNCT
ejpam-3479	252	36	using	use	VERB
ejpam-3479	252	37	(	(	PUNCT
ejpam-3479	252	38	40	40	NUM
ejpam-3479	252	39	)	)	PUNCT
ejpam-3479	252	40	and	and	CCONJ
ejpam-3479	252	41	(	(	PUNCT
ejpam-3479	252	42	42	42	NUM
ejpam-3479	252	43	)	)	PUNCT
ejpam-3479	252	44	,	,	PUNCT
ejpam-3479	252	45	we	we	PRON
ejpam-3479	252	46	obtain	obtain	VERB
ejpam-3479	252	47	‖∂ρj	‖∂ρj	NOUN
ejpam-3479	252	48	∂ν	∂ν	PROPN
ejpam-3479	252	49	‖2l2(u×γ	‖2l2(u×γ	PROPN
ejpam-3479	252	50	)	)	PUNCT
ejpam-3479	252	51	≤	≤	NOUN
ejpam-3479	252	52	c.	c.	NOUN
ejpam-3479	252	53	(	(	PUNCT
ejpam-3479	252	54	43	43	NUM
ejpam-3479	252	55	)	)	PUNCT
ejpam-3479	252	56	step	step	NOUN
ejpam-3479	252	57	2	2	NUM
ejpam-3479	252	58	.	.	PUNCT
ejpam-3479	253	1	let	let	VERB
ejpam-3479	253	2	l2	l2	NOUN
ejpam-3479	253	3	(	(	PUNCT
ejpam-3479	253	4	1	1	NUM
ejpam-3479	253	5	θ	θ	NOUN
ejpam-3479	253	6	,	,	PUNCT
ejpam-3479	253	7	u	u	PRON
ejpam-3479	253	8	×	×	NOUN
ejpam-3479	253	9	γ	γ	NOUN
ejpam-3479	253	10	)	)	PUNCT
ejpam-3479	253	11	=	=	PUNCT
ejpam-3479	254	1	{	{	PUNCT
ejpam-3479	254	2	ρ	ρ	PROPN
ejpam-3479	254	3	∈	∈	PROPN
ejpam-3479	255	1	l2(u	l2(u	X
ejpam-3479	255	2	×	×	PROPN
ejpam-3479	255	3	ω	ω	PROPN
ejpam-3479	255	4	)	)	PUNCT
ejpam-3479	255	5	;	;	PUNCT
ejpam-3479	255	6	∫	∫	PROPN
ejpam-3479	255	7	u	u	NOUN
ejpam-3479	255	8	∫	∫	PROPN
ejpam-3479	255	9	γ	γ	PROPN
ejpam-3479	255	10	1	1	NUM
ejpam-3479	255	11	θ2	θ2	PROPN
ejpam-3479	255	12	∣∣∣∣∂ρj∂ν	∣∣∣∣∂ρj∂ν	PROPN
ejpam-3479	255	13	∣∣∣∣2	∣∣∣∣2	PROPN
ejpam-3479	255	14	dtdadγ	dtdadγ	PROPN
ejpam-3479	255	15	<	<	X
ejpam-3479	255	16	∞	∞	PROPN
ejpam-3479	255	17	}	}	PUNCT
ejpam-3479	255	18	.	.	PUNCT
ejpam-3479	256	1	then	then	ADV
ejpam-3479	256	2	in	in	ADP
ejpam-3479	256	3	view	view	NOUN
ejpam-3479	256	4	of	of	ADP
ejpam-3479	256	5	(	(	PUNCT
ejpam-3479	256	6	40	40	NUM
ejpam-3479	256	7	)	)	PUNCT
ejpam-3479	256	8	and	and	CCONJ
ejpam-3479	256	9	(	(	PUNCT
ejpam-3479	256	10	43	43	NUM
ejpam-3479	256	11	)	)	PUNCT
ejpam-3479	256	12	,	,	PUNCT
ejpam-3479	256	13	we	we	PRON
ejpam-3479	256	14	deduce	deduce	VERB
ejpam-3479	256	15	from	from	ADP
ejpam-3479	256	16	(	(	PUNCT
ejpam-3479	256	17	34	34	NUM
ejpam-3479	256	18	)	)	PUNCT
ejpam-3479	256	19	that	that	PRON
ejpam-3479	256	20	,	,	PUNCT
ejpam-3479	256	21	(	(	PUNCT
ejpam-3479	256	22	∂ρ	∂ρ	PROPN
ejpam-3479	256	23	∂t	∂t	PROPN
ejpam-3479	256	24	+	+	CCONJ
ejpam-3479	256	25	∂ρ	∂ρ	PROPN
ejpam-3479	256	26	∂a	∂a	NOUN
ejpam-3479	256	27	)	)	PUNCT
ejpam-3479	256	28	,	,	PUNCT
ejpam-3479	256	29	(	(	PUNCT
ejpam-3479	256	30	∂ρj	∂ρj	PROPN
ejpam-3479	256	31	∂ν	∂ν	PROPN
ejpam-3479	256	32	)	)	PUNCT
ejpam-3479	256	33	,	,	PUNCT
ejpam-3479	256	34	(	(	PUNCT
ejpam-3479	256	35	∇ρj	∇ρj	NOUN
ejpam-3479	256	36	)	)	PUNCT
ejpam-3479	256	37	,	,	PUNCT
ejpam-3479	256	38	(	(	PUNCT
ejpam-3479	256	39	ρj	ρj	NOUN
ejpam-3479	256	40	)	)	PUNCT
ejpam-3479	256	41	and	and	CCONJ
ejpam-3479	256	42	(	(	PUNCT
ejpam-3479	256	43	∆ρj	∆ρj	X
ejpam-3479	256	44	)	)	PUNCT
ejpam-3479	256	45	are	be	AUX
ejpam-3479	256	46	bounded	bound	VERB
ejpam-3479	256	47	in	in	ADP
ejpam-3479	256	48	l2	l2	NOUN
ejpam-3479	256	49	(	(	PUNCT
ejpam-3479	256	50	1	1	NUM
ejpam-3479	256	51	θ	θ	NOUN
ejpam-3479	256	52	,	,	PUNCT
ejpam-3479	256	53	u	u	PRON
ejpam-3479	256	54	×	×	NOUN
ejpam-3479	256	55	γ	γ	NOUN
ejpam-3479	256	56	)	)	PUNCT
ejpam-3479	256	57	.	.	PUNCT
ejpam-3479	257	1	let	let	VERB
ejpam-3479	257	2	us	we	PRON
ejpam-3479	257	3	the	the	DET
ejpam-3479	257	4	take	take	VERB
ejpam-3479	257	5	a	a	DET
ejpam-3479	257	6	subsequence	subsequence	NOUN
ejpam-3479	257	7	still	still	ADV
ejpam-3479	257	8	denoted	denote	VERB
ejpam-3479	257	9	by	by	ADP
ejpam-3479	257	10	(	(	PUNCT
ejpam-3479	257	11	ρj	ρj	NOUN
ejpam-3479	257	12	)	)	PUNCT
ejpam-3479	257	13	such	such	ADJ
ejpam-3479	257	14	that	that	SCONJ
ejpam-3479	257	15	ρj	ρj	NOUN
ejpam-3479	257	16	⇀	⇀	NUM
ejpam-3479	257	17	ρ	ρ	NUM
ejpam-3479	257	18	weakly	weakly	ADJ
ejpam-3479	257	19	in	in	ADP
ejpam-3479	257	20	l2	l2	NOUN
ejpam-3479	257	21	(	(	PUNCT
ejpam-3479	257	22	1	1	NUM
ejpam-3479	257	23	θ	θ	NOUN
ejpam-3479	257	24	,	,	PUNCT
ejpam-3479	257	25	u	u	PRON
ejpam-3479	257	26	×	×	PROPN
ejpam-3479	257	27	γ	γ	PROPN
ejpam-3479	257	28	)	)	PUNCT
ejpam-3479	257	29	,	,	PUNCT
ejpam-3479	257	30	(	(	PUNCT
ejpam-3479	257	31	44	44	NUM
ejpam-3479	257	32	)	)	PUNCT
ejpam-3479	257	33	∂ρj	∂ρj	PROPN
ejpam-3479	257	34	∂ν	∂ν	PROPN
ejpam-3479	258	1	⇀	⇀	PROPN
ejpam-3479	258	2	∂ρ	∂ρ	PROPN
ejpam-3479	259	1	∂ν	∂ν	PRON
ejpam-3479	259	2	weakly	weakly	ADV
ejpam-3479	259	3	in	in	ADP
ejpam-3479	259	4	l2	l2	NOUN
ejpam-3479	259	5	(	(	PUNCT
ejpam-3479	259	6	1	1	NUM
ejpam-3479	259	7	θ	θ	NOUN
ejpam-3479	259	8	,	,	PUNCT
ejpam-3479	259	9	u	u	PRON
ejpam-3479	259	10	×	×	PROPN
ejpam-3479	259	11	γ	γ	X
ejpam-3479	259	12	)	)	PUNCT
ejpam-3479	259	13	.	.	PUNCT
ejpam-3479	260	1	(	(	PUNCT
ejpam-3479	260	2	45	45	NUM
ejpam-3479	260	3	)	)	PUNCT
ejpam-3479	260	4	then	then	ADV
ejpam-3479	260	5	follows	follow	VERB
ejpam-3479	260	6	from	from	ADP
ejpam-3479	260	7	(	(	PUNCT
ejpam-3479	260	8	28	28	NUM
ejpam-3479	260	9	)	)	PUNCT
ejpam-3479	260	10	−	−	PROPN
ejpam-3479	260	11	(	(	PUNCT
ejpam-3479	260	12	30	30	NUM
ejpam-3479	260	13	)	)	PUNCT
ejpam-3479	260	14	and	and	CCONJ
ejpam-3479	260	15	the	the	DET
ejpam-3479	260	16	definition	definition	NOUN
ejpam-3479	260	17	of	of	ADP
ejpam-3479	260	18	1	1	NUM
ejpam-3479	260	19	θ	θ	NOUN
ejpam-3479	260	20	given	give	VERB
ejpam-3479	260	21	by	by	ADP
ejpam-3479	260	22	(	(	PUNCT
ejpam-3479	260	23	31	31	NUM
ejpam-3479	260	24	)	)	PUNCT
ejpam-3479	260	25	that	that	SCONJ
ejpam-3479	260	26	(	(	PUNCT
ejpam-3479	260	27	ρj	ρj	NOUN
ejpam-3479	260	28	)	)	PUNCT
ejpam-3479	260	29	and	and	CCONJ
ejpam-3479	260	30	(	(	PUNCT
ejpam-3479	260	31	∆ρj	∆ρj	X
ejpam-3479	260	32	)	)	PUNCT
ejpam-3479	260	33	are	be	AUX
ejpam-3479	260	34	bounded	bound	VERB
ejpam-3479	260	35	in	in	ADP
ejpam-3479	260	36	l2(]β	l2(]β	PROPN
ejpam-3479	260	37	,	,	PUNCT
ejpam-3479	260	38	t	t	NOUN
ejpam-3479	261	1	−	−	PROPN
ejpam-3479	261	2	β[×]α	β[×]α	PROPN
ejpam-3479	261	3	,	,	PUNCT
ejpam-3479	261	4	a−	a−	PROPN
ejpam-3479	261	5	α[×ω	α[×ω	NUM
ejpam-3479	261	6	)	)	PUNCT
ejpam-3479	261	7	for	for	ADP
ejpam-3479	261	8	any	any	DET
ejpam-3479	261	9	β	β	NOUN
ejpam-3479	261	10	>	>	X
ejpam-3479	261	11	0	0	PUNCT
ejpam-3479	261	12	and	and	CCONJ
ejpam-3479	261	13	any	any	DET
ejpam-3479	261	14	α	α	NOUN
ejpam-3479	261	15	>	>	X
ejpam-3479	261	16	0	0	NUM
ejpam-3479	261	17	.	.	PUNCT
ejpam-3479	262	1	in	in	ADP
ejpam-3479	262	2	particular	particular	ADJ
ejpam-3479	262	3	,	,	PUNCT
ejpam-3479	262	4	for	for	ADP
ejpam-3479	262	5	all	all	DET
ejpam-3479	262	6	β	β	X
ejpam-3479	262	7	>	>	X
ejpam-3479	262	8	0	0	PUNCT
ejpam-3479	262	9	and	and	CCONJ
ejpam-3479	262	10	any	any	DET
ejpam-3479	262	11	α	α	NOUN
ejpam-3479	262	12	>	>	X
ejpam-3479	262	13	0	0	NUM
ejpam-3479	262	14	,	,	PUNCT
ejpam-3479	262	15	we	we	PRON
ejpam-3479	262	16	have	have	VERB
ejpam-3479	262	17	ρj	ρj	NOUN
ejpam-3479	262	18	⇀	⇀	NOUN
ejpam-3479	262	19	ρ	ρ	NUM
ejpam-3479	262	20	weakly	weakly	ADJ
ejpam-3479	262	21	in	in	ADP
ejpam-3479	262	22	l2(]β	l2(]β	PROPN
ejpam-3479	262	23	,	,	PUNCT
ejpam-3479	262	24	t	t	NOUN
ejpam-3479	263	1	−	−	PROPN
ejpam-3479	263	2	β[×]α	β[×]α	PROPN
ejpam-3479	263	3	,	,	PUNCT
ejpam-3479	263	4	a−	a−	PROPN
ejpam-3479	263	5	α[×ω	α[×ω	NUM
ejpam-3479	263	6	)	)	PUNCT
ejpam-3479	264	1	∂ρj	∂ρj	PROPN
ejpam-3479	264	2	∂ν	∂ν	PROPN
ejpam-3479	265	1	⇀	⇀	PROPN
ejpam-3479	265	2	∂ρ	∂ρ	PROPN
ejpam-3479	266	1	∂ν	∂ν	NOUN
ejpam-3479	266	2	weakly	weakly	ADV
ejpam-3479	266	3	in	in	ADP
ejpam-3479	266	4	l2(]β	l2(]β	PROPN
ejpam-3479	266	5	,	,	PUNCT
ejpam-3479	266	6	t	t	NOUN
ejpam-3479	267	1	−	−	PROPN
ejpam-3479	267	2	β[×]α	β[×]α	PROPN
ejpam-3479	267	3	,	,	PUNCT
ejpam-3479	267	4	a−	a−	PROPN
ejpam-3479	267	5	α[×σ	α[×σ	NOUN
ejpam-3479	267	6	)	)	PUNCT
ejpam-3479	267	7	.	.	PUNCT
ejpam-3479	268	1	which	which	PRON
ejpam-3479	268	2	implies	imply	VERB
ejpam-3479	268	3	that	that	SCONJ
ejpam-3479	268	4	m.soma	m.soma	ADV
ejpam-3479	268	5	,	,	PUNCT
ejpam-3479	268	6	s.	s.	PROPN
ejpam-3479	268	7	sawadogo	sawadogo	PROPN
ejpam-3479	268	8	/	/	SYM
ejpam-3479	268	9	eur	eur	PROPN
ejpam-3479	268	10	.	.	PUNCT
ejpam-3479	269	1	j.	j.	PROPN
ejpam-3479	269	2	pure	pure	PROPN
ejpam-3479	269	3	appl	appl	PROPN
ejpam-3479	269	4	.	.	PROPN
ejpam-3479	269	5	math	math	PROPN
ejpam-3479	269	6	,	,	PUNCT
ejpam-3479	269	7	12	12	NUM
ejpam-3479	269	8	(	(	PUNCT
ejpam-3479	269	9	3	3	NUM
ejpam-3479	269	10	)	)	PUNCT
ejpam-3479	269	11	(	(	PUNCT
ejpam-3479	269	12	2019	2019	NUM
ejpam-3479	269	13	)	)	PUNCT
ejpam-3479	269	14	,	,	PUNCT
ejpam-3479	269	15	1277	1277	NUM
ejpam-3479	269	16	-	-	SYM
ejpam-3479	269	17	1296	1296	NUM
ejpam-3479	269	18	1289	1289	NUM
ejpam-3479	269	19	ρj	ρj	NOUN
ejpam-3479	269	20	⇀	⇀	NUM
ejpam-3479	269	21	ρ	ρ	NUM
ejpam-3479	269	22	weakly	weakly	ADJ
ejpam-3479	269	23	in	in	ADP
ejpam-3479	269	24	d′(q	d′(q	NOUN
ejpam-3479	269	25	)	)	PUNCT
ejpam-3479	269	26	∂ρj	∂ρj	NOUN
ejpam-3479	269	27	∂ν	∂ν	PROPN
ejpam-3479	270	1	⇀	⇀	PROPN
ejpam-3479	270	2	∂ρ	∂ρ	PROPN
ejpam-3479	271	1	∂ν	∂ν	NOUN
ejpam-3479	271	2	weakly	weakly	ADV
ejpam-3479	271	3	in	in	ADP
ejpam-3479	271	4	d′(σ	d′(σ	PROPN
ejpam-3479	271	5	)	)	PUNCT
ejpam-3479	271	6	.	.	PUNCT
ejpam-3479	272	1	therefore	therefore	ADV
ejpam-3479	272	2	,	,	PUNCT
ejpam-3479	272	3	we	we	PRON
ejpam-3479	272	4	get	get	VERB
ejpam-3479	272	5	from	from	ADP
ejpam-3479	272	6	(	(	PUNCT
ejpam-3479	272	7	38	38	NUM
ejpam-3479	272	8	)	)	PUNCT
ejpam-3479	272	9	and	and	CCONJ
ejpam-3479	272	10	(	(	PUNCT
ejpam-3479	272	11	43	43	NUM
ejpam-3479	272	12	)	)	PUNCT
ejpam-3479	272	13	that	that	PRON
ejpam-3479	272	14	lρj	lρj	VERB
ejpam-3479	272	15	−→	−→	ADV
ejpam-3479	272	16	lρ	lρ	ADP
ejpam-3479	272	17	=	=	SYM
ejpam-3479	272	18	0	0	PUNCT
ejpam-3479	272	19	strongly	strongly	ADV
ejpam-3479	272	20	in	in	ADP
ejpam-3479	272	21	l2(u	l2(u	PROPN
ejpam-3479	272	22	×	×	PROPN
ejpam-3479	272	23	ω	ω	PROPN
ejpam-3479	272	24	)	)	PUNCT
ejpam-3479	272	25	,	,	PUNCT
ejpam-3479	272	26	(	(	PUNCT
ejpam-3479	272	27	46	46	X
ejpam-3479	272	28	)	)	PUNCT
ejpam-3479	272	29	∂ρj	∂ρj	PROPN
ejpam-3479	272	30	∂ν	∂ν	PROPN
ejpam-3479	273	1	⇀	⇀	PROPN
ejpam-3479	273	2	∂ρ	∂ρ	PROPN
ejpam-3479	273	3	∂ν	∂ν	PRON
ejpam-3479	274	1	strongly	strongly	ADV
ejpam-3479	274	2	in	in	ADP
ejpam-3479	274	3	l2(u	l2(u	PROPN
ejpam-3479	274	4	×	×	PROPN
ejpam-3479	274	5	γ	γ	NOUN
ejpam-3479	274	6	)	)	PUNCT
ejpam-3479	274	7	.	.	PUNCT
ejpam-3479	275	1	(	(	PUNCT
ejpam-3479	275	2	47	47	NUM
ejpam-3479	275	3	)	)	PUNCT
ejpam-3479	275	4	and	and	CCONJ
ejpam-3479	275	5	,	,	PUNCT
ejpam-3479	275	6	since	since	SCONJ
ejpam-3479	275	7	p	p	NOUN
ejpam-3479	275	8	is	be	AUX
ejpam-3479	275	9	a	a	DET
ejpam-3479	275	10	compact	compact	ADJ
ejpam-3479	275	11	operator	operator	NOUN
ejpam-3479	275	12	,	,	PUNCT
ejpam-3479	275	13	we	we	PRON
ejpam-3479	275	14	deduce	deduce	VERB
ejpam-3479	275	15	from	from	ADP
ejpam-3479	275	16	(	(	PUNCT
ejpam-3479	275	17	47	47	NUM
ejpam-3479	275	18	)	)	PUNCT
ejpam-3479	276	1	that	that	SCONJ
ejpam-3479	276	2	p	p	PROPN
ejpam-3479	276	3	∂ρj	∂ρj	PROPN
ejpam-3479	276	4	∂ν	∂ν	PROPN
ejpam-3479	276	5	−→	−→	NOUN
ejpam-3479	276	6	p	p	PROPN
ejpam-3479	276	7	∂ρ	∂ρ	PROPN
ejpam-3479	276	8	∂ν	∂ν	PRON
ejpam-3479	276	9	strongly	strongly	ADV
ejpam-3479	276	10	in	in	ADP
ejpam-3479	276	11	l2(u	l2(u	PROPN
ejpam-3479	276	12	×	×	PROPN
ejpam-3479	276	13	γ	γ	PROPN
ejpam-3479	276	14	)	)	PUNCT
ejpam-3479	276	15	.	.	PUNCT
ejpam-3479	277	1	(	(	PUNCT
ejpam-3479	277	2	48	48	NUM
ejpam-3479	277	3	)	)	PUNCT
ejpam-3479	277	4	in	in	ADP
ejpam-3479	277	5	view	view	NOUN
ejpam-3479	277	6	of	of	ADP
ejpam-3479	277	7	(	(	PUNCT
ejpam-3479	277	8	39	39	NUM
ejpam-3479	277	9	)	)	PUNCT
ejpam-3479	277	10	,	,	PUNCT
ejpam-3479	277	11	we	we	PRON
ejpam-3479	277	12	also	also	ADV
ejpam-3479	277	13	have	have	VERB
ejpam-3479	277	14	∂ρj	∂ρj	PROPN
ejpam-3479	277	15	∂ν	∂ν	PROPN
ejpam-3479	278	1	−	−	PROPN
ejpam-3479	279	1	p	p	PROPN
ejpam-3479	279	2	∂ρj	∂ρj	PROPN
ejpam-3479	279	3	∂ν	∂ν	PROPN
ejpam-3479	279	4	−→	−→	NOUN
ejpam-3479	279	5	0	0	NUM
ejpam-3479	279	6	strongly	strongly	ADV
ejpam-3479	279	7	in	in	ADP
ejpam-3479	279	8	l2(u	l2(u	PROPN
ejpam-3479	279	9	×	×	PROPN
ejpam-3479	279	10	γ	γ	NOUN
ejpam-3479	279	11	)	)	PUNCT
ejpam-3479	279	12	.	.	PUNCT
ejpam-3479	280	1	(	(	PUNCT
ejpam-3479	280	2	49	49	NUM
ejpam-3479	280	3	)	)	PUNCT
ejpam-3479	280	4	thus	thus	ADV
ejpam-3479	280	5	combining	combine	VERB
ejpam-3479	280	6	(	(	PUNCT
ejpam-3479	280	7	48	48	NUM
ejpam-3479	280	8	)	)	PUNCT
ejpam-3479	280	9	and	and	CCONJ
ejpam-3479	280	10	(	(	PUNCT
ejpam-3479	280	11	49	49	NUM
ejpam-3479	280	12	)	)	PUNCT
ejpam-3479	280	13	,	,	PUNCT
ejpam-3479	280	14	we	we	PRON
ejpam-3479	280	15	get	get	VERB
ejpam-3479	280	16	p	p	PROPN
ejpam-3479	280	17	∂ρj	∂ρj	PROPN
ejpam-3479	280	18	∂ν	∂ν	PROPN
ejpam-3479	281	1	−→	−→	PROPN
ejpam-3479	282	1	∂ρj	∂ρj	PROPN
ejpam-3479	282	2	∂ν	∂ν	PROPN
ejpam-3479	282	3	strongly	strongly	ADV
ejpam-3479	282	4	in	in	ADP
ejpam-3479	282	5	l2(u	l2(u	PROPN
ejpam-3479	282	6	×	×	PROPN
ejpam-3479	282	7	γ	γ	PROPN
ejpam-3479	282	8	)	)	PUNCT
ejpam-3479	282	9	.	.	PUNCT
ejpam-3479	283	1	(	(	PUNCT
ejpam-3479	283	2	50	50	NUM
ejpam-3479	283	3	)	)	PUNCT
ejpam-3479	283	4	thanks	thank	NOUN
ejpam-3479	283	5	to	to	ADP
ejpam-3479	283	6	the	the	DET
ejpam-3479	283	7	uniqueness	uniqueness	NOUN
ejpam-3479	283	8	of	of	ADP
ejpam-3479	283	9	the	the	DET
ejpam-3479	283	10	limit	limit	NOUN
ejpam-3479	283	11	in	in	ADP
ejpam-3479	283	12	l2(u	l2(u	PROPN
ejpam-3479	283	13	×	×	PROPN
ejpam-3479	283	14	γ	γ	PROPN
ejpam-3479	283	15	)	)	PUNCT
ejpam-3479	283	16	,	,	PUNCT
ejpam-3479	283	17	the	the	DET
ejpam-3479	283	18	convergence	convergence	NOUN
ejpam-3479	283	19	relations	relation	NOUN
ejpam-3479	283	20	(	(	PUNCT
ejpam-3479	283	21	48)-(49	48)-(49	NOUN
ejpam-3479	283	22	)	)	PUNCT
ejpam-3479	283	23	and	and	CCONJ
ejpam-3479	283	24	(	(	PUNCT
ejpam-3479	283	25	50	50	NUM
ejpam-3479	283	26	)	)	PUNCT
ejpam-3479	283	27	imply	imply	VERB
ejpam-3479	283	28	that	that	SCONJ
ejpam-3479	283	29	p	p	PRON
ejpam-3479	283	30	∂ρ	∂ρ	PROPN
ejpam-3479	283	31	∂ν	∂ν	X
ejpam-3479	283	32	=	=	PUNCT
ejpam-3479	283	33	∂ρ	∂ρ	PROPN
ejpam-3479	283	34	∂νχγ	∂νχγ	VERB
ejpam-3479	283	35	.	.	PUNCT
ejpam-3479	284	1	this	this	PRON
ejpam-3479	284	2	means	mean	VERB
ejpam-3479	284	3	that	that	SCONJ
ejpam-3479	284	4	∂ρ	∂ρ	PROPN
ejpam-3479	284	5	∂νχγ	∂νχγ	VERB
ejpam-3479	284	6	∈	∈	PROPN
ejpam-3479	284	7	y	y	NOUN
ejpam-3479	284	8	.	.	PUNCT
ejpam-3479	285	1	we	we	PRON
ejpam-3479	285	2	thus	thus	ADV
ejpam-3479	285	3	have	have	AUX
ejpam-3479	285	4	proved	prove	VERB
ejpam-3479	285	5	that	that	SCONJ
ejpam-3479	285	6	ρ	ρ	PROPN
ejpam-3479	285	7	verifies	verifie	NOUN
ejpam-3479	285	8	(	(	PUNCT
ejpam-3479	285	9	35	35	NUM
ejpam-3479	285	10	)	)	PUNCT
ejpam-3479	285	11	.	.	PUNCT
ejpam-3479	286	1	hence	hence	ADV
ejpam-3479	286	2	thanks	thank	NOUN
ejpam-3479	286	3	to	to	ADP
ejpam-3479	286	4	lemma	lemma	PROPN
ejpam-3479	286	5	2	2	NUM
ejpam-3479	286	6	,	,	PUNCT
ejpam-3479	286	7	ρ	ρ	PROPN
ejpam-3479	286	8	is	be	AUX
ejpam-3479	286	9	identically	identically	ADV
ejpam-3479	286	10	zero	zero	NUM
ejpam-3479	286	11	.	.	PUNCT
ejpam-3479	287	1	therefore	therefore	ADV
ejpam-3479	287	2	,	,	PUNCT
ejpam-3479	287	3	(	(	PUNCT
ejpam-3479	287	4	50	50	NUM
ejpam-3479	287	5	)	)	PUNCT
ejpam-3479	287	6	becomes	become	VERB
ejpam-3479	287	7	∂ρj	∂ρj	PROPN
ejpam-3479	287	8	∂ν	∂ν	PROPN
ejpam-3479	287	9	−→	−→	NOUN
ejpam-3479	287	10	0	0	NUM
ejpam-3479	287	11	strongly	strongly	ADV
ejpam-3479	287	12	in	in	ADP
ejpam-3479	287	13	l2(u	l2(u	PROPN
ejpam-3479	287	14	×	×	PROPN
ejpam-3479	287	15	γ	γ	PROPN
ejpam-3479	287	16	)	)	PUNCT
ejpam-3479	287	17	.	.	PUNCT
ejpam-3479	288	1	(	(	PUNCT
ejpam-3479	288	2	51	51	NUM
ejpam-3479	288	3	)	)	PUNCT
ejpam-3479	288	4	step	step	NOUN
ejpam-3479	288	5	3	3	NUM
ejpam-3479	288	6	.	.	PUNCT
ejpam-3479	289	1	since	since	SCONJ
ejpam-3479	289	2	ρj	ρj	PROPN
ejpam-3479	289	3	∈	∈	PROPN
ejpam-3479	289	4	ν	ν	NOUN
ejpam-3479	289	5	,	,	PUNCT
ejpam-3479	289	6	it	it	PRON
ejpam-3479	289	7	follows	follow	VERB
ejpam-3479	289	8	from	from	ADP
ejpam-3479	289	9	the	the	DET
ejpam-3479	289	10	observability	observability	NOUN
ejpam-3479	289	11	inequality	inequality	NOUN
ejpam-3479	289	12	(	(	PUNCT
ejpam-3479	289	13	34	34	NUM
ejpam-3479	289	14	)	)	PUNCT
ejpam-3479	289	15	that∫	that∫	NOUN
ejpam-3479	289	16	u	u	NOUN
ejpam-3479	289	17	∫	∫	PROPN
ejpam-3479	289	18	ω	ω	PROPN
ejpam-3479	289	19	1	1	NUM
ejpam-3479	289	20	θ2	θ2	ADP
ejpam-3479	289	21	|∂ρj	|∂ρj	X
ejpam-3479	290	1	∂ν	∂ν	PROPN
ejpam-3479	290	2	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	290	3	≤	≤	PROPN
ejpam-3479	290	4	c1	c1	PROPN
ejpam-3479	290	5	[	[	X
ejpam-3479	290	6	∫	∫	X
ejpam-3479	290	7	q	q	PROPN
ejpam-3479	290	8	|lρj	|lρj	NOUN
ejpam-3479	290	9	|2	|2	NUM
ejpam-3479	291	1	dtdadx+	dtdadx+	CCONJ
ejpam-3479	291	2	∫	∫	X
ejpam-3479	291	3	u	u	NOUN
ejpam-3479	291	4	∫	∫	PROPN
ejpam-3479	291	5	γ	γ	X
ejpam-3479	291	6	|∂ρj	|∂ρj	X
ejpam-3479	291	7	∂ν	∂ν	PROPN
ejpam-3479	291	8	|2dtdadγ	|2dtdadγ	PROPN
ejpam-3479	291	9	]	]	PUNCT
ejpam-3479	291	10	.	.	PUNCT
ejpam-3479	292	1	therefore	therefore	ADV
ejpam-3479	292	2	passing	pass	VERB
ejpam-3479	292	3	this	this	DET
ejpam-3479	292	4	latter	latter	ADJ
ejpam-3479	292	5	inequality	inequality	NOUN
ejpam-3479	292	6	to	to	ADP
ejpam-3479	292	7	the	the	DET
ejpam-3479	292	8	limit	limit	NOUN
ejpam-3479	292	9	while	while	SCONJ
ejpam-3479	292	10	using	use	VERB
ejpam-3479	292	11	(	(	PUNCT
ejpam-3479	292	12	46	46	NUM
ejpam-3479	292	13	)	)	PUNCT
ejpam-3479	292	14	and	and	CCONJ
ejpam-3479	292	15	(	(	PUNCT
ejpam-3479	292	16	51	51	NUM
ejpam-3479	292	17	)	)	PUNCT
ejpam-3479	292	18	,	,	PUNCT
ejpam-3479	292	19	we	we	PRON
ejpam-3479	292	20	obtain	obtain	VERB
ejpam-3479	292	21	lim	lim	PROPN
ejpam-3479	292	22	j−→∞	j−→∞	PROPN
ejpam-3479	292	23	∫	∫	PROPN
ejpam-3479	293	1	u	u	PROPN
ejpam-3479	293	2	∫	∫	PROPN
ejpam-3479	293	3	ω	ω	X
ejpam-3479	293	4	|∂ρj	|∂ρj	X
ejpam-3479	294	1	∂ν	∂ν	ADP
ejpam-3479	294	2	|2dtdadx	|2dtdadx	PROPN
ejpam-3479	294	3	=	=	SYM
ejpam-3479	294	4	0	0	NUM
ejpam-3479	294	5	.	.	PUNCT
ejpam-3479	295	1	the	the	DET
ejpam-3479	295	2	contradiction	contradiction	NOUN
ejpam-3479	295	3	occurs	occur	VERB
ejpam-3479	295	4	with	with	ADP
ejpam-3479	295	5	(	(	PUNCT
ejpam-3479	295	6	40	40	NUM
ejpam-3479	295	7	)	)	PUNCT
ejpam-3479	295	8	.	.	PUNCT
ejpam-3479	296	1	m.soma	m.soma	ADV
ejpam-3479	296	2	,	,	PUNCT
ejpam-3479	296	3	s.	s.	PROPN
ejpam-3479	296	4	sawadogo	sawadogo	PROPN
ejpam-3479	296	5	/	/	SYM
ejpam-3479	296	6	eur	eur	PROPN
ejpam-3479	296	7	.	.	PUNCT
ejpam-3479	297	1	j.	j.	PROPN
ejpam-3479	297	2	pure	pure	PROPN
ejpam-3479	297	3	appl	appl	PROPN
ejpam-3479	297	4	.	.	PROPN
ejpam-3479	297	5	math	math	PROPN
ejpam-3479	297	6	,	,	PUNCT
ejpam-3479	297	7	12	12	NUM
ejpam-3479	297	8	(	(	PUNCT
ejpam-3479	297	9	3	3	NUM
ejpam-3479	297	10	)	)	PUNCT
ejpam-3479	297	11	(	(	PUNCT
ejpam-3479	297	12	2019	2019	NUM
ejpam-3479	297	13	)	)	PUNCT
ejpam-3479	297	14	,	,	PUNCT
ejpam-3479	297	15	1277	1277	NUM
ejpam-3479	297	16	-	-	SYM
ejpam-3479	297	17	1296	1296	NUM
ejpam-3479	297	18	1290	1290	NUM
ejpam-3479	297	19	3.2	3.2	NUM
ejpam-3479	297	20	.	.	PUNCT
ejpam-3479	298	1	proof	proof	NOUN
ejpam-3479	298	2	of	of	ADP
ejpam-3479	298	3	theorem	theorem	NOUN
ejpam-3479	298	4	2	2	NUM
ejpam-3479	298	5	in	in	ADP
ejpam-3479	298	6	this	this	DET
ejpam-3479	298	7	subsection	subsection	NOUN
ejpam-3479	298	8	,	,	PUNCT
ejpam-3479	298	9	we	we	PRON
ejpam-3479	298	10	are	be	AUX
ejpam-3479	298	11	concerned	concerned	ADJ
ejpam-3479	298	12	with	with	ADP
ejpam-3479	298	13	the	the	DET
ejpam-3479	298	14	proof	proof	NOUN
ejpam-3479	298	15	of	of	ADP
ejpam-3479	298	16	theorem	theorem	NOUN
ejpam-3479	298	17	2	2	NUM
ejpam-3479	298	18	.	.	X
ejpam-3479	299	1	that	that	PRON
ejpam-3479	299	2	is	is	ADV
ejpam-3479	299	3	,	,	PUNCT
ejpam-3479	299	4	the	the	DET
ejpam-3479	299	5	optimality	optimality	NOUN
ejpam-3479	299	6	system	system	NOUN
ejpam-3479	299	7	for	for	ADP
ejpam-3479	299	8	the	the	DET
ejpam-3479	299	9	control	control	NOUN
ejpam-3479	299	10	v̂	v̂	NOUN
ejpam-3479	299	11	such	such	ADJ
ejpam-3479	299	12	that	that	SCONJ
ejpam-3479	299	13	the	the	DET
ejpam-3479	299	14	pair	pair	NOUN
ejpam-3479	299	15	(	(	PUNCT
ejpam-3479	299	16	v̂	v̂	NOUN
ejpam-3479	299	17	;	;	PUNCT
ejpam-3479	299	18	q̂	q̂	NUM
ejpam-3479	299	19	)	)	PUNCT
ejpam-3479	299	20	verifies	verifie	NOUN
ejpam-3479	299	21	(	(	PUNCT
ejpam-3479	299	22	14)−	14)−	NUM
ejpam-3479	299	23	(	(	PUNCT
ejpam-3479	299	24	16	16	NUM
ejpam-3479	299	25	)	)	PUNCT
ejpam-3479	299	26	.	.	PUNCT
ejpam-3479	300	1	since	since	SCONJ
ejpam-3479	300	2	a	a	DET
ejpam-3479	300	3	classical	classical	ADJ
ejpam-3479	300	4	way	way	NOUN
ejpam-3479	300	5	to	to	PART
ejpam-3479	300	6	derive	derive	VERB
ejpam-3479	300	7	this	this	DET
ejpam-3479	300	8	optimality	optimality	NOUN
ejpam-3479	300	9	system	system	NOUN
ejpam-3479	300	10	is	be	AUX
ejpam-3479	300	11	the	the	DET
ejpam-3479	300	12	method	method	NOUN
ejpam-3479	300	13	of	of	ADP
ejpam-3479	300	14	penalization	penalization	NOUN
ejpam-3479	300	15	due	due	ADP
ejpam-3479	300	16	to	to	ADP
ejpam-3479	300	17	j.l.lions	j.l.lion	NOUN
ejpam-3479	300	18	[	[	X
ejpam-3479	300	19	11	11	NUM
ejpam-3479	300	20	]	]	PUNCT
ejpam-3479	300	21	,	,	PUNCT
ejpam-3479	300	22	here	here	ADV
ejpam-3479	300	23	we	we	PRON
ejpam-3479	300	24	use	use	VERB
ejpam-3479	300	25	this	this	DET
ejpam-3479	300	26	method	method	NOUN
ejpam-3479	300	27	.	.	PUNCT
ejpam-3479	301	1	step	step	NOUN
ejpam-3479	301	2	1	1	NUM
ejpam-3479	301	3	.	.	PUNCT
ejpam-3479	302	1	let	let	VERB
ejpam-3479	302	2	w0	w0	PROPN
ejpam-3479	302	3	be	be	AUX
ejpam-3479	302	4	defined	define	VERB
ejpam-3479	302	5	by	by	ADP
ejpam-3479	302	6	(	(	PUNCT
ejpam-3479	302	7	27	27	NUM
ejpam-3479	302	8	)	)	PUNCT
ejpam-3479	302	9	.	.	PUNCT
ejpam-3479	303	1	if	if	SCONJ
ejpam-3479	303	2	v	v	NUM
ejpam-3479	303	3	∈	∈	X
ejpam-3479	303	4	y	y	PROPN
ejpam-3479	303	5	⊥	⊥	PROPN
ejpam-3479	303	6	and	and	CCONJ
ejpam-3479	303	7	q	q	NOUN
ejpam-3479	303	8	is	be	AUX
ejpam-3479	303	9	solution	solution	NOUN
ejpam-3479	303	10	of	of	ADP
ejpam-3479	303	11	(	(	PUNCT
ejpam-3479	303	12	15	15	NUM
ejpam-3479	303	13	)	)	PUNCT
ejpam-3479	303	14	then	then	ADV
ejpam-3479	303	15	q(0	q(0	PROPN
ejpam-3479	303	16	,	,	PUNCT
ejpam-3479	303	17	.	.	PUNCT
ejpam-3479	303	18	,	,	PUNCT
ejpam-3479	303	19	.	.	PUNCT
ejpam-3479	303	20	)	)	PUNCT
ejpam-3479	304	1	∈	∈	PROPN
ejpam-3479	304	2	l2(qa	l2(qa	PROPN
ejpam-3479	304	3	)	)	PUNCT
ejpam-3479	304	4	and	and	CCONJ
ejpam-3479	304	5	we	we	PRON
ejpam-3479	304	6	can	can	AUX
ejpam-3479	304	7	define	define	VERB
ejpam-3479	304	8	the	the	DET
ejpam-3479	304	9	functional	functional	ADJ
ejpam-3479	304	10	jε(v	jε(v	NOUN
ejpam-3479	304	11	)	)	PUNCT
ejpam-3479	304	12	=	=	SYM
ejpam-3479	304	13	1	1	NUM
ejpam-3479	304	14	2	2	NUM
ejpam-3479	304	15	‖w0	‖w0	NOUN
ejpam-3479	304	16	−	−	PROPN
ejpam-3479	304	17	v‖2l2(u×γ	v‖2l2(u×γ	NUM
ejpam-3479	304	18	)	)	PUNCT
ejpam-3479	305	1	+	+	CCONJ
ejpam-3479	305	2	1	1	NUM
ejpam-3479	305	3	2ε	2ε	NUM
ejpam-3479	305	4	‖q(0	‖q(0	PROPN
ejpam-3479	305	5	,	,	PUNCT
ejpam-3479	305	6	.	.	PUNCT
ejpam-3479	305	7	,	,	PUNCT
ejpam-3479	305	8	.)‖2l2(qa	.)‖2l2(qa	PROPN
ejpam-3479	305	9	)	)	PUNCT
ejpam-3479	305	10	.	.	PUNCT
ejpam-3479	306	1	(	(	PUNCT
ejpam-3479	306	2	52	52	NUM
ejpam-3479	306	3	)	)	PUNCT
ejpam-3479	306	4	we	we	PRON
ejpam-3479	306	5	consider	consider	VERB
ejpam-3479	306	6	the	the	DET
ejpam-3479	306	7	optimal	optimal	ADJ
ejpam-3479	306	8	control	control	NOUN
ejpam-3479	306	9	problem	problem	NOUN
ejpam-3479	306	10	:	:	PUNCT
ejpam-3479	306	11	find	find	VERB
ejpam-3479	306	12	vε	vε	ADP
ejpam-3479	306	13	∈	∈	PROPN
ejpam-3479	306	14	y	y	PROPN
ejpam-3479	306	15	⊥	⊥	NOUN
ejpam-3479	307	1	such	such	ADJ
ejpam-3479	307	2	that	that	SCONJ
ejpam-3479	307	3	jε(vε	jε(vε	PROPN
ejpam-3479	307	4	)	)	PUNCT
ejpam-3479	307	5	=	=	SYM
ejpam-3479	307	6	min	min	NOUN
ejpam-3479	307	7	v∈y	v∈y	NOUN
ejpam-3479	307	8	⊥	⊥	PROPN
ejpam-3479	307	9	jε(v	jε(v	NOUN
ejpam-3479	307	10	)	)	PUNCT
ejpam-3479	307	11	(	(	PUNCT
ejpam-3479	307	12	53	53	NUM
ejpam-3479	307	13	)	)	PUNCT
ejpam-3479	307	14	since	since	SCONJ
ejpam-3479	307	15	y	y	PROPN
ejpam-3479	307	16	⊥	⊥	PROPN
ejpam-3479	307	17	is	be	AUX
ejpam-3479	307	18	a	a	DET
ejpam-3479	307	19	closed	closed	ADJ
ejpam-3479	307	20	and	and	CCONJ
ejpam-3479	307	21	convex	convex	NOUN
ejpam-3479	307	22	subset	subset	NOUN
ejpam-3479	307	23	of	of	ADP
ejpam-3479	307	24	l2(u	l2(u	PROPN
ejpam-3479	307	25	×	×	PROPN
ejpam-3479	307	26	γ	γ	NOUN
ejpam-3479	307	27	)	)	PUNCT
ejpam-3479	307	28	,	,	PUNCT
ejpam-3479	307	29	it	it	PRON
ejpam-3479	307	30	is	be	AUX
ejpam-3479	307	31	classical	classical	ADJ
ejpam-3479	307	32	to	to	PART
ejpam-3479	307	33	prove	prove	VERB
ejpam-3479	307	34	that	that	SCONJ
ejpam-3479	307	35	there	there	PRON
ejpam-3479	307	36	exists	exist	VERB
ejpam-3479	307	37	a	a	DET
ejpam-3479	307	38	unique	unique	ADJ
ejpam-3479	307	39	solution	solution	NOUN
ejpam-3479	307	40	to	to	ADP
ejpam-3479	307	41	(	(	PUNCT
ejpam-3479	307	42	53	53	NUM
ejpam-3479	307	43	)	)	PUNCT
ejpam-3479	307	44	.	.	PUNCT
ejpam-3479	308	1	if	if	SCONJ
ejpam-3479	308	2	we	we	PRON
ejpam-3479	308	3	write	write	VERB
ejpam-3479	308	4	qε	qε	ADV
ejpam-3479	308	5	the	the	DET
ejpam-3479	308	6	solution	solution	NOUN
ejpam-3479	308	7	of	of	ADP
ejpam-3479	308	8	(	(	PUNCT
ejpam-3479	308	9	15	15	NUM
ejpam-3479	308	10	)	)	PUNCT
ejpam-3479	308	11	corresponding	correspond	VERB
ejpam-3479	308	12	to	to	PART
ejpam-3479	308	13	vε	vε	VERB
ejpam-3479	308	14	using	use	VERB
ejpam-3479	308	15	an	an	DET
ejpam-3479	308	16	adjoint	adjoint	NOUN
ejpam-3479	308	17	state	state	NOUN
ejpam-3479	308	18	ρε	ρε	PROPN
ejpam-3479	308	19	,	,	PUNCT
ejpam-3479	308	20	we	we	PRON
ejpam-3479	308	21	have	have	VERB
ejpam-3479	308	22	that	that	SCONJ
ejpam-3479	308	23	the	the	DET
ejpam-3479	308	24	triplet	triplet	NOUN
ejpam-3479	308	25	(	(	PUNCT
ejpam-3479	308	26	qε	qε	INTJ
ejpam-3479	308	27	,	,	PUNCT
ejpam-3479	308	28	ρε	ρε	PROPN
ejpam-3479	308	29	vε	vε	NOUN
ejpam-3479	308	30	)	)	PUNCT
ejpam-3479	308	31	is	be	AUX
ejpam-3479	308	32	solution	solution	NOUN
ejpam-3479	308	33	of	of	ADP
ejpam-3479	308	34	the	the	DET
ejpam-3479	308	35	first	first	ADJ
ejpam-3479	308	36	order	order	NOUN
ejpam-3479	308	37	optimality	optimality	NOUN
ejpam-3479	308	38	system:	system:	NOUN
ejpam-3479	308	39	l∗qε	l∗qε	ADJ
ejpam-3479	308	40	=	=	SYM
ejpam-3479	308	41	βqε(t	βqε(t	NOUN
ejpam-3479	308	42	,	,	PUNCT
ejpam-3479	308	43	0	0	NUM
ejpam-3479	308	44	,	,	PUNCT
ejpam-3479	308	45	x	x	NOUN
ejpam-3479	308	46	)	)	PUNCT
ejpam-3479	308	47	in	in	ADP
ejpam-3479	308	48	q	q	NOUN
ejpam-3479	308	49	,	,	PUNCT
ejpam-3479	308	50	qε(t	qε(t	NOUN
ejpam-3479	308	51	,	,	PUNCT
ejpam-3479	308	52	a	a	DET
ejpam-3479	308	53	,	,	PUNCT
ejpam-3479	308	54	x	x	NOUN
ejpam-3479	308	55	)	)	PUNCT
ejpam-3479	309	1	=	=	SYM
ejpam-3479	309	2	0	0	NUM
ejpam-3479	310	1	in	in	ADP
ejpam-3479	310	2	qa	qa	PROPN
ejpam-3479	310	3	,	,	PUNCT
ejpam-3479	310	4	qε(t	qε(t	NOUN
ejpam-3479	310	5	,	,	PUNCT
ejpam-3479	310	6	a	a	DET
ejpam-3479	310	7	,	,	PUNCT
ejpam-3479	310	8	x	x	NOUN
ejpam-3479	310	9	)	)	PUNCT
ejpam-3479	310	10	=	=	SYM
ejpam-3479	310	11	0	0	NUM
ejpam-3479	310	12	in	in	ADP
ejpam-3479	310	13	qt	qt	NOUN
ejpam-3479	310	14	,	,	PUNCT
ejpam-3479	310	15	qε	qε	ADV
ejpam-3479	310	16	=	=	PUNCT
ejpam-3479	310	17	h0χo	h0χo	X
ejpam-3479	310	18	+	+	CCONJ
ejpam-3479	310	19	(	(	PUNCT
ejpam-3479	310	20	w0	w0	PROPN
ejpam-3479	310	21	−	−	PROPN
ejpam-3479	310	22	vε)χγ	vε)χγ	X
ejpam-3479	310	23	on	on	ADP
ejpam-3479	310	24	σ	σ	PROPN
ejpam-3479	310	25	,	,	PUNCT
ejpam-3479	310	26	(	(	PUNCT
ejpam-3479	310	27	54	54	NUM
ejpam-3479	310	28	)	)	PUNCT
ejpam-3479	310	29			NUM
ejpam-3479	310	30	lρε	lρε	NOUN
ejpam-3479	311	1	=	=	NOUN
ejpam-3479	311	2	0	0	NUM
ejpam-3479	311	3	in	in	ADP
ejpam-3479	311	4	q	q	PROPN
ejpam-3479	311	5	,	,	PUNCT
ejpam-3479	311	6	ρε(0	ρε(0	PROPN
ejpam-3479	311	7	,	,	PUNCT
ejpam-3479	311	8	a	a	PRON
ejpam-3479	311	9	,	,	PUNCT
ejpam-3479	311	10	x	x	NOUN
ejpam-3479	311	11	)	)	PUNCT
ejpam-3479	311	12	=	=	SYM
ejpam-3479	311	13	1	1	NUM
ejpam-3479	311	14	ε	ε	PROPN
ejpam-3479	311	15	qε(0	qε(0	PROPN
ejpam-3479	311	16	,	,	PUNCT
ejpam-3479	311	17	a	a	PRON
ejpam-3479	311	18	,	,	PUNCT
ejpam-3479	311	19	x	x	NOUN
ejpam-3479	311	20	)	)	PUNCT
ejpam-3479	311	21	in	in	ADP
ejpam-3479	311	22	qa	qa	PROPN
ejpam-3479	311	23	,	,	PUNCT
ejpam-3479	311	24	ρε(t	ρε(t	PROPN
ejpam-3479	311	25	,	,	PUNCT
ejpam-3479	311	26	0	0	NUM
ejpam-3479	311	27	,	,	PUNCT
ejpam-3479	311	28	x	x	NOUN
ejpam-3479	311	29	)	)	PUNCT
ejpam-3479	311	30	=	=	SYM
ejpam-3479	312	1	∫	∫	PROPN
ejpam-3479	312	2	a	a	DET
ejpam-3479	312	3	0	0	NUM
ejpam-3479	312	4	β(t	β(t	PROPN
ejpam-3479	312	5	,	,	PUNCT
ejpam-3479	312	6	a	a	PRON
ejpam-3479	312	7	,	,	PUNCT
ejpam-3479	312	8	x)ρε(t	x)ρε(t	PROPN
ejpam-3479	312	9	,	,	PUNCT
ejpam-3479	312	10	a	a	PRON
ejpam-3479	312	11	,	,	PUNCT
ejpam-3479	312	12	x)da	x)da	PROPN
ejpam-3479	312	13	in	in	ADP
ejpam-3479	312	14	qt	qt	NOUN
ejpam-3479	312	15	,	,	PUNCT
ejpam-3479	312	16	ρε	ρε	PROPN
ejpam-3479	312	17	=	=	NOUN
ejpam-3479	312	18	0	0	NUM
ejpam-3479	312	19	on	on	ADP
ejpam-3479	312	20	σ	σ	PROPN
ejpam-3479	312	21	,	,	PUNCT
ejpam-3479	312	22	(	(	PUNCT
ejpam-3479	312	23	55	55	NUM
ejpam-3479	312	24	)	)	PUNCT
ejpam-3479	312	25	vε	vε	NOUN
ejpam-3479	312	26	=	=	PUNCT
ejpam-3479	312	27	(	(	PUNCT
ejpam-3479	312	28	w0χγ	w0χγ	PROPN
ejpam-3479	312	29	−	−	PROPN
ejpam-3479	312	30	∂ρε	∂ρε	PROPN
ejpam-3479	312	31	∂ν	∂ν	PRON
ejpam-3479	312	32	χγ)−	χγ)−	VERB
ejpam-3479	312	33	p	p	X
ejpam-3479	312	34	(	(	PUNCT
ejpam-3479	312	35	w0χγ	w0χγ	PROPN
ejpam-3479	312	36	−	−	PROPN
ejpam-3479	312	37	∂ρε	∂ρε	PROPN
ejpam-3479	312	38	∂ν	∂ν	PRON
ejpam-3479	312	39	χγ	χγ	PROPN
ejpam-3479	312	40	)	)	PUNCT
ejpam-3479	312	41	∈	∈	PROPN
ejpam-3479	312	42	y	y	PROPN
ejpam-3479	312	43	⊥.	⊥.	PROPN
ejpam-3479	312	44	(	(	PUNCT
ejpam-3479	312	45	56	56	NUM
ejpam-3479	312	46	)	)	PUNCT
ejpam-3479	312	47	step	step	NOUN
ejpam-3479	312	48	2	2	NUM
ejpam-3479	312	49	.	.	PUNCT
ejpam-3479	312	50	multiplying	multiply	VERB
ejpam-3479	312	51	the	the	DET
ejpam-3479	312	52	state	state	NOUN
ejpam-3479	312	53	equation	equation	NOUN
ejpam-3479	312	54	(	(	PUNCT
ejpam-3479	312	55	54	54	NUM
ejpam-3479	312	56	)	)	PUNCT
ejpam-3479	312	57	by	by	ADP
ejpam-3479	312	58	ρε	ρε	NOUN
ejpam-3479	312	59	and	and	CCONJ
ejpam-3479	312	60	integrating	integrate	VERB
ejpam-3479	312	61	by	by	ADP
ejpam-3479	312	62	parts	part	NOUN
ejpam-3479	312	63	over	over	ADP
ejpam-3479	312	64	q	q	NOUN
ejpam-3479	312	65	,	,	PUNCT
ejpam-3479	312	66	we	we	PRON
ejpam-3479	312	67	get	get	VERB
ejpam-3479	312	68	1	1	NUM
ejpam-3479	312	69	ε	ε	PROPN
ejpam-3479	312	70	‖qε(0	‖qε(0	NOUN
ejpam-3479	312	71	,	,	PUNCT
ejpam-3479	312	72	.	.	PUNCT
ejpam-3479	312	73	,	,	PUNCT
ejpam-3479	312	74	.)‖2l2(qa	.)‖2l2(qa	PROPN
ejpam-3479	312	75	)	)	PUNCT
ejpam-3479	313	1	=	=	SYM
ejpam-3479	313	2	∫	∫	PUNCT
ejpam-3479	314	1	u	u	NOUN
ejpam-3479	314	2	∫	∫	PROPN
ejpam-3479	314	3	o	o	PROPN
ejpam-3479	314	4	h0	h0	PROPN
ejpam-3479	314	5	∂ρε	∂ρε	PROPN
ejpam-3479	314	6	∂ν	∂ν	PRON
ejpam-3479	314	7	dtdγ	dtdγ	PROPN
ejpam-3479	315	1	+	+	NUM
ejpam-3479	315	2	∫	∫	PROPN
ejpam-3479	315	3	u	u	X
ejpam-3479	315	4	∫	∫	PROPN
ejpam-3479	315	5	γ	γ	X
ejpam-3479	315	6	(	(	PUNCT
ejpam-3479	315	7	w0	w0	PROPN
ejpam-3479	315	8	−	−	PROPN
ejpam-3479	315	9	vε	vε	NOUN
ejpam-3479	315	10	)	)	PUNCT
ejpam-3479	315	11	∂ρε	∂ρε	PROPN
ejpam-3479	315	12	∂ν	∂ν	NOUN
ejpam-3479	315	13	dtdγ	dtdγ	PROPN
ejpam-3479	315	14	.	.	PUNCT
ejpam-3479	316	1	m.soma	m.soma	ADV
ejpam-3479	316	2	,	,	PUNCT
ejpam-3479	316	3	s.	s.	PROPN
ejpam-3479	316	4	sawadogo	sawadogo	PROPN
ejpam-3479	316	5	/	/	SYM
ejpam-3479	316	6	eur	eur	PROPN
ejpam-3479	316	7	.	.	PUNCT
ejpam-3479	317	1	j.	j.	PROPN
ejpam-3479	317	2	pure	pure	PROPN
ejpam-3479	317	3	appl	appl	PROPN
ejpam-3479	317	4	.	.	PROPN
ejpam-3479	317	5	math	math	PROPN
ejpam-3479	317	6	,	,	PUNCT
ejpam-3479	317	7	12	12	NUM
ejpam-3479	317	8	(	(	PUNCT
ejpam-3479	317	9	3	3	NUM
ejpam-3479	317	10	)	)	PUNCT
ejpam-3479	317	11	(	(	PUNCT
ejpam-3479	317	12	2019	2019	NUM
ejpam-3479	317	13	)	)	PUNCT
ejpam-3479	317	14	,	,	PUNCT
ejpam-3479	317	15	1277	1277	NUM
ejpam-3479	317	16	-	-	SYM
ejpam-3479	317	17	1296	1296	NUM
ejpam-3479	317	18	1291	1291	NUM
ejpam-3479	317	19	which	which	PRON
ejpam-3479	317	20	in	in	ADP
ejpam-3479	317	21	view	view	NOUN
ejpam-3479	317	22	of	of	ADP
ejpam-3479	317	23	(	(	PUNCT
ejpam-3479	317	24	56	56	NUM
ejpam-3479	317	25	)	)	PUNCT
ejpam-3479	317	26	and	and	CCONJ
ejpam-3479	317	27	the	the	DET
ejpam-3479	317	28	fact	fact	NOUN
ejpam-3479	317	29	that	that	SCONJ
ejpam-3479	317	30	vε	vε	VERB
ejpam-3479	317	31	∈	∈	PRON
ejpam-3479	317	32	y	y	PROPN
ejpam-3479	317	33	⊥	⊥	NOUN
ejpam-3479	317	34	give	give	VERB
ejpam-3479	317	35	1	1	NUM
ejpam-3479	317	36	ε	ε	PROPN
ejpam-3479	317	37	‖qε(0	‖qε(0	PROPN
ejpam-3479	317	38	,	,	PUNCT
ejpam-3479	317	39	.	.	PUNCT
ejpam-3479	317	40	,	,	PUNCT
ejpam-3479	317	41	.)‖2l2(qa	.)‖2l2(qa	PROPN
ejpam-3479	317	42	)	)	PUNCT
ejpam-3479	318	1	=	=	SYM
ejpam-3479	318	2	∫	∫	PUNCT
ejpam-3479	319	1	u	u	NOUN
ejpam-3479	319	2	∫	∫	PROPN
ejpam-3479	319	3	o	o	PROPN
ejpam-3479	319	4	h0	h0	PROPN
ejpam-3479	319	5	∂ρε	∂ρε	PROPN
ejpam-3479	319	6	∂ν	∂ν	PRON
ejpam-3479	319	7	dtdγ	dtdγ	PROPN
ejpam-3479	320	1	+	+	NUM
ejpam-3479	320	2	∫	∫	PROPN
ejpam-3479	320	3	u	u	X
ejpam-3479	320	4	∫	∫	PROPN
ejpam-3479	320	5	γ	γ	X
ejpam-3479	320	6	(	(	PUNCT
ejpam-3479	320	7	w0	w0	PROPN
ejpam-3479	320	8	−	−	PROPN
ejpam-3479	320	9	vε)(w0	vε)(w0	NOUN
ejpam-3479	320	10	−	−	PROPN
ejpam-3479	320	11	vε	vε	VERB
ejpam-3479	320	12	−	−	PROPN
ejpam-3479	320	13	p	p	NOUN
ejpam-3479	320	14	(	(	PUNCT
ejpam-3479	320	15	w0χγ	w0χγ	PROPN
ejpam-3479	320	16	−	−	PROPN
ejpam-3479	320	17	∂ρε	∂ρε	PROPN
ejpam-3479	320	18	∂ν	∂ν	PROPN
ejpam-3479	320	19	χγ))dtdγ	χγ))dtdγ	PROPN
ejpam-3479	320	20	.	.	PUNCT
ejpam-3479	321	1	=	=	PRON
ejpam-3479	321	2	∫	∫	PROPN
ejpam-3479	322	1	u	u	NOUN
ejpam-3479	322	2	∫	∫	PROPN
ejpam-3479	322	3	o	o	PROPN
ejpam-3479	322	4	h0	h0	PROPN
ejpam-3479	322	5	∂ρε	∂ρε	PROPN
ejpam-3479	322	6	∂ν	∂ν	NOUN
ejpam-3479	322	7	dtdγ	dtdγ	ADJ
ejpam-3479	322	8	−	−	PROPN
ejpam-3479	322	9	‖w0	‖w0	NOUN
ejpam-3479	322	10	−	−	NOUN
ejpam-3479	322	11	vε‖l2(u×γ	vε‖l2(u×γ	NOUN
ejpam-3479	322	12	)	)	PUNCT
ejpam-3479	323	1	+	+	CCONJ
ejpam-3479	323	2	‖pw0χγ‖l2(u×γ	‖pw0χγ‖l2(u×γ	PUNCT
ejpam-3479	323	3	)	)	PUNCT
ejpam-3479	324	1	+	+	NUM
ejpam-3479	324	2	∫	∫	PROPN
ejpam-3479	324	3	u	u	X
ejpam-3479	324	4	∫	∫	PROPN
ejpam-3479	324	5	γ	γ	PROPN
ejpam-3479	324	6	w0	w0	PROPN
ejpam-3479	324	7	∂ρε	∂ρε	PROPN
ejpam-3479	324	8	∂ν	∂ν	PROPN
ejpam-3479	324	9	dtdγ	dtdγ	NOUN
ejpam-3479	324	10	.	.	PUNCT
ejpam-3479	325	1	as	as	SCONJ
ejpam-3479	325	2	on	on	ADP
ejpam-3479	325	3	u	u	PROPN
ejpam-3479	325	4	×	×	PROPN
ejpam-3479	325	5	γ	γ	PROPN
ejpam-3479	325	6	w0	w0	PROPN
ejpam-3479	325	7	−	−	PROPN
ejpam-3479	325	8	vε	vε	NOUN
ejpam-3479	325	9	=	=	PUNCT
ejpam-3479	325	10	pw0χγ	pw0χγ	NOUN
ejpam-3479	325	11	+	+	CCONJ
ejpam-3479	325	12	(	(	PUNCT
ejpam-3479	325	13	i	i	PRON
ejpam-3479	325	14	−	−	PROPN
ejpam-3479	325	15	p	p	NOUN
ejpam-3479	325	16	)	)	PUNCT
ejpam-3479	325	17	∂ρε	∂ρε	PROPN
ejpam-3479	325	18	∂ν	∂ν	NOUN
ejpam-3479	325	19	χγ	χγ	VERB
ejpam-3479	325	20	.	.	PUNCT
ejpam-3479	326	1	we	we	PRON
ejpam-3479	326	2	have	have	VERB
ejpam-3479	326	3	that	that	PRON
ejpam-3479	326	4	‖w0	‖w0	PRON
ejpam-3479	326	5	−	−	NOUN
ejpam-3479	326	6	vε‖l2(u×γ	vε‖l2(u×γ	NOUN
ejpam-3479	326	7	)	)	PUNCT
ejpam-3479	326	8	=	=	SYM
ejpam-3479	326	9	‖(i	‖(i	NOUN
ejpam-3479	326	10	−	−	PROPN
ejpam-3479	326	11	p	p	NOUN
ejpam-3479	326	12	)	)	PUNCT
ejpam-3479	326	13	∂ρε	∂ρε	PROPN
ejpam-3479	326	14	∂ν	∂ν	PROPN
ejpam-3479	326	15	χγ‖2l2(u×γ	χγ‖2l2(u×γ	ADV
ejpam-3479	326	16	)	)	PUNCT
ejpam-3479	327	1	+	+	CCONJ
ejpam-3479	327	2	‖pw0χγ‖2l2(u×γ	‖pw0χγ‖2l2(u×γ	X
ejpam-3479	327	3	)	)	PUNCT
ejpam-3479	327	4	so	so	SCONJ
ejpam-3479	327	5	that	that	SCONJ
ejpam-3479	327	6	1	1	NUM
ejpam-3479	327	7	ε	ε	PROPN
ejpam-3479	327	8	‖qε(0	‖qε(0	PROPN
ejpam-3479	327	9	,	,	PUNCT
ejpam-3479	327	10	.	.	PUNCT
ejpam-3479	327	11	,	,	PUNCT
ejpam-3479	327	12	.)‖2l2(qa	.)‖2l2(qa	PROPN
ejpam-3479	327	13	)	)	PUNCT
ejpam-3479	328	1	+	+	NUM
ejpam-3479	328	2	‖(i	‖(i	NOUN
ejpam-3479	328	3	−	−	NOUN
ejpam-3479	328	4	p	p	NOUN
ejpam-3479	328	5	)	)	PUNCT
ejpam-3479	328	6	∂ρε	∂ρε	PROPN
ejpam-3479	328	7	∂ν	∂ν	PROPN
ejpam-3479	328	8	χγ‖2l2(u×γ	χγ‖2l2(u×γ	ADV
ejpam-3479	328	9	)	)	PUNCT
ejpam-3479	329	1	=	=	SYM
ejpam-3479	329	2	∫	∫	PUNCT
ejpam-3479	330	1	u	u	NOUN
ejpam-3479	330	2	∫	∫	PROPN
ejpam-3479	330	3	o	o	PROPN
ejpam-3479	330	4	h0	h0	PROPN
ejpam-3479	330	5	∂ρε	∂ρε	PROPN
ejpam-3479	330	6	∂ν	∂ν	PRON
ejpam-3479	330	7	dtdγ	dtdγ	PROPN
ejpam-3479	331	1	+	+	NUM
ejpam-3479	331	2	∫	∫	PROPN
ejpam-3479	331	3	u	u	X
ejpam-3479	331	4	∫	∫	PROPN
ejpam-3479	331	5	γ	γ	PROPN
ejpam-3479	331	6	w0	w0	PROPN
ejpam-3479	331	7	∂ρε	∂ρε	PROPN
ejpam-3479	331	8	∂ν	∂ν	PROPN
ejpam-3479	331	9	dtdγ	dtdγ	NOUN
ejpam-3479	331	10	.	.	PUNCT
ejpam-3479	332	1	this	this	PRON
ejpam-3479	332	2	implies	imply	VERB
ejpam-3479	332	3	that	that	SCONJ
ejpam-3479	332	4	1	1	NUM
ejpam-3479	332	5	ε	ε	PROPN
ejpam-3479	332	6	‖qε(0	‖qε(0	PROPN
ejpam-3479	332	7	,	,	PUNCT
ejpam-3479	332	8	.	.	PUNCT
ejpam-3479	332	9	,	,	PUNCT
ejpam-3479	332	10	.)‖2l2(qa	.)‖2l2(qa	PROPN
ejpam-3479	332	11	)	)	PUNCT
ejpam-3479	333	1	+	+	NUM
ejpam-3479	333	2	‖(i	‖(i	NOUN
ejpam-3479	333	3	−	−	NOUN
ejpam-3479	333	4	p	p	NOUN
ejpam-3479	333	5	)	)	PUNCT
ejpam-3479	333	6	∂ρε	∂ρε	PROPN
ejpam-3479	333	7	∂ν	∂ν	PROPN
ejpam-3479	333	8	χγ‖2l2(u×γ	χγ‖2l2(u×γ	ADV
ejpam-3479	333	9	)	)	PUNCT
ejpam-3479	333	10	≤	≤	NUM
ejpam-3479	333	11	(	(	PUNCT
ejpam-3479	333	12	∫	∫	PROPN
ejpam-3479	333	13	u	u	X
ejpam-3479	333	14	∫	∫	PROPN
ejpam-3479	333	15	o	o	X
ejpam-3479	333	16	(	(	PUNCT
ejpam-3479	333	17	θh0)2dtdγ	θh0)2dtdγ	NOUN
ejpam-3479	333	18	)	)	PUNCT
ejpam-3479	333	19	1	1	NUM
ejpam-3479	333	20	2	2	NUM
ejpam-3479	333	21	(	(	PUNCT
ejpam-3479	333	22	∫	∫	PROPN
ejpam-3479	333	23	u	u	NOUN
ejpam-3479	333	24	∫	∫	PROPN
ejpam-3479	333	25	γ	γ	PROPN
ejpam-3479	333	26	1	1	NUM
ejpam-3479	333	27	θ2	θ2	PROPN
ejpam-3479	333	28	∂ρε	∂ρε	PROPN
ejpam-3479	333	29	∂ν	∂ν	VERB
ejpam-3479	333	30	2	2	NUM
ejpam-3479	333	31	dtdγ	dtdγ	ADJ
ejpam-3479	333	32	)	)	PUNCT
ejpam-3479	333	33	1	1	NUM
ejpam-3479	333	34	2	2	NUM
ejpam-3479	333	35	+	+	CCONJ
ejpam-3479	333	36	(	(	PUNCT
ejpam-3479	333	37	∫	∫	PROPN
ejpam-3479	333	38	u	u	NOUN
ejpam-3479	333	39	∫	∫	PROPN
ejpam-3479	333	40	o	o	X
ejpam-3479	333	41	(	(	PUNCT
ejpam-3479	333	42	θw0)2dtdγ	θw0)2dtdγ	PROPN
ejpam-3479	333	43	)	)	PUNCT
ejpam-3479	333	44	1	1	NUM
ejpam-3479	333	45	2	2	NUM
ejpam-3479	333	46	(	(	PUNCT
ejpam-3479	333	47	∫	∫	PROPN
ejpam-3479	333	48	u	u	NOUN
ejpam-3479	333	49	∫	∫	PROPN
ejpam-3479	333	50	γ	γ	PROPN
ejpam-3479	333	51	1	1	NUM
ejpam-3479	333	52	θ2	θ2	PROPN
ejpam-3479	333	53	∂ρε	∂ρε	PROPN
ejpam-3479	333	54	∂ν	∂ν	VERB
ejpam-3479	333	55	2	2	NUM
ejpam-3479	333	56	dtdγ	dtdγ	ADJ
ejpam-3479	333	57	)	)	PUNCT
ejpam-3479	333	58	1	1	NUM
ejpam-3479	333	59	2	2	NUM
ejpam-3479	333	60	.	.	PUNCT
ejpam-3479	334	1	(	(	PUNCT
ejpam-3479	334	2	57	57	NUM
ejpam-3479	334	3	)	)	PUNCT
ejpam-3479	334	4	if	if	SCONJ
ejpam-3479	334	5	we	we	PRON
ejpam-3479	334	6	apply	apply	VERB
ejpam-3479	334	7	the	the	DET
ejpam-3479	334	8	adapted	adapted	ADJ
ejpam-3479	334	9	carleman	carleman	ADJ
ejpam-3479	334	10	inequality	inequality	NOUN
ejpam-3479	334	11	(	(	PUNCT
ejpam-3479	334	12	37	37	NUM
ejpam-3479	334	13	)	)	PUNCT
ejpam-3479	334	14	to	to	ADP
ejpam-3479	334	15	ρε	ρε	NOUN
ejpam-3479	334	16	we	we	PRON
ejpam-3479	334	17	obtain∫	obtain∫	VERB
ejpam-3479	334	18	u	u	NOUN
ejpam-3479	334	19	∫	∫	PROPN
ejpam-3479	334	20	γ	γ	PROPN
ejpam-3479	334	21	1	1	NUM
ejpam-3479	334	22	θ2	θ2	PROPN
ejpam-3479	334	23	|∂ρε	|∂ρε	PROPN
ejpam-3479	335	1	∂ν	∂ν	PROPN
ejpam-3479	335	2	|2dtdγ	|2dtdγ	PROPN
ejpam-3479	335	3	≤	≤	NUM
ejpam-3479	336	1	c	c	NOUN
ejpam-3479	336	2	∫	∫	PROPN
ejpam-3479	336	3	u	u	NOUN
ejpam-3479	336	4	∫	∫	PROPN
ejpam-3479	336	5	γ	γ	X
ejpam-3479	336	6	|(i	|(i	PROPN
ejpam-3479	336	7	−	−	PROPN
ejpam-3479	336	8	p	p	NOUN
ejpam-3479	336	9	)	)	PUNCT
ejpam-3479	336	10	∂ρε	∂ρε	PROPN
ejpam-3479	336	11	∂ν	∂ν	PROPN
ejpam-3479	336	12	χγ	χγ	ADP
ejpam-3479	336	13	|2dtdaγ	|2dtdaγ	PROPN
ejpam-3479	336	14	,	,	PUNCT
ejpam-3479	336	15	(	(	PUNCT
ejpam-3479	336	16	58	58	NUM
ejpam-3479	336	17	)	)	PUNCT
ejpam-3479	336	18	where	where	SCONJ
ejpam-3479	336	19	c	c	X
ejpam-3479	336	20	>	>	X
ejpam-3479	336	21	0	0	NUM
ejpam-3479	336	22	is	be	AUX
ejpam-3479	336	23	independent	independent	ADJ
ejpam-3479	336	24	of	of	ADP
ejpam-3479	336	25	ε	ε	PROPN
ejpam-3479	336	26	.	.	PROPN
ejpam-3479	336	27	from	from	ADP
ejpam-3479	336	28	(	(	PUNCT
ejpam-3479	336	29	57	57	NUM
ejpam-3479	336	30	)	)	PUNCT
ejpam-3479	336	31	,	,	PUNCT
ejpam-3479	336	32	the	the	DET
ejpam-3479	336	33	choice	choice	NOUN
ejpam-3479	336	34	of	of	ADP
ejpam-3479	336	35	w0	w0	PROPN
ejpam-3479	336	36	∈	∈	PROPN
ejpam-3479	336	37	yθ	yθ	NOUN
ejpam-3479	336	38	and	and	CCONJ
ejpam-3479	336	39	the	the	DET
ejpam-3479	336	40	hypothesis	hypothesis	NOUN
ejpam-3479	336	41	on	on	ADP
ejpam-3479	336	42	h0	h0	PROPN
ejpam-3479	336	43	,	,	PUNCT
ejpam-3479	336	44	we	we	PRON
ejpam-3479	336	45	deduce	deduce	VERB
ejpam-3479	336	46	that	that	SCONJ
ejpam-3479	336	47	1	1	NUM
ejpam-3479	336	48	ε‖qε(0	ε‖qε(0	NOUN
ejpam-3479	336	49	,	,	PUNCT
ejpam-3479	336	50	.	.	PUNCT
ejpam-3479	337	1	,	,	PUNCT
ejpam-3479	337	2	.)‖	.)‖	PROPN
ejpam-3479	337	3	2	2	NUM
ejpam-3479	337	4	l2(qa	l2(qa	PROPN
ejpam-3479	337	5	)	)	PUNCT
ejpam-3479	337	6	+	+	CCONJ
ejpam-3479	337	7	1	1	NUM
ejpam-3479	337	8	2‖(i	2‖(i	NUM
ejpam-3479	337	9	−	−	PROPN
ejpam-3479	337	10	p	p	NOUN
ejpam-3479	337	11	)	)	PUNCT
ejpam-3479	337	12	∂ρε∂ν	∂ρε∂ν	VERB
ejpam-3479	337	13	χγ‖	χγ‖	PROPN
ejpam-3479	337	14	2	2	NUM
ejpam-3479	337	15	l2(u×γ	l2(u×γ	PROPN
ejpam-3479	337	16	)	)	PUNCT
ejpam-3479	337	17	≤	≤	NOUN
ejpam-3479	338	1	c	c	X
ejpam-3479	338	2	(	(	PUNCT
ejpam-3479	338	3	∫	∫	PROPN
ejpam-3479	338	4	u	u	NOUN
ejpam-3479	338	5	∫	∫	PROPN
ejpam-3479	338	6	ω	ω	PROPN
ejpam-3479	338	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	338	8	+	+	CCONJ
ejpam-3479	338	9	∫	∫	PROPN
ejpam-3479	338	10	u	u	X
ejpam-3479	338	11	∫	∫	NOUN
ejpam-3479	338	12	o	o	NOUN
ejpam-3479	338	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	338	14	)	)	PUNCT
ejpam-3479	338	15	1	1	NUM
ejpam-3479	338	16	2	2	NUM
ejpam-3479	338	17	(	(	PUNCT
ejpam-3479	338	18	59	59	NUM
ejpam-3479	338	19	)	)	PUNCT
ejpam-3479	338	20	and	and	CCONJ
ejpam-3479	338	21	then	then	ADV
ejpam-3479	338	22	‖vε‖2l2(u×ω	‖vε‖2l2(u×ω	NOUN
ejpam-3479	338	23	)	)	PUNCT
ejpam-3479	338	24	≤	≤	NUM
ejpam-3479	339	1	c	c	X
ejpam-3479	339	2	(	(	PUNCT
ejpam-3479	339	3	∫	∫	PROPN
ejpam-3479	339	4	u	u	NOUN
ejpam-3479	339	5	∫	∫	PROPN
ejpam-3479	339	6	γ	γ	X
ejpam-3479	339	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	339	8	+	+	CCONJ
ejpam-3479	339	9	∫	∫	PROPN
ejpam-3479	339	10	u	u	X
ejpam-3479	339	11	∫	∫	NOUN
ejpam-3479	339	12	o	o	NOUN
ejpam-3479	339	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	339	14	)	)	PUNCT
ejpam-3479	339	15	1	1	NUM
ejpam-3479	339	16	2	2	NUM
ejpam-3479	339	17	(	(	PUNCT
ejpam-3479	339	18	60	60	NUM
ejpam-3479	339	19	)	)	PUNCT
ejpam-3479	339	20	m.soma	m.soma	NOUN
ejpam-3479	339	21	,	,	PUNCT
ejpam-3479	339	22	s.	s.	PROPN
ejpam-3479	339	23	sawadogo	sawadogo	PROPN
ejpam-3479	339	24	/	/	SYM
ejpam-3479	339	25	eur	eur	PROPN
ejpam-3479	339	26	.	.	PUNCT
ejpam-3479	340	1	j.	j.	PROPN
ejpam-3479	340	2	pure	pure	PROPN
ejpam-3479	340	3	appl	appl	PROPN
ejpam-3479	340	4	.	.	PROPN
ejpam-3479	340	5	math	math	PROPN
ejpam-3479	340	6	,	,	PUNCT
ejpam-3479	340	7	12	12	NUM
ejpam-3479	340	8	(	(	PUNCT
ejpam-3479	340	9	3	3	NUM
ejpam-3479	340	10	)	)	PUNCT
ejpam-3479	340	11	(	(	PUNCT
ejpam-3479	340	12	2019	2019	NUM
ejpam-3479	340	13	)	)	PUNCT
ejpam-3479	340	14	,	,	PUNCT
ejpam-3479	340	15	1277	1277	NUM
ejpam-3479	340	16	-	-	SYM
ejpam-3479	340	17	1296	1296	NUM
ejpam-3479	340	18	1292	1292	NUM
ejpam-3479	340	19	‖qεχω‖2l2(u×γ	‖qεχω‖2l2(u×γ	NUM
ejpam-3479	340	20	)	)	PUNCT
ejpam-3479	340	21	≤	≤	NOUN
ejpam-3479	341	1	c	c	X
ejpam-3479	341	2	(	(	PUNCT
ejpam-3479	341	3	∫	∫	PROPN
ejpam-3479	341	4	u	u	NOUN
ejpam-3479	341	5	∫	∫	PROPN
ejpam-3479	341	6	γ	γ	X
ejpam-3479	341	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	341	8	+	+	CCONJ
ejpam-3479	341	9	∫	∫	PROPN
ejpam-3479	341	10	u	u	X
ejpam-3479	341	11	∫	∫	NOUN
ejpam-3479	341	12	o	o	NOUN
ejpam-3479	341	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	341	14	)	)	PUNCT
ejpam-3479	341	15	1	1	NUM
ejpam-3479	341	16	2	2	NUM
ejpam-3479	341	17	(	(	PUNCT
ejpam-3479	341	18	61	61	NUM
ejpam-3479	341	19	)	)	PUNCT
ejpam-3479	341	20	in	in	ADP
ejpam-3479	341	21	view	view	NOUN
ejpam-3479	341	22	of	of	ADP
ejpam-3479	341	23	(	(	PUNCT
ejpam-3479	341	24	58	58	NUM
ejpam-3479	341	25	)	)	PUNCT
ejpam-3479	341	26	and	and	CCONJ
ejpam-3479	341	27	(	(	PUNCT
ejpam-3479	341	28	59	59	NUM
ejpam-3479	341	29	)	)	PUNCT
ejpam-3479	341	30	,	,	PUNCT
ejpam-3479	341	31	we	we	PRON
ejpam-3479	341	32	get	get	VERB
ejpam-3479	341	33	‖1	‖1	PROPN
ejpam-3479	341	34	θ	θ	PROPN
ejpam-3479	341	35	∂ρε	∂ρε	PROPN
ejpam-3479	341	36	∂ν	∂ν	ADP
ejpam-3479	341	37	‖l2(σ	‖l2(σ	NOUN
ejpam-3479	341	38	)	)	PUNCT
ejpam-3479	341	39	≤	≤	NUM
ejpam-3479	342	1	c	c	X
ejpam-3479	342	2	(	(	PUNCT
ejpam-3479	342	3	∫	∫	PROPN
ejpam-3479	342	4	u	u	NOUN
ejpam-3479	342	5	∫	∫	PROPN
ejpam-3479	342	6	γ	γ	X
ejpam-3479	342	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	342	8	+	+	CCONJ
ejpam-3479	342	9	∫	∫	PROPN
ejpam-3479	342	10	u	u	X
ejpam-3479	342	11	∫	∫	NOUN
ejpam-3479	342	12	o	o	NOUN
ejpam-3479	342	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	342	14	)	)	PUNCT
ejpam-3479	342	15	1	1	NUM
ejpam-3479	342	16	2	2	NUM
ejpam-3479	342	17	(	(	PUNCT
ejpam-3479	342	18	62	62	NUM
ejpam-3479	342	19	)	)	PUNCT
ejpam-3479	342	20	and	and	CCONJ
ejpam-3479	342	21	using	use	VERB
ejpam-3479	342	22	(	(	PUNCT
ejpam-3479	342	23	59	59	NUM
ejpam-3479	342	24	)	)	PUNCT
ejpam-3479	342	25	and	and	CCONJ
ejpam-3479	342	26	the	the	DET
ejpam-3479	342	27	fact	fact	NOUN
ejpam-3479	342	28	that	that	SCONJ
ejpam-3479	342	29	1	1	NUM
ejpam-3479	342	30	θ	θ	NOUN
ejpam-3479	342	31	is	be	AUX
ejpam-3479	342	32	bounded	bound	VERB
ejpam-3479	342	33	,	,	PUNCT
ejpam-3479	342	34	we	we	PRON
ejpam-3479	342	35	have	have	VERB
ejpam-3479	342	36	‖1	‖1	NOUN
ejpam-3479	342	37	θ	θ	PROPN
ejpam-3479	342	38	p	p	X
ejpam-3479	342	39	∂ρε	∂ρε	PROPN
ejpam-3479	342	40	∂ν	∂ν	PRON
ejpam-3479	342	41	‖l2(u×γ	‖l2(u×γ	NOUN
ejpam-3479	342	42	)	)	PUNCT
ejpam-3479	342	43	≤	≤	NOUN
ejpam-3479	343	1	c	c	X
ejpam-3479	343	2	(	(	PUNCT
ejpam-3479	343	3	∫	∫	PROPN
ejpam-3479	343	4	u	u	NOUN
ejpam-3479	343	5	∫	∫	PROPN
ejpam-3479	343	6	γ	γ	X
ejpam-3479	343	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	343	8	+	+	CCONJ
ejpam-3479	343	9	∫	∫	PROPN
ejpam-3479	343	10	u	u	X
ejpam-3479	343	11	∫	∫	NOUN
ejpam-3479	343	12	o	o	NOUN
ejpam-3479	343	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	343	14	)	)	PUNCT
ejpam-3479	343	15	1	1	NUM
ejpam-3479	343	16	2	2	NUM
ejpam-3479	343	17	therefore	therefore	ADV
ejpam-3479	343	18	,	,	PUNCT
ejpam-3479	343	19	y	y	PROPN
ejpam-3479	343	20	being	be	AUX
ejpam-3479	343	21	a	a	DET
ejpam-3479	343	22	finite	finite	ADJ
ejpam-3479	343	23	dimensional	dimensional	ADJ
ejpam-3479	343	24	vector	vector	NOUN
ejpam-3479	343	25	subspace	subspace	NOUN
ejpam-3479	343	26	of	of	ADP
ejpam-3479	343	27	l2(u	l2(u	PROPN
ejpam-3479	343	28	×	×	NOUN
ejpam-3479	343	29	γ),we	γ),we	PRON
ejpam-3479	343	30	deduce	deduce	VERB
ejpam-3479	343	31	that	that	SCONJ
ejpam-3479	343	32	‖p	‖p	PROPN
ejpam-3479	343	33	∂ρε	∂ρε	PROPN
ejpam-3479	343	34	∂ν	∂ν	PRON
ejpam-3479	343	35	‖l2(u×γ	‖l2(u×γ	NOUN
ejpam-3479	343	36	)	)	PUNCT
ejpam-3479	343	37	≤	≤	NOUN
ejpam-3479	344	1	c	c	X
ejpam-3479	344	2	(	(	PUNCT
ejpam-3479	344	3	∫	∫	PROPN
ejpam-3479	344	4	u	u	NOUN
ejpam-3479	344	5	∫	∫	PROPN
ejpam-3479	344	6	γ	γ	X
ejpam-3479	344	7	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	344	8	+	+	CCONJ
ejpam-3479	344	9	∫	∫	PROPN
ejpam-3479	344	10	u	u	X
ejpam-3479	344	11	∫	∫	NOUN
ejpam-3479	344	12	o	o	NOUN
ejpam-3479	344	13	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	344	14	)	)	PUNCT
ejpam-3479	344	15	1	1	NUM
ejpam-3479	344	16	2	2	NUM
ejpam-3479	344	17	(	(	PUNCT
ejpam-3479	344	18	63	63	NUM
ejpam-3479	344	19	)	)	PUNCT
ejpam-3479	344	20	from	from	ADP
ejpam-3479	344	21	which	which	PRON
ejpam-3479	344	22	we	we	PRON
ejpam-3479	344	23	deduce	deduce	VERB
ejpam-3479	344	24	by	by	ADP
ejpam-3479	344	25	using	use	VERB
ejpam-3479	344	26	(	(	PUNCT
ejpam-3479	344	27	59	59	NUM
ejpam-3479	344	28	)	)	PUNCT
ejpam-3479	344	29	that	that	PRON
ejpam-3479	344	30	‖∂ρε	‖∂ρε	VERB
ejpam-3479	344	31	∂ν	∂ν	PRON
ejpam-3479	344	32	‖l2(u×γ	‖l2(u×γ	NOUN
ejpam-3479	344	33	)	)	PUNCT
ejpam-3479	344	34	≤	≤	NOUN
ejpam-3479	344	35	c	c	X
ejpam-3479	344	36	(	(	PUNCT
ejpam-3479	344	37	∫	∫	PROPN
ejpam-3479	344	38	u	u	NOUN
ejpam-3479	344	39	∫	∫	PROPN
ejpam-3479	344	40	γ	γ	X
ejpam-3479	344	41	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	344	42	+	+	CCONJ
ejpam-3479	344	43	∫	∫	PROPN
ejpam-3479	344	44	u	u	X
ejpam-3479	344	45	∫	∫	NOUN
ejpam-3479	344	46	o	o	NOUN
ejpam-3479	344	47	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	344	48	)	)	PUNCT
ejpam-3479	344	49	1	1	NUM
ejpam-3479	344	50	2	2	NUM
ejpam-3479	344	51	(	(	PUNCT
ejpam-3479	344	52	64	64	NUM
ejpam-3479	344	53	)	)	PUNCT
ejpam-3479	344	54	using	use	VERB
ejpam-3479	344	55	proposition	proposition	NOUN
ejpam-3479	344	56	2	2	NUM
ejpam-3479	344	57	,	,	PUNCT
ejpam-3479	344	58	we	we	PRON
ejpam-3479	344	59	have	have	VERB
ejpam-3479	344	60	that∫	that∫	PROPN
ejpam-3479	344	61	u	u	PROPN
ejpam-3479	344	62	∫	∫	PROPN
ejpam-3479	344	63	ω	ω	PROPN
ejpam-3479	344	64	1	1	NUM
ejpam-3479	344	65	θ2	θ2	PROPN
ejpam-3479	344	66	(	(	PUNCT
ejpam-3479	344	67	|∂ρε	|∂ρε	X
ejpam-3479	344	68	∂ν	∂ν	X
ejpam-3479	344	69	|2	|2	NUM
ejpam-3479	344	70	+	+	CCONJ
ejpam-3479	344	71	|∆ρε	|∆ρε	NOUN
ejpam-3479	344	72	|2	|2	NUM
ejpam-3479	345	1	+	+	CCONJ
ejpam-3479	345	2	|∇ρε	|∇ρε	PRON
ejpam-3479	345	3	|2	|2	NUM
ejpam-3479	345	4	+	+	CCONJ
ejpam-3479	345	5	|ρε	|ρε	NUM
ejpam-3479	345	6	|2)dtdadγ	|2)dtdadγ	VERB
ejpam-3479	345	7	≤	≤	NUM
ejpam-3479	345	8	c	c	NOUN
ejpam-3479	345	9	(	(	PUNCT
ejpam-3479	345	10	∫	∫	PROPN
ejpam-3479	345	11	u	u	NOUN
ejpam-3479	345	12	∫	∫	PROPN
ejpam-3479	345	13	γ	γ	X
ejpam-3479	345	14	θ2|w0|2dtdadγ	θ2|w0|2dtdadγ	PROPN
ejpam-3479	345	15	+	+	CCONJ
ejpam-3479	345	16	∫	∫	PROPN
ejpam-3479	345	17	u	u	X
ejpam-3479	345	18	∫	∫	NOUN
ejpam-3479	345	19	o	o	NOUN
ejpam-3479	345	20	θ2|h0|2dtdadγ	θ2|h0|2dtdadγ	PROPN
ejpam-3479	345	21	)	)	PUNCT
ejpam-3479	345	22	1	1	NUM
ejpam-3479	345	23	2	2	NUM
ejpam-3479	345	24	(	(	PUNCT
ejpam-3479	345	25	65	65	NUM
ejpam-3479	345	26	)	)	PUNCT
ejpam-3479	345	27	step	step	NOUN
ejpam-3479	345	28	3	3	NUM
ejpam-3479	345	29	.	.	PUNCT
ejpam-3479	346	1	we	we	PRON
ejpam-3479	346	2	prove	prove	VERB
ejpam-3479	346	3	the	the	DET
ejpam-3479	346	4	convergence	convergence	NOUN
ejpam-3479	346	5	of	of	ADP
ejpam-3479	346	6	(	(	PUNCT
ejpam-3479	346	7	vε	vε	ADJ
ejpam-3479	346	8	,	,	PUNCT
ejpam-3479	346	9	qε)ε	qε)ε	PROPN
ejpam-3479	346	10	and	and	CCONJ
ejpam-3479	346	11	ρε	ρε	NOUN
ejpam-3479	346	12	towards	towards	ADP
ejpam-3479	346	13	v̂	v̂	NOUN
ejpam-3479	346	14	,	,	PUNCT
ejpam-3479	346	15	q̂	q̂	PUNCT
ejpam-3479	346	16	and	and	CCONJ
ejpam-3479	346	17	ρ	ρ	NOUN
ejpam-3479	346	18	as	as	ADP
ejpam-3479	346	19	ε	ε	PROPN
ejpam-3479	346	20	−→	−→	NOUN
ejpam-3479	346	21	0	0	NUM
ejpam-3479	346	22	.	.	PUNCT
ejpam-3479	347	1	according	accord	VERB
ejpam-3479	347	2	to	to	ADP
ejpam-3479	347	3	(	(	PUNCT
ejpam-3479	347	4	60	60	NUM
ejpam-3479	347	5	)	)	PUNCT
ejpam-3479	347	6	,	,	PUNCT
ejpam-3479	347	7	(	(	PUNCT
ejpam-3479	347	8	61	61	NUM
ejpam-3479	347	9	)	)	PUNCT
ejpam-3479	347	10	and	and	CCONJ
ejpam-3479	347	11	(	(	PUNCT
ejpam-3479	347	12	62	62	NUM
ejpam-3479	347	13	)	)	PUNCT
ejpam-3479	347	14	we	we	PRON
ejpam-3479	347	15	can	can	AUX
ejpam-3479	347	16	extract	extract	VERB
ejpam-3479	347	17	subsequences	subsequence	NOUN
ejpam-3479	347	18	of	of	ADP
ejpam-3479	347	19	(	(	PUNCT
ejpam-3479	347	20	vε	vε	ADJ
ejpam-3479	347	21	,	,	PUNCT
ejpam-3479	347	22	qε)ε	qε)ε	PROPN
ejpam-3479	347	23	(	(	PUNCT
ejpam-3479	347	24	still	still	ADV
ejpam-3479	347	25	called	call	VERB
ejpam-3479	347	26	(	(	PUNCT
ejpam-3479	347	27	vε	vε	ADJ
ejpam-3479	347	28	,	,	PUNCT
ejpam-3479	347	29	qε)ε	qε)ε	PROPN
ejpam-3479	347	30	)	)	PUNCT
ejpam-3479	347	31	such	such	ADJ
ejpam-3479	347	32	that	that	PRON
ejpam-3479	347	33	vε	vε	VERB
ejpam-3479	347	34	⇀	⇀	X
ejpam-3479	347	35	ṽ	ṽ	PROPN
ejpam-3479	347	36	weakly	weakly	ADV
ejpam-3479	347	37	in	in	ADP
ejpam-3479	347	38	l2(u	l2(u	PROPN
ejpam-3479	347	39	×	×	PROPN
ejpam-3479	347	40	γ	γ	NOUN
ejpam-3479	347	41	)	)	PUNCT
ejpam-3479	347	42	,	,	PUNCT
ejpam-3479	347	43	(	(	PUNCT
ejpam-3479	347	44	66	66	NUM
ejpam-3479	347	45	)	)	PUNCT
ejpam-3479	347	46	qε	qε	VERB
ejpam-3479	347	47	⇀	⇀	PRON
ejpam-3479	347	48	q̃	q̃	NOUN
ejpam-3479	347	49	weakly	weakly	ADV
ejpam-3479	347	50	in	in	ADP
ejpam-3479	347	51	l2(u	l2(u	PROPN
ejpam-3479	347	52	;	;	PUNCT
ejpam-3479	347	53	h1	h1	PROPN
ejpam-3479	347	54	0	0	NUM
ejpam-3479	347	55	(	(	PUNCT
ejpam-3479	347	56	ω	ω	NOUN
ejpam-3479	347	57	)	)	PUNCT
ejpam-3479	347	58	)	)	PUNCT
ejpam-3479	347	59	,	,	PUNCT
ejpam-3479	347	60	(	(	PUNCT
ejpam-3479	347	61	67	67	NUM
ejpam-3479	347	62	)	)	PUNCT
ejpam-3479	347	63	1	1	NUM
ejpam-3479	347	64	θ	θ	NOUN
ejpam-3479	347	65	ρε	ρε	NOUN
ejpam-3479	347	66	⇀	⇀	PUNCT
ejpam-3479	347	67	ρ̃	ρ̃	PROPN
ejpam-3479	347	68	weakly	weakly	ADJ
ejpam-3479	347	69	in	in	ADP
ejpam-3479	347	70	l2	l2	NOUN
ejpam-3479	347	71	(	(	PUNCT
ejpam-3479	347	72	1	1	NUM
ejpam-3479	347	73	θ	θ	PROPN
ejpam-3479	347	74	,	,	PUNCT
ejpam-3479	347	75	q	q	NOUN
ejpam-3479	347	76	)	)	PUNCT
ejpam-3479	347	77	.	.	PUNCT
ejpam-3479	348	1	(	(	PUNCT
ejpam-3479	348	2	68	68	NUM
ejpam-3479	348	3	)	)	PUNCT
ejpam-3479	348	4	as	as	SCONJ
ejpam-3479	348	5	vε	vε	ADV
ejpam-3479	348	6	belong	belong	VERB
ejpam-3479	348	7	to	to	ADP
ejpam-3479	348	8	y	y	PROPN
ejpam-3479	348	9	⊥	⊥	NOUN
ejpam-3479	348	10	which	which	PRON
ejpam-3479	348	11	is	be	AUX
ejpam-3479	348	12	closed	close	VERB
ejpam-3479	348	13	vector	vector	NOUN
ejpam-3479	348	14	subspace	subspace	NOUN
ejpam-3479	348	15	of	of	ADP
ejpam-3479	348	16	l2(u	l2(u	PROPN
ejpam-3479	348	17	×	×	PROPN
ejpam-3479	348	18	γ	γ	PROPN
ejpam-3479	348	19	)	)	PUNCT
ejpam-3479	348	20	,	,	PUNCT
ejpam-3479	348	21	we	we	PRON
ejpam-3479	348	22	have	have	VERB
ejpam-3479	348	23	ṽ	ṽ	PROPN
ejpam-3479	348	24	∈	∈	PROPN
ejpam-3479	348	25	y	y	PROPN
ejpam-3479	348	26	⊥.	⊥.	PROPN
ejpam-3479	348	27	(	(	PUNCT
ejpam-3479	348	28	69	69	NUM
ejpam-3479	348	29	)	)	PUNCT
ejpam-3479	348	30	m.soma	m.soma	NOUN
ejpam-3479	348	31	,	,	PUNCT
ejpam-3479	348	32	s.	s.	PROPN
ejpam-3479	348	33	sawadogo	sawadogo	PROPN
ejpam-3479	348	34	/	/	SYM
ejpam-3479	348	35	eur	eur	PROPN
ejpam-3479	348	36	.	.	PUNCT
ejpam-3479	349	1	j.	j.	PROPN
ejpam-3479	349	2	pure	pure	PROPN
ejpam-3479	349	3	appl	appl	PROPN
ejpam-3479	349	4	.	.	PROPN
ejpam-3479	349	5	math	math	PROPN
ejpam-3479	349	6	,	,	PUNCT
ejpam-3479	349	7	12	12	NUM
ejpam-3479	349	8	(	(	PUNCT
ejpam-3479	349	9	3	3	NUM
ejpam-3479	349	10	)	)	PUNCT
ejpam-3479	349	11	(	(	PUNCT
ejpam-3479	349	12	2019	2019	NUM
ejpam-3479	349	13	)	)	PUNCT
ejpam-3479	349	14	,	,	PUNCT
ejpam-3479	349	15	1277	1277	NUM
ejpam-3479	349	16	-	-	SYM
ejpam-3479	349	17	1296	1296	NUM
ejpam-3479	349	18	1293	1293	NUM
ejpam-3479	349	19	the	the	DET
ejpam-3479	349	20	traces	trace	NOUN
ejpam-3479	349	21	(	(	PUNCT
ejpam-3479	349	22	q̃(0	q̃(0	ADV
ejpam-3479	349	23	,	,	PUNCT
ejpam-3479	349	24	.	.	PUNCT
ejpam-3479	349	25	,	,	PUNCT
ejpam-3479	349	26	.	.	PUNCT
ejpam-3479	349	27	)	)	PUNCT
ejpam-3479	349	28	,	,	PUNCT
ejpam-3479	349	29	q̃	q̃	PROPN
ejpam-3479	349	30	(	(	PUNCT
ejpam-3479	349	31	.	.	PUNCT
ejpam-3479	349	32	,	,	PUNCT
ejpam-3479	349	33	0	0	NUM
ejpam-3479	349	34	,	,	PUNCT
ejpam-3479	349	35	.	.	PUNCT
ejpam-3479	349	36	)	)	PUNCT
ejpam-3479	349	37	)	)	PUNCT
ejpam-3479	349	38	,	,	PUNCT
ejpam-3479	349	39	(	(	PUNCT
ejpam-3479	349	40	q̃(t	q̃(t	PROPN
ejpam-3479	349	41	,	,	PUNCT
ejpam-3479	349	42	.	.	PUNCT
ejpam-3479	349	43	,	,	PUNCT
ejpam-3479	349	44	.	.	PUNCT
ejpam-3479	349	45	)	)	PUNCT
ejpam-3479	349	46	,	,	PUNCT
ejpam-3479	349	47	q̃	q̃	PROPN
ejpam-3479	349	48	(	(	PUNCT
ejpam-3479	349	49	.	.	NUM
ejpam-3479	349	50	,	,	PUNCT
ejpam-3479	349	51	a	a	PRON
ejpam-3479	349	52	,	,	PUNCT
ejpam-3479	349	53	.	.	PUNCT
ejpam-3479	349	54	)	)	PUNCT
ejpam-3479	349	55	)	)	PUNCT
ejpam-3479	350	1	and	and	CCONJ
ejpam-3479	350	2	∂q̃	∂q̃	NOUN
ejpam-3479	350	3	∂ν	∂ν	PRON
ejpam-3479	350	4	exists	exist	VERB
ejpam-3479	350	5	and	and	CCONJ
ejpam-3479	350	6	belong	belong	VERB
ejpam-3479	350	7	respectively	respectively	ADV
ejpam-3479	350	8	to	to	ADP
ejpam-3479	350	9	(	(	PUNCT
ejpam-3479	350	10	l2(qa))2	l2(qa))2	NUM
ejpam-3479	350	11	×	×	NOUN
ejpam-3479	350	12	(	(	PUNCT
ejpam-3479	350	13	l2(qt	l2(qt	PROPN
ejpam-3479	350	14	)	)	PUNCT
ejpam-3479	350	15	)	)	PUNCT
ejpam-3479	350	16	2	2	NUM
ejpam-3479	350	17	and	and	CCONJ
ejpam-3479	350	18	l2(σ)(see	l2(σ)(see	VERB
ejpam-3479	351	1	[	[	X
ejpam-3479	351	2	8	8	NUM
ejpam-3479	351	3	]	]	NUM
ejpam-3479	351	4	)	)	PUNCT
ejpam-3479	351	5	.	.	PUNCT
ejpam-3479	352	1	so	so	ADV
ejpam-3479	352	2	,	,	PUNCT
ejpam-3479	352	3	using	use	VERB
ejpam-3479	352	4	(	(	PUNCT
ejpam-3479	352	5	66	66	NUM
ejpam-3479	352	6	)	)	PUNCT
ejpam-3479	352	7	and	and	CCONJ
ejpam-3479	352	8	(	(	PUNCT
ejpam-3479	352	9	67	67	NUM
ejpam-3479	352	10	)	)	PUNCT
ejpam-3479	352	11	while	while	SCONJ
ejpam-3479	352	12	passing	pass	VERB
ejpam-3479	352	13	(	(	PUNCT
ejpam-3479	352	14	54	54	NUM
ejpam-3479	352	15	)	)	PUNCT
ejpam-3479	352	16	to	to	ADP
ejpam-3479	352	17	the	the	DET
ejpam-3479	352	18	limit	limit	NOUN
ejpam-3479	352	19	as	as	ADP
ejpam-3479	352	20	ε	ε	PROPN
ejpam-3479	352	21	−→	−→	NOUN
ejpam-3479	352	22	0	0	NUM
ejpam-3479	352	23	,	,	PUNCT
ejpam-3479	352	24	we	we	PRON
ejpam-3479	352	25	can	can	AUX
ejpam-3479	352	26	prove	prove	VERB
ejpam-3479	352	27	that	that	SCONJ
ejpam-3479	352	28	q̃	q̃	PROPN
ejpam-3479	352	29	is	be	AUX
ejpam-3479	352	30	solution	solution	NOUN
ejpam-3479	352	31	of	of	PROPN
ejpam-3479	352	32	l∗q̃	l∗q̃	PROPN
ejpam-3479	352	33	=	=	SYM
ejpam-3479	352	34	βq̃(t	βq̃(t	NOUN
ejpam-3479	352	35	,	,	PUNCT
ejpam-3479	352	36	0	0	NUM
ejpam-3479	352	37	,	,	PUNCT
ejpam-3479	352	38	x	x	NOUN
ejpam-3479	352	39	)	)	PUNCT
ejpam-3479	352	40	in	in	ADP
ejpam-3479	352	41	q	q	NOUN
ejpam-3479	352	42	,	,	PUNCT
ejpam-3479	352	43	q̃(t	q̃(t	PROPN
ejpam-3479	352	44	,	,	PUNCT
ejpam-3479	352	45	a	a	PRON
ejpam-3479	352	46	,	,	PUNCT
ejpam-3479	352	47	x	x	NOUN
ejpam-3479	352	48	)	)	PUNCT
ejpam-3479	352	49	=	=	SYM
ejpam-3479	352	50	0	0	NUM
ejpam-3479	353	1	in	in	ADP
ejpam-3479	353	2	qa	qa	PROPN
ejpam-3479	353	3	,	,	PUNCT
ejpam-3479	353	4	q̃(t	q̃(t	PROPN
ejpam-3479	353	5	,	,	PUNCT
ejpam-3479	353	6	a	a	PRON
ejpam-3479	353	7	,	,	PUNCT
ejpam-3479	353	8	x	x	NOUN
ejpam-3479	353	9	)	)	PUNCT
ejpam-3479	353	10	=	=	SYM
ejpam-3479	353	11	0	0	NUM
ejpam-3479	354	1	in	in	ADP
ejpam-3479	354	2	qt	qt	NOUN
ejpam-3479	354	3	,	,	PUNCT
ejpam-3479	354	4	q̃	q̃	PROPN
ejpam-3479	354	5	=	=	PUNCT
ejpam-3479	354	6	h0χo	h0χo	PROPN
ejpam-3479	354	7	+	+	CCONJ
ejpam-3479	354	8	(	(	PUNCT
ejpam-3479	354	9	w0	w0	PROPN
ejpam-3479	354	10	−	−	PROPN
ejpam-3479	354	11	ṽ)χγ	ṽ)χγ	PROPN
ejpam-3479	354	12	on	on	ADP
ejpam-3479	354	13	σ	σ	PROPN
ejpam-3479	354	14	,	,	PUNCT
ejpam-3479	354	15	(	(	PUNCT
ejpam-3479	354	16	70	70	NUM
ejpam-3479	354	17	)	)	PUNCT
ejpam-3479	354	18	and	and	CCONJ
ejpam-3479	354	19	it	it	PRON
ejpam-3479	354	20	follows	follow	VERB
ejpam-3479	354	21	from	from	ADP
ejpam-3479	354	22	(	(	PUNCT
ejpam-3479	354	23	59	59	NUM
ejpam-3479	354	24	)	)	PUNCT
ejpam-3479	354	25	that	that	SCONJ
ejpam-3479	354	26	qε(0	qε(0	NOUN
ejpam-3479	354	27	,	,	PUNCT
ejpam-3479	354	28	.	.	PUNCT
ejpam-3479	354	29	,	,	PUNCT
ejpam-3479	354	30	.	.	PUNCT
ejpam-3479	354	31	)	)	PUNCT
ejpam-3479	355	1	⇀	⇀	PUNCT
ejpam-3479	356	1	q̃(0	q̃(0	ADV
ejpam-3479	356	2	,	,	PUNCT
ejpam-3479	356	3	.	.	PUNCT
ejpam-3479	356	4	,	,	PUNCT
ejpam-3479	356	5	.	.	PUNCT
ejpam-3479	356	6	)	)	PUNCT
ejpam-3479	357	1	=	=	SYM
ejpam-3479	357	2	0	0	PUNCT
ejpam-3479	357	3	weakly	weakly	ADV
ejpam-3479	357	4	in	in	ADP
ejpam-3479	357	5	l2(q	l2(q	PROPN
ejpam-3479	357	6	)	)	PUNCT
ejpam-3479	357	7	.	.	PUNCT
ejpam-3479	358	1	(	(	PUNCT
ejpam-3479	358	2	71	71	NUM
ejpam-3479	358	3	)	)	PUNCT
ejpam-3479	358	4	in	in	ADP
ejpam-3479	358	5	view	view	NOUN
ejpam-3479	358	6	of	of	ADP
ejpam-3479	358	7	(	(	PUNCT
ejpam-3479	358	8	69	69	NUM
ejpam-3479	358	9	)	)	PUNCT
ejpam-3479	358	10	,	,	PUNCT
ejpam-3479	358	11	(	(	PUNCT
ejpam-3479	358	12	70	70	NUM
ejpam-3479	358	13	)	)	PUNCT
ejpam-3479	358	14	and	and	CCONJ
ejpam-3479	358	15	(	(	PUNCT
ejpam-3479	358	16	71	71	NUM
ejpam-3479	358	17	)	)	PUNCT
ejpam-3479	358	18	,	,	PUNCT
ejpam-3479	358	19	(	(	PUNCT
ejpam-3479	358	20	υ̃	υ̃	PROPN
ejpam-3479	358	21	,	,	PUNCT
ejpam-3479	358	22	q̃	q̃	PROPN
ejpam-3479	358	23	)	)	PUNCT
ejpam-3479	358	24	verifies	verifie	NOUN
ejpam-3479	358	25	the	the	DET
ejpam-3479	358	26	null	null	ADJ
ejpam-3479	358	27	controllability	controllability	NOUN
ejpam-3479	358	28	(	(	PUNCT
ejpam-3479	358	29	14)−	14)−	NUM
ejpam-3479	358	30	(	(	PUNCT
ejpam-3479	358	31	16	16	NUM
ejpam-3479	358	32	)	)	PUNCT
ejpam-3479	358	33	and	and	CCONJ
ejpam-3479	358	34	there	there	PRON
ejpam-3479	358	35	exists	exist	VERB
ejpam-3479	358	36	a	a	DET
ejpam-3479	358	37	solution	solution	NOUN
ejpam-3479	358	38	to	to	ADP
ejpam-3479	358	39	the	the	DET
ejpam-3479	358	40	boundary	boundary	ADJ
ejpam-3479	358	41	null	null	ADJ
ejpam-3479	358	42	controllability	controllability	NOUN
ejpam-3479	358	43	problem	problem	NOUN
ejpam-3479	358	44	.	.	PUNCT
ejpam-3479	359	1	moreover	moreover	ADV
ejpam-3479	359	2	,	,	PUNCT
ejpam-3479	359	3	it	it	PRON
ejpam-3479	359	4	is	be	AUX
ejpam-3479	359	5	clear	clear	ADJ
ejpam-3479	359	6	from	from	ADP
ejpam-3479	359	7	(	(	PUNCT
ejpam-3479	359	8	68	68	NUM
ejpam-3479	359	9	)	)	PUNCT
ejpam-3479	359	10	that	that	PRON
ejpam-3479	359	11	ρ̃	ρ̃	PROPN
ejpam-3479	359	12	satisfies	satisfies	PROPN
ejpam-3479	359	13	lρ̃	lρ̃	PART
ejpam-3479	359	14	=	=	NOUN
ejpam-3479	359	15	0	0	NUM
ejpam-3479	359	16	in	in	ADP
ejpam-3479	359	17	q	q	PROPN
ejpam-3479	359	18	ρ̃(t	ρ̃(t	PROPN
ejpam-3479	359	19	,	,	PUNCT
ejpam-3479	359	20	0	0	NUM
ejpam-3479	359	21	,	,	PUNCT
ejpam-3479	359	22	x	x	X
ejpam-3479	359	23	)	)	PUNCT
ejpam-3479	359	24	=	=	SYM
ejpam-3479	360	1	∫	∫	PROPN
ejpam-3479	360	2	a	a	DET
ejpam-3479	360	3	0	0	NUM
ejpam-3479	360	4	β(t	β(t	PROPN
ejpam-3479	360	5	,	,	PUNCT
ejpam-3479	360	6	a	a	PRON
ejpam-3479	360	7	,	,	PUNCT
ejpam-3479	360	8	x)ρ̃(t	x)ρ̃(t	PROPN
ejpam-3479	360	9	,	,	PUNCT
ejpam-3479	360	10	a	a	PRON
ejpam-3479	360	11	,	,	PUNCT
ejpam-3479	360	12	x)da	x)da	PROPN
ejpam-3479	360	13	in	in	ADP
ejpam-3479	360	14	qt	qt	NOUN
ejpam-3479	360	15	,	,	PUNCT
ejpam-3479	360	16	ρ̃	ρ̃	PROPN
ejpam-3479	360	17	=	=	SYM
ejpam-3479	360	18	0	0	NUM
ejpam-3479	360	19	on	on	ADP
ejpam-3479	360	20	σ	σ	PROPN
ejpam-3479	360	21	from	from	ADP
ejpam-3479	360	22	(	(	PUNCT
ejpam-3479	360	23	64	64	NUM
ejpam-3479	360	24	)	)	PUNCT
ejpam-3479	360	25	∂ρε	∂ρε	NOUN
ejpam-3479	360	26	∂ν	∂ν	PRON
ejpam-3479	361	1	⇀	⇀	PROPN
ejpam-3479	361	2	∂ρ̃	∂ρ̃	PROPN
ejpam-3479	361	3	∂ν	∂ν	PRON
ejpam-3479	361	4	weakly	weakly	ADV
ejpam-3479	361	5	in	in	ADP
ejpam-3479	361	6	l2(u	l2(u	PROPN
ejpam-3479	361	7	×	×	PROPN
ejpam-3479	361	8	γ	γ	NOUN
ejpam-3479	361	9	)	)	PUNCT
ejpam-3479	361	10	(	(	PUNCT
ejpam-3479	361	11	72	72	NUM
ejpam-3479	361	12	)	)	PUNCT
ejpam-3479	361	13	we	we	PRON
ejpam-3479	361	14	know	know	VERB
ejpam-3479	361	15	on	on	ADP
ejpam-3479	361	16	the	the	DET
ejpam-3479	361	17	one	one	NUM
ejpam-3479	361	18	hand	hand	NOUN
ejpam-3479	361	19	that	that	PRON
ejpam-3479	361	20	(	(	PUNCT
ejpam-3479	361	21	ṽ	ṽ	PROPN
ejpam-3479	361	22	,	,	PUNCT
ejpam-3479	361	23	q̃	q̃	PROPN
ejpam-3479	361	24	)	)	PUNCT
ejpam-3479	361	25	is	be	AUX
ejpam-3479	361	26	solution	solution	NOUN
ejpam-3479	361	27	to	to	ADP
ejpam-3479	361	28	null	null	ADJ
ejpam-3479	361	29	controllability	controllability	NOUN
ejpam-3479	361	30	(	(	PUNCT
ejpam-3479	361	31	14)−	14)−	NUM
ejpam-3479	361	32	(	(	PUNCT
ejpam-3479	361	33	16	16	NUM
ejpam-3479	361	34	)	)	PUNCT
ejpam-3479	361	35	,	,	PUNCT
ejpam-3479	361	36	and	and	CCONJ
ejpam-3479	361	37	on	on	ADP
ejpam-3479	361	38	the	the	DET
ejpam-3479	361	39	other	other	ADJ
ejpam-3479	361	40	other	other	ADJ
ejpam-3479	361	41	hand	hand	NOUN
ejpam-3479	361	42	that	that	PRON
ejpam-3479	361	43	,	,	PUNCT
ejpam-3479	361	44	there	there	PRON
ejpam-3479	361	45	exists	exist	VERB
ejpam-3479	361	46	a	a	DET
ejpam-3479	361	47	unique	unique	ADJ
ejpam-3479	361	48	v̂	v̂	PRON
ejpam-3479	361	49	∈	∈	NOUN
ejpam-3479	361	50	ε	ε	NOUN
ejpam-3479	361	51	such	such	ADJ
ejpam-3479	361	52	that	that	PRON
ejpam-3479	361	53	(	(	PUNCT
ejpam-3479	361	54	w0	w0	PROPN
ejpam-3479	361	55	−	−	PROPN
ejpam-3479	361	56	v̂	v̂	NOUN
ejpam-3479	361	57	)	)	PUNCT
ejpam-3479	361	58	is	be	AUX
ejpam-3479	361	59	of	of	ADP
ejpam-3479	361	60	minimal	minimal	ADJ
ejpam-3479	361	61	norm	norm	NOUN
ejpam-3479	361	62	in	in	ADP
ejpam-3479	361	63	l2(u	l2(u	PROPN
ejpam-3479	361	64	×γ	×γ	ADV
ejpam-3479	361	65	)	)	PUNCT
ejpam-3479	361	66	.	.	PUNCT
ejpam-3479	362	1	if	if	SCONJ
ejpam-3479	362	2	we	we	PRON
ejpam-3479	362	3	denote	denote	VERB
ejpam-3479	362	4	by	by	ADP
ejpam-3479	362	5	q̂	q̂	X
ejpam-3479	362	6	the	the	DET
ejpam-3479	362	7	corresponding	corresponding	ADJ
ejpam-3479	362	8	solution	solution	NOUN
ejpam-3479	362	9	to	to	ADP
ejpam-3479	362	10	(	(	PUNCT
ejpam-3479	362	11	15	15	NUM
ejpam-3479	362	12	)	)	PUNCT
ejpam-3479	362	13	,	,	PUNCT
ejpam-3479	362	14	we	we	PRON
ejpam-3479	362	15	have	have	VERB
ejpam-3479	362	16	q̂(0	q̂(0	NUM
ejpam-3479	362	17	,	,	PUNCT
ejpam-3479	362	18	.	.	PUNCT
ejpam-3479	362	19	,	,	PUNCT
ejpam-3479	362	20	.	.	PUNCT
ejpam-3479	362	21	)	)	PUNCT
ejpam-3479	363	1	=	=	SYM
ejpam-3479	363	2	0	0	PUNCT
ejpam-3479	364	1	and	and	CCONJ
ejpam-3479	364	2	,	,	PUNCT
ejpam-3479	364	3	as	as	SCONJ
ejpam-3479	364	4	ṽ	ṽ	PROPN
ejpam-3479	364	5	∈	∈	PROPN
ejpam-3479	364	6	e	e	NOUN
ejpam-3479	364	7	,	,	PUNCT
ejpam-3479	364	8	1	1	NUM
ejpam-3479	364	9	2	2	NUM
ejpam-3479	364	10	‖w0	‖w0	NOUN
ejpam-3479	364	11	−	−	PROPN
ejpam-3479	364	12	vε‖2l2(u×γ	vε‖2l2(u×γ	NOUN
ejpam-3479	364	13	)	)	PUNCT
ejpam-3479	364	14	≤	≤	NUM
ejpam-3479	365	1	jε(vε	jε(vε	ADJ
ejpam-3479	365	2	)	)	PUNCT
ejpam-3479	365	3	≤	≤	NUM
ejpam-3479	365	4	jε(v̂	jε(v̂	PROPN
ejpam-3479	365	5	)	)	PUNCT
ejpam-3479	365	6	=	=	SYM
ejpam-3479	365	7	1	1	NUM
ejpam-3479	365	8	2	2	NUM
ejpam-3479	365	9	‖w0	‖w0	NOUN
ejpam-3479	365	10	−	−	PROPN
ejpam-3479	365	11	v̂‖2l2(u×γ	v̂‖2l2(u×γ	PROPN
ejpam-3479	365	12	)	)	PUNCT
ejpam-3479	365	13	and	and	CCONJ
ejpam-3479	365	14	1	1	NUM
ejpam-3479	365	15	2	2	NUM
ejpam-3479	365	16	‖w0	‖w0	NOUN
ejpam-3479	365	17	−	−	PROPN
ejpam-3479	365	18	v̂‖2l2(u×γ	v̂‖2l2(u×γ	PROPN
ejpam-3479	365	19	)	)	PUNCT
ejpam-3479	365	20	≤	≤	NUM
ejpam-3479	365	21	1	1	NUM
ejpam-3479	365	22	2	2	NUM
ejpam-3479	365	23	‖w0	‖w0	NOUN
ejpam-3479	365	24	−	−	PROPN
ejpam-3479	365	25	vε‖2l2(u×γ	vε‖2l2(u×γ	NOUN
ejpam-3479	365	26	)	)	PUNCT
ejpam-3479	365	27	using	use	VERB
ejpam-3479	365	28	(	(	PUNCT
ejpam-3479	365	29	66	66	NUM
ejpam-3479	365	30	)	)	PUNCT
ejpam-3479	365	31	lim	lim	PROPN
ejpam-3479	365	32	inf	inf	PROPN
ejpam-3479	365	33	ε−→0	ε−→0	PROPN
ejpam-3479	365	34	1	1	NUM
ejpam-3479	365	35	2	2	NUM
ejpam-3479	365	36	‖w0	‖w0	NOUN
ejpam-3479	365	37	−	−	PROPN
ejpam-3479	365	38	vε‖2l2(u×γ	vε‖2l2(u×γ	NOUN
ejpam-3479	365	39	)	)	PUNCT
ejpam-3479	365	40	≥	≥	NOUN
ejpam-3479	365	41	1	1	NUM
ejpam-3479	365	42	2	2	NUM
ejpam-3479	365	43	‖w0	‖w0	NOUN
ejpam-3479	365	44	−	−	PROPN
ejpam-3479	365	45	v̂‖2l2(u×γ	v̂‖2l2(u×γ	PROPN
ejpam-3479	365	46	)	)	PUNCT
ejpam-3479	365	47	m.soma	m.soma	NOUN
ejpam-3479	365	48	,	,	PUNCT
ejpam-3479	365	49	s.	s.	PROPN
ejpam-3479	365	50	sawadogo	sawadogo	PROPN
ejpam-3479	365	51	/	/	SYM
ejpam-3479	365	52	eur	eur	PROPN
ejpam-3479	365	53	.	.	PUNCT
ejpam-3479	366	1	j.	j.	PROPN
ejpam-3479	366	2	pure	pure	PROPN
ejpam-3479	366	3	appl	appl	PROPN
ejpam-3479	366	4	.	.	PROPN
ejpam-3479	366	5	math	math	PROPN
ejpam-3479	366	6	,	,	PUNCT
ejpam-3479	366	7	12	12	NUM
ejpam-3479	366	8	(	(	PUNCT
ejpam-3479	366	9	3	3	NUM
ejpam-3479	366	10	)	)	PUNCT
ejpam-3479	366	11	(	(	PUNCT
ejpam-3479	366	12	2019	2019	NUM
ejpam-3479	366	13	)	)	PUNCT
ejpam-3479	366	14	,	,	PUNCT
ejpam-3479	366	15	1277	1277	NUM
ejpam-3479	366	16	-	-	SYM
ejpam-3479	366	17	1296	1296	NUM
ejpam-3479	366	18	1294	1294	NUM
ejpam-3479	366	19	hence	hence	ADV
ejpam-3479	366	20	,	,	PUNCT
ejpam-3479	366	21	ṽ	ṽ	PROPN
ejpam-3479	366	22	=	=	PROPN
ejpam-3479	366	23	v̂	v̂	X
ejpam-3479	366	24	and	and	CCONJ
ejpam-3479	366	25	vε	vε	VERB
ejpam-3479	366	26	⇀	⇀	X
ejpam-3479	366	27	ṽ	ṽ	PROPN
ejpam-3479	366	28	strongly	strongly	ADV
ejpam-3479	366	29	in	in	ADP
ejpam-3479	366	30	l2(u	l2(u	PROPN
ejpam-3479	366	31	×	×	PROPN
ejpam-3479	366	32	γ	γ	PROPN
ejpam-3479	366	33	)	)	PUNCT
ejpam-3479	366	34	.	.	PUNCT
ejpam-3479	367	1	writing	write	VERB
ejpam-3479	367	2	ρ̃	ρ̃	PROPN
ejpam-3479	367	3	=	=	SYM
ejpam-3479	367	4	ρ̂	ρ̂	NUM
ejpam-3479	367	5	,	,	PUNCT
ejpam-3479	367	6	we	we	PRON
ejpam-3479	367	7	obtain	obtain	VERB
ejpam-3479	367	8	v̂	v̂	NOUN
ejpam-3479	367	9	=	=	PUNCT
ejpam-3479	368	1	(	(	PUNCT
ejpam-3479	368	2	i	i	PRON
ejpam-3479	368	3	−	−	PROPN
ejpam-3479	368	4	p	p	NOUN
ejpam-3479	368	5	)	)	PUNCT
ejpam-3479	368	6	(	(	PUNCT
ejpam-3479	368	7	w0χγ	w0χγ	PROPN
ejpam-3479	368	8	−	−	NOUN
ejpam-3479	368	9	∂ρ̂	∂ρ̂	VERB
ejpam-3479	368	10	∂ν	∂ν	PRON
ejpam-3479	368	11	χγ	χγ	VERB
ejpam-3479	368	12	)	)	PUNCT
ejpam-3479	368	13	.	.	PUNCT
ejpam-3479	369	1	4	4	X
ejpam-3479	369	2	.	.	X
ejpam-3479	369	3	formulation	formulation	NOUN
ejpam-3479	369	4	of	of	ADP
ejpam-3479	369	5	the	the	DET
ejpam-3479	369	6	sentinel	sentinel	NOUN
ejpam-3479	369	7	with	with	ADP
ejpam-3479	369	8	given	give	VERB
ejpam-3479	369	9	sensitivity	sensitivity	NOUN
ejpam-3479	369	10	and	and	CCONJ
ejpam-3479	369	11	identification	identification	NOUN
ejpam-3479	369	12	of	of	ADP
ejpam-3479	369	13	parameters	parameter	NOUN
ejpam-3479	369	14	λi	λi	ADP
ejpam-3479	369	15	according	accord	VERB
ejpam-3479	369	16	to	to	ADP
ejpam-3479	369	17	theorem	theorem	NOUN
ejpam-3479	369	18	2	2	NUM
ejpam-3479	369	19	,	,	PUNCT
ejpam-3479	369	20	if	if	SCONJ
ejpam-3479	369	21	we	we	PRON
ejpam-3479	369	22	replace	replace	VERB
ejpam-3479	369	23	in	in	ADP
ejpam-3479	369	24	(	(	PUNCT
ejpam-3479	369	25	4	4	NUM
ejpam-3479	369	26	)	)	PUNCT
ejpam-3479	369	27	w	w	NOUN
ejpam-3479	369	28	by	by	ADP
ejpam-3479	369	29	ŵ	ŵ	X
ejpam-3479	369	30	=	=	SYM
ejpam-3479	369	31	p	p	X
ejpam-3479	369	32	(	(	PUNCT
ejpam-3479	369	33	w0	w0	PROPN
ejpam-3479	369	34	)	)	PUNCT
ejpam-3479	369	35	+	+	CCONJ
ejpam-3479	369	36	(	(	PUNCT
ejpam-3479	369	37	i	i	PRON
ejpam-3479	369	38	−	−	PROPN
ejpam-3479	369	39	p	p	NOUN
ejpam-3479	369	40	)	)	PUNCT
ejpam-3479	369	41	(	(	PUNCT
ejpam-3479	369	42	∂ρ̂	∂ρ̂	VERB
ejpam-3479	369	43	∂ν	∂ν	PROPN
ejpam-3479	369	44	χγ	χγ	PROPN
ejpam-3479	369	45	)	)	PUNCT
ejpam-3479	369	46	,	,	PUNCT
ejpam-3479	369	47	the	the	DET
ejpam-3479	369	48	function	function	NOUN
ejpam-3479	369	49	s	s	AUX
ejpam-3479	369	50	defined	define	VERB
ejpam-3479	369	51	by	by	ADP
ejpam-3479	369	52	s(λ	s(λ	PROPN
ejpam-3479	369	53	,	,	PUNCT
ejpam-3479	369	54	τ	τ	X
ejpam-3479	369	55	)	)	PUNCT
ejpam-3479	369	56	=	=	SYM
ejpam-3479	370	1	∫	∫	PUNCT
ejpam-3479	370	2	u	u	NOUN
ejpam-3479	370	3	∫	∫	PROPN
ejpam-3479	370	4	o	o	PROPN
ejpam-3479	370	5	h0	h0	PROPN
ejpam-3479	370	6	∂y	∂y	PROPN
ejpam-3479	370	7	∂ν	∂ν	PROPN
ejpam-3479	370	8	(	(	PUNCT
ejpam-3479	370	9	λ	λ	PROPN
ejpam-3479	370	10	,	,	PUNCT
ejpam-3479	370	11	τ)dtdadγ	τ)dtdadγ	PUNCT
ejpam-3479	371	1	+	+	CCONJ
ejpam-3479	371	2	∫	∫	X
ejpam-3479	371	3	u	u	X
ejpam-3479	371	4	∫	∫	PROPN
ejpam-3479	371	5	γ	γ	X
ejpam-3479	371	6	(	(	PUNCT
ejpam-3479	371	7	p	p	X
ejpam-3479	371	8	(	(	PUNCT
ejpam-3479	371	9	w0	w0	PROPN
ejpam-3479	371	10	)	)	PUNCT
ejpam-3479	371	11	+	+	CCONJ
ejpam-3479	371	12	(	(	PUNCT
ejpam-3479	371	13	i	i	PRON
ejpam-3479	371	14	−	−	PROPN
ejpam-3479	371	15	p	p	NOUN
ejpam-3479	371	16	)	)	PUNCT
ejpam-3479	371	17	(	(	PUNCT
ejpam-3479	371	18	∂ρ̂	∂ρ̂	VERB
ejpam-3479	371	19	∂ν	∂ν	PRON
ejpam-3479	371	20	χγ	χγ	PROPN
ejpam-3479	371	21	)	)	PUNCT
ejpam-3479	371	22	)	)	PUNCT
ejpam-3479	372	1	∂y	∂y	PRON
ejpam-3479	372	2	∂ν	∂ν	PROPN
ejpam-3479	372	3	(	(	PUNCT
ejpam-3479	372	4	λ	λ	PROPN
ejpam-3479	372	5	,	,	PUNCT
ejpam-3479	372	6	τ)dtdadγ	τ)dtdadγ	NUM
ejpam-3479	372	7	,	,	PUNCT
ejpam-3479	372	8	is	be	AUX
ejpam-3479	372	9	such	such	ADJ
ejpam-3479	372	10	that	that	SCONJ
ejpam-3479	372	11	(	(	PUNCT
ejpam-3479	372	12	ŵ	ŵ	X
ejpam-3479	372	13	,	,	PUNCT
ejpam-3479	372	14	s(ŵ	s(ŵ	NOUN
ejpam-3479	372	15	)	)	PUNCT
ejpam-3479	372	16	)	)	PUNCT
ejpam-3479	372	17	verified	verify	VERB
ejpam-3479	372	18	the	the	DET
ejpam-3479	372	19	sentinel	sentinel	ADJ
ejpam-3479	372	20	problem	problem	NOUN
ejpam-3479	372	21	(	(	PUNCT
ejpam-3479	372	22	4)−	4)−	NOUN
ejpam-3479	372	23	(	(	PUNCT
ejpam-3479	372	24	7	7	NUM
ejpam-3479	372	25	)	)	PUNCT
ejpam-3479	372	26	.	.	PUNCT
ejpam-3479	373	1	to	to	PART
ejpam-3479	373	2	estimate	estimate	VERB
ejpam-3479	373	3	the	the	DET
ejpam-3479	373	4	parameters	parameter	NOUN
ejpam-3479	373	5	λi	λi	SYM
ejpam-3479	373	6	,	,	PUNCT
ejpam-3479	373	7	one	one	NUM
ejpam-3479	373	8	proceeds	proceed	NOUN
ejpam-3479	373	9	as	as	SCONJ
ejpam-3479	373	10	follows	follow	VERB
ejpam-3479	373	11	:	:	PUNCT
ejpam-3479	373	12	assume	assume	VERB
ejpam-3479	373	13	that	that	SCONJ
ejpam-3479	373	14	the	the	DET
ejpam-3479	373	15	solution	solution	NOUN
ejpam-3479	373	16	of	of	ADP
ejpam-3479	373	17	(	(	PUNCT
ejpam-3479	373	18	1	1	NUM
ejpam-3479	373	19	)	)	PUNCT
ejpam-3479	373	20	when	when	SCONJ
ejpam-3479	373	21	λ	λ	X
ejpam-3479	373	22	=	=	SYM
ejpam-3479	373	23	0	0	NUM
ejpam-3479	373	24	and	and	CCONJ
ejpam-3479	373	25	τ	τ	X
ejpam-3479	373	26	=	=	SYM
ejpam-3479	373	27	0	0	NUM
ejpam-3479	373	28	is	be	AUX
ejpam-3479	373	29	known	know	VERB
ejpam-3479	373	30	.	.	PUNCT
ejpam-3479	374	1	then	then	ADV
ejpam-3479	374	2	,	,	PUNCT
ejpam-3479	374	3	one	one	PRON
ejpam-3479	374	4	has	have	VERB
ejpam-3479	374	5	the	the	DET
ejpam-3479	374	6	following	follow	VERB
ejpam-3479	374	7	information	information	NOUN
ejpam-3479	374	8	s(λ	s(λ	PROPN
ejpam-3479	374	9	,	,	PUNCT
ejpam-3479	374	10	τ)−	τ)−	PROPN
ejpam-3479	374	11	s(0	s(0	PROPN
ejpam-3479	374	12	,	,	PUNCT
ejpam-3479	374	13	0	0	NUM
ejpam-3479	374	14	)	)	PUNCT
ejpam-3479	375	1	≈	≈	PROPN
ejpam-3479	375	2	m∑	m∑	INTJ
ejpam-3479	375	3	i=1	i=1	PROPN
ejpam-3479	375	4	λi	λi	ADP
ejpam-3479	375	5	∂s	∂s	PROPN
ejpam-3479	375	6	∂λi	∂λi	PROPN
ejpam-3479	375	7	(	(	PUNCT
ejpam-3479	375	8	0	0	NUM
ejpam-3479	375	9	,	,	PUNCT
ejpam-3479	375	10	0	0	NUM
ejpam-3479	375	11	)	)	PUNCT
ejpam-3479	375	12	.	.	PUNCT
ejpam-3479	376	1	therefore	therefore	ADV
ejpam-3479	376	2	,	,	PUNCT
ejpam-3479	376	3	fixing	fix	VERB
ejpam-3479	376	4	i	i	PRON
ejpam-3479	376	5	∈	∈	PROPN
ejpam-3479	376	6	{	{	PUNCT
ejpam-3479	376	7	1	1	NUM
ejpam-3479	376	8	,	,	PUNCT
ejpam-3479	376	9	.	.	PUNCT
ejpam-3479	376	10	.	.	PUNCT
ejpam-3479	376	11	.	.	PUNCT
ejpam-3479	377	1	,	,	PUNCT
ejpam-3479	377	2	m	m	VERB
ejpam-3479	377	3	}	}	PUNCT
ejpam-3479	377	4	and	and	CCONJ
ejpam-3479	377	5	choosing	choose	VERB
ejpam-3479	377	6	∂s	∂s	PROPN
ejpam-3479	377	7	∂λj	∂λj	PROPN
ejpam-3479	377	8	(	(	PUNCT
ejpam-3479	377	9	0	0	NUM
ejpam-3479	377	10	,	,	PUNCT
ejpam-3479	377	11	0	0	NUM
ejpam-3479	377	12	)	)	PUNCT
ejpam-3479	377	13	=	=	SYM
ejpam-3479	377	14	0	0	NUM
ejpam-3479	377	15	for	for	ADP
ejpam-3479	377	16	j	j	PROPN
ejpam-3479	377	17	6=	6=	PROPN
ejpam-3479	377	18	i	i	PRON
ejpam-3479	377	19	and	and	CCONJ
ejpam-3479	377	20	∂s	∂s	PROPN
ejpam-3479	377	21	∂λi	∂λi	PROPN
ejpam-3479	377	22	(	(	PUNCT
ejpam-3479	377	23	0	0	NUM
ejpam-3479	377	24	,	,	PUNCT
ejpam-3479	377	25	0	0	NUM
ejpam-3479	377	26	)	)	PUNCT
ejpam-3479	377	27	=	=	SYM
ejpam-3479	377	28	ci	ci	NOUN
ejpam-3479	377	29	,	,	PUNCT
ejpam-3479	377	30	one	one	NOUN
ejpam-3479	377	31	obtains	obtain	VERB
ejpam-3479	377	32	the	the	DET
ejpam-3479	377	33	following	following	ADJ
ejpam-3479	377	34	estimate	estimate	NOUN
ejpam-3479	377	35	of	of	ADP
ejpam-3479	377	36	the	the	DET
ejpam-3479	377	37	parameter	parameter	NOUN
ejpam-3479	377	38	λi	λi	X
ejpam-3479	377	39	:	:	PUNCT
ejpam-3479	377	40	λi	λi	PROPN
ejpam-3479	377	41	≈	≈	PROPN
ejpam-3479	377	42	1	1	NUM
ejpam-3479	377	43	ci	ci	NOUN
ejpam-3479	377	44	(	(	PUNCT
ejpam-3479	377	45	s(λ	s(λ	PROPN
ejpam-3479	377	46	,	,	PUNCT
ejpam-3479	377	47	τ)−	τ)−	PROPN
ejpam-3479	377	48	s(0	s(0	PROPN
ejpam-3479	377	49	,	,	PUNCT
ejpam-3479	377	50	0	0	NUM
ejpam-3479	377	51	)	)	PUNCT
ejpam-3479	377	52	)	)	PUNCT
ejpam-3479	377	53	,	,	PUNCT
ejpam-3479	377	54	we	we	PRON
ejpam-3479	377	55	deduce	deduce	VERB
ejpam-3479	377	56	that	that	PRON
ejpam-3479	377	57	λi	λi	ADP
ejpam-3479	377	58	≈	≈	PROPN
ejpam-3479	377	59	1	1	PROPN
ejpam-3479	377	60	ci	ci	PROPN
ejpam-3479	377	61	{	{	PUNCT
ejpam-3479	377	62	∫	∫	PROPN
ejpam-3479	377	63	u	u	NOUN
ejpam-3479	377	64	∫	∫	PROPN
ejpam-3479	377	65	o	o	PROPN
ejpam-3479	377	66	h0	h0	PROPN
ejpam-3479	377	67	(	(	PUNCT
ejpam-3479	377	68	m0	m0	PROPN
ejpam-3479	377	69	−	−	PROPN
ejpam-3479	377	70	∂y0	∂y0	PROPN
ejpam-3479	377	71	∂ν	∂ν	PROPN
ejpam-3479	377	72	dtdadγ	dtdadγ	ADV
ejpam-3479	377	73	)	)	PUNCT
ejpam-3479	377	74	}	}	PUNCT
ejpam-3479	377	75	+	+	CCONJ
ejpam-3479	377	76	1	1	NUM
ejpam-3479	377	77	ci	ci	NOUN
ejpam-3479	377	78	{	{	PUNCT
ejpam-3479	377	79	∫	∫	PROPN
ejpam-3479	377	80	u	u	NOUN
ejpam-3479	377	81	∫	∫	PROPN
ejpam-3479	377	82	γ	γ	X
ejpam-3479	377	83	(	(	PUNCT
ejpam-3479	377	84	p	p	X
ejpam-3479	377	85	(	(	PUNCT
ejpam-3479	377	86	w0	w0	PROPN
ejpam-3479	377	87	)	)	PUNCT
ejpam-3479	377	88	+	+	CCONJ
ejpam-3479	378	1	(	(	PUNCT
ejpam-3479	379	1	i	i	PRON
ejpam-3479	379	2	−	−	PROPN
ejpam-3479	379	3	p	p	NOUN
ejpam-3479	379	4	)	)	PUNCT
ejpam-3479	379	5	(	(	PUNCT
ejpam-3479	379	6	∂ρ̂	∂ρ̂	VERB
ejpam-3479	379	7	∂ν	∂ν	PROPN
ejpam-3479	379	8	χγ	χγ	PROPN
ejpam-3479	379	9	)	)	PUNCT
ejpam-3479	379	10	)	)	PUNCT
ejpam-3479	380	1	(	(	PUNCT
ejpam-3479	380	2	m0	m0	PROPN
ejpam-3479	380	3	−	−	PROPN
ejpam-3479	380	4	∂y0	∂y0	PROPN
ejpam-3479	380	5	∂ν	∂ν	PROPN
ejpam-3479	380	6	)	)	PUNCT
ejpam-3479	380	7	dtdadγ	dtdadγ	PROPN
ejpam-3479	380	8	}	}	PUNCT
ejpam-3479	380	9	,	,	PUNCT
ejpam-3479	380	10	where	where	SCONJ
ejpam-3479	380	11	m0	m0	NOUN
ejpam-3479	380	12	is	be	AUX
ejpam-3479	380	13	a	a	DET
ejpam-3479	380	14	measure	measure	NOUN
ejpam-3479	380	15	of	of	ADP
ejpam-3479	380	16	the	the	DET
ejpam-3479	380	17	flux	flux	NOUN
ejpam-3479	380	18	of	of	ADP
ejpam-3479	380	19	the	the	DET
ejpam-3479	380	20	population	population	NOUN
ejpam-3479	380	21	taken	take	VERB
ejpam-3479	380	22	on	on	ADP
ejpam-3479	380	23	the	the	DET
ejpam-3479	380	24	observatory	observatory	ADJ
ejpam-3479	380	25	o	o	NOUN
ejpam-3479	380	26	∪	∪	ADP
ejpam-3479	380	27	γ	γ	NOUN
ejpam-3479	380	28	and	and	CCONJ
ejpam-3479	380	29	y0	y0	PROPN
ejpam-3479	380	30	is	be	AUX
ejpam-3479	380	31	solution	solution	NOUN
ejpam-3479	380	32	of	of	ADP
ejpam-3479	380	33	(	(	PUNCT
ejpam-3479	380	34	1	1	NUM
ejpam-3479	380	35	)	)	PUNCT
ejpam-3479	380	36	when	when	SCONJ
ejpam-3479	380	37	λ	λ	X
ejpam-3479	380	38	=	=	SYM
ejpam-3479	380	39	0	0	NUM
ejpam-3479	380	40	and	and	CCONJ
ejpam-3479	380	41	τ	τ	X
ejpam-3479	380	42	=	=	SYM
ejpam-3479	380	43	0	0	PROPN
ejpam-3479	380	44	.	.	PUNCT
ejpam-3479	381	1	references	reference	NOUN
ejpam-3479	381	2	1295	1295	NUM
ejpam-3479	381	3	references	reference	NOUN
ejpam-3479	381	4	[	[	X
ejpam-3479	381	5	1	1	NUM
ejpam-3479	381	6	]	]	PUNCT
ejpam-3479	381	7	m.langlais	m.langlais	NOUN
ejpam-3479	381	8	,	,	PUNCT
ejpam-3479	381	9	age	age	NOUN
ejpam-3479	381	10	-	-	PUNCT
ejpam-3479	381	11	dependent	dependent	ADJ
ejpam-3479	381	12	population	population	NOUN
ejpam-3479	381	13	diffusion	diffusion	NOUN
ejpam-3479	381	14	with	with	ADP
ejpam-3479	381	15	external	external	ADJ
ejpam-3479	381	16	constraint	constraint	NOUN
ejpam-3479	381	17	.	.	PUNCT
ejpam-3479	382	1	j.math.biology	j.math.biology	NOUN
ejpam-3479	382	2	14(1982):77	14(1982):77	PROPN
ejpam-3479	382	3	-	-	SYM
ejpam-3479	382	4	94	94	NUM
ejpam-3479	382	5	.	.	PUNCT
ejpam-3479	383	1	[	[	X
ejpam-3479	383	2	2	2	NUM
ejpam-3479	383	3	]	]	PUNCT
ejpam-3479	383	4	b.ainseba	b.ainseba	NOUN
ejpam-3479	383	5	,	,	PUNCT
ejpam-3479	383	6	exact	exact	ADJ
ejpam-3479	383	7	and	and	CCONJ
ejpam-3479	383	8	approximate	approximate	ADJ
ejpam-3479	383	9	controllability	controllability	NOUN
ejpam-3479	383	10	of	of	ADP
ejpam-3479	383	11	age	age	NOUN
ejpam-3479	383	12	and	and	CCONJ
ejpam-3479	383	13	space	space	NOUN
ejpam-3479	383	14	population	population	NOUN
ejpam-3479	383	15	dynamics	dynamic	NOUN
ejpam-3479	383	16	structured	structure	VERB
ejpam-3479	383	17	model.j.math.anal.app.(2002	model.j.math.anal.app.(2002	NOUN
ejpam-3479	383	18	)	)	PUNCT
ejpam-3479	383	19	.	.	PUNCT
ejpam-3479	384	1	[	[	X
ejpam-3479	384	2	3	3	X
ejpam-3479	384	3	]	]	PUNCT
ejpam-3479	384	4	b.ainseba	b.ainseba	NOUN
ejpam-3479	384	5	et	et	PROPN
ejpam-3479	384	6	m.langlais	m.langlais	PROPN
ejpam-3479	384	7	,	,	PUNCT
ejpam-3479	384	8	on	on	ADP
ejpam-3479	384	9	a	a	DET
ejpam-3479	384	10	population	population	NOUN
ejpam-3479	384	11	dynamics	dynamic	NOUN
ejpam-3479	384	12	control	control	VERB
ejpam-3479	384	13	problem	problem	NOUN
ejpam-3479	384	14	with	with	ADP
ejpam-3479	384	15	age	age	NOUN
ejpam-3479	384	16	dependence	dependence	NOUN
ejpam-3479	384	17	and	and	CCONJ
ejpam-3479	384	18	spatial	spatial	ADJ
ejpam-3479	384	19	structure.journal	structure.journal	PROPN
ejpam-3479	384	20	of	of	ADP
ejpam-3479	384	21	mathematical	mathematical	ADJ
ejpam-3479	384	22	analysis	analysis	NOUN
ejpam-3479	384	23	and	and	CCONJ
ejpam-3479	384	24	applications	application	NOUN
ejpam-3479	384	25	248(2000),455–474	248(2000),455–474	PROPN
ejpam-3479	384	26	.	.	PUNCT
ejpam-3479	385	1	[	[	X
ejpam-3479	385	2	4	4	X
ejpam-3479	385	3	]	]	PUNCT
ejpam-3479	385	4	b.	b.	PROPN
ejpam-3479	385	5	ainseba	ainseba	NOUN
ejpam-3479	385	6	et	et	PROPN
ejpam-3479	385	7	m.langlais	m.langlais	PROPN
ejpam-3479	385	8	,	,	PUNCT
ejpam-3479	385	9	sur	sur	PROPN
ejpam-3479	385	10	un	un	PROPN
ejpam-3479	385	11	probléme	probléme	PROPN
ejpam-3479	385	12	de	de	PROPN
ejpam-3479	385	13	contrle	contrle	PROPN
ejpam-3479	385	14	d’une	d’une	NUM
ejpam-3479	385	15	population	population	NOUN
ejpam-3479	385	16	structurée	structurée	PROPN
ejpam-3479	385	17	en	en	PROPN
ejpam-3479	385	18	ge	ge	PROPN
ejpam-3479	385	19	et	et	PROPN
ejpam-3479	385	20	en	en	PROPN
ejpam-3479	385	21	espace.c.r.acad.sci.paris	espace.c.r.acad.sci.paris	PROPN
ejpam-3479	385	22	,	,	PUNCT
ejpam-3479	385	23	t.323(1996	t.323(1996	PROPN
ejpam-3479	385	24	)	)	PUNCT
ejpam-3479	385	25	,	,	PUNCT
ejpam-3479	385	26	serie	serie	X
ejpam-3479	385	27	i	i	PRON
ejpam-3479	385	28	,	,	PUNCT
ejpam-3479	385	29	p.269–274	p.269–274	NOUN
ejpam-3479	385	30	.	.	PUNCT
ejpam-3479	386	1	[	[	X
ejpam-3479	386	2	5	5	NUM
ejpam-3479	386	3	]	]	PUNCT
ejpam-3479	386	4	b.ainseba	b.ainseba	NOUN
ejpam-3479	386	5	and	and	CCONJ
ejpam-3479	386	6	s.anita	s.anita	PROPN
ejpam-3479	386	7	,	,	PUNCT
ejpam-3479	386	8	local	local	ADJ
ejpam-3479	386	9	exact	exact	ADJ
ejpam-3479	386	10	controllability	controllability	NOUN
ejpam-3479	386	11	of	of	ADP
ejpam-3479	386	12	the	the	DET
ejpam-3479	386	13	age	age	NOUN
ejpam-3479	386	14	-	-	PUNCT
ejpam-3479	386	15	dependent	dependent	ADJ
ejpam-3479	386	16	population	population	NOUN
ejpam-3479	386	17	dynamics	dynamic	NOUN
ejpam-3479	386	18	with	with	ADP
ejpam-3479	386	19	diffusion	diffusion	NOUN
ejpam-3479	386	20	.	.	PUNCT
ejpam-3479	387	1	abstract	abstract	PROPN
ejpam-3479	387	2	appl.anal.6(2001	appl.anal.6(2001	PROPN
ejpam-3479	387	3	)	)	PUNCT
ejpam-3479	387	4	357	357	NUM
ejpam-3479	387	5	-	-	SYM
ejpam-3479	387	6	368	368	NUM
ejpam-3479	387	7	.	.	PUNCT
ejpam-3479	388	1	[	[	X
ejpam-3479	388	2	6	6	NUM
ejpam-3479	388	3	]	]	ADJ
ejpam-3479	388	4	h.brezis	h.brezi	NOUN
ejpam-3479	388	5	,	,	PUNCT
ejpam-3479	388	6	analyse	analyse	PROPN
ejpam-3479	388	7	fonctionnelle.théorie	fonctionnelle.théorie	PROPN
ejpam-3479	388	8	et	et	NOUN
ejpam-3479	388	9	application	application	NOUN
ejpam-3479	388	10	.	.	PUNCT
ejpam-3479	389	1	masson(1983	masson(1983	NUM
ejpam-3479	389	2	)	)	PUNCT
ejpam-3479	390	1	[	[	X
ejpam-3479	390	2	7	7	X
ejpam-3479	390	3	]	]	PUNCT
ejpam-3479	390	4	a.fursikov	a.fursikov	NOUN
ejpam-3479	390	5	,	,	PUNCT
ejpam-3479	390	6	o.imanualov	o.imanualov	NOUN
ejpam-3479	390	7	,	,	PUNCT
ejpam-3479	390	8	controllability	controllability	NOUN
ejpam-3479	390	9	of	of	ADP
ejpam-3479	390	10	evolution	evolution	NOUN
ejpam-3479	390	11	equation.lecture	equation.lecture	NOUN
ejpam-3479	390	12	notes	note	NOUN
ejpam-3479	390	13	series	series	PROPN
ejpam-3479	390	14	34	34	NUM
ejpam-3479	390	15	,	,	PUNCT
ejpam-3479	390	16	rim	rim	PROPN
ejpam-3479	390	17	-	-	PUNCT
ejpam-3479	390	18	garc	garc	PROPN
ejpam-3479	390	19	,	,	PUNCT
ejpam-3479	390	20	seoul	seoul	PROPN
ejpam-3479	390	21	national	national	PROPN
ejpam-3479	390	22	university,1996	university,1996	PROPN
ejpam-3479	390	23	.	.	PUNCT
ejpam-3479	391	1	[	[	X
ejpam-3479	391	2	8	8	NUM
ejpam-3479	391	3	]	]	SYM
ejpam-3479	391	4	m.giovanna	m.giovanna	NOUN
ejpam-3479	391	5	and	and	CCONJ
ejpam-3479	391	6	m.langlais	m.langlais	NOUN
ejpam-3479	391	7	,	,	PUNCT
ejpam-3479	391	8	age	age	NOUN
ejpam-3479	391	9	-	-	PUNCT
ejpam-3479	391	10	dependent	dependent	ADJ
ejpam-3479	391	11	population	population	NOUN
ejpam-3479	391	12	diffusion	diffusion	NOUN
ejpam-3479	391	13	with	with	ADP
ejpam-3479	391	14	external	external	ADJ
ejpam-3479	391	15	constraint	constraint	NOUN
ejpam-3479	391	16	.	.	PUNCT
ejpam-3479	392	1	j.math.biology(1982	j.math.biology(1982	NOUN
ejpam-3479	392	2	)	)	PUNCT
ejpam-3479	392	3	14:77	14:77	NUM
ejpam-3479	392	4	-	-	SYM
ejpam-3479	392	5	94	94	NUM
ejpam-3479	392	6	.	.	PUNCT
ejpam-3479	393	1	[	[	X
ejpam-3479	393	2	9	9	NUM
ejpam-3479	393	3	]	]	X
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ejpam-3479	393	5	and	and	CCONJ
ejpam-3479	393	6	o.nakoulima	o.nakoulima	NOUN
ejpam-3479	393	7	,	,	PUNCT
ejpam-3479	393	8	sentinels	sentinel	NOUN
ejpam-3479	393	9	with	with	ADP
ejpam-3479	393	10	given	give	VERB
ejpam-3479	393	11	sensitivity	sensitivity	NOUN
ejpam-3479	393	12	.	.	PUNCT
ejpam-3479	394	1	european	european	PROPN
ejpam-3479	394	2	journal	journal	PROPN
ejpam-3479	394	3	of	of	ADP
ejpam-3479	394	4	applied	apply	VERB
ejpam-3479	394	5	mathematics	mathematic	NOUN
ejpam-3479	394	6	,	,	PUNCT
ejpam-3479	394	7	vol.19(2008	vol.19(2008	NOUN
ejpam-3479	394	8	)	)	PUNCT
ejpam-3479	394	9	,	,	PUNCT
ejpam-3479	394	10	pp.21	pp.21	NOUN
ejpam-3479	394	11	-	-	SYM
ejpam-3479	394	12	40	40	NUM
ejpam-3479	394	13	.	.	PUNCT
ejpam-3479	395	1	[	[	X
ejpam-3479	395	2	10	10	NUM
ejpam-3479	395	3	]	]	X
ejpam-3479	395	4	g.m.mophou	g.m.mophou	NOUN
ejpam-3479	395	5	and	and	CCONJ
ejpam-3479	395	6	j.p.puel	j.p.puel	PROPN
ejpam-3479	395	7	,	,	PUNCT
ejpam-3479	395	8	boundary	boundary	ADJ
ejpam-3479	395	9	sentinels	sentinel	NOUN
ejpam-3479	395	10	with	with	ADP
ejpam-3479	395	11	given	give	VERB
ejpam-3479	395	12	sensitivity.rev.mat.complut	sensitivity.rev.mat.complut	NOUN
ejpam-3479	395	13	.	.	PUNCT
ejpam-3479	395	14	vol.22(2009	vol.22(2009	NUM
ejpam-3479	395	15	)	)	PUNCT
ejpam-3479	395	16	,	,	PUNCT
ejpam-3479	395	17	no.1,165	no.1,165	PROPN
ejpam-3479	395	18	-	-	PUNCT
ejpam-3479	395	19	185	185	NUM
ejpam-3479	395	20	.	.	PUNCT
ejpam-3479	396	1	[	[	X
ejpam-3479	396	2	11	11	NUM
ejpam-3479	396	3	]	]	PUNCT
ejpam-3479	396	4	j.l.lions	j.l.lion	NOUN
ejpam-3479	396	5	,	,	PUNCT
ejpam-3479	396	6	sentinelles	sentinelle	NOUN
ejpam-3479	396	7	pour	pour	VERB
ejpam-3479	396	8	les	le	NOUN
ejpam-3479	396	9	systemes	systeme	NOUN
ejpam-3479	396	10	distribués	distribués	AUX
ejpam-3479	396	11	données	donnée	NOUN
ejpam-3479	396	12	incompltes.recherches	incompltes.recherches	X
ejpam-3479	396	13	en	en	ADP
ejpam-3479	396	14	mathématiques	mathématiques	PROPN
ejpam-3479	396	15	appliques	applique	NOUN
ejpam-3479	396	16	,	,	PUNCT
ejpam-3479	396	17	vol.21	vol.21	NOUN
ejpam-3479	396	18	,	,	PUNCT
ejpam-3479	396	19	masson	masson	PROPN
ejpam-3479	396	20	,	,	PUNCT
ejpam-3479	396	21	paris,1992	paris,1992	NOUN
ejpam-3479	396	22	.	.	PUNCT
ejpam-3479	397	1	[	[	X
ejpam-3479	397	2	12	12	NUM
ejpam-3479	397	3	]	]	X
ejpam-3479	397	4	j.l.lions	j.l.lion	NOUN
ejpam-3479	397	5	and	and	CCONJ
ejpam-3479	397	6	e.magenes	e.magene	NOUN
ejpam-3479	397	7	,	,	PUNCT
ejpam-3479	397	8	problémes	problémes	PROPN
ejpam-3479	397	9	aux	aux	PROPN
ejpam-3479	397	10	limites	limites	X
ejpam-3479	397	11	non	non	PROPN
ejpam-3479	397	12	homogénes	homogénes	PROPN
ejpam-3479	397	13	et	et	PROPN
ejpam-3479	397	14	applications	application	NOUN
ejpam-3479	397	15	.	.	PUNCT
ejpam-3479	398	1	paris	paris	PROPN
ejpam-3479	398	2	,	,	PUNCT
ejpam-3479	398	3	dunod,1968,vol	dunod,1968,vol	PROPN
ejpam-3479	398	4	.	.	PUNCT
ejpam-3479	399	1	1et	1et	ADJ
ejpam-3479	399	2	2	2	NUM
ejpam-3479	400	1	[	[	SYM
ejpam-3479	400	2	13	13	NUM
ejpam-3479	400	3	]	]	X
ejpam-3479	400	4	o.	o.	PROPN
ejpam-3479	400	5	nakoulima	nakoulima	PROPN
ejpam-3479	400	6	,	,	PUNCT
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ejpam-3479	400	8	zéro	zéro	NUM
ejpam-3479	400	9	avec	avec	X
ejpam-3479	400	10	contraintes	contraintes	PROPN
ejpam-3479	400	11	sur	sur	PROPN
ejpam-3479	400	12	le	le	X
ejpam-3479	400	13	contrle	contrle	PROPN
ejpam-3479	400	14	.	.	PUNCT
ejpam-3479	401	1	c.r.acad.sci	c.r.acad.sci	PROPN
ejpam-3479	401	2	.	.	PUNCT
ejpam-3479	402	1	paris	paris	PROPN
ejpam-3479	402	2	,	,	PUNCT
ejpam-3479	402	3	ser.i	ser.i	PROPN
ejpam-3479	402	4	339/6	339/6	NUM
ejpam-3479	402	5	(	(	PUNCT
ejpam-3479	402	6	2004	2004	NUM
ejpam-3479	402	7	)	)	PUNCT
ejpam-3479	402	8	405	405	NUM
ejpam-3479	402	9	-	-	SYM
ejpam-3479	402	10	410	410	NUM
ejpam-3479	402	11	.	.	PUNCT
ejpam-3479	403	1	[	[	X
ejpam-3479	403	2	14	14	NUM
ejpam-3479	403	3	]	]	X
ejpam-3479	403	4	o.	o.	PROPN
ejpam-3479	403	5	nakoulima	nakoulima	PROPN
ejpam-3479	403	6	,	,	PUNCT
ejpam-3479	403	7	a	a	DET
ejpam-3479	403	8	revision	revision	NOUN
ejpam-3479	403	9	of	of	ADP
ejpam-3479	403	10	j.-l	j.-l	PROPN
ejpam-3479	403	11	.	.	PUNCT
ejpam-3479	404	1	lions	lion	NOUN
ejpam-3479	404	2	’	'	PUNCT
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ejpam-3479	404	5	sentinels	sentinel	NOUN
ejpam-3479	404	6	.	.	PUNCT
ejpam-3479	405	1	portugal	portugal	PROPN
ejpam-3479	405	2	.	.	PUNCT
ejpam-3479	405	3	math	math	PROPN
ejpam-3479	405	4	.	.	PUNCT
ejpam-3479	406	1	(	(	PUNCT
ejpam-3479	406	2	n.s	n.s	PROPN
ejpam-3479	406	3	)	)	PUNCT
ejpam-3479	406	4	vol.65	vol.65	PROPN
ejpam-3479	406	5	,	,	PUNCT
ejpam-3479	406	6	fasc	fasc	PROPN
ejpam-3479	406	7	.	.	PROPN
ejpam-3479	406	8	1(2008	1(2008	NUM
ejpam-3479	406	9	)	)	PUNCT
ejpam-3479	406	10	,	,	PUNCT
ejpam-3479	406	11	1	1	NUM
ejpam-3479	406	12	-	-	SYM
ejpam-3479	406	13	22	22	NUM
ejpam-3479	406	14	.	.	PUNCT
ejpam-3479	407	1	[	[	X
ejpam-3479	407	2	15	15	NUM
ejpam-3479	407	3	]	]	X
ejpam-3479	407	4	o.nakoulima	o.nakoulima	NOUN
ejpam-3479	407	5	and	and	CCONJ
ejpam-3479	407	6	s.sawadogo	s.sawadogo	ADJ
ejpam-3479	407	7	,	,	PUNCT
ejpam-3479	407	8	internal	internal	ADJ
ejpam-3479	407	9	pollution	pollution	NOUN
ejpam-3479	407	10	and	and	CCONJ
ejpam-3479	407	11	discriminating	discriminate	VERB
ejpam-3479	407	12	sentinel	sentinel	NOUN
ejpam-3479	407	13	in	in	ADP
ejpam-3479	407	14	population	population	NOUN
ejpam-3479	407	15	dynamics	dynamic	NOUN
ejpam-3479	407	16	problem	problem	NOUN
ejpam-3479	407	17	.	.	PUNCT
ejpam-3479	408	1	international	international	ADJ
ejpam-3479	408	2	journal	journal	PROPN
ejpam-3479	408	3	of	of	ADP
ejpam-3479	408	4	evolution	evolution	NOUN
ejpam-3479	408	5	equations	equation	NOUN
ejpam-3479	408	6	,	,	PUNCT
ejpam-3479	408	7	vol	vol	NOUN
ejpam-3479	408	8	2	2	NUM
ejpam-3479	408	9	,	,	PUNCT
ejpam-3479	408	10	n01,pp.29	n01,pp.29	NOUN
ejpam-3479	408	11	-	-	NOUN
ejpam-3479	408	12	46	46	NUM
ejpam-3479	408	13	,	,	PUNCT
ejpam-3479	408	14	2007	2007	NUM
ejpam-3479	408	15	.	.	PUNCT
ejpam-3479	409	1	references	reference	NOUN
ejpam-3479	409	2	1296	1296	NUM
ejpam-3479	409	3	[	[	X
ejpam-3479	409	4	16	16	NUM
ejpam-3479	409	5	]	]	SYM
ejpam-3479	409	6	s.sawadogo	s.sawadogo	NOUN
ejpam-3479	409	7	,	,	PUNCT
ejpam-3479	409	8	control	control	NOUN
ejpam-3479	409	9	of	of	ADP
ejpam-3479	409	10	a	a	DET
ejpam-3479	409	11	migration	migration	NOUN
ejpam-3479	409	12	problem	problem	NOUN
ejpam-3479	409	13	of	of	ADP
ejpam-3479	409	14	a	a	DET
ejpam-3479	409	15	population	population	NOUN
ejpam-3479	409	16	by	by	ADP
ejpam-3479	409	17	the	the	DET
ejpam-3479	409	18	sentinel	sentinel	ADJ
ejpam-3479	409	19	method	method	NOUN
ejpam-3479	409	20	,	,	PUNCT
ejpam-3479	409	21	journal	journal	NOUN
ejpam-3479	409	22	of	of	ADP
ejpam-3479	409	23	nonlinear	nonlinear	ADJ
ejpam-3479	409	24	evolution	evolution	NOUN
ejpam-3479	409	25	equation	equation	NOUN
ejpam-3479	409	26	and	and	CCONJ
ejpam-3479	409	27	application	application	NOUN
ejpam-3479	409	28	,	,	PUNCT
ejpam-3479	409	29	i	i	PROPN
ejpam-3479	409	30	d	d	PROPN
ejpam-3479	409	31	jneea-1810291	jneea-1810291	PROPN
ejpam-3479	409	32	(	(	PUNCT
ejpam-3479	409	33	accepted	accept	VERB
ejpam-3479	409	34	for	for	ADP
ejpam-3479	409	35	publication	publication	NOUN
ejpam-3479	409	36	)	)	PUNCT
ejpam-3479	410	1	[	[	X
ejpam-3479	410	2	17	17	NUM
ejpam-3479	410	3	]	]	PUNCT
ejpam-3479	410	4	a.	a.	NOUN
ejpam-3479	410	5	ouédraogo	ouédraogo	PROPN
ejpam-3479	410	6	,	,	PUNCT
ejpam-3479	410	7	o.	o.	NOUN
ejpam-3479	410	8	traoré	traoré	NOUN
ejpam-3479	410	9	,	,	PUNCT
ejpam-3479	410	10	sur	sur	PROPN
ejpam-3479	410	11	un	un	PROPN
ejpam-3479	410	12	probléme	probléme	PROPN
ejpam-3479	410	13	de	de	X
ejpam-3479	410	14	dynamique	dynamique	PROPN
ejpam-3479	410	15	des	des	PROPN
ejpam-3479	410	16	populations	population	NOUN
ejpam-3479	410	17	,	,	PUNCT
ejpam-3479	410	18	imhotep	imhotep	NOUN
ejpam-3479	410	19	.	.	PUNCT
ejpam-3479	411	1	vol	vol	NOUN
ejpam-3479	411	2	4	4	NUM
ejpam-3479	411	3	n01(2003	n01(2003	NOUN
ejpam-3479	411	4	)	)	PUNCT
ejpam-3479	411	5	.	.	PUNCT
ejpam-3479	412	1	[	[	X
ejpam-3479	412	2	18	18	NUM
ejpam-3479	412	3	]	]	X
ejpam-3479	412	4	o.	o.	NOUN
ejpam-3479	412	5	traoré	traoré	NOUN
ejpam-3479	412	6	,	,	PUNCT
ejpam-3479	412	7	null	null	ADJ
ejpam-3479	412	8	controllability	controllability	NOUN
ejpam-3479	412	9	of	of	ADP
ejpam-3479	412	10	a	a	DET
ejpam-3479	412	11	nonlinear	nonlinear	ADJ
ejpam-3479	412	12	population	population	NOUN
ejpam-3479	412	13	dynamics	dynamic	NOUN
ejpam-3479	412	14	problem	problem	NOUN
ejpam-3479	412	15	,	,	PUNCT
ejpam-3479	412	16	e	e	PROPN
ejpam-3479	412	17	international	international	ADJ
ejpam-3479	412	18	journal	journal	NOUN
ejpam-3479	412	19	of	of	ADP
ejpam-3479	412	20	mathematics	mathematics	PROPN
ejpam-3479	412	21	and	and	CCONJ
ejpam-3479	412	22	mathematical	mathematical	ADJ
ejpam-3479	412	23	sciences	science	NOUN
ejpam-3479	412	24	,	,	PUNCT
ejpam-3479	412	25	vol	vol	NOUN
ejpam-3479	412	26	26	26	NUM
ejpam-3479	412	27	,	,	PUNCT
ejpam-3479	412	28	article	article	NOUN
ejpam-3479	412	29	i	i	PROPN
ejpam-3479	412	30	d	d	PROPN
ejpam-3479	412	31	49279	49279	NUM
ejpam-3479	412	32	,	,	PUNCT
ejpam-3479	412	33	pp	pp	ADJ
ejpam-3479	412	34	.	.	PUNCT
ejpam-3479	413	1	1	1	NUM
ejpam-3479	413	2	-	-	SYM
ejpam-3479	413	3	20	20	NUM
ejpam-3479	413	4	.	.	PUNCT
ejpam-3479	414	1	[	[	X
ejpam-3479	414	2	19	19	NUM
ejpam-3479	414	3	]	]	X
ejpam-3479	414	4	j.	j.	PROPN
ejpam-3479	414	5	c.	c.	PROPN
ejpam-3479	414	6	saut	saut	PROPN
ejpam-3479	414	7	and	and	CCONJ
ejpam-3479	414	8	b.	b.	PROPN
ejpam-3479	414	9	scheure	scheure	NOUN
ejpam-3479	414	10	,	,	PUNCT
ejpam-3479	414	11	unique	unique	ADJ
ejpam-3479	414	12	continuation	continuation	NOUN
ejpam-3479	414	13	for	for	ADP
ejpam-3479	414	14	some	some	DET
ejpam-3479	414	15	evolution	evolution	NOUN
ejpam-3479	414	16	equation	equation	NOUN
ejpam-3479	414	17	,	,	PUNCT
ejpam-3479	414	18	j.differential	j.differential	ADJ
ejpam-3479	414	19	equation	equation	NOUN
ejpam-3479	414	20	,	,	PUNCT
ejpam-3479	414	21	66	66	NUM
ejpam-3479	414	22	(	(	PUNCT
ejpam-3479	414	23	1987	1987	NUM
ejpam-3479	414	24	)	)	PUNCT
ejpam-3479	414	25	n0.1	n0.1	PROPN
ejpam-3479	414	26	,	,	PUNCT
ejpam-3479	414	27	118	118	NUM
ejpam-3479	414	28	-	-	SYM
ejpam-3479	414	29	139	139	NUM
ejpam-3479	414	30	.	.	PUNCT
ejpam-3479	415	1	[	[	X
ejpam-3479	415	2	20	20	NUM
ejpam-3479	415	3	]	]	PUNCT
ejpam-3479	415	4	j.-p	j.-p	PROPN
ejpam-3479	415	5	.	.	PUNCT
ejpam-3479	416	1	kernévez	kernévez	PROPN
ejpam-3479	416	2	,	,	PUNCT
ejpam-3479	416	3	the	the	DET
ejpam-3479	416	4	sentinel	sentinel	ADJ
ejpam-3479	416	5	method	method	NOUN
ejpam-3479	416	6	and	and	CCONJ
ejpam-3479	416	7	its	its	PRON
ejpam-3479	416	8	application	application	NOUN
ejpam-3479	416	9	to	to	ADP
ejpam-3479	416	10	environmental	environmental	ADJ
ejpam-3479	416	11	pollution	pollution	NOUN
ejpam-3479	416	12	problem	problem	NOUN
ejpam-3479	416	13	,	,	PUNCT
ejpam-3479	416	14	crc	crc	PROPN
ejpam-3479	416	15	mathematical	mathematical	PROPN
ejpam-3479	416	16	modelling	modelling	NOUN
ejpam-3479	416	17	series	series	PROPN
ejpam-3479	416	18	,	,	PUNCT
ejpam-3479	416	19	crc	crc	PROPN
ejpam-3479	416	20	press	press	PROPN
ejpam-3479	416	21	,	,	PUNCT
ejpam-3479	416	22	boca	boca	PROPN
ejpam-3479	416	23	raton	raton	PROPN
ejpam-3479	416	24	,	,	PUNCT
ejpam-3479	416	25	fl	fl	PROPN
ejpam-3479	416	26	,	,	PUNCT
ejpam-3479	416	27	(	(	PUNCT
ejpam-3479	416	28	1997	1997	NUM
ejpam-3479	416	29	)	)	PUNCT
ejpam-3479	416	30	.	.	PUNCT
ejpam-3479	417	1	[	[	X
ejpam-3479	417	2	21	21	NUM
ejpam-3479	417	3	]	]	X
ejpam-3479	417	4	y.	y.	PROPN
ejpam-3479	417	5	simporé	simporé	PROPN
ejpam-3479	417	6	and	and	CCONJ
ejpam-3479	417	7	o.	o.	PROPN
ejpam-3479	417	8	traoré	traoré	NOUN
ejpam-3479	417	9	,	,	PUNCT
ejpam-3479	417	10	null	null	ADJ
ejpam-3479	417	11	controllability	controllability	NOUN
ejpam-3479	417	12	of	of	ADP
ejpam-3479	417	13	a	a	DET
ejpam-3479	417	14	nonlinear	nonlinear	ADJ
ejpam-3479	417	15	dissipative	dissipative	ADJ
ejpam-3479	417	16	system	system	NOUN
ejpam-3479	417	17	and	and	CCONJ
ejpam-3479	417	18	application	application	NOUN
ejpam-3479	417	19	to	to	ADP
ejpam-3479	417	20	the	the	DET
ejpam-3479	417	21	detection	detection	NOUN
ejpam-3479	417	22	of	of	ADP
ejpam-3479	417	23	the	the	DET
ejpam-3479	417	24	incomplete	incomplete	ADJ
ejpam-3479	417	25	parameter	parameter	NOUN
ejpam-3479	417	26	for	for	ADP
ejpam-3479	417	27	a	a	DET
ejpam-3479	417	28	nonlinear	nonlinear	ADJ
ejpam-3479	417	29	population	population	NOUN
ejpam-3479	417	30	dynamics	dynamic	NOUN
ejpam-3479	417	31	model	model	NOUN
ejpam-3479	417	32	,	,	PUNCT
ejpam-3479	417	33	international	international	ADJ
ejpam-3479	417	34	journal	journal	NOUN
ejpam-3479	417	35	of	of	ADP
ejpam-3479	417	36	mathematics	mathematics	PROPN
ejpam-3479	417	37	and	and	CCONJ
ejpam-3479	417	38	mathematical	mathematical	ADJ
ejpam-3479	417	39	sciences	science	NOUN
ejpam-3479	417	40	article	article	NOUN
ejpam-3479	417	41	i	i	PROPN
ejpam-3479	417	42	d	d	PROPN
ejpam-3479	417	43	2820613	2820613	NUM
ejpam-3479	417	44	,	,	PUNCT
ejpam-3479	417	45	(	(	PUNCT
ejpam-3479	417	46	2016	2016	NUM
ejpam-3479	417	47	)	)	PUNCT
ejpam-3479	417	48	.	.	PUNCT
ejpam-3479	418	1	[	[	X
ejpam-3479	418	2	22	22	NUM
ejpam-3479	418	3	]	]	PUNCT
ejpam-3479	418	4	lions	lion	NOUN
ejpam-3479	418	5	,	,	PUNCT
ejpam-3479	418	6	j.l	j.l	PROPN
ejpam-3479	418	7	.	.	PROPN
ejpam-3479	418	8	and	and	CCONJ
ejpam-3479	418	9	magenes	magene	NOUN
ejpam-3479	418	10	,	,	PUNCT
ejpam-3479	418	11	e.	e.	PROPN
ejpam-3479	418	12	nonhomogenous	nonhomogenous	PROPN
ejpam-3479	418	13	boundary	boundary	ADJ
ejpam-3479	418	14	value	value	NOUN
ejpam-3479	418	15	problem	problem	NOUN
ejpam-3479	418	16	and	and	CCONJ
ejpam-3479	418	17	applications	application	NOUN
ejpam-3479	418	18	,	,	PUNCT
ejpam-3479	418	19	grundlehren	grundlehren	PROPN
ejpam-3479	418	20	b	b	PROPN
ejpam-3479	418	21	,	,	PUNCT
ejpam-3479	418	22	181(1972	181(1972	NUM
ejpam-3479	418	23	)	)	PUNCT
ejpam-3479	418	24	,	,	PUNCT
ejpam-3479	418	25	springer	springer	NOUN
ejpam-3479	418	26	verlag	verlag	PROPN
ejpam-3479	418	27	.	.	PUNCT