id	sid	tid	token	lemma	pos
ejpam-3459	1	1	european	european	PROPN
ejpam-3459	1	2	journal	journal	PROPN
ejpam-3459	1	3	of	of	ADP
ejpam-3459	1	4	pure	pure	ADJ
ejpam-3459	1	5	and	and	CCONJ
ejpam-3459	1	6	applied	apply	VERB
ejpam-3459	1	7	mathematics	mathematic	NOUN
ejpam-3459	1	8	vol	vol	NOUN
ejpam-3459	1	9	.	.	PROPN
ejpam-3459	2	1	12	12	NUM
ejpam-3459	2	2	,	,	PUNCT
ejpam-3459	2	3	no	no	INTJ
ejpam-3459	2	4	.	.	NOUN
ejpam-3459	2	5	3	3	NUM
ejpam-3459	2	6	,	,	PUNCT
ejpam-3459	2	7	2019	2019	NUM
ejpam-3459	2	8	,	,	PUNCT
ejpam-3459	2	9	870	870	NUM
ejpam-3459	2	10	-	-	SYM
ejpam-3459	2	11	892	892	NUM
ejpam-3459	2	12	issn	issn	PROPN
ejpam-3459	2	13	1307	1307	NUM
ejpam-3459	2	14	-	-	SYM
ejpam-3459	2	15	5543	5543	NUM
ejpam-3459	2	16	–	–	PUNCT
ejpam-3459	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3459	2	18	published	publish	VERB
ejpam-3459	2	19	by	by	ADP
ejpam-3459	2	20	new	new	PROPN
ejpam-3459	2	21	york	york	PROPN
ejpam-3459	2	22	business	business	PROPN
ejpam-3459	2	23	global	global	PROPN
ejpam-3459	2	24	simultaneous	simultaneous	ADJ
ejpam-3459	2	25	null	null	ADJ
ejpam-3459	2	26	controllability	controllability	NOUN
ejpam-3459	2	27	for	for	ADP
ejpam-3459	2	28	two	two	NUM
ejpam-3459	2	29	stroke	stroke	NOUN
ejpam-3459	2	30	nonlinear	nonlinear	PROPN
ejpam-3459	2	31	systems	system	NOUN
ejpam-3459	2	32	:	:	PUNCT
ejpam-3459	2	33	application	application	NOUN
ejpam-3459	2	34	to	to	ADP
ejpam-3459	2	35	the	the	DET
ejpam-3459	2	36	sentinel	sentinel	NOUN
ejpam-3459	2	37	of	of	ADP
ejpam-3459	2	38	detection	detection	NOUN
ejpam-3459	2	39	in	in	ADP
ejpam-3459	2	40	population	population	NOUN
ejpam-3459	2	41	dynamics	dynamic	NOUN
ejpam-3459	2	42	model	model	NOUN
ejpam-3459	2	43	with	with	ADP
ejpam-3459	2	44	incomplete	incomplete	ADJ
ejpam-3459	2	45	data	datum	NOUN
ejpam-3459	2	46	cédric	cédric	PROPN
ejpam-3459	2	47	kpèbbèwèrè	kpèbbèwèrè	PROPN
ejpam-3459	2	48	somé1	somé1	NOUN
ejpam-3459	2	49	,	,	PUNCT
ejpam-3459	2	50	somdouda	somdouda	NOUN
ejpam-3459	2	51	sawadogo2,∗	sawadogo2,∗	PROPN
ejpam-3459	2	52	1	1	NUM
ejpam-3459	2	53	département	département	PROPN
ejpam-3459	2	54	de	de	X
ejpam-3459	2	55	mathématiques	mathématiques	PROPN
ejpam-3459	2	56	,	,	PUNCT
ejpam-3459	2	57	sciences	science	NOUN
ejpam-3459	2	58	exactes	exact	VERB
ejpam-3459	2	59	et	et	NOUN
ejpam-3459	2	60	appliquées	appliquée	NOUN
ejpam-3459	2	61	,	,	PUNCT
ejpam-3459	2	62	université	université	ADJ
ejpam-3459	2	63	joseph	joseph	PROPN
ejpam-3459	2	64	ki	ki	PROPN
ejpam-3459	2	65	-	-	PUNCT
ejpam-3459	2	66	zerbo	zerbo	PROPN
ejpam-3459	2	67	,	,	PUNCT
ejpam-3459	2	68	ouagadougou	ouagadougou	PROPN
ejpam-3459	2	69	,	,	PUNCT
ejpam-3459	2	70	burkina	burkina	PROPN
ejpam-3459	2	71	faso	faso	PROPN
ejpam-3459	2	72	2	2	NUM
ejpam-3459	2	73	département	département	PROPN
ejpam-3459	2	74	de	de	X
ejpam-3459	2	75	mathématiques	mathématiques	PROPN
ejpam-3459	2	76	,	,	PUNCT
ejpam-3459	2	77	institut	institut	PROPN
ejpam-3459	2	78	des	des	PROPN
ejpam-3459	2	79	sciences	sciences	PROPN
ejpam-3459	2	80	,	,	PUNCT
ejpam-3459	2	81	ouagadougou	ouagadougou	PROPN
ejpam-3459	2	82	,	,	PUNCT
ejpam-3459	2	83	burkina	burkina	PROPN
ejpam-3459	2	84	faso	faso	PROPN
ejpam-3459	2	85	abstract	abstract	PROPN
ejpam-3459	2	86	.	.	PUNCT
ejpam-3459	3	1	this	this	DET
ejpam-3459	3	2	paper	paper	NOUN
ejpam-3459	3	3	deals	deal	NOUN
ejpam-3459	3	4	with	with	ADP
ejpam-3459	3	5	the	the	DET
ejpam-3459	3	6	simultaneous	simultaneous	ADJ
ejpam-3459	3	7	null	null	ADJ
ejpam-3459	3	8	controllability	controllability	NOUN
ejpam-3459	3	9	for	for	ADP
ejpam-3459	3	10	some	some	DET
ejpam-3459	3	11	nonlinear	nonlinear	ADJ
ejpam-3459	3	12	two	two	NUM
ejpam-3459	3	13	stroke	stroke	NOUN
ejpam-3459	3	14	systems	system	NOUN
ejpam-3459	3	15	.	.	PUNCT
ejpam-3459	4	1	we	we	PRON
ejpam-3459	4	2	shall	shall	AUX
ejpam-3459	4	3	solve	solve	VERB
ejpam-3459	4	4	this	this	DET
ejpam-3459	4	5	problem	problem	NOUN
ejpam-3459	4	6	by	by	ADP
ejpam-3459	4	7	transforming	transform	VERB
ejpam-3459	4	8	the	the	DET
ejpam-3459	4	9	simultaneous	simultaneous	ADJ
ejpam-3459	4	10	null	null	ADJ
ejpam-3459	4	11	controllability	controllability	NOUN
ejpam-3459	4	12	of	of	ADP
ejpam-3459	4	13	uncoupled	uncoupled	ADJ
ejpam-3459	4	14	initial	initial	ADJ
ejpam-3459	4	15	systems	system	NOUN
ejpam-3459	4	16	into	into	ADP
ejpam-3459	4	17	a	a	DET
ejpam-3459	4	18	null	null	ADJ
ejpam-3459	4	19	controllability	controllability	NOUN
ejpam-3459	4	20	of	of	ADP
ejpam-3459	4	21	a	a	DET
ejpam-3459	4	22	coupled	couple	VERB
ejpam-3459	4	23	system	system	NOUN
ejpam-3459	4	24	via	via	ADP
ejpam-3459	4	25	a	a	DET
ejpam-3459	4	26	change	change	NOUN
ejpam-3459	4	27	of	of	ADP
ejpam-3459	4	28	variables	variable	NOUN
ejpam-3459	4	29	.	.	PUNCT
ejpam-3459	5	1	this	this	DET
ejpam-3459	5	2	last	last	ADJ
ejpam-3459	5	3	problem	problem	NOUN
ejpam-3459	5	4	is	be	AUX
ejpam-3459	5	5	solved	solve	VERB
ejpam-3459	5	6	thanks	thank	NOUN
ejpam-3459	5	7	to	to	ADP
ejpam-3459	5	8	a	a	DET
ejpam-3459	5	9	global	global	ADJ
ejpam-3459	5	10	carleman	carleman	NOUN
ejpam-3459	5	11	inequality	inequality	NOUN
ejpam-3459	5	12	,	,	PUNCT
ejpam-3459	5	13	appropriates	appropriate	VERB
ejpam-3459	5	14	estimates	estimate	NOUN
ejpam-3459	5	15	adapted	adapt	VERB
ejpam-3459	5	16	to	to	ADP
ejpam-3459	5	17	the	the	DET
ejpam-3459	5	18	system	system	NOUN
ejpam-3459	5	19	and	and	CCONJ
ejpam-3459	5	20	via	via	ADP
ejpam-3459	5	21	some	some	DET
ejpam-3459	5	22	fixed	fix	VERB
ejpam-3459	5	23	point	point	NOUN
ejpam-3459	5	24	theorems	theorem	NOUN
ejpam-3459	5	25	.	.	PUNCT
ejpam-3459	6	1	the	the	DET
ejpam-3459	6	2	obtained	obtain	VERB
ejpam-3459	6	3	results	result	NOUN
ejpam-3459	6	4	are	be	AUX
ejpam-3459	6	5	used	use	VERB
ejpam-3459	6	6	to	to	PART
ejpam-3459	6	7	build	build	VERB
ejpam-3459	6	8	a	a	DET
ejpam-3459	6	9	simultaneous	simultaneous	ADJ
ejpam-3459	6	10	sentinel	sentinel	NOUN
ejpam-3459	6	11	of	of	ADP
ejpam-3459	6	12	detection	detection	NOUN
ejpam-3459	6	13	in	in	ADP
ejpam-3459	6	14	a	a	DET
ejpam-3459	6	15	population	population	NOUN
ejpam-3459	6	16	dynamics	dynamic	NOUN
ejpam-3459	6	17	model	model	NOUN
ejpam-3459	6	18	with	with	ADP
ejpam-3459	6	19	incomplete	incomplete	ADJ
ejpam-3459	6	20	data	datum	NOUN
ejpam-3459	6	21	.	.	PUNCT
ejpam-3459	7	1	2010	2010	NUM
ejpam-3459	7	2	mathematics	mathematic	NOUN
ejpam-3459	7	3	subject	subject	NOUN
ejpam-3459	7	4	classifications	classification	NOUN
ejpam-3459	7	5	:	:	PUNCT
ejpam-3459	7	6	49j20	49j20	NUM
ejpam-3459	7	7	,	,	PUNCT
ejpam-3459	7	8	93b05	93b05	NUM
ejpam-3459	7	9	,	,	PUNCT
ejpam-3459	7	10	92d25	92d25	NUM
ejpam-3459	7	11	,	,	PUNCT
ejpam-3459	7	12	35q92,35q93	35q92,35q93	NUM
ejpam-3459	7	13	key	key	ADJ
ejpam-3459	7	14	words	word	NOUN
ejpam-3459	7	15	and	and	CCONJ
ejpam-3459	7	16	phrases	phrase	NOUN
ejpam-3459	7	17	:	:	PUNCT
ejpam-3459	7	18	population	population	NOUN
ejpam-3459	7	19	dynamics	dynamic	NOUN
ejpam-3459	7	20	,	,	PUNCT
ejpam-3459	7	21	null	null	ADJ
ejpam-3459	7	22	controllability	controllability	NOUN
ejpam-3459	7	23	,	,	PUNCT
ejpam-3459	7	24	carleman	carleman	ADJ
ejpam-3459	7	25	inequality	inequality	NOUN
ejpam-3459	7	26	,	,	PUNCT
ejpam-3459	7	27	simultaneous	simultaneous	ADJ
ejpam-3459	7	28	sentinel	sentinel	NOUN
ejpam-3459	7	29	1	1	NUM
ejpam-3459	7	30	.	.	PUNCT
ejpam-3459	8	1	introduction	introduction	NOUN
ejpam-3459	8	2	let	let	VERB
ejpam-3459	8	3	ω	ω	NOUN
ejpam-3459	8	4	be	be	AUX
ejpam-3459	8	5	a	a	DET
ejpam-3459	8	6	bounded	bounded	ADJ
ejpam-3459	8	7	open	open	ADJ
ejpam-3459	8	8	subset	subset	NOUN
ejpam-3459	8	9	of	of	ADP
ejpam-3459	8	10	rn	rn	PROPN
ejpam-3459	8	11	,	,	PUNCT
ejpam-3459	8	12	n	n	PROPN
ejpam-3459	8	13	∈	∈	PROPN
ejpam-3459	8	14	{	{	PUNCT
ejpam-3459	8	15	1	1	NUM
ejpam-3459	8	16	,	,	PUNCT
ejpam-3459	8	17	2	2	NUM
ejpam-3459	8	18	,	,	PUNCT
ejpam-3459	8	19	3	3	NUM
ejpam-3459	8	20	}	}	PUNCT
ejpam-3459	8	21	with	with	ADP
ejpam-3459	8	22	boundary	boundary	ADJ
ejpam-3459	8	23	γ	γ	NOUN
ejpam-3459	8	24	of	of	ADP
ejpam-3459	8	25	class	class	PROPN
ejpam-3459	8	26	c2	c2	PROPN
ejpam-3459	8	27	.	.	PUNCT
ejpam-3459	9	1	let	let	VERB
ejpam-3459	9	2	ω	ω	PROPN
ejpam-3459	9	3	⊂	⊂	PROPN
ejpam-3459	9	4	ω	ω	PROPN
ejpam-3459	9	5	be	be	AUX
ejpam-3459	9	6	an	an	DET
ejpam-3459	9	7	open	open	ADJ
ejpam-3459	9	8	nonempty	nonempty	NOUN
ejpam-3459	9	9	subset	subset	VERB
ejpam-3459	9	10	.	.	PUNCT
ejpam-3459	10	1	for	for	ADP
ejpam-3459	10	2	a	a	DET
ejpam-3459	10	3	time	time	NOUN
ejpam-3459	10	4	t	t	X
ejpam-3459	10	5	>	>	X
ejpam-3459	10	6	0	0	PUNCT
ejpam-3459	11	1	and	and	CCONJ
ejpam-3459	11	2	the	the	DET
ejpam-3459	11	3	common	common	ADJ
ejpam-3459	11	4	life	life	NOUN
ejpam-3459	11	5	expectancy	expectancy	NOUN
ejpam-3459	11	6	a	a	DET
ejpam-3459	11	7	>	>	X
ejpam-3459	11	8	0	0	NUM
ejpam-3459	11	9	of	of	ADP
ejpam-3459	11	10	species	specie	NOUN
ejpam-3459	11	11	,	,	PUNCT
ejpam-3459	11	12	we	we	PRON
ejpam-3459	11	13	set	set	VERB
ejpam-3459	11	14	u	u	PRON
ejpam-3459	11	15	=	=	SYM
ejpam-3459	11	16	(	(	PUNCT
ejpam-3459	11	17	0	0	NUM
ejpam-3459	11	18	,	,	PUNCT
ejpam-3459	11	19	t	t	NOUN
ejpam-3459	11	20	)	)	PUNCT
ejpam-3459	11	21	×	×	NOUN
ejpam-3459	11	22	(	(	PUNCT
ejpam-3459	11	23	0	0	NUM
ejpam-3459	11	24	,	,	PUNCT
ejpam-3459	11	25	a	a	PRON
ejpam-3459	11	26	)	)	PUNCT
ejpam-3459	11	27	,	,	PUNCT
ejpam-3459	11	28	q	q	NOUN
ejpam-3459	11	29	=	=	PUNCT
ejpam-3459	11	30	u	u	NOUN
ejpam-3459	11	31	×	×	PROPN
ejpam-3459	11	32	ω	ω	PROPN
ejpam-3459	11	33	,	,	PUNCT
ejpam-3459	11	34	qω	qω	ADP
ejpam-3459	11	35	=	=	PRON
ejpam-3459	11	36	u	u	PROPN
ejpam-3459	11	37	×	×	PROPN
ejpam-3459	11	38	ω	ω	PROPN
ejpam-3459	11	39	,	,	PUNCT
ejpam-3459	11	40	qt	qt	NOUN
ejpam-3459	11	41	=	=	SYM
ejpam-3459	11	42	(	(	PUNCT
ejpam-3459	11	43	0,t	0,t	PROPN
ejpam-3459	11	44	)	)	PUNCT
ejpam-3459	11	45	×	×	PROPN
ejpam-3459	11	46	ω	ω	PROPN
ejpam-3459	11	47	,	,	PUNCT
ejpam-3459	11	48	qa	qa	PROPN
ejpam-3459	11	49	=	=	SYM
ejpam-3459	11	50	(	(	PUNCT
ejpam-3459	11	51	0,a	0,a	PROPN
ejpam-3459	11	52	)	)	PUNCT
ejpam-3459	11	53	×	×	PROPN
ejpam-3459	11	54	ω	ω	PROPN
ejpam-3459	11	55	,	,	PUNCT
ejpam-3459	11	56	σ	σ	PROPN
ejpam-3459	11	57	=	=	PUNCT
ejpam-3459	11	58	u	u	PROPN
ejpam-3459	11	59	×	×	PROPN
ejpam-3459	11	60	γ	γ	X
ejpam-3459	11	61	,	,	PUNCT
ejpam-3459	11	62	σt	σt	ADP
ejpam-3459	11	63	=	=	SYM
ejpam-3459	11	64	(	(	PUNCT
ejpam-3459	11	65	0	0	NUM
ejpam-3459	11	66	,	,	PUNCT
ejpam-3459	11	67	t	t	PROPN
ejpam-3459	11	68	)	)	PUNCT
ejpam-3459	11	69	×	×	PROPN
ejpam-3459	11	70	γ	γ	NOUN
ejpam-3459	12	1	and	and	CCONJ
ejpam-3459	12	2	we	we	PRON
ejpam-3459	12	3	consider	consider	VERB
ejpam-3459	12	4	the	the	DET
ejpam-3459	12	5	following	follow	VERB
ejpam-3459	12	6	∗corresponding	∗corresponde	VERB
ejpam-3459	12	7	author	author	NOUN
ejpam-3459	12	8	.	.	PUNCT
ejpam-3459	13	1	doi	doi	NOUN
ejpam-3459	13	2	:	:	PUNCT
ejpam-3459	13	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3459	https://doi.org/10.29020/nybg.ejpam.v12i3.3459	NOUN
ejpam-3459	13	4	email	email	NOUN
ejpam-3459	13	5	addresses	address	NOUN
ejpam-3459	13	6	:	:	PUNCT
ejpam-3459	13	7	cedrickpebsom@yahoo.fr	cedrickpebsom@yahoo.fr	PROPN
ejpam-3459	13	8	(	(	PUNCT
ejpam-3459	13	9	c.	c.	PROPN
ejpam-3459	13	10	k.	k.	PROPN
ejpam-3459	13	11	somé	somé	PROPN
ejpam-3459	13	12	)	)	PUNCT
ejpam-3459	13	13	,	,	PUNCT
ejpam-3459	13	14	sawasom@yahoo.fr	sawasom@yahoo.fr	PROPN
ejpam-3459	13	15	(	(	PUNCT
ejpam-3459	13	16	s.	s.	PROPN
ejpam-3459	13	17	sawadogo	sawadogo	PROPN
ejpam-3459	13	18	)	)	PUNCT
ejpam-3459	13	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3459	14	1	870	870	NUM
ejpam-3459	14	2	c	c	X
ejpam-3459	14	3	©	©	PROPN
ejpam-3459	14	4	2019	2019	NUM
ejpam-3459	14	5	ejpam	ejpam	NOUN
ejpam-3459	14	6	all	all	DET
ejpam-3459	14	7	rights	right	NOUN
ejpam-3459	14	8	reserved	reserve	VERB
ejpam-3459	14	9	.	.	PUNCT
ejpam-3459	15	1	c.	c.	PROPN
ejpam-3459	15	2	k.	k.	PROPN
ejpam-3459	15	3	somé	somé	PROPN
ejpam-3459	15	4	,	,	PUNCT
ejpam-3459	15	5	s.	s.	PROPN
ejpam-3459	15	6	sawadogo	sawadogo	PROPN
ejpam-3459	15	7	/	/	SYM
ejpam-3459	15	8	eur	eur	PROPN
ejpam-3459	15	9	.	.	PUNCT
ejpam-3459	16	1	j.	j.	PROPN
ejpam-3459	16	2	pure	pure	PROPN
ejpam-3459	16	3	appl	appl	PROPN
ejpam-3459	16	4	.	.	PROPN
ejpam-3459	16	5	math	math	PROPN
ejpam-3459	16	6	,	,	PUNCT
ejpam-3459	16	7	12	12	NUM
ejpam-3459	16	8	(	(	PUNCT
ejpam-3459	16	9	3	3	NUM
ejpam-3459	16	10	)	)	PUNCT
ejpam-3459	16	11	(	(	PUNCT
ejpam-3459	16	12	2019	2019	NUM
ejpam-3459	16	13	)	)	PUNCT
ejpam-3459	16	14	,	,	PUNCT
ejpam-3459	16	15	870	870	NUM
ejpam-3459	16	16	-	-	SYM
ejpam-3459	16	17	892	892	NUM
ejpam-3459	16	18	871	871	NUM
ejpam-3459	16	19	nonlinear	nonlinear	ADJ
ejpam-3459	16	20	two	two	NUM
ejpam-3459	16	21	stroke	stroke	NOUN
ejpam-3459	16	22	systems	system	NOUN
ejpam-3459	16	23	:	:	PUNCT
ejpam-3459	16	24			PROPN
ejpam-3459	16	25	−∂q1	−∂q1	PROPN
ejpam-3459	16	26	∂t	∂t	PROPN
ejpam-3459	16	27	−	−	PROPN
ejpam-3459	16	28	∂q1	∂q1	VERB
ejpam-3459	16	29	∂a	∂a	NOUN
ejpam-3459	16	30	−∆q1	−∆q1	NOUN
ejpam-3459	16	31	+	+	CCONJ
ejpam-3459	16	32	µ1q1	µ1q1	X
ejpam-3459	16	33	=	=	PRON
ejpam-3459	16	34	β1f	β1f	X
ejpam-3459	16	35	(	(	PUNCT
ejpam-3459	16	36	∫	∫	PROPN
ejpam-3459	16	37	a	a	DET
ejpam-3459	16	38	0	0	NUM
ejpam-3459	16	39	β1q1da	β1q1da	PROPN
ejpam-3459	16	40	)	)	PUNCT
ejpam-3459	17	1	q1(t	q1(t	ADP
ejpam-3459	17	2	,	,	PUNCT
ejpam-3459	17	3	0	0	NUM
ejpam-3459	17	4	,	,	PUNCT
ejpam-3459	17	5	x	x	PRON
ejpam-3459	17	6	)	)	PUNCT
ejpam-3459	17	7	+	+	NUM
ejpam-3459	17	8	h+	h+	X
ejpam-3459	17	9	wχω	wχω	PROPN
ejpam-3459	17	10	in	in	ADP
ejpam-3459	17	11	q	q	NOUN
ejpam-3459	17	12	,	,	PUNCT
ejpam-3459	17	13	−∂q2	−∂q2	PROPN
ejpam-3459	17	14	∂t	∂t	PROPN
ejpam-3459	17	15	−	−	PROPN
ejpam-3459	17	16	∂q2	∂q2	PROPN
ejpam-3459	17	17	∂a	∂a	PROPN
ejpam-3459	17	18	−∆q2	−∆q2	NOUN
ejpam-3459	18	1	+	+	CCONJ
ejpam-3459	18	2	µ2q2	µ2q2	X
ejpam-3459	18	3	=	=	ADJ
ejpam-3459	18	4	β2	β2	PROPN
ejpam-3459	18	5	g	g	PROPN
ejpam-3459	18	6	(	(	PUNCT
ejpam-3459	18	7	∫	∫	PROPN
ejpam-3459	18	8	a	a	DET
ejpam-3459	18	9	0	0	NUM
ejpam-3459	18	10	β2q2da	β2q2da	PUNCT
ejpam-3459	18	11	)	)	PUNCT
ejpam-3459	19	1	q2(t	q2(t	PROPN
ejpam-3459	19	2	,	,	PUNCT
ejpam-3459	19	3	0	0	NUM
ejpam-3459	19	4	,	,	PUNCT
ejpam-3459	19	5	x	x	PRON
ejpam-3459	19	6	)	)	PUNCT
ejpam-3459	19	7	+	+	NUM
ejpam-3459	19	8	h+	h+	AUX
ejpam-3459	19	9	wχω	wχω	PROPN
ejpam-3459	19	10	in	in	ADP
ejpam-3459	19	11	q	q	PROPN
ejpam-3459	19	12	,	,	PUNCT
ejpam-3459	19	13	q1(t	q1(t	PROPN
ejpam-3459	19	14	,	,	PUNCT
ejpam-3459	19	15	a	a	DET
ejpam-3459	19	16	,	,	PUNCT
ejpam-3459	19	17	x	x	NOUN
ejpam-3459	19	18	)	)	PUNCT
ejpam-3459	19	19	=	=	SYM
ejpam-3459	20	1	q2(t	q2(t	PROPN
ejpam-3459	20	2	,	,	PUNCT
ejpam-3459	20	3	a	a	PRON
ejpam-3459	20	4	,	,	PUNCT
ejpam-3459	20	5	x	x	NOUN
ejpam-3459	20	6	)	)	PUNCT
ejpam-3459	20	7	=	=	SYM
ejpam-3459	20	8	0	0	NUM
ejpam-3459	21	1	in	in	ADP
ejpam-3459	21	2	qa	qa	PROPN
ejpam-3459	21	3	,	,	PUNCT
ejpam-3459	21	4	q1(t	q1(t	PROPN
ejpam-3459	21	5	,	,	PUNCT
ejpam-3459	21	6	a	a	PRON
ejpam-3459	21	7	,	,	PUNCT
ejpam-3459	21	8	x	x	NOUN
ejpam-3459	21	9	)	)	PUNCT
ejpam-3459	21	10	=	=	SYM
ejpam-3459	21	11	q2(t	q2(t	PROPN
ejpam-3459	21	12	,	,	PUNCT
ejpam-3459	21	13	a	a	PRON
ejpam-3459	21	14	,	,	PUNCT
ejpam-3459	21	15	x	x	NOUN
ejpam-3459	21	16	)	)	PUNCT
ejpam-3459	21	17	=	=	SYM
ejpam-3459	21	18	0	0	NUM
ejpam-3459	21	19	in	in	ADP
ejpam-3459	21	20	qt	qt	NOUN
ejpam-3459	21	21	,	,	PUNCT
ejpam-3459	21	22	q1	q1	PROPN
ejpam-3459	21	23	=	=	SYM
ejpam-3459	21	24	q2	q2	PROPN
ejpam-3459	21	25	=	=	SYM
ejpam-3459	21	26	0	0	NUM
ejpam-3459	22	1	on	on	ADP
ejpam-3459	22	2	σ	σ	PROPN
ejpam-3459	22	3	,	,	PUNCT
ejpam-3459	22	4	(	(	PUNCT
ejpam-3459	22	5	1	1	NUM
ejpam-3459	22	6	)	)	PUNCT
ejpam-3459	22	7	for	for	ADP
ejpam-3459	22	8	some	some	DET
ejpam-3459	22	9	functions	function	NOUN
ejpam-3459	22	10	f	f	X
ejpam-3459	22	11	,	,	PUNCT
ejpam-3459	22	12	g	g	PROPN
ejpam-3459	22	13	defined	define	VERB
ejpam-3459	22	14	on	on	ADP
ejpam-3459	22	15	r.	r.	PROPN
ejpam-3459	22	16	we	we	PRON
ejpam-3459	22	17	assume	assume	VERB
ejpam-3459	22	18	that	that	SCONJ
ejpam-3459	22	19	(	(	PUNCT
ejpam-3459	22	20	h0	h0	PROPN
ejpam-3459	22	21	)	)	PUNCT
ejpam-3459	22	22	the	the	DET
ejpam-3459	22	23	functions	function	NOUN
ejpam-3459	22	24	f	f	X
ejpam-3459	22	25	,	,	PUNCT
ejpam-3459	22	26	g	g	PROPN
ejpam-3459	22	27	belong	belong	VERB
ejpam-3459	22	28	to	to	ADP
ejpam-3459	22	29	l∞(r	l∞(r	NOUN
ejpam-3459	22	30	)	)	PUNCT
ejpam-3459	22	31	and	and	CCONJ
ejpam-3459	22	32	f	f	PROPN
ejpam-3459	22	33	(	(	PUNCT
ejpam-3459	22	34	0	0	NUM
ejpam-3459	22	35	)	)	PUNCT
ejpam-3459	22	36	=	=	SYM
ejpam-3459	22	37	g(0	g(0	PROPN
ejpam-3459	22	38	)	)	PUNCT
ejpam-3459	22	39	=	=	SYM
ejpam-3459	23	1	0	0	X
ejpam-3459	23	2	.	.	PUNCT
ejpam-3459	24	1	the	the	DET
ejpam-3459	24	2	simultaneous	simultaneous	ADJ
ejpam-3459	24	3	null	null	ADJ
ejpam-3459	24	4	controllability	controllability	NOUN
ejpam-3459	24	5	problem	problem	NOUN
ejpam-3459	24	6	can	can	AUX
ejpam-3459	24	7	be	be	AUX
ejpam-3459	24	8	stated	state	VERB
ejpam-3459	24	9	as	as	SCONJ
ejpam-3459	24	10	follows	follow	VERB
ejpam-3459	24	11	:	:	PUNCT
ejpam-3459	24	12	given	give	VERB
ejpam-3459	24	13	h	h	NOUN
ejpam-3459	24	14	∈	∈	PROPN
ejpam-3459	24	15	l2(q	l2(q	PROPN
ejpam-3459	24	16	)	)	PUNCT
ejpam-3459	24	17	find	find	VERB
ejpam-3459	24	18	w	w	ADP
ejpam-3459	24	19	∈	∈	PROPN
ejpam-3459	24	20	l2(qω	l2(qω	PROPN
ejpam-3459	24	21	)	)	PUNCT
ejpam-3459	24	22	such	such	ADJ
ejpam-3459	24	23	that	that	SCONJ
ejpam-3459	24	24	the	the	DET
ejpam-3459	24	25	solution	solution	NOUN
ejpam-3459	24	26	of	of	ADP
ejpam-3459	24	27	(	(	PUNCT
ejpam-3459	24	28	1	1	X
ejpam-3459	24	29	)	)	PUNCT
ejpam-3459	24	30	satisfies	satisfy	VERB
ejpam-3459	24	31	q1(0	q1(0	PROPN
ejpam-3459	24	32	,	,	PUNCT
ejpam-3459	24	33	a	a	PRON
ejpam-3459	24	34	,	,	PUNCT
ejpam-3459	24	35	x	x	NOUN
ejpam-3459	24	36	)	)	PUNCT
ejpam-3459	25	1	=	=	SYM
ejpam-3459	25	2	q2(0	q2(0	PROPN
ejpam-3459	25	3	,	,	PUNCT
ejpam-3459	25	4	a	a	PRON
ejpam-3459	25	5	,	,	PUNCT
ejpam-3459	25	6	x	x	NOUN
ejpam-3459	25	7	)	)	PUNCT
ejpam-3459	25	8	=	=	SYM
ejpam-3459	25	9	0	0	NUM
ejpam-3459	26	1	a.e	a.e	NOUN
ejpam-3459	26	2	(	(	PUNCT
ejpam-3459	26	3	a	a	PRON
ejpam-3459	26	4	,	,	PUNCT
ejpam-3459	26	5	x	x	NOUN
ejpam-3459	26	6	)	)	PUNCT
ejpam-3459	26	7	in	in	ADP
ejpam-3459	26	8	qa	qa	PROPN
ejpam-3459	26	9	.	.	PUNCT
ejpam-3459	27	1	(	(	PUNCT
ejpam-3459	27	2	2	2	X
ejpam-3459	27	3	)	)	PUNCT
ejpam-3459	27	4	the	the	DET
ejpam-3459	27	5	null	null	ADJ
ejpam-3459	27	6	controllability	controllability	NOUN
ejpam-3459	27	7	problem	problem	NOUN
ejpam-3459	27	8	for	for	ADP
ejpam-3459	27	9	one	one	NUM
ejpam-3459	27	10	two	two	NUM
ejpam-3459	27	11	stroke	stroke	NOUN
ejpam-3459	27	12	system	system	NOUN
ejpam-3459	27	13	with	with	ADP
ejpam-3459	27	14	one	one	NUM
ejpam-3459	27	15	and	and	CCONJ
ejpam-3459	27	16	only	only	ADV
ejpam-3459	27	17	one	one	NUM
ejpam-3459	27	18	control	control	NOUN
ejpam-3459	27	19	is	be	AUX
ejpam-3459	27	20	well	well	ADV
ejpam-3459	27	21	understood	understand	VERB
ejpam-3459	27	22	:	:	PUNCT
ejpam-3459	27	23	it	it	PRON
ejpam-3459	27	24	has	have	AUX
ejpam-3459	27	25	been	be	AUX
ejpam-3459	27	26	studied	study	VERB
ejpam-3459	27	27	by	by	ADP
ejpam-3459	27	28	several	several	ADJ
ejpam-3459	27	29	authors	author	NOUN
ejpam-3459	27	30	using	use	VERB
ejpam-3459	27	31	different	different	ADJ
ejpam-3459	27	32	methods	method	NOUN
ejpam-3459	27	33	.	.	PUNCT
ejpam-3459	28	1	we	we	PRON
ejpam-3459	28	2	refer	refer	VERB
ejpam-3459	28	3	to	to	ADP
ejpam-3459	28	4	b.	b.	PROPN
ejpam-3459	28	5	ainseba	ainseba	PROPN
ejpam-3459	28	6	and	and	CCONJ
ejpam-3459	28	7	m.	m.	NOUN
ejpam-3459	28	8	langlais	langlais	PROPN
ejpam-3459	29	1	[	[	X
ejpam-3459	29	2	2	2	NUM
ejpam-3459	29	3	]	]	PUNCT
ejpam-3459	29	4	,	,	PUNCT
ejpam-3459	29	5	b.	b.	PROPN
ejpam-3459	29	6	ainseba	ainseba	PROPN
ejpam-3459	29	7	and	and	CCONJ
ejpam-3459	30	1	s.	s.	PROPN
ejpam-3459	30	2	anita	anita	PROPN
ejpam-3459	31	1	[	[	X
ejpam-3459	31	2	3	3	NUM
ejpam-3459	31	3	]	]	PUNCT
ejpam-3459	31	4	.	.	PUNCT
ejpam-3459	32	1	we	we	PRON
ejpam-3459	32	2	also	also	ADV
ejpam-3459	32	3	refer	refer	VERB
ejpam-3459	32	4	to	to	ADP
ejpam-3459	32	5	s.	s.	PROPN
ejpam-3459	32	6	sawadogo	sawadogo	PROPN
ejpam-3459	33	1	[	[	X
ejpam-3459	33	2	9	9	NUM
ejpam-3459	33	3	]	]	PUNCT
ejpam-3459	33	4	,	,	PUNCT
ejpam-3459	34	1	o.	o.	PROPN
ejpam-3459	34	2	traoré	traoré	PUNCT
ejpam-3459	35	1	[	[	X
ejpam-3459	35	2	12	12	NUM
ejpam-3459	35	3	]	]	PUNCT
ejpam-3459	35	4	,	,	PUNCT
ejpam-3459	35	5	y.	y.	PROPN
ejpam-3459	35	6	simporé	simporé	PROPN
ejpam-3459	35	7	and	and	CCONJ
ejpam-3459	35	8	o.	o.	ADJ
ejpam-3459	35	9	traoré	traoré	NOUN
ejpam-3459	36	1	[	[	X
ejpam-3459	36	2	10	10	NUM
ejpam-3459	36	3	]	]	PUNCT
ejpam-3459	36	4	and	and	CCONJ
ejpam-3459	36	5	their	their	PRON
ejpam-3459	36	6	bibliography	bibliography	NOUN
ejpam-3459	36	7	for	for	ADP
ejpam-3459	36	8	other	other	ADJ
ejpam-3459	36	9	related	relate	VERB
ejpam-3459	36	10	controllability	controllability	NOUN
ejpam-3459	36	11	problems	problem	NOUN
ejpam-3459	36	12	.	.	PUNCT
ejpam-3459	37	1	as	as	ADV
ejpam-3459	37	2	far	far	ADV
ejpam-3459	37	3	as	as	SCONJ
ejpam-3459	37	4	we	we	PRON
ejpam-3459	37	5	know	know	VERB
ejpam-3459	37	6	,	,	PUNCT
ejpam-3459	37	7	there	there	PRON
ejpam-3459	37	8	is	be	VERB
ejpam-3459	37	9	no	no	DET
ejpam-3459	37	10	results	result	NOUN
ejpam-3459	37	11	on	on	ADP
ejpam-3459	37	12	simultaneous	simultaneous	ADJ
ejpam-3459	37	13	null	null	ADJ
ejpam-3459	37	14	controllability	controllability	NOUN
ejpam-3459	37	15	for	for	ADP
ejpam-3459	37	16	nonlinear	nonlinear	ADJ
ejpam-3459	37	17	two	two	NUM
ejpam-3459	37	18	stroke	stroke	NOUN
ejpam-3459	37	19	systems	system	NOUN
ejpam-3459	37	20	.	.	PUNCT
ejpam-3459	38	1	in	in	ADP
ejpam-3459	38	2	this	this	DET
ejpam-3459	38	3	paper	paper	NOUN
ejpam-3459	38	4	we	we	PRON
ejpam-3459	38	5	focus	focus	VERB
ejpam-3459	38	6	on	on	ADP
ejpam-3459	38	7	the	the	DET
ejpam-3459	38	8	previous	previous	ADJ
ejpam-3459	38	9	problem	problem	NOUN
ejpam-3459	38	10	in	in	ADP
ejpam-3459	38	11	order	order	NOUN
ejpam-3459	38	12	to	to	PART
ejpam-3459	38	13	applicate	applicate	VERB
ejpam-3459	38	14	it	it	PRON
ejpam-3459	38	15	to	to	PART
ejpam-3459	38	16	build	build	VERB
ejpam-3459	38	17	a	a	DET
ejpam-3459	38	18	simultaneous	simultaneous	ADJ
ejpam-3459	38	19	sentinel	sentinel	NOUN
ejpam-3459	38	20	of	of	ADP
ejpam-3459	38	21	detection	detection	NOUN
ejpam-3459	38	22	in	in	ADP
ejpam-3459	38	23	population	population	NOUN
ejpam-3459	38	24	dynamics	dynamic	NOUN
ejpam-3459	38	25	problem	problem	NOUN
ejpam-3459	38	26	with	with	ADP
ejpam-3459	38	27	incomplete	incomplete	ADJ
ejpam-3459	38	28	data	datum	NOUN
ejpam-3459	38	29	.	.	PUNCT
ejpam-3459	39	1	the	the	DET
ejpam-3459	39	2	remainder	remainder	NOUN
ejpam-3459	39	3	of	of	ADP
ejpam-3459	39	4	this	this	DET
ejpam-3459	39	5	paper	paper	NOUN
ejpam-3459	39	6	is	be	AUX
ejpam-3459	39	7	organized	organize	VERB
ejpam-3459	39	8	as	as	SCONJ
ejpam-3459	39	9	follows	follow	VERB
ejpam-3459	39	10	:	:	PUNCT
ejpam-3459	39	11	in	in	ADP
ejpam-3459	39	12	order	order	NOUN
ejpam-3459	39	13	to	to	PART
ejpam-3459	39	14	well	well	ADV
ejpam-3459	39	15	pose	pose	VERB
ejpam-3459	39	16	our	our	PRON
ejpam-3459	39	17	problem	problem	NOUN
ejpam-3459	39	18	,	,	PUNCT
ejpam-3459	39	19	in	in	ADP
ejpam-3459	39	20	section	section	NOUN
ejpam-3459	39	21	2	2	NUM
ejpam-3459	39	22	we	we	PRON
ejpam-3459	39	23	make	make	VERB
ejpam-3459	39	24	some	some	DET
ejpam-3459	39	25	assumptions	assumption	NOUN
ejpam-3459	39	26	,	,	PUNCT
ejpam-3459	39	27	transform	transform	VERB
ejpam-3459	39	28	the	the	DET
ejpam-3459	39	29	system	system	NOUN
ejpam-3459	39	30	(	(	PUNCT
ejpam-3459	39	31	1	1	NUM
ejpam-3459	39	32	)	)	PUNCT
ejpam-3459	39	33	into	into	ADP
ejpam-3459	39	34	an	an	DET
ejpam-3459	39	35	equivalent	equivalent	ADJ
ejpam-3459	39	36	cascade	cascade	NOUN
ejpam-3459	39	37	problem	problem	NOUN
ejpam-3459	39	38	and	and	CCONJ
ejpam-3459	39	39	we	we	PRON
ejpam-3459	39	40	state	state	VERB
ejpam-3459	39	41	the	the	DET
ejpam-3459	39	42	main	main	ADJ
ejpam-3459	39	43	result	result	NOUN
ejpam-3459	39	44	of	of	ADP
ejpam-3459	39	45	this	this	DET
ejpam-3459	39	46	paper	paper	NOUN
ejpam-3459	39	47	.	.	PUNCT
ejpam-3459	40	1	in	in	ADP
ejpam-3459	40	2	section	section	NOUN
ejpam-3459	40	3	3	3	NUM
ejpam-3459	40	4	,	,	PUNCT
ejpam-3459	40	5	we	we	PRON
ejpam-3459	40	6	state	state	VERB
ejpam-3459	40	7	first	first	ADV
ejpam-3459	40	8	some	some	DET
ejpam-3459	40	9	carleman	carleman	NOUN
ejpam-3459	40	10	’s	’s	PART
ejpam-3459	40	11	inequalities	inequality	NOUN
ejpam-3459	40	12	that	that	PRON
ejpam-3459	40	13	we	we	PRON
ejpam-3459	40	14	had	have	AUX
ejpam-3459	40	15	established	establish	VERB
ejpam-3459	40	16	in	in	ADP
ejpam-3459	40	17	[	[	X
ejpam-3459	40	18	11	11	NUM
ejpam-3459	40	19	]	]	PUNCT
ejpam-3459	40	20	.	.	PUNCT
ejpam-3459	41	1	afterwards	afterwards	ADV
ejpam-3459	41	2	,	,	PUNCT
ejpam-3459	41	3	we	we	PRON
ejpam-3459	41	4	study	study	VERB
ejpam-3459	41	5	the	the	DET
ejpam-3459	41	6	controllability	controllability	NOUN
ejpam-3459	41	7	for	for	ADP
ejpam-3459	41	8	a	a	DET
ejpam-3459	41	9	linear	linear	ADJ
ejpam-3459	41	10	intermediate	intermediate	ADJ
ejpam-3459	41	11	problem	problem	NOUN
ejpam-3459	41	12	and	and	CCONJ
ejpam-3459	41	13	for	for	ADP
ejpam-3459	41	14	another	another	DET
ejpam-3459	41	15	nonlinear	nonlinear	NOUN
ejpam-3459	41	16	.	.	PUNCT
ejpam-3459	42	1	the	the	DET
ejpam-3459	42	2	section	section	NOUN
ejpam-3459	42	3	4	4	NUM
ejpam-3459	42	4	is	be	AUX
ejpam-3459	42	5	devoted	devote	VERB
ejpam-3459	42	6	to	to	ADP
ejpam-3459	42	7	the	the	DET
ejpam-3459	42	8	proof	proof	NOUN
ejpam-3459	42	9	of	of	ADP
ejpam-3459	42	10	the	the	DET
ejpam-3459	42	11	main	main	ADJ
ejpam-3459	42	12	result	result	NOUN
ejpam-3459	42	13	and	and	CCONJ
ejpam-3459	42	14	in	in	ADP
ejpam-3459	42	15	the	the	DET
ejpam-3459	42	16	last	last	ADJ
ejpam-3459	42	17	section	section	NOUN
ejpam-3459	42	18	we	we	PRON
ejpam-3459	42	19	use	use	VERB
ejpam-3459	42	20	the	the	DET
ejpam-3459	42	21	result	result	NOUN
ejpam-3459	42	22	obtained	obtain	VERB
ejpam-3459	42	23	in	in	ADP
ejpam-3459	42	24	section	section	NOUN
ejpam-3459	42	25	4	4	NUM
ejpam-3459	42	26	to	to	PART
ejpam-3459	42	27	build	build	VERB
ejpam-3459	42	28	a	a	DET
ejpam-3459	42	29	simultaneous	simultaneous	ADJ
ejpam-3459	42	30	sentinel	sentinel	NOUN
ejpam-3459	42	31	.	.	PUNCT
ejpam-3459	43	1	2	2	X
ejpam-3459	43	2	.	.	NOUN
ejpam-3459	43	3	assumptions	assumption	NOUN
ejpam-3459	43	4	and	and	CCONJ
ejpam-3459	43	5	main	main	ADJ
ejpam-3459	43	6	result	result	NOUN
ejpam-3459	43	7	for	for	ADP
ejpam-3459	43	8	the	the	DET
ejpam-3459	43	9	sequel	sequel	NOUN
ejpam-3459	43	10	,	,	PUNCT
ejpam-3459	43	11	the	the	DET
ejpam-3459	43	12	following	follow	VERB
ejpam-3459	43	13	assumptions	assumption	NOUN
ejpam-3459	43	14	hold	hold	VERB
ejpam-3459	43	15	:	:	PUNCT
ejpam-3459	43	16	(	(	PUNCT
ejpam-3459	43	17	h1	h1	PROPN
ejpam-3459	43	18	)	)	PUNCT
ejpam-3459	43	19			PUNCT
ejpam-3459	43	20	(	(	PUNCT
ejpam-3459	43	21	µi	µi	PROPN
ejpam-3459	43	22	,	,	PUNCT
ejpam-3459	43	23	∇µi	∇µi	PROPN
ejpam-3459	43	24	)	)	PUNCT
ejpam-3459	43	25	∈	∈	PROPN
ejpam-3459	43	26	(	(	PUNCT
ejpam-3459	43	27	l∞(q))n+1	l∞(q))n+1	PROPN
ejpam-3459	43	28	for	for	ADP
ejpam-3459	43	29	all	all	PRON
ejpam-3459	43	30	i	i	PRON
ejpam-3459	43	31	∈	∈	PROPN
ejpam-3459	43	32	{	{	PUNCT
ejpam-3459	43	33	1	1	NUM
ejpam-3459	43	34	;	;	PUNCT
ejpam-3459	43	35	2	2	NUM
ejpam-3459	43	36	}	}	PUNCT
ejpam-3459	43	37	,	,	PUNCT
ejpam-3459	43	38	n	n	X
ejpam-3459	43	39	∈	∈	PROPN
ejpam-3459	43	40	{	{	PUNCT
ejpam-3459	43	41	1	1	NUM
ejpam-3459	43	42	,	,	PUNCT
ejpam-3459	43	43	2	2	NUM
ejpam-3459	43	44	,	,	PUNCT
ejpam-3459	43	45	3	3	NUM
ejpam-3459	43	46	}	}	PUNCT
ejpam-3459	43	47	,	,	PUNCT
ejpam-3459	43	48	µi	µi	ADP
ejpam-3459	43	49	≥	≥	NOUN
ejpam-3459	43	50	0	0	NUM
ejpam-3459	43	51	in	in	ADP
ejpam-3459	43	52	q	q	NOUN
ejpam-3459	43	53	for	for	ADP
ejpam-3459	43	54	all	all	PRON
ejpam-3459	43	55	i	i	PRON
ejpam-3459	43	56	∈	∈	PROPN
ejpam-3459	43	57	{	{	PUNCT
ejpam-3459	43	58	1	1	NUM
ejpam-3459	43	59	;	;	PUNCT
ejpam-3459	43	60	2	2	NUM
ejpam-3459	43	61	}	}	PUNCT
ejpam-3459	43	62	,	,	PUNCT
ejpam-3459	43	63	µ1	µ1	PROPN
ejpam-3459	43	64	6=	6=	PROPN
ejpam-3459	43	65	µ2	µ2	PROPN
ejpam-3459	43	66	in	in	ADP
ejpam-3459	43	67	qω	qω	PROPN
ejpam-3459	43	68	.	.	PUNCT
ejpam-3459	44	1	c.	c.	PROPN
ejpam-3459	44	2	k.	k.	PROPN
ejpam-3459	44	3	somé	somé	PROPN
ejpam-3459	44	4	,	,	PUNCT
ejpam-3459	44	5	s.	s.	PROPN
ejpam-3459	44	6	sawadogo	sawadogo	PROPN
ejpam-3459	44	7	/	/	SYM
ejpam-3459	44	8	eur	eur	PROPN
ejpam-3459	44	9	.	.	PUNCT
ejpam-3459	45	1	j.	j.	PROPN
ejpam-3459	45	2	pure	pure	PROPN
ejpam-3459	45	3	appl	appl	PROPN
ejpam-3459	45	4	.	.	PROPN
ejpam-3459	45	5	math	math	PROPN
ejpam-3459	45	6	,	,	PUNCT
ejpam-3459	45	7	12	12	NUM
ejpam-3459	45	8	(	(	PUNCT
ejpam-3459	45	9	3	3	NUM
ejpam-3459	45	10	)	)	PUNCT
ejpam-3459	45	11	(	(	PUNCT
ejpam-3459	45	12	2019	2019	NUM
ejpam-3459	45	13	)	)	PUNCT
ejpam-3459	45	14	,	,	PUNCT
ejpam-3459	45	15	870	870	NUM
ejpam-3459	45	16	-	-	SYM
ejpam-3459	45	17	892	892	NUM
ejpam-3459	45	18	872	872	NUM
ejpam-3459	45	19	(	(	PUNCT
ejpam-3459	45	20	h2	h2	PROPN
ejpam-3459	45	21	)	)	PUNCT
ejpam-3459	45	22	{	{	PUNCT
ejpam-3459	45	23	βi	βi	PROPN
ejpam-3459	45	24	∈	∈	PROPN
ejpam-3459	45	25	c2(q	c2(q	PROPN
ejpam-3459	45	26	)	)	PUNCT
ejpam-3459	45	27	for	for	ADP
ejpam-3459	45	28	all	all	PRON
ejpam-3459	45	29	i	i	PRON
ejpam-3459	45	30	∈	∈	PROPN
ejpam-3459	45	31	{	{	PUNCT
ejpam-3459	45	32	1	1	NUM
ejpam-3459	45	33	;	;	PUNCT
ejpam-3459	45	34	2	2	NUM
ejpam-3459	45	35	}	}	PUNCT
ejpam-3459	45	36	,	,	PUNCT
ejpam-3459	45	37	βi	βi	PRON
ejpam-3459	45	38	≥	≥	NOUN
ejpam-3459	45	39	0	0	NUM
ejpam-3459	45	40	in	in	ADP
ejpam-3459	45	41	q	q	NOUN
ejpam-3459	45	42	for	for	ADP
ejpam-3459	45	43	all	all	PRON
ejpam-3459	45	44	i	i	PRON
ejpam-3459	45	45	∈	∈	PROPN
ejpam-3459	45	46	{	{	PUNCT
ejpam-3459	45	47	1	1	NUM
ejpam-3459	45	48	;	;	PUNCT
ejpam-3459	45	49	2	2	NUM
ejpam-3459	45	50	}	}	PUNCT
ejpam-3459	45	51	.	.	PUNCT
ejpam-3459	46	1	(	(	PUNCT
ejpam-3459	46	2	h3	h3	NOUN
ejpam-3459	46	3	)	)	PUNCT
ejpam-3459	46	4	there	there	PRON
ejpam-3459	46	5	exists	exist	VERB
ejpam-3459	46	6	positive	positive	ADJ
ejpam-3459	46	7	constants	constant	NOUN
ejpam-3459	46	8	non	non	PRON
ejpam-3459	46	9	null	null	ADJ
ejpam-3459	46	10	a0	a0	PROPN
ejpam-3459	46	11	and	and	CCONJ
ejpam-3459	46	12	a1	a1	NOUN
ejpam-3459	46	13	with	with	ADP
ejpam-3459	46	14	a0	a0	PROPN
ejpam-3459	46	15	<	<	X
ejpam-3459	46	16	a1	a1	PROPN
ejpam-3459	46	17	<	<	X
ejpam-3459	46	18	a	a	DET
ejpam-3459	46	19	such	such	ADJ
ejpam-3459	46	20	that	that	PRON
ejpam-3459	46	21	for	for	ADP
ejpam-3459	46	22	each	each	DET
ejpam-3459	46	23	i	i	PRON
ejpam-3459	46	24	∈	∈	PROPN
ejpam-3459	46	25	{	{	PUNCT
ejpam-3459	46	26	1	1	NUM
ejpam-3459	46	27	;	;	PUNCT
ejpam-3459	46	28	2	2	NUM
ejpam-3459	46	29	}	}	PUNCT
ejpam-3459	46	30	,	,	PUNCT
ejpam-3459	46	31	βi(t	βi(t	ADP
ejpam-3459	46	32	,	,	PUNCT
ejpam-3459	46	33	a	a	DET
ejpam-3459	46	34	,	,	PUNCT
ejpam-3459	46	35	x	x	NOUN
ejpam-3459	46	36	)	)	PUNCT
ejpam-3459	46	37	=	=	SYM
ejpam-3459	46	38	0	0	NUM
ejpam-3459	47	1	a.e	a.e	PROPN
ejpam-3459	47	2	(	(	PUNCT
ejpam-3459	47	3	t	t	PROPN
ejpam-3459	47	4	,	,	PUNCT
ejpam-3459	47	5	a	a	PRON
ejpam-3459	47	6	,	,	PUNCT
ejpam-3459	47	7	x	x	NOUN
ejpam-3459	47	8	)	)	PUNCT
ejpam-3459	47	9	∈	∈	PROPN
ejpam-3459	47	10	(	(	PUNCT
ejpam-3459	47	11	0	0	NUM
ejpam-3459	47	12	,	,	PUNCT
ejpam-3459	47	13	t	t	NOUN
ejpam-3459	47	14	)	)	PUNCT
ejpam-3459	47	15	×	×	NOUN
ejpam-3459	47	16	(	(	PUNCT
ejpam-3459	47	17	[	[	X
ejpam-3459	47	18	0	0	NUM
ejpam-3459	47	19	,	,	PUNCT
ejpam-3459	47	20	a0	a0	PROPN
ejpam-3459	47	21	]	]	PUNCT
ejpam-3459	47	22	∪	∪	ADP
ejpam-3459	47	23	[	[	X
ejpam-3459	47	24	a1	a1	NOUN
ejpam-3459	47	25	,	,	PUNCT
ejpam-3459	47	26	a])×	a])×	PROPN
ejpam-3459	47	27	ω	ω	PROPN
ejpam-3459	47	28	.	.	PUNCT
ejpam-3459	48	1	under	under	ADP
ejpam-3459	48	2	the	the	DET
ejpam-3459	48	3	assumptions	assumption	NOUN
ejpam-3459	48	4	(	(	PUNCT
ejpam-3459	48	5	h0	h0	NOUN
ejpam-3459	48	6	)	)	PUNCT
ejpam-3459	48	7	−	−	PROPN
ejpam-3459	48	8	(	(	PUNCT
ejpam-3459	48	9	h3	h3	NOUN
ejpam-3459	48	10	)	)	PUNCT
ejpam-3459	48	11	,	,	PUNCT
ejpam-3459	48	12	for	for	ADP
ejpam-3459	48	13	all	all	DET
ejpam-3459	48	14	h	h	NOUN
ejpam-3459	48	15	∈	∈	PROPN
ejpam-3459	48	16	l2(q	l2(q	PROPN
ejpam-3459	48	17	)	)	PUNCT
ejpam-3459	48	18	,	,	PUNCT
ejpam-3459	48	19	w	w	PROPN
ejpam-3459	48	20	∈	∈	PROPN
ejpam-3459	48	21	l2(qω	l2(qω	PROPN
ejpam-3459	48	22	)	)	PUNCT
ejpam-3459	48	23	the	the	DET
ejpam-3459	48	24	system	system	NOUN
ejpam-3459	48	25	(	(	PUNCT
ejpam-3459	48	26	1	1	X
ejpam-3459	48	27	)	)	PUNCT
ejpam-3459	48	28	admits	admit	VERB
ejpam-3459	48	29	an	an	DET
ejpam-3459	48	30	unique	unique	ADJ
ejpam-3459	48	31	solution	solution	NOUN
ejpam-3459	48	32	(	(	PUNCT
ejpam-3459	48	33	q1	q1	PROPN
ejpam-3459	48	34	,	,	PUNCT
ejpam-3459	48	35	q2	q2	NOUN
ejpam-3459	48	36	)	)	PUNCT
ejpam-3459	48	37	in	in	ADP
ejpam-3459	48	38	l2(u	l2(u	PROPN
ejpam-3459	48	39	,	,	PUNCT
ejpam-3459	48	40	h1	h1	PROPN
ejpam-3459	48	41	0	0	NUM
ejpam-3459	49	1	(	(	PUNCT
ejpam-3459	49	2	ω))2	ω))2	NOUN
ejpam-3459	49	3	such	such	ADJ
ejpam-3459	49	4	that	that	SCONJ
ejpam-3459	49	5	∂qi	∂qi	PROPN
ejpam-3459	49	6	∂t	∂t	PROPN
ejpam-3459	50	1	+	+	CCONJ
ejpam-3459	51	1	∂qi	∂qi	PROPN
ejpam-3459	51	2	∂a	∂a	NOUN
ejpam-3459	51	3	∈	∈	PROPN
ejpam-3459	51	4	l2(u	l2(u	PROPN
ejpam-3459	51	5	;	;	PUNCT
ejpam-3459	51	6	h−1(ω	h−1(ω	PROPN
ejpam-3459	51	7	)	)	PUNCT
ejpam-3459	51	8	)	)	PUNCT
ejpam-3459	51	9	where	where	SCONJ
ejpam-3459	51	10	h−1(ω	h−1(ω	PROPN
ejpam-3459	51	11	)	)	PUNCT
ejpam-3459	51	12	is	be	AUX
ejpam-3459	51	13	the	the	DET
ejpam-3459	51	14	dual	dual	ADJ
ejpam-3459	51	15	of	of	ADP
ejpam-3459	51	16	the	the	DET
ejpam-3459	51	17	hilbert	hilbert	PROPN
ejpam-3459	51	18	space	space	NOUN
ejpam-3459	51	19	h1	h1	NOUN
ejpam-3459	51	20	0	0	NUM
ejpam-3459	51	21	(	(	PUNCT
ejpam-3459	51	22	ω	ω	NOUN
ejpam-3459	51	23	)	)	PUNCT
ejpam-3459	51	24	.	.	PUNCT
ejpam-3459	52	1	moreover	moreover	ADV
ejpam-3459	52	2	(	(	PUNCT
ejpam-3459	52	3	q1	q1	PROPN
ejpam-3459	52	4	,	,	PUNCT
ejpam-3459	52	5	q2	q2	NOUN
ejpam-3459	52	6	)	)	PUNCT
ejpam-3459	52	7	belong	belong	VERB
ejpam-3459	52	8	to	to	ADP
ejpam-3459	52	9	c((0	c((0	PROPN
ejpam-3459	52	10	,	,	PUNCT
ejpam-3459	52	11	t	t	PROPN
ejpam-3459	52	12	)	)	PUNCT
ejpam-3459	52	13	;	;	PUNCT
ejpam-3459	52	14	l2(qa	l2(qa	PROPN
ejpam-3459	52	15	)	)	PUNCT
ejpam-3459	52	16	)	)	PUNCT
ejpam-3459	52	17	∩	∩	PROPN
ejpam-3459	52	18	c((0	c((0	PROPN
ejpam-3459	52	19	,	,	PUNCT
ejpam-3459	52	20	a);l2(qt	a);l2(qt	NOUN
ejpam-3459	52	21	)	)	PUNCT
ejpam-3459	52	22	)	)	PUNCT
ejpam-3459	52	23	∩	∩	PROPN
ejpam-3459	53	1	l2(u	l2(u	PROPN
ejpam-3459	53	2	,	,	PUNCT
ejpam-3459	53	3	h1	h1	NOUN
ejpam-3459	53	4	0	0	NUM
ejpam-3459	53	5	(	(	PUNCT
ejpam-3459	53	6	ω))2	ω))2	NOUN
ejpam-3459	53	7	(	(	PUNCT
ejpam-3459	53	8	see	see	VERB
ejpam-3459	53	9	lemma	lemma	PROPN
ejpam-3459	53	10	0	0	PUNCT
ejpam-3459	54	1	in	in	ADP
ejpam-3459	54	2	[	[	X
ejpam-3459	54	3	5	5	NUM
ejpam-3459	54	4	]	]	NUM
ejpam-3459	54	5	)	)	PUNCT
ejpam-3459	54	6	.	.	PUNCT
ejpam-3459	54	7	remark	remark	PROPN
ejpam-3459	54	8	1	1	NUM
ejpam-3459	54	9	.	.	PUNCT
ejpam-3459	54	10	assume	assume	VERB
ejpam-3459	54	11	that	that	SCONJ
ejpam-3459	54	12	(	(	PUNCT
ejpam-3459	54	13	h1	h1	PROPN
ejpam-3459	54	14	)	)	PUNCT
ejpam-3459	54	15	holds	hold	VERB
ejpam-3459	54	16	and	and	CCONJ
ejpam-3459	54	17	set	set	VERB
ejpam-3459	54	18	p1	p1	PROPN
ejpam-3459	54	19	=	=	PROPN
ejpam-3459	54	20	q1	q1	PROPN
ejpam-3459	54	21	+	+	NUM
ejpam-3459	54	22	q2	q2	NOUN
ejpam-3459	54	23	;	;	PUNCT
ejpam-3459	54	24	p2	p2	PROPN
ejpam-3459	54	25	=	=	PROPN
ejpam-3459	54	26	q1	q1	PROPN
ejpam-3459	54	27	−	−	PROPN
ejpam-3459	54	28	q2	q2	NOUN
ejpam-3459	54	29	.	.	PUNCT
ejpam-3459	55	1	(	(	PUNCT
ejpam-3459	55	2	3	3	NUM
ejpam-3459	55	3	)	)	PUNCT
ejpam-3459	55	4	thus	thus	ADV
ejpam-3459	55	5	,	,	PUNCT
ejpam-3459	55	6	the	the	DET
ejpam-3459	55	7	condition	condition	NOUN
ejpam-3459	55	8	(	(	PUNCT
ejpam-3459	55	9	2	2	X
ejpam-3459	55	10	)	)	PUNCT
ejpam-3459	55	11	is	be	AUX
ejpam-3459	55	12	equivalent	equivalent	ADJ
ejpam-3459	55	13	to	to	ADP
ejpam-3459	55	14	p1(0	p1(0	PROPN
ejpam-3459	55	15	,	,	PUNCT
ejpam-3459	55	16	a	a	PRON
ejpam-3459	55	17	,	,	PUNCT
ejpam-3459	55	18	x	x	NOUN
ejpam-3459	55	19	)	)	PUNCT
ejpam-3459	55	20	=	=	SYM
ejpam-3459	55	21	p2(0	p2(0	NOUN
ejpam-3459	55	22	,	,	PUNCT
ejpam-3459	55	23	a	a	PRON
ejpam-3459	55	24	,	,	PUNCT
ejpam-3459	55	25	x	x	NOUN
ejpam-3459	55	26	)	)	PUNCT
ejpam-3459	56	1	=	=	SYM
ejpam-3459	56	2	0	0	NUM
ejpam-3459	56	3	a.e	a.e	NOUN
ejpam-3459	56	4	(	(	PUNCT
ejpam-3459	56	5	a	a	PRON
ejpam-3459	56	6	,	,	PUNCT
ejpam-3459	56	7	x	x	NOUN
ejpam-3459	56	8	)	)	PUNCT
ejpam-3459	56	9	in	in	ADP
ejpam-3459	56	10	qa	qa	PROPN
ejpam-3459	56	11	.	.	PUNCT
ejpam-3459	57	1	the	the	DET
ejpam-3459	57	2	following	follow	VERB
ejpam-3459	57	3	changes	change	NOUN
ejpam-3459	57	4	are	be	AUX
ejpam-3459	57	5	required	require	VERB
ejpam-3459	57	6	:	:	PUNCT
ejpam-3459	57	7	µ̂1	µ̂1	ADP
ejpam-3459	57	8	=	=	SYM
ejpam-3459	57	9	1	1	NUM
ejpam-3459	57	10	2(µ1	2(µ1	NUM
ejpam-3459	57	11	+	+	CCONJ
ejpam-3459	57	12	µ2	µ2	PROPN
ejpam-3459	57	13	)	)	PUNCT
ejpam-3459	57	14	,	,	PUNCT
ejpam-3459	57	15	µ̂2	µ̂2	PUNCT
ejpam-3459	57	16	=	=	NOUN
ejpam-3459	57	17	1	1	NUM
ejpam-3459	57	18	2(µ1	2(µ1	NUM
ejpam-3459	57	19	−	−	NOUN
ejpam-3459	57	20	µ2	µ2	PROPN
ejpam-3459	57	21	)	)	PUNCT
ejpam-3459	57	22	,	,	PUNCT
ejpam-3459	57	23	f	f	X
ejpam-3459	57	24	=	=	SYM
ejpam-3459	57	25	2h	2h	NUM
ejpam-3459	57	26	,	,	PUNCT
ejpam-3459	57	27	k	k	PROPN
ejpam-3459	57	28	=	=	SYM
ejpam-3459	57	29	2w	2w	NUM
ejpam-3459	57	30	,	,	PUNCT
ejpam-3459	57	31	β̂1(p1	β̂1(p1	NOUN
ejpam-3459	57	32	,	,	PUNCT
ejpam-3459	57	33	p2	p2	X
ejpam-3459	57	34	)	)	PUNCT
ejpam-3459	57	35	=	=	SYM
ejpam-3459	57	36	1	1	NUM
ejpam-3459	57	37	2	2	NUM
ejpam-3459	57	38	[	[	PUNCT
ejpam-3459	57	39	β1f	β1f	X
ejpam-3459	57	40	(	(	PUNCT
ejpam-3459	57	41	1	1	NUM
ejpam-3459	57	42	2	2	NUM
ejpam-3459	57	43	∫	∫	NOUN
ejpam-3459	57	44	a	a	DET
ejpam-3459	57	45	0	0	NUM
ejpam-3459	57	46	β1(p1	β1(p1	NOUN
ejpam-3459	57	47	+	+	CCONJ
ejpam-3459	57	48	p2)da	p2)da	ADJ
ejpam-3459	57	49	)	)	PUNCT
ejpam-3459	58	1	+	+	CCONJ
ejpam-3459	58	2	β2	β2	VERB
ejpam-3459	58	3	g	g	PROPN
ejpam-3459	58	4	(	(	PUNCT
ejpam-3459	58	5	1	1	NUM
ejpam-3459	58	6	2	2	NUM
ejpam-3459	58	7	∫	∫	NOUN
ejpam-3459	58	8	a	a	DET
ejpam-3459	58	9	0	0	NUM
ejpam-3459	58	10	β2(p1	β2(p1	NUM
ejpam-3459	58	11	−	−	NOUN
ejpam-3459	58	12	p2)da	p2)da	PROPN
ejpam-3459	58	13	)	)	PUNCT
ejpam-3459	58	14	]	]	PUNCT
ejpam-3459	58	15	,	,	PUNCT
ejpam-3459	58	16	β̂2(p1	β̂2(p1	NOUN
ejpam-3459	58	17	,	,	PUNCT
ejpam-3459	58	18	p2	p2	X
ejpam-3459	58	19	)	)	PUNCT
ejpam-3459	58	20	=	=	SYM
ejpam-3459	58	21	1	1	NUM
ejpam-3459	58	22	2	2	NUM
ejpam-3459	58	23	[	[	PUNCT
ejpam-3459	58	24	β1f	β1f	X
ejpam-3459	58	25	(	(	PUNCT
ejpam-3459	58	26	1	1	NUM
ejpam-3459	58	27	2	2	NUM
ejpam-3459	58	28	∫	∫	NOUN
ejpam-3459	58	29	a	a	DET
ejpam-3459	58	30	0	0	NUM
ejpam-3459	58	31	β1(p1	β1(p1	NOUN
ejpam-3459	58	32	+	+	CCONJ
ejpam-3459	58	33	p2)da	p2)da	ADJ
ejpam-3459	58	34	)	)	PUNCT
ejpam-3459	58	35	−	−	PROPN
ejpam-3459	59	1	β2	β2	PROPN
ejpam-3459	59	2	g	g	PROPN
ejpam-3459	59	3	(	(	PUNCT
ejpam-3459	59	4	1	1	NUM
ejpam-3459	59	5	2	2	NUM
ejpam-3459	59	6	∫	∫	NOUN
ejpam-3459	59	7	a	a	DET
ejpam-3459	59	8	0	0	NUM
ejpam-3459	59	9	β2(p1	β2(p1	NUM
ejpam-3459	59	10	−	−	NOUN
ejpam-3459	59	11	p2)da	p2)da	PROPN
ejpam-3459	59	12	)	)	PUNCT
ejpam-3459	59	13	]	]	PUNCT
ejpam-3459	59	14	.	.	PUNCT
ejpam-3459	60	1	then	then	ADV
ejpam-3459	60	2	,	,	PUNCT
ejpam-3459	60	3	the	the	DET
ejpam-3459	60	4	null	null	ADJ
ejpam-3459	60	5	controllability	controllability	NOUN
ejpam-3459	60	6	problem	problem	NOUN
ejpam-3459	60	7	(	(	PUNCT
ejpam-3459	60	8	1)-(2	1)-(2	NUM
ejpam-3459	60	9	)	)	PUNCT
ejpam-3459	60	10	is	be	AUX
ejpam-3459	60	11	equivalent	equivalent	ADJ
ejpam-3459	60	12	to	to	ADP
ejpam-3459	60	13	the	the	DET
ejpam-3459	60	14	problem	problem	NOUN
ejpam-3459	60	15	:	:	PUNCT
ejpam-3459	60	16	for	for	ADP
ejpam-3459	60	17	any	any	DET
ejpam-3459	60	18	µ̂1	µ̂1	NOUN
ejpam-3459	60	19	,	,	PUNCT
ejpam-3459	60	20	µ̂2	µ̂2	PUNCT
ejpam-3459	60	21	∈	∈	PROPN
ejpam-3459	60	22	l∞(q	l∞(q	NOUN
ejpam-3459	60	23	)	)	PUNCT
ejpam-3459	60	24	and	and	CCONJ
ejpam-3459	60	25	for	for	ADP
ejpam-3459	60	26	f	f	PROPN
ejpam-3459	60	27	∈	∈	PROPN
ejpam-3459	60	28	l2(q	l2(q	PROPN
ejpam-3459	60	29	)	)	PUNCT
ejpam-3459	60	30	find	find	VERB
ejpam-3459	60	31	a	a	DET
ejpam-3459	60	32	control	control	NOUN
ejpam-3459	60	33	k	k	PROPN
ejpam-3459	60	34	∈	∈	PROPN
ejpam-3459	60	35	l2(qω	l2(qω	PROPN
ejpam-3459	60	36	)	)	PUNCT
ejpam-3459	60	37	(	(	PUNCT
ejpam-3459	60	38	4	4	X
ejpam-3459	60	39	)	)	PUNCT
ejpam-3459	60	40	such	such	ADJ
ejpam-3459	60	41	that	that	SCONJ
ejpam-3459	60	42	the	the	DET
ejpam-3459	60	43	pair	pair	NOUN
ejpam-3459	60	44	p	p	X
ejpam-3459	60	45	=	=	X
ejpam-3459	60	46	(	(	PUNCT
ejpam-3459	60	47	p1	p1	PROPN
ejpam-3459	60	48	,	,	PUNCT
ejpam-3459	60	49	p2	p2	NOUN
ejpam-3459	60	50	)	)	PUNCT
ejpam-3459	60	51	solution	solution	NOUN
ejpam-3459	60	52	of	of	ADP
ejpam-3459	60	53	the	the	DET
ejpam-3459	60	54	system	system	PROPN
ejpam-3459	60	55	−∂p1	−∂p1	NOUN
ejpam-3459	60	56	∂t	∂t	PROPN
ejpam-3459	60	57	−	−	NOUN
ejpam-3459	60	58	∂p1	∂p1	NOUN
ejpam-3459	60	59	∂a	∂a	PROPN
ejpam-3459	60	60	−∆p1	−∆p1	NOUN
ejpam-3459	60	61	+	+	CCONJ
ejpam-3459	60	62	µ̂1p1	µ̂1p1	ADJ
ejpam-3459	60	63	+	+	NUM
ejpam-3459	60	64	µ̂2p2	µ̂2p2	NOUN
ejpam-3459	60	65	=	=	SYM
ejpam-3459	60	66	β̂1(p)p1(t	β̂1(p)p1(t	NUM
ejpam-3459	60	67	,	,	PUNCT
ejpam-3459	60	68	0	0	NUM
ejpam-3459	60	69	,	,	PUNCT
ejpam-3459	60	70	x	x	NOUN
ejpam-3459	60	71	)	)	PUNCT
ejpam-3459	60	72	+	+	CCONJ
ejpam-3459	60	73	β̂2(p)p2(t	β̂2(p)p2(t	ADJ
ejpam-3459	60	74	,	,	PUNCT
ejpam-3459	60	75	0	0	NUM
ejpam-3459	60	76	,	,	PUNCT
ejpam-3459	60	77	x	x	NOUN
ejpam-3459	60	78	)	)	PUNCT
ejpam-3459	61	1	+	+	NUM
ejpam-3459	61	2	f	f	NOUN
ejpam-3459	61	3	+	+	NUM
ejpam-3459	61	4	kχω	kχω	NOUN
ejpam-3459	61	5	in	in	ADP
ejpam-3459	61	6	q	q	PROPN
ejpam-3459	61	7	,	,	PUNCT
ejpam-3459	61	8	−∂p2	−∂p2	PROPN
ejpam-3459	61	9	∂t	∂t	PROPN
ejpam-3459	61	10	−	−	PROPN
ejpam-3459	61	11	∂p2	∂p2	PROPN
ejpam-3459	61	12	∂a	∂a	PROPN
ejpam-3459	61	13	−∆p2	−∆p2	NOUN
ejpam-3459	61	14	+	+	CCONJ
ejpam-3459	61	15	µ̂1p2	µ̂1p2	VERB
ejpam-3459	61	16	+	+	NUM
ejpam-3459	61	17	µ̂2p1	µ̂2p1	NOUN
ejpam-3459	61	18	=	=	SYM
ejpam-3459	61	19	β̂2(p)p1(t	β̂2(p)p1(t	PROPN
ejpam-3459	61	20	,	,	PUNCT
ejpam-3459	61	21	0	0	NUM
ejpam-3459	61	22	,	,	PUNCT
ejpam-3459	61	23	x	x	NOUN
ejpam-3459	61	24	)	)	PUNCT
ejpam-3459	61	25	+	+	CCONJ
ejpam-3459	61	26	β̂1(p)p2(t	β̂1(p)p2(t	PROPN
ejpam-3459	61	27	,	,	PUNCT
ejpam-3459	61	28	0	0	NUM
ejpam-3459	61	29	,	,	PUNCT
ejpam-3459	61	30	x	x	NOUN
ejpam-3459	61	31	)	)	PUNCT
ejpam-3459	61	32	in	in	ADP
ejpam-3459	61	33	q	q	NOUN
ejpam-3459	61	34	,	,	PUNCT
ejpam-3459	61	35	p1	p1	NOUN
ejpam-3459	61	36	=	=	NOUN
ejpam-3459	61	37	p2	p2	PROPN
ejpam-3459	61	38	=	=	SYM
ejpam-3459	61	39	0	0	NUM
ejpam-3459	61	40	on	on	ADP
ejpam-3459	61	41	∑	∑	PROPN
ejpam-3459	61	42	,	,	PUNCT
ejpam-3459	61	43	p1(t	p1(t	PROPN
ejpam-3459	61	44	,	,	PUNCT
ejpam-3459	61	45	a	a	PRON
ejpam-3459	61	46	,	,	PUNCT
ejpam-3459	61	47	x	x	NOUN
ejpam-3459	61	48	)	)	PUNCT
ejpam-3459	61	49	=	=	SYM
ejpam-3459	61	50	p2(t	p2(t	PROPN
ejpam-3459	61	51	,	,	PUNCT
ejpam-3459	61	52	a	a	PRON
ejpam-3459	61	53	,	,	PUNCT
ejpam-3459	61	54	x	x	NOUN
ejpam-3459	61	55	)	)	PUNCT
ejpam-3459	61	56	=	=	SYM
ejpam-3459	61	57	0	0	NUM
ejpam-3459	62	1	in	in	ADP
ejpam-3459	62	2	qa	qa	PROPN
ejpam-3459	62	3	,	,	PUNCT
ejpam-3459	62	4	p1(t	p1(t	PROPN
ejpam-3459	62	5	,	,	PUNCT
ejpam-3459	62	6	a	a	PRON
ejpam-3459	62	7	,	,	PUNCT
ejpam-3459	62	8	x	x	NOUN
ejpam-3459	62	9	)	)	PUNCT
ejpam-3459	62	10	=	=	SYM
ejpam-3459	62	11	p2(t	p2(t	PROPN
ejpam-3459	62	12	,	,	PUNCT
ejpam-3459	62	13	a	a	PRON
ejpam-3459	62	14	,	,	PUNCT
ejpam-3459	62	15	x	x	NOUN
ejpam-3459	62	16	)	)	PUNCT
ejpam-3459	62	17	=	=	SYM
ejpam-3459	62	18	0	0	NUM
ejpam-3459	62	19	in	in	ADP
ejpam-3459	62	20	qt	qt	NOUN
ejpam-3459	62	21	,	,	PUNCT
ejpam-3459	62	22	(	(	PUNCT
ejpam-3459	62	23	5	5	X
ejpam-3459	62	24	)	)	PUNCT
ejpam-3459	62	25	satisfies	satisfy	VERB
ejpam-3459	62	26	p1(0	p1(0	PROPN
ejpam-3459	62	27	,	,	PUNCT
ejpam-3459	62	28	a	a	PRON
ejpam-3459	62	29	,	,	PUNCT
ejpam-3459	62	30	x	x	NOUN
ejpam-3459	62	31	)	)	PUNCT
ejpam-3459	62	32	=	=	SYM
ejpam-3459	62	33	p2(0	p2(0	NOUN
ejpam-3459	62	34	,	,	PUNCT
ejpam-3459	62	35	a	a	PRON
ejpam-3459	62	36	,	,	PUNCT
ejpam-3459	62	37	x	x	NOUN
ejpam-3459	62	38	)	)	PUNCT
ejpam-3459	62	39	=	=	SYM
ejpam-3459	62	40	0	0	NUM
ejpam-3459	63	1	in	in	ADP
ejpam-3459	63	2	qa	qa	PROPN
ejpam-3459	63	3	.	.	PUNCT
ejpam-3459	64	1	(	(	PUNCT
ejpam-3459	64	2	6	6	X
ejpam-3459	64	3	)	)	PUNCT
ejpam-3459	64	4	notice	notice	NOUN
ejpam-3459	64	5	that	that	SCONJ
ejpam-3459	64	6	system	system	NOUN
ejpam-3459	64	7	(	(	PUNCT
ejpam-3459	64	8	5	5	X
ejpam-3459	64	9	)	)	PUNCT
ejpam-3459	64	10	admits	admit	VERB
ejpam-3459	64	11	an	an	DET
ejpam-3459	64	12	unique	unique	ADJ
ejpam-3459	64	13	solution	solution	NOUN
ejpam-3459	64	14	(	(	PUNCT
ejpam-3459	64	15	p1	p1	NOUN
ejpam-3459	64	16	,	,	PUNCT
ejpam-3459	64	17	p2	p2	PROPN
ejpam-3459	64	18	)	)	PUNCT
ejpam-3459	64	19	in	in	ADP
ejpam-3459	64	20	(	(	PUNCT
ejpam-3459	64	21	c((0	c((0	PROPN
ejpam-3459	64	22	,	,	PUNCT
ejpam-3459	64	23	t	t	PROPN
ejpam-3459	64	24	)	)	PUNCT
ejpam-3459	64	25	;	;	PUNCT
ejpam-3459	65	1	l2(qa))∩c((0	l2(qa))∩c((0	PROPN
ejpam-3459	65	2	,	,	PUNCT
ejpam-3459	65	3	a);l2(qt	a);l2(qt	PROPN
ejpam-3459	65	4	)	)	PUNCT
ejpam-3459	65	5	)	)	PUNCT
ejpam-3459	65	6	∩	∩	PROPN
ejpam-3459	65	7	l2(u	l2(u	PROPN
ejpam-3459	65	8	,	,	PUNCT
ejpam-3459	65	9	h1	h1	PROPN
ejpam-3459	65	10	0	0	NUM
ejpam-3459	65	11	(	(	PUNCT
ejpam-3459	65	12	ω	ω	NOUN
ejpam-3459	65	13	)	)	PUNCT
ejpam-3459	65	14	)	)	PUNCT
ejpam-3459	65	15	)	)	PUNCT
ejpam-3459	65	16	2	2	NUM
ejpam-3459	65	17	for	for	ADP
ejpam-3459	65	18	each	each	DET
ejpam-3459	65	19	control	control	NOUN
ejpam-3459	65	20	k	k	PROPN
ejpam-3459	65	21	verifying	verifying	NOUN
ejpam-3459	65	22	(	(	PUNCT
ejpam-3459	65	23	4	4	NUM
ejpam-3459	65	24	)	)	PUNCT
ejpam-3459	65	25	.	.	PUNCT
ejpam-3459	66	1	the	the	DET
ejpam-3459	66	2	main	main	ADJ
ejpam-3459	66	3	goal	goal	NOUN
ejpam-3459	66	4	of	of	ADP
ejpam-3459	66	5	this	this	DET
ejpam-3459	66	6	paper	paper	NOUN
ejpam-3459	66	7	is	be	AUX
ejpam-3459	66	8	to	to	PART
ejpam-3459	66	9	prove	prove	VERB
ejpam-3459	66	10	the	the	DET
ejpam-3459	66	11	following	following	ADJ
ejpam-3459	66	12	result	result	NOUN
ejpam-3459	66	13	:	:	PUNCT
ejpam-3459	66	14	c.	c.	PROPN
ejpam-3459	66	15	k.	k.	PROPN
ejpam-3459	66	16	somé	somé	PROPN
ejpam-3459	66	17	,	,	PUNCT
ejpam-3459	66	18	s.	s.	PROPN
ejpam-3459	66	19	sawadogo	sawadogo	PROPN
ejpam-3459	66	20	/	/	SYM
ejpam-3459	66	21	eur	eur	PROPN
ejpam-3459	66	22	.	.	PUNCT
ejpam-3459	67	1	j.	j.	PROPN
ejpam-3459	67	2	pure	pure	PROPN
ejpam-3459	67	3	appl	appl	PROPN
ejpam-3459	67	4	.	.	PROPN
ejpam-3459	67	5	math	math	PROPN
ejpam-3459	67	6	,	,	PUNCT
ejpam-3459	67	7	12	12	NUM
ejpam-3459	67	8	(	(	PUNCT
ejpam-3459	67	9	3	3	NUM
ejpam-3459	67	10	)	)	PUNCT
ejpam-3459	67	11	(	(	PUNCT
ejpam-3459	67	12	2019	2019	NUM
ejpam-3459	67	13	)	)	PUNCT
ejpam-3459	67	14	,	,	PUNCT
ejpam-3459	67	15	870	870	NUM
ejpam-3459	67	16	-	-	SYM
ejpam-3459	67	17	892	892	NUM
ejpam-3459	67	18	873	873	NUM
ejpam-3459	67	19	theorem	theorem	NOUN
ejpam-3459	67	20	1	1	NUM
ejpam-3459	67	21	.	.	PUNCT
ejpam-3459	68	1	let	let	VERB
ejpam-3459	68	2	ω	ω	PRON
ejpam-3459	68	3	be	be	AUX
ejpam-3459	68	4	an	an	DET
ejpam-3459	68	5	open	open	ADJ
ejpam-3459	68	6	subset	subset	NOUN
ejpam-3459	68	7	of	of	ADP
ejpam-3459	68	8	rn	rn	PROPN
ejpam-3459	68	9	with	with	ADP
ejpam-3459	68	10	boundary	boundary	ADJ
ejpam-3459	68	11	γ	γ	NOUN
ejpam-3459	68	12	of	of	ADP
ejpam-3459	68	13	class	class	NOUN
ejpam-3459	68	14	c2	c2	PROPN
ejpam-3459	68	15	and	and	CCONJ
ejpam-3459	69	1	ω	ω	PROPN
ejpam-3459	69	2	be	be	AUX
ejpam-3459	69	3	a	a	DET
ejpam-3459	69	4	non	non	X
ejpam-3459	69	5	empty	empty	ADJ
ejpam-3459	69	6	subset	subset	NOUN
ejpam-3459	69	7	of	of	ADP
ejpam-3459	69	8	ω	ω	PROPN
ejpam-3459	69	9	.	.	PUNCT
ejpam-3459	70	1	assume	assume	VERB
ejpam-3459	70	2	that	that	SCONJ
ejpam-3459	70	3	the	the	DET
ejpam-3459	70	4	hypothesis	hypothesis	NOUN
ejpam-3459	70	5	(	(	PUNCT
ejpam-3459	70	6	h0	h0	NOUN
ejpam-3459	70	7	)	)	PUNCT
ejpam-3459	70	8	−	−	PROPN
ejpam-3459	70	9	(	(	PUNCT
ejpam-3459	70	10	h3	h3	NOUN
ejpam-3459	70	11	)	)	PUNCT
ejpam-3459	70	12	hold	hold	VERB
ejpam-3459	70	13	.	.	PUNCT
ejpam-3459	71	1	there	there	PRON
ejpam-3459	71	2	exists	exist	VERB
ejpam-3459	71	3	a	a	DET
ejpam-3459	71	4	positive	positive	ADJ
ejpam-3459	71	5	real	real	ADJ
ejpam-3459	71	6	function	function	NOUN
ejpam-3459	71	7	θ	θ	PROPN
ejpam-3459	71	8	(	(	PUNCT
ejpam-3459	71	9	θ	θ	NOUN
ejpam-3459	71	10	is	be	AUX
ejpam-3459	71	11	defined	define	VERB
ejpam-3459	71	12	by	by	ADP
ejpam-3459	71	13	(	(	PUNCT
ejpam-3459	71	14	13	13	NUM
ejpam-3459	71	15	)	)	PUNCT
ejpam-3459	71	16	)	)	PUNCT
ejpam-3459	71	17	such	such	ADJ
ejpam-3459	71	18	that	that	PRON
ejpam-3459	71	19	for	for	ADP
ejpam-3459	71	20	any	any	DET
ejpam-3459	71	21	function	function	NOUN
ejpam-3459	71	22	f	f	PROPN
ejpam-3459	71	23	∈	∈	PROPN
ejpam-3459	71	24	l2	l2	NOUN
ejpam-3459	71	25	(	(	PUNCT
ejpam-3459	71	26	q	q	X
ejpam-3459	71	27	)	)	PUNCT
ejpam-3459	71	28	with	with	ADP
ejpam-3459	71	29	θf	θf	PUNCT
ejpam-3459	71	30	∈	∈	NOUN
ejpam-3459	71	31	l2	l2	NOUN
ejpam-3459	71	32	(	(	PUNCT
ejpam-3459	71	33	q	q	NOUN
ejpam-3459	71	34	)	)	PUNCT
ejpam-3459	71	35	,	,	PUNCT
ejpam-3459	71	36	there	there	PRON
ejpam-3459	71	37	exists	exist	VERB
ejpam-3459	71	38	an	an	DET
ejpam-3459	71	39	unique	unique	ADJ
ejpam-3459	71	40	control	control	NOUN
ejpam-3459	71	41	k̃	k̃	PROPN
ejpam-3459	71	42	,	,	PUNCT
ejpam-3459	71	43	of	of	ADP
ejpam-3459	71	44	minimal	minimal	ADJ
ejpam-3459	71	45	norm	norm	NOUN
ejpam-3459	71	46	in	in	ADP
ejpam-3459	71	47	l2(qω	l2(qω	PROPN
ejpam-3459	71	48	)	)	PUNCT
ejpam-3459	71	49	such	such	ADJ
ejpam-3459	71	50	that	that	SCONJ
ejpam-3459	71	51	(	(	PUNCT
ejpam-3459	71	52	k̃	k̃	PROPN
ejpam-3459	71	53	,	,	PUNCT
ejpam-3459	71	54	p̃1	p̃1	PROPN
ejpam-3459	71	55	,	,	PUNCT
ejpam-3459	71	56	p̃2	p̃2	PROPN
ejpam-3459	71	57	)	)	PUNCT
ejpam-3459	71	58	is	be	AUX
ejpam-3459	71	59	solution	solution	NOUN
ejpam-3459	71	60	of	of	ADP
ejpam-3459	71	61	the	the	DET
ejpam-3459	71	62	simultaneous	simultaneous	ADJ
ejpam-3459	71	63	null	null	ADJ
ejpam-3459	71	64	controllability	controllability	NOUN
ejpam-3459	71	65	problem	problem	NOUN
ejpam-3459	71	66	(	(	PUNCT
ejpam-3459	71	67	5)-(6	5)-(6	NUM
ejpam-3459	71	68	)	)	PUNCT
ejpam-3459	71	69	.	.	PUNCT
ejpam-3459	72	1	moreover	moreover	ADV
ejpam-3459	72	2	,	,	PUNCT
ejpam-3459	72	3	the	the	DET
ejpam-3459	72	4	control	control	NOUN
ejpam-3459	72	5	k̃	k̃	PROPN
ejpam-3459	72	6	is	be	AUX
ejpam-3459	72	7	given	give	VERB
ejpam-3459	72	8	by	by	ADP
ejpam-3459	72	9	k̃	k̃	PROPN
ejpam-3459	72	10	=	=	PROPN
ejpam-3459	72	11	η̃1χω	η̃1χω	X
ejpam-3459	72	12	(	(	PUNCT
ejpam-3459	72	13	7	7	NUM
ejpam-3459	72	14	)	)	PUNCT
ejpam-3459	72	15	and	and	CCONJ
ejpam-3459	72	16	verifies	verifie	NOUN
ejpam-3459	72	17	‖k̃‖l2(qω	‖k̃‖l2(qω	VERB
ejpam-3459	72	18	)	)	PUNCT
ejpam-3459	72	19	≤	≤	NUM
ejpam-3459	73	1	c	c	NOUN
ejpam-3459	73	2	(	(	PUNCT
ejpam-3459	73	3	‖θf‖l2(q	‖θf‖l2(q	NUM
ejpam-3459	73	4	)	)	PUNCT
ejpam-3459	73	5	+	+	CCONJ
ejpam-3459	73	6	‖f‖l2(q	‖f‖l2(q	NUM
ejpam-3459	73	7	)	)	PUNCT
ejpam-3459	73	8	)	)	PUNCT
ejpam-3459	74	1	(	(	PUNCT
ejpam-3459	74	2	8)	8)	NUM
ejpam-3459	74	3	where	where	SCONJ
ejpam-3459	74	4	η̃	η̃	PROPN
ejpam-3459	74	5	=	=	SYM
ejpam-3459	74	6	(	(	PUNCT
ejpam-3459	74	7	η̃1	η̃1	PROPN
ejpam-3459	74	8	,	,	PUNCT
ejpam-3459	74	9	η̃2	η̃2	PROPN
ejpam-3459	74	10	)	)	PUNCT
ejpam-3459	74	11	satisfies	satisfies	NOUN
ejpam-3459	74	12	∂η̃1	∂η̃1	NOUN
ejpam-3459	75	1	∂t	∂t	PROPN
ejpam-3459	75	2	+	+	CCONJ
ejpam-3459	75	3	∂η̃1	∂η̃1	PROPN
ejpam-3459	75	4	∂a	∂a	PROPN
ejpam-3459	75	5	−∆η̃1	−∆η̃1	PROPN
ejpam-3459	75	6	+	+	CCONJ
ejpam-3459	75	7	µ̂1η̃1	µ̂1η̃1	PRON
ejpam-3459	75	8	+	+	CCONJ
ejpam-3459	75	9	µ̂2η̃2	µ̂2η̃2	X
ejpam-3459	75	10	=	=	SYM
ejpam-3459	75	11	0	0	NUM
ejpam-3459	75	12	in	in	ADP
ejpam-3459	75	13	q	q	NOUN
ejpam-3459	75	14	,	,	PUNCT
ejpam-3459	75	15	∂η̃2	∂η̃2	VERB
ejpam-3459	75	16	∂t	∂t	PROPN
ejpam-3459	76	1	+	+	NUM
ejpam-3459	76	2	∂η̃2	∂η̃2	NOUN
ejpam-3459	76	3	∂a	∂a	ADP
ejpam-3459	76	4	−∆η̃2	−∆η̃2	PROPN
ejpam-3459	76	5	+	+	CCONJ
ejpam-3459	76	6	µ̂1η̃2	µ̂1η̃2	PROPN
ejpam-3459	76	7	+	+	CCONJ
ejpam-3459	76	8	µ̂2η̃1	µ̂2η̃1	PROPN
ejpam-3459	76	9	=	=	NOUN
ejpam-3459	76	10	0	0	NUM
ejpam-3459	76	11	in	in	ADP
ejpam-3459	76	12	q	q	NOUN
ejpam-3459	76	13	,	,	PUNCT
ejpam-3459	76	14	η̃1	η̃1	PROPN
ejpam-3459	76	15	=	=	PUNCT
ejpam-3459	76	16	η̃2	η̃2	PROPN
ejpam-3459	76	17	=	=	SYM
ejpam-3459	76	18	0	0	NUM
ejpam-3459	76	19	on	on	ADP
ejpam-3459	76	20	σ	σ	PROPN
ejpam-3459	76	21	,	,	PUNCT
ejpam-3459	76	22	η̃1(t	η̃1(t	PROPN
ejpam-3459	76	23	,	,	PUNCT
ejpam-3459	76	24	0	0	NUM
ejpam-3459	76	25	,	,	PUNCT
ejpam-3459	76	26	x	x	NOUN
ejpam-3459	76	27	)	)	PUNCT
ejpam-3459	76	28	=	=	SYM
ejpam-3459	77	1	∫	∫	PROPN
ejpam-3459	78	1	a	a	PRON
ejpam-3459	78	2	0	0	NUM
ejpam-3459	78	3	(	(	PUNCT
ejpam-3459	78	4	β̂1(p)η̃1	β̂1(p)η̃1	PROPN
ejpam-3459	78	5	+	+	CCONJ
ejpam-3459	78	6	β̂2(p)η̃2	β̂2(p)η̃2	PROPN
ejpam-3459	78	7	)	)	PUNCT
ejpam-3459	78	8	da	da	NOUN
ejpam-3459	78	9	in	in	ADP
ejpam-3459	78	10	qt	qt	NOUN
ejpam-3459	78	11	,	,	PUNCT
ejpam-3459	78	12	η̃2(t	η̃2(t	PROPN
ejpam-3459	78	13	,	,	PUNCT
ejpam-3459	78	14	0	0	NUM
ejpam-3459	78	15	,	,	PUNCT
ejpam-3459	78	16	x	x	X
ejpam-3459	78	17	)	)	PUNCT
ejpam-3459	79	1	=	=	SYM
ejpam-3459	79	2	∫	∫	PROPN
ejpam-3459	80	1	a	a	DET
ejpam-3459	80	2	0	0	NUM
ejpam-3459	80	3	(	(	PUNCT
ejpam-3459	80	4	β̂2(p)η̃1	β̂2(p)η̃1	PROPN
ejpam-3459	80	5	+	+	CCONJ
ejpam-3459	80	6	β̂1(p)η̃2	β̂1(p)η̃2	NOUN
ejpam-3459	80	7	)	)	PUNCT
ejpam-3459	80	8	da	da	NOUN
ejpam-3459	80	9	in	in	ADP
ejpam-3459	80	10	qt	qt	NOUN
ejpam-3459	80	11	.	.	PUNCT
ejpam-3459	81	1	(	(	PUNCT
ejpam-3459	81	2	9	9	NUM
ejpam-3459	81	3	)	)	PUNCT
ejpam-3459	81	4	with	with	ADP
ejpam-3459	81	5	p̃	p̃	PROPN
ejpam-3459	81	6	=	=	PUNCT
ejpam-3459	81	7	(	(	PUNCT
ejpam-3459	81	8	p̃1	p̃1	PROPN
ejpam-3459	81	9	,	,	PUNCT
ejpam-3459	81	10	p̃2	p̃2	PROPN
ejpam-3459	81	11	)	)	PUNCT
ejpam-3459	81	12	.	.	PUNCT
ejpam-3459	82	1	3	3	X
ejpam-3459	82	2	.	.	X
ejpam-3459	82	3	null	null	ADJ
ejpam-3459	82	4	controllability	controllability	PROPN
ejpam-3459	82	5	result	result	NOUN
ejpam-3459	82	6	for	for	ADP
ejpam-3459	82	7	some	some	DET
ejpam-3459	82	8	coupled	couple	VERB
ejpam-3459	82	9	models	model	NOUN
ejpam-3459	82	10	before	before	ADP
ejpam-3459	82	11	tackling	tackle	VERB
ejpam-3459	82	12	the	the	DET
ejpam-3459	82	13	controllability	controllability	NOUN
ejpam-3459	82	14	problem	problem	NOUN
ejpam-3459	82	15	,	,	PUNCT
ejpam-3459	82	16	we	we	PRON
ejpam-3459	82	17	will	will	AUX
ejpam-3459	82	18	state	state	VERB
ejpam-3459	82	19	the	the	DET
ejpam-3459	82	20	following	follow	VERB
ejpam-3459	82	21	results	result	NOUN
ejpam-3459	82	22	.	.	PUNCT
ejpam-3459	83	1	3.1	3.1	NUM
ejpam-3459	83	2	.	.	PUNCT
ejpam-3459	83	3	global	global	ADJ
ejpam-3459	83	4	carleman	carleman	PROPN
ejpam-3459	83	5	’s	’s	PART
ejpam-3459	83	6	inequality	inequality	NOUN
ejpam-3459	83	7	and	and	CCONJ
ejpam-3459	83	8	observability	observability	NOUN
ejpam-3459	83	9	inequality	inequality	NOUN
ejpam-3459	83	10	result	result	NOUN
ejpam-3459	83	11	for	for	ADP
ejpam-3459	83	12	any	any	DET
ejpam-3459	83	13	positive	positive	ADJ
ejpam-3459	83	14	parameters	parameter	NOUN
ejpam-3459	83	15	λ	λ	PROPN
ejpam-3459	83	16	and	and	CCONJ
ejpam-3459	83	17	τ	τ	PROPN
ejpam-3459	83	18	,	,	PUNCT
ejpam-3459	83	19	we	we	PRON
ejpam-3459	83	20	define	define	VERB
ejpam-3459	83	21	the	the	DET
ejpam-3459	83	22	positive	positive	ADJ
ejpam-3459	83	23	functions	function	NOUN
ejpam-3459	83	24	:	:	PUNCT
ejpam-3459	83	25	α(t	α(t	PROPN
ejpam-3459	83	26	,	,	PUNCT
ejpam-3459	83	27	a	a	PRON
ejpam-3459	83	28	,	,	PUNCT
ejpam-3459	83	29	x	x	NOUN
ejpam-3459	83	30	)	)	PUNCT
ejpam-3459	83	31	=	=	PUNCT
ejpam-3459	84	1	τ	τ	X
ejpam-3459	84	2	e	e	NOUN
ejpam-3459	84	3	4	4	NUM
ejpam-3459	84	4	3λ‖ψ‖∞	3λ‖ψ‖∞	NUM
ejpam-3459	84	5	−	−	PROPN
ejpam-3459	84	6	eλψ(x	eλψ(x	PROPN
ejpam-3459	84	7	)	)	PUNCT
ejpam-3459	84	8	at	at	ADP
ejpam-3459	84	9	(	(	PUNCT
ejpam-3459	84	10	t	t	PROPN
ejpam-3459	84	11	−	−	PROPN
ejpam-3459	84	12	t	t	PROPN
ejpam-3459	84	13	)	)	PUNCT
ejpam-3459	84	14	and	and	CCONJ
ejpam-3459	84	15	ϕ(t	ϕ(t	PROPN
ejpam-3459	84	16	,	,	PUNCT
ejpam-3459	84	17	a	a	PRON
ejpam-3459	84	18	,	,	PUNCT
ejpam-3459	84	19	x	x	NOUN
ejpam-3459	84	20	)	)	PUNCT
ejpam-3459	84	21	=	=	SYM
ejpam-3459	84	22	eλψ(x	eλψ(x	PROPN
ejpam-3459	84	23	)	)	PUNCT
ejpam-3459	84	24	at	at	ADP
ejpam-3459	84	25	(	(	PUNCT
ejpam-3459	84	26	t	t	PROPN
ejpam-3459	84	27	−	−	PROPN
ejpam-3459	84	28	t	t	PROPN
ejpam-3459	84	29	)	)	PUNCT
ejpam-3459	84	30	,	,	PUNCT
ejpam-3459	84	31	∀	∀	X
ejpam-3459	84	32	(	(	PUNCT
ejpam-3459	84	33	t	t	PROPN
ejpam-3459	84	34	,	,	PUNCT
ejpam-3459	84	35	a	a	PRON
ejpam-3459	84	36	,	,	PUNCT
ejpam-3459	84	37	x	x	NOUN
ejpam-3459	84	38	)	)	PUNCT
ejpam-3459	84	39	∈	∈	PROPN
ejpam-3459	84	40	q.	q.	NOUN
ejpam-3459	84	41	remark	remark	NOUN
ejpam-3459	84	42	2	2	NUM
ejpam-3459	84	43	.	.	PUNCT
ejpam-3459	85	1	as	as	ADP
ejpam-3459	85	2	a	a	DET
ejpam-3459	85	3	reminder	reminder	NOUN
ejpam-3459	85	4	(	(	PUNCT
ejpam-3459	85	5	see	see	VERB
ejpam-3459	85	6	[	[	X
ejpam-3459	85	7	4	4	NUM
ejpam-3459	85	8	]	]	PUNCT
ejpam-3459	85	9	)	)	PUNCT
ejpam-3459	85	10	the	the	DET
ejpam-3459	85	11	function	function	NOUN
ejpam-3459	85	12	ψ	ψ	X
ejpam-3459	85	13	∈	∈	PROPN
ejpam-3459	85	14	c2(ω	c2(ω	PRON
ejpam-3459	85	15	)	)	PUNCT
ejpam-3459	85	16	is	be	AUX
ejpam-3459	85	17	such	such	ADJ
ejpam-3459	85	18	that	that	SCONJ
ejpam-3459	85	19	:	:	PUNCT
ejpam-3459	85	20	∀x	∀x	X
ejpam-3459	85	21	∈	∈	PROPN
ejpam-3459	85	22	ω	ω	NOUN
ejpam-3459	85	23	;	;	PUNCT
ejpam-3459	85	24	ψ(x	ψ(x	PROPN
ejpam-3459	85	25	)	)	PUNCT
ejpam-3459	85	26	>	>	X
ejpam-3459	85	27	0	0	NUM
ejpam-3459	86	1	;	;	PUNCT
ejpam-3459	86	2	∀x	∀x	NUM
ejpam-3459	86	3	∈	∈	PROPN
ejpam-3459	86	4	γ	γ	X
ejpam-3459	86	5	,	,	PUNCT
ejpam-3459	86	6	ψ(x	ψ(x	NOUN
ejpam-3459	86	7	)	)	PUNCT
ejpam-3459	86	8	=	=	SYM
ejpam-3459	86	9	0	0	NUM
ejpam-3459	86	10	and	and	CCONJ
ejpam-3459	86	11	∀x	∀x	NOUN
ejpam-3459	86	12	∈	∈	PROPN
ejpam-3459	86	13	ω	ω	NUM
ejpam-3459	86	14	\	\	PROPN
ejpam-3459	86	15	ω0	ω0	PROPN
ejpam-3459	86	16	,	,	PUNCT
ejpam-3459	86	17	∇ψ(x	∇ψ(x	NOUN
ejpam-3459	86	18	)	)	PUNCT
ejpam-3459	86	19	6=	6=	ADP
ejpam-3459	86	20	0	0	NUM
ejpam-3459	86	21	where	where	SCONJ
ejpam-3459	86	22	ω0	ω0	PROPN
ejpam-3459	86	23	is	be	AUX
ejpam-3459	86	24	an	an	DET
ejpam-3459	86	25	open	open	ADJ
ejpam-3459	86	26	set	set	NOUN
ejpam-3459	86	27	such	such	ADJ
ejpam-3459	86	28	that	that	SCONJ
ejpam-3459	86	29	ω0	ω0	PROPN
ejpam-3459	86	30	⊂	⊂	PROPN
ejpam-3459	86	31	ω	ω	PROPN
ejpam-3459	87	1	⊂	⊂	PROPN
ejpam-3459	87	2	ω	ω	PROPN
ejpam-3459	87	3	.	.	PUNCT
ejpam-3459	88	1	in	in	ADP
ejpam-3459	88	2	the	the	DET
ejpam-3459	88	3	sequel	sequel	NOUN
ejpam-3459	88	4	:	:	PUNCT
ejpam-3459	88	5	•	•	X
ejpam-3459	88	6	c	c	X
ejpam-3459	88	7	represent	represent	VERB
ejpam-3459	88	8	different	different	ADJ
ejpam-3459	88	9	positive	positive	ADJ
ejpam-3459	88	10	constants	constant	NOUN
ejpam-3459	88	11	,	,	PUNCT
ejpam-3459	88	12	•	•	ADP
ejpam-3459	88	13	we	we	PRON
ejpam-3459	88	14	will	will	AUX
ejpam-3459	88	15	use	use	VERB
ejpam-3459	88	16	the	the	DET
ejpam-3459	88	17	following	follow	VERB
ejpam-3459	88	18	notations	notation	NOUN
ejpam-3459	88	19	:	:	PUNCT
ejpam-3459	88	20	v	v	X
ejpam-3459	88	21	=	=	SYM
ejpam-3459	88	22	{	{	PUNCT
ejpam-3459	88	23	ρ	ρ	PROPN
ejpam-3459	88	24	∈	∈	PROPN
ejpam-3459	88	25	c∞	c∞	PROPN
ejpam-3459	88	26	(	(	PUNCT
ejpam-3459	88	27	q	q	NOUN
ejpam-3459	88	28	)	)	PUNCT
ejpam-3459	88	29	such	such	ADJ
ejpam-3459	88	30	that	that	PRON
ejpam-3459	88	31	ρ|σ	ρ|σ	PUNCT
ejpam-3459	89	1	=	=	NOUN
ejpam-3459	89	2	0	0	NUM
ejpam-3459	89	3	}	}	PUNCT
ejpam-3459	89	4	;	;	PUNCT
ejpam-3459	89	5	w	w	X
ejpam-3459	89	6	=	=	PUNCT
ejpam-3459	89	7	v	v	NUM
ejpam-3459	89	8	×	×	NOUN
ejpam-3459	89	9	v	v	NOUN
ejpam-3459	89	10	,	,	PUNCT
ejpam-3459	89	11	c.	c.	PROPN
ejpam-3459	89	12	k.	k.	PROPN
ejpam-3459	89	13	somé	somé	PROPN
ejpam-3459	89	14	,	,	PUNCT
ejpam-3459	89	15	s.	s.	PROPN
ejpam-3459	89	16	sawadogo	sawadogo	PROPN
ejpam-3459	89	17	/	/	SYM
ejpam-3459	89	18	eur	eur	PROPN
ejpam-3459	89	19	.	.	PUNCT
ejpam-3459	90	1	j.	j.	PROPN
ejpam-3459	90	2	pure	pure	PROPN
ejpam-3459	90	3	appl	appl	PROPN
ejpam-3459	90	4	.	.	PROPN
ejpam-3459	90	5	math	math	PROPN
ejpam-3459	90	6	,	,	PUNCT
ejpam-3459	90	7	12	12	NUM
ejpam-3459	90	8	(	(	PUNCT
ejpam-3459	90	9	3	3	NUM
ejpam-3459	90	10	)	)	PUNCT
ejpam-3459	90	11	(	(	PUNCT
ejpam-3459	90	12	2019	2019	NUM
ejpam-3459	90	13	)	)	PUNCT
ejpam-3459	90	14	,	,	PUNCT
ejpam-3459	90	15	870	870	NUM
ejpam-3459	90	16	-	-	SYM
ejpam-3459	90	17	892	892	NUM
ejpam-3459	90	18	874	874	NUM
ejpam-3459	91	1	lρ	lρ	ADP
ejpam-3459	91	2	=	=	PUNCT
ejpam-3459	91	3	−∂ρ	−∂ρ	PROPN
ejpam-3459	91	4	∂t	∂t	PROPN
ejpam-3459	91	5	−	−	PROPN
ejpam-3459	91	6	∂ρ	∂ρ	PROPN
ejpam-3459	92	1	∂a	∂a	NOUN
ejpam-3459	92	2	−∆ρ	−∆ρ	NUM
ejpam-3459	92	3	;	;	PUNCT
ejpam-3459	92	4	l∗ρ	l∗ρ	PROPN
ejpam-3459	93	1	=	=	SYM
ejpam-3459	93	2	∂ρ	∂ρ	PROPN
ejpam-3459	93	3	∂t	∂t	PROPN
ejpam-3459	93	4	+	+	CCONJ
ejpam-3459	93	5	∂ρ	∂ρ	PROPN
ejpam-3459	94	1	∂a	∂a	NOUN
ejpam-3459	94	2	−∆ρ	−∆ρ	NUM
ejpam-3459	94	3	m(ρ1	m(ρ1	NOUN
ejpam-3459	94	4	,	,	PUNCT
ejpam-3459	94	5	ρ2	ρ2	NOUN
ejpam-3459	94	6	)	)	PUNCT
ejpam-3459	94	7	=	=	PUNCT
ejpam-3459	95	1	l∗ρ1	l∗ρ1	VERB
ejpam-3459	96	1	+	+	CCONJ
ejpam-3459	96	2	µ̂1ρ1	µ̂1ρ1	NOUN
ejpam-3459	96	3	+	+	CCONJ
ejpam-3459	96	4	µ̂2ρ2	µ̂2ρ2	NOUN
ejpam-3459	96	5	;	;	PUNCT
ejpam-3459	96	6	n(ρ1	n(ρ1	NOUN
ejpam-3459	96	7	,	,	PUNCT
ejpam-3459	96	8	ρ2	ρ2	NOUN
ejpam-3459	96	9	)	)	PUNCT
ejpam-3459	96	10	=	=	PUNCT
ejpam-3459	96	11	l∗ρ2	l∗ρ2	X
ejpam-3459	97	1	+	+	PUNCT
ejpam-3459	97	2	µ̂1ρ2	µ̂1ρ2	NOUN
ejpam-3459	97	3	+	+	NUM
ejpam-3459	97	4	µ̂2ρ1	µ̂2ρ1	X
ejpam-3459	97	5	.	.	PUNCT
ejpam-3459	98	1	‖	‖	PROPN
ejpam-3459	98	2	µ̂1	µ̂1	PROPN
ejpam-3459	98	3	,	,	PUNCT
ejpam-3459	98	4	µ̂2	µ̂2	PUNCT
ejpam-3459	98	5	‖2∞=‖	‖2∞=‖	VERB
ejpam-3459	98	6	µ̂1	µ̂1	ADJ
ejpam-3459	99	1	‖2∞	‖2∞	PROPN
ejpam-3459	99	2	+	+	CCONJ
ejpam-3459	99	3	‖	‖	PROPN
ejpam-3459	99	4	µ̂2	µ̂2	NOUN
ejpam-3459	99	5	‖2∞	‖2∞	NOUN
ejpam-3459	99	6	and	and	CCONJ
ejpam-3459	99	7	dq	dq	NOUN
ejpam-3459	99	8	=	=	PUNCT
ejpam-3459	99	9	dtdadx	dtdadx	NOUN
ejpam-3459	99	10	theorem	theorem	ADJ
ejpam-3459	99	11	2	2	NUM
ejpam-3459	99	12	.	.	PUNCT
ejpam-3459	100	1	[	[	X
ejpam-3459	100	2	11	11	NUM
ejpam-3459	100	3	]	]	PUNCT
ejpam-3459	100	4	there	there	PRON
ejpam-3459	100	5	exists	exist	VERB
ejpam-3459	100	6	λ0	λ0	NOUN
ejpam-3459	100	7	>	>	X
ejpam-3459	100	8	0	0	PUNCT
ejpam-3459	100	9	,	,	PUNCT
ejpam-3459	100	10	τ0	τ0	PROPN
ejpam-3459	100	11	>	>	X
ejpam-3459	100	12	0	0	PUNCT
ejpam-3459	100	13	and	and	CCONJ
ejpam-3459	100	14	a	a	DET
ejpam-3459	100	15	positive	positive	ADJ
ejpam-3459	100	16	constant	constant	ADJ
ejpam-3459	100	17	c	c	NOUN
ejpam-3459	100	18	such	such	ADJ
ejpam-3459	100	19	that	that	PRON
ejpam-3459	100	20	for	for	ADP
ejpam-3459	100	21	all	all	DET
ejpam-3459	100	22	λ	λ	PROPN
ejpam-3459	100	23	≥	≥	NOUN
ejpam-3459	100	24	λ0	λ0	NOUN
ejpam-3459	100	25	,	,	PUNCT
ejpam-3459	100	26	τ	τ	PROPN
ejpam-3459	100	27	≥	≥	NOUN
ejpam-3459	100	28	τ0	τ0	NOUN
ejpam-3459	100	29	and	and	CCONJ
ejpam-3459	100	30	for	for	ADP
ejpam-3459	100	31	all	all	PRON
ejpam-3459	100	32	s	s	PART
ejpam-3459	100	33	≥	≥	NOUN
ejpam-3459	100	34	−3	−3	ADV
ejpam-3459	100	35	,	,	PUNCT
ejpam-3459	100	36	the	the	DET
ejpam-3459	100	37	inequality∫	inequality∫	ADJ
ejpam-3459	100	38	q	q	NOUN
ejpam-3459	100	39	(	(	PUNCT
ejpam-3459	100	40	1	1	NUM
ejpam-3459	100	41	λ	λ	NOUN
ejpam-3459	100	42	∣∣∣∣∂ρ∂t	∣∣∣∣∂ρ∂t	ADJ
ejpam-3459	100	43	+	+	SYM
ejpam-3459	100	44	∂ρ	∂ρ	NOUN
ejpam-3459	100	45	∂a	∂a	NOUN
ejpam-3459	100	46	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3459	100	47	+	+	CCONJ
ejpam-3459	100	48	1	1	NUM
ejpam-3459	100	49	λ	λ	NOUN
ejpam-3459	100	50	|∆ρ|2	|∆ρ|2	NOUN
ejpam-3459	101	1	+	+	CCONJ
ejpam-3459	102	1	λτ2ϕ2	λτ2ϕ2	X
ejpam-3459	102	2	|∇ρ|2	|∇ρ|2	NOUN
ejpam-3459	102	3	+	+	CCONJ
ejpam-3459	102	4	λ4τ4ϕ4	λ4τ4ϕ4	CCONJ
ejpam-3459	102	5	|ρ|2	|ρ|2	NOUN
ejpam-3459	102	6	)	)	PUNCT
ejpam-3459	102	7	ϕ2s−1e−2αdq	ϕ2s−1e−2αdq	NOUN
ejpam-3459	102	8	≤	≤	PROPN
ejpam-3459	102	9	c	c	X
ejpam-3459	102	10	(	(	PUNCT
ejpam-3459	102	11	τ	τ	PROPN
ejpam-3459	102	12	∫	∫	PROPN
ejpam-3459	102	13	q	q	PROPN
ejpam-3459	102	14	∣∣∣∣∂ρ∂t	∣∣∣∣∂ρ∂t	PROPN
ejpam-3459	102	15	+	+	NUM
ejpam-3459	102	16	∂ρ	∂ρ	PROPN
ejpam-3459	102	17	∂a	∂a	PROPN
ejpam-3459	102	18	±∆ρ	±∆ρ	ADJ
ejpam-3459	102	19	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3459	102	20	ϕ2se−2αdq	ϕ2se−2αdq	NOUN
ejpam-3459	102	21	+	+	CCONJ
ejpam-3459	102	22	λ4τ4	λ4τ4	NOUN
ejpam-3459	102	23	∫	∫	PROPN
ejpam-3459	102	24	t	t	PROPN
ejpam-3459	102	25	0	0	NUM
ejpam-3459	102	26	∫	∫	PROPN
ejpam-3459	102	27	a	a	DET
ejpam-3459	102	28	0	0	NUM
ejpam-3459	102	29	∫	∫	PROPN
ejpam-3459	102	30	ω	ω	NUM
ejpam-3459	102	31	|ρ|2	|ρ|2	PROPN
ejpam-3459	102	32	ϕ2s+3e−2αdq	ϕ2s+3e−2αdq	PROPN
ejpam-3459	102	33	)	)	PUNCT
ejpam-3459	102	34	(	(	PUNCT
ejpam-3459	102	35	10	10	NUM
ejpam-3459	102	36	)	)	PUNCT
ejpam-3459	102	37	holds	hold	VERB
ejpam-3459	102	38	for	for	ADP
ejpam-3459	102	39	any	any	DET
ejpam-3459	102	40	function	function	NOUN
ejpam-3459	102	41	ρ	ρ	PROPN
ejpam-3459	102	42	∈	∈	PROPN
ejpam-3459	102	43	v	v	ADP
ejpam-3459	102	44	such	such	DET
ejpam-3459	102	45	that	that	SCONJ
ejpam-3459	102	46	the	the	DET
ejpam-3459	102	47	member	member	NOUN
ejpam-3459	102	48	on	on	ADP
ejpam-3459	102	49	the	the	DET
ejpam-3459	102	50	right	right	ADJ
ejpam-3459	102	51	hand	hand	NOUN
ejpam-3459	102	52	side	side	NOUN
ejpam-3459	102	53	of	of	ADP
ejpam-3459	102	54	the	the	DET
ejpam-3459	102	55	inequality	inequality	NOUN
ejpam-3459	102	56	(	(	PUNCT
ejpam-3459	102	57	10	10	NUM
ejpam-3459	102	58	)	)	PUNCT
ejpam-3459	102	59	is	be	AUX
ejpam-3459	102	60	finite	finite	PROPN
ejpam-3459	102	61	.	.	PUNCT
ejpam-3459	103	1	lemma	lemma	PROPN
ejpam-3459	103	2	1	1	NUM
ejpam-3459	103	3	.	.	PUNCT
ejpam-3459	104	1	[	[	X
ejpam-3459	104	2	11	11	NUM
ejpam-3459	104	3	]	]	PUNCT
ejpam-3459	104	4	let	let	VERB
ejpam-3459	104	5	c	c	NOUN
ejpam-3459	104	6	be	be	AUX
ejpam-3459	104	7	the	the	DET
ejpam-3459	104	8	constant	constant	ADJ
ejpam-3459	104	9	given	give	VERB
ejpam-3459	104	10	by	by	ADP
ejpam-3459	104	11	the	the	DET
ejpam-3459	104	12	theorem	theorem	NOUN
ejpam-3459	104	13	2	2	X
ejpam-3459	104	14	.	.	X
ejpam-3459	104	15	assume	assume	VERB
ejpam-3459	104	16	that	that	SCONJ
ejpam-3459	104	17	for	for	ADP
ejpam-3459	104	18	λ	λ	PROPN
ejpam-3459	104	19	≥	≥	NOUN
ejpam-3459	104	20	λ0	λ0	NOUN
ejpam-3459	104	21	,	,	PUNCT
ejpam-3459	104	22	τ	τ	X
ejpam-3459	104	23	≥	≥	NOUN
ejpam-3459	104	24	1	1	NUM
ejpam-3459	104	25	and	and	CCONJ
ejpam-3459	104	26	s	s	X
ejpam-3459	104	27	≥	≥	NOUN
ejpam-3459	104	28	−3	−3	ADV
ejpam-3459	104	29	,	,	PUNCT
ejpam-3459	104	30	there	there	PRON
ejpam-3459	104	31	exists	exist	VERB
ejpam-3459	104	32	a	a	DET
ejpam-3459	104	33	constant	constant	ADJ
ejpam-3459	104	34	b0	b0	NOUN
ejpam-3459	104	35	>	>	X
ejpam-3459	104	36	0	0	PROPN
ejpam-3459	104	37	and	and	CCONJ
ejpam-3459	104	38	a	a	DET
ejpam-3459	104	39	set	set	NOUN
ejpam-3459	104	40	ωb	ωb	NOUN
ejpam-3459	105	1	such	such	ADJ
ejpam-3459	105	2	that	that	PRON
ejpam-3459	105	3	ωb	ωb	PROPN
ejpam-3459	105	4	⊂	⊂	PROPN
ejpam-3459	105	5	ω	ω	PROPN
ejpam-3459	105	6	and	and	CCONJ
ejpam-3459	105	7	|µ̂2|	|µ̂2|	PRON
ejpam-3459	105	8	≥	≥	PROPN
ejpam-3459	105	9	b0	b0	NOUN
ejpam-3459	105	10	in	in	ADP
ejpam-3459	105	11	(	(	PUNCT
ejpam-3459	105	12	0	0	NUM
ejpam-3459	105	13	;	;	PUNCT
ejpam-3459	105	14	t	t	X
ejpam-3459	105	15	)	)	PUNCT
ejpam-3459	105	16	×	×	NOUN
ejpam-3459	105	17	(	(	PUNCT
ejpam-3459	105	18	0	0	NUM
ejpam-3459	105	19	;	;	PUNCT
ejpam-3459	105	20	a)×	a)×	DET
ejpam-3459	105	21	ωb	ωb	NOUN
ejpam-3459	105	22	.	.	PUNCT
ejpam-3459	106	1	(	(	PUNCT
ejpam-3459	106	2	11	11	NUM
ejpam-3459	106	3	)	)	PUNCT
ejpam-3459	106	4	then	then	ADV
ejpam-3459	106	5	,	,	PUNCT
ejpam-3459	106	6	for	for	ADP
ejpam-3459	106	7	all	all	DET
ejpam-3459	106	8	r	r	NOUN
ejpam-3459	106	9	∈	∈	NOUN
ejpam-3459	107	1	[	[	X
ejpam-3459	107	2	0	0	NUM
ejpam-3459	107	3	;	;	PUNCT
ejpam-3459	107	4	2	2	NUM
ejpam-3459	107	5	[	[	NOUN
ejpam-3459	107	6	,	,	PUNCT
ejpam-3459	107	7	there	there	PRON
ejpam-3459	107	8	exists	exist	VERB
ejpam-3459	107	9	a	a	DET
ejpam-3459	107	10	constant	constant	ADJ
ejpam-3459	107	11	c	c	NOUN
ejpam-3459	107	12	=	=	PUNCT
ejpam-3459	107	13	c(a	c(a	PROPN
ejpam-3459	107	14	,	,	PUNCT
ejpam-3459	107	15	t	t	PROPN
ejpam-3459	107	16	,	,	PUNCT
ejpam-3459	107	17	‖	‖	PROPN
ejpam-3459	107	18	µ̂1	µ̂1	NOUN
ejpam-3459	107	19	,	,	PUNCT
ejpam-3459	107	20	µ̂2	µ̂2	PROPN
ejpam-3459	107	21	‖∞	‖∞	PROPN
ejpam-3459	107	22	,	,	PUNCT
ejpam-3459	107	23	b0	b0	NOUN
ejpam-3459	107	24	,	,	PUNCT
ejpam-3459	107	25	r	r	NOUN
ejpam-3459	107	26	)	)	PUNCT
ejpam-3459	107	27	such	such	ADJ
ejpam-3459	107	28	that	that	PRON
ejpam-3459	107	29	for	for	ADP
ejpam-3459	107	30	all	all	DET
ejpam-3459	107	31	ρ	ρ	NOUN
ejpam-3459	107	32	=	=	SYM
ejpam-3459	107	33	(	(	PUNCT
ejpam-3459	107	34	ρ1	ρ1	NOUN
ejpam-3459	107	35	,	,	PUNCT
ejpam-3459	107	36	ρ2	ρ2	NOUN
ejpam-3459	107	37	)	)	PUNCT
ejpam-3459	107	38	∈	∈	PROPN
ejpam-3459	107	39	w	w	PROPN
ejpam-3459	107	40	,	,	PUNCT
ejpam-3459	107	41	we	we	PRON
ejpam-3459	107	42	have	have	VERB
ejpam-3459	107	43	:	:	PUNCT
ejpam-3459	107	44	∫	∫	PROPN
ejpam-3459	107	45	t	t	PROPN
ejpam-3459	107	46	0	0	NUM
ejpam-3459	107	47	∫	∫	PROPN
ejpam-3459	107	48	a	a	DET
ejpam-3459	107	49	0	0	NUM
ejpam-3459	107	50	∫	∫	PROPN
ejpam-3459	107	51	ω′	ω′	PROPN
ejpam-3459	107	52	(	(	PUNCT
ejpam-3459	107	53	|ρ1|2	|ρ1|2	X
ejpam-3459	107	54	+	+	NUM
ejpam-3459	107	55	|ρ2|2	|ρ2|2	NUM
ejpam-3459	107	56	)	)	PUNCT
ejpam-3459	107	57	e−2αdq	e−2αdq	NOUN
ejpam-3459	107	58	≤	≤	NUM
ejpam-3459	107	59	c	c	PROPN
ejpam-3459	107	60	(	(	PUNCT
ejpam-3459	107	61	∫	∫	PROPN
ejpam-3459	107	62	q	q	X
ejpam-3459	107	63	[	[	PUNCT
ejpam-3459	107	64	|m(ρ)|2	|m(ρ)|2	X
ejpam-3459	107	65	+	+	CCONJ
ejpam-3459	107	66	|n(ρ)|2	|n(ρ)|2	X
ejpam-3459	107	67	]	]	PUNCT
ejpam-3459	107	68	ϕ2se−2αdq	ϕ2se−2αdq	PROPN
ejpam-3459	107	69	+	+	CCONJ
ejpam-3459	107	70	∫	∫	PROPN
ejpam-3459	107	71	qω	qω	PROPN
ejpam-3459	107	72	|ρ1|2	|ρ1|2	PROPN
ejpam-3459	107	73	e−rαdq	e−rαdq	PROPN
ejpam-3459	107	74	)	)	PUNCT
ejpam-3459	107	75	(	(	PUNCT
ejpam-3459	107	76	12	12	NUM
ejpam-3459	107	77	)	)	PUNCT
ejpam-3459	107	78	with	with	ADP
ejpam-3459	107	79	ω′	ω′	PROPN
ejpam-3459	107	80	⊂	⊂	X
ejpam-3459	107	81	ωb	ωb	PROPN
ejpam-3459	107	82	.	.	PUNCT
ejpam-3459	107	83	setting	set	VERB
ejpam-3459	107	84	θ	θ	NOUN
ejpam-3459	107	85	=	=	PUNCT
ejpam-3459	107	86	eα	eα	PROPN
ejpam-3459	107	87	and	and	CCONJ
ejpam-3459	107	88	δ	δ	PROPN
ejpam-3459	107	89	=	=	SYM
ejpam-3459	107	90	θ	θ	PROPN
ejpam-3459	107	91	r	r	NOUN
ejpam-3459	107	92	2−1	2−1	NUM
ejpam-3459	107	93	,	,	PUNCT
ejpam-3459	107	94	(	(	PUNCT
ejpam-3459	107	95	13	13	NUM
ejpam-3459	107	96	)	)	PUNCT
ejpam-3459	107	97	we	we	PRON
ejpam-3459	107	98	have	have	VERB
ejpam-3459	107	99	the	the	DET
ejpam-3459	107	100	following	follow	VERB
ejpam-3459	107	101	result	result	NOUN
ejpam-3459	107	102	lemma	lemma	PROPN
ejpam-3459	107	103	2	2	X
ejpam-3459	107	104	.	.	PUNCT
ejpam-3459	108	1	[	[	X
ejpam-3459	108	2	11	11	NUM
ejpam-3459	108	3	]	]	PUNCT
ejpam-3459	108	4	under	under	ADP
ejpam-3459	108	5	the	the	DET
ejpam-3459	108	6	hypothesis	hypothesis	NOUN
ejpam-3459	108	7	of	of	ADP
ejpam-3459	108	8	the	the	DET
ejpam-3459	108	9	lemma	lemma	PROPN
ejpam-3459	108	10	1	1	NUM
ejpam-3459	108	11	,	,	PUNCT
ejpam-3459	108	12	for	for	ADP
ejpam-3459	108	13	all	all	DET
ejpam-3459	108	14	ρ	ρ	NOUN
ejpam-3459	108	15	=	=	SYM
ejpam-3459	108	16	(	(	PUNCT
ejpam-3459	108	17	ρ1	ρ1	NOUN
ejpam-3459	108	18	,	,	PUNCT
ejpam-3459	108	19	ρ2	ρ2	NOUN
ejpam-3459	108	20	)	)	PUNCT
ejpam-3459	108	21	∈	∈	PROPN
ejpam-3459	108	22	w	w	PROPN
ejpam-3459	108	23	,	,	PUNCT
ejpam-3459	108	24	there	there	PRON
ejpam-3459	108	25	exists	exist	VERB
ejpam-3459	108	26	a	a	DET
ejpam-3459	108	27	positive	positive	ADJ
ejpam-3459	108	28	constant	constant	ADJ
ejpam-3459	108	29	c	c	NOUN
ejpam-3459	108	30	=	=	PUNCT
ejpam-3459	108	31	c(a	c(a	PROPN
ejpam-3459	108	32	,	,	PUNCT
ejpam-3459	108	33	t	t	PROPN
ejpam-3459	108	34	,	,	PUNCT
ejpam-3459	108	35	‖	‖	PROPN
ejpam-3459	108	36	aµ	aµ	PROPN
ejpam-3459	108	37	,	,	PUNCT
ejpam-3459	108	38	bµ	bµ	PROPN
ejpam-3459	108	39	‖∞	‖∞	PROPN
ejpam-3459	108	40	,	,	PUNCT
ejpam-3459	108	41	c0	c0	NOUN
ejpam-3459	108	42	,	,	PUNCT
ejpam-3459	108	43	r	r	NOUN
ejpam-3459	108	44	)	)	PUNCT
ejpam-3459	109	1	such	such	ADJ
ejpam-3459	109	2	that∫	that∫	NOUN
ejpam-3459	109	3	q	q	PROPN
ejpam-3459	109	4	1	1	NUM
ejpam-3459	109	5	θ2	θ2	PROPN
ejpam-3459	109	6	(	(	PUNCT
ejpam-3459	109	7	|ρ1|2	|ρ1|2	X
ejpam-3459	109	8	+	+	X
ejpam-3459	109	9	|ρ2|2	|ρ2|2	NUM
ejpam-3459	109	10	)	)	PUNCT
ejpam-3459	109	11	dq	dq	ADP
ejpam-3459	109	12	≤	≤	NUM
ejpam-3459	109	13	c	c	PROPN
ejpam-3459	109	14	(	(	PUNCT
ejpam-3459	109	15	∫	∫	PROPN
ejpam-3459	109	16	q	q	PROPN
ejpam-3459	109	17	(	(	PUNCT
ejpam-3459	109	18	|m(ρ)|2	|m(ρ)|2	X
ejpam-3459	109	19	+	+	CCONJ
ejpam-3459	109	20	|n(ρ)|2	|n(ρ)|2	X
ejpam-3459	109	21	)	)	PUNCT
ejpam-3459	109	22	dq	dq	PROPN
ejpam-3459	109	23	+	+	CCONJ
ejpam-3459	109	24	∫	∫	PROPN
ejpam-3459	109	25	qω	qω	PROPN
ejpam-3459	109	26	δ2	δ2	VERB
ejpam-3459	109	27	|ρ1|2	|ρ1|2	X
ejpam-3459	109	28	dq	dq	PROPN
ejpam-3459	109	29	)	)	PUNCT
ejpam-3459	109	30	.	.	PUNCT
ejpam-3459	110	1	(	(	PUNCT
ejpam-3459	110	2	14	14	NUM
ejpam-3459	110	3	)	)	PUNCT
ejpam-3459	110	4	at	at	ADP
ejpam-3459	110	5	last	last	ADV
ejpam-3459	110	6	,	,	PUNCT
ejpam-3459	110	7	we	we	PRON
ejpam-3459	110	8	deduct	deduct	VERB
ejpam-3459	110	9	the	the	DET
ejpam-3459	110	10	following	follow	VERB
ejpam-3459	110	11	result	result	NOUN
ejpam-3459	110	12	.	.	PUNCT
ejpam-3459	111	1	proposition	proposition	NOUN
ejpam-3459	111	2	1	1	NUM
ejpam-3459	111	3	.	.	PUNCT
ejpam-3459	112	1	[	[	X
ejpam-3459	112	2	11	11	NUM
ejpam-3459	112	3	]	]	PUNCT
ejpam-3459	112	4	under	under	ADP
ejpam-3459	112	5	the	the	DET
ejpam-3459	112	6	hypothesis	hypothesis	NOUN
ejpam-3459	112	7	of	of	ADP
ejpam-3459	112	8	the	the	DET
ejpam-3459	112	9	lemma	lemma	PROPN
ejpam-3459	112	10	2	2	NUM
ejpam-3459	112	11	,	,	PUNCT
ejpam-3459	112	12	there	there	PRON
ejpam-3459	112	13	exists	exist	VERB
ejpam-3459	112	14	a	a	DET
ejpam-3459	112	15	positive	positive	ADJ
ejpam-3459	112	16	constant	constant	ADJ
ejpam-3459	112	17	c	c	NOUN
ejpam-3459	112	18	such	such	ADJ
ejpam-3459	112	19	that	that	PRON
ejpam-3459	112	20	for	for	ADP
ejpam-3459	112	21	all	all	DET
ejpam-3459	112	22	ρ	ρ	NOUN
ejpam-3459	112	23	=	=	PUNCT
ejpam-3459	112	24	(	(	PUNCT
ejpam-3459	112	25	ρ1	ρ1	NOUN
ejpam-3459	112	26	,	,	PUNCT
ejpam-3459	112	27	ρ2	ρ2	NOUN
ejpam-3459	112	28	)	)	PUNCT
ejpam-3459	112	29	∈	∈	PROPN
ejpam-3459	112	30	w	w	PROPN
ejpam-3459	112	31	,	,	PUNCT
ejpam-3459	112	32	we	we	PRON
ejpam-3459	112	33	have∫	have∫	VERB
ejpam-3459	112	34	t	t	NOUN
ejpam-3459	112	35	0	0	NUM
ejpam-3459	113	1	∫	∫	PROPN
ejpam-3459	113	2	ω	ω	PROPN
ejpam-3459	113	3	(	(	PUNCT
ejpam-3459	113	4	|ρ1(t	|ρ1(t	PROPN
ejpam-3459	113	5	,	,	PUNCT
ejpam-3459	113	6	0	0	NUM
ejpam-3459	113	7	,	,	PUNCT
ejpam-3459	113	8	x)|2	x)|2	PROPN
ejpam-3459	113	9	+	+	CCONJ
ejpam-3459	113	10	|ρ2(t	|ρ2(t	PROPN
ejpam-3459	113	11	,	,	PUNCT
ejpam-3459	113	12	0	0	NUM
ejpam-3459	113	13	,	,	PUNCT
ejpam-3459	113	14	x)|2	x)|2	PROPN
ejpam-3459	113	15	)	)	PUNCT
ejpam-3459	114	1	dxdt+	dxdt+	X
ejpam-3459	114	2	∫	∫	PROPN
ejpam-3459	114	3	a	a	DET
ejpam-3459	114	4	0	0	NUM
ejpam-3459	114	5	∫	∫	PROPN
ejpam-3459	114	6	ω	ω	PROPN
ejpam-3459	114	7	(	(	PUNCT
ejpam-3459	114	8	|ρ1(0	|ρ1(0	PROPN
ejpam-3459	114	9	,	,	PUNCT
ejpam-3459	114	10	a	a	PRON
ejpam-3459	114	11	,	,	PUNCT
ejpam-3459	114	12	x)|2	x)|2	PROPN
ejpam-3459	114	13	+	+	CCONJ
ejpam-3459	114	14	|ρ2(0	|ρ2(0	PROPN
ejpam-3459	114	15	,	,	PUNCT
ejpam-3459	114	16	a	a	PRON
ejpam-3459	114	17	,	,	PUNCT
ejpam-3459	114	18	x)|2	x)|2	PROPN
ejpam-3459	114	19	)	)	PUNCT
ejpam-3459	115	1	dxda	dxda	VERB
ejpam-3459	115	2	≤	≤	NUM
ejpam-3459	115	3	c	c	PROPN
ejpam-3459	115	4	(	(	PUNCT
ejpam-3459	115	5	∫	∫	PROPN
ejpam-3459	115	6	q	q	PROPN
ejpam-3459	115	7	(	(	PUNCT
ejpam-3459	115	8	|m(ρ)|2	|m(ρ)|2	X
ejpam-3459	115	9	+	+	CCONJ
ejpam-3459	115	10	|n(ρ)|2	|n(ρ)|2	X
ejpam-3459	115	11	)	)	PUNCT
ejpam-3459	115	12	dq	dq	PROPN
ejpam-3459	116	1	+	+	CCONJ
ejpam-3459	116	2	∫	∫	PROPN
ejpam-3459	116	3	qω	qω	PROPN
ejpam-3459	116	4	δ2	δ2	VERB
ejpam-3459	116	5	|ρ1|2	|ρ1|2	X
ejpam-3459	116	6	dq	dq	NOUN
ejpam-3459	116	7	)	)	PUNCT
ejpam-3459	116	8	(	(	PUNCT
ejpam-3459	116	9	15	15	NUM
ejpam-3459	116	10	)	)	PUNCT
ejpam-3459	116	11	c.	c.	PROPN
ejpam-3459	116	12	k.	k.	PROPN
ejpam-3459	116	13	somé	somé	PROPN
ejpam-3459	116	14	,	,	PUNCT
ejpam-3459	116	15	s.	s.	PROPN
ejpam-3459	116	16	sawadogo	sawadogo	PROPN
ejpam-3459	116	17	/	/	SYM
ejpam-3459	116	18	eur	eur	PROPN
ejpam-3459	116	19	.	.	PUNCT
ejpam-3459	117	1	j.	j.	PROPN
ejpam-3459	117	2	pure	pure	PROPN
ejpam-3459	117	3	appl	appl	PROPN
ejpam-3459	117	4	.	.	PROPN
ejpam-3459	117	5	math	math	PROPN
ejpam-3459	117	6	,	,	PUNCT
ejpam-3459	117	7	12	12	NUM
ejpam-3459	117	8	(	(	PUNCT
ejpam-3459	117	9	3	3	NUM
ejpam-3459	117	10	)	)	PUNCT
ejpam-3459	117	11	(	(	PUNCT
ejpam-3459	117	12	2019	2019	NUM
ejpam-3459	117	13	)	)	PUNCT
ejpam-3459	117	14	,	,	PUNCT
ejpam-3459	117	15	870	870	NUM
ejpam-3459	117	16	-	-	SYM
ejpam-3459	117	17	892	892	NUM
ejpam-3459	117	18	875	875	NUM
ejpam-3459	117	19	3.2	3.2	NUM
ejpam-3459	117	20	.	.	PUNCT
ejpam-3459	118	1	study	study	NOUN
ejpam-3459	118	2	of	of	ADP
ejpam-3459	118	3	the	the	DET
ejpam-3459	118	4	linear	linear	ADJ
ejpam-3459	118	5	case	case	NOUN
ejpam-3459	118	6	:	:	PUNCT
ejpam-3459	118	7	in	in	ADP
ejpam-3459	118	8	this	this	DET
ejpam-3459	118	9	paragraph	paragraph	NOUN
ejpam-3459	118	10	,	,	PUNCT
ejpam-3459	118	11	we	we	PRON
ejpam-3459	118	12	study	study	VERB
ejpam-3459	118	13	the	the	DET
ejpam-3459	118	14	following	follow	VERB
ejpam-3459	118	15	problem	problem	NOUN
ejpam-3459	118	16	:	:	PUNCT
ejpam-3459	118	17	for	for	ADP
ejpam-3459	118	18	given	give	VERB
ejpam-3459	118	19	functions	function	NOUN
ejpam-3459	118	20	µ̃1	µ̃1	PROPN
ejpam-3459	118	21	,	,	PUNCT
ejpam-3459	118	22	µ̃2	µ̃2	PROPN
ejpam-3459	118	23	,	,	PUNCT
ejpam-3459	118	24	b1	b1	NOUN
ejpam-3459	118	25	,	,	PUNCT
ejpam-3459	118	26	b2	b2	NOUN
ejpam-3459	118	27	∈	∈	PROPN
ejpam-3459	118	28	l2(qt	l2(qt	PROPN
ejpam-3459	118	29	)	)	PUNCT
ejpam-3459	118	30	,	,	PUNCT
ejpam-3459	118	31	β̃1	β̃1	PROPN
ejpam-3459	118	32	,	,	PUNCT
ejpam-3459	118	33	β̃2	β̃2	PROPN
ejpam-3459	118	34	∈	∈	PROPN
ejpam-3459	118	35	c2(q	c2(q	PROPN
ejpam-3459	118	36	)	)	PUNCT
ejpam-3459	118	37	and	and	CCONJ
ejpam-3459	118	38	f	f	PROPN
ejpam-3459	118	39	∈	∈	PROPN
ejpam-3459	118	40	l2(q	l2(q	PROPN
ejpam-3459	118	41	)	)	PUNCT
ejpam-3459	118	42	find	find	VERB
ejpam-3459	118	43	v	v	ADP
ejpam-3459	118	44	∈	∈	PROPN
ejpam-3459	118	45	l2(qω	l2(qω	PROPN
ejpam-3459	118	46	)	)	PUNCT
ejpam-3459	118	47	such	such	ADJ
ejpam-3459	118	48	that	that	SCONJ
ejpam-3459	118	49	the	the	DET
ejpam-3459	118	50	solution	solution	NOUN
ejpam-3459	118	51	(	(	PUNCT
ejpam-3459	118	52	z1	z1	NOUN
ejpam-3459	118	53	,	,	PUNCT
ejpam-3459	118	54	z2	z2	PROPN
ejpam-3459	118	55	)	)	PUNCT
ejpam-3459	118	56	of	of	ADP
ejpam-3459	118	57	:	:	PUNCT
ejpam-3459	118	58			PROPN
ejpam-3459	118	59	−∂z1	−∂z1	PROPN
ejpam-3459	118	60	∂t	∂t	PROPN
ejpam-3459	118	61	−	−	NUM
ejpam-3459	118	62	∂z1	∂z1	NOUN
ejpam-3459	118	63	∂a	∂a	VERB
ejpam-3459	118	64	−∆z1	−∆z1	NOUN
ejpam-3459	118	65	+	+	CCONJ
ejpam-3459	118	66	µ̃1z1	µ̃1z1	PROPN
ejpam-3459	118	67	+	+	CCONJ
ejpam-3459	118	68	µ̃2z2	µ̃2z2	PROPN
ejpam-3459	118	69	=	=	SYM
ejpam-3459	118	70	g1(t	g1(t	PROPN
ejpam-3459	118	71	,	,	PUNCT
ejpam-3459	118	72	a	a	PRON
ejpam-3459	118	73	,	,	PUNCT
ejpam-3459	118	74	x)z1(t	x)z1(t	X
ejpam-3459	118	75	,	,	PUNCT
ejpam-3459	118	76	0	0	NUM
ejpam-3459	118	77	,	,	PUNCT
ejpam-3459	118	78	x	x	X
ejpam-3459	118	79	)	)	PUNCT
ejpam-3459	119	1	+	+	NUM
ejpam-3459	119	2	f	f	X
ejpam-3459	119	3	+	+	CCONJ
ejpam-3459	119	4	vχω	vχω	PROPN
ejpam-3459	120	1	+	+	PROPN
ejpam-3459	120	2	g2(t	g2(t	PROPN
ejpam-3459	120	3	,	,	PUNCT
ejpam-3459	120	4	a	a	PRON
ejpam-3459	120	5	,	,	PUNCT
ejpam-3459	120	6	x)z2(t	x)z2(t	PROPN
ejpam-3459	120	7	,	,	PUNCT
ejpam-3459	120	8	0	0	NUM
ejpam-3459	120	9	,	,	PUNCT
ejpam-3459	120	10	x	x	NOUN
ejpam-3459	120	11	)	)	PUNCT
ejpam-3459	120	12	in	in	ADP
ejpam-3459	120	13	q	q	PROPN
ejpam-3459	120	14	−∂z2	−∂z2	PROPN
ejpam-3459	120	15	∂t	∂t	PROPN
ejpam-3459	120	16	−	−	PROPN
ejpam-3459	120	17	∂z2	∂z2	PROPN
ejpam-3459	120	18	∂a	∂a	PROPN
ejpam-3459	120	19	−∆z2	−∆z2	NOUN
ejpam-3459	120	20	+	+	CCONJ
ejpam-3459	120	21	µ̃1z2	µ̃1z2	PROPN
ejpam-3459	120	22	+	+	CCONJ
ejpam-3459	120	23	µ̃2z1	µ̃2z1	PROPN
ejpam-3459	120	24	=	=	SYM
ejpam-3459	120	25	g2(t	g2(t	PROPN
ejpam-3459	120	26	,	,	PUNCT
ejpam-3459	120	27	a	a	PRON
ejpam-3459	120	28	,	,	PUNCT
ejpam-3459	120	29	x)z1(t	x)z1(t	X
ejpam-3459	120	30	,	,	PUNCT
ejpam-3459	120	31	0	0	NUM
ejpam-3459	120	32	,	,	PUNCT
ejpam-3459	120	33	x	x	X
ejpam-3459	120	34	)	)	PUNCT
ejpam-3459	121	1	+	+	ADJ
ejpam-3459	121	2	g1(t	g1(t	PROPN
ejpam-3459	121	3	,	,	PUNCT
ejpam-3459	121	4	a	a	PRON
ejpam-3459	121	5	,	,	PUNCT
ejpam-3459	121	6	x)z2(t	x)z2(t	PROPN
ejpam-3459	121	7	,	,	PUNCT
ejpam-3459	121	8	0	0	NUM
ejpam-3459	121	9	,	,	PUNCT
ejpam-3459	121	10	x	x	NOUN
ejpam-3459	121	11	)	)	PUNCT
ejpam-3459	121	12	in	in	ADP
ejpam-3459	121	13	q	q	PROPN
ejpam-3459	121	14	zi	zi	PROPN
ejpam-3459	121	15	=	=	PUNCT
ejpam-3459	121	16	0	0	NUM
ejpam-3459	121	17	on	on	ADP
ejpam-3459	121	18	σ	σ	PROPN
ejpam-3459	121	19	,	,	PUNCT
ejpam-3459	121	20	i	i	NOUN
ejpam-3459	121	21	=	=	NOUN
ejpam-3459	121	22	1	1	NUM
ejpam-3459	121	23	,	,	PUNCT
ejpam-3459	121	24	2	2	NUM
ejpam-3459	121	25	zi(t	zi(t	NOUN
ejpam-3459	121	26	,	,	PUNCT
ejpam-3459	121	27	a	a	DET
ejpam-3459	121	28	,	,	PUNCT
ejpam-3459	121	29	x	x	NOUN
ejpam-3459	121	30	)	)	PUNCT
ejpam-3459	121	31	=	=	SYM
ejpam-3459	121	32	0	0	NUM
ejpam-3459	121	33	in	in	ADP
ejpam-3459	121	34	qa	qa	PROPN
ejpam-3459	121	35	,	,	PUNCT
ejpam-3459	121	36	i	i	PRON
ejpam-3459	121	37	=	=	NOUN
ejpam-3459	121	38	1	1	NUM
ejpam-3459	121	39	,	,	PUNCT
ejpam-3459	121	40	2	2	NUM
ejpam-3459	121	41	zi(t	zi(t	NOUN
ejpam-3459	121	42	,	,	PUNCT
ejpam-3459	121	43	a	a	DET
ejpam-3459	121	44	,	,	PUNCT
ejpam-3459	121	45	x	x	NOUN
ejpam-3459	121	46	)	)	PUNCT
ejpam-3459	121	47	=	=	SYM
ejpam-3459	121	48	0	0	NUM
ejpam-3459	121	49	in	in	ADP
ejpam-3459	121	50	qt	qt	NOUN
ejpam-3459	121	51	,	,	PUNCT
ejpam-3459	121	52	i	i	PRON
ejpam-3459	121	53	=	=	NOUN
ejpam-3459	121	54	1	1	NUM
ejpam-3459	121	55	,	,	PUNCT
ejpam-3459	121	56	2	2	NUM
ejpam-3459	121	57	(	(	PUNCT
ejpam-3459	121	58	16	16	NUM
ejpam-3459	121	59	)	)	PUNCT
ejpam-3459	121	60	verifies	verifie	NOUN
ejpam-3459	121	61	zi(0	zi(0	NUM
ejpam-3459	121	62	,	,	PUNCT
ejpam-3459	121	63	a	a	PRON
ejpam-3459	121	64	,	,	PUNCT
ejpam-3459	121	65	x	x	NOUN
ejpam-3459	121	66	)	)	PUNCT
ejpam-3459	122	1	=	=	SYM
ejpam-3459	122	2	0	0	NUM
ejpam-3459	123	1	in	in	ADP
ejpam-3459	123	2	qa	qa	PROPN
ejpam-3459	123	3	,	,	PUNCT
ejpam-3459	123	4	i	i	PRON
ejpam-3459	123	5	=	=	NOUN
ejpam-3459	123	6	1	1	NUM
ejpam-3459	123	7	,	,	PUNCT
ejpam-3459	123	8	2	2	NUM
ejpam-3459	123	9	.	.	PUNCT
ejpam-3459	123	10	(	(	PUNCT
ejpam-3459	123	11	17	17	NUM
ejpam-3459	123	12	)	)	PUNCT
ejpam-3459	123	13	where	where	SCONJ
ejpam-3459	123	14	,	,	PUNCT
ejpam-3459	123	15	g1(t	g1(t	PROPN
ejpam-3459	123	16	,	,	PUNCT
ejpam-3459	123	17	a	a	DET
ejpam-3459	123	18	,	,	PUNCT
ejpam-3459	123	19	x	x	NOUN
ejpam-3459	123	20	)	)	PUNCT
ejpam-3459	123	21	=	=	SYM
ejpam-3459	123	22	β̃1(t	β̃1(t	PROPN
ejpam-3459	123	23	,	,	PUNCT
ejpam-3459	123	24	a	a	DET
ejpam-3459	123	25	,	,	PUNCT
ejpam-3459	123	26	x)b1(t	x)b1(t	PROPN
ejpam-3459	123	27	,	,	PUNCT
ejpam-3459	123	28	x	x	X
ejpam-3459	123	29	)	)	PUNCT
ejpam-3459	123	30	+	+	CCONJ
ejpam-3459	123	31	β̃2(t	β̃2(t	PROPN
ejpam-3459	123	32	,	,	PUNCT
ejpam-3459	123	33	a	a	PRON
ejpam-3459	123	34	,	,	PUNCT
ejpam-3459	123	35	x)b2(t	x)b2(t	PROPN
ejpam-3459	123	36	,	,	PUNCT
ejpam-3459	123	37	x	x	X
ejpam-3459	123	38	)	)	PUNCT
ejpam-3459	123	39	g2(t	g2(t	PROPN
ejpam-3459	123	40	,	,	PUNCT
ejpam-3459	123	41	a	a	PRON
ejpam-3459	123	42	,	,	PUNCT
ejpam-3459	123	43	x	x	NOUN
ejpam-3459	123	44	)	)	PUNCT
ejpam-3459	123	45	=	=	SYM
ejpam-3459	124	1	β̃1(t	β̃1(t	PROPN
ejpam-3459	124	2	,	,	PUNCT
ejpam-3459	124	3	a	a	DET
ejpam-3459	124	4	,	,	PUNCT
ejpam-3459	124	5	x)b1(t	x)b1(t	PROPN
ejpam-3459	124	6	,	,	PUNCT
ejpam-3459	124	7	x)−	x)−	PROPN
ejpam-3459	124	8	β̃2(t	β̃2(t	PROPN
ejpam-3459	124	9	,	,	PUNCT
ejpam-3459	124	10	a	a	PRON
ejpam-3459	124	11	,	,	PUNCT
ejpam-3459	124	12	x)b2(t	x)b2(t	PROPN
ejpam-3459	124	13	,	,	PUNCT
ejpam-3459	124	14	x	x	NOUN
ejpam-3459	124	15	)	)	PUNCT
ejpam-3459	124	16	and	and	CCONJ
ejpam-3459	124	17	for	for	ADP
ejpam-3459	124	18	all	all	PRON
ejpam-3459	124	19	i	i	PRON
ejpam-3459	124	20	∈	∈	PROPN
ejpam-3459	124	21	{	{	PUNCT
ejpam-3459	124	22	1	1	NUM
ejpam-3459	124	23	,	,	PUNCT
ejpam-3459	124	24	2	2	NUM
ejpam-3459	124	25	}	}	PUNCT
ejpam-3459	124	26	,	,	PUNCT
ejpam-3459	124	27	µ̃i	µ̃i	ADJ
ejpam-3459	124	28	verifies	verifie	NOUN
ejpam-3459	124	29	(	(	PUNCT
ejpam-3459	124	30	h1	h1	PROPN
ejpam-3459	124	31	)	)	PUNCT
ejpam-3459	124	32	,	,	PUNCT
ejpam-3459	124	33	β̃i	β̃i	ADP
ejpam-3459	124	34	satisfies	satisfie	NOUN
ejpam-3459	124	35	(	(	PUNCT
ejpam-3459	124	36	h2)−	h2)−	X
ejpam-3459	124	37	(	(	PUNCT
ejpam-3459	124	38	h3	h3	NOUN
ejpam-3459	124	39	)	)	PUNCT
ejpam-3459	124	40	.	.	PUNCT
ejpam-3459	125	1	we	we	PRON
ejpam-3459	125	2	can	can	AUX
ejpam-3459	125	3	state	state	VERB
ejpam-3459	125	4	the	the	DET
ejpam-3459	125	5	following	following	ADJ
ejpam-3459	125	6	result	result	NOUN
ejpam-3459	125	7	:	:	PUNCT
ejpam-3459	125	8	theorem	theorem	NOUN
ejpam-3459	125	9	3	3	X
ejpam-3459	125	10	.	.	PUNCT
ejpam-3459	125	11	suppose	suppose	VERB
ejpam-3459	125	12	that	that	SCONJ
ejpam-3459	125	13	assumptions	assumption	NOUN
ejpam-3459	125	14	(	(	PUNCT
ejpam-3459	125	15	h1	h1	PROPN
ejpam-3459	125	16	)	)	PUNCT
ejpam-3459	125	17	−	−	PROPN
ejpam-3459	125	18	(	(	PUNCT
ejpam-3459	125	19	h3	h3	NOUN
ejpam-3459	125	20	)	)	PUNCT
ejpam-3459	125	21	hold	hold	NOUN
ejpam-3459	125	22	and	and	CCONJ
ejpam-3459	125	23	b1	b1	NOUN
ejpam-3459	125	24	,	,	PUNCT
ejpam-3459	125	25	b2	b2	NOUN
ejpam-3459	125	26	∈	∈	PROPN
ejpam-3459	125	27	l2(qt	l2(qt	PROPN
ejpam-3459	125	28	)	)	PUNCT
ejpam-3459	125	29	.	.	PUNCT
ejpam-3459	126	1	for	for	ADP
ejpam-3459	126	2	any	any	DET
ejpam-3459	126	3	function	function	NOUN
ejpam-3459	126	4	f	f	PROPN
ejpam-3459	126	5	∈	∈	PROPN
ejpam-3459	126	6	l2(q	l2(q	PROPN
ejpam-3459	126	7	)	)	PUNCT
ejpam-3459	126	8	such	such	ADJ
ejpam-3459	126	9	that	that	SCONJ
ejpam-3459	126	10	θf	θf	ADP
ejpam-3459	126	11	∈	∈	PROPN
ejpam-3459	126	12	l2(q	l2(q	PROPN
ejpam-3459	126	13	)	)	PUNCT
ejpam-3459	126	14	,	,	PUNCT
ejpam-3459	126	15	there	there	PRON
ejpam-3459	126	16	exists	exist	VERB
ejpam-3459	126	17	a	a	DET
ejpam-3459	126	18	control	control	NOUN
ejpam-3459	126	19	ṽ	ṽ	PROPN
ejpam-3459	126	20	in	in	ADP
ejpam-3459	126	21	l2(qω	l2(qω	PROPN
ejpam-3459	126	22	)	)	PUNCT
ejpam-3459	126	23	such	such	ADJ
ejpam-3459	126	24	that	that	SCONJ
ejpam-3459	126	25	(	(	PUNCT
ejpam-3459	126	26	ṽ	ṽ	PROPN
ejpam-3459	126	27	,	,	PUNCT
ejpam-3459	126	28	z̃1	z̃1	PROPN
ejpam-3459	126	29	,	,	PUNCT
ejpam-3459	126	30	z̃2	z̃2	NUM
ejpam-3459	126	31	)	)	PUNCT
ejpam-3459	126	32	is	be	AUX
ejpam-3459	126	33	solution	solution	NOUN
ejpam-3459	126	34	of	of	ADP
ejpam-3459	126	35	simultaneous	simultaneous	ADJ
ejpam-3459	126	36	null	null	ADJ
ejpam-3459	126	37	controllability	controllability	NOUN
ejpam-3459	126	38	problem	problem	NOUN
ejpam-3459	126	39	(	(	PUNCT
ejpam-3459	126	40	16)-(17	16)-(17	NUM
ejpam-3459	126	41	)	)	PUNCT
ejpam-3459	126	42	.	.	PUNCT
ejpam-3459	127	1	moreover	moreover	ADV
ejpam-3459	127	2	,	,	PUNCT
ejpam-3459	127	3	(	(	PUNCT
ejpam-3459	127	4	ṽ	ṽ	PROPN
ejpam-3459	127	5	,	,	PUNCT
ejpam-3459	127	6	z̃1	z̃1	PROPN
ejpam-3459	127	7	,	,	PUNCT
ejpam-3459	127	8	z̃2	z̃2	NUM
ejpam-3459	127	9	)	)	PUNCT
ejpam-3459	127	10	verifies	verifie	NOUN
ejpam-3459	127	11	ṽ	ṽ	PROPN
ejpam-3459	127	12	=	=	SYM
ejpam-3459	127	13	ũ1χω	ũ1χω	NOUN
ejpam-3459	127	14	(	(	PUNCT
ejpam-3459	127	15	18	18	NUM
ejpam-3459	127	16	)	)	PUNCT
ejpam-3459	127	17	‖z̃1‖l2(u	‖z̃1‖l2(u	NOUN
ejpam-3459	127	18	;	;	PUNCT
ejpam-3459	127	19	h1(ω	h1(ω	PROPN
ejpam-3459	127	20	)	)	PUNCT
ejpam-3459	128	1	≤	≤	NUM
ejpam-3459	128	2	c	c	X
ejpam-3459	128	3	(	(	PUNCT
ejpam-3459	128	4	‖θf‖l2(q	‖θf‖l2(q	NUM
ejpam-3459	128	5	)	)	PUNCT
ejpam-3459	128	6	+	+	CCONJ
ejpam-3459	128	7	‖f‖l2(q	‖f‖l2(q	NUM
ejpam-3459	128	8	)	)	PUNCT
ejpam-3459	128	9	)	)	PUNCT
ejpam-3459	129	1	(	(	PUNCT
ejpam-3459	129	2	19	19	NUM
ejpam-3459	129	3	)	)	PUNCT
ejpam-3459	129	4	‖z̃2‖l2(u	‖z̃2‖l2(u	PROPN
ejpam-3459	129	5	;	;	PUNCT
ejpam-3459	129	6	h1(ω	h1(ω	PROPN
ejpam-3459	129	7	)	)	PUNCT
ejpam-3459	130	1	≤	≤	NUM
ejpam-3459	131	1	c	c	X
ejpam-3459	131	2	(	(	PUNCT
ejpam-3459	131	3	‖θf‖l2(q	‖θf‖l2(q	NUM
ejpam-3459	131	4	)	)	PUNCT
ejpam-3459	132	1	+	+	CCONJ
ejpam-3459	132	2	‖f‖l2(q	‖f‖l2(q	NUM
ejpam-3459	132	3	)	)	PUNCT
ejpam-3459	132	4	)	)	PUNCT
ejpam-3459	133	1	(	(	PUNCT
ejpam-3459	133	2	20	20	NUM
ejpam-3459	133	3	)	)	PUNCT
ejpam-3459	133	4	where	where	SCONJ
ejpam-3459	133	5	ũ	ũ	PROPN
ejpam-3459	133	6	=	=	X
ejpam-3459	133	7	(	(	PUNCT
ejpam-3459	133	8	ũ1	ũ1	PROPN
ejpam-3459	133	9	,	,	PUNCT
ejpam-3459	133	10	ũ2	ũ2	PROPN
ejpam-3459	133	11	)	)	PUNCT
ejpam-3459	133	12	satisfies	satisfies	NOUN
ejpam-3459	133	13	∂ũ1	∂ũ1	NOUN
ejpam-3459	133	14	∂t	∂t	PROPN
ejpam-3459	133	15	+	+	CCONJ
ejpam-3459	133	16	∂ũ1	∂ũ1	NOUN
ejpam-3459	133	17	∂a	∂a	ADP
ejpam-3459	133	18	−∆ũ1	−∆ũ1	NOUN
ejpam-3459	133	19	+	+	CCONJ
ejpam-3459	133	20	µ̃1ũ1	µ̃1ũ1	ADJ
ejpam-3459	133	21	+	+	ADJ
ejpam-3459	133	22	µ̃2ũ2	µ̃2ũ2	NOUN
ejpam-3459	133	23	=	=	SYM
ejpam-3459	133	24	0	0	NUM
ejpam-3459	133	25	in	in	ADP
ejpam-3459	133	26	q	q	NOUN
ejpam-3459	133	27	,	,	PUNCT
ejpam-3459	133	28	∂ũ2	∂ũ2	PUNCT
ejpam-3459	134	1	∂t	∂t	PROPN
ejpam-3459	134	2	+	+	CCONJ
ejpam-3459	134	3	∂ũ2	∂ũ2	X
ejpam-3459	135	1	∂a	∂a	ADP
ejpam-3459	135	2	−∆ũ2	−∆ũ2	NOUN
ejpam-3459	135	3	+	+	CCONJ
ejpam-3459	135	4	µ̃1ũ2	µ̃1ũ2	PROPN
ejpam-3459	135	5	+	+	CCONJ
ejpam-3459	135	6	µ̃2ũ1	µ̃2ũ1	PROPN
ejpam-3459	135	7	=	=	SYM
ejpam-3459	135	8	0	0	NUM
ejpam-3459	135	9	in	in	ADP
ejpam-3459	135	10	q	q	NOUN
ejpam-3459	135	11	,	,	PUNCT
ejpam-3459	135	12	ũ1(0	ũ1(0	NOUN
ejpam-3459	135	13	,	,	PUNCT
ejpam-3459	135	14	a	a	DET
ejpam-3459	135	15	,	,	PUNCT
ejpam-3459	135	16	x	x	NOUN
ejpam-3459	135	17	)	)	PUNCT
ejpam-3459	135	18	=	=	SYM
ejpam-3459	135	19	ũ2(0	ũ2(0	NOUN
ejpam-3459	135	20	,	,	PUNCT
ejpam-3459	135	21	a	a	DET
ejpam-3459	135	22	,	,	PUNCT
ejpam-3459	135	23	x	x	NOUN
ejpam-3459	135	24	)	)	PUNCT
ejpam-3459	135	25	=	=	SYM
ejpam-3459	135	26	0	0	NUM
ejpam-3459	136	1	in	in	ADP
ejpam-3459	136	2	qa	qa	PROPN
ejpam-3459	136	3	,	,	PUNCT
ejpam-3459	136	4	ũ1	ũ1	PROPN
ejpam-3459	136	5	=	=	SYM
ejpam-3459	136	6	ũ2	ũ2	PROPN
ejpam-3459	136	7	=	=	SYM
ejpam-3459	136	8	0	0	NUM
ejpam-3459	136	9	on	on	ADP
ejpam-3459	136	10	σ	σ	PROPN
ejpam-3459	136	11	,	,	PUNCT
ejpam-3459	136	12	ũ1(t	ũ1(t	PROPN
ejpam-3459	136	13	,	,	PUNCT
ejpam-3459	136	14	0	0	NUM
ejpam-3459	136	15	,	,	PUNCT
ejpam-3459	136	16	x	x	NOUN
ejpam-3459	136	17	)	)	PUNCT
ejpam-3459	136	18	=	=	SYM
ejpam-3459	136	19	υ1(ũ	υ1(ũ	PROPN
ejpam-3459	136	20	)	)	PUNCT
ejpam-3459	136	21	in	in	ADP
ejpam-3459	136	22	qt	qt	NOUN
ejpam-3459	136	23	,	,	PUNCT
ejpam-3459	136	24	ũ2(t	ũ2(t	PROPN
ejpam-3459	136	25	,	,	PUNCT
ejpam-3459	136	26	0	0	NUM
ejpam-3459	136	27	,	,	PUNCT
ejpam-3459	136	28	x	x	NOUN
ejpam-3459	136	29	)	)	PUNCT
ejpam-3459	136	30	=	=	SYM
ejpam-3459	136	31	υ2(ũ	υ2(ũ	PROPN
ejpam-3459	136	32	)	)	PUNCT
ejpam-3459	136	33	in	in	ADP
ejpam-3459	136	34	qt	qt	NOUN
ejpam-3459	136	35	.	.	PUNCT
ejpam-3459	137	1	(	(	PUNCT
ejpam-3459	137	2	21	21	NUM
ejpam-3459	137	3	)	)	PUNCT
ejpam-3459	137	4	c.	c.	PROPN
ejpam-3459	137	5	k.	k.	PROPN
ejpam-3459	137	6	somé	somé	PROPN
ejpam-3459	137	7	,	,	PUNCT
ejpam-3459	137	8	s.	s.	PROPN
ejpam-3459	137	9	sawadogo	sawadogo	PROPN
ejpam-3459	137	10	/	/	SYM
ejpam-3459	137	11	eur	eur	PROPN
ejpam-3459	137	12	.	.	PUNCT
ejpam-3459	138	1	j.	j.	PROPN
ejpam-3459	138	2	pure	pure	PROPN
ejpam-3459	138	3	appl	appl	PROPN
ejpam-3459	138	4	.	.	PROPN
ejpam-3459	138	5	math	math	PROPN
ejpam-3459	138	6	,	,	PUNCT
ejpam-3459	138	7	12	12	NUM
ejpam-3459	138	8	(	(	PUNCT
ejpam-3459	138	9	3	3	NUM
ejpam-3459	138	10	)	)	PUNCT
ejpam-3459	138	11	(	(	PUNCT
ejpam-3459	138	12	2019	2019	NUM
ejpam-3459	138	13	)	)	PUNCT
ejpam-3459	138	14	,	,	PUNCT
ejpam-3459	138	15	870	870	NUM
ejpam-3459	138	16	-	-	SYM
ejpam-3459	138	17	892	892	NUM
ejpam-3459	138	18	876	876	NUM
ejpam-3459	138	19	where	where	SCONJ
ejpam-3459	138	20	υ1(ũ	υ1(ũ	PROPN
ejpam-3459	138	21	)	)	PUNCT
ejpam-3459	139	1	=	=	PROPN
ejpam-3459	139	2	b1	b1	PROPN
ejpam-3459	139	3	∫	∫	PROPN
ejpam-3459	139	4	a	a	DET
ejpam-3459	139	5	0	0	NUM
ejpam-3459	139	6	β̃1(ũ1	β̃1(ũ1	PROPN
ejpam-3459	139	7	+	+	CCONJ
ejpam-3459	139	8	ũ2)da+	ũ2)da+	NUM
ejpam-3459	139	9	b2	b2	PROPN
ejpam-3459	139	10	∫	∫	PROPN
ejpam-3459	139	11	a	a	DET
ejpam-3459	139	12	0	0	NUM
ejpam-3459	139	13	β̃2(ũ1	β̃2(ũ1	PUNCT
ejpam-3459	139	14	−	−	PROPN
ejpam-3459	139	15	ũ2)da	ũ2)da	ADJ
ejpam-3459	139	16	υ2(ũ	υ2(ũ	PROPN
ejpam-3459	139	17	)	)	PUNCT
ejpam-3459	140	1	=	=	PUNCT
ejpam-3459	140	2	b1	b1	PROPN
ejpam-3459	140	3	∫	∫	PROPN
ejpam-3459	140	4	a	a	DET
ejpam-3459	140	5	0	0	NUM
ejpam-3459	140	6	β̃1(ũ1	β̃1(ũ1	PROPN
ejpam-3459	140	7	+	+	CCONJ
ejpam-3459	140	8	ũ2)da+	ũ2)da+	NUM
ejpam-3459	140	9	b2	b2	PROPN
ejpam-3459	140	10	∫	∫	PROPN
ejpam-3459	140	11	a	a	DET
ejpam-3459	140	12	0	0	NUM
ejpam-3459	140	13	β̃2(ũ2	β̃2(ũ2	PUNCT
ejpam-3459	140	14	−	−	PROPN
ejpam-3459	140	15	ũ1)da	ũ1)da	ADJ
ejpam-3459	140	16	proof	proof	NOUN
ejpam-3459	140	17	.	.	PUNCT
ejpam-3459	141	1	we	we	PRON
ejpam-3459	141	2	will	will	AUX
ejpam-3459	141	3	do	do	VERB
ejpam-3459	141	4	it	it	PRON
ejpam-3459	141	5	in	in	ADP
ejpam-3459	141	6	two	two	NUM
ejpam-3459	141	7	steps	step	NOUN
ejpam-3459	141	8	as	as	SCONJ
ejpam-3459	141	9	follows	follow	VERB
ejpam-3459	141	10	:	:	PUNCT
ejpam-3459	141	11	step	step	NOUN
ejpam-3459	141	12	1	1	NUM
ejpam-3459	141	13	:	:	PUNCT
ejpam-3459	141	14	there	there	PRON
ejpam-3459	141	15	exists	exist	VERB
ejpam-3459	141	16	a	a	DET
ejpam-3459	141	17	control	control	NOUN
ejpam-3459	141	18	vε	vε	NOUN
ejpam-3459	141	19	that	that	PRON
ejpam-3459	141	20	leads	lead	VERB
ejpam-3459	141	21	to	to	ADP
ejpam-3459	141	22	extinction	extinction	NOUN
ejpam-3459	141	23	each	each	DET
ejpam-3459	141	24	distribution	distribution	NOUN
ejpam-3459	141	25	z1ε	z1ε	PUNCT
ejpam-3459	141	26	,	,	PUNCT
ejpam-3459	141	27	z2ε	z2ε	PROPN
ejpam-3459	141	28	.	.	PUNCT
ejpam-3459	142	1	for	for	ADP
ejpam-3459	142	2	any	any	DET
ejpam-3459	142	3	ε	ε	PROPN
ejpam-3459	142	4	>	>	X
ejpam-3459	142	5	0	0	PROPN
ejpam-3459	142	6	,	,	PUNCT
ejpam-3459	142	7	we	we	PRON
ejpam-3459	142	8	consider	consider	VERB
ejpam-3459	142	9	the	the	DET
ejpam-3459	142	10	functional	functional	ADJ
ejpam-3459	142	11	defined	define	VERB
ejpam-3459	142	12	on	on	ADP
ejpam-3459	142	13	l2(qω	l2(qω	PROPN
ejpam-3459	142	14	)	)	PUNCT
ejpam-3459	142	15	by	by	ADP
ejpam-3459	142	16	jε(v	jε(v	NOUN
ejpam-3459	142	17	)	)	PUNCT
ejpam-3459	142	18	=	=	SYM
ejpam-3459	142	19	1	1	NUM
ejpam-3459	142	20	2	2	NUM
ejpam-3459	142	21	‖v‖2l2(qω	‖v‖2l2(qω	NUM
ejpam-3459	142	22	)	)	PUNCT
ejpam-3459	143	1	+	+	CCONJ
ejpam-3459	143	2	1	1	NUM
ejpam-3459	143	3	2ε	2ε	NUM
ejpam-3459	143	4	∫	∫	PROPN
ejpam-3459	143	5	qa	qa	PROPN
ejpam-3459	143	6	(	(	PUNCT
ejpam-3459	143	7	z2	z2	PROPN
ejpam-3459	143	8	1(0	1(0	PROPN
ejpam-3459	143	9	,	,	PUNCT
ejpam-3459	143	10	a	a	PRON
ejpam-3459	143	11	,	,	PUNCT
ejpam-3459	143	12	x	x	NOUN
ejpam-3459	143	13	)	)	PUNCT
ejpam-3459	143	14	+	+	CCONJ
ejpam-3459	143	15	z2	z2	PROPN
ejpam-3459	143	16	2(0	2(0	NUM
ejpam-3459	143	17	,	,	PUNCT
ejpam-3459	143	18	a	a	PRON
ejpam-3459	143	19	,	,	PUNCT
ejpam-3459	143	20	x	x	NOUN
ejpam-3459	143	21	)	)	PUNCT
ejpam-3459	143	22	)	)	PUNCT
ejpam-3459	144	1	dqa	dqa	INTJ
ejpam-3459	144	2	,	,	PUNCT
ejpam-3459	144	3	(	(	PUNCT
ejpam-3459	144	4	22	22	NUM
ejpam-3459	144	5	)	)	PUNCT
ejpam-3459	144	6	where	where	SCONJ
ejpam-3459	144	7	z	z	NOUN
ejpam-3459	144	8	=	=	SYM
ejpam-3459	144	9	(	(	PUNCT
ejpam-3459	144	10	z1	z1	PROPN
ejpam-3459	144	11	,	,	PUNCT
ejpam-3459	144	12	z2	z2	PROPN
ejpam-3459	144	13	)	)	PUNCT
ejpam-3459	144	14	is	be	AUX
ejpam-3459	144	15	solution	solution	NOUN
ejpam-3459	144	16	of	of	ADP
ejpam-3459	144	17	(	(	PUNCT
ejpam-3459	144	18	16	16	NUM
ejpam-3459	144	19	)	)	PUNCT
ejpam-3459	144	20	.	.	PUNCT
ejpam-3459	145	1	it	it	PRON
ejpam-3459	145	2	is	be	AUX
ejpam-3459	145	3	clear	clear	ADJ
ejpam-3459	145	4	that	that	SCONJ
ejpam-3459	145	5	jε	jε	NOUN
ejpam-3459	145	6	is	be	AUX
ejpam-3459	145	7	continuous	continuous	ADJ
ejpam-3459	145	8	,	,	PUNCT
ejpam-3459	145	9	convex	convex	ADJ
ejpam-3459	145	10	and	and	CCONJ
ejpam-3459	145	11	coercive	coercive	ADJ
ejpam-3459	145	12	on	on	ADP
ejpam-3459	145	13	l2(qω	l2(qω	PROPN
ejpam-3459	145	14	)	)	PUNCT
ejpam-3459	145	15	.	.	PUNCT
ejpam-3459	146	1	hence	hence	ADV
ejpam-3459	146	2	,	,	PUNCT
ejpam-3459	146	3	the	the	DET
ejpam-3459	146	4	minimization	minimization	NOUN
ejpam-3459	146	5	problem	problem	NOUN
ejpam-3459	146	6	of	of	ADP
ejpam-3459	146	7	jε	jε	PROPN
ejpam-3459	146	8	admits	admit	VERB
ejpam-3459	146	9	at	at	ADV
ejpam-3459	146	10	least	least	ADV
ejpam-3459	146	11	one	one	NUM
ejpam-3459	146	12	solution	solution	NOUN
ejpam-3459	146	13	vε	vε	ADP
ejpam-3459	146	14	associated	associate	VERB
ejpam-3459	146	15	to	to	ADP
ejpam-3459	146	16	(	(	PUNCT
ejpam-3459	146	17	z1ε	z1ε	X
ejpam-3459	146	18	,	,	PUNCT
ejpam-3459	146	19	z2ε	z2ε	NOUN
ejpam-3459	146	20	)	)	PUNCT
ejpam-3459	146	21	solution	solution	NOUN
ejpam-3459	146	22	of	of	ADP
ejpam-3459	146	23	(	(	PUNCT
ejpam-3459	146	24	16	16	NUM
ejpam-3459	146	25	)	)	PUNCT
ejpam-3459	146	26	.	.	PUNCT
ejpam-3459	147	1	from	from	ADP
ejpam-3459	147	2	the	the	DET
ejpam-3459	147	3	maximum	maximum	ADJ
ejpam-3459	147	4	principle	principle	NOUN
ejpam-3459	147	5	(	(	PUNCT
ejpam-3459	147	6	see	see	VERB
ejpam-3459	147	7	[	[	X
ejpam-3459	147	8	10	10	NUM
ejpam-3459	147	9	]	]	NUM
ejpam-3459	147	10	)	)	PUNCT
ejpam-3459	147	11	,	,	PUNCT
ejpam-3459	147	12	we	we	PRON
ejpam-3459	147	13	get	get	VERB
ejpam-3459	147	14	vε	vε	ADP
ejpam-3459	147	15	=	=	PUNCT
ejpam-3459	147	16	η1εχω	η1εχω	PROPN
ejpam-3459	147	17	in	in	ADP
ejpam-3459	147	18	q	q	X
ejpam-3459	147	19	(	(	PUNCT
ejpam-3459	147	20	23	23	NUM
ejpam-3459	147	21	)	)	PUNCT
ejpam-3459	147	22	where	where	SCONJ
ejpam-3459	147	23	ηε	ηε	NOUN
ejpam-3459	147	24	=	=	SYM
ejpam-3459	147	25	(	(	PUNCT
ejpam-3459	147	26	η1ε	η1ε	X
ejpam-3459	147	27	,	,	PUNCT
ejpam-3459	147	28	η2ε	η2ε	NOUN
ejpam-3459	147	29	)	)	PUNCT
ejpam-3459	147	30	verifies	verifie	NOUN
ejpam-3459	147	31	the	the	DET
ejpam-3459	147	32	system	system	NOUN
ejpam-3459	148	1			PROPN
ejpam-3459	148	2	∂η1ε	∂η1ε	X
ejpam-3459	149	1	∂t	∂t	PROPN
ejpam-3459	149	2	+	+	CCONJ
ejpam-3459	149	3	∂η1ε	∂η1ε	PROPN
ejpam-3459	150	1	∂a	∂a	NOUN
ejpam-3459	150	2	−∆η1ε	−∆η1ε	NOUN
ejpam-3459	150	3	+	+	CCONJ
ejpam-3459	150	4	µ̃1η1ε	µ̃1η1ε	X
ejpam-3459	150	5	+	+	SYM
ejpam-3459	150	6	µ̃2η2ε	µ̃2η2ε	NOUN
ejpam-3459	150	7	=	=	NOUN
ejpam-3459	150	8	0	0	NUM
ejpam-3459	150	9	in	in	ADP
ejpam-3459	150	10	q	q	NOUN
ejpam-3459	150	11	,	,	PUNCT
ejpam-3459	150	12	∂η2ε	∂η2ε	PROPN
ejpam-3459	150	13	∂t	∂t	PROPN
ejpam-3459	150	14	+	+	CCONJ
ejpam-3459	150	15	∂η2ε	∂η2ε	NOUN
ejpam-3459	150	16	∂a	∂a	NOUN
ejpam-3459	150	17	−∆η2ε	−∆η2ε	NOUN
ejpam-3459	150	18	+	+	CCONJ
ejpam-3459	150	19	µ̃1η2ε	µ̃1η2ε	NOUN
ejpam-3459	150	20	+	+	X
ejpam-3459	150	21	µ̃2η1ε	µ̃2η1ε	NOUN
ejpam-3459	150	22	=	=	PUNCT
ejpam-3459	150	23	0	0	NUM
ejpam-3459	151	1	in	in	ADP
ejpam-3459	151	2	q	q	PROPN
ejpam-3459	151	3	,	,	PUNCT
ejpam-3459	151	4	η1ε	η1ε	X
ejpam-3459	151	5	=	=	PUNCT
ejpam-3459	151	6	η2ε	η2ε	NOUN
ejpam-3459	151	7	=	=	SYM
ejpam-3459	151	8	0	0	NUM
ejpam-3459	151	9	on	on	ADP
ejpam-3459	151	10	σ	σ	PROPN
ejpam-3459	151	11	,	,	PUNCT
ejpam-3459	151	12	η1ε(0	η1ε(0	PROPN
ejpam-3459	151	13	,	,	PUNCT
ejpam-3459	151	14	a	a	PRON
ejpam-3459	151	15	,	,	PUNCT
ejpam-3459	151	16	x	x	NOUN
ejpam-3459	151	17	)	)	PUNCT
ejpam-3459	151	18	=	=	SYM
ejpam-3459	151	19	−1	−1	NOUN
ejpam-3459	151	20	εz1ε(0	εz1ε(0	PROPN
ejpam-3459	151	21	,	,	PUNCT
ejpam-3459	151	22	a	a	PRON
ejpam-3459	151	23	,	,	PUNCT
ejpam-3459	151	24	x	x	NOUN
ejpam-3459	151	25	)	)	PUNCT
ejpam-3459	151	26	in	in	ADP
ejpam-3459	151	27	qa	qa	PROPN
ejpam-3459	151	28	,	,	PUNCT
ejpam-3459	151	29	η2ε(0	η2ε(0	PROPN
ejpam-3459	151	30	,	,	PUNCT
ejpam-3459	151	31	a	a	DET
ejpam-3459	151	32	,	,	PUNCT
ejpam-3459	151	33	x	x	NOUN
ejpam-3459	151	34	)	)	PUNCT
ejpam-3459	151	35	=	=	SYM
ejpam-3459	151	36	−1	−1	NOUN
ejpam-3459	151	37	εz2ε(0	εz2ε(0	PROPN
ejpam-3459	151	38	,	,	PUNCT
ejpam-3459	151	39	a	a	PRON
ejpam-3459	151	40	,	,	PUNCT
ejpam-3459	151	41	x	x	NOUN
ejpam-3459	151	42	)	)	PUNCT
ejpam-3459	151	43	in	in	ADP
ejpam-3459	151	44	qa	qa	PROPN
ejpam-3459	151	45	,	,	PUNCT
ejpam-3459	151	46	η1ε(t	η1ε(t	PROPN
ejpam-3459	151	47	,	,	PUNCT
ejpam-3459	151	48	0	0	NUM
ejpam-3459	151	49	,	,	PUNCT
ejpam-3459	151	50	x	x	NOUN
ejpam-3459	151	51	)	)	PUNCT
ejpam-3459	151	52	=	=	SYM
ejpam-3459	151	53	υ1(ηε	υ1(ηε	PROPN
ejpam-3459	151	54	)	)	PUNCT
ejpam-3459	151	55	in	in	ADP
ejpam-3459	151	56	qt	qt	NOUN
ejpam-3459	151	57	η2ε(t	η2ε(t	NOUN
ejpam-3459	151	58	,	,	PUNCT
ejpam-3459	151	59	0	0	NUM
ejpam-3459	151	60	,	,	PUNCT
ejpam-3459	151	61	x	x	NOUN
ejpam-3459	151	62	)	)	PUNCT
ejpam-3459	151	63	=	=	SYM
ejpam-3459	151	64	υ2(ηε	υ2(ηε	PROPN
ejpam-3459	151	65	)	)	PUNCT
ejpam-3459	151	66	in	in	ADP
ejpam-3459	151	67	qt	qt	NOUN
ejpam-3459	151	68	,	,	PUNCT
ejpam-3459	151	69	(	(	PUNCT
ejpam-3459	151	70	24	24	NUM
ejpam-3459	151	71	)	)	PUNCT
ejpam-3459	151	72	herein	herein	NOUN
ejpam-3459	151	73	zε	zε	NOUN
ejpam-3459	151	74	=	=	PUNCT
ejpam-3459	151	75	(	(	PUNCT
ejpam-3459	151	76	z1ε	z1ε	X
ejpam-3459	151	77	,	,	PUNCT
ejpam-3459	151	78	z2ε	z2ε	NOUN
ejpam-3459	151	79	)	)	PUNCT
ejpam-3459	151	80	is	be	AUX
ejpam-3459	151	81	the	the	DET
ejpam-3459	151	82	solution	solution	NOUN
ejpam-3459	151	83	of	of	ADP
ejpam-3459	151	84	(	(	PUNCT
ejpam-3459	151	85	16	16	NUM
ejpam-3459	151	86	)	)	PUNCT
ejpam-3459	151	87	associated	associate	VERB
ejpam-3459	151	88	to	to	PART
ejpam-3459	151	89	vε	vε	VERB
ejpam-3459	151	90	.	.	PUNCT
ejpam-3459	152	1	let	let	VERB
ejpam-3459	152	2	us	we	PRON
ejpam-3459	152	3	multiply	multiply	VERB
ejpam-3459	152	4	the	the	DET
ejpam-3459	152	5	first	first	ADJ
ejpam-3459	152	6	(	(	PUNCT
ejpam-3459	152	7	with	with	ADP
ejpam-3459	152	8	v	v	NOUN
ejpam-3459	152	9	=	=	SYM
ejpam-3459	152	10	vε	vε	NOUN
ejpam-3459	152	11	and	and	CCONJ
ejpam-3459	152	12	z1	z1	NOUN
ejpam-3459	152	13	=	=	PUNCT
ejpam-3459	152	14	z1ε	z1ε	X
ejpam-3459	152	15	)	)	PUNCT
ejpam-3459	152	16	and	and	CCONJ
ejpam-3459	152	17	the	the	DET
ejpam-3459	152	18	second	second	ADJ
ejpam-3459	152	19	(	(	PUNCT
ejpam-3459	152	20	with	with	ADP
ejpam-3459	152	21	z2	z2	PROPN
ejpam-3459	152	22	=	=	SYM
ejpam-3459	152	23	z2ε	z2ε	X
ejpam-3459	152	24	)	)	PUNCT
ejpam-3459	152	25	equalities	equality	NOUN
ejpam-3459	152	26	of	of	ADP
ejpam-3459	152	27	(	(	PUNCT
ejpam-3459	152	28	16	16	NUM
ejpam-3459	152	29	)	)	PUNCT
ejpam-3459	152	30	by	by	ADP
ejpam-3459	152	31	η1ε	η1ε	INTJ
ejpam-3459	152	32	and	and	CCONJ
ejpam-3459	152	33	η2ε	η2ε	NOUN
ejpam-3459	152	34	respectively	respectively	ADV
ejpam-3459	152	35	,	,	PUNCT
ejpam-3459	152	36	and	and	CCONJ
ejpam-3459	152	37	integrate	integrate	VERB
ejpam-3459	152	38	each	each	DET
ejpam-3459	152	39	equality	equality	NOUN
ejpam-3459	152	40	by	by	ADP
ejpam-3459	152	41	parts	part	NOUN
ejpam-3459	152	42	over	over	ADP
ejpam-3459	152	43	q.	q.	NOUN
ejpam-3459	152	44	using	use	VERB
ejpam-3459	152	45	(	(	PUNCT
ejpam-3459	152	46	24	24	NUM
ejpam-3459	152	47	)	)	PUNCT
ejpam-3459	152	48	we	we	PRON
ejpam-3459	152	49	deduct	deduct	VERB
ejpam-3459	152	50	that∫	that∫	NOUN
ejpam-3459	152	51	q	q	PROPN
ejpam-3459	153	1	(	(	PUNCT
ejpam-3459	153	2	−f)η1εdq	−f)η1εdq	NOUN
ejpam-3459	153	3	=	=	SYM
ejpam-3459	153	4	‖vε‖2l2(qω	‖vε‖2l2(qω	PROPN
ejpam-3459	153	5	)	)	PUNCT
ejpam-3459	154	1	+	+	CCONJ
ejpam-3459	154	2	1	1	NUM
ejpam-3459	154	3	ε‖z1ε(0	ε‖z1ε(0	NOUN
ejpam-3459	154	4	,	,	PUNCT
ejpam-3459	154	5	·	·	PUNCT
ejpam-3459	154	6	,	,	PUNCT
ejpam-3459	154	7	·	·	PUNCT
ejpam-3459	154	8	)	)	PUNCT
ejpam-3459	154	9	‖2l2(q	‖2l2(q	X
ejpam-3459	154	10	)	)	PUNCT
ejpam-3459	155	1	+	+	CCONJ
ejpam-3459	155	2	1	1	NUM
ejpam-3459	155	3	ε‖z2ε(0	ε‖z2ε(0	ADJ
ejpam-3459	155	4	,	,	PUNCT
ejpam-3459	155	5	·	·	PUNCT
ejpam-3459	155	6	,	,	PUNCT
ejpam-3459	155	7	·	·	PUNCT
ejpam-3459	155	8	)	)	PUNCT
ejpam-3459	155	9	‖2l2(q	‖2l2(q	X
ejpam-3459	155	10	)	)	PUNCT
ejpam-3459	155	11	.	.	PUNCT
ejpam-3459	156	1	(	(	PUNCT
ejpam-3459	156	2	25	25	NUM
ejpam-3459	156	3	)	)	PUNCT
ejpam-3459	156	4	elsewhere	elsewhere	ADV
ejpam-3459	156	5	,	,	PUNCT
ejpam-3459	156	6	young	young	PROPN
ejpam-3459	156	7	’s	’s	PART
ejpam-3459	156	8	inequality	inequality	NOUN
ejpam-3459	156	9	gives	give	VERB
ejpam-3459	156	10	:	:	PUNCT
ejpam-3459	156	11	∫	∫	PROPN
ejpam-3459	156	12	q	q	PROPN
ejpam-3459	156	13	|fη1ε	|fη1ε	PRON
ejpam-3459	157	1	|	|	ADV
ejpam-3459	157	2	dq	dq	NOUN
ejpam-3459	157	3	≤	≤	NUM
ejpam-3459	157	4	2c‖θf‖2l2(q	2c‖θf‖2l2(q	NUM
ejpam-3459	157	5	)	)	PUNCT
ejpam-3459	158	1	+	+	CCONJ
ejpam-3459	158	2	1	1	NUM
ejpam-3459	158	3	2c	2c	NUM
ejpam-3459	158	4	∫	∫	NOUN
ejpam-3459	158	5	q	q	PROPN
ejpam-3459	158	6	1	1	NUM
ejpam-3459	158	7	θ2	θ2	PROPN
ejpam-3459	158	8	η2	η2	VERB
ejpam-3459	158	9	1εdq	1εdq	NUM
ejpam-3459	158	10	for	for	ADP
ejpam-3459	158	11	any	any	DET
ejpam-3459	158	12	c	c	PROPN
ejpam-3459	158	13	>	>	X
ejpam-3459	158	14	0	0	NUM
ejpam-3459	158	15	.	.	NOUN
ejpam-3459	158	16	thus,∫	thus,∫	DET
ejpam-3459	159	1	q	q	PROPN
ejpam-3459	159	2	(	(	PUNCT
ejpam-3459	159	3	−f)η1ε	−f)η1ε	PROPN
ejpam-3459	159	4	≤	≤	NUM
ejpam-3459	159	5	2c‖θf‖2l2(q	2c‖θf‖2l2(q	NUM
ejpam-3459	159	6	)	)	PUNCT
ejpam-3459	160	1	+	+	CCONJ
ejpam-3459	160	2	1	1	NUM
ejpam-3459	160	3	2c	2c	NUM
ejpam-3459	160	4	∫	∫	NOUN
ejpam-3459	160	5	q	q	PROPN
ejpam-3459	160	6	1	1	NUM
ejpam-3459	160	7	θ2	θ2	PROPN
ejpam-3459	160	8	(	(	PUNCT
ejpam-3459	160	9	η2	η2	X
ejpam-3459	160	10	1ε	1ε	NOUN
ejpam-3459	160	11	+	+	CCONJ
ejpam-3459	161	1	η2	η2	ADJ
ejpam-3459	161	2	2ε	2ε	NOUN
ejpam-3459	161	3	)	)	PUNCT
ejpam-3459	161	4	dq	dq	PROPN
ejpam-3459	161	5	.	.	PUNCT
ejpam-3459	161	6	c.	c.	PROPN
ejpam-3459	161	7	k.	k.	PROPN
ejpam-3459	161	8	somé	somé	PROPN
ejpam-3459	161	9	,	,	PUNCT
ejpam-3459	161	10	s.	s.	PROPN
ejpam-3459	161	11	sawadogo	sawadogo	PROPN
ejpam-3459	161	12	/	/	SYM
ejpam-3459	161	13	eur	eur	PROPN
ejpam-3459	161	14	.	.	PUNCT
ejpam-3459	162	1	j.	j.	PROPN
ejpam-3459	162	2	pure	pure	PROPN
ejpam-3459	162	3	appl	appl	PROPN
ejpam-3459	162	4	.	.	PROPN
ejpam-3459	162	5	math	math	PROPN
ejpam-3459	162	6	,	,	PUNCT
ejpam-3459	162	7	12	12	NUM
ejpam-3459	162	8	(	(	PUNCT
ejpam-3459	162	9	3	3	NUM
ejpam-3459	162	10	)	)	PUNCT
ejpam-3459	162	11	(	(	PUNCT
ejpam-3459	162	12	2019	2019	NUM
ejpam-3459	162	13	)	)	PUNCT
ejpam-3459	162	14	,	,	PUNCT
ejpam-3459	162	15	870	870	NUM
ejpam-3459	162	16	-	-	SYM
ejpam-3459	162	17	892	892	NUM
ejpam-3459	162	18	877	877	NUM
ejpam-3459	162	19	the	the	DET
ejpam-3459	162	20	lemma	lemma	PROPN
ejpam-3459	162	21	2	2	NUM
ejpam-3459	162	22	allows	allow	VERB
ejpam-3459	162	23	,	,	PUNCT
ejpam-3459	162	24	choosing	choose	VERB
ejpam-3459	162	25	c	c	NUM
ejpam-3459	162	26	,	,	PUNCT
ejpam-3459	162	27	the	the	DET
ejpam-3459	162	28	constant	constant	ADJ
ejpam-3459	162	29	defined	define	VERB
ejpam-3459	162	30	therein	therein	ADV
ejpam-3459	162	31	,	,	PUNCT
ejpam-3459	162	32	to	to	PART
ejpam-3459	162	33	deduct	deduct	VERB
ejpam-3459	162	34	that∫	that∫	NOUN
ejpam-3459	162	35	q	q	PROPN
ejpam-3459	163	1	(	(	PUNCT
ejpam-3459	163	2	−f)η1εdq	−f)η1εdq	NOUN
ejpam-3459	163	3	≤	≤	ADV
ejpam-3459	163	4	2c‖θf‖2l2(q	2c‖θf‖2l2(q	NUM
ejpam-3459	163	5	)	)	PUNCT
ejpam-3459	164	1	+	+	CCONJ
ejpam-3459	164	2	1	1	NUM
ejpam-3459	164	3	2	2	NUM
ejpam-3459	164	4	‖vε‖2l2(g	‖vε‖2l2(g	NOUN
ejpam-3459	164	5	)	)	PUNCT
ejpam-3459	164	6	.	.	PUNCT
ejpam-3459	165	1	(	(	PUNCT
ejpam-3459	165	2	26	26	NUM
ejpam-3459	165	3	)	)	PUNCT
ejpam-3459	165	4	from	from	ADP
ejpam-3459	165	5	(	(	PUNCT
ejpam-3459	165	6	25	25	NUM
ejpam-3459	165	7	)	)	PUNCT
ejpam-3459	165	8	and	and	CCONJ
ejpam-3459	165	9	(	(	PUNCT
ejpam-3459	165	10	26	26	NUM
ejpam-3459	165	11	)	)	PUNCT
ejpam-3459	165	12	one	one	NOUN
ejpam-3459	165	13	obtains	obtain	VERB
ejpam-3459	165	14	:	:	PUNCT
ejpam-3459	165	15	‖vε‖l2(g	‖vε‖l2(g	NUM
ejpam-3459	165	16	)	)	PUNCT
ejpam-3459	165	17	≤	≤	NUM
ejpam-3459	165	18	2	2	NUM
ejpam-3459	165	19	√	√	NUM
ejpam-3459	165	20	c‖θf‖l2(q	c‖θf‖l2(q	NUM
ejpam-3459	165	21	)	)	PUNCT
ejpam-3459	165	22	(	(	PUNCT
ejpam-3459	165	23	27	27	NUM
ejpam-3459	165	24	)	)	PUNCT
ejpam-3459	165	25	‖z1ε(0	‖z1ε(0	PROPN
ejpam-3459	165	26	,	,	PUNCT
ejpam-3459	165	27	·	·	PUNCT
ejpam-3459	165	28	,	,	PUNCT
ejpam-3459	165	29	·	·	PUNCT
ejpam-3459	165	30	)	)	PUNCT
ejpam-3459	165	31	‖l2(q	‖l2(q	PROPN
ejpam-3459	165	32	)	)	PUNCT
ejpam-3459	165	33	≤	≤	NOUN
ejpam-3459	165	34	√	√	ADP
ejpam-3459	165	35	2εc‖θf‖l2(q	2εc‖θf‖l2(q	NUM
ejpam-3459	165	36	)	)	PUNCT
ejpam-3459	165	37	(	(	PUNCT
ejpam-3459	165	38	28	28	NUM
ejpam-3459	165	39	)	)	PUNCT
ejpam-3459	165	40	‖z2ε(0	‖z2ε(0	PROPN
ejpam-3459	165	41	,	,	PUNCT
ejpam-3459	165	42	·	·	PUNCT
ejpam-3459	165	43	,	,	PUNCT
ejpam-3459	165	44	·	·	PUNCT
ejpam-3459	165	45	)	)	PUNCT
ejpam-3459	165	46	‖l2(q	‖l2(q	PROPN
ejpam-3459	165	47	)	)	PUNCT
ejpam-3459	165	48	≤	≤	NOUN
ejpam-3459	165	49	√	√	ADP
ejpam-3459	165	50	2εc‖θf‖l2(q	2εc‖θf‖l2(q	NUM
ejpam-3459	165	51	)	)	PUNCT
ejpam-3459	165	52	(	(	PUNCT
ejpam-3459	165	53	29	29	NUM
ejpam-3459	165	54	)	)	PUNCT
ejpam-3459	165	55	we	we	PRON
ejpam-3459	165	56	can	can	AUX
ejpam-3459	165	57	extract	extract	VERB
ejpam-3459	165	58	subsequences	subsequence	NOUN
ejpam-3459	165	59	denoted	denote	VERB
ejpam-3459	165	60	again	again	ADV
ejpam-3459	165	61	(	(	PUNCT
ejpam-3459	165	62	vε)ε	vε)ε	PROPN
ejpam-3459	165	63	and	and	CCONJ
ejpam-3459	165	64	(	(	PUNCT
ejpam-3459	165	65	zε)ε	zε)ε	X
ejpam-3459	165	66	such	such	ADJ
ejpam-3459	165	67	that	that	PRON
ejpam-3459	165	68	vε	vε	VERB
ejpam-3459	165	69	⇀	⇀	X
ejpam-3459	165	70	ṽ	ṽ	PROPN
ejpam-3459	165	71	weakly	weakly	ADV
ejpam-3459	165	72	in	in	ADP
ejpam-3459	165	73	l2(qω	l2(qω	PROPN
ejpam-3459	165	74	)	)	PUNCT
ejpam-3459	165	75	and	and	CCONJ
ejpam-3459	165	76	ziε	ziε	NOUN
ejpam-3459	166	1	⇀	⇀	INTJ
ejpam-3459	167	1	z̃i	z̃i	INTJ
ejpam-3459	167	2	,	,	PUNCT
ejpam-3459	167	3	i	i	PRON
ejpam-3459	167	4	=	=	NOUN
ejpam-3459	167	5	1	1	NUM
ejpam-3459	167	6	,	,	PUNCT
ejpam-3459	167	7	2	2	NUM
ejpam-3459	167	8	weakly	weakly	ADV
ejpam-3459	167	9	in	in	ADP
ejpam-3459	167	10	l2(u	l2(u	PROPN
ejpam-3459	167	11	,	,	PUNCT
ejpam-3459	167	12	h1	h1	PROPN
ejpam-3459	167	13	0	0	NUM
ejpam-3459	167	14	(	(	PUNCT
ejpam-3459	167	15	ω	ω	NOUN
ejpam-3459	167	16	)	)	PUNCT
ejpam-3459	167	17	)	)	PUNCT
ejpam-3459	167	18	.	.	PUNCT
ejpam-3459	168	1	note	note	VERB
ejpam-3459	168	2	that	that	SCONJ
ejpam-3459	168	3	(	(	PUNCT
ejpam-3459	168	4	z̃1	z̃1	X
ejpam-3459	168	5	,	,	PUNCT
ejpam-3459	168	6	z̃2	z̃2	NUM
ejpam-3459	168	7	)	)	PUNCT
ejpam-3459	168	8	is	be	AUX
ejpam-3459	168	9	the	the	DET
ejpam-3459	168	10	unique	unique	ADJ
ejpam-3459	168	11	couple	couple	NOUN
ejpam-3459	168	12	solution	solution	NOUN
ejpam-3459	168	13	of	of	ADP
ejpam-3459	168	14	(	(	PUNCT
ejpam-3459	168	15	16)-(17	16)-(17	NUM
ejpam-3459	168	16	)	)	PUNCT
ejpam-3459	168	17	associated	associate	VERB
ejpam-3459	168	18	to	to	ADP
ejpam-3459	168	19	ṽ.	ṽ.	PROPN
ejpam-3459	168	20	in	in	ADP
ejpam-3459	168	21	the	the	DET
ejpam-3459	168	22	same	same	ADJ
ejpam-3459	168	23	ways	way	NOUN
ejpam-3459	168	24	,	,	PUNCT
ejpam-3459	168	25	it	it	PRON
ejpam-3459	168	26	follows	follow	VERB
ejpam-3459	168	27	that	that	SCONJ
ejpam-3459	168	28	(	(	PUNCT
ejpam-3459	168	29	η1ε	η1ε	X
ejpam-3459	168	30	,	,	PUNCT
ejpam-3459	168	31	η2ε	η2ε	NOUN
ejpam-3459	168	32	)	)	PUNCT
ejpam-3459	168	33	converge	converge	VERB
ejpam-3459	168	34	weakly	weakly	ADV
ejpam-3459	168	35	to	to	ADP
ejpam-3459	168	36	(	(	PUNCT
ejpam-3459	168	37	η̃1	η̃1	PROPN
ejpam-3459	168	38	,	,	PUNCT
ejpam-3459	168	39	η̃2	η̃2	PROPN
ejpam-3459	168	40	)	)	PUNCT
ejpam-3459	168	41	and	and	CCONJ
ejpam-3459	168	42	that	that	SCONJ
ejpam-3459	168	43	(	(	PUNCT
ejpam-3459	168	44	η̃1	η̃1	PROPN
ejpam-3459	168	45	,	,	PUNCT
ejpam-3459	168	46	η̃2	η̃2	PROPN
ejpam-3459	168	47	)	)	PUNCT
ejpam-3459	168	48	satisfies	satisfie	NOUN
ejpam-3459	168	49	(	(	PUNCT
ejpam-3459	168	50	21	21	NUM
ejpam-3459	168	51	)	)	PUNCT
ejpam-3459	168	52	.	.	PUNCT
ejpam-3459	169	1	from	from	ADP
ejpam-3459	169	2	(	(	PUNCT
ejpam-3459	169	3	23	23	NUM
ejpam-3459	169	4	)	)	PUNCT
ejpam-3459	169	5	and	and	CCONJ
ejpam-3459	169	6	(	(	PUNCT
ejpam-3459	169	7	27	27	NUM
ejpam-3459	169	8	)	)	PUNCT
ejpam-3459	169	9	we	we	PRON
ejpam-3459	169	10	obtain	obtain	VERB
ejpam-3459	169	11	that	that	DET
ejpam-3459	169	12	ṽ	ṽ	NOUN
ejpam-3459	169	13	=	=	PUNCT
ejpam-3459	169	14	η̃1χω	η̃1χω	NOUN
ejpam-3459	169	15	in	in	ADP
ejpam-3459	169	16	q.	q.	PROPN
ejpam-3459	169	17	step	step	NOUN
ejpam-3459	169	18	2	2	NUM
ejpam-3459	169	19	:	:	PUNCT
ejpam-3459	169	20	now	now	ADV
ejpam-3459	169	21	we	we	PRON
ejpam-3459	169	22	prove	prove	VERB
ejpam-3459	169	23	the	the	DET
ejpam-3459	169	24	inequalities	inequality	NOUN
ejpam-3459	169	25	(	(	PUNCT
ejpam-3459	169	26	19)and	19)and	NUM
ejpam-3459	169	27	(	(	PUNCT
ejpam-3459	169	28	20	20	NUM
ejpam-3459	169	29	)	)	PUNCT
ejpam-3459	169	30	.	.	PUNCT
ejpam-3459	170	1	let	let	VERB
ejpam-3459	170	2	set	set	VERB
ejpam-3459	170	3	ẑiε	ẑiε	NOUN
ejpam-3459	170	4	=	=	SYM
ejpam-3459	170	5	e−λ0tziε	e−λ0tziε	NOUN
ejpam-3459	170	6	,	,	PUNCT
ejpam-3459	170	7	i	i	PRON
ejpam-3459	170	8	=	=	NOUN
ejpam-3459	170	9	1	1	NUM
ejpam-3459	170	10	,	,	PUNCT
ejpam-3459	170	11	2	2	NUM
ejpam-3459	170	12	where	where	SCONJ
ejpam-3459	170	13	(	(	PUNCT
ejpam-3459	170	14	z1ε	z1ε	X
ejpam-3459	170	15	,	,	PUNCT
ejpam-3459	170	16	z2ε	z2ε	NOUN
ejpam-3459	170	17	)	)	PUNCT
ejpam-3459	170	18	verifies	verifie	NOUN
ejpam-3459	170	19	(	(	PUNCT
ejpam-3459	170	20	16)-(17	16)-(17	NUM
ejpam-3459	170	21	)	)	PUNCT
ejpam-3459	170	22	and	and	CCONJ
ejpam-3459	170	23	λ0	λ0	NOUN
ejpam-3459	170	24	is	be	AUX
ejpam-3459	170	25	a	a	DET
ejpam-3459	170	26	positive	positive	ADJ
ejpam-3459	170	27	real	real	ADJ
ejpam-3459	170	28	constant	constant	ADJ
ejpam-3459	170	29	.	.	PUNCT
ejpam-3459	171	1	then	then	ADV
ejpam-3459	171	2	ẑ1ε	ẑ1ε	X
ejpam-3459	171	3	,	,	PUNCT
ejpam-3459	171	4	ẑ2ε	ẑ2ε	NUM
ejpam-3459	171	5	verify	verify	VERB
ejpam-3459	171	6	the	the	DET
ejpam-3459	171	7	system	system	PROPN
ejpam-3459	171	8	−∂ẑ1ε	−∂ẑ1ε	NOUN
ejpam-3459	171	9	∂t	∂t	PROPN
ejpam-3459	172	1	−	−	PROPN
ejpam-3459	173	1	∂ẑ1ε	∂ẑ1ε	PROPN
ejpam-3459	174	1	∂a	∂a	PROPN
ejpam-3459	174	2	−∆ẑ1ε	−∆ẑ1ε	PROPN
ejpam-3459	175	1	+	+	CCONJ
ejpam-3459	175	2	µ̂1ẑ1ε	µ̂1ẑ1ε	PROPN
ejpam-3459	175	3	+	+	CCONJ
ejpam-3459	175	4	µ̃2ẑ2ε	µ̃2ẑ2ε	PROPN
ejpam-3459	175	5	=	=	SYM
ejpam-3459	175	6	ĝ1(t	ĝ1(t	PROPN
ejpam-3459	175	7	,	,	PUNCT
ejpam-3459	175	8	a	a	PRON
ejpam-3459	175	9	,	,	PUNCT
ejpam-3459	175	10	x)z1ε(t	x)z1ε(t	PROPN
ejpam-3459	175	11	,	,	PUNCT
ejpam-3459	175	12	0	0	NUM
ejpam-3459	175	13	,	,	PUNCT
ejpam-3459	175	14	x	x	PRON
ejpam-3459	175	15	)	)	PUNCT
ejpam-3459	175	16	+	+	CCONJ
ejpam-3459	175	17	f̂	f̂	NUM
ejpam-3459	175	18	+	+	CCONJ
ejpam-3459	175	19	v̂εχω	v̂εχω	VERB
ejpam-3459	175	20	+	+	CCONJ
ejpam-3459	175	21	ĝ2(t	ĝ2(t	NOUN
ejpam-3459	175	22	,	,	PUNCT
ejpam-3459	175	23	a	a	PRON
ejpam-3459	175	24	,	,	PUNCT
ejpam-3459	175	25	x)z2ε(t	x)z2ε(t	PROPN
ejpam-3459	175	26	,	,	PUNCT
ejpam-3459	175	27	0	0	NUM
ejpam-3459	175	28	,	,	PUNCT
ejpam-3459	175	29	x	x	NOUN
ejpam-3459	175	30	)	)	PUNCT
ejpam-3459	175	31	in	in	ADP
ejpam-3459	175	32	q	q	PROPN
ejpam-3459	175	33	−∂ẑ2ε	−∂ẑ2ε	PROPN
ejpam-3459	175	34	∂t	∂t	PROPN
ejpam-3459	176	1	−	−	PROPN
ejpam-3459	176	2	∂ẑ2ε	∂ẑ2ε	PUNCT
ejpam-3459	177	1	∂a	∂a	PROPN
ejpam-3459	177	2	−∆ẑ2ε	−∆ẑ2ε	NOUN
ejpam-3459	177	3	+	+	CCONJ
ejpam-3459	177	4	µ̂1ẑ2ε	µ̂1ẑ2ε	PROPN
ejpam-3459	177	5	+	+	CCONJ
ejpam-3459	177	6	µ̃2ẑ1ε	µ̃2ẑ1ε	PROPN
ejpam-3459	177	7	=	=	SYM
ejpam-3459	177	8	ĝ2(t	ĝ2(t	NOUN
ejpam-3459	177	9	,	,	PUNCT
ejpam-3459	177	10	a	a	PRON
ejpam-3459	177	11	,	,	PUNCT
ejpam-3459	177	12	x)z1ε(t	x)z1ε(t	PROPN
ejpam-3459	177	13	,	,	PUNCT
ejpam-3459	177	14	0	0	NUM
ejpam-3459	177	15	,	,	PUNCT
ejpam-3459	177	16	x	x	PRON
ejpam-3459	177	17	)	)	PUNCT
ejpam-3459	177	18	+	+	CCONJ
ejpam-3459	177	19	ĝ1(t	ĝ1(t	ADJ
ejpam-3459	177	20	,	,	PUNCT
ejpam-3459	177	21	a	a	PRON
ejpam-3459	177	22	,	,	PUNCT
ejpam-3459	177	23	x)z2ε(t	x)z2ε(t	PROPN
ejpam-3459	177	24	,	,	PUNCT
ejpam-3459	177	25	0	0	NUM
ejpam-3459	177	26	,	,	PUNCT
ejpam-3459	177	27	x	x	NOUN
ejpam-3459	177	28	)	)	PUNCT
ejpam-3459	177	29	in	in	ADP
ejpam-3459	177	30	q	q	PROPN
ejpam-3459	177	31	ẑiε	ẑiε	PROPN
ejpam-3459	177	32	=	=	NOUN
ejpam-3459	177	33	0	0	NUM
ejpam-3459	177	34	on	on	ADP
ejpam-3459	177	35	σ	σ	PROPN
ejpam-3459	177	36	,	,	PUNCT
ejpam-3459	177	37	i	i	NOUN
ejpam-3459	177	38	=	=	NOUN
ejpam-3459	177	39	1	1	NUM
ejpam-3459	177	40	,	,	PUNCT
ejpam-3459	177	41	2	2	NUM
ejpam-3459	177	42	ẑiε(t	ẑiε(t	NOUN
ejpam-3459	177	43	,	,	PUNCT
ejpam-3459	177	44	a	a	PRON
ejpam-3459	177	45	,	,	PUNCT
ejpam-3459	177	46	x	x	NOUN
ejpam-3459	177	47	)	)	PUNCT
ejpam-3459	177	48	=	=	SYM
ejpam-3459	177	49	0	0	NUM
ejpam-3459	178	1	in	in	ADP
ejpam-3459	178	2	qa	qa	PROPN
ejpam-3459	178	3	,	,	PUNCT
ejpam-3459	178	4	i	i	PRON
ejpam-3459	178	5	=	=	NOUN
ejpam-3459	178	6	1	1	NUM
ejpam-3459	178	7	,	,	PUNCT
ejpam-3459	178	8	2	2	NUM
ejpam-3459	178	9	ẑiε(t	ẑiε(t	NOUN
ejpam-3459	178	10	,	,	PUNCT
ejpam-3459	178	11	a	a	DET
ejpam-3459	178	12	,	,	PUNCT
ejpam-3459	178	13	x	x	NOUN
ejpam-3459	178	14	)	)	PUNCT
ejpam-3459	178	15	=	=	SYM
ejpam-3459	178	16	0	0	NUM
ejpam-3459	178	17	in	in	ADP
ejpam-3459	178	18	qt	qt	NOUN
ejpam-3459	178	19	,	,	PUNCT
ejpam-3459	178	20	i	i	PRON
ejpam-3459	178	21	=	=	NOUN
ejpam-3459	178	22	1	1	NUM
ejpam-3459	178	23	,	,	PUNCT
ejpam-3459	178	24	2	2	NUM
ejpam-3459	178	25	(	(	PUNCT
ejpam-3459	178	26	30	30	NUM
ejpam-3459	178	27	)	)	PUNCT
ejpam-3459	178	28	where	where	SCONJ
ejpam-3459	178	29	:	:	PUNCT
ejpam-3459	178	30	ĝi	ĝi	PROPN
ejpam-3459	178	31	=	=	PROPN
ejpam-3459	178	32	e−λ0tgi	e−λ0tgi	PROPN
ejpam-3459	178	33	,	,	PUNCT
ejpam-3459	178	34	f̂	f̂	NUM
ejpam-3459	178	35	=	=	SYM
ejpam-3459	178	36	e−λ0tf	e−λ0tf	PROPN
ejpam-3459	178	37	,	,	PUNCT
ejpam-3459	178	38	v̂ε	v̂ε	X
ejpam-3459	178	39	=	=	PUNCT
ejpam-3459	178	40	e−λ0tvε	e−λ0tvε	PROPN
ejpam-3459	178	41	and	and	CCONJ
ejpam-3459	178	42	µ̂1	µ̂1	PUNCT
ejpam-3459	178	43	=	=	PUNCT
ejpam-3459	178	44	µ̃1	µ̃1	NOUN
ejpam-3459	178	45	+	+	NOUN
ejpam-3459	178	46	λ0	λ0	NOUN
ejpam-3459	178	47	.	.	PUNCT
ejpam-3459	179	1	multiplying	multiply	VERB
ejpam-3459	179	2	the	the	DET
ejpam-3459	179	3	first	first	ADJ
ejpam-3459	179	4	and	and	CCONJ
ejpam-3459	179	5	the	the	DET
ejpam-3459	179	6	second	second	ADJ
ejpam-3459	179	7	equations	equation	NOUN
ejpam-3459	179	8	of	of	ADP
ejpam-3459	179	9	(	(	PUNCT
ejpam-3459	179	10	30	30	NUM
ejpam-3459	179	11	)	)	PUNCT
ejpam-3459	179	12	by	by	ADP
ejpam-3459	179	13	ẑ1ε	ẑ1ε	NUM
ejpam-3459	179	14	and	and	CCONJ
ejpam-3459	179	15	ẑ2ε	ẑ2ε	NUM
ejpam-3459	179	16	respectively	respectively	ADV
ejpam-3459	179	17	,	,	PUNCT
ejpam-3459	179	18	and	and	CCONJ
ejpam-3459	179	19	integrating	integrate	VERB
ejpam-3459	179	20	by	by	ADP
ejpam-3459	179	21	parts	part	NOUN
ejpam-3459	179	22	over	over	ADP
ejpam-3459	179	23	q	q	NOUN
ejpam-3459	179	24	,	,	PUNCT
ejpam-3459	179	25	we	we	PRON
ejpam-3459	179	26	have	have	VERB
ejpam-3459	179	27	thanks	thank	NOUN
ejpam-3459	179	28	to	to	ADP
ejpam-3459	179	29	young	young	PROPN
ejpam-3459	179	30	’s	’s	PART
ejpam-3459	179	31	inequality	inequality	NOUN
ejpam-3459	179	32	:	:	PUNCT
ejpam-3459	179	33	∫	∫	PROPN
ejpam-3459	179	34	q	q	PROPN
ejpam-3459	179	35	|∇ẑ1ε|2	|∇ẑ1ε|2	PROPN
ejpam-3459	179	36	dq+	dq+	PROPN
ejpam-3459	179	37	γ1	γ1	PROPN
ejpam-3459	179	38	∫	∫	PROPN
ejpam-3459	179	39	q	q	PROPN
ejpam-3459	179	40	|ẑ1ε|2dq−	|ẑ1ε|2dq−	PROPN
ejpam-3459	179	41	‖µ̃2‖∞	‖µ̃2‖∞	PROPN
ejpam-3459	180	1	2c1	2c1	NUM
ejpam-3459	180	2	∫	∫	PROPN
ejpam-3459	180	3	q	q	PROPN
ejpam-3459	180	4	|ẑ2ε|2dq+	|ẑ2ε|2dq+	X
ejpam-3459	180	5	(	(	PUNCT
ejpam-3459	180	6	1−	1−	NUM
ejpam-3459	180	7	a	a	DET
ejpam-3459	180	8	2c2	2c2	NUM
ejpam-3459	180	9	)	)	PUNCT
ejpam-3459	180	10	∫	∫	PROPN
ejpam-3459	180	11	qt	qt	PROPN
ejpam-3459	180	12	ẑ2	ẑ2	PROPN
ejpam-3459	180	13	1ε(t	1ε(t	PROPN
ejpam-3459	180	14	,	,	PUNCT
ejpam-3459	180	15	0	0	NUM
ejpam-3459	180	16	,	,	PUNCT
ejpam-3459	180	17	x)dqt	x)dqt	PROPN
ejpam-3459	181	1	+	+	CCONJ
ejpam-3459	182	1	∫	∫	PROPN
ejpam-3459	182	2	qa	qa	PROPN
ejpam-3459	182	3	ẑ2	ẑ2	PROPN
ejpam-3459	182	4	1ε(0	1ε(0	NUM
ejpam-3459	182	5	,	,	PUNCT
ejpam-3459	182	6	a	a	DET
ejpam-3459	182	7	,	,	PUNCT
ejpam-3459	182	8	x)dqa	x)dqa	ADJ
ejpam-3459	182	9	−	−	NOUN
ejpam-3459	182	10	a	a	DET
ejpam-3459	182	11	2c3	2c3	NUM
ejpam-3459	182	12	∫	∫	NOUN
ejpam-3459	182	13	qt	qt	PROPN
ejpam-3459	182	14	ẑ2	ẑ2	PROPN
ejpam-3459	182	15	2ε(t	2ε(t	PROPN
ejpam-3459	182	16	,	,	PUNCT
ejpam-3459	182	17	0	0	NUM
ejpam-3459	182	18	,	,	PUNCT
ejpam-3459	182	19	x)dqt	x)dqt	PROPN
ejpam-3459	182	20	≤	≤	ADV
ejpam-3459	182	21	1	1	NUM
ejpam-3459	182	22	2c4	2c4	NUM
ejpam-3459	182	23	∫	∫	PROPN
ejpam-3459	182	24	q	q	NOUN
ejpam-3459	182	25	∣∣∣f̂	∣∣∣f̂	NOUN
ejpam-3459	182	26	∣∣∣	∣∣∣	X
ejpam-3459	182	27	dq+	dq+	NOUN
ejpam-3459	182	28	1	1	NUM
ejpam-3459	182	29	2c5	2c5	NUM
ejpam-3459	182	30	∫	∫	PROPN
ejpam-3459	182	31	g	g	PROPN
ejpam-3459	182	32	v̂2	v̂2	VERB
ejpam-3459	182	33	εdq	εdq	NOUN
ejpam-3459	182	34	(	(	PUNCT
ejpam-3459	182	35	31	31	NUM
ejpam-3459	182	36	)	)	PUNCT
ejpam-3459	182	37	and∫	and∫	NOUN
ejpam-3459	182	38	q	q	PROPN
ejpam-3459	182	39	|∇ẑ2ε|2	|∇ẑ2ε|2	PROPN
ejpam-3459	182	40	dq+	dq+	PROPN
ejpam-3459	182	41	γ2	γ2	PROPN
ejpam-3459	182	42	∫	∫	PROPN
ejpam-3459	182	43	q	q	PROPN
ejpam-3459	182	44	|ẑ2ε|2dq−	|ẑ2ε|2dq−	PROPN
ejpam-3459	182	45	‖µ̃2‖∞	‖µ̃2‖∞	SYM
ejpam-3459	182	46	2k1	2k1	NUM
ejpam-3459	182	47	∫	∫	PROPN
ejpam-3459	182	48	q	q	PROPN
ejpam-3459	182	49	|ẑ1ε|2dq+	|ẑ1ε|2dq+	PROPN
ejpam-3459	182	50	(	(	PUNCT
ejpam-3459	182	51	1−	1−	NUM
ejpam-3459	182	52	a	a	DET
ejpam-3459	182	53	2k3	2k3	NUM
ejpam-3459	182	54	)	)	PUNCT
ejpam-3459	182	55	∫	∫	PROPN
ejpam-3459	182	56	qt	qt	PROPN
ejpam-3459	182	57	ẑ2	ẑ2	PROPN
ejpam-3459	182	58	2ε(t	2ε(t	PROPN
ejpam-3459	182	59	,	,	PUNCT
ejpam-3459	182	60	0	0	NUM
ejpam-3459	182	61	,	,	PUNCT
ejpam-3459	182	62	x)dqt	x)dqt	PROPN
ejpam-3459	182	63	c.	c.	PROPN
ejpam-3459	182	64	k.	k.	PROPN
ejpam-3459	182	65	somé	somé	PROPN
ejpam-3459	182	66	,	,	PUNCT
ejpam-3459	182	67	s.	s.	PROPN
ejpam-3459	182	68	sawadogo	sawadogo	PROPN
ejpam-3459	182	69	/	/	SYM
ejpam-3459	182	70	eur	eur	PROPN
ejpam-3459	182	71	.	.	PUNCT
ejpam-3459	183	1	j.	j.	PROPN
ejpam-3459	183	2	pure	pure	PROPN
ejpam-3459	183	3	appl	appl	PROPN
ejpam-3459	183	4	.	.	PROPN
ejpam-3459	183	5	math	math	PROPN
ejpam-3459	183	6	,	,	PUNCT
ejpam-3459	183	7	12	12	NUM
ejpam-3459	183	8	(	(	PUNCT
ejpam-3459	183	9	3	3	NUM
ejpam-3459	183	10	)	)	PUNCT
ejpam-3459	183	11	(	(	PUNCT
ejpam-3459	183	12	2019	2019	NUM
ejpam-3459	183	13	)	)	PUNCT
ejpam-3459	183	14	,	,	PUNCT
ejpam-3459	183	15	870	870	NUM
ejpam-3459	183	16	-	-	SYM
ejpam-3459	183	17	892	892	NUM
ejpam-3459	183	18	878	878	NUM
ejpam-3459	183	19	+	+	CCONJ
ejpam-3459	183	20	∫	∫	PROPN
ejpam-3459	183	21	qa	qa	PROPN
ejpam-3459	183	22	ẑ2	ẑ2	SYM
ejpam-3459	183	23	2ε(0	2ε(0	PROPN
ejpam-3459	183	24	,	,	PUNCT
ejpam-3459	183	25	a	a	PRON
ejpam-3459	183	26	,	,	PUNCT
ejpam-3459	183	27	x)dqa	x)dqa	ADJ
ejpam-3459	183	28	−	−	PROPN
ejpam-3459	183	29	‖µ̃1‖∞	‖µ̃1‖∞	NUM
ejpam-3459	183	30	2k2	2k2	NUM
ejpam-3459	183	31	‖∞	‖∞	PROPN
ejpam-3459	183	32	∫	∫	PROPN
ejpam-3459	183	33	qt	qt	PROPN
ejpam-3459	183	34	ẑ2	ẑ2	PROPN
ejpam-3459	183	35	1ε(t	1ε(t	PROPN
ejpam-3459	183	36	,	,	PUNCT
ejpam-3459	183	37	0	0	NUM
ejpam-3459	183	38	,	,	PUNCT
ejpam-3459	183	39	x)dqt	x)dqt	PROPN
ejpam-3459	183	40	≤	≤	X
ejpam-3459	183	41	0	0	NUM
ejpam-3459	183	42	(	(	PUNCT
ejpam-3459	183	43	32	32	NUM
ejpam-3459	183	44	)	)	PUNCT
ejpam-3459	184	1	where	where	SCONJ
ejpam-3459	184	2	:	:	PUNCT
ejpam-3459	184	3	γ1	γ1	NOUN
ejpam-3459	184	4	=	=	NOUN
ejpam-3459	184	5	λ0	λ0	NOUN
ejpam-3459	184	6	−	−	PROPN
ejpam-3459	184	7	2c1‖µ̃2‖∞	2c1‖µ̃2‖∞	NUM
ejpam-3459	184	8	−	−	PROPN
ejpam-3459	184	9	4a	4a	NOUN
ejpam-3459	184	10	(	(	PUNCT
ejpam-3459	184	11	c2	c2	PROPN
ejpam-3459	184	12	+	+	CCONJ
ejpam-3459	184	13	c3	c3	PROPN
ejpam-3459	184	14	)	)	PUNCT
ejpam-3459	184	15	‖β̃1	‖β̃1	PROPN
ejpam-3459	184	16	,	,	PUNCT
ejpam-3459	184	17	β̃2‖2∞‖b1	β̃2‖2∞‖b1	NOUN
ejpam-3459	184	18	,	,	PUNCT
ejpam-3459	184	19	b2‖2qt	b2‖2qt	ADP
ejpam-3459	184	20	−	−	PROPN
ejpam-3459	184	21	‖µ̃1‖∞	‖µ̃1‖∞	PUNCT
ejpam-3459	184	22	−	−	PROPN
ejpam-3459	184	23	2c5	2c5	PROPN
ejpam-3459	184	24	,	,	PUNCT
ejpam-3459	184	25	γ2	γ2	NOUN
ejpam-3459	184	26	=	=	SYM
ejpam-3459	184	27	λ0	λ0	NOUN
ejpam-3459	184	28	−	−	NOUN
ejpam-3459	184	29	2k1‖µ̃1‖∞	2k1‖µ̃1‖∞	NUM
ejpam-3459	184	30	−	−	NOUN
ejpam-3459	184	31	4a	4a	NOUN
ejpam-3459	184	32	(	(	PUNCT
ejpam-3459	184	33	k2	k2	PROPN
ejpam-3459	184	34	+	+	PROPN
ejpam-3459	184	35	k3	k3	ADJ
ejpam-3459	184	36	)	)	PUNCT
ejpam-3459	184	37	‖β̃1	‖β̃1	PROPN
ejpam-3459	184	38	,	,	PUNCT
ejpam-3459	184	39	β̃2‖2∞‖b1	β̃2‖2∞‖b1	NOUN
ejpam-3459	184	40	,	,	PUNCT
ejpam-3459	184	41	b2‖2qt	b2‖2qt	ADP
ejpam-3459	184	42	−	−	PROPN
ejpam-3459	184	43	‖µ̃1‖∞	‖µ̃1‖∞	PUNCT
ejpam-3459	184	44	and	and	CCONJ
ejpam-3459	184	45	the	the	DET
ejpam-3459	184	46	ci	ci	NOUN
ejpam-3459	184	47	,	,	PUNCT
ejpam-3459	184	48	ki	ki	PROPN
ejpam-3459	184	49	are	be	AUX
ejpam-3459	184	50	young	young	PROPN
ejpam-3459	184	51	’s	’s	PART
ejpam-3459	184	52	constants	constant	NOUN
ejpam-3459	184	53	for	for	ADP
ejpam-3459	184	54	i	i	PROPN
ejpam-3459	184	55	=	=	NOUN
ejpam-3459	184	56	1	1	NUM
ejpam-3459	184	57	,	,	PUNCT
ejpam-3459	184	58	2	2	NUM
ejpam-3459	184	59	,	,	PUNCT
ejpam-3459	184	60	3	3	NUM
ejpam-3459	184	61	,	,	PUNCT
ejpam-3459	184	62	5	5	NUM
ejpam-3459	184	63	.	.	PUNCT
ejpam-3459	184	64	summing	sum	VERB
ejpam-3459	184	65	(	(	PUNCT
ejpam-3459	184	66	31	31	NUM
ejpam-3459	184	67	)	)	PUNCT
ejpam-3459	184	68	and	and	CCONJ
ejpam-3459	184	69	(	(	PUNCT
ejpam-3459	184	70	32	32	NUM
ejpam-3459	184	71	)	)	PUNCT
ejpam-3459	184	72	,	,	PUNCT
ejpam-3459	184	73	one	one	PRON
ejpam-3459	184	74	obtains	obtain	VERB
ejpam-3459	184	75	:	:	PUNCT
ejpam-3459	184	76	∫	∫	PROPN
ejpam-3459	184	77	q	q	PROPN
ejpam-3459	184	78	|∇ẑ1ε|2	|∇ẑ1ε|2	PROPN
ejpam-3459	184	79	dq+	dq+	PROPN
ejpam-3459	184	80	π1	π1	PROPN
ejpam-3459	185	1	∫	∫	PROPN
ejpam-3459	185	2	q	q	PROPN
ejpam-3459	185	3	|ẑ1ε|2dq+	|ẑ1ε|2dq+	PROPN
ejpam-3459	185	4	∫	∫	PROPN
ejpam-3459	186	1	q	q	PROPN
ejpam-3459	186	2	|∇ẑ2ε|2	|∇ẑ2ε|2	PROPN
ejpam-3459	186	3	dq+	dq+	PROPN
ejpam-3459	186	4	π2	π2	PROPN
ejpam-3459	186	5	∫	∫	PROPN
ejpam-3459	186	6	q	q	PROPN
ejpam-3459	186	7	|ẑ2ε|2dq+	|ẑ2ε|2dq+	X
ejpam-3459	186	8	(	(	PUNCT
ejpam-3459	186	9	1−	1−	NUM
ejpam-3459	186	10	a	a	DET
ejpam-3459	186	11	2c2	2c2	NUM
ejpam-3459	186	12	−	−	NOUN
ejpam-3459	186	13	a	a	DET
ejpam-3459	186	14	2k3	2k3	NUM
ejpam-3459	186	15	)	)	PUNCT
ejpam-3459	186	16	∫	∫	PROPN
ejpam-3459	186	17	qt	qt	PROPN
ejpam-3459	186	18	ẑ2	ẑ2	PROPN
ejpam-3459	186	19	1ε(t	1ε(t	PROPN
ejpam-3459	186	20	,	,	PUNCT
ejpam-3459	186	21	0	0	NUM
ejpam-3459	186	22	,	,	PUNCT
ejpam-3459	186	23	x)dqt	x)dqt	PROPN
ejpam-3459	187	1	+	+	CCONJ
ejpam-3459	187	2	(	(	PUNCT
ejpam-3459	187	3	1−	1−	NUM
ejpam-3459	187	4	a	a	DET
ejpam-3459	187	5	2c3	2c3	NUM
ejpam-3459	187	6	−	−	NOUN
ejpam-3459	187	7	a	a	DET
ejpam-3459	187	8	2k2	2k2	NUM
ejpam-3459	187	9	)	)	PUNCT
ejpam-3459	187	10	∫	∫	PROPN
ejpam-3459	187	11	qt	qt	PROPN
ejpam-3459	187	12	ẑ2	ẑ2	PROPN
ejpam-3459	187	13	2ε(t	2ε(t	PROPN
ejpam-3459	187	14	,	,	PUNCT
ejpam-3459	187	15	0	0	NUM
ejpam-3459	187	16	,	,	PUNCT
ejpam-3459	187	17	x)dqt	x)dqt	PROPN
ejpam-3459	188	1	+	+	CCONJ
ejpam-3459	189	1	∫	∫	PROPN
ejpam-3459	189	2	qa	qa	PROPN
ejpam-3459	189	3	ẑ2	ẑ2	PROPN
ejpam-3459	189	4	1ε(0	1ε(0	NUM
ejpam-3459	189	5	,	,	PUNCT
ejpam-3459	189	6	a	a	PRON
ejpam-3459	189	7	,	,	PUNCT
ejpam-3459	190	1	x)dqa	x)dqa	PROPN
ejpam-3459	190	2	+	+	NUM
ejpam-3459	190	3	∫	∫	PROPN
ejpam-3459	190	4	qa	qa	PROPN
ejpam-3459	190	5	ẑ2	ẑ2	SYM
ejpam-3459	190	6	2ε(0	2ε(0	PROPN
ejpam-3459	190	7	,	,	PUNCT
ejpam-3459	190	8	a	a	PRON
ejpam-3459	190	9	,	,	PUNCT
ejpam-3459	190	10	x)dqa	x)dqa	ADJ
ejpam-3459	190	11	≤	≤	ADJ
ejpam-3459	190	12	1	1	NUM
ejpam-3459	190	13	2c4	2c4	NUM
ejpam-3459	190	14	∫	∫	PROPN
ejpam-3459	190	15	q	q	NOUN
ejpam-3459	190	16	∣∣∣f̂	∣∣∣f̂	NOUN
ejpam-3459	190	17	∣∣∣	∣∣∣	X
ejpam-3459	190	18	dq+	dq+	NOUN
ejpam-3459	190	19	1	1	NUM
ejpam-3459	190	20	2c5	2c5	NUM
ejpam-3459	190	21	∫	∫	PROPN
ejpam-3459	190	22	g	g	PROPN
ejpam-3459	190	23	v̂2	v̂2	VERB
ejpam-3459	190	24	εdq	εdq	X
ejpam-3459	190	25	(	(	PUNCT
ejpam-3459	190	26	33	33	NUM
ejpam-3459	190	27	)	)	PUNCT
ejpam-3459	190	28	with	with	ADP
ejpam-3459	190	29	:	:	PUNCT
ejpam-3459	190	30	π1	π1	NOUN
ejpam-3459	190	31	=	=	SYM
ejpam-3459	190	32	γ1	γ1	PROPN
ejpam-3459	190	33	−	−	PROPN
ejpam-3459	190	34	‖µ̃2‖∞	‖µ̃2‖∞	SYM
ejpam-3459	190	35	2k1	2k1	NUM
ejpam-3459	190	36	and	and	CCONJ
ejpam-3459	190	37	π2	π2	NOUN
ejpam-3459	190	38	=	=	SYM
ejpam-3459	190	39	γ2	γ2	NOUN
ejpam-3459	190	40	−	−	PROPN
ejpam-3459	190	41	‖µ̃2‖∞	‖µ̃2‖∞	SYM
ejpam-3459	190	42	2c1	2c1	NUM
ejpam-3459	190	43	.	.	PUNCT
ejpam-3459	191	1	choosing	choose	VERB
ejpam-3459	191	2	λ0	λ0	NOUN
ejpam-3459	191	3	and	and	CCONJ
ejpam-3459	191	4	the	the	DET
ejpam-3459	191	5	young	young	PROPN
ejpam-3459	191	6	’s	’s	PART
ejpam-3459	191	7	constants	constant	NOUN
ejpam-3459	191	8	such	such	ADJ
ejpam-3459	191	9	that	that	SCONJ
ejpam-3459	191	10	:	:	PUNCT
ejpam-3459	191	11	λ0	λ0	NOUN
ejpam-3459	191	12	≥	≥	NOUN
ejpam-3459	191	13	max	max	PROPN
ejpam-3459	191	14	{	{	PUNCT
ejpam-3459	191	15	2c1‖µ̃2‖∞	2c1‖µ̃2‖∞	NUM
ejpam-3459	191	16	+	+	NUM
ejpam-3459	191	17	4a	4a	X
ejpam-3459	191	18	(	(	PUNCT
ejpam-3459	191	19	c2	c2	PROPN
ejpam-3459	191	20	+	+	CCONJ
ejpam-3459	191	21	c3	c3	PROPN
ejpam-3459	191	22	)	)	PUNCT
ejpam-3459	191	23	‖β̃1	‖β̃1	PROPN
ejpam-3459	191	24	,	,	PUNCT
ejpam-3459	191	25	β̃2‖2∞‖b1	β̃2‖2∞‖b1	NOUN
ejpam-3459	191	26	,	,	PUNCT
ejpam-3459	191	27	b2‖2qt	b2‖2qt	VERB
ejpam-3459	191	28	+	+	CCONJ
ejpam-3459	191	29	‖µ̃1‖∞	‖µ̃1‖∞	NUM
ejpam-3459	192	1	+	+	NUM
ejpam-3459	192	2	2c5	2c5	PROPN
ejpam-3459	192	3	+	+	CCONJ
ejpam-3459	192	4	‖µ̃2‖∞	‖µ̃2‖∞	SYM
ejpam-3459	192	5	2k1	2k1	NUM
ejpam-3459	192	6	+	+	NUM
ejpam-3459	192	7	1	1	NUM
ejpam-3459	192	8	;	;	PUNCT
ejpam-3459	192	9	2k1‖µ̃1‖∞	2k1‖µ̃1‖∞	NUM
ejpam-3459	193	1	+	+	NUM
ejpam-3459	193	2	4a	4a	X
ejpam-3459	193	3	(	(	PUNCT
ejpam-3459	193	4	k2	k2	PROPN
ejpam-3459	193	5	+	+	PROPN
ejpam-3459	193	6	k3	k3	ADJ
ejpam-3459	193	7	)	)	PUNCT
ejpam-3459	193	8	‖β̃1	‖β̃1	PROPN
ejpam-3459	193	9	,	,	PUNCT
ejpam-3459	193	10	β̃2‖2∞‖b1	β̃2‖2∞‖b1	NOUN
ejpam-3459	193	11	,	,	PUNCT
ejpam-3459	193	12	b2‖2qt	b2‖2qt	VERB
ejpam-3459	193	13	+	+	CCONJ
ejpam-3459	193	14	‖µ̃1	‖µ̃1	NOUN
ejpam-3459	193	15	+	+	X
ejpam-3459	193	16	‖µ̃2‖∞	‖µ̃2‖∞	X
ejpam-3459	193	17	2c1	2c1	NUM
ejpam-3459	194	1	+	+	CCONJ
ejpam-3459	194	2	1	1	NUM
ejpam-3459	194	3	}	}	PUNCT
ejpam-3459	194	4	and	and	CCONJ
ejpam-3459	194	5	min	min	PROPN
ejpam-3459	194	6	{	{	PUNCT
ejpam-3459	194	7	1−	1−	NUM
ejpam-3459	194	8	a	a	DET
ejpam-3459	194	9	2c2	2c2	NUM
ejpam-3459	194	10	−	−	NOUN
ejpam-3459	194	11	a	a	DET
ejpam-3459	194	12	2k3	2k3	NUM
ejpam-3459	194	13	,	,	PUNCT
ejpam-3459	194	14	1−	1−	NUM
ejpam-3459	194	15	a	a	DET
ejpam-3459	194	16	2c3	2c3	NUM
ejpam-3459	194	17	−	−	NOUN
ejpam-3459	194	18	a	a	DET
ejpam-3459	194	19	2k2	2k2	NUM
ejpam-3459	194	20	}	}	PUNCT
ejpam-3459	194	21	≥	≥	NOUN
ejpam-3459	194	22	1	1	NUM
ejpam-3459	194	23	,	,	PUNCT
ejpam-3459	194	24	one	one	NUM
ejpam-3459	194	25	deducts	deduct	NOUN
ejpam-3459	194	26	from	from	ADP
ejpam-3459	194	27	(	(	PUNCT
ejpam-3459	194	28	27	27	NUM
ejpam-3459	194	29	)	)	PUNCT
ejpam-3459	194	30	and	and	CCONJ
ejpam-3459	194	31	(	(	PUNCT
ejpam-3459	194	32	33	33	NUM
ejpam-3459	194	33	)	)	PUNCT
ejpam-3459	194	34	that∫	that∫	NOUN
ejpam-3459	194	35	q	q	PROPN
ejpam-3459	194	36	|∇ẑ1ε|2	|∇ẑ1ε|2	PROPN
ejpam-3459	194	37	dq+	dq+	PROPN
ejpam-3459	194	38	∫	∫	PROPN
ejpam-3459	194	39	q	q	PROPN
ejpam-3459	194	40	|ẑ1ε|2dq	|ẑ1ε|2dq	VERB
ejpam-3459	194	41	≤	≤	PUNCT
ejpam-3459	194	42	c	c	NOUN
ejpam-3459	194	43	(	(	PUNCT
ejpam-3459	194	44	‖f̂‖2l2(q	‖f̂‖2l2(q	NOUN
ejpam-3459	194	45	)	)	PUNCT
ejpam-3459	195	1	+	+	CCONJ
ejpam-3459	195	2	‖θf̂‖l2(q	‖θf̂‖l2(q	NOUN
ejpam-3459	195	3	)	)	PUNCT
ejpam-3459	195	4	)	)	PUNCT
ejpam-3459	196	1	(	(	PUNCT
ejpam-3459	196	2	34)∫	34)∫	NUM
ejpam-3459	196	3	q	q	NOUN
ejpam-3459	196	4	|∇ẑ2ε|2	|∇ẑ2ε|2	PROPN
ejpam-3459	196	5	dq+	dq+	INTJ
ejpam-3459	196	6	∫	∫	PROPN
ejpam-3459	196	7	q	q	X
ejpam-3459	196	8	|ẑ2ε|2dq	|ẑ2ε|2dq	PROPN
ejpam-3459	196	9	≤	≤	PROPN
ejpam-3459	196	10	c	c	NOUN
ejpam-3459	196	11	(	(	PUNCT
ejpam-3459	196	12	‖f̂‖2l2(q	‖f̂‖2l2(q	NOUN
ejpam-3459	196	13	)	)	PUNCT
ejpam-3459	196	14	+	+	CCONJ
ejpam-3459	196	15	‖θf̂‖l2(q	‖θf̂‖l2(q	NOUN
ejpam-3459	196	16	)	)	PUNCT
ejpam-3459	196	17	)	)	PUNCT
ejpam-3459	197	1	(	(	PUNCT
ejpam-3459	197	2	35)∫	35)∫	NUM
ejpam-3459	197	3	qt	qt	ADP
ejpam-3459	197	4	ẑ2	ẑ2	PROPN
ejpam-3459	197	5	1ε(t	1ε(t	PROPN
ejpam-3459	197	6	,	,	PUNCT
ejpam-3459	197	7	0	0	NUM
ejpam-3459	197	8	,	,	PUNCT
ejpam-3459	197	9	x)dqt	x)dqt	PROPN
ejpam-3459	197	10	≤	≤	PROPN
ejpam-3459	198	1	c	c	X
ejpam-3459	198	2	(	(	PUNCT
ejpam-3459	198	3	‖f̂‖2l2(q	‖f̂‖2l2(q	NOUN
ejpam-3459	198	4	)	)	PUNCT
ejpam-3459	198	5	+	+	CCONJ
ejpam-3459	198	6	‖θf̂‖l2(q	‖θf̂‖l2(q	NOUN
ejpam-3459	198	7	)	)	PUNCT
ejpam-3459	198	8	)	)	PUNCT
ejpam-3459	199	1	(	(	PUNCT
ejpam-3459	199	2	36)∫	36)∫	NUM
ejpam-3459	199	3	qt	qt	PROPN
ejpam-3459	199	4	ẑ2	ẑ2	PROPN
ejpam-3459	199	5	2ε(t	2ε(t	PROPN
ejpam-3459	199	6	,	,	PUNCT
ejpam-3459	199	7	0	0	NUM
ejpam-3459	199	8	,	,	PUNCT
ejpam-3459	199	9	x)dqt	x)dqt	PROPN
ejpam-3459	199	10	≤	≤	PROPN
ejpam-3459	199	11	c	c	X
ejpam-3459	199	12	(	(	PUNCT
ejpam-3459	199	13	‖f̂‖2l2(q	‖f̂‖2l2(q	NOUN
ejpam-3459	199	14	)	)	PUNCT
ejpam-3459	199	15	+	+	CCONJ
ejpam-3459	199	16	‖θf̂‖l2(q	‖θf̂‖l2(q	NOUN
ejpam-3459	199	17	)	)	PUNCT
ejpam-3459	199	18	)	)	PUNCT
ejpam-3459	199	19	(	(	PUNCT
ejpam-3459	199	20	37	37	NUM
ejpam-3459	199	21	)	)	PUNCT
ejpam-3459	199	22	consequently	consequently	ADV
ejpam-3459	199	23	,	,	PUNCT
ejpam-3459	199	24	the	the	DET
ejpam-3459	199	25	sequences	sequence	NOUN
ejpam-3459	199	26	(	(	PUNCT
ejpam-3459	199	27	ẑ1ε)ε	ẑ1ε)ε	NOUN
ejpam-3459	199	28	,	,	PUNCT
ejpam-3459	199	29	(	(	PUNCT
ejpam-3459	199	30	ẑ2ε)ε	ẑ2ε)ε	X
ejpam-3459	199	31	,	,	PUNCT
ejpam-3459	199	32	(	(	PUNCT
ejpam-3459	199	33	ẑ1ε	ẑ1ε	X
ejpam-3459	199	34	(	(	PUNCT
ejpam-3459	199	35	·	·	PUNCT
ejpam-3459	199	36	,	,	PUNCT
ejpam-3459	199	37	0	0	NUM
ejpam-3459	199	38	,	,	PUNCT
ejpam-3459	199	39	·	·	PUNCT
ejpam-3459	199	40	)	)	PUNCT
ejpam-3459	199	41	)	)	PUNCT
ejpam-3459	199	42	ε	ε	PROPN
ejpam-3459	199	43	and	and	CCONJ
ejpam-3459	199	44	(	(	PUNCT
ejpam-3459	199	45	ẑ2ε	ẑ2ε	NUM
ejpam-3459	199	46	(	(	PUNCT
ejpam-3459	199	47	·	·	PUNCT
ejpam-3459	199	48	,	,	PUNCT
ejpam-3459	199	49	0	0	NUM
ejpam-3459	199	50	,	,	PUNCT
ejpam-3459	199	51	·	·	PUNCT
ejpam-3459	199	52	)	)	PUNCT
ejpam-3459	199	53	)	)	PUNCT
ejpam-3459	199	54	ε	ε	PROPN
ejpam-3459	199	55	are	be	AUX
ejpam-3459	199	56	bounded	bound	VERB
ejpam-3459	199	57	respectively	respectively	ADV
ejpam-3459	199	58	in	in	ADP
ejpam-3459	199	59	l2(u	l2(u	PROPN
ejpam-3459	199	60	,	,	PUNCT
ejpam-3459	199	61	h1	h1	PROPN
ejpam-3459	199	62	0	0	NUM
ejpam-3459	199	63	(	(	PUNCT
ejpam-3459	199	64	q	q	NOUN
ejpam-3459	199	65	)	)	PUNCT
ejpam-3459	199	66	)	)	PUNCT
ejpam-3459	199	67	and	and	CCONJ
ejpam-3459	199	68	l2(qt	l2(qt	PROPN
ejpam-3459	199	69	)	)	PUNCT
ejpam-3459	199	70	.	.	PUNCT
ejpam-3459	200	1	that	that	PRON
ejpam-3459	200	2	ends	end	VERB
ejpam-3459	200	3	this	this	DET
ejpam-3459	200	4	proof	proof	NOUN
ejpam-3459	200	5	,	,	PUNCT
ejpam-3459	200	6	thanks	thank	NOUN
ejpam-3459	200	7	to	to	PART
ejpam-3459	200	8	limit	limit	VERB
ejpam-3459	200	9	’s	’s	PART
ejpam-3459	200	10	results	result	NOUN
ejpam-3459	200	11	obtained	obtain	VERB
ejpam-3459	200	12	in	in	ADP
ejpam-3459	200	13	the	the	DET
ejpam-3459	200	14	step	step	NOUN
ejpam-3459	200	15	1	1	NUM
ejpam-3459	200	16	.	.	PUNCT
ejpam-3459	201	1	c.	c.	PROPN
ejpam-3459	201	2	k.	k.	PROPN
ejpam-3459	201	3	somé	somé	PROPN
ejpam-3459	201	4	,	,	PUNCT
ejpam-3459	201	5	s.	s.	PROPN
ejpam-3459	201	6	sawadogo	sawadogo	PROPN
ejpam-3459	201	7	/	/	SYM
ejpam-3459	201	8	eur	eur	PROPN
ejpam-3459	201	9	.	.	PUNCT
ejpam-3459	202	1	j.	j.	PROPN
ejpam-3459	202	2	pure	pure	PROPN
ejpam-3459	202	3	appl	appl	PROPN
ejpam-3459	202	4	.	.	PROPN
ejpam-3459	202	5	math	math	PROPN
ejpam-3459	202	6	,	,	PUNCT
ejpam-3459	202	7	12	12	NUM
ejpam-3459	202	8	(	(	PUNCT
ejpam-3459	202	9	3	3	NUM
ejpam-3459	202	10	)	)	PUNCT
ejpam-3459	202	11	(	(	PUNCT
ejpam-3459	202	12	2019	2019	NUM
ejpam-3459	202	13	)	)	PUNCT
ejpam-3459	202	14	,	,	PUNCT
ejpam-3459	202	15	870	870	NUM
ejpam-3459	202	16	-	-	SYM
ejpam-3459	202	17	892	892	NUM
ejpam-3459	202	18	879	879	NUM
ejpam-3459	202	19	3.3	3.3	NUM
ejpam-3459	202	20	.	.	PUNCT
ejpam-3459	203	1	study	study	NOUN
ejpam-3459	203	2	of	of	ADP
ejpam-3459	203	3	the	the	DET
ejpam-3459	203	4	nonlinear	nonlinear	ADJ
ejpam-3459	203	5	case	case	NOUN
ejpam-3459	203	6	let	let	VERB
ejpam-3459	203	7	bi(t	bi(t	NOUN
ejpam-3459	203	8	,	,	PUNCT
ejpam-3459	203	9	x	x	X
ejpam-3459	203	10	)	)	PUNCT
ejpam-3459	203	11	=	=	SYM
ejpam-3459	203	12	ti	ti	NOUN
ejpam-3459	203	13	(	(	PUNCT
ejpam-3459	203	14	∫	∫	PROPN
ejpam-3459	203	15	a	a	DET
ejpam-3459	203	16	0	0	NUM
ejpam-3459	203	17	βi(t	βi(t	PROPN
ejpam-3459	203	18	,	,	PUNCT
ejpam-3459	203	19	a	a	PRON
ejpam-3459	203	20	,	,	PUNCT
ejpam-3459	203	21	x)zi(t	x)zi(t	ADJ
ejpam-3459	203	22	,	,	PUNCT
ejpam-3459	203	23	a	a	PRON
ejpam-3459	203	24	,	,	PUNCT
ejpam-3459	203	25	x)da	x)da	PROPN
ejpam-3459	203	26	)	)	PUNCT
ejpam-3459	203	27	,	,	PUNCT
ejpam-3459	203	28	i	i	PRON
ejpam-3459	203	29	=	=	NOUN
ejpam-3459	203	30	1	1	NUM
ejpam-3459	203	31	;	;	PUNCT
ejpam-3459	203	32	2	2	NUM
ejpam-3459	203	33	where	where	SCONJ
ejpam-3459	203	34	ti	ti	NOUN
ejpam-3459	203	35	∈	∈	PROPN
ejpam-3459	203	36	l∞(r	l∞(r	PROPN
ejpam-3459	203	37	)	)	PUNCT
ejpam-3459	203	38	,	,	PUNCT
ejpam-3459	203	39	βi	βi	VERB
ejpam-3459	203	40	i	i	NOUN
ejpam-3459	203	41	=	=	NOUN
ejpam-3459	203	42	1	1	NUM
ejpam-3459	203	43	,	,	PUNCT
ejpam-3459	203	44	2	2	NUM
ejpam-3459	203	45	verify	verify	NOUN
ejpam-3459	203	46	(	(	PUNCT
ejpam-3459	203	47	h2)−	h2)−	NOUN
ejpam-3459	203	48	(	(	PUNCT
ejpam-3459	203	49	h3	h3	NOUN
ejpam-3459	203	50	)	)	PUNCT
ejpam-3459	203	51	.	.	PUNCT
ejpam-3459	204	1	we	we	PRON
ejpam-3459	204	2	study	study	VERB
ejpam-3459	204	3	here	here	ADV
ejpam-3459	204	4	,	,	PUNCT
ejpam-3459	204	5	the	the	DET
ejpam-3459	204	6	null	null	ADJ
ejpam-3459	204	7	controllability	controllability	NOUN
ejpam-3459	204	8	of	of	ADP
ejpam-3459	204	9	the	the	DET
ejpam-3459	204	10	following	follow	VERB
ejpam-3459	204	11	system	system	NOUN
ejpam-3459	204	12	:	:	PUNCT
ejpam-3459	205	1			PROPN
ejpam-3459	205	2	−∂z1	−∂z1	PROPN
ejpam-3459	205	3	∂t	∂t	PROPN
ejpam-3459	206	1	−	−	NUM
ejpam-3459	206	2	∂z1	∂z1	NOUN
ejpam-3459	206	3	∂a	∂a	VERB
ejpam-3459	206	4	−∆z1	−∆z1	NOUN
ejpam-3459	206	5	+	+	CCONJ
ejpam-3459	206	6	µ̃1z1	µ̃1z1	PROPN
ejpam-3459	206	7	+	+	CCONJ
ejpam-3459	206	8	µ̃2z2	µ̃2z2	PROPN
ejpam-3459	206	9	=	=	SYM
ejpam-3459	206	10	β1t1(ξ1)z1(t	β1t1(ξ1)z1(t	PROPN
ejpam-3459	206	11	,	,	PUNCT
ejpam-3459	206	12	0	0	NUM
ejpam-3459	206	13	,	,	PUNCT
ejpam-3459	206	14	x	x	NOUN
ejpam-3459	206	15	)	)	PUNCT
ejpam-3459	207	1	+	+	NUM
ejpam-3459	207	2	f	f	X
ejpam-3459	207	3	+	+	CCONJ
ejpam-3459	207	4	vχω	vχω	PROPN
ejpam-3459	208	1	+	+	CCONJ
ejpam-3459	208	2	β2t2(ξ2)z2(t	β2t2(ξ2)z2(t	PROPN
ejpam-3459	208	3	,	,	PUNCT
ejpam-3459	208	4	0	0	NUM
ejpam-3459	208	5	,	,	PUNCT
ejpam-3459	208	6	x	x	NOUN
ejpam-3459	208	7	)	)	PUNCT
ejpam-3459	208	8	in	in	ADP
ejpam-3459	208	9	q	q	PROPN
ejpam-3459	208	10	−∂z2	−∂z2	PROPN
ejpam-3459	208	11	∂t	∂t	PROPN
ejpam-3459	208	12	−	−	PROPN
ejpam-3459	208	13	∂z2	∂z2	PROPN
ejpam-3459	208	14	∂a	∂a	PROPN
ejpam-3459	208	15	−∆z2	−∆z2	NOUN
ejpam-3459	208	16	+	+	CCONJ
ejpam-3459	208	17	µ̃1z2	µ̃1z2	PROPN
ejpam-3459	208	18	+	+	CCONJ
ejpam-3459	208	19	µ̃2z1	µ̃2z1	PROPN
ejpam-3459	208	20	=	=	SYM
ejpam-3459	208	21	β1t2(ξ2)z1(t	β1t2(ξ2)z1(t	PROPN
ejpam-3459	208	22	,	,	PUNCT
ejpam-3459	208	23	0	0	NUM
ejpam-3459	208	24	,	,	PUNCT
ejpam-3459	208	25	x	x	NOUN
ejpam-3459	208	26	)	)	PUNCT
ejpam-3459	209	1	+	+	CCONJ
ejpam-3459	209	2	β2t1(ξ1)z2(t	β2t1(ξ1)z2(t	NOUN
ejpam-3459	209	3	,	,	PUNCT
ejpam-3459	209	4	0	0	NUM
ejpam-3459	209	5	,	,	PUNCT
ejpam-3459	209	6	x	x	NOUN
ejpam-3459	209	7	)	)	PUNCT
ejpam-3459	209	8	in	in	ADP
ejpam-3459	209	9	q	q	PROPN
ejpam-3459	209	10	zi	zi	PROPN
ejpam-3459	209	11	=	=	PUNCT
ejpam-3459	209	12	0	0	NUM
ejpam-3459	209	13	on	on	ADP
ejpam-3459	209	14	σ	σ	PROPN
ejpam-3459	209	15	,	,	PUNCT
ejpam-3459	209	16	i	i	NOUN
ejpam-3459	209	17	=	=	NOUN
ejpam-3459	209	18	1	1	NUM
ejpam-3459	209	19	,	,	PUNCT
ejpam-3459	209	20	2	2	NUM
ejpam-3459	209	21	zi(t	zi(t	NOUN
ejpam-3459	209	22	,	,	PUNCT
ejpam-3459	209	23	a	a	PRON
ejpam-3459	209	24	,	,	PUNCT
ejpam-3459	209	25	x	x	NOUN
ejpam-3459	209	26	)	)	PUNCT
ejpam-3459	209	27	=	=	SYM
ejpam-3459	209	28	0	0	NUM
ejpam-3459	210	1	in	in	ADP
ejpam-3459	210	2	qa	qa	PROPN
ejpam-3459	210	3	,	,	PUNCT
ejpam-3459	210	4	i	i	PRON
ejpam-3459	210	5	=	=	NOUN
ejpam-3459	210	6	1	1	NUM
ejpam-3459	210	7	,	,	PUNCT
ejpam-3459	210	8	2	2	NUM
ejpam-3459	210	9	zi(t	zi(t	NOUN
ejpam-3459	210	10	,	,	PUNCT
ejpam-3459	210	11	a	a	DET
ejpam-3459	210	12	,	,	PUNCT
ejpam-3459	210	13	x	x	NOUN
ejpam-3459	210	14	)	)	PUNCT
ejpam-3459	210	15	=	=	SYM
ejpam-3459	210	16	0	0	NUM
ejpam-3459	211	1	in	in	ADP
ejpam-3459	211	2	qt	qt	NOUN
ejpam-3459	211	3	,	,	PUNCT
ejpam-3459	211	4	i	i	PRON
ejpam-3459	211	5	=	=	NOUN
ejpam-3459	211	6	1	1	NUM
ejpam-3459	211	7	,	,	PUNCT
ejpam-3459	211	8	2	2	NUM
ejpam-3459	211	9	(	(	PUNCT
ejpam-3459	211	10	38	38	NUM
ejpam-3459	211	11	)	)	PUNCT
ejpam-3459	211	12	the	the	DET
ejpam-3459	211	13	system	system	NOUN
ejpam-3459	211	14	(	(	PUNCT
ejpam-3459	211	15	38	38	NUM
ejpam-3459	211	16	)	)	PUNCT
ejpam-3459	211	17	is	be	AUX
ejpam-3459	211	18	nonlinear	nonlinear	ADJ
ejpam-3459	211	19	.	.	PUNCT
ejpam-3459	212	1	let	let	VERB
ejpam-3459	212	2	a	a	PRON
ejpam-3459	212	3	=	=	PUNCT
ejpam-3459	212	4	{	{	PUNCT
ejpam-3459	212	5	ṽ	ṽ	PROPN
ejpam-3459	212	6	∈	∈	PROPN
ejpam-3459	212	7	l2(qω	l2(qω	PROPN
ejpam-3459	212	8	)	)	PUNCT
ejpam-3459	212	9	:	:	PUNCT
ejpam-3459	212	10	(	(	PUNCT
ejpam-3459	212	11	z̃1	z̃1	X
ejpam-3459	212	12	,	,	PUNCT
ejpam-3459	212	13	z̃2	z̃2	NUM
ejpam-3459	212	14	)	)	PUNCT
ejpam-3459	212	15	solves	solve	NOUN
ejpam-3459	212	16	(	(	PUNCT
ejpam-3459	212	17	38	38	NUM
ejpam-3459	212	18	)	)	PUNCT
ejpam-3459	212	19	,	,	PUNCT
ejpam-3459	212	20	verifies	verifie	NOUN
ejpam-3459	212	21	(	(	PUNCT
ejpam-3459	212	22	17	17	NUM
ejpam-3459	212	23	)	)	PUNCT
ejpam-3459	212	24	and	and	CCONJ
ejpam-3459	212	25	ṽ	ṽ	PROPN
ejpam-3459	212	26	satifies	satifie	NOUN
ejpam-3459	212	27	(	(	PUNCT
ejpam-3459	212	28	27	27	NUM
ejpam-3459	212	29	)	)	PUNCT
ejpam-3459	212	30	}	}	PUNCT
ejpam-3459	212	31	,	,	PUNCT
ejpam-3459	212	32	n	n	PROPN
ejpam-3459	212	33	=	=	SYM
ejpam-3459	212	34	l2(qt	l2(qt	PROPN
ejpam-3459	212	35	)	)	PUNCT
ejpam-3459	212	36	×	×	PROPN
ejpam-3459	212	37	l2(qt	l2(qt	PROPN
ejpam-3459	212	38	)	)	PUNCT
ejpam-3459	212	39	,	,	PUNCT
ejpam-3459	212	40	and	and	CCONJ
ejpam-3459	212	41	define	define	VERB
ejpam-3459	212	42	the	the	DET
ejpam-3459	212	43	multivalued	multivalued	ADJ
ejpam-3459	212	44	mapping	mapping	NOUN
ejpam-3459	212	45	:	:	PUNCT
ejpam-3459	213	1	λ	λ	X
ejpam-3459	213	2	:	:	PUNCT
ejpam-3459	213	3	n	n	PRON
ejpam-3459	213	4	−→	−→	NOUN
ejpam-3459	213	5	2n	2n	NUM
ejpam-3459	213	6	,	,	PUNCT
ejpam-3459	213	7	(	(	PUNCT
ejpam-3459	213	8	ξ1	ξ1	NOUN
ejpam-3459	213	9	,	,	PUNCT
ejpam-3459	213	10	ξ2	ξ2	ADJ
ejpam-3459	213	11	)	)	PUNCT
ejpam-3459	213	12	7−→	7−→	PROPN
ejpam-3459	213	13	λ(ξ1	λ(ξ1	NOUN
ejpam-3459	213	14	,	,	PUNCT
ejpam-3459	213	15	ξ2	ξ2	NOUN
ejpam-3459	213	16	)	)	PUNCT
ejpam-3459	213	17	by	by	ADP
ejpam-3459	213	18	λ(ξ1	λ(ξ1	ADP
ejpam-3459	213	19	,	,	PUNCT
ejpam-3459	213	20	ξ2	ξ2	ADJ
ejpam-3459	213	21	)	)	PUNCT
ejpam-3459	213	22	=	=	PRON
ejpam-3459	213	23	{	{	PUNCT
ejpam-3459	213	24	(	(	PUNCT
ejpam-3459	213	25	∫	∫	PROPN
ejpam-3459	213	26	a	a	PRON
ejpam-3459	213	27	0	0	NUM
ejpam-3459	213	28	β1z̃1da	β1z̃1da	NOUN
ejpam-3459	213	29	,	,	PUNCT
ejpam-3459	213	30	∫	∫	PROPN
ejpam-3459	213	31	a	a	DET
ejpam-3459	213	32	0	0	NUM
ejpam-3459	213	33	β2z̃2da	β2z̃2da	NOUN
ejpam-3459	213	34	)	)	PUNCT
ejpam-3459	213	35	:	:	PUNCT
ejpam-3459	213	36	(	(	PUNCT
ejpam-3459	213	37	z̃1	z̃1	X
ejpam-3459	213	38	,	,	PUNCT
ejpam-3459	213	39	z̃2	z̃2	NUM
ejpam-3459	213	40	)	)	PUNCT
ejpam-3459	213	41	is	be	AUX
ejpam-3459	213	42	associated	associate	VERB
ejpam-3459	213	43	to	to	ADP
ejpam-3459	213	44	ṽ	ṽ	PROPN
ejpam-3459	213	45	∈	∈	PROPN
ejpam-3459	213	46	a	a	PRON
ejpam-3459	213	47	}	}	PUNCT
ejpam-3459	213	48	.	.	PUNCT
ejpam-3459	214	1	the	the	DET
ejpam-3459	214	2	null	null	ADJ
ejpam-3459	214	3	controllability	controllability	NOUN
ejpam-3459	214	4	problem	problem	NOUN
ejpam-3459	214	5	of	of	ADP
ejpam-3459	214	6	(	(	PUNCT
ejpam-3459	214	7	38	38	NUM
ejpam-3459	214	8	)	)	PUNCT
ejpam-3459	214	9	is	be	AUX
ejpam-3459	214	10	reduced	reduce	VERB
ejpam-3459	214	11	to	to	PART
ejpam-3459	214	12	find	find	VERB
ejpam-3459	214	13	a	a	DET
ejpam-3459	214	14	fixed	fix	VERB
ejpam-3459	214	15	point	point	NOUN
ejpam-3459	214	16	of	of	ADP
ejpam-3459	214	17	λ	λ	PROPN
ejpam-3459	214	18	.	.	PUNCT
ejpam-3459	215	1	in	in	ADP
ejpam-3459	215	2	order	order	NOUN
ejpam-3459	215	3	to	to	PART
ejpam-3459	215	4	use	use	VERB
ejpam-3459	215	5	the	the	DET
ejpam-3459	215	6	generalization	generalization	NOUN
ejpam-3459	215	7	of	of	ADP
ejpam-3459	215	8	the	the	DET
ejpam-3459	215	9	leray	leray	ADJ
ejpam-3459	215	10	-	-	PUNCT
ejpam-3459	215	11	schauder	schauder	NOUN
ejpam-3459	215	12	’s	’s	PART
ejpam-3459	215	13	fixed	fix	VERB
ejpam-3459	215	14	point	point	NOUN
ejpam-3459	215	15	theorem	theorem	VERB
ejpam-3459	215	16	,	,	PUNCT
ejpam-3459	215	17	we	we	PRON
ejpam-3459	215	18	set	set	VERB
ejpam-3459	215	19	nρ	nρ	PROPN
ejpam-3459	215	20	=	=	PUNCT
ejpam-3459	215	21	{	{	PUNCT
ejpam-3459	215	22	(	(	PUNCT
ejpam-3459	215	23	ξ1	ξ1	NOUN
ejpam-3459	215	24	,	,	PUNCT
ejpam-3459	215	25	ξ2	ξ2	ADJ
ejpam-3459	215	26	)	)	PUNCT
ejpam-3459	215	27	∈	∈	PROPN
ejpam-3459	216	1	n	n	CCONJ
ejpam-3459	216	2	:	:	PUNCT
ejpam-3459	216	3	∃ρ	∃ρ	PROPN
ejpam-3459	216	4	∈	∈	PROPN
ejpam-3459	216	5	(	(	PUNCT
ejpam-3459	216	6	0	0	NUM
ejpam-3459	216	7	,	,	PUNCT
ejpam-3459	216	8	1	1	NUM
ejpam-3459	216	9	)	)	PUNCT
ejpam-3459	216	10	,	,	PUNCT
ejpam-3459	216	11	(	(	PUNCT
ejpam-3459	216	12	ξ1	ξ1	NOUN
ejpam-3459	216	13	,	,	PUNCT
ejpam-3459	216	14	ξ2	ξ2	ADJ
ejpam-3459	216	15	)	)	PUNCT
ejpam-3459	216	16	∈	∈	PROPN
ejpam-3459	216	17	ρλ(ξ1	ρλ(ξ1	NUM
ejpam-3459	216	18	,	,	PUNCT
ejpam-3459	216	19	ξ2	ξ2	NOUN
ejpam-3459	216	20	)	)	PUNCT
ejpam-3459	216	21	}	}	PUNCT
ejpam-3459	216	22	.	.	PUNCT
ejpam-3459	217	1	the	the	DET
ejpam-3459	217	2	following	follow	VERB
ejpam-3459	217	3	proposition	proposition	NOUN
ejpam-3459	217	4	is	be	AUX
ejpam-3459	217	5	a	a	DET
ejpam-3459	217	6	direct	direct	ADJ
ejpam-3459	217	7	consequence	consequence	NOUN
ejpam-3459	217	8	of	of	ADP
ejpam-3459	217	9	the	the	DET
ejpam-3459	217	10	leray	leray	ADJ
ejpam-3459	217	11	-	-	PUNCT
ejpam-3459	217	12	schauder	schauder	NOUN
ejpam-3459	217	13	’s	’s	PART
ejpam-3459	217	14	fixed	fix	VERB
ejpam-3459	217	15	point	point	NOUN
ejpam-3459	217	16	theorem	theorem	NOUN
ejpam-3459	217	17	(	(	PUNCT
ejpam-3459	217	18	see	see	VERB
ejpam-3459	217	19	[	[	X
ejpam-3459	217	20	1	1	NUM
ejpam-3459	217	21	]	]	NUM
ejpam-3459	217	22	)	)	PUNCT
ejpam-3459	217	23	.	.	PUNCT
ejpam-3459	218	1	proposition	proposition	NOUN
ejpam-3459	218	2	2	2	NUM
ejpam-3459	218	3	.	.	PUNCT
ejpam-3459	219	1	under	under	ADP
ejpam-3459	219	2	the	the	DET
ejpam-3459	219	3	assumptions	assumption	NOUN
ejpam-3459	219	4	(	(	PUNCT
ejpam-3459	219	5	h1)−	h1)−	PROPN
ejpam-3459	219	6	(	(	PUNCT
ejpam-3459	219	7	h3	h3	NOUN
ejpam-3459	219	8	)	)	PUNCT
ejpam-3459	219	9	,	,	PUNCT
ejpam-3459	219	10	the	the	DET
ejpam-3459	219	11	multivalued	multivalue	VERB
ejpam-3459	219	12	mapping	mapping	NOUN
ejpam-3459	219	13	λ	λ	PROPN
ejpam-3459	219	14	admits	admit	VERB
ejpam-3459	219	15	at	at	ADP
ejpam-3459	219	16	least	least	ADV
ejpam-3459	219	17	one	one	NUM
ejpam-3459	219	18	fixed	fix	VERB
ejpam-3459	219	19	point	point	NOUN
ejpam-3459	219	20	.	.	PUNCT
ejpam-3459	220	1	proof	proof	NOUN
ejpam-3459	220	2	.	.	PUNCT
ejpam-3459	221	1	we	we	PRON
ejpam-3459	221	2	proceed	proceed	VERB
ejpam-3459	221	3	in	in	ADP
ejpam-3459	221	4	four	four	NUM
ejpam-3459	221	5	steps	step	NOUN
ejpam-3459	221	6	:	:	PUNCT
ejpam-3459	221	7	step	step	NOUN
ejpam-3459	221	8	1	1	NUM
ejpam-3459	221	9	:	:	PUNCT
ejpam-3459	221	10	nρ	nρ	PROPN
ejpam-3459	221	11	is	be	AUX
ejpam-3459	221	12	bounded	bound	VERB
ejpam-3459	221	13	in	in	ADP
ejpam-3459	221	14	n	n	PROPN
ejpam-3459	221	15	.	.	PUNCT
ejpam-3459	222	1	let	let	VERB
ejpam-3459	222	2	(	(	PUNCT
ejpam-3459	223	1	ξ1	ξ1	NOUN
ejpam-3459	223	2	,	,	PUNCT
ejpam-3459	223	3	ξ2	ξ2	ADJ
ejpam-3459	223	4	)	)	PUNCT
ejpam-3459	223	5	∈	∈	PROPN
ejpam-3459	223	6	nρ	nρ	PROPN
ejpam-3459	223	7	.	.	PUNCT
ejpam-3459	224	1	then	then	ADV
ejpam-3459	224	2	,	,	PUNCT
ejpam-3459	224	3	there	there	PRON
ejpam-3459	224	4	exists	exist	VERB
ejpam-3459	224	5	ρ	ρ	PROPN
ejpam-3459	224	6	∈	∈	PROPN
ejpam-3459	224	7	(	(	PUNCT
ejpam-3459	224	8	0	0	NUM
ejpam-3459	224	9	,	,	PUNCT
ejpam-3459	224	10	1	1	NUM
ejpam-3459	224	11	)	)	PUNCT
ejpam-3459	224	12	,	,	PUNCT
ejpam-3459	224	13	z̃1	z̃1	PROPN
ejpam-3459	224	14	,	,	PUNCT
ejpam-3459	224	15	z̃2	z̃2	PROPN
ejpam-3459	224	16	such	such	ADJ
ejpam-3459	224	17	that	that	DET
ejpam-3459	224	18	ξ1	ξ1	NOUN
ejpam-3459	224	19	=	=	SYM
ejpam-3459	225	1	ρ	ρ	PROPN
ejpam-3459	225	2	∫	∫	PROPN
ejpam-3459	225	3	a	a	DET
ejpam-3459	225	4	0	0	NUM
ejpam-3459	225	5	β1z̃1da	β1z̃1da	PROPN
ejpam-3459	225	6	and	and	CCONJ
ejpam-3459	225	7	ξ2	ξ2	NOUN
ejpam-3459	225	8	=	=	SYM
ejpam-3459	225	9	ρ	ρ	PROPN
ejpam-3459	225	10	∫	∫	PROPN
ejpam-3459	225	11	a	a	DET
ejpam-3459	225	12	0	0	NUM
ejpam-3459	225	13	β2z̃2da	β2z̃2da	NOUN
ejpam-3459	225	14	.	.	PUNCT
ejpam-3459	226	1	then	then	ADV
ejpam-3459	226	2	,	,	PUNCT
ejpam-3459	226	3	∫	∫	PROPN
ejpam-3459	226	4	qt	qt	NOUN
ejpam-3459	226	5	|ξi|2dqt	|ξi|2dqt	ADV
ejpam-3459	226	6	≤	≤	NOUN
ejpam-3459	226	7	‖β1	‖β1	ADJ
ejpam-3459	226	8	,	,	PUNCT
ejpam-3459	226	9	β2‖2∞	β2‖2∞	PROPN
ejpam-3459	226	10	∫	∫	PROPN
ejpam-3459	226	11	q	q	PROPN
ejpam-3459	226	12	z̃	z̃	PROPN
ejpam-3459	226	13	2	2	NUM
ejpam-3459	227	1	i	i	PRON
ejpam-3459	227	2	dq	dq	VERB
ejpam-3459	227	3	,	,	PUNCT
ejpam-3459	227	4	i	i	PRON
ejpam-3459	227	5	=	=	NOUN
ejpam-3459	227	6	1	1	NUM
ejpam-3459	227	7	;	;	PUNCT
ejpam-3459	227	8	2	2	NUM
ejpam-3459	227	9	.	.	PUNCT
ejpam-3459	228	1	so	so	ADV
ejpam-3459	228	2	,	,	PUNCT
ejpam-3459	228	3	‖ξ1‖l2(qt	‖ξ1‖l2(qt	NOUN
ejpam-3459	228	4	)	)	PUNCT
ejpam-3459	229	1	+	+	PUNCT
ejpam-3459	229	2	‖ξ2‖l2(qt	‖ξ2‖l2(qt	NOUN
ejpam-3459	229	3	)	)	PUNCT
ejpam-3459	229	4	≤	≤	NOUN
ejpam-3459	230	1	‖β1	‖β1	PROPN
ejpam-3459	230	2	,	,	PUNCT
ejpam-3459	230	3	β2‖∞	β2‖∞	PRON
ejpam-3459	230	4	(	(	PUNCT
ejpam-3459	230	5	‖z̃1‖l2(q	‖z̃1‖l2(q	NOUN
ejpam-3459	230	6	)	)	PUNCT
ejpam-3459	231	1	+	+	CCONJ
ejpam-3459	231	2	‖z̃2‖l2(q	‖z̃2‖l2(q	NOUN
ejpam-3459	231	3	)	)	PUNCT
ejpam-3459	231	4	)	)	PUNCT
ejpam-3459	232	1	(	(	PUNCT
ejpam-3459	232	2	39	39	NUM
ejpam-3459	232	3	)	)	PUNCT
ejpam-3459	232	4	from	from	ADP
ejpam-3459	232	5	the	the	DET
ejpam-3459	232	6	theorem	theorem	NOUN
ejpam-3459	232	7	3	3	NUM
ejpam-3459	232	8	,	,	PUNCT
ejpam-3459	232	9	one	one	NUM
ejpam-3459	232	10	deducts	deduct	NOUN
ejpam-3459	232	11	that	that	PRON
ejpam-3459	232	12	there	there	PRON
ejpam-3459	232	13	exists	exist	VERB
ejpam-3459	232	14	a	a	DET
ejpam-3459	232	15	positive	positive	ADJ
ejpam-3459	232	16	constant	constant	ADJ
ejpam-3459	232	17	c	c	NOUN
ejpam-3459	232	18	such	such	ADJ
ejpam-3459	232	19	that	that	DET
ejpam-3459	232	20	‖ξ1‖l2(qt	‖ξ1‖l2(qt	NOUN
ejpam-3459	232	21	)	)	PUNCT
ejpam-3459	233	1	+	+	CCONJ
ejpam-3459	233	2	‖ξ2‖l)2(qt	‖ξ2‖l)2(qt	VERB
ejpam-3459	233	3	)	)	PUNCT
ejpam-3459	233	4	≤	≤	NOUN
ejpam-3459	233	5	2c‖β1	2c‖β1	NUM
ejpam-3459	233	6	,	,	PUNCT
ejpam-3459	233	7	β2‖∞	β2‖∞	PUNCT
ejpam-3459	233	8	(	(	PUNCT
ejpam-3459	233	9	‖θf‖l2(q	‖θf‖l2(q	NUM
ejpam-3459	233	10	)	)	PUNCT
ejpam-3459	233	11	+	+	CCONJ
ejpam-3459	233	12	‖f‖l2(q	‖f‖l2(q	NUM
ejpam-3459	233	13	)	)	PUNCT
ejpam-3459	233	14	)	)	PUNCT
ejpam-3459	234	1	(	(	PUNCT
ejpam-3459	234	2	40	40	NUM
ejpam-3459	234	3	)	)	PUNCT
ejpam-3459	234	4	hence	hence	ADV
ejpam-3459	234	5	,	,	PUNCT
ejpam-3459	234	6	nρ	nρ	PROPN
ejpam-3459	234	7	is	be	AUX
ejpam-3459	234	8	bounded	bound	VERB
ejpam-3459	234	9	in	in	ADP
ejpam-3459	234	10	n	n	PROPN
ejpam-3459	234	11	since	since	SCONJ
ejpam-3459	234	12	l2(u	l2(u	PRON
ejpam-3459	234	13	;	;	PUNCT
ejpam-3459	234	14	h1(ω	h1(ω	PROPN
ejpam-3459	234	15	)	)	PUNCT
ejpam-3459	234	16	)	)	PUNCT
ejpam-3459	235	1	⊂	⊂	PROPN
ejpam-3459	235	2	l2(q	l2(q	PROPN
ejpam-3459	235	3	)	)	PUNCT
ejpam-3459	235	4	.	.	PUNCT
ejpam-3459	236	1	c.	c.	PROPN
ejpam-3459	236	2	k.	k.	PROPN
ejpam-3459	236	3	somé	somé	PROPN
ejpam-3459	236	4	,	,	PUNCT
ejpam-3459	236	5	s.	s.	PROPN
ejpam-3459	236	6	sawadogo	sawadogo	PROPN
ejpam-3459	236	7	/	/	SYM
ejpam-3459	236	8	eur	eur	PROPN
ejpam-3459	236	9	.	.	PUNCT
ejpam-3459	237	1	j.	j.	PROPN
ejpam-3459	237	2	pure	pure	PROPN
ejpam-3459	237	3	appl	appl	PROPN
ejpam-3459	237	4	.	.	PROPN
ejpam-3459	237	5	math	math	PROPN
ejpam-3459	237	6	,	,	PUNCT
ejpam-3459	237	7	12	12	NUM
ejpam-3459	237	8	(	(	PUNCT
ejpam-3459	237	9	3	3	NUM
ejpam-3459	237	10	)	)	PUNCT
ejpam-3459	237	11	(	(	PUNCT
ejpam-3459	237	12	2019	2019	NUM
ejpam-3459	237	13	)	)	PUNCT
ejpam-3459	237	14	,	,	PUNCT
ejpam-3459	237	15	870	870	NUM
ejpam-3459	237	16	-	-	SYM
ejpam-3459	237	17	892	892	NUM
ejpam-3459	237	18	880	880	NUM
ejpam-3459	237	19	step	step	NOUN
ejpam-3459	237	20	2	2	NUM
ejpam-3459	237	21	:	:	PUNCT
ejpam-3459	237	22	for	for	ADP
ejpam-3459	237	23	all	all	DET
ejpam-3459	237	24	(	(	PUNCT
ejpam-3459	237	25	ξ1	ξ1	NOUN
ejpam-3459	237	26	,	,	PUNCT
ejpam-3459	237	27	ξ2	ξ2	ADJ
ejpam-3459	237	28	)	)	PUNCT
ejpam-3459	237	29	∈	∈	PROPN
ejpam-3459	237	30	n	n	NOUN
ejpam-3459	237	31	,	,	PUNCT
ejpam-3459	237	32	λ(ξ1	λ(ξ1	ADJ
ejpam-3459	237	33	,	,	PUNCT
ejpam-3459	237	34	ξ2	ξ2	NOUN
ejpam-3459	237	35	)	)	PUNCT
ejpam-3459	237	36	is	be	AUX
ejpam-3459	237	37	closed	close	VERB
ejpam-3459	237	38	and	and	CCONJ
ejpam-3459	237	39	convex	convex	NOUN
ejpam-3459	237	40	subset	subset	NOUN
ejpam-3459	237	41	of	of	ADP
ejpam-3459	237	42	n	n	PROPN
ejpam-3459	237	43	.	.	PUNCT
ejpam-3459	238	1	let	let	VERB
ejpam-3459	238	2	(	(	PUNCT
ejpam-3459	238	3	ξ1	ξ1	NOUN
ejpam-3459	238	4	,	,	PUNCT
ejpam-3459	238	5	ξ2	ξ2	ADJ
ejpam-3459	238	6	)	)	PUNCT
ejpam-3459	238	7	∈	∈	PROPN
ejpam-3459	238	8	λ(ξ1	λ(ξ1	X
ejpam-3459	238	9	,	,	PUNCT
ejpam-3459	238	10	ξ2	ξ2	NOUN
ejpam-3459	238	11	)	)	PUNCT
ejpam-3459	238	12	.	.	PUNCT
ejpam-3459	239	1	under	under	ADP
ejpam-3459	239	2	the	the	DET
ejpam-3459	239	3	assumptions	assumption	NOUN
ejpam-3459	239	4	(	(	PUNCT
ejpam-3459	239	5	h1	h1	PROPN
ejpam-3459	239	6	)	)	PUNCT
ejpam-3459	239	7	−	−	PROPN
ejpam-3459	239	8	(	(	PUNCT
ejpam-3459	239	9	h3	h3	NOUN
ejpam-3459	239	10	)	)	PUNCT
ejpam-3459	239	11	,	,	PUNCT
ejpam-3459	239	12	the	the	DET
ejpam-3459	239	13	system	system	NOUN
ejpam-3459	239	14	(	(	PUNCT
ejpam-3459	239	15	38	38	NUM
ejpam-3459	239	16	)	)	PUNCT
ejpam-3459	239	17	admits	admit	VERB
ejpam-3459	239	18	a	a	DET
ejpam-3459	239	19	solution	solution	NOUN
ejpam-3459	239	20	and	and	CCONJ
ejpam-3459	239	21	the	the	DET
ejpam-3459	239	22	corresponding	corresponding	ADJ
ejpam-3459	239	23	control	control	NOUN
ejpam-3459	239	24	verifies	verifie	NOUN
ejpam-3459	239	25	(	(	PUNCT
ejpam-3459	239	26	27	27	NUM
ejpam-3459	239	27	)	)	PUNCT
ejpam-3459	239	28	.	.	PUNCT
ejpam-3459	240	1	so	so	ADV
ejpam-3459	240	2	,	,	PUNCT
ejpam-3459	240	3	the	the	DET
ejpam-3459	240	4	set	set	NOUN
ejpam-3459	240	5	λ(ξ1	λ(ξ1	ADP
ejpam-3459	240	6	,	,	PUNCT
ejpam-3459	240	7	ξ2	ξ2	NOUN
ejpam-3459	240	8	)	)	PUNCT
ejpam-3459	240	9	is	be	AUX
ejpam-3459	240	10	non	non	X
ejpam-3459	240	11	empty	empty	ADJ
ejpam-3459	240	12	.	.	PUNCT
ejpam-3459	241	1	elsewhere	elsewhere	ADV
ejpam-3459	241	2	,	,	PUNCT
ejpam-3459	241	3	like	like	ADP
ejpam-3459	241	4	the	the	DET
ejpam-3459	241	5	mapping	mapping	NOUN
ejpam-3459	241	6	(	(	PUNCT
ejpam-3459	241	7	ξ1	ξ1	NOUN
ejpam-3459	241	8	,	,	PUNCT
ejpam-3459	241	9	ξ2	ξ2	ADJ
ejpam-3459	241	10	)	)	PUNCT
ejpam-3459	241	11	7−→	7−→	NOUN
ejpam-3459	241	12	(	(	PUNCT
ejpam-3459	241	13	z̃1	z̃1	PROPN
ejpam-3459	241	14	,	,	PUNCT
ejpam-3459	241	15	z̃2	z̃2	NUM
ejpam-3459	241	16	)	)	PUNCT
ejpam-3459	241	17	is	be	AUX
ejpam-3459	241	18	affine	affine	ADJ
ejpam-3459	241	19	,	,	PUNCT
ejpam-3459	241	20	then	then	ADV
ejpam-3459	241	21	,	,	PUNCT
ejpam-3459	241	22	the	the	DET
ejpam-3459	241	23	set	set	NOUN
ejpam-3459	241	24	λ(ξ1	λ(ξ1	ADP
ejpam-3459	241	25	,	,	PUNCT
ejpam-3459	241	26	ξ2	ξ2	NOUN
ejpam-3459	241	27	)	)	PUNCT
ejpam-3459	241	28	is	be	AUX
ejpam-3459	241	29	convex	convex	ADJ
ejpam-3459	241	30	.	.	PUNCT
ejpam-3459	242	1	there	there	PRON
ejpam-3459	242	2	rest	rest	VERB
ejpam-3459	242	3	to	to	PART
ejpam-3459	242	4	prove	prove	VERB
ejpam-3459	242	5	that	that	SCONJ
ejpam-3459	242	6	this	this	DET
ejpam-3459	242	7	set	set	NOUN
ejpam-3459	242	8	is	be	AUX
ejpam-3459	242	9	closed	closed	ADJ
ejpam-3459	242	10	.	.	PUNCT
ejpam-3459	243	1	let	let	VERB
ejpam-3459	243	2	(	(	PUNCT
ejpam-3459	243	3	η1n	η1n	PROPN
ejpam-3459	243	4	,	,	PUNCT
ejpam-3459	243	5	η2n)n	η2n)n	PROPN
ejpam-3459	243	6	⊂	⊂	PROPN
ejpam-3459	243	7	λ(ξ1	λ(ξ1	X
ejpam-3459	243	8	,	,	PUNCT
ejpam-3459	243	9	ξ2	ξ2	NOUN
ejpam-3459	243	10	)	)	PUNCT
ejpam-3459	243	11	which	which	PRON
ejpam-3459	243	12	converges	converge	VERB
ejpam-3459	243	13	strongly	strongly	ADV
ejpam-3459	243	14	towards	towards	ADP
ejpam-3459	243	15	(	(	PUNCT
ejpam-3459	243	16	η1	η1	NOUN
ejpam-3459	243	17	,	,	PUNCT
ejpam-3459	243	18	η2	η2	NOUN
ejpam-3459	243	19	)	)	PUNCT
ejpam-3459	243	20	in	in	ADP
ejpam-3459	243	21	n	n	PROPN
ejpam-3459	243	22	.	.	PUNCT
ejpam-3459	244	1	then	then	ADV
ejpam-3459	244	2	,	,	PUNCT
ejpam-3459	244	3	for	for	ADP
ejpam-3459	244	4	each	each	DET
ejpam-3459	244	5	n	n	PRON
ejpam-3459	244	6	∈	∈	PROPN
ejpam-3459	244	7	n	n	CCONJ
ejpam-3459	244	8	,	,	PUNCT
ejpam-3459	244	9	there	there	PRON
ejpam-3459	244	10	exists	exist	VERB
ejpam-3459	244	11	a	a	DET
ejpam-3459	244	12	control	control	NOUN
ejpam-3459	244	13	ṽn	ṽn	VERB
ejpam-3459	244	14	∈	∈	PROPN
ejpam-3459	244	15	a	a	PRON
ejpam-3459	244	16	and	and	CCONJ
ejpam-3459	244	17	a	a	DET
ejpam-3459	244	18	corresponding	corresponding	ADJ
ejpam-3459	244	19	solution	solution	NOUN
ejpam-3459	244	20	(	(	PUNCT
ejpam-3459	244	21	z̃1n	z̃1n	NOUN
ejpam-3459	244	22	,	,	PUNCT
ejpam-3459	244	23	z̃2n	z̃2n	NUM
ejpam-3459	244	24	)	)	PUNCT
ejpam-3459	244	25	of	of	ADP
ejpam-3459	244	26	(	(	PUNCT
ejpam-3459	244	27	38	38	NUM
ejpam-3459	244	28	)	)	PUNCT
ejpam-3459	244	29	such	such	ADJ
ejpam-3459	244	30	that	that	SCONJ
ejpam-3459	244	31	ηin	ηin	PROPN
ejpam-3459	244	32	=	=	PROPN
ejpam-3459	244	33	∫	∫	PROPN
ejpam-3459	244	34	a	a	DET
ejpam-3459	244	35	0	0	NUM
ejpam-3459	244	36	βiz̃in	βiz̃in	PROPN
ejpam-3459	244	37	,	,	PUNCT
ejpam-3459	244	38	i	i	PRON
ejpam-3459	244	39	=	=	NOUN
ejpam-3459	244	40	1	1	NUM
ejpam-3459	244	41	,	,	PUNCT
ejpam-3459	244	42	2	2	NUM
ejpam-3459	244	43	.	.	NUM
ejpam-3459	244	44	from	from	ADP
ejpam-3459	244	45	the	the	DET
ejpam-3459	244	46	inequalities	inequality	NOUN
ejpam-3459	244	47	(	(	PUNCT
ejpam-3459	244	48	27	27	NUM
ejpam-3459	244	49	)	)	PUNCT
ejpam-3459	244	50	,	,	PUNCT
ejpam-3459	244	51	(	(	PUNCT
ejpam-3459	244	52	34	34	NUM
ejpam-3459	244	53	)	)	PUNCT
ejpam-3459	244	54	and	and	CCONJ
ejpam-3459	244	55	(	(	PUNCT
ejpam-3459	244	56	35	35	NUM
ejpam-3459	244	57	)	)	PUNCT
ejpam-3459	244	58	one	one	NOUN
ejpam-3459	244	59	deduces	deduce	VERB
ejpam-3459	244	60	that	that	PRON
ejpam-3459	244	61	(	(	PUNCT
ejpam-3459	244	62	z̃1n	z̃1n	NOUN
ejpam-3459	244	63	,	,	PUNCT
ejpam-3459	244	64	z̃2n	z̃2n	ADV
ejpam-3459	244	65	)	)	PUNCT
ejpam-3459	244	66	and	and	CCONJ
ejpam-3459	244	67	ṽn	ṽn	NOUN
ejpam-3459	244	68	are	be	AUX
ejpam-3459	244	69	bounded	bound	VERB
ejpam-3459	244	70	respectively	respectively	ADV
ejpam-3459	244	71	in	in	ADP
ejpam-3459	244	72	(	(	PUNCT
ejpam-3459	244	73	l2(q))2	l2(q))2	NOUN
ejpam-3459	244	74	and	and	CCONJ
ejpam-3459	244	75	l2(qω	l2(qω	PROPN
ejpam-3459	244	76	)	)	PUNCT
ejpam-3459	244	77	.	.	PUNCT
ejpam-3459	245	1	thus	thus	ADV
ejpam-3459	245	2	,	,	PUNCT
ejpam-3459	245	3	(	(	PUNCT
ejpam-3459	245	4	η1n	η1n	NOUN
ejpam-3459	245	5	,	,	PUNCT
ejpam-3459	245	6	η2n	η2n	VERB
ejpam-3459	245	7	)	)	PUNCT
ejpam-3459	245	8	is	be	AUX
ejpam-3459	245	9	bounded	bound	VERB
ejpam-3459	245	10	in	in	ADP
ejpam-3459	245	11	n	n	PROPN
ejpam-3459	245	12	.	.	PUNCT
ejpam-3459	246	1	hence	hence	ADV
ejpam-3459	246	2	,	,	PUNCT
ejpam-3459	246	3	we	we	PRON
ejpam-3459	246	4	can	can	AUX
ejpam-3459	246	5	extract	extract	VERB
ejpam-3459	246	6	subsequences	subsequence	NOUN
ejpam-3459	246	7	denoted	denote	VERB
ejpam-3459	246	8	still	still	ADV
ejpam-3459	246	9	(	(	PUNCT
ejpam-3459	246	10	z̃1n	z̃1n	NOUN
ejpam-3459	246	11	,	,	PUNCT
ejpam-3459	246	12	z̃2n	z̃2n	NUM
ejpam-3459	246	13	)	)	PUNCT
ejpam-3459	246	14	,	,	PUNCT
ejpam-3459	246	15	ṽn	ṽn	VERB
ejpam-3459	246	16	and	and	CCONJ
ejpam-3459	246	17	(	(	PUNCT
ejpam-3459	246	18	η1n	η1n	NOUN
ejpam-3459	246	19	,	,	PUNCT
ejpam-3459	246	20	η2n	η2n	NOUN
ejpam-3459	246	21	)	)	PUNCT
ejpam-3459	246	22	respectively	respectively	ADV
ejpam-3459	246	23	such	such	ADJ
ejpam-3459	246	24	that	that	SCONJ
ejpam-3459	246	25	(	(	PUNCT
ejpam-3459	246	26	z̃1n	z̃1n	NOUN
ejpam-3459	246	27	,	,	PUNCT
ejpam-3459	246	28	z̃2n	z̃2n	NUM
ejpam-3459	246	29	)	)	PUNCT
ejpam-3459	246	30	,	,	PUNCT
ejpam-3459	246	31	ṽn	ṽn	VERB
ejpam-3459	246	32	and	and	CCONJ
ejpam-3459	246	33	(	(	PUNCT
ejpam-3459	246	34	η1n	η1n	NOUN
ejpam-3459	246	35	,	,	PUNCT
ejpam-3459	246	36	η2n	η2n	NOUN
ejpam-3459	246	37	)	)	PUNCT
ejpam-3459	246	38	converge	converge	VERB
ejpam-3459	246	39	weakly	weakly	ADV
ejpam-3459	246	40	towards	towards	ADP
ejpam-3459	246	41	(	(	PUNCT
ejpam-3459	246	42	z̃1	z̃1	PROPN
ejpam-3459	246	43	,	,	PUNCT
ejpam-3459	246	44	z̃2	z̃2	NUM
ejpam-3459	246	45	)	)	PUNCT
ejpam-3459	246	46	,	,	PUNCT
ejpam-3459	246	47	ṽ	ṽ	PROPN
ejpam-3459	246	48	and	and	CCONJ
ejpam-3459	246	49	(	(	PUNCT
ejpam-3459	246	50	η1	η1	NOUN
ejpam-3459	246	51	,	,	PUNCT
ejpam-3459	246	52	η2	η2	NOUN
ejpam-3459	246	53	)	)	PUNCT
ejpam-3459	246	54	respectively	respectively	ADV
ejpam-3459	246	55	in	in	ADP
ejpam-3459	246	56	(	(	PUNCT
ejpam-3459	246	57	l2(q))2	l2(q))2	NOUN
ejpam-3459	246	58	,	,	PUNCT
ejpam-3459	246	59	l2(qω	l2(qω	PROPN
ejpam-3459	246	60	)	)	PUNCT
ejpam-3459	246	61	and	and	CCONJ
ejpam-3459	246	62	n	n	ADV
ejpam-3459	246	63	with	with	ADP
ejpam-3459	246	64	ηi	ηi	PROPN
ejpam-3459	246	65	=	=	SYM
ejpam-3459	246	66	∫	∫	PROPN
ejpam-3459	246	67	a	a	DET
ejpam-3459	246	68	0	0	NUM
ejpam-3459	246	69	βiz̃ida	βiz̃ida	NUM
ejpam-3459	246	70	,	,	PUNCT
ejpam-3459	246	71	i	i	PRON
ejpam-3459	246	72	=	=	NOUN
ejpam-3459	246	73	1	1	NUM
ejpam-3459	246	74	;	;	PUNCT
ejpam-3459	246	75	2	2	NUM
ejpam-3459	246	76	.	.	X
ejpam-3459	246	77	notice	notice	VERB
ejpam-3459	246	78	that	that	SCONJ
ejpam-3459	246	79	(	(	PUNCT
ejpam-3459	246	80	z̃1	z̃1	X
ejpam-3459	246	81	,	,	PUNCT
ejpam-3459	246	82	z̃2	z̃2	NUM
ejpam-3459	246	83	)	)	PUNCT
ejpam-3459	246	84	is	be	AUX
ejpam-3459	246	85	solution	solution	NOUN
ejpam-3459	246	86	of	of	ADP
ejpam-3459	246	87	(	(	PUNCT
ejpam-3459	246	88	38	38	NUM
ejpam-3459	246	89	)	)	PUNCT
ejpam-3459	246	90	and	and	CCONJ
ejpam-3459	246	91	ṽ	ṽ	PROPN
ejpam-3459	246	92	verifies	verifie	NOUN
ejpam-3459	246	93	(	(	PUNCT
ejpam-3459	246	94	27	27	NUM
ejpam-3459	246	95	)	)	PUNCT
ejpam-3459	246	96	.	.	PUNCT
ejpam-3459	247	1	so	so	ADV
ejpam-3459	247	2	,	,	PUNCT
ejpam-3459	247	3	(	(	PUNCT
ejpam-3459	247	4	z̃1	z̃1	X
ejpam-3459	247	5	,	,	PUNCT
ejpam-3459	247	6	z̃2	z̃2	NUM
ejpam-3459	247	7	)	)	PUNCT
ejpam-3459	247	8	satisfies	satisfie	NOUN
ejpam-3459	247	9	(	(	PUNCT
ejpam-3459	247	10	17	17	NUM
ejpam-3459	247	11	)	)	PUNCT
ejpam-3459	247	12	.	.	PUNCT
ejpam-3459	248	1	as	as	ADP
ejpam-3459	248	2	consequence	consequence	NOUN
ejpam-3459	248	3	,	,	PUNCT
ejpam-3459	248	4	(	(	PUNCT
ejpam-3459	248	5	η1	η1	NOUN
ejpam-3459	248	6	,	,	PUNCT
ejpam-3459	248	7	η2	η2	ADJ
ejpam-3459	248	8	)	)	PUNCT
ejpam-3459	248	9	∈	∈	PROPN
ejpam-3459	248	10	λ(ξ1	λ(ξ1	X
ejpam-3459	248	11	,	,	PUNCT
ejpam-3459	248	12	ξ2	ξ2	NOUN
ejpam-3459	248	13	)	)	PUNCT
ejpam-3459	248	14	.	.	PUNCT
ejpam-3459	249	1	step	step	NOUN
ejpam-3459	249	2	3	3	NUM
ejpam-3459	249	3	:	:	PUNCT
ejpam-3459	249	4	λ	λ	NOUN
ejpam-3459	249	5	is	be	AUX
ejpam-3459	249	6	a	a	DET
ejpam-3459	249	7	compact	compact	ADJ
ejpam-3459	249	8	multivalued	multivalue	VERB
ejpam-3459	249	9	mapping	mapping	NOUN
ejpam-3459	249	10	.	.	PUNCT
ejpam-3459	250	1	let	let	VERB
ejpam-3459	250	2	b	b	X
ejpam-3459	250	3	be	be	AUX
ejpam-3459	250	4	a	a	DET
ejpam-3459	250	5	bounded	bounded	ADJ
ejpam-3459	250	6	subset	subset	NOUN
ejpam-3459	250	7	of	of	ADP
ejpam-3459	250	8	n	n	PROPN
ejpam-3459	250	9	,	,	PUNCT
ejpam-3459	250	10	(	(	PUNCT
ejpam-3459	250	11	ξ1	ξ1	NOUN
ejpam-3459	250	12	,	,	PUNCT
ejpam-3459	250	13	ξ2	ξ2	ADJ
ejpam-3459	250	14	)	)	PUNCT
ejpam-3459	250	15	∈	∈	PROPN
ejpam-3459	250	16	b.	b.	PROPN
ejpam-3459	250	17	let	let	VERB
ejpam-3459	250	18	(	(	PUNCT
ejpam-3459	250	19	ρ1n	ρ1n	INTJ
ejpam-3459	250	20	,	,	PUNCT
ejpam-3459	250	21	ρ2n	ρ2n	PROPN
ejpam-3459	250	22	)	)	PUNCT
ejpam-3459	250	23	∈	∈	PROPN
ejpam-3459	250	24	λ(ξ1	λ(ξ1	NOUN
ejpam-3459	250	25	,	,	PUNCT
ejpam-3459	250	26	ξ2	ξ2	NOUN
ejpam-3459	250	27	)	)	PUNCT
ejpam-3459	250	28	.	.	PUNCT
ejpam-3459	251	1	then	then	ADV
ejpam-3459	251	2	,	,	PUNCT
ejpam-3459	251	3	for	for	ADP
ejpam-3459	251	4	all	all	DET
ejpam-3459	251	5	n	n	DET
ejpam-3459	251	6	∈	∈	PROPN
ejpam-3459	251	7	n	n	CCONJ
ejpam-3459	251	8	,	,	PUNCT
ejpam-3459	251	9	there	there	PRON
ejpam-3459	251	10	exists	exist	VERB
ejpam-3459	251	11	(	(	PUNCT
ejpam-3459	251	12	z̃1n	z̃1n	NOUN
ejpam-3459	251	13	,	,	PUNCT
ejpam-3459	251	14	z̃2n	z̃2n	NUM
ejpam-3459	251	15	)	)	PUNCT
ejpam-3459	251	16	,	,	PUNCT
ejpam-3459	251	17	solution	solution	NOUN
ejpam-3459	251	18	of	of	ADP
ejpam-3459	251	19	(	(	PUNCT
ejpam-3459	251	20	38	38	NUM
ejpam-3459	251	21	)	)	PUNCT
ejpam-3459	251	22	,	,	PUNCT
ejpam-3459	251	23	and	and	CCONJ
ejpam-3459	251	24	ṽn	ṽn	VERB
ejpam-3459	251	25	in	in	ADP
ejpam-3459	251	26	(	(	PUNCT
ejpam-3459	251	27	l2(q	l2(q	PROPN
ejpam-3459	251	28	)	)	PUNCT
ejpam-3459	251	29	)	)	PUNCT
ejpam-3459	251	30	2	2	NUM
ejpam-3459	251	31	and	and	CCONJ
ejpam-3459	251	32	l2(qω	l2(qω	PROPN
ejpam-3459	251	33	)	)	PUNCT
ejpam-3459	251	34	respectively	respectively	ADV
ejpam-3459	251	35	such	such	ADJ
ejpam-3459	251	36	that	that	DET
ejpam-3459	251	37	ρin	ρin	NOUN
ejpam-3459	251	38	=	=	X
ejpam-3459	251	39	∫	∫	PROPN
ejpam-3459	251	40	a	a	DET
ejpam-3459	251	41	0	0	NUM
ejpam-3459	251	42	βiz̃inda	βiz̃inda	NOUN
ejpam-3459	251	43	,	,	PUNCT
ejpam-3459	251	44	i	i	PRON
ejpam-3459	251	45	=	=	NOUN
ejpam-3459	251	46	1	1	NUM
ejpam-3459	251	47	;	;	PUNCT
ejpam-3459	251	48	2	2	NUM
ejpam-3459	251	49	and	and	CCONJ
ejpam-3459	251	50	ṽn	ṽn	VERB
ejpam-3459	251	51	satisfies	satisfie	NOUN
ejpam-3459	251	52	(	(	PUNCT
ejpam-3459	251	53	27	27	NUM
ejpam-3459	251	54	)	)	PUNCT
ejpam-3459	251	55	.	.	PUNCT
ejpam-3459	252	1	so	so	ADV
ejpam-3459	252	2	,	,	PUNCT
ejpam-3459	252	3	(	(	PUNCT
ejpam-3459	252	4	ṽn)n	ṽn)n	NOUN
ejpam-3459	252	5	is	be	AUX
ejpam-3459	252	6	bounded	bound	VERB
ejpam-3459	252	7	in	in	ADP
ejpam-3459	252	8	l2(qω	l2(qω	PROPN
ejpam-3459	252	9	)	)	PUNCT
ejpam-3459	252	10	.	.	PUNCT
ejpam-3459	253	1	proceeding	proceed	VERB
ejpam-3459	253	2	in	in	ADP
ejpam-3459	253	3	the	the	DET
ejpam-3459	253	4	similar	similar	ADJ
ejpam-3459	253	5	ways	way	NOUN
ejpam-3459	253	6	that	that	PRON
ejpam-3459	253	7	the	the	DET
ejpam-3459	253	8	step	step	NOUN
ejpam-3459	253	9	2	2	NUM
ejpam-3459	253	10	of	of	ADP
ejpam-3459	253	11	the	the	DET
ejpam-3459	253	12	proof	proof	NOUN
ejpam-3459	253	13	of	of	ADP
ejpam-3459	253	14	the	the	DET
ejpam-3459	253	15	theorem	theorem	NOUN
ejpam-3459	253	16	3	3	NUM
ejpam-3459	253	17	,	,	PUNCT
ejpam-3459	253	18	one	one	NUM
ejpam-3459	253	19	deducts	deduct	NOUN
ejpam-3459	253	20	from	from	ADP
ejpam-3459	253	21	(	(	PUNCT
ejpam-3459	253	22	27	27	NUM
ejpam-3459	253	23	)	)	PUNCT
ejpam-3459	253	24	,	,	PUNCT
ejpam-3459	253	25	(	(	PUNCT
ejpam-3459	253	26	34)-(37	34)-(37	NUM
ejpam-3459	253	27	)	)	PUNCT
ejpam-3459	253	28	and	and	CCONJ
ejpam-3459	253	29	the	the	DET
ejpam-3459	253	30	fact	fact	NOUN
ejpam-3459	253	31	that	that	SCONJ
ejpam-3459	253	32	h1(ω	h1(ω	PROPN
ejpam-3459	253	33	)	)	PUNCT
ejpam-3459	253	34	⊂	⊂	PROPN
ejpam-3459	253	35	l2(ω	l2(ω	PROPN
ejpam-3459	253	36	)	)	PUNCT
ejpam-3459	253	37	that	that	SCONJ
ejpam-3459	253	38	(	(	PUNCT
ejpam-3459	253	39	z̃1n	z̃1n	NOUN
ejpam-3459	253	40	,	,	PUNCT
ejpam-3459	253	41	z̃2n)n	z̃2n)n	NOUN
ejpam-3459	253	42	is	be	AUX
ejpam-3459	253	43	bounded	bound	VERB
ejpam-3459	253	44	in	in	ADP
ejpam-3459	253	45	(	(	PUNCT
ejpam-3459	253	46	l2(q	l2(q	PROPN
ejpam-3459	253	47	)	)	PUNCT
ejpam-3459	253	48	)	)	PUNCT
ejpam-3459	253	49	2	2	NUM
ejpam-3459	253	50	,	,	PUNCT
ejpam-3459	253	51	and	and	CCONJ
ejpam-3459	253	52	then	then	ADV
ejpam-3459	253	53	,	,	PUNCT
ejpam-3459	253	54	(	(	PUNCT
ejpam-3459	253	55	ρ1n	ρ1n	INTJ
ejpam-3459	253	56	,	,	PUNCT
ejpam-3459	253	57	ρ2n	ρ2n	PROPN
ejpam-3459	253	58	)	)	PUNCT
ejpam-3459	253	59	is	be	AUX
ejpam-3459	253	60	bounded	bound	VERB
ejpam-3459	253	61	in	in	ADP
ejpam-3459	253	62	n	n	PROPN
ejpam-3459	253	63	.	.	PUNCT
ejpam-3459	254	1	thus	thus	ADV
ejpam-3459	254	2	,	,	PUNCT
ejpam-3459	254	3	there	there	PRON
ejpam-3459	254	4	exists	exist	VERB
ejpam-3459	254	5	subsequences	subsequence	NOUN
ejpam-3459	254	6	of	of	ADP
ejpam-3459	254	7	(	(	PUNCT
ejpam-3459	254	8	z̃1n	z̃1n	PROPN
ejpam-3459	254	9	,	,	PUNCT
ejpam-3459	254	10	z̃2n	z̃2n	ADV
ejpam-3459	254	11	)	)	PUNCT
ejpam-3459	254	12	and	and	CCONJ
ejpam-3459	254	13	ṽn	ṽn	VERB
ejpam-3459	254	14	also	also	ADV
ejpam-3459	254	15	denoted	denote	VERB
ejpam-3459	254	16	by	by	ADP
ejpam-3459	254	17	(	(	PUNCT
ejpam-3459	254	18	z̃1n	z̃1n	PROPN
ejpam-3459	254	19	,	,	PUNCT
ejpam-3459	254	20	z̃2n	z̃2n	PROPN
ejpam-3459	254	21	)	)	PUNCT
ejpam-3459	254	22	which	which	PRON
ejpam-3459	254	23	converges	converge	VERB
ejpam-3459	254	24	weakly	weakly	ADV
ejpam-3459	254	25	in	in	ADP
ejpam-3459	254	26	(	(	PUNCT
ejpam-3459	254	27	l2(q	l2(q	NOUN
ejpam-3459	254	28	)	)	PUNCT
ejpam-3459	254	29	)	)	PUNCT
ejpam-3459	254	30	2	2	NUM
ejpam-3459	254	31	and	and	CCONJ
ejpam-3459	254	32	l2(qω	l2(qω	PROPN
ejpam-3459	254	33	)	)	PUNCT
ejpam-3459	254	34	.	.	PUNCT
ejpam-3459	255	1	moreover	moreover	ADV
ejpam-3459	255	2	,	,	PUNCT
ejpam-3459	255	3	the	the	DET
ejpam-3459	255	4	subsequences	subsequence	NOUN
ejpam-3459	255	5	ρin	ρin	NOUN
ejpam-3459	255	6	=	=	SYM
ejpam-3459	255	7	∫	∫	PROPN
ejpam-3459	255	8	a	a	DET
ejpam-3459	255	9	0	0	NUM
ejpam-3459	255	10	βiz̃inda	βiz̃inda	NOUN
ejpam-3459	255	11	,	,	PUNCT
ejpam-3459	255	12	i	i	PRON
ejpam-3459	255	13	=	=	NOUN
ejpam-3459	255	14	1	1	NUM
ejpam-3459	255	15	;	;	PUNCT
ejpam-3459	255	16	2	2	NUM
ejpam-3459	255	17	of	of	ADP
ejpam-3459	255	18	(	(	PUNCT
ejpam-3459	255	19	ρin)n	ρin)n	PROPN
ejpam-3459	255	20	verify	verify	VERB
ejpam-3459	255	21	the	the	DET
ejpam-3459	255	22	following	follow	VERB
ejpam-3459	255	23	system	system	NOUN
ejpam-3459	255	24	:	:	PUNCT
ejpam-3459	255	25			NUM
ejpam-3459	256	1	−∂ρ1n	−∂ρ1n	PROPN
ejpam-3459	257	1	∂t	∂t	PROPN
ejpam-3459	257	2	−∆ρ1n	−∆ρ1n	PROPN
ejpam-3459	258	1	+	+	CCONJ
ejpam-3459	258	2	∫	∫	PROPN
ejpam-3459	258	3	a	a	DET
ejpam-3459	258	4	0	0	PUNCT
ejpam-3459	258	5	µ̂1β1z̃1nda+	µ̂1β1z̃1nda+	NOUN
ejpam-3459	258	6	∫	∫	NOUN
ejpam-3459	258	7	a	a	PRON
ejpam-3459	258	8	0	0	NUM
ejpam-3459	258	9	β1µ2z̃2nda	β1µ2z̃2nda	PUNCT
ejpam-3459	258	10	=	=	SYM
ejpam-3459	258	11	k1(ξn	k1(ξn	PROPN
ejpam-3459	258	12	)	)	PUNCT
ejpam-3459	258	13	in	in	ADP
ejpam-3459	258	14	qt	qt	NOUN
ejpam-3459	258	15	−∂ρ2n	−∂ρ2n	NOUN
ejpam-3459	259	1	∂t	∂t	PROPN
ejpam-3459	259	2	−∆ρ2n	−∆ρ2n	PROPN
ejpam-3459	260	1	+	+	CCONJ
ejpam-3459	260	2	∫	∫	PROPN
ejpam-3459	260	3	a	a	DET
ejpam-3459	260	4	0	0	NUM
ejpam-3459	260	5	µ̂1β2z̃2nda+	µ̂1β2z̃2nda+	PROPN
ejpam-3459	260	6	∫	∫	NOUN
ejpam-3459	260	7	a	a	DET
ejpam-3459	260	8	0	0	NUM
ejpam-3459	260	9	β2µ2z̃1nda	β2µ2z̃1nda	PUNCT
ejpam-3459	260	10	=	=	SYM
ejpam-3459	260	11	k2(ξn	k2(ξn	PROPN
ejpam-3459	260	12	)	)	PUNCT
ejpam-3459	260	13	in	in	ADP
ejpam-3459	260	14	qt	qt	NOUN
ejpam-3459	260	15	ρ1n	ρ1n	X
ejpam-3459	261	1	=	=	PUNCT
ejpam-3459	261	2	ρ2n	ρ2n	PUNCT
ejpam-3459	261	3	=	=	PUNCT
ejpam-3459	261	4	0	0	NUM
ejpam-3459	261	5	on	on	ADP
ejpam-3459	261	6	σt	σt	ADP
ejpam-3459	261	7	ρ1n(0	ρ1n(0	PROPN
ejpam-3459	261	8	,	,	PUNCT
ejpam-3459	261	9	x	x	NOUN
ejpam-3459	261	10	)	)	PUNCT
ejpam-3459	261	11	=	=	SYM
ejpam-3459	261	12	ρ2n(0	ρ2n(0	PROPN
ejpam-3459	261	13	,	,	PUNCT
ejpam-3459	261	14	x	x	NOUN
ejpam-3459	261	15	)	)	PUNCT
ejpam-3459	262	1	=	=	SYM
ejpam-3459	262	2	0	0	NUM
ejpam-3459	262	3	in	in	ADP
ejpam-3459	262	4	ω	ω	NUM
ejpam-3459	262	5	ρ1n(t	ρ1n(t	PROPN
ejpam-3459	262	6	,	,	PUNCT
ejpam-3459	262	7	x	x	X
ejpam-3459	262	8	)	)	PUNCT
ejpam-3459	262	9	=	=	SYM
ejpam-3459	262	10	ρ2n(t	ρ2n(t	PROPN
ejpam-3459	262	11	,	,	PUNCT
ejpam-3459	262	12	x	x	NOUN
ejpam-3459	262	13	)	)	PUNCT
ejpam-3459	262	14	=	=	SYM
ejpam-3459	262	15	0	0	NUM
ejpam-3459	262	16	in	in	ADP
ejpam-3459	262	17	ω	ω	PROPN
ejpam-3459	262	18	(	(	PUNCT
ejpam-3459	262	19	41	41	NUM
ejpam-3459	262	20	)	)	PUNCT
ejpam-3459	262	21	where	where	SCONJ
ejpam-3459	262	22	σt	σt	ADV
ejpam-3459	262	23	=	=	SYM
ejpam-3459	262	24	(	(	PUNCT
ejpam-3459	262	25	0	0	NUM
ejpam-3459	262	26	,	,	PUNCT
ejpam-3459	262	27	t	t	NOUN
ejpam-3459	262	28	)	)	PUNCT
ejpam-3459	262	29	×	×	PROPN
ejpam-3459	262	30	γ	γ	X
ejpam-3459	262	31	,	,	PUNCT
ejpam-3459	262	32	µ̂1	µ̂1	PUNCT
ejpam-3459	262	33	=	=	PUNCT
ejpam-3459	262	34	µ1	µ1	PROPN
ejpam-3459	262	35	+	+	SYM
ejpam-3459	262	36	λ0	λ0	NOUN
ejpam-3459	262	37	and	and	CCONJ
ejpam-3459	262	38	for	for	ADP
ejpam-3459	262	39	all	all	PRON
ejpam-3459	262	40	n	n	PRON
ejpam-3459	262	41	∈	∈	PROPN
ejpam-3459	262	42	n	n	CCONJ
ejpam-3459	262	43	,	,	PUNCT
ejpam-3459	262	44	k1n(ξ	k1n(ξ	PROPN
ejpam-3459	262	45	)	)	PUNCT
ejpam-3459	262	46	=	=	PUNCT
ejpam-3459	263	1	−	−	PROPN
ejpam-3459	263	2	∫	∫	PROPN
ejpam-3459	263	3	a	a	PRON
ejpam-3459	263	4	0	0	NUM
ejpam-3459	263	5	(	(	PUNCT
ejpam-3459	263	6	∂β1	∂β1	ADP
ejpam-3459	263	7	∂t	∂t	PROPN
ejpam-3459	263	8	+	+	CCONJ
ejpam-3459	263	9	∂β1	∂β1	PROPN
ejpam-3459	264	1	∂a	∂a	NOUN
ejpam-3459	264	2	+	+	NUM
ejpam-3459	264	3	∆β1	∆β1	NOUN
ejpam-3459	264	4	+	+	CCONJ
ejpam-3459	264	5	µ2β2	µ2β2	PROPN
ejpam-3459	264	6	)	)	PUNCT
ejpam-3459	264	7	z̃1nda+	z̃1nda+	NOUN
ejpam-3459	264	8	∫	∫	PROPN
ejpam-3459	264	9	a	a	DET
ejpam-3459	264	10	0	0	NUM
ejpam-3459	264	11	β1(f	β1(f	PUNCT
ejpam-3459	264	12	+	+	NUM
ejpam-3459	264	13	ṽnχω)da	ṽnχω)da	PROPN
ejpam-3459	264	14	+	+	CCONJ
ejpam-3459	264	15	∫	∫	PROPN
ejpam-3459	264	16	a	a	DET
ejpam-3459	264	17	0	0	NUM
ejpam-3459	264	18	β2	β2	NOUN
ejpam-3459	264	19	1t1(ξ1n)z̃1n(t	1t1(ξ1n)z̃1n(t	NUM
ejpam-3459	264	20	,	,	PUNCT
ejpam-3459	264	21	0	0	NUM
ejpam-3459	264	22	,	,	PUNCT
ejpam-3459	264	23	x)da+	x)da+	PUNCT
ejpam-3459	264	24	∫	∫	PROPN
ejpam-3459	265	1	a	a	DET
ejpam-3459	265	2	0	0	NUM
ejpam-3459	265	3	β1β2t2(ξ2n)z̃2n(t	β1β2t2(ξ2n)z̃2n(t	PROPN
ejpam-3459	265	4	,	,	PUNCT
ejpam-3459	265	5	0	0	NUM
ejpam-3459	265	6	,	,	PUNCT
ejpam-3459	265	7	x)da	x)da	PROPN
ejpam-3459	265	8	−	−	PROPN
ejpam-3459	266	1	2	2	NUM
ejpam-3459	266	2	n∑	n∑	NOUN
ejpam-3459	266	3	i=1	i=1	PROPN
ejpam-3459	267	1	∫	∫	PROPN
ejpam-3459	267	2	a	a	DET
ejpam-3459	267	3	0	0	NUM
ejpam-3459	267	4	∂β1	∂β1	NOUN
ejpam-3459	267	5	∂xi	∂xi	NOUN
ejpam-3459	267	6	.	.	PUNCT
ejpam-3459	268	1	∂z̃1n	∂z̃1n	PUNCT
ejpam-3459	268	2	∂xi	∂xi	PROPN
ejpam-3459	268	3	da	da	PROPN
ejpam-3459	268	4	c.	c.	PROPN
ejpam-3459	268	5	k.	k.	PROPN
ejpam-3459	268	6	somé	somé	PROPN
ejpam-3459	268	7	,	,	PUNCT
ejpam-3459	268	8	s.	s.	PROPN
ejpam-3459	268	9	sawadogo	sawadogo	PROPN
ejpam-3459	268	10	/	/	SYM
ejpam-3459	268	11	eur	eur	PROPN
ejpam-3459	268	12	.	.	PUNCT
ejpam-3459	269	1	j.	j.	PROPN
ejpam-3459	269	2	pure	pure	PROPN
ejpam-3459	269	3	appl	appl	PROPN
ejpam-3459	269	4	.	.	PROPN
ejpam-3459	269	5	math	math	PROPN
ejpam-3459	269	6	,	,	PUNCT
ejpam-3459	269	7	12	12	NUM
ejpam-3459	269	8	(	(	PUNCT
ejpam-3459	269	9	3	3	NUM
ejpam-3459	269	10	)	)	PUNCT
ejpam-3459	269	11	(	(	PUNCT
ejpam-3459	269	12	2019	2019	NUM
ejpam-3459	269	13	)	)	PUNCT
ejpam-3459	269	14	,	,	PUNCT
ejpam-3459	269	15	870	870	NUM
ejpam-3459	269	16	-	-	SYM
ejpam-3459	269	17	892	892	NUM
ejpam-3459	269	18	881	881	NUM
ejpam-3459	269	19	k2n(ξ	k2n(ξ	NOUN
ejpam-3459	269	20	)	)	PUNCT
ejpam-3459	269	21	=	=	PUNCT
ejpam-3459	270	1	−	−	PROPN
ejpam-3459	270	2	∫	∫	PROPN
ejpam-3459	270	3	a	a	PRON
ejpam-3459	270	4	0	0	NUM
ejpam-3459	271	1	(	(	PUNCT
ejpam-3459	271	2	∂β2	∂β2	ADJ
ejpam-3459	271	3	∂t	∂t	PROPN
ejpam-3459	271	4	+	+	CCONJ
ejpam-3459	272	1	∂β2	∂β2	ADJ
ejpam-3459	272	2	∂a	∂a	NOUN
ejpam-3459	272	3	+	+	NUM
ejpam-3459	272	4	∆β2	∆β2	PROPN
ejpam-3459	272	5	+	+	CCONJ
ejpam-3459	272	6	µ2β1	µ2β1	X
ejpam-3459	272	7	)	)	PUNCT
ejpam-3459	272	8	z̃2nda+	z̃2nda+	NOUN
ejpam-3459	272	9	∫	∫	PROPN
ejpam-3459	272	10	a	a	DET
ejpam-3459	272	11	0	0	NUM
ejpam-3459	272	12	β2	β2	NOUN
ejpam-3459	272	13	2t1(ξ1n)z̃2n(t	2t1(ξ1n)z̃2n(t	NUM
ejpam-3459	272	14	,	,	PUNCT
ejpam-3459	272	15	0	0	NUM
ejpam-3459	272	16	,	,	PUNCT
ejpam-3459	273	1	x)da	x)da	PROPN
ejpam-3459	273	2	+	+	CCONJ
ejpam-3459	274	1	∫	∫	PROPN
ejpam-3459	274	2	a	a	DET
ejpam-3459	274	3	0	0	NUM
ejpam-3459	274	4	β1β2t2(ξ2n)z̃1n(t	β1β2t2(ξ2n)z̃1n(t	NOUN
ejpam-3459	274	5	,	,	PUNCT
ejpam-3459	274	6	0	0	NUM
ejpam-3459	274	7	,	,	PUNCT
ejpam-3459	274	8	x)da−	x)da−	PROPN
ejpam-3459	274	9	2	2	NUM
ejpam-3459	274	10	n∑	n∑	NOUN
ejpam-3459	274	11	i=1	i=1	PROPN
ejpam-3459	274	12	∫	∫	PROPN
ejpam-3459	275	1	a	a	DET
ejpam-3459	275	2	0	0	NUM
ejpam-3459	275	3	∂β2	∂β2	ADJ
ejpam-3459	275	4	∂xi	∂xi	NOUN
ejpam-3459	275	5	.	.	PUNCT
ejpam-3459	276	1	∂z̃2n	∂z̃2n	PROPN
ejpam-3459	276	2	∂xi	∂xi	PROPN
ejpam-3459	276	3	da	da	VERB
ejpam-3459	276	4	under	under	ADP
ejpam-3459	276	5	the	the	DET
ejpam-3459	276	6	assumptions	assumption	NOUN
ejpam-3459	276	7	(	(	PUNCT
ejpam-3459	276	8	h1)−	h1)−	PROPN
ejpam-3459	276	9	(	(	PUNCT
ejpam-3459	276	10	h3	h3	NOUN
ejpam-3459	276	11	)	)	PUNCT
ejpam-3459	276	12	the	the	DET
ejpam-3459	276	13	boundedness	boundedness	NOUN
ejpam-3459	276	14	of	of	ADP
ejpam-3459	276	15	b	b	PROPN
ejpam-3459	276	16	and	and	CCONJ
ejpam-3459	276	17	of	of	ADP
ejpam-3459	276	18	sequences	sequence	NOUN
ejpam-3459	276	19	(	(	PUNCT
ejpam-3459	276	20	z̃in)n	z̃in)n	NOUN
ejpam-3459	276	21	i	i	NOUN
ejpam-3459	276	22	=	=	NOUN
ejpam-3459	276	23	1	1	NUM
ejpam-3459	276	24	;	;	PUNCT
ejpam-3459	276	25	2	2	NUM
ejpam-3459	276	26	,	,	PUNCT
ejpam-3459	276	27	from	from	ADP
ejpam-3459	276	28	(	(	PUNCT
ejpam-3459	276	29	27	27	NUM
ejpam-3459	276	30	)	)	PUNCT
ejpam-3459	276	31	,	,	PUNCT
ejpam-3459	276	32	(	(	PUNCT
ejpam-3459	276	33	34)-(37	34)-(37	NUM
ejpam-3459	276	34	)	)	PUNCT
ejpam-3459	276	35	,	,	PUNCT
ejpam-3459	276	36	one	one	NUM
ejpam-3459	276	37	deducts	deduct	NOUN
ejpam-3459	276	38	that	that	PRON
ejpam-3459	276	39	there	there	PRON
ejpam-3459	276	40	exists	exist	VERB
ejpam-3459	276	41	positive	positive	ADJ
ejpam-3459	276	42	constants	constant	NOUN
ejpam-3459	276	43	ci	ci	NOUN
ejpam-3459	276	44	which	which	PRON
ejpam-3459	276	45	depend	depend	VERB
ejpam-3459	276	46	on	on	ADP
ejpam-3459	276	47	‖∇βi‖∞	‖∇βi‖∞	PRON
ejpam-3459	276	48	,	,	PUNCT
ejpam-3459	276	49	‖β1	‖β1	PROPN
ejpam-3459	276	50	,	,	PUNCT
ejpam-3459	276	51	β2‖2∞	β2‖2∞	PROPN
ejpam-3459	276	52	,	,	PUNCT
ejpam-3459	276	53	‖t1	‖t1	PROPN
ejpam-3459	276	54	,	,	PUNCT
ejpam-3459	276	55	t2‖∞	t2‖∞	PROPN
ejpam-3459	276	56	for	for	ADP
ejpam-3459	276	57	i	i	PRON
ejpam-3459	276	58	=	=	NOUN
ejpam-3459	276	59	1	1	NUM
ejpam-3459	276	60	;	;	PUNCT
ejpam-3459	276	61	2	2	NUM
ejpam-3459	276	62	such	such	ADJ
ejpam-3459	276	63	that	that	DET
ejpam-3459	276	64	‖ki(ξn)‖2l2(qt	‖ki(ξn)‖2l2(qt	NOUN
ejpam-3459	276	65	)	)	PUNCT
ejpam-3459	277	1	≤	≤	NOUN
ejpam-3459	277	2	ci	ci	NOUN
ejpam-3459	277	3	(	(	PUNCT
ejpam-3459	277	4	‖θf‖2l2(qω	‖θf‖2l2(qω	NOUN
ejpam-3459	277	5	)	)	PUNCT
ejpam-3459	277	6	+	+	CCONJ
ejpam-3459	277	7	‖f‖2l2(q	‖f‖2l2(q	NOUN
ejpam-3459	277	8	)	)	PUNCT
ejpam-3459	277	9	)	)	PUNCT
ejpam-3459	277	10	(	(	PUNCT
ejpam-3459	277	11	42	42	X
ejpam-3459	277	12	)	)	PUNCT
ejpam-3459	277	13	now	now	ADV
ejpam-3459	277	14	,	,	PUNCT
ejpam-3459	277	15	multiplying	multiply	VERB
ejpam-3459	277	16	the	the	DET
ejpam-3459	277	17	first	first	ADJ
ejpam-3459	277	18	and	and	CCONJ
ejpam-3459	277	19	the	the	DET
ejpam-3459	277	20	second	second	ADJ
ejpam-3459	277	21	equations	equation	NOUN
ejpam-3459	277	22	of	of	ADP
ejpam-3459	277	23	(	(	PUNCT
ejpam-3459	277	24	41	41	NUM
ejpam-3459	277	25	)	)	PUNCT
ejpam-3459	277	26	by	by	ADP
ejpam-3459	277	27	ρ1n	ρ1n	INTJ
ejpam-3459	277	28	and	and	CCONJ
ejpam-3459	277	29	ρ2n	ρ2n	PROPN
ejpam-3459	277	30	respectively	respectively	ADV
ejpam-3459	277	31	and	and	CCONJ
ejpam-3459	277	32	proceeding	proceed	VERB
ejpam-3459	277	33	by	by	ADP
ejpam-3459	277	34	integrations	integration	NOUN
ejpam-3459	277	35	by	by	ADP
ejpam-3459	277	36	parts	part	NOUN
ejpam-3459	277	37	over	over	ADP
ejpam-3459	277	38	qt	qt	NOUN
ejpam-3459	277	39	,	,	PUNCT
ejpam-3459	277	40	one	one	NUM
ejpam-3459	277	41	has∫	has∫	NOUN
ejpam-3459	277	42	qt	qt	ADP
ejpam-3459	277	43	|∇ρ1n	|∇ρ1n	PROPN
ejpam-3459	277	44	|2dqt	|2dqt	PROPN
ejpam-3459	278	1	+	+	NOUN
ejpam-3459	279	1	λ0	λ0	NOUN
ejpam-3459	279	2	∫	∫	NOUN
ejpam-3459	279	3	qt	qt	PROPN
ejpam-3459	279	4	ρ2	ρ2	PROPN
ejpam-3459	279	5	1ndqt	1ndqt	PROPN
ejpam-3459	279	6	=	=	SYM
ejpam-3459	279	7	∫	∫	PROPN
ejpam-3459	279	8	qt	qt	PROPN
ejpam-3459	279	9	(	(	PUNCT
ejpam-3459	279	10	k1(ξn)−	k1(ξn)−	NOUN
ejpam-3459	279	11	∫	∫	PROPN
ejpam-3459	279	12	a	a	PRON
ejpam-3459	279	13	0	0	NUM
ejpam-3459	279	14	β1(µ̃1z̃1n	β1(µ̃1z̃1n	PUNCT
ejpam-3459	279	15	+	+	NOUN
ejpam-3459	279	16	µ̃2z̃2n)da	µ̃2z̃2n)da	ADJ
ejpam-3459	279	17	)	)	PUNCT
ejpam-3459	279	18	ρ1ndqt	ρ1ndqt	PROPN
ejpam-3459	279	19	since	since	SCONJ
ejpam-3459	279	20	z̃1n	z̃1n	PROPN
ejpam-3459	279	21	,	,	PUNCT
ejpam-3459	279	22	z̃2n	z̃2n	ADV
ejpam-3459	279	23	verify	verify	VERB
ejpam-3459	279	24	(	(	PUNCT
ejpam-3459	279	25	35)-(36	35)-(36	NUM
ejpam-3459	279	26	)	)	PUNCT
ejpam-3459	279	27	,	,	PUNCT
ejpam-3459	279	28	one	one	NUM
ejpam-3459	279	29	deducts	deduct	NOUN
ejpam-3459	279	30	that	that	PRON
ejpam-3459	279	31	k1(ξn)−	k1(ξn)−	NOUN
ejpam-3459	279	32	∫	∫	VERB
ejpam-3459	279	33	a	a	PRON
ejpam-3459	279	34	0	0	NUM
ejpam-3459	279	35	β1(µ̃1z̃1n	β1(µ̃1z̃1n	PUNCT
ejpam-3459	280	1	+	+	NOUN
ejpam-3459	280	2	µ̃2z̃2n)da	µ̃2z̃2n)da	ADJ
ejpam-3459	280	3	verifies	verifie	NOUN
ejpam-3459	280	4	(	(	PUNCT
ejpam-3459	280	5	42	42	NUM
ejpam-3459	280	6	)	)	PUNCT
ejpam-3459	280	7	.	.	PUNCT
ejpam-3459	281	1	so	so	ADV
ejpam-3459	281	2	,	,	PUNCT
ejpam-3459	281	3	using	use	VERB
ejpam-3459	281	4	young	young	ADJ
ejpam-3459	281	5	inequality	inequality	NOUN
ejpam-3459	281	6	,	,	PUNCT
ejpam-3459	281	7	one	one	NUM
ejpam-3459	281	8	has∫	has∫	NOUN
ejpam-3459	281	9	qt	qt	ADP
ejpam-3459	281	10	|∇ρ1n	|∇ρ1n	PROPN
ejpam-3459	281	11	|2dqt	|2dqt	PROPN
ejpam-3459	282	1	+	+	CCONJ
ejpam-3459	283	1	(	(	PUNCT
ejpam-3459	283	2	λ0	λ0	NOUN
ejpam-3459	283	3	−	−	NOUN
ejpam-3459	283	4	λ1	λ1	ADJ
ejpam-3459	283	5	2	2	NUM
ejpam-3459	283	6	)	)	PUNCT
ejpam-3459	283	7	∫	∫	PROPN
ejpam-3459	283	8	qt	qt	PROPN
ejpam-3459	283	9	ρ2	ρ2	PROPN
ejpam-3459	283	10	1ndqt	1ndqt	PROPN
ejpam-3459	283	11	≤	≤	PROPN
ejpam-3459	283	12	c1	c1	NOUN
ejpam-3459	283	13	2λ1	2λ1	NUM
ejpam-3459	284	1	(	(	PUNCT
ejpam-3459	284	2	‖θf‖2l2(qω	‖θf‖2l2(qω	NOUN
ejpam-3459	284	3	)	)	PUNCT
ejpam-3459	285	1	+	+	CCONJ
ejpam-3459	285	2	‖f‖2l2(q	‖f‖2l2(q	NOUN
ejpam-3459	285	3	)	)	PUNCT
ejpam-3459	285	4	)	)	PUNCT
ejpam-3459	286	1	(	(	PUNCT
ejpam-3459	286	2	43	43	NUM
ejpam-3459	286	3	)	)	PUNCT
ejpam-3459	286	4	by	by	ADP
ejpam-3459	286	5	analogy	analogy	NOUN
ejpam-3459	286	6	we	we	PRON
ejpam-3459	286	7	show	show	VERB
ejpam-3459	286	8	that∫	that∫	PROPN
ejpam-3459	286	9	qt	qt	PROPN
ejpam-3459	286	10	|∇ρ2n	|∇ρ2n	PROPN
ejpam-3459	286	11	|2dqt	|2dqt	PROPN
ejpam-3459	286	12	+	+	CCONJ
ejpam-3459	286	13	(	(	PUNCT
ejpam-3459	286	14	λ0	λ0	NOUN
ejpam-3459	286	15	−	−	NOUN
ejpam-3459	286	16	λ2	λ2	NOUN
ejpam-3459	286	17	2	2	NUM
ejpam-3459	286	18	)	)	PUNCT
ejpam-3459	286	19	∫	∫	PROPN
ejpam-3459	286	20	qt	qt	PROPN
ejpam-3459	286	21	ρ2	ρ2	PROPN
ejpam-3459	286	22	2ndqt	2ndqt	PROPN
ejpam-3459	286	23	≤	≤	PROPN
ejpam-3459	286	24	c2	c2	PROPN
ejpam-3459	286	25	2λ2	2λ2	NUM
ejpam-3459	286	26	(	(	PUNCT
ejpam-3459	286	27	‖θf‖2l2(qω	‖θf‖2l2(qω	NOUN
ejpam-3459	286	28	)	)	PUNCT
ejpam-3459	287	1	+	+	CCONJ
ejpam-3459	287	2	‖f‖2l2(q	‖f‖2l2(q	NOUN
ejpam-3459	287	3	)	)	PUNCT
ejpam-3459	287	4	)	)	PUNCT
ejpam-3459	288	1	(	(	PUNCT
ejpam-3459	288	2	44	44	X
ejpam-3459	288	3	)	)	PUNCT
ejpam-3459	288	4	taking	take	VERB
ejpam-3459	288	5	λ0−1	λ0−1	PROPN
ejpam-3459	288	6	≥	≥	NOUN
ejpam-3459	288	7	max(λ12	max(λ12	PROPN
ejpam-3459	288	8	,	,	PUNCT
ejpam-3459	288	9	λ2	λ2	NOUN
ejpam-3459	288	10	2	2	NUM
ejpam-3459	288	11	)	)	PUNCT
ejpam-3459	288	12	,	,	PUNCT
ejpam-3459	288	13	one	one	NUM
ejpam-3459	288	14	deducts	deduct	NOUN
ejpam-3459	288	15	that	that	PRON
ejpam-3459	288	16	(	(	PUNCT
ejpam-3459	288	17	ρ1n)n	ρ1n)n	PROPN
ejpam-3459	288	18	and	and	CCONJ
ejpam-3459	288	19	(	(	PUNCT
ejpam-3459	288	20	ρ2n)n	ρ2n)n	PROPN
ejpam-3459	288	21	are	be	AUX
ejpam-3459	288	22	bounded	bound	VERB
ejpam-3459	288	23	in	in	ADP
ejpam-3459	288	24	l2((0	l2((0	PROPN
ejpam-3459	288	25	,	,	PUNCT
ejpam-3459	288	26	t	t	PROPN
ejpam-3459	288	27	)	)	PUNCT
ejpam-3459	288	28	;	;	PUNCT
ejpam-3459	288	29	h1(ω	h1(ω	PROPN
ejpam-3459	288	30	)	)	PUNCT
ejpam-3459	288	31	)	)	PUNCT
ejpam-3459	288	32	.	.	PUNCT
ejpam-3459	289	1	let	let	AUX
ejpam-3459	289	2	remark	remark	VERB
ejpam-3459	289	3	that	that	SCONJ
ejpam-3459	289	4	the	the	DET
ejpam-3459	289	5	system	system	NOUN
ejpam-3459	289	6	(	(	PUNCT
ejpam-3459	289	7	41	41	NUM
ejpam-3459	289	8	)	)	PUNCT
ejpam-3459	289	9	is	be	AUX
ejpam-3459	289	10	equivalent	equivalent	ADJ
ejpam-3459	289	11	to	to	ADP
ejpam-3459	289	12	the	the	DET
ejpam-3459	289	13	system	system	PROPN
ejpam-3459	289	14	−∂ρ1n	−∂ρ1n	PROPN
ejpam-3459	290	1	∂t	∂t	PROPN
ejpam-3459	290	2	−∆ρ1n	−∆ρ1n	PROPN
ejpam-3459	291	1	+	+	CCONJ
ejpam-3459	291	2	λ0ρ1n	λ0ρ1n	X
ejpam-3459	291	3	=	=	SYM
ejpam-3459	291	4	k	k	X
ejpam-3459	291	5	′1(ξn	′1(ξn	PROPN
ejpam-3459	291	6	)	)	PUNCT
ejpam-3459	291	7	in	in	ADP
ejpam-3459	291	8	qt	qt	NOUN
ejpam-3459	291	9	−∂ρ2n	−∂ρ2n	NOUN
ejpam-3459	292	1	∂t	∂t	PROPN
ejpam-3459	292	2	−∆ρ2n	−∆ρ2n	PROPN
ejpam-3459	292	3	+	+	CCONJ
ejpam-3459	292	4	λ0ρ2n	λ0ρ2n	PUNCT
ejpam-3459	292	5	=	=	SYM
ejpam-3459	292	6	k	k	PROPN
ejpam-3459	292	7	′2(ξn	′2(ξn	PROPN
ejpam-3459	292	8	)	)	PUNCT
ejpam-3459	293	1	in	in	ADP
ejpam-3459	293	2	qt	qt	NOUN
ejpam-3459	293	3	ρ1n	ρ1n	X
ejpam-3459	293	4	=	=	PUNCT
ejpam-3459	293	5	ρ2n	ρ2n	PUNCT
ejpam-3459	293	6	=	=	PUNCT
ejpam-3459	293	7	0	0	NUM
ejpam-3459	293	8	on	on	ADP
ejpam-3459	293	9	σt	σt	ADP
ejpam-3459	293	10	ρ1n(0	ρ1n(0	PROPN
ejpam-3459	293	11	,	,	PUNCT
ejpam-3459	293	12	x	x	NOUN
ejpam-3459	293	13	)	)	PUNCT
ejpam-3459	293	14	=	=	SYM
ejpam-3459	293	15	ρ2n(0	ρ2n(0	PROPN
ejpam-3459	293	16	,	,	PUNCT
ejpam-3459	293	17	x	x	NOUN
ejpam-3459	293	18	)	)	PUNCT
ejpam-3459	293	19	=	=	SYM
ejpam-3459	293	20	0	0	NUM
ejpam-3459	293	21	in	in	ADP
ejpam-3459	293	22	ω	ω	NUM
ejpam-3459	293	23	ρ1n(t	ρ1n(t	PROPN
ejpam-3459	293	24	,	,	PUNCT
ejpam-3459	293	25	x	x	X
ejpam-3459	293	26	)	)	PUNCT
ejpam-3459	293	27	=	=	SYM
ejpam-3459	293	28	ρ2n(t	ρ2n(t	PROPN
ejpam-3459	293	29	,	,	PUNCT
ejpam-3459	293	30	x	x	NOUN
ejpam-3459	293	31	)	)	PUNCT
ejpam-3459	293	32	=	=	SYM
ejpam-3459	293	33	0	0	NUM
ejpam-3459	293	34	in	in	ADP
ejpam-3459	293	35	ω	ω	PROPN
ejpam-3459	293	36	(	(	PUNCT
ejpam-3459	293	37	45	45	NUM
ejpam-3459	293	38	)	)	PUNCT
ejpam-3459	293	39	with	with	ADP
ejpam-3459	293	40	k	k	PROPN
ejpam-3459	293	41	′1	′1	PROPN
ejpam-3459	293	42	=	=	SYM
ejpam-3459	293	43	k1(ξn	k1(ξn	PROPN
ejpam-3459	293	44	)	)	PUNCT
ejpam-3459	294	1	−	−	NOUN
ejpam-3459	294	2	∫	∫	PROPN
ejpam-3459	294	3	a	a	DET
ejpam-3459	294	4	0	0	NUM
ejpam-3459	294	5	β1(µ1z̃1n	β1(µ1z̃1n	PROPN
ejpam-3459	294	6	+	+	CCONJ
ejpam-3459	294	7	µ2z̃2n)da	µ2z̃2n)da	ADJ
ejpam-3459	294	8	,	,	PUNCT
ejpam-3459	294	9	k	k	X
ejpam-3459	294	10	′2	′2	X
ejpam-3459	294	11	=	=	SYM
ejpam-3459	294	12	k2(ξn	k2(ξn	PROPN
ejpam-3459	294	13	)	)	PUNCT
ejpam-3459	294	14	−	−	NUM
ejpam-3459	295	1	∫	∫	PROPN
ejpam-3459	295	2	a	a	DET
ejpam-3459	295	3	0	0	NUM
ejpam-3459	295	4	β2(µ1z̃2n	β2(µ1z̃2n	PROPN
ejpam-3459	295	5	+	+	CCONJ
ejpam-3459	295	6	µ2z̃1n)da	µ2z̃1n)da	ADJ
ejpam-3459	295	7	and	and	CCONJ
ejpam-3459	295	8	(	(	PUNCT
ejpam-3459	295	9	45	45	NUM
ejpam-3459	295	10	)	)	PUNCT
ejpam-3459	295	11	is	be	AUX
ejpam-3459	295	12	a	a	DET
ejpam-3459	295	13	system	system	NOUN
ejpam-3459	295	14	of	of	ADP
ejpam-3459	295	15	retrograde	retrograde	ADJ
ejpam-3459	295	16	heat	heat	NOUN
ejpam-3459	295	17	equations	equation	NOUN
ejpam-3459	295	18	which	which	PRON
ejpam-3459	295	19	the	the	DET
ejpam-3459	295	20	source	source	NOUN
ejpam-3459	295	21	terms	term	NOUN
ejpam-3459	295	22	are	be	AUX
ejpam-3459	295	23	bounded	bound	VERB
ejpam-3459	295	24	in	in	ADP
ejpam-3459	295	25	l2(qt	l2(qt	PROPN
ejpam-3459	295	26	)	)	PUNCT
ejpam-3459	295	27	and	and	CCONJ
ejpam-3459	295	28	the	the	DET
ejpam-3459	295	29	distributions	distribution	NOUN
ejpam-3459	295	30	are	be	AUX
ejpam-3459	295	31	bounded	bound	VERB
ejpam-3459	295	32	in	in	ADP
ejpam-3459	295	33	l2((0	l2((0	PROPN
ejpam-3459	295	34	,	,	PUNCT
ejpam-3459	295	35	t	t	PROPN
ejpam-3459	295	36	)	)	PUNCT
ejpam-3459	295	37	;	;	PUNCT
ejpam-3459	295	38	h1(ω	h1(ω	PROPN
ejpam-3459	295	39	)	)	PUNCT
ejpam-3459	295	40	)	)	PUNCT
ejpam-3459	295	41	.	.	PUNCT
ejpam-3459	296	1	so	so	ADV
ejpam-3459	296	2	,	,	PUNCT
ejpam-3459	296	3	the	the	DET
ejpam-3459	296	4	sequences	sequence	NOUN
ejpam-3459	296	5	(	(	PUNCT
ejpam-3459	296	6	ρ1n	ρ1n	PROPN
ejpam-3459	296	7	∂t	∂t	PROPN
ejpam-3459	296	8	)	)	PUNCT
ejpam-3459	296	9	n	n	PROPN
ejpam-3459	296	10	and	and	CCONJ
ejpam-3459	296	11	(	(	PUNCT
ejpam-3459	296	12	ρ2n	ρ2n	PROPN
ejpam-3459	296	13	∂t	∂t	PROPN
ejpam-3459	296	14	)	)	PUNCT
ejpam-3459	296	15	n	n	CCONJ
ejpam-3459	296	16	are	be	AUX
ejpam-3459	296	17	bounded	bound	VERB
ejpam-3459	296	18	in	in	ADP
ejpam-3459	296	19	l2((0	l2((0	PROPN
ejpam-3459	296	20	,	,	PUNCT
ejpam-3459	296	21	t	t	PROPN
ejpam-3459	296	22	)	)	PUNCT
ejpam-3459	296	23	;	;	PUNCT
ejpam-3459	296	24	h−1(ω	h−1(ω	PROPN
ejpam-3459	296	25	)	)	PUNCT
ejpam-3459	296	26	)	)	PUNCT
ejpam-3459	296	27	.	.	PUNCT
ejpam-3459	297	1	thus	thus	ADV
ejpam-3459	297	2	,	,	PUNCT
ejpam-3459	297	3	we	we	PRON
ejpam-3459	297	4	deduct	deduct	VERB
ejpam-3459	297	5	from	from	ADP
ejpam-3459	297	6	aubin	aubin	PROPN
ejpam-3459	297	7	-	-	PUNCT
ejpam-3459	297	8	lions	lion	NOUN
ejpam-3459	297	9	lemma	lemma	PROPN
ejpam-3459	297	10	that	that	SCONJ
ejpam-3459	297	11	there	there	PRON
ejpam-3459	297	12	exists	exist	VERB
ejpam-3459	297	13	subsequences	subsequence	NOUN
ejpam-3459	297	14	(	(	PUNCT
ejpam-3459	297	15	ρ1nk	ρ1nk	X
ejpam-3459	297	16	)	)	PUNCT
ejpam-3459	297	17	k	k	NOUN
ejpam-3459	297	18	and	and	CCONJ
ejpam-3459	297	19	(	(	PUNCT
ejpam-3459	297	20	ρ2nk	ρ2nk	PUNCT
ejpam-3459	297	21	)	)	PUNCT
ejpam-3459	297	22	k	k	PROPN
ejpam-3459	297	23	of	of	ADP
ejpam-3459	297	24	(	(	PUNCT
ejpam-3459	297	25	ρ1n)n	ρ1n)n	PROPN
ejpam-3459	297	26	and	and	CCONJ
ejpam-3459	297	27	(	(	PUNCT
ejpam-3459	297	28	ρ2n)n	ρ2n)n	PROPN
ejpam-3459	297	29	respectively	respectively	ADV
ejpam-3459	297	30	that	that	PRON
ejpam-3459	297	31	converge	converge	VERB
ejpam-3459	297	32	strongly	strongly	ADV
ejpam-3459	297	33	towards	towards	ADP
ejpam-3459	297	34	ρ1	ρ1	NOUN
ejpam-3459	297	35	and	and	CCONJ
ejpam-3459	297	36	ρ2	ρ2	NOUN
ejpam-3459	297	37	respectively	respectively	ADV
ejpam-3459	297	38	in	in	ADP
ejpam-3459	297	39	l2(qt	l2(qt	PROPN
ejpam-3459	297	40	)	)	PUNCT
ejpam-3459	297	41	.	.	PUNCT
ejpam-3459	298	1	hence	hence	ADV
ejpam-3459	298	2	,	,	PUNCT
ejpam-3459	298	3	(	(	PUNCT
ejpam-3459	298	4	ρ1n)n	ρ1n)n	PROPN
ejpam-3459	298	5	and	and	CCONJ
ejpam-3459	298	6	(	(	PUNCT
ejpam-3459	298	7	ρ2n)n	ρ2n)n	PROPN
ejpam-3459	298	8	c.	c.	PROPN
ejpam-3459	298	9	k.	k.	PROPN
ejpam-3459	298	10	somé	somé	PROPN
ejpam-3459	298	11	,	,	PUNCT
ejpam-3459	298	12	s.	s.	PROPN
ejpam-3459	298	13	sawadogo	sawadogo	PROPN
ejpam-3459	298	14	/	/	SYM
ejpam-3459	298	15	eur	eur	PROPN
ejpam-3459	298	16	.	.	PUNCT
ejpam-3459	299	1	j.	j.	PROPN
ejpam-3459	299	2	pure	pure	PROPN
ejpam-3459	299	3	appl	appl	PROPN
ejpam-3459	299	4	.	.	PROPN
ejpam-3459	299	5	math	math	PROPN
ejpam-3459	299	6	,	,	PUNCT
ejpam-3459	299	7	12	12	NUM
ejpam-3459	299	8	(	(	PUNCT
ejpam-3459	299	9	3	3	NUM
ejpam-3459	299	10	)	)	PUNCT
ejpam-3459	299	11	(	(	PUNCT
ejpam-3459	299	12	2019	2019	NUM
ejpam-3459	299	13	)	)	PUNCT
ejpam-3459	299	14	,	,	PUNCT
ejpam-3459	299	15	870	870	NUM
ejpam-3459	299	16	-	-	SYM
ejpam-3459	299	17	892	892	NUM
ejpam-3459	299	18	882	882	NUM
ejpam-3459	299	19	converge	converge	NOUN
ejpam-3459	299	20	weakly	weakly	ADJ
ejpam-3459	299	21	towards	towards	ADP
ejpam-3459	299	22	ρ1	ρ1	NOUN
ejpam-3459	299	23	and	and	CCONJ
ejpam-3459	299	24	ρ2	ρ2	NOUN
ejpam-3459	299	25	respectively	respectively	ADV
ejpam-3459	299	26	in	in	ADP
ejpam-3459	299	27	l2(qt	l2(qt	PROPN
ejpam-3459	299	28	)	)	PUNCT
ejpam-3459	299	29	.	.	PUNCT
ejpam-3459	300	1	elsewhere	elsewhere	ADV
ejpam-3459	300	2	,	,	PUNCT
ejpam-3459	300	3	there	there	PRON
ejpam-3459	300	4	exists	exist	VERB
ejpam-3459	300	5	subsequences	subsequence	NOUN
ejpam-3459	300	6	(	(	PUNCT
ejpam-3459	300	7	z̃ink	z̃ink	NOUN
ejpam-3459	300	8	)	)	PUNCT
ejpam-3459	300	9	k	k	PROPN
ejpam-3459	300	10	of	of	ADP
ejpam-3459	300	11	z̃in	z̃in	PROPN
ejpam-3459	300	12	,	,	PUNCT
ejpam-3459	300	13	i	i	PRON
ejpam-3459	300	14	=	=	NOUN
ejpam-3459	300	15	1	1	NUM
ejpam-3459	300	16	,	,	PUNCT
ejpam-3459	300	17	2	2	NUM
ejpam-3459	300	18	associated	associate	VERB
ejpam-3459	300	19	to	to	ADP
ejpam-3459	300	20	(	(	PUNCT
ejpam-3459	300	21	ρink	ρink	INTJ
ejpam-3459	300	22	)	)	PUNCT
ejpam-3459	300	23	k	k	NOUN
ejpam-3459	300	24	,	,	PUNCT
ejpam-3459	300	25	i	i	PRON
ejpam-3459	300	26	=	=	NOUN
ejpam-3459	300	27	1	1	NUM
ejpam-3459	300	28	,	,	PUNCT
ejpam-3459	300	29	2	2	NUM
ejpam-3459	300	30	respectively	respectively	ADV
ejpam-3459	300	31	that	that	PRON
ejpam-3459	300	32	converge	converge	VERB
ejpam-3459	300	33	weakly	weakly	ADV
ejpam-3459	300	34	towards	towards	ADP
ejpam-3459	300	35	z̃i	z̃i	PROPN
ejpam-3459	300	36	,	,	PUNCT
ejpam-3459	300	37	i	i	PRON
ejpam-3459	300	38	=	=	NOUN
ejpam-3459	300	39	1	1	NUM
ejpam-3459	300	40	,	,	PUNCT
ejpam-3459	300	41	2	2	NUM
ejpam-3459	300	42	respectively	respectively	ADV
ejpam-3459	300	43	in	in	ADP
ejpam-3459	300	44	l2(u	l2(u	PROPN
ejpam-3459	300	45	;	;	PUNCT
ejpam-3459	300	46	h1(ω	h1(ω	PROPN
ejpam-3459	300	47	)	)	PUNCT
ejpam-3459	300	48	)	)	PUNCT
ejpam-3459	300	49	,	,	PUNCT
ejpam-3459	300	50	say	say	VERB
ejpam-3459	300	51	us	we	PRON
ejpam-3459	300	52	more	more	ADV
ejpam-3459	300	53	precisely	precisely	ADV
ejpam-3459	300	54	in	in	ADP
ejpam-3459	300	55	l2(q	l2(q	PROPN
ejpam-3459	300	56	)	)	PUNCT
ejpam-3459	300	57	,	,	PUNCT
ejpam-3459	300	58	since	since	ADV
ejpam-3459	300	59	,	,	PUNCT
ejpam-3459	300	60	l2(u	l2(u	PROPN
ejpam-3459	300	61	;	;	PUNCT
ejpam-3459	300	62	h1(ω	h1(ω	PROPN
ejpam-3459	300	63	)	)	PUNCT
ejpam-3459	300	64	)	)	PUNCT
ejpam-3459	301	1	⊂	⊂	PROPN
ejpam-3459	301	2	l2(q	l2(q	PROPN
ejpam-3459	301	3	)	)	PUNCT
ejpam-3459	301	4	.	.	PUNCT
ejpam-3459	302	1	thus	thus	ADV
ejpam-3459	302	2	,	,	PUNCT
ejpam-3459	302	3	we	we	PRON
ejpam-3459	302	4	have	have	AUX
ejpam-3459	302	5	firsly	firsly	ADV
ejpam-3459	302	6	ρink	ρink	ADJ
ejpam-3459	302	7	⇀	⇀	PROPN
ejpam-3459	303	1	ρi	ρi	INTJ
ejpam-3459	303	2	weakly	weakly	ADV
ejpam-3459	303	3	in	in	ADP
ejpam-3459	303	4	l2(qt	l2(qt	PROPN
ejpam-3459	303	5	)	)	PUNCT
ejpam-3459	304	1	i	i	PRON
ejpam-3459	304	2	=	=	NOUN
ejpam-3459	304	3	1	1	NUM
ejpam-3459	304	4	;	;	PUNCT
ejpam-3459	304	5	2	2	NUM
ejpam-3459	304	6	(	(	PUNCT
ejpam-3459	304	7	46	46	NUM
ejpam-3459	304	8	)	)	PUNCT
ejpam-3459	304	9	and	and	CCONJ
ejpam-3459	304	10	secondly	secondly	ADV
ejpam-3459	304	11	ρink	ρink	VERB
ejpam-3459	304	12	⇀	⇀	NUM
ejpam-3459	304	13	∫	∫	PROPN
ejpam-3459	304	14	a	a	DET
ejpam-3459	304	15	0	0	NUM
ejpam-3459	304	16	βiz̃ida	βiz̃ida	PRON
ejpam-3459	304	17	weakly	weakly	ADJ
ejpam-3459	304	18	in	in	ADP
ejpam-3459	304	19	l2(qt	l2(qt	PROPN
ejpam-3459	304	20	)	)	PUNCT
ejpam-3459	305	1	i	i	PRON
ejpam-3459	305	2	=	=	NOUN
ejpam-3459	305	3	1	1	NUM
ejpam-3459	305	4	;	;	PUNCT
ejpam-3459	305	5	2	2	NUM
ejpam-3459	305	6	,	,	PUNCT
ejpam-3459	305	7	(	(	PUNCT
ejpam-3459	305	8	47	47	NUM
ejpam-3459	305	9	)	)	PUNCT
ejpam-3459	305	10	then	then	ADV
ejpam-3459	305	11	,	,	PUNCT
ejpam-3459	305	12	from	from	ADP
ejpam-3459	305	13	the	the	DET
ejpam-3459	305	14	uniqueness	uniqueness	NOUN
ejpam-3459	305	15	of	of	ADP
ejpam-3459	305	16	the	the	DET
ejpam-3459	305	17	limit	limit	NOUN
ejpam-3459	305	18	,	,	PUNCT
ejpam-3459	305	19	for	for	ADP
ejpam-3459	305	20	all	all	PRON
ejpam-3459	305	21	i	i	PRON
ejpam-3459	305	22	∈	∈	PROPN
ejpam-3459	305	23	{	{	PUNCT
ejpam-3459	305	24	1	1	NUM
ejpam-3459	305	25	,	,	PUNCT
ejpam-3459	305	26	2	2	NUM
ejpam-3459	305	27	}	}	PUNCT
ejpam-3459	305	28	,	,	PUNCT
ejpam-3459	305	29	one	one	NUM
ejpam-3459	305	30	deducts	deduct	NOUN
ejpam-3459	305	31	that	that	PRON
ejpam-3459	305	32	ρi	ρi	VERB
ejpam-3459	305	33	=	=	SYM
ejpam-3459	305	34	∫	∫	PROPN
ejpam-3459	305	35	a	a	DET
ejpam-3459	305	36	0	0	NUM
ejpam-3459	305	37	βiz̃ida	βiz̃ida	PRON
ejpam-3459	305	38	.	.	PUNCT
ejpam-3459	306	1	(	(	PUNCT
ejpam-3459	306	2	48	48	NUM
ejpam-3459	306	3	)	)	PUNCT
ejpam-3459	306	4	similarly	similarly	ADV
ejpam-3459	306	5	,	,	PUNCT
ejpam-3459	306	6	we	we	PRON
ejpam-3459	306	7	can	can	AUX
ejpam-3459	306	8	prove	prove	VERB
ejpam-3459	306	9	that	that	SCONJ
ejpam-3459	306	10	(	(	PUNCT
ejpam-3459	306	11	ṽn)n	ṽn)n	NOUN
ejpam-3459	306	12	converges	converge	VERB
ejpam-3459	306	13	towards	towards	ADP
ejpam-3459	306	14	ṽ	ṽ	PROPN
ejpam-3459	306	15	∈	∈	PROPN
ejpam-3459	306	16	l2(qω	l2(qω	PROPN
ejpam-3459	306	17	)	)	PUNCT
ejpam-3459	306	18	.	.	PUNCT
ejpam-3459	307	1	moreover	moreover	ADV
ejpam-3459	307	2	,	,	PUNCT
ejpam-3459	307	3	(	(	PUNCT
ejpam-3459	307	4	z̃1	z̃1	X
ejpam-3459	307	5	,	,	PUNCT
ejpam-3459	307	6	z̃2	z̃2	NUM
ejpam-3459	307	7	)	)	PUNCT
ejpam-3459	307	8	verifies	verifie	NOUN
ejpam-3459	307	9	(	(	PUNCT
ejpam-3459	307	10	38	38	NUM
ejpam-3459	307	11	)	)	PUNCT
ejpam-3459	307	12	and	and	CCONJ
ejpam-3459	307	13	ṽ	ṽ	PROPN
ejpam-3459	307	14	satisfies	satisfie	NOUN
ejpam-3459	307	15	(	(	PUNCT
ejpam-3459	307	16	27	27	NUM
ejpam-3459	307	17	)	)	PUNCT
ejpam-3459	307	18	.	.	PUNCT
ejpam-3459	308	1	from	from	ADP
ejpam-3459	308	2	the	the	DET
ejpam-3459	308	3	theorem	theorem	ADJ
ejpam-3459	308	4	3	3	NUM
ejpam-3459	308	5	,	,	PUNCT
ejpam-3459	308	6	one	one	NUM
ejpam-3459	308	7	deducts	deduct	NOUN
ejpam-3459	308	8	that	that	PRON
ejpam-3459	308	9	z̃i	z̃i	PROPN
ejpam-3459	308	10	,	,	PUNCT
ejpam-3459	308	11	i	i	PRON
ejpam-3459	308	12	=	=	NOUN
ejpam-3459	308	13	1	1	NUM
ejpam-3459	308	14	;	;	PUNCT
ejpam-3459	308	15	2	2	NUM
ejpam-3459	308	16	satisfies	satisfie	NOUN
ejpam-3459	308	17	(	(	PUNCT
ejpam-3459	308	18	17	17	NUM
ejpam-3459	308	19	)	)	PUNCT
ejpam-3459	308	20	.	.	PUNCT
ejpam-3459	309	1	step	step	NOUN
ejpam-3459	309	2	4	4	NUM
ejpam-3459	309	3	:	:	PUNCT
ejpam-3459	309	4	λ	λ	NOUN
ejpam-3459	309	5	is	be	AUX
ejpam-3459	309	6	upper	upper	ADJ
ejpam-3459	309	7	semi	semi	ADJ
ejpam-3459	309	8	-	-	ADJ
ejpam-3459	309	9	continuous	continuous	ADJ
ejpam-3459	309	10	on	on	ADP
ejpam-3459	309	11	n	n	PROPN
ejpam-3459	309	12	.	.	PUNCT
ejpam-3459	310	1	let	let	VERB
ejpam-3459	310	2	k	k	PRON
ejpam-3459	310	3	be	be	AUX
ejpam-3459	310	4	a	a	DET
ejpam-3459	310	5	closed	closed	ADJ
ejpam-3459	310	6	subset	subset	NOUN
ejpam-3459	310	7	of	of	ADP
ejpam-3459	310	8	n	n	PROPN
ejpam-3459	310	9	.	.	PUNCT
ejpam-3459	311	1	let	let	VERB
ejpam-3459	311	2	(	(	PUNCT
ejpam-3459	311	3	k1n	k1n	NOUN
ejpam-3459	311	4	,	,	PUNCT
ejpam-3459	311	5	k2n)n	k2n)n	PROPN
ejpam-3459	311	6	⊂	⊂	PROPN
ejpam-3459	311	7	λ−1(k	λ−1(k	PROPN
ejpam-3459	311	8	)	)	PUNCT
ejpam-3459	311	9	that	that	PRON
ejpam-3459	311	10	converges	converge	VERB
ejpam-3459	311	11	strongly	strongly	ADV
ejpam-3459	311	12	towards	towards	ADP
ejpam-3459	311	13	(	(	PUNCT
ejpam-3459	311	14	k1	k1	X
ejpam-3459	311	15	,	,	PUNCT
ejpam-3459	311	16	k2	k2	NOUN
ejpam-3459	311	17	)	)	PUNCT
ejpam-3459	311	18	in	in	ADP
ejpam-3459	311	19	n	n	PROPN
ejpam-3459	311	20	.	.	PUNCT
ejpam-3459	312	1	then	then	ADV
ejpam-3459	312	2	,	,	PUNCT
ejpam-3459	312	3	(	(	PUNCT
ejpam-3459	312	4	k1n	k1n	NOUN
ejpam-3459	312	5	,	,	PUNCT
ejpam-3459	312	6	k2n)n	k2n)n	PROPN
ejpam-3459	312	7	is	be	AUX
ejpam-3459	312	8	bounded	bound	VERB
ejpam-3459	312	9	in	in	ADP
ejpam-3459	312	10	n	n	PROPN
ejpam-3459	312	11	.	.	PUNCT
ejpam-3459	313	1	since	since	SCONJ
ejpam-3459	313	2	λ−1(k	λ−1(k	PROPN
ejpam-3459	313	3	)	)	PUNCT
ejpam-3459	313	4	=	=	PRON
ejpam-3459	313	5	{	{	PUNCT
ejpam-3459	313	6	(	(	PUNCT
ejpam-3459	313	7	k1	k1	NOUN
ejpam-3459	313	8	,	,	PUNCT
ejpam-3459	313	9	k2	k2	ADJ
ejpam-3459	313	10	)	)	PUNCT
ejpam-3459	313	11	∈	∈	PROPN
ejpam-3459	313	12	k	k	X
ejpam-3459	313	13	:	:	PUNCT
ejpam-3459	313	14	λ(k1	λ(k1	ADJ
ejpam-3459	313	15	,	,	PUNCT
ejpam-3459	313	16	k2	k2	ADJ
ejpam-3459	313	17	)	)	PUNCT
ejpam-3459	313	18	∩k	∩k	NOUN
ejpam-3459	313	19	6=	6=	ADP
ejpam-3459	313	20	∅	∅	NOUN
ejpam-3459	313	21	}	}	PUNCT
ejpam-3459	313	22	,	,	PUNCT
ejpam-3459	313	23	there	there	PRON
ejpam-3459	313	24	exists	exist	VERB
ejpam-3459	313	25	,	,	PUNCT
ejpam-3459	313	26	a	a	DET
ejpam-3459	313	27	sequence	sequence	NOUN
ejpam-3459	313	28	(	(	PUNCT
ejpam-3459	313	29	ρ1n	ρ1n	INTJ
ejpam-3459	313	30	,	,	PUNCT
ejpam-3459	314	1	ρ2n)n	ρ2n)n	PROPN
ejpam-3459	314	2	∈	∈	PROPN
ejpam-3459	314	3	k	k	PROPN
ejpam-3459	314	4	that	that	PRON
ejpam-3459	314	5	belongs	belong	VERB
ejpam-3459	314	6	to	to	ADP
ejpam-3459	314	7	λ(k1n	λ(k1n	PROPN
ejpam-3459	314	8	,	,	PUNCT
ejpam-3459	314	9	k2n	k2n	PROPN
ejpam-3459	314	10	)	)	PUNCT
ejpam-3459	314	11	.	.	PUNCT
ejpam-3459	315	1	now	now	ADV
ejpam-3459	315	2	,	,	PUNCT
ejpam-3459	315	3	proceeding	proceed	VERB
ejpam-3459	315	4	as	as	ADP
ejpam-3459	315	5	in	in	ADP
ejpam-3459	315	6	the	the	DET
ejpam-3459	315	7	previous	previous	ADJ
ejpam-3459	315	8	step	step	NOUN
ejpam-3459	315	9	with	with	ADP
ejpam-3459	315	10	k	k	PROPN
ejpam-3459	315	11	instead	instead	ADV
ejpam-3459	315	12	of	of	ADP
ejpam-3459	315	13	b	b	NOUN
ejpam-3459	315	14	and	and	CCONJ
ejpam-3459	315	15	with	with	ADP
ejpam-3459	315	16	λ−1(k1n	λ−1(k1n	ADJ
ejpam-3459	315	17	,	,	PUNCT
ejpam-3459	315	18	k2n	k2n	PROPN
ejpam-3459	315	19	)	)	PUNCT
ejpam-3459	315	20	instead	instead	ADV
ejpam-3459	315	21	of	of	ADP
ejpam-3459	315	22	λ−1(ξ1	λ−1(ξ1	PRON
ejpam-3459	315	23	,	,	PUNCT
ejpam-3459	315	24	ξ2	ξ2	NOUN
ejpam-3459	315	25	)	)	PUNCT
ejpam-3459	315	26	,	,	PUNCT
ejpam-3459	315	27	one	one	PRON
ejpam-3459	315	28	deduces	deduce	VERB
ejpam-3459	315	29	that	that	SCONJ
ejpam-3459	315	30	there	there	PRON
ejpam-3459	315	31	exists	exist	VERB
ejpam-3459	315	32	subsequences	subsequence	NOUN
ejpam-3459	315	33	still	still	ADV
ejpam-3459	315	34	denoted	denote	VERB
ejpam-3459	315	35	by	by	ADP
ejpam-3459	315	36	(	(	PUNCT
ejpam-3459	315	37	ρ1n	ρ1n	INTJ
ejpam-3459	315	38	,	,	PUNCT
ejpam-3459	315	39	ρ2n	ρ2n	PROPN
ejpam-3459	315	40	)	)	PUNCT
ejpam-3459	315	41	and	and	CCONJ
ejpam-3459	315	42	(	(	PUNCT
ejpam-3459	315	43	ṽn	ṽn	PROPN
ejpam-3459	315	44	)	)	PUNCT
ejpam-3459	315	45	which	which	PRON
ejpam-3459	315	46	converge	converge	VERB
ejpam-3459	315	47	weakly	weakly	ADV
ejpam-3459	315	48	to	to	ADP
ejpam-3459	315	49	(	(	PUNCT
ejpam-3459	315	50	ρ1	ρ1	NOUN
ejpam-3459	315	51	,	,	PUNCT
ejpam-3459	315	52	ρ2	ρ2	NOUN
ejpam-3459	315	53	)	)	PUNCT
ejpam-3459	315	54	and	and	CCONJ
ejpam-3459	315	55	ṽ	ṽ	PROPN
ejpam-3459	315	56	respectively	respectively	ADV
ejpam-3459	315	57	in	in	ADP
ejpam-3459	315	58	n	n	NOUN
ejpam-3459	315	59	and	and	CCONJ
ejpam-3459	315	60	l2(qω	l2(qω	PROPN
ejpam-3459	315	61	)	)	PUNCT
ejpam-3459	315	62	,	,	PUNCT
ejpam-3459	315	63	and	and	CCONJ
ejpam-3459	315	64	for	for	ADP
ejpam-3459	315	65	all	all	PRON
ejpam-3459	315	66	i	i	PRON
ejpam-3459	315	67	∈	∈	PROPN
ejpam-3459	315	68	{	{	PUNCT
ejpam-3459	315	69	1	1	NUM
ejpam-3459	315	70	,	,	PUNCT
ejpam-3459	315	71	2	2	NUM
ejpam-3459	315	72	}	}	PUNCT
ejpam-3459	315	73	,	,	PUNCT
ejpam-3459	315	74	there	there	PRON
ejpam-3459	315	75	exists	exist	VERB
ejpam-3459	315	76	z̃i	z̃i	PROPN
ejpam-3459	315	77	∈	∈	PROPN
ejpam-3459	316	1	l2(u	l2(u	PROPN
ejpam-3459	316	2	,	,	PUNCT
ejpam-3459	316	3	h2(ω	h2(ω	NOUN
ejpam-3459	316	4	)	)	PUNCT
ejpam-3459	316	5	)	)	PUNCT
ejpam-3459	316	6	such	such	ADJ
ejpam-3459	316	7	that	that	SCONJ
ejpam-3459	316	8	ρin	ρin	NOUN
ejpam-3459	316	9	verifies	verifie	NOUN
ejpam-3459	316	10	(	(	PUNCT
ejpam-3459	316	11	47	47	NUM
ejpam-3459	316	12	)	)	PUNCT
ejpam-3459	316	13	.	.	PUNCT
ejpam-3459	317	1	so	so	ADV
ejpam-3459	317	2	,	,	PUNCT
ejpam-3459	317	3	for	for	ADP
ejpam-3459	317	4	all	all	PRON
ejpam-3459	317	5	i	i	PRON
ejpam-3459	317	6	∈	∈	PROPN
ejpam-3459	317	7	{	{	PUNCT
ejpam-3459	317	8	1	1	NUM
ejpam-3459	317	9	,	,	PUNCT
ejpam-3459	317	10	2	2	NUM
ejpam-3459	317	11	}	}	PUNCT
ejpam-3459	317	12	,	,	PUNCT
ejpam-3459	317	13	ρi	ρi	PROPN
ejpam-3459	317	14	verifies	verifie	NOUN
ejpam-3459	317	15	(	(	PUNCT
ejpam-3459	317	16	48	48	NUM
ejpam-3459	317	17	)	)	PUNCT
ejpam-3459	317	18	.	.	PUNCT
ejpam-3459	318	1	let	let	AUX
ejpam-3459	318	2	mention	mention	VERB
ejpam-3459	318	3	that	that	PRON
ejpam-3459	318	4	(	(	PUNCT
ejpam-3459	318	5	z̃1	z̃1	X
ejpam-3459	318	6	,	,	PUNCT
ejpam-3459	318	7	z̃2	z̃2	NUM
ejpam-3459	318	8	)	)	PUNCT
ejpam-3459	318	9	solves	solve	NOUN
ejpam-3459	318	10	(	(	PUNCT
ejpam-3459	318	11	38	38	NUM
ejpam-3459	318	12	)	)	PUNCT
ejpam-3459	318	13	,	,	PUNCT
ejpam-3459	318	14	ṽ	ṽ	PROPN
ejpam-3459	318	15	verifies	verifie	NOUN
ejpam-3459	318	16	(	(	PUNCT
ejpam-3459	318	17	27	27	NUM
ejpam-3459	318	18	)	)	PUNCT
ejpam-3459	318	19	and	and	CCONJ
ejpam-3459	318	20	z̃i	z̃i	VERB
ejpam-3459	318	21	i	i	NOUN
ejpam-3459	318	22	=	=	NOUN
ejpam-3459	318	23	1	1	NUM
ejpam-3459	318	24	,	,	PUNCT
ejpam-3459	318	25	2	2	NUM
ejpam-3459	318	26	satisfies	satisfie	NOUN
ejpam-3459	318	27	(	(	PUNCT
ejpam-3459	318	28	17	17	NUM
ejpam-3459	318	29	)	)	PUNCT
ejpam-3459	318	30	.	.	PUNCT
ejpam-3459	319	1	consequently	consequently	ADV
ejpam-3459	319	2	,	,	PUNCT
ejpam-3459	319	3	(	(	PUNCT
ejpam-3459	319	4	ρ1	ρ1	NOUN
ejpam-3459	319	5	,	,	PUNCT
ejpam-3459	319	6	ρ2	ρ2	NOUN
ejpam-3459	319	7	)	)	PUNCT
ejpam-3459	319	8	∈	∈	PROPN
ejpam-3459	319	9	λ(k1	λ(k1	PROPN
ejpam-3459	319	10	,	,	PUNCT
ejpam-3459	319	11	k2	k2	NOUN
ejpam-3459	319	12	)	)	PUNCT
ejpam-3459	319	13	(	(	PUNCT
ejpam-3459	319	14	49	49	NUM
ejpam-3459	319	15	)	)	PUNCT
ejpam-3459	319	16	from	from	ADP
ejpam-3459	319	17	(	(	PUNCT
ejpam-3459	319	18	43	43	NUM
ejpam-3459	319	19	)	)	PUNCT
ejpam-3459	319	20	,	,	PUNCT
ejpam-3459	319	21	(	(	PUNCT
ejpam-3459	319	22	44	44	NUM
ejpam-3459	319	23	)	)	PUNCT
ejpam-3459	319	24	and	and	CCONJ
ejpam-3459	319	25	lions	lion	NOUN
ejpam-3459	319	26	-	-	PUNCT
ejpam-3459	319	27	aubin	aubin	PROPN
ejpam-3459	319	28	lemma	lemma	PROPN
ejpam-3459	320	1	one	one	NUM
ejpam-3459	320	2	deduces	deduce	VERB
ejpam-3459	320	3	that	that	SCONJ
ejpam-3459	320	4	the	the	DET
ejpam-3459	320	5	subsequence	subsequence	NOUN
ejpam-3459	320	6	(	(	PUNCT
ejpam-3459	320	7	ρ1n	ρ1n	INTJ
ejpam-3459	320	8	,	,	PUNCT
ejpam-3459	320	9	ρ2n	ρ2n	PROPN
ejpam-3459	320	10	)	)	PUNCT
ejpam-3459	320	11	of	of	ADP
ejpam-3459	320	12	the	the	DET
ejpam-3459	320	13	closed	closed	ADJ
ejpam-3459	320	14	set	set	NOUN
ejpam-3459	320	15	k	k	NOUN
ejpam-3459	320	16	,	,	PUNCT
ejpam-3459	320	17	converges	converge	VERB
ejpam-3459	320	18	strongly	strongly	ADV
ejpam-3459	320	19	towards	towards	ADP
ejpam-3459	320	20	(	(	PUNCT
ejpam-3459	320	21	ρ1	ρ1	NOUN
ejpam-3459	320	22	,	,	PUNCT
ejpam-3459	320	23	ρ2	ρ2	NOUN
ejpam-3459	320	24	)	)	PUNCT
ejpam-3459	320	25	in	in	ADP
ejpam-3459	320	26	n	n	PROPN
ejpam-3459	320	27	.	.	PUNCT
ejpam-3459	321	1	then	then	ADV
ejpam-3459	321	2	,	,	PUNCT
ejpam-3459	321	3	(	(	PUNCT
ejpam-3459	321	4	ρ1	ρ1	NOUN
ejpam-3459	321	5	,	,	PUNCT
ejpam-3459	321	6	ρ2	ρ2	NOUN
ejpam-3459	321	7	)	)	PUNCT
ejpam-3459	321	8	∈	∈	PROPN
ejpam-3459	321	9	k.	k.	PROPN
ejpam-3459	321	10	(	(	PUNCT
ejpam-3459	321	11	50	50	NUM
ejpam-3459	321	12	)	)	PUNCT
ejpam-3459	321	13	(	(	PUNCT
ejpam-3459	321	14	49	49	NUM
ejpam-3459	321	15	)	)	PUNCT
ejpam-3459	321	16	and	and	CCONJ
ejpam-3459	321	17	(	(	PUNCT
ejpam-3459	321	18	50	50	NUM
ejpam-3459	321	19	)	)	PUNCT
ejpam-3459	321	20	say	say	VERB
ejpam-3459	321	21	that	that	SCONJ
ejpam-3459	321	22	(	(	PUNCT
ejpam-3459	321	23	k1	k1	X
ejpam-3459	321	24	,	,	PUNCT
ejpam-3459	321	25	k2	k2	ADJ
ejpam-3459	321	26	)	)	PUNCT
ejpam-3459	321	27	∈	∈	PROPN
ejpam-3459	321	28	λ−1(k	λ−1(k	PROPN
ejpam-3459	321	29	)	)	PUNCT
ejpam-3459	321	30	.	.	PUNCT
ejpam-3459	322	1	4	4	X
ejpam-3459	322	2	.	.	X
ejpam-3459	322	3	proof	proof	NOUN
ejpam-3459	322	4	of	of	ADP
ejpam-3459	322	5	the	the	DET
ejpam-3459	322	6	main	main	ADJ
ejpam-3459	322	7	result	result	NOUN
ejpam-3459	322	8	in	in	ADP
ejpam-3459	322	9	this	this	DET
ejpam-3459	322	10	section	section	NOUN
ejpam-3459	322	11	,	,	PUNCT
ejpam-3459	322	12	we	we	PRON
ejpam-3459	322	13	study	study	VERB
ejpam-3459	322	14	the	the	DET
ejpam-3459	322	15	controllability	controllability	NOUN
ejpam-3459	322	16	of	of	ADP
ejpam-3459	322	17	the	the	DET
ejpam-3459	322	18	(	(	PUNCT
ejpam-3459	322	19	8)-(9	8)-(9	NUM
ejpam-3459	322	20	)	)	PUNCT
ejpam-3459	322	21	.	.	PUNCT
ejpam-3459	323	1	in	in	ADP
ejpam-3459	323	2	view	view	NOUN
ejpam-3459	323	3	of	of	ADP
ejpam-3459	323	4	the	the	DET
ejpam-3459	323	5	above	above	ADJ
ejpam-3459	323	6	,	,	PUNCT
ejpam-3459	323	7	let	let	VERB
ejpam-3459	323	8	’s	’s	NOUN
ejpam-3459	323	9	set	set	VERB
ejpam-3459	323	10	for	for	ADP
ejpam-3459	323	11	any	any	PRON
ejpam-3459	324	1	ξ	ξ	PROPN
ejpam-3459	324	2	=	=	SYM
ejpam-3459	324	3	(	(	PUNCT
ejpam-3459	324	4	ξ1	ξ1	PROPN
ejpam-3459	324	5	,	,	PUNCT
ejpam-3459	324	6	ξ2	ξ2	ADJ
ejpam-3459	324	7	)	)	PUNCT
ejpam-3459	324	8	∈	∈	PROPN
ejpam-3459	324	9	l2(qt	l2(qt	PROPN
ejpam-3459	324	10	)	)	PUNCT
ejpam-3459	324	11	×	×	PROPN
ejpam-3459	324	12	l2(qt	l2(qt	PROPN
ejpam-3459	324	13	)	)	PUNCT
ejpam-3459	324	14	t1(ξ	t1(ξ	NUM
ejpam-3459	324	15	)	)	PUNCT
ejpam-3459	324	16	=	=	SYM
ejpam-3459	324	17	f	f	PROPN
ejpam-3459	324	18	(	(	PUNCT
ejpam-3459	324	19	ξ1	ξ1	PROPN
ejpam-3459	324	20	+	+	CCONJ
ejpam-3459	324	21	ξ2	ξ2	ADJ
ejpam-3459	324	22	)	)	PUNCT
ejpam-3459	324	23	;	;	PUNCT
ejpam-3459	324	24	t2(ξ	t2(ξ	X
ejpam-3459	324	25	)	)	PUNCT
ejpam-3459	324	26	=	=	NOUN
ejpam-3459	324	27	g(ξ1	g(ξ1	NOUN
ejpam-3459	324	28	−	−	PROPN
ejpam-3459	324	29	ξ2	ξ2	NOUN
ejpam-3459	324	30	)	)	PUNCT
ejpam-3459	324	31	,	,	PUNCT
ejpam-3459	324	32	g1(ξ	g1(ξ	NOUN
ejpam-3459	324	33	)	)	PUNCT
ejpam-3459	324	34	=	=	SYM
ejpam-3459	324	35	β1(t	β1(t	PROPN
ejpam-3459	324	36	,	,	PUNCT
ejpam-3459	324	37	a	a	PRON
ejpam-3459	324	38	,	,	PUNCT
ejpam-3459	324	39	x)t1(ξ	x)t1(ξ	NUM
ejpam-3459	324	40	)	)	PUNCT
ejpam-3459	324	41	+	+	CCONJ
ejpam-3459	324	42	β2(t	β2(t	PROPN
ejpam-3459	324	43	,	,	PUNCT
ejpam-3459	324	44	a	a	PRON
ejpam-3459	324	45	,	,	PUNCT
ejpam-3459	324	46	x)t2(ξ	x)t2(ξ	PROPN
ejpam-3459	324	47	)	)	PUNCT
ejpam-3459	324	48	,	,	PUNCT
ejpam-3459	324	49	g2(ξ	g2(ξ	X
ejpam-3459	324	50	)	)	PUNCT
ejpam-3459	324	51	=	=	SYM
ejpam-3459	324	52	β1(t	β1(t	PROPN
ejpam-3459	324	53	,	,	PUNCT
ejpam-3459	324	54	a	a	PRON
ejpam-3459	324	55	,	,	PUNCT
ejpam-3459	324	56	x)t1(ξ)−	x)t1(ξ)−	PROPN
ejpam-3459	324	57	β2(t	β2(t	PROPN
ejpam-3459	324	58	,	,	PUNCT
ejpam-3459	324	59	a	a	PRON
ejpam-3459	324	60	,	,	PUNCT
ejpam-3459	324	61	x)t2(ξ	x)t2(ξ	PROPN
ejpam-3459	324	62	)	)	PUNCT
ejpam-3459	324	63	.	.	PUNCT
ejpam-3459	325	1	(	(	PUNCT
ejpam-3459	325	2	51	51	NUM
ejpam-3459	325	3	)	)	PUNCT
ejpam-3459	325	4	c.	c.	PROPN
ejpam-3459	325	5	k.	k.	PROPN
ejpam-3459	325	6	somé	somé	PROPN
ejpam-3459	325	7	,	,	PUNCT
ejpam-3459	325	8	s.	s.	PROPN
ejpam-3459	325	9	sawadogo	sawadogo	PROPN
ejpam-3459	325	10	/	/	SYM
ejpam-3459	325	11	eur	eur	PROPN
ejpam-3459	325	12	.	.	PUNCT
ejpam-3459	326	1	j.	j.	PROPN
ejpam-3459	326	2	pure	pure	PROPN
ejpam-3459	326	3	appl	appl	PROPN
ejpam-3459	326	4	.	.	PROPN
ejpam-3459	326	5	math	math	PROPN
ejpam-3459	326	6	,	,	PUNCT
ejpam-3459	326	7	12	12	NUM
ejpam-3459	326	8	(	(	PUNCT
ejpam-3459	326	9	3	3	NUM
ejpam-3459	326	10	)	)	PUNCT
ejpam-3459	326	11	(	(	PUNCT
ejpam-3459	326	12	2019	2019	NUM
ejpam-3459	326	13	)	)	PUNCT
ejpam-3459	326	14	,	,	PUNCT
ejpam-3459	326	15	870	870	NUM
ejpam-3459	326	16	-	-	SYM
ejpam-3459	326	17	892	892	NUM
ejpam-3459	326	18	883	883	NUM
ejpam-3459	326	19	now	now	ADV
ejpam-3459	326	20	,	,	PUNCT
ejpam-3459	326	21	we	we	PRON
ejpam-3459	326	22	consider	consider	VERB
ejpam-3459	326	23	the	the	DET
ejpam-3459	326	24	system	system	NOUN
ejpam-3459	326	25	that	that	PRON
ejpam-3459	326	26	follows	follows	PROPN
ejpam-3459	326	27	−∂p̂1ε	−∂p̂1ε	PROPN
ejpam-3459	327	1	∂t	∂t	PROPN
ejpam-3459	327	2	−	−	PROPN
ejpam-3459	327	3	∂p̂1ε	∂p̂1ε	PROPN
ejpam-3459	327	4	∂a	∂a	PROPN
ejpam-3459	327	5	−∆p̂1ε	−∆p̂1ε	NOUN
ejpam-3459	327	6	+	+	CCONJ
ejpam-3459	328	1	µ̃1p̂1ε	µ̃1p̂1ε	PROPN
ejpam-3459	328	2	+	+	CCONJ
ejpam-3459	328	3	µ2p̂2ε	µ2p̂2ε	PROPN
ejpam-3459	328	4	=	=	PROPN
ejpam-3459	328	5	g1(ξ)p̂1ε(t	g1(ξ)p̂1ε(t	NOUN
ejpam-3459	328	6	,	,	PUNCT
ejpam-3459	328	7	0	0	NUM
ejpam-3459	328	8	,	,	PUNCT
ejpam-3459	328	9	x	x	PRON
ejpam-3459	328	10	)	)	PUNCT
ejpam-3459	328	11	+	+	CCONJ
ejpam-3459	328	12	f̂	f̂	NUM
ejpam-3459	328	13	+	+	CCONJ
ejpam-3459	328	14	v̂εχω	v̂εχω	VERB
ejpam-3459	328	15	+	+	ADJ
ejpam-3459	328	16	g2(ξ)p̂2ε(t	g2(ξ)p̂2ε(t	NOUN
ejpam-3459	328	17	,	,	PUNCT
ejpam-3459	328	18	0	0	NUM
ejpam-3459	328	19	,	,	PUNCT
ejpam-3459	328	20	x	x	NOUN
ejpam-3459	328	21	)	)	PUNCT
ejpam-3459	328	22	in	in	ADP
ejpam-3459	328	23	q	q	NOUN
ejpam-3459	328	24	,	,	PUNCT
ejpam-3459	328	25	−∂p̂2ε	−∂p̂2ε	VERB
ejpam-3459	328	26	∂t	∂t	PROPN
ejpam-3459	328	27	−	−	PROPN
ejpam-3459	328	28	∂p̂2ε	∂p̂2ε	PROPN
ejpam-3459	328	29	∂a	∂a	PROPN
ejpam-3459	328	30	−∆p̂2ε	−∆p̂2ε	NOUN
ejpam-3459	328	31	+	+	CCONJ
ejpam-3459	328	32	µ̃1p̂2ε	µ̃1p̂2ε	PROPN
ejpam-3459	328	33	+	+	CCONJ
ejpam-3459	328	34	µ2p̂1ε	µ2p̂1ε	PROPN
ejpam-3459	328	35	=	=	SYM
ejpam-3459	328	36	g2(ξ)p̂1ε(t	g2(ξ)p̂1ε(t	NOUN
ejpam-3459	328	37	,	,	PUNCT
ejpam-3459	328	38	0	0	NUM
ejpam-3459	328	39	,	,	PUNCT
ejpam-3459	328	40	x	x	X
ejpam-3459	328	41	)	)	PUNCT
ejpam-3459	328	42	+	+	NOUN
ejpam-3459	328	43	g1(ξ)p̂2ε(t	g1(ξ)p̂2ε(t	NOUN
ejpam-3459	328	44	,	,	PUNCT
ejpam-3459	328	45	0	0	NUM
ejpam-3459	328	46	,	,	PUNCT
ejpam-3459	328	47	x	x	NOUN
ejpam-3459	328	48	)	)	PUNCT
ejpam-3459	328	49	in	in	ADP
ejpam-3459	328	50	q	q	NOUN
ejpam-3459	328	51	,	,	PUNCT
ejpam-3459	328	52	p̂1ε	p̂1ε	NOUN
ejpam-3459	328	53	=	=	SYM
ejpam-3459	328	54	p̂2ε	p̂2ε	ADJ
ejpam-3459	328	55	=	=	SYM
ejpam-3459	328	56	0	0	NUM
ejpam-3459	328	57	on	on	ADP
ejpam-3459	328	58	σ	σ	PROPN
ejpam-3459	328	59	,	,	PUNCT
ejpam-3459	328	60	p̂1ε(t	p̂1ε(t	PROPN
ejpam-3459	328	61	,	,	PUNCT
ejpam-3459	328	62	a	a	PRON
ejpam-3459	328	63	,	,	PUNCT
ejpam-3459	328	64	x	x	NOUN
ejpam-3459	328	65	)	)	PUNCT
ejpam-3459	328	66	=	=	SYM
ejpam-3459	328	67	p̂2ε(t	p̂2ε(t	PROPN
ejpam-3459	328	68	,	,	PUNCT
ejpam-3459	328	69	a	a	PRON
ejpam-3459	328	70	,	,	PUNCT
ejpam-3459	328	71	x	x	NOUN
ejpam-3459	328	72	)	)	PUNCT
ejpam-3459	328	73	=	=	SYM
ejpam-3459	328	74	0	0	NUM
ejpam-3459	329	1	in	in	ADP
ejpam-3459	329	2	qa	qa	PROPN
ejpam-3459	329	3	,	,	PUNCT
ejpam-3459	329	4	p̂1ε(t	p̂1ε(t	PROPN
ejpam-3459	329	5	,	,	PUNCT
ejpam-3459	329	6	a	a	PRON
ejpam-3459	329	7	,	,	PUNCT
ejpam-3459	329	8	x	x	NOUN
ejpam-3459	329	9	)	)	PUNCT
ejpam-3459	329	10	=	=	SYM
ejpam-3459	329	11	p̂2ε(t	p̂2ε(t	PROPN
ejpam-3459	329	12	,	,	PUNCT
ejpam-3459	329	13	a	a	PRON
ejpam-3459	329	14	,	,	PUNCT
ejpam-3459	329	15	x	x	NOUN
ejpam-3459	329	16	)	)	PUNCT
ejpam-3459	329	17	=	=	SYM
ejpam-3459	329	18	0	0	NUM
ejpam-3459	330	1	in	in	ADP
ejpam-3459	330	2	qt	qt	NOUN
ejpam-3459	330	3	,	,	PUNCT
ejpam-3459	330	4	(	(	PUNCT
ejpam-3459	330	5	52	52	NUM
ejpam-3459	330	6	)	)	PUNCT
ejpam-3459	330	7	where	where	SCONJ
ejpam-3459	330	8	:	:	PUNCT
ejpam-3459	330	9	p̂iε	p̂iε	VERB
ejpam-3459	330	10	=	=	SYM
ejpam-3459	330	11	e−λ0tpiε	e−λ0tpiε	NOUN
ejpam-3459	330	12	,	,	PUNCT
ejpam-3459	330	13	i	i	PRON
ejpam-3459	330	14	=	=	NOUN
ejpam-3459	330	15	1	1	NUM
ejpam-3459	330	16	;	;	PUNCT
ejpam-3459	330	17	2	2	NUM
ejpam-3459	330	18	,	,	PUNCT
ejpam-3459	330	19	f̂	f̂	NUM
ejpam-3459	330	20	=	=	SYM
ejpam-3459	330	21	e−λ0tf	e−λ0tf	PROPN
ejpam-3459	330	22	,	,	PUNCT
ejpam-3459	330	23	µ̃1	µ̃1	NOUN
ejpam-3459	330	24	=	=	SYM
ejpam-3459	330	25	µ̃1	µ̃1	NOUN
ejpam-3459	330	26	+	+	CCONJ
ejpam-3459	330	27	λ0	λ0	NOUN
ejpam-3459	330	28	and	and	CCONJ
ejpam-3459	330	29	v̂ε	v̂ε	NOUN
ejpam-3459	330	30	=	=	PUNCT
ejpam-3459	330	31	e−λ0tvε	e−λ0tvε	PROPN
ejpam-3459	330	32	for	for	ADP
ejpam-3459	330	33	any	any	DET
ejpam-3459	330	34	λ0	λ0	NOUN
ejpam-3459	330	35	≥	≥	NOUN
ejpam-3459	330	36	0	0	NUM
ejpam-3459	330	37	with	with	ADP
ejpam-3459	330	38	(	(	PUNCT
ejpam-3459	330	39	p1ε	p1ε	PROPN
ejpam-3459	330	40	,	,	PUNCT
ejpam-3459	330	41	p2ε	p2ε	PROPN
ejpam-3459	330	42	)	)	PUNCT
ejpam-3459	330	43	a	a	DET
ejpam-3459	330	44	solution	solution	NOUN
ejpam-3459	330	45	of	of	ADP
ejpam-3459	330	46	(	(	PUNCT
ejpam-3459	330	47	8)	8)	NUM
ejpam-3459	330	48	associated	associate	VERB
ejpam-3459	330	49	to	to	PART
ejpam-3459	330	50	vε	vε	VERB
ejpam-3459	330	51	.	.	PUNCT
ejpam-3459	331	1	the	the	DET
ejpam-3459	331	2	controllability	controllability	NOUN
ejpam-3459	331	3	of	of	ADP
ejpam-3459	331	4	the	the	DET
ejpam-3459	331	5	system	system	NOUN
ejpam-3459	331	6	(	(	PUNCT
ejpam-3459	331	7	8)	8)	NUM
ejpam-3459	331	8	-(9	-(9	NOUN
ejpam-3459	331	9	)	)	PUNCT
ejpam-3459	331	10	is	be	AUX
ejpam-3459	331	11	summarized	summarize	VERB
ejpam-3459	331	12	in	in	ADP
ejpam-3459	331	13	the	the	DET
ejpam-3459	331	14	study	study	NOUN
ejpam-3459	331	15	of	of	ADP
ejpam-3459	331	16	the	the	DET
ejpam-3459	331	17	null	null	ADJ
ejpam-3459	331	18	controllability	controllability	NOUN
ejpam-3459	331	19	of	of	ADP
ejpam-3459	331	20	system	system	NOUN
ejpam-3459	331	21	(	(	PUNCT
ejpam-3459	331	22	52	52	NUM
ejpam-3459	331	23	)	)	PUNCT
ejpam-3459	331	24	.	.	PUNCT
ejpam-3459	332	1	we	we	PRON
ejpam-3459	332	2	consider	consider	VERB
ejpam-3459	332	3	the	the	DET
ejpam-3459	332	4	operator	operator	NOUN
ejpam-3459	332	5	λ̂	λ̂	NUM
ejpam-3459	332	6	from	from	ADP
ejpam-3459	332	7	n	n	PROPN
ejpam-3459	332	8	=	=	SYM
ejpam-3459	332	9	l2(qt	l2(qt	PROPN
ejpam-3459	332	10	)	)	PUNCT
ejpam-3459	332	11	×	×	PROPN
ejpam-3459	332	12	l2(qt	l2(qt	PROPN
ejpam-3459	332	13	)	)	PUNCT
ejpam-3459	332	14	into	into	ADP
ejpam-3459	332	15	2n	2n	NUM
ejpam-3459	332	16	defined	define	VERB
ejpam-3459	332	17	by	by	ADP
ejpam-3459	332	18	(	(	PUNCT
ejpam-3459	332	19	ξ1	ξ1	NOUN
ejpam-3459	332	20	,	,	PUNCT
ejpam-3459	332	21	ξ2	ξ2	ADJ
ejpam-3459	332	22	)	)	PUNCT
ejpam-3459	332	23	7−→	7−→	NOUN
ejpam-3459	332	24	λ̂(ξ1	λ̂(ξ1	NOUN
ejpam-3459	332	25	,	,	PUNCT
ejpam-3459	332	26	ξ2	ξ2	NOUN
ejpam-3459	332	27	)	)	PUNCT
ejpam-3459	333	1	=	=	PUNCT
ejpam-3459	334	1	λξ2(ξ1)×	λξ2(ξ1)×	X
ejpam-3459	334	2	λξ1(ξ2	λξ1(ξ2	NOUN
ejpam-3459	334	3	)	)	PUNCT
ejpam-3459	334	4	(	(	PUNCT
ejpam-3459	334	5	53	53	NUM
ejpam-3459	334	6	)	)	PUNCT
ejpam-3459	334	7	such	such	ADJ
ejpam-3459	334	8	that	that	SCONJ
ejpam-3459	334	9	λξ2(ξ1	λξ2(ξ1	NOUN
ejpam-3459	334	10	)	)	PUNCT
ejpam-3459	334	11	=	=	SYM
ejpam-3459	334	12	{	{	PUNCT
ejpam-3459	334	13	∫	∫	PROPN
ejpam-3459	334	14	a	a	DET
ejpam-3459	334	15	0	0	NUM
ejpam-3459	334	16	β1	β1	NOUN
ejpam-3459	334	17	(	(	PUNCT
ejpam-3459	334	18	p̂1ε(ξ1	p̂1ε(ξ1	PROPN
ejpam-3459	334	19	)	)	PUNCT
ejpam-3459	334	20	+	+	NUM
ejpam-3459	334	21	p̂2ε(ξ2	p̂2ε(ξ2	NOUN
ejpam-3459	334	22	)	)	PUNCT
ejpam-3459	334	23	)	)	PUNCT
ejpam-3459	334	24	da	da	NOUN
ejpam-3459	334	25	}	}	PUNCT
ejpam-3459	334	26	λξ1(ξ2	λξ1(ξ2	NOUN
ejpam-3459	334	27	)	)	PUNCT
ejpam-3459	334	28	=	=	PRON
ejpam-3459	335	1	{	{	PUNCT
ejpam-3459	335	2	∫	∫	PROPN
ejpam-3459	335	3	a	a	DET
ejpam-3459	335	4	0	0	NUM
ejpam-3459	335	5	β2	β2	NOUN
ejpam-3459	335	6	(	(	PUNCT
ejpam-3459	335	7	p̂1ε(ξ1)−	p̂1ε(ξ1)−	NOUN
ejpam-3459	335	8	p̂2ε(ξ2	p̂2ε(ξ2	NOUN
ejpam-3459	335	9	)	)	PUNCT
ejpam-3459	335	10	)	)	PUNCT
ejpam-3459	335	11	da	da	NOUN
ejpam-3459	335	12	}	}	PUNCT
ejpam-3459	335	13	where	where	SCONJ
ejpam-3459	335	14	(	(	PUNCT
ejpam-3459	335	15	p̂1ε(ξ1	p̂1ε(ξ1	NOUN
ejpam-3459	335	16	)	)	PUNCT
ejpam-3459	335	17	,	,	PUNCT
ejpam-3459	335	18	p̂2ε(ξ2	p̂2ε(ξ2	NOUN
ejpam-3459	335	19	)	)	PUNCT
ejpam-3459	335	20	)	)	PUNCT
ejpam-3459	335	21	solves	solve	NOUN
ejpam-3459	335	22	(	(	PUNCT
ejpam-3459	335	23	52	52	NUM
ejpam-3459	335	24	)	)	PUNCT
ejpam-3459	335	25	,	,	PUNCT
ejpam-3459	335	26	verifies	verifie	NOUN
ejpam-3459	335	27	(	(	PUNCT
ejpam-3459	335	28	28)-(29	28)-(29	NOUN
ejpam-3459	335	29	)	)	PUNCT
ejpam-3459	335	30	and	and	CCONJ
ejpam-3459	335	31	the	the	DET
ejpam-3459	335	32	associated	associated	ADJ
ejpam-3459	335	33	control	control	NOUN
ejpam-3459	335	34	v̂ε	v̂ε	X
ejpam-3459	335	35	satisfies	satisfie	NOUN
ejpam-3459	335	36	(	(	PUNCT
ejpam-3459	335	37	27	27	NUM
ejpam-3459	335	38	)	)	PUNCT
ejpam-3459	335	39	.	.	PUNCT
ejpam-3459	336	1	the	the	DET
ejpam-3459	336	2	controllability	controllability	NOUN
ejpam-3459	336	3	of	of	ADP
ejpam-3459	336	4	(	(	PUNCT
ejpam-3459	336	5	52	52	NUM
ejpam-3459	336	6	)	)	PUNCT
ejpam-3459	336	7	is	be	AUX
ejpam-3459	336	8	summarized	summarize	VERB
ejpam-3459	336	9	to	to	ADP
ejpam-3459	336	10	the	the	DET
ejpam-3459	336	11	study	study	NOUN
ejpam-3459	336	12	of	of	ADP
ejpam-3459	336	13	the	the	DET
ejpam-3459	336	14	existence	existence	NOUN
ejpam-3459	336	15	of	of	ADP
ejpam-3459	336	16	a	a	DET
ejpam-3459	336	17	fixed	fix	VERB
ejpam-3459	336	18	point	point	NOUN
ejpam-3459	336	19	of	of	ADP
ejpam-3459	336	20	the	the	DET
ejpam-3459	336	21	mapping	mapping	NOUN
ejpam-3459	336	22	λ̂	λ̂	X
ejpam-3459	337	1	[	[	X
ejpam-3459	337	2	8	8	NUM
ejpam-3459	337	3	]	]	PUNCT
ejpam-3459	337	4	.	.	PUNCT
ejpam-3459	338	1	we	we	PRON
ejpam-3459	338	2	are	be	AUX
ejpam-3459	338	3	going	go	VERB
ejpam-3459	338	4	to	to	PART
ejpam-3459	338	5	show	show	VERB
ejpam-3459	338	6	that	that	SCONJ
ejpam-3459	338	7	λ̂	λ̂	PRON
ejpam-3459	338	8	admits	admit	VERB
ejpam-3459	338	9	a	a	DET
ejpam-3459	338	10	fixed	fixed	ADJ
ejpam-3459	338	11	point	point	NOUN
ejpam-3459	338	12	.	.	PUNCT
ejpam-3459	339	1	to	to	PART
ejpam-3459	339	2	do	do	VERB
ejpam-3459	339	3	that	that	PRON
ejpam-3459	339	4	,	,	PUNCT
ejpam-3459	339	5	we	we	PRON
ejpam-3459	339	6	have	have	VERB
ejpam-3459	339	7	to	to	PART
ejpam-3459	339	8	demonstrate	demonstrate	VERB
ejpam-3459	339	9	that	that	SCONJ
ejpam-3459	339	10	for	for	ADP
ejpam-3459	339	11	each	each	DET
ejpam-3459	339	12	(	(	PUNCT
ejpam-3459	339	13	ξ1	ξ1	NOUN
ejpam-3459	339	14	,	,	PUNCT
ejpam-3459	339	15	ξ2	ξ2	ADJ
ejpam-3459	339	16	)	)	PUNCT
ejpam-3459	339	17	∈	∈	PROPN
ejpam-3459	339	18	n	n	NOUN
ejpam-3459	339	19	,	,	PUNCT
ejpam-3459	339	20	λξ2(ξ1	λξ2(ξ1	ADJ
ejpam-3459	339	21	)	)	PUNCT
ejpam-3459	339	22	and	and	CCONJ
ejpam-3459	339	23	λξ1(ξ2	λξ1(ξ2	NUM
ejpam-3459	339	24	)	)	PUNCT
ejpam-3459	339	25	are	be	AUX
ejpam-3459	339	26	bounbed	bounbe	VERB
ejpam-3459	339	27	closed	closed	ADJ
ejpam-3459	339	28	convex	convex	NOUN
ejpam-3459	339	29	sets	set	NOUN
ejpam-3459	339	30	in	in	ADP
ejpam-3459	339	31	l2(qt	l2(qt	PROPN
ejpam-3459	339	32	)	)	PUNCT
ejpam-3459	339	33	and	and	CCONJ
ejpam-3459	339	34	λ̂(ξ1	λ̂(ξ1	NOUN
ejpam-3459	339	35	,	,	PUNCT
ejpam-3459	339	36	ξ2	ξ2	NOUN
ejpam-3459	339	37	)	)	PUNCT
ejpam-3459	339	38	is	be	AUX
ejpam-3459	339	39	upper	upper	ADJ
ejpam-3459	339	40	semicontinuous	semicontinuous	NOUN
ejpam-3459	339	41	.	.	PUNCT
ejpam-3459	340	1	let	let	AUX
ejpam-3459	340	2	set	set	VERB
ejpam-3459	340	3	y1(ξ)(t	y1(ξ)(t	PROPN
ejpam-3459	340	4	,	,	PUNCT
ejpam-3459	340	5	x	x	X
ejpam-3459	340	6	)	)	PUNCT
ejpam-3459	341	1	=	=	SYM
ejpam-3459	341	2	∫	∫	PROPN
ejpam-3459	341	3	a	a	DET
ejpam-3459	341	4	0	0	NUM
ejpam-3459	341	5	β1p̂1ε(ξ1)da+	β1p̂1ε(ξ1)da+	NUM
ejpam-3459	341	6	∫	∫	PROPN
ejpam-3459	341	7	a	a	DET
ejpam-3459	341	8	0	0	NUM
ejpam-3459	341	9	β1p̂2ε(ξ2)da	β1p̂2ε(ξ2)da	ADJ
ejpam-3459	341	10	(	(	PUNCT
ejpam-3459	341	11	54	54	NUM
ejpam-3459	341	12	)	)	PUNCT
ejpam-3459	341	13	y2(ξ)(t	y2(ξ)(t	PROPN
ejpam-3459	341	14	,	,	PUNCT
ejpam-3459	341	15	x	x	X
ejpam-3459	341	16	)	)	PUNCT
ejpam-3459	341	17	=	=	SYM
ejpam-3459	342	1	∫	∫	PROPN
ejpam-3459	342	2	a	a	DET
ejpam-3459	342	3	0	0	NUM
ejpam-3459	342	4	β2p̂1ε(ξ1)da−	β2p̂1ε(ξ1)da−	NUM
ejpam-3459	342	5	∫	∫	PROPN
ejpam-3459	342	6	a	a	DET
ejpam-3459	342	7	0	0	NUM
ejpam-3459	342	8	β2p̂2ε(ξ2)da	β2p̂2ε(ξ2)da	NOUN
ejpam-3459	342	9	(	(	PUNCT
ejpam-3459	342	10	55	55	NUM
ejpam-3459	342	11	)	)	PUNCT
ejpam-3459	342	12	proceeding	proceed	VERB
ejpam-3459	342	13	as	as	ADP
ejpam-3459	342	14	in	in	ADP
ejpam-3459	342	15	the	the	DET
ejpam-3459	342	16	step	step	NOUN
ejpam-3459	342	17	2	2	NUM
ejpam-3459	342	18	of	of	ADP
ejpam-3459	342	19	the	the	DET
ejpam-3459	342	20	proof	proof	NOUN
ejpam-3459	342	21	of	of	ADP
ejpam-3459	342	22	the	the	DET
ejpam-3459	342	23	proposition	proposition	NOUN
ejpam-3459	342	24	3	3	NUM
ejpam-3459	342	25	,	,	PUNCT
ejpam-3459	342	26	one	one	NUM
ejpam-3459	342	27	deducts	deduct	NOUN
ejpam-3459	342	28	from	from	ADP
ejpam-3459	342	29	(	(	PUNCT
ejpam-3459	342	30	41)-(42	41)-(42	ADV
ejpam-3459	342	31	)	)	PUNCT
ejpam-3459	342	32	that	that	PRON
ejpam-3459	342	33	yi(ξ	yi(ξ	PUNCT
ejpam-3459	342	34	)	)	PUNCT
ejpam-3459	342	35	,	,	PUNCT
ejpam-3459	342	36	i	i	PRON
ejpam-3459	342	37	=	=	NOUN
ejpam-3459	342	38	1	1	NUM
ejpam-3459	342	39	;	;	PUNCT
ejpam-3459	342	40	2	2	NUM
ejpam-3459	342	41	verify	verify	VERB
ejpam-3459	342	42	for	for	ADP
ejpam-3459	342	43	any	any	DET
ejpam-3459	342	44	positive	positive	ADJ
ejpam-3459	342	45	real	real	ADJ
ejpam-3459	342	46	λ0	λ0	NOUN
ejpam-3459	342	47	the	the	DET
ejpam-3459	342	48	following	follow	VERB
ejpam-3459	342	49	system	system	NOUN
ejpam-3459	342	50	:	:	PUNCT
ejpam-3459	342	51			NOUN
ejpam-3459	342	52	−∂yi(ξ	−∂yi(ξ	ADV
ejpam-3459	342	53	)	)	PUNCT
ejpam-3459	343	1	∂t	∂t	PROPN
ejpam-3459	343	2	−∆yi(ξ	−∆yi(ξ	X
ejpam-3459	343	3	)	)	PUNCT
ejpam-3459	344	1	+	+	CCONJ
ejpam-3459	344	2	λ0yi	λ0yi	X
ejpam-3459	344	3	=	=	SYM
ejpam-3459	344	4	ri(ξ	ri(ξ	NOUN
ejpam-3459	344	5	)	)	PUNCT
ejpam-3459	344	6	in	in	ADP
ejpam-3459	344	7	qt	qt	NOUN
ejpam-3459	344	8	yi(ξ	yi(ξ	PUNCT
ejpam-3459	344	9	)	)	PUNCT
ejpam-3459	345	1	=	=	SYM
ejpam-3459	345	2	0	0	NUM
ejpam-3459	346	1	on	on	ADP
ejpam-3459	346	2	σt	σt	ADP
ejpam-3459	346	3	yi(ξ)(0	yi(ξ)(0	PROPN
ejpam-3459	346	4	,	,	PUNCT
ejpam-3459	346	5	x	x	X
ejpam-3459	346	6	)	)	PUNCT
ejpam-3459	346	7	=	=	SYM
ejpam-3459	346	8	0	0	NUM
ejpam-3459	347	1	in	in	ADP
ejpam-3459	347	2	ω	ω	PROPN
ejpam-3459	347	3	(	(	PUNCT
ejpam-3459	347	4	56	56	NUM
ejpam-3459	347	5	)	)	PUNCT
ejpam-3459	347	6	c.	c.	PROPN
ejpam-3459	347	7	k.	k.	PROPN
ejpam-3459	347	8	somé	somé	PROPN
ejpam-3459	347	9	,	,	PUNCT
ejpam-3459	347	10	s.	s.	PROPN
ejpam-3459	347	11	sawadogo	sawadogo	PROPN
ejpam-3459	347	12	/	/	SYM
ejpam-3459	347	13	eur	eur	PROPN
ejpam-3459	347	14	.	.	PUNCT
ejpam-3459	348	1	j.	j.	PROPN
ejpam-3459	348	2	pure	pure	PROPN
ejpam-3459	348	3	appl	appl	PROPN
ejpam-3459	348	4	.	.	PROPN
ejpam-3459	348	5	math	math	PROPN
ejpam-3459	348	6	,	,	PUNCT
ejpam-3459	348	7	12	12	NUM
ejpam-3459	348	8	(	(	PUNCT
ejpam-3459	348	9	3	3	NUM
ejpam-3459	348	10	)	)	PUNCT
ejpam-3459	348	11	(	(	PUNCT
ejpam-3459	348	12	2019	2019	NUM
ejpam-3459	348	13	)	)	PUNCT
ejpam-3459	348	14	,	,	PUNCT
ejpam-3459	348	15	870	870	NUM
ejpam-3459	348	16	-	-	SYM
ejpam-3459	348	17	892	892	NUM
ejpam-3459	348	18	884	884	NUM
ejpam-3459	348	19	where	where	SCONJ
ejpam-3459	348	20	r1(ξ	r1(ξ	NOUN
ejpam-3459	348	21	)	)	PUNCT
ejpam-3459	348	22	=	=	PUNCT
ejpam-3459	349	1	−	−	PROPN
ejpam-3459	349	2	∫	∫	PROPN
ejpam-3459	349	3	a	a	PRON
ejpam-3459	349	4	0	0	NUM
ejpam-3459	349	5	(	(	PUNCT
ejpam-3459	349	6	∂β1	∂β1	ADP
ejpam-3459	349	7	∂t	∂t	PROPN
ejpam-3459	349	8	+	+	CCONJ
ejpam-3459	349	9	∂β1	∂β1	PROPN
ejpam-3459	350	1	∂a	∂a	NOUN
ejpam-3459	350	2	+	+	CCONJ
ejpam-3459	350	3	∆β1	∆β1	X
ejpam-3459	350	4	+	+	CCONJ
ejpam-3459	350	5	(	(	PUNCT
ejpam-3459	350	6	µ1	µ1	PROPN
ejpam-3459	350	7	+	+	CCONJ
ejpam-3459	350	8	µ2)β1	µ2)β1	NOUN
ejpam-3459	350	9	)	)	PUNCT
ejpam-3459	350	10	(	(	PUNCT
ejpam-3459	350	11	p̂1ε(ξ1	p̂1ε(ξ1	NOUN
ejpam-3459	350	12	)	)	PUNCT
ejpam-3459	350	13	+	+	NOUN
ejpam-3459	350	14	p̂2ε(ξ2))da	p̂2ε(ξ2))da	PROPN
ejpam-3459	351	1	+	+	NUM
ejpam-3459	351	2	∫	∫	PROPN
ejpam-3459	351	3	a	a	DET
ejpam-3459	351	4	0	0	NUM
ejpam-3459	351	5	β1(g1(ξ)p̂1ε(ξ1)(t	β1(g1(ξ)p̂1ε(ξ1)(t	NOUN
ejpam-3459	351	6	,	,	PUNCT
ejpam-3459	351	7	0	0	NUM
ejpam-3459	351	8	,	,	PUNCT
ejpam-3459	351	9	x	x	X
ejpam-3459	351	10	)	)	PUNCT
ejpam-3459	352	1	+	+	SYM
ejpam-3459	352	2	g2(ξ)p̂2ε(ξ2)(t	g2(ξ)p̂2ε(ξ2)(t	PROPN
ejpam-3459	352	3	,	,	PUNCT
ejpam-3459	352	4	0	0	NUM
ejpam-3459	352	5	,	,	PUNCT
ejpam-3459	352	6	x	x	PRON
ejpam-3459	352	7	)	)	PUNCT
ejpam-3459	352	8	+	+	CCONJ
ejpam-3459	352	9	f̂	f̂	NUM
ejpam-3459	352	10	+	+	CCONJ
ejpam-3459	352	11	v̂εχω)da	v̂εχω)da	PROPN
ejpam-3459	352	12	+	+	CCONJ
ejpam-3459	352	13	∫	∫	PROPN
ejpam-3459	352	14	a	a	DET
ejpam-3459	352	15	0	0	NUM
ejpam-3459	352	16	β2	β2	NOUN
ejpam-3459	352	17	(	(	PUNCT
ejpam-3459	352	18	g2(ξ)p̂1ε(ξ1)(t	g2(ξ)p̂1ε(ξ1)(t	PROPN
ejpam-3459	352	19	,	,	PUNCT
ejpam-3459	352	20	0	0	NUM
ejpam-3459	352	21	,	,	PUNCT
ejpam-3459	352	22	x	x	X
ejpam-3459	352	23	)	)	PUNCT
ejpam-3459	353	1	+	+	PROPN
ejpam-3459	353	2	g1(ξ)p̂2ε(ξ2)(t	g1(ξ)p̂2ε(ξ2)(t	NOUN
ejpam-3459	353	3	,	,	PUNCT
ejpam-3459	353	4	0	0	NUM
ejpam-3459	353	5	,	,	PUNCT
ejpam-3459	353	6	x	x	NOUN
ejpam-3459	353	7	)	)	PUNCT
ejpam-3459	353	8	)	)	PUNCT
ejpam-3459	354	1	da	da	NOUN
ejpam-3459	354	2	−	−	NOUN
ejpam-3459	354	3	2	2	NUM
ejpam-3459	354	4	n∑	n∑	NOUN
ejpam-3459	354	5	i=1	i=1	PROPN
ejpam-3459	355	1	∫	∫	PROPN
ejpam-3459	355	2	a	a	DET
ejpam-3459	355	3	0	0	NUM
ejpam-3459	355	4	∂β1	∂β1	NOUN
ejpam-3459	355	5	∂xi	∂xi	NOUN
ejpam-3459	355	6	.	.	PUNCT
ejpam-3459	356	1	(	(	PUNCT
ejpam-3459	356	2	∂p̂1ε	∂p̂1ε	X
ejpam-3459	356	3	∂xi	∂xi	PROPN
ejpam-3459	356	4	+	+	CCONJ
ejpam-3459	356	5	∂p̂2ε	∂p̂2ε	PROPN
ejpam-3459	356	6	∂xi	∂xi	PROPN
ejpam-3459	356	7	)	)	PUNCT
ejpam-3459	356	8	da	da	PROPN
ejpam-3459	356	9	r2(ξ	r2(ξ	NOUN
ejpam-3459	356	10	)	)	PUNCT
ejpam-3459	356	11	=	=	VERB
ejpam-3459	357	1	∫	∫	PROPN
ejpam-3459	358	1	a	a	PRON
ejpam-3459	358	2	0	0	NUM
ejpam-3459	359	1	(	(	PUNCT
ejpam-3459	359	2	∂β2	∂β2	ADJ
ejpam-3459	359	3	∂t	∂t	PROPN
ejpam-3459	359	4	+	+	CCONJ
ejpam-3459	360	1	∂β2	∂β2	ADJ
ejpam-3459	360	2	∂a	∂a	NOUN
ejpam-3459	360	3	+	+	NUM
ejpam-3459	360	4	∆β2	∆β2	PROPN
ejpam-3459	360	5	+	+	CCONJ
ejpam-3459	360	6	β2(µ1	β2(µ1	NOUN
ejpam-3459	360	7	−	−	NOUN
ejpam-3459	360	8	µ2	µ2	PROPN
ejpam-3459	360	9	)	)	PUNCT
ejpam-3459	360	10	)	)	PUNCT
ejpam-3459	361	1	(	(	PUNCT
ejpam-3459	361	2	p̂1ε(ξ1)−	p̂1ε(ξ1)−	NOUN
ejpam-3459	361	3	p̂2ε(ξ2))da	p̂2ε(ξ2))da	PROPN
ejpam-3459	361	4	+	+	NUM
ejpam-3459	361	5	∫	∫	PROPN
ejpam-3459	361	6	a	a	DET
ejpam-3459	361	7	0	0	NUM
ejpam-3459	361	8	β2(g1(ξ)p̂1ε(t	β2(g1(ξ)p̂1ε(t	NOUN
ejpam-3459	361	9	,	,	PUNCT
ejpam-3459	361	10	0	0	NUM
ejpam-3459	361	11	,	,	PUNCT
ejpam-3459	361	12	x	x	X
ejpam-3459	361	13	)	)	PUNCT
ejpam-3459	361	14	+	+	NOUN
ejpam-3459	361	15	g2(ξ)p̂2ε(t	g2(ξ)p̂2ε(t	NOUN
ejpam-3459	361	16	,	,	PUNCT
ejpam-3459	361	17	0	0	NUM
ejpam-3459	361	18	,	,	PUNCT
ejpam-3459	361	19	x	x	PRON
ejpam-3459	361	20	)	)	PUNCT
ejpam-3459	361	21	+	+	CCONJ
ejpam-3459	361	22	f̂	f̂	NUM
ejpam-3459	361	23	+	+	CCONJ
ejpam-3459	361	24	v̂εχω)da	v̂εχω)da	PROPN
ejpam-3459	361	25	−	−	PROPN
ejpam-3459	361	26	∫	∫	PROPN
ejpam-3459	361	27	a	a	DET
ejpam-3459	361	28	0	0	NUM
ejpam-3459	361	29	β2	β2	NOUN
ejpam-3459	361	30	(	(	PUNCT
ejpam-3459	361	31	g2(ξ)p̂1ε(t	g2(ξ)p̂1ε(t	NOUN
ejpam-3459	361	32	,	,	PUNCT
ejpam-3459	361	33	0	0	NUM
ejpam-3459	361	34	,	,	PUNCT
ejpam-3459	361	35	x	x	X
ejpam-3459	361	36	)	)	PUNCT
ejpam-3459	361	37	+	+	NOUN
ejpam-3459	361	38	g1(ξ)p̂2ε(t	g1(ξ)p̂2ε(t	NOUN
ejpam-3459	361	39	,	,	PUNCT
ejpam-3459	361	40	0	0	NUM
ejpam-3459	361	41	,	,	PUNCT
ejpam-3459	361	42	x	x	NOUN
ejpam-3459	361	43	)	)	PUNCT
ejpam-3459	361	44	)	)	PUNCT
ejpam-3459	361	45	da	da	NOUN
ejpam-3459	361	46	−	−	NOUN
ejpam-3459	361	47	2	2	NUM
ejpam-3459	361	48	n∑	n∑	NOUN
ejpam-3459	362	1	i=1	i=1	PROPN
ejpam-3459	363	1	∫	∫	PROPN
ejpam-3459	364	1	a	a	DET
ejpam-3459	364	2	0	0	NUM
ejpam-3459	364	3	∂β2	∂β2	ADJ
ejpam-3459	364	4	∂xi	∂xi	NOUN
ejpam-3459	364	5	.	.	PUNCT
ejpam-3459	365	1	(	(	PUNCT
ejpam-3459	365	2	∂p̂1ε	∂p̂1ε	X
ejpam-3459	365	3	∂xi	∂xi	PROPN
ejpam-3459	365	4	−	−	PROPN
ejpam-3459	365	5	∂p̂2ε	∂p̂2ε	SYM
ejpam-3459	365	6	∂xi	∂xi	PROPN
ejpam-3459	365	7	)	)	PUNCT
ejpam-3459	365	8	da	da	PROPN
ejpam-3459	365	9	.	.	PUNCT
ejpam-3459	366	1	under	under	ADP
ejpam-3459	366	2	the	the	DET
ejpam-3459	366	3	hypothesis	hypothesis	NOUN
ejpam-3459	366	4	(	(	PUNCT
ejpam-3459	366	5	h1	h1	PROPN
ejpam-3459	366	6	)	)	PUNCT
ejpam-3459	366	7	−	−	PROPN
ejpam-3459	366	8	(	(	PUNCT
ejpam-3459	366	9	h4	h4	PROPN
ejpam-3459	366	10	)	)	PUNCT
ejpam-3459	366	11	,	,	PUNCT
ejpam-3459	366	12	taking	take	VERB
ejpam-3459	366	13	λ0	λ0	NOUN
ejpam-3459	366	14	as	as	ADP
ejpam-3459	366	15	in	in	ADP
ejpam-3459	366	16	the	the	DET
ejpam-3459	366	17	proof	proof	NOUN
ejpam-3459	366	18	of	of	ADP
ejpam-3459	366	19	the	the	DET
ejpam-3459	366	20	theorem	theorem	NOUN
ejpam-3459	366	21	1	1	NUM
ejpam-3459	366	22	,	,	PUNCT
ejpam-3459	366	23	one	one	NUM
ejpam-3459	366	24	deducts	deduct	NOUN
ejpam-3459	366	25	from	from	ADP
ejpam-3459	366	26	(	(	PUNCT
ejpam-3459	366	27	27	27	NUM
ejpam-3459	366	28	)	)	PUNCT
ejpam-3459	366	29	,	,	PUNCT
ejpam-3459	366	30	(	(	PUNCT
ejpam-3459	366	31	34)-(37	34)-(37	NUM
ejpam-3459	366	32	)	)	PUNCT
ejpam-3459	366	33	that	that	SCONJ
ejpam-3459	366	34	there	there	PRON
ejpam-3459	366	35	exists	exist	VERB
ejpam-3459	366	36	a	a	DET
ejpam-3459	366	37	positive	positive	ADJ
ejpam-3459	366	38	reals	real	NOUN
ejpam-3459	366	39	c1	c1	NOUN
ejpam-3459	366	40	,	,	PUNCT
ejpam-3459	366	41	c2	c2	PROPN
ejpam-3459	366	42	which	which	PRON
ejpam-3459	366	43	depend	depend	VERB
ejpam-3459	366	44	on	on	ADP
ejpam-3459	366	45	‖β1	‖β1	PROPN
ejpam-3459	366	46	,	,	PUNCT
ejpam-3459	366	47	β2‖∞	β2‖∞	PROPN
ejpam-3459	366	48	,	,	PUNCT
ejpam-3459	366	49	‖f	‖f	ADJ
ejpam-3459	366	50	,	,	PUNCT
ejpam-3459	366	51	g‖∞	g‖∞	NOUN
ejpam-3459	366	52	and	and	CCONJ
ejpam-3459	366	53	‖µ1	‖µ1	NOUN
ejpam-3459	366	54	,	,	PUNCT
ejpam-3459	366	55	µ2‖∞	µ2‖∞	NOUN
ejpam-3459	366	56	such	such	ADJ
ejpam-3459	366	57	that	that	SCONJ
ejpam-3459	366	58	‖r1(ξ)‖2∞	‖r1(ξ)‖2∞	PROPN
ejpam-3459	366	59	≤	≤	PROPN
ejpam-3459	366	60	c1	c1	PROPN
ejpam-3459	366	61	(	(	PUNCT
ejpam-3459	366	62	‖θf‖2l2(qω	‖θf‖2l2(qω	NOUN
ejpam-3459	366	63	)	)	PUNCT
ejpam-3459	366	64	+	+	CCONJ
ejpam-3459	366	65	‖f‖2q	‖f‖2q	PROPN
ejpam-3459	366	66	)	)	PUNCT
ejpam-3459	366	67	(	(	PUNCT
ejpam-3459	366	68	57	57	NUM
ejpam-3459	366	69	)	)	PUNCT
ejpam-3459	366	70	‖r2(ξ)‖2∞	‖r2(ξ)‖2∞	NOUN
ejpam-3459	366	71	≤	≤	PROPN
ejpam-3459	366	72	c2	c2	PROPN
ejpam-3459	366	73	(	(	PUNCT
ejpam-3459	366	74	‖θf‖2l2(qω	‖θf‖2l2(qω	NOUN
ejpam-3459	366	75	)	)	PUNCT
ejpam-3459	366	76	+	+	PROPN
ejpam-3459	366	77	‖f‖2q	‖f‖2q	PROPN
ejpam-3459	366	78	)	)	PUNCT
ejpam-3459	366	79	.	.	PUNCT
ejpam-3459	367	1	(	(	PUNCT
ejpam-3459	367	2	58	58	X
ejpam-3459	367	3	)	)	PUNCT
ejpam-3459	367	4	multiplying	multiply	VERB
ejpam-3459	367	5	respectively	respectively	ADV
ejpam-3459	367	6	the	the	DET
ejpam-3459	367	7	first	first	ADJ
ejpam-3459	367	8	equation	equation	NOUN
ejpam-3459	367	9	of	of	ADP
ejpam-3459	367	10	(	(	PUNCT
ejpam-3459	367	11	56	56	NUM
ejpam-3459	367	12	)	)	PUNCT
ejpam-3459	367	13	by	by	ADP
ejpam-3459	367	14	yi(ξ	yi(ξ	NOUN
ejpam-3459	367	15	)	)	PUNCT
ejpam-3459	367	16	,	,	PUNCT
ejpam-3459	367	17	i	i	PRON
ejpam-3459	367	18	=	=	NOUN
ejpam-3459	367	19	1	1	NUM
ejpam-3459	367	20	;	;	PUNCT
ejpam-3459	367	21	2	2	NUM
ejpam-3459	367	22	and	and	CCONJ
ejpam-3459	367	23	by	by	ADP
ejpam-3459	367	24	integrating	integrate	VERB
ejpam-3459	367	25	by	by	ADP
ejpam-3459	367	26	parts	part	NOUN
ejpam-3459	367	27	over	over	ADP
ejpam-3459	367	28	qt	qt	NOUN
ejpam-3459	367	29	,	,	PUNCT
ejpam-3459	367	30	we	we	PRON
ejpam-3459	367	31	show	show	VERB
ejpam-3459	367	32	(	(	PUNCT
ejpam-3459	367	33	using	use	VERB
ejpam-3459	367	34	young	young	PROPN
ejpam-3459	367	35	’s	’s	PART
ejpam-3459	367	36	inequality	inequality	NOUN
ejpam-3459	367	37	as	as	ADP
ejpam-3459	367	38	in	in	ADP
ejpam-3459	367	39	the	the	DET
ejpam-3459	367	40	step	step	NOUN
ejpam-3459	367	41	2	2	NUM
ejpam-3459	367	42	of	of	ADP
ejpam-3459	367	43	the	the	DET
ejpam-3459	367	44	proof	proof	NOUN
ejpam-3459	367	45	of	of	ADP
ejpam-3459	367	46	the	the	DET
ejpam-3459	367	47	proposition	proposition	NOUN
ejpam-3459	367	48	3	3	NUM
ejpam-3459	367	49	)	)	PUNCT
ejpam-3459	367	50	that	that	SCONJ
ejpam-3459	367	51	yi	yi	PROPN
ejpam-3459	367	52	,	,	PUNCT
ejpam-3459	367	53	i	i	PRON
ejpam-3459	367	54	=	=	NOUN
ejpam-3459	367	55	1	1	NUM
ejpam-3459	367	56	;	;	PUNCT
ejpam-3459	367	57	2	2	NUM
ejpam-3459	367	58	are	be	AUX
ejpam-3459	367	59	bounded	bound	VERB
ejpam-3459	367	60	in	in	ADP
ejpam-3459	367	61	l2(0	l2(0	PROPN
ejpam-3459	367	62	,	,	PUNCT
ejpam-3459	367	63	t	t	PROPN
ejpam-3459	367	64	;	;	PUNCT
ejpam-3459	367	65	h1	h1	PROPN
ejpam-3459	367	66	0	0	NUM
ejpam-3459	367	67	(	(	PUNCT
ejpam-3459	367	68	ω	ω	NOUN
ejpam-3459	367	69	)	)	PUNCT
ejpam-3459	367	70	)	)	PUNCT
ejpam-3459	367	71	.	.	PUNCT
ejpam-3459	368	1	thus	thus	ADV
ejpam-3459	368	2	,	,	PUNCT
ejpam-3459	368	3	for	for	ADP
ejpam-3459	368	4	each	each	DET
ejpam-3459	368	5	i	i	PRON
ejpam-3459	368	6	∈	∈	PROPN
ejpam-3459	368	7	{	{	PUNCT
ejpam-3459	368	8	1	1	NUM
ejpam-3459	368	9	;	;	PUNCT
ejpam-3459	368	10	2	2	NUM
ejpam-3459	368	11	}	}	PUNCT
ejpam-3459	368	12	,	,	PUNCT
ejpam-3459	368	13	the	the	DET
ejpam-3459	368	14	system	system	NOUN
ejpam-3459	368	15	(	(	PUNCT
ejpam-3459	368	16	56	56	NUM
ejpam-3459	368	17	)	)	PUNCT
ejpam-3459	368	18	is	be	AUX
ejpam-3459	368	19	a	a	DET
ejpam-3459	368	20	retrograde	retrograde	ADJ
ejpam-3459	368	21	heat	heat	NOUN
ejpam-3459	368	22	equation	equation	NOUN
ejpam-3459	368	23	with	with	ADP
ejpam-3459	368	24	the	the	DET
ejpam-3459	368	25	source	source	NOUN
ejpam-3459	368	26	term	term	NOUN
ejpam-3459	368	27	and	and	CCONJ
ejpam-3459	368	28	the	the	DET
ejpam-3459	368	29	initial	initial	ADJ
ejpam-3459	368	30	condition	condition	NOUN
ejpam-3459	368	31	are	be	AUX
ejpam-3459	368	32	bounded	bound	VERB
ejpam-3459	368	33	respectively	respectively	ADV
ejpam-3459	368	34	in	in	ADP
ejpam-3459	368	35	l2(qt	l2(qt	PROPN
ejpam-3459	368	36	)	)	PUNCT
ejpam-3459	368	37	and	and	CCONJ
ejpam-3459	368	38	l2(q	l2(q	PROPN
ejpam-3459	368	39	)	)	PUNCT
ejpam-3459	368	40	.	.	PUNCT
ejpam-3459	369	1	moreover	moreover	ADV
ejpam-3459	369	2	,	,	PUNCT
ejpam-3459	369	3	yi	yi	NOUN
ejpam-3459	369	4	,	,	PUNCT
ejpam-3459	369	5	∂yi(ξ	∂yi(ξ	PROPN
ejpam-3459	369	6	)	)	PUNCT
ejpam-3459	370	1	∂t	∂t	PROPN
ejpam-3459	370	2	i	i	NOUN
ejpam-3459	370	3	=	=	NOUN
ejpam-3459	370	4	1	1	NUM
ejpam-3459	370	5	,	,	PUNCT
ejpam-3459	370	6	2	2	NUM
ejpam-3459	370	7	are	be	AUX
ejpam-3459	370	8	bounded	bound	VERB
ejpam-3459	370	9	respectively	respectively	ADV
ejpam-3459	370	10	in	in	ADP
ejpam-3459	370	11	l2(0	l2(0	NOUN
ejpam-3459	370	12	,	,	PUNCT
ejpam-3459	370	13	t	t	NOUN
ejpam-3459	370	14	;	;	PUNCT
ejpam-3459	370	15	h1	h1	PROPN
ejpam-3459	370	16	0	0	NUM
ejpam-3459	370	17	(	(	PUNCT
ejpam-3459	370	18	ω	ω	NOUN
ejpam-3459	370	19	)	)	PUNCT
ejpam-3459	370	20	)	)	PUNCT
ejpam-3459	370	21	and	and	CCONJ
ejpam-3459	370	22	l2(0	l2(0	PROPN
ejpam-3459	370	23	,	,	PUNCT
ejpam-3459	370	24	t	t	PROPN
ejpam-3459	370	25	;	;	PUNCT
ejpam-3459	370	26	h−1(ω	h−1(ω	PROPN
ejpam-3459	370	27	)	)	PUNCT
ejpam-3459	370	28	)	)	PUNCT
ejpam-3459	370	29	.	.	PUNCT
ejpam-3459	371	1	consequently	consequently	ADV
ejpam-3459	371	2	,	,	PUNCT
ejpam-3459	371	3	we	we	PRON
ejpam-3459	371	4	conclude	conclude	VERB
ejpam-3459	371	5	,	,	PUNCT
ejpam-3459	371	6	thanks	thank	NOUN
ejpam-3459	371	7	to	to	ADP
ejpam-3459	371	8	lions	lion	NOUN
ejpam-3459	371	9	-	-	PUNCT
ejpam-3459	371	10	aubin	aubin	PROPN
ejpam-3459	371	11	lemma	lemma	PROPN
ejpam-3459	371	12	,	,	PUNCT
ejpam-3459	371	13	that	that	SCONJ
ejpam-3459	371	14	λξi	λξi	VERB
ejpam-3459	371	15	i	i	NOUN
ejpam-3459	371	16	=	=	NOUN
ejpam-3459	371	17	1	1	NUM
ejpam-3459	371	18	,	,	PUNCT
ejpam-3459	371	19	2	2	NUM
ejpam-3459	371	20	are	be	AUX
ejpam-3459	371	21	bounded	bound	VERB
ejpam-3459	371	22	and	and	CCONJ
ejpam-3459	371	23	compact	compact	ADJ
ejpam-3459	371	24	in	in	ADP
ejpam-3459	371	25	l2(qt	l2(qt	PROPN
ejpam-3459	371	26	)	)	PUNCT
ejpam-3459	371	27	.	.	PUNCT
ejpam-3459	372	1	thus	thus	ADV
ejpam-3459	372	2	,	,	PUNCT
ejpam-3459	372	3	λ̂	λ̂	X
ejpam-3459	372	4	is	be	AUX
ejpam-3459	372	5	bounded	bound	VERB
ejpam-3459	372	6	and	and	CCONJ
ejpam-3459	372	7	compact	compact	ADJ
ejpam-3459	372	8	in	in	ADP
ejpam-3459	372	9	n	n	PROPN
ejpam-3459	372	10	.	.	PUNCT
ejpam-3459	373	1	now	now	ADV
ejpam-3459	373	2	,	,	PUNCT
ejpam-3459	373	3	let	let	VERB
ejpam-3459	373	4	k	k	PROPN
ejpam-3459	373	5	a	a	DET
ejpam-3459	373	6	closed	closed	ADJ
ejpam-3459	373	7	subset	subset	NOUN
ejpam-3459	373	8	of	of	ADP
ejpam-3459	373	9	n	n	PROPN
ejpam-3459	373	10	.	.	PUNCT
ejpam-3459	374	1	let	let	VERB
ejpam-3459	374	2	(	(	PUNCT
ejpam-3459	374	3	ξ1n	ξ1n	ADJ
ejpam-3459	374	4	,	,	PUNCT
ejpam-3459	374	5	ξ2n)n	ξ2n)n	PROPN
ejpam-3459	374	6	⊂	⊂	ADJ
ejpam-3459	374	7	λ̂−1(k	λ̂−1(k	PROPN
ejpam-3459	374	8	)	)	PUNCT
ejpam-3459	374	9	that	that	PRON
ejpam-3459	374	10	converges	converge	VERB
ejpam-3459	374	11	strongly	strongly	ADV
ejpam-3459	374	12	towards	towards	ADP
ejpam-3459	374	13	(	(	PUNCT
ejpam-3459	374	14	ξ1	ξ1	NOUN
ejpam-3459	374	15	,	,	PUNCT
ejpam-3459	374	16	ξ2	ξ2	NOUN
ejpam-3459	374	17	)	)	PUNCT
ejpam-3459	374	18	in	in	ADP
ejpam-3459	374	19	n	n	PROPN
ejpam-3459	374	20	.	.	PUNCT
ejpam-3459	375	1	then	then	ADV
ejpam-3459	375	2	,	,	PUNCT
ejpam-3459	375	3	(	(	PUNCT
ejpam-3459	375	4	(	(	PUNCT
ejpam-3459	375	5	ξ1n	ξ1n	ADJ
ejpam-3459	375	6	,	,	PUNCT
ejpam-3459	375	7	ξ2n))n	ξ2n))n	PROPN
ejpam-3459	375	8	is	be	AUX
ejpam-3459	375	9	bounded	bound	VERB
ejpam-3459	375	10	in	in	ADP
ejpam-3459	375	11	n	n	PROPN
ejpam-3459	375	12	.	.	PUNCT
ejpam-3459	376	1	let	let	AUX
ejpam-3459	376	2	remember	remember	VERB
ejpam-3459	376	3	that	that	PRON
ejpam-3459	376	4	λ̂−1(k	λ̂−1(k	NOUN
ejpam-3459	376	5	)	)	PUNCT
ejpam-3459	376	6	=	=	SYM
ejpam-3459	377	1	{	{	PUNCT
ejpam-3459	377	2	(	(	PUNCT
ejpam-3459	377	3	ξ1	ξ1	NOUN
ejpam-3459	377	4	,	,	PUNCT
ejpam-3459	377	5	ξ2	ξ2	ADJ
ejpam-3459	377	6	)	)	PUNCT
ejpam-3459	377	7	∈	∈	PROPN
ejpam-3459	377	8	k	k	NOUN
ejpam-3459	377	9	:	:	PUNCT
ejpam-3459	377	10	λ(ξ1	λ(ξ1	ADJ
ejpam-3459	377	11	,	,	PUNCT
ejpam-3459	377	12	ξ2	ξ2	ADJ
ejpam-3459	377	13	)	)	PUNCT
ejpam-3459	377	14	∩	∩	PROPN
ejpam-3459	377	15	k	k	PROPN
ejpam-3459	377	16	6=	6=	PROPN
ejpam-3459	377	17	∅	∅	NOUN
ejpam-3459	377	18	}	}	PUNCT
ejpam-3459	377	19	.	.	PUNCT
ejpam-3459	378	1	so	so	ADV
ejpam-3459	378	2	,	,	PUNCT
ejpam-3459	378	3	there	there	PRON
ejpam-3459	378	4	exists	exist	VERB
ejpam-3459	378	5	a	a	DET
ejpam-3459	378	6	sequence	sequence	NOUN
ejpam-3459	378	7	(	(	PUNCT
ejpam-3459	378	8	y1n	y1n	PROPN
ejpam-3459	378	9	,	,	PUNCT
ejpam-3459	378	10	y2n)n	y2n)n	PROPN
ejpam-3459	378	11	∈	∈	PROPN
ejpam-3459	378	12	k	k	PROPN
ejpam-3459	378	13	that	that	PRON
ejpam-3459	378	14	belongs	belong	VERB
ejpam-3459	378	15	to	to	ADP
ejpam-3459	378	16	λ−1	λ−1	PROPN
ejpam-3459	378	17	ξ2	ξ2	PROPN
ejpam-3459	378	18	(	(	PUNCT
ejpam-3459	378	19	ξ1n	ξ1n	ADJ
ejpam-3459	378	20	)	)	PUNCT
ejpam-3459	378	21	×	×	NOUN
ejpam-3459	378	22	λ−1	λ−1	PROPN
ejpam-3459	378	23	ξ1	ξ1	NOUN
ejpam-3459	378	24	(	(	PUNCT
ejpam-3459	378	25	ξ2n	ξ2n	PROPN
ejpam-3459	378	26	)	)	PUNCT
ejpam-3459	378	27	=	=	PUNCT
ejpam-3459	379	1	λ̂−1(ξ1n	λ̂−1(ξ1n	ADJ
ejpam-3459	379	2	,	,	PUNCT
ejpam-3459	379	3	ξ2n	ξ2n	PROPN
ejpam-3459	379	4	)	)	PUNCT
ejpam-3459	379	5	such	such	ADJ
ejpam-3459	379	6	that	that	SCONJ
ejpam-3459	379	7	y1n	y1n	PROPN
ejpam-3459	379	8	and	and	CCONJ
ejpam-3459	379	9	y2n	y2n	NOUN
ejpam-3459	379	10	verifies	verifie	NOUN
ejpam-3459	379	11	respectively	respectively	ADV
ejpam-3459	379	12	(	(	PUNCT
ejpam-3459	379	13	54	54	NUM
ejpam-3459	379	14	)	)	PUNCT
ejpam-3459	379	15	and	and	CCONJ
ejpam-3459	379	16	(	(	PUNCT
ejpam-3459	379	17	55	55	NUM
ejpam-3459	379	18	)	)	PUNCT
ejpam-3459	379	19	with	with	ADP
ejpam-3459	379	20	respectively	respectively	ADV
ejpam-3459	379	21	ξ1n	ξ1n	ADJ
ejpam-3459	379	22	and	and	CCONJ
ejpam-3459	379	23	ξ2n	ξ2n	PROPN
ejpam-3459	379	24	instead	instead	ADV
ejpam-3459	379	25	of	of	ADP
ejpam-3459	379	26	ξ1	ξ1	NOUN
ejpam-3459	379	27	and	and	CCONJ
ejpam-3459	379	28	ξ2	ξ2	NOUN
ejpam-3459	379	29	,	,	PUNCT
ejpam-3459	379	30	and	and	CCONJ
ejpam-3459	379	31	moreover	moreover	ADV
ejpam-3459	379	32	,	,	PUNCT
ejpam-3459	379	33	the	the	DET
ejpam-3459	379	34	pair	pair	NOUN
ejpam-3459	379	35	(	(	PUNCT
ejpam-3459	379	36	p̂1ε(ξ1n	p̂1ε(ξ1n	NOUN
ejpam-3459	379	37	)	)	PUNCT
ejpam-3459	379	38	,	,	PUNCT
ejpam-3459	379	39	p̂2ε(ξ2n	p̂2ε(ξ2n	PROPN
ejpam-3459	379	40	)	)	PUNCT
ejpam-3459	379	41	)	)	PUNCT
ejpam-3459	379	42	satisfies	satisfie	NOUN
ejpam-3459	379	43	(	(	PUNCT
ejpam-3459	379	44	52	52	NUM
ejpam-3459	379	45	)	)	PUNCT
ejpam-3459	379	46	and	and	CCONJ
ejpam-3459	379	47	the	the	DET
ejpam-3459	379	48	associated	associated	ADJ
ejpam-3459	379	49	control	control	NOUN
ejpam-3459	379	50	v̂ε	v̂ε	NUM
ejpam-3459	380	1	verifies	verifie	NOUN
ejpam-3459	380	2	(	(	PUNCT
ejpam-3459	380	3	27	27	NUM
ejpam-3459	380	4	)	)	PUNCT
ejpam-3459	380	5	.	.	PUNCT
ejpam-3459	381	1	using	use	VERB
ejpam-3459	381	2	c.	c.	PROPN
ejpam-3459	381	3	k.	k.	PROPN
ejpam-3459	381	4	somé	somé	PROPN
ejpam-3459	381	5	,	,	PUNCT
ejpam-3459	381	6	s.	s.	PROPN
ejpam-3459	381	7	sawadogo	sawadogo	PROPN
ejpam-3459	381	8	/	/	SYM
ejpam-3459	381	9	eur	eur	PROPN
ejpam-3459	381	10	.	.	PUNCT
ejpam-3459	382	1	j.	j.	PROPN
ejpam-3459	382	2	pure	pure	PROPN
ejpam-3459	382	3	appl	appl	PROPN
ejpam-3459	382	4	.	.	PROPN
ejpam-3459	382	5	math	math	PROPN
ejpam-3459	382	6	,	,	PUNCT
ejpam-3459	382	7	12	12	NUM
ejpam-3459	382	8	(	(	PUNCT
ejpam-3459	382	9	3	3	NUM
ejpam-3459	382	10	)	)	PUNCT
ejpam-3459	382	11	(	(	PUNCT
ejpam-3459	382	12	2019	2019	NUM
ejpam-3459	382	13	)	)	PUNCT
ejpam-3459	382	14	,	,	PUNCT
ejpam-3459	382	15	870	870	NUM
ejpam-3459	382	16	-	-	SYM
ejpam-3459	382	17	892	892	NUM
ejpam-3459	382	18	885	885	NUM
ejpam-3459	382	19	(	(	PUNCT
ejpam-3459	382	20	56	56	NUM
ejpam-3459	382	21	)	)	PUNCT
ejpam-3459	382	22	and	and	CCONJ
ejpam-3459	382	23	the	the	DET
ejpam-3459	382	24	estimations	estimation	NOUN
ejpam-3459	382	25	(	(	PUNCT
ejpam-3459	382	26	34)-(37	34)-(37	NUM
ejpam-3459	382	27	)	)	PUNCT
ejpam-3459	382	28	,	,	PUNCT
ejpam-3459	382	29	we	we	PRON
ejpam-3459	382	30	show	show	VERB
ejpam-3459	382	31	(	(	PUNCT
ejpam-3459	382	32	as	as	ADP
ejpam-3459	382	33	the	the	DET
ejpam-3459	382	34	step	step	NOUN
ejpam-3459	382	35	4	4	NUM
ejpam-3459	382	36	in	in	ADP
ejpam-3459	382	37	the	the	DET
ejpam-3459	382	38	section	section	NOUN
ejpam-3459	382	39	4	4	NUM
ejpam-3459	382	40	)	)	PUNCT
ejpam-3459	382	41	that	that	SCONJ
ejpam-3459	382	42	the	the	DET
ejpam-3459	382	43	sequel	sequel	NOUN
ejpam-3459	382	44	(	(	PUNCT
ejpam-3459	382	45	yin)n	yin)n	PROPN
ejpam-3459	382	46	,	,	PUNCT
ejpam-3459	382	47	i	i	PRON
ejpam-3459	382	48	=	=	NOUN
ejpam-3459	382	49	1	1	NUM
ejpam-3459	382	50	,	,	PUNCT
ejpam-3459	382	51	2	2	NUM
ejpam-3459	382	52	converge	converge	VERB
ejpam-3459	382	53	strongly	strongly	ADV
ejpam-3459	382	54	to	to	ADP
ejpam-3459	382	55	yi	yi	PROPN
ejpam-3459	382	56	i	i	NOUN
ejpam-3459	382	57	=	=	NOUN
ejpam-3459	382	58	1	1	NUM
ejpam-3459	382	59	,	,	PUNCT
ejpam-3459	382	60	2	2	NUM
ejpam-3459	382	61	.	.	PUNCT
ejpam-3459	382	62	since	since	SCONJ
ejpam-3459	382	63	p̂iε(ξin	p̂iε(ξin	NOUN
ejpam-3459	382	64	)	)	PUNCT
ejpam-3459	382	65	,	,	PUNCT
ejpam-3459	382	66	i	i	PRON
ejpam-3459	382	67	=	=	NOUN
ejpam-3459	382	68	1	1	NUM
ejpam-3459	382	69	,	,	PUNCT
ejpam-3459	382	70	2	2	NUM
ejpam-3459	382	71	and	and	CCONJ
ejpam-3459	382	72	η1ε(ξ1n	η1ε(ξ1n	ADV
ejpam-3459	382	73	)	)	PUNCT
ejpam-3459	382	74	are	be	AUX
ejpam-3459	382	75	bounded	bound	VERB
ejpam-3459	382	76	independently	independently	ADV
ejpam-3459	382	77	to	to	ADP
ejpam-3459	382	78	(	(	PUNCT
ejpam-3459	382	79	ξin	ξin	PROPN
ejpam-3459	382	80	)	)	PUNCT
ejpam-3459	382	81	,	,	PUNCT
ejpam-3459	383	1	i	i	PRON
ejpam-3459	383	2	=	=	NOUN
ejpam-3459	383	3	1	1	NUM
ejpam-3459	383	4	;	;	PUNCT
ejpam-3459	383	5	2	2	NUM
ejpam-3459	383	6	,	,	PUNCT
ejpam-3459	383	7	then	then	ADV
ejpam-3459	383	8	,	,	PUNCT
ejpam-3459	383	9	for	for	ADP
ejpam-3459	383	10	all	all	DET
ejpam-3459	383	11	n	n	CCONJ
ejpam-3459	383	12	,	,	PUNCT
ejpam-3459	383	13	ri(ξn	ri(ξn	NOUN
ejpam-3459	383	14	)	)	PUNCT
ejpam-3459	384	1	i	i	PRON
ejpam-3459	385	1	=	=	NOUN
ejpam-3459	385	2	1	1	NUM
ejpam-3459	385	3	,	,	PUNCT
ejpam-3459	385	4	2	2	NUM
ejpam-3459	385	5	are	be	AUX
ejpam-3459	385	6	bounded	bound	VERB
ejpam-3459	385	7	in	in	ADP
ejpam-3459	385	8	l2(qt	l2(qt	PROPN
ejpam-3459	385	9	)	)	PUNCT
ejpam-3459	385	10	.	.	PUNCT
ejpam-3459	386	1	consequently	consequently	ADV
ejpam-3459	386	2	,	,	PUNCT
ejpam-3459	386	3	one	one	PRON
ejpam-3459	386	4	can	can	AUX
ejpam-3459	386	5	extract	extract	VERB
ejpam-3459	386	6	a	a	DET
ejpam-3459	386	7	subsequence	subsequence	NOUN
ejpam-3459	386	8	still	still	ADV
ejpam-3459	386	9	denoted	denote	VERB
ejpam-3459	386	10	by	by	ADP
ejpam-3459	386	11	yin	yin	PROPN
ejpam-3459	386	12	,	,	PUNCT
ejpam-3459	386	13	ri(ξn	ri(ξn	NOUN
ejpam-3459	386	14	)	)	PUNCT
ejpam-3459	386	15	i	i	PRON
ejpam-3459	387	1	=	=	NOUN
ejpam-3459	387	2	1	1	NUM
ejpam-3459	387	3	,	,	PUNCT
ejpam-3459	387	4	2	2	NUM
ejpam-3459	387	5	such	such	ADJ
ejpam-3459	387	6	that	that	DET
ejpam-3459	387	7	yin	yin	PROPN
ejpam-3459	387	8	−→	−→	NOUN
ejpam-3459	387	9	yi	yi	PROPN
ejpam-3459	387	10	in	in	ADP
ejpam-3459	387	11	l2(qt	l2(qt	PROPN
ejpam-3459	387	12	)	)	PUNCT
ejpam-3459	388	1	i	i	PRON
ejpam-3459	388	2	=	=	NOUN
ejpam-3459	388	3	1	1	NUM
ejpam-3459	388	4	,	,	PUNCT
ejpam-3459	388	5	2	2	NUM
ejpam-3459	388	6	;	;	PUNCT
ejpam-3459	388	7	ri(ξn	ri(ξn	NOUN
ejpam-3459	388	8	)	)	PUNCT
ejpam-3459	388	9	−→	−→	NOUN
ejpam-3459	388	10	ri(ξ	ri(ξ	NOUN
ejpam-3459	388	11	)	)	PUNCT
ejpam-3459	389	1	i	i	PRON
ejpam-3459	389	2	=	=	NOUN
ejpam-3459	389	3	1	1	NUM
ejpam-3459	389	4	,	,	PUNCT
ejpam-3459	389	5	2	2	NUM
ejpam-3459	389	6	;	;	PUNCT
ejpam-3459	389	7	∫	∫	PROPN
ejpam-3459	389	8	a	a	DET
ejpam-3459	389	9	0	0	NUM
ejpam-3459	389	10	µ̃1β̃ip̂iε(ξin	µ̃1β̃ip̂iε(ξin	NOUN
ejpam-3459	389	11	)	)	PUNCT
ejpam-3459	390	1	−→	−→	NOUN
ejpam-3459	390	2	∫	∫	PROPN
ejpam-3459	390	3	a	a	DET
ejpam-3459	390	4	0	0	NUM
ejpam-3459	390	5	µ̃1βip̂iε(ξi)da	µ̃1βip̂iε(ξi)da	NOUN
ejpam-3459	390	6	weakly	weakly	ADJ
ejpam-3459	390	7	in	in	ADP
ejpam-3459	390	8	l2(qt	l2(qt	PROPN
ejpam-3459	390	9	)	)	PUNCT
ejpam-3459	391	1	i	i	PRON
ejpam-3459	391	2	=	=	NOUN
ejpam-3459	391	3	1	1	NUM
ejpam-3459	391	4	,	,	PUNCT
ejpam-3459	391	5	2	2	NUM
ejpam-3459	391	6	;	;	PUNCT
ejpam-3459	391	7	∫	∫	PROPN
ejpam-3459	391	8	a	a	DET
ejpam-3459	391	9	0	0	NUM
ejpam-3459	391	10	µ̃1β1p̂2ε(ξ2n)da	µ̃1β1p̂2ε(ξ2n)da	ADJ
ejpam-3459	391	11	−→	−→	NOUN
ejpam-3459	392	1	∫	∫	NOUN
ejpam-3459	392	2	a	a	DET
ejpam-3459	392	3	0	0	NUM
ejpam-3459	392	4	µ̃1β1p̂2ε(ξ2)da	µ̃1β1p̂2ε(ξ2)da	PUNCT
ejpam-3459	392	5	weakly	weakly	ADJ
ejpam-3459	392	6	in	in	ADP
ejpam-3459	392	7	l2(qt	l2(qt	PROPN
ejpam-3459	392	8	)	)	PUNCT
ejpam-3459	392	9	;	;	PUNCT
ejpam-3459	392	10	∫	∫	PROPN
ejpam-3459	392	11	a	a	DET
ejpam-3459	392	12	0	0	PUNCT
ejpam-3459	392	13	µ2β2p̂1ε(ξ1n)da	µ2β2p̂1ε(ξ1n)da	ADJ
ejpam-3459	392	14	−→	−→	ADJ
ejpam-3459	392	15	∫	∫	PROPN
ejpam-3459	392	16	a	a	DET
ejpam-3459	392	17	0	0	NUM
ejpam-3459	392	18	µ2β2p̂1ε(ξ1)da	µ2β2p̂1ε(ξ1)da	NOUN
ejpam-3459	392	19	weakly	weakly	ADJ
ejpam-3459	392	20	in	in	ADP
ejpam-3459	392	21	l2(qt	l2(qt	PROPN
ejpam-3459	392	22	)	)	PUNCT
ejpam-3459	392	23	;	;	PUNCT
ejpam-3459	392	24	so	so	CCONJ
ejpam-3459	392	25	,	,	PUNCT
ejpam-3459	392	26	for	for	ADP
ejpam-3459	392	27	each	each	DET
ejpam-3459	392	28	i	i	PRON
ejpam-3459	392	29	∈	∈	PROPN
ejpam-3459	392	30	{	{	PUNCT
ejpam-3459	392	31	1	1	NUM
ejpam-3459	392	32	;	;	PUNCT
ejpam-3459	392	33	2	2	NUM
ejpam-3459	392	34	}	}	PUNCT
ejpam-3459	392	35	,	,	PUNCT
ejpam-3459	392	36	yi(ξ	yi(ξ	NOUN
ejpam-3459	392	37	)	)	PUNCT
ejpam-3459	392	38	is	be	AUX
ejpam-3459	392	39	solution	solution	NOUN
ejpam-3459	392	40	of	of	ADP
ejpam-3459	392	41	(	(	PUNCT
ejpam-3459	392	42	56	56	NUM
ejpam-3459	392	43	)	)	PUNCT
ejpam-3459	392	44	,	,	PUNCT
ejpam-3459	392	45	(	(	PUNCT
ejpam-3459	392	46	p̂1ε(ξ1	p̂1ε(ξ1	NOUN
ejpam-3459	392	47	)	)	PUNCT
ejpam-3459	392	48	,	,	PUNCT
ejpam-3459	392	49	p̂2ε(ξ2	p̂2ε(ξ2	NOUN
ejpam-3459	392	50	)	)	PUNCT
ejpam-3459	392	51	)	)	PUNCT
ejpam-3459	392	52	solves	solve	NOUN
ejpam-3459	392	53	(	(	PUNCT
ejpam-3459	392	54	52	52	NUM
ejpam-3459	392	55	)	)	PUNCT
ejpam-3459	392	56	and	and	CCONJ
ejpam-3459	392	57	the	the	DET
ejpam-3459	392	58	associated	associated	ADJ
ejpam-3459	392	59	control	control	NOUN
ejpam-3459	392	60	v̂ε	v̂ε	X
ejpam-3459	393	1	=	=	SYM
ejpam-3459	393	2	η1(ξ1	η1(ξ1	NOUN
ejpam-3459	393	3	)	)	PUNCT
ejpam-3459	393	4	verifies	verifie	NOUN
ejpam-3459	393	5	(	(	PUNCT
ejpam-3459	393	6	29	29	NUM
ejpam-3459	393	7	)	)	PUNCT
ejpam-3459	393	8	.	.	PUNCT
ejpam-3459	394	1	hence	hence	ADV
ejpam-3459	394	2	,	,	PUNCT
ejpam-3459	394	3	(	(	PUNCT
ejpam-3459	394	4	y1	y1	INTJ
ejpam-3459	394	5	,	,	PUNCT
ejpam-3459	394	6	y2	y2	NOUN
ejpam-3459	394	7	)	)	PUNCT
ejpam-3459	394	8	∈	∈	PROPN
ejpam-3459	395	1	λ−1	λ−1	PROPN
ejpam-3459	395	2	ξ2	ξ2	PROPN
ejpam-3459	395	3	(	(	PUNCT
ejpam-3459	395	4	ξ1	ξ1	NOUN
ejpam-3459	395	5	)	)	PUNCT
ejpam-3459	395	6	×	×	NOUN
ejpam-3459	396	1	λ−1	λ−1	PROPN
ejpam-3459	396	2	ξ1	ξ1	NOUN
ejpam-3459	396	3	(	(	PUNCT
ejpam-3459	396	4	ξ2	ξ2	NOUN
ejpam-3459	396	5	)	)	PUNCT
ejpam-3459	396	6	and	and	CCONJ
ejpam-3459	396	7	so	so	ADV
ejpam-3459	396	8	,	,	PUNCT
ejpam-3459	396	9	(	(	PUNCT
ejpam-3459	396	10	ξ1	ξ1	NOUN
ejpam-3459	396	11	,	,	PUNCT
ejpam-3459	396	12	ξ2	ξ2	ADJ
ejpam-3459	396	13	)	)	PUNCT
ejpam-3459	396	14	∈	∈	PROPN
ejpam-3459	396	15	λ̂−1(k	λ̂−1(k	NOUN
ejpam-3459	396	16	)	)	PUNCT
ejpam-3459	396	17	.	.	PUNCT
ejpam-3459	397	1	endly	endly	ADV
ejpam-3459	397	2	,	,	PUNCT
ejpam-3459	397	3	since	since	SCONJ
ejpam-3459	397	4	ξ1	ξ1	PROPN
ejpam-3459	397	5	7−→	7−→	PROPN
ejpam-3459	397	6	p̂1ε	p̂1ε	ADV
ejpam-3459	397	7	and	and	CCONJ
ejpam-3459	397	8	ξ2	ξ2	PROPN
ejpam-3459	397	9	7−→	7−→	PROPN
ejpam-3459	397	10	p̂2ε	p̂2ε	ADJ
ejpam-3459	397	11	are	be	AUX
ejpam-3459	397	12	affine	affine	ADJ
ejpam-3459	397	13	,	,	PUNCT
ejpam-3459	397	14	then	then	ADV
ejpam-3459	397	15	λξ2(ξ1	λξ2(ξ1	NOUN
ejpam-3459	397	16	)	)	PUNCT
ejpam-3459	397	17	and	and	CCONJ
ejpam-3459	397	18	λξ1(ξ2	λξ1(ξ2	NUM
ejpam-3459	397	19	)	)	PUNCT
ejpam-3459	397	20	are	be	AUX
ejpam-3459	397	21	nonempty	nonempty	ADJ
ejpam-3459	397	22	convex	convex	NOUN
ejpam-3459	397	23	sets	set	NOUN
ejpam-3459	397	24	in	in	ADP
ejpam-3459	397	25	l2(qt	l2(qt	PROPN
ejpam-3459	397	26	)	)	PUNCT
ejpam-3459	397	27	.	.	PUNCT
ejpam-3459	398	1	thus	thus	ADV
ejpam-3459	398	2	,	,	PUNCT
ejpam-3459	398	3	the	the	DET
ejpam-3459	398	4	gragh	gragh	PROPN
ejpam-3459	398	5	g	g	PROPN
ejpam-3459	398	6	λ̂	λ̂	X
ejpam-3459	398	7	=	=	SYM
ejpam-3459	398	8	{	{	PUNCT
ejpam-3459	398	9	〈	〈	PROPN
ejpam-3459	398	10	(	(	PUNCT
ejpam-3459	398	11	ξ1	ξ1	NOUN
ejpam-3459	398	12	,	,	PUNCT
ejpam-3459	398	13	ξ2	ξ2	NOUN
ejpam-3459	398	14	)	)	PUNCT
ejpam-3459	398	15	,	,	PUNCT
ejpam-3459	398	16	λ̂(ξ1	λ̂(ξ1	NOUN
ejpam-3459	398	17	,	,	PUNCT
ejpam-3459	398	18	ξ2	ξ2	ADJ
ejpam-3459	398	19	)	)	PUNCT
ejpam-3459	398	20	〉	〉	PROPN
ejpam-3459	398	21	}	}	PUNCT
ejpam-3459	398	22	of	of	ADP
ejpam-3459	398	23	λ̂	λ̂	NUM
ejpam-3459	398	24	is	be	AUX
ejpam-3459	398	25	closed	closed	ADJ
ejpam-3459	398	26	.	.	PUNCT
ejpam-3459	399	1	then	then	ADV
ejpam-3459	399	2	,	,	PUNCT
ejpam-3459	399	3	λ̂(ξ1	λ̂(ξ1	ADJ
ejpam-3459	399	4	,	,	PUNCT
ejpam-3459	399	5	ξ2	ξ2	NOUN
ejpam-3459	399	6	)	)	PUNCT
ejpam-3459	399	7	=	=	PUNCT
ejpam-3459	400	1	λξ2(ξ1	λξ2(ξ1	NOUN
ejpam-3459	400	2	)	)	PUNCT
ejpam-3459	400	3	×	×	NOUN
ejpam-3459	400	4	λξ1(ξ2	λξ1(ξ2	NOUN
ejpam-3459	400	5	)	)	PUNCT
ejpam-3459	400	6	is	be	AUX
ejpam-3459	400	7	upper	upper	ADJ
ejpam-3459	400	8	semicontinuous	semicontinuous	NOUN
ejpam-3459	400	9	,	,	PUNCT
ejpam-3459	400	10	and	and	CCONJ
ejpam-3459	400	11	from	from	ADP
ejpam-3459	400	12	the	the	DET
ejpam-3459	400	13	kakutani	kakutani	NOUN
ejpam-3459	400	14	’s	’s	PART
ejpam-3459	400	15	fixed	fix	VERB
ejpam-3459	400	16	point	point	NOUN
ejpam-3459	400	17	theorem	theorem	VERB
ejpam-3459	400	18	[	[	X
ejpam-3459	400	19	8	8	NUM
ejpam-3459	400	20	]	]	PUNCT
ejpam-3459	400	21	,	,	PUNCT
ejpam-3459	400	22	we	we	PRON
ejpam-3459	400	23	conclude	conclude	VERB
ejpam-3459	400	24	that	that	SCONJ
ejpam-3459	400	25	λ̂	λ̂	X
ejpam-3459	400	26	admits	admit	VERB
ejpam-3459	400	27	a	a	DET
ejpam-3459	400	28	fixed	fixed	ADJ
ejpam-3459	400	29	point	point	NOUN
ejpam-3459	400	30	.	.	PUNCT
ejpam-3459	401	1	more	more	ADV
ejpam-3459	401	2	precisely	precisely	ADV
ejpam-3459	401	3	,	,	PUNCT
ejpam-3459	401	4	there	there	PRON
ejpam-3459	401	5	exists	exist	VERB
ejpam-3459	401	6	ξ	ξ	PROPN
ejpam-3459	401	7	=	=	SYM
ejpam-3459	401	8	(	(	PUNCT
ejpam-3459	401	9	ξ1	ξ1	PROPN
ejpam-3459	401	10	,	,	PUNCT
ejpam-3459	401	11	ξ2	ξ2	ADJ
ejpam-3459	401	12	)	)	PUNCT
ejpam-3459	401	13	∈	∈	PROPN
ejpam-3459	401	14	n	n	PRON
ejpam-3459	401	15	such	such	ADJ
ejpam-3459	401	16	that	that	DET
ejpam-3459	401	17	λ̂(ξ	λ̂(ξ	NOUN
ejpam-3459	401	18	)	)	PUNCT
ejpam-3459	401	19	=	=	SYM
ejpam-3459	402	1	ξ	ξ	X
ejpam-3459	402	2	=	=	SYM
ejpam-3459	402	3	(	(	PUNCT
ejpam-3459	402	4	∫	∫	PROPN
ejpam-3459	402	5	a	a	DET
ejpam-3459	402	6	0	0	NUM
ejpam-3459	402	7	β1(p̂1ε(ξ1	β1(p̂1ε(ξ1	NUM
ejpam-3459	402	8	)	)	PUNCT
ejpam-3459	402	9	+	+	CCONJ
ejpam-3459	402	10	p̂2ε(ξ2))da	p̂2ε(ξ2))da	PROPN
ejpam-3459	402	11	,	,	PUNCT
ejpam-3459	402	12	∫	∫	PROPN
ejpam-3459	402	13	a	a	PRON
ejpam-3459	402	14	0	0	NUM
ejpam-3459	402	15	β2(p̂1ε(ξ1)−	β2(p̂1ε(ξ1)−	PROPN
ejpam-3459	402	16	p̂2ε(ξ2))da	p̂2ε(ξ2))da	PROPN
ejpam-3459	402	17	)	)	PUNCT
ejpam-3459	402	18	where	where	SCONJ
ejpam-3459	402	19	(	(	PUNCT
ejpam-3459	402	20	p̂1ε	p̂1ε	ADV
ejpam-3459	402	21	,	,	PUNCT
ejpam-3459	402	22	p̂2ε	p̂2ε	NUM
ejpam-3459	402	23	)	)	PUNCT
ejpam-3459	402	24	is	be	AUX
ejpam-3459	402	25	solution	solution	NOUN
ejpam-3459	402	26	of	of	ADP
ejpam-3459	402	27	the	the	DET
ejpam-3459	402	28	system	system	NOUN
ejpam-3459	402	29	(	(	PUNCT
ejpam-3459	402	30	52	52	NUM
ejpam-3459	402	31	)	)	PUNCT
ejpam-3459	402	32	with	with	ADP
ejpam-3459	402	33	g1	g1	PROPN
ejpam-3459	402	34	(	(	PUNCT
ejpam-3459	402	35	∫	∫	PROPN
ejpam-3459	402	36	a	a	DET
ejpam-3459	402	37	0	0	NUM
ejpam-3459	402	38	βp̂εda	βp̂εda	PUNCT
ejpam-3459	402	39	)	)	PUNCT
ejpam-3459	403	1	=	=	SYM
ejpam-3459	403	2	β1(t	β1(t	PROPN
ejpam-3459	403	3	,	,	PUNCT
ejpam-3459	403	4	a	a	PRON
ejpam-3459	403	5	,	,	PUNCT
ejpam-3459	403	6	x)f	x)f	X
ejpam-3459	403	7	(	(	PUNCT
ejpam-3459	403	8	∫	∫	PROPN
ejpam-3459	403	9	a	a	PRON
ejpam-3459	403	10	0	0	PUNCT
ejpam-3459	403	11	β1(p̂1ε	β1(p̂1ε	PROPN
ejpam-3459	403	12	+	+	NUM
ejpam-3459	403	13	p̂2ε)da	p̂2ε)da	ADJ
ejpam-3459	403	14	)	)	PUNCT
ejpam-3459	403	15	+	+	CCONJ
ejpam-3459	403	16	β2(t	β2(t	PROPN
ejpam-3459	403	17	,	,	PUNCT
ejpam-3459	403	18	a	a	PRON
ejpam-3459	403	19	,	,	PUNCT
ejpam-3459	403	20	x)g	x)g	X
ejpam-3459	403	21	(	(	PUNCT
ejpam-3459	403	22	∫	∫	PROPN
ejpam-3459	403	23	a	a	PRON
ejpam-3459	403	24	0	0	NUM
ejpam-3459	403	25	β2(p̂1ε	β2(p̂1ε	NOUN
ejpam-3459	403	26	−	−	PROPN
ejpam-3459	403	27	p̂2ε)da	p̂2ε)da	PROPN
ejpam-3459	403	28	)	)	PUNCT
ejpam-3459	403	29	g2	g2	PROPN
ejpam-3459	403	30	(	(	PUNCT
ejpam-3459	403	31	∫	∫	PROPN
ejpam-3459	403	32	a	a	PRON
ejpam-3459	403	33	0	0	NUM
ejpam-3459	403	34	β2p̂εda	β2p̂εda	NOUN
ejpam-3459	403	35	)	)	PUNCT
ejpam-3459	404	1	=	=	SYM
ejpam-3459	404	2	β1(t	β1(t	PROPN
ejpam-3459	404	3	,	,	PUNCT
ejpam-3459	404	4	a	a	PRON
ejpam-3459	404	5	,	,	PUNCT
ejpam-3459	404	6	x)f	x)f	X
ejpam-3459	404	7	(	(	PUNCT
ejpam-3459	404	8	∫	∫	PROPN
ejpam-3459	404	9	a	a	PRON
ejpam-3459	404	10	0	0	PUNCT
ejpam-3459	404	11	β1(p̂1ε	β1(p̂1ε	PROPN
ejpam-3459	404	12	+	+	NUM
ejpam-3459	404	13	p̂2ε)da	p̂2ε)da	ADJ
ejpam-3459	404	14	)	)	PUNCT
ejpam-3459	404	15	−	−	ADP
ejpam-3459	405	1	β2(t	β2(t	PROPN
ejpam-3459	405	2	,	,	PUNCT
ejpam-3459	405	3	a	a	PRON
ejpam-3459	405	4	,	,	PUNCT
ejpam-3459	405	5	x)g	x)g	X
ejpam-3459	405	6	(	(	PUNCT
ejpam-3459	405	7	∫	∫	PROPN
ejpam-3459	405	8	a	a	PRON
ejpam-3459	405	9	0	0	NUM
ejpam-3459	405	10	β2(p̂1ε	β2(p̂1ε	NOUN
ejpam-3459	405	11	−	−	PROPN
ejpam-3459	405	12	p̂2ε)da	p̂2ε)da	PROPN
ejpam-3459	405	13	)	)	PUNCT
ejpam-3459	405	14	.	.	PUNCT
ejpam-3459	406	1	instead	instead	ADV
ejpam-3459	406	2	of	of	ADP
ejpam-3459	406	3	g1(ξ	g1(ξ	NOUN
ejpam-3459	406	4	)	)	PUNCT
ejpam-3459	406	5	and	and	CCONJ
ejpam-3459	406	6	g2(ξ	g2(ξ	X
ejpam-3459	406	7	)	)	PUNCT
ejpam-3459	406	8	respectively	respectively	ADV
ejpam-3459	406	9	.	.	PUNCT
ejpam-3459	407	1	c.	c.	PROPN
ejpam-3459	407	2	k.	k.	PROPN
ejpam-3459	407	3	somé	somé	PROPN
ejpam-3459	407	4	,	,	PUNCT
ejpam-3459	407	5	s.	s.	PROPN
ejpam-3459	407	6	sawadogo	sawadogo	PROPN
ejpam-3459	407	7	/	/	SYM
ejpam-3459	407	8	eur	eur	PROPN
ejpam-3459	407	9	.	.	PUNCT
ejpam-3459	408	1	j.	j.	PROPN
ejpam-3459	408	2	pure	pure	PROPN
ejpam-3459	408	3	appl	appl	PROPN
ejpam-3459	408	4	.	.	PROPN
ejpam-3459	408	5	math	math	PROPN
ejpam-3459	408	6	,	,	PUNCT
ejpam-3459	408	7	12	12	NUM
ejpam-3459	408	8	(	(	PUNCT
ejpam-3459	408	9	3	3	NUM
ejpam-3459	408	10	)	)	PUNCT
ejpam-3459	408	11	(	(	PUNCT
ejpam-3459	408	12	2019	2019	NUM
ejpam-3459	408	13	)	)	PUNCT
ejpam-3459	408	14	,	,	PUNCT
ejpam-3459	408	15	870	870	NUM
ejpam-3459	408	16	-	-	SYM
ejpam-3459	408	17	892	892	NUM
ejpam-3459	408	18	886	886	NUM
ejpam-3459	408	19	5	5	NUM
ejpam-3459	408	20	.	.	PUNCT
ejpam-3459	408	21	application	application	NOUN
ejpam-3459	408	22	to	to	ADP
ejpam-3459	408	23	the	the	DET
ejpam-3459	408	24	sentinel	sentinel	NOUN
ejpam-3459	408	25	of	of	ADP
ejpam-3459	408	26	detection	detection	NOUN
ejpam-3459	408	27	we	we	PRON
ejpam-3459	408	28	consider	consider	VERB
ejpam-3459	408	29	for	for	ADP
ejpam-3459	408	30	given	give	VERB
ejpam-3459	408	31	positive	positive	ADJ
ejpam-3459	408	32	functions	function	NOUN
ejpam-3459	408	33	gi	gi	X
ejpam-3459	408	34	=	=	SYM
ejpam-3459	408	35	1	1	NUM
ejpam-3459	408	36	;	;	PUNCT
ejpam-3459	408	37	2	2	NUM
ejpam-3459	408	38	the	the	DET
ejpam-3459	408	39	following	follow	VERB
ejpam-3459	408	40	systems	system	NOUN
ejpam-3459	408	41	:	:	PUNCT
ejpam-3459	408	42			PROPN
ejpam-3459	408	43	∂yi	∂yi	PROPN
ejpam-3459	408	44	∂t	∂t	PROPN
ejpam-3459	409	1	+	+	CCONJ
ejpam-3459	409	2	∂yi	∂yi	PROPN
ejpam-3459	409	3	∂a	∂a	PROPN
ejpam-3459	409	4	−∆yi	−∆yi	NOUN
ejpam-3459	409	5	+	+	NOUN
ejpam-3459	409	6	µiyi	µiyi	NOUN
ejpam-3459	409	7	=	=	SYM
ejpam-3459	409	8	0	0	NUM
ejpam-3459	409	9	in	in	ADP
ejpam-3459	409	10	q	q	PROPN
ejpam-3459	409	11	,	,	PUNCT
ejpam-3459	409	12	yi(0	yi(0	PROPN
ejpam-3459	409	13	,	,	PUNCT
ejpam-3459	409	14	a	a	PRON
ejpam-3459	409	15	,	,	PUNCT
ejpam-3459	409	16	x	x	NOUN
ejpam-3459	409	17	)	)	PUNCT
ejpam-3459	409	18	=	=	SYM
ejpam-3459	409	19	y0	y0	NOUN
ejpam-3459	409	20	i	i	NOUN
ejpam-3459	409	21	+	+	CCONJ
ejpam-3459	410	1	τiŷ	τiŷ	ADV
ejpam-3459	410	2	0	0	PUNCT
ejpam-3459	411	1	i	i	PRON
ejpam-3459	411	2	in	in	ADP
ejpam-3459	411	3	qa	qa	PROPN
ejpam-3459	411	4	,	,	PUNCT
ejpam-3459	411	5	yi(t	yi(t	PROPN
ejpam-3459	411	6	,	,	PUNCT
ejpam-3459	411	7	0	0	NUM
ejpam-3459	411	8	,	,	PUNCT
ejpam-3459	411	9	x	x	X
ejpam-3459	411	10	)	)	PUNCT
ejpam-3459	411	11	=	=	SYM
ejpam-3459	411	12	gi	gi	INTJ
ejpam-3459	411	13	(	(	PUNCT
ejpam-3459	411	14	∫	∫	PROPN
ejpam-3459	411	15	a	a	DET
ejpam-3459	411	16	0	0	NUM
ejpam-3459	411	17	βiyida	βiyida	NOUN
ejpam-3459	411	18	)	)	PUNCT
ejpam-3459	411	19	in	in	ADP
ejpam-3459	411	20	qt	qt	NOUN
ejpam-3459	411	21	,	,	PUNCT
ejpam-3459	411	22	yi	yi	PROPN
ejpam-3459	411	23	=	=	PUNCT
ejpam-3459	411	24	{	{	PUNCT
ejpam-3459	411	25	gi	gi	X
ejpam-3459	412	1	+	+	CCONJ
ejpam-3459	412	2	λiĝi	λiĝi	INTJ
ejpam-3459	412	3	on	on	ADP
ejpam-3459	412	4	σi	σi	PROPN
ejpam-3459	412	5	,	,	PUNCT
ejpam-3459	412	6	0	0	NUM
ejpam-3459	412	7	on	on	ADP
ejpam-3459	412	8	σ	σ	PROPN
ejpam-3459	412	9	\	\	PROPN
ejpam-3459	412	10	σi	σi	PROPN
ejpam-3459	412	11	.	.	PUNCT
ejpam-3459	413	1	(	(	PUNCT
ejpam-3459	413	2	59	59	NUM
ejpam-3459	413	3	)	)	PUNCT
ejpam-3459	413	4	where	where	SCONJ
ejpam-3459	413	5	σi	σi	NOUN
ejpam-3459	413	6	=	=	SYM
ejpam-3459	413	7	(	(	PUNCT
ejpam-3459	413	8	0	0	NUM
ejpam-3459	413	9	,	,	PUNCT
ejpam-3459	413	10	t	t	NOUN
ejpam-3459	413	11	)	)	PUNCT
ejpam-3459	413	12	×	×	NOUN
ejpam-3459	413	13	(	(	PUNCT
ejpam-3459	413	14	0	0	NUM
ejpam-3459	413	15	,	,	PUNCT
ejpam-3459	413	16	a	a	PRON
ejpam-3459	413	17	)	)	PUNCT
ejpam-3459	413	18	×	×	NOUN
ejpam-3459	413	19	γi	γi	INTJ
ejpam-3459	413	20	i	i	NOUN
ejpam-3459	413	21	=	=	NOUN
ejpam-3459	413	22	1	1	NUM
ejpam-3459	413	23	;	;	PUNCT
ejpam-3459	413	24	2	2	NUM
ejpam-3459	413	25	,	,	PUNCT
ejpam-3459	413	26	the	the	DET
ejpam-3459	413	27	γi	γi	NOUN
ejpam-3459	413	28	,	,	PUNCT
ejpam-3459	413	29	i	i	PRON
ejpam-3459	413	30	=	=	NOUN
ejpam-3459	413	31	1	1	NUM
ejpam-3459	413	32	;	;	PUNCT
ejpam-3459	413	33	2	2	NUM
ejpam-3459	413	34	are	be	AUX
ejpam-3459	413	35	such	such	ADJ
ejpam-3459	413	36	that	that	SCONJ
ejpam-3459	413	37	γ1	γ1	NOUN
ejpam-3459	413	38	∪	∪	ADP
ejpam-3459	413	39	γ2	γ2	NOUN
ejpam-3459	413	40	=	=	SYM
ejpam-3459	413	41	γ	γ	X
ejpam-3459	413	42	and	and	CCONJ
ejpam-3459	413	43	γ	γ	X
ejpam-3459	413	44	=	=	SYM
ejpam-3459	413	45	∂ω	∂ω	PROPN
ejpam-3459	413	46	is	be	AUX
ejpam-3459	413	47	the	the	DET
ejpam-3459	413	48	smooth	smooth	ADJ
ejpam-3459	413	49	boundary	boundary	NOUN
ejpam-3459	413	50	of	of	ADP
ejpam-3459	413	51	ω	ω	PROPN
ejpam-3459	413	52	,	,	PUNCT
ejpam-3459	413	53	the	the	DET
ejpam-3459	413	54	functions	function	NOUN
ejpam-3459	413	55	µi	µi	PROPN
ejpam-3459	413	56	,	,	PUNCT
ejpam-3459	413	57	βi	βi	PRON
ejpam-3459	413	58	and	and	CCONJ
ejpam-3459	413	59	the	the	DET
ejpam-3459	413	60	reals	reals	PROPN
ejpam-3459	413	61	t	t	PROPN
ejpam-3459	413	62	,	,	PUNCT
ejpam-3459	413	63	a	a	PRON
ejpam-3459	413	64	are	be	AUX
ejpam-3459	413	65	defined	define	VERB
ejpam-3459	413	66	respectively	respectively	ADV
ejpam-3459	413	67	as	as	ADP
ejpam-3459	413	68	in	in	ADP
ejpam-3459	413	69	section	section	NOUN
ejpam-3459	413	70	1	1	NUM
ejpam-3459	413	71	.	.	PUNCT
ejpam-3459	414	1	y(t	y(t	PROPN
ejpam-3459	414	2	,	,	PUNCT
ejpam-3459	414	3	a	a	PRON
ejpam-3459	414	4	,	,	PUNCT
ejpam-3459	414	5	x	x	X
ejpam-3459	414	6	)	)	PUNCT
ejpam-3459	414	7	is	be	AUX
ejpam-3459	414	8	the	the	DET
ejpam-3459	414	9	distribution	distribution	NOUN
ejpam-3459	414	10	of	of	ADP
ejpam-3459	414	11	individuals	individual	NOUN
ejpam-3459	414	12	of	of	ADP
ejpam-3459	414	13	age	age	NOUN
ejpam-3459	414	14	a	a	DET
ejpam-3459	414	15	at	at	ADP
ejpam-3459	414	16	time	time	NOUN
ejpam-3459	414	17	t	t	NOUN
ejpam-3459	414	18	and	and	CCONJ
ejpam-3459	414	19	location	location	NOUN
ejpam-3459	414	20	x	x	SYM
ejpam-3459	414	21	∈	∈	PROPN
ejpam-3459	414	22	ω	ω	PROPN
ejpam-3459	414	23	.	.	PUNCT
ejpam-3459	415	1	the	the	DET
ejpam-3459	415	2	expressions	expression	NOUN
ejpam-3459	415	3	∫	∫	INTJ
ejpam-3459	415	4	a	a	DET
ejpam-3459	415	5	0	0	NUM
ejpam-3459	415	6	βiyida	βiyida	ADJ
ejpam-3459	415	7	,	,	PUNCT
ejpam-3459	415	8	i	i	PRON
ejpam-3459	415	9	=	=	NOUN
ejpam-3459	415	10	1	1	NUM
ejpam-3459	415	11	;	;	PUNCT
ejpam-3459	415	12	2	2	NUM
ejpam-3459	415	13	denote	denote	VERB
ejpam-3459	415	14	the	the	DET
ejpam-3459	415	15	distribution	distribution	NOUN
ejpam-3459	415	16	of	of	ADP
ejpam-3459	415	17	newborn	newborn	ADJ
ejpam-3459	415	18	individuals	individual	NOUN
ejpam-3459	415	19	at	at	ADP
ejpam-3459	415	20	time	time	NOUN
ejpam-3459	415	21	t	t	NOUN
ejpam-3459	415	22	and	and	CCONJ
ejpam-3459	415	23	location	location	NOUN
ejpam-3459	415	24	x.	x.	NOUN
ejpam-3459	415	25	in	in	ADP
ejpam-3459	415	26	an	an	DET
ejpam-3459	415	27	ovipare	ovipare	NOUN
ejpam-3459	415	28	species	specie	NOUN
ejpam-3459	415	29	it	it	PRON
ejpam-3459	415	30	represents	represent	VERB
ejpam-3459	415	31	the	the	DET
ejpam-3459	415	32	total	total	ADJ
ejpam-3459	415	33	eggs	egg	NOUN
ejpam-3459	415	34	hatch	hatch	NOUN
ejpam-3459	415	35	at	at	ADP
ejpam-3459	415	36	time	time	NOUN
ejpam-3459	415	37	t	t	PROPN
ejpam-3459	415	38	and	and	CCONJ
ejpam-3459	415	39	the	the	DET
ejpam-3459	415	40	position	position	NOUN
ejpam-3459	415	41	x	x	PUNCT
ejpam-3459	415	42	and	and	CCONJ
ejpam-3459	415	43	gi	gi	INTJ
ejpam-3459	415	44	(	(	PUNCT
ejpam-3459	415	45	∫	∫	PROPN
ejpam-3459	415	46	a	a	DET
ejpam-3459	415	47	0	0	NUM
ejpam-3459	415	48	βiyida	βiyida	NOUN
ejpam-3459	415	49	)	)	PUNCT
ejpam-3459	415	50	denote	denote	VERB
ejpam-3459	415	51	the	the	DET
ejpam-3459	415	52	distribution	distribution	NOUN
ejpam-3459	415	53	of	of	ADP
ejpam-3459	415	54	eggs	egg	NOUN
ejpam-3459	415	55	that	that	PRON
ejpam-3459	415	56	at	at	ADP
ejpam-3459	415	57	time	time	NOUN
ejpam-3459	415	58	t	t	PROPN
ejpam-3459	415	59	and	and	CCONJ
ejpam-3459	415	60	the	the	DET
ejpam-3459	415	61	position	position	NOUN
ejpam-3459	415	62	x.	x.	VERB
ejpam-3459	416	1	the	the	DET
ejpam-3459	416	2	functions	function	NOUN
ejpam-3459	416	3	gi	gi	VERB
ejpam-3459	416	4	i	i	NOUN
ejpam-3459	416	5	=	=	NOUN
ejpam-3459	417	1	1	1	NUM
ejpam-3459	417	2	;	;	PUNCT
ejpam-3459	417	3	2	2	NUM
ejpam-3459	417	4	are	be	AUX
ejpam-3459	417	5	of	of	ADP
ejpam-3459	417	6	class	class	NOUN
ejpam-3459	417	7	c1	c1	NOUN
ejpam-3459	417	8	,	,	PUNCT
ejpam-3459	417	9	globally	globally	ADV
ejpam-3459	417	10	lipschitz	lipschitz	NOUN
ejpam-3459	417	11	and	and	CCONJ
ejpam-3459	417	12	their	their	PRON
ejpam-3459	417	13	derivate	derivate	NOUN
ejpam-3459	417	14	functions	function	NOUN
ejpam-3459	417	15	verify	verify	VERB
ejpam-3459	417	16	g′i(0	g′i(0	NUM
ejpam-3459	417	17	)	)	PUNCT
ejpam-3459	418	1	=	=	SYM
ejpam-3459	418	2	0	0	NUM
ejpam-3459	418	3	and	and	CCONJ
ejpam-3459	418	4	moreover	moreover	ADV
ejpam-3459	418	5	g′i	g′i	VERB
ejpam-3459	418	6	∈	∈	PROPN
ejpam-3459	418	7	l∞(r	l∞(r	NOUN
ejpam-3459	418	8	)	)	PUNCT
ejpam-3459	418	9	are	be	AUX
ejpam-3459	418	10	globally	globally	ADV
ejpam-3459	418	11	lipschitz	lipschitz	ADJ
ejpam-3459	418	12	.	.	PUNCT
ejpam-3459	419	1	the	the	DET
ejpam-3459	419	2	system	system	NOUN
ejpam-3459	419	3	(	(	PUNCT
ejpam-3459	419	4	59	59	NUM
ejpam-3459	419	5	)	)	PUNCT
ejpam-3459	419	6	describes	describe	VERB
ejpam-3459	419	7	the	the	DET
ejpam-3459	419	8	evolution	evolution	NOUN
ejpam-3459	419	9	of	of	ADP
ejpam-3459	419	10	the	the	DET
ejpam-3459	419	11	populations	population	NOUN
ejpam-3459	419	12	under	under	ADP
ejpam-3459	419	13	the	the	DET
ejpam-3459	419	14	inhospitable	inhospitable	ADJ
ejpam-3459	419	15	boundary	boundary	ADJ
ejpam-3459	419	16	conditions	condition	NOUN
ejpam-3459	419	17	when	when	SCONJ
ejpam-3459	419	18	the	the	DET
ejpam-3459	419	19	flux	flux	NOUN
ejpam-3459	419	20	of	of	ADP
ejpam-3459	419	21	population	population	NOUN
ejpam-3459	419	22	takes	take	VERB
ejpam-3459	419	23	the	the	DET
ejpam-3459	419	24	form	form	NOUN
ejpam-3459	419	25	−∇y(t	−∇y(t	PROPN
ejpam-3459	419	26	,	,	PUNCT
ejpam-3459	419	27	a	a	DET
ejpam-3459	419	28	,	,	PUNCT
ejpam-3459	419	29	x	x	NOUN
ejpam-3459	419	30	)	)	PUNCT
ejpam-3459	419	31	.	.	PUNCT
ejpam-3459	420	1	as	as	ADP
ejpam-3459	420	2	for	for	ADP
ejpam-3459	420	3	the	the	DET
ejpam-3459	420	4	initial	initial	ADJ
ejpam-3459	420	5	and	and	CCONJ
ejpam-3459	420	6	boundary	boundary	ADJ
ejpam-3459	420	7	conditions	condition	NOUN
ejpam-3459	420	8	of	of	ADP
ejpam-3459	420	9	(	(	PUNCT
ejpam-3459	420	10	59	59	NUM
ejpam-3459	420	11	)	)	PUNCT
ejpam-3459	420	12	,	,	PUNCT
ejpam-3459	420	13	y0	y0	NOUN
ejpam-3459	420	14	i	i	PRON
ejpam-3459	420	15	and	and	CCONJ
ejpam-3459	420	16	gi	gi	INTJ
ejpam-3459	420	17	are	be	AUX
ejpam-3459	420	18	given	give	VERB
ejpam-3459	420	19	respectively	respectively	ADV
ejpam-3459	420	20	in	in	ADP
ejpam-3459	420	21	l2(qa)τiŷ	l2(qa)τiŷ	PROPN
ejpam-3459	420	22	0	0	PUNCT
ejpam-3459	421	1	i	i	PRON
ejpam-3459	421	2	,	,	PUNCT
ejpam-3459	421	3	λiĝi	λiĝi	INTJ
ejpam-3459	421	4	i	i	PRON
ejpam-3459	421	5	=	=	NOUN
ejpam-3459	421	6	1	1	NUM
ejpam-3459	421	7	;	;	PUNCT
ejpam-3459	421	8	2	2	NUM
ejpam-3459	421	9	are	be	AUX
ejpam-3459	421	10	unknown	unknown	ADJ
ejpam-3459	421	11	where	where	SCONJ
ejpam-3459	421	12	τi	τi	NOUN
ejpam-3459	421	13	,	,	PUNCT
ejpam-3459	421	14	λi	λi	ADP
ejpam-3459	421	15	i	i	NOUN
ejpam-3459	421	16	=	=	NOUN
ejpam-3459	421	17	1	1	NUM
ejpam-3459	421	18	;	;	PUNCT
ejpam-3459	421	19	2	2	NUM
ejpam-3459	421	20	are	be	AUX
ejpam-3459	421	21	reals	real	NOUN
ejpam-3459	421	22	.	.	PUNCT
ejpam-3459	422	1	as	as	ADP
ejpam-3459	422	2	a	a	DET
ejpam-3459	422	3	matter	matter	NOUN
ejpam-3459	422	4	of	of	ADP
ejpam-3459	422	5	fact	fact	NOUN
ejpam-3459	422	6	the	the	DET
ejpam-3459	422	7	terms	term	NOUN
ejpam-3459	422	8	y0	y0	VERB
ejpam-3459	422	9	i	i	PRON
ejpam-3459	422	10	+	+	CCONJ
ejpam-3459	423	1	τiŷ	τiŷ	ADV
ejpam-3459	423	2	0	0	PUNCT
ejpam-3459	424	1	i	i	PRON
ejpam-3459	424	2	and	and	CCONJ
ejpam-3459	424	3	gi	gi	VERB
ejpam-3459	425	1	+	+	CCONJ
ejpam-3459	425	2	λiĝi	λiĝi	INTJ
ejpam-3459	425	3	are	be	AUX
ejpam-3459	425	4	qualified	qualified	ADJ
ejpam-3459	425	5	as	as	ADP
ejpam-3459	425	6	incomplete	incomplete	ADJ
ejpam-3459	425	7	data	datum	NOUN
ejpam-3459	425	8	.	.	PUNCT
ejpam-3459	426	1	suppose	suppose	VERB
ejpam-3459	426	2	that	that	SCONJ
ejpam-3459	426	3	:	:	PUNCT
ejpam-3459	426	4	(	(	PUNCT
ejpam-3459	426	5	i	i	NOUN
ejpam-3459	426	6	)	)	PUNCT
ejpam-3459	426	7	for	for	ADP
ejpam-3459	426	8	i=1;2	i=1;2	PROPN
ejpam-3459	426	9	ĝi	ĝi	X
ejpam-3459	426	10	∈	∈	PROPN
ejpam-3459	426	11	l2(σi	l2(σi	PROPN
ejpam-3459	426	12	)	)	PUNCT
ejpam-3459	426	13	and	and	CCONJ
ejpam-3459	426	14	‖ĝi‖l2(σi	‖ĝi‖l2(σi	NUM
ejpam-3459	426	15	)	)	PUNCT
ejpam-3459	426	16	≤	≤	NUM
ejpam-3459	426	17	1	1	NUM
ejpam-3459	426	18	,	,	PUNCT
ejpam-3459	426	19	(	(	PUNCT
ejpam-3459	426	20	ii	ii	NOUN
ejpam-3459	426	21	)	)	PUNCT
ejpam-3459	426	22	for	for	ADP
ejpam-3459	426	23	i=1;2	i=1;2	PROPN
ejpam-3459	426	24	ŷ0	ŷ0	PROPN
ejpam-3459	426	25	i	i	PROPN
ejpam-3459	426	26	∈	∈	PROPN
ejpam-3459	426	27	l2(qa	l2(qa	PROPN
ejpam-3459	426	28	)	)	PUNCT
ejpam-3459	426	29	and	and	CCONJ
ejpam-3459	426	30	‖ŷ0	‖ŷ0	PROPN
ejpam-3459	426	31	i	i	PRON
ejpam-3459	426	32	‖l2(qa	‖l2(qa	PROPN
ejpam-3459	426	33	)	)	PUNCT
ejpam-3459	426	34	≤	≤	NUM
ejpam-3459	426	35	1	1	NUM
ejpam-3459	426	36	,	,	PUNCT
ejpam-3459	426	37	(	(	PUNCT
ejpam-3459	426	38	iii	iii	NOUN
ejpam-3459	426	39	)	)	PUNCT
ejpam-3459	426	40	for	for	ADP
ejpam-3459	426	41	i	i	PRON
ejpam-3459	426	42	=	=	NOUN
ejpam-3459	426	43	1	1	NUM
ejpam-3459	426	44	;	;	PUNCT
ejpam-3459	426	45	2	2	NUM
ejpam-3459	426	46	the	the	DET
ejpam-3459	426	47	reals	real	NOUN
ejpam-3459	426	48	τi	τi	VERB
ejpam-3459	426	49	and	and	CCONJ
ejpam-3459	426	50	λi	λi	X
ejpam-3459	426	51	are	be	AUX
ejpam-3459	426	52	unknown	unknown	ADJ
ejpam-3459	426	53	and	and	CCONJ
ejpam-3459	426	54	small	small	ADJ
ejpam-3459	426	55	enough	enough	ADV
ejpam-3459	426	56	.	.	PUNCT
ejpam-3459	427	1	it	it	PRON
ejpam-3459	427	2	is	be	AUX
ejpam-3459	427	3	now	now	ADV
ejpam-3459	427	4	assumed	assume	VERB
ejpam-3459	427	5	that	that	SCONJ
ejpam-3459	427	6	measures	measure	NOUN
ejpam-3459	427	7	yiobs	yiob	NOUN
ejpam-3459	427	8	,	,	PUNCT
ejpam-3459	427	9	i	i	PRON
ejpam-3459	427	10	=	=	NOUN
ejpam-3459	427	11	1	1	NUM
ejpam-3459	427	12	;	;	PUNCT
ejpam-3459	427	13	2	2	NUM
ejpam-3459	427	14	are	be	AUX
ejpam-3459	427	15	available	available	ADJ
ejpam-3459	427	16	on	on	ADP
ejpam-3459	427	17	qo	qo	NOUN
ejpam-3459	427	18	=	=	PUNCT
ejpam-3459	427	19	u×o	u×o	PROPN
ejpam-3459	427	20	where	where	SCONJ
ejpam-3459	427	21	o	o	PROPN
ejpam-3459	427	22	⊂	⊂	PROPN
ejpam-3459	427	23	ω	ω	PROPN
ejpam-3459	427	24	is	be	AUX
ejpam-3459	427	25	the	the	DET
ejpam-3459	427	26	observation	observation	NOUN
ejpam-3459	427	27	set	set	VERB
ejpam-3459	427	28	and	and	CCONJ
ejpam-3459	427	29	o	o	NOUN
ejpam-3459	427	30	∩	∩	PROPN
ejpam-3459	427	31	ω	ω	PROPN
ejpam-3459	427	32	6=	6=	ADP
ejpam-3459	427	33	∅.	∅.	NOUN
ejpam-3459	427	34	assume	assume	VERB
ejpam-3459	427	35	moreover	moreover	ADV
ejpam-3459	427	36	that	that	SCONJ
ejpam-3459	427	37	yi	yi	NOUN
ejpam-3459	427	38	=	=	SYM
ejpam-3459	427	39	yiobs	yiob	NOUN
ejpam-3459	427	40	=	=	SYM
ejpam-3459	427	41	m0i	m0i	NOUN
ejpam-3459	427	42	,	,	PUNCT
ejpam-3459	427	43	i	i	PRON
ejpam-3459	427	44	=	=	NOUN
ejpam-3459	427	45	1	1	NUM
ejpam-3459	427	46	;	;	PUNCT
ejpam-3459	427	47	2	2	NUM
ejpam-3459	427	48	on	on	ADP
ejpam-3459	427	49	qo	qo	NOUN
ejpam-3459	427	50	.	.	PUNCT
ejpam-3459	428	1	(	(	PUNCT
ejpam-3459	428	2	60	60	NUM
ejpam-3459	428	3	)	)	PUNCT
ejpam-3459	428	4	where	where	SCONJ
ejpam-3459	428	5	m0i	m0i	NOUN
ejpam-3459	428	6	,	,	PUNCT
ejpam-3459	428	7	i	i	PRON
ejpam-3459	428	8	=	=	NOUN
ejpam-3459	428	9	1	1	NUM
ejpam-3459	428	10	;	;	PUNCT
ejpam-3459	428	11	2	2	NUM
ejpam-3459	428	12	are	be	AUX
ejpam-3459	428	13	known	know	VERB
ejpam-3459	428	14	functions	function	NOUN
ejpam-3459	428	15	belonging	belong	VERB
ejpam-3459	428	16	to	to	ADP
ejpam-3459	428	17	l2(qo	l2(qo	PROPN
ejpam-3459	428	18	)	)	PUNCT
ejpam-3459	428	19	.	.	PUNCT
ejpam-3459	429	1	the	the	DET
ejpam-3459	429	2	aim	aim	NOUN
ejpam-3459	429	3	is	be	AUX
ejpam-3459	429	4	to	to	PART
ejpam-3459	429	5	calculate	calculate	VERB
ejpam-3459	429	6	the	the	DET
ejpam-3459	429	7	pollution	pollution	NOUN
ejpam-3459	429	8	terms	term	NOUN
ejpam-3459	429	9	λ1ĝ1	λ1ĝ1	ADJ
ejpam-3459	429	10	and	and	CCONJ
ejpam-3459	429	11	λ2ĝ2	λ2ĝ2	ADJ
ejpam-3459	429	12	independently	independently	ADV
ejpam-3459	429	13	from	from	ADP
ejpam-3459	429	14	the	the	DET
ejpam-3459	429	15	missing	miss	VERB
ejpam-3459	429	16	terms	term	NOUN
ejpam-3459	429	17	τ1ŷ	τ1ŷ	PUNCT
ejpam-3459	429	18	0	0	NUM
ejpam-3459	429	19	1	1	NUM
ejpam-3459	429	20	and	and	CCONJ
ejpam-3459	429	21	τ2ŷ	τ2ŷ	PROPN
ejpam-3459	429	22	0	0	NUM
ejpam-3459	429	23	2	2	NUM
ejpam-3459	429	24	with	with	ADP
ejpam-3459	429	25	one	one	NUM
ejpam-3459	429	26	and	and	CCONJ
ejpam-3459	429	27	only	only	ADV
ejpam-3459	429	28	one	one	NUM
ejpam-3459	429	29	sentinel	sentinel	NOUN
ejpam-3459	429	30	.	.	PUNCT
ejpam-3459	430	1	one	one	NUM
ejpam-3459	430	2	of	of	ADP
ejpam-3459	430	3	the	the	DET
ejpam-3459	430	4	methods	method	NOUN
ejpam-3459	430	5	to	to	PART
ejpam-3459	430	6	solve	solve	VERB
ejpam-3459	430	7	this	this	DET
ejpam-3459	430	8	problem	problem	NOUN
ejpam-3459	430	9	is	be	AUX
ejpam-3459	430	10	the	the	DET
ejpam-3459	430	11	least	least	ADJ
ejpam-3459	430	12	squares	square	NOUN
ejpam-3459	430	13	method	method	NOUN
ejpam-3459	430	14	.	.	PUNCT
ejpam-3459	431	1	the	the	DET
ejpam-3459	431	2	sentinel	sentinel	ADJ
ejpam-3459	431	3	concept	concept	NOUN
ejpam-3459	431	4	was	be	AUX
ejpam-3459	431	5	introduced	introduce	VERB
ejpam-3459	431	6	by	by	ADP
ejpam-3459	431	7	j.l	j.l	PROPN
ejpam-3459	431	8	.	.	PUNCT
ejpam-3459	431	9	lions	lion	NOUN
ejpam-3459	432	1	[	[	X
ejpam-3459	432	2	7	7	X
ejpam-3459	432	3	]	]	PUNCT
ejpam-3459	432	4	to	to	PART
ejpam-3459	432	5	study	study	VERB
ejpam-3459	432	6	the	the	DET
ejpam-3459	432	7	systems	system	NOUN
ejpam-3459	432	8	with	with	ADP
ejpam-3459	432	9	incomplete	incomplete	ADJ
ejpam-3459	432	10	data	datum	NOUN
ejpam-3459	432	11	.	.	PUNCT
ejpam-3459	433	1	this	this	DET
ejpam-3459	433	2	concept	concept	NOUN
ejpam-3459	433	3	relies	rely	VERB
ejpam-3459	433	4	on	on	ADP
ejpam-3459	433	5	the	the	DET
ejpam-3459	433	6	following	follow	VERB
ejpam-3459	433	7	elements	element	NOUN
ejpam-3459	433	8	:	:	PUNCT
ejpam-3459	433	9	the	the	DET
ejpam-3459	433	10	state	state	NOUN
ejpam-3459	433	11	y	y	PROPN
ejpam-3459	433	12	described	describe	VERB
ejpam-3459	433	13	by	by	ADP
ejpam-3459	433	14	a	a	DET
ejpam-3459	433	15	equation	equation	NOUN
ejpam-3459	433	16	or	or	CCONJ
ejpam-3459	433	17	a	a	DET
ejpam-3459	433	18	partial	partial	ADJ
ejpam-3459	433	19	differential	differential	NOUN
ejpam-3459	433	20	equations	equation	NOUN
ejpam-3459	433	21	system	system	NOUN
ejpam-3459	433	22	,	,	PUNCT
ejpam-3459	433	23	an	an	DET
ejpam-3459	433	24	observation	observation	NOUN
ejpam-3459	433	25	function	function	NOUN
ejpam-3459	433	26	yobs	yob	NOUN
ejpam-3459	433	27	defined	define	VERB
ejpam-3459	433	28	on	on	ADP
ejpam-3459	433	29	u	u	PROPN
ejpam-3459	433	30	×	×	NOUN
ejpam-3459	433	31	o	o	INTJ
ejpam-3459	433	32	where	where	SCONJ
ejpam-3459	433	33	o	o	NOUN
ejpam-3459	433	34	is	be	AUX
ejpam-3459	433	35	the	the	DET
ejpam-3459	433	36	observation	observation	NOUN
ejpam-3459	433	37	set	set	VERB
ejpam-3459	433	38	and	and	CCONJ
ejpam-3459	433	39	a	a	DET
ejpam-3459	433	40	control	control	NOUN
ejpam-3459	433	41	function	function	VERB
ejpam-3459	433	42	v	v	NOUN
ejpam-3459	433	43	to	to	PART
ejpam-3459	433	44	be	be	AUX
ejpam-3459	433	45	determined	determine	VERB
ejpam-3459	433	46	.	.	PUNCT
ejpam-3459	434	1	many	many	ADJ
ejpam-3459	434	2	papers	paper	NOUN
ejpam-3459	434	3	use	use	VERB
ejpam-3459	434	4	the	the	DET
ejpam-3459	434	5	definition	definition	NOUN
ejpam-3459	434	6	of	of	ADP
ejpam-3459	434	7	lions	lion	NOUN
ejpam-3459	434	8	in	in	ADP
ejpam-3459	434	9	the	the	DET
ejpam-3459	434	10	theoretical	theoretical	ADJ
ejpam-3459	434	11	aspect	aspect	NOUN
ejpam-3459	434	12	.	.	PUNCT
ejpam-3459	435	1	as	as	ADP
ejpam-3459	435	2	to	to	ADP
ejpam-3459	435	3	applications	application	NOUN
ejpam-3459	435	4	,	,	PUNCT
ejpam-3459	435	5	we	we	PRON
ejpam-3459	435	6	quote	quote	VERB
ejpam-3459	435	7	s.	s.	PROPN
ejpam-3459	435	8	sawadogo	sawadogo	VERB
ejpam-3459	435	9	in	in	ADP
ejpam-3459	435	10	[	[	X
ejpam-3459	435	11	9	9	NUM
ejpam-3459	435	12	]	]	PUNCT
ejpam-3459	435	13	who	who	PRON
ejpam-3459	435	14	studied	study	VERB
ejpam-3459	435	15	the	the	DET
ejpam-3459	435	16	detection	detection	NOUN
ejpam-3459	435	17	of	of	ADP
ejpam-3459	435	18	incomplete	incomplete	ADJ
ejpam-3459	435	19	parameters	parameter	NOUN
ejpam-3459	435	20	for	for	ADP
ejpam-3459	435	21	a	a	DET
ejpam-3459	435	22	c.	c.	PROPN
ejpam-3459	435	23	k.	k.	PROPN
ejpam-3459	435	24	somé	somé	PROPN
ejpam-3459	435	25	,	,	PUNCT
ejpam-3459	435	26	s.	s.	PROPN
ejpam-3459	435	27	sawadogo	sawadogo	PROPN
ejpam-3459	435	28	/	/	SYM
ejpam-3459	435	29	eur	eur	PROPN
ejpam-3459	435	30	.	.	PUNCT
ejpam-3459	436	1	j.	j.	PROPN
ejpam-3459	436	2	pure	pure	PROPN
ejpam-3459	436	3	appl	appl	PROPN
ejpam-3459	436	4	.	.	PROPN
ejpam-3459	436	5	math	math	PROPN
ejpam-3459	436	6	,	,	PUNCT
ejpam-3459	436	7	12	12	NUM
ejpam-3459	436	8	(	(	PUNCT
ejpam-3459	436	9	3	3	NUM
ejpam-3459	436	10	)	)	PUNCT
ejpam-3459	436	11	(	(	PUNCT
ejpam-3459	436	12	2019	2019	NUM
ejpam-3459	436	13	)	)	PUNCT
ejpam-3459	436	14	,	,	PUNCT
ejpam-3459	436	15	870	870	NUM
ejpam-3459	436	16	-	-	SYM
ejpam-3459	436	17	892	892	NUM
ejpam-3459	436	18	887	887	NUM
ejpam-3459	436	19	linear	linear	ADJ
ejpam-3459	436	20	population	population	NOUN
ejpam-3459	436	21	dynamic	dynamic	ADJ
ejpam-3459	436	22	model	model	NOUN
ejpam-3459	436	23	.	.	PUNCT
ejpam-3459	437	1	in	in	ADP
ejpam-3459	437	2	[	[	X
ejpam-3459	437	3	10	10	NUM
ejpam-3459	437	4	]	]	PUNCT
ejpam-3459	437	5	the	the	DET
ejpam-3459	437	6	author	author	NOUN
ejpam-3459	437	7	made	make	VERB
ejpam-3459	437	8	the	the	DET
ejpam-3459	437	9	same	same	ADJ
ejpam-3459	437	10	study	study	NOUN
ejpam-3459	437	11	for	for	ADP
ejpam-3459	437	12	a	a	DET
ejpam-3459	437	13	nonlinear	nonlinear	ADJ
ejpam-3459	437	14	population	population	NOUN
ejpam-3459	437	15	dynamic	dynamic	ADJ
ejpam-3459	437	16	model	model	NOUN
ejpam-3459	437	17	.	.	PUNCT
ejpam-3459	438	1	for	for	ADP
ejpam-3459	438	2	the	the	DET
ejpam-3459	438	3	sentinel	sentinel	ADJ
ejpam-3459	438	4	concept	concept	NOUN
ejpam-3459	438	5	we	we	PRON
ejpam-3459	438	6	refer	refer	VERB
ejpam-3459	438	7	to	to	ADP
ejpam-3459	438	8	[	[	X
ejpam-3459	438	9	9	9	NUM
ejpam-3459	438	10	,	,	PUNCT
ejpam-3459	438	11	10	10	NUM
ejpam-3459	438	12	]	]	PUNCT
ejpam-3459	438	13	and	and	CCONJ
ejpam-3459	438	14	the	the	DET
ejpam-3459	438	15	references	reference	NOUN
ejpam-3459	438	16	therein	therein	ADV
ejpam-3459	438	17	.	.	PUNCT
ejpam-3459	439	1	in	in	ADP
ejpam-3459	439	2	this	this	DET
ejpam-3459	439	3	paragraph	paragraph	NOUN
ejpam-3459	439	4	we	we	PRON
ejpam-3459	439	5	study	study	VERB
ejpam-3459	439	6	the	the	DET
ejpam-3459	439	7	simultaneous	simultaneous	ADJ
ejpam-3459	439	8	sentinel	sentinel	NOUN
ejpam-3459	439	9	concept	concept	NOUN
ejpam-3459	439	10	for	for	ADP
ejpam-3459	439	11	a	a	DET
ejpam-3459	439	12	coupled	couple	VERB
ejpam-3459	439	13	nonlinear	nonlinear	ADJ
ejpam-3459	439	14	population	population	NOUN
ejpam-3459	439	15	dynamic	dynamic	ADJ
ejpam-3459	439	16	model	model	NOUN
ejpam-3459	439	17	.	.	PUNCT
ejpam-3459	440	1	we	we	PRON
ejpam-3459	440	2	begin	begin	VERB
ejpam-3459	440	3	by	by	ADP
ejpam-3459	440	4	the	the	DET
ejpam-3459	440	5	following	follow	VERB
ejpam-3459	440	6	proposition	proposition	NOUN
ejpam-3459	440	7	proposition	proposition	NOUN
ejpam-3459	440	8	3	3	NUM
ejpam-3459	440	9	.	.	X
ejpam-3459	441	1	for	for	ADP
ejpam-3459	441	2	each	each	DET
ejpam-3459	441	3	i	i	NOUN
ejpam-3459	441	4	=	=	NOUN
ejpam-3459	441	5	1	1	NUM
ejpam-3459	441	6	;	;	PUNCT
ejpam-3459	441	7	2	2	NUM
ejpam-3459	441	8	,	,	PUNCT
ejpam-3459	441	9	the	the	DET
ejpam-3459	441	10	functions	function	NOUN
ejpam-3459	441	11	λi	λi	ADP
ejpam-3459	441	12	7−→	7−→	PROPN
ejpam-3459	441	13	yi(λi	yi(λi	PROPN
ejpam-3459	441	14	,	,	PUNCT
ejpam-3459	441	15	τi	τi	PROPN
ejpam-3459	441	16	)	)	PUNCT
ejpam-3459	441	17	and	and	CCONJ
ejpam-3459	441	18	τi	τi	VERB
ejpam-3459	441	19	7−→	7−→	PROPN
ejpam-3459	441	20	yi(λi	yi(λi	PROPN
ejpam-3459	441	21	,	,	PUNCT
ejpam-3459	441	22	τi	τi	PROPN
ejpam-3459	441	23	)	)	PUNCT
ejpam-3459	441	24	are	be	AUX
ejpam-3459	441	25	differentiable	differentiable	ADJ
ejpam-3459	441	26	at	at	ADP
ejpam-3459	441	27	the	the	DET
ejpam-3459	441	28	point	point	NOUN
ejpam-3459	441	29	0	0	NUM
ejpam-3459	441	30	.	.	PUNCT
ejpam-3459	442	1	proof	proof	NOUN
ejpam-3459	442	2	.	.	PUNCT
ejpam-3459	443	1	let	let	VERB
ejpam-3459	443	2	ŷi(t	ŷi(t	PROPN
ejpam-3459	443	3	,	,	PUNCT
ejpam-3459	443	4	a	a	DET
ejpam-3459	443	5	,	,	PUNCT
ejpam-3459	443	6	x	x	NOUN
ejpam-3459	443	7	)	)	PUNCT
ejpam-3459	443	8	=	=	PUNCT
ejpam-3459	443	9	e−λ0	e−λ0	ADP
ejpam-3459	443	10	t	t	PROPN
ejpam-3459	443	11	(	(	PUNCT
ejpam-3459	443	12	yi(λi	yi(λi	PROPN
ejpam-3459	443	13	,	,	PUNCT
ejpam-3459	443	14	τi)−	τi)−	PUNCT
ejpam-3459	443	15	y0i	y0i	PROPN
ejpam-3459	443	16	)	)	PUNCT
ejpam-3459	444	1	i	i	PRON
ejpam-3459	444	2	=	=	NOUN
ejpam-3459	444	3	1	1	NUM
ejpam-3459	444	4	;	;	PUNCT
ejpam-3459	444	5	2	2	NUM
ejpam-3459	444	6	with	with	ADP
ejpam-3459	444	7	y0i	y0i	PROPN
ejpam-3459	444	8	=	=	SYM
ejpam-3459	444	9	yi(λi	yi(λi	PROPN
ejpam-3459	444	10	,	,	PUNCT
ejpam-3459	444	11	0	0	NUM
ejpam-3459	444	12	)	)	PUNCT
ejpam-3459	444	13	and	and	CCONJ
ejpam-3459	444	14	for	for	ADP
ejpam-3459	444	15	each	each	DET
ejpam-3459	444	16	i	i	NOUN
ejpam-3459	444	17	=	=	NOUN
ejpam-3459	444	18	1	1	NUM
ejpam-3459	444	19	;	;	PUNCT
ejpam-3459	444	20	2	2	NUM
ejpam-3459	444	21	,	,	PUNCT
ejpam-3459	444	22	yi(λi	yi(λi	PROPN
ejpam-3459	444	23	,	,	PUNCT
ejpam-3459	444	24	τi	τi	NOUN
ejpam-3459	444	25	)	)	PUNCT
ejpam-3459	444	26	and	and	CCONJ
ejpam-3459	444	27	y0i	y0i	ADV
ejpam-3459	444	28	solve	solve	VERB
ejpam-3459	444	29	(	(	PUNCT
ejpam-3459	444	30	59	59	NUM
ejpam-3459	444	31	)	)	PUNCT
ejpam-3459	444	32	.	.	PUNCT
ejpam-3459	445	1	then	then	ADV
ejpam-3459	445	2	ŷi	ŷi	PROPN
ejpam-3459	445	3	i	i	NOUN
ejpam-3459	445	4	=	=	NOUN
ejpam-3459	445	5	1	1	NUM
ejpam-3459	445	6	;	;	PUNCT
ejpam-3459	445	7	2	2	NUM
ejpam-3459	445	8	verify	verify	PROPN
ejpam-3459	445	9	∂ŷi	∂ŷi	PROPN
ejpam-3459	445	10	∂t	∂t	PROPN
ejpam-3459	446	1	+	+	CCONJ
ejpam-3459	446	2	∂ŷi	∂ŷi	ADV
ejpam-3459	446	3	∂a	∂a	ADP
ejpam-3459	446	4	−∆ŷi	−∆ŷi	PUNCT
ejpam-3459	446	5	+	+	CCONJ
ejpam-3459	446	6	(	(	PUNCT
ejpam-3459	446	7	µi	µi	ADP
ejpam-3459	446	8	+	+	ADJ
ejpam-3459	446	9	λ0)ŷi	λ0)ŷi	NOUN
ejpam-3459	446	10	=	=	NOUN
ejpam-3459	446	11	0	0	NUM
ejpam-3459	446	12	in	in	ADP
ejpam-3459	446	13	q	q	PROPN
ejpam-3459	446	14	,	,	PUNCT
ejpam-3459	446	15	ŷi(0	ŷi(0	PRON
ejpam-3459	446	16	,	,	PUNCT
ejpam-3459	446	17	a	a	PRON
ejpam-3459	446	18	,	,	PUNCT
ejpam-3459	446	19	x	x	NOUN
ejpam-3459	446	20	)	)	PUNCT
ejpam-3459	447	1	=	=	SYM
ejpam-3459	448	1	τiŷ	τiŷ	ADV
ejpam-3459	448	2	0	0	PUNCT
ejpam-3459	449	1	i	i	PRON
ejpam-3459	449	2	in	in	ADP
ejpam-3459	449	3	qa	qa	PROPN
ejpam-3459	449	4	,	,	PUNCT
ejpam-3459	449	5	ŷi(t	ŷi(t	PROPN
ejpam-3459	449	6	,	,	PUNCT
ejpam-3459	449	7	0	0	NUM
ejpam-3459	449	8	,	,	PUNCT
ejpam-3459	449	9	x	x	NOUN
ejpam-3459	449	10	)	)	PUNCT
ejpam-3459	449	11	=	=	PUNCT
ejpam-3459	449	12	e−λ0	e−λ0	ADP
ejpam-3459	449	13	t	t	PROPN
ejpam-3459	449	14	(	(	PUNCT
ejpam-3459	449	15	gi	gi	INTJ
ejpam-3459	449	16	(	(	PUNCT
ejpam-3459	449	17	∫	∫	PROPN
ejpam-3459	449	18	a	a	PRON
ejpam-3459	449	19	0	0	NUM
ejpam-3459	449	20	βiyida	βiyida	ADJ
ejpam-3459	449	21	)	)	PUNCT
ejpam-3459	449	22	−gi	−gi	NOUN
ejpam-3459	449	23	(	(	PUNCT
ejpam-3459	449	24	∫	∫	PROPN
ejpam-3459	449	25	a	a	PRON
ejpam-3459	449	26	0	0	NUM
ejpam-3459	449	27	βiy0ida	βiy0ida	NOUN
ejpam-3459	449	28	)	)	PUNCT
ejpam-3459	449	29	)	)	PUNCT
ejpam-3459	449	30	in	in	ADP
ejpam-3459	449	31	qt	qt	NOUN
ejpam-3459	449	32	,	,	PUNCT
ejpam-3459	449	33	ŷi	ŷi	PROPN
ejpam-3459	449	34	=	=	NOUN
ejpam-3459	449	35	0	0	NUM
ejpam-3459	449	36	on	on	ADP
ejpam-3459	449	37	σ	σ	PROPN
ejpam-3459	449	38	.	.	PUNCT
ejpam-3459	450	1	(	(	PUNCT
ejpam-3459	450	2	61	61	NUM
ejpam-3459	450	3	)	)	PUNCT
ejpam-3459	450	4	system	system	NOUN
ejpam-3459	450	5	(	(	PUNCT
ejpam-3459	450	6	61	61	NUM
ejpam-3459	450	7	)	)	PUNCT
ejpam-3459	450	8	is	be	AUX
ejpam-3459	450	9	this	this	DET
ejpam-3459	450	10	one	one	NOUN
ejpam-3459	450	11	obtained	obtain	VERB
ejpam-3459	450	12	in	in	ADP
ejpam-3459	450	13	the	the	DET
ejpam-3459	450	14	proof	proof	NOUN
ejpam-3459	450	15	of	of	ADP
ejpam-3459	450	16	the	the	DET
ejpam-3459	450	17	proposition	proposition	NOUN
ejpam-3459	450	18	9	9	NUM
ejpam-3459	450	19	in	in	ADP
ejpam-3459	450	20	[	[	X
ejpam-3459	450	21	10	10	NUM
ejpam-3459	450	22	]	]	PUNCT
ejpam-3459	450	23	with	with	ADP
ejpam-3459	450	24	here	here	ADV
ejpam-3459	450	25	βi(t	βi(t	NOUN
ejpam-3459	450	26	,	,	PUNCT
ejpam-3459	450	27	a	a	DET
ejpam-3459	450	28	,	,	PUNCT
ejpam-3459	450	29	x	x	NOUN
ejpam-3459	450	30	)	)	PUNCT
ejpam-3459	450	31	,	,	PUNCT
ejpam-3459	450	32	gi	gi	VERB
ejpam-3459	450	33	respectively	respectively	ADV
ejpam-3459	450	34	in	in	ADP
ejpam-3459	450	35	the	the	DET
ejpam-3459	450	36	place	place	NOUN
ejpam-3459	450	37	of	of	ADP
ejpam-3459	450	38	β(a	β(a	PROPN
ejpam-3459	450	39	)	)	PUNCT
ejpam-3459	450	40	,	,	PUNCT
ejpam-3459	450	41	f	f	PROPN
ejpam-3459	450	42	and	and	CCONJ
ejpam-3459	450	43	τi	τi	VERB
ejpam-3459	450	44	=	=	SYM
ejpam-3459	450	45	τ	τ	PROPN
ejpam-3459	450	46	,	,	PUNCT
ejpam-3459	450	47	λi	λi	X
ejpam-3459	450	48	=	=	NOUN
ejpam-3459	450	49	λ	λ	X
ejpam-3459	450	50	i	i	NOUN
ejpam-3459	450	51	=	=	NOUN
ejpam-3459	450	52	1	1	NUM
ejpam-3459	450	53	;	;	PUNCT
ejpam-3459	450	54	2	2	X
ejpam-3459	450	55	.	.	X
ejpam-3459	450	56	let	let	VERB
ejpam-3459	450	57	multiply	multiply	ADV
ejpam-3459	450	58	(	(	PUNCT
ejpam-3459	450	59	61	61	NUM
ejpam-3459	450	60	)	)	PUNCT
ejpam-3459	450	61	by	by	ADP
ejpam-3459	450	62	ŷi	ŷi	NOUN
ejpam-3459	450	63	and	and	CCONJ
ejpam-3459	450	64	integrate	integrate	VERB
ejpam-3459	450	65	by	by	ADP
ejpam-3459	450	66	parts	part	NOUN
ejpam-3459	450	67	over	over	ADP
ejpam-3459	450	68	q.	q.	PROPN
ejpam-3459	450	69	since	since	SCONJ
ejpam-3459	450	70	gi	gi	NOUN
ejpam-3459	450	71	,	,	PUNCT
ejpam-3459	450	72	i	i	PRON
ejpam-3459	450	73	=	=	NOUN
ejpam-3459	450	74	1	1	NUM
ejpam-3459	450	75	;	;	PUNCT
ejpam-3459	450	76	2	2	NUM
ejpam-3459	450	77	is	be	AUX
ejpam-3459	450	78	globally	globally	ADV
ejpam-3459	450	79	lipschitz	lipschitz	ADJ
ejpam-3459	450	80	,	,	PUNCT
ejpam-3459	450	81	proceeding	proceed	VERB
ejpam-3459	450	82	as	as	ADP
ejpam-3459	450	83	in	in	ADP
ejpam-3459	450	84	[	[	X
ejpam-3459	450	85	10	10	NUM
ejpam-3459	450	86	]	]	PUNCT
ejpam-3459	450	87	,	,	PUNCT
ejpam-3459	450	88	we	we	PRON
ejpam-3459	450	89	have	have	VERB
ejpam-3459	450	90	‖ŷi	‖ŷi	ADV
ejpam-3459	450	91	(	(	PUNCT
ejpam-3459	450	92	·	·	PUNCT
ejpam-3459	450	93	,	,	PUNCT
ejpam-3459	450	94	0	0	NUM
ejpam-3459	450	95	,	,	PUNCT
ejpam-3459	450	96	·	·	PUNCT
ejpam-3459	450	97	)	)	PUNCT
ejpam-3459	450	98	‖l2(qt	‖l2(qt	X
ejpam-3459	450	99	)	)	PUNCT
ejpam-3459	450	100	≤	≤	NOUN
ejpam-3459	450	101	c‖βi‖2∞‖ŷi‖l2(qt	c‖βi‖2∞‖ŷi‖l2(qt	PROPN
ejpam-3459	450	102	)	)	PUNCT
ejpam-3459	450	103	.	.	PUNCT
ejpam-3459	451	1	(	(	PUNCT
ejpam-3459	451	2	62	62	X
ejpam-3459	451	3	)	)	PUNCT
ejpam-3459	451	4	one	one	NUM
ejpam-3459	451	5	deducts	deduct	NOUN
ejpam-3459	451	6	from	from	ADP
ejpam-3459	451	7	(	(	PUNCT
ejpam-3459	451	8	62	62	NUM
ejpam-3459	451	9	)	)	PUNCT
ejpam-3459	451	10	that	that	PRON
ejpam-3459	451	11	‖∇ŷi‖l2(qt	‖∇ŷi‖l2(qt	ADV
ejpam-3459	451	12	)	)	PUNCT
ejpam-3459	452	1	+	+	CCONJ
ejpam-3459	452	2	‖ŷi‖l2(qt	‖ŷi‖l2(qt	X
ejpam-3459	452	3	)	)	PUNCT
ejpam-3459	452	4	≤	≤	NUM
ejpam-3459	452	5	cτ2	cτ2	NOUN
ejpam-3459	452	6	i	i	PRON
ejpam-3459	452	7	.	.	PUNCT
ejpam-3459	453	1	(	(	PUNCT
ejpam-3459	453	2	63	63	NUM
ejpam-3459	453	3	)	)	PUNCT
ejpam-3459	453	4	according	accord	VERB
ejpam-3459	453	5	to	to	ADP
ejpam-3459	453	6	the	the	DET
ejpam-3459	453	7	expression	expression	NOUN
ejpam-3459	453	8	of	of	ADP
ejpam-3459	453	9	ŷi	ŷi	PROPN
ejpam-3459	453	10	and	and	CCONJ
ejpam-3459	453	11	the	the	DET
ejpam-3459	453	12	relation	relation	NOUN
ejpam-3459	453	13	(	(	PUNCT
ejpam-3459	453	14	61	61	NUM
ejpam-3459	453	15	)	)	PUNCT
ejpam-3459	453	16	,	,	PUNCT
ejpam-3459	453	17	we	we	PRON
ejpam-3459	453	18	get	get	VERB
ejpam-3459	453	19	yi	yi	NOUN
ejpam-3459	453	20	converges	converge	VERB
ejpam-3459	453	21	uniformly	uniformly	ADV
ejpam-3459	453	22	to	to	ADP
ejpam-3459	453	23	y0i	y0i	PROPN
ejpam-3459	453	24	on	on	ADP
ejpam-3459	453	25	q	q	PROPN
ejpam-3459	453	26	and	and	CCONJ
ejpam-3459	453	27	∫	∫	PROPN
ejpam-3459	453	28	a	a	DET
ejpam-3459	453	29	0	0	NUM
ejpam-3459	453	30	βiyi(λi	βiyi(λi	NOUN
ejpam-3459	453	31	,	,	PUNCT
ejpam-3459	453	32	τi)da	τi)da	PRON
ejpam-3459	453	33	converges	converge	VERB
ejpam-3459	453	34	uniformly	uniformly	ADV
ejpam-3459	453	35	to	to	PART
ejpam-3459	453	36	∫	∫	VERB
ejpam-3459	453	37	a	a	DET
ejpam-3459	453	38	0	0	NUM
ejpam-3459	453	39	βiy0ida	βiy0ida	PRON
ejpam-3459	453	40	on	on	ADP
ejpam-3459	453	41	qt	qt	NOUN
ejpam-3459	453	42	.	.	PUNCT
ejpam-3459	454	1	set	set	VERB
ejpam-3459	454	2	now	now	ADV
ejpam-3459	454	3	zτi	zτi	X
ejpam-3459	454	4	=	=	SYM
ejpam-3459	454	5	ŷi	ŷi	PROPN
ejpam-3459	454	6	τi	τi	ADV
ejpam-3459	454	7	and	and	CCONJ
ejpam-3459	454	8	pτi	pτi	PROPN
ejpam-3459	454	9	=	=	PROPN
ejpam-3459	454	10	zτi	zτi	PROPN
ejpam-3459	454	11	−	−	PROPN
ejpam-3459	454	12	zi	zi	PROPN
ejpam-3459	454	13	for	for	ADP
ejpam-3459	454	14	i	i	PRON
ejpam-3459	454	15	=	=	NOUN
ejpam-3459	454	16	1	1	NUM
ejpam-3459	454	17	;	;	PUNCT
ejpam-3459	454	18	2	2	NUM
ejpam-3459	454	19	,	,	PUNCT
ejpam-3459	454	20	where	where	SCONJ
ejpam-3459	454	21	zi	zi	NOUN
ejpam-3459	454	22	verifies	verifies	PROPN
ejpam-3459	454	23	∂zi	∂zi	PROPN
ejpam-3459	454	24	∂t	∂t	PROPN
ejpam-3459	454	25	+	+	CCONJ
ejpam-3459	454	26	∂zi	∂zi	PROPN
ejpam-3459	454	27	∂a	∂a	PROPN
ejpam-3459	454	28	−∆zi	−∆zi	NOUN
ejpam-3459	454	29	+	+	CCONJ
ejpam-3459	454	30	µizi	µizi	NOUN
ejpam-3459	454	31	=	=	NOUN
ejpam-3459	454	32	0	0	NUM
ejpam-3459	454	33	in	in	ADP
ejpam-3459	454	34	q	q	PROPN
ejpam-3459	454	35	,	,	PUNCT
ejpam-3459	454	36	zi(0	zi(0	PROPN
ejpam-3459	454	37	,	,	PUNCT
ejpam-3459	454	38	a	a	PRON
ejpam-3459	454	39	,	,	PUNCT
ejpam-3459	454	40	x	x	NOUN
ejpam-3459	454	41	)	)	PUNCT
ejpam-3459	455	1	=	=	SYM
ejpam-3459	455	2	ŷ0	ŷ0	NOUN
ejpam-3459	455	3	i	i	PRON
ejpam-3459	455	4	in	in	ADP
ejpam-3459	455	5	qa	qa	PROPN
ejpam-3459	455	6	,	,	PUNCT
ejpam-3459	455	7	zi(t	zi(t	NOUN
ejpam-3459	455	8	,	,	PUNCT
ejpam-3459	455	9	0	0	NUM
ejpam-3459	455	10	,	,	PUNCT
ejpam-3459	455	11	x	x	NOUN
ejpam-3459	455	12	)	)	PUNCT
ejpam-3459	455	13	=	=	SYM
ejpam-3459	455	14	g′i	g′i	NOUN
ejpam-3459	455	15	(	(	PUNCT
ejpam-3459	455	16	∫	∫	PROPN
ejpam-3459	455	17	a	a	PRON
ejpam-3459	455	18	0	0	NUM
ejpam-3459	455	19	βiy0ida	βiy0ida	NOUN
ejpam-3459	455	20	)	)	PUNCT
ejpam-3459	455	21	∫	∫	PROPN
ejpam-3459	456	1	a	a	DET
ejpam-3459	456	2	0	0	NUM
ejpam-3459	456	3	βizida	βizida	ADJ
ejpam-3459	456	4	in	in	ADP
ejpam-3459	456	5	qt	qt	NOUN
ejpam-3459	456	6	,	,	PUNCT
ejpam-3459	456	7	yi	yi	PROPN
ejpam-3459	456	8	=	=	NOUN
ejpam-3459	456	9	0	0	NUM
ejpam-3459	456	10	on	on	ADP
ejpam-3459	456	11	σ	σ	PROPN
ejpam-3459	456	12	.	.	PUNCT
ejpam-3459	457	1	(	(	PUNCT
ejpam-3459	457	2	64	64	NUM
ejpam-3459	457	3	)	)	PUNCT
ejpam-3459	457	4	we	we	PRON
ejpam-3459	457	5	show	show	VERB
ejpam-3459	457	6	as	as	ADP
ejpam-3459	457	7	in	in	ADP
ejpam-3459	457	8	[	[	X
ejpam-3459	457	9	10	10	NUM
ejpam-3459	457	10	]	]	PUNCT
ejpam-3459	457	11	that	that	PRON
ejpam-3459	457	12	:	:	PUNCT
ejpam-3459	457	13	pτi	pτi	VERB
ejpam-3459	457	14	−→	−→	NOUN
ejpam-3459	457	15	0	0	NUM
ejpam-3459	457	16	,	,	PUNCT
ejpam-3459	457	17	zτi	zτi	PROPN
ejpam-3459	457	18	−→	−→	NOUN
ejpam-3459	457	19	zi	zi	PROPN
ejpam-3459	458	1	i	i	NOUN
ejpam-3459	458	2	=	=	NOUN
ejpam-3459	458	3	1	1	NUM
ejpam-3459	458	4	;	;	PUNCT
ejpam-3459	458	5	2	2	NUM
ejpam-3459	458	6	respectively	respectively	ADV
ejpam-3459	458	7	in	in	ADP
ejpam-3459	458	8	l2	l2	NOUN
ejpam-3459	458	9	(	(	PUNCT
ejpam-3459	458	10	u	u	NOUN
ejpam-3459	458	11	;	;	PUNCT
ejpam-3459	458	12	h1	h1	PROPN
ejpam-3459	458	13	0	0	NUM
ejpam-3459	458	14	(	(	PUNCT
ejpam-3459	458	15	ω	ω	NOUN
ejpam-3459	458	16	)	)	PUNCT
ejpam-3459	458	17	)	)	PUNCT
ejpam-3459	458	18	as	as	ADP
ejpam-3459	458	19	τi	τi	ADV
ejpam-3459	458	20	→	→	SYM
ejpam-3459	458	21	0	0	X
ejpam-3459	458	22	.	.	PUNCT
ejpam-3459	459	1	c.	c.	PROPN
ejpam-3459	459	2	k.	k.	PROPN
ejpam-3459	459	3	somé	somé	PROPN
ejpam-3459	459	4	,	,	PUNCT
ejpam-3459	459	5	s.	s.	PROPN
ejpam-3459	459	6	sawadogo	sawadogo	PROPN
ejpam-3459	459	7	/	/	SYM
ejpam-3459	459	8	eur	eur	PROPN
ejpam-3459	459	9	.	.	PUNCT
ejpam-3459	460	1	j.	j.	PROPN
ejpam-3459	460	2	pure	pure	PROPN
ejpam-3459	460	3	appl	appl	PROPN
ejpam-3459	460	4	.	.	PROPN
ejpam-3459	460	5	math	math	PROPN
ejpam-3459	460	6	,	,	PUNCT
ejpam-3459	460	7	12	12	NUM
ejpam-3459	460	8	(	(	PUNCT
ejpam-3459	460	9	3	3	NUM
ejpam-3459	460	10	)	)	PUNCT
ejpam-3459	460	11	(	(	PUNCT
ejpam-3459	460	12	2019	2019	NUM
ejpam-3459	460	13	)	)	PUNCT
ejpam-3459	460	14	,	,	PUNCT
ejpam-3459	460	15	870	870	NUM
ejpam-3459	460	16	-	-	SYM
ejpam-3459	460	17	892	892	NUM
ejpam-3459	460	18	888	888	NUM
ejpam-3459	460	19	likewise	likewise	ADV
ejpam-3459	460	20	let	let	VERB
ejpam-3459	460	21	ûi(t	ûi(t	NOUN
ejpam-3459	460	22	,	,	PUNCT
ejpam-3459	460	23	a	a	PRON
ejpam-3459	460	24	,	,	PUNCT
ejpam-3459	460	25	x	x	NOUN
ejpam-3459	460	26	)	)	PUNCT
ejpam-3459	460	27	=	=	PUNCT
ejpam-3459	460	28	e−λ0	e−λ0	ADP
ejpam-3459	460	29	t	t	PROPN
ejpam-3459	460	30	(	(	PUNCT
ejpam-3459	460	31	yi(λi	yi(λi	PROPN
ejpam-3459	460	32	,	,	PUNCT
ejpam-3459	460	33	τi)−	τi)−	PUNCT
ejpam-3459	460	34	yi0	yi0	PROPN
ejpam-3459	460	35	)	)	PUNCT
ejpam-3459	461	1	i	i	PRON
ejpam-3459	461	2	=	=	NOUN
ejpam-3459	461	3	1	1	NUM
ejpam-3459	461	4	;	;	PUNCT
ejpam-3459	461	5	2	2	NUM
ejpam-3459	461	6	with	with	ADP
ejpam-3459	461	7	yi0	yi0	NOUN
ejpam-3459	462	1	=	=	SYM
ejpam-3459	462	2	yi(0	yi(0	PROPN
ejpam-3459	462	3	,	,	PUNCT
ejpam-3459	462	4	τi	τi	NOUN
ejpam-3459	462	5	)	)	PUNCT
ejpam-3459	462	6	and	and	CCONJ
ejpam-3459	462	7	for	for	ADP
ejpam-3459	462	8	each	each	DET
ejpam-3459	462	9	i	i	NOUN
ejpam-3459	462	10	=	=	NOUN
ejpam-3459	462	11	1	1	NUM
ejpam-3459	462	12	;	;	PUNCT
ejpam-3459	462	13	2	2	NUM
ejpam-3459	462	14	,	,	PUNCT
ejpam-3459	462	15	yi(λi	yi(λi	PROPN
ejpam-3459	462	16	,	,	PUNCT
ejpam-3459	462	17	τi	τi	NOUN
ejpam-3459	462	18	)	)	PUNCT
ejpam-3459	462	19	and	and	CCONJ
ejpam-3459	462	20	yi0	yi0	NOUN
ejpam-3459	462	21	solve	solve	VERB
ejpam-3459	462	22	(	(	PUNCT
ejpam-3459	462	23	59	59	NUM
ejpam-3459	462	24	)	)	PUNCT
ejpam-3459	462	25	.	.	PUNCT
ejpam-3459	463	1	then	then	ADV
ejpam-3459	463	2	ûi	ûi	PROPN
ejpam-3459	463	3	,	,	PUNCT
ejpam-3459	463	4	i	i	PRON
ejpam-3459	463	5	=	=	NOUN
ejpam-3459	463	6	1	1	NUM
ejpam-3459	463	7	;	;	PUNCT
ejpam-3459	463	8	2	2	NUM
ejpam-3459	463	9	verify	verify	PROPN
ejpam-3459	463	10	∂ûi	∂ûi	PROPN
ejpam-3459	463	11	∂t	∂t	PROPN
ejpam-3459	463	12	+	+	CCONJ
ejpam-3459	463	13	∂ûi	∂ûi	PROPN
ejpam-3459	464	1	∂a	∂a	PROPN
ejpam-3459	464	2	−∆ûi	−∆ûi	PROPN
ejpam-3459	465	1	+	+	CCONJ
ejpam-3459	465	2	(	(	PUNCT
ejpam-3459	465	3	µi	µi	INTJ
ejpam-3459	465	4	+	+	NUM
ejpam-3459	465	5	λ0)ûi	λ0)ûi	NOUN
ejpam-3459	465	6	=	=	X
ejpam-3459	465	7	0	0	NUM
ejpam-3459	465	8	in	in	ADP
ejpam-3459	465	9	q	q	PROPN
ejpam-3459	465	10	,	,	PUNCT
ejpam-3459	465	11	ûi(0	ûi(0	PROPN
ejpam-3459	465	12	,	,	PUNCT
ejpam-3459	465	13	a	a	PRON
ejpam-3459	465	14	,	,	PUNCT
ejpam-3459	465	15	x	x	NOUN
ejpam-3459	465	16	)	)	PUNCT
ejpam-3459	465	17	=	=	SYM
ejpam-3459	465	18	0	0	NUM
ejpam-3459	466	1	in	in	ADP
ejpam-3459	466	2	qa	qa	PROPN
ejpam-3459	466	3	,	,	PUNCT
ejpam-3459	466	4	ûi(t	ûi(t	PROPN
ejpam-3459	466	5	,	,	PUNCT
ejpam-3459	466	6	0	0	NUM
ejpam-3459	466	7	,	,	PUNCT
ejpam-3459	466	8	x	x	NOUN
ejpam-3459	466	9	)	)	PUNCT
ejpam-3459	466	10	=	=	PUNCT
ejpam-3459	466	11	e−λ0	e−λ0	ADP
ejpam-3459	466	12	t	t	PROPN
ejpam-3459	466	13	(	(	PUNCT
ejpam-3459	466	14	gi	gi	INTJ
ejpam-3459	466	15	(	(	PUNCT
ejpam-3459	466	16	∫	∫	PROPN
ejpam-3459	466	17	a	a	PRON
ejpam-3459	466	18	0	0	NUM
ejpam-3459	466	19	βiyida	βiyida	ADJ
ejpam-3459	466	20	)	)	PUNCT
ejpam-3459	466	21	−gi	−gi	NOUN
ejpam-3459	466	22	(	(	PUNCT
ejpam-3459	466	23	∫	∫	PROPN
ejpam-3459	466	24	a	a	DET
ejpam-3459	466	25	0	0	NUM
ejpam-3459	466	26	βiy0ida	βiy0ida	NOUN
ejpam-3459	466	27	)	)	PUNCT
ejpam-3459	466	28	)	)	PUNCT
ejpam-3459	466	29	in	in	ADP
ejpam-3459	466	30	qt	qt	NOUN
ejpam-3459	466	31	,	,	PUNCT
ejpam-3459	466	32	ûi	ûi	PROPN
ejpam-3459	466	33	=	=	PRON
ejpam-3459	466	34	{	{	PUNCT
ejpam-3459	466	35	λiĝi	λiĝi	PROPN
ejpam-3459	466	36	on	on	ADP
ejpam-3459	466	37	σi	σi	PROPN
ejpam-3459	466	38	0	0	NUM
ejpam-3459	466	39	on	on	ADP
ejpam-3459	466	40	σ	σ	PROPN
ejpam-3459	466	41	\	\	PROPN
ejpam-3459	466	42	σi	σi	PROPN
ejpam-3459	466	43	.	.	PUNCT
ejpam-3459	467	1	(	(	PUNCT
ejpam-3459	467	2	65	65	NUM
ejpam-3459	467	3	)	)	PUNCT
ejpam-3459	467	4	multiplying	multiplying	NOUN
ejpam-3459	467	5	(	(	PUNCT
ejpam-3459	467	6	65	65	NUM
ejpam-3459	467	7	)	)	PUNCT
ejpam-3459	467	8	by	by	ADP
ejpam-3459	467	9	ûi	ûi	PROPN
ejpam-3459	467	10	and	and	CCONJ
ejpam-3459	467	11	by	by	ADP
ejpam-3459	467	12	integrating	integrate	VERB
ejpam-3459	467	13	by	by	ADP
ejpam-3459	467	14	parts	part	NOUN
ejpam-3459	467	15	over	over	ADP
ejpam-3459	467	16	q	q	NOUN
ejpam-3459	467	17	,	,	PUNCT
ejpam-3459	467	18	we	we	PRON
ejpam-3459	467	19	have	have	VERB
ejpam-3459	467	20	1	1	NUM
ejpam-3459	467	21	2	2	NUM
ejpam-3459	467	22	∫	∫	NOUN
ejpam-3459	467	23	qa	qa	PROPN
ejpam-3459	468	1	û2	û2	PROPN
ejpam-3459	469	1	i	i	X
ejpam-3459	469	2	(	(	PUNCT
ejpam-3459	469	3	t	t	PROPN
ejpam-3459	469	4	,	,	PUNCT
ejpam-3459	469	5	a	a	PRON
ejpam-3459	469	6	,	,	PUNCT
ejpam-3459	469	7	x)dqa	x)dqa	ADJ
ejpam-3459	469	8	+	+	NUM
ejpam-3459	469	9	1	1	NUM
ejpam-3459	469	10	2	2	NUM
ejpam-3459	469	11	∫	∫	NOUN
ejpam-3459	469	12	qt	qt	NOUN
ejpam-3459	469	13	û2	û2	PROPN
ejpam-3459	470	1	i	i	X
ejpam-3459	470	2	(	(	PUNCT
ejpam-3459	470	3	t	t	PROPN
ejpam-3459	470	4	,	,	PUNCT
ejpam-3459	470	5	a	a	PRON
ejpam-3459	470	6	,	,	PUNCT
ejpam-3459	470	7	x)dqt	x)dqt	PROPN
ejpam-3459	471	1	+	+	CCONJ
ejpam-3459	471	2	∫	∫	PROPN
ejpam-3459	471	3	q	q	NOUN
ejpam-3459	471	4	|∇ûi|2dq	|∇ûi|2dq	NOUN
ejpam-3459	471	5	+	+	CCONJ
ejpam-3459	471	6	∫	∫	PROPN
ejpam-3459	471	7	q	q	PROPN
ejpam-3459	472	1	(	(	PUNCT
ejpam-3459	472	2	µi	µi	PROPN
ejpam-3459	472	3	+	+	CCONJ
ejpam-3459	472	4	λ0)û2	λ0)û2	X
ejpam-3459	472	5	i	i	NOUN
ejpam-3459	472	6	dq	dq	NOUN
ejpam-3459	472	7	=	=	PUNCT
ejpam-3459	473	1	τi	τi	ADP
ejpam-3459	473	2	∫	∫	PROPN
ejpam-3459	474	1	σi	σi	PROPN
ejpam-3459	474	2	∂ûi	∂ûi	PROPN
ejpam-3459	474	3	∂σi	∂σi	PROPN
ejpam-3459	474	4	ĝidσi	ĝidσi	VERB
ejpam-3459	475	1	+	+	NOUN
ejpam-3459	475	2	1	1	NUM
ejpam-3459	475	3	2	2	NUM
ejpam-3459	475	4	∫	∫	NOUN
ejpam-3459	475	5	qt	qt	NOUN
ejpam-3459	475	6	û2	û2	PROPN
ejpam-3459	476	1	i	i	X
ejpam-3459	476	2	(	(	PUNCT
ejpam-3459	476	3	t	t	PROPN
ejpam-3459	476	4	,	,	PUNCT
ejpam-3459	476	5	0	0	NUM
ejpam-3459	476	6	,	,	PUNCT
ejpam-3459	476	7	x)dqt	x)dqt	PROPN
ejpam-3459	476	8	(	(	PUNCT
ejpam-3459	476	9	66	66	NUM
ejpam-3459	476	10	)	)	PUNCT
ejpam-3459	476	11	from	from	ADP
ejpam-3459	476	12	(	(	PUNCT
ejpam-3459	476	13	62	62	NUM
ejpam-3459	476	14	)	)	PUNCT
ejpam-3459	476	15	,	,	PUNCT
ejpam-3459	476	16	taking	take	VERB
ejpam-3459	476	17	λ0	λ0	NOUN
ejpam-3459	476	18	=	=	SYM
ejpam-3459	476	19	1	1	NUM
ejpam-3459	476	20	+	+	NUM
ejpam-3459	476	21	c‖βi‖2∞	c‖βi‖2∞	NOUN
ejpam-3459	476	22	,	,	PUNCT
ejpam-3459	476	23	one	one	NUM
ejpam-3459	476	24	has	have	VERB
ejpam-3459	476	25	‖ûi‖2l2(q	‖ûi‖2l2(q	NUM
ejpam-3459	476	26	)	)	PUNCT
ejpam-3459	477	1	+	+	CCONJ
ejpam-3459	477	2	‖∇ûi‖2(l2(q))n	‖∇ûi‖2(l2(q))n	NOUN
ejpam-3459	477	3	≤	≤	NUM
ejpam-3459	477	4	λi	λi	ADP
ejpam-3459	477	5	∫	∫	PROPN
ejpam-3459	478	1	σi	σi	INTJ
ejpam-3459	478	2	∇ûiĝidσi	∇ûiĝidσi	INTJ
ejpam-3459	478	3	(	(	PUNCT
ejpam-3459	478	4	67	67	NUM
ejpam-3459	478	5	)	)	PUNCT
ejpam-3459	478	6	using	use	VERB
ejpam-3459	478	7	young	young	ADJ
ejpam-3459	478	8	inequality	inequality	NOUN
ejpam-3459	478	9	and	and	CCONJ
ejpam-3459	478	10	according	accord	VERB
ejpam-3459	478	11	to	to	ADP
ejpam-3459	478	12	hypothesis	hypothesis	NOUN
ejpam-3459	478	13	(	(	PUNCT
ejpam-3459	478	14	i	i	NOUN
ejpam-3459	478	15	)	)	PUNCT
ejpam-3459	478	16	,	,	PUNCT
ejpam-3459	478	17	there	there	PRON
ejpam-3459	478	18	exists	exist	VERB
ejpam-3459	478	19	a	a	DET
ejpam-3459	478	20	positive	positive	ADJ
ejpam-3459	478	21	constant	constant	NOUN
ejpam-3459	478	22	cy	cy	ADP
ejpam-3459	478	23	such	such	ADJ
ejpam-3459	478	24	that	that	DET
ejpam-3459	478	25	‖ûi‖2l2(q	‖ûi‖2l2(q	NUM
ejpam-3459	478	26	)	)	PUNCT
ejpam-3459	479	1	+	+	CCONJ
ejpam-3459	479	2	‖∇ûi‖2(l2(q))n	‖∇ûi‖2(l2(q))n	NOUN
ejpam-3459	479	3	≤	≤	NUM
ejpam-3459	479	4	λ2i	λ2i	PROPN
ejpam-3459	479	5	2cy	2cy	NOUN
ejpam-3459	479	6	.	.	PUNCT
ejpam-3459	480	1	(	(	PUNCT
ejpam-3459	480	2	68	68	NUM
ejpam-3459	480	3	)	)	PUNCT
ejpam-3459	480	4	then	then	ADV
ejpam-3459	480	5	ŷi	ŷi	PROPN
ejpam-3459	480	6	converges	converge	VERB
ejpam-3459	480	7	uniformly	uniformly	ADV
ejpam-3459	480	8	to	to	PART
ejpam-3459	480	9	yi0	yi0	VERB
ejpam-3459	480	10	on	on	ADP
ejpam-3459	480	11	q	q	PROPN
ejpam-3459	480	12	and	and	CCONJ
ejpam-3459	480	13	from	from	ADP
ejpam-3459	480	14	the	the	DET
ejpam-3459	480	15	regularity	regularity	NOUN
ejpam-3459	480	16	of	of	ADP
ejpam-3459	480	17	gi	gi	NOUN
ejpam-3459	480	18	,	,	PUNCT
ejpam-3459	480	19	i	i	PRON
ejpam-3459	480	20	=	=	NOUN
ejpam-3459	480	21	1	1	NUM
ejpam-3459	480	22	;	;	PUNCT
ejpam-3459	480	23	2	2	NUM
ejpam-3459	480	24	we	we	PRON
ejpam-3459	480	25	proove	proove	VERB
ejpam-3459	480	26	that	that	SCONJ
ejpam-3459	480	27	∫	∫	PROPN
ejpam-3459	480	28	a	a	DET
ejpam-3459	480	29	0	0	NUM
ejpam-3459	480	30	βiyi(λi	βiyi(λi	NOUN
ejpam-3459	480	31	,	,	PUNCT
ejpam-3459	480	32	τi)da	τi)da	PRON
ejpam-3459	480	33	converges	converge	VERB
ejpam-3459	480	34	uniformly	uniformly	ADV
ejpam-3459	480	35	to	to	PART
ejpam-3459	480	36	∫	∫	VERB
ejpam-3459	480	37	a	a	DET
ejpam-3459	480	38	0	0	NUM
ejpam-3459	480	39	βiyi0da	βiyi0da	NOUN
ejpam-3459	480	40	on	on	ADP
ejpam-3459	480	41	qt	qt	NOUN
ejpam-3459	480	42	.	.	PUNCT
ejpam-3459	481	1	one	one	NUM
ejpam-3459	481	2	deducts	deduct	NOUN
ejpam-3459	481	3	from	from	ADP
ejpam-3459	481	4	the	the	DET
ejpam-3459	481	5	proposition	proposition	NOUN
ejpam-3459	481	6	9	9	NUM
ejpam-3459	481	7	in	in	ADP
ejpam-3459	481	8	[	[	X
ejpam-3459	481	9	10	10	NUM
ejpam-3459	481	10	]	]	PUNCT
ejpam-3459	481	11	,	,	PUNCT
ejpam-3459	481	12	that	that	SCONJ
ejpam-3459	481	13	the	the	DET
ejpam-3459	481	14	functions	function	NOUN
ejpam-3459	481	15	λi	λi	ADP
ejpam-3459	481	16	7−→	7−→	PROPN
ejpam-3459	481	17	y(λi	y(λi	PROPN
ejpam-3459	481	18	,	,	PUNCT
ejpam-3459	481	19	τi	τi	ADP
ejpam-3459	481	20	)	)	PUNCT
ejpam-3459	481	21	i	i	PRON
ejpam-3459	482	1	=	=	NOUN
ejpam-3459	482	2	1	1	NUM
ejpam-3459	482	3	;	;	PUNCT
ejpam-3459	482	4	2	2	NUM
ejpam-3459	482	5	are	be	AUX
ejpam-3459	482	6	differentiable	differentiable	ADJ
ejpam-3459	482	7	.	.	PUNCT
ejpam-3459	483	1	set	set	VERB
ejpam-3459	483	2	now	now	ADV
ejpam-3459	483	3	zλi	zλi	PROPN
ejpam-3459	483	4	=	=	SYM
ejpam-3459	483	5	ûi	ûi	PROPN
ejpam-3459	483	6	λi	λi	NOUN
ejpam-3459	483	7	and	and	CCONJ
ejpam-3459	483	8	pλi	pλi	NOUN
ejpam-3459	483	9	=	=	SYM
ejpam-3459	483	10	zλi	zλi	PROPN
ejpam-3459	483	11	−	−	PROPN
ejpam-3459	483	12	zi	zi	PROPN
ejpam-3459	483	13	for	for	ADP
ejpam-3459	483	14	i	i	PRON
ejpam-3459	483	15	=	=	NOUN
ejpam-3459	483	16	1	1	NUM
ejpam-3459	483	17	;	;	PUNCT
ejpam-3459	483	18	2	2	NUM
ejpam-3459	483	19	,	,	PUNCT
ejpam-3459	483	20	where	where	SCONJ
ejpam-3459	483	21	zi	zi	NOUN
ejpam-3459	483	22	verifies	verifies	VERB
ejpam-3459	483	23	∂zi	∂zi	PROPN
ejpam-3459	483	24	∂t	∂t	PROPN
ejpam-3459	483	25	+	+	CCONJ
ejpam-3459	483	26	∂zi	∂zi	PROPN
ejpam-3459	483	27	∂a	∂a	PROPN
ejpam-3459	483	28	−∆zi	−∆zi	NOUN
ejpam-3459	483	29	+	+	CCONJ
ejpam-3459	483	30	µizi	µizi	NOUN
ejpam-3459	483	31	=	=	NOUN
ejpam-3459	483	32	0	0	NUM
ejpam-3459	483	33	in	in	ADP
ejpam-3459	483	34	q	q	PROPN
ejpam-3459	483	35	,	,	PUNCT
ejpam-3459	483	36	zi(0	zi(0	PROPN
ejpam-3459	483	37	,	,	PUNCT
ejpam-3459	483	38	a	a	PRON
ejpam-3459	483	39	,	,	PUNCT
ejpam-3459	483	40	x	x	NOUN
ejpam-3459	483	41	)	)	PUNCT
ejpam-3459	483	42	=	=	SYM
ejpam-3459	483	43	0	0	NUM
ejpam-3459	483	44	in	in	ADP
ejpam-3459	483	45	qa	qa	PROPN
ejpam-3459	483	46	,	,	PUNCT
ejpam-3459	483	47	zi(t	zi(t	NOUN
ejpam-3459	483	48	,	,	PUNCT
ejpam-3459	483	49	0	0	NUM
ejpam-3459	483	50	,	,	PUNCT
ejpam-3459	483	51	x	x	NOUN
ejpam-3459	483	52	)	)	PUNCT
ejpam-3459	483	53	=	=	SYM
ejpam-3459	483	54	g′i	g′i	NOUN
ejpam-3459	483	55	(	(	PUNCT
ejpam-3459	483	56	∫	∫	PROPN
ejpam-3459	483	57	a	a	PRON
ejpam-3459	483	58	0	0	NUM
ejpam-3459	483	59	βiy0ida	βiy0ida	NOUN
ejpam-3459	483	60	)	)	PUNCT
ejpam-3459	483	61	∫	∫	PROPN
ejpam-3459	484	1	a	a	DET
ejpam-3459	484	2	0	0	NUM
ejpam-3459	484	3	βizida	βizida	ADJ
ejpam-3459	484	4	in	in	ADP
ejpam-3459	484	5	qt	qt	NOUN
ejpam-3459	484	6	,	,	PUNCT
ejpam-3459	484	7	yi	yi	PROPN
ejpam-3459	484	8	=	=	NOUN
ejpam-3459	484	9	{	{	PUNCT
ejpam-3459	484	10	ĝi	ĝi	PROPN
ejpam-3459	484	11	on	on	ADP
ejpam-3459	484	12	σi	σi	PRON
ejpam-3459	484	13	0	0	NUM
ejpam-3459	484	14	on	on	ADP
ejpam-3459	484	15	σ	σ	PROPN
ejpam-3459	484	16	\	\	PROPN
ejpam-3459	484	17	σi	σi	PROPN
ejpam-3459	484	18	.	.	PUNCT
ejpam-3459	485	1	(	(	PUNCT
ejpam-3459	485	2	69	69	NUM
ejpam-3459	485	3	)	)	PUNCT
ejpam-3459	485	4	c.	c.	PROPN
ejpam-3459	485	5	k.	k.	PROPN
ejpam-3459	485	6	somé	somé	PROPN
ejpam-3459	485	7	,	,	PUNCT
ejpam-3459	485	8	s.	s.	PROPN
ejpam-3459	485	9	sawadogo	sawadogo	PROPN
ejpam-3459	485	10	/	/	SYM
ejpam-3459	485	11	eur	eur	PROPN
ejpam-3459	485	12	.	.	PUNCT
ejpam-3459	486	1	j.	j.	PROPN
ejpam-3459	486	2	pure	pure	PROPN
ejpam-3459	486	3	appl	appl	PROPN
ejpam-3459	486	4	.	.	PROPN
ejpam-3459	486	5	math	math	PROPN
ejpam-3459	486	6	,	,	PUNCT
ejpam-3459	486	7	12	12	NUM
ejpam-3459	486	8	(	(	PUNCT
ejpam-3459	486	9	3	3	NUM
ejpam-3459	486	10	)	)	PUNCT
ejpam-3459	486	11	(	(	PUNCT
ejpam-3459	486	12	2019	2019	NUM
ejpam-3459	486	13	)	)	PUNCT
ejpam-3459	486	14	,	,	PUNCT
ejpam-3459	486	15	870	870	NUM
ejpam-3459	486	16	-	-	SYM
ejpam-3459	486	17	892	892	NUM
ejpam-3459	486	18	889	889	NUM
ejpam-3459	486	19	then	then	ADV
ejpam-3459	486	20	pλi	pλi	NOUN
ejpam-3459	486	21	solves	solves	PROPN
ejpam-3459	486	22	∂pλi	∂pλi	CCONJ
ejpam-3459	486	23	∂t	∂t	PROPN
ejpam-3459	487	1	+	+	CCONJ
ejpam-3459	487	2	∂pλi	∂pλi	ADJ
ejpam-3459	487	3	∂a	∂a	PROPN
ejpam-3459	487	4	−∆pλi	−∆pλi	ADJ
ejpam-3459	487	5	+	+	CCONJ
ejpam-3459	487	6	µipλi	µipλi	NOUN
ejpam-3459	487	7	=	=	SYM
ejpam-3459	487	8	0	0	NUM
ejpam-3459	487	9	in	in	ADP
ejpam-3459	487	10	q	q	NOUN
ejpam-3459	487	11	,	,	PUNCT
ejpam-3459	487	12	pλi	pλi	NOUN
ejpam-3459	487	13	(	(	PUNCT
ejpam-3459	487	14	0	0	NUM
ejpam-3459	487	15	,	,	PUNCT
ejpam-3459	487	16	a	a	PRON
ejpam-3459	487	17	,	,	PUNCT
ejpam-3459	487	18	x	x	NOUN
ejpam-3459	487	19	)	)	PUNCT
ejpam-3459	487	20	=	=	SYM
ejpam-3459	487	21	0	0	NUM
ejpam-3459	488	1	in	in	ADP
ejpam-3459	488	2	qa	qa	PROPN
ejpam-3459	488	3	,	,	PUNCT
ejpam-3459	488	4	pλi(t	pλi(t	PROPN
ejpam-3459	488	5	,	,	PUNCT
ejpam-3459	488	6	0	0	NUM
ejpam-3459	488	7	,	,	PUNCT
ejpam-3459	488	8	x	x	NOUN
ejpam-3459	488	9	)	)	PUNCT
ejpam-3459	488	10	=	=	PUNCT
ejpam-3459	488	11	e−λ0	e−λ0	ADP
ejpam-3459	488	12	t	t	X
ejpam-3459	488	13	[	[	PUNCT
ejpam-3459	488	14	gi	gi	X
ejpam-3459	488	15	(	(	PUNCT
ejpam-3459	488	16	∫	∫	PROPN
ejpam-3459	488	17	a	a	PRON
ejpam-3459	488	18	0	0	NUM
ejpam-3459	488	19	βiyida	βiyida	ADJ
ejpam-3459	488	20	)	)	PUNCT
ejpam-3459	488	21	−gi	−gi	NOUN
ejpam-3459	488	22	(	(	PUNCT
ejpam-3459	488	23	∫	∫	PROPN
ejpam-3459	488	24	a	a	DET
ejpam-3459	488	25	0	0	NUM
ejpam-3459	488	26	βiy0ida	βiy0ida	NOUN
ejpam-3459	488	27	)	)	PUNCT
ejpam-3459	488	28	]	]	PUNCT
ejpam-3459	489	1	−g′i	−g′i	PRON
ejpam-3459	489	2	(	(	PUNCT
ejpam-3459	489	3	∫	∫	PROPN
ejpam-3459	489	4	a	a	PRON
ejpam-3459	489	5	0	0	NUM
ejpam-3459	489	6	βiy0ida	βiy0ida	NOUN
ejpam-3459	489	7	)	)	PUNCT
ejpam-3459	489	8	∫	∫	PROPN
ejpam-3459	490	1	a	a	DET
ejpam-3459	490	2	0	0	NUM
ejpam-3459	490	3	βizida	βizida	ADJ
ejpam-3459	490	4	in	in	ADP
ejpam-3459	490	5	qt	qt	NOUN
ejpam-3459	490	6	,	,	PUNCT
ejpam-3459	490	7	pλi	pλi	NOUN
ejpam-3459	490	8	=	=	SYM
ejpam-3459	490	9	0	0	NUM
ejpam-3459	490	10	on	on	ADP
ejpam-3459	490	11	σ	σ	PROPN
ejpam-3459	490	12	.	.	PUNCT
ejpam-3459	491	1	(	(	PUNCT
ejpam-3459	491	2	70	70	X
ejpam-3459	491	3	)	)	PUNCT
ejpam-3459	491	4	we	we	PRON
ejpam-3459	491	5	obtain	obtain	VERB
ejpam-3459	491	6	the	the	DET
ejpam-3459	491	7	equality	equality	NOUN
ejpam-3459	491	8	(	(	PUNCT
ejpam-3459	491	9	66	66	NUM
ejpam-3459	491	10	)	)	PUNCT
ejpam-3459	491	11	when	when	SCONJ
ejpam-3459	491	12	we	we	PRON
ejpam-3459	491	13	multiply	multiply	VERB
ejpam-3459	491	14	(	(	PUNCT
ejpam-3459	491	15	70	70	NUM
ejpam-3459	491	16	)	)	PUNCT
ejpam-3459	491	17	by	by	ADP
ejpam-3459	491	18	pλi	pλi	NOUN
ejpam-3459	491	19	and	and	CCONJ
ejpam-3459	491	20	integrate	integrate	VERB
ejpam-3459	491	21	by	by	ADP
ejpam-3459	491	22	parts	part	NOUN
ejpam-3459	491	23	over	over	ADP
ejpam-3459	491	24	q.	q.	NOUN
ejpam-3459	491	25	from	from	ADP
ejpam-3459	491	26	the	the	DET
ejpam-3459	491	27	fact	fact	NOUN
ejpam-3459	491	28	that	that	SCONJ
ejpam-3459	491	29	the	the	DET
ejpam-3459	491	30	functions	function	NOUN
ejpam-3459	491	31	gi	gi	VERB
ejpam-3459	491	32	i	i	NOUN
ejpam-3459	491	33	=	=	NOUN
ejpam-3459	492	1	1	1	NUM
ejpam-3459	492	2	;	;	PUNCT
ejpam-3459	492	3	2	2	NUM
ejpam-3459	492	4	are	be	AUX
ejpam-3459	492	5	globally	globally	ADV
ejpam-3459	492	6	lipschitz	lipschitz	ADJ
ejpam-3459	492	7	and	and	CCONJ
ejpam-3459	492	8	λi	λi	NOUN
ejpam-3459	492	9	7−→	7−→	PROPN
ejpam-3459	492	10	yi(λi	yi(λi	PROPN
ejpam-3459	492	11	,	,	PUNCT
ejpam-3459	492	12	τi	τi	CCONJ
ejpam-3459	492	13	)	)	PUNCT
ejpam-3459	492	14	converge	converge	VERB
ejpam-3459	492	15	uniformly	uniformly	ADV
ejpam-3459	492	16	,	,	PUNCT
ejpam-3459	492	17	one	one	PRON
ejpam-3459	492	18	deduces	deduce	VERB
ejpam-3459	492	19	that	that	SCONJ
ejpam-3459	492	20	the	the	DET
ejpam-3459	492	21	functions	function	NOUN
ejpam-3459	492	22	λi	λi	ADP
ejpam-3459	492	23	7−→	7−→	PROPN
ejpam-3459	492	24	yi(λi	yi(λi	PROPN
ejpam-3459	492	25	,	,	PUNCT
ejpam-3459	492	26	τi	τi	ADP
ejpam-3459	492	27	)	)	PUNCT
ejpam-3459	492	28	i	i	PRON
ejpam-3459	492	29	=	=	NOUN
ejpam-3459	492	30	1	1	NUM
ejpam-3459	492	31	;	;	PUNCT
ejpam-3459	492	32	2	2	NUM
ejpam-3459	492	33	are	be	AUX
ejpam-3459	492	34	differentiable	differentiable	ADJ
ejpam-3459	492	35	(	(	PUNCT
ejpam-3459	492	36	see	see	VERB
ejpam-3459	492	37	proposition	proposition	NOUN
ejpam-3459	492	38	9	9	NUM
ejpam-3459	492	39	in	in	ADP
ejpam-3459	492	40	[	[	X
ejpam-3459	492	41	10	10	NUM
ejpam-3459	492	42	]	]	NUM
ejpam-3459	492	43	)	)	PUNCT
ejpam-3459	492	44	.	.	PUNCT
ejpam-3459	493	1	in	in	ADP
ejpam-3459	493	2	the	the	DET
ejpam-3459	493	3	sequel	sequel	NOUN
ejpam-3459	493	4	,	,	PUNCT
ejpam-3459	493	5	we	we	PRON
ejpam-3459	493	6	consider	consider	VERB
ejpam-3459	493	7	for	for	ADP
ejpam-3459	493	8	h	h	NOUN
ejpam-3459	493	9	∈	∈	PROPN
ejpam-3459	493	10	l2(qo	l2(qo	PROPN
ejpam-3459	493	11	)	)	PUNCT
ejpam-3459	493	12	and	and	CCONJ
ejpam-3459	493	13	w	w	PROPN
ejpam-3459	493	14	∈	∈	PROPN
ejpam-3459	493	15	l2(qω	l2(qω	PROPN
ejpam-3459	493	16	)	)	PUNCT
ejpam-3459	493	17	,	,	PUNCT
ejpam-3459	493	18	the	the	DET
ejpam-3459	493	19	following	follow	VERB
ejpam-3459	493	20	functionals	functional	NOUN
ejpam-3459	493	21	:	:	PUNCT
ejpam-3459	493	22	si(λi	si(λi	ADJ
ejpam-3459	493	23	,	,	PUNCT
ejpam-3459	493	24	τi	τi	NOUN
ejpam-3459	493	25	)	)	PUNCT
ejpam-3459	493	26	=	=	SYM
ejpam-3459	493	27	∫	∫	PROPN
ejpam-3459	493	28	qo	qo	PROPN
ejpam-3459	493	29	hyi(λi	hyi(λi	PRON
ejpam-3459	493	30	,	,	PUNCT
ejpam-3459	493	31	τi)dq+	τi)dq+	ADJ
ejpam-3459	493	32	∫	∫	PROPN
ejpam-3459	493	33	qω	qω	PROPN
ejpam-3459	493	34	wyi(λi	wyi(λi	NOUN
ejpam-3459	493	35	,	,	PUNCT
ejpam-3459	493	36	τi)dq	τi)dq	PUNCT
ejpam-3459	493	37	i	i	PRON
ejpam-3459	493	38	=	=	NOUN
ejpam-3459	493	39	1	1	NUM
ejpam-3459	493	40	;	;	PUNCT
ejpam-3459	493	41	2	2	NUM
ejpam-3459	493	42	.	.	PUNCT
ejpam-3459	493	43	(	(	PUNCT
ejpam-3459	493	44	71	71	NUM
ejpam-3459	493	45	)	)	PUNCT
ejpam-3459	493	46	we	we	PRON
ejpam-3459	493	47	obtain	obtain	VERB
ejpam-3459	493	48	from	from	ADP
ejpam-3459	493	49	the	the	DET
ejpam-3459	493	50	proposition	proposition	NOUN
ejpam-3459	493	51	3	3	NUM
ejpam-3459	493	52	the	the	DET
ejpam-3459	493	53	following	following	ADJ
ejpam-3459	493	54	result	result	NOUN
ejpam-3459	493	55	.	.	PUNCT
ejpam-3459	494	1	corollary	corollary	ADJ
ejpam-3459	494	2	1	1	NUM
ejpam-3459	494	3	.	.	PUNCT
ejpam-3459	495	1	the	the	DET
ejpam-3459	495	2	functionals	functional	NOUN
ejpam-3459	495	3	si	si	INTJ
ejpam-3459	495	4	i	i	NOUN
ejpam-3459	495	5	=	=	PROPN
ejpam-3459	495	6	1	1	NUM
ejpam-3459	495	7	;	;	PUNCT
ejpam-3459	495	8	2	2	NUM
ejpam-3459	495	9	are	be	AUX
ejpam-3459	495	10	differentiable	differentiable	ADJ
ejpam-3459	495	11	at	at	ADP
ejpam-3459	495	12	the	the	DET
ejpam-3459	495	13	point	point	NOUN
ejpam-3459	495	14	(	(	PUNCT
ejpam-3459	495	15	0	0	NUM
ejpam-3459	495	16	,	,	PUNCT
ejpam-3459	495	17	0	0	NUM
ejpam-3459	495	18	)	)	PUNCT
ejpam-3459	495	19	and	and	CCONJ
ejpam-3459	495	20	∂si	∂si	PROPN
ejpam-3459	495	21	∂τi	∂τi	PROPN
ejpam-3459	495	22	(	(	PUNCT
ejpam-3459	495	23	0	0	NUM
ejpam-3459	495	24	,	,	PUNCT
ejpam-3459	495	25	0	0	NUM
ejpam-3459	495	26	)	)	PUNCT
ejpam-3459	495	27	=	=	SYM
ejpam-3459	496	1	∫	∫	PROPN
ejpam-3459	497	1	qo	qo	PROPN
ejpam-3459	498	1	hyτidq+	hyτidq+	X
ejpam-3459	498	2	∫	∫	PROPN
ejpam-3459	498	3	qω	qω	NOUN
ejpam-3459	498	4	wyτidq	wyτidq	NOUN
ejpam-3459	498	5	i	i	PRON
ejpam-3459	498	6	=	=	NOUN
ejpam-3459	498	7	1	1	NUM
ejpam-3459	498	8	;	;	PUNCT
ejpam-3459	498	9	2	2	NUM
ejpam-3459	498	10	(	(	PUNCT
ejpam-3459	498	11	72	72	NUM
ejpam-3459	498	12	)	)	PUNCT
ejpam-3459	498	13	∂si	∂si	PROPN
ejpam-3459	498	14	∂λi	∂λi	PROPN
ejpam-3459	498	15	(	(	PUNCT
ejpam-3459	498	16	0	0	NUM
ejpam-3459	498	17	,	,	PUNCT
ejpam-3459	498	18	0	0	NUM
ejpam-3459	498	19	)	)	PUNCT
ejpam-3459	498	20	=	=	SYM
ejpam-3459	499	1	∫	∫	PROPN
ejpam-3459	499	2	qo	qo	PROPN
ejpam-3459	500	1	hyλidq+	hyλidq+	X
ejpam-3459	500	2	∫	∫	PROPN
ejpam-3459	500	3	qω	qω	INTJ
ejpam-3459	500	4	wyλidq	wyλidq	NOUN
ejpam-3459	500	5	i	i	PRON
ejpam-3459	500	6	=	=	NOUN
ejpam-3459	500	7	1	1	NUM
ejpam-3459	500	8	;	;	PUNCT
ejpam-3459	500	9	2	2	NUM
ejpam-3459	500	10	(	(	PUNCT
ejpam-3459	500	11	73	73	NUM
ejpam-3459	500	12	)	)	PUNCT
ejpam-3459	500	13	where	where	SCONJ
ejpam-3459	500	14	for	for	ADP
ejpam-3459	500	15	each	each	DET
ejpam-3459	500	16	i	i	NOUN
ejpam-3459	500	17	=	=	NOUN
ejpam-3459	500	18	1	1	NUM
ejpam-3459	500	19	;	;	PUNCT
ejpam-3459	500	20	2	2	NUM
ejpam-3459	500	21	,	,	PUNCT
ejpam-3459	500	22	yτi	yτi	NOUN
ejpam-3459	500	23	solves	solve	VERB
ejpam-3459	500	24	the	the	DET
ejpam-3459	500	25	system	system	NOUN
ejpam-3459	500	26	:	:	PUNCT
ejpam-3459	500	27			ADV
ejpam-3459	500	28	∂yτi	∂yτi	PROPN
ejpam-3459	501	1	∂t	∂t	PROPN
ejpam-3459	501	2	+	+	CCONJ
ejpam-3459	501	3	∂yτi	∂yτi	X
ejpam-3459	501	4	∂a	∂a	PROPN
ejpam-3459	501	5	−∆yτi	−∆yτi	NOUN
ejpam-3459	501	6	+	+	CCONJ
ejpam-3459	501	7	µiyτi	µiyτi	ADJ
ejpam-3459	501	8	=	=	NOUN
ejpam-3459	501	9	0	0	NUM
ejpam-3459	501	10	in	in	ADP
ejpam-3459	501	11	q	q	NOUN
ejpam-3459	501	12	,	,	PUNCT
ejpam-3459	501	13	yτi(0	yτi(0	NOUN
ejpam-3459	501	14	,	,	PUNCT
ejpam-3459	501	15	a	a	DET
ejpam-3459	501	16	,	,	PUNCT
ejpam-3459	501	17	x	x	NOUN
ejpam-3459	501	18	)	)	PUNCT
ejpam-3459	501	19	=	=	SYM
ejpam-3459	501	20	ŷ0(a	ŷ0(a	PROPN
ejpam-3459	501	21	,	,	PUNCT
ejpam-3459	501	22	x	x	NOUN
ejpam-3459	501	23	)	)	PUNCT
ejpam-3459	501	24	in	in	ADP
ejpam-3459	501	25	qa	qa	PROPN
ejpam-3459	501	26	,	,	PUNCT
ejpam-3459	501	27	yτi(t	yτi(t	PROPN
ejpam-3459	501	28	,	,	PUNCT
ejpam-3459	501	29	0	0	NUM
ejpam-3459	501	30	,	,	PUNCT
ejpam-3459	501	31	x	x	NOUN
ejpam-3459	501	32	)	)	PUNCT
ejpam-3459	501	33	=	=	SYM
ejpam-3459	501	34	g′i	g′i	NOUN
ejpam-3459	501	35	(	(	PUNCT
ejpam-3459	501	36	∫	∫	PROPN
ejpam-3459	501	37	a	a	PRON
ejpam-3459	501	38	0	0	NUM
ejpam-3459	501	39	βiy0ida	βiy0ida	NOUN
ejpam-3459	501	40	)	)	PUNCT
ejpam-3459	501	41	∫	∫	PROPN
ejpam-3459	502	1	a	a	DET
ejpam-3459	502	2	0	0	NUM
ejpam-3459	502	3	βizida	βizida	ADJ
ejpam-3459	502	4	in	in	ADP
ejpam-3459	502	5	qt	qt	NOUN
ejpam-3459	502	6	,	,	PUNCT
ejpam-3459	502	7	yτi	yτi	NOUN
ejpam-3459	502	8	=	=	NOUN
ejpam-3459	502	9	0	0	NUM
ejpam-3459	502	10	on	on	ADP
ejpam-3459	502	11	σ	σ	PROPN
ejpam-3459	502	12	,	,	PUNCT
ejpam-3459	502	13	(	(	PUNCT
ejpam-3459	502	14	74	74	NUM
ejpam-3459	502	15	)	)	PUNCT
ejpam-3459	502	16	and	and	CCONJ
ejpam-3459	502	17	yλi	yλi	NOUN
ejpam-3459	502	18	solves	solve	VERB
ejpam-3459	502	19	the	the	DET
ejpam-3459	502	20	system	system	PROPN
ejpam-3459	502	21	∂yλi	∂yλi	SCONJ
ejpam-3459	502	22	∂t	∂t	PROPN
ejpam-3459	502	23	+	+	CCONJ
ejpam-3459	502	24	∂yλi	∂yλi	ADV
ejpam-3459	502	25	∂a	∂a	NOUN
ejpam-3459	502	26	−∆yλi	−∆yλi	ADV
ejpam-3459	502	27	+	+	CCONJ
ejpam-3459	502	28	µiyλi	µiyλi	ADV
ejpam-3459	502	29	=	=	SYM
ejpam-3459	502	30	0	0	NUM
ejpam-3459	502	31	in	in	ADP
ejpam-3459	502	32	q	q	ADJ
ejpam-3459	502	33	,	,	PUNCT
ejpam-3459	502	34	yλi	yλi	NOUN
ejpam-3459	502	35	(	(	PUNCT
ejpam-3459	502	36	0	0	NUM
ejpam-3459	502	37	,	,	PUNCT
ejpam-3459	502	38	a	a	PRON
ejpam-3459	502	39	,	,	PUNCT
ejpam-3459	502	40	x	x	NOUN
ejpam-3459	502	41	)	)	PUNCT
ejpam-3459	502	42	=	=	SYM
ejpam-3459	502	43	0	0	NUM
ejpam-3459	503	1	in	in	ADP
ejpam-3459	503	2	qa	qa	PROPN
ejpam-3459	503	3	,	,	PUNCT
ejpam-3459	503	4	yλi	yλi	PROPN
ejpam-3459	503	5	(	(	PUNCT
ejpam-3459	503	6	t	t	PROPN
ejpam-3459	503	7	,	,	PUNCT
ejpam-3459	503	8	0	0	NUM
ejpam-3459	503	9	,	,	PUNCT
ejpam-3459	503	10	x	x	NOUN
ejpam-3459	503	11	)	)	PUNCT
ejpam-3459	503	12	=	=	SYM
ejpam-3459	503	13	g′i	g′i	NOUN
ejpam-3459	503	14	(	(	PUNCT
ejpam-3459	503	15	∫	∫	PROPN
ejpam-3459	503	16	a	a	PRON
ejpam-3459	503	17	0	0	NUM
ejpam-3459	503	18	βiy0ida	βiy0ida	NOUN
ejpam-3459	503	19	)	)	PUNCT
ejpam-3459	503	20	∫	∫	PROPN
ejpam-3459	504	1	a	a	DET
ejpam-3459	504	2	0	0	NUM
ejpam-3459	504	3	βiyλi	βiyλi	NOUN
ejpam-3459	504	4	da	da	NOUN
ejpam-3459	504	5	in	in	ADP
ejpam-3459	504	6	qt	qt	NOUN
ejpam-3459	504	7	,	,	PUNCT
ejpam-3459	504	8	yλi	yλi	NOUN
ejpam-3459	504	9	=	=	PUNCT
ejpam-3459	504	10	{	{	PUNCT
ejpam-3459	504	11	ĝi	ĝi	PROPN
ejpam-3459	504	12	on	on	ADP
ejpam-3459	504	13	σi	σi	PRON
ejpam-3459	504	14	0	0	NUM
ejpam-3459	504	15	on	on	ADP
ejpam-3459	504	16	σ	σ	PROPN
ejpam-3459	504	17	\	\	PROPN
ejpam-3459	504	18	σi	σi	PROPN
ejpam-3459	504	19	.	.	PUNCT
ejpam-3459	505	1	(	(	PUNCT
ejpam-3459	505	2	75	75	NUM
ejpam-3459	505	3	)	)	PUNCT
ejpam-3459	505	4	c.	c.	PROPN
ejpam-3459	505	5	k.	k.	PROPN
ejpam-3459	505	6	somé	somé	PROPN
ejpam-3459	505	7	,	,	PUNCT
ejpam-3459	505	8	s.	s.	PROPN
ejpam-3459	505	9	sawadogo	sawadogo	PROPN
ejpam-3459	505	10	/	/	SYM
ejpam-3459	505	11	eur	eur	PROPN
ejpam-3459	505	12	.	.	PUNCT
ejpam-3459	506	1	j.	j.	PROPN
ejpam-3459	506	2	pure	pure	PROPN
ejpam-3459	506	3	appl	appl	PROPN
ejpam-3459	506	4	.	.	PROPN
ejpam-3459	506	5	math	math	PROPN
ejpam-3459	506	6	,	,	PUNCT
ejpam-3459	506	7	12	12	NUM
ejpam-3459	506	8	(	(	PUNCT
ejpam-3459	506	9	3	3	NUM
ejpam-3459	506	10	)	)	PUNCT
ejpam-3459	506	11	(	(	PUNCT
ejpam-3459	506	12	2019	2019	NUM
ejpam-3459	506	13	)	)	PUNCT
ejpam-3459	506	14	,	,	PUNCT
ejpam-3459	506	15	870	870	NUM
ejpam-3459	506	16	-	-	SYM
ejpam-3459	506	17	892	892	NUM
ejpam-3459	506	18	890	890	NUM
ejpam-3459	506	19	moreover	moreover	ADV
ejpam-3459	506	20	yλi	yλi	NOUN
ejpam-3459	506	21	,	,	PUNCT
ejpam-3459	506	22	yτi	yτi	NOUN
ejpam-3459	506	23	∈	∈	PROPN
ejpam-3459	506	24	c((0	c((0	PROPN
ejpam-3459	506	25	,	,	PUNCT
ejpam-3459	506	26	t	t	PROPN
ejpam-3459	506	27	)	)	PUNCT
ejpam-3459	506	28	;	;	PUNCT
ejpam-3459	506	29	l2(qa	l2(qa	PROPN
ejpam-3459	506	30	)	)	PUNCT
ejpam-3459	506	31	)	)	PUNCT
ejpam-3459	506	32	∩	∩	PROPN
ejpam-3459	506	33	c((0	c((0	PROPN
ejpam-3459	506	34	,	,	PUNCT
ejpam-3459	506	35	a);l2(qt	a);l2(qt	NOUN
ejpam-3459	506	36	)	)	PUNCT
ejpam-3459	506	37	)	)	PUNCT
ejpam-3459	506	38	∩	∩	PROPN
ejpam-3459	507	1	l2(u	l2(u	PROPN
ejpam-3459	507	2	,	,	PUNCT
ejpam-3459	507	3	h1	h1	PROPN
ejpam-3459	507	4	0	0	NUM
ejpam-3459	507	5	(	(	PUNCT
ejpam-3459	507	6	ω	ω	NOUN
ejpam-3459	507	7	)	)	PUNCT
ejpam-3459	507	8	)	)	PUNCT
ejpam-3459	508	1	i	i	PRON
ejpam-3459	508	2	=	=	NOUN
ejpam-3459	508	3	1	1	NUM
ejpam-3459	508	4	;	;	PUNCT
ejpam-3459	508	5	2	2	NUM
ejpam-3459	508	6	.	.	PUNCT
ejpam-3459	508	7	(	(	PUNCT
ejpam-3459	508	8	76	76	NUM
ejpam-3459	508	9	)	)	PUNCT
ejpam-3459	508	10	proof	proof	NOUN
ejpam-3459	508	11	.	.	PUNCT
ejpam-3459	509	1	we	we	PRON
ejpam-3459	509	2	know	know	VERB
ejpam-3459	509	3	that	that	SCONJ
ejpam-3459	509	4	for	for	ADP
ejpam-3459	509	5	each	each	DET
ejpam-3459	509	6	pair	pair	NOUN
ejpam-3459	509	7	(	(	PUNCT
ejpam-3459	509	8	λi	λi	NOUN
ejpam-3459	509	9	,	,	PUNCT
ejpam-3459	509	10	τi	τi	ADJ
ejpam-3459	509	11	)	)	PUNCT
ejpam-3459	509	12	∈	∈	NOUN
ejpam-3459	509	13	r2	r2	NOUN
ejpam-3459	509	14	,	,	PUNCT
ejpam-3459	509	15	(	(	PUNCT
ejpam-3459	509	16	59	59	NUM
ejpam-3459	509	17	)	)	PUNCT
ejpam-3459	509	18	admits	admit	VERB
ejpam-3459	509	19	an	an	DET
ejpam-3459	509	20	unique	unique	ADJ
ejpam-3459	509	21	solution	solution	NOUN
ejpam-3459	509	22	y(λi	y(λi	NUM
ejpam-3459	509	23	,	,	PUNCT
ejpam-3459	509	24	τi	τi	ADP
ejpam-3459	509	25	)	)	PUNCT
ejpam-3459	509	26	in	in	ADP
ejpam-3459	509	27	c((0	c((0	PROPN
ejpam-3459	509	28	,	,	PUNCT
ejpam-3459	509	29	t	t	PROPN
ejpam-3459	509	30	)	)	PUNCT
ejpam-3459	509	31	;	;	PUNCT
ejpam-3459	509	32	l2(qa	l2(qa	PROPN
ejpam-3459	509	33	)	)	PUNCT
ejpam-3459	509	34	)	)	PUNCT
ejpam-3459	510	1	∩	∩	PROPN
ejpam-3459	510	2	c((0	c((0	PROPN
ejpam-3459	510	3	,	,	PUNCT
ejpam-3459	510	4	a);l2(qt	a);l2(qt	NOUN
ejpam-3459	510	5	)	)	PUNCT
ejpam-3459	510	6	)	)	PUNCT
ejpam-3459	511	1	∩	∩	PROPN
ejpam-3459	511	2	l2(u	l2(u	PROPN
ejpam-3459	511	3	,	,	PUNCT
ejpam-3459	511	4	h1	h1	NOUN
ejpam-3459	511	5	0	0	NUM
ejpam-3459	511	6	(	(	PUNCT
ejpam-3459	511	7	ω))2	ω))2	NOUN
ejpam-3459	511	8	(	(	PUNCT
ejpam-3459	511	9	see	see	VERB
ejpam-3459	511	10	[	[	X
ejpam-3459	511	11	5	5	NUM
ejpam-3459	511	12	]	]	NUM
ejpam-3459	511	13	)	)	PUNCT
ejpam-3459	511	14	.	.	PUNCT
ejpam-3459	512	1	we	we	PRON
ejpam-3459	512	2	have	have	VERB
ejpam-3459	512	3	si(λi	si(λi	PROPN
ejpam-3459	512	4	=	=	SYM
ejpam-3459	512	5	0	0	NUM
ejpam-3459	512	6	,	,	PUNCT
ejpam-3459	512	7	τi	τi	NOUN
ejpam-3459	512	8	)	)	PUNCT
ejpam-3459	512	9	=	=	SYM
ejpam-3459	513	1	∫	∫	PROPN
ejpam-3459	514	1	qo	qo	PROPN
ejpam-3459	514	2	hy(λi	hy(λi	PROPN
ejpam-3459	514	3	=	=	SYM
ejpam-3459	514	4	0	0	NUM
ejpam-3459	514	5	,	,	PUNCT
ejpam-3459	514	6	τi)dq+	τi)dq+	NOUN
ejpam-3459	514	7	∫	∫	PROPN
ejpam-3459	515	1	qω	qω	NOUN
ejpam-3459	515	2	wy(λi	wy(λi	PROPN
ejpam-3459	515	3	=	=	SYM
ejpam-3459	515	4	0	0	NUM
ejpam-3459	515	5	,	,	PUNCT
ejpam-3459	515	6	τi)dq	τi)dq	PUNCT
ejpam-3459	515	7	.	.	PUNCT
ejpam-3459	516	1	so	so	ADV
ejpam-3459	516	2	si(λi	si(λi	ADV
ejpam-3459	516	3	=	=	SYM
ejpam-3459	516	4	0	0	NUM
ejpam-3459	516	5	,	,	PUNCT
ejpam-3459	516	6	τi)−	τi)−	NOUN
ejpam-3459	516	7	si(0	si(0	NOUN
ejpam-3459	516	8	,	,	PUNCT
ejpam-3459	516	9	0	0	NUM
ejpam-3459	516	10	)	)	PUNCT
ejpam-3459	516	11	τi	τi	VERB
ejpam-3459	517	1	=	=	SYM
ejpam-3459	517	2	∫	∫	PROPN
ejpam-3459	517	3	qo	qo	PROPN
ejpam-3459	517	4	h	h	PROPN
ejpam-3459	517	5	y(λi	y(λi	PROPN
ejpam-3459	517	6	=	=	SYM
ejpam-3459	517	7	0	0	NUM
ejpam-3459	517	8	,	,	PUNCT
ejpam-3459	517	9	τi)−	τi)−	PUNCT
ejpam-3459	517	10	yi(0	yi(0	PROPN
ejpam-3459	517	11	,	,	PUNCT
ejpam-3459	517	12	0	0	NUM
ejpam-3459	517	13	)	)	PUNCT
ejpam-3459	517	14	τi	τi	VERB
ejpam-3459	517	15	dq	dq	ADP
ejpam-3459	518	1	+	+	CCONJ
ejpam-3459	518	2	∫	∫	PROPN
ejpam-3459	518	3	qω	qω	CCONJ
ejpam-3459	518	4	w	w	PROPN
ejpam-3459	518	5	y(λi	y(λi	PROPN
ejpam-3459	518	6	=	=	SYM
ejpam-3459	518	7	0	0	NUM
ejpam-3459	518	8	,	,	PUNCT
ejpam-3459	518	9	τi)−	τi)−	PUNCT
ejpam-3459	519	1	yi(0	yi(0	PROPN
ejpam-3459	519	2	,	,	PUNCT
ejpam-3459	519	3	0	0	NUM
ejpam-3459	519	4	)	)	PUNCT
ejpam-3459	519	5	τi	τi	VERB
ejpam-3459	519	6	dq	dq	ADP
ejpam-3459	519	7	passing	pass	VERB
ejpam-3459	519	8	to	to	ADP
ejpam-3459	519	9	the	the	DET
ejpam-3459	519	10	limit	limit	NOUN
ejpam-3459	519	11	as	as	ADP
ejpam-3459	519	12	τi	τi	ADV
ejpam-3459	519	13	→	→	SYM
ejpam-3459	519	14	0	0	NUM
ejpam-3459	519	15	one	one	NUM
ejpam-3459	519	16	obtain	obtain	NOUN
ejpam-3459	519	17	(	(	PUNCT
ejpam-3459	519	18	72	72	NUM
ejpam-3459	519	19	)	)	PUNCT
ejpam-3459	519	20	.	.	PUNCT
ejpam-3459	520	1	likewise	likewise	ADV
ejpam-3459	520	2	,	,	PUNCT
ejpam-3459	520	3	since	since	SCONJ
ejpam-3459	520	4	y(λi	y(λi	PROPN
ejpam-3459	520	5	=	=	SYM
ejpam-3459	520	6	0	0	NUM
ejpam-3459	520	7	,	,	PUNCT
ejpam-3459	520	8	τi	τi	ADJ
ejpam-3459	520	9	)	)	PUNCT
ejpam-3459	520	10	−	−	PROPN
ejpam-3459	520	11	yi(0	yi(0	PROPN
ejpam-3459	520	12	,	,	PUNCT
ejpam-3459	520	13	0	0	NUM
ejpam-3459	520	14	)	)	PUNCT
ejpam-3459	520	15	verifies	verifie	NOUN
ejpam-3459	520	16	(	(	PUNCT
ejpam-3459	520	17	61	61	NUM
ejpam-3459	520	18	)	)	PUNCT
ejpam-3459	520	19	with	with	ADP
ejpam-3459	520	20	λ0	λ0	NOUN
ejpam-3459	520	21	=	=	SYM
ejpam-3459	520	22	0	0	NUM
ejpam-3459	520	23	,	,	PUNCT
ejpam-3459	520	24	then	then	ADV
ejpam-3459	520	25	from	from	ADP
ejpam-3459	520	26	the	the	DET
ejpam-3459	520	27	regularities	regularity	NOUN
ejpam-3459	520	28	of	of	ADP
ejpam-3459	520	29	the	the	DET
ejpam-3459	520	30	functions	function	NOUN
ejpam-3459	520	31	gi	gi	ADP
ejpam-3459	520	32	1	1	NUM
ejpam-3459	520	33	;	;	PUNCT
ejpam-3459	520	34	2	2	NUM
ejpam-3459	520	35	and	and	CCONJ
ejpam-3459	520	36	from	from	ADP
ejpam-3459	520	37	the	the	DET
ejpam-3459	520	38	proposition	proposition	NOUN
ejpam-3459	520	39	3	3	NUM
ejpam-3459	520	40	,	,	PUNCT
ejpam-3459	520	41	one	one	PRON
ejpam-3459	520	42	shows	show	VERB
ejpam-3459	520	43	that	that	PRON
ejpam-3459	520	44	yτi	yτi	NOUN
ejpam-3459	521	1	=	=	PROPN
ejpam-3459	521	2	lim	lim	PROPN
ejpam-3459	521	3	τi→0	τi→0	PROPN
ejpam-3459	521	4	y(λi	y(λi	PROPN
ejpam-3459	521	5	=	=	SYM
ejpam-3459	521	6	0	0	NUM
ejpam-3459	521	7	,	,	PUNCT
ejpam-3459	521	8	τi)−	τi)−	PUNCT
ejpam-3459	521	9	yi(0	yi(0	PROPN
ejpam-3459	521	10	,	,	PUNCT
ejpam-3459	521	11	0	0	NUM
ejpam-3459	521	12	)	)	PUNCT
ejpam-3459	521	13	τi	τi	ADP
ejpam-3459	521	14	solves	solve	NOUN
ejpam-3459	521	15	(	(	PUNCT
ejpam-3459	521	16	74	74	NUM
ejpam-3459	521	17	)	)	PUNCT
ejpam-3459	521	18	and	and	CCONJ
ejpam-3459	521	19	verifies	verifie	NOUN
ejpam-3459	521	20	(	(	PUNCT
ejpam-3459	521	21	76	76	NUM
ejpam-3459	521	22	)	)	PUNCT
ejpam-3459	521	23	for	for	ADP
ejpam-3459	521	24	i	i	PRON
ejpam-3459	521	25	=	=	NOUN
ejpam-3459	521	26	1	1	NUM
ejpam-3459	521	27	;	;	PUNCT
ejpam-3459	521	28	2	2	NUM
ejpam-3459	521	29	.	.	X
ejpam-3459	522	1	in	in	ADP
ejpam-3459	522	2	the	the	DET
ejpam-3459	522	3	same	same	ADJ
ejpam-3459	522	4	ways	way	NOUN
ejpam-3459	522	5	setting	set	VERB
ejpam-3459	522	6	yλi	yλi	NOUN
ejpam-3459	522	7	=	=	PUNCT
ejpam-3459	522	8	lim	lim	PROPN
ejpam-3459	522	9	λi→0	λi→0	PROPN
ejpam-3459	522	10	y(λi	y(λi	PROPN
ejpam-3459	522	11	,	,	PUNCT
ejpam-3459	522	12	τi	τi	ADP
ejpam-3459	522	13	=	=	SYM
ejpam-3459	522	14	0)−	0)−	PUNCT
ejpam-3459	523	1	yi(0	yi(0	PROPN
ejpam-3459	523	2	,	,	PUNCT
ejpam-3459	523	3	0	0	NUM
ejpam-3459	523	4	)	)	PUNCT
ejpam-3459	523	5	λi	λi	VERB
ejpam-3459	523	6	,	,	PUNCT
ejpam-3459	523	7	we	we	PRON
ejpam-3459	523	8	proof	proof	VERB
ejpam-3459	523	9	that	that	SCONJ
ejpam-3459	523	10	yλi	yλi	NOUN
ejpam-3459	523	11	satisfies	satisfie	NOUN
ejpam-3459	523	12	(	(	PUNCT
ejpam-3459	523	13	73	73	NUM
ejpam-3459	523	14	)	)	PUNCT
ejpam-3459	523	15	,	,	PUNCT
ejpam-3459	523	16	(	(	PUNCT
ejpam-3459	523	17	75	75	NUM
ejpam-3459	523	18	)	)	PUNCT
ejpam-3459	523	19	and	and	CCONJ
ejpam-3459	523	20	(	(	PUNCT
ejpam-3459	523	21	76	76	NUM
ejpam-3459	523	22	)	)	PUNCT
ejpam-3459	523	23	.	.	PUNCT
ejpam-3459	524	1	remark	remark	PROPN
ejpam-3459	524	2	3	3	NUM
ejpam-3459	524	3	.	.	PUNCT
ejpam-3459	525	1	si	si	PROPN
ejpam-3459	526	1	i	i	NOUN
ejpam-3459	526	2	=	=	PROPN
ejpam-3459	526	3	1	1	NUM
ejpam-3459	526	4	;	;	PUNCT
ejpam-3459	526	5	2	2	NUM
ejpam-3459	526	6	is	be	AUX
ejpam-3459	526	7	say	say	VERB
ejpam-3459	526	8	to	to	PART
ejpam-3459	526	9	be	be	AUX
ejpam-3459	526	10	a	a	DET
ejpam-3459	526	11	simultaneous	simultaneous	ADJ
ejpam-3459	526	12	sentinel	sentinel	NOUN
ejpam-3459	526	13	if	if	SCONJ
ejpam-3459	526	14	there	there	PRON
ejpam-3459	526	15	exists	exist	VERB
ejpam-3459	526	16	a	a	DET
ejpam-3459	526	17	control	control	NOUN
ejpam-3459	526	18	w	w	PROPN
ejpam-3459	526	19	∈	∈	PROPN
ejpam-3459	526	20	l2(qω	l2(qω	PROPN
ejpam-3459	526	21	)	)	PUNCT
ejpam-3459	527	1	such	such	ADJ
ejpam-3459	527	2	that	that	SCONJ
ejpam-3459	527	3	∂si	∂si	PROPN
ejpam-3459	527	4	∂τi	∂τi	PROPN
ejpam-3459	527	5	(	(	PUNCT
ejpam-3459	527	6	0	0	NUM
ejpam-3459	527	7	,	,	PUNCT
ejpam-3459	527	8	0	0	NUM
ejpam-3459	527	9	)	)	PUNCT
ejpam-3459	527	10	=	=	SYM
ejpam-3459	528	1	0	0	PUNCT
ejpam-3459	529	1	i	i	NOUN
ejpam-3459	529	2	=	=	NOUN
ejpam-3459	529	3	1	1	NUM
ejpam-3459	529	4	;	;	PUNCT
ejpam-3459	529	5	2	2	NUM
ejpam-3459	529	6	(	(	PUNCT
ejpam-3459	529	7	77	77	NUM
ejpam-3459	529	8	)	)	PUNCT
ejpam-3459	529	9	and	and	CCONJ
ejpam-3459	529	10	‖w‖l2(qω	‖w‖l2(qω	PROPN
ejpam-3459	529	11	=	=	SYM
ejpam-3459	529	12	min	min	PROPN
ejpam-3459	529	13	{	{	PUNCT
ejpam-3459	529	14	‖k‖l2(qω	‖k‖l2(qω	NOUN
ejpam-3459	529	15	:	:	PUNCT
ejpam-3459	529	16	k	k	PROPN
ejpam-3459	529	17	∈	∈	PROPN
ejpam-3459	529	18	l2(qω	l2(qω	PROPN
ejpam-3459	529	19	)	)	PUNCT
ejpam-3459	529	20	and	and	CCONJ
ejpam-3459	529	21	k	k	PROPN
ejpam-3459	529	22	verifies	verifie	NOUN
ejpam-3459	529	23	(	(	PUNCT
ejpam-3459	529	24	77	77	NUM
ejpam-3459	529	25	)	)	PUNCT
ejpam-3459	529	26	}	}	PUNCT
ejpam-3459	529	27	(	(	PUNCT
ejpam-3459	529	28	78	78	NUM
ejpam-3459	529	29	)	)	PUNCT
ejpam-3459	529	30	following	follow	VERB
ejpam-3459	529	31	[	[	X
ejpam-3459	529	32	9	9	NUM
ejpam-3459	529	33	,	,	PUNCT
ejpam-3459	529	34	10	10	NUM
ejpam-3459	529	35	]	]	PUNCT
ejpam-3459	529	36	,	,	PUNCT
ejpam-3459	529	37	we	we	PRON
ejpam-3459	529	38	show	show	VERB
ejpam-3459	529	39	that	that	SCONJ
ejpam-3459	529	40	the	the	DET
ejpam-3459	529	41	simultaneous	simultaneous	ADJ
ejpam-3459	529	42	sentinel	sentinel	ADJ
ejpam-3459	529	43	problem	problem	NOUN
ejpam-3459	529	44	is	be	AUX
ejpam-3459	529	45	equivalent	equivalent	ADJ
ejpam-3459	529	46	to	to	ADP
ejpam-3459	529	47	the	the	DET
ejpam-3459	529	48	following	follow	VERB
ejpam-3459	529	49	null	null	ADJ
ejpam-3459	529	50	controllability	controllability	NOUN
ejpam-3459	529	51	problem	problem	NOUN
ejpam-3459	529	52	:	:	PUNCT
ejpam-3459	529	53	find	find	VERB
ejpam-3459	529	54	w	w	ADP
ejpam-3459	529	55	∈	∈	PROPN
ejpam-3459	529	56	l2(qω	l2(qω	PROPN
ejpam-3459	529	57	)	)	PUNCT
ejpam-3459	529	58	with	with	ADP
ejpam-3459	529	59	minimal	minimal	ADJ
ejpam-3459	529	60	norm	norm	NOUN
ejpam-3459	529	61	such	such	ADJ
ejpam-3459	529	62	that	that	SCONJ
ejpam-3459	529	63	(	(	PUNCT
ejpam-3459	529	64	q1	q1	PROPN
ejpam-3459	529	65	,	,	PUNCT
ejpam-3459	529	66	q2	q2	NOUN
ejpam-3459	529	67	)	)	PUNCT
ejpam-3459	529	68	satisfies	satisfies	PROPN
ejpam-3459	529	69	−∂qi	−∂qi	NOUN
ejpam-3459	530	1	∂t	∂t	PROPN
ejpam-3459	530	2	−	−	PROPN
ejpam-3459	530	3	∂qi	∂qi	PROPN
ejpam-3459	530	4	∂a	∂a	PROPN
ejpam-3459	530	5	−∆qi	−∆qi	NOUN
ejpam-3459	531	1	+	+	CCONJ
ejpam-3459	531	2	µiqi	µiqi	NOUN
ejpam-3459	531	3	=	=	SYM
ejpam-3459	531	4	βig	βig	NOUN
ejpam-3459	532	1	′	′	NUM
ejpam-3459	532	2	i	i	PRON
ejpam-3459	532	3	(	(	PUNCT
ejpam-3459	532	4	∫	∫	PROPN
ejpam-3459	532	5	a	a	PRON
ejpam-3459	532	6	0	0	NUM
ejpam-3459	532	7	β1y0ida	β1y0ida	NUM
ejpam-3459	532	8	)	)	PUNCT
ejpam-3459	532	9	qi(t	qi(t	NOUN
ejpam-3459	532	10	,	,	PUNCT
ejpam-3459	532	11	0	0	NUM
ejpam-3459	532	12	,	,	PUNCT
ejpam-3459	532	13	x	x	PRON
ejpam-3459	532	14	)	)	PUNCT
ejpam-3459	532	15	+	+	CCONJ
ejpam-3459	532	16	hχo	hχo	ADJ
ejpam-3459	532	17	+	+	NUM
ejpam-3459	532	18	wχω	wχω	PROPN
ejpam-3459	532	19	in	in	ADP
ejpam-3459	532	20	q	q	NOUN
ejpam-3459	532	21	,	,	PUNCT
ejpam-3459	532	22	qi(t	qi(t	PROPN
ejpam-3459	532	23	,	,	PUNCT
ejpam-3459	532	24	a	a	DET
ejpam-3459	532	25	,	,	PUNCT
ejpam-3459	532	26	x	x	NOUN
ejpam-3459	532	27	)	)	PUNCT
ejpam-3459	532	28	=	=	SYM
ejpam-3459	532	29	0	0	NUM
ejpam-3459	533	1	in	in	ADP
ejpam-3459	533	2	qa	qa	PROPN
ejpam-3459	533	3	,	,	PUNCT
ejpam-3459	533	4	qi(t	qi(t	PROPN
ejpam-3459	533	5	,	,	PUNCT
ejpam-3459	533	6	a	a	DET
ejpam-3459	533	7	,	,	PUNCT
ejpam-3459	533	8	x	x	NOUN
ejpam-3459	533	9	)	)	PUNCT
ejpam-3459	533	10	=	=	SYM
ejpam-3459	533	11	0	0	NUM
ejpam-3459	533	12	in	in	ADP
ejpam-3459	533	13	qt	qt	NOUN
ejpam-3459	533	14	,	,	PUNCT
ejpam-3459	533	15	qi	qi	PROPN
ejpam-3459	533	16	=	=	SYM
ejpam-3459	533	17	0	0	NUM
ejpam-3459	533	18	on	on	ADP
ejpam-3459	533	19	σ	σ	PROPN
ejpam-3459	533	20	,	,	PUNCT
ejpam-3459	533	21	(	(	PUNCT
ejpam-3459	533	22	79	79	NUM
ejpam-3459	533	23	)	)	PUNCT
ejpam-3459	533	24	and	and	CCONJ
ejpam-3459	533	25	q1(0	q1(0	PROPN
ejpam-3459	533	26	,	,	PUNCT
ejpam-3459	533	27	a	a	PRON
ejpam-3459	533	28	,	,	PUNCT
ejpam-3459	533	29	x	x	NOUN
ejpam-3459	533	30	)	)	PUNCT
ejpam-3459	534	1	=	=	SYM
ejpam-3459	534	2	q2(0	q2(0	PROPN
ejpam-3459	534	3	,	,	PUNCT
ejpam-3459	534	4	a	a	PRON
ejpam-3459	534	5	,	,	PUNCT
ejpam-3459	534	6	x	x	NOUN
ejpam-3459	534	7	)	)	PUNCT
ejpam-3459	534	8	=	=	SYM
ejpam-3459	534	9	0	0	NUM
ejpam-3459	535	1	in	in	ADP
ejpam-3459	535	2	qa	qa	PROPN
ejpam-3459	535	3	(	(	PUNCT
ejpam-3459	535	4	80	80	NUM
ejpam-3459	535	5	)	)	PUNCT
ejpam-3459	535	6	‖w‖l2(qω	‖w‖l2(qω	NOUN
ejpam-3459	535	7	)	)	PUNCT
ejpam-3459	535	8	=	=	SYM
ejpam-3459	535	9	min	min	PROPN
ejpam-3459	535	10	k∈e	k∈e	PROPN
ejpam-3459	535	11	{	{	PUNCT
ejpam-3459	535	12	‖k‖	‖k‖	PROPN
ejpam-3459	535	13	}	}	PUNCT
ejpam-3459	535	14	(	(	PUNCT
ejpam-3459	535	15	81	81	NUM
ejpam-3459	535	16	)	)	PUNCT
ejpam-3459	535	17	where	where	SCONJ
ejpam-3459	535	18	e	e	NOUN
ejpam-3459	535	19	=	=	PRON
ejpam-3459	535	20	{	{	PUNCT
ejpam-3459	535	21	k	k	PROPN
ejpam-3459	535	22	∈	∈	PROPN
ejpam-3459	535	23	l2(qω	l2(qω	PROPN
ejpam-3459	535	24	)	)	PUNCT
ejpam-3459	535	25	such	such	ADJ
ejpam-3459	535	26	that	that	SCONJ
ejpam-3459	535	27	(	(	PUNCT
ejpam-3459	535	28	k	k	X
ejpam-3459	535	29	,	,	PUNCT
ejpam-3459	535	30	si	si	NOUN
ejpam-3459	535	31	)	)	PUNCT
ejpam-3459	535	32	satisfies	satisfie	NOUN
ejpam-3459	535	33	(	(	PUNCT
ejpam-3459	535	34	71	71	NUM
ejpam-3459	535	35	)	)	PUNCT
ejpam-3459	535	36	and	and	CCONJ
ejpam-3459	535	37	(	(	PUNCT
ejpam-3459	535	38	77	77	NUM
ejpam-3459	535	39	)	)	PUNCT
ejpam-3459	535	40	}	}	PUNCT
ejpam-3459	535	41	.	.	PUNCT
ejpam-3459	536	1	references	reference	NOUN
ejpam-3459	536	2	891	891	NUM
ejpam-3459	536	3	remark	remark	NOUN
ejpam-3459	536	4	4	4	NUM
ejpam-3459	536	5	.	.	PUNCT
ejpam-3459	536	6	setting	set	VERB
ejpam-3459	536	7	g′1	g′1	NOUN
ejpam-3459	536	8	=	=	SYM
ejpam-3459	536	9	f	f	PROPN
ejpam-3459	536	10	and	and	CCONJ
ejpam-3459	536	11	g′2	g′2	NOUN
ejpam-3459	536	12	=	=	PRON
ejpam-3459	537	1	g	g	PROPN
ejpam-3459	537	2	the	the	DET
ejpam-3459	537	3	problem	problem	NOUN
ejpam-3459	537	4	(	(	PUNCT
ejpam-3459	537	5	79)-(80	79)-(80	NUM
ejpam-3459	537	6	)	)	PUNCT
ejpam-3459	537	7	is	be	AUX
ejpam-3459	537	8	exactly	exactly	ADV
ejpam-3459	537	9	the	the	DET
ejpam-3459	537	10	problem	problem	NOUN
ejpam-3459	537	11	(	(	PUNCT
ejpam-3459	537	12	1	1	NUM
ejpam-3459	537	13	)	)	PUNCT
ejpam-3459	537	14	that	that	SCONJ
ejpam-3459	537	15	we	we	PRON
ejpam-3459	537	16	have	have	AUX
ejpam-3459	537	17	solved	solve	VERB
ejpam-3459	537	18	.	.	PUNCT
ejpam-3459	538	1	since	since	SCONJ
ejpam-3459	538	2	e	e	PROPN
ejpam-3459	538	3	is	be	AUX
ejpam-3459	538	4	closed	close	VERB
ejpam-3459	538	5	and	and	CCONJ
ejpam-3459	538	6	convex	convex	PROPN
ejpam-3459	538	7	subset	subset	NOUN
ejpam-3459	538	8	of	of	ADP
ejpam-3459	538	9	l2(qω	l2(qω	PROPN
ejpam-3459	538	10	)	)	PUNCT
ejpam-3459	538	11	,	,	PUNCT
ejpam-3459	538	12	we	we	PRON
ejpam-3459	538	13	can	can	AUX
ejpam-3459	538	14	obtain	obtain	VERB
ejpam-3459	538	15	w	w	NOUN
ejpam-3459	538	16	to	to	PART
ejpam-3459	538	17	be	be	AUX
ejpam-3459	538	18	of	of	ADP
ejpam-3459	538	19	minimal	minimal	ADJ
ejpam-3459	538	20	norm	norm	NOUN
ejpam-3459	538	21	in	in	ADP
ejpam-3459	538	22	l2(qω	l2(qω	PROPN
ejpam-3459	538	23	)	)	PUNCT
ejpam-3459	538	24	by	by	ADP
ejpam-3459	538	25	minimizing	minimize	VERB
ejpam-3459	538	26	the	the	DET
ejpam-3459	538	27	norm	norm	NOUN
ejpam-3459	538	28	of	of	ADP
ejpam-3459	538	29	k	k	NOUN
ejpam-3459	538	30	,	,	PUNCT
ejpam-3459	538	31	when	when	SCONJ
ejpam-3459	538	32	k	k	PROPN
ejpam-3459	538	33	∈	∈	PROPN
ejpam-3459	538	34	e.	e.	PROPN
ejpam-3459	538	35	6	6	NUM
ejpam-3459	538	36	.	.	PUNCT
ejpam-3459	538	37	detection	detection	NOUN
ejpam-3459	538	38	of	of	ADP
ejpam-3459	538	39	the	the	DET
ejpam-3459	538	40	pollution	pollution	NOUN
ejpam-3459	538	41	term	term	NOUN
ejpam-3459	539	1	λiĝi	λiĝi	INTJ
ejpam-3459	539	2	i	i	PRON
ejpam-3459	539	3	=	=	NOUN
ejpam-3459	539	4	1	1	NUM
ejpam-3459	539	5	;	;	PUNCT
ejpam-3459	539	6	2	2	X
ejpam-3459	539	7	.	.	X
ejpam-3459	540	1	we	we	PRON
ejpam-3459	540	2	know	know	VERB
ejpam-3459	540	3	from	from	ADP
ejpam-3459	540	4	the	the	DET
ejpam-3459	540	5	corollary	corollary	ADJ
ejpam-3459	540	6	1	1	NUM
ejpam-3459	540	7	that	that	SCONJ
ejpam-3459	540	8	for	for	ADP
ejpam-3459	540	9	each	each	DET
ejpam-3459	540	10	i	i	NOUN
ejpam-3459	540	11	=	=	NOUN
ejpam-3459	540	12	1	1	NUM
ejpam-3459	540	13	;	;	PUNCT
ejpam-3459	540	14	2	2	NUM
ejpam-3459	540	15	the	the	DET
ejpam-3459	540	16	function	function	NOUN
ejpam-3459	540	17	yλi	yλi	NOUN
ejpam-3459	540	18	=	=	PUNCT
ejpam-3459	541	1	lim	lim	PROPN
ejpam-3459	541	2	λi→0	λi→0	PROPN
ejpam-3459	541	3	y(λi	y(λi	PROPN
ejpam-3459	541	4	,	,	PUNCT
ejpam-3459	541	5	0)−	0)−	PUNCT
ejpam-3459	542	1	yi(0	yi(0	PROPN
ejpam-3459	542	2	,	,	PUNCT
ejpam-3459	542	3	0	0	NUM
ejpam-3459	542	4	)	)	PUNCT
ejpam-3459	542	5	λi	λi	ADP
ejpam-3459	542	6	(	(	PUNCT
ejpam-3459	542	7	82	82	NUM
ejpam-3459	542	8	)	)	PUNCT
ejpam-3459	542	9	solve	solve	NOUN
ejpam-3459	542	10	(	(	PUNCT
ejpam-3459	542	11	75	75	NUM
ejpam-3459	542	12	)	)	PUNCT
ejpam-3459	542	13	.	.	PUNCT
ejpam-3459	543	1	using	use	VERB
ejpam-3459	543	2	the	the	DET
ejpam-3459	543	3	taylor	taylor	PROPN
ejpam-3459	543	4	formula	formula	NOUN
ejpam-3459	543	5	at	at	ADP
ejpam-3459	543	6	the	the	DET
ejpam-3459	543	7	neighbourhood	neighbourhood	NOUN
ejpam-3459	543	8	of	of	ADP
ejpam-3459	543	9	(	(	PUNCT
ejpam-3459	543	10	0	0	NUM
ejpam-3459	543	11	;	;	PUNCT
ejpam-3459	543	12	0	0	X
ejpam-3459	543	13	)	)	PUNCT
ejpam-3459	543	14	we	we	PRON
ejpam-3459	543	15	have	have	VERB
ejpam-3459	543	16	:	:	PUNCT
ejpam-3459	543	17	si(λi	si(λi	ADV
ejpam-3459	543	18	,	,	PUNCT
ejpam-3459	543	19	τi	τi	ADJ
ejpam-3459	543	20	)	)	PUNCT
ejpam-3459	544	1	≈	≈	PROPN
ejpam-3459	544	2	si(0	si(0	PROPN
ejpam-3459	544	3	,	,	PUNCT
ejpam-3459	544	4	0	0	NUM
ejpam-3459	544	5	)	)	PUNCT
ejpam-3459	545	1	+	+	CCONJ
ejpam-3459	545	2	λi	λi	ADP
ejpam-3459	545	3	∂si	∂si	PROPN
ejpam-3459	545	4	∂λi	∂λi	PROPN
ejpam-3459	545	5	(	(	PUNCT
ejpam-3459	545	6	0	0	NUM
ejpam-3459	545	7	,	,	PUNCT
ejpam-3459	545	8	0	0	NUM
ejpam-3459	545	9	)	)	PUNCT
ejpam-3459	546	1	+	+	CCONJ
ejpam-3459	546	2	τi	τi	ADP
ejpam-3459	546	3	∂si	∂si	PROPN
ejpam-3459	546	4	∂τi	∂τi	PROPN
ejpam-3459	546	5	(	(	PUNCT
ejpam-3459	546	6	0	0	NUM
ejpam-3459	546	7	,	,	PUNCT
ejpam-3459	546	8	0	0	NUM
ejpam-3459	546	9	)	)	PUNCT
ejpam-3459	546	10	,	,	PUNCT
ejpam-3459	546	11	i	i	PRON
ejpam-3459	546	12	=	=	NOUN
ejpam-3459	546	13	1	1	NUM
ejpam-3459	546	14	;	;	PUNCT
ejpam-3459	546	15	2	2	NUM
ejpam-3459	546	16	.	.	PUNCT
ejpam-3459	546	17	(	(	PUNCT
ejpam-3459	546	18	83	83	NUM
ejpam-3459	546	19	)	)	PUNCT
ejpam-3459	546	20	according	accord	VERB
ejpam-3459	546	21	to	to	ADP
ejpam-3459	546	22	(	(	PUNCT
ejpam-3459	546	23	77	77	NUM
ejpam-3459	546	24	)	)	PUNCT
ejpam-3459	546	25	,	,	PUNCT
ejpam-3459	546	26	one	one	NUM
ejpam-3459	546	27	deducts	deduct	NOUN
ejpam-3459	546	28	from	from	ADP
ejpam-3459	546	29	(	(	PUNCT
ejpam-3459	546	30	71	71	NUM
ejpam-3459	546	31	)	)	PUNCT
ejpam-3459	546	32	,	,	PUNCT
ejpam-3459	546	33	(	(	PUNCT
ejpam-3459	546	34	73	73	NUM
ejpam-3459	546	35	)	)	PUNCT
ejpam-3459	546	36	and	and	CCONJ
ejpam-3459	546	37	from	from	ADP
ejpam-3459	546	38	the	the	DET
ejpam-3459	546	39	expression	expression	NOUN
ejpam-3459	546	40	of	of	ADP
ejpam-3459	546	41	si(0	si(0	PROPN
ejpam-3459	546	42	,	,	PUNCT
ejpam-3459	546	43	0	0	NUM
ejpam-3459	546	44	)	)	PUNCT
ejpam-3459	546	45	that	that	SCONJ
ejpam-3459	546	46	(	(	PUNCT
ejpam-3459	546	47	83	83	NUM
ejpam-3459	546	48	)	)	PUNCT
ejpam-3459	546	49	is	be	AUX
ejpam-3459	546	50	equivalent	equivalent	ADJ
ejpam-3459	546	51	to∫	to∫	INTJ
ejpam-3459	546	52	q	q	PROPN
ejpam-3459	547	1	(	(	PUNCT
ejpam-3459	547	2	hχo	hχo	PROPN
ejpam-3459	547	3	+	+	CCONJ
ejpam-3459	547	4	wχω)yi(λi	wχω)yi(λi	NUM
ejpam-3459	547	5	,	,	PUNCT
ejpam-3459	547	6	τi)dq	τi)dq	PUNCT
ejpam-3459	547	7	=	=	SYM
ejpam-3459	548	1	∫	∫	PROPN
ejpam-3459	548	2	q	q	PROPN
ejpam-3459	548	3	(	(	PUNCT
ejpam-3459	548	4	hχo	hχo	PROPN
ejpam-3459	548	5	+	+	X
ejpam-3459	548	6	wχω)yi(0	wχω)yi(0	PROPN
ejpam-3459	548	7	,	,	PUNCT
ejpam-3459	548	8	0)dq+	0)dq+	PROPN
ejpam-3459	548	9	λi	λi	NOUN
ejpam-3459	548	10	∫	∫	PROPN
ejpam-3459	548	11	q	q	PROPN
ejpam-3459	549	1	(	(	PUNCT
ejpam-3459	549	2	hχo	hχo	NOUN
ejpam-3459	549	3	+	+	CCONJ
ejpam-3459	549	4	wχω)yλidq	wχω)yλidq	NOUN
ejpam-3459	549	5	(	(	PUNCT
ejpam-3459	549	6	84	84	NUM
ejpam-3459	549	7	)	)	PUNCT
ejpam-3459	549	8	thanks	thank	NOUN
ejpam-3459	549	9	to	to	ADP
ejpam-3459	549	10	(	(	PUNCT
ejpam-3459	549	11	60	60	NUM
ejpam-3459	549	12	)	)	PUNCT
ejpam-3459	549	13	,	,	PUNCT
ejpam-3459	549	14	the	the	DET
ejpam-3459	549	15	equality	equality	NOUN
ejpam-3459	549	16	(	(	PUNCT
ejpam-3459	549	17	84	84	NUM
ejpam-3459	549	18	)	)	PUNCT
ejpam-3459	549	19	becomes	become	VERB
ejpam-3459	549	20	λi	λi	ADP
ejpam-3459	549	21	∫	∫	PROPN
ejpam-3459	549	22	q	q	PROPN
ejpam-3459	550	1	(	(	PUNCT
ejpam-3459	550	2	hχo	hχo	ADJ
ejpam-3459	550	3	+	+	CCONJ
ejpam-3459	550	4	wχω)yλidq	wχω)yλidq	NOUN
ejpam-3459	550	5	=	=	SYM
ejpam-3459	550	6	∫	∫	PROPN
ejpam-3459	551	1	q	q	PROPN
ejpam-3459	552	1	(	(	PUNCT
ejpam-3459	552	2	hχo	hχo	ADJ
ejpam-3459	552	3	+	+	CCONJ
ejpam-3459	552	4	wχω)(m0i	wχω)(m0i	NOUN
ejpam-3459	552	5	−	−	PROPN
ejpam-3459	553	1	yi(0	yi(0	PROPN
ejpam-3459	553	2	,	,	PUNCT
ejpam-3459	553	3	0))dq	0))dq	NUM
ejpam-3459	553	4	,	,	PUNCT
ejpam-3459	553	5	i	i	PRON
ejpam-3459	553	6	=	=	NOUN
ejpam-3459	553	7	1	1	NUM
ejpam-3459	553	8	;	;	PUNCT
ejpam-3459	553	9	2	2	NUM
ejpam-3459	553	10	.	.	PUNCT
ejpam-3459	553	11	(	(	PUNCT
ejpam-3459	553	12	85	85	NUM
ejpam-3459	553	13	)	)	PUNCT
ejpam-3459	553	14	elsewhere	elsewhere	ADV
ejpam-3459	553	15	,	,	PUNCT
ejpam-3459	553	16	multiplying	multiply	VERB
ejpam-3459	553	17	the	the	DET
ejpam-3459	553	18	first	first	ADJ
ejpam-3459	553	19	equation	equation	NOUN
ejpam-3459	553	20	of	of	ADP
ejpam-3459	553	21	(	(	PUNCT
ejpam-3459	553	22	79	79	NUM
ejpam-3459	553	23	)	)	PUNCT
ejpam-3459	553	24	by	by	ADP
ejpam-3459	553	25	yλi	yλi	NOUN
ejpam-3459	553	26	,	,	PUNCT
ejpam-3459	553	27	i	i	PRON
ejpam-3459	553	28	=	=	NOUN
ejpam-3459	553	29	1	1	NUM
ejpam-3459	553	30	;	;	PUNCT
ejpam-3459	553	31	2	2	NUM
ejpam-3459	553	32	and	and	CCONJ
ejpam-3459	553	33	by	by	ADP
ejpam-3459	553	34	integratings	integrating	NOUN
ejpam-3459	553	35	by	by	ADP
ejpam-3459	553	36	parts	part	NOUN
ejpam-3459	553	37	over	over	ADP
ejpam-3459	553	38	q	q	NOUN
ejpam-3459	553	39	,	,	PUNCT
ejpam-3459	553	40	we	we	PRON
ejpam-3459	553	41	have	have	VERB
ejpam-3459	553	42	thanks	thank	NOUN
ejpam-3459	553	43	to	to	ADP
ejpam-3459	553	44	(	(	PUNCT
ejpam-3459	553	45	75	75	NUM
ejpam-3459	553	46	)	)	PUNCT
ejpam-3459	553	47	and	and	CCONJ
ejpam-3459	553	48	(	(	PUNCT
ejpam-3459	553	49	80)∫	80)∫	NUM
ejpam-3459	553	50	σi	σi	PRON
ejpam-3459	554	1	ĝi	ĝi	PROPN
ejpam-3459	555	1	∂qi	∂qi	PROPN
ejpam-3459	555	2	∂σ	∂σ	PROPN
ejpam-3459	555	3	dς	dς	VERB
ejpam-3459	556	1	=	=	SYM
ejpam-3459	556	2	∫	∫	PROPN
ejpam-3459	556	3	q	q	PROPN
ejpam-3459	557	1	(	(	PUNCT
ejpam-3459	557	2	hχo	hχo	NOUN
ejpam-3459	557	3	+	+	CCONJ
ejpam-3459	557	4	wχω)yλidq	wχω)yλidq	NOUN
ejpam-3459	557	5	i	i	PRON
ejpam-3459	557	6	=	=	NOUN
ejpam-3459	557	7	1	1	NUM
ejpam-3459	557	8	;	;	PUNCT
ejpam-3459	557	9	2	2	NUM
ejpam-3459	557	10	.	.	PUNCT
ejpam-3459	557	11	(	(	PUNCT
ejpam-3459	557	12	86	86	NUM
ejpam-3459	557	13	)	)	PUNCT
ejpam-3459	557	14	where	where	SCONJ
ejpam-3459	557	15	σ	σ	PROPN
ejpam-3459	557	16	is	be	AUX
ejpam-3459	557	17	the	the	DET
ejpam-3459	557	18	external	external	ADJ
ejpam-3459	557	19	unitary	unitary	ADJ
ejpam-3459	557	20	normal	normal	ADJ
ejpam-3459	557	21	vector	vector	NOUN
ejpam-3459	557	22	of	of	ADP
ejpam-3459	557	23	γ	γ	PROPN
ejpam-3459	557	24	.	.	PROPN
ejpam-3459	558	1	then	then	ADV
ejpam-3459	558	2	(	(	PUNCT
ejpam-3459	558	3	73	73	NUM
ejpam-3459	558	4	)	)	PUNCT
ejpam-3459	558	5	becames∫	becames∫	NOUN
ejpam-3459	559	1	σi	σi	INTJ
ejpam-3459	559	2	λiĝi	λiĝi	PROPN
ejpam-3459	560	1	∂qi	∂qi	PROPN
ejpam-3459	560	2	∂σ	∂σ	PROPN
ejpam-3459	560	3	dς	dς	VERB
ejpam-3459	561	1	≈	≈	PROPN
ejpam-3459	561	2	∫	∫	PROPN
ejpam-3459	561	3	q	q	PROPN
ejpam-3459	561	4	(	(	PUNCT
ejpam-3459	561	5	hχo	hχo	ADJ
ejpam-3459	561	6	+	+	CCONJ
ejpam-3459	561	7	wχω)(m0i	wχω)(m0i	NOUN
ejpam-3459	561	8	−	−	PROPN
ejpam-3459	562	1	yi(0	yi(0	PROPN
ejpam-3459	562	2	,	,	PUNCT
ejpam-3459	562	3	0))dq	0))dq	NUM
ejpam-3459	562	4	,	,	PUNCT
ejpam-3459	562	5	i	i	PRON
ejpam-3459	562	6	=	=	NOUN
ejpam-3459	562	7	1	1	NUM
ejpam-3459	562	8	;	;	PUNCT
ejpam-3459	562	9	2	2	NUM
ejpam-3459	562	10	.	.	PUNCT
ejpam-3459	562	11	(	(	PUNCT
ejpam-3459	562	12	87	87	NUM
ejpam-3459	562	13	)	)	PUNCT
ejpam-3459	562	14	since	since	SCONJ
ejpam-3459	562	15	qi	qi	PROPN
ejpam-3459	562	16	,	,	PUNCT
ejpam-3459	562	17	h	h	NOUN
ejpam-3459	562	18	,	,	PUNCT
ejpam-3459	562	19	w	w	PROPN
ejpam-3459	562	20	,	,	PUNCT
ejpam-3459	562	21	and	and	CCONJ
ejpam-3459	562	22	yi(0	yi(0	PROPN
ejpam-3459	562	23	,	,	PUNCT
ejpam-3459	562	24	0	0	NUM
ejpam-3459	562	25	)	)	PUNCT
ejpam-3459	562	26	i	i	PRON
ejpam-3459	563	1	=	=	NOUN
ejpam-3459	563	2	1	1	NUM
ejpam-3459	563	3	;	;	PUNCT
ejpam-3459	563	4	2	2	NUM
ejpam-3459	563	5	are	be	AUX
ejpam-3459	563	6	known	know	VERB
ejpam-3459	563	7	,	,	PUNCT
ejpam-3459	563	8	(	(	PUNCT
ejpam-3459	563	9	87	87	NUM
ejpam-3459	563	10	)	)	PUNCT
ejpam-3459	563	11	is	be	AUX
ejpam-3459	563	12	a	a	DET
ejpam-3459	563	13	integral	integral	ADJ
ejpam-3459	563	14	equation	equation	NOUN
ejpam-3459	563	15	in	in	ADP
ejpam-3459	563	16	λiĝi	λiĝi	PROPN
ejpam-3459	563	17	that	that	PRON
ejpam-3459	563	18	supply	supply	VERB
ejpam-3459	563	19	some	some	DET
ejpam-3459	563	20	informations	information	NOUN
ejpam-3459	563	21	on	on	ADP
ejpam-3459	563	22	the	the	DET
ejpam-3459	563	23	terms	term	NOUN
ejpam-3459	564	1	λiĝi	λiĝi	INTJ
ejpam-3459	564	2	i	i	PRON
ejpam-3459	564	3	=	=	NOUN
ejpam-3459	564	4	1	1	NUM
ejpam-3459	564	5	;	;	PUNCT
ejpam-3459	564	6	2	2	NUM
ejpam-3459	564	7	.	.	NUM
ejpam-3459	564	8	references	reference	NOUN
ejpam-3459	564	9	[	[	X
ejpam-3459	565	1	1	1	NUM
ejpam-3459	565	2	]	]	PUNCT
ejpam-3459	565	3	c.	c.	PROPN
ejpam-3459	565	4	avramescu	avramescu	PROPN
ejpam-3459	565	5	.	.	PUNCT
ejpam-3459	566	1	a	a	DET
ejpam-3459	566	2	fixed	fix	VERB
ejpam-3459	566	3	point	point	NOUN
ejpam-3459	566	4	theorem	theorem	NOUN
ejpam-3459	566	5	for	for	ADP
ejpam-3459	566	6	multivalued	multivalued	ADJ
ejpam-3459	566	7	mappings	mapping	NOUN
ejpam-3459	566	8	.	.	PUNCT
ejpam-3459	567	1	electronic	electronic	ADJ
ejpam-3459	567	2	journal	journal	NOUN
ejpam-3459	567	3	of	of	ADP
ejpam-3459	567	4	qualitative	qualitative	ADJ
ejpam-3459	567	5	theory	theory	NOUN
ejpam-3459	567	6	of	of	ADP
ejpam-3459	567	7	differential	differential	ADJ
ejpam-3459	567	8	equations	equation	NOUN
ejpam-3459	567	9	,	,	PUNCT
ejpam-3459	567	10	2004:1–10	2004:1–10	NUM
ejpam-3459	567	11	,	,	PUNCT
ejpam-3459	567	12	2004	2004	NUM
ejpam-3459	567	13	.	.	PUNCT
ejpam-3459	568	1	[	[	X
ejpam-3459	568	2	2	2	X
ejpam-3459	568	3	]	]	PUNCT
ejpam-3459	568	4	b.ainseba	b.ainseba	NOUN
ejpam-3459	568	5	et	et	PROPN
ejpam-3459	568	6	m.langlais	m.langlais	PROPN
ejpam-3459	568	7	.	.	PUNCT
ejpam-3459	569	1	on	on	ADP
ejpam-3459	569	2	a	a	DET
ejpam-3459	569	3	population	population	NOUN
ejpam-3459	569	4	dynamics	dynamic	NOUN
ejpam-3459	569	5	control	control	VERB
ejpam-3459	569	6	problem	problem	NOUN
ejpam-3459	569	7	with	with	ADP
ejpam-3459	569	8	age	age	NOUN
ejpam-3459	569	9	dependence	dependence	NOUN
ejpam-3459	569	10	and	and	CCONJ
ejpam-3459	569	11	spatial	spatial	ADJ
ejpam-3459	569	12	structure.journal	structure.journal	PROPN
ejpam-3459	569	13	of	of	ADP
ejpam-3459	569	14	mathematical	mathematical	ADJ
ejpam-3459	569	15	analysis	analysis	NOUN
ejpam-3459	569	16	and	and	CCONJ
ejpam-3459	569	17	applications	application	NOUN
ejpam-3459	569	18	248,455–474(2000	248,455–474(2000	NUM
ejpam-3459	569	19	)	)	PUNCT
ejpam-3459	569	20	.	.	PUNCT
ejpam-3459	570	1	references	reference	NOUN
ejpam-3459	570	2	892	892	NUM
ejpam-3459	571	1	[	[	X
ejpam-3459	571	2	3	3	NUM
ejpam-3459	571	3	]	]	PUNCT
ejpam-3459	571	4	b.ainseba	b.ainseba	NOUN
ejpam-3459	571	5	and	and	CCONJ
ejpam-3459	571	6	s.anita	s.anita	PROPN
ejpam-3459	571	7	.	.	PUNCT
ejpam-3459	572	1	local	local	ADJ
ejpam-3459	572	2	exact	exact	ADJ
ejpam-3459	572	3	controllability	controllability	NOUN
ejpam-3459	572	4	of	of	ADP
ejpam-3459	572	5	the	the	DET
ejpam-3459	572	6	age	age	NOUN
ejpam-3459	572	7	-	-	PUNCT
ejpam-3459	572	8	dependent	dependent	ADJ
ejpam-3459	572	9	population	population	NOUN
ejpam-3459	572	10	dynamics	dynamic	NOUN
ejpam-3459	572	11	with	with	ADP
ejpam-3459	572	12	diffusion.abstract	diffusion.abstract	PROPN
ejpam-3459	572	13	appl.anal.6(2001	appl.anal.6(2001	NOUN
ejpam-3459	572	14	)	)	PUNCT
ejpam-3459	572	15	357	357	NUM
ejpam-3459	572	16	-	-	SYM
ejpam-3459	572	17	368	368	NUM
ejpam-3459	572	18	.	.	PUNCT
ejpam-3459	573	1	[	[	X
ejpam-3459	573	2	4	4	NUM
ejpam-3459	573	3	]	]	X
ejpam-3459	573	4	a.	a.	NOUN
ejpam-3459	573	5	v.	v.	ADP
ejpam-3459	573	6	fursikov	fursikov	PROPN
ejpam-3459	573	7	and	and	CCONJ
ejpam-3459	573	8	o.	o.	PROPN
ejpam-3459	573	9	yu	yu	PROPN
ejpam-3459	573	10	.	.	PROPN
ejpam-3459	573	11	imanuvilov	imanuvilov	PROPN
ejpam-3459	573	12	.	.	PUNCT
ejpam-3459	574	1	controllability	controllability	NOUN
ejpam-3459	574	2	of	of	ADP
ejpam-3459	574	3	evolution	evolution	NOUN
ejpam-3459	574	4	equations	equation	NOUN
ejpam-3459	574	5	.	.	PUNCT
ejpam-3459	575	1	lecture	lecture	NOUN
ejpam-3459	575	2	notes	note	NOUN
ejpam-3459	575	3	series	series	PROPN
ejpam-3459	575	4	,	,	PUNCT
ejpam-3459	575	5	vol	vol	NOUN
ejpam-3459	575	6	.	.	PROPN
ejpam-3459	575	7	34	34	NUM
ejpam-3459	575	8	,	,	PUNCT
ejpam-3459	575	9	seoul	seoul	PROPN
ejpam-3459	575	10	national	national	PROPN
ejpam-3459	575	11	university	university	PROPN
ejpam-3459	575	12	research	research	PROPN
ejpam-3459	575	13	institute	institute	PROPN
ejpam-3459	575	14	of	of	ADP
ejpam-3459	575	15	mathematics	mathematics	PROPN
ejpam-3459	575	16	global	global	ADJ
ejpam-3459	575	17	analysis	analysis	NOUN
ejpam-3459	575	18	research	research	NOUN
ejpam-3459	575	19	center	center	NOUN
ejpam-3459	575	20	,	,	PUNCT
ejpam-3459	575	21	seoul	seoul	PROPN
ejpam-3459	575	22	,	,	PUNCT
ejpam-3459	575	23	1996	1996	NUM
ejpam-3459	575	24	.	.	PUNCT
ejpam-3459	576	1	[	[	X
ejpam-3459	576	2	5	5	NUM
ejpam-3459	576	3	]	]	PUNCT
ejpam-3459	576	4	m.	m.	NOUN
ejpam-3459	576	5	g.	g.	PROPN
ejpam-3459	576	6	garoni	garoni	PROPN
ejpam-3459	576	7	m.	m.	PROPN
ejpam-3459	576	8	langlais	langlais	PROPN
ejpam-3459	576	9	.	.	PUNCT
ejpam-3459	577	1	age	age	NOUN
ejpam-3459	577	2	-	-	PUNCT
ejpam-3459	577	3	dependance	dependance	NOUN
ejpam-3459	577	4	population	population	NOUN
ejpam-3459	577	5	diffusion	diffusion	NOUN
ejpam-3459	577	6	with	with	ADP
ejpam-3459	577	7	external	external	ADJ
ejpam-3459	577	8	contraint	contraint	NOUN
ejpam-3459	577	9	.	.	PUNCT
ejpam-3459	578	1	journal	journal	PROPN
ejpam-3459	578	2	of	of	ADP
ejpam-3459	578	3	mathematical	mathematical	ADJ
ejpam-3459	578	4	biology	biology	NOUN
ejpam-3459	578	5	14:77–94	14:77–94	NUM
ejpam-3459	578	6	,	,	PUNCT
ejpam-3459	578	7	1982	1982	NUM
ejpam-3459	578	8	.	.	PUNCT
ejpam-3459	579	1	[	[	X
ejpam-3459	579	2	6	6	NUM
ejpam-3459	579	3	]	]	PUNCT
ejpam-3459	579	4	j.	j.	PROPN
ejpam-3459	579	5	klamka	klamka	PROPN
ejpam-3459	579	6	.	.	PROPN
ejpam-3459	579	7	schauder	schauder	PROPN
ejpam-3459	579	8	’s	’s	PART
ejpam-3459	579	9	fixed	fix	VERB
ejpam-3459	579	10	-	-	PUNCT
ejpam-3459	579	11	point	point	NOUN
ejpam-3459	579	12	theorem	theorem	NOUN
ejpam-3459	579	13	in	in	ADP
ejpam-3459	579	14	nonlinear	nonlinear	ADJ
ejpam-3459	579	15	controllability	controllability	NOUN
ejpam-3459	579	16	problems	problem	NOUN
ejpam-3459	579	17	.	.	PUNCT
ejpam-3459	580	1	control	control	NOUN
ejpam-3459	580	2	and	and	CCONJ
ejpam-3459	580	3	cybernetics	cybernetic	NOUN
ejpam-3459	580	4	,	,	PUNCT
ejpam-3459	580	5	29(1):153–165	29(1):153–165	NUM
ejpam-3459	580	6	,	,	PUNCT
ejpam-3459	580	7	2000	2000	NUM
ejpam-3459	580	8	.	.	PUNCT
ejpam-3459	581	1	[	[	X
ejpam-3459	581	2	7	7	X
ejpam-3459	581	3	]	]	X
ejpam-3459	581	4	j.l	j.l	PROPN
ejpam-3459	581	5	.	.	PROPN
ejpam-3459	581	6	lions	lion	NOUN
ejpam-3459	581	7	.	.	PUNCT
ejpam-3459	582	1	sentinelle	sentinelle	PROPN
ejpam-3459	582	2	pour	pour	VERB
ejpam-3459	582	3	les	les	X
ejpam-3459	582	4	systèmes	système	NOUN
ejpam-3459	582	5	distribués	distribués	PROPN
ejpam-3459	582	6	à	à	PROPN
ejpam-3459	582	7	données	donnée	NOUN
ejpam-3459	582	8	incomplètes	incomplètes	PROPN
ejpam-3459	582	9	.	.	PUNCT
ejpam-3459	583	1	masson	masson	PROPN
ejpam-3459	583	2	,	,	PUNCT
ejpam-3459	583	3	rma	rma	PROPN
ejpam-3459	583	4	,	,	PUNCT
ejpam-3459	583	5	paris	paris	PROPN
ejpam-3459	583	6	,	,	PUNCT
ejpam-3459	583	7	france	france	PROPN
ejpam-3459	583	8	,	,	PUNCT
ejpam-3459	583	9	21	21	NUM
ejpam-3459	583	10	,	,	PUNCT
ejpam-3459	583	11	1992	1992	NUM
ejpam-3459	583	12	.	.	PUNCT
ejpam-3459	584	1	[	[	X
ejpam-3459	584	2	8	8	NUM
ejpam-3459	584	3	]	]	X
ejpam-3459	584	4	g.	g.	PROPN
ejpam-3459	584	5	modi	modi	PROPN
ejpam-3459	584	6	,	,	PUNCT
ejpam-3459	584	7	s.	s.	PROPN
ejpam-3459	584	8	duraphe	duraphe	PROPN
ejpam-3459	584	9	,	,	PUNCT
ejpam-3459	584	10	a.	a.	PROPN
ejpam-3459	584	11	gupta	gupta	PROPN
ejpam-3459	584	12	,	,	PUNCT
ejpam-3459	584	13	v.	v.	ADP
ejpam-3459	584	14	singh	singh	PROPN
ejpam-3459	584	15	.	.	PUNCT
ejpam-3459	585	1	application	application	NOUN
ejpam-3459	585	2	of	of	ADP
ejpam-3459	585	3	fixed	fix	VERB
ejpam-3459	585	4	point	point	NOUN
ejpam-3459	585	5	theorem	theorem	VERB
ejpam-3459	585	6	in	in	ADP
ejpam-3459	585	7	game	game	NOUN
ejpam-3459	585	8	theory	theory	NOUN
ejpam-3459	585	9	.	.	PUNCT
ejpam-3459	586	1	international	international	ADJ
ejpam-3459	586	2	journal	journal	PROPN
ejpam-3459	586	3	of	of	ADP
ejpam-3459	586	4	scientific	scientific	ADJ
ejpam-3459	586	5	and	and	CCONJ
ejpam-3459	586	6	innovative	innovative	ADJ
ejpam-3459	586	7	mathematical	mathematical	ADJ
ejpam-3459	586	8	research,2(5):469–473	research,2(5):469–473	NOUN
ejpam-3459	586	9	,	,	PUNCT
ejpam-3459	586	10	may	may	AUX
ejpam-3459	586	11	2014	2014	NUM
ejpam-3459	586	12	.	.	PUNCT
ejpam-3459	587	1	[	[	X
ejpam-3459	587	2	9	9	NUM
ejpam-3459	587	3	]	]	PUNCT
ejpam-3459	587	4	s.	s.	PROPN
ejpam-3459	587	5	sawadogo	sawadogo	PROPN
ejpam-3459	587	6	.	.	PUNCT
ejpam-3459	588	1	parameters	parameter	NOUN
ejpam-3459	588	2	identification	identification	NOUN
ejpam-3459	588	3	in	in	ADP
ejpam-3459	588	4	population	population	NOUN
ejpam-3459	588	5	dynamics	dynamic	NOUN
ejpam-3459	588	6	problem	problem	NOUN
ejpam-3459	588	7	.	.	PUNCT
ejpam-3459	589	1	african	african	ADJ
ejpam-3459	589	2	diaspora	diaspora	PROPN
ejpam-3459	589	3	journal	journal	PROPN
ejpam-3459	589	4	of	of	ADP
ejpam-3459	589	5	mathematics	mathematic	NOUN
ejpam-3459	589	6	,	,	PUNCT
ejpam-3459	589	7	13(2):81–99	13(2):81–99	NUM
ejpam-3459	589	8	,	,	PUNCT
ejpam-3459	589	9	2012	2012	NUM
ejpam-3459	589	10	.	.	PUNCT
ejpam-3459	590	1	[	[	X
ejpam-3459	590	2	10	10	NUM
ejpam-3459	590	3	]	]	X
ejpam-3459	590	4	y.	y.	PROPN
ejpam-3459	590	5	simporé	simporé	PROPN
ejpam-3459	590	6	,	,	PUNCT
ejpam-3459	590	7	o.	o.	PROPN
ejpam-3459	590	8	traoré.	traoré.	PROPN
ejpam-3459	590	9	null	null	NOUN
ejpam-3459	590	10	controllability	controllability	NOUN
ejpam-3459	590	11	of	of	ADP
ejpam-3459	590	12	a	a	DET
ejpam-3459	590	13	nonlinear	nonlinear	ADJ
ejpam-3459	590	14	dissipative	dissipative	ADJ
ejpam-3459	590	15	system	system	NOUN
ejpam-3459	590	16	and	and	CCONJ
ejpam-3459	590	17	application	application	NOUN
ejpam-3459	590	18	to	to	ADP
ejpam-3459	590	19	the	the	DET
ejpam-3459	590	20	detection	detection	NOUN
ejpam-3459	590	21	of	of	ADP
ejpam-3459	590	22	the	the	DET
ejpam-3459	590	23	incomplete	incomplete	ADJ
ejpam-3459	590	24	parameter	parameter	NOUN
ejpam-3459	590	25	for	for	ADP
ejpam-3459	590	26	a	a	DET
ejpam-3459	590	27	nonlinear	nonlinear	ADJ
ejpam-3459	590	28	population	population	NOUN
ejpam-3459	590	29	dynamics	dynamic	NOUN
ejpam-3459	590	30	model	model	NOUN
ejpam-3459	590	31	.	.	PUNCT
ejpam-3459	591	1	international	international	ADJ
ejpam-3459	591	2	journal	journal	PROPN
ejpam-3459	591	3	of	of	ADP
ejpam-3459	591	4	mathematics	mathematics	PROPN
ejpam-3459	591	5	and	and	CCONJ
ejpam-3459	591	6	mathematical	mathematical	ADJ
ejpam-3459	591	7	sciences	science	NOUN
ejpam-3459	591	8	2016	2016	NUM
ejpam-3459	591	9	,	,	PUNCT
ejpam-3459	591	10	article	article	NOUN
ejpam-3459	591	11	i	i	PROPN
ejpam-3459	591	12	d	d	PROPN
ejpam-3459	591	13	2820613	2820613	NUM
ejpam-3459	591	14	,	,	PUNCT
ejpam-3459	591	15	9	9	NUM
ejpam-3459	591	16	pages	page	NOUN
ejpam-3459	591	17	.	.	PUNCT
ejpam-3459	592	1	[	[	X
ejpam-3459	592	2	11	11	NUM
ejpam-3459	592	3	]	]	X
ejpam-3459	592	4	c.	c.	PROPN
ejpam-3459	592	5	k.	k.	PROPN
ejpam-3459	592	6	somé	somé	PROPN
ejpam-3459	592	7	,	,	PUNCT
ejpam-3459	592	8	s.	s.	PROPN
ejpam-3459	592	9	sawadogo	sawadogo	PROPN
ejpam-3459	592	10	,	,	PUNCT
ejpam-3459	592	11	m.	m.	NOUN
ejpam-3459	592	12	kéré.	kéré.	PROPN
ejpam-3459	592	13	simultaneous	simultaneous	ADJ
ejpam-3459	592	14	null	null	ADJ
ejpam-3459	592	15	controllability	controllability	NOUN
ejpam-3459	592	16	for	for	ADP
ejpam-3459	592	17	a	a	DET
ejpam-3459	592	18	system	system	NOUN
ejpam-3459	592	19	of	of	ADP
ejpam-3459	592	20	two	two	NUM
ejpam-3459	592	21	stroke	stroke	NOUN
ejpam-3459	592	22	equations	equation	NOUN
ejpam-3459	592	23	.	.	PUNCT
ejpam-3459	593	1	journal	journal	PROPN
ejpam-3459	593	2	of	of	ADP
ejpam-3459	593	3	nonlinear	nonlinear	ADJ
ejpam-3459	593	4	evolution	evolution	NOUN
ejpam-3459	593	5	equations	equation	NOUN
ejpam-3459	593	6	and	and	CCONJ
ejpam-3459	593	7	applications	application	NOUN
ejpam-3459	593	8	,	,	PUNCT
ejpam-3459	593	9	article	article	NOUN
ejpam-3459	593	10	i	i	PROPN
ejpam-3459	593	11	d	d	PROPN
ejpam-3459	593	12	jneea-1809292	jneea-1809292	PROPN
ejpam-3459	593	13	(	(	PUNCT
ejpam-3459	593	14	accepted	accept	VERB
ejpam-3459	593	15	for	for	ADP
ejpam-3459	593	16	publication	publication	NOUN
ejpam-3459	593	17	)	)	PUNCT
ejpam-3459	593	18	.	.	PUNCT
ejpam-3459	594	1	[	[	X
ejpam-3459	594	2	12	12	NUM
ejpam-3459	594	3	]	]	X
ejpam-3459	594	4	o.	o.	PROPN
ejpam-3459	594	5	traoré.	traoré.	PROPN
ejpam-3459	594	6	null	null	NOUN
ejpam-3459	594	7	controllability	controllability	NOUN
ejpam-3459	594	8	of	of	ADP
ejpam-3459	594	9	a	a	DET
ejpam-3459	594	10	nonlinear	nonlinear	ADJ
ejpam-3459	594	11	population	population	NOUN
ejpam-3459	594	12	dynamics	dynamic	NOUN
ejpam-3459	594	13	problem	problem	NOUN
ejpam-3459	594	14	,	,	PUNCT
ejpam-3459	594	15	international	international	ADJ
ejpam-3459	594	16	journal	journal	NOUN
ejpam-3459	594	17	of	of	ADP
ejpam-3459	594	18	mathematics	mathematics	PROPN
ejpam-3459	594	19	and	and	CCONJ
ejpam-3459	594	20	mathematical	mathematical	ADJ
ejpam-3459	594	21	sciences	science	NOUN
ejpam-3459	594	22	,	,	PUNCT
ejpam-3459	594	23	vol	vol	NOUN
ejpam-3459	594	24	.	.	PUNCT
ejpam-3459	594	25	2006	2006	NUM
ejpam-3459	594	26	,	,	PUNCT
ejpam-3459	594	27	2006	2006	NUM
ejpam-3459	594	28	,	,	PUNCT
ejpam-3459	594	29	pp	pp	ADJ
ejpam-3459	594	30	.	.	PUNCT
ejpam-3459	595	1	1	1	NUM
ejpam-3459	595	2	-	-	SYM
ejpam-3459	595	3	20	20	NUM
ejpam-3459	595	4	.	.	PUNCT