id	sid	tid	token	lemma	pos
ejpam-3903	1	1	european	european	PROPN
ejpam-3903	1	2	journal	journal	PROPN
ejpam-3903	1	3	of	of	ADP
ejpam-3903	1	4	pure	pure	ADJ
ejpam-3903	1	5	and	and	CCONJ
ejpam-3903	1	6	applied	apply	VERB
ejpam-3903	1	7	mathematics	mathematic	NOUN
ejpam-3903	1	8	vol	vol	NOUN
ejpam-3903	1	9	.	.	PUNCT
ejpam-3903	2	1	14	14	NUM
ejpam-3903	2	2	,	,	PUNCT
ejpam-3903	2	3	no	no	INTJ
ejpam-3903	2	4	.	.	NOUN
ejpam-3903	2	5	1	1	NUM
ejpam-3903	2	6	,	,	PUNCT
ejpam-3903	2	7	2021	2021	NUM
ejpam-3903	2	8	,	,	PUNCT
ejpam-3903	2	9	82	82	NUM
ejpam-3903	2	10	-	-	SYM
ejpam-3903	2	11	111	111	NUM
ejpam-3903	2	12	issn	issn	PROPN
ejpam-3903	2	13	1307	1307	NUM
ejpam-3903	2	14	-	-	SYM
ejpam-3903	2	15	5543	5543	NUM
ejpam-3903	2	16	–	–	PUNCT
ejpam-3903	2	17	ejpam.com	ejpam.com	X
ejpam-3903	2	18	published	publish	VERB
ejpam-3903	2	19	by	by	ADP
ejpam-3903	2	20	new	new	PROPN
ejpam-3903	2	21	york	york	PROPN
ejpam-3903	2	22	business	business	PROPN
ejpam-3903	2	23	global	global	ADJ
ejpam-3903	2	24	existence	existence	NOUN
ejpam-3903	2	25	of	of	ADP
ejpam-3903	2	26	weak	weak	ADJ
ejpam-3903	2	27	solution	solution	NOUN
ejpam-3903	2	28	of	of	ADP
ejpam-3903	2	29	navier	navier	NOUN
ejpam-3903	2	30	-	-	PUNCT
ejpam-3903	2	31	stokes	stokes	PROPN
ejpam-3903	2	32	-	-	PUNCT
ejpam-3903	2	33	fourier	fourier	NOUN
ejpam-3903	2	34	system	system	NOUN
ejpam-3903	2	35	with	with	ADP
ejpam-3903	2	36	a	a	DET
ejpam-3903	2	37	new	new	ADJ
ejpam-3903	2	38	successive	successive	ADJ
ejpam-3903	2	39	approximation	approximation	NOUN
ejpam-3903	2	40	method	method	NOUN
ejpam-3903	2	41	rabe	rabe	NOUN
ejpam-3903	2	42	bade	bade	PROPN
ejpam-3903	2	43	1,∗	1,∗	PROPN
ejpam-3903	2	44	,	,	PUNCT
ejpam-3903	2	45	hedia	hedia	NOUN
ejpam-3903	2	46	chaker2	chaker2	NOUN
ejpam-3903	2	47	1	1	NUM
ejpam-3903	2	48	department	department	NOUN
ejpam-3903	2	49	of	of	ADP
ejpam-3903	2	50	mathematics	mathematics	PROPN
ejpam-3903	2	51	and	and	CCONJ
ejpam-3903	2	52	computer	computer	NOUN
ejpam-3903	2	53	sciences	science	NOUN
ejpam-3903	2	54	faculty	faculty	NOUN
ejpam-3903	2	55	of	of	ADP
ejpam-3903	2	56	science	science	NOUN
ejpam-3903	2	57	and	and	CCONJ
ejpam-3903	2	58	technology	technology	NOUN
ejpam-3903	2	59	,	,	PUNCT
ejpam-3903	2	60	abdou	abdou	PROPN
ejpam-3903	2	61	moumouni	moumouni	PROPN
ejpam-3903	2	62	university	university	PROPN
ejpam-3903	2	63	,	,	PUNCT
ejpam-3903	2	64	bp	bp	PROPN
ejpam-3903	2	65	:	:	PUNCT
ejpam-3903	2	66	10662	10662	NUM
ejpam-3903	2	67	niamey	niamey	NOUN
ejpam-3903	2	68	,	,	PUNCT
ejpam-3903	2	69	niger	niger	NOUN
ejpam-3903	2	70	2	2	NUM
ejpam-3903	2	71	lamsin	lamsin	NOUN
ejpam-3903	2	72	,	,	PUNCT
ejpam-3903	2	73	national	national	ADJ
ejpam-3903	2	74	school	school	NOUN
ejpam-3903	2	75	of	of	ADP
ejpam-3903	2	76	engineers	engineer	NOUN
ejpam-3903	2	77	of	of	ADP
ejpam-3903	2	78	tunis	tunis	NOUN
ejpam-3903	2	79	,	,	PUNCT
ejpam-3903	2	80	university	university	NOUN
ejpam-3903	2	81	of	of	ADP
ejpam-3903	2	82	tunis	tunis	PROPN
ejpam-3903	2	83	el	el	PROPN
ejpam-3903	2	84	-	-	PROPN
ejpam-3903	2	85	manar	manar	PROPN
ejpam-3903	2	86	,	,	PUNCT
ejpam-3903	2	87	bp:37	bp:37	PROPN
ejpam-3903	2	88	,	,	PUNCT
ejpam-3903	2	89	1002	1002	NUM
ejpam-3903	2	90	-	-	PUNCT
ejpam-3903	2	91	tunis	tunis	NOUN
ejpam-3903	2	92	,	,	PUNCT
ejpam-3903	2	93	tunisia	tunisia	NOUN
ejpam-3903	2	94	abstract	abstract	NOUN
ejpam-3903	2	95	.	.	PUNCT
ejpam-3903	3	1	in	in	ADP
ejpam-3903	3	2	this	this	DET
ejpam-3903	3	3	paper	paper	NOUN
ejpam-3903	3	4	we	we	PRON
ejpam-3903	3	5	prove	prove	VERB
ejpam-3903	3	6	the	the	DET
ejpam-3903	3	7	existence	existence	NOUN
ejpam-3903	3	8	of	of	ADP
ejpam-3903	3	9	a	a	DET
ejpam-3903	3	10	weak	weak	ADJ
ejpam-3903	3	11	solution	solution	NOUN
ejpam-3903	3	12	of	of	ADP
ejpam-3903	3	13	the	the	DET
ejpam-3903	3	14	complete	complete	ADJ
ejpam-3903	3	15	compressible	compressible	ADJ
ejpam-3903	3	16	navier	navier	NOUN
ejpam-3903	3	17	-	-	PUNCT
ejpam-3903	3	18	stokes	stoke	NOUN
ejpam-3903	3	19	system	system	NOUN
ejpam-3903	3	20	.	.	PUNCT
ejpam-3903	4	1	we	we	PRON
ejpam-3903	4	2	follow	follow	VERB
ejpam-3903	4	3	an	an	DET
ejpam-3903	4	4	previous	previous	ADJ
ejpam-3903	4	5	work	work	NOUN
ejpam-3903	4	6	where	where	SCONJ
ejpam-3903	4	7	we	we	PRON
ejpam-3903	4	8	added	add	VERB
ejpam-3903	4	9	an	an	DET
ejpam-3903	4	10	artificial	artificial	ADJ
ejpam-3903	4	11	viscosity	viscosity	NOUN
ejpam-3903	4	12	in	in	ADP
ejpam-3903	4	13	the	the	DET
ejpam-3903	4	14	continuity	continuity	NOUN
ejpam-3903	4	15	equation	equation	NOUN
ejpam-3903	4	16	and	and	CCONJ
ejpam-3903	4	17	then	then	ADV
ejpam-3903	4	18	rewrite	rewrite	VERB
ejpam-3903	4	19	the	the	DET
ejpam-3903	4	20	system	system	NOUN
ejpam-3903	4	21	in	in	ADP
ejpam-3903	4	22	hyperbolic	hyperbolic	ADJ
ejpam-3903	4	23	and	and	CCONJ
ejpam-3903	4	24	symmetric	symmetric	ADJ
ejpam-3903	4	25	form	form	NOUN
ejpam-3903	4	26	.	.	PUNCT
ejpam-3903	5	1	our	our	PRON
ejpam-3903	5	2	study	study	NOUN
ejpam-3903	5	3	is	be	AUX
ejpam-3903	5	4	based	base	VERB
ejpam-3903	5	5	on	on	ADP
ejpam-3903	5	6	the	the	DET
ejpam-3903	5	7	symmetric	symmetric	ADJ
ejpam-3903	5	8	hyperbolic	hyperbolic	ADJ
ejpam-3903	5	9	theory	theory	NOUN
ejpam-3903	5	10	.	.	PUNCT
ejpam-3903	6	1	we	we	PRON
ejpam-3903	6	2	use	use	VERB
ejpam-3903	6	3	for	for	ADP
ejpam-3903	6	4	this	this	DET
ejpam-3903	6	5	aim	aim	NOUN
ejpam-3903	6	6	a	a	DET
ejpam-3903	6	7	successive	successive	ADJ
ejpam-3903	6	8	approximation	approximation	NOUN
ejpam-3903	6	9	in	in	ADP
ejpam-3903	6	10	time	time	NOUN
ejpam-3903	6	11	to	to	PART
ejpam-3903	6	12	show	show	VERB
ejpam-3903	6	13	the	the	DET
ejpam-3903	6	14	existence	existence	NOUN
ejpam-3903	6	15	of	of	ADP
ejpam-3903	6	16	the	the	DET
ejpam-3903	6	17	hyperbolic	hyperbolic	ADJ
ejpam-3903	6	18	system	system	NOUN
ejpam-3903	6	19	solution	solution	NOUN
ejpam-3903	6	20	and	and	CCONJ
ejpam-3903	6	21	by	by	ADP
ejpam-3903	6	22	the	the	DET
ejpam-3903	6	23	fixed	fix	VERB
ejpam-3903	6	24	point	point	NOUN
ejpam-3903	6	25	theorem	theorem	VERB
ejpam-3903	6	26	the	the	DET
ejpam-3903	6	27	compacity	compacity	NOUN
ejpam-3903	6	28	property	property	NOUN
ejpam-3903	6	29	of	of	ADP
ejpam-3903	6	30	some	some	DET
ejpam-3903	6	31	appropriate	appropriate	ADJ
ejpam-3903	6	32	sobolev	sobolev	NOUN
ejpam-3903	6	33	spaces	space	NOUN
ejpam-3903	6	34	and	and	CCONJ
ejpam-3903	6	35	some	some	PRON
ejpam-3903	6	36	established	establish	VERB
ejpam-3903	6	37	a	a	DET
ejpam-3903	6	38	priori	priori	ADJ
ejpam-3903	6	39	estimates	estimate	NOUN
ejpam-3903	6	40	we	we	PRON
ejpam-3903	6	41	can	can	AUX
ejpam-3903	6	42	pass	pass	VERB
ejpam-3903	6	43	to	to	ADP
ejpam-3903	6	44	several	several	ADJ
ejpam-3903	6	45	limits	limit	NOUN
ejpam-3903	6	46	to	to	PART
ejpam-3903	6	47	prove	prove	VERB
ejpam-3903	6	48	our	our	PRON
ejpam-3903	6	49	result	result	NOUN
ejpam-3903	6	50	.	.	PUNCT
ejpam-3903	7	1	as	as	ADP
ejpam-3903	7	2	state	state	NOUN
ejpam-3903	7	3	law	law	NOUN
ejpam-3903	7	4	,	,	PUNCT
ejpam-3903	7	5	we	we	PRON
ejpam-3903	7	6	use	use	VERB
ejpam-3903	7	7	the	the	DET
ejpam-3903	7	8	stiffened	stiffen	VERB
ejpam-3903	7	9	gas	gas	NOUN
ejpam-3903	7	10	law	law	NOUN
ejpam-3903	7	11	.	.	PUNCT
ejpam-3903	8	1	2020	2020	NUM
ejpam-3903	8	2	mathematics	mathematic	NOUN
ejpam-3903	8	3	subject	subject	NOUN
ejpam-3903	8	4	classifications	classification	NOUN
ejpam-3903	8	5	:	:	PUNCT
ejpam-3903	8	6	76n06	76n06	NUM
ejpam-3903	8	7	,	,	PUNCT
ejpam-3903	8	8	35d30	35d30	NUM
ejpam-3903	8	9	,	,	PUNCT
ejpam-3903	8	10	47j25	47j25	NUM
ejpam-3903	8	11	key	key	ADJ
ejpam-3903	8	12	words	word	NOUN
ejpam-3903	8	13	and	and	CCONJ
ejpam-3903	8	14	phrases	phrase	NOUN
ejpam-3903	8	15	:	:	PUNCT
ejpam-3903	8	16	fluid	fluid	ADJ
ejpam-3903	8	17	dynamic	dynamic	ADJ
ejpam-3903	8	18	,	,	PUNCT
ejpam-3903	8	19	weak	weak	ADJ
ejpam-3903	8	20	solution	solution	NOUN
ejpam-3903	8	21	,	,	PUNCT
ejpam-3903	8	22	iterative	iterative	NOUN
ejpam-3903	8	23	procedures	procedure	NOUN
ejpam-3903	8	24	.	.	PUNCT
ejpam-3903	9	1	1	1	X
ejpam-3903	9	2	.	.	X
ejpam-3903	9	3	introduction	introduction	NOUN
ejpam-3903	9	4	the	the	DET
ejpam-3903	9	5	compressible	compressible	ADJ
ejpam-3903	9	6	navier	navier	NOUN
ejpam-3903	9	7	-	-	PUNCT
ejpam-3903	9	8	stokes	stoke	NOUN
ejpam-3903	9	9	equations	equation	NOUN
ejpam-3903	9	10	describe	describe	VERB
ejpam-3903	9	11	a	a	DET
ejpam-3903	9	12	viscous	viscous	ADJ
ejpam-3903	9	13	fluid	fluid	NOUN
ejpam-3903	9	14	flow	flow	NOUN
ejpam-3903	9	15	in	in	ADP
ejpam-3903	9	16	a	a	DET
ejpam-3903	9	17	bounded	bounded	ADJ
ejpam-3903	9	18	tridimensional	tridimensional	ADJ
ejpam-3903	9	19	domain	domain	NOUN
ejpam-3903	9	20	,	,	PUNCT
ejpam-3903	9	21	they	they	PRON
ejpam-3903	9	22	are	be	AUX
ejpam-3903	9	23	given	give	VERB
ejpam-3903	9	24	by:	by:	PROPN
ejpam-3903	9	25	∂ρ	∂ρ	PROPN
ejpam-3903	9	26	∂t	∂t	PROPN
ejpam-3903	10	1	+	+	PROPN
ejpam-3903	10	2	∇	∇	X
ejpam-3903	10	3	·	·	PUNCT
ejpam-3903	10	4	(	(	PUNCT
ejpam-3903	10	5	ρu	ρu	NOUN
ejpam-3903	10	6	)	)	PUNCT
ejpam-3903	10	7	=	=	SYM
ejpam-3903	10	8	0	0	NUM
ejpam-3903	10	9	,	,	PUNCT
ejpam-3903	10	10	∂ρu	∂ρu	NOUN
ejpam-3903	10	11	∂t	∂t	PROPN
ejpam-3903	10	12	+	+	NOUN
ejpam-3903	10	13	∇	∇	X
ejpam-3903	10	14	·	·	PUNCT
ejpam-3903	10	15	(	(	PUNCT
ejpam-3903	10	16	ρu⊗u)−	ρu⊗u)−	X
ejpam-3903	10	17	µ4u−	µ4u−	X
ejpam-3903	10	18	(	(	PUNCT
ejpam-3903	10	19	µ	µ	X
ejpam-3903	10	20	3	3	NUM
ejpam-3903	10	21	+	+	CCONJ
ejpam-3903	10	22	λ)∇(∇	λ)∇(∇	PROPN
ejpam-3903	10	23	·	·	PUNCT
ejpam-3903	10	24	u	u	X
ejpam-3903	10	25	)	)	PUNCT
ejpam-3903	10	26	+	+	PROPN
ejpam-3903	10	27	∇p	∇p	PROPN
ejpam-3903	10	28	=	=	SYM
ejpam-3903	10	29	f	f	PROPN
ejpam-3903	10	30	,	,	PUNCT
ejpam-3903	10	31	∂ρe	∂ρe	PROPN
ejpam-3903	10	32	∂t	∂t	PROPN
ejpam-3903	11	1	+	+	NOUN
ejpam-3903	11	2	∇	∇	X
ejpam-3903	11	3	·	·	PUNCT
ejpam-3903	11	4	(	(	PUNCT
ejpam-3903	11	5	(	(	PUNCT
ejpam-3903	11	6	ρe	ρe	INTJ
ejpam-3903	11	7	+	+	CCONJ
ejpam-3903	11	8	p	p	X
ejpam-3903	11	9	)	)	PUNCT
ejpam-3903	11	10	u	u	NOUN
ejpam-3903	11	11	)	)	PUNCT
ejpam-3903	11	12	=	=	SYM
ejpam-3903	11	13	−∇	−∇	NOUN
ejpam-3903	11	14	·	·	PUNCT
ejpam-3903	11	15	(	(	PUNCT
ejpam-3903	11	16	q−	q−	PROPN
ejpam-3903	12	1	[	[	X
ejpam-3903	12	2	µ	µ	X
ejpam-3903	12	3	(	(	PUNCT
ejpam-3903	12	4	∇u	∇u	PROPN
ejpam-3903	12	5	+	+	NOUN
ejpam-3903	12	6	∇ut	∇ut	ADJ
ejpam-3903	12	7	)	)	PUNCT
ejpam-3903	13	1	+	+	CCONJ
ejpam-3903	13	2	(	(	PUNCT
ejpam-3903	13	3	λ−	λ−	PROPN
ejpam-3903	13	4	2	2	NUM
ejpam-3903	13	5	3	3	NUM
ejpam-3903	13	6	µ	µ	X
ejpam-3903	13	7	)	)	PUNCT
ejpam-3903	13	8	id∇	id∇	X
ejpam-3903	13	9	·	·	PUNCT
ejpam-3903	13	10	u]u	u]u	X
ejpam-3903	13	11	)	)	PUNCT
ejpam-3903	14	1	+	+	PUNCT
ejpam-3903	14	2	u	u	NOUN
ejpam-3903	14	3	·	·	SYM
ejpam-3903	14	4	f	f	X
ejpam-3903	14	5	.	.	PUNCT
ejpam-3903	15	1	(	(	PUNCT
ejpam-3903	15	2	1	1	X
ejpam-3903	15	3	)	)	PUNCT
ejpam-3903	15	4	where	where	SCONJ
ejpam-3903	15	5	ρ	ρ	PROPN
ejpam-3903	15	6	is	be	AUX
ejpam-3903	15	7	the	the	DET
ejpam-3903	15	8	density	density	NOUN
ejpam-3903	15	9	,	,	PUNCT
ejpam-3903	15	10	u	u	NOUN
ejpam-3903	15	11	=	=	PUNCT
ejpam-3903	15	12	(	(	PUNCT
ejpam-3903	15	13	u1	u1	PROPN
ejpam-3903	15	14	,	,	PUNCT
ejpam-3903	15	15	u2	u2	NOUN
ejpam-3903	15	16	,	,	PUNCT
ejpam-3903	15	17	u3	u3	PROPN
ejpam-3903	15	18	)	)	PUNCT
ejpam-3903	15	19	are	be	AUX
ejpam-3903	15	20	the	the	DET
ejpam-3903	15	21	velocity	velocity	NOUN
ejpam-3903	15	22	components	component	NOUN
ejpam-3903	15	23	,	,	PUNCT
ejpam-3903	15	24	p	p	NOUN
ejpam-3903	15	25	is	be	AUX
ejpam-3903	15	26	the	the	DET
ejpam-3903	15	27	pressure	pressure	NOUN
ejpam-3903	15	28	,	,	PUNCT
ejpam-3903	15	29	e	e	X
ejpam-3903	15	30	is	be	AUX
ejpam-3903	15	31	the	the	DET
ejpam-3903	15	32	tolal	tolal	NOUN
ejpam-3903	15	33	energy	energy	NOUN
ejpam-3903	15	34	,	,	PUNCT
ejpam-3903	15	35	f	f	PROPN
ejpam-3903	15	36	is	be	AUX
ejpam-3903	15	37	the	the	DET
ejpam-3903	15	38	external	external	ADJ
ejpam-3903	15	39	force	force	NOUN
ejpam-3903	15	40	and	and	CCONJ
ejpam-3903	15	41	q	q	NOUN
ejpam-3903	15	42	is	be	AUX
ejpam-3903	15	43	the	the	DET
ejpam-3903	15	44	heat	heat	NOUN
ejpam-3903	15	45	flux	flux	NOUN
ejpam-3903	15	46	.	.	PUNCT
ejpam-3903	16	1	∗corresponding	∗corresponde	VERB
ejpam-3903	16	2	author	author	NOUN
ejpam-3903	16	3	.	.	PUNCT
ejpam-3903	17	1	doi	doi	NOUN
ejpam-3903	17	2	:	:	PUNCT
ejpam-3903	17	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3903	https://doi.org/10.29020/nybg.ejpam.v14i1.3903	PRON
ejpam-3903	17	4	email	email	NOUN
ejpam-3903	17	5	addresses	address	NOUN
ejpam-3903	17	6	:	:	PUNCT
ejpam-3903	17	7	baderabe@yahoo.fr	baderabe@yahoo.fr	PROPN
ejpam-3903	17	8	(	(	PUNCT
ejpam-3903	17	9	r.	r.	PROPN
ejpam-3903	17	10	bade	bade	PROPN
ejpam-3903	17	11	)	)	PUNCT
ejpam-3903	17	12	,	,	PUNCT
ejpam-3903	17	13	hedia.chaker@enit.rnu.tn	hedia.chaker@enit.rnu.tn	INTJ
ejpam-3903	17	14	(	(	PUNCT
ejpam-3903	17	15	h.	h.	PROPN
ejpam-3903	17	16	chaker	chaker	PROPN
ejpam-3903	17	17	)	)	PUNCT
ejpam-3903	17	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3903	18	1	82	82	NUM
ejpam-3903	19	1	c	c	X
ejpam-3903	19	2	©	©	PROPN
ejpam-3903	19	3	2021	2021	NUM
ejpam-3903	19	4	ejpam	ejpam	VERB
ejpam-3903	19	5	all	all	DET
ejpam-3903	19	6	rights	right	NOUN
ejpam-3903	19	7	reserved	reserve	VERB
ejpam-3903	19	8	.	.	PUNCT
ejpam-3903	20	1	r.	r.	PROPN
ejpam-3903	20	2	bade	bade	PROPN
ejpam-3903	20	3	,	,	PUNCT
ejpam-3903	20	4	h.	h.	PROPN
ejpam-3903	20	5	chaker	chaker	PROPN
ejpam-3903	20	6	/	/	SYM
ejpam-3903	20	7	eur	eur	PROPN
ejpam-3903	20	8	.	.	PUNCT
ejpam-3903	21	1	j.	j.	PROPN
ejpam-3903	21	2	pure	pure	PROPN
ejpam-3903	21	3	appl	appl	PROPN
ejpam-3903	21	4	.	.	PROPN
ejpam-3903	21	5	math	math	PROPN
ejpam-3903	21	6	,	,	PUNCT
ejpam-3903	21	7	14	14	NUM
ejpam-3903	21	8	(	(	PUNCT
ejpam-3903	21	9	1	1	NUM
ejpam-3903	21	10	)	)	PUNCT
ejpam-3903	21	11	(	(	PUNCT
ejpam-3903	21	12	2021	2021	NUM
ejpam-3903	21	13	)	)	PUNCT
ejpam-3903	21	14	,	,	PUNCT
ejpam-3903	21	15	82	82	NUM
ejpam-3903	21	16	-	-	SYM
ejpam-3903	21	17	111	111	NUM
ejpam-3903	21	18	83	83	NUM
ejpam-3903	21	19	the	the	DET
ejpam-3903	21	20	mathematical	mathematical	ADJ
ejpam-3903	21	21	analysis	analysis	NOUN
ejpam-3903	21	22	of	of	ADP
ejpam-3903	21	23	these	these	DET
ejpam-3903	21	24	equations	equation	NOUN
ejpam-3903	21	25	was	be	AUX
ejpam-3903	21	26	made	make	VERB
ejpam-3903	21	27	only	only	ADV
ejpam-3903	21	28	recently	recently	ADV
ejpam-3903	21	29	with	with	ADP
ejpam-3903	21	30	the	the	DET
ejpam-3903	21	31	works	work	NOUN
ejpam-3903	21	32	of	of	ADP
ejpam-3903	21	33	[	[	X
ejpam-3903	21	34	16	16	NUM
ejpam-3903	21	35	]	]	X
ejpam-3903	21	36	,	,	PUNCT
ejpam-3903	21	37	in	in	ADP
ejpam-3903	21	38	particular	particular	ADJ
ejpam-3903	21	39	in	in	ADP
ejpam-3903	21	40	the	the	DET
ejpam-3903	21	41	case	case	NOUN
ejpam-3903	21	42	of	of	ADP
ejpam-3903	21	43	barotropic	barotropic	NOUN
ejpam-3903	21	44	fluids	fluid	NOUN
ejpam-3903	21	45	p	p	PROPN
ejpam-3903	21	46	(	(	PUNCT
ejpam-3903	21	47	ρ	ρ	NOUN
ejpam-3903	21	48	)	)	PUNCT
ejpam-3903	21	49	=	=	SYM
ejpam-3903	21	50	aργ	aργ	NOUN
ejpam-3903	21	51	.	.	PUNCT
ejpam-3903	22	1	the	the	DET
ejpam-3903	22	2	author	author	NOUN
ejpam-3903	22	3	had	have	AUX
ejpam-3903	22	4	established	establish	VERB
ejpam-3903	22	5	a	a	DET
ejpam-3903	22	6	regularity	regularity	NOUN
ejpam-3903	22	7	result	result	NOUN
ejpam-3903	22	8	of	of	ADP
ejpam-3903	22	9	weak	weak	ADJ
ejpam-3903	22	10	solution	solution	NOUN
ejpam-3903	22	11	under	under	ADP
ejpam-3903	22	12	certain	certain	ADJ
ejpam-3903	22	13	conditions	condition	NOUN
ejpam-3903	22	14	related	relate	VERB
ejpam-3903	22	15	to	to	ADP
ejpam-3903	22	16	γ	γ	PROPN
ejpam-3903	22	17	.	.	PUNCT
ejpam-3903	23	1	studying	study	VERB
ejpam-3903	23	2	a	a	DET
ejpam-3903	23	3	more	more	ADV
ejpam-3903	23	4	general	general	ADJ
ejpam-3903	23	5	case	case	NOUN
ejpam-3903	23	6	,	,	PUNCT
ejpam-3903	23	7	[	[	X
ejpam-3903	23	8	9	9	NUM
ejpam-3903	23	9	]	]	PUNCT
ejpam-3903	23	10	had	have	AUX
ejpam-3903	23	11	looked	look	VERB
ejpam-3903	23	12	the	the	DET
ejpam-3903	23	13	case	case	NOUN
ejpam-3903	23	14	of	of	ADP
ejpam-3903	23	15	non	non	ADJ
ejpam-3903	23	16	-	-	ADJ
ejpam-3903	23	17	monotone	monotone	ADJ
ejpam-3903	23	18	pressure	pressure	NOUN
ejpam-3903	23	19	-	-	PUNCT
ejpam-3903	23	20	law	law	NOUN
ejpam-3903	23	21	.	.	PUNCT
ejpam-3903	24	1	[	[	X
ejpam-3903	24	2	7	7	NUM
ejpam-3903	24	3	,	,	PUNCT
ejpam-3903	24	4	8	8	NUM
ejpam-3903	24	5	]	]	PUNCT
ejpam-3903	24	6	was	be	AUX
ejpam-3903	24	7	interested	interested	ADJ
ejpam-3903	24	8	in	in	ADP
ejpam-3903	24	9	the	the	DET
ejpam-3903	24	10	system	system	NOUN
ejpam-3903	24	11	in	in	ADP
ejpam-3903	24	12	dimension	dimension	NOUN
ejpam-3903	24	13	two	two	NUM
ejpam-3903	24	14	where	where	SCONJ
ejpam-3903	24	15	he	he	PRON
ejpam-3903	24	16	refined	refine	VERB
ejpam-3903	24	17	the	the	DET
ejpam-3903	24	18	conditions	condition	NOUN
ejpam-3903	24	19	on	on	ADP
ejpam-3903	24	20	the	the	DET
ejpam-3903	24	21	initial	initial	ADJ
ejpam-3903	24	22	data	datum	NOUN
ejpam-3903	24	23	.	.	PUNCT
ejpam-3903	25	1	the	the	DET
ejpam-3903	25	2	author	author	NOUN
ejpam-3903	25	3	established	establish	VERB
ejpam-3903	25	4	a	a	DET
ejpam-3903	25	5	regularity	regularity	NOUN
ejpam-3903	25	6	result	result	NOUN
ejpam-3903	25	7	with	with	ADP
ejpam-3903	25	8	periodic	periodic	ADJ
ejpam-3903	25	9	boundary	boundary	ADJ
ejpam-3903	25	10	conditions	condition	NOUN
ejpam-3903	25	11	and	and	CCONJ
ejpam-3903	25	12	especially	especially	ADV
ejpam-3903	25	13	in	in	ADP
ejpam-3903	25	14	prevision	prevision	NOUN
ejpam-3903	25	15	of	of	ADP
ejpam-3903	25	16	possible	possible	ADJ
ejpam-3903	25	17	appearance	appearance	NOUN
ejpam-3903	25	18	of	of	ADP
ejpam-3903	25	19	the	the	DET
ejpam-3903	25	20	vacuum	vacuum	NOUN
ejpam-3903	25	21	.	.	PUNCT
ejpam-3903	26	1	in	in	ADP
ejpam-3903	26	2	the	the	DET
ejpam-3903	26	3	case	case	NOUN
ejpam-3903	26	4	of	of	ADP
ejpam-3903	26	5	the	the	DET
ejpam-3903	26	6	complete	complete	ADJ
ejpam-3903	26	7	navier	navier	NOUN
ejpam-3903	26	8	-	-	PUNCT
ejpam-3903	26	9	stokes	stoke	NOUN
ejpam-3903	26	10	equation	equation	NOUN
ejpam-3903	26	11	,	,	PUNCT
ejpam-3903	26	12	with	with	ADP
ejpam-3903	26	13	heat	heat	NOUN
ejpam-3903	26	14	conduction	conduction	NOUN
ejpam-3903	26	15	,	,	PUNCT
ejpam-3903	26	16	[	[	X
ejpam-3903	26	17	16	16	NUM
ejpam-3903	26	18	]	]	PUNCT
ejpam-3903	26	19	had	have	AUX
ejpam-3903	26	20	sketched	sketch	VERB
ejpam-3903	26	21	the	the	DET
ejpam-3903	26	22	existence	existence	NOUN
ejpam-3903	26	23	of	of	ADP
ejpam-3903	26	24	global	global	ADJ
ejpam-3903	26	25	weak	weak	ADJ
ejpam-3903	26	26	solution	solution	NOUN
ejpam-3903	26	27	by	by	ADP
ejpam-3903	26	28	compactness	compactness	NOUN
ejpam-3903	26	29	arguments	argument	NOUN
ejpam-3903	26	30	and	and	CCONJ
ejpam-3903	26	31	some	some	DET
ejpam-3903	26	32	a	a	DET
ejpam-3903	26	33	priori	priori	ADJ
ejpam-3903	26	34	estimates	estimate	NOUN
ejpam-3903	26	35	.	.	PUNCT
ejpam-3903	27	1	however	however	ADV
ejpam-3903	27	2	,	,	PUNCT
ejpam-3903	27	3	the	the	DET
ejpam-3903	27	4	author	author	NOUN
ejpam-3903	27	5	indicated	indicate	VERB
ejpam-3903	27	6	that	that	SCONJ
ejpam-3903	27	7	these	these	DET
ejpam-3903	27	8	a	a	DET
ejpam-3903	27	9	priori	priori	ADJ
ejpam-3903	27	10	estimates	estimate	NOUN
ejpam-3903	27	11	are	be	AUX
ejpam-3903	27	12	very	very	ADV
ejpam-3903	27	13	difficult	difficult	ADJ
ejpam-3903	27	14	to	to	PART
ejpam-3903	27	15	be	be	AUX
ejpam-3903	27	16	establish	establish	VERB
ejpam-3903	27	17	and	and	CCONJ
ejpam-3903	27	18	sometimes	sometimes	ADV
ejpam-3903	27	19	unavailable	unavailable	ADJ
ejpam-3903	27	20	except	except	SCONJ
ejpam-3903	27	21	in	in	ADP
ejpam-3903	27	22	a	a	DET
ejpam-3903	27	23	very	very	ADV
ejpam-3903	27	24	restrictive	restrictive	ADJ
ejpam-3903	27	25	cases	case	NOUN
ejpam-3903	27	26	.	.	PUNCT
ejpam-3903	28	1	more	more	ADV
ejpam-3903	28	2	recently	recently	ADV
ejpam-3903	28	3	,	,	PUNCT
ejpam-3903	28	4	[	[	X
ejpam-3903	28	5	19	19	NUM
ejpam-3903	28	6	]	]	PUNCT
ejpam-3903	28	7	made	make	VERB
ejpam-3903	28	8	a	a	DET
ejpam-3903	28	9	major	major	ADJ
ejpam-3903	28	10	contribution	contribution	NOUN
ejpam-3903	28	11	in	in	ADP
ejpam-3903	28	12	the	the	DET
ejpam-3903	28	13	development	development	NOUN
ejpam-3903	28	14	of	of	ADP
ejpam-3903	28	15	the	the	DET
ejpam-3903	28	16	general	general	ADJ
ejpam-3903	28	17	mathematical	mathematical	ADJ
ejpam-3903	28	18	theory	theory	NOUN
ejpam-3903	28	19	of	of	ADP
ejpam-3903	28	20	this	this	DET
ejpam-3903	28	21	system	system	NOUN
ejpam-3903	28	22	without	without	ADP
ejpam-3903	28	23	any	any	DET
ejpam-3903	28	24	limitation	limitation	NOUN
ejpam-3903	28	25	on	on	ADP
ejpam-3903	28	26	the	the	DET
ejpam-3903	28	27	data	data	NOUN
ejpam-3903	28	28	size	size	NOUN
ejpam-3903	28	29	.	.	PUNCT
ejpam-3903	29	1	the	the	DET
ejpam-3903	29	2	authors	author	NOUN
ejpam-3903	29	3	proved	prove	VERB
ejpam-3903	29	4	the	the	DET
ejpam-3903	29	5	existence	existence	NOUN
ejpam-3903	29	6	of	of	ADP
ejpam-3903	29	7	a	a	DET
ejpam-3903	29	8	variational	variational	ADJ
ejpam-3903	29	9	solution	solution	NOUN
ejpam-3903	29	10	using	use	VERB
ejpam-3903	29	11	a	a	DET
ejpam-3903	29	12	series	series	NOUN
ejpam-3903	29	13	of	of	ADP
ejpam-3903	29	14	approximations	approximation	NOUN
ejpam-3903	29	15	:	:	PUNCT
ejpam-3903	29	16	artificial	artificial	ADJ
ejpam-3903	29	17	pressure	pressure	NOUN
ejpam-3903	29	18	,	,	PUNCT
ejpam-3903	29	19	relaxation	relaxation	NOUN
ejpam-3903	29	20	in	in	ADP
ejpam-3903	29	21	the	the	DET
ejpam-3903	29	22	continuity	continuity	NOUN
ejpam-3903	29	23	equation	equation	NOUN
ejpam-3903	29	24	and	and	CCONJ
ejpam-3903	29	25	finally	finally	ADV
ejpam-3903	29	26	a	a	DET
ejpam-3903	29	27	regularized	regularize	VERB
ejpam-3903	29	28	thermal	thermal	ADJ
ejpam-3903	29	29	energy	energy	NOUN
ejpam-3903	29	30	equation	equation	NOUN
ejpam-3903	29	31	.	.	PUNCT
ejpam-3903	30	1	passing	pass	VERB
ejpam-3903	30	2	to	to	ADP
ejpam-3903	30	3	the	the	DET
ejpam-3903	30	4	limit	limit	NOUN
ejpam-3903	30	5	they	they	PRON
ejpam-3903	30	6	obtain	obtain	VERB
ejpam-3903	30	7	their	their	PRON
ejpam-3903	30	8	variational	variational	ADJ
ejpam-3903	30	9	solution	solution	NOUN
ejpam-3903	30	10	of	of	ADP
ejpam-3903	30	11	the	the	DET
ejpam-3903	30	12	navier	navier	NOUN
ejpam-3903	30	13	-	-	PUNCT
ejpam-3903	30	14	stokes	stoke	NOUN
ejpam-3903	30	15	equations	equation	NOUN
ejpam-3903	30	16	.	.	PUNCT
ejpam-3903	31	1	although	although	SCONJ
ejpam-3903	31	2	the	the	DET
ejpam-3903	31	3	theory	theory	NOUN
ejpam-3903	31	4	is	be	AUX
ejpam-3903	31	5	very	very	ADV
ejpam-3903	31	6	nice	nice	ADJ
ejpam-3903	31	7	,	,	PUNCT
ejpam-3903	31	8	the	the	DET
ejpam-3903	31	9	question	question	NOUN
ejpam-3903	31	10	of	of	ADP
ejpam-3903	31	11	the	the	DET
ejpam-3903	31	12	physical	physical	ADJ
ejpam-3903	31	13	sense	sense	NOUN
ejpam-3903	31	14	of	of	ADP
ejpam-3903	31	15	these	these	DET
ejpam-3903	31	16	approximations	approximation	NOUN
ejpam-3903	31	17	could	could	AUX
ejpam-3903	31	18	possibly	possibly	ADV
ejpam-3903	31	19	arise	arise	VERB
ejpam-3903	31	20	.	.	PUNCT
ejpam-3903	32	1	with	with	ADP
ejpam-3903	32	2	another	another	DET
ejpam-3903	32	3	approach	approach	NOUN
ejpam-3903	32	4	,	,	PUNCT
ejpam-3903	32	5	[	[	X
ejpam-3903	32	6	9	9	NUM
ejpam-3903	32	7	,	,	PUNCT
ejpam-3903	32	8	10	10	NUM
ejpam-3903	32	9	]	]	PUNCT
ejpam-3903	32	10	justify	justify	VERB
ejpam-3903	32	11	the	the	DET
ejpam-3903	32	12	existence	existence	NOUN
ejpam-3903	32	13	of	of	ADP
ejpam-3903	32	14	a	a	DET
ejpam-3903	32	15	variational	variational	ADJ
ejpam-3903	32	16	solution	solution	NOUN
ejpam-3903	32	17	using	use	VERB
ejpam-3903	32	18	in	in	ADP
ejpam-3903	32	19	addition	addition	NOUN
ejpam-3903	32	20	some	some	DET
ejpam-3903	32	21	a	a	DET
ejpam-3903	32	22	priori	priori	ADJ
ejpam-3903	32	23	estimates	estimate	NOUN
ejpam-3903	32	24	.	.	PUNCT
ejpam-3903	33	1	in	in	ADP
ejpam-3903	33	2	this	this	DET
ejpam-3903	33	3	work	work	NOUN
ejpam-3903	33	4	,	,	PUNCT
ejpam-3903	33	5	we	we	PRON
ejpam-3903	33	6	establish	establish	VERB
ejpam-3903	33	7	the	the	DET
ejpam-3903	33	8	existence	existence	NOUN
ejpam-3903	33	9	of	of	ADP
ejpam-3903	33	10	a	a	DET
ejpam-3903	33	11	weak	weak	ADJ
ejpam-3903	33	12	solution	solution	NOUN
ejpam-3903	33	13	for	for	ADP
ejpam-3903	33	14	the	the	DET
ejpam-3903	33	15	compressible	compressible	ADJ
ejpam-3903	33	16	navierstokes	navierstoke	NOUN
ejpam-3903	33	17	system	system	NOUN
ejpam-3903	33	18	using	use	VERB
ejpam-3903	33	19	the	the	DET
ejpam-3903	33	20	theory	theory	NOUN
ejpam-3903	33	21	of	of	ADP
ejpam-3903	33	22	the	the	DET
ejpam-3903	33	23	symmetric	symmetric	ADJ
ejpam-3903	33	24	hyperbolic	hyperbolic	ADJ
ejpam-3903	33	25	system	system	NOUN
ejpam-3903	33	26	[	[	X
ejpam-3903	33	27	11	11	NUM
ejpam-3903	33	28	,	,	PUNCT
ejpam-3903	33	29	13	13	NUM
ejpam-3903	33	30	,	,	PUNCT
ejpam-3903	33	31	17	17	NUM
ejpam-3903	33	32	]	]	PUNCT
ejpam-3903	33	33	.	.	PUNCT
ejpam-3903	34	1	for	for	ADP
ejpam-3903	34	2	that	that	DET
ejpam-3903	34	3	purpose	purpose	NOUN
ejpam-3903	34	4	,	,	PUNCT
ejpam-3903	34	5	we	we	PRON
ejpam-3903	34	6	add	add	VERB
ejpam-3903	34	7	an	an	DET
ejpam-3903	34	8	artificial	artificial	ADJ
ejpam-3903	34	9	viscosity	viscosity	NOUN
ejpam-3903	34	10	term	term	NOUN
ejpam-3903	34	11	−ε4ρ	−ε4ρ	PROPN
ejpam-3903	34	12	in	in	ADP
ejpam-3903	34	13	the	the	DET
ejpam-3903	34	14	continuity	continuity	NOUN
ejpam-3903	34	15	equation	equation	NOUN
ejpam-3903	34	16	.	.	PUNCT
ejpam-3903	35	1	classically	classically	ADV
ejpam-3903	35	2	this	this	DET
ejpam-3903	35	3	artificial	artificial	ADJ
ejpam-3903	35	4	viscosity	viscosity	NOUN
ejpam-3903	35	5	is	be	AUX
ejpam-3903	35	6	added	add	VERB
ejpam-3903	35	7	to	to	PART
ejpam-3903	35	8	regularize	regularize	VERB
ejpam-3903	35	9	the	the	DET
ejpam-3903	35	10	solution	solution	NOUN
ejpam-3903	35	11	,	,	PUNCT
ejpam-3903	35	12	but	but	CCONJ
ejpam-3903	35	13	here	here	ADV
ejpam-3903	35	14	we	we	PRON
ejpam-3903	35	15	add	add	VERB
ejpam-3903	35	16	it	it	PRON
ejpam-3903	35	17	in	in	ADP
ejpam-3903	35	18	the	the	DET
ejpam-3903	35	19	aim	aim	NOUN
ejpam-3903	35	20	of	of	ADP
ejpam-3903	35	21	rewriting	rewrite	VERB
ejpam-3903	35	22	and	and	CCONJ
ejpam-3903	35	23	obtaining	obtain	VERB
ejpam-3903	35	24	a	a	DET
ejpam-3903	35	25	hyperbolic	hyperbolic	ADJ
ejpam-3903	35	26	system	system	NOUN
ejpam-3903	35	27	from	from	ADP
ejpam-3903	35	28	compressible	compressible	ADJ
ejpam-3903	35	29	navier	navier	NOUN
ejpam-3903	35	30	-	-	PUNCT
ejpam-3903	35	31	stokes	stoke	NOUN
ejpam-3903	35	32	equations	equation	NOUN
ejpam-3903	35	33	.	.	PUNCT
ejpam-3903	36	1	after	after	ADP
ejpam-3903	36	2	adding	add	VERB
ejpam-3903	36	3	−ε4ρ	−ε4ρ	PROPN
ejpam-3903	36	4	,	,	PUNCT
ejpam-3903	36	5	we	we	PRON
ejpam-3903	36	6	make	make	VERB
ejpam-3903	36	7	a	a	DET
ejpam-3903	36	8	change	change	NOUN
ejpam-3903	36	9	of	of	ADP
ejpam-3903	36	10	variable	variable	NOUN
ejpam-3903	36	11	similar	similar	ADJ
ejpam-3903	36	12	to	to	ADP
ejpam-3903	36	13	that	that	PRON
ejpam-3903	36	14	used	use	VERB
ejpam-3903	36	15	by	by	ADP
ejpam-3903	36	16	[	[	X
ejpam-3903	36	17	5	5	NUM
ejpam-3903	36	18	]	]	PUNCT
ejpam-3903	36	19	.	.	PUNCT
ejpam-3903	37	1	with	with	ADP
ejpam-3903	37	2	this	this	DET
ejpam-3903	37	3	change	change	NOUN
ejpam-3903	37	4	of	of	ADP
ejpam-3903	37	5	variable	variable	NOUN
ejpam-3903	37	6	,	,	PUNCT
ejpam-3903	37	7	we	we	PRON
ejpam-3903	37	8	come	come	VERB
ejpam-3903	37	9	down	down	ADP
ejpam-3903	37	10	to	to	ADP
ejpam-3903	37	11	a	a	DET
ejpam-3903	37	12	system	system	NOUN
ejpam-3903	37	13	of	of	ADP
ejpam-3903	37	14	order	order	NOUN
ejpam-3903	37	15	1	1	NUM
ejpam-3903	37	16	.	.	PUNCT
ejpam-3903	38	1	a	a	DET
ejpam-3903	38	2	semi	semi	NOUN
ejpam-3903	38	3	-	-	ADJ
ejpam-3903	38	4	discretization	discretization	NOUN
ejpam-3903	38	5	in	in	ADP
ejpam-3903	38	6	time	time	NOUN
ejpam-3903	38	7	and	and	CCONJ
ejpam-3903	38	8	a	a	DET
ejpam-3903	38	9	linearization	linearization	NOUN
ejpam-3903	38	10	of	of	ADP
ejpam-3903	38	11	the	the	DET
ejpam-3903	38	12	obtained	obtain	VERB
ejpam-3903	38	13	system	system	NOUN
ejpam-3903	38	14	allow	allow	VERB
ejpam-3903	38	15	us	we	PRON
ejpam-3903	38	16	to	to	PART
ejpam-3903	38	17	use	use	VERB
ejpam-3903	38	18	the	the	DET
ejpam-3903	38	19	results	result	NOUN
ejpam-3903	38	20	of	of	ADP
ejpam-3903	38	21	[	[	X
ejpam-3903	38	22	13	13	NUM
ejpam-3903	38	23	]	]	PUNCT
ejpam-3903	38	24	.	.	PUNCT
ejpam-3903	39	1	by	by	ADP
ejpam-3903	39	2	a	a	DET
ejpam-3903	39	3	fixed	fix	VERB
ejpam-3903	39	4	point	point	NOUN
ejpam-3903	39	5	theorem	theorem	VERB
ejpam-3903	39	6	we	we	PRON
ejpam-3903	39	7	show	show	VERB
ejpam-3903	39	8	the	the	DET
ejpam-3903	39	9	existence	existence	NOUN
ejpam-3903	39	10	of	of	ADP
ejpam-3903	39	11	the	the	DET
ejpam-3903	39	12	solution	solution	NOUN
ejpam-3903	39	13	of	of	ADP
ejpam-3903	39	14	the	the	DET
ejpam-3903	39	15	stationary	stationary	ADJ
ejpam-3903	39	16	,	,	PUNCT
ejpam-3903	39	17	nonlinear	nonlinear	ADJ
ejpam-3903	39	18	system	system	NOUN
ejpam-3903	39	19	.	.	PUNCT
ejpam-3903	40	1	then	then	ADV
ejpam-3903	40	2	by	by	ADP
ejpam-3903	40	3	some	some	DET
ejpam-3903	40	4	a	a	DET
ejpam-3903	40	5	priori	priori	ADJ
ejpam-3903	40	6	estimates	estimate	NOUN
ejpam-3903	40	7	we	we	PRON
ejpam-3903	40	8	can	can	AUX
ejpam-3903	40	9	pass	pass	VERB
ejpam-3903	40	10	to	to	PART
ejpam-3903	40	11	limit	limit	VERB
ejpam-3903	40	12	in	in	ADP
ejpam-3903	40	13	time	time	NOUN
ejpam-3903	40	14	(	(	PUNCT
ejpam-3903	40	15	4t→	4t→	NOUN
ejpam-3903	40	16	0	0	NUM
ejpam-3903	40	17	)	)	PUNCT
ejpam-3903	40	18	and	and	CCONJ
ejpam-3903	40	19	after	after	ADP
ejpam-3903	40	20	when	when	SCONJ
ejpam-3903	40	21	ε→	ε→	PROPN
ejpam-3903	40	22	0	0	NUM
ejpam-3903	40	23	we	we	PRON
ejpam-3903	40	24	justify	justify	VERB
ejpam-3903	40	25	the	the	DET
ejpam-3903	40	26	existence	existence	NOUN
ejpam-3903	40	27	of	of	ADP
ejpam-3903	40	28	navier	navier	NOUN
ejpam-3903	40	29	-	-	PUNCT
ejpam-3903	40	30	stokes	stoke	VERB
ejpam-3903	40	31	weak	weak	ADJ
ejpam-3903	40	32	solution	solution	NOUN
ejpam-3903	40	33	.	.	PUNCT
ejpam-3903	41	1	the	the	DET
ejpam-3903	41	2	outline	outline	NOUN
ejpam-3903	41	3	of	of	ADP
ejpam-3903	41	4	this	this	DET
ejpam-3903	41	5	paper	paper	NOUN
ejpam-3903	41	6	is	be	AUX
ejpam-3903	41	7	organized	organize	VERB
ejpam-3903	41	8	as	as	ADP
ejpam-3903	41	9	follow	follow	NOUN
ejpam-3903	41	10	.	.	PUNCT
ejpam-3903	42	1	in	in	ADP
ejpam-3903	42	2	section	section	NOUN
ejpam-3903	42	3	2	2	NUM
ejpam-3903	42	4	we	we	PRON
ejpam-3903	42	5	will	will	AUX
ejpam-3903	42	6	present	present	VERB
ejpam-3903	42	7	the	the	DET
ejpam-3903	42	8	added	add	VERB
ejpam-3903	42	9	system	system	NOUN
ejpam-3903	42	10	and	and	CCONJ
ejpam-3903	42	11	our	our	PRON
ejpam-3903	42	12	main	main	ADJ
ejpam-3903	42	13	results	result	NOUN
ejpam-3903	42	14	.	.	PUNCT
ejpam-3903	43	1	in	in	ADP
ejpam-3903	43	2	section	section	NOUN
ejpam-3903	43	3	3	3	NUM
ejpam-3903	43	4	we	we	PRON
ejpam-3903	43	5	will	will	AUX
ejpam-3903	43	6	prove	prove	VERB
ejpam-3903	43	7	that	that	SCONJ
ejpam-3903	43	8	the	the	DET
ejpam-3903	43	9	density	density	NOUN
ejpam-3903	43	10	in	in	ADP
ejpam-3903	43	11	the	the	DET
ejpam-3903	43	12	added	add	VERB
ejpam-3903	43	13	system	system	NOUN
ejpam-3903	43	14	remain	remain	VERB
ejpam-3903	43	15	strictly	strictly	ADV
ejpam-3903	43	16	positive	positive	ADJ
ejpam-3903	43	17	when	when	SCONJ
ejpam-3903	43	18	its	its	PRON
ejpam-3903	43	19	initial	initial	ADJ
ejpam-3903	43	20	value	value	NOUN
ejpam-3903	43	21	is	be	AUX
ejpam-3903	43	22	positive	positive	ADJ
ejpam-3903	43	23	.	.	PUNCT
ejpam-3903	44	1	in	in	ADP
ejpam-3903	44	2	section	section	NOUN
ejpam-3903	44	3	4	4	NUM
ejpam-3903	44	4	we	we	PRON
ejpam-3903	44	5	show	show	VERB
ejpam-3903	44	6	how	how	SCONJ
ejpam-3903	44	7	we	we	PRON
ejpam-3903	44	8	obtain	obtain	VERB
ejpam-3903	44	9	the	the	DET
ejpam-3903	44	10	hyperbolic	hyperbolic	ADJ
ejpam-3903	44	11	system	system	NOUN
ejpam-3903	44	12	and	and	CCONJ
ejpam-3903	44	13	we	we	PRON
ejpam-3903	44	14	will	will	AUX
ejpam-3903	44	15	present	present	VERB
ejpam-3903	44	16	the	the	DET
ejpam-3903	44	17	successive	successive	ADJ
ejpam-3903	44	18	approximations	approximation	NOUN
ejpam-3903	44	19	which	which	PRON
ejpam-3903	44	20	allows	allow	VERB
ejpam-3903	44	21	us	we	PRON
ejpam-3903	44	22	to	to	PART
ejpam-3903	44	23	construct	construct	VERB
ejpam-3903	44	24	and	and	CCONJ
ejpam-3903	44	25	prove	prove	VERB
ejpam-3903	44	26	the	the	DET
ejpam-3903	44	27	existence	existence	NOUN
ejpam-3903	44	28	of	of	ADP
ejpam-3903	44	29	the	the	DET
ejpam-3903	44	30	weak	weak	ADJ
ejpam-3903	44	31	solution	solution	NOUN
ejpam-3903	44	32	of	of	ADP
ejpam-3903	44	33	the	the	DET
ejpam-3903	44	34	obtained	obtain	VERB
ejpam-3903	44	35	system	system	NOUN
ejpam-3903	44	36	.	.	PUNCT
ejpam-3903	45	1	finally	finally	ADV
ejpam-3903	45	2	in	in	ADP
ejpam-3903	45	3	section	section	NOUN
ejpam-3903	45	4	5	5	NUM
ejpam-3903	45	5	we	we	PRON
ejpam-3903	45	6	pass	pass	VERB
ejpam-3903	45	7	to	to	PART
ejpam-3903	45	8	limit	limit	VERB
ejpam-3903	45	9	in	in	ADP
ejpam-3903	45	10	the	the	DET
ejpam-3903	45	11	artificial	artificial	ADJ
ejpam-3903	45	12	viscosity	viscosity	NOUN
ejpam-3903	45	13	and	and	CCONJ
ejpam-3903	45	14	then	then	ADV
ejpam-3903	45	15	we	we	PRON
ejpam-3903	45	16	prove	prove	VERB
ejpam-3903	45	17	the	the	DET
ejpam-3903	45	18	existence	existence	NOUN
ejpam-3903	45	19	of	of	ADP
ejpam-3903	45	20	the	the	DET
ejpam-3903	45	21	weak	weak	ADJ
ejpam-3903	45	22	solution	solution	NOUN
ejpam-3903	45	23	for	for	ADP
ejpam-3903	45	24	the	the	DET
ejpam-3903	45	25	compressible	compressible	ADJ
ejpam-3903	45	26	navier	navier	NOUN
ejpam-3903	45	27	-	-	PUNCT
ejpam-3903	45	28	stokes	stoke	NOUN
ejpam-3903	45	29	system	system	NOUN
ejpam-3903	45	30	.	.	PUNCT
ejpam-3903	46	1	2	2	X
ejpam-3903	46	2	.	.	NUM
ejpam-3903	46	3	preliminaries	preliminary	NOUN
ejpam-3903	46	4	and	and	CCONJ
ejpam-3903	46	5	main	main	ADJ
ejpam-3903	46	6	results	result	NOUN
ejpam-3903	46	7	let	let	VERB
ejpam-3903	46	8	us	we	PRON
ejpam-3903	46	9	consider	consider	VERB
ejpam-3903	46	10	a	a	DET
ejpam-3903	46	11	bounded	bounded	ADJ
ejpam-3903	46	12	domain	domain	NOUN
ejpam-3903	46	13	ω	ω	NOUN
ejpam-3903	46	14	of	of	ADP
ejpam-3903	46	15	r3	r3	PROPN
ejpam-3903	46	16	with	with	ADP
ejpam-3903	46	17	the	the	DET
ejpam-3903	46	18	boundary	boundary	ADJ
ejpam-3903	46	19	∂ω	∂ω	PROPN
ejpam-3903	46	20	is	be	AUX
ejpam-3903	46	21	supposed	suppose	VERB
ejpam-3903	46	22	to	to	PART
ejpam-3903	46	23	be	be	AUX
ejpam-3903	46	24	enough	enough	ADV
ejpam-3903	46	25	regular	regular	ADJ
ejpam-3903	46	26	,	,	PUNCT
ejpam-3903	46	27	[	[	X
ejpam-3903	46	28	0	0	NUM
ejpam-3903	46	29	,	,	PUNCT
ejpam-3903	46	30	t	t	PROPN
ejpam-3903	46	31	]	]	PUNCT
ejpam-3903	46	32	be	be	AUX
ejpam-3903	46	33	a	a	DET
ejpam-3903	46	34	time	time	NOUN
ejpam-3903	46	35	interval	interval	NOUN
ejpam-3903	46	36	with	with	ADP
ejpam-3903	46	37	t	t	PROPN
ejpam-3903	46	38	>	>	X
ejpam-3903	46	39	0	0	X
ejpam-3903	46	40	.	.	PUNCT
ejpam-3903	47	1	we	we	PRON
ejpam-3903	47	2	assume	assume	VERB
ejpam-3903	47	3	that	that	SCONJ
ejpam-3903	47	4	heat	heat	NOUN
ejpam-3903	47	5	flux	flux	NOUN
ejpam-3903	47	6	q	q	PROPN
ejpam-3903	47	7	is	be	AUX
ejpam-3903	47	8	r.	r.	PROPN
ejpam-3903	47	9	bade	bade	PROPN
ejpam-3903	47	10	,	,	PUNCT
ejpam-3903	47	11	h.	h.	PROPN
ejpam-3903	47	12	chaker	chaker	PROPN
ejpam-3903	47	13	/	/	SYM
ejpam-3903	47	14	eur	eur	PROPN
ejpam-3903	47	15	.	.	PUNCT
ejpam-3903	48	1	j.	j.	PROPN
ejpam-3903	48	2	pure	pure	PROPN
ejpam-3903	48	3	appl	appl	PROPN
ejpam-3903	48	4	.	.	PROPN
ejpam-3903	48	5	math	math	PROPN
ejpam-3903	48	6	,	,	PUNCT
ejpam-3903	48	7	14	14	NUM
ejpam-3903	48	8	(	(	PUNCT
ejpam-3903	48	9	1	1	NUM
ejpam-3903	48	10	)	)	PUNCT
ejpam-3903	48	11	(	(	PUNCT
ejpam-3903	48	12	2021	2021	NUM
ejpam-3903	48	13	)	)	PUNCT
ejpam-3903	48	14	,	,	PUNCT
ejpam-3903	48	15	82	82	NUM
ejpam-3903	48	16	-	-	SYM
ejpam-3903	48	17	111	111	NUM
ejpam-3903	48	18	84	84	NUM
ejpam-3903	48	19	determined	determine	VERB
ejpam-3903	48	20	by	by	ADP
ejpam-3903	48	21	the	the	DET
ejpam-3903	48	22	fourier	fourier	NOUN
ejpam-3903	48	23	’s	’s	PART
ejpam-3903	48	24	law	law	NOUN
ejpam-3903	48	25	(	(	PUNCT
ejpam-3903	48	26	q	q	NOUN
ejpam-3903	48	27	=	=	SYM
ejpam-3903	48	28	−k∇θ	−k∇θ	NUM
ejpam-3903	48	29	,	,	PUNCT
ejpam-3903	48	30	with	with	ADP
ejpam-3903	48	31	k	k	PROPN
ejpam-3903	48	32	is	be	AUX
ejpam-3903	48	33	the	the	DET
ejpam-3903	48	34	thermal	thermal	ADJ
ejpam-3903	48	35	conductivity	conductivity	NOUN
ejpam-3903	48	36	of	of	ADP
ejpam-3903	48	37	the	the	DET
ejpam-3903	48	38	fluid	fluid	NOUN
ejpam-3903	48	39	)	)	PUNCT
ejpam-3903	48	40	and	and	CCONJ
ejpam-3903	48	41	the	the	DET
ejpam-3903	48	42	pressure	pressure	NOUN
ejpam-3903	48	43	p	p	NOUN
ejpam-3903	48	44	,	,	PUNCT
ejpam-3903	48	45	the	the	DET
ejpam-3903	48	46	internal	internal	ADJ
ejpam-3903	48	47	energy	energy	NOUN
ejpam-3903	48	48	e	e	NOUN
ejpam-3903	48	49	are	be	AUX
ejpam-3903	48	50	described	describe	VERB
ejpam-3903	48	51	by	by	ADP
ejpam-3903	48	52	the	the	DET
ejpam-3903	48	53	following	follow	VERB
ejpam-3903	48	54	state	state	NOUN
ejpam-3903	48	55	laws	law	NOUN
ejpam-3903	48	56	[	[	X
ejpam-3903	48	57	1	1	NUM
ejpam-3903	48	58	,	,	PUNCT
ejpam-3903	48	59	3	3	NUM
ejpam-3903	48	60	,	,	PUNCT
ejpam-3903	48	61	18	18	NUM
ejpam-3903	48	62	,	,	PUNCT
ejpam-3903	48	63	20	20	NUM
ejpam-3903	48	64	]	]	PUNCT
ejpam-3903	48	65	:	:	PUNCT
ejpam-3903	48	66	p	p	X
ejpam-3903	48	67	(	(	PUNCT
ejpam-3903	48	68	ρ	ρ	PROPN
ejpam-3903	48	69	,	,	PUNCT
ejpam-3903	48	70	e	e	NOUN
ejpam-3903	48	71	)	)	PUNCT
ejpam-3903	48	72	=	=	SYM
ejpam-3903	48	73	(	(	PUNCT
ejpam-3903	48	74	γ	γ	X
ejpam-3903	48	75	−	−	PROPN
ejpam-3903	48	76	1)ρe−	1)ρe−	NUM
ejpam-3903	48	77	γp∞	γp∞	PROPN
ejpam-3903	48	78	and	and	CCONJ
ejpam-3903	48	79	e(ρ	e(ρ	PROPN
ejpam-3903	48	80	,	,	PUNCT
ejpam-3903	48	81	θ	θ	PROPN
ejpam-3903	48	82	)	)	PUNCT
ejpam-3903	49	1	=	=	SYM
ejpam-3903	49	2	p∞	p∞	PROPN
ejpam-3903	49	3	ρ	ρ	NOUN
ejpam-3903	49	4	+	+	X
ejpam-3903	49	5	cvθ	cvθ	NOUN
ejpam-3903	49	6	.	.	PUNCT
ejpam-3903	50	1	(	(	PUNCT
ejpam-3903	50	2	2	2	NUM
ejpam-3903	50	3	)	)	PUNCT
ejpam-3903	50	4	where	where	SCONJ
ejpam-3903	50	5	γ	γ	PROPN
ejpam-3903	50	6	and	and	CCONJ
ejpam-3903	50	7	p∞	p∞	PROPN
ejpam-3903	50	8	are	be	AUX
ejpam-3903	50	9	given	give	VERB
ejpam-3903	50	10	constants	constant	NOUN
ejpam-3903	50	11	depending	depend	VERB
ejpam-3903	50	12	on	on	ADP
ejpam-3903	50	13	the	the	DET
ejpam-3903	50	14	fluid	fluid	NOUN
ejpam-3903	50	15	,	,	PUNCT
ejpam-3903	50	16	cv	cv	PROPN
ejpam-3903	50	17	is	be	AUX
ejpam-3903	50	18	the	the	DET
ejpam-3903	50	19	specific	specific	ADJ
ejpam-3903	50	20	heat	heat	NOUN
ejpam-3903	50	21	at	at	ADP
ejpam-3903	50	22	constant	constant	ADJ
ejpam-3903	50	23	volume	volume	NOUN
ejpam-3903	50	24	and	and	CCONJ
ejpam-3903	50	25	θ	θ	PROPN
ejpam-3903	50	26	is	be	AUX
ejpam-3903	50	27	the	the	DET
ejpam-3903	50	28	temperature	temperature	NOUN
ejpam-3903	50	29	.	.	PUNCT
ejpam-3903	51	1	the	the	DET
ejpam-3903	51	2	relationship	relationship	NOUN
ejpam-3903	51	3	between	between	ADP
ejpam-3903	51	4	the	the	DET
ejpam-3903	51	5	total	total	ADJ
ejpam-3903	51	6	energy	energy	NOUN
ejpam-3903	51	7	e	e	NOUN
ejpam-3903	51	8	and	and	CCONJ
ejpam-3903	51	9	the	the	DET
ejpam-3903	51	10	internal	internal	ADJ
ejpam-3903	51	11	energy	energy	NOUN
ejpam-3903	51	12	is	be	AUX
ejpam-3903	51	13	:	:	PUNCT
ejpam-3903	51	14	e	e	X
ejpam-3903	51	15	=	=	PUNCT
ejpam-3903	51	16	ρe+	ρe+	PROPN
ejpam-3903	51	17	‖u‖2	‖u‖2	ADJ
ejpam-3903	51	18	2	2	NUM
ejpam-3903	51	19	.	.	PUNCT
ejpam-3903	52	1	we	we	PRON
ejpam-3903	52	2	add	add	VERB
ejpam-3903	52	3	an	an	DET
ejpam-3903	52	4	artificial	artificial	ADJ
ejpam-3903	52	5	viscosity	viscosity	NOUN
ejpam-3903	52	6	term	term	NOUN
ejpam-3903	52	7	−ε4ρ	−ε4ρ	PROPN
ejpam-3903	52	8	in	in	ADP
ejpam-3903	52	9	the	the	DET
ejpam-3903	52	10	continuity	continuity	NOUN
ejpam-3903	52	11	equation	equation	NOUN
ejpam-3903	52	12	of	of	ADP
ejpam-3903	52	13	the	the	DET
ejpam-3903	52	14	system	system	NOUN
ejpam-3903	52	15	(	(	PUNCT
ejpam-3903	52	16	1	1	NUM
ejpam-3903	52	17	)	)	PUNCT
ejpam-3903	52	18	,	,	PUNCT
ejpam-3903	52	19	we	we	PRON
ejpam-3903	52	20	obtain	obtain	VERB
ejpam-3903	52	21	:	:	PUNCT
ejpam-3903	52	22	(	(	PUNCT
ejpam-3903	52	23	see	see	VERB
ejpam-3903	52	24	[	[	X
ejpam-3903	52	25	4]):	4]):	NUM
ejpam-3903	52	26	∂ρε	∂ρε	PROPN
ejpam-3903	52	27	∂t	∂t	PROPN
ejpam-3903	53	1	+	+	NOUN
ejpam-3903	53	2	∇	∇	X
ejpam-3903	53	3	·	·	PUNCT
ejpam-3903	53	4	(	(	PUNCT
ejpam-3903	53	5	ρεuε)−	ρεuε)−	X
ejpam-3903	53	6	ε4ρε	ε4ρε	PUNCT
ejpam-3903	53	7	=	=	SYM
ejpam-3903	53	8	0	0	PROPN
ejpam-3903	53	9	,	,	PUNCT
ejpam-3903	54	1	ρε	ρε	PROPN
ejpam-3903	54	2	∂uε	∂uε	PROPN
ejpam-3903	54	3	∂t	∂t	PROPN
ejpam-3903	55	1	+	+	CCONJ
ejpam-3903	55	2	ρε(uε	ρε(uε	PROPN
ejpam-3903	56	1	·	·	PUNCT
ejpam-3903	56	2	∇)uε	∇)uε	PROPN
ejpam-3903	56	3	−	−	NOUN
ejpam-3903	56	4	µ4uε	µ4uε	PUNCT
ejpam-3903	56	5	−	−	PROPN
ejpam-3903	56	6	(	(	PUNCT
ejpam-3903	56	7	µ	µ	X
ejpam-3903	56	8	3	3	NUM
ejpam-3903	56	9	+	+	CCONJ
ejpam-3903	56	10	λ)∇(∇	λ)∇(∇	PROPN
ejpam-3903	56	11	·	·	PUNCT
ejpam-3903	56	12	uε	uε	PROPN
ejpam-3903	56	13	)	)	PUNCT
ejpam-3903	56	14	+	+	NUM
ejpam-3903	56	15	cv(γ	cv(γ	NUM
ejpam-3903	56	16	−	−	PROPN
ejpam-3903	56	17	1)θ∇ρε	1)θ∇ρε	NUM
ejpam-3903	57	1	+	+	NOUN
ejpam-3903	57	2	(	(	PUNCT
ejpam-3903	57	3	γ	γ	X
ejpam-3903	57	4	−	−	PROPN
ejpam-3903	57	5	1)ρε∇θε	1)ρε∇θε	NUM
ejpam-3903	57	6	=	=	SYM
ejpam-3903	57	7	f	f	PROPN
ejpam-3903	57	8	,	,	PUNCT
ejpam-3903	57	9	ρεcv	ρεcv	VERB
ejpam-3903	57	10	∂θε	∂θε	ADJ
ejpam-3903	57	11	∂t	∂t	PROPN
ejpam-3903	58	1	+	+	NUM
ejpam-3903	58	2	ρεcvuε	ρεcvuε	PROPN
ejpam-3903	58	3	·	·	PUNCT
ejpam-3903	58	4	∇θε	∇θε	PROPN
ejpam-3903	58	5	−	−	NOUN
ejpam-3903	58	6	k4θε	k4θε	X
ejpam-3903	58	7	−	−	PROPN
ejpam-3903	58	8	(	(	PUNCT
ejpam-3903	58	9	λ−	λ−	PROPN
ejpam-3903	58	10	2	2	NUM
ejpam-3903	58	11	3	3	NUM
ejpam-3903	58	12	µ	µ	X
ejpam-3903	58	13	)	)	PUNCT
ejpam-3903	59	1	|∇	|∇	PROPN
ejpam-3903	59	2	·	·	PUNCT
ejpam-3903	59	3	uε|2	uε|2	PROPN
ejpam-3903	59	4	−	−	PROPN
ejpam-3903	59	5	µ	µ	NOUN
ejpam-3903	59	6	2	2	NUM
ejpam-3903	59	7	|∇uε	|∇uε	X
ejpam-3903	59	8	+	+	NOUN
ejpam-3903	59	9	∇utε	∇utε	ADJ
ejpam-3903	59	10	|2	|2	NOUN
ejpam-3903	59	11	+	+	ADJ
ejpam-3903	59	12	ρεuε	ρεuε	NOUN
ejpam-3903	59	13	·	·	PUNCT
ejpam-3903	59	14	∇	∇	X
ejpam-3903	59	15	(	(	PUNCT
ejpam-3903	59	16	uε	uε	NOUN
ejpam-3903	59	17	·	·	PUNCT
ejpam-3903	59	18	uε	uε	NOUN
ejpam-3903	59	19	2	2	NUM
ejpam-3903	59	20	)	)	PUNCT
ejpam-3903	60	1	+	+	CCONJ
ejpam-3903	60	2	(	(	PUNCT
ejpam-3903	60	3	γ	γ	PROPN
ejpam-3903	60	4	−	−	PROPN
ejpam-3903	60	5	1)ρεcvθε∇	1)ρεcvθε∇	NUM
ejpam-3903	60	6	·	·	PUNCT
ejpam-3903	60	7	uε	uε	NOUN
ejpam-3903	60	8	=	=	SYM
ejpam-3903	60	9	0	0	PROPN
ejpam-3903	60	10	,	,	PUNCT
ejpam-3903	60	11	ρε|t=0	ρε|t=0	NOUN
ejpam-3903	60	12	=	=	SYM
ejpam-3903	60	13	ρ0	ρ0	PROPN
ejpam-3903	60	14	,	,	PUNCT
ejpam-3903	60	15	uε|t=0	uε|t=0	PROPN
ejpam-3903	60	16	=	=	SYM
ejpam-3903	60	17	u0	u0	PROPN
ejpam-3903	60	18	,	,	PUNCT
ejpam-3903	60	19	θε|t=0	θε|t=0	PROPN
ejpam-3903	60	20	=	=	SYM
ejpam-3903	60	21	θ0	θ0	PROPN
ejpam-3903	60	22	,	,	PUNCT
ejpam-3903	60	23	uε|∂ω	uε|∂ω	X
ejpam-3903	60	24	=	=	SYM
ejpam-3903	60	25	ub	ub	PROPN
ejpam-3903	60	26	,	,	PUNCT
ejpam-3903	60	27	θε|∂ω	θε|∂ω	X
ejpam-3903	61	1	=	=	SYM
ejpam-3903	61	2	θb	θb	PROPN
ejpam-3903	61	3	.	.	PUNCT
ejpam-3903	62	1	(	(	PUNCT
ejpam-3903	62	2	3	3	X
ejpam-3903	62	3	)	)	PUNCT
ejpam-3903	62	4	to	to	PART
ejpam-3903	62	5	close	close	VERB
ejpam-3903	62	6	the	the	DET
ejpam-3903	62	7	system	system	NOUN
ejpam-3903	62	8	(	(	PUNCT
ejpam-3903	62	9	3	3	NUM
ejpam-3903	62	10	)	)	PUNCT
ejpam-3903	62	11	,	,	PUNCT
ejpam-3903	62	12	we	we	PRON
ejpam-3903	62	13	need	need	VERB
ejpam-3903	62	14	an	an	DET
ejpam-3903	62	15	additional	additional	ADJ
ejpam-3903	62	16	boundary	boundary	ADJ
ejpam-3903	62	17	condition	condition	NOUN
ejpam-3903	62	18	on	on	ADP
ejpam-3903	62	19	ρε	ρε	NOUN
ejpam-3903	62	20	given	give	VERB
ejpam-3903	62	21	by	by	ADP
ejpam-3903	62	22	:	:	PUNCT
ejpam-3903	62	23	ε	ε	PROPN
ejpam-3903	62	24	∂ρε	∂ρε	PROPN
ejpam-3903	62	25	∂n	∂n	PROPN
ejpam-3903	62	26	=	=	NOUN
ejpam-3903	62	27	0	0	PROPN
ejpam-3903	62	28	.	.	PUNCT
ejpam-3903	63	1	(	(	PUNCT
ejpam-3903	63	2	4	4	X
ejpam-3903	63	3	)	)	PUNCT
ejpam-3903	63	4	in	in	ADP
ejpam-3903	63	5	all	all	DET
ejpam-3903	63	6	the	the	DET
ejpam-3903	63	7	sequel	sequel	NOUN
ejpam-3903	63	8	we	we	PRON
ejpam-3903	63	9	assume	assume	VERB
ejpam-3903	63	10	that	that	SCONJ
ejpam-3903	63	11	the	the	DET
ejpam-3903	63	12	following	follow	VERB
ejpam-3903	63	13	assumptions	assumption	NOUN
ejpam-3903	63	14	are	be	AUX
ejpam-3903	63	15	hold	hold	ADJ
ejpam-3903	63	16	:	:	PUNCT
ejpam-3903	63	17	(	(	PUNCT
ejpam-3903	63	18	h1	h1	PROPN
ejpam-3903	63	19	)	)	PUNCT
ejpam-3903	63	20	{	{	PUNCT
ejpam-3903	63	21	the	the	DET
ejpam-3903	63	22	viscosities	viscosity	NOUN
ejpam-3903	63	23	verify	verify	VERB
ejpam-3903	63	24	:	:	PUNCT
ejpam-3903	63	25	0	0	NUM
ejpam-3903	63	26	<	<	X
ejpam-3903	63	27	λ+	λ+	PUNCT
ejpam-3903	63	28	2	2	NUM
ejpam-3903	63	29	3	3	NUM
ejpam-3903	63	30	µ	µ	NUM
ejpam-3903	63	31	6	6	NUM
ejpam-3903	63	32	4	4	NUM
ejpam-3903	63	33	3	3	NUM
ejpam-3903	63	34	µ	µ	NOUN
ejpam-3903	63	35	,	,	PUNCT
ejpam-3903	63	36	s	s	PART
ejpam-3903	63	37	∈	∈	NOUN
ejpam-3903	63	38	r	r	NOUN
ejpam-3903	63	39	such	such	ADJ
ejpam-3903	63	40	that	that	PRON
ejpam-3903	63	41	s	s	NOUN
ejpam-3903	63	42	≥	≥	NOUN
ejpam-3903	63	43	5	5	NUM
ejpam-3903	63	44	2	2	NUM
ejpam-3903	63	45	,	,	PUNCT
ejpam-3903	63	46	(	(	PUNCT
ejpam-3903	63	47	h2	h2	NOUN
ejpam-3903	63	48	)	)	PUNCT
ejpam-3903	64	1			NOUN
ejpam-3903	64	2	f	f	PROPN
ejpam-3903	64	3	∈	∈	PROPN
ejpam-3903	64	4	(	(	PUNCT
ejpam-3903	64	5	l∞(0	l∞(0	NUM
ejpam-3903	64	6	,	,	PUNCT
ejpam-3903	64	7	t	t	PROPN
ejpam-3903	64	8	;	;	PUNCT
ejpam-3903	64	9	hs(ω)3))3	hs(ω)3))3	PROPN
ejpam-3903	64	10	,	,	PUNCT
ejpam-3903	64	11	ub	ub	NOUN
ejpam-3903	64	12	∈	∈	PROPN
ejpam-3903	64	13	(	(	PUNCT
ejpam-3903	64	14	w	w	PROPN
ejpam-3903	64	15	1,∞(0	1,∞(0	PROPN
ejpam-3903	64	16	,	,	PUNCT
ejpam-3903	64	17	t	t	PROPN
ejpam-3903	64	18	;	;	PUNCT
ejpam-3903	64	19	hs+	hs+	VERB
ejpam-3903	64	20	3	3	NUM
ejpam-3903	64	21	2	2	NUM
ejpam-3903	64	22	(	(	PUNCT
ejpam-3903	64	23	∂ω)3))3	∂ω)3))3	PROPN
ejpam-3903	64	24	,	,	PUNCT
ejpam-3903	64	25	θb	θb	ADP
ejpam-3903	64	26	∈w	∈w	VERB
ejpam-3903	64	27	1,∞(0	1,∞(0	PRON
ejpam-3903	64	28	,	,	PUNCT
ejpam-3903	64	29	t	t	PROPN
ejpam-3903	64	30	;	;	PUNCT
ejpam-3903	64	31	hs+	hs+	VERB
ejpam-3903	64	32	3	3	NUM
ejpam-3903	64	33	2	2	NUM
ejpam-3903	64	34	(	(	PUNCT
ejpam-3903	64	35	∂ω	∂ω	PROPN
ejpam-3903	64	36	)	)	PUNCT
ejpam-3903	64	37	)	)	PUNCT
ejpam-3903	64	38	,	,	PUNCT
ejpam-3903	64	39	(	(	PUNCT
ejpam-3903	64	40	h3	h3	NOUN
ejpam-3903	64	41	)	)	PUNCT
ejpam-3903	64	42			NUM
ejpam-3903	65	1	ρ0	ρ0	PROPN
ejpam-3903	65	2	∈	∈	PROPN
ejpam-3903	65	3	hs(ω	hs(ω	PRON
ejpam-3903	65	4	)	)	PUNCT
ejpam-3903	65	5	∩w	∩w	ADJ
ejpam-3903	65	6	1,∞(ω	1,∞(ω	NUM
ejpam-3903	65	7	)	)	PUNCT
ejpam-3903	65	8	,	,	PUNCT
ejpam-3903	65	9	u0	u0	PROPN
ejpam-3903	65	10	∈	∈	PROPN
ejpam-3903	65	11	(	(	PUNCT
ejpam-3903	65	12	hs(ω))3	hs(ω))3	PROPN
ejpam-3903	65	13	∩	∩	X
ejpam-3903	65	14	(	(	PUNCT
ejpam-3903	65	15	w	w	PROPN
ejpam-3903	65	16	1,∞(ω))3	1,∞(ω))3	PROPN
ejpam-3903	65	17	,	,	PUNCT
ejpam-3903	65	18	θ0	θ0	PROPN
ejpam-3903	65	19	∈	∈	PROPN
ejpam-3903	65	20	hs(ω	hs(ω	PRON
ejpam-3903	65	21	)	)	PUNCT
ejpam-3903	65	22	∩w	∩w	ADJ
ejpam-3903	65	23	1,∞(ω	1,∞(ω	NUM
ejpam-3903	65	24	)	)	PUNCT
ejpam-3903	65	25	,	,	PUNCT
ejpam-3903	65	26	ρ0	ρ0	PROPN
ejpam-3903	65	27	>	>	X
ejpam-3903	65	28	ρ̄	ρ̄	PROPN
ejpam-3903	65	29	with	with	ADP
ejpam-3903	65	30	ρ̄	ρ̄	NOUN
ejpam-3903	65	31	∈	∈	PROPN
ejpam-3903	65	32	r+	r+	PUNCT
ejpam-3903	65	33	∗	∗	NOUN
ejpam-3903	65	34	.	.	PUNCT
ejpam-3903	66	1	we	we	PRON
ejpam-3903	66	2	denote	denote	VERB
ejpam-3903	66	3	l2	l2	NOUN
ejpam-3903	66	4	(	(	PUNCT
ejpam-3903	66	5	·	·	PUNCT
ejpam-3903	66	6	)	)	PUNCT
ejpam-3903	66	7	,	,	PUNCT
ejpam-3903	66	8	l∞	l∞	NOUN
ejpam-3903	66	9	(	(	PUNCT
ejpam-3903	66	10	·	·	PUNCT
ejpam-3903	66	11	)	)	PUNCT
ejpam-3903	66	12	,	,	PUNCT
ejpam-3903	66	13	hs	hs	PROPN
ejpam-3903	66	14	(	(	PUNCT
ejpam-3903	66	15	·	·	PUNCT
ejpam-3903	66	16	)	)	PUNCT
ejpam-3903	66	17	and	and	CCONJ
ejpam-3903	66	18	w	w	PROPN
ejpam-3903	66	19	1,∞	1,∞	PROPN
ejpam-3903	66	20	(	(	PUNCT
ejpam-3903	66	21	·	·	PUNCT
ejpam-3903	66	22	)	)	PUNCT
ejpam-3903	66	23	the	the	DET
ejpam-3903	66	24	usual	usual	ADJ
ejpam-3903	66	25	lebesgue	lebesgue	NOUN
ejpam-3903	66	26	and	and	CCONJ
ejpam-3903	66	27	sobolev	sobolev	NOUN
ejpam-3903	66	28	spaces	space	NOUN
ejpam-3903	66	29	and	and	CCONJ
ejpam-3903	66	30	||	||	NUM
ejpam-3903	66	31	·	·	PUNCT
ejpam-3903	67	1	||l2	||l2	NOUN
ejpam-3903	67	2	,	,	PUNCT
ejpam-3903	67	3	||	||	X
ejpam-3903	67	4	·	·	PUNCT
ejpam-3903	68	1	||l∞	||l∞	NOUN
ejpam-3903	68	2	,	,	PUNCT
ejpam-3903	68	3	||	||	NOUN
ejpam-3903	68	4	·	·	PUNCT
ejpam-3903	68	5	||hs	||hs	NOUN
ejpam-3903	68	6	and	and	CCONJ
ejpam-3903	68	7	||	||	NUM
ejpam-3903	68	8	·	·	PUNCT
ejpam-3903	68	9	||w	||w	NOUN
ejpam-3903	68	10	1,∞	1,∞	NUM
ejpam-3903	68	11	their	their	PRON
ejpam-3903	68	12	corresponding	correspond	VERB
ejpam-3903	68	13	norms	norm	NOUN
ejpam-3903	68	14	(	(	PUNCT
ejpam-3903	68	15	see	see	VERB
ejpam-3903	68	16	[	[	X
ejpam-3903	68	17	2	2	NUM
ejpam-3903	68	18	]	]	NUM
ejpam-3903	68	19	)	)	PUNCT
ejpam-3903	68	20	.	.	PUNCT
ejpam-3903	69	1	in	in	ADP
ejpam-3903	69	2	all	all	DET
ejpam-3903	69	3	the	the	DET
ejpam-3903	69	4	following	following	NOUN
ejpam-3903	69	5	we	we	PRON
ejpam-3903	69	6	will	will	AUX
ejpam-3903	69	7	adopte	adopte	VERB
ejpam-3903	69	8	the	the	DET
ejpam-3903	69	9	following	follow	VERB
ejpam-3903	69	10	notation	notation	NOUN
ejpam-3903	69	11	:	:	PUNCT
ejpam-3903	69	12	||·||	||·||	NOUN
ejpam-3903	69	13	l2	l2	NOUN
ejpam-3903	69	14	(	(	PUNCT
ejpam-3903	69	15	0,t	0,t	NOUN
ejpam-3903	69	16	;	;	PUNCT
ejpam-3903	69	17	hs(ω	hs(ω	NUM
ejpam-3903	69	18	)	)	PUNCT
ejpam-3903	69	19	)	)	PUNCT
ejpam-3903	70	1	=	=	NOUN
ejpam-3903	70	2	||·||2,s	||·||2,	NOUN
ejpam-3903	70	3	,	,	PUNCT
ejpam-3903	70	4	||·||	||·||	NOUN
ejpam-3903	70	5	l∞	l∞	NOUN
ejpam-3903	70	6	(	(	PUNCT
ejpam-3903	70	7	0,t	0,t	NOUN
ejpam-3903	70	8	;	;	PUNCT
ejpam-3903	70	9	hs(ω	hs(ω	NUM
ejpam-3903	70	10	)	)	PUNCT
ejpam-3903	70	11	)	)	PUNCT
ejpam-3903	71	1	=	=	PUNCT
ejpam-3903	71	2	||·||∞,s	||·||∞,s	NOUN
ejpam-3903	71	3	,	,	PUNCT
ejpam-3903	71	4	||·||	||·||	NOUN
ejpam-3903	71	5	l∞	l∞	NOUN
ejpam-3903	71	6	(	(	PUNCT
ejpam-3903	71	7	0,t	0,t	NOUN
ejpam-3903	71	8	;	;	PUNCT
ejpam-3903	71	9	l∞(ω	l∞(ω	X
ejpam-3903	71	10	)	)	PUNCT
ejpam-3903	71	11	)	)	PUNCT
ejpam-3903	72	1	=	=	PUNCT
ejpam-3903	72	2	||·||∞,∞	||·||∞,∞	X
ejpam-3903	72	3	we	we	PRON
ejpam-3903	72	4	are	be	AUX
ejpam-3903	72	5	now	now	ADV
ejpam-3903	72	6	able	able	ADJ
ejpam-3903	72	7	to	to	PART
ejpam-3903	72	8	announce	announce	VERB
ejpam-3903	72	9	our	our	PRON
ejpam-3903	72	10	main	main	ADJ
ejpam-3903	72	11	results	result	NOUN
ejpam-3903	72	12	:	:	PUNCT
ejpam-3903	72	13	r.	r.	PROPN
ejpam-3903	72	14	bade	bade	PROPN
ejpam-3903	72	15	,	,	PUNCT
ejpam-3903	72	16	h.	h.	PROPN
ejpam-3903	72	17	chaker	chaker	PROPN
ejpam-3903	72	18	/	/	SYM
ejpam-3903	72	19	eur	eur	PROPN
ejpam-3903	72	20	.	.	PUNCT
ejpam-3903	73	1	j.	j.	PROPN
ejpam-3903	73	2	pure	pure	PROPN
ejpam-3903	73	3	appl	appl	PROPN
ejpam-3903	73	4	.	.	PROPN
ejpam-3903	73	5	math	math	PROPN
ejpam-3903	73	6	,	,	PUNCT
ejpam-3903	73	7	14	14	NUM
ejpam-3903	73	8	(	(	PUNCT
ejpam-3903	73	9	1	1	NUM
ejpam-3903	73	10	)	)	PUNCT
ejpam-3903	73	11	(	(	PUNCT
ejpam-3903	73	12	2021	2021	NUM
ejpam-3903	73	13	)	)	PUNCT
ejpam-3903	73	14	,	,	PUNCT
ejpam-3903	73	15	82	82	NUM
ejpam-3903	73	16	-	-	SYM
ejpam-3903	73	17	111	111	NUM
ejpam-3903	73	18	85	85	NUM
ejpam-3903	73	19	theorem	theorem	NOUN
ejpam-3903	73	20	1	1	NUM
ejpam-3903	73	21	.	.	PUNCT
ejpam-3903	74	1	under	under	ADP
ejpam-3903	74	2	assumptions	assumption	NOUN
ejpam-3903	74	3	(	(	PUNCT
ejpam-3903	74	4	h1	h1	PROPN
ejpam-3903	74	5	)	)	PUNCT
ejpam-3903	74	6	,	,	PUNCT
ejpam-3903	74	7	(	(	PUNCT
ejpam-3903	74	8	h2	h2	NOUN
ejpam-3903	74	9	)	)	PUNCT
ejpam-3903	74	10	and	and	CCONJ
ejpam-3903	74	11	(	(	PUNCT
ejpam-3903	74	12	h3	h3	NOUN
ejpam-3903	74	13	)	)	PUNCT
ejpam-3903	74	14	,	,	PUNCT
ejpam-3903	74	15	suppose	suppose	VERB
ejpam-3903	74	16	that	that	SCONJ
ejpam-3903	74	17	the	the	DET
ejpam-3903	74	18	state	state	NOUN
ejpam-3903	74	19	law	law	NOUN
ejpam-3903	74	20	is	be	AUX
ejpam-3903	74	21	given	give	VERB
ejpam-3903	74	22	by	by	ADP
ejpam-3903	74	23	(	(	PUNCT
ejpam-3903	74	24	2	2	NUM
ejpam-3903	74	25	)	)	PUNCT
ejpam-3903	74	26	.	.	PUNCT
ejpam-3903	75	1	then	then	ADV
ejpam-3903	75	2	for	for	ADP
ejpam-3903	75	3	any	any	DET
ejpam-3903	75	4	fixed	fix	VERB
ejpam-3903	75	5	time	time	NOUN
ejpam-3903	75	6	t	t	PROPN
ejpam-3903	75	7	>	>	X
ejpam-3903	75	8	0	0	PUNCT
ejpam-3903	76	1	the	the	DET
ejpam-3903	76	2	system	system	NOUN
ejpam-3903	76	3	(	(	PUNCT
ejpam-3903	76	4	3	3	X
ejpam-3903	76	5	)	)	PUNCT
ejpam-3903	76	6	has	have	VERB
ejpam-3903	76	7	a	a	DET
ejpam-3903	76	8	solution	solution	NOUN
ejpam-3903	76	9	(	(	PUNCT
ejpam-3903	76	10	ρε	ρε	PROPN
ejpam-3903	76	11	,	,	PUNCT
ejpam-3903	76	12	uε	uε	NOUN
ejpam-3903	76	13	,	,	PUNCT
ejpam-3903	76	14	θε	θε	NOUN
ejpam-3903	76	15	)	)	PUNCT
ejpam-3903	76	16	such	such	ADJ
ejpam-3903	76	17	that	that	SCONJ
ejpam-3903	76	18	:	:	PUNCT
ejpam-3903	76	19	(	(	PUNCT
ejpam-3903	76	20	ρε	ρε	NOUN
ejpam-3903	76	21	,	,	PUNCT
ejpam-3903	76	22	θε	θε	NOUN
ejpam-3903	76	23	)	)	PUNCT
ejpam-3903	76	24	∈	∈	PROPN
ejpam-3903	76	25	(	(	PUNCT
ejpam-3903	76	26	l∞(0	l∞(0	X
ejpam-3903	76	27	,	,	PUNCT
ejpam-3903	76	28	t	t	NOUN
ejpam-3903	76	29	;	;	PUNCT
ejpam-3903	76	30	hs(ω	hs(ω	NUM
ejpam-3903	76	31	)	)	PUNCT
ejpam-3903	76	32	)	)	PUNCT
ejpam-3903	76	33	)	)	PUNCT
ejpam-3903	76	34	2	2	NUM
ejpam-3903	76	35	and	and	CCONJ
ejpam-3903	76	36	(	(	PUNCT
ejpam-3903	76	37	∂ρε	∂ρε	PROPN
ejpam-3903	76	38	∂t	∂t	PROPN
ejpam-3903	76	39	,	,	PUNCT
ejpam-3903	76	40	∂θε	∂θε	PROPN
ejpam-3903	76	41	∂t	∂t	PROPN
ejpam-3903	76	42	)	)	PUNCT
ejpam-3903	76	43	∈	∈	PROPN
ejpam-3903	76	44	(	(	PUNCT
ejpam-3903	76	45	l2(0	l2(0	NOUN
ejpam-3903	76	46	,	,	PUNCT
ejpam-3903	76	47	t	t	NOUN
ejpam-3903	76	48	;	;	PUNCT
ejpam-3903	76	49	hs(ω	hs(ω	NUM
ejpam-3903	76	50	)	)	PUNCT
ejpam-3903	76	51	)	)	PUNCT
ejpam-3903	76	52	)	)	PUNCT
ejpam-3903	76	53	2	2	NUM
ejpam-3903	76	54	uε	uε	NOUN
ejpam-3903	76	55	∈	∈	PROPN
ejpam-3903	76	56	(	(	PUNCT
ejpam-3903	76	57	l∞	l∞	NOUN
ejpam-3903	76	58	(	(	PUNCT
ejpam-3903	76	59	0	0	NUM
ejpam-3903	76	60	,	,	PUNCT
ejpam-3903	76	61	t	t	NOUN
ejpam-3903	76	62	;	;	PUNCT
ejpam-3903	76	63	hs(ω	hs(ω	NUM
ejpam-3903	76	64	)	)	PUNCT
ejpam-3903	76	65	)	)	PUNCT
ejpam-3903	76	66	)	)	PUNCT
ejpam-3903	76	67	3	3	NUM
ejpam-3903	76	68	and	and	CCONJ
ejpam-3903	76	69	∂uε	∂uε	PROPN
ejpam-3903	76	70	∂t	∂t	PROPN
ejpam-3903	76	71	∈	∈	PROPN
ejpam-3903	76	72	(	(	PUNCT
ejpam-3903	76	73	l2	l2	NOUN
ejpam-3903	76	74	(	(	PUNCT
ejpam-3903	76	75	0	0	NUM
ejpam-3903	76	76	,	,	PUNCT
ejpam-3903	76	77	t	t	NOUN
ejpam-3903	76	78	;	;	PUNCT
ejpam-3903	76	79	hs(ω	hs(ω	NUM
ejpam-3903	76	80	)	)	PUNCT
ejpam-3903	76	81	)	)	PUNCT
ejpam-3903	76	82	)	)	PUNCT
ejpam-3903	76	83	3	3	X
ejpam-3903	76	84	.	.	PUNCT
ejpam-3903	77	1	in	in	ADP
ejpam-3903	77	2	addition	addition	NOUN
ejpam-3903	77	3	we	we	PRON
ejpam-3903	77	4	have	have	VERB
ejpam-3903	77	5	:	:	PUNCT
ejpam-3903	77	6	ρε	ρε	X
ejpam-3903	77	7	>	>	X
ejpam-3903	77	8	ρ̄	ρ̄	NOUN
ejpam-3903	77	9	exp−kt	exp−kt	NOUN
ejpam-3903	77	10	and	and	CCONJ
ejpam-3903	77	11	‖uε‖l∞	‖uε‖l∞	PROPN
ejpam-3903	77	12	(	(	PUNCT
ejpam-3903	77	13	0,t	0,t	PROPN
ejpam-3903	77	14	;	;	PUNCT
ejpam-3903	77	15	w	w	NOUN
ejpam-3903	77	16	1,∞(ω	1,∞(ω	NUM
ejpam-3903	77	17	)	)	PUNCT
ejpam-3903	77	18	)	)	PUNCT
ejpam-3903	77	19	≤	≤	PUNCT
ejpam-3903	78	1	k	k	X
ejpam-3903	78	2	,	,	PUNCT
ejpam-3903	78	3	where	where	SCONJ
ejpam-3903	78	4	k	k	PROPN
ejpam-3903	78	5	is	be	AUX
ejpam-3903	78	6	a	a	DET
ejpam-3903	78	7	constant	constant	ADJ
ejpam-3903	78	8	independent	independent	NOUN
ejpam-3903	78	9	of	of	ADP
ejpam-3903	78	10	ε	ε	PROPN
ejpam-3903	78	11	.	.	PUNCT
ejpam-3903	78	12	theorem	theorem	PROPN
ejpam-3903	78	13	2	2	NUM
ejpam-3903	78	14	.	.	PUNCT
ejpam-3903	79	1	let	let	VERB
ejpam-3903	79	2	(	(	PUNCT
ejpam-3903	79	3	ρε	ρε	PROPN
ejpam-3903	79	4	,	,	PUNCT
ejpam-3903	79	5	uε	uε	PROPN
ejpam-3903	79	6	,	,	PUNCT
ejpam-3903	79	7	θε	θε	NOUN
ejpam-3903	79	8	)	)	PUNCT
ejpam-3903	79	9	be	be	AUX
ejpam-3903	79	10	a	a	DET
ejpam-3903	79	11	solution	solution	NOUN
ejpam-3903	79	12	given	give	VERB
ejpam-3903	79	13	by	by	ADP
ejpam-3903	79	14	the	the	DET
ejpam-3903	79	15	theorem	theorem	NOUN
ejpam-3903	79	16	1	1	X
ejpam-3903	79	17	.	.	PUNCT
ejpam-3903	80	1	then	then	ADV
ejpam-3903	80	2	,	,	PUNCT
ejpam-3903	80	3	up	up	ADP
ejpam-3903	80	4	to	to	ADP
ejpam-3903	80	5	extracting	extract	VERB
ejpam-3903	80	6	subsequence	subsequence	NOUN
ejpam-3903	80	7	,	,	PUNCT
ejpam-3903	80	8	we	we	PRON
ejpam-3903	80	9	have	have	VERB
ejpam-3903	80	10	the	the	DET
ejpam-3903	80	11	following	follow	VERB
ejpam-3903	80	12	convergence	convergence	NOUN
ejpam-3903	80	13	when	when	SCONJ
ejpam-3903	80	14	ε	ε	PROPN
ejpam-3903	80	15	goes	go	VERB
ejpam-3903	80	16	to	to	ADP
ejpam-3903	80	17	zero	zero	NUM
ejpam-3903	80	18	:	:	PUNCT
ejpam-3903	80	19	ρε	ρε	PROPN
ejpam-3903	80	20	⇀	⇀	NUM
ejpam-3903	80	21	ρ	ρ	NUM
ejpam-3903	80	22	weakly-∗	weakly-∗	NOUN
ejpam-3903	80	23	in	in	ADP
ejpam-3903	80	24	l∞	l∞	NOUN
ejpam-3903	80	25	(	(	PUNCT
ejpam-3903	80	26	0	0	NUM
ejpam-3903	80	27	,	,	PUNCT
ejpam-3903	80	28	t	t	NOUN
ejpam-3903	80	29	;	;	PUNCT
ejpam-3903	80	30	hs(ω	hs(ω	NUM
ejpam-3903	80	31	)	)	PUNCT
ejpam-3903	80	32	)	)	PUNCT
ejpam-3903	80	33	,	,	PUNCT
ejpam-3903	81	1	∂ρε	∂ρε	PROPN
ejpam-3903	81	2	∂t	∂t	PROPN
ejpam-3903	81	3	⇀	⇀	PROPN
ejpam-3903	81	4	∂ρ	∂ρ	PROPN
ejpam-3903	82	1	∂t	∂t	PROPN
ejpam-3903	82	2	weakly	weakly	ADJ
ejpam-3903	82	3	in	in	ADP
ejpam-3903	82	4	l2	l2	NOUN
ejpam-3903	82	5	(	(	PUNCT
ejpam-3903	82	6	0	0	NUM
ejpam-3903	82	7	,	,	PUNCT
ejpam-3903	82	8	t	t	NOUN
ejpam-3903	82	9	;	;	PUNCT
ejpam-3903	82	10	l2(ω	l2(ω	X
ejpam-3903	82	11	)	)	PUNCT
ejpam-3903	82	12	)	)	PUNCT
ejpam-3903	83	1	,	,	PUNCT
ejpam-3903	83	2	θε	θε	NOUN
ejpam-3903	83	3	⇀	⇀	NUM
ejpam-3903	84	1	θ	θ	NOUN
ejpam-3903	84	2	weakly-∗	weakly-∗	NOUN
ejpam-3903	84	3	in	in	ADP
ejpam-3903	84	4	l∞	l∞	NOUN
ejpam-3903	84	5	(	(	PUNCT
ejpam-3903	84	6	0	0	NUM
ejpam-3903	84	7	,	,	PUNCT
ejpam-3903	84	8	t	t	NOUN
ejpam-3903	84	9	;	;	PUNCT
ejpam-3903	84	10	hs(ω	hs(ω	NUM
ejpam-3903	84	11	)	)	PUNCT
ejpam-3903	84	12	)	)	PUNCT
ejpam-3903	84	13	,	,	PUNCT
ejpam-3903	85	1	∂θε	∂θε	ADJ
ejpam-3903	85	2	∂t	∂t	PROPN
ejpam-3903	85	3	⇀	⇀	PUNCT
ejpam-3903	86	1	∂θ	∂θ	PROPN
ejpam-3903	87	1	∂t	∂t	PROPN
ejpam-3903	87	2	weakly	weakly	ADJ
ejpam-3903	87	3	in	in	ADP
ejpam-3903	87	4	l2	l2	NOUN
ejpam-3903	87	5	(	(	PUNCT
ejpam-3903	87	6	0	0	NUM
ejpam-3903	87	7	,	,	PUNCT
ejpam-3903	87	8	t	t	NOUN
ejpam-3903	87	9	;	;	PUNCT
ejpam-3903	87	10	l2(ω	l2(ω	X
ejpam-3903	87	11	)	)	PUNCT
ejpam-3903	87	12	)	)	PUNCT
ejpam-3903	87	13	,	,	PUNCT
ejpam-3903	87	14	uε	uε	NOUN
ejpam-3903	87	15	⇀	⇀	NUM
ejpam-3903	88	1	u	u	PROPN
ejpam-3903	88	2	weakly-∗	weakly-∗	NOUN
ejpam-3903	88	3	in	in	ADP
ejpam-3903	88	4	(	(	PUNCT
ejpam-3903	88	5	l∞	l∞	NOUN
ejpam-3903	88	6	(	(	PUNCT
ejpam-3903	88	7	0	0	NUM
ejpam-3903	88	8	,	,	PUNCT
ejpam-3903	88	9	t	t	NOUN
ejpam-3903	88	10	;	;	PUNCT
ejpam-3903	88	11	hs(ω	hs(ω	NUM
ejpam-3903	88	12	)	)	PUNCT
ejpam-3903	88	13	)	)	PUNCT
ejpam-3903	88	14	)	)	PUNCT
ejpam-3903	88	15	3	3	NUM
ejpam-3903	88	16	,	,	PUNCT
ejpam-3903	88	17	∂uε	∂uε	NOUN
ejpam-3903	88	18	∂t	∂t	PROPN
ejpam-3903	89	1	⇀	⇀	NUM
ejpam-3903	90	1	∂u	∂u	PROPN
ejpam-3903	90	2	∂t	∂t	PROPN
ejpam-3903	90	3	weakly	weakly	ADV
ejpam-3903	90	4	in	in	ADP
ejpam-3903	90	5	(	(	PUNCT
ejpam-3903	90	6	l2	l2	NOUN
ejpam-3903	90	7	(	(	PUNCT
ejpam-3903	90	8	0	0	NUM
ejpam-3903	90	9	,	,	PUNCT
ejpam-3903	90	10	t	t	NOUN
ejpam-3903	90	11	;	;	PUNCT
ejpam-3903	90	12	l2(ω	l2(ω	NUM
ejpam-3903	90	13	)	)	PUNCT
ejpam-3903	90	14	)	)	PUNCT
ejpam-3903	90	15	)	)	PUNCT
ejpam-3903	90	16	3	3	NUM
ejpam-3903	90	17	,	,	PUNCT
ejpam-3903	90	18	where	where	SCONJ
ejpam-3903	90	19	(	(	PUNCT
ejpam-3903	90	20	ρ	ρ	NOUN
ejpam-3903	90	21	,	,	PUNCT
ejpam-3903	90	22	u	u	NOUN
ejpam-3903	90	23	,	,	PUNCT
ejpam-3903	90	24	θ	θ	NOUN
ejpam-3903	90	25	)	)	PUNCT
ejpam-3903	90	26	is	be	AUX
ejpam-3903	90	27	a	a	DET
ejpam-3903	90	28	solution	solution	NOUN
ejpam-3903	90	29	of	of	ADP
ejpam-3903	90	30	the	the	DET
ejpam-3903	90	31	system	system	NOUN
ejpam-3903	90	32	(	(	PUNCT
ejpam-3903	90	33	1	1	NUM
ejpam-3903	90	34	)	)	PUNCT
ejpam-3903	90	35	.	.	PUNCT
ejpam-3903	91	1	the	the	DET
ejpam-3903	91	2	proof	proof	NOUN
ejpam-3903	91	3	of	of	ADP
ejpam-3903	91	4	these	these	DET
ejpam-3903	91	5	two	two	NUM
ejpam-3903	91	6	theorems	theorem	NOUN
ejpam-3903	91	7	will	will	AUX
ejpam-3903	91	8	be	be	AUX
ejpam-3903	91	9	done	do	VERB
ejpam-3903	91	10	in	in	ADP
ejpam-3903	91	11	several	several	ADJ
ejpam-3903	91	12	steps	step	NOUN
ejpam-3903	91	13	.	.	PUNCT
ejpam-3903	92	1	in	in	ADP
ejpam-3903	92	2	section	section	NOUN
ejpam-3903	92	3	4	4	NUM
ejpam-3903	92	4	we	we	PRON
ejpam-3903	92	5	shortly	shortly	ADV
ejpam-3903	92	6	recall	recall	VERB
ejpam-3903	92	7	how	how	SCONJ
ejpam-3903	92	8	to	to	PART
ejpam-3903	92	9	rewrite	rewrite	VERB
ejpam-3903	92	10	the	the	DET
ejpam-3903	92	11	system	system	NOUN
ejpam-3903	92	12	(	(	PUNCT
ejpam-3903	92	13	3	3	NUM
ejpam-3903	92	14	)	)	PUNCT
ejpam-3903	92	15	in	in	ADP
ejpam-3903	92	16	the	the	DET
ejpam-3903	92	17	hyperbolic	hyperbolic	ADJ
ejpam-3903	92	18	form	form	NOUN
ejpam-3903	92	19	,	,	PUNCT
ejpam-3903	92	20	his	his	PRON
ejpam-3903	92	21	symmetrization	symmetrization	NOUN
ejpam-3903	92	22	and	and	CCONJ
ejpam-3903	92	23	the	the	DET
ejpam-3903	92	24	study	study	NOUN
ejpam-3903	92	25	of	of	ADP
ejpam-3903	92	26	deduced	deduce	VERB
ejpam-3903	92	27	operators	operator	NOUN
ejpam-3903	92	28	that	that	PRON
ejpam-3903	92	29	we	we	PRON
ejpam-3903	92	30	be	be	AUX
ejpam-3903	92	31	used	use	VERB
ejpam-3903	92	32	in	in	ADP
ejpam-3903	92	33	the	the	DET
ejpam-3903	92	34	demonstrations	demonstration	NOUN
ejpam-3903	92	35	(	(	PUNCT
ejpam-3903	92	36	see	see	VERB
ejpam-3903	92	37	[	[	X
ejpam-3903	92	38	4	4	X
ejpam-3903	92	39	]	]	PUNCT
ejpam-3903	92	40	for	for	ADP
ejpam-3903	92	41	details	detail	NOUN
ejpam-3903	92	42	)	)	PUNCT
ejpam-3903	92	43	.	.	PUNCT
ejpam-3903	93	1	the	the	DET
ejpam-3903	93	2	proof	proof	NOUN
ejpam-3903	93	3	of	of	ADP
ejpam-3903	93	4	theorem	theorem	NOUN
ejpam-3903	93	5	1	1	NUM
ejpam-3903	93	6	will	will	AUX
ejpam-3903	93	7	be	be	AUX
ejpam-3903	93	8	given	give	VERB
ejpam-3903	93	9	in	in	ADP
ejpam-3903	93	10	section	section	NOUN
ejpam-3903	93	11	4	4	NUM
ejpam-3903	93	12	and	and	CCONJ
ejpam-3903	93	13	for	for	ADP
ejpam-3903	93	14	the	the	DET
ejpam-3903	93	15	theorem	theorem	NOUN
ejpam-3903	93	16	2	2	NUM
ejpam-3903	93	17	in	in	ADP
ejpam-3903	93	18	section	section	NOUN
ejpam-3903	93	19	5	5	NUM
ejpam-3903	93	20	.	.	NOUN
ejpam-3903	93	21	3	3	NUM
ejpam-3903	93	22	.	.	X
ejpam-3903	93	23	positivity	positivity	NOUN
ejpam-3903	93	24	of	of	ADP
ejpam-3903	93	25	the	the	DET
ejpam-3903	93	26	density	density	NOUN
ejpam-3903	93	27	before	before	SCONJ
ejpam-3903	93	28	we	we	PRON
ejpam-3903	93	29	begin	begin	VERB
ejpam-3903	93	30	our	our	PRON
ejpam-3903	93	31	demonstrations	demonstration	NOUN
ejpam-3903	93	32	,	,	PUNCT
ejpam-3903	93	33	we	we	PRON
ejpam-3903	93	34	have	have	VERB
ejpam-3903	93	35	to	to	PART
ejpam-3903	93	36	verify	verify	VERB
ejpam-3903	93	37	that	that	SCONJ
ejpam-3903	93	38	the	the	DET
ejpam-3903	93	39	density	density	NOUN
ejpam-3903	93	40	ρε	ρε	PROPN
ejpam-3903	93	41	remains	remain	VERB
ejpam-3903	93	42	strictly	strictly	ADV
ejpam-3903	93	43	positive	positive	ADJ
ejpam-3903	93	44	in	in	ADP
ejpam-3903	93	45	time	time	NOUN
ejpam-3903	93	46	if	if	SCONJ
ejpam-3903	93	47	its	its	PRON
ejpam-3903	93	48	initial	initial	ADJ
ejpam-3903	93	49	value	value	NOUN
ejpam-3903	93	50	is	be	AUX
ejpam-3903	93	51	greater	great	ADJ
ejpam-3903	93	52	than	than	ADP
ejpam-3903	93	53	a	a	DET
ejpam-3903	93	54	positive	positive	ADJ
ejpam-3903	93	55	quantity	quantity	NOUN
ejpam-3903	93	56	.	.	PUNCT
ejpam-3903	94	1	for	for	ADP
ejpam-3903	94	2	this	this	PRON
ejpam-3903	94	3	,	,	PUNCT
ejpam-3903	94	4	we	we	PRON
ejpam-3903	94	5	take	take	VERB
ejpam-3903	94	6	the	the	DET
ejpam-3903	94	7	first	first	ADJ
ejpam-3903	94	8	equation	equation	NOUN
ejpam-3903	94	9	of	of	ADP
ejpam-3903	94	10	the	the	DET
ejpam-3903	94	11	system	system	NOUN
ejpam-3903	94	12	(	(	PUNCT
ejpam-3903	94	13	3	3	NUM
ejpam-3903	94	14	):	):	PUNCT
ejpam-3903	94	15	∂ρε	∂ρε	PROPN
ejpam-3903	94	16	∂t	∂t	PROPN
ejpam-3903	95	1	+	+	NOUN
ejpam-3903	95	2	∇	∇	X
ejpam-3903	95	3	·	·	PUNCT
ejpam-3903	95	4	(	(	PUNCT
ejpam-3903	95	5	ρεuε)−	ρεuε)−	X
ejpam-3903	95	6	ε4ρε	ε4ρε	PUNCT
ejpam-3903	95	7	=	=	SYM
ejpam-3903	95	8	0	0	X
ejpam-3903	95	9	.	.	PUNCT
ejpam-3903	96	1	(	(	PUNCT
ejpam-3903	96	2	5	5	X
ejpam-3903	96	3	)	)	PUNCT
ejpam-3903	96	4	an	an	DET
ejpam-3903	96	5	implicit	implicit	ADJ
ejpam-3903	96	6	semi	semi	ADJ
ejpam-3903	96	7	-	-	ADJ
ejpam-3903	96	8	discretization	discretization	NOUN
ejpam-3903	96	9	in	in	ADP
ejpam-3903	96	10	time	time	NOUN
ejpam-3903	96	11	of	of	ADP
ejpam-3903	96	12	the	the	DET
ejpam-3903	96	13	equation	equation	NOUN
ejpam-3903	96	14	(	(	PUNCT
ejpam-3903	96	15	5	5	X
ejpam-3903	96	16	)	)	PUNCT
ejpam-3903	96	17	gives	give	VERB
ejpam-3903	96	18	:	:	PUNCT
ejpam-3903	96	19	1	1	NUM
ejpam-3903	96	20	4	4	NUM
ejpam-3903	96	21	t	t	NOUN
ejpam-3903	96	22	ρn+1	ρn+1	NUM
ejpam-3903	96	23	ε	ε	PROPN
ejpam-3903	96	24	+	+	PROPN
ejpam-3903	96	25	∇	∇	X
ejpam-3903	96	26	·	·	PUNCT
ejpam-3903	96	27	(	(	PUNCT
ejpam-3903	96	28	ρn+1	ρn+1	NUM
ejpam-3903	96	29	ε	ε	PROPN
ejpam-3903	96	30	un+1	un+1	PROPN
ejpam-3903	96	31	ε	ε	PROPN
ejpam-3903	96	32	)	)	PUNCT
ejpam-3903	96	33	−	−	PROPN
ejpam-3903	97	1	ε4ρn+1	ε4ρn+1	NOUN
ejpam-3903	97	2	ε	ε	PROPN
ejpam-3903	97	3	=	=	SYM
ejpam-3903	97	4	1	1	NUM
ejpam-3903	97	5	4	4	NUM
ejpam-3903	97	6	t	t	NOUN
ejpam-3903	97	7	ρε	ρε	PROPN
ejpam-3903	97	8	n.	n.	NOUN
ejpam-3903	97	9	(	(	PUNCT
ejpam-3903	97	10	6	6	NUM
ejpam-3903	97	11	)	)	PUNCT
ejpam-3903	97	12	r.	r.	NOUN
ejpam-3903	97	13	bade	bade	PROPN
ejpam-3903	97	14	,	,	PUNCT
ejpam-3903	97	15	h.	h.	PROPN
ejpam-3903	97	16	chaker	chaker	PROPN
ejpam-3903	97	17	/	/	SYM
ejpam-3903	97	18	eur	eur	PROPN
ejpam-3903	97	19	.	.	PUNCT
ejpam-3903	98	1	j.	j.	PROPN
ejpam-3903	98	2	pure	pure	PROPN
ejpam-3903	98	3	appl	appl	PROPN
ejpam-3903	98	4	.	.	PROPN
ejpam-3903	98	5	math	math	PROPN
ejpam-3903	98	6	,	,	PUNCT
ejpam-3903	98	7	14	14	NUM
ejpam-3903	98	8	(	(	PUNCT
ejpam-3903	98	9	1	1	NUM
ejpam-3903	98	10	)	)	PUNCT
ejpam-3903	98	11	(	(	PUNCT
ejpam-3903	98	12	2021	2021	NUM
ejpam-3903	98	13	)	)	PUNCT
ejpam-3903	98	14	,	,	PUNCT
ejpam-3903	98	15	82	82	NUM
ejpam-3903	98	16	-	-	SYM
ejpam-3903	98	17	111	111	NUM
ejpam-3903	98	18	86	86	NUM
ejpam-3903	98	19	to	to	PART
ejpam-3903	98	20	justify	justify	VERB
ejpam-3903	98	21	this	this	DET
ejpam-3903	98	22	strict	strict	ADJ
ejpam-3903	98	23	positivity	positivity	NOUN
ejpam-3903	98	24	,	,	PUNCT
ejpam-3903	98	25	we	we	PRON
ejpam-3903	98	26	considered	consider	VERB
ejpam-3903	98	27	a	a	DET
ejpam-3903	98	28	more	more	ADV
ejpam-3903	98	29	general	general	ADJ
ejpam-3903	98	30	convection	convection	NOUN
ejpam-3903	98	31	-	-	PUNCT
ejpam-3903	98	32	diffusion	diffusion	NOUN
ejpam-3903	98	33	equation	equation	NOUN
ejpam-3903	98	34	.	.	PUNCT
ejpam-3903	99	1	so	so	ADV
ejpam-3903	99	2	,	,	PUNCT
ejpam-3903	99	3	we	we	PRON
ejpam-3903	99	4	have	have	VERB
ejpam-3903	99	5	the	the	DET
ejpam-3903	99	6	following	follow	VERB
ejpam-3903	99	7	results	result	NOUN
ejpam-3903	99	8	:	:	PUNCT
ejpam-3903	99	9	lemma	lemma	PROPN
ejpam-3903	99	10	1	1	X
ejpam-3903	99	11	.	.	PUNCT
ejpam-3903	100	1	let	let	VERB
ejpam-3903	100	2	v	v	X
ejpam-3903	100	3	∈	∈	PROPN
ejpam-3903	100	4	(	(	PUNCT
ejpam-3903	100	5	w1,∞(ω))3	w1,∞(ω))3	PROPN
ejpam-3903	100	6	,	,	PUNCT
ejpam-3903	100	7	h	h	NOUN
ejpam-3903	100	8	∈	∈	PROPN
ejpam-3903	100	9	l∞(ω	l∞(ω	NOUN
ejpam-3903	100	10	)	)	PUNCT
ejpam-3903	100	11	,	,	PUNCT
ejpam-3903	101	1	k	k	PROPN
ejpam-3903	101	2	a	a	DET
ejpam-3903	101	3	constant	constant	ADJ
ejpam-3903	101	4	as	as	ADP
ejpam-3903	101	5	‖v‖w1,∞	‖v‖w1,∞	X
ejpam-3903	101	6	6	6	NUM
ejpam-3903	101	7	k.	k.	ADV
ejpam-3903	101	8	then	then	ADV
ejpam-3903	101	9	the	the	DET
ejpam-3903	101	10	solution	solution	NOUN
ejpam-3903	101	11	ρ	ρ	NOUN
ejpam-3903	101	12	of	of	ADP
ejpam-3903	101	13	the	the	DET
ejpam-3903	101	14	problem:	problem:	ADJ
ejpam-3903	101	15	σρ+∇	σρ+∇	NOUN
ejpam-3903	101	16	·	·	PUNCT
ejpam-3903	101	17	(	(	PUNCT
ejpam-3903	101	18	ρv)−	ρv)−	X
ejpam-3903	101	19	ε4ρ	ε4ρ	X
ejpam-3903	101	20	=	=	PUNCT
ejpam-3903	101	21	σh	σh	PROPN
ejpam-3903	101	22	in	in	ADP
ejpam-3903	101	23	ω	ω	PROPN
ejpam-3903	101	24	,	,	PUNCT
ejpam-3903	101	25	ε	ε	PROPN
ejpam-3903	101	26	∂ρ	∂ρ	PROPN
ejpam-3903	101	27	∂n	∂n	PROPN
ejpam-3903	101	28	=	=	SYM
ejpam-3903	101	29	0	0	NUM
ejpam-3903	101	30	,	,	PUNCT
ejpam-3903	101	31	v	v	NOUN
ejpam-3903	101	32	=	=	SYM
ejpam-3903	101	33	0	0	NUM
ejpam-3903	101	34	on	on	ADP
ejpam-3903	101	35	∂ω	∂ω	PROPN
ejpam-3903	101	36	,	,	PUNCT
ejpam-3903	101	37	(	(	PUNCT
ejpam-3903	101	38	7	7	X
ejpam-3903	101	39	)	)	PUNCT
ejpam-3903	101	40	verify	verify	NOUN
ejpam-3903	101	41	:	:	PUNCT
ejpam-3903	101	42	for	for	ADP
ejpam-3903	101	43	all	all	PRON
ejpam-3903	101	44	ρ̄	ρ̄	NOUN
ejpam-3903	101	45	>	>	SYM
ejpam-3903	101	46	0	0	NUM
ejpam-3903	101	47	such	such	ADJ
ejpam-3903	101	48	as	as	ADP
ejpam-3903	101	49	h	h	PROPN
ejpam-3903	101	50	>	>	X
ejpam-3903	101	51	ρ̄	ρ̄	NOUN
ejpam-3903	101	52	we	we	PRON
ejpam-3903	101	53	have	have	VERB
ejpam-3903	101	54	ρ	ρ	PROPN
ejpam-3903	101	55	>	>	X
ejpam-3903	101	56	ρ̄	ρ̄	PROPN
ejpam-3903	101	57	exp−	exp−	PROPN
ejpam-3903	101	58	k	k	PROPN
ejpam-3903	101	59	σ	σ	PROPN
ejpam-3903	101	60	.	.	PUNCT
ejpam-3903	102	1	proof	proof	NOUN
ejpam-3903	102	2	.	.	PUNCT
ejpam-3903	103	1	using	use	VERB
ejpam-3903	103	2	the	the	DET
ejpam-3903	103	3	same	same	ADJ
ejpam-3903	103	4	idea	idea	NOUN
ejpam-3903	103	5	like	like	ADP
ejpam-3903	103	6	in	in	ADP
ejpam-3903	103	7	[	[	X
ejpam-3903	103	8	6	6	NUM
ejpam-3903	103	9	]	]	PUNCT
ejpam-3903	103	10	,	,	PUNCT
ejpam-3903	103	11	we	we	PRON
ejpam-3903	103	12	set	set	VERB
ejpam-3903	103	13	:	:	PUNCT
ejpam-3903	103	14	ρ̃	ρ̃	PROPN
ejpam-3903	103	15	=	=	SYM
ejpam-3903	103	16	ρ	ρ	PROPN
ejpam-3903	103	17	−	−	PROPN
ejpam-3903	103	18	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	103	19	,	,	PUNCT
ejpam-3903	103	20	with	with	ADP
ejpam-3903	103	21	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	103	22	=	=	PUNCT
ejpam-3903	103	23	ρ̄	ρ̄	PROPN
ejpam-3903	103	24	exp−	exp−	PROPN
ejpam-3903	103	25	k	k	PROPN
ejpam-3903	103	26	σ	σ	PROPN
ejpam-3903	103	27	.	.	PUNCT
ejpam-3903	104	1	ρ̃	ρ̃	PROPN
ejpam-3903	104	2	is	be	AUX
ejpam-3903	104	3	then	then	ADV
ejpam-3903	104	4	solution	solution	NOUN
ejpam-3903	104	5	of	of	ADP
ejpam-3903	104	6	:	:	PUNCT
ejpam-3903	104	7	σρ̃+∇	σρ̃+∇	NOUN
ejpam-3903	104	8	·	·	PUNCT
ejpam-3903	104	9	(	(	PUNCT
ejpam-3903	104	10	ρv)−	ρv)−	X
ejpam-3903	104	11	ε4ρ̃	ε4ρ̃	X
ejpam-3903	104	12	=	=	SYM
ejpam-3903	104	13	σ	σ	PROPN
ejpam-3903	104	14	(	(	PUNCT
ejpam-3903	104	15	h−	h−	PROPN
ejpam-3903	104	16	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	104	17	)	)	PUNCT
ejpam-3903	104	18	.	.	PUNCT
ejpam-3903	105	1	(	(	PUNCT
ejpam-3903	105	2	8)	8)	NUM
ejpam-3903	105	3	using	use	VERB
ejpam-3903	105	4	the	the	DET
ejpam-3903	105	5	same	same	ADJ
ejpam-3903	105	6	decomposition	decomposition	NOUN
ejpam-3903	105	7	like	like	ADP
ejpam-3903	105	8	in	in	ADP
ejpam-3903	105	9	[	[	X
ejpam-3903	105	10	19	19	NUM
ejpam-3903	105	11	]	]	X
ejpam-3903	105	12	:	:	PUNCT
ejpam-3903	105	13	ρ̃	ρ̃	PROPN
ejpam-3903	105	14	=	=	SYM
ejpam-3903	105	15	ρ̃+	ρ̃+	NUM
ejpam-3903	105	16	−	−	PROPN
ejpam-3903	105	17	ρ̃+	ρ̃+	NOUN
ejpam-3903	105	18	,	,	PUNCT
ejpam-3903	105	19	where	where	SCONJ
ejpam-3903	105	20	:	:	PUNCT
ejpam-3903	105	21	ρ̃+	ρ̃+	X
ejpam-3903	105	22	=	=	SYM
ejpam-3903	105	23	{	{	PUNCT
ejpam-3903	105	24	ρ̃	ρ̃	PROPN
ejpam-3903	105	25	if	if	SCONJ
ejpam-3903	105	26	ρ̃	ρ̃	PROPN
ejpam-3903	105	27	>	>	SYM
ejpam-3903	105	28	0	0	NUM
ejpam-3903	105	29	,	,	PUNCT
ejpam-3903	105	30	0	0	NUM
ejpam-3903	105	31	if	if	SCONJ
ejpam-3903	105	32	not	not	PART
ejpam-3903	105	33	.	.	PUNCT
ejpam-3903	106	1	ρ̃−	ρ̃−	NOUN
ejpam-3903	107	1	=	=	PUNCT
ejpam-3903	107	2	{	{	PUNCT
ejpam-3903	107	3	−ρ̃	−ρ̃	NOUN
ejpam-3903	107	4	if	if	SCONJ
ejpam-3903	107	5	ρ̃	ρ̃	PROPN
ejpam-3903	107	6	<	<	X
ejpam-3903	107	7	0	0	NUM
ejpam-3903	107	8	,	,	PUNCT
ejpam-3903	107	9	0	0	NUM
ejpam-3903	107	10	if	if	SCONJ
ejpam-3903	107	11	not	not	PART
ejpam-3903	107	12	.	.	PUNCT
ejpam-3903	108	1	(	(	PUNCT
ejpam-3903	108	2	9	9	X
ejpam-3903	108	3	)	)	PUNCT
ejpam-3903	108	4	∂j	∂j	NOUN
ejpam-3903	108	5	ρ̃	ρ̃	PROPN
ejpam-3903	108	6	+	+	NUM
ejpam-3903	108	7	=	=	SYM
ejpam-3903	108	8	{	{	PUNCT
ejpam-3903	108	9	∂j	∂j	NOUN
ejpam-3903	108	10	ρ̃	ρ̃	PROPN
ejpam-3903	108	11	if	if	SCONJ
ejpam-3903	108	12	ρ̃	ρ̃	PROPN
ejpam-3903	108	13	>	>	SYM
ejpam-3903	108	14	0	0	NUM
ejpam-3903	108	15	,	,	PUNCT
ejpam-3903	108	16	0	0	NUM
ejpam-3903	108	17	if	if	SCONJ
ejpam-3903	108	18	not	not	PART
ejpam-3903	108	19	.	.	PUNCT
ejpam-3903	109	1	∂j	∂j	NOUN
ejpam-3903	109	2	ρ̃	ρ̃	PROPN
ejpam-3903	109	3	−	−	PROPN
ejpam-3903	109	4	=	=	PUNCT
ejpam-3903	109	5	{	{	PUNCT
ejpam-3903	109	6	−∂j	−∂j	ADP
ejpam-3903	109	7	ρ̃	ρ̃	PROPN
ejpam-3903	109	8	if	if	SCONJ
ejpam-3903	109	9	ρ̃	ρ̃	PROPN
ejpam-3903	109	10	<	<	X
ejpam-3903	109	11	0	0	NUM
ejpam-3903	109	12	,	,	PUNCT
ejpam-3903	109	13	0	0	NUM
ejpam-3903	109	14	if	if	SCONJ
ejpam-3903	109	15	not	not	PART
ejpam-3903	109	16	.	.	PUNCT
ejpam-3903	110	1	(	(	PUNCT
ejpam-3903	110	2	10	10	NUM
ejpam-3903	110	3	)	)	PUNCT
ejpam-3903	110	4	multiplying	multiplying	NOUN
ejpam-3903	110	5	(	(	PUNCT
ejpam-3903	110	6	8)	8)	NUM
ejpam-3903	110	7	by	by	ADP
ejpam-3903	110	8	the	the	DET
ejpam-3903	110	9	test	test	NOUN
ejpam-3903	110	10	function	function	NOUN
ejpam-3903	110	11	η̃−	η̃−	NOUN
ejpam-3903	110	12	=	=	SYM
ejpam-3903	110	13	−(ρ̃−	−(ρ̃−	PROPN
ejpam-3903	110	14	+	+	CCONJ
ejpam-3903	110	15	l)β	l)β	X
ejpam-3903	110	16	with	with	ADP
ejpam-3903	110	17	β	β	X
ejpam-3903	110	18	∈	∈	PROPN
ejpam-3903	111	1	[	[	X
ejpam-3903	111	2	0	0	NUM
ejpam-3903	111	3	,	,	PUNCT
ejpam-3903	111	4	1	1	NUM
ejpam-3903	111	5	]	]	PUNCT
ejpam-3903	111	6	,	,	PUNCT
ejpam-3903	111	7	one	one	PRON
ejpam-3903	111	8	obtain	obtain	VERB
ejpam-3903	111	9	:	:	PUNCT
ejpam-3903	111	10	−	−	PROPN
ejpam-3903	111	11	∫	∫	PROPN
ejpam-3903	111	12	ω	ω	PROPN
ejpam-3903	111	13	σρ̃(ρ̃−	σρ̃(ρ̃−	PROPN
ejpam-3903	112	1	+	+	PROPN
ejpam-3903	112	2	l)β	l)β	X
ejpam-3903	113	1	−	−	PROPN
ejpam-3903	113	2	∫	∫	PROPN
ejpam-3903	113	3	ω	ω	X
ejpam-3903	113	4	ε∇ρ̃∇(ρ̃−	ε∇ρ̃∇(ρ̃−	X
ejpam-3903	113	5	+	+	CCONJ
ejpam-3903	113	6	l)β	l)β	X
ejpam-3903	113	7	+	+	CCONJ
ejpam-3903	113	8	∫	∫	PROPN
ejpam-3903	113	9	ω	ω	NUM
ejpam-3903	113	10	σ(h−	σ(h−	NOUN
ejpam-3903	113	11	ρ̄∞)(ρ̃−	ρ̄∞)(ρ̃−	PROPN
ejpam-3903	113	12	+	+	SYM
ejpam-3903	113	13	l)β	l)β	X
ejpam-3903	113	14	=	=	PUNCT
ejpam-3903	114	1	−	−	PROPN
ejpam-3903	114	2	∫	∫	PROPN
ejpam-3903	114	3	ω	ω	NUM
ejpam-3903	114	4	ρv∇(ρ̃−	ρv∇(ρ̃−	PROPN
ejpam-3903	114	5	+	+	NUM
ejpam-3903	114	6	l)β	l)β	X
ejpam-3903	114	7	(	(	PUNCT
ejpam-3903	114	8	11	11	NUM
ejpam-3903	114	9	)	)	PUNCT
ejpam-3903	114	10	the	the	DET
ejpam-3903	114	11	different	different	ADJ
ejpam-3903	114	12	terms	term	NOUN
ejpam-3903	114	13	of	of	ADP
ejpam-3903	114	14	equality	equality	NOUN
ejpam-3903	114	15	(	(	PUNCT
ejpam-3903	114	16	11	11	NUM
ejpam-3903	114	17	)	)	PUNCT
ejpam-3903	114	18	are	be	AUX
ejpam-3903	114	19	estimated	estimate	VERB
ejpam-3903	114	20	by	by	ADP
ejpam-3903	114	21	:	:	PUNCT
ejpam-3903	114	22	ε	ε	PROPN
ejpam-3903	114	23	∫	∫	PROPN
ejpam-3903	114	24	ω∇ρ̃∇(ρ̃−	ω∇ρ̃∇(ρ̃−	PUNCT
ejpam-3903	114	25	+	+	NUM
ejpam-3903	114	26	l)β	l)β	X
ejpam-3903	114	27	=	=	PUNCT
ejpam-3903	114	28	−ε	−ε	PROPN
ejpam-3903	114	29	∫	∫	PROPN
ejpam-3903	114	30	ω∇ρ̃	ω∇ρ̃	PROPN
ejpam-3903	114	31	−∇(ρ̃−	−∇(ρ̃−	PROPN
ejpam-3903	115	1	+	+	CCONJ
ejpam-3903	116	1	l)β	l)β	X
ejpam-3903	117	1	=	=	PUNCT
ejpam-3903	117	2	−ε	−ε	PROPN
ejpam-3903	117	3	∫	∫	PROPN
ejpam-3903	117	4	ω∇(ρ̃−	ω∇(ρ̃−	PROPN
ejpam-3903	117	5	+	+	NUM
ejpam-3903	117	6	l)∇(ρ̃−	l)∇(ρ̃−	PROPN
ejpam-3903	117	7	+	+	CCONJ
ejpam-3903	117	8	l)β	l)β	X
ejpam-3903	117	9	=	=	SYM
ejpam-3903	117	10	−ε	−ε	PROPN
ejpam-3903	117	11	∫	∫	PROPN
ejpam-3903	118	1	ω	ω	PROPN
ejpam-3903	118	2	β(ρ̃−	β(ρ̃−	PROPN
ejpam-3903	119	1	+	+	CCONJ
ejpam-3903	119	2	l)β−1|∇(ρ̃−	l)β−1|∇(ρ̃−	NUM
ejpam-3903	119	3	+	+	NUM
ejpam-3903	119	4	l)|2	l)|2	NOUN
ejpam-3903	119	5	.	.	PUNCT
ejpam-3903	120	1	(	(	PUNCT
ejpam-3903	120	2	12	12	NUM
ejpam-3903	120	3	)	)	PUNCT
ejpam-3903	120	4	setting	set	VERB
ejpam-3903	120	5	ρ	ρ	NOUN
ejpam-3903	120	6	=	=	SYM
ejpam-3903	120	7	(	(	PUNCT
ejpam-3903	120	8	ρ̃+	ρ̃+	NUM
ejpam-3903	120	9	l	l	NOUN
ejpam-3903	120	10	)	)	PUNCT
ejpam-3903	121	1	+	+	CCONJ
ejpam-3903	121	2	(	(	PUNCT
ejpam-3903	121	3	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	121	4	−	−	PROPN
ejpam-3903	121	5	l	l	NOUN
ejpam-3903	121	6	)	)	PUNCT
ejpam-3903	121	7	one	one	PRON
ejpam-3903	121	8	can	can	AUX
ejpam-3903	121	9	found:∣∣	found:∣∣	VERB
ejpam-3903	121	10	∫	∫	PROPN
ejpam-3903	121	11	ω	ω	NUM
ejpam-3903	121	12	ρv∇(ρ̃−+	ρv∇(ρ̃−+	X
ejpam-3903	121	13	l)β	l)β	X
ejpam-3903	121	14	∣∣	∣∣	X
ejpam-3903	121	15	=	=	SYM
ejpam-3903	121	16	∣∣	∣∣	NUM
ejpam-3903	121	17	∫	∫	PROPN
ejpam-3903	121	18	ω	ω	PROPN
ejpam-3903	121	19	v(ρ̃−	v(ρ̃−	PROPN
ejpam-3903	122	1	+	+	CCONJ
ejpam-3903	122	2	l)∇(ρ̃−	l)∇(ρ̃−	PROPN
ejpam-3903	122	3	+	+	CCONJ
ejpam-3903	122	4	l)β	l)β	ADJ
ejpam-3903	122	5	−	−	NOUN
ejpam-3903	122	6	(	(	PUNCT
ejpam-3903	122	7	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	122	8	−	−	PROPN
ejpam-3903	122	9	l	l	NOUN
ejpam-3903	122	10	)	)	PUNCT
ejpam-3903	122	11	∫	∫	PROPN
ejpam-3903	122	12	ω(∇	ω(∇	X
ejpam-3903	122	13	·	·	PUNCT
ejpam-3903	122	14	v)(ρ̃−	v)(ρ̃−	PUNCT
ejpam-3903	123	1	+	+	NUM
ejpam-3903	123	2	l)β	l)β	X
ejpam-3903	123	3	∣∣	∣∣	NUM
ejpam-3903	123	4	≤	≤	NUM
ejpam-3903	123	5	kβ	kβ	PRON
ejpam-3903	123	6	∫	∫	PROPN
ejpam-3903	123	7	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	124	1	+	+	NUM
ejpam-3903	125	1	l)β∇(ρ̃−	l)β∇(ρ̃−	PROPN
ejpam-3903	126	1	+	+	X
ejpam-3903	126	2	l	l	NOUN
ejpam-3903	126	3	)	)	PUNCT
ejpam-3903	127	1	+	+	ADJ
ejpam-3903	127	2	k(ρ̄∞	k(ρ̄∞	X
ejpam-3903	127	3	+	+	X
ejpam-3903	127	4	l	l	NOUN
ejpam-3903	127	5	)	)	PUNCT
ejpam-3903	127	6	∫	∫	PROPN
ejpam-3903	127	7	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	127	8	+	+	CCONJ
ejpam-3903	127	9	l)β	l)β	X
ejpam-3903	127	10	≤	≤	NUM
ejpam-3903	127	11	k	k	PROPN
ejpam-3903	127	12	∫	∫	PROPN
ejpam-3903	127	13	ω	ω	PROPN
ejpam-3903	127	14	β(ρ̃−	β(ρ̃−	PROPN
ejpam-3903	127	15	+	+	NUM
ejpam-3903	127	16	l	l	NOUN
ejpam-3903	127	17	)	)	PUNCT
ejpam-3903	127	18	β+1	β+1	NUM
ejpam-3903	127	19	2	2	NUM
ejpam-3903	127	20	(	(	PUNCT
ejpam-3903	127	21	ρ̃−	ρ̃−	PROPN
ejpam-3903	127	22	+	+	NUM
ejpam-3903	127	23	l	l	NOUN
ejpam-3903	127	24	)	)	PUNCT
ejpam-3903	127	25	β−1	β−1	SYM
ejpam-3903	127	26	2	2	NUM
ejpam-3903	127	27	∇(ρ̃−	∇(ρ̃−	X
ejpam-3903	127	28	+	+	CCONJ
ejpam-3903	127	29	l	l	NOUN
ejpam-3903	127	30	)	)	PUNCT
ejpam-3903	128	1	+	+	ADJ
ejpam-3903	128	2	k(ρ̄∞	k(ρ̄∞	X
ejpam-3903	128	3	+	+	X
ejpam-3903	128	4	l	l	NOUN
ejpam-3903	128	5	)	)	PUNCT
ejpam-3903	128	6	∫	∫	PROPN
ejpam-3903	128	7	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	129	1	+	+	CCONJ
ejpam-3903	129	2	l)β	l)β	X
ejpam-3903	129	3	≤	≤	NUM
ejpam-3903	129	4	kβ‖ρ̃−	kβ‖ρ̃−	VERB
ejpam-3903	130	1	+	+	NUM
ejpam-3903	130	2	l‖	l‖	NOUN
ejpam-3903	130	3	β+1	β+1	NUM
ejpam-3903	130	4	2	2	NUM
ejpam-3903	130	5	lβ+1	lβ+1	PROPN
ejpam-3903	130	6	√∫	√∫	PROPN
ejpam-3903	130	7	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	130	8	+	+	CCONJ
ejpam-3903	130	9	l)β−1|∇(ρ̃−	l)β−1|∇(ρ̃−	NUM
ejpam-3903	130	10	+	+	NUM
ejpam-3903	130	11	l)|2	l)|2	X
ejpam-3903	130	12	+	+	ADJ
ejpam-3903	130	13	k(ρ̄∞	k(ρ̄∞	X
ejpam-3903	130	14	+	+	X
ejpam-3903	130	15	l	l	NOUN
ejpam-3903	130	16	)	)	PUNCT
ejpam-3903	130	17	∫	∫	PROPN
ejpam-3903	130	18	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	131	1	+	+	CCONJ
ejpam-3903	131	2	l)β	l)β	X
ejpam-3903	131	3	≤	≤	NUM
ejpam-3903	131	4	βk2	βk2	VERB
ejpam-3903	131	5	2ε	2ε	NOUN
ejpam-3903	131	6	‖ρ̃	‖ρ̃	PUNCT
ejpam-3903	131	7	−	−	PROPN
ejpam-3903	132	1	+	+	CCONJ
ejpam-3903	132	2	l‖β+1	l‖β+1	ADJ
ejpam-3903	132	3	lβ+1	lβ+1	PROPN
ejpam-3903	132	4	+	+	CCONJ
ejpam-3903	132	5	εβ	εβ	PROPN
ejpam-3903	132	6	2	2	NUM
ejpam-3903	132	7	∫	∫	NOUN
ejpam-3903	132	8	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	132	9	+	+	CCONJ
ejpam-3903	132	10	l)β−1|∇(ρ̃−	l)β−1|∇(ρ̃−	NUM
ejpam-3903	132	11	+	+	NUM
ejpam-3903	132	12	l)|2	l)|2	X
ejpam-3903	132	13	+	+	ADJ
ejpam-3903	132	14	k(ρ̄∞	k(ρ̄∞	X
ejpam-3903	132	15	+	+	X
ejpam-3903	132	16	l	l	NOUN
ejpam-3903	132	17	)	)	PUNCT
ejpam-3903	132	18	∫	∫	PROPN
ejpam-3903	132	19	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	132	20	+	+	CCONJ
ejpam-3903	132	21	l)β	l)β	X
ejpam-3903	132	22	.	.	PUNCT
ejpam-3903	133	1	(	(	PUNCT
ejpam-3903	133	2	13	13	NUM
ejpam-3903	133	3	)	)	PUNCT
ejpam-3903	133	4	r.	r.	NOUN
ejpam-3903	133	5	bade	bade	PROPN
ejpam-3903	133	6	,	,	PUNCT
ejpam-3903	133	7	h.	h.	PROPN
ejpam-3903	133	8	chaker	chaker	PROPN
ejpam-3903	133	9	/	/	SYM
ejpam-3903	133	10	eur	eur	PROPN
ejpam-3903	133	11	.	.	PUNCT
ejpam-3903	134	1	j.	j.	PROPN
ejpam-3903	134	2	pure	pure	PROPN
ejpam-3903	134	3	appl	appl	PROPN
ejpam-3903	134	4	.	.	PROPN
ejpam-3903	134	5	math	math	PROPN
ejpam-3903	134	6	,	,	PUNCT
ejpam-3903	134	7	14	14	NUM
ejpam-3903	134	8	(	(	PUNCT
ejpam-3903	134	9	1	1	NUM
ejpam-3903	134	10	)	)	PUNCT
ejpam-3903	134	11	(	(	PUNCT
ejpam-3903	134	12	2021	2021	NUM
ejpam-3903	134	13	)	)	PUNCT
ejpam-3903	134	14	,	,	PUNCT
ejpam-3903	134	15	82	82	NUM
ejpam-3903	134	16	-	-	SYM
ejpam-3903	134	17	111	111	NUM
ejpam-3903	134	18	87	87	NUM
ejpam-3903	134	19	since	since	SCONJ
ejpam-3903	134	20	the	the	DET
ejpam-3903	134	21	left	left	ADJ
ejpam-3903	134	22	terms	term	NOUN
ejpam-3903	134	23	in	in	ADP
ejpam-3903	134	24	(	(	PUNCT
ejpam-3903	134	25	11	11	NUM
ejpam-3903	134	26	)	)	PUNCT
ejpam-3903	134	27	being	be	AUX
ejpam-3903	134	28	positive	positive	ADJ
ejpam-3903	134	29	,	,	PUNCT
ejpam-3903	134	30	using	use	VERB
ejpam-3903	134	31	(	(	PUNCT
ejpam-3903	134	32	12	12	NUM
ejpam-3903	134	33	)	)	PUNCT
ejpam-3903	134	34	and	and	CCONJ
ejpam-3903	134	35	(	(	PUNCT
ejpam-3903	134	36	13	13	X
ejpam-3903	134	37	)	)	PUNCT
ejpam-3903	134	38	we	we	PRON
ejpam-3903	134	39	get	get	VERB
ejpam-3903	134	40	:	:	PUNCT
ejpam-3903	134	41	−	−	PROPN
ejpam-3903	134	42	∫	∫	PROPN
ejpam-3903	134	43	ω	ω	PROPN
ejpam-3903	134	44	σρ̃(ρ̃−	σρ̃(ρ̃−	PROPN
ejpam-3903	134	45	+	+	CCONJ
ejpam-3903	134	46	l)β	l)β	ADJ
ejpam-3903	134	47	≤	≤	NUM
ejpam-3903	134	48	βk2	βk2	VERB
ejpam-3903	134	49	2ε	2ε	NOUN
ejpam-3903	134	50	‖ρ̃	‖ρ̃	PUNCT
ejpam-3903	134	51	−	−	PROPN
ejpam-3903	135	1	+	+	SYM
ejpam-3903	135	2	l‖β+1	l‖β+1	ADJ
ejpam-3903	135	3	lβ+1	lβ+1	ADJ
ejpam-3903	135	4	+	+	ADJ
ejpam-3903	135	5	k(l	k(l	NOUN
ejpam-3903	135	6	+	+	CCONJ
ejpam-3903	135	7	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	135	8	)	)	PUNCT
ejpam-3903	135	9	∫	∫	PROPN
ejpam-3903	135	10	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	136	1	+	+	CCONJ
ejpam-3903	136	2	l)β	l)β	X
ejpam-3903	136	3	−	−	PROPN
ejpam-3903	136	4	σ	σ	NUM
ejpam-3903	136	5	∫	∫	PROPN
ejpam-3903	136	6	ω(h−	ω(h−	PROPN
ejpam-3903	136	7	ρ̄∞)(ρ̃−	ρ̄∞)(ρ̃−	PROPN
ejpam-3903	136	8	+	+	CCONJ
ejpam-3903	136	9	l)β	l)β	ADJ
ejpam-3903	136	10	≤	≤	NUM
ejpam-3903	136	11	βk2	βk2	VERB
ejpam-3903	136	12	2ε	2ε	NOUN
ejpam-3903	136	13	‖ρ̃	‖ρ̃	PUNCT
ejpam-3903	136	14	−	−	PROPN
ejpam-3903	137	1	+	+	CCONJ
ejpam-3903	137	2	l‖β+1	l‖β+1	ADP
ejpam-3903	137	3	lβ+1	lβ+1	ADJ
ejpam-3903	137	4	−	−	PROPN
ejpam-3903	137	5	σ	σ	PROPN
ejpam-3903	137	6	∫	∫	PROPN
ejpam-3903	137	7	ω	ω	PROPN
ejpam-3903	137	8	(	(	PUNCT
ejpam-3903	137	9	h−	h−	PROPN
ejpam-3903	137	10	ρ̄∞(1	ρ̄∞(1	NOUN
ejpam-3903	137	11	+	+	CCONJ
ejpam-3903	137	12	k	k	PROPN
ejpam-3903	137	13	σ	σ	PROPN
ejpam-3903	137	14	)	)	PUNCT
ejpam-3903	137	15	)	)	PUNCT
ejpam-3903	137	16	(	(	PUNCT
ejpam-3903	137	17	ρ̃−	ρ̃−	PROPN
ejpam-3903	137	18	+	+	NUM
ejpam-3903	137	19	l	l	NOUN
ejpam-3903	137	20	)	)	PUNCT
ejpam-3903	137	21	β	β	X
ejpam-3903	138	1	+	+	PROPN
ejpam-3903	138	2	kl	kl	PROPN
ejpam-3903	138	3	∫	∫	PROPN
ejpam-3903	138	4	ω(ρ̃−	ω(ρ̃−	PROPN
ejpam-3903	138	5	+	+	CCONJ
ejpam-3903	138	6	l)β	l)β	X
ejpam-3903	138	7	.	.	PUNCT
ejpam-3903	139	1	(	(	PUNCT
ejpam-3903	139	2	14	14	NUM
ejpam-3903	139	3	)	)	PUNCT
ejpam-3903	139	4	with	with	ADP
ejpam-3903	139	5	the	the	DET
ejpam-3903	139	6	taylor	taylor	PROPN
ejpam-3903	139	7	polynomial	polynomial	NOUN
ejpam-3903	139	8	of	of	ADP
ejpam-3903	139	9	order	order	NOUN
ejpam-3903	139	10	1	1	NUM
ejpam-3903	139	11	one	one	NUM
ejpam-3903	139	12	obtain	obtain	NOUN
ejpam-3903	139	13	:	:	PUNCT
ejpam-3903	139	14	ρ̄	ρ̄	NUM
ejpam-3903	139	15	>	>	X
ejpam-3903	139	16	ρ̄∞	ρ̄∞	PROPN
ejpam-3903	139	17	exp	exp	PROPN
ejpam-3903	139	18	(	(	PUNCT
ejpam-3903	139	19	k	k	PROPN
ejpam-3903	139	20	σ	σ	PROPN
ejpam-3903	139	21	)	)	PUNCT
ejpam-3903	139	22	>	>	X
ejpam-3903	140	1	ρ̄∞(1	ρ̄∞(1	NOUN
ejpam-3903	140	2	+	+	CCONJ
ejpam-3903	140	3	k	k	PROPN
ejpam-3903	140	4	σ	σ	PROPN
ejpam-3903	140	5	)	)	PUNCT
ejpam-3903	140	6	,	,	PUNCT
ejpam-3903	140	7	then	then	ADV
ejpam-3903	140	8	we	we	PRON
ejpam-3903	140	9	have	have	VERB
ejpam-3903	140	10	:	:	PUNCT
ejpam-3903	140	11	0	0	PUNCT
ejpam-3903	140	12	<	<	X
ejpam-3903	140	13	h−	h−	PROPN
ejpam-3903	140	14	ρ̄	ρ̄	NUM
ejpam-3903	140	15	6	6	NUM
ejpam-3903	140	16	h−	h−	NOUN
ejpam-3903	140	17	ρ̄∞(1	ρ̄∞(1	NOUN
ejpam-3903	140	18	+	+	CCONJ
ejpam-3903	140	19	k	k	PROPN
ejpam-3903	140	20	σ	σ	PROPN
ejpam-3903	140	21	)	)	PUNCT
ejpam-3903	140	22	.	.	PUNCT
ejpam-3903	141	1	then	then	ADV
ejpam-3903	141	2	,	,	PUNCT
ejpam-3903	141	3	the	the	DET
ejpam-3903	141	4	inequality	inequality	NOUN
ejpam-3903	141	5	(	(	PUNCT
ejpam-3903	141	6	14	14	NUM
ejpam-3903	141	7	)	)	PUNCT
ejpam-3903	141	8	becomes	become	VERB
ejpam-3903	141	9	:	:	PUNCT
ejpam-3903	141	10	−	−	PROPN
ejpam-3903	141	11	∫	∫	PROPN
ejpam-3903	141	12	ω	ω	PROPN
ejpam-3903	141	13	σρ̃(ρ̃−	σρ̃(ρ̃−	PROPN
ejpam-3903	141	14	+	+	CCONJ
ejpam-3903	141	15	l)β	l)β	ADJ
ejpam-3903	141	16	≤	≤	NUM
ejpam-3903	141	17	βk2	βk2	VERB
ejpam-3903	141	18	2ε	2ε	NOUN
ejpam-3903	141	19	‖ρ̃−	‖ρ̃−	PUNCT
ejpam-3903	142	1	+	+	PUNCT
ejpam-3903	142	2	l‖β+1	l‖β+1	ADJ
ejpam-3903	142	3	lβ+1	lβ+1	PROPN
ejpam-3903	143	1	+	+	ADJ
ejpam-3903	143	2	kl	kl	PROPN
ejpam-3903	143	3	∫	∫	PROPN
ejpam-3903	143	4	ω	ω	PROPN
ejpam-3903	143	5	(	(	PUNCT
ejpam-3903	143	6	ρ̃−	ρ̃−	PROPN
ejpam-3903	143	7	+	+	X
ejpam-3903	143	8	l)β	l)β	X
ejpam-3903	143	9	.	.	PUNCT
ejpam-3903	144	1	if	if	SCONJ
ejpam-3903	144	2	l	l	NOUN
ejpam-3903	144	3	−→	−→	NOUN
ejpam-3903	144	4	0	0	NUM
ejpam-3903	144	5	,	,	PUNCT
ejpam-3903	144	6	we	we	PRON
ejpam-3903	144	7	get	get	VERB
ejpam-3903	144	8	:	:	PUNCT
ejpam-3903	144	9	(	(	PUNCT
ejpam-3903	144	10	σ	σ	NOUN
ejpam-3903	144	11	−	−	PROPN
ejpam-3903	144	12	βk2	βk2	NOUN
ejpam-3903	144	13	2ε	2ε	NUM
ejpam-3903	144	14	)	)	PUNCT
ejpam-3903	145	1	‖ρ̃−‖β+1	‖ρ̃−‖β+1	PUNCT
ejpam-3903	145	2	lβ+1	lβ+1	ADJ
ejpam-3903	145	3	≤	≤	ADJ
ejpam-3903	145	4	0	0	NUM
ejpam-3903	145	5	.	.	PUNCT
ejpam-3903	146	1	choosing	choose	VERB
ejpam-3903	146	2	β	β	PRON
ejpam-3903	146	3	<	<	X
ejpam-3903	146	4	inf(1	inf(1	NOUN
ejpam-3903	146	5	,	,	PUNCT
ejpam-3903	146	6	2σε	2σε	PROPN
ejpam-3903	146	7	k2	k2	PROPN
ejpam-3903	146	8	)	)	PUNCT
ejpam-3903	146	9	,	,	PUNCT
ejpam-3903	146	10	one	one	PRON
ejpam-3903	146	11	obtain	obtain	VERB
ejpam-3903	146	12	ρ̃−	ρ̃−	NOUN
ejpam-3903	146	13	=	=	SYM
ejpam-3903	146	14	0	0	NUM
ejpam-3903	146	15	which	which	PRON
ejpam-3903	146	16	means	mean	VERB
ejpam-3903	146	17	that	that	SCONJ
ejpam-3903	146	18	ρ	ρ	PROPN
ejpam-3903	146	19	>	>	X
ejpam-3903	146	20	ρ̄	ρ̄	PROPN
ejpam-3903	146	21	exp−	exp−	PROPN
ejpam-3903	146	22	k	k	PROPN
ejpam-3903	146	23	σ	σ	PROPN
ejpam-3903	146	24	.	.	PUNCT
ejpam-3903	147	1	�	�	PROPN
ejpam-3903	147	2	lemma	lemma	PROPN
ejpam-3903	147	3	2	2	X
ejpam-3903	147	4	.	.	PUNCT
ejpam-3903	148	1	for	for	ADP
ejpam-3903	148	2	s	s	PRON
ejpam-3903	148	3	≥	≥	NUM
ejpam-3903	148	4	5	5	NUM
ejpam-3903	148	5	2	2	NUM
ejpam-3903	148	6	,	,	PUNCT
ejpam-3903	148	7	let	let	VERB
ejpam-3903	148	8	v	v	X
ejpam-3903	148	9	∈	∈	PROPN
ejpam-3903	148	10	(	(	PUNCT
ejpam-3903	148	11	hs+2(ω))3	hs+2(ω))3	PROPN
ejpam-3903	148	12	,	,	PUNCT
ejpam-3903	148	13	h	h	PROPN
ejpam-3903	148	14	∈	∈	PROPN
ejpam-3903	148	15	l∞(ω	l∞(ω	NOUN
ejpam-3903	148	16	)	)	PUNCT
ejpam-3903	148	17	,	,	PUNCT
ejpam-3903	149	1	v∗	v∗	PROPN
ejpam-3903	149	2	∈	∈	PROPN
ejpam-3903	149	3	(	(	PUNCT
ejpam-3903	149	4	hs+	hs+	NOUN
ejpam-3903	149	5	3	3	NUM
ejpam-3903	149	6	2	2	NUM
ejpam-3903	149	7	(	(	PUNCT
ejpam-3903	149	8	∂ω))3	∂ω))3	PROPN
ejpam-3903	149	9	.	.	PUNCT
ejpam-3903	150	1	for	for	ADP
ejpam-3903	150	2	all	all	DET
ejpam-3903	150	3	σ	σ	PROPN
ejpam-3903	150	4	>	>	X
ejpam-3903	150	5	k2	k2	PROPN
ejpam-3903	150	6	ε	ε	PROPN
ejpam-3903	150	7	+	+	CCONJ
ejpam-3903	150	8	k	k	PROPN
ejpam-3903	150	9	,	,	PUNCT
ejpam-3903	150	10	where	where	SCONJ
ejpam-3903	150	11	k	k	PROPN
ejpam-3903	150	12	is	be	AUX
ejpam-3903	150	13	a	a	DET
ejpam-3903	150	14	constant	constant	ADJ
ejpam-3903	150	15	such	such	ADJ
ejpam-3903	150	16	as	as	ADP
ejpam-3903	150	17	‖v‖hs+2	‖v‖hs+2	PROPN
ejpam-3903	150	18	6	6	NUM
ejpam-3903	150	19	k.	k.	NOUN
ejpam-3903	150	20	then	then	ADV
ejpam-3903	150	21	,	,	PUNCT
ejpam-3903	150	22	the	the	DET
ejpam-3903	150	23	solution	solution	NOUN
ejpam-3903	150	24	ρ	ρ	NOUN
ejpam-3903	150	25	of	of	ADP
ejpam-3903	150	26	the	the	DET
ejpam-3903	150	27	problem	problem	NOUN
ejpam-3903	150	28	:	:	PUNCT
ejpam-3903	150	29			PUNCT
ejpam-3903	150	30	σρ+∇	σρ+∇	X
ejpam-3903	150	31	·	·	PUNCT
ejpam-3903	150	32	(	(	PUNCT
ejpam-3903	150	33	ρv)−	ρv)−	X
ejpam-3903	150	34	ε4ρ	ε4ρ	X
ejpam-3903	150	35	=	=	PUNCT
ejpam-3903	150	36	σh	σh	PROPN
ejpam-3903	150	37	in	in	ADP
ejpam-3903	150	38	ω	ω	PROPN
ejpam-3903	150	39	,	,	PUNCT
ejpam-3903	150	40	ε	ε	PROPN
ejpam-3903	150	41	∂ρ	∂ρ	PROPN
ejpam-3903	150	42	∂n	∂n	PROPN
ejpam-3903	150	43	=	=	SYM
ejpam-3903	150	44	0	0	NUM
ejpam-3903	150	45	,	,	PUNCT
ejpam-3903	150	46	v	v	NOUN
ejpam-3903	150	47	=	=	SYM
ejpam-3903	150	48	v∗	v∗	PROPN
ejpam-3903	150	49	on	on	ADP
ejpam-3903	150	50	∂ω	∂ω	PROPN
ejpam-3903	150	51	,	,	PUNCT
ejpam-3903	150	52	(	(	PUNCT
ejpam-3903	150	53	15	15	X
ejpam-3903	150	54	)	)	PUNCT
ejpam-3903	150	55	verify	verify	VERB
ejpam-3903	150	56	the	the	DET
ejpam-3903	150	57	following	follow	VERB
ejpam-3903	150	58	properties	property	NOUN
ejpam-3903	150	59	:	:	PUNCT
ejpam-3903	150	60	i	i	NOUN
ejpam-3903	150	61	)	)	PUNCT
ejpam-3903	150	62	if	if	SCONJ
ejpam-3903	150	63	h	h	PROPN
ejpam-3903	150	64	>	>	X
ejpam-3903	150	65	0	0	PUNCT
ejpam-3903	151	1	then	then	ADV
ejpam-3903	151	2	ρ	ρ	PROPN
ejpam-3903	151	3	>	>	X
ejpam-3903	151	4	0	0	PROPN
ejpam-3903	151	5	,	,	PUNCT
ejpam-3903	151	6	ii	ii	NOUN
ejpam-3903	151	7	)	)	PUNCT
ejpam-3903	151	8	let	let	VERB
ejpam-3903	151	9	ρ̄	ρ̄	NOUN
ejpam-3903	151	10	>	>	X
ejpam-3903	151	11	0	0	NUM
ejpam-3903	151	12	,	,	PUNCT
ejpam-3903	151	13	if	if	SCONJ
ejpam-3903	151	14	h	h	PROPN
ejpam-3903	151	15	>	>	X
ejpam-3903	151	16	ρ̄	ρ̄	PROPN
ejpam-3903	152	1	then	then	ADV
ejpam-3903	152	2	ρ	ρ	PROPN
ejpam-3903	152	3	>	>	X
ejpam-3903	152	4	ρ̄	ρ̄	PROPN
ejpam-3903	152	5	exp−	exp−	PROPN
ejpam-3903	152	6	k	k	PROPN
ejpam-3903	152	7	σ	σ	PROPN
ejpam-3903	152	8	.	.	PUNCT
ejpam-3903	153	1	proof	proof	NOUN
ejpam-3903	153	2	.	.	PUNCT
ejpam-3903	154	1	i	i	PRON
ejpam-3903	154	2	):	):	PUNCT
ejpam-3903	154	3	we	we	PRON
ejpam-3903	154	4	have	have	VERB
ejpam-3903	154	5	v∗	v∗	PROPN
ejpam-3903	154	6	∈	∈	PROPN
ejpam-3903	154	7	(	(	PUNCT
ejpam-3903	154	8	hs+	hs+	NOUN
ejpam-3903	154	9	3	3	NUM
ejpam-3903	154	10	2	2	NUM
ejpam-3903	154	11	(	(	PUNCT
ejpam-3903	154	12	∂ω))3	∂ω))3	PROPN
ejpam-3903	154	13	,	,	PUNCT
ejpam-3903	154	14	then	then	ADV
ejpam-3903	154	15	there	there	PRON
ejpam-3903	154	16	exist	exist	VERB
ejpam-3903	154	17	ṽ∗	ṽ∗	ADP
ejpam-3903	154	18	∈	∈	PROPN
ejpam-3903	154	19	(	(	PUNCT
ejpam-3903	154	20	hs+2(ω))3	hs+2(ω))3	NOUN
ejpam-3903	154	21	such	such	ADJ
ejpam-3903	154	22	that	that	DET
ejpam-3903	154	23	ṽ∗|∂ω	ṽ∗|∂ω	NUM
ejpam-3903	154	24	=	=	SYM
ejpam-3903	154	25	v∗	v∗	NOUN
ejpam-3903	154	26	;	;	PUNCT
ejpam-3903	154	27	let	let	VERB
ejpam-3903	154	28	set	set	VERB
ejpam-3903	154	29	ṽ	ṽ	PROPN
ejpam-3903	154	30	=	=	SYM
ejpam-3903	154	31	v	v	ADP
ejpam-3903	154	32	−	−	PROPN
ejpam-3903	154	33	ṽ∗.	ṽ∗.	NOUN
ejpam-3903	154	34	according	accord	VERB
ejpam-3903	154	35	to	to	ADP
ejpam-3903	154	36	the	the	DET
ejpam-3903	154	37	sobolev	sobolev	NOUN
ejpam-3903	154	38	embendding	embendding	NOUN
ejpam-3903	154	39	theorem	theorem	NOUN
ejpam-3903	154	40	(	(	PUNCT
ejpam-3903	154	41	see	see	VERB
ejpam-3903	154	42	[	[	X
ejpam-3903	154	43	2	2	NUM
ejpam-3903	154	44	]	]	PUNCT
ejpam-3903	154	45	)	)	PUNCT
ejpam-3903	154	46	and	and	CCONJ
ejpam-3903	154	47	the	the	DET
ejpam-3903	154	48	fact	fact	NOUN
ejpam-3903	154	49	that	that	SCONJ
ejpam-3903	154	50	s	s	VERB
ejpam-3903	154	51	>	>	X
ejpam-3903	154	52	5	5	NUM
ejpam-3903	154	53	2	2	NUM
ejpam-3903	154	54	>	>	SYM
ejpam-3903	154	55	3	3	NUM
ejpam-3903	154	56	2	2	NUM
ejpam-3903	154	57	−	−	NOUN
ejpam-3903	154	58	1	1	NUM
ejpam-3903	154	59	;	;	PUNCT
ejpam-3903	154	60	we	we	PRON
ejpam-3903	154	61	have	have	VERB
ejpam-3903	154	62	ṽ	ṽ	PROPN
ejpam-3903	154	63	∈	∈	PROPN
ejpam-3903	154	64	(	(	PUNCT
ejpam-3903	154	65	w	w	NOUN
ejpam-3903	154	66	1,∞(ω))3	1,∞(ω))3	NUM
ejpam-3903	154	67	,	,	PUNCT
ejpam-3903	154	68	so	so	ADV
ejpam-3903	154	69	replacing	replace	VERB
ejpam-3903	154	70	v	v	NOUN
ejpam-3903	154	71	=	=	SYM
ejpam-3903	154	72	ṽ	ṽ	PROPN
ejpam-3903	154	73	+	+	CCONJ
ejpam-3903	154	74	ṽ∗	ṽ∗	PROPN
ejpam-3903	154	75	in	in	ADP
ejpam-3903	154	76	(	(	PUNCT
ejpam-3903	154	77	15	15	NUM
ejpam-3903	154	78	)	)	PUNCT
ejpam-3903	154	79	,	,	PUNCT
ejpam-3903	154	80	ρ	ρ	PROPN
ejpam-3903	154	81	is	be	AUX
ejpam-3903	154	82	then	then	ADV
ejpam-3903	154	83	solution	solution	NOUN
ejpam-3903	154	84	of	of	ADP
ejpam-3903	154	85	the	the	DET
ejpam-3903	154	86	following	follow	VERB
ejpam-3903	154	87	system:	system:	NOUN
ejpam-3903	154	88	σρ+∇	σρ+∇	PROPN
ejpam-3903	154	89	·	·	PUNCT
ejpam-3903	154	90	(	(	PUNCT
ejpam-3903	154	91	ρṽ	ρṽ	NOUN
ejpam-3903	154	92	)	)	PUNCT
ejpam-3903	155	1	+	+	NUM
ejpam-3903	155	2	ε4ρ	ε4ρ	X
ejpam-3903	155	3	=	=	SYM
ejpam-3903	155	4	σh−∇	σh−∇	PROPN
ejpam-3903	155	5	·	·	PUNCT
ejpam-3903	155	6	(	(	PUNCT
ejpam-3903	155	7	ρṽ∗	ρṽ∗	NOUN
ejpam-3903	155	8	)	)	PUNCT
ejpam-3903	155	9	in	in	ADP
ejpam-3903	155	10	ω	ω	PROPN
ejpam-3903	155	11	,	,	PUNCT
ejpam-3903	155	12	ε	ε	PROPN
ejpam-3903	155	13	∂ρ	∂ρ	PROPN
ejpam-3903	155	14	∂n	∂n	PROPN
ejpam-3903	155	15	=	=	SYM
ejpam-3903	155	16	0	0	PROPN
ejpam-3903	155	17	,	,	PUNCT
ejpam-3903	155	18	ṽ	ṽ	PROPN
ejpam-3903	155	19	=	=	SYM
ejpam-3903	155	20	0	0	NUM
ejpam-3903	155	21	on	on	ADP
ejpam-3903	155	22	∂ω	∂ω	PROPN
ejpam-3903	155	23	.	.	PUNCT
ejpam-3903	156	1	(	(	PUNCT
ejpam-3903	156	2	16	16	NUM
ejpam-3903	156	3	)	)	PUNCT
ejpam-3903	156	4	r.	r.	PROPN
ejpam-3903	156	5	bade	bade	PROPN
ejpam-3903	156	6	,	,	PUNCT
ejpam-3903	156	7	h.	h.	PROPN
ejpam-3903	156	8	chaker	chaker	PROPN
ejpam-3903	156	9	/	/	SYM
ejpam-3903	156	10	eur	eur	PROPN
ejpam-3903	156	11	.	.	PUNCT
ejpam-3903	157	1	j.	j.	PROPN
ejpam-3903	157	2	pure	pure	PROPN
ejpam-3903	157	3	appl	appl	PROPN
ejpam-3903	157	4	.	.	PROPN
ejpam-3903	157	5	math	math	PROPN
ejpam-3903	157	6	,	,	PUNCT
ejpam-3903	157	7	14	14	NUM
ejpam-3903	157	8	(	(	PUNCT
ejpam-3903	157	9	1	1	NUM
ejpam-3903	157	10	)	)	PUNCT
ejpam-3903	157	11	(	(	PUNCT
ejpam-3903	157	12	2021	2021	NUM
ejpam-3903	157	13	)	)	PUNCT
ejpam-3903	157	14	,	,	PUNCT
ejpam-3903	157	15	82	82	NUM
ejpam-3903	157	16	-	-	SYM
ejpam-3903	157	17	111	111	NUM
ejpam-3903	157	18	88	88	NUM
ejpam-3903	157	19	considering	consider	VERB
ejpam-3903	157	20	the	the	DET
ejpam-3903	157	21	same	same	ADJ
ejpam-3903	157	22	test	test	NOUN
ejpam-3903	157	23	function	function	NOUN
ejpam-3903	157	24	η−	η−	PROPN
ejpam-3903	157	25	=	=	SYM
ejpam-3903	157	26	−(ρ−+	−(ρ−+	PROPN
ejpam-3903	157	27	l)β	l)β	PUNCT
ejpam-3903	157	28	and	and	CCONJ
ejpam-3903	157	29	also	also	ADV
ejpam-3903	157	30	use	use	VERB
ejpam-3903	157	31	the	the	DET
ejpam-3903	157	32	same	same	ADJ
ejpam-3903	157	33	decomposition	decomposition	NOUN
ejpam-3903	157	34	of	of	ADP
ejpam-3903	157	35	the	the	DET
ejpam-3903	157	36	density	density	NOUN
ejpam-3903	157	37	ρ	ρ	PROPN
ejpam-3903	157	38	=	=	SYM
ejpam-3903	157	39	ρ+	ρ+	NOUN
ejpam-3903	157	40	+	+	CCONJ
ejpam-3903	158	1	ρ−	ρ−	NOUN
ejpam-3903	158	2	,	,	PUNCT
ejpam-3903	158	3	we	we	PRON
ejpam-3903	158	4	get	get	VERB
ejpam-3903	158	5	:	:	PUNCT
ejpam-3903	158	6	−σ	−σ	NOUN
ejpam-3903	158	7	∫	∫	PROPN
ejpam-3903	158	8	ω	ω	NUM
ejpam-3903	158	9	ρ(ρ−	ρ(ρ−	PROPN
ejpam-3903	158	10	+	+	CCONJ
ejpam-3903	158	11	l)β	l)β	X
ejpam-3903	159	1	+	+	CCONJ
ejpam-3903	159	2	ε	ε	PROPN
ejpam-3903	159	3	∫	∫	PROPN
ejpam-3903	159	4	ω	ω	PROPN
ejpam-3903	160	1	∇ρ∇(ρ−	∇ρ∇(ρ−	X
ejpam-3903	160	2	+	+	CCONJ
ejpam-3903	160	3	l)β	l)β	X
ejpam-3903	160	4	+	+	CCONJ
ejpam-3903	160	5	σ	σ	NUM
ejpam-3903	160	6	∫	∫	PROPN
ejpam-3903	160	7	ω	ω	NUM
ejpam-3903	160	8	h(ρ−	h(ρ−	NOUN
ejpam-3903	160	9	+	+	CCONJ
ejpam-3903	160	10	l)β	l)β	X
ejpam-3903	160	11	=	=	PUNCT
ejpam-3903	160	12	−	−	PROPN
ejpam-3903	160	13	∫	∫	PROPN
ejpam-3903	160	14	ω	ω	NUM
ejpam-3903	160	15	ρṽ∇(ρ−	ρṽ∇(ρ−	PROPN
ejpam-3903	160	16	+	+	CCONJ
ejpam-3903	160	17	l)β	l)β	X
ejpam-3903	161	1	+	+	CCONJ
ejpam-3903	161	2	∫	∫	PROPN
ejpam-3903	161	3	ω	ω	NUM
ejpam-3903	161	4	ρ(∇	ρ(∇	PROPN
ejpam-3903	161	5	·	·	PUNCT
ejpam-3903	161	6	ṽ∗)(ρ−	ṽ∗)(ρ−	NOUN
ejpam-3903	161	7	+	+	CCONJ
ejpam-3903	161	8	l)β	l)β	X
ejpam-3903	162	1	+	+	CCONJ
ejpam-3903	162	2	∫	∫	PROPN
ejpam-3903	162	3	ω	ω	PROPN
ejpam-3903	162	4	ṽ∗(∇ρ)(ρ−	ṽ∗(∇ρ)(ρ−	PROPN
ejpam-3903	162	5	+	+	X
ejpam-3903	162	6	l)β	l)β	X
ejpam-3903	162	7	.	.	PUNCT
ejpam-3903	163	1	(	(	PUNCT
ejpam-3903	163	2	17	17	NUM
ejpam-3903	163	3	)	)	PUNCT
ejpam-3903	163	4	the	the	DET
ejpam-3903	163	5	differents	different	NOUN
ejpam-3903	163	6	terms	term	NOUN
ejpam-3903	163	7	in	in	ADP
ejpam-3903	163	8	the	the	DET
ejpam-3903	163	9	equality	equality	NOUN
ejpam-3903	163	10	(	(	PUNCT
ejpam-3903	163	11	17	17	NUM
ejpam-3903	163	12	)	)	PUNCT
ejpam-3903	163	13	can	can	AUX
ejpam-3903	163	14	be	be	AUX
ejpam-3903	163	15	estimated	estimate	VERB
ejpam-3903	163	16	as	as	ADP
ejpam-3903	163	17	follow	follow	NOUN
ejpam-3903	163	18	:	:	PUNCT
ejpam-3903	163	19	|	|	ADV
ejpam-3903	163	20	∫	∫	PROPN
ejpam-3903	164	1	ω	ω	NUM
ejpam-3903	164	2	ρṽ∇(ρ−	ρṽ∇(ρ−	PROPN
ejpam-3903	164	3	+	+	CCONJ
ejpam-3903	164	4	l)β|	l)β|	PROPN
ejpam-3903	164	5	≤	≤	NUM
ejpam-3903	164	6	kβ	kβ	PRON
ejpam-3903	164	7	∫	∫	PROPN
ejpam-3903	164	8	ω(ρ−	ω(ρ−	X
ejpam-3903	164	9	+	+	CCONJ
ejpam-3903	164	10	l)β∇(ρ−	l)β∇(ρ−	VERB
ejpam-3903	164	11	+	+	CCONJ
ejpam-3903	164	12	l	l	NOUN
ejpam-3903	164	13	)	)	PUNCT
ejpam-3903	165	1	+	+	CCONJ
ejpam-3903	165	2	l|	l|	ADJ
ejpam-3903	165	3	∫	∫	PROPN
ejpam-3903	165	4	ω	ω	NUM
ejpam-3903	165	5	ṽ∇(ρ−	ṽ∇(ρ−	PROPN
ejpam-3903	165	6	+	+	CCONJ
ejpam-3903	165	7	l)β|	l)β|	PROPN
ejpam-3903	165	8	≤	≤	NOUN
ejpam-3903	165	9	βk2	βk2	VERB
ejpam-3903	165	10	2ε	2ε	ADJ
ejpam-3903	165	11	‖ρ	‖ρ	NOUN
ejpam-3903	165	12	−	−	PROPN
ejpam-3903	166	1	+	+	CCONJ
ejpam-3903	166	2	l‖β+1	l‖β+1	ADJ
ejpam-3903	166	3	lβ+1	lβ+1	PROPN
ejpam-3903	166	4	+	+	CCONJ
ejpam-3903	166	5	βε	βε	PROPN
ejpam-3903	166	6	2	2	NUM
ejpam-3903	166	7	∫	∫	NOUN
ejpam-3903	166	8	ω(ρ−	ω(ρ−	X
ejpam-3903	166	9	+	+	CCONJ
ejpam-3903	166	10	l)β−1|∇(ρ−	l)β−1|∇(ρ−	PROPN
ejpam-3903	166	11	+	+	NUM
ejpam-3903	166	12	l)|2	l)|2	NOUN
ejpam-3903	166	13	+	+	X
ejpam-3903	166	14	lk|ω|	lk|ω|	ADP
ejpam-3903	166	15	1	1	NUM
ejpam-3903	166	16	β+1	β+1	PROPN
ejpam-3903	166	17	‖ρ−	‖ρ−	PROPN
ejpam-3903	166	18	+	+	CCONJ
ejpam-3903	166	19	l‖β	l‖β	ADJ
ejpam-3903	166	20	lβ+1	lβ+1	ADJ
ejpam-3903	166	21	,	,	PUNCT
ejpam-3903	166	22	(	(	PUNCT
ejpam-3903	166	23	18	18	NUM
ejpam-3903	166	24	)	)	PUNCT
ejpam-3903	167	1	|	|	ADV
ejpam-3903	167	2	∫	∫	PROPN
ejpam-3903	167	3	ω	ω	NUM
ejpam-3903	167	4	ρ(∇	ρ(∇	PROPN
ejpam-3903	167	5	·	·	PUNCT
ejpam-3903	167	6	ṽ∗)(ρ−	ṽ∗)(ρ−	NOUN
ejpam-3903	168	1	+	+	CCONJ
ejpam-3903	168	2	l)β|	l)β|	NOUN
ejpam-3903	168	3	=	=	PUNCT
ejpam-3903	169	1	|	|	ADV
ejpam-3903	169	2	∫	∫	PROPN
ejpam-3903	169	3	ω	ω	PROPN
ejpam-3903	169	4	(	(	PUNCT
ejpam-3903	169	5	ρ−	ρ−	NOUN
ejpam-3903	169	6	+	+	CCONJ
ejpam-3903	169	7	l)(∇	l)(∇	NOUN
ejpam-3903	169	8	·	·	PUNCT
ejpam-3903	169	9	ṽ∗)(ρ−	ṽ∗)(ρ−	NOUN
ejpam-3903	169	10	+	+	CCONJ
ejpam-3903	169	11	l)β	l)β	X
ejpam-3903	170	1	−	−	NOUN
ejpam-3903	170	2	l	l	NOUN
ejpam-3903	170	3	∫	∫	PROPN
ejpam-3903	170	4	ω	ω	PROPN
ejpam-3903	170	5	(	(	PUNCT
ejpam-3903	170	6	∇	∇	X
ejpam-3903	170	7	·	·	PUNCT
ejpam-3903	170	8	ṽ∗)(ρ−	ṽ∗)(ρ−	NOUN
ejpam-3903	170	9	+	+	CCONJ
ejpam-3903	170	10	l)β|	l)β|	PROPN
ejpam-3903	170	11	≤	≤	NOUN
ejpam-3903	171	1	k	k	PROPN
ejpam-3903	171	2	∫	∫	PROPN
ejpam-3903	171	3	ω(ρ−	ω(ρ−	PROPN
ejpam-3903	171	4	+	+	CCONJ
ejpam-3903	171	5	l)β+1	l)β+1	PROPN
ejpam-3903	171	6	+	+	CCONJ
ejpam-3903	171	7	lk	lk	PROPN
ejpam-3903	171	8	∫	∫	PROPN
ejpam-3903	171	9	ω(ρ−	ω(ρ−	X
ejpam-3903	171	10	+	+	CCONJ
ejpam-3903	171	11	l)β	l)β	X
ejpam-3903	171	12	≤	≤	NUM
ejpam-3903	171	13	k‖ρ−	k‖ρ−	NOUN
ejpam-3903	171	14	+	+	SYM
ejpam-3903	171	15	l‖β+1	l‖β+1	X
ejpam-3903	171	16	lβ+1	lβ+1	ADJ
ejpam-3903	172	1	+	+	CCONJ
ejpam-3903	172	2	lk|ω|	lk|ω|	NOUN
ejpam-3903	172	3	1	1	NUM
ejpam-3903	172	4	β+1	β+1	PROPN
ejpam-3903	172	5	‖ρ−	‖ρ−	PROPN
ejpam-3903	172	6	+	+	CCONJ
ejpam-3903	172	7	l‖β	l‖β	ADJ
ejpam-3903	172	8	lβ+1	lβ+1	ADJ
ejpam-3903	172	9	,	,	PUNCT
ejpam-3903	172	10	(	(	PUNCT
ejpam-3903	172	11	19	19	NUM
ejpam-3903	172	12	)	)	PUNCT
ejpam-3903	172	13	|	|	ADV
ejpam-3903	172	14	∫	∫	PROPN
ejpam-3903	172	15	ω	ω	PROPN
ejpam-3903	172	16	ṽ∗(∇ρ)(ρ−	ṽ∗(∇ρ)(ρ−	PROPN
ejpam-3903	172	17	+	+	CCONJ
ejpam-3903	172	18	l)β|	l)β|	X
ejpam-3903	172	19	≤	≤	PUNCT
ejpam-3903	173	1	k	k	PROPN
ejpam-3903	173	2	∫	∫	PROPN
ejpam-3903	173	3	ω(∇(ρ−	ω(∇(ρ−	NOUN
ejpam-3903	174	1	+	+	CCONJ
ejpam-3903	174	2	l))(ρ−	l))(ρ−	NOUN
ejpam-3903	174	3	+	+	CCONJ
ejpam-3903	174	4	l	l	NOUN
ejpam-3903	174	5	)	)	PUNCT
ejpam-3903	174	6	β−1	β−1	SYM
ejpam-3903	174	7	2	2	NUM
ejpam-3903	174	8	(	(	PUNCT
ejpam-3903	174	9	ρ−	ρ−	NOUN
ejpam-3903	174	10	+	+	NUM
ejpam-3903	174	11	l	l	NOUN
ejpam-3903	174	12	)	)	PUNCT
ejpam-3903	174	13	β+1	β+1	PRON
ejpam-3903	174	14	2	2	NUM
ejpam-3903	174	15	≤	≤	NUM
ejpam-3903	174	16	εβ	εβ	PROPN
ejpam-3903	174	17	2	2	NUM
ejpam-3903	174	18	∫	∫	PROPN
ejpam-3903	174	19	ω	ω	NUM
ejpam-3903	174	20	|∇(ρ−	|∇(ρ−	PROPN
ejpam-3903	174	21	+	+	CCONJ
ejpam-3903	174	22	l)|2(ρ−	l)|2(ρ−	NOUN
ejpam-3903	174	23	+	+	CCONJ
ejpam-3903	174	24	l)β−1	l)β−1	PROPN
ejpam-3903	174	25	+	+	X
ejpam-3903	174	26	k2	k2	X
ejpam-3903	175	1	2εβ‖ρ	2εβ‖ρ	NUM
ejpam-3903	175	2	−	−	PROPN
ejpam-3903	176	1	+	+	CCONJ
ejpam-3903	176	2	l‖β+1	l‖β+1	ADJ
ejpam-3903	176	3	lβ+1	lβ+1	ADJ
ejpam-3903	176	4	.	.	PUNCT
ejpam-3903	177	1	(	(	PUNCT
ejpam-3903	177	2	20	20	NUM
ejpam-3903	177	3	)	)	PUNCT
ejpam-3903	177	4	using	use	VERB
ejpam-3903	177	5	inequalities	inequality	NOUN
ejpam-3903	177	6	(	(	PUNCT
ejpam-3903	177	7	18	18	NUM
ejpam-3903	177	8	)	)	PUNCT
ejpam-3903	177	9	to	to	ADP
ejpam-3903	177	10	(	(	PUNCT
ejpam-3903	177	11	20	20	NUM
ejpam-3903	177	12	)	)	PUNCT
ejpam-3903	177	13	into	into	ADP
ejpam-3903	177	14	(	(	PUNCT
ejpam-3903	177	15	17	17	NUM
ejpam-3903	177	16	)	)	PUNCT
ejpam-3903	177	17	and	and	CCONJ
ejpam-3903	177	18	h	h	NOUN
ejpam-3903	177	19	being	be	AUX
ejpam-3903	177	20	positive	positive	ADJ
ejpam-3903	177	21	we	we	PRON
ejpam-3903	177	22	get	get	VERB
ejpam-3903	177	23	:	:	PUNCT
ejpam-3903	177	24	−σ	−σ	NOUN
ejpam-3903	177	25	∫	∫	PROPN
ejpam-3903	177	26	ω	ω	NUM
ejpam-3903	177	27	ρ(ρ−	ρ(ρ−	PROPN
ejpam-3903	177	28	+	+	CCONJ
ejpam-3903	177	29	l)β	l)β	ADJ
ejpam-3903	177	30	≤	≤	NOUN
ejpam-3903	177	31	(	(	PUNCT
ejpam-3903	177	32	βk2	βk2	PRON
ejpam-3903	177	33	2ε	2ε	NOUN
ejpam-3903	177	34	+	+	CCONJ
ejpam-3903	177	35	k2	k2	PROPN
ejpam-3903	177	36	2εβ	2εβ	NOUN
ejpam-3903	178	1	+	+	PROPN
ejpam-3903	178	2	k	k	NOUN
ejpam-3903	178	3	)	)	PUNCT
ejpam-3903	178	4	‖ρ−	‖ρ−	PROPN
ejpam-3903	179	1	+	+	PUNCT
ejpam-3903	179	2	l‖β+1	l‖β+1	X
ejpam-3903	179	3	lβ+1	lβ+1	ADJ
ejpam-3903	179	4	+	+	X
ejpam-3903	179	5	2lk|ω|	2lk|ω|	NOUN
ejpam-3903	179	6	1	1	NUM
ejpam-3903	179	7	β+1	β+1	PROPN
ejpam-3903	179	8	‖ρ−	‖ρ−	PROPN
ejpam-3903	179	9	+	+	CCONJ
ejpam-3903	179	10	l‖β	l‖β	ADJ
ejpam-3903	179	11	lβ+1	lβ+1	ADJ
ejpam-3903	179	12	.	.	PUNCT
ejpam-3903	180	1	(	(	PUNCT
ejpam-3903	180	2	21	21	NUM
ejpam-3903	180	3	)	)	PUNCT
ejpam-3903	181	1	so	so	ADV
ejpam-3903	181	2	when	when	SCONJ
ejpam-3903	181	3	l	l	NOUN
ejpam-3903	181	4	−→	−→	NOUN
ejpam-3903	181	5	0	0	NUM
ejpam-3903	181	6	,	,	PUNCT
ejpam-3903	181	7	we	we	PRON
ejpam-3903	181	8	obtain	obtain	VERB
ejpam-3903	181	9	:(	:(	X
ejpam-3903	182	1	σ	σ	PROPN
ejpam-3903	182	2	−k2β	−k2β	NUM
ejpam-3903	182	3	2	2	NUM
ejpam-3903	182	4	+	+	SYM
ejpam-3903	182	5	1	1	NUM
ejpam-3903	182	6	2βε	2βε	ADJ
ejpam-3903	182	7	−k	−k	NOUN
ejpam-3903	182	8	)	)	PUNCT
ejpam-3903	183	1	‖ρ−‖β+1	‖ρ−‖β+1	ADJ
ejpam-3903	183	2	lβ+1	lβ+1	ADJ
ejpam-3903	183	3	≤	≤	NOUN
ejpam-3903	183	4	0	0	NUM
ejpam-3903	183	5	.	.	PUNCT
ejpam-3903	184	1	(	(	PUNCT
ejpam-3903	184	2	22	22	NUM
ejpam-3903	184	3	)	)	PUNCT
ejpam-3903	184	4	let	let	AUX
ejpam-3903	184	5	set	set	VERB
ejpam-3903	184	6	:	:	PUNCT
ejpam-3903	184	7	σ	σ	PROPN
ejpam-3903	184	8	−k2	−k2	PROPN
ejpam-3903	184	9	β2	β2	NOUN
ejpam-3903	184	10	+	+	NOUN
ejpam-3903	184	11	1	1	NUM
ejpam-3903	184	12	2βε	2βε	ADJ
ejpam-3903	184	13	−k	−k	NOUN
ejpam-3903	184	14	=	=	SYM
ejpam-3903	184	15	f(β	f(β	PROPN
ejpam-3903	184	16	)	)	PUNCT
ejpam-3903	184	17	2εβ	2εβ	NOUN
ejpam-3903	184	18	,	,	PUNCT
ejpam-3903	184	19	(	(	PUNCT
ejpam-3903	184	20	23	23	NUM
ejpam-3903	184	21	)	)	PUNCT
ejpam-3903	184	22	where	where	SCONJ
ejpam-3903	184	23	,	,	PUNCT
ejpam-3903	184	24	f(β	f(β	PROPN
ejpam-3903	184	25	)	)	PUNCT
ejpam-3903	184	26	=	=	PUNCT
ejpam-3903	185	1	−k2β2	−k2β2	PROPN
ejpam-3903	185	2	+	+	NUM
ejpam-3903	185	3	2εβ(σ	2εβ(σ	NUM
ejpam-3903	185	4	−k)−k2	−k)−k2	NOUN
ejpam-3903	185	5	.	.	PUNCT
ejpam-3903	186	1	since	since	SCONJ
ejpam-3903	186	2	σ	σ	PROPN
ejpam-3903	186	3	>	>	X
ejpam-3903	186	4	k2	k2	PROPN
ejpam-3903	186	5	ε	ε	PROPN
ejpam-3903	186	6	+	+	PROPN
ejpam-3903	186	7	k	k	PROPN
ejpam-3903	186	8	,	,	PUNCT
ejpam-3903	186	9	we	we	PRON
ejpam-3903	186	10	have	have	VERB
ejpam-3903	186	11	f	f	PROPN
ejpam-3903	186	12	′(β	′(β	PROPN
ejpam-3903	186	13	)	)	PUNCT
ejpam-3903	186	14	=	=	NOUN
ejpam-3903	187	1	−2k2β	−2k2β	NOUN
ejpam-3903	188	1	+	+	CCONJ
ejpam-3903	188	2	2ε(σ	2ε(σ	NUM
ejpam-3903	188	3	−k	−k	NOUN
ejpam-3903	188	4	)	)	PUNCT
ejpam-3903	188	5	is	be	AUX
ejpam-3903	188	6	strictly	strictly	ADV
ejpam-3903	188	7	positive	positive	ADJ
ejpam-3903	188	8	on	on	ADP
ejpam-3903	188	9	[	[	X
ejpam-3903	188	10	0	0	NUM
ejpam-3903	188	11	,	,	PUNCT
ejpam-3903	188	12	1	1	NUM
ejpam-3903	188	13	]	]	PUNCT
ejpam-3903	188	14	and	and	CCONJ
ejpam-3903	188	15	r.	r.	PROPN
ejpam-3903	188	16	bade	bade	PROPN
ejpam-3903	188	17	,	,	PUNCT
ejpam-3903	188	18	h.	h.	PROPN
ejpam-3903	188	19	chaker	chaker	PROPN
ejpam-3903	188	20	/	/	SYM
ejpam-3903	188	21	eur	eur	PROPN
ejpam-3903	188	22	.	.	PUNCT
ejpam-3903	189	1	j.	j.	PROPN
ejpam-3903	189	2	pure	pure	PROPN
ejpam-3903	189	3	appl	appl	PROPN
ejpam-3903	189	4	.	.	PROPN
ejpam-3903	189	5	math	math	PROPN
ejpam-3903	189	6	,	,	PUNCT
ejpam-3903	189	7	14	14	NUM
ejpam-3903	189	8	(	(	PUNCT
ejpam-3903	189	9	1	1	NUM
ejpam-3903	189	10	)	)	PUNCT
ejpam-3903	189	11	(	(	PUNCT
ejpam-3903	189	12	2021	2021	NUM
ejpam-3903	189	13	)	)	PUNCT
ejpam-3903	189	14	,	,	PUNCT
ejpam-3903	189	15	82	82	NUM
ejpam-3903	189	16	-	-	SYM
ejpam-3903	189	17	111	111	NUM
ejpam-3903	189	18	89	89	NUM
ejpam-3903	189	19	f(0	f(0	NOUN
ejpam-3903	189	20	)	)	PUNCT
ejpam-3903	189	21	=	=	PUNCT
ejpam-3903	190	1	−k2	−k2	X
ejpam-3903	190	2	<	<	X
ejpam-3903	190	3	0	0	NUM
ejpam-3903	190	4	,	,	PUNCT
ejpam-3903	190	5	f(1	f(1	PROPN
ejpam-3903	190	6	)	)	PUNCT
ejpam-3903	190	7	=	=	SYM
ejpam-3903	190	8	−2k2	−2k2	SYM
ejpam-3903	191	1	+	+	NUM
ejpam-3903	191	2	2ε(σ	2ε(σ	NUM
ejpam-3903	191	3	−	−	PROPN
ejpam-3903	191	4	k	k	NOUN
ejpam-3903	191	5	)	)	PUNCT
ejpam-3903	191	6	>	>	X
ejpam-3903	191	7	0	0	NUM
ejpam-3903	191	8	,	,	PUNCT
ejpam-3903	191	9	then	then	ADV
ejpam-3903	191	10	there	there	PRON
ejpam-3903	191	11	exist	exist	VERB
ejpam-3903	191	12	an	an	DET
ejpam-3903	191	13	unique	unique	ADJ
ejpam-3903	191	14	β1	β1	NOUN
ejpam-3903	191	15	∈]0	∈]0	NOUN
ejpam-3903	191	16	,	,	PUNCT
ejpam-3903	191	17	1	1	NUM
ejpam-3903	191	18	[	[	PUNCT
ejpam-3903	191	19	such	such	ADJ
ejpam-3903	191	20	as	as	ADP
ejpam-3903	191	21	f(β1	f(β1	NOUN
ejpam-3903	191	22	)	)	PUNCT
ejpam-3903	192	1	=	=	SYM
ejpam-3903	192	2	0	0	X
ejpam-3903	192	3	.	.	PUNCT
ejpam-3903	192	4	choosing	choose	VERB
ejpam-3903	192	5	β	β	NOUN
ejpam-3903	192	6	∈]β1	∈]β1	NOUN
ejpam-3903	192	7	,	,	PUNCT
ejpam-3903	192	8	1	1	NUM
ejpam-3903	192	9	[	[	X
ejpam-3903	192	10	,	,	PUNCT
ejpam-3903	192	11	we	we	PRON
ejpam-3903	192	12	have	have	VERB
ejpam-3903	192	13	σ	σ	NUM
ejpam-3903	192	14	−k2	−k2	PROPN
ejpam-3903	192	15	β2	β2	NOUN
ejpam-3903	192	16	+	+	NOUN
ejpam-3903	192	17	1	1	NUM
ejpam-3903	192	18	2βε	2βε	ADJ
ejpam-3903	192	19	−k	−k	NOUN
ejpam-3903	192	20	>	>	X
ejpam-3903	192	21	0	0	X
ejpam-3903	192	22	.	.	PUNCT
ejpam-3903	193	1	we	we	PRON
ejpam-3903	193	2	conclude	conclude	VERB
ejpam-3903	193	3	that	that	DET
ejpam-3903	193	4	ρ−	ρ−	NOUN
ejpam-3903	193	5	=	=	PUNCT
ejpam-3903	193	6	0	0	NUM
ejpam-3903	193	7	,	,	PUNCT
ejpam-3903	193	8	so	so	ADV
ejpam-3903	193	9	ρ	ρ	PROPN
ejpam-3903	193	10	>	>	X
ejpam-3903	193	11	0	0	PROPN
ejpam-3903	193	12	.	.	PUNCT
ejpam-3903	193	13	ii	ii	PROPN
ejpam-3903	193	14	):	):	PUNCT
ejpam-3903	193	15	by	by	ADP
ejpam-3903	193	16	setting	set	VERB
ejpam-3903	193	17	ρ̃	ρ̃	PROPN
ejpam-3903	193	18	=	=	SYM
ejpam-3903	193	19	ρ−	ρ−	NOUN
ejpam-3903	193	20	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	193	21	;	;	PUNCT
ejpam-3903	193	22	ρ̃	ρ̃	PROPN
ejpam-3903	193	23	is	be	AUX
ejpam-3903	193	24	then	then	ADV
ejpam-3903	193	25	solution	solution	NOUN
ejpam-3903	193	26	of:	of:	PUNCT
ejpam-3903	193	27	σρ̃+∇	σρ̃+∇	NOUN
ejpam-3903	193	28	·	·	PUNCT
ejpam-3903	193	29	(	(	PUNCT
ejpam-3903	193	30	ρṽ)−	ρṽ)−	PRON
ejpam-3903	193	31	ε4ρ̃	ε4ρ̃	NOUN
ejpam-3903	193	32	=	=	X
ejpam-3903	193	33	σ(h−	σ(h−	NOUN
ejpam-3903	193	34	ρ̄∞)−∇	ρ̄∞)−∇	NUM
ejpam-3903	193	35	·	·	PUNCT
ejpam-3903	193	36	(	(	PUNCT
ejpam-3903	193	37	ρṽ∗	ρṽ∗	NOUN
ejpam-3903	193	38	)	)	PUNCT
ejpam-3903	193	39	,	,	PUNCT
ejpam-3903	193	40	ε	ε	PROPN
ejpam-3903	193	41	∂ρ̃	∂ρ̃	PROPN
ejpam-3903	193	42	∂n	∂n	PROPN
ejpam-3903	193	43	=	=	SYM
ejpam-3903	193	44	0	0	NUM
ejpam-3903	193	45	,	,	PUNCT
ejpam-3903	193	46	ṽ	ṽ	PROPN
ejpam-3903	193	47	=	=	SYM
ejpam-3903	193	48	0	0	NUM
ejpam-3903	193	49	on	on	ADP
ejpam-3903	193	50	∂ω	∂ω	PROPN
ejpam-3903	193	51	.	.	PUNCT
ejpam-3903	194	1	(	(	PUNCT
ejpam-3903	194	2	24	24	NUM
ejpam-3903	194	3	)	)	PUNCT
ejpam-3903	194	4	we	we	PRON
ejpam-3903	194	5	use	use	VERB
ejpam-3903	194	6	the	the	DET
ejpam-3903	194	7	decomposition	decomposition	NOUN
ejpam-3903	194	8	(	(	PUNCT
ejpam-3903	194	9	9	9	NUM
ejpam-3903	194	10	)	)	PUNCT
ejpam-3903	194	11	and	and	CCONJ
ejpam-3903	194	12	(	(	PUNCT
ejpam-3903	194	13	10	10	NUM
ejpam-3903	194	14	)	)	PUNCT
ejpam-3903	194	15	.	.	PUNCT
ejpam-3903	195	1	so	so	ADV
ejpam-3903	195	2	multiplying	multiply	VERB
ejpam-3903	195	3	(	(	PUNCT
ejpam-3903	195	4	24	24	NUM
ejpam-3903	195	5	)	)	PUNCT
ejpam-3903	195	6	by	by	ADP
ejpam-3903	195	7	the	the	DET
ejpam-3903	195	8	test	test	NOUN
ejpam-3903	195	9	function	function	NOUN
ejpam-3903	195	10	η̃−	η̃−	NOUN
ejpam-3903	195	11	=	=	SYM
ejpam-3903	195	12	−(ρ̃−	−(ρ̃−	PROPN
ejpam-3903	195	13	+	+	PUNCT
ejpam-3903	195	14	l)β	l)β	PROPN
ejpam-3903	195	15	,	,	PUNCT
ejpam-3903	195	16	we	we	PRON
ejpam-3903	195	17	obtain	obtain	VERB
ejpam-3903	195	18	after	after	ADP
ejpam-3903	195	19	integration	integration	NOUN
ejpam-3903	195	20	by	by	ADP
ejpam-3903	195	21	parts	part	NOUN
ejpam-3903	195	22	:	:	PUNCT
ejpam-3903	195	23	−σ	−σ	NOUN
ejpam-3903	195	24	∫	∫	PROPN
ejpam-3903	195	25	ω	ω	PROPN
ejpam-3903	195	26	ρ̃(ρ̃−	ρ̃(ρ̃−	X
ejpam-3903	196	1	+	+	CCONJ
ejpam-3903	196	2	l)β	l)β	X
ejpam-3903	196	3	−	−	PROPN
ejpam-3903	196	4	ε	ε	PROPN
ejpam-3903	196	5	∫	∫	PROPN
ejpam-3903	196	6	ω	ω	PROPN
ejpam-3903	196	7	∇ρ̃∇(ρ̃−	∇ρ̃∇(ρ̃−	PROPN
ejpam-3903	197	1	+	+	CCONJ
ejpam-3903	197	2	l)β	l)β	X
ejpam-3903	197	3	+	+	CCONJ
ejpam-3903	197	4	σ	σ	NUM
ejpam-3903	197	5	∫	∫	PROPN
ejpam-3903	197	6	ω	ω	PROPN
ejpam-3903	197	7	(	(	PUNCT
ejpam-3903	197	8	h−	h−	PROPN
ejpam-3903	197	9	ρ̄∞)(ρ̃−	ρ̄∞)(ρ̃−	PROPN
ejpam-3903	197	10	+	+	NUM
ejpam-3903	197	11	l)β	l)β	X
ejpam-3903	197	12	=	=	PUNCT
ejpam-3903	197	13	−	−	PROPN
ejpam-3903	197	14	∫	∫	PROPN
ejpam-3903	197	15	ω	ω	PROPN
ejpam-3903	197	16	ρṽ∇(ρ̃−	ρṽ∇(ρ̃−	PROPN
ejpam-3903	197	17	+	+	CCONJ
ejpam-3903	197	18	l)β	l)β	X
ejpam-3903	197	19	+	+	CCONJ
ejpam-3903	197	20	∫	∫	PROPN
ejpam-3903	197	21	ω	ω	NUM
ejpam-3903	197	22	ρ(∇	ρ(∇	PROPN
ejpam-3903	197	23	·	·	PUNCT
ejpam-3903	197	24	ṽ∗)(ρ̃−	ṽ∗)(ρ̃−	PROPN
ejpam-3903	197	25	+	+	CCONJ
ejpam-3903	197	26	l)β	l)β	X
ejpam-3903	197	27	+	+	CCONJ
ejpam-3903	197	28	∫	∫	PROPN
ejpam-3903	197	29	ω	ω	PROPN
ejpam-3903	197	30	ṽ∗(∇ρ)(ρ̃−	ṽ∗(∇ρ)(ρ̃−	PROPN
ejpam-3903	197	31	+	+	X
ejpam-3903	197	32	l)β	l)β	X
ejpam-3903	197	33	(	(	PUNCT
ejpam-3903	197	34	25	25	NUM
ejpam-3903	197	35	)	)	PUNCT
ejpam-3903	197	36	by	by	ADP
ejpam-3903	197	37	taking	take	VERB
ejpam-3903	197	38	the	the	DET
ejpam-3903	197	39	modulus	modulus	NOUN
ejpam-3903	197	40	,	,	PUNCT
ejpam-3903	197	41	we	we	PRON
ejpam-3903	197	42	follow	follow	VERB
ejpam-3903	197	43	the	the	DET
ejpam-3903	197	44	same	same	ADJ
ejpam-3903	197	45	procedure	procedure	NOUN
ejpam-3903	197	46	as	as	ADP
ejpam-3903	197	47	above	above	ADV
ejpam-3903	197	48	to	to	PART
ejpam-3903	197	49	justify	justify	VERB
ejpam-3903	197	50	that	that	SCONJ
ejpam-3903	197	51	ρ̃−	ρ̃−	PROPN
ejpam-3903	197	52	=	=	SYM
ejpam-3903	197	53	0	0	X
ejpam-3903	197	54	.	.	PUNCT
ejpam-3903	198	1	this	this	PRON
ejpam-3903	198	2	allows	allow	VERB
ejpam-3903	198	3	us	we	PRON
ejpam-3903	198	4	to	to	PART
ejpam-3903	198	5	conclude	conclude	VERB
ejpam-3903	198	6	.	.	PUNCT
ejpam-3903	199	1	�	�	PROPN
ejpam-3903	199	2	4	4	NUM
ejpam-3903	199	3	.	.	X
ejpam-3903	199	4	hyperbolization	hyperbolization	NOUN
ejpam-3903	199	5	,	,	PUNCT
ejpam-3903	199	6	demonstration	demonstration	NOUN
ejpam-3903	199	7	of	of	ADP
ejpam-3903	199	8	the	the	DET
ejpam-3903	199	9	theorem	theorem	NOUN
ejpam-3903	199	10	1	1	NUM
ejpam-3903	199	11	the	the	DET
ejpam-3903	199	12	rewriting	rewriting	NOUN
ejpam-3903	199	13	of	of	ADP
ejpam-3903	199	14	the	the	DET
ejpam-3903	199	15	system	system	NOUN
ejpam-3903	199	16	(	(	PUNCT
ejpam-3903	199	17	3	3	NUM
ejpam-3903	199	18	)	)	PUNCT
ejpam-3903	199	19	in	in	ADP
ejpam-3903	199	20	hyperbolic	hyperbolic	ADJ
ejpam-3903	199	21	form	form	NOUN
ejpam-3903	199	22	was	be	AUX
ejpam-3903	199	23	presented	present	VERB
ejpam-3903	199	24	in	in	ADP
ejpam-3903	199	25	[	[	X
ejpam-3903	199	26	4	4	NUM
ejpam-3903	199	27	]	]	PUNCT
ejpam-3903	199	28	and	and	CCONJ
ejpam-3903	199	29	inspired	inspire	VERB
ejpam-3903	199	30	by	by	ADP
ejpam-3903	199	31	[	[	X
ejpam-3903	199	32	5	5	NUM
ejpam-3903	199	33	]	]	PUNCT
ejpam-3903	199	34	.	.	PUNCT
ejpam-3903	200	1	its	its	PRON
ejpam-3903	200	2	consist	consist	NOUN
ejpam-3903	200	3	to	to	PART
ejpam-3903	200	4	set	set	VERB
ejpam-3903	200	5	:	:	PUNCT
ejpam-3903	200	6	wε	wε	X
ejpam-3903	200	7	=	=	SYM
ejpam-3903	200	8	(	(	PUNCT
ejpam-3903	200	9	uε	uε	PROPN
ejpam-3903	200	10	,	,	PUNCT
ejpam-3903	200	11	d1uε	d1uε	PUNCT
ejpam-3903	200	12	,	,	PUNCT
ejpam-3903	200	13	d2uε	d2uε	X
ejpam-3903	200	14	,	,	PUNCT
ejpam-3903	200	15	d3uε	d3uε	NOUN
ejpam-3903	200	16	)	)	PUNCT
ejpam-3903	200	17	,	,	PUNCT
ejpam-3903	200	18	(	(	PUNCT
ejpam-3903	200	19	26	26	NUM
ejpam-3903	200	20	)	)	PUNCT
ejpam-3903	200	21	with	with	ADP
ejpam-3903	200	22	uε	uε	PROPN
ejpam-3903	200	23	=	=	SYM
ejpam-3903	200	24	(	(	PUNCT
ejpam-3903	200	25	ρε	ρε	PROPN
ejpam-3903	200	26	,	,	PUNCT
ejpam-3903	200	27	uε	uε	NOUN
ejpam-3903	200	28	,	,	PUNCT
ejpam-3903	200	29	θε	θε	NOUN
ejpam-3903	200	30	)	)	PUNCT
ejpam-3903	200	31	and	and	CCONJ
ejpam-3903	200	32	di	di	NOUN
ejpam-3903	200	33	=	=	SYM
ejpam-3903	200	34	∂	∂	NUM
ejpam-3903	200	35	∂xi	∂xi	NOUN
ejpam-3903	200	36	for	for	ADP
ejpam-3903	200	37	i	i	PROPN
ejpam-3903	200	38	=	=	SYM
ejpam-3903	200	39	1	1	NUM
ejpam-3903	200	40	,	,	PUNCT
ejpam-3903	200	41	2	2	NUM
ejpam-3903	200	42	,	,	PUNCT
ejpam-3903	200	43	3	3	NUM
ejpam-3903	200	44	.	.	PUNCT
ejpam-3903	200	45	(	(	PUNCT
ejpam-3903	200	46	27	27	NUM
ejpam-3903	200	47	)	)	PUNCT
ejpam-3903	200	48	let	let	AUX
ejpam-3903	200	49	set	set	VERB
ejpam-3903	200	50	α	α	NOUN
ejpam-3903	200	51	=	=	PUNCT
ejpam-3903	200	52	λ+	λ+	PUNCT
ejpam-3903	200	53	4	4	NUM
ejpam-3903	200	54	3	3	NUM
ejpam-3903	200	55	µ	µ	NOUN
ejpam-3903	200	56	,	,	PUNCT
ejpam-3903	200	57	β	β	X
ejpam-3903	200	58	=	=	PUNCT
ejpam-3903	200	59	λ+	λ+	PUNCT
ejpam-3903	200	60	µ	µ	X
ejpam-3903	200	61	3	3	NUM
ejpam-3903	200	62	and	and	CCONJ
ejpam-3903	200	63	δ	δ	PROPN
ejpam-3903	200	64	=	=	SYM
ejpam-3903	200	65	λ−	λ−	PROPN
ejpam-3903	200	66	2	2	NUM
ejpam-3903	200	67	3	3	NUM
ejpam-3903	200	68	µ.	µ.	NOUN
ejpam-3903	200	69	(	(	PUNCT
ejpam-3903	200	70	28	28	NUM
ejpam-3903	200	71	)	)	PUNCT
ejpam-3903	200	72	one	one	NOUN
ejpam-3903	200	73	can	can	AUX
ejpam-3903	200	74	found	find	VERB
ejpam-3903	200	75	in	in	ADP
ejpam-3903	200	76	[	[	X
ejpam-3903	200	77	4	4	X
ejpam-3903	200	78	]	]	PUNCT
ejpam-3903	200	79	the	the	DET
ejpam-3903	200	80	proof	proof	NOUN
ejpam-3903	200	81	of	of	ADP
ejpam-3903	200	82	the	the	DET
ejpam-3903	200	83	following	following	ADJ
ejpam-3903	200	84	result	result	NOUN
ejpam-3903	200	85	:	:	PUNCT
ejpam-3903	200	86	proposition	proposition	NOUN
ejpam-3903	200	87	1	1	NUM
ejpam-3903	200	88	.	.	PUNCT
ejpam-3903	201	1	(	(	PUNCT
ejpam-3903	201	2	[	[	X
ejpam-3903	201	3	4	4	NUM
ejpam-3903	201	4	]	]	PUNCT
ejpam-3903	201	5	)	)	PUNCT
ejpam-3903	201	6	under	under	ADP
ejpam-3903	201	7	assumption	assumption	NOUN
ejpam-3903	201	8	(	(	PUNCT
ejpam-3903	201	9	h1	h1	PROPN
ejpam-3903	201	10	)	)	PUNCT
ejpam-3903	201	11	and	and	CCONJ
ejpam-3903	201	12	using	use	VERB
ejpam-3903	201	13	the	the	DET
ejpam-3903	201	14	change	change	NOUN
ejpam-3903	201	15	of	of	ADP
ejpam-3903	201	16	variables	variable	NOUN
ejpam-3903	201	17	(	(	PUNCT
ejpam-3903	201	18	26)-(27	26)-(27	NUM
ejpam-3903	201	19	)	)	PUNCT
ejpam-3903	201	20	,	,	PUNCT
ejpam-3903	201	21	the	the	DET
ejpam-3903	201	22	system	system	NOUN
ejpam-3903	201	23	(	(	PUNCT
ejpam-3903	201	24	3	3	X
ejpam-3903	201	25	)	)	PUNCT
ejpam-3903	201	26	can	can	AUX
ejpam-3903	201	27	be	be	AUX
ejpam-3903	201	28	rewrite	rewrite	VERB
ejpam-3903	201	29	as:	as:	PROPN
ejpam-3903	201	30	a0(wε	a0(wε	NUM
ejpam-3903	201	31	)	)	PUNCT
ejpam-3903	201	32	∂wε	∂wε	PROPN
ejpam-3903	201	33	∂t	∂t	PROPN
ejpam-3903	202	1	+	+	CCONJ
ejpam-3903	202	2	3∑	3∑	PROPN
ejpam-3903	202	3	i=1	i=1	PROPN
ejpam-3903	202	4	aiε	aiε	ADJ
ejpam-3903	202	5	∂wε	∂wε	PROPN
ejpam-3903	202	6	∂xi	∂xi	NOUN
ejpam-3903	202	7	+	+	CCONJ
ejpam-3903	202	8	k(wε)wε	k(wε)wε	NOUN
ejpam-3903	202	9	=	=	SYM
ejpam-3903	202	10	f	f	NOUN
ejpam-3903	202	11	,	,	PUNCT
ejpam-3903	202	12	wε|t=0	wε|t=0	PROPN
ejpam-3903	202	13	=	=	SYM
ejpam-3903	202	14	(	(	PUNCT
ejpam-3903	202	15	ρ0	ρ0	PROPN
ejpam-3903	202	16	,	,	PUNCT
ejpam-3903	202	17	u0	u0	ADJ
ejpam-3903	202	18	,	,	PUNCT
ejpam-3903	202	19	θ0	θ0	PROPN
ejpam-3903	202	20	,	,	PUNCT
ejpam-3903	202	21	0	0	NUM
ejpam-3903	202	22	,	,	PUNCT
ejpam-3903	202	23	.	.	PUNCT
ejpam-3903	202	24	.	.	PUNCT
ejpam-3903	203	1	.	.	PUNCT
ejpam-3903	204	1	,	,	PUNCT
ejpam-3903	204	2	0	0	NUM
ejpam-3903	204	3	)	)	PUNCT
ejpam-3903	204	4	,	,	PUNCT
ejpam-3903	204	5	wε|∂ω	wε|∂ω	PROPN
ejpam-3903	204	6	=	=	PUNCT
ejpam-3903	204	7	(	(	PUNCT
ejpam-3903	204	8	0	0	NUM
ejpam-3903	204	9	,	,	PUNCT
ejpam-3903	204	10	ub	ub	PROPN
ejpam-3903	204	11	,	,	PUNCT
ejpam-3903	204	12	θb	θb	PROPN
ejpam-3903	204	13	,	,	PUNCT
ejpam-3903	204	14	0	0	NUM
ejpam-3903	204	15	,	,	PUNCT
ejpam-3903	204	16	.	.	PUNCT
ejpam-3903	204	17	.	.	PUNCT
ejpam-3903	204	18	.	.	PUNCT
ejpam-3903	205	1	,	,	PUNCT
ejpam-3903	205	2	0	0	NUM
ejpam-3903	205	3	)	)	PUNCT
ejpam-3903	205	4	,	,	PUNCT
ejpam-3903	205	5	(	(	PUNCT
ejpam-3903	205	6	(	(	PUNCT
ejpam-3903	205	7	wε)6n1	wε)6n1	ADJ
ejpam-3903	205	8	+	+	ADJ
ejpam-3903	205	9	(	(	PUNCT
ejpam-3903	205	10	wε)11n2	wε)11n2	PROPN
ejpam-3903	205	11	+	+	CCONJ
ejpam-3903	205	12	(	(	PUNCT
ejpam-3903	205	13	wε)16n3	wε)16n3	PROPN
ejpam-3903	205	14	)	)	PUNCT
ejpam-3903	206	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3903	206	2	∂ω	∂ω	ADJ
ejpam-3903	206	3	=	=	SYM
ejpam-3903	206	4	0	0	X
ejpam-3903	206	5	.	.	PUNCT
ejpam-3903	207	1	(	(	PUNCT
ejpam-3903	207	2	29	29	NUM
ejpam-3903	207	3	)	)	PUNCT
ejpam-3903	207	4	r.	r.	PROPN
ejpam-3903	207	5	bade	bade	PROPN
ejpam-3903	207	6	,	,	PUNCT
ejpam-3903	207	7	h.	h.	PROPN
ejpam-3903	207	8	chaker	chaker	PROPN
ejpam-3903	207	9	/	/	SYM
ejpam-3903	207	10	eur	eur	PROPN
ejpam-3903	207	11	.	.	PUNCT
ejpam-3903	208	1	j.	j.	PROPN
ejpam-3903	208	2	pure	pure	PROPN
ejpam-3903	208	3	appl	appl	PROPN
ejpam-3903	208	4	.	.	PROPN
ejpam-3903	208	5	math	math	PROPN
ejpam-3903	208	6	,	,	PUNCT
ejpam-3903	208	7	14	14	NUM
ejpam-3903	208	8	(	(	PUNCT
ejpam-3903	208	9	1	1	NUM
ejpam-3903	208	10	)	)	PUNCT
ejpam-3903	208	11	(	(	PUNCT
ejpam-3903	208	12	2021	2021	NUM
ejpam-3903	208	13	)	)	PUNCT
ejpam-3903	208	14	,	,	PUNCT
ejpam-3903	208	15	82	82	NUM
ejpam-3903	208	16	-	-	SYM
ejpam-3903	208	17	111	111	NUM
ejpam-3903	208	18	90	90	NUM
ejpam-3903	208	19	where	where	SCONJ
ejpam-3903	208	20	n	n	ADV
ejpam-3903	208	21	=	=	SYM
ejpam-3903	208	22	(	(	PUNCT
ejpam-3903	208	23	n1	n1	PROPN
ejpam-3903	208	24	,	,	PUNCT
ejpam-3903	208	25	n2	n2	ADJ
ejpam-3903	208	26	,	,	PUNCT
ejpam-3903	208	27	n3)t	n3)t	PROPN
ejpam-3903	208	28	is	be	AUX
ejpam-3903	208	29	the	the	DET
ejpam-3903	208	30	outward	outward	ADJ
ejpam-3903	208	31	normal	normal	ADJ
ejpam-3903	208	32	vector	vector	NOUN
ejpam-3903	208	33	,	,	PUNCT
ejpam-3903	208	34	a0(wε	a0(wε	NUM
ejpam-3903	208	35	)	)	PUNCT
ejpam-3903	208	36	,	,	PUNCT
ejpam-3903	208	37	aiε	aiε	PROPN
ejpam-3903	208	38	(	(	PUNCT
ejpam-3903	208	39	i=1	i=1	X
ejpam-3903	208	40	..	..	PUNCT
ejpam-3903	208	41	3	3	NUM
ejpam-3903	208	42	)	)	PUNCT
ejpam-3903	208	43	,	,	PUNCT
ejpam-3903	208	44	kε(wε	kε(wε	PROPN
ejpam-3903	208	45	)	)	PUNCT
ejpam-3903	208	46	are	be	AUX
ejpam-3903	208	47	matrix	matrix	NOUN
ejpam-3903	208	48	in	in	ADP
ejpam-3903	208	49	m20(r	m20(r	NOUN
ejpam-3903	208	50	)	)	PUNCT
ejpam-3903	208	51	and	and	CCONJ
ejpam-3903	208	52	kε(wε	kε(wε	PROPN
ejpam-3903	208	53	)	)	PUNCT
ejpam-3903	208	54	contains	contain	VERB
ejpam-3903	208	55	all	all	DET
ejpam-3903	208	56	non	non	ADJ
ejpam-3903	208	57	-	-	ADJ
ejpam-3903	208	58	linear	linear	ADJ
ejpam-3903	208	59	terms	term	NOUN
ejpam-3903	208	60	.	.	PUNCT
ejpam-3903	209	1	in	in	ADP
ejpam-3903	209	2	addition	addition	NOUN
ejpam-3903	209	3	there	there	PRON
ejpam-3903	209	4	exist	exist	VERB
ejpam-3903	209	5	a	a	DET
ejpam-3903	209	6	positive	positive	ADJ
ejpam-3903	209	7	definte	definte	NOUN
ejpam-3903	209	8	matrix	matrix	NOUN
ejpam-3903	209	9	s	s	PROPN
ejpam-3903	209	10	which	which	PRON
ejpam-3903	209	11	symmetrizes	symmetrize	VERB
ejpam-3903	209	12	the	the	DET
ejpam-3903	209	13	system	system	NOUN
ejpam-3903	209	14	(	(	PUNCT
ejpam-3903	209	15	29	29	NUM
ejpam-3903	209	16	)	)	PUNCT
ejpam-3903	209	17	.	.	PUNCT
ejpam-3903	210	1	the	the	DET
ejpam-3903	210	2	corresponding	corresponding	ADJ
ejpam-3903	210	3	boundary	boundary	ADJ
ejpam-3903	210	4	conditions	condition	NOUN
ejpam-3903	210	5	are	be	AUX
ejpam-3903	210	6	also	also	ADV
ejpam-3903	210	7	rewrite	rewrite	VERB
ejpam-3903	210	8	like	like	ADP
ejpam-3903	210	9	in	in	ADP
ejpam-3903	210	10	[	[	X
ejpam-3903	210	11	13	13	NUM
ejpam-3903	210	12	]	]	PUNCT
ejpam-3903	210	13	.	.	PUNCT
ejpam-3903	211	1	we	we	PRON
ejpam-3903	211	2	obtain:	obtain:	PROPN
ejpam-3903	211	3	(	(	PUNCT
ejpam-3903	211	4	sa0(wε	sa0(wε	PROPN
ejpam-3903	211	5	)	)	PUNCT
ejpam-3903	211	6	)	)	PUNCT
ejpam-3903	212	1	∂wε	∂wε	PROPN
ejpam-3903	212	2	∂t	∂t	PROPN
ejpam-3903	213	1	+	+	CCONJ
ejpam-3903	213	2	3∑	3∑	NUM
ejpam-3903	213	3	i=1	i=1	PROPN
ejpam-3903	213	4	(	(	PUNCT
ejpam-3903	213	5	saiε	saiε	NOUN
ejpam-3903	213	6	)	)	PUNCT
ejpam-3903	213	7	∂wε	∂wε	PROPN
ejpam-3903	213	8	∂xi	∂xi	NOUN
ejpam-3903	213	9	+	+	CCONJ
ejpam-3903	213	10	(	(	PUNCT
ejpam-3903	213	11	skε)(wε)wε	skε)(wε)wε	NOUN
ejpam-3903	213	12	=	=	SYM
ejpam-3903	213	13	sf	sf	PROPN
ejpam-3903	213	14	,	,	PUNCT
ejpam-3903	213	15	(	(	PUNCT
ejpam-3903	213	16	bε	bε	NOUN
ejpam-3903	213	17	−mε)wε	−mε)wε	X
ejpam-3903	213	18	=	=	SYM
ejpam-3903	213	19	g	g	NOUN
ejpam-3903	213	20	,	,	PUNCT
ejpam-3903	213	21	(	(	PUNCT
ejpam-3903	213	22	30	30	NUM
ejpam-3903	213	23	)	)	PUNCT
ejpam-3903	213	24	with	with	ADP
ejpam-3903	213	25	bε	bε	NOUN
ejpam-3903	213	26	=	=	PUNCT
ejpam-3903	213	27	3∑	3∑	NUM
ejpam-3903	213	28	i=1	i=1	PRON
ejpam-3903	213	29	ni(saiε	ni(saiε	PROPN
ejpam-3903	213	30	)	)	PUNCT
ejpam-3903	213	31	.	.	PUNCT
ejpam-3903	214	1	the	the	DET
ejpam-3903	214	2	matrix	matrix	NOUN
ejpam-3903	214	3	mε	mε	PROPN
ejpam-3903	214	4	∈	∈	PROPN
ejpam-3903	214	5	m20(r	m20(r	NOUN
ejpam-3903	214	6	)	)	PUNCT
ejpam-3903	214	7	and	and	CCONJ
ejpam-3903	214	8	the	the	DET
ejpam-3903	214	9	vector	vector	NOUN
ejpam-3903	214	10	g	g	PROPN
ejpam-3903	214	11	∈	∈	PROPN
ejpam-3903	214	12	r20	r20	NOUN
ejpam-3903	214	13	are	be	AUX
ejpam-3903	214	14	obtained	obtain	VERB
ejpam-3903	214	15	in	in	ADP
ejpam-3903	214	16	accordance	accordance	NOUN
ejpam-3903	214	17	with	with	ADP
ejpam-3903	214	18	the	the	DET
ejpam-3903	214	19	change	change	NOUN
ejpam-3903	214	20	of	of	ADP
ejpam-3903	214	21	variables	variable	NOUN
ejpam-3903	214	22	and	and	CCONJ
ejpam-3903	214	23	:	:	PUNCT
ejpam-3903	214	24	gi	gi	X
ejpam-3903	214	25	=	=	SYM
ejpam-3903	214	26	0	0	PROPN
ejpam-3903	215	1	for	for	ADP
ejpam-3903	215	2	i	i	PRON
ejpam-3903	215	3	=	=	SYM
ejpam-3903	215	4	1	1	NUM
ejpam-3903	215	5	,	,	PUNCT
ejpam-3903	215	6	6	6	NUM
ejpam-3903	215	7	,	,	PUNCT
ejpam-3903	215	8	g11	g11	NOUN
ejpam-3903	215	9	=	=	SYM
ejpam-3903	215	10	g16	g16	PROPN
ejpam-3903	215	11	=	=	SYM
ejpam-3903	215	12	0	0	PROPN
ejpam-3903	215	13	,	,	PUNCT
ejpam-3903	215	14	g7	g7	PROPN
ejpam-3903	215	15	=	=	SYM
ejpam-3903	215	16	−2(αn1u	−2(αn1u	PROPN
ejpam-3903	215	17	1	1	NUM
ejpam-3903	215	18	b	b	X
ejpam-3903	215	19	+	+	CCONJ
ejpam-3903	215	20	βn2u	βn2u	PROPN
ejpam-3903	215	21	2	2	NUM
ejpam-3903	215	22	b	b	NOUN
ejpam-3903	215	23	+	+	CCONJ
ejpam-3903	215	24	βn3u	βn3u	PROPN
ejpam-3903	215	25	3	3	NUM
ejpam-3903	215	26	b	b	NOUN
ejpam-3903	215	27	)	)	PUNCT
ejpam-3903	215	28	,	,	PUNCT
ejpam-3903	215	29	g8	g8	PROPN
ejpam-3903	215	30	=	=	SYM
ejpam-3903	215	31	−2µn1u	−2µn1u	PROPN
ejpam-3903	215	32	2	2	NUM
ejpam-3903	215	33	b	b	NOUN
ejpam-3903	215	34	,	,	PUNCT
ejpam-3903	215	35	g9	g9	PROPN
ejpam-3903	215	36	=	=	SYM
ejpam-3903	215	37	−2µn1u	−2µn1u	PROPN
ejpam-3903	215	38	3	3	NUM
ejpam-3903	215	39	b	b	PROPN
ejpam-3903	215	40	,	,	PUNCT
ejpam-3903	215	41	g10	g10	PROPN
ejpam-3903	215	42	=	=	SYM
ejpam-3903	215	43	−2kn1θb	−2kn1θb	PROPN
ejpam-3903	215	44	,	,	PUNCT
ejpam-3903	215	45	g12	g12	PROPN
ejpam-3903	215	46	=	=	SYM
ejpam-3903	215	47	−2µn2u	−2µn2u	PROPN
ejpam-3903	215	48	1	1	NUM
ejpam-3903	215	49	b	b	PROPN
ejpam-3903	215	50	,	,	PUNCT
ejpam-3903	215	51	g13	g13	PROPN
ejpam-3903	215	52	=	=	SYM
ejpam-3903	215	53	−2(βn1u	−2(βn1u	PROPN
ejpam-3903	215	54	1	1	NUM
ejpam-3903	215	55	b	b	PROPN
ejpam-3903	215	56	+	+	CCONJ
ejpam-3903	215	57	αn2u	αn2u	PROPN
ejpam-3903	215	58	2	2	NUM
ejpam-3903	215	59	b	b	NOUN
ejpam-3903	215	60	+	+	CCONJ
ejpam-3903	215	61	βn3u	βn3u	PROPN
ejpam-3903	215	62	3	3	NUM
ejpam-3903	215	63	b	b	NOUN
ejpam-3903	215	64	)	)	PUNCT
ejpam-3903	215	65	,	,	PUNCT
ejpam-3903	215	66	g14	g14	X
ejpam-3903	215	67	=	=	SYM
ejpam-3903	215	68	−2µn2u	−2µn2u	PROPN
ejpam-3903	215	69	3	3	NUM
ejpam-3903	215	70	b	b	NOUN
ejpam-3903	215	71	,	,	PUNCT
ejpam-3903	215	72	g15	g15	PROPN
ejpam-3903	215	73	=	=	SYM
ejpam-3903	215	74	−2kn2θb	−2kn2θb	NOUN
ejpam-3903	215	75	,	,	PUNCT
ejpam-3903	215	76	g17	g17	NOUN
ejpam-3903	215	77	=	=	SYM
ejpam-3903	216	1	−2µn3u	−2µn3u	PROPN
ejpam-3903	216	2	1	1	NUM
ejpam-3903	216	3	b	b	NOUN
ejpam-3903	216	4	,	,	PUNCT
ejpam-3903	216	5	g18	g18	PROPN
ejpam-3903	216	6	=	=	PUNCT
ejpam-3903	217	1	−2µn3u	−2µn3u	PROPN
ejpam-3903	217	2	2	2	NUM
ejpam-3903	217	3	b	b	NOUN
ejpam-3903	217	4	,	,	PUNCT
ejpam-3903	217	5	g19	g19	PROPN
ejpam-3903	217	6	=	=	SYM
ejpam-3903	217	7	−2(βn1u	−2(βn1u	PROPN
ejpam-3903	217	8	1	1	NUM
ejpam-3903	217	9	b	b	PROPN
ejpam-3903	217	10	+	+	CCONJ
ejpam-3903	217	11	βn2u	βn2u	PROPN
ejpam-3903	217	12	2	2	NUM
ejpam-3903	217	13	b	b	NOUN
ejpam-3903	217	14	+	+	SYM
ejpam-3903	217	15	αn3u	αn3u	PROPN
ejpam-3903	217	16	3	3	NUM
ejpam-3903	217	17	b	b	NOUN
ejpam-3903	217	18	)	)	PUNCT
ejpam-3903	217	19	,	,	PUNCT
ejpam-3903	217	20	g20	g20	NOUN
ejpam-3903	217	21	=	=	NOUN
ejpam-3903	217	22	−2kn3θb	−2kn3θb	NOUN
ejpam-3903	217	23	.	.	PUNCT
ejpam-3903	218	1	notation	notation	NOUN
ejpam-3903	218	2	:	:	PUNCT
ejpam-3903	218	3	for	for	ADP
ejpam-3903	218	4	simplicity	simplicity	NOUN
ejpam-3903	218	5	,	,	PUNCT
ejpam-3903	218	6	in	in	ADP
ejpam-3903	218	7	all	all	DET
ejpam-3903	218	8	the	the	DET
ejpam-3903	218	9	following	following	NOUN
ejpam-3903	218	10	we	we	PRON
ejpam-3903	218	11	will	will	AUX
ejpam-3903	218	12	denote	denote	VERB
ejpam-3903	218	13	by	by	ADP
ejpam-3903	218	14	:	:	PUNCT
ejpam-3903	218	15	1	1	NUM
ejpam-3903	218	16	)	)	PUNCT
ejpam-3903	218	17	(	(	PUNCT
ejpam-3903	218	18	sa0(w	sa0(w	NOUN
ejpam-3903	218	19	)	)	PUNCT
ejpam-3903	218	20	)	)	PUNCT
ejpam-3903	219	1	=	=	SYM
ejpam-3903	219	2	a0(w	a0(w	PROPN
ejpam-3903	219	3	)	)	PUNCT
ejpam-3903	219	4	,	,	PUNCT
ejpam-3903	219	5	(	(	PUNCT
ejpam-3903	219	6	saiε	saiε	NOUN
ejpam-3903	219	7	)	)	PUNCT
ejpam-3903	219	8	=	=	VERB
ejpam-3903	220	1	aiε	aiε	ADJ
ejpam-3903	220	2	,	,	PUNCT
ejpam-3903	220	3	(	(	PUNCT
ejpam-3903	220	4	skε	skε	NOUN
ejpam-3903	220	5	)	)	PUNCT
ejpam-3903	220	6	=	=	SYM
ejpam-3903	220	7	kε	kε	PROPN
ejpam-3903	220	8	2	2	NUM
ejpam-3903	220	9	)	)	PUNCT
ejpam-3903	220	10	a0	a0	NOUN
ejpam-3903	220	11	=	=	SYM
ejpam-3903	220	12	(	(	PUNCT
ejpam-3903	220	13	id5	id5	VERB
ejpam-3903	220	14	0	0	NUM
ejpam-3903	220	15	0	0	NUM
ejpam-3903	220	16	0	0	NUM
ejpam-3903	220	17	)	)	PUNCT
ejpam-3903	220	18	,	,	PUNCT
ejpam-3903	220	19	id5	id5	X
ejpam-3903	220	20	is	be	AUX
ejpam-3903	220	21	an	an	DET
ejpam-3903	220	22	identity	identity	NOUN
ejpam-3903	220	23	matrix	matrix	NOUN
ejpam-3903	220	24	in	in	ADP
ejpam-3903	220	25	m5(r	m5(r	PROPN
ejpam-3903	220	26	)	)	PUNCT
ejpam-3903	220	27	.	.	PUNCT
ejpam-3903	221	1	before	before	SCONJ
ejpam-3903	221	2	we	we	PRON
ejpam-3903	221	3	present	present	VERB
ejpam-3903	221	4	our	our	PRON
ejpam-3903	221	5	approach	approach	NOUN
ejpam-3903	221	6	for	for	ADP
ejpam-3903	221	7	the	the	DET
ejpam-3903	221	8	construction	construction	NOUN
ejpam-3903	221	9	of	of	ADP
ejpam-3903	221	10	the	the	DET
ejpam-3903	221	11	weak	weak	ADJ
ejpam-3903	221	12	solution	solution	NOUN
ejpam-3903	221	13	for	for	ADP
ejpam-3903	221	14	the	the	DET
ejpam-3903	221	15	system	system	NOUN
ejpam-3903	221	16	(	(	PUNCT
ejpam-3903	221	17	30	30	NUM
ejpam-3903	221	18	)	)	PUNCT
ejpam-3903	221	19	,	,	PUNCT
ejpam-3903	221	20	note	note	VERB
ejpam-3903	221	21	that	that	SCONJ
ejpam-3903	221	22	by	by	ADP
ejpam-3903	221	23	the	the	DET
ejpam-3903	221	24	assumption	assumption	NOUN
ejpam-3903	221	25	(	(	PUNCT
ejpam-3903	221	26	h2	h2	NOUN
ejpam-3903	221	27	)	)	PUNCT
ejpam-3903	221	28	we	we	PRON
ejpam-3903	221	29	have	have	VERB
ejpam-3903	221	30	g	g	PROPN
ejpam-3903	221	31	∈w1,∞(0	∈w1,∞(0	PROPN
ejpam-3903	221	32	,	,	PUNCT
ejpam-3903	221	33	t	t	PROPN
ejpam-3903	221	34	;	;	PUNCT
ejpam-3903	221	35	hs+	hs+	VERB
ejpam-3903	221	36	3	3	NUM
ejpam-3903	221	37	2	2	NUM
ejpam-3903	221	38	(	(	PUNCT
ejpam-3903	221	39	∂ω))20	∂ω))20	NOUN
ejpam-3903	221	40	,	,	PUNCT
ejpam-3903	221	41	and	and	CCONJ
ejpam-3903	221	42	by	by	ADP
ejpam-3903	221	43	the	the	DET
ejpam-3903	221	44	trace	trace	NOUN
ejpam-3903	221	45	theorem	theorem	NOUN
ejpam-3903	221	46	(	(	PUNCT
ejpam-3903	221	47	see	see	VERB
ejpam-3903	221	48	[	[	X
ejpam-3903	221	49	15	15	NUM
ejpam-3903	221	50	]	]	NUM
ejpam-3903	221	51	)	)	PUNCT
ejpam-3903	221	52	,	,	PUNCT
ejpam-3903	221	53	for	for	ADP
ejpam-3903	221	54	ub	ub	PROPN
ejpam-3903	221	55	∈w1,∞(0	∈w1,∞(0	PROPN
ejpam-3903	221	56	,	,	PUNCT
ejpam-3903	221	57	t	t	PROPN
ejpam-3903	221	58	;	;	PUNCT
ejpam-3903	221	59	hs+	hs+	VERB
ejpam-3903	221	60	3	3	NUM
ejpam-3903	221	61	2	2	NUM
ejpam-3903	221	62	(	(	PUNCT
ejpam-3903	221	63	∂ω)3	∂ω)3	NOUN
ejpam-3903	221	64	)	)	PUNCT
ejpam-3903	221	65	and	and	CCONJ
ejpam-3903	221	66	θb	θb	ADP
ejpam-3903	221	67	∈w1,∞(0	∈w1,∞(0	PROPN
ejpam-3903	221	68	,	,	PUNCT
ejpam-3903	221	69	t	t	PROPN
ejpam-3903	221	70	;	;	PUNCT
ejpam-3903	221	71	hs+	hs+	VERB
ejpam-3903	221	72	3	3	NUM
ejpam-3903	221	73	2	2	NUM
ejpam-3903	221	74	(	(	PUNCT
ejpam-3903	221	75	∂ω	∂ω	PROPN
ejpam-3903	221	76	)	)	PUNCT
ejpam-3903	221	77	)	)	PUNCT
ejpam-3903	222	1	there	there	PRON
ejpam-3903	222	2	exist	exist	VERB
ejpam-3903	222	3	(	(	PUNCT
ejpam-3903	222	4	wg	wg	PROPN
ejpam-3903	222	5	)	)	PUNCT
ejpam-3903	222	6	2	2	NUM
ejpam-3903	222	7	,	,	PUNCT
ejpam-3903	222	8	(	(	PUNCT
ejpam-3903	222	9	wg	wg	PROPN
ejpam-3903	222	10	)	)	PUNCT
ejpam-3903	222	11	3	3	NUM
ejpam-3903	222	12	,	,	PUNCT
ejpam-3903	222	13	(	(	PUNCT
ejpam-3903	222	14	wg	wg	PROPN
ejpam-3903	222	15	)	)	PUNCT
ejpam-3903	222	16	4	4	NUM
ejpam-3903	222	17	,	,	PUNCT
ejpam-3903	222	18	(	(	PUNCT
ejpam-3903	222	19	wg	wg	PROPN
ejpam-3903	222	20	)	)	PUNCT
ejpam-3903	222	21	5	5	NUM
ejpam-3903	222	22	in	in	ADP
ejpam-3903	222	23	w1,∞(0	w1,∞(0	PROPN
ejpam-3903	222	24	,	,	PUNCT
ejpam-3903	222	25	t	t	PROPN
ejpam-3903	222	26	;	;	PUNCT
ejpam-3903	222	27	hs+2(ω	hs+2(ω	ADV
ejpam-3903	222	28	)	)	PUNCT
ejpam-3903	222	29	)	)	PUNCT
ejpam-3903	222	30	such	such	ADJ
ejpam-3903	222	31	as	as	ADP
ejpam-3903	222	32	:	:	PUNCT
ejpam-3903	222	33	(	(	PUNCT
ejpam-3903	222	34	wg	wg	PROPN
ejpam-3903	222	35	)	)	PUNCT
ejpam-3903	222	36	2|∂ω	2|∂ω	NUM
ejpam-3903	222	37	=	=	PUNCT
ejpam-3903	222	38	u1	u1	PROPN
ejpam-3903	222	39	b	b	PROPN
ejpam-3903	222	40	,	,	PUNCT
ejpam-3903	222	41	(	(	PUNCT
ejpam-3903	222	42	wg	wg	PROPN
ejpam-3903	222	43	)	)	PUNCT
ejpam-3903	222	44	3|∂ω	3|∂ω	NUM
ejpam-3903	223	1	=	=	PUNCT
ejpam-3903	223	2	u2	u2	PROPN
ejpam-3903	223	3	b	b	PROPN
ejpam-3903	223	4	,	,	PUNCT
ejpam-3903	223	5	(	(	PUNCT
ejpam-3903	223	6	wg	wg	PROPN
ejpam-3903	223	7	)	)	PUNCT
ejpam-3903	223	8	4|∂ω	4|∂ω	NUM
ejpam-3903	224	1	=	=	SYM
ejpam-3903	224	2	u3	u3	PROPN
ejpam-3903	224	3	b	b	PROPN
ejpam-3903	224	4	,	,	PUNCT
ejpam-3903	224	5	(	(	PUNCT
ejpam-3903	224	6	wg	wg	PROPN
ejpam-3903	224	7	)	)	PUNCT
ejpam-3903	224	8	5|∂ω	5|∂ω	PROPN
ejpam-3903	224	9	=	=	SYM
ejpam-3903	224	10	θb	θb	X
ejpam-3903	224	11	.	.	PUNCT
ejpam-3903	225	1	setting	set	VERB
ejpam-3903	225	2	:	:	PUNCT
ejpam-3903	225	3	zg	zg	PROPN
ejpam-3903	225	4	=	=	SYM
ejpam-3903	225	5	(	(	PUNCT
ejpam-3903	225	6	0	0	NUM
ejpam-3903	225	7	,	,	PUNCT
ejpam-3903	225	8	(	(	PUNCT
ejpam-3903	225	9	wg	wg	PROPN
ejpam-3903	225	10	)	)	PUNCT
ejpam-3903	225	11	2	2	NUM
ejpam-3903	225	12	,	,	PUNCT
ejpam-3903	225	13	(	(	PUNCT
ejpam-3903	225	14	wg	wg	PROPN
ejpam-3903	225	15	)	)	PUNCT
ejpam-3903	225	16	3	3	NUM
ejpam-3903	225	17	,	,	PUNCT
ejpam-3903	225	18	(	(	PUNCT
ejpam-3903	225	19	wg	wg	PROPN
ejpam-3903	225	20	)	)	PUNCT
ejpam-3903	225	21	4	4	NUM
ejpam-3903	225	22	,	,	PUNCT
ejpam-3903	225	23	(	(	PUNCT
ejpam-3903	225	24	wg	wg	PROPN
ejpam-3903	225	25	)	)	PUNCT
ejpam-3903	225	26	5	5	NUM
ejpam-3903	225	27	)	)	PUNCT
ejpam-3903	225	28	,	,	PUNCT
ejpam-3903	225	29	we	we	PRON
ejpam-3903	225	30	obtain	obtain	VERB
ejpam-3903	225	31	:	:	PUNCT
ejpam-3903	225	32	wg	wg	PROPN
ejpam-3903	226	1	=	=	PUNCT
ejpam-3903	227	1	(	(	PUNCT
ejpam-3903	227	2	zg	zg	PROPN
ejpam-3903	227	3	,	,	PUNCT
ejpam-3903	227	4	d1z	d1z	ADP
ejpam-3903	227	5	g	g	NOUN
ejpam-3903	227	6	,	,	PUNCT
ejpam-3903	227	7	d2z	d2z	X
ejpam-3903	227	8	g	g	NOUN
ejpam-3903	227	9	,	,	PUNCT
ejpam-3903	227	10	d3z	d3z	NOUN
ejpam-3903	227	11	g	g	NOUN
ejpam-3903	227	12	)	)	PUNCT
ejpam-3903	227	13	∈	∈	PROPN
ejpam-3903	227	14	l∞(0	l∞(0	PROPN
ejpam-3903	227	15	,	,	PUNCT
ejpam-3903	227	16	t	t	PROPN
ejpam-3903	227	17	;	;	PUNCT
ejpam-3903	227	18	hs+1(ω)20	hs+1(ω)20	X
ejpam-3903	227	19	)	)	PUNCT
ejpam-3903	227	20	(	(	PUNCT
ejpam-3903	227	21	31	31	NUM
ejpam-3903	227	22	)	)	PUNCT
ejpam-3903	227	23	r.	r.	PROPN
ejpam-3903	227	24	bade	bade	PROPN
ejpam-3903	227	25	,	,	PUNCT
ejpam-3903	227	26	h.	h.	PROPN
ejpam-3903	227	27	chaker	chaker	PROPN
ejpam-3903	227	28	/	/	SYM
ejpam-3903	227	29	eur	eur	PROPN
ejpam-3903	227	30	.	.	PUNCT
ejpam-3903	228	1	j.	j.	PROPN
ejpam-3903	228	2	pure	pure	PROPN
ejpam-3903	228	3	appl	appl	PROPN
ejpam-3903	228	4	.	.	PROPN
ejpam-3903	228	5	math	math	PROPN
ejpam-3903	228	6	,	,	PUNCT
ejpam-3903	228	7	14	14	NUM
ejpam-3903	228	8	(	(	PUNCT
ejpam-3903	228	9	1	1	NUM
ejpam-3903	228	10	)	)	PUNCT
ejpam-3903	228	11	(	(	PUNCT
ejpam-3903	228	12	2021	2021	NUM
ejpam-3903	228	13	)	)	PUNCT
ejpam-3903	228	14	,	,	PUNCT
ejpam-3903	228	15	82	82	NUM
ejpam-3903	228	16	-	-	SYM
ejpam-3903	228	17	111	111	NUM
ejpam-3903	228	18	91	91	NUM
ejpam-3903	228	19	4.1	4.1	NUM
ejpam-3903	228	20	.	.	PUNCT
ejpam-3903	229	1	construction	construction	NOUN
ejpam-3903	229	2	of	of	ADP
ejpam-3903	229	3	successive	successive	ADJ
ejpam-3903	229	4	approximations	approximation	NOUN
ejpam-3903	229	5	for	for	ADP
ejpam-3903	229	6	the	the	DET
ejpam-3903	229	7	existence	existence	NOUN
ejpam-3903	229	8	study	study	NOUN
ejpam-3903	229	9	of	of	ADP
ejpam-3903	229	10	a	a	DET
ejpam-3903	229	11	weak	weak	ADJ
ejpam-3903	229	12	solution	solution	NOUN
ejpam-3903	229	13	of	of	ADP
ejpam-3903	229	14	the	the	DET
ejpam-3903	229	15	system	system	NOUN
ejpam-3903	229	16	(	(	PUNCT
ejpam-3903	229	17	30	30	NUM
ejpam-3903	229	18	)	)	PUNCT
ejpam-3903	229	19	,	,	PUNCT
ejpam-3903	229	20	we	we	PRON
ejpam-3903	229	21	use	use	VERB
ejpam-3903	229	22	a	a	DET
ejpam-3903	229	23	process	process	NOUN
ejpam-3903	229	24	of	of	ADP
ejpam-3903	229	25	successive	successive	ADJ
ejpam-3903	229	26	construction	construction	NOUN
ejpam-3903	229	27	of	of	ADP
ejpam-3903	229	28	a	a	DET
ejpam-3903	229	29	solution	solution	NOUN
ejpam-3903	229	30	.	.	PUNCT
ejpam-3903	230	1	one	one	PRON
ejpam-3903	230	2	can	can	AUX
ejpam-3903	230	3	found	find	VERB
ejpam-3903	230	4	the	the	DET
ejpam-3903	230	5	used	use	VERB
ejpam-3903	230	6	of	of	ADP
ejpam-3903	230	7	this	this	DET
ejpam-3903	230	8	approach	approach	NOUN
ejpam-3903	230	9	in	in	ADP
ejpam-3903	230	10	[	[	X
ejpam-3903	230	11	5	5	NUM
ejpam-3903	230	12	,	,	PUNCT
ejpam-3903	230	13	21	21	NUM
ejpam-3903	230	14	]	]	PUNCT
ejpam-3903	230	15	,	,	PUNCT
ejpam-3903	230	16	or	or	CCONJ
ejpam-3903	230	17	in	in	ADP
ejpam-3903	230	18	the	the	DET
ejpam-3903	230	19	continuous	continuous	ADJ
ejpam-3903	230	20	version	version	NOUN
ejpam-3903	230	21	in	in	ADP
ejpam-3903	230	22	[	[	X
ejpam-3903	230	23	22	22	NUM
ejpam-3903	230	24	]	]	PUNCT
ejpam-3903	230	25	.	.	PUNCT
ejpam-3903	231	1	thus	thus	ADV
ejpam-3903	231	2	in	in	ADP
ejpam-3903	231	3	the	the	DET
ejpam-3903	231	4	first	first	ADJ
ejpam-3903	231	5	step	step	NOUN
ejpam-3903	231	6	,	,	PUNCT
ejpam-3903	231	7	we	we	PRON
ejpam-3903	231	8	perform	perform	VERB
ejpam-3903	231	9	a	a	DET
ejpam-3903	231	10	implicite	implicite	NOUN
ejpam-3903	231	11	semidiscretization	semidiscretization	NOUN
ejpam-3903	231	12	in	in	ADP
ejpam-3903	231	13	time	time	NOUN
ejpam-3903	231	14	.	.	PUNCT
ejpam-3903	232	1	so	so	ADV
ejpam-3903	232	2	,	,	PUNCT
ejpam-3903	232	3	let	let	VERB
ejpam-3903	232	4	n	n	PRON
ejpam-3903	232	5	be	be	AUX
ejpam-3903	232	6	a	a	DET
ejpam-3903	232	7	given	give	VERB
ejpam-3903	232	8	integer	integer	NOUN
ejpam-3903	232	9	,	,	PUNCT
ejpam-3903	232	10	we	we	PRON
ejpam-3903	232	11	subdivide	subdivide	VERB
ejpam-3903	232	12	[	[	X
ejpam-3903	232	13	0	0	NUM
ejpam-3903	232	14	,	,	PUNCT
ejpam-3903	232	15	t	t	NOUN
ejpam-3903	232	16	]	]	PUNCT
ejpam-3903	232	17	into	into	ADP
ejpam-3903	232	18	n	n	PROPN
ejpam-3903	232	19	intervals	interval	NOUN
ejpam-3903	232	20	with	with	ADP
ejpam-3903	232	21	the	the	DET
ejpam-3903	232	22	time	time	NOUN
ejpam-3903	232	23	step	step	NOUN
ejpam-3903	232	24	is	be	AUX
ejpam-3903	232	25	4	4	NUM
ejpam-3903	232	26	t	t	NOUN
ejpam-3903	232	27	=	=	SYM
ejpam-3903	232	28	t	t	PROPN
ejpam-3903	232	29	n	n	NOUN
ejpam-3903	232	30	,	,	PUNCT
ejpam-3903	232	31	we	we	PRON
ejpam-3903	232	32	denote	denote	VERB
ejpam-3903	232	33	wn(x	wn(x	NOUN
ejpam-3903	232	34	)	)	PUNCT
ejpam-3903	232	35	=	=	SYM
ejpam-3903	232	36	w(tn	w(tn	PROPN
ejpam-3903	232	37	,	,	PUNCT
ejpam-3903	232	38	x	x	NOUN
ejpam-3903	232	39	)	)	PUNCT
ejpam-3903	232	40	.	.	PUNCT
ejpam-3903	233	1	the	the	DET
ejpam-3903	233	2	essential	essential	ADJ
ejpam-3903	233	3	idea	idea	NOUN
ejpam-3903	233	4	of	of	ADP
ejpam-3903	233	5	our	our	PRON
ejpam-3903	233	6	study	study	NOUN
ejpam-3903	233	7	is	be	AUX
ejpam-3903	233	8	based	base	VERB
ejpam-3903	233	9	on	on	ADP
ejpam-3903	233	10	use	use	NOUN
ejpam-3903	233	11	of	of	ADP
ejpam-3903	233	12	the	the	DET
ejpam-3903	233	13	following	follow	VERB
ejpam-3903	233	14	algorithm	algorithm	NOUN
ejpam-3903	233	15	:	:	PUNCT
ejpam-3903	233	16	•	•	NUM
ejpam-3903	233	17	initialization	initialization	NOUN
ejpam-3903	233	18	:	:	PUNCT
ejpam-3903	233	19	wn	wn	PROPN
ejpam-3903	233	20	=	=	PUNCT
ejpam-3903	233	21	w0	w0	PROPN
ejpam-3903	233	22	•	•	NUM
ejpam-3903	233	23	by	by	ADP
ejpam-3903	233	24	using	use	VERB
ejpam-3903	233	25	the	the	DET
ejpam-3903	233	26	semi	semi	ADJ
ejpam-3903	233	27	-	-	NOUN
ejpam-3903	233	28	discretization	discretization	NOUN
ejpam-3903	233	29	in	in	ADP
ejpam-3903	233	30	time	time	NOUN
ejpam-3903	233	31	of	of	ADP
ejpam-3903	233	32	the	the	DET
ejpam-3903	233	33	system	system	NOUN
ejpam-3903	233	34	(	(	PUNCT
ejpam-3903	233	35	30	30	NUM
ejpam-3903	233	36	)	)	PUNCT
ejpam-3903	233	37	,	,	PUNCT
ejpam-3903	233	38	we	we	PRON
ejpam-3903	233	39	construct	construct	VERB
ejpam-3903	233	40	the	the	DET
ejpam-3903	233	41	sequence	sequence	NOUN
ejpam-3903	233	42	wn+1	wn+1	NOUN
ejpam-3903	233	43	solution	solution	NOUN
ejpam-3903	233	44	of:	of:	NUM
ejpam-3903	233	45	a0(wn	a0(wn	NUM
ejpam-3903	233	46	)	)	PUNCT
ejpam-3903	233	47	4	4	NUM
ejpam-3903	233	48	t	t	NOUN
ejpam-3903	233	49	wn+1	wn+1	NOUN
ejpam-3903	233	50	+	+	CCONJ
ejpam-3903	234	1	3∑	3∑	NUM
ejpam-3903	234	2	i=1	i=1	ADP
ejpam-3903	234	3	aiε	aiε	CCONJ
ejpam-3903	234	4	∂wn+1	∂wn+1	ADJ
ejpam-3903	234	5	∂xi	∂xi	NOUN
ejpam-3903	234	6	+	+	CCONJ
ejpam-3903	234	7	kε(w	kε(w	VERB
ejpam-3903	234	8	n+1)wn+1	n+1)wn+1	NOUN
ejpam-3903	234	9	=	=	SYM
ejpam-3903	234	10	fn+1	fn+1	X
ejpam-3903	234	11	+	+	NUM
ejpam-3903	234	12	a0(wn	a0(wn	NOUN
ejpam-3903	234	13	)	)	PUNCT
ejpam-3903	234	14	4	4	NUM
ejpam-3903	234	15	t	t	NOUN
ejpam-3903	234	16	wn	wn	PROPN
ejpam-3903	234	17	,	,	PUNCT
ejpam-3903	234	18	(	(	PUNCT
ejpam-3903	234	19	bε	bε	NOUN
ejpam-3903	234	20	−mε)w	−mε)w	PROPN
ejpam-3903	234	21	n+1	n+1	PROPN
ejpam-3903	234	22	=	=	PUNCT
ejpam-3903	234	23	gn+1	gn+1	PROPN
ejpam-3903	234	24	·	·	PUNCT
ejpam-3903	234	25	(	(	PUNCT
ejpam-3903	234	26	32	32	NUM
ejpam-3903	234	27	)	)	PUNCT
ejpam-3903	234	28	•	•	NOUN
ejpam-3903	234	29	by	by	ADP
ejpam-3903	234	30	linearizing	linearize	VERB
ejpam-3903	234	31	le	le	X
ejpam-3903	234	32	system	system	NOUN
ejpam-3903	234	33	(	(	PUNCT
ejpam-3903	234	34	32	32	NUM
ejpam-3903	234	35	)	)	PUNCT
ejpam-3903	234	36	we	we	PRON
ejpam-3903	234	37	construct	construct	VERB
ejpam-3903	234	38	the	the	DET
ejpam-3903	234	39	sequence	sequence	NOUN
ejpam-3903	234	40	wn+1	wn+1	VERB
ejpam-3903	234	41	k+1	k+1	NOUN
ejpam-3903	234	42	solution	solution	NOUN
ejpam-3903	234	43	of:	of:	NUM
ejpam-3903	234	44	a0(wn	a0(wn	NUM
ejpam-3903	234	45	)	)	PUNCT
ejpam-3903	234	46	4	4	NUM
ejpam-3903	234	47	t	t	NOUN
ejpam-3903	234	48	wn+1	wn+1	VERB
ejpam-3903	234	49	k+1	k+1	X
ejpam-3903	235	1	+	+	CCONJ
ejpam-3903	235	2	3∑	3∑	NUM
ejpam-3903	235	3	i=1	i=1	ADP
ejpam-3903	235	4	aiε	aiε	ADV
ejpam-3903	235	5	∂wn+1	∂wn+1	VERB
ejpam-3903	235	6	k+1	k+1	DET
ejpam-3903	235	7	∂xi	∂xi	NOUN
ejpam-3903	235	8	+	+	CCONJ
ejpam-3903	235	9	kε(w	kε(w	VERB
ejpam-3903	235	10	n+1	n+1	PROPN
ejpam-3903	235	11	k	k	X
ejpam-3903	235	12	)	)	PUNCT
ejpam-3903	235	13	wn+1	wn+1	VERB
ejpam-3903	235	14	k+1	k+1	X
ejpam-3903	235	15	=	=	SYM
ejpam-3903	235	16	fn+1	fn+1	PROPN
ejpam-3903	235	17	+	+	NUM
ejpam-3903	235	18	a0(wn	a0(wn	NOUN
ejpam-3903	235	19	)	)	PUNCT
ejpam-3903	235	20	4	4	NUM
ejpam-3903	235	21	t	t	NOUN
ejpam-3903	235	22	wn	wn	PROPN
ejpam-3903	235	23	,	,	PUNCT
ejpam-3903	235	24	(	(	PUNCT
ejpam-3903	235	25	bε	bε	NOUN
ejpam-3903	235	26	−mε)w	−mε)w	PROPN
ejpam-3903	235	27	n+1	n+1	PROPN
ejpam-3903	235	28	k+1	k+1	X
ejpam-3903	235	29	=	=	SYM
ejpam-3903	235	30	gn+1	gn+1	PROPN
ejpam-3903	235	31	·	·	PUNCT
ejpam-3903	235	32	(	(	PUNCT
ejpam-3903	235	33	33	33	NUM
ejpam-3903	235	34	)	)	PUNCT
ejpam-3903	235	35	•	•	NOUN
ejpam-3903	235	36	convergences	convergence	NOUN
ejpam-3903	235	37	−	−	NOUN
ejpam-3903	235	38	with	with	ADP
ejpam-3903	235	39	the	the	DET
ejpam-3903	235	40	fixed	fix	VERB
ejpam-3903	235	41	point	point	NOUN
ejpam-3903	235	42	theorem	theorem	VERB
ejpam-3903	235	43	,	,	PUNCT
ejpam-3903	235	44	we	we	PRON
ejpam-3903	235	45	prove	prove	VERB
ejpam-3903	235	46	:	:	PUNCT
ejpam-3903	235	47	wn+1	wn+1	VERB
ejpam-3903	235	48	k+1	k+1	X
ejpam-3903	235	49	→wn+1	→wn+1	ADJ
ejpam-3903	235	50	,	,	PUNCT
ejpam-3903	235	51	when	when	SCONJ
ejpam-3903	235	52	k	k	PROPN
ejpam-3903	235	53	→	→	SYM
ejpam-3903	235	54	+	+	PROPN
ejpam-3903	235	55	∞	∞	PROPN
ejpam-3903	235	56	and	and	CCONJ
ejpam-3903	235	57	where	where	SCONJ
ejpam-3903	235	58	wn+1	wn+1	NOUN
ejpam-3903	235	59	is	be	AUX
ejpam-3903	235	60	a	a	DET
ejpam-3903	235	61	solution	solution	NOUN
ejpam-3903	235	62	of	of	ADP
ejpam-3903	235	63	(	(	PUNCT
ejpam-3903	235	64	32	32	NUM
ejpam-3903	235	65	)	)	PUNCT
ejpam-3903	235	66	.	.	PUNCT
ejpam-3903	236	1	−	−	NOUN
ejpam-3903	237	1	by	by	ADP
ejpam-3903	237	2	some	some	DET
ejpam-3903	237	3	a	a	DET
ejpam-3903	237	4	priori	priori	ADJ
ejpam-3903	237	5	estimations	estimation	NOUN
ejpam-3903	237	6	,	,	PUNCT
ejpam-3903	237	7	we	we	PRON
ejpam-3903	237	8	prove	prove	VERB
ejpam-3903	237	9	:	:	PUNCT
ejpam-3903	237	10	wn+1	wn+1	VERB
ejpam-3903	237	11	→wε	→wε	NOUN
ejpam-3903	237	12	,	,	PUNCT
ejpam-3903	237	13	when	when	SCONJ
ejpam-3903	237	14	n→	n→	ADV
ejpam-3903	237	15	+	+	ADJ
ejpam-3903	237	16	∞	∞	PROPN
ejpam-3903	237	17	and	and	CCONJ
ejpam-3903	237	18	where	where	SCONJ
ejpam-3903	237	19	wε	wε	X
ejpam-3903	237	20	is	be	AUX
ejpam-3903	237	21	a	a	DET
ejpam-3903	237	22	solution	solution	NOUN
ejpam-3903	237	23	of	of	ADP
ejpam-3903	237	24	(	(	PUNCT
ejpam-3903	237	25	30	30	NUM
ejpam-3903	237	26	)	)	PUNCT
ejpam-3903	237	27	.	.	PUNCT
ejpam-3903	238	1	4.1.1	4.1.1	X
ejpam-3903	238	2	.	.	PUNCT
ejpam-3903	239	1	existence	existence	NOUN
ejpam-3903	239	2	of	of	ADP
ejpam-3903	239	3	w1	w1	PROPN
ejpam-3903	239	4	1	1	NUM
ejpam-3903	239	5	to	to	PART
ejpam-3903	239	6	prove	prove	VERB
ejpam-3903	239	7	the	the	DET
ejpam-3903	239	8	existence	existence	NOUN
ejpam-3903	239	9	of	of	ADP
ejpam-3903	239	10	the	the	DET
ejpam-3903	239	11	sequence	sequence	NOUN
ejpam-3903	239	12	(	(	PUNCT
ejpam-3903	239	13	w1	w1	NOUN
ejpam-3903	239	14	k	k	PROPN
ejpam-3903	239	15	)	)	PUNCT
ejpam-3903	239	16	,	,	PUNCT
ejpam-3903	239	17	we	we	PRON
ejpam-3903	239	18	begin	begin	VERB
ejpam-3903	239	19	with	with	ADP
ejpam-3903	239	20	the	the	DET
ejpam-3903	239	21	existence	existence	NOUN
ejpam-3903	239	22	of	of	ADP
ejpam-3903	239	23	w1	w1	NOUN
ejpam-3903	239	24	1	1	NUM
ejpam-3903	239	25	by	by	ADP
ejpam-3903	239	26	initializing	initialize	VERB
ejpam-3903	239	27	with	with	ADP
ejpam-3903	239	28	w1	w1	NOUN
ejpam-3903	239	29	0	0	NUM
ejpam-3903	239	30	=	=	SYM
ejpam-3903	239	31	w0	w0	PROPN
ejpam-3903	239	32	.	.	PUNCT
ejpam-3903	240	1	thus	thus	ADV
ejpam-3903	240	2	w1	w1	NOUN
ejpam-3903	240	3	1	1	NUM
ejpam-3903	240	4	will	will	AUX
ejpam-3903	240	5	be	be	AUX
ejpam-3903	240	6	solution	solution	NOUN
ejpam-3903	240	7	of:	of:	PROPN
ejpam-3903	240	8	a0(w0	a0(w0	NOUN
ejpam-3903	240	9	)	)	PUNCT
ejpam-3903	240	10	4	4	NUM
ejpam-3903	240	11	t	t	NOUN
ejpam-3903	240	12	w1	w1	NOUN
ejpam-3903	240	13	1	1	NUM
ejpam-3903	241	1	+	+	NUM
ejpam-3903	241	2	3∑	3∑	NUM
ejpam-3903	241	3	i=1	i=1	INTJ
ejpam-3903	241	4	aiε	aiε	ADJ
ejpam-3903	241	5	∂w1	∂w1	PROPN
ejpam-3903	241	6	1	1	NUM
ejpam-3903	241	7	∂xi	∂xi	NOUN
ejpam-3903	241	8	+	+	CCONJ
ejpam-3903	241	9	kε(w	kε(w	VERB
ejpam-3903	241	10	0)w1	0)w1	PRON
ejpam-3903	241	11	1	1	NUM
ejpam-3903	241	12	=	=	SYM
ejpam-3903	241	13	f1	f1	NOUN
ejpam-3903	241	14	+	+	CCONJ
ejpam-3903	241	15	a0(w0	a0(w0	NOUN
ejpam-3903	241	16	)	)	PUNCT
ejpam-3903	241	17	4	4	NUM
ejpam-3903	241	18	t	t	NOUN
ejpam-3903	241	19	w0	w0	NOUN
ejpam-3903	241	20	,	,	PUNCT
ejpam-3903	241	21	(	(	PUNCT
ejpam-3903	241	22	bε	bε	NOUN
ejpam-3903	241	23	−mε)w	−mε)w	ADJ
ejpam-3903	241	24	1	1	NUM
ejpam-3903	241	25	1	1	NUM
ejpam-3903	241	26	=	=	NOUN
ejpam-3903	241	27	g1	g1	X
ejpam-3903	241	28	.	.	PUNCT
ejpam-3903	242	1	(	(	PUNCT
ejpam-3903	242	2	34	34	NUM
ejpam-3903	242	3	)	)	PUNCT
ejpam-3903	242	4	r.	r.	PROPN
ejpam-3903	242	5	bade	bade	PROPN
ejpam-3903	242	6	,	,	PUNCT
ejpam-3903	242	7	h.	h.	PROPN
ejpam-3903	242	8	chaker	chaker	PROPN
ejpam-3903	242	9	/	/	SYM
ejpam-3903	242	10	eur	eur	PROPN
ejpam-3903	242	11	.	.	PUNCT
ejpam-3903	243	1	j.	j.	PROPN
ejpam-3903	243	2	pure	pure	PROPN
ejpam-3903	243	3	appl	appl	PROPN
ejpam-3903	243	4	.	.	PROPN
ejpam-3903	243	5	math	math	PROPN
ejpam-3903	243	6	,	,	PUNCT
ejpam-3903	243	7	14	14	NUM
ejpam-3903	243	8	(	(	PUNCT
ejpam-3903	243	9	1	1	NUM
ejpam-3903	243	10	)	)	PUNCT
ejpam-3903	243	11	(	(	PUNCT
ejpam-3903	243	12	2021	2021	NUM
ejpam-3903	243	13	)	)	PUNCT
ejpam-3903	243	14	,	,	PUNCT
ejpam-3903	243	15	82	82	NUM
ejpam-3903	243	16	-	-	SYM
ejpam-3903	243	17	111	111	NUM
ejpam-3903	243	18	92	92	NUM
ejpam-3903	243	19	definition	definition	NOUN
ejpam-3903	243	20	1	1	NUM
ejpam-3903	243	21	.	.	PUNCT
ejpam-3903	244	1	w1	w1	NOUN
ejpam-3903	244	2	1	1	NUM
ejpam-3903	244	3	is	be	AUX
ejpam-3903	244	4	called	call	VERB
ejpam-3903	244	5	a	a	DET
ejpam-3903	244	6	weak	weak	ADJ
ejpam-3903	244	7	solution	solution	NOUN
ejpam-3903	244	8	of	of	ADP
ejpam-3903	244	9	(	(	PUNCT
ejpam-3903	244	10	34	34	NUM
ejpam-3903	244	11	)	)	PUNCT
ejpam-3903	244	12	if	if	SCONJ
ejpam-3903	244	13	w1	w1	NOUN
ejpam-3903	244	14	1	1	NUM
ejpam-3903	244	15	∈	∈	NOUN
ejpam-3903	244	16	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	244	17	and	and	CCONJ
ejpam-3903	244	18	for	for	ADP
ejpam-3903	244	19	all	all	DET
ejpam-3903	244	20	test	test	NOUN
ejpam-3903	244	21	function	function	NOUN
ejpam-3903	244	22	v	v	ADP
ejpam-3903	244	23	∈	∈	PROPN
ejpam-3903	244	24	h1	h1	NOUN
ejpam-3903	244	25	0	0	PUNCT
ejpam-3903	245	1	(	(	PUNCT
ejpam-3903	245	2	ω)20	ω)20	NOUN
ejpam-3903	245	3	we	we	PRON
ejpam-3903	245	4	have	have	VERB
ejpam-3903	245	5	<	<	X
ejpam-3903	245	6	w1	w1	NOUN
ejpam-3903	245	7	1,ψ	1,ψ	PROPN
ejpam-3903	245	8	∗v	∗v	NOUN
ejpam-3903	245	9	>	>	PUNCT
ejpam-3903	246	1	=	=	SYM
ejpam-3903	246	2	<	<	X
ejpam-3903	246	3	g	g	PROPN
ejpam-3903	246	4	,	,	PUNCT
ejpam-3903	246	5	v	v	X
ejpam-3903	246	6	>	>	X
ejpam-3903	246	7	,	,	PUNCT
ejpam-3903	246	8	(	(	PUNCT
ejpam-3903	246	9	35	35	NUM
ejpam-3903	246	10	)	)	PUNCT
ejpam-3903	246	11	where	where	SCONJ
ejpam-3903	246	12	g	g	NOUN
ejpam-3903	246	13	=	=	SYM
ejpam-3903	246	14	f1	f1	PROPN
ejpam-3903	246	15	+	+	CCONJ
ejpam-3903	246	16	a0(w0	a0(w0	NOUN
ejpam-3903	246	17	)	)	PUNCT
ejpam-3903	246	18	4	4	NUM
ejpam-3903	246	19	t	t	NOUN
ejpam-3903	246	20	w0	w0	PROPN
ejpam-3903	246	21	and	and	CCONJ
ejpam-3903	246	22	ψ∗	ψ∗	NOUN
ejpam-3903	246	23	is	be	AUX
ejpam-3903	246	24	the	the	DET
ejpam-3903	246	25	adjoint	adjoint	NOUN
ejpam-3903	246	26	operator	operator	NOUN
ejpam-3903	246	27	of	of	ADP
ejpam-3903	246	28	ψ	ψ	X
ejpam-3903	246	29	(	(	PUNCT
ejpam-3903	246	30	·	·	PUNCT
ejpam-3903	246	31	)	)	PUNCT
ejpam-3903	246	32	=	=	SYM
ejpam-3903	246	33	a0(w0	a0(w0	NOUN
ejpam-3903	246	34	)	)	PUNCT
ejpam-3903	246	35	4	4	NUM
ejpam-3903	246	36	t	t	NOUN
ejpam-3903	246	37	(	(	PUNCT
ejpam-3903	246	38	·	·	PUNCT
ejpam-3903	246	39	)	)	PUNCT
ejpam-3903	247	1	+	+	PUNCT
ejpam-3903	247	2	3∑	3∑	NUM
ejpam-3903	247	3	i=1	i=1	PRON
ejpam-3903	247	4	aiε	aiε	ADJ
ejpam-3903	247	5	∂	∂	NUM
ejpam-3903	247	6	(	(	PUNCT
ejpam-3903	247	7	·	·	PUNCT
ejpam-3903	247	8	)	)	PUNCT
ejpam-3903	247	9	∂xi	∂xi	NOUN
ejpam-3903	247	10	+	+	CCONJ
ejpam-3903	247	11	kε(w	kε(w	ADJ
ejpam-3903	247	12	0	0	NUM
ejpam-3903	247	13	)	)	PUNCT
ejpam-3903	247	14	(	(	PUNCT
ejpam-3903	247	15	·	·	PUNCT
ejpam-3903	247	16	)	)	PUNCT
ejpam-3903	247	17	.	.	PUNCT
ejpam-3903	248	1	the	the	DET
ejpam-3903	248	2	existence	existence	NOUN
ejpam-3903	248	3	of	of	ADP
ejpam-3903	248	4	w1	w1	NOUN
ejpam-3903	248	5	1	1	NUM
ejpam-3903	248	6	is	be	AUX
ejpam-3903	248	7	given	give	VERB
ejpam-3903	248	8	by	by	ADP
ejpam-3903	248	9	following	follow	VERB
ejpam-3903	248	10	result	result	NOUN
ejpam-3903	248	11	:	:	PUNCT
ejpam-3903	248	12	proposition	proposition	NOUN
ejpam-3903	248	13	2	2	NUM
ejpam-3903	248	14	.	.	PUNCT
ejpam-3903	249	1	let	let	VERB
ejpam-3903	249	2	that	that	DET
ejpam-3903	249	3	assumptions	assumption	NOUN
ejpam-3903	249	4	(	(	PUNCT
ejpam-3903	249	5	h2	h2	NOUN
ejpam-3903	249	6	)	)	PUNCT
ejpam-3903	249	7	and	and	CCONJ
ejpam-3903	249	8	(	(	PUNCT
ejpam-3903	249	9	h3	h3	NOUN
ejpam-3903	249	10	)	)	PUNCT
ejpam-3903	249	11	hold	hold	VERB
ejpam-3903	249	12	.	.	PUNCT
ejpam-3903	250	1	then	then	ADV
ejpam-3903	250	2	the	the	DET
ejpam-3903	250	3	system	system	NOUN
ejpam-3903	250	4	(	(	PUNCT
ejpam-3903	250	5	34	34	NUM
ejpam-3903	250	6	)	)	PUNCT
ejpam-3903	250	7	admit	admit	VERB
ejpam-3903	250	8	a	a	DET
ejpam-3903	250	9	weak	weak	ADJ
ejpam-3903	250	10	solution	solution	NOUN
ejpam-3903	250	11	w1	w1	NOUN
ejpam-3903	250	12	1	1	NUM
ejpam-3903	250	13	∈	∈	PROPN
ejpam-3903	250	14	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	250	15	.	.	PUNCT
ejpam-3903	251	1	in	in	ADP
ejpam-3903	251	2	addition	addition	NOUN
ejpam-3903	251	3	if	if	SCONJ
ejpam-3903	251	4	w1	w1	NOUN
ejpam-3903	251	5	1	1	NUM
ejpam-3903	251	6	∈	∈	NOUN
ejpam-3903	251	7	h1(ω)20	h1(ω)20	PUNCT
ejpam-3903	251	8	we	we	PRON
ejpam-3903	251	9	have	have	VERB
ejpam-3903	251	10	uniqueness	uniqueness	NOUN
ejpam-3903	251	11	.	.	PUNCT
ejpam-3903	252	1	moreover	moreover	ADV
ejpam-3903	252	2	if	if	SCONJ
ejpam-3903	252	3	f1	f1	PROPN
ejpam-3903	252	4	+	+	CCONJ
ejpam-3903	252	5	a0(w0	a0(w0	NOUN
ejpam-3903	252	6	)	)	PUNCT
ejpam-3903	252	7	4	4	NUM
ejpam-3903	252	8	t	t	NOUN
ejpam-3903	252	9	w0	w0	PROPN
ejpam-3903	252	10	∈	∈	PROPN
ejpam-3903	252	11	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	252	12	,	,	PUNCT
ejpam-3903	252	13	g1	g1	PROPN
ejpam-3903	252	14	∈	∈	PROPN
ejpam-3903	252	15	hs+	hs+	NOUN
ejpam-3903	252	16	3	3	NUM
ejpam-3903	252	17	2	2	NUM
ejpam-3903	252	18	(	(	PUNCT
ejpam-3903	252	19	∂ω)20	∂ω)20	PROPN
ejpam-3903	252	20	,	,	PUNCT
ejpam-3903	252	21	then	then	ADV
ejpam-3903	252	22	the	the	DET
ejpam-3903	252	23	system	system	NOUN
ejpam-3903	252	24	(	(	PUNCT
ejpam-3903	252	25	34	34	NUM
ejpam-3903	252	26	)	)	PUNCT
ejpam-3903	252	27	admit	admit	VERB
ejpam-3903	252	28	a	a	DET
ejpam-3903	252	29	weak	weak	ADJ
ejpam-3903	252	30	solution	solution	NOUN
ejpam-3903	252	31	w1	w1	NOUN
ejpam-3903	252	32	1	1	NUM
ejpam-3903	252	33	∈	∈	PROPN
ejpam-3903	252	34	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	252	35	.	.	PUNCT
ejpam-3903	253	1	in	in	ADP
ejpam-3903	253	2	addition	addition	NOUN
ejpam-3903	253	3	we	we	PRON
ejpam-3903	253	4	have	have	VERB
ejpam-3903	253	5	(	(	PUNCT
ejpam-3903	253	6	w1	w1	NOUN
ejpam-3903	253	7	1)1	1)1	PROPN
ejpam-3903	253	8	>	>	SYM
ejpam-3903	253	9	ρ̄	ρ̄	NUM
ejpam-3903	253	10	exp(−4tk	exp(−4tk	PROPN
ejpam-3903	253	11	)	)	PUNCT
ejpam-3903	253	12	,	,	PUNCT
ejpam-3903	253	13	with	with	ADP
ejpam-3903	253	14	k	k	PROPN
ejpam-3903	253	15	given	give	VERB
ejpam-3903	253	16	by	by	ADP
ejpam-3903	253	17	(	(	PUNCT
ejpam-3903	253	18	49	49	NUM
ejpam-3903	253	19	)	)	PUNCT
ejpam-3903	253	20	.	.	PUNCT
ejpam-3903	254	1	proof	proof	NOUN
ejpam-3903	254	2	.	.	PUNCT
ejpam-3903	255	1	by	by	ADP
ejpam-3903	255	2	the	the	DET
ejpam-3903	255	3	assumptions	assumption	NOUN
ejpam-3903	255	4	(	(	PUNCT
ejpam-3903	255	5	h2	h2	NOUN
ejpam-3903	255	6	)	)	PUNCT
ejpam-3903	255	7	and	and	CCONJ
ejpam-3903	255	8	(	(	PUNCT
ejpam-3903	255	9	h3	h3	NOUN
ejpam-3903	255	10	)	)	PUNCT
ejpam-3903	255	11	,	,	PUNCT
ejpam-3903	255	12	we	we	PRON
ejpam-3903	255	13	have	have	VERB
ejpam-3903	255	14	f1	f1	NOUN
ejpam-3903	255	15	+	+	CCONJ
ejpam-3903	255	16	a0(w0	a0(w0	NOUN
ejpam-3903	255	17	)	)	PUNCT
ejpam-3903	255	18	4	4	NUM
ejpam-3903	255	19	t	t	NOUN
ejpam-3903	255	20	w0	w0	PROPN
ejpam-3903	255	21	∈	∈	PROPN
ejpam-3903	255	22	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	255	23	.	.	PUNCT
ejpam-3903	256	1	in	in	ADP
ejpam-3903	256	2	the	the	DET
ejpam-3903	256	3	aim	aim	NOUN
ejpam-3903	256	4	to	to	PART
ejpam-3903	256	5	homogeneous	homogeneous	VERB
ejpam-3903	256	6	the	the	DET
ejpam-3903	256	7	boundary	boundary	ADJ
ejpam-3903	256	8	conditions	condition	NOUN
ejpam-3903	256	9	of	of	ADP
ejpam-3903	256	10	the	the	DET
ejpam-3903	256	11	system	system	NOUN
ejpam-3903	256	12	(	(	PUNCT
ejpam-3903	256	13	34	34	NUM
ejpam-3903	256	14	)	)	PUNCT
ejpam-3903	256	15	,	,	PUNCT
ejpam-3903	256	16	let	let	VERB
ejpam-3903	256	17	us	we	PRON
ejpam-3903	256	18	set	set	VERB
ejpam-3903	256	19	:	:	PUNCT
ejpam-3903	256	20	w1∗	w1∗	NOUN
ejpam-3903	256	21	1	1	NUM
ejpam-3903	256	22	=	=	SYM
ejpam-3903	256	23	w1	w1	PROPN
ejpam-3903	256	24	1	1	NUM
ejpam-3903	257	1	−w1	−w1	NOUN
ejpam-3903	257	2	g	g	NOUN
ejpam-3903	257	3	,	,	PUNCT
ejpam-3903	257	4	(	(	PUNCT
ejpam-3903	257	5	36	36	NUM
ejpam-3903	257	6	)	)	PUNCT
ejpam-3903	257	7	w1∗	w1∗	NOUN
ejpam-3903	257	8	1	1	NUM
ejpam-3903	257	9	is	be	AUX
ejpam-3903	257	10	then	then	ADV
ejpam-3903	257	11	solution	solution	NOUN
ejpam-3903	257	12	of:	of:	PROPN
ejpam-3903	257	13	(	(	PUNCT
ejpam-3903	257	14	a0(w0	a0(w0	NOUN
ejpam-3903	257	15	)	)	PUNCT
ejpam-3903	257	16	4	4	NUM
ejpam-3903	257	17	t	t	NOUN
ejpam-3903	257	18	+	+	CCONJ
ejpam-3903	257	19	kε(w	kε(w	X
ejpam-3903	257	20	0	0	NUM
ejpam-3903	257	21	)	)	PUNCT
ejpam-3903	257	22	)	)	PUNCT
ejpam-3903	258	1	w1∗	w1∗	NOUN
ejpam-3903	258	2	1	1	NUM
ejpam-3903	259	1	+	+	NUM
ejpam-3903	259	2	3∑	3∑	NUM
ejpam-3903	259	3	i=1	i=1	PRON
ejpam-3903	259	4	aiε	aiε	ADJ
ejpam-3903	259	5	∂w1∗	∂w1∗	ADJ
ejpam-3903	259	6	1	1	NUM
ejpam-3903	259	7	∂xi	∂xi	PROPN
ejpam-3903	259	8	=	=	SYM
ejpam-3903	259	9	f1	f1	PROPN
ejpam-3903	259	10	+	+	CCONJ
ejpam-3903	259	11	a0(w0	a0(w0	NOUN
ejpam-3903	259	12	)	)	PUNCT
ejpam-3903	259	13	4	4	NUM
ejpam-3903	259	14	t	t	NOUN
ejpam-3903	259	15	w0	w0	PROPN
ejpam-3903	259	16	−	−	PROPN
ejpam-3903	259	17	(	(	PUNCT
ejpam-3903	259	18	a0(w0	a0(w0	NOUN
ejpam-3903	259	19	)	)	PUNCT
ejpam-3903	259	20	4	4	NUM
ejpam-3903	259	21	t	t	NOUN
ejpam-3903	259	22	+	+	CCONJ
ejpam-3903	259	23	kε(w	kε(w	X
ejpam-3903	259	24	0	0	NUM
ejpam-3903	259	25	)	)	PUNCT
ejpam-3903	259	26	)	)	PUNCT
ejpam-3903	260	1	w1	w1	NOUN
ejpam-3903	260	2	g	g	NOUN
ejpam-3903	260	3	−	−	PROPN
ejpam-3903	260	4	3∑	3∑	PROPN
ejpam-3903	260	5	i=1	i=1	PRON
ejpam-3903	260	6	aiε	aiε	ADP
ejpam-3903	260	7	∂w1	∂w1	PROPN
ejpam-3903	260	8	g	g	PROPN
ejpam-3903	260	9	∂xi	∂xi	PROPN
ejpam-3903	260	10	,	,	PUNCT
ejpam-3903	260	11	(	(	PUNCT
ejpam-3903	260	12	b−m)w1∗	b−m)w1∗	NOUN
ejpam-3903	260	13	1	1	NUM
ejpam-3903	260	14	=	=	SYM
ejpam-3903	260	15	0	0	NUM
ejpam-3903	260	16	.	.	PUNCT
ejpam-3903	261	1	(	(	PUNCT
ejpam-3903	261	2	37	37	NUM
ejpam-3903	261	3	)	)	PUNCT
ejpam-3903	261	4	let	let	AUX
ejpam-3903	261	5	define	define	VERB
ejpam-3903	261	6	the	the	DET
ejpam-3903	261	7	operator	operator	NOUN
ejpam-3903	261	8	:	:	PUNCT
ejpam-3903	261	9	<	<	X
ejpam-3903	261	10	(	(	PUNCT
ejpam-3903	261	11	w0,w0	w0,w0	PROPN
ejpam-3903	261	12	)	)	PUNCT
ejpam-3903	261	13	(	(	PUNCT
ejpam-3903	261	14	·	·	PUNCT
ejpam-3903	261	15	)	)	PUNCT
ejpam-3903	262	1	=	=	PRON
ejpam-3903	262	2	(	(	PUNCT
ejpam-3903	262	3	a0(w0	a0(w0	NOUN
ejpam-3903	262	4	)	)	PUNCT
ejpam-3903	262	5	4	4	NUM
ejpam-3903	262	6	t	t	NOUN
ejpam-3903	262	7	+	+	CCONJ
ejpam-3903	262	8	kε(w	kε(w	X
ejpam-3903	262	9	0	0	NUM
ejpam-3903	262	10	)	)	PUNCT
ejpam-3903	262	11	)	)	PUNCT
ejpam-3903	263	1	(	(	PUNCT
ejpam-3903	263	2	·	·	PUNCT
ejpam-3903	263	3	)	)	PUNCT
ejpam-3903	264	1	+	+	CCONJ
ejpam-3903	264	2	d∑	d∑	PROPN
ejpam-3903	264	3	i=1	i=1	PROPN
ejpam-3903	264	4	aiε	aiε	ADJ
ejpam-3903	264	5	∂	∂	NUM
ejpam-3903	264	6	(	(	PUNCT
ejpam-3903	264	7	·	·	PUNCT
ejpam-3903	264	8	)	)	PUNCT
ejpam-3903	264	9	∂xi	∂xi	NOUN
ejpam-3903	264	10	.	.	PUNCT
ejpam-3903	265	1	(	(	PUNCT
ejpam-3903	265	2	38	38	NUM
ejpam-3903	265	3	)	)	PUNCT
ejpam-3903	265	4	(	(	PUNCT
ejpam-3903	265	5	<	<	X
ejpam-3903	265	6	+	+	X
ejpam-3903	265	7	<	<	X
ejpam-3903	265	8	∗	∗	NOUN
ejpam-3903	265	9	)	)	PUNCT
ejpam-3903	265	10	is	be	AUX
ejpam-3903	265	11	positive	positive	ADJ
ejpam-3903	265	12	(	(	PUNCT
ejpam-3903	265	13	see	see	VERB
ejpam-3903	265	14	for	for	ADP
ejpam-3903	265	15	instance	instance	NOUN
ejpam-3903	265	16	[	[	X
ejpam-3903	265	17	4	4	NUM
ejpam-3903	265	18	]	]	PUNCT
ejpam-3903	265	19	,	,	PUNCT
ejpam-3903	265	20	proposition	proposition	NOUN
ejpam-3903	265	21	2	2	NUM
ejpam-3903	265	22	)	)	PUNCT
ejpam-3903	265	23	.	.	PUNCT
ejpam-3903	266	1	do	do	VERB
ejpam-3903	266	2	to	to	ADP
ejpam-3903	266	3	[	[	X
ejpam-3903	266	4	13	13	NUM
ejpam-3903	266	5	]	]	PUNCT
ejpam-3903	266	6	,	,	PUNCT
ejpam-3903	266	7	we	we	PRON
ejpam-3903	266	8	can	can	AUX
ejpam-3903	266	9	deduce	deduce	VERB
ejpam-3903	266	10	the	the	DET
ejpam-3903	266	11	existence	existence	NOUN
ejpam-3903	266	12	of	of	ADP
ejpam-3903	266	13	a	a	DET
ejpam-3903	266	14	weak	weak	ADJ
ejpam-3903	266	15	solution	solution	NOUN
ejpam-3903	266	16	in	in	ADP
ejpam-3903	266	17	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	266	18	.	.	PUNCT
ejpam-3903	267	1	moreover	moreover	ADV
ejpam-3903	267	2	if	if	SCONJ
ejpam-3903	267	3	the	the	DET
ejpam-3903	267	4	solution	solution	NOUN
ejpam-3903	267	5	is	be	AUX
ejpam-3903	267	6	in	in	ADP
ejpam-3903	267	7	h1(ω)20	h1(ω)20	PROPN
ejpam-3903	267	8	we	we	PRON
ejpam-3903	267	9	have	have	VERB
ejpam-3903	267	10	r.	r.	PROPN
ejpam-3903	267	11	bade	bade	PROPN
ejpam-3903	267	12	,	,	PUNCT
ejpam-3903	267	13	h.	h.	PROPN
ejpam-3903	267	14	chaker	chaker	PROPN
ejpam-3903	267	15	/	/	SYM
ejpam-3903	267	16	eur	eur	PROPN
ejpam-3903	267	17	.	.	PUNCT
ejpam-3903	268	1	j.	j.	PROPN
ejpam-3903	268	2	pure	pure	PROPN
ejpam-3903	268	3	appl	appl	PROPN
ejpam-3903	268	4	.	.	PROPN
ejpam-3903	268	5	math	math	PROPN
ejpam-3903	268	6	,	,	PUNCT
ejpam-3903	268	7	14	14	NUM
ejpam-3903	268	8	(	(	PUNCT
ejpam-3903	268	9	1	1	NUM
ejpam-3903	268	10	)	)	PUNCT
ejpam-3903	268	11	(	(	PUNCT
ejpam-3903	268	12	2021	2021	NUM
ejpam-3903	268	13	)	)	PUNCT
ejpam-3903	268	14	,	,	PUNCT
ejpam-3903	268	15	82	82	NUM
ejpam-3903	268	16	-	-	SYM
ejpam-3903	268	17	111	111	NUM
ejpam-3903	268	18	93	93	NUM
ejpam-3903	268	19	uniqueness	uniqueness	NOUN
ejpam-3903	268	20	and	and	CCONJ
ejpam-3903	268	21	the	the	DET
ejpam-3903	268	22	following	follow	VERB
ejpam-3903	268	23	estimate	estimate	NOUN
ejpam-3903	268	24	:	:	PUNCT
ejpam-3903	268	25	‖w1∗	‖w1∗	PROPN
ejpam-3903	268	26	1	1	NUM
ejpam-3903	268	27	‖l2	‖l2	PROPN
ejpam-3903	268	28	≤	≤	ADJ
ejpam-3903	268	29	2	2	NUM
ejpam-3903	268	30	υ(ε,4	υ(ε,4	PROPN
ejpam-3903	268	31	t	t	NOUN
ejpam-3903	268	32	)	)	PUNCT
ejpam-3903	268	33	(	(	PUNCT
ejpam-3903	268	34	‖f1‖l2	‖f1‖l2	VERB
ejpam-3903	268	35	+	+	CCONJ
ejpam-3903	268	36	1	1	NUM
ejpam-3903	268	37	4	4	NUM
ejpam-3903	268	38	t	t	NOUN
ejpam-3903	268	39	‖a0(w0)w0‖l2	‖a0(w0)w0‖l2	NUM
ejpam-3903	269	1	+	+	CCONJ
ejpam-3903	269	2	1	1	NUM
ejpam-3903	269	3	4	4	NUM
ejpam-3903	269	4	t	t	NOUN
ejpam-3903	269	5	‖a0(w0)w1	‖a0(w0)w1	ADJ
ejpam-3903	269	6	g‖l2	g‖l2	PROPN
ejpam-3903	270	1	+	+	PROPN
ejpam-3903	270	2	‖kε(w	‖kε(w	PROPN
ejpam-3903	270	3	0)w1	0)w1	PRON
ejpam-3903	271	1	g	g	NOUN
ejpam-3903	271	2	+	+	NOUN
ejpam-3903	271	3	3∑	3∑	NUM
ejpam-3903	271	4	i=1	i=1	PRON
ejpam-3903	271	5	aiε	aiε	PRON
ejpam-3903	271	6	∂w1	∂w1	PROPN
ejpam-3903	271	7	g	g	PROPN
ejpam-3903	271	8	∂xi	∂xi	PROPN
ejpam-3903	271	9	‖l2	‖l2	VERB
ejpam-3903	271	10	)	)	PUNCT
ejpam-3903	271	11	≤	≤	NUM
ejpam-3903	271	12	2	2	NUM
ejpam-3903	271	13	υ(ε,4	υ(ε,4	PROPN
ejpam-3903	271	14	t	t	NOUN
ejpam-3903	271	15	)	)	PUNCT
ejpam-3903	271	16	(	(	PUNCT
ejpam-3903	271	17	‖f1‖l2	‖f1‖l2	VERB
ejpam-3903	271	18	+	+	CCONJ
ejpam-3903	271	19	c03(w0	c03(w0	ADJ
ejpam-3903	271	20	)	)	PUNCT
ejpam-3903	271	21	4	4	NUM
ejpam-3903	271	22	t	t	NOUN
ejpam-3903	271	23	‖a0w	‖a0w	NOUN
ejpam-3903	271	24	0‖l2	0‖l2	NOUN
ejpam-3903	272	1	+	+	CCONJ
ejpam-3903	272	2	(	(	PUNCT
ejpam-3903	272	3	1	1	NUM
ejpam-3903	272	4	+	+	NUM
ejpam-3903	272	5	1	1	NUM
ejpam-3903	272	6	4	4	NUM
ejpam-3903	272	7	t	t	NOUN
ejpam-3903	272	8	)	)	PUNCT
ejpam-3903	273	1	c1(w0)‖w1	c1(w0)‖w1	PUNCT
ejpam-3903	274	1	g‖l2	g‖l2	X
ejpam-3903	274	2	+	+	CCONJ
ejpam-3903	274	3	c̃‖w1	c̃‖w1	NOUN
ejpam-3903	274	4	g‖h1	g‖h1	PROPN
ejpam-3903	274	5	)	)	PUNCT
ejpam-3903	274	6	·	·	PUNCT
ejpam-3903	275	1	υ(ε,4	υ(ε,4	NUM
ejpam-3903	275	2	t	t	NOUN
ejpam-3903	275	3	)	)	PUNCT
ejpam-3903	275	4	is	be	AUX
ejpam-3903	275	5	the	the	DET
ejpam-3903	275	6	constant	constant	ADJ
ejpam-3903	275	7	positivity	positivity	NOUN
ejpam-3903	275	8	of	of	ADP
ejpam-3903	275	9	(	(	PUNCT
ejpam-3903	275	10	<	<	X
ejpam-3903	275	11	+	+	X
ejpam-3903	275	12	<	<	X
ejpam-3903	275	13	∗	∗	NOUN
ejpam-3903	275	14	)	)	PUNCT
ejpam-3903	275	15	.	.	PUNCT
ejpam-3903	276	1	using	use	VERB
ejpam-3903	276	2	(	(	PUNCT
ejpam-3903	276	3	36	36	NUM
ejpam-3903	276	4	)	)	PUNCT
ejpam-3903	276	5	,	,	PUNCT
ejpam-3903	276	6	we	we	PRON
ejpam-3903	276	7	obtain	obtain	VERB
ejpam-3903	276	8	:	:	PUNCT
ejpam-3903	276	9	‖w1	‖w1	NOUN
ejpam-3903	276	10	1‖l2	1‖l2	X
ejpam-3903	276	11	≤	≤	NUM
ejpam-3903	276	12	2	2	NUM
ejpam-3903	276	13	υ(ε,4	υ(ε,4	PROPN
ejpam-3903	276	14	t	t	NOUN
ejpam-3903	276	15	)	)	PUNCT
ejpam-3903	276	16	(	(	PUNCT
ejpam-3903	276	17	‖f1‖l2	‖f1‖l2	VERB
ejpam-3903	276	18	+	+	CCONJ
ejpam-3903	276	19	c03(w0	c03(w0	ADJ
ejpam-3903	276	20	)	)	PUNCT
ejpam-3903	276	21	4	4	NUM
ejpam-3903	276	22	t	t	NOUN
ejpam-3903	276	23	‖a0w	‖a0w	NOUN
ejpam-3903	276	24	0‖l2	0‖l2	NOUN
ejpam-3903	276	25	+	+	CCONJ
ejpam-3903	277	1	(	(	PUNCT
ejpam-3903	277	2	1	1	NUM
ejpam-3903	277	3	+	+	NUM
ejpam-3903	277	4	1	1	NUM
ejpam-3903	277	5	4	4	NUM
ejpam-3903	277	6	t	t	NOUN
ejpam-3903	277	7	)	)	PUNCT
ejpam-3903	278	1	c1(w0)‖w1	c1(w0)‖w1	PUNCT
ejpam-3903	279	1	g‖l2	g‖l2	PRON
ejpam-3903	280	1	+	+	NOUN
ejpam-3903	280	2	c̃‖w1	c̃‖w1	NOUN
ejpam-3903	280	3	g‖h1	g‖h1	X
ejpam-3903	280	4	)	)	PUNCT
ejpam-3903	281	1	+	+	CCONJ
ejpam-3903	281	2	‖w1	‖w1	CCONJ
ejpam-3903	281	3	g‖l2	g‖l2	PROPN
ejpam-3903	281	4	where	where	SCONJ
ejpam-3903	281	5	c03(w0	c03(w0	ADJ
ejpam-3903	281	6	)	)	PUNCT
ejpam-3903	281	7	=	=	PUNCT
ejpam-3903	281	8	sup(1	sup(1	NOUN
ejpam-3903	281	9	,	,	PUNCT
ejpam-3903	281	10	‖w0‖l∞	‖w0‖l∞	PROPN
ejpam-3903	281	11	,	,	PUNCT
ejpam-3903	281	12	cv‖w0‖l∞	cv‖w0‖l∞	NOUN
ejpam-3903	281	13	)	)	PUNCT
ejpam-3903	281	14	c04(w0	c04(w0	NOUN
ejpam-3903	281	15	)	)	PUNCT
ejpam-3903	281	16	=	=	SYM
ejpam-3903	281	17	max	max	PROPN
ejpam-3903	281	18	16j620	16j620	NOUN
ejpam-3903	281	19	5∑	5∑	PROPN
ejpam-3903	281	20	i=1	i=1	PROPN
ejpam-3903	281	21	|(kε)ij(w	|(kε)ij(w	NUM
ejpam-3903	281	22	0)|	0)|	NOUN
ejpam-3903	281	23	,	,	PUNCT
ejpam-3903	281	24	c1(w0	c1(w0	NOUN
ejpam-3903	281	25	)	)	PUNCT
ejpam-3903	281	26	=	=	SYM
ejpam-3903	281	27	sup(c03(w0	sup(c03(w0	NOUN
ejpam-3903	281	28	)	)	PUNCT
ejpam-3903	281	29	,	,	PUNCT
ejpam-3903	281	30	c04(w0	c04(w0	NOUN
ejpam-3903	281	31	)	)	PUNCT
ejpam-3903	281	32	)	)	PUNCT
ejpam-3903	282	1	c̃	c̃	PROPN
ejpam-3903	282	2	=	=	SYM
ejpam-3903	282	3	sup(µ	sup(µ	PROPN
ejpam-3903	282	4	,	,	PUNCT
ejpam-3903	282	5	β	β	X
ejpam-3903	282	6	,	,	PUNCT
ejpam-3903	282	7	α	α	PROPN
ejpam-3903	282	8	,	,	PUNCT
ejpam-3903	282	9	k	k	NOUN
ejpam-3903	282	10	)	)	PUNCT
ejpam-3903	282	11	a	a	DET
ejpam-3903	282	12	constant	constant	ADJ
ejpam-3903	282	13	independente	independente	NOUN
ejpam-3903	282	14	to	to	ADP
ejpam-3903	282	15	ε	ε	PROPN
ejpam-3903	282	16	.	.	PUNCT
ejpam-3903	283	1	by	by	ADP
ejpam-3903	283	2	construction	construction	NOUN
ejpam-3903	283	3	of	of	ADP
ejpam-3903	283	4	wg	wg	PROPN
ejpam-3903	283	5	(	(	PUNCT
ejpam-3903	283	6	equality	equality	NOUN
ejpam-3903	283	7	(	(	PUNCT
ejpam-3903	283	8	31	31	NUM
ejpam-3903	283	9	)	)	PUNCT
ejpam-3903	283	10	)	)	PUNCT
ejpam-3903	283	11	,	,	PUNCT
ejpam-3903	283	12	have	have	VERB
ejpam-3903	283	13	:	:	PUNCT
ejpam-3903	283	14	(	(	PUNCT
ejpam-3903	283	15	wg	wg	PROPN
ejpam-3903	283	16	)	)	PUNCT
ejpam-3903	283	17	1	1	NUM
ejpam-3903	283	18	,	,	PUNCT
ejpam-3903	283	19	(	(	PUNCT
ejpam-3903	283	20	wg	wg	PROPN
ejpam-3903	283	21	)	)	PUNCT
ejpam-3903	283	22	6	6	NUM
ejpam-3903	283	23	,	,	PUNCT
ejpam-3903	283	24	(	(	PUNCT
ejpam-3903	283	25	wg	wg	PROPN
ejpam-3903	283	26	)	)	PUNCT
ejpam-3903	283	27	11	11	NUM
ejpam-3903	283	28	,	,	PUNCT
ejpam-3903	283	29	and	and	CCONJ
ejpam-3903	283	30	(	(	PUNCT
ejpam-3903	283	31	wg	wg	PROPN
ejpam-3903	283	32	)	)	PUNCT
ejpam-3903	283	33	16	16	NUM
ejpam-3903	283	34	are	be	AUX
ejpam-3903	283	35	all	all	ADV
ejpam-3903	283	36	equal	equal	ADJ
ejpam-3903	283	37	to	to	ADP
ejpam-3903	283	38	zero	zero	NUM
ejpam-3903	283	39	.	.	PUNCT
ejpam-3903	284	1	for	for	ADP
ejpam-3903	284	2	the	the	DET
ejpam-3903	284	3	second	second	ADJ
ejpam-3903	284	4	part	part	NOUN
ejpam-3903	284	5	of	of	ADP
ejpam-3903	284	6	the	the	DET
ejpam-3903	284	7	proposition	proposition	NOUN
ejpam-3903	284	8	,	,	PUNCT
ejpam-3903	284	9	let	let	VERB
ejpam-3903	284	10	us	we	PRON
ejpam-3903	284	11	choose	choose	VERB
ejpam-3903	284	12	a	a	DET
ejpam-3903	284	13	test	test	NOUN
ejpam-3903	284	14	function	function	NOUN
ejpam-3903	284	15	test	test	NOUN
ejpam-3903	284	16	v	v	ADP
ejpam-3903	284	17	∈	∈	NOUN
ejpam-3903	284	18	v	v	NOUN
ejpam-3903	284	19	with	with	ADP
ejpam-3903	284	20	v	v	NOUN
ejpam-3903	284	21	=	=	PUNCT
ejpam-3903	284	22	{	{	PUNCT
ejpam-3903	284	23	v	v	NOUN
ejpam-3903	284	24	∈	∈	NOUN
ejpam-3903	284	25	d(ω)20	d(ω)20	NOUN
ejpam-3903	284	26	/	/	SYM
ejpam-3903	284	27	vi+5	vi+5	NOUN
ejpam-3903	284	28	=	=	PUNCT
ejpam-3903	284	29	d1vi	d1vi	NOUN
ejpam-3903	284	30	,	,	PUNCT
ejpam-3903	284	31	vi+10	vi+10	NOUN
ejpam-3903	284	32	=	=	PUNCT
ejpam-3903	284	33	d2vi	d2vi	X
ejpam-3903	284	34	,	,	PUNCT
ejpam-3903	284	35	vi+15	vi+15	PROPN
ejpam-3903	284	36	=	=	PUNCT
ejpam-3903	284	37	d3vi	d3vi	ADP
ejpam-3903	284	38	,	,	PUNCT
ejpam-3903	284	39	for	for	ADP
ejpam-3903	284	40	i	i	PROPN
ejpam-3903	284	41	=	=	SYM
ejpam-3903	284	42	1	1	NUM
ejpam-3903	284	43	,	,	PUNCT
ejpam-3903	284	44	5	5	NUM
ejpam-3903	284	45	}	}	PUNCT
ejpam-3903	284	46	.	.	PUNCT
ejpam-3903	285	1	one	one	PRON
ejpam-3903	285	2	can	can	AUX
ejpam-3903	285	3	remark	remark	VERB
ejpam-3903	285	4	that	that	SCONJ
ejpam-3903	285	5	:	:	PUNCT
ejpam-3903	285	6	<	<	X
ejpam-3903	285	7	aiεw	aiεw	NOUN
ejpam-3903	285	8	1∗	1∗	NUM
ejpam-3903	285	9	1	1	NUM
ejpam-3903	285	10	,	,	PUNCT
ejpam-3903	285	11	v	v	NOUN
ejpam-3903	285	12	>	>	X
ejpam-3903	285	13	=	=	SYM
ejpam-3903	285	14	0	0	PUNCT
ejpam-3903	285	15	for	for	ADP
ejpam-3903	285	16	i	i	PRON
ejpam-3903	285	17	=	=	SYM
ejpam-3903	285	18	1	1	NUM
ejpam-3903	285	19	·	·	PUNCT
ejpam-3903	285	20	·	·	PUNCT
ejpam-3903	285	21	·	·	PUNCT
ejpam-3903	286	1	3	3	X
ejpam-3903	286	2	.	.	PUNCT
ejpam-3903	286	3	thus	thus	ADV
ejpam-3903	286	4	,	,	PUNCT
ejpam-3903	286	5	for	for	ADP
ejpam-3903	286	6	v	v	ADP
ejpam-3903	286	7	∈	∈	NUM
ejpam-3903	286	8	v	v	ADP
ejpam-3903	286	9	we	we	PRON
ejpam-3903	286	10	obtain	obtain	VERB
ejpam-3903	286	11	<	<	X
ejpam-3903	286	12	a0(w0	a0(w0	NOUN
ejpam-3903	286	13	)	)	PUNCT
ejpam-3903	286	14	4	4	NUM
ejpam-3903	286	15	t	t	NOUN
ejpam-3903	286	16	w1∗	w1∗	NOUN
ejpam-3903	286	17	1	1	NUM
ejpam-3903	286	18	,	,	PUNCT
ejpam-3903	286	19	v	v	PART
ejpam-3903	286	20	>	>	X
ejpam-3903	287	1	+	+	CCONJ
ejpam-3903	287	2	<	<	X
ejpam-3903	287	3	kε(w	kε(w	X
ejpam-3903	287	4	0)w1∗	0)w1∗	NOUN
ejpam-3903	287	5	1	1	NUM
ejpam-3903	287	6	,	,	PUNCT
ejpam-3903	287	7	v	v	PART
ejpam-3903	287	8	>	>	X
ejpam-3903	287	9	=	=	NOUN
ejpam-3903	287	10	<	<	X
ejpam-3903	287	11	f1	f1	NOUN
ejpam-3903	287	12	+	+	CCONJ
ejpam-3903	287	13	a0(w0	a0(w0	NOUN
ejpam-3903	287	14	)	)	PUNCT
ejpam-3903	287	15	4	4	NUM
ejpam-3903	287	16	t	t	NOUN
ejpam-3903	287	17	w0∗	w0∗	NUM
ejpam-3903	287	18	,	,	PUNCT
ejpam-3903	287	19	v	v	ADP
ejpam-3903	287	20	>	>	X
ejpam-3903	288	1	+	+	X
ejpam-3903	288	2	<	<	X
ejpam-3903	288	3	hε(w	hε(w	X
ejpam-3903	288	4	0)w1	0)w1	PROPN
ejpam-3903	288	5	g	g	PROPN
ejpam-3903	288	6	,	,	PUNCT
ejpam-3903	288	7	v	v	X
ejpam-3903	288	8	>	>	X
ejpam-3903	288	9	−	−	X
ejpam-3903	288	10	<	<	X
ejpam-3903	288	11	a0(w0	a0(w0	NOUN
ejpam-3903	288	12	)	)	PUNCT
ejpam-3903	288	13	4	4	NUM
ejpam-3903	288	14	t	t	NOUN
ejpam-3903	288	15	(	(	PUNCT
ejpam-3903	288	16	w1	w1	NOUN
ejpam-3903	288	17	g	g	PROPN
ejpam-3903	288	18	−w0	−w0	PROPN
ejpam-3903	288	19	g	g	PROPN
ejpam-3903	288	20	)	)	PUNCT
ejpam-3903	288	21	,	,	PUNCT
ejpam-3903	288	22	v	v	X
ejpam-3903	288	23	>	>	X
ejpam-3903	288	24	(	(	PUNCT
ejpam-3903	288	25	39	39	NUM
ejpam-3903	288	26	)	)	PUNCT
ejpam-3903	288	27	where	where	SCONJ
ejpam-3903	288	28	hε(w	hε(w	PUNCT
ejpam-3903	288	29	0)w1	0)w1	PROPN
ejpam-3903	288	30	g	g	NOUN
ejpam-3903	288	31	=	=	X
ejpam-3903	288	32	kε(w	kε(w	VERB
ejpam-3903	288	33	0)w1	0)w1	NOUN
ejpam-3903	288	34	g	g	NOUN
ejpam-3903	289	1	+	+	CCONJ
ejpam-3903	289	2	d∑	d∑	PROPN
ejpam-3903	289	3	i=1	i=1	PROPN
ejpam-3903	290	1	aiε	aiε	VERB
ejpam-3903	290	2	∂w1	∂w1	PROPN
ejpam-3903	290	3	g	g	PROPN
ejpam-3903	290	4	∂xi	∂xi	PROPN
ejpam-3903	290	5	·	·	PUNCT
ejpam-3903	290	6	(	(	PUNCT
ejpam-3903	290	7	40	40	NUM
ejpam-3903	290	8	)	)	PUNCT
ejpam-3903	290	9	using	use	VERB
ejpam-3903	290	10	the	the	DET
ejpam-3903	290	11	fact	fact	NOUN
ejpam-3903	290	12	that	that	SCONJ
ejpam-3903	290	13	in	in	ADP
ejpam-3903	290	14	the	the	DET
ejpam-3903	290	15	expression	expression	NOUN
ejpam-3903	290	16	of	of	ADP
ejpam-3903	290	17	hε(w	hε(w	X
ejpam-3903	290	18	0)w1	0)w1	PROPN
ejpam-3903	290	19	g	g	ADP
ejpam-3903	290	20	only	only	ADJ
ejpam-3903	290	21	elements	element	NOUN
ejpam-3903	290	22	at	at	ADP
ejpam-3903	290	23	the	the	DET
ejpam-3903	290	24	five	five	NUM
ejpam-3903	290	25	first	first	ADJ
ejpam-3903	290	26	lines	line	NOUN
ejpam-3903	290	27	are	be	AUX
ejpam-3903	290	28	not	not	PART
ejpam-3903	290	29	equal	equal	ADJ
ejpam-3903	290	30	to	to	ADP
ejpam-3903	290	31	zero	zero	NUM
ejpam-3903	290	32	.	.	PUNCT
ejpam-3903	291	1	we	we	PRON
ejpam-3903	291	2	decompose	decompose	VERB
ejpam-3903	291	3	the	the	DET
ejpam-3903	291	4	matrix	matrix	NOUN
ejpam-3903	291	5	kε(w	kε(w	VERB
ejpam-3903	291	6	0	0	NUM
ejpam-3903	291	7	)	)	PUNCT
ejpam-3903	291	8	as	as	ADP
ejpam-3903	291	9	follow	follow	VERB
ejpam-3903	291	10	:	:	PUNCT
ejpam-3903	291	11	kε(w	kε(w	PROPN
ejpam-3903	291	12	0	0	NUM
ejpam-3903	291	13	)	)	PUNCT
ejpam-3903	291	14	=	=	VERB
ejpam-3903	291	15	d−a0	d−a0	NOUN
ejpam-3903	291	16	+	+	CCONJ
ejpam-3903	291	17	r1(w0	r1(w0	NOUN
ejpam-3903	291	18	)	)	PUNCT
ejpam-3903	291	19	+	+	CCONJ
ejpam-3903	291	20	r2(w0	r2(w0	NOUN
ejpam-3903	291	21	)	)	PUNCT
ejpam-3903	291	22	,	,	PUNCT
ejpam-3903	291	23	(	(	PUNCT
ejpam-3903	291	24	41	41	NUM
ejpam-3903	291	25	)	)	PUNCT
ejpam-3903	291	26	r.	r.	PROPN
ejpam-3903	291	27	bade	bade	PROPN
ejpam-3903	291	28	,	,	PUNCT
ejpam-3903	291	29	h.	h.	PROPN
ejpam-3903	291	30	chaker	chaker	PROPN
ejpam-3903	291	31	/	/	SYM
ejpam-3903	291	32	eur	eur	PROPN
ejpam-3903	291	33	.	.	PUNCT
ejpam-3903	292	1	j.	j.	PROPN
ejpam-3903	292	2	pure	pure	PROPN
ejpam-3903	292	3	appl	appl	PROPN
ejpam-3903	292	4	.	.	PROPN
ejpam-3903	292	5	math	math	PROPN
ejpam-3903	292	6	,	,	PUNCT
ejpam-3903	292	7	14	14	NUM
ejpam-3903	292	8	(	(	PUNCT
ejpam-3903	292	9	1	1	NUM
ejpam-3903	292	10	)	)	PUNCT
ejpam-3903	292	11	(	(	PUNCT
ejpam-3903	292	12	2021	2021	NUM
ejpam-3903	292	13	)	)	PUNCT
ejpam-3903	292	14	,	,	PUNCT
ejpam-3903	292	15	82	82	NUM
ejpam-3903	292	16	-	-	SYM
ejpam-3903	292	17	111	111	NUM
ejpam-3903	292	18	94	94	NUM
ejpam-3903	293	1	where	where	SCONJ
ejpam-3903	293	2	:	:	PUNCT
ejpam-3903	293	3	d	d	X
ejpam-3903	293	4	=	=	SYM
ejpam-3903	293	5			ADJ
ejpam-3903	293	6	0	0	NUM
ejpam-3903	293	7	0	0	NUM
ejpam-3903	293	8	0	0	NUM
ejpam-3903	293	9	0	0	NUM
ejpam-3903	293	10	0	0	NUM
ejpam-3903	293	11	k22	k22	NOUN
ejpam-3903	293	12	k23	k23	NOUN
ejpam-3903	293	13	k24	k24	PROPN
ejpam-3903	293	14	0	0	NUM
ejpam-3903	293	15	k32	k32	PROPN
ejpam-3903	293	16	k33	k33	PROPN
ejpam-3903	293	17	k34	k34	PROPN
ejpam-3903	293	18	0	0	NUM
ejpam-3903	293	19	k42	k42	PROPN
ejpam-3903	293	20	k43	k43	PROPN
ejpam-3903	293	21	k44	k44	PROPN
ejpam-3903	293	22			NOUN
ejpam-3903	293	23	,	,	PUNCT
ejpam-3903	293	24	r1	r1	NOUN
ejpam-3903	293	25	=	=	PUNCT
ejpam-3903	293	26			PROPN
ejpam-3903	293	27	k11	k11	NOUN
ejpam-3903	293	28	0	0	NUM
ejpam-3903	293	29	0	0	NUM
ejpam-3903	293	30	0	0	NUM
ejpam-3903	293	31	0	0	NUM
ejpam-3903	293	32	0	0	NUM
ejpam-3903	293	33	0	0	NUM
ejpam-3903	293	34	0	0	NUM
ejpam-3903	293	35	0	0	NUM
ejpam-3903	293	36	0	0	NUM
ejpam-3903	293	37	0	0	NUM
ejpam-3903	293	38	0	0	NUM
ejpam-3903	293	39	0	0	NUM
ejpam-3903	293	40	0	0	NUM
ejpam-3903	293	41	0	0	NUM
ejpam-3903	293	42	0	0	NUM
ejpam-3903	293	43			NOUN
ejpam-3903	293	44	,	,	PUNCT
ejpam-3903	293	45	r2	r2	PROPN
ejpam-3903	293	46	=	=	PUNCT
ejpam-3903	293	47			PROPN
ejpam-3903	293	48	0	0	NUM
ejpam-3903	293	49	k12	k12	PROPN
ejpam-3903	293	50	k13	k13	PROPN
ejpam-3903	293	51	k14	k14	PROPN
ejpam-3903	293	52	0	0	NUM
ejpam-3903	293	53	0	0	NUM
ejpam-3903	293	54	0	0	NUM
ejpam-3903	293	55	0	0	NUM
ejpam-3903	293	56	0	0	NUM
ejpam-3903	293	57	0	0	NUM
ejpam-3903	293	58	0	0	NUM
ejpam-3903	293	59	0	0	NUM
ejpam-3903	293	60	0	0	NUM
ejpam-3903	293	61	0	0	NUM
ejpam-3903	293	62	0	0	NUM
ejpam-3903	293	63	0	0	NUM
ejpam-3903	293	64			NOUN
ejpam-3903	293	65	,	,	PUNCT
ejpam-3903	293	66	with	with	ADP
ejpam-3903	293	67	k11	k11	NOUN
ejpam-3903	293	68	=	=	SYM
ejpam-3903	293	69			NOUN
ejpam-3903	293	70	w7	w7	ADJ
ejpam-3903	293	71	+	+	CCONJ
ejpam-3903	293	72	w13	w13	PROPN
ejpam-3903	293	73	+	+	CCONJ
ejpam-3903	293	74	w19	w19	PROPN
ejpam-3903	293	75	w6	w6	PROPN
ejpam-3903	293	76	w11	w11	PROPN
ejpam-3903	293	77	w16	w16	PROPN
ejpam-3903	293	78	0	0	PROPN
ejpam-3903	294	1	(	(	PUNCT
ejpam-3903	294	2	γ	γ	PROPN
ejpam-3903	294	3	−	−	PROPN
ejpam-3903	294	4	1)cvw10	1)cvw10	NUM
ejpam-3903	294	5	w1w7	w1w7	PROPN
ejpam-3903	294	6	w1w12	w1w12	PROPN
ejpam-3903	294	7	w1w17	w1w17	PROPN
ejpam-3903	294	8	(	(	PUNCT
ejpam-3903	294	9	γ	γ	PROPN
ejpam-3903	294	10	−	−	PROPN
ejpam-3903	294	11	1)cvw6	1)cvw6	PROPN
ejpam-3903	294	12	(	(	PUNCT
ejpam-3903	294	13	γ	γ	PROPN
ejpam-3903	294	14	−	−	PROPN
ejpam-3903	294	15	1)cvw15	1)cvw15	PROPN
ejpam-3903	294	16	w1w8	w1w8	PROPN
ejpam-3903	294	17	w1w13	w1w13	PROPN
ejpam-3903	294	18	w1w18	w1w18	PROPN
ejpam-3903	294	19	(	(	PUNCT
ejpam-3903	294	20	γ	γ	X
ejpam-3903	294	21	−	−	PROPN
ejpam-3903	294	22	1)cvw11	1)cvw11	NUM
ejpam-3903	294	23	(	(	PUNCT
ejpam-3903	294	24	γ	γ	PROPN
ejpam-3903	294	25	−	−	PROPN
ejpam-3903	294	26	1)cvw20	1)cvw20	NUM
ejpam-3903	294	27	w1w9	w1w9	PRON
ejpam-3903	294	28	w1w14	w1w14	VERB
ejpam-3903	294	29	w1w19	w1w19	PROPN
ejpam-3903	294	30	(	(	PUNCT
ejpam-3903	294	31	γ	γ	PROPN
ejpam-3903	294	32	−	−	PROPN
ejpam-3903	294	33	1)cvw16	1)cvw16	NUM
ejpam-3903	294	34	t1	t1	PROPN
ejpam-3903	294	35	t2	t2	PROPN
ejpam-3903	294	36	t3	t3	PROPN
ejpam-3903	294	37	t4	t4	PROPN
ejpam-3903	294	38	t5	t5	PROPN
ejpam-3903	294	39			NOUN
ejpam-3903	294	40	and	and	CCONJ
ejpam-3903	294	41	t1	t1	NOUN
ejpam-3903	294	42	=	=	PUNCT
ejpam-3903	294	43	cv(w2w10	cv(w2w10	PROPN
ejpam-3903	294	44	+	+	CCONJ
ejpam-3903	294	45	w3w15	w3w15	PROPN
ejpam-3903	294	46	+	+	CCONJ
ejpam-3903	294	47	w4w20	w4w20	PROPN
ejpam-3903	294	48	)	)	PUNCT
ejpam-3903	294	49	,	,	PUNCT
ejpam-3903	294	50	t2	t2	NOUN
ejpam-3903	294	51	=	=	SYM
ejpam-3903	294	52	w1(w2w7	w1(w2w7	PROPN
ejpam-3903	294	53	+	+	CCONJ
ejpam-3903	294	54	w3w8	w3w8	X
ejpam-3903	294	55	+	+	NUM
ejpam-3903	294	56	w4w9	w4w9	ADJ
ejpam-3903	294	57	)	)	PUNCT
ejpam-3903	294	58	,	,	PUNCT
ejpam-3903	294	59	t3	t3	PROPN
ejpam-3903	294	60	=	=	PUNCT
ejpam-3903	294	61	w1(w2w12	w1(w2w12	PROPN
ejpam-3903	294	62	+	+	NUM
ejpam-3903	294	63	w3w13	w3w13	ADJ
ejpam-3903	294	64	+	+	CCONJ
ejpam-3903	294	65	w4w14	w4w14	NOUN
ejpam-3903	294	66	)	)	PUNCT
ejpam-3903	294	67	,	,	PUNCT
ejpam-3903	294	68	t4	t4	PROPN
ejpam-3903	294	69	=	=	SYM
ejpam-3903	294	70	w1(w2w17	w1(w2w17	X
ejpam-3903	294	71	+	+	X
ejpam-3903	294	72	w3w18	w3w18	X
ejpam-3903	294	73	+	+	CCONJ
ejpam-3903	294	74	w4w19	w4w19	NUM
ejpam-3903	294	75	)	)	PUNCT
ejpam-3903	294	76	,	,	PUNCT
ejpam-3903	294	77	t5	t5	PROPN
ejpam-3903	294	78	=	=	SYM
ejpam-3903	294	79	cvw1(w7	cvw1(w7	PROPN
ejpam-3903	294	80	+	+	CCONJ
ejpam-3903	294	81	w13	w13	PROPN
ejpam-3903	294	82	+	+	CCONJ
ejpam-3903	294	83	w19	w19	PROPN
ejpam-3903	294	84	)	)	PUNCT
ejpam-3903	294	85	.	.	PUNCT
ejpam-3903	295	1	(	(	PUNCT
ejpam-3903	295	2	k12)ij	k12)ij	PROPN
ejpam-3903	295	3	=	=	PUNCT
ejpam-3903	295	4			NOUN
ejpam-3903	295	5	−δ(w7	−δ(w7	PROPN
ejpam-3903	295	6	+	+	CCONJ
ejpam-3903	295	7	w13	w13	PROPN
ejpam-3903	295	8	+	+	CCONJ
ejpam-3903	295	9	w19)−	w19)−	X
ejpam-3903	295	10	µw7	µw7	ADV
ejpam-3903	295	11	if	if	SCONJ
ejpam-3903	295	12	(	(	PUNCT
ejpam-3903	295	13	i	i	PROPN
ejpam-3903	295	14	,	,	PUNCT
ejpam-3903	295	15	j	j	PROPN
ejpam-3903	295	16	)	)	PUNCT
ejpam-3903	295	17	=	=	PUNCT
ejpam-3903	295	18	(	(	PUNCT
ejpam-3903	295	19	5	5	NUM
ejpam-3903	295	20	,	,	PUNCT
ejpam-3903	295	21	2	2	NUM
ejpam-3903	295	22	)	)	PUNCT
ejpam-3903	295	23	,	,	PUNCT
ejpam-3903	295	24	−µ	−µ	NOUN
ejpam-3903	295	25	2	2	NUM
ejpam-3903	295	26	(	(	PUNCT
ejpam-3903	295	27	w8	w8	NOUN
ejpam-3903	295	28	+	+	NUM
ejpam-3903	295	29	w12	w12	NOUN
ejpam-3903	295	30	)	)	PUNCT
ejpam-3903	295	31	if	if	SCONJ
ejpam-3903	295	32	(	(	PUNCT
ejpam-3903	295	33	i	i	PROPN
ejpam-3903	295	34	,	,	PUNCT
ejpam-3903	295	35	j	j	PROPN
ejpam-3903	295	36	)	)	PUNCT
ejpam-3903	295	37	=	=	PUNCT
ejpam-3903	295	38	(	(	PUNCT
ejpam-3903	295	39	5	5	NUM
ejpam-3903	295	40	,	,	PUNCT
ejpam-3903	295	41	3	3	NUM
ejpam-3903	295	42	)	)	PUNCT
ejpam-3903	295	43	,	,	PUNCT
ejpam-3903	295	44	−µ	−µ	NOUN
ejpam-3903	295	45	2	2	NUM
ejpam-3903	295	46	(	(	PUNCT
ejpam-3903	295	47	w9	w9	PROPN
ejpam-3903	295	48	+	+	SYM
ejpam-3903	295	49	w17	w17	PROPN
ejpam-3903	295	50	)	)	PUNCT
ejpam-3903	295	51	if	if	SCONJ
ejpam-3903	295	52	(	(	PUNCT
ejpam-3903	295	53	i	i	PRON
ejpam-3903	295	54	,	,	PUNCT
ejpam-3903	295	55	j	j	PROPN
ejpam-3903	295	56	)	)	PUNCT
ejpam-3903	295	57	=	=	PUNCT
ejpam-3903	295	58	(	(	PUNCT
ejpam-3903	295	59	5	5	NUM
ejpam-3903	295	60	,	,	PUNCT
ejpam-3903	295	61	4	4	NUM
ejpam-3903	295	62	)	)	PUNCT
ejpam-3903	295	63	,	,	PUNCT
ejpam-3903	295	64	0	0	NUM
ejpam-3903	295	65	if	if	SCONJ
ejpam-3903	295	66	not	not	PART
ejpam-3903	295	67	.	.	PUNCT
ejpam-3903	296	1	(	(	PUNCT
ejpam-3903	296	2	k13)ij	k13)ij	NOUN
ejpam-3903	296	3	=	=	PUNCT
ejpam-3903	296	4			NOUN
ejpam-3903	296	5	−µ	−µ	NOUN
ejpam-3903	296	6	2	2	NUM
ejpam-3903	296	7	(	(	PUNCT
ejpam-3903	296	8	w8	w8	NOUN
ejpam-3903	296	9	+	+	NUM
ejpam-3903	296	10	w12	w12	NOUN
ejpam-3903	296	11	)	)	PUNCT
ejpam-3903	296	12	if	if	SCONJ
ejpam-3903	296	13	(	(	PUNCT
ejpam-3903	296	14	i	i	PROPN
ejpam-3903	296	15	,	,	PUNCT
ejpam-3903	296	16	j	j	PROPN
ejpam-3903	296	17	)	)	PUNCT
ejpam-3903	296	18	=	=	PUNCT
ejpam-3903	296	19	(	(	PUNCT
ejpam-3903	296	20	5	5	NUM
ejpam-3903	296	21	,	,	PUNCT
ejpam-3903	296	22	2	2	NUM
ejpam-3903	296	23	)	)	PUNCT
ejpam-3903	296	24	,	,	PUNCT
ejpam-3903	296	25	−δ(w7	−δ(w7	PROPN
ejpam-3903	296	26	+	+	CCONJ
ejpam-3903	296	27	w13	w13	PROPN
ejpam-3903	296	28	+	+	CCONJ
ejpam-3903	296	29	w19)−	w19)−	X
ejpam-3903	296	30	µw13	µw13	PROPN
ejpam-3903	296	31	if	if	SCONJ
ejpam-3903	296	32	(	(	PUNCT
ejpam-3903	296	33	i	i	PROPN
ejpam-3903	296	34	,	,	PUNCT
ejpam-3903	296	35	j	j	PROPN
ejpam-3903	296	36	)	)	PUNCT
ejpam-3903	296	37	=	=	PUNCT
ejpam-3903	296	38	(	(	PUNCT
ejpam-3903	296	39	5	5	NUM
ejpam-3903	296	40	,	,	PUNCT
ejpam-3903	296	41	3	3	NUM
ejpam-3903	296	42	)	)	PUNCT
ejpam-3903	296	43	,	,	PUNCT
ejpam-3903	296	44	−µ	−µ	NOUN
ejpam-3903	296	45	2	2	NUM
ejpam-3903	296	46	(	(	PUNCT
ejpam-3903	296	47	w14	w14	NOUN
ejpam-3903	296	48	+	+	CCONJ
ejpam-3903	296	49	w18	w18	NOUN
ejpam-3903	296	50	)	)	PUNCT
ejpam-3903	296	51	if	if	SCONJ
ejpam-3903	296	52	(	(	PUNCT
ejpam-3903	296	53	i	i	PRON
ejpam-3903	296	54	,	,	PUNCT
ejpam-3903	296	55	j	j	PROPN
ejpam-3903	296	56	)	)	PUNCT
ejpam-3903	296	57	=	=	PUNCT
ejpam-3903	296	58	(	(	PUNCT
ejpam-3903	296	59	5	5	NUM
ejpam-3903	296	60	,	,	PUNCT
ejpam-3903	296	61	4	4	NUM
ejpam-3903	296	62	)	)	PUNCT
ejpam-3903	296	63	,	,	PUNCT
ejpam-3903	296	64	0	0	NUM
ejpam-3903	296	65	if	if	SCONJ
ejpam-3903	296	66	not	not	PART
ejpam-3903	296	67	.	.	PUNCT
ejpam-3903	297	1	(	(	PUNCT
ejpam-3903	297	2	k14)ij	k14)ij	NOUN
ejpam-3903	297	3	=	=	SYM
ejpam-3903	297	4			NOUN
ejpam-3903	297	5	−µ	−µ	NOUN
ejpam-3903	297	6	2	2	NUM
ejpam-3903	297	7	(	(	PUNCT
ejpam-3903	297	8	w9	w9	PROPN
ejpam-3903	297	9	+	+	SYM
ejpam-3903	297	10	w17	w17	PROPN
ejpam-3903	297	11	)	)	PUNCT
ejpam-3903	297	12	if	if	SCONJ
ejpam-3903	297	13	(	(	PUNCT
ejpam-3903	297	14	i	i	PRON
ejpam-3903	297	15	,	,	PUNCT
ejpam-3903	297	16	j	j	PROPN
ejpam-3903	297	17	)	)	PUNCT
ejpam-3903	297	18	=	=	PUNCT
ejpam-3903	297	19	(	(	PUNCT
ejpam-3903	297	20	5	5	NUM
ejpam-3903	297	21	,	,	PUNCT
ejpam-3903	297	22	2	2	NUM
ejpam-3903	297	23	)	)	PUNCT
ejpam-3903	297	24	,	,	PUNCT
ejpam-3903	297	25	−µ	−µ	NOUN
ejpam-3903	297	26	2	2	NUM
ejpam-3903	297	27	(	(	PUNCT
ejpam-3903	297	28	w8	w8	NOUN
ejpam-3903	297	29	+	+	CCONJ
ejpam-3903	297	30	w14	w14	PROPN
ejpam-3903	297	31	)	)	PUNCT
ejpam-3903	298	1	if	if	SCONJ
ejpam-3903	298	2	(	(	PUNCT
ejpam-3903	298	3	i	i	PRON
ejpam-3903	298	4	,	,	PUNCT
ejpam-3903	298	5	j	j	PROPN
ejpam-3903	298	6	)	)	PUNCT
ejpam-3903	298	7	=	=	PUNCT
ejpam-3903	298	8	(	(	PUNCT
ejpam-3903	298	9	5	5	NUM
ejpam-3903	298	10	,	,	PUNCT
ejpam-3903	298	11	3	3	NUM
ejpam-3903	298	12	)	)	PUNCT
ejpam-3903	298	13	,	,	PUNCT
ejpam-3903	298	14	−δ(w7	−δ(w7	PROPN
ejpam-3903	298	15	+	+	CCONJ
ejpam-3903	298	16	w13	w13	PROPN
ejpam-3903	298	17	+	+	CCONJ
ejpam-3903	298	18	w19)−	w19)−	X
ejpam-3903	298	19	µw19	µw19	PROPN
ejpam-3903	298	20	if	if	SCONJ
ejpam-3903	298	21	(	(	PUNCT
ejpam-3903	298	22	i	i	PROPN
ejpam-3903	298	23	,	,	PUNCT
ejpam-3903	298	24	j	j	PROPN
ejpam-3903	298	25	)	)	PUNCT
ejpam-3903	298	26	=	=	PUNCT
ejpam-3903	299	1	(	(	PUNCT
ejpam-3903	299	2	5	5	NUM
ejpam-3903	299	3	,	,	PUNCT
ejpam-3903	299	4	4	4	NUM
ejpam-3903	299	5	)	)	PUNCT
ejpam-3903	299	6	,	,	PUNCT
ejpam-3903	299	7	0	0	NUM
ejpam-3903	299	8	if	if	SCONJ
ejpam-3903	299	9	not	not	PART
ejpam-3903	299	10	.	.	PUNCT
ejpam-3903	300	1	k22	k22	NOUN
ejpam-3903	300	2	=	=	SYM
ejpam-3903	300	3			NOUN
ejpam-3903	300	4	ε	ε	PROPN
ejpam-3903	300	5	0	0	NUM
ejpam-3903	300	6	0	0	NUM
ejpam-3903	300	7	0	0	NUM
ejpam-3903	300	8	0	0	NUM
ejpam-3903	300	9	0	0	NUM
ejpam-3903	300	10	α	α	NOUN
ejpam-3903	300	11	0	0	NUM
ejpam-3903	300	12	0	0	NUM
ejpam-3903	300	13	0	0	NUM
ejpam-3903	300	14	0	0	NUM
ejpam-3903	300	15	0	0	NUM
ejpam-3903	300	16	µ	µ	X
ejpam-3903	300	17	0	0	NUM
ejpam-3903	300	18	0	0	NUM
ejpam-3903	300	19	0	0	NUM
ejpam-3903	300	20	0	0	NUM
ejpam-3903	300	21	0	0	NUM
ejpam-3903	300	22	µ	µ	X
ejpam-3903	300	23	0	0	NUM
ejpam-3903	300	24	0	0	NUM
ejpam-3903	300	25	0	0	NUM
ejpam-3903	300	26	0	0	NUM
ejpam-3903	300	27	0	0	NUM
ejpam-3903	300	28	k	k	NOUN
ejpam-3903	300	29			NOUN
ejpam-3903	300	30	,	,	PUNCT
ejpam-3903	300	31	k33	k33	NOUN
ejpam-3903	300	32	=	=	SYM
ejpam-3903	300	33			NOUN
ejpam-3903	300	34	ε	ε	PROPN
ejpam-3903	300	35	0	0	NUM
ejpam-3903	300	36	0	0	NUM
ejpam-3903	300	37	0	0	NUM
ejpam-3903	300	38	0	0	NUM
ejpam-3903	300	39	0	0	NUM
ejpam-3903	300	40	µ	µ	X
ejpam-3903	300	41	0	0	NUM
ejpam-3903	300	42	0	0	NUM
ejpam-3903	300	43	0	0	NUM
ejpam-3903	300	44	0	0	NUM
ejpam-3903	300	45	0	0	NUM
ejpam-3903	301	1	α	α	NOUN
ejpam-3903	301	2	0	0	NUM
ejpam-3903	301	3	0	0	NUM
ejpam-3903	301	4	0	0	NUM
ejpam-3903	301	5	0	0	NUM
ejpam-3903	301	6	0	0	NUM
ejpam-3903	301	7	µ	µ	X
ejpam-3903	301	8	0	0	NUM
ejpam-3903	301	9	0	0	NUM
ejpam-3903	301	10	0	0	NUM
ejpam-3903	301	11	0	0	NUM
ejpam-3903	301	12	0	0	NUM
ejpam-3903	302	1	k	k	NOUN
ejpam-3903	302	2			NOUN
ejpam-3903	302	3	,	,	PUNCT
ejpam-3903	302	4	k44	k44	NOUN
ejpam-3903	302	5	=	=	PUNCT
ejpam-3903	302	6			NOUN
ejpam-3903	302	7	ε	ε	PROPN
ejpam-3903	302	8	0	0	NUM
ejpam-3903	302	9	0	0	NUM
ejpam-3903	302	10	0	0	NUM
ejpam-3903	302	11	0	0	NUM
ejpam-3903	302	12	0	0	NUM
ejpam-3903	302	13	µ	µ	X
ejpam-3903	302	14	0	0	NUM
ejpam-3903	302	15	0	0	NUM
ejpam-3903	302	16	0	0	NUM
ejpam-3903	302	17	0	0	NUM
ejpam-3903	302	18	0	0	NUM
ejpam-3903	302	19	µ	µ	X
ejpam-3903	302	20	0	0	NUM
ejpam-3903	302	21	0	0	NUM
ejpam-3903	302	22	0	0	NUM
ejpam-3903	302	23	0	0	NUM
ejpam-3903	302	24	0	0	NUM
ejpam-3903	302	25	α	α	NOUN
ejpam-3903	302	26	0	0	NUM
ejpam-3903	302	27	0	0	NUM
ejpam-3903	302	28	0	0	NUM
ejpam-3903	302	29	0	0	NUM
ejpam-3903	302	30	0	0	NUM
ejpam-3903	302	31	k	k	NOUN
ejpam-3903	302	32			NOUN
ejpam-3903	302	33	,	,	PUNCT
ejpam-3903	302	34	r.	r.	PROPN
ejpam-3903	302	35	bade	bade	PROPN
ejpam-3903	302	36	,	,	PUNCT
ejpam-3903	302	37	h.	h.	PROPN
ejpam-3903	302	38	chaker	chaker	PROPN
ejpam-3903	302	39	/	/	SYM
ejpam-3903	302	40	eur	eur	PROPN
ejpam-3903	302	41	.	.	PUNCT
ejpam-3903	303	1	j.	j.	PROPN
ejpam-3903	303	2	pure	pure	PROPN
ejpam-3903	303	3	appl	appl	PROPN
ejpam-3903	303	4	.	.	PROPN
ejpam-3903	303	5	math	math	PROPN
ejpam-3903	303	6	,	,	PUNCT
ejpam-3903	303	7	14	14	NUM
ejpam-3903	303	8	(	(	PUNCT
ejpam-3903	303	9	1	1	NUM
ejpam-3903	303	10	)	)	PUNCT
ejpam-3903	303	11	(	(	PUNCT
ejpam-3903	303	12	2021	2021	NUM
ejpam-3903	303	13	)	)	PUNCT
ejpam-3903	303	14	,	,	PUNCT
ejpam-3903	303	15	82	82	NUM
ejpam-3903	303	16	-	-	SYM
ejpam-3903	303	17	111	111	NUM
ejpam-3903	303	18	95	95	NUM
ejpam-3903	303	19	(	(	PUNCT
ejpam-3903	303	20	k23)ij	k23)ij	X
ejpam-3903	303	21	=	=	SYM
ejpam-3903	303	22	{	{	PUNCT
ejpam-3903	303	23	β	β	X
ejpam-3903	303	24	if	if	SCONJ
ejpam-3903	303	25	(	(	PUNCT
ejpam-3903	303	26	i	i	PROPN
ejpam-3903	303	27	,	,	PUNCT
ejpam-3903	303	28	j	j	PROPN
ejpam-3903	303	29	)	)	PUNCT
ejpam-3903	303	30	=	=	PUNCT
ejpam-3903	303	31	(	(	PUNCT
ejpam-3903	303	32	2	2	NUM
ejpam-3903	303	33	,	,	PUNCT
ejpam-3903	303	34	3	3	NUM
ejpam-3903	303	35	)	)	PUNCT
ejpam-3903	303	36	,	,	PUNCT
ejpam-3903	303	37	0	0	NUM
ejpam-3903	303	38	if	if	SCONJ
ejpam-3903	303	39	not	not	PART
ejpam-3903	303	40	.	.	PUNCT
ejpam-3903	304	1	(	(	PUNCT
ejpam-3903	304	2	k32)ij	k32)ij	PROPN
ejpam-3903	304	3	=	=	SYM
ejpam-3903	304	4	{	{	PUNCT
ejpam-3903	304	5	β	β	X
ejpam-3903	304	6	if	if	SCONJ
ejpam-3903	304	7	(	(	PUNCT
ejpam-3903	304	8	i	i	PROPN
ejpam-3903	304	9	,	,	PUNCT
ejpam-3903	304	10	j	j	PROPN
ejpam-3903	304	11	)	)	PUNCT
ejpam-3903	304	12	=	=	PUNCT
ejpam-3903	304	13	(	(	PUNCT
ejpam-3903	304	14	3	3	NUM
ejpam-3903	304	15	,	,	PUNCT
ejpam-3903	304	16	2	2	NUM
ejpam-3903	304	17	)	)	PUNCT
ejpam-3903	304	18	,	,	PUNCT
ejpam-3903	304	19	0	0	NUM
ejpam-3903	304	20	if	if	SCONJ
ejpam-3903	304	21	not	not	PART
ejpam-3903	304	22	.	.	PUNCT
ejpam-3903	305	1	(	(	PUNCT
ejpam-3903	305	2	k42)ij	k42)ij	X
ejpam-3903	305	3	=	=	PUNCT
ejpam-3903	305	4	{	{	PUNCT
ejpam-3903	305	5	β	β	X
ejpam-3903	305	6	if	if	SCONJ
ejpam-3903	305	7	(	(	PUNCT
ejpam-3903	305	8	i	i	PROPN
ejpam-3903	305	9	,	,	PUNCT
ejpam-3903	305	10	j	j	PROPN
ejpam-3903	305	11	)	)	PUNCT
ejpam-3903	305	12	=	=	PUNCT
ejpam-3903	305	13	(	(	PUNCT
ejpam-3903	305	14	4	4	NUM
ejpam-3903	305	15	,	,	PUNCT
ejpam-3903	305	16	2	2	NUM
ejpam-3903	305	17	)	)	PUNCT
ejpam-3903	305	18	,	,	PUNCT
ejpam-3903	305	19	0	0	NUM
ejpam-3903	305	20	if	if	SCONJ
ejpam-3903	305	21	not	not	PART
ejpam-3903	305	22	.	.	PUNCT
ejpam-3903	306	1	(	(	PUNCT
ejpam-3903	306	2	k24)ij	k24)ij	PROPN
ejpam-3903	306	3	=	=	SYM
ejpam-3903	306	4	{	{	PUNCT
ejpam-3903	306	5	β	β	X
ejpam-3903	306	6	if	if	SCONJ
ejpam-3903	306	7	(	(	PUNCT
ejpam-3903	306	8	i	i	PROPN
ejpam-3903	306	9	,	,	PUNCT
ejpam-3903	306	10	j	j	PROPN
ejpam-3903	306	11	)	)	PUNCT
ejpam-3903	306	12	=	=	PUNCT
ejpam-3903	306	13	(	(	PUNCT
ejpam-3903	306	14	2	2	NUM
ejpam-3903	306	15	,	,	PUNCT
ejpam-3903	306	16	4	4	NUM
ejpam-3903	306	17	)	)	PUNCT
ejpam-3903	306	18	,	,	PUNCT
ejpam-3903	306	19	0	0	NUM
ejpam-3903	306	20	if	if	SCONJ
ejpam-3903	306	21	not	not	PART
ejpam-3903	306	22	.	.	PUNCT
ejpam-3903	307	1	(	(	PUNCT
ejpam-3903	307	2	k34)ij	k34)ij	PROPN
ejpam-3903	307	3	=	=	SYM
ejpam-3903	307	4	{	{	PUNCT
ejpam-3903	307	5	β	β	X
ejpam-3903	307	6	if	if	SCONJ
ejpam-3903	307	7	(	(	PUNCT
ejpam-3903	307	8	i	i	PROPN
ejpam-3903	307	9	,	,	PUNCT
ejpam-3903	307	10	j	j	PROPN
ejpam-3903	307	11	)	)	PUNCT
ejpam-3903	307	12	=	=	PUNCT
ejpam-3903	307	13	(	(	PUNCT
ejpam-3903	307	14	3	3	NUM
ejpam-3903	307	15	,	,	PUNCT
ejpam-3903	307	16	4	4	NUM
ejpam-3903	307	17	)	)	PUNCT
ejpam-3903	307	18	,	,	PUNCT
ejpam-3903	307	19	0	0	NUM
ejpam-3903	307	20	if	if	SCONJ
ejpam-3903	307	21	not	not	PART
ejpam-3903	307	22	.	.	PUNCT
ejpam-3903	308	1	(	(	PUNCT
ejpam-3903	308	2	k43)ij	k43)ij	PROPN
ejpam-3903	308	3	=	=	SYM
ejpam-3903	308	4	{	{	PUNCT
ejpam-3903	308	5	β	β	X
ejpam-3903	308	6	if	if	SCONJ
ejpam-3903	308	7	(	(	PUNCT
ejpam-3903	308	8	i	i	PROPN
ejpam-3903	308	9	,	,	PUNCT
ejpam-3903	308	10	j	j	PROPN
ejpam-3903	308	11	)	)	PUNCT
ejpam-3903	308	12	=	=	PUNCT
ejpam-3903	308	13	(	(	PUNCT
ejpam-3903	308	14	4	4	NUM
ejpam-3903	308	15	,	,	PUNCT
ejpam-3903	308	16	3	3	NUM
ejpam-3903	308	17	)	)	PUNCT
ejpam-3903	308	18	,	,	PUNCT
ejpam-3903	308	19	0	0	NUM
ejpam-3903	308	20	if	if	SCONJ
ejpam-3903	308	21	not	not	PART
ejpam-3903	308	22	.	.	PUNCT
ejpam-3903	309	1	multiplying	multiply	VERB
ejpam-3903	309	2	the	the	DET
ejpam-3903	309	3	equality	equality	NOUN
ejpam-3903	309	4	(	(	PUNCT
ejpam-3903	309	5	39	39	NUM
ejpam-3903	309	6	)	)	PUNCT
ejpam-3903	309	7	by	by	ADP
ejpam-3903	309	8	4	4	NUM
ejpam-3903	309	9	t	t	NOUN
ejpam-3903	309	10	and	and	CCONJ
ejpam-3903	309	11	using	use	VERB
ejpam-3903	309	12	the	the	DET
ejpam-3903	309	13	decomposition	decomposition	NOUN
ejpam-3903	309	14	(	(	PUNCT
ejpam-3903	309	15	41	41	NUM
ejpam-3903	309	16	)	)	PUNCT
ejpam-3903	309	17	we	we	PRON
ejpam-3903	309	18	have	have	AUX
ejpam-3903	309	19	:	:	PUNCT
ejpam-3903	309	20	<	<	X
ejpam-3903	309	21	a0(w0)w1∗	a0(w0)w1∗	ADJ
ejpam-3903	309	22	1	1	NUM
ejpam-3903	309	23	,	,	PUNCT
ejpam-3903	309	24	a0v	a0v	PROPN
ejpam-3903	309	25	>	>	X
ejpam-3903	310	1	+4	+4	PROPN
ejpam-3903	310	2	t	t	X
ejpam-3903	310	3	<	<	X
ejpam-3903	310	4	dw1∗	dw1∗	PROPN
ejpam-3903	310	5	1	1	NUM
ejpam-3903	310	6	,	,	PUNCT
ejpam-3903	310	7	v	v	PART
ejpam-3903	310	8	>	>	X
ejpam-3903	310	9	+4	+4	PROPN
ejpam-3903	310	10	t	t	X
ejpam-3903	310	11	<	<	X
ejpam-3903	310	12	r2(w0)w1∗	r2(w0)w1∗	NOUN
ejpam-3903	310	13	1	1	NUM
ejpam-3903	310	14	,	,	PUNCT
ejpam-3903	310	15	v	v	PART
ejpam-3903	310	16	>	>	X
ejpam-3903	310	17	=	=	SYM
ejpam-3903	310	18	4	4	NUM
ejpam-3903	310	19	t	t	NOUN
ejpam-3903	310	20	<	<	X
ejpam-3903	310	21	f1,a0v	f1,a0v	PROPN
ejpam-3903	310	22	>	>	X
ejpam-3903	311	1	+	+	X
ejpam-3903	311	2	<	<	X
ejpam-3903	311	3	a0(w0)w0∗,a0v	a0(w0)w0∗,a0v	NOUN
ejpam-3903	311	4	>	>	X
ejpam-3903	312	1	+4	+4	PROPN
ejpam-3903	312	2	t	t	X
ejpam-3903	312	3	<	<	X
ejpam-3903	312	4	(	(	PUNCT
ejpam-3903	312	5	a0	a0	PROPN
ejpam-3903	312	6	−r1(w0))w1∗	−r1(w0))w1∗	PROPN
ejpam-3903	312	7	1	1	NUM
ejpam-3903	312	8	,	,	PUNCT
ejpam-3903	312	9	a0v	a0v	PROPN
ejpam-3903	312	10	>	>	X
ejpam-3903	313	1	−4	−4	PROPN
ejpam-3903	313	2	t	t	X
ejpam-3903	313	3	<	<	X
ejpam-3903	313	4	hε(w	hε(w	X
ejpam-3903	313	5	0)w1	0)w1	PROPN
ejpam-3903	313	6	g	g	PROPN
ejpam-3903	313	7	,	,	PUNCT
ejpam-3903	313	8	a0v	a0v	PROPN
ejpam-3903	313	9	>	>	X
ejpam-3903	313	10	−	−	X
ejpam-3903	313	11	<	<	X
ejpam-3903	313	12	a0(w0)(w1	a0(w0)(w1	X
ejpam-3903	313	13	g	g	PROPN
ejpam-3903	314	1	−w0	−w0	PROPN
ejpam-3903	315	1	g),a0v	g),a0v	PROPN
ejpam-3903	315	2	>	>	PUNCT
ejpam-3903	315	3	one	one	PRON
ejpam-3903	315	4	can	can	AUX
ejpam-3903	315	5	note	note	VERB
ejpam-3903	315	6	that	that	SCONJ
ejpam-3903	315	7	all	all	DET
ejpam-3903	315	8	elements	element	NOUN
ejpam-3903	315	9	of	of	ADP
ejpam-3903	315	10	r2	r2	PROPN
ejpam-3903	315	11	(	(	PUNCT
ejpam-3903	315	12	·	·	PUNCT
ejpam-3903	315	13	)	)	PUNCT
ejpam-3903	315	14	are	be	AUX
ejpam-3903	315	15	equal	equal	ADJ
ejpam-3903	315	16	to	to	ADP
ejpam-3903	315	17	zero	zero	NUM
ejpam-3903	315	18	except	except	SCONJ
ejpam-3903	315	19	somes	some	NOUN
ejpam-3903	315	20	of	of	ADP
ejpam-3903	315	21	the	the	DET
ejpam-3903	315	22	fifth	fifth	ADJ
ejpam-3903	315	23	line	line	NOUN
ejpam-3903	315	24	,	,	PUNCT
ejpam-3903	315	25	then	then	ADV
ejpam-3903	315	26	we	we	PRON
ejpam-3903	315	27	get	get	VERB
ejpam-3903	315	28	sup	sup	NOUN
ejpam-3903	315	29	v	v	ADP
ejpam-3903	315	30	∈v	∈v	NOUN
ejpam-3903	315	31	|	|	ADV
ejpam-3903	315	32	<	<	X
ejpam-3903	315	33	a0(w0)w1∗	a0(w0)w1∗	ADJ
ejpam-3903	315	34	1	1	NUM
ejpam-3903	315	35	,	,	PUNCT
ejpam-3903	315	36	a0v	a0v	PROPN
ejpam-3903	315	37	>	>	X
ejpam-3903	316	1	|	|	ADV
ejpam-3903	316	2	‖a0v	‖a0v	PROPN
ejpam-3903	316	3	‖h−s	‖h−s	PROPN
ejpam-3903	316	4	6	6	NUM
ejpam-3903	316	5	sup	sup	NOUN
ejpam-3903	316	6	v	v	ADP
ejpam-3903	316	7	∈v	∈v	PROPN
ejpam-3903	316	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3903	316	9	<	<	X
ejpam-3903	316	10	a0(w0)w1∗	a0(w0)w1∗	ADJ
ejpam-3903	316	11	1	1	NUM
ejpam-3903	316	12	,	,	PUNCT
ejpam-3903	316	13	a0v	a0v	PROPN
ejpam-3903	316	14	>	>	X
ejpam-3903	316	15	‖a0v	‖a0v	PROPN
ejpam-3903	316	16	‖h−s	‖h−s	PROPN
ejpam-3903	317	1	+4	+4	PROPN
ejpam-3903	317	2	t	t	X
ejpam-3903	317	3	<	<	X
ejpam-3903	317	4	dw1∗	dw1∗	PROPN
ejpam-3903	317	5	1	1	NUM
ejpam-3903	317	6	,	,	PUNCT
ejpam-3903	317	7	v	v	PART
ejpam-3903	317	8	>	>	X
ejpam-3903	317	9	‖v	‖v	NOUN
ejpam-3903	318	1	‖h−s+1	‖h−s+1	PROPN
ejpam-3903	318	2	+4	+4	PROPN
ejpam-3903	318	3	t	t	X
ejpam-3903	318	4	<	<	X
ejpam-3903	318	5	r2(w0)w1∗	r2(w0)w1∗	NOUN
ejpam-3903	318	6	1	1	NUM
ejpam-3903	318	7	,	,	PUNCT
ejpam-3903	318	8	a0v	a0v	PROPN
ejpam-3903	318	9	>	>	X
ejpam-3903	318	10	‖a0v	‖a0v	PROPN
ejpam-3903	318	11	‖h−s	‖h−s	X
ejpam-3903	318	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3903	318	13	6	6	NUM
ejpam-3903	318	14	4t‖f1‖hs	4t‖f1‖hs	NUM
ejpam-3903	318	15	+	+	CCONJ
ejpam-3903	318	16	c03(w0)‖a0w0∗‖hs+	c03(w0)‖a0w0∗‖hs+	ADJ
ejpam-3903	318	17	4t(c	4t(c	PROPN
ejpam-3903	318	18	+	+	CCONJ
ejpam-3903	318	19	c‖w0‖3l∞)‖a0w1∗	c‖w0‖3l∞)‖a0w1∗	NOUN
ejpam-3903	318	20	1	1	NUM
ejpam-3903	318	21	‖hs	‖hs	PROPN
ejpam-3903	318	22	+4t(c	+4t(c	NUM
ejpam-3903	318	23	+	+	NUM
ejpam-3903	318	24	c‖w0‖3l∞)‖w1	c‖w0‖3l∞)‖w1	PROPN
ejpam-3903	318	25	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	318	26	+	+	NUM
ejpam-3903	318	27	c03(w0)‖a0(w1	c03(w0)‖a0(w1	NOUN
ejpam-3903	318	28	g	g	ADP
ejpam-3903	318	29	−w0	−w0	PROPN
ejpam-3903	318	30	g)‖hs	g)‖h	VERB
ejpam-3903	318	31	where	where	SCONJ
ejpam-3903	318	32	c	c	NOUN
ejpam-3903	318	33	=	=	SYM
ejpam-3903	318	34	sup	sup	NOUN
ejpam-3903	318	35	(	(	PUNCT
ejpam-3903	318	36	3	3	NUM
ejpam-3903	318	37	,	,	PUNCT
ejpam-3903	318	38	3cv	3cv	NOUN
ejpam-3903	318	39	,	,	PUNCT
ejpam-3903	318	40	(	(	PUNCT
ejpam-3903	318	41	γ	γ	PROPN
ejpam-3903	318	42	−	−	PROPN
ejpam-3903	318	43	1)cv	1)cv	NUM
ejpam-3903	318	44	,	,	PUNCT
ejpam-3903	318	45	µ	µ	NOUN
ejpam-3903	318	46	,	,	PUNCT
ejpam-3903	318	47	β	β	X
ejpam-3903	318	48	,	,	PUNCT
ejpam-3903	318	49	α	α	PROPN
ejpam-3903	318	50	,	,	PUNCT
ejpam-3903	318	51	k	k	PROPN
ejpam-3903	318	52	)	)	PUNCT
ejpam-3903	318	53	by	by	ADP
ejpam-3903	318	54	definition	definition	NOUN
ejpam-3903	318	55	of	of	ADP
ejpam-3903	318	56	the	the	DET
ejpam-3903	318	57	hs	hs	PROPN
ejpam-3903	318	58	norm	norm	NOUN
ejpam-3903	318	59	given	give	VERB
ejpam-3903	318	60	in	in	ADP
ejpam-3903	318	61	[	[	X
ejpam-3903	318	62	12	12	NUM
ejpam-3903	318	63	]	]	PUNCT
ejpam-3903	318	64	,	,	PUNCT
ejpam-3903	318	65	we	we	PRON
ejpam-3903	318	66	finally	finally	ADV
ejpam-3903	318	67	deduce	deduce	VERB
ejpam-3903	318	68	:	:	PUNCT
ejpam-3903	318	69	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	318	70	1	1	NUM
ejpam-3903	318	71	‖hs	‖hs	NUM
ejpam-3903	318	72	≤	≤	NUM
ejpam-3903	318	73	4	4	NUM
ejpam-3903	318	74	t	t	NOUN
ejpam-3903	318	75	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	318	76	)	)	PUNCT
ejpam-3903	318	77	‖f1‖hs	‖f1‖hs	PUNCT
ejpam-3903	319	1	+	+	PUNCT
ejpam-3903	319	2	c03(w0	c03(w0	ADJ
ejpam-3903	319	3	)	)	PUNCT
ejpam-3903	319	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	319	5	)	)	PUNCT
ejpam-3903	319	6	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	320	1	+4	+4	PROPN
ejpam-3903	320	2	t	t	X
ejpam-3903	320	3	c	c	NOUN
ejpam-3903	320	4	+	+	CCONJ
ejpam-3903	320	5	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	320	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	320	7	)	)	PUNCT
ejpam-3903	320	8	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	320	9	1	1	NUM
ejpam-3903	320	10	‖hs	‖hs	NUM
ejpam-3903	320	11	+4	+4	PROPN
ejpam-3903	320	12	t	t	NOUN
ejpam-3903	320	13	c	c	NOUN
ejpam-3903	320	14	+	+	CCONJ
ejpam-3903	320	15	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	320	16	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	320	17	)	)	PUNCT
ejpam-3903	320	18	‖w1	‖w1	PART
ejpam-3903	320	19	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	321	1	+	+	CCONJ
ejpam-3903	321	2	c03(w0	c03(w0	ADJ
ejpam-3903	321	3	)	)	PUNCT
ejpam-3903	321	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	321	5	)	)	PUNCT
ejpam-3903	321	6	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	321	7	g	g	PROPN
ejpam-3903	321	8	−w0	−w0	PROPN
ejpam-3903	321	9	g)‖hs	g)‖hs	PROPN
ejpam-3903	321	10	,	,	PUNCT
ejpam-3903	321	11	(	(	PUNCT
ejpam-3903	321	12	42	42	NUM
ejpam-3903	321	13	)	)	PUNCT
ejpam-3903	321	14	with	with	ADP
ejpam-3903	321	15	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	321	16	)	)	PUNCT
ejpam-3903	321	17	is	be	AUX
ejpam-3903	321	18	a	a	DET
ejpam-3903	321	19	strict	strict	ADJ
ejpam-3903	321	20	positive	positive	ADJ
ejpam-3903	321	21	constant	constant	ADJ
ejpam-3903	321	22	independent	independent	NOUN
ejpam-3903	321	23	to	to	AUX
ejpam-3903	321	24	ε	ε	PROPN
ejpam-3903	321	25	given	give	VERB
ejpam-3903	321	26	by	by	ADP
ejpam-3903	321	27	:	:	PUNCT
ejpam-3903	321	28	c01(ρ̄∞	c01(ρ̄∞	PROPN
ejpam-3903	321	29	)	)	PUNCT
ejpam-3903	321	30	=	=	SYM
ejpam-3903	321	31	inf(1	inf(1	NOUN
ejpam-3903	321	32	,	,	PUNCT
ejpam-3903	321	33	ρ̄∞	ρ̄∞	NOUN
ejpam-3903	321	34	,	,	PUNCT
ejpam-3903	321	35	cvρ̄∞	cvρ̄∞	PROPN
ejpam-3903	321	36	)	)	PUNCT
ejpam-3903	321	37	·	·	PUNCT
ejpam-3903	321	38	(	(	PUNCT
ejpam-3903	321	39	43	43	X
ejpam-3903	321	40	)	)	PUNCT
ejpam-3903	321	41	r.	r.	PROPN
ejpam-3903	321	42	bade	bade	PROPN
ejpam-3903	321	43	,	,	PUNCT
ejpam-3903	321	44	h.	h.	PROPN
ejpam-3903	321	45	chaker	chaker	PROPN
ejpam-3903	321	46	/	/	SYM
ejpam-3903	321	47	eur	eur	PROPN
ejpam-3903	321	48	.	.	PUNCT
ejpam-3903	322	1	j.	j.	PROPN
ejpam-3903	322	2	pure	pure	PROPN
ejpam-3903	322	3	appl	appl	PROPN
ejpam-3903	322	4	.	.	PROPN
ejpam-3903	322	5	math	math	PROPN
ejpam-3903	322	6	,	,	PUNCT
ejpam-3903	322	7	14	14	NUM
ejpam-3903	322	8	(	(	PUNCT
ejpam-3903	322	9	1	1	NUM
ejpam-3903	322	10	)	)	PUNCT
ejpam-3903	322	11	(	(	PUNCT
ejpam-3903	322	12	2021	2021	NUM
ejpam-3903	322	13	)	)	PUNCT
ejpam-3903	322	14	,	,	PUNCT
ejpam-3903	322	15	82	82	NUM
ejpam-3903	322	16	-	-	SYM
ejpam-3903	322	17	111	111	NUM
ejpam-3903	322	18	96	96	NUM
ejpam-3903	322	19	the	the	DET
ejpam-3903	322	20	discrete	discrete	ADJ
ejpam-3903	322	21	grönwall	grönwall	PROPN
ejpam-3903	322	22	’s	’s	PART
ejpam-3903	322	23	inequality	inequality	NOUN
ejpam-3903	322	24	allows	allow	VERB
ejpam-3903	322	25	us	we	PRON
ejpam-3903	322	26	to	to	PART
ejpam-3903	322	27	deduct	deduct	VERB
ejpam-3903	322	28	:	:	PUNCT
ejpam-3903	322	29	ä	ä	PROPN
ejpam-3903	322	30	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	322	31	1	1	NUM
ejpam-3903	322	32	‖hs	‖hs	NUM
ejpam-3903	322	33	≤m	≤m	NOUN
ejpam-3903	322	34	exp	exp	NOUN
ejpam-3903	322	35	4	4	NUM
ejpam-3903	322	36	t	t	NOUN
ejpam-3903	322	37	c	c	NOUN
ejpam-3903	322	38	+	+	CCONJ
ejpam-3903	322	39	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	322	40	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	322	41	)	)	PUNCT
ejpam-3903	322	42	,	,	PUNCT
ejpam-3903	322	43	(	(	PUNCT
ejpam-3903	322	44	44	44	NUM
ejpam-3903	322	45	)	)	PUNCT
ejpam-3903	322	46	where	where	SCONJ
ejpam-3903	322	47	m	m	VERB
ejpam-3903	322	48	=	=	SYM
ejpam-3903	322	49	4	4	NUM
ejpam-3903	322	50	t	t	NOUN
ejpam-3903	322	51	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	322	52	)	)	PUNCT
ejpam-3903	322	53	‖f1‖hs	‖f1‖hs	PUNCT
ejpam-3903	323	1	+	+	PUNCT
ejpam-3903	323	2	c03(w0	c03(w0	ADJ
ejpam-3903	323	3	)	)	PUNCT
ejpam-3903	323	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	323	5	)	)	PUNCT
ejpam-3903	323	6	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	324	1	+4	+4	PROPN
ejpam-3903	324	2	t	t	X
ejpam-3903	324	3	c	c	NOUN
ejpam-3903	324	4	+	+	CCONJ
ejpam-3903	324	5	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	324	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	324	7	)	)	PUNCT
ejpam-3903	324	8	‖w1	‖w1	PART
ejpam-3903	324	9	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	325	1	+	+	CCONJ
ejpam-3903	325	2	c03(w0	c03(w0	ADJ
ejpam-3903	325	3	)	)	PUNCT
ejpam-3903	325	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	325	5	)	)	PUNCT
ejpam-3903	325	6	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	325	7	g	g	PROPN
ejpam-3903	325	8	−w0	−w0	PROPN
ejpam-3903	325	9	g)‖hs	g)‖hs	PROPN
ejpam-3903	325	10	.	.	PUNCT
ejpam-3903	326	1	from	from	ADP
ejpam-3903	326	2	inequality	inequality	NOUN
ejpam-3903	326	3	(	(	PUNCT
ejpam-3903	326	4	44	44	NUM
ejpam-3903	326	5	)	)	PUNCT
ejpam-3903	326	6	we	we	PRON
ejpam-3903	326	7	obtain	obtain	VERB
ejpam-3903	326	8	:	:	PUNCT
ejpam-3903	326	9	‖a0w1	‖a0w1	PROPN
ejpam-3903	326	10	1‖hs	1‖hs	PROPN
ejpam-3903	326	11	≤m	≤m	PROPN
ejpam-3903	326	12	exp	exp	NOUN
ejpam-3903	326	13	4	4	NUM
ejpam-3903	326	14	t	t	NOUN
ejpam-3903	326	15	c	c	NOUN
ejpam-3903	326	16	+	+	CCONJ
ejpam-3903	326	17	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	326	18	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	326	19	)	)	PUNCT
ejpam-3903	326	20	+	+	NUM
ejpam-3903	326	21	‖a0wg‖hs	‖a0wg‖hs	PRON
ejpam-3903	326	22	.	.	PUNCT
ejpam-3903	327	1	(	(	PUNCT
ejpam-3903	327	2	45	45	NUM
ejpam-3903	327	3	)	)	PUNCT
ejpam-3903	327	4	so	so	ADV
ejpam-3903	327	5	with	with	ADP
ejpam-3903	327	6	the	the	DET
ejpam-3903	327	7	compactly	compactly	ADV
ejpam-3903	327	8	embedded	embed	VERB
ejpam-3903	327	9	of	of	ADP
ejpam-3903	327	10	hs−1	hs−1	PROPN
ejpam-3903	327	11	into	into	ADP
ejpam-3903	327	12	l∞	l∞	NOUN
ejpam-3903	327	13	,	,	PUNCT
ejpam-3903	327	14	we	we	PRON
ejpam-3903	327	15	obtain	obtain	VERB
ejpam-3903	327	16	:	:	PUNCT
ejpam-3903	327	17	‖w1∗	‖w1∗	PROPN
ejpam-3903	327	18	1	1	NUM
ejpam-3903	327	19	‖l∞	‖l∞	PROPN
ejpam-3903	327	20	≤	≤	ADJ
ejpam-3903	327	21	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	327	22	1	1	NUM
ejpam-3903	327	23	‖hs	‖hs	PROPN
ejpam-3903	327	24	≤mt	≤mt	PROPN
ejpam-3903	327	25	exp	exp	NOUN
ejpam-3903	327	26	t	t	PROPN
ejpam-3903	327	27	c	c	PROPN
ejpam-3903	328	1	+	+	CCONJ
ejpam-3903	328	2	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	328	3	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	328	4	)	)	PUNCT
ejpam-3903	328	5	,	,	PUNCT
ejpam-3903	328	6	(	(	PUNCT
ejpam-3903	328	7	46	46	NUM
ejpam-3903	328	8	)	)	PUNCT
ejpam-3903	328	9	where	where	SCONJ
ejpam-3903	328	10	mt	mt	PROPN
ejpam-3903	328	11	is	be	AUX
ejpam-3903	328	12	a	a	DET
ejpam-3903	328	13	constant	constant	ADJ
ejpam-3903	328	14	independent	independent	NOUN
ejpam-3903	328	15	of	of	ADP
ejpam-3903	328	16	ε	ε	PROPN
ejpam-3903	328	17	and	and	CCONJ
ejpam-3903	328	18	of	of	ADP
ejpam-3903	328	19	4	4	NUM
ejpam-3903	328	20	t	t	NOUN
ejpam-3903	328	21	,	,	PUNCT
ejpam-3903	328	22	given	give	VERB
ejpam-3903	328	23	by	by	ADP
ejpam-3903	328	24	:	:	PUNCT
ejpam-3903	328	25	mt	mt	PROPN
ejpam-3903	328	26	=	=	PROPN
ejpam-3903	328	27	t	t	PROPN
ejpam-3903	328	28	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	328	29	)	)	PUNCT
ejpam-3903	328	30	‖f‖∞,s	‖f‖∞,s	PUNCT
ejpam-3903	329	1	+	+	CCONJ
ejpam-3903	329	2	c03(w0	c03(w0	ADJ
ejpam-3903	329	3	)	)	PUNCT
ejpam-3903	329	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	329	5	)	)	PUNCT
ejpam-3903	329	6	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	330	1	+	+	NUM
ejpam-3903	330	2	t	t	X
ejpam-3903	330	3	c	c	NOUN
ejpam-3903	330	4	+	+	CCONJ
ejpam-3903	331	1	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	331	2	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	331	3	)	)	PUNCT
ejpam-3903	331	4	‖wg‖∞,s+1	‖wg‖∞,s+1	ADP
ejpam-3903	331	5	+	+	SYM
ejpam-3903	331	6	2c03(w0	2c03(w0	NUM
ejpam-3903	331	7	)	)	PUNCT
ejpam-3903	331	8	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	331	9	)	)	PUNCT
ejpam-3903	331	10	‖a0wg‖∞,s	‖a0wg‖∞,s	PROPN
ejpam-3903	331	11	(	(	PUNCT
ejpam-3903	331	12	47	47	NUM
ejpam-3903	331	13	)	)	PUNCT
ejpam-3903	332	1	finally	finally	ADV
ejpam-3903	332	2	we	we	PRON
ejpam-3903	332	3	have	have	VERB
ejpam-3903	332	4	the	the	DET
ejpam-3903	332	5	estimate	estimate	NOUN
ejpam-3903	332	6	:	:	PUNCT
ejpam-3903	333	1	‖w1	‖w1	NOUN
ejpam-3903	333	2	1‖l∞	1‖l∞	NUM
ejpam-3903	333	3	≤	≤	NUM
ejpam-3903	333	4	k	k	X
ejpam-3903	333	5	(	(	PUNCT
ejpam-3903	333	6	48	48	NUM
ejpam-3903	333	7	)	)	PUNCT
ejpam-3903	333	8	with	with	ADP
ejpam-3903	333	9	k	k	PROPN
ejpam-3903	333	10	=	=	PROPN
ejpam-3903	333	11	mt	mt	PROPN
ejpam-3903	333	12	exp	exp	NOUN
ejpam-3903	333	13	t	t	PROPN
ejpam-3903	333	14	c	c	PROPN
ejpam-3903	333	15	+	+	CCONJ
ejpam-3903	333	16	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	333	17	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	333	18	)	)	PUNCT
ejpam-3903	333	19	+	+	NUM
ejpam-3903	333	20	‖wg‖∞,s	‖wg‖∞,s	PROPN
ejpam-3903	333	21	.	.	PUNCT
ejpam-3903	333	22	�	�	PROPN
ejpam-3903	333	23	(	(	PUNCT
ejpam-3903	333	24	49	49	NUM
ejpam-3903	333	25	)	)	PUNCT
ejpam-3903	333	26	4.1.2	4.1.2	NUM
ejpam-3903	333	27	.	.	PUNCT
ejpam-3903	334	1	existence	existence	NOUN
ejpam-3903	334	2	of	of	ADP
ejpam-3903	334	3	w1	w1	NOUN
ejpam-3903	334	4	k+1	k+1	X
ejpam-3903	334	5	in	in	ADP
ejpam-3903	334	6	this	this	DET
ejpam-3903	334	7	part	part	NOUN
ejpam-3903	334	8	,	,	PUNCT
ejpam-3903	334	9	we	we	PRON
ejpam-3903	334	10	will	will	AUX
ejpam-3903	334	11	establish	establish	VERB
ejpam-3903	334	12	the	the	DET
ejpam-3903	334	13	existence	existence	NOUN
ejpam-3903	334	14	of	of	ADP
ejpam-3903	334	15	w1	w1	NOUN
ejpam-3903	334	16	k+1	k+1	PROPN
ejpam-3903	334	17	,	,	PUNCT
ejpam-3903	334	18	weak	weak	ADJ
ejpam-3903	334	19	solution	solution	NOUN
ejpam-3903	334	20	of	of	ADP
ejpam-3903	334	21	the	the	DET
ejpam-3903	334	22	following	follow	VERB
ejpam-3903	334	23	system:	system:	NOUN
ejpam-3903	334	24	a0(w0	a0(w0	NOUN
ejpam-3903	334	25	)	)	PUNCT
ejpam-3903	334	26	4	4	NUM
ejpam-3903	334	27	t	t	NOUN
ejpam-3903	334	28	w1	w1	NOUN
ejpam-3903	334	29	k+1	k+1	NOUN
ejpam-3903	335	1	+	+	CCONJ
ejpam-3903	335	2	3∑	3∑	NUM
ejpam-3903	335	3	i=1	i=1	INTJ
ejpam-3903	335	4	aiε	aiε	ADV
ejpam-3903	335	5	∂w1	∂w1	PROPN
ejpam-3903	335	6	k+1	k+1	PRON
ejpam-3903	335	7	∂xi	∂xi	PROPN
ejpam-3903	335	8	+	+	CCONJ
ejpam-3903	335	9	kε(w	kε(w	ADJ
ejpam-3903	335	10	1	1	NUM
ejpam-3903	335	11	k)w1	k)w1	PROPN
ejpam-3903	335	12	k+1	k+1	X
ejpam-3903	335	13	=	=	SYM
ejpam-3903	335	14	f1	f1	NOUN
ejpam-3903	335	15	+	+	CCONJ
ejpam-3903	335	16	a0(w0	a0(w0	NOUN
ejpam-3903	335	17	)	)	PUNCT
ejpam-3903	335	18	4	4	NUM
ejpam-3903	335	19	t	t	NOUN
ejpam-3903	335	20	w0	w0	NOUN
ejpam-3903	335	21	,	,	PUNCT
ejpam-3903	335	22	(	(	PUNCT
ejpam-3903	335	23	b−m)w1	b−m)w1	X
ejpam-3903	335	24	k+1	k+1	NOUN
ejpam-3903	335	25	=	=	PUNCT
ejpam-3903	335	26	g1	g1	PROPN
ejpam-3903	335	27	.	.	PUNCT
ejpam-3903	336	1	(	(	PUNCT
ejpam-3903	336	2	50	50	NUM
ejpam-3903	336	3	)	)	PUNCT
ejpam-3903	336	4	in	in	ADP
ejpam-3903	336	5	fact	fact	NOUN
ejpam-3903	336	6	we	we	PRON
ejpam-3903	336	7	have	have	VERB
ejpam-3903	336	8	the	the	DET
ejpam-3903	336	9	following	follow	VERB
ejpam-3903	336	10	result	result	NOUN
ejpam-3903	336	11	:	:	PUNCT
ejpam-3903	336	12	r.	r.	PROPN
ejpam-3903	336	13	bade	bade	PROPN
ejpam-3903	336	14	,	,	PUNCT
ejpam-3903	336	15	h.	h.	PROPN
ejpam-3903	336	16	chaker	chaker	PROPN
ejpam-3903	336	17	/	/	SYM
ejpam-3903	336	18	eur	eur	PROPN
ejpam-3903	336	19	.	.	PUNCT
ejpam-3903	337	1	j.	j.	PROPN
ejpam-3903	337	2	pure	pure	PROPN
ejpam-3903	337	3	appl	appl	PROPN
ejpam-3903	337	4	.	.	PROPN
ejpam-3903	337	5	math	math	PROPN
ejpam-3903	337	6	,	,	PUNCT
ejpam-3903	337	7	14	14	NUM
ejpam-3903	337	8	(	(	PUNCT
ejpam-3903	337	9	1	1	NUM
ejpam-3903	337	10	)	)	PUNCT
ejpam-3903	337	11	(	(	PUNCT
ejpam-3903	337	12	2021	2021	NUM
ejpam-3903	337	13	)	)	PUNCT
ejpam-3903	337	14	,	,	PUNCT
ejpam-3903	337	15	82	82	NUM
ejpam-3903	337	16	-	-	SYM
ejpam-3903	337	17	111	111	NUM
ejpam-3903	337	18	97	97	NUM
ejpam-3903	337	19	proposition	proposition	NOUN
ejpam-3903	337	20	3	3	NUM
ejpam-3903	337	21	.	.	PUNCT
ejpam-3903	338	1	let	let	VERB
ejpam-3903	338	2	the	the	DET
ejpam-3903	338	3	assumptions	assumption	NOUN
ejpam-3903	338	4	(	(	PUNCT
ejpam-3903	338	5	h2	h2	NOUN
ejpam-3903	338	6	)	)	PUNCT
ejpam-3903	338	7	and	and	CCONJ
ejpam-3903	338	8	(	(	PUNCT
ejpam-3903	338	9	h3	h3	NOUN
ejpam-3903	338	10	)	)	PUNCT
ejpam-3903	338	11	hold	hold	VERB
ejpam-3903	338	12	,	,	PUNCT
ejpam-3903	338	13	then	then	ADV
ejpam-3903	338	14	the	the	DET
ejpam-3903	338	15	system	system	NOUN
ejpam-3903	338	16	(	(	PUNCT
ejpam-3903	338	17	50	50	NUM
ejpam-3903	338	18	)	)	PUNCT
ejpam-3903	338	19	admit	admit	VERB
ejpam-3903	338	20	a	a	DET
ejpam-3903	338	21	weak	weak	ADJ
ejpam-3903	338	22	solution	solution	NOUN
ejpam-3903	338	23	w1	w1	NOUN
ejpam-3903	338	24	k+1	k+1	X
ejpam-3903	338	25	∈	∈	PROPN
ejpam-3903	338	26	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	338	27	.	.	PUNCT
ejpam-3903	339	1	in	in	ADP
ejpam-3903	339	2	addition	addition	NOUN
ejpam-3903	339	3	if	if	SCONJ
ejpam-3903	339	4	w1	w1	NOUN
ejpam-3903	339	5	k+1	k+1	X
ejpam-3903	339	6	∈	∈	PROPN
ejpam-3903	339	7	h1(ω)20	h1(ω)20	PUNCT
ejpam-3903	339	8	this	this	DET
ejpam-3903	339	9	solution	solution	NOUN
ejpam-3903	339	10	is	be	AUX
ejpam-3903	339	11	unique	unique	ADJ
ejpam-3903	339	12	.	.	PUNCT
ejpam-3903	340	1	if	if	SCONJ
ejpam-3903	340	2	f1	f1	PROPN
ejpam-3903	340	3	+	+	CCONJ
ejpam-3903	340	4	a0(w0	a0(w0	NOUN
ejpam-3903	340	5	)	)	PUNCT
ejpam-3903	340	6	4	4	NUM
ejpam-3903	340	7	t	t	NOUN
ejpam-3903	340	8	w0	w0	PROPN
ejpam-3903	340	9	∈	∈	PROPN
ejpam-3903	340	10	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	340	11	,	,	PUNCT
ejpam-3903	340	12	g1	g1	PROPN
ejpam-3903	340	13	∈	∈	PROPN
ejpam-3903	340	14	hs+	hs+	NOUN
ejpam-3903	340	15	3	3	NUM
ejpam-3903	340	16	2	2	NUM
ejpam-3903	340	17	(	(	PUNCT
ejpam-3903	340	18	∂ω)20	∂ω)20	PROPN
ejpam-3903	340	19	,	,	PUNCT
ejpam-3903	340	20	then	then	ADV
ejpam-3903	340	21	the	the	DET
ejpam-3903	340	22	weak	weak	ADJ
ejpam-3903	340	23	solution	solution	NOUN
ejpam-3903	340	24	of	of	ADP
ejpam-3903	340	25	the	the	DET
ejpam-3903	340	26	system	system	NOUN
ejpam-3903	340	27	(	(	PUNCT
ejpam-3903	340	28	34	34	NUM
ejpam-3903	340	29	):	):	PUNCT
ejpam-3903	340	30	w1	w1	NOUN
ejpam-3903	340	31	k+1	k+1	NOUN
ejpam-3903	340	32	∈	∈	PROPN
ejpam-3903	340	33	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	340	34	.	.	PUNCT
ejpam-3903	341	1	we	we	PRON
ejpam-3903	341	2	have	have	VERB
ejpam-3903	341	3	(	(	PUNCT
ejpam-3903	341	4	w1	w1	PROPN
ejpam-3903	341	5	k+1)1	k+1)1	PROPN
ejpam-3903	341	6	>	>	SYM
ejpam-3903	341	7	ρ̄	ρ̄	PROPN
ejpam-3903	341	8	exp(−k4	exp(−k4	PROPN
ejpam-3903	341	9	t	t	PROPN
ejpam-3903	341	10	)	)	PUNCT
ejpam-3903	341	11	.	.	PUNCT
ejpam-3903	342	1	proof	proof	NOUN
ejpam-3903	342	2	.	.	PUNCT
ejpam-3903	343	1	we	we	PRON
ejpam-3903	343	2	use	use	VERB
ejpam-3903	343	3	recurrence	recurrence	NOUN
ejpam-3903	343	4	and	and	CCONJ
ejpam-3903	343	5	follow	follow	VERB
ejpam-3903	343	6	the	the	DET
ejpam-3903	343	7	same	same	ADJ
ejpam-3903	343	8	approach	approach	NOUN
ejpam-3903	343	9	as	as	ADP
ejpam-3903	343	10	in	in	ADP
ejpam-3903	343	11	the	the	DET
ejpam-3903	343	12	proposition	proposition	NOUN
ejpam-3903	343	13	2	2	NUM
ejpam-3903	343	14	.	.	PUNCT
ejpam-3903	344	1	so	so	ADV
ejpam-3903	344	2	in	in	ADP
ejpam-3903	344	3	the	the	DET
ejpam-3903	344	4	second	second	ADJ
ejpam-3903	344	5	step	step	NOUN
ejpam-3903	344	6	we	we	PRON
ejpam-3903	344	7	will	will	AUX
ejpam-3903	344	8	construct	construct	VERB
ejpam-3903	344	9	w1	w1	PROPN
ejpam-3903	344	10	2	2	NUM
ejpam-3903	344	11	starting	start	VERB
ejpam-3903	344	12	from	from	ADP
ejpam-3903	344	13	w1	w1	NOUN
ejpam-3903	344	14	1	1	NUM
ejpam-3903	344	15	given	give	VERB
ejpam-3903	344	16	by	by	ADP
ejpam-3903	344	17	the	the	DET
ejpam-3903	344	18	proposition	proposition	NOUN
ejpam-3903	344	19	2	2	NUM
ejpam-3903	344	20	.	.	PUNCT
ejpam-3903	345	1	then	then	ADV
ejpam-3903	345	2	we	we	PRON
ejpam-3903	345	3	will	will	AUX
ejpam-3903	345	4	get	get	VERB
ejpam-3903	345	5	the	the	DET
ejpam-3903	345	6	following	follow	VERB
ejpam-3903	345	7	estimates	estimate	NOUN
ejpam-3903	345	8	:	:	PUNCT
ejpam-3903	345	9	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	345	10	2	2	NUM
ejpam-3903	345	11	‖hs	‖hs	PROPN
ejpam-3903	345	12	≤	≤	NOUN
ejpam-3903	345	13	(	(	PUNCT
ejpam-3903	345	14	4	4	NUM
ejpam-3903	345	15	t	t	NOUN
ejpam-3903	345	16	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	345	17	)	)	PUNCT
ejpam-3903	345	18	‖f1‖hs	‖f1‖hs	PUNCT
ejpam-3903	346	1	+	+	PUNCT
ejpam-3903	346	2	c03(w0	c03(w0	ADJ
ejpam-3903	346	3	)	)	PUNCT
ejpam-3903	346	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	346	5	)	)	PUNCT
ejpam-3903	346	6	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	347	1	+4	+4	PROPN
ejpam-3903	347	2	t	t	X
ejpam-3903	347	3	c	c	NOUN
ejpam-3903	347	4	+	+	CCONJ
ejpam-3903	347	5	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	347	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	347	7	)	)	PUNCT
ejpam-3903	347	8	‖w1	‖w1	PART
ejpam-3903	347	9	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	348	1	+	+	CCONJ
ejpam-3903	348	2	c03(w0	c03(w0	ADJ
ejpam-3903	348	3	)	)	PUNCT
ejpam-3903	348	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	348	5	)	)	PUNCT
ejpam-3903	348	6	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	348	7	g	g	PROPN
ejpam-3903	348	8	−w0	−w0	PROPN
ejpam-3903	348	9	g)‖hs	g)‖hs	PROPN
ejpam-3903	348	10	)	)	PUNCT
ejpam-3903	348	11	exp	exp	NOUN
ejpam-3903	348	12	4	4	NUM
ejpam-3903	348	13	t	t	NOUN
ejpam-3903	348	14	c	c	NOUN
ejpam-3903	348	15	+	+	CCONJ
ejpam-3903	348	16	c‖w1∗	c‖w1∗	PRON
ejpam-3903	348	17	1	1	NUM
ejpam-3903	348	18	‖3l∞	‖3l∞	NOUN
ejpam-3903	348	19	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	348	20	)	)	PUNCT
ejpam-3903	348	21	,	,	PUNCT
ejpam-3903	348	22	(	(	PUNCT
ejpam-3903	348	23	51	51	NUM
ejpam-3903	348	24	)	)	PUNCT
ejpam-3903	348	25	‖w1∗	‖w1∗	NOUN
ejpam-3903	348	26	2	2	NUM
ejpam-3903	348	27	‖l∞	‖l∞	PROPN
ejpam-3903	348	28	≤	≤	NUM
ejpam-3903	348	29	(	(	PUNCT
ejpam-3903	348	30	t	t	PROPN
ejpam-3903	348	31	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	348	32	)	)	PUNCT
ejpam-3903	348	33	‖f‖∞,s	‖f‖∞,s	PUNCT
ejpam-3903	349	1	+	+	CCONJ
ejpam-3903	349	2	c03(w0	c03(w0	ADJ
ejpam-3903	349	3	)	)	PUNCT
ejpam-3903	349	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	349	5	)	)	PUNCT
ejpam-3903	349	6	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	350	1	+	+	NUM
ejpam-3903	350	2	t	t	X
ejpam-3903	350	3	c	c	NOUN
ejpam-3903	350	4	+	+	CCONJ
ejpam-3903	351	1	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	351	2	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	351	3	)	)	PUNCT
ejpam-3903	351	4	‖wg‖∞,s+1	‖wg‖∞,s+1	ADP
ejpam-3903	351	5	+	+	PUNCT
ejpam-3903	351	6	c03(w0	c03(w0	ADJ
ejpam-3903	351	7	)	)	PUNCT
ejpam-3903	351	8	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	351	9	)	)	PUNCT
ejpam-3903	351	10	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	351	11	g	g	PROPN
ejpam-3903	351	12	−w0	−w0	PROPN
ejpam-3903	351	13	g)‖∞,s	g)‖∞,s	NOUN
ejpam-3903	351	14	)	)	PUNCT
ejpam-3903	351	15	exp	exp	NOUN
ejpam-3903	351	16	t	t	PROPN
ejpam-3903	351	17	c	c	PROPN
ejpam-3903	351	18	+	+	CCONJ
ejpam-3903	351	19	c‖w1∗	c‖w1∗	PRON
ejpam-3903	351	20	1	1	NUM
ejpam-3903	351	21	‖3l∞	‖3l∞	NOUN
ejpam-3903	351	22	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	351	23	)	)	PUNCT
ejpam-3903	351	24	.	.	PUNCT
ejpam-3903	352	1	(	(	PUNCT
ejpam-3903	352	2	52	52	NUM
ejpam-3903	352	3	)	)	PUNCT
ejpam-3903	352	4	note	note	NOUN
ejpam-3903	352	5	here	here	ADV
ejpam-3903	352	6	that	that	SCONJ
ejpam-3903	352	7	we	we	PRON
ejpam-3903	352	8	can	can	AUX
ejpam-3903	352	9	not	not	PART
ejpam-3903	352	10	continue	continue	VERB
ejpam-3903	352	11	the	the	DET
ejpam-3903	352	12	recurrence	recurrence	NOUN
ejpam-3903	352	13	only	only	ADV
ejpam-3903	352	14	if	if	SCONJ
ejpam-3903	352	15	these	these	DET
ejpam-3903	352	16	estimates	estimate	NOUN
ejpam-3903	352	17	are	be	AUX
ejpam-3903	352	18	uniform	uniform	ADJ
ejpam-3903	352	19	in	in	ADP
ejpam-3903	352	20	the	the	DET
ejpam-3903	352	21	sense	sense	NOUN
ejpam-3903	352	22	that	that	SCONJ
ejpam-3903	352	23	t	t	PROPN
ejpam-3903	352	24	c	c	PROPN
ejpam-3903	352	25	+	+	CCONJ
ejpam-3903	352	26	c‖w1∗	c‖w1∗	PRON
ejpam-3903	352	27	1	1	NUM
ejpam-3903	352	28	‖3l∞	‖3l∞	NOUN
ejpam-3903	352	29	c01(ρ̄	c01(ρ̄	NOUN
ejpam-3903	352	30	)	)	PUNCT
ejpam-3903	352	31	remains	remain	VERB
ejpam-3903	352	32	lower	low	ADJ
ejpam-3903	352	33	than	than	ADP
ejpam-3903	352	34	a	a	DET
ejpam-3903	352	35	quantity	quantity	NOUN
ejpam-3903	352	36	independent	independent	ADJ
ejpam-3903	352	37	of	of	ADP
ejpam-3903	352	38	the	the	DET
ejpam-3903	352	39	iteration	iteration	NOUN
ejpam-3903	352	40	.	.	PUNCT
ejpam-3903	353	1	for	for	ADP
ejpam-3903	353	2	this	this	DET
ejpam-3903	353	3	aim	aim	NOUN
ejpam-3903	353	4	let	let	VERB
ejpam-3903	353	5	us	we	PRON
ejpam-3903	353	6	consider	consider	VERB
ejpam-3903	353	7	the	the	DET
ejpam-3903	353	8	term	term	NOUN
ejpam-3903	353	9	m	m	AUX
ejpam-3903	353	10	defined	define	VERB
ejpam-3903	353	11	by	by	ADP
ejpam-3903	353	12	:	:	PUNCT
ejpam-3903	353	13	m	m	PROPN
ejpam-3903	353	14	=	=	SYM
ejpam-3903	353	15	t̃	t̃	PROPN
ejpam-3903	353	16	c	c	NOUN
ejpam-3903	353	17	+	+	CCONJ
ejpam-3903	353	18	c‖w0‖3l∞	c‖w0‖3l∞	PROPN
ejpam-3903	353	19	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	353	20	)	)	PUNCT
ejpam-3903	353	21	,	,	PUNCT
ejpam-3903	353	22	(	(	PUNCT
ejpam-3903	353	23	53	53	NUM
ejpam-3903	353	24	)	)	PUNCT
ejpam-3903	353	25	where	where	SCONJ
ejpam-3903	353	26	t̃	t̃	PROPN
ejpam-3903	353	27	is	be	AUX
ejpam-3903	353	28	an	an	DET
ejpam-3903	353	29	enough	enough	ADJ
ejpam-3903	353	30	time	time	NOUN
ejpam-3903	353	31	to	to	PART
ejpam-3903	353	32	have	have	VERB
ejpam-3903	353	33	t	t	PROPN
ejpam-3903	353	34	c	c	PROPN
ejpam-3903	353	35	+	+	CCONJ
ejpam-3903	353	36	c‖w1∗	c‖w1∗	PRON
ejpam-3903	353	37	1	1	NUM
ejpam-3903	353	38	‖3l∞	‖3l∞	NOUN
ejpam-3903	353	39	c01(ρ̄	c01(ρ̄	NOUN
ejpam-3903	353	40	)	)	PUNCT
ejpam-3903	353	41	6	6	NUM
ejpam-3903	353	42	m.	m.	NOUN
ejpam-3903	353	43	we	we	PRON
ejpam-3903	353	44	will	will	AUX
ejpam-3903	353	45	note	note	VERB
ejpam-3903	353	46	in	in	ADP
ejpam-3903	353	47	the	the	DET
ejpam-3903	353	48	sequel	sequel	NOUN
ejpam-3903	353	49	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	353	50	)	)	PUNCT
ejpam-3903	353	51	as	as	ADP
ejpam-3903	353	52	:	:	PUNCT
ejpam-3903	353	53	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	353	54	)	)	PUNCT
ejpam-3903	353	55	=	=	PROPN
ejpam-3903	353	56	inf	inf	NOUN
ejpam-3903	353	57	(	(	PUNCT
ejpam-3903	353	58	1	1	NUM
ejpam-3903	353	59	,	,	PUNCT
ejpam-3903	353	60	ρ̄	ρ̄	NOUN
ejpam-3903	353	61	exp(−t̃	exp(−t̃	PROPN
ejpam-3903	353	62	k̃	k̃	PROPN
ejpam-3903	353	63	)	)	PUNCT
ejpam-3903	353	64	,	,	PUNCT
ejpam-3903	353	65	cvρ̄	cvρ̄	NOUN
ejpam-3903	354	1	exp(−t̃	exp(−t̃	PROPN
ejpam-3903	354	2	k̃	k̃	PROPN
ejpam-3903	354	3	)	)	PUNCT
ejpam-3903	354	4	)	)	PUNCT
ejpam-3903	354	5	,	,	PUNCT
ejpam-3903	354	6	(	(	PUNCT
ejpam-3903	354	7	54	54	NUM
ejpam-3903	354	8	)	)	PUNCT
ejpam-3903	354	9	with	with	ADP
ejpam-3903	354	10	k̃	k̃	PROPN
ejpam-3903	354	11	=	=	SYM
ejpam-3903	354	12	mt̃	mt̃	PROPN
ejpam-3903	354	13	expt̃m+	expt̃m+	PROPN
ejpam-3903	354	14	‖wg‖l∞(0,t̃	‖wg‖l∞(0,t̃	NOUN
ejpam-3903	354	15	;	;	PUNCT
ejpam-3903	354	16	l∞(ω)20	l∞(ω)20	VERB
ejpam-3903	354	17	)	)	PUNCT
ejpam-3903	354	18	·	·	PUNCT
ejpam-3903	354	19	(	(	PUNCT
ejpam-3903	354	20	55	55	NUM
ejpam-3903	354	21	)	)	PUNCT
ejpam-3903	354	22	r.	r.	PROPN
ejpam-3903	354	23	bade	bade	PROPN
ejpam-3903	354	24	,	,	PUNCT
ejpam-3903	354	25	h.	h.	PROPN
ejpam-3903	354	26	chaker	chaker	PROPN
ejpam-3903	354	27	/	/	SYM
ejpam-3903	354	28	eur	eur	PROPN
ejpam-3903	354	29	.	.	PUNCT
ejpam-3903	355	1	j.	j.	PROPN
ejpam-3903	355	2	pure	pure	PROPN
ejpam-3903	355	3	appl	appl	PROPN
ejpam-3903	355	4	.	.	PROPN
ejpam-3903	355	5	math	math	PROPN
ejpam-3903	355	6	,	,	PUNCT
ejpam-3903	355	7	14	14	NUM
ejpam-3903	355	8	(	(	PUNCT
ejpam-3903	355	9	1	1	NUM
ejpam-3903	355	10	)	)	PUNCT
ejpam-3903	355	11	(	(	PUNCT
ejpam-3903	355	12	2021	2021	NUM
ejpam-3903	355	13	)	)	PUNCT
ejpam-3903	355	14	,	,	PUNCT
ejpam-3903	355	15	82	82	NUM
ejpam-3903	355	16	-	-	SYM
ejpam-3903	355	17	111	111	NUM
ejpam-3903	355	18	98	98	NUM
ejpam-3903	355	19	using	use	VERB
ejpam-3903	355	20	the	the	DET
ejpam-3903	355	21	estimation	estimation	NOUN
ejpam-3903	355	22	(	(	PUNCT
ejpam-3903	355	23	46	46	NUM
ejpam-3903	355	24	)	)	PUNCT
ejpam-3903	355	25	and	and	CCONJ
ejpam-3903	355	26	the	the	DET
ejpam-3903	355	27	equality	equality	NOUN
ejpam-3903	355	28	(	(	PUNCT
ejpam-3903	355	29	47	47	NUM
ejpam-3903	355	30	)	)	PUNCT
ejpam-3903	355	31	we	we	PRON
ejpam-3903	355	32	get	get	VERB
ejpam-3903	355	33	:	:	PUNCT
ejpam-3903	355	34	t	t	PROPN
ejpam-3903	355	35	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	355	36	)	)	PUNCT
ejpam-3903	355	37	(	(	PUNCT
ejpam-3903	355	38	c	c	NOUN
ejpam-3903	355	39	+	+	CCONJ
ejpam-3903	355	40	c‖w1∗	c‖w1∗	ADP
ejpam-3903	355	41	1	1	NUM
ejpam-3903	355	42	‖3l∞	‖3l∞	NOUN
ejpam-3903	355	43	)	)	PUNCT
ejpam-3903	355	44	6	6	NUM
ejpam-3903	355	45	t	t	PROPN
ejpam-3903	355	46	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	355	47	)	)	PUNCT
ejpam-3903	355	48	(	(	PUNCT
ejpam-3903	355	49	c	c	X
ejpam-3903	355	50	+	+	CCONJ
ejpam-3903	355	51	ck3	ck3	PROPN
ejpam-3903	355	52	)	)	PUNCT
ejpam-3903	355	53	6	6	NUM
ejpam-3903	355	54	t	t	NOUN
ejpam-3903	355	55	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	355	56	)	)	PUNCT
ejpam-3903	356	1	[	[	PUNCT
ejpam-3903	356	2	c	c	NOUN
ejpam-3903	356	3	+	+	X
ejpam-3903	356	4	c	c	PROPN
ejpam-3903	356	5	(	(	PUNCT
ejpam-3903	356	6	t	t	PROPN
ejpam-3903	356	7	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	356	8	)	)	PUNCT
ejpam-3903	356	9	‖f‖l∞(0,t̃	‖f‖l∞(0,t̃	PROPN
ejpam-3903	356	10	;	;	PUNCT
ejpam-3903	356	11	hs(ω)20	hs(ω)20	ADJ
ejpam-3903	356	12	+	+	CCONJ
ejpam-3903	356	13	c03(w0	c03(w0	ADJ
ejpam-3903	356	14	)	)	PUNCT
ejpam-3903	356	15	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	356	16	)	)	PUNCT
ejpam-3903	356	17	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	357	1	+	+	PROPN
ejpam-3903	357	2	m‖wg‖l∞(0,t̃	m‖wg‖l∞(0,t̃	ADJ
ejpam-3903	357	3	;	;	PUNCT
ejpam-3903	357	4	hs+1(ω)20	hs+1(ω)20	X
ejpam-3903	357	5	)	)	PUNCT
ejpam-3903	357	6	+	+	SYM
ejpam-3903	357	7	2c03(w0	2c03(w0	NUM
ejpam-3903	357	8	)	)	PUNCT
ejpam-3903	357	9	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	357	10	)	)	PUNCT
ejpam-3903	357	11	‖a0wg‖l∞(0,t̃	‖a0wg‖l∞(0,t̃	PROPN
ejpam-3903	357	12	;	;	PUNCT
ejpam-3903	357	13	hs(ω)20	hs(ω)20	ADJ
ejpam-3903	357	14	)	)	PUNCT
ejpam-3903	357	15	)	)	PUNCT
ejpam-3903	357	16	3	3	NUM
ejpam-3903	357	17	exp3	exp3	NOUN
ejpam-3903	357	18	m	m	VERB
ejpam-3903	357	19	]	]	PUNCT
ejpam-3903	357	20	,	,	PUNCT
ejpam-3903	357	21	(	(	PUNCT
ejpam-3903	357	22	56	56	NUM
ejpam-3903	357	23	)	)	PUNCT
ejpam-3903	357	24	where	where	SCONJ
ejpam-3903	357	25	we	we	PRON
ejpam-3903	357	26	have	have	AUX
ejpam-3903	357	27	set	set	VERB
ejpam-3903	357	28	:	:	PUNCT
ejpam-3903	357	29	k	k	PROPN
ejpam-3903	357	30	=	=	PROPN
ejpam-3903	357	31	mt	mt	PROPN
ejpam-3903	357	32	expm	expm	NOUN
ejpam-3903	357	33	.	.	PUNCT
ejpam-3903	358	1	(	(	PUNCT
ejpam-3903	358	2	57	57	NUM
ejpam-3903	358	3	)	)	PUNCT
ejpam-3903	358	4	we	we	PRON
ejpam-3903	358	5	wish	wish	VERB
ejpam-3903	358	6	that	that	SCONJ
ejpam-3903	358	7	the	the	DET
ejpam-3903	358	8	right	right	ADJ
ejpam-3903	358	9	term	term	NOUN
ejpam-3903	358	10	in	in	ADP
ejpam-3903	358	11	the	the	DET
ejpam-3903	358	12	estimate	estimate	NOUN
ejpam-3903	358	13	(	(	PUNCT
ejpam-3903	358	14	56	56	NUM
ejpam-3903	358	15	)	)	PUNCT
ejpam-3903	358	16	be	be	AUX
ejpam-3903	358	17	majoreted	majorete	VERB
ejpam-3903	358	18	by	by	ADP
ejpam-3903	358	19	m.	m.	NOUN
ejpam-3903	358	20	thus	thus	ADV
ejpam-3903	358	21	,	,	PUNCT
ejpam-3903	358	22	we	we	PRON
ejpam-3903	358	23	rewrite	rewrite	VERB
ejpam-3903	358	24	the	the	DET
ejpam-3903	358	25	difference	difference	NOUN
ejpam-3903	358	26	between	between	ADP
ejpam-3903	358	27	the	the	DET
ejpam-3903	358	28	right	right	ADJ
ejpam-3903	358	29	term	term	NOUN
ejpam-3903	358	30	of	of	ADP
ejpam-3903	358	31	(	(	PUNCT
ejpam-3903	358	32	56	56	NUM
ejpam-3903	358	33	)	)	PUNCT
ejpam-3903	358	34	and	and	CCONJ
ejpam-3903	358	35	m	m	VERB
ejpam-3903	358	36	as	as	ADP
ejpam-3903	358	37	a	a	DET
ejpam-3903	358	38	polynomial	polynomial	ADJ
ejpam-3903	358	39	function	function	NOUN
ejpam-3903	358	40	in	in	ADP
ejpam-3903	358	41	t	t	PROPN
ejpam-3903	358	42	:	:	PUNCT
ejpam-3903	358	43	gm(t	gm(t	X
ejpam-3903	358	44	)	)	PUNCT
ejpam-3903	359	1	=	=	SYM
ejpam-3903	359	2	a3	a3	NOUN
ejpam-3903	359	3	1	1	NUM
ejpam-3903	359	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	5	)	)	PUNCT
ejpam-3903	359	6	exp3	exp3	PROPN
ejpam-3903	359	7	m	m	PROPN
ejpam-3903	359	8	t	t	PROPN
ejpam-3903	359	9	4	4	NUM
ejpam-3903	359	10	+	+	SYM
ejpam-3903	359	11	3	3	NUM
ejpam-3903	359	12	a2	a2	PROPN
ejpam-3903	359	13	1a2	1a2	NUM
ejpam-3903	359	14	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	15	)	)	PUNCT
ejpam-3903	359	16	exp3	exp3	PROPN
ejpam-3903	359	17	m	m	PROPN
ejpam-3903	359	18	t	t	PROPN
ejpam-3903	359	19	3	3	NUM
ejpam-3903	359	20	+	+	SYM
ejpam-3903	359	21	3	3	NUM
ejpam-3903	359	22	a1a	a1a	PROPN
ejpam-3903	359	23	2	2	NUM
ejpam-3903	359	24	2	2	NUM
ejpam-3903	359	25	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	26	)	)	PUNCT
ejpam-3903	359	27	exp3	exp3	PROPN
ejpam-3903	359	28	m	m	PROPN
ejpam-3903	359	29	t	t	NOUN
ejpam-3903	359	30	2	2	NUM
ejpam-3903	359	31	+	+	CCONJ
ejpam-3903	359	32	c	c	NOUN
ejpam-3903	359	33	+	+	SYM
ejpam-3903	359	34	a3	a3	VERB
ejpam-3903	359	35	2	2	NUM
ejpam-3903	359	36	exp3	exp3	PROPN
ejpam-3903	359	37	m	m	VERB
ejpam-3903	359	38	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	39	)	)	PUNCT
ejpam-3903	359	40	t	t	PROPN
ejpam-3903	359	41	−m	−m	NOUN
ejpam-3903	359	42	,	,	PUNCT
ejpam-3903	359	43	where	where	SCONJ
ejpam-3903	359	44	:	:	PUNCT
ejpam-3903	359	45	a1	a1	NOUN
ejpam-3903	359	46	=	=	SYM
ejpam-3903	359	47	c	c	PROPN
ejpam-3903	359	48	‖f‖l∞(0,t̃	‖f‖l∞(0,t̃	NOUN
ejpam-3903	359	49	;	;	PUNCT
ejpam-3903	359	50	hs(ω	hs(ω	NUM
ejpam-3903	359	51	)	)	PUNCT
ejpam-3903	359	52	)	)	PUNCT
ejpam-3903	359	53	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	54	)	)	PUNCT
ejpam-3903	359	55	,	,	PUNCT
ejpam-3903	359	56	a2	a2	PROPN
ejpam-3903	359	57	=	=	SYM
ejpam-3903	359	58	c	c	PROPN
ejpam-3903	359	59	(	(	PUNCT
ejpam-3903	359	60	c03(w0	c03(w0	ADJ
ejpam-3903	359	61	)	)	PUNCT
ejpam-3903	359	62	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	359	63	)	)	PUNCT
ejpam-3903	359	64	‖a0w0∗‖hs	‖a0w0∗‖hs	NOUN
ejpam-3903	360	1	+	+	PROPN
ejpam-3903	360	2	m‖wg‖l∞(0,t̃	m‖wg‖l∞(0,t̃	ADJ
ejpam-3903	360	3	;	;	PUNCT
ejpam-3903	360	4	hs+1(ω)20	hs+1(ω)20	X
ejpam-3903	360	5	)	)	PUNCT
ejpam-3903	360	6	+	+	SYM
ejpam-3903	360	7	2c03(w0	2c03(w0	NUM
ejpam-3903	360	8	)	)	PUNCT
ejpam-3903	360	9	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	360	10	)	)	PUNCT
ejpam-3903	360	11	‖a0wg‖l∞(0,t̃	‖a0wg‖l∞(0,t̃	PROPN
ejpam-3903	360	12	;	;	PUNCT
ejpam-3903	360	13	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	360	14	)	)	PUNCT
ejpam-3903	360	15	)	)	PUNCT
ejpam-3903	360	16	.	.	PUNCT
ejpam-3903	361	1	we	we	PRON
ejpam-3903	361	2	expect	expect	VERB
ejpam-3903	361	3	to	to	PART
ejpam-3903	361	4	have	have	VERB
ejpam-3903	361	5	:	:	PUNCT
ejpam-3903	361	6	gm(t	gm(t	X
ejpam-3903	361	7	)	)	PUNCT
ejpam-3903	361	8	6	6	NUM
ejpam-3903	361	9	0	0	NUM
ejpam-3903	361	10	·	·	PUNCT
ejpam-3903	361	11	let	let	VERB
ejpam-3903	361	12	e	e	PRON
ejpam-3903	361	13	be	be	AUX
ejpam-3903	361	14	a	a	DET
ejpam-3903	361	15	subset	subset	NOUN
ejpam-3903	361	16	of	of	ADP
ejpam-3903	361	17	r+	r+	NOUN
ejpam-3903	361	18	containing	contain	VERB
ejpam-3903	361	19	the	the	DET
ejpam-3903	361	20	zeros	zero	NOUN
ejpam-3903	361	21	of	of	ADP
ejpam-3903	361	22	the	the	DET
ejpam-3903	361	23	function	function	NOUN
ejpam-3903	361	24	gm	gm	PROPN
ejpam-3903	361	25	:	:	PUNCT
ejpam-3903	361	26	e	e	X
ejpam-3903	361	27	=	=	PRON
ejpam-3903	361	28	{	{	PUNCT
ejpam-3903	361	29	t	t	PROPN
ejpam-3903	361	30	∈	∈	PROPN
ejpam-3903	361	31	r+	r+	NOUN
ejpam-3903	361	32	such	such	ADJ
ejpam-3903	361	33	as	as	ADP
ejpam-3903	361	34	gm(t	gm(t	NOUN
ejpam-3903	361	35	)	)	PUNCT
ejpam-3903	361	36	=	=	SYM
ejpam-3903	362	1	0	0	X
ejpam-3903	362	2	}	}	PUNCT
ejpam-3903	362	3	.	.	PUNCT
ejpam-3903	363	1	first	first	ADV
ejpam-3903	363	2	one	one	NUM
ejpam-3903	363	3	can	can	AUX
ejpam-3903	363	4	note	note	VERB
ejpam-3903	363	5	that	that	SCONJ
ejpam-3903	363	6	the	the	DET
ejpam-3903	363	7	e	e	NOUN
ejpam-3903	363	8	is	be	AUX
ejpam-3903	363	9	not	not	PART
ejpam-3903	363	10	empty	empty	ADJ
ejpam-3903	363	11	,	,	PUNCT
ejpam-3903	363	12	indeed	indeed	ADV
ejpam-3903	363	13	gm(t	gm(t	ADV
ejpam-3903	363	14	)	)	PUNCT
ejpam-3903	363	15	is	be	AUX
ejpam-3903	363	16	a	a	DET
ejpam-3903	363	17	polynomial	polynomial	ADJ
ejpam-3903	363	18	function	function	NOUN
ejpam-3903	363	19	of	of	ADP
ejpam-3903	363	20	degree	degree	NOUN
ejpam-3903	363	21	four	four	NUM
ejpam-3903	363	22	which	which	PRON
ejpam-3903	363	23	is	be	AUX
ejpam-3903	363	24	negative	negative	ADJ
ejpam-3903	363	25	at	at	ADP
ejpam-3903	363	26	t	t	PROPN
ejpam-3903	363	27	=	=	SYM
ejpam-3903	363	28	0	0	NUM
ejpam-3903	363	29	,	,	PUNCT
ejpam-3903	363	30	and	and	CCONJ
ejpam-3903	363	31	is	be	AUX
ejpam-3903	363	32	tends	tend	VERB
ejpam-3903	363	33	towards	towards	ADP
ejpam-3903	363	34	+	+	NOUN
ejpam-3903	363	35	∞	∞	PROPN
ejpam-3903	363	36	when	when	SCONJ
ejpam-3903	363	37	t	t	PROPN
ejpam-3903	363	38	→	→	SYM
ejpam-3903	363	39	+	+	PROPN
ejpam-3903	363	40	∞.	∞.	PROPN
ejpam-3903	363	41	thus	thus	ADV
ejpam-3903	363	42	there	there	PRON
ejpam-3903	363	43	exists	exist	VERB
ejpam-3903	363	44	at	at	ADP
ejpam-3903	363	45	least	least	ADV
ejpam-3903	363	46	one	one	NUM
ejpam-3903	363	47	t	t	NOUN
ejpam-3903	363	48	∈	∈	NOUN
ejpam-3903	363	49	r	r	NOUN
ejpam-3903	363	50	such	such	ADJ
ejpam-3903	363	51	as	as	ADP
ejpam-3903	363	52	gm(t	gm(t	PUNCT
ejpam-3903	363	53	)	)	PUNCT
ejpam-3903	364	1	=	=	SYM
ejpam-3903	364	2	0	0	X
ejpam-3903	364	3	.	.	PUNCT
ejpam-3903	365	1	thus	thus	ADV
ejpam-3903	365	2	we	we	PRON
ejpam-3903	365	3	takes	take	VERB
ejpam-3903	365	4	t0	t0	PROPN
ejpam-3903	365	5	as	as	SCONJ
ejpam-3903	365	6	follows	follow	VERB
ejpam-3903	365	7	:	:	PUNCT
ejpam-3903	365	8	t0	t0	PROPN
ejpam-3903	365	9	=	=	PROPN
ejpam-3903	365	10	inf	inf	PROPN
ejpam-3903	365	11	t∈[0,+∞	t∈[0,+∞	ADP
ejpam-3903	365	12	[	[	PUNCT
ejpam-3903	365	13	e	e	X
ejpam-3903	365	14	(	(	PUNCT
ejpam-3903	365	15	58	58	NUM
ejpam-3903	365	16	)	)	PUNCT
ejpam-3903	365	17	consequently	consequently	ADV
ejpam-3903	365	18	,	,	PUNCT
ejpam-3903	365	19	for	for	ADP
ejpam-3903	365	20	any	any	DET
ejpam-3903	365	21	t	t	NOUN
ejpam-3903	365	22	∈	∈	PROPN
ejpam-3903	366	1	[	[	X
ejpam-3903	366	2	0	0	NUM
ejpam-3903	366	3	,	,	PUNCT
ejpam-3903	366	4	t0	t0	PROPN
ejpam-3903	366	5	[	[	PUNCT
ejpam-3903	366	6	we	we	PRON
ejpam-3903	366	7	have	have	AUX
ejpam-3903	366	8	gm(t	gm(t	NOUN
ejpam-3903	366	9	)	)	PUNCT
ejpam-3903	366	10	6	6	NUM
ejpam-3903	366	11	0	0	NUM
ejpam-3903	366	12	.	.	PUNCT
ejpam-3903	367	1	we	we	PRON
ejpam-3903	367	2	then	then	ADV
ejpam-3903	367	3	obtain	obtain	VERB
ejpam-3903	367	4	the	the	DET
ejpam-3903	367	5	following	follow	VERB
ejpam-3903	367	6	uniform	uniform	ADJ
ejpam-3903	367	7	estimate	estimate	NOUN
ejpam-3903	367	8	:	:	PUNCT
ejpam-3903	367	9	‖a0w1∗	‖a0w1∗	PROPN
ejpam-3903	367	10	2	2	NUM
ejpam-3903	367	11	‖hs	‖hs	PROPN
ejpam-3903	367	12	≤	≤	NOUN
ejpam-3903	367	13	(	(	PUNCT
ejpam-3903	367	14	4	4	NUM
ejpam-3903	367	15	t	t	NOUN
ejpam-3903	367	16	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	367	17	)	)	PUNCT
ejpam-3903	367	18	‖f1‖hs	‖f1‖hs	PUNCT
ejpam-3903	368	1	+	+	PUNCT
ejpam-3903	368	2	c03(w0	c03(w0	ADJ
ejpam-3903	368	3	)	)	PUNCT
ejpam-3903	368	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	368	5	)	)	PUNCT
ejpam-3903	368	6	‖a0w0∗‖hs	‖a0w0∗‖h	VERB
ejpam-3903	368	7	+	+	PROPN
ejpam-3903	368	8	m‖w1	m‖w1	ADJ
ejpam-3903	368	9	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	368	10	+	+	CCONJ
ejpam-3903	368	11	c03(w0	c03(w0	ADJ
ejpam-3903	368	12	)	)	PUNCT
ejpam-3903	368	13	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	368	14	)	)	PUNCT
ejpam-3903	368	15	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	368	16	g	g	PROPN
ejpam-3903	368	17	−w0	−w0	PROPN
ejpam-3903	368	18	g)‖hs	g)‖hs	PROPN
ejpam-3903	368	19	)	)	PUNCT
ejpam-3903	368	20	expm	expm	NOUN
ejpam-3903	368	21	(	(	PUNCT
ejpam-3903	368	22	59	59	NUM
ejpam-3903	368	23	)	)	PUNCT
ejpam-3903	368	24	r.	r.	PROPN
ejpam-3903	368	25	bade	bade	PROPN
ejpam-3903	368	26	,	,	PUNCT
ejpam-3903	368	27	h.	h.	PROPN
ejpam-3903	368	28	chaker	chaker	PROPN
ejpam-3903	368	29	/	/	SYM
ejpam-3903	368	30	eur	eur	PROPN
ejpam-3903	368	31	.	.	PUNCT
ejpam-3903	369	1	j.	j.	PROPN
ejpam-3903	369	2	pure	pure	PROPN
ejpam-3903	369	3	appl	appl	PROPN
ejpam-3903	369	4	.	.	PROPN
ejpam-3903	369	5	math	math	PROPN
ejpam-3903	369	6	,	,	PUNCT
ejpam-3903	369	7	14	14	NUM
ejpam-3903	369	8	(	(	PUNCT
ejpam-3903	369	9	1	1	NUM
ejpam-3903	369	10	)	)	PUNCT
ejpam-3903	369	11	(	(	PUNCT
ejpam-3903	369	12	2021	2021	NUM
ejpam-3903	369	13	)	)	PUNCT
ejpam-3903	369	14	,	,	PUNCT
ejpam-3903	369	15	82	82	NUM
ejpam-3903	369	16	-	-	SYM
ejpam-3903	369	17	111	111	NUM
ejpam-3903	369	18	99	99	NUM
ejpam-3903	369	19	and	and	CCONJ
ejpam-3903	369	20	‖w1	‖w1	PROPN
ejpam-3903	369	21	2‖l∞	2‖l∞	NUM
ejpam-3903	369	22	≤	≤	NOUN
ejpam-3903	369	23	(	(	PUNCT
ejpam-3903	369	24	t	t	PROPN
ejpam-3903	369	25	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	369	26	)	)	PUNCT
ejpam-3903	369	27	t‖f‖∞,s	t‖f‖∞,s	NOUN
ejpam-3903	370	1	+	+	CCONJ
ejpam-3903	370	2	c03(w0	c03(w0	ADJ
ejpam-3903	370	3	)	)	PUNCT
ejpam-3903	370	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	370	5	)	)	PUNCT
ejpam-3903	370	6	‖a0w0∗‖hs	‖a0w0∗‖h	VERB
ejpam-3903	370	7	+	+	PUNCT
ejpam-3903	370	8	m‖wg‖∞,s+1	m‖wg‖∞,s+1	NOUN
ejpam-3903	370	9	+	+	CCONJ
ejpam-3903	370	10	c03(w0	c03(w0	ADJ
ejpam-3903	370	11	)	)	PUNCT
ejpam-3903	370	12	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	370	13	)	)	PUNCT
ejpam-3903	370	14	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	370	15	g	g	PROPN
ejpam-3903	370	16	−w0	−w0	PROPN
ejpam-3903	370	17	g)‖hs	g)‖hs	PROPN
ejpam-3903	370	18	)	)	PUNCT
ejpam-3903	371	1	expm+‖wg‖∞,∞.	expm+‖wg‖∞,∞.	PROPN
ejpam-3903	371	2	(	(	PUNCT
ejpam-3903	371	3	60	60	NUM
ejpam-3903	371	4	)	)	PUNCT
ejpam-3903	371	5	finally	finally	ADV
ejpam-3903	371	6	we	we	PRON
ejpam-3903	371	7	have	have	AUX
ejpam-3903	371	8	by	by	ADP
ejpam-3903	371	9	recurrence	recurrence	NOUN
ejpam-3903	371	10	:	:	PUNCT
ejpam-3903	371	11	‖a0w1	‖a0w1	PUNCT
ejpam-3903	372	1	k‖hs	k‖hs	PROPN
ejpam-3903	372	2	≤	≤	NOUN
ejpam-3903	372	3	(	(	PUNCT
ejpam-3903	372	4	4	4	NUM
ejpam-3903	372	5	t	t	NOUN
ejpam-3903	372	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	372	7	)	)	PUNCT
ejpam-3903	372	8	‖f1‖hs	‖f1‖hs	PUNCT
ejpam-3903	373	1	+	+	PUNCT
ejpam-3903	373	2	c03(w0	c03(w0	ADJ
ejpam-3903	373	3	)	)	PUNCT
ejpam-3903	373	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	373	5	)	)	PUNCT
ejpam-3903	373	6	‖a0w0∗‖hs	‖a0w0∗‖h	VERB
ejpam-3903	373	7	+	+	PROPN
ejpam-3903	373	8	m‖w1	m‖w1	ADJ
ejpam-3903	373	9	g‖hs+1	g‖hs+1	NOUN
ejpam-3903	373	10	+	+	CCONJ
ejpam-3903	373	11	c03(w0	c03(w0	ADJ
ejpam-3903	373	12	)	)	PUNCT
ejpam-3903	373	13	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	373	14	)	)	PUNCT
ejpam-3903	373	15	‖a0(w1	‖a0(w1	NOUN
ejpam-3903	373	16	g	g	PROPN
ejpam-3903	373	17	−w0	−w0	PROPN
ejpam-3903	373	18	g)‖hs	g)‖hs	PROPN
ejpam-3903	373	19	)	)	PUNCT
ejpam-3903	374	1	expm+‖a0w1	expm+‖a0w1	ADP
ejpam-3903	374	2	g‖hs	g‖hs	PROPN
ejpam-3903	374	3	(	(	PUNCT
ejpam-3903	374	4	61	61	NUM
ejpam-3903	374	5	)	)	PUNCT
ejpam-3903	375	1	‖w1	‖w1	VERB
ejpam-3903	375	2	k‖l∞	k‖l∞	VERB
ejpam-3903	375	3	≤	≤	NUM
ejpam-3903	375	4	(	(	PUNCT
ejpam-3903	375	5	t	t	PROPN
ejpam-3903	375	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	375	7	)	)	PUNCT
ejpam-3903	375	8	‖f‖∞,s	‖f‖∞,s	PUNCT
ejpam-3903	376	1	+	+	CCONJ
ejpam-3903	376	2	c03(w0	c03(w0	ADJ
ejpam-3903	376	3	)	)	PUNCT
ejpam-3903	376	4	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	376	5	)	)	PUNCT
ejpam-3903	376	6	‖a0w0∗‖hs	‖a0w0∗‖h	VERB
ejpam-3903	377	1	+	+	PUNCT
ejpam-3903	377	2	m‖wg‖∞,s+1	m‖wg‖∞,s+1	NOUN
ejpam-3903	377	3	+	+	CCONJ
ejpam-3903	377	4	2c03(w0	2c03(w0	NUM
ejpam-3903	377	5	)	)	PUNCT
ejpam-3903	377	6	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	377	7	)	)	PUNCT
ejpam-3903	377	8	‖a0wg‖∞,s	‖a0wg‖∞,s	NOUN
ejpam-3903	377	9	)	)	PUNCT
ejpam-3903	378	1	expm+‖wg‖∞,∞.	expm+‖wg‖∞,∞.	PROPN
ejpam-3903	378	2	�	�	PROPN
ejpam-3903	378	3	(	(	PUNCT
ejpam-3903	378	4	62	62	NUM
ejpam-3903	378	5	)	)	PUNCT
ejpam-3903	378	6	4.1.3	4.1.3	NUM
ejpam-3903	378	7	.	.	PUNCT
ejpam-3903	378	8	passing	pass	VERB
ejpam-3903	378	9	to	to	ADP
ejpam-3903	378	10	the	the	DET
ejpam-3903	378	11	limit	limit	NOUN
ejpam-3903	378	12	k	k	PROPN
ejpam-3903	378	13	→∞	→∞	NOUN
ejpam-3903	378	14	we	we	PRON
ejpam-3903	378	15	have	have	AUX
ejpam-3903	378	16	shown	show	VERB
ejpam-3903	378	17	in	in	ADP
ejpam-3903	378	18	the	the	DET
ejpam-3903	378	19	paragraphs	paragraph	NOUN
ejpam-3903	378	20	4.1.1	4.1.1	NUM
ejpam-3903	378	21	and	and	CCONJ
ejpam-3903	378	22	4.1.2	4.1.2	NUM
ejpam-3903	378	23	the	the	DET
ejpam-3903	378	24	existence	existence	NOUN
ejpam-3903	378	25	of	of	ADP
ejpam-3903	378	26	the	the	DET
ejpam-3903	378	27	sequence	sequence	NOUN
ejpam-3903	378	28	(	(	PUNCT
ejpam-3903	378	29	w1	w1	NOUN
ejpam-3903	378	30	k+1	k+1	PROPN
ejpam-3903	378	31	)	)	PUNCT
ejpam-3903	378	32	,	,	PUNCT
ejpam-3903	378	33	here	here	ADV
ejpam-3903	378	34	we	we	PRON
ejpam-3903	378	35	will	will	AUX
ejpam-3903	378	36	show	show	VERB
ejpam-3903	378	37	that	that	SCONJ
ejpam-3903	378	38	this	this	DET
ejpam-3903	378	39	sequence	sequence	NOUN
ejpam-3903	378	40	converge	converge	VERB
ejpam-3903	378	41	and	and	CCONJ
ejpam-3903	378	42	its	its	PRON
ejpam-3903	378	43	limit	limit	NOUN
ejpam-3903	378	44	is	be	AUX
ejpam-3903	378	45	solution	solution	NOUN
ejpam-3903	378	46	of	of	ADP
ejpam-3903	378	47	the	the	DET
ejpam-3903	378	48	following	follow	VERB
ejpam-3903	378	49	system:	system:	NOUN
ejpam-3903	378	50	a0(w0	a0(w0	NOUN
ejpam-3903	378	51	)	)	PUNCT
ejpam-3903	378	52	4	4	NUM
ejpam-3903	378	53	t	t	NOUN
ejpam-3903	378	54	w1	w1	NOUN
ejpam-3903	378	55	+	+	CCONJ
ejpam-3903	378	56	3∑	3∑	NUM
ejpam-3903	378	57	i=1	i=1	NOUN
ejpam-3903	378	58	aiε	aiε	CCONJ
ejpam-3903	378	59	∂w1	∂w1	PROPN
ejpam-3903	378	60	∂xi	∂xi	PROPN
ejpam-3903	378	61	+	+	CCONJ
ejpam-3903	378	62	kε(w	kε(w	PROPN
ejpam-3903	378	63	1)w1	1)w1	NUM
ejpam-3903	378	64	=	=	SYM
ejpam-3903	378	65	f1	f1	NOUN
ejpam-3903	378	66	+	+	CCONJ
ejpam-3903	378	67	a0(w0	a0(w0	NOUN
ejpam-3903	378	68	)	)	PUNCT
ejpam-3903	378	69	4	4	NUM
ejpam-3903	378	70	t	t	NOUN
ejpam-3903	378	71	w0	w0	NOUN
ejpam-3903	378	72	,	,	PUNCT
ejpam-3903	378	73	(	(	PUNCT
ejpam-3903	378	74	b−m)w1	b−m)w1	X
ejpam-3903	378	75	=	=	PUNCT
ejpam-3903	378	76	g1	g1	PROPN
ejpam-3903	378	77	.	.	PUNCT
ejpam-3903	379	1	(	(	PUNCT
ejpam-3903	379	2	63	63	NUM
ejpam-3903	379	3	)	)	PUNCT
ejpam-3903	379	4	let	let	VERB
ejpam-3903	379	5	us	we	PRON
ejpam-3903	379	6	set	set	VERB
ejpam-3903	379	7	:	:	PUNCT
ejpam-3903	379	8	rs	rs	PROPN
ejpam-3903	379	9	=	=	SYM
ejpam-3903	379	10	mt	mt	PROPN
ejpam-3903	379	11	expm+‖wg‖∞,∞	expm+‖wg‖∞,∞	PROPN
ejpam-3903	379	12	(	(	PUNCT
ejpam-3903	379	13	64	64	NUM
ejpam-3903	379	14	)	)	PUNCT
ejpam-3903	379	15	lemma	lemma	PROPN
ejpam-3903	380	1	3	3	X
ejpam-3903	380	2	.	.	PUNCT
ejpam-3903	381	1	let	let	VERB
ejpam-3903	381	2	b	b	X
ejpam-3903	381	3	be	be	AUX
ejpam-3903	381	4	a	a	DET
ejpam-3903	381	5	ball	ball	NOUN
ejpam-3903	381	6	of	of	ADP
ejpam-3903	381	7	hs(ω)20	hs(ω)20	NOUN
ejpam-3903	381	8	with	with	ADP
ejpam-3903	381	9	radius	radius	ADJ
ejpam-3903	381	10	rs	rs	NOUN
ejpam-3903	381	11	given	give	VERB
ejpam-3903	381	12	by	by	ADP
ejpam-3903	381	13	(	(	PUNCT
ejpam-3903	381	14	64	64	NUM
ejpam-3903	381	15	)	)	PUNCT
ejpam-3903	381	16	.	.	PUNCT
ejpam-3903	382	1	then	then	ADV
ejpam-3903	382	2	the	the	DET
ejpam-3903	382	3	function	function	NOUN
ejpam-3903	382	4	g	g	PROPN
ejpam-3903	382	5	defined	define	VERB
ejpam-3903	382	6	by	by	ADP
ejpam-3903	382	7	:	:	PUNCT
ejpam-3903	382	8	g	g	NOUN
ejpam-3903	382	9	:	:	PUNCT
ejpam-3903	382	10	(	(	PUNCT
ejpam-3903	382	11	b	b	X
ejpam-3903	382	12	−→	−→	NOUN
ejpam-3903	382	13	b	b	PROPN
ejpam-3903	382	14	w1	w1	NOUN
ejpam-3903	382	15	k	k	PROPN
ejpam-3903	382	16	−→	−→	NOUN
ejpam-3903	382	17	g(w1	g(w1	ADJ
ejpam-3903	382	18	k	k	NOUN
ejpam-3903	382	19	)	)	PUNCT
ejpam-3903	382	20	=	=	SYM
ejpam-3903	382	21	w1	w1	PROPN
ejpam-3903	382	22	k+1	k+1	X
ejpam-3903	382	23	)	)	PUNCT
ejpam-3903	382	24	admits	admit	VERB
ejpam-3903	382	25	an	an	DET
ejpam-3903	382	26	unique	unique	ADJ
ejpam-3903	382	27	fixed	fix	VERB
ejpam-3903	382	28	point	point	NOUN
ejpam-3903	382	29	w1	w1	NOUN
ejpam-3903	382	30	which	which	PRON
ejpam-3903	382	31	is	be	AUX
ejpam-3903	382	32	solution	solution	NOUN
ejpam-3903	382	33	of	of	ADP
ejpam-3903	382	34	the	the	DET
ejpam-3903	382	35	system	system	NOUN
ejpam-3903	382	36	(	(	PUNCT
ejpam-3903	382	37	63	63	NUM
ejpam-3903	382	38	)	)	PUNCT
ejpam-3903	382	39	.	.	PUNCT
ejpam-3903	383	1	in	in	ADP
ejpam-3903	383	2	addition	addition	NOUN
ejpam-3903	383	3	we	we	PRON
ejpam-3903	383	4	have	have	VERB
ejpam-3903	383	5	w1	w1	NOUN
ejpam-3903	383	6	∈	∈	PROPN
ejpam-3903	383	7	l∞(ω)20	l∞(ω)20	VERB
ejpam-3903	383	8	with	with	ADP
ejpam-3903	383	9	(	(	PUNCT
ejpam-3903	383	10	w1)1	w1)1	X
ejpam-3903	383	11	>	>	X
ejpam-3903	383	12	ρ̄	ρ̄	NUM
ejpam-3903	383	13	exp(−4trs	exp(−4trs	PROPN
ejpam-3903	383	14	)	)	PUNCT
ejpam-3903	383	15	·	·	PUNCT
ejpam-3903	383	16	r.	r.	PROPN
ejpam-3903	383	17	bade	bade	PROPN
ejpam-3903	383	18	,	,	PUNCT
ejpam-3903	383	19	h.	h.	PROPN
ejpam-3903	383	20	chaker	chaker	PROPN
ejpam-3903	383	21	/	/	SYM
ejpam-3903	383	22	eur	eur	PROPN
ejpam-3903	383	23	.	.	PUNCT
ejpam-3903	384	1	j.	j.	PROPN
ejpam-3903	384	2	pure	pure	PROPN
ejpam-3903	384	3	appl	appl	PROPN
ejpam-3903	384	4	.	.	PROPN
ejpam-3903	384	5	math	math	PROPN
ejpam-3903	384	6	,	,	PUNCT
ejpam-3903	384	7	14	14	NUM
ejpam-3903	384	8	(	(	PUNCT
ejpam-3903	384	9	1	1	NUM
ejpam-3903	384	10	)	)	PUNCT
ejpam-3903	384	11	(	(	PUNCT
ejpam-3903	384	12	2021	2021	NUM
ejpam-3903	384	13	)	)	PUNCT
ejpam-3903	384	14	,	,	PUNCT
ejpam-3903	384	15	82	82	NUM
ejpam-3903	384	16	-	-	SYM
ejpam-3903	384	17	111	111	NUM
ejpam-3903	384	18	100	100	NUM
ejpam-3903	384	19	proof	proof	NOUN
ejpam-3903	384	20	.	.	PUNCT
ejpam-3903	385	1	let	let	VERB
ejpam-3903	385	2	w1	w1	PROPN
ejpam-3903	385	3	k	k	PROPN
ejpam-3903	385	4	and	and	CCONJ
ejpam-3903	385	5	w1	w1	NOUN
ejpam-3903	385	6	k+1	k+1	X
ejpam-3903	385	7	be	be	AUX
ejpam-3903	385	8	two	two	NUM
ejpam-3903	385	9	successive	successive	ADJ
ejpam-3903	385	10	solutions	solution	NOUN
ejpam-3903	385	11	of	of	ADP
ejpam-3903	385	12	(	(	PUNCT
ejpam-3903	385	13	50	50	NUM
ejpam-3903	385	14	)	)	PUNCT
ejpam-3903	385	15	then	then	ADV
ejpam-3903	385	16	we	we	PRON
ejpam-3903	385	17	have	have	VERB
ejpam-3903	385	18	:	:	PUNCT
ejpam-3903	385	19	a0(w0	a0(w0	NOUN
ejpam-3903	385	20	)	)	PUNCT
ejpam-3903	385	21	4	4	NUM
ejpam-3903	385	22	t	t	NOUN
ejpam-3903	385	23	w1	w1	NOUN
ejpam-3903	385	24	k+1	k+1	NOUN
ejpam-3903	386	1	+	+	CCONJ
ejpam-3903	386	2	3∑	3∑	NUM
ejpam-3903	386	3	i=1	i=1	INTJ
ejpam-3903	386	4	aiε	aiε	ADV
ejpam-3903	386	5	∂w1	∂w1	PROPN
ejpam-3903	386	6	k+1	k+1	PRON
ejpam-3903	386	7	∂xi	∂xi	PROPN
ejpam-3903	386	8	+	+	CCONJ
ejpam-3903	386	9	kε(w	kε(w	ADJ
ejpam-3903	386	10	1	1	NUM
ejpam-3903	386	11	k)w1	k)w1	PROPN
ejpam-3903	386	12	k+1	k+1	X
ejpam-3903	386	13	=	=	SYM
ejpam-3903	386	14	f1	f1	NOUN
ejpam-3903	386	15	+	+	CCONJ
ejpam-3903	386	16	a0(w0	a0(w0	NOUN
ejpam-3903	386	17	)	)	PUNCT
ejpam-3903	386	18	4	4	NUM
ejpam-3903	386	19	t	t	NOUN
ejpam-3903	386	20	w0	w0	NOUN
ejpam-3903	386	21	,	,	PUNCT
ejpam-3903	386	22	(	(	PUNCT
ejpam-3903	386	23	65	65	X
ejpam-3903	386	24	)	)	PUNCT
ejpam-3903	386	25	a0(w0	a0(w0	NOUN
ejpam-3903	386	26	)	)	PUNCT
ejpam-3903	386	27	4	4	NUM
ejpam-3903	386	28	t	t	NOUN
ejpam-3903	386	29	w1	w1	NOUN
ejpam-3903	386	30	k	k	PROPN
ejpam-3903	387	1	+	+	PUNCT
ejpam-3903	388	1	3∑	3∑	NUM
ejpam-3903	388	2	i=1	i=1	INTJ
ejpam-3903	388	3	aiε	aiε	PRON
ejpam-3903	388	4	∂w1	∂w1	PROPN
ejpam-3903	388	5	k	k	PROPN
ejpam-3903	388	6	∂xi	∂xi	PROPN
ejpam-3903	388	7	+	+	CCONJ
ejpam-3903	388	8	kε(w	kε(w	X
ejpam-3903	388	9	1	1	NUM
ejpam-3903	388	10	k−1)w1	k−1)w1	ADP
ejpam-3903	388	11	k	k	PROPN
ejpam-3903	388	12	=	=	PUNCT
ejpam-3903	388	13	f1	f1	PROPN
ejpam-3903	388	14	+	+	CCONJ
ejpam-3903	388	15	a0(w0	a0(w0	NOUN
ejpam-3903	388	16	)	)	PUNCT
ejpam-3903	388	17	4	4	NUM
ejpam-3903	388	18	t	t	NOUN
ejpam-3903	388	19	w0	w0	NOUN
ejpam-3903	388	20	.	.	PUNCT
ejpam-3903	389	1	(	(	PUNCT
ejpam-3903	389	2	66	66	NUM
ejpam-3903	389	3	)	)	PUNCT
ejpam-3903	389	4	the	the	DET
ejpam-3903	389	5	difference	difference	NOUN
ejpam-3903	389	6	between	between	ADP
ejpam-3903	389	7	(	(	PUNCT
ejpam-3903	389	8	65	65	NUM
ejpam-3903	389	9	)	)	PUNCT
ejpam-3903	389	10	and	and	CCONJ
ejpam-3903	389	11	(	(	PUNCT
ejpam-3903	389	12	66	66	NUM
ejpam-3903	389	13	)	)	PUNCT
ejpam-3903	389	14	gives	give	VERB
ejpam-3903	389	15	:	:	PUNCT
ejpam-3903	390	1	[	[	X
ejpam-3903	390	2	a0(w0	a0(w0	NOUN
ejpam-3903	390	3	)	)	PUNCT
ejpam-3903	390	4	4	4	NUM
ejpam-3903	390	5	t	t	NOUN
ejpam-3903	390	6	+	+	CCONJ
ejpam-3903	390	7	kε(w	kε(w	VERB
ejpam-3903	390	8	1	1	NUM
ejpam-3903	390	9	k	k	NOUN
ejpam-3903	390	10	)	)	PUNCT
ejpam-3903	390	11	]	]	X
ejpam-3903	390	12	(	(	PUNCT
ejpam-3903	390	13	w1	w1	NOUN
ejpam-3903	390	14	k+1	k+1	PROPN
ejpam-3903	390	15	−w1	−w1	PROPN
ejpam-3903	390	16	k	k	PROPN
ejpam-3903	390	17	)	)	PUNCT
ejpam-3903	391	1	+	+	PUNCT
ejpam-3903	391	2	3∑	3∑	NUM
ejpam-3903	391	3	i=1	i=1	NUM
ejpam-3903	391	4	aiε	aiε	PRON
ejpam-3903	391	5	∂	∂	NUM
ejpam-3903	391	6	∂xi	∂xi	NOUN
ejpam-3903	391	7	(	(	PUNCT
ejpam-3903	391	8	w1	w1	NOUN
ejpam-3903	391	9	k+1	k+1	PROPN
ejpam-3903	391	10	−w1	−w1	PROPN
ejpam-3903	391	11	k	k	PROPN
ejpam-3903	391	12	)	)	PUNCT
ejpam-3903	392	1	=	=	PUNCT
ejpam-3903	393	1	[	[	PUNCT
ejpam-3903	393	2	kε(w	kε(w	X
ejpam-3903	393	3	1	1	NUM
ejpam-3903	393	4	k−1)−kε(w	k−1)−kε(w	PROPN
ejpam-3903	393	5	1	1	NUM
ejpam-3903	393	6	k	k	NOUN
ejpam-3903	393	7	)	)	PUNCT
ejpam-3903	393	8	]	]	PUNCT
ejpam-3903	393	9	(	(	PUNCT
ejpam-3903	393	10	w1	w1	NOUN
ejpam-3903	393	11	k	k	PROPN
ejpam-3903	393	12	)	)	PUNCT
ejpam-3903	393	13	.	.	PUNCT
ejpam-3903	394	1	a	a	DET
ejpam-3903	394	2	scalar	scalar	ADJ
ejpam-3903	394	3	product	product	NOUN
ejpam-3903	394	4	with	with	ADP
ejpam-3903	394	5	w1	w1	NOUN
ejpam-3903	394	6	k+1−w1	k+1−w1	PROPN
ejpam-3903	394	7	k	k	PROPN
ejpam-3903	394	8	and	and	CCONJ
ejpam-3903	394	9	using	use	VERB
ejpam-3903	394	10	the	the	DET
ejpam-3903	394	11	fact	fact	NOUN
ejpam-3903	394	12	that	that	SCONJ
ejpam-3903	394	13	:	:	PUNCT
ejpam-3903	394	14	the	the	DET
ejpam-3903	394	15	matrix	matrix	NOUN
ejpam-3903	394	16	aiε	aiε	VERB
ejpam-3903	394	17	are	be	AUX
ejpam-3903	394	18	symmetric	symmetric	ADJ
ejpam-3903	394	19	,	,	PUNCT
ejpam-3903	394	20	w1	w1	NOUN
ejpam-3903	394	21	k+1	k+1	PROPN
ejpam-3903	394	22	−w1	−w1	PROPN
ejpam-3903	394	23	k	k	PROPN
ejpam-3903	394	24	=	=	PUNCT
ejpam-3903	394	25	w1∗	w1∗	PROPN
ejpam-3903	394	26	k+1	k+1	NOUN
ejpam-3903	394	27	−w1∗	−w1∗	NOUN
ejpam-3903	394	28	k	k	NOUN
ejpam-3903	394	29	and	and	CCONJ
ejpam-3903	394	30	the	the	DET
ejpam-3903	394	31	operator	operator	NOUN
ejpam-3903	395	1	<	<	X
ejpam-3903	395	2	+	+	NOUN
ejpam-3903	395	3	<	<	X
ejpam-3903	395	4	∗	∗	NOUN
ejpam-3903	395	5	is	be	AUX
ejpam-3903	395	6	positive	positive	ADJ
ejpam-3903	395	7	we	we	PRON
ejpam-3903	395	8	obtain	obtain	VERB
ejpam-3903	395	9	:	:	PUNCT
ejpam-3903	395	10	<	<	X
ejpam-3903	395	11	(	(	PUNCT
ejpam-3903	395	12	<	<	X
ejpam-3903	395	13	+	+	X
ejpam-3903	395	14	<	<	X
ejpam-3903	395	15	∗)(w0,w1	∗)(w0,w1	PROPN
ejpam-3903	395	16	k)(w	k)(w	ADJ
ejpam-3903	395	17	1	1	NUM
ejpam-3903	395	18	k+1	k+1	PRON
ejpam-3903	395	19	−w1	−w1	NOUN
ejpam-3903	395	20	k),w1	k),w1	NOUN
ejpam-3903	395	21	k+1	k+1	PROPN
ejpam-3903	395	22	−w1	−w1	PROPN
ejpam-3903	395	23	k	k	X
ejpam-3903	395	24	>	>	PUNCT
ejpam-3903	395	25	>	>	X
ejpam-3903	395	26	2	2	NUM
ejpam-3903	395	27	υ(ε,4t)‖w1	υ(ε,4t)‖w1	VERB
ejpam-3903	395	28	k+1	k+1	PROPN
ejpam-3903	395	29	−w1	−w1	PROPN
ejpam-3903	395	30	k‖2l2	k‖2l2	PROPN
ejpam-3903	395	31	(	(	PUNCT
ejpam-3903	395	32	67	67	NUM
ejpam-3903	395	33	)	)	PUNCT
ejpam-3903	395	34	and	and	CCONJ
ejpam-3903	395	35	<	<	X
ejpam-3903	395	36	(	(	PUNCT
ejpam-3903	395	37	<	<	X
ejpam-3903	395	38	+	+	X
ejpam-3903	395	39	<	<	X
ejpam-3903	395	40	∗)(w0,w1	∗)(w0,w1	PROPN
ejpam-3903	395	41	k)(w	k)(w	ADJ
ejpam-3903	395	42	1	1	NUM
ejpam-3903	395	43	k+1	k+1	PRON
ejpam-3903	395	44	−w1	−w1	NOUN
ejpam-3903	395	45	k),w1	k),w1	NOUN
ejpam-3903	395	46	k+1	k+1	PROPN
ejpam-3903	395	47	−w1	−w1	PROPN
ejpam-3903	395	48	k	k	X
ejpam-3903	395	49	>	>	PUNCT
ejpam-3903	395	50	>	>	X
ejpam-3903	395	51	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	395	52	)	)	PUNCT
ejpam-3903	395	53	4	4	NUM
ejpam-3903	395	54	t	t	NOUN
ejpam-3903	395	55	‖a0	‖a0	NOUN
ejpam-3903	395	56	(	(	PUNCT
ejpam-3903	395	57	w1	w1	NOUN
ejpam-3903	395	58	k+1	k+1	PROPN
ejpam-3903	395	59	−w1	−w1	PROPN
ejpam-3903	395	60	k	k	PROPN
ejpam-3903	395	61	)	)	PUNCT
ejpam-3903	395	62	‖2l2	‖2l2	PROPN
ejpam-3903	395	63	.	.	PUNCT
ejpam-3903	396	1	(	(	PUNCT
ejpam-3903	396	2	68	68	NUM
ejpam-3903	396	3	)	)	PUNCT
ejpam-3903	396	4	by	by	ADP
ejpam-3903	396	5	the	the	DET
ejpam-3903	396	6	obtained	obtain	VERB
ejpam-3903	396	7	result	result	NOUN
ejpam-3903	396	8	in	in	ADP
ejpam-3903	396	9	[	[	X
ejpam-3903	396	10	4	4	NUM
ejpam-3903	396	11	]	]	X
ejpam-3903	396	12	(	(	PUNCT
ejpam-3903	396	13	lemma	lemma	PROPN
ejpam-3903	396	14	2	2	X
ejpam-3903	396	15	)	)	PUNCT
ejpam-3903	396	16	we	we	PRON
ejpam-3903	396	17	have	have	VERB
ejpam-3903	396	18	:	:	PUNCT
ejpam-3903	396	19	<	<	X
ejpam-3903	396	20	[	[	PUNCT
ejpam-3903	396	21	kε(w	kε(w	X
ejpam-3903	396	22	1	1	NUM
ejpam-3903	396	23	k−1)−kε(w	k−1)−kε(w	PROPN
ejpam-3903	396	24	1	1	NUM
ejpam-3903	396	25	k	k	NOUN
ejpam-3903	396	26	)	)	PUNCT
ejpam-3903	396	27	]	]	PUNCT
ejpam-3903	397	1	w1	w1	PROPN
ejpam-3903	397	2	k	k	PROPN
ejpam-3903	397	3	,	,	PUNCT
ejpam-3903	397	4	w	w	PROPN
ejpam-3903	397	5	1	1	NUM
ejpam-3903	397	6	k+1	k+1	PRON
ejpam-3903	397	7	−w1	−w1	PROPN
ejpam-3903	397	8	k	k	PROPN
ejpam-3903	397	9	>	>	PROPN
ejpam-3903	397	10	6	6	NUM
ejpam-3903	397	11	c	c	NOUN
ejpam-3903	397	12	w	w	PROPN
ejpam-3903	397	13	1,∞‖w1	1,∞‖w1	NUM
ejpam-3903	397	14	k	k	PROPN
ejpam-3903	398	1	−w1	−w1	PROPN
ejpam-3903	398	2	k−1‖l2‖a0	k−1‖l2‖a0	PROPN
ejpam-3903	398	3	(	(	PUNCT
ejpam-3903	398	4	w1	w1	NOUN
ejpam-3903	398	5	k+1	k+1	PROPN
ejpam-3903	398	6	−w1	−w1	PROPN
ejpam-3903	398	7	k	k	PROPN
ejpam-3903	398	8	)	)	PUNCT
ejpam-3903	398	9	‖l2	‖l2	VERB
ejpam-3903	398	10	,	,	PUNCT
ejpam-3903	398	11	(	(	PUNCT
ejpam-3903	398	12	69	69	NUM
ejpam-3903	398	13	)	)	PUNCT
ejpam-3903	398	14	where	where	SCONJ
ejpam-3903	398	15	the	the	DET
ejpam-3903	398	16	constant	constant	ADJ
ejpam-3903	398	17	cw	cw	NOUN
ejpam-3903	398	18	1,∞	1,∞	PROPN
ejpam-3903	398	19	is	be	AUX
ejpam-3903	398	20	defined	define	VERB
ejpam-3903	398	21	as	as	ADP
ejpam-3903	398	22	follow	follow	NOUN
ejpam-3903	398	23	:	:	PUNCT
ejpam-3903	398	24	cw	cw	NOUN
ejpam-3903	398	25	1,∞	1,∞	NUM
ejpam-3903	399	1	=	=	SYM
ejpam-3903	400	1	max	max	PROPN
ejpam-3903	400	2	16j620	16j620	NOUN
ejpam-3903	401	1	20∑	20∑	NUM
ejpam-3903	402	1	i=1	i=1	PROPN
ejpam-3903	402	2	sup	sup	NOUN
ejpam-3903	402	3	‖w1	‖w1	PROPN
ejpam-3903	402	4	k−1	k−1	PROPN
ejpam-3903	403	1	‖l∞6rs	‖l∞6rs	NUM
ejpam-3903	403	2	‖w1	‖w1	PROPN
ejpam-3903	403	3	k	k	NOUN
ejpam-3903	403	4	‖l∞6rs	‖l∞6rs	NUM
ejpam-3903	403	5	∣∣∣∣(n	∣∣∣∣(n	NOUN
ejpam-3903	404	1	[	[	X
ejpam-3903	404	2	w1	w1	NOUN
ejpam-3903	404	3	k−1,w	k−1,w	NOUN
ejpam-3903	404	4	1	1	NUM
ejpam-3903	404	5	k	k	NOUN
ejpam-3903	404	6	,	,	PUNCT
ejpam-3903	404	7	w	w	PROPN
ejpam-3903	404	8	1	1	NUM
ejpam-3903	404	9	k	k	NOUN
ejpam-3903	404	10	]	]	PUNCT
ejpam-3903	404	11	)	)	PUNCT
ejpam-3903	404	12	ij	ij	INTJ
ejpam-3903	404	13	∣∣∣∣.	∣∣∣∣.	PROPN
ejpam-3903	404	14	(	(	PUNCT
ejpam-3903	404	15	70	70	NUM
ejpam-3903	404	16	)	)	PUNCT
ejpam-3903	404	17	using	use	VERB
ejpam-3903	404	18	the	the	DET
ejpam-3903	404	19	inequality	inequality	NOUN
ejpam-3903	404	20	(	(	PUNCT
ejpam-3903	404	21	69	69	NUM
ejpam-3903	404	22	)	)	PUNCT
ejpam-3903	404	23	into	into	ADP
ejpam-3903	404	24	(	(	PUNCT
ejpam-3903	404	25	67	67	NUM
ejpam-3903	404	26	)	)	PUNCT
ejpam-3903	404	27	we	we	PRON
ejpam-3903	404	28	get	get	VERB
ejpam-3903	404	29	:	:	PUNCT
ejpam-3903	404	30	2υ(ε,4t)‖w1	2υ(ε,4t)‖w1	NUM
ejpam-3903	404	31	k+1	k+1	PROPN
ejpam-3903	404	32	−w1	−w1	VERB
ejpam-3903	404	33	k‖2l2	k‖2l2	PROPN
ejpam-3903	404	34	6	6	NUM
ejpam-3903	404	35	c(rs)‖w1	c(rs)‖w1	PROPN
ejpam-3903	404	36	k	k	PROPN
ejpam-3903	405	1	−w1	−w1	PROPN
ejpam-3903	405	2	k−1‖l2‖a0	k−1‖l2‖a0	PROPN
ejpam-3903	405	3	(	(	PUNCT
ejpam-3903	405	4	w1	w1	NOUN
ejpam-3903	405	5	k+1	k+1	PROPN
ejpam-3903	405	6	−w1	−w1	PROPN
ejpam-3903	405	7	k	k	PROPN
ejpam-3903	405	8	)	)	PUNCT
ejpam-3903	405	9	‖l2	‖l2	X
ejpam-3903	405	10	.	.	PUNCT
ejpam-3903	406	1	(	(	PUNCT
ejpam-3903	406	2	71	71	NUM
ejpam-3903	406	3	)	)	PUNCT
ejpam-3903	406	4	the	the	DET
ejpam-3903	406	5	inequality	inequality	NOUN
ejpam-3903	406	6	(	(	PUNCT
ejpam-3903	406	7	68	68	NUM
ejpam-3903	406	8	)	)	PUNCT
ejpam-3903	406	9	allows	allow	VERB
ejpam-3903	406	10	us	we	PRON
ejpam-3903	406	11	to	to	PART
ejpam-3903	406	12	deduce	deduce	VERB
ejpam-3903	406	13	:	:	PUNCT
ejpam-3903	407	1	‖a0	‖a0	PROPN
ejpam-3903	407	2	(	(	PUNCT
ejpam-3903	407	3	w1	w1	NOUN
ejpam-3903	407	4	k+1	k+1	PROPN
ejpam-3903	407	5	−w1	−w1	PROPN
ejpam-3903	407	6	k	k	PROPN
ejpam-3903	407	7	)	)	PUNCT
ejpam-3903	407	8	‖l2	‖l2	VERB
ejpam-3903	407	9	6	6	NUM
ejpam-3903	407	10	c(rs	c(rs	NOUN
ejpam-3903	407	11	)	)	PUNCT
ejpam-3903	407	12	4	4	NUM
ejpam-3903	407	13	t	t	NOUN
ejpam-3903	407	14	c01(ρ̄	c01(ρ̄	PROPN
ejpam-3903	407	15	)	)	PUNCT
ejpam-3903	407	16	‖w1	‖w1	PROPN
ejpam-3903	407	17	k	k	PROPN
ejpam-3903	407	18	−w1	−w1	PROPN
ejpam-3903	407	19	k−1‖l2	k−1‖l2	PROPN
ejpam-3903	407	20	.	.	PUNCT
ejpam-3903	408	1	(	(	PUNCT
ejpam-3903	408	2	72	72	X
ejpam-3903	408	3	)	)	PUNCT
ejpam-3903	408	4	r.	r.	NOUN
ejpam-3903	408	5	bade	bade	PROPN
ejpam-3903	408	6	,	,	PUNCT
ejpam-3903	408	7	h.	h.	PROPN
ejpam-3903	408	8	chaker	chaker	PROPN
ejpam-3903	408	9	/	/	SYM
ejpam-3903	408	10	eur	eur	PROPN
ejpam-3903	408	11	.	.	PUNCT
ejpam-3903	409	1	j.	j.	PROPN
ejpam-3903	409	2	pure	pure	PROPN
ejpam-3903	409	3	appl	appl	PROPN
ejpam-3903	409	4	.	.	PROPN
ejpam-3903	409	5	math	math	PROPN
ejpam-3903	409	6	,	,	PUNCT
ejpam-3903	409	7	14	14	NUM
ejpam-3903	409	8	(	(	PUNCT
ejpam-3903	409	9	1	1	NUM
ejpam-3903	409	10	)	)	PUNCT
ejpam-3903	409	11	(	(	PUNCT
ejpam-3903	409	12	2021	2021	NUM
ejpam-3903	409	13	)	)	PUNCT
ejpam-3903	409	14	,	,	PUNCT
ejpam-3903	409	15	82	82	NUM
ejpam-3903	409	16	-	-	SYM
ejpam-3903	409	17	111	111	NUM
ejpam-3903	409	18	101	101	NUM
ejpam-3903	409	19	the	the	DET
ejpam-3903	409	20	time	time	NOUN
ejpam-3903	409	21	step	step	NOUN
ejpam-3903	409	22	4	4	NUM
ejpam-3903	409	23	t	t	AUX
ejpam-3903	409	24	being	be	AUX
ejpam-3903	409	25	intended	intend	VERB
ejpam-3903	409	26	to	to	PART
ejpam-3903	409	27	goes	go	VERB
ejpam-3903	409	28	to	to	ADP
ejpam-3903	409	29	zero	zero	NUM
ejpam-3903	409	30	before	before	ADP
ejpam-3903	409	31	ε	ε	PROPN
ejpam-3903	409	32	,	,	PUNCT
ejpam-3903	409	33	taking	take	VERB
ejpam-3903	409	34	(	(	PUNCT
ejpam-3903	409	35	72	72	NUM
ejpam-3903	409	36	)	)	PUNCT
ejpam-3903	409	37	into	into	ADP
ejpam-3903	409	38	(	(	PUNCT
ejpam-3903	409	39	71	71	NUM
ejpam-3903	409	40	)	)	PUNCT
ejpam-3903	409	41	it	it	PRON
ejpam-3903	409	42	follow	follow	VERB
ejpam-3903	409	43	:	:	PUNCT
ejpam-3903	409	44	‖w1	‖w1	ADP
ejpam-3903	410	1	k+1	k+1	PROPN
ejpam-3903	410	2	−w1	−w1	PROPN
ejpam-3903	410	3	k‖2l2	k‖2l2	PROPN
ejpam-3903	410	4	≤	≤	PROPN
ejpam-3903	410	5	4tc2(rs	4tc2(rs	NUM
ejpam-3903	410	6	)	)	PUNCT
ejpam-3903	410	7	4εc01(ρ̄	4εc01(ρ̄	NUM
ejpam-3903	410	8	)	)	PUNCT
ejpam-3903	411	1	‖w1	‖w1	PROPN
ejpam-3903	411	2	k	k	PROPN
ejpam-3903	412	1	−w1	−w1	PROPN
ejpam-3903	412	2	k−1‖2l2	k−1‖2l2	PROPN
ejpam-3903	412	3	.	.	PUNCT
ejpam-3903	413	1	(	(	PUNCT
ejpam-3903	413	2	73	73	NUM
ejpam-3903	413	3	)	)	PUNCT
ejpam-3903	413	4	choosing	choose	VERB
ejpam-3903	413	5	the	the	DET
ejpam-3903	413	6	time	time	NOUN
ejpam-3903	413	7	step	step	NOUN
ejpam-3903	413	8	such	such	ADJ
ejpam-3903	413	9	that4	that4	NOUN
ejpam-3903	413	10	t	t	PROPN
ejpam-3903	413	11	<	<	X
ejpam-3903	413	12	4εc01(ρ̄	4εc01(ρ̄	PROPN
ejpam-3903	413	13	)	)	PUNCT
ejpam-3903	413	14	c2(rs	c2(rs	PROPN
ejpam-3903	413	15	)	)	PUNCT
ejpam-3903	413	16	,	,	PUNCT
ejpam-3903	413	17	we	we	PRON
ejpam-3903	413	18	deduce	deduce	VERB
ejpam-3903	413	19	that	that	SCONJ
ejpam-3903	413	20	g	g	PROPN
ejpam-3903	413	21	is	be	AUX
ejpam-3903	413	22	strictly	strictly	ADV
ejpam-3903	413	23	l2	l2	NOUN
ejpam-3903	413	24	-	-	PUNCT
ejpam-3903	413	25	contraction	contraction	NOUN
ejpam-3903	413	26	.	.	PUNCT
ejpam-3903	414	1	hence	hence	ADV
ejpam-3903	414	2	there	there	PRON
ejpam-3903	414	3	exist	exist	VERB
ejpam-3903	414	4	an	an	DET
ejpam-3903	414	5	unique	unique	ADJ
ejpam-3903	414	6	w1	w1	NOUN
ejpam-3903	414	7	∈	∈	NOUN
ejpam-3903	414	8	l2(ω)20	l2(ω)20	VERB
ejpam-3903	414	9	such	such	ADJ
ejpam-3903	414	10	as	as	ADP
ejpam-3903	414	11	g(w1	g(w1	ADJ
ejpam-3903	414	12	)	)	PUNCT
ejpam-3903	414	13	=	=	SYM
ejpam-3903	414	14	w1	w1	NOUN
ejpam-3903	414	15	.	.	PUNCT
ejpam-3903	415	1	it	it	PRON
ejpam-3903	415	2	remains	remain	VERB
ejpam-3903	415	3	to	to	PART
ejpam-3903	415	4	prove	prove	VERB
ejpam-3903	415	5	that	that	SCONJ
ejpam-3903	415	6	w1	w1	NOUN
ejpam-3903	415	7	∈	∈	PROPN
ejpam-3903	415	8	hs(ω	hs(ω	NUM
ejpam-3903	415	9	)	)	PUNCT
ejpam-3903	415	10	.	.	PUNCT
ejpam-3903	416	1	by	by	ADP
ejpam-3903	416	2	sobolev	sobolev	PROPN
ejpam-3903	416	3	spaces	space	NOUN
ejpam-3903	416	4	interpolation	interpolation	NOUN
ejpam-3903	416	5	:	:	PUNCT
ejpam-3903	416	6	for	for	ADP
ejpam-3903	416	7	all	all	DET
ejpam-3903	416	8	reels	reel	NOUN
ejpam-3903	416	9	s	s	PRON
ejpam-3903	416	10	,	,	PUNCT
ejpam-3903	416	11	s′	s′	VERB
ejpam-3903	416	12	with	with	ADP
ejpam-3903	416	13	0	0	NUM
ejpam-3903	416	14	<	<	X
ejpam-3903	416	15	s′	s′	X
ejpam-3903	416	16	<	<	X
ejpam-3903	416	17	s,∃	s,∃	PUNCT
ejpam-3903	416	18	c(s	c(	NOUN
ejpam-3903	416	19	,	,	PUNCT
ejpam-3903	416	20	ω	ω	NOUN
ejpam-3903	416	21	)	)	PUNCT
ejpam-3903	416	22	,	,	PUNCT
ejpam-3903	416	23	such	such	ADJ
ejpam-3903	416	24	that	that	SCONJ
ejpam-3903	416	25	‖w1	‖w1	PROPN
ejpam-3903	416	26	k	k	PROPN
ejpam-3903	416	27	−w1	−w1	PROPN
ejpam-3903	416	28	l	l	PROPN
ejpam-3903	416	29	‖hs′	‖hs′	X
ejpam-3903	416	30	6	6	NUM
ejpam-3903	416	31	c(s	c(	NOUN
ejpam-3903	416	32	,	,	PUNCT
ejpam-3903	416	33	ω)‖w1	ω)‖w1	NOUN
ejpam-3903	416	34	k	k	PROPN
ejpam-3903	416	35	−w1	−w1	PROPN
ejpam-3903	416	36	l	l	PROPN
ejpam-3903	416	37	‖	‖	PROPN
ejpam-3903	416	38	1−	1−	NUM
ejpam-3903	416	39	s	s	NOUN
ejpam-3903	416	40	′	′	NOUN
ejpam-3903	416	41	s	s	NOUN
ejpam-3903	416	42	l2	l2	NOUN
ejpam-3903	416	43	‖w1	‖w1	CCONJ
ejpam-3903	416	44	k	k	PROPN
ejpam-3903	416	45	−w1	−w1	PROPN
ejpam-3903	416	46	l	l	PROPN
ejpam-3903	416	47	‖	‖	PROPN
ejpam-3903	416	48	s′	s′	PROPN
ejpam-3903	416	49	s	s	X
ejpam-3903	416	50	hs	hs	PROPN
ejpam-3903	416	51	6	6	NUM
ejpam-3903	416	52	2r	2r	NUM
ejpam-3903	416	53	s′	s′	VERB
ejpam-3903	416	54	s	s	PART
ejpam-3903	416	55	s	s	X
ejpam-3903	416	56	c(s	c(	NOUN
ejpam-3903	416	57	,	,	PUNCT
ejpam-3903	416	58	ω)‖w1	ω)‖w1	NOUN
ejpam-3903	416	59	k	k	PROPN
ejpam-3903	416	60	−w1	−w1	PROPN
ejpam-3903	416	61	l	l	PROPN
ejpam-3903	416	62	‖	‖	PROPN
ejpam-3903	417	1	1−	1−	NUM
ejpam-3903	417	2	s	s	NOUN
ejpam-3903	417	3	′	′	NOUN
ejpam-3903	417	4	s	s	NOUN
ejpam-3903	417	5	l2	l2	NOUN
ejpam-3903	417	6	.	.	PUNCT
ejpam-3903	418	1	(	(	PUNCT
ejpam-3903	418	2	74	74	NUM
ejpam-3903	418	3	)	)	PUNCT
ejpam-3903	418	4	according	accord	VERB
ejpam-3903	418	5	to	to	ADP
ejpam-3903	418	6	(	(	PUNCT
ejpam-3903	418	7	73	73	NUM
ejpam-3903	418	8	)	)	PUNCT
ejpam-3903	418	9	,	,	PUNCT
ejpam-3903	418	10	(	(	PUNCT
ejpam-3903	418	11	w1	w1	PROPN
ejpam-3903	418	12	k	k	NOUN
ejpam-3903	418	13	)	)	PUNCT
ejpam-3903	418	14	is	be	AUX
ejpam-3903	418	15	a	a	DET
ejpam-3903	418	16	cauchy	cauchy	ADJ
ejpam-3903	418	17	sequence	sequence	NOUN
ejpam-3903	418	18	in	in	ADP
ejpam-3903	418	19	hs′(ω	hs′(ω	PROPN
ejpam-3903	418	20	)	)	PUNCT
ejpam-3903	418	21	.	.	PUNCT
ejpam-3903	419	1	so	so	ADV
ejpam-3903	419	2	choosing	choose	VERB
ejpam-3903	419	3	s′	s′	NUM
ejpam-3903	419	4	≥	≥	NUM
ejpam-3903	419	5	5	5	NUM
ejpam-3903	419	6	2	2	NUM
ejpam-3903	419	7	we	we	PRON
ejpam-3903	419	8	have	have	VERB
ejpam-3903	419	9	w1	w1	PROPN
ejpam-3903	419	10	k	k	PROPN
ejpam-3903	419	11	−→w1	−→w1	PROPN
ejpam-3903	419	12	in	in	ADP
ejpam-3903	419	13	hs′(ω	hs′(ω	PROPN
ejpam-3903	419	14	)	)	PUNCT
ejpam-3903	419	15	.	.	PUNCT
ejpam-3903	420	1	by	by	ADP
ejpam-3903	420	2	duality	duality	NOUN
ejpam-3903	420	3	product	product	NOUN
ejpam-3903	420	4	of	of	ADP
ejpam-3903	420	5	sobolev	sobolev	NOUN
ejpam-3903	420	6	spaces	space	NOUN
ejpam-3903	420	7	we	we	PRON
ejpam-3903	420	8	have	have	VERB
ejpam-3903	420	9	:	:	PUNCT
ejpam-3903	420	10	<	<	X
ejpam-3903	420	11	φ	φ	PROPN
ejpam-3903	420	12	,	,	PUNCT
ejpam-3903	420	13	w1	w1	PROPN
ejpam-3903	420	14	k	k	PROPN
ejpam-3903	420	15	>	>	PUNCT
ejpam-3903	420	16	−→	−→	ADJ
ejpam-3903	420	17	<	<	X
ejpam-3903	420	18	φ	φ	PROPN
ejpam-3903	420	19	,	,	PUNCT
ejpam-3903	420	20	w1	w1	PROPN
ejpam-3903	420	21	>	>	X
ejpam-3903	420	22	∀	∀	PUNCT
ejpam-3903	420	23	φ	φ	PROPN
ejpam-3903	420	24	∈	∈	PROPN
ejpam-3903	420	25	h−s′(ω	h−s′(ω	NOUN
ejpam-3903	420	26	)	)	PUNCT
ejpam-3903	420	27	,	,	PUNCT
ejpam-3903	420	28	and	and	CCONJ
ejpam-3903	420	29	by	by	ADP
ejpam-3903	420	30	density	density	NOUN
ejpam-3903	420	31	of	of	ADP
ejpam-3903	420	32	h−s	h−s	PROPN
ejpam-3903	420	33	′	′	NUM
ejpam-3903	420	34	(	(	PUNCT
ejpam-3903	420	35	ω	ω	NOUN
ejpam-3903	420	36	)	)	PUNCT
ejpam-3903	420	37	in	in	ADP
ejpam-3903	420	38	h−s(ω	h−s(ω	NOUN
ejpam-3903	420	39	)	)	PUNCT
ejpam-3903	420	40	,	,	PUNCT
ejpam-3903	420	41	we	we	PRON
ejpam-3903	420	42	have	have	VERB
ejpam-3903	420	43	:	:	PUNCT
ejpam-3903	420	44	<	<	X
ejpam-3903	420	45	φ	φ	PROPN
ejpam-3903	420	46	,	,	PUNCT
ejpam-3903	420	47	w1	w1	PROPN
ejpam-3903	420	48	k	k	PROPN
ejpam-3903	420	49	>	>	PUNCT
ejpam-3903	420	50	−→	−→	ADJ
ejpam-3903	420	51	<	<	X
ejpam-3903	420	52	φ	φ	PROPN
ejpam-3903	420	53	,	,	PUNCT
ejpam-3903	420	54	w1	w1	PROPN
ejpam-3903	420	55	>	>	X
ejpam-3903	420	56	∀	∀	PUNCT
ejpam-3903	420	57	φ	φ	PROPN
ejpam-3903	420	58	∈	∈	PROPN
ejpam-3903	420	59	h−s(ω	h−s(ω	NOUN
ejpam-3903	420	60	)	)	PUNCT
ejpam-3903	420	61	.	.	PUNCT
ejpam-3903	421	1	�	�	PROPN
ejpam-3903	421	2	now	now	ADV
ejpam-3903	421	3	we	we	PRON
ejpam-3903	421	4	are	be	AUX
ejpam-3903	421	5	able	able	ADJ
ejpam-3903	421	6	to	to	PART
ejpam-3903	421	7	pass	pass	VERB
ejpam-3903	421	8	to	to	ADP
ejpam-3903	421	9	the	the	DET
ejpam-3903	421	10	limit	limit	NOUN
ejpam-3903	421	11	in	in	ADP
ejpam-3903	421	12	the	the	DET
ejpam-3903	421	13	system	system	NOUN
ejpam-3903	421	14	(	(	PUNCT
ejpam-3903	421	15	50	50	NUM
ejpam-3903	421	16	)	)	PUNCT
ejpam-3903	421	17	.	.	PUNCT
ejpam-3903	422	1	by	by	ADP
ejpam-3903	422	2	term	term	NOUN
ejpam-3903	422	3	by	by	ADP
ejpam-3903	422	4	term	term	NOUN
ejpam-3903	422	5	convergence	convergence	NOUN
ejpam-3903	422	6	we	we	PRON
ejpam-3903	422	7	obtain	obtain	VERB
ejpam-3903	422	8	that	that	DET
ejpam-3903	422	9	w1	w1	NOUN
ejpam-3903	422	10	is	be	AUX
ejpam-3903	422	11	a	a	DET
ejpam-3903	422	12	solution	solution	NOUN
ejpam-3903	422	13	of	of	ADP
ejpam-3903	422	14	the	the	DET
ejpam-3903	422	15	system	system	NOUN
ejpam-3903	422	16	(	(	PUNCT
ejpam-3903	422	17	63	63	NUM
ejpam-3903	422	18	)	)	PUNCT
ejpam-3903	422	19	.	.	PUNCT
ejpam-3903	423	1	by	by	ADP
ejpam-3903	423	2	construction	construction	NOUN
ejpam-3903	423	3	of	of	ADP
ejpam-3903	423	4	the	the	DET
ejpam-3903	423	5	matrix	matrix	NOUN
ejpam-3903	423	6	a0	a0	NOUN
ejpam-3903	423	7	,	,	PUNCT
ejpam-3903	423	8	aiε(i	aiε(i	PROPN
ejpam-3903	423	9	=	=	NOUN
ejpam-3903	423	10	.	.	PUNCT
ejpam-3903	423	11	.	.	PUNCT
ejpam-3903	423	12	.	.	PUNCT
ejpam-3903	424	1	3	3	X
ejpam-3903	424	2	)	)	PUNCT
ejpam-3903	424	3	and	and	CCONJ
ejpam-3903	424	4	kiε	kiε	PROPN
ejpam-3903	424	5	,	,	PUNCT
ejpam-3903	424	6	the	the	DET
ejpam-3903	424	7	last	last	ADJ
ejpam-3903	424	8	fifteen	fifteen	ADJ
ejpam-3903	424	9	lines	line	NOUN
ejpam-3903	424	10	of	of	ADP
ejpam-3903	424	11	the	the	DET
ejpam-3903	424	12	system	system	NOUN
ejpam-3903	424	13	(	(	PUNCT
ejpam-3903	424	14	63	63	NUM
ejpam-3903	424	15	)	)	PUNCT
ejpam-3903	424	16	gives	give	VERB
ejpam-3903	424	17	that	that	DET
ejpam-3903	424	18	w1	w1	NOUN
ejpam-3903	424	19	have	have	AUX
ejpam-3903	424	20	exactly	exactly	ADV
ejpam-3903	424	21	the	the	DET
ejpam-3903	424	22	following	follow	VERB
ejpam-3903	424	23	form	form	NOUN
ejpam-3903	424	24	:	:	PUNCT
ejpam-3903	424	25	w1	w1	NOUN
ejpam-3903	424	26	=	=	SYM
ejpam-3903	424	27	(	(	PUNCT
ejpam-3903	424	28	u1	u1	PROPN
ejpam-3903	424	29	,	,	PUNCT
ejpam-3903	424	30	d1u	d1u	PROPN
ejpam-3903	424	31	1	1	NUM
ejpam-3903	424	32	,	,	PUNCT
ejpam-3903	424	33	d2u	d2u	ADV
ejpam-3903	424	34	1	1	NUM
ejpam-3903	424	35	,	,	PUNCT
ejpam-3903	424	36	d3u	d3u	PROPN
ejpam-3903	424	37	1	1	NUM
ejpam-3903	424	38	)	)	PUNCT
ejpam-3903	424	39	with	with	ADP
ejpam-3903	424	40	u1	u1	NOUN
ejpam-3903	424	41	=	=	SYM
ejpam-3903	425	1	(	(	PUNCT
ejpam-3903	425	2	(	(	PUNCT
ejpam-3903	425	3	w1)1,w	w1)1,w	NOUN
ejpam-3903	425	4	1)2	1)2	NUM
ejpam-3903	425	5	,	,	PUNCT
ejpam-3903	425	6	(	(	PUNCT
ejpam-3903	425	7	w1)3	w1)3	ADV
ejpam-3903	425	8	,	,	PUNCT
ejpam-3903	425	9	(	(	PUNCT
ejpam-3903	425	10	w1)4	w1)4	ADV
ejpam-3903	425	11	,	,	PUNCT
ejpam-3903	425	12	w1)5	w1)5	NUM
ejpam-3903	425	13	)	)	PUNCT
ejpam-3903	425	14	and	and	CCONJ
ejpam-3903	425	15	di	di	NOUN
ejpam-3903	425	16	=	=	SYM
ejpam-3903	425	17	∂	∂	NUM
ejpam-3903	425	18	∂xi	∂xi	NOUN
ejpam-3903	425	19	for	for	ADP
ejpam-3903	425	20	i	i	PROPN
ejpam-3903	425	21	=	=	SYM
ejpam-3903	425	22	1	1	NUM
ejpam-3903	425	23	,	,	PUNCT
ejpam-3903	425	24	2	2	NUM
ejpam-3903	425	25	,	,	PUNCT
ejpam-3903	425	26	3	3	NUM
ejpam-3903	425	27	(	(	PUNCT
ejpam-3903	425	28	75	75	NUM
ejpam-3903	425	29	)	)	PUNCT
ejpam-3903	425	30	the	the	DET
ejpam-3903	425	31	estimate	estimate	NOUN
ejpam-3903	425	32	(	(	PUNCT
ejpam-3903	425	33	48	48	NUM
ejpam-3903	425	34	)	)	PUNCT
ejpam-3903	425	35	being	be	AUX
ejpam-3903	425	36	true	true	ADJ
ejpam-3903	425	37	for	for	ADP
ejpam-3903	425	38	the	the	DET
ejpam-3903	425	39	sequence	sequence	NOUN
ejpam-3903	425	40	(	(	PUNCT
ejpam-3903	425	41	w1	w1	NOUN
ejpam-3903	425	42	k+1	k+1	PROPN
ejpam-3903	425	43	)	)	PUNCT
ejpam-3903	425	44	,	,	PUNCT
ejpam-3903	425	45	the	the	DET
ejpam-3903	425	46	limit	limit	NOUN
ejpam-3903	425	47	also	also	ADV
ejpam-3903	425	48	verify	verify	VERB
ejpam-3903	425	49	the	the	DET
ejpam-3903	425	50	same	same	ADJ
ejpam-3903	425	51	estimate	estimate	NOUN
ejpam-3903	425	52	.	.	PUNCT
ejpam-3903	426	1	then	then	ADV
ejpam-3903	426	2	we	we	PRON
ejpam-3903	426	3	have	have	VERB
ejpam-3903	426	4	v	v	NOUN
ejpam-3903	426	5	=	=	SYM
ejpam-3903	426	6	(	(	PUNCT
ejpam-3903	426	7	(	(	PUNCT
ejpam-3903	426	8	w1)2	w1)2	NUM
ejpam-3903	426	9	,	,	PUNCT
ejpam-3903	426	10	(	(	PUNCT
ejpam-3903	426	11	w1)3	w1)3	ADV
ejpam-3903	426	12	,	,	PUNCT
ejpam-3903	426	13	(	(	PUNCT
ejpam-3903	426	14	w1)4	w1)4	CCONJ
ejpam-3903	426	15	)	)	PUNCT
ejpam-3903	426	16	∈	∈	PROPN
ejpam-3903	426	17	w1,∞(ω)3	w1,∞(ω)3	X
ejpam-3903	426	18	and	and	CCONJ
ejpam-3903	426	19	according	accord	VERB
ejpam-3903	426	20	to	to	ADP
ejpam-3903	426	21	lemma	lemma	PROPN
ejpam-3903	426	22	2	2	NUM
ejpam-3903	426	23	we	we	PRON
ejpam-3903	426	24	deduce	deduce	VERB
ejpam-3903	426	25	that	that	PRON
ejpam-3903	426	26	(	(	PUNCT
ejpam-3903	426	27	w1)1	w1)1	X
ejpam-3903	426	28	>	>	X
ejpam-3903	426	29	ρ̄	ρ̄	NUM
ejpam-3903	426	30	exp(−4trs	exp(−4trs	PROPN
ejpam-3903	426	31	)	)	PUNCT
ejpam-3903	426	32	.	.	PUNCT
ejpam-3903	427	1	4.1.4	4.1.4	X
ejpam-3903	427	2	.	.	PUNCT
ejpam-3903	428	1	existence	existence	NOUN
ejpam-3903	428	2	of	of	ADP
ejpam-3903	428	3	wn+1	wn+1	NOUN
ejpam-3903	428	4	k+1	k+1	X
ejpam-3903	428	5	and	and	CCONJ
ejpam-3903	428	6	passing	pass	VERB
ejpam-3903	428	7	to	to	PART
ejpam-3903	428	8	limit	limit	VERB
ejpam-3903	428	9	k	k	PROPN
ejpam-3903	428	10	→∞	→∞	PROPN
ejpam-3903	428	11	in	in	ADP
ejpam-3903	428	12	the	the	DET
ejpam-3903	428	13	paragraph	paragraph	NOUN
ejpam-3903	428	14	4.1.2	4.1.2	NUM
ejpam-3903	428	15	,	,	PUNCT
ejpam-3903	428	16	we	we	PRON
ejpam-3903	428	17	have	have	AUX
ejpam-3903	428	18	proved	prove	VERB
ejpam-3903	428	19	the	the	DET
ejpam-3903	428	20	existence	existence	NOUN
ejpam-3903	428	21	of	of	ADP
ejpam-3903	428	22	(	(	PUNCT
ejpam-3903	428	23	w1	w1	NOUN
ejpam-3903	428	24	k+1	k+1	NOUN
ejpam-3903	428	25	)	)	PUNCT
ejpam-3903	428	26	solution	solution	NOUN
ejpam-3903	428	27	of	of	ADP
ejpam-3903	428	28	(	(	PUNCT
ejpam-3903	428	29	50	50	NUM
ejpam-3903	428	30	)	)	PUNCT
ejpam-3903	428	31	,	,	PUNCT
ejpam-3903	428	32	whose	whose	DET
ejpam-3903	428	33	limit	limit	NOUN
ejpam-3903	428	34	w1	w1	NOUN
ejpam-3903	428	35	is	be	AUX
ejpam-3903	428	36	solution	solution	NOUN
ejpam-3903	428	37	of	of	ADP
ejpam-3903	428	38	the	the	DET
ejpam-3903	428	39	system	system	NOUN
ejpam-3903	428	40	(	(	PUNCT
ejpam-3903	428	41	63	63	NUM
ejpam-3903	428	42	)	)	PUNCT
ejpam-3903	428	43	(	(	PUNCT
ejpam-3903	428	44	paragraph	paragraph	NOUN
ejpam-3903	428	45	4.1.3	4.1.3	NUM
ejpam-3903	428	46	)	)	PUNCT
ejpam-3903	428	47	.	.	PUNCT
ejpam-3903	429	1	now	now	ADV
ejpam-3903	429	2	we	we	PRON
ejpam-3903	429	3	construct	construct	VERB
ejpam-3903	429	4	the	the	DET
ejpam-3903	429	5	sequence	sequence	NOUN
ejpam-3903	429	6	(	(	PUNCT
ejpam-3903	429	7	w2	w2	NOUN
ejpam-3903	429	8	k+1	k+1	PROPN
ejpam-3903	429	9	)	)	PUNCT
ejpam-3903	429	10	whose	whose	DET
ejpam-3903	429	11	first	first	ADJ
ejpam-3903	429	12	term	term	NOUN
ejpam-3903	429	13	w2	w2	NOUN
ejpam-3903	429	14	0	0	NUM
ejpam-3903	429	15	=	=	SYM
ejpam-3903	429	16	w1	w1	PROPN
ejpam-3903	429	17	.	.	PUNCT
ejpam-3903	430	1	according	accord	VERB
ejpam-3903	430	2	to	to	ADP
ejpam-3903	430	3	the	the	DET
ejpam-3903	430	4	lemma	lemma	PROPN
ejpam-3903	430	5	3	3	NUM
ejpam-3903	430	6	and	and	CCONJ
ejpam-3903	430	7	the	the	DET
ejpam-3903	430	8	positivity	positivity	NOUN
ejpam-3903	430	9	of	of	ADP
ejpam-3903	430	10	the	the	DET
ejpam-3903	430	11	operator	operator	NOUN
ejpam-3903	430	12	<	<	X
ejpam-3903	430	13	+	+	NOUN
ejpam-3903	430	14	<	<	X
ejpam-3903	430	15	∗	∗	NOUN
ejpam-3903	430	16	,	,	PUNCT
ejpam-3903	430	17	one	one	NUM
ejpam-3903	430	18	obtain	obtain	VERB
ejpam-3903	430	19	the	the	DET
ejpam-3903	430	20	existence	existence	NOUN
ejpam-3903	430	21	of	of	ADP
ejpam-3903	430	22	(	(	PUNCT
ejpam-3903	430	23	w2	w2	NOUN
ejpam-3903	430	24	1	1	NUM
ejpam-3903	430	25	)	)	PUNCT
ejpam-3903	430	26	,	,	PUNCT
ejpam-3903	430	27	and	and	CCONJ
ejpam-3903	430	28	moreover	moreover	ADV
ejpam-3903	430	29	we	we	PRON
ejpam-3903	430	30	have	have	VERB
ejpam-3903	430	31	(	(	PUNCT
ejpam-3903	430	32	w2	w2	NOUN
ejpam-3903	430	33	1)1	1)1	PROPN
ejpam-3903	430	34	>	>	SYM
ejpam-3903	430	35	ρ̄	ρ̄	NUM
ejpam-3903	430	36	exp(−24trs	exp(−24trs	PROPN
ejpam-3903	430	37	)	)	PUNCT
ejpam-3903	430	38	.	.	PUNCT
ejpam-3903	431	1	then	then	ADV
ejpam-3903	431	2	,	,	PUNCT
ejpam-3903	431	3	by	by	ADP
ejpam-3903	431	4	recurrence	recurrence	NOUN
ejpam-3903	431	5	we	we	PRON
ejpam-3903	431	6	have	have	VERB
ejpam-3903	431	7	the	the	DET
ejpam-3903	431	8	existence	existence	NOUN
ejpam-3903	431	9	of	of	ADP
ejpam-3903	431	10	(	(	PUNCT
ejpam-3903	431	11	w2	w2	NOUN
ejpam-3903	431	12	k+1	k+1	PROPN
ejpam-3903	431	13	)	)	PUNCT
ejpam-3903	431	14	.	.	PUNCT
ejpam-3903	432	1	we	we	PRON
ejpam-3903	432	2	repeat	repeat	VERB
ejpam-3903	432	3	the	the	DET
ejpam-3903	432	4	process	process	NOUN
ejpam-3903	432	5	in	in	ADP
ejpam-3903	432	6	the	the	DET
ejpam-3903	432	7	same	same	ADJ
ejpam-3903	432	8	way	way	NOUN
ejpam-3903	432	9	,	,	PUNCT
ejpam-3903	432	10	so	so	ADV
ejpam-3903	432	11	successively	successively	ADV
ejpam-3903	432	12	we	we	PRON
ejpam-3903	432	13	construct	construct	VERB
ejpam-3903	432	14	the	the	DET
ejpam-3903	432	15	sequence	sequence	NOUN
ejpam-3903	432	16	(	(	PUNCT
ejpam-3903	432	17	wn+1	wn+1	NOUN
ejpam-3903	432	18	k+1	k+1	NOUN
ejpam-3903	432	19	)	)	PUNCT
ejpam-3903	432	20	solution	solution	NOUN
ejpam-3903	432	21	of	of	ADP
ejpam-3903	432	22	the	the	DET
ejpam-3903	432	23	sytem	sytem	NOUN
ejpam-3903	432	24	(	(	PUNCT
ejpam-3903	432	25	33	33	NUM
ejpam-3903	432	26	)	)	PUNCT
ejpam-3903	432	27	and	and	CCONJ
ejpam-3903	432	28	whose	whose	DET
ejpam-3903	432	29	existence	existence	NOUN
ejpam-3903	432	30	is	be	AUX
ejpam-3903	432	31	given	give	VERB
ejpam-3903	432	32	by	by	ADP
ejpam-3903	432	33	the	the	DET
ejpam-3903	432	34	following	follow	VERB
ejpam-3903	432	35	result	result	NOUN
ejpam-3903	432	36	:	:	PUNCT
ejpam-3903	432	37	r.	r.	PROPN
ejpam-3903	432	38	bade	bade	PROPN
ejpam-3903	432	39	,	,	PUNCT
ejpam-3903	432	40	h.	h.	PROPN
ejpam-3903	432	41	chaker	chaker	PROPN
ejpam-3903	432	42	/	/	SYM
ejpam-3903	432	43	eur	eur	PROPN
ejpam-3903	432	44	.	.	PUNCT
ejpam-3903	433	1	j.	j.	PROPN
ejpam-3903	433	2	pure	pure	PROPN
ejpam-3903	433	3	appl	appl	PROPN
ejpam-3903	433	4	.	.	PROPN
ejpam-3903	433	5	math	math	PROPN
ejpam-3903	433	6	,	,	PUNCT
ejpam-3903	433	7	14	14	NUM
ejpam-3903	433	8	(	(	PUNCT
ejpam-3903	433	9	1	1	NUM
ejpam-3903	433	10	)	)	PUNCT
ejpam-3903	433	11	(	(	PUNCT
ejpam-3903	433	12	2021	2021	NUM
ejpam-3903	433	13	)	)	PUNCT
ejpam-3903	433	14	,	,	PUNCT
ejpam-3903	433	15	82	82	NUM
ejpam-3903	433	16	-	-	SYM
ejpam-3903	433	17	111	111	NUM
ejpam-3903	433	18	102	102	NUM
ejpam-3903	433	19	proposition	proposition	NOUN
ejpam-3903	433	20	4	4	NUM
ejpam-3903	433	21	.	.	PUNCT
ejpam-3903	433	22	suppose	suppose	VERB
ejpam-3903	433	23	that	that	SCONJ
ejpam-3903	433	24	fn+1	fn+1	ADJ
ejpam-3903	433	25	+	+	NUM
ejpam-3903	433	26	a0(wn	a0(wn	NOUN
ejpam-3903	433	27	)	)	PUNCT
ejpam-3903	433	28	4	4	NUM
ejpam-3903	433	29	t	t	NOUN
ejpam-3903	433	30	wn	wn	PROPN
ejpam-3903	433	31	∈	∈	PROPN
ejpam-3903	433	32	l2(ω)20	l2(ω)20	PUNCT
ejpam-3903	433	33	and	and	CCONJ
ejpam-3903	433	34	gn+1	gn+1	PROPN
ejpam-3903	433	35	∈	∈	PROPN
ejpam-3903	433	36	hs+	hs+	NOUN
ejpam-3903	433	37	3	3	NUM
ejpam-3903	433	38	2	2	NUM
ejpam-3903	433	39	(	(	PUNCT
ejpam-3903	433	40	∂ω)20	∂ω)20	PROPN
ejpam-3903	433	41	,	,	PUNCT
ejpam-3903	433	42	then	then	ADV
ejpam-3903	433	43	the	the	DET
ejpam-3903	433	44	system	system	NOUN
ejpam-3903	433	45	(	(	PUNCT
ejpam-3903	433	46	33	33	NUM
ejpam-3903	433	47	)	)	PUNCT
ejpam-3903	433	48	admit	admit	VERB
ejpam-3903	433	49	a	a	DET
ejpam-3903	433	50	weak	weak	ADJ
ejpam-3903	433	51	solution	solution	NOUN
ejpam-3903	433	52	wn+1	wn+1	VERB
ejpam-3903	433	53	k+1	k+1	X
ejpam-3903	433	54	∈	∈	PROPN
ejpam-3903	433	55	l2(ω)20	l2(ω)20	PROPN
ejpam-3903	433	56	.	.	PUNCT
ejpam-3903	434	1	in	in	ADP
ejpam-3903	434	2	addition	addition	NOUN
ejpam-3903	434	3	if	if	SCONJ
ejpam-3903	434	4	wn+1	wn+1	VERB
ejpam-3903	434	5	k+1	k+1	X
ejpam-3903	434	6	∈	∈	PROPN
ejpam-3903	434	7	h1(ω)20	h1(ω)20	PROPN
ejpam-3903	434	8	,	,	PUNCT
ejpam-3903	434	9	then	then	ADV
ejpam-3903	434	10	this	this	DET
ejpam-3903	434	11	solution	solution	NOUN
ejpam-3903	434	12	is	be	AUX
ejpam-3903	434	13	unique	unique	ADJ
ejpam-3903	434	14	.	.	PUNCT
ejpam-3903	435	1	if	if	SCONJ
ejpam-3903	435	2	fn+1	fn+1	ADJ
ejpam-3903	435	3	+	+	NUM
ejpam-3903	435	4	a0(wn	a0(wn	NOUN
ejpam-3903	435	5	)	)	PUNCT
ejpam-3903	435	6	4	4	NUM
ejpam-3903	435	7	t	t	NOUN
ejpam-3903	435	8	wn	wn	PROPN
ejpam-3903	435	9	∈	∈	PROPN
ejpam-3903	435	10	hs(ω)20	hs(ω)20	ADJ
ejpam-3903	435	11	,	,	PUNCT
ejpam-3903	435	12	gn+1	gn+1	PROPN
ejpam-3903	435	13	∈	∈	PROPN
ejpam-3903	435	14	hs+	hs+	NOUN
ejpam-3903	435	15	3	3	NUM
ejpam-3903	435	16	2	2	NUM
ejpam-3903	435	17	(	(	PUNCT
ejpam-3903	435	18	∂ω)20	∂ω)20	PROPN
ejpam-3903	435	19	then	then	ADV
ejpam-3903	435	20	the	the	DET
ejpam-3903	435	21	system	system	NOUN
ejpam-3903	435	22	(	(	PUNCT
ejpam-3903	435	23	33	33	NUM
ejpam-3903	435	24	)	)	PUNCT
ejpam-3903	435	25	admit	admit	VERB
ejpam-3903	435	26	a	a	DET
ejpam-3903	435	27	weak	weak	ADJ
ejpam-3903	435	28	solution	solution	NOUN
ejpam-3903	435	29	wn+1	wn+1	VERB
ejpam-3903	435	30	k+1	k+1	X
ejpam-3903	435	31	∈	∈	PROPN
ejpam-3903	435	32	h	h	NOUN
ejpam-3903	435	33	s(ω)20	s(ω)20	PROPN
ejpam-3903	435	34	.	.	PUNCT
ejpam-3903	436	1	in	in	ADP
ejpam-3903	436	2	addition	addition	NOUN
ejpam-3903	436	3	,	,	PUNCT
ejpam-3903	436	4	we	we	PRON
ejpam-3903	436	5	have	have	AUX
ejpam-3903	436	6	(	(	PUNCT
ejpam-3903	436	7	wn+1	wn+1	VERB
ejpam-3903	436	8	k+1)1	k+1)1	PROPN
ejpam-3903	436	9	>	>	SYM
ejpam-3903	436	10	ρ̄	ρ̄	ADJ
ejpam-3903	436	11	exp(−(n+	exp(−(n+	NOUN
ejpam-3903	436	12	1)4trs	1)4trs	NUM
ejpam-3903	436	13	)	)	PUNCT
ejpam-3903	436	14	proof	proof	NOUN
ejpam-3903	436	15	.	.	PUNCT
ejpam-3903	437	1	use	use	VERB
ejpam-3903	437	2	the	the	DET
ejpam-3903	437	3	same	same	ADJ
ejpam-3903	437	4	demarche	demarche	NOUN
ejpam-3903	437	5	as	as	ADP
ejpam-3903	437	6	in	in	ADP
ejpam-3903	437	7	the	the	DET
ejpam-3903	437	8	existence	existence	NOUN
ejpam-3903	437	9	of	of	ADP
ejpam-3903	437	10	w1	w1	PROPN
ejpam-3903	437	11	1	1	NUM
ejpam-3903	437	12	.	.	PUNCT
ejpam-3903	437	13	�	�	PROPN
ejpam-3903	437	14	at	at	ADP
ejpam-3903	437	15	the	the	DET
ejpam-3903	437	16	limit	limit	NOUN
ejpam-3903	437	17	with	with	ADP
ejpam-3903	437	18	the	the	DET
ejpam-3903	437	19	same	same	ADJ
ejpam-3903	437	20	argument	argument	NOUN
ejpam-3903	437	21	of	of	ADP
ejpam-3903	437	22	the	the	DET
ejpam-3903	437	23	fixed	fix	VERB
ejpam-3903	437	24	point	point	NOUN
ejpam-3903	437	25	theorem	theorem	VERB
ejpam-3903	437	26	one	one	PRON
ejpam-3903	437	27	can	can	AUX
ejpam-3903	437	28	get	get	VERB
ejpam-3903	437	29	wn+1	wn+1	ADJ
ejpam-3903	437	30	solution	solution	NOUN
ejpam-3903	437	31	of	of	ADP
ejpam-3903	437	32	the	the	DET
ejpam-3903	437	33	system	system	NOUN
ejpam-3903	437	34	(	(	PUNCT
ejpam-3903	437	35	32	32	NUM
ejpam-3903	437	36	)	)	PUNCT
ejpam-3903	437	37	.	.	PUNCT
ejpam-3903	438	1	4.2	4.2	NUM
ejpam-3903	438	2	.	.	PUNCT
ejpam-3903	439	1	a	a	DET
ejpam-3903	439	2	priori	priori	ADJ
ejpam-3903	439	3	estimations	estimation	NOUN
ejpam-3903	439	4	lemma	lemma	PROPN
ejpam-3903	439	5	4	4	X
ejpam-3903	439	6	.	.	PUNCT
ejpam-3903	440	1	under	under	ADP
ejpam-3903	440	2	assumptions	assumption	NOUN
ejpam-3903	440	3	(	(	PUNCT
ejpam-3903	440	4	h2	h2	NOUN
ejpam-3903	440	5	)	)	PUNCT
ejpam-3903	440	6	and	and	CCONJ
ejpam-3903	440	7	(	(	PUNCT
ejpam-3903	440	8	h3	h3	NOUN
ejpam-3903	440	9	)	)	PUNCT
ejpam-3903	440	10	,	,	PUNCT
ejpam-3903	440	11	the	the	DET
ejpam-3903	440	12	following	follow	VERB
ejpam-3903	440	13	estimations	estimation	NOUN
ejpam-3903	440	14	hold	hold	VERB
ejpam-3903	440	15	:	:	PUNCT
ejpam-3903	440	16	i	i	NOUN
ejpam-3903	440	17	)	)	PUNCT
ejpam-3903	440	18	‖a0wn‖hs	‖a0wn‖hs	PUNCT
ejpam-3903	441	1	≤	≤	NUM
ejpam-3903	441	2	c(t	c(t	PROPN
ejpam-3903	441	3	,	,	PUNCT
ejpam-3903	441	4	f	f	PROPN
ejpam-3903	441	5	,	,	PUNCT
ejpam-3903	441	6	wg	wg	PROPN
ejpam-3903	441	7	)	)	PUNCT
ejpam-3903	441	8	,	,	PUNCT
ejpam-3903	441	9	ii	ii	PROPN
ejpam-3903	441	10	)	)	PUNCT
ejpam-3903	441	11	4	4	NUM
ejpam-3903	441	12	t	t	NOUN
ejpam-3903	441	13	n∑	n∑	PROPN
ejpam-3903	441	14	i=0	i=0	PROPN
ejpam-3903	441	15	‖a0(wi	‖a0(wi	NUM
ejpam-3903	441	16	)	)	PUNCT
ejpam-3903	441	17	wi+1	wi+1	PRON
ejpam-3903	441	18	−wi	−wi	NUM
ejpam-3903	441	19	4	4	NUM
ejpam-3903	441	20	t	t	NOUN
ejpam-3903	441	21	‖2l2	‖2l2	PROPN
ejpam-3903	441	22	≤	≤	PROPN
ejpam-3903	441	23	c(t	c(t	PROPN
ejpam-3903	441	24	,	,	PUNCT
ejpam-3903	441	25	f	f	PROPN
ejpam-3903	441	26	,	,	PUNCT
ejpam-3903	441	27	wg	wg	PROPN
ejpam-3903	441	28	)	)	PUNCT
ejpam-3903	441	29	,	,	PUNCT
ejpam-3903	441	30	iii	iii	X
ejpam-3903	441	31	)	)	PUNCT
ejpam-3903	441	32	4	4	NUM
ejpam-3903	441	33	t	t	NOUN
ejpam-3903	441	34	n∑	n∑	PROPN
ejpam-3903	441	35	i=0	i=0	PROPN
ejpam-3903	441	36	‖	‖	PROPN
ejpam-3903	441	37	1	1	NUM
ejpam-3903	441	38	4	4	NUM
ejpam-3903	441	39	t	t	NOUN
ejpam-3903	441	40	a0	a0	NOUN
ejpam-3903	441	41	(	(	PUNCT
ejpam-3903	441	42	wi+1	wi+1	NOUN
ejpam-3903	441	43	−wi	−wi	NOUN
ejpam-3903	441	44	)	)	PUNCT
ejpam-3903	441	45	‖2l2	‖2l2	PROPN
ejpam-3903	441	46	≤	≤	NUM
ejpam-3903	441	47	c(t	c(t	PROPN
ejpam-3903	441	48	,	,	PUNCT
ejpam-3903	441	49	f	f	PROPN
ejpam-3903	441	50	,	,	PUNCT
ejpam-3903	441	51	wg	wg	PROPN
ejpam-3903	441	52	)	)	PUNCT
ejpam-3903	441	53	,	,	PUNCT
ejpam-3903	441	54	(	(	PUNCT
ejpam-3903	441	55	76	76	NUM
ejpam-3903	441	56	)	)	PUNCT
ejpam-3903	441	57	with	with	ADP
ejpam-3903	441	58	c(t	c(t	PROPN
ejpam-3903	441	59	,	,	PUNCT
ejpam-3903	441	60	f	f	PROPN
ejpam-3903	441	61	,	,	PUNCT
ejpam-3903	441	62	wg	wg	PROPN
ejpam-3903	441	63	)	)	PUNCT
ejpam-3903	441	64	is	be	AUX
ejpam-3903	441	65	a	a	DET
ejpam-3903	441	66	constante	constante	ADJ
ejpam-3903	441	67	independente	independente	NOUN
ejpam-3903	441	68	of	of	ADP
ejpam-3903	441	69	ε	ε	PROPN
ejpam-3903	441	70	and	and	CCONJ
ejpam-3903	441	71	4	4	NUM
ejpam-3903	441	72	t.	t.	NOUN
ejpam-3903	441	73	proof	proof	NOUN
ejpam-3903	441	74	.	.	PUNCT
ejpam-3903	442	1	i	i	PRON
ejpam-3903	442	2	):	):	PUNCT
ejpam-3903	442	3	let	let	VERB
ejpam-3903	442	4	wn+1	wn+1	PRON
ejpam-3903	442	5	be	be	AUX
ejpam-3903	442	6	the	the	DET
ejpam-3903	442	7	solution	solution	NOUN
ejpam-3903	442	8	of	of	ADP
ejpam-3903	442	9	the	the	DET
ejpam-3903	442	10	following	follow	VERB
ejpam-3903	442	11	system	system	NOUN
ejpam-3903	442	12	:	:	PUNCT
ejpam-3903	442	13	a0(wn	a0(wn	NUM
ejpam-3903	442	14	)	)	PUNCT
ejpam-3903	442	15	4	4	NUM
ejpam-3903	442	16	t	t	NOUN
ejpam-3903	442	17	(	(	PUNCT
ejpam-3903	442	18	wn+1	wn+1	NOUN
ejpam-3903	442	19	−wn	−wn	NOUN
ejpam-3903	442	20	)	)	PUNCT
ejpam-3903	443	1	+	+	CCONJ
ejpam-3903	444	1	3∑	3∑	NUM
ejpam-3903	444	2	i=1	i=1	NOUN
ejpam-3903	444	3	aiε	aiε	ADJ
ejpam-3903	444	4	∂w(n+1)∗	∂w(n+1)∗	ADJ
ejpam-3903	444	5	∂xi	∂xi	NOUN
ejpam-3903	444	6	+	+	CCONJ
ejpam-3903	444	7	kε(w	kε(w	VERB
ejpam-3903	444	8	n+1)w(n+1)∗	n+1)w(n+1)∗	PROPN
ejpam-3903	444	9	=	=	SYM
ejpam-3903	444	10	fn+1	fn+1	X
ejpam-3903	444	11	−hε(w	−hε(w	VERB
ejpam-3903	444	12	n+1)wn+1	n+1)wn+1	NOUN
ejpam-3903	444	13	g	g	NOUN
ejpam-3903	444	14	,	,	PUNCT
ejpam-3903	444	15	with	with	ADP
ejpam-3903	444	16	hε(w	hε(w	X
ejpam-3903	444	17	n+1)wn+1	n+1)wn+1	NOUN
ejpam-3903	444	18	g	g	NOUN
ejpam-3903	444	19	=	=	PUNCT
ejpam-3903	444	20	kε(w	kε(w	NOUN
ejpam-3903	444	21	n+1)wn+1	n+1)wn+1	VERB
ejpam-3903	444	22	g	g	NOUN
ejpam-3903	444	23	+	+	NOUN
ejpam-3903	445	1	3∑	3∑	NUM
ejpam-3903	445	2	i=1	i=1	ADP
ejpam-3903	445	3	aiε	aiε	CCONJ
ejpam-3903	445	4	∂wn+1	∂wn+1	VERB
ejpam-3903	445	5	g	g	ADP
ejpam-3903	445	6	∂xi	∂xi	PROPN
ejpam-3903	445	7	.	.	PUNCT
ejpam-3903	446	1	using	use	VERB
ejpam-3903	446	2	the	the	DET
ejpam-3903	446	3	same	same	ADJ
ejpam-3903	446	4	decomposition	decomposition	NOUN
ejpam-3903	446	5	of	of	ADP
ejpam-3903	446	6	kε	kε	PROPN
ejpam-3903	446	7	as	as	ADP
ejpam-3903	446	8	previously	previously	ADV
ejpam-3903	446	9	,	,	PUNCT
ejpam-3903	446	10	we	we	PRON
ejpam-3903	446	11	get	get	VERB
ejpam-3903	446	12	:	:	PUNCT
ejpam-3903	446	13	<	<	X
ejpam-3903	446	14	a0(wn	a0(wn	NOUN
ejpam-3903	446	15	)	)	PUNCT
ejpam-3903	446	16	4	4	NUM
ejpam-3903	446	17	t	t	NOUN
ejpam-3903	446	18	(	(	PUNCT
ejpam-3903	446	19	wn+1	wn+1	VERB
ejpam-3903	446	20	−wn),a0v	−wn),a0v	X
ejpam-3903	446	21	>	>	X
ejpam-3903	446	22	+	+	PUNCT
ejpam-3903	446	23	<	<	X
ejpam-3903	446	24	dwn+1	dwn+1	PROPN
ejpam-3903	446	25	,	,	PUNCT
ejpam-3903	446	26	v	v	X
ejpam-3903	446	27	>	>	X
ejpam-3903	447	1	+	+	X
ejpam-3903	447	2	<	<	X
ejpam-3903	447	3	r2(wn+1)wn+1,a0v	r2(wn+1)wn+1,a0v	PROPN
ejpam-3903	447	4	>	>	X
ejpam-3903	447	5	=	=	X
ejpam-3903	447	6	<	<	X
ejpam-3903	447	7	fn+1,a0v	fn+1,a0v	PROPN
ejpam-3903	447	8	>	>	X
ejpam-3903	448	1	+	+	X
ejpam-3903	448	2	<	<	X
ejpam-3903	448	3	[	[	PUNCT
ejpam-3903	448	4	a0	a0	PROPN
ejpam-3903	448	5	−r1(wn+1	−r1(wn+1	PROPN
ejpam-3903	448	6	)	)	PUNCT
ejpam-3903	448	7	]	]	PUNCT
ejpam-3903	448	8	w(n+1)∗,a0v	w(n+1)∗,a0v	PUNCT
ejpam-3903	448	9	>	>	X
ejpam-3903	448	10	+	+	CCONJ
ejpam-3903	448	11	<	<	X
ejpam-3903	448	12	hε(w	hε(w	X
ejpam-3903	448	13	n+1)wn+1	n+1)wn+1	NOUN
ejpam-3903	448	14	g	g	PROPN
ejpam-3903	448	15	,	,	PUNCT
ejpam-3903	448	16	a0v	a0v	PROPN
ejpam-3903	448	17	>	>	X
ejpam-3903	448	18	.	.	PUNCT
ejpam-3903	449	1	(	(	PUNCT
ejpam-3903	449	2	77	77	X
ejpam-3903	449	3	)	)	PUNCT
ejpam-3903	449	4	it	it	PRON
ejpam-3903	449	5	follows	follow	VERB
ejpam-3903	449	6	that	that	PRON
ejpam-3903	449	7	:	:	PUNCT
ejpam-3903	449	8	sup	sup	NOUN
ejpam-3903	449	9	v	v	ADP
ejpam-3903	449	10	∈v	∈v	NOUN
ejpam-3903	449	11	|	|	ADV
ejpam-3903	449	12	<	<	X
ejpam-3903	449	13	a0(wn	a0(wn	NUM
ejpam-3903	449	14	)	)	PUNCT
ejpam-3903	449	15	4	4	NUM
ejpam-3903	449	16	t	t	NOUN
ejpam-3903	449	17	(	(	PUNCT
ejpam-3903	449	18	wn+1	wn+1	VERB
ejpam-3903	449	19	−wn),a0v	−wn),a0v	X
ejpam-3903	449	20	>	>	X
ejpam-3903	450	1	|	|	ADV
ejpam-3903	450	2	‖a0v	‖a0v	PROPN
ejpam-3903	450	3	‖h−s	‖h−s	PROPN
ejpam-3903	450	4	6	6	NUM
ejpam-3903	450	5	‖fn+1‖hs	‖fn+1‖hs	NOUN
ejpam-3903	450	6	+	+	X
ejpam-3903	450	7	(	(	PUNCT
ejpam-3903	450	8	c	c	NOUN
ejpam-3903	450	9	+	+	CCONJ
ejpam-3903	450	10	cr3	cr3	NOUN
ejpam-3903	450	11	s)‖a0w	s)‖a0w	NOUN
ejpam-3903	450	12	n+1‖hs	n+1‖hs	PUNCT
ejpam-3903	451	1	+	+	ADJ
ejpam-3903	451	2	(	(	PUNCT
ejpam-3903	451	3	c	c	NOUN
ejpam-3903	451	4	+	+	NUM
ejpam-3903	451	5	cr3	cr3	PROPN
ejpam-3903	451	6	s)‖wn+1	s)‖wn+1	PROPN
ejpam-3903	451	7	g	g	PROPN
ejpam-3903	451	8	‖hs	‖hs	PUNCT
ejpam-3903	451	9	+	+	PUNCT
ejpam-3903	451	10	c̃‖wn+1	c̃‖wn+1	NOUN
ejpam-3903	451	11	g	g	NOUN
ejpam-3903	451	12	‖hs+1	‖hs+1	PROPN
ejpam-3903	451	13	,	,	PUNCT
ejpam-3903	451	14	r.	r.	PROPN
ejpam-3903	451	15	bade	bade	PROPN
ejpam-3903	451	16	,	,	PUNCT
ejpam-3903	451	17	h.	h.	PROPN
ejpam-3903	451	18	chaker	chaker	PROPN
ejpam-3903	451	19	/	/	SYM
ejpam-3903	451	20	eur	eur	PROPN
ejpam-3903	451	21	.	.	PUNCT
ejpam-3903	452	1	j.	j.	PROPN
ejpam-3903	452	2	pure	pure	PROPN
ejpam-3903	452	3	appl	appl	PROPN
ejpam-3903	452	4	.	.	PROPN
ejpam-3903	452	5	math	math	PROPN
ejpam-3903	452	6	,	,	PUNCT
ejpam-3903	452	7	14	14	NUM
ejpam-3903	452	8	(	(	PUNCT
ejpam-3903	452	9	1	1	NUM
ejpam-3903	452	10	)	)	PUNCT
ejpam-3903	452	11	(	(	PUNCT
ejpam-3903	452	12	2021	2021	NUM
ejpam-3903	452	13	)	)	PUNCT
ejpam-3903	452	14	,	,	PUNCT
ejpam-3903	452	15	82	82	NUM
ejpam-3903	452	16	-	-	SYM
ejpam-3903	452	17	111	111	NUM
ejpam-3903	452	18	103	103	NUM
ejpam-3903	452	19	then	then	ADV
ejpam-3903	452	20	,	,	PUNCT
ejpam-3903	452	21	‖a0(wn)(wn+1	‖a0(wn)(wn+1	NOUN
ejpam-3903	452	22	−wn)‖hs	−wn)‖hs	PROPN
ejpam-3903	452	23	6	6	NUM
ejpam-3903	452	24	4t‖fn+1‖hs	4t‖fn+1‖hs	NUM
ejpam-3903	452	25	+	+	CCONJ
ejpam-3903	452	26	(	(	PUNCT
ejpam-3903	452	27	c	c	X
ejpam-3903	452	28	+	+	NUM
ejpam-3903	452	29	cr3	cr3	PROPN
ejpam-3903	452	30	s	s	PROPN
ejpam-3903	452	31	)	)	PUNCT
ejpam-3903	452	32	(	(	PUNCT
ejpam-3903	452	33	4t‖a0w	4t‖a0w	NOUN
ejpam-3903	452	34	n+1‖hs	n+1‖hs	VERB
ejpam-3903	452	35	+4t‖wn+1	+4t‖wn+1	PROPN
ejpam-3903	452	36	g	g	PROPN
ejpam-3903	452	37	‖hs	‖hs	NUM
ejpam-3903	452	38	)	)	PUNCT
ejpam-3903	453	1	+	+	CCONJ
ejpam-3903	453	2	c̃4t‖wn+1	c̃4t‖wn+1	VERB
ejpam-3903	453	3	g	g	NOUN
ejpam-3903	453	4	‖hs+1	‖hs+1	NOUN
ejpam-3903	453	5	.	.	PUNCT
ejpam-3903	454	1	(	(	PUNCT
ejpam-3903	454	2	78	78	NUM
ejpam-3903	454	3	)	)	PUNCT
ejpam-3903	454	4	now	now	ADV
ejpam-3903	454	5	we	we	PRON
ejpam-3903	454	6	set	set	VERB
ejpam-3903	454	7	:	:	PUNCT
ejpam-3903	454	8	crs01	crs01	NOUN
ejpam-3903	454	9	(	(	PUNCT
ejpam-3903	454	10	ρ̄	ρ̄	NUM
ejpam-3903	454	11	)	)	PUNCT
ejpam-3903	454	12	=	=	SYM
ejpam-3903	454	13	inf	inf	NOUN
ejpam-3903	454	14	(	(	PUNCT
ejpam-3903	454	15	1	1	NUM
ejpam-3903	454	16	,	,	PUNCT
ejpam-3903	454	17	ρ̄	ρ̄	NOUN
ejpam-3903	454	18	exp(−t	exp(−t	PROPN
ejpam-3903	454	19	rs	rs	NOUN
ejpam-3903	454	20	)	)	PUNCT
ejpam-3903	454	21	,	,	PUNCT
ejpam-3903	454	22	cvρ̄	cvρ̄	NOUN
ejpam-3903	455	1	exp(−t	exp(−t	PROPN
ejpam-3903	455	2	rs	rs	PROPN
ejpam-3903	455	3	)	)	PUNCT
ejpam-3903	455	4	)	)	PUNCT
ejpam-3903	456	1	(	(	PUNCT
ejpam-3903	456	2	79	79	X
ejpam-3903	456	3	)	)	PUNCT
ejpam-3903	456	4	we	we	PRON
ejpam-3903	456	5	get	get	VERB
ejpam-3903	456	6	finally	finally	ADV
ejpam-3903	456	7	:	:	PUNCT
ejpam-3903	456	8	‖a0w	‖a0w	VERB
ejpam-3903	456	9	n+1‖hs	n+1‖hs	PROPN
ejpam-3903	456	10	6	6	NUM
ejpam-3903	456	11	4	4	NUM
ejpam-3903	456	12	t	t	NOUN
ejpam-3903	456	13	crs01	crs01	NOUN
ejpam-3903	456	14	(	(	PUNCT
ejpam-3903	456	15	ρ̄	ρ̄	NOUN
ejpam-3903	456	16	)	)	PUNCT
ejpam-3903	456	17	‖fn+1‖hs	‖fn+1‖hs	VERB
ejpam-3903	456	18	+4tc	+4tc	PROPN
ejpam-3903	457	1	+	+	CCONJ
ejpam-3903	457	2	cr3	cr3	PROPN
ejpam-3903	457	3	s	s	PROPN
ejpam-3903	457	4	crs01	crs01	NOUN
ejpam-3903	457	5	(	(	PUNCT
ejpam-3903	457	6	ρ̄	ρ̄	NOUN
ejpam-3903	457	7	)	)	PUNCT
ejpam-3903	457	8	‖a0w	‖a0w	PROPN
ejpam-3903	457	9	n+1‖hs	n+1‖hs	VERB
ejpam-3903	457	10	+4tc	+4tc	PROPN
ejpam-3903	458	1	+	+	CCONJ
ejpam-3903	458	2	cr3	cr3	PROPN
ejpam-3903	458	3	s	s	PROPN
ejpam-3903	458	4	crs01	crs01	NOUN
ejpam-3903	458	5	(	(	PUNCT
ejpam-3903	458	6	ρ̄	ρ̄	NOUN
ejpam-3903	458	7	)	)	PUNCT
ejpam-3903	458	8	‖wn+1	‖wn+1	PUNCT
ejpam-3903	458	9	g	g	PROPN
ejpam-3903	458	10	‖hs	‖hs	NUM
ejpam-3903	458	11	+4	+4	PROPN
ejpam-3903	458	12	t	t	NOUN
ejpam-3903	458	13	c̃	c̃	PROPN
ejpam-3903	458	14	crs01	crs01	NOUN
ejpam-3903	458	15	(	(	PUNCT
ejpam-3903	458	16	ρ̄	ρ̄	NOUN
ejpam-3903	458	17	)	)	PUNCT
ejpam-3903	458	18	‖wn+1	‖wn+1	PUNCT
ejpam-3903	458	19	g	g	NOUN
ejpam-3903	458	20	‖hs+1	‖hs+1	NOUN
ejpam-3903	458	21	+	+	NUM
ejpam-3903	458	22	‖a0w	‖a0w	PROPN
ejpam-3903	458	23	n‖hs	n‖hs	PROPN
ejpam-3903	458	24	.	.	PUNCT
ejpam-3903	459	1	(	(	PUNCT
ejpam-3903	459	2	80	80	NUM
ejpam-3903	459	3	)	)	PUNCT
ejpam-3903	459	4	by	by	ADP
ejpam-3903	459	5	summation	summation	NOUN
ejpam-3903	459	6	we	we	PRON
ejpam-3903	459	7	have	have	VERB
ejpam-3903	459	8	:	:	PUNCT
ejpam-3903	459	9	‖a0w	‖a0w	VERB
ejpam-3903	459	10	n+1‖hs	n+1‖hs	PROPN
ejpam-3903	459	11	6	6	NUM
ejpam-3903	459	12	4	4	NUM
ejpam-3903	459	13	t	t	NOUN
ejpam-3903	459	14	crs01	crs01	NOUN
ejpam-3903	459	15	(	(	PUNCT
ejpam-3903	459	16	ρ̄	ρ̄	NOUN
ejpam-3903	459	17	)	)	PUNCT
ejpam-3903	459	18	n∑	n∑	PROPN
ejpam-3903	460	1	i=1	i=1	PROPN
ejpam-3903	460	2	‖fi+1‖hs	‖fi+1‖hs	VERB
ejpam-3903	460	3	+4tc	+4tc	PROPN
ejpam-3903	461	1	+	+	CCONJ
ejpam-3903	461	2	cr3	cr3	PROPN
ejpam-3903	461	3	s	s	PROPN
ejpam-3903	461	4	crs01	crs01	NOUN
ejpam-3903	461	5	(	(	PUNCT
ejpam-3903	461	6	ρ̄	ρ̄	NOUN
ejpam-3903	461	7	)	)	PUNCT
ejpam-3903	461	8	n∑	n∑	PROPN
ejpam-3903	461	9	i=1	i=1	PROPN
ejpam-3903	461	10	‖a0w	‖a0w	PROPN
ejpam-3903	461	11	i+1‖hs	i+1‖hs	NOUN
ejpam-3903	461	12	+4tc	+4tc	PROPN
ejpam-3903	462	1	+	+	CCONJ
ejpam-3903	462	2	cr3	cr3	PROPN
ejpam-3903	462	3	s	s	PROPN
ejpam-3903	462	4	crs01	crs01	NOUN
ejpam-3903	462	5	(	(	PUNCT
ejpam-3903	462	6	ρ̄	ρ̄	NOUN
ejpam-3903	462	7	)	)	PUNCT
ejpam-3903	462	8	n∑	n∑	PROPN
ejpam-3903	462	9	i=1	i=1	PROPN
ejpam-3903	462	10	‖wi+1	‖wi+1	ADV
ejpam-3903	462	11	g	g	PROPN
ejpam-3903	462	12	‖hs	‖hs	NUM
ejpam-3903	462	13	+4	+4	PROPN
ejpam-3903	462	14	t	t	X
ejpam-3903	462	15	c̃	c̃	PROPN
ejpam-3903	462	16	crs01	crs01	NOUN
ejpam-3903	462	17	(	(	PUNCT
ejpam-3903	462	18	ρ̄	ρ̄	NOUN
ejpam-3903	462	19	)	)	PUNCT
ejpam-3903	462	20	n∑	n∑	PROPN
ejpam-3903	462	21	i=1	i=1	PROPN
ejpam-3903	462	22	‖wi+1	‖wi+1	ADV
ejpam-3903	462	23	g	g	NOUN
ejpam-3903	462	24	‖hs+1	‖hs+1	NOUN
ejpam-3903	462	25	+	+	NUM
ejpam-3903	462	26	‖a0w	‖a0w	PROPN
ejpam-3903	462	27	0‖hs	0‖h	NOUN
ejpam-3903	462	28	.	.	PUNCT
ejpam-3903	463	1	(	(	PUNCT
ejpam-3903	463	2	81	81	NUM
ejpam-3903	463	3	)	)	PUNCT
ejpam-3903	463	4	by	by	ADP
ejpam-3903	463	5	the	the	DET
ejpam-3903	463	6	grönwall	grönwall	PROPN
ejpam-3903	463	7	’s	’s	PART
ejpam-3903	463	8	inequality	inequality	NOUN
ejpam-3903	463	9	we	we	PRON
ejpam-3903	463	10	deduce	deduce	VERB
ejpam-3903	463	11	:	:	PUNCT
ejpam-3903	463	12	‖a0w	‖a0w	PROPN
ejpam-3903	463	13	n‖hs	n‖hs	PROPN
ejpam-3903	463	14	6	6	NUM
ejpam-3903	463	15	(	(	PUNCT
ejpam-3903	463	16	t	t	NOUN
ejpam-3903	463	17	crs01	crs01	NOUN
ejpam-3903	463	18	(	(	PUNCT
ejpam-3903	463	19	ρ̄	ρ̄	NOUN
ejpam-3903	463	20	)	)	PUNCT
ejpam-3903	463	21	‖f‖∞,s	‖f‖∞,s	NOUN
ejpam-3903	464	1	+	+	CCONJ
ejpam-3903	464	2	ct‖wg‖∞,s+1	ct‖wg‖∞,s+1	ADJ
ejpam-3903	464	3	+	+	CCONJ
ejpam-3903	464	4	‖a0w	‖a0w	PROPN
ejpam-3903	464	5	0‖hs	0‖h	NOUN
ejpam-3903	464	6	)	)	PUNCT
ejpam-3903	464	7	expm	expm	NOUN
ejpam-3903	464	8	,	,	PUNCT
ejpam-3903	464	9	(	(	PUNCT
ejpam-3903	464	10	82	82	NUM
ejpam-3903	464	11	)	)	PUNCT
ejpam-3903	464	12	where	where	SCONJ
ejpam-3903	464	13	m	m	NOUN
ejpam-3903	464	14	is	be	AUX
ejpam-3903	464	15	given	give	VERB
ejpam-3903	464	16	by	by	ADP
ejpam-3903	464	17	(	(	PUNCT
ejpam-3903	464	18	53	53	NUM
ejpam-3903	464	19	)	)	PUNCT
ejpam-3903	464	20	.	.	PUNCT
ejpam-3903	465	1	by	by	ADP
ejpam-3903	465	2	assumptions	assumption	NOUN
ejpam-3903	465	3	(	(	PUNCT
ejpam-3903	465	4	h2	h2	NOUN
ejpam-3903	465	5	)	)	PUNCT
ejpam-3903	465	6	and	and	CCONJ
ejpam-3903	465	7	(	(	PUNCT
ejpam-3903	465	8	h3	h3	NOUN
ejpam-3903	465	9	)	)	PUNCT
ejpam-3903	465	10	,	,	PUNCT
ejpam-3903	465	11	we	we	PRON
ejpam-3903	465	12	deduce	deduce	VERB
ejpam-3903	465	13	i	i	PRON
ejpam-3903	465	14	)	)	PUNCT
ejpam-3903	465	15	.	.	PUNCT
ejpam-3903	466	1	for	for	ADP
ejpam-3903	466	2	the	the	DET
ejpam-3903	466	3	proof	proof	NOUN
ejpam-3903	466	4	of	of	ADP
ejpam-3903	466	5	ii	ii	PROPN
ejpam-3903	466	6	)	)	PUNCT
ejpam-3903	466	7	,	,	PUNCT
ejpam-3903	466	8	let	let	VERB
ejpam-3903	466	9	us	we	PRON
ejpam-3903	466	10	consider	consider	VERB
ejpam-3903	466	11	two	two	NUM
ejpam-3903	466	12	successive	successive	ADJ
ejpam-3903	466	13	solutions	solution	NOUN
ejpam-3903	466	14	wn+1	wn+1	NOUN
ejpam-3903	466	15	and	and	CCONJ
ejpam-3903	466	16	wn	wn	PROPN
ejpam-3903	466	17	of	of	ADP
ejpam-3903	466	18	the	the	DET
ejpam-3903	466	19	system	system	NOUN
ejpam-3903	466	20	(	(	PUNCT
ejpam-3903	466	21	32	32	NUM
ejpam-3903	466	22	)	)	PUNCT
ejpam-3903	466	23	,	,	PUNCT
ejpam-3903	466	24	using	use	VERB
ejpam-3903	466	25	the	the	DET
ejpam-3903	466	26	same	same	ADJ
ejpam-3903	466	27	change	change	NOUN
ejpam-3903	466	28	of	of	ADP
ejpam-3903	466	29	variable	variable	NOUN
ejpam-3903	466	30	like	like	ADP
ejpam-3903	466	31	(	(	PUNCT
ejpam-3903	466	32	36	36	NUM
ejpam-3903	466	33	)	)	PUNCT
ejpam-3903	466	34	and	and	CCONJ
ejpam-3903	466	35	setting	set	VERB
ejpam-3903	466	36	:	:	PUNCT
ejpam-3903	466	37	(	(	PUNCT
ejpam-3903	466	38	∂w)n+1	∂w)n+1	NOUN
ejpam-3903	466	39	n	n	PROPN
ejpam-3903	466	40	=	=	SYM
ejpam-3903	466	41	w(n+1)∗−wn∗	w(n+1)∗−wn∗	PROPN
ejpam-3903	466	42	,	,	PUNCT
ejpam-3903	466	43	we	we	PRON
ejpam-3903	466	44	get	get	VERB
ejpam-3903	466	45	:	:	PUNCT
ejpam-3903	466	46	a0(wn	a0(wn	NUM
ejpam-3903	466	47	)	)	PUNCT
ejpam-3903	466	48	4	4	NUM
ejpam-3903	466	49	t	t	NOUN
ejpam-3903	466	50	(	(	PUNCT
ejpam-3903	466	51	∂w)n+1	∂w)n+1	PROPN
ejpam-3903	466	52	n	n	PROPN
ejpam-3903	466	53	+	+	NUM
ejpam-3903	466	54	3∑	3∑	NUM
ejpam-3903	466	55	i=1	i=1	NUM
ejpam-3903	466	56	aiε	aiε	PRON
ejpam-3903	466	57	∂	∂	NUM
ejpam-3903	466	58	∂xi	∂xi	NOUN
ejpam-3903	466	59	(	(	PUNCT
ejpam-3903	466	60	(	(	PUNCT
ejpam-3903	466	61	∂w)n+1	∂w)n+1	NOUN
ejpam-3903	466	62	n	n	X
ejpam-3903	466	63	)	)	PUNCT
ejpam-3903	467	1	+	+	CCONJ
ejpam-3903	467	2	kε(w	kε(w	X
ejpam-3903	467	3	n+1)(∂w)n+1	n+1)(∂w)n+1	X
ejpam-3903	467	4	n	n	X
ejpam-3903	467	5	+	+	CCONJ
ejpam-3903	467	6	(	(	PUNCT
ejpam-3903	467	7	kε(w	kε(w	NOUN
ejpam-3903	467	8	n+1)−kε(w	n+1)−kε(w	NUM
ejpam-3903	467	9	n	n	CCONJ
ejpam-3903	467	10	)	)	PUNCT
ejpam-3903	467	11	)	)	PUNCT
ejpam-3903	467	12	wn∗	wn∗	NOUN
ejpam-3903	468	1	=	=	SYM
ejpam-3903	468	2	fn+1	fn+1	NOUN
ejpam-3903	468	3	−	−	PROPN
ejpam-3903	468	4	fn	fn	NOUN
ejpam-3903	469	1	+	+	NOUN
ejpam-3903	469	2	a0(wn−1	a0(wn−1	NUM
ejpam-3903	469	3	)	)	PUNCT
ejpam-3903	469	4	4	4	NUM
ejpam-3903	469	5	t	t	NOUN
ejpam-3903	469	6	(	(	PUNCT
ejpam-3903	469	7	∂w)nn−1	∂w)nn−1	PROPN
ejpam-3903	469	8	−	−	PROPN
ejpam-3903	469	9	(	(	PUNCT
ejpam-3903	469	10	hε(w	hε(w	X
ejpam-3903	469	11	n+1)−hε(w	n+1)−hε(w	PROPN
ejpam-3903	469	12	n	n	CCONJ
ejpam-3903	469	13	)	)	PUNCT
ejpam-3903	469	14	)	)	PUNCT
ejpam-3903	469	15	wn+1	wn+1	VERB
ejpam-3903	469	16	g	g	PROPN
ejpam-3903	469	17	−hε(w	−hε(w	PROPN
ejpam-3903	469	18	n)(wn+1	n)(wn+1	PROPN
ejpam-3903	469	19	g	g	NOUN
ejpam-3903	469	20	−wn	−wn	NOUN
ejpam-3903	469	21	g	g	PROPN
ejpam-3903	469	22	)	)	PUNCT
ejpam-3903	469	23	·	·	PUNCT
ejpam-3903	469	24	(	(	PUNCT
ejpam-3903	469	25	83	83	NUM
ejpam-3903	469	26	)	)	PUNCT
ejpam-3903	469	27	r.	r.	PROPN
ejpam-3903	469	28	bade	bade	PROPN
ejpam-3903	469	29	,	,	PUNCT
ejpam-3903	469	30	h.	h.	PROPN
ejpam-3903	469	31	chaker	chaker	PROPN
ejpam-3903	469	32	/	/	SYM
ejpam-3903	469	33	eur	eur	PROPN
ejpam-3903	469	34	.	.	PUNCT
ejpam-3903	470	1	j.	j.	PROPN
ejpam-3903	470	2	pure	pure	PROPN
ejpam-3903	470	3	appl	appl	PROPN
ejpam-3903	470	4	.	.	PROPN
ejpam-3903	470	5	math	math	PROPN
ejpam-3903	470	6	,	,	PUNCT
ejpam-3903	470	7	14	14	NUM
ejpam-3903	470	8	(	(	PUNCT
ejpam-3903	470	9	1	1	NUM
ejpam-3903	470	10	)	)	PUNCT
ejpam-3903	470	11	(	(	PUNCT
ejpam-3903	470	12	2021	2021	NUM
ejpam-3903	470	13	)	)	PUNCT
ejpam-3903	470	14	,	,	PUNCT
ejpam-3903	470	15	82	82	NUM
ejpam-3903	470	16	-	-	SYM
ejpam-3903	470	17	111	111	NUM
ejpam-3903	470	18	104	104	NUM
ejpam-3903	470	19	by	by	ADP
ejpam-3903	470	20	the	the	DET
ejpam-3903	470	21	lemma	lemma	PROPN
ejpam-3903	470	22	2	2	NUM
ejpam-3903	470	23	,	,	PUNCT
ejpam-3903	470	24	proved	prove	VERB
ejpam-3903	470	25	in	in	ADP
ejpam-3903	470	26	[	[	X
ejpam-3903	470	27	4	4	NUM
ejpam-3903	470	28	]	]	PUNCT
ejpam-3903	470	29	,	,	PUNCT
ejpam-3903	470	30	we	we	PRON
ejpam-3903	470	31	rewrite	rewrite	VERB
ejpam-3903	470	32	(	(	PUNCT
ejpam-3903	470	33	83	83	NUM
ejpam-3903	470	34	)	)	PUNCT
ejpam-3903	470	35	as	as	SCONJ
ejpam-3903	470	36	follow	follow	VERB
ejpam-3903	470	37	:	:	PUNCT
ejpam-3903	470	38	[	[	PUNCT
ejpam-3903	470	39	a0(wn	a0(wn	NUM
ejpam-3903	470	40	)	)	PUNCT
ejpam-3903	470	41	4	4	NUM
ejpam-3903	470	42	t	t	NOUN
ejpam-3903	470	43	+	+	CCONJ
ejpam-3903	470	44	kε(w	kε(w	NOUN
ejpam-3903	470	45	n+1	n+1	PROPN
ejpam-3903	470	46	)	)	PUNCT
ejpam-3903	471	1	+	+	NOUN
ejpam-3903	471	2	n	n	CCONJ
ejpam-3903	471	3	[	[	X
ejpam-3903	471	4	wn+1,wn	wn+1,wn	PROPN
ejpam-3903	471	5	,	,	PUNCT
ejpam-3903	471	6	wn∗	wn∗	NOUN
ejpam-3903	471	7	]	]	PUNCT
ejpam-3903	471	8	]	]	PUNCT
ejpam-3903	471	9	(	(	PUNCT
ejpam-3903	471	10	∂w)n+1	∂w)n+1	NOUN
ejpam-3903	471	11	n	n	PROPN
ejpam-3903	471	12	+	+	NUM
ejpam-3903	471	13	3∑	3∑	NUM
ejpam-3903	471	14	i=1	i=1	NUM
ejpam-3903	471	15	aiε	aiε	PRON
ejpam-3903	471	16	∂	∂	NUM
ejpam-3903	471	17	∂xi	∂xi	NOUN
ejpam-3903	471	18	(	(	PUNCT
ejpam-3903	471	19	(	(	PUNCT
ejpam-3903	471	20	∂w)n+1	∂w)n+1	NOUN
ejpam-3903	471	21	n	n	X
ejpam-3903	471	22	)	)	PUNCT
ejpam-3903	471	23	=	=	SYM
ejpam-3903	471	24	fn+1	fn+1	ADP
ejpam-3903	471	25	−	−	NOUN
ejpam-3903	472	1	fn	fn	NOUN
ejpam-3903	473	1	+	+	NOUN
ejpam-3903	473	2	a0(wn−1	a0(wn−1	NUM
ejpam-3903	473	3	)	)	PUNCT
ejpam-3903	473	4	4	4	NUM
ejpam-3903	473	5	t	t	NOUN
ejpam-3903	473	6	(	(	PUNCT
ejpam-3903	473	7	∂w)nn−1	∂w)nn−1	PROPN
ejpam-3903	473	8	−kε(w	−kε(w	PROPN
ejpam-3903	473	9	n+1)(wn+1	n+1)(wn+1	PROPN
ejpam-3903	473	10	g	g	NOUN
ejpam-3903	473	11	−wn	−wn	NOUN
ejpam-3903	473	12	g	g	NOUN
ejpam-3903	473	13	)	)	PUNCT
ejpam-3903	473	14	−	−	PROPN
ejpam-3903	473	15	(	(	PUNCT
ejpam-3903	473	16	kε(w	kε(w	NOUN
ejpam-3903	473	17	n+1)−kε(w	n+1)−kε(w	NUM
ejpam-3903	473	18	n	n	CCONJ
ejpam-3903	473	19	)	)	PUNCT
ejpam-3903	473	20	)	)	PUNCT
ejpam-3903	474	1	wn	wn	INTJ
ejpam-3903	475	1	g	g	PROPN
ejpam-3903	475	2	−	−	PROPN
ejpam-3903	476	1	3∑	3∑	PROPN
ejpam-3903	476	2	i=1	i=1	PROPN
ejpam-3903	476	3	aiε	aiε	PRON
ejpam-3903	476	4	∂	∂	NUM
ejpam-3903	476	5	∂xi	∂xi	NOUN
ejpam-3903	476	6	(	(	PUNCT
ejpam-3903	476	7	wn+1	wn+1	VERB
ejpam-3903	476	8	g	g	NOUN
ejpam-3903	476	9	−wn	−wn	NOUN
ejpam-3903	476	10	g	g	NOUN
ejpam-3903	476	11	)	)	PUNCT
ejpam-3903	476	12	(	(	PUNCT
ejpam-3903	476	13	84	84	NUM
ejpam-3903	476	14	)	)	PUNCT
ejpam-3903	476	15	applying	apply	VERB
ejpam-3903	476	16	the	the	DET
ejpam-3903	476	17	proposition	proposition	NOUN
ejpam-3903	476	18	3	3	NUM
ejpam-3903	476	19	of	of	ADP
ejpam-3903	476	20	[	[	X
ejpam-3903	476	21	4	4	X
ejpam-3903	476	22	]	]	PUNCT
ejpam-3903	476	23	to	to	ADP
ejpam-3903	476	24	the	the	DET
ejpam-3903	476	25	system	system	NOUN
ejpam-3903	476	26	(	(	PUNCT
ejpam-3903	476	27	84	84	NUM
ejpam-3903	476	28	)	)	PUNCT
ejpam-3903	476	29	we	we	PRON
ejpam-3903	476	30	have	have	AUX
ejpam-3903	476	31	:	:	PUNCT
ejpam-3903	476	32	‖a0(wn	‖a0(wn	NUM
ejpam-3903	476	33	)	)	PUNCT
ejpam-3903	476	34	4	4	NUM
ejpam-3903	476	35	t	t	NOUN
ejpam-3903	476	36	(	(	PUNCT
ejpam-3903	476	37	wn+1	wn+1	VERB
ejpam-3903	476	38	−wn	−wn	NOUN
ejpam-3903	476	39	)	)	PUNCT
ejpam-3903	476	40	‖l2	‖l2	VERB
ejpam-3903	476	41	6	6	NUM
ejpam-3903	476	42	2‖fn+1	2‖fn+1	NUM
ejpam-3903	476	43	−	−	NOUN
ejpam-3903	476	44	fn‖l2	fn‖l2	NOUN
ejpam-3903	476	45	+	+	CCONJ
ejpam-3903	477	1	2‖a0(wn−1	2‖a0(wn−1	NUM
ejpam-3903	477	2	)	)	PUNCT
ejpam-3903	477	3	4	4	NUM
ejpam-3903	477	4	t	t	NOUN
ejpam-3903	477	5	(	(	PUNCT
ejpam-3903	477	6	wn	wn	PROPN
ejpam-3903	477	7	−wn−1)‖l2	−wn−1)‖l2	PROPN
ejpam-3903	477	8	+2‖kε(w	+2‖kε(w	NUM
ejpam-3903	477	9	n)‖l∞‖wn+1	n)‖l∞‖wn+1	NOUN
ejpam-3903	477	10	g	g	NOUN
ejpam-3903	477	11	−wn	−wn	NOUN
ejpam-3903	477	12	g	g	ADP
ejpam-3903	478	1	‖l2	‖l2	ADJ
ejpam-3903	478	2	+	+	X
ejpam-3903	478	3	2‖n	2‖n	NUM
ejpam-3903	478	4	[	[	X
ejpam-3903	478	5	wn+1,wn	wn+1,wn	PROPN
ejpam-3903	478	6	,	,	PUNCT
ejpam-3903	478	7	wn∗]‖l∞‖wn+1	wn∗]‖l∞‖wn+1	VERB
ejpam-3903	478	8	g	g	NOUN
ejpam-3903	478	9	−wn	−wn	NOUN
ejpam-3903	478	10	g	g	PRON
ejpam-3903	478	11	‖l2	‖l2	ADJ
ejpam-3903	478	12	+2‖a0(wn−1	+2‖a0(wn−1	ADJ
ejpam-3903	478	13	)	)	PUNCT
ejpam-3903	478	14	4	4	NUM
ejpam-3903	478	15	t	t	NOUN
ejpam-3903	478	16	(	(	PUNCT
ejpam-3903	478	17	wn	wn	PROPN
ejpam-3903	478	18	g	g	PROPN
ejpam-3903	478	19	−wn−1	−wn−1	X
ejpam-3903	478	20	g	g	NOUN
ejpam-3903	478	21	)	)	PUNCT
ejpam-3903	478	22	‖l2	‖l2	VERB
ejpam-3903	478	23	+	+	NOUN
ejpam-3903	478	24	‖a0(wn	‖a0(wn	NUM
ejpam-3903	478	25	)	)	PUNCT
ejpam-3903	478	26	4	4	NUM
ejpam-3903	478	27	t	t	NOUN
ejpam-3903	478	28	(	(	PUNCT
ejpam-3903	478	29	wn+1	wn+1	VERB
ejpam-3903	478	30	g	g	NOUN
ejpam-3903	478	31	−wn	−wn	NOUN
ejpam-3903	478	32	g	g	NOUN
ejpam-3903	478	33	)	)	PUNCT
ejpam-3903	478	34	‖l2	‖l2	VERB
ejpam-3903	478	35	or∥∥∥∥a0(wn	or∥∥∥∥a0(wn	NOUN
ejpam-3903	478	36	)	)	PUNCT
ejpam-3903	478	37	4	4	NUM
ejpam-3903	478	38	t	t	NOUN
ejpam-3903	478	39	(	(	PUNCT
ejpam-3903	478	40	wn+1	wn+1	VERB
ejpam-3903	478	41	−wn	−wn	NOUN
ejpam-3903	478	42	)	)	PUNCT
ejpam-3903	478	43	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3903	478	44	l2	l2	NOUN
ejpam-3903	478	45	6	6	NUM
ejpam-3903	478	46	2‖fn+1	2‖fn+1	NUM
ejpam-3903	478	47	−	−	NOUN
ejpam-3903	478	48	fn‖l2	fn‖l2	NOUN
ejpam-3903	478	49	+	+	CCONJ
ejpam-3903	478	50	2	2	NUM
ejpam-3903	478	51	∥∥∥∥a0(wn−1	∥∥∥∥a0(wn−1	NUM
ejpam-3903	478	52	)	)	PUNCT
ejpam-3903	478	53	4	4	NUM
ejpam-3903	478	54	t	t	NOUN
ejpam-3903	478	55	(	(	PUNCT
ejpam-3903	478	56	wn	wn	PROPN
ejpam-3903	478	57	−wn−1	−wn−1	PROPN
ejpam-3903	478	58	)	)	PUNCT
ejpam-3903	478	59	∥∥∥∥	∥∥∥∥	NUM
ejpam-3903	478	60	l2	l2	NOUN
ejpam-3903	478	61	+2	+2	PROPN
ejpam-3903	478	62	∥∥∥∥a0(wn−1	∥∥∥∥a0(wn−1	NUM
ejpam-3903	478	63	)	)	PUNCT
ejpam-3903	478	64	4	4	NUM
ejpam-3903	478	65	t	t	NOUN
ejpam-3903	478	66	(	(	PUNCT
ejpam-3903	478	67	wn	wn	PROPN
ejpam-3903	478	68	g	g	PROPN
ejpam-3903	478	69	−wn−1	−wn−1	X
ejpam-3903	478	70	g	g	NOUN
ejpam-3903	478	71	)	)	PUNCT
ejpam-3903	478	72	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3903	478	73	l2	l2	NOUN
ejpam-3903	478	74	+	+	CCONJ
ejpam-3903	478	75	∥∥∥∥a0(wn	∥∥∥∥a0(wn	NOUN
ejpam-3903	478	76	)	)	PUNCT
ejpam-3903	478	77	4	4	NUM
ejpam-3903	478	78	t	t	NOUN
ejpam-3903	478	79	(	(	PUNCT
ejpam-3903	478	80	wn+1	wn+1	VERB
ejpam-3903	478	81	g	g	NOUN
ejpam-3903	478	82	−wn	−wn	NOUN
ejpam-3903	478	83	g	g	NOUN
ejpam-3903	478	84	)	)	PUNCT
ejpam-3903	478	85	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3903	478	86	l2	l2	NOUN
ejpam-3903	478	87	+	+	NOUN
ejpam-3903	478	88	c(rs)‖wn+1	c(rs)‖wn+1	NOUN
ejpam-3903	478	89	g	g	NOUN
ejpam-3903	478	90	−wn	−wn	NOUN
ejpam-3903	478	91	g	g	PROPN
ejpam-3903	478	92	‖l2	‖l2	ADV
ejpam-3903	478	93	squared	square	VERB
ejpam-3903	478	94	,	,	PUNCT
ejpam-3903	478	95	one	one	NUM
ejpam-3903	478	96	obtain:∥∥∥∥a0(wn	obtain:∥∥∥∥a0(wn	NOUN
ejpam-3903	478	97	)	)	PUNCT
ejpam-3903	478	98	4	4	NUM
ejpam-3903	478	99	t	t	NOUN
ejpam-3903	478	100	(	(	PUNCT
ejpam-3903	478	101	wn+1	wn+1	VERB
ejpam-3903	478	102	−wn	−wn	NOUN
ejpam-3903	478	103	)	)	PUNCT
ejpam-3903	478	104	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	478	105	l2	l2	NOUN
ejpam-3903	478	106	6	6	NUM
ejpam-3903	478	107	c‖fn+1	c‖fn+1	NOUN
ejpam-3903	478	108	−	−	PROPN
ejpam-3903	478	109	fn‖2l2	fn‖2l2	PROPN
ejpam-3903	479	1	+	+	CCONJ
ejpam-3903	479	2	1	1	NUM
ejpam-3903	479	3	2	2	NUM
ejpam-3903	479	4	∥∥∥∥a0(wn−1	∥∥∥∥a0(wn−1	NUM
ejpam-3903	479	5	)	)	PUNCT
ejpam-3903	479	6	4	4	NUM
ejpam-3903	479	7	t	t	NOUN
ejpam-3903	479	8	(	(	PUNCT
ejpam-3903	479	9	wn	wn	PROPN
ejpam-3903	479	10	−wn−1	−wn−1	PROPN
ejpam-3903	479	11	)	)	PUNCT
ejpam-3903	479	12	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	479	13	l2	l2	NOUN
ejpam-3903	479	14	+	+	CCONJ
ejpam-3903	479	15	c	c	NOUN
ejpam-3903	479	16	∥∥∥∥a0(wn−1	∥∥∥∥a0(wn−1	NUM
ejpam-3903	479	17	)	)	PUNCT
ejpam-3903	479	18	4	4	NUM
ejpam-3903	479	19	t	t	NOUN
ejpam-3903	479	20	(	(	PUNCT
ejpam-3903	479	21	wn	wn	PROPN
ejpam-3903	479	22	g	g	PROPN
ejpam-3903	479	23	−wn−1	−wn−1	X
ejpam-3903	479	24	g	g	PROPN
ejpam-3903	479	25	)	)	PUNCT
ejpam-3903	479	26	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	479	27	l2	l2	NOUN
ejpam-3903	479	28	+	+	CCONJ
ejpam-3903	479	29	c	c	NOUN
ejpam-3903	479	30	∥∥∥∥a0(wn	∥∥∥∥a0(wn	NOUN
ejpam-3903	479	31	)	)	PUNCT
ejpam-3903	479	32	4	4	NUM
ejpam-3903	479	33	t	t	NOUN
ejpam-3903	479	34	(	(	PUNCT
ejpam-3903	479	35	wn+1	wn+1	VERB
ejpam-3903	479	36	g	g	NOUN
ejpam-3903	479	37	−wn	−wn	NOUN
ejpam-3903	479	38	g	g	NOUN
ejpam-3903	479	39	)	)	PUNCT
ejpam-3903	479	40	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	479	41	l2	l2	NOUN
ejpam-3903	479	42	+	+	NOUN
ejpam-3903	479	43	c(rs	c(rs	PROPN
ejpam-3903	479	44	)	)	PUNCT
ejpam-3903	479	45	2‖wn+1	2‖wn+1	NUM
ejpam-3903	479	46	g	g	NOUN
ejpam-3903	479	47	−wn	−wn	NOUN
ejpam-3903	479	48	g	g	ADP
ejpam-3903	479	49	‖2l2	‖2l2	PROPN
ejpam-3903	479	50	(	(	PUNCT
ejpam-3903	479	51	85	85	NUM
ejpam-3903	479	52	)	)	PUNCT
ejpam-3903	479	53	with	with	ADP
ejpam-3903	479	54	c	c	PROPN
ejpam-3903	479	55	a	a	DET
ejpam-3903	479	56	positive	positive	ADJ
ejpam-3903	479	57	constant	constant	NOUN
ejpam-3903	479	58	.	.	PUNCT
ejpam-3903	480	1	the	the	DET
ejpam-3903	480	2	inequality	inequality	NOUN
ejpam-3903	480	3	(	(	PUNCT
ejpam-3903	480	4	85	85	NUM
ejpam-3903	480	5	)	)	PUNCT
ejpam-3903	480	6	remains	remain	VERB
ejpam-3903	480	7	true	true	ADJ
ejpam-3903	480	8	for	for	ADP
ejpam-3903	480	9	i	i	PROPN
ejpam-3903	480	10	=	=	NOUN
ejpam-3903	480	11	1	1	NUM
ejpam-3903	480	12	,	,	PUNCT
ejpam-3903	480	13	2	2	NUM
ejpam-3903	480	14	,	,	PUNCT
ejpam-3903	480	15	·	·	PUNCT
ejpam-3903	480	16	·	·	PUNCT
ejpam-3903	480	17	·	·	PUNCT
ejpam-3903	480	18	n	n	CCONJ
ejpam-3903	480	19	,	,	PUNCT
ejpam-3903	480	20	by	by	ADP
ejpam-3903	480	21	summation	summation	NOUN
ejpam-3903	480	22	,	,	PUNCT
ejpam-3903	480	23	we	we	PRON
ejpam-3903	480	24	get	get	VERB
ejpam-3903	480	25	:	:	PUNCT
ejpam-3903	480	26	n∑	n∑	PROPN
ejpam-3903	480	27	i=1	i=1	PROPN
ejpam-3903	480	28	∥∥∥∥a0(wi−1	∥∥∥∥a0(wi−1	PROPN
ejpam-3903	480	29	)	)	PUNCT
ejpam-3903	480	30	4	4	NUM
ejpam-3903	480	31	t	t	NOUN
ejpam-3903	480	32	(	(	PUNCT
ejpam-3903	480	33	wi+1	wi+1	NOUN
ejpam-3903	480	34	−wi	−wi	NOUN
ejpam-3903	480	35	)	)	PUNCT
ejpam-3903	480	36	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	480	37	l2	l2	NOUN
ejpam-3903	480	38	6	6	NUM
ejpam-3903	480	39	c	c	NOUN
ejpam-3903	480	40	n∑	n∑	NOUN
ejpam-3903	481	1	i	i	PRON
ejpam-3903	481	2	∥∥fi+1	∥∥fi+1	NOUN
ejpam-3903	481	3	−	−	PROPN
ejpam-3903	481	4	fi	fi	NOUN
ejpam-3903	481	5	∥∥2	∥∥2	NOUN
ejpam-3903	481	6	l2	l2	NOUN
ejpam-3903	482	1	+	+	CCONJ
ejpam-3903	483	1	c	c	PROPN
ejpam-3903	483	2	n∑	n∑	NOUN
ejpam-3903	483	3	i	i	PRON
ejpam-3903	483	4	∥∥∥∥a0(wi−1	∥∥∥∥a0(wi−1	PROPN
ejpam-3903	483	5	)	)	PUNCT
ejpam-3903	483	6	4	4	NUM
ejpam-3903	483	7	t	t	NOUN
ejpam-3903	483	8	(	(	PUNCT
ejpam-3903	483	9	wi	wi	PROPN
ejpam-3903	483	10	g	g	PROPN
ejpam-3903	483	11	−wi−1	−wi−1	CCONJ
ejpam-3903	483	12	g	g	PROPN
ejpam-3903	483	13	)	)	PUNCT
ejpam-3903	483	14	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	483	15	l2	l2	NOUN
ejpam-3903	484	1	+	+	NOUN
ejpam-3903	484	2	c	c	PROPN
ejpam-3903	484	3	n∑	n∑	VERB
ejpam-3903	484	4	i	i	PRON
ejpam-3903	484	5	∥∥∥∥a0(wi	∥∥∥∥a0(wi	VERB
ejpam-3903	484	6	)	)	PUNCT
ejpam-3903	484	7	4	4	NUM
ejpam-3903	484	8	t	t	NOUN
ejpam-3903	484	9	(	(	PUNCT
ejpam-3903	484	10	wi+1	wi+1	ADV
ejpam-3903	484	11	g	g	NOUN
ejpam-3903	484	12	−wi	−wi	NUM
ejpam-3903	484	13	g	g	NOUN
ejpam-3903	484	14	)	)	PUNCT
ejpam-3903	484	15	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	484	16	l2	l2	NOUN
ejpam-3903	484	17	+	+	CCONJ
ejpam-3903	484	18	c(rs	c(rs	PROPN
ejpam-3903	484	19	)	)	PUNCT
ejpam-3903	484	20	2	2	NUM
ejpam-3903	485	1	n∑	n∑	NOUN
ejpam-3903	485	2	i	i	PRON
ejpam-3903	485	3	∥∥wi+1	∥∥wi+1	VERB
ejpam-3903	485	4	g	g	NOUN
ejpam-3903	485	5	−wi	−wi	NUM
ejpam-3903	485	6	g	g	PROPN
ejpam-3903	485	7	∥∥2	∥∥2	PROPN
ejpam-3903	485	8	l2	l2	NOUN
ejpam-3903	485	9	.	.	PUNCT
ejpam-3903	486	1	(	(	PUNCT
ejpam-3903	486	2	86	86	NUM
ejpam-3903	486	3	)	)	PUNCT
ejpam-3903	486	4	r.	r.	PROPN
ejpam-3903	486	5	bade	bade	PROPN
ejpam-3903	486	6	,	,	PUNCT
ejpam-3903	486	7	h.	h.	PROPN
ejpam-3903	486	8	chaker	chaker	PROPN
ejpam-3903	486	9	/	/	SYM
ejpam-3903	486	10	eur	eur	PROPN
ejpam-3903	486	11	.	.	PUNCT
ejpam-3903	487	1	j.	j.	PROPN
ejpam-3903	487	2	pure	pure	PROPN
ejpam-3903	487	3	appl	appl	PROPN
ejpam-3903	487	4	.	.	PROPN
ejpam-3903	487	5	math	math	PROPN
ejpam-3903	487	6	,	,	PUNCT
ejpam-3903	487	7	14	14	NUM
ejpam-3903	487	8	(	(	PUNCT
ejpam-3903	487	9	1	1	NUM
ejpam-3903	487	10	)	)	PUNCT
ejpam-3903	487	11	(	(	PUNCT
ejpam-3903	487	12	2021	2021	NUM
ejpam-3903	487	13	)	)	PUNCT
ejpam-3903	487	14	,	,	PUNCT
ejpam-3903	487	15	82	82	NUM
ejpam-3903	487	16	-	-	SYM
ejpam-3903	487	17	111	111	NUM
ejpam-3903	487	18	105	105	NUM
ejpam-3903	487	19	multiplying	multiplying	NOUN
ejpam-3903	487	20	by	by	ADP
ejpam-3903	487	21	4	4	NUM
ejpam-3903	487	22	t	t	NOUN
ejpam-3903	487	23	we	we	PRON
ejpam-3903	487	24	have	have	VERB
ejpam-3903	487	25	:	:	PUNCT
ejpam-3903	487	26	4	4	NUM
ejpam-3903	487	27	t	t	NUM
ejpam-3903	487	28	n∑	n∑	NOUN
ejpam-3903	487	29	i=1	i=1	PROPN
ejpam-3903	487	30	∥∥∥∥a0(wi−1	∥∥∥∥a0(wi−1	PROPN
ejpam-3903	487	31	)	)	PUNCT
ejpam-3903	487	32	4	4	NUM
ejpam-3903	487	33	t	t	NOUN
ejpam-3903	487	34	(	(	PUNCT
ejpam-3903	487	35	wi+1	wi+1	NOUN
ejpam-3903	487	36	−wi	−wi	NOUN
ejpam-3903	487	37	)	)	PUNCT
ejpam-3903	487	38	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	487	39	l2	l2	NOUN
ejpam-3903	487	40	6	6	NUM
ejpam-3903	487	41	4tc	4tc	ADJ
ejpam-3903	487	42	n∑	n∑	NOUN
ejpam-3903	488	1	i	i	PRON
ejpam-3903	488	2	∥∥fi+1	∥∥fi+1	NOUN
ejpam-3903	488	3	−	−	PROPN
ejpam-3903	488	4	fi	fi	NOUN
ejpam-3903	488	5	∥∥2	∥∥2	NOUN
ejpam-3903	488	6	l2	l2	NOUN
ejpam-3903	489	1	+4	+4	PROPN
ejpam-3903	489	2	t	t	PROPN
ejpam-3903	489	3	n∑	n∑	NOUN
ejpam-3903	489	4	i	i	PRON
ejpam-3903	489	5	∥∥∥∥a0(wi−1	∥∥∥∥a0(wi−1	PROPN
ejpam-3903	489	6	)	)	PUNCT
ejpam-3903	489	7	4	4	NUM
ejpam-3903	489	8	t	t	NOUN
ejpam-3903	489	9	(	(	PUNCT
ejpam-3903	489	10	wi+1	wi+1	ADV
ejpam-3903	489	11	g	g	NOUN
ejpam-3903	489	12	−wi	−wi	NUM
ejpam-3903	489	13	g	g	NOUN
ejpam-3903	489	14	)	)	PUNCT
ejpam-3903	489	15	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	489	16	l2	l2	NOUN
ejpam-3903	489	17	+4	+4	PROPN
ejpam-3903	489	18	t	t	PROPN
ejpam-3903	489	19	n∑	n∑	NOUN
ejpam-3903	490	1	i	i	PRON
ejpam-3903	490	2	∥∥∥∥a0(wi	∥∥∥∥a0(wi	ADV
ejpam-3903	490	3	)	)	PUNCT
ejpam-3903	490	4	4	4	NUM
ejpam-3903	490	5	t	t	NOUN
ejpam-3903	490	6	(	(	PUNCT
ejpam-3903	490	7	wi+1	wi+1	ADV
ejpam-3903	490	8	g	g	NOUN
ejpam-3903	490	9	−wi	−wi	NUM
ejpam-3903	490	10	g	g	NOUN
ejpam-3903	490	11	)	)	PUNCT
ejpam-3903	490	12	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	490	13	l2	l2	NOUN
ejpam-3903	490	14	+24tc(rs	+24tc(rs	NOUN
ejpam-3903	490	15	)	)	PUNCT
ejpam-3903	490	16	2	2	NUM
ejpam-3903	490	17	n∑	n∑	NOUN
ejpam-3903	490	18	i	i	PRON
ejpam-3903	490	19	∥∥wi+1	∥∥wi+1	VERB
ejpam-3903	490	20	g	g	NOUN
ejpam-3903	491	1	‖2l2	‖2l2	PROPN
ejpam-3903	491	2	+	+	CCONJ
ejpam-3903	491	3	‖wi	‖wi	NUM
ejpam-3903	491	4	g	g	PROPN
ejpam-3903	491	5	∥∥2	∥∥2	PROPN
ejpam-3903	491	6	l2	l2	NOUN
ejpam-3903	491	7	.	.	PUNCT
ejpam-3903	492	1	finally	finally	ADV
ejpam-3903	492	2	we	we	PRON
ejpam-3903	492	3	obtain	obtain	VERB
ejpam-3903	492	4	ii	ii	NOUN
ejpam-3903	492	5	)	)	PUNCT
ejpam-3903	492	6	,	,	PUNCT
ejpam-3903	492	7	with	with	ADP
ejpam-3903	492	8	:	:	PUNCT
ejpam-3903	492	9	4	4	NUM
ejpam-3903	492	10	t	t	NUM
ejpam-3903	492	11	n∑	n∑	NOUN
ejpam-3903	492	12	i=1	i=1	PROPN
ejpam-3903	492	13	∥∥∥∥a0(wi−1	∥∥∥∥a0(wi−1	PROPN
ejpam-3903	492	14	)	)	PUNCT
ejpam-3903	492	15	4	4	NUM
ejpam-3903	492	16	t	t	NOUN
ejpam-3903	492	17	(	(	PUNCT
ejpam-3903	492	18	wi+1	wi+1	NOUN
ejpam-3903	492	19	−wi	−wi	NOUN
ejpam-3903	492	20	)	)	PUNCT
ejpam-3903	492	21	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	492	22	l2	l2	NOUN
ejpam-3903	492	23	6	6	NUM
ejpam-3903	492	24	tc	tc	NOUN
ejpam-3903	492	25	(	(	PUNCT
ejpam-3903	492	26	‖f‖2∞,2	‖f‖2∞,2	PROPN
ejpam-3903	492	27	+	+	CCONJ
ejpam-3903	492	28	‖a0wg‖2w1,∞(0,t	‖a0wg‖2w1,∞(0,t	NOUN
ejpam-3903	492	29	;	;	PUNCT
ejpam-3903	492	30	l2(ω)20	l2(ω)20	X
ejpam-3903	492	31	)	)	PUNCT
ejpam-3903	493	1	+	+	CCONJ
ejpam-3903	493	2	‖wg‖2∞,2	‖wg‖2∞,2	NOUN
ejpam-3903	493	3	)	)	PUNCT
ejpam-3903	493	4	for	for	ADP
ejpam-3903	493	5	iii	iii	NOUN
ejpam-3903	493	6	)	)	PUNCT
ejpam-3903	493	7	,	,	PUNCT
ejpam-3903	493	8	we	we	PRON
ejpam-3903	493	9	multiply	multiply	VERB
ejpam-3903	493	10	(	(	PUNCT
ejpam-3903	493	11	86	86	NUM
ejpam-3903	493	12	)	)	PUNCT
ejpam-3903	493	13	by	by	ADP
ejpam-3903	493	14	4	4	NUM
ejpam-3903	493	15	t	t	NOUN
ejpam-3903	493	16	,	,	PUNCT
ejpam-3903	493	17	which	which	PRON
ejpam-3903	493	18	implies	imply	VERB
ejpam-3903	493	19	4	4	NUM
ejpam-3903	493	20	t	t	NOUN
ejpam-3903	493	21	n∑	n∑	NOUN
ejpam-3903	493	22	i=1	i=1	PROPN
ejpam-3903	493	23	∥∥∥∥a0	∥∥∥∥a0	NOUN
ejpam-3903	493	24	4	4	NUM
ejpam-3903	493	25	t	t	NOUN
ejpam-3903	493	26	(	(	PUNCT
ejpam-3903	493	27	wi+1	wi+1	NOUN
ejpam-3903	493	28	−wi	−wi	NOUN
ejpam-3903	493	29	)	)	PUNCT
ejpam-3903	493	30	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	493	31	l2	l2	NOUN
ejpam-3903	493	32	6	6	NUM
ejpam-3903	493	33	4	4	NUM
ejpam-3903	494	1	t	t	NOUN
ejpam-3903	494	2	c	c	NOUN
ejpam-3903	494	3	c01	c01	PROPN
ejpam-3903	494	4	n∑	n∑	PROPN
ejpam-3903	495	1	i	i	PROPN
ejpam-3903	496	1	∥∥fi+1	∥∥fi+1	VERB
ejpam-3903	496	2	−	−	PROPN
ejpam-3903	496	3	fi	fi	NOUN
ejpam-3903	496	4	∥∥2	∥∥2	NOUN
ejpam-3903	496	5	l2	l2	NOUN
ejpam-3903	496	6	+	+	CCONJ
ejpam-3903	497	1	24tc03	24tc03	NUM
ejpam-3903	497	2	c01	c01	NOUN
ejpam-3903	497	3	n∑	n∑	PROPN
ejpam-3903	498	1	i	i	PRON
ejpam-3903	498	2	∥∥∥∥a0	∥∥∥∥a0	NOUN
ejpam-3903	498	3	4	4	NUM
ejpam-3903	498	4	t	t	NOUN
ejpam-3903	498	5	(	(	PUNCT
ejpam-3903	498	6	wi+1	wi+1	ADV
ejpam-3903	498	7	g	g	NOUN
ejpam-3903	498	8	−wi	−wi	NUM
ejpam-3903	498	9	g	g	NOUN
ejpam-3903	498	10	)	)	PUNCT
ejpam-3903	498	11	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	498	12	l2	l2	NOUN
ejpam-3903	498	13	+24tc(rs	+24tc(rs	NOUN
ejpam-3903	498	14	)	)	PUNCT
ejpam-3903	498	15	2	2	NUM
ejpam-3903	499	1	c01	c01	NOUN
ejpam-3903	500	1	n∑	n∑	INTJ
ejpam-3903	501	1	i	i	PRON
ejpam-3903	501	2	∥∥wi+1	∥∥wi+1	VERB
ejpam-3903	501	3	g	g	NOUN
ejpam-3903	501	4	‖2l2	‖2l2	PROPN
ejpam-3903	501	5	+	+	CCONJ
ejpam-3903	501	6	‖wi	‖wi	NUM
ejpam-3903	501	7	g	g	PROPN
ejpam-3903	501	8	∥∥2	∥∥2	PROPN
ejpam-3903	501	9	l2	l2	NOUN
ejpam-3903	501	10	,	,	PUNCT
ejpam-3903	501	11	and	and	CCONJ
ejpam-3903	501	12	finally	finally	ADV
ejpam-3903	501	13	we	we	PRON
ejpam-3903	501	14	obtain	obtain	VERB
ejpam-3903	501	15	:	:	PUNCT
ejpam-3903	501	16	4	4	NUM
ejpam-3903	501	17	t	t	NOUN
ejpam-3903	501	18	n∑	n∑	NOUN
ejpam-3903	501	19	i=1	i=1	PROPN
ejpam-3903	501	20	∥∥∥∥a0	∥∥∥∥a0	NOUN
ejpam-3903	501	21	4	4	NUM
ejpam-3903	501	22	t	t	NOUN
ejpam-3903	501	23	(	(	PUNCT
ejpam-3903	501	24	wi+1	wi+1	NOUN
ejpam-3903	501	25	−wi	−wi	NOUN
ejpam-3903	501	26	)	)	PUNCT
ejpam-3903	501	27	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3903	501	28	l2	l2	NOUN
ejpam-3903	501	29	6	6	NUM
ejpam-3903	501	30	tc	tc	NOUN
ejpam-3903	501	31	(	(	PUNCT
ejpam-3903	501	32	‖f‖2∞,2	‖f‖2∞,2	PROPN
ejpam-3903	501	33	+	+	CCONJ
ejpam-3903	501	34	‖a0wg‖2w1,∞(0,t	‖a0wg‖2w1,∞(0,t	NOUN
ejpam-3903	501	35	;	;	PUNCT
ejpam-3903	501	36	l2(ω)20	l2(ω)20	X
ejpam-3903	501	37	)	)	PUNCT
ejpam-3903	502	1	+	+	CCONJ
ejpam-3903	502	2	‖wg‖2∞,2	‖wg‖2∞,2	NOUN
ejpam-3903	502	3	)	)	PUNCT
ejpam-3903	502	4	.	.	PUNCT
ejpam-3903	503	1	�	�	PROPN
ejpam-3903	503	2	4.2.1	4.2.1	NUM
ejpam-3903	503	3	.	.	PUNCT
ejpam-3903	504	1	passing	pass	VERB
ejpam-3903	504	2	to	to	PART
ejpam-3903	504	3	limit	limit	VERB
ejpam-3903	504	4	m→∞	m→∞	NOUN
ejpam-3903	504	5	the	the	DET
ejpam-3903	504	6	a	a	DET
ejpam-3903	504	7	priori	priori	ADJ
ejpam-3903	504	8	estimates	estimate	NOUN
ejpam-3903	504	9	given	give	VERB
ejpam-3903	504	10	by	by	ADP
ejpam-3903	504	11	the	the	DET
ejpam-3903	504	12	lemma	lemma	PROPN
ejpam-3903	504	13	4	4	NUM
ejpam-3903	504	14	allow	allow	VERB
ejpam-3903	504	15	us	we	PRON
ejpam-3903	504	16	to	to	PART
ejpam-3903	504	17	pass	pass	VERB
ejpam-3903	504	18	to	to	ADP
ejpam-3903	504	19	the	the	DET
ejpam-3903	504	20	limit	limit	NOUN
ejpam-3903	504	21	in	in	ADP
ejpam-3903	504	22	non	non	ADJ
ejpam-3903	504	23	-	-	ADJ
ejpam-3903	504	24	linear	linear	ADJ
ejpam-3903	504	25	terms	term	NOUN
ejpam-3903	504	26	.	.	PUNCT
ejpam-3903	505	1	but	but	CCONJ
ejpam-3903	505	2	to	to	PART
ejpam-3903	505	3	be	be	AUX
ejpam-3903	505	4	able	able	ADJ
ejpam-3903	505	5	to	to	PART
ejpam-3903	505	6	do	do	VERB
ejpam-3903	505	7	it	it	PRON
ejpam-3903	505	8	,	,	PUNCT
ejpam-3903	505	9	we	we	PRON
ejpam-3903	505	10	introduce	introduce	VERB
ejpam-3903	505	11	the	the	DET
ejpam-3903	505	12	approximate	approximate	ADJ
ejpam-3903	505	13	functions	function	NOUN
ejpam-3903	505	14	on	on	ADP
ejpam-3903	505	15	[	[	X
ejpam-3903	505	16	0	0	NUM
ejpam-3903	505	17	,	,	PUNCT
ejpam-3903	505	18	t	t	NOUN
ejpam-3903	505	19	]	]	PUNCT
ejpam-3903	505	20	and	and	CCONJ
ejpam-3903	505	21	which	which	PRON
ejpam-3903	505	22	are	be	AUX
ejpam-3903	505	23	defined	define	VERB
ejpam-3903	505	24	as	as	SCONJ
ejpam-3903	505	25	follows	follow	VERB
ejpam-3903	505	26	:	:	PUNCT
ejpam-3903	505	27	v∗m(t	v∗m(t	VERB
ejpam-3903	505	28	)	)	PUNCT
ejpam-3903	506	1	=	=	SYM
ejpam-3903	506	2	wn	wn	PROPN
ejpam-3903	507	1	+	+	CCONJ
ejpam-3903	507	2	1	1	NUM
ejpam-3903	507	3	k	k	NOUN
ejpam-3903	507	4	(	(	PUNCT
ejpam-3903	507	5	wn+1	wn+1	PROPN
ejpam-3903	507	6	−wn)(t−	−wn)(t−	PROPN
ejpam-3903	507	7	nk	nk	PROPN
ejpam-3903	507	8	)	)	PUNCT
ejpam-3903	507	9	∀t	∀t	PROPN
ejpam-3903	507	10	∈	∈	PROPN
ejpam-3903	508	1	[	[	X
ejpam-3903	508	2	nk	nk	PROPN
ejpam-3903	508	3	,	,	PUNCT
ejpam-3903	508	4	(	(	PUNCT
ejpam-3903	508	5	n+	n+	X
ejpam-3903	508	6	1)k	1)k	NUM
ejpam-3903	508	7	[	[	X
ejpam-3903	508	8	,	,	PUNCT
ejpam-3903	508	9	vm(t	vm(t	ADJ
ejpam-3903	508	10	)	)	PUNCT
ejpam-3903	508	11	=	=	SYM
ejpam-3903	508	12	wn	wn	PROPN
ejpam-3903	508	13	∀t	∀t	PROPN
ejpam-3903	508	14	∈	∈	PROPN
ejpam-3903	509	1	[	[	X
ejpam-3903	509	2	nk	nk	PROPN
ejpam-3903	509	3	,	,	PUNCT
ejpam-3903	509	4	(	(	PUNCT
ejpam-3903	509	5	n+	n+	X
ejpam-3903	509	6	1)k	1)k	NUM
ejpam-3903	509	7	]	]	X
ejpam-3903	509	8	(	(	PUNCT
ejpam-3903	509	9	87	87	NUM
ejpam-3903	509	10	)	)	PUNCT
ejpam-3903	509	11	with	with	ADP
ejpam-3903	509	12	k	k	PROPN
ejpam-3903	509	13	=	=	SYM
ejpam-3903	509	14	t	t	PROPN
ejpam-3903	509	15	m	m	NOUN
ejpam-3903	509	16	.	.	PUNCT
ejpam-3903	510	1	so	so	ADV
ejpam-3903	510	2	we	we	PRON
ejpam-3903	510	3	have	have	VERB
ejpam-3903	510	4	the	the	DET
ejpam-3903	510	5	following	follow	VERB
ejpam-3903	510	6	result	result	NOUN
ejpam-3903	510	7	:	:	PUNCT
ejpam-3903	511	1	lemma	lemma	PROPN
ejpam-3903	511	2	5	5	X
ejpam-3903	511	3	.	.	PUNCT
ejpam-3903	511	4	let	let	AUX
ejpam-3903	511	5	suppose	suppose	VERB
ejpam-3903	511	6	that	that	SCONJ
ejpam-3903	511	7	the	the	DET
ejpam-3903	511	8	assumptions	assumption	NOUN
ejpam-3903	511	9	(	(	PUNCT
ejpam-3903	511	10	h2	h2	NOUN
ejpam-3903	511	11	)	)	PUNCT
ejpam-3903	511	12	and	and	CCONJ
ejpam-3903	511	13	(	(	PUNCT
ejpam-3903	511	14	h3	h3	NOUN
ejpam-3903	511	15	)	)	PUNCT
ejpam-3903	511	16	hold	hold	VERB
ejpam-3903	511	17	,	,	PUNCT
ejpam-3903	511	18	then	then	ADV
ejpam-3903	511	19	up	up	ADP
ejpam-3903	511	20	to	to	PART
ejpam-3903	511	21	extract	extract	VERB
ejpam-3903	511	22	sub	sub	NOUN
ejpam-3903	511	23	sequences	sequence	NOUN
ejpam-3903	511	24	of	of	ADP
ejpam-3903	511	25	v∗m	v∗m	NUM
ejpam-3903	511	26	and	and	CCONJ
ejpam-3903	511	27	vm	vm	PROPN
ejpam-3903	511	28	,	,	PUNCT
ejpam-3903	511	29	if	if	SCONJ
ejpam-3903	511	30	necessary	necessary	ADJ
ejpam-3903	511	31	(	(	PUNCT
ejpam-3903	511	32	which	which	PRON
ejpam-3903	511	33	we	we	PRON
ejpam-3903	511	34	will	will	AUX
ejpam-3903	511	35	note	note	VERB
ejpam-3903	511	36	in	in	ADP
ejpam-3903	511	37	the	the	DET
ejpam-3903	511	38	same	same	ADJ
ejpam-3903	511	39	maner	maner	NOUN
ejpam-3903	511	40	)	)	PUNCT
ejpam-3903	511	41	we	we	PRON
ejpam-3903	511	42	have	have	VERB
ejpam-3903	511	43	the	the	DET
ejpam-3903	511	44	following	follow	VERB
ejpam-3903	511	45	convergences	convergence	NOUN
ejpam-3903	511	46	:	:	PUNCT
ejpam-3903	511	47	r.	r.	PROPN
ejpam-3903	511	48	bade	bade	PROPN
ejpam-3903	511	49	,	,	PUNCT
ejpam-3903	511	50	h.	h.	PROPN
ejpam-3903	511	51	chaker	chaker	PROPN
ejpam-3903	511	52	/	/	SYM
ejpam-3903	511	53	eur	eur	PROPN
ejpam-3903	511	54	.	.	PUNCT
ejpam-3903	512	1	j.	j.	PROPN
ejpam-3903	512	2	pure	pure	PROPN
ejpam-3903	512	3	appl	appl	PROPN
ejpam-3903	512	4	.	.	PROPN
ejpam-3903	512	5	math	math	PROPN
ejpam-3903	512	6	,	,	PUNCT
ejpam-3903	512	7	14	14	NUM
ejpam-3903	512	8	(	(	PUNCT
ejpam-3903	512	9	1	1	NUM
ejpam-3903	512	10	)	)	PUNCT
ejpam-3903	512	11	(	(	PUNCT
ejpam-3903	512	12	2021	2021	NUM
ejpam-3903	512	13	)	)	PUNCT
ejpam-3903	512	14	,	,	PUNCT
ejpam-3903	512	15	82	82	NUM
ejpam-3903	512	16	-	-	SYM
ejpam-3903	512	17	111	111	NUM
ejpam-3903	512	18	106	106	NUM
ejpam-3903	512	19	a	a	PRON
ejpam-3903	512	20	)	)	PUNCT
ejpam-3903	512	21	a0v	a0v	PROPN
ejpam-3903	512	22	∗	∗	NOUN
ejpam-3903	512	23	m	m	VERB
ejpam-3903	512	24	⇀	⇀	X
ejpam-3903	512	25	a0v	a0v	PROPN
ejpam-3903	512	26	weakly	weakly	ADV
ejpam-3903	512	27	in	in	ADP
ejpam-3903	512	28	l2(0	l2(0	PROPN
ejpam-3903	512	29	,	,	PUNCT
ejpam-3903	512	30	t	t	NOUN
ejpam-3903	512	31	;	;	PUNCT
ejpam-3903	512	32	hs(ω)20	hs(ω)20	ADJ
ejpam-3903	512	33	)	)	PUNCT
ejpam-3903	512	34	,	,	PUNCT
ejpam-3903	512	35	b	b	X
ejpam-3903	512	36	)	)	PUNCT
ejpam-3903	512	37	a0v	a0v	PROPN
ejpam-3903	512	38	m	m	VERB
ejpam-3903	512	39	⇀	⇀	PROPN
ejpam-3903	512	40	a0v	a0v	PROPN
ejpam-3903	512	41	weakly	weakly	ADV
ejpam-3903	512	42	in	in	ADP
ejpam-3903	512	43	l2(0	l2(0	PROPN
ejpam-3903	512	44	,	,	PUNCT
ejpam-3903	512	45	t	t	NOUN
ejpam-3903	512	46	;	;	PUNCT
ejpam-3903	512	47	hs(ω)20	hs(ω)20	ADJ
ejpam-3903	512	48	)	)	PUNCT
ejpam-3903	512	49	,	,	PUNCT
ejpam-3903	512	50	c	c	X
ejpam-3903	512	51	)	)	PUNCT
ejpam-3903	512	52	v∗m	v∗m	NOUN
ejpam-3903	512	53	and	and	CCONJ
ejpam-3903	512	54	vm	vm	NOUN
ejpam-3903	513	1	⇀	⇀	PROPN
ejpam-3903	513	2	v	v	ADP
ejpam-3903	513	3	weakly-∗	weakly-∗	NOUN
ejpam-3903	513	4	in	in	ADP
ejpam-3903	513	5	l∞(0	l∞(0	PRON
ejpam-3903	513	6	,	,	PUNCT
ejpam-3903	513	7	t	t	PROPN
ejpam-3903	513	8	;	;	PUNCT
ejpam-3903	513	9	hs−1(ω)20	hs−1(ω)20	NUM
ejpam-3903	513	10	)	)	PUNCT
ejpam-3903	513	11	,	,	PUNCT
ejpam-3903	513	12	d	d	X
ejpam-3903	513	13	)	)	PUNCT
ejpam-3903	514	1	d	d	NOUN
ejpam-3903	514	2	dt	dt	X
ejpam-3903	514	3	(	(	PUNCT
ejpam-3903	514	4	a0v	a0v	PROPN
ejpam-3903	514	5	∗	∗	PROPN
ejpam-3903	514	6	m	m	PROPN
ejpam-3903	514	7	)	)	PUNCT
ejpam-3903	514	8	⇀	⇀	PUNCT
ejpam-3903	515	1	d	d	NOUN
ejpam-3903	515	2	dt	dt	X
ejpam-3903	515	3	(	(	PUNCT
ejpam-3903	515	4	a0v	a0v	PROPN
ejpam-3903	515	5	)	)	PUNCT
ejpam-3903	515	6	weakly	weakly	ADJ
ejpam-3903	515	7	in	in	ADP
ejpam-3903	515	8	l2(0	l2(0	PROPN
ejpam-3903	515	9	,	,	PUNCT
ejpam-3903	515	10	t	t	NOUN
ejpam-3903	515	11	;	;	PUNCT
ejpam-3903	515	12	l2(ω)20	l2(ω)20	NUM
ejpam-3903	515	13	)	)	PUNCT
ejpam-3903	515	14	.	.	PUNCT
ejpam-3903	516	1	proof	proof	NOUN
ejpam-3903	516	2	.	.	PUNCT
ejpam-3903	517	1	by	by	ADP
ejpam-3903	517	2	construction	construction	NOUN
ejpam-3903	517	3	of	of	ADP
ejpam-3903	517	4	the	the	DET
ejpam-3903	517	5	functions	function	NOUN
ejpam-3903	517	6	v∗m	v∗m	NOUN
ejpam-3903	517	7	,	,	PUNCT
ejpam-3903	517	8	vm	vm	PROPN
ejpam-3903	517	9	and	and	CCONJ
ejpam-3903	517	10	the	the	DET
ejpam-3903	517	11	estimation	estimation	NOUN
ejpam-3903	517	12	i	i	NOUN
ejpam-3903	517	13	)	)	PUNCT
ejpam-3903	517	14	of	of	ADP
ejpam-3903	517	15	the	the	DET
ejpam-3903	517	16	lemma	lemma	PROPN
ejpam-3903	517	17	4	4	NUM
ejpam-3903	517	18	,	,	PUNCT
ejpam-3903	517	19	we	we	PRON
ejpam-3903	517	20	have	have	AUX
ejpam-3903	517	21	a0v∗m	a0v∗m	NUM
ejpam-3903	517	22	and	and	CCONJ
ejpam-3903	517	23	a0vm	a0vm	VERB
ejpam-3903	517	24	are	be	AUX
ejpam-3903	517	25	bounded	bound	VERB
ejpam-3903	517	26	in	in	ADP
ejpam-3903	517	27	l∞(0	l∞(0	PRON
ejpam-3903	517	28	,	,	PUNCT
ejpam-3903	517	29	t	t	PROPN
ejpam-3903	517	30	;	;	PUNCT
ejpam-3903	517	31	hs(ω)20	hs(ω)20	X
ejpam-3903	517	32	)	)	PUNCT
ejpam-3903	517	33	thus	thus	ADV
ejpam-3903	517	34	we	we	PRON
ejpam-3903	517	35	have	have	VERB
ejpam-3903	517	36	the	the	DET
ejpam-3903	517	37	weak-∗	weak-∗	ADJ
ejpam-3903	517	38	convergence	convergence	NOUN
ejpam-3903	517	39	of	of	ADP
ejpam-3903	517	40	the	the	DET
ejpam-3903	517	41	two	two	NUM
ejpam-3903	517	42	sequences	sequence	NOUN
ejpam-3903	517	43	in	in	ADP
ejpam-3903	517	44	l∞(0	l∞(0	PRON
ejpam-3903	517	45	,	,	PUNCT
ejpam-3903	517	46	t	t	PROPN
ejpam-3903	517	47	;	;	PUNCT
ejpam-3903	517	48	hs(ω))20	hs(ω))20	PROPN
ejpam-3903	517	49	.	.	PUNCT
ejpam-3903	518	1	by	by	ADP
ejpam-3903	518	2	compact	compact	ADJ
ejpam-3903	518	3	embedded	embed	VERB
ejpam-3903	518	4	we	we	PRON
ejpam-3903	518	5	get	get	VERB
ejpam-3903	518	6	a	a	PRON
ejpam-3903	518	7	)	)	PUNCT
ejpam-3903	518	8	and	and	CCONJ
ejpam-3903	518	9	b	b	X
ejpam-3903	518	10	)	)	PUNCT
ejpam-3903	518	11	.	.	PUNCT
ejpam-3903	519	1	notice	notice	VERB
ejpam-3903	519	2	that	that	SCONJ
ejpam-3903	519	3	a0v∗m	a0v∗m	PUNCT
ejpam-3903	519	4	and	and	CCONJ
ejpam-3903	519	5	a0vm	a0vm	AUX
ejpam-3903	519	6	represent	represent	VERB
ejpam-3903	519	7	the	the	DET
ejpam-3903	519	8	first	first	ADJ
ejpam-3903	519	9	five	five	NUM
ejpam-3903	519	10	variables	variable	NOUN
ejpam-3903	519	11	of	of	ADP
ejpam-3903	519	12	v∗m	v∗m	NUM
ejpam-3903	519	13	and	and	CCONJ
ejpam-3903	519	14	vm	vm	PROPN
ejpam-3903	519	15	thus	thus	ADV
ejpam-3903	519	16	,	,	PUNCT
ejpam-3903	519	17	v∗m	v∗m	NUM
ejpam-3903	519	18	et	et	NOUN
ejpam-3903	519	19	vm	vm	PROPN
ejpam-3903	519	20	are	be	AUX
ejpam-3903	519	21	bounded	bound	VERB
ejpam-3903	519	22	in	in	ADP
ejpam-3903	519	23	l∞(0	l∞(0	PRON
ejpam-3903	519	24	,	,	PUNCT
ejpam-3903	519	25	t	t	NOUN
ejpam-3903	519	26	;	;	PUNCT
ejpam-3903	519	27	hs−1(ω)20	hs−1(ω)20	NUM
ejpam-3903	519	28	)	)	PUNCT
ejpam-3903	519	29	.	.	PUNCT
ejpam-3903	520	1	then	then	ADV
ejpam-3903	520	2	we	we	PRON
ejpam-3903	520	3	have	have	VERB
ejpam-3903	520	4	c	c	NOUN
ejpam-3903	520	5	)	)	PUNCT
ejpam-3903	520	6	.	.	PUNCT
ejpam-3903	521	1	finally	finally	ADV
ejpam-3903	521	2	d	d	X
ejpam-3903	521	3	)	)	PUNCT
ejpam-3903	521	4	come	come	VERB
ejpam-3903	521	5	from	from	ADP
ejpam-3903	521	6	iii	iii	NOUN
ejpam-3903	521	7	)	)	PUNCT
ejpam-3903	521	8	of	of	ADP
ejpam-3903	521	9	the	the	DET
ejpam-3903	521	10	lemma	lemma	PROPN
ejpam-3903	521	11	4	4	NUM
ejpam-3903	521	12	.	.	PUNCT
ejpam-3903	522	1	it	it	PRON
ejpam-3903	522	2	remains	remain	VERB
ejpam-3903	522	3	to	to	PART
ejpam-3903	522	4	prove	prove	VERB
ejpam-3903	522	5	that	that	SCONJ
ejpam-3903	522	6	v∗m	v∗m	NOUN
ejpam-3903	522	7	and	and	CCONJ
ejpam-3903	522	8	vm	vm	PROPN
ejpam-3903	522	9	have	have	VERB
ejpam-3903	522	10	the	the	DET
ejpam-3903	522	11	same	same	ADJ
ejpam-3903	522	12	limit	limit	NOUN
ejpam-3903	522	13	when	when	SCONJ
ejpam-3903	522	14	m→∞.	m→∞.	PROPN
ejpam-3903	522	15	for	for	ADP
ejpam-3903	522	16	that	that	PRON
ejpam-3903	522	17	,	,	PUNCT
ejpam-3903	522	18	one	one	PRON
ejpam-3903	522	19	can	can	AUX
ejpam-3903	522	20	remark	remark	VERB
ejpam-3903	522	21	that	that	SCONJ
ejpam-3903	522	22	:	:	PUNCT
ejpam-3903	522	23	a0v∗m(t)−a0vm(t	a0v∗m(t)−a0vm(t	NOUN
ejpam-3903	522	24	)	)	PUNCT
ejpam-3903	522	25	=	=	PUNCT
ejpam-3903	522	26	t−	t−	PROPN
ejpam-3903	522	27	nk	nk	PROPN
ejpam-3903	522	28	k	k	PROPN
ejpam-3903	522	29	(	(	PUNCT
ejpam-3903	522	30	a0wn+1	a0wn+1	PROPN
ejpam-3903	522	31	−a0wn	−a0wn	NOUN
ejpam-3903	522	32	)	)	PUNCT
ejpam-3903	522	33	∀t	∀t	PROPN
ejpam-3903	522	34	∈	∈	PROPN
ejpam-3903	523	1	[	[	X
ejpam-3903	523	2	nk	nk	PROPN
ejpam-3903	523	3	,	,	PUNCT
ejpam-3903	523	4	(	(	PUNCT
ejpam-3903	523	5	n+	n+	X
ejpam-3903	523	6	1)k	1)k	NUM
ejpam-3903	523	7	]	]	X
ejpam-3903	523	8	∫	∫	PROPN
ejpam-3903	523	9	(	(	PUNCT
ejpam-3903	523	10	n+1)k	n+1)k	PROPN
ejpam-3903	523	11	nk	nk	PROPN
ejpam-3903	523	12	|a0v∗m(t)−a0vm(t)|2	|a0v∗m(t)−a0vm(t)|2	NOUN
ejpam-3903	523	13	dt	dt	NOUN
ejpam-3903	523	14	=	=	SYM
ejpam-3903	523	15	|a0wn+1	|a0wn+1	PROPN
ejpam-3903	523	16	−a0wn|2	−a0wn|2	PROPN
ejpam-3903	523	17	∫	∫	PROPN
ejpam-3903	523	18	(	(	PUNCT
ejpam-3903	523	19	n+1)k	n+1)k	PROPN
ejpam-3903	523	20	nk	nk	PROPN
ejpam-3903	523	21	(	(	PUNCT
ejpam-3903	523	22	τ	τ	PROPN
ejpam-3903	523	23	−	−	PROPN
ejpam-3903	523	24	nk	nk	PROPN
ejpam-3903	523	25	k	k	PROPN
ejpam-3903	523	26	)	)	PUNCT
ejpam-3903	523	27	2	2	NUM
ejpam-3903	523	28	dτ	dτ	NOUN
ejpam-3903	523	29	=	=	PROPN
ejpam-3903	523	30	k2	k2	ADJ
ejpam-3903	523	31	3	3	NUM
ejpam-3903	523	32	|a0wn+1	|a0wn+1	PROPN
ejpam-3903	523	33	−a0wn|2	−a0wn|2	PROPN
ejpam-3903	523	34	,	,	PUNCT
ejpam-3903	523	35	so	so	ADV
ejpam-3903	523	36	,	,	PUNCT
ejpam-3903	523	37	by	by	ADP
ejpam-3903	523	38	summation	summation	NOUN
ejpam-3903	523	39	,	,	PUNCT
ejpam-3903	523	40	we	we	PRON
ejpam-3903	523	41	obtain	obtain	VERB
ejpam-3903	523	42	:	:	PUNCT
ejpam-3903	523	43	‖a0v∗m	‖a0v∗m	NUM
ejpam-3903	523	44	−a0vm‖2,2	−a0vm‖2,2	NOUN
ejpam-3903	523	45	≤	≤	PUNCT
ejpam-3903	524	1	ck	ck	PROPN
ejpam-3903	524	2	3	3	NUM
ejpam-3903	524	3	.	.	PUNCT
ejpam-3903	525	1	passing	pass	VERB
ejpam-3903	525	2	to	to	ADP
ejpam-3903	525	3	the	the	DET
ejpam-3903	525	4	limit	limit	NOUN
ejpam-3903	525	5	m	m	AUX
ejpam-3903	525	6	→	→	SYM
ejpam-3903	525	7	+	+	NUM
ejpam-3903	525	8	∞	∞	PROPN
ejpam-3903	525	9	which	which	PRON
ejpam-3903	525	10	means	mean	VERB
ejpam-3903	525	11	k	k	PROPN
ejpam-3903	525	12	→	→	SYM
ejpam-3903	525	13	0	0	NUM
ejpam-3903	525	14	,	,	PUNCT
ejpam-3903	525	15	we	we	PRON
ejpam-3903	525	16	have	have	VERB
ejpam-3903	525	17	:	:	PUNCT
ejpam-3903	525	18	a0v∗	a0v∗	X
ejpam-3903	525	19	=	=	SYM
ejpam-3903	525	20	a0v	a0v	PROPN
ejpam-3903	525	21	and	and	CCONJ
ejpam-3903	525	22	consequently	consequently	ADV
ejpam-3903	525	23	v∗	v∗	PROPN
ejpam-3903	525	24	=	=	PUNCT
ejpam-3903	526	1	v.	v.	PROPN
ejpam-3903	526	2	�	�	PROPN
ejpam-3903	526	3	now	now	ADV
ejpam-3903	526	4	we	we	PRON
ejpam-3903	526	5	can	can	AUX
ejpam-3903	526	6	announce	announce	VERB
ejpam-3903	526	7	the	the	DET
ejpam-3903	526	8	result	result	NOUN
ejpam-3903	526	9	which	which	PRON
ejpam-3903	526	10	allows	allow	VERB
ejpam-3903	526	11	us	we	PRON
ejpam-3903	526	12	to	to	PART
ejpam-3903	526	13	pass	pass	VERB
ejpam-3903	526	14	to	to	ADP
ejpam-3903	526	15	the	the	DET
ejpam-3903	526	16	limit	limit	NOUN
ejpam-3903	526	17	in	in	ADP
ejpam-3903	526	18	the	the	DET
ejpam-3903	526	19	nonlinear	nonlinear	ADJ
ejpam-3903	526	20	term	term	NOUN
ejpam-3903	526	21	.	.	PUNCT
ejpam-3903	527	1	lemma	lemma	PROPN
ejpam-3903	527	2	6	6	NUM
ejpam-3903	527	3	.	.	PUNCT
ejpam-3903	528	1	let	let	VERB
ejpam-3903	528	2	us	we	PRON
ejpam-3903	528	3	suppose	suppose	VERB
ejpam-3903	528	4	that	that	SCONJ
ejpam-3903	528	5	the	the	DET
ejpam-3903	528	6	assumptions	assumption	NOUN
ejpam-3903	528	7	(	(	PUNCT
ejpam-3903	528	8	h1	h1	PROPN
ejpam-3903	528	9	)	)	PUNCT
ejpam-3903	528	10	,	,	PUNCT
ejpam-3903	528	11	(	(	PUNCT
ejpam-3903	528	12	h2	h2	NOUN
ejpam-3903	528	13	)	)	PUNCT
ejpam-3903	528	14	and	and	CCONJ
ejpam-3903	528	15	(	(	PUNCT
ejpam-3903	528	16	h3	h3	NOUN
ejpam-3903	528	17	)	)	PUNCT
ejpam-3903	528	18	hold	hold	VERB
ejpam-3903	528	19	,	,	PUNCT
ejpam-3903	528	20	then	then	ADV
ejpam-3903	528	21	up	up	ADP
ejpam-3903	528	22	to	to	PART
ejpam-3903	528	23	subsequence	subsequence	VERB
ejpam-3903	528	24	,	,	PUNCT
ejpam-3903	528	25	we	we	PRON
ejpam-3903	528	26	have	have	VERB
ejpam-3903	528	27	:	:	PUNCT
ejpam-3903	528	28	1	1	NUM
ejpam-3903	528	29	)	)	PUNCT
ejpam-3903	528	30	vm	vm	NOUN
ejpam-3903	528	31	1	1	NUM
ejpam-3903	528	32	⇀	⇀	PROPN
ejpam-3903	528	33	w1	w1	NOUN
ejpam-3903	528	34	weakly-∗	weakly-∗	NOUN
ejpam-3903	528	35	in	in	ADP
ejpam-3903	528	36	l∞(0	l∞(0	PRON
ejpam-3903	528	37	,	,	PUNCT
ejpam-3903	528	38	t	t	NOUN
ejpam-3903	528	39	;	;	PUNCT
ejpam-3903	528	40	l2(ω	l2(ω	NUM
ejpam-3903	528	41	)	)	PUNCT
ejpam-3903	528	42	)	)	PUNCT
ejpam-3903	528	43	,	,	PUNCT
ejpam-3903	528	44	2	2	X
ejpam-3903	528	45	)	)	PUNCT
ejpam-3903	528	46	vm	vm	NOUN
ejpam-3903	529	1	i	i	PRON
ejpam-3903	529	2	→wi	→wi	VERB
ejpam-3903	529	3	strongly	strongly	ADV
ejpam-3903	529	4	in	in	ADP
ejpam-3903	529	5	l2(0	l2(0	NOUN
ejpam-3903	529	6	,	,	PUNCT
ejpam-3903	529	7	t	t	NOUN
ejpam-3903	529	8	;	;	PUNCT
ejpam-3903	529	9	l4(ω	l4(ω	X
ejpam-3903	529	10	)	)	PUNCT
ejpam-3903	529	11	)	)	PUNCT
ejpam-3903	530	1	,	,	PUNCT
ejpam-3903	530	2	3	3	X
ejpam-3903	530	3	)	)	PUNCT
ejpam-3903	530	4	vm	vm	NOUN
ejpam-3903	531	1	i	i	PRON
ejpam-3903	531	2	→wi	→wi	VERB
ejpam-3903	531	3	strongly	strongly	ADV
ejpam-3903	531	4	in	in	ADP
ejpam-3903	531	5	l2(0	l2(0	NOUN
ejpam-3903	531	6	,	,	PUNCT
ejpam-3903	531	7	t	t	NOUN
ejpam-3903	531	8	;	;	PUNCT
ejpam-3903	531	9	l6(ω	l6(ω	PROPN
ejpam-3903	531	10	)	)	PUNCT
ejpam-3903	531	11	)	)	PUNCT
ejpam-3903	531	12	,	,	PUNCT
ejpam-3903	531	13	4	4	X
ejpam-3903	531	14	)	)	PUNCT
ejpam-3903	531	15	vm	vm	NOUN
ejpam-3903	532	1	i	i	PRON
ejpam-3903	532	2	vm	vm	PROPN
ejpam-3903	532	3	j	j	PROPN
ejpam-3903	532	4	⇀	⇀	PROPN
ejpam-3903	532	5	wiwj	wiwj	ADP
ejpam-3903	532	6	weakly	weakly	ADJ
ejpam-3903	532	7	l2(0	l2(0	NOUN
ejpam-3903	532	8	,	,	PUNCT
ejpam-3903	532	9	t	t	NOUN
ejpam-3903	532	10	;	;	PUNCT
ejpam-3903	532	11	l2(ω	l2(ω	NUM
ejpam-3903	532	12	)	)	PUNCT
ejpam-3903	532	13	)	)	PUNCT
ejpam-3903	532	14	,	,	PUNCT
ejpam-3903	532	15	r.	r.	PROPN
ejpam-3903	532	16	bade	bade	PROPN
ejpam-3903	532	17	,	,	PUNCT
ejpam-3903	532	18	h.	h.	PROPN
ejpam-3903	532	19	chaker	chaker	PROPN
ejpam-3903	532	20	/	/	SYM
ejpam-3903	532	21	eur	eur	PROPN
ejpam-3903	532	22	.	.	PUNCT
ejpam-3903	533	1	j.	j.	PROPN
ejpam-3903	533	2	pure	pure	PROPN
ejpam-3903	533	3	appl	appl	PROPN
ejpam-3903	533	4	.	.	PROPN
ejpam-3903	533	5	math	math	PROPN
ejpam-3903	533	6	,	,	PUNCT
ejpam-3903	533	7	14	14	NUM
ejpam-3903	533	8	(	(	PUNCT
ejpam-3903	533	9	1	1	NUM
ejpam-3903	533	10	)	)	PUNCT
ejpam-3903	533	11	(	(	PUNCT
ejpam-3903	533	12	2021	2021	NUM
ejpam-3903	533	13	)	)	PUNCT
ejpam-3903	533	14	,	,	PUNCT
ejpam-3903	533	15	82	82	NUM
ejpam-3903	533	16	-	-	SYM
ejpam-3903	533	17	111	111	NUM
ejpam-3903	533	18	107	107	NUM
ejpam-3903	533	19	5	5	NUM
ejpam-3903	533	20	)	)	PUNCT
ejpam-3903	533	21	vm	vm	NOUN
ejpam-3903	534	1	i	i	PRON
ejpam-3903	534	2	vm	vm	PROPN
ejpam-3903	534	3	j	j	PROPN
ejpam-3903	534	4	vm	vm	PROPN
ejpam-3903	534	5	r	r	PROPN
ejpam-3903	534	6	⇀	⇀	PROPN
ejpam-3903	534	7	wiwjwr	wiwjwr	AUX
ejpam-3903	534	8	weakly	weakly	ADV
ejpam-3903	534	9	in	in	ADP
ejpam-3903	534	10	l2(0	l2(0	NOUN
ejpam-3903	534	11	,	,	PUNCT
ejpam-3903	534	12	t	t	NOUN
ejpam-3903	534	13	;	;	PUNCT
ejpam-3903	534	14	l2(ω	l2(ω	NUM
ejpam-3903	534	15	)	)	PUNCT
ejpam-3903	534	16	)	)	PUNCT
ejpam-3903	534	17	,	,	PUNCT
ejpam-3903	534	18	6	6	X
ejpam-3903	534	19	)	)	PUNCT
ejpam-3903	534	20	vm	vm	PROPN
ejpam-3903	534	21	1	1	NUM
ejpam-3903	534	22	vm	vm	PROPN
ejpam-3903	535	1	i	i	PRON
ejpam-3903	535	2	vm	vm	PROPN
ejpam-3903	535	3	j	j	PROPN
ejpam-3903	535	4	vm	vm	PROPN
ejpam-3903	535	5	r	r	NOUN
ejpam-3903	535	6	⇀	⇀	PROPN
ejpam-3903	535	7	w1wiwjwr	w1wiwjwr	ADV
ejpam-3903	535	8	weakly	weakly	ADV
ejpam-3903	535	9	in	in	ADP
ejpam-3903	535	10	l2(0	l2(0	NOUN
ejpam-3903	535	11	,	,	PUNCT
ejpam-3903	535	12	t	t	NOUN
ejpam-3903	535	13	;	;	PUNCT
ejpam-3903	535	14	l2(ω	l2(ω	NOUN
ejpam-3903	535	15	)	)	PUNCT
ejpam-3903	535	16	)	)	PUNCT
ejpam-3903	535	17	,	,	PUNCT
ejpam-3903	535	18	with	with	ADP
ejpam-3903	535	19	1	1	NUM
ejpam-3903	535	20	≤	≤	NUM
ejpam-3903	535	21	i	i	PROPN
ejpam-3903	535	22	,	,	PUNCT
ejpam-3903	535	23	j	j	PROPN
ejpam-3903	535	24	,	,	PUNCT
ejpam-3903	535	25	r	r	NOUN
ejpam-3903	535	26	≤	≤	NUM
ejpam-3903	535	27	20	20	NUM
ejpam-3903	535	28	.	.	PUNCT
ejpam-3903	536	1	proof	proof	NOUN
ejpam-3903	536	2	.	.	PUNCT
ejpam-3903	537	1	the	the	DET
ejpam-3903	537	2	point	point	NOUN
ejpam-3903	537	3	1	1	NUM
ejpam-3903	537	4	)	)	PUNCT
ejpam-3903	537	5	is	be	AUX
ejpam-3903	537	6	a	a	DET
ejpam-3903	537	7	direct	direct	ADJ
ejpam-3903	537	8	deduction	deduction	NOUN
ejpam-3903	537	9	of	of	ADP
ejpam-3903	537	10	the	the	DET
ejpam-3903	537	11	point	point	NOUN
ejpam-3903	537	12	c	c	NOUN
ejpam-3903	537	13	)	)	PUNCT
ejpam-3903	537	14	of	of	ADP
ejpam-3903	537	15	the	the	DET
ejpam-3903	537	16	lemma	lemma	PROPN
ejpam-3903	537	17	5	5	NUM
ejpam-3903	537	18	.	.	PUNCT
ejpam-3903	538	1	form	form	VERB
ejpam-3903	538	2	the	the	DET
ejpam-3903	538	3	apriori	apriori	NOUN
ejpam-3903	538	4	estimates	estimate	NOUN
ejpam-3903	538	5	,	,	PUNCT
ejpam-3903	538	6	we	we	PRON
ejpam-3903	538	7	have	have	AUX
ejpam-3903	538	8	(	(	PUNCT
ejpam-3903	538	9	vm	vm	NOUN
ejpam-3903	538	10	i	i	PROPN
ejpam-3903	538	11	)	)	PUNCT
ejpam-3903	538	12	is	be	AUX
ejpam-3903	538	13	bounded	bound	VERB
ejpam-3903	538	14	in	in	ADP
ejpam-3903	538	15	l2(0	l2(0	PROPN
ejpam-3903	538	16	,	,	PUNCT
ejpam-3903	538	17	t	t	PROPN
ejpam-3903	538	18	;	;	PUNCT
ejpam-3903	538	19	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	538	20	)	)	PUNCT
ejpam-3903	538	21	)	)	PUNCT
ejpam-3903	538	22	,	,	PUNCT
ejpam-3903	538	23	thus	thus	ADV
ejpam-3903	538	24	(	(	PUNCT
ejpam-3903	538	25	vm	vm	PROPN
ejpam-3903	538	26	i	i	NOUN
ejpam-3903	538	27	)	)	PUNCT
ejpam-3903	538	28	converge	converge	VERB
ejpam-3903	538	29	weakly	weakly	ADV
ejpam-3903	538	30	in	in	ADP
ejpam-3903	538	31	l2(0	l2(0	NOUN
ejpam-3903	538	32	,	,	PUNCT
ejpam-3903	538	33	t	t	PROPN
ejpam-3903	538	34	;	;	PUNCT
ejpam-3903	538	35	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	538	36	)	)	PUNCT
ejpam-3903	538	37	)	)	PUNCT
ejpam-3903	538	38	.	.	PUNCT
ejpam-3903	539	1	for	for	ADP
ejpam-3903	539	2	s	s	PRON
ejpam-3903	539	3	≥	≥	NOUN
ejpam-3903	539	4	3	3	NUM
ejpam-3903	539	5	2	2	NUM
ejpam-3903	539	6	+	+	NUM
ejpam-3903	539	7	1	1	NUM
ejpam-3903	539	8	,	,	PUNCT
ejpam-3903	539	9	we	we	PRON
ejpam-3903	539	10	have	have	VERB
ejpam-3903	539	11	the	the	DET
ejpam-3903	539	12	compact	compact	ADJ
ejpam-3903	539	13	embendding	embendding	NOUN
ejpam-3903	539	14	of	of	ADP
ejpam-3903	539	15	hs−1(ω	hs−1(ω	NOUN
ejpam-3903	539	16	)	)	PUNCT
ejpam-3903	539	17	in	in	ADP
ejpam-3903	539	18	l4(ω	l4(ω	PROPN
ejpam-3903	539	19	)	)	PUNCT
ejpam-3903	539	20	(	(	PUNCT
ejpam-3903	539	21	see	see	VERB
ejpam-3903	539	22	[	[	X
ejpam-3903	539	23	2	2	NUM
ejpam-3903	539	24	]	]	NUM
ejpam-3903	539	25	)	)	PUNCT
ejpam-3903	539	26	,	,	PUNCT
ejpam-3903	539	27	so	so	CCONJ
ejpam-3903	539	28	by	by	SCONJ
ejpam-3903	539	29	the	the	DET
ejpam-3903	539	30	compacity	compacity	NOUN
ejpam-3903	539	31	theorem	theorem	NOUN
ejpam-3903	539	32	do	do	AUX
ejpam-3903	539	33	to	to	ADP
ejpam-3903	539	34	[	[	X
ejpam-3903	539	35	14	14	NUM
ejpam-3903	539	36	]	]	PUNCT
ejpam-3903	539	37	,	,	PUNCT
ejpam-3903	539	38	we	we	PRON
ejpam-3903	539	39	have	have	VERB
ejpam-3903	539	40	that	that	PRON
ejpam-3903	539	41	(	(	PUNCT
ejpam-3903	539	42	vm	vm	PROPN
ejpam-3903	539	43	i	i	NOUN
ejpam-3903	539	44	)	)	PUNCT
ejpam-3903	539	45	converge	converge	VERB
ejpam-3903	539	46	strongly	strongly	ADV
ejpam-3903	539	47	in	in	ADP
ejpam-3903	539	48	l2(0	l2(0	NOUN
ejpam-3903	539	49	,	,	PUNCT
ejpam-3903	539	50	t	t	NOUN
ejpam-3903	539	51	;	;	PUNCT
ejpam-3903	539	52	l4(ω	l4(ω	X
ejpam-3903	539	53	)	)	PUNCT
ejpam-3903	539	54	)	)	PUNCT
ejpam-3903	539	55	.	.	PUNCT
ejpam-3903	540	1	so	so	ADV
ejpam-3903	540	2	we	we	PRON
ejpam-3903	540	3	have	have	VERB
ejpam-3903	540	4	the	the	DET
ejpam-3903	540	5	point	point	NOUN
ejpam-3903	540	6	2	2	NUM
ejpam-3903	540	7	)	)	PUNCT
ejpam-3903	540	8	.	.	PUNCT
ejpam-3903	541	1	by	by	ADP
ejpam-3903	541	2	the	the	DET
ejpam-3903	541	3	same	same	ADJ
ejpam-3903	541	4	argument	argument	NOUN
ejpam-3903	541	5	one	one	PRON
ejpam-3903	541	6	can	can	AUX
ejpam-3903	541	7	obtain	obtain	VERB
ejpam-3903	541	8	the	the	DET
ejpam-3903	541	9	point	point	NOUN
ejpam-3903	541	10	3	3	NUM
ejpam-3903	541	11	)	)	PUNCT
ejpam-3903	541	12	.	.	PUNCT
ejpam-3903	542	1	for	for	ADP
ejpam-3903	542	2	the	the	DET
ejpam-3903	542	3	point	point	NOUN
ejpam-3903	542	4	4	4	NUM
ejpam-3903	542	5	)	)	PUNCT
ejpam-3903	542	6	,	,	PUNCT
ejpam-3903	542	7	we	we	PRON
ejpam-3903	542	8	have	have	VERB
ejpam-3903	542	9	(	(	PUNCT
ejpam-3903	542	10	vm	vm	NOUN
ejpam-3903	542	11	i	i	PROPN
ejpam-3903	542	12	)	)	PUNCT
ejpam-3903	542	13	and	and	CCONJ
ejpam-3903	542	14	(	(	PUNCT
ejpam-3903	542	15	vm	vm	PROPN
ejpam-3903	542	16	j	j	PROPN
ejpam-3903	542	17	)	)	PUNCT
ejpam-3903	542	18	are	be	AUX
ejpam-3903	542	19	bounded	bound	VERB
ejpam-3903	542	20	in	in	ADP
ejpam-3903	542	21	l2(0	l2(0	PROPN
ejpam-3903	542	22	,	,	PUNCT
ejpam-3903	542	23	t	t	NOUN
ejpam-3903	542	24	;	;	PUNCT
ejpam-3903	542	25	l4(ω	l4(ω	X
ejpam-3903	542	26	)	)	PUNCT
ejpam-3903	542	27	)	)	PUNCT
ejpam-3903	542	28	,	,	PUNCT
ejpam-3903	542	29	thus	thus	ADV
ejpam-3903	542	30	(	(	PUNCT
ejpam-3903	542	31	vm	vm	PROPN
ejpam-3903	542	32	i	i	PROPN
ejpam-3903	542	33	vm	vm	PROPN
ejpam-3903	542	34	j	j	PROPN
ejpam-3903	542	35	)	)	PUNCT
ejpam-3903	542	36	is	be	AUX
ejpam-3903	542	37	bounded	bound	VERB
ejpam-3903	542	38	in	in	ADP
ejpam-3903	542	39	l2(0	l2(0	PROPN
ejpam-3903	542	40	,	,	PUNCT
ejpam-3903	542	41	t	t	NOUN
ejpam-3903	542	42	;	;	PUNCT
ejpam-3903	542	43	l2(ω	l2(ω	X
ejpam-3903	542	44	)	)	PUNCT
ejpam-3903	542	45	)	)	PUNCT
ejpam-3903	542	46	hence	hence	ADV
ejpam-3903	542	47	it	it	PRON
ejpam-3903	542	48	converges	converge	VERB
ejpam-3903	542	49	weakly	weakly	ADJ
ejpam-3903	542	50	towards	towards	ADP
ejpam-3903	542	51	a	a	DET
ejpam-3903	542	52	limit	limit	NOUN
ejpam-3903	542	53	that	that	PRON
ejpam-3903	542	54	we	we	PRON
ejpam-3903	542	55	note	note	VERB
ejpam-3903	542	56	ψij	ψij	VERB
ejpam-3903	542	57	.	.	PUNCT
ejpam-3903	543	1	to	to	PART
ejpam-3903	543	2	justify	justify	VERB
ejpam-3903	543	3	the	the	DET
ejpam-3903	543	4	equality	equality	NOUN
ejpam-3903	543	5	ψij	ψij	NOUN
ejpam-3903	543	6	=	=	NOUN
ejpam-3903	543	7	wiwj	wiwj	NOUN
ejpam-3903	543	8	,	,	PUNCT
ejpam-3903	543	9	we	we	PRON
ejpam-3903	543	10	takes	take	VERB
ejpam-3903	543	11	q	q	NOUN
ejpam-3903	543	12	=	=	PUNCT
ejpam-3903	544	1	[	[	X
ejpam-3903	544	2	0	0	NUM
ejpam-3903	544	3	,	,	PUNCT
ejpam-3903	544	4	t	t	X
ejpam-3903	545	1	[	[	X
ejpam-3903	545	2	×ω	×ω	ADV
ejpam-3903	545	3	,	,	PUNCT
ejpam-3903	545	4	thus	thus	ADV
ejpam-3903	545	5	we	we	PRON
ejpam-3903	545	6	have	have	VERB
ejpam-3903	545	7	:	:	PUNCT
ejpam-3903	545	8	<	<	X
ejpam-3903	545	9	vm	vm	X
ejpam-3903	546	1	i	i	PRON
ejpam-3903	546	2	vm	vm	PROPN
ejpam-3903	546	3	j	j	PROPN
ejpam-3903	546	4	,	,	PUNCT
ejpam-3903	546	5	φ	φ	PROPN
ejpam-3903	546	6	>	>	X
ejpam-3903	547	1	=	=	X
ejpam-3903	547	2	<	<	X
ejpam-3903	547	3	vm	vm	X
ejpam-3903	547	4	i	i	PRON
ejpam-3903	547	5	,	,	PUNCT
ejpam-3903	547	6	v	v	PROPN
ejpam-3903	547	7	m	m	PROPN
ejpam-3903	547	8	j	j	PROPN
ejpam-3903	547	9	φ	φ	PROPN
ejpam-3903	547	10	>	>	PROPN
ejpam-3903	547	11	,	,	PUNCT
ejpam-3903	547	12	∀	∀	NUM
ejpam-3903	547	13	φ	φ	PROPN
ejpam-3903	547	14	∈	∈	PROPN
ejpam-3903	547	15	d(q	d(q	PROPN
ejpam-3903	547	16	)	)	PUNCT
ejpam-3903	547	17	by	by	ADP
ejpam-3903	547	18	the	the	DET
ejpam-3903	547	19	point	point	NOUN
ejpam-3903	547	20	2	2	NUM
ejpam-3903	547	21	)	)	PUNCT
ejpam-3903	547	22	,	,	PUNCT
ejpam-3903	547	23	we	we	PRON
ejpam-3903	547	24	have	have	VERB
ejpam-3903	547	25	vm	vm	PROPN
ejpam-3903	547	26	i	i	PRON
ejpam-3903	547	27	is	be	AUX
ejpam-3903	547	28	bounded	bound	VERB
ejpam-3903	547	29	in	in	ADP
ejpam-3903	547	30	l2(0	l2(0	PROPN
ejpam-3903	547	31	,	,	PUNCT
ejpam-3903	547	32	t	t	NOUN
ejpam-3903	547	33	;	;	PUNCT
ejpam-3903	547	34	l2(ω	l2(ω	NUM
ejpam-3903	547	35	)	)	PUNCT
ejpam-3903	547	36	)	)	PUNCT
ejpam-3903	547	37	,	,	PUNCT
ejpam-3903	547	38	then	then	ADV
ejpam-3903	547	39	converge	converge	VERB
ejpam-3903	547	40	weakly	weakly	ADV
ejpam-3903	547	41	,	,	PUNCT
ejpam-3903	547	42	on	on	ADP
ejpam-3903	547	43	the	the	DET
ejpam-3903	547	44	other	other	ADJ
ejpam-3903	547	45	hand	hand	NOUN
ejpam-3903	547	46	we	we	PRON
ejpam-3903	547	47	have	have	VERB
ejpam-3903	547	48	the	the	DET
ejpam-3903	547	49	strong	strong	ADJ
ejpam-3903	547	50	convergence	convergence	NOUN
ejpam-3903	547	51	of	of	ADP
ejpam-3903	547	52	vm	vm	PROPN
ejpam-3903	547	53	j	j	PROPN
ejpam-3903	547	54	φ	φ	PROPN
ejpam-3903	547	55	in	in	ADP
ejpam-3903	547	56	l2(0	l2(0	PROPN
ejpam-3903	547	57	,	,	PUNCT
ejpam-3903	547	58	t	t	NOUN
ejpam-3903	547	59	;	;	PUNCT
ejpam-3903	547	60	l2(ω	l2(ω	NUM
ejpam-3903	547	61	)	)	PUNCT
ejpam-3903	547	62	)	)	PUNCT
ejpam-3903	547	63	.	.	PUNCT
ejpam-3903	548	1	it	it	PRON
ejpam-3903	548	2	result	result	VERB
ejpam-3903	548	3	that:∫	that:∫	ADP
ejpam-3903	548	4	q	q	X
ejpam-3903	548	5	vm	vm	PROPN
ejpam-3903	549	1	i	i	PRON
ejpam-3903	549	2	vm	vm	PROPN
ejpam-3903	549	3	j	j	PROPN
ejpam-3903	549	4	φ	φ	PROPN
ejpam-3903	549	5	dxdt	dxdt	PROPN
ejpam-3903	550	1	−→	−→	ADJ
ejpam-3903	550	2	∫	∫	PROPN
ejpam-3903	550	3	q	q	PROPN
ejpam-3903	550	4	wiwjφ	wiwjφ	PROPN
ejpam-3903	550	5	dxdt	dxdt	PROPN
ejpam-3903	550	6	∀	∀	X
ejpam-3903	550	7	φ	φ	PROPN
ejpam-3903	550	8	∈	∈	PROPN
ejpam-3903	550	9	d(q	d(q	PROPN
ejpam-3903	550	10	)	)	PUNCT
ejpam-3903	550	11	.	.	PUNCT
ejpam-3903	551	1	for	for	ADP
ejpam-3903	551	2	the	the	DET
ejpam-3903	551	3	point	point	NOUN
ejpam-3903	551	4	5	5	NUM
ejpam-3903	551	5	)	)	PUNCT
ejpam-3903	551	6	,	,	PUNCT
ejpam-3903	551	7	given	give	VERB
ejpam-3903	551	8	that	that	SCONJ
ejpam-3903	551	9	(	(	PUNCT
ejpam-3903	551	10	3	3	NUM
ejpam-3903	551	11	2	2	NUM
ejpam-3903	551	12	,	,	PUNCT
ejpam-3903	551	13	3	3	NUM
ejpam-3903	551	14	)	)	PUNCT
ejpam-3903	551	15	are	be	AUX
ejpam-3903	551	16	conjugate	conjugate	ADJ
ejpam-3903	551	17	,	,	PUNCT
ejpam-3903	551	18	we	we	PRON
ejpam-3903	551	19	have	have	VERB
ejpam-3903	551	20	the	the	DET
ejpam-3903	551	21	following	follow	VERB
ejpam-3903	551	22	estimate	estimate	NOUN
ejpam-3903	551	23	:	:	PUNCT
ejpam-3903	551	24	‖(vm	‖(vm	PROPN
ejpam-3903	552	1	i	i	PRON
ejpam-3903	552	2	vm	vm	PROPN
ejpam-3903	552	3	j	j	PROPN
ejpam-3903	552	4	vm	vm	PROPN
ejpam-3903	552	5	r	r	PROPN
ejpam-3903	552	6	)	)	PUNCT
ejpam-3903	552	7	(	(	PUNCT
ejpam-3903	552	8	t)‖2l2	t)‖2l2	PROPN
ejpam-3903	552	9	≤	≤	PROPN
ejpam-3903	552	10	‖(vm	‖(vm	VERB
ejpam-3903	552	11	i	i	PRON
ejpam-3903	552	12	vm	vm	PROPN
ejpam-3903	552	13	j	j	PROPN
ejpam-3903	552	14	)	)	PUNCT
ejpam-3903	552	15	(	(	PUNCT
ejpam-3903	552	16	t)‖2l3‖vr(t)‖2l6	t)‖2l3‖vr(t)‖2l6	NUM
ejpam-3903	552	17	≤	≤	NOUN
ejpam-3903	552	18	(	(	PUNCT
ejpam-3903	552	19	‖vm	‖vm	NUM
ejpam-3903	552	20	i	i	PRON
ejpam-3903	552	21	(	(	PUNCT
ejpam-3903	552	22	t)‖l6‖vm	t)‖l6‖vm	PROPN
ejpam-3903	552	23	j	j	PROPN
ejpam-3903	552	24	(	(	PUNCT
ejpam-3903	552	25	t)‖l6‖vm	t)‖l6‖vm	PROPN
ejpam-3903	552	26	r	r	NOUN
ejpam-3903	552	27	(	(	PUNCT
ejpam-3903	552	28	t)‖l6	t)‖l6	PROPN
ejpam-3903	552	29	)	)	PUNCT
ejpam-3903	552	30	2	2	NUM
ejpam-3903	552	31	.	.	PUNCT
ejpam-3903	553	1	the	the	DET
ejpam-3903	553	2	sequence	sequence	NOUN
ejpam-3903	553	3	(	(	PUNCT
ejpam-3903	553	4	vm	vm	PROPN
ejpam-3903	553	5	i	i	PRON
ejpam-3903	553	6	vm	vm	PROPN
ejpam-3903	553	7	j	j	PROPN
ejpam-3903	553	8	vm	vm	PROPN
ejpam-3903	553	9	r	r	PROPN
ejpam-3903	553	10	)	)	PUNCT
ejpam-3903	553	11	is	be	AUX
ejpam-3903	553	12	then	then	ADV
ejpam-3903	553	13	bounded	bound	VERB
ejpam-3903	553	14	in	in	ADP
ejpam-3903	553	15	l2(0	l2(0	PROPN
ejpam-3903	553	16	,	,	PUNCT
ejpam-3903	553	17	t	t	NOUN
ejpam-3903	553	18	;	;	PUNCT
ejpam-3903	553	19	l2(ω	l2(ω	NUM
ejpam-3903	553	20	)	)	PUNCT
ejpam-3903	553	21	)	)	PUNCT
ejpam-3903	554	1	so	so	SCONJ
ejpam-3903	554	2	it	it	PRON
ejpam-3903	554	3	converges	converge	VERB
ejpam-3903	554	4	weakly	weakly	ADJ
ejpam-3903	554	5	towards	towards	ADP
ejpam-3903	554	6	φijr	φijr	PROPN
ejpam-3903	554	7	.	.	PUNCT
ejpam-3903	555	1	for	for	ADP
ejpam-3903	555	2	the	the	DET
ejpam-3903	555	3	equality	equality	NOUN
ejpam-3903	555	4	φijr	φijr	PROPN
ejpam-3903	555	5	=	=	PUNCT
ejpam-3903	555	6	wiwjwr	wiwjwr	NOUN
ejpam-3903	555	7	,	,	PUNCT
ejpam-3903	555	8	we	we	PRON
ejpam-3903	555	9	juste	juste	VERB
ejpam-3903	555	10	follow	follow	VERB
ejpam-3903	555	11	the	the	DET
ejpam-3903	555	12	same	same	ADJ
ejpam-3903	555	13	way	way	NOUN
ejpam-3903	555	14	as	as	ADV
ejpam-3903	555	15	previously	previously	ADV
ejpam-3903	555	16	.	.	PUNCT
ejpam-3903	556	1	the	the	DET
ejpam-3903	556	2	point	point	NOUN
ejpam-3903	556	3	6	6	NUM
ejpam-3903	556	4	)	)	PUNCT
ejpam-3903	556	5	is	be	AUX
ejpam-3903	556	6	a	a	DET
ejpam-3903	556	7	deduction	deduction	NOUN
ejpam-3903	556	8	of	of	ADP
ejpam-3903	556	9	1	1	NUM
ejpam-3903	556	10	)	)	PUNCT
ejpam-3903	556	11	and	and	CCONJ
ejpam-3903	556	12	5	5	NUM
ejpam-3903	556	13	)	)	PUNCT
ejpam-3903	556	14	.	.	PUNCT
ejpam-3903	557	1	�	�	PROPN
ejpam-3903	557	2	lemma	lemma	PROPN
ejpam-3903	557	3	7	7	X
ejpam-3903	557	4	.	.	PUNCT
ejpam-3903	558	1	under	under	ADP
ejpam-3903	558	2	the	the	DET
ejpam-3903	558	3	same	same	ADJ
ejpam-3903	558	4	assumptions	assumption	NOUN
ejpam-3903	558	5	like	like	ADP
ejpam-3903	558	6	in	in	ADP
ejpam-3903	558	7	the	the	DET
ejpam-3903	558	8	lemma	lemma	PROPN
ejpam-3903	558	9	5	5	NUM
ejpam-3903	558	10	,	,	PUNCT
ejpam-3903	558	11	the	the	DET
ejpam-3903	558	12	following	follow	VERB
ejpam-3903	558	13	convergence	convergence	NOUN
ejpam-3903	558	14	hold	hold	VERB
ejpam-3903	558	15	:	:	PUNCT
ejpam-3903	558	16	a0v	a0v	PROPN
ejpam-3903	558	17	m	m	VERB
ejpam-3903	558	18	d	d	NOUN
ejpam-3903	558	19	dt	dt	X
ejpam-3903	558	20	(	(	PUNCT
ejpam-3903	558	21	a0v	a0v	PROPN
ejpam-3903	558	22	∗	∗	PROPN
ejpam-3903	558	23	m	m	PROPN
ejpam-3903	558	24	)	)	PUNCT
ejpam-3903	559	1	⇀	⇀	PROPN
ejpam-3903	560	1	a0v	a0v	PROPN
ejpam-3903	561	1	d	d	X
ejpam-3903	561	2	dt	dt	X
ejpam-3903	561	3	(	(	PUNCT
ejpam-3903	561	4	a0v	a0v	PROPN
ejpam-3903	561	5	)	)	PUNCT
ejpam-3903	561	6	weakly	weakly	ADJ
ejpam-3903	561	7	in	in	ADP
ejpam-3903	561	8	l2(0	l2(0	PROPN
ejpam-3903	561	9	,	,	PUNCT
ejpam-3903	561	10	t	t	PROPN
ejpam-3903	561	11	;	;	PUNCT
ejpam-3903	561	12	l2(ω))20	l2(ω))20	X
ejpam-3903	561	13	.	.	PUNCT
ejpam-3903	561	14	proof	proof	NOUN
ejpam-3903	561	15	.	.	PUNCT
ejpam-3903	562	1	from	from	ADP
ejpam-3903	562	2	the	the	DET
ejpam-3903	562	3	estimation	estimation	NOUN
ejpam-3903	562	4	ii	ii	PROPN
ejpam-3903	562	5	)	)	PUNCT
ejpam-3903	562	6	of	of	ADP
ejpam-3903	562	7	the	the	DET
ejpam-3903	562	8	lemma	lemma	PROPN
ejpam-3903	562	9	4	4	NUM
ejpam-3903	562	10	we	we	PRON
ejpam-3903	562	11	deduce	deduce	VERB
ejpam-3903	562	12	that	that	SCONJ
ejpam-3903	562	13	a0v	a0v	PROPN
ejpam-3903	562	14	m	m	PROPN
ejpam-3903	562	15	d	d	NOUN
ejpam-3903	562	16	dt	dt	X
ejpam-3903	562	17	(	(	PUNCT
ejpam-3903	562	18	a0v	a0v	PROPN
ejpam-3903	562	19	∗	∗	PROPN
ejpam-3903	562	20	m	m	PROPN
ejpam-3903	562	21	)	)	PUNCT
ejpam-3903	562	22	is	be	AUX
ejpam-3903	562	23	bounded	bound	VERB
ejpam-3903	562	24	in	in	ADP
ejpam-3903	562	25	l2(0	l2(0	PROPN
ejpam-3903	562	26	,	,	PUNCT
ejpam-3903	562	27	t	t	NOUN
ejpam-3903	562	28	;	;	PUNCT
ejpam-3903	562	29	l2(ω)20	l2(ω)20	NUM
ejpam-3903	562	30	)	)	PUNCT
ejpam-3903	562	31	,	,	PUNCT
ejpam-3903	562	32	hence	hence	ADV
ejpam-3903	562	33	it	it	PRON
ejpam-3903	562	34	follow	follow	VERB
ejpam-3903	562	35	the	the	DET
ejpam-3903	562	36	weak	weak	ADJ
ejpam-3903	562	37	converge	converge	NOUN
ejpam-3903	562	38	to	to	ADP
ejpam-3903	562	39	φ	φ	PROPN
ejpam-3903	562	40	in	in	ADP
ejpam-3903	562	41	the	the	DET
ejpam-3903	562	42	same	same	ADJ
ejpam-3903	562	43	space	space	NOUN
ejpam-3903	562	44	.	.	PUNCT
ejpam-3903	563	1	to	to	PART
ejpam-3903	563	2	justify	justify	VERB
ejpam-3903	563	3	the	the	DET
ejpam-3903	563	4	equality	equality	NOUN
ejpam-3903	563	5	φ	φ	NOUN
ejpam-3903	563	6	=	=	SYM
ejpam-3903	563	7	a0v	a0v	PROPN
ejpam-3903	563	8	d	d	X
ejpam-3903	563	9	dt	dt	X
ejpam-3903	563	10	(	(	PUNCT
ejpam-3903	563	11	a0v	a0v	PROPN
ejpam-3903	563	12	)	)	PUNCT
ejpam-3903	563	13	,	,	PUNCT
ejpam-3903	563	14	we	we	PRON
ejpam-3903	563	15	have	have	VERB
ejpam-3903	563	16	:	:	PUNCT
ejpam-3903	563	17	firstly	firstly	ADV
ejpam-3903	563	18	the	the	DET
ejpam-3903	563	19	estimate	estimate	NOUN
ejpam-3903	563	20	i	i	X
ejpam-3903	563	21	)	)	PUNCT
ejpam-3903	563	22	of	of	ADP
ejpam-3903	563	23	lemma	lemma	PROPN
ejpam-3903	563	24	4	4	NUM
ejpam-3903	563	25	r.	r.	PROPN
ejpam-3903	563	26	bade	bade	PROPN
ejpam-3903	563	27	,	,	PUNCT
ejpam-3903	563	28	h.	h.	PROPN
ejpam-3903	563	29	chaker	chaker	PROPN
ejpam-3903	563	30	/	/	SYM
ejpam-3903	563	31	eur	eur	PROPN
ejpam-3903	563	32	.	.	PUNCT
ejpam-3903	564	1	j.	j.	PROPN
ejpam-3903	564	2	pure	pure	PROPN
ejpam-3903	564	3	appl	appl	PROPN
ejpam-3903	564	4	.	.	PROPN
ejpam-3903	564	5	math	math	PROPN
ejpam-3903	564	6	,	,	PUNCT
ejpam-3903	564	7	14	14	NUM
ejpam-3903	564	8	(	(	PUNCT
ejpam-3903	564	9	1	1	NUM
ejpam-3903	564	10	)	)	PUNCT
ejpam-3903	564	11	(	(	PUNCT
ejpam-3903	564	12	2021	2021	NUM
ejpam-3903	564	13	)	)	PUNCT
ejpam-3903	564	14	,	,	PUNCT
ejpam-3903	564	15	82	82	NUM
ejpam-3903	564	16	-	-	SYM
ejpam-3903	564	17	111	111	NUM
ejpam-3903	564	18	108	108	NUM
ejpam-3903	564	19	guarantees	guarantee	VERB
ejpam-3903	564	20	the	the	DET
ejpam-3903	564	21	weak	weak	ADJ
ejpam-3903	564	22	convergence	convergence	NOUN
ejpam-3903	564	23	of	of	ADP
ejpam-3903	564	24	a0v	a0v	PROPN
ejpam-3903	564	25	m	m	VERB
ejpam-3903	564	26	in	in	ADP
ejpam-3903	564	27	l∞(0	l∞(0	PRON
ejpam-3903	564	28	,	,	PUNCT
ejpam-3903	564	29	t	t	NOUN
ejpam-3903	564	30	;	;	PUNCT
ejpam-3903	564	31	hs(ω	hs(ω	NUM
ejpam-3903	564	32	)	)	PUNCT
ejpam-3903	564	33	)	)	PUNCT
ejpam-3903	565	1	and	and	CCONJ
ejpam-3903	565	2	due	due	ADP
ejpam-3903	565	3	to	to	ADP
ejpam-3903	565	4	the	the	DET
ejpam-3903	565	5	compact	compact	ADJ
ejpam-3903	565	6	embendding	embendding	NOUN
ejpam-3903	565	7	hs(ω	hs(ω	NUM
ejpam-3903	565	8	)	)	PUNCT
ejpam-3903	565	9	↪	↪	PROPN
ejpam-3903	565	10	→	→	SYM
ejpam-3903	565	11	l2(ω	l2(ω	NUM
ejpam-3903	565	12	)	)	PUNCT
ejpam-3903	565	13	,	,	PUNCT
ejpam-3903	565	14	we	we	PRON
ejpam-3903	565	15	have	have	VERB
ejpam-3903	565	16	the	the	DET
ejpam-3903	565	17	strong	strong	ADJ
ejpam-3903	565	18	convergence	convergence	NOUN
ejpam-3903	565	19	of	of	ADP
ejpam-3903	565	20	a0v	a0v	PROPN
ejpam-3903	565	21	m	m	VERB
ejpam-3903	565	22	in	in	ADP
ejpam-3903	565	23	l∞(0	l∞(0	PRON
ejpam-3903	565	24	,	,	PUNCT
ejpam-3903	565	25	t	t	NOUN
ejpam-3903	565	26	;	;	PUNCT
ejpam-3903	565	27	l2(ω	l2(ω	NUM
ejpam-3903	565	28	)	)	PUNCT
ejpam-3903	565	29	)	)	PUNCT
ejpam-3903	565	30	,	,	PUNCT
ejpam-3903	565	31	and	and	CCONJ
ejpam-3903	565	32	as	as	ADP
ejpam-3903	565	33	t	t	PROPN
ejpam-3903	565	34	<	<	X
ejpam-3903	565	35	∞	∞	PROPN
ejpam-3903	565	36	,	,	PUNCT
ejpam-3903	565	37	the	the	DET
ejpam-3903	565	38	strong	strong	ADJ
ejpam-3903	565	39	convergence	convergence	NOUN
ejpam-3903	565	40	also	also	ADV
ejpam-3903	565	41	holds	hold	VERB
ejpam-3903	565	42	in	in	ADP
ejpam-3903	565	43	l2(0	l2(0	NOUN
ejpam-3903	565	44	,	,	PUNCT
ejpam-3903	565	45	t	t	NOUN
ejpam-3903	565	46	;	;	PUNCT
ejpam-3903	565	47	l2(ω	l2(ω	NUM
ejpam-3903	565	48	)	)	PUNCT
ejpam-3903	565	49	)	)	PUNCT
ejpam-3903	565	50	.	.	PUNCT
ejpam-3903	566	1	and	and	CCONJ
ejpam-3903	566	2	secondly	secondly	ADV
ejpam-3903	566	3	,	,	PUNCT
ejpam-3903	566	4	the	the	DET
ejpam-3903	566	5	point	point	NOUN
ejpam-3903	566	6	d	d	NOUN
ejpam-3903	566	7	)	)	PUNCT
ejpam-3903	566	8	of	of	ADP
ejpam-3903	566	9	lemma	lemma	PROPN
ejpam-3903	566	10	7	7	NUM
ejpam-3903	566	11	gives	give	VERB
ejpam-3903	566	12	us	we	PRON
ejpam-3903	566	13	the	the	DET
ejpam-3903	566	14	weak	weak	ADJ
ejpam-3903	566	15	convergence	convergence	NOUN
ejpam-3903	566	16	of	of	ADP
ejpam-3903	566	17	d	d	X
ejpam-3903	566	18	dt	dt	X
ejpam-3903	566	19	(	(	PUNCT
ejpam-3903	566	20	a0v	a0v	PROPN
ejpam-3903	566	21	∗	∗	PROPN
ejpam-3903	566	22	m	m	PROPN
ejpam-3903	566	23	)	)	PUNCT
ejpam-3903	566	24	in	in	ADP
ejpam-3903	566	25	l2(0	l2(0	NOUN
ejpam-3903	566	26	,	,	PUNCT
ejpam-3903	566	27	t	t	NOUN
ejpam-3903	566	28	;	;	PUNCT
ejpam-3903	566	29	l2(ω))5	l2(ω))5	NOUN
ejpam-3903	566	30	.	.	PUNCT
ejpam-3903	567	1	thus	thus	ADV
ejpam-3903	567	2	,	,	PUNCT
ejpam-3903	567	3	equality	equality	NOUN
ejpam-3903	567	4	is	be	AUX
ejpam-3903	567	5	obtained	obtain	VERB
ejpam-3903	567	6	in	in	ADP
ejpam-3903	567	7	the	the	DET
ejpam-3903	567	8	same	same	ADJ
ejpam-3903	567	9	way	way	NOUN
ejpam-3903	567	10	as	as	ADV
ejpam-3903	567	11	previously	previously	ADV
ejpam-3903	567	12	.	.	PUNCT
ejpam-3903	568	1	�	�	PROPN
ejpam-3903	568	2	lemma	lemma	PROPN
ejpam-3903	568	3	8	8	NUM
ejpam-3903	568	4	.	.	PUNCT
ejpam-3903	568	5	kε(v	kε(v	PROPN
ejpam-3903	569	1	m)vm	m)vm	PROPN
ejpam-3903	569	2	⇀	⇀	PROPN
ejpam-3903	569	3	kε(w)w	kε(w)w	VERB
ejpam-3903	569	4	weakly	weakly	ADJ
ejpam-3903	569	5	in	in	ADP
ejpam-3903	569	6	l2(0	l2(0	NOUN
ejpam-3903	569	7	,	,	PUNCT
ejpam-3903	569	8	t	t	PROPN
ejpam-3903	569	9	;	;	PUNCT
ejpam-3903	569	10	l2(ω))20	l2(ω))20	NUM
ejpam-3903	569	11	when	when	SCONJ
ejpam-3903	569	12	m→∞	m→∞	NOUN
ejpam-3903	569	13	proof	proof	NOUN
ejpam-3903	569	14	.	.	PUNCT
ejpam-3903	570	1	performing	perform	VERB
ejpam-3903	570	2	the	the	DET
ejpam-3903	570	3	vector	vector	NOUN
ejpam-3903	570	4	-	-	PUNCT
ejpam-3903	570	5	matrix	matrix	NOUN
ejpam-3903	570	6	product	product	NOUN
ejpam-3903	570	7	kε(v	kε(v	PROPN
ejpam-3903	570	8	m)vm	m)vm	PROPN
ejpam-3903	570	9	,	,	PUNCT
ejpam-3903	570	10	the	the	DET
ejpam-3903	570	11	result	result	NOUN
ejpam-3903	570	12	is	be	AUX
ejpam-3903	570	13	a	a	DET
ejpam-3903	570	14	consequence	consequence	NOUN
ejpam-3903	570	15	of	of	ADP
ejpam-3903	570	16	the	the	DET
ejpam-3903	570	17	lemma	lemma	PROPN
ejpam-3903	570	18	6	6	NUM
ejpam-3903	570	19	.	.	PUNCT
ejpam-3903	570	20	�	�	PROPN
ejpam-3903	570	21	we	we	PRON
ejpam-3903	570	22	now	now	ADV
ejpam-3903	570	23	be	be	VERB
ejpam-3903	570	24	able	able	ADJ
ejpam-3903	570	25	to	to	PART
ejpam-3903	570	26	pass	pass	VERB
ejpam-3903	570	27	to	to	ADP
ejpam-3903	570	28	the	the	DET
ejpam-3903	570	29	limit	limit	NOUN
ejpam-3903	570	30	in	in	ADP
ejpam-3903	570	31	the	the	DET
ejpam-3903	570	32	weak	weak	ADJ
ejpam-3903	570	33	sense	sense	NOUN
ejpam-3903	570	34	in	in	ADP
ejpam-3903	570	35	the	the	DET
ejpam-3903	570	36	following	follow	VERB
ejpam-3903	570	37	system	system	NOUN
ejpam-3903	570	38	:	:	PUNCT
ejpam-3903	570	39	<	<	X
ejpam-3903	570	40	a0(vm	a0(vm	PROPN
ejpam-3903	570	41	)	)	PUNCT
ejpam-3903	570	42	d	d	NOUN
ejpam-3903	570	43	dt	dt	X
ejpam-3903	570	44	(	(	PUNCT
ejpam-3903	570	45	a0(v∗m	a0(v∗m	NOUN
ejpam-3903	570	46	)	)	PUNCT
ejpam-3903	570	47	)	)	PUNCT
ejpam-3903	570	48	,	,	PUNCT
ejpam-3903	570	49	φ	φ	X
ejpam-3903	570	50	>	>	X
ejpam-3903	571	1	+	+	X
ejpam-3903	571	2	<	<	X
ejpam-3903	571	3	3∑	3∑	NUM
ejpam-3903	571	4	i=1	i=1	NOUN
ejpam-3903	571	5	aiε	aiε	CCONJ
ejpam-3903	571	6	∂v∗m	∂v∗m	PROPN
ejpam-3903	571	7	∂xi	∂xi	PROPN
ejpam-3903	571	8	,	,	PUNCT
ejpam-3903	571	9	φ	φ	PROPN
ejpam-3903	571	10	>	>	X
ejpam-3903	572	1	+	+	X
ejpam-3903	572	2	<	<	X
ejpam-3903	572	3	kε(v	kε(v	X
ejpam-3903	572	4	m)v∗m	m)v∗m	X
ejpam-3903	572	5	,	,	PUNCT
ejpam-3903	572	6	φ	φ	NOUN
ejpam-3903	572	7	>	>	X
ejpam-3903	572	8	=	=	X
ejpam-3903	572	9	<	<	X
ejpam-3903	572	10	f	f	PROPN
ejpam-3903	572	11	,	,	PUNCT
ejpam-3903	572	12	φ	φ	PROPN
ejpam-3903	572	13	>	>	X
ejpam-3903	572	14	,	,	PUNCT
ejpam-3903	572	15	∀φ	∀φ	X
ejpam-3903	572	16	∈	∈	PROPN
ejpam-3903	572	17	d(q)20	d(q)20	VERB
ejpam-3903	572	18	with	with	ADP
ejpam-3903	572	19	q	q	NOUN
ejpam-3903	572	20	=	=	PUNCT
ejpam-3903	573	1	[	[	X
ejpam-3903	573	2	0	0	NUM
ejpam-3903	573	3	,	,	PUNCT
ejpam-3903	573	4	t	t	X
ejpam-3903	574	1	[	[	X
ejpam-3903	574	2	×ω	×ω	X
ejpam-3903	574	3	.	.	PUNCT
ejpam-3903	575	1	applying	apply	VERB
ejpam-3903	575	2	the	the	DET
ejpam-3903	575	3	lemmas	lemma	NOUN
ejpam-3903	575	4	7	7	NUM
ejpam-3903	575	5	and	and	CCONJ
ejpam-3903	575	6	8	8	NUM
ejpam-3903	575	7	we	we	PRON
ejpam-3903	575	8	get	get	VERB
ejpam-3903	575	9	:	:	PUNCT
ejpam-3903	575	10	for	for	ADP
ejpam-3903	575	11	all	all	DET
ejpam-3903	575	12	test	test	NOUN
ejpam-3903	575	13	function	function	NOUN
ejpam-3903	575	14	φ	φ	PROPN
ejpam-3903	575	15	∈	∈	PROPN
ejpam-3903	576	1	d(q)20	d(q)20	PROPN
ejpam-3903	576	2	:	:	PUNCT
ejpam-3903	576	3	<	<	X
ejpam-3903	576	4	a0(wε	a0(wε	NUM
ejpam-3903	576	5	)	)	PUNCT
ejpam-3903	576	6	∂	∂	NOUN
ejpam-3903	577	1	∂t	∂t	PROPN
ejpam-3903	577	2	(	(	PUNCT
ejpam-3903	577	3	a0(wε	a0(wε	PROPN
ejpam-3903	577	4	)	)	PUNCT
ejpam-3903	577	5	)	)	PUNCT
ejpam-3903	577	6	,	,	PUNCT
ejpam-3903	577	7	φ	φ	X
ejpam-3903	577	8	>	>	X
ejpam-3903	578	1	+	+	X
ejpam-3903	578	2	<	<	X
ejpam-3903	578	3	3∑	3∑	NUM
ejpam-3903	578	4	i=1	i=1	PROPN
ejpam-3903	578	5	aiε	aiε	ADJ
ejpam-3903	578	6	∂wε	∂wε	PROPN
ejpam-3903	578	7	∂xi	∂xi	PROPN
ejpam-3903	578	8	,	,	PUNCT
ejpam-3903	578	9	φ	φ	PROPN
ejpam-3903	578	10	>	>	X
ejpam-3903	579	1	+	+	CCONJ
ejpam-3903	579	2	<	<	X
ejpam-3903	579	3	kε(w	kε(w	PRON
ejpam-3903	579	4	ε)wε	ε)wε	PROPN
ejpam-3903	579	5	,	,	PUNCT
ejpam-3903	579	6	φ	φ	NOUN
ejpam-3903	579	7	>	>	X
ejpam-3903	579	8	=	=	X
ejpam-3903	579	9	<	<	X
ejpam-3903	579	10	f	f	PROPN
ejpam-3903	579	11	,	,	PUNCT
ejpam-3903	579	12	φ	φ	PROPN
ejpam-3903	579	13	>	>	X
ejpam-3903	579	14	,	,	PUNCT
ejpam-3903	579	15	hence	hence	ADV
ejpam-3903	579	16	a0w	a0w	PROPN
ejpam-3903	579	17	ε	ε	PROPN
ejpam-3903	579	18	is	be	AUX
ejpam-3903	579	19	a	a	DET
ejpam-3903	579	20	weak	weak	ADJ
ejpam-3903	579	21	solution	solution	NOUN
ejpam-3903	579	22	of	of	ADP
ejpam-3903	579	23	the	the	DET
ejpam-3903	579	24	system	system	NOUN
ejpam-3903	579	25	(	(	PUNCT
ejpam-3903	579	26	3	3	NUM
ejpam-3903	579	27	)	)	PUNCT
ejpam-3903	579	28	.	.	PUNCT
ejpam-3903	580	1	�	�	PROPN
ejpam-3903	580	2	5	5	NUM
ejpam-3903	580	3	.	.	PUNCT
ejpam-3903	581	1	passing	pass	VERB
ejpam-3903	581	2	to	to	PART
ejpam-3903	581	3	limit	limit	VERB
ejpam-3903	581	4	ε	ε	PROPN
ejpam-3903	581	5	−→	−→	NOUN
ejpam-3903	581	6	0	0	NUM
ejpam-3903	581	7	,	,	PUNCT
ejpam-3903	581	8	démonstration	démonstration	PROPN
ejpam-3903	581	9	of	of	ADP
ejpam-3903	581	10	the	the	DET
ejpam-3903	581	11	theorem	theorem	NOUN
ejpam-3903	581	12	2	2	NUM
ejpam-3903	581	13	in	in	ADP
ejpam-3903	581	14	this	this	DET
ejpam-3903	581	15	section	section	NOUN
ejpam-3903	581	16	,	,	PUNCT
ejpam-3903	581	17	we	we	PRON
ejpam-3903	581	18	will	will	AUX
ejpam-3903	581	19	pass	pass	VERB
ejpam-3903	581	20	to	to	ADP
ejpam-3903	581	21	the	the	DET
ejpam-3903	581	22	limit	limit	NOUN
ejpam-3903	581	23	ε→	ε→	X
ejpam-3903	581	24	0	0	NUM
ejpam-3903	582	1	in	in	ADP
ejpam-3903	582	2	wε	wε	NUM
ejpam-3903	582	3	solution	solution	NOUN
ejpam-3903	582	4	of	of	ADP
ejpam-3903	582	5	(	(	PUNCT
ejpam-3903	582	6	3	3	NUM
ejpam-3903	582	7	)	)	PUNCT
ejpam-3903	582	8	.	.	PUNCT
ejpam-3903	583	1	by	by	ADP
ejpam-3903	583	2	definition	definition	NOUN
ejpam-3903	583	3	of	of	ADP
ejpam-3903	583	4	the	the	DET
ejpam-3903	583	5	matrix	matrix	NOUN
ejpam-3903	583	6	a0	a0	NOUN
ejpam-3903	583	7	,	,	PUNCT
ejpam-3903	583	8	we	we	PRON
ejpam-3903	583	9	have	have	VERB
ejpam-3903	583	10	:	:	PUNCT
ejpam-3903	583	11	a0w	a0w	NOUN
ejpam-3903	583	12	ε	ε	X
ejpam-3903	583	13	=	=	PUNCT
ejpam-3903	583	14	(	(	PUNCT
ejpam-3903	583	15	ρε	ρε	PROPN
ejpam-3903	583	16	,	,	PUNCT
ejpam-3903	583	17	uε	uε	NOUN
ejpam-3903	583	18	,	,	PUNCT
ejpam-3903	583	19	θε	θε	NOUN
ejpam-3903	583	20	,	,	PUNCT
ejpam-3903	583	21	0	0	NUM
ejpam-3903	583	22	,	,	PUNCT
ejpam-3903	583	23	.	.	PUNCT
ejpam-3903	583	24	.	.	PUNCT
ejpam-3903	583	25	.	.	PUNCT
ejpam-3903	584	1	,	,	PUNCT
ejpam-3903	584	2	0)t	0)t	INTJ
ejpam-3903	584	3	.	.	PUNCT
ejpam-3903	585	1	so	so	ADV
ejpam-3903	585	2	by	by	ADP
ejpam-3903	585	3	the	the	DET
ejpam-3903	585	4	theorem	theorem	NOUN
ejpam-3903	585	5	1	1	NUM
ejpam-3903	585	6	we	we	PRON
ejpam-3903	585	7	have	have	VERB
ejpam-3903	585	8	:	:	PUNCT
ejpam-3903	585	9	‖a0w	‖a0w	PROPN
ejpam-3903	585	10	ε‖∞,s	ε‖∞,s	NOUN
ejpam-3903	585	11	6	6	NUM
ejpam-3903	585	12	c	c	NOUN
ejpam-3903	585	13	and	and	CCONJ
ejpam-3903	585	14	‖d0w	‖d0w	VERB
ejpam-3903	585	15	ε‖2,s−1	ε‖2,s−1	NOUN
ejpam-3903	585	16	6	6	NUM
ejpam-3903	585	17	c	c	NOUN
ejpam-3903	585	18	where	where	SCONJ
ejpam-3903	585	19	c	c	NOUN
ejpam-3903	585	20	is	be	AUX
ejpam-3903	585	21	a	a	DET
ejpam-3903	585	22	positive	positive	ADJ
ejpam-3903	585	23	constant	constant	ADJ
ejpam-3903	585	24	independente	independente	NOUN
ejpam-3903	585	25	to	to	ADP
ejpam-3903	585	26	ε	ε	PROPN
ejpam-3903	585	27	and	and	CCONJ
ejpam-3903	585	28	d0	d0	PROPN
ejpam-3903	585	29	∈m(r20	∈m(r20	NUM
ejpam-3903	585	30	)	)	PUNCT
ejpam-3903	585	31	a	a	DET
ejpam-3903	585	32	matrix	matrix	NOUN
ejpam-3903	585	33	given	give	VERB
ejpam-3903	585	34	by	by	ADP
ejpam-3903	585	35	:	:	PUNCT
ejpam-3903	585	36	(	(	PUNCT
ejpam-3903	585	37	d0)ij	d0)ij	NOUN
ejpam-3903	585	38	=	=	SYM
ejpam-3903	585	39	{	{	PUNCT
ejpam-3903	585	40	1	1	NUM
ejpam-3903	585	41	if	if	SCONJ
ejpam-3903	585	42	i	i	PRON
ejpam-3903	585	43	=	=	SYM
ejpam-3903	585	44	j	j	PROPN
ejpam-3903	585	45	with	with	ADP
ejpam-3903	585	46	i	i	PRON
ejpam-3903	585	47	/∈	/∈	PUNCT
ejpam-3903	586	1	(	(	PUNCT
ejpam-3903	586	2	6	6	NUM
ejpam-3903	586	3	,	,	PUNCT
ejpam-3903	586	4	11	11	NUM
ejpam-3903	586	5	,	,	PUNCT
ejpam-3903	586	6	16	16	NUM
ejpam-3903	586	7	)	)	PUNCT
ejpam-3903	586	8	0	0	PUNCT
ejpam-3903	587	1	if	if	SCONJ
ejpam-3903	587	2	not	not	PART
ejpam-3903	587	3	(	(	PUNCT
ejpam-3903	587	4	88	88	NUM
ejpam-3903	587	5	)	)	PUNCT
ejpam-3903	587	6	then	then	ADV
ejpam-3903	587	7	,	,	PUNCT
ejpam-3903	587	8	extracting	extract	VERB
ejpam-3903	587	9	subsequence	subsequence	NOUN
ejpam-3903	587	10	if	if	SCONJ
ejpam-3903	587	11	necessary	necessary	ADJ
ejpam-3903	587	12	,	,	PUNCT
ejpam-3903	587	13	we	we	PRON
ejpam-3903	587	14	have	have	VERB
ejpam-3903	587	15	the	the	DET
ejpam-3903	587	16	convergence	convergence	NOUN
ejpam-3903	587	17	of	of	ADP
ejpam-3903	587	18	wε	wε	PRON
ejpam-3903	587	19	to	to	PART
ejpam-3903	587	20	w	w	VERB
ejpam-3903	587	21	in	in	ADP
ejpam-3903	587	22	l∞(0	l∞(0	ADJ
ejpam-3903	587	23	,	,	PUNCT
ejpam-3903	587	24	t	t	PROPN
ejpam-3903	587	25	,	,	PUNCT
ejpam-3903	587	26	hs(ω))20	hs(ω))20	PROPN
ejpam-3903	587	27	.	.	PUNCT
ejpam-3903	588	1	it	it	PRON
ejpam-3903	588	2	remains	remain	VERB
ejpam-3903	588	3	now	now	ADV
ejpam-3903	588	4	to	to	PART
ejpam-3903	588	5	verify	verify	VERB
ejpam-3903	588	6	that	that	SCONJ
ejpam-3903	588	7	the	the	DET
ejpam-3903	588	8	limit	limit	NOUN
ejpam-3903	588	9	a0w	a0w	NOUN
ejpam-3903	588	10	is	be	AUX
ejpam-3903	588	11	solution	solution	NOUN
ejpam-3903	588	12	of	of	ADP
ejpam-3903	588	13	the	the	DET
ejpam-3903	588	14	system	system	NOUN
ejpam-3903	588	15	(	(	PUNCT
ejpam-3903	588	16	1	1	X
ejpam-3903	588	17	)	)	PUNCT
ejpam-3903	588	18	which	which	PRON
ejpam-3903	588	19	means	mean	VERB
ejpam-3903	588	20	to	to	PART
ejpam-3903	588	21	show	show	VERB
ejpam-3903	588	22	that	that	SCONJ
ejpam-3903	588	23	:	:	PUNCT
ejpam-3903	588	24	∂wi	∂wi	PROPN
ejpam-3903	588	25	∂xj	∂xj	NOUN
ejpam-3903	588	26	=	=	SYM
ejpam-3903	588	27	wi+5j	wi+5j	NOUN
ejpam-3903	588	28	for	for	ADP
ejpam-3903	588	29	i	i	PROPN
ejpam-3903	588	30	=	=	NOUN
ejpam-3903	588	31	1	1	NUM
ejpam-3903	588	32	,	,	PUNCT
ejpam-3903	588	33	.	.	PUNCT
ejpam-3903	588	34	.	.	PUNCT
ejpam-3903	589	1	.	.	PUNCT
ejpam-3903	590	1	,	,	PUNCT
ejpam-3903	590	2	5	5	NUM
ejpam-3903	590	3	and	and	CCONJ
ejpam-3903	590	4	j	j	NOUN
ejpam-3903	590	5	=	=	SYM
ejpam-3903	590	6	1	1	NUM
ejpam-3903	590	7	,	,	PUNCT
ejpam-3903	590	8	.	.	PUNCT
ejpam-3903	590	9	.	.	PUNCT
ejpam-3903	591	1	.	.	PUNCT
ejpam-3903	592	1	,	,	PUNCT
ejpam-3903	592	2	3	3	X
ejpam-3903	592	3	(	(	PUNCT
ejpam-3903	592	4	89	89	NUM
ejpam-3903	592	5	)	)	PUNCT
ejpam-3903	592	6	we	we	PRON
ejpam-3903	592	7	have	have	VERB
ejpam-3903	592	8	(	(	PUNCT
ejpam-3903	592	9	wε)1	wε)1	PROPN
ejpam-3903	592	10	∈	∈	PROPN
ejpam-3903	592	11	l2(0	l2(0	NOUN
ejpam-3903	592	12	,	,	PUNCT
ejpam-3903	592	13	t	t	PROPN
ejpam-3903	592	14	;	;	PUNCT
ejpam-3903	592	15	hs(ω))20	hs(ω))20	PROPN
ejpam-3903	592	16	,	,	PUNCT
ejpam-3903	592	17	which	which	PRON
ejpam-3903	592	18	gives:∥∥∥∥∂wε	gives:∥∥∥∥∂wε	PROPN
ejpam-3903	592	19	1	1	NUM
ejpam-3903	592	20	∂x1	∂x1	NOUN
ejpam-3903	592	21	∥∥∥∥	∥∥∥∥	NUM
ejpam-3903	592	22	hs−1	hs−1	ADJ
ejpam-3903	592	23	6	6	NUM
ejpam-3903	592	24	‖wε	‖wε	NUM
ejpam-3903	592	25	1‖hs	1‖h	NOUN
ejpam-3903	592	26	6	6	NUM
ejpam-3903	592	27	c∥∥∥∥∂wε	c∥∥∥∥∂wε	NOUN
ejpam-3903	592	28	1	1	NUM
ejpam-3903	592	29	∂x1	∂x1	NOUN
ejpam-3903	592	30	∥∥∥∥	∥∥∥∥	NUM
ejpam-3903	592	31	l2	l2	NOUN
ejpam-3903	593	1	6	6	NUM
ejpam-3903	593	2	‖wε	‖wε	NUM
ejpam-3903	593	3	1‖hs	1‖h	NOUN
ejpam-3903	593	4	6	6	NUM
ejpam-3903	593	5	c	c	NOUN
ejpam-3903	593	6	references	reference	NOUN
ejpam-3903	593	7	109	109	NUM
ejpam-3903	593	8	(	(	PUNCT
ejpam-3903	593	9	wε)1	wε)1	NOUN
ejpam-3903	593	10	being	be	AUX
ejpam-3903	593	11	bounded	bound	VERB
ejpam-3903	593	12	in	in	ADP
ejpam-3903	593	13	l2(0	l2(0	PROPN
ejpam-3903	593	14	,	,	PUNCT
ejpam-3903	593	15	t	t	NOUN
ejpam-3903	593	16	;	;	PUNCT
ejpam-3903	593	17	hs(ω	hs(ω	NUM
ejpam-3903	593	18	)	)	PUNCT
ejpam-3903	593	19	)	)	PUNCT
ejpam-3903	593	20	,	,	PUNCT
ejpam-3903	593	21	one	one	PRON
ejpam-3903	593	22	can	can	AUX
ejpam-3903	593	23	deduce	deduce	VERB
ejpam-3903	593	24	that	that	PRON
ejpam-3903	593	25	,	,	PUNCT
ejpam-3903	593	26	∂wε	∂wε	PROPN
ejpam-3903	593	27	1	1	NUM
ejpam-3903	593	28	∂x1	∂x1	NOUN
ejpam-3903	593	29	=	=	PUNCT
ejpam-3903	593	30	(	(	PUNCT
ejpam-3903	593	31	wε)6	wε)6	PROPN
ejpam-3903	593	32	is	be	AUX
ejpam-3903	593	33	bounded	bound	VERB
ejpam-3903	593	34	in	in	ADP
ejpam-3903	593	35	l2(0	l2(0	PROPN
ejpam-3903	593	36	,	,	PUNCT
ejpam-3903	593	37	t	t	PROPN
ejpam-3903	593	38	;	;	PUNCT
ejpam-3903	593	39	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	593	40	)	)	PUNCT
ejpam-3903	593	41	)	)	PUNCT
ejpam-3903	593	42	.	.	PUNCT
ejpam-3903	594	1	consequently	consequently	ADV
ejpam-3903	594	2	their	their	PRON
ejpam-3903	594	3	exist	exist	ADJ
ejpam-3903	594	4	subsequence	subsequence	NOUN
ejpam-3903	594	5	noted	note	VERB
ejpam-3903	594	6	again	again	ADV
ejpam-3903	594	7	∂wε	∂wε	PROPN
ejpam-3903	594	8	1	1	NUM
ejpam-3903	594	9	∂x1	∂x1	NOUN
ejpam-3903	594	10	which	which	PRON
ejpam-3903	594	11	converges	converge	VERB
ejpam-3903	594	12	weakly	weakly	ADJ
ejpam-3903	594	13	to	to	ADP
ejpam-3903	594	14	w	w	NOUN
ejpam-3903	594	15	in	in	ADP
ejpam-3903	594	16	l2(0	l2(0	NOUN
ejpam-3903	594	17	,	,	PUNCT
ejpam-3903	594	18	t	t	PROPN
ejpam-3903	594	19	;	;	PUNCT
ejpam-3903	594	20	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	594	21	)	)	PUNCT
ejpam-3903	594	22	)	)	PUNCT
ejpam-3903	594	23	.	.	PUNCT
ejpam-3903	595	1	on	on	ADP
ejpam-3903	595	2	the	the	DET
ejpam-3903	595	3	other	other	ADJ
ejpam-3903	595	4	hand	hand	NOUN
ejpam-3903	595	5	we	we	PRON
ejpam-3903	595	6	have	have	VERB
ejpam-3903	595	7	wε	wε	NUM
ejpam-3903	595	8	1	1	NUM
ejpam-3903	595	9	converge	converge	VERB
ejpam-3903	595	10	strongly	strongly	ADV
ejpam-3903	595	11	to	to	ADP
ejpam-3903	595	12	−→w1	−→w1	PROPN
ejpam-3903	595	13	in	in	ADP
ejpam-3903	595	14	l2(0	l2(0	NOUN
ejpam-3903	595	15	,	,	PUNCT
ejpam-3903	595	16	t	t	NOUN
ejpam-3903	595	17	;	;	PUNCT
ejpam-3903	595	18	hs(ω	hs(ω	NUM
ejpam-3903	595	19	)	)	PUNCT
ejpam-3903	595	20	)	)	PUNCT
ejpam-3903	595	21	,	,	PUNCT
ejpam-3903	595	22	which	which	PRON
ejpam-3903	595	23	gives	give	VERB
ejpam-3903	595	24	w	w	NOUN
ejpam-3903	595	25	=	=	PUNCT
ejpam-3903	595	26	∂w1	∂w1	ADJ
ejpam-3903	595	27	∂x1	∂x1	NOUN
ejpam-3903	595	28	.	.	PUNCT
ejpam-3903	596	1	this	this	PRON
ejpam-3903	596	2	allows	allow	VERB
ejpam-3903	596	3	us	we	PRON
ejpam-3903	596	4	to	to	PART
ejpam-3903	596	5	deduce	deduce	VERB
ejpam-3903	596	6	the	the	DET
ejpam-3903	596	7	following	follow	VERB
ejpam-3903	596	8	convergences	convergence	NOUN
ejpam-3903	596	9	:	:	PUNCT
ejpam-3903	596	10	∂(wε)1	∂(wε)1	PROPN
ejpam-3903	596	11	∂x1	∂x1	PROPN
ejpam-3903	596	12	−→	−→	NOUN
ejpam-3903	596	13	∂w1	∂w1	PROPN
ejpam-3903	596	14	∂x1	∂x1	PROPN
ejpam-3903	596	15	in	in	ADP
ejpam-3903	596	16	l2(0	l2(0	PROPN
ejpam-3903	596	17	,	,	PUNCT
ejpam-3903	596	18	t	t	PROPN
ejpam-3903	596	19	;	;	PUNCT
ejpam-3903	596	20	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	596	21	)	)	PUNCT
ejpam-3903	596	22	)	)	PUNCT
ejpam-3903	597	1	(	(	PUNCT
ejpam-3903	597	2	wε)6	wε)6	PROPN
ejpam-3903	597	3	−→	−→	NOUN
ejpam-3903	597	4	w6	w6	PROPN
ejpam-3903	597	5	in	in	ADP
ejpam-3903	597	6	l2(0	l2(0	PROPN
ejpam-3903	597	7	,	,	PUNCT
ejpam-3903	597	8	t	t	PROPN
ejpam-3903	597	9	;	;	PUNCT
ejpam-3903	597	10	hs−1(ω	hs−1(ω	PROPN
ejpam-3903	597	11	)	)	PUNCT
ejpam-3903	597	12	)	)	PUNCT
ejpam-3903	597	13	by	by	ADP
ejpam-3903	597	14	equality	equality	NOUN
ejpam-3903	597	15	of	of	ADP
ejpam-3903	597	16	sequences	sequence	NOUN
ejpam-3903	597	17	and	and	CCONJ
ejpam-3903	597	18	their	their	PRON
ejpam-3903	597	19	limits	limit	NOUN
ejpam-3903	597	20	,	,	PUNCT
ejpam-3903	597	21	we	we	PRON
ejpam-3903	597	22	have	have	VERB
ejpam-3903	597	23	:	:	PUNCT
ejpam-3903	597	24	∂w1	∂w1	PROPN
ejpam-3903	597	25	∂x1	∂x1	NOUN
ejpam-3903	597	26	=	=	SYM
ejpam-3903	597	27	w6	w6	PROPN
ejpam-3903	597	28	.	.	PUNCT
ejpam-3903	598	1	we	we	PRON
ejpam-3903	598	2	repeat	repeat	VERB
ejpam-3903	598	3	the	the	DET
ejpam-3903	598	4	same	same	ADJ
ejpam-3903	598	5	calculation	calculation	NOUN
ejpam-3903	598	6	for	for	ADP
ejpam-3903	598	7	∂w1	∂w1	PROPN
ejpam-3903	598	8	∂x2	∂x2	NOUN
ejpam-3903	598	9	=	=	SYM
ejpam-3903	598	10	w11	w11	PROPN
ejpam-3903	598	11	,	,	PUNCT
ejpam-3903	598	12	which	which	PRON
ejpam-3903	598	13	finally	finally	ADV
ejpam-3903	598	14	gives	give	VERB
ejpam-3903	598	15	:	:	PUNCT
ejpam-3903	598	16	a0w	a0w	VERB
ejpam-3903	598	17	∈	∈	NOUN
ejpam-3903	598	18	l∞(0	l∞(0	PRON
ejpam-3903	598	19	,	,	PUNCT
ejpam-3903	598	20	t	t	NOUN
ejpam-3903	598	21	;	;	PUNCT
ejpam-3903	598	22	hs(ω	hs(ω	NUM
ejpam-3903	598	23	)	)	PUNCT
ejpam-3903	598	24	)	)	PUNCT
ejpam-3903	598	25	∂	∂	NUM
ejpam-3903	599	1	∂t	∂t	PROPN
ejpam-3903	599	2	(	(	PUNCT
ejpam-3903	599	3	a0w	a0w	NOUN
ejpam-3903	599	4	)	)	PUNCT
ejpam-3903	599	5	∈	∈	PROPN
ejpam-3903	599	6	l2(0	l2(0	NOUN
ejpam-3903	599	7	,	,	PUNCT
ejpam-3903	599	8	t	t	NOUN
ejpam-3903	599	9	;	;	PUNCT
ejpam-3903	599	10	l2(ω	l2(ω	X
ejpam-3903	599	11	)	)	PUNCT
ejpam-3903	599	12	)	)	PUNCT
ejpam-3903	600	1	the	the	DET
ejpam-3903	600	2	verification	verification	NOUN
ejpam-3903	600	3	of	of	ADP
ejpam-3903	600	4	a0w	a0w	NOUN
ejpam-3903	600	5	solution	solution	NOUN
ejpam-3903	600	6	of	of	ADP
ejpam-3903	600	7	the	the	DET
ejpam-3903	600	8	compressible	compressible	ADJ
ejpam-3903	600	9	navier	navier	NOUN
ejpam-3903	600	10	-	-	PUNCT
ejpam-3903	600	11	stokes	stoke	NOUN
ejpam-3903	600	12	system	system	NOUN
ejpam-3903	600	13	(	(	PUNCT
ejpam-3903	600	14	1	1	X
ejpam-3903	600	15	)	)	PUNCT
ejpam-3903	600	16	is	be	AUX
ejpam-3903	600	17	done	do	VERB
ejpam-3903	600	18	in	in	ADP
ejpam-3903	600	19	the	the	DET
ejpam-3903	600	20	same	same	ADJ
ejpam-3903	600	21	way	way	NOUN
ejpam-3903	600	22	as	as	ADP
ejpam-3903	600	23	before	before	ADV
ejpam-3903	600	24	.	.	PUNCT
ejpam-3903	601	1	6	6	X
ejpam-3903	601	2	.	.	X
ejpam-3903	601	3	conclusion	conclusion	NOUN
ejpam-3903	601	4	in	in	ADP
ejpam-3903	601	5	this	this	DET
ejpam-3903	601	6	work	work	NOUN
ejpam-3903	601	7	we	we	PRON
ejpam-3903	601	8	have	have	AUX
ejpam-3903	601	9	proved	prove	VERB
ejpam-3903	601	10	the	the	DET
ejpam-3903	601	11	existence	existence	NOUN
ejpam-3903	601	12	of	of	ADP
ejpam-3903	601	13	a	a	DET
ejpam-3903	601	14	weak	weak	ADJ
ejpam-3903	601	15	solution	solution	NOUN
ejpam-3903	601	16	of	of	ADP
ejpam-3903	601	17	the	the	DET
ejpam-3903	601	18	navier	navier	NOUN
ejpam-3903	601	19	-	-	PUNCT
ejpam-3903	601	20	stokesfourier	stokesfourier	NOUN
ejpam-3903	601	21	system	system	NOUN
ejpam-3903	601	22	if	if	SCONJ
ejpam-3903	601	23	the	the	DET
ejpam-3903	601	24	second	second	ADJ
ejpam-3903	601	25	member	member	NOUN
ejpam-3903	601	26	remains	remain	VERB
ejpam-3903	601	27	bounded	bound	VERB
ejpam-3903	601	28	in	in	ADP
ejpam-3903	601	29	time	time	NOUN
ejpam-3903	601	30	and	and	CCONJ
ejpam-3903	601	31	with	with	ADP
ejpam-3903	601	32	a	a	DET
ejpam-3903	601	33	certain	certain	ADJ
ejpam-3903	601	34	regularity	regularity	NOUN
ejpam-3903	601	35	in	in	ADP
ejpam-3903	601	36	spaces	space	NOUN
ejpam-3903	601	37	.	.	PUNCT
ejpam-3903	602	1	the	the	DET
ejpam-3903	602	2	justification	justification	NOUN
ejpam-3903	602	3	is	be	AUX
ejpam-3903	602	4	based	base	VERB
ejpam-3903	602	5	on	on	ADP
ejpam-3903	602	6	a	a	DET
ejpam-3903	602	7	reduction	reduction	NOUN
ejpam-3903	602	8	of	of	ADP
ejpam-3903	602	9	the	the	DET
ejpam-3903	602	10	system	system	NOUN
ejpam-3903	602	11	order	order	NOUN
ejpam-3903	602	12	due	due	ADP
ejpam-3903	602	13	to	to	ADP
ejpam-3903	602	14	the	the	DET
ejpam-3903	602	15	add	add	NOUN
ejpam-3903	602	16	of	of	ADP
ejpam-3903	602	17	a	a	DET
ejpam-3903	602	18	diffusion	diffusion	NOUN
ejpam-3903	602	19	in	in	ADP
ejpam-3903	602	20	the	the	DET
ejpam-3903	602	21	continuity	continuity	NOUN
ejpam-3903	602	22	equation	equation	NOUN
ejpam-3903	602	23	.	.	PUNCT
ejpam-3903	603	1	however	however	ADV
ejpam-3903	603	2	,	,	PUNCT
ejpam-3903	603	3	we	we	PRON
ejpam-3903	603	4	prove	prove	VERB
ejpam-3903	603	5	that	that	SCONJ
ejpam-3903	603	6	this	this	DET
ejpam-3903	603	7	addition	addition	NOUN
ejpam-3903	603	8	preserves	preserve	VERB
ejpam-3903	603	9	the	the	DET
ejpam-3903	603	10	positivity	positivity	NOUN
ejpam-3903	603	11	of	of	ADP
ejpam-3903	603	12	the	the	DET
ejpam-3903	603	13	density	density	NOUN
ejpam-3903	603	14	as	as	ADV
ejpam-3903	603	15	long	long	ADV
ejpam-3903	603	16	as	as	SCONJ
ejpam-3903	603	17	there	there	PRON
ejpam-3903	603	18	is	be	VERB
ejpam-3903	603	19	not	not	PART
ejpam-3903	603	20	a	a	DET
ejpam-3903	603	21	vacuum	vacuum	NOUN
ejpam-3903	603	22	at	at	ADP
ejpam-3903	603	23	the	the	DET
ejpam-3903	603	24	initial	initial	ADJ
ejpam-3903	603	25	time	time	NOUN
ejpam-3903	603	26	.	.	PUNCT
ejpam-3903	604	1	the	the	DET
ejpam-3903	604	2	treatment	treatment	NOUN
ejpam-3903	604	3	of	of	ADP
ejpam-3903	604	4	the	the	DET
ejpam-3903	604	5	nonlinearity	nonlinearity	NOUN
ejpam-3903	604	6	of	of	ADP
ejpam-3903	604	7	the	the	DET
ejpam-3903	604	8	navier	navier	NOUN
ejpam-3903	604	9	-	-	PUNCT
ejpam-3903	604	10	stokes	stokes	PROPN
ejpam-3903	604	11	-	-	PUNCT
ejpam-3903	604	12	fourier	fourier	NOUN
ejpam-3903	604	13	system	system	NOUN
ejpam-3903	604	14	is	be	AUX
ejpam-3903	604	15	done	do	VERB
ejpam-3903	604	16	by	by	ADP
ejpam-3903	604	17	a	a	DET
ejpam-3903	604	18	successive	successive	ADJ
ejpam-3903	604	19	approximation	approximation	NOUN
ejpam-3903	604	20	and	and	CCONJ
ejpam-3903	604	21	the	the	DET
ejpam-3903	604	22	passage	passage	NOUN
ejpam-3903	604	23	to	to	ADP
ejpam-3903	604	24	the	the	DET
ejpam-3903	604	25	limit	limit	NOUN
ejpam-3903	604	26	was	be	AUX
ejpam-3903	604	27	possible	possible	ADJ
ejpam-3903	604	28	thanks	thank	NOUN
ejpam-3903	604	29	to	to	ADP
ejpam-3903	604	30	some	some	DET
ejpam-3903	604	31	a	a	DET
ejpam-3903	604	32	priori	priori	ADJ
ejpam-3903	604	33	estimations	estimation	NOUN
ejpam-3903	604	34	.	.	PUNCT
ejpam-3903	605	1	references	reference	NOUN
ejpam-3903	605	2	[	[	X
ejpam-3903	605	3	1	1	NUM
ejpam-3903	605	4	]	]	X
ejpam-3903	605	5	r	r	NOUN
ejpam-3903	605	6	abgrall	abgrall	NOUN
ejpam-3903	605	7	and	and	CCONJ
ejpam-3903	605	8	r	r	NOUN
ejpam-3903	605	9	saurel	saurel	NOUN
ejpam-3903	605	10	.	.	PUNCT
ejpam-3903	606	1	a	a	DET
ejpam-3903	606	2	simple	simple	ADJ
ejpam-3903	606	3	method	method	NOUN
ejpam-3903	606	4	for	for	ADP
ejpam-3903	606	5	compressible	compressible	ADJ
ejpam-3903	606	6	multiphase	multiphase	NOUN
ejpam-3903	606	7	flows	flow	NOUN
ejpam-3903	606	8	.	.	PUNCT
ejpam-3903	607	1	siam	siam	PROPN
ejpam-3903	607	2	j.	j.	PROPN
ejpam-3903	607	3	sci	sci	PROPN
ejpam-3903	607	4	.	.	PUNCT
ejpam-3903	608	1	comput	comput	PROPN
ejpam-3903	608	2	.	.	PUNCT
ejpam-3903	608	3	,	,	PUNCT
ejpam-3903	609	1	21(3):1115–1145	21(3):1115–1145	NUM
ejpam-3903	609	2	,	,	PUNCT
ejpam-3903	609	3	1999	1999	NUM
ejpam-3903	609	4	.	.	PUNCT
ejpam-3903	610	1	[	[	X
ejpam-3903	610	2	2	2	NUM
ejpam-3903	610	3	]	]	X
ejpam-3903	610	4	r	r	NOUN
ejpam-3903	610	5	a	a	DET
ejpam-3903	610	6	adams	adams	PROPN
ejpam-3903	610	7	.	.	PUNCT
ejpam-3903	611	1	sobolev	sobolev	PROPN
ejpam-3903	611	2	spaces	space	VERB
ejpam-3903	611	3	.	.	PUNCT
ejpam-3903	612	1	academic	academic	ADJ
ejpam-3903	612	2	press	press	NOUN
ejpam-3903	612	3	,	,	PUNCT
ejpam-3903	612	4	new	new	PROPN
ejpam-3903	612	5	york	york	PROPN
ejpam-3903	612	6	,	,	PUNCT
ejpam-3903	612	7	1975	1975	NUM
ejpam-3903	612	8	.	.	PUNCT
ejpam-3903	613	1	[	[	X
ejpam-3903	613	2	3	3	X
ejpam-3903	613	3	]	]	PUNCT
ejpam-3903	613	4	n	n	CCONJ
ejpam-3903	613	5	andrainov	andrainov	NOUN
ejpam-3903	613	6	and	and	CCONJ
ejpam-3903	613	7	w	w	PROPN
ejpam-3903	613	8	s	s	PROPN
ejpam-3903	613	9	richard	richard	PROPN
ejpam-3903	613	10	.	.	PUNCT
ejpam-3903	614	1	a	a	DET
ejpam-3903	614	2	simple	simple	ADJ
ejpam-3903	614	3	method	method	NOUN
ejpam-3903	614	4	for	for	ADP
ejpam-3903	614	5	compressible	compressible	ADJ
ejpam-3903	614	6	multiphase	multiphase	NOUN
ejpam-3903	614	7	mixture	mixture	NOUN
ejpam-3903	614	8	and	and	CCONJ
ejpam-3903	614	9	interfaces	interface	NOUN
ejpam-3903	614	10	.	.	PUNCT
ejpam-3903	615	1	int	int	NOUN
ejpam-3903	615	2	.	.	PUNCT
ejpam-3903	616	1	j.	j.	PROPN
ejpam-3903	616	2	num	num	PROPN
ejpam-3903	616	3	.	.	PROPN
ejpam-3903	616	4	meth	meth	PROPN
ejpam-3903	616	5	.	.	PUNCT
ejpam-3903	617	1	fluids	fluid	NOUN
ejpam-3903	617	2	,	,	PUNCT
ejpam-3903	617	3	41:109–131	41:109–131	PROPN
ejpam-3903	617	4	,	,	PUNCT
ejpam-3903	617	5	2003	2003	NUM
ejpam-3903	617	6	.	.	PUNCT
ejpam-3903	618	1	references	reference	NOUN
ejpam-3903	618	2	110	110	NUM
ejpam-3903	618	3	[	[	X
ejpam-3903	618	4	4	4	NUM
ejpam-3903	618	5	]	]	X
ejpam-3903	618	6	r	r	NOUN
ejpam-3903	618	7	bade	bade	NOUN
ejpam-3903	618	8	and	and	CCONJ
ejpam-3903	618	9	h	h	PROPN
ejpam-3903	618	10	chaker	chaker	PROPN
ejpam-3903	618	11	.	.	PUNCT
ejpam-3903	619	1	hyperbolisation	hyperbolisation	NOUN
ejpam-3903	619	2	of	of	ADP
ejpam-3903	619	3	second	second	ADJ
ejpam-3903	619	4	partial	partial	ADJ
ejpam-3903	619	5	differential	differential	NOUN
ejpam-3903	619	6	equation	equation	NOUN
ejpam-3903	619	7	:	:	PUNCT
ejpam-3903	619	8	application	application	NOUN
ejpam-3903	619	9	to	to	ADP
ejpam-3903	619	10	navier	navier	NOUN
ejpam-3903	619	11	-	-	PUNCT
ejpam-3903	619	12	stokes	stokes	PROPN
ejpam-3903	619	13	-	-	PUNCT
ejpam-3903	619	14	fourier	fourier	NOUN
ejpam-3903	619	15	system	system	NOUN
ejpam-3903	619	16	.	.	PUNCT
ejpam-3903	620	1	far	far	PROPN
ejpam-3903	620	2	east	east	PROPN
ejpam-3903	620	3	journal	journal	PROPN
ejpam-3903	620	4	of	of	ADP
ejpam-3903	620	5	mathematical	mathematical	ADJ
ejpam-3903	620	6	sciences	science	NOUN
ejpam-3903	620	7	,	,	PUNCT
ejpam-3903	620	8	110(1):93–112	110(1):93–112	NUM
ejpam-3903	620	9	,	,	PUNCT
ejpam-3903	620	10	2019	2019	NUM
ejpam-3903	620	11	.	.	PUNCT
ejpam-3903	621	1	[	[	X
ejpam-3903	621	2	5	5	NUM
ejpam-3903	621	3	]	]	PUNCT
ejpam-3903	621	4	h	h	NOUN
ejpam-3903	621	5	chaker	chaker	PROPN
ejpam-3903	621	6	.	.	PUNCT
ejpam-3903	622	1	sur	sur	PROPN
ejpam-3903	622	2	un	un	PROPN
ejpam-3903	622	3	problème	problème	PROPN
ejpam-3903	622	4	d’écoulement	d’écoulement	PROPN
ejpam-3903	622	5	en	en	PROPN
ejpam-3903	622	6	milieu	milieu	PROPN
ejpam-3903	622	7	lagunaire	lagunaire	PROPN
ejpam-3903	622	8	:	:	PUNCT
ejpam-3903	622	9	analyse	analyse	PROPN
ejpam-3903	622	10	mathématique	mathématique	PROPN
ejpam-3903	622	11	et	et	PROPN
ejpam-3903	622	12	approximation	approximation	NOUN
ejpam-3903	622	13	numérique	numérique	NOUN
ejpam-3903	622	14	de	de	X
ejpam-3903	622	15	la	la	NOUN
ejpam-3903	622	16	solution	solution	NOUN
ejpam-3903	622	17	.	.	PUNCT
ejpam-3903	623	1	phd	phd	NOUN
ejpam-3903	623	2	thesis	thesis	NOUN
ejpam-3903	623	3	,	,	PUNCT
ejpam-3903	623	4	université	université	ADJ
ejpam-3903	623	5	de	de	X
ejpam-3903	623	6	tunis	tunis	PROPN
ejpam-3903	623	7	el	el	PROPN
ejpam-3903	623	8	-	-	PUNCT
ejpam-3903	623	9	manar	manar	PROPN
ejpam-3903	623	10	,	,	PUNCT
ejpam-3903	623	11	tunisie	tunisie	PROPN
ejpam-3903	623	12	,	,	PUNCT
ejpam-3903	623	13	1991	1991	NUM
ejpam-3903	623	14	.	.	PUNCT
ejpam-3903	624	1	[	[	X
ejpam-3903	624	2	6	6	NUM
ejpam-3903	624	3	]	]	X
ejpam-3903	624	4	r	r	NOUN
ejpam-3903	624	5	danchin	danchin	NOUN
ejpam-3903	624	6	,	,	PUNCT
ejpam-3903	624	7	f	f	PROPN
ejpam-3903	624	8	fanelli	fanelli	PROPN
ejpam-3903	624	9	,	,	PUNCT
ejpam-3903	624	10	and	and	CCONJ
ejpam-3903	624	11	m	m	PROPN
ejpam-3903	624	12	paicu	paicu	NOUN
ejpam-3903	624	13	.	.	PUNCT
ejpam-3903	625	1	a	a	DET
ejpam-3903	625	2	well	well	ADV
ejpam-3903	625	3	-	-	PUNCT
ejpam-3903	625	4	posedness	posedness	NOUN
ejpam-3903	625	5	result	result	NOUN
ejpam-3903	625	6	for	for	ADP
ejpam-3903	625	7	viscous	viscous	ADJ
ejpam-3903	625	8	compressible	compressible	ADJ
ejpam-3903	625	9	fluids	fluid	NOUN
ejpam-3903	625	10	with	with	ADP
ejpam-3903	625	11	only	only	ADV
ejpam-3903	625	12	bounded	bounded	ADJ
ejpam-3903	625	13	density	density	NOUN
ejpam-3903	625	14	.	.	PUNCT
ejpam-3903	626	1	analysis	analysis	NOUN
ejpam-3903	626	2	pde	pde	NOUN
ejpam-3903	626	3	,	,	PUNCT
ejpam-3903	626	4	13(1):275–316	13(1):275–316	NUM
ejpam-3903	626	5	,	,	PUNCT
ejpam-3903	626	6	2020	2020	NUM
ejpam-3903	626	7	.	.	PUNCT
ejpam-3903	627	1	[	[	X
ejpam-3903	627	2	7	7	NUM
ejpam-3903	627	3	]	]	SYM
ejpam-3903	627	4	b	b	X
ejpam-3903	627	5	desjardins	desjardin	NOUN
ejpam-3903	627	6	.	.	PUNCT
ejpam-3903	628	1	sur	sur	PROPN
ejpam-3903	628	2	la	la	PROPN
ejpam-3903	628	3	régularité	régularité	PROPN
ejpam-3903	628	4	des	des	X
ejpam-3903	628	5	solutions	solution	NOUN
ejpam-3903	628	6	faibles	faible	VERB
ejpam-3903	628	7	des	des	X
ejpam-3903	628	8	équations	équations	PROPN
ejpam-3903	628	9	de	de	X
ejpam-3903	628	10	navier	navier	NOUN
ejpam-3903	628	11	-	-	PUNCT
ejpam-3903	628	12	stokes	stoke	NOUN
ejpam-3903	628	13	isentropique	isentropique	NOUN
ejpam-3903	628	14	en	en	ADP
ejpam-3903	628	15	dimension	dimension	NOUN
ejpam-3903	628	16	deux	deux	PROPN
ejpam-3903	628	17	.	.	PROPN
ejpam-3903	629	1	in	in	ADP
ejpam-3903	629	2	séminaire	séminaire	PROPN
ejpam-3903	629	3	e.	e.	PROPN
ejpam-3903	629	4	d.	d.	PROPN
ejpam-3903	629	5	p.	p.	PROPN
ejpam-3903	629	6	exposé	exposé	PROPN
ejpam-3903	630	1	n	n	PROPN
ejpam-3903	630	2	iii	iii	NOUN
ejpam-3903	630	3	,	,	PUNCT
ejpam-3903	630	4	centre	centre	PROPN
ejpam-3903	630	5	mathématiques	mathématiques	PROPN
ejpam-3903	630	6	laurent	laurent	PROPN
ejpam-3903	630	7	schwartz	schwartz	PROPN
ejpam-3903	630	8	,	,	PUNCT
ejpam-3903	630	9	1997	1997	NUM
ejpam-3903	630	10	-	-	SYM
ejpam-3903	630	11	1998	1998	NUM
ejpam-3903	630	12	.	.	PUNCT
ejpam-3903	631	1	[	[	X
ejpam-3903	631	2	8	8	NUM
ejpam-3903	631	3	]	]	SYM
ejpam-3903	631	4	b	b	X
ejpam-3903	631	5	desjardins	desjardin	NOUN
ejpam-3903	631	6	.	.	PUNCT
ejpam-3903	632	1	on	on	ADP
ejpam-3903	632	2	weak	weak	ADJ
ejpam-3903	632	3	solutions	solution	NOUN
ejpam-3903	632	4	of	of	ADP
ejpam-3903	632	5	compressible	compressible	ADJ
ejpam-3903	632	6	isentropic	isentropic	NOUN
ejpam-3903	632	7	navier	navier	NOUN
ejpam-3903	632	8	-	-	PUNCT
ejpam-3903	632	9	stokes	stokes	PROPN
ejpam-3903	632	10	equations	equation	NOUN
ejpam-3903	632	11	.	.	PUNCT
ejpam-3903	633	1	appl	appl	PROPN
ejpam-3903	633	2	.	.	PROPN
ejpam-3903	633	3	math	math	PROPN
ejpam-3903	633	4	.	.	PUNCT
ejpam-3903	634	1	lett	lett	PROPN
ejpam-3903	634	2	.	.	PROPN
ejpam-3903	634	3	,	,	PUNCT
ejpam-3903	634	4	12:107–111	12:107–111	PROPN
ejpam-3903	634	5	,	,	PUNCT
ejpam-3903	634	6	1999	1999	NUM
ejpam-3903	634	7	.	.	PUNCT
ejpam-3903	635	1	[	[	X
ejpam-3903	635	2	9	9	NUM
ejpam-3903	635	3	]	]	PUNCT
ejpam-3903	635	4	e	e	NOUN
ejpam-3903	635	5	feireisl	feireisl	NOUN
ejpam-3903	635	6	.	.	PUNCT
ejpam-3903	636	1	compressible	compressible	ADJ
ejpam-3903	636	2	navier	navier	NOUN
ejpam-3903	636	3	-	-	PUNCT
ejpam-3903	636	4	stokes	stoke	NOUN
ejpam-3903	636	5	equations	equation	NOUN
ejpam-3903	636	6	with	with	ADP
ejpam-3903	636	7	a	a	DET
ejpam-3903	636	8	non	non	ADJ
ejpam-3903	636	9	-	-	ADJ
ejpam-3903	636	10	monotone	monotone	ADJ
ejpam-3903	636	11	pressure	pressure	NOUN
ejpam-3903	636	12	law	law	NOUN
ejpam-3903	636	13	.	.	PUNCT
ejpam-3903	637	1	journal	journal	PROPN
ejpam-3903	637	2	.	.	PUNCT
ejpam-3903	638	1	of	of	ADP
ejpam-3903	638	2	differential	differential	ADJ
ejpam-3903	638	3	equations	equation	NOUN
ejpam-3903	638	4	,	,	PUNCT
ejpam-3903	638	5	184:97–108	184:97–108	NUM
ejpam-3903	638	6	,	,	PUNCT
ejpam-3903	638	7	2002	2002	NUM
ejpam-3903	638	8	.	.	PUNCT
ejpam-3903	639	1	[	[	X
ejpam-3903	639	2	10	10	NUM
ejpam-3903	639	3	]	]	X
ejpam-3903	639	4	e	e	NOUN
ejpam-3903	639	5	feireisl	feireisl	NOUN
ejpam-3903	639	6	.	.	PUNCT
ejpam-3903	640	1	mathematical	mathematical	ADJ
ejpam-3903	640	2	theory	theory	NOUN
ejpam-3903	640	3	of	of	ADP
ejpam-3903	640	4	compressible	compressible	ADJ
ejpam-3903	640	5	,	,	PUNCT
ejpam-3903	640	6	viscous	viscous	ADJ
ejpam-3903	640	7	and	and	CCONJ
ejpam-3903	640	8	heat	heat	NOUN
ejpam-3903	640	9	conduction	conduction	NOUN
ejpam-3903	640	10	fluids	fluid	NOUN
ejpam-3903	640	11	.	.	PUNCT
ejpam-3903	641	1	computers	computer	NOUN
ejpam-3903	641	2	and	and	CCONJ
ejpam-3903	641	3	math	math	NOUN
ejpam-3903	641	4	.	.	PUNCT
ejpam-3903	642	1	with	with	ADP
ejpam-3903	642	2	appl	appl	PROPN
ejpam-3903	642	3	.	.	PROPN
ejpam-3903	642	4	,	,	PUNCT
ejpam-3903	642	5	53:461–490	53:461–490	PROPN
ejpam-3903	642	6	,	,	PUNCT
ejpam-3903	642	7	2007	2007	NUM
ejpam-3903	642	8	.	.	PUNCT
ejpam-3903	643	1	[	[	X
ejpam-3903	643	2	11	11	NUM
ejpam-3903	643	3	]	]	X
ejpam-3903	643	4	k	k	NOUN
ejpam-3903	643	5	o	o	NOUN
ejpam-3903	643	6	freidrichs	freidrich	NOUN
ejpam-3903	643	7	.	.	PUNCT
ejpam-3903	644	1	symmetric	symmetric	ADJ
ejpam-3903	644	2	positive	positive	ADJ
ejpam-3903	644	3	linear	linear	PROPN
ejpam-3903	644	4	differential	differential	NOUN
ejpam-3903	644	5	equations	equation	NOUN
ejpam-3903	644	6	.	.	PUNCT
ejpam-3903	645	1	comm	comm	NOUN
ejpam-3903	645	2	.	.	PUNCT
ejpam-3903	646	1	on	on	ADP
ejpam-3903	646	2	pure	pure	ADJ
ejpam-3903	646	3	and	and	CCONJ
ejpam-3903	646	4	appl	appl	NOUN
ejpam-3903	646	5	.	.	PROPN
ejpam-3903	646	6	math	math	PROPN
ejpam-3903	646	7	.	.	PUNCT
ejpam-3903	646	8	,	,	PUNCT
ejpam-3903	646	9	xi:333–418	xi:333–418	PROPN
ejpam-3903	646	10	,	,	PUNCT
ejpam-3903	646	11	1958	1958	NUM
ejpam-3903	646	12	.	.	PUNCT
ejpam-3903	647	1	[	[	X
ejpam-3903	647	2	12	12	NUM
ejpam-3903	647	3	]	]	X
ejpam-3903	647	4	d	d	X
ejpam-3903	647	5	p	p	NOUN
ejpam-3903	647	6	lax	lax	NOUN
ejpam-3903	647	7	.	.	PUNCT
ejpam-3903	648	1	on	on	ADP
ejpam-3903	648	2	cauchy	cauchy	PROPN
ejpam-3903	648	3	problem	problem	NOUN
ejpam-3903	648	4	for	for	ADP
ejpam-3903	648	5	hyperbolic	hyperbolic	ADJ
ejpam-3903	648	6	equations	equation	NOUN
ejpam-3903	648	7	and	and	CCONJ
ejpam-3903	648	8	the	the	DET
ejpam-3903	648	9	differentiability	differentiability	NOUN
ejpam-3903	648	10	of	of	ADP
ejpam-3903	648	11	solutions	solution	NOUN
ejpam-3903	648	12	of	of	ADP
ejpam-3903	648	13	elliptic	elliptic	ADJ
ejpam-3903	648	14	equations	equation	NOUN
ejpam-3903	648	15	.	.	PUNCT
ejpam-3903	649	1	comm	comm	NOUN
ejpam-3903	649	2	.	.	PUNCT
ejpam-3903	650	1	on	on	ADP
ejpam-3903	650	2	pure	pure	ADJ
ejpam-3903	650	3	and	and	CCONJ
ejpam-3903	650	4	appl	appl	NOUN
ejpam-3903	650	5	.	.	PROPN
ejpam-3903	650	6	math	math	PROPN
ejpam-3903	650	7	.	.	PUNCT
ejpam-3903	650	8	,	,	PUNCT
ejpam-3903	650	9	6:615–633	6:615–633	PROPN
ejpam-3903	650	10	,	,	PUNCT
ejpam-3903	650	11	1955	1955	NUM
ejpam-3903	650	12	.	.	PUNCT
ejpam-3903	651	1	[	[	X
ejpam-3903	651	2	13	13	NUM
ejpam-3903	651	3	]	]	X
ejpam-3903	651	4	p	p	X
ejpam-3903	651	5	lesaint	lesaint	PROPN
ejpam-3903	651	6	.	.	PUNCT
ejpam-3903	652	1	finite	finite	PROPN
ejpam-3903	652	2	element	element	NOUN
ejpam-3903	652	3	methods	method	NOUN
ejpam-3903	652	4	for	for	ADP
ejpam-3903	652	5	symmetric	symmetric	ADJ
ejpam-3903	652	6	hyperbolic	hyperbolic	ADJ
ejpam-3903	652	7	equation	equation	NOUN
ejpam-3903	652	8	.	.	PUNCT
ejpam-3903	653	1	num	num	PROPN
ejpam-3903	653	2	.	.	PROPN
ejpam-3903	653	3	math	math	NOUN
ejpam-3903	653	4	.	.	PUNCT
ejpam-3903	653	5	,	,	PUNCT
ejpam-3903	653	6	21:244–255	21:244–255	NUM
ejpam-3903	653	7	,	,	PUNCT
ejpam-3903	653	8	1973	1973	NUM
ejpam-3903	653	9	.	.	PUNCT
ejpam-3903	654	1	[	[	X
ejpam-3903	654	2	14	14	NUM
ejpam-3903	654	3	]	]	SYM
ejpam-3903	654	4	j	j	PROPN
ejpam-3903	654	5	l	l	NOUN
ejpam-3903	654	6	lions	lion	NOUN
ejpam-3903	654	7	.	.	PUNCT
ejpam-3903	655	1	quelques	quelque	NOUN
ejpam-3903	655	2	méthodes	méthodes	PROPN
ejpam-3903	655	3	de	de	PROPN
ejpam-3903	655	4	résoluion	résoluion	PROPN
ejpam-3903	655	5	des	des	PROPN
ejpam-3903	655	6	problèmes	problèmes	PROPN
ejpam-3903	655	7	aux	aux	PROPN
ejpam-3903	655	8	limites	limites	X
ejpam-3903	655	9	non	non	ADJ
ejpam-3903	655	10	-	-	NOUN
ejpam-3903	655	11	linéaires	linéaire	NOUN
ejpam-3903	655	12	.	.	PUNCT
ejpam-3903	656	1	dunod	dunod	PROPN
ejpam-3903	656	2	,	,	PUNCT
ejpam-3903	656	3	paris	paris	PROPN
ejpam-3903	656	4	,	,	PUNCT
ejpam-3903	656	5	1975	1975	NUM
ejpam-3903	656	6	.	.	PUNCT
ejpam-3903	657	1	[	[	X
ejpam-3903	657	2	15	15	NUM
ejpam-3903	657	3	]	]	X
ejpam-3903	657	4	j	j	PROPN
ejpam-3903	657	5	l	l	NOUN
ejpam-3903	657	6	lions	lion	NOUN
ejpam-3903	657	7	and	and	CCONJ
ejpam-3903	657	8	e	e	NOUN
ejpam-3903	657	9	magenes	magene	NOUN
ejpam-3903	657	10	.	.	PUNCT
ejpam-3903	658	1	problèmes	problèmes	PROPN
ejpam-3903	658	2	aux	aux	PROPN
ejpam-3903	658	3	limites	limites	PROPN
ejpam-3903	658	4	non	non	PROPN
ejpam-3903	658	5	homogènes	homogènes	PROPN
ejpam-3903	658	6	,	,	PUNCT
ejpam-3903	658	7	volume	volume	NOUN
ejpam-3903	658	8	1	1	NUM
ejpam-3903	658	9	.	.	PUNCT
ejpam-3903	658	10	dunod	dunod	PROPN
ejpam-3903	658	11	,	,	PUNCT
ejpam-3903	658	12	paris	paris	PROPN
ejpam-3903	658	13	,	,	PUNCT
ejpam-3903	658	14	1968	1968	NUM
ejpam-3903	658	15	.	.	PUNCT
ejpam-3903	659	1	[	[	X
ejpam-3903	659	2	16	16	NUM
ejpam-3903	659	3	]	]	PUNCT
ejpam-3903	659	4	p	p	X
ejpam-3903	659	5	l	l	NOUN
ejpam-3903	659	6	lions	lion	NOUN
ejpam-3903	659	7	.	.	PUNCT
ejpam-3903	660	1	mathematical	mathematical	ADJ
ejpam-3903	660	2	topics	topic	NOUN
ejpam-3903	660	3	in	in	ADP
ejpam-3903	660	4	fluid	fluid	ADJ
ejpam-3903	660	5	mechanics	mechanic	NOUN
ejpam-3903	660	6	,	,	PUNCT
ejpam-3903	660	7	compressible	compressible	ADJ
ejpam-3903	660	8	models	model	NOUN
ejpam-3903	660	9	,	,	PUNCT
ejpam-3903	660	10	volume	volume	NOUN
ejpam-3903	660	11	2	2	NUM
ejpam-3903	660	12	.	.	PUNCT
ejpam-3903	661	1	oxford	oxford	PROPN
ejpam-3903	661	2	sciences	sciences	PROPN
ejpam-3903	661	3	publications	publication	NOUN
ejpam-3903	661	4	,	,	PUNCT
ejpam-3903	661	5	oxford	oxford	PROPN
ejpam-3903	661	6	,	,	PUNCT
ejpam-3903	661	7	1998	1998	NUM
ejpam-3903	661	8	.	.	PUNCT
ejpam-3903	662	1	[	[	X
ejpam-3903	662	2	17	17	NUM
ejpam-3903	662	3	]	]	PUNCT
ejpam-3903	662	4	a	a	DET
ejpam-3903	662	5	majda	majda	NOUN
ejpam-3903	662	6	.	.	PUNCT
ejpam-3903	663	1	compressible	compressible	ADJ
ejpam-3903	663	2	fluid	fluid	NOUN
ejpam-3903	663	3	flows	flow	NOUN
ejpam-3903	663	4	and	and	CCONJ
ejpam-3903	663	5	systems	system	NOUN
ejpam-3903	663	6	of	of	ADP
ejpam-3903	663	7	conservation	conservation	NOUN
ejpam-3903	663	8	laws	law	NOUN
ejpam-3903	663	9	in	in	ADP
ejpam-3903	663	10	several	several	ADJ
ejpam-3903	663	11	space	space	NOUN
ejpam-3903	663	12	variables	variable	NOUN
ejpam-3903	663	13	.	.	PUNCT
ejpam-3903	664	1	springer	springer	NOUN
ejpam-3903	664	2	verlag	verlag	PROPN
ejpam-3903	664	3	,	,	PUNCT
ejpam-3903	664	4	1984	1984	NUM
ejpam-3903	664	5	.	.	PUNCT
ejpam-3903	665	1	[	[	X
ejpam-3903	665	2	18	18	NUM
ejpam-3903	665	3	]	]	X
ejpam-3903	665	4	j	j	PROPN
ejpam-3903	665	5	massoni	massoni	PROPN
ejpam-3903	665	6	,	,	PUNCT
ejpam-3903	665	7	r	r	NOUN
ejpam-3903	665	8	saurel	saurel	NOUN
ejpam-3903	665	9	,	,	PUNCT
ejpam-3903	665	10	b	b	X
ejpam-3903	665	11	nkonga	nkonga	NOUN
ejpam-3903	665	12	,	,	PUNCT
ejpam-3903	665	13	and	and	CCONJ
ejpam-3903	665	14	r	r	NOUN
ejpam-3903	665	15	abgrall	abgrall	NOUN
ejpam-3903	665	16	.	.	PUNCT
ejpam-3903	666	1	some	some	DET
ejpam-3903	666	2	models	model	NOUN
ejpam-3903	666	3	and	and	CCONJ
ejpam-3903	666	4	eulerian	eulerian	ADJ
ejpam-3903	666	5	methods	method	NOUN
ejpam-3903	666	6	for	for	ADP
ejpam-3903	666	7	interface	interface	NOUN
ejpam-3903	666	8	problems	problem	NOUN
ejpam-3903	666	9	between	between	ADP
ejpam-3903	666	10	compressible	compressible	ADJ
ejpam-3903	666	11	fluids	fluid	NOUN
ejpam-3903	666	12	with	with	ADP
ejpam-3903	666	13	heat	heat	NOUN
ejpam-3903	666	14	transfert	transfert	PROPN
ejpam-3903	666	15	.	.	PUNCT
ejpam-3903	667	1	int	int	PROPN
ejpam-3903	667	2	.	.	PUNCT
ejpam-3903	668	1	j.	j.	PROPN
ejpam-3903	668	2	of	of	ADP
ejpam-3903	668	3	heat	heat	PROPN
ejpam-3903	668	4	and	and	CCONJ
ejpam-3903	668	5	mass	mass	NOUN
ejpam-3903	668	6	transf	transf	NOUN
ejpam-3903	668	7	,	,	PUNCT
ejpam-3903	668	8	41(6):1287–1307	41(6):1287–1307	NUM
ejpam-3903	668	9	,	,	PUNCT
ejpam-3903	668	10	2002	2002	NUM
ejpam-3903	668	11	.	.	PUNCT
ejpam-3903	669	1	references	reference	NOUN
ejpam-3903	669	2	111	111	NUM
ejpam-3903	670	1	[	[	X
ejpam-3903	670	2	19	19	NUM
ejpam-3903	670	3	]	]	PUNCT
ejpam-3903	670	4	a	a	DET
ejpam-3903	670	5	novotný	novotný	NOUN
ejpam-3903	670	6	and	and	CCONJ
ejpam-3903	670	7	i	i	PRON
ejpam-3903	670	8	straskraba	straskraba	PROPN
ejpam-3903	670	9	.	.	PUNCT
ejpam-3903	671	1	introduction	introduction	NOUN
ejpam-3903	671	2	to	to	ADP
ejpam-3903	671	3	the	the	DET
ejpam-3903	671	4	theory	theory	NOUN
ejpam-3903	671	5	of	of	ADP
ejpam-3903	671	6	compressible	compressible	ADJ
ejpam-3903	671	7	flow	flow	NOUN
ejpam-3903	671	8	.	.	PUNCT
ejpam-3903	672	1	oxford	oxford	PROPN
ejpam-3903	672	2	university	university	PROPN
ejpam-3903	672	3	press	press	NOUN
ejpam-3903	672	4	,	,	PUNCT
ejpam-3903	672	5	oxford	oxford	PROPN
ejpam-3903	672	6	,	,	PUNCT
ejpam-3903	672	7	2004	2004	NUM
ejpam-3903	672	8	.	.	PUNCT
ejpam-3903	673	1	[	[	X
ejpam-3903	673	2	20	20	NUM
ejpam-3903	673	3	]	]	PUNCT
ejpam-3903	673	4	s	s	PART
ejpam-3903	673	5	rouy	rouy	NOUN
ejpam-3903	673	6	.	.	PUNCT
ejpam-3903	674	1	modélisation	modélisation	NOUN
ejpam-3903	674	2	mathématique	mathématique	NOUN
ejpam-3903	674	3	et	et	NOUN
ejpam-3903	674	4	numérique	numérique	NOUN
ejpam-3903	674	5	d’écoulement	d’écoulement	NOUN
ejpam-3903	674	6	diphasique	diphasique	ADJ
ejpam-3903	674	7	compressible	compressible	NOUN
ejpam-3903	674	8	.	.	PUNCT
ejpam-3903	675	1	application	application	NOUN
ejpam-3903	675	2	au	au	PROPN
ejpam-3903	675	3	cas	cas	PROPN
ejpam-3903	675	4	industriel	industriel	PROPN
ejpam-3903	675	5	d’un	d’un	PROPN
ejpam-3903	675	6	générateur	générateur	PROPN
ejpam-3903	675	7	de	de	X
ejpam-3903	675	8	gaz	gaz	PROPN
ejpam-3903	675	9	.	.	PUNCT
ejpam-3903	676	1	phd	phd	NOUN
ejpam-3903	676	2	thesis	thesis	NOUN
ejpam-3903	676	3	,	,	PUNCT
ejpam-3903	676	4	université	université	ADJ
ejpam-3903	676	5	de	de	X
ejpam-3903	676	6	toulon	toulon	PROPN
ejpam-3903	676	7	et	et	PROPN
ejpam-3903	676	8	var	var	PROPN
ejpam-3903	676	9	,	,	PUNCT
ejpam-3903	676	10	toulon	toulon	PROPN
ejpam-3903	676	11	,	,	PUNCT
ejpam-3903	676	12	2000	2000	NUM
ejpam-3903	676	13	.	.	PUNCT
ejpam-3903	677	1	[	[	X
ejpam-3903	677	2	21	21	NUM
ejpam-3903	677	3	]	]	X
ejpam-3903	677	4	a	a	DET
ejpam-3903	677	5	valli	valli	NOUN
ejpam-3903	677	6	.	.	PUNCT
ejpam-3903	678	1	an	an	DET
ejpam-3903	678	2	existence	existence	NOUN
ejpam-3903	678	3	theorem	theorem	VERB
ejpam-3903	678	4	for	for	ADP
ejpam-3903	678	5	compressible	compressible	ADJ
ejpam-3903	678	6	viscous	viscous	ADJ
ejpam-3903	678	7	fluids	fluid	NOUN
ejpam-3903	678	8	.	.	PUNCT
ejpam-3903	679	1	annali	annali	PROPN
ejpam-3903	679	2	di	di	PROPN
ejpam-3903	679	3	mathematica	mathematica	PROPN
ejpam-3903	679	4	pura	pura	PROPN
ejpam-3903	679	5	ed	ed	PROPN
ejpam-3903	679	6	applicata	applicata	PROPN
ejpam-3903	679	7	,	,	PUNCT
ejpam-3903	679	8	130:197–213	130:197–213	NUM
ejpam-3903	679	9	,	,	PUNCT
ejpam-3903	679	10	1982	1982	NUM
ejpam-3903	679	11	.	.	PUNCT
ejpam-3903	680	1	[	[	X
ejpam-3903	680	2	22	22	NUM
ejpam-3903	680	3	]	]	X
ejpam-3903	680	4	y	y	PROPN
ejpam-3903	680	5	zhou	zhou	PROPN
ejpam-3903	680	6	,	,	PUNCT
ejpam-3903	680	7	l	l	PROPN
ejpam-3903	680	8	peng	peng	PROPN
ejpam-3903	680	9	,	,	PUNCT
ejpam-3903	680	10	and	and	CCONJ
ejpam-3903	680	11	y.	y.	PROPN
ejpam-3903	680	12	huang	huang	PROPN
ejpam-3903	680	13	.	.	PUNCT
ejpam-3903	681	1	existence	existence	PROPN
ejpam-3903	681	2	and	and	CCONJ
ejpam-3903	681	3	hölder	hölder	VERB
ejpam-3903	681	4	continuity	continuity	NOUN
ejpam-3903	681	5	of	of	ADP
ejpam-3903	681	6	solutions	solution	NOUN
ejpam-3903	681	7	for	for	ADP
ejpam-3903	681	8	timefractional	timefractional	ADJ
ejpam-3903	681	9	navier	navier	NOUN
ejpam-3903	681	10	-	-	PUNCT
ejpam-3903	681	11	stokes	stoke	NOUN
ejpam-3903	681	12	equations	equation	NOUN
ejpam-3903	681	13	.	.	PUNCT
ejpam-3903	682	1	mathematical	mathematical	ADJ
ejpam-3903	682	2	methods	method	NOUN
ejpam-3903	682	3	in	in	ADP
ejpam-3903	682	4	the	the	DET
ejpam-3903	682	5	applied	apply	VERB
ejpam-3903	682	6	sciences	science	NOUN
ejpam-3903	682	7	,	,	PUNCT
ejpam-3903	682	8	41(17):7830–7838	41(17):7830–7838	NUM
ejpam-3903	682	9	,	,	PUNCT
ejpam-3903	682	10	2018	2018	NUM
ejpam-3903	682	11	.	.	PUNCT