id	sid	tid	token	lemma	pos
ejpam-4674	1	1	european	european	PROPN
ejpam-4674	1	2	journal	journal	PROPN
ejpam-4674	1	3	of	of	ADP
ejpam-4674	1	4	pure	pure	ADJ
ejpam-4674	1	5	and	and	CCONJ
ejpam-4674	1	6	applied	apply	VERB
ejpam-4674	1	7	mathematics	mathematic	NOUN
ejpam-4674	1	8	vol	vol	NOUN
ejpam-4674	1	9	.	.	PUNCT
ejpam-4674	2	1	16	16	NUM
ejpam-4674	2	2	,	,	PUNCT
ejpam-4674	2	3	no	no	INTJ
ejpam-4674	2	4	.	.	NOUN
ejpam-4674	2	5	1	1	NUM
ejpam-4674	2	6	,	,	PUNCT
ejpam-4674	2	7	2023	2023	NUM
ejpam-4674	2	8	,	,	PUNCT
ejpam-4674	2	9	404	404	NUM
ejpam-4674	2	10	-	-	SYM
ejpam-4674	2	11	417	417	NUM
ejpam-4674	2	12	issn	issn	PROPN
ejpam-4674	2	13	1307	1307	NUM
ejpam-4674	2	14	-	-	SYM
ejpam-4674	2	15	5543	5543	NUM
ejpam-4674	2	16	–	–	PUNCT
ejpam-4674	3	1	ejpam.com	ejpam.com	X
ejpam-4674	3	2	published	publish	VERB
ejpam-4674	3	3	by	by	ADP
ejpam-4674	3	4	new	new	PROPN
ejpam-4674	3	5	york	york	PROPN
ejpam-4674	3	6	business	business	PROPN
ejpam-4674	3	7	global	global	PROPN
ejpam-4674	3	8	isogeometric	isogeometric	ADJ
ejpam-4674	3	9	analysis	analysis	NOUN
ejpam-4674	3	10	approximation	approximation	NOUN
ejpam-4674	3	11	of	of	ADP
ejpam-4674	3	12	linear	linear	PROPN
ejpam-4674	3	13	elliptic	elliptic	ADJ
ejpam-4674	3	14	equations	equation	NOUN
ejpam-4674	3	15	with	with	ADP
ejpam-4674	3	16	l1	l1	PROPN
ejpam-4674	3	17	data	data	VERB
ejpam-4674	3	18	yibour	yibour	PRON
ejpam-4674	3	19	corentin	corentin	PROPN
ejpam-4674	3	20	bassonon1	bassonon1	PROPN
ejpam-4674	3	21	,	,	PUNCT
ejpam-4674	3	22	arouna	arouna	PROPN
ejpam-4674	3	23	ouédraogo1,∗	ouédraogo1,∗	PROPN
ejpam-4674	3	24	1	1	NUM
ejpam-4674	3	25	département	département	PROPN
ejpam-4674	3	26	de	de	X
ejpam-4674	3	27	mathématiques	mathématiques	PROPN
ejpam-4674	3	28	,	,	PUNCT
ejpam-4674	3	29	laboratoire	laboratoire	PROPN
ejpam-4674	3	30	de	de	X
ejpam-4674	3	31	mathématiques	mathématiques	PROPN
ejpam-4674	3	32	,	,	PUNCT
ejpam-4674	3	33	informatique	informatique	PROPN
ejpam-4674	3	34	et	et	NOUN
ejpam-4674	3	35	applications	application	NOUN
ejpam-4674	3	36	(	(	PUNCT
ejpam-4674	3	37	l@mia	l@mia	NOUN
ejpam-4674	3	38	)	)	PUNCT
ejpam-4674	3	39	,	,	PUNCT
ejpam-4674	3	40	université	université	ADJ
ejpam-4674	3	41	norbert	norbert	PROPN
ejpam-4674	3	42	zongo	zongo	PROPN
ejpam-4674	3	43	,	,	PUNCT
ejpam-4674	3	44	koudougou	koudougou	PROPN
ejpam-4674	3	45	,	,	PUNCT
ejpam-4674	3	46	burkina	burkina	PROPN
ejpam-4674	3	47	faso	faso	PROPN
ejpam-4674	3	48	abstract	abstract	PROPN
ejpam-4674	3	49	.	.	PUNCT
ejpam-4674	4	1	isogeometric	isogeometric	ADJ
ejpam-4674	4	2	analysis	analysis	NOUN
ejpam-4674	4	3	(	(	PUNCT
ejpam-4674	4	4	iga	iga	PROPN
ejpam-4674	4	5	)	)	PUNCT
ejpam-4674	4	6	is	be	AUX
ejpam-4674	4	7	a	a	DET
ejpam-4674	4	8	recent	recent	ADJ
ejpam-4674	4	9	technique	technique	NOUN
ejpam-4674	4	10	for	for	ADP
ejpam-4674	4	11	the	the	DET
ejpam-4674	4	12	discretization	discretization	NOUN
ejpam-4674	4	13	of	of	ADP
ejpam-4674	4	14	partial	partial	ADJ
ejpam-4674	4	15	differential	differential	ADJ
ejpam-4674	4	16	equations	equation	NOUN
ejpam-4674	4	17	(	(	PUNCT
ejpam-4674	4	18	pdes	pde	NOUN
ejpam-4674	4	19	)	)	PUNCT
ejpam-4674	4	20	.	.	PUNCT
ejpam-4674	5	1	the	the	DET
ejpam-4674	5	2	main	main	ADJ
ejpam-4674	5	3	feature	feature	NOUN
ejpam-4674	5	4	of	of	ADP
ejpam-4674	5	5	the	the	DET
ejpam-4674	5	6	method	method	NOUN
ejpam-4674	5	7	is	be	AUX
ejpam-4674	5	8	the	the	DET
ejpam-4674	5	9	ability	ability	NOUN
ejpam-4674	5	10	to	to	PART
ejpam-4674	5	11	maintain	maintain	VERB
ejpam-4674	5	12	the	the	DET
ejpam-4674	5	13	same	same	ADJ
ejpam-4674	5	14	exact	exact	ADJ
ejpam-4674	5	15	description	description	NOUN
ejpam-4674	5	16	of	of	ADP
ejpam-4674	5	17	the	the	DET
ejpam-4674	5	18	computational	computational	ADJ
ejpam-4674	5	19	geometry	geometry	NOUN
ejpam-4674	5	20	domain	domain	NOUN
ejpam-4674	5	21	throughout	throughout	ADP
ejpam-4674	5	22	the	the	DET
ejpam-4674	5	23	analysis	analysis	NOUN
ejpam-4674	5	24	process	process	NOUN
ejpam-4674	5	25	,	,	PUNCT
ejpam-4674	5	26	including	include	VERB
ejpam-4674	5	27	refinement	refinement	NOUN
ejpam-4674	5	28	.	.	PUNCT
ejpam-4674	6	1	in	in	ADP
ejpam-4674	6	2	the	the	DET
ejpam-4674	6	3	present	present	ADJ
ejpam-4674	6	4	paper	paper	NOUN
ejpam-4674	6	5	,	,	PUNCT
ejpam-4674	6	6	we	we	PRON
ejpam-4674	6	7	consider	consider	VERB
ejpam-4674	6	8	,	,	PUNCT
ejpam-4674	6	9	in	in	ADP
ejpam-4674	6	10	dimension	dimension	NOUN
ejpam-4674	6	11	d	d	X
ejpam-4674	6	12	≥	≥	NUM
ejpam-4674	6	13	2	2	NUM
ejpam-4674	6	14	the	the	DET
ejpam-4674	6	15	isogeometric	isogeometric	ADJ
ejpam-4674	6	16	analysis	analysis	NOUN
ejpam-4674	6	17	approximation	approximation	NOUN
ejpam-4674	6	18	of	of	ADP
ejpam-4674	6	19	second	second	ADJ
ejpam-4674	6	20	order	order	NOUN
ejpam-4674	6	21	elliptic	elliptic	ADJ
ejpam-4674	6	22	equations	equation	NOUN
ejpam-4674	6	23	in	in	ADP
ejpam-4674	6	24	divergence	divergence	NOUN
ejpam-4674	6	25	form	form	NOUN
ejpam-4674	6	26	with	with	ADP
ejpam-4674	6	27	right	right	ADJ
ejpam-4674	6	28	-	-	PUNCT
ejpam-4674	6	29	hand	hand	NOUN
ejpam-4674	6	30	side	side	NOUN
ejpam-4674	6	31	in	in	ADP
ejpam-4674	6	32	l1	l1	PROPN
ejpam-4674	6	33	.	.	PUNCT
ejpam-4674	7	1	we	we	PRON
ejpam-4674	7	2	assume	assume	VERB
ejpam-4674	7	3	that	that	SCONJ
ejpam-4674	7	4	the	the	DET
ejpam-4674	7	5	family	family	NOUN
ejpam-4674	7	6	of	of	ADP
ejpam-4674	7	7	meshes	meshes	PROPN
ejpam-4674	7	8	is	be	AUX
ejpam-4674	7	9	shape	shape	NOUN
ejpam-4674	7	10	regular	regular	ADV
ejpam-4674	7	11	and	and	CCONJ
ejpam-4674	7	12	satisfies	satisfy	VERB
ejpam-4674	7	13	the	the	DET
ejpam-4674	7	14	discrete	discrete	ADJ
ejpam-4674	7	15	maximum	maximum	ADJ
ejpam-4674	7	16	principle	principle	NOUN
ejpam-4674	7	17	.	.	PUNCT
ejpam-4674	8	1	when	when	SCONJ
ejpam-4674	8	2	the	the	DET
ejpam-4674	8	3	righthand	righthand	NOUN
ejpam-4674	8	4	side	side	NOUN
ejpam-4674	8	5	belongs	belong	VERB
ejpam-4674	8	6	to	to	ADP
ejpam-4674	8	7	l1(ω	l1(ω	PROPN
ejpam-4674	8	8	)	)	PUNCT
ejpam-4674	8	9	,	,	PUNCT
ejpam-4674	8	10	we	we	PRON
ejpam-4674	8	11	prove	prove	VERB
ejpam-4674	8	12	that	that	SCONJ
ejpam-4674	8	13	the	the	DET
ejpam-4674	8	14	unique	unique	ADJ
ejpam-4674	8	15	solution	solution	NOUN
ejpam-4674	8	16	of	of	ADP
ejpam-4674	8	17	the	the	DET
ejpam-4674	8	18	discrete	discrete	ADJ
ejpam-4674	8	19	problem	problem	NOUN
ejpam-4674	8	20	converges	converge	VERB
ejpam-4674	8	21	to	to	ADP
ejpam-4674	8	22	the	the	DET
ejpam-4674	8	23	unique	unique	ADJ
ejpam-4674	8	24	renormalized	renormalize	VERB
ejpam-4674	8	25	solution	solution	NOUN
ejpam-4674	8	26	in	in	ADP
ejpam-4674	8	27	w	w	PROPN
ejpam-4674	8	28	1,q	1,q	NUM
ejpam-4674	8	29	0	0	NUM
ejpam-4674	8	30	(	(	PUNCT
ejpam-4674	8	31	ω	ω	NOUN
ejpam-4674	8	32	)	)	PUNCT
ejpam-4674	8	33	,	,	PUNCT
ejpam-4674	9	1	1	1	NUM
ejpam-4674	9	2	≤	≤	NOUN
ejpam-4674	9	3	q	q	NOUN
ejpam-4674	9	4	<	<	X
ejpam-4674	9	5	d	d	SYM
ejpam-4674	9	6	d−	d−	PROPN
ejpam-4674	9	7	1	1	NUM
ejpam-4674	9	8	.	.	PUNCT
ejpam-4674	10	1	we	we	PRON
ejpam-4674	10	2	also	also	ADV
ejpam-4674	10	3	prove	prove	VERB
ejpam-4674	10	4	some	some	DET
ejpam-4674	10	5	error	error	NOUN
ejpam-4674	10	6	estimates	estimate	NOUN
ejpam-4674	10	7	and	and	CCONJ
ejpam-4674	10	8	include	include	VERB
ejpam-4674	10	9	numerical	numerical	ADJ
ejpam-4674	10	10	tests	test	NOUN
ejpam-4674	10	11	for	for	ADP
ejpam-4674	10	12	data	datum	NOUN
ejpam-4674	10	13	with	with	ADP
ejpam-4674	10	14	low	low	ADJ
ejpam-4674	10	15	smoothness	smoothness	NOUN
ejpam-4674	10	16	.	.	PUNCT
ejpam-4674	11	1	2020	2020	NUM
ejpam-4674	11	2	mathematics	mathematic	NOUN
ejpam-4674	11	3	subject	subject	NOUN
ejpam-4674	11	4	classifications	classification	NOUN
ejpam-4674	11	5	:	:	PUNCT
ejpam-4674	11	6	65n30	65n30	NUM
ejpam-4674	11	7	,	,	PUNCT
ejpam-4674	11	8	35j25	35j25	NUM
ejpam-4674	11	9	key	key	ADJ
ejpam-4674	11	10	words	word	NOUN
ejpam-4674	11	11	and	and	CCONJ
ejpam-4674	11	12	phrases	phrase	NOUN
ejpam-4674	11	13	:	:	PUNCT
ejpam-4674	11	14	isogeometric	isogeometric	ADJ
ejpam-4674	11	15	analysis	analysis	NOUN
ejpam-4674	11	16	,	,	PUNCT
ejpam-4674	11	17	nurbs	nurbs	NOUN
ejpam-4674	11	18	approximation	approximation	NOUN
ejpam-4674	11	19	,	,	PUNCT
ejpam-4674	11	20	l1	l1	PROPN
ejpam-4674	11	21	data	data	PROPN
ejpam-4674	11	22	,	,	PUNCT
ejpam-4674	11	23	renormalized	renormalize	VERB
ejpam-4674	11	24	solution	solution	NOUN
ejpam-4674	11	25	1	1	NUM
ejpam-4674	11	26	.	.	PUNCT
ejpam-4674	12	1	introduction	introduction	NOUN
ejpam-4674	12	2	this	this	DET
ejpam-4674	12	3	paper	paper	NOUN
ejpam-4674	12	4	is	be	AUX
ejpam-4674	12	5	devoted	devote	VERB
ejpam-4674	12	6	to	to	ADP
ejpam-4674	12	7	the	the	DET
ejpam-4674	12	8	isogeometric	isogeometric	ADJ
ejpam-4674	12	9	analysis	analysis	NOUN
ejpam-4674	12	10	approximation	approximation	NOUN
ejpam-4674	12	11	of	of	ADP
ejpam-4674	12	12	second	second	ADJ
ejpam-4674	12	13	order	order	NOUN
ejpam-4674	12	14	linear	linear	VERB
ejpam-4674	12	15	elliptic	elliptic	ADJ
ejpam-4674	12	16	equations	equation	NOUN
ejpam-4674	12	17	in	in	ADP
ejpam-4674	12	18	divergence	divergence	NOUN
ejpam-4674	12	19	form	form	NOUN
ejpam-4674	12	20	with	with	ADP
ejpam-4674	12	21	l1	l1	PROPN
ejpam-4674	12	22	-	-	PUNCT
ejpam-4674	12	23	data	data	PROPN
ejpam-4674	12	24	.	.	PUNCT
ejpam-4674	13	1	we	we	PRON
ejpam-4674	13	2	study	study	VERB
ejpam-4674	13	3	the	the	DET
ejpam-4674	13	4	following	follow	VERB
ejpam-4674	13	5	problem	problem	NOUN
ejpam-4674	13	6	{	{	PUNCT
ejpam-4674	13	7	−div	−div	X
ejpam-4674	13	8	(	(	PUNCT
ejpam-4674	13	9	a∇u	a∇u	PROPN
ejpam-4674	13	10	)	)	PUNCT
ejpam-4674	13	11	=	=	SYM
ejpam-4674	13	12	f	f	PROPN
ejpam-4674	13	13	in	in	ADP
ejpam-4674	13	14	ω	ω	PROPN
ejpam-4674	13	15	,	,	PUNCT
ejpam-4674	13	16	u	u	NOUN
ejpam-4674	13	17	=	=	NOUN
ejpam-4674	13	18	0	0	NUM
ejpam-4674	13	19	on	on	ADP
ejpam-4674	13	20	∂ω	∂ω	PROPN
ejpam-4674	13	21	,	,	PUNCT
ejpam-4674	13	22	(	(	PUNCT
ejpam-4674	13	23	1	1	X
ejpam-4674	13	24	)	)	PUNCT
ejpam-4674	13	25	where	where	SCONJ
ejpam-4674	13	26	ω	ω	NOUN
ejpam-4674	13	27	is	be	AUX
ejpam-4674	13	28	an	an	DET
ejpam-4674	13	29	open	open	ADJ
ejpam-4674	13	30	,	,	PUNCT
ejpam-4674	13	31	bounded	bound	VERB
ejpam-4674	13	32	and	and	CCONJ
ejpam-4674	13	33	lipschitz	lipschitz	VERB
ejpam-4674	13	34	set	set	NOUN
ejpam-4674	13	35	of	of	ADP
ejpam-4674	13	36	rd	rd	PROPN
ejpam-4674	13	37	,	,	PUNCT
ejpam-4674	13	38	with	with	ADP
ejpam-4674	13	39	d	d	PROPN
ejpam-4674	13	40	=	=	SYM
ejpam-4674	13	41	2	2	NUM
ejpam-4674	13	42	or	or	CCONJ
ejpam-4674	13	43	d	d	NOUN
ejpam-4674	13	44	=	=	SYM
ejpam-4674	13	45	3	3	NUM
ejpam-4674	13	46	,	,	PUNCT
ejpam-4674	13	47	a	a	PRON
ejpam-4674	13	48	is	be	AUX
ejpam-4674	13	49	a	a	DET
ejpam-4674	13	50	coercive	coercive	ADJ
ejpam-4674	13	51	matrix	matrix	NOUN
ejpam-4674	13	52	with	with	ADP
ejpam-4674	13	53	coefficients	coefficient	NOUN
ejpam-4674	13	54	in	in	ADP
ejpam-4674	13	55	l∞(ω	l∞(ω	NOUN
ejpam-4674	13	56	)	)	PUNCT
ejpam-4674	13	57	and	and	CCONJ
ejpam-4674	13	58	f	f	PROPN
ejpam-4674	13	59	belongs	belong	VERB
ejpam-4674	13	60	to	to	ADP
ejpam-4674	13	61	l1(ω	l1(ω	PROPN
ejpam-4674	13	62	)	)	PUNCT
ejpam-4674	13	63	.	.	PUNCT
ejpam-4674	14	1	this	this	DET
ejpam-4674	14	2	problem	problem	NOUN
ejpam-4674	14	3	frequently	frequently	ADV
ejpam-4674	14	4	appears	appear	VERB
ejpam-4674	14	5	in	in	ADP
ejpam-4674	14	6	applied	applied	ADJ
ejpam-4674	14	7	sciences	science	NOUN
ejpam-4674	14	8	,	,	PUNCT
ejpam-4674	14	9	being	be	AUX
ejpam-4674	14	10	one	one	NUM
ejpam-4674	14	11	of	of	ADP
ejpam-4674	14	12	the	the	DET
ejpam-4674	14	13	basic	basic	ADJ
ejpam-4674	14	14	problems	problem	NOUN
ejpam-4674	14	15	∗corresponding	∗corresponde	VERB
ejpam-4674	14	16	author	author	NOUN
ejpam-4674	14	17	.	.	PUNCT
ejpam-4674	15	1	doi	doi	NOUN
ejpam-4674	15	2	:	:	PUNCT
ejpam-4674	15	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4674	https://doi.org/10.29020/nybg.ejpam.v16i1.4674	NUM
ejpam-4674	15	4	email	email	NOUN
ejpam-4674	15	5	addresses	address	NOUN
ejpam-4674	15	6	:	:	PUNCT
ejpam-4674	15	7	corentinbassonon@gmail.com	corentinbassonon@gmail.com	X
ejpam-4674	15	8	(	(	PUNCT
ejpam-4674	15	9	y.	y.	PROPN
ejpam-4674	15	10	c.	c.	PROPN
ejpam-4674	15	11	bassonon	bassonon	PROPN
ejpam-4674	15	12	)	)	PUNCT
ejpam-4674	15	13	,	,	PUNCT
ejpam-4674	15	14	arounaoued2002@yahoo.fr	arounaoued2002@yahoo.fr	PROPN
ejpam-4674	15	15	(	(	PUNCT
ejpam-4674	15	16	a.	a.	NOUN
ejpam-4674	15	17	ouédraogo	ouédraogo	PROPN
ejpam-4674	15	18	)	)	PUNCT
ejpam-4674	15	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4674	16	1	404	404	NUM
ejpam-4674	17	1	©	©	ADP
ejpam-4674	17	2	2023	2023	NUM
ejpam-4674	17	3	ejpam	ejpam	NOUN
ejpam-4674	17	4	all	all	DET
ejpam-4674	17	5	rights	right	NOUN
ejpam-4674	17	6	reserved	reserve	VERB
ejpam-4674	17	7	.	.	PUNCT
ejpam-4674	18	1	y.	y.	PROPN
ejpam-4674	18	2	c.	c.	PROPN
ejpam-4674	18	3	bassonon	bassonon	PROPN
ejpam-4674	18	4	,	,	PUNCT
ejpam-4674	18	5	a.	a.	NOUN
ejpam-4674	18	6	ouédraogo	ouédraogo	PROPN
ejpam-4674	18	7	/	/	SYM
ejpam-4674	18	8	eur	eur	PROPN
ejpam-4674	18	9	.	.	PUNCT
ejpam-4674	19	1	j.	j.	PROPN
ejpam-4674	19	2	pure	pure	PROPN
ejpam-4674	19	3	appl	appl	PROPN
ejpam-4674	19	4	.	.	PROPN
ejpam-4674	19	5	math	math	PROPN
ejpam-4674	19	6	,	,	PUNCT
ejpam-4674	19	7	16	16	NUM
ejpam-4674	19	8	(	(	PUNCT
ejpam-4674	19	9	1	1	NUM
ejpam-4674	19	10	)	)	PUNCT
ejpam-4674	19	11	(	(	PUNCT
ejpam-4674	19	12	2023	2023	NUM
ejpam-4674	19	13	)	)	PUNCT
ejpam-4674	19	14	,	,	PUNCT
ejpam-4674	19	15	404	404	NUM
ejpam-4674	19	16	-	-	SYM
ejpam-4674	19	17	417	417	NUM
ejpam-4674	19	18	405	405	NUM
ejpam-4674	19	19	in	in	ADP
ejpam-4674	19	20	mathematical	mathematical	ADJ
ejpam-4674	19	21	fluid	fluid	ADJ
ejpam-4674	19	22	mechanics	mechanic	NOUN
ejpam-4674	19	23	(	(	PUNCT
ejpam-4674	19	24	see	see	VERB
ejpam-4674	19	25	[	[	X
ejpam-4674	19	26	7	7	NUM
ejpam-4674	19	27	,	,	PUNCT
ejpam-4674	19	28	9	9	NUM
ejpam-4674	19	29	]	]	PUNCT
ejpam-4674	19	30	)	)	PUNCT
ejpam-4674	19	31	.	.	PUNCT
ejpam-4674	20	1	for	for	ADP
ejpam-4674	20	2	this	this	DET
ejpam-4674	20	3	class	class	NOUN
ejpam-4674	20	4	of	of	ADP
ejpam-4674	20	5	problems	problem	NOUN
ejpam-4674	20	6	,	,	PUNCT
ejpam-4674	20	7	the	the	DET
ejpam-4674	20	8	maximum	maximum	ADJ
ejpam-4674	20	9	principle	principle	NOUN
ejpam-4674	20	10	is	be	AUX
ejpam-4674	20	11	required	require	VERB
ejpam-4674	20	12	to	to	PART
ejpam-4674	20	13	obtain	obtain	VERB
ejpam-4674	20	14	physically	physically	ADV
ejpam-4674	20	15	admissible	admissible	ADJ
ejpam-4674	20	16	solutions	solution	NOUN
ejpam-4674	20	17	.	.	PUNCT
ejpam-4674	21	1	the	the	DET
ejpam-4674	21	2	problem	problem	NOUN
ejpam-4674	21	3	(	(	PUNCT
ejpam-4674	21	4	1	1	X
ejpam-4674	21	5	)	)	PUNCT
ejpam-4674	21	6	has	have	AUX
ejpam-4674	21	7	been	be	AUX
ejpam-4674	21	8	studied	study	VERB
ejpam-4674	21	9	in	in	ADP
ejpam-4674	21	10	[	[	X
ejpam-4674	21	11	3	3	X
ejpam-4674	21	12	]	]	PUNCT
ejpam-4674	21	13	by	by	ADP
ejpam-4674	21	14	the	the	DET
ejpam-4674	21	15	standard	standard	ADJ
ejpam-4674	21	16	finite	finite	ADJ
ejpam-4674	21	17	element	element	NOUN
ejpam-4674	21	18	method	method	NOUN
ejpam-4674	21	19	(	(	PUNCT
ejpam-4674	21	20	fem	fem	PROPN
ejpam-4674	21	21	)	)	PUNCT
ejpam-4674	21	22	.	.	PUNCT
ejpam-4674	22	1	the	the	DET
ejpam-4674	22	2	authors	author	NOUN
ejpam-4674	22	3	proved	prove	VERB
ejpam-4674	22	4	that	that	SCONJ
ejpam-4674	22	5	the	the	DET
ejpam-4674	22	6	discrete	discrete	ADJ
ejpam-4674	22	7	solution	solution	NOUN
ejpam-4674	22	8	converges	converge	VERB
ejpam-4674	22	9	in	in	ADP
ejpam-4674	22	10	w	w	PROPN
ejpam-4674	22	11	1,q	1,q	NUM
ejpam-4674	22	12	0	0	NUM
ejpam-4674	22	13	(	(	PUNCT
ejpam-4674	22	14	ω	ω	NOUN
ejpam-4674	22	15	)	)	PUNCT
ejpam-4674	22	16	,	,	PUNCT
ejpam-4674	22	17	1	1	NUM
ejpam-4674	22	18	≤	≤	NOUN
ejpam-4674	22	19	q	q	NOUN
ejpam-4674	22	20	<	<	X
ejpam-4674	22	21	d	d	SYM
ejpam-4674	22	22	d−	d−	PROPN
ejpam-4674	22	23	1	1	NUM
ejpam-4674	22	24	to	to	ADP
ejpam-4674	22	25	the	the	DET
ejpam-4674	22	26	unique	unique	ADJ
ejpam-4674	22	27	renormalized	renormalize	VERB
ejpam-4674	22	28	solution	solution	NOUN
ejpam-4674	22	29	(	(	PUNCT
ejpam-4674	22	30	see	see	VERB
ejpam-4674	22	31	[	[	X
ejpam-4674	22	32	6	6	NUM
ejpam-4674	22	33	]	]	PUNCT
ejpam-4674	22	34	for	for	ADP
ejpam-4674	22	35	existence	existence	NOUN
ejpam-4674	22	36	and	and	CCONJ
ejpam-4674	22	37	uniqueness	uniqueness	NOUN
ejpam-4674	22	38	of	of	ADP
ejpam-4674	22	39	renormalized	renormalize	VERB
ejpam-4674	22	40	solution	solution	NOUN
ejpam-4674	22	41	)	)	PUNCT
ejpam-4674	22	42	.	.	PUNCT
ejpam-4674	23	1	the	the	DET
ejpam-4674	23	2	isogeometric	isogeometric	ADJ
ejpam-4674	23	3	analysis	analysis	NOUN
ejpam-4674	23	4	based	base	VERB
ejpam-4674	23	5	on	on	ADP
ejpam-4674	23	6	nurbs	nurbs	X
ejpam-4674	23	7	(	(	PUNCT
ejpam-4674	23	8	non	non	ADJ
ejpam-4674	23	9	-	-	ADJ
ejpam-4674	23	10	uniform	uniform	ADJ
ejpam-4674	23	11	rational	rational	ADJ
ejpam-4674	23	12	b	b	NOUN
ejpam-4674	23	13	-	-	PUNCT
ejpam-4674	23	14	splines	spline	NOUN
ejpam-4674	23	15	)	)	PUNCT
ejpam-4674	23	16	,	,	PUNCT
ejpam-4674	23	17	which	which	PRON
ejpam-4674	23	18	possesses	possess	VERB
ejpam-4674	23	19	improved	improved	ADJ
ejpam-4674	23	20	properties	property	NOUN
ejpam-4674	23	21	,	,	PUNCT
ejpam-4674	23	22	is	be	AUX
ejpam-4674	23	23	a	a	DET
ejpam-4674	23	24	generalization	generalization	NOUN
ejpam-4674	23	25	of	of	ADP
ejpam-4674	23	26	classical	classical	ADJ
ejpam-4674	23	27	finite	finite	ADJ
ejpam-4674	23	28	element	element	NOUN
ejpam-4674	23	29	method	method	NOUN
ejpam-4674	23	30	.	.	PUNCT
ejpam-4674	24	1	nurbs	nurb	NOUN
ejpam-4674	24	2	are	be	AUX
ejpam-4674	24	3	capable	capable	ADJ
ejpam-4674	24	4	of	of	ADP
ejpam-4674	24	5	more	more	ADV
ejpam-4674	24	6	precise	precise	ADJ
ejpam-4674	24	7	geometric	geometric	ADJ
ejpam-4674	24	8	representation	representation	NOUN
ejpam-4674	24	9	of	of	ADP
ejpam-4674	24	10	complex	complex	ADJ
ejpam-4674	24	11	objects	object	NOUN
ejpam-4674	24	12	and	and	CCONJ
ejpam-4674	24	13	can	can	AUX
ejpam-4674	24	14	exactly	exactly	ADV
ejpam-4674	24	15	represent	represent	VERB
ejpam-4674	24	16	many	many	ADJ
ejpam-4674	24	17	engineered	engineer	VERB
ejpam-4674	24	18	shapes	shape	NOUN
ejpam-4674	24	19	.	.	PUNCT
ejpam-4674	25	1	iga	iga	PROPN
ejpam-4674	25	2	also	also	ADV
ejpam-4674	25	3	simplifies	simplify	VERB
ejpam-4674	25	4	mesh	mesh	NOUN
ejpam-4674	25	5	refinement	refinement	NOUN
ejpam-4674	25	6	because	because	SCONJ
ejpam-4674	25	7	the	the	DET
ejpam-4674	25	8	geometry	geometry	NOUN
ejpam-4674	25	9	is	be	AUX
ejpam-4674	25	10	fixed	fix	VERB
ejpam-4674	25	11	at	at	ADP
ejpam-4674	25	12	the	the	DET
ejpam-4674	25	13	coarsest	coarse	ADJ
ejpam-4674	25	14	level	level	NOUN
ejpam-4674	25	15	of	of	ADP
ejpam-4674	25	16	refinement	refinement	NOUN
ejpam-4674	25	17	and	and	CCONJ
ejpam-4674	25	18	is	be	AUX
ejpam-4674	25	19	unchanged	unchanged	ADJ
ejpam-4674	25	20	throughout	throughout	ADP
ejpam-4674	25	21	the	the	DET
ejpam-4674	25	22	refinement	refinement	NOUN
ejpam-4674	25	23	process	process	NOUN
ejpam-4674	25	24	.	.	PUNCT
ejpam-4674	26	1	the	the	DET
ejpam-4674	26	2	rest	rest	NOUN
ejpam-4674	26	3	of	of	ADP
ejpam-4674	26	4	the	the	DET
ejpam-4674	26	5	paper	paper	NOUN
ejpam-4674	26	6	is	be	AUX
ejpam-4674	26	7	organized	organize	VERB
ejpam-4674	26	8	as	as	SCONJ
ejpam-4674	26	9	follows	follow	VERB
ejpam-4674	26	10	:	:	PUNCT
ejpam-4674	26	11	in	in	ADP
ejpam-4674	26	12	section	section	NOUN
ejpam-4674	26	13	2	2	NUM
ejpam-4674	26	14	,	,	PUNCT
ejpam-4674	26	15	we	we	PRON
ejpam-4674	26	16	gives	give	VERB
ejpam-4674	26	17	setting	setting	NOUN
ejpam-4674	26	18	of	of	ADP
ejpam-4674	26	19	the	the	DET
ejpam-4674	26	20	problem	problem	NOUN
ejpam-4674	26	21	and	and	CCONJ
ejpam-4674	26	22	main	main	ADJ
ejpam-4674	26	23	result	result	NOUN
ejpam-4674	26	24	.	.	PUNCT
ejpam-4674	27	1	we	we	PRON
ejpam-4674	27	2	recall	recall	VERB
ejpam-4674	27	3	brievly	brievly	NOUN
ejpam-4674	27	4	the	the	DET
ejpam-4674	27	5	isogeometric	isogeometric	ADJ
ejpam-4674	27	6	analysis	analysis	NOUN
ejpam-4674	27	7	method	method	NOUN
ejpam-4674	27	8	.	.	PUNCT
ejpam-4674	28	1	in	in	ADP
ejpam-4674	28	2	section	section	NOUN
ejpam-4674	28	3	3	3	NUM
ejpam-4674	28	4	,	,	PUNCT
ejpam-4674	28	5	we	we	PRON
ejpam-4674	28	6	study	study	VERB
ejpam-4674	28	7	the	the	DET
ejpam-4674	28	8	convergence	convergence	NOUN
ejpam-4674	28	9	analysis	analysis	NOUN
ejpam-4674	28	10	and	and	CCONJ
ejpam-4674	28	11	we	we	PRON
ejpam-4674	28	12	obtain	obtain	VERB
ejpam-4674	28	13	the	the	DET
ejpam-4674	28	14	error	error	NOUN
ejpam-4674	28	15	estimates	estimate	NOUN
ejpam-4674	28	16	for	for	ADP
ejpam-4674	28	17	data	datum	NOUN
ejpam-4674	28	18	in	in	ADP
ejpam-4674	28	19	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	28	20	)	)	PUNCT
ejpam-4674	28	21	for	for	ADP
ejpam-4674	28	22	1	1	NUM
ejpam-4674	28	23	<	<	NOUN
ejpam-4674	28	24	r	r	NOUN
ejpam-4674	28	25	<	<	X
ejpam-4674	28	26	2	2	NUM
ejpam-4674	28	27	.	.	NOUN
ejpam-4674	28	28	to	to	PART
ejpam-4674	28	29	finish	finish	VERB
ejpam-4674	28	30	,	,	PUNCT
ejpam-4674	28	31	we	we	PRON
ejpam-4674	28	32	give	give	VERB
ejpam-4674	28	33	numerical	numerical	ADJ
ejpam-4674	28	34	result	result	NOUN
ejpam-4674	28	35	.	.	PUNCT
ejpam-4674	29	1	the	the	DET
ejpam-4674	29	2	novelty	novelty	NOUN
ejpam-4674	29	3	in	in	ADP
ejpam-4674	29	4	our	our	PRON
ejpam-4674	29	5	work	work	NOUN
ejpam-4674	29	6	is	be	AUX
ejpam-4674	29	7	the	the	DET
ejpam-4674	29	8	convergence	convergence	NOUN
ejpam-4674	29	9	result	result	NOUN
ejpam-4674	29	10	in	in	ADP
ejpam-4674	29	11	w	w	PROPN
ejpam-4674	29	12	1,q	1,q	NUM
ejpam-4674	29	13	0	0	NUM
ejpam-4674	29	14	(	(	PUNCT
ejpam-4674	29	15	ω	ω	NOUN
ejpam-4674	29	16	)	)	PUNCT
ejpam-4674	29	17	,	,	PUNCT
ejpam-4674	29	18	obtained	obtain	VERB
ejpam-4674	29	19	for	for	ADP
ejpam-4674	29	20	approximate	approximate	ADJ
ejpam-4674	29	21	solutions	solution	NOUN
ejpam-4674	29	22	of	of	ADP
ejpam-4674	29	23	(	(	PUNCT
ejpam-4674	29	24	1	1	NUM
ejpam-4674	29	25	)	)	PUNCT
ejpam-4674	29	26	in	in	ADP
ejpam-4674	29	27	nurbs	nurb	NOUN
ejpam-4674	29	28	space	space	NOUN
ejpam-4674	29	29	.	.	PUNCT
ejpam-4674	30	1	2	2	X
ejpam-4674	30	2	.	.	X
ejpam-4674	30	3	preliminary	preliminary	ADJ
ejpam-4674	30	4	2.1	2.1	NUM
ejpam-4674	30	5	.	.	PUNCT
ejpam-4674	30	6	renormalized	renormalize	VERB
ejpam-4674	30	7	solution	solution	NOUN
ejpam-4674	30	8	we	we	PRON
ejpam-4674	30	9	investigate	investigate	VERB
ejpam-4674	30	10	the	the	DET
ejpam-4674	30	11	poisson	poisson	NOUN
ejpam-4674	30	12	’s	’s	PART
ejpam-4674	30	13	problem	problem	NOUN
ejpam-4674	30	14	with	with	ADP
ejpam-4674	30	15	homogeneous	homogeneous	ADJ
ejpam-4674	30	16	boundary	boundary	ADJ
ejpam-4674	30	17	conditions	condition	NOUN
ejpam-4674	30	18	under	under	ADP
ejpam-4674	30	19	the	the	DET
ejpam-4674	30	20	following	follow	VERB
ejpam-4674	30	21	conditions	condition	NOUN
ejpam-4674	30	22	:	:	PUNCT
ejpam-4674	30	23	the	the	DET
ejpam-4674	30	24	matrix	matrix	NOUN
ejpam-4674	30	25	a	a	PRON
ejpam-4674	30	26	is	be	AUX
ejpam-4674	30	27	such	such	ADJ
ejpam-4674	30	28	that	that	SCONJ
ejpam-4674	30	29	a	a	DET
ejpam-4674	30	30	∈	∈	PROPN
ejpam-4674	30	31	l∞(ω)d×d	l∞(ω)d×d	NOUN
ejpam-4674	30	32	,	,	PUNCT
ejpam-4674	30	33	(	(	PUNCT
ejpam-4674	30	34	2	2	X
ejpam-4674	30	35	)	)	PUNCT
ejpam-4674	30	36	a.e	a.e	NOUN
ejpam-4674	30	37	.	.	PUNCT
ejpam-4674	30	38	x	x	SYM
ejpam-4674	30	39	∈	∈	PROPN
ejpam-4674	30	40	ω	ω	PROPN
ejpam-4674	30	41	,	,	PUNCT
ejpam-4674	30	42	∀ϕ	∀ϕ	PROPN
ejpam-4674	30	43	∈	∈	PROPN
ejpam-4674	30	44	rd	rd	PROPN
ejpam-4674	30	45	,	,	PUNCT
ejpam-4674	30	46	a(x)ϕ	a(x)ϕ	PROPN
ejpam-4674	30	47	·	·	PUNCT
ejpam-4674	30	48	ϕ	ϕ	X
ejpam-4674	30	49	≥	≥	NOUN
ejpam-4674	30	50	α|ϕ|2	α|ϕ|2	ADJ
ejpam-4674	30	51	,	,	PUNCT
ejpam-4674	30	52	(	(	PUNCT
ejpam-4674	30	53	3	3	X
ejpam-4674	30	54	)	)	PUNCT
ejpam-4674	30	55	for	for	ADP
ejpam-4674	30	56	some	some	DET
ejpam-4674	30	57	α	α	NOUN
ejpam-4674	30	58	>	>	X
ejpam-4674	30	59	0	0	NUM
ejpam-4674	30	60	,	,	PUNCT
ejpam-4674	30	61	and	and	CCONJ
ejpam-4674	30	62	the	the	DET
ejpam-4674	30	63	right	right	ADJ
ejpam-4674	30	64	-	-	PUNCT
ejpam-4674	30	65	hand	hand	NOUN
ejpam-4674	30	66	side	side	NOUN
ejpam-4674	30	67	f	f	PROPN
ejpam-4674	30	68	is	be	AUX
ejpam-4674	30	69	such	such	ADJ
ejpam-4674	30	70	that	that	SCONJ
ejpam-4674	30	71	f	f	PROPN
ejpam-4674	30	72	∈	∈	PROPN
ejpam-4674	30	73	l1(ω	l1(ω	PROPN
ejpam-4674	30	74	)	)	PUNCT
ejpam-4674	30	75	.	.	PUNCT
ejpam-4674	31	1	(	(	PUNCT
ejpam-4674	31	2	4	4	X
ejpam-4674	31	3	)	)	PUNCT
ejpam-4674	31	4	we	we	PRON
ejpam-4674	31	5	give	give	VERB
ejpam-4674	31	6	the	the	DET
ejpam-4674	31	7	definition	definition	NOUN
ejpam-4674	31	8	of	of	ADP
ejpam-4674	31	9	the	the	DET
ejpam-4674	31	10	renormalized	renormalize	VERB
ejpam-4674	31	11	solution	solution	NOUN
ejpam-4674	31	12	of	of	ADP
ejpam-4674	31	13	problem(1	problem(1	NOUN
ejpam-4674	31	14	)	)	PUNCT
ejpam-4674	31	15	.	.	PUNCT
ejpam-4674	32	1	definition	definition	NOUN
ejpam-4674	32	2	2.1	2.1	NUM
ejpam-4674	32	3	.	.	PUNCT
ejpam-4674	33	1	a	a	DET
ejpam-4674	33	2	function	function	NOUN
ejpam-4674	33	3	u	u	NOUN
ejpam-4674	33	4	is	be	AUX
ejpam-4674	33	5	a	a	DET
ejpam-4674	33	6	renormalized	renormalized	ADJ
ejpam-4674	33	7	solution	solution	NOUN
ejpam-4674	33	8	of	of	ADP
ejpam-4674	33	9	(	(	PUNCT
ejpam-4674	33	10	1	1	X
ejpam-4674	33	11	)	)	PUNCT
ejpam-4674	33	12	if	if	SCONJ
ejpam-4674	33	13	u	u	PRON
ejpam-4674	33	14	satisfies	satisfy	VERB
ejpam-4674	33	15	u	u	PROPN
ejpam-4674	33	16	∈	∈	PROPN
ejpam-4674	33	17	l1(ω	l1(ω	PROPN
ejpam-4674	33	18	)	)	PUNCT
ejpam-4674	33	19	,	,	PUNCT
ejpam-4674	33	20	(	(	PUNCT
ejpam-4674	33	21	5	5	X
ejpam-4674	33	22	)	)	PUNCT
ejpam-4674	33	23	∀k	∀k	NOUN
ejpam-4674	33	24	>	>	X
ejpam-4674	33	25	0	0	NUM
ejpam-4674	33	26	,	,	PUNCT
ejpam-4674	33	27	tk(u	tk(u	NUM
ejpam-4674	33	28	)	)	PUNCT
ejpam-4674	33	29	∈	∈	PROPN
ejpam-4674	33	30	h1	h1	NOUN
ejpam-4674	33	31	0	0	NUM
ejpam-4674	33	32	(	(	PUNCT
ejpam-4674	33	33	ω	ω	NOUN
ejpam-4674	33	34	)	)	PUNCT
ejpam-4674	33	35	,	,	PUNCT
ejpam-4674	33	36	(	(	PUNCT
ejpam-4674	33	37	6	6	X
ejpam-4674	33	38	)	)	PUNCT
ejpam-4674	33	39	lim	lim	NOUN
ejpam-4674	33	40	k−→∞	k−→∞	PROPN
ejpam-4674	33	41	1	1	NUM
ejpam-4674	33	42	k	k	PROPN
ejpam-4674	33	43	∫	∫	PROPN
ejpam-4674	33	44	ω	ω	PROPN
ejpam-4674	33	45	|∇tk(u)|2dx	|∇tk(u)|2dx	VERB
ejpam-4674	33	46	=	=	SYM
ejpam-4674	33	47	0	0	NUM
ejpam-4674	33	48	,	,	PUNCT
ejpam-4674	33	49	(	(	PUNCT
ejpam-4674	33	50	7)	7)	NUM
ejpam-4674	33	51	∀k	∀k	NOUN
ejpam-4674	33	52	>	>	X
ejpam-4674	33	53	0	0	NUM
ejpam-4674	33	54	,	,	PUNCT
ejpam-4674	33	55	∀s	∀s	PROPN
ejpam-4674	33	56	∈	∈	PROPN
ejpam-4674	33	57	c1	c1	PROPN
ejpam-4674	33	58	c	c	PROPN
ejpam-4674	33	59	(	(	PUNCT
ejpam-4674	33	60	r	r	NOUN
ejpam-4674	33	61	)	)	PUNCT
ejpam-4674	33	62	with	with	ADP
ejpam-4674	33	63	supps	supp	NOUN
ejpam-4674	33	64	⊂	⊂	PROPN
ejpam-4674	34	1	[	[	X
ejpam-4674	34	2	−k,+k	−k,+k	X
ejpam-4674	34	3	]	]	X
ejpam-4674	34	4	,	,	PUNCT
ejpam-4674	34	5	∀v	∀v	PROPN
ejpam-4674	34	6	∈	∈	PROPN
ejpam-4674	34	7	h1	h1	NOUN
ejpam-4674	34	8	0	0	NUM
ejpam-4674	34	9	(	(	PUNCT
ejpam-4674	34	10	ω	ω	NOUN
ejpam-4674	34	11	)	)	PUNCT
ejpam-4674	34	12	∩	∩	PROPN
ejpam-4674	34	13	l∞(ω),∫	l∞(ω),∫	PROPN
ejpam-4674	34	14	ω	ω	NUM
ejpam-4674	34	15	a∇tk(u)∇vs(u)dx+	a∇tk(u)∇vs(u)dx+	NOUN
ejpam-4674	34	16	∫	∫	PROPN
ejpam-4674	34	17	ω	ω	PROPN
ejpam-4674	34	18	a∇tk(u)∇tk(u)s	a∇tk(u)∇tk(u)s	PROPN
ejpam-4674	34	19	′(u)vdx	′(u)vdx	PUNCT
ejpam-4674	34	20	=	=	SYM
ejpam-4674	34	21	∫	∫	PROPN
ejpam-4674	34	22	ω	ω	PROPN
ejpam-4674	34	23	fs(u)vdx	fs(u)vdx	PROPN
ejpam-4674	34	24	.	.	PUNCT
ejpam-4674	35	1	(	(	PUNCT
ejpam-4674	35	2	8)	8)	NUM
ejpam-4674	35	3	y.	y.	PROPN
ejpam-4674	35	4	c.	c.	PROPN
ejpam-4674	35	5	bassonon	bassonon	PROPN
ejpam-4674	35	6	,	,	PUNCT
ejpam-4674	35	7	a.	a.	NOUN
ejpam-4674	35	8	ouédraogo	ouédraogo	PROPN
ejpam-4674	35	9	/	/	SYM
ejpam-4674	35	10	eur	eur	PROPN
ejpam-4674	35	11	.	.	PUNCT
ejpam-4674	36	1	j.	j.	PROPN
ejpam-4674	36	2	pure	pure	PROPN
ejpam-4674	36	3	appl	appl	PROPN
ejpam-4674	36	4	.	.	PROPN
ejpam-4674	36	5	math	math	PROPN
ejpam-4674	36	6	,	,	PUNCT
ejpam-4674	36	7	16	16	NUM
ejpam-4674	36	8	(	(	PUNCT
ejpam-4674	36	9	1	1	NUM
ejpam-4674	36	10	)	)	PUNCT
ejpam-4674	36	11	(	(	PUNCT
ejpam-4674	36	12	2023	2023	NUM
ejpam-4674	36	13	)	)	PUNCT
ejpam-4674	36	14	,	,	PUNCT
ejpam-4674	36	15	404	404	NUM
ejpam-4674	36	16	-	-	SYM
ejpam-4674	36	17	417	417	NUM
ejpam-4674	36	18	406	406	NUM
ejpam-4674	36	19	as	as	ADP
ejpam-4674	36	20	tk(u	tk(u	NOUN
ejpam-4674	36	21	)	)	PUNCT
ejpam-4674	36	22	∈	∈	PROPN
ejpam-4674	36	23	h1	h1	NOUN
ejpam-4674	36	24	0	0	NUM
ejpam-4674	36	25	(	(	PUNCT
ejpam-4674	36	26	ω	ω	NOUN
ejpam-4674	36	27	)	)	PUNCT
ejpam-4674	36	28	,	,	PUNCT
ejpam-4674	36	29	every	every	DET
ejpam-4674	36	30	term	term	NOUN
ejpam-4674	36	31	makes	make	VERB
ejpam-4674	36	32	sense	sense	NOUN
ejpam-4674	36	33	in	in	ADP
ejpam-4674	36	34	(	(	PUNCT
ejpam-4674	36	35	8)	8)	NUM
ejpam-4674	36	36	.	.	PUNCT
ejpam-4674	37	1	when	when	SCONJ
ejpam-4674	37	2	f	f	PROPN
ejpam-4674	37	3	belongs	belong	VERB
ejpam-4674	37	4	to	to	ADP
ejpam-4674	37	5	l1(ω	l1(ω	PROPN
ejpam-4674	37	6	)	)	PUNCT
ejpam-4674	37	7	∩h−1(ω	∩h−1(ω	PROPN
ejpam-4674	37	8	)	)	PUNCT
ejpam-4674	37	9	,	,	PUNCT
ejpam-4674	37	10	the	the	DET
ejpam-4674	37	11	usual	usual	ADJ
ejpam-4674	37	12	weak	weak	ADJ
ejpam-4674	37	13	solution	solution	NOUN
ejpam-4674	37	14	of	of	ADP
ejpam-4674	37	15	(	(	PUNCT
ejpam-4674	37	16	1	1	NUM
ejpam-4674	37	17	)	)	PUNCT
ejpam-4674	37	18	,	,	PUNCT
ejpam-4674	37	19	namely	namely	NOUN
ejpam-4674	38	1	∀u	∀u	NOUN
ejpam-4674	38	2	∈	∈	NOUN
ejpam-4674	38	3	h1	h1	NOUN
ejpam-4674	38	4	0	0	NUM
ejpam-4674	38	5	(	(	PUNCT
ejpam-4674	38	6	ω	ω	NOUN
ejpam-4674	38	7	)	)	PUNCT
ejpam-4674	38	8	,	,	PUNCT
ejpam-4674	38	9	∀v	∀v	PROPN
ejpam-4674	38	10	∈	∈	PROPN
ejpam-4674	38	11	h1	h1	NOUN
ejpam-4674	38	12	0	0	NUM
ejpam-4674	38	13	(	(	PUNCT
ejpam-4674	38	14	ω	ω	NOUN
ejpam-4674	38	15	)	)	PUNCT
ejpam-4674	38	16	,	,	PUNCT
ejpam-4674	38	17	∫	∫	PROPN
ejpam-4674	38	18	ω	ω	PROPN
ejpam-4674	38	19	a∇u∇vdx	a∇u∇vdx	PROPN
ejpam-4674	38	20	=	=	SYM
ejpam-4674	38	21	∫	∫	PROPN
ejpam-4674	38	22	ω	ω	NUM
ejpam-4674	38	23	fvdx	fvdx	NOUN
ejpam-4674	38	24	,	,	PUNCT
ejpam-4674	38	25	(	(	PUNCT
ejpam-4674	38	26	9	9	X
ejpam-4674	38	27	)	)	PUNCT
ejpam-4674	38	28	is	be	AUX
ejpam-4674	38	29	also	also	ADV
ejpam-4674	38	30	a	a	DET
ejpam-4674	38	31	renormalized	renormalized	ADJ
ejpam-4674	38	32	solution	solution	NOUN
ejpam-4674	38	33	of	of	ADP
ejpam-4674	38	34	(	(	PUNCT
ejpam-4674	38	35	1	1	NUM
ejpam-4674	38	36	)	)	PUNCT
ejpam-4674	38	37	and	and	CCONJ
ejpam-4674	38	38	conversly	conversly	ADV
ejpam-4674	38	39	.	.	PUNCT
ejpam-4674	39	1	2.2	2.2	NUM
ejpam-4674	39	2	.	.	PUNCT
ejpam-4674	40	1	nurbs	nurb	NOUN
ejpam-4674	40	2	-	-	PUNCT
ejpam-4674	40	3	based	base	VERB
ejpam-4674	40	4	isogeometric	isogeometric	ADJ
ejpam-4674	40	5	analysis	analysis	NOUN
ejpam-4674	40	6	here	here	ADV
ejpam-4674	41	1	,	,	PUNCT
ejpam-4674	41	2	we	we	PRON
ejpam-4674	41	3	recall	recall	VERB
ejpam-4674	41	4	the	the	DET
ejpam-4674	41	5	basic	basic	ADJ
ejpam-4674	41	6	concepts	concept	NOUN
ejpam-4674	41	7	of	of	ADP
ejpam-4674	41	8	the	the	DET
ejpam-4674	41	9	b	b	NOUN
ejpam-4674	41	10	-	-	PUNCT
ejpam-4674	41	11	splines	spline	NOUN
ejpam-4674	41	12	and	and	CCONJ
ejpam-4674	41	13	nurbs	nurb	NOUN
ejpam-4674	41	14	basis	basis	NOUN
ejpam-4674	41	15	functions	function	NOUN
ejpam-4674	41	16	and	and	CCONJ
ejpam-4674	41	17	geometrical	geometrical	ADJ
ejpam-4674	41	18	representation	representation	NOUN
ejpam-4674	41	19	.	.	PUNCT
ejpam-4674	42	1	nurbs	nurb	NOUN
ejpam-4674	42	2	are	be	AUX
ejpam-4674	42	3	built	build	VERB
ejpam-4674	42	4	from	from	ADP
ejpam-4674	42	5	b	b	NOUN
ejpam-4674	42	6	-	-	PUNCT
ejpam-4674	42	7	splines	spline	NOUN
ejpam-4674	42	8	.	.	PUNCT
ejpam-4674	43	1	a	a	DET
ejpam-4674	43	2	knot	knot	ADJ
ejpam-4674	43	3	vector	vector	NOUN
ejpam-4674	43	4	in	in	ADP
ejpam-4674	43	5	one	one	NUM
ejpam-4674	43	6	dimenion	dimenion	NOUN
ejpam-4674	43	7	is	be	AUX
ejpam-4674	43	8	a	a	DET
ejpam-4674	43	9	set	set	NOUN
ejpam-4674	43	10	of	of	ADP
ejpam-4674	43	11	coordinates	coordinate	NOUN
ejpam-4674	43	12	in	in	ADP
ejpam-4674	43	13	the	the	DET
ejpam-4674	43	14	parametric	parametric	ADJ
ejpam-4674	43	15	space	space	NOUN
ejpam-4674	43	16	,	,	PUNCT
ejpam-4674	43	17	written	write	VERB
ejpam-4674	43	18	ξ	ξ	PROPN
ejpam-4674	43	19	=	=	PRON
ejpam-4674	43	20	{	{	PUNCT
ejpam-4674	43	21	ξ1	ξ1	NOUN
ejpam-4674	43	22	,	,	PUNCT
ejpam-4674	43	23	ξ2	ξ2	ADJ
ejpam-4674	43	24	,	,	PUNCT
ejpam-4674	43	25	...	...	PUNCT
ejpam-4674	43	26	,	,	PUNCT
ejpam-4674	43	27	ξn+p+1	ξn+p+1	PROPN
ejpam-4674	43	28	}	}	PUNCT
ejpam-4674	43	29	,	,	PUNCT
ejpam-4674	43	30	where	where	SCONJ
ejpam-4674	43	31	ξi	ξi	NOUN
ejpam-4674	43	32	is	be	AUX
ejpam-4674	43	33	the	the	DET
ejpam-4674	43	34	i	i	PROPN
ejpam-4674	43	35	-knot	-knot	PROPN
ejpam-4674	43	36	index	index	NOUN
ejpam-4674	44	1	i	i	PRON
ejpam-4674	44	2	∈	∈	PROPN
ejpam-4674	44	3	{	{	PUNCT
ejpam-4674	44	4	1	1	NUM
ejpam-4674	44	5	,	,	PUNCT
ejpam-4674	44	6	...	...	PUNCT
ejpam-4674	44	7	,	,	PUNCT
ejpam-4674	44	8	n	n	PROPN
ejpam-4674	44	9	+	+	X
ejpam-4674	44	10	p	p	X
ejpam-4674	45	1	+	+	ADJ
ejpam-4674	45	2	1	1	NUM
ejpam-4674	45	3	}	}	PUNCT
ejpam-4674	45	4	characterized	characterize	VERB
ejpam-4674	45	5	by	by	ADP
ejpam-4674	45	6	the	the	DET
ejpam-4674	45	7	polynomial	polynomial	ADJ
ejpam-4674	45	8	degree	degree	NOUN
ejpam-4674	45	9	p	p	NOUN
ejpam-4674	45	10	and	and	CCONJ
ejpam-4674	45	11	the	the	DET
ejpam-4674	45	12	number	number	NOUN
ejpam-4674	45	13	of	of	ADP
ejpam-4674	45	14	basis	basis	NOUN
ejpam-4674	45	15	functions	function	NOUN
ejpam-4674	45	16	n	n	CCONJ
ejpam-4674	45	17	defining	define	VERB
ejpam-4674	45	18	the	the	DET
ejpam-4674	45	19	b	b	NOUN
ejpam-4674	45	20	-	-	PUNCT
ejpam-4674	45	21	splines	spline	NOUN
ejpam-4674	45	22	basis	basis	NOUN
ejpam-4674	45	23	,	,	PUNCT
ejpam-4674	45	24	respectively	respectively	ADV
ejpam-4674	45	25	.	.	PUNCT
ejpam-4674	46	1	by	by	ADP
ejpam-4674	46	2	convention	convention	NOUN
ejpam-4674	46	3	,	,	PUNCT
ejpam-4674	46	4	we	we	PRON
ejpam-4674	46	5	assume	assume	VERB
ejpam-4674	46	6	that	that	SCONJ
ejpam-4674	46	7	ξ1	ξ1	NOUN
ejpam-4674	46	8	=	=	SYM
ejpam-4674	46	9	0	0	NUM
ejpam-4674	46	10	and	and	CCONJ
ejpam-4674	46	11	ξn+p+1	ξn+p+1	NUM
ejpam-4674	46	12	=	=	SYM
ejpam-4674	46	13	1	1	X
ejpam-4674	46	14	.	.	PUNCT
ejpam-4674	47	1	the	the	DET
ejpam-4674	47	2	consequence	consequence	NOUN
ejpam-4674	47	3	is	be	AUX
ejpam-4674	47	4	that	that	SCONJ
ejpam-4674	47	5	parametric	parametric	ADJ
ejpam-4674	47	6	domain	domain	NOUN
ejpam-4674	47	7	is	be	AUX
ejpam-4674	47	8	defined	define	VERB
ejpam-4674	47	9	as	as	ADP
ejpam-4674	47	10	ω̂	ω̂	NUM
ejpam-4674	47	11	:	:	PUNCT
ejpam-4674	47	12	=	=	SYM
ejpam-4674	47	13	(	(	PUNCT
ejpam-4674	47	14	ξ1	ξ1	NOUN
ejpam-4674	47	15	,	,	PUNCT
ejpam-4674	47	16	ξn+p+1	ξn+p+1	NOUN
ejpam-4674	47	17	)	)	PUNCT
ejpam-4674	47	18	=	=	SYM
ejpam-4674	48	1	(	(	PUNCT
ejpam-4674	48	2	0	0	NUM
ejpam-4674	48	3	,	,	PUNCT
ejpam-4674	48	4	1	1	NUM
ejpam-4674	48	5	)	)	PUNCT
ejpam-4674	48	6	⊂	⊂	PROPN
ejpam-4674	48	7	r.	r.	PROPN
ejpam-4674	48	8	knots	knots	PROPN
ejpam-4674	48	9	may	may	AUX
ejpam-4674	48	10	be	be	AUX
ejpam-4674	48	11	repeated	repeat	VERB
ejpam-4674	48	12	with	with	ADP
ejpam-4674	48	13	the	the	DET
ejpam-4674	48	14	number	number	NOUN
ejpam-4674	48	15	of	of	ADP
ejpam-4674	48	16	repetitions	repetition	NOUN
ejpam-4674	48	17	indicating	indicate	VERB
ejpam-4674	48	18	its	its	PRON
ejpam-4674	48	19	multiplicity	multiplicity	NOUN
ejpam-4674	48	20	.	.	PUNCT
ejpam-4674	49	1	to	to	PART
ejpam-4674	49	2	investigate	investigate	VERB
ejpam-4674	49	3	the	the	DET
ejpam-4674	49	4	concept	concept	NOUN
ejpam-4674	49	5	of	of	ADP
ejpam-4674	49	6	mesh	mesh	NOUN
ejpam-4674	49	7	elements	element	NOUN
ejpam-4674	49	8	in	in	ADP
ejpam-4674	49	9	the	the	DET
ejpam-4674	49	10	parametric	parametric	ADJ
ejpam-4674	49	11	domain	domain	NOUN
ejpam-4674	49	12	,	,	PUNCT
ejpam-4674	49	13	we	we	PRON
ejpam-4674	49	14	collect	collect	VERB
ejpam-4674	49	15	all	all	DET
ejpam-4674	49	16	the	the	DET
ejpam-4674	49	17	r	r	NOUN
ejpam-4674	49	18	distinct	distinct	ADJ
ejpam-4674	49	19	and	and	CCONJ
ejpam-4674	49	20	ordered	order	VERB
ejpam-4674	49	21	knots	knot	NOUN
ejpam-4674	49	22	of	of	ADP
ejpam-4674	49	23	ξ	ξ	PROPN
ejpam-4674	49	24	,	,	PUNCT
ejpam-4674	49	25	say	say	VERB
ejpam-4674	49	26	ζj	ζj	PROPN
ejpam-4674	49	27	for	for	ADP
ejpam-4674	49	28	j	j	PROPN
ejpam-4674	49	29	=	=	SYM
ejpam-4674	49	30	1	1	NUM
ejpam-4674	49	31	,	,	PUNCT
ejpam-4674	49	32	...	...	PUNCT
ejpam-4674	49	33	,	,	PUNCT
ejpam-4674	49	34	r	r	NOUN
ejpam-4674	49	35	into	into	ADP
ejpam-4674	49	36	a	a	DET
ejpam-4674	49	37	vector	vector	NOUN
ejpam-4674	49	38	z	z	NOUN
ejpam-4674	49	39	=	=	SYM
ejpam-4674	49	40	{	{	PUNCT
ejpam-4674	49	41	ζ1	ζ1	NOUN
ejpam-4674	49	42	,	,	PUNCT
ejpam-4674	49	43	...	...	PUNCT
ejpam-4674	49	44	,	,	PUNCT
ejpam-4674	49	45	ζr	ζr	ADP
ejpam-4674	49	46	}	}	PUNCT
ejpam-4674	49	47	with	with	ADP
ejpam-4674	49	48	ζ1	ζ1	PROPN
ejpam-4674	49	49	≡	≡	PROPN
ejpam-4674	49	50	ξ1	ξ1	PROPN
ejpam-4674	49	51	=	=	SYM
ejpam-4674	49	52	0	0	NUM
ejpam-4674	49	53	and	and	CCONJ
ejpam-4674	49	54	ζr	ζr	ADP
ejpam-4674	49	55	≡	≡	PROPN
ejpam-4674	49	56	ξn+p+1	ξn+p+1	PROPN
ejpam-4674	49	57	=	=	SYM
ejpam-4674	49	58	1	1	X
ejpam-4674	49	59	.	.	PUNCT
ejpam-4674	50	1	in	in	ADP
ejpam-4674	50	2	particular	particular	ADJ
ejpam-4674	50	3	,	,	PUNCT
ejpam-4674	50	4	the	the	DET
ejpam-4674	50	5	one	one	NUM
ejpam-4674	50	6	dimensional	dimensional	ADJ
ejpam-4674	50	7	mesh	mesh	NOUN
ejpam-4674	50	8	over	over	ADP
ejpam-4674	50	9	ω̂	ω̂	NUM
ejpam-4674	50	10	,	,	PUNCT
ejpam-4674	50	11	say	say	VERB
ejpam-4674	50	12	qh	qh	NOUN
ejpam-4674	50	13	,	,	PUNCT
ejpam-4674	50	14	is	be	AUX
ejpam-4674	50	15	given	give	VERB
ejpam-4674	50	16	by	by	ADP
ejpam-4674	50	17	qh	qh	NOUN
ejpam-4674	50	18	:	:	PUNCT
ejpam-4674	50	19	=	=	PRON
ejpam-4674	50	20	{	{	PUNCT
ejpam-4674	50	21	q	q	NOUN
ejpam-4674	50	22	=	=	X
ejpam-4674	50	23	(	(	PUNCT
ejpam-4674	50	24	ζj	ζj	NOUN
ejpam-4674	50	25	,	,	PUNCT
ejpam-4674	50	26	ζj+1	ζj+1	PROPN
ejpam-4674	50	27	)	)	PUNCT
ejpam-4674	50	28	:	:	PUNCT
ejpam-4674	51	1	j	j	X
ejpam-4674	51	2	=	=	SYM
ejpam-4674	51	3	1	1	NUM
ejpam-4674	51	4	,	,	PUNCT
ejpam-4674	51	5	...	...	PUNCT
ejpam-4674	51	6	,	,	PUNCT
ejpam-4674	51	7	r	r	NOUN
ejpam-4674	51	8	−	−	PROPN
ejpam-4674	51	9	1	1	NUM
ejpam-4674	51	10	}	}	PUNCT
ejpam-4674	51	11	;	;	PUNCT
ejpam-4674	51	12	we	we	PRON
ejpam-4674	51	13	denote	denote	VERB
ejpam-4674	51	14	by	by	ADP
ejpam-4674	51	15	h	h	NOUN
ejpam-4674	51	16	:	:	PUNCT
ejpam-4674	51	17	=	=	SYM
ejpam-4674	52	1	max{hq	max{hq	X
ejpam-4674	52	2	:	:	PUNCT
ejpam-4674	52	3	q	q	PROPN
ejpam-4674	52	4	∈	∈	PROPN
ejpam-4674	52	5	qh	qh	NOUN
ejpam-4674	52	6	}	}	PUNCT
ejpam-4674	52	7	,	,	PUNCT
ejpam-4674	52	8	where	where	SCONJ
ejpam-4674	52	9	hq	hq	NOUN
ejpam-4674	52	10	:	:	PUNCT
ejpam-4674	52	11	=	=	SYM
ejpam-4674	52	12	diam(q	diam(q	PROPN
ejpam-4674	52	13	)	)	PUNCT
ejpam-4674	52	14	∀q	∀q	PROPN
ejpam-4674	52	15	∈	∈	PROPN
ejpam-4674	52	16	qh	qh	PROPN
ejpam-4674	52	17	(	(	PUNCT
ejpam-4674	52	18	10	10	NUM
ejpam-4674	52	19	)	)	PUNCT
ejpam-4674	52	20	the	the	DET
ejpam-4674	52	21	global	global	ADJ
ejpam-4674	52	22	mesh	mesh	NOUN
ejpam-4674	52	23	size	size	NOUN
ejpam-4674	52	24	in	in	ADP
ejpam-4674	52	25	the	the	DET
ejpam-4674	52	26	parametric	parametric	ADJ
ejpam-4674	52	27	domain	domain	NOUN
ejpam-4674	52	28	ω̂.	ω̂.	NOUN
ejpam-4674	52	29	by	by	ADP
ejpam-4674	52	30	means	mean	NOUN
ejpam-4674	52	31	of	of	ADP
ejpam-4674	52	32	the	the	DET
ejpam-4674	52	33	cox	cox	PROPN
ejpam-4674	52	34	-	-	PUNCT
ejpam-4674	52	35	de	de	X
ejpam-4674	52	36	boor	boor	ADJ
ejpam-4674	52	37	recursion	recursion	NOUN
ejpam-4674	52	38	formula	formula	NOUN
ejpam-4674	52	39	,	,	PUNCT
ejpam-4674	52	40	(	(	PUNCT
ejpam-4674	52	41	see	see	VERB
ejpam-4674	52	42	[	[	X
ejpam-4674	52	43	5	5	NUM
ejpam-4674	52	44	]	]	PUNCT
ejpam-4674	52	45	,	,	PUNCT
ejpam-4674	52	46	[	[	X
ejpam-4674	52	47	10	10	NUM
ejpam-4674	52	48	]	]	NUM
ejpam-4674	52	49	)	)	PUNCT
ejpam-4674	52	50	,	,	PUNCT
ejpam-4674	52	51	univariate	univariate	ADJ
ejpam-4674	52	52	b	b	NUM
ejpam-4674	52	53	-	-	PUNCT
ejpam-4674	52	54	splines	spline	NOUN
ejpam-4674	52	55	basis	basis	NOUN
ejpam-4674	52	56	functions	function	NOUN
ejpam-4674	52	57	ni	ni	PROPN
ejpam-4674	52	58	:	:	PUNCT
ejpam-4674	52	59	ω̂	ω̂	PUNCT
ejpam-4674	52	60	−→	−→	NOUN
ejpam-4674	52	61	r	r	NOUN
ejpam-4674	52	62	for	for	ADP
ejpam-4674	52	63	i	i	PRON
ejpam-4674	52	64	=	=	NOUN
ejpam-4674	52	65	1	1	NUM
ejpam-4674	52	66	,	,	PUNCT
ejpam-4674	52	67	...	...	PUNCT
ejpam-4674	52	68	,	,	PUNCT
ejpam-4674	52	69	n	n	CCONJ
ejpam-4674	52	70	,	,	PUNCT
ejpam-4674	52	71	are	be	AUX
ejpam-4674	52	72	built	build	VERB
ejpam-4674	52	73	as	as	ADP
ejpam-4674	52	74	piecewise	piecewise	NOUN
ejpam-4674	52	75	polynomials	polynomial	NOUN
ejpam-4674	52	76	of	of	ADP
ejpam-4674	52	77	degree	degree	NOUN
ejpam-4674	52	78	p	p	NOUN
ejpam-4674	52	79	with	with	ADP
ejpam-4674	52	80	compact	compact	ADJ
ejpam-4674	52	81	support	support	NOUN
ejpam-4674	52	82	over	over	ADP
ejpam-4674	52	83	the	the	DET
ejpam-4674	52	84	interval	interval	NOUN
ejpam-4674	52	85	(	(	PUNCT
ejpam-4674	52	86	ξi	ξi	NOUN
ejpam-4674	52	87	,	,	PUNCT
ejpam-4674	52	88	ξi+p+1	ξi+p+1	NUM
ejpam-4674	52	89	)	)	PUNCT
ejpam-4674	52	90	.	.	PUNCT
ejpam-4674	53	1	the	the	DET
ejpam-4674	53	2	basis	basis	NOUN
ejpam-4674	53	3	functions	function	NOUN
ejpam-4674	53	4	are	be	AUX
ejpam-4674	53	5	everywhere	everywhere	ADV
ejpam-4674	53	6	pointwise	pointwise	VERB
ejpam-4674	53	7	nonnegative	nonnegative	ADJ
ejpam-4674	53	8	and	and	CCONJ
ejpam-4674	53	9	c∞−continuous	c∞−continuous	ADJ
ejpam-4674	53	10	,	,	PUNCT
ejpam-4674	53	11	except	except	SCONJ
ejpam-4674	53	12	in	in	ADP
ejpam-4674	53	13	the	the	DET
ejpam-4674	53	14	knot	knot	NOUN
ejpam-4674	53	15	values	value	NOUN
ejpam-4674	53	16	ζj	ζj	X
ejpam-4674	53	17	,	,	PUNCT
ejpam-4674	53	18	where	where	SCONJ
ejpam-4674	53	19	they	they	PRON
ejpam-4674	53	20	are	be	AUX
ejpam-4674	53	21	only	only	ADV
ejpam-4674	53	22	cp−mj−	cp−mj−	ADV
ejpam-4674	53	23	continuous	continuous	ADJ
ejpam-4674	53	24	.	.	PUNCT
ejpam-4674	54	1	in	in	ADP
ejpam-4674	54	2	particular	particular	ADJ
ejpam-4674	54	3	,	,	PUNCT
ejpam-4674	54	4	we	we	PRON
ejpam-4674	54	5	define	define	VERB
ejpam-4674	54	6	for	for	ADP
ejpam-4674	54	7	all	all	PRON
ejpam-4674	54	8	j	j	NOUN
ejpam-4674	54	9	=	=	SYM
ejpam-4674	54	10	1	1	NUM
ejpam-4674	54	11	,	,	PUNCT
ejpam-4674	54	12	...	...	PUNCT
ejpam-4674	54	13	,	,	PUNCT
ejpam-4674	55	1	r	r	X
ejpam-4674	55	2	,	,	PUNCT
ejpam-4674	55	3	the	the	DET
ejpam-4674	55	4	smoothness	smoothness	ADJ
ejpam-4674	55	5	integer	integer	NOUN
ejpam-4674	55	6	parameters	parameter	NOUN
ejpam-4674	55	7	kj	kj	NOUN
ejpam-4674	55	8	=	=	PROPN
ejpam-4674	55	9	p	p	X
ejpam-4674	55	10	−	−	PROPN
ejpam-4674	55	11	mj	mj	NOUN
ejpam-4674	55	12	+	+	NOUN
ejpam-4674	55	13	1	1	NUM
ejpam-4674	55	14	such	such	ADJ
ejpam-4674	55	15	that	that	SCONJ
ejpam-4674	55	16	0	0	NUM
ejpam-4674	55	17	≤	≤	NUM
ejpam-4674	55	18	kj	kj	NOUN
ejpam-4674	55	19	≤	≤	PROPN
ejpam-4674	55	20	p	p	X
ejpam-4674	55	21	,	,	PUNCT
ejpam-4674	55	22	we	we	PRON
ejpam-4674	55	23	collect	collect	VERB
ejpam-4674	55	24	them	they	PRON
ejpam-4674	55	25	in	in	ADP
ejpam-4674	55	26	a	a	DET
ejpam-4674	55	27	vector	vector	NOUN
ejpam-4674	55	28	k	k	NOUN
ejpam-4674	55	29	=	=	PUNCT
ejpam-4674	55	30	{	{	PUNCT
ejpam-4674	55	31	k1	k1	PROPN
ejpam-4674	55	32	,	,	PUNCT
ejpam-4674	55	33	...	...	PUNCT
ejpam-4674	55	34	,	,	PUNCT
ejpam-4674	55	35	kr	kr	PROPN
ejpam-4674	55	36	}	}	PUNCT
ejpam-4674	55	37	,	,	PUNCT
ejpam-4674	55	38	and	and	CCONJ
ejpam-4674	55	39	we	we	PRON
ejpam-4674	55	40	introduce	introduce	VERB
ejpam-4674	55	41	the	the	DET
ejpam-4674	55	42	minimum	minimum	ADJ
ejpam-4674	55	43	integer	integer	NOUN
ejpam-4674	55	44	parameter	parameter	NOUN
ejpam-4674	55	45	kmin	kmin	NOUN
ejpam-4674	55	46	:	:	PUNCT
ejpam-4674	55	47	=	=	SYM
ejpam-4674	55	48	min	min	PROPN
ejpam-4674	55	49	j=2,	j=2,	PROPN
ejpam-4674	55	50	...	...	PUNCT
ejpam-4674	55	51	,r−1	,r−1	PUNCT
ejpam-4674	55	52	{	{	PUNCT
ejpam-4674	55	53	kj	kj	NOUN
ejpam-4674	55	54	}	}	PUNCT
ejpam-4674	55	55	.	.	PUNCT
ejpam-4674	56	1	the	the	DET
ejpam-4674	56	2	b	b	NUM
ejpam-4674	56	3	-	-	PUNCT
ejpam-4674	56	4	splines	spline	NOUN
ejpam-4674	56	5	space	space	NOUN
ejpam-4674	56	6	built	build	VERB
ejpam-4674	56	7	from	from	ADP
ejpam-4674	56	8	the	the	DET
ejpam-4674	56	9	basis	basis	NOUN
ejpam-4674	56	10	function	function	NOUN
ejpam-4674	56	11	in	in	ADP
ejpam-4674	56	12	the	the	DET
ejpam-4674	56	13	parametric	parametric	ADJ
ejpam-4674	56	14	domain	domain	NOUN
ejpam-4674	56	15	ω̂	ω̂	PUNCT
ejpam-4674	56	16	reads	read	VERB
ejpam-4674	56	17	:	:	PUNCT
ejpam-4674	56	18	sh	sh	INTJ
ejpam-4674	56	19	:	:	PUNCT
ejpam-4674	57	1	=	=	SYM
ejpam-4674	57	2	span{ni}ni=1	span{ni}ni=1	ADJ
ejpam-4674	57	3	.	.	PUNCT
ejpam-4674	58	1	(	(	PUNCT
ejpam-4674	58	2	11	11	NUM
ejpam-4674	58	3	)	)	PUNCT
ejpam-4674	58	4	by	by	ADP
ejpam-4674	58	5	definition	definition	NOUN
ejpam-4674	58	6	,	,	PUNCT
ejpam-4674	58	7	the	the	DET
ejpam-4674	58	8	b	b	NOUN
ejpam-4674	58	9	-	-	PUNCT
ejpam-4674	58	10	splines	spline	NOUN
ejpam-4674	58	11	in	in	ADP
ejpam-4674	58	12	sh	sh	PROPN
ejpam-4674	58	13	are	be	AUX
ejpam-4674	58	14	globally	globally	ADV
ejpam-4674	58	15	ckmin−continuous	ckmin−continuous	ADJ
ejpam-4674	58	16	.	.	PUNCT
ejpam-4674	59	1	y.	y.	PROPN
ejpam-4674	59	2	c.	c.	PROPN
ejpam-4674	59	3	bassonon	bassonon	PROPN
ejpam-4674	59	4	,	,	PUNCT
ejpam-4674	59	5	a.	a.	NOUN
ejpam-4674	59	6	ouédraogo	ouédraogo	PROPN
ejpam-4674	59	7	/	/	SYM
ejpam-4674	59	8	eur	eur	PROPN
ejpam-4674	59	9	.	.	PUNCT
ejpam-4674	60	1	j.	j.	PROPN
ejpam-4674	60	2	pure	pure	PROPN
ejpam-4674	60	3	appl	appl	PROPN
ejpam-4674	60	4	.	.	PROPN
ejpam-4674	60	5	math	math	PROPN
ejpam-4674	60	6	,	,	PUNCT
ejpam-4674	60	7	16	16	NUM
ejpam-4674	60	8	(	(	PUNCT
ejpam-4674	60	9	1	1	NUM
ejpam-4674	60	10	)	)	PUNCT
ejpam-4674	60	11	(	(	PUNCT
ejpam-4674	60	12	2023	2023	NUM
ejpam-4674	60	13	)	)	PUNCT
ejpam-4674	60	14	,	,	PUNCT
ejpam-4674	60	15	404	404	NUM
ejpam-4674	60	16	-	-	SYM
ejpam-4674	60	17	417	417	NUM
ejpam-4674	60	18	407	407	NUM
ejpam-4674	60	19	for	for	ADP
ejpam-4674	60	20	each	each	DET
ejpam-4674	60	21	multi	multi	ADJ
ejpam-4674	60	22	-	-	NOUN
ejpam-4674	60	23	index	index	NOUN
ejpam-4674	60	24	i	i	PRON
ejpam-4674	60	25	:	:	PUNCT
ejpam-4674	60	26	=	=	SYM
ejpam-4674	60	27	(	(	PUNCT
ejpam-4674	60	28	i1	i1	PROPN
ejpam-4674	60	29	,	,	PUNCT
ejpam-4674	60	30	...	...	PUNCT
ejpam-4674	60	31	,	,	PUNCT
ejpam-4674	60	32	iκ	iκ	X
ejpam-4674	60	33	)	)	PUNCT
ejpam-4674	60	34	in	in	ADP
ejpam-4674	60	35	the	the	DET
ejpam-4674	60	36	set	set	NOUN
ejpam-4674	61	1	i	i	PRON
ejpam-4674	61	2	=	=	PUNCT
ejpam-4674	61	3	{	{	PUNCT
ejpam-4674	61	4	i	i	NOUN
ejpam-4674	61	5	=	=	SYM
ejpam-4674	61	6	(	(	PUNCT
ejpam-4674	61	7	i1	i1	PROPN
ejpam-4674	61	8	,	,	PUNCT
ejpam-4674	61	9	...	...	PUNCT
ejpam-4674	61	10	,	,	PUNCT
ejpam-4674	61	11	iκ	iκ	NUM
ejpam-4674	61	12	)	)	PUNCT
ejpam-4674	61	13	:	:	PUNCT
ejpam-4674	61	14	0	0	NUM
ejpam-4674	61	15	≤	≤	NUM
ejpam-4674	61	16	iα	iα	VERB
ejpam-4674	61	17	≤	≤	NUM
ejpam-4674	61	18	nα	nα	VERB
ejpam-4674	61	19	,	,	PUNCT
ejpam-4674	61	20	for	for	ADP
ejpam-4674	61	21	1	1	NUM
ejpam-4674	61	22	≤	≤	NUM
ejpam-4674	61	23	α	α	PRON
ejpam-4674	61	24	≤	≤	NUM
ejpam-4674	61	25	κ	κ	X
ejpam-4674	61	26	}	}	PUNCT
ejpam-4674	61	27	,	,	PUNCT
ejpam-4674	61	28	we	we	PRON
ejpam-4674	61	29	define	define	VERB
ejpam-4674	61	30	the	the	DET
ejpam-4674	61	31	multivariate	multivariate	NOUN
ejpam-4674	61	32	b	b	NOUN
ejpam-4674	61	33	-	-	PUNCT
ejpam-4674	61	34	splines	spline	NOUN
ejpam-4674	61	35	basis	basis	NOUN
ejpam-4674	61	36	functions	function	NOUN
ejpam-4674	61	37	as	as	ADP
ejpam-4674	61	38	:	:	PUNCT
ejpam-4674	61	39	ni	ni	PROPN
ejpam-4674	61	40	:	:	PUNCT
ejpam-4674	61	41	ω̂	ω̂	PUNCT
ejpam-4674	61	42	→	→	SYM
ejpam-4674	61	43	r	r	NOUN
ejpam-4674	61	44	,	,	PUNCT
ejpam-4674	61	45	ni(η	ni(η	PUNCT
ejpam-4674	61	46	)	)	PUNCT
ejpam-4674	61	47	:	:	PUNCT
ejpam-4674	62	1	=	=	SYM
ejpam-4674	62	2	κ∏	κ∏	PROPN
ejpam-4674	62	3	α=1	α=1	X
ejpam-4674	62	4	nα	nα	ADP
ejpam-4674	62	5	iα(ηα	iα(ηα	PROPN
ejpam-4674	62	6	)	)	PUNCT
ejpam-4674	62	7	,	,	PUNCT
ejpam-4674	62	8	(	(	PUNCT
ejpam-4674	62	9	12	12	NUM
ejpam-4674	62	10	)	)	PUNCT
ejpam-4674	62	11	and	and	CCONJ
ejpam-4674	62	12	we	we	PRON
ejpam-4674	62	13	denote	denote	VERB
ejpam-4674	62	14	the	the	DET
ejpam-4674	62	15	tensor	tensor	NOUN
ejpam-4674	62	16	product	product	NOUN
ejpam-4674	62	17	b	b	NOUN
ejpam-4674	62	18	-	-	PUNCT
ejpam-4674	62	19	splines	spline	NOUN
ejpam-4674	62	20	space	space	NOUN
ejpam-4674	62	21	,	,	PUNCT
ejpam-4674	62	22	as	as	ADP
ejpam-4674	62	23	:	:	PUNCT
ejpam-4674	62	24	sh	sh	INTJ
ejpam-4674	62	25	:	:	PUNCT
ejpam-4674	62	26	=	=	NOUN
ejpam-4674	62	27	span{ni}i∈i	span{ni}i∈i	ADV
ejpam-4674	62	28	.	.	PUNCT
ejpam-4674	63	1	(	(	PUNCT
ejpam-4674	63	2	13	13	NUM
ejpam-4674	63	3	)	)	PUNCT
ejpam-4674	63	4	uniand	uniand	NOUN
ejpam-4674	63	5	multivariate	multivariate	NOUN
ejpam-4674	63	6	nurbs	nurbs	NOUN
ejpam-4674	63	7	basis	basis	NOUN
ejpam-4674	63	8	functions	function	NOUN
ejpam-4674	63	9	are	be	AUX
ejpam-4674	63	10	defined	define	VERB
ejpam-4674	63	11	on	on	ADP
ejpam-4674	63	12	the	the	DET
ejpam-4674	63	13	parametric	parametric	ADJ
ejpam-4674	63	14	domain	domain	NOUN
ejpam-4674	63	15	ω̂	ω̂	PUNCT
ejpam-4674	63	16	=	=	SYM
ejpam-4674	63	17	(	(	PUNCT
ejpam-4674	63	18	0	0	NUM
ejpam-4674	63	19	,	,	PUNCT
ejpam-4674	63	20	1)κ	1)κ	NOUN
ejpam-4674	63	21	once	once	ADV
ejpam-4674	63	22	provided	provide	VERB
ejpam-4674	63	23	κ	κ	PRON
ejpam-4674	63	24	knot	knot	NOUN
ejpam-4674	63	25	vectors	vector	NOUN
ejpam-4674	63	26	ξα	ξα	VERB
ejpam-4674	63	27	for	for	ADP
ejpam-4674	63	28	α	α	NOUN
ejpam-4674	63	29	=	=	SYM
ejpam-4674	63	30	1	1	NUM
ejpam-4674	63	31	,	,	PUNCT
ejpam-4674	63	32	...	...	PUNCT
ejpam-4674	63	33	,	,	PUNCT
ejpam-4674	63	34	κ	κ	NOUN
ejpam-4674	63	35	and	and	CCONJ
ejpam-4674	63	36	the	the	DET
ejpam-4674	63	37	corresponding	corresponding	ADJ
ejpam-4674	63	38	b	b	X
ejpam-4674	63	39	-	-	PUNCT
ejpam-4674	63	40	splines	spline	NOUN
ejpam-4674	63	41	basis	basis	NOUN
ejpam-4674	63	42	{	{	PUNCT
ejpam-4674	63	43	ni}i∈i	ni}i∈i	INTJ
ejpam-4674	63	44	,	,	PUNCT
ejpam-4674	63	45	by	by	ADP
ejpam-4674	63	46	introducing	introduce	VERB
ejpam-4674	63	47	a	a	DET
ejpam-4674	63	48	set	set	NOUN
ejpam-4674	63	49	of	of	ADP
ejpam-4674	63	50	real	real	ADJ
ejpam-4674	63	51	numbers	number	NOUN
ejpam-4674	63	52	ω	ω	NOUN
ejpam-4674	63	53	=	=	SYM
ejpam-4674	63	54	{	{	PUNCT
ejpam-4674	63	55	ωi}i∈i	ωi}i∈i	PROPN
ejpam-4674	63	56	,	,	PUNCT
ejpam-4674	63	57	called	call	VERB
ejpam-4674	63	58	the	the	DET
ejpam-4674	63	59	weights	weight	NOUN
ejpam-4674	63	60	.	.	PUNCT
ejpam-4674	64	1	we	we	PRON
ejpam-4674	64	2	assume	assume	VERB
ejpam-4674	64	3	that	that	SCONJ
ejpam-4674	64	4	the	the	DET
ejpam-4674	64	5	weights	weight	NOUN
ejpam-4674	64	6	are	be	AUX
ejpam-4674	64	7	positive	positive	ADJ
ejpam-4674	64	8	and	and	CCONJ
ejpam-4674	64	9	we	we	PRON
ejpam-4674	64	10	define	define	VERB
ejpam-4674	64	11	a	a	DET
ejpam-4674	64	12	positive	positive	ADJ
ejpam-4674	64	13	scalar	scalar	ADJ
ejpam-4674	64	14	piecewise	piecewise	NOUN
ejpam-4674	64	15	polynomial	polynomial	ADJ
ejpam-4674	64	16	function	function	NOUN
ejpam-4674	64	17	,	,	PUNCT
ejpam-4674	64	18	called	call	VERB
ejpam-4674	64	19	weighting	weight	VERB
ejpam-4674	64	20	function	function	NOUN
ejpam-4674	64	21	,	,	PUNCT
ejpam-4674	64	22	as	as	ADP
ejpam-4674	64	23	:	:	PUNCT
ejpam-4674	64	24	w	w	X
ejpam-4674	64	25	:	:	PUNCT
ejpam-4674	64	26	ω̂	ω̂	PUNCT
ejpam-4674	64	27	→	→	SYM
ejpam-4674	64	28	r	r	X
ejpam-4674	64	29	,	,	PUNCT
ejpam-4674	64	30	w	w	PROPN
ejpam-4674	64	31	(	(	PUNCT
ejpam-4674	64	32	η	η	NOUN
ejpam-4674	64	33	)	)	PUNCT
ejpam-4674	64	34	:	:	PUNCT
ejpam-4674	65	1	=	=	PUNCT
ejpam-4674	65	2	∑	∑	ADP
ejpam-4674	65	3	i∈i	i∈i	ADJ
ejpam-4674	65	4	ωini(η	ωini(η	PROPN
ejpam-4674	65	5	)	)	PUNCT
ejpam-4674	65	6	.	.	PUNCT
ejpam-4674	66	1	(	(	PUNCT
ejpam-4674	66	2	14	14	NUM
ejpam-4674	66	3	)	)	PUNCT
ejpam-4674	66	4	the	the	DET
ejpam-4674	66	5	i	i	PROPN
ejpam-4674	66	6	-	-	PUNCT
ejpam-4674	66	7	th	th	VERB
ejpam-4674	66	8	multivariate	multivariate	NOUN
ejpam-4674	66	9	nurbs	nurbs	NOUN
ejpam-4674	66	10	basis	basis	NOUN
ejpam-4674	66	11	function	function	NOUN
ejpam-4674	66	12	is	be	AUX
ejpam-4674	66	13	defined	define	VERB
ejpam-4674	66	14	as	as	ADP
ejpam-4674	66	15	ri	ri	PROPN
ejpam-4674	66	16	:	:	PUNCT
ejpam-4674	66	17	ω̂	ω̂	PUNCT
ejpam-4674	66	18	→	→	SYM
ejpam-4674	66	19	r	r	NOUN
ejpam-4674	66	20	,	,	PUNCT
ejpam-4674	66	21	ri(η	ri(η	NOUN
ejpam-4674	66	22	)	)	PUNCT
ejpam-4674	67	1	=	=	SYM
ejpam-4674	67	2	ni(η)ωi	ni(η)ωi	PROPN
ejpam-4674	67	3	w	w	PROPN
ejpam-4674	67	4	(	(	PUNCT
ejpam-4674	67	5	η	η	NOUN
ejpam-4674	67	6	)	)	PUNCT
ejpam-4674	67	7	∀i	∀i	NOUN
ejpam-4674	67	8	∈	∈	PROPN
ejpam-4674	67	9	i	i	PRON
ejpam-4674	67	10	,	,	PUNCT
ejpam-4674	67	11	(	(	PUNCT
ejpam-4674	67	12	15	15	NUM
ejpam-4674	67	13	)	)	PUNCT
ejpam-4674	67	14	and	and	CCONJ
ejpam-4674	67	15	the	the	DET
ejpam-4674	67	16	corresponding	correspond	VERB
ejpam-4674	67	17	nurbs	nurb	NOUN
ejpam-4674	67	18	space	space	NOUN
ejpam-4674	67	19	over	over	ADP
ejpam-4674	67	20	the	the	DET
ejpam-4674	67	21	parametric	parametric	ADJ
ejpam-4674	67	22	domain	domain	NOUN
ejpam-4674	67	23	ω	ω	NOUN
ejpam-4674	67	24	reads	read	VERB
ejpam-4674	67	25	:	:	PUNCT
ejpam-4674	67	26	nh	nh	PROPN
ejpam-4674	67	27	:	:	PUNCT
ejpam-4674	67	28	=	=	SYM
ejpam-4674	67	29	span{ri}i∈i	span{ri}i∈i	X
ejpam-4674	67	30	.	.	PUNCT
ejpam-4674	68	1	(	(	PUNCT
ejpam-4674	68	2	16	16	NUM
ejpam-4674	68	3	)	)	PUNCT
ejpam-4674	68	4	therefore	therefore	ADV
ejpam-4674	68	5	,	,	PUNCT
ejpam-4674	68	6	we	we	PRON
ejpam-4674	68	7	consider	consider	VERB
ejpam-4674	68	8	the	the	DET
ejpam-4674	68	9	nurbs	nurbs	NOUN
ejpam-4674	68	10	space	space	NOUN
ejpam-4674	68	11	over	over	ADP
ejpam-4674	68	12	the	the	DET
ejpam-4674	68	13	parametric	parametric	ADJ
ejpam-4674	68	14	domain	domain	NOUN
ejpam-4674	68	15	ω̂	ω̂	PUNCT
ejpam-4674	68	16	of	of	ADP
ejpam-4674	68	17	(	(	PUNCT
ejpam-4674	68	18	16	16	NUM
ejpam-4674	68	19	)	)	PUNCT
ejpam-4674	68	20	and	and	CCONJ
ejpam-4674	68	21	a	a	DET
ejpam-4674	68	22	set	set	NOUN
ejpam-4674	68	23	of	of	ADP
ejpam-4674	68	24	control	control	NOUN
ejpam-4674	68	25	points	point	NOUN
ejpam-4674	68	26	{	{	PUNCT
ejpam-4674	68	27	pi}i∈i	pi}i∈i	INTJ
ejpam-4674	68	28	⊂	⊂	PROPN
ejpam-4674	68	29	rd.then	rd.then	NOUN
ejpam-4674	68	30	a	a	DET
ejpam-4674	68	31	nurbs	nurbs	NOUN
ejpam-4674	68	32	geometry	geometry	NOUN
ejpam-4674	68	33	ω	ω	PROPN
ejpam-4674	68	34	in	in	ADP
ejpam-4674	68	35	rd	rd	PROPN
ejpam-4674	68	36	is	be	AUX
ejpam-4674	68	37	defined	define	VERB
ejpam-4674	68	38	from	from	ADP
ejpam-4674	68	39	the	the	DET
ejpam-4674	68	40	parametric	parametric	ADJ
ejpam-4674	68	41	domain	domain	NOUN
ejpam-4674	68	42	ω̂	ω̂	PUNCT
ejpam-4674	68	43	=	=	SYM
ejpam-4674	68	44	(	(	PUNCT
ejpam-4674	68	45	0	0	NUM
ejpam-4674	68	46	,	,	PUNCT
ejpam-4674	68	47	1)κ	1)κ	NUM
ejpam-4674	68	48	by	by	ADP
ejpam-4674	68	49	means	mean	NOUN
ejpam-4674	68	50	of	of	ADP
ejpam-4674	68	51	the	the	DET
ejpam-4674	68	52	geometrical	geometrical	ADJ
ejpam-4674	68	53	mapping	mapping	NOUN
ejpam-4674	68	54	:	:	PUNCT
ejpam-4674	68	55	x	x	SYM
ejpam-4674	68	56	:	:	PUNCT
ejpam-4674	68	57	ω̂	ω̂	PUNCT
ejpam-4674	68	58	→	→	SYM
ejpam-4674	68	59	ω	ω	PROPN
ejpam-4674	68	60	⊆	⊆	NUM
ejpam-4674	68	61	rd	rd	NOUN
ejpam-4674	68	62	x(η	x(η	PROPN
ejpam-4674	68	63	)	)	PUNCT
ejpam-4674	69	1	=	=	PUNCT
ejpam-4674	69	2	∑	∑	PUNCT
ejpam-4674	69	3	i∈i	i∈i	ADJ
ejpam-4674	69	4	ri(η)pi	ri(η)pi	NOUN
ejpam-4674	69	5	.	.	PUNCT
ejpam-4674	70	1	(	(	PUNCT
ejpam-4674	70	2	17	17	NUM
ejpam-4674	70	3	)	)	PUNCT
ejpam-4674	70	4	by	by	ADP
ejpam-4674	70	5	means	mean	NOUN
ejpam-4674	70	6	of	of	ADP
ejpam-4674	70	7	the	the	DET
ejpam-4674	70	8	geometrical	geometrical	ADJ
ejpam-4674	70	9	mapping	mapping	NOUN
ejpam-4674	70	10	(	(	PUNCT
ejpam-4674	70	11	17	17	NUM
ejpam-4674	70	12	)	)	PUNCT
ejpam-4674	70	13	,	,	PUNCT
ejpam-4674	70	14	we	we	PRON
ejpam-4674	70	15	define	define	VERB
ejpam-4674	70	16	the	the	DET
ejpam-4674	70	17	physical	physical	ADJ
ejpam-4674	70	18	mesh	mesh	NOUN
ejpam-4674	70	19	kh	kh	PROPN
ejpam-4674	70	20	in	in	ADP
ejpam-4674	70	21	the	the	DET
ejpam-4674	70	22	computational	computational	ADJ
ejpam-4674	70	23	domain	domain	NOUN
ejpam-4674	70	24	ω	ω	NOUN
ejpam-4674	70	25	,	,	PUNCT
ejpam-4674	70	26	whose	whose	DET
ejpam-4674	70	27	elements	element	NOUN
ejpam-4674	70	28	are	be	AUX
ejpam-4674	70	29	obatained	obataine	VERB
ejpam-4674	70	30	as	as	ADP
ejpam-4674	70	31	the	the	DET
ejpam-4674	70	32	image	image	NOUN
ejpam-4674	70	33	of	of	ADP
ejpam-4674	70	34	the	the	DET
ejpam-4674	70	35	elements	element	NOUN
ejpam-4674	70	36	in	in	ADP
ejpam-4674	70	37	the	the	DET
ejpam-4674	70	38	parametric	parametric	ADJ
ejpam-4674	70	39	domain	domain	NOUN
ejpam-4674	70	40	,	,	PUNCT
ejpam-4674	70	41	i.e.	i.e.	X
ejpam-4674	70	42	:	:	PUNCT
ejpam-4674	70	43	kh	kh	X
ejpam-4674	70	44	:	:	PUNCT
ejpam-4674	70	45	=	=	PRON
ejpam-4674	70	46	{	{	PUNCT
ejpam-4674	70	47	k	k	X
ejpam-4674	70	48	=	=	SYM
ejpam-4674	70	49	x(q	x(q	PROPN
ejpam-4674	70	50	)	)	PUNCT
ejpam-4674	70	51	:	:	PUNCT
ejpam-4674	70	52	q	q	PUNCT
ejpam-4674	70	53	∈	∈	PROPN
ejpam-4674	70	54	qh	qh	NOUN
ejpam-4674	70	55	}	}	PUNCT
ejpam-4674	70	56	.	.	PUNCT
ejpam-4674	71	1	we	we	PRON
ejpam-4674	71	2	denote	denote	VERB
ejpam-4674	71	3	the	the	DET
ejpam-4674	71	4	global	global	ADJ
ejpam-4674	71	5	mesh	mesh	NOUN
ejpam-4674	71	6	size	size	NOUN
ejpam-4674	71	7	of	of	ADP
ejpam-4674	71	8	the	the	DET
ejpam-4674	71	9	mesh	mesh	NOUN
ejpam-4674	71	10	in	in	ADP
ejpam-4674	71	11	the	the	DET
ejpam-4674	71	12	physical	physical	ADJ
ejpam-4674	71	13	domain	domain	NOUN
ejpam-4674	71	14	by	by	ADP
ejpam-4674	71	15	h	h	NOUN
ejpam-4674	71	16	:	:	PUNCT
ejpam-4674	71	17	=	=	SYM
ejpam-4674	71	18	max{hk	max{hk	NOUN
ejpam-4674	71	19	:	:	PUNCT
ejpam-4674	71	20	k	k	PROPN
ejpam-4674	71	21	∈	∈	PROPN
ejpam-4674	71	22	kh	kh	PROPN
ejpam-4674	71	23	}	}	PUNCT
ejpam-4674	71	24	,	,	PUNCT
ejpam-4674	71	25	with	with	ADP
ejpam-4674	71	26	hk	hk	PROPN
ejpam-4674	71	27	:	:	PUNCT
ejpam-4674	71	28	=	=	SYM
ejpam-4674	71	29	∥∇x∥l∞(k)ĥk̂	∥∇x∥l∞(k)ĥk̂	PROPN
ejpam-4674	71	30	and	and	CCONJ
ejpam-4674	71	31	ĥ	ĥ	X
ejpam-4674	71	32	k̂	k̂	X
ejpam-4674	71	33	=	=	SYM
ejpam-4674	71	34	diam(k̂	diam(k̂	NOUN
ejpam-4674	71	35	)	)	PUNCT
ejpam-4674	71	36	.	.	PUNCT
ejpam-4674	72	1	further	far	ADV
ejpam-4674	72	2	,	,	PUNCT
ejpam-4674	72	3	we	we	PRON
ejpam-4674	72	4	assume	assume	VERB
ejpam-4674	72	5	that	that	SCONJ
ejpam-4674	72	6	the	the	DET
ejpam-4674	72	7	physical	physical	ADJ
ejpam-4674	72	8	mesh	mesh	NOUN
ejpam-4674	72	9	is	be	AUX
ejpam-4674	72	10	quasi	quasi	ADJ
ejpam-4674	72	11	-	-	ADJ
ejpam-4674	72	12	uniform	uniform	ADJ
ejpam-4674	72	13	,	,	PUNCT
ejpam-4674	72	14	i.e.	i.e.	X
ejpam-4674	72	15	there	there	PRON
ejpam-4674	72	16	exists	exist	VERB
ejpam-4674	72	17	a	a	DET
ejpam-4674	72	18	positive	positive	ADJ
ejpam-4674	72	19	constant	constant	ADJ
ejpam-4674	72	20	cu	cu	PROPN
ejpam-4674	72	21	,	,	PUNCT
ejpam-4674	72	22	independent	independent	ADJ
ejpam-4674	72	23	of	of	ADP
ejpam-4674	72	24	h	h	NOUN
ejpam-4674	72	25	,	,	PUNCT
ejpam-4674	72	26	such	such	ADJ
ejpam-4674	72	27	that	that	SCONJ
ejpam-4674	72	28	hk	hk	PROPN
ejpam-4674	72	29	≤	≤	PROPN
ejpam-4674	72	30	h	h	NOUN
ejpam-4674	72	31	≤	≤	PROPN
ejpam-4674	72	32	cuhk	cuhk	NOUN
ejpam-4674	72	33	∀k	∀k	X
ejpam-4674	72	34	∈	∈	PROPN
ejpam-4674	72	35	kh	kh	PROPN
ejpam-4674	72	36	.	.	PUNCT
ejpam-4674	73	1	(	(	PUNCT
ejpam-4674	73	2	18	18	NUM
ejpam-4674	73	3	)	)	PUNCT
ejpam-4674	73	4	y.	y.	PROPN
ejpam-4674	73	5	c.	c.	PROPN
ejpam-4674	73	6	bassonon	bassonon	PROPN
ejpam-4674	73	7	,	,	PUNCT
ejpam-4674	73	8	a.	a.	NOUN
ejpam-4674	73	9	ouédraogo	ouédraogo	PROPN
ejpam-4674	73	10	/	/	SYM
ejpam-4674	73	11	eur	eur	PROPN
ejpam-4674	73	12	.	.	PUNCT
ejpam-4674	74	1	j.	j.	PROPN
ejpam-4674	74	2	pure	pure	PROPN
ejpam-4674	74	3	appl	appl	PROPN
ejpam-4674	74	4	.	.	PROPN
ejpam-4674	74	5	math	math	PROPN
ejpam-4674	74	6	,	,	PUNCT
ejpam-4674	74	7	16	16	NUM
ejpam-4674	74	8	(	(	PUNCT
ejpam-4674	74	9	1	1	NUM
ejpam-4674	74	10	)	)	PUNCT
ejpam-4674	74	11	(	(	PUNCT
ejpam-4674	74	12	2023	2023	NUM
ejpam-4674	74	13	)	)	PUNCT
ejpam-4674	74	14	,	,	PUNCT
ejpam-4674	74	15	404	404	NUM
ejpam-4674	74	16	-	-	SYM
ejpam-4674	74	17	417	417	NUM
ejpam-4674	74	18	408	408	NUM
ejpam-4674	74	19	moreover	moreover	ADV
ejpam-4674	74	20	,	,	PUNCT
ejpam-4674	74	21	we	we	PRON
ejpam-4674	74	22	define	define	VERB
ejpam-4674	74	23	the	the	DET
ejpam-4674	74	24	space	space	NOUN
ejpam-4674	74	25	of	of	ADP
ejpam-4674	74	26	nurbs	nurb	NOUN
ejpam-4674	74	27	in	in	ADP
ejpam-4674	74	28	the	the	DET
ejpam-4674	74	29	domain	domain	NOUN
ejpam-4674	74	30	ω	ω	NOUN
ejpam-4674	74	31	as	as	ADP
ejpam-4674	74	32	the	the	DET
ejpam-4674	74	33	push	push	NOUN
ejpam-4674	74	34	-	-	PUNCT
ejpam-4674	74	35	forward	forward	NOUN
ejpam-4674	74	36	of	of	ADP
ejpam-4674	74	37	the	the	DET
ejpam-4674	74	38	space	space	NOUN
ejpam-4674	74	39	nh	nh	PROPN
ejpam-4674	74	40	of	of	ADP
ejpam-4674	74	41	(	(	PUNCT
ejpam-4674	74	42	16	16	NUM
ejpam-4674	74	43	)	)	PUNCT
ejpam-4674	74	44	,	,	PUNCT
ejpam-4674	74	45	i.e.	i.e.	X
ejpam-4674	74	46	:	:	PUNCT
ejpam-4674	74	47	vh	vh	NOUN
ejpam-4674	74	48	:	:	PUNCT
ejpam-4674	74	49	=	=	NOUN
ejpam-4674	74	50	span{ri	span{ri	VERB
ejpam-4674	74	51	◦	◦	VERB
ejpam-4674	74	52	x−1}i∈i	x−1}i∈i	NOUN
ejpam-4674	74	53	=	=	SYM
ejpam-4674	74	54	span{ri}i∈i	span{ri}i∈i	NOUN
ejpam-4674	74	55	,	,	PUNCT
ejpam-4674	74	56	(	(	PUNCT
ejpam-4674	74	57	19	19	NUM
ejpam-4674	74	58	)	)	PUNCT
ejpam-4674	74	59	where	where	SCONJ
ejpam-4674	74	60	{	{	PUNCT
ejpam-4674	74	61	ri}i∈i	ri}i∈i	NOUN
ejpam-4674	74	62	is	be	AUX
ejpam-4674	74	63	the	the	DET
ejpam-4674	74	64	nurbs	nurbs	NOUN
ejpam-4674	74	65	basis	basis	NOUN
ejpam-4674	74	66	in	in	ADP
ejpam-4674	74	67	the	the	DET
ejpam-4674	74	68	physical	physical	ADJ
ejpam-4674	74	69	domain	domain	NOUN
ejpam-4674	74	70	,	,	PUNCT
ejpam-4674	74	71	with	with	ADP
ejpam-4674	74	72	ri	ri	PROPN
ejpam-4674	74	73	:	:	PUNCT
ejpam-4674	74	74	=	=	SYM
ejpam-4674	74	75	ri	ri	PROPN
ejpam-4674	74	76	◦	◦	PROPN
ejpam-4674	74	77	x−1	x−1	PROPN
ejpam-4674	74	78	for	for	ADP
ejpam-4674	74	79	all	all	PRON
ejpam-4674	74	80	i	i	PRON
ejpam-4674	74	81	∈	∈	PROPN
ejpam-4674	74	82	i.	i.	NOUN
ejpam-4674	74	83	the	the	DET
ejpam-4674	74	84	geometrical	geometrical	ADJ
ejpam-4674	74	85	mapping	mapping	NOUN
ejpam-4674	74	86	(	(	PUNCT
ejpam-4674	74	87	17	17	NUM
ejpam-4674	74	88	)	)	PUNCT
ejpam-4674	74	89	is	be	AUX
ejpam-4674	74	90	assumed	assume	VERB
ejpam-4674	74	91	to	to	PART
ejpam-4674	74	92	be	be	AUX
ejpam-4674	74	93	invertible	invertible	ADJ
ejpam-4674	74	94	a.e	a.e	PROPN
ejpam-4674	74	95	.	.	PROPN
ejpam-4674	75	1	in	in	ADP
ejpam-4674	75	2	ω	ω	PROPN
ejpam-4674	75	3	,	,	PUNCT
ejpam-4674	75	4	with	with	ADP
ejpam-4674	75	5	smooth	smooth	ADJ
ejpam-4674	75	6	inverse	inverse	NOUN
ejpam-4674	75	7	on	on	ADP
ejpam-4674	75	8	each	each	DET
ejpam-4674	75	9	element	element	NOUN
ejpam-4674	75	10	k	k	PROPN
ejpam-4674	75	11	of	of	ADP
ejpam-4674	75	12	the	the	DET
ejpam-4674	75	13	physical	physical	ADJ
ejpam-4674	75	14	mesh	mesh	NOUN
ejpam-4674	75	15	kh	kh	PROPN
ejpam-4674	75	16	.	.	PUNCT
ejpam-4674	76	1	in	in	ADP
ejpam-4674	76	2	our	our	PRON
ejpam-4674	76	3	analysis	analysis	NOUN
ejpam-4674	76	4	,	,	PUNCT
ejpam-4674	76	5	we	we	PRON
ejpam-4674	76	6	restricted	restrict	VERB
ejpam-4674	76	7	ourselves	ourselves	PRON
ejpam-4674	76	8	to	to	ADP
ejpam-4674	76	9	the	the	DET
ejpam-4674	76	10	case	case	NOUN
ejpam-4674	76	11	d	d	X
ejpam-4674	76	12	=	=	SYM
ejpam-4674	76	13	κ	κ	NOUN
ejpam-4674	76	14	.	.	NOUN
ejpam-4674	76	15	in	in	ADP
ejpam-4674	76	16	standard	standard	ADJ
ejpam-4674	76	17	fem	fem	PROPN
ejpam-4674	76	18	,	,	PUNCT
ejpam-4674	76	19	the	the	DET
ejpam-4674	76	20	space	space	NOUN
ejpam-4674	76	21	vh	vh	PROPN
ejpam-4674	76	22	is	be	AUX
ejpam-4674	76	23	a	a	DET
ejpam-4674	76	24	space	space	NOUN
ejpam-4674	76	25	of	of	ADP
ejpam-4674	76	26	piecewise	piecewise	NOUN
ejpam-4674	76	27	polynomials	polynomial	NOUN
ejpam-4674	76	28	.	.	PUNCT
ejpam-4674	77	1	in	in	ADP
ejpam-4674	77	2	an	an	DET
ejpam-4674	77	3	iga	iga	PROPN
ejpam-4674	77	4	context	context	NOUN
ejpam-4674	77	5	,	,	PUNCT
ejpam-4674	77	6	as	as	SCONJ
ejpam-4674	77	7	introduced	introduce	VERB
ejpam-4674	77	8	in	in	ADP
ejpam-4674	77	9	[	[	X
ejpam-4674	77	10	8	8	NUM
ejpam-4674	77	11	]	]	PUNCT
ejpam-4674	77	12	,	,	PUNCT
ejpam-4674	77	13	this	this	DET
ejpam-4674	77	14	space	space	NOUN
ejpam-4674	77	15	is	be	AUX
ejpam-4674	77	16	formed	form	VERB
ejpam-4674	77	17	by	by	ADP
ejpam-4674	77	18	nurbs	nurb	NOUN
ejpam-4674	77	19	functions	function	NOUN
ejpam-4674	77	20	.	.	PUNCT
ejpam-4674	78	1	for	for	ADP
ejpam-4674	78	2	this	this	PRON
ejpam-4674	78	3	,	,	PUNCT
ejpam-4674	78	4	we	we	PRON
ejpam-4674	78	5	introduce	introduce	VERB
ejpam-4674	78	6	finite	finite	ADJ
ejpam-4674	78	7	-	-	ADJ
ejpam-4674	78	8	dimensional	dimensional	ADJ
ejpam-4674	78	9	spaces	space	NOUN
ejpam-4674	78	10	on	on	ADP
ejpam-4674	78	11	the	the	DET
ejpam-4674	78	12	patch	patch	NOUN
ejpam-4674	78	13	(	(	PUNCT
ejpam-4674	78	14	0	0	NUM
ejpam-4674	78	15	,	,	PUNCT
ejpam-4674	78	16	1)d	1)d	NUM
ejpam-4674	78	17	.	.	PUNCT
ejpam-4674	79	1	the	the	DET
ejpam-4674	79	2	approximate	approximate	ADJ
ejpam-4674	79	3	solution	solution	NOUN
ejpam-4674	79	4	uh	uh	INTJ
ejpam-4674	79	5	of	of	ADP
ejpam-4674	79	6	problem	problem	NOUN
ejpam-4674	79	7	(	(	PUNCT
ejpam-4674	79	8	9	9	NUM
ejpam-4674	79	9	)	)	PUNCT
ejpam-4674	79	10	is	be	AUX
ejpam-4674	79	11	obtained	obtain	VERB
ejpam-4674	79	12	by	by	ADP
ejpam-4674	79	13	solving	solve	VERB
ejpam-4674	79	14	the	the	DET
ejpam-4674	79	15	following	follow	VERB
ejpam-4674	79	16	problem:	problem:	PART
ejpam-4674	79	17	find	find	VERB
ejpam-4674	79	18	uh	uh	INTJ
ejpam-4674	79	19	∈	∈	PROPN
ejpam-4674	79	20	v	v	NOUN
ejpam-4674	79	21	h	h	NOUN
ejpam-4674	79	22	,	,	PUNCT
ejpam-4674	79	23	∀vh	∀vh	PROPN
ejpam-4674	79	24	∈	∈	PROPN
ejpam-4674	79	25	v	v	PROPN
ejpam-4674	79	26	h	h	NOUN
ejpam-4674	79	27	,	,	PUNCT
ejpam-4674	79	28	∫	∫	PROPN
ejpam-4674	79	29	ω	ω	PROPN
ejpam-4674	79	30	a∇uh∇vhdx	a∇uh∇vhdx	ADP
ejpam-4674	79	31	=	=	SYM
ejpam-4674	79	32	∫	∫	PROPN
ejpam-4674	79	33	ω	ω	NUM
ejpam-4674	79	34	fvhdx	fvhdx	NOUN
ejpam-4674	79	35	,	,	PUNCT
ejpam-4674	79	36	(	(	PUNCT
ejpam-4674	79	37	20	20	NUM
ejpam-4674	79	38	)	)	PUNCT
ejpam-4674	79	39	where	where	SCONJ
ejpam-4674	79	40	v	v	NOUN
ejpam-4674	79	41	h	h	NOUN
ejpam-4674	79	42	:	:	PUNCT
ejpam-4674	80	1	=	=	SYM
ejpam-4674	80	2	vh	vh	PROPN
ejpam-4674	80	3	∩h1	∩h1	NUM
ejpam-4674	80	4	0	0	SYM
ejpam-4674	80	5	(	(	PUNCT
ejpam-4674	80	6	ω	ω	NOUN
ejpam-4674	80	7	)	)	PUNCT
ejpam-4674	80	8	,	,	PUNCT
ejpam-4674	80	9	and	and	CCONJ
ejpam-4674	80	10	vh	vh	PROPN
ejpam-4674	80	11	is	be	AUX
ejpam-4674	80	12	a	a	DET
ejpam-4674	80	13	nurbs	nurbs	NOUN
ejpam-4674	80	14	space	space	NOUN
ejpam-4674	80	15	described	describe	VERB
ejpam-4674	80	16	in	in	ADP
ejpam-4674	80	17	(	(	PUNCT
ejpam-4674	80	18	19	19	NUM
ejpam-4674	80	19	)	)	PUNCT
ejpam-4674	80	20	.	.	PUNCT
ejpam-4674	81	1	in	in	ADP
ejpam-4674	81	2	our	our	PRON
ejpam-4674	81	3	framework	framework	NOUN
ejpam-4674	81	4	we	we	PRON
ejpam-4674	81	5	prefer	prefer	VERB
ejpam-4674	81	6	to	to	PART
ejpam-4674	81	7	define	define	VERB
ejpam-4674	81	8	this	this	DET
ejpam-4674	81	9	space	space	NOUN
ejpam-4674	81	10	in	in	ADP
ejpam-4674	81	11	the	the	DET
ejpam-4674	81	12	following	follow	VERB
ejpam-4674	81	13	general	general	ADJ
ejpam-4674	81	14	way	way	NOUN
ejpam-4674	81	15	,	,	PUNCT
ejpam-4674	81	16	(	(	PUNCT
ejpam-4674	81	17	see	see	VERB
ejpam-4674	81	18	[	[	X
ejpam-4674	81	19	1	1	NUM
ejpam-4674	81	20	]	]	PUNCT
ejpam-4674	81	21	):	):	PUNCT
ejpam-4674	81	22	v	v	NOUN
ejpam-4674	81	23	h	h	NOUN
ejpam-4674	81	24	=	=	PUNCT
ejpam-4674	81	25	{	{	PUNCT
ejpam-4674	81	26	vh	vh	PROPN
ejpam-4674	81	27	∈	∈	PROPN
ejpam-4674	81	28	h1	h1	PROPN
ejpam-4674	81	29	0	0	NUM
ejpam-4674	81	30	(	(	PUNCT
ejpam-4674	81	31	ω	ω	NOUN
ejpam-4674	81	32	)	)	PUNCT
ejpam-4674	81	33	:	:	PUNCT
ejpam-4674	81	34	vh	vh	PROPN
ejpam-4674	81	35	=	=	NOUN
ejpam-4674	81	36	v̂h	v̂h	NOUN
ejpam-4674	81	37	◦	◦	NOUN
ejpam-4674	81	38	x−1	x−1	PROPN
ejpam-4674	81	39	∈	∈	PROPN
ejpam-4674	81	40	v̂h	v̂h	NOUN
ejpam-4674	81	41	}	}	PUNCT
ejpam-4674	81	42	.	.	PUNCT
ejpam-4674	82	1	(	(	PUNCT
ejpam-4674	82	2	21	21	NUM
ejpam-4674	82	3	)	)	PUNCT
ejpam-4674	82	4	v̂	v̂	NUM
ejpam-4674	82	5	h	h	NOUN
ejpam-4674	82	6	is	be	AUX
ejpam-4674	82	7	a	a	DET
ejpam-4674	82	8	discrete	discrete	ADJ
ejpam-4674	82	9	space	space	NOUN
ejpam-4674	82	10	defined	define	VERB
ejpam-4674	82	11	in	in	ADP
ejpam-4674	82	12	the	the	DET
ejpam-4674	82	13	parametric	parametric	ADJ
ejpam-4674	82	14	domain	domain	NOUN
ejpam-4674	82	15	ω̂	ω̂	PUNCT
ejpam-4674	82	16	such	such	ADJ
ejpam-4674	82	17	that	that	SCONJ
ejpam-4674	82	18	v̂	v̂	NUM
ejpam-4674	82	19	h	h	NOUN
ejpam-4674	82	20	=	=	PRON
ejpam-4674	82	21	{	{	PUNCT
ejpam-4674	82	22	vh	vh	NOUN
ejpam-4674	82	23	:	:	PUNCT
ejpam-4674	82	24	(	(	PUNCT
ejpam-4674	82	25	0	0	NUM
ejpam-4674	82	26	,	,	PUNCT
ejpam-4674	82	27	1)d	1)d	NUM
ejpam-4674	82	28	−→	−→	PROPN
ejpam-4674	82	29	rd	rd	NOUN
ejpam-4674	82	30	|	|	NOUN
ejpam-4674	82	31	v̂h	v̂h	X
ejpam-4674	82	32	=	=	SYM
ejpam-4674	82	33	vh	vh	PROPN
ejpam-4674	82	34	◦	◦	PROPN
ejpam-4674	83	1	x	x	PROPN
ejpam-4674	83	2	,	,	PUNCT
ejpam-4674	83	3	vh	vh	PROPN
ejpam-4674	83	4	∈	∈	PROPN
ejpam-4674	83	5	v	v	ADP
ejpam-4674	83	6	h	h	NOUN
ejpam-4674	83	7	}	}	PUNCT
ejpam-4674	83	8	.	.	PUNCT
ejpam-4674	84	1	note	note	VERB
ejpam-4674	84	2	that	that	SCONJ
ejpam-4674	84	3	the	the	DET
ejpam-4674	84	4	discrete	discrete	ADJ
ejpam-4674	84	5	problem	problem	NOUN
ejpam-4674	84	6	(	(	PUNCT
ejpam-4674	84	7	20	20	NUM
ejpam-4674	84	8	)	)	PUNCT
ejpam-4674	84	9	has	have	VERB
ejpam-4674	84	10	a	a	DET
ejpam-4674	84	11	unique	unique	ADJ
ejpam-4674	84	12	solution	solution	NOUN
ejpam-4674	84	13	.	.	PUNCT
ejpam-4674	85	1	indeed	indeed	ADV
ejpam-4674	85	2	,	,	PUNCT
ejpam-4674	85	3	it	it	PRON
ejpam-4674	85	4	is	be	AUX
ejpam-4674	85	5	square	square	ADJ
ejpam-4674	85	6	system	system	NOUN
ejpam-4674	85	7	of	of	ADP
ejpam-4674	85	8	linear	linear	ADJ
ejpam-4674	85	9	equations	equation	NOUN
ejpam-4674	85	10	in	in	ADP
ejpam-4674	85	11	finite	finite	ADJ
ejpam-4674	85	12	dimension	dimension	NOUN
ejpam-4674	85	13	,	,	PUNCT
ejpam-4674	85	14	and	and	CCONJ
ejpam-4674	85	15	the	the	DET
ejpam-4674	85	16	integral	integral	ADJ
ejpam-4674	85	17	in	in	ADP
ejpam-4674	85	18	the	the	DET
ejpam-4674	85	19	right	right	ADJ
ejpam-4674	85	20	-	-	PUNCT
ejpam-4674	85	21	hand	hand	NOUN
ejpam-4674	85	22	side	side	NOUN
ejpam-4674	85	23	is	be	AUX
ejpam-4674	85	24	well	well	ADV
ejpam-4674	85	25	-	-	PUNCT
ejpam-4674	85	26	defined	define	VERB
ejpam-4674	85	27	because	because	SCONJ
ejpam-4674	85	28	the	the	DET
ejpam-4674	85	29	functions	function	NOUN
ejpam-4674	85	30	of	of	ADP
ejpam-4674	85	31	v	v	NOUN
ejpam-4674	85	32	h	h	NOUN
ejpam-4674	85	33	belong	belong	VERB
ejpam-4674	85	34	to	to	ADP
ejpam-4674	85	35	l∞(ω	l∞(ω	ADJ
ejpam-4674	85	36	)	)	PUNCT
ejpam-4674	85	37	.	.	PUNCT
ejpam-4674	86	1	we	we	PRON
ejpam-4674	86	2	denote	denote	VERB
ejpam-4674	86	3	ah(uh	ah(uh	PROPN
ejpam-4674	86	4	,	,	PUNCT
ejpam-4674	86	5	vh	vh	PROPN
ejpam-4674	86	6	)	)	PUNCT
ejpam-4674	86	7	:	:	PUNCT
ejpam-4674	87	1	=	=	SYM
ejpam-4674	87	2	∫	∫	PROPN
ejpam-4674	87	3	ω	ω	PROPN
ejpam-4674	87	4	a∇uh∇vhdx	a∇uh∇vhdx	PROPN
ejpam-4674	87	5	,	,	PUNCT
ejpam-4674	87	6	the	the	DET
ejpam-4674	87	7	bilinear	bilinear	ADJ
ejpam-4674	87	8	form	form	NOUN
ejpam-4674	87	9	of	of	ADP
ejpam-4674	87	10	(	(	PUNCT
ejpam-4674	87	11	20	20	NUM
ejpam-4674	87	12	)	)	PUNCT
ejpam-4674	87	13	.	.	PUNCT
ejpam-4674	88	1	since	since	SCONJ
ejpam-4674	88	2	splines	spline	NOUN
ejpam-4674	88	3	are	be	AUX
ejpam-4674	88	4	not	not	PART
ejpam-4674	88	5	in	in	ADP
ejpam-4674	88	6	general	general	ADJ
ejpam-4674	88	7	interpolatory	interpolatory	NOUN
ejpam-4674	88	8	,	,	PUNCT
ejpam-4674	88	9	a	a	DET
ejpam-4674	88	10	common	common	ADJ
ejpam-4674	88	11	way	way	NOUN
ejpam-4674	88	12	to	to	PART
ejpam-4674	88	13	define	define	VERB
ejpam-4674	88	14	projection	projection	NOUN
ejpam-4674	88	15	is	be	AUX
ejpam-4674	88	16	by	by	ADP
ejpam-4674	88	17	giving	give	VERB
ejpam-4674	88	18	a	a	DET
ejpam-4674	88	19	dual	dual	ADJ
ejpam-4674	88	20	basis	basis	NOUN
ejpam-4674	88	21	.	.	PUNCT
ejpam-4674	89	1	given	give	VERB
ejpam-4674	89	2	a	a	DET
ejpam-4674	89	3	function	function	NOUN
ejpam-4674	89	4	v̂	v̂	ADP
ejpam-4674	89	5	∈	∈	PROPN
ejpam-4674	89	6	l2(ω̂	l2(ω̂	PROPN
ejpam-4674	89	7	)	)	PUNCT
ejpam-4674	89	8	defined	define	VERB
ejpam-4674	89	9	in	in	ADP
ejpam-4674	89	10	the	the	DET
ejpam-4674	89	11	parametric	parametric	ADJ
ejpam-4674	89	12	domain	domain	NOUN
ejpam-4674	89	13	ω̂	ω̂	NUM
ejpam-4674	89	14	,	,	PUNCT
ejpam-4674	89	15	we	we	PRON
ejpam-4674	89	16	use	use	VERB
ejpam-4674	89	17	the	the	DET
ejpam-4674	89	18	projective	projective	ADJ
ejpam-4674	89	19	operator	operator	NOUN
ejpam-4674	89	20	over	over	ADP
ejpam-4674	89	21	the	the	DET
ejpam-4674	89	22	b	b	NOUN
ejpam-4674	89	23	-	-	PUNCT
ejpam-4674	89	24	splines	spline	NOUN
ejpam-4674	89	25	space	space	NOUN
ejpam-4674	89	26	sh	sh	PROPN
ejpam-4674	89	27	,	,	PUNCT
ejpam-4674	89	28	say	say	VERB
ejpam-4674	89	29	πsh	πsh	INTJ
ejpam-4674	89	30	,	,	PUNCT
ejpam-4674	89	31	introduced	introduce	VERB
ejpam-4674	89	32	in	in	ADP
ejpam-4674	89	33	[	[	X
ejpam-4674	89	34	1	1	NUM
ejpam-4674	89	35	]	]	PUNCT
ejpam-4674	89	36	and	and	CCONJ
ejpam-4674	89	37	defined	define	VERB
ejpam-4674	89	38	as	as	ADP
ejpam-4674	89	39	:	:	PUNCT
ejpam-4674	89	40	πsh	πsh	NOUN
ejpam-4674	89	41	:	:	PUNCT
ejpam-4674	89	42	l2(ω̂	l2(ω̂	NUM
ejpam-4674	89	43	)	)	PUNCT
ejpam-4674	89	44	→	→	SYM
ejpam-4674	89	45	sh	sh	PROPN
ejpam-4674	89	46	,	,	PUNCT
ejpam-4674	89	47	πsh	πsh	X
ejpam-4674	89	48	v̂	v̂	PRON
ejpam-4674	89	49	:	:	PUNCT
ejpam-4674	89	50	=	=	PUNCT
ejpam-4674	89	51	∑	∑	PUNCT
ejpam-4674	89	52	i∈i	i∈i	ADJ
ejpam-4674	89	53	λi(v̂)ni	λi(v̂)ni	PROPN
ejpam-4674	89	54	,	,	PUNCT
ejpam-4674	89	55	(	(	PUNCT
ejpam-4674	89	56	22	22	NUM
ejpam-4674	89	57	)	)	PUNCT
ejpam-4674	89	58	where	where	SCONJ
ejpam-4674	89	59	the	the	DET
ejpam-4674	89	60	linear	linear	NOUN
ejpam-4674	89	61	functionals	functional	VERB
ejpam-4674	89	62	λj	λj	X
ejpam-4674	89	63	∈	∈	PROPN
ejpam-4674	89	64	l2(ω̂)′	l2(ω̂)′	PROPN
ejpam-4674	89	65	determine	determine	VERB
ejpam-4674	89	66	the	the	DET
ejpam-4674	89	67	dual	dual	ADJ
ejpam-4674	89	68	basis	basis	NOUN
ejpam-4674	89	69	for	for	ADP
ejpam-4674	89	70	the	the	DET
ejpam-4674	89	71	set	set	NOUN
ejpam-4674	89	72	of	of	ADP
ejpam-4674	89	73	b	b	NOUN
ejpam-4674	89	74	-	-	PUNCT
ejpam-4674	89	75	splines	spline	NOUN
ejpam-4674	89	76	[	[	X
ejpam-4674	89	77	11	11	NUM
ejpam-4674	89	78	]	]	PUNCT
ejpam-4674	89	79	,	,	PUNCT
ejpam-4674	89	80	i.e.	i.e.	X
ejpam-4674	89	81	they	they	PRON
ejpam-4674	89	82	are	be	AUX
ejpam-4674	89	83	such	such	ADJ
ejpam-4674	89	84	that	that	DET
ejpam-4674	89	85	λj(ni	λj(ni	PROPN
ejpam-4674	89	86	)	)	PUNCT
ejpam-4674	90	1	:	:	PUNCT
ejpam-4674	90	2	=	=	SYM
ejpam-4674	90	3	δj	δj	ADP
ejpam-4674	90	4	,	,	PUNCT
ejpam-4674	90	5	i	i	PRON
ejpam-4674	90	6	for	for	ADP
ejpam-4674	90	7	i	i	PRON
ejpam-4674	90	8	,	,	PUNCT
ejpam-4674	90	9	j	j	PROPN
ejpam-4674	90	10	∈	∈	PROPN
ejpam-4674	90	11	i.	i.	NOUN
ejpam-4674	91	1	the	the	DET
ejpam-4674	91	2	corresponding	corresponding	ADJ
ejpam-4674	91	3	projective	projective	ADJ
ejpam-4674	91	4	operator	operator	NOUN
ejpam-4674	91	5	over	over	ADP
ejpam-4674	91	6	the	the	DET
ejpam-4674	91	7	nurbs	nurbs	NOUN
ejpam-4674	91	8	space	space	PROPN
ejpam-4674	91	9	nh	nh	PROPN
ejpam-4674	91	10	in	in	ADP
ejpam-4674	91	11	the	the	DET
ejpam-4674	91	12	parametric	parametric	ADJ
ejpam-4674	91	13	domain	domain	NOUN
ejpam-4674	91	14	(	(	PUNCT
ejpam-4674	91	15	16	16	NUM
ejpam-4674	91	16	)	)	PUNCT
ejpam-4674	91	17	,	,	PUNCT
ejpam-4674	91	18	say	say	VERB
ejpam-4674	91	19	πnh	πnh	VERB
ejpam-4674	91	20	,	,	PUNCT
ejpam-4674	91	21	is	be	AUX
ejpam-4674	91	22	defined	define	VERB
ejpam-4674	91	23	y.	y.	PROPN
ejpam-4674	91	24	c.	c.	PROPN
ejpam-4674	91	25	bassonon	bassonon	PROPN
ejpam-4674	91	26	,	,	PUNCT
ejpam-4674	91	27	a.	a.	NOUN
ejpam-4674	91	28	ouédraogo	ouédraogo	PROPN
ejpam-4674	91	29	/	/	SYM
ejpam-4674	91	30	eur	eur	PROPN
ejpam-4674	91	31	.	.	PUNCT
ejpam-4674	92	1	j.	j.	PROPN
ejpam-4674	92	2	pure	pure	PROPN
ejpam-4674	92	3	appl	appl	PROPN
ejpam-4674	92	4	.	.	PROPN
ejpam-4674	92	5	math	math	PROPN
ejpam-4674	92	6	,	,	PUNCT
ejpam-4674	92	7	16	16	NUM
ejpam-4674	92	8	(	(	PUNCT
ejpam-4674	92	9	1	1	NUM
ejpam-4674	92	10	)	)	PUNCT
ejpam-4674	92	11	(	(	PUNCT
ejpam-4674	92	12	2023	2023	NUM
ejpam-4674	92	13	)	)	PUNCT
ejpam-4674	92	14	,	,	PUNCT
ejpam-4674	92	15	404	404	NUM
ejpam-4674	92	16	-	-	SYM
ejpam-4674	92	17	417	417	NUM
ejpam-4674	92	18	409	409	NUM
ejpam-4674	92	19	by	by	ADP
ejpam-4674	92	20	means	mean	NOUN
ejpam-4674	92	21	of	of	ADP
ejpam-4674	92	22	πsh	πsh	NOUN
ejpam-4674	92	23	and	and	CCONJ
ejpam-4674	92	24	the	the	DET
ejpam-4674	92	25	definition	definition	NOUN
ejpam-4674	92	26	of	of	ADP
ejpam-4674	92	27	the	the	DET
ejpam-4674	92	28	nurbs	nurbs	NOUN
ejpam-4674	92	29	basis	basis	NOUN
ejpam-4674	92	30	functions	function	NOUN
ejpam-4674	92	31	of	of	ADP
ejpam-4674	92	32	(	(	PUNCT
ejpam-4674	92	33	15	15	NUM
ejpam-4674	92	34	)	)	PUNCT
ejpam-4674	92	35	through	through	ADP
ejpam-4674	92	36	the	the	DET
ejpam-4674	92	37	weighting	weighting	NOUN
ejpam-4674	92	38	function	function	NOUN
ejpam-4674	92	39	w	w	PROPN
ejpam-4674	92	40	of	of	ADP
ejpam-4674	92	41	(	(	PUNCT
ejpam-4674	92	42	14	14	NUM
ejpam-4674	92	43	)	)	PUNCT
ejpam-4674	92	44	.	.	PUNCT
ejpam-4674	93	1	in	in	ADP
ejpam-4674	93	2	particular	particular	ADJ
ejpam-4674	93	3	,	,	PUNCT
ejpam-4674	93	4	πnh	πnh	ADJ
ejpam-4674	93	5	reads	read	NOUN
ejpam-4674	93	6	:	:	PUNCT
ejpam-4674	93	7	πnh	πnh	VERB
ejpam-4674	93	8	:	:	PUNCT
ejpam-4674	93	9	l2(ω̂	l2(ω̂	X
ejpam-4674	93	10	)	)	PUNCT
ejpam-4674	93	11	→	→	SYM
ejpam-4674	93	12	nh	nh	PROPN
ejpam-4674	93	13	,	,	PUNCT
ejpam-4674	93	14	πnh	πnh	VERB
ejpam-4674	93	15	v̂	v̂	PRON
ejpam-4674	93	16	:	:	PUNCT
ejpam-4674	93	17	=	=	PRON
ejpam-4674	93	18	πsh	πsh	X
ejpam-4674	93	19	(	(	PUNCT
ejpam-4674	93	20	wv̂	wv̂	PROPN
ejpam-4674	93	21	)	)	PUNCT
ejpam-4674	93	22	w	w	NOUN
ejpam-4674	93	23	,	,	PUNCT
ejpam-4674	93	24	(	(	PUNCT
ejpam-4674	93	25	23	23	NUM
ejpam-4674	93	26	)	)	PUNCT
ejpam-4674	93	27	for	for	ADP
ejpam-4674	93	28	all	all	PRON
ejpam-4674	93	29	v̂	v̂	NUM
ejpam-4674	93	30	∈	∈	PROPN
ejpam-4674	93	31	l2(ω̂	l2(ω̂	NOUN
ejpam-4674	93	32	)	)	PUNCT
ejpam-4674	93	33	.	.	PUNCT
ejpam-4674	94	1	in	in	ADP
ejpam-4674	94	2	this	this	DET
ejpam-4674	94	3	manner	manner	NOUN
ejpam-4674	94	4	,	,	PUNCT
ejpam-4674	94	5	the	the	DET
ejpam-4674	94	6	projective	projective	ADJ
ejpam-4674	94	7	operator	operator	NOUN
ejpam-4674	94	8	over	over	ADP
ejpam-4674	94	9	vh	vh	PROPN
ejpam-4674	94	10	,	,	PUNCT
ejpam-4674	94	11	the	the	DET
ejpam-4674	94	12	nurbs	nurbs	NOUN
ejpam-4674	94	13	space	space	NOUN
ejpam-4674	94	14	in	in	ADP
ejpam-4674	94	15	the	the	DET
ejpam-4674	94	16	physical	physical	ADJ
ejpam-4674	94	17	domain	domain	NOUN
ejpam-4674	94	18	ω	ω	NOUN
ejpam-4674	94	19	defined	define	VERB
ejpam-4674	94	20	in	in	ADP
ejpam-4674	94	21	(	(	PUNCT
ejpam-4674	94	22	19	19	NUM
ejpam-4674	94	23	)	)	PUNCT
ejpam-4674	94	24	as	as	ADP
ejpam-4674	94	25	the	the	DET
ejpam-4674	94	26	push	push	NOUN
ejpam-4674	94	27	-	-	PUNCT
ejpam-4674	94	28	forward	forward	NOUN
ejpam-4674	94	29	of	of	ADP
ejpam-4674	94	30	the	the	DET
ejpam-4674	94	31	space	space	NOUN
ejpam-4674	94	32	nh	nh	PROPN
ejpam-4674	94	33	,	,	PUNCT
ejpam-4674	94	34	is	be	AUX
ejpam-4674	94	35	given	give	VERB
ejpam-4674	94	36	by	by	ADP
ejpam-4674	94	37	:	:	PUNCT
ejpam-4674	94	38	πvh	πvh	NOUN
ejpam-4674	94	39	:	:	PUNCT
ejpam-4674	94	40	l2(ω	l2(ω	X
ejpam-4674	94	41	)	)	PUNCT
ejpam-4674	94	42	→	→	SYM
ejpam-4674	94	43	vh	vh	PROPN
ejpam-4674	94	44	,	,	PUNCT
ejpam-4674	94	45	πvhv	πvhv	NOUN
ejpam-4674	94	46	:	:	PUNCT
ejpam-4674	94	47	=	=	SYM
ejpam-4674	94	48	(	(	PUNCT
ejpam-4674	94	49	πnh	πnh	X
ejpam-4674	94	50	(	(	PUNCT
ejpam-4674	94	51	v̂	v̂	NOUN
ejpam-4674	94	52	)	)	PUNCT
ejpam-4674	94	53	)	)	PUNCT
ejpam-4674	95	1	◦	◦	NOUN
ejpam-4674	95	2	x−1	x−1	PROPN
ejpam-4674	95	3	.	.	PUNCT
ejpam-4674	96	1	(	(	PUNCT
ejpam-4674	96	2	24	24	NUM
ejpam-4674	96	3	)	)	PUNCT
ejpam-4674	96	4	the	the	DET
ejpam-4674	96	5	following	follow	VERB
ejpam-4674	96	6	result	result	NOUN
ejpam-4674	96	7	is	be	AUX
ejpam-4674	96	8	proved	prove	VERB
ejpam-4674	96	9	in	in	ADP
ejpam-4674	96	10	[	[	X
ejpam-4674	96	11	2	2	NUM
ejpam-4674	96	12	]	]	PUNCT
ejpam-4674	96	13	and	and	CCONJ
ejpam-4674	96	14	shows	show	VERB
ejpam-4674	96	15	that	that	SCONJ
ejpam-4674	96	16	πvh	πvh	NOUN
ejpam-4674	96	17	is	be	AUX
ejpam-4674	96	18	actually	actually	ADV
ejpam-4674	96	19	a	a	DET
ejpam-4674	96	20	projector	projector	NOUN
ejpam-4674	96	21	on	on	ADP
ejpam-4674	96	22	vh	vh	PROPN
ejpam-4674	96	23	.	.	PUNCT
ejpam-4674	97	1	proposition	proposition	NOUN
ejpam-4674	97	2	2.1	2.1	NUM
ejpam-4674	97	3	.	.	PUNCT
ejpam-4674	98	1	its	its	PRON
ejpam-4674	98	2	holds	hold	VERB
ejpam-4674	98	3	that	that	DET
ejpam-4674	98	4	πvhvh	πvhvh	NOUN
ejpam-4674	98	5	=	=	SYM
ejpam-4674	98	6	vh	vh	PROPN
ejpam-4674	98	7	for	for	ADP
ejpam-4674	98	8	all	all	DET
ejpam-4674	98	9	vh	vh	PROPN
ejpam-4674	98	10	∈	∈	PROPN
ejpam-4674	98	11	vh	vh	PROPN
ejpam-4674	98	12	.	.	PUNCT
ejpam-4674	99	1	that	that	PRON
ejpam-4674	99	2	is	is	ADV
ejpam-4674	99	3	,	,	PUNCT
ejpam-4674	99	4	πvh	πvh	PROPN
ejpam-4674	99	5	is	be	AUX
ejpam-4674	99	6	a	a	DET
ejpam-4674	99	7	projector	projector	NOUN
ejpam-4674	99	8	.	.	PUNCT
ejpam-4674	100	1	now	now	ADV
ejpam-4674	100	2	,	,	PUNCT
ejpam-4674	100	3	we	we	PRON
ejpam-4674	100	4	define	define	VERB
ejpam-4674	100	5	the	the	DET
ejpam-4674	100	6	real	real	ADJ
ejpam-4674	100	7	number	number	NOUN
ejpam-4674	100	8	dij	dij	NOUN
ejpam-4674	101	1	=	=	SYM
ejpam-4674	101	2	∫	∫	PROPN
ejpam-4674	101	3	ω	ω	PROPN
ejpam-4674	101	4	a∇λi∇λjdx	a∇λi∇λjdx	PROPN
ejpam-4674	101	5	;	;	PUNCT
ejpam-4674	101	6	(	(	PUNCT
ejpam-4674	101	7	25	25	NUM
ejpam-4674	101	8	)	)	PUNCT
ejpam-4674	101	9	this	this	PRON
ejpam-4674	101	10	defines	define	VERB
ejpam-4674	101	11	an	an	DET
ejpam-4674	101	12	i	i	PRON
ejpam-4674	101	13	×	×	NOUN
ejpam-4674	102	1	i	i	PRON
ejpam-4674	102	2	matrix	matrix	VERB
ejpam-4674	102	3	d.	d.	PROPN
ejpam-4674	102	4	here	here	ADV
ejpam-4674	102	5	,	,	PUNCT
ejpam-4674	102	6	d	d	NOUN
ejpam-4674	102	7	satisfies	satisfy	VERB
ejpam-4674	102	8	∀i	∀i	NOUN
ejpam-4674	102	9	∈	∈	PROPN
ejpam-4674	102	10	i	i	PRON
ejpam-4674	102	11	,	,	PUNCT
ejpam-4674	102	12	dii	dii	PROPN
ejpam-4674	102	13	−	−	PROPN
ejpam-4674	102	14	∑	∑	PROPN
ejpam-4674	102	15	j∈i	j∈i	PROPN
ejpam-4674	102	16	,	,	PUNCT
ejpam-4674	102	17	j	j	PROPN
ejpam-4674	102	18	̸=i	̸=i	PROPN
ejpam-4674	102	19	|dij	|dij	VERB
ejpam-4674	102	20	|	|	ADV
ejpam-4674	102	21	≥	≥	NOUN
ejpam-4674	102	22	0	0	NUM
ejpam-4674	102	23	.	.	PUNCT
ejpam-4674	103	1	(	(	PUNCT
ejpam-4674	103	2	26	26	NUM
ejpam-4674	103	3	)	)	PUNCT
ejpam-4674	103	4	d	d	NOUN
ejpam-4674	103	5	is	be	AUX
ejpam-4674	103	6	assumed	assume	VERB
ejpam-4674	103	7	to	to	PART
ejpam-4674	103	8	be	be	AUX
ejpam-4674	103	9	diagonally	diagonally	ADV
ejpam-4674	103	10	dominant	dominant	ADJ
ejpam-4674	103	11	matrix	matrix	NOUN
ejpam-4674	103	12	.	.	PUNCT
ejpam-4674	104	1	this	this	DET
ejpam-4674	104	2	assumption	assumption	NOUN
ejpam-4674	104	3	is	be	AUX
ejpam-4674	104	4	close	close	ADJ
ejpam-4674	104	5	to	to	ADP
ejpam-4674	104	6	the	the	DET
ejpam-4674	104	7	usual	usual	ADJ
ejpam-4674	104	8	assumption	assumption	NOUN
ejpam-4674	104	9	which	which	PRON
ejpam-4674	104	10	ensures	ensure	VERB
ejpam-4674	104	11	the	the	DET
ejpam-4674	104	12	discrete	discrete	ADJ
ejpam-4674	104	13	maximum	maximum	ADJ
ejpam-4674	104	14	principle	principle	NOUN
ejpam-4674	104	15	.	.	PUNCT
ejpam-4674	105	1	lemma	lemma	PROPN
ejpam-4674	105	2	1	1	NUM
ejpam-4674	105	3	.	.	PUNCT
ejpam-4674	106	1	the	the	DET
ejpam-4674	106	2	matrix	matrix	NOUN
ejpam-4674	106	3	d(sh	d(sh	PROPN
ejpam-4674	106	4	)	)	PUNCT
ejpam-4674	106	5	is	be	AUX
ejpam-4674	106	6	an	an	DET
ejpam-4674	106	7	m	m	NOUN
ejpam-4674	106	8	-	-	NOUN
ejpam-4674	106	9	matrix	matrix	NOUN
ejpam-4674	106	10	and	and	CCONJ
ejpam-4674	106	11	satisfies	satisfie	NOUN
ejpam-4674	106	12	property	property	NOUN
ejpam-4674	106	13	(	(	PUNCT
ejpam-4674	106	14	26	26	NUM
ejpam-4674	106	15	)	)	PUNCT
ejpam-4674	106	16	,	,	PUNCT
ejpam-4674	106	17	∀	∀	NUM
ejpam-4674	106	18	sh	sh	ADP
ejpam-4674	106	19	∈	∈	PROPN
ejpam-4674	106	20	v	v	ADP
ejpam-4674	106	21	h.	h.	PROPN
ejpam-4674	106	22	the	the	DET
ejpam-4674	106	23	coerciveness	coerciveness	NOUN
ejpam-4674	106	24	of	of	ADP
ejpam-4674	106	25	the	the	DET
ejpam-4674	106	26	bilinear	bilinear	NOUN
ejpam-4674	106	27	form	form	NOUN
ejpam-4674	106	28	ah	ah	INTJ
ejpam-4674	106	29	is	be	AUX
ejpam-4674	106	30	the	the	DET
ejpam-4674	106	31	a	a	DET
ejpam-4674	106	32	consequence	consequence	NOUN
ejpam-4674	106	33	of	of	ADP
ejpam-4674	106	34	this	this	DET
ejpam-4674	106	35	lemma	lemma	PROPN
ejpam-4674	106	36	:	:	PUNCT
ejpam-4674	106	37	ah(vh	ah(vh	PROPN
ejpam-4674	106	38	,	,	PUNCT
ejpam-4674	106	39	vh	vh	PROPN
ejpam-4674	106	40	)	)	PUNCT
ejpam-4674	106	41	≥	≥	NOUN
ejpam-4674	106	42	α∥∇vh∥22	α∥∇vh∥22	NUM
ejpam-4674	106	43	,	,	PUNCT
ejpam-4674	106	44	∀vh	∀vh	PROPN
ejpam-4674	106	45	∈	∈	PROPN
ejpam-4674	106	46	v	v	PROPN
ejpam-4674	106	47	h.	h.	PROPN
ejpam-4674	106	48	(	(	PUNCT
ejpam-4674	106	49	27	27	NUM
ejpam-4674	106	50	)	)	PUNCT
ejpam-4674	106	51	3	3	NUM
ejpam-4674	106	52	.	.	X
ejpam-4674	106	53	convergence	convergence	NOUN
ejpam-4674	106	54	analysis	analysis	NOUN
ejpam-4674	106	55	and	and	CCONJ
ejpam-4674	106	56	error	error	NOUN
ejpam-4674	106	57	estimates	estimate	NOUN
ejpam-4674	106	58	in	in	ADP
ejpam-4674	106	59	this	this	DET
ejpam-4674	106	60	section	section	NOUN
ejpam-4674	106	61	,	,	PUNCT
ejpam-4674	106	62	we	we	PRON
ejpam-4674	106	63	give	give	VERB
ejpam-4674	106	64	a	a	DET
ejpam-4674	106	65	priori	priori	ADJ
ejpam-4674	106	66	estimates	estimate	NOUN
ejpam-4674	106	67	on	on	ADP
ejpam-4674	106	68	the	the	DET
ejpam-4674	106	69	solution	solution	NOUN
ejpam-4674	106	70	uh	uh	INTJ
ejpam-4674	106	71	of	of	ADP
ejpam-4674	106	72	(	(	PUNCT
ejpam-4674	106	73	20	20	NUM
ejpam-4674	106	74	)	)	PUNCT
ejpam-4674	106	75	.	.	PUNCT
ejpam-4674	107	1	these	these	DET
ejpam-4674	107	2	results	result	NOUN
ejpam-4674	107	3	allow	allow	VERB
ejpam-4674	107	4	to	to	PART
ejpam-4674	107	5	prove	prove	VERB
ejpam-4674	107	6	our	our	PRON
ejpam-4674	107	7	main	main	ADJ
ejpam-4674	107	8	result	result	NOUN
ejpam-4674	107	9	.	.	PUNCT
ejpam-4674	108	1	theorem	theorem	NOUN
ejpam-4674	108	2	2	2	NUM
ejpam-4674	108	3	.	.	PUNCT
ejpam-4674	109	1	(	(	PUNCT
ejpam-4674	109	2	see	see	VERB
ejpam-4674	109	3	[	[	X
ejpam-4674	109	4	4	4	NUM
ejpam-4674	109	5	]	]	PUNCT
ejpam-4674	109	6	)	)	PUNCT
ejpam-4674	110	1	assume	assume	VERB
ejpam-4674	110	2	that	that	SCONJ
ejpam-4674	110	3	a	a	DET
ejpam-4674	110	4	satisfies	satisfie	NOUN
ejpam-4674	110	5	(	(	PUNCT
ejpam-4674	110	6	3	3	NUM
ejpam-4674	110	7	)	)	PUNCT
ejpam-4674	110	8	and	and	CCONJ
ejpam-4674	110	9	(	(	PUNCT
ejpam-4674	110	10	27	27	NUM
ejpam-4674	110	11	)	)	PUNCT
ejpam-4674	110	12	.	.	PUNCT
ejpam-4674	111	1	then	then	ADV
ejpam-4674	111	2	,	,	PUNCT
ejpam-4674	111	3	for	for	ADP
ejpam-4674	111	4	every	every	DET
ejpam-4674	111	5	h	h	NOUN
ejpam-4674	111	6	>	>	X
ejpam-4674	111	7	0	0	NUM
ejpam-4674	111	8	,	,	PUNCT
ejpam-4674	111	9	let	let	VERB
ejpam-4674	111	10	uh	uh	INTJ
ejpam-4674	111	11	the	the	DET
ejpam-4674	111	12	unique	unique	ADJ
ejpam-4674	111	13	solution	solution	NOUN
ejpam-4674	111	14	of	of	ADP
ejpam-4674	111	15	problem	problem	NOUN
ejpam-4674	111	16	(	(	PUNCT
ejpam-4674	111	17	20	20	NUM
ejpam-4674	111	18	)	)	PUNCT
ejpam-4674	111	19	,	,	PUNCT
ejpam-4674	111	20	then	then	ADV
ejpam-4674	111	21	{	{	PUNCT
ejpam-4674	111	22	uh}h>0	uh}h>0	PROPN
ejpam-4674	111	23	is	be	AUX
ejpam-4674	111	24	bounded	bound	VERB
ejpam-4674	111	25	in	in	ADP
ejpam-4674	111	26	w	w	PROPN
ejpam-4674	111	27	1,q	1,q	NUM
ejpam-4674	111	28	0	0	NUM
ejpam-4674	111	29	(	(	PUNCT
ejpam-4674	111	30	ω	ω	NOUN
ejpam-4674	111	31	)	)	PUNCT
ejpam-4674	111	32	(	(	PUNCT
ejpam-4674	112	1	1	1	NUM
ejpam-4674	112	2	≤	≤	NUM
ejpam-4674	112	3	q	q	NOUN
ejpam-4674	112	4	<	<	X
ejpam-4674	112	5	d	d	X
ejpam-4674	112	6	d−	d−	PROPN
ejpam-4674	112	7	1	1	NUM
ejpam-4674	112	8	)	)	PUNCT
ejpam-4674	112	9	and	and	CCONJ
ejpam-4674	112	10	there	there	PRON
ejpam-4674	112	11	exists	exist	VERB
ejpam-4674	112	12	a	a	DET
ejpam-4674	112	13	constant	constant	ADJ
ejpam-4674	112	14	c	c	NOUN
ejpam-4674	112	15	>	>	X
ejpam-4674	112	16	0	0	PUNCT
ejpam-4674	112	17	independent	independent	NOUN
ejpam-4674	112	18	of	of	ADP
ejpam-4674	112	19	h	h	NOUN
ejpam-4674	112	20	,	,	PUNCT
ejpam-4674	112	21	such	such	ADJ
ejpam-4674	112	22	that	that	SCONJ
ejpam-4674	112	23	∥uh∥w	∥uh∥w	PROPN
ejpam-4674	112	24	1,q	1,q	NUM
ejpam-4674	112	25	0	0	NUM
ejpam-4674	112	26	(	(	PUNCT
ejpam-4674	112	27	ω	ω	NOUN
ejpam-4674	112	28	)	)	PUNCT
ejpam-4674	112	29	≤	≤	NOUN
ejpam-4674	112	30	c∥f∥l1(ω	c∥f∥l1(ω	NOUN
ejpam-4674	112	31	)	)	PUNCT
ejpam-4674	112	32	.	.	PUNCT
ejpam-4674	113	1	(	(	PUNCT
ejpam-4674	113	2	28	28	X
ejpam-4674	113	3	)	)	PUNCT
ejpam-4674	113	4	y.	y.	PROPN
ejpam-4674	113	5	c.	c.	PROPN
ejpam-4674	113	6	bassonon	bassonon	PROPN
ejpam-4674	113	7	,	,	PUNCT
ejpam-4674	113	8	a.	a.	NOUN
ejpam-4674	113	9	ouédraogo	ouédraogo	PROPN
ejpam-4674	113	10	/	/	SYM
ejpam-4674	113	11	eur	eur	PROPN
ejpam-4674	113	12	.	.	PUNCT
ejpam-4674	114	1	j.	j.	PROPN
ejpam-4674	114	2	pure	pure	PROPN
ejpam-4674	114	3	appl	appl	PROPN
ejpam-4674	114	4	.	.	PROPN
ejpam-4674	114	5	math	math	PROPN
ejpam-4674	114	6	,	,	PUNCT
ejpam-4674	114	7	16	16	NUM
ejpam-4674	114	8	(	(	PUNCT
ejpam-4674	114	9	1	1	NUM
ejpam-4674	114	10	)	)	PUNCT
ejpam-4674	114	11	(	(	PUNCT
ejpam-4674	114	12	2023	2023	NUM
ejpam-4674	114	13	)	)	PUNCT
ejpam-4674	114	14	,	,	PUNCT
ejpam-4674	114	15	404	404	NUM
ejpam-4674	114	16	-	-	SYM
ejpam-4674	114	17	417	417	NUM
ejpam-4674	114	18	410	410	NUM
ejpam-4674	114	19	proposition	proposition	NOUN
ejpam-4674	114	20	3.1	3.1	NUM
ejpam-4674	114	21	.	.	PUNCT
ejpam-4674	115	1	under	under	ADP
ejpam-4674	115	2	assumption	assumption	NOUN
ejpam-4674	115	3	(	(	PUNCT
ejpam-4674	115	4	26	26	NUM
ejpam-4674	115	5	)	)	PUNCT
ejpam-4674	115	6	,	,	PUNCT
ejpam-4674	115	7	on	on	ADP
ejpam-4674	115	8	has	have	AUX
ejpam-4674	115	9	for	for	ADP
ejpam-4674	115	10	every	every	DET
ejpam-4674	115	11	vh	vh	PROPN
ejpam-4674	115	12	∈	∈	PROPN
ejpam-4674	115	13	v	v	ADP
ejpam-4674	115	14	h	h	NOUN
ejpam-4674	115	15	and	and	CCONJ
ejpam-4674	115	16	every	every	DET
ejpam-4674	115	17	k	k	X
ejpam-4674	115	18	>	>	X
ejpam-4674	115	19	0∫	0∫	PROPN
ejpam-4674	115	20	ω	ω	NUM
ejpam-4674	115	21	a∇	a∇	PROPN
ejpam-4674	115	22	(	(	PUNCT
ejpam-4674	115	23	vh	vh	PROPN
ejpam-4674	115	24	−πvh(tk(vh	−πvh(tk(vh	PROPN
ejpam-4674	115	25	)	)	PUNCT
ejpam-4674	115	26	)	)	PUNCT
ejpam-4674	115	27	)	)	PUNCT
ejpam-4674	115	28	∇πvh(tk(vh))dx	∇πvh(tk(vh))dx	VERB
ejpam-4674	115	29	≥	≥	NOUN
ejpam-4674	115	30	0	0	NUM
ejpam-4674	115	31	.	.	PUNCT
ejpam-4674	116	1	(	(	PUNCT
ejpam-4674	116	2	29	29	NUM
ejpam-4674	116	3	)	)	PUNCT
ejpam-4674	116	4	proof	proof	NOUN
ejpam-4674	116	5	.	.	PUNCT
ejpam-4674	117	1	we	we	PRON
ejpam-4674	117	2	use	use	VERB
ejpam-4674	117	3	the	the	DET
ejpam-4674	117	4	technique	technique	NOUN
ejpam-4674	117	5	applied	apply	VERB
ejpam-4674	117	6	in	in	ADP
ejpam-4674	117	7	[	[	X
ejpam-4674	117	8	3	3	NUM
ejpam-4674	117	9	]	]	PUNCT
ejpam-4674	117	10	.	.	PUNCT
ejpam-4674	118	1	since	since	SCONJ
ejpam-4674	118	2	vh	vh	PROPN
ejpam-4674	118	3	=	=	SYM
ejpam-4674	118	4	∑	∑	PROPN
ejpam-4674	118	5	i∈i	i∈i	ADJ
ejpam-4674	118	6	vh(xi)λi	vh(xi)λi	NOUN
ejpam-4674	118	7	and	and	CCONJ
ejpam-4674	118	8	πvh(tk(vh	πvh(tk(vh	PROPN
ejpam-4674	118	9	)	)	PUNCT
ejpam-4674	118	10	)	)	PUNCT
ejpam-4674	119	1	=	=	PUNCT
ejpam-4674	119	2	∑	∑	PROPN
ejpam-4674	119	3	i∈i	i∈i	ADJ
ejpam-4674	119	4	tk(vh)(xi)λi	tk(vh)(xi)λi	PROPN
ejpam-4674	119	5	,	,	PUNCT
ejpam-4674	119	6	using	use	VERB
ejpam-4674	119	7	the	the	DET
ejpam-4674	119	8	definition	definition	NOUN
ejpam-4674	119	9	(	(	PUNCT
ejpam-4674	119	10	26	26	NUM
ejpam-4674	119	11	)	)	PUNCT
ejpam-4674	119	12	of	of	ADP
ejpam-4674	119	13	dij	dij	INTJ
ejpam-4674	119	14	,	,	PUNCT
ejpam-4674	119	15	we	we	PRON
ejpam-4674	119	16	have∫	have∫	VERB
ejpam-4674	119	17	ω	ω	NUM
ejpam-4674	119	18	a∇	a∇	PROPN
ejpam-4674	119	19	(	(	PUNCT
ejpam-4674	119	20	vh	vh	PROPN
ejpam-4674	119	21	−πvh(tk(vh	−πvh(tk(vh	PROPN
ejpam-4674	119	22	)	)	PUNCT
ejpam-4674	119	23	)	)	PUNCT
ejpam-4674	119	24	)	)	PUNCT
ejpam-4674	119	25	∇πvh(tk(vh))dx	∇πvh(tk(vh))dx	NOUN
ejpam-4674	119	26	=	=	PUNCT
ejpam-4674	120	1	=	=	PUNCT
ejpam-4674	120	2	∑	∑	PUNCT
ejpam-4674	120	3	i	i	PROPN
ejpam-4674	120	4	,	,	PUNCT
ejpam-4674	120	5	j∈i	j∈i	PROPN
ejpam-4674	120	6	dij	dij	PROPN
ejpam-4674	120	7	(	(	PUNCT
ejpam-4674	120	8	vh(xi)−	vh(xi)−	NOUN
ejpam-4674	120	9	tk(vh(xi	tk(vh(xi	NUM
ejpam-4674	120	10	)	)	PUNCT
ejpam-4674	120	11	)	)	PUNCT
ejpam-4674	120	12	)	)	PUNCT
ejpam-4674	120	13	tk(vh(xj	tk(vh(xj	X
ejpam-4674	120	14	)	)	PUNCT
ejpam-4674	120	15	)	)	PUNCT
ejpam-4674	121	1	=	=	PUNCT
ejpam-4674	121	2	∑	∑	PROPN
ejpam-4674	121	3	i∈i	i∈i	ADJ
ejpam-4674	121	4	si	si	NOUN
ejpam-4674	121	5	,	,	PUNCT
ejpam-4674	121	6	where	where	SCONJ
ejpam-4674	121	7	xi	xi	X
ejpam-4674	121	8	=	=	SYM
ejpam-4674	121	9	(	(	PUNCT
ejpam-4674	121	10	ξi+1	ξi+1	NUM
ejpam-4674	121	11	+	+	CCONJ
ejpam-4674	121	12	...	...	PUNCT
ejpam-4674	121	13	+	+	CCONJ
ejpam-4674	121	14	ξi+p)/p	ξi+p)/p	NOUN
ejpam-4674	121	15	and	and	CCONJ
ejpam-4674	121	16	si	si	NOUN
ejpam-4674	121	17	=	=	ADJ
ejpam-4674	121	18	dii	dii	PROPN
ejpam-4674	121	19	(	(	PUNCT
ejpam-4674	121	20	vh(xi)−	vh(xi)−	NOUN
ejpam-4674	121	21	tk(vh(xi	tk(vh(xi	NUM
ejpam-4674	121	22	)	)	PUNCT
ejpam-4674	121	23	)	)	PUNCT
ejpam-4674	121	24	)	)	PUNCT
ejpam-4674	121	25	tk(vh(xi))+	tk(vh(xi))+	VERB
ejpam-4674	121	26	+	+	NUM
ejpam-4674	121	27	∑	∑	PROPN
ejpam-4674	121	28	j∈i	j∈i	PROPN
ejpam-4674	121	29	,	,	PUNCT
ejpam-4674	121	30	j	j	PROPN
ejpam-4674	122	1	̸=i	̸=i	PROPN
ejpam-4674	122	2	dij	dij	PROPN
ejpam-4674	122	3	(	(	PUNCT
ejpam-4674	122	4	vh(xi)−	vh(xi)−	NOUN
ejpam-4674	122	5	tk(vh(xi	tk(vh(xi	NUM
ejpam-4674	122	6	)	)	PUNCT
ejpam-4674	122	7	)	)	PUNCT
ejpam-4674	122	8	)	)	PUNCT
ejpam-4674	123	1	tk(vh(xj	tk(vh(xj	NUM
ejpam-4674	123	2	)	)	PUNCT
ejpam-4674	123	3	)	)	PUNCT
ejpam-4674	123	4	.	.	PUNCT
ejpam-4674	124	1	fix	fix	NOUN
ejpam-4674	124	2	i	i	PRON
ejpam-4674	124	3	∈	∈	PROPN
ejpam-4674	124	4	i.	i.	NOUN
ejpam-4674	124	5	if	if	SCONJ
ejpam-4674	124	6	|vh(xi)|	|vh(xi)|	VERB
ejpam-4674	124	7	≤	≤	ADV
ejpam-4674	124	8	k	k	PROPN
ejpam-4674	124	9	,	,	PUNCT
ejpam-4674	124	10	then	then	ADV
ejpam-4674	124	11	vh(xi)−	vh(xi)−	PROPN
ejpam-4674	124	12	tk(vh(xi	tk(vh(xi	NOUN
ejpam-4674	124	13	)	)	PUNCT
ejpam-4674	124	14	)	)	PUNCT
ejpam-4674	125	1	=	=	SYM
ejpam-4674	125	2	0	0	PUNCT
ejpam-4674	125	3	and	and	CCONJ
ejpam-4674	125	4	si	si	X
ejpam-4674	125	5	=	=	ADJ
ejpam-4674	125	6	0	0	PROPN
ejpam-4674	125	7	.	.	PUNCT
ejpam-4674	126	1	if	if	SCONJ
ejpam-4674	126	2	|vh(xi)|	|vh(xi)|	PROPN
ejpam-4674	126	3	>	>	X
ejpam-4674	127	1	k	k	X
ejpam-4674	127	2	,	,	PUNCT
ejpam-4674	127	3	then	then	ADV
ejpam-4674	127	4	(	(	PUNCT
ejpam-4674	127	5	vh(xi)−	vh(xi)−	NOUN
ejpam-4674	127	6	tk(vh(xi	tk(vh(xi	NUM
ejpam-4674	127	7	)	)	PUNCT
ejpam-4674	127	8	)	)	PUNCT
ejpam-4674	127	9	)	)	PUNCT
ejpam-4674	128	1	tk(vh(xi	tk(vh(xi	X
ejpam-4674	128	2	)	)	PUNCT
ejpam-4674	128	3	)	)	PUNCT
ejpam-4674	129	1	=	=	SYM
ejpam-4674	129	2	|vh(xi)−	|vh(xi)−	NOUN
ejpam-4674	129	3	tk(vh(xi))|k	tk(vh(xi))|k	NOUN
ejpam-4674	129	4	.	.	PUNCT
ejpam-4674	130	1	since	since	SCONJ
ejpam-4674	130	2	|tk(vh(xj))|	|tk(vh(xj))|	NOUN
ejpam-4674	130	3	≤	≤	PROPN
ejpam-4674	130	4	k	k	NOUN
ejpam-4674	130	5	for	for	ADP
ejpam-4674	130	6	every	every	DET
ejpam-4674	130	7	j	j	PROPN
ejpam-4674	130	8	,	,	PUNCT
ejpam-4674	130	9	one	one	PRON
ejpam-4674	130	10	has	have	VERB
ejpam-4674	130	11	si	si	PROPN
ejpam-4674	130	12	≥	≥	NOUN
ejpam-4674	130	13	dii|vh(xi)−	dii|vh(xi)−	PROPN
ejpam-4674	130	14	tk(vh(xi))|k	tk(vh(xi))|k	PROPN
ejpam-4674	130	15	−	−	PROPN
ejpam-4674	130	16	∑	∑	SYM
ejpam-4674	130	17	j∈i	j∈i	PROPN
ejpam-4674	130	18	,	,	PUNCT
ejpam-4674	130	19	j	j	PROPN
ejpam-4674	130	20	̸=i	̸=i	PROPN
ejpam-4674	130	21	|dij	|dij	VERB
ejpam-4674	130	22	||vh(xi)−	||vh(xi)−	PROPN
ejpam-4674	130	23	tk(vh(xi))|k	tk(vh(xi))|k	NOUN
ejpam-4674	130	24	=	=	SYM
ejpam-4674	130	25	|vh(xi)−	|vh(xi)−	NOUN
ejpam-4674	130	26	tk(vh(xi))|k	tk(vh(xi))|k	NOUN
ejpam-4674	130	27	(	(	PUNCT
ejpam-4674	130	28	dii	dii	PROPN
ejpam-4674	130	29	−	−	PROPN
ejpam-4674	130	30	∑	∑	PROPN
ejpam-4674	130	31	j∈i	j∈i	PROPN
ejpam-4674	130	32	,	,	PUNCT
ejpam-4674	130	33	j	j	PROPN
ejpam-4674	130	34	̸=i	̸=i	PROPN
ejpam-4674	130	35	|dij	|dij	VERB
ejpam-4674	130	36	|	|	ADV
ejpam-4674	130	37	)	)	PUNCT
ejpam-4674	130	38	≥	≥	NOUN
ejpam-4674	130	39	0	0	NUM
ejpam-4674	130	40	,	,	PUNCT
ejpam-4674	130	41	owing	owe	VERB
ejpam-4674	130	42	the	the	DET
ejpam-4674	130	43	hypothesis	hypothesis	NOUN
ejpam-4674	130	44	(	(	PUNCT
ejpam-4674	130	45	26	26	NUM
ejpam-4674	130	46	)	)	PUNCT
ejpam-4674	130	47	.	.	PUNCT
ejpam-4674	131	1	this	this	PRON
ejpam-4674	131	2	proves	prove	VERB
ejpam-4674	131	3	that	that	SCONJ
ejpam-4674	131	4	∀i	∀i	NOUN
ejpam-4674	131	5	∈	∈	PROPN
ejpam-4674	131	6	i	i	PRON
ejpam-4674	131	7	,	,	PUNCT
ejpam-4674	131	8	si	si	X
ejpam-4674	131	9	≥	≥	PROPN
ejpam-4674	131	10	0	0	NUM
ejpam-4674	131	11	,	,	PUNCT
ejpam-4674	131	12	and	and	CCONJ
ejpam-4674	131	13	therefore	therefore	ADV
ejpam-4674	131	14	we	we	PRON
ejpam-4674	131	15	obtain	obtain	VERB
ejpam-4674	131	16	(	(	PUNCT
ejpam-4674	131	17	29	29	NUM
ejpam-4674	131	18	)	)	PUNCT
ejpam-4674	131	19	.	.	PUNCT
ejpam-4674	132	1	now	now	ADV
ejpam-4674	132	2	,	,	PUNCT
ejpam-4674	132	3	we	we	PRON
ejpam-4674	132	4	establish	establish	VERB
ejpam-4674	132	5	a	a	DET
ejpam-4674	132	6	priori	priori	ADJ
ejpam-4674	132	7	estimate	estimate	NOUN
ejpam-4674	132	8	on	on	ADP
ejpam-4674	132	9	the	the	DET
ejpam-4674	132	10	solution	solution	NOUN
ejpam-4674	132	11	uh	uh	INTJ
ejpam-4674	132	12	of	of	ADP
ejpam-4674	132	13	(	(	PUNCT
ejpam-4674	132	14	20	20	NUM
ejpam-4674	132	15	)	)	PUNCT
ejpam-4674	132	16	.	.	PUNCT
ejpam-4674	133	1	y.	y.	PROPN
ejpam-4674	133	2	c.	c.	PROPN
ejpam-4674	133	3	bassonon	bassonon	PROPN
ejpam-4674	133	4	,	,	PUNCT
ejpam-4674	133	5	a.	a.	NOUN
ejpam-4674	133	6	ouédraogo	ouédraogo	PROPN
ejpam-4674	133	7	/	/	SYM
ejpam-4674	133	8	eur	eur	PROPN
ejpam-4674	133	9	.	.	PUNCT
ejpam-4674	134	1	j.	j.	PROPN
ejpam-4674	134	2	pure	pure	PROPN
ejpam-4674	134	3	appl	appl	PROPN
ejpam-4674	134	4	.	.	PROPN
ejpam-4674	134	5	math	math	PROPN
ejpam-4674	134	6	,	,	PUNCT
ejpam-4674	134	7	16	16	NUM
ejpam-4674	134	8	(	(	PUNCT
ejpam-4674	134	9	1	1	NUM
ejpam-4674	134	10	)	)	PUNCT
ejpam-4674	134	11	(	(	PUNCT
ejpam-4674	134	12	2023	2023	NUM
ejpam-4674	134	13	)	)	PUNCT
ejpam-4674	134	14	,	,	PUNCT
ejpam-4674	134	15	404	404	NUM
ejpam-4674	134	16	-	-	SYM
ejpam-4674	134	17	417	417	NUM
ejpam-4674	134	18	411	411	NUM
ejpam-4674	134	19	proposition	proposition	NOUN
ejpam-4674	134	20	3.2	3.2	NUM
ejpam-4674	134	21	.	.	PUNCT
ejpam-4674	135	1	under	under	ADP
ejpam-4674	135	2	the	the	DET
ejpam-4674	135	3	assumptions	assumption	NOUN
ejpam-4674	135	4	(	(	PUNCT
ejpam-4674	135	5	2.1	2.1	NUM
ejpam-4674	135	6	)	)	PUNCT
ejpam-4674	135	7	,	,	PUNCT
ejpam-4674	135	8	(	(	PUNCT
ejpam-4674	135	9	3	3	NUM
ejpam-4674	135	10	)	)	PUNCT
ejpam-4674	135	11	,	,	PUNCT
ejpam-4674	135	12	(	(	PUNCT
ejpam-4674	135	13	4	4	NUM
ejpam-4674	135	14	)	)	PUNCT
ejpam-4674	135	15	,	,	PUNCT
ejpam-4674	135	16	(	(	PUNCT
ejpam-4674	135	17	10	10	NUM
ejpam-4674	135	18	)	)	PUNCT
ejpam-4674	135	19	,	,	PUNCT
ejpam-4674	135	20	(	(	PUNCT
ejpam-4674	135	21	18	18	NUM
ejpam-4674	135	22	)	)	PUNCT
ejpam-4674	135	23	and	and	CCONJ
ejpam-4674	135	24	(	(	PUNCT
ejpam-4674	135	25	26	26	NUM
ejpam-4674	135	26	)	)	PUNCT
ejpam-4674	135	27	.	.	PUNCT
ejpam-4674	136	1	then	then	ADV
ejpam-4674	136	2	the	the	DET
ejpam-4674	136	3	unique	unique	ADJ
ejpam-4674	136	4	solution	solution	NOUN
ejpam-4674	136	5	uh	uh	INTJ
ejpam-4674	136	6	of	of	ADP
ejpam-4674	136	7	(	(	PUNCT
ejpam-4674	136	8	20	20	NUM
ejpam-4674	136	9	)	)	PUNCT
ejpam-4674	136	10	satisfies	satisfie	NOUN
ejpam-4674	136	11	for	for	ADP
ejpam-4674	136	12	every	every	DET
ejpam-4674	136	13	h	h	NOUN
ejpam-4674	136	14	>	>	X
ejpam-4674	136	15	0	0	PUNCT
ejpam-4674	136	16	and	and	CCONJ
ejpam-4674	136	17	every	every	DET
ejpam-4674	136	18	k	k	X
ejpam-4674	136	19	>	>	PUNCT
ejpam-4674	136	20	0∫	0∫	PROPN
ejpam-4674	136	21	ω	ω	NUM
ejpam-4674	136	22	a∇πvh(tk(uh))∇πvh(tk(uh))dx	a∇πvh(tk(uh))∇πvh(tk(uh))dx	ADJ
ejpam-4674	136	23	≤	≤	NUM
ejpam-4674	136	24	∫	∫	PROPN
ejpam-4674	136	25	ω	ω	NUM
ejpam-4674	136	26	fπvh(tk(uh))dx	fπvh(tk(uh))dx	PROPN
ejpam-4674	136	27	.	.	PUNCT
ejpam-4674	137	1	(	(	PUNCT
ejpam-4674	137	2	30	30	NUM
ejpam-4674	137	3	)	)	PUNCT
ejpam-4674	137	4	in	in	ADP
ejpam-4674	137	5	particular	particular	ADJ
ejpam-4674	137	6	,	,	PUNCT
ejpam-4674	137	7	uh	uh	INTJ
ejpam-4674	137	8	satisfies	satisfy	VERB
ejpam-4674	137	9	α	α	X
ejpam-4674	137	10	∫	∫	PROPN
ejpam-4674	137	11	ω	ω	PROPN
ejpam-4674	137	12	|∇πvh(tk(uh))|2dx	|∇πvh(tk(uh))|2dx	PROPN
ejpam-4674	137	13	≤	≤	PROPN
ejpam-4674	137	14	k∥f∥l1(ω	k∥f∥l1(ω	NOUN
ejpam-4674	137	15	)	)	PUNCT
ejpam-4674	137	16	.	.	PUNCT
ejpam-4674	138	1	(	(	PUNCT
ejpam-4674	138	2	31	31	NUM
ejpam-4674	138	3	)	)	PUNCT
ejpam-4674	138	4	proof	proof	NOUN
ejpam-4674	138	5	.	.	PUNCT
ejpam-4674	139	1	since	since	SCONJ
ejpam-4674	139	2	tk(uh	tk(uh	PROPN
ejpam-4674	139	3	)	)	PUNCT
ejpam-4674	139	4	is	be	AUX
ejpam-4674	139	5	continuous	continuous	ADJ
ejpam-4674	139	6	,	,	PUNCT
ejpam-4674	139	7	the	the	DET
ejpam-4674	139	8	function	function	NOUN
ejpam-4674	139	9	πvh(tk(uh	πvh(tk(uh	PROPN
ejpam-4674	139	10	)	)	PUNCT
ejpam-4674	139	11	)	)	PUNCT
ejpam-4674	139	12	belongs	belong	VERB
ejpam-4674	139	13	to	to	ADP
ejpam-4674	139	14	vh	vh	PROPN
ejpam-4674	139	15	.	.	PUNCT
ejpam-4674	140	1	using	use	VERB
ejpam-4674	140	2	this	this	DET
ejpam-4674	140	3	function	function	NOUN
ejpam-4674	140	4	as	as	ADP
ejpam-4674	140	5	test	test	NOUN
ejpam-4674	140	6	function	function	NOUN
ejpam-4674	140	7	in	in	ADP
ejpam-4674	140	8	(	(	PUNCT
ejpam-4674	140	9	20	20	NUM
ejpam-4674	140	10	)	)	PUNCT
ejpam-4674	140	11	we	we	PRON
ejpam-4674	140	12	have∫	have∫	AUX
ejpam-4674	140	13	ω	ω	PUNCT
ejpam-4674	140	14	a∇uh∇πvh(tk(uh))dx	a∇uh∇πvh(tk(uh))dx	X
ejpam-4674	140	15	=	=	SYM
ejpam-4674	140	16	∫	∫	PROPN
ejpam-4674	140	17	ω	ω	NUM
ejpam-4674	140	18	fπvh(tk(uh))dx	fπvh(tk(uh))dx	PROPN
ejpam-4674	140	19	.	.	PUNCT
ejpam-4674	141	1	(	(	PUNCT
ejpam-4674	141	2	32	32	NUM
ejpam-4674	141	3	)	)	PUNCT
ejpam-4674	141	4	proposition	proposition	NOUN
ejpam-4674	141	5	(	(	PUNCT
ejpam-4674	141	6	3.1	3.1	NUM
ejpam-4674	141	7	)	)	PUNCT
ejpam-4674	141	8	shows	show	VERB
ejpam-4674	141	9	that∫	that∫	PROPN
ejpam-4674	141	10	ω	ω	NUM
ejpam-4674	141	11	a∇	a∇	PROPN
ejpam-4674	141	12	(	(	PUNCT
ejpam-4674	141	13	vh	vh	PROPN
ejpam-4674	141	14	−πvh(tk(vh	−πvh(tk(vh	PROPN
ejpam-4674	141	15	)	)	PUNCT
ejpam-4674	141	16	)	)	PUNCT
ejpam-4674	141	17	)	)	PUNCT
ejpam-4674	141	18	∇πvh(tk(vh))dx	∇πvh(tk(vh))dx	VERB
ejpam-4674	141	19	≥	≥	NUM
ejpam-4674	141	20	0	0	NUM
ejpam-4674	141	21	,	,	PUNCT
ejpam-4674	141	22	which	which	PRON
ejpam-4674	141	23	immediately	immediately	ADV
ejpam-4674	141	24	implies	imply	VERB
ejpam-4674	141	25	(	(	PUNCT
ejpam-4674	141	26	30	30	NUM
ejpam-4674	141	27	)	)	PUNCT
ejpam-4674	141	28	.	.	PUNCT
ejpam-4674	142	1	as	as	ADP
ejpam-4674	142	2	a	a	DET
ejpam-4674	142	3	consequence	consequence	NOUN
ejpam-4674	142	4	,	,	PUNCT
ejpam-4674	142	5	we	we	PRON
ejpam-4674	142	6	consider	consider	VERB
ejpam-4674	142	7	(	(	PUNCT
ejpam-4674	142	8	30	30	NUM
ejpam-4674	142	9	)	)	PUNCT
ejpam-4674	142	10	and	and	CCONJ
ejpam-4674	142	11	the	the	DET
ejpam-4674	142	12	coercivity	coercivity	NOUN
ejpam-4674	142	13	(	(	PUNCT
ejpam-4674	142	14	3	3	NUM
ejpam-4674	142	15	)	)	PUNCT
ejpam-4674	142	16	of	of	ADP
ejpam-4674	142	17	a	a	PRON
ejpam-4674	142	18	to	to	PART
ejpam-4674	142	19	obtain	obtain	VERB
ejpam-4674	142	20	(	(	PUNCT
ejpam-4674	142	21	31	31	NUM
ejpam-4674	142	22	)	)	PUNCT
ejpam-4674	142	23	.	.	PUNCT
ejpam-4674	143	1	our	our	PRON
ejpam-4674	143	2	main	main	ADJ
ejpam-4674	143	3	result	result	NOUN
ejpam-4674	143	4	is	be	AUX
ejpam-4674	143	5	the	the	DET
ejpam-4674	143	6	following	following	NOUN
ejpam-4674	143	7	.	.	PUNCT
ejpam-4674	144	1	theorem	theorem	NOUN
ejpam-4674	144	2	3	3	NUM
ejpam-4674	144	3	.	.	PUNCT
ejpam-4674	145	1	under	under	ADP
ejpam-4674	145	2	the	the	DET
ejpam-4674	145	3	assumptions	assumption	NOUN
ejpam-4674	145	4	of	of	ADP
ejpam-4674	145	5	proposition	proposition	NOUN
ejpam-4674	145	6	(	(	PUNCT
ejpam-4674	145	7	3.2	3.2	NUM
ejpam-4674	145	8	)	)	PUNCT
ejpam-4674	145	9	,	,	PUNCT
ejpam-4674	145	10	the	the	DET
ejpam-4674	145	11	unique	unique	ADJ
ejpam-4674	145	12	solution	solution	NOUN
ejpam-4674	145	13	uh	uh	INTJ
ejpam-4674	145	14	of	of	ADP
ejpam-4674	145	15	(	(	PUNCT
ejpam-4674	145	16	20	20	NUM
ejpam-4674	145	17	)	)	PUNCT
ejpam-4674	145	18	satisfies	satisfie	NOUN
ejpam-4674	145	19	for	for	ADP
ejpam-4674	145	20	every	every	DET
ejpam-4674	145	21	k	k	PROPN
ejpam-4674	145	22	>	>	X
ejpam-4674	145	23	0	0	PUNCT
ejpam-4674	145	24	and	and	CCONJ
ejpam-4674	145	25	for	for	ADP
ejpam-4674	145	26	every	every	DET
ejpam-4674	145	27	q	q	NOUN
ejpam-4674	145	28	with	with	ADP
ejpam-4674	145	29	1	1	NUM
ejpam-4674	145	30	≤	≤	NOUN
ejpam-4674	145	31	q	q	NOUN
ejpam-4674	145	32	<	<	X
ejpam-4674	145	33	d	d	SYM
ejpam-4674	145	34	d−	d−	PROPN
ejpam-4674	145	35	1	1	NUM
ejpam-4674	145	36	uh	uh	INTJ
ejpam-4674	145	37	−→	−→	NOUN
ejpam-4674	145	38	u	u	NOUN
ejpam-4674	145	39	strongly	strongly	ADV
ejpam-4674	145	40	in	in	ADP
ejpam-4674	145	41	w	w	PROPN
ejpam-4674	145	42	1,q	1,q	NUM
ejpam-4674	145	43	0	0	NUM
ejpam-4674	145	44	(	(	PUNCT
ejpam-4674	145	45	ω	ω	NOUN
ejpam-4674	145	46	)	)	PUNCT
ejpam-4674	145	47	,	,	PUNCT
ejpam-4674	145	48	(	(	PUNCT
ejpam-4674	145	49	33	33	NUM
ejpam-4674	145	50	)	)	PUNCT
ejpam-4674	145	51	when	when	SCONJ
ejpam-4674	145	52	the	the	DET
ejpam-4674	145	53	mesh	mesh	NOUN
ejpam-4674	145	54	size	size	NOUN
ejpam-4674	145	55	h	h	NOUN
ejpam-4674	145	56	tends	tend	VERB
ejpam-4674	145	57	to	to	ADP
ejpam-4674	145	58	zero	zero	NUM
ejpam-4674	145	59	,	,	PUNCT
ejpam-4674	145	60	where	where	SCONJ
ejpam-4674	145	61	u	u	NOUN
ejpam-4674	145	62	is	be	AUX
ejpam-4674	145	63	the	the	DET
ejpam-4674	145	64	unique	unique	ADJ
ejpam-4674	145	65	renormalized	renormalize	VERB
ejpam-4674	145	66	solution	solution	NOUN
ejpam-4674	145	67	of	of	ADP
ejpam-4674	145	68	(	(	PUNCT
ejpam-4674	145	69	1	1	NUM
ejpam-4674	145	70	)	)	PUNCT
ejpam-4674	145	71	.	.	PUNCT
ejpam-4674	146	1	proof	proof	NOUN
ejpam-4674	146	2	.	.	PUNCT
ejpam-4674	147	1	let	let	VERB
ejpam-4674	147	2	us	we	PRON
ejpam-4674	147	3	consider	consider	VERB
ejpam-4674	147	4	(	(	PUNCT
ejpam-4674	147	5	f	f	X
ejpam-4674	147	6	ε	ε	PROPN
ejpam-4674	147	7	)	)	PUNCT
ejpam-4674	147	8	ε	ε	PROPN
ejpam-4674	147	9	,	,	PUNCT
ejpam-4674	147	10	a	a	DET
ejpam-4674	147	11	sequence	sequence	NOUN
ejpam-4674	147	12	of	of	ADP
ejpam-4674	147	13	functions	function	NOUN
ejpam-4674	147	14	such	such	ADJ
ejpam-4674	147	15	that	that	SCONJ
ejpam-4674	147	16	f	f	PROPN
ejpam-4674	147	17	ε	ε	PROPN
ejpam-4674	147	18	∈	∈	PROPN
ejpam-4674	147	19	l2(ω	l2(ω	PROPN
ejpam-4674	147	20	)	)	PUNCT
ejpam-4674	147	21	,	,	PUNCT
ejpam-4674	147	22	f	f	PROPN
ejpam-4674	147	23	ε	ε	PROPN
ejpam-4674	147	24	−→	−→	NOUN
ejpam-4674	147	25	f	f	X
ejpam-4674	147	26	strongly	strongly	ADV
ejpam-4674	147	27	in	in	ADP
ejpam-4674	147	28	l1(ω	l1(ω	PROPN
ejpam-4674	147	29	)	)	PUNCT
ejpam-4674	147	30	.	.	PUNCT
ejpam-4674	148	1	we	we	PRON
ejpam-4674	148	2	can	can	AUX
ejpam-4674	148	3	take	take	VERB
ejpam-4674	148	4	for	for	ADP
ejpam-4674	148	5	example	example	NOUN
ejpam-4674	148	6	f	f	PROPN
ejpam-4674	148	7	ε	ε	PROPN
ejpam-4674	148	8	=	=	SYM
ejpam-4674	148	9	t	t	PROPN
ejpam-4674	148	10	1	1	NUM
ejpam-4674	148	11	ε	ε	PROPN
ejpam-4674	148	12	(	(	PUNCT
ejpam-4674	148	13	f	f	NOUN
ejpam-4674	148	14	)	)	PUNCT
ejpam-4674	148	15	.	.	PUNCT
ejpam-4674	149	1	let	let	VERB
ejpam-4674	149	2	uεh	uεh	PROPN
ejpam-4674	149	3	be	be	AUX
ejpam-4674	149	4	the	the	DET
ejpam-4674	149	5	unique	unique	ADJ
ejpam-4674	149	6	solution	solution	NOUN
ejpam-4674	149	7	of	of	ADP
ejpam-4674	149	8	problem	problem	NOUN
ejpam-4674	149	9	(	(	PUNCT
ejpam-4674	149	10	20	20	NUM
ejpam-4674	149	11	)	)	PUNCT
ejpam-4674	149	12	with	with	ADP
ejpam-4674	149	13	regularized	regularize	VERB
ejpam-4674	149	14	data	datum	NOUN
ejpam-4674	149	15	f	f	PROPN
ejpam-4674	149	16	ε	ε	PROPN
ejpam-4674	149	17	∈	∈	PROPN
ejpam-4674	149	18	l2(ω	l2(ω	PROPN
ejpam-4674	149	19	)	)	PUNCT
ejpam-4674	149	20	.	.	PUNCT
ejpam-4674	150	1	then	then	ADV
ejpam-4674	150	2	uh	uh	INTJ
ejpam-4674	150	3	−	−	PROPN
ejpam-4674	150	4	uεh	uεh	PROPN
ejpam-4674	150	5	satisfies	satisfies	PUNCT
ejpam-4674	150	6	uh	uh	INTJ
ejpam-4674	150	7	−	−	PUNCT
ejpam-4674	150	8	uεh	uεh	PROPN
ejpam-4674	150	9	∈	∈	PROPN
ejpam-4674	150	10	v	v	NOUN
ejpam-4674	150	11	h	h	NOUN
ejpam-4674	150	12	,	,	PUNCT
ejpam-4674	150	13	∀vh	∀vh	PROPN
ejpam-4674	150	14	∈	∈	PROPN
ejpam-4674	150	15	v	v	PROPN
ejpam-4674	150	16	h	h	NOUN
ejpam-4674	150	17	,	,	PUNCT
ejpam-4674	150	18	∫	∫	PROPN
ejpam-4674	150	19	ω	ω	PROPN
ejpam-4674	151	1	a∇(uh	a∇(uh	PROPN
ejpam-4674	151	2	−	−	PROPN
ejpam-4674	152	1	uεh)∇vhdx	uεh)∇vhdx	PROPN
ejpam-4674	152	2	=	=	SYM
ejpam-4674	152	3	∫	∫	PROPN
ejpam-4674	152	4	ω	ω	PROPN
ejpam-4674	152	5	(	(	PUNCT
ejpam-4674	152	6	f	f	PROPN
ejpam-4674	152	7	−	−	PROPN
ejpam-4674	152	8	f	f	PROPN
ejpam-4674	152	9	ε)vhdx	ε)vhdx	PROPN
ejpam-4674	152	10	.	.	PUNCT
ejpam-4674	153	1	y.	y.	PROPN
ejpam-4674	153	2	c.	c.	PROPN
ejpam-4674	153	3	bassonon	bassonon	PROPN
ejpam-4674	153	4	,	,	PUNCT
ejpam-4674	153	5	a.	a.	NOUN
ejpam-4674	153	6	ouédraogo	ouédraogo	PROPN
ejpam-4674	153	7	/	/	SYM
ejpam-4674	153	8	eur	eur	PROPN
ejpam-4674	153	9	.	.	PUNCT
ejpam-4674	154	1	j.	j.	PROPN
ejpam-4674	154	2	pure	pure	PROPN
ejpam-4674	154	3	appl	appl	PROPN
ejpam-4674	154	4	.	.	PROPN
ejpam-4674	154	5	math	math	PROPN
ejpam-4674	154	6	,	,	PUNCT
ejpam-4674	154	7	16	16	NUM
ejpam-4674	154	8	(	(	PUNCT
ejpam-4674	154	9	1	1	NUM
ejpam-4674	154	10	)	)	PUNCT
ejpam-4674	154	11	(	(	PUNCT
ejpam-4674	154	12	2023	2023	NUM
ejpam-4674	154	13	)	)	PUNCT
ejpam-4674	154	14	,	,	PUNCT
ejpam-4674	154	15	404	404	NUM
ejpam-4674	154	16	-	-	SYM
ejpam-4674	154	17	417	417	NUM
ejpam-4674	154	18	412	412	NUM
ejpam-4674	154	19	we	we	PRON
ejpam-4674	154	20	consider	consider	VERB
ejpam-4674	154	21	this	this	DET
ejpam-4674	154	22	problem	problem	NOUN
ejpam-4674	154	23	and	and	CCONJ
ejpam-4674	154	24	we	we	PRON
ejpam-4674	154	25	apply	apply	VERB
ejpam-4674	154	26	estimate	estimate	NOUN
ejpam-4674	154	27	(	(	PUNCT
ejpam-4674	154	28	31	31	NUM
ejpam-4674	154	29	)	)	PUNCT
ejpam-4674	154	30	.	.	PUNCT
ejpam-4674	155	1	we	we	PRON
ejpam-4674	155	2	have	have	VERB
ejpam-4674	155	3	for	for	ADP
ejpam-4674	155	4	every	every	PRON
ejpam-4674	155	5	k	k	PROPN
ejpam-4674	155	6	>	>	X
ejpam-4674	155	7	0	0	PROPN
ejpam-4674	155	8	,	,	PUNCT
ejpam-4674	155	9	every	every	DET
ejpam-4674	155	10	h	h	NOUN
ejpam-4674	155	11	>	>	X
ejpam-4674	155	12	0	0	PUNCT
ejpam-4674	156	1	and	and	CCONJ
ejpam-4674	156	2	every	every	DET
ejpam-4674	156	3	ε	ε	PROPN
ejpam-4674	156	4	>	>	X
ejpam-4674	156	5	0	0	PUNCT
ejpam-4674	157	1	α	α	PRON
ejpam-4674	157	2	∫	∫	PROPN
ejpam-4674	157	3	ω	ω	X
ejpam-4674	157	4	∣∣∣∇πvh	∣∣∣∇πvh	X
ejpam-4674	157	5	(	(	PUNCT
ejpam-4674	157	6	tk(uh	tk(uh	PROPN
ejpam-4674	157	7	−	−	ADP
ejpam-4674	157	8	uεh	uεh	PROPN
ejpam-4674	157	9	)	)	PUNCT
ejpam-4674	157	10	)	)	PUNCT
ejpam-4674	157	11	∣∣∣2dx	∣∣∣2dx	PROPN
ejpam-4674	158	1	≤	≤	NOUN
ejpam-4674	158	2	k∥f	k∥f	NOUN
ejpam-4674	158	3	−	−	PROPN
ejpam-4674	158	4	f	f	PROPN
ejpam-4674	158	5	ε∥l1(ω	ε∥l1(ω	PROPN
ejpam-4674	158	6	)	)	PUNCT
ejpam-4674	158	7	,	,	PUNCT
ejpam-4674	158	8	next	next	ADV
ejpam-4674	158	9	,	,	PUNCT
ejpam-4674	158	10	applying	apply	VERB
ejpam-4674	158	11	theorem	theorem	NOUN
ejpam-4674	158	12	2.1	2.1	NUM
ejpam-4674	158	13	of	of	ADP
ejpam-4674	158	14	[	[	X
ejpam-4674	158	15	3	3	NUM
ejpam-4674	158	16	]	]	PUNCT
ejpam-4674	158	17	and	and	CCONJ
ejpam-4674	158	18	using	use	VERB
ejpam-4674	158	19	theorem	theorem	NOUN
ejpam-4674	158	20	2	2	NUM
ejpam-4674	158	21	,	,	PUNCT
ejpam-4674	158	22	we	we	PRON
ejpam-4674	158	23	deduce	deduce	VERB
ejpam-4674	158	24	that	that	SCONJ
ejpam-4674	158	25	,	,	PUNCT
ejpam-4674	158	26	for	for	ADP
ejpam-4674	158	27	every	every	DET
ejpam-4674	158	28	q	q	NOUN
ejpam-4674	158	29	with	with	ADP
ejpam-4674	158	30	1	1	NUM
ejpam-4674	158	31	≤	≤	NOUN
ejpam-4674	158	32	q	q	NOUN
ejpam-4674	158	33	<	<	X
ejpam-4674	158	34	d	d	SYM
ejpam-4674	158	35	d−	d−	PROPN
ejpam-4674	158	36	1	1	NUM
ejpam-4674	158	37	,	,	PUNCT
ejpam-4674	158	38	every	every	DET
ejpam-4674	158	39	h	h	NOUN
ejpam-4674	158	40	>	>	X
ejpam-4674	158	41	0	0	PUNCT
ejpam-4674	158	42	and	and	CCONJ
ejpam-4674	158	43	every	every	DET
ejpam-4674	158	44	ε	ε	PROPN
ejpam-4674	158	45	>	>	X
ejpam-4674	158	46	0	0	NUM
ejpam-4674	158	47	∥uh	∥uh	PROPN
ejpam-4674	158	48	−	−	PROPN
ejpam-4674	158	49	uεh∥w	uεh∥w	INTJ
ejpam-4674	158	50	1,q	1,q	NUM
ejpam-4674	158	51	0	0	NUM
ejpam-4674	158	52	(	(	PUNCT
ejpam-4674	158	53	ω	ω	NOUN
ejpam-4674	158	54	)	)	PUNCT
ejpam-4674	158	55	≤	≤	NOUN
ejpam-4674	158	56	c2	c2	PROPN
ejpam-4674	158	57	1	1	NUM
ejpam-4674	158	58	α	α	PROPN
ejpam-4674	159	1	∥f	∥f	PROPN
ejpam-4674	159	2	−	−	X
ejpam-4674	160	1	f	f	PROPN
ejpam-4674	160	2	ε∥l1(ω	ε∥l1(ω	NOUN
ejpam-4674	160	3	)	)	PUNCT
ejpam-4674	160	4	,	,	PUNCT
ejpam-4674	160	5	(	(	PUNCT
ejpam-4674	160	6	34	34	NUM
ejpam-4674	160	7	)	)	PUNCT
ejpam-4674	160	8	where	where	SCONJ
ejpam-4674	160	9	c2	c2	PROPN
ejpam-4674	160	10	is	be	AUX
ejpam-4674	160	11	a	a	DET
ejpam-4674	160	12	constant	constant	ADJ
ejpam-4674	160	13	which	which	PRON
ejpam-4674	160	14	depends	depend	VERB
ejpam-4674	160	15	of	of	ADP
ejpam-4674	160	16	d	d	NOUN
ejpam-4674	160	17	and	and	CCONJ
ejpam-4674	160	18	q.	q.	PROPN
ejpam-4674	160	19	on	on	ADP
ejpam-4674	160	20	the	the	DET
ejpam-4674	160	21	other	other	ADJ
ejpam-4674	160	22	hand	hand	NOUN
ejpam-4674	160	23	,	,	PUNCT
ejpam-4674	160	24	since	since	SCONJ
ejpam-4674	160	25	f	f	PROPN
ejpam-4674	160	26	ε	ε	PROPN
ejpam-4674	160	27	∈	∈	PROPN
ejpam-4674	160	28	l2(ω	l2(ω	PROPN
ejpam-4674	160	29	)	)	PUNCT
ejpam-4674	160	30	and	and	CCONJ
ejpam-4674	160	31	the	the	DET
ejpam-4674	160	32	fact	fact	NOUN
ejpam-4674	160	33	that	that	SCONJ
ejpam-4674	160	34	the	the	DET
ejpam-4674	160	35	physical	physical	ADJ
ejpam-4674	160	36	mesh	mesh	NOUN
ejpam-4674	160	37	is	be	AUX
ejpam-4674	160	38	quasi	quasi	ADJ
ejpam-4674	160	39	-	-	ADJ
ejpam-4674	160	40	uniform	uniform	ADJ
ejpam-4674	160	41	under	under	ADP
ejpam-4674	160	42	hypothesis	hypothesis	NOUN
ejpam-4674	160	43	(	(	PUNCT
ejpam-4674	160	44	10	10	NUM
ejpam-4674	160	45	)	)	PUNCT
ejpam-4674	160	46	and	and	CCONJ
ejpam-4674	160	47	(	(	PUNCT
ejpam-4674	160	48	18	18	NUM
ejpam-4674	160	49	)	)	PUNCT
ejpam-4674	161	1	,	,	PUNCT
ejpam-4674	161	2	we	we	PRON
ejpam-4674	161	3	have	have	VERB
ejpam-4674	161	4	that	that	PRON
ejpam-4674	161	5	,	,	PUNCT
ejpam-4674	161	6	for	for	ADP
ejpam-4674	161	7	any	any	DET
ejpam-4674	161	8	ε	ε	PROPN
ejpam-4674	161	9	>	>	X
ejpam-4674	161	10	0	0	NUM
ejpam-4674	162	1	lim	lim	PROPN
ejpam-4674	162	2	h−→0	h−→0	PROPN
ejpam-4674	162	3	∥uεh	∥uεh	PROPN
ejpam-4674	162	4	−	−	PROPN
ejpam-4674	162	5	uε∥h1	uε∥h1	NOUN
ejpam-4674	162	6	0	0	NUM
ejpam-4674	163	1	(	(	PUNCT
ejpam-4674	163	2	ω	ω	NOUN
ejpam-4674	163	3	)	)	PUNCT
ejpam-4674	164	1	=	=	SYM
ejpam-4674	164	2	0	0	NUM
ejpam-4674	164	3	,	,	PUNCT
ejpam-4674	164	4	(	(	PUNCT
ejpam-4674	164	5	35	35	NUM
ejpam-4674	164	6	)	)	PUNCT
ejpam-4674	164	7	where	where	SCONJ
ejpam-4674	164	8	uε	uε	PROPN
ejpam-4674	164	9	is	be	AUX
ejpam-4674	164	10	the	the	DET
ejpam-4674	164	11	unique	unique	ADJ
ejpam-4674	164	12	solution	solution	NOUN
ejpam-4674	164	13	of	of	VERB
ejpam-4674	164	14	uε	uε	PROPN
ejpam-4674	164	15	∈	∈	PROPN
ejpam-4674	164	16	h1	h1	PROPN
ejpam-4674	164	17	0	0	NUM
ejpam-4674	164	18	(	(	PUNCT
ejpam-4674	164	19	ω	ω	NOUN
ejpam-4674	164	20	)	)	PUNCT
ejpam-4674	164	21	,	,	PUNCT
ejpam-4674	164	22	−div(a∇uε	−div(a∇uε	ADJ
ejpam-4674	164	23	)	)	PUNCT
ejpam-4674	165	1	=	=	SYM
ejpam-4674	165	2	f	f	X
ejpam-4674	165	3	ε	ε	PROPN
ejpam-4674	165	4	in	in	ADP
ejpam-4674	165	5	d′(ω	d′(ω	PROPN
ejpam-4674	165	6	)	)	PUNCT
ejpam-4674	165	7	.	.	PUNCT
ejpam-4674	166	1	(	(	PUNCT
ejpam-4674	166	2	36	36	NUM
ejpam-4674	166	3	)	)	PUNCT
ejpam-4674	166	4	finally	finally	ADV
ejpam-4674	166	5	,	,	PUNCT
ejpam-4674	166	6	the	the	DET
ejpam-4674	166	7	function	function	NOUN
ejpam-4674	166	8	uε	uε	NOUN
ejpam-4674	166	9	,	,	PUNCT
ejpam-4674	166	10	which	which	PRON
ejpam-4674	166	11	is	be	AUX
ejpam-4674	166	12	the	the	DET
ejpam-4674	166	13	unique	unique	ADJ
ejpam-4674	166	14	weak	weak	ADJ
ejpam-4674	166	15	solution	solution	NOUN
ejpam-4674	166	16	of	of	ADP
ejpam-4674	166	17	(	(	PUNCT
ejpam-4674	166	18	36	36	NUM
ejpam-4674	166	19	)	)	PUNCT
ejpam-4674	166	20	,	,	PUNCT
ejpam-4674	166	21	is	be	AUX
ejpam-4674	166	22	also	also	ADV
ejpam-4674	166	23	the	the	DET
ejpam-4674	166	24	unique	unique	ADJ
ejpam-4674	166	25	renormalized	renormalize	VERB
ejpam-4674	166	26	solution	solution	NOUN
ejpam-4674	166	27	in	in	ADP
ejpam-4674	166	28	the	the	DET
ejpam-4674	166	29	sense	sense	NOUN
ejpam-4674	166	30	of	of	ADP
ejpam-4674	166	31	definition	definition	NOUN
ejpam-4674	166	32	1.1	1.1	NUM
ejpam-4674	166	33	of	of	ADP
ejpam-4674	166	34	the	the	DET
ejpam-4674	166	35	problem	problem	PUNCT
ejpam-4674	166	36	−div(a∇uε	−div(a∇uε	NOUN
ejpam-4674	166	37	)	)	PUNCT
ejpam-4674	167	1	=	=	SYM
ejpam-4674	167	2	f	f	X
ejpam-4674	167	3	ε	ε	PROPN
ejpam-4674	167	4	in	in	ADP
ejpam-4674	167	5	ω	ω	PROPN
ejpam-4674	167	6	,	,	PUNCT
ejpam-4674	167	7	uε	uε	X
ejpam-4674	167	8	=	=	NOUN
ejpam-4674	167	9	0	0	NUM
ejpam-4674	167	10	on	on	ADP
ejpam-4674	167	11	∂ω	∂ω	PROPN
ejpam-4674	167	12	.	.	PUNCT
ejpam-4674	168	1	(	(	PUNCT
ejpam-4674	168	2	37	37	NUM
ejpam-4674	168	3	)	)	PUNCT
ejpam-4674	168	4	we	we	PRON
ejpam-4674	168	5	consider	consider	VERB
ejpam-4674	168	6	u	u	PRON
ejpam-4674	168	7	and	and	CCONJ
ejpam-4674	168	8	uε	uε	ADP
ejpam-4674	168	9	the	the	DET
ejpam-4674	168	10	unique	unique	ADJ
ejpam-4674	168	11	renormalized	renormalize	VERB
ejpam-4674	168	12	solutions	solution	NOUN
ejpam-4674	168	13	of	of	ADP
ejpam-4674	168	14	(	(	PUNCT
ejpam-4674	168	15	1	1	NUM
ejpam-4674	168	16	)	)	PUNCT
ejpam-4674	168	17	and	and	CCONJ
ejpam-4674	168	18	(	(	PUNCT
ejpam-4674	168	19	37	37	NUM
ejpam-4674	168	20	)	)	PUNCT
ejpam-4674	168	21	respectively	respectively	ADV
ejpam-4674	168	22	.	.	PUNCT
ejpam-4674	169	1	we	we	PRON
ejpam-4674	169	2	have	have	VERB
ejpam-4674	169	3	,	,	PUNCT
ejpam-4674	169	4	indeed	indeed	ADV
ejpam-4674	169	5	the	the	DET
ejpam-4674	169	6	continuous	continuous	ADJ
ejpam-4674	169	7	dependence	dependence	NOUN
ejpam-4674	169	8	of	of	ADP
ejpam-4674	169	9	the	the	DET
ejpam-4674	169	10	renormalized	renormalize	VERB
ejpam-4674	169	11	solution	solution	NOUN
ejpam-4674	169	12	with	with	ADP
ejpam-4674	169	13	respect	respect	NOUN
ejpam-4674	169	14	to	to	ADP
ejpam-4674	169	15	the	the	DET
ejpam-4674	169	16	data	datum	NOUN
ejpam-4674	169	17	implies	imply	VERB
ejpam-4674	169	18	that	that	SCONJ
ejpam-4674	169	19	∥uε	∥uε	VERB
ejpam-4674	169	20	−	−	PROPN
ejpam-4674	169	21	u∥	u∥	PROPN
ejpam-4674	169	22	w	w	PROPN
ejpam-4674	169	23	1,q	1,q	NUM
ejpam-4674	169	24	0	0	NUM
ejpam-4674	169	25	(	(	PUNCT
ejpam-4674	169	26	ω	ω	NOUN
ejpam-4674	169	27	)	)	PUNCT
ejpam-4674	169	28	≤	≤	NOUN
ejpam-4674	169	29	c3	c3	NOUN
ejpam-4674	169	30	1	1	NUM
ejpam-4674	169	31	α	α	NOUN
ejpam-4674	169	32	∥f	∥f	PROPN
ejpam-4674	169	33	ε	ε	PROPN
ejpam-4674	169	34	−	−	NOUN
ejpam-4674	169	35	f∥l1(ω	f∥l1(ω	NOUN
ejpam-4674	169	36	)	)	PUNCT
ejpam-4674	169	37	.	.	PUNCT
ejpam-4674	170	1	(	(	PUNCT
ejpam-4674	170	2	38	38	NUM
ejpam-4674	170	3	)	)	PUNCT
ejpam-4674	170	4	for	for	ADP
ejpam-4674	170	5	every	every	DET
ejpam-4674	170	6	q	q	NOUN
ejpam-4674	170	7	with	with	ADP
ejpam-4674	170	8	1	1	NUM
ejpam-4674	170	9	≤	≤	NOUN
ejpam-4674	170	10	q	q	NOUN
ejpam-4674	170	11	<	<	X
ejpam-4674	170	12	d	d	SYM
ejpam-4674	170	13	d−	d−	PROPN
ejpam-4674	170	14	1	1	NUM
ejpam-4674	170	15	.	.	PUNCT
ejpam-4674	171	1	inequality	inequality	NOUN
ejpam-4674	171	2	(	(	PUNCT
ejpam-4674	171	3	38	38	NUM
ejpam-4674	171	4	)	)	PUNCT
ejpam-4674	171	5	is	be	AUX
ejpam-4674	171	6	given	give	VERB
ejpam-4674	171	7	by	by	ADP
ejpam-4674	171	8	theorem	theorem	NOUN
ejpam-4674	171	9	1.2	1.2	NUM
ejpam-4674	171	10	in	in	ADP
ejpam-4674	171	11	[	[	X
ejpam-4674	171	12	3	3	NUM
ejpam-4674	171	13	]	]	PUNCT
ejpam-4674	171	14	.	.	PUNCT
ejpam-4674	172	1	writing	write	VERB
ejpam-4674	172	2	now	now	ADV
ejpam-4674	172	3	∥uh	∥uh	PUNCT
ejpam-4674	173	1	−	−	NOUN
ejpam-4674	173	2	u∥	u∥	PROPN
ejpam-4674	173	3	w	w	PROPN
ejpam-4674	173	4	1,q	1,q	NUM
ejpam-4674	173	5	0	0	NUM
ejpam-4674	173	6	(	(	PUNCT
ejpam-4674	173	7	ω	ω	NOUN
ejpam-4674	173	8	)	)	PUNCT
ejpam-4674	173	9	≤	≤	NOUN
ejpam-4674	173	10	∥uh	∥uh	PRON
ejpam-4674	174	1	−	−	NOUN
ejpam-4674	174	2	uεh∥w	uεh∥w	INTJ
ejpam-4674	174	3	1,q	1,q	NUM
ejpam-4674	174	4	0	0	NUM
ejpam-4674	174	5	(	(	PUNCT
ejpam-4674	174	6	ω	ω	NOUN
ejpam-4674	174	7	)	)	PUNCT
ejpam-4674	175	1	+	+	CCONJ
ejpam-4674	175	2	∥uεh	∥uεh	NUM
ejpam-4674	175	3	−	−	PROPN
ejpam-4674	176	1	uε∥	uε∥	PROPN
ejpam-4674	176	2	w	w	PROPN
ejpam-4674	176	3	1,q	1,q	NUM
ejpam-4674	176	4	0	0	NUM
ejpam-4674	176	5	(	(	PUNCT
ejpam-4674	176	6	ω	ω	NOUN
ejpam-4674	176	7	)	)	PUNCT
ejpam-4674	176	8	+	+	SYM
ejpam-4674	176	9	∥uε	∥uε	NOUN
ejpam-4674	176	10	−	−	NOUN
ejpam-4674	176	11	u∥	u∥	PROPN
ejpam-4674	176	12	w	w	PROPN
ejpam-4674	176	13	1,q	1,q	NUM
ejpam-4674	176	14	0	0	NUM
ejpam-4674	176	15	(	(	PUNCT
ejpam-4674	176	16	ω	ω	NOUN
ejpam-4674	176	17	)	)	PUNCT
ejpam-4674	176	18	and	and	CCONJ
ejpam-4674	176	19	using	use	VERB
ejpam-4674	176	20	(	(	PUNCT
ejpam-4674	176	21	34	34	NUM
ejpam-4674	176	22	)	)	PUNCT
ejpam-4674	176	23	,	,	PUNCT
ejpam-4674	176	24	(	(	PUNCT
ejpam-4674	176	25	35	35	NUM
ejpam-4674	176	26	)	)	PUNCT
ejpam-4674	176	27	and	and	CCONJ
ejpam-4674	176	28	(	(	PUNCT
ejpam-4674	176	29	38	38	NUM
ejpam-4674	176	30	)	)	PUNCT
ejpam-4674	176	31	,	,	PUNCT
ejpam-4674	176	32	we	we	PRON
ejpam-4674	176	33	have	have	AUX
ejpam-4674	176	34	proved	prove	VERB
ejpam-4674	176	35	that	that	SCONJ
ejpam-4674	176	36	for	for	ADP
ejpam-4674	176	37	every	every	DET
ejpam-4674	176	38	ε	ε	PROPN
ejpam-4674	176	39	>	>	X
ejpam-4674	176	40	0	0	PUNCT
ejpam-4674	177	1	and	and	CCONJ
ejpam-4674	177	2	every	every	DET
ejpam-4674	177	3	q	q	NOUN
ejpam-4674	177	4	with	with	ADP
ejpam-4674	177	5	1	1	NUM
ejpam-4674	177	6	≤	≤	NOUN
ejpam-4674	177	7	q	q	NOUN
ejpam-4674	177	8	<	<	X
ejpam-4674	177	9	d	d	SYM
ejpam-4674	177	10	d−	d−	PROPN
ejpam-4674	177	11	1	1	NUM
ejpam-4674	177	12	lim	lim	PROPN
ejpam-4674	177	13	sup	sup	PROPN
ejpam-4674	177	14	h−→0	h−→0	PROPN
ejpam-4674	177	15	∥uh	∥uh	PROPN
ejpam-4674	178	1	−	−	NOUN
ejpam-4674	178	2	u∥	u∥	PROPN
ejpam-4674	178	3	w	w	PROPN
ejpam-4674	178	4	1,q	1,q	NUM
ejpam-4674	178	5	0	0	NUM
ejpam-4674	178	6	(	(	PUNCT
ejpam-4674	178	7	ω	ω	NOUN
ejpam-4674	178	8	)	)	PUNCT
ejpam-4674	178	9	≤	≤	NOUN
ejpam-4674	178	10	(	(	PUNCT
ejpam-4674	178	11	c1	c1	PROPN
ejpam-4674	178	12	,	,	PUNCT
ejpam-4674	178	13	c2	c2	PROPN
ejpam-4674	178	14	,	,	PUNCT
ejpam-4674	178	15	c3	c3	PROPN
ejpam-4674	178	16	)	)	PUNCT
ejpam-4674	178	17	1	1	NUM
ejpam-4674	178	18	α	α	X
ejpam-4674	178	19	∥f	∥f	PROPN
ejpam-4674	178	20	ε	ε	PROPN
ejpam-4674	178	21	−	−	NOUN
ejpam-4674	178	22	f∥l1(ω	f∥l1(ω	NOUN
ejpam-4674	178	23	)	)	PUNCT
ejpam-4674	178	24	.	.	PUNCT
ejpam-4674	179	1	y.	y.	PROPN
ejpam-4674	179	2	c.	c.	PROPN
ejpam-4674	179	3	bassonon	bassonon	PROPN
ejpam-4674	179	4	,	,	PUNCT
ejpam-4674	179	5	a.	a.	NOUN
ejpam-4674	179	6	ouédraogo	ouédraogo	PROPN
ejpam-4674	179	7	/	/	SYM
ejpam-4674	179	8	eur	eur	PROPN
ejpam-4674	179	9	.	.	PUNCT
ejpam-4674	180	1	j.	j.	PROPN
ejpam-4674	180	2	pure	pure	PROPN
ejpam-4674	180	3	appl	appl	PROPN
ejpam-4674	180	4	.	.	PROPN
ejpam-4674	180	5	math	math	PROPN
ejpam-4674	180	6	,	,	PUNCT
ejpam-4674	180	7	16	16	NUM
ejpam-4674	180	8	(	(	PUNCT
ejpam-4674	180	9	1	1	NUM
ejpam-4674	180	10	)	)	PUNCT
ejpam-4674	180	11	(	(	PUNCT
ejpam-4674	180	12	2023	2023	NUM
ejpam-4674	180	13	)	)	PUNCT
ejpam-4674	180	14	,	,	PUNCT
ejpam-4674	180	15	404	404	NUM
ejpam-4674	180	16	-	-	SYM
ejpam-4674	180	17	417	417	NUM
ejpam-4674	180	18	413	413	NUM
ejpam-4674	180	19	taking	take	VERB
ejpam-4674	180	20	the	the	DET
ejpam-4674	180	21	limit	limit	NOUN
ejpam-4674	180	22	when	when	SCONJ
ejpam-4674	180	23	ε	ε	PROPN
ejpam-4674	180	24	tends	tend	VERB
ejpam-4674	180	25	to	to	ADP
ejpam-4674	180	26	zero	zero	NUM
ejpam-4674	180	27	proves	prove	VERB
ejpam-4674	180	28	(	(	PUNCT
ejpam-4674	180	29	33	33	NUM
ejpam-4674	180	30	)	)	PUNCT
ejpam-4674	180	31	.	.	PUNCT
ejpam-4674	181	1	for	for	ADP
ejpam-4674	181	2	every	every	DET
ejpam-4674	181	3	r	r	NOUN
ejpam-4674	181	4	with	with	ADP
ejpam-4674	181	5	1	1	NUM
ejpam-4674	181	6	<	<	X
ejpam-4674	181	7	r	r	NOUN
ejpam-4674	181	8	<	<	X
ejpam-4674	181	9	+	+	NOUN
ejpam-4674	181	10	∞	∞	PROPN
ejpam-4674	181	11	,	,	PUNCT
ejpam-4674	181	12	we	we	PRON
ejpam-4674	181	13	denote	denote	VERB
ejpam-4674	181	14	by	by	ADP
ejpam-4674	181	15	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	181	16	)	)	PUNCT
ejpam-4674	182	1	the	the	DET
ejpam-4674	182	2	marcinkiewicz	marcinkiewicz	ADJ
ejpam-4674	182	3	space	space	NOUN
ejpam-4674	182	4	whose	whose	DET
ejpam-4674	182	5	norm	norm	NOUN
ejpam-4674	182	6	is	be	AUX
ejpam-4674	182	7	defined	define	VERB
ejpam-4674	182	8	by	by	ADP
ejpam-4674	182	9	∥f∥lr,∞(ω	∥f∥lr,∞(ω	NOUN
ejpam-4674	182	10	)	)	PUNCT
ejpam-4674	182	11	=	=	SYM
ejpam-4674	182	12	sup	sup	NOUN
ejpam-4674	182	13	ν>0	ν>0	NOUN
ejpam-4674	182	14	(	(	PUNCT
ejpam-4674	182	15	ν	ν	X
ejpam-4674	182	16	∣∣∣{x	∣∣∣{x	PROPN
ejpam-4674	182	17	∈	∈	PROPN
ejpam-4674	182	18	ω	ω	NOUN
ejpam-4674	182	19	:	:	PUNCT
ejpam-4674	183	1	|f(x)|	|f(x)|	NOUN
ejpam-4674	183	2	≥	≥	NUM
ejpam-4674	183	3	ν	ν	NOUN
ejpam-4674	183	4	}	}	PUNCT
ejpam-4674	183	5	∣∣∣1	∣∣∣1	PROPN
ejpam-4674	183	6	/	/	SYM
ejpam-4674	183	7	r	r	NOUN
ejpam-4674	183	8	)	)	PUNCT
ejpam-4674	183	9	.	.	PUNCT
ejpam-4674	184	1	(	(	PUNCT
ejpam-4674	184	2	39	39	NUM
ejpam-4674	184	3	)	)	PUNCT
ejpam-4674	184	4	next	next	ADV
ejpam-4674	184	5	,	,	PUNCT
ejpam-4674	184	6	error	error	NOUN
ejpam-4674	184	7	estimates	estimate	NOUN
ejpam-4674	184	8	for	for	ADP
ejpam-4674	184	9	data	datum	NOUN
ejpam-4674	184	10	f	f	PROPN
ejpam-4674	184	11	∈	∈	PROPN
ejpam-4674	184	12	lr,∞(ω	lr,∞(ω	PROPN
ejpam-4674	184	13	)	)	PUNCT
ejpam-4674	184	14	may	may	AUX
ejpam-4674	184	15	be	be	AUX
ejpam-4674	184	16	derived	derive	VERB
ejpam-4674	184	17	using	use	VERB
ejpam-4674	184	18	the	the	DET
ejpam-4674	184	19	techniques	technique	NOUN
ejpam-4674	184	20	introduced	introduce	VERB
ejpam-4674	184	21	in	in	ADP
ejpam-4674	184	22	[	[	X
ejpam-4674	184	23	3	3	NUM
ejpam-4674	184	24	]	]	PUNCT
ejpam-4674	184	25	.	.	PUNCT
ejpam-4674	185	1	theorem	theorem	ADJ
ejpam-4674	185	2	4	4	NUM
ejpam-4674	185	3	.	.	PUNCT
ejpam-4674	186	1	under	under	ADP
ejpam-4674	186	2	the	the	DET
ejpam-4674	186	3	assumptions	assumption	NOUN
ejpam-4674	186	4	of	of	ADP
ejpam-4674	186	5	theorem	theorem	ADJ
ejpam-4674	186	6	2.2	2.2	NUM
ejpam-4674	186	7	and	and	CCONJ
ejpam-4674	186	8	f	f	PROPN
ejpam-4674	186	9	∈	∈	PROPN
ejpam-4674	186	10	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	186	11	)	)	PUNCT
ejpam-4674	186	12	for	for	ADP
ejpam-4674	186	13	some	some	DET
ejpam-4674	186	14	r	r	NOUN
ejpam-4674	186	15	with	with	ADP
ejpam-4674	186	16	1	1	NUM
ejpam-4674	186	17	<	<	X
ejpam-4674	186	18	r	r	NOUN
ejpam-4674	186	19	<	<	X
ejpam-4674	186	20	2	2	NUM
ejpam-4674	186	21	,	,	PUNCT
ejpam-4674	186	22	there	there	PRON
ejpam-4674	186	23	exists	exist	VERB
ejpam-4674	186	24	a	a	DET
ejpam-4674	186	25	constant	constant	ADJ
ejpam-4674	186	26	c	c	NOUN
ejpam-4674	186	27	independent	independent	NOUN
ejpam-4674	186	28	of	of	ADP
ejpam-4674	186	29	the	the	DET
ejpam-4674	186	30	mesh	mesh	NOUN
ejpam-4674	186	31	size	size	NOUN
ejpam-4674	186	32	h	h	NOUN
ejpam-4674	186	33	such	such	ADJ
ejpam-4674	186	34	that	that	SCONJ
ejpam-4674	186	35	we	we	PRON
ejpam-4674	186	36	have	have	VERB
ejpam-4674	186	37	the	the	DET
ejpam-4674	186	38	error	error	NOUN
ejpam-4674	186	39	estimate	estimate	NOUN
ejpam-4674	186	40	∥uh	∥uh	PUNCT
ejpam-4674	187	1	−	−	NOUN
ejpam-4674	187	2	u∥	u∥	PROPN
ejpam-4674	187	3	w	w	PROPN
ejpam-4674	187	4	1,q	1,q	NUM
ejpam-4674	187	5	0	0	NUM
ejpam-4674	187	6	(	(	PUNCT
ejpam-4674	187	7	ω	ω	NOUN
ejpam-4674	187	8	)	)	PUNCT
ejpam-4674	187	9	≤	≤	NOUN
ejpam-4674	188	1	ch2(1−	ch2(1−	PUNCT
ejpam-4674	188	2	1	1	NUM
ejpam-4674	188	3	r	r	NOUN
ejpam-4674	188	4	)	)	PUNCT
ejpam-4674	188	5	∥f∥lr,∞(ω	∥f∥lr,∞(ω	NOUN
ejpam-4674	188	6	)	)	PUNCT
ejpam-4674	188	7	.	.	PUNCT
ejpam-4674	189	1	(	(	PUNCT
ejpam-4674	189	2	40	40	NUM
ejpam-4674	189	3	)	)	PUNCT
ejpam-4674	189	4	proof	proof	NOUN
ejpam-4674	189	5	.	.	PUNCT
ejpam-4674	190	1	we	we	PRON
ejpam-4674	190	2	assume	assume	VERB
ejpam-4674	190	3	that	that	SCONJ
ejpam-4674	190	4	f	f	PROPN
ejpam-4674	190	5	belongs	belong	VERB
ejpam-4674	190	6	to	to	ADP
ejpam-4674	190	7	the	the	DET
ejpam-4674	190	8	marcinkiewicz	marcinkiewicz	ADJ
ejpam-4674	190	9	space	space	NOUN
ejpam-4674	190	10	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	190	11	)	)	PUNCT
ejpam-4674	190	12	for	for	ADP
ejpam-4674	190	13	some	some	DET
ejpam-4674	190	14	r	r	NOUN
ejpam-4674	190	15	with	with	ADP
ejpam-4674	190	16	1	1	NUM
ejpam-4674	190	17	<	<	X
ejpam-4674	190	18	r	r	NOUN
ejpam-4674	190	19	<	<	X
ejpam-4674	190	20	2	2	NUM
ejpam-4674	190	21	(	(	PUNCT
ejpam-4674	190	22	this	this	PRON
ejpam-4674	190	23	holds	hold	VERB
ejpam-4674	190	24	in	in	ADP
ejpam-4674	190	25	particular	particular	ADJ
ejpam-4674	190	26	if	if	SCONJ
ejpam-4674	190	27	f	f	PROPN
ejpam-4674	190	28	belongs	belong	VERB
ejpam-4674	190	29	to	to	ADP
ejpam-4674	190	30	lr(ω	lr(ω	PROPN
ejpam-4674	190	31	)	)	PUNCT
ejpam-4674	190	32	)	)	PUNCT
ejpam-4674	190	33	.	.	PUNCT
ejpam-4674	191	1	for	for	ADP
ejpam-4674	191	2	every	every	DET
ejpam-4674	191	3	ε	ε	PROPN
ejpam-4674	191	4	>	>	X
ejpam-4674	191	5	0	0	PROPN
ejpam-4674	191	6	,	,	PUNCT
ejpam-4674	191	7	we	we	PRON
ejpam-4674	191	8	set	set	VERB
ejpam-4674	191	9	f	f	PROPN
ejpam-4674	191	10	ε	ε	PROPN
ejpam-4674	191	11	=	=	SYM
ejpam-4674	191	12	t	t	PROPN
ejpam-4674	191	13	1	1	NUM
ejpam-4674	191	14	ε	ε	PROPN
ejpam-4674	191	15	(	(	PUNCT
ejpam-4674	191	16	f	f	PROPN
ejpam-4674	191	17	)	)	PUNCT
ejpam-4674	191	18	,	,	PUNCT
ejpam-4674	191	19	which	which	PRON
ejpam-4674	191	20	belongs	belong	VERB
ejpam-4674	191	21	to	to	ADP
ejpam-4674	191	22	l∞(ω	l∞(ω	ADJ
ejpam-4674	191	23	)	)	PUNCT
ejpam-4674	191	24	⊂	⊂	PROPN
ejpam-4674	191	25	l2(ω	l2(ω	PROPN
ejpam-4674	191	26	)	)	PUNCT
ejpam-4674	191	27	,	,	PUNCT
ejpam-4674	191	28	and	and	CCONJ
ejpam-4674	191	29	we	we	PRON
ejpam-4674	191	30	denote	denote	VERB
ejpam-4674	191	31	by	by	ADP
ejpam-4674	191	32	uεh	uεh	NOUN
ejpam-4674	191	33	the	the	DET
ejpam-4674	191	34	solution	solution	NOUN
ejpam-4674	191	35	of	of	ADP
ejpam-4674	191	36	(	(	PUNCT
ejpam-4674	191	37	20	20	NUM
ejpam-4674	191	38	)	)	PUNCT
ejpam-4674	191	39	with	with	ADP
ejpam-4674	191	40	right	right	ADJ
ejpam-4674	191	41	-	-	PUNCT
ejpam-4674	191	42	hand	hand	NOUN
ejpam-4674	191	43	side	side	NOUN
ejpam-4674	191	44	f	f	PROPN
ejpam-4674	191	45	ε	ε	PROPN
ejpam-4674	191	46	.	.	PUNCT
ejpam-4674	191	47	defining	define	VERB
ejpam-4674	191	48	also	also	ADV
ejpam-4674	191	49	uε	uε	INTJ
ejpam-4674	191	50	at	at	ADP
ejpam-4674	191	51	the	the	DET
ejpam-4674	191	52	solution	solution	NOUN
ejpam-4674	191	53	of	of	ADP
ejpam-4674	191	54	(	(	PUNCT
ejpam-4674	191	55	36	36	NUM
ejpam-4674	191	56	)	)	PUNCT
ejpam-4674	191	57	,	,	PUNCT
ejpam-4674	191	58	we	we	PRON
ejpam-4674	191	59	write	write	VERB
ejpam-4674	191	60	for	for	ADP
ejpam-4674	191	61	every	every	DET
ejpam-4674	191	62	q	q	NOUN
ejpam-4674	191	63	with	with	ADP
ejpam-4674	191	64	1	1	NUM
ejpam-4674	191	65	≤	≤	NOUN
ejpam-4674	191	66	q	q	NOUN
ejpam-4674	191	67	<	<	X
ejpam-4674	191	68	d	d	SYM
ejpam-4674	191	69	d−	d−	PROPN
ejpam-4674	191	70	1	1	NUM
ejpam-4674	191	71	∥uh	∥uh	ADP
ejpam-4674	191	72	−	−	NOUN
ejpam-4674	192	1	u∥	u∥	PROPN
ejpam-4674	193	1	w	w	PROPN
ejpam-4674	193	2	1,q	1,q	NUM
ejpam-4674	193	3	0	0	NUM
ejpam-4674	193	4	(	(	PUNCT
ejpam-4674	193	5	ω	ω	NOUN
ejpam-4674	193	6	)	)	PUNCT
ejpam-4674	193	7	≤	≤	NOUN
ejpam-4674	193	8	∥uh	∥uh	PRON
ejpam-4674	194	1	−	−	NOUN
ejpam-4674	194	2	uεh∥w	uεh∥w	INTJ
ejpam-4674	194	3	1,q	1,q	NUM
ejpam-4674	194	4	0	0	NUM
ejpam-4674	194	5	(	(	PUNCT
ejpam-4674	194	6	ω	ω	NOUN
ejpam-4674	194	7	)	)	PUNCT
ejpam-4674	195	1	+	+	CCONJ
ejpam-4674	195	2	∥uεh	∥uεh	NUM
ejpam-4674	195	3	−	−	PROPN
ejpam-4674	196	1	uε∥	uε∥	PROPN
ejpam-4674	196	2	w	w	PROPN
ejpam-4674	196	3	1,q	1,q	NUM
ejpam-4674	196	4	0	0	NUM
ejpam-4674	196	5	(	(	PUNCT
ejpam-4674	196	6	ω	ω	NOUN
ejpam-4674	196	7	)	)	PUNCT
ejpam-4674	196	8	+	+	SYM
ejpam-4674	196	9	∥uε	∥uε	NOUN
ejpam-4674	196	10	−	−	NOUN
ejpam-4674	196	11	u∥	u∥	PROPN
ejpam-4674	196	12	w	w	PROPN
ejpam-4674	196	13	1,q	1,q	NUM
ejpam-4674	196	14	0	0	NUM
ejpam-4674	196	15	(	(	PUNCT
ejpam-4674	196	16	ω	ω	NOUN
ejpam-4674	196	17	)	)	PUNCT
ejpam-4674	196	18	.	.	PUNCT
ejpam-4674	197	1	(	(	PUNCT
ejpam-4674	197	2	41	41	NUM
ejpam-4674	197	3	)	)	PUNCT
ejpam-4674	197	4	we	we	PRON
ejpam-4674	197	5	have	have	VERB
ejpam-4674	197	6	for	for	ADP
ejpam-4674	197	7	a	a	DET
ejpam-4674	197	8	new	new	ADJ
ejpam-4674	197	9	constant	constant	ADJ
ejpam-4674	197	10	c	c	NOUN
ejpam-4674	197	11	(	(	PUNCT
ejpam-4674	197	12	which	which	PRON
ejpam-4674	197	13	depends	depend	VERB
ejpam-4674	197	14	on	on	ADP
ejpam-4674	197	15	q	q	PROPN
ejpam-4674	197	16	,	,	PUNCT
ejpam-4674	197	17	ω	ω	PROPN
ejpam-4674	197	18	,	,	PUNCT
ejpam-4674	197	19	)	)	PUNCT
ejpam-4674	197	20	∥uεh	∥uεh	PROPN
ejpam-4674	197	21	−	−	PROPN
ejpam-4674	198	1	uε∥	uε∥	PROPN
ejpam-4674	198	2	w	w	PROPN
ejpam-4674	198	3	1,q	1,q	NUM
ejpam-4674	198	4	0	0	NUM
ejpam-4674	198	5	(	(	PUNCT
ejpam-4674	198	6	ω	ω	NOUN
ejpam-4674	198	7	)	)	PUNCT
ejpam-4674	198	8	≤	≤	NOUN
ejpam-4674	198	9	ch∥f	ch∥f	VERB
ejpam-4674	198	10	ε∥l2(ω	ε∥l2(ω	ADV
ejpam-4674	198	11	)	)	PUNCT
ejpam-4674	198	12	.	.	PUNCT
ejpam-4674	199	1	using	use	VERB
ejpam-4674	199	2	then	then	ADV
ejpam-4674	199	3	(	(	PUNCT
ejpam-4674	199	4	34	34	NUM
ejpam-4674	199	5	)	)	PUNCT
ejpam-4674	199	6	and	and	CCONJ
ejpam-4674	199	7	(	(	PUNCT
ejpam-4674	199	8	38	38	NUM
ejpam-4674	199	9	)	)	PUNCT
ejpam-4674	199	10	,	,	PUNCT
ejpam-4674	199	11	we	we	PRON
ejpam-4674	199	12	deduce	deduce	VERB
ejpam-4674	199	13	that	that	PRON
ejpam-4674	199	14	for	for	ADP
ejpam-4674	199	15	a	a	DET
ejpam-4674	199	16	new	new	ADJ
ejpam-4674	199	17	constant	constant	ADJ
ejpam-4674	199	18	c	c	NOUN
ejpam-4674	199	19	,	,	PUNCT
ejpam-4674	199	20	which	which	PRON
ejpam-4674	199	21	is	be	AUX
ejpam-4674	199	22	independent	independent	ADJ
ejpam-4674	199	23	of	of	ADP
ejpam-4674	199	24	ε	ε	PROPN
ejpam-4674	199	25	,	,	PUNCT
ejpam-4674	199	26	h	h	NOUN
ejpam-4674	199	27	and	and	CCONJ
ejpam-4674	199	28	f	f	PROPN
ejpam-4674	199	29	(	(	PUNCT
ejpam-4674	199	30	but	but	CCONJ
ejpam-4674	199	31	depends	depend	VERB
ejpam-4674	199	32	on	on	ADP
ejpam-4674	199	33	d	d	PROPN
ejpam-4674	199	34	,	,	PUNCT
ejpam-4674	199	35	q	q	NOUN
ejpam-4674	199	36	,	,	PUNCT
ejpam-4674	199	37	ω	ω	NOUN
ejpam-4674	199	38	)	)	PUNCT
ejpam-4674	199	39	,	,	PUNCT
ejpam-4674	199	40	one	one	PRON
ejpam-4674	199	41	has	have	VERB
ejpam-4674	199	42	∥uh	∥uh	PROPN
ejpam-4674	200	1	−	−	NOUN
ejpam-4674	200	2	u∥	u∥	PROPN
ejpam-4674	200	3	w	w	PROPN
ejpam-4674	200	4	1,q	1,q	NUM
ejpam-4674	200	5	0	0	NUM
ejpam-4674	200	6	(	(	PUNCT
ejpam-4674	200	7	ω	ω	NOUN
ejpam-4674	200	8	)	)	PUNCT
ejpam-4674	200	9	≤	≤	PUNCT
ejpam-4674	200	10	c	c	X
ejpam-4674	200	11	(	(	PUNCT
ejpam-4674	200	12	∥f	∥f	INTJ
ejpam-4674	200	13	−	−	PROPN
ejpam-4674	200	14	f	f	PROPN
ejpam-4674	200	15	ε∥l1(ω	ε∥l1(ω	NOUN
ejpam-4674	200	16	)	)	PUNCT
ejpam-4674	200	17	+	+	NUM
ejpam-4674	200	18	h∥f	h∥f	NOUN
ejpam-4674	200	19	ε∥l2(ω	ε∥l2(ω	ADV
ejpam-4674	200	20	)	)	PUNCT
ejpam-4674	200	21	)	)	PUNCT
ejpam-4674	200	22	.	.	PUNCT
ejpam-4674	201	1	(	(	PUNCT
ejpam-4674	201	2	42	42	X
ejpam-4674	201	3	)	)	PUNCT
ejpam-4674	201	4	we	we	PRON
ejpam-4674	201	5	now	now	ADV
ejpam-4674	201	6	estimate	estimate	VERB
ejpam-4674	201	7	the	the	DET
ejpam-4674	201	8	right	right	ADJ
ejpam-4674	201	9	-	-	PUNCT
ejpam-4674	201	10	hand	hand	NOUN
ejpam-4674	201	11	side	side	NOUN
ejpam-4674	201	12	of	of	ADP
ejpam-4674	201	13	this	this	DET
ejpam-4674	201	14	inequality	inequality	NOUN
ejpam-4674	201	15	by	by	ADP
ejpam-4674	201	16	considering	consider	VERB
ejpam-4674	201	17	∥g∥plp(ω	∥g∥plp(ω	PROPN
ejpam-4674	201	18	)	)	PUNCT
ejpam-4674	201	19	=	=	PUNCT
ejpam-4674	202	1	p	p	X
ejpam-4674	202	2	∫	∫	PROPN
ejpam-4674	203	1	+	+	PROPN
ejpam-4674	203	2	∞	∞	PROPN
ejpam-4674	203	3	0	0	NUM
ejpam-4674	203	4	tp−1	tp−1	PROPN
ejpam-4674	203	5	∣∣∣{x	∣∣∣{x	NOUN
ejpam-4674	203	6	∈	∈	PROPN
ejpam-4674	203	7	ω	ω	NOUN
ejpam-4674	203	8	:	:	PUNCT
ejpam-4674	204	1	|g(x)|	|g(x)|	NOUN
ejpam-4674	204	2	≥	≥	ADP
ejpam-4674	204	3	t	t	NOUN
ejpam-4674	204	4	}	}	PUNCT
ejpam-4674	204	5	∣∣∣dt	∣∣∣dt	PROPN
ejpam-4674	204	6	,	,	PUNCT
ejpam-4674	204	7	which	which	PRON
ejpam-4674	204	8	gives	give	VERB
ejpam-4674	204	9			NUM
ejpam-4674	204	10	∥f	∥f	PROPN
ejpam-4674	204	11	−	−	PUNCT
ejpam-4674	204	12	f	f	PROPN
ejpam-4674	204	13	ε∥l1(ω	ε∥l1(ω	NOUN
ejpam-4674	204	14	)	)	PUNCT
ejpam-4674	204	15	=	=	SYM
ejpam-4674	205	1	∫	∫	PROPN
ejpam-4674	206	1	+	+	NUM
ejpam-4674	206	2	∞	∞	PROPN
ejpam-4674	206	3	0	0	NUM
ejpam-4674	206	4	∣∣∣{x	∣∣∣{x	PROPN
ejpam-4674	206	5	∈	∈	PROPN
ejpam-4674	206	6	ω	ω	NOUN
ejpam-4674	206	7	:	:	PUNCT
ejpam-4674	206	8	|f(x)−	|f(x)−	PROPN
ejpam-4674	206	9	t	t	PROPN
ejpam-4674	206	10	1	1	NUM
ejpam-4674	206	11	ε	ε	PROPN
ejpam-4674	206	12	(	(	PUNCT
ejpam-4674	206	13	f)(x)|	f)(x)|	PROPN
ejpam-4674	206	14	≥	≥	X
ejpam-4674	206	15	t	t	PROPN
ejpam-4674	206	16	}	}	PUNCT
ejpam-4674	206	17	∣∣∣dt	∣∣∣dt	PROPN
ejpam-4674	206	18	=	=	SYM
ejpam-4674	206	19	∫	∫	PROPN
ejpam-4674	207	1	+	+	NUM
ejpam-4674	207	2	∞	∞	PROPN
ejpam-4674	207	3	0	0	NUM
ejpam-4674	207	4	∣∣∣{x	∣∣∣{x	PROPN
ejpam-4674	207	5	∈	∈	PROPN
ejpam-4674	207	6	ω	ω	NOUN
ejpam-4674	207	7	:	:	PUNCT
ejpam-4674	207	8	|f(x)−	|f(x)−	NOUN
ejpam-4674	207	9	1	1	NUM
ejpam-4674	207	10	ε	ε	PROPN
ejpam-4674	207	11	|	|	ADV
ejpam-4674	207	12	≥	≥	X
ejpam-4674	207	13	t	t	PROPN
ejpam-4674	207	14	}	}	PUNCT
ejpam-4674	207	15	∣∣∣dt	∣∣∣dt	PROPN
ejpam-4674	207	16	=	=	SYM
ejpam-4674	207	17	∫	∫	PROPN
ejpam-4674	208	1	+	+	SYM
ejpam-4674	208	2	∞	∞	PROPN
ejpam-4674	208	3	1	1	NUM
ejpam-4674	208	4	ε	ε	PROPN
ejpam-4674	208	5	∣∣∣{x	∣∣∣{x	PROPN
ejpam-4674	208	6	∈	∈	PROPN
ejpam-4674	208	7	ω	ω	NOUN
ejpam-4674	208	8	:	:	PUNCT
ejpam-4674	209	1	|f(x)|	|f(x)|	NOUN
ejpam-4674	209	2	≥	≥	X
ejpam-4674	209	3	t	t	NOUN
ejpam-4674	209	4	}	}	PUNCT
ejpam-4674	209	5	∣∣∣dt	∣∣∣dt	X
ejpam-4674	209	6	,	,	PUNCT
ejpam-4674	209	7	(	(	PUNCT
ejpam-4674	209	8	43	43	NUM
ejpam-4674	209	9	)	)	PUNCT
ejpam-4674	209	10	y.	y.	PROPN
ejpam-4674	209	11	c.	c.	PROPN
ejpam-4674	209	12	bassonon	bassonon	PROPN
ejpam-4674	209	13	,	,	PUNCT
ejpam-4674	209	14	a.	a.	NOUN
ejpam-4674	209	15	ouédraogo	ouédraogo	PROPN
ejpam-4674	209	16	/	/	SYM
ejpam-4674	209	17	eur	eur	PROPN
ejpam-4674	209	18	.	.	PUNCT
ejpam-4674	210	1	j.	j.	PROPN
ejpam-4674	210	2	pure	pure	PROPN
ejpam-4674	210	3	appl	appl	PROPN
ejpam-4674	210	4	.	.	PROPN
ejpam-4674	210	5	math	math	PROPN
ejpam-4674	210	6	,	,	PUNCT
ejpam-4674	210	7	16	16	NUM
ejpam-4674	210	8	(	(	PUNCT
ejpam-4674	210	9	1	1	NUM
ejpam-4674	210	10	)	)	PUNCT
ejpam-4674	210	11	(	(	PUNCT
ejpam-4674	210	12	2023	2023	NUM
ejpam-4674	210	13	)	)	PUNCT
ejpam-4674	210	14	,	,	PUNCT
ejpam-4674	210	15	404	404	NUM
ejpam-4674	210	16	-	-	SYM
ejpam-4674	210	17	417	417	NUM
ejpam-4674	210	18	414	414	NUM
ejpam-4674	210	19	and	and	CCONJ
ejpam-4674	210	20			PROPN
ejpam-4674	210	21	∥f	∥f	PROPN
ejpam-4674	210	22	ε∥2l2(ω	ε∥2l2(ω	ADV
ejpam-4674	210	23	)	)	PUNCT
ejpam-4674	210	24	=	=	SYM
ejpam-4674	211	1	2	2	NUM
ejpam-4674	211	2	∫	∫	NOUN
ejpam-4674	211	3	+	+	NOUN
ejpam-4674	211	4	∞	∞	PROPN
ejpam-4674	211	5	0	0	NUM
ejpam-4674	211	6	t	t	PROPN
ejpam-4674	211	7	∣∣∣{x	∣∣∣{x	NOUN
ejpam-4674	211	8	∈	∈	PROPN
ejpam-4674	211	9	ω	ω	NOUN
ejpam-4674	211	10	:	:	PUNCT
ejpam-4674	211	11	|t	|t	PROPN
ejpam-4674	211	12	1	1	NUM
ejpam-4674	211	13	ε	ε	PROPN
ejpam-4674	211	14	(	(	PUNCT
ejpam-4674	211	15	f)(x)|	f)(x)|	PROPN
ejpam-4674	211	16	≥	≥	X
ejpam-4674	211	17	t	t	PROPN
ejpam-4674	211	18	}	}	PUNCT
ejpam-4674	211	19	∣∣∣dt	∣∣∣dt	X
ejpam-4674	211	20	=	=	SYM
ejpam-4674	211	21	2	2	NUM
ejpam-4674	211	22	∫	∫	NOUN
ejpam-4674	211	23	1	1	NUM
ejpam-4674	211	24	ε	ε	PROPN
ejpam-4674	211	25	0	0	NUM
ejpam-4674	211	26	t	t	PROPN
ejpam-4674	211	27	∣∣∣{x	∣∣∣{x	PROPN
ejpam-4674	211	28	∈	∈	PROPN
ejpam-4674	211	29	ω	ω	NOUN
ejpam-4674	211	30	:	:	PUNCT
ejpam-4674	211	31	|f(x)|	|f(x)|	NOUN
ejpam-4674	211	32	≥	≥	X
ejpam-4674	211	33	t	t	NOUN
ejpam-4674	211	34	}	}	PUNCT
ejpam-4674	211	35	∣∣∣dt	∣∣∣dt	X
ejpam-4674	211	36	.	.	PUNCT
ejpam-4674	212	1	(	(	PUNCT
ejpam-4674	212	2	44	44	NUM
ejpam-4674	212	3	)	)	PUNCT
ejpam-4674	212	4	by	by	ADP
ejpam-4674	212	5	the	the	DET
ejpam-4674	212	6	norm	norm	NOUN
ejpam-4674	212	7	in	in	ADP
ejpam-4674	212	8	the	the	DET
ejpam-4674	212	9	marcinkiewicz	marcinkiewicz	ADJ
ejpam-4674	212	10	space	space	NOUN
ejpam-4674	212	11	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	212	12	)	)	PUNCT
ejpam-4674	212	13	define	define	VERB
ejpam-4674	212	14	in	in	ADP
ejpam-4674	212	15	(	(	PUNCT
ejpam-4674	212	16	39	39	NUM
ejpam-4674	212	17	)	)	PUNCT
ejpam-4674	213	1	,	,	PUNCT
ejpam-4674	213	2	we	we	PRON
ejpam-4674	213	3	have∣∣∣{x	have∣∣∣{x	PROPN
ejpam-4674	213	4	∈	∈	PROPN
ejpam-4674	213	5	ω	ω	NOUN
ejpam-4674	213	6	:	:	PUNCT
ejpam-4674	213	7	|f(x)|	|f(x)|	NOUN
ejpam-4674	213	8	≥	≥	X
ejpam-4674	213	9	t	t	NOUN
ejpam-4674	213	10	}	}	PUNCT
ejpam-4674	213	11	∣∣∣	∣∣∣	ADJ
ejpam-4674	213	12	≤	≤	NUM
ejpam-4674	213	13	min	min	NOUN
ejpam-4674	213	14	{	{	PUNCT
ejpam-4674	213	15	|ω|	|ω|	PROPN
ejpam-4674	213	16	,	,	PUNCT
ejpam-4674	213	17	∥f∥rlr,∞(ω	∥f∥rlr,∞(ω	NOUN
ejpam-4674	213	18	)	)	PUNCT
ejpam-4674	213	19	tr	tr	VERB
ejpam-4674	213	20	}	}	PUNCT
ejpam-4674	213	21	,	,	PUNCT
ejpam-4674	213	22	and	and	CCONJ
ejpam-4674	213	23	thus	thus	ADV
ejpam-4674	213	24			PROPN
ejpam-4674	213	25	∥f	∥f	PROPN
ejpam-4674	213	26	−	−	X
ejpam-4674	213	27	f	f	PROPN
ejpam-4674	213	28	ε∥l1(ω	ε∥l1(ω	NOUN
ejpam-4674	213	29	)	)	PUNCT
ejpam-4674	213	30	≤	≤	NUM
ejpam-4674	213	31	1	1	NUM
ejpam-4674	213	32	r	r	NOUN
ejpam-4674	213	33	−	−	NUM
ejpam-4674	213	34	1	1	NUM
ejpam-4674	213	35	εr−1∥f∥rlr,∞(ω	εr−1∥f∥rlr,∞(ω	NOUN
ejpam-4674	213	36	)	)	PUNCT
ejpam-4674	213	37	,	,	PUNCT
ejpam-4674	213	38	∥f	∥f	PROPN
ejpam-4674	213	39	ε∥l2(ω	ε∥l2(ω	ADV
ejpam-4674	213	40	)	)	PUNCT
ejpam-4674	213	41	≤	≤	NOUN
ejpam-4674	213	42	√	√	NUM
ejpam-4674	213	43	2	2	NUM
ejpam-4674	213	44	2−	2−	NUM
ejpam-4674	213	45	r	r	NOUN
ejpam-4674	213	46	1	1	NUM
ejpam-4674	213	47	ε1−	ε1−	NOUN
ejpam-4674	213	48	r	r	NOUN
ejpam-4674	213	49	2	2	NUM
ejpam-4674	213	50	∥f∥	∥f∥	NOUN
ejpam-4674	213	51	r	r	NOUN
ejpam-4674	213	52	2	2	NUM
ejpam-4674	213	53	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	213	54	)	)	PUNCT
ejpam-4674	213	55	.	.	PUNCT
ejpam-4674	214	1	(	(	PUNCT
ejpam-4674	214	2	45	45	NUM
ejpam-4674	214	3	)	)	PUNCT
ejpam-4674	214	4	then	then	ADV
ejpam-4674	214	5	,	,	PUNCT
ejpam-4674	214	6	(	(	PUNCT
ejpam-4674	214	7	42	42	X
ejpam-4674	214	8	)	)	PUNCT
ejpam-4674	214	9	gives	give	VERB
ejpam-4674	214	10	∥uh	∥uh	PUNCT
ejpam-4674	215	1	−	−	NOUN
ejpam-4674	215	2	u∥	u∥	PROPN
ejpam-4674	215	3	w	w	PROPN
ejpam-4674	215	4	1,q	1,q	NUM
ejpam-4674	215	5	0	0	NUM
ejpam-4674	215	6	(	(	PUNCT
ejpam-4674	215	7	ω	ω	NOUN
ejpam-4674	215	8	)	)	PUNCT
ejpam-4674	215	9	)	)	PUNCT
ejpam-4674	216	1	≤	≤	NUM
ejpam-4674	216	2	c	c	NOUN
ejpam-4674	216	3	(	(	PUNCT
ejpam-4674	216	4	1	1	NUM
ejpam-4674	216	5	r	r	NOUN
ejpam-4674	216	6	−	−	NUM
ejpam-4674	216	7	1	1	NUM
ejpam-4674	216	8	εr−1∥f∥rlr,∞(ω	εr−1∥f∥rlr,∞(ω	NOUN
ejpam-4674	216	9	)	)	PUNCT
ejpam-4674	216	10	+	+	CCONJ
ejpam-4674	216	11	√	√	NUM
ejpam-4674	216	12	2	2	NUM
ejpam-4674	216	13	2−	2−	NUM
ejpam-4674	216	14	r	r	NOUN
ejpam-4674	216	15	h	h	NOUN
ejpam-4674	216	16	ε1−	ε1−	NOUN
ejpam-4674	216	17	r	r	NOUN
ejpam-4674	216	18	2	2	NUM
ejpam-4674	216	19	∥f∥	∥f∥	NOUN
ejpam-4674	216	20	r	r	NOUN
ejpam-4674	216	21	2	2	NUM
ejpam-4674	216	22	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	216	23	)	)	PUNCT
ejpam-4674	216	24	)	)	PUNCT
ejpam-4674	216	25	.	.	PUNCT
ejpam-4674	217	1	taking	take	VERB
ejpam-4674	217	2	in	in	ADP
ejpam-4674	217	3	this	this	DET
ejpam-4674	217	4	inequality	inequality	NOUN
ejpam-4674	217	5	ε	ε	PROPN
ejpam-4674	217	6	=	=	SYM
ejpam-4674	217	7	h	h	NOUN
ejpam-4674	217	8	2	2	NUM
ejpam-4674	217	9	r	r	NOUN
ejpam-4674	217	10	∥f∥	∥f∥	NUM
ejpam-4674	217	11	r	r	NOUN
ejpam-4674	217	12	2	2	NUM
ejpam-4674	217	13	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	217	14	)	)	PUNCT
ejpam-4674	217	15	yields	yield	NOUN
ejpam-4674	217	16	,	,	PUNCT
ejpam-4674	217	17	for	for	ADP
ejpam-4674	217	18	every	every	DET
ejpam-4674	217	19	q	q	NOUN
ejpam-4674	217	20	with	with	ADP
ejpam-4674	217	21	1	1	NUM
ejpam-4674	217	22	≤	≤	NOUN
ejpam-4674	217	23	q	q	NOUN
ejpam-4674	217	24	<	<	X
ejpam-4674	217	25	d	d	SYM
ejpam-4674	217	26	d−	d−	PROPN
ejpam-4674	217	27	1	1	NUM
ejpam-4674	217	28	and	and	CCONJ
ejpam-4674	217	29	for	for	ADP
ejpam-4674	217	30	every	every	DET
ejpam-4674	217	31	h	h	NOUN
ejpam-4674	217	32	>	>	X
ejpam-4674	217	33	0	0	NUM
ejpam-4674	217	34	,	,	PUNCT
ejpam-4674	217	35	we	we	PRON
ejpam-4674	217	36	obtain	obtain	VERB
ejpam-4674	217	37	∥uh	∥uh	PUNCT
ejpam-4674	218	1	−	−	NOUN
ejpam-4674	218	2	u∥	u∥	PROPN
ejpam-4674	218	3	w	w	PROPN
ejpam-4674	218	4	1,q	1,q	NUM
ejpam-4674	218	5	0	0	NUM
ejpam-4674	218	6	(	(	PUNCT
ejpam-4674	218	7	ω	ω	NOUN
ejpam-4674	218	8	)	)	PUNCT
ejpam-4674	218	9	≤	≤	PUNCT
ejpam-4674	219	1	c	c	X
ejpam-4674	219	2	(	(	PUNCT
ejpam-4674	219	3	d	d	NOUN
ejpam-4674	219	4	,	,	PUNCT
ejpam-4674	219	5	q	q	NOUN
ejpam-4674	219	6	,	,	PUNCT
ejpam-4674	219	7	r	r	NOUN
ejpam-4674	219	8	,	,	PUNCT
ejpam-4674	219	9	|ω|	|ω|	PROPN
ejpam-4674	219	10	,	,	PUNCT
ejpam-4674	219	11	)	)	PUNCT
ejpam-4674	219	12	h2(1−	h2(1−	VERB
ejpam-4674	219	13	1	1	NUM
ejpam-4674	219	14	r	r	NOUN
ejpam-4674	219	15	)	)	PUNCT
ejpam-4674	219	16	∥f∥rlr,∞(ω	∥f∥rlr,∞(ω	NOUN
ejpam-4674	219	17	)	)	PUNCT
ejpam-4674	219	18	.	.	PUNCT
ejpam-4674	220	1	4	4	X
ejpam-4674	220	2	.	.	X
ejpam-4674	220	3	numerical	numerical	ADJ
ejpam-4674	220	4	implementation	implementation	NOUN
ejpam-4674	220	5	in	in	ADP
ejpam-4674	220	6	this	this	DET
ejpam-4674	220	7	section	section	NOUN
ejpam-4674	220	8	,	,	PUNCT
ejpam-4674	220	9	we	we	PRON
ejpam-4674	220	10	give	give	VERB
ejpam-4674	220	11	the	the	DET
ejpam-4674	220	12	numerical	numerical	ADJ
ejpam-4674	220	13	tests	test	NOUN
ejpam-4674	220	14	to	to	PART
ejpam-4674	220	15	attest	attest	VERB
ejpam-4674	220	16	our	our	PRON
ejpam-4674	220	17	main	main	ADJ
ejpam-4674	220	18	error	error	NOUN
ejpam-4674	220	19	estimate	estimate	NOUN
ejpam-4674	220	20	result	result	NOUN
ejpam-4674	220	21	,	,	PUNCT
ejpam-4674	220	22	namely	namely	ADV
ejpam-4674	220	23	theorem	theorem	ADJ
ejpam-4674	220	24	(	(	PUNCT
ejpam-4674	220	25	4	4	NUM
ejpam-4674	220	26	)	)	PUNCT
ejpam-4674	220	27	.	.	PUNCT
ejpam-4674	221	1	we	we	PRON
ejpam-4674	221	2	consider	consider	VERB
ejpam-4674	221	3	in	in	ADP
ejpam-4674	221	4	this	this	DET
ejpam-4674	221	5	paper	paper	NOUN
ejpam-4674	221	6	for	for	ADP
ejpam-4674	221	7	the	the	DET
ejpam-4674	221	8	numerical	numerical	ADJ
ejpam-4674	221	9	test	test	NOUN
ejpam-4674	221	10	a	a	DET
ejpam-4674	221	11	simple	simple	ADJ
ejpam-4674	221	12	geometry	geometry	NOUN
ejpam-4674	221	13	:	:	PUNCT
ejpam-4674	221	14	a	a	DET
ejpam-4674	221	15	quarter	quarter	NOUN
ejpam-4674	221	16	of	of	ADP
ejpam-4674	221	17	a	a	DET
ejpam-4674	221	18	ring	ring	NOUN
ejpam-4674	221	19	with	with	ADP
ejpam-4674	221	20	inner	inner	ADJ
ejpam-4674	221	21	and	and	CCONJ
ejpam-4674	221	22	outer	outer	ADJ
ejpam-4674	221	23	radius	radius	NOUN
ejpam-4674	221	24	equal	equal	ADJ
ejpam-4674	221	25	to	to	ADP
ejpam-4674	221	26	1	1	NUM
ejpam-4674	221	27	or	or	CCONJ
ejpam-4674	221	28	2	2	NUM
ejpam-4674	221	29	,	,	PUNCT
ejpam-4674	221	30	respectively	respectively	ADV
ejpam-4674	221	31	,	,	PUNCT
ejpam-4674	221	32	and	and	CCONJ
ejpam-4674	221	33	described	describe	VERB
ejpam-4674	221	34	through	through	ADP
ejpam-4674	221	35	a	a	DET
ejpam-4674	221	36	quadratic	quadratic	ADJ
ejpam-4674	221	37	nurbs	nurb	NOUN
ejpam-4674	221	38	parametrization	parametrization	NOUN
ejpam-4674	221	39	,	,	PUNCT
ejpam-4674	221	40	as	as	ADP
ejpam-4674	221	41	the	the	DET
ejpam-4674	221	42	one	one	NUM
ejpam-4674	221	43	in	in	ADP
ejpam-4674	221	44	figure	figure	NOUN
ejpam-4674	221	45	1	1	NUM
ejpam-4674	221	46	.	.	PUNCT
ejpam-4674	222	1	we	we	PRON
ejpam-4674	222	2	solve	solve	VERB
ejpam-4674	222	3	the	the	DET
ejpam-4674	222	4	initial	initial	ADJ
ejpam-4674	222	5	problem	problem	NOUN
ejpam-4674	222	6	(	(	PUNCT
ejpam-4674	222	7	1	1	NUM
ejpam-4674	222	8	)	)	PUNCT
ejpam-4674	222	9	with	with	ADP
ejpam-4674	222	10	a(x	a(x	NOUN
ejpam-4674	222	11	)	)	PUNCT
ejpam-4674	222	12	the	the	DET
ejpam-4674	222	13	identity	identity	NOUN
ejpam-4674	222	14	matrix	matrix	NOUN
ejpam-4674	222	15	.	.	PUNCT
ejpam-4674	223	1	this	this	DET
ejpam-4674	223	2	matrix	matrix	NOUN
ejpam-4674	223	3	satisfy	satisfy	VERB
ejpam-4674	223	4	the	the	DET
ejpam-4674	223	5	assumptions	assumption	NOUN
ejpam-4674	223	6	of	of	ADP
ejpam-4674	223	7	theorem	theorem	NOUN
ejpam-4674	223	8	(	(	PUNCT
ejpam-4674	223	9	3	3	NUM
ejpam-4674	223	10	)	)	PUNCT
ejpam-4674	223	11	,	,	PUNCT
ejpam-4674	223	12	namely	namely	ADV
ejpam-4674	223	13	(	(	PUNCT
ejpam-4674	223	14	2	2	NUM
ejpam-4674	223	15	)	)	PUNCT
ejpam-4674	223	16	,	,	PUNCT
ejpam-4674	223	17	(	(	PUNCT
ejpam-4674	223	18	3	3	NUM
ejpam-4674	223	19	)	)	PUNCT
ejpam-4674	223	20	,	,	PUNCT
ejpam-4674	223	21	(	(	PUNCT
ejpam-4674	223	22	4	4	NUM
ejpam-4674	223	23	)	)	PUNCT
ejpam-4674	223	24	,	,	PUNCT
ejpam-4674	223	25	(	(	PUNCT
ejpam-4674	223	26	10	10	NUM
ejpam-4674	223	27	)	)	PUNCT
ejpam-4674	223	28	,	,	PUNCT
ejpam-4674	223	29	(	(	PUNCT
ejpam-4674	223	30	18	18	NUM
ejpam-4674	223	31	)	)	PUNCT
ejpam-4674	223	32	and	and	CCONJ
ejpam-4674	223	33	(	(	PUNCT
ejpam-4674	223	34	26	26	NUM
ejpam-4674	223	35	)	)	PUNCT
ejpam-4674	223	36	,	,	PUNCT
ejpam-4674	223	37	are	be	AUX
ejpam-4674	223	38	satisfied	satisfied	ADJ
ejpam-4674	223	39	.	.	PUNCT
ejpam-4674	224	1	the	the	DET
ejpam-4674	224	2	right	right	ADJ
ejpam-4674	224	3	-	-	PUNCT
ejpam-4674	224	4	hand	hand	NOUN
ejpam-4674	224	5	side	side	NOUN
ejpam-4674	224	6	f	f	PROPN
ejpam-4674	224	7	is	be	AUX
ejpam-4674	224	8	imposed	impose	VERB
ejpam-4674	224	9	to	to	PART
ejpam-4674	224	10	obtain	obtain	VERB
ejpam-4674	224	11	the	the	DET
ejpam-4674	224	12	renormalized	renormalize	VERB
ejpam-4674	224	13	solution	solution	NOUN
ejpam-4674	224	14	u	u	NOUN
ejpam-4674	224	15	=	=	PROPN
ejpam-4674	224	16	ex1	ex1	PROPN
ejpam-4674	224	17	sin(x2	sin(x2	NOUN
ejpam-4674	224	18	)	)	PUNCT
ejpam-4674	224	19	.	.	PUNCT
ejpam-4674	225	1	we	we	PRON
ejpam-4674	225	2	solve	solve	VERB
ejpam-4674	225	3	the	the	DET
ejpam-4674	225	4	problem	problem	NOUN
ejpam-4674	225	5	ina	ina	PROPN
ejpam-4674	225	6	set	set	VERB
ejpam-4674	225	7	of	of	ADP
ejpam-4674	225	8	successively	successively	ADV
ejpam-4674	225	9	refined	refined	ADJ
ejpam-4674	225	10	meshes	mesh	NOUN
ejpam-4674	225	11	,	,	PUNCT
ejpam-4674	225	12	the	the	DET
ejpam-4674	225	13	coarest	coar	ADJ
ejpam-4674	225	14	three	three	NUM
ejpam-4674	225	15	meshes	mesh	NOUN
ejpam-4674	225	16	are	be	AUX
ejpam-4674	225	17	plotted	plot	VERB
ejpam-4674	225	18	in	in	ADP
ejpam-4674	225	19	figure	figure	NOUN
ejpam-4674	225	20	1	1	NUM
ejpam-4674	225	21	,	,	PUNCT
ejpam-4674	225	22	for	for	ADP
ejpam-4674	225	23	degree	degree	NOUN
ejpam-4674	225	24	p	p	NOUN
ejpam-4674	225	25	varying	vary	VERB
ejpam-4674	225	26	from	from	ADP
ejpam-4674	225	27	2	2	NUM
ejpam-4674	225	28	to	to	ADP
ejpam-4674	225	29	4	4	NUM
ejpam-4674	225	30	,	,	PUNCT
ejpam-4674	225	31	and	and	CCONJ
ejpam-4674	225	32	in	in	ADP
ejpam-4674	225	33	nurbs	nurbs	NOUN
ejpam-4674	225	34	spaces	space	NOUN
ejpam-4674	225	35	of	of	ADP
ejpam-4674	225	36	maximum	maximum	ADJ
ejpam-4674	225	37	(	(	PUNCT
ejpam-4674	225	38	cp−1	cp−1	NOUN
ejpam-4674	225	39	)	)	PUNCT
ejpam-4674	225	40	and	and	CCONJ
ejpam-4674	225	41	minimum	minimum	NOUN
ejpam-4674	225	42	(	(	PUNCT
ejpam-4674	225	43	c0	c0	NOUN
ejpam-4674	225	44	)	)	PUNCT
ejpam-4674	225	45	continuity	continuity	NOUN
ejpam-4674	225	46	.	.	PUNCT
ejpam-4674	226	1	in	in	ADP
ejpam-4674	226	2	figure	figure	NOUN
ejpam-4674	226	3	2	2	NUM
ejpam-4674	226	4	,	,	PUNCT
ejpam-4674	226	5	we	we	PRON
ejpam-4674	226	6	present	present	VERB
ejpam-4674	226	7	the	the	DET
ejpam-4674	226	8	error	error	NOUN
ejpam-4674	226	9	in	in	ADP
ejpam-4674	226	10	the	the	DET
ejpam-4674	226	11	w	w	PROPN
ejpam-4674	226	12	1,q	1,q	NUM
ejpam-4674	226	13	0	0	NUM
ejpam-4674	226	14	-norm	-norm	NOUN
ejpam-4674	226	15	with	with	ADP
ejpam-4674	226	16	respect	respect	NOUN
ejpam-4674	226	17	to	to	ADP
ejpam-4674	226	18	the	the	DET
ejpam-4674	226	19	mesh	mesh	NOUN
ejpam-4674	226	20	size	size	NOUN
ejpam-4674	226	21	h	h	NOUN
ejpam-4674	226	22	,	,	PUNCT
ejpam-4674	226	23	and	and	CCONJ
ejpam-4674	226	24	with	with	ADP
ejpam-4674	226	25	respect	respect	NOUN
ejpam-4674	226	26	to	to	ADP
ejpam-4674	226	27	the	the	DET
ejpam-4674	226	28	number	number	NOUN
ejpam-4674	226	29	of	of	ADP
ejpam-4674	226	30	degree	degree	NOUN
ejpam-4674	226	31	of	of	ADP
ejpam-4674	226	32	freedom	freedom	NOUN
ejpam-4674	226	33	.	.	PUNCT
ejpam-4674	227	1	the	the	DET
ejpam-4674	227	2	result	result	NOUN
ejpam-4674	227	3	in	in	ADP
ejpam-4674	227	4	terms	term	NOUN
ejpam-4674	227	5	of	of	ADP
ejpam-4674	227	6	the	the	DET
ejpam-4674	227	7	mesh	mesh	NOUN
ejpam-4674	227	8	size	size	NOUN
ejpam-4674	227	9	confirm	confirm	VERB
ejpam-4674	227	10	the	the	DET
ejpam-4674	227	11	estimate	estimate	NOUN
ejpam-4674	227	12	of	of	ADP
ejpam-4674	227	13	theorem	theorem	NOUN
ejpam-4674	227	14	(	(	PUNCT
ejpam-4674	227	15	4	4	NUM
ejpam-4674	227	16	)	)	PUNCT
ejpam-4674	227	17	when	when	SCONJ
ejpam-4674	227	18	we	we	PRON
ejpam-4674	227	19	take	take	VERB
ejpam-4674	227	20	for	for	ADP
ejpam-4674	227	21	example	example	NOUN
ejpam-4674	227	22	y.	y.	PROPN
ejpam-4674	227	23	c.	c.	PROPN
ejpam-4674	227	24	bassonon	bassonon	PROPN
ejpam-4674	227	25	,	,	PUNCT
ejpam-4674	227	26	a.	a.	NOUN
ejpam-4674	227	27	ouédraogo	ouédraogo	PROPN
ejpam-4674	227	28	/	/	SYM
ejpam-4674	227	29	eur	eur	PROPN
ejpam-4674	227	30	.	.	PUNCT
ejpam-4674	228	1	j.	j.	PROPN
ejpam-4674	228	2	pure	pure	PROPN
ejpam-4674	228	3	appl	appl	PROPN
ejpam-4674	228	4	.	.	PROPN
ejpam-4674	228	5	math	math	PROPN
ejpam-4674	228	6	,	,	PUNCT
ejpam-4674	228	7	16	16	NUM
ejpam-4674	228	8	(	(	PUNCT
ejpam-4674	228	9	1	1	NUM
ejpam-4674	228	10	)	)	PUNCT
ejpam-4674	228	11	(	(	PUNCT
ejpam-4674	228	12	2023	2023	NUM
ejpam-4674	228	13	)	)	PUNCT
ejpam-4674	228	14	,	,	PUNCT
ejpam-4674	228	15	404	404	NUM
ejpam-4674	228	16	-	-	SYM
ejpam-4674	228	17	417	417	NUM
ejpam-4674	228	18	415	415	NUM
ejpam-4674	228	19	figure	figure	NOUN
ejpam-4674	228	20	1	1	NUM
ejpam-4674	228	21	:	:	PUNCT
ejpam-4674	228	22	mesh	mesh	NOUN
ejpam-4674	228	23	parametrization	parametrization	NOUN
ejpam-4674	228	24	.	.	PUNCT
ejpam-4674	229	1	f(x	f(x	NOUN
ejpam-4674	229	2	)	)	PUNCT
ejpam-4674	230	1	=	=	SYM
ejpam-4674	230	2	1	1	NUM
ejpam-4674	230	3	|x|2	|x|2	NOUN
ejpam-4674	230	4	/	/	SYM
ejpam-4674	230	5	r	r	NOUN
ejpam-4674	230	6	∈	∈	PROPN
ejpam-4674	230	7	lr,∞(ω	lr,∞(ω	NOUN
ejpam-4674	230	8	)	)	PUNCT
ejpam-4674	230	9	.	.	PUNCT
ejpam-4674	231	1	in	in	ADP
ejpam-4674	231	2	terms	term	NOUN
ejpam-4674	231	3	of	of	ADP
ejpam-4674	231	4	the	the	DET
ejpam-4674	231	5	degrees	degree	NOUN
ejpam-4674	231	6	of	of	ADP
ejpam-4674	231	7	freedom	freedom	NOUN
ejpam-4674	231	8	,	,	PUNCT
ejpam-4674	231	9	the	the	DET
ejpam-4674	231	10	results	result	NOUN
ejpam-4674	231	11	always	always	ADV
ejpam-4674	231	12	converges	converge	VERB
ejpam-4674	231	13	like	like	ADP
ejpam-4674	231	14	o(n	o(n	NOUN
ejpam-4674	231	15	−p/2	−p/2	ADJ
ejpam-4674	231	16	dof	dof	NOUN
ejpam-4674	231	17	)	)	PUNCT
ejpam-4674	231	18	where	where	SCONJ
ejpam-4674	231	19	ndof	ndof	NOUN
ejpam-4674	231	20	is	be	AUX
ejpam-4674	231	21	the	the	DET
ejpam-4674	231	22	number	number	NOUN
ejpam-4674	231	23	of	of	ADP
ejpam-4674	231	24	degrees	degree	NOUN
ejpam-4674	231	25	of	of	ADP
ejpam-4674	231	26	freedom	freedom	NOUN
ejpam-4674	231	27	(	(	PUNCT
ejpam-4674	231	28	a	a	NOUN
ejpam-4674	231	29	)	)	PUNCT
ejpam-4674	231	30	error	error	NOUN
ejpam-4674	231	31	in	in	ADP
ejpam-4674	231	32	the	the	DET
ejpam-4674	231	33	terms	term	NOUN
ejpam-4674	231	34	of	of	ADP
ejpam-4674	231	35	the	the	DET
ejpam-4674	231	36	mesh	mesh	NOUN
ejpam-4674	231	37	size	size	NOUN
ejpam-4674	231	38	.	.	PUNCT
ejpam-4674	232	1	(	(	PUNCT
ejpam-4674	232	2	b	b	X
ejpam-4674	232	3	)	)	PUNCT
ejpam-4674	232	4	error	error	NOUN
ejpam-4674	232	5	in	in	ADP
ejpam-4674	232	6	terms	term	NOUN
ejpam-4674	232	7	of	of	ADP
ejpam-4674	232	8	the	the	DET
ejpam-4674	232	9	degrees	degree	NOUN
ejpam-4674	232	10	of	of	ADP
ejpam-4674	232	11	freedom	freedom	NOUN
ejpam-4674	232	12	.	.	PUNCT
ejpam-4674	233	1	figure	figure	NOUN
ejpam-4674	233	2	2	2	NUM
ejpam-4674	233	3	:	:	PUNCT
ejpam-4674	233	4	error	error	NOUN
ejpam-4674	233	5	estimates	estimate	NOUN
ejpam-4674	233	6	in	in	ADP
ejpam-4674	233	7	the	the	DET
ejpam-4674	233	8	w	w	PROPN
ejpam-4674	233	9	1,1	1,1	NUM
ejpam-4674	233	10	0	0	NUM
ejpam-4674	233	11	norm	norm	NOUN
ejpam-4674	233	12	in	in	ADP
ejpam-4674	233	13	the	the	DET
ejpam-4674	233	14	quarter	quarter	NOUN
ejpam-4674	233	15	-	-	PUNCT
ejpam-4674	233	16	ring	ring	NOUN
ejpam-4674	233	17	:	:	PUNCT
ejpam-4674	233	18	error	error	NOUN
ejpam-4674	233	19	in	in	ADP
ejpam-4674	233	20	terms	term	NOUN
ejpam-4674	233	21	of	of	ADP
ejpam-4674	233	22	(	(	PUNCT
ejpam-4674	233	23	a	a	X
ejpam-4674	233	24	)	)	PUNCT
ejpam-4674	233	25	the	the	DET
ejpam-4674	233	26	mesh	mesh	NOUN
ejpam-4674	233	27	size	size	NOUN
ejpam-4674	233	28	,	,	PUNCT
ejpam-4674	233	29	and	and	CCONJ
ejpam-4674	233	30	(	(	PUNCT
ejpam-4674	233	31	b	b	X
ejpam-4674	233	32	)	)	PUNCT
ejpam-4674	233	33	the	the	DET
ejpam-4674	233	34	degrees	degree	NOUN
ejpam-4674	233	35	of	of	ADP
ejpam-4674	233	36	freedom	freedom	NOUN
ejpam-4674	233	37	.	.	PUNCT
ejpam-4674	234	1	references	reference	NOUN
ejpam-4674	234	2	416	416	NUM
ejpam-4674	234	3	5	5	NUM
ejpam-4674	234	4	.	.	PUNCT
ejpam-4674	234	5	conclusion	conclusion	NOUN
ejpam-4674	234	6	in	in	ADP
ejpam-4674	234	7	this	this	DET
ejpam-4674	234	8	paper	paper	NOUN
ejpam-4674	234	9	,	,	PUNCT
ejpam-4674	234	10	we	we	PRON
ejpam-4674	234	11	discussed	discuss	VERB
ejpam-4674	234	12	in	in	ADP
ejpam-4674	234	13	dimension	dimension	NOUN
ejpam-4674	234	14	d	d	X
ejpam-4674	234	15	≥	≥	NUM
ejpam-4674	234	16	2	2	NUM
ejpam-4674	234	17	,	,	PUNCT
ejpam-4674	234	18	the	the	DET
ejpam-4674	234	19	isogeometric	isogeometric	ADJ
ejpam-4674	234	20	analysis	analysis	NOUN
ejpam-4674	234	21	approximation	approximation	NOUN
ejpam-4674	234	22	of	of	ADP
ejpam-4674	234	23	second	second	ADJ
ejpam-4674	234	24	order	order	NOUN
ejpam-4674	234	25	elliptic	elliptic	ADJ
ejpam-4674	234	26	equations	equation	NOUN
ejpam-4674	234	27	in	in	ADP
ejpam-4674	234	28	divergence	divergence	NOUN
ejpam-4674	234	29	form	form	NOUN
ejpam-4674	234	30	with	with	ADP
ejpam-4674	234	31	right	right	ADJ
ejpam-4674	234	32	-	-	PUNCT
ejpam-4674	234	33	hand	hand	NOUN
ejpam-4674	234	34	side	side	NOUN
ejpam-4674	234	35	in	in	ADP
ejpam-4674	234	36	l1	l1	PROPN
ejpam-4674	234	37	.	.	PUNCT
ejpam-4674	235	1	we	we	PRON
ejpam-4674	235	2	have	have	AUX
ejpam-4674	235	3	proven	prove	VERB
ejpam-4674	235	4	that	that	SCONJ
ejpam-4674	235	5	the	the	DET
ejpam-4674	235	6	unique	unique	ADJ
ejpam-4674	235	7	solution	solution	NOUN
ejpam-4674	235	8	of	of	ADP
ejpam-4674	235	9	the	the	DET
ejpam-4674	235	10	discrete	discrete	ADJ
ejpam-4674	235	11	problem	problem	NOUN
ejpam-4674	235	12	converges	converge	VERB
ejpam-4674	235	13	,	,	PUNCT
ejpam-4674	235	14	in	in	ADP
ejpam-4674	235	15	nurbs	nurbs	NOUN
ejpam-4674	235	16	space	space	NOUN
ejpam-4674	235	17	,	,	PUNCT
ejpam-4674	235	18	to	to	ADP
ejpam-4674	235	19	the	the	DET
ejpam-4674	235	20	unique	unique	ADJ
ejpam-4674	235	21	renormalized	renormalize	VERB
ejpam-4674	235	22	solution	solution	NOUN
ejpam-4674	235	23	in	in	ADP
ejpam-4674	235	24	w	w	PROPN
ejpam-4674	235	25	1,q	1,q	NUM
ejpam-4674	235	26	0	0	NUM
ejpam-4674	235	27	(	(	PUNCT
ejpam-4674	235	28	ω	ω	NOUN
ejpam-4674	235	29	)	)	PUNCT
ejpam-4674	235	30	,	,	PUNCT
ejpam-4674	235	31	1	1	NUM
ejpam-4674	235	32	≤	≤	NOUN
ejpam-4674	235	33	q	q	NOUN
ejpam-4674	235	34	<	<	X
ejpam-4674	235	35	d	d	SYM
ejpam-4674	235	36	d−	d−	PROPN
ejpam-4674	235	37	1	1	NUM
ejpam-4674	235	38	.	.	PUNCT
ejpam-4674	236	1	we	we	PRON
ejpam-4674	236	2	have	have	AUX
ejpam-4674	236	3	also	also	ADV
ejpam-4674	236	4	studied	study	VERB
ejpam-4674	236	5	the	the	DET
ejpam-4674	236	6	convergence	convergence	NOUN
ejpam-4674	236	7	analysis	analysis	NOUN
ejpam-4674	236	8	and	and	CCONJ
ejpam-4674	236	9	we	we	PRON
ejpam-4674	236	10	have	have	AUX
ejpam-4674	236	11	obtained	obtain	VERB
ejpam-4674	236	12	the	the	DET
ejpam-4674	236	13	error	error	NOUN
ejpam-4674	236	14	estimates	estimate	NOUN
ejpam-4674	236	15	for	for	ADP
ejpam-4674	236	16	data	datum	NOUN
ejpam-4674	236	17	in	in	ADP
ejpam-4674	236	18	lr;∞(ω	lr;∞(ω	NOUN
ejpam-4674	236	19	)	)	PUNCT
ejpam-4674	236	20	for	for	ADP
ejpam-4674	236	21	1	1	NUM
ejpam-4674	236	22	<	<	X
ejpam-4674	236	23	r	r	NOUN
ejpam-4674	236	24	<	<	X
ejpam-4674	236	25	2	2	NUM
ejpam-4674	236	26	.	.	NOUN
ejpam-4674	236	27	to	to	PART
ejpam-4674	236	28	finish	finish	VERB
ejpam-4674	236	29	,	,	PUNCT
ejpam-4674	236	30	we	we	PRON
ejpam-4674	236	31	gave	give	VERB
ejpam-4674	236	32	numerical	numerical	ADJ
ejpam-4674	236	33	results	result	NOUN
ejpam-4674	236	34	using	use	VERB
ejpam-4674	236	35	python	python	NOUN
ejpam-4674	236	36	.	.	PUNCT
ejpam-4674	237	1	references	reference	NOUN
ejpam-4674	237	2	[	[	X
ejpam-4674	237	3	1	1	NUM
ejpam-4674	237	4	]	]	X
ejpam-4674	237	5	y.	y.	PROPN
ejpam-4674	237	6	bazilevs	bazilevs	PROPN
ejpam-4674	237	7	,	,	PUNCT
ejpam-4674	237	8	l.	l.	PROPN
ejpam-4674	237	9	beirão	beirão	PROPN
ejpam-4674	237	10	da	da	PROPN
ejpam-4674	237	11	veiga	veiga	PROPN
ejpam-4674	237	12	,	,	PUNCT
ejpam-4674	237	13	j.	j.	PROPN
ejpam-4674	237	14	a.	a.	PROPN
ejpam-4674	237	15	cottrell	cottrell	PROPN
ejpam-4674	237	16	,	,	PUNCT
ejpam-4674	237	17	t.	t.	PROPN
ejpam-4674	237	18	j.	j.	PROPN
ejpam-4674	237	19	r.	r.	PROPN
ejpam-4674	237	20	hughes	hughes	PROPN
ejpam-4674	237	21	,	,	PUNCT
ejpam-4674	237	22	and	and	CCONJ
ejpam-4674	237	23	g.	g.	PROPN
ejpam-4674	237	24	sangalli	sangalli	PROPN
ejpam-4674	237	25	.	.	PUNCT
ejpam-4674	238	1	isogeometric	isogeometric	ADJ
ejpam-4674	238	2	analysis	analysis	NOUN
ejpam-4674	238	3	:	:	PUNCT
ejpam-4674	238	4	approximation	approximation	NOUN
ejpam-4674	238	5	,	,	PUNCT
ejpam-4674	238	6	stability	stability	NOUN
ejpam-4674	238	7	and	and	CCONJ
ejpam-4674	238	8	error	error	NOUN
ejpam-4674	238	9	estimates	estimate	NOUN
ejpam-4674	238	10	for	for	ADP
ejpam-4674	238	11	h	h	NOUN
ejpam-4674	238	12	-	-	PUNCT
ejpam-4674	238	13	refined	refined	ADJ
ejpam-4674	238	14	meshes	mesh	NOUN
ejpam-4674	238	15	.	.	PUNCT
ejpam-4674	239	1	math	math	NOUN
ejpam-4674	239	2	.	.	PUNCT
ejpam-4674	240	1	models	model	NOUN
ejpam-4674	240	2	methods	method	NOUN
ejpam-4674	240	3	appl	appl	PROPN
ejpam-4674	240	4	.	.	PUNCT
ejpam-4674	241	1	sci	sci	PROPN
ejpam-4674	241	2	.	.	PROPN
ejpam-4674	241	3	,	,	PUNCT
ejpam-4674	241	4	16(7):1031–1090	16(7):1031–1090	NUM
ejpam-4674	241	5	,	,	PUNCT
ejpam-4674	241	6	2006	2006	NUM
ejpam-4674	241	7	.	.	PUNCT
ejpam-4674	242	1	[	[	X
ejpam-4674	242	2	2	2	NUM
ejpam-4674	242	3	]	]	PUNCT
ejpam-4674	242	4	a.	a.	NOUN
ejpam-4674	242	5	buffa	buffa	NOUN
ejpam-4674	242	6	,	,	PUNCT
ejpam-4674	242	7	g.	g.	PROPN
ejpam-4674	242	8	sangalli	sangalli	PROPN
ejpam-4674	242	9	,	,	PUNCT
ejpam-4674	242	10	and	and	CCONJ
ejpam-4674	242	11	r.	r.	PROPN
ejpam-4674	242	12	vázquez	vázquez	PROPN
ejpam-4674	242	13	.	.	PROPN
ejpam-4674	242	14	isogeometric	isogeometric	ADJ
ejpam-4674	242	15	analysis	analysis	NOUN
ejpam-4674	242	16	in	in	ADP
ejpam-4674	242	17	electromagnetics	electromagnetic	NOUN
ejpam-4674	242	18	:	:	PUNCT
ejpam-4674	242	19	b	b	X
ejpam-4674	242	20	-	-	PUNCT
ejpam-4674	242	21	splines	spline	NOUN
ejpam-4674	242	22	approximation	approximation	NOUN
ejpam-4674	242	23	.	.	PUNCT
ejpam-4674	243	1	comput	comput	NOUN
ejpam-4674	243	2	.	.	PUNCT
ejpam-4674	244	1	methods	method	NOUN
ejpam-4674	244	2	appl	appl	PROPN
ejpam-4674	244	3	.	.	PROPN
ejpam-4674	244	4	mech	mech	PROPN
ejpam-4674	244	5	.	.	PUNCT
ejpam-4674	245	1	eng	eng	PROPN
ejpam-4674	245	2	.	.	PROPN
ejpam-4674	245	3	,	,	PUNCT
ejpam-4674	245	4	199(17	199(17	PROPN
ejpam-4674	245	5	-	-	PUNCT
ejpam-4674	245	6	20):1143–1152	20):1143–1152	NUM
ejpam-4674	245	7	,	,	PUNCT
ejpam-4674	245	8	2010	2010	NUM
ejpam-4674	245	9	.	.	PUNCT
ejpam-4674	246	1	[	[	X
ejpam-4674	246	2	3	3	X
ejpam-4674	246	3	]	]	X
ejpam-4674	246	4	j.	j.	PROPN
ejpam-4674	246	5	casado	casado	PROPN
ejpam-4674	246	6	-	-	PUNCT
ejpam-4674	246	7	dı́az	dı́az	PROPN
ejpam-4674	246	8	,	,	PUNCT
ejpam-4674	246	9	t.	t.	NOUN
ejpam-4674	246	10	chacón	chacón	PROPN
ejpam-4674	246	11	rebollo	rebollo	NOUN
ejpam-4674	246	12	,	,	PUNCT
ejpam-4674	246	13	v.	v.	ADP
ejpam-4674	246	14	girault	girault	NOUN
ejpam-4674	246	15	,	,	PUNCT
ejpam-4674	246	16	m.	m.	NOUN
ejpam-4674	246	17	gómez	gómez	PROPN
ejpam-4674	246	18	mármol	mármol	PROPN
ejpam-4674	246	19	,	,	PUNCT
ejpam-4674	246	20	and	and	CCONJ
ejpam-4674	246	21	f.	f.	PROPN
ejpam-4674	246	22	murat	murat	PROPN
ejpam-4674	246	23	.	.	PUNCT
ejpam-4674	247	1	finite	finite	PROPN
ejpam-4674	247	2	elements	element	NOUN
ejpam-4674	247	3	approximation	approximation	NOUN
ejpam-4674	247	4	of	of	ADP
ejpam-4674	247	5	second	second	ADJ
ejpam-4674	247	6	order	order	NOUN
ejpam-4674	247	7	linear	linear	VERB
ejpam-4674	247	8	elliptic	elliptic	ADJ
ejpam-4674	247	9	equations	equation	NOUN
ejpam-4674	247	10	in	in	ADP
ejpam-4674	247	11	divergence	divergence	NOUN
ejpam-4674	247	12	form	form	NOUN
ejpam-4674	247	13	with	with	ADP
ejpam-4674	247	14	right	right	ADJ
ejpam-4674	247	15	-	-	PUNCT
ejpam-4674	247	16	hand	hand	NOUN
ejpam-4674	247	17	side	side	NOUN
ejpam-4674	247	18	in	in	ADP
ejpam-4674	247	19	l1	l1	PROPN
ejpam-4674	247	20	.	.	PUNCT
ejpam-4674	248	1	numer	numer	PROPN
ejpam-4674	248	2	.	.	PUNCT
ejpam-4674	248	3	math	math	PROPN
ejpam-4674	248	4	.	.	PUNCT
ejpam-4674	248	5	,	,	PUNCT
ejpam-4674	249	1	105(3):337–374	105(3):337–374	NUM
ejpam-4674	249	2	,	,	PUNCT
ejpam-4674	249	3	2007	2007	NUM
ejpam-4674	249	4	.	.	PUNCT
ejpam-4674	250	1	[	[	X
ejpam-4674	250	2	4	4	X
ejpam-4674	250	3	]	]	PUNCT
ejpam-4674	250	4	t.	t.	NOUN
ejpam-4674	250	5	chacón	chacón	PROPN
ejpam-4674	250	6	rebollo	rebollo	PROPN
ejpam-4674	250	7	,	,	PUNCT
ejpam-4674	250	8	e.	e.	PROPN
ejpam-4674	250	9	d.	d.	PROPN
ejpam-4674	250	10	fernández	fernández	PROPN
ejpam-4674	250	11	nieto	nieto	PROPN
ejpam-4674	250	12	,	,	PUNCT
ejpam-4674	250	13	and	and	CCONJ
ejpam-4674	250	14	m.	m.	NOUN
ejpam-4674	250	15	gómez	gómez	PROPN
ejpam-4674	250	16	mármol	mármol	PROPN
ejpam-4674	250	17	.	.	PUNCT
ejpam-4674	251	1	some	some	DET
ejpam-4674	251	2	remarks	remark	NOUN
ejpam-4674	251	3	on	on	ADP
ejpam-4674	251	4	a	a	DET
ejpam-4674	251	5	model	model	NOUN
ejpam-4674	251	6	for	for	ADP
ejpam-4674	251	7	the	the	DET
ejpam-4674	251	8	atmospheric	atmospheric	ADJ
ejpam-4674	251	9	pressure	pressure	NOUN
ejpam-4674	251	10	in	in	ADP
ejpam-4674	251	11	ocean	ocean	NOUN
ejpam-4674	251	12	dynamics	dynamic	NOUN
ejpam-4674	251	13	.	.	PUNCT
ejpam-4674	252	1	in	in	ADP
ejpam-4674	252	2	numerical	numerical	ADJ
ejpam-4674	252	3	mathematics	mathematic	NOUN
ejpam-4674	252	4	and	and	CCONJ
ejpam-4674	252	5	advanced	advanced	ADJ
ejpam-4674	252	6	applications	application	NOUN
ejpam-4674	252	7	.	.	PUNCT
ejpam-4674	253	1	proceedings	proceeding	NOUN
ejpam-4674	253	2	of	of	ADP
ejpam-4674	253	3	enumath	enumath	NOUN
ejpam-4674	253	4	2005	2005	NUM
ejpam-4674	253	5	,	,	PUNCT
ejpam-4674	253	6	the	the	DET
ejpam-4674	253	7	6th	6th	ADJ
ejpam-4674	253	8	european	european	ADJ
ejpam-4674	253	9	conference	conference	NOUN
ejpam-4674	253	10	on	on	ADP
ejpam-4674	253	11	numerical	numerical	ADJ
ejpam-4674	253	12	mathematics	mathematic	NOUN
ejpam-4674	253	13	and	and	CCONJ
ejpam-4674	253	14	advanced	advanced	ADJ
ejpam-4674	253	15	applications	application	NOUN
ejpam-4674	253	16	,	,	PUNCT
ejpam-4674	253	17	santiago	santiago	PROPN
ejpam-4674	253	18	de	de	PROPN
ejpam-4674	253	19	compostela	compostela	PROPN
ejpam-4674	253	20	,	,	PUNCT
ejpam-4674	253	21	spain	spain	PROPN
ejpam-4674	253	22	,	,	PUNCT
ejpam-4674	253	23	july	july	PROPN
ejpam-4674	253	24	18–22	18–22	NUM
ejpam-4674	253	25	,	,	PUNCT
ejpam-4674	253	26	2005	2005	NUM
ejpam-4674	253	27	.	.	PUNCT
ejpam-4674	253	28	,	,	PUNCT
ejpam-4674	253	29	pages	page	NOUN
ejpam-4674	253	30	279–287	279–287	NUM
ejpam-4674	253	31	.	.	PUNCT
ejpam-4674	254	1	berlin	berlin	ADJ
ejpam-4674	254	2	:	:	PUNCT
ejpam-4674	254	3	springer	springer	NOUN
ejpam-4674	254	4	,	,	PUNCT
ejpam-4674	254	5	2006	2006	NUM
ejpam-4674	254	6	.	.	PUNCT
ejpam-4674	255	1	[	[	X
ejpam-4674	255	2	5	5	X
ejpam-4674	255	3	]	]	PUNCT
ejpam-4674	255	4	j.	j.	PROPN
ejpam-4674	255	5	austin	austin	PROPN
ejpam-4674	255	6	cottrell	cottrell	PROPN
ejpam-4674	255	7	,	,	PUNCT
ejpam-4674	255	8	thomas	thomas	PROPN
ejpam-4674	255	9	j.	j.	PROPN
ejpam-4674	255	10	r.	r.	PROPN
ejpam-4674	255	11	hughes	hughes	PROPN
ejpam-4674	255	12	,	,	PUNCT
ejpam-4674	255	13	and	and	CCONJ
ejpam-4674	255	14	yuri	yuri	PROPN
ejpam-4674	255	15	bazilevs	bazilevs	PROPN
ejpam-4674	255	16	.	.	PUNCT
ejpam-4674	256	1	isogeometric	isogeometric	ADJ
ejpam-4674	256	2	analysis	analysis	NOUN
ejpam-4674	256	3	.	.	PUNCT
ejpam-4674	257	1	toward	toward	ADP
ejpam-4674	257	2	integration	integration	NOUN
ejpam-4674	257	3	of	of	ADP
ejpam-4674	257	4	cad	cad	PROPN
ejpam-4674	257	5	and	and	CCONJ
ejpam-4674	257	6	fea	fea	PROPN
ejpam-4674	257	7	.	.	PUNCT
ejpam-4674	258	1	hoboken	hoboken	PROPN
ejpam-4674	258	2	,	,	PUNCT
ejpam-4674	258	3	nj	nj	PROPN
ejpam-4674	258	4	:	:	PUNCT
ejpam-4674	258	5	john	john	PROPN
ejpam-4674	258	6	wiley	wiley	PROPN
ejpam-4674	258	7	&	&	CCONJ
ejpam-4674	258	8	sons	son	NOUN
ejpam-4674	258	9	,	,	PUNCT
ejpam-4674	258	10	2009	2009	NUM
ejpam-4674	258	11	.	.	PUNCT
ejpam-4674	259	1	[	[	X
ejpam-4674	259	2	6	6	NUM
ejpam-4674	259	3	]	]	X
ejpam-4674	259	4	gianni	gianni	PROPN
ejpam-4674	259	5	dal	dal	PROPN
ejpam-4674	259	6	maso	maso	PROPN
ejpam-4674	259	7	,	,	PUNCT
ejpam-4674	259	8	françois	françois	PROPN
ejpam-4674	259	9	murat	murat	NOUN
ejpam-4674	259	10	,	,	PUNCT
ejpam-4674	259	11	luigi	luigi	PROPN
ejpam-4674	259	12	orsina	orsina	PROPN
ejpam-4674	259	13	,	,	PUNCT
ejpam-4674	259	14	and	and	CCONJ
ejpam-4674	259	15	alain	alain	PROPN
ejpam-4674	259	16	prignet	prignet	PROPN
ejpam-4674	259	17	.	.	PUNCT
ejpam-4674	260	1	renormalization	renormalization	NOUN
ejpam-4674	260	2	solutions	solution	NOUN
ejpam-4674	260	3	of	of	ADP
ejpam-4674	260	4	elliptic	elliptic	ADJ
ejpam-4674	260	5	equations	equation	NOUN
ejpam-4674	260	6	with	with	ADP
ejpam-4674	260	7	general	general	ADJ
ejpam-4674	260	8	measure	measure	NOUN
ejpam-4674	260	9	data	datum	NOUN
ejpam-4674	260	10	.	.	PUNCT
ejpam-4674	261	1	ann	ann	PROPN
ejpam-4674	261	2	.	.	PROPN
ejpam-4674	261	3	sc	sc	PROPN
ejpam-4674	261	4	.	.	PROPN
ejpam-4674	261	5	norm	norm	PROPN
ejpam-4674	261	6	.	.	PUNCT
ejpam-4674	262	1	super	super	ADJ
ejpam-4674	262	2	.	.	PUNCT
ejpam-4674	262	3	pisa	pisa	PROPN
ejpam-4674	262	4	,	,	PUNCT
ejpam-4674	262	5	cl	cl	NOUN
ejpam-4674	262	6	.	.	PUNCT
ejpam-4674	263	1	sci	sci	PROPN
ejpam-4674	263	2	.	.	PROPN
ejpam-4674	263	3	,	,	PUNCT
ejpam-4674	263	4	iv	iv	X
ejpam-4674	263	5	.	.	PUNCT
ejpam-4674	263	6	ser	ser	PROPN
ejpam-4674	263	7	.	.	PROPN
ejpam-4674	263	8	,	,	PUNCT
ejpam-4674	263	9	28(4):741–808	28(4):741–808	PROPN
ejpam-4674	263	10	,	,	PUNCT
ejpam-4674	263	11	1999	1999	NUM
ejpam-4674	263	12	.	.	PUNCT
ejpam-4674	264	1	[	[	X
ejpam-4674	264	2	7	7	X
ejpam-4674	264	3	]	]	X
ejpam-4674	264	4	b.	b.	PROPN
ejpam-4674	264	5	faraj	faraj	PROPN
ejpam-4674	264	6	and	and	CCONJ
ejpam-4674	264	7	m.	m.	PROPN
ejpam-4674	264	8	modanli	modanli	PROPN
ejpam-4674	264	9	.	.	PUNCT
ejpam-4674	265	1	using	use	VERB
ejpam-4674	265	2	difference	difference	NOUN
ejpam-4674	265	3	scheme	scheme	NOUN
ejpam-4674	265	4	method	method	NOUN
ejpam-4674	265	5	for	for	ADP
ejpam-4674	265	6	the	the	DET
ejpam-4674	265	7	numerical	numerical	ADJ
ejpam-4674	265	8	solution	solution	NOUN
ejpam-4674	265	9	of	of	ADP
ejpam-4674	265	10	telegraph	telegraph	NOUN
ejpam-4674	265	11	partial	partial	ADJ
ejpam-4674	265	12	differential	differential	NOUN
ejpam-4674	265	13	equation	equation	NOUN
ejpam-4674	265	14	.	.	PUNCT
ejpam-4674	266	1	journal	journal	NOUN
ejpam-4674	266	2	of	of	ADP
ejpam-4674	266	3	garmian	garmian	PROPN
ejpam-4674	266	4	university	university	NOUN
ejpam-4674	266	5	,	,	PUNCT
ejpam-4674	266	6	4(icbs	4(icbs	X
ejpam-4674	266	7	conference):157–163	conference):157–163	NOUN
ejpam-4674	266	8	,	,	PUNCT
ejpam-4674	266	9	2017	2017	NUM
ejpam-4674	266	10	.	.	PUNCT
ejpam-4674	267	1	[	[	X
ejpam-4674	267	2	8	8	X
ejpam-4674	267	3	]	]	PUNCT
ejpam-4674	267	4	t.	t.	PROPN
ejpam-4674	267	5	j.	j.	PROPN
ejpam-4674	267	6	r.	r.	PROPN
ejpam-4674	267	7	hughes	hughes	PROPN
ejpam-4674	267	8	,	,	PUNCT
ejpam-4674	267	9	j.	j.	PROPN
ejpam-4674	267	10	a.	a.	PROPN
ejpam-4674	267	11	cottrell	cottrell	PROPN
ejpam-4674	267	12	,	,	PUNCT
ejpam-4674	267	13	and	and	CCONJ
ejpam-4674	267	14	y.	y.	PROPN
ejpam-4674	267	15	bazilevs	bazilevs	PROPN
ejpam-4674	267	16	.	.	PUNCT
ejpam-4674	268	1	isogeometric	isogeometric	ADJ
ejpam-4674	268	2	analysis	analysis	NOUN
ejpam-4674	268	3	:	:	PUNCT
ejpam-4674	268	4	cad	cad	NOUN
ejpam-4674	268	5	,	,	PUNCT
ejpam-4674	268	6	finite	finite	ADJ
ejpam-4674	268	7	elements	element	NOUN
ejpam-4674	268	8	,	,	PUNCT
ejpam-4674	268	9	nurbs	nurb	NOUN
ejpam-4674	268	10	,	,	PUNCT
ejpam-4674	268	11	exact	exact	ADJ
ejpam-4674	268	12	geometry	geometry	NOUN
ejpam-4674	268	13	and	and	CCONJ
ejpam-4674	268	14	mesh	mesh	NOUN
ejpam-4674	268	15	refinement	refinement	NOUN
ejpam-4674	268	16	.	.	PUNCT
ejpam-4674	269	1	comput	comput	NOUN
ejpam-4674	269	2	.	.	PUNCT
ejpam-4674	270	1	methods	method	NOUN
ejpam-4674	270	2	appl	appl	PROPN
ejpam-4674	270	3	.	.	PROPN
ejpam-4674	270	4	mech	mech	PROPN
ejpam-4674	270	5	.	.	PUNCT
ejpam-4674	271	1	eng	eng	PROPN
ejpam-4674	271	2	.	.	PROPN
ejpam-4674	271	3	,	,	PUNCT
ejpam-4674	271	4	194(39	194(39	NUM
ejpam-4674	271	5	-	-	SYM
ejpam-4674	271	6	41):4135–4195	41):4135–4195	PROPN
ejpam-4674	271	7	,	,	PUNCT
ejpam-4674	271	8	2005	2005	NUM
ejpam-4674	271	9	.	.	PUNCT
ejpam-4674	272	1	references	reference	NOUN
ejpam-4674	272	2	417	417	NUM
ejpam-4674	272	3	[	[	X
ejpam-4674	272	4	9	9	NUM
ejpam-4674	272	5	]	]	PUNCT
ejpam-4674	272	6	m.	m.	NOUN
ejpam-4674	272	7	modanli	modanli	PROPN
ejpam-4674	272	8	,	,	PUNCT
ejpam-4674	272	9	b.	b.	PROPN
ejpam-4674	272	10	m.	m.	PROPN
ejpam-4674	272	11	faraj	faraj	PROPN
ejpam-4674	272	12	,	,	PUNCT
ejpam-4674	272	13	and	and	CCONJ
ejpam-4674	272	14	f.w	f.w	PROPN
ejpam-4674	272	15	.	.	PROPN
ejpam-4674	272	16	ahmed	ahmed	PROPN
ejpam-4674	272	17	.	.	PUNCT
ejpam-4674	273	1	using	use	VERB
ejpam-4674	273	2	matrix	matrix	NOUN
ejpam-4674	273	3	stability	stability	NOUN
ejpam-4674	273	4	for	for	ADP
ejpam-4674	273	5	variable	variable	ADJ
ejpam-4674	273	6	telegraph	telegraph	NOUN
ejpam-4674	273	7	partial	partial	ADJ
ejpam-4674	273	8	differential	differential	NOUN
ejpam-4674	273	9	equation	equation	NOUN
ejpam-4674	273	10	.	.	PUNCT
ejpam-4674	274	1	int	int	NOUN
ejpam-4674	274	2	.	.	PUNCT
ejpam-4674	275	1	j.	j.	PROPN
ejpam-4674	275	2	optim	optim	PROPN
ejpam-4674	275	3	.	.	PUNCT
ejpam-4674	276	1	control	control	PROPN
ejpam-4674	276	2	,	,	PUNCT
ejpam-4674	276	3	theor	theor	PROPN
ejpam-4674	276	4	.	.	PUNCT
ejpam-4674	277	1	appl	appl	PROPN
ejpam-4674	277	2	.	.	PROPN
ejpam-4674	277	3	,	,	PUNCT
ejpam-4674	277	4	10(2):237	10(2):237	NUM
ejpam-4674	277	5	–	–	PUNCT
ejpam-4674	277	6	243	243	NUM
ejpam-4674	277	7	,	,	PUNCT
ejpam-4674	277	8	2020	2020	NUM
ejpam-4674	277	9	.	.	PUNCT
ejpam-4674	278	1	[	[	X
ejpam-4674	278	2	10	10	NUM
ejpam-4674	278	3	]	]	X
ejpam-4674	278	4	les	les	X
ejpam-4674	278	5	piegl	piegl	PROPN
ejpam-4674	278	6	and	and	CCONJ
ejpam-4674	278	7	wayne	wayne	PROPN
ejpam-4674	278	8	tiller	tiller	NOUN
ejpam-4674	278	9	.	.	PUNCT
ejpam-4674	279	1	the	the	DET
ejpam-4674	279	2	nurbs	nurbs	NOUN
ejpam-4674	279	3	books	book	NOUN
ejpam-4674	279	4	.	.	PUNCT
ejpam-4674	280	1	berlin	berlin	ADJ
ejpam-4674	280	2	:	:	PUNCT
ejpam-4674	280	3	springer	springer	NOUN
ejpam-4674	280	4	,	,	PUNCT
ejpam-4674	280	5	2nd	2nd	ADJ
ejpam-4674	280	6	ed	ed	NOUN
ejpam-4674	280	7	.	.	PUNCT
ejpam-4674	280	8	edition	edition	PROPN
ejpam-4674	280	9	,	,	PUNCT
ejpam-4674	280	10	1997	1997	NUM
ejpam-4674	280	11	.	.	PUNCT
ejpam-4674	281	1	[	[	X
ejpam-4674	281	2	11	11	NUM
ejpam-4674	281	3	]	]	X
ejpam-4674	281	4	larry	larry	PROPN
ejpam-4674	281	5	l.	l.	PROPN
ejpam-4674	281	6	schumaker	schumaker	PROPN
ejpam-4674	281	7	.	.	PUNCT
ejpam-4674	281	8	spline	spline	PROPN
ejpam-4674	281	9	functions	function	NOUN
ejpam-4674	281	10	:	:	PUNCT
ejpam-4674	281	11	basic	basic	ADJ
ejpam-4674	281	12	theory	theory	NOUN
ejpam-4674	281	13	.	.	PUNCT
ejpam-4674	282	1	camb	camb	PROPN
ejpam-4674	282	2	.	.	PUNCT
ejpam-4674	283	1	math	math	PROPN
ejpam-4674	283	2	.	.	PUNCT
ejpam-4674	284	1	libr	libr	PROPN
ejpam-4674	284	2	.	.	PUNCT
ejpam-4674	285	1	cambridge	cambridge	PROPN
ejpam-4674	285	2	:	:	PUNCT
ejpam-4674	285	3	cambridge	cambridge	PROPN
ejpam-4674	285	4	university	university	PROPN
ejpam-4674	285	5	press	press	NOUN
ejpam-4674	285	6	,	,	PUNCT
ejpam-4674	285	7	2007	2007	NUM
ejpam-4674	285	8	.	.	PUNCT