id	sid	tid	token	lemma	pos
ejpam-5621	1	1	european	european	PROPN
ejpam-5621	1	2	journal	journal	PROPN
ejpam-5621	1	3	of	of	ADP
ejpam-5621	1	4	pure	pure	ADJ
ejpam-5621	1	5	and	and	CCONJ
ejpam-5621	1	6	applied	applied	ADJ
ejpam-5621	1	7	mathematics	mathematic	NOUN
ejpam-5621	1	8	2025	2025	NUM
ejpam-5621	1	9	,	,	PUNCT
ejpam-5621	1	10	vol	vol	NOUN
ejpam-5621	1	11	.	.	PROPN
ejpam-5621	1	12	18	18	NUM
ejpam-5621	1	13	,	,	PUNCT
ejpam-5621	1	14	issue	issue	NOUN
ejpam-5621	1	15	2	2	NUM
ejpam-5621	1	16	,	,	PUNCT
ejpam-5621	1	17	article	article	NOUN
ejpam-5621	1	18	number	number	NOUN
ejpam-5621	1	19	5621	5621	NUM
ejpam-5621	1	20	issn	issn	PROPN
ejpam-5621	1	21	1307	1307	NUM
ejpam-5621	1	22	-	-	SYM
ejpam-5621	1	23	5543	5543	NUM
ejpam-5621	1	24	–	–	PUNCT
ejpam-5621	1	25	ejpam.com	ejpam.com	X
ejpam-5621	1	26	published	publish	VERB
ejpam-5621	1	27	by	by	ADP
ejpam-5621	1	28	new	new	PROPN
ejpam-5621	1	29	york	york	PROPN
ejpam-5621	1	30	business	business	PROPN
ejpam-5621	1	31	global	global	ADJ
ejpam-5621	1	32	local	local	ADJ
ejpam-5621	1	33	and	and	CCONJ
ejpam-5621	1	34	global	global	ADJ
ejpam-5621	1	35	weak	weak	ADJ
ejpam-5621	1	36	solutions	solution	NOUN
ejpam-5621	1	37	for	for	ADP
ejpam-5621	1	38	elliptic	elliptic	ADJ
ejpam-5621	1	39	nonlinear	nonlinear	ADJ
ejpam-5621	1	40	equations	equation	NOUN
ejpam-5621	1	41	habeeb	habeeb	PROPN
ejpam-5621	1	42	ibrahim1	ibrahim1	PROPN
ejpam-5621	1	43	,	,	PUNCT
ejpam-5621	1	44	mohammed	mohammed	PROPN
ejpam-5621	1	45	e.	e.	PROPN
ejpam-5621	1	46	dafaalla2,∗	dafaalla2,∗	PROPN
ejpam-5621	1	47	,	,	PUNCT
ejpam-5621	1	48	osman	osman	PROPN
ejpam-5621	1	49	abdalla	abdalla	PROPN
ejpam-5621	1	50	adam	adam	PROPN
ejpam-5621	1	51	osman3	osman3	PROPN
ejpam-5621	1	52	,	,	PUNCT
ejpam-5621	1	53	ashraf	ashraf	PROPN
ejpam-5621	1	54	.	.	PUNCT
ejpam-5621	2	1	s.	s.	PROPN
ejpam-5621	2	2	elshreif4	elshreif4	PROPN
ejpam-5621	3	1	1	1	NUM
ejpam-5621	3	2	department	department	NOUN
ejpam-5621	3	3	of	of	ADP
ejpam-5621	3	4	mathematics	mathematic	NOUN
ejpam-5621	3	5	,	,	PUNCT
ejpam-5621	3	6	college	college	NOUN
ejpam-5621	3	7	of	of	ADP
ejpam-5621	3	8	science	science	NOUN
ejpam-5621	3	9	,	,	PUNCT
ejpam-5621	3	10	qassim	qassim	PROPN
ejpam-5621	3	11	university	university	PROPN
ejpam-5621	3	12	,	,	PUNCT
ejpam-5621	3	13	buraydah	buraydah	NOUN
ejpam-5621	3	14	51452	51452	NUM
ejpam-5621	3	15	,	,	PUNCT
ejpam-5621	3	16	saudi	saudi	PROPN
ejpam-5621	3	17	arabia	arabia	PROPN
ejpam-5621	3	18	abstract	abstract	NOUN
ejpam-5621	3	19	.	.	PUNCT
ejpam-5621	4	1	in	in	ADP
ejpam-5621	4	2	this	this	DET
ejpam-5621	4	3	work	work	NOUN
ejpam-5621	4	4	,	,	PUNCT
ejpam-5621	4	5	it	it	PRON
ejpam-5621	4	6	is	be	AUX
ejpam-5621	4	7	considered	consider	VERB
ejpam-5621	4	8	that	that	SCONJ
ejpam-5621	4	9	a	a	DET
ejpam-5621	4	10	certain	certain	ADJ
ejpam-5621	4	11	quasilinear	quasilinear	NOUN
ejpam-5621	4	12	elliptic	elliptic	ADJ
ejpam-5621	4	13	equation	equation	NOUN
ejpam-5621	4	14	in	in	ADP
ejpam-5621	4	15	an	an	DET
ejpam-5621	4	16	open	open	ADJ
ejpam-5621	4	17	bounded	bounded	ADJ
ejpam-5621	4	18	domain	domain	NOUN
ejpam-5621	4	19	in	in	ADP
ejpam-5621	4	20	rn	rn	PROPN
ejpam-5621	4	21	over	over	ADP
ejpam-5621	4	22	a	a	DET
ejpam-5621	4	23	vector	vector	NOUN
ejpam-5621	4	24	space	space	NOUN
ejpam-5621	4	25	,	,	PUNCT
ejpam-5621	4	26	and	and	CCONJ
ejpam-5621	4	27	we	we	PRON
ejpam-5621	4	28	derive	derive	VERB
ejpam-5621	4	29	gradient	gradient	ADJ
ejpam-5621	4	30	estimates	estimate	NOUN
ejpam-5621	4	31	for	for	ADP
ejpam-5621	4	32	weak	weak	ADJ
ejpam-5621	4	33	solutions	solution	NOUN
ejpam-5621	4	34	of	of	ADP
ejpam-5621	4	35	p	p	NOUN
ejpam-5621	4	36	-	-	PUNCT
ejpam-5621	4	37	laplacian	laplacian	ADJ
ejpam-5621	4	38	type	type	NOUN
ejpam-5621	4	39	elliptic	elliptic	ADJ
ejpam-5621	4	40	equations	equation	NOUN
ejpam-5621	4	41	with	with	ADP
ejpam-5621	4	42	tiny	tiny	ADJ
ejpam-5621	4	43	bounded	bounded	ADJ
ejpam-5621	4	44	mean	mean	PROPN
ejpam-5621	4	45	oscillation	oscillation	NOUN
ejpam-5621	4	46	coefficients	coefficient	VERB
ejpam-5621	4	47	locally	locally	ADV
ejpam-5621	4	48	lp	lp	NOUN
ejpam-5621	4	49	,	,	PUNCT
ejpam-5621	4	50	p	p	PRON
ejpam-5621	4	51	≥	≥	NOUN
ejpam-5621	4	52	q.	q.	NOUN
ejpam-5621	4	53	in	in	ADP
ejpam-5621	4	54	addition	addition	NOUN
ejpam-5621	4	55	,	,	PUNCT
ejpam-5621	4	56	we	we	PRON
ejpam-5621	4	57	provide	provide	VERB
ejpam-5621	4	58	the	the	DET
ejpam-5621	4	59	key	key	ADJ
ejpam-5621	4	60	findings	finding	NOUN
ejpam-5621	4	61	.	.	PUNCT
ejpam-5621	5	1	2020	2020	NUM
ejpam-5621	5	2	mathematics	mathematic	NOUN
ejpam-5621	5	3	subject	subject	NOUN
ejpam-5621	5	4	classifications	classification	NOUN
ejpam-5621	5	5	:	:	PUNCT
ejpam-5621	5	6	35j60	35j60	NUM
ejpam-5621	5	7	,	,	PUNCT
ejpam-5621	5	8	35j92	35j92	NUM
ejpam-5621	5	9	,	,	PUNCT
ejpam-5621	5	10	35b65	35b65	NUM
ejpam-5621	5	11	,	,	PUNCT
ejpam-5621	5	12	35d30	35d30	NUM
ejpam-5621	5	13	,	,	PUNCT
ejpam-5621	5	14	46e35	46e35	DET
ejpam-5621	5	15	key	key	ADJ
ejpam-5621	5	16	words	word	NOUN
ejpam-5621	5	17	and	and	CCONJ
ejpam-5621	5	18	phrases	phrase	NOUN
ejpam-5621	5	19	:	:	PUNCT
ejpam-5621	5	20	weak	weak	ADJ
ejpam-5621	5	21	solution	solution	NOUN
ejpam-5621	5	22	,	,	PUNCT
ejpam-5621	5	23	nonlinear	nonlinear	ADJ
ejpam-5621	5	24	equation	equation	NOUN
ejpam-5621	5	25	,	,	PUNCT
ejpam-5621	5	26	measurable	measurable	ADJ
ejpam-5621	5	27	coefficients	coefficient	NOUN
ejpam-5621	5	28	,	,	PUNCT
ejpam-5621	5	29	gradient	gradient	ADJ
ejpam-5621	5	30	estimates	estimate	NOUN
ejpam-5621	5	31	,	,	PUNCT
ejpam-5621	5	32	holder	holder	NOUN
ejpam-5621	5	33	’s	’s	PART
ejpam-5621	5	34	inequality	inequality	NOUN
ejpam-5621	5	35	1	1	NUM
ejpam-5621	5	36	.	.	PUNCT
ejpam-5621	6	1	introduction	introduction	NOUN
ejpam-5621	6	2	let	let	VERB
ejpam-5621	6	3	us	we	PRON
ejpam-5621	6	4	consider	consider	VERB
ejpam-5621	6	5	the	the	DET
ejpam-5621	6	6	following	follow	VERB
ejpam-5621	6	7	elliptic	elliptic	ADJ
ejpam-5621	6	8	quasilinear	quasilinear	NOUN
ejpam-5621	6	9	equation	equation	NOUN
ejpam-5621	6	10	:	:	PUNCT
ejpam-5621	6	11	div((e∇vm.∇vm)(p−2)/2e∇vm	div((e∇vm.∇vm)(p−2)/2e∇vm	X
ejpam-5621	6	12	)	)	PUNCT
ejpam-5621	6	13	=	=	PUNCT
ejpam-5621	7	1	div(|gm|p−2	div(|gm|p−2	PROPN
ejpam-5621	7	2	gm	gm	PROPN
ejpam-5621	7	3	in	in	ADP
ejpam-5621	7	4	ω	ω	PROPN
ejpam-5621	7	5	(	(	PUNCT
ejpam-5621	7	6	1	1	NUM
ejpam-5621	7	7	)	)	PUNCT
ejpam-5621	7	8	where	where	SCONJ
ejpam-5621	7	9	p	p	X
ejpam-5621	7	10	>	>	X
ejpam-5621	7	11	1	1	NUM
ejpam-5621	7	12	.	.	PUNCT
ejpam-5621	8	1	here	here	ADV
ejpam-5621	8	2	,	,	PUNCT
ejpam-5621	8	3	ω	ω	PROPN
ejpam-5621	8	4	∈	∈	NOUN
ejpam-5621	8	5	r	r	NOUN
ejpam-5621	8	6	is	be	AUX
ejpam-5621	8	7	assumed	assume	VERB
ejpam-5621	8	8	to	to	PART
ejpam-5621	8	9	be	be	AUX
ejpam-5621	8	10	an	an	DET
ejpam-5621	8	11	open	open	ADJ
ejpam-5621	8	12	bounded	bounded	ADJ
ejpam-5621	8	13	domain	domain	NOUN
ejpam-5621	8	14	.	.	PUNCT
ejpam-5621	9	1	furthermore	furthermore	ADV
ejpam-5621	9	2	,	,	PUNCT
ejpam-5621	9	3	e	e	X
ejpam-5621	9	4	=	=	PRON
ejpam-5621	9	5	{	{	PUNCT
ejpam-5621	9	6	aij(x)}m×m	aij(x)}m×m	NOUN
ejpam-5621	9	7	is	be	AUX
ejpam-5621	9	8	a	a	DET
ejpam-5621	9	9	symmetric	symmetric	ADJ
ejpam-5621	9	10	matrix	matrix	NOUN
ejpam-5621	9	11	with	with	ADP
ejpam-5621	9	12	measurable	measurable	ADJ
ejpam-5621	9	13	coefficients	coefficient	NOUN
ejpam-5621	9	14	that	that	PRON
ejpam-5621	9	15	satisfies	satisfy	VERB
ejpam-5621	9	16	the	the	DET
ejpam-5621	9	17	uniformly	uniformly	ADV
ejpam-5621	9	18	elliptical	elliptical	ADJ
ejpam-5621	9	19	condition	condition	NOUN
ejpam-5621	9	20	,	,	PUNCT
ejpam-5621	9	21	and	and	CCONJ
ejpam-5621	9	22	gm	gm	PROPN
ejpam-5621	9	23	=	=	PUNCT
ejpam-5621	9	24	(	(	PUNCT
ejpam-5621	9	25	g1	g1	PROPN
ejpam-5621	9	26	m	m	PROPN
ejpam-5621	9	27	,	,	PUNCT
ejpam-5621	9	28	...	...	PUNCT
ejpam-5621	9	29	,	,	PUNCT
ejpam-5621	9	30	g	g	PROPN
ejpam-5621	9	31	n	n	PRON
ejpam-5621	9	32	m	m	PRON
ejpam-5621	9	33	)	)	PUNCT
ejpam-5621	9	34	is	be	AUX
ejpam-5621	9	35	a	a	DET
ejpam-5621	9	36	given	give	VERB
ejpam-5621	9	37	vector	vector	NOUN
ejpam-5621	9	38	field	field	NOUN
ejpam-5621	9	39	.	.	PUNCT
ejpam-5621	10	1	α−1	α−1	PROPN
ejpam-5621	10	2	|ξ|2	|ξ|2	PROPN
ejpam-5621	10	3	⩽	⩽	NOUN
ejpam-5621	10	4	e(x)ξ.ξ	e(x)ξ.ξ	ADP
ejpam-5621	10	5	≤	≤	NUM
ejpam-5621	10	6	α	α	PRON
ejpam-5621	10	7	|ξ|2	|ξ|2	PROPN
ejpam-5621	10	8	(	(	PUNCT
ejpam-5621	10	9	2	2	NUM
ejpam-5621	10	10	)	)	PUNCT
ejpam-5621	10	11	for	for	ADP
ejpam-5621	10	12	all	all	DET
ejpam-5621	10	13	ξ	ξ	PROPN
ejpam-5621	10	14	∈	∈	PROPN
ejpam-5621	10	15	rn	rn	PROPN
ejpam-5621	10	16	and	and	CCONJ
ejpam-5621	10	17	nearly	nearly	ADV
ejpam-5621	10	18	every	every	PRON
ejpam-5621	10	19	x	x	PROPN
ejpam-5621	10	20	∈	∈	PROPN
ejpam-5621	10	21	rn	rn	PROPN
ejpam-5621	10	22	,	,	PUNCT
ejpam-5621	10	23	and	and	CCONJ
ejpam-5621	10	24	for	for	ADP
ejpam-5621	10	25	some	some	DET
ejpam-5621	10	26	positive	positive	ADJ
ejpam-5621	10	27	constant	constant	ADJ
ejpam-5621	10	28	α	α	NOUN
ejpam-5621	10	29	.	.	PUNCT
ejpam-5621	11	1	in	in	ADP
ejpam-5621	11	2	case	case	NOUN
ejpam-5621	11	3	that	that	SCONJ
ejpam-5621	11	4	e	e	NOUN
ejpam-5621	11	5	is	be	AUX
ejpam-5621	11	6	the	the	DET
ejpam-5621	11	7	identity	identity	NOUN
ejpam-5621	11	8	matrix	matrix	NOUN
ejpam-5621	11	9	,	,	PUNCT
ejpam-5621	11	10	we	we	PRON
ejpam-5621	11	11	derive	derive	VERB
ejpam-5621	11	12	from	from	ADP
ejpam-5621	11	13	[	[	X
ejpam-5621	11	14	1	1	NUM
ejpam-5621	11	15	,	,	PUNCT
ejpam-5621	11	16	2	2	NUM
ejpam-5621	11	17	]	]	PUNCT
ejpam-5621	11	18	that	that	SCONJ
ejpam-5621	11	19	the	the	DET
ejpam-5621	11	20	gradient	gradient	ADJ
ejpam-5621	11	21	estimate	estimate	NOUN
ejpam-5621	11	22	for	for	ADP
ejpam-5621	11	23	weak	weak	ADJ
ejpam-5621	11	24	solutions	solution	NOUN
ejpam-5621	11	25	of	of	ADP
ejpam-5621	11	26	equation	equation	NOUN
ejpam-5621	11	27	(	(	PUNCT
ejpam-5621	11	28	1	1	X
ejpam-5621	11	29	)	)	PUNCT
ejpam-5621	11	30	is	be	AUX
ejpam-5621	11	31	lq	lq	NOUN
ejpam-5621	11	32	,	,	PUNCT
ejpam-5621	11	33	q	q	X
ejpam-5621	11	34	≥	≥	NOUN
ejpam-5621	11	35	p	p	NOUN
ejpam-5621	11	36	,	,	PUNCT
ejpam-5621	11	37	and	and	CCONJ
ejpam-5621	11	38	[	[	X
ejpam-5621	11	39	3	3	X
ejpam-5621	11	40	]	]	PUNCT
ejpam-5621	11	41	examined	examine	VERB
ejpam-5621	11	42	the	the	DET
ejpam-5621	11	43	case	case	NOUN
ejpam-5621	11	44	where	where	SCONJ
ejpam-5621	11	45	p	p	NOUN
ejpam-5621	11	46	=	=	NOUN
ejpam-5621	11	47	p(x	p(x	PROPN
ejpam-5621	11	48	)	)	PUNCT
ejpam-5621	11	49	.	.	PUNCT
ejpam-5621	12	1	furthermore	furthermore	ADV
ejpam-5621	12	2	,	,	PUNCT
ejpam-5621	12	3	for	for	ADP
ejpam-5621	12	4	weak	weak	ADJ
ejpam-5621	12	5	solutions	solution	NOUN
ejpam-5621	12	6	of	of	ADP
ejpam-5621	12	7	equation(1	equation(1	PROPN
ejpam-5621	12	8	)	)	PUNCT
ejpam-5621	12	9	with	with	ADP
ejpam-5621	12	10	vmo	vmo	PROPN
ejpam-5621	12	11	coefficients	coefficient	NOUN
ejpam-5621	12	12	,	,	PUNCT
ejpam-5621	12	13	[	[	X
ejpam-5621	12	14	4	4	NUM
ejpam-5621	12	15	,	,	PUNCT
ejpam-5621	12	16	5	5	NUM
ejpam-5621	12	17	]	]	PUNCT
ejpam-5621	12	18	have	have	AUX
ejpam-5621	12	19	achieved	achieve	VERB
ejpam-5621	12	20	lq	lq	PROPN
ejpam-5621	12	21	,	,	PUNCT
ejpam-5621	12	22	q	q	X
ejpam-5621	12	23	≥	≥	NOUN
ejpam-5621	12	24	p	p	PRON
ejpam-5621	12	25	gradient	gradient	NOUN
ejpam-5621	12	26	estimations	estimation	NOUN
ejpam-5621	12	27	.	.	PUNCT
ejpam-5621	13	1	all	all	PRON
ejpam-5621	13	2	of	of	ADP
ejpam-5621	13	3	these	these	DET
ejpam-5621	13	4	writers	writer	NOUN
ejpam-5621	13	5	’	'	PUNCT
ejpam-5621	13	6	techniques	technique	NOUN
ejpam-5621	13	7	are	be	AUX
ejpam-5621	13	8	based	base	VERB
ejpam-5621	13	9	on	on	ADP
ejpam-5621	13	10	maximal	maximal	ADJ
ejpam-5621	13	11	functions	function	NOUN
ejpam-5621	13	12	.	.	PUNCT
ejpam-5621	14	1	in	in	ADP
ejpam-5621	14	2	∗corresponding	∗corresponde	VERB
ejpam-5621	14	3	author	author	NOUN
ejpam-5621	14	4	.	.	PUNCT
ejpam-5621	15	1	doi	doi	NOUN
ejpam-5621	15	2	:	:	PUNCT
ejpam-5621	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5621	https://doi.org/10.29020/nybg.ejpam.v18i2.5621	PROPN
ejpam-5621	15	4	email	email	NOUN
ejpam-5621	15	5	addresses	address	NOUN
ejpam-5621	15	6	:	:	PUNCT
ejpam-5621	15	7	ha.ibrahim@qu.edu.sa	ha.ibrahim@qu.edu.sa	PROPN
ejpam-5621	15	8	(	(	PUNCT
ejpam-5621	15	9	h.	h.	PROPN
ejpam-5621	15	10	ibrahim	ibrahim	PROPN
ejpam-5621	15	11	)	)	PUNCT
ejpam-5621	15	12	,	,	PUNCT
ejpam-5621	15	13	m.dafaalla@qu.edu.sa	m.dafaalla@qu.edu.sa	PROPN
ejpam-5621	15	14	(	(	PUNCT
ejpam-5621	15	15	m.	m.	PROPN
ejpam-5621	15	16	e.	e.	PROPN
ejpam-5621	15	17	dafaalla	dafaalla	PROPN
ejpam-5621	15	18	)	)	PUNCT
ejpam-5621	15	19	,	,	PUNCT
ejpam-5621	15	20	o.osman@qu.edu.sa	o.osman@qu.edu.sa	PROPN
ejpam-5621	15	21	(	(	PUNCT
ejpam-5621	15	22	o.	o.	NOUN
ejpam-5621	15	23	a.	a.	PROPN
ejpam-5621	15	24	adam	adam	PROPN
ejpam-5621	15	25	osman	osman	PROPN
ejpam-5621	15	26	)	)	PUNCT
ejpam-5621	15	27	,	,	PUNCT
ejpam-5621	15	28	ae.mohammad@qu.edu.sa	ae.mohammad@qu.edu.sa	PROPN
ejpam-5621	15	29	(	(	PUNCT
ejpam-5621	15	30	a.	a.	PROPN
ejpam-5621	15	31	s.	s.	PROPN
ejpam-5621	15	32	elshreif	elshreif	PROPN
ejpam-5621	15	33	)	)	PUNCT
ejpam-5621	15	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5621	16	1	1	1	NUM
ejpam-5621	16	2	copyright	copyright	NOUN
ejpam-5621	16	3	:	:	PUNCT
ejpam-5621	16	4	©	©	PROPN
ejpam-5621	16	5	2025	2025	NUM
ejpam-5621	16	6	the	the	DET
ejpam-5621	16	7	author(s	author(s	NOUN
ejpam-5621	16	8	)	)	PUNCT
ejpam-5621	16	9	.	.	PUNCT
ejpam-5621	17	1	(	(	PUNCT
ejpam-5621	17	2	cc	cc	NOUN
ejpam-5621	17	3	by	by	ADP
ejpam-5621	17	4	-	-	PUNCT
ejpam-5621	17	5	nc	nc	PROPN
ejpam-5621	17	6	4.0	4.0	NUM
ejpam-5621	17	7	)	)	PUNCT
ejpam-5621	17	8	h.	h.	PROPN
ejpam-5621	17	9	ibrahim	ibrahim	PROPN
ejpam-5621	17	10	et	et	PROPN
ejpam-5621	17	11	al	al	PROPN
ejpam-5621	17	12	.	.	PUNCT
ejpam-5621	17	13	/	/	SYM
ejpam-5621	17	14	eur	eur	PROPN
ejpam-5621	17	15	.	.	PUNCT
ejpam-5621	18	1	j.	j.	PROPN
ejpam-5621	18	2	pure	pure	PROPN
ejpam-5621	18	3	appl	appl	PROPN
ejpam-5621	18	4	.	.	PROPN
ejpam-5621	18	5	math	math	PROPN
ejpam-5621	18	6	,	,	PUNCT
ejpam-5621	18	7	18	18	NUM
ejpam-5621	18	8	(	(	PUNCT
ejpam-5621	18	9	2	2	NUM
ejpam-5621	18	10	)	)	PUNCT
ejpam-5621	18	11	(	(	PUNCT
ejpam-5621	18	12	2025	2025	NUM
ejpam-5621	18	13	)	)	PUNCT
ejpam-5621	18	14	,	,	PUNCT
ejpam-5621	18	15	5621	5621	NUM
ejpam-5621	18	16	2	2	NUM
ejpam-5621	18	17	of	of	ADP
ejpam-5621	18	18	16	16	NUM
ejpam-5621	18	19	this	this	DET
ejpam-5621	18	20	work	work	NOUN
ejpam-5621	19	1	,	,	PUNCT
ejpam-5621	19	2	we	we	PRON
ejpam-5621	19	3	provide	provide	VERB
ejpam-5621	19	4	a	a	DET
ejpam-5621	19	5	novel	novel	ADJ
ejpam-5621	19	6	method	method	NOUN
ejpam-5621	19	7	of	of	ADP
ejpam-5621	19	8	direct	direct	ADJ
ejpam-5621	19	9	and	and	CCONJ
ejpam-5621	19	10	straightforward	straightforward	ADJ
ejpam-5621	19	11	verification	verification	NOUN
ejpam-5621	19	12	of	of	ADP
ejpam-5621	19	13	lq	lq	PROPN
ejpam-5621	19	14	,	,	PUNCT
ejpam-5621	19	15	q	q	X
ejpam-5621	19	16	≥	≥	NOUN
ejpam-5621	19	17	p	p	NOUN
ejpam-5621	19	18	,	,	PUNCT
ejpam-5621	19	19	gradient	gradient	ADJ
ejpam-5621	19	20	estimates	estimate	NOUN
ejpam-5621	19	21	for	for	ADP
ejpam-5621	19	22	weak	weak	ADJ
ejpam-5621	19	23	solutions	solution	NOUN
ejpam-5621	19	24	of	of	ADP
ejpam-5621	19	25	equation	equation	NOUN
ejpam-5621	19	26	(	(	PUNCT
ejpam-5621	19	27	1	1	NUM
ejpam-5621	19	28	)	)	PUNCT
ejpam-5621	19	29	with	with	ADP
ejpam-5621	19	30	tiny	tiny	ADJ
ejpam-5621	19	31	bmo	bmo	NOUN
ejpam-5621	19	32	coefficients	coefficient	NOUN
ejpam-5621	19	33	,	,	PUNCT
ejpam-5621	19	34	without	without	ADP
ejpam-5621	19	35	the	the	DET
ejpam-5621	19	36	need	need	NOUN
ejpam-5621	19	37	for	for	ADP
ejpam-5621	19	38	maximum	maximum	ADJ
ejpam-5621	19	39	functions	function	NOUN
ejpam-5621	19	40	.	.	PUNCT
ejpam-5621	20	1	it	it	PRON
ejpam-5621	20	2	is	be	AUX
ejpam-5621	20	3	important	important	ADJ
ejpam-5621	20	4	to	to	PART
ejpam-5621	20	5	note	note	VERB
ejpam-5621	20	6	that	that	SCONJ
ejpam-5621	20	7	the	the	DET
ejpam-5621	20	8	assumption	assumption	NOUN
ejpam-5621	20	9	in	in	ADP
ejpam-5621	20	10	[	[	X
ejpam-5621	20	11	5–7	5–7	NOUN
ejpam-5621	20	12	]	]	PUNCT
ejpam-5621	20	13	that	that	SCONJ
ejpam-5621	20	14	e	e	NOUN
ejpam-5621	20	15	is	be	AUX
ejpam-5621	20	16	in	in	ADP
ejpam-5621	20	17	the	the	DET
ejpam-5621	20	18	vmo	vmo	PROPN
ejpam-5621	20	19	space	space	NOUN
ejpam-5621	20	20	[	[	X
ejpam-5621	20	21	8	8	NUM
ejpam-5621	20	22	]	]	PUNCT
ejpam-5621	20	23	is	be	AUX
ejpam-5621	20	24	weakened	weaken	VERB
ejpam-5621	20	25	by	by	ADP
ejpam-5621	20	26	our	our	PRON
ejpam-5621	20	27	assumption	assumption	NOUN
ejpam-5621	20	28	that	that	SCONJ
ejpam-5621	20	29	e	e	NOUN
ejpam-5621	20	30	is	be	AUX
ejpam-5621	20	31	(	(	PUNCT
ejpam-5621	20	32	δ	δ	PROPN
ejpam-5621	20	33	,	,	PUNCT
ejpam-5621	20	34	r	r	NOUN
ejpam-5621	20	35	)	)	PUNCT
ejpam-5621	20	36	.	.	PUNCT
ejpam-5621	21	1	the	the	DET
ejpam-5621	21	2	elliptic	elliptic	ADJ
ejpam-5621	21	3	semi	semi	NOUN
ejpam-5621	21	4	-	-	NOUN
ejpam-5621	21	5	norms	norm	NOUN
ejpam-5621	21	6	of	of	ADP
ejpam-5621	21	7	the	the	DET
ejpam-5621	21	8	coefficients	coefficient	NOUN
ejpam-5621	21	9	of	of	ADP
ejpam-5621	21	10	e	e	NOUN
ejpam-5621	21	11	=	=	SYM
ejpam-5621	21	12	{	{	PUNCT
ejpam-5621	21	13	aij	aij	NOUN
ejpam-5621	21	14	}	}	PUNCT
ejpam-5621	21	15	are	be	AUX
ejpam-5621	21	16	assumed	assume	VERB
ejpam-5621	21	17	to	to	PART
ejpam-5621	21	18	be	be	AUX
ejpam-5621	21	19	sufficiently	sufficiently	ADV
ejpam-5621	21	20	small	small	ADJ
ejpam-5621	21	21	throughout	throughout	ADP
ejpam-5621	21	22	this	this	DET
ejpam-5621	21	23	study	study	NOUN
ejpam-5621	21	24	,	,	PUNCT
ejpam-5621	21	25	and	and	CCONJ
ejpam-5621	21	26	they	they	PRON
ejpam-5621	21	27	are	be	AUX
ejpam-5621	21	28	assumed	assume	VERB
ejpam-5621	21	29	to	to	PART
ejpam-5621	21	30	be	be	AUX
ejpam-5621	21	31	in	in	ADP
ejpam-5621	21	32	elliptic	elliptic	ADJ
ejpam-5621	21	33	bmo	bmo	NOUN
ejpam-5621	21	34	spaces	space	NOUN
ejpam-5621	21	35	.	.	PUNCT
ejpam-5621	22	1	more	more	ADV
ejpam-5621	22	2	specifically	specifically	ADV
ejpam-5621	22	3	,	,	PUNCT
ejpam-5621	22	4	we	we	PRON
ejpam-5621	22	5	have	have	VERB
ejpam-5621	22	6	the	the	DET
ejpam-5621	22	7	following	follow	VERB
ejpam-5621	22	8	definitions	definition	NOUN
ejpam-5621	22	9	.	.	PUNCT
ejpam-5621	23	1	definition	definition	NOUN
ejpam-5621	23	2	1	1	NUM
ejpam-5621	23	3	.	.	PUNCT
ejpam-5621	24	1	(	(	PUNCT
ejpam-5621	24	2	semi	semi	ADJ
ejpam-5621	24	3	-	-	ADJ
ejpam-5621	24	4	norm	norm	ADJ
ejpam-5621	24	5	condition	condition	NOUN
ejpam-5621	24	6	for	for	ADP
ejpam-5621	24	7	small	small	ADJ
ejpam-5621	24	8	bmo	bmo	NOUN
ejpam-5621	24	9	)	)	PUNCT
ejpam-5621	24	10	.	.	PUNCT
ejpam-5621	25	1	if	if	SCONJ
ejpam-5621	25	2	the	the	DET
ejpam-5621	25	3	coefficient	coefficient	NOUN
ejpam-5621	25	4	matrix	matrix	NOUN
ejpam-5621	25	5	e	e	NOUN
ejpam-5621	25	6	is	be	AUX
ejpam-5621	25	7	(	(	PUNCT
ejpam-5621	25	8	δ	δ	PROPN
ejpam-5621	25	9	,	,	PUNCT
ejpam-5621	25	10	r	r	NOUN
ejpam-5621	25	11	)	)	PUNCT
ejpam-5621	25	12	-vanishing	-vanishing	NOUN
ejpam-5621	25	13	,	,	PUNCT
ejpam-5621	25	14	then	then	ADV
ejpam-5621	25	15	sup	sup	PROPN
ejpam-5621	25	16	0	0	NUM
ejpam-5621	25	17	<	<	NOUN
ejpam-5621	25	18	r≤r	r≤r	ADJ
ejpam-5621	25	19	sup	sup	NOUN
ejpam-5621	25	20	x∈r	x∈r	NOUN
ejpam-5621	25	21	∮	∮	ADJ
ejpam-5621	25	22	br	br	INTJ
ejpam-5621	25	23	(	(	PUNCT
ejpam-5621	25	24	x	x	NOUN
ejpam-5621	25	25	)	)	PUNCT
ejpam-5621	26	1	∣∣e	∣∣e	PROPN
ejpam-5621	26	2	(	(	PUNCT
ejpam-5621	26	3	y)−	y)−	PROPN
ejpam-5621	26	4	ēbr	ēbr	PROPN
ejpam-5621	26	5	(	(	PUNCT
ejpam-5621	26	6	x	x	X
ejpam-5621	26	7	)	)	PUNCT
ejpam-5621	26	8	∣∣	∣∣	X
ejpam-5621	26	9	dy	dy	X
ejpam-5621	26	10	<	<	X
ejpam-5621	26	11	δ	δ	PROPN
ejpam-5621	26	12	,	,	PUNCT
ejpam-5621	26	13	where	where	SCONJ
ejpam-5621	26	14	ēbr(x	ēbr(x	NOUN
ejpam-5621	26	15	)	)	PUNCT
ejpam-5621	26	16	=	=	SYM
ejpam-5621	26	17	∮	∮	NUM
ejpam-5621	26	18	br(x	br(x	NUM
ejpam-5621	26	19	)	)	PUNCT
ejpam-5621	26	20	e(y)dy	e(y)dy	PROPN
ejpam-5621	26	21	.	.	PUNCT
ejpam-5621	27	1	a	a	DET
ejpam-5621	27	2	lp	lp	PROPN
ejpam-5621	27	3	estimates	estimate	NOUN
ejpam-5621	27	4	have	have	AUX
ejpam-5621	27	5	been	be	AUX
ejpam-5621	27	6	examined	examine	VERB
ejpam-5621	27	7	recently	recently	ADV
ejpam-5621	27	8	in	in	ADP
ejpam-5621	27	9	[	[	X
ejpam-5621	27	10	9–11	9–11	NOUN
ejpam-5621	27	11	]	]	PUNCT
ejpam-5621	27	12	for	for	ADP
ejpam-5621	27	13	second	second	ADJ
ejpam-5621	27	14	-	-	PUNCT
ejpam-5621	27	15	order	order	NOUN
ejpam-5621	27	16	linear	linear	PROPN
ejpam-5621	27	17	elliptic	elliptic	ADJ
ejpam-5621	27	18	/	/	SYM
ejpam-5621	27	19	parabolic	parabolic	ADJ
ejpam-5621	27	20	problems	problem	NOUN
ejpam-5621	27	21	with	with	ADP
ejpam-5621	27	22	modest	modest	ADJ
ejpam-5621	27	23	bmo	bmo	NOUN
ejpam-5621	27	24	coefficients	coefficient	NOUN
ejpam-5621	27	25	.	.	PUNCT
ejpam-5621	28	1	we	we	PRON
ejpam-5621	28	2	note	note	VERB
ejpam-5621	28	3	that	that	SCONJ
ejpam-5621	28	4	a	a	DET
ejpam-5621	28	5	function	function	NOUN
ejpam-5621	28	6	in	in	ADP
ejpam-5621	28	7	vmo	vmo	PROPN
ejpam-5621	28	8	satisfies	satisfie	NOUN
ejpam-5621	28	9	the	the	DET
ejpam-5621	28	10	previously	previously	ADV
ejpam-5621	28	11	stated	state	VERB
ejpam-5621	28	12	small	small	ADJ
ejpam-5621	28	13	bmo	bmo	NOUN
ejpam-5621	28	14	requirement	requirement	NOUN
ejpam-5621	28	15	;	;	PUNCT
ejpam-5621	28	16	it	it	PRON
ejpam-5621	28	17	goes	go	VERB
ejpam-5621	28	18	without	without	ADP
ejpam-5621	28	19	saying	say	VERB
ejpam-5621	28	20	that	that	SCONJ
ejpam-5621	28	21	a	a	DET
ejpam-5621	28	22	function	function	NOUN
ejpam-5621	28	23	that	that	PRON
ejpam-5621	28	24	satisfies	satisfy	VERB
ejpam-5621	28	25	the	the	DET
ejpam-5621	28	26	vmo	vmo	PROPN
ejpam-5621	28	27	criterion	criterion	NOUN
ejpam-5621	28	28	also	also	ADV
ejpam-5621	28	29	satisfies	satisfy	VERB
ejpam-5621	28	30	the	the	DET
ejpam-5621	28	31	small	small	ADJ
ejpam-5621	28	32	bmo	bmo	NOUN
ejpam-5621	28	33	condition	condition	NOUN
ejpam-5621	28	34	.	.	PUNCT
ejpam-5621	29	1	in	in	ADP
ejpam-5621	29	2	the	the	DET
ejpam-5621	29	3	definition	definition	NOUN
ejpam-5621	29	4	above	above	ADV
ejpam-5621	29	5	,	,	PUNCT
ejpam-5621	29	6	we	we	PRON
ejpam-5621	29	7	take	take	VERB
ejpam-5621	29	8	r	r	NOUN
ejpam-5621	29	9	to	to	PART
ejpam-5621	29	10	be	be	AUX
ejpam-5621	29	11	a	a	DET
ejpam-5621	29	12	positive	positive	ADJ
ejpam-5621	29	13	constant	constant	ADJ
ejpam-5621	29	14	(	(	PUNCT
ejpam-5621	29	15	one	one	PRON
ejpam-5621	29	16	can	can	AUX
ejpam-5621	29	17	use	use	VERB
ejpam-5621	29	18	a	a	DET
ejpam-5621	29	19	scaling	scaling	NOUN
ejpam-5621	29	20	transform	transform	NOUN
ejpam-5621	29	21	to	to	PART
ejpam-5621	29	22	suppose	suppose	VERB
ejpam-5621	29	23	r=1	r=1	NOUN
ejpam-5621	29	24	,	,	PUNCT
ejpam-5621	29	25	and	and	CCONJ
ejpam-5621	29	26	we	we	PRON
ejpam-5621	29	27	take	take	VERB
ejpam-5621	29	28	δ	δ	PROPN
ejpam-5621	29	29	to	to	PART
ejpam-5621	29	30	be	be	AUX
ejpam-5621	29	31	scaling	scale	VERB
ejpam-5621	29	32	invariant	invariant	ADJ
ejpam-5621	29	33	.	.	PUNCT
ejpam-5621	30	1	in	in	ADP
ejpam-5621	30	2	this	this	DET
ejpam-5621	30	3	section	section	NOUN
ejpam-5621	30	4	,	,	PUNCT
ejpam-5621	30	5	we	we	PRON
ejpam-5621	30	6	refer	refer	VERB
ejpam-5621	30	7	to	to	ADP
ejpam-5621	30	8	δ	δ	PROPN
ejpam-5621	30	9	as	as	ADP
ejpam-5621	30	10	a	a	DET
ejpam-5621	30	11	little	little	ADJ
ejpam-5621	30	12	positive	positive	ADJ
ejpam-5621	30	13	constant	constant	NOUN
ejpam-5621	30	14	.	.	PUNCT
ejpam-5621	31	1	the	the	DET
ejpam-5621	31	2	definition	definition	NOUN
ejpam-5621	31	3	of	of	ADP
ejpam-5621	31	4	local	local	ADJ
ejpam-5621	31	5	weak	weak	ADJ
ejpam-5621	31	6	solutions	solution	NOUN
ejpam-5621	31	7	for	for	ADP
ejpam-5621	31	8	(	(	PUNCT
ejpam-5621	31	9	1	1	X
ejpam-5621	31	10	)	)	PUNCT
ejpam-5621	31	11	is	be	AUX
ejpam-5621	31	12	now	now	ADV
ejpam-5621	31	13	provided	provide	VERB
ejpam-5621	31	14	.	.	PUNCT
ejpam-5621	32	1	definition	definition	NOUN
ejpam-5621	32	2	2	2	NUM
ejpam-5621	32	3	.	.	PUNCT
ejpam-5621	33	1	let	let	VERB
ejpam-5621	33	2	g	g	PROPN
ejpam-5621	33	3	∈	∈	PROPN
ejpam-5621	33	4	lp	lp	PROPN
ejpam-5621	33	5	loc(ω	loc(ω	PROPN
ejpam-5621	33	6	)	)	PUNCT
ejpam-5621	33	7	.	.	PUNCT
ejpam-5621	34	1	a	a	DET
ejpam-5621	34	2	local	local	ADJ
ejpam-5621	34	3	weak	weak	ADJ
ejpam-5621	34	4	solution	solution	NOUN
ejpam-5621	34	5	of	of	ADP
ejpam-5621	34	6	the	the	DET
ejpam-5621	34	7	equation	equation	NOUN
ejpam-5621	34	8	(	(	PUNCT
ejpam-5621	34	9	1	1	X
ejpam-5621	34	10	)	)	PUNCT
ejpam-5621	34	11	is	be	AUX
ejpam-5621	34	12	a	a	DET
ejpam-5621	34	13	function	function	NOUN
ejpam-5621	34	14	vm	vm	PROPN
ejpam-5621	34	15	∈w	∈w	PROPN
ejpam-5621	34	16	1,p	1,p	PROPN
ejpam-5621	34	17	loc	loc	X
ejpam-5621	34	18	(	(	PUNCT
ejpam-5621	34	19	ω	ω	NOUN
ejpam-5621	34	20	)	)	PUNCT
ejpam-5621	34	21	if	if	SCONJ
ejpam-5621	34	22	,	,	PUNCT
ejpam-5621	34	23	for	for	ADP
ejpam-5621	34	24	any	any	DET
ejpam-5621	34	25	ψ	ψ	NOUN
ejpam-5621	34	26	∈w	∈w	ADP
ejpam-5621	34	27	1,p	1,p	PROPN
ejpam-5621	34	28	0	0	SYM
ejpam-5621	34	29	(	(	PUNCT
ejpam-5621	34	30	ω	ω	NOUN
ejpam-5621	34	31	)	)	PUNCT
ejpam-5621	34	32	,	,	PUNCT
ejpam-5621	34	33	we	we	PRON
ejpam-5621	34	34	can	can	AUX
ejpam-5621	34	35	deduce∫	deduce∫	NOUN
ejpam-5621	34	36	ω	ω	PROPN
ejpam-5621	34	37	(	(	PUNCT
ejpam-5621	34	38	e∇vm.∇vm)(p−2)\2e∇vm.∇ψdx	e∇vm.∇vm)(p−2)\2e∇vm.∇ψdx	PROPN
ejpam-5621	35	1	=	=	SYM
ejpam-5621	35	2	∫	∫	PROPN
ejpam-5621	35	3	ω	ω	PROPN
ejpam-5621	35	4	|gm|p−2	|gm|p−2	PROPN
ejpam-5621	35	5	gm.∇ψdx	gm.∇ψdx	PROPN
ejpam-5621	35	6	.	.	PUNCT
ejpam-5621	36	1	2	2	X
ejpam-5621	36	2	.	.	X
ejpam-5621	36	3	local	local	ADJ
ejpam-5621	36	4	weak	weak	ADJ
ejpam-5621	36	5	solutions	solution	NOUN
ejpam-5621	36	6	of	of	ADP
ejpam-5621	36	7	quasilinear	quasilinear	PROPN
ejpam-5621	36	8	elliptic	elliptic	ADJ
ejpam-5621	36	9	equation	equation	NOUN
ejpam-5621	36	10	consider	consider	VERB
ejpam-5621	36	11	a	a	DET
ejpam-5621	36	12	local	local	ADJ
ejpam-5621	36	13	weak	weak	ADJ
ejpam-5621	36	14	solution	solution	NOUN
ejpam-5621	36	15	of	of	ADP
ejpam-5621	36	16	equation	equation	NOUN
ejpam-5621	36	17	(	(	PUNCT
ejpam-5621	36	18	1	1	X
ejpam-5621	36	19	)	)	PUNCT
ejpam-5621	36	20	vn	vn	PROPN
ejpam-5621	36	21	∈w	∈w	PROPN
ejpam-5621	36	22	1,p	1,p	PROPN
ejpam-5621	36	23	loc	loc	X
ejpam-5621	36	24	(	(	PUNCT
ejpam-5621	36	25	ω	ω	PROPN
ejpam-5621	36	26	)	)	PUNCT
ejpam-5621	36	27	,	,	PUNCT
ejpam-5621	36	28	we	we	PRON
ejpam-5621	36	29	state	state	VERB
ejpam-5621	36	30	some	some	DET
ejpam-5621	36	31	preliminary	preliminary	ADJ
ejpam-5621	36	32	lemmas	lemma	NOUN
ejpam-5621	36	33	.	.	PUNCT
ejpam-5621	37	1	lemma	lemma	PROPN
ejpam-5621	37	2	1	1	NUM
ejpam-5621	37	3	.	.	PUNCT
ejpam-5621	37	4	suppose	suppose	VERB
ejpam-5621	37	5	that	that	SCONJ
ejpam-5621	37	6	b3	b3	PROPN
ejpam-5621	37	7	⊂	⊂	PROPN
ejpam-5621	37	8	ω	ω	PROPN
ejpam-5621	37	9	.	.	PUNCT
ejpam-5621	38	1	then	then	ADV
ejpam-5621	38	2	we	we	PRON
ejpam-5621	38	3	have∫	have∫	VERB
ejpam-5621	38	4	b1	b1	VERB
ejpam-5621	38	5	|∇vm|q	|∇vm|q	NOUN
ejpam-5621	38	6	dx	dx	PROPN
ejpam-5621	38	7	≤	≤	PROPN
ejpam-5621	38	8	c	c	PROPN
ejpam-5621	38	9	{	{	PUNCT
ejpam-5621	38	10	∫	∫	PROPN
ejpam-5621	38	11	b3	b3	PROPN
ejpam-5621	38	12	|vm|q	|vm|q	PROPN
ejpam-5621	38	13	dx+	dx+	ADJ
ejpam-5621	38	14	∫	∫	PROPN
ejpam-5621	38	15	b3	b3	PROPN
ejpam-5621	38	16	|gm|q	|gm|q	PROPN
ejpam-5621	38	17	dx	dx	PROPN
ejpam-5621	38	18	}	}	PUNCT
ejpam-5621	38	19	(	(	PUNCT
ejpam-5621	38	20	3	3	X
ejpam-5621	38	21	)	)	PUNCT
ejpam-5621	38	22	where	where	SCONJ
ejpam-5621	38	23	c	c	NOUN
ejpam-5621	38	24	is	be	AUX
ejpam-5621	38	25	solely	solely	ADV
ejpam-5621	38	26	dependent	dependent	ADJ
ejpam-5621	38	27	on	on	ADP
ejpam-5621	38	28	m	m	PROPN
ejpam-5621	38	29	,	,	PUNCT
ejpam-5621	38	30	q	q	PUNCT
ejpam-5621	38	31	and	and	CCONJ
ejpam-5621	38	32	α	α	X
ejpam-5621	39	1	[	[	X
ejpam-5621	39	2	8	8	NUM
ejpam-5621	39	3	]	]	PUNCT
ejpam-5621	39	4	.	.	PUNCT
ejpam-5621	40	1	proof	proof	NOUN
ejpam-5621	40	2	.	.	PUNCT
ejpam-5621	41	1	it	it	PRON
ejpam-5621	41	2	is	be	AUX
ejpam-5621	41	3	possible	possible	ADJ
ejpam-5621	41	4	to	to	PART
ejpam-5621	41	5	choose	choose	VERB
ejpam-5621	41	6	the	the	DET
ejpam-5621	41	7	test	test	NOUN
ejpam-5621	41	8	function	function	NOUN
ejpam-5621	41	9	ψ	ψ	X
ejpam-5621	41	10	=	=	NOUN
ejpam-5621	41	11	ζpv	ζpv	NOUN
ejpam-5621	41	12	∈w	∈w	VERB
ejpam-5621	41	13	1,p	1,p	PROPN
ejpam-5621	41	14	0	0	SYM
ejpam-5621	41	15	(	(	PUNCT
ejpam-5621	41	16	ω	ω	NOUN
ejpam-5621	41	17	)	)	PUNCT
ejpam-5621	41	18	,	,	PUNCT
ejpam-5621	41	19	where	where	SCONJ
ejpam-5621	41	20	ζ	ζ	X
ejpam-5621	41	21	∈	∈	PROPN
ejpam-5621	41	22	c∞	c∞	PROPN
ejpam-5621	41	23	0	0	NUM
ejpam-5621	41	24	(	(	PUNCT
ejpam-5621	41	25	rn	rn	NOUN
ejpam-5621	41	26	)	)	PUNCT
ejpam-5621	41	27	represents	represent	VERB
ejpam-5621	41	28	a	a	DET
ejpam-5621	41	29	cut	cut	VERB
ejpam-5621	41	30	-	-	PUNCT
ejpam-5621	41	31	off	off	ADP
ejpam-5621	41	32	function	function	NOUN
ejpam-5621	41	33	that	that	PRON
ejpam-5621	41	34	is	be	AUX
ejpam-5621	41	35	satisfied	satisfied	ADJ
ejpam-5621	41	36	.	.	PUNCT
ejpam-5621	42	1	0	0	NUM
ejpam-5621	43	1	≤	≤	NUM
ejpam-5621	43	2	ζ	ζ	NOUN
ejpam-5621	43	3	≤	≤	NUM
ejpam-5621	43	4	1	1	NUM
ejpam-5621	43	5	,	,	PUNCT
ejpam-5621	43	6	ζ	ζ	PROPN
ejpam-5621	43	7	≡	≡	PROPN
ejpam-5621	43	8	1	1	NUM
ejpam-5621	43	9	in	in	ADP
ejpam-5621	43	10	b1	b1	NOUN
ejpam-5621	43	11	,	,	PUNCT
ejpam-5621	43	12	ζ	ζ	PROPN
ejpam-5621	43	13	≡	≡	PROPN
ejpam-5621	43	14	0	0	NUM
ejpam-5621	43	15	in	in	ADP
ejpam-5621	43	16	rn	rn	PROPN
ejpam-5621	43	17	\b2	\b2	PROPN
ejpam-5621	43	18	.	.	PUNCT
ejpam-5621	44	1	h.	h.	PROPN
ejpam-5621	44	2	ibrahim	ibrahim	PROPN
ejpam-5621	44	3	et	et	PROPN
ejpam-5621	44	4	al	al	PROPN
ejpam-5621	44	5	.	.	PUNCT
ejpam-5621	44	6	/	/	SYM
ejpam-5621	44	7	eur	eur	PROPN
ejpam-5621	44	8	.	.	PUNCT
ejpam-5621	45	1	j.	j.	PROPN
ejpam-5621	45	2	pure	pure	PROPN
ejpam-5621	45	3	appl	appl	PROPN
ejpam-5621	45	4	.	.	PROPN
ejpam-5621	45	5	math	math	PROPN
ejpam-5621	45	6	,	,	PUNCT
ejpam-5621	45	7	18	18	NUM
ejpam-5621	45	8	(	(	PUNCT
ejpam-5621	45	9	2	2	NUM
ejpam-5621	45	10	)	)	PUNCT
ejpam-5621	45	11	(	(	PUNCT
ejpam-5621	45	12	2025	2025	NUM
ejpam-5621	45	13	)	)	PUNCT
ejpam-5621	45	14	,	,	PUNCT
ejpam-5621	45	15	5621	5621	NUM
ejpam-5621	45	16	3	3	NUM
ejpam-5621	45	17	of	of	ADP
ejpam-5621	45	18	16	16	NUM
ejpam-5621	45	19	therefore	therefore	ADV
ejpam-5621	45	20	,	,	PUNCT
ejpam-5621	45	21	by	by	ADP
ejpam-5621	45	22	definition	definition	NOUN
ejpam-5621	45	23	1	1	NUM
ejpam-5621	45	24	,	,	PUNCT
ejpam-5621	45	25	we	we	PRON
ejpam-5621	45	26	get∫	get∫	PROPN
ejpam-5621	45	27	b3	b3	PROPN
ejpam-5621	45	28	(	(	PUNCT
ejpam-5621	45	29	e∇vm.∇vm)(p−2)\2e∇vm.∇(ζpvm)dx	e∇vm.∇vm)(p−2)\2e∇vm.∇(ζpvm)dx	NOUN
ejpam-5621	45	30	=	=	SYM
ejpam-5621	45	31	∫	∫	PROPN
ejpam-5621	45	32	b3	b3	PROPN
ejpam-5621	45	33	|gm|p−2	|gm|p−2	PROPN
ejpam-5621	45	34	gm.∇(ζpvm)dx	gm.∇(ζpvm)dx	VERB
ejpam-5621	45	35	the	the	DET
ejpam-5621	45	36	resulting	result	VERB
ejpam-5621	45	37	expression	expression	NOUN
ejpam-5621	45	38	should	should	AUX
ejpam-5621	45	39	be	be	AUX
ejpam-5621	45	40	written	write	VERB
ejpam-5621	45	41	as	as	ADP
ejpam-5621	45	42	i1	i1	PROPN
ejpam-5621	45	43	=	=	PROPN
ejpam-5621	45	44	i2	i2	PROPN
ejpam-5621	45	45	+	+	CCONJ
ejpam-5621	45	46	i3	i3	NOUN
ejpam-5621	45	47	+	+	CCONJ
ejpam-5621	45	48	i4	i4	PROPN
ejpam-5621	45	49	where	where	SCONJ
ejpam-5621	45	50	,	,	PUNCT
ejpam-5621	45	51	i1	i1	PROPN
ejpam-5621	45	52	=	=	SYM
ejpam-5621	45	53	∫	∫	PROPN
ejpam-5621	45	54	b3	b3	PROPN
ejpam-5621	45	55	ζp(e∇vm.∇vm)p\2dx	ζp(e∇vm.∇vm)p\2dx	PROPN
ejpam-5621	45	56	,	,	PUNCT
ejpam-5621	45	57	i2	i2	PROPN
ejpam-5621	45	58	=	=	PUNCT
ejpam-5621	45	59	−	−	PROPN
ejpam-5621	45	60	∫	∫	PROPN
ejpam-5621	45	61	b3	b3	PROPN
ejpam-5621	45	62	pζp−1vm(e∇vm.∇vm)(p−2)\2(e∇vm.∇ζ)dx	pζp−1vm(e∇vm.∇vm)(p−2)\2(e∇vm.∇ζ)dx	NOUN
ejpam-5621	45	63	,	,	PUNCT
ejpam-5621	45	64	i3	i3	NOUN
ejpam-5621	45	65	=	=	SYM
ejpam-5621	45	66	∫	∫	PROPN
ejpam-5621	45	67	b3	b3	PROPN
ejpam-5621	45	68	ζp	ζp	ADP
ejpam-5621	45	69	|gm|p−2	|gm|p−2	PROPN
ejpam-5621	45	70	gm.∇vmdx	gm.∇vmdx	PROPN
ejpam-5621	45	71	,	,	PUNCT
ejpam-5621	45	72	i4	i4	PROPN
ejpam-5621	45	73	=	=	SYM
ejpam-5621	45	74	∫	∫	PROPN
ejpam-5621	45	75	b3	b3	PROPN
ejpam-5621	45	76	pζp−1vm	pζp−1vm	PROPN
ejpam-5621	45	77	|gm|p−2	|gm|p−2	PROPN
ejpam-5621	45	78	gm.∇ζdx	gm.∇ζdx	PROPN
ejpam-5621	45	79	.	.	PUNCT
ejpam-5621	46	1	the	the	DET
ejpam-5621	46	2	estimation	estimation	NOUN
ejpam-5621	46	3	of	of	ADP
ejpam-5621	46	4	i1	i1	PROPN
ejpam-5621	46	5	.	.	PUNCT
ejpam-5621	47	1	the	the	DET
ejpam-5621	47	2	uniformly	uniformly	ADV
ejpam-5621	47	3	elliptic	elliptic	ADJ
ejpam-5621	47	4	equation	equation	NOUN
ejpam-5621	47	5	(	(	PUNCT
ejpam-5621	47	6	2	2	X
ejpam-5621	47	7	)	)	PUNCT
ejpam-5621	47	8	dictates	dictate	VERB
ejpam-5621	47	9	that	that	SCONJ
ejpam-5621	47	10	i1	i1	PROPN
ejpam-5621	47	11	=	=	SYM
ejpam-5621	47	12	∫	∫	PROPN
ejpam-5621	47	13	b3	b3	PROPN
ejpam-5621	47	14	ζp(e∇vm.∇vm)p\2dx	ζp(e∇vm.∇vm)p\2dx	PROPN
ejpam-5621	47	15	≥	≥	NOUN
ejpam-5621	47	16	1	1	NUM
ejpam-5621	47	17	α	α	NUM
ejpam-5621	47	18	∫	∫	PROPN
ejpam-5621	47	19	b3	b3	PROPN
ejpam-5621	47	20	ζp	ζp	PROPN
ejpam-5621	47	21	|∇vm|p	|∇vm|p	PROPN
ejpam-5621	47	22	dx	dx	PROPN
ejpam-5621	47	23	.	.	PUNCT
ejpam-5621	48	1	the	the	DET
ejpam-5621	48	2	estimation	estimation	NOUN
ejpam-5621	48	3	of	of	ADP
ejpam-5621	48	4	i2	i2	PROPN
ejpam-5621	48	5	can	can	AUX
ejpam-5621	48	6	be	be	AUX
ejpam-5621	48	7	derived	derive	VERB
ejpam-5621	48	8	using	use	VERB
ejpam-5621	48	9	the	the	DET
ejpam-5621	48	10	uniformly	uniformly	ADV
ejpam-5621	48	11	elliptic	elliptic	ADJ
ejpam-5621	48	12	condition	condition	NOUN
ejpam-5621	48	13	(	(	PUNCT
ejpam-5621	48	14	2	2	NUM
ejpam-5621	48	15	)	)	PUNCT
ejpam-5621	48	16	and	and	CCONJ
ejpam-5621	48	17	young	young	PROPN
ejpam-5621	48	18	’s	’s	PART
ejpam-5621	48	19	inequality	inequality	NOUN
ejpam-5621	48	20	with	with	ADP
ejpam-5621	48	21	respect	respect	NOUN
ejpam-5621	48	22	to	to	ADP
ejpam-5621	48	23	τ	τ	PROPN
ejpam-5621	48	24	.	.	PUNCT
ejpam-5621	49	1	i2	i2	PROPN
ejpam-5621	49	2	≤	≤	PROPN
ejpam-5621	49	3	c	c	PROPN
ejpam-5621	49	4	∫	∫	PROPN
ejpam-5621	49	5	b3	b3	PROPN
ejpam-5621	49	6	ζp−1	ζp−1	PROPN
ejpam-5621	49	7	|∇vm|p−1	|∇vm|p−1	NUM
ejpam-5621	49	8	|vm|	|vm|	PROPN
ejpam-5621	49	9	dx	dx	PROPN
ejpam-5621	49	10	≤	≤	NUM
ejpam-5621	49	11	τ	τ	PROPN
ejpam-5621	49	12	∫	∫	PROPN
ejpam-5621	49	13	b3	b3	PROPN
ejpam-5621	49	14	ζp	ζp	PROPN
ejpam-5621	49	15	|∇vm|p	|∇vm|p	ADJ
ejpam-5621	49	16	dx+	dx+	PROPN
ejpam-5621	49	17	c(τ	c(τ	PROPN
ejpam-5621	49	18	)	)	PUNCT
ejpam-5621	49	19	∫	∫	PROPN
ejpam-5621	49	20	b3	b3	PROPN
ejpam-5621	49	21	|vm|p	|vm|p	PROPN
ejpam-5621	49	22	dx	dx	PROPN
ejpam-5621	49	23	.	.	PUNCT
ejpam-5621	50	1	the	the	DET
ejpam-5621	50	2	estimation	estimation	NOUN
ejpam-5621	50	3	of	of	ADP
ejpam-5621	50	4	i3	i3	NOUN
ejpam-5621	50	5	can	can	AUX
ejpam-5621	50	6	be	be	AUX
ejpam-5621	50	7	derived	derive	VERB
ejpam-5621	50	8	from	from	ADP
ejpam-5621	50	9	young	young	PROPN
ejpam-5621	50	10	’s	’s	PART
ejpam-5621	50	11	inequality	inequality	NOUN
ejpam-5621	50	12	.	.	PUNCT
ejpam-5621	51	1	i3	i3	NOUN
ejpam-5621	51	2	≤	≤	PUNCT
ejpam-5621	51	3	τ	τ	PROPN
ejpam-5621	51	4	∫	∫	PROPN
ejpam-5621	51	5	b3	b3	PROPN
ejpam-5621	51	6	ζp	ζp	PROPN
ejpam-5621	51	7	|∇vm|p	|∇vm|p	ADJ
ejpam-5621	51	8	dx+	dx+	PROPN
ejpam-5621	51	9	c(τ	c(τ	PROPN
ejpam-5621	51	10	)	)	PUNCT
ejpam-5621	51	11	∫	∫	PROPN
ejpam-5621	51	12	b3	b3	PROPN
ejpam-5621	51	13	|gm|p	|gm|p	PROPN
ejpam-5621	51	14	dx	dx	PROPN
ejpam-5621	51	15	.	.	PUNCT
ejpam-5621	52	1	the	the	DET
ejpam-5621	52	2	estimation	estimation	NOUN
ejpam-5621	52	3	of	of	ADP
ejpam-5621	52	4	i4	i4	PROPN
ejpam-5621	52	5	can	can	AUX
ejpam-5621	52	6	be	be	AUX
ejpam-5621	52	7	derived	derive	VERB
ejpam-5621	52	8	from	from	ADP
ejpam-5621	52	9	young	young	PROPN
ejpam-5621	52	10	’s	’s	PART
ejpam-5621	52	11	inequality	inequality	NOUN
ejpam-5621	52	12	.	.	PUNCT
ejpam-5621	53	1	i4	i4	PROPN
ejpam-5621	53	2	≤	≤	PROPN
ejpam-5621	53	3	c	c	PROPN
ejpam-5621	53	4	{	{	PUNCT
ejpam-5621	53	5	∫	∫	PROPN
ejpam-5621	53	6	b3	b3	PROPN
ejpam-5621	53	7	|vm|p	|vm|p	PROPN
ejpam-5621	53	8	dx+	dx+	ADJ
ejpam-5621	53	9	∫	∫	PROPN
ejpam-5621	53	10	b3	b3	PROPN
ejpam-5621	53	11	|gm|p	|gm|p	PROPN
ejpam-5621	53	12	dx	dx	PROPN
ejpam-5621	53	13	}	}	PUNCT
ejpam-5621	53	14	.	.	PUNCT
ejpam-5621	54	1	we	we	PRON
ejpam-5621	54	2	conclude	conclude	VERB
ejpam-5621	54	3	that	that	SCONJ
ejpam-5621	54	4	by	by	ADP
ejpam-5621	54	5	summing	sum	VERB
ejpam-5621	54	6	all	all	DET
ejpam-5621	54	7	the	the	DET
ejpam-5621	54	8	estimates	estimate	NOUN
ejpam-5621	54	9	of	of	ADP
ejpam-5621	54	10	ij(1	ij(1	PROPN
ejpam-5621	54	11	⩽	⩽	PROPN
ejpam-5621	54	12	j	j	PROPN
ejpam-5621	54	13	≤	≤	ADJ
ejpam-5621	54	14	4	4	NUM
ejpam-5621	54	15	)	)	PUNCT
ejpam-5621	54	16	,	,	PUNCT
ejpam-5621	54	17	1	1	NUM
ejpam-5621	54	18	α	α	NUM
ejpam-5621	54	19	∫	∫	PROPN
ejpam-5621	54	20	b3	b3	PROPN
ejpam-5621	54	21	ζp	ζp	PROPN
ejpam-5621	54	22	|∇vm|p	|∇vm|p	PROPN
ejpam-5621	54	23	dx	dx	PROPN
ejpam-5621	54	24	≤	≤	PROPN
ejpam-5621	54	25	2τ	2τ	NUM
ejpam-5621	54	26	∫	∫	PROPN
ejpam-5621	54	27	b3	b3	PROPN
ejpam-5621	54	28	ζp	ζp	PROPN
ejpam-5621	54	29	|∇vm|p	|∇vm|p	ADJ
ejpam-5621	54	30	dx+	dx+	PROPN
ejpam-5621	54	31	c(τ	c(τ	PROPN
ejpam-5621	54	32	)	)	PUNCT
ejpam-5621	54	33	∫	∫	PROPN
ejpam-5621	54	34	b3	b3	PROPN
ejpam-5621	54	35	(	(	PUNCT
ejpam-5621	54	36	vpmdx+	vpmdx+	NUM
ejpam-5621	54	37	|gm|p)dx	|gm|p)dx	NOUN
ejpam-5621	54	38	.	.	PUNCT
ejpam-5621	54	39	by	by	ADP
ejpam-5621	54	40	choosing	choose	VERB
ejpam-5621	54	41	τ	τ	X
ejpam-5621	54	42	=	=	SYM
ejpam-5621	54	43	1	1	NUM
ejpam-5621	54	44	(	(	PUNCT
ejpam-5621	54	45	4α	4α	NOUN
ejpam-5621	54	46	)	)	PUNCT
ejpam-5621	54	47	,	,	PUNCT
ejpam-5621	54	48	and	and	CCONJ
ejpam-5621	54	49	referring	refer	VERB
ejpam-5621	54	50	back	back	ADV
ejpam-5621	54	51	to	to	ADP
ejpam-5621	54	52	the	the	DET
ejpam-5621	54	53	definition	definition	NOUN
ejpam-5621	54	54	of	of	ADP
ejpam-5621	54	55	ζ	ζ	NOUN
ejpam-5621	54	56	the	the	DET
ejpam-5621	54	57	proof	proof	NOUN
ejpam-5621	54	58	is	be	AUX
ejpam-5621	54	59	successfully	successfully	ADV
ejpam-5621	54	60	concluded	conclude	VERB
ejpam-5621	54	61	.	.	PUNCT
ejpam-5621	55	1	henceforth	henceforth	ADV
ejpam-5621	55	2	,	,	PUNCT
ejpam-5621	55	3	it	it	PRON
ejpam-5621	55	4	is	be	AUX
ejpam-5621	55	5	assumed	assume	VERB
ejpam-5621	55	6	that	that	SCONJ
ejpam-5621	55	7	q	q	NOUN
ejpam-5621	55	8	is	be	AUX
ejpam-5621	55	9	greater	great	ADJ
ejpam-5621	55	10	than	than	SCONJ
ejpam-5621	55	11	p.	p.	NOUN
ejpam-5621	55	12	now	now	ADV
ejpam-5621	55	13	let	let	VERB
ejpam-5621	55	14	q1	q1	NOUN
ejpam-5621	55	15	=	=	NOUN
ejpam-5621	55	16	:	:	PUNCT
ejpam-5621	55	17	q	q	X
ejpam-5621	56	1	+	+	CCONJ
ejpam-5621	56	2	p	p	X
ejpam-5621	56	3	2	2	NUM
ejpam-5621	56	4	∈	∈	NOUN
ejpam-5621	56	5	(	(	PUNCT
ejpam-5621	56	6	p	p	NOUN
ejpam-5621	56	7	,	,	PUNCT
ejpam-5621	56	8	q	q	NOUN
ejpam-5621	56	9	)	)	PUNCT
ejpam-5621	56	10	.	.	PUNCT
ejpam-5621	57	1	we	we	PRON
ejpam-5621	57	2	recall	recall	VERB
ejpam-5621	57	3	a	a	DET
ejpam-5621	57	4	well	well	ADV
ejpam-5621	57	5	-	-	PUNCT
ejpam-5621	57	6	known	know	VERB
ejpam-5621	57	7	result	result	NOUN
ejpam-5621	57	8	of	of	ADP
ejpam-5621	57	9	[	[	X
ejpam-5621	57	10	1	1	NUM
ejpam-5621	57	11	]	]	PUNCT
ejpam-5621	57	12	.	.	PUNCT
ejpam-5621	58	1	h.	h.	PROPN
ejpam-5621	58	2	ibrahim	ibrahim	PROPN
ejpam-5621	58	3	et	et	PROPN
ejpam-5621	58	4	al	al	PROPN
ejpam-5621	58	5	.	.	PUNCT
ejpam-5621	58	6	/	/	SYM
ejpam-5621	58	7	eur	eur	PROPN
ejpam-5621	58	8	.	.	PUNCT
ejpam-5621	59	1	j.	j.	PROPN
ejpam-5621	59	2	pure	pure	PROPN
ejpam-5621	59	3	appl	appl	PROPN
ejpam-5621	59	4	.	.	PROPN
ejpam-5621	59	5	math	math	PROPN
ejpam-5621	59	6	,	,	PUNCT
ejpam-5621	59	7	18	18	NUM
ejpam-5621	59	8	(	(	PUNCT
ejpam-5621	59	9	2	2	NUM
ejpam-5621	59	10	)	)	PUNCT
ejpam-5621	59	11	(	(	PUNCT
ejpam-5621	59	12	2025	2025	NUM
ejpam-5621	59	13	)	)	PUNCT
ejpam-5621	59	14	,	,	PUNCT
ejpam-5621	59	15	5621	5621	NUM
ejpam-5621	59	16	4	4	NUM
ejpam-5621	59	17	of	of	ADP
ejpam-5621	59	18	16	16	NUM
ejpam-5621	59	19	lemma	lemma	PROPN
ejpam-5621	59	20	2	2	NUM
ejpam-5621	59	21	.	.	PUNCT
ejpam-5621	59	22	assumes	assume	VERB
ejpam-5621	59	23	that	that	SCONJ
ejpam-5621	59	24	vn	vn	PROPN
ejpam-5621	59	25	∈	∈	PROPN
ejpam-5621	59	26	w	w	PROPN
ejpam-5621	59	27	1,p	1,p	PROPN
ejpam-5621	59	28	loc	loc	X
ejpam-5621	59	29	(	(	PUNCT
ejpam-5621	59	30	ω	ω	NOUN
ejpam-5621	59	31	)	)	PUNCT
ejpam-5621	59	32	is	be	AUX
ejpam-5621	59	33	a	a	DET
ejpam-5621	59	34	local	local	ADJ
ejpam-5621	59	35	weak	weak	ADJ
ejpam-5621	59	36	solution	solution	NOUN
ejpam-5621	59	37	of	of	ADP
ejpam-5621	59	38	the	the	DET
ejpam-5621	59	39	equation	equation	NOUN
ejpam-5621	59	40	(	(	PUNCT
ejpam-5621	59	41	1	1	NUM
ejpam-5621	59	42	)	)	PUNCT
ejpam-5621	59	43	and	and	CCONJ
ejpam-5621	59	44	g	g	PROPN
ejpam-5621	59	45	∈	∈	PROPN
ejpam-5621	59	46	lq1(ω	lq1(ω	PROPN
ejpam-5621	59	47	)	)	PUNCT
ejpam-5621	59	48	.	.	PUNCT
ejpam-5621	60	1	consequently	consequently	ADV
ejpam-5621	60	2	,	,	PUNCT
ejpam-5621	60	3	we	we	PRON
ejpam-5621	60	4	have	have	VERB
ejpam-5621	60	5	q2	q2	NOUN
ejpam-5621	60	6	,	,	PUNCT
ejpam-5621	60	7	p	p	X
ejpam-5621	60	8	<	<	X
ejpam-5621	60	9	q2	q2	X
ejpam-5621	60	10	<	<	X
ejpam-5621	60	11	q1	q1	PROPN
ejpam-5621	60	12	in	in	ADP
ejpam-5621	60	13	which:(∮	which:(∮	PROPN
ejpam-5621	60	14	bs(x1	bs(x1	NOUN
ejpam-5621	60	15	)	)	PUNCT
ejpam-5621	60	16	|∇vm|q2	|∇vm|q2	NUM
ejpam-5621	60	17	dx	dx	PROPN
ejpam-5621	60	18	)	)	PUNCT
ejpam-5621	61	1	1	1	NUM
ejpam-5621	61	2	q2	q2	NOUN
ejpam-5621	61	3	≤	≤	NOUN
ejpam-5621	61	4	c	c	X
ejpam-5621	61	5			PUNCT
ejpam-5621	61	6	(	(	PUNCT
ejpam-5621	61	7	∮	∮	NUM
ejpam-5621	61	8	b2s(x1	b2s(x1	ADJ
ejpam-5621	61	9	)	)	PUNCT
ejpam-5621	61	10	|∇vm|p	|∇vm|p	ADP
ejpam-5621	61	11	dx	dx	PROPN
ejpam-5621	61	12	)	)	PUNCT
ejpam-5621	61	13	1	1	NUM
ejpam-5621	61	14	p	p	NOUN
ejpam-5621	61	15	+	+	X
ejpam-5621	61	16	(	(	PUNCT
ejpam-5621	61	17	∮	∮	ADJ
ejpam-5621	61	18	b2s(x1	b2s(x1	ADJ
ejpam-5621	61	19	)	)	PUNCT
ejpam-5621	61	20	|gm|q1	|gm|q1	NOUN
ejpam-5621	61	21	dx	dx	PROPN
ejpam-5621	61	22	)	)	PUNCT
ejpam-5621	61	23	1	1	NUM
ejpam-5621	61	24	q1	q1	NOUN
ejpam-5621	61	25			PROPN
ejpam-5621	61	26	,	,	PUNCT
ejpam-5621	61	27	for	for	ADP
ejpam-5621	61	28	each	each	DET
ejpam-5621	61	29	b2s(x1	b2s(x1	PROPN
ejpam-5621	61	30	)	)	PUNCT
ejpam-5621	61	31	⊂	⊂	PROPN
ejpam-5621	61	32	ω	ω	PROPN
ejpam-5621	61	33	,	,	PUNCT
ejpam-5621	61	34	with	with	ADP
ejpam-5621	61	35	condition	condition	NOUN
ejpam-5621	61	36	that	that	SCONJ
ejpam-5621	61	37	q2	q2	NOUN
ejpam-5621	61	38	and	and	CCONJ
ejpam-5621	61	39	c	c	PROPN
ejpam-5621	61	40	are	be	AUX
ejpam-5621	61	41	dependent	dependent	ADJ
ejpam-5621	61	42	solely	solely	ADV
ejpam-5621	61	43	on	on	ADP
ejpam-5621	61	44	n	n	CCONJ
ejpam-5621	61	45	,	,	PUNCT
ejpam-5621	61	46	p	p	X
ejpam-5621	61	47	,	,	PUNCT
ejpam-5621	61	48	q	q	X
ejpam-5621	61	49	,	,	PUNCT
ejpam-5621	61	50	α	α	X
ejpam-5621	61	51	.	.	PUNCT
ejpam-5621	62	1	following	follow	VERB
ejpam-5621	62	2	this	this	PRON
ejpam-5621	62	3	,	,	PUNCT
ejpam-5621	62	4	we	we	PRON
ejpam-5621	62	5	present	present	VERB
ejpam-5621	62	6	two	two	NUM
ejpam-5621	62	7	lemmas	lemma	NOUN
ejpam-5621	62	8	that	that	PRON
ejpam-5621	62	9	are	be	AUX
ejpam-5621	62	10	critical	critical	ADJ
ejpam-5621	62	11	in	in	ADP
ejpam-5621	62	12	order	order	NOUN
ejpam-5621	62	13	to	to	PART
ejpam-5621	62	14	derive	derive	VERB
ejpam-5621	62	15	the	the	DET
ejpam-5621	62	16	primary	primary	ADJ
ejpam-5621	62	17	result	result	NOUN
ejpam-5621	62	18	:	:	PUNCT
ejpam-5621	62	19	the	the	DET
ejpam-5621	62	20	two	two	NUM
ejpam-5621	62	21	lemmas	lemma	NOUN
ejpam-5621	62	22	are	be	AUX
ejpam-5621	62	23	significantly	significantly	ADV
ejpam-5621	62	24	impacted	impact	VERB
ejpam-5621	62	25	by	by	ADP
ejpam-5621	62	26	[	[	X
ejpam-5621	62	27	6	6	NUM
ejpam-5621	62	28	,	,	PUNCT
ejpam-5621	62	29	7	7	NUM
ejpam-5621	62	30	]	]	PUNCT
ejpam-5621	62	31	.	.	PUNCT
ejpam-5621	63	1	we	we	PRON
ejpam-5621	63	2	compose	compose	VERB
ejpam-5621	63	3	λ0	λ0	NOUN
ejpam-5621	63	4	=	=	SYM
ejpam-5621	63	5	{	{	PUNCT
ejpam-5621	63	6	(	(	PUNCT
ejpam-5621	63	7	∮	∮	NUM
ejpam-5621	63	8	b2	b2	NOUN
ejpam-5621	63	9	|∇vm|p	|∇vm|p	ADP
ejpam-5621	63	10	dx	dx	PROPN
ejpam-5621	63	11	)	)	PUNCT
ejpam-5621	63	12	1	1	NUM
ejpam-5621	64	1	p	p	NOUN
ejpam-5621	64	2	+	+	NOUN
ejpam-5621	64	3	1	1	NUM
ejpam-5621	64	4	δ	δ	PROPN
ejpam-5621	64	5	(	(	PUNCT
ejpam-5621	64	6	∮	∮	NUM
ejpam-5621	64	7	b2	b2	NOUN
ejpam-5621	64	8	|gm|q1	|gm|q1	NOUN
ejpam-5621	64	9	dx	dx	PROPN
ejpam-5621	64	10	)	)	PUNCT
ejpam-5621	64	11	1	1	NUM
ejpam-5621	64	12	q1	q1	PROPN
ejpam-5621	64	13	}	}	PUNCT
ejpam-5621	64	14	,	,	PUNCT
ejpam-5621	64	15	(	(	PUNCT
ejpam-5621	64	16	4	4	NUM
ejpam-5621	64	17	)	)	PUNCT
ejpam-5621	64	18	and	and	CCONJ
ejpam-5621	64	19	a(λ	a(λ	PROPN
ejpam-5621	64	20	)	)	PUNCT
ejpam-5621	64	21	=	=	PRON
ejpam-5621	65	1	{	{	PUNCT
ejpam-5621	65	2	x	x	PUNCT
ejpam-5621	65	3	∈	∈	PROPN
ejpam-5621	65	4	b1	b1	NOUN
ejpam-5621	65	5	:	:	PUNCT
ejpam-5621	65	6	|∇vm|	|∇vm|	X
ejpam-5621	65	7	>	>	X
ejpam-5621	65	8	λ	λ	X
ejpam-5621	65	9	}	}	PUNCT
ejpam-5621	65	10	for	for	ADP
ejpam-5621	65	11	λ	λ	PROPN
ejpam-5621	65	12	>	>	X
ejpam-5621	65	13	0	0	NUM
ejpam-5621	65	14	,	,	PUNCT
ejpam-5621	65	15	whereas	whereas	SCONJ
ejpam-5621	65	16	δ	δ	PROPN
ejpam-5621	65	17	>	>	X
ejpam-5621	65	18	0	0	NUM
ejpam-5621	65	19	will	will	AUX
ejpam-5621	65	20	be	be	AUX
ejpam-5621	65	21	selected	select	VERB
ejpam-5621	65	22	at	at	ADP
ejpam-5621	65	23	a	a	DET
ejpam-5621	65	24	later	later	ADJ
ejpam-5621	65	25	time	time	NOUN
ejpam-5621	65	26	.	.	PUNCT
ejpam-5621	66	1	by	by	ADP
ejpam-5621	66	2	ensuring	ensure	VERB
ejpam-5621	66	3	that	that	PRON
ejpam-5621	66	4	|∇vm|	|∇vm|	NOUN
ejpam-5621	66	5	is	be	AUX
ejpam-5621	66	6	constrained	constrain	VERB
ejpam-5621	66	7	within	within	ADP
ejpam-5621	66	8	the	the	DET
ejpam-5621	66	9	range	range	NOUN
ejpam-5621	66	10	b1	b1	NOUN
ejpam-5621	66	11	\a(λ	\a(λ	NOUN
ejpam-5621	66	12	)	)	PUNCT
ejpam-5621	66	13	for	for	ADP
ejpam-5621	66	14	any	any	DET
ejpam-5621	66	15	fixed	fix	VERB
ejpam-5621	66	16	λ	λ	PROPN
ejpam-5621	66	17	>	>	X
ejpam-5621	66	18	0	0	PROPN
ejpam-5621	66	19	,	,	PUNCT
ejpam-5621	66	20	our	our	PRON
ejpam-5621	66	21	analysis	analysis	NOUN
ejpam-5621	66	22	is	be	AUX
ejpam-5621	66	23	directed	direct	VERB
ejpam-5621	66	24	towards	towards	ADP
ejpam-5621	66	25	the	the	DET
ejpam-5621	66	26	level	level	NOUN
ejpam-5621	66	27	set	set	VERB
ejpam-5621	66	28	a(λ	a(λ	ADV
ejpam-5621	66	29	)	)	PUNCT
ejpam-5621	66	30	.	.	PUNCT
ejpam-5621	67	1	at	at	ADP
ejpam-5621	67	2	this	this	DET
ejpam-5621	67	3	juncture	juncture	NOUN
ejpam-5621	67	4	,	,	PUNCT
ejpam-5621	67	5	a(λ	a(λ	ADV
ejpam-5621	67	6	)	)	PUNCT
ejpam-5621	67	7	shall	shall	AUX
ejpam-5621	67	8	be	be	AUX
ejpam-5621	67	9	decomposed	decompose	VERB
ejpam-5621	67	10	into	into	ADP
ejpam-5621	67	11	a	a	DET
ejpam-5621	67	12	set	set	NOUN
ejpam-5621	67	13	of	of	ADP
ejpam-5621	67	14	disjoint	disjoint	NOUN
ejpam-5621	67	15	spheres	sphere	NOUN
ejpam-5621	67	16	.	.	PUNCT
ejpam-5621	68	1	lemma	lemma	PROPN
ejpam-5621	68	2	3	3	X
ejpam-5621	68	3	.	.	PUNCT
ejpam-5621	68	4	suppose	suppose	VERB
ejpam-5621	69	1	that	that	SCONJ
ejpam-5621	69	2	λ	λ	PROPN
ejpam-5621	69	3	≥	≥	PRON
ejpam-5621	69	4	λ∗	λ∗	NOUN
ejpam-5621	70	1	=	=	SYM
ejpam-5621	70	2	26n\pλ0	26n\pλ0	NUM
ejpam-5621	70	3	,	,	PUNCT
ejpam-5621	70	4	there	there	PRON
ejpam-5621	70	5	exists	exist	VERB
ejpam-5621	70	6	a	a	DET
ejpam-5621	70	7	family	family	NOUN
ejpam-5621	70	8	of	of	ADP
ejpam-5621	70	9	disjoint	disjoint	NOUN
ejpam-5621	70	10	balls	ball	NOUN
ejpam-5621	70	11	{	{	PUNCT
ejpam-5621	70	12	b0	b0	NOUN
ejpam-5621	70	13	i	i	PRON
ejpam-5621	70	14	}	}	PUNCT
ejpam-5621	70	15	i∈n	i∈n	NOUN
ejpam-5621	71	1	=	=	NOUN
ejpam-5621	71	2	{	{	PUNCT
ejpam-5621	71	3	bpxi	bpxi	PROPN
ejpam-5621	71	4	(	(	PUNCT
ejpam-5621	71	5	xi	xi	PROPN
ejpam-5621	71	6	)	)	PUNCT
ejpam-5621	71	7	}	}	PUNCT
ejpam-5621	71	8	i∈n	i∈n	NOUN
ejpam-5621	71	9	,	,	PUNCT
ejpam-5621	71	10	xi	xi	PROPN
ejpam-5621	71	11	∈	∈	PROPN
ejpam-5621	71	12	a(λ	a(λ	PROPN
ejpam-5621	71	13	)	)	PUNCT
ejpam-5621	71	14	,	,	PUNCT
ejpam-5621	71	15	such	such	ADJ
ejpam-5621	71	16	that	that	SCONJ
ejpam-5621	71	17	0	0	NUM
ejpam-5621	71	18	<	<	X
ejpam-5621	71	19	pxi	pxi	NOUN
ejpam-5621	71	20	<	<	X
ejpam-5621	71	21	1	1	NUM
ejpam-5621	71	22	\	\	PROPN
ejpam-5621	71	23	25	25	NUM
ejpam-5621	71	24	.	.	PUNCT
ejpam-5621	72	1	and	and	CCONJ
ejpam-5621	72	2	(	(	PUNCT
ejpam-5621	72	3	∮	∮	NUM
ejpam-5621	72	4	b0	b0	VERB
ejpam-5621	72	5	i	i	PRON
ejpam-5621	72	6	|∇vm|p	|∇vm|p	PROPN
ejpam-5621	72	7	dx	dx	PROPN
ejpam-5621	72	8	)	)	PUNCT
ejpam-5621	72	9	1	1	NUM
ejpam-5621	73	1	p	p	NOUN
ejpam-5621	73	2	+	+	NOUN
ejpam-5621	73	3	1	1	NUM
ejpam-5621	73	4	δ	δ	PROPN
ejpam-5621	73	5	(	(	PUNCT
ejpam-5621	73	6	∮	∮	NUM
ejpam-5621	73	7	b0	b0	NOUN
ejpam-5621	73	8	i	i	PRON
ejpam-5621	73	9	|gm|q1	|gm|q1	NOUN
ejpam-5621	73	10	dx	dx	PROPN
ejpam-5621	73	11	)	)	PUNCT
ejpam-5621	73	12	1	1	NUM
ejpam-5621	73	13	q1	q1	NOUN
ejpam-5621	73	14	=	=	SYM
ejpam-5621	73	15	λ	λ	PROPN
ejpam-5621	73	16	.	.	PUNCT
ejpam-5621	74	1	furthermore	furthermore	ADV
ejpam-5621	74	2	,	,	PUNCT
ejpam-5621	74	3	we	we	PRON
ejpam-5621	74	4	have	have	VERB
ejpam-5621	74	5	e	e	X
ejpam-5621	74	6	(	(	PUNCT
ejpam-5621	74	7	λ	λ	X
ejpam-5621	74	8	)	)	PUNCT
ejpam-5621	74	9	⊂	⊂	PROPN
ejpam-5621	74	10	⋃	⋃	PROPN
ejpam-5621	74	11	i∈n	i∈n	NOUN
ejpam-5621	74	12	b1	b1	NOUN
ejpam-5621	74	13	i	i	PRON
ejpam-5621	74	14	,	,	PUNCT
ejpam-5621	74	15	where	where	SCONJ
ejpam-5621	74	16	bj	bj	VERB
ejpam-5621	74	17	i	i	PRON
ejpam-5621	74	18	=	=	NOUN
ejpam-5621	74	19	:	:	PUNCT
ejpam-5621	74	20	2j+2b0	2j+2b0	NUM
ejpam-5621	74	21	i	i	PRON
ejpam-5621	74	22	and	and	CCONJ
ejpam-5621	74	23	pxi	pxi	NOUN
ejpam-5621	74	24	<	<	X
ejpam-5621	74	25	s	s	X
ejpam-5621	74	26	<	<	X
ejpam-5621	74	27	1	1	NUM
ejpam-5621	74	28	for	for	ADP
ejpam-5621	74	29	all	all	PRON
ejpam-5621	74	30	i	i	PRON
ejpam-5621	74	31	values	value	VERB
ejpam-5621	74	32	1	1	NUM
ejpam-5621	74	33	,	,	PUNCT
ejpam-5621	74	34	2	2	NUM
ejpam-5621	74	35	,	,	PUNCT
ejpam-5621	74	36	and	and	CCONJ
ejpam-5621	74	37	3.(∮	3.(∮	NUM
ejpam-5621	74	38	bs(xi	bs(xi	ADJ
ejpam-5621	74	39	)	)	PUNCT
ejpam-5621	75	1	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	75	2	)	)	PUNCT
ejpam-5621	75	3	1	1	X
ejpam-5621	75	4	/	/	SYM
ejpam-5621	75	5	p	p	X
ejpam-5621	76	1	+	+	NOUN
ejpam-5621	76	2	1	1	NUM
ejpam-5621	76	3	δ	δ	PROPN
ejpam-5621	76	4	(	(	PUNCT
ejpam-5621	76	5	∮	∮	NUM
ejpam-5621	76	6	bs(xi	bs(xi	ADJ
ejpam-5621	76	7	)	)	PUNCT
ejpam-5621	76	8	|gm|q1dx	|gm|q1dx	NOUN
ejpam-5621	76	9	)	)	PUNCT
ejpam-5621	76	10	1	1	NUM
ejpam-5621	76	11	/	/	SYM
ejpam-5621	76	12	q1	q1	PROPN
ejpam-5621	76	13	≤	≤	NUM
ejpam-5621	76	14	λ	λ	PROPN
ejpam-5621	76	15	.	.	PUNCT
ejpam-5621	76	16	proof	proof	NOUN
ejpam-5621	76	17	.	.	PUNCT
ejpam-5621	77	1	(	(	PUNCT
ejpam-5621	77	2	i	i	NOUN
ejpam-5621	77	3	)	)	PUNCT
ejpam-5621	77	4	for	for	ADP
ejpam-5621	77	5	the	the	DET
ejpam-5621	77	6	sake	sake	NOUN
ejpam-5621	77	7	of	of	ADP
ejpam-5621	77	8	expediency	expediency	NOUN
ejpam-5621	77	9	,	,	PUNCT
ejpam-5621	77	10	we	we	PRON
ejpam-5621	77	11	signify	signify	VERB
ejpam-5621	77	12	:	:	PUNCT
ejpam-5621	77	13	j	j	PROPN
ejpam-5621	78	1	[	[	X
ejpam-5621	78	2	b	b	X
ejpam-5621	78	3	]	]	X
ejpam-5621	78	4	=	=	PUNCT
ejpam-5621	78	5	∮	∮	NOUN
ejpam-5621	78	6	b	b	X
ejpam-5621	78	7	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	78	8	1	1	NOUN
ejpam-5621	78	9	/	/	SYM
ejpam-5621	78	10	p	p	NOUN
ejpam-5621	78	11	+	+	NOUN
ejpam-5621	78	12	1	1	NUM
ejpam-5621	78	13	δ	δ	PROPN
ejpam-5621	78	14	∫	∫	NUM
ejpam-5621	78	15	b	b	PROPN
ejpam-5621	78	16	|gm|q1dx	|gm|q1dx	PRON
ejpam-5621	78	17	1	1	NOUN
ejpam-5621	78	18	/	/	SYM
ejpam-5621	78	19	q1	q1	PROPN
ejpam-5621	78	20	.	.	PUNCT
ejpam-5621	79	1	h.	h.	PROPN
ejpam-5621	79	2	ibrahim	ibrahim	PROPN
ejpam-5621	79	3	et	et	PROPN
ejpam-5621	79	4	al	al	PROPN
ejpam-5621	79	5	.	.	PUNCT
ejpam-5621	79	6	/	/	SYM
ejpam-5621	79	7	eur	eur	PROPN
ejpam-5621	79	8	.	.	PUNCT
ejpam-5621	80	1	j.	j.	PROPN
ejpam-5621	80	2	pure	pure	PROPN
ejpam-5621	80	3	appl	appl	PROPN
ejpam-5621	80	4	.	.	PROPN
ejpam-5621	80	5	math	math	PROPN
ejpam-5621	80	6	,	,	PUNCT
ejpam-5621	80	7	18	18	NUM
ejpam-5621	80	8	(	(	PUNCT
ejpam-5621	80	9	2	2	NUM
ejpam-5621	80	10	)	)	PUNCT
ejpam-5621	80	11	(	(	PUNCT
ejpam-5621	80	12	2025	2025	NUM
ejpam-5621	80	13	)	)	PUNCT
ejpam-5621	80	14	,	,	PUNCT
ejpam-5621	80	15	5621	5621	NUM
ejpam-5621	80	16	5	5	NUM
ejpam-5621	80	17	of	of	ADP
ejpam-5621	80	18	16	16	NUM
ejpam-5621	80	19	now	now	ADV
ejpam-5621	80	20	we	we	PRON
ejpam-5621	80	21	assert	assert	VERB
ejpam-5621	80	22	that	that	PRON
ejpam-5621	80	23	:	:	PUNCT
ejpam-5621	80	24	sup	sup	NOUN
ejpam-5621	80	25	ω∈b1	ω∈b1	VERB
ejpam-5621	80	26	sup	sup	PROPN
ejpam-5621	80	27	1/25≤λ≤1	1/25≤λ≤1	PROPN
ejpam-5621	80	28	j	j	PROPN
ejpam-5621	81	1	[	[	X
ejpam-5621	81	2	bp	bp	PROPN
ejpam-5621	81	3	(	(	PUNCT
ejpam-5621	81	4	ω	ω	NOUN
ejpam-5621	81	5	)	)	PUNCT
ejpam-5621	81	6	]	]	PUNCT
ejpam-5621	81	7	≤	≤	ADV
ejpam-5621	81	8	2	2	NUM
ejpam-5621	81	9	6n	6n	NOUN
ejpam-5621	81	10	p	p	NOUN
ejpam-5621	81	11	λ0	λ0	NOUN
ejpam-5621	81	12	=	=	NOUN
ejpam-5621	81	13	:	:	PUNCT
ejpam-5621	81	14	λ∗.	λ∗.	X
ejpam-5621	81	15	(	(	PUNCT
ejpam-5621	81	16	5	5	NUM
ejpam-5621	81	17	)	)	PUNCT
ejpam-5621	81	18	in	in	ADP
ejpam-5621	81	19	order	order	NOUN
ejpam-5621	81	20	to	to	PART
ejpam-5621	81	21	demonstrate	demonstrate	VERB
ejpam-5621	81	22	this	this	PRON
ejpam-5621	81	23	,	,	PUNCT
ejpam-5621	81	24	assign	assign	VERB
ejpam-5621	81	25	any	any	DET
ejpam-5621	81	26	ω	ω	NUM
ejpam-5621	81	27	∈	∈	PROPN
ejpam-5621	81	28	b1	b1	NOUN
ejpam-5621	81	29	and	and	CCONJ
ejpam-5621	81	30	1/25	1/25	NUM
ejpam-5621	81	31	≤	≤	NOUN
ejpam-5621	81	32	p	p	NOUN
ejpam-5621	81	33	≤	≤	NUM
ejpam-5621	81	34	1	1	NUM
ejpam-5621	81	35	.	.	PUNCT
ejpam-5621	81	36	from	from	ADP
ejpam-5621	81	37	the	the	DET
ejpam-5621	81	38	equation	equation	NOUN
ejpam-5621	81	39	bj	bj	ADP
ejpam-5621	81	40	i	i	NOUN
ejpam-5621	81	41	=	=	PROPN
ejpam-5621	82	1	2j+2b0	2j+2b0	NUM
ejpam-5621	82	2	i	i	PRON
ejpam-5621	82	3	:	:	PUNCT
ejpam-5621	82	4	j=1,2,3	j=1,2,3	NUM
ejpam-5621	82	5	,	,	PUNCT
ejpam-5621	82	6	we	we	PRON
ejpam-5621	82	7	get	get	VERB
ejpam-5621	82	8	that	that	DET
ejpam-5621	82	9	b2	b2	NOUN
ejpam-5621	82	10	=	=	SYM
ejpam-5621	82	11	25bp(ω	25bp(ω	PROPN
ejpam-5621	82	12	)	)	PUNCT
ejpam-5621	82	13	.	.	PUNCT
ejpam-5621	83	1	and	and	CCONJ
ejpam-5621	83	2	we	we	PRON
ejpam-5621	83	3	can	can	AUX
ejpam-5621	83	4	easily	easily	ADV
ejpam-5621	83	5	see	see	VERB
ejpam-5621	83	6	that	that	PRON
ejpam-5621	83	7	:	:	PUNCT
ejpam-5621	83	8	(	(	PUNCT
ejpam-5621	83	9	|b2|	|b2|	NOUN
ejpam-5621	83	10	|bp	|bp	NOUN
ejpam-5621	83	11	(	(	PUNCT
ejpam-5621	83	12	ω)|	ω)|	ADJ
ejpam-5621	83	13	)	)	PUNCT
ejpam-5621	83	14	1	1	NUM
ejpam-5621	83	15	p	p	NOUN
ejpam-5621	83	16	≤	≤	NUM
ejpam-5621	83	17	2	2	NUM
ejpam-5621	83	18	5	5	NUM
ejpam-5621	83	19	p	p	NOUN
ejpam-5621	83	20	≤	≤	NUM
ejpam-5621	83	21	2	2	NUM
ejpam-5621	83	22	6n	6n	NOUN
ejpam-5621	83	23	p	p	NOUN
ejpam-5621	83	24	,	,	PUNCT
ejpam-5621	83	25	n	n	NOUN
ejpam-5621	83	26	=	=	SYM
ejpam-5621	83	27	1	1	NUM
ejpam-5621	83	28	,	,	PUNCT
ejpam-5621	83	29	2	2	NUM
ejpam-5621	83	30	,	,	PUNCT
ejpam-5621	83	31	...	...	PUNCT
ejpam-5621	83	32	.	.	PUNCT
ejpam-5621	84	1	(	(	PUNCT
ejpam-5621	84	2	6	6	NUM
ejpam-5621	84	3	)	)	PUNCT
ejpam-5621	84	4	then	then	ADV
ejpam-5621	84	5	by	by	ADP
ejpam-5621	84	6	using	use	VERB
ejpam-5621	84	7	equations	equation	NOUN
ejpam-5621	84	8	(	(	PUNCT
ejpam-5621	84	9	4	4	NUM
ejpam-5621	84	10	)	)	PUNCT
ejpam-5621	84	11	,	,	PUNCT
ejpam-5621	84	12	(	(	PUNCT
ejpam-5621	84	13	5	5	NUM
ejpam-5621	84	14	)	)	PUNCT
ejpam-5621	84	15	and	and	CCONJ
ejpam-5621	84	16	(	(	PUNCT
ejpam-5621	84	17	6	6	X
ejpam-5621	84	18	)	)	PUNCT
ejpam-5621	84	19	we	we	PRON
ejpam-5621	84	20	can	can	AUX
ejpam-5621	84	21	deduce	deduce	VERB
ejpam-5621	84	22	that:(∮	that:(∮	ADP
ejpam-5621	84	23	bp(ω	bp(ω	NOUN
ejpam-5621	84	24	)	)	PUNCT
ejpam-5621	84	25	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	84	26	)	)	PUNCT
ejpam-5621	85	1	1	1	NUM
ejpam-5621	85	2	/	/	SYM
ejpam-5621	85	3	p	p	NOUN
ejpam-5621	85	4	≤	≤	NOUN
ejpam-5621	85	5	(	(	PUNCT
ejpam-5621	85	6	|b2|	|b2|	NOUN
ejpam-5621	85	7	|bp(ω)|	|bp(ω)|	PROPN
ejpam-5621	85	8	1	1	NUM
ejpam-5621	85	9	p	p	NOUN
ejpam-5621	85	10	(	(	PUNCT
ejpam-5621	85	11	∮	∮	NUM
ejpam-5621	85	12	b2	b2	NOUN
ejpam-5621	85	13	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	85	14	)	)	PUNCT
ejpam-5621	85	15	1	1	NUM
ejpam-5621	85	16	p	p	NOUN
ejpam-5621	85	17	≤	≤	NOUN
ejpam-5621	85	18	26n	26n	NUM
ejpam-5621	85	19	/	/	SYM
ejpam-5621	85	20	p	p	X
ejpam-5621	85	21	(	(	PUNCT
ejpam-5621	85	22	∮	∮	NUM
ejpam-5621	85	23	b2	b2	NOUN
ejpam-5621	85	24	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	85	25	)	)	PUNCT
ejpam-5621	85	26	1	1	NUM
ejpam-5621	85	27	p	p	NOUN
ejpam-5621	85	28	.	.	PUNCT
ejpam-5621	86	1	in	in	ADP
ejpam-5621	86	2	a	a	DET
ejpam-5621	86	3	similar	similar	ADJ
ejpam-5621	86	4	fashion	fashion	NOUN
ejpam-5621	86	5	,	,	PUNCT
ejpam-5621	86	6	we	we	PRON
ejpam-5621	86	7	have(∮	have(∮	VERB
ejpam-5621	86	8	br	br	PROPN
ejpam-5621	86	9	(	(	PUNCT
ejpam-5621	86	10	ω	ω	NOUN
ejpam-5621	86	11	)	)	PUNCT
ejpam-5621	86	12	|gm|q1	|gm|q1	NOUN
ejpam-5621	86	13	dy	dy	NOUN
ejpam-5621	86	14	)	)	PUNCT
ejpam-5621	86	15	1	1	NUM
ejpam-5621	86	16	q1	q1	NOUN
ejpam-5621	86	17	≤	≤	NUM
ejpam-5621	86	18	2	2	NUM
ejpam-5621	86	19	6n	6n	PROPN
ejpam-5621	86	20	q1	q1	PROPN
ejpam-5621	86	21	(	(	PUNCT
ejpam-5621	86	22	∮	∮	NUM
ejpam-5621	86	23	b2	b2	NOUN
ejpam-5621	86	24	|gm|q1	|gm|q1	NOUN
ejpam-5621	86	25	dx	dx	PROPN
ejpam-5621	86	26	)	)	PUNCT
ejpam-5621	86	27	1	1	NUM
ejpam-5621	86	28	q1	q1	NOUN
ejpam-5621	86	29	.	.	PUNCT
ejpam-5621	87	1	as	as	ADP
ejpam-5621	87	2	a	a	DET
ejpam-5621	87	3	result	result	NOUN
ejpam-5621	87	4	of	of	ADP
ejpam-5621	87	5	combining	combine	VERB
ejpam-5621	87	6	the	the	DET
ejpam-5621	87	7	aforementioned	aforementioned	ADJ
ejpam-5621	87	8	two	two	NUM
ejpam-5621	87	9	inequalities	inequality	NOUN
ejpam-5621	87	10	with	with	ADP
ejpam-5621	87	11	the	the	DET
ejpam-5621	87	12	definitions	definition	NOUN
ejpam-5621	87	13	of	of	ADP
ejpam-5621	87	14	λ0	λ0	NOUN
ejpam-5621	87	15	and	and	CCONJ
ejpam-5621	87	16	q1	q1	PROPN
ejpam-5621	87	17	,	,	PUNCT
ejpam-5621	87	18	we	we	PRON
ejpam-5621	87	19	can	can	AUX
ejpam-5621	87	20	conclude	conclude	VERB
ejpam-5621	87	21	that	that	PRON
ejpam-5621	87	22	(	(	PUNCT
ejpam-5621	87	23	4	4	X
ejpam-5621	87	24	)	)	PUNCT
ejpam-5621	87	25	is	be	AUX
ejpam-5621	87	26	valid	valid	ADJ
ejpam-5621	87	27	.	.	PUNCT
ejpam-5621	88	1	(	(	PUNCT
ejpam-5621	88	2	ii	ii	NOUN
ejpam-5621	88	3	)	)	PUNCT
ejpam-5621	88	4	define	define	VERB
ejpam-5621	88	5	λ0	λ0	NOUN
ejpam-5621	88	6	as	as	ADP
ejpam-5621	88	7	λ	λ	PROPN
ejpam-5621	88	8	≥	≥	NOUN
ejpam-5621	88	9	λ∗	λ∗	NOUN
ejpam-5621	88	10	=	=	X
ejpam-5621	88	11	26n	26n	X
ejpam-5621	88	12	/	/	SYM
ejpam-5621	88	13	pλ0	pλ0	NOUN
ejpam-5621	88	14	.	.	PUNCT
ejpam-5621	89	1	in	in	ADP
ejpam-5621	89	2	the	the	DET
ejpam-5621	89	3	case	case	NOUN
ejpam-5621	89	4	of	of	ADP
ejpam-5621	89	5	ω	ω	PROPN
ejpam-5621	89	6	∈	∈	PROPN
ejpam-5621	89	7	a(λ	a(λ	PROPN
ejpam-5621	89	8	)	)	PUNCT
ejpam-5621	89	9	,	,	PUNCT
ejpam-5621	89	10	a	a	DET
ejpam-5621	89	11	variant	variant	NOUN
ejpam-5621	89	12	of	of	ADP
ejpam-5621	89	13	lebesgue	lebesgue	NOUN
ejpam-5621	89	14	’s	’s	PART
ejpam-5621	89	15	differentiation	differentiation	NOUN
ejpam-5621	89	16	theorem	theorem	NOUN
ejpam-5621	89	17	provides	provide	VERB
ejpam-5621	89	18	the	the	DET
ejpam-5621	89	19	following	following	NOUN
ejpam-5621	89	20	:	:	PUNCT
ejpam-5621	90	1	lim	lim	PROPN
ejpam-5621	90	2	p→0	p→0	PROPN
ejpam-5621	90	3	j	j	PROPN
ejpam-5621	91	1	[	[	X
ejpam-5621	91	2	bp	bp	PROPN
ejpam-5621	91	3	(	(	PUNCT
ejpam-5621	91	4	ω	ω	NOUN
ejpam-5621	91	5	)	)	PUNCT
ejpam-5621	91	6	]	]	PUNCT
ejpam-5621	91	7	>	>	X
ejpam-5621	91	8	λ	λ	PROPN
ejpam-5621	91	9	.	.	PROPN
ejpam-5621	91	10	which	which	PRON
ejpam-5621	91	11	indicates	indicate	VERB
ejpam-5621	91	12	the	the	DET
ejpam-5621	91	13	existence	existence	NOUN
ejpam-5621	91	14	of	of	ADP
ejpam-5621	91	15	a	a	DET
ejpam-5621	91	16	p	p	X
ejpam-5621	91	17	>	>	X
ejpam-5621	91	18	0	0	NUM
ejpam-5621	91	19	that	that	PRON
ejpam-5621	91	20	satisfies	satisfy	VERB
ejpam-5621	91	21	j	j	PROPN
ejpam-5621	92	1	[	[	X
ejpam-5621	92	2	bp	bp	PROPN
ejpam-5621	92	3	(	(	PUNCT
ejpam-5621	92	4	ω	ω	NOUN
ejpam-5621	92	5	)	)	PUNCT
ejpam-5621	92	6	]	]	PUNCT
ejpam-5621	92	7	>	>	X
ejpam-5621	92	8	λ	λ	X
ejpam-5621	92	9	.	.	PUNCT
ejpam-5621	92	10	consequently	consequently	ADV
ejpam-5621	92	11	,	,	PUNCT
ejpam-5621	92	12	starting	start	VERB
ejpam-5621	92	13	from	from	ADP
ejpam-5621	92	14	step	step	NOUN
ejpam-5621	92	15	(	(	PUNCT
ejpam-5621	92	16	i	i	NOUN
ejpam-5621	92	17	)	)	PUNCT
ejpam-5621	92	18	,	,	PUNCT
ejpam-5621	92	19	we	we	PRON
ejpam-5621	92	20	can	can	AUX
ejpam-5621	92	21	choose	choose	VERB
ejpam-5621	92	22	a	a	DET
ejpam-5621	92	23	radius	radius	NOUN
ejpam-5621	92	24	pω	pω	X
ejpam-5621	92	25	∈	∈	PROPN
ejpam-5621	92	26	(	(	PUNCT
ejpam-5621	92	27	0	0	NUM
ejpam-5621	92	28	,	,	PUNCT
ejpam-5621	92	29	1/25	1/25	NUM
ejpam-5621	92	30	]	]	PUNCT
ejpam-5621	93	1	[	[	X
ejpam-5621	93	2	8	8	NUM
ejpam-5621	93	3	]	]	PUNCT
ejpam-5621	93	4	,	,	PUNCT
ejpam-5621	93	5	and	and	CCONJ
ejpam-5621	93	6	such	such	ADJ
ejpam-5621	93	7	that	that	DET
ejpam-5621	93	8	j	j	PROPN
ejpam-5621	94	1	[	[	X
ejpam-5621	94	2	bpw	bpw	PROPN
ejpam-5621	94	3	(	(	PUNCT
ejpam-5621	94	4	ω	ω	NOUN
ejpam-5621	94	5	)	)	PUNCT
ejpam-5621	94	6	]	]	PUNCT
ejpam-5621	95	1	=	=	PUNCT
ejpam-5621	95	2	λ	λ	X
ejpam-5621	95	3	.	.	PUNCT
ejpam-5621	96	1	furthermore	furthermore	ADV
ejpam-5621	96	2	,	,	PUNCT
ejpam-5621	96	3	that	that	PRON
ejpam-5621	96	4	for	for	ADP
ejpam-5621	96	5	pω	pω	NOUN
ejpam-5621	96	6	<	<	X
ejpam-5621	96	7	p	p	X
ejpam-5621	96	8	≤	≤	ADJ
ejpam-5621	96	9	1	1	NUM
ejpam-5621	96	10	and	and	CCONJ
ejpam-5621	96	11	j	j	PROPN
ejpam-5621	97	1	[	[	X
ejpam-5621	97	2	bp	bp	PROPN
ejpam-5621	97	3	(	(	PUNCT
ejpam-5621	97	4	ω	ω	NOUN
ejpam-5621	97	5	)	)	PUNCT
ejpam-5621	97	6	]	]	PUNCT
ejpam-5621	98	1	<	<	X
ejpam-5621	98	2	λ	λ	X
ejpam-5621	98	3	.	.	PROPN
ejpam-5621	98	4	based	base	VERB
ejpam-5621	98	5	on	on	ADP
ejpam-5621	98	6	the	the	DET
ejpam-5621	98	7	aforementioned	aforementione	VERB
ejpam-5621	98	8	argument	argument	NOUN
ejpam-5621	98	9	for	for	ADP
ejpam-5621	98	10	.	.	PUNCT
ejpam-5621	99	1	ω	ω	PROPN
ejpam-5621	99	2	∈	∈	PROPN
ejpam-5621	99	3	a(λ	a(λ	PROPN
ejpam-5621	99	4	)	)	PUNCT
ejpam-5621	99	5	,	,	PUNCT
ejpam-5621	99	6	the	the	DET
ejpam-5621	99	7	ball	ball	NOUN
ejpam-5621	99	8	bpω(ω	bpω(ω	PROPN
ejpam-5621	99	9	)	)	PUNCT
ejpam-5621	99	10	can	can	AUX
ejpam-5621	99	11	be	be	AUX
ejpam-5621	99	12	constructed	construct	VERB
ejpam-5621	99	13	as	as	ADP
ejpam-5621	99	14	described	describe	VERB
ejpam-5621	99	15	above	above	ADV
ejpam-5621	99	16	.	.	PUNCT
ejpam-5621	100	1	hence	hence	ADV
ejpam-5621	100	2	,	,	PUNCT
ejpam-5621	100	3	by	by	ADP
ejpam-5621	100	4	employing	employ	VERB
ejpam-5621	100	5	vitali	vitali	PROPN
ejpam-5621	100	6	’s	’s	PART
ejpam-5621	100	7	covering	cover	VERB
ejpam-5621	100	8	lemma	lemma	PROPN
ejpam-5621	100	9	,	,	PUNCT
ejpam-5621	100	10	it	it	PRON
ejpam-5621	100	11	is	be	AUX
ejpam-5621	100	12	possible	possible	ADJ
ejpam-5621	100	13	to	to	PART
ejpam-5621	100	14	identify	identify	VERB
ejpam-5621	100	15	a	a	DET
ejpam-5621	100	16	set	set	NOUN
ejpam-5621	100	17	of	of	ADP
ejpam-5621	100	18	disjoint	disjoint	NOUN
ejpam-5621	100	19	orbs	orbs	NOUN
ejpam-5621	100	20	denoted	denote	VERB
ejpam-5621	100	21	as	as	ADP
ejpam-5621	100	22	{	{	PUNCT
ejpam-5621	100	23	b0	b0	NOUN
ejpam-5621	100	24	i	i	PRON
ejpam-5621	100	25	}	}	PUNCT
ejpam-5621	100	26	i∈n	i∈n	NOUN
ejpam-5621	100	27	=	=	PRON
ejpam-5621	100	28	{	{	PUNCT
ejpam-5621	100	29	bpxi	bpxi	PROPN
ejpam-5621	100	30	(	(	PUNCT
ejpam-5621	100	31	xi)}i∈n	xi)}i∈n	PROPN
ejpam-5621	100	32	where	where	SCONJ
ejpam-5621	100	33	xi	xi	PROPN
ejpam-5621	100	34	∈	∈	PROPN
ejpam-5621	100	35	a(λ	a(λ	ADV
ejpam-5621	100	36	)	)	PUNCT
ejpam-5621	100	37	in	in	ADP
ejpam-5621	100	38	order	order	NOUN
ejpam-5621	100	39	to	to	PART
ejpam-5621	100	40	validate	validate	VERB
ejpam-5621	100	41	the	the	DET
ejpam-5621	100	42	lemma	lemma	PROPN
ejpam-5621	100	43	’s	’s	PART
ejpam-5621	100	44	conclusions	conclusion	NOUN
ejpam-5621	100	45	.	.	PUNCT
ejpam-5621	101	1	we	we	PRON
ejpam-5621	101	2	now	now	ADV
ejpam-5621	101	3	have	have	VERB
ejpam-5621	101	4	a	a	DET
ejpam-5621	101	5	comprehensive	comprehensive	ADJ
ejpam-5621	101	6	proof	proof	NOUN
ejpam-5621	101	7	.	.	PUNCT
ejpam-5621	102	1	at	at	ADP
ejpam-5621	102	2	present	present	ADJ
ejpam-5621	102	3	,	,	PUNCT
ejpam-5621	102	4	the	the	DET
ejpam-5621	102	5	subsequent	subsequent	ADJ
ejpam-5621	102	6	estimates	estimate	NOUN
ejpam-5621	102	7	of	of	ADP
ejpam-5621	102	8	spheres	sphere	NOUN
ejpam-5621	102	9	{	{	PUNCT
ejpam-5621	102	10	b0	b0	NOUN
ejpam-5621	102	11	i	i	PRON
ejpam-5621	102	12	}	}	PUNCT
ejpam-5621	102	13	are	be	AUX
ejpam-5621	102	14	obtained	obtain	VERB
ejpam-5621	102	15	.	.	PUNCT
ejpam-5621	103	1	h.	h.	PROPN
ejpam-5621	103	2	ibrahim	ibrahim	PROPN
ejpam-5621	103	3	et	et	PROPN
ejpam-5621	103	4	al	al	PROPN
ejpam-5621	103	5	.	.	PUNCT
ejpam-5621	103	6	/	/	SYM
ejpam-5621	103	7	eur	eur	PROPN
ejpam-5621	103	8	.	.	PUNCT
ejpam-5621	104	1	j.	j.	PROPN
ejpam-5621	104	2	pure	pure	PROPN
ejpam-5621	104	3	appl	appl	PROPN
ejpam-5621	104	4	.	.	PROPN
ejpam-5621	104	5	math	math	PROPN
ejpam-5621	104	6	,	,	PUNCT
ejpam-5621	104	7	18	18	NUM
ejpam-5621	104	8	(	(	PUNCT
ejpam-5621	104	9	2	2	NUM
ejpam-5621	104	10	)	)	PUNCT
ejpam-5621	104	11	(	(	PUNCT
ejpam-5621	104	12	2025	2025	NUM
ejpam-5621	104	13	)	)	PUNCT
ejpam-5621	104	14	,	,	PUNCT
ejpam-5621	104	15	5621	5621	NUM
ejpam-5621	104	16	6	6	NUM
ejpam-5621	104	17	of	of	ADP
ejpam-5621	104	18	16	16	NUM
ejpam-5621	104	19	lemma	lemma	PROPN
ejpam-5621	104	20	4	4	NUM
ejpam-5621	104	21	.	.	PUNCT
ejpam-5621	105	1	by	by	ADP
ejpam-5621	105	2	employing	employ	VERB
ejpam-5621	105	3	the	the	DET
ejpam-5621	105	4	identical	identical	ADJ
ejpam-5621	105	5	hypothesis	hypothesis	NOUN
ejpam-5621	105	6	and	and	CCONJ
ejpam-5621	105	7	outcomes	outcome	NOUN
ejpam-5621	105	8	as	as	ADP
ejpam-5621	105	9	in	in	ADP
ejpam-5621	105	10	lemma	lemma	PROPN
ejpam-5621	105	11	(	(	PUNCT
ejpam-5621	105	12	6	6	NUM
ejpam-5621	105	13	)	)	PUNCT
ejpam-5621	105	14	,	,	PUNCT
ejpam-5621	105	15	we	we	PRON
ejpam-5621	105	16	obtain	obtain	VERB
ejpam-5621	105	17	∣∣b0	∣∣b0	NOUN
ejpam-5621	105	18	i	i	PRON
ejpam-5621	105	19	∣∣	∣∣	VERB
ejpam-5621	106	1	≤	≤	ADV
ejpam-5621	106	2	c	c	NOUN
ejpam-5621	106	3	(	(	PUNCT
ejpam-5621	106	4	1	1	NUM
ejpam-5621	106	5	λp	λp	X
ejpam-5621	106	6	∫	∫	PROPN
ejpam-5621	106	7	{	{	PUNCT
ejpam-5621	106	8	x∈b0	x∈b0	PROPN
ejpam-5621	106	9	i	i	PRON
ejpam-5621	106	10	:	:	PUNCT
ejpam-5621	106	11	|∇vm|>λ	|∇vm|>λ	X
ejpam-5621	106	12	4	4	NUM
ejpam-5621	106	13	}	}	SYM
ejpam-5621	106	14	|∇vm|pdx+	|∇vm|pdx+	NUM
ejpam-5621	106	15	1	1	NUM
ejpam-5621	106	16	λq1δq1	λq1δq1	ADJ
ejpam-5621	106	17	∫	∫	PROPN
ejpam-5621	106	18	{	{	PUNCT
ejpam-5621	106	19	x∈b0	x∈b0	PROPN
ejpam-5621	107	1	i	i	PRON
ejpam-5621	107	2	:	:	PUNCT
ejpam-5621	107	3	|f	|f	PROPN
ejpam-5621	107	4	|	|	ADV
ejpam-5621	107	5	>	>	X
ejpam-5621	107	6	δλ	δλ	PROPN
ejpam-5621	107	7	4	4	NUM
ejpam-5621	107	8	}	}	PUNCT
ejpam-5621	107	9	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	107	10	)	)	PUNCT
ejpam-5621	107	11	,	,	PUNCT
ejpam-5621	107	12	where	where	SCONJ
ejpam-5621	107	13	c	c	NOUN
ejpam-5621	107	14	=	=	SYM
ejpam-5621	107	15	c(p	c(p	PROPN
ejpam-5621	107	16	,	,	PUNCT
ejpam-5621	107	17	q1	q1	PROPN
ejpam-5621	107	18	)	)	PUNCT
ejpam-5621	107	19	=	=	SYM
ejpam-5621	107	20	2q1/[1−	2q1/[1−	NOUN
ejpam-5621	107	21	(	(	PUNCT
ejpam-5621	107	22	1/2)p	1/2)p	NUM
ejpam-5621	107	23	−	−	NOUN
ejpam-5621	107	24	(	(	PUNCT
ejpam-5621	107	25	1/2)q1	1/2)q1	X
ejpam-5621	107	26	]	]	PUNCT
ejpam-5621	107	27	.	.	PUNCT
ejpam-5621	108	1	proof	proof	NOUN
ejpam-5621	108	2	.	.	PUNCT
ejpam-5621	109	1	as	as	SCONJ
ejpam-5621	109	2	shown	show	VERB
ejpam-5621	109	3	in	in	ADP
ejpam-5621	109	4	the	the	DET
ejpam-5621	109	5	lemma	lemma	PROPN
ejpam-5621	109	6	above,(∫	above,(∫	PROPN
ejpam-5621	109	7	b0	b0	PROPN
ejpam-5621	109	8	i	i	PRON
ejpam-5621	109	9	|∇vm|pdx+	|∇vm|pdx+	NOUN
ejpam-5621	109	10	1	1	NUM
ejpam-5621	109	11	δ	δ	NOUN
ejpam-5621	109	12	∫	∫	PROPN
ejpam-5621	109	13	b0	b0	NOUN
ejpam-5621	109	14	i	i	PRON
ejpam-5621	109	15	|gm|1	|gm|1	PUNCT
ejpam-5621	109	16	/	/	SYM
ejpam-5621	109	17	q1dx	q1dx	NOUN
ejpam-5621	109	18	)	)	PUNCT
ejpam-5621	110	1	=	=	SYM
ejpam-5621	110	2	λ	λ	NOUN
ejpam-5621	110	3	,	,	PUNCT
ejpam-5621	110	4	thus	thus	ADV
ejpam-5621	110	5	,	,	PUNCT
ejpam-5621	110	6	signifying	signify	VERB
ejpam-5621	110	7	that	that	DET
ejpam-5621	110	8	|b0	|b0	NOUN
ejpam-5621	111	1	i	i	PRON
ejpam-5621	111	2	|	|	ADV
ejpam-5621	111	3	≤	≤	NUM
ejpam-5621	111	4	2p	2p	NOUN
ejpam-5621	111	5	λp	λp	X
ejpam-5621	111	6	∫	∫	PROPN
ejpam-5621	111	7	b0	b0	PROPN
ejpam-5621	111	8	i	i	PRON
ejpam-5621	111	9	|∇vm|pdx+	|∇vm|pdx+	NOUN
ejpam-5621	111	10	2q1	2q1	NUM
ejpam-5621	111	11	λq1δq1	λq1δq1	ADJ
ejpam-5621	111	12	∫	∫	PROPN
ejpam-5621	111	13	b0	b0	PROPN
ejpam-5621	111	14	i	i	PRON
ejpam-5621	111	15	|gm|	|gm|	PROPN
ejpam-5621	111	16	1	1	NUM
ejpam-5621	111	17	q1	q1	PROPN
ejpam-5621	111	18	dx	dx	PROPN
ejpam-5621	111	19	(	(	PUNCT
ejpam-5621	111	20	7	7	NUM
ejpam-5621	111	21	)	)	PUNCT
ejpam-5621	111	22	given	give	VERB
ejpam-5621	111	23	that	that	DET
ejpam-5621	111	24	one	one	NUM
ejpam-5621	111	25	of	of	ADP
ejpam-5621	111	26	the	the	DET
ejpam-5621	111	27	subsequent	subsequent	ADJ
ejpam-5621	111	28	inequalities	inequality	NOUN
ejpam-5621	111	29	must	must	AUX
ejpam-5621	111	30	hold	hold	VERB
ejpam-5621	111	31	true	true	ADJ
ejpam-5621	111	32	:	:	PUNCT
ejpam-5621	111	33	λ/2	λ/2	NUM
ejpam-5621	111	34	≤	≤	NUM
ejpam-5621	111	35	(	(	PUNCT
ejpam-5621	111	36	∫	∫	PROPN
ejpam-5621	111	37	b0	b0	NOUN
ejpam-5621	111	38	i	i	PROPN
ejpam-5621	111	39	|∇vm|pdx	|∇vm|pdx	NOUN
ejpam-5621	111	40	)	)	PUNCT
ejpam-5621	111	41	1	1	NUM
ejpam-5621	111	42	p	p	NOUN
ejpam-5621	111	43	,	,	PUNCT
ejpam-5621	111	44	or	or	CCONJ
ejpam-5621	111	45	λ/2	λ/2	NUM
ejpam-5621	111	46	≤	≤	NUM
ejpam-5621	111	47	1	1	NUM
ejpam-5621	111	48	δ	δ	PROPN
ejpam-5621	111	49	(	(	PUNCT
ejpam-5621	111	50	∫	∫	PROPN
ejpam-5621	111	51	b0	b0	NOUN
ejpam-5621	111	52	i	i	PRON
ejpam-5621	111	53	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	111	54	)	)	PUNCT
ejpam-5621	111	55	1	1	NUM
ejpam-5621	111	56	q1	q1	NOUN
ejpam-5621	111	57	.	.	PUNCT
ejpam-5621	112	1	as	as	ADP
ejpam-5621	112	2	a	a	DET
ejpam-5621	112	3	result	result	NOUN
ejpam-5621	112	4	,	,	PUNCT
ejpam-5621	112	5	we	we	PRON
ejpam-5621	112	6	obtain	obtain	VERB
ejpam-5621	112	7	the	the	DET
ejpam-5621	112	8	following	following	NOUN
ejpam-5621	112	9	by	by	ADP
ejpam-5621	112	10	dividing	divide	VERB
ejpam-5621	112	11	the	the	DET
ejpam-5621	112	12	right	right	ADJ
ejpam-5621	112	13	-	-	PUNCT
ejpam-5621	112	14	hand	hand	NOUN
ejpam-5621	112	15	side	side	NOUN
ejpam-5621	112	16	of	of	ADP
ejpam-5621	112	17	equation	equation	NOUN
ejpam-5621	112	18	(	(	PUNCT
ejpam-5621	112	19	6	6	NUM
ejpam-5621	112	20	)	)	PUNCT
ejpam-5621	112	21	into	into	ADP
ejpam-5621	112	22	two	two	NUM
ejpam-5621	112	23	integrals	integral	NOUN
ejpam-5621	112	24	:	:	PUNCT
ejpam-5621	112	25	∣∣b0	∣∣b0	NOUN
ejpam-5621	112	26	i	i	PRON
ejpam-5621	112	27	∣∣	∣∣	VERB
ejpam-5621	112	28	≤	≤	ADV
ejpam-5621	112	29	c	c	NOUN
ejpam-5621	112	30	(	(	PUNCT
ejpam-5621	112	31	2p	2p	NOUN
ejpam-5621	112	32	λp	λp	ADP
ejpam-5621	112	33	∮	∮	NUM
ejpam-5621	112	34	{	{	PUNCT
ejpam-5621	112	35	x∈b0	x∈b0	NOUN
ejpam-5621	112	36	i	i	PRON
ejpam-5621	112	37	:	:	PUNCT
ejpam-5621	112	38	|∇vm|>λ/4	|∇vm|>λ/4	PROPN
ejpam-5621	112	39	}	}	PUNCT
ejpam-5621	112	40	|∇vm|p	|∇vm|p	ADJ
ejpam-5621	112	41	dx+	dx+	NOUN
ejpam-5621	112	42	(	(	PUNCT
ejpam-5621	112	43	1/2)q1	1/2)q1	ADV
ejpam-5621	112	44	∣∣b0	∣∣b0	NOUN
ejpam-5621	112	45	i	i	PRON
ejpam-5621	112	46	∣∣	∣∣	VERB
ejpam-5621	112	47	)	)	PUNCT
ejpam-5621	113	1	+	+	CCONJ
ejpam-5621	113	2	2q1	2q1	NUM
ejpam-5621	113	3	λq1δq1	λq1δq1	ADJ
ejpam-5621	113	4	∫	∫	PROPN
ejpam-5621	113	5	{	{	PUNCT
ejpam-5621	113	6	x∈b0	x∈b0	PROPN
ejpam-5621	114	1	i	i	PRON
ejpam-5621	114	2	:	:	PUNCT
ejpam-5621	114	3	|f	|f	PROPN
ejpam-5621	114	4	|>δλ/4	|>δλ/4	PROPN
ejpam-5621	114	5	}	}	PUNCT
ejpam-5621	114	6	|gm|q1	|gm|q1	NUM
ejpam-5621	114	7	dx+	dx+	NOUN
ejpam-5621	114	8	(	(	PUNCT
ejpam-5621	114	9	1/2)q1	1/2)q1	ADV
ejpam-5621	114	10	∣∣b0	∣∣b0	NOUN
ejpam-5621	114	11	i	i	PRON
ejpam-5621	114	12	∣∣	∣∣	NUM
ejpam-5621	114	13	we	we	PRON
ejpam-5621	114	14	have	have	AUX
ejpam-5621	114	15	therefore	therefore	ADV
ejpam-5621	114	16	arrived	arrive	VERB
ejpam-5621	114	17	at	at	ADP
ejpam-5621	114	18	the	the	DET
ejpam-5621	114	19	intended	intend	VERB
ejpam-5621	114	20	estimation	estimation	NOUN
ejpam-5621	114	21	.	.	PUNCT
ejpam-5621	115	1	it	it	PRON
ejpam-5621	115	2	is	be	AUX
ejpam-5621	115	3	adequate	adequate	ADJ
ejpam-5621	115	4	to	to	PART
ejpam-5621	115	5	regard	regard	VERB
ejpam-5621	115	6	the	the	DET
ejpam-5621	115	7	proof	proof	NOUN
ejpam-5621	115	8	of	of	ADP
ejpam-5621	115	9	theorem	theorem	NOUN
ejpam-5621	115	10	1	1	NUM
ejpam-5621	115	11	in	in	ADP
ejpam-5621	115	12	section	section	NOUN
ejpam-5621	115	13	four	four	NUM
ejpam-5621	115	14	as	as	ADP
ejpam-5621	115	15	an	an	DET
ejpam-5621	115	16	a	a	DET
ejpam-5621	115	17	priori	priori	ADJ
ejpam-5621	115	18	estimate	estimate	NOUN
ejpam-5621	115	19	in	in	ADP
ejpam-5621	115	20	the	the	DET
ejpam-5621	115	21	subsequent	subsequent	ADJ
ejpam-5621	115	22	discussion	discussion	NOUN
ejpam-5621	115	23	,	,	PUNCT
ejpam-5621	115	24	thus	thus	ADV
ejpam-5621	115	25	presuming	presume	VERB
ejpam-5621	115	26	that	that	SCONJ
ejpam-5621	115	27	∇vm	∇vm	PROPN
ejpam-5621	115	28	∈	∈	PROPN
ejpam-5621	115	29	lq	lq	ADP
ejpam-5621	115	30	loc	loc	PROPN
ejpam-5621	115	31	(	(	PUNCT
ejpam-5621	115	32	ω	ω	NOUN
ejpam-5621	115	33	)	)	PUNCT
ejpam-5621	115	34	.	.	PUNCT
ejpam-5621	116	1	one	one	PRON
ejpam-5621	116	2	can	can	AUX
ejpam-5621	116	3	easily	easily	ADV
ejpam-5621	116	4	eliminate	eliminate	VERB
ejpam-5621	116	5	this	this	DET
ejpam-5621	116	6	assumption	assumption	NOUN
ejpam-5621	116	7	using	use	VERB
ejpam-5621	116	8	a	a	DET
ejpam-5621	116	9	standard	standard	ADJ
ejpam-5621	116	10	approximation	approximation	NOUN
ejpam-5621	116	11	argument	argument	NOUN
ejpam-5621	116	12	,	,	PUNCT
ejpam-5621	116	13	such	such	ADJ
ejpam-5621	116	14	as	as	ADP
ejpam-5621	116	15	the	the	DET
ejpam-5621	116	16	one	one	NOUN
ejpam-5621	116	17	presented	present	VERB
ejpam-5621	116	18	in	in	ADP
ejpam-5621	116	19	[	[	X
ejpam-5621	116	20	12	12	NUM
ejpam-5621	116	21	,	,	PUNCT
ejpam-5621	116	22	13	13	NUM
ejpam-5621	116	23	]	]	PUNCT
ejpam-5621	116	24	.	.	PUNCT
ejpam-5621	117	1	by	by	ADP
ejpam-5621	117	2	considering	consider	VERB
ejpam-5621	117	3	lemma	lemma	PROPN
ejpam-5621	117	4	3	3	NUM
ejpam-5621	117	5	and	and	CCONJ
ejpam-5621	117	6	λ	λ	PROPN
ejpam-5621	117	7	≥	≥	NOUN
ejpam-5621	117	8	λ∗	λ∗	NOUN
ejpam-5621	117	9	=	=	NOUN
ejpam-5621	117	10	2	2	NUM
ejpam-5621	117	11	6n	6n	NOUN
ejpam-5621	117	12	p	p	X
ejpam-5621	117	13	·	·	PUNCT
ejpam-5621	117	14	λ0	λ0	NOUN
ejpam-5621	117	15	,	,	PUNCT
ejpam-5621	117	16	it	it	PRON
ejpam-5621	117	17	is	be	AUX
ejpam-5621	117	18	possible	possible	ADJ
ejpam-5621	117	19	to	to	PART
ejpam-5621	117	20	generate	generate	VERB
ejpam-5621	117	21	a	a	DET
ejpam-5621	117	22	set	set	NOUN
ejpam-5621	117	23	of	of	ADP
ejpam-5621	117	24	disjoint	disjoint	NOUN
ejpam-5621	117	25	balls	ball	NOUN
ejpam-5621	117	26	denoted	denote	VERB
ejpam-5621	117	27	as	as	ADP
ejpam-5621	117	28	{	{	PUNCT
ejpam-5621	117	29	b0	b0	NOUN
ejpam-5621	117	30	i	i	PRON
ejpam-5621	117	31	}	}	PUNCT
ejpam-5621	117	32	i∈n	i∈n	NOUN
ejpam-5621	118	1	=	=	NOUN
ejpam-5621	118	2	{	{	PUNCT
ejpam-5621	118	3	bpxi	bpxi	PROPN
ejpam-5621	118	4	(	(	PUNCT
ejpam-5621	118	5	xi	xi	PROPN
ejpam-5621	118	6	)	)	PUNCT
ejpam-5621	118	7	}	}	PUNCT
ejpam-5621	118	8	i∈n	i∈n	NOUN
ejpam-5621	118	9	,	,	PUNCT
ejpam-5621	118	10	xi	xi	PROPN
ejpam-5621	118	11	∈	∈	PROPN
ejpam-5621	118	12	a	a	DET
ejpam-5621	118	13	(	(	PUNCT
ejpam-5621	118	14	λ	λ	NOUN
ejpam-5621	118	15	)	)	PUNCT
ejpam-5621	118	16	.	.	PUNCT
ejpam-5621	119	1	adjust	adjust	VERB
ejpam-5621	119	2	any	any	DET
ejpam-5621	119	3	i	i	PROPN
ejpam-5621	119	4	∈	∈	PROPN
ejpam-5621	119	5	n	n	ADV
ejpam-5621	119	6	and	and	CCONJ
ejpam-5621	119	7	set	set	VERB
ejpam-5621	119	8	vmλ	vmλ	NOUN
ejpam-5621	119	9	=	=	SYM
ejpam-5621	119	10	um	um	INTJ
ejpam-5621	119	11	/	/	SYM
ejpam-5621	119	12	λ	λ	PROPN
ejpam-5621	119	13	and	and	CCONJ
ejpam-5621	119	14	gmλ	gmλ	X
ejpam-5621	119	15	=	=	SYM
ejpam-5621	119	16	gm	gm	PROPN
ejpam-5621	119	17	/	/	SYM
ejpam-5621	119	18	λ	λ	PROPN
ejpam-5621	119	19	.	.	PUNCT
ejpam-5621	120	1	h.	h.	PROPN
ejpam-5621	120	2	ibrahim	ibrahim	PROPN
ejpam-5621	120	3	et	et	PROPN
ejpam-5621	120	4	al	al	PROPN
ejpam-5621	120	5	.	.	PUNCT
ejpam-5621	120	6	/	/	SYM
ejpam-5621	120	7	eur	eur	PROPN
ejpam-5621	120	8	.	.	PUNCT
ejpam-5621	121	1	j.	j.	PROPN
ejpam-5621	121	2	pure	pure	PROPN
ejpam-5621	121	3	appl	appl	PROPN
ejpam-5621	121	4	.	.	PROPN
ejpam-5621	121	5	math	math	PROPN
ejpam-5621	121	6	,	,	PUNCT
ejpam-5621	121	7	18	18	NUM
ejpam-5621	121	8	(	(	PUNCT
ejpam-5621	121	9	2	2	NUM
ejpam-5621	121	10	)	)	PUNCT
ejpam-5621	121	11	(	(	PUNCT
ejpam-5621	121	12	2025	2025	NUM
ejpam-5621	121	13	)	)	PUNCT
ejpam-5621	121	14	,	,	PUNCT
ejpam-5621	121	15	5621	5621	NUM
ejpam-5621	121	16	7	7	NUM
ejpam-5621	121	17	of	of	ADP
ejpam-5621	121	18	16	16	NUM
ejpam-5621	121	19	subsequently	subsequently	ADV
ejpam-5621	121	20	,	,	PUNCT
ejpam-5621	121	21	vmλ	vmλ	NOUN
ejpam-5621	121	22	remains	remain	VERB
ejpam-5621	121	23	a	a	DET
ejpam-5621	121	24	local	local	ADJ
ejpam-5621	121	25	weak	weak	ADJ
ejpam-5621	121	26	solution	solution	NOUN
ejpam-5621	121	27	of	of	ADP
ejpam-5621	121	28	(	(	PUNCT
ejpam-5621	121	29	1	1	NUM
ejpam-5621	121	30	)	)	PUNCT
ejpam-5621	121	31	,	,	PUNCT
ejpam-5621	121	32	where	where	SCONJ
ejpam-5621	121	33	gmλ	gmλ	PROPN
ejpam-5621	121	34	assumes	assume	VERB
ejpam-5621	121	35	the	the	DET
ejpam-5621	121	36	place	place	NOUN
ejpam-5621	121	37	of	of	ADP
ejpam-5621	121	38	gm	gm	PROPN
ejpam-5621	121	39	.	.	PUNCT
ejpam-5621	122	1	consequently	consequently	ADV
ejpam-5621	122	2	,	,	PUNCT
ejpam-5621	122	3	lemma	lemma	PROPN
ejpam-5621	122	4	(	(	PUNCT
ejpam-5621	122	5	3	3	X
ejpam-5621	122	6	)	)	PUNCT
ejpam-5621	122	7	dictates	dictate	VERB
ejpam-5621	122	8	that∫	that∫	PROPN
ejpam-5621	122	9	b	b	PROPN
ejpam-5621	123	1	j	j	PROPN
ejpam-5621	123	2	i	i	PRON
ejpam-5621	123	3	|∇vmλ	|∇vmλ	VERB
ejpam-5621	123	4	|p	|p	PRON
ejpam-5621	123	5	dx	dx	PROPN
ejpam-5621	123	6	≤	≤	NUM
ejpam-5621	123	7	1	1	NUM
ejpam-5621	123	8	and	and	CCONJ
ejpam-5621	123	9	∫	∫	PROPN
ejpam-5621	123	10	bj	bj	ADP
ejpam-5621	123	11	i	i	PRON
ejpam-5621	123	12	|gm|q1	|gm|q1	NOUN
ejpam-5621	123	13	dx	dx	PROPN
ejpam-5621	123	14	≤	≤	NUM
ejpam-5621	123	15	λq1	λq1	NOUN
ejpam-5621	123	16	(	(	PUNCT
ejpam-5621	123	17	8)	8)	NUM
ejpam-5621	123	18	in	in	ADP
ejpam-5621	123	19	the	the	DET
ejpam-5621	123	20	case	case	NOUN
ejpam-5621	124	1	i	i	NOUN
ejpam-5621	124	2	=	=	NOUN
ejpam-5621	124	3	1	1	NUM
ejpam-5621	124	4	,	,	PUNCT
ejpam-5621	124	5	2	2	NUM
ejpam-5621	124	6	,	,	PUNCT
ejpam-5621	124	7	3	3	NUM
ejpam-5621	124	8	,	,	PUNCT
ejpam-5621	124	9	bi	bi	PROPN
ejpam-5621	124	10	j	j	PROPN
ejpam-5621	124	11	is	be	AUX
ejpam-5621	124	12	defined	define	VERB
ejpam-5621	124	13	in	in	ADP
ejpam-5621	124	14	lemma	lemma	PROPN
ejpam-5621	124	15	2	2	NUM
ejpam-5621	124	16	as	as	ADP
ejpam-5621	124	17	bi	bi	PROPN
ejpam-5621	124	18	j	j	PROPN
ejpam-5621	124	19	=	=	PRON
ejpam-5621	124	20	:	:	PUNCT
ejpam-5621	124	21	2i+2b0	2i+2b0	NOUN
ejpam-5621	124	22	i	i	PRON
ejpam-5621	124	23	denote	denote	VERB
ejpam-5621	124	24	the	the	DET
ejpam-5621	124	25	weak	weak	ADJ
ejpam-5621	124	26	solution	solution	NOUN
ejpam-5621	124	27	of	of	ADP
ejpam-5621	124	28	the	the	DET
ejpam-5621	124	29	reference	reference	NOUN
ejpam-5621	124	30	equation	equation	NOUN
ejpam-5621	124	31	as	as	ADP
ejpam-5621	124	32	:	:	PUNCT
ejpam-5621	124	33	{	{	PUNCT
ejpam-5621	124	34	div	div	X
ejpam-5621	124	35	(	(	PUNCT
ejpam-5621	124	36	ēbs∇um	ēbs∇um	PROPN
ejpam-5621	124	37	·	·	SYM
ejpam-5621	124	38	∇umēbs∇um	∇umēbs∇um	PROPN
ejpam-5621	124	39	)	)	PUNCT
ejpam-5621	125	1	=	=	SYM
ejpam-5621	125	2	0	0	NUM
ejpam-5621	126	1	in	in	ADP
ejpam-5621	126	2	bs	bs	INTJ
ejpam-5621	126	3	um	um	INTJ
ejpam-5621	126	4	=	=	SYM
ejpam-5621	126	5	fm	fm	PROPN
ejpam-5621	126	6	in	in	ADP
ejpam-5621	126	7	bs	bs	X
ejpam-5621	126	8	(	(	PUNCT
ejpam-5621	126	9	9	9	NUM
ejpam-5621	126	10	)	)	PUNCT
ejpam-5621	126	11	3	3	NUM
ejpam-5621	126	12	.	.	PUNCT
ejpam-5621	127	1	the	the	DET
ejpam-5621	127	2	global	global	ADJ
ejpam-5621	127	3	weak	weak	ADJ
ejpam-5621	127	4	solutions	solution	NOUN
ejpam-5621	127	5	and	and	CCONJ
ejpam-5621	127	6	grading	grading	NOUN
ejpam-5621	127	7	estimates	estimate	NOUN
ejpam-5621	127	8	definition	definition	NOUN
ejpam-5621	127	9	3	3	X
ejpam-5621	127	10	.	.	PUNCT
ejpam-5621	128	1	let	let	VERB
ejpam-5621	128	2	f	f	PROPN
ejpam-5621	128	3	∈	∈	PROPN
ejpam-5621	128	4	w	w	PROPN
ejpam-5621	128	5	1,p(bs	1,p(bs	NUM
ejpam-5621	128	6	)	)	PUNCT
ejpam-5621	128	7	be	be	AUX
ejpam-5621	128	8	assumed	assume	VERB
ejpam-5621	128	9	.	.	PUNCT
ejpam-5621	129	1	it	it	PRON
ejpam-5621	129	2	is	be	AUX
ejpam-5621	129	3	stated	state	VERB
ejpam-5621	129	4	that	that	SCONJ
ejpam-5621	129	5	um	um	INTJ
ejpam-5621	129	6	∈	∈	PROPN
ejpam-5621	129	7	w	w	PROPN
ejpam-5621	129	8	1,p(bs	1,p(bs	NUM
ejpam-5621	129	9	)	)	PUNCT
ejpam-5621	129	10	is	be	AUX
ejpam-5621	129	11	a	a	DET
ejpam-5621	129	12	weak	weak	ADJ
ejpam-5621	129	13	solution	solution	NOUN
ejpam-5621	129	14	of	of	ADP
ejpam-5621	129	15	the	the	DET
ejpam-5621	129	16	system	system	NOUN
ejpam-5621	129	17	um	um	INTJ
ejpam-5621	129	18	−	−	PROPN
ejpam-5621	129	19	gm	gm	PROPN
ejpam-5621	129	20	∈w	∈w	VERB
ejpam-5621	129	21	1,p	1,p	PROPN
ejpam-5621	129	22	0	0	NUM
ejpam-5621	129	23	(	(	PUNCT
ejpam-5621	129	24	bs	bs	NOUN
ejpam-5621	129	25	)	)	PUNCT
ejpam-5621	129	26	is	be	AUX
ejpam-5621	129	27	a	a	DET
ejpam-5621	129	28	weak	weak	ADJ
ejpam-5621	129	29	solution	solution	NOUN
ejpam-5621	129	30	of	of	ADP
ejpam-5621	129	31	{	{	PUNCT
ejpam-5621	129	32	div	div	X
ejpam-5621	129	33	(	(	PUNCT
ejpam-5621	129	34	ēbs∇um	ēbs∇um	PROPN
ejpam-5621	129	35	·	·	SYM
ejpam-5621	129	36	∇umēbs∇um	∇umēbs∇um	PROPN
ejpam-5621	129	37	)	)	PUNCT
ejpam-5621	130	1	=	=	SYM
ejpam-5621	130	2	0	0	NUM
ejpam-5621	131	1	in	in	ADP
ejpam-5621	131	2	bs	bs	NOUN
ejpam-5621	131	3	,	,	PUNCT
ejpam-5621	131	4	um	um	INTJ
ejpam-5621	131	5	=	=	SYM
ejpam-5621	131	6	fm	fm	NOUN
ejpam-5621	131	7	on	on	ADP
ejpam-5621	131	8	∂bs	∂bs	PROPN
ejpam-5621	131	9	.	.	PUNCT
ejpam-5621	132	1	let	let	VERB
ejpam-5621	132	2	∫	∫	PROPN
ejpam-5621	132	3	bs	bs	INTJ
ejpam-5621	132	4	(	(	PUNCT
ejpam-5621	132	5	ēbs∇um	ēbs∇um	PROPN
ejpam-5621	132	6	·	·	SYM
ejpam-5621	132	7	∇umēbs∇um	∇umēbs∇um	PROPN
ejpam-5621	132	8	·	·	PUNCT
ejpam-5621	132	9	∇ψdx	∇ψdx	X
ejpam-5621	132	10	)	)	PUNCT
ejpam-5621	133	1	=	=	SYM
ejpam-5621	133	2	0	0	NUM
ejpam-5621	133	3	,	,	PUNCT
ejpam-5621	133	4	with	with	ADP
ejpam-5621	133	5	any	any	DET
ejpam-5621	133	6	ψ	ψ	ADP
ejpam-5621	133	7	∈w	∈w	NOUN
ejpam-5621	133	8	1,p	1,p	PROPN
ejpam-5621	133	9	0	0	NUM
ejpam-5621	133	10	(	(	PUNCT
ejpam-5621	133	11	bs	bs	NOUN
ejpam-5621	133	12	)	)	PUNCT
ejpam-5621	133	13	.	.	PUNCT
ejpam-5621	134	1	the	the	DET
ejpam-5621	134	2	following	follow	VERB
ejpam-5621	134	3	are	be	AUX
ejpam-5621	134	4	recollections	recollection	NOUN
ejpam-5621	134	5	of	of	ADP
ejpam-5621	134	6	estimates	estimate	NOUN
ejpam-5621	134	7	for	for	ADP
ejpam-5621	134	8	um	um	INTJ
ejpam-5621	134	9	to	to	ADP
ejpam-5621	134	10	[	[	X
ejpam-5621	134	11	5	5	NUM
ejpam-5621	134	12	,	,	PUNCT
ejpam-5621	134	13	12]:∫	12]:∫	NUM
ejpam-5621	134	14	bs	bs	NOUN
ejpam-5621	134	15	|∇um|pdx	|∇um|pdx	PROPN
ejpam-5621	134	16	≤	≤	PROPN
ejpam-5621	134	17	c	c	NOUN
ejpam-5621	134	18	∫	∫	PROPN
ejpam-5621	134	19	bs	bs	PROPN
ejpam-5621	134	20	|∇vm|pdx	|∇vm|pdx	PROPN
ejpam-5621	134	21	,	,	PUNCT
ejpam-5621	134	22	(	(	PUNCT
ejpam-5621	134	23	10	10	NUM
ejpam-5621	134	24	)	)	PUNCT
ejpam-5621	134	25	and	and	CCONJ
ejpam-5621	134	26	sup	sup	PROPN
ejpam-5621	134	27	bp	bp	PROPN
ejpam-5621	134	28	|∇um|	|∇um|	PUNCT
ejpam-5621	134	29	≤	≤	NUM
ejpam-5621	134	30	c	c	X
ejpam-5621	134	31	(	(	PUNCT
ejpam-5621	134	32	∫	∫	PROPN
ejpam-5621	134	33	bs	bs	PROPN
ejpam-5621	134	34	|∇um|pdx	|∇um|pdx	PROPN
ejpam-5621	134	35	)	)	PUNCT
ejpam-5621	134	36	)	)	PUNCT
ejpam-5621	134	37	1	1	NUM
ejpam-5621	134	38	p	p	NOUN
ejpam-5621	134	39	(	(	PUNCT
ejpam-5621	134	40	11	11	NUM
ejpam-5621	134	41	)	)	PUNCT
ejpam-5621	134	42	in	in	ADP
ejpam-5621	134	43	the	the	DET
ejpam-5621	134	44	range	range	NOUN
ejpam-5621	134	45	p	p	X
ejpam-5621	134	46	∈	∈	PROPN
ejpam-5621	134	47	(	(	PUNCT
ejpam-5621	134	48	0	0	NUM
ejpam-5621	134	49	,	,	PUNCT
ejpam-5621	134	50	s/2	s/2	NOUN
ejpam-5621	134	51	]	]	PUNCT
ejpam-5621	134	52	,	,	PUNCT
ejpam-5621	134	53	with	with	ADP
ejpam-5621	134	54	c	c	NOUN
ejpam-5621	134	55	=	=	SYM
ejpam-5621	134	56	c(n	c(n	PROPN
ejpam-5621	134	57	,	,	PUNCT
ejpam-5621	134	58	p	p	X
ejpam-5621	134	59	,	,	PUNCT
ejpam-5621	134	60	α	α	NOUN
ejpam-5621	134	61	)	)	PUNCT
ejpam-5621	134	62	.	.	PUNCT
ejpam-5621	135	1	moreover	moreover	ADV
ejpam-5621	135	2	,	,	PUNCT
ejpam-5621	135	3	we	we	PRON
ejpam-5621	135	4	can	can	AUX
ejpam-5621	135	5	derive	derive	VERB
ejpam-5621	135	6	the	the	DET
ejpam-5621	135	7	subsequent	subsequent	ADJ
ejpam-5621	135	8	significant	significant	ADJ
ejpam-5621	135	9	outcome	outcome	NOUN
ejpam-5621	135	10	.	.	PUNCT
ejpam-5621	136	1	lemma	lemma	PROPN
ejpam-5621	136	2	5	5	NUM
ejpam-5621	136	3	.	.	PUNCT
ejpam-5621	137	1	there	there	PRON
ejpam-5621	137	2	exists	exist	VERB
ejpam-5621	137	3	a	a	DET
ejpam-5621	137	4	small	small	ADJ
ejpam-5621	137	5	value	value	NOUN
ejpam-5621	137	6	of	of	ADP
ejpam-5621	137	7	δ	δ	PROPN
ejpam-5621	137	8	=	=	SYM
ejpam-5621	137	9	δ(ϵ	δ(ϵ	PROPN
ejpam-5621	137	10	)	)	PUNCT
ejpam-5621	137	11	>	>	X
ejpam-5621	137	12	0	0	PUNCT
ejpam-5621	138	1	for	for	ADP
ejpam-5621	138	2	all	all	DET
ejpam-5621	138	3	values	value	NOUN
ejpam-5621	138	4	of	of	ADP
ejpam-5621	138	5	ϵ	ϵ	NOUN
ejpam-5621	138	6	,	,	PUNCT
ejpam-5621	138	7	such	such	ADJ
ejpam-5621	138	8	that	that	SCONJ
ejpam-5621	138	9	if	if	SCONJ
ejpam-5621	138	10	vm	vm	PROPN
ejpam-5621	138	11	is	be	AUX
ejpam-5621	138	12	a	a	DET
ejpam-5621	138	13	local	local	ADJ
ejpam-5621	138	14	weak	weak	ADJ
ejpam-5621	138	15	solution	solution	NOUN
ejpam-5621	138	16	of	of	ADP
ejpam-5621	138	17	(	(	PUNCT
ejpam-5621	138	18	1	1	NUM
ejpam-5621	138	19	)	)	PUNCT
ejpam-5621	138	20	in	in	ADP
ejpam-5621	138	21	ω	ω	PROPN
ejpam-5621	138	22	with	with	ADP
ejpam-5621	138	23	b4	b4	PROPN
ejpam-5621	138	24	⊂	⊂	PROPN
ejpam-5621	138	25	ω	ω	PROPN
ejpam-5621	138	26	,	,	PUNCT
ejpam-5621	138	27	then∫	then∫	NOUN
ejpam-5621	138	28	b2	b2	NOUN
ejpam-5621	138	29	∣∣e	∣∣e	NOUN
ejpam-5621	138	30	−	−	PROPN
ejpam-5621	138	31	ēb2	ēb2	PROPN
ejpam-5621	138	32	∣∣dx	∣∣dx	VERB
ejpam-5621	138	33	≤	≤	PROPN
ejpam-5621	138	34	δ	δ	PROPN
ejpam-5621	138	35	,	,	PUNCT
ejpam-5621	138	36	(	(	PUNCT
ejpam-5621	138	37	12	12	NUM
ejpam-5621	138	38	)	)	PUNCT
ejpam-5621	138	39	and	and	CCONJ
ejpam-5621	138	40	∫	∫	PROPN
ejpam-5621	138	41	b4	b4	PROPN
ejpam-5621	138	42	|∇vm|pdx	|∇vm|pdx	PROPN
ejpam-5621	138	43	≤	≤	PROPN
ejpam-5621	138	44	1	1	NUM
ejpam-5621	138	45	and	and	CCONJ
ejpam-5621	138	46	∫	∫	PROPN
ejpam-5621	138	47	b4	b4	PROPN
ejpam-5621	138	48	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	138	49	≤	≤	ADV
ejpam-5621	139	1	δq1	δq1	NOUN
ejpam-5621	139	2	.	.	PUNCT
ejpam-5621	140	1	(	(	PUNCT
ejpam-5621	140	2	13	13	NUM
ejpam-5621	140	3	)	)	PUNCT
ejpam-5621	140	4	consequently	consequently	ADV
ejpam-5621	140	5	,	,	PUNCT
ejpam-5621	140	6	n0	n0	X
ejpam-5621	140	7	>	>	SYM
ejpam-5621	140	8	1	1	NUM
ejpam-5621	140	9	exists	exist	VERB
ejpam-5621	140	10	and	and	CCONJ
ejpam-5621	140	11	is	be	AUX
ejpam-5621	140	12	denoted	denote	VERB
ejpam-5621	140	13	by	by	ADP
ejpam-5621	140	14	u	u	NOUN
ejpam-5621	140	15	in	in	ADP
ejpam-5621	140	16	b2	b2	NOUN
ejpam-5621	140	17	as	as	ADP
ejpam-5621	140	18	the	the	DET
ejpam-5621	140	19	weak	weak	ADJ
ejpam-5621	140	20	solution	solution	NOUN
ejpam-5621	140	21	to	to	ADP
ejpam-5621	140	22	(	(	PUNCT
ejpam-5621	140	23	1	1	X
ejpam-5621	140	24	)	)	PUNCT
ejpam-5621	140	25	h.	h.	PROPN
ejpam-5621	140	26	ibrahim	ibrahim	PROPN
ejpam-5621	141	1	et	et	PROPN
ejpam-5621	141	2	al	al	PROPN
ejpam-5621	141	3	.	.	PUNCT
ejpam-5621	141	4	/	/	SYM
ejpam-5621	141	5	eur	eur	PROPN
ejpam-5621	141	6	.	.	PUNCT
ejpam-5621	142	1	j.	j.	PROPN
ejpam-5621	142	2	pure	pure	PROPN
ejpam-5621	142	3	appl	appl	PROPN
ejpam-5621	142	4	.	.	PROPN
ejpam-5621	142	5	math	math	PROPN
ejpam-5621	142	6	,	,	PUNCT
ejpam-5621	142	7	18	18	NUM
ejpam-5621	142	8	(	(	PUNCT
ejpam-5621	142	9	2	2	NUM
ejpam-5621	142	10	)	)	PUNCT
ejpam-5621	142	11	(	(	PUNCT
ejpam-5621	142	12	2025	2025	NUM
ejpam-5621	142	13	)	)	PUNCT
ejpam-5621	142	14	,	,	PUNCT
ejpam-5621	142	15	5621	5621	NUM
ejpam-5621	142	16	8	8	NUM
ejpam-5621	142	17	of	of	ADP
ejpam-5621	142	18	16	16	NUM
ejpam-5621	142	19	proof	proof	NOUN
ejpam-5621	142	20	.	.	PUNCT
ejpam-5621	143	1	based	base	VERB
ejpam-5621	143	2	on	on	ADP
ejpam-5621	143	3	(	(	PUNCT
ejpam-5621	143	4	1	1	NUM
ejpam-5621	143	5	)	)	PUNCT
ejpam-5621	143	6	,	,	PUNCT
ejpam-5621	143	7	(	(	PUNCT
ejpam-5621	143	8	2	2	NUM
ejpam-5621	143	9	)	)	PUNCT
ejpam-5621	143	10	,	,	PUNCT
ejpam-5621	143	11	and	and	CCONJ
ejpam-5621	143	12	(	(	PUNCT
ejpam-5621	143	13	4	4	NUM
ejpam-5621	143	14	)	)	PUNCT
ejpam-5621	143	15	,	,	PUNCT
ejpam-5621	143	16	it	it	PRON
ejpam-5621	143	17	can	can	AUX
ejpam-5621	143	18	be	be	AUX
ejpam-5621	143	19	deduced	deduce	VERB
ejpam-5621	143	20	that	that	SCONJ
ejpam-5621	143	21	the	the	DET
ejpam-5621	143	22	weak	weak	ADJ
ejpam-5621	143	23	solutions	solution	NOUN
ejpam-5621	143	24	of	of	ADP
ejpam-5621	143	25	(	(	PUNCT
ejpam-5621	143	26	1	1	NUM
ejpam-5621	143	27	)	)	PUNCT
ejpam-5621	143	28	in	in	ADP
ejpam-5621	143	29	ω	ω	PROPN
ejpam-5621	143	30	and	and	CCONJ
ejpam-5621	143	31	(	(	PUNCT
ejpam-5621	143	32	2	2	NUM
ejpam-5621	143	33	)	)	PUNCT
ejpam-5621	143	34	in	in	ADP
ejpam-5621	143	35	b2	b2	NOUN
ejpam-5621	143	36	,	,	PUNCT
ejpam-5621	143	37	respectively	respectively	ADV
ejpam-5621	143	38	,	,	PUNCT
ejpam-5621	143	39	are	be	AUX
ejpam-5621	143	40	denoted	denote	VERB
ejpam-5621	143	41	as	as	ADP
ejpam-5621	143	42	vm	vm	PROPN
ejpam-5621	143	43	and	and	CCONJ
ejpam-5621	143	44	um	um	INTJ
ejpam-5621	143	45	.	.	PUNCT
ejpam-5621	144	1	it	it	PRON
ejpam-5621	144	2	is	be	AUX
ejpam-5621	144	3	sufficient	sufficient	ADJ
ejpam-5621	144	4	to	to	PART
ejpam-5621	144	5	select	select	VERB
ejpam-5621	144	6	the	the	DET
ejpam-5621	144	7	test	test	NOUN
ejpam-5621	144	8	function	function	NOUN
ejpam-5621	144	9	ψ	ψ	X
ejpam-5621	144	10	=	=	X
ejpam-5621	144	11	um	um	INTJ
ejpam-5621	144	12	−	−	PROPN
ejpam-5621	144	13	vm	vm	PROPN
ejpam-5621	144	14	∈	∈	PROPN
ejpam-5621	144	15	w	w	PROPN
ejpam-5621	144	16	1,p	1,p	PROPN
ejpam-5621	144	17	0	0	NUM
ejpam-5621	144	18	(	(	PUNCT
ejpam-5621	144	19	b2	b2	NOUN
ejpam-5621	144	20	)	)	PUNCT
ejpam-5621	144	21	,	,	PUNCT
ejpam-5621	144	22	and	and	CCONJ
ejpam-5621	144	23	a	a	DET
ejpam-5621	144	24	straightforward	straightforward	ADJ
ejpam-5621	144	25	calculation	calculation	NOUN
ejpam-5621	144	26	yields	yield	VERB
ejpam-5621	144	27	the	the	DET
ejpam-5621	144	28	following	follow	VERB
ejpam-5621	144	29	expression	expression	NOUN
ejpam-5621	144	30	:	:	PUNCT
ejpam-5621	144	31	i1	i1	PROPN
ejpam-5621	144	32	=	=	PROPN
ejpam-5621	144	33	i2	i2	PROPN
ejpam-5621	144	34	+	+	CCONJ
ejpam-5621	144	35	i3	i3	NOUN
ejpam-5621	144	36	,	,	PUNCT
ejpam-5621	144	37	where	where	SCONJ
ejpam-5621	144	38	i1	i1	PROPN
ejpam-5621	144	39	=	=	SYM
ejpam-5621	144	40	∫	∫	PROPN
ejpam-5621	144	41	b2	b2	PROPN
ejpam-5621	144	42	(	(	PUNCT
ejpam-5621	144	43	ēb2∇um	ēb2∇um	PROPN
ejpam-5621	144	44	·	·	SYM
ejpam-5621	144	45	∇um	∇um	NUM
ejpam-5621	144	46	)	)	PUNCT
ejpam-5621	144	47	p−2	p−2	NOUN
ejpam-5621	144	48	2	2	NUM
ejpam-5621	144	49	eb2∇u−	eb2∇u−	X
ejpam-5621	144	50	(	(	PUNCT
ejpam-5621	144	51	êb2∇vm	êb2∇vm	PROPN
ejpam-5621	144	52	·	·	PUNCT
ejpam-5621	144	53	∇vm	∇vm	PROPN
ejpam-5621	144	54	)	)	PUNCT
ejpam-5621	144	55	p−2	p−2	NOUN
ejpam-5621	144	56	2	2	NUM
ejpam-5621	144	57	āb2∇vm	āb2∇vm	X
ejpam-5621	144	58	)	)	PUNCT
ejpam-5621	144	59	.∇(u−	.∇(u−	PUNCT
ejpam-5621	145	1	vm)dx	vm)dx	ADP
ejpam-5621	145	2	,	,	PUNCT
ejpam-5621	145	3	i2	i2	PROPN
ejpam-5621	145	4	=	=	SYM
ejpam-5621	145	5	∫	∫	PROPN
ejpam-5621	145	6	b2	b2	PROPN
ejpam-5621	145	7	(	(	PUNCT
ejpam-5621	145	8	(	(	PUNCT
ejpam-5621	145	9	e∇vm	e∇vm	X
ejpam-5621	145	10	·	·	PUNCT
ejpam-5621	145	11	∇vm)(p−2)/2ē∇vm	∇vm)(p−2)/2ē∇vm	PROPN
ejpam-5621	145	12	−	−	PROPN
ejpam-5621	145	13	(	(	PUNCT
ejpam-5621	145	14	ēb2∇vm	ēb2∇vm	X
ejpam-5621	145	15	·	·	PUNCT
ejpam-5621	145	16	∇vm)(p−2)/2ēb2∇vm	∇vm)(p−2)/2ēb2∇vm	NUM
ejpam-5621	145	17	)	)	PUNCT
ejpam-5621	145	18	·	·	PUNCT
ejpam-5621	146	1	∇(um	∇(um	NOUN
ejpam-5621	146	2	−	−	NOUN
ejpam-5621	147	1	vm)dx	vm)dx	NOUN
ejpam-5621	147	2	,	,	PUNCT
ejpam-5621	147	3	i3	i3	NOUN
ejpam-5621	147	4	=	=	SYM
ejpam-5621	147	5	−	−	PROPN
ejpam-5621	147	6	∫	∫	PROPN
ejpam-5621	147	7	b2	b2	NOUN
ejpam-5621	147	8	|gm|p−2	|gm|p−2	PROPN
ejpam-5621	147	9	g	g	NOUN
ejpam-5621	147	10	·	·	PUNCT
ejpam-5621	147	11	∇	∇	X
ejpam-5621	147	12	(	(	PUNCT
ejpam-5621	147	13	um	um	INTJ
ejpam-5621	147	14	−	−	PROPN
ejpam-5621	147	15	vm	vm	PROPN
ejpam-5621	147	16	)	)	PUNCT
ejpam-5621	147	17	dx	dx	PROPN
ejpam-5621	147	18	.	.	PUNCT
ejpam-5621	148	1	the	the	DET
ejpam-5621	148	2	estimation	estimation	NOUN
ejpam-5621	148	3	of	of	ADP
ejpam-5621	148	4	i1	i1	PROPN
ejpam-5621	148	5	.	.	PUNCT
ejpam-5621	149	1	two	two	NUM
ejpam-5621	149	2	instances	instance	NOUN
ejpam-5621	149	3	are	be	AUX
ejpam-5621	149	4	distinguished	distinguish	VERB
ejpam-5621	149	5	.	.	PUNCT
ejpam-5621	150	1	given	give	VERB
ejpam-5621	150	2	case	case	NOUN
ejpam-5621	150	3	1	1	NUM
ejpam-5621	150	4	.	.	PUNCT
ejpam-5621	150	5	p	p	X
ejpam-5621	150	6	≥	≥	NOUN
ejpam-5621	150	7	2	2	NUM
ejpam-5621	150	8	,	,	PUNCT
ejpam-5621	150	9	the	the	DET
ejpam-5621	150	10	elementary	elementary	ADJ
ejpam-5621	150	11	inequality	inequality	NOUN
ejpam-5621	150	12	is	be	AUX
ejpam-5621	150	13	applied	apply	VERB
ejpam-5621	150	14	.	.	PUNCT
ejpam-5621	151	1	(	(	PUNCT
ejpam-5621	151	2	ēb2ζ	ēb2ζ	X
ejpam-5621	151	3	·	·	PUNCT
ejpam-5621	151	4	ζ	ζ	X
ejpam-5621	151	5	)	)	PUNCT
ejpam-5621	151	6	p−2	p−2	NOUN
ejpam-5621	151	7	2	2	NUM
ejpam-5621	151	8	ēb2ζ	ēb2ζ	NUM
ejpam-5621	151	9	−	−	PROPN
ejpam-5621	151	10	(	(	PUNCT
ejpam-5621	151	11	ēb2η	ēb2η	NUM
ejpam-5621	151	12	·	·	PUNCT
ejpam-5621	151	13	η	η	PROPN
ejpam-5621	151	14	)	)	PUNCT
ejpam-5621	151	15	p−2	p−2	PROPN
ejpam-5621	151	16	2	2	NUM
ejpam-5621	151	17	ēb2η	ēb2η	NUM
ejpam-5621	151	18	)	)	PUNCT
ejpam-5621	151	19	·	·	PUNCT
ejpam-5621	152	1	(	(	PUNCT
ejpam-5621	152	2	ζ	ζ	NOUN
ejpam-5621	152	3	−	−	PROPN
ejpam-5621	152	4	η	η	PROPN
ejpam-5621	152	5	)	)	PUNCT
ejpam-5621	152	6	≥	≥	NOUN
ejpam-5621	152	7	c|ζ	c|ζ	ADP
ejpam-5621	152	8	−	−	PROPN
ejpam-5621	152	9	η|p	η|p	NOUN
ejpam-5621	152	10	,	,	PUNCT
ejpam-5621	152	11	we	we	PRON
ejpam-5621	152	12	have	have	AUX
ejpam-5621	152	13	,	,	PUNCT
ejpam-5621	152	14	for	for	ADP
ejpam-5621	152	15	every	every	DET
ejpam-5621	152	16	ζ	ζ	NOUN
ejpam-5621	152	17	,	,	PUNCT
ejpam-5621	152	18	η	η	PROPN
ejpam-5621	152	19	∈	∈	PROPN
ejpam-5621	152	20	rn	rn	PROPN
ejpam-5621	152	21	where	where	SCONJ
ejpam-5621	152	22	c	c	NOUN
ejpam-5621	152	23	=	=	SYM
ejpam-5621	152	24	c(p	c(p	NOUN
ejpam-5621	152	25	,	,	PUNCT
ejpam-5621	152	26	α	α	NOUN
ejpam-5621	152	27	)	)	PUNCT
ejpam-5621	152	28	,	,	PUNCT
ejpam-5621	152	29	:	:	PUNCT
ejpam-5621	152	30	i1	i1	PROPN
ejpam-5621	152	31	≥	≥	PROPN
ejpam-5621	152	32	c	c	PROPN
ejpam-5621	152	33	∫	∫	PROPN
ejpam-5621	152	34	b2	b2	PROPN
ejpam-5621	152	35	|∇(vm	|∇(vm	PROPN
ejpam-5621	152	36	−	−	PROPN
ejpam-5621	152	37	um)|pdx	um)|pdx	PROPN
ejpam-5621	152	38	.	.	PUNCT
ejpam-5621	152	39	case	case	NOUN
ejpam-5621	152	40	2	2	NUM
ejpam-5621	152	41	:	:	PUNCT
ejpam-5621	152	42	applying	apply	VERB
ejpam-5621	152	43	the	the	DET
ejpam-5621	152	44	rudimentary	rudimentary	ADJ
ejpam-5621	152	45	inequality	inequality	NOUN
ejpam-5621	152	46	to	to	ADP
ejpam-5621	152	47	1	1	NUM
ejpam-5621	152	48	<	<	X
ejpam-5621	152	49	p	p	X
ejpam-5621	152	50	<	<	X
ejpam-5621	152	51	2	2	NUM
ejpam-5621	152	52	.	.	PUNCT
ejpam-5621	153	1	|ζ	|ζ	PROPN
ejpam-5621	153	2	−	−	PROPN
ejpam-5621	153	3	η|p	η|p	PROPN
ejpam-5621	153	4	≤	≤	NUM
ejpam-5621	153	5	cτ	cτ	ADP
ejpam-5621	153	6	p−2	p−2	PROPN
ejpam-5621	153	7	p	p	X
ejpam-5621	153	8	(	(	PUNCT
ejpam-5621	153	9	(	(	PUNCT
ejpam-5621	153	10	ēb2ζ	ēb2ζ	X
ejpam-5621	153	11	·	·	PUNCT
ejpam-5621	153	12	ζ	ζ	X
ejpam-5621	153	13	)	)	PUNCT
ejpam-5621	153	14	p−2	p−2	NOUN
ejpam-5621	153	15	2	2	NUM
ejpam-5621	153	16	ēb2ζ	ēb2ζ	NUM
ejpam-5621	153	17	−	−	PROPN
ejpam-5621	153	18	(	(	PUNCT
ejpam-5621	153	19	ēb2η	ēb2η	NUM
ejpam-5621	153	20	·	·	PUNCT
ejpam-5621	153	21	η	η	PROPN
ejpam-5621	153	22	)	)	PUNCT
ejpam-5621	153	23	p−2	p−2	PROPN
ejpam-5621	153	24	2	2	NUM
ejpam-5621	153	25	ēb2η	ēb2η	NUM
ejpam-5621	153	26	)	)	PUNCT
ejpam-5621	153	27	·	·	PUNCT
ejpam-5621	154	1	(	(	PUNCT
ejpam-5621	154	2	ζ	ζ	NOUN
ejpam-5621	154	3	−	−	PROPN
ejpam-5621	154	4	η	η	PROPN
ejpam-5621	154	5	)	)	PUNCT
ejpam-5621	155	1	+	+	NUM
ejpam-5621	155	2	τ	τ	X
ejpam-5621	155	3	|η|p	|η|p	PROPN
ejpam-5621	155	4	.	.	PUNCT
ejpam-5621	156	1	we	we	PRON
ejpam-5621	156	2	have	have	VERB
ejpam-5621	156	3	the	the	DET
ejpam-5621	156	4	following	following	NOUN
ejpam-5621	156	5	for	for	ADP
ejpam-5621	156	6	each	each	DET
ejpam-5621	156	7	ζ	ζ	NOUN
ejpam-5621	156	8	,	,	PUNCT
ejpam-5621	156	9	η	η	PROPN
ejpam-5621	156	10	∈	∈	PROPN
ejpam-5621	156	11	rn	rn	PROPN
ejpam-5621	156	12	and	and	CCONJ
ejpam-5621	156	13	each	each	DET
ejpam-5621	156	14	τ	τ	PROPN
ejpam-5621	156	15	∈	∈	PROPN
ejpam-5621	156	16	(	(	PUNCT
ejpam-5621	156	17	0	0	NUM
ejpam-5621	156	18	,	,	PUNCT
ejpam-5621	156	19	1	1	NUM
ejpam-5621	156	20	)	)	PUNCT
ejpam-5621	156	21	where	where	SCONJ
ejpam-5621	156	22	c	c	NOUN
ejpam-5621	156	23	=	=	SYM
ejpam-5621	156	24	c(p	c(p	NOUN
ejpam-5621	156	25	,	,	PUNCT
ejpam-5621	156	26	α	α	NOUN
ejpam-5621	156	27	):	):	PUNCT
ejpam-5621	156	28	i1	i1	PROPN
ejpam-5621	156	29	+	+	CCONJ
ejpam-5621	156	30	τ	τ	PROPN
ejpam-5621	156	31	∫	∫	PROPN
ejpam-5621	156	32	b2	b2	PROPN
ejpam-5621	156	33	|∇vm|pdx	|∇vm|pdx	PROPN
ejpam-5621	156	34	≥	≥	NOUN
ejpam-5621	156	35	c	c	NOUN
ejpam-5621	156	36	(	(	PUNCT
ejpam-5621	156	37	τ	τ	PROPN
ejpam-5621	156	38	)	)	PUNCT
ejpam-5621	156	39	∫	∫	PROPN
ejpam-5621	156	40	b2	b2	PROPN
ejpam-5621	156	41	|∇	|∇	PROPN
ejpam-5621	156	42	(	(	PUNCT
ejpam-5621	156	43	vm	vm	NOUN
ejpam-5621	156	44	−	−	PROPN
ejpam-5621	157	1	um)|pdx	um)|pdx	PROPN
ejpam-5621	157	2	.	.	PUNCT
ejpam-5621	158	1	approximation	approximation	NOUN
ejpam-5621	158	2	of	of	ADP
ejpam-5621	158	3	implementing	implement	VERB
ejpam-5621	158	4	a	a	DET
ejpam-5621	158	5	fundamental	fundamental	ADJ
ejpam-5621	158	6	inequality∣∣∣(eζ	inequality∣∣∣(eζ	X
ejpam-5621	158	7	·	·	PUNCT
ejpam-5621	158	8	ζ)(p−2)/2eζ	ζ)(p−2)/2eζ	NUM
ejpam-5621	158	9	−	−	PROPN
ejpam-5621	158	10	(	(	PUNCT
ejpam-5621	158	11	ēb2ζ	ēb2ζ	X
ejpam-5621	158	12	·	·	PUNCT
ejpam-5621	158	13	ζ)(p−2)/2ēb2ζ	ζ)(p−2)/2ēb2ζ	ADP
ejpam-5621	158	14	∣∣∣	∣∣∣	ADJ
ejpam-5621	158	15	≤	≤	NUM
ejpam-5621	159	1	c	c	NOUN
ejpam-5621	159	2	∣∣e	∣∣e	PROPN
ejpam-5621	160	1	−	−	PROPN
ejpam-5621	160	2	ēb2	ēb2	X
ejpam-5621	160	3	∣∣	∣∣	X
ejpam-5621	160	4	|ζ|p−1	|ζ|p−1	X
ejpam-5621	160	5	.	.	PUNCT
ejpam-5621	161	1	we	we	PRON
ejpam-5621	161	2	have	have	VERB
ejpam-5621	161	3	,	,	PUNCT
ejpam-5621	161	4	for	for	ADP
ejpam-5621	161	5	each	each	DET
ejpam-5621	161	6	o	o	NOUN
ejpam-5621	161	7	,	,	PUNCT
ejpam-5621	161	8	η	η	PROPN
ejpam-5621	161	9	∈	∈	PROPN
ejpam-5621	161	10	rn	rn	PROPN
ejpam-5621	161	11	where	where	SCONJ
ejpam-5621	161	12	c	c	NOUN
ejpam-5621	161	13	=	=	SYM
ejpam-5621	161	14	c(p	c(p	NOUN
ejpam-5621	161	15	,	,	PUNCT
ejpam-5621	161	16	α	α	NOUN
ejpam-5621	161	17	)	)	PUNCT
ejpam-5621	161	18	,	,	PUNCT
ejpam-5621	161	19	by	by	ADP
ejpam-5621	161	20	employing	employ	VERB
ejpam-5621	161	21	young	young	PROPN
ejpam-5621	161	22	’s	’s	PART
ejpam-5621	161	23	inequality	inequality	NOUN
ejpam-5621	161	24	with	with	ADP
ejpam-5621	161	25	and	and	CCONJ
ejpam-5621	161	26	holder	holder	NOUN
ejpam-5621	161	27	’s	’s	PART
ejpam-5621	161	28	inequality	inequality	NOUN
ejpam-5621	161	29	.	.	PUNCT
ejpam-5621	162	1	i2	i2	PROPN
ejpam-5621	162	2	≤	≤	PROPN
ejpam-5621	162	3	c	c	PROPN
ejpam-5621	162	4	∫	∫	PROPN
ejpam-5621	162	5	b2	b2	PROPN
ejpam-5621	162	6	∣∣e	∣∣e	PROPN
ejpam-5621	162	7	−	−	PROPN
ejpam-5621	162	8	ēb2	ēb2	NOUN
ejpam-5621	162	9	∣∣	∣∣	NUM
ejpam-5621	162	10	|∇vm|p−1	|∇vm|p−1	NUM
ejpam-5621	162	11	|∇	|∇	X
ejpam-5621	162	12	(	(	PUNCT
ejpam-5621	162	13	vm	vm	NOUN
ejpam-5621	162	14	−	−	PROPN
ejpam-5621	162	15	um)|	um)|	PROPN
ejpam-5621	162	16	dx	dx	PROPN
ejpam-5621	162	17	≤	≤	PROPN
ejpam-5621	162	18	c	c	X
ejpam-5621	162	19	(	(	PUNCT
ejpam-5621	162	20	τ	τ	PROPN
ejpam-5621	162	21	)	)	PUNCT
ejpam-5621	162	22	∫	∫	PROPN
ejpam-5621	162	23	b2	b2	PROPN
ejpam-5621	162	24	∣∣e	∣∣e	PROPN
ejpam-5621	162	25	−	−	PROPN
ejpam-5621	162	26	ē	ē	ADV
ejpam-5621	162	27	∣∣	∣∣	PROPN
ejpam-5621	162	28	p	p	PROPN
ejpam-5621	162	29	p−1	p−1	PROPN
ejpam-5621	162	30	|∇vm|pdx+	|∇vm|pdx+	NOUN
ejpam-5621	162	31	τ	τ	PROPN
ejpam-5621	162	32	∫	∫	PROPN
ejpam-5621	162	33	b2	b2	PROPN
ejpam-5621	162	34	|∇(vm	|∇(vm	PROPN
ejpam-5621	162	35	−	−	PROPN
ejpam-5621	162	36	um)|pdx	um)|pdx	PROPN
ejpam-5621	162	37	≤	≤	PROPN
ejpam-5621	162	38	c(τ	c(τ	PROPN
ejpam-5621	162	39	)	)	PUNCT
ejpam-5621	162	40	(	(	PUNCT
ejpam-5621	162	41	∫	∫	PROPN
ejpam-5621	162	42	b2	b2	PROPN
ejpam-5621	162	43	∣∣e	∣∣e	PROPN
ejpam-5621	162	44	−	−	PROPN
ejpam-5621	162	45	ēb2	ēb2	PROPN
ejpam-5621	162	46	∣∣pq2/[(p−1)(q2−p	∣∣pq2/[(p−1)(q2−p	NOUN
ejpam-5621	162	47	)	)	PUNCT
ejpam-5621	162	48	]	]	PUNCT
ejpam-5621	162	49	dx	dx	PROPN
ejpam-5621	162	50	)	)	PUNCT
ejpam-5621	162	51	(	(	PUNCT
ejpam-5621	162	52	q2−p)/q2(∫	q2−p)/q2(∫	X
ejpam-5621	162	53	b2	b2	NOUN
ejpam-5621	162	54	|∇vm|q2dx	|∇vm|q2dx	ADV
ejpam-5621	162	55	)	)	PUNCT
ejpam-5621	163	1	p	p	X
ejpam-5621	163	2	/	/	SYM
ejpam-5621	163	3	q2	q2	NOUN
ejpam-5621	163	4	+	+	ADP
ejpam-5621	163	5	τ	τ	PROPN
ejpam-5621	163	6	∫	∫	PROPN
ejpam-5621	163	7	b2	b2	PROPN
ejpam-5621	163	8	|∇(vm	|∇(vm	PROPN
ejpam-5621	163	9	−	−	PROPN
ejpam-5621	163	10	um)|pdx	um)|pdx	PROPN
ejpam-5621	163	11	.	.	PUNCT
ejpam-5621	164	1	we	we	PRON
ejpam-5621	164	2	observe	observe	VERB
ejpam-5621	164	3	that	that	SCONJ
ejpam-5621	164	4	(	(	PUNCT
ejpam-5621	164	5	∫	∫	PROPN
ejpam-5621	164	6	b2	b2	PROPN
ejpam-5621	164	7	∣∣e	∣∣e	PROPN
ejpam-5621	164	8	−	−	PROPN
ejpam-5621	164	9	ēb2	ēb2	PROPN
ejpam-5621	164	10	∣∣pq2/[(p−1)(q2−p	∣∣pq2/[(p−1)(q2−p	NOUN
ejpam-5621	164	11	)	)	PUNCT
ejpam-5621	164	12	]	]	PUNCT
ejpam-5621	164	13	dx	dx	PROPN
ejpam-5621	164	14	)	)	PUNCT
ejpam-5621	164	15	(	(	PUNCT
ejpam-5621	164	16	q2−p)/q2	q2−p)/q2	PROPN
ejpam-5621	164	17	≤	≤	X
ejpam-5621	164	18	(	(	PUNCT
ejpam-5621	164	19	2α)(p	2α)(p	NUM
ejpam-5621	164	20	2+q2−p)/[q2(p−1	2+q2−p)/[q2(p−1	NUM
ejpam-5621	164	21	)	)	PUNCT
ejpam-5621	164	22	]	]	PUNCT
ejpam-5621	164	23	(	(	PUNCT
ejpam-5621	164	24	∫	∫	PROPN
ejpam-5621	164	25	b2	b2	PROPN
ejpam-5621	164	26	∣∣e	∣∣e	PROPN
ejpam-5621	164	27	−	−	PROPN
ejpam-5621	164	28	ēb2	ēb2	NOUN
ejpam-5621	164	29	∣∣dx)(q2−p)/q2	∣∣dx)(q2−p)/q2	NOUN
ejpam-5621	164	30	≤	≤	NUM
ejpam-5621	164	31	cδ(q2−p)/q2	cδ(q2−p)/q2	PROPN
ejpam-5621	164	32	h.	h.	PROPN
ejpam-5621	164	33	ibrahim	ibrahim	PROPN
ejpam-5621	164	34	et	et	PROPN
ejpam-5621	164	35	al	al	PROPN
ejpam-5621	164	36	.	.	PUNCT
ejpam-5621	164	37	/	/	SYM
ejpam-5621	164	38	eur	eur	PROPN
ejpam-5621	164	39	.	.	PUNCT
ejpam-5621	165	1	j.	j.	PROPN
ejpam-5621	165	2	pure	pure	PROPN
ejpam-5621	165	3	appl	appl	PROPN
ejpam-5621	165	4	.	.	PROPN
ejpam-5621	165	5	math	math	PROPN
ejpam-5621	165	6	,	,	PUNCT
ejpam-5621	165	7	18	18	NUM
ejpam-5621	165	8	(	(	PUNCT
ejpam-5621	165	9	2	2	NUM
ejpam-5621	165	10	)	)	PUNCT
ejpam-5621	165	11	(	(	PUNCT
ejpam-5621	165	12	2025	2025	NUM
ejpam-5621	165	13	)	)	PUNCT
ejpam-5621	165	14	,	,	PUNCT
ejpam-5621	165	15	5621	5621	NUM
ejpam-5621	165	16	9	9	NUM
ejpam-5621	165	17	of	of	ADP
ejpam-5621	165	18	16	16	NUM
ejpam-5621	165	19	due	due	ADP
ejpam-5621	165	20	to	to	ADP
ejpam-5621	165	21	the	the	DET
ejpam-5621	165	22	outcomes	outcome	NOUN
ejpam-5621	165	23	of	of	ADP
ejpam-5621	165	24	(	(	PUNCT
ejpam-5621	165	25	2	2	NUM
ejpam-5621	165	26	)	)	PUNCT
ejpam-5621	165	27	and	and	CCONJ
ejpam-5621	165	28	(	(	PUNCT
ejpam-5621	165	29	3	3	NUM
ejpam-5621	165	30	)	)	PUNCT
ejpam-5621	165	31	,	,	PUNCT
ejpam-5621	165	32	and(∫	and(∫	NOUN
ejpam-5621	165	33	b2	b2	PROPN
ejpam-5621	165	34	|∇vm|	|∇vm|	PROPN
ejpam-5621	165	35	q2	q2	NOUN
ejpam-5621	165	36	dx	dx	PROPN
ejpam-5621	165	37	)	)	PUNCT
ejpam-5621	166	1	p	p	X
ejpam-5621	166	2	/	/	SYM
ejpam-5621	166	3	q2	q2	NOUN
ejpam-5621	166	4	≤	≤	NOUN
ejpam-5621	166	5	c	c	PROPN
ejpam-5621	167	1	[	[	X
ejpam-5621	167	2	(	(	PUNCT
ejpam-5621	167	3	∫	∫	PROPN
ejpam-5621	167	4	b4	b4	PROPN
ejpam-5621	167	5	|∇vm|pdx	|∇vm|pdx	PROPN
ejpam-5621	167	6	)	)	PUNCT
ejpam-5621	167	7	1	1	NUM
ejpam-5621	168	1	p	p	NOUN
ejpam-5621	168	2	+	+	NUM
ejpam-5621	168	3	∫	∫	PROPN
ejpam-5621	168	4	b4	b4	PROPN
ejpam-5621	168	5	(	(	PUNCT
ejpam-5621	168	6	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	168	7	)	)	PUNCT
ejpam-5621	168	8	1	1	NUM
ejpam-5621	168	9	q1	q1	NOUN
ejpam-5621	168	10	]	]	PUNCT
ejpam-5621	168	11	p	p	X
ejpam-5621	168	12	≤	≤	NOUN
ejpam-5621	168	13	c	c	X
ejpam-5621	168	14	,	,	PUNCT
ejpam-5621	168	15	by	by	ADP
ejpam-5621	168	16	virtue	virtue	NOUN
ejpam-5621	168	17	of	of	ADP
ejpam-5621	168	18	lemma	lemma	PROPN
ejpam-5621	168	19	4	4	NUM
ejpam-5621	168	20	and	and	CCONJ
ejpam-5621	168	21	equation	equation	NOUN
ejpam-5621	168	22	(	(	PUNCT
ejpam-5621	168	23	13	13	NUM
ejpam-5621	168	24	)	)	PUNCT
ejpam-5621	168	25	,	,	PUNCT
ejpam-5621	168	26	with	with	ADP
ejpam-5621	168	27	c	c	NOUN
ejpam-5621	168	28	denoting	denote	VERB
ejpam-5621	168	29	the	the	DET
ejpam-5621	168	30	set	set	NOUN
ejpam-5621	168	31	c	c	NOUN
ejpam-5621	168	32	=	=	SYM
ejpam-5621	168	33	c(m	c(m	PROPN
ejpam-5621	168	34	,	,	PUNCT
ejpam-5621	168	35	p	p	X
ejpam-5621	168	36	,	,	PUNCT
ejpam-5621	168	37	q1	q1	PROPN
ejpam-5621	168	38	,	,	PUNCT
ejpam-5621	168	39	α	α	NOUN
ejpam-5621	168	40	)	)	PUNCT
ejpam-5621	168	41	.	.	PUNCT
ejpam-5621	169	1	in	in	ADP
ejpam-5621	169	2	this	this	DET
ejpam-5621	169	3	context	context	NOUN
ejpam-5621	169	4	,	,	PUNCT
ejpam-5621	169	5	the	the	DET
ejpam-5621	169	6	assumption	assumption	NOUN
ejpam-5621	169	7	that	that	SCONJ
ejpam-5621	169	8	δ	δ	PROPN
ejpam-5621	169	9	<	<	X
ejpam-5621	169	10	1	1	X
ejpam-5621	169	11	.	.	PUNCT
ejpam-5621	170	1	we	we	PRON
ejpam-5621	170	2	thus	thus	ADV
ejpam-5621	170	3	conclude	conclude	VERB
ejpam-5621	170	4	that	that	SCONJ
ejpam-5621	170	5	i2	i2	PROPN
ejpam-5621	170	6	≤	≤	NOUN
ejpam-5621	170	7	c(τ)δ(q2−p)/q2	c(τ)δ(q2−p)/q2	NOUN
ejpam-5621	170	8	+	+	CCONJ
ejpam-5621	170	9	τ	τ	PROPN
ejpam-5621	170	10	∫	∫	PROPN
ejpam-5621	170	11	b2	b2	PROPN
ejpam-5621	170	12	|∇(vm	|∇(vm	PROPN
ejpam-5621	170	13	−	−	PROPN
ejpam-5621	170	14	um)|p	um)|p	ADJ
ejpam-5621	170	15	dx	dx	PROPN
ejpam-5621	170	16	.	.	PUNCT
ejpam-5621	171	1	the	the	DET
ejpam-5621	171	2	estimation	estimation	NOUN
ejpam-5621	171	3	of	of	ADP
ejpam-5621	171	4	i3	i3	NOUN
ejpam-5621	171	5	can	can	AUX
ejpam-5621	171	6	be	be	AUX
ejpam-5621	171	7	obtained	obtain	VERB
ejpam-5621	171	8	by	by	ADP
ejpam-5621	171	9	applying	apply	VERB
ejpam-5621	171	10	young	young	PROPN
ejpam-5621	171	11	’s	’s	PART
ejpam-5621	171	12	inequality	inequality	NOUN
ejpam-5621	171	13	with	with	ADP
ejpam-5621	171	14	τ	τ	PROPN
ejpam-5621	171	15	and	and	CCONJ
ejpam-5621	171	16	holder	holder	NOUN
ejpam-5621	171	17	’s	’s	PART
ejpam-5621	171	18	inequality	inequality	NOUN
ejpam-5621	171	19	i3	i3	PROPN
ejpam-5621	171	20	≤	≤	PUNCT
ejpam-5621	171	21	τ	τ	PROPN
ejpam-5621	171	22	∫	∫	PROPN
ejpam-5621	171	23	b2	b2	PROPN
ejpam-5621	171	24	|∇	|∇	PROPN
ejpam-5621	171	25	(	(	PUNCT
ejpam-5621	171	26	vm	vm	NOUN
ejpam-5621	171	27	−	−	NOUN
ejpam-5621	171	28	um)|pdx+	um)|pdx+	PROPN
ejpam-5621	172	1	c	c	PROPN
ejpam-5621	172	2	(	(	PUNCT
ejpam-5621	172	3	τ	τ	PROPN
ejpam-5621	172	4	)	)	PUNCT
ejpam-5621	172	5	∫	∫	PROPN
ejpam-5621	172	6	b2	b2	PROPN
ejpam-5621	172	7	|gm|pdx	|gm|pdx	PROPN
ejpam-5621	172	8	≤	≤	PROPN
ejpam-5621	172	9	τ	τ	PROPN
ejpam-5621	172	10	∫	∫	PROPN
ejpam-5621	172	11	b2	b2	PROPN
ejpam-5621	172	12	|∇(vm	|∇(vm	PROPN
ejpam-5621	172	13	−	−	PROPN
ejpam-5621	172	14	um)|pdx+	um)|pdx+	PROPN
ejpam-5621	172	15	c(τ	c(τ	PROPN
ejpam-5621	172	16	)	)	PUNCT
ejpam-5621	172	17	(	(	PUNCT
ejpam-5621	172	18	∫	∫	PROPN
ejpam-5621	172	19	b2	b2	PROPN
ejpam-5621	172	20	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	172	21	)	)	PUNCT
ejpam-5621	172	22	p	p	X
ejpam-5621	172	23	/	/	SYM
ejpam-5621	172	24	q1	q1	NOUN
ejpam-5621	172	25	≤	≤	NUM
ejpam-5621	172	26	τ	τ	PROPN
ejpam-5621	172	27	∫	∫	PROPN
ejpam-5621	172	28	b2	b2	PROPN
ejpam-5621	172	29	|∇(vm	|∇(vm	PROPN
ejpam-5621	172	30	−	−	PROPN
ejpam-5621	172	31	um)|pdx+	um)|pdx+	PROPN
ejpam-5621	172	32	c(τ)δp	c(τ)δp	PART
ejpam-5621	172	33	.	.	PUNCT
ejpam-5621	173	1	we	we	PRON
ejpam-5621	173	2	derive	derive	VERB
ejpam-5621	173	3	by	by	ADP
ejpam-5621	173	4	summing	sum	VERB
ejpam-5621	173	5	all	all	DET
ejpam-5621	173	6	the	the	DET
ejpam-5621	173	7	estimates	estimate	NOUN
ejpam-5621	173	8	of	of	ADP
ejpam-5621	173	9	ii	ii	PROPN
ejpam-5621	173	10	(	(	PUNCT
ejpam-5621	173	11	1	1	NUM
ejpam-5621	173	12	≤	≤	NUM
ejpam-5621	173	13	i	i	X
ejpam-5621	173	14	≤	≤	NOUN
ejpam-5621	173	15	3	3	NUM
ejpam-5621	173	16	):	):	PUNCT
ejpam-5621	173	17	c(τ	c(τ	PROPN
ejpam-5621	173	18	)	)	PUNCT
ejpam-5621	173	19	∫	∫	PROPN
ejpam-5621	173	20	b2	b2	PROPN
ejpam-5621	173	21	|∇(vm	|∇(vm	PROPN
ejpam-5621	173	22	−	−	PROPN
ejpam-5621	173	23	um)|pdx	um)|pdx	PROPN
ejpam-5621	173	24	≤	≤	PROPN
ejpam-5621	173	25	2τ	2τ	NUM
ejpam-5621	173	26	∫	∫	PROPN
ejpam-5621	173	27	b2	b2	PROPN
ejpam-5621	173	28	|∇(vm	|∇(vm	PROPN
ejpam-5621	173	29	−	−	PROPN
ejpam-5621	174	1	um)|pdx	um)|pdx	PROPN
ejpam-5621	175	1	+	+	PROPN
ejpam-5621	175	2	τ	τ	PROPN
ejpam-5621	175	3	∫	∫	PROPN
ejpam-5621	175	4	b2	b2	PROPN
ejpam-5621	175	5	|∇vm|pdx+	|∇vm|pdx+	NOUN
ejpam-5621	175	6	c(τ	c(τ	PROPN
ejpam-5621	175	7	)	)	PUNCT
ejpam-5621	175	8	[	[	PUNCT
ejpam-5621	175	9	δ(q2−p)/q2	δ(q2−p)/q2	NOUN
ejpam-5621	175	10	+	+	CCONJ
ejpam-5621	175	11	δp	δp	ADV
ejpam-5621	175	12	]	]	PUNCT
ejpam-5621	175	13	.	.	PUNCT
ejpam-5621	176	1	we	we	PRON
ejpam-5621	176	2	reach	reach	VERB
ejpam-5621	176	3	the	the	DET
ejpam-5621	176	4	following	follow	VERB
ejpam-5621	176	5	conclusion	conclusion	NOUN
ejpam-5621	176	6	by	by	ADP
ejpam-5621	176	7	selecting	select	VERB
ejpam-5621	176	8	a	a	DET
ejpam-5621	176	9	small	small	ADJ
ejpam-5621	176	10	constant	constant	ADJ
ejpam-5621	176	11	τ	τ	X
ejpam-5621	176	12	>	>	X
ejpam-5621	176	13	0	0	NUM
ejpam-5621	176	14	such	such	ADJ
ejpam-5621	176	15	that	that	SCONJ
ejpam-5621	176	16	0	0	NUM
ejpam-5621	176	17	<	<	X
ejpam-5621	176	18	τ	τ	PROPN
ejpam-5621	176	19	≪	≪	VERB
ejpam-5621	176	20	δ	δ	PROPN
ejpam-5621	176	21	<	<	X
ejpam-5621	176	22	1	1	NUM
ejpam-5621	176	23	,	,	PUNCT
ejpam-5621	176	24	and	and	CCONJ
ejpam-5621	176	25	then	then	ADV
ejpam-5621	176	26	applying	apply	VERB
ejpam-5621	176	27	(	(	PUNCT
ejpam-5621	176	28	13):∫	13):∫	NUM
ejpam-5621	176	29	b2	b2	NOUN
ejpam-5621	176	30	|∇(vm	|∇(vm	PROPN
ejpam-5621	176	31	−	−	PROPN
ejpam-5621	176	32	um)|pdx	um)|pdx	PROPN
ejpam-5621	176	33	≤	≤	PROPN
ejpam-5621	176	34	c	c	X
ejpam-5621	176	35	[	[	PUNCT
ejpam-5621	176	36	δ	δ	PROPN
ejpam-5621	176	37	+	+	CCONJ
ejpam-5621	176	38	δ	δ	PROPN
ejpam-5621	176	39	q2−p	q2−p	PROPN
ejpam-5621	176	40	q2	q2	NOUN
ejpam-5621	176	41	+	+	CCONJ
ejpam-5621	176	42	δp	δp	ADP
ejpam-5621	176	43	]	]	PUNCT
ejpam-5621	176	44	=	=	PUNCT
ejpam-5621	176	45	εp	εp	PROPN
ejpam-5621	176	46	,	,	PUNCT
ejpam-5621	176	47	by	by	ADP
ejpam-5621	176	48	choosing	choose	VERB
ejpam-5621	176	49	that	that	PRON
ejpam-5621	176	50	fulfills	fulfill	VERB
ejpam-5621	176	51	the	the	DET
ejpam-5621	176	52	final	final	ADJ
ejpam-5621	176	53	inequality	inequality	NOUN
ejpam-5621	176	54	stated	state	VERB
ejpam-5621	176	55	earlier	early	ADV
ejpam-5621	176	56	.	.	PUNCT
ejpam-5621	177	1	this	this	PRON
ejpam-5621	177	2	concludes	conclude	VERB
ejpam-5621	177	3	the	the	DET
ejpam-5621	177	4	evidence	evidence	NOUN
ejpam-5621	177	5	.	.	PUNCT
ejpam-5621	178	1	define	define	VERB
ejpam-5621	178	2	(	(	PUNCT
ejpam-5621	178	3	1	1	NUM
ejpam-5621	178	4	)	)	PUNCT
ejpam-5621	178	5	and	and	CCONJ
ejpam-5621	178	6	(	(	PUNCT
ejpam-5621	178	7	2	2	X
ejpam-5621	178	8	)	)	PUNCT
ejpam-5621	178	9	with	with	ADP
ejpam-5621	178	10	the	the	DET
ejpam-5621	178	11	same	same	ADJ
ejpam-5621	178	12	value	value	NOUN
ejpam-5621	178	13	of	of	ADP
ejpam-5621	178	14	δ	δ	PROPN
ejpam-5621	178	15	as	as	ADP
ejpam-5621	178	16	in	in	ADP
ejpam-5621	178	17	lemma	lemma	PROPN
ejpam-5621	178	18	2	2	NUM
ejpam-5621	178	19	.	.	PUNCT
ejpam-5621	178	20	as	as	SCONJ
ejpam-5621	178	21	stated	state	VERB
ejpam-5621	178	22	at	at	ADP
ejpam-5621	178	23	the	the	DET
ejpam-5621	178	24	outset	outset	NOUN
ejpam-5621	178	25	of	of	ADP
ejpam-5621	178	26	this	this	DET
ejpam-5621	178	27	segment	segment	NOUN
ejpam-5621	178	28	,	,	PUNCT
ejpam-5621	178	29	e	e	PROPN
ejpam-5621	178	30	is	be	AUX
ejpam-5621	178	31	vanishing	vanish	VERB
ejpam-5621	178	32	(	(	PUNCT
ejpam-5621	178	33	δ	δ	PROPN
ejpam-5621	178	34	,	,	PUNCT
ejpam-5621	178	35	1	1	NUM
ejpam-5621	178	36	)	)	PUNCT
ejpam-5621	178	37	.	.	PUNCT
ejpam-5621	179	1	thus	thus	ADV
ejpam-5621	179	2	(	(	PUNCT
ejpam-5621	179	3	perci)∫	perci)∫	AUX
ejpam-5621	179	4	bj	bj	NOUN
ejpam-5621	179	5	i	i	PRON
ejpam-5621	179	6	|e	|e	VERB
ejpam-5621	179	7	−	−	NOUN
ejpam-5621	179	8	ē	ē	ADV
ejpam-5621	179	9	bj	bj	VERB
ejpam-5621	179	10	i	i	PRON
ejpam-5621	179	11	|dx|	|dx|	VERB
ejpam-5621	179	12	≤	≤	NUM
ejpam-5621	179	13	δ	δ	PROPN
ejpam-5621	179	14	,	,	PUNCT
ejpam-5621	179	15	(	(	PUNCT
ejpam-5621	179	16	14	14	NUM
ejpam-5621	179	17	)	)	PUNCT
ejpam-5621	179	18	given	give	VERB
ejpam-5621	179	19	that	that	SCONJ
ejpam-5621	179	20	the	the	DET
ejpam-5621	179	21	radiuses	radius	NOUN
ejpam-5621	179	22	of	of	ADP
ejpam-5621	179	23	bj	bj	NOUN
ejpam-5621	179	24	i	i	PRON
ejpam-5621	179	25	(	(	PUNCT
ejpam-5621	179	26	0	0	NUM
ejpam-5621	179	27	≤	≤	NUM
ejpam-5621	179	28	j	j	PROPN
ejpam-5621	179	29	≤	≤	ADV
ejpam-5621	179	30	3	3	NUM
ejpam-5621	179	31	)	)	PUNCT
ejpam-5621	179	32	are	be	AUX
ejpam-5621	179	33	not	not	PART
ejpam-5621	179	34	greater	great	ADJ
ejpam-5621	179	35	than	than	ADP
ejpam-5621	179	36	1	1	NUM
ejpam-5621	179	37	for	for	ADP
ejpam-5621	179	38	j	j	PROPN
ejpam-5621	179	39	=	=	SYM
ejpam-5621	179	40	0	0	NUM
ejpam-5621	179	41	,	,	PUNCT
ejpam-5621	179	42	1	1	NUM
ejpam-5621	179	43	,	,	PUNCT
ejpam-5621	179	44	2	2	NUM
ejpam-5621	179	45	,	,	PUNCT
ejpam-5621	179	46	3	3	NUM
ejpam-5621	179	47	.	.	PUNCT
ejpam-5621	180	1	the	the	DET
ejpam-5621	180	2	scaling	scaling	ADJ
ejpam-5621	180	3	invariant	invariant	ADJ
ejpam-5621	180	4	form	form	NOUN
ejpam-5621	180	5	of	of	ADP
ejpam-5621	180	6	lemma	lemma	PROPN
ejpam-5621	180	7	2	2	NUM
ejpam-5621	180	8	is	be	AUX
ejpam-5621	180	9	then	then	ADV
ejpam-5621	180	10	obtained	obtain	VERB
ejpam-5621	180	11	by	by	ADP
ejpam-5621	180	12	recalling	recall	VERB
ejpam-5621	180	13	(	(	PUNCT
ejpam-5621	180	14	7	7	NUM
ejpam-5621	180	15	)	)	PUNCT
ejpam-5621	180	16	.	.	PUNCT
ejpam-5621	181	1	lemma	lemma	PROPN
ejpam-5621	181	2	6	6	NUM
ejpam-5621	181	3	.	.	PUNCT
ejpam-5621	181	4	considers	consider	VERB
ejpam-5621	181	5	the	the	DET
ejpam-5621	181	6	assumption	assumption	NOUN
ejpam-5621	181	7	that	that	PRON
ejpam-5621	181	8	λ	λ	PROPN
ejpam-5621	181	9	≥	≥	PRON
ejpam-5621	181	10	λ∗.	λ∗.	X
ejpam-5621	181	11	in	in	ADP
ejpam-5621	181	12	the	the	DET
ejpam-5621	181	13	case	case	NOUN
ejpam-5621	181	14	where	where	SCONJ
ejpam-5621	181	15	ε	ε	PROPN
ejpam-5621	181	16	is	be	AUX
ejpam-5621	181	17	greater	great	ADJ
ejpam-5621	181	18	than	than	ADP
ejpam-5621	181	19	zero	zero	NUM
ejpam-5621	181	20	,	,	PUNCT
ejpam-5621	181	21	there	there	PRON
ejpam-5621	181	22	is	be	VERB
ejpam-5621	181	23	a	a	DET
ejpam-5621	181	24	small	small	ADJ
ejpam-5621	181	25	δ	δ	NOUN
ejpam-5621	181	26	=	=	SYM
ejpam-5621	181	27	δ(ε	δ(ε	PROPN
ejpam-5621	181	28	)	)	PUNCT
ejpam-5621	181	29	>	>	X
ejpam-5621	181	30	0	0	NUM
ejpam-5621	181	31	such	such	ADJ
ejpam-5621	181	32	that	that	SCONJ
ejpam-5621	181	33	n0	n0	PROPN
ejpam-5621	181	34	is	be	AUX
ejpam-5621	181	35	greater	great	ADJ
ejpam-5621	181	36	than	than	ADP
ejpam-5621	181	37	one	one	NUM
ejpam-5621	181	38	and	and	CCONJ
ejpam-5621	181	39	vm	vm	PROPN
ejpam-5621	181	40	is	be	AUX
ejpam-5621	181	41	a	a	DET
ejpam-5621	181	42	local	local	ADJ
ejpam-5621	181	43	weak	weak	ADJ
ejpam-5621	181	44	solution	solution	NOUN
ejpam-5621	181	45	of	of	ADP
ejpam-5621	181	46	in	in	ADP
ejpam-5621	181	47	ω	ω	PROPN
ejpam-5621	181	48	with	with	ADP
ejpam-5621	181	49	b3	b3	PROPN
ejpam-5621	181	50	i	i	PROPN
ejpam-5621	181	51	⊂	⊂	PROPN
ejpam-5621	181	52	ω	ω	PROPN
ejpam-5621	181	53	.	.	PUNCT
ejpam-5621	181	54	sup	sup	PROPN
ejpam-5621	181	55	b2	b2	NOUN
ejpam-5621	181	56	i	i	PRON
ejpam-5621	181	57	∣∣∣∇(um)iλ	∣∣∣∇(um)iλ	ADJ
ejpam-5621	181	58	∣∣∣	∣∣∣	ADJ
ejpam-5621	181	59	≤	≤	PROPN
ejpam-5621	181	60	n0	n0	X
ejpam-5621	181	61	and	and	CCONJ
ejpam-5621	181	62	∫	∫	PROPN
ejpam-5621	181	63	b2	b2	PROPN
ejpam-5621	182	1	i	i	PRON
ejpam-5621	182	2	∣∣∇	∣∣∇	PROPN
ejpam-5621	182	3	(	(	PUNCT
ejpam-5621	182	4	vmλ	vmλ	NOUN
ejpam-5621	182	5	−	−	PROPN
ejpam-5621	182	6	(	(	PUNCT
ejpam-5621	182	7	vm)iλ	vm)iλ	NOUN
ejpam-5621	182	8	)	)	PUNCT
ejpam-5621	182	9	∣∣pdx	∣∣pdx	PROPN
ejpam-5621	182	10	≤	≤	NOUN
ejpam-5621	182	11	εp	εp	ADP
ejpam-5621	182	12	.	.	PUNCT
ejpam-5621	183	1	(	(	PUNCT
ejpam-5621	183	2	15	15	NUM
ejpam-5621	183	3	)	)	PUNCT
ejpam-5621	183	4	in	in	ADP
ejpam-5621	183	5	this	this	DET
ejpam-5621	183	6	context	context	NOUN
ejpam-5621	183	7	,	,	PUNCT
ejpam-5621	183	8	(	(	PUNCT
ejpam-5621	183	9	um)iλ	um)iλ	PROPN
ejpam-5621	183	10	denotes	denote	VERB
ejpam-5621	183	11	the	the	DET
ejpam-5621	183	12	weak	weak	ADJ
ejpam-5621	183	13	solution	solution	NOUN
ejpam-5621	183	14	of	of	ADP
ejpam-5621	183	15	equation	equation	NOUN
ejpam-5621	183	16	(	(	PUNCT
ejpam-5621	183	17	2	2	NUM
ejpam-5621	183	18	)	)	PUNCT
ejpam-5621	183	19	in	in	ADP
ejpam-5621	183	20	b2	b2	NOUN
ejpam-5621	184	1	i	i	PRON
ejpam-5621	184	2	,	,	PUNCT
ejpam-5621	184	3	where	where	SCONJ
ejpam-5621	184	4	vmλ	vmλ	NOUN
ejpam-5621	184	5	substitutes	substitute	VERB
ejpam-5621	184	6	for	for	ADP
ejpam-5621	184	7	vm	vm	PROPN
ejpam-5621	184	8	.	.	PUNCT
ejpam-5621	185	1	h.	h.	PROPN
ejpam-5621	185	2	ibrahim	ibrahim	PROPN
ejpam-5621	185	3	et	et	PROPN
ejpam-5621	185	4	al	al	PROPN
ejpam-5621	185	5	.	.	PUNCT
ejpam-5621	185	6	/	/	SYM
ejpam-5621	185	7	eur	eur	PROPN
ejpam-5621	185	8	.	.	PUNCT
ejpam-5621	186	1	j.	j.	PROPN
ejpam-5621	186	2	pure	pure	PROPN
ejpam-5621	186	3	appl	appl	PROPN
ejpam-5621	186	4	.	.	PROPN
ejpam-5621	186	5	math	math	PROPN
ejpam-5621	186	6	,	,	PUNCT
ejpam-5621	186	7	18	18	NUM
ejpam-5621	186	8	(	(	PUNCT
ejpam-5621	186	9	2	2	NUM
ejpam-5621	186	10	)	)	PUNCT
ejpam-5621	186	11	(	(	PUNCT
ejpam-5621	186	12	2025	2025	NUM
ejpam-5621	186	13	)	)	PUNCT
ejpam-5621	186	14	,	,	PUNCT
ejpam-5621	186	15	5621	5621	NUM
ejpam-5621	186	16	10	10	NUM
ejpam-5621	186	17	of	of	ADP
ejpam-5621	186	18	16	16	NUM
ejpam-5621	186	19	proof	proof	NOUN
ejpam-5621	186	20	.	.	PUNCT
ejpam-5621	187	1	resealing	reseal	VERB
ejpam-5621	187	2	the	the	DET
ejpam-5621	187	3	definitions	definition	NOUN
ejpam-5621	187	4	of	of	ADP
ejpam-5621	187	5	bj	bj	NOUN
ejpam-5621	187	6	i	i	PRON
ejpam-5621	187	7	for	for	ADP
ejpam-5621	187	8	j	j	PROPN
ejpam-5621	187	9	=	=	SYM
ejpam-5621	187	10	0	0	NUM
ejpam-5621	187	11	,	,	PUNCT
ejpam-5621	187	12	1	1	NUM
ejpam-5621	187	13	,	,	PUNCT
ejpam-5621	187	14	2	2	NUM
ejpam-5621	187	15	,	,	PUNCT
ejpam-5621	187	16	3	3	NUM
ejpam-5621	187	17	,	,	PUNCT
ejpam-5621	187	18	we	we	PRON
ejpam-5621	187	19	establish	establish	X
ejpam-5621	187	20	(	(	PUNCT
ejpam-5621	187	21	vm)iλ	vm)iλ	X
ejpam-5621	187	22	(	(	PUNCT
ejpam-5621	187	23	x	x	NOUN
ejpam-5621	187	24	)	)	PUNCT
ejpam-5621	187	25	=	=	SYM
ejpam-5621	187	26	vλm(23pxix	vλm(23pxix	NOUN
ejpam-5621	187	27	)	)	PUNCT
ejpam-5621	187	28	23pzi	23pzi	NOUN
ejpam-5621	187	29	,	,	PUNCT
ejpam-5621	187	30	(	(	PUNCT
ejpam-5621	187	31	gm)iλ	gm)iλ	X
ejpam-5621	187	32	(	(	PUNCT
ejpam-5621	187	33	x	x	NOUN
ejpam-5621	187	34	)	)	PUNCT
ejpam-5621	187	35	=	=	NOUN
ejpam-5621	187	36	gmλ(2	gmλ(2	ADJ
ejpam-5621	187	37	3pxix	3pxix	NUM
ejpam-5621	187	38	)	)	PUNCT
ejpam-5621	187	39	,	,	PUNCT
ejpam-5621	187	40	ei(x	ei(x	NUM
ejpam-5621	187	41	)	)	PUNCT
ejpam-5621	187	42	=	=	SYM
ejpam-5621	187	43	e(23pxix	e(23pxix	NOUN
ejpam-5621	187	44	)	)	PUNCT
ejpam-5621	187	45	,	,	PUNCT
ejpam-5621	187	46	x	x	PROPN
ejpam-5621	187	47	∈	∈	PROPN
ejpam-5621	187	48	b4	b4	NOUN
ejpam-5621	187	49	.	.	PUNCT
ejpam-5621	188	1	(	(	PUNCT
ejpam-5621	188	2	vm)iλ	vm)iλ	NOUN
ejpam-5621	188	3	is	be	AUX
ejpam-5621	188	4	therefore	therefore	ADV
ejpam-5621	188	5	a	a	DET
ejpam-5621	188	6	local	local	ADJ
ejpam-5621	188	7	weak	weak	ADJ
ejpam-5621	188	8	solution	solution	NOUN
ejpam-5621	188	9	of	of	ADP
ejpam-5621	188	10	div	div	X
ejpam-5621	188	11	(	(	PUNCT
ejpam-5621	188	12	ei∇	ei∇	X
ejpam-5621	188	13	(	(	PUNCT
ejpam-5621	188	14	vm)iλ	vm)iλ	PUNCT
ejpam-5621	188	15	·	·	PUNCT
ejpam-5621	188	16	∇(vm)iλ	∇(vm)iλ	NOUN
ejpam-5621	188	17	)	)	PUNCT
ejpam-5621	188	18	(	(	PUNCT
ejpam-5621	188	19	p−2)/2	p−2)/2	VERB
ejpam-5621	188	20	ei∇(vm)iλ	ei∇(vm)iλ	NOUN
ejpam-5621	188	21	=	=	SYM
ejpam-5621	188	22	div	div	X
ejpam-5621	188	23	(	(	PUNCT
ejpam-5621	188	24	|(gm)iλ|p−2(gm)iλ	|(gm)iλ|p−2(gm)iλ	PROPN
ejpam-5621	188	25	)	)	PUNCT
ejpam-5621	188	26	in	in	ADP
ejpam-5621	188	27	b4	b4	NOUN
ejpam-5621	188	28	.	.	PUNCT
ejpam-5621	189	1	it	it	PRON
ejpam-5621	189	2	is	be	AUX
ejpam-5621	189	3	easily	easily	ADV
ejpam-5621	189	4	discernible	discernible	ADJ
ejpam-5621	189	5	from	from	ADP
ejpam-5621	189	6	equations	equation	NOUN
ejpam-5621	189	7	(	(	PUNCT
ejpam-5621	189	8	7	7	NUM
ejpam-5621	189	9	)	)	PUNCT
ejpam-5621	189	10	and	and	CCONJ
ejpam-5621	189	11	(	(	PUNCT
ejpam-5621	189	12	14	14	NUM
ejpam-5621	189	13	)	)	PUNCT
ejpam-5621	189	14	that∫	that∫	NOUN
ejpam-5621	189	15	b4	b4	PROPN
ejpam-5621	189	16	∣∣∣∇(vm)iλ(x	∣∣∣∇(vm)iλ(x	PROPN
ejpam-5621	189	17	)	)	PUNCT
ejpam-5621	190	1	∣∣∣pdx	∣∣∣pdx	PROPN
ejpam-5621	190	2	≤	≤	NUM
ejpam-5621	190	3	1	1	NUM
ejpam-5621	190	4	,	,	PUNCT
ejpam-5621	190	5	∫	∫	PROPN
ejpam-5621	190	6	b4	b4	PROPN
ejpam-5621	190	7	∣∣∣(gm)iλ	∣∣∣(gm)iλ	PROPN
ejpam-5621	191	1	∣∣∣pdx	∣∣∣pdx	PROPN
ejpam-5621	191	2	≤	≤	PUNCT
ejpam-5621	191	3	δp	δp	ADP
ejpam-5621	191	4	and	and	CCONJ
ejpam-5621	191	5	∫	∫	PROPN
ejpam-5621	191	6	b2	b2	PROPN
ejpam-5621	191	7	∣∣ei	∣∣ei	PROPN
ejpam-5621	191	8	−	−	PROPN
ejpam-5621	191	9	ēi	ēi	NOUN
ejpam-5621	191	10	b2	b2	NOUN
ejpam-5621	191	11	∣∣pdx	∣∣pdx	PROPN
ejpam-5621	191	12	≤	≤	PROPN
ejpam-5621	191	13	δ	δ	PROPN
ejpam-5621	191	14	.	.	PUNCT
ejpam-5621	192	1	lemma	lemma	PROPN
ejpam-5621	192	2	1	1	NUM
ejpam-5621	192	3	subsequently	subsequently	ADV
ejpam-5621	192	4	states	state	VERB
ejpam-5621	192	5	that	that	SCONJ
ejpam-5621	192	6	a	a	DET
ejpam-5621	192	7	weak	weak	ADJ
ejpam-5621	192	8	solution	solution	NOUN
ejpam-5621	192	9	of	of	ADP
ejpam-5621	192	10	{	{	PUNCT
ejpam-5621	192	11	div	div	X
ejpam-5621	192	12	(	(	PUNCT
ejpam-5621	192	13	ēi	ēi	NOUN
ejpam-5621	192	14	b2	b2	NOUN
ejpam-5621	192	15	∇um	∇um	NOUN
ejpam-5621	192	16	·	·	PUNCT
ejpam-5621	192	17	∇umēi	∇umēi	NOUN
ejpam-5621	192	18	b2	b2	NOUN
ejpam-5621	192	19	∇um	∇um	NOUN
ejpam-5621	192	20	)	)	PUNCT
ejpam-5621	192	21	=	=	SYM
ejpam-5621	192	22	0	0	NUM
ejpam-5621	192	23	in	in	ADP
ejpam-5621	192	24	b2	b2	NOUN
ejpam-5621	192	25	um	um	INTJ
ejpam-5621	192	26	=	=	PUNCT
ejpam-5621	192	27	(	(	PUNCT
ejpam-5621	192	28	vm)iλ	vm)iλ	ADP
ejpam-5621	192	29	on	on	ADP
ejpam-5621	192	30	∂b2	∂b2	NOUN
ejpam-5621	192	31	in	in	ADP
ejpam-5621	192	32	the	the	DET
ejpam-5621	192	33	form	form	NOUN
ejpam-5621	192	34	that	that	PRON
ejpam-5621	192	35	sup	sup	NOUN
ejpam-5621	192	36	b1	b1	NOUN
ejpam-5621	192	37	|∇um|	|∇um|	NOUN
ejpam-5621	192	38	≤	≤	NOUN
ejpam-5621	192	39	n0	n0	X
ejpam-5621	192	40	and	and	CCONJ
ejpam-5621	192	41	∫	∫	PROPN
ejpam-5621	192	42	b2	b2	PROPN
ejpam-5621	192	43	∣∣∣∇	∣∣∣∇	PROPN
ejpam-5621	192	44	(	(	PUNCT
ejpam-5621	192	45	vm)iλ	vm)iλ	X
ejpam-5621	192	46	−	−	PROPN
ejpam-5621	192	47	um	um	INTJ
ejpam-5621	192	48	∣∣∣p	∣∣∣p	NOUN
ejpam-5621	192	49	dx	dx	PROPN
ejpam-5621	192	50	≤	≤	PROPN
ejpam-5621	192	51	εp	εp	ADP
ejpam-5621	192	52	at	at	ADP
ejpam-5621	192	53	this	this	DET
ejpam-5621	192	54	moment	moment	NOUN
ejpam-5621	192	55	,	,	PUNCT
ejpam-5621	192	56	we	we	PRON
ejpam-5621	192	57	define	define	VERB
ejpam-5621	192	58	(	(	PUNCT
ejpam-5621	192	59	um)iλ	um)iλ	PROPN
ejpam-5621	192	60	in	in	ADP
ejpam-5621	192	61	b2	b2	NOUN
ejpam-5621	192	62	i	i	PRON
ejpam-5621	192	63	by	by	ADP
ejpam-5621	192	64	um	um	INTJ
ejpam-5621	192	65	(	(	PUNCT
ejpam-5621	192	66	x	x	NOUN
ejpam-5621	192	67	)	)	PUNCT
ejpam-5621	192	68	=	=	SYM
ejpam-5621	192	69	1	1	NUM
ejpam-5621	192	70	23pxi	23pxi	NOUN
ejpam-5621	192	71	(	(	PUNCT
ejpam-5621	192	72	um)iλ	um)iλ	PROPN
ejpam-5621	192	73	(	(	PUNCT
ejpam-5621	192	74	23pxix	23pxix	NUM
ejpam-5621	192	75	)	)	PUNCT
ejpam-5621	192	76	,	,	PUNCT
ejpam-5621	192	77	x	x	PUNCT
ejpam-5621	192	78	∈	∈	PROPN
ejpam-5621	192	79	b2	b2	NOUN
ejpam-5621	192	80	.	.	PUNCT
ejpam-5621	193	1	then	then	ADV
ejpam-5621	193	2	,	,	PUNCT
ejpam-5621	193	3	by	by	ADP
ejpam-5621	193	4	modifying	modify	VERB
ejpam-5621	193	5	the	the	DET
ejpam-5621	193	6	variables	variable	NOUN
ejpam-5621	193	7	,	,	PUNCT
ejpam-5621	193	8	the	the	DET
ejpam-5621	193	9	conclusion	conclusion	NOUN
ejpam-5621	193	10	of	of	ADP
ejpam-5621	193	11	lemma	lemma	PROPN
ejpam-5621	193	12	3	3	NUM
ejpam-5621	193	13	is	be	AUX
ejpam-5621	193	14	reestablished	reestablish	VERB
ejpam-5621	193	15	.	.	PUNCT
ejpam-5621	194	1	such	such	ADJ
ejpam-5621	194	2	concludes	conclude	VERB
ejpam-5621	194	3	the	the	DET
ejpam-5621	194	4	evidence	evidence	NOUN
ejpam-5621	194	5	.	.	PUNCT
ejpam-5621	195	1	4	4	X
ejpam-5621	195	2	.	.	NUM
ejpam-5621	195	3	local	local	ADJ
ejpam-5621	195	4	and	and	CCONJ
ejpam-5621	195	5	gradient	gradient	ADJ
ejpam-5621	195	6	estimates	estimate	NOUN
ejpam-5621	195	7	for	for	ADP
ejpam-5621	195	8	elliptic	elliptic	ADJ
ejpam-5621	195	9	nonlinear	nonlinear	ADJ
ejpam-5621	195	10	equations	equation	NOUN
ejpam-5621	195	11	:	:	PUNCT
ejpam-5621	195	12	theorem	theorem	NOUN
ejpam-5621	195	13	1	1	NUM
ejpam-5621	195	14	.	.	PUNCT
ejpam-5621	195	15	considers	consider	VERB
ejpam-5621	195	16	the	the	DET
ejpam-5621	195	17	case	case	NOUN
ejpam-5621	195	18	where	where	SCONJ
ejpam-5621	195	19	q	q	PROPN
ejpam-5621	195	20	≥	≥	NOUN
ejpam-5621	195	21	p.	p.	NOUN
ejpam-5621	195	22	considers	consider	VERB
ejpam-5621	195	23	vm	vm	PROPN
ejpam-5621	195	24	to	to	PART
ejpam-5621	195	25	be	be	AUX
ejpam-5621	195	26	a	a	DET
ejpam-5621	195	27	feeble	feeble	ADJ
ejpam-5621	195	28	local	local	ADJ
ejpam-5621	195	29	solution	solution	NOUN
ejpam-5621	195	30	to	to	ADP
ejpam-5621	195	31	(	(	PUNCT
ejpam-5621	195	32	1	1	NUM
ejpam-5621	195	33	)	)	PUNCT
ejpam-5621	195	34	.	.	PUNCT
ejpam-5621	196	1	subsequently	subsequently	ADV
ejpam-5621	196	2	,	,	PUNCT
ejpam-5621	196	3	a	a	DET
ejpam-5621	196	4	small	small	ADJ
ejpam-5621	196	5	value	value	NOUN
ejpam-5621	196	6	of	of	ADP
ejpam-5621	196	7	δ	δ	PROPN
ejpam-5621	196	8	=	=	SYM
ejpam-5621	196	9	δ(n	δ(n	PROPN
ejpam-5621	196	10	,	,	PUNCT
ejpam-5621	196	11	p	p	X
ejpam-5621	196	12	,	,	PUNCT
ejpam-5621	196	13	q	q	X
ejpam-5621	196	14	,	,	PUNCT
ejpam-5621	196	15	α	α	NOUN
ejpam-5621	196	16	,	,	PUNCT
ejpam-5621	196	17	r	r	NOUN
ejpam-5621	196	18	)	)	PUNCT
ejpam-5621	196	19	>	>	X
ejpam-5621	196	20	0	0	PUNCT
ejpam-5621	196	21	is	be	AUX
ejpam-5621	196	22	present	present	ADJ
ejpam-5621	196	23	,	,	PUNCT
ejpam-5621	196	24	such	such	ADJ
ejpam-5621	196	25	that	that	PRON
ejpam-5621	196	26	for	for	ADP
ejpam-5621	196	27	every	every	DET
ejpam-5621	196	28	elliptical	elliptical	ADJ
ejpam-5621	196	29	function	function	NOUN
ejpam-5621	196	30	and	and	CCONJ
ejpam-5621	196	31	vanishing	vanish	VERB
ejpam-5621	196	32	(	(	PUNCT
ejpam-5621	196	33	δ	δ	PROPN
ejpam-5621	196	34	,	,	PUNCT
ejpam-5621	196	35	r	r	NOUN
ejpam-5621	196	36	)	)	PUNCT
ejpam-5621	196	37	,	,	PUNCT
ejpam-5621	196	38	as	as	ADV
ejpam-5621	196	39	well	well	ADV
ejpam-5621	196	40	as	as	ADP
ejpam-5621	196	41	for	for	ADP
ejpam-5621	196	42	every	every	DET
ejpam-5621	196	43	f	f	NOUN
ejpam-5621	196	44	with	with	ADP
ejpam-5621	196	45	gm	gm	PROPN
ejpam-5621	196	46	∈	∈	PROPN
ejpam-5621	196	47	lq	lq	VERB
ejpam-5621	196	48	loc(ω;r	loc(ω;r	PROPN
ejpam-5621	196	49	n	n	CCONJ
ejpam-5621	196	50	)	)	PUNCT
ejpam-5621	196	51	,	,	PUNCT
ejpam-5621	196	52	we	we	PRON
ejpam-5621	196	53	can	can	AUX
ejpam-5621	196	54	deduce	deduce	VERB
ejpam-5621	196	55	:	:	PUNCT
ejpam-5621	196	56	∫	∫	PROPN
ejpam-5621	196	57	br(x0	br(x0	NOUN
ejpam-5621	196	58	)	)	PUNCT
ejpam-5621	196	59	|∇vm|qdx	|∇vm|qdx	PROPN
ejpam-5621	196	60	≤	≤	NUM
ejpam-5621	196	61	c	c	NOUN
ejpam-5621	197	1	[	[	X
ejpam-5621	197	2	∫	∫	PROPN
ejpam-5621	197	3	b4r(x0	b4r(x0	PROPN
ejpam-5621	197	4	)	)	PUNCT
ejpam-5621	197	5	|vm|qdx+	|vm|qdx+	NOUN
ejpam-5621	197	6	∫	∫	PROPN
ejpam-5621	197	7	b4r(x0	b4r(x0	PROPN
ejpam-5621	197	8	)	)	PUNCT
ejpam-5621	197	9	|gm|qdx	|gm|qdx	NOUN
ejpam-5621	197	10	]	]	PUNCT
ejpam-5621	197	11	.	.	PUNCT
ejpam-5621	198	1	(	(	PUNCT
ejpam-5621	198	2	16	16	NUM
ejpam-5621	198	3	)	)	PUNCT
ejpam-5621	198	4	the	the	DET
ejpam-5621	198	5	constant	constant	ADJ
ejpam-5621	198	6	c	c	NOUN
ejpam-5621	198	7	is	be	AUX
ejpam-5621	198	8	independent	independent	ADJ
ejpam-5621	198	9	of	of	ADP
ejpam-5621	198	10	vmand	vmand	NOUN
ejpam-5621	198	11	gm	gm	PROPN
ejpam-5621	198	12	where	where	SCONJ
ejpam-5621	198	13	b4r(x0	b4r(x0	NOUN
ejpam-5621	198	14	)	)	PUNCT
ejpam-5621	199	1	⊂	⊂	PROPN
ejpam-5621	199	2	ω	ω	PROPN
ejpam-5621	199	3	.	.	PUNCT
ejpam-5621	200	1	our	our	PRON
ejpam-5621	200	2	strategy	strategy	NOUN
ejpam-5621	200	3	is	be	AUX
ejpam-5621	200	4	substantially	substantially	ADV
ejpam-5621	200	5	shaped	shape	VERB
ejpam-5621	200	6	by	by	ADP
ejpam-5621	200	7	[	[	X
ejpam-5621	200	8	5	5	NUM
ejpam-5621	200	9	,	,	PUNCT
ejpam-5621	200	10	14	14	NUM
ejpam-5621	200	11	]	]	PUNCT
ejpam-5621	200	12	.	.	PUNCT
ejpam-5621	201	1	h.	h.	PROPN
ejpam-5621	201	2	ibrahim	ibrahim	PROPN
ejpam-5621	201	3	et	et	PROPN
ejpam-5621	201	4	al	al	PROPN
ejpam-5621	201	5	.	.	PUNCT
ejpam-5621	201	6	/	/	SYM
ejpam-5621	201	7	eur	eur	PROPN
ejpam-5621	201	8	.	.	PUNCT
ejpam-5621	202	1	j.	j.	PROPN
ejpam-5621	202	2	pure	pure	PROPN
ejpam-5621	202	3	appl	appl	PROPN
ejpam-5621	202	4	.	.	PROPN
ejpam-5621	202	5	math	math	PROPN
ejpam-5621	202	6	,	,	PUNCT
ejpam-5621	202	7	18	18	NUM
ejpam-5621	202	8	(	(	PUNCT
ejpam-5621	202	9	2	2	NUM
ejpam-5621	202	10	)	)	PUNCT
ejpam-5621	202	11	(	(	PUNCT
ejpam-5621	202	12	2025	2025	NUM
ejpam-5621	202	13	)	)	PUNCT
ejpam-5621	202	14	,	,	PUNCT
ejpam-5621	202	15	5621	5621	NUM
ejpam-5621	202	16	11	11	NUM
ejpam-5621	202	17	of	of	ADP
ejpam-5621	202	18	16	16	NUM
ejpam-5621	202	19	proof	proof	NOUN
ejpam-5621	202	20	.	.	PUNCT
ejpam-5621	203	1	(	(	PUNCT
ejpam-5621	203	2	i	i	NOUN
ejpam-5621	203	3	)	)	PUNCT
ejpam-5621	203	4	for	for	ADP
ejpam-5621	203	5	q	q	NOUN
ejpam-5621	203	6	=	=	SYM
ejpam-5621	203	7	p	p	NOUN
ejpam-5621	203	8	,	,	PUNCT
ejpam-5621	203	9	the	the	DET
ejpam-5621	203	10	proof	proof	NOUN
ejpam-5621	203	11	is	be	AUX
ejpam-5621	203	12	uncomplicated	uncomplicated	ADJ
ejpam-5621	203	13	.	.	PUNCT
ejpam-5621	204	1	(	(	PUNCT
ejpam-5621	204	2	ii	ii	X
ejpam-5621	204	3	)	)	PUNCT
ejpam-5621	204	4	lemma	lemma	PROPN
ejpam-5621	204	5	(	(	PUNCT
ejpam-5621	204	6	3	3	X
ejpam-5621	204	7	)	)	PUNCT
ejpam-5621	204	8	states	state	VERB
ejpam-5621	204	9	that	that	SCONJ
ejpam-5621	204	10	for	for	ADP
ejpam-5621	204	11	all	all	DET
ejpam-5621	204	12	λ	λ	PROPN
ejpam-5621	204	13	≥	≥	PRON
ejpam-5621	204	14	λ∗	λ∗	PROPN
ejpam-5621	204	15	,	,	PUNCT
ejpam-5621	204	16	we	we	PRON
ejpam-5621	204	17	obtain∣∣{x	obtain∣∣{x	PROPN
ejpam-5621	204	18	∈	∈	PROPN
ejpam-5621	204	19	b1	b1	NOUN
ejpam-5621	204	20	i	i	PRON
ejpam-5621	204	21	:	:	PUNCT
ejpam-5621	204	22	|∇vm|	|∇vm|	X
ejpam-5621	204	23	>	>	X
ejpam-5621	204	24	2n0λ	2n0λ	NUM
ejpam-5621	204	25	}	}	PUNCT
ejpam-5621	204	26	∣∣	∣∣	NUM
ejpam-5621	204	27	=	=	PUNCT
ejpam-5621	204	28	∣∣{x	∣∣{x	PROPN
ejpam-5621	204	29	∈	∈	PROPN
ejpam-5621	204	30	b1	b1	NOUN
ejpam-5621	204	31	i	i	PRON
ejpam-5621	204	32	:	:	PUNCT
ejpam-5621	204	33	|∇vmλ|	|∇vmλ|	X
ejpam-5621	204	34	>	>	X
ejpam-5621	204	35	2n0	2n0	NUM
ejpam-5621	204	36	}	}	PUNCT
ejpam-5621	204	37	∣∣	∣∣	X
ejpam-5621	204	38	≤	≤	NUM
ejpam-5621	204	39	∣∣∣{x	∣∣∣{x	NOUN
ejpam-5621	204	40	∈	∈	PROPN
ejpam-5621	204	41	b1	b1	NOUN
ejpam-5621	205	1	i	i	PRON
ejpam-5621	205	2	:	:	PUNCT
ejpam-5621	205	3	∣∣∣∇(vmλ	∣∣∣∇(vmλ	VERB
ejpam-5621	205	4	−	−	PROPN
ejpam-5621	205	5	(	(	PUNCT
ejpam-5621	205	6	vm)iλ	vm)iλ	ADP
ejpam-5621	205	7	∣∣∣	∣∣∣	X
ejpam-5621	205	8	>	>	X
ejpam-5621	205	9	n0	n0	PROPN
ejpam-5621	205	10	}	}	PUNCT
ejpam-5621	205	11	∣∣∣	∣∣∣	NOUN
ejpam-5621	205	12	+	+	CCONJ
ejpam-5621	205	13	∣∣∣{x	∣∣∣{x	PROPN
ejpam-5621	205	14	∈	∈	PROPN
ejpam-5621	205	15	b1	b1	NOUN
ejpam-5621	205	16	i	i	PRON
ejpam-5621	205	17	:	:	PUNCT
ejpam-5621	205	18	∣∣∣∇(um)iλ	∣∣∣∇(um)iλ	ADJ
ejpam-5621	205	19	∣∣∣	∣∣∣	NOUN
ejpam-5621	205	20	>	>	X
ejpam-5621	205	21	n0	n0	ADJ
ejpam-5621	205	22	}	}	PUNCT
ejpam-5621	205	23	∣∣∣	∣∣∣	NOUN
ejpam-5621	205	24	=	=	SYM
ejpam-5621	205	25	∣∣∣{x	∣∣∣{x	NOUN
ejpam-5621	205	26	∈	∈	PROPN
ejpam-5621	205	27	b1	b1	NOUN
ejpam-5621	205	28	i	i	PRON
ejpam-5621	205	29	:	:	PUNCT
ejpam-5621	205	30	∣∣∣∇(umλ	∣∣∣∇(umλ	ADJ
ejpam-5621	205	31	−	−	X
ejpam-5621	205	32	(	(	PUNCT
ejpam-5621	205	33	um)iλ	um)iλ	PROPN
ejpam-5621	205	34	)	)	PUNCT
ejpam-5621	205	35	∣∣∣	∣∣∣	NOUN
ejpam-5621	205	36	>	>	X
ejpam-5621	205	37	n0	n0	PROPN
ejpam-5621	205	38	}	}	PUNCT
ejpam-5621	205	39	∣∣∣	∣∣∣	ADJ
ejpam-5621	205	40	≤	≤	NUM
ejpam-5621	205	41	1	1	NUM
ejpam-5621	205	42	np	np	PART
ejpam-5621	205	43	0	0	NUM
ejpam-5621	205	44	∫	∫	NOUN
ejpam-5621	205	45	b2	b2	PROPN
ejpam-5621	205	46	i	i	PRON
ejpam-5621	205	47	∣∣∣∇(vm	∣∣∣∇(vm	X
ejpam-5621	205	48	−	−	PROPN
ejpam-5621	205	49	(	(	PUNCT
ejpam-5621	205	50	um)iλ	um)iλ	NOUN
ejpam-5621	205	51	)	)	PUNCT
ejpam-5621	205	52	∣∣∣pdz	∣∣∣pdz	NOUN
ejpam-5621	205	53	≤	≤	NOUN
ejpam-5621	205	54	εp|b2	εp|b2	NOUN
ejpam-5621	206	1	i	i	PRON
ejpam-5621	206	2	|	|	ADV
ejpam-5621	206	3	np	np	INTJ
ejpam-5621	206	4	0	0	NUM
ejpam-5621	207	1	=	=	SYM
ejpam-5621	207	2	24nεp|b0	24nεp|b0	NUM
ejpam-5621	208	1	i	i	PRON
ejpam-5621	208	2	|	|	ADV
ejpam-5621	208	3	np	np	INTJ
ejpam-5621	208	4	0	0	NUM
ejpam-5621	208	5	.	.	PUNCT
ejpam-5621	209	1	consequently	consequently	ADV
ejpam-5621	209	2	,	,	PUNCT
ejpam-5621	209	3	as	as	SCONJ
ejpam-5621	209	4	shown	show	VERB
ejpam-5621	209	5	in	in	ADP
ejpam-5621	209	6	lemma	lemma	PROPN
ejpam-5621	209	7	2	2	NUM
ejpam-5621	209	8	,	,	PUNCT
ejpam-5621	209	9	that∣∣{x	that∣∣{x	PROPN
ejpam-5621	209	10	∈	∈	PROPN
ejpam-5621	209	11	b1	b1	NOUN
ejpam-5621	209	12	i	i	PRON
ejpam-5621	209	13	:	:	PUNCT
ejpam-5621	209	14	|∇vm|	|∇vm|	X
ejpam-5621	209	15	>	>	X
ejpam-5621	209	16	2n0λ	2n0λ	NUM
ejpam-5621	209	17	}	}	PUNCT
ejpam-5621	209	18	∣∣	∣∣	X
ejpam-5621	210	1	≤	≤	PUNCT
ejpam-5621	210	2	c	c	X
ejpam-5621	210	3	(	(	PUNCT
ejpam-5621	210	4	εp	εp	ADP
ejpam-5621	210	5	1	1	NUM
ejpam-5621	210	6	λp	λp	NOUN
ejpam-5621	210	7	∫	∫	PROPN
ejpam-5621	210	8	{	{	PUNCT
ejpam-5621	210	9	x∈b0	x∈b0	PROPN
ejpam-5621	211	1	i	i	PRON
ejpam-5621	211	2	:	:	PUNCT
ejpam-5621	211	3	|∇vm	|∇vm	NOUN
ejpam-5621	211	4	>	>	X
ejpam-5621	211	5	λ	λ	PROPN
ejpam-5621	211	6	4	4	NUM
ejpam-5621	211	7	|	|	ADV
ejpam-5621	211	8	}	}	PUNCT
ejpam-5621	211	9	|∇vm|p	|∇vm|p	ADP
ejpam-5621	211	10	dx	dx	PROPN
ejpam-5621	211	11	)	)	PUNCT
ejpam-5621	212	1	+	+	CCONJ
ejpam-5621	212	2	1	1	NUM
ejpam-5621	212	3	λq1δq1	λq1δq1	PRON
ejpam-5621	212	4	(	(	PUNCT
ejpam-5621	212	5	∫	∫	PROPN
ejpam-5621	212	6	{	{	PUNCT
ejpam-5621	212	7	x∈b0	x∈b0	PROPN
ejpam-5621	213	1	i	i	PRON
ejpam-5621	213	2	:	:	PUNCT
ejpam-5621	213	3	|g|>δλ/4	|g|>δλ/4	PROPN
ejpam-5621	213	4	}	}	PUNCT
ejpam-5621	213	5	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	213	6	)	)	PUNCT
ejpam-5621	213	7	.	.	PUNCT
ejpam-5621	214	1	in	in	ADP
ejpam-5621	214	2	the	the	DET
ejpam-5621	214	3	given	give	VERB
ejpam-5621	214	4	context	context	NOUN
ejpam-5621	214	5	,	,	PUNCT
ejpam-5621	214	6	c	c	NOUN
ejpam-5621	214	7	=	=	SYM
ejpam-5621	214	8	c(n	c(n	PROPN
ejpam-5621	214	9	,	,	PUNCT
ejpam-5621	214	10	p	p	X
ejpam-5621	214	11	,	,	PUNCT
ejpam-5621	214	12	q1	q1	PROPN
ejpam-5621	214	13	,	,	PUNCT
ejpam-5621	214	14	α	α	NOUN
ejpam-5621	214	15	)	)	PUNCT
ejpam-5621	214	16	.	.	PUNCT
ejpam-5621	215	1	keeping	keep	VERB
ejpam-5621	215	2	in	in	ADP
ejpam-5621	215	3	mind	mind	NOUN
ejpam-5621	215	4	that	that	SCONJ
ejpam-5621	215	5	the	the	DET
ejpam-5621	215	6	spheres	sphere	NOUN
ejpam-5621	215	7	are	be	AUX
ejpam-5621	215	8	disconnected	disconnected	ADJ
ejpam-5621	215	9	and	and	CCONJ
ejpam-5621	215	10	⋃	⋃	ADV
ejpam-5621	215	11	i∈n	i∈n	NOUN
ejpam-5621	215	12	b1	b1	NOUN
ejpam-5621	215	13	i	i	PRON
ejpam-5621	215	14	⊃	⊃	X
ejpam-5621	215	15	a(λ	a(λ	ADV
ejpam-5621	215	16	)	)	PUNCT
ejpam-5621	215	17	=	=	PRON
ejpam-5621	215	18	{	{	PUNCT
ejpam-5621	215	19	x	x	PUNCT
ejpam-5621	215	20	∈	∈	PROPN
ejpam-5621	215	21	b1	b1	NOUN
ejpam-5621	215	22	:	:	PUNCT
ejpam-5621	215	23	|∇vm|	|∇vm|	X
ejpam-5621	215	24	>	>	X
ejpam-5621	215	25	λ	λ	X
ejpam-5621	215	26	}	}	PUNCT
ejpam-5621	215	27	.	.	PUNCT
ejpam-5621	216	1	we	we	PRON
ejpam-5621	216	2	obtain	obtain	VERB
ejpam-5621	216	3	the	the	DET
ejpam-5621	216	4	following	following	NOUN
ejpam-5621	216	5	by	by	ADP
ejpam-5621	216	6	summing	sum	VERB
ejpam-5621	216	7	i	i	PRON
ejpam-5621	216	8	∈	∈	PROPN
ejpam-5621	216	9	n	n	CCONJ
ejpam-5621	216	10	in	in	ADP
ejpam-5621	216	11	the	the	DET
ejpam-5621	216	12	inequality	inequality	NOUN
ejpam-5621	216	13	above	above	ADV
ejpam-5621	216	14	for	for	ADP
ejpam-5621	216	15	any	any	DET
ejpam-5621	216	16	λ	λ	PROPN
ejpam-5621	216	17	≥	≥	NUM
ejpam-5621	216	18	λ∗	λ∗	NOUN
ejpam-5621	216	19	:	:	PUNCT
ejpam-5621	216	20	|{x	|{x	PUNCT
ejpam-5621	216	21	∈	∈	PROPN
ejpam-5621	216	22	b1	b1	NOUN
ejpam-5621	216	23	:	:	PUNCT
ejpam-5621	216	24	|∇vm|	|∇vm|	X
ejpam-5621	216	25	>	>	X
ejpam-5621	216	26	2n0λ}|	2n0λ}|	NUM
ejpam-5621	216	27	≤	≤	NOUN
ejpam-5621	216	28	∑	∑	PUNCT
ejpam-5621	216	29	i	i	PROPN
ejpam-5621	216	30	∣∣{x	∣∣{x	PROPN
ejpam-5621	216	31	∈	∈	PROPN
ejpam-5621	216	32	b1	b1	NOUN
ejpam-5621	216	33	i	i	PRON
ejpam-5621	216	34	:	:	PUNCT
ejpam-5621	216	35	|∇vm|	|∇vm|	X
ejpam-5621	216	36	>	>	X
ejpam-5621	216	37	2n0λ	2n0λ	NUM
ejpam-5621	216	38	}	}	PUNCT
ejpam-5621	216	39	∣∣	∣∣	PROPN
ejpam-5621	216	40	≤	≤	NUM
ejpam-5621	216	41	cεp	cεp	NOUN
ejpam-5621	216	42	(	(	PUNCT
ejpam-5621	216	43	1	1	NUM
ejpam-5621	216	44	λp	λp	X
ejpam-5621	216	45	∫	∫	PROPN
ejpam-5621	216	46	{	{	PUNCT
ejpam-5621	216	47	x∈b2:|∇vm|>λ	x∈b2:|∇vm|>λ	X
ejpam-5621	216	48	4	4	NUM
ejpam-5621	216	49	}	}	SYM
ejpam-5621	216	50	|∇vm|pdx+	|∇vm|pdx+	NUM
ejpam-5621	216	51	1	1	NUM
ejpam-5621	216	52	λq1δq1	λq1δq1	ADJ
ejpam-5621	217	1	∫	∫	PROPN
ejpam-5621	217	2	{	{	PUNCT
ejpam-5621	217	3	x∈b2:|gm|	x∈b2:|gm|	PROPN
ejpam-5621	217	4	>	>	X
ejpam-5621	217	5	δλ	δλ	PROPN
ejpam-5621	217	6	4	4	NUM
ejpam-5621	217	7	}	}	PUNCT
ejpam-5621	217	8	|gm|q1dx	|gm|q1dx	PROPN
ejpam-5621	217	9	)	)	PUNCT
ejpam-5621	217	10	(	(	PUNCT
ejpam-5621	217	11	17	17	NUM
ejpam-5621	217	12	)	)	PUNCT
ejpam-5621	217	13	in	in	ADP
ejpam-5621	217	14	the	the	DET
ejpam-5621	217	15	case	case	NOUN
ejpam-5621	217	16	of	of	ADP
ejpam-5621	217	17	any	any	DET
ejpam-5621	217	18	λ	λ	NOUN
ejpam-5621	217	19	≥	≥	NUM
ejpam-5621	217	20	λ∗.	λ∗.	X
ejpam-5621	217	21	we	we	PRON
ejpam-5621	217	22	compute	compute	VERB
ejpam-5621	217	23	while	while	SCONJ
ejpam-5621	217	24	recalling	recall	VERB
ejpam-5621	217	25	the	the	DET
ejpam-5621	217	26	standard	standard	ADJ
ejpam-5621	217	27	argument	argument	NOUN
ejpam-5621	217	28	of	of	ADP
ejpam-5621	217	29	measure	measure	NOUN
ejpam-5621	217	30	theory	theory	NOUN
ejpam-5621	217	31	.	.	PUNCT
ejpam-5621	218	1	∫	∫	PROPN
ejpam-5621	218	2	b1	b1	PROPN
ejpam-5621	218	3	|∇vm|q	|∇vm|q	CCONJ
ejpam-5621	218	4	dz	dz	PROPN
ejpam-5621	218	5	=	=	PUNCT
ejpam-5621	218	6	q	q	NOUN
ejpam-5621	218	7	∫∞	∫∞	NOUN
ejpam-5621	218	8	0	0	PUNCT
ejpam-5621	219	1	µq−1	µq−1	PRON
ejpam-5621	219	2	|{x	|{x	SYM
ejpam-5621	219	3	∈	∈	PROPN
ejpam-5621	219	4	b1	b1	NOUN
ejpam-5621	219	5	:	:	PUNCT
ejpam-5621	219	6	|∇vm|	|∇vm|	X
ejpam-5621	219	7	>	>	X
ejpam-5621	219	8	µ}|	µ}|	NOUN
ejpam-5621	219	9	dµ	dµ	PRON
ejpam-5621	219	10	=	=	PUNCT
ejpam-5621	219	11	q	q	PUNCT
ejpam-5621	219	12	∫	∫	PROPN
ejpam-5621	220	1	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	220	2	0	0	NUM
ejpam-5621	221	1	µq−1	µq−1	ADJ
ejpam-5621	221	2	|{x	|{x	SYM
ejpam-5621	221	3	∈	∈	PROPN
ejpam-5621	221	4	b1	b1	NOUN
ejpam-5621	221	5	:	:	PUNCT
ejpam-5621	221	6	|∇vm|	|∇vm|	X
ejpam-5621	221	7	>	>	X
ejpam-5621	221	8	µ}|	µ}|	PROPN
ejpam-5621	221	9	dµ+	dµ+	NOUN
ejpam-5621	221	10	q	q	PROPN
ejpam-5621	221	11	∫∞	∫∞	NOUN
ejpam-5621	221	12	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	221	13	µq−1	µq−1	PROPN
ejpam-5621	221	14	|{x	|{x	CCONJ
ejpam-5621	221	15	∈	∈	PROPN
ejpam-5621	221	16	b1	b1	NOUN
ejpam-5621	221	17	:	:	PUNCT
ejpam-5621	221	18	|∇vm|	|∇vm|	X
ejpam-5621	221	19	>	>	X
ejpam-5621	221	20	µ}|	µ}|	NOUN
ejpam-5621	221	21	dµ	dµ	PRON
ejpam-5621	221	22	=	=	PUNCT
ejpam-5621	221	23	q	q	PUNCT
ejpam-5621	221	24	∫	∫	PROPN
ejpam-5621	221	25	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	221	26	0	0	NUM
ejpam-5621	222	1	µq−1	µq−1	ADJ
ejpam-5621	222	2	|{x	|{x	SYM
ejpam-5621	222	3	∈	∈	PROPN
ejpam-5621	222	4	b1	b1	NOUN
ejpam-5621	222	5	:	:	PUNCT
ejpam-5621	222	6	|∇vm|	|∇vm|	X
ejpam-5621	222	7	>	>	X
ejpam-5621	222	8	µ}|	µ}|	VERB
ejpam-5621	222	9	dµ	dµ	ADP
ejpam-5621	223	1	+	+	NOUN
ejpam-5621	223	2	q	q	X
ejpam-5621	223	3	∫∞	∫∞	NOUN
ejpam-5621	223	4	λ∗	λ∗	PROPN
ejpam-5621	223	5	(	(	PUNCT
ejpam-5621	223	6	2n0λ	2n0λ	NUM
ejpam-5621	223	7	)	)	PUNCT
ejpam-5621	223	8	q−1	q−1	PROPN
ejpam-5621	223	9	|{x	|{x	X
ejpam-5621	223	10	∈	∈	PROPN
ejpam-5621	223	11	b1	b1	NOUN
ejpam-5621	223	12	:	:	PUNCT
ejpam-5621	223	13	|∇vm|	|∇vm|	X
ejpam-5621	223	14	>	>	X
ejpam-5621	223	15	2n0λ}|	2n0λ}|	NUM
ejpam-5621	223	16	d(2n0λ	d(2n0λ	NOUN
ejpam-5621	223	17	)	)	PUNCT
ejpam-5621	224	1	=	=	NOUN
ejpam-5621	224	2	:	:	PUNCT
ejpam-5621	224	3	j1	j1	PROPN
ejpam-5621	224	4	+	+	CCONJ
ejpam-5621	224	5	j2	j2	PROPN
ejpam-5621	224	6	.	.	PROPN
ejpam-5621	224	7	estimation	estimation	NOUN
ejpam-5621	224	8	of	of	ADP
ejpam-5621	224	9	j1	j1	PROPN
ejpam-5621	224	10	:	:	PUNCT
ejpam-5621	224	11	it	it	PRON
ejpam-5621	224	12	can	can	AUX
ejpam-5621	224	13	be	be	AUX
ejpam-5621	224	14	deduced	deduce	VERB
ejpam-5621	224	15	from	from	ADP
ejpam-5621	224	16	the	the	DET
ejpam-5621	224	17	definitions	definition	NOUN
ejpam-5621	224	18	of	of	ADP
ejpam-5621	224	19	λ∗	λ∗	NOUN
ejpam-5621	224	20	and	and	CCONJ
ejpam-5621	224	21	λ0	λ0	NOUN
ejpam-5621	224	22	that	that	DET
ejpam-5621	224	23	λq∗	λq∗	NOUN
ejpam-5621	225	1	=	=	SYM
ejpam-5621	225	2	26nq	26nq	PROPN
ejpam-5621	225	3	/	/	SYM
ejpam-5621	225	4	pλq0	pλq0	PROPN
ejpam-5621	225	5	≤	≤	PROPN
ejpam-5621	225	6	c	c	NOUN
ejpam-5621	225	7	{	{	PUNCT
ejpam-5621	225	8	(	(	PUNCT
ejpam-5621	225	9	∫	∫	PROPN
ejpam-5621	225	10	b2	b2	PROPN
ejpam-5621	225	11	|∇vm|p	|∇vm|p	PROPN
ejpam-5621	225	12	dx	dx	PROPN
ejpam-5621	225	13	)	)	PUNCT
ejpam-5621	226	1	q	q	PROPN
ejpam-5621	227	1	p	p	NOUN
ejpam-5621	227	2	+	+	NOUN
ejpam-5621	227	3	1	1	NUM
ejpam-5621	227	4	δq	δq	PART
ejpam-5621	227	5	(	(	PUNCT
ejpam-5621	227	6	∫	∫	PROPN
ejpam-5621	227	7	b2	b2	PROPN
ejpam-5621	227	8	|gm|q1	|gm|q1	NOUN
ejpam-5621	227	9	dx	dx	PROPN
ejpam-5621	227	10	)	)	PUNCT
ejpam-5621	227	11	q	q	PROPN
ejpam-5621	227	12	q1	q1	PROPN
ejpam-5621	227	13	}	}	PUNCT
ejpam-5621	227	14	.	.	PUNCT
ejpam-5621	228	1	(	(	PUNCT
ejpam-5621	228	2	18	18	NUM
ejpam-5621	228	3	)	)	PUNCT
ejpam-5621	228	4	consequently	consequently	ADV
ejpam-5621	228	5	,	,	PUNCT
ejpam-5621	228	6	lemma	lemma	PROPN
ejpam-5621	228	7	(	(	PUNCT
ejpam-5621	228	8	1	1	NUM
ejpam-5621	228	9	)	)	PUNCT
ejpam-5621	228	10	and	and	CCONJ
ejpam-5621	228	11	holder	holder	NOUN
ejpam-5621	228	12	’s	’s	PART
ejpam-5621	228	13	inequality	inequality	NOUN
ejpam-5621	228	14	dictate	dictate	VERB
ejpam-5621	228	15	that	that	SCONJ
ejpam-5621	228	16	λq∗	λq∗	NOUN
ejpam-5621	228	17	≤	≤	NUM
ejpam-5621	229	1	c	c	X
ejpam-5621	230	1	[	[	X
ejpam-5621	230	2	(	(	PUNCT
ejpam-5621	230	3	∫	∫	PROPN
ejpam-5621	230	4	b4	b4	PROPN
ejpam-5621	230	5	|vm|p	|vm|p	PROPN
ejpam-5621	230	6	dx+	dx+	ADJ
ejpam-5621	230	7	∫	∫	PROPN
ejpam-5621	230	8	b4	b4	PROPN
ejpam-5621	230	9	|gm|p	|gm|p	PROPN
ejpam-5621	230	10	dx	dx	PROPN
ejpam-5621	230	11	)	)	PUNCT
ejpam-5621	231	1	q	q	PROPN
ejpam-5621	232	1	p	p	NOUN
ejpam-5621	232	2	+	+	NOUN
ejpam-5621	232	3	1	1	NUM
ejpam-5621	232	4	δq	δq	PART
ejpam-5621	232	5	(	(	PUNCT
ejpam-5621	232	6	∫	∫	PROPN
ejpam-5621	232	7	b2	b2	PROPN
ejpam-5621	232	8	|gm|q1	|gm|q1	NOUN
ejpam-5621	232	9	dx	dx	PROPN
ejpam-5621	232	10	)	)	PUNCT
ejpam-5621	232	11	q	q	PROPN
ejpam-5621	232	12	q1	q1	PROPN
ejpam-5621	232	13	]	]	PUNCT
ejpam-5621	232	14	≤	≤	NUM
ejpam-5621	232	15	c	c	X
ejpam-5621	233	1	[	[	X
ejpam-5621	233	2	(	(	PUNCT
ejpam-5621	233	3	∫	∫	PROPN
ejpam-5621	233	4	b4	b4	PROPN
ejpam-5621	233	5	|vm|pdx	|vm|pdx	VERB
ejpam-5621	233	6	)	)	PUNCT
ejpam-5621	233	7	q	q	X
ejpam-5621	233	8	/	/	SYM
ejpam-5621	234	1	p	p	X
ejpam-5621	234	2	+	+	CCONJ
ejpam-5621	234	3	(	(	PUNCT
ejpam-5621	234	4	∫	∫	PROPN
ejpam-5621	234	5	b4	b4	PROPN
ejpam-5621	234	6	|gm|pdx	|gm|pdx	PROPN
ejpam-5621	234	7	)	)	PUNCT
ejpam-5621	235	1	q	q	X
ejpam-5621	235	2	/	/	SYM
ejpam-5621	236	1	p	p	X
ejpam-5621	236	2	+	+	NOUN
ejpam-5621	236	3	1	1	NUM
ejpam-5621	236	4	δq	δq	ADP
ejpam-5621	236	5	∫	∫	PROPN
ejpam-5621	236	6	b2	b2	PROPN
ejpam-5621	236	7	|gm|qdx	|gm|qdx	NOUN
ejpam-5621	236	8	]	]	PUNCT
ejpam-5621	236	9	≤	≤	PROPN
ejpam-5621	236	10	c	c	X
ejpam-5621	236	11	{	{	PUNCT
ejpam-5621	236	12	∫	∫	PROPN
ejpam-5621	236	13	b4	b4	PROPN
ejpam-5621	236	14	|vm|qdx+	|vm|qdx+	PROPN
ejpam-5621	236	15	∫	∫	PROPN
ejpam-5621	236	16	b4	b4	PROPN
ejpam-5621	236	17	|gm|qdx	|gm|qdx	PROPN
ejpam-5621	236	18	}	}	PUNCT
ejpam-5621	236	19	.	.	PUNCT
ejpam-5621	237	1	h.	h.	PROPN
ejpam-5621	237	2	ibrahim	ibrahim	PROPN
ejpam-5621	237	3	et	et	PROPN
ejpam-5621	237	4	al	al	PROPN
ejpam-5621	237	5	.	.	PUNCT
ejpam-5621	237	6	/	/	SYM
ejpam-5621	237	7	eur	eur	PROPN
ejpam-5621	237	8	.	.	PUNCT
ejpam-5621	238	1	j.	j.	PROPN
ejpam-5621	238	2	pure	pure	PROPN
ejpam-5621	238	3	appl	appl	PROPN
ejpam-5621	238	4	.	.	PROPN
ejpam-5621	238	5	math	math	PROPN
ejpam-5621	238	6	,	,	PUNCT
ejpam-5621	238	7	18	18	NUM
ejpam-5621	238	8	(	(	PUNCT
ejpam-5621	238	9	2	2	NUM
ejpam-5621	238	10	)	)	PUNCT
ejpam-5621	238	11	(	(	PUNCT
ejpam-5621	238	12	2025	2025	NUM
ejpam-5621	238	13	)	)	PUNCT
ejpam-5621	238	14	,	,	PUNCT
ejpam-5621	238	15	5621	5621	NUM
ejpam-5621	238	16	12	12	NUM
ejpam-5621	238	17	of	of	ADP
ejpam-5621	238	18	16	16	NUM
ejpam-5621	238	19	from	from	ADP
ejpam-5621	238	20	[	[	X
ejpam-5621	238	21	14	14	NUM
ejpam-5621	238	22	]	]	PUNCT
ejpam-5621	238	23	we	we	PRON
ejpam-5621	238	24	see	see	VERB
ejpam-5621	238	25	that	that	SCONJ
ejpam-5621	238	26	,	,	PUNCT
ejpam-5621	238	27	1	1	NUM
ejpam-5621	238	28	δq	δq	PROPN
ejpam-5621	238	29	→	→	SYM
ejpam-5621	238	30	0	0	NUM
ejpam-5621	238	31	,	,	PUNCT
ejpam-5621	238	32	and	and	CCONJ
ejpam-5621	238	33	we	we	PRON
ejpam-5621	238	34	have	have	VERB
ejpam-5621	238	35	:	:	PUNCT
ejpam-5621	238	36	λq∗	λq∗	X
ejpam-5621	238	37	≤	≤	PROPN
ejpam-5621	239	1	c	c	X
ejpam-5621	239	2	{	{	PUNCT
ejpam-5621	239	3	∫	∫	PROPN
ejpam-5621	239	4	b4	b4	PROPN
ejpam-5621	239	5	|vm|qdx+	|vm|qdx+	PROPN
ejpam-5621	239	6	∫	∫	PROPN
ejpam-5621	239	7	b4	b4	PROPN
ejpam-5621	239	8	|gm|qdx	|gm|qdx	ADV
ejpam-5621	239	9	}	}	PUNCT
ejpam-5621	239	10	.	.	PUNCT
ejpam-5621	240	1	hence	hence	ADV
ejpam-5621	240	2	,	,	PUNCT
ejpam-5621	240	3	we	we	PRON
ejpam-5621	240	4	ascertain	ascertain	VERB
ejpam-5621	240	5	j1	j1	PROPN
ejpam-5621	240	6	≤	≤	NUM
ejpam-5621	240	7	(	(	PUNCT
ejpam-5621	240	8	2n0λ∗	2n0λ∗	NOUN
ejpam-5621	240	9	)	)	PUNCT
ejpam-5621	240	10	q	q	NOUN
ejpam-5621	240	11	|b1|	|b1|	NOUN
ejpam-5621	240	12	≤	≤	PROPN
ejpam-5621	240	13	c	c	PROPN
ejpam-5621	240	14	{	{	PUNCT
ejpam-5621	240	15	∫	∫	PROPN
ejpam-5621	240	16	b4	b4	PROPN
ejpam-5621	240	17	|vm|qdx+	|vm|qdx+	PROPN
ejpam-5621	240	18	∫	∫	PROPN
ejpam-5621	240	19	b4	b4	PROPN
ejpam-5621	240	20	|gm|qdx	|gm|qdx	PROPN
ejpam-5621	240	21	}	}	PUNCT
ejpam-5621	240	22	,	,	PUNCT
ejpam-5621	240	23	where	where	SCONJ
ejpam-5621	240	24	c	c	NOUN
ejpam-5621	240	25	=	=	SYM
ejpam-5621	240	26	c(n	c(n	PROPN
ejpam-5621	240	27	,	,	PUNCT
ejpam-5621	240	28	p	p	X
ejpam-5621	240	29	,	,	PUNCT
ejpam-5621	240	30	q	q	X
ejpam-5621	240	31	,	,	PUNCT
ejpam-5621	240	32	α	α	NOUN
ejpam-5621	240	33	)	)	PUNCT
ejpam-5621	240	34	.	.	PUNCT
ejpam-5621	241	1	probability	probability	NOUN
ejpam-5621	241	2	of	of	ADP
ejpam-5621	241	3	j2	j2	PROPN
ejpam-5621	241	4	.	.	PUNCT
ejpam-5621	242	1	by	by	ADP
ejpam-5621	242	2	deriving	derive	VERB
ejpam-5621	242	3	from	from	ADP
ejpam-5621	242	4	(	(	PUNCT
ejpam-5621	242	5	17	17	NUM
ejpam-5621	242	6	)	)	PUNCT
ejpam-5621	242	7	,	,	PUNCT
ejpam-5621	242	8	we	we	PRON
ejpam-5621	242	9	obtain	obtain	VERB
ejpam-5621	242	10	that	that	SCONJ
ejpam-5621	242	11	j2	j2	PROPN
ejpam-5621	242	12	≤	≤	PROPN
ejpam-5621	242	13	cεp	cεp	NOUN
ejpam-5621	242	14	{	{	PUNCT
ejpam-5621	242	15	∫∞	∫∞	NOUN
ejpam-5621	242	16	0	0	PUNCT
ejpam-5621	242	17	λq−p−1	λq−p−1	X
ejpam-5621	242	18	∫	∫	PROPN
ejpam-5621	242	19	{	{	PUNCT
ejpam-5621	242	20	x∈b2:|∇vm|>λ/4	x∈b2:|∇vm|>λ/4	PROPN
ejpam-5621	242	21	}	}	PUNCT
ejpam-5621	242	22	|∇vm|pdxdλ	|∇vm|pdxdλ	VERB
ejpam-5621	243	1	+	+	CCONJ
ejpam-5621	243	2	1	1	NUM
ejpam-5621	243	3	δq1	δq1	NOUN
ejpam-5621	243	4	∫∞	∫∞	NOUN
ejpam-5621	243	5	0	0	PUNCT
ejpam-5621	244	1	λq−q1−1	λq−q1−1	ADJ
ejpam-5621	244	2	∫	∫	PROPN
ejpam-5621	244	3	{	{	PUNCT
ejpam-5621	244	4	x∈b2:|gm|>δλ/4	x∈b2:|gm|>δλ/4	PROPN
ejpam-5621	244	5	}	}	PUNCT
ejpam-5621	244	6	|gm|q1dxdλ	|gm|q1dxdλ	NUM
ejpam-5621	244	7	}	}	PUNCT
ejpam-5621	244	8	.	.	PUNCT
ejpam-5621	245	1	considering	consider	VERB
ejpam-5621	245	2	that∫	that∫	PROPN
ejpam-5621	245	3	rn	rn	PROPN
ejpam-5621	245	4	|fm|βdx	|fm|βdx	NOUN
ejpam-5621	245	5	=	=	SYM
ejpam-5621	245	6	(	(	PUNCT
ejpam-5621	245	7	β	β	NOUN
ejpam-5621	245	8	−	−	PROPN
ejpam-5621	245	9	λ	λ	PROPN
ejpam-5621	245	10	)	)	PUNCT
ejpam-5621	245	11	∫	∫	PROPN
ejpam-5621	245	12	∞	∞	PROPN
ejpam-5621	245	13	0	0	NUM
ejpam-5621	245	14	µβ−α−1	µβ−α−1	NUM
ejpam-5621	245	15	∫	∫	PROPN
ejpam-5621	245	16	{	{	PUNCT
ejpam-5621	245	17	x∈rn:|fm|>µ	x∈rn:|fm|>µ	PROPN
ejpam-5621	245	18	}	}	PUNCT
ejpam-5621	245	19	fm	fm	PROPN
ejpam-5621	245	20	αdxdµ.	αdxdµ.	NOUN
ejpam-5621	245	21	given	give	VERB
ejpam-5621	245	22	β	β	PRON
ejpam-5621	245	23	>	>	X
ejpam-5621	245	24	λ	λ	X
ejpam-5621	245	25	>	>	X
ejpam-5621	245	26	1	1	NUM
ejpam-5621	245	27	,	,	PUNCT
ejpam-5621	245	28	we	we	PRON
ejpam-5621	245	29	obtain	obtain	VERB
ejpam-5621	245	30	j2	j2	NOUN
ejpam-5621	245	31	≤	≤	PROPN
ejpam-5621	245	32	c1ε	c1ε	ADP
ejpam-5621	245	33	p	p	DET
ejpam-5621	245	34	∫	∫	PROPN
ejpam-5621	245	35	b2	b2	PROPN
ejpam-5621	245	36	|∇um|qdx+	|∇um|qdx+	NOUN
ejpam-5621	245	37	c2ε	c2ε	PROPN
ejpam-5621	245	38	p	p	NOUN
ejpam-5621	245	39	∫	∫	PROPN
ejpam-5621	245	40	b2	b2	PROPN
ejpam-5621	245	41	|fm|qdx	|fm|qdx	ADV
ejpam-5621	245	42	,	,	PUNCT
ejpam-5621	245	43	in	in	ADP
ejpam-5621	245	44	that	that	PRON
ejpam-5621	245	45	where	where	SCONJ
ejpam-5621	245	46	c1	c1	PROPN
ejpam-5621	245	47	=	=	PUNCT
ejpam-5621	245	48	c1(n	c1(n	PROPN
ejpam-5621	245	49	,	,	PUNCT
ejpam-5621	245	50	p	p	X
ejpam-5621	245	51	,	,	PUNCT
ejpam-5621	245	52	q	q	ADJ
ejpam-5621	245	53	,	,	PUNCT
ejpam-5621	245	54	α	α	NOUN
ejpam-5621	245	55	)	)	PUNCT
ejpam-5621	245	56	and	and	CCONJ
ejpam-5621	245	57	c2	c2	PROPN
ejpam-5621	245	58	=	=	SYM
ejpam-5621	245	59	c2(n	c2(n	PROPN
ejpam-5621	245	60	,	,	PUNCT
ejpam-5621	245	61	p	p	X
ejpam-5621	245	62	,	,	PUNCT
ejpam-5621	245	63	q	q	X
ejpam-5621	245	64	,	,	PUNCT
ejpam-5621	245	65	α	α	PROPN
ejpam-5621	245	66	,	,	PUNCT
ejpam-5621	245	67	δ	δ	PROPN
ejpam-5621	245	68	)	)	PUNCT
ejpam-5621	245	69	.	.	PUNCT
ejpam-5621	246	1	we	we	PRON
ejpam-5621	246	2	obtain	obtain	VERB
ejpam-5621	246	3	by	by	ADP
ejpam-5621	246	4	combining	combine	VERB
ejpam-5621	246	5	the	the	DET
ejpam-5621	246	6	estimates	estimate	NOUN
ejpam-5621	246	7	of	of	ADP
ejpam-5621	246	8	j1	j1	PROPN
ejpam-5621	246	9	and	and	CCONJ
ejpam-5621	246	10	j2.∫	j2.∫	CCONJ
ejpam-5621	246	11	b1	b1	NOUN
ejpam-5621	246	12	|∇vm|qdx	|∇vm|qdx	NOUN
ejpam-5621	246	13	≤	≤	NOUN
ejpam-5621	246	14	c1ε	c1ε	ADP
ejpam-5621	246	15	p	p	DET
ejpam-5621	246	16	∫	∫	PROPN
ejpam-5621	246	17	b2	b2	PROPN
ejpam-5621	246	18	|∇vm|qdx+	|∇vm|qdx+	PROPN
ejpam-5621	246	19	c3	c3	PROPN
ejpam-5621	246	20	∫	∫	PROPN
ejpam-5621	246	21	b4	b4	PROPN
ejpam-5621	246	22	(	(	PUNCT
ejpam-5621	246	23	|vm|q	|vm|q	X
ejpam-5621	246	24	+	+	NUM
ejpam-5621	246	25	|gm|q	|gm|q	NOUN
ejpam-5621	246	26	)	)	PUNCT
ejpam-5621	246	27	dx	dx	PROPN
ejpam-5621	246	28	,	,	PUNCT
ejpam-5621	246	29	c3	c3	NOUN
ejpam-5621	246	30	=	=	PUNCT
ejpam-5621	246	31	c3(n	c3(n	PROPN
ejpam-5621	246	32	,	,	PUNCT
ejpam-5621	246	33	p	p	X
ejpam-5621	246	34	,	,	PUNCT
ejpam-5621	246	35	q	q	X
ejpam-5621	246	36	,	,	PUNCT
ejpam-5621	246	37	α	α	PROPN
ejpam-5621	246	38	,	,	PUNCT
ejpam-5621	246	39	δ	δ	PROPN
ejpam-5621	246	40	,	,	PUNCT
ejpam-5621	246	41	ε	ε	PROPN
ejpam-5621	246	42	)	)	PUNCT
ejpam-5621	246	43	.	.	PUNCT
ejpam-5621	247	1	using	use	VERB
ejpam-5621	247	2	a	a	DET
ejpam-5621	247	3	covering	covering	NOUN
ejpam-5621	247	4	and	and	CCONJ
ejpam-5621	247	5	iteration	iteration	NOUN
ejpam-5621	247	6	argument	argument	NOUN
ejpam-5621	247	7	to	to	ADP
ejpam-5621	247	8	[	[	X
ejpam-5621	247	9	15	15	NUM
ejpam-5621	247	10	,	,	PUNCT
ejpam-5621	247	11	16	16	NUM
ejpam-5621	247	12	]	]	PUNCT
ejpam-5621	247	13	to	to	PART
ejpam-5621	247	14	re	re	AUX
ejpam-5621	247	15	incorporate	incorporate	VERB
ejpam-5621	247	16	at	at	ADP
ejpam-5621	247	17	the	the	DET
ejpam-5621	247	18	right	right	ADJ
ejpam-5621	247	19	-	-	PUNCT
ejpam-5621	247	20	hand	hand	NOUN
ejpam-5621	247	21	side	side	NOUN
ejpam-5621	247	22	the	the	DET
ejpam-5621	247	23	first	first	ADJ
ejpam-5621	247	24	integral	integral	NOUN
ejpam-5621	247	25	in	in	ADP
ejpam-5621	247	26	the	the	DET
ejpam-5621	247	27	aforementioned	aforementioned	ADJ
ejpam-5621	247	28	inequality	inequality	NOUN
ejpam-5621	247	29	while	while	SCONJ
ejpam-5621	247	30	selecting	select	VERB
ejpam-5621	247	31	a	a	DET
ejpam-5621	247	32	suitable	suitable	ADJ
ejpam-5621	247	33	ε	ε	NOUN
ejpam-5621	247	34	such	such	ADJ
ejpam-5621	247	35	that	that	SCONJ
ejpam-5621	247	36	c1ε	c1ε	PROPN
ejpam-5621	247	37	p	p	NOUN
ejpam-5621	247	38	=	=	SYM
ejpam-5621	247	39	1/2	1/2	NUM
ejpam-5621	247	40	,	,	PUNCT
ejpam-5621	247	41	we	we	PRON
ejpam-5621	247	42	obtain	obtain	VERB
ejpam-5621	247	43	the	the	DET
ejpam-5621	247	44	following:∫	following:∫	NOUN
ejpam-5621	247	45	b1	b1	NOUN
ejpam-5621	247	46	|∇vm|q	|∇vm|q	NOUN
ejpam-5621	247	47	dx	dx	PROPN
ejpam-5621	247	48	≤	≤	PROPN
ejpam-5621	247	49	c	c	PROPN
ejpam-5621	247	50	{	{	PUNCT
ejpam-5621	247	51	∫	∫	PROPN
ejpam-5621	247	52	b4	b4	PROPN
ejpam-5621	247	53	|vm|q	|vm|q	X
ejpam-5621	247	54	dx+	dx+	ADJ
ejpam-5621	247	55	∫	∫	PROPN
ejpam-5621	247	56	b4	b4	PROPN
ejpam-5621	247	57	|gm|q	|gm|q	PROPN
ejpam-5621	247	58	dx	dx	PROPN
ejpam-5621	247	59	}	}	PUNCT
ejpam-5621	247	60	.	.	PUNCT
ejpam-5621	248	1	by	by	ADP
ejpam-5621	248	2	performing	perform	VERB
ejpam-5621	248	3	a	a	DET
ejpam-5621	248	4	shift	shift	NOUN
ejpam-5621	248	5	and	and	CCONJ
ejpam-5621	248	6	scaling	scaling	NOUN
ejpam-5621	248	7	transform	transform	NOUN
ejpam-5621	248	8	,	,	PUNCT
ejpam-5621	248	9	the	the	DET
ejpam-5621	248	10	proof	proof	NOUN
ejpam-5621	248	11	of	of	ADP
ejpam-5621	248	12	the	the	DET
ejpam-5621	248	13	main	main	ADJ
ejpam-5621	248	14	result	result	NOUN
ejpam-5621	248	15	can	can	AUX
ejpam-5621	248	16	be	be	AUX
ejpam-5621	248	17	completed	complete	VERB
ejpam-5621	248	18	.	.	PUNCT
ejpam-5621	249	1	corollary	corollary	ADJ
ejpam-5621	249	2	1	1	NUM
ejpam-5621	249	3	.	.	PUNCT
ejpam-5621	249	4	considers	consider	VERB
ejpam-5621	249	5	vm	vm	PROPN
ejpam-5621	249	6	to	to	PART
ejpam-5621	249	7	be	be	AUX
ejpam-5621	249	8	a	a	DET
ejpam-5621	249	9	sequence	sequence	NOUN
ejpam-5621	249	10	of	of	ADP
ejpam-5621	249	11	local	local	ADJ
ejpam-5621	249	12	weak	weak	ADJ
ejpam-5621	249	13	solutions	solution	NOUN
ejpam-5621	249	14	to	to	ADP
ejpam-5621	249	15	equation	equation	NOUN
ejpam-5621	249	16	(	(	PUNCT
ejpam-5621	249	17	1	1	NUM
ejpam-5621	249	18	)	)	PUNCT
ejpam-5621	249	19	,	,	PUNCT
ejpam-5621	249	20	assuming	assume	VERB
ejpam-5621	249	21	that	that	SCONJ
ejpam-5621	249	22	ε	ε	PROPN
ejpam-5621	249	23	is	be	AUX
ejpam-5621	249	24	greater	great	ADJ
ejpam-5621	249	25	than	than	ADP
ejpam-5621	249	26	zero	zero	NUM
ejpam-5621	249	27	.	.	PUNCT
ejpam-5621	250	1	subsequently	subsequently	ADV
ejpam-5621	250	2	,	,	PUNCT
ejpam-5621	250	3	a	a	DET
ejpam-5621	250	4	small	small	ADJ
ejpam-5621	250	5	value	value	NOUN
ejpam-5621	250	6	of	of	ADP
ejpam-5621	250	7	δ	δ	PROPN
ejpam-5621	250	8	=	=	SYM
ejpam-5621	250	9	δ(n	δ(n	PROPN
ejpam-5621	250	10	,	,	PUNCT
ejpam-5621	250	11	1+ε	1+ε	NUM
ejpam-5621	250	12	,	,	PUNCT
ejpam-5621	250	13	1+ε	1+ε	NUM
ejpam-5621	250	14	ε	ε	PROPN
ejpam-5621	250	15	,	,	PUNCT
ejpam-5621	250	16	α	α	NOUN
ejpam-5621	250	17	,	,	PUNCT
ejpam-5621	250	18	r	r	NOUN
ejpam-5621	250	19	)	)	PUNCT
ejpam-5621	250	20	>	>	X
ejpam-5621	251	1	θ	θ	PROPN
ejpam-5621	252	1	h.	h.	PROPN
ejpam-5621	252	2	ibrahim	ibrahim	PROPN
ejpam-5621	252	3	et	et	PROPN
ejpam-5621	252	4	al	al	PROPN
ejpam-5621	252	5	.	.	PUNCT
ejpam-5621	252	6	/	/	SYM
ejpam-5621	252	7	eur	eur	PROPN
ejpam-5621	252	8	.	.	PUNCT
ejpam-5621	253	1	j.	j.	PROPN
ejpam-5621	253	2	pure	pure	PROPN
ejpam-5621	253	3	appl	appl	PROPN
ejpam-5621	253	4	.	.	PROPN
ejpam-5621	253	5	math	math	PROPN
ejpam-5621	253	6	,	,	PUNCT
ejpam-5621	253	7	18	18	NUM
ejpam-5621	253	8	(	(	PUNCT
ejpam-5621	253	9	2	2	NUM
ejpam-5621	253	10	)	)	PUNCT
ejpam-5621	253	11	(	(	PUNCT
ejpam-5621	253	12	2025	2025	NUM
ejpam-5621	253	13	)	)	PUNCT
ejpam-5621	253	14	,	,	PUNCT
ejpam-5621	253	15	5621	5621	NUM
ejpam-5621	253	16	13	13	NUM
ejpam-5621	253	17	of	of	ADP
ejpam-5621	253	18	16	16	NUM
ejpam-5621	253	19	is	be	AUX
ejpam-5621	253	20	present	present	ADJ
ejpam-5621	253	21	,	,	PUNCT
ejpam-5621	253	22	such	such	ADJ
ejpam-5621	253	23	that	that	PRON
ejpam-5621	253	24	for	for	ADP
ejpam-5621	253	25	every	every	PRON
ejpam-5621	253	26	elliptically	elliptically	ADV
ejpam-5621	253	27	shaped	shape	VERB
ejpam-5621	253	28	and	and	CCONJ
ejpam-5621	253	29	vanished	vanish	VERB
ejpam-5621	253	30	set	set	VERB
ejpam-5621	253	31	e(δ	e(δ	PROPN
ejpam-5621	253	32	,	,	PUNCT
ejpam-5621	253	33	r	r	NOUN
ejpam-5621	253	34	)	)	PUNCT
ejpam-5621	253	35	and	and	CCONJ
ejpam-5621	253	36	every	every	PRON
ejpam-5621	253	37	set	set	VERB
ejpam-5621	253	38	gm	gm	PROPN
ejpam-5621	253	39	with	with	ADP
ejpam-5621	253	40	gm	gm	PROPN
ejpam-5621	253	41	∈	∈	PROPN
ejpam-5621	253	42	l	l	NOUN
ejpam-5621	253	43	1+ϵ	1+ϵ	NUM
ejpam-5621	253	44	ϵ	ϵ	PRON
ejpam-5621	253	45	loc	loc	X
ejpam-5621	253	46	(	(	PUNCT
ejpam-5621	253	47	ω;rn	ω;rn	ADJ
ejpam-5621	253	48	)	)	PUNCT
ejpam-5621	253	49	,	,	PUNCT
ejpam-5621	253	50	we	we	PRON
ejpam-5621	253	51	can	can	AUX
ejpam-5621	253	52	deduce:∫	deduce:∫	PROPN
ejpam-5621	253	53	br(x0	br(x0	VERB
ejpam-5621	253	54	)	)	PUNCT
ejpam-5621	254	1	∑s	∑s	PROPN
ejpam-5621	255	1	m=1	m=1	X
ejpam-5621	255	2	|∇vm|	|∇vm|	NOUN
ejpam-5621	255	3	1+ϵ	1+ϵ	NUM
ejpam-5621	255	4	ϵ	ϵ	X
ejpam-5621	255	5	dx	dx	PROPN
ejpam-5621	255	6	≤	≤	NUM
ejpam-5621	255	7	c̄	c̄	PROPN
ejpam-5621	256	1	[	[	X
ejpam-5621	256	2	∫	∫	NUM
ejpam-5621	256	3	b4r(x0	b4r(x0	PROPN
ejpam-5621	256	4	)	)	PUNCT
ejpam-5621	256	5	∑s	∑s	PROPN
ejpam-5621	256	6	m=1	m=1	PROPN
ejpam-5621	257	1	|vm|	|vm|	NOUN
ejpam-5621	257	2	1+ε	1+ε	NUM
ejpam-5621	257	3	ε	ε	PROPN
ejpam-5621	257	4	dx+	dx+	ADJ
ejpam-5621	257	5	∫	∫	PROPN
ejpam-5621	257	6	b4r(x0	b4r(x0	PROPN
ejpam-5621	257	7	)	)	PUNCT
ejpam-5621	258	1	∑s	∑s	PROPN
ejpam-5621	258	2	m=1	m=1	X
ejpam-5621	259	1	|gm|	|gm|	NOUN
ejpam-5621	259	2	1+ε	1+ε	NUM
ejpam-5621	259	3	ε	ε	PROPN
ejpam-5621	259	4	dx	dx	PROPN
ejpam-5621	259	5	]	]	PUNCT
ejpam-5621	259	6	where	where	SCONJ
ejpam-5621	259	7	c̄	c̄	PROPN
ejpam-5621	259	8	is	be	AUX
ejpam-5621	259	9	a	a	DET
ejpam-5621	259	10	constant	constant	ADJ
ejpam-5621	259	11	that	that	PRON
ejpam-5621	259	12	is	be	AUX
ejpam-5621	259	13	not	not	PART
ejpam-5621	259	14	dependent	dependent	ADJ
ejpam-5621	259	15	on	on	ADP
ejpam-5621	259	16	um	um	INTJ
ejpam-5621	259	17	and	and	CCONJ
ejpam-5621	259	18	gm	gm	PROPN
ejpam-5621	259	19	,	,	PUNCT
ejpam-5621	259	20	and	and	CCONJ
ejpam-5621	259	21	b4r(x0	b4r(x0	PROPN
ejpam-5621	259	22	)	)	PUNCT
ejpam-5621	260	1	⊂	⊂	PROPN
ejpam-5621	260	2	ω	ω	PROPN
ejpam-5621	260	3	.	.	PUNCT
ejpam-5621	261	1	proof	proof	NOUN
ejpam-5621	261	2	.	.	PUNCT
ejpam-5621	262	1	lemma	lemma	PROPN
ejpam-5621	262	2	2	2	NUM
ejpam-5621	262	3	states	state	VERB
ejpam-5621	262	4	that	that	SCONJ
ejpam-5621	262	5	for	for	ADP
ejpam-5621	262	6	any	any	DET
ejpam-5621	262	7	λ	λ	NOUN
ejpam-5621	262	8	=	=	PROPN
ejpam-5621	262	9	λ∗	λ∗	PROPN
ejpam-5621	263	1	+	+	CCONJ
ejpam-5621	263	2	ϵ	ϵ	X
ejpam-5621	263	3	,	,	PUNCT
ejpam-5621	263	4	we	we	PRON
ejpam-5621	263	5	obtain	obtain	VERB
ejpam-5621	263	6	1/	1/	NUM
ejpam-5621	263	7	(	(	PUNCT
ejpam-5621	263	8	2x	2x	NUM
ejpam-5621	263	9	∈	∈	PROPN
ejpam-5621	263	10	b1	b1	NOUN
ejpam-5621	263	11	i	i	PRON
ejpam-5621	263	12	:	:	PUNCT
ejpam-5621	264	1	∑s	∑s	PROPN
ejpam-5621	264	2	m=1	m=1	X
ejpam-5621	264	3	|vm|	|vm|	NOUN
ejpam-5621	264	4	>	>	X
ejpam-5621	264	5	2n0(λ∗	2n0(λ∗	NUM
ejpam-5621	265	1	+	+	CCONJ
ejpam-5621	265	2	ϵ	ϵ	X
ejpam-5621	265	3	)	)	PUNCT
ejpam-5621	265	4	)	)	PUNCT
ejpam-5621	266	1	1/2	1/2	NUM
ejpam-5621	266	2	=	=	SYM
ejpam-5621	266	3	1/	1/	NUM
ejpam-5621	266	4	{	{	PUNCT
ejpam-5621	266	5	x	x	SYM
ejpam-5621	266	6	∈	∈	PROPN
ejpam-5621	266	7	b1	b1	NOUN
ejpam-5621	267	1	i	i	PRON
ejpam-5621	267	2	:	:	PUNCT
ejpam-5621	267	3	∑s	∑s	PROPN
ejpam-5621	267	4	m=1	m=1	X
ejpam-5621	267	5	|(vm)λ∗+ϵ|	|(vm)λ∗+ϵ|	NOUN
ejpam-5621	267	6	>	>	X
ejpam-5621	267	7	2n0	2n0	NUM
ejpam-5621	267	8	}	}	SYM
ejpam-5621	267	9	1/2	1/2	NUM
ejpam-5621	267	10	≤	≤	NUM
ejpam-5621	267	11	1/{x	1/{x	NUM
ejpam-5621	267	12	∈	∈	NOUN
ejpam-5621	267	13	b1	b1	NOUN
ejpam-5621	267	14	i	i	PRON
ejpam-5621	267	15	:	:	PUNCT
ejpam-5621	267	16	∑s	∑s	PROPN
ejpam-5621	267	17	m=1	m=1	X
ejpam-5621	267	18	∣∣∣((vm)λ∗+ε	∣∣∣((vm)λ∗+ε	ADJ
ejpam-5621	267	19	−	−	PROPN
ejpam-5621	267	20	(	(	PUNCT
ejpam-5621	267	21	um)iλ∗+ε	um)iλ∗+ε	ADJ
ejpam-5621	267	22	)	)	PUNCT
ejpam-5621	267	23	∣∣∣	∣∣∣	ADP
ejpam-5621	267	24	>	>	X
ejpam-5621	267	25	n0	n0	PROPN
ejpam-5621	267	26	}	}	PUNCT
ejpam-5621	267	27	1/2	1/2	NUM
ejpam-5621	267	28	+	+	NUM
ejpam-5621	267	29	∣∣∣{x	∣∣∣{x	PROPN
ejpam-5621	267	30	∈	∈	PROPN
ejpam-5621	267	31	b1	b1	NOUN
ejpam-5621	267	32	i	i	PRON
ejpam-5621	267	33	:	:	PUNCT
ejpam-5621	267	34	∣∣∣∇(um)iλ∗+ε	∣∣∣∇(um)iλ∗+ε	ADP
ejpam-5621	267	35	∣∣∣	∣∣∣	ADJ
ejpam-5621	267	36	>	>	X
ejpam-5621	267	37	n0	n0	ADJ
ejpam-5621	267	38	}	}	PUNCT
ejpam-5621	267	39	∣∣∣	∣∣∣	NOUN
ejpam-5621	267	40	=	=	SYM
ejpam-5621	267	41	1/{x	1/{x	NUM
ejpam-5621	267	42	∈	∈	NOUN
ejpam-5621	267	43	b1	b1	NOUN
ejpam-5621	267	44	i	i	PRON
ejpam-5621	267	45	:	:	PUNCT
ejpam-5621	267	46	∑s	∑s	PROPN
ejpam-5621	267	47	m=1	m=1	X
ejpam-5621	267	48	∣∣∣∇((vm)λ∗+ε	∣∣∣∇((vm)λ∗+ε	ADJ
ejpam-5621	267	49	−	−	PROPN
ejpam-5621	267	50	(	(	PUNCT
ejpam-5621	267	51	um)iλ∗+ε	um)iλ∗+ε	ADJ
ejpam-5621	267	52	)	)	PUNCT
ejpam-5621	267	53	∣∣∣	∣∣∣	ADP
ejpam-5621	267	54	>	>	X
ejpam-5621	267	55	n0	n0	PROPN
ejpam-5621	267	56	}	}	PUNCT
ejpam-5621	267	57	1/2	1/2	NUM
ejpam-5621	267	58	≤	≤	NUM
ejpam-5621	267	59	1	1	NUM
ejpam-5621	268	1	n1+ε	n1+ε	PROPN
ejpam-5621	268	2	0	0	NUM
ejpam-5621	268	3	∫	∫	PROPN
ejpam-5621	268	4	b2	b2	NOUN
ejpam-5621	269	1	i	i	NOUN
ejpam-5621	269	2	∑s	∑s	PROPN
ejpam-5621	270	1	m=1	m=1	X
ejpam-5621	270	2	∣∣∣∇(vm)λ∗+ε	∣∣∣∇(vm)λ∗+ε	PROPN
ejpam-5621	270	3	−	−	PROPN
ejpam-5621	270	4	(	(	PUNCT
ejpam-5621	270	5	um)iλ∗+ε	um)iλ∗+ε	ADV
ejpam-5621	270	6	)	)	PUNCT
ejpam-5621	270	7	∣∣∣1+ε	∣∣∣1+ε	NOUN
ejpam-5621	270	8	dz	dz	NOUN
ejpam-5621	270	9	≤	≤	NUM
ejpam-5621	270	10	ε1+ε|b2	ε1+ε|b2	NOUN
ejpam-5621	271	1	i	i	PRON
ejpam-5621	271	2	|	|	ADV
ejpam-5621	271	3	n1+ε	n1+ε	VERB
ejpam-5621	271	4	0	0	NUM
ejpam-5621	272	1	=	=	SYM
ejpam-5621	272	2	24nε1+ε|b0	24nε1+ε|b0	NOUN
ejpam-5621	273	1	i	i	PRON
ejpam-5621	273	2	|	|	ADV
ejpam-5621	273	3	n1+ε	n1+ε	PROPN
ejpam-5621	273	4	0	0	NUM
ejpam-5621	273	5	,	,	PUNCT
ejpam-5621	273	6	consequently	consequently	ADV
ejpam-5621	273	7	,	,	PUNCT
ejpam-5621	273	8	as	as	SCONJ
ejpam-5621	273	9	shown	show	VERB
ejpam-5621	273	10	in	in	ADP
ejpam-5621	273	11	lemma	lemma	PROPN
ejpam-5621	273	12	3	3	NUM
ejpam-5621	273	13	that	that	SCONJ
ejpam-5621	273	14	1/	1/	NUM
ejpam-5621	273	15	(	(	PUNCT
ejpam-5621	273	16	≤	≤	X
ejpam-5621	273	17	{	{	PUNCT
ejpam-5621	273	18	2x	2x	NUM
ejpam-5621	273	19	∈	∈	PROPN
ejpam-5621	273	20	b1	b1	NOUN
ejpam-5621	273	21	i	i	PRON
ejpam-5621	273	22	:	:	PUNCT
ejpam-5621	273	23	s∑	s∑	PROPN
ejpam-5621	273	24	m=1	m=1	X
ejpam-5621	274	1	|∇vm|	|∇vm|	X
ejpam-5621	274	2	>	>	X
ejpam-5621	274	3	2n0(λ∗	2n0(λ∗	NUM
ejpam-5621	275	1	+	+	CCONJ
ejpam-5621	275	2	ϵ	ϵ	X
ejpam-5621	275	3	)	)	PUNCT
ejpam-5621	275	4	)	)	PUNCT
ejpam-5621	275	5	1/2	1/2	NUM
ejpam-5621	275	6	≤	≤	NUM
ejpam-5621	275	7	c̄ε1+ε	c̄ε1+ε	NOUN
ejpam-5621	275	8	1	1	NUM
ejpam-5621	275	9	λ1+ε	λ1+ε	PROPN
ejpam-5621	275	10	∫	∫	PROPN
ejpam-5621	275	11	{	{	PUNCT
ejpam-5621	275	12	x∈b0	x∈b0	PROPN
ejpam-5621	276	1	i	i	PRON
ejpam-5621	276	2	:	:	PUNCT
ejpam-5621	276	3	∑s	∑s	PROPN
ejpam-5621	276	4	m=1	m=1	X
ejpam-5621	276	5	|∇vm|>(λ∗+ε)/4	|∇vm|>(λ∗+ε)/4	ADV
ejpam-5621	276	6	}	}	PUNCT
ejpam-5621	276	7	s∑	s∑	PROPN
ejpam-5621	276	8	m=1	m=1	AUX
ejpam-5621	276	9	|∇vm|1+δdx	|∇vm|1+δdx	NOUN
ejpam-5621	276	10	in	in	ADP
ejpam-5621	276	11	that	that	PRON
ejpam-5621	276	12	where	where	SCONJ
ejpam-5621	276	13	c̄	c̄	PROPN
ejpam-5621	276	14	=	=	SYM
ejpam-5621	276	15	c̄(n	c̄(n	PROPN
ejpam-5621	276	16	,	,	PUNCT
ejpam-5621	276	17	1	1	NUM
ejpam-5621	276	18	+	+	CCONJ
ejpam-5621	276	19	ϵ	ϵ	NUM
ejpam-5621	276	20	,	,	PUNCT
ejpam-5621	276	21	(	(	PUNCT
ejpam-5621	276	22	1+ϵ	1+ϵ	NUM
ejpam-5621	276	23	ϵ	ϵ	NOUN
ejpam-5621	276	24	)	)	PUNCT
ejpam-5621	276	25	1	1	NUM
ejpam-5621	276	26	,	,	PUNCT
ejpam-5621	276	27	α	α	NOUN
ejpam-5621	276	28	)	)	PUNCT
ejpam-5621	276	29	.	.	PUNCT
ejpam-5621	277	1	bearing	bear	VERB
ejpam-5621	277	2	in	in	ADP
ejpam-5621	277	3	mind	mind	NOUN
ejpam-5621	277	4	that	that	SCONJ
ejpam-5621	277	5	the	the	DET
ejpam-5621	277	6	spheres	sphere	NOUN
ejpam-5621	277	7	are	be	AUX
ejpam-5621	277	8	disconnected	disconnected	ADJ
ejpam-5621	277	9	and	and	CCONJ
ejpam-5621	277	10	∪	∪	ADJ
ejpam-5621	277	11	i∈n	i∈n	NOUN
ejpam-5621	277	12	b1	b1	NOUN
ejpam-5621	277	13	i	i	PRON
ejpam-5621	277	14	⊃	⊃	VERB
ejpam-5621	277	15	a	a	PRON
ejpam-5621	277	16	(	(	PUNCT
ejpam-5621	277	17	λ∗	λ∗	NOUN
ejpam-5621	277	18	+	+	CCONJ
ejpam-5621	277	19	ε	ε	PROPN
ejpam-5621	277	20	)	)	PUNCT
ejpam-5621	277	21	=	=	PRON
ejpam-5621	278	1	{	{	PUNCT
ejpam-5621	278	2	x	x	PUNCT
ejpam-5621	278	3	∈	∈	PROPN
ejpam-5621	278	4	b1	b1	NOUN
ejpam-5621	278	5	:	:	PUNCT
ejpam-5621	278	6	s∑	s∑	PROPN
ejpam-5621	278	7	m=1	m=1	X
ejpam-5621	278	8	|∇vm|	|∇vm|	X
ejpam-5621	278	9	>	>	X
ejpam-5621	278	10	(	(	PUNCT
ejpam-5621	278	11	λ∗	λ∗	NOUN
ejpam-5621	278	12	+	+	CCONJ
ejpam-5621	278	13	ε	ε	PROPN
ejpam-5621	278	14	)	)	PUNCT
ejpam-5621	278	15	}	}	PUNCT
ejpam-5621	278	16	,	,	PUNCT
ejpam-5621	278	17	for	for	ADP
ejpam-5621	278	18	any	any	DET
ejpam-5621	278	19	λ	λ	NOUN
ejpam-5621	278	20	=	=	PROPN
ejpam-5621	278	21	λ∗	λ∗	PROPN
ejpam-5621	278	22	+	+	CCONJ
ejpam-5621	278	23	ε	ε	PROPN
ejpam-5621	278	24	,	,	PUNCT
ejpam-5621	278	25	and	and	CCONJ
ejpam-5621	278	26	by	by	ADP
ejpam-5621	278	27	aggregating	aggregate	VERB
ejpam-5621	278	28	the	the	DET
ejpam-5621	278	29	terms	term	NOUN
ejpam-5621	278	30	in	in	ADP
ejpam-5621	278	31	the	the	DET
ejpam-5621	278	32	aforementioned	aforementioned	ADJ
ejpam-5621	278	33	inequality	inequality	NOUN
ejpam-5621	278	34	,	,	PUNCT
ejpam-5621	278	35	we	we	PRON
ejpam-5621	278	36	obtain	obtain	VERB
ejpam-5621	278	37	1/	1/	NUM
ejpam-5621	278	38	(	(	PUNCT
ejpam-5621	278	39	{	{	PUNCT
ejpam-5621	278	40	2x	2x	NUM
ejpam-5621	278	41	∈	∈	PROPN
ejpam-5621	278	42	b1	b1	NOUN
ejpam-5621	278	43	:	:	PUNCT
ejpam-5621	279	1	∑s	∑s	PROPN
ejpam-5621	279	2	m=1	m=1	X
ejpam-5621	279	3	|∇vm|	|∇vm|	X
ejpam-5621	279	4	>	>	X
ejpam-5621	279	5	2n0(λ∗	2n0(λ∗	NUM
ejpam-5621	279	6	+	+	CCONJ
ejpam-5621	279	7	ε)})1/2	ε)})1/2	NUM
ejpam-5621	279	8	≤	≤	NOUN
ejpam-5621	279	9	∑	∑	PUNCT
ejpam-5621	279	10	i	i	PRON
ejpam-5621	279	11	1/{2x	1/{2x	PROPN
ejpam-5621	279	12	∈	∈	PROPN
ejpam-5621	279	13	b1	b1	NOUN
ejpam-5621	279	14	i	i	PRON
ejpam-5621	279	15	:	:	PUNCT
ejpam-5621	280	1	∑s	∑s	PROPN
ejpam-5621	280	2	m=1	m=1	X
ejpam-5621	280	3	|∇vm|	|∇vm|	X
ejpam-5621	280	4	>	>	X
ejpam-5621	280	5	2n0(λ∗	2n0(λ∗	NUM
ejpam-5621	280	6	+	+	CCONJ
ejpam-5621	280	7	ε)}1/2	ε)}1/2	PROPN
ejpam-5621	280	8	≤	≤	X
ejpam-5621	280	9	c̄ε1+ε	c̄ε1+ε	NOUN
ejpam-5621	280	10	1	1	NUM
ejpam-5621	280	11	λ1+ε	λ1+ε	PROPN
ejpam-5621	280	12	∫	∫	PROPN
ejpam-5621	280	13	{	{	PUNCT
ejpam-5621	280	14	x∈b2	x∈b2	ADV
ejpam-5621	280	15	:	:	PUNCT
ejpam-5621	281	1	∑s	∑s	PROPN
ejpam-5621	281	2	m=1	m=1	X
ejpam-5621	281	3	|∇vm|>(λ∗+ε)/4	|∇vm|>(λ∗+ε)/4	VERB
ejpam-5621	281	4	}	}	PUNCT
ejpam-5621	281	5	∑s	∑s	PROPN
ejpam-5621	281	6	m=1	m=1	X
ejpam-5621	281	7	|∇vm|1+εdx	|∇vm|1+εdx	VERB
ejpam-5621	281	8	1	1	NUM
ejpam-5621	281	9	λ	λ	NOUN
ejpam-5621	281	10	(	(	PUNCT
ejpam-5621	281	11	1+ε	1+ε	PROPN
ejpam-5621	281	12	ε	ε	PROPN
ejpam-5621	281	13	)	)	PUNCT
ejpam-5621	281	14	1δ	1δ	NUM
ejpam-5621	281	15	(	(	PUNCT
ejpam-5621	281	16	1+ε	1+ε	NUM
ejpam-5621	281	17	ε	ε	PROPN
ejpam-5621	281	18	)	)	PUNCT
ejpam-5621	281	19	1	1	NUM
ejpam-5621	281	20	∫	∫	NOUN
ejpam-5621	281	21	{	{	PUNCT
ejpam-5621	281	22	x∈b2	x∈b2	ADV
ejpam-5621	281	23	:	:	PUNCT
ejpam-5621	281	24	∑s	∑s	PROPN
ejpam-5621	281	25	m=1	m=1	X
ejpam-5621	281	26	|gm|>δ(λ∗+ε)/4	|gm|>δ(λ∗+ε)/4	VERB
ejpam-5621	281	27	}	}	PUNCT
ejpam-5621	281	28	∑s	∑s	PROPN
ejpam-5621	281	29	m=1	m=1	X
ejpam-5621	281	30	|gm|	|gm|	PROPN
ejpam-5621	281	31	(	(	PUNCT
ejpam-5621	281	32	1+ε	1+ε	NUM
ejpam-5621	281	33	ε	ε	PROPN
ejpam-5621	281	34	)	)	PUNCT
ejpam-5621	281	35	1dx	1dx	NOUN
ejpam-5621	281	36	)	)	PUNCT
ejpam-5621	281	37	,	,	PUNCT
ejpam-5621	281	38	(	(	PUNCT
ejpam-5621	281	39	19	19	NUM
ejpam-5621	281	40	)	)	PUNCT
ejpam-5621	281	41	for	for	ADP
ejpam-5621	281	42	whatever	whatever	PRON
ejpam-5621	281	43	.	.	PUNCT
ejpam-5621	282	1	we	we	PRON
ejpam-5621	282	2	compute	compute	VERB
ejpam-5621	282	3	while	while	SCONJ
ejpam-5621	282	4	recalling	recall	VERB
ejpam-5621	282	5	the	the	DET
ejpam-5621	282	6	standard	standard	ADJ
ejpam-5621	282	7	argument	argument	NOUN
ejpam-5621	282	8	of	of	ADP
ejpam-5621	282	9	measure	measure	NOUN
ejpam-5621	282	10	theory.∫	theory.∫	PROPN
ejpam-5621	282	11	b1	b1	PROPN
ejpam-5621	282	12	∑s	∑s	PROPN
ejpam-5621	283	1	m=1	m=1	X
ejpam-5621	283	2	|∇vm|	|∇vm|	ADV
ejpam-5621	283	3	(	(	PUNCT
ejpam-5621	283	4	1+ε	1+ε	PROPN
ejpam-5621	283	5	ε	ε	NOUN
ejpam-5621	283	6	)	)	PUNCT
ejpam-5621	283	7	dz	dz	PROPN
ejpam-5621	283	8	=	=	SYM
ejpam-5621	283	9	(	(	PUNCT
ejpam-5621	283	10	1+ε	1+ε	PROPN
ejpam-5621	283	11	ε	ε	PROPN
ejpam-5621	283	12	)	)	PUNCT
ejpam-5621	283	13	∫∞	∫∞	NOUN
ejpam-5621	283	14	0	0	SYM
ejpam-5621	284	1	µ	µ	X
ejpam-5621	284	2	(	(	PUNCT
ejpam-5621	284	3	1+ε	1+ε	PROPN
ejpam-5621	284	4	ε	ε	NOUN
ejpam-5621	284	5	)	)	PUNCT
ejpam-5621	284	6	−11/{2x	−11/{2x	PROPN
ejpam-5621	284	7	∈	∈	PROPN
ejpam-5621	284	8	b1	b1	NOUN
ejpam-5621	284	9	:	:	PUNCT
ejpam-5621	284	10	∑s	∑s	PROPN
ejpam-5621	284	11	m=1	m=1	X
ejpam-5621	284	12	|∇vm|	|∇vm|	X
ejpam-5621	284	13	>	>	X
ejpam-5621	284	14	µ}1/2dµ	µ}1/2dµ	NOUN
ejpam-5621	284	15	=	=	SYM
ejpam-5621	284	16	(	(	PUNCT
ejpam-5621	284	17	1+ε	1+ε	NUM
ejpam-5621	284	18	ε	ε	PROPN
ejpam-5621	284	19	)	)	PUNCT
ejpam-5621	284	20	∫	∫	PROPN
ejpam-5621	285	1	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	285	2	0	0	NUM
ejpam-5621	285	3	µ	µ	X
ejpam-5621	285	4	(	(	PUNCT
ejpam-5621	285	5	1+ε	1+ε	PROPN
ejpam-5621	285	6	ε	ε	NOUN
ejpam-5621	285	7	)	)	PUNCT
ejpam-5621	285	8	−11/{2x	−11/{2x	PROPN
ejpam-5621	285	9	∈	∈	PROPN
ejpam-5621	285	10	b1	b1	NOUN
ejpam-5621	285	11	:	:	PUNCT
ejpam-5621	285	12	∑s	∑s	PROPN
ejpam-5621	285	13	m=1	m=1	X
ejpam-5621	285	14	|∇vm|	|∇vm|	X
ejpam-5621	285	15	>	>	X
ejpam-5621	285	16	µ}1/2dµ	µ}1/2dµ	ADJ
ejpam-5621	285	17	+	+	NOUN
ejpam-5621	285	18	(	(	PUNCT
ejpam-5621	285	19	1+ε	1+ε	PROPN
ejpam-5621	285	20	ε	ε	PROPN
ejpam-5621	285	21	)	)	PUNCT
ejpam-5621	285	22	∫∞	∫∞	NOUN
ejpam-5621	285	23	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	285	24	µ	µ	PROPN
ejpam-5621	285	25	(	(	PUNCT
ejpam-5621	285	26	1+ε	1+ε	PROPN
ejpam-5621	285	27	ε	ε	NOUN
ejpam-5621	285	28	)	)	PUNCT
ejpam-5621	285	29	−11/{2x	−11/{2x	PROPN
ejpam-5621	285	30	∈	∈	PROPN
ejpam-5621	285	31	b1	b1	NOUN
ejpam-5621	285	32	:	:	PUNCT
ejpam-5621	286	1	∑s	∑s	PROPN
ejpam-5621	286	2	m=1	m=1	X
ejpam-5621	286	3	|∇vm|	|∇vm|	X
ejpam-5621	286	4	>	>	X
ejpam-5621	286	5	µ}1/2dµ	µ}1/2dµ	NOUN
ejpam-5621	286	6	=	=	SYM
ejpam-5621	286	7	(	(	PUNCT
ejpam-5621	286	8	1+ε	1+ε	NUM
ejpam-5621	286	9	ε	ε	PROPN
ejpam-5621	286	10	)	)	PUNCT
ejpam-5621	286	11	∫	∫	PROPN
ejpam-5621	287	1	2n0λ∗	2n0λ∗	PROPN
ejpam-5621	287	2	0	0	NUM
ejpam-5621	287	3	µ	µ	X
ejpam-5621	287	4	(	(	PUNCT
ejpam-5621	287	5	1+ε	1+ε	PROPN
ejpam-5621	287	6	ε	ε	NOUN
ejpam-5621	287	7	)	)	PUNCT
ejpam-5621	287	8	−11/{2x	−11/{2x	PROPN
ejpam-5621	287	9	∈	∈	PROPN
ejpam-5621	287	10	b1	b1	NOUN
ejpam-5621	287	11	:	:	PUNCT
ejpam-5621	287	12	∑s	∑s	PROPN
ejpam-5621	287	13	m=1	m=1	X
ejpam-5621	287	14	|∇vm|	|∇vm|	X
ejpam-5621	287	15	>	>	X
ejpam-5621	287	16	µ}1/2dµ	µ}1/2dµ	ADJ
ejpam-5621	287	17	+	+	CCONJ
ejpam-5621	287	18	(	(	PUNCT
ejpam-5621	287	19	1+ε	1+ε	NUM
ejpam-5621	287	20	ε	ε	PROPN
ejpam-5621	287	21	)	)	PUNCT
ejpam-5621	287	22	∫∞	∫∞	NOUN
ejpam-5621	287	23	λ∗	λ∗	PROPN
ejpam-5621	287	24	(	(	PUNCT
ejpam-5621	287	25	2n0	2n0	NUM
ejpam-5621	287	26	(	(	PUNCT
ejpam-5621	287	27	λ∗	λ∗	PROPN
ejpam-5621	287	28	+	+	CCONJ
ejpam-5621	287	29	ε	ε	PROPN
ejpam-5621	287	30	)	)	PUNCT
ejpam-5621	287	31	)	)	PUNCT
ejpam-5621	287	32	(	(	PUNCT
ejpam-5621	287	33	1+ε	1+ε	NUM
ejpam-5621	287	34	ε	ε	NOUN
ejpam-5621	287	35	)	)	PUNCT
ejpam-5621	287	36	−1k.d(2n0(λ∗	−1k.d(2n0(λ∗	PROPN
ejpam-5621	287	37	+	+	CCONJ
ejpam-5621	287	38	ε	ε	PROPN
ejpam-5621	287	39	)	)	PUNCT
ejpam-5621	287	40	}	}	PUNCT
ejpam-5621	287	41	,	,	PUNCT
ejpam-5621	287	42	h.	h.	PROPN
ejpam-5621	287	43	ibrahim	ibrahim	PROPN
ejpam-5621	287	44	et	et	PROPN
ejpam-5621	287	45	al	al	PROPN
ejpam-5621	287	46	.	.	PUNCT
ejpam-5621	287	47	/	/	SYM
ejpam-5621	287	48	eur	eur	PROPN
ejpam-5621	287	49	.	.	PUNCT
ejpam-5621	288	1	j.	j.	PROPN
ejpam-5621	288	2	pure	pure	PROPN
ejpam-5621	288	3	appl	appl	PROPN
ejpam-5621	288	4	.	.	PROPN
ejpam-5621	288	5	math	math	PROPN
ejpam-5621	288	6	,	,	PUNCT
ejpam-5621	288	7	18	18	NUM
ejpam-5621	288	8	(	(	PUNCT
ejpam-5621	288	9	2	2	NUM
ejpam-5621	288	10	)	)	PUNCT
ejpam-5621	288	11	(	(	PUNCT
ejpam-5621	288	12	2025	2025	NUM
ejpam-5621	288	13	)	)	PUNCT
ejpam-5621	288	14	,	,	PUNCT
ejpam-5621	288	15	5621	5621	NUM
ejpam-5621	288	16	14	14	NUM
ejpam-5621	288	17	of	of	ADP
ejpam-5621	288	18	16	16	NUM
ejpam-5621	288	19	where	where	SCONJ
ejpam-5621	288	20	k	k	NOUN
ejpam-5621	288	21	=	=	PRON
ejpam-5621	288	22	(	(	PUNCT
ejpam-5621	288	23	1/2x	1/2x	NUM
ejpam-5621	288	24	∈	∈	PROPN
ejpam-5621	288	25	b1	b1	NOUN
ejpam-5621	288	26	:	:	PUNCT
ejpam-5621	288	27	s∑	s∑	PROPN
ejpam-5621	288	28	m=1	m=1	X
ejpam-5621	288	29	|∇vm|	|∇vm|	X
ejpam-5621	288	30	>	>	X
ejpam-5621	288	31	2n0(λ∗	2n0(λ∗	NUM
ejpam-5621	289	1	+	+	CCONJ
ejpam-5621	289	2	ε	ε	PROPN
ejpam-5621	289	3	)	)	PUNCT
ejpam-5621	289	4	)	)	PUNCT
ejpam-5621	290	1	1/2	1/2	NUM
ejpam-5621	291	1	=	=	NUM
ejpam-5621	291	2	:	:	PUNCT
ejpam-5621	291	3	j1	j1	PROPN
ejpam-5621	291	4	+	+	CCONJ
ejpam-5621	291	5	j2	j2	PROPN
ejpam-5621	291	6	.	.	PROPN
ejpam-5621	291	7	probability	probability	NOUN
ejpam-5621	291	8	of	of	ADP
ejpam-5621	291	9	j1	j1	PROPN
ejpam-5621	291	10	.	.	PUNCT
ejpam-5621	292	1	it	it	PRON
ejpam-5621	292	2	can	can	AUX
ejpam-5621	292	3	be	be	AUX
ejpam-5621	292	4	deduced	deduce	VERB
ejpam-5621	292	5	from	from	ADP
ejpam-5621	292	6	the	the	DET
ejpam-5621	292	7	definitions	definition	NOUN
ejpam-5621	292	8	of	of	ADP
ejpam-5621	292	9	λ∗and	λ∗and	NOUN
ejpam-5621	292	10	λ0	λ0	NOUN
ejpam-5621	292	11	that	that	PRON
ejpam-5621	293	1	λ	λ	PROPN
ejpam-5621	293	2	(	(	PUNCT
ejpam-5621	293	3	1+ε	1+ε	NUM
ejpam-5621	293	4	ε	ε	NOUN
ejpam-5621	293	5	)	)	PUNCT
ejpam-5621	293	6	∗	∗	NOUN
ejpam-5621	293	7	=	=	SYM
ejpam-5621	293	8	26n	26n	NUM
ejpam-5621	293	9	(	(	PUNCT
ejpam-5621	293	10	1+ε	1+ε	NUM
ejpam-5621	293	11	ε	ε	PROPN
ejpam-5621	293	12	)	)	PUNCT
ejpam-5621	293	13	/(1+ε)λ	/(1+ε)λ	PUNCT
ejpam-5621	294	1	(	(	PUNCT
ejpam-5621	294	2	1+ε	1+ε	NUM
ejpam-5621	294	3	ε	ε	NOUN
ejpam-5621	294	4	)	)	PUNCT
ejpam-5621	294	5	0	0	NUM
ejpam-5621	295	1	≤	≤	NUM
ejpam-5621	295	2	c̄	c̄	NUM
ejpam-5621	295	3	(	(	PUNCT
ejpam-5621	295	4	(	(	PUNCT
ejpam-5621	295	5	∫	∫	PROPN
ejpam-5621	295	6	b2	b2	PROPN
ejpam-5621	295	7	∑s	∑s	PROPN
ejpam-5621	295	8	m=1	m=1	X
ejpam-5621	296	1	|∇vm|(1+ε)dx	|∇vm|(1+ε)dx	ADJ
ejpam-5621	296	2	)	)	PUNCT
ejpam-5621	296	3	(	(	PUNCT
ejpam-5621	296	4	1+ε	1+ε	NUM
ejpam-5621	296	5	ε	ε	NOUN
ejpam-5621	296	6	)	)	PUNCT
ejpam-5621	296	7	/(1+ε	/(1+ε	X
ejpam-5621	296	8	)	)	PUNCT
ejpam-5621	297	1	+	+	CCONJ
ejpam-5621	297	2	1	1	NUM
ejpam-5621	297	3	δ	δ	PROPN
ejpam-5621	297	4	(	(	PUNCT
ejpam-5621	297	5	1+ε	1+ε	PROPN
ejpam-5621	297	6	ε	ε	PROPN
ejpam-5621	297	7	)	)	PUNCT
ejpam-5621	297	8	(	(	PUNCT
ejpam-5621	297	9	∫	∫	PROPN
ejpam-5621	297	10	b2	b2	PROPN
ejpam-5621	297	11	∑s	∑s	PROPN
ejpam-5621	297	12	m=1	m=1	X
ejpam-5621	297	13	|gm|	|gm|	PROPN
ejpam-5621	297	14	(	(	PUNCT
ejpam-5621	297	15	1+ε	1+ε	NUM
ejpam-5621	297	16	ε	ε	PROPN
ejpam-5621	297	17	)	)	PUNCT
ejpam-5621	297	18	1dx	1dx	NOUN
ejpam-5621	297	19	)	)	PUNCT
ejpam-5621	297	20	(	(	PUNCT
ejpam-5621	297	21	1+ε	1+ε	NUM
ejpam-5621	297	22	ε	ε	NOUN
ejpam-5621	297	23	)	)	PUNCT
ejpam-5621	297	24	/	/	SYM
ejpam-5621	297	25	(	(	PUNCT
ejpam-5621	297	26	1+ε	1+ε	NUM
ejpam-5621	297	27	ε	ε	PROPN
ejpam-5621	297	28	)	)	PUNCT
ejpam-5621	297	29	1	1	NUM
ejpam-5621	297	30	.	.	PUNCT
ejpam-5621	297	31	)	)	PUNCT
ejpam-5621	298	1	consequently	consequently	ADV
ejpam-5621	298	2	,	,	PUNCT
ejpam-5621	298	3	lemma	lemma	PROPN
ejpam-5621	298	4	3	3	NUM
ejpam-5621	298	5	and	and	CCONJ
ejpam-5621	298	6	holder	holder	NOUN
ejpam-5621	298	7	’s	’s	PART
ejpam-5621	298	8	inequality	inequality	NOUN
ejpam-5621	298	9	dictate	dictate	VERB
ejpam-5621	298	10	that	that	SCONJ
ejpam-5621	298	11	λ	λ	PROPN
ejpam-5621	298	12	(	(	PUNCT
ejpam-5621	298	13	1+ε	1+ε	NUM
ejpam-5621	298	14	ε	ε	NOUN
ejpam-5621	298	15	)	)	PUNCT
ejpam-5621	298	16	∗	∗	NOUN
ejpam-5621	298	17	≤	≤	NUM
ejpam-5621	298	18	c̄	c̄	PROPN
ejpam-5621	298	19	(	(	PUNCT
ejpam-5621	298	20	∫	∫	PROPN
ejpam-5621	298	21	b4	b4	PROPN
ejpam-5621	298	22	∑s	∑s	PROPN
ejpam-5621	298	23	m=1	m=1	PROPN
ejpam-5621	298	24	|vm|(1+ε)dx+	|vm|(1+ε)dx+	NOUN
ejpam-5621	298	25	∫	∫	NOUN
ejpam-5621	298	26	b4	b4	NOUN
ejpam-5621	298	27	∑s	∑s	PROPN
ejpam-5621	299	1	m=1	m=1	X
ejpam-5621	299	2	|gm|(1+ε)dx	|gm|(1+ε)dx	NOUN
ejpam-5621	299	3	)	)	PUNCT
ejpam-5621	299	4	(	(	PUNCT
ejpam-5621	299	5	1+ε	1+ε	NUM
ejpam-5621	299	6	ε	ε	NOUN
ejpam-5621	299	7	)	)	PUNCT
ejpam-5621	299	8	/(1+ε	/(1+ε	X
ejpam-5621	299	9	)	)	PUNCT
ejpam-5621	300	1	+	+	CCONJ
ejpam-5621	300	2	1	1	NUM
ejpam-5621	300	3	δ	δ	PROPN
ejpam-5621	300	4	(	(	PUNCT
ejpam-5621	300	5	1+ε	1+ε	PROPN
ejpam-5621	300	6	ε	ε	PROPN
ejpam-5621	300	7	)	)	PUNCT
ejpam-5621	300	8	(	(	PUNCT
ejpam-5621	300	9	∫	∫	PROPN
ejpam-5621	300	10	b2	b2	PROPN
ejpam-5621	300	11	∑s	∑s	PROPN
ejpam-5621	300	12	m=1	m=1	X
ejpam-5621	300	13	|gm|	|gm|	PROPN
ejpam-5621	300	14	(	(	PUNCT
ejpam-5621	300	15	1+ε	1+ε	NUM
ejpam-5621	300	16	ε	ε	PROPN
ejpam-5621	300	17	)	)	PUNCT
ejpam-5621	300	18	1dx	1dx	X
ejpam-5621	300	19	)	)	PUNCT
ejpam-5621	300	20	(	(	PUNCT
ejpam-5621	300	21	1+ε	1+ε	NUM
ejpam-5621	300	22	ε	ε	NOUN
ejpam-5621	300	23	)	)	PUNCT
ejpam-5621	300	24	/	/	SYM
ejpam-5621	300	25	(	(	PUNCT
ejpam-5621	300	26	1+ε	1+ε	NUM
ejpam-5621	300	27	ε	ε	PROPN
ejpam-5621	300	28	)	)	PUNCT
ejpam-5621	300	29	1	1	NUM
ejpam-5621	300	30	)	)	PUNCT
ejpam-5621	300	31	≤	≤	NUM
ejpam-5621	300	32	c̄	c̄	PROPN
ejpam-5621	300	33	{	{	PUNCT
ejpam-5621	300	34	(	(	PUNCT
ejpam-5621	300	35	∫	∫	PROPN
ejpam-5621	300	36	b4	b4	PROPN
ejpam-5621	300	37	∑s	∑s	PROPN
ejpam-5621	300	38	m=1	m=1	X
ejpam-5621	300	39	|vm|(1+ε)dx	|vm|(1+ε)dx	ADJ
ejpam-5621	300	40	)	)	PUNCT
ejpam-5621	300	41	(	(	PUNCT
ejpam-5621	300	42	1+ε	1+ε	NUM
ejpam-5621	300	43	ε	ε	NOUN
ejpam-5621	300	44	)	)	PUNCT
ejpam-5621	300	45	/(1+ε	/(1+ε	X
ejpam-5621	300	46	)	)	PUNCT
ejpam-5621	301	1	+	+	CCONJ
ejpam-5621	301	2	(	(	PUNCT
ejpam-5621	301	3	∫	∫	PROPN
ejpam-5621	301	4	b4	b4	PROPN
ejpam-5621	301	5	∑s	∑s	PROPN
ejpam-5621	302	1	m=1	m=1	X
ejpam-5621	302	2	|gm|(1+ε)dx	|gm|(1+ε)dx	NOUN
ejpam-5621	302	3	)	)	PUNCT
ejpam-5621	302	4	(	(	PUNCT
ejpam-5621	302	5	1+ε	1+ε	NUM
ejpam-5621	302	6	ε	ε	NOUN
ejpam-5621	302	7	)	)	PUNCT
ejpam-5621	302	8	/(1+ε	/(1+ε	X
ejpam-5621	302	9	)	)	PUNCT
ejpam-5621	303	1	+	+	CCONJ
ejpam-5621	303	2	1	1	NUM
ejpam-5621	303	3	δ	δ	PROPN
ejpam-5621	303	4	(	(	PUNCT
ejpam-5621	303	5	1+ε	1+ε	PROPN
ejpam-5621	303	6	ε	ε	PROPN
ejpam-5621	303	7	)	)	PUNCT
ejpam-5621	303	8	∫	∫	PROPN
ejpam-5621	303	9	b2	b2	PROPN
ejpam-5621	303	10	∑s	∑s	PROPN
ejpam-5621	303	11	m=1	m=1	X
ejpam-5621	303	12	|gm|	|gm|	PROPN
ejpam-5621	303	13	(	(	PUNCT
ejpam-5621	303	14	1+ε	1+ε	NUM
ejpam-5621	303	15	ε	ε	PROPN
ejpam-5621	303	16	)	)	PUNCT
ejpam-5621	303	17	dx	dx	PROPN
ejpam-5621	303	18	≤	≤	PROPN
ejpam-5621	303	19	c̄	c̄	PROPN
ejpam-5621	303	20	{	{	PUNCT
ejpam-5621	303	21	∫	∫	PROPN
ejpam-5621	303	22	b4	b4	PROPN
ejpam-5621	303	23	∑s	∑s	PROPN
ejpam-5621	303	24	m=1	m=1	PROPN
ejpam-5621	303	25	|vm|	|vm|	PROPN
ejpam-5621	303	26	(	(	PUNCT
ejpam-5621	303	27	1+ε	1+ε	PROPN
ejpam-5621	303	28	ε	ε	NOUN
ejpam-5621	303	29	)	)	PUNCT
ejpam-5621	303	30	dx+	dx+	NOUN
ejpam-5621	303	31	∫	∫	PROPN
ejpam-5621	303	32	b4	b4	PROPN
ejpam-5621	303	33	∑s	∑s	PROPN
ejpam-5621	303	34	m=1	m=1	X
ejpam-5621	303	35	|gm|	|gm|	PROPN
ejpam-5621	303	36	(	(	PUNCT
ejpam-5621	303	37	1+ε	1+ε	PROPN
ejpam-5621	303	38	ε	ε	PROPN
ejpam-5621	303	39	)	)	PUNCT
ejpam-5621	303	40	dx	dx	PROPN
ejpam-5621	303	41	}	}	PUNCT
ejpam-5621	303	42	.	.	PUNCT
ejpam-5621	304	1	hence	hence	ADV
ejpam-5621	304	2	,	,	PUNCT
ejpam-5621	304	3	we	we	PRON
ejpam-5621	304	4	ascertain	ascertain	VERB
ejpam-5621	304	5	j1	j1	PROPN
ejpam-5621	304	6	≤	≤	NUM
ejpam-5621	304	7	(	(	PUNCT
ejpam-5621	304	8	2n0λ∗	2n0λ∗	NOUN
ejpam-5621	304	9	)	)	PUNCT
ejpam-5621	304	10	(	(	PUNCT
ejpam-5621	304	11	1+ε	1+ε	NUM
ejpam-5621	304	12	ε	ε	NOUN
ejpam-5621	304	13	)	)	PUNCT
ejpam-5621	304	14	|b1|	|b1|	NOUN
ejpam-5621	304	15	≤	≤	ADV
ejpam-5621	304	16	c̄	c̄	PROPN
ejpam-5621	304	17	{	{	PUNCT
ejpam-5621	304	18	∫	∫	NOUN
ejpam-5621	304	19	b4	b4	PROPN
ejpam-5621	304	20	s∑	s∑	PROPN
ejpam-5621	304	21	m=1	m=1	PROPN
ejpam-5621	304	22	|vm|	|vm|	PROPN
ejpam-5621	304	23	(	(	PUNCT
ejpam-5621	304	24	1+ε	1+ε	PROPN
ejpam-5621	304	25	ε	ε	NOUN
ejpam-5621	304	26	)	)	PUNCT
ejpam-5621	304	27	dx+	dx+	NOUN
ejpam-5621	304	28	∫	∫	PROPN
ejpam-5621	304	29	b4	b4	PROPN
ejpam-5621	304	30	s∑	s∑	PROPN
ejpam-5621	304	31	m=1	m=1	PROPN
ejpam-5621	304	32	|gm|	|gm|	PROPN
ejpam-5621	304	33	(	(	PUNCT
ejpam-5621	304	34	1+ε	1+ε	PROPN
ejpam-5621	304	35	ε	ε	PROPN
ejpam-5621	304	36	)	)	PUNCT
ejpam-5621	304	37	dx	dx	PROPN
ejpam-5621	304	38	}	}	PUNCT
ejpam-5621	304	39	,	,	PUNCT
ejpam-5621	304	40	where	where	SCONJ
ejpam-5621	304	41	c̄	c̄	PROPN
ejpam-5621	304	42	=	=	SYM
ejpam-5621	304	43	c̄(n	c̄(n	PROPN
ejpam-5621	304	44	,	,	PUNCT
ejpam-5621	304	45	1	1	NUM
ejpam-5621	304	46	+	+	CCONJ
ejpam-5621	304	47	ε	ε	PROPN
ejpam-5621	304	48	,	,	PUNCT
ejpam-5621	304	49	(	(	PUNCT
ejpam-5621	304	50	1+ε	1+ε	PROPN
ejpam-5621	304	51	ε	ε	PROPN
ejpam-5621	304	52	)	)	PUNCT
ejpam-5621	304	53	,	,	PUNCT
ejpam-5621	304	54	α	α	X
ejpam-5621	304	55	)	)	PUNCT
ejpam-5621	304	56	.	.	PUNCT
ejpam-5621	305	1	j2	j2	PROPN
ejpam-5621	305	2	estimation	estimation	NOUN
ejpam-5621	305	3	is	be	AUX
ejpam-5621	305	4	derived	derive	VERB
ejpam-5621	305	5	from	from	ADP
ejpam-5621	305	6	(	(	PUNCT
ejpam-5621	305	7	18	18	NUM
ejpam-5621	305	8	)	)	PUNCT
ejpam-5621	305	9	as	as	SCONJ
ejpam-5621	305	10	follows	follow	VERB
ejpam-5621	305	11	:	:	PUNCT
ejpam-5621	305	12	c̄ε(1+ε	c̄ε(1+ε	NUM
ejpam-5621	305	13	)	)	PUNCT
ejpam-5621	305	14			PUNCT
ejpam-5621	305	15	∫∞	∫∞	NOUN
ejpam-5621	305	16	0	0	PUNCT
ejpam-5621	306	1	(	(	PUNCT
ejpam-5621	306	2	λ∗	λ∗	PROPN
ejpam-5621	306	3	+	+	CCONJ
ejpam-5621	306	4	ε	ε	PROPN
ejpam-5621	306	5	)	)	PUNCT
ejpam-5621	306	6	(	(	PUNCT
ejpam-5621	306	7	1+ε	1+ε	NUM
ejpam-5621	306	8	ε	ε	NOUN
ejpam-5621	306	9	)	)	PUNCT
ejpam-5621	306	10	−(1+ε)−1	−(1+ε)−1	PROPN
ejpam-5621	306	11	∫	∫	PROPN
ejpam-5621	306	12	{	{	PUNCT
ejpam-5621	306	13	x∈b2	x∈b2	ADV
ejpam-5621	306	14	:	:	PUNCT
ejpam-5621	306	15	∑s	∑s	PROPN
ejpam-5621	306	16	m=1|∇vm|>(λ∗+ε)/4	m=1|∇vm|>(λ∗+ε)/4	PROPN
ejpam-5621	306	17	}	}	PUNCT
ejpam-5621	306	18	∑s	∑s	PROPN
ejpam-5621	306	19	m=1	m=1	X
ejpam-5621	306	20	|∇vm|(1+ε	|∇vm|(1+ε	NOUN
ejpam-5621	306	21	)	)	PUNCT
ejpam-5621	306	22	dxd	dxd	PROPN
ejpam-5621	306	23	(	(	PUNCT
ejpam-5621	306	24	λ∗	λ∗	PROPN
ejpam-5621	306	25	+	+	CCONJ
ejpam-5621	306	26	ε	ε	PROPN
ejpam-5621	306	27	)	)	PUNCT
ejpam-5621	306	28	+	+	CCONJ
ejpam-5621	306	29	1	1	NUM
ejpam-5621	306	30	δ	δ	NOUN
ejpam-5621	306	31	(	(	PUNCT
ejpam-5621	306	32	1+ε	1+ε	PROPN
ejpam-5621	306	33	ε	ε	PROPN
ejpam-5621	306	34	)	)	PUNCT
ejpam-5621	306	35	1	1	NUM
ejpam-5621	306	36	∫∞	∫∞	NOUN
ejpam-5621	306	37	0	0	PUNCT
ejpam-5621	307	1	(	(	PUNCT
ejpam-5621	307	2	λ∗	λ∗	PROPN
ejpam-5621	307	3	+	+	CCONJ
ejpam-5621	307	4	ε	ε	PROPN
ejpam-5621	307	5	)	)	PUNCT
ejpam-5621	307	6	considering	consider	VERB
ejpam-5621	307	7	that∫	that∫	PROPN
ejpam-5621	307	8	rn	rn	PROPN
ejpam-5621	307	9	|f	|f	PROPN
ejpam-5621	307	10	|βdx	|βdx	PROPN
ejpam-5621	307	11	=	=	PUNCT
ejpam-5621	307	12	(	(	PUNCT
ejpam-5621	307	13	β	β	NOUN
ejpam-5621	307	14	−	−	PROPN
ejpam-5621	307	15	λ	λ	PROPN
ejpam-5621	307	16	)	)	PUNCT
ejpam-5621	307	17	∫	∫	PROPN
ejpam-5621	307	18	∞	∞	PROPN
ejpam-5621	307	19	0	0	NUM
ejpam-5621	307	20	µβ−λ−1	µβ−λ−1	X
ejpam-5621	307	21	∫	∫	PROPN
ejpam-5621	307	22	{	{	PUNCT
ejpam-5621	307	23	x∈rm:|f	x∈rm:|f	PROPN
ejpam-5621	307	24	|>µ	|>µ	NOUN
ejpam-5621	307	25	}	}	PUNCT
ejpam-5621	307	26	fλdxdµ.	fλdxdµ.	NOUN
ejpam-5621	307	27	given	give	VERB
ejpam-5621	307	28	β	β	PRON
ejpam-5621	307	29	>	>	X
ejpam-5621	307	30	λ	λ	X
ejpam-5621	307	31	>	>	X
ejpam-5621	307	32	1	1	NUM
ejpam-5621	307	33	,	,	PUNCT
ejpam-5621	307	34	we	we	PRON
ejpam-5621	307	35	obtain	obtain	VERB
ejpam-5621	307	36	j2	j2	PROPN
ejpam-5621	307	37	≤	≤	PROPN
ejpam-5621	307	38	c̄1ε	c̄1ε	NOUN
ejpam-5621	307	39	(	(	PUNCT
ejpam-5621	307	40	1+ε	1+ε	NUM
ejpam-5621	307	41	)	)	PUNCT
ejpam-5621	307	42	∫	∫	PROPN
ejpam-5621	307	43	b2	b2	NOUN
ejpam-5621	308	1	s∑	s∑	PROPN
ejpam-5621	308	2	m=1	m=1	PROPN
ejpam-5621	308	3	|∇vm|	|∇vm|	ADV
ejpam-5621	308	4	(	(	PUNCT
ejpam-5621	308	5	1+ε	1+ε	PROPN
ejpam-5621	308	6	ε	ε	NOUN
ejpam-5621	308	7	)	)	PUNCT
ejpam-5621	308	8	dx+	dx+	NOUN
ejpam-5621	308	9	c̄2ε	c̄2ε	NOUN
ejpam-5621	308	10	(	(	PUNCT
ejpam-5621	308	11	1+ε	1+ε	NUM
ejpam-5621	308	12	)	)	PUNCT
ejpam-5621	308	13	∫	∫	PROPN
ejpam-5621	308	14	b2	b2	NOUN
ejpam-5621	308	15	s∑	s∑	PROPN
ejpam-5621	308	16	m=1	m=1	PROPN
ejpam-5621	308	17	|gm|	|gm|	PROPN
ejpam-5621	308	18	(	(	PUNCT
ejpam-5621	308	19	1+ε	1+ε	PROPN
ejpam-5621	308	20	ε	ε	PROPN
ejpam-5621	308	21	)	)	PUNCT
ejpam-5621	308	22	dx	dx	PROPN
ejpam-5621	308	23	,	,	PUNCT
ejpam-5621	308	24	h.	h.	PROPN
ejpam-5621	308	25	ibrahim	ibrahim	PROPN
ejpam-5621	308	26	et	et	PROPN
ejpam-5621	308	27	al	al	PROPN
ejpam-5621	308	28	.	.	PUNCT
ejpam-5621	308	29	/	/	SYM
ejpam-5621	308	30	eur	eur	PROPN
ejpam-5621	308	31	.	.	PUNCT
ejpam-5621	309	1	j.	j.	PROPN
ejpam-5621	309	2	pure	pure	PROPN
ejpam-5621	309	3	appl	appl	PROPN
ejpam-5621	309	4	.	.	PROPN
ejpam-5621	309	5	math	math	PROPN
ejpam-5621	309	6	,	,	PUNCT
ejpam-5621	309	7	18	18	NUM
ejpam-5621	309	8	(	(	PUNCT
ejpam-5621	309	9	2	2	NUM
ejpam-5621	309	10	)	)	PUNCT
ejpam-5621	309	11	(	(	PUNCT
ejpam-5621	309	12	2025	2025	NUM
ejpam-5621	309	13	)	)	PUNCT
ejpam-5621	309	14	,	,	PUNCT
ejpam-5621	309	15	5621	5621	NUM
ejpam-5621	309	16	15	15	NUM
ejpam-5621	309	17	of	of	ADP
ejpam-5621	309	18	16	16	NUM
ejpam-5621	309	19	where	where	SCONJ
ejpam-5621	309	20	c̄1	c̄1	X
ejpam-5621	309	21	=	=	SYM
ejpam-5621	309	22	c̄1(n	c̄1(n	NOUN
ejpam-5621	309	23	,	,	PUNCT
ejpam-5621	309	24	1	1	NUM
ejpam-5621	309	25	+	+	CCONJ
ejpam-5621	309	26	ε	ε	PROPN
ejpam-5621	309	27	,	,	PUNCT
ejpam-5621	309	28	(	(	PUNCT
ejpam-5621	309	29	1+ε	1+ε	PROPN
ejpam-5621	309	30	ε	ε	PROPN
ejpam-5621	309	31	)	)	PUNCT
ejpam-5621	309	32	,	,	PUNCT
ejpam-5621	309	33	α	α	X
ejpam-5621	309	34	)	)	PUNCT
ejpam-5621	309	35	and	and	CCONJ
ejpam-5621	309	36	c̄2	c̄2	NUM
ejpam-5621	309	37	=	=	SYM
ejpam-5621	309	38	c̄2(n	c̄2(n	PROPN
ejpam-5621	309	39	,	,	PUNCT
ejpam-5621	309	40	1	1	NUM
ejpam-5621	309	41	+	+	CCONJ
ejpam-5621	309	42	ε	ε	PROPN
ejpam-5621	309	43	,	,	PUNCT
ejpam-5621	309	44	(	(	PUNCT
ejpam-5621	309	45	1+ε	1+ε	PROPN
ejpam-5621	309	46	ε	ε	PROPN
ejpam-5621	309	47	)	)	PUNCT
ejpam-5621	309	48	,	,	PUNCT
ejpam-5621	309	49	α	α	X
ejpam-5621	309	50	)	)	PUNCT
ejpam-5621	309	51	.	.	PUNCT
ejpam-5621	310	1	we	we	PRON
ejpam-5621	310	2	obtain	obtain	VERB
ejpam-5621	310	3	by	by	ADP
ejpam-5621	310	4	combining	combine	VERB
ejpam-5621	310	5	the	the	DET
ejpam-5621	310	6	estimates	estimate	NOUN
ejpam-5621	310	7	of	of	ADP
ejpam-5621	310	8	j1	j1	PROPN
ejpam-5621	310	9	and	and	CCONJ
ejpam-5621	310	10	j2.∫	j2.∫	NOUN
ejpam-5621	310	11	b1	b1	NOUN
ejpam-5621	310	12	s∑	s∑	PROPN
ejpam-5621	310	13	m=1	m=1	PROPN
ejpam-5621	310	14	|∇vm|	|∇vm|	ADV
ejpam-5621	310	15	(	(	PUNCT
ejpam-5621	310	16	1+ε	1+ε	PROPN
ejpam-5621	310	17	ε	ε	PROPN
ejpam-5621	310	18	)	)	PUNCT
ejpam-5621	310	19	dx	dx	PROPN
ejpam-5621	310	20	≤	≤	PROPN
ejpam-5621	310	21	c̄1ε	c̄1ε	NOUN
ejpam-5621	310	22	(	(	PUNCT
ejpam-5621	310	23	1+ε	1+ε	NUM
ejpam-5621	310	24	)	)	PUNCT
ejpam-5621	310	25	∫	∫	PROPN
ejpam-5621	310	26	b2	b2	NOUN
ejpam-5621	310	27	s∑	s∑	PROPN
ejpam-5621	310	28	m=1	m=1	PROPN
ejpam-5621	310	29	|∇vm|	|∇vm|	ADV
ejpam-5621	310	30	(	(	PUNCT
ejpam-5621	310	31	1+ε	1+ε	PROPN
ejpam-5621	310	32	ε	ε	NOUN
ejpam-5621	310	33	)	)	PUNCT
ejpam-5621	310	34	dx+	dx+	ADJ
ejpam-5621	310	35	c̄3	c̄3	PROPN
ejpam-5621	310	36	∫	∫	PROPN
ejpam-5621	310	37	b4	b4	PROPN
ejpam-5621	310	38	s∑	s∑	PROPN
ejpam-5621	310	39	m=1	m=1	X
ejpam-5621	310	40	(	(	PUNCT
ejpam-5621	310	41	|vm|	|vm|	PROPN
ejpam-5621	310	42	(	(	PUNCT
ejpam-5621	310	43	1+ε	1+ε	NUM
ejpam-5621	310	44	ε	ε	PROPN
ejpam-5621	310	45	)	)	PUNCT
ejpam-5621	311	1	+	+	CCONJ
ejpam-5621	311	2	|gm|	|gm|	ADV
ejpam-5621	311	3	(	(	PUNCT
ejpam-5621	311	4	1+ε	1+ε	NUM
ejpam-5621	311	5	ε	ε	PROPN
ejpam-5621	311	6	)	)	PUNCT
ejpam-5621	311	7	)	)	PUNCT
ejpam-5621	311	8	dx	dx	PROPN
ejpam-5621	311	9	,	,	PUNCT
ejpam-5621	311	10	in	in	ADP
ejpam-5621	311	11	that	that	PRON
ejpam-5621	311	12	where	where	SCONJ
ejpam-5621	311	13	c̄3	c̄3	NOUN
ejpam-5621	311	14	=	=	SYM
ejpam-5621	311	15	c̄3(n	c̄3(n	NOUN
ejpam-5621	311	16	,	,	PUNCT
ejpam-5621	311	17	1	1	NUM
ejpam-5621	311	18	+	+	CCONJ
ejpam-5621	311	19	ε	ε	PROPN
ejpam-5621	311	20	,	,	PUNCT
ejpam-5621	311	21	(	(	PUNCT
ejpam-5621	311	22	1+ε	1+ε	PROPN
ejpam-5621	311	23	ε	ε	PROPN
ejpam-5621	311	24	)	)	PUNCT
ejpam-5621	311	25	,	,	PUNCT
ejpam-5621	311	26	α	α	PROPN
ejpam-5621	311	27	,	,	PUNCT
ejpam-5621	311	28	δ	δ	PROPN
ejpam-5621	311	29	,	,	PUNCT
ejpam-5621	311	30	ε	ε	PROPN
ejpam-5621	311	31	)	)	PUNCT
ejpam-5621	311	32	.	.	PUNCT
ejpam-5621	312	1	by	by	ADP
ejpam-5621	312	2	choosing	choose	VERB
ejpam-5621	312	3	an	an	DET
ejpam-5621	312	4	appropriate	appropriate	ADJ
ejpam-5621	312	5	ε	ε	NOUN
ejpam-5621	312	6	such	such	ADJ
ejpam-5621	312	7	that	that	DET
ejpam-5621	312	8	c̄1ε	c̄1ε	NOUN
ejpam-5621	312	9	(	(	PUNCT
ejpam-5621	312	10	1+ε	1+ε	NUM
ejpam-5621	312	11	)	)	PUNCT
ejpam-5621	312	12	=	=	SYM
ejpam-5621	312	13	1/2	1/2	NUM
ejpam-5621	312	14	and	and	CCONJ
ejpam-5621	312	15	employing	employ	VERB
ejpam-5621	312	16	a	a	DET
ejpam-5621	312	17	covering	covering	NOUN
ejpam-5621	312	18	and	and	CCONJ
ejpam-5621	312	19	iteration	iteration	NOUN
ejpam-5621	312	20	argument	argument	NOUN
ejpam-5621	312	21	to	to	PART
ejpam-5621	312	22	reabsorb	reabsorb	VERB
ejpam-5621	312	23	at	at	ADP
ejpam-5621	312	24	the	the	DET
ejpam-5621	312	25	righthand	righthand	NOUN
ejpam-5621	312	26	side	side	NOUN
ejpam-5621	312	27	of	of	ADP
ejpam-5621	312	28	the	the	DET
ejpam-5621	312	29	initial	initial	ADJ
ejpam-5621	312	30	integral	integral	NOUN
ejpam-5621	312	31	in	in	ADP
ejpam-5621	312	32	the	the	DET
ejpam-5621	312	33	aforementioned	aforementioned	ADJ
ejpam-5621	312	34	inequality	inequality	NOUN
ejpam-5621	312	35	,	,	PUNCT
ejpam-5621	312	36	we	we	PRON
ejpam-5621	312	37	obtain	obtain	VERB
ejpam-5621	312	38	the	the	DET
ejpam-5621	312	39	following	following	ADJ
ejpam-5621	312	40	result	result	NOUN
ejpam-5621	312	41	:	:	PUNCT
ejpam-5621	312	42	∫	∫	PROPN
ejpam-5621	312	43	b1	b1	PROPN
ejpam-5621	312	44	s∑	s∑	PROPN
ejpam-5621	312	45	m=1	m=1	PROPN
ejpam-5621	312	46	|∇vm|	|∇vm|	ADV
ejpam-5621	312	47	(	(	PUNCT
ejpam-5621	312	48	1+ε	1+ε	PROPN
ejpam-5621	312	49	ε	ε	NOUN
ejpam-5621	312	50	)	)	PUNCT
ejpam-5621	312	51	dx	dx	PROPN
ejpam-5621	312	52	≤	≤	PROPN
ejpam-5621	312	53	c̄	c̄	PROPN
ejpam-5621	312	54	{	{	PUNCT
ejpam-5621	312	55	∫	∫	NOUN
ejpam-5621	312	56	b4	b4	PROPN
ejpam-5621	312	57	s∑	s∑	PROPN
ejpam-5621	313	1	m=1	m=1	PROPN
ejpam-5621	313	2	|vm|	|vm|	PROPN
ejpam-5621	313	3	(	(	PUNCT
ejpam-5621	313	4	1+ε	1+ε	PROPN
ejpam-5621	313	5	ε	ε	NOUN
ejpam-5621	313	6	)	)	PUNCT
ejpam-5621	313	7	dx+	dx+	NOUN
ejpam-5621	313	8	∫	∫	PROPN
ejpam-5621	313	9	b4	b4	PROPN
ejpam-5621	313	10	s∑	s∑	PROPN
ejpam-5621	313	11	m=1	m=1	PROPN
ejpam-5621	313	12	|gm|	|gm|	PROPN
ejpam-5621	313	13	(	(	PUNCT
ejpam-5621	313	14	1+ε	1+ε	PROPN
ejpam-5621	313	15	ε	ε	PROPN
ejpam-5621	313	16	)	)	PUNCT
ejpam-5621	313	17	dx	dx	PROPN
ejpam-5621	313	18	}	}	PUNCT
ejpam-5621	313	19	.	.	PUNCT
ejpam-5621	314	1	by	by	ADP
ejpam-5621	314	2	performing	perform	VERB
ejpam-5621	314	3	a	a	DET
ejpam-5621	314	4	shift	shift	NOUN
ejpam-5621	314	5	and	and	CCONJ
ejpam-5621	314	6	scaling	scaling	NOUN
ejpam-5621	314	7	transform	transform	NOUN
ejpam-5621	314	8	,	,	PUNCT
ejpam-5621	314	9	the	the	DET
ejpam-5621	314	10	proof	proof	NOUN
ejpam-5621	314	11	can	can	AUX
ejpam-5621	314	12	be	be	AUX
ejpam-5621	314	13	completed	complete	VERB
ejpam-5621	314	14	.	.	PUNCT
ejpam-5621	315	1	5	5	X
ejpam-5621	315	2	.	.	X
ejpam-5621	315	3	conclusion	conclusion	NOUN
ejpam-5621	315	4	this	this	DET
ejpam-5621	315	5	study	study	NOUN
ejpam-5621	315	6	meticulously	meticulously	ADV
ejpam-5621	315	7	established	establish	VERB
ejpam-5621	315	8	the	the	DET
ejpam-5621	315	9	foundational	foundational	ADJ
ejpam-5621	315	10	groundwork	groundwork	NOUN
ejpam-5621	315	11	for	for	ADP
ejpam-5621	315	12	analyzing	analyze	VERB
ejpam-5621	315	13	nonlinear	nonlinear	ADJ
ejpam-5621	315	14	elliptic	elliptic	ADJ
ejpam-5621	315	15	equations	equation	NOUN
ejpam-5621	315	16	of	of	ADP
ejpam-5621	315	17	p	p	NOUN
ejpam-5621	315	18	-	-	PUNCT
ejpam-5621	315	19	laplacian	laplacian	ADJ
ejpam-5621	315	20	type	type	NOUN
ejpam-5621	315	21	.	.	PUNCT
ejpam-5621	316	1	we	we	PRON
ejpam-5621	316	2	began	begin	VERB
ejpam-5621	316	3	by	by	ADP
ejpam-5621	316	4	rigorously	rigorously	ADV
ejpam-5621	316	5	defining	define	VERB
ejpam-5621	316	6	key	key	ADJ
ejpam-5621	316	7	concepts	concept	NOUN
ejpam-5621	316	8	,	,	PUNCT
ejpam-5621	316	9	including	include	VERB
ejpam-5621	316	10	the	the	DET
ejpam-5621	316	11	small	small	ADJ
ejpam-5621	316	12	bounded	bounded	ADJ
ejpam-5621	316	13	mean	mean	PROPN
ejpam-5621	316	14	oscillation	oscillation	NOUN
ejpam-5621	316	15	semi	semi	ADJ
ejpam-5621	316	16	-	-	ADJ
ejpam-5621	316	17	norm	norm	ADJ
ejpam-5621	316	18	condition	condition	NOUN
ejpam-5621	316	19	,	,	PUNCT
ejpam-5621	316	20	which	which	PRON
ejpam-5621	316	21	quantifies	quantify	VERB
ejpam-5621	316	22	the	the	DET
ejpam-5621	316	23	oscillation	oscillation	NOUN
ejpam-5621	316	24	of	of	ADP
ejpam-5621	316	25	coefficients	coefficient	NOUN
ejpam-5621	316	26	.	.	PUNCT
ejpam-5621	317	1	furthermore	furthermore	ADV
ejpam-5621	317	2	,	,	PUNCT
ejpam-5621	317	3	we	we	PRON
ejpam-5621	317	4	provided	provide	VERB
ejpam-5621	317	5	precise	precise	ADJ
ejpam-5621	317	6	definitions	definition	NOUN
ejpam-5621	317	7	for	for	ADP
ejpam-5621	317	8	both	both	CCONJ
ejpam-5621	317	9	local	local	ADJ
ejpam-5621	317	10	and	and	CCONJ
ejpam-5621	317	11	global	global	ADJ
ejpam-5621	317	12	weak	weak	ADJ
ejpam-5621	317	13	solutions	solution	NOUN
ejpam-5621	317	14	of	of	ADP
ejpam-5621	317	15	the	the	DET
ejpam-5621	317	16	equation	equation	NOUN
ejpam-5621	317	17	under	under	ADP
ejpam-5621	317	18	consideration	consideration	NOUN
ejpam-5621	317	19	,	,	PUNCT
ejpam-5621	317	20	ensuring	ensure	VERB
ejpam-5621	317	21	a	a	DET
ejpam-5621	317	22	clear	clear	ADJ
ejpam-5621	317	23	understanding	understanding	NOUN
ejpam-5621	317	24	of	of	ADP
ejpam-5621	317	25	the	the	DET
ejpam-5621	317	26	solution	solution	NOUN
ejpam-5621	317	27	spaces	space	VERB
ejpam-5621	317	28	.	.	PUNCT
ejpam-5621	318	1	crucial	crucial	ADJ
ejpam-5621	318	2	lemmas	lemma	NOUN
ejpam-5621	318	3	were	be	AUX
ejpam-5621	318	4	derived	derive	VERB
ejpam-5621	318	5	to	to	PART
ejpam-5621	318	6	support	support	VERB
ejpam-5621	318	7	the	the	DET
ejpam-5621	318	8	main	main	ADJ
ejpam-5621	318	9	theorem	theorem	NOUN
ejpam-5621	318	10	,	,	PUNCT
ejpam-5621	318	11	laying	lay	VERB
ejpam-5621	318	12	a	a	DET
ejpam-5621	318	13	solid	solid	ADJ
ejpam-5621	318	14	analytical	analytical	ADJ
ejpam-5621	318	15	framework	framework	NOUN
ejpam-5621	318	16	for	for	ADP
ejpam-5621	318	17	the	the	DET
ejpam-5621	318	18	subsequent	subsequent	ADJ
ejpam-5621	318	19	investigation	investigation	NOUN
ejpam-5621	318	20	.	.	PUNCT
ejpam-5621	319	1	building	build	VERB
ejpam-5621	319	2	upon	upon	SCONJ
ejpam-5621	319	3	these	these	DET
ejpam-5621	319	4	definitions	definition	NOUN
ejpam-5621	319	5	and	and	CCONJ
ejpam-5621	319	6	lemmas	lemma	NOUN
ejpam-5621	319	7	,	,	PUNCT
ejpam-5621	319	8	the	the	DET
ejpam-5621	319	9	core	core	NOUN
ejpam-5621	319	10	contribution	contribution	NOUN
ejpam-5621	319	11	of	of	ADP
ejpam-5621	319	12	this	this	DET
ejpam-5621	319	13	work	work	NOUN
ejpam-5621	319	14	lies	lie	VERB
ejpam-5621	319	15	in	in	ADP
ejpam-5621	319	16	the	the	DET
ejpam-5621	319	17	proof	proof	NOUN
ejpam-5621	319	18	of	of	ADP
ejpam-5621	319	19	the	the	DET
ejpam-5621	319	20	main	main	ADJ
ejpam-5621	319	21	result	result	NOUN
ejpam-5621	319	22	theorem	theorem	VERB
ejpam-5621	319	23	.	.	PUNCT
ejpam-5621	320	1	this	this	PRON
ejpam-5621	320	2	theorem	theorem	VERB
ejpam-5621	320	3	successfully	successfully	ADV
ejpam-5621	320	4	derives	derive	VERB
ejpam-5621	320	5	local	local	ADJ
ejpam-5621	320	6	gradient	gradient	NOUN
ejpam-5621	320	7	estimates	estimate	NOUN
ejpam-5621	320	8	for	for	ADP
ejpam-5621	320	9	the	the	DET
ejpam-5621	320	10	aforementioned	aforementioned	ADJ
ejpam-5621	320	11	nonlinear	nonlinear	ADJ
ejpam-5621	320	12	elliptic	elliptic	ADJ
ejpam-5621	320	13	equations	equation	NOUN
ejpam-5621	320	14	,	,	PUNCT
ejpam-5621	320	15	specifically	specifically	ADV
ejpam-5621	320	16	those	those	PRON
ejpam-5621	320	17	featuring	feature	VERB
ejpam-5621	320	18	bounded	bound	VERB
ejpam-5621	320	19	mean	mean	ADJ
ejpam-5621	320	20	oscillation	oscillation	NOUN
ejpam-5621	320	21	coefficients	coefficient	NOUN
ejpam-5621	320	22	.	.	PUNCT
ejpam-5621	321	1	these	these	DET
ejpam-5621	321	2	estimates	estimate	NOUN
ejpam-5621	321	3	provide	provide	VERB
ejpam-5621	321	4	valuable	valuable	ADJ
ejpam-5621	321	5	insights	insight	NOUN
ejpam-5621	321	6	into	into	ADP
ejpam-5621	321	7	the	the	DET
ejpam-5621	321	8	regularity	regularity	NOUN
ejpam-5621	321	9	and	and	CCONJ
ejpam-5621	321	10	behavior	behavior	NOUN
ejpam-5621	321	11	of	of	ADP
ejpam-5621	321	12	solutions	solution	NOUN
ejpam-5621	321	13	,	,	PUNCT
ejpam-5621	321	14	particularly	particularly	ADV
ejpam-5621	321	15	concerning	concern	VERB
ejpam-5621	321	16	the	the	DET
ejpam-5621	321	17	gradient	gradient	NOUN
ejpam-5621	321	18	’s	’s	PART
ejpam-5621	321	19	control	control	NOUN
ejpam-5621	321	20	within	within	ADP
ejpam-5621	321	21	localized	localized	ADJ
ejpam-5621	321	22	domains	domain	NOUN
ejpam-5621	321	23	.	.	PUNCT
ejpam-5621	322	1	the	the	DET
ejpam-5621	322	2	successful	successful	ADJ
ejpam-5621	322	3	derivation	derivation	NOUN
ejpam-5621	322	4	of	of	ADP
ejpam-5621	322	5	these	these	DET
ejpam-5621	322	6	gradient	gradient	ADJ
ejpam-5621	322	7	estimates	estimate	NOUN
ejpam-5621	322	8	signifies	signify	VERB
ejpam-5621	322	9	a	a	DET
ejpam-5621	322	10	significant	significant	ADJ
ejpam-5621	322	11	advancement	advancement	NOUN
ejpam-5621	322	12	in	in	ADP
ejpam-5621	322	13	the	the	DET
ejpam-5621	322	14	understanding	understanding	NOUN
ejpam-5621	322	15	of	of	ADP
ejpam-5621	322	16	p	p	NOUN
ejpam-5621	322	17	-	-	PUNCT
ejpam-5621	322	18	laplacian	laplacian	ADJ
ejpam-5621	322	19	type	type	NOUN
ejpam-5621	322	20	equations	equation	NOUN
ejpam-5621	322	21	with	with	ADP
ejpam-5621	322	22	non	non	ADJ
ejpam-5621	322	23	-	-	ADJ
ejpam-5621	322	24	smooth	smooth	ADJ
ejpam-5621	322	25	coefficients	coefficient	NOUN
ejpam-5621	322	26	.	.	PUNCT
ejpam-5621	323	1	author	author	NOUN
ejpam-5621	323	2	contributions	contribution	NOUN
ejpam-5621	323	3	all	all	DET
ejpam-5621	323	4	authors	author	NOUN
ejpam-5621	323	5	contributed	contribute	VERB
ejpam-5621	323	6	equally	equally	ADV
ejpam-5621	323	7	to	to	ADP
ejpam-5621	323	8	the	the	DET
ejpam-5621	323	9	writing	writing	NOUN
ejpam-5621	323	10	of	of	ADP
ejpam-5621	323	11	this	this	DET
ejpam-5621	323	12	article	article	NOUN
ejpam-5621	323	13	.	.	PUNCT
ejpam-5621	324	1	all	all	DET
ejpam-5621	324	2	authors	author	NOUN
ejpam-5621	324	3	have	have	AUX
ejpam-5621	324	4	accepted	accept	VERB
ejpam-5621	324	5	responsibility	responsibility	NOUN
ejpam-5621	324	6	for	for	ADP
ejpam-5621	324	7	the	the	DET
ejpam-5621	324	8	entire	entire	ADJ
ejpam-5621	324	9	content	content	NOUN
ejpam-5621	324	10	of	of	ADP
ejpam-5621	324	11	the	the	DET
ejpam-5621	324	12	manuscript	manuscript	NOUN
ejpam-5621	324	13	and	and	CCONJ
ejpam-5621	324	14	approved	approve	VERB
ejpam-5621	324	15	its	its	PRON
ejpam-5621	324	16	submission	submission	NOUN
ejpam-5621	324	17	.	.	PUNCT
ejpam-5621	325	1	conflicts	conflict	NOUN
ejpam-5621	325	2	of	of	ADP
ejpam-5621	325	3	interest	interest	NOUN
ejpam-5621	325	4	all	all	DET
ejpam-5621	325	5	authors	author	NOUN
ejpam-5621	325	6	confirm	confirm	VERB
ejpam-5621	325	7	that	that	SCONJ
ejpam-5621	325	8	they	they	PRON
ejpam-5621	325	9	have	have	VERB
ejpam-5621	325	10	no	no	DET
ejpam-5621	325	11	conflict	conflict	NOUN
ejpam-5621	325	12	of	of	ADP
ejpam-5621	325	13	interest	interest	NOUN
ejpam-5621	325	14	.	.	PUNCT
ejpam-5621	326	1	h.	h.	PROPN
ejpam-5621	326	2	ibrahim	ibrahim	PROPN
ejpam-5621	326	3	et	et	PROPN
ejpam-5621	326	4	al	al	PROPN
ejpam-5621	326	5	.	.	PUNCT
ejpam-5621	326	6	/	/	SYM
ejpam-5621	326	7	eur	eur	PROPN
ejpam-5621	326	8	.	.	PUNCT
ejpam-5621	327	1	j.	j.	PROPN
ejpam-5621	327	2	pure	pure	PROPN
ejpam-5621	327	3	appl	appl	PROPN
ejpam-5621	327	4	.	.	PROPN
ejpam-5621	327	5	math	math	PROPN
ejpam-5621	327	6	,	,	PUNCT
ejpam-5621	327	7	18	18	NUM
ejpam-5621	327	8	(	(	PUNCT
ejpam-5621	327	9	2	2	NUM
ejpam-5621	327	10	)	)	PUNCT
ejpam-5621	327	11	(	(	PUNCT
ejpam-5621	327	12	2025	2025	NUM
ejpam-5621	327	13	)	)	PUNCT
ejpam-5621	327	14	,	,	PUNCT
ejpam-5621	327	15	5621	5621	NUM
ejpam-5621	327	16	16	16	NUM
ejpam-5621	327	17	of	of	ADP
ejpam-5621	327	18	16	16	NUM
ejpam-5621	327	19	acknowledgements	acknowledgement	NOUN
ejpam-5621	327	20	the	the	DET
ejpam-5621	327	21	researchers	researcher	NOUN
ejpam-5621	327	22	would	would	AUX
ejpam-5621	327	23	like	like	VERB
ejpam-5621	327	24	to	to	PART
ejpam-5621	327	25	thank	thank	VERB
ejpam-5621	327	26	the	the	DET
ejpam-5621	327	27	deanship	deanship	NOUN
ejpam-5621	327	28	of	of	ADP
ejpam-5621	327	29	graduate	graduate	NOUN
ejpam-5621	327	30	studies	study	NOUN
ejpam-5621	327	31	and	and	CCONJ
ejpam-5621	327	32	scientific	scientific	ADJ
ejpam-5621	327	33	research	research	NOUN
ejpam-5621	327	34	at	at	ADP
ejpam-5621	327	35	qassim	qassim	PROPN
ejpam-5621	327	36	university	university	PROPN
ejpam-5621	327	37	for	for	ADP
ejpam-5621	327	38	financial	financial	ADJ
ejpam-5621	327	39	support	support	NOUN
ejpam-5621	327	40	(	(	PUNCT
ejpam-5621	327	41	qu	qu	NOUN
ejpam-5621	327	42	-	-	NOUN
ejpam-5621	327	43	apc-2025	apc-2025	NOUN
ejpam-5621	327	44	)	)	PUNCT
ejpam-5621	327	45	.	.	PUNCT
ejpam-5621	328	1	references	reference	NOUN
ejpam-5621	328	2	[	[	X
ejpam-5621	328	3	1	1	X
ejpam-5621	328	4	]	]	PUNCT
ejpam-5621	328	5	j.	j.	PROPN
ejpam-5621	328	6	manfredi	manfredi	PROPN
ejpam-5621	328	7	e.	e.	PROPN
ejpam-5621	328	8	dibenedetto	dibenedetto	PROPN
ejpam-5621	328	9	.	.	PUNCT
ejpam-5621	329	1	gradient	gradient	ADJ
ejpam-5621	329	2	estimates	estimate	NOUN
ejpam-5621	329	3	for	for	ADP
ejpam-5621	329	4	the	the	DET
ejpam-5621	329	5	p(x)-laplacean	p(x)-laplacean	ADJ
ejpam-5621	329	6	system	system	NOUN
ejpam-5621	329	7	.	.	PUNCT
ejpam-5621	330	1	j.	j.	PROPN
ejpam-5621	330	2	reine	reine	PROPN
ejpam-5621	330	3	angew	angew	PROPN
ejpam-5621	330	4	,	,	PUNCT
ejpam-5621	330	5	115:1107–1134	115:1107–1134	NUM
ejpam-5621	330	6	,	,	PUNCT
ejpam-5621	330	7	1993	1993	NUM
ejpam-5621	330	8	.	.	PUNCT
ejpam-5621	331	1	[	[	X
ejpam-5621	331	2	2	2	X
ejpam-5621	331	3	]	]	PUNCT
ejpam-5621	331	4	t.	t.	NOUN
ejpam-5621	331	5	iwaniec	iwaniec	PROPN
ejpam-5621	331	6	.	.	PUNCT
ejpam-5621	332	1	projections	projection	NOUN
ejpam-5621	332	2	onto	onto	ADP
ejpam-5621	332	3	gradient	gradient	ADJ
ejpam-5621	332	4	fields	field	NOUN
ejpam-5621	332	5	and	and	CCONJ
ejpam-5621	332	6	lp	lp	NOUN
ejpam-5621	332	7	-	-	NOUN
ejpam-5621	332	8	estimates	estimate	NOUN
ejpam-5621	332	9	for	for	ADP
ejpam-5621	332	10	degenerated	degenerated	ADJ
ejpam-5621	332	11	elliptic	elliptic	ADJ
ejpam-5621	332	12	operators	operator	NOUN
ejpam-5621	332	13	.	.	PUNCT
ejpam-5621	333	1	studia	studia	PROPN
ejpam-5621	333	2	math	math	PROPN
ejpam-5621	333	3	,	,	PUNCT
ejpam-5621	333	4	75:293–312	75:293–312	PROPN
ejpam-5621	333	5	,	,	PUNCT
ejpam-5621	333	6	1983	1983	NUM
ejpam-5621	333	7	.	.	PUNCT
ejpam-5621	334	1	[	[	X
ejpam-5621	334	2	3	3	X
ejpam-5621	334	3	]	]	X
ejpam-5621	334	4	e.	e.	PROPN
ejpam-5621	334	5	acerbi	acerbi	PROPN
ejpam-5621	334	6	and	and	CCONJ
ejpam-5621	334	7	g.	g.	PROPN
ejpam-5621	334	8	mingione	mingione	PROPN
ejpam-5621	334	9	.	.	PUNCT
ejpam-5621	335	1	gradient	gradient	NOUN
ejpam-5621	335	2	estimates	estimate	NOUN
ejpam-5621	335	3	for	for	ADP
ejpam-5621	335	4	the	the	DET
ejpam-5621	335	5	p(x)-laplacean	p(x)-laplacean	ADJ
ejpam-5621	335	6	system	system	NOUN
ejpam-5621	335	7	.	.	PUNCT
ejpam-5621	336	1	j.	j.	PROPN
ejpam-5621	336	2	reine	reine	PROPN
ejpam-5621	336	3	angew	angew	PROPN
ejpam-5621	336	4	,	,	PUNCT
ejpam-5621	336	5	584:117–148	584:117–148	NUM
ejpam-5621	336	6	,	,	PUNCT
ejpam-5621	336	7	2005	2005	NUM
ejpam-5621	336	8	.	.	PUNCT
ejpam-5621	337	1	[	[	X
ejpam-5621	337	2	4	4	NUM
ejpam-5621	337	3	]	]	X
ejpam-5621	337	4	k	k	PROPN
ejpam-5621	337	5	habib	habib	PROPN
ejpam-5621	337	6	,	,	PUNCT
ejpam-5621	337	7	y	y	PROPN
ejpam-5621	337	8	rohen	rohen	NOUN
ejpam-5621	337	9	,	,	PUNCT
ejpam-5621	337	10	n	n	X
ejpam-5621	337	11	saleem	saleem	VERB
ejpam-5621	337	12	,	,	PUNCT
ejpam-5621	337	13	m	m	VERB
ejpam-5621	337	14	aphane	aphane	ADJ
ejpam-5621	337	15	,	,	PUNCT
ejpam-5621	337	16	and	and	CCONJ
ejpam-5621	337	17	a	a	DET
ejpam-5621	337	18	rzzaque	rzzaque	NOUN
ejpam-5621	337	19	.	.	PUNCT
ejpam-5621	338	1	convergence	convergence	NOUN
ejpam-5621	338	2	of	of	ADP
ejpam-5621	338	3	fibonacci	fibonacci	NOUN
ejpam-5621	338	4	–	–	PUNCT
ejpam-5621	338	5	ishikawa	ishikawa	PROPN
ejpam-5621	338	6	iteration	iteration	NOUN
ejpam-5621	338	7	procedure	procedure	NOUN
ejpam-5621	338	8	for	for	ADP
ejpam-5621	338	9	monotone	monotone	ADJ
ejpam-5621	338	10	asymptotically	asymptotically	ADV
ejpam-5621	338	11	nonexpansive	nonexpansive	ADJ
ejpam-5621	338	12	mappings	mapping	NOUN
ejpam-5621	338	13	.	.	PUNCT
ejpam-5621	339	1	journal	journal	PROPN
ejpam-5621	339	2	of	of	ADP
ejpam-5621	339	3	inequalities	inequality	NOUN
ejpam-5621	339	4	and	and	CCONJ
ejpam-5621	339	5	applications	application	NOUN
ejpam-5621	339	6	,	,	PUNCT
ejpam-5621	339	7	81	81	NUM
ejpam-5621	339	8	,	,	PUNCT
ejpam-5621	339	9	2024	2024	NUM
ejpam-5621	339	10	.	.	PUNCT
ejpam-5621	340	1	[	[	X
ejpam-5621	340	2	5	5	X
ejpam-5621	340	3	]	]	PUNCT
ejpam-5621	340	4	s.	s.	PROPN
ejpam-5621	340	5	zhou	zhou	PROPN
ejpam-5621	340	6	j.	j.	PROPN
ejpam-5621	340	7	kinnunen	kinnunen	PROPN
ejpam-5621	340	8	.	.	PUNCT
ejpam-5621	341	1	a	a	DET
ejpam-5621	341	2	local	local	ADJ
ejpam-5621	341	3	estimate	estimate	NOUN
ejpam-5621	341	4	for	for	ADP
ejpam-5621	341	5	nonlinear	nonlinear	ADJ
ejpam-5621	341	6	equations	equation	NOUN
ejpam-5621	341	7	with	with	ADP
ejpam-5621	341	8	discontinuous	discontinuous	ADJ
ejpam-5621	341	9	coefficients	coefficient	NOUN
ejpam-5621	341	10	,	,	PUNCT
ejpam-5621	341	11	comm	comm	NOUN
ejpam-5621	341	12	.	.	PUNCT
ejpam-5621	342	1	partial	partial	ADJ
ejpam-5621	342	2	differential	differential	NOUN
ejpam-5621	342	3	equations	equation	NOUN
ejpam-5621	342	4	,	,	PUNCT
ejpam-5621	342	5	24:2043–2068	24:2043–2068	NUM
ejpam-5621	342	6	,	,	PUNCT
ejpam-5621	342	7	1999	1999	NUM
ejpam-5621	342	8	.	.	PUNCT
ejpam-5621	343	1	[	[	X
ejpam-5621	343	2	6	6	NUM
ejpam-5621	343	3	]	]	PUNCT
ejpam-5621	343	4	e.	e.	PROPN
ejpam-5621	343	5	acerbi	acerbi	PROPN
ejpam-5621	343	6	and	and	CCONJ
ejpam-5621	343	7	g.	g.	PROPN
ejpam-5621	343	8	mingione	mingione	PROPN
ejpam-5621	343	9	.	.	PUNCT
ejpam-5621	344	1	unbounded	unbounded	ADJ
ejpam-5621	344	2	weak	weak	ADJ
ejpam-5621	344	3	solutions	solution	NOUN
ejpam-5621	344	4	to	to	PART
ejpam-5621	344	5	strongly	strongly	ADV
ejpam-5621	344	6	q	q	ADJ
ejpam-5621	344	7	-	-	ADJ
ejpam-5621	344	8	nonlinear	nonlinear	ADJ
ejpam-5621	344	9	elliptic	elliptic	ADJ
ejpam-5621	344	10	systems	system	NOUN
ejpam-5621	344	11	.	.	PUNCT
ejpam-5621	345	1	j	j	PROPN
ejpam-5621	345	2	math	math	PROPN
ejpam-5621	345	3	sci	sci	PROPN
ejpam-5621	345	4	,	,	PUNCT
ejpam-5621	345	5	276:15–36	276:15–36	NUM
ejpam-5621	345	6	,	,	PUNCT
ejpam-5621	345	7	2023	2023	NUM
ejpam-5621	345	8	.	.	PUNCT
ejpam-5621	346	1	[	[	X
ejpam-5621	346	2	7	7	X
ejpam-5621	346	3	]	]	X
ejpam-5621	346	4	g.	g.	PROPN
ejpam-5621	346	5	cupini	cupini	PROPN
ejpam-5621	346	6	,	,	PUNCT
ejpam-5621	346	7	p.	p.	NOUN
ejpam-5621	346	8	marcellini	marcellini	PROPN
ejpam-5621	346	9	,	,	PUNCT
ejpam-5621	346	10	and	and	CCONJ
ejpam-5621	346	11	e.	e.	PROPN
ejpam-5621	346	12	mascolo	mascolo	PROPN
ejpam-5621	346	13	.	.	PUNCT
ejpam-5621	347	1	local	local	ADJ
ejpam-5621	347	2	boundedness	boundedness	NOUN
ejpam-5621	347	3	of	of	ADP
ejpam-5621	347	4	weak	weak	ADJ
ejpam-5621	347	5	solutions	solution	NOUN
ejpam-5621	347	6	to	to	ADP
ejpam-5621	347	7	elliptic	elliptic	ADJ
ejpam-5621	347	8	equations	equation	NOUN
ejpam-5621	347	9	with	with	ADP
ejpam-5621	347	10	p	p	X
ejpam-5621	347	11	,	,	PUNCT
ejpam-5621	347	12	q	q	NOUN
ejpam-5621	347	13	-	-	PUNCT
ejpam-5621	347	14	growth[j	growth[j	X
ejpam-5621	347	15	]	]	PUNCT
ejpam-5621	347	16	.	.	PUNCT
ejpam-5621	348	1	journal	journal	PROPN
ejpam-5621	348	2	für	für	AUX
ejpam-5621	348	3	die	die	VERB
ejpam-5621	348	4	reine	reine	PROPN
ejpam-5621	348	5	und	und	PROPN
ejpam-5621	348	6	angewandte	angewandte	PROPN
ejpam-5621	348	7	mathematik	mathematik	PROPN
ejpam-5621	348	8	,	,	PUNCT
ejpam-5621	348	9	584:117–148	584:117–148	NUM
ejpam-5621	348	10	,	,	PUNCT
ejpam-5621	348	11	2005	2005	NUM
ejpam-5621	348	12	.	.	PUNCT
ejpam-5621	349	1	[	[	X
ejpam-5621	349	2	8	8	NUM
ejpam-5621	349	3	]	]	PUNCT
ejpam-5621	349	4	fengping	fengpe	VERB
ejpam-5621	349	5	yao	yao	PROPN
ejpam-5621	349	6	and	and	CCONJ
ejpam-5621	349	7	caifang	caifang	PROPN
ejpam-5621	349	8	wang	wang	PROPN
ejpam-5621	349	9	.	.	PUNCT
ejpam-5621	350	1	local	local	ADJ
ejpam-5621	350	2	gradient	gradient	NOUN
ejpam-5621	350	3	estimates	estimate	NOUN
ejpam-5621	350	4	for	for	ADP
ejpam-5621	350	5	nonlinear	nonlinear	ADJ
ejpam-5621	350	6	elliptic	elliptic	ADJ
ejpam-5621	350	7	equations	equation	NOUN
ejpam-5621	350	8	.	.	PUNCT
ejpam-5621	351	1	j.	j.	PROPN
ejpam-5621	351	2	math	math	PROPN
ejpam-5621	351	3	.	.	PUNCT
ejpam-5621	352	1	anal	anal	PROPN
ejpam-5621	352	2	.	.	PUNCT
ejpam-5621	352	3	appl	appl	PROPN
ejpam-5621	352	4	.	.	PROPN
ejpam-5621	352	5	,	,	PUNCT
ejpam-5621	352	6	338:427–437	338:427–437	NUM
ejpam-5621	352	7	,	,	PUNCT
ejpam-5621	352	8	2008	2008	NUM
ejpam-5621	352	9	.	.	PUNCT
ejpam-5621	353	1	[	[	X
ejpam-5621	353	2	9	9	NUM
ejpam-5621	353	3	]	]	PUNCT
ejpam-5621	353	4	n	n	DET
ejpam-5621	353	5	saleem	saleem	NOUN
ejpam-5621	353	6	,	,	PUNCT
ejpam-5621	353	7	m	m	PROPN
ejpam-5621	353	8	rashid	rashid	PROPN
ejpam-5621	353	9	,	,	PUNCT
ejpam-5621	353	10	f	f	PROPN
ejpam-5621	353	11	jarad	jarad	PROPN
ejpam-5621	353	12	,	,	PUNCT
ejpam-5621	353	13	and	and	CCONJ
ejpam-5621	353	14	a	a	DET
ejpam-5621	353	15	kalsoom	kalsoom	NOUN
ejpam-5621	353	16	.	.	PUNCT
ejpam-5621	354	1	convergence	convergence	NOUN
ejpam-5621	354	2	of	of	ADP
ejpam-5621	354	3	generalized	generalized	ADJ
ejpam-5621	354	4	quasinonexpansive	quasinonexpansive	NOUN
ejpam-5621	354	5	mappings	mapping	NOUN
ejpam-5621	354	6	in	in	ADP
ejpam-5621	354	7	hyperbolic	hyperbolic	ADJ
ejpam-5621	354	8	space	space	NOUN
ejpam-5621	354	9	.	.	PUNCT
ejpam-5621	355	1	journal	journal	NOUN
ejpam-5621	355	2	of	of	ADP
ejpam-5621	355	3	function	function	NOUN
ejpam-5621	355	4	spaces	space	NOUN
ejpam-5621	355	5	,	,	PUNCT
ejpam-5621	355	6	2022:1–10	2022:1–10	NUM
ejpam-5621	355	7	,	,	PUNCT
ejpam-5621	355	8	2002	2002	NUM
ejpam-5621	355	9	.	.	PUNCT
ejpam-5621	356	1	[	[	X
ejpam-5621	356	2	10	10	NUM
ejpam-5621	356	3	]	]	X
ejpam-5621	356	4	s.	s.	PROPN
ejpam-5621	356	5	byun	byun	PROPN
ejpam-5621	356	6	and	and	CCONJ
ejpam-5621	356	7	l.	l.	PROPN
ejpam-5621	356	8	wang	wang	PROPN
ejpam-5621	356	9	.	.	PUNCT
ejpam-5621	357	1	elliptic	elliptic	ADJ
ejpam-5621	357	2	equations	equation	NOUN
ejpam-5621	357	3	with	with	ADP
ejpam-5621	357	4	bmo	bmo	PROPN
ejpam-5621	357	5	coefficients	coefficient	NOUN
ejpam-5621	357	6	in	in	ADP
ejpam-5621	357	7	reifenberg	reifenberg	PROPN
ejpam-5621	357	8	domains	domain	NOUN
ejpam-5621	357	9	.	.	PUNCT
ejpam-5621	358	1	comm	comm	NOUN
ejpam-5621	358	2	.	.	PUNCT
ejpam-5621	359	1	pure	pure	ADJ
ejpam-5621	359	2	appl	appl	PROPN
ejpam-5621	359	3	,	,	PUNCT
ejpam-5621	359	4	57(10):1283	57(10):1283	NUM
ejpam-5621	359	5	–	–	PUNCT
ejpam-5621	359	6	1310	1310	NUM
ejpam-5621	359	7	,	,	PUNCT
ejpam-5621	359	8	2004	2004	NUM
ejpam-5621	359	9	.	.	PUNCT
ejpam-5621	360	1	[	[	X
ejpam-5621	360	2	11	11	NUM
ejpam-5621	360	3	]	]	PUNCT
ejpam-5621	360	4	s.	s.	PROPN
ejpam-5621	360	5	byun	byun	PROPN
ejpam-5621	360	6	and	and	CCONJ
ejpam-5621	360	7	l.	l.	PROPN
ejpam-5621	360	8	wang	wang	PROPN
ejpam-5621	360	9	.	.	PUNCT
ejpam-5621	361	1	parabolic	parabolic	PROPN
ejpam-5621	361	2	equations	equation	NOUN
ejpam-5621	361	3	in	in	ADP
ejpam-5621	361	4	reifenberg	reifenberg	PROPN
ejpam-5621	361	5	domains	domain	NOUN
ejpam-5621	361	6	.	.	PUNCT
ejpam-5621	362	1	arch	arch	NOUN
ejpam-5621	362	2	.	.	PUNCT
ejpam-5621	363	1	ration	ration	NOUN
ejpam-5621	363	2	.	.	PUNCT
ejpam-5621	364	1	mech	mech	PROPN
ejpam-5621	364	2	.	.	PUNCT
ejpam-5621	365	1	anal	anal	ADJ
ejpam-5621	365	2	,	,	PUNCT
ejpam-5621	365	3	176:271	176:271	NOUN
ejpam-5621	365	4	–	–	PUNCT
ejpam-5621	365	5	301	301	NUM
ejpam-5621	365	6	,	,	PUNCT
ejpam-5621	365	7	2005	2005	NUM
ejpam-5621	365	8	.	.	PUNCT
ejpam-5621	366	1	[	[	X
ejpam-5621	366	2	12	12	NUM
ejpam-5621	366	3	]	]	PUNCT
ejpam-5621	366	4	p.	p.	NOUN
ejpam-5621	366	5	tolksdorf	tolksdorf	PROPN
ejpam-5621	366	6	.	.	PUNCT
ejpam-5621	367	1	regularity	regularity	NOUN
ejpam-5621	367	2	for	for	ADP
ejpam-5621	367	3	a	a	DET
ejpam-5621	367	4	more	more	ADV
ejpam-5621	367	5	general	general	ADJ
ejpam-5621	367	6	class	class	NOUN
ejpam-5621	367	7	of	of	ADP
ejpam-5621	367	8	quasilinear	quasilinear	PROPN
ejpam-5621	367	9	elliptic	elliptic	ADJ
ejpam-5621	367	10	equations	equation	NOUN
ejpam-5621	367	11	.	.	PUNCT
ejpam-5621	368	1	j.	j.	PROPN
ejpam-5621	368	2	differential	differential	PROPN
ejpam-5621	368	3	equations	equation	NOUN
ejpam-5621	368	4	,	,	PUNCT
ejpam-5621	368	5	51(1):126–150	51(1):126–150	NOUN
ejpam-5621	368	6	,	,	PUNCT
ejpam-5621	368	7	1984	1984	NUM
ejpam-5621	368	8	.	.	PUNCT
ejpam-5621	369	1	[	[	X
ejpam-5621	369	2	13	13	NUM
ejpam-5621	369	3	]	]	SYM
ejpam-5621	369	4	x	x	SYM
ejpam-5621	369	5	su	su	PROPN
ejpam-5621	369	6	,	,	PUNCT
ejpam-5621	369	7	e	e	PROPN
ejpam-5621	369	8	valdinoci	valdinoci	NOUN
ejpam-5621	369	9	b	b	PROPN
ejpam-5621	369	10	,	,	PUNCT
ejpam-5621	369	11	y	y	PROPN
ejpam-5621	369	12	wei	wei	PROPN
ejpam-5621	369	13	,	,	PUNCT
ejpam-5621	369	14	and	and	CCONJ
ejpam-5621	369	15	j	j	PROPN
ejpam-5621	369	16	zhang	zhang	PROPN
ejpam-5621	369	17	.	.	PUNCT
ejpam-5621	370	1	on	on	ADP
ejpam-5621	370	2	some	some	DET
ejpam-5621	370	3	regularity	regularity	NOUN
ejpam-5621	370	4	properties	property	NOUN
ejpam-5621	370	5	of	of	ADP
ejpam-5621	370	6	mixed	mixed	ADJ
ejpam-5621	370	7	local	local	ADJ
ejpam-5621	370	8	and	and	CCONJ
ejpam-5621	370	9	nonlocal	nonlocal	ADJ
ejpam-5621	370	10	elliptic	elliptic	ADJ
ejpam-5621	370	11	equations	equation	NOUN
ejpam-5621	370	12	.	.	PUNCT
ejpam-5621	371	1	journal	journal	PROPN
ejpam-5621	371	2	of	of	ADP
ejpam-5621	371	3	differential	differential	ADJ
ejpam-5621	371	4	equations	equation	NOUN
ejpam-5621	371	5	,	,	PUNCT
ejpam-5621	371	6	416(1):576	416(1):576	NOUN
ejpam-5621	371	7	–	–	PUNCT
ejpam-5621	371	8	613	613	NUM
ejpam-5621	371	9	,	,	PUNCT
ejpam-5621	371	10	2025	2025	NUM
ejpam-5621	371	11	.	.	PUNCT
ejpam-5621	372	1	[	[	X
ejpam-5621	372	2	14	14	NUM
ejpam-5621	372	3	]	]	X
ejpam-5621	372	4	e.	e.	PROPN
ejpam-5621	372	5	acerbi	acerbi	PROPN
ejpam-5621	372	6	and	and	CCONJ
ejpam-5621	372	7	g.	g.	PROPN
ejpam-5621	372	8	mingione	mingione	PROPN
ejpam-5621	372	9	.	.	PUNCT
ejpam-5621	373	1	gradient	gradient	NOUN
ejpam-5621	373	2	estimates	estimate	NOUN
ejpam-5621	373	3	for	for	ADP
ejpam-5621	373	4	a	a	DET
ejpam-5621	373	5	class	class	NOUN
ejpam-5621	373	6	of	of	ADP
ejpam-5621	373	7	parabolic	parabolic	NOUN
ejpam-5621	373	8	systems	system	NOUN
ejpam-5621	373	9	.	.	PUNCT
ejpam-5621	374	1	duke	duke	PROPN
ejpam-5621	374	2	math	math	PROPN
ejpam-5621	374	3	.	.	PUNCT
ejpam-5621	375	1	j.	j.	PROPN
ejpam-5621	375	2	,	,	PUNCT
ejpam-5621	375	3	136:285–320	136:285–320	NUM
ejpam-5621	375	4	,	,	PUNCT
ejpam-5621	375	5	2007	2007	NUM
ejpam-5621	375	6	.	.	PUNCT
ejpam-5621	376	1	[	[	X
ejpam-5621	376	2	15	15	NUM
ejpam-5621	376	3	]	]	X
ejpam-5621	376	4	y.	y.	PROPN
ejpam-5621	376	5	chen	chen	PROPN
ejpam-5621	376	6	and	and	CCONJ
ejpam-5621	376	7	l.	l.	PROPN
ejpam-5621	376	8	wu	wu	PROPN
ejpam-5621	376	9	.	.	PUNCT
ejpam-5621	377	1	on	on	ADP
ejpam-5621	377	2	the	the	DET
ejpam-5621	377	3	higher	high	ADJ
ejpam-5621	377	4	integrability	integrability	NOUN
ejpam-5621	377	5	of	of	ADP
ejpam-5621	377	6	the	the	DET
ejpam-5621	377	7	gradient	gradient	NOUN
ejpam-5621	377	8	of	of	ADP
ejpam-5621	377	9	weak	weak	ADJ
ejpam-5621	377	10	solutions	solution	NOUN
ejpam-5621	377	11	of	of	ADP
ejpam-5621	377	12	certain	certain	ADJ
ejpam-5621	377	13	degenerate	degenerate	ADJ
ejpam-5621	377	14	elliptic	elliptic	ADJ
ejpam-5621	377	15	systems	system	NOUN
ejpam-5621	377	16	.	.	PUNCT
ejpam-5621	378	1	amer	amer	PROPN
ejpam-5621	378	2	.	.	PUNCT
ejpam-5621	379	1	j.	j.	PROPN
ejpam-5621	379	2	math	math	PROPN
ejpam-5621	379	3	,	,	PUNCT
ejpam-5621	379	4	ri	ri	PROPN
ejpam-5621	379	5	,	,	PUNCT
ejpam-5621	379	6	1998	1998	NUM
ejpam-5621	379	7	.	.	PUNCT
ejpam-5621	380	1	[	[	X
ejpam-5621	380	2	16	16	NUM
ejpam-5621	380	3	]	]	PUNCT
ejpam-5621	380	4	m.	m.	NOUN
ejpam-5621	380	5	giquinta	giquinta	NOUN
ejpam-5621	380	6	.	.	PUNCT
ejpam-5621	381	1	multiple	multiple	ADJ
ejpam-5621	381	2	integrals	integral	NOUN
ejpam-5621	381	3	in	in	ADP
ejpam-5621	381	4	the	the	DET
ejpam-5621	381	5	calculus	calculus	NOUN
ejpam-5621	381	6	of	of	ADP
ejpam-5621	381	7	variations	variation	NOUN
ejpam-5621	381	8	and	and	CCONJ
ejpam-5621	381	9	nonlinear	nonlinear	ADJ
ejpam-5621	381	10	elliptic	elliptic	ADJ
ejpam-5621	381	11	systems	system	NOUN
ejpam-5621	381	12	.	.	PUNCT
ejpam-5621	382	1	princeton	princeton	PROPN
ejpam-5621	382	2	university	university	PROPN
ejpam-5621	382	3	press	press	PROPN
ejpam-5621	382	4	,	,	PUNCT
ejpam-5621	382	5	princeton	princeton	PROPN
ejpam-5621	382	6	,	,	PUNCT
ejpam-5621	382	7	nj	nj	PROPN
ejpam-5621	382	8	,	,	PUNCT
ejpam-5621	382	9	1983	1983	NUM
ejpam-5621	382	10	.	.	PUNCT