id	sid	tid	token	lemma	pos
ejpam-6266	1	1	european	european	PROPN
ejpam-6266	1	2	journal	journal	PROPN
ejpam-6266	1	3	of	of	ADP
ejpam-6266	1	4	pure	pure	ADJ
ejpam-6266	1	5	and	and	CCONJ
ejpam-6266	1	6	applied	applied	ADJ
ejpam-6266	1	7	mathematics	mathematic	NOUN
ejpam-6266	1	8	2025	2025	NUM
ejpam-6266	1	9	,	,	PUNCT
ejpam-6266	1	10	vol	vol	NOUN
ejpam-6266	1	11	.	.	PROPN
ejpam-6266	1	12	18	18	NUM
ejpam-6266	1	13	,	,	PUNCT
ejpam-6266	1	14	issue	issue	NOUN
ejpam-6266	1	15	4	4	NUM
ejpam-6266	1	16	,	,	PUNCT
ejpam-6266	1	17	article	article	NOUN
ejpam-6266	1	18	number	number	NOUN
ejpam-6266	1	19	6266	6266	NUM
ejpam-6266	1	20	issn	issn	PROPN
ejpam-6266	1	21	1307	1307	NUM
ejpam-6266	1	22	-	-	SYM
ejpam-6266	1	23	5543	5543	NUM
ejpam-6266	1	24	–	–	PUNCT
ejpam-6266	1	25	ejpam.com	ejpam.com	X
ejpam-6266	1	26	published	publish	VERB
ejpam-6266	1	27	by	by	ADP
ejpam-6266	1	28	new	new	PROPN
ejpam-6266	1	29	york	york	PROPN
ejpam-6266	1	30	business	business	PROPN
ejpam-6266	1	31	global	global	PROPN
ejpam-6266	1	32	global	global	ADJ
ejpam-6266	1	33	well	well	PROPN
ejpam-6266	1	34	posedness	posedness	NOUN
ejpam-6266	1	35	for	for	ADP
ejpam-6266	1	36	damped	damped	ADJ
ejpam-6266	1	37	wave	wave	NOUN
ejpam-6266	1	38	models	model	NOUN
ejpam-6266	1	39	with	with	ADP
ejpam-6266	1	40	damping	damp	VERB
ejpam-6266	1	41	in	in	ADP
ejpam-6266	1	42	the	the	DET
ejpam-6266	1	43	memory	memory	NOUN
ejpam-6266	1	44	tayeb	tayeb	PROPN
ejpam-6266	1	45	hadj	hadj	PROPN
ejpam-6266	1	46	kaddour1	kaddour1	PROPN
ejpam-6266	1	47	,	,	PUNCT
ejpam-6266	1	48	ali	ali	PROPN
ejpam-6266	1	49	hakem2	hakem2	PROPN
ejpam-6266	1	50	,	,	PUNCT
ejpam-6266	1	51	abdelkader	abdelkader	PROPN
ejpam-6266	1	52	benali3	benali3	PROPN
ejpam-6266	1	53	,	,	PUNCT
ejpam-6266	1	54	ibrahim	ibrahim	PROPN
ejpam-6266	1	55	alraddadi4,∗	alraddadi4,∗	NOUN
ejpam-6266	1	56	,	,	PUNCT
ejpam-6266	1	57	hijaz	hijaz	PROPN
ejpam-6266	1	58	ahmad4,5,6,7	ahmad4,5,6,7	NOUN
ejpam-6266	1	59	,	,	PUNCT
ejpam-6266	1	60	taha	taha	PROPN
ejpam-6266	1	61	radwan8	radwan8	PROPN
ejpam-6266	1	62	,	,	PUNCT
ejpam-6266	1	63	dragan	dragan	VERB
ejpam-6266	1	64	pamucar9,∗	pamucar9,∗	ADJ
ejpam-6266	1	65	1	1	NUM
ejpam-6266	1	66	department	department	NOUN
ejpam-6266	1	67	of	of	ADP
ejpam-6266	1	68	mathematics	mathematic	NOUN
ejpam-6266	1	69	,	,	PUNCT
ejpam-6266	1	70	faculty	faculty	NOUN
ejpam-6266	1	71	of	of	ADP
ejpam-6266	1	72	exact	exact	ADJ
ejpam-6266	1	73	science	science	NOUN
ejpam-6266	1	74	and	and	CCONJ
ejpam-6266	1	75	informatics	informatic	NOUN
ejpam-6266	1	76	,	,	PUNCT
ejpam-6266	1	77	hassiba	hassiba	PROPN
ejpam-6266	1	78	benbouali	benbouali	PROPN
ejpam-6266	1	79	university	university	PROPN
ejpam-6266	1	80	of	of	ADP
ejpam-6266	1	81	chlef	chlef	PROPN
ejpam-6266	1	82	,	,	PUNCT
ejpam-6266	1	83	chlef	chlef	PROPN
ejpam-6266	1	84	,	,	PUNCT
ejpam-6266	1	85	algeria	algeria	PROPN
ejpam-6266	1	86	2	2	NUM
ejpam-6266	1	87	department	department	NOUN
ejpam-6266	1	88	of	of	ADP
ejpam-6266	1	89	technology	technology	NOUN
ejpam-6266	1	90	,	,	PUNCT
ejpam-6266	1	91	laboratory	laboratory	PROPN
ejpam-6266	1	92	acedp	acedp	PROPN
ejpam-6266	1	93	,	,	PUNCT
ejpam-6266	1	94	djilali	djilali	PROPN
ejpam-6266	1	95	liabès	liabès	NOUN
ejpam-6266	1	96	university	university	PROPN
ejpam-6266	1	97	of	of	ADP
ejpam-6266	1	98	sidi	sidi	NOUN
ejpam-6266	1	99	belabbes	belabbe	NOUN
ejpam-6266	1	100	,	,	PUNCT
ejpam-6266	1	101	sidi	sidi	NOUN
ejpam-6266	1	102	belabbes	belabbe	NOUN
ejpam-6266	1	103	,	,	PUNCT
ejpam-6266	1	104	algeria	algeria	PROPN
ejpam-6266	1	105	3	3	NUM
ejpam-6266	1	106	department	department	NOUN
ejpam-6266	1	107	of	of	ADP
ejpam-6266	1	108	mathematics	mathematic	NOUN
ejpam-6266	1	109	,	,	PUNCT
ejpam-6266	1	110	faculty	faculty	NOUN
ejpam-6266	1	111	of	of	ADP
ejpam-6266	1	112	exact	exact	ADJ
ejpam-6266	1	113	science	science	NOUN
ejpam-6266	1	114	and	and	CCONJ
ejpam-6266	1	115	informatics	informatic	NOUN
ejpam-6266	1	116	,	,	PUNCT
ejpam-6266	1	117	laboratory	laboratory	NOUN
ejpam-6266	1	118	of	of	ADP
ejpam-6266	1	119	mathematics	mathematic	NOUN
ejpam-6266	1	120	and	and	CCONJ
ejpam-6266	1	121	its	its	PRON
ejpam-6266	1	122	applications	application	NOUN
ejpam-6266	1	123	lma	lma	PROPN
ejpam-6266	1	124	,	,	PUNCT
ejpam-6266	1	125	hassiba	hassiba	PROPN
ejpam-6266	1	126	benbouali	benbouali	PROPN
ejpam-6266	1	127	university	university	PROPN
ejpam-6266	1	128	of	of	ADP
ejpam-6266	1	129	chlef	chlef	PROPN
ejpam-6266	1	130	,	,	PUNCT
ejpam-6266	1	131	algeria	algeria	PROPN
ejpam-6266	1	132	4	4	NUM
ejpam-6266	1	133	vsb	vsb	PROPN
ejpam-6266	1	134	–	–	PUNCT
ejpam-6266	1	135	technical	technical	ADJ
ejpam-6266	1	136	university	university	PROPN
ejpam-6266	1	137	of	of	ADP
ejpam-6266	1	138	ostrava	ostrava	PROPN
ejpam-6266	1	139	,	,	PUNCT
ejpam-6266	1	140	ceet	ceet	PROPN
ejpam-6266	1	141	,	,	PUNCT
ejpam-6266	1	142	enet	enet	PROPN
ejpam-6266	1	143	centre	centre	PROPN
ejpam-6266	1	144	,	,	PUNCT
ejpam-6266	1	145	17	17	NUM
ejpam-6266	1	146	.	.	PUNCT
ejpam-6266	2	1	listopadu	listopadu	ADJ
ejpam-6266	2	2	2172/15	2172/15	NUM
ejpam-6266	2	3	,	,	PUNCT
ejpam-6266	2	4	708	708	NUM
ejpam-6266	2	5	00	00	NUM
ejpam-6266	2	6	ostrava	ostrava	PROPN
ejpam-6266	2	7	–	–	PUNCT
ejpam-6266	2	8	poruba	poruba	PROPN
ejpam-6266	2	9	,	,	PUNCT
ejpam-6266	2	10	czech	czech	PROPN
ejpam-6266	2	11	republic	republic	PROPN
ejpam-6266	2	12	5	5	NUM
ejpam-6266	2	13	department	department	NOUN
ejpam-6266	2	14	of	of	ADP
ejpam-6266	2	15	mathematics	mathematic	NOUN
ejpam-6266	2	16	,	,	PUNCT
ejpam-6266	2	17	faculty	faculty	NOUN
ejpam-6266	2	18	of	of	ADP
ejpam-6266	2	19	science	science	NOUN
ejpam-6266	2	20	,	,	PUNCT
ejpam-6266	2	21	islamic	islamic	PROPN
ejpam-6266	2	22	university	university	PROPN
ejpam-6266	2	23	of	of	ADP
ejpam-6266	2	24	madinah	madinah	PROPN
ejpam-6266	2	25	,	,	PUNCT
ejpam-6266	2	26	madinah	madinah	PROPN
ejpam-6266	2	27	,	,	PUNCT
ejpam-6266	2	28	saudi	saudi	PROPN
ejpam-6266	2	29	arabia	arabia	PROPN
ejpam-6266	2	30	6	6	NUM
ejpam-6266	2	31	operational	operational	ADJ
ejpam-6266	2	32	research	research	NOUN
ejpam-6266	2	33	center	center	NOUN
ejpam-6266	2	34	in	in	ADP
ejpam-6266	2	35	healthcare	healthcare	PROPN
ejpam-6266	2	36	,	,	PUNCT
ejpam-6266	2	37	near	near	ADP
ejpam-6266	2	38	east	east	PROPN
ejpam-6266	2	39	university	university	PROPN
ejpam-6266	2	40	,	,	PUNCT
ejpam-6266	2	41	nicosia	nicosia	PROPN
ejpam-6266	2	42	/	/	SYM
ejpam-6266	2	43	trnc	trnc	PROPN
ejpam-6266	2	44	,	,	PUNCT
ejpam-6266	2	45	99138	99138	NUM
ejpam-6266	2	46	mersin	mersin	PROPN
ejpam-6266	2	47	10	10	NUM
ejpam-6266	2	48	,	,	PUNCT
ejpam-6266	2	49	turkey	turkey	PROPN
ejpam-6266	2	50	7	7	NUM
ejpam-6266	2	51	department	department	NOUN
ejpam-6266	2	52	of	of	ADP
ejpam-6266	2	53	mathematics	mathematic	NOUN
ejpam-6266	2	54	,	,	PUNCT
ejpam-6266	2	55	college	college	NOUN
ejpam-6266	2	56	of	of	ADP
ejpam-6266	2	57	science	science	PROPN
ejpam-6266	2	58	,	,	PUNCT
ejpam-6266	2	59	korea	korea	PROPN
ejpam-6266	2	60	university	university	PROPN
ejpam-6266	2	61	,	,	PUNCT
ejpam-6266	2	62	145	145	NUM
ejpam-6266	2	63	anam	anam	PROPN
ejpam-6266	2	64	-	-	PUNCT
ejpam-6266	2	65	ro	ro	ADJ
ejpam-6266	2	66	,	,	PUNCT
ejpam-6266	2	67	seongbuk	seongbuk	NOUN
ejpam-6266	2	68	-	-	PUNCT
ejpam-6266	2	69	gu	gu	NOUN
ejpam-6266	2	70	,	,	PUNCT
ejpam-6266	2	71	seoul	seoul	PROPN
ejpam-6266	2	72	02841	02841	PROPN
ejpam-6266	2	73	,	,	PUNCT
ejpam-6266	2	74	south	south	PROPN
ejpam-6266	2	75	korea	korea	PROPN
ejpam-6266	2	76	8	8	PROPN
ejpam-6266	2	77	department	department	PROPN
ejpam-6266	2	78	of	of	ADP
ejpam-6266	2	79	management	management	NOUN
ejpam-6266	2	80	information	information	NOUN
ejpam-6266	2	81	systems	system	NOUN
ejpam-6266	2	82	,	,	PUNCT
ejpam-6266	2	83	college	college	NOUN
ejpam-6266	2	84	of	of	ADP
ejpam-6266	2	85	business	business	NOUN
ejpam-6266	2	86	and	and	CCONJ
ejpam-6266	2	87	economics	economic	NOUN
ejpam-6266	2	88	,	,	PUNCT
ejpam-6266	2	89	qassim	qassim	PROPN
ejpam-6266	2	90	university	university	PROPN
ejpam-6266	2	91	,	,	PUNCT
ejpam-6266	2	92	buraydah	buraydah	NOUN
ejpam-6266	2	93	51452	51452	NUM
ejpam-6266	2	94	,	,	PUNCT
ejpam-6266	2	95	saudi	saudi	PROPN
ejpam-6266	2	96	arabia	arabia	PROPN
ejpam-6266	2	97	9	9	NUM
ejpam-6266	2	98	széchenyi	széchenyi	PROPN
ejpam-6266	2	99	istván	istván	PROPN
ejpam-6266	2	100	university	university	PROPN
ejpam-6266	2	101	,	,	PUNCT
ejpam-6266	2	102	győr	győr	PROPN
ejpam-6266	2	103	,	,	PUNCT
ejpam-6266	2	104	hungary	hungary	PROPN
ejpam-6266	2	105	abstract	abstract	NOUN
ejpam-6266	2	106	.	.	PUNCT
ejpam-6266	3	1	this	this	DET
ejpam-6266	3	2	paper	paper	NOUN
ejpam-6266	3	3	aims	aim	VERB
ejpam-6266	3	4	to	to	PART
ejpam-6266	3	5	study	study	VERB
ejpam-6266	3	6	the	the	DET
ejpam-6266	3	7	cauchy	cauchy	ADJ
ejpam-6266	3	8	problem	problem	NOUN
ejpam-6266	3	9	for	for	ADP
ejpam-6266	3	10	damped	damped	NOUN
ejpam-6266	3	11	wave	wave	NOUN
ejpam-6266	3	12	models	model	NOUN
ejpam-6266	3	13	with	with	ADP
ejpam-6266	3	14	a	a	DET
ejpam-6266	3	15	dissipative	dissipative	ADJ
ejpam-6266	3	16	memory	memory	NOUN
ejpam-6266	3	17	term	term	NOUN
ejpam-6266	3	18	.	.	PUNCT
ejpam-6266	4	1	the	the	DET
ejpam-6266	4	2	main	main	ADJ
ejpam-6266	4	3	objective	objective	NOUN
ejpam-6266	4	4	is	be	AUX
ejpam-6266	4	5	to	to	PART
ejpam-6266	4	6	establish	establish	VERB
ejpam-6266	4	7	global	global	ADJ
ejpam-6266	4	8	(	(	PUNCT
ejpam-6266	4	9	in	in	ADP
ejpam-6266	4	10	time	time	NOUN
ejpam-6266	4	11	)	)	PUNCT
ejpam-6266	4	12	well	well	ADJ
ejpam-6266	4	13	-	-	PUNCT
ejpam-6266	4	14	posedness	posedness	NOUN
ejpam-6266	4	15	results	result	NOUN
ejpam-6266	4	16	for	for	ADP
ejpam-6266	4	17	both	both	PRON
ejpam-6266	4	18	energy	energy	NOUN
ejpam-6266	4	19	solutions	solution	NOUN
ejpam-6266	4	20	and	and	CCONJ
ejpam-6266	4	21	higher	high	ADJ
ejpam-6266	4	22	-	-	PUNCT
ejpam-6266	4	23	regularity	regularity	NOUN
ejpam-6266	4	24	solutions	solution	NOUN
ejpam-6266	4	25	,	,	PUNCT
ejpam-6266	4	26	determine	determine	VERB
ejpam-6266	4	27	the	the	DET
ejpam-6266	4	28	critical	critical	ADJ
ejpam-6266	4	29	exponent	exponent	NOUN
ejpam-6266	4	30	in	in	ADP
ejpam-6266	4	31	the	the	DET
ejpam-6266	4	32	fujita	fujita	NOUN
ejpam-6266	4	33	sense	sense	NOUN
ejpam-6266	4	34	,	,	PUNCT
ejpam-6266	4	35	and	and	CCONJ
ejpam-6266	4	36	investigate	investigate	VERB
ejpam-6266	4	37	the	the	DET
ejpam-6266	4	38	influence	influence	NOUN
ejpam-6266	4	39	of	of	ADP
ejpam-6266	4	40	nonlinear	nonlinear	ADJ
ejpam-6266	4	41	memory	memory	NOUN
ejpam-6266	4	42	on	on	ADP
ejpam-6266	4	43	the	the	DET
ejpam-6266	4	44	fujita	fujita	PROPN
ejpam-6266	4	45	exponent	exponent	NOUN
ejpam-6266	4	46	.	.	PUNCT
ejpam-6266	5	1	using	use	VERB
ejpam-6266	5	2	modern	modern	ADJ
ejpam-6266	5	3	tools	tool	NOUN
ejpam-6266	5	4	from	from	ADP
ejpam-6266	5	5	harmonic	harmonic	ADJ
ejpam-6266	5	6	analysis	analysis	NOUN
ejpam-6266	5	7	and	and	CCONJ
ejpam-6266	5	8	the	the	DET
ejpam-6266	5	9	banach	banach	ADV
ejpam-6266	5	10	fixed	fix	VERB
ejpam-6266	5	11	point	point	NOUN
ejpam-6266	5	12	method	method	NOUN
ejpam-6266	5	13	,	,	PUNCT
ejpam-6266	5	14	we	we	PRON
ejpam-6266	5	15	show	show	VERB
ejpam-6266	5	16	several	several	ADJ
ejpam-6266	5	17	results	result	NOUN
ejpam-6266	5	18	by	by	ADP
ejpam-6266	5	19	taking	take	VERB
ejpam-6266	5	20	into	into	ADP
ejpam-6266	5	21	consideration	consideration	NOUN
ejpam-6266	5	22	different	different	ADJ
ejpam-6266	5	23	regularity	regularity	NOUN
ejpam-6266	5	24	properties	property	NOUN
ejpam-6266	5	25	of	of	ADP
ejpam-6266	5	26	the	the	DET
ejpam-6266	5	27	initial	initial	ADJ
ejpam-6266	5	28	data	datum	NOUN
ejpam-6266	5	29	.	.	PUNCT
ejpam-6266	6	1	2020	2020	NUM
ejpam-6266	6	2	mathematics	mathematics	PROPN
ejpam-6266	6	3	subject	subject	NOUN
ejpam-6266	6	4	classifications	classification	NOUN
ejpam-6266	6	5	:	:	PUNCT
ejpam-6266	6	6	35l15	35l15	NUM
ejpam-6266	6	7	,	,	PUNCT
ejpam-6266	6	8	35l71	35l71	NUM
ejpam-6266	6	9	,	,	PUNCT
ejpam-6266	6	10	35b44	35b44	NUM
ejpam-6266	6	11	,	,	PUNCT
ejpam-6266	6	12	35l05	35l05	NUM
ejpam-6266	6	13	,	,	PUNCT
ejpam-6266	6	14	33c15	33c15	NUM
ejpam-6266	6	15	key	key	ADJ
ejpam-6266	6	16	words	word	NOUN
ejpam-6266	6	17	and	and	CCONJ
ejpam-6266	6	18	phrases	phrase	NOUN
ejpam-6266	6	19	:	:	PUNCT
ejpam-6266	6	20	damped	damp	VERB
ejpam-6266	6	21	wave	wave	NOUN
ejpam-6266	6	22	equation	equation	NOUN
ejpam-6266	6	23	,	,	PUNCT
ejpam-6266	6	24	nonlinear	nonlinear	ADJ
ejpam-6266	6	25	memory	memory	NOUN
ejpam-6266	6	26	,	,	PUNCT
ejpam-6266	6	27	cauchy	cauchy	PROPN
ejpam-6266	6	28	problem	problem	NOUN
ejpam-6266	6	29	,	,	PUNCT
ejpam-6266	6	30	energy	energy	NOUN
ejpam-6266	6	31	solutions	solution	NOUN
ejpam-6266	6	32	,	,	PUNCT
ejpam-6266	6	33	matsumura	matsumura	ADJ
ejpam-6266	6	34	type	type	NOUN
ejpam-6266	6	35	estimates	estimate	NOUN
ejpam-6266	6	36	,	,	PUNCT
ejpam-6266	6	37	fixed	fix	VERB
ejpam-6266	6	38	point	point	NOUN
ejpam-6266	6	39	theorem	theorem	VERB
ejpam-6266	6	40	∗corresponding	∗corresponde	VERB
ejpam-6266	6	41	author	author	NOUN
ejpam-6266	6	42	.	.	PUNCT
ejpam-6266	7	1	∗corresponding	∗corresponde	VERB
ejpam-6266	7	2	author	author	NOUN
ejpam-6266	7	3	.	.	PUNCT
ejpam-6266	8	1	doi	doi	NOUN
ejpam-6266	8	2	:	:	PUNCT
ejpam-6266	8	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6266	https://doi.org/10.29020/nybg.ejpam.v18i4.6266	NOUN
ejpam-6266	8	4	email	email	NOUN
ejpam-6266	8	5	addresses	address	NOUN
ejpam-6266	8	6	:	:	PUNCT
ejpam-6266	8	7	t.hadjkaddour@univ-chlef.dz	t.hadjkaddour@univ-chlef.dz	X
ejpam-6266	8	8	(	(	PUNCT
ejpam-6266	8	9	t.	t.	PROPN
ejpam-6266	8	10	hadj	hadj	PROPN
ejpam-6266	8	11	kaddour	kaddour	PROPN
ejpam-6266	8	12	)	)	PUNCT
ejpam-6266	8	13	,	,	PUNCT
ejpam-6266	9	1	hakemali@yahoo.com	hakemali@yahoo.com	PRON
ejpam-6266	9	2	(	(	PUNCT
ejpam-6266	9	3	a.	a.	NOUN
ejpam-6266	9	4	hakem	hakem	PROPN
ejpam-6266	9	5	)	)	PUNCT
ejpam-6266	9	6	,	,	PUNCT
ejpam-6266	9	7	benali4848@gmail.com	benali4848@gmail.com	X
ejpam-6266	10	1	(	(	PUNCT
ejpam-6266	10	2	a.	a.	NOUN
ejpam-6266	10	3	benali	benali	PROPN
ejpam-6266	10	4	)	)	PUNCT
ejpam-6266	10	5	,	,	PUNCT
ejpam-6266	11	1	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-6266	11	2	(	(	PUNCT
ejpam-6266	11	3	i.	i.	NOUN
ejpam-6266	11	4	alraddadi	alraddadi	PROPN
ejpam-6266	11	5	)	)	PUNCT
ejpam-6266	11	6	,	,	PUNCT
ejpam-6266	11	7	hijaz.ahmad@iu.edu.sa	hijaz.ahmad@iu.edu.sa	PROPN
ejpam-6266	11	8	(	(	PUNCT
ejpam-6266	11	9	h.	h.	PROPN
ejpam-6266	11	10	ahmad	ahmad	PROPN
ejpam-6266	11	11	)	)	PUNCT
ejpam-6266	11	12	,	,	PUNCT
ejpam-6266	11	13	t.radwan@qu.edu.sa	t.radwan@qu.edu.sa	PROPN
ejpam-6266	11	14	(	(	PUNCT
ejpam-6266	11	15	t.	t.	NOUN
ejpam-6266	11	16	radwan	radwan	PROPN
ejpam-6266	11	17	)	)	PUNCT
ejpam-6266	11	18	,	,	PUNCT
ejpam-6266	11	19	pamucar.dragan@sze.hu	pamucar.dragan@sze.hu	PROPN
ejpam-6266	11	20	(	(	PUNCT
ejpam-6266	11	21	d.	d.	PROPN
ejpam-6266	11	22	pamucar	pamucar	PROPN
ejpam-6266	11	23	)	)	PUNCT
ejpam-6266	11	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6266	11	25	1	1	NUM
ejpam-6266	11	26	copyright	copyright	NOUN
ejpam-6266	11	27	:	:	PUNCT
ejpam-6266	12	1	©	©	PROPN
ejpam-6266	12	2	2025	2025	NUM
ejpam-6266	12	3	the	the	DET
ejpam-6266	12	4	author(s	author(s	NOUN
ejpam-6266	12	5	)	)	PUNCT
ejpam-6266	12	6	.	.	PUNCT
ejpam-6266	13	1	(	(	PUNCT
ejpam-6266	13	2	cc	cc	NOUN
ejpam-6266	13	3	by	by	ADP
ejpam-6266	13	4	-	-	PUNCT
ejpam-6266	13	5	nc	nc	PROPN
ejpam-6266	13	6	4.0	4.0	NUM
ejpam-6266	13	7	)	)	PUNCT
ejpam-6266	13	8	t.	t.	PROPN
ejpam-6266	13	9	hadj	hadj	PROPN
ejpam-6266	13	10	kaddour	kaddour	PROPN
ejpam-6266	13	11	et	et	PROPN
ejpam-6266	13	12	al	al	PROPN
ejpam-6266	13	13	.	.	PUNCT
ejpam-6266	13	14	/	/	SYM
ejpam-6266	13	15	eur	eur	PROPN
ejpam-6266	13	16	.	.	PUNCT
ejpam-6266	14	1	j.	j.	PROPN
ejpam-6266	14	2	pure	pure	PROPN
ejpam-6266	14	3	appl	appl	PROPN
ejpam-6266	14	4	.	.	PROPN
ejpam-6266	14	5	math	math	PROPN
ejpam-6266	14	6	,	,	PUNCT
ejpam-6266	14	7	18	18	NUM
ejpam-6266	14	8	(	(	PUNCT
ejpam-6266	14	9	4	4	NUM
ejpam-6266	14	10	)	)	PUNCT
ejpam-6266	14	11	(	(	PUNCT
ejpam-6266	14	12	2025	2025	NUM
ejpam-6266	14	13	)	)	PUNCT
ejpam-6266	14	14	,	,	PUNCT
ejpam-6266	14	15	6266	6266	NUM
ejpam-6266	14	16	2	2	NUM
ejpam-6266	14	17	of	of	ADP
ejpam-6266	14	18	24	24	NUM
ejpam-6266	14	19	1	1	NUM
ejpam-6266	14	20	.	.	PUNCT
ejpam-6266	15	1	introduction	introduction	NOUN
ejpam-6266	15	2	in	in	ADP
ejpam-6266	15	3	this	this	DET
ejpam-6266	15	4	paper	paper	NOUN
ejpam-6266	15	5	,	,	PUNCT
ejpam-6266	15	6	we	we	PRON
ejpam-6266	15	7	are	be	AUX
ejpam-6266	15	8	interesting	interesting	ADJ
ejpam-6266	15	9	in	in	ADP
ejpam-6266	15	10	the	the	DET
ejpam-6266	15	11	study	study	NOUN
ejpam-6266	15	12	of	of	ADP
ejpam-6266	15	13	a	a	DET
ejpam-6266	15	14	cauchy	cauchy	ADJ
ejpam-6266	15	15	problem	problem	NOUN
ejpam-6266	15	16	for	for	ADP
ejpam-6266	15	17	a	a	DET
ejpam-6266	15	18	damped	damped	ADJ
ejpam-6266	15	19	wave	wave	NOUN
ejpam-6266	15	20	model	model	NOUN
ejpam-6266	15	21	with	with	ADP
ejpam-6266	15	22	dissipative	dissipative	ADJ
ejpam-6266	15	23	term	term	NOUN
ejpam-6266	15	24	as	as	ADP
ejpam-6266	15	25	fractional	fractional	ADJ
ejpam-6266	15	26	semilinear	semilinear	NOUN
ejpam-6266	15	27	power	power	NOUN
ejpam-6266	15	28	-	-	PUNCT
ejpam-6266	15	29	type	type	NOUN
ejpam-6266	15	30	non	non	NOUN
ejpam-6266	15	31	-	-	NOUN
ejpam-6266	15	32	linearity	linearity	NOUN
ejpam-6266	15	33	on	on	ADP
ejpam-6266	15	34	the	the	DET
ejpam-6266	15	35	righthand	righthand	NOUN
ejpam-6266	15	36	side	side	NOUN
ejpam-6266	15	37	.	.	PUNCT
ejpam-6266	16	1	the	the	DET
ejpam-6266	16	2	most	most	ADV
ejpam-6266	16	3	important	important	ADJ
ejpam-6266	16	4	gaol	gaol	NOUN
ejpam-6266	16	5	is	be	AUX
ejpam-6266	16	6	to	to	PART
ejpam-6266	16	7	study	study	VERB
ejpam-6266	16	8	carefully	carefully	ADV
ejpam-6266	16	9	the	the	DET
ejpam-6266	16	10	influence	influence	NOUN
ejpam-6266	16	11	of	of	ADP
ejpam-6266	16	12	the	the	DET
ejpam-6266	16	13	dissipative	dissipative	ADJ
ejpam-6266	16	14	memory	memory	NOUN
ejpam-6266	16	15	term	term	NOUN
ejpam-6266	16	16	on	on	ADP
ejpam-6266	16	17	the	the	DET
ejpam-6266	16	18	range	range	NOUN
ejpam-6266	16	19	of	of	ADP
ejpam-6266	16	20	global	global	ADJ
ejpam-6266	16	21	(	(	PUNCT
ejpam-6266	16	22	in	in	ADP
ejpam-6266	16	23	time	time	NOUN
ejpam-6266	16	24	)	)	PUNCT
ejpam-6266	16	25	existence	existence	NOUN
ejpam-6266	16	26	of	of	ADP
ejpam-6266	16	27	energy	energy	NOUN
ejpam-6266	16	28	solutions	solution	NOUN
ejpam-6266	16	29	for	for	ADP
ejpam-6266	16	30	different	different	ADJ
ejpam-6266	16	31	regularities	regularity	NOUN
ejpam-6266	16	32	.	.	PUNCT
ejpam-6266	17	1	in	in	ADP
ejpam-6266	17	2	order	order	NOUN
ejpam-6266	17	3	to	to	PART
ejpam-6266	17	4	satisfy	satisfy	VERB
ejpam-6266	17	5	our	our	PRON
ejpam-6266	17	6	aim	aim	NOUN
ejpam-6266	17	7	we	we	PRON
ejpam-6266	17	8	prove	prove	VERB
ejpam-6266	17	9	several	several	ADJ
ejpam-6266	17	10	results	result	NOUN
ejpam-6266	17	11	of	of	ADP
ejpam-6266	17	12	global	global	ADJ
ejpam-6266	17	13	existence	existence	NOUN
ejpam-6266	17	14	and	and	CCONJ
ejpam-6266	17	15	find	find	VERB
ejpam-6266	17	16	the	the	DET
ejpam-6266	17	17	critical	critical	ADJ
ejpam-6266	17	18	exponent	exponent	NOUN
ejpam-6266	17	19	in	in	ADP
ejpam-6266	17	20	fujita	fujita	PROPN
ejpam-6266	17	21	sense	sense	NOUN
ejpam-6266	17	22	for	for	ADP
ejpam-6266	17	23	our	our	PRON
ejpam-6266	17	24	model	model	NOUN
ejpam-6266	17	25	by	by	ADP
ejpam-6266	17	26	using	use	VERB
ejpam-6266	17	27	matsumura	matsumura	ADJ
ejpam-6266	17	28	type	type	NOUN
ejpam-6266	17	29	estimates	estimate	NOUN
ejpam-6266	17	30	and	and	CCONJ
ejpam-6266	17	31	banach	banach	ADV
ejpam-6266	17	32	fixed	fix	VERB
ejpam-6266	17	33	point	point	NOUN
ejpam-6266	17	34	theorem	theorem	VERB
ejpam-6266	17	35	.	.	PROPN
ejpam-6266	18	1	for	for	ADP
ejpam-6266	18	2	physical	physical	ADJ
ejpam-6266	18	3	application	application	NOUN
ejpam-6266	18	4	we	we	PRON
ejpam-6266	18	5	refer	refer	VERB
ejpam-6266	18	6	the	the	DET
ejpam-6266	18	7	reader	reader	NOUN
ejpam-6266	18	8	to	to	PART
ejpam-6266	18	9	check	check	VERB
ejpam-6266	18	10	eg	eg	NOUN
ejpam-6266	18	11	.	.	PUNCT
ejpam-6266	19	1	[	[	X
ejpam-6266	19	2	1–5	1–5	X
ejpam-6266	19	3	]	]	X
ejpam-6266	19	4	and	and	CCONJ
ejpam-6266	19	5	the	the	DET
ejpam-6266	19	6	references	reference	NOUN
ejpam-6266	19	7	therein	therein	ADV
ejpam-6266	19	8	.	.	PUNCT
ejpam-6266	20	1	first	first	ADV
ejpam-6266	20	2	,	,	PUNCT
ejpam-6266	20	3	let	let	VERB
ejpam-6266	20	4	us	we	PRON
ejpam-6266	20	5	introduce	introduce	VERB
ejpam-6266	20	6	some	some	DET
ejpam-6266	20	7	crucial	crucial	ADJ
ejpam-6266	20	8	notations	notation	NOUN
ejpam-6266	20	9	used	use	VERB
ejpam-6266	20	10	throughout	throughout	ADP
ejpam-6266	20	11	this	this	DET
ejpam-6266	20	12	paper	paper	NOUN
ejpam-6266	20	13	notations	notation	NOUN
ejpam-6266	20	14	•	•	ADP
ejpam-6266	20	15	(	(	PUNCT
ejpam-6266	20	16	x)+	x)+	NUM
ejpam-6266	20	17	=	=	SYM
ejpam-6266	20	18	max{x	max{x	PROPN
ejpam-6266	20	19	,	,	PUNCT
ejpam-6266	20	20	0	0	NUM
ejpam-6266	20	21	}	}	PUNCT
ejpam-6266	20	22	:	:	PUNCT
ejpam-6266	20	23	the	the	DET
ejpam-6266	20	24	positive	positive	ADJ
ejpam-6266	20	25	part	part	NOUN
ejpam-6266	20	26	of	of	ADP
ejpam-6266	20	27	x.	x.	PROPN
ejpam-6266	20	28	•	•	PROPN
ejpam-6266	20	29	ut	ut	PROPN
ejpam-6266	20	30	:	:	PUNCT
ejpam-6266	20	31	the	the	DET
ejpam-6266	20	32	first	first	ADJ
ejpam-6266	20	33	partial	partial	ADJ
ejpam-6266	20	34	differential	differential	NOUN
ejpam-6266	20	35	of	of	ADP
ejpam-6266	20	36	u	u	NOUN
ejpam-6266	20	37	with	with	ADP
ejpam-6266	20	38	respect	respect	NOUN
ejpam-6266	20	39	to	to	ADP
ejpam-6266	20	40	t.	t.	NOUN
ejpam-6266	20	41	•	•	NOUN
ejpam-6266	20	42	∗x	∗x	NOUN
ejpam-6266	20	43	:	:	PUNCT
ejpam-6266	20	44	the	the	DET
ejpam-6266	20	45	convolution	convolution	NOUN
ejpam-6266	20	46	product	product	NOUN
ejpam-6266	20	47	with	with	ADP
ejpam-6266	20	48	respect	respect	NOUN
ejpam-6266	20	49	to	to	ADP
ejpam-6266	20	50	the	the	DET
ejpam-6266	20	51	x−variable	x−variable	PROPN
ejpam-6266	20	52	.	.	PUNCT
ejpam-6266	21	1	•	•	NUM
ejpam-6266	21	2	p∗	p∗	ADJ
ejpam-6266	21	3	or	or	CCONJ
ejpam-6266	21	4	pfuj	pfuj	NOUN
ejpam-6266	21	5	:	:	PUNCT
ejpam-6266	21	6	the	the	DET
ejpam-6266	21	7	critical	critical	ADJ
ejpam-6266	21	8	exponent	exponent	NOUN
ejpam-6266	21	9	in	in	ADP
ejpam-6266	21	10	fujita	fujita	PROPN
ejpam-6266	21	11	sense	sense	NOUN
ejpam-6266	21	12	.	.	PUNCT
ejpam-6266	22	1	•	•	PUNCT
ejpam-6266	22	2	|d|σ	|d|σ	ADJ
ejpam-6266	22	3	:	:	PUNCT
ejpam-6266	22	4	pseudo	pseudo	NOUN
ejpam-6266	22	5	-	-	NOUN
ejpam-6266	22	6	differential	differential	ADJ
ejpam-6266	22	7	operator	operator	NOUN
ejpam-6266	22	8	of	of	ADP
ejpam-6266	22	9	order	order	NOUN
ejpam-6266	22	10	σ	σ	PROPN
ejpam-6266	22	11	.	.	PROPN
ejpam-6266	22	12	•	•	NUM
ejpam-6266	22	13	ḣ	ḣ	PROPN
ejpam-6266	22	14	:	:	PUNCT
ejpam-6266	22	15	homogeneous	homogeneous	ADJ
ejpam-6266	22	16	sobolev	sobolev	NOUN
ejpam-6266	22	17	space	space	NOUN
ejpam-6266	22	18	.	.	PUNCT
ejpam-6266	23	1	2	2	X
ejpam-6266	23	2	.	.	X
ejpam-6266	23	3	background	background	NOUN
ejpam-6266	23	4	and	and	CCONJ
ejpam-6266	23	5	preliminaries	preliminary	NOUN
ejpam-6266	23	6	2.1	2.1	NUM
ejpam-6266	23	7	.	.	PUNCT
ejpam-6266	23	8	background	background	NOUN
ejpam-6266	23	9	and	and	CCONJ
ejpam-6266	23	10	motivation	motivation	NOUN
ejpam-6266	23	11	recently	recently	ADV
ejpam-6266	23	12	the	the	DET
ejpam-6266	23	13	damped	damped	NOUN
ejpam-6266	23	14	wave	wave	NOUN
ejpam-6266	23	15	equation	equation	NOUN
ejpam-6266	23	16	utt	utt	PROPN
ejpam-6266	24	1	−∆u+	−∆u+	NOUN
ejpam-6266	24	2	ut	ut	PROPN
ejpam-6266	25	1	=	=	SYM
ejpam-6266	25	2	∫	∫	PROPN
ejpam-6266	25	3	t	t	PROPN
ejpam-6266	25	4	0	0	NUM
ejpam-6266	25	5	(	(	PUNCT
ejpam-6266	25	6	t−	t−	PROPN
ejpam-6266	25	7	τ)−γ	τ)−γ	X
ejpam-6266	25	8	|u(τ	|u(τ	ADJ
ejpam-6266	25	9	,	,	PUNCT
ejpam-6266	25	10	·	·	PUNCT
ejpam-6266	25	11	)	)	PUNCT
ejpam-6266	25	12	|pdτ	|pdτ	NOUN
ejpam-6266	25	13	,	,	PUNCT
ejpam-6266	25	14	(	(	PUNCT
ejpam-6266	25	15	t	t	PROPN
ejpam-6266	25	16	,	,	PUNCT
ejpam-6266	25	17	x	x	NOUN
ejpam-6266	25	18	)	)	PUNCT
ejpam-6266	25	19	∈	∈	PROPN
ejpam-6266	25	20	(	(	PUNCT
ejpam-6266	25	21	0,∞)×	0,∞)×	NUM
ejpam-6266	25	22	rn	rn	PROPN
ejpam-6266	25	23	,	,	PUNCT
ejpam-6266	25	24	(	(	PUNCT
ejpam-6266	25	25	1	1	X
ejpam-6266	25	26	)	)	PUNCT
ejpam-6266	25	27	is	be	AUX
ejpam-6266	25	28	considered	consider	VERB
ejpam-6266	25	29	by	by	ADP
ejpam-6266	25	30	a.	a.	NOUN
ejpam-6266	25	31	fino	fino	PROPN
ejpam-6266	25	32	in	in	ADP
ejpam-6266	25	33	[	[	X
ejpam-6266	25	34	6	6	NUM
ejpam-6266	25	35	]	]	PUNCT
ejpam-6266	25	36	where	where	SCONJ
ejpam-6266	25	37	he	he	PRON
ejpam-6266	25	38	proved	prove	VERB
ejpam-6266	25	39	the	the	DET
ejpam-6266	25	40	global	global	ADJ
ejpam-6266	25	41	(	(	PUNCT
ejpam-6266	25	42	in	in	ADP
ejpam-6266	25	43	time	time	NOUN
ejpam-6266	25	44	)	)	PUNCT
ejpam-6266	25	45	existence	existence	NOUN
ejpam-6266	25	46	of	of	ADP
ejpam-6266	25	47	energy	energy	NOUN
ejpam-6266	25	48	solution	solution	NOUN
ejpam-6266	25	49	by	by	ADP
ejpam-6266	25	50	using	use	VERB
ejpam-6266	25	51	the	the	DET
ejpam-6266	25	52	weighted	weight	VERB
ejpam-6266	25	53	energy	energy	NOUN
ejpam-6266	25	54	method	method	NOUN
ejpam-6266	25	55	and	and	CCONJ
ejpam-6266	25	56	blow	blow	NOUN
ejpam-6266	25	57	-	-	PUNCT
ejpam-6266	25	58	up	up	ADP
ejpam-6266	25	59	results	result	NOUN
ejpam-6266	25	60	by	by	ADP
ejpam-6266	25	61	the	the	DET
ejpam-6266	25	62	test	test	NOUN
ejpam-6266	25	63	function	function	NOUN
ejpam-6266	25	64	method	method	NOUN
ejpam-6266	25	65	.	.	PUNCT
ejpam-6266	26	1	in	in	ADP
ejpam-6266	26	2	particular	particular	ADJ
ejpam-6266	26	3	he	he	PRON
ejpam-6266	26	4	showed	show	VERB
ejpam-6266	26	5	that	that	SCONJ
ejpam-6266	26	6	the	the	DET
ejpam-6266	26	7	critical	critical	ADJ
ejpam-6266	26	8	exponent	exponent	NOUN
ejpam-6266	26	9	in	in	ADP
ejpam-6266	26	10	fujita	fujita	PROPN
ejpam-6266	26	11	sense	sense	NOUN
ejpam-6266	26	12	in	in	ADP
ejpam-6266	26	13	the	the	DET
ejpam-6266	26	14	l1	l1	PROPN
ejpam-6266	26	15	∩	∩	PROPN
ejpam-6266	26	16	l2−theory	l2−theory	NOUN
ejpam-6266	26	17	for	for	ADP
ejpam-6266	26	18	the	the	DET
ejpam-6266	26	19	cauchy	cauchy	ADJ
ejpam-6266	26	20	problem	problem	NOUN
ejpam-6266	26	21	of	of	ADP
ejpam-6266	26	22	equation	equation	NOUN
ejpam-6266	26	23	(	(	PUNCT
ejpam-6266	26	24	1	1	X
ejpam-6266	26	25	)	)	PUNCT
ejpam-6266	26	26	is	be	AUX
ejpam-6266	26	27	p∗(n	p∗(n	PROPN
ejpam-6266	26	28	,	,	PUNCT
ejpam-6266	26	29	γ	γ	NOUN
ejpam-6266	26	30	)	)	PUNCT
ejpam-6266	26	31	=	=	SYM
ejpam-6266	26	32	max	max	PROPN
ejpam-6266	26	33	{	{	PUNCT
ejpam-6266	26	34	pγ(n	pγ(n	PROPN
ejpam-6266	26	35	)	)	PUNCT
ejpam-6266	26	36	;	;	PUNCT
ejpam-6266	26	37	1	1	NUM
ejpam-6266	26	38	γ	γ	NOUN
ejpam-6266	26	39	}	}	PUNCT
ejpam-6266	26	40	,	,	PUNCT
ejpam-6266	26	41	where	where	SCONJ
ejpam-6266	26	42	pγ(n	pγ(n	VERB
ejpam-6266	26	43	)	)	PUNCT
ejpam-6266	26	44	=	=	SYM
ejpam-6266	26	45	1	1	NUM
ejpam-6266	26	46	+	+	NUM
ejpam-6266	26	47	2(2−	2(2−	NUM
ejpam-6266	26	48	γ	γ	NOUN
ejpam-6266	26	49	)	)	PUNCT
ejpam-6266	26	50	(	(	PUNCT
ejpam-6266	26	51	n−	n−	NOUN
ejpam-6266	26	52	2(1−	2(1−	NUM
ejpam-6266	26	53	γ))+	γ))+	VERB
ejpam-6266	26	54	,	,	PUNCT
ejpam-6266	26	55	(	(	PUNCT
ejpam-6266	26	56	2	2	X
ejpam-6266	26	57	)	)	PUNCT
ejpam-6266	26	58	where	where	SCONJ
ejpam-6266	26	59	(	(	PUNCT
ejpam-6266	26	60	x)+	x)+	PROPN
ejpam-6266	26	61	stands	stand	VERB
ejpam-6266	26	62	for	for	ADP
ejpam-6266	26	63	the	the	DET
ejpam-6266	26	64	positive	positive	ADJ
ejpam-6266	26	65	part	part	NOUN
ejpam-6266	26	66	of	of	ADP
ejpam-6266	26	67	x	x	PRON
ejpam-6266	26	68	,	,	PUNCT
ejpam-6266	26	69	this	this	PRON
ejpam-6266	26	70	means	mean	VERB
ejpam-6266	26	71	that	that	SCONJ
ejpam-6266	26	72	(	(	PUNCT
ejpam-6266	26	73	n−	n−	NOUN
ejpam-6266	26	74	2(1−	2(1−	NUM
ejpam-6266	26	75	γ))+	γ))+	NOUN
ejpam-6266	26	76	=	=	SYM
ejpam-6266	26	77	max{n−	max{n−	NOUN
ejpam-6266	26	78	2(1−γ	2(1−γ	NUM
ejpam-6266	26	79	)	)	PUNCT
ejpam-6266	26	80	,	,	PUNCT
ejpam-6266	26	81	0	0	NUM
ejpam-6266	26	82	}	}	PUNCT
ejpam-6266	26	83	.	.	PUNCT
ejpam-6266	27	1	in	in	ADP
ejpam-6266	27	2	[	[	X
ejpam-6266	27	3	7	7	NUM
ejpam-6266	27	4	]	]	PUNCT
ejpam-6266	27	5	,	,	PUNCT
ejpam-6266	27	6	where	where	SCONJ
ejpam-6266	27	7	the	the	DET
ejpam-6266	27	8	same	same	ADJ
ejpam-6266	27	9	model	model	NOUN
ejpam-6266	27	10	is	be	AUX
ejpam-6266	27	11	considered	consider	VERB
ejpam-6266	27	12	,	,	PUNCT
ejpam-6266	27	13	m.	m.	NOUN
ejpam-6266	27	14	d’abbicco	d’abbicco	NOUN
ejpam-6266	27	15	has	have	AUX
ejpam-6266	27	16	improved	improve	VERB
ejpam-6266	27	17	some	some	DET
ejpam-6266	27	18	results	result	NOUN
ejpam-6266	27	19	of	of	ADP
ejpam-6266	27	20	global	global	ADJ
ejpam-6266	27	21	existence	existence	NOUN
ejpam-6266	27	22	by	by	ADP
ejpam-6266	27	23	using	use	VERB
ejpam-6266	27	24	matsumura	matsumura	ADJ
ejpam-6266	27	25	type	type	NOUN
ejpam-6266	27	26	estimates	estimate	NOUN
ejpam-6266	27	27	but	but	CCONJ
ejpam-6266	27	28	he	he	PRON
ejpam-6266	27	29	did	do	AUX
ejpam-6266	27	30	n’t	not	PART
ejpam-6266	27	31	investigate	investigate	VERB
ejpam-6266	27	32	blow	blow	NOUN
ejpam-6266	27	33	-	-	PUNCT
ejpam-6266	27	34	up	up	NOUN
ejpam-6266	27	35	.	.	PUNCT
ejpam-6266	28	1	in	in	ADP
ejpam-6266	28	2	particular	particular	ADJ
ejpam-6266	28	3	he	he	PRON
ejpam-6266	28	4	proposed	propose	VERB
ejpam-6266	28	5	the	the	DET
ejpam-6266	28	6	same	same	ADJ
ejpam-6266	28	7	critical	critical	ADJ
ejpam-6266	28	8	exponent	exponent	NOUN
ejpam-6266	28	9	proposed	propose	VERB
ejpam-6266	28	10	in	in	ADP
ejpam-6266	28	11	[	[	X
ejpam-6266	28	12	6	6	NUM
ejpam-6266	28	13	]	]	PUNCT
ejpam-6266	28	14	.	.	PUNCT
ejpam-6266	29	1	in	in	ADP
ejpam-6266	29	2	fact	fact	NOUN
ejpam-6266	29	3	the	the	DET
ejpam-6266	29	4	authors	author	NOUN
ejpam-6266	29	5	proved	prove	VERB
ejpam-6266	29	6	in	in	ADP
ejpam-6266	29	7	[	[	X
ejpam-6266	29	8	6	6	NUM
ejpam-6266	29	9	]	]	PUNCT
ejpam-6266	29	10	and	and	CCONJ
ejpam-6266	29	11	[	[	X
ejpam-6266	29	12	7	7	X
ejpam-6266	29	13	]	]	PUNCT
ejpam-6266	29	14	that	that	SCONJ
ejpam-6266	29	15	the	the	DET
ejpam-6266	29	16	term	term	NOUN
ejpam-6266	29	17	utt	utt	NOUN
ejpam-6266	29	18	does	do	AUX
ejpam-6266	29	19	not	not	PART
ejpam-6266	29	20	influence	influence	VERB
ejpam-6266	29	21	the	the	DET
ejpam-6266	29	22	critical	critical	ADJ
ejpam-6266	29	23	exponent	exponent	NOUN
ejpam-6266	29	24	since	since	SCONJ
ejpam-6266	29	25	t.	t.	PROPN
ejpam-6266	29	26	hadj	hadj	PROPN
ejpam-6266	29	27	kaddour	kaddour	PROPN
ejpam-6266	29	28	et	et	PROPN
ejpam-6266	29	29	al	al	PROPN
ejpam-6266	29	30	.	.	PUNCT
ejpam-6266	29	31	/	/	SYM
ejpam-6266	29	32	eur	eur	PROPN
ejpam-6266	29	33	.	.	PUNCT
ejpam-6266	30	1	j.	j.	PROPN
ejpam-6266	30	2	pure	pure	PROPN
ejpam-6266	30	3	appl	appl	PROPN
ejpam-6266	30	4	.	.	PROPN
ejpam-6266	30	5	math	math	PROPN
ejpam-6266	30	6	,	,	PUNCT
ejpam-6266	30	7	18	18	NUM
ejpam-6266	30	8	(	(	PUNCT
ejpam-6266	30	9	4	4	NUM
ejpam-6266	30	10	)	)	PUNCT
ejpam-6266	30	11	(	(	PUNCT
ejpam-6266	30	12	2025	2025	NUM
ejpam-6266	30	13	)	)	PUNCT
ejpam-6266	30	14	,	,	PUNCT
ejpam-6266	30	15	6266	6266	NUM
ejpam-6266	30	16	3	3	NUM
ejpam-6266	30	17	of	of	ADP
ejpam-6266	30	18	24	24	NUM
ejpam-6266	30	19	cazenave	cazenave	NOUN
ejpam-6266	30	20	et	et	PROPN
ejpam-6266	30	21	al	al	PROPN
ejpam-6266	30	22	proved	prove	VERB
ejpam-6266	30	23	in	in	ADP
ejpam-6266	30	24	[	[	X
ejpam-6266	30	25	8	8	NUM
ejpam-6266	30	26	]	]	PUNCT
ejpam-6266	30	27	that	that	SCONJ
ejpam-6266	30	28	the	the	DET
ejpam-6266	30	29	critical	critical	ADJ
ejpam-6266	30	30	exponent	exponent	NOUN
ejpam-6266	30	31	is	be	AUX
ejpam-6266	30	32	the	the	DET
ejpam-6266	30	33	same	same	ADJ
ejpam-6266	30	34	(	(	PUNCT
ejpam-6266	30	35	2	2	NUM
ejpam-6266	30	36	)	)	PUNCT
ejpam-6266	30	37	for	for	ADP
ejpam-6266	30	38	the	the	DET
ejpam-6266	30	39	corresponding	corresponding	ADJ
ejpam-6266	30	40	heat	heat	NOUN
ejpam-6266	30	41	equation	equation	NOUN
ejpam-6266	30	42	with	with	ADP
ejpam-6266	30	43	non	non	ADJ
ejpam-6266	30	44	linear	linear	PROPN
ejpam-6266	30	45	memory	memory	NOUN
ejpam-6266	30	46	ut	ut	PROPN
ejpam-6266	30	47	−∆u	−∆u	X
ejpam-6266	31	1	=	=	SYM
ejpam-6266	31	2	∫	∫	PROPN
ejpam-6266	31	3	t	t	PROPN
ejpam-6266	31	4	0	0	NUM
ejpam-6266	31	5	(	(	PUNCT
ejpam-6266	31	6	t−	t−	PROPN
ejpam-6266	31	7	τ)−γu(τ	τ)−γu(τ	PROPN
ejpam-6266	31	8	,	,	PUNCT
ejpam-6266	31	9	·	·	PUNCT
ejpam-6266	31	10	)	)	PUNCT
ejpam-6266	31	11	|u(τ	|u(τ	ADJ
ejpam-6266	31	12	,	,	PUNCT
ejpam-6266	31	13	·	·	PUNCT
ejpam-6266	31	14	)	)	PUNCT
ejpam-6266	31	15	|p−1dτ	|p−1dτ	PROPN
ejpam-6266	31	16	,	,	PUNCT
ejpam-6266	31	17	(	(	PUNCT
ejpam-6266	31	18	t	t	PROPN
ejpam-6266	31	19	,	,	PUNCT
ejpam-6266	31	20	x	x	NOUN
ejpam-6266	31	21	)	)	PUNCT
ejpam-6266	31	22	∈	∈	PROPN
ejpam-6266	31	23	(	(	PUNCT
ejpam-6266	31	24	0,∞)×	0,∞)×	NUM
ejpam-6266	31	25	rn	rn	X
ejpam-6266	31	26	.	.	PROPN
ejpam-6266	32	1	(	(	PUNCT
ejpam-6266	32	2	3	3	X
ejpam-6266	32	3	)	)	PUNCT
ejpam-6266	32	4	in	in	ADP
ejpam-6266	32	5	the	the	DET
ejpam-6266	32	6	other	other	ADJ
ejpam-6266	32	7	hand	hand	NOUN
ejpam-6266	32	8	,	,	PUNCT
ejpam-6266	32	9	the	the	DET
ejpam-6266	32	10	semilinear	semilinear	PROPN
ejpam-6266	32	11	cauchy	cauchy	PROPN
ejpam-6266	32	12	problem	problem	NOUN
ejpam-6266	32	13	corresponding	correspond	VERB
ejpam-6266	32	14	to	to	ADP
ejpam-6266	32	15	(	(	PUNCT
ejpam-6266	32	16	1	1	NUM
ejpam-6266	32	17	)	)	PUNCT
ejpam-6266	32	18	utt	utt	NOUN
ejpam-6266	32	19	−∆u+	−∆u+	NOUN
ejpam-6266	32	20	ut	ut	PROPN
ejpam-6266	33	1	=	=	SYM
ejpam-6266	33	2	|u|p	|u|p	PROPN
ejpam-6266	33	3	,	,	PUNCT
ejpam-6266	33	4	(	(	PUNCT
ejpam-6266	33	5	4	4	X
ejpam-6266	33	6	)	)	PUNCT
ejpam-6266	33	7	is	be	AUX
ejpam-6266	33	8	considered	consider	VERB
ejpam-6266	33	9	by	by	ADP
ejpam-6266	33	10	many	many	ADJ
ejpam-6266	33	11	authors	author	NOUN
ejpam-6266	33	12	,	,	PUNCT
ejpam-6266	33	13	we	we	PRON
ejpam-6266	33	14	refer	refer	VERB
ejpam-6266	33	15	the	the	DET
ejpam-6266	33	16	reader	reader	NOUN
ejpam-6266	33	17	to	to	ADP
ejpam-6266	33	18	eg	eg	NOUN
ejpam-6266	33	19	.	.	PUNCT
ejpam-6266	34	1	[	[	X
ejpam-6266	34	2	9	9	NUM
ejpam-6266	34	3	]	]	PUNCT
ejpam-6266	34	4	,	,	PUNCT
ejpam-6266	34	5	[	[	X
ejpam-6266	34	6	10	10	NUM
ejpam-6266	34	7	]	]	PUNCT
ejpam-6266	34	8	where	where	SCONJ
ejpam-6266	34	9	they	they	PRON
ejpam-6266	34	10	showed	show	VERB
ejpam-6266	34	11	that	that	SCONJ
ejpam-6266	34	12	the	the	DET
ejpam-6266	34	13	critical	critical	ADJ
ejpam-6266	34	14	exponent	exponent	NOUN
ejpam-6266	34	15	in	in	ADP
ejpam-6266	34	16	the	the	DET
ejpam-6266	34	17	l1	l1	PROPN
ejpam-6266	34	18	∩	∩	ADJ
ejpam-6266	34	19	l2	l2	NOUN
ejpam-6266	34	20	theory	theory	NOUN
ejpam-6266	34	21	for	for	ADP
ejpam-6266	34	22	cauchy	cauchy	ADJ
ejpam-6266	34	23	problem	problem	NOUN
ejpam-6266	34	24	of	of	ADP
ejpam-6266	34	25	(	(	PUNCT
ejpam-6266	34	26	4	4	NUM
ejpam-6266	34	27	)	)	PUNCT
ejpam-6266	34	28	is	be	AUX
ejpam-6266	34	29	the	the	DET
ejpam-6266	34	30	fujita	fujita	PROPN
ejpam-6266	34	31	exponent	exponent	PROPN
ejpam-6266	34	32	pfuj	pfuj	PROPN
ejpam-6266	34	33	=	=	PROPN
ejpam-6266	34	34	1	1	NUM
ejpam-6266	34	35	+	+	NUM
ejpam-6266	34	36	n	n	DET
ejpam-6266	34	37	2	2	NUM
ejpam-6266	34	38	.	.	PUNCT
ejpam-6266	35	1	(	(	PUNCT
ejpam-6266	35	2	5	5	NUM
ejpam-6266	35	3	)	)	PUNCT
ejpam-6266	35	4	in	in	ADP
ejpam-6266	35	5	the	the	DET
ejpam-6266	35	6	recent	recent	ADJ
ejpam-6266	35	7	paper	paper	NOUN
ejpam-6266	35	8	[	[	X
ejpam-6266	35	9	11	11	NUM
ejpam-6266	35	10	]	]	PUNCT
ejpam-6266	35	11	,	,	PUNCT
ejpam-6266	35	12	we	we	PRON
ejpam-6266	35	13	proved	prove	VERB
ejpam-6266	35	14	that	that	SCONJ
ejpam-6266	35	15	some	some	DET
ejpam-6266	35	16	class	class	NOUN
ejpam-6266	35	17	of	of	ADP
ejpam-6266	35	18	effective	effective	ADJ
ejpam-6266	35	19	damping	damp	VERB
ejpam-6266	35	20	influence	influence	NOUN
ejpam-6266	35	21	the	the	DET
ejpam-6266	35	22	critical	critical	ADJ
ejpam-6266	35	23	exponent	exponent	NOUN
ejpam-6266	35	24	in	in	ADP
ejpam-6266	35	25	fujita	fujita	PROPN
ejpam-6266	35	26	sense	sense	NOUN
ejpam-6266	35	27	.	.	PUNCT
ejpam-6266	36	1	in	in	ADP
ejpam-6266	36	2	this	this	DET
ejpam-6266	36	3	paper	paper	NOUN
ejpam-6266	36	4	we	we	PRON
ejpam-6266	36	5	will	will	AUX
ejpam-6266	36	6	show	show	VERB
ejpam-6266	36	7	that	that	SCONJ
ejpam-6266	36	8	the	the	DET
ejpam-6266	36	9	dissipative	dissipative	ADJ
ejpam-6266	36	10	nonlinear	nonlinear	NOUN
ejpam-6266	36	11	memory	memory	NOUN
ejpam-6266	36	12	dominates	dominate	VERB
ejpam-6266	36	13	the	the	DET
ejpam-6266	36	14	damping	damp	VERB
ejpam-6266	36	15	term	term	NOUN
ejpam-6266	36	16	ut	ut	INTJ
ejpam-6266	36	17	by	by	ADP
ejpam-6266	36	18	considering	consider	VERB
ejpam-6266	36	19	the	the	DET
ejpam-6266	36	20	following	follow	VERB
ejpam-6266	36	21	cauchy	cauchy	PROPN
ejpam-6266	36	22	problem	problem	NOUN
ejpam-6266	36	23	:	:	PUNCT
ejpam-6266	37	1	utt	utt	PROPN
ejpam-6266	37	2	−∆u+	−∆u+	NOUN
ejpam-6266	37	3	ut	ut	PROPN
ejpam-6266	37	4	=	=	SYM
ejpam-6266	38	1	∫	∫	PROPN
ejpam-6266	38	2	t	t	PROPN
ejpam-6266	38	3	0	0	NUM
ejpam-6266	38	4	(	(	PUNCT
ejpam-6266	38	5	t−	t−	PROPN
ejpam-6266	38	6	τ)−γ	τ)−γ	PUNCT
ejpam-6266	38	7	|ut(τ	|ut(τ	PROPN
ejpam-6266	38	8	,	,	PUNCT
ejpam-6266	38	9	x)|p	x)|p	PROPN
ejpam-6266	38	10	dτ	dτ	PROPN
ejpam-6266	38	11	,	,	PUNCT
ejpam-6266	38	12	(	(	PUNCT
ejpam-6266	38	13	t	t	PROPN
ejpam-6266	38	14	,	,	PUNCT
ejpam-6266	38	15	x	x	NOUN
ejpam-6266	38	16	)	)	PUNCT
ejpam-6266	38	17	∈	∈	PROPN
ejpam-6266	38	18	(	(	PUNCT
ejpam-6266	38	19	0,∞)×	0,∞)×	NUM
ejpam-6266	38	20	rn	rn	PROPN
ejpam-6266	38	21	,	,	PUNCT
ejpam-6266	38	22	u(0	u(0	PROPN
ejpam-6266	38	23	,	,	PUNCT
ejpam-6266	38	24	x	x	NOUN
ejpam-6266	38	25	)	)	PUNCT
ejpam-6266	38	26	=	=	SYM
ejpam-6266	38	27	u0(x	u0(x	NOUN
ejpam-6266	38	28	)	)	PUNCT
ejpam-6266	38	29	,	,	PUNCT
ejpam-6266	38	30	ut(0	ut(0	PROPN
ejpam-6266	38	31	,	,	PUNCT
ejpam-6266	38	32	x	x	NOUN
ejpam-6266	38	33	)	)	PUNCT
ejpam-6266	38	34	=	=	SYM
ejpam-6266	38	35	u1(x	u1(x	NOUN
ejpam-6266	38	36	)	)	PUNCT
ejpam-6266	38	37	,	,	PUNCT
ejpam-6266	38	38	x	x	PROPN
ejpam-6266	38	39	∈	∈	PROPN
ejpam-6266	38	40	rn	rn	PROPN
ejpam-6266	38	41	,	,	PUNCT
ejpam-6266	38	42	(	(	PUNCT
ejpam-6266	38	43	6	6	NUM
ejpam-6266	38	44	)	)	PUNCT
ejpam-6266	38	45	where	where	SCONJ
ejpam-6266	38	46	γ	γ	X
ejpam-6266	38	47	∈	∈	PROPN
ejpam-6266	38	48	(	(	PUNCT
ejpam-6266	38	49	0	0	NUM
ejpam-6266	38	50	,	,	PUNCT
ejpam-6266	38	51	1	1	NUM
ejpam-6266	38	52	)	)	PUNCT
ejpam-6266	38	53	and	and	CCONJ
ejpam-6266	38	54	p	p	X
ejpam-6266	38	55	>	>	X
ejpam-6266	38	56	1	1	X
ejpam-6266	38	57	.	.	PUNCT
ejpam-6266	39	1	here	here	ADV
ejpam-6266	39	2	,	,	PUNCT
ejpam-6266	39	3	the	the	DET
ejpam-6266	39	4	dissipative	dissipative	ADJ
ejpam-6266	39	5	memory	memory	NOUN
ejpam-6266	39	6	has	have	VERB
ejpam-6266	39	7	to	to	PART
ejpam-6266	39	8	be	be	AUX
ejpam-6266	39	9	seen	see	VERB
ejpam-6266	39	10	as	as	ADP
ejpam-6266	39	11	riemannliouville	riemannliouville	NOUN
ejpam-6266	39	12	fractional	fractional	ADJ
ejpam-6266	39	13	integral	integral	ADJ
ejpam-6266	39	14	to	to	ADP
ejpam-6266	39	15	a	a	DET
ejpam-6266	39	16	constant	constant	ADJ
ejpam-6266	39	17	up	up	ADP
ejpam-6266	39	18	of	of	ADP
ejpam-6266	39	19	|ut|p	|ut|p	PROPN
ejpam-6266	39	20	.	.	PUNCT
ejpam-6266	40	1	for	for	ADP
ejpam-6266	40	2	this	this	DET
ejpam-6266	40	3	reason	reason	NOUN
ejpam-6266	40	4	the	the	DET
ejpam-6266	40	5	non	non	ADJ
ejpam-6266	40	6	linear	linear	ADJ
ejpam-6266	40	7	term	term	NOUN
ejpam-6266	40	8	in	in	ADP
ejpam-6266	40	9	(	(	PUNCT
ejpam-6266	40	10	6	6	NUM
ejpam-6266	40	11	)	)	PUNCT
ejpam-6266	40	12	is	be	AUX
ejpam-6266	40	13	interpreted	interpret	VERB
ejpam-6266	40	14	as	as	ADP
ejpam-6266	40	15	a	a	DET
ejpam-6266	40	16	fractional	fractional	ADJ
ejpam-6266	40	17	power	power	NOUN
ejpam-6266	40	18	type	type	NOUN
ejpam-6266	40	19	non	non	ADJ
ejpam-6266	40	20	linearity	linearity	NOUN
ejpam-6266	40	21	.	.	PUNCT
ejpam-6266	41	1	finally	finally	ADV
ejpam-6266	41	2	,	,	PUNCT
ejpam-6266	41	3	we	we	PRON
ejpam-6266	41	4	finish	finish	VERB
ejpam-6266	41	5	this	this	DET
ejpam-6266	41	6	discussion	discussion	NOUN
ejpam-6266	41	7	by	by	ADP
ejpam-6266	41	8	the	the	DET
ejpam-6266	41	9	connexion	connexion	NOUN
ejpam-6266	41	10	between	between	ADP
ejpam-6266	41	11	the	the	DET
ejpam-6266	41	12	semilinar	semilinar	NOUN
ejpam-6266	41	13	damped	damp	VERB
ejpam-6266	41	14	wave	wave	NOUN
ejpam-6266	41	15	equation	equation	NOUN
ejpam-6266	41	16	and	and	CCONJ
ejpam-6266	41	17	the	the	DET
ejpam-6266	41	18	damped	damped	NOUN
ejpam-6266	41	19	wave	wave	NOUN
ejpam-6266	41	20	equation	equation	NOUN
ejpam-6266	41	21	with	with	ADP
ejpam-6266	41	22	non	non	ADJ
ejpam-6266	41	23	linear	linear	PROPN
ejpam-6266	41	24	memory	memory	NOUN
ejpam-6266	41	25	by	by	ADP
ejpam-6266	41	26	noting	note	VERB
ejpam-6266	41	27	that∫	that∫	PROPN
ejpam-6266	41	28	t	t	PROPN
ejpam-6266	41	29	0	0	NUM
ejpam-6266	42	1	(	(	PUNCT
ejpam-6266	42	2	t−	t−	PROPN
ejpam-6266	42	3	s)−γ	s)−γ	PROPN
ejpam-6266	42	4	|u(s	|u(s	PROPN
ejpam-6266	42	5	,	,	PUNCT
ejpam-6266	42	6	·	·	PUNCT
ejpam-6266	42	7	)	)	PUNCT
ejpam-6266	42	8	|p	|p	VERB
ejpam-6266	42	9	ds	ds	ADJ
ejpam-6266	42	10	−→	−→	NOUN
ejpam-6266	42	11	γ(1−	γ(1−	PROPN
ejpam-6266	42	12	γ)|u(t	γ)|u(t	PROPN
ejpam-6266	42	13	,	,	PUNCT
ejpam-6266	42	14	·	·	PUNCT
ejpam-6266	42	15	)	)	PUNCT
ejpam-6266	42	16	|p	|p	PROPN
ejpam-6266	42	17	as	as	ADP
ejpam-6266	42	18	γ	γ	X
ejpam-6266	42	19	−→	−→	NOUN
ejpam-6266	42	20	1	1	NUM
ejpam-6266	42	21	,	,	PUNCT
ejpam-6266	42	22	(	(	PUNCT
ejpam-6266	42	23	7	7	X
ejpam-6266	42	24	)	)	PUNCT
ejpam-6266	42	25	in	in	ADP
ejpam-6266	42	26	distribution	distribution	NOUN
ejpam-6266	42	27	sense	sense	NOUN
ejpam-6266	42	28	,	,	PUNCT
ejpam-6266	42	29	where	where	SCONJ
ejpam-6266	42	30	γ	γ	PROPN
ejpam-6266	42	31	is	be	AUX
ejpam-6266	42	32	the	the	DET
ejpam-6266	42	33	euler	euler	PROPN
ejpam-6266	42	34	gamma	gamma	PROPN
ejpam-6266	42	35	function	function	PROPN
ejpam-6266	42	36	.	.	PUNCT
ejpam-6266	43	1	for	for	ADP
ejpam-6266	43	2	this	this	DET
ejpam-6266	43	3	reason	reason	NOUN
ejpam-6266	43	4	we	we	PRON
ejpam-6266	43	5	have	have	VERB
ejpam-6266	43	6	lim	lim	PROPN
ejpam-6266	43	7	γ→1	γ→1	SYM
ejpam-6266	43	8	p∗(n	p∗(n	PROPN
ejpam-6266	43	9	,	,	PUNCT
ejpam-6266	43	10	γ	γ	NOUN
ejpam-6266	43	11	)	)	PUNCT
ejpam-6266	43	12	=	=	SYM
ejpam-6266	43	13	pfuj	pfuj	NOUN
ejpam-6266	43	14	,	,	PUNCT
ejpam-6266	43	15	(	(	PUNCT
ejpam-6266	43	16	8)	8)	NUM
ejpam-6266	43	17	2.2	2.2	NUM
ejpam-6266	43	18	.	.	PUNCT
ejpam-6266	44	1	representation	representation	NOUN
ejpam-6266	44	2	of	of	ADP
ejpam-6266	44	3	the	the	DET
ejpam-6266	44	4	solution	solution	NOUN
ejpam-6266	44	5	the	the	DET
ejpam-6266	44	6	presence	presence	NOUN
ejpam-6266	44	7	of	of	ADP
ejpam-6266	44	8	the	the	DET
ejpam-6266	44	9	nonlinear	nonlinear	ADJ
ejpam-6266	44	10	term	term	NOUN
ejpam-6266	44	11	on	on	ADP
ejpam-6266	44	12	the	the	DET
ejpam-6266	44	13	right	right	ADJ
ejpam-6266	44	14	-	-	PUNCT
ejpam-6266	44	15	hand	hand	NOUN
ejpam-6266	44	16	side	side	NOUN
ejpam-6266	44	17	suggests	suggest	VERB
ejpam-6266	44	18	to	to	ADP
ejpam-6266	44	19	us	we	PRON
ejpam-6266	44	20	the	the	DET
ejpam-6266	44	21	apply	apply	VERB
ejpam-6266	44	22	the	the	DET
ejpam-6266	44	23	duhamel	duhamel	PROPN
ejpam-6266	44	24	’s	’s	PART
ejpam-6266	44	25	principle	principle	NOUN
ejpam-6266	44	26	where	where	SCONJ
ejpam-6266	44	27	the	the	DET
ejpam-6266	44	28	study	study	NOUN
ejpam-6266	44	29	of	of	ADP
ejpam-6266	44	30	the	the	DET
ejpam-6266	44	31	cauchy	cauchy	ADJ
ejpam-6266	44	32	problem	problem	NOUN
ejpam-6266	44	33	(	(	PUNCT
ejpam-6266	44	34	6	6	NUM
ejpam-6266	44	35	)	)	PUNCT
ejpam-6266	44	36	reduces	reduce	VERB
ejpam-6266	44	37	to	to	ADP
ejpam-6266	44	38	the	the	DET
ejpam-6266	44	39	study	study	NOUN
ejpam-6266	44	40	of	of	ADP
ejpam-6266	44	41	the	the	DET
ejpam-6266	44	42	following	follow	VERB
ejpam-6266	44	43	cauchy	cauchy	PROPN
ejpam-6266	44	44	problem	problem	NOUN
ejpam-6266	44	45	:	:	PUNCT
ejpam-6266	45	1	utt	utt	PROPN
ejpam-6266	45	2	−∆u+	−∆u+	NOUN
ejpam-6266	45	3	ut	ut	PROPN
ejpam-6266	46	1	=	=	SYM
ejpam-6266	46	2	0	0	PROPN
ejpam-6266	46	3	,	,	PUNCT
ejpam-6266	46	4	(	(	PUNCT
ejpam-6266	46	5	t	t	PROPN
ejpam-6266	46	6	,	,	PUNCT
ejpam-6266	46	7	x	x	NOUN
ejpam-6266	46	8	)	)	PUNCT
ejpam-6266	46	9	∈	∈	PROPN
ejpam-6266	46	10	(	(	PUNCT
ejpam-6266	46	11	0,∞)×	0,∞)×	NUM
ejpam-6266	46	12	rn	rn	PROPN
ejpam-6266	46	13	,	,	PUNCT
ejpam-6266	46	14	u(0	u(0	PROPN
ejpam-6266	46	15	,	,	PUNCT
ejpam-6266	46	16	x	x	NOUN
ejpam-6266	46	17	)	)	PUNCT
ejpam-6266	46	18	=	=	SYM
ejpam-6266	46	19	u0(x	u0(x	NOUN
ejpam-6266	46	20	)	)	PUNCT
ejpam-6266	46	21	,	,	PUNCT
ejpam-6266	46	22	ut(0	ut(0	PROPN
ejpam-6266	46	23	,	,	PUNCT
ejpam-6266	46	24	x	x	NOUN
ejpam-6266	46	25	)	)	PUNCT
ejpam-6266	46	26	=	=	SYM
ejpam-6266	47	1	u1(x	u1(x	NOUN
ejpam-6266	47	2	)	)	PUNCT
ejpam-6266	48	1	,	,	PUNCT
ejpam-6266	48	2	x	x	PROPN
ejpam-6266	48	3	∈	∈	PROPN
ejpam-6266	48	4	rn	rn	PROPN
ejpam-6266	48	5	,	,	PUNCT
ejpam-6266	48	6	(	(	PUNCT
ejpam-6266	48	7	9	9	NUM
ejpam-6266	48	8	)	)	PUNCT
ejpam-6266	48	9	and	and	CCONJ
ejpam-6266	48	10	the	the	DET
ejpam-6266	48	11	family	family	NOUN
ejpam-6266	48	12	of	of	ADP
ejpam-6266	48	13	parameter	parameter	NOUN
ejpam-6266	48	14	-	-	PUNCT
ejpam-6266	48	15	dependent	dependent	ADJ
ejpam-6266	48	16	cauchy	cauchy	NOUN
ejpam-6266	48	17	problems	problem	NOUN
ejpam-6266	48	18	vtt	vtt	PROPN
ejpam-6266	48	19	−∆v	−∆v	PROPN
ejpam-6266	49	1	+	+	CCONJ
ejpam-6266	49	2	vt	vt	PROPN
ejpam-6266	49	3	=	=	SYM
ejpam-6266	49	4	0	0	PROPN
ejpam-6266	49	5	,	,	PUNCT
ejpam-6266	49	6	(	(	PUNCT
ejpam-6266	49	7	t	t	PROPN
ejpam-6266	49	8	,	,	PUNCT
ejpam-6266	49	9	x	x	NOUN
ejpam-6266	49	10	)	)	PUNCT
ejpam-6266	49	11	∈	∈	PROPN
ejpam-6266	49	12	(	(	PUNCT
ejpam-6266	49	13	τ,∞)×	τ,∞)×	PROPN
ejpam-6266	49	14	rn	rn	PROPN
ejpam-6266	49	15	,	,	PUNCT
ejpam-6266	49	16	v(τ	v(τ	PROPN
ejpam-6266	49	17	,	,	PUNCT
ejpam-6266	49	18	x	x	NOUN
ejpam-6266	49	19	)	)	PUNCT
ejpam-6266	49	20	=	=	SYM
ejpam-6266	49	21	0	0	NUM
ejpam-6266	49	22	,	,	PUNCT
ejpam-6266	49	23	x	x	PROPN
ejpam-6266	49	24	∈	∈	PROPN
ejpam-6266	49	25	rn	rn	PROPN
ejpam-6266	49	26	,	,	PUNCT
ejpam-6266	49	27	τ	τ	PROPN
ejpam-6266	49	28	≥	≥	NOUN
ejpam-6266	49	29	0	0	NUM
ejpam-6266	49	30	,	,	PUNCT
ejpam-6266	49	31	vt(τ	vt(τ	NOUN
ejpam-6266	49	32	,	,	PUNCT
ejpam-6266	49	33	x	x	X
ejpam-6266	49	34	)	)	PUNCT
ejpam-6266	49	35	=	=	SYM
ejpam-6266	49	36	h(τ	h(τ	PROPN
ejpam-6266	49	37	,	,	PUNCT
ejpam-6266	49	38	x	x	NOUN
ejpam-6266	49	39	)	)	PUNCT
ejpam-6266	49	40	:	:	PUNCT
ejpam-6266	50	1	=	=	SYM
ejpam-6266	50	2	∫	∫	PROPN
ejpam-6266	50	3	τ	τ	PROPN
ejpam-6266	50	4	0	0	NUM
ejpam-6266	50	5	(	(	PUNCT
ejpam-6266	50	6	τ	τ	X
ejpam-6266	50	7	−	−	PROPN
ejpam-6266	50	8	s)−γ	s)−γ	X
ejpam-6266	50	9	|ut(s	|ut(s	X
ejpam-6266	50	10	,	,	PUNCT
ejpam-6266	50	11	x)|p	x)|p	NOUN
ejpam-6266	50	12	ds	ds	PROPN
ejpam-6266	50	13	,	,	PUNCT
ejpam-6266	50	14	x	x	PROPN
ejpam-6266	50	15	∈	∈	PROPN
ejpam-6266	50	16	rn	rn	PROPN
ejpam-6266	50	17	,	,	PUNCT
ejpam-6266	50	18	τ	τ	PROPN
ejpam-6266	50	19	≥	≥	NOUN
ejpam-6266	50	20	0	0	NUM
ejpam-6266	50	21	.	.	PUNCT
ejpam-6266	51	1	(	(	PUNCT
ejpam-6266	51	2	10	10	NUM
ejpam-6266	51	3	)	)	PUNCT
ejpam-6266	51	4	t.	t.	NOUN
ejpam-6266	51	5	hadj	hadj	PROPN
ejpam-6266	51	6	kaddour	kaddour	PROPN
ejpam-6266	51	7	et	et	PROPN
ejpam-6266	51	8	al	al	PROPN
ejpam-6266	51	9	.	.	PUNCT
ejpam-6266	51	10	/	/	SYM
ejpam-6266	51	11	eur	eur	PROPN
ejpam-6266	51	12	.	.	PUNCT
ejpam-6266	52	1	j.	j.	PROPN
ejpam-6266	52	2	pure	pure	PROPN
ejpam-6266	52	3	appl	appl	PROPN
ejpam-6266	52	4	.	.	PROPN
ejpam-6266	52	5	math	math	PROPN
ejpam-6266	52	6	,	,	PUNCT
ejpam-6266	52	7	18	18	NUM
ejpam-6266	52	8	(	(	PUNCT
ejpam-6266	52	9	4	4	NUM
ejpam-6266	52	10	)	)	PUNCT
ejpam-6266	52	11	(	(	PUNCT
ejpam-6266	52	12	2025	2025	NUM
ejpam-6266	52	13	)	)	PUNCT
ejpam-6266	52	14	,	,	PUNCT
ejpam-6266	52	15	6266	6266	NUM
ejpam-6266	52	16	4	4	NUM
ejpam-6266	52	17	of	of	ADP
ejpam-6266	52	18	24	24	NUM
ejpam-6266	52	19	denoting	denote	VERB
ejpam-6266	52	20	v	v	NOUN
ejpam-6266	52	21	=	=	SYM
ejpam-6266	52	22	v(t	v(t	X
ejpam-6266	52	23	,	,	PUNCT
ejpam-6266	52	24	τ	τ	PROPN
ejpam-6266	52	25	,	,	PUNCT
ejpam-6266	52	26	x	x	X
ejpam-6266	52	27	)	)	PUNCT
ejpam-6266	52	28	the	the	DET
ejpam-6266	52	29	solution	solution	NOUN
ejpam-6266	52	30	of	of	ADP
ejpam-6266	52	31	cauchy	cauchy	ADJ
ejpam-6266	52	32	problem	problem	NOUN
ejpam-6266	52	33	(	(	PUNCT
ejpam-6266	52	34	10	10	NUM
ejpam-6266	52	35	)	)	PUNCT
ejpam-6266	52	36	,	,	PUNCT
ejpam-6266	52	37	and	and	CCONJ
ejpam-6266	52	38	ulin	ulin	PROPN
ejpam-6266	52	39	=	=	SYM
ejpam-6266	52	40	ulin(t	ulin(t	PROPN
ejpam-6266	52	41	,	,	PUNCT
ejpam-6266	52	42	x	x	X
ejpam-6266	52	43	)	)	PUNCT
ejpam-6266	52	44	the	the	DET
ejpam-6266	52	45	solution	solution	NOUN
ejpam-6266	52	46	of	of	ADP
ejpam-6266	52	47	cauchy	cauchy	ADJ
ejpam-6266	52	48	problem	problem	NOUN
ejpam-6266	52	49	(	(	PUNCT
ejpam-6266	52	50	9	9	NUM
ejpam-6266	52	51	)	)	PUNCT
ejpam-6266	52	52	,	,	PUNCT
ejpam-6266	52	53	then	then	ADV
ejpam-6266	52	54	the	the	DET
ejpam-6266	52	55	solution	solution	NOUN
ejpam-6266	52	56	u	u	NOUN
ejpam-6266	52	57	=	=	SYM
ejpam-6266	52	58	u(t	u(t	NOUN
ejpam-6266	52	59	,	,	PUNCT
ejpam-6266	52	60	x	x	NOUN
ejpam-6266	52	61	)	)	PUNCT
ejpam-6266	52	62	of	of	ADP
ejpam-6266	52	63	the	the	DET
ejpam-6266	52	64	cauchy	cauchy	ADJ
ejpam-6266	52	65	problem	problem	NOUN
ejpam-6266	52	66	(	(	PUNCT
ejpam-6266	52	67	6	6	NUM
ejpam-6266	52	68	)	)	PUNCT
ejpam-6266	52	69	is	be	AUX
ejpam-6266	52	70	formally	formally	ADV
ejpam-6266	52	71	given	give	VERB
ejpam-6266	52	72	by	by	ADP
ejpam-6266	52	73	u(t	u(t	NOUN
ejpam-6266	52	74	,	,	PUNCT
ejpam-6266	52	75	x	x	NOUN
ejpam-6266	52	76	)	)	PUNCT
ejpam-6266	52	77	=	=	SYM
ejpam-6266	52	78	ulin(t	ulin(t	PROPN
ejpam-6266	52	79	,	,	PUNCT
ejpam-6266	52	80	x	x	NOUN
ejpam-6266	52	81	)	)	PUNCT
ejpam-6266	52	82	+	+	CCONJ
ejpam-6266	52	83	unl(t	unl(t	PROPN
ejpam-6266	52	84	,	,	PUNCT
ejpam-6266	52	85	x	x	NOUN
ejpam-6266	52	86	)	)	PUNCT
ejpam-6266	52	87	,	,	PUNCT
ejpam-6266	52	88	(	(	PUNCT
ejpam-6266	52	89	11	11	NUM
ejpam-6266	52	90	)	)	PUNCT
ejpam-6266	52	91	where	where	SCONJ
ejpam-6266	52	92	unl(t	unl(t	PROPN
ejpam-6266	52	93	,	,	PUNCT
ejpam-6266	52	94	x	x	NOUN
ejpam-6266	52	95	)	)	PUNCT
ejpam-6266	52	96	:	:	PUNCT
ejpam-6266	53	1	=	=	SYM
ejpam-6266	53	2	∫	∫	PROPN
ejpam-6266	53	3	t	t	PROPN
ejpam-6266	53	4	0	0	NUM
ejpam-6266	54	1	v(t	v(t	PROPN
ejpam-6266	54	2	,	,	PUNCT
ejpam-6266	54	3	τ	τ	PROPN
ejpam-6266	54	4	,	,	PUNCT
ejpam-6266	54	5	x	x	NOUN
ejpam-6266	54	6	)	)	PUNCT
ejpam-6266	54	7	dτ	dτ	NOUN
ejpam-6266	54	8	.	.	PUNCT
ejpam-6266	54	9	by	by	ADP
ejpam-6266	54	10	using	use	VERB
ejpam-6266	54	11	fourier	fourier	NOUN
ejpam-6266	54	12	transform	transform	NOUN
ejpam-6266	54	13	argument	argument	NOUN
ejpam-6266	54	14	,	,	PUNCT
ejpam-6266	54	15	the	the	DET
ejpam-6266	54	16	solution	solution	NOUN
ejpam-6266	54	17	ulin	ulin	NOUN
ejpam-6266	54	18	=	=	SYM
ejpam-6266	54	19	ulin(t	ulin(t	PROPN
ejpam-6266	54	20	,	,	PUNCT
ejpam-6266	54	21	x	x	NOUN
ejpam-6266	54	22	)	)	PUNCT
ejpam-6266	54	23	of	of	ADP
ejpam-6266	54	24	cauchy	cauchy	PROPN
ejpam-6266	54	25	problem	problem	NOUN
ejpam-6266	54	26	(	(	PUNCT
ejpam-6266	54	27	9	9	NUM
ejpam-6266	54	28	)	)	PUNCT
ejpam-6266	54	29	is	be	AUX
ejpam-6266	54	30	given	give	VERB
ejpam-6266	54	31	by	by	ADP
ejpam-6266	54	32	ulin(t	ulin(t	PROPN
ejpam-6266	54	33	,	,	PUNCT
ejpam-6266	54	34	x	x	NOUN
ejpam-6266	54	35	)	)	PUNCT
ejpam-6266	54	36	=	=	SYM
ejpam-6266	54	37	e0(t	e0(t	PROPN
ejpam-6266	54	38	,	,	PUNCT
ejpam-6266	54	39	0	0	NUM
ejpam-6266	54	40	,	,	PUNCT
ejpam-6266	54	41	x	x	NOUN
ejpam-6266	54	42	)	)	PUNCT
ejpam-6266	54	43	∗x	∗x	ADV
ejpam-6266	54	44	u0(x	u0(x	NUM
ejpam-6266	54	45	)	)	PUNCT
ejpam-6266	54	46	+	+	X
ejpam-6266	54	47	e1(t	e1(t	PROPN
ejpam-6266	54	48	,	,	PUNCT
ejpam-6266	54	49	0	0	NUM
ejpam-6266	54	50	,	,	PUNCT
ejpam-6266	54	51	x	x	NOUN
ejpam-6266	54	52	)	)	PUNCT
ejpam-6266	54	53	∗x	∗x	PUNCT
ejpam-6266	54	54	u1(x	u1(x	ADJ
ejpam-6266	54	55	)	)	PUNCT
ejpam-6266	54	56	,	,	PUNCT
ejpam-6266	54	57	(	(	PUNCT
ejpam-6266	54	58	12	12	NUM
ejpam-6266	54	59	)	)	PUNCT
ejpam-6266	55	1	where	where	SCONJ
ejpam-6266	55	2	e0	e0	PROPN
ejpam-6266	55	3	=	=	SYM
ejpam-6266	55	4	e0(t	e0(t	PROPN
ejpam-6266	55	5	,	,	PUNCT
ejpam-6266	55	6	0	0	NUM
ejpam-6266	55	7	,	,	PUNCT
ejpam-6266	55	8	x	x	NOUN
ejpam-6266	55	9	)	)	PUNCT
ejpam-6266	55	10	and	and	CCONJ
ejpam-6266	55	11	e1	e1	PROPN
ejpam-6266	55	12	=	=	SYM
ejpam-6266	55	13	e1(t	e1(t	PROPN
ejpam-6266	55	14	,	,	PUNCT
ejpam-6266	55	15	0	0	NUM
ejpam-6266	55	16	,	,	PUNCT
ejpam-6266	55	17	x	x	X
ejpam-6266	55	18	)	)	PUNCT
ejpam-6266	55	19	are	be	AUX
ejpam-6266	55	20	the	the	DET
ejpam-6266	55	21	fundamental	fundamental	ADJ
ejpam-6266	55	22	solutions	solution	NOUN
ejpam-6266	55	23	for	for	ADP
ejpam-6266	55	24	the	the	DET
ejpam-6266	55	25	cauchy	cauchy	ADJ
ejpam-6266	55	26	problem	problem	NOUN
ejpam-6266	55	27	(	(	PUNCT
ejpam-6266	55	28	9	9	NUM
ejpam-6266	55	29	)	)	PUNCT
ejpam-6266	55	30	,	,	PUNCT
ejpam-6266	55	31	that	that	ADV
ejpam-6266	55	32	is	is	ADV
ejpam-6266	55	33	,	,	PUNCT
ejpam-6266	55	34	e0	e0	PROPN
ejpam-6266	55	35	corresponds	correspond	VERB
ejpam-6266	55	36	to	to	ADP
ejpam-6266	55	37	the	the	DET
ejpam-6266	55	38	initial	initial	ADJ
ejpam-6266	55	39	data	datum	NOUN
ejpam-6266	55	40	(	(	PUNCT
ejpam-6266	55	41	u0	u0	ADJ
ejpam-6266	55	42	,	,	PUNCT
ejpam-6266	55	43	u1	u1	NOUN
ejpam-6266	55	44	)	)	PUNCT
ejpam-6266	55	45	=	=	PUNCT
ejpam-6266	56	1	(	(	PUNCT
ejpam-6266	56	2	δ0	δ0	NOUN
ejpam-6266	56	3	,	,	PUNCT
ejpam-6266	56	4	0	0	NUM
ejpam-6266	56	5	)	)	PUNCT
ejpam-6266	56	6	and	and	CCONJ
ejpam-6266	56	7	e1	e1	PROPN
ejpam-6266	56	8	=	=	SYM
ejpam-6266	56	9	e1(t	e1(t	PROPN
ejpam-6266	56	10	,	,	PUNCT
ejpam-6266	56	11	0	0	NUM
ejpam-6266	56	12	,	,	PUNCT
ejpam-6266	56	13	x	x	X
ejpam-6266	56	14	)	)	PUNCT
ejpam-6266	56	15	corresponds	correspond	VERB
ejpam-6266	56	16	to	to	ADP
ejpam-6266	56	17	the	the	DET
ejpam-6266	56	18	initial	initial	ADJ
ejpam-6266	56	19	data	datum	NOUN
ejpam-6266	56	20	(	(	PUNCT
ejpam-6266	56	21	u0	u0	ADJ
ejpam-6266	56	22	,	,	PUNCT
ejpam-6266	56	23	u1	u1	NOUN
ejpam-6266	56	24	)	)	PUNCT
ejpam-6266	56	25	=	=	SYM
ejpam-6266	57	1	(	(	PUNCT
ejpam-6266	57	2	0	0	NUM
ejpam-6266	57	3	,	,	PUNCT
ejpam-6266	57	4	δ0	δ0	NOUN
ejpam-6266	57	5	)	)	PUNCT
ejpam-6266	57	6	,	,	PUNCT
ejpam-6266	57	7	where	where	SCONJ
ejpam-6266	57	8	δ0	δ0	NOUN
ejpam-6266	57	9	denotes	denote	VERB
ejpam-6266	57	10	the	the	DET
ejpam-6266	57	11	dirac	dirac	PROPN
ejpam-6266	57	12	delta	delta	NOUN
ejpam-6266	57	13	-	-	PUNCT
ejpam-6266	57	14	distribution	distribution	NOUN
ejpam-6266	57	15	supported	support	VERB
ejpam-6266	57	16	in	in	ADP
ejpam-6266	57	17	0	0	NUM
ejpam-6266	57	18	.	.	PUNCT
ejpam-6266	58	1	here	here	ADV
ejpam-6266	58	2	and	and	CCONJ
ejpam-6266	58	3	in	in	ADP
ejpam-6266	58	4	the	the	DET
ejpam-6266	58	5	sequel	sequel	NOUN
ejpam-6266	58	6	,	,	PUNCT
ejpam-6266	58	7	∗x	∗x	ADJ
ejpam-6266	58	8	denotes	denote	NOUN
ejpam-6266	58	9	for	for	ADP
ejpam-6266	58	10	the	the	DET
ejpam-6266	58	11	convolution	convolution	NOUN
ejpam-6266	58	12	with	with	ADP
ejpam-6266	58	13	respect	respect	NOUN
ejpam-6266	58	14	to	to	ADP
ejpam-6266	58	15	the	the	DET
ejpam-6266	58	16	x−variables	x−variables	PROPN
ejpam-6266	58	17	.	.	PUNCT
ejpam-6266	59	1	similarly	similarly	ADV
ejpam-6266	59	2	,	,	PUNCT
ejpam-6266	59	3	the	the	DET
ejpam-6266	59	4	solution	solution	NOUN
ejpam-6266	59	5	v	v	ADP
ejpam-6266	59	6	=	=	SYM
ejpam-6266	59	7	v(t	v(t	X
ejpam-6266	59	8	,	,	PUNCT
ejpam-6266	59	9	τ	τ	PROPN
ejpam-6266	59	10	,	,	PUNCT
ejpam-6266	59	11	x	x	NOUN
ejpam-6266	59	12	)	)	PUNCT
ejpam-6266	59	13	of	of	ADP
ejpam-6266	59	14	the	the	DET
ejpam-6266	59	15	cauchy	cauchy	ADJ
ejpam-6266	59	16	problem	problem	NOUN
ejpam-6266	59	17	(	(	PUNCT
ejpam-6266	59	18	10	10	NUM
ejpam-6266	59	19	)	)	PUNCT
ejpam-6266	59	20	is	be	AUX
ejpam-6266	59	21	given	give	VERB
ejpam-6266	59	22	by	by	ADP
ejpam-6266	59	23	v(t	v(t	PROPN
ejpam-6266	59	24	,	,	PUNCT
ejpam-6266	59	25	τ	τ	PROPN
ejpam-6266	59	26	,	,	PUNCT
ejpam-6266	59	27	x	x	NOUN
ejpam-6266	59	28	)	)	PUNCT
ejpam-6266	59	29	=	=	SYM
ejpam-6266	59	30	e1(t	e1(t	PROPN
ejpam-6266	59	31	,	,	PUNCT
ejpam-6266	59	32	τ	τ	X
ejpam-6266	59	33	,	,	PUNCT
ejpam-6266	59	34	x	x	NOUN
ejpam-6266	59	35	)	)	PUNCT
ejpam-6266	59	36	∗x	∗x	PROPN
ejpam-6266	59	37	h(τ	h(τ	PROPN
ejpam-6266	59	38	,	,	PUNCT
ejpam-6266	59	39	u	u	NOUN
ejpam-6266	59	40	)	)	PUNCT
ejpam-6266	59	41	,	,	PUNCT
ejpam-6266	59	42	where	where	SCONJ
ejpam-6266	59	43	h(τ	h(τ	PROPN
ejpam-6266	59	44	,	,	PUNCT
ejpam-6266	59	45	u	u	NOUN
ejpam-6266	59	46	)	)	PUNCT
ejpam-6266	59	47	=	=	SYM
ejpam-6266	60	1	∫	∫	PROPN
ejpam-6266	60	2	τ	τ	PROPN
ejpam-6266	60	3	0	0	NUM
ejpam-6266	60	4	(	(	PUNCT
ejpam-6266	60	5	τ	τ	X
ejpam-6266	60	6	−	−	PROPN
ejpam-6266	60	7	s)−γ	s)−γ	X
ejpam-6266	60	8	|ut(s	|ut(s	X
ejpam-6266	60	9	,	,	PUNCT
ejpam-6266	60	10	x)|p	x)|p	PROPN
ejpam-6266	60	11	ds	ds	PROPN
ejpam-6266	60	12	,	,	PUNCT
ejpam-6266	60	13	t	t	PROPN
ejpam-6266	60	14	>	>	X
ejpam-6266	60	15	τ	τ	PROPN
ejpam-6266	60	16	≥	≥	PROPN
ejpam-6266	60	17	0	0	NUM
ejpam-6266	60	18	,	,	PUNCT
ejpam-6266	60	19	(	(	PUNCT
ejpam-6266	60	20	13	13	NUM
ejpam-6266	60	21	)	)	PUNCT
ejpam-6266	60	22	since	since	SCONJ
ejpam-6266	60	23	v(τ	v(τ	PROPN
ejpam-6266	60	24	,	,	PUNCT
ejpam-6266	60	25	x	x	NOUN
ejpam-6266	60	26	)	)	PUNCT
ejpam-6266	60	27	=	=	SYM
ejpam-6266	60	28	0	0	NUM
ejpam-6266	60	29	for	for	ADP
ejpam-6266	60	30	all	all	DET
ejpam-6266	60	31	x	x	SYM
ejpam-6266	60	32	∈	∈	PROPN
ejpam-6266	60	33	rn	rn	PROPN
ejpam-6266	60	34	and	and	CCONJ
ejpam-6266	60	35	τ	τ	PROPN
ejpam-6266	60	36	≥	≥	NOUN
ejpam-6266	60	37	0	0	NUM
ejpam-6266	60	38	.	.	PUNCT
ejpam-6266	61	1	by	by	ADP
ejpam-6266	61	2	using	use	VERB
ejpam-6266	61	3	(	(	PUNCT
ejpam-6266	61	4	11	11	NUM
ejpam-6266	61	5	)	)	PUNCT
ejpam-6266	61	6	,	,	PUNCT
ejpam-6266	61	7	(	(	PUNCT
ejpam-6266	61	8	12	12	NUM
ejpam-6266	61	9	)	)	PUNCT
ejpam-6266	61	10	and	and	CCONJ
ejpam-6266	61	11	(	(	PUNCT
ejpam-6266	61	12	13	13	NUM
ejpam-6266	61	13	)	)	PUNCT
ejpam-6266	61	14	the	the	DET
ejpam-6266	61	15	solution	solution	NOUN
ejpam-6266	61	16	of	of	ADP
ejpam-6266	61	17	the	the	DET
ejpam-6266	61	18	cauchy	cauchy	ADJ
ejpam-6266	61	19	problem	problem	NOUN
ejpam-6266	61	20	(	(	PUNCT
ejpam-6266	61	21	6	6	NUM
ejpam-6266	61	22	)	)	PUNCT
ejpam-6266	61	23	is	be	AUX
ejpam-6266	61	24	formally	formally	ADV
ejpam-6266	61	25	given	give	VERB
ejpam-6266	61	26	as	as	ADP
ejpam-6266	61	27	a	a	DET
ejpam-6266	61	28	solution	solution	NOUN
ejpam-6266	61	29	of	of	ADP
ejpam-6266	61	30	the	the	DET
ejpam-6266	61	31	fixed	fix	VERB
ejpam-6266	61	32	point	point	NOUN
ejpam-6266	61	33	equation	equation	NOUN
ejpam-6266	61	34	u(t	u(t	NOUN
ejpam-6266	61	35	,	,	PUNCT
ejpam-6266	61	36	x	x	NOUN
ejpam-6266	61	37	)	)	PUNCT
ejpam-6266	61	38	=	=	SYM
ejpam-6266	62	1	e0(t	e0(t	PROPN
ejpam-6266	62	2	,	,	PUNCT
ejpam-6266	62	3	0	0	NUM
ejpam-6266	62	4	,	,	PUNCT
ejpam-6266	62	5	x	x	NOUN
ejpam-6266	62	6	)	)	PUNCT
ejpam-6266	62	7	∗x	∗x	ADV
ejpam-6266	62	8	u0(x	u0(x	NUM
ejpam-6266	62	9	)	)	PUNCT
ejpam-6266	62	10	+	+	X
ejpam-6266	62	11	e1(t	e1(t	PROPN
ejpam-6266	62	12	,	,	PUNCT
ejpam-6266	62	13	0	0	NUM
ejpam-6266	62	14	,	,	PUNCT
ejpam-6266	62	15	x	x	NOUN
ejpam-6266	62	16	)	)	PUNCT
ejpam-6266	62	17	∗x	∗x	PUNCT
ejpam-6266	62	18	u1(x	u1(x	NOUN
ejpam-6266	62	19	)	)	PUNCT
ejpam-6266	63	1	+	+	CCONJ
ejpam-6266	63	2	∫	∫	PROPN
ejpam-6266	63	3	t	t	PROPN
ejpam-6266	63	4	0	0	NUM
ejpam-6266	63	5	e1(t	e1(t	PROPN
ejpam-6266	63	6	,	,	PUNCT
ejpam-6266	63	7	τ	τ	X
ejpam-6266	63	8	,	,	PUNCT
ejpam-6266	63	9	x	x	NOUN
ejpam-6266	63	10	)	)	PUNCT
ejpam-6266	63	11	∗x	∗x	PROPN
ejpam-6266	63	12	h(τ	h(τ	PROPN
ejpam-6266	63	13	,	,	PUNCT
ejpam-6266	63	14	u	u	NOUN
ejpam-6266	63	15	)	)	PUNCT
ejpam-6266	63	16	dτ	dτ	PROPN
ejpam-6266	63	17	.	.	PROPN
ejpam-6266	64	1	since	since	SCONJ
ejpam-6266	64	2	the	the	DET
ejpam-6266	64	3	coefficients	coefficient	NOUN
ejpam-6266	64	4	of	of	ADP
ejpam-6266	64	5	the	the	DET
ejpam-6266	64	6	linear	linear	ADJ
ejpam-6266	64	7	problem	problem	NOUN
ejpam-6266	64	8	(	(	PUNCT
ejpam-6266	64	9	9	9	X
ejpam-6266	64	10	)	)	PUNCT
ejpam-6266	64	11	associated	associate	VERB
ejpam-6266	64	12	to	to	ADP
ejpam-6266	64	13	the	the	DET
ejpam-6266	64	14	cauchy	cauchy	ADJ
ejpam-6266	64	15	problem	problem	NOUN
ejpam-6266	64	16	(	(	PUNCT
ejpam-6266	64	17	6	6	NUM
ejpam-6266	64	18	)	)	PUNCT
ejpam-6266	64	19	are	be	AUX
ejpam-6266	64	20	constants	constant	NOUN
ejpam-6266	64	21	then	then	ADV
ejpam-6266	64	22	the	the	DET
ejpam-6266	64	23	considered	considered	ADJ
ejpam-6266	64	24	model	model	NOUN
ejpam-6266	64	25	(	(	PUNCT
ejpam-6266	64	26	6	6	NUM
ejpam-6266	64	27	)	)	PUNCT
ejpam-6266	64	28	is	be	AUX
ejpam-6266	64	29	invariant	invariant	ADJ
ejpam-6266	64	30	by	by	ADP
ejpam-6266	64	31	translation	translation	NOUN
ejpam-6266	64	32	.	.	PUNCT
ejpam-6266	65	1	for	for	ADP
ejpam-6266	65	2	this	this	DET
ejpam-6266	65	3	reason	reason	NOUN
ejpam-6266	65	4	we	we	PRON
ejpam-6266	65	5	can	can	AUX
ejpam-6266	65	6	make	make	VERB
ejpam-6266	65	7	a	a	DET
ejpam-6266	65	8	shift	shift	NOUN
ejpam-6266	65	9	of	of	ADP
ejpam-6266	65	10	the	the	DET
ejpam-6266	65	11	solution	solution	NOUN
ejpam-6266	65	12	in	in	ADP
ejpam-6266	65	13	the	the	DET
ejpam-6266	65	14	non	non	ADJ
ejpam-6266	65	15	linear	linear	ADJ
ejpam-6266	65	16	part	part	NOUN
ejpam-6266	65	17	.	.	PUNCT
ejpam-6266	66	1	in	in	ADP
ejpam-6266	66	2	this	this	DET
ejpam-6266	66	3	way	way	NOUN
ejpam-6266	66	4	,	,	PUNCT
ejpam-6266	66	5	the	the	DET
ejpam-6266	66	6	solution	solution	NOUN
ejpam-6266	66	7	of	of	ADP
ejpam-6266	66	8	cauchy	cauchy	ADJ
ejpam-6266	66	9	problem	problem	NOUN
ejpam-6266	66	10	(	(	PUNCT
ejpam-6266	66	11	6	6	NUM
ejpam-6266	66	12	)	)	PUNCT
ejpam-6266	66	13	is	be	AUX
ejpam-6266	66	14	formally	formally	ADV
ejpam-6266	66	15	represented	represent	VERB
ejpam-6266	66	16	as	as	ADP
ejpam-6266	66	17	u(t	u(t	NOUN
ejpam-6266	66	18	,	,	PUNCT
ejpam-6266	66	19	x	x	NOUN
ejpam-6266	66	20	)	)	PUNCT
ejpam-6266	66	21	=	=	SYM
ejpam-6266	67	1	e0(t	e0(t	PROPN
ejpam-6266	67	2	,	,	PUNCT
ejpam-6266	67	3	0	0	NUM
ejpam-6266	67	4	,	,	PUNCT
ejpam-6266	67	5	x	x	NOUN
ejpam-6266	67	6	)	)	PUNCT
ejpam-6266	67	7	∗x	∗x	ADV
ejpam-6266	67	8	u0(x	u0(x	NUM
ejpam-6266	67	9	)	)	PUNCT
ejpam-6266	67	10	+	+	X
ejpam-6266	67	11	e1(t	e1(t	PROPN
ejpam-6266	67	12	,	,	PUNCT
ejpam-6266	67	13	0	0	NUM
ejpam-6266	67	14	,	,	PUNCT
ejpam-6266	67	15	x	x	NOUN
ejpam-6266	67	16	)	)	PUNCT
ejpam-6266	67	17	∗x	∗x	PUNCT
ejpam-6266	67	18	u1(x	u1(x	NOUN
ejpam-6266	67	19	)	)	PUNCT
ejpam-6266	68	1	+	+	CCONJ
ejpam-6266	69	1	∫	∫	PROPN
ejpam-6266	69	2	t	t	PROPN
ejpam-6266	69	3	0	0	NUM
ejpam-6266	69	4	e1(t−	e1(t−	PROPN
ejpam-6266	69	5	τ	τ	PROPN
ejpam-6266	69	6	,	,	PUNCT
ejpam-6266	69	7	0	0	NUM
ejpam-6266	69	8	,	,	PUNCT
ejpam-6266	69	9	x	x	X
ejpam-6266	69	10	)	)	PUNCT
ejpam-6266	69	11	∗x	∗x	PROPN
ejpam-6266	69	12	h(τ	h(τ	PROPN
ejpam-6266	69	13	,	,	PUNCT
ejpam-6266	69	14	u	u	NOUN
ejpam-6266	69	15	)	)	PUNCT
ejpam-6266	69	16	dτ	dτ	NOUN
ejpam-6266	69	17	.	.	PROPN
ejpam-6266	70	1	(	(	PUNCT
ejpam-6266	70	2	14	14	NUM
ejpam-6266	70	3	)	)	PUNCT
ejpam-6266	70	4	now	now	ADV
ejpam-6266	70	5	,	,	PUNCT
ejpam-6266	70	6	let	let	VERB
ejpam-6266	70	7	us	we	PRON
ejpam-6266	70	8	introduce	introduce	VERB
ejpam-6266	70	9	some	some	DET
ejpam-6266	70	10	notations	notation	NOUN
ejpam-6266	70	11	that	that	PRON
ejpam-6266	70	12	will	will	AUX
ejpam-6266	70	13	be	be	AUX
ejpam-6266	70	14	used	use	VERB
ejpam-6266	70	15	in	in	ADP
ejpam-6266	70	16	the	the	DET
ejpam-6266	70	17	sequel	sequel	NOUN
ejpam-6266	70	18	.	.	PUNCT
ejpam-6266	71	1	for	for	ADP
ejpam-6266	71	2	all	all	DET
ejpam-6266	71	3	t	t	PROPN
ejpam-6266	71	4	>	>	X
ejpam-6266	71	5	0	0	PUNCT
ejpam-6266	72	1	we	we	PRON
ejpam-6266	72	2	denote	denote	VERB
ejpam-6266	72	3	by	by	ADP
ejpam-6266	72	4	x(t	x(t	PROPN
ejpam-6266	72	5	)	)	PUNCT
ejpam-6266	72	6	the	the	DET
ejpam-6266	72	7	space	space	NOUN
ejpam-6266	72	8	of	of	ADP
ejpam-6266	72	9	solutions	solution	NOUN
ejpam-6266	72	10	to	to	ADP
ejpam-6266	72	11	the	the	DET
ejpam-6266	72	12	cauchy	cauchy	ADJ
ejpam-6266	72	13	problem	problem	NOUN
ejpam-6266	72	14	(	(	PUNCT
ejpam-6266	72	15	6	6	NUM
ejpam-6266	72	16	)	)	PUNCT
ejpam-6266	72	17	.	.	PUNCT
ejpam-6266	73	1	for	for	ADP
ejpam-6266	73	2	all	all	DET
ejpam-6266	73	3	u	u	NOUN
ejpam-6266	73	4	∈	∈	PROPN
ejpam-6266	73	5	x(t	x(t	PROPN
ejpam-6266	73	6	)	)	PUNCT
ejpam-6266	73	7	we	we	PRON
ejpam-6266	73	8	define	define	VERB
ejpam-6266	73	9	the	the	DET
ejpam-6266	73	10	mapping	mapping	NOUN
ejpam-6266	73	11	n	n	NOUN
ejpam-6266	73	12	as	as	SCONJ
ejpam-6266	73	13	follows	follow	VERB
ejpam-6266	73	14	:	:	PUNCT
ejpam-6266	73	15	n	n	X
ejpam-6266	73	16	:	:	PUNCT
ejpam-6266	73	17	u	u	NOUN
ejpam-6266	73	18	∈	∈	PROPN
ejpam-6266	73	19	x(t	x(t	PROPN
ejpam-6266	73	20	)	)	PUNCT
ejpam-6266	73	21	→	→	SYM
ejpam-6266	73	22	n(u	n(u	PROPN
ejpam-6266	73	23	)	)	PUNCT
ejpam-6266	73	24	=	=	SYM
ejpam-6266	74	1	e0(t	e0(t	PROPN
ejpam-6266	74	2	,	,	PUNCT
ejpam-6266	74	3	0	0	NUM
ejpam-6266	74	4	,	,	PUNCT
ejpam-6266	74	5	x	x	NOUN
ejpam-6266	74	6	)	)	PUNCT
ejpam-6266	74	7	∗	∗	NOUN
ejpam-6266	74	8	u0(x	u0(x	NOUN
ejpam-6266	74	9	)	)	PUNCT
ejpam-6266	74	10	+	+	X
ejpam-6266	74	11	e1(t	e1(t	PROPN
ejpam-6266	74	12	,	,	PUNCT
ejpam-6266	74	13	0	0	NUM
ejpam-6266	74	14	,	,	PUNCT
ejpam-6266	74	15	x	x	NOUN
ejpam-6266	74	16	)	)	PUNCT
ejpam-6266	74	17	∗	∗	NOUN
ejpam-6266	74	18	u1(x	u1(x	NOUN
ejpam-6266	74	19	)	)	PUNCT
ejpam-6266	75	1	+	+	CCONJ
ejpam-6266	75	2	∫	∫	PROPN
ejpam-6266	75	3	t	t	PROPN
ejpam-6266	75	4	0	0	NUM
ejpam-6266	75	5	e1(t−	e1(t−	PROPN
ejpam-6266	75	6	τ	τ	PROPN
ejpam-6266	75	7	,	,	PUNCT
ejpam-6266	75	8	0	0	NUM
ejpam-6266	75	9	,	,	PUNCT
ejpam-6266	75	10	x	x	X
ejpam-6266	75	11	)	)	PUNCT
ejpam-6266	75	12	∗x	∗x	PROPN
ejpam-6266	75	13	h(τ	h(τ	PROPN
ejpam-6266	75	14	,	,	PUNCT
ejpam-6266	75	15	u	u	NOUN
ejpam-6266	75	16	)	)	PUNCT
ejpam-6266	75	17	dτ	dτ	NOUN
ejpam-6266	75	18	.	.	PUNCT
ejpam-6266	75	19	t.	t.	PROPN
ejpam-6266	75	20	hadj	hadj	PROPN
ejpam-6266	75	21	kaddour	kaddour	PROPN
ejpam-6266	75	22	et	et	PROPN
ejpam-6266	75	23	al	al	PROPN
ejpam-6266	75	24	.	.	PUNCT
ejpam-6266	75	25	/	/	SYM
ejpam-6266	75	26	eur	eur	PROPN
ejpam-6266	75	27	.	.	PUNCT
ejpam-6266	76	1	j.	j.	PROPN
ejpam-6266	76	2	pure	pure	PROPN
ejpam-6266	76	3	appl	appl	PROPN
ejpam-6266	76	4	.	.	PROPN
ejpam-6266	76	5	math	math	PROPN
ejpam-6266	76	6	,	,	PUNCT
ejpam-6266	76	7	18	18	NUM
ejpam-6266	76	8	(	(	PUNCT
ejpam-6266	76	9	4	4	NUM
ejpam-6266	76	10	)	)	PUNCT
ejpam-6266	76	11	(	(	PUNCT
ejpam-6266	76	12	2025	2025	NUM
ejpam-6266	76	13	)	)	PUNCT
ejpam-6266	76	14	,	,	PUNCT
ejpam-6266	76	15	6266	6266	NUM
ejpam-6266	76	16	5	5	NUM
ejpam-6266	76	17	of	of	ADP
ejpam-6266	76	18	24	24	NUM
ejpam-6266	76	19	our	our	PRON
ejpam-6266	76	20	main	main	ADJ
ejpam-6266	76	21	strategy	strategy	NOUN
ejpam-6266	76	22	is	be	AUX
ejpam-6266	76	23	to	to	PART
ejpam-6266	76	24	prove	prove	VERB
ejpam-6266	76	25	well	well	ADJ
ejpam-6266	76	26	-	-	PUNCT
ejpam-6266	76	27	posedness	posedness	NOUN
ejpam-6266	76	28	results	result	NOUN
ejpam-6266	76	29	for	for	ADP
ejpam-6266	76	30	solutions	solution	NOUN
ejpam-6266	76	31	to	to	ADP
ejpam-6266	76	32	(	(	PUNCT
ejpam-6266	76	33	6	6	NUM
ejpam-6266	76	34	)	)	PUNCT
ejpam-6266	76	35	as	as	ADP
ejpam-6266	76	36	solutions	solution	NOUN
ejpam-6266	76	37	of	of	ADP
ejpam-6266	76	38	the	the	DET
ejpam-6266	76	39	fixed	fix	VERB
ejpam-6266	76	40	point	point	NOUN
ejpam-6266	76	41	equation	equation	NOUN
ejpam-6266	76	42	u	u	NOUN
ejpam-6266	76	43	=	=	PROPN
ejpam-6266	76	44	n(u	n(u	PROPN
ejpam-6266	76	45	)	)	PUNCT
ejpam-6266	76	46	by	by	ADP
ejpam-6266	76	47	proving	prove	VERB
ejpam-6266	76	48	the	the	DET
ejpam-6266	76	49	following	follow	VERB
ejpam-6266	76	50	inequalities	inequality	NOUN
ejpam-6266	76	51	for	for	ADP
ejpam-6266	76	52	all	all	DET
ejpam-6266	76	53	u	u	NOUN
ejpam-6266	76	54	,	,	PUNCT
ejpam-6266	76	55	v	v	NOUN
ejpam-6266	76	56	∈	∈	PROPN
ejpam-6266	76	57	x(t	x(t	PROPN
ejpam-6266	76	58	):	):	PUNCT
ejpam-6266	76	59	‖nu‖x(t	‖nu‖x(t	PROPN
ejpam-6266	76	60	)	)	PUNCT
ejpam-6266	76	61	≤	≤	NUM
ejpam-6266	76	62	c‖(u0	c‖(u0	NOUN
ejpam-6266	76	63	,	,	PUNCT
ejpam-6266	76	64	u1)‖aσ	u1)‖aσ	PROPN
ejpam-6266	76	65	,	,	PUNCT
ejpam-6266	76	66	m	m	VERB
ejpam-6266	76	67	+	+	CCONJ
ejpam-6266	76	68	c‖u‖px(t	c‖u‖px(t	NUM
ejpam-6266	76	69	)	)	PUNCT
ejpam-6266	76	70	,	,	PUNCT
ejpam-6266	76	71	(	(	PUNCT
ejpam-6266	76	72	15	15	NUM
ejpam-6266	76	73	)	)	PUNCT
ejpam-6266	76	74	‖nu−nv‖x(t	‖nu−nv‖x(t	SYM
ejpam-6266	76	75	)	)	PUNCT
ejpam-6266	76	76	≤	≤	NUM
ejpam-6266	76	77	c‖u−	c‖u−	NOUN
ejpam-6266	76	78	v‖x(t	v‖x(t	PROPN
ejpam-6266	76	79	)	)	PUNCT
ejpam-6266	76	80	(	(	PUNCT
ejpam-6266	76	81	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	76	82	x(t	x(t	PROPN
ejpam-6266	76	83	)	)	PUNCT
ejpam-6266	77	1	+	+	CCONJ
ejpam-6266	77	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	77	3	x(t	x(t	PROPN
ejpam-6266	77	4	)	)	PUNCT
ejpam-6266	77	5	)	)	PUNCT
ejpam-6266	77	6	,	,	PUNCT
ejpam-6266	77	7	(	(	PUNCT
ejpam-6266	77	8	16	16	NUM
ejpam-6266	77	9	)	)	PUNCT
ejpam-6266	77	10	where	where	SCONJ
ejpam-6266	77	11	the	the	DET
ejpam-6266	77	12	norm	norm	NOUN
ejpam-6266	77	13	‖·‖x(t	‖·‖x(t	PROPN
ejpam-6266	77	14	)	)	PUNCT
ejpam-6266	77	15	in	in	ADP
ejpam-6266	77	16	x(t	x(t	PROPN
ejpam-6266	77	17	)	)	PUNCT
ejpam-6266	77	18	will	will	AUX
ejpam-6266	77	19	be	be	AUX
ejpam-6266	77	20	defined	define	VERB
ejpam-6266	77	21	later	later	ADV
ejpam-6266	77	22	in	in	ADP
ejpam-6266	77	23	a	a	DET
ejpam-6266	77	24	suitable	suitable	ADJ
ejpam-6266	77	25	way	way	NOUN
ejpam-6266	77	26	and	and	CCONJ
ejpam-6266	77	27	makes	make	VERB
ejpam-6266	77	28	x(t	x(t	PROPN
ejpam-6266	77	29	)	)	PUNCT
ejpam-6266	77	30	as	as	ADP
ejpam-6266	77	31	a	a	DET
ejpam-6266	77	32	banach	banach	NOUN
ejpam-6266	77	33	space	space	NOUN
ejpam-6266	77	34	.	.	PUNCT
ejpam-6266	78	1	for	for	ADP
ejpam-6266	78	2	the	the	DET
ejpam-6266	78	3	further	further	ADJ
ejpam-6266	78	4	considerations	consideration	NOUN
ejpam-6266	78	5	we	we	PRON
ejpam-6266	78	6	introduce	introduce	VERB
ejpam-6266	78	7	the	the	DET
ejpam-6266	78	8	scale	scale	NOUN
ejpam-6266	78	9	{	{	PUNCT
ejpam-6266	78	10	am	am	NOUN
ejpam-6266	78	11	,	,	PUNCT
ejpam-6266	78	12	σ	σ	NOUN
ejpam-6266	78	13	}	}	PUNCT
ejpam-6266	78	14	of	of	ADP
ejpam-6266	78	15	banach	banach	NOUN
ejpam-6266	78	16	spaces	space	NOUN
ejpam-6266	78	17	with	with	ADP
ejpam-6266	78	18	σ	σ	PROPN
ejpam-6266	78	19	≥	≥	NUM
ejpam-6266	78	20	1	1	NUM
ejpam-6266	78	21	and	and	CCONJ
ejpam-6266	78	22	m	m	PROPN
ejpam-6266	78	23	∈	∈	PROPN
ejpam-6266	79	1	[	[	X
ejpam-6266	79	2	1	1	NUM
ejpam-6266	79	3	,	,	PUNCT
ejpam-6266	79	4	2	2	NUM
ejpam-6266	79	5	)	)	PUNCT
ejpam-6266	79	6	,	,	PUNCT
ejpam-6266	79	7	where	where	SCONJ
ejpam-6266	79	8	am	be	AUX
ejpam-6266	79	9	,	,	PUNCT
ejpam-6266	79	10	σ	σ	PROPN
ejpam-6266	79	11	=	=	SYM
ejpam-6266	79	12	am	am	NOUN
ejpam-6266	79	13	,	,	PUNCT
ejpam-6266	79	14	σ(rn	σ(rn	PROPN
ejpam-6266	79	15	)	)	PUNCT
ejpam-6266	79	16	=	=	SYM
ejpam-6266	79	17	(	(	PUNCT
ejpam-6266	79	18	hσ(rn	hσ(rn	PROPN
ejpam-6266	79	19	)	)	PUNCT
ejpam-6266	79	20	∩	∩	PROPN
ejpam-6266	79	21	lm(rn	lm(rn	PROPN
ejpam-6266	79	22	)	)	PUNCT
ejpam-6266	79	23	)	)	PUNCT
ejpam-6266	80	1	×	×	NOUN
ejpam-6266	80	2	(	(	PUNCT
ejpam-6266	80	3	hσ−1(rn	hσ−1(rn	PROPN
ejpam-6266	80	4	)	)	PUNCT
ejpam-6266	80	5	∩	∩	NOUN
ejpam-6266	80	6	lm(rn	lm(rn	PROPN
ejpam-6266	80	7	)	)	PUNCT
ejpam-6266	80	8	)	)	PUNCT
ejpam-6266	80	9	.	.	PUNCT
ejpam-6266	81	1	(	(	PUNCT
ejpam-6266	81	2	17	17	NUM
ejpam-6266	81	3	)	)	PUNCT
ejpam-6266	81	4	2.3	2.3	NUM
ejpam-6266	81	5	.	.	PUNCT
ejpam-6266	81	6	outline	outline	NOUN
ejpam-6266	81	7	of	of	ADP
ejpam-6266	81	8	this	this	DET
ejpam-6266	81	9	paper	paper	NOUN
ejpam-6266	81	10	this	this	DET
ejpam-6266	81	11	paper	paper	NOUN
ejpam-6266	81	12	is	be	AUX
ejpam-6266	81	13	structured	structure	VERB
ejpam-6266	81	14	to	to	PART
ejpam-6266	81	15	help	help	VERB
ejpam-6266	81	16	the	the	DET
ejpam-6266	81	17	reader	reader	NOUN
ejpam-6266	81	18	clearly	clearly	ADV
ejpam-6266	81	19	understand	understand	VERB
ejpam-6266	81	20	its	its	PRON
ejpam-6266	81	21	objectives	objective	NOUN
ejpam-6266	81	22	.	.	PUNCT
ejpam-6266	82	1	it	it	PRON
ejpam-6266	82	2	consists	consist	VERB
ejpam-6266	82	3	of	of	ADP
ejpam-6266	82	4	six	six	NUM
ejpam-6266	82	5	sections	section	NOUN
ejpam-6266	82	6	and	and	CCONJ
ejpam-6266	82	7	an	an	DET
ejpam-6266	82	8	appendix	appendix	NOUN
ejpam-6266	82	9	.	.	PUNCT
ejpam-6266	83	1	section	section	NOUN
ejpam-6266	83	2	1	1	NUM
ejpam-6266	83	3	provides	provide	VERB
ejpam-6266	83	4	the	the	DET
ejpam-6266	83	5	work	work	NOUN
ejpam-6266	83	6	and	and	CCONJ
ejpam-6266	83	7	outlines	outline	VERB
ejpam-6266	83	8	its	its	PRON
ejpam-6266	83	9	purpose	purpose	NOUN
ejpam-6266	83	10	.	.	PUNCT
ejpam-6266	84	1	section	section	NOUN
ejpam-6266	84	2	2	2	NUM
ejpam-6266	84	3	presents	present	VERB
ejpam-6266	84	4	the	the	DET
ejpam-6266	84	5	background	background	NOUN
ejpam-6266	84	6	and	and	CCONJ
ejpam-6266	84	7	preliminaries	preliminary	NOUN
ejpam-6266	84	8	,	,	PUNCT
ejpam-6266	84	9	including	include	VERB
ejpam-6266	84	10	the	the	DET
ejpam-6266	84	11	strategy	strategy	NOUN
ejpam-6266	84	12	of	of	ADP
ejpam-6266	84	13	proof	proof	NOUN
ejpam-6266	84	14	.	.	PUNCT
ejpam-6266	85	1	in	in	ADP
ejpam-6266	85	2	section	section	NOUN
ejpam-6266	85	3	3	3	NUM
ejpam-6266	85	4	,	,	PUNCT
ejpam-6266	85	5	we	we	PRON
ejpam-6266	85	6	states	state	VERB
ejpam-6266	85	7	the	the	DET
ejpam-6266	85	8	main	main	ADJ
ejpam-6266	85	9	results	result	NOUN
ejpam-6266	85	10	,	,	PUNCT
ejpam-6266	85	11	which	which	PRON
ejpam-6266	85	12	are	be	AUX
ejpam-6266	85	13	proved	prove	VERB
ejpam-6266	85	14	in	in	ADP
ejpam-6266	85	15	section	section	NOUN
ejpam-6266	85	16	4	4	NUM
ejpam-6266	85	17	.	.	PUNCT
ejpam-6266	86	1	for	for	ADP
ejpam-6266	86	2	brevity	brevity	NOUN
ejpam-6266	86	3	,	,	PUNCT
ejpam-6266	86	4	the	the	DET
ejpam-6266	86	5	proof	proof	NOUN
ejpam-6266	86	6	of	of	ADP
ejpam-6266	86	7	theorem	theorem	ADJ
ejpam-6266	86	8	4	4	NUM
ejpam-6266	86	9	is	be	AUX
ejpam-6266	86	10	omitted	omit	VERB
ejpam-6266	86	11	and	and	CCONJ
ejpam-6266	86	12	breviary	breviary	NOUN
ejpam-6266	86	13	discussed	discuss	VERB
ejpam-6266	86	14	since	since	SCONJ
ejpam-6266	86	15	it	it	PRON
ejpam-6266	86	16	follows	follow	VERB
ejpam-6266	86	17	the	the	DET
ejpam-6266	86	18	same	same	ADJ
ejpam-6266	86	19	arguments	argument	NOUN
ejpam-6266	86	20	as	as	ADP
ejpam-6266	86	21	the	the	DET
ejpam-6266	86	22	proof	proof	NOUN
ejpam-6266	86	23	of	of	ADP
ejpam-6266	86	24	theorem	theorem	ADJ
ejpam-6266	86	25	3	3	NUM
ejpam-6266	86	26	.	.	PUNCT
ejpam-6266	86	27	section	section	NOUN
ejpam-6266	86	28	5	5	NUM
ejpam-6266	86	29	concludes	conclude	VERB
ejpam-6266	86	30	the	the	DET
ejpam-6266	86	31	paper	paper	NOUN
ejpam-6266	86	32	,	,	PUNCT
ejpam-6266	86	33	highlighting	highlight	VERB
ejpam-6266	86	34	in	in	ADP
ejpam-6266	86	35	particular	particular	ADJ
ejpam-6266	86	36	its	its	PRON
ejpam-6266	86	37	novelty	novelty	NOUN
ejpam-6266	86	38	and	and	CCONJ
ejpam-6266	86	39	main	main	ADJ
ejpam-6266	86	40	contributions	contribution	NOUN
ejpam-6266	86	41	.	.	PUNCT
ejpam-6266	87	1	section	section	NOUN
ejpam-6266	87	2	6	6	NUM
ejpam-6266	87	3	contains	contain	VERB
ejpam-6266	87	4	our	our	PRON
ejpam-6266	87	5	acknowledgements	acknowledgement	NOUN
ejpam-6266	87	6	,	,	PUNCT
ejpam-6266	87	7	followed	follow	VERB
ejpam-6266	87	8	by	by	ADP
ejpam-6266	87	9	a	a	DET
ejpam-6266	87	10	bibliography	bibliography	NOUN
ejpam-6266	87	11	arranged	arrange	VERB
ejpam-6266	87	12	in	in	ADP
ejpam-6266	87	13	alphabetical	alphabetical	ADJ
ejpam-6266	87	14	order	order	NOUN
ejpam-6266	87	15	.	.	PUNCT
ejpam-6266	88	1	the	the	DET
ejpam-6266	88	2	paper	paper	NOUN
ejpam-6266	88	3	ends	end	VERB
ejpam-6266	88	4	with	with	ADP
ejpam-6266	88	5	an	an	DET
ejpam-6266	88	6	appendix	appendix	NOUN
ejpam-6266	88	7	,	,	PUNCT
ejpam-6266	88	8	which	which	PRON
ejpam-6266	88	9	gathers	gather	VERB
ejpam-6266	88	10	the	the	DET
ejpam-6266	88	11	main	main	ADJ
ejpam-6266	88	12	tools	tool	NOUN
ejpam-6266	88	13	used	use	VERB
ejpam-6266	88	14	,	,	PUNCT
ejpam-6266	88	15	especially	especially	ADV
ejpam-6266	88	16	in	in	ADP
ejpam-6266	88	17	section	section	NOUN
ejpam-6266	88	18	4	4	NUM
ejpam-6266	88	19	,	,	PUNCT
ejpam-6266	88	20	together	together	ADV
ejpam-6266	88	21	with	with	ADP
ejpam-6266	88	22	additional	additional	ADJ
ejpam-6266	88	23	remarks	remark	NOUN
ejpam-6266	88	24	.	.	PUNCT
ejpam-6266	89	1	throughout	throughout	ADP
ejpam-6266	89	2	the	the	DET
ejpam-6266	89	3	present	present	ADJ
ejpam-6266	89	4	paper	paper	NOUN
ejpam-6266	89	5	we	we	PRON
ejpam-6266	89	6	write	write	VERB
ejpam-6266	89	7	f	f	PROPN
ejpam-6266	89	8	.	.	PUNCT
ejpam-6266	90	1	g	g	PROPN
ejpam-6266	90	2	when	when	SCONJ
ejpam-6266	90	3	there	there	PRON
ejpam-6266	90	4	exists	exist	VERB
ejpam-6266	90	5	a	a	DET
ejpam-6266	90	6	constant	constant	ADJ
ejpam-6266	90	7	c	c	NOUN
ejpam-6266	90	8	>	>	X
ejpam-6266	90	9	0	0	NUM
ejpam-6266	90	10	such	such	ADJ
ejpam-6266	90	11	that	that	SCONJ
ejpam-6266	90	12	f	f	PROPN
ejpam-6266	90	13	≤	≤	PROPN
ejpam-6266	90	14	cg	cg	NOUN
ejpam-6266	90	15	,	,	PUNCT
ejpam-6266	90	16	and	and	CCONJ
ejpam-6266	90	17	f	f	X
ejpam-6266	90	18	≈	≈	PROPN
ejpam-6266	90	19	g	g	PROPN
ejpam-6266	90	20	when	when	SCONJ
ejpam-6266	90	21	g	g	PROPN
ejpam-6266	90	22	.	.	PUNCT
ejpam-6266	91	1	f	f	PROPN
ejpam-6266	91	2	.	.	PUNCT
ejpam-6266	92	1	g.	g.	PROPN
ejpam-6266	92	2	nonnegative	nonnegative	PROPN
ejpam-6266	92	3	constants	constant	NOUN
ejpam-6266	92	4	c	c	PROPN
ejpam-6266	92	5	or	or	CCONJ
ejpam-6266	92	6	cj	cj	NOUN
ejpam-6266	92	7	,	,	PUNCT
ejpam-6266	92	8	j	j	PROPN
ejpam-6266	92	9	∈	∈	PROPN
ejpam-6266	92	10	n	n	CCONJ
ejpam-6266	92	11	,	,	PUNCT
ejpam-6266	92	12	are	be	AUX
ejpam-6266	92	13	always	always	ADV
ejpam-6266	92	14	supposed	suppose	VERB
ejpam-6266	92	15	to	to	PART
ejpam-6266	92	16	be	be	AUX
ejpam-6266	92	17	independent	independent	ADJ
ejpam-6266	92	18	of	of	ADP
ejpam-6266	92	19	t	t	PROPN
ejpam-6266	92	20	>	>	X
ejpam-6266	92	21	0	0	X
ejpam-6266	92	22	.	.	PUNCT
ejpam-6266	93	1	for	for	ADP
ejpam-6266	93	2	the	the	DET
ejpam-6266	93	3	sake	sake	NOUN
ejpam-6266	93	4	of	of	ADP
ejpam-6266	93	5	brevity	brevity	NOUN
ejpam-6266	93	6	we	we	PRON
ejpam-6266	93	7	sometimes	sometimes	ADV
ejpam-6266	93	8	put	put	VERB
ejpam-6266	93	9	for	for	ADP
ejpam-6266	93	10	all	all	DET
ejpam-6266	93	11	n	n	PRON
ejpam-6266	93	12	∈	∈	PROPN
ejpam-6266	93	13	n∗	n∗	NOUN
ejpam-6266	93	14	and	and	CCONJ
ejpam-6266	93	15	(	(	PUNCT
ejpam-6266	93	16	k	k	X
ejpam-6266	93	17	,	,	PUNCT
ejpam-6266	93	18	j	j	NOUN
ejpam-6266	93	19	)	)	PUNCT
ejpam-6266	93	20	∈	∈	PROPN
ejpam-6266	93	21	n2	n2	PROPN
ejpam-6266	93	22	j	j	PROPN
ejpam-6266	93	23	(	(	PUNCT
ejpam-6266	93	24	k	k	X
ejpam-6266	93	25	,	,	PUNCT
ejpam-6266	93	26	j	j	PROPN
ejpam-6266	93	27	)	)	PUNCT
ejpam-6266	93	28	n	n	PROPN
ejpam-6266	93	29	(	(	PUNCT
ejpam-6266	93	30	t	t	NOUN
ejpam-6266	93	31	)	)	PUNCT
ejpam-6266	93	32	=	=	SYM
ejpam-6266	94	1	∫	∫	PROPN
ejpam-6266	94	2	t	t	PROPN
ejpam-6266	94	3	0	0	NUM
ejpam-6266	95	1	(	(	PUNCT
ejpam-6266	95	2	1	1	NUM
ejpam-6266	95	3	+	+	CCONJ
ejpam-6266	95	4	t−	t−	PROPN
ejpam-6266	95	5	τ)−	τ)−	PROPN
ejpam-6266	95	6	n	n	CCONJ
ejpam-6266	95	7	4	4	NUM
ejpam-6266	95	8	−	−	NOUN
ejpam-6266	95	9	k	k	SYM
ejpam-6266	95	10	2	2	NUM
ejpam-6266	95	11	−j	−j	NOUN
ejpam-6266	95	12	∫	∫	PROPN
ejpam-6266	95	13	τ	τ	X
ejpam-6266	95	14	0	0	NUM
ejpam-6266	95	15	(	(	PUNCT
ejpam-6266	95	16	τ	τ	X
ejpam-6266	95	17	−	−	NOUN
ejpam-6266	95	18	s)−γ(1	s)−γ(1	PROPN
ejpam-6266	95	19	+	+	PUNCT
ejpam-6266	95	20	s)−βdsdτ	s)−βdsdτ	PROPN
ejpam-6266	95	21	.	.	PUNCT
ejpam-6266	96	1	(	(	PUNCT
ejpam-6266	96	2	18	18	NUM
ejpam-6266	96	3	)	)	SYM
ejpam-6266	96	4	3	3	NUM
ejpam-6266	96	5	.	.	X
ejpam-6266	96	6	main	main	ADJ
ejpam-6266	96	7	result	result	NOUN
ejpam-6266	96	8	3.1	3.1	NUM
ejpam-6266	96	9	.	.	PUNCT
ejpam-6266	96	10	global	global	ADJ
ejpam-6266	96	11	existence	existence	NOUN
ejpam-6266	96	12	of	of	ADP
ejpam-6266	96	13	energy	energy	NOUN
ejpam-6266	96	14	solution	solution	NOUN
ejpam-6266	96	15	in	in	ADP
ejpam-6266	96	16	low	low	ADJ
ejpam-6266	96	17	dimension	dimension	NOUN
ejpam-6266	96	18	in	in	ADP
ejpam-6266	96	19	term	term	NOUN
ejpam-6266	96	20	of	of	ADP
ejpam-6266	96	21	comparison	comparison	NOUN
ejpam-6266	96	22	,	,	PUNCT
ejpam-6266	96	23	the	the	DET
ejpam-6266	96	24	dissipative	dissipative	ADJ
ejpam-6266	96	25	term	term	NOUN
ejpam-6266	96	26	ut	ut	PROPN
ejpam-6266	96	27	does	do	AUX
ejpam-6266	96	28	not	not	PART
ejpam-6266	96	29	influence	influence	VERB
ejpam-6266	96	30	the	the	DET
ejpam-6266	96	31	critical	critical	ADJ
ejpam-6266	96	32	exponent	exponent	NOUN
ejpam-6266	96	33	since	since	SCONJ
ejpam-6266	96	34	the	the	DET
ejpam-6266	96	35	two	two	NUM
ejpam-6266	96	36	models	model	NOUN
ejpam-6266	96	37	(	(	PUNCT
ejpam-6266	96	38	3	3	NUM
ejpam-6266	96	39	)	)	PUNCT
ejpam-6266	96	40	and	and	CCONJ
ejpam-6266	96	41	(	(	PUNCT
ejpam-6266	96	42	1	1	X
ejpam-6266	96	43	)	)	PUNCT
ejpam-6266	96	44	have	have	VERB
ejpam-6266	96	45	the	the	DET
ejpam-6266	96	46	same	same	ADJ
ejpam-6266	96	47	critical	critical	ADJ
ejpam-6266	96	48	exponent	exponent	NOUN
ejpam-6266	96	49	in	in	ADP
ejpam-6266	96	50	fujita	fujita	PROPN
ejpam-6266	96	51	sense	sense	NOUN
ejpam-6266	96	52	.	.	PUNCT
ejpam-6266	97	1	in	in	ADP
ejpam-6266	97	2	the	the	DET
ejpam-6266	97	3	other	other	ADJ
ejpam-6266	97	4	hand	hand	NOUN
ejpam-6266	97	5	,	,	PUNCT
ejpam-6266	97	6	one	one	PRON
ejpam-6266	97	7	can	can	AUX
ejpam-6266	97	8	note	note	VERB
ejpam-6266	97	9	that	that	SCONJ
ejpam-6266	97	10	the	the	DET
ejpam-6266	97	11	non	non	ADJ
ejpam-6266	97	12	linear	linear	PROPN
ejpam-6266	97	13	memory	memory	NOUN
ejpam-6266	97	14	influence	influence	NOUN
ejpam-6266	97	15	the	the	DET
ejpam-6266	97	16	critical	critical	ADJ
ejpam-6266	97	17	exponent	exponent	NOUN
ejpam-6266	97	18	by	by	ADP
ejpam-6266	97	19	comparing	compare	VERB
ejpam-6266	97	20	the	the	DET
ejpam-6266	97	21	critical	critical	ADJ
ejpam-6266	97	22	exponent	exponent	NOUN
ejpam-6266	97	23	of	of	ADP
ejpam-6266	97	24	(	(	PUNCT
ejpam-6266	97	25	1	1	NUM
ejpam-6266	97	26	)	)	PUNCT
ejpam-6266	97	27	and	and	CCONJ
ejpam-6266	97	28	(	(	PUNCT
ejpam-6266	97	29	4	4	NUM
ejpam-6266	97	30	)	)	PUNCT
ejpam-6266	97	31	and	and	CCONJ
ejpam-6266	97	32	there	there	PRON
ejpam-6266	97	33	is	be	VERB
ejpam-6266	97	34	continuity	continuity	NOUN
ejpam-6266	97	35	with	with	ADP
ejpam-6266	97	36	respect	respect	NOUN
ejpam-6266	97	37	to	to	ADP
ejpam-6266	97	38	γ	γ	PROPN
ejpam-6266	97	39	(	(	PUNCT
ejpam-6266	97	40	see	see	PROPN
ejpam-6266	97	41	(	(	PUNCT
ejpam-6266	97	42	8)	8)	NUM
ejpam-6266	97	43	)	)	PUNCT
ejpam-6266	97	44	.	.	PUNCT
ejpam-6266	98	1	in	in	ADP
ejpam-6266	98	2	this	this	DET
ejpam-6266	98	3	section	section	NOUN
ejpam-6266	98	4	we	we	PRON
ejpam-6266	98	5	study	study	VERB
ejpam-6266	98	6	the	the	DET
ejpam-6266	98	7	influence	influence	NOUN
ejpam-6266	98	8	of	of	ADP
ejpam-6266	98	9	the	the	DET
ejpam-6266	98	10	damping	damp	VERB
ejpam-6266	98	11	term	term	NOUN
ejpam-6266	98	12	in	in	ADP
ejpam-6266	98	13	the	the	DET
ejpam-6266	98	14	memory	memory	NOUN
ejpam-6266	98	15	on	on	ADP
ejpam-6266	98	16	the	the	DET
ejpam-6266	98	17	critical	critical	ADJ
ejpam-6266	98	18	exponent	exponent	NOUN
ejpam-6266	98	19	by	by	ADP
ejpam-6266	98	20	comparing	compare	VERB
ejpam-6266	98	21	the	the	DET
ejpam-6266	98	22	critical	critical	ADJ
ejpam-6266	98	23	exponent	exponent	NOUN
ejpam-6266	98	24	of	of	ADP
ejpam-6266	98	25	cauchy	cauchy	PROPN
ejpam-6266	98	26	problem	problem	NOUN
ejpam-6266	98	27	(	(	PUNCT
ejpam-6266	98	28	6	6	NUM
ejpam-6266	98	29	)	)	PUNCT
ejpam-6266	98	30	with	with	ADP
ejpam-6266	98	31	the	the	DET
ejpam-6266	98	32	one	one	NOUN
ejpam-6266	98	33	obtained	obtain	VERB
ejpam-6266	98	34	for	for	ADP
ejpam-6266	98	35	(	(	PUNCT
ejpam-6266	98	36	1	1	NUM
ejpam-6266	98	37	)	)	PUNCT
ejpam-6266	98	38	.	.	PUNCT
ejpam-6266	99	1	for	for	ADP
ejpam-6266	99	2	this	this	DET
ejpam-6266	99	3	reason	reason	NOUN
ejpam-6266	99	4	,	,	PUNCT
ejpam-6266	99	5	we	we	PRON
ejpam-6266	99	6	begin	begin	VERB
ejpam-6266	99	7	by	by	ADP
ejpam-6266	99	8	taking	take	VERB
ejpam-6266	99	9	m	m	PROPN
ejpam-6266	99	10	=	=	PUNCT
ejpam-6266	99	11	σ	σ	NOUN
ejpam-6266	99	12	=	=	NOUN
ejpam-6266	99	13	1	1	NUM
ejpam-6266	99	14	in	in	ADP
ejpam-6266	99	15	(	(	PUNCT
ejpam-6266	99	16	17	17	NUM
ejpam-6266	99	17	)	)	PUNCT
ejpam-6266	99	18	.	.	PUNCT
ejpam-6266	100	1	in	in	ADP
ejpam-6266	100	2	section	section	NOUN
ejpam-6266	100	3	3.3	3.3	NUM
ejpam-6266	100	4	,	,	PUNCT
ejpam-6266	100	5	we	we	PRON
ejpam-6266	100	6	will	will	AUX
ejpam-6266	100	7	see	see	VERB
ejpam-6266	100	8	that	that	SCONJ
ejpam-6266	100	9	the	the	DET
ejpam-6266	100	10	range	range	NOUN
ejpam-6266	100	11	of	of	ADP
ejpam-6266	100	12	admissible	admissible	ADJ
ejpam-6266	100	13	p	p	NOUN
ejpam-6266	100	14	for	for	ADP
ejpam-6266	100	15	global	global	ADJ
ejpam-6266	100	16	existence	existence	NOUN
ejpam-6266	100	17	can	can	AUX
ejpam-6266	100	18	not	not	PART
ejpam-6266	100	19	be	be	AUX
ejpam-6266	100	20	improved	improve	VERB
ejpam-6266	100	21	even	even	ADV
ejpam-6266	100	22	by	by	ADP
ejpam-6266	100	23	adding	add	VERB
ejpam-6266	100	24	an	an	DET
ejpam-6266	100	25	additional	additional	ADJ
ejpam-6266	100	26	regularity	regularity	NOUN
ejpam-6266	100	27	.	.	PUNCT
ejpam-6266	101	1	so	so	ADV
ejpam-6266	101	2	,	,	PUNCT
ejpam-6266	101	3	let	let	VERB
ejpam-6266	101	4	us	we	PRON
ejpam-6266	101	5	fix	fix	VERB
ejpam-6266	101	6	in	in	ADP
ejpam-6266	101	7	this	this	DET
ejpam-6266	101	8	section	section	NOUN
ejpam-6266	101	9	m	m	NOUN
ejpam-6266	101	10	=	=	SYM
ejpam-6266	101	11	σ	σ	PROPN
ejpam-6266	101	12	=	=	NOUN
ejpam-6266	101	13	1	1	NUM
ejpam-6266	101	14	in	in	ADP
ejpam-6266	101	15	(	(	PUNCT
ejpam-6266	101	16	17	17	NUM
ejpam-6266	101	17	)	)	PUNCT
ejpam-6266	101	18	,	,	PUNCT
ejpam-6266	101	19	t.	t.	PROPN
ejpam-6266	101	20	hadj	hadj	PROPN
ejpam-6266	101	21	kaddour	kaddour	PROPN
ejpam-6266	101	22	et	et	PROPN
ejpam-6266	101	23	al	al	PROPN
ejpam-6266	101	24	.	.	PUNCT
ejpam-6266	101	25	/	/	SYM
ejpam-6266	101	26	eur	eur	PROPN
ejpam-6266	101	27	.	.	PUNCT
ejpam-6266	102	1	j.	j.	PROPN
ejpam-6266	102	2	pure	pure	PROPN
ejpam-6266	102	3	appl	appl	PROPN
ejpam-6266	102	4	.	.	PROPN
ejpam-6266	102	5	math	math	PROPN
ejpam-6266	102	6	,	,	PUNCT
ejpam-6266	102	7	18	18	NUM
ejpam-6266	102	8	(	(	PUNCT
ejpam-6266	102	9	4	4	NUM
ejpam-6266	102	10	)	)	PUNCT
ejpam-6266	102	11	(	(	PUNCT
ejpam-6266	102	12	2025	2025	NUM
ejpam-6266	102	13	)	)	PUNCT
ejpam-6266	102	14	,	,	PUNCT
ejpam-6266	102	15	6266	6266	NUM
ejpam-6266	102	16	6	6	NUM
ejpam-6266	102	17	of	of	ADP
ejpam-6266	102	18	24	24	NUM
ejpam-6266	102	19	that	that	PRON
ejpam-6266	102	20	is	be	AUX
ejpam-6266	102	21	the	the	DET
ejpam-6266	102	22	data	datum	NOUN
ejpam-6266	102	23	are	be	AUX
ejpam-6266	102	24	from	from	ADP
ejpam-6266	102	25	the	the	DET
ejpam-6266	102	26	energy	energy	NOUN
ejpam-6266	102	27	space	space	NOUN
ejpam-6266	102	28	without	without	ADP
ejpam-6266	102	29	additional	additional	ADJ
ejpam-6266	102	30	regularity	regularity	NOUN
ejpam-6266	102	31	(	(	PUNCT
ejpam-6266	102	32	ie	ie	X
ejpam-6266	102	33	.	.	PUNCT
ejpam-6266	102	34	m	m	VERB
ejpam-6266	102	35	=	=	NOUN
ejpam-6266	102	36	1	1	NUM
ejpam-6266	102	37	in	in	ADP
ejpam-6266	102	38	(	(	PUNCT
ejpam-6266	102	39	17	17	NUM
ejpam-6266	102	40	)	)	PUNCT
ejpam-6266	102	41	)	)	PUNCT
ejpam-6266	102	42	,	,	PUNCT
ejpam-6266	102	43	and	and	CCONJ
ejpam-6266	102	44	set	set	VERB
ejpam-6266	102	45	for	for	ADP
ejpam-6266	102	46	all	all	DET
ejpam-6266	102	47	n	n	DET
ejpam-6266	102	48	≥	≥	NOUN
ejpam-6266	102	49	1	1	NUM
ejpam-6266	102	50	and	and	CCONJ
ejpam-6266	102	51	γ	γ	PROPN
ejpam-6266	102	52	∈	∈	PROPN
ejpam-6266	102	53	(	(	PUNCT
ejpam-6266	102	54	0	0	NUM
ejpam-6266	102	55	,	,	PUNCT
ejpam-6266	102	56	1	1	X
ejpam-6266	102	57	)	)	PUNCT
ejpam-6266	102	58	pγ	pγ	NOUN
ejpam-6266	102	59	=	=	SYM
ejpam-6266	102	60	pγ(n	pγ(n	X
ejpam-6266	102	61	)	)	PUNCT
ejpam-6266	102	62	:	:	PUNCT
ejpam-6266	103	1	=	=	SYM
ejpam-6266	103	2	1	1	NUM
ejpam-6266	103	3	γ	γ	X
ejpam-6266	103	4	.	.	PUNCT
ejpam-6266	104	1	(	(	PUNCT
ejpam-6266	104	2	19	19	NUM
ejpam-6266	104	3	)	)	PUNCT
ejpam-6266	104	4	then	then	ADV
ejpam-6266	104	5	we	we	PRON
ejpam-6266	104	6	have	have	AUX
ejpam-6266	104	7	theorem	theorem	VERB
ejpam-6266	104	8	1	1	NUM
ejpam-6266	104	9	.	.	PUNCT
ejpam-6266	104	10	assume	assume	VERB
ejpam-6266	104	11	that	that	SCONJ
ejpam-6266	104	12	γ	γ	PROPN
ejpam-6266	104	13	∈	∈	PROPN
ejpam-6266	104	14	(	(	PUNCT
ejpam-6266	104	15	1/2	1/2	NUM
ejpam-6266	104	16	,	,	PUNCT
ejpam-6266	104	17	1	1	NUM
ejpam-6266	104	18	)	)	PUNCT
ejpam-6266	104	19	and	and	CCONJ
ejpam-6266	104	20	p	p	X
ejpam-6266	104	21	>	>	X
ejpam-6266	104	22	pγ	pγ	VERB
ejpam-6266	104	23	for	for	ADP
ejpam-6266	104	24	n	n	NOUN
ejpam-6266	104	25	=	=	SYM
ejpam-6266	104	26	1	1	NUM
ejpam-6266	104	27	or	or	CCONJ
ejpam-6266	104	28	γ	γ	PRON
ejpam-6266	104	29	∈	∈	PROPN
ejpam-6266	104	30	(	(	PUNCT
ejpam-6266	104	31	0	0	NUM
ejpam-6266	104	32	,	,	PUNCT
ejpam-6266	104	33	1	1	NUM
ejpam-6266	104	34	)	)	PUNCT
ejpam-6266	104	35	and	and	CCONJ
ejpam-6266	104	36	p	p	X
ejpam-6266	104	37	>	>	X
ejpam-6266	104	38	pγ	pγ	VERB
ejpam-6266	104	39	for	for	ADP
ejpam-6266	104	40	n	n	NOUN
ejpam-6266	104	41	=	=	SYM
ejpam-6266	104	42	2	2	NUM
ejpam-6266	104	43	.	.	PUNCT
ejpam-6266	104	44	then	then	ADV
ejpam-6266	104	45	there	there	PRON
ejpam-6266	104	46	exists	exist	VERB
ejpam-6266	104	47	ε	ε	PROPN
ejpam-6266	104	48	>	>	X
ejpam-6266	104	49	0	0	NUM
ejpam-6266	104	50	such	such	ADJ
ejpam-6266	104	51	that	that	PRON
ejpam-6266	104	52	for	for	ADP
ejpam-6266	104	53	any	any	DET
ejpam-6266	104	54	initial	initial	ADJ
ejpam-6266	104	55	data	datum	NOUN
ejpam-6266	104	56	(	(	PUNCT
ejpam-6266	104	57	u0	u0	ADJ
ejpam-6266	104	58	,	,	PUNCT
ejpam-6266	104	59	u1	u1	NOUN
ejpam-6266	104	60	)	)	PUNCT
ejpam-6266	104	61	∈	∈	PROPN
ejpam-6266	105	1	a1,1	a1,1	NOUN
ejpam-6266	105	2	:	:	PUNCT
ejpam-6266	105	3	=	=	PUNCT
ejpam-6266	105	4	h1	h1	PROPN
ejpam-6266	105	5	∩	∩	ADJ
ejpam-6266	105	6	l1	l1	PROPN
ejpam-6266	105	7	×	×	PROPN
ejpam-6266	105	8	l2	l2	PROPN
ejpam-6266	105	9	∩	∩	X
ejpam-6266	105	10	l1	l1	PROPN
ejpam-6266	105	11	with	with	ADP
ejpam-6266	105	12	‖(u0	‖(u0	PROPN
ejpam-6266	105	13	,	,	PUNCT
ejpam-6266	105	14	u1)‖a1,1	u1)‖a1,1	ADV
ejpam-6266	105	15	≤	≤	PROPN
ejpam-6266	105	16	ε	ε	PROPN
ejpam-6266	105	17	,	,	PUNCT
ejpam-6266	105	18	there	there	PRON
ejpam-6266	105	19	exists	exist	VERB
ejpam-6266	105	20	a	a	DET
ejpam-6266	105	21	unique	unique	ADJ
ejpam-6266	105	22	global	global	NOUN
ejpam-6266	105	23	(	(	PUNCT
ejpam-6266	105	24	in	in	ADP
ejpam-6266	105	25	time	time	NOUN
ejpam-6266	105	26	)	)	PUNCT
ejpam-6266	105	27	solution	solution	NOUN
ejpam-6266	105	28	to	to	ADP
ejpam-6266	105	29	cauchy	cauchy	ADJ
ejpam-6266	105	30	problem	problem	NOUN
ejpam-6266	105	31	(	(	PUNCT
ejpam-6266	105	32	6	6	NUM
ejpam-6266	105	33	)	)	PUNCT
ejpam-6266	105	34	u	u	NOUN
ejpam-6266	105	35	∈	∈	PROPN
ejpam-6266	105	36	c	c	X
ejpam-6266	105	37	(	(	PUNCT
ejpam-6266	105	38	[	[	X
ejpam-6266	105	39	0,∞),h1	0,∞),h1	NUM
ejpam-6266	105	40	)	)	PUNCT
ejpam-6266	105	41	∩	∩	ADJ
ejpam-6266	105	42	c1	c1	NOUN
ejpam-6266	105	43	(	(	PUNCT
ejpam-6266	105	44	[	[	X
ejpam-6266	105	45	0,∞	0,∞	NOUN
ejpam-6266	105	46	)	)	PUNCT
ejpam-6266	105	47	,	,	PUNCT
ejpam-6266	105	48	l2	l2	NOUN
ejpam-6266	105	49	)	)	PUNCT
ejpam-6266	105	50	.	.	PUNCT
ejpam-6266	106	1	moreover	moreover	ADV
ejpam-6266	106	2	,	,	PUNCT
ejpam-6266	106	3	the	the	DET
ejpam-6266	106	4	solution	solution	NOUN
ejpam-6266	106	5	satisfies	satisfy	VERB
ejpam-6266	106	6	the	the	DET
ejpam-6266	106	7	following	follow	VERB
ejpam-6266	106	8	matsumura	matsumura	ADJ
ejpam-6266	106	9	type	type	NOUN
ejpam-6266	106	10	decay	decay	NOUN
ejpam-6266	106	11	estimates	estimate	NOUN
ejpam-6266	106	12	‖u(t	‖u(t	NOUN
ejpam-6266	106	13	,	,	PUNCT
ejpam-6266	106	14	·	·	PUNCT
ejpam-6266	106	15	)	)	PUNCT
ejpam-6266	106	16	‖l2	‖l2	X
ejpam-6266	106	17	.	.	PUNCT
ejpam-6266	107	1	(	(	PUNCT
ejpam-6266	107	2	1	1	X
ejpam-6266	107	3	+	+	X
ejpam-6266	107	4	t)−	t)−	PROPN
ejpam-6266	107	5	n	n	PRON
ejpam-6266	107	6	4	4	NUM
ejpam-6266	107	7	−γ+1‖(u0	−γ+1‖(u0	NOUN
ejpam-6266	107	8	,	,	PUNCT
ejpam-6266	107	9	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	107	10	,	,	PUNCT
ejpam-6266	107	11	‖∇u(t	‖∇u(t	PROPN
ejpam-6266	107	12	,	,	PUNCT
ejpam-6266	107	13	·	·	PUNCT
ejpam-6266	107	14	)	)	PUNCT
ejpam-6266	107	15	‖l2	‖l2	VERB
ejpam-6266	107	16	.	.	PUNCT
ejpam-6266	108	1	{	{	PUNCT
ejpam-6266	108	2	(	(	PUNCT
ejpam-6266	108	3	1	1	NUM
ejpam-6266	108	4	+	+	NUM
ejpam-6266	108	5	t	t	NOUN
ejpam-6266	108	6	)	)	PUNCT
ejpam-6266	108	7	1	1	NUM
ejpam-6266	108	8	4	4	NUM
ejpam-6266	108	9	−γ‖(u0	−γ‖(u0	NUM
ejpam-6266	108	10	,	,	PUNCT
ejpam-6266	108	11	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	108	12	if	if	SCONJ
ejpam-6266	108	13	n	n	PROPN
ejpam-6266	108	14	=	=	SYM
ejpam-6266	108	15	1	1	NUM
ejpam-6266	108	16	,	,	PUNCT
ejpam-6266	108	17	(	(	PUNCT
ejpam-6266	108	18	1	1	NUM
ejpam-6266	108	19	+	+	NUM
ejpam-6266	108	20	t)−γ	t)−γ	PRON
ejpam-6266	108	21	log(2	log(2	NOUN
ejpam-6266	108	22	+	+	CCONJ
ejpam-6266	109	1	t)‖(u0	t)‖(u0	ADJ
ejpam-6266	109	2	,	,	PUNCT
ejpam-6266	109	3	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	109	4	if	if	SCONJ
ejpam-6266	109	5	n	n	PROPN
ejpam-6266	109	6	=	=	SYM
ejpam-6266	109	7	2	2	NUM
ejpam-6266	109	8	,	,	PUNCT
ejpam-6266	109	9	‖∂j	‖∂j	VERB
ejpam-6266	109	10	t∇ku(t	t∇ku(t	NOUN
ejpam-6266	109	11	,	,	PUNCT
ejpam-6266	109	12	·	·	PUNCT
ejpam-6266	109	13	)	)	PUNCT
ejpam-6266	109	14	‖l2	‖l2	X
ejpam-6266	109	15	.	.	PUNCT
ejpam-6266	110	1	(	(	PUNCT
ejpam-6266	110	2	1	1	NUM
ejpam-6266	110	3	+	+	NUM
ejpam-6266	110	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	110	5	,	,	PUNCT
ejpam-6266	110	6	u1)‖a1,1	u1)‖a1,1	ADV
ejpam-6266	110	7	for	for	ADP
ejpam-6266	110	8	all	all	DET
ejpam-6266	110	9	j	j	PROPN
ejpam-6266	110	10	≥	≥	NUM
ejpam-6266	110	11	1	1	NUM
ejpam-6266	110	12	and	and	CCONJ
ejpam-6266	110	13	k	k	PROPN
ejpam-6266	110	14	≥	≥	NUM
ejpam-6266	110	15	2	2	NUM
ejpam-6266	110	16	.	.	NOUN
ejpam-6266	110	17	3.2	3.2	NUM
ejpam-6266	110	18	.	.	PUNCT
ejpam-6266	111	1	global	global	ADJ
ejpam-6266	111	2	existence	existence	NOUN
ejpam-6266	111	3	in	in	ADP
ejpam-6266	111	4	high	high	ADJ
ejpam-6266	111	5	dimension	dimension	NOUN
ejpam-6266	111	6	in	in	ADP
ejpam-6266	111	7	section	section	NOUN
ejpam-6266	111	8	3.1	3.1	NUM
ejpam-6266	111	9	we	we	PRON
ejpam-6266	111	10	presented	present	VERB
ejpam-6266	111	11	global	global	ADJ
ejpam-6266	111	12	existence	existence	NOUN
ejpam-6266	111	13	for	for	ADP
ejpam-6266	111	14	low	low	ADJ
ejpam-6266	111	15	dimension	dimension	NOUN
ejpam-6266	111	16	(	(	PUNCT
ejpam-6266	111	17	n	n	NOUN
ejpam-6266	111	18	=	=	SYM
ejpam-6266	111	19	1	1	NUM
ejpam-6266	111	20	and	and	CCONJ
ejpam-6266	111	21	n	n	CCONJ
ejpam-6266	111	22	=	=	NOUN
ejpam-6266	111	23	2	2	NUM
ejpam-6266	111	24	)	)	PUNCT
ejpam-6266	111	25	.	.	PUNCT
ejpam-6266	112	1	in	in	ADP
ejpam-6266	112	2	that	that	DET
ejpam-6266	112	3	case	case	NOUN
ejpam-6266	112	4	the	the	DET
ejpam-6266	112	5	admissible	admissible	ADJ
ejpam-6266	112	6	range	range	NOUN
ejpam-6266	112	7	for	for	ADP
ejpam-6266	112	8	p	p	PROPN
ejpam-6266	112	9	is	be	AUX
ejpam-6266	112	10	superiorly	superiorly	ADV
ejpam-6266	112	11	unbounded	unbounded	ADJ
ejpam-6266	112	12	.	.	PUNCT
ejpam-6266	113	1	in	in	ADP
ejpam-6266	113	2	space	space	NOUN
ejpam-6266	113	3	dimensional	dimensional	ADJ
ejpam-6266	113	4	n	n	X
ejpam-6266	113	5	≥	≥	NUM
ejpam-6266	113	6	3	3	NUM
ejpam-6266	113	7	,	,	PUNCT
ejpam-6266	113	8	there	there	PRON
ejpam-6266	113	9	appears	appear	VERB
ejpam-6266	113	10	an	an	DET
ejpam-6266	113	11	upper	upper	ADJ
ejpam-6266	113	12	bound	bind	VERB
ejpam-6266	113	13	for	for	ADP
ejpam-6266	113	14	the	the	DET
ejpam-6266	113	15	admissible	admissible	ADJ
ejpam-6266	113	16	values	value	NOUN
ejpam-6266	113	17	for	for	ADP
ejpam-6266	113	18	p.	p.	NOUN
ejpam-6266	113	19	this	this	DET
ejpam-6266	113	20	upper	upper	ADJ
ejpam-6266	113	21	bound	bound	NOUN
ejpam-6266	113	22	is	be	AUX
ejpam-6266	113	23	caused	cause	VERB
ejpam-6266	113	24	by	by	ADP
ejpam-6266	113	25	the	the	DET
ejpam-6266	113	26	application	application	NOUN
ejpam-6266	113	27	of	of	ADP
ejpam-6266	113	28	gagliardo	gagliardo	NOUN
ejpam-6266	113	29	-	-	PUNCT
ejpam-6266	113	30	nirenberg	nirenberg	NOUN
ejpam-6266	113	31	inequality	inequality	NOUN
ejpam-6266	113	32	(	(	PUNCT
ejpam-6266	113	33	see	see	VERB
ejpam-6266	113	34	condition	condition	NOUN
ejpam-6266	113	35	108	108	NUM
ejpam-6266	113	36	)	)	PUNCT
ejpam-6266	113	37	.	.	PUNCT
ejpam-6266	114	1	so	so	ADV
ejpam-6266	114	2	,	,	PUNCT
ejpam-6266	114	3	let	let	VERB
ejpam-6266	114	4	us	we	PRON
ejpam-6266	114	5	,	,	PUNCT
ejpam-6266	114	6	first	first	ADV
ejpam-6266	114	7	,	,	PUNCT
ejpam-6266	114	8	state	state	NOUN
ejpam-6266	114	9	the	the	DET
ejpam-6266	114	10	global	global	ADJ
ejpam-6266	114	11	(	(	PUNCT
ejpam-6266	114	12	in	in	ADP
ejpam-6266	114	13	time	time	NOUN
ejpam-6266	114	14	)	)	PUNCT
ejpam-6266	114	15	existence	existence	NOUN
ejpam-6266	114	16	results	result	NOUN
ejpam-6266	114	17	theorem	theorem	VERB
ejpam-6266	114	18	2	2	X
ejpam-6266	114	19	.	.	PUNCT
ejpam-6266	115	1	let	let	VERB
ejpam-6266	115	2	n	n	PRON
ejpam-6266	115	3	≥	≥	NOUN
ejpam-6266	115	4	3	3	X
ejpam-6266	115	5	.	.	PUNCT
ejpam-6266	115	6	assume	assume	VERB
ejpam-6266	115	7	that	that	SCONJ
ejpam-6266	115	8	γ	γ	PROPN
ejpam-6266	115	9	∈	∈	PROPN
ejpam-6266	115	10	(	(	PUNCT
ejpam-6266	115	11	n−2	n−2	PROPN
ejpam-6266	115	12	n	n	PROPN
ejpam-6266	115	13	,	,	PUNCT
ejpam-6266	115	14	1	1	NUM
ejpam-6266	115	15	)	)	PUNCT
ejpam-6266	115	16	and	and	CCONJ
ejpam-6266	115	17	pγ	pγ	VERB
ejpam-6266	115	18	<	<	X
ejpam-6266	115	19	p	p	X
ejpam-6266	115	20	≤	≤	NUM
ejpam-6266	115	21	pgn	pgn	NOUN
ejpam-6266	115	22	:	:	PUNCT
ejpam-6266	115	23	=	=	SYM
ejpam-6266	115	24	n	n	PRON
ejpam-6266	115	25	n−2	n−2	PROPN
ejpam-6266	115	26	.	.	PUNCT
ejpam-6266	116	1	then	then	ADV
ejpam-6266	116	2	there	there	PRON
ejpam-6266	116	3	exists	exist	VERB
ejpam-6266	116	4	ε	ε	PROPN
ejpam-6266	116	5	>	>	X
ejpam-6266	116	6	0	0	NUM
ejpam-6266	116	7	such	such	ADJ
ejpam-6266	116	8	that	that	PRON
ejpam-6266	116	9	for	for	ADP
ejpam-6266	116	10	any	any	DET
ejpam-6266	116	11	initial	initial	ADJ
ejpam-6266	116	12	data	datum	NOUN
ejpam-6266	116	13	(	(	PUNCT
ejpam-6266	116	14	u0	u0	ADJ
ejpam-6266	116	15	,	,	PUNCT
ejpam-6266	116	16	u1	u1	NOUN
ejpam-6266	116	17	)	)	PUNCT
ejpam-6266	116	18	∈	∈	PROPN
ejpam-6266	117	1	a1,1	a1,1	NOUN
ejpam-6266	117	2	:	:	PUNCT
ejpam-6266	117	3	=	=	PUNCT
ejpam-6266	117	4	h1	h1	PROPN
ejpam-6266	117	5	∩	∩	ADJ
ejpam-6266	117	6	l1	l1	PROPN
ejpam-6266	117	7	×	×	PROPN
ejpam-6266	117	8	l2	l2	PROPN
ejpam-6266	117	9	∩	∩	X
ejpam-6266	117	10	l1	l1	PROPN
ejpam-6266	117	11	with	with	ADP
ejpam-6266	117	12	‖(u0	‖(u0	PROPN
ejpam-6266	117	13	,	,	PUNCT
ejpam-6266	117	14	u1)‖a1,1	u1)‖a1,1	ADV
ejpam-6266	117	15	≤	≤	PROPN
ejpam-6266	117	16	ε	ε	PROPN
ejpam-6266	117	17	,	,	PUNCT
ejpam-6266	117	18	there	there	PRON
ejpam-6266	117	19	exists	exist	VERB
ejpam-6266	117	20	a	a	DET
ejpam-6266	117	21	unique	unique	ADJ
ejpam-6266	117	22	global	global	NOUN
ejpam-6266	117	23	(	(	PUNCT
ejpam-6266	117	24	in	in	ADP
ejpam-6266	117	25	time	time	NOUN
ejpam-6266	117	26	)	)	PUNCT
ejpam-6266	117	27	solution	solution	NOUN
ejpam-6266	117	28	to	to	ADP
ejpam-6266	117	29	cauchy	cauchy	ADJ
ejpam-6266	117	30	problem	problem	NOUN
ejpam-6266	117	31	(	(	PUNCT
ejpam-6266	117	32	6	6	NUM
ejpam-6266	117	33	)	)	PUNCT
ejpam-6266	117	34	u	u	NOUN
ejpam-6266	117	35	∈	∈	PROPN
ejpam-6266	117	36	c	c	X
ejpam-6266	117	37	(	(	PUNCT
ejpam-6266	117	38	[	[	X
ejpam-6266	117	39	0,∞),h1	0,∞),h1	NUM
ejpam-6266	117	40	)	)	PUNCT
ejpam-6266	117	41	∩	∩	ADJ
ejpam-6266	117	42	c1	c1	NOUN
ejpam-6266	117	43	(	(	PUNCT
ejpam-6266	117	44	[	[	X
ejpam-6266	117	45	0,∞	0,∞	NOUN
ejpam-6266	117	46	)	)	PUNCT
ejpam-6266	117	47	,	,	PUNCT
ejpam-6266	117	48	l2	l2	NOUN
ejpam-6266	117	49	)	)	PUNCT
ejpam-6266	117	50	.	.	PUNCT
ejpam-6266	118	1	moreover	moreover	ADV
ejpam-6266	118	2	,	,	PUNCT
ejpam-6266	118	3	the	the	DET
ejpam-6266	118	4	solution	solution	NOUN
ejpam-6266	118	5	satisfies	satisfy	VERB
ejpam-6266	118	6	the	the	DET
ejpam-6266	118	7	following	follow	VERB
ejpam-6266	118	8	matsumura	matsumura	ADJ
ejpam-6266	118	9	type	type	NOUN
ejpam-6266	118	10	decay	decay	NOUN
ejpam-6266	118	11	estimates	estimate	NOUN
ejpam-6266	118	12	‖u(t	‖u(t	NOUN
ejpam-6266	118	13	,	,	PUNCT
ejpam-6266	118	14	·	·	PUNCT
ejpam-6266	118	15	)	)	PUNCT
ejpam-6266	118	16	‖l2	‖l2	VERB
ejpam-6266	118	17	.	.	PUNCT
ejpam-6266	119	1			PUNCT
ejpam-6266	119	2	(	(	PUNCT
ejpam-6266	119	3	1	1	NUM
ejpam-6266	119	4	+	+	NUM
ejpam-6266	119	5	t	t	NOUN
ejpam-6266	119	6	)	)	PUNCT
ejpam-6266	119	7	1	1	NUM
ejpam-6266	119	8	4	4	NUM
ejpam-6266	119	9	−γ‖(u0	−γ‖(u0	NUM
ejpam-6266	119	10	,	,	PUNCT
ejpam-6266	119	11	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	119	12	if	if	SCONJ
ejpam-6266	119	13	n	n	PROPN
ejpam-6266	119	14	=	=	SYM
ejpam-6266	119	15	3	3	NUM
ejpam-6266	119	16	,	,	PUNCT
ejpam-6266	119	17	(	(	PUNCT
ejpam-6266	119	18	1	1	NUM
ejpam-6266	119	19	+	+	NUM
ejpam-6266	119	20	t)−γ	t)−γ	PRON
ejpam-6266	119	21	log(2	log(2	NOUN
ejpam-6266	119	22	+	+	CCONJ
ejpam-6266	119	23	t)‖(u0	t)‖(u0	ADJ
ejpam-6266	119	24	,	,	PUNCT
ejpam-6266	119	25	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	119	26	if	if	SCONJ
ejpam-6266	119	27	n	n	PROPN
ejpam-6266	119	28	=	=	SYM
ejpam-6266	119	29	4	4	NUM
ejpam-6266	119	30	,	,	PUNCT
ejpam-6266	119	31	(	(	PUNCT
ejpam-6266	119	32	1	1	NUM
ejpam-6266	119	33	+	+	NUM
ejpam-6266	119	34	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	119	35	,	,	PUNCT
ejpam-6266	119	36	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	119	37	if	if	SCONJ
ejpam-6266	119	38	n	n	PRON
ejpam-6266	119	39	≥	≥	NOUN
ejpam-6266	119	40	5	5	NUM
ejpam-6266	119	41	,	,	PUNCT
ejpam-6266	119	42	(	(	PUNCT
ejpam-6266	119	43	20	20	NUM
ejpam-6266	119	44	)	)	PUNCT
ejpam-6266	119	45	‖u(t	‖u(t	NUM
ejpam-6266	119	46	,	,	PUNCT
ejpam-6266	119	47	·	·	PUNCT
ejpam-6266	119	48	)	)	PUNCT
ejpam-6266	119	49	‖ḣ1/2	‖ḣ1/2	PROPN
ejpam-6266	119	50	.	.	PUNCT
ejpam-6266	120	1	{	{	PUNCT
ejpam-6266	120	2	(	(	PUNCT
ejpam-6266	120	3	1	1	NUM
ejpam-6266	120	4	+	+	NUM
ejpam-6266	120	5	t)−γ	t)−γ	PRON
ejpam-6266	120	6	log(2	log(2	NOUN
ejpam-6266	120	7	+	+	CCONJ
ejpam-6266	120	8	t)‖(u0	t)‖(u0	ADJ
ejpam-6266	120	9	,	,	PUNCT
ejpam-6266	120	10	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	120	11	if	if	SCONJ
ejpam-6266	120	12	n	n	PROPN
ejpam-6266	120	13	=	=	SYM
ejpam-6266	120	14	3	3	NUM
ejpam-6266	120	15	,	,	PUNCT
ejpam-6266	120	16	(	(	PUNCT
ejpam-6266	120	17	1	1	NUM
ejpam-6266	120	18	+	+	NUM
ejpam-6266	120	19	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	120	20	,	,	PUNCT
ejpam-6266	120	21	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	120	22	if	if	SCONJ
ejpam-6266	120	23	n	n	PRON
ejpam-6266	120	24	≥	≥	NOUN
ejpam-6266	120	25	4	4	NUM
ejpam-6266	120	26	,	,	PUNCT
ejpam-6266	120	27	(	(	PUNCT
ejpam-6266	120	28	21	21	NUM
ejpam-6266	120	29	)	)	PUNCT
ejpam-6266	120	30	‖∇u(t	‖∇u(t	PROPN
ejpam-6266	120	31	,	,	PUNCT
ejpam-6266	120	32	·	·	PUNCT
ejpam-6266	120	33	)	)	PUNCT
ejpam-6266	120	34	‖l2	‖l2	X
ejpam-6266	120	35	.	.	PUNCT
ejpam-6266	121	1	(	(	PUNCT
ejpam-6266	121	2	1	1	NUM
ejpam-6266	121	3	+	+	NUM
ejpam-6266	121	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	121	5	,	,	PUNCT
ejpam-6266	121	6	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	121	7	,	,	PUNCT
ejpam-6266	121	8	(	(	PUNCT
ejpam-6266	121	9	22	22	NUM
ejpam-6266	121	10	)	)	PUNCT
ejpam-6266	121	11	‖∂tu(t	‖∂tu(t	PROPN
ejpam-6266	121	12	,	,	PUNCT
ejpam-6266	121	13	·	·	PUNCT
ejpam-6266	121	14	)	)	PUNCT
ejpam-6266	121	15	‖l2	‖l2	X
ejpam-6266	121	16	.	.	PUNCT
ejpam-6266	122	1	(	(	PUNCT
ejpam-6266	122	2	1	1	NUM
ejpam-6266	122	3	+	+	NUM
ejpam-6266	122	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	122	5	,	,	PUNCT
ejpam-6266	122	6	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	122	7	.	.	PUNCT
ejpam-6266	123	1	(	(	PUNCT
ejpam-6266	123	2	23	23	NUM
ejpam-6266	123	3	)	)	PUNCT
ejpam-6266	123	4	t.	t.	NOUN
ejpam-6266	123	5	hadj	hadj	PROPN
ejpam-6266	123	6	kaddour	kaddour	PROPN
ejpam-6266	123	7	et	et	PROPN
ejpam-6266	123	8	al	al	PROPN
ejpam-6266	123	9	.	.	PUNCT
ejpam-6266	123	10	/	/	SYM
ejpam-6266	123	11	eur	eur	PROPN
ejpam-6266	123	12	.	.	PUNCT
ejpam-6266	124	1	j.	j.	PROPN
ejpam-6266	124	2	pure	pure	PROPN
ejpam-6266	124	3	appl	appl	PROPN
ejpam-6266	124	4	.	.	PROPN
ejpam-6266	124	5	math	math	PROPN
ejpam-6266	124	6	,	,	PUNCT
ejpam-6266	124	7	18	18	NUM
ejpam-6266	124	8	(	(	PUNCT
ejpam-6266	124	9	4	4	NUM
ejpam-6266	124	10	)	)	PUNCT
ejpam-6266	124	11	(	(	PUNCT
ejpam-6266	124	12	2025	2025	NUM
ejpam-6266	124	13	)	)	PUNCT
ejpam-6266	124	14	,	,	PUNCT
ejpam-6266	124	15	6266	6266	NUM
ejpam-6266	124	16	7	7	NUM
ejpam-6266	124	17	of	of	ADP
ejpam-6266	124	18	24	24	NUM
ejpam-6266	124	19	3.3	3.3	NUM
ejpam-6266	124	20	.	.	PUNCT
ejpam-6266	125	1	global	global	ADJ
ejpam-6266	125	2	existence	existence	NOUN
ejpam-6266	125	3	of	of	ADP
ejpam-6266	125	4	high	high	ADJ
ejpam-6266	125	5	regular	regular	ADJ
ejpam-6266	125	6	solution	solution	NOUN
ejpam-6266	125	7	with	with	ADP
ejpam-6266	125	8	additional	additional	ADJ
ejpam-6266	125	9	regularity	regularity	NOUN
ejpam-6266	125	10	m	m	NOUN
ejpam-6266	125	11	∈	∈	NOUN
ejpam-6266	126	1	[	[	X
ejpam-6266	126	2	1	1	NUM
ejpam-6266	126	3	,	,	PUNCT
ejpam-6266	126	4	2	2	NUM
ejpam-6266	126	5	)	)	PUNCT
ejpam-6266	126	6	in	in	ADP
ejpam-6266	126	7	this	this	DET
ejpam-6266	126	8	section	section	NOUN
ejpam-6266	126	9	we	we	PRON
ejpam-6266	126	10	require	require	VERB
ejpam-6266	126	11	an	an	DET
ejpam-6266	126	12	additional	additional	ADJ
ejpam-6266	126	13	regularity	regularity	NOUN
ejpam-6266	126	14	on	on	ADP
ejpam-6266	126	15	the	the	DET
ejpam-6266	126	16	data	datum	NOUN
ejpam-6266	126	17	.	.	PUNCT
ejpam-6266	127	1	however	however	ADV
ejpam-6266	127	2	,	,	PUNCT
ejpam-6266	127	3	we	we	PRON
ejpam-6266	127	4	choose	choose	VERB
ejpam-6266	127	5	m	m	PRON
ejpam-6266	127	6	∈	∈	NOUN
ejpam-6266	127	7	(	(	PUNCT
ejpam-6266	127	8	1	1	NUM
ejpam-6266	127	9	,	,	PUNCT
ejpam-6266	127	10	2	2	NUM
ejpam-6266	127	11	)	)	PUNCT
ejpam-6266	127	12	and	and	CCONJ
ejpam-6266	127	13	σ	σ	X
ejpam-6266	127	14	>	>	X
ejpam-6266	127	15	1	1	NUM
ejpam-6266	127	16	in	in	ADP
ejpam-6266	127	17	the	the	DET
ejpam-6266	127	18	data	data	NOUN
ejpam-6266	127	19	space	space	NOUN
ejpam-6266	127	20	(	(	PUNCT
ejpam-6266	127	21	17	17	NUM
ejpam-6266	127	22	)	)	PUNCT
ejpam-6266	127	23	.	.	PUNCT
ejpam-6266	128	1	the	the	DET
ejpam-6266	128	2	purpose	purpose	NOUN
ejpam-6266	128	3	of	of	ADP
ejpam-6266	128	4	this	this	DET
ejpam-6266	128	5	section	section	NOUN
ejpam-6266	128	6	is	be	AUX
ejpam-6266	128	7	to	to	PART
ejpam-6266	128	8	show	show	VERB
ejpam-6266	128	9	that	that	SCONJ
ejpam-6266	128	10	the	the	DET
ejpam-6266	128	11	regularity	regularity	NOUN
ejpam-6266	128	12	of	of	ADP
ejpam-6266	128	13	the	the	DET
ejpam-6266	128	14	data	datum	NOUN
ejpam-6266	128	15	does	do	AUX
ejpam-6266	128	16	not	not	PART
ejpam-6266	128	17	influence	influence	VERB
ejpam-6266	128	18	the	the	DET
ejpam-6266	128	19	critical	critical	ADJ
ejpam-6266	128	20	exponent	exponent	NOUN
ejpam-6266	128	21	,	,	PUNCT
ejpam-6266	128	22	although	although	SCONJ
ejpam-6266	128	23	the	the	DET
ejpam-6266	128	24	additional	additional	ADJ
ejpam-6266	128	25	regularity	regularity	NOUN
ejpam-6266	128	26	improve	improve	VERB
ejpam-6266	128	27	somehow	somehow	ADV
ejpam-6266	128	28	the	the	DET
ejpam-6266	128	29	range	range	NOUN
ejpam-6266	128	30	of	of	ADP
ejpam-6266	128	31	admissible	admissible	ADJ
ejpam-6266	128	32	p	p	NOUN
ejpam-6266	128	33	as	as	SCONJ
ejpam-6266	128	34	it	it	PRON
ejpam-6266	128	35	is	be	AUX
ejpam-6266	128	36	well	well	ADV
ejpam-6266	128	37	known	know	VERB
ejpam-6266	128	38	.	.	PUNCT
ejpam-6266	129	1	first	first	ADV
ejpam-6266	129	2	,	,	PUNCT
ejpam-6266	129	3	let	let	VERB
ejpam-6266	129	4	us	we	PRON
ejpam-6266	129	5	set	set	VERB
ejpam-6266	129	6	for	for	ADP
ejpam-6266	129	7	all	all	DET
ejpam-6266	129	8	n	n	DET
ejpam-6266	129	9	≥	≥	NOUN
ejpam-6266	129	10	3	3	NUM
ejpam-6266	129	11	,	,	PUNCT
ejpam-6266	129	12	m	m	VERB
ejpam-6266	129	13	∈	∈	NOUN
ejpam-6266	129	14	(	(	PUNCT
ejpam-6266	129	15	1	1	NUM
ejpam-6266	129	16	,	,	PUNCT
ejpam-6266	129	17	2	2	NUM
ejpam-6266	129	18	)	)	PUNCT
ejpam-6266	129	19	,	,	PUNCT
ejpam-6266	129	20	γ	γ	PROPN
ejpam-6266	129	21	∈	∈	PROPN
ejpam-6266	129	22	(	(	PUNCT
ejpam-6266	129	23	0	0	NUM
ejpam-6266	129	24	,	,	PUNCT
ejpam-6266	129	25	1	1	NUM
ejpam-6266	129	26	)	)	PUNCT
ejpam-6266	129	27	and	and	CCONJ
ejpam-6266	129	28	σ	σ	NOUN
ejpam-6266	129	29	>	>	X
ejpam-6266	129	30	1	1	NUM
ejpam-6266	129	31	pγ	pγ	NOUN
ejpam-6266	129	32	,	,	PUNCT
ejpam-6266	129	33	m(n	m(n	X
ejpam-6266	129	34	)	)	PUNCT
ejpam-6266	129	35	=	=	SYM
ejpam-6266	129	36	1	1	NUM
ejpam-6266	129	37	γ	γ	X
ejpam-6266	129	38	.	.	PUNCT
ejpam-6266	130	1	(	(	PUNCT
ejpam-6266	130	2	24	24	NUM
ejpam-6266	130	3	)	)	PUNCT
ejpam-6266	130	4	then	then	ADV
ejpam-6266	130	5	we	we	PRON
ejpam-6266	130	6	have	have	AUX
ejpam-6266	130	7	theorem	theorem	VERB
ejpam-6266	130	8	3	3	NUM
ejpam-6266	130	9	.	.	PUNCT
ejpam-6266	130	10	assume	assume	VERB
ejpam-6266	130	11	that	that	SCONJ
ejpam-6266	130	12	n	n	PROPN
ejpam-6266	130	13	≥	≥	NUM
ejpam-6266	130	14	3	3	NUM
ejpam-6266	130	15	,	,	PUNCT
ejpam-6266	130	16	σ	σ	PROPN
ejpam-6266	130	17	∈	∈	PROPN
ejpam-6266	130	18	(	(	PUNCT
ejpam-6266	130	19	1	1	NUM
ejpam-6266	130	20	,	,	PUNCT
ejpam-6266	130	21	n2	n2	NOUN
ejpam-6266	130	22	)	)	PUNCT
ejpam-6266	130	23	,	,	PUNCT
ejpam-6266	130	24	γ	γ	PROPN
ejpam-6266	130	25	∈	∈	PROPN
ejpam-6266	130	26	(	(	PUNCT
ejpam-6266	130	27	0	0	NUM
ejpam-6266	130	28	,	,	PUNCT
ejpam-6266	130	29	1	1	NUM
ejpam-6266	130	30	)	)	PUNCT
ejpam-6266	130	31	and	and	CCONJ
ejpam-6266	130	32	m	m	PROPN
ejpam-6266	130	33	∈	∈	NOUN
ejpam-6266	130	34	(	(	PUNCT
ejpam-6266	130	35	1	1	NUM
ejpam-6266	130	36	,	,	PUNCT
ejpam-6266	130	37	2	2	NUM
ejpam-6266	130	38	)	)	PUNCT
ejpam-6266	130	39	such	such	ADJ
ejpam-6266	130	40	that	that	SCONJ
ejpam-6266	130	41	n	n	PROPN
ejpam-6266	130	42	2	2	NUM
ejpam-6266	130	43	(	(	PUNCT
ejpam-6266	130	44	1	1	NUM
ejpam-6266	130	45	m	m	NOUN
ejpam-6266	130	46	−	−	NUM
ejpam-6266	130	47	1	1	NUM
ejpam-6266	130	48	2	2	NUM
ejpam-6266	130	49	)	)	PUNCT
ejpam-6266	130	50	<	<	X
ejpam-6266	130	51	1	1	NUM
ejpam-6266	130	52	,	,	PUNCT
ejpam-6266	130	53	n	n	PRON
ejpam-6266	130	54	2	2	NUM
ejpam-6266	130	55	(	(	PUNCT
ejpam-6266	130	56	1	1	NUM
ejpam-6266	130	57	m	m	NOUN
ejpam-6266	130	58	−	−	NUM
ejpam-6266	130	59	1	1	NUM
ejpam-6266	130	60	2	2	NUM
ejpam-6266	130	61	)	)	PUNCT
ejpam-6266	131	1	+	+	CCONJ
ejpam-6266	131	2	σ	σ	PROPN
ejpam-6266	131	3	2	2	NUM
ejpam-6266	131	4	>	>	SYM
ejpam-6266	131	5	1	1	NUM
ejpam-6266	131	6	,	,	PUNCT
ejpam-6266	131	7	(	(	PUNCT
ejpam-6266	131	8	25	25	NUM
ejpam-6266	131	9	)	)	PUNCT
ejpam-6266	131	10	and	and	CCONJ
ejpam-6266	131	11	p	p	NOUN
ejpam-6266	131	12	satisfies	satisfy	VERB
ejpam-6266	131	13	the	the	DET
ejpam-6266	131	14	condition	condition	NOUN
ejpam-6266	131	15	p	p	PROPN
ejpam-6266	131	16	>	>	X
ejpam-6266	131	17	max	max	PROPN
ejpam-6266	131	18	{	{	PUNCT
ejpam-6266	131	19	dσe	dσe	PROPN
ejpam-6266	131	20	;	;	PUNCT
ejpam-6266	131	21	pγ	pγ	PRON
ejpam-6266	131	22	,	,	PUNCT
ejpam-6266	131	23	m(n	m(n	NOUN
ejpam-6266	131	24	)	)	PUNCT
ejpam-6266	131	25	}	}	PUNCT
ejpam-6266	131	26	,	,	PUNCT
ejpam-6266	131	27	(	(	PUNCT
ejpam-6266	131	28	26	26	NUM
ejpam-6266	131	29	)	)	PUNCT
ejpam-6266	131	30	then	then	ADV
ejpam-6266	131	31	,	,	PUNCT
ejpam-6266	131	32	there	there	PRON
ejpam-6266	131	33	exists	exist	VERB
ejpam-6266	131	34	a	a	DET
ejpam-6266	131	35	positive	positive	ADJ
ejpam-6266	131	36	constant	constant	ADJ
ejpam-6266	131	37	ε0	ε0	NOUN
ejpam-6266	131	38	such	such	ADJ
ejpam-6266	131	39	that	that	PRON
ejpam-6266	131	40	for	for	ADP
ejpam-6266	131	41	any	any	DET
ejpam-6266	131	42	initial	initial	ADJ
ejpam-6266	131	43	data	datum	NOUN
ejpam-6266	131	44	(	(	PUNCT
ejpam-6266	131	45	u0	u0	ADJ
ejpam-6266	131	46	,	,	PUNCT
ejpam-6266	131	47	u1	u1	NOUN
ejpam-6266	131	48	)	)	PUNCT
ejpam-6266	131	49	∈	∈	PROPN
ejpam-6266	131	50	am	be	AUX
ejpam-6266	131	51	,	,	PUNCT
ejpam-6266	131	52	σ(rn	σ(rn	PROPN
ejpam-6266	131	53	)	)	PUNCT
ejpam-6266	131	54	satisfying	satisfy	VERB
ejpam-6266	131	55	‖(u0	‖(u0	PROPN
ejpam-6266	131	56	,	,	PUNCT
ejpam-6266	131	57	u1)‖am	u1)‖am	PROPN
ejpam-6266	131	58	,	,	PUNCT
ejpam-6266	131	59	σ	σ	PROPN
ejpam-6266	131	60	≤	≤	X
ejpam-6266	131	61	ε	ε	PROPN
ejpam-6266	131	62	for	for	ADP
ejpam-6266	131	63	all	all	DET
ejpam-6266	131	64	ε	ε	PROPN
ejpam-6266	131	65	≤	≤	ADJ
ejpam-6266	131	66	ε0	ε0	PROPN
ejpam-6266	131	67	,	,	PUNCT
ejpam-6266	131	68	there	there	PRON
ejpam-6266	131	69	is	be	VERB
ejpam-6266	131	70	a	a	DET
ejpam-6266	131	71	uniquely	uniquely	ADV
ejpam-6266	131	72	determined	determined	ADJ
ejpam-6266	131	73	global	global	ADJ
ejpam-6266	131	74	(	(	PUNCT
ejpam-6266	131	75	in	in	ADP
ejpam-6266	131	76	time	time	NOUN
ejpam-6266	131	77	)	)	PUNCT
ejpam-6266	131	78	energy	energy	NOUN
ejpam-6266	131	79	solution	solution	NOUN
ejpam-6266	131	80	u	u	NOUN
ejpam-6266	131	81	∈	∈	PROPN
ejpam-6266	131	82	c	c	X
ejpam-6266	131	83	(	(	PUNCT
ejpam-6266	131	84	[	[	X
ejpam-6266	131	85	0,∞),hσ	0,∞),hσ	NUM
ejpam-6266	131	86	)	)	PUNCT
ejpam-6266	131	87	∩	∩	ADJ
ejpam-6266	131	88	c1	c1	NOUN
ejpam-6266	131	89	(	(	PUNCT
ejpam-6266	131	90	[	[	X
ejpam-6266	131	91	0,∞),hσ−1	0,∞),hσ−1	PROPN
ejpam-6266	131	92	)	)	PUNCT
ejpam-6266	131	93	to	to	ADP
ejpam-6266	131	94	the	the	DET
ejpam-6266	131	95	cauchy	cauchy	ADJ
ejpam-6266	131	96	problem	problem	NOUN
ejpam-6266	131	97	(	(	PUNCT
ejpam-6266	131	98	6	6	NUM
ejpam-6266	131	99	)	)	PUNCT
ejpam-6266	131	100	.	.	PUNCT
ejpam-6266	132	1	moreover	moreover	ADV
ejpam-6266	132	2	,	,	PUNCT
ejpam-6266	132	3	the	the	DET
ejpam-6266	132	4	solution	solution	NOUN
ejpam-6266	132	5	satisfies	satisfy	VERB
ejpam-6266	132	6	the	the	DET
ejpam-6266	132	7	following	follow	VERB
ejpam-6266	132	8	estimates	estimate	NOUN
ejpam-6266	132	9	:	:	PUNCT
ejpam-6266	132	10	‖u(t	‖u(t	NUM
ejpam-6266	132	11	,	,	PUNCT
ejpam-6266	132	12	·	·	PUNCT
ejpam-6266	132	13	)	)	PUNCT
ejpam-6266	132	14	‖l2	‖l2	X
ejpam-6266	132	15	.	.	PUNCT
ejpam-6266	133	1	(	(	PUNCT
ejpam-6266	133	2	1	1	NUM
ejpam-6266	133	3	+	+	NUM
ejpam-6266	133	4	t)1−	t)1−	NOUN
ejpam-6266	133	5	n	n	ADP
ejpam-6266	133	6	2	2	NUM
ejpam-6266	133	7	(	(	PUNCT
ejpam-6266	133	8	1	1	NUM
ejpam-6266	133	9	m	m	NOUN
ejpam-6266	133	10	−	−	NUM
ejpam-6266	133	11	1	1	NUM
ejpam-6266	133	12	2	2	NUM
ejpam-6266	133	13	)	)	PUNCT
ejpam-6266	133	14	−γ‖(u0	−γ‖(u0	PROPN
ejpam-6266	133	15	,	,	PUNCT
ejpam-6266	133	16	u1)‖am	u1)‖am	PROPN
ejpam-6266	133	17	,	,	PUNCT
ejpam-6266	133	18	σ	σ	PROPN
ejpam-6266	133	19	,	,	PUNCT
ejpam-6266	133	20	‖|d|σu(t	‖|d|σu(t	PROPN
ejpam-6266	133	21	,	,	PUNCT
ejpam-6266	133	22	·	·	PUNCT
ejpam-6266	133	23	)	)	PUNCT
ejpam-6266	133	24	‖l2	‖l2	X
ejpam-6266	133	25	.	.	PUNCT
ejpam-6266	134	1	(	(	PUNCT
ejpam-6266	134	2	1	1	NUM
ejpam-6266	134	3	+	+	NUM
ejpam-6266	134	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	134	5	,	,	PUNCT
ejpam-6266	134	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	134	7	,	,	PUNCT
ejpam-6266	134	8	σ	σ	PROPN
ejpam-6266	134	9	,	,	PUNCT
ejpam-6266	134	10	‖ut(t	‖ut(t	PROPN
ejpam-6266	134	11	,	,	PUNCT
ejpam-6266	134	12	·	·	PUNCT
ejpam-6266	134	13	)	)	PUNCT
ejpam-6266	134	14	‖l2	‖l2	X
ejpam-6266	134	15	.	.	PUNCT
ejpam-6266	135	1	(	(	PUNCT
ejpam-6266	135	2	1	1	NUM
ejpam-6266	135	3	+	+	NUM
ejpam-6266	135	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	135	5	,	,	PUNCT
ejpam-6266	135	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	135	7	,	,	PUNCT
ejpam-6266	135	8	σ	σ	NOUN
ejpam-6266	135	9	,	,	PUNCT
ejpam-6266	135	10	‖|d|σ−1ut(t	‖|d|σ−1ut(t	PROPN
ejpam-6266	135	11	,	,	PUNCT
ejpam-6266	135	12	·	·	PUNCT
ejpam-6266	135	13	)	)	PUNCT
ejpam-6266	135	14	‖l2	‖l2	X
ejpam-6266	135	15	.	.	PUNCT
ejpam-6266	136	1	(	(	PUNCT
ejpam-6266	136	2	1	1	NUM
ejpam-6266	136	3	+	+	NUM
ejpam-6266	136	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	136	5	,	,	PUNCT
ejpam-6266	136	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	136	7	,	,	PUNCT
ejpam-6266	136	8	σ	σ	PROPN
ejpam-6266	136	9	.	.	PUNCT
ejpam-6266	137	1	the	the	DET
ejpam-6266	137	2	second	second	ADJ
ejpam-6266	137	3	result	result	NOUN
ejpam-6266	137	4	we	we	PRON
ejpam-6266	137	5	have	have	VERB
ejpam-6266	137	6	is	be	AUX
ejpam-6266	137	7	theorem	theorem	VERB
ejpam-6266	137	8	4	4	NUM
ejpam-6266	137	9	.	.	PUNCT
ejpam-6266	138	1	let	let	VERB
ejpam-6266	138	2	us	we	PRON
ejpam-6266	138	3	assume	assume	VERB
ejpam-6266	138	4	n	n	PRON
ejpam-6266	138	5	≥	≥	NUM
ejpam-6266	138	6	3	3	NUM
ejpam-6266	138	7	,	,	PUNCT
ejpam-6266	138	8	σ	σ	PROPN
ejpam-6266	138	9	∈	∈	PROPN
ejpam-6266	138	10	(	(	PUNCT
ejpam-6266	138	11	1	1	NUM
ejpam-6266	138	12	,	,	PUNCT
ejpam-6266	138	13	n2	n2	NOUN
ejpam-6266	138	14	)	)	PUNCT
ejpam-6266	138	15	,	,	PUNCT
ejpam-6266	138	16	γ	γ	PROPN
ejpam-6266	138	17	∈	∈	PROPN
ejpam-6266	138	18	(	(	PUNCT
ejpam-6266	138	19	0	0	NUM
ejpam-6266	138	20	,	,	PUNCT
ejpam-6266	138	21	1	1	NUM
ejpam-6266	138	22	)	)	PUNCT
ejpam-6266	138	23	and	and	CCONJ
ejpam-6266	138	24	m	m	PROPN
ejpam-6266	138	25	∈	∈	PROPN
ejpam-6266	139	1	[	[	X
ejpam-6266	139	2	1	1	NUM
ejpam-6266	139	3	,	,	PUNCT
ejpam-6266	139	4	2	2	NUM
ejpam-6266	139	5	)	)	PUNCT
ejpam-6266	139	6	such	such	ADJ
ejpam-6266	139	7	that	that	SCONJ
ejpam-6266	139	8	n	n	PROPN
ejpam-6266	139	9	2	2	NUM
ejpam-6266	139	10	(	(	PUNCT
ejpam-6266	139	11	1	1	NUM
ejpam-6266	139	12	m	m	NOUN
ejpam-6266	139	13	−	−	NUM
ejpam-6266	139	14	1	1	NUM
ejpam-6266	139	15	2	2	NUM
ejpam-6266	139	16	)	)	PUNCT
ejpam-6266	139	17	≥	≥	NOUN
ejpam-6266	139	18	1	1	NUM
ejpam-6266	139	19	,	,	PUNCT
ejpam-6266	139	20	(	(	PUNCT
ejpam-6266	139	21	27	27	NUM
ejpam-6266	139	22	)	)	PUNCT
ejpam-6266	139	23	and	and	CCONJ
ejpam-6266	139	24	p	p	NOUN
ejpam-6266	139	25	satisfies	satisfy	VERB
ejpam-6266	139	26	the	the	DET
ejpam-6266	139	27	condition	condition	NOUN
ejpam-6266	139	28	max	max	PROPN
ejpam-6266	139	29	{	{	PUNCT
ejpam-6266	139	30	dσe	dσe	PROPN
ejpam-6266	139	31	;	;	PUNCT
ejpam-6266	139	32	pγ	pγ	PRON
ejpam-6266	139	33	,	,	PUNCT
ejpam-6266	139	34	m(n	m(n	PROPN
ejpam-6266	139	35	)	)	PUNCT
ejpam-6266	139	36	}	}	PUNCT
ejpam-6266	140	1	<	<	X
ejpam-6266	140	2	p	p	X
ejpam-6266	140	3	≤	≤	NUM
ejpam-6266	140	4	pgn	pgn	NOUN
ejpam-6266	140	5	:	:	PUNCT
ejpam-6266	140	6	=	=	SYM
ejpam-6266	140	7	n	n	PRON
ejpam-6266	140	8	n−	n−	PROPN
ejpam-6266	140	9	2	2	NUM
ejpam-6266	140	10	,	,	PUNCT
ejpam-6266	140	11	(	(	PUNCT
ejpam-6266	140	12	28	28	NUM
ejpam-6266	140	13	)	)	PUNCT
ejpam-6266	140	14	t.	t.	PROPN
ejpam-6266	140	15	hadj	hadj	PROPN
ejpam-6266	140	16	kaddour	kaddour	PROPN
ejpam-6266	140	17	et	et	PROPN
ejpam-6266	140	18	al	al	PROPN
ejpam-6266	140	19	.	.	PUNCT
ejpam-6266	140	20	/	/	SYM
ejpam-6266	140	21	eur	eur	PROPN
ejpam-6266	140	22	.	.	PUNCT
ejpam-6266	141	1	j.	j.	PROPN
ejpam-6266	141	2	pure	pure	PROPN
ejpam-6266	141	3	appl	appl	PROPN
ejpam-6266	141	4	.	.	PROPN
ejpam-6266	141	5	math	math	PROPN
ejpam-6266	141	6	,	,	PUNCT
ejpam-6266	141	7	18	18	NUM
ejpam-6266	141	8	(	(	PUNCT
ejpam-6266	141	9	4	4	NUM
ejpam-6266	141	10	)	)	PUNCT
ejpam-6266	141	11	(	(	PUNCT
ejpam-6266	141	12	2025	2025	NUM
ejpam-6266	141	13	)	)	PUNCT
ejpam-6266	141	14	,	,	PUNCT
ejpam-6266	141	15	6266	6266	NUM
ejpam-6266	141	16	8	8	NUM
ejpam-6266	141	17	of	of	ADP
ejpam-6266	141	18	24	24	NUM
ejpam-6266	141	19	then	then	ADV
ejpam-6266	142	1	,	,	PUNCT
ejpam-6266	142	2	there	there	PRON
ejpam-6266	142	3	exists	exist	VERB
ejpam-6266	142	4	a	a	DET
ejpam-6266	142	5	positive	positive	ADJ
ejpam-6266	142	6	constant	constant	ADJ
ejpam-6266	142	7	ε0	ε0	NOUN
ejpam-6266	142	8	such	such	ADJ
ejpam-6266	142	9	that	that	PRON
ejpam-6266	142	10	for	for	ADP
ejpam-6266	142	11	any	any	DET
ejpam-6266	142	12	initial	initial	ADJ
ejpam-6266	142	13	data	datum	NOUN
ejpam-6266	142	14	(	(	PUNCT
ejpam-6266	142	15	u0	u0	ADJ
ejpam-6266	142	16	,	,	PUNCT
ejpam-6266	142	17	u1	u1	NOUN
ejpam-6266	142	18	)	)	PUNCT
ejpam-6266	142	19	∈	∈	PROPN
ejpam-6266	142	20	am	be	AUX
ejpam-6266	142	21	,	,	PUNCT
ejpam-6266	142	22	σ(rn)satisfying	σ(rn)satisfye	VERB
ejpam-6266	142	23	‖(u0	‖(u0	PROPN
ejpam-6266	142	24	,	,	PUNCT
ejpam-6266	142	25	u1)‖am	u1)‖am	PROPN
ejpam-6266	142	26	,	,	PUNCT
ejpam-6266	142	27	σ	σ	PROPN
ejpam-6266	142	28	≤	≤	X
ejpam-6266	142	29	ε	ε	PROPN
ejpam-6266	142	30	for	for	ADP
ejpam-6266	142	31	all	all	DET
ejpam-6266	142	32	ε	ε	PROPN
ejpam-6266	142	33	≤	≤	ADJ
ejpam-6266	142	34	ε0	ε0	PROPN
ejpam-6266	142	35	,	,	PUNCT
ejpam-6266	142	36	there	there	PRON
ejpam-6266	142	37	is	be	VERB
ejpam-6266	142	38	a	a	DET
ejpam-6266	142	39	uniquely	uniquely	ADV
ejpam-6266	142	40	determined	determined	ADJ
ejpam-6266	142	41	global	global	ADJ
ejpam-6266	142	42	(	(	PUNCT
ejpam-6266	142	43	in	in	ADP
ejpam-6266	142	44	time	time	NOUN
ejpam-6266	142	45	)	)	PUNCT
ejpam-6266	142	46	energy	energy	NOUN
ejpam-6266	142	47	solution	solution	NOUN
ejpam-6266	142	48	u	u	NOUN
ejpam-6266	142	49	∈	∈	PROPN
ejpam-6266	142	50	c	c	X
ejpam-6266	142	51	(	(	PUNCT
ejpam-6266	142	52	[	[	X
ejpam-6266	142	53	0,∞),hσ	0,∞),hσ	NUM
ejpam-6266	142	54	)	)	PUNCT
ejpam-6266	142	55	∩	∩	ADJ
ejpam-6266	142	56	c1	c1	NOUN
ejpam-6266	142	57	(	(	PUNCT
ejpam-6266	142	58	[	[	X
ejpam-6266	142	59	0,∞),hσ−1	0,∞),hσ−1	PROPN
ejpam-6266	142	60	)	)	PUNCT
ejpam-6266	142	61	to	to	ADP
ejpam-6266	142	62	the	the	DET
ejpam-6266	142	63	cauchy	cauchy	ADJ
ejpam-6266	142	64	problem	problem	NOUN
ejpam-6266	142	65	(	(	PUNCT
ejpam-6266	142	66	6	6	NUM
ejpam-6266	142	67	)	)	PUNCT
ejpam-6266	142	68	.	.	PUNCT
ejpam-6266	143	1	moreover	moreover	ADV
ejpam-6266	143	2	,	,	PUNCT
ejpam-6266	143	3	the	the	DET
ejpam-6266	143	4	solution	solution	NOUN
ejpam-6266	143	5	satisfies	satisfy	VERB
ejpam-6266	143	6	the	the	DET
ejpam-6266	143	7	following	follow	VERB
ejpam-6266	143	8	estimates	estimate	NOUN
ejpam-6266	143	9	:	:	PUNCT
ejpam-6266	143	10	‖u(t	‖u(t	NUM
ejpam-6266	143	11	,	,	PUNCT
ejpam-6266	143	12	·	·	PUNCT
ejpam-6266	143	13	)	)	PUNCT
ejpam-6266	143	14	‖l2	‖l2	VERB
ejpam-6266	143	15	.	.	PUNCT
ejpam-6266	144	1	{	{	PUNCT
ejpam-6266	144	2	(	(	PUNCT
ejpam-6266	144	3	1	1	NUM
ejpam-6266	144	4	+	+	NUM
ejpam-6266	144	5	t)−γ	t)−γ	PRON
ejpam-6266	144	6	log(2	log(2	NOUN
ejpam-6266	144	7	+	+	CCONJ
ejpam-6266	144	8	t)‖(u0	t)‖(u0	NOUN
ejpam-6266	144	9	,	,	PUNCT
ejpam-6266	144	10	u1)‖am	u1)‖am	PROPN
ejpam-6266	144	11	,	,	PUNCT
ejpam-6266	144	12	σ	σ	PROPN
ejpam-6266	144	13	if	if	SCONJ
ejpam-6266	144	14	n	n	PRON
ejpam-6266	144	15	≥	≥	NOUN
ejpam-6266	144	16	4	4	NUM
ejpam-6266	144	17	and	and	CCONJ
ejpam-6266	144	18	m	m	PROPN
ejpam-6266	144	19	=	=	NOUN
ejpam-6266	144	20	2n	2n	NUM
ejpam-6266	144	21	n+4	n+4	NUM
ejpam-6266	144	22	,	,	PUNCT
ejpam-6266	144	23	(	(	PUNCT
ejpam-6266	144	24	1	1	NUM
ejpam-6266	144	25	+	+	NUM
ejpam-6266	144	26	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	144	27	,	,	PUNCT
ejpam-6266	144	28	u1)‖am	u1)‖am	PROPN
ejpam-6266	144	29	,	,	PUNCT
ejpam-6266	144	30	σ	σ	PROPN
ejpam-6266	144	31	else	else	ADV
ejpam-6266	144	32	,	,	PUNCT
ejpam-6266	144	33	‖|d|σu(t	‖|d|σu(t	PROPN
ejpam-6266	144	34	,	,	PUNCT
ejpam-6266	144	35	·	·	PUNCT
ejpam-6266	144	36	)	)	PUNCT
ejpam-6266	144	37	‖l2	‖l2	X
ejpam-6266	144	38	.	.	PUNCT
ejpam-6266	145	1	(	(	PUNCT
ejpam-6266	145	2	1	1	NUM
ejpam-6266	145	3	+	+	NUM
ejpam-6266	145	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	145	5	,	,	PUNCT
ejpam-6266	145	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	145	7	,	,	PUNCT
ejpam-6266	145	8	σ	σ	PROPN
ejpam-6266	145	9	,	,	PUNCT
ejpam-6266	145	10	‖ut(t	‖ut(t	PROPN
ejpam-6266	145	11	,	,	PUNCT
ejpam-6266	145	12	·	·	PUNCT
ejpam-6266	145	13	)	)	PUNCT
ejpam-6266	145	14	‖l2	‖l2	X
ejpam-6266	145	15	.	.	PUNCT
ejpam-6266	146	1	(	(	PUNCT
ejpam-6266	146	2	1	1	NUM
ejpam-6266	146	3	+	+	NUM
ejpam-6266	146	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	146	5	,	,	PUNCT
ejpam-6266	146	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	146	7	,	,	PUNCT
ejpam-6266	146	8	σ	σ	NOUN
ejpam-6266	146	9	,	,	PUNCT
ejpam-6266	146	10	‖|d|σ−1ut(t	‖|d|σ−1ut(t	PROPN
ejpam-6266	146	11	,	,	PUNCT
ejpam-6266	146	12	·	·	PUNCT
ejpam-6266	146	13	)	)	PUNCT
ejpam-6266	146	14	‖l2	‖l2	X
ejpam-6266	146	15	.	.	PUNCT
ejpam-6266	147	1	(	(	PUNCT
ejpam-6266	147	2	1	1	NUM
ejpam-6266	147	3	+	+	NUM
ejpam-6266	147	4	t)−γ‖(u0	t)−γ‖(u0	PROPN
ejpam-6266	147	5	,	,	PUNCT
ejpam-6266	147	6	u1)‖am	u1)‖am	PROPN
ejpam-6266	147	7	,	,	PUNCT
ejpam-6266	147	8	σ	σ	PROPN
ejpam-6266	147	9	.	.	PUNCT
ejpam-6266	148	1	4	4	X
ejpam-6266	148	2	.	.	X
ejpam-6266	148	3	proof	proof	NOUN
ejpam-6266	148	4	of	of	ADP
ejpam-6266	148	5	the	the	DET
ejpam-6266	148	6	results	result	NOUN
ejpam-6266	148	7	4.1	4.1	NUM
ejpam-6266	148	8	.	.	PUNCT
ejpam-6266	149	1	proof	proof	NOUN
ejpam-6266	149	2	of	of	ADP
ejpam-6266	149	3	theorems	theorem	NOUN
ejpam-6266	149	4	1	1	NUM
ejpam-6266	149	5	and	and	CCONJ
ejpam-6266	149	6	2	2	NUM
ejpam-6266	149	7	4.1.1	4.1.1	NUM
ejpam-6266	149	8	.	.	PUNCT
ejpam-6266	150	1	proof	proof	NOUN
ejpam-6266	150	2	of	of	ADP
ejpam-6266	150	3	theorem	theorem	ADJ
ejpam-6266	150	4	1	1	NUM
ejpam-6266	150	5	let	let	VERB
ejpam-6266	150	6	us	we	PRON
ejpam-6266	150	7	introduce	introduce	VERB
ejpam-6266	150	8	,	,	PUNCT
ejpam-6266	150	9	for	for	ADP
ejpam-6266	150	10	t	t	PROPN
ejpam-6266	150	11	>	>	X
ejpam-6266	150	12	0	0	PROPN
ejpam-6266	150	13	,	,	PUNCT
ejpam-6266	150	14	the	the	DET
ejpam-6266	150	15	space	space	NOUN
ejpam-6266	150	16	of	of	ADP
ejpam-6266	150	17	energy	energy	NOUN
ejpam-6266	150	18	solutions	solution	NOUN
ejpam-6266	150	19	x(t	x(t	PROPN
ejpam-6266	150	20	)	)	PUNCT
ejpam-6266	151	1	=	=	PUNCT
ejpam-6266	152	1	c	c	NOUN
ejpam-6266	152	2	(	(	PUNCT
ejpam-6266	152	3	[	[	X
ejpam-6266	152	4	0	0	NUM
ejpam-6266	152	5	,	,	PUNCT
ejpam-6266	152	6	t	t	X
ejpam-6266	152	7	]	]	PUNCT
ejpam-6266	152	8	,	,	PUNCT
ejpam-6266	152	9	h1(r	h1(r	NOUN
ejpam-6266	152	10	)	)	PUNCT
ejpam-6266	152	11	)	)	PUNCT
ejpam-6266	152	12	∩	∩	PROPN
ejpam-6266	152	13	c1	c1	NOUN
ejpam-6266	152	14	(	(	PUNCT
ejpam-6266	152	15	[	[	X
ejpam-6266	152	16	0	0	NUM
ejpam-6266	152	17	,	,	PUNCT
ejpam-6266	152	18	t	t	X
ejpam-6266	152	19	]	]	PUNCT
ejpam-6266	152	20	,	,	PUNCT
ejpam-6266	152	21	l2(r	l2(r	PROPN
ejpam-6266	152	22	)	)	PUNCT
ejpam-6266	152	23	)	)	PUNCT
ejpam-6266	152	24	(	(	PUNCT
ejpam-6266	152	25	29	29	NUM
ejpam-6266	152	26	)	)	PUNCT
ejpam-6266	152	27	with	with	ADP
ejpam-6266	152	28	the	the	DET
ejpam-6266	152	29	norm	norm	NOUN
ejpam-6266	152	30	‖u‖x(t	‖u‖x(t	PROPN
ejpam-6266	152	31	)	)	PUNCT
ejpam-6266	152	32	=	=	SYM
ejpam-6266	152	33	sup	sup	NOUN
ejpam-6266	152	34	0≤t≤t	0≤t≤t	NUM
ejpam-6266	152	35	{	{	PUNCT
ejpam-6266	152	36	(	(	PUNCT
ejpam-6266	152	37	1	1	NUM
ejpam-6266	152	38	+	+	NUM
ejpam-6266	152	39	t	t	PROPN
ejpam-6266	152	40	)	)	PUNCT
ejpam-6266	152	41	n	n	PRON
ejpam-6266	152	42	4	4	NUM
ejpam-6266	152	43	+	+	NOUN
ejpam-6266	152	44	γ−1‖u(t	γ−1‖u(t	PROPN
ejpam-6266	152	45	,	,	PUNCT
ejpam-6266	152	46	·	·	PUNCT
ejpam-6266	152	47	)	)	PUNCT
ejpam-6266	152	48	‖l2	‖l2	VERB
ejpam-6266	152	49	+	+	CCONJ
ejpam-6266	152	50	`	`	PUNCT
ejpam-6266	152	51	n(t	n(t	PROPN
ejpam-6266	152	52	)	)	PUNCT
ejpam-6266	152	53	−1(1	−1(1	ADJ
ejpam-6266	152	54	+	+	CCONJ
ejpam-6266	152	55	t)γ‖∇u(t	t)γ‖∇u(t	PROPN
ejpam-6266	152	56	,	,	PUNCT
ejpam-6266	152	57	·	·	PUNCT
ejpam-6266	152	58	)	)	PUNCT
ejpam-6266	152	59	‖l2	‖l2	VERB
ejpam-6266	152	60	+	+	ADJ
ejpam-6266	152	61	(	(	PUNCT
ejpam-6266	152	62	1	1	NUM
ejpam-6266	152	63	+	+	NUM
ejpam-6266	152	64	t)γ‖ut(t	t)γ‖ut(t	NOUN
ejpam-6266	152	65	,	,	PUNCT
ejpam-6266	152	66	·	·	PUNCT
ejpam-6266	152	67	)	)	PUNCT
ejpam-6266	153	1	‖l2	‖l2	VERB
ejpam-6266	153	2	+	+	PUNCT
ejpam-6266	153	3	(	(	PUNCT
ejpam-6266	153	4	1	1	NUM
ejpam-6266	153	5	+	+	CCONJ
ejpam-6266	153	6	t)γ‖∇ut(t	t)γ‖∇ut(t	PROPN
ejpam-6266	153	7	,	,	PUNCT
ejpam-6266	153	8	·	·	PUNCT
ejpam-6266	153	9	)	)	PUNCT
ejpam-6266	153	10	‖l2	‖l2	VERB
ejpam-6266	153	11	}	}	PUNCT
ejpam-6266	153	12	,	,	PUNCT
ejpam-6266	153	13	(	(	PUNCT
ejpam-6266	153	14	30	30	NUM
ejpam-6266	153	15	)	)	PUNCT
ejpam-6266	153	16	where	where	SCONJ
ejpam-6266	153	17	`	`	PUNCT
ejpam-6266	153	18	n(t	n(t	PROPN
ejpam-6266	153	19	)	)	PUNCT
ejpam-6266	153	20	=	=	PRON
ejpam-6266	153	21	{	{	PUNCT
ejpam-6266	153	22	(	(	PUNCT
ejpam-6266	153	23	1	1	NUM
ejpam-6266	153	24	+	+	NUM
ejpam-6266	153	25	t	t	NOUN
ejpam-6266	153	26	)	)	PUNCT
ejpam-6266	153	27	1	1	NUM
ejpam-6266	153	28	4	4	NUM
ejpam-6266	153	29	if	if	SCONJ
ejpam-6266	153	30	n	n	NOUN
ejpam-6266	153	31	=	=	SYM
ejpam-6266	153	32	1	1	NUM
ejpam-6266	153	33	,	,	PUNCT
ejpam-6266	153	34	log(2	log(2	NOUN
ejpam-6266	153	35	+	+	CCONJ
ejpam-6266	153	36	t	t	X
ejpam-6266	153	37	)	)	PUNCT
ejpam-6266	153	38	if	if	SCONJ
ejpam-6266	153	39	n	n	NOUN
ejpam-6266	153	40	=	=	SYM
ejpam-6266	153	41	2	2	X
ejpam-6266	153	42	.	.	PUNCT
ejpam-6266	153	43	(	(	PUNCT
ejpam-6266	153	44	31	31	NUM
ejpam-6266	153	45	)	)	PUNCT
ejpam-6266	153	46	first	first	ADV
ejpam-6266	153	47	,	,	PUNCT
ejpam-6266	153	48	let	let	VERB
ejpam-6266	153	49	us	we	PRON
ejpam-6266	153	50	prove	prove	VERB
ejpam-6266	153	51	the	the	DET
ejpam-6266	153	52	inequality	inequality	NOUN
ejpam-6266	153	53	(	(	PUNCT
ejpam-6266	153	54	15	15	NUM
ejpam-6266	153	55	)	)	PUNCT
ejpam-6266	153	56	.	.	PUNCT
ejpam-6266	154	1	the	the	DET
ejpam-6266	154	2	inequality	inequality	NOUN
ejpam-6266	154	3	‖ulin‖x(t	‖ulin‖x(t	X
ejpam-6266	154	4	)	)	PUNCT
ejpam-6266	154	5	.	.	PUNCT
ejpam-6266	155	1	‖(u0	‖(u0	PROPN
ejpam-6266	155	2	,	,	PUNCT
ejpam-6266	155	3	u1)‖a1,1	u1)‖a1,1	PROPN
ejpam-6266	155	4	is	be	AUX
ejpam-6266	155	5	an	an	DET
ejpam-6266	155	6	immediate	immediate	ADJ
ejpam-6266	155	7	consequence	consequence	NOUN
ejpam-6266	155	8	of	of	ADP
ejpam-6266	155	9	proposition	proposition	NOUN
ejpam-6266	155	10	1	1	NUM
ejpam-6266	155	11	and	and	CCONJ
ejpam-6266	155	12	corollary	corollary	ADJ
ejpam-6266	155	13	1	1	NUM
ejpam-6266	155	14	for	for	ADP
ejpam-6266	155	15	τ	τ	PROPN
ejpam-6266	155	16	=	=	SYM
ejpam-6266	155	17	0	0	PROPN
ejpam-6266	155	18	and	and	CCONJ
ejpam-6266	155	19	h(0	h(0	PROPN
ejpam-6266	155	20	,	,	PUNCT
ejpam-6266	155	21	u(x	u(x	NOUN
ejpam-6266	155	22	)	)	PUNCT
ejpam-6266	155	23	)	)	PUNCT
ejpam-6266	156	1	=	=	PUNCT
ejpam-6266	156	2	u1(x	u1(x	NOUN
ejpam-6266	156	3	)	)	PUNCT
ejpam-6266	156	4	.	.	PUNCT
ejpam-6266	157	1	it	it	PRON
ejpam-6266	157	2	remains	remain	VERB
ejpam-6266	157	3	to	to	PART
ejpam-6266	157	4	show	show	VERB
ejpam-6266	157	5	the	the	DET
ejpam-6266	157	6	inequality	inequality	NOUN
ejpam-6266	157	7	‖unl‖x(t	‖unl‖x(t	PRON
ejpam-6266	157	8	)	)	PUNCT
ejpam-6266	157	9	.	.	PUNCT
ejpam-6266	158	1	‖u‖px(t	‖u‖px(t	PROPN
ejpam-6266	158	2	)	)	PUNCT
ejpam-6266	158	3	.	.	PUNCT
ejpam-6266	159	1	(	(	PUNCT
ejpam-6266	159	2	32	32	X
ejpam-6266	159	3	)	)	PUNCT
ejpam-6266	159	4	taking	take	VERB
ejpam-6266	159	5	into	into	ADP
ejpam-6266	159	6	account	account	NOUN
ejpam-6266	159	7	the	the	DET
ejpam-6266	159	8	results	result	NOUN
ejpam-6266	159	9	of	of	ADP
ejpam-6266	159	10	corollary	corollary	ADJ
ejpam-6266	159	11	1	1	NUM
ejpam-6266	159	12	we	we	PRON
ejpam-6266	159	13	have	have	VERB
ejpam-6266	159	14	‖unl(t	‖unl(t	NOUN
ejpam-6266	159	15	,	,	PUNCT
ejpam-6266	159	16	·	·	PUNCT
ejpam-6266	159	17	)	)	PUNCT
ejpam-6266	159	18	‖l2	‖l2	VERB
ejpam-6266	159	19	.	.	PUNCT
ejpam-6266	160	1	∫	∫	PROPN
ejpam-6266	160	2	t	t	PROPN
ejpam-6266	160	3	0	0	NUM
ejpam-6266	161	1	(	(	PUNCT
ejpam-6266	161	2	1	1	NUM
ejpam-6266	161	3	+	+	CCONJ
ejpam-6266	161	4	t−	t−	PROPN
ejpam-6266	161	5	τ)−	τ)−	PROPN
ejpam-6266	161	6	n	n	CCONJ
ejpam-6266	161	7	4	4	NUM
ejpam-6266	161	8	∫	∫	NOUN
ejpam-6266	161	9	τ	τ	X
ejpam-6266	161	10	0	0	NUM
ejpam-6266	161	11	(	(	PUNCT
ejpam-6266	161	12	τ	τ	PROPN
ejpam-6266	161	13	−	−	PROPN
ejpam-6266	161	14	s)−γ‖|ut(s	s)−γ‖|ut(s	PROPN
ejpam-6266	161	15	,	,	PUNCT
ejpam-6266	161	16	·	·	PUNCT
ejpam-6266	161	17	)	)	PUNCT
ejpam-6266	161	18	|p‖l1∩l2	|p‖l1∩l2	NOUN
ejpam-6266	161	19	dsdτ	dsdτ	NOUN
ejpam-6266	161	20	.	.	PUNCT
ejpam-6266	162	1	(	(	PUNCT
ejpam-6266	162	2	33	33	NUM
ejpam-6266	162	3	)	)	PUNCT
ejpam-6266	162	4	t.	t.	PROPN
ejpam-6266	162	5	hadj	hadj	PROPN
ejpam-6266	162	6	kaddour	kaddour	PROPN
ejpam-6266	162	7	et	et	PROPN
ejpam-6266	162	8	al	al	PROPN
ejpam-6266	162	9	.	.	PUNCT
ejpam-6266	162	10	/	/	SYM
ejpam-6266	162	11	eur	eur	PROPN
ejpam-6266	162	12	.	.	PUNCT
ejpam-6266	163	1	j.	j.	PROPN
ejpam-6266	163	2	pure	pure	PROPN
ejpam-6266	163	3	appl	appl	PROPN
ejpam-6266	163	4	.	.	PROPN
ejpam-6266	163	5	math	math	PROPN
ejpam-6266	163	6	,	,	PUNCT
ejpam-6266	163	7	18	18	NUM
ejpam-6266	163	8	(	(	PUNCT
ejpam-6266	163	9	4	4	NUM
ejpam-6266	163	10	)	)	PUNCT
ejpam-6266	163	11	(	(	PUNCT
ejpam-6266	163	12	2025	2025	NUM
ejpam-6266	163	13	)	)	PUNCT
ejpam-6266	163	14	,	,	PUNCT
ejpam-6266	163	15	6266	6266	NUM
ejpam-6266	163	16	9	9	NUM
ejpam-6266	163	17	of	of	ADP
ejpam-6266	163	18	24	24	NUM
ejpam-6266	163	19	since	since	SCONJ
ejpam-6266	163	20	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	163	21	,	,	PUNCT
ejpam-6266	163	22	·	·	PUNCT
ejpam-6266	163	23	)	)	PUNCT
ejpam-6266	163	24	|p‖l1∩l2	|p‖l1∩l2	NOUN
ejpam-6266	163	25	=	=	SYM
ejpam-6266	163	26	‖ut(s	‖ut(s	PROPN
ejpam-6266	163	27	,	,	PUNCT
ejpam-6266	163	28	·	·	PUNCT
ejpam-6266	163	29	)	)	PUNCT
ejpam-6266	163	30	‖plp∩l2p	‖plp∩l2p	ADV
ejpam-6266	163	31	=	=	SYM
ejpam-6266	163	32	‖ut(s	‖ut(s	PROPN
ejpam-6266	163	33	,	,	PUNCT
ejpam-6266	163	34	·	·	PUNCT
ejpam-6266	163	35	)	)	PUNCT
ejpam-6266	163	36	‖plp	‖plp	X
ejpam-6266	163	37	+	+	ADJ
ejpam-6266	163	38	‖ut(s	‖ut(s	X
ejpam-6266	163	39	,	,	PUNCT
ejpam-6266	163	40	·	·	PUNCT
ejpam-6266	163	41	)	)	PUNCT
ejpam-6266	164	1	‖pl2p	‖pl2p	PROPN
ejpam-6266	164	2	,	,	PUNCT
ejpam-6266	164	3	then	then	ADV
ejpam-6266	164	4	,	,	PUNCT
ejpam-6266	164	5	it	it	PRON
ejpam-6266	164	6	is	be	AUX
ejpam-6266	164	7	obvious	obvious	ADJ
ejpam-6266	164	8	that	that	SCONJ
ejpam-6266	164	9	one	one	PRON
ejpam-6266	164	10	has	have	VERB
ejpam-6266	164	11	to	to	PART
ejpam-6266	164	12	estimate	estimate	VERB
ejpam-6266	164	13	the	the	DET
ejpam-6266	164	14	norms	norm	NOUN
ejpam-6266	164	15	:	:	PUNCT
ejpam-6266	164	16	‖|ut(s	‖|ut(s	NUM
ejpam-6266	164	17	,	,	PUNCT
ejpam-6266	164	18	·	·	PUNCT
ejpam-6266	164	19	)	)	PUNCT
ejpam-6266	164	20	‖plp	‖plp	NOUN
ejpam-6266	164	21	and	and	CCONJ
ejpam-6266	164	22	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	164	23	,	,	PUNCT
ejpam-6266	164	24	·	·	PUNCT
ejpam-6266	164	25	)	)	PUNCT
ejpam-6266	164	26	‖pl2p	‖pl2p	PROPN
ejpam-6266	164	27	.	.	PUNCT
ejpam-6266	165	1	for	for	ADP
ejpam-6266	165	2	this	this	DET
ejpam-6266	165	3	purpose	purpose	NOUN
ejpam-6266	165	4	,	,	PUNCT
ejpam-6266	165	5	we	we	PRON
ejpam-6266	165	6	apply	apply	VERB
ejpam-6266	165	7	the	the	DET
ejpam-6266	165	8	classical	classical	ADJ
ejpam-6266	165	9	gagliardo	gagliardo	NOUN
ejpam-6266	165	10	-	-	PUNCT
ejpam-6266	165	11	nirenberg	nirenberg	NOUN
ejpam-6266	165	12	inequality	inequality	NOUN
ejpam-6266	165	13	(	(	PUNCT
ejpam-6266	165	14	107	107	NUM
ejpam-6266	165	15	)	)	PUNCT
ejpam-6266	165	16	.	.	PUNCT
ejpam-6266	166	1	in	in	ADP
ejpam-6266	166	2	this	this	DET
ejpam-6266	166	3	way	way	NOUN
ejpam-6266	166	4	we	we	PRON
ejpam-6266	166	5	obtain	obtain	VERB
ejpam-6266	166	6	for	for	ADP
ejpam-6266	166	7	j	j	PROPN
ejpam-6266	166	8	=	=	SYM
ejpam-6266	166	9	1	1	NUM
ejpam-6266	166	10	,	,	PUNCT
ejpam-6266	166	11	2	2	NUM
ejpam-6266	166	12	the	the	DET
ejpam-6266	166	13	chain	chain	NOUN
ejpam-6266	166	14	of	of	ADP
ejpam-6266	166	15	inequalities	inequality	NOUN
ejpam-6266	166	16	‖ut(s	‖ut(s	PUNCT
ejpam-6266	166	17	,	,	PUNCT
ejpam-6266	166	18	·	·	PUNCT
ejpam-6266	166	19	)	)	PUNCT
ejpam-6266	166	20	‖pljp	‖pljp	NOUN
ejpam-6266	166	21	.	.	PUNCT
ejpam-6266	167	1	‖ut(s	‖ut(s	PUNCT
ejpam-6266	167	2	,	,	PUNCT
ejpam-6266	167	3	·	·	PUNCT
ejpam-6266	167	4	)	)	PUNCT
ejpam-6266	167	5	‖	‖	PROPN
ejpam-6266	168	1	p(1−θj(p	p(1−θj(p	PROPN
ejpam-6266	168	2	)	)	PUNCT
ejpam-6266	168	3	)	)	PUNCT
ejpam-6266	168	4	l2	l2	NOUN
ejpam-6266	168	5	‖∇ut(s	‖∇ut(s	PROPN
ejpam-6266	168	6	,	,	PUNCT
ejpam-6266	168	7	·	·	PUNCT
ejpam-6266	168	8	)	)	PUNCT
ejpam-6266	168	9	‖	‖	PROPN
ejpam-6266	168	10	pθj(p	pθj(p	PROPN
ejpam-6266	168	11	)	)	PUNCT
ejpam-6266	168	12	l2	l2	NOUN
ejpam-6266	168	13	.	.	PUNCT
ejpam-6266	169	1	(	(	PUNCT
ejpam-6266	169	2	1	1	NUM
ejpam-6266	169	3	+	+	NUM
ejpam-6266	169	4	s)−γp‖u‖px(t	s)−γp‖u‖px(t	PROPN
ejpam-6266	169	5	)	)	PUNCT
ejpam-6266	169	6	.	.	PUNCT
ejpam-6266	170	1	(	(	PUNCT
ejpam-6266	170	2	1	1	X
ejpam-6266	170	3	+	+	CCONJ
ejpam-6266	170	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	170	5	)	)	PUNCT
ejpam-6266	170	6	,	,	PUNCT
ejpam-6266	170	7	(	(	PUNCT
ejpam-6266	170	8	34	34	NUM
ejpam-6266	170	9	)	)	PUNCT
ejpam-6266	170	10	where	where	SCONJ
ejpam-6266	170	11	θj(p	θj(p	NOUN
ejpam-6266	170	12	)	)	PUNCT
ejpam-6266	170	13	=	=	SYM
ejpam-6266	171	1	n	n	CCONJ
ejpam-6266	171	2	(	(	PUNCT
ejpam-6266	171	3	1	1	NUM
ejpam-6266	171	4	2	2	NUM
ejpam-6266	171	5	−	−	NUM
ejpam-6266	171	6	1	1	NUM
ejpam-6266	171	7	jp	jp	NOUN
ejpam-6266	171	8	)	)	PUNCT
ejpam-6266	171	9	,	,	PUNCT
ejpam-6266	171	10	(	(	PUNCT
ejpam-6266	171	11	35	35	NUM
ejpam-6266	171	12	)	)	PUNCT
ejpam-6266	171	13	θj(p	θj(p	PROPN
ejpam-6266	171	14	)	)	PUNCT
ejpam-6266	171	15	∈	∈	PROPN
ejpam-6266	172	1	[	[	X
ejpam-6266	172	2	0	0	NUM
ejpam-6266	172	3	,	,	PUNCT
ejpam-6266	172	4	1	1	NUM
ejpam-6266	172	5	]	]	PUNCT
ejpam-6266	173	1	if	if	SCONJ
ejpam-6266	173	2	and	and	CCONJ
ejpam-6266	173	3	only	only	ADV
ejpam-6266	173	4	if	if	SCONJ
ejpam-6266	173	5	p	p	NOUN
ejpam-6266	173	6	≥	≥	PUNCT
ejpam-6266	173	7	2	2	NUM
ejpam-6266	173	8	since	since	SCONJ
ejpam-6266	173	9	n	n	ADV
ejpam-6266	173	10	≤	≤	NOUN
ejpam-6266	173	11	2	2	NUM
ejpam-6266	173	12	,	,	PUNCT
ejpam-6266	173	13	and	and	CCONJ
ejpam-6266	173	14	β	β	X
ejpam-6266	173	15	=	=	SYM
ejpam-6266	173	16	γp	γp	PROPN
ejpam-6266	173	17	.	.	PUNCT
ejpam-6266	174	1	(	(	PUNCT
ejpam-6266	174	2	36	36	NUM
ejpam-6266	174	3	)	)	PUNCT
ejpam-6266	174	4	taking	take	VERB
ejpam-6266	174	5	j	j	PROPN
ejpam-6266	174	6	=	=	SYM
ejpam-6266	174	7	1	1	NUM
ejpam-6266	174	8	and	and	CCONJ
ejpam-6266	174	9	j	j	NOUN
ejpam-6266	174	10	=	=	SYM
ejpam-6266	174	11	2	2	NUM
ejpam-6266	174	12	in	in	ADP
ejpam-6266	174	13	(	(	PUNCT
ejpam-6266	174	14	34	34	NUM
ejpam-6266	174	15	)	)	PUNCT
ejpam-6266	174	16	,	,	PUNCT
ejpam-6266	174	17	respectively	respectively	ADV
ejpam-6266	174	18	,	,	PUNCT
ejpam-6266	174	19	we	we	PRON
ejpam-6266	174	20	find	find	VERB
ejpam-6266	174	21	‖u(s	‖u(	NOUN
ejpam-6266	174	22	,	,	PUNCT
ejpam-6266	174	23	·	·	PUNCT
ejpam-6266	174	24	)	)	PUNCT
ejpam-6266	174	25	‖p	‖p	PROPN
ejpam-6266	175	1	lp∩l2p	lp∩l2p	PROPN
ejpam-6266	175	2	.	.	PUNCT
ejpam-6266	176	1	(	(	PUNCT
ejpam-6266	176	2	1	1	NUM
ejpam-6266	176	3	+	+	CCONJ
ejpam-6266	176	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	176	5	)	)	PUNCT
ejpam-6266	176	6	.	.	PUNCT
ejpam-6266	177	1	(	(	PUNCT
ejpam-6266	177	2	37	37	NUM
ejpam-6266	177	3	)	)	PUNCT
ejpam-6266	177	4	noting	note	VERB
ejpam-6266	177	5	that	that	SCONJ
ejpam-6266	177	6	β	β	NOUN
ejpam-6266	177	7	>	>	X
ejpam-6266	177	8	1	1	NUM
ejpam-6266	177	9	if	if	SCONJ
ejpam-6266	177	10	and	and	CCONJ
ejpam-6266	177	11	only	only	ADV
ejpam-6266	177	12	if	if	SCONJ
ejpam-6266	177	13	p	p	X
ejpam-6266	177	14	>	>	X
ejpam-6266	177	15	1	1	NUM
ejpam-6266	177	16	γ	γ	X
ejpam-6266	177	17	.	.	PUNCT
ejpam-6266	178	1	including	include	VERB
ejpam-6266	178	2	(	(	PUNCT
ejpam-6266	178	3	37	37	NUM
ejpam-6266	178	4	)	)	PUNCT
ejpam-6266	178	5	in	in	ADP
ejpam-6266	178	6	(	(	PUNCT
ejpam-6266	178	7	33	33	NUM
ejpam-6266	178	8	)	)	PUNCT
ejpam-6266	178	9	we	we	PRON
ejpam-6266	178	10	find	find	VERB
ejpam-6266	178	11	‖unl(t	‖unl(t	NOUN
ejpam-6266	178	12	,	,	PUNCT
ejpam-6266	178	13	·	·	PUNCT
ejpam-6266	178	14	)	)	PUNCT
ejpam-6266	178	15	‖l2	‖l2	VERB
ejpam-6266	178	16	.	.	PUNCT
ejpam-6266	179	1	j	j	PROPN
ejpam-6266	179	2	(	(	PUNCT
ejpam-6266	179	3	0,0	0,0	NUM
ejpam-6266	179	4	)	)	PUNCT
ejpam-6266	179	5	n	n	CCONJ
ejpam-6266	179	6	(	(	PUNCT
ejpam-6266	179	7	t)‖u‖px(t	t)‖u‖px(t	PROPN
ejpam-6266	179	8	)	)	PUNCT
ejpam-6266	179	9	,	,	PUNCT
ejpam-6266	179	10	(	(	PUNCT
ejpam-6266	179	11	38	38	NUM
ejpam-6266	179	12	)	)	PUNCT
ejpam-6266	179	13	where	where	SCONJ
ejpam-6266	179	14	j	j	PROPN
ejpam-6266	179	15	(	(	PUNCT
ejpam-6266	179	16	0,0	0,0	NUM
ejpam-6266	179	17	)	)	PUNCT
ejpam-6266	179	18	n	n	CCONJ
ejpam-6266	179	19	(	(	PUNCT
ejpam-6266	179	20	t	t	NOUN
ejpam-6266	179	21	)	)	PUNCT
ejpam-6266	179	22	is	be	AUX
ejpam-6266	179	23	defined	define	VERB
ejpam-6266	179	24	by	by	ADP
ejpam-6266	179	25	(	(	PUNCT
ejpam-6266	179	26	18	18	NUM
ejpam-6266	179	27	)	)	PUNCT
ejpam-6266	179	28	(	(	PUNCT
ejpam-6266	179	29	case	case	NOUN
ejpam-6266	179	30	:	:	PUNCT
ejpam-6266	179	31	k	k	PROPN
ejpam-6266	179	32	=	=	PUNCT
ejpam-6266	179	33	j	j	PROPN
ejpam-6266	179	34	=	=	NOUN
ejpam-6266	179	35	0	0	NUM
ejpam-6266	179	36	)	)	PUNCT
ejpam-6266	179	37	.	.	PUNCT
ejpam-6266	180	1	since	since	SCONJ
ejpam-6266	180	2	β	β	X
ejpam-6266	180	3	>	>	X
ejpam-6266	180	4	1	1	NUM
ejpam-6266	180	5	we	we	PRON
ejpam-6266	180	6	estimate	estimate	VERB
ejpam-6266	180	7	j	j	PROPN
ejpam-6266	180	8	(	(	PUNCT
ejpam-6266	180	9	0,0	0,0	NUM
ejpam-6266	180	10	)	)	PUNCT
ejpam-6266	180	11	n	n	CCONJ
ejpam-6266	180	12	(	(	PUNCT
ejpam-6266	180	13	t	t	PROPN
ejpam-6266	180	14	)	)	PUNCT
ejpam-6266	180	15	by	by	ADP
ejpam-6266	180	16	using	use	VERB
ejpam-6266	180	17	lemma	lemma	PROPN
ejpam-6266	180	18	1	1	NUM
ejpam-6266	180	19	as	as	SCONJ
ejpam-6266	180	20	follows	follow	VERB
ejpam-6266	180	21	:	:	PUNCT
ejpam-6266	180	22	j	j	PROPN
ejpam-6266	180	23	(	(	PUNCT
ejpam-6266	180	24	0,0	0,0	NUM
ejpam-6266	180	25	)	)	PUNCT
ejpam-6266	180	26	n	n	PROPN
ejpam-6266	180	27	(	(	PUNCT
ejpam-6266	180	28	t	t	PROPN
ejpam-6266	180	29	)	)	PUNCT
ejpam-6266	180	30	.	.	PUNCT
ejpam-6266	181	1	(	(	PUNCT
ejpam-6266	181	2	1	1	X
ejpam-6266	181	3	+	+	X
ejpam-6266	181	4	t)−	t)−	PROPN
ejpam-6266	181	5	n	n	CCONJ
ejpam-6266	181	6	4	4	NUM
ejpam-6266	181	7	+1−γ	+1−γ	NOUN
ejpam-6266	181	8	.	.	PUNCT
ejpam-6266	182	1	(	(	PUNCT
ejpam-6266	182	2	39	39	NUM
ejpam-6266	182	3	)	)	PUNCT
ejpam-6266	182	4	then	then	ADV
ejpam-6266	182	5	,	,	PUNCT
ejpam-6266	182	6	introducing	introduce	VERB
ejpam-6266	182	7	the	the	DET
ejpam-6266	182	8	estimate	estimate	NOUN
ejpam-6266	182	9	(	(	PUNCT
ejpam-6266	182	10	39	39	NUM
ejpam-6266	182	11	)	)	PUNCT
ejpam-6266	182	12	into	into	ADP
ejpam-6266	182	13	(	(	PUNCT
ejpam-6266	182	14	38	38	NUM
ejpam-6266	182	15	)	)	PUNCT
ejpam-6266	182	16	we	we	PRON
ejpam-6266	182	17	find	find	VERB
ejpam-6266	182	18	‖unl(t	‖unl(t	NOUN
ejpam-6266	182	19	,	,	PUNCT
ejpam-6266	182	20	·	·	PUNCT
ejpam-6266	182	21	)	)	PUNCT
ejpam-6266	182	22	‖l2	‖l2	X
ejpam-6266	182	23	.	.	PUNCT
ejpam-6266	183	1	(	(	PUNCT
ejpam-6266	183	2	1	1	X
ejpam-6266	183	3	+	+	X
ejpam-6266	183	4	t)−	t)−	PROPN
ejpam-6266	183	5	n	n	PRON
ejpam-6266	183	6	4	4	NUM
ejpam-6266	183	7	+1−γ‖u‖px(t	+1−γ‖u‖px(t	PROPN
ejpam-6266	183	8	)	)	PUNCT
ejpam-6266	183	9	.	.	PUNCT
ejpam-6266	184	1	(	(	PUNCT
ejpam-6266	184	2	40	40	NUM
ejpam-6266	184	3	)	)	PUNCT
ejpam-6266	184	4	now	now	ADV
ejpam-6266	184	5	we	we	PRON
ejpam-6266	184	6	deal	deal	VERB
ejpam-6266	184	7	with	with	ADP
ejpam-6266	184	8	‖∂j	‖∂j	NOUN
ejpam-6266	184	9	t∇kunl(t	t∇kunl(t	PROPN
ejpam-6266	184	10	,	,	PUNCT
ejpam-6266	184	11	·	·	PUNCT
ejpam-6266	184	12	)	)	PUNCT
ejpam-6266	184	13	‖l2	‖l2	VERB
ejpam-6266	184	14	for	for	ADP
ejpam-6266	184	15	all	all	DET
ejpam-6266	184	16	k	k	PROPN
ejpam-6266	184	17	,	,	PUNCT
ejpam-6266	184	18	j	j	PROPN
ejpam-6266	184	19	∈	∈	PROPN
ejpam-6266	184	20	n	n	PRON
ejpam-6266	184	21	such	such	ADJ
ejpam-6266	184	22	that	that	SCONJ
ejpam-6266	184	23	1	1	NUM
ejpam-6266	184	24	≤	≤	NUM
ejpam-6266	184	25	k+	k+	NOUN
ejpam-6266	185	1	j	j	PROPN
ejpam-6266	185	2	≤	≤	ADV
ejpam-6266	185	3	2	2	NUM
ejpam-6266	185	4	.	.	PUNCT
ejpam-6266	185	5	again	again	ADV
ejpam-6266	185	6	,	,	PUNCT
ejpam-6266	185	7	taking	take	VERB
ejpam-6266	185	8	into	into	ADP
ejpam-6266	185	9	account	account	NOUN
ejpam-6266	185	10	the	the	DET
ejpam-6266	185	11	results	result	NOUN
ejpam-6266	185	12	of	of	ADP
ejpam-6266	185	13	corollary	corollary	ADJ
ejpam-6266	185	14	1	1	NUM
ejpam-6266	185	15	we	we	PRON
ejpam-6266	185	16	have	have	VERB
ejpam-6266	185	17	the	the	DET
ejpam-6266	185	18	estimate	estimate	NOUN
ejpam-6266	185	19	‖∂j	‖∂j	NOUN
ejpam-6266	185	20	t∇kunl(t	t∇kunl(t	PROPN
ejpam-6266	185	21	,	,	PUNCT
ejpam-6266	185	22	·	·	PUNCT
ejpam-6266	185	23	)	)	PUNCT
ejpam-6266	185	24	‖l2	‖l2	VERB
ejpam-6266	185	25	.	.	PUNCT
ejpam-6266	186	1	∫	∫	PROPN
ejpam-6266	186	2	t	t	PROPN
ejpam-6266	186	3	0	0	NUM
ejpam-6266	187	1	(	(	PUNCT
ejpam-6266	187	2	1	1	NUM
ejpam-6266	187	3	+	+	CCONJ
ejpam-6266	187	4	t−	t−	PROPN
ejpam-6266	187	5	τ)−	τ)−	PROPN
ejpam-6266	187	6	n	n	CCONJ
ejpam-6266	187	7	4	4	NUM
ejpam-6266	187	8	−	−	NOUN
ejpam-6266	187	9	k	k	SYM
ejpam-6266	187	10	2	2	NUM
ejpam-6266	187	11	−j	−j	NOUN
ejpam-6266	187	12	∫	∫	PROPN
ejpam-6266	187	13	τ	τ	X
ejpam-6266	187	14	0	0	NUM
ejpam-6266	187	15	(	(	PUNCT
ejpam-6266	187	16	τ	τ	PROPN
ejpam-6266	187	17	−	−	PROPN
ejpam-6266	187	18	s)−γ‖|ut(s	s)−γ‖|ut(s	PROPN
ejpam-6266	187	19	,	,	PUNCT
ejpam-6266	187	20	·	·	PUNCT
ejpam-6266	187	21	)	)	PUNCT
ejpam-6266	187	22	|p‖l1∩l2	|p‖l1∩l2	NOUN
ejpam-6266	187	23	dsdτ	dsdτ	NOUN
ejpam-6266	187	24	.	.	PUNCT
ejpam-6266	188	1	using	use	VERB
ejpam-6266	188	2	the	the	DET
ejpam-6266	188	3	estimate	estimate	NOUN
ejpam-6266	188	4	(	(	PUNCT
ejpam-6266	188	5	37	37	NUM
ejpam-6266	188	6	)	)	PUNCT
ejpam-6266	188	7	we	we	PRON
ejpam-6266	188	8	get	get	VERB
ejpam-6266	188	9	‖∇k∂j	‖∇k∂j	PROPN
ejpam-6266	188	10	t	t	PROPN
ejpam-6266	188	11	u	u	PROPN
ejpam-6266	188	12	nl(t	nl(t	NOUN
ejpam-6266	188	13	,	,	PUNCT
ejpam-6266	188	14	·	·	PUNCT
ejpam-6266	188	15	)	)	PUNCT
ejpam-6266	188	16	‖l2	‖l2	VERB
ejpam-6266	188	17	.	.	PUNCT
ejpam-6266	189	1	j	j	PROPN
ejpam-6266	189	2	(	(	PUNCT
ejpam-6266	189	3	k	k	X
ejpam-6266	189	4	,	,	PUNCT
ejpam-6266	189	5	j	j	PROPN
ejpam-6266	189	6	)	)	PUNCT
ejpam-6266	189	7	n	n	PROPN
ejpam-6266	189	8	(	(	PUNCT
ejpam-6266	189	9	t)‖u‖px(t	t)‖u‖px(t	PROPN
ejpam-6266	189	10	)	)	PUNCT
ejpam-6266	189	11	,	,	PUNCT
ejpam-6266	189	12	(	(	PUNCT
ejpam-6266	189	13	41	41	NUM
ejpam-6266	189	14	)	)	PUNCT
ejpam-6266	189	15	t.	t.	NOUN
ejpam-6266	189	16	hadj	hadj	PROPN
ejpam-6266	189	17	kaddour	kaddour	PROPN
ejpam-6266	189	18	et	et	PROPN
ejpam-6266	189	19	al	al	PROPN
ejpam-6266	189	20	.	.	PUNCT
ejpam-6266	189	21	/	/	SYM
ejpam-6266	189	22	eur	eur	PROPN
ejpam-6266	189	23	.	.	PUNCT
ejpam-6266	190	1	j.	j.	PROPN
ejpam-6266	190	2	pure	pure	PROPN
ejpam-6266	190	3	appl	appl	PROPN
ejpam-6266	190	4	.	.	PROPN
ejpam-6266	190	5	math	math	PROPN
ejpam-6266	190	6	,	,	PUNCT
ejpam-6266	190	7	18	18	NUM
ejpam-6266	190	8	(	(	PUNCT
ejpam-6266	190	9	4	4	NUM
ejpam-6266	190	10	)	)	PUNCT
ejpam-6266	190	11	(	(	PUNCT
ejpam-6266	190	12	2025	2025	NUM
ejpam-6266	190	13	)	)	PUNCT
ejpam-6266	190	14	,	,	PUNCT
ejpam-6266	190	15	6266	6266	NUM
ejpam-6266	190	16	10	10	NUM
ejpam-6266	190	17	of	of	ADP
ejpam-6266	190	18	24	24	NUM
ejpam-6266	190	19	where	where	SCONJ
ejpam-6266	190	20	j	j	PROPN
ejpam-6266	190	21	(	(	PUNCT
ejpam-6266	190	22	k	k	PROPN
ejpam-6266	190	23	,	,	PUNCT
ejpam-6266	190	24	j	j	PROPN
ejpam-6266	190	25	)	)	PUNCT
ejpam-6266	190	26	n	n	PROPN
ejpam-6266	190	27	(	(	PUNCT
ejpam-6266	190	28	t	t	PROPN
ejpam-6266	190	29	)	)	PUNCT
ejpam-6266	190	30	is	be	AUX
ejpam-6266	190	31	defined	define	VERB
ejpam-6266	190	32	by	by	ADP
ejpam-6266	190	33	(	(	PUNCT
ejpam-6266	190	34	18	18	NUM
ejpam-6266	190	35	)	)	PUNCT
ejpam-6266	190	36	.	.	PUNCT
ejpam-6266	191	1	since	since	SCONJ
ejpam-6266	191	2	β	β	X
ejpam-6266	191	3	>	>	X
ejpam-6266	191	4	1	1	NUM
ejpam-6266	191	5	we	we	PRON
ejpam-6266	191	6	may	may	AUX
ejpam-6266	191	7	estimate	estimate	VERB
ejpam-6266	191	8	j	j	PROPN
ejpam-6266	191	9	(	(	PUNCT
ejpam-6266	191	10	k	k	X
ejpam-6266	191	11	,	,	PUNCT
ejpam-6266	191	12	j	j	PROPN
ejpam-6266	191	13	)	)	PUNCT
ejpam-6266	191	14	n	n	PROPN
ejpam-6266	191	15	(	(	PUNCT
ejpam-6266	191	16	t	t	PROPN
ejpam-6266	191	17	)	)	PUNCT
ejpam-6266	191	18	,	,	PUNCT
ejpam-6266	191	19	after	after	ADP
ejpam-6266	191	20	using	use	VERB
ejpam-6266	191	21	lemma	lemma	PROPN
ejpam-6266	191	22	1	1	NUM
ejpam-6266	191	23	as	as	SCONJ
ejpam-6266	191	24	follows	follow	VERB
ejpam-6266	191	25	:	:	PUNCT
ejpam-6266	191	26	j	j	PROPN
ejpam-6266	191	27	(	(	PUNCT
ejpam-6266	191	28	k	k	X
ejpam-6266	191	29	,	,	PUNCT
ejpam-6266	191	30	j	j	PROPN
ejpam-6266	191	31	)	)	PUNCT
ejpam-6266	191	32	n	n	PROPN
ejpam-6266	191	33	(	(	PUNCT
ejpam-6266	191	34	t	t	PROPN
ejpam-6266	191	35	)	)	PUNCT
ejpam-6266	191	36	.	.	PUNCT
ejpam-6266	192	1			PUNCT
ejpam-6266	192	2	(	(	PUNCT
ejpam-6266	192	3	1	1	NUM
ejpam-6266	192	4	+	+	NUM
ejpam-6266	192	5	t)−	t)−	PROPN
ejpam-6266	192	6	3	3	NUM
ejpam-6266	192	7	4	4	NUM
ejpam-6266	192	8	if	if	SCONJ
ejpam-6266	192	9	n	n	NOUN
ejpam-6266	192	10	=	=	SYM
ejpam-6266	192	11	k	k	NOUN
ejpam-6266	192	12	=	=	SYM
ejpam-6266	192	13	1	1	NUM
ejpam-6266	192	14	and	and	CCONJ
ejpam-6266	192	15	j	j	PROPN
ejpam-6266	192	16	=	=	SYM
ejpam-6266	192	17	0	0	PROPN
ejpam-6266	192	18	,	,	PUNCT
ejpam-6266	192	19	(	(	PUNCT
ejpam-6266	192	20	1	1	NUM
ejpam-6266	192	21	+	+	NUM
ejpam-6266	192	22	t)−γ	t)−γ	PRON
ejpam-6266	192	23	log(2	log(2	NOUN
ejpam-6266	192	24	+	+	CCONJ
ejpam-6266	192	25	t	t	X
ejpam-6266	192	26	)	)	PUNCT
ejpam-6266	192	27	if	if	SCONJ
ejpam-6266	192	28	n	n	NOUN
ejpam-6266	192	29	=	=	SYM
ejpam-6266	192	30	2	2	NUM
ejpam-6266	192	31	,	,	PUNCT
ejpam-6266	192	32	k	k	NOUN
ejpam-6266	192	33	=	=	SYM
ejpam-6266	192	34	1	1	NUM
ejpam-6266	192	35	and	and	CCONJ
ejpam-6266	192	36	j	j	PROPN
ejpam-6266	192	37	=	=	SYM
ejpam-6266	192	38	0	0	PROPN
ejpam-6266	192	39	,	,	PUNCT
ejpam-6266	192	40	(	(	PUNCT
ejpam-6266	192	41	1	1	NUM
ejpam-6266	192	42	+	+	SYM
ejpam-6266	192	43	t)−γ	t)−γ	PRON
ejpam-6266	192	44	if	if	SCONJ
ejpam-6266	192	45	n	n	NOUN
ejpam-6266	192	46	=	=	SYM
ejpam-6266	192	47	1	1	NUM
ejpam-6266	192	48	,	,	PUNCT
ejpam-6266	192	49	2	2	NUM
ejpam-6266	192	50	and	and	CCONJ
ejpam-6266	192	51	k	k	PROPN
ejpam-6266	192	52	+	+	PROPN
ejpam-6266	192	53	j	j	PROPN
ejpam-6266	192	54	≥	≥	NUM
ejpam-6266	192	55	1	1	NUM
ejpam-6266	192	56	.	.	PUNCT
ejpam-6266	192	57	(	(	PUNCT
ejpam-6266	192	58	42	42	X
ejpam-6266	192	59	)	)	PUNCT
ejpam-6266	192	60	putting	put	VERB
ejpam-6266	192	61	(	(	PUNCT
ejpam-6266	192	62	42	42	NUM
ejpam-6266	192	63	)	)	PUNCT
ejpam-6266	192	64	into	into	ADP
ejpam-6266	192	65	(	(	PUNCT
ejpam-6266	192	66	41	41	NUM
ejpam-6266	192	67	)	)	PUNCT
ejpam-6266	192	68	we	we	PRON
ejpam-6266	192	69	derive	derive	VERB
ejpam-6266	192	70	the	the	DET
ejpam-6266	192	71	estimates	estimate	NOUN
ejpam-6266	192	72	‖∇unl(t	‖∇unl(t	PROPN
ejpam-6266	192	73	,	,	PUNCT
ejpam-6266	192	74	·	·	PUNCT
ejpam-6266	192	75	)	)	PUNCT
ejpam-6266	192	76	‖l2	‖l2	VERB
ejpam-6266	192	77	.	.	PUNCT
ejpam-6266	193	1			PRON
ejpam-6266	193	2	(	(	PUNCT
ejpam-6266	193	3	1	1	X
ejpam-6266	193	4	+	+	CCONJ
ejpam-6266	193	5	t)−	t)−	PROPN
ejpam-6266	193	6	3	3	NUM
ejpam-6266	193	7	4	4	NUM
ejpam-6266	193	8	‖u‖px(t	‖u‖px(t	NOUN
ejpam-6266	193	9	)	)	PUNCT
ejpam-6266	193	10	if	if	SCONJ
ejpam-6266	193	11	n	n	NOUN
ejpam-6266	193	12	=	=	SYM
ejpam-6266	193	13	k	k	NOUN
ejpam-6266	193	14	=	=	SYM
ejpam-6266	193	15	1	1	NUM
ejpam-6266	193	16	and	and	CCONJ
ejpam-6266	193	17	j	j	PROPN
ejpam-6266	193	18	=	=	SYM
ejpam-6266	193	19	0	0	PROPN
ejpam-6266	193	20	,	,	PUNCT
ejpam-6266	193	21	(	(	PUNCT
ejpam-6266	193	22	1	1	NUM
ejpam-6266	193	23	+	+	NUM
ejpam-6266	193	24	t)−γ	t)−γ	PRON
ejpam-6266	193	25	log(2	log(2	NOUN
ejpam-6266	193	26	+	+	CCONJ
ejpam-6266	193	27	t)‖u‖px(t	t)‖u‖px(t	PROPN
ejpam-6266	193	28	)	)	PUNCT
ejpam-6266	193	29	if	if	SCONJ
ejpam-6266	193	30	n	n	NOUN
ejpam-6266	193	31	=	=	SYM
ejpam-6266	193	32	2	2	NUM
ejpam-6266	193	33	,	,	PUNCT
ejpam-6266	193	34	k	k	NOUN
ejpam-6266	193	35	=	=	SYM
ejpam-6266	193	36	1	1	NUM
ejpam-6266	193	37	and	and	CCONJ
ejpam-6266	193	38	j	j	PROPN
ejpam-6266	193	39	=	=	SYM
ejpam-6266	193	40	0	0	PROPN
ejpam-6266	193	41	,	,	PUNCT
ejpam-6266	193	42	(	(	PUNCT
ejpam-6266	193	43	1	1	NUM
ejpam-6266	193	44	+	+	NUM
ejpam-6266	193	45	t)−γ‖u‖px(t	t)−γ‖u‖px(t	PROPN
ejpam-6266	193	46	)	)	PUNCT
ejpam-6266	193	47	if	if	SCONJ
ejpam-6266	193	48	n	n	NOUN
ejpam-6266	193	49	=	=	SYM
ejpam-6266	193	50	1	1	NUM
ejpam-6266	193	51	,	,	PUNCT
ejpam-6266	193	52	2	2	NUM
ejpam-6266	193	53	and	and	CCONJ
ejpam-6266	193	54	1	1	NUM
ejpam-6266	193	55	≤	≤	NUM
ejpam-6266	193	56	k	k	PROPN
ejpam-6266	194	1	+	+	NUM
ejpam-6266	194	2	j	j	PROPN
ejpam-6266	194	3	≤	≤	ADV
ejpam-6266	194	4	2	2	NUM
ejpam-6266	194	5	.	.	PUNCT
ejpam-6266	194	6	(	(	PUNCT
ejpam-6266	194	7	43	43	NUM
ejpam-6266	194	8	)	)	PUNCT
ejpam-6266	194	9	then	then	ADV
ejpam-6266	194	10	,	,	PUNCT
ejpam-6266	194	11	the	the	DET
ejpam-6266	194	12	inequality	inequality	NOUN
ejpam-6266	194	13	(	(	PUNCT
ejpam-6266	194	14	32	32	NUM
ejpam-6266	194	15	)	)	PUNCT
ejpam-6266	194	16	is	be	AUX
ejpam-6266	194	17	concluded	conclude	VERB
ejpam-6266	194	18	from	from	ADP
ejpam-6266	194	19	(	(	PUNCT
ejpam-6266	194	20	43	43	NUM
ejpam-6266	194	21	)	)	PUNCT
ejpam-6266	194	22	,	,	PUNCT
ejpam-6266	194	23	(	(	PUNCT
ejpam-6266	194	24	40	40	NUM
ejpam-6266	194	25	)	)	PUNCT
ejpam-6266	194	26	and	and	CCONJ
ejpam-6266	194	27	the	the	DET
ejpam-6266	194	28	definition	definition	NOUN
ejpam-6266	194	29	(	(	PUNCT
ejpam-6266	194	30	30	30	NUM
ejpam-6266	194	31	)	)	PUNCT
ejpam-6266	194	32	of	of	ADP
ejpam-6266	194	33	the	the	DET
ejpam-6266	194	34	norm	norm	NOUN
ejpam-6266	194	35	in	in	ADP
ejpam-6266	194	36	x(t	x(t	PROPN
ejpam-6266	194	37	)	)	PUNCT
ejpam-6266	194	38	.	.	PUNCT
ejpam-6266	195	1	now	now	ADV
ejpam-6266	195	2	,	,	PUNCT
ejpam-6266	195	3	let	let	VERB
ejpam-6266	195	4	us	we	PRON
ejpam-6266	195	5	turn	turn	VERB
ejpam-6266	195	6	to	to	ADP
ejpam-6266	195	7	the	the	DET
ejpam-6266	195	8	inequality	inequality	NOUN
ejpam-6266	195	9	(	(	PUNCT
ejpam-6266	195	10	16	16	NUM
ejpam-6266	195	11	)	)	PUNCT
ejpam-6266	195	12	.	.	PUNCT
ejpam-6266	196	1	by	by	ADP
ejpam-6266	196	2	definition	definition	NOUN
ejpam-6266	196	3	of	of	ADP
ejpam-6266	196	4	the	the	DET
ejpam-6266	196	5	operator	operator	NOUN
ejpam-6266	196	6	n	n	NOUN
ejpam-6266	196	7	and	and	CCONJ
ejpam-6266	196	8	the	the	DET
ejpam-6266	196	9	results	result	NOUN
ejpam-6266	196	10	of	of	ADP
ejpam-6266	196	11	corollary	corollary	ADJ
ejpam-6266	196	12	1	1	NUM
ejpam-6266	196	13	,	,	PUNCT
ejpam-6266	196	14	we	we	PRON
ejpam-6266	196	15	have	have	VERB
ejpam-6266	196	16	‖(nu−nv)(t	‖(nu−nv)(t	PROPN
ejpam-6266	196	17	,	,	PUNCT
ejpam-6266	196	18	·	·	PUNCT
ejpam-6266	196	19	)	)	PUNCT
ejpam-6266	196	20	‖l2	‖l2	VERB
ejpam-6266	196	21	.	.	PUNCT
ejpam-6266	197	1	∫	∫	PROPN
ejpam-6266	197	2	t	t	PROPN
ejpam-6266	197	3	0	0	NUM
ejpam-6266	198	1	(	(	PUNCT
ejpam-6266	198	2	1	1	NUM
ejpam-6266	198	3	+	+	CCONJ
ejpam-6266	198	4	t−	t−	PROPN
ejpam-6266	198	5	τ)−	τ)−	PROPN
ejpam-6266	198	6	n	n	CCONJ
ejpam-6266	198	7	4	4	NUM
ejpam-6266	198	8	×	×	NOUN
ejpam-6266	198	9	∫	∫	PROPN
ejpam-6266	198	10	τ	τ	X
ejpam-6266	198	11	0	0	NUM
ejpam-6266	199	1	(	(	PUNCT
ejpam-6266	199	2	τ	τ	X
ejpam-6266	199	3	−	−	PROPN
ejpam-6266	199	4	s)−γ	s)−γ	PRON
ejpam-6266	199	5	∥∥|ut(s	∥∥|ut(s	PROPN
ejpam-6266	199	6	,	,	PUNCT
ejpam-6266	199	7	·	·	PUNCT
ejpam-6266	199	8	)	)	PUNCT
ejpam-6266	199	9	|p	|p	NOUN
ejpam-6266	199	10	−	−	ADP
ejpam-6266	199	11	|vt(s	|vt(s	PROPN
ejpam-6266	199	12	,	,	PUNCT
ejpam-6266	199	13	·	·	PUNCT
ejpam-6266	199	14	)	)	PUNCT
ejpam-6266	199	15	|p	|p	VERB
ejpam-6266	199	16	∥∥	∥∥	X
ejpam-6266	199	17	l1∩l2	l1∩l2	PROPN
ejpam-6266	199	18	dsdτ	dsdτ	PROPN
ejpam-6266	199	19	.	.	PUNCT
ejpam-6266	200	1	(	(	PUNCT
ejpam-6266	200	2	44	44	NUM
ejpam-6266	200	3	)	)	PUNCT
ejpam-6266	200	4	then	then	ADV
ejpam-6266	200	5	we	we	PRON
ejpam-6266	200	6	have	have	VERB
ejpam-6266	200	7	to	to	PART
ejpam-6266	200	8	estimate	estimate	VERB
ejpam-6266	200	9	‖|ut(s	‖|ut(s	PRON
ejpam-6266	200	10	,	,	PUNCT
ejpam-6266	200	11	·	·	PUNCT
ejpam-6266	200	12	)	)	PUNCT
ejpam-6266	200	13	|p	|p	NOUN
ejpam-6266	200	14	−	−	ADP
ejpam-6266	200	15	|vt(s	|vt(s	PROPN
ejpam-6266	200	16	,	,	PUNCT
ejpam-6266	200	17	·	·	PUNCT
ejpam-6266	200	18	)	)	PUNCT
ejpam-6266	200	19	|p‖l1	|p‖l1	NOUN
ejpam-6266	200	20	and	and	CCONJ
ejpam-6266	200	21	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	200	22	,	,	PUNCT
ejpam-6266	200	23	·	·	PUNCT
ejpam-6266	200	24	)	)	PUNCT
ejpam-6266	200	25	|p	|p	NOUN
ejpam-6266	200	26	−	−	ADP
ejpam-6266	200	27	|vt(s	|vt(s	PROPN
ejpam-6266	200	28	,	,	PUNCT
ejpam-6266	200	29	·	·	PUNCT
ejpam-6266	200	30	)	)	PUNCT
ejpam-6266	200	31	|p‖l2	|p‖l2	VERB
ejpam-6266	200	32	.	.	PUNCT
ejpam-6266	201	1	first	first	ADV
ejpam-6266	201	2	,	,	PUNCT
ejpam-6266	201	3	we	we	PRON
ejpam-6266	201	4	have	have	VERB
ejpam-6266	201	5	by	by	ADP
ejpam-6266	201	6	hölder	hölder	PROPN
ejpam-6266	201	7	’s	’s	PART
ejpam-6266	201	8	inequality	inequality	NOUN
ejpam-6266	201	9	for	for	ADP
ejpam-6266	201	10	j	j	PROPN
ejpam-6266	201	11	=	=	SYM
ejpam-6266	201	12	1	1	NUM
ejpam-6266	201	13	,	,	PUNCT
ejpam-6266	201	14	2	2	NUM
ejpam-6266	201	15	,	,	PUNCT
ejpam-6266	201	16	‖|ut|p	‖|ut|p	NOUN
ejpam-6266	201	17	−	−	PROPN
ejpam-6266	201	18	|vt|p‖lj	|vt|p‖lj	NOUN
ejpam-6266	201	19	.	.	PUNCT
ejpam-6266	202	1	‖ut	‖ut	PROPN
ejpam-6266	203	1	−	−	NUM
ejpam-6266	203	2	vt‖ljp	vt‖ljp	NOUN
ejpam-6266	203	3	(	(	PUNCT
ejpam-6266	203	4	‖ut‖p−1	‖ut‖p−1	CCONJ
ejpam-6266	203	5	ljp	ljp	NOUN
ejpam-6266	203	6	+	+	CCONJ
ejpam-6266	203	7	‖vt‖p−1	‖vt‖p−1	X
ejpam-6266	203	8	ljp	ljp	NOUN
ejpam-6266	203	9	)	)	PUNCT
ejpam-6266	203	10	.	.	PUNCT
ejpam-6266	204	1	(	(	PUNCT
ejpam-6266	204	2	45	45	NUM
ejpam-6266	204	3	)	)	PUNCT
ejpam-6266	204	4	then	then	ADV
ejpam-6266	204	5	,	,	PUNCT
ejpam-6266	204	6	the	the	DET
ejpam-6266	204	7	aim	aim	NOUN
ejpam-6266	204	8	is	be	AUX
ejpam-6266	204	9	to	to	PART
ejpam-6266	204	10	estimate	estimate	VERB
ejpam-6266	204	11	the	the	DET
ejpam-6266	204	12	following	follow	VERB
ejpam-6266	204	13	terms	term	NOUN
ejpam-6266	204	14	for	for	ADP
ejpam-6266	204	15	j	j	PROPN
ejpam-6266	204	16	=	=	SYM
ejpam-6266	204	17	1	1	NUM
ejpam-6266	204	18	and	and	CCONJ
ejpam-6266	204	19	j	j	NOUN
ejpam-6266	204	20	=	=	NOUN
ejpam-6266	204	21	2	2	NUM
ejpam-6266	204	22	:	:	PUNCT
ejpam-6266	204	23	‖ut	‖ut	PROPN
ejpam-6266	205	1	−	−	NUM
ejpam-6266	205	2	vt‖ljp	vt‖ljp	NOUN
ejpam-6266	205	3	,	,	PUNCT
ejpam-6266	205	4	‖ut‖p−1	‖ut‖p−1	NOUN
ejpam-6266	205	5	ljp	ljp	NOUN
ejpam-6266	205	6	and	and	CCONJ
ejpam-6266	205	7	‖vt‖p−1	‖vt‖p−1	NOUN
ejpam-6266	205	8	ljp	ljp	NOUN
ejpam-6266	205	9	.	.	PUNCT
ejpam-6266	206	1	let	let	VERB
ejpam-6266	206	2	us	we	PRON
ejpam-6266	206	3	begin	begin	VERB
ejpam-6266	206	4	with	with	ADP
ejpam-6266	206	5	the	the	DET
ejpam-6266	206	6	estimate	estimate	NOUN
ejpam-6266	206	7	of	of	ADP
ejpam-6266	206	8	the	the	DET
ejpam-6266	206	9	term	term	NOUN
ejpam-6266	206	10	‖ut(s	‖ut(s	PUNCT
ejpam-6266	206	11	,	,	PUNCT
ejpam-6266	206	12	·	·	PUNCT
ejpam-6266	206	13	)	)	PUNCT
ejpam-6266	206	14	−	−	NOUN
ejpam-6266	206	15	vt(s	vt(s	PROPN
ejpam-6266	206	16	,	,	PUNCT
ejpam-6266	206	17	·	·	PUNCT
ejpam-6266	206	18	)	)	PUNCT
ejpam-6266	206	19	‖ljp	‖ljp	NOUN
ejpam-6266	206	20	.	.	PUNCT
ejpam-6266	207	1	by	by	ADP
ejpam-6266	207	2	using	use	VERB
ejpam-6266	207	3	gagliardonirenberg	gagliardonirenberg	PROPN
ejpam-6266	207	4	inequality	inequality	NOUN
ejpam-6266	207	5	(	(	PUNCT
ejpam-6266	207	6	107	107	NUM
ejpam-6266	207	7	)	)	PUNCT
ejpam-6266	207	8	with	with	ADP
ejpam-6266	207	9	k	k	PROPN
ejpam-6266	207	10	=	=	SYM
ejpam-6266	207	11	1	1	NUM
ejpam-6266	207	12	and	and	CCONJ
ejpam-6266	207	13	q	q	NOUN
ejpam-6266	207	14	=	=	PUNCT
ejpam-6266	207	15	p	p	X
ejpam-6266	207	16	we	we	PRON
ejpam-6266	207	17	estimate	estimate	VERB
ejpam-6266	207	18	‖ut(s	‖ut(s	PUNCT
ejpam-6266	207	19	,	,	PUNCT
ejpam-6266	207	20	·	·	PUNCT
ejpam-6266	207	21	)	)	PUNCT
ejpam-6266	207	22	−	−	NOUN
ejpam-6266	207	23	vt(s	vt(s	PROPN
ejpam-6266	207	24	,	,	PUNCT
ejpam-6266	207	25	·	·	PUNCT
ejpam-6266	207	26	)	)	PUNCT
ejpam-6266	207	27	‖ljp	‖ljp	NOUN
ejpam-6266	207	28	.	.	PUNCT
ejpam-6266	208	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	208	2	,	,	PUNCT
ejpam-6266	208	3	·	·	PUNCT
ejpam-6266	208	4	)	)	PUNCT
ejpam-6266	209	1	−	−	NOUN
ejpam-6266	209	2	vt(s	vt(s	PROPN
ejpam-6266	209	3	,	,	PUNCT
ejpam-6266	209	4	·	·	PUNCT
ejpam-6266	209	5	)	)	PUNCT
ejpam-6266	209	6	‖	‖	PROPN
ejpam-6266	209	7	1−θj(p	1−θj(p	X
ejpam-6266	209	8	)	)	PUNCT
ejpam-6266	209	9	l2	l2	NOUN
ejpam-6266	209	10	∥∥|∇k(ut	∥∥|∇k(ut	ADJ
ejpam-6266	209	11	−	−	PROPN
ejpam-6266	209	12	vt)(s	vt)(s	PROPN
ejpam-6266	209	13	,	,	PUNCT
ejpam-6266	209	14	·	·	PUNCT
ejpam-6266	209	15	)	)	PUNCT
ejpam-6266	209	16	∥∥θj(p	∥∥θj(p	NOUN
ejpam-6266	209	17	)	)	PUNCT
ejpam-6266	209	18	l2	l2	NOUN
ejpam-6266	209	19	.	.	PUNCT
ejpam-6266	210	1	(	(	PUNCT
ejpam-6266	210	2	1	1	NUM
ejpam-6266	210	3	+	+	NUM
ejpam-6266	210	4	s)−γ(1−θj(p))(1	s)−γ(1−θj(p))(1	NOUN
ejpam-6266	211	1	+	+	CCONJ
ejpam-6266	211	2	s)−γθj(p)‖u−	s)−γθj(p)‖u−	PROPN
ejpam-6266	211	3	v‖x(t	v‖x(t	PROPN
ejpam-6266	211	4	)	)	PUNCT
ejpam-6266	211	5	.	.	PUNCT
ejpam-6266	212	1	(	(	PUNCT
ejpam-6266	212	2	1	1	NUM
ejpam-6266	212	3	+	+	CCONJ
ejpam-6266	212	4	s)−γ‖u−	s)−γ‖u−	PUNCT
ejpam-6266	212	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	212	6	)	)	PUNCT
ejpam-6266	212	7	,	,	PUNCT
ejpam-6266	212	8	(	(	PUNCT
ejpam-6266	212	9	46	46	NUM
ejpam-6266	212	10	)	)	PUNCT
ejpam-6266	212	11	where	where	SCONJ
ejpam-6266	212	12	θj(p	θj(p	VERB
ejpam-6266	212	13	)	)	PUNCT
ejpam-6266	212	14	is	be	AUX
ejpam-6266	212	15	defined	define	VERB
ejpam-6266	212	16	(	(	PUNCT
ejpam-6266	212	17	35	35	NUM
ejpam-6266	212	18	)	)	PUNCT
ejpam-6266	212	19	.	.	PUNCT
ejpam-6266	213	1	we	we	PRON
ejpam-6266	213	2	use	use	VERB
ejpam-6266	213	3	the	the	DET
ejpam-6266	213	4	same	same	ADJ
ejpam-6266	213	5	tools	tool	NOUN
ejpam-6266	213	6	to	to	PART
ejpam-6266	213	7	estimate	estimate	VERB
ejpam-6266	213	8	‖ut(s	‖ut(s	PRON
ejpam-6266	213	9	,	,	PUNCT
ejpam-6266	213	10	·	·	PUNCT
ejpam-6266	213	11	)	)	PUNCT
ejpam-6266	213	12	‖p−1	‖p−1	PUNCT
ejpam-6266	213	13	ljp	ljp	NOUN
ejpam-6266	213	14	.	.	PUNCT
ejpam-6266	214	1	we	we	PRON
ejpam-6266	214	2	get	get	VERB
ejpam-6266	214	3	‖ut(s	‖ut(s	NUM
ejpam-6266	214	4	,	,	PUNCT
ejpam-6266	214	5	·	·	PUNCT
ejpam-6266	214	6	)	)	PUNCT
ejpam-6266	214	7	‖p−1	‖p−1	PUNCT
ejpam-6266	214	8	ljp	ljp	NOUN
ejpam-6266	214	9	.	.	PUNCT
ejpam-6266	215	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	215	2	,	,	PUNCT
ejpam-6266	215	3	·	·	PUNCT
ejpam-6266	215	4	)	)	PUNCT
ejpam-6266	215	5	‖	‖	PROPN
ejpam-6266	215	6	(	(	PUNCT
ejpam-6266	215	7	p−1)(1−θj(p	p−1)(1−θj(p	NOUN
ejpam-6266	215	8	)	)	PUNCT
ejpam-6266	215	9	)	)	PUNCT
ejpam-6266	216	1	l2	l2	NOUN
ejpam-6266	216	2	‖∇ut(s	‖∇ut(s	PROPN
ejpam-6266	216	3	,	,	PUNCT
ejpam-6266	216	4	·	·	PUNCT
ejpam-6266	216	5	)	)	PUNCT
ejpam-6266	216	6	‖	‖	PROPN
ejpam-6266	216	7	(	(	PUNCT
ejpam-6266	216	8	p−1)θj(p	p−1)θj(p	PROPN
ejpam-6266	216	9	)	)	PUNCT
ejpam-6266	216	10	l2	l2	NOUN
ejpam-6266	216	11	t.	t.	PROPN
ejpam-6266	216	12	hadj	hadj	PROPN
ejpam-6266	216	13	kaddour	kaddour	PROPN
ejpam-6266	216	14	et	et	PROPN
ejpam-6266	216	15	al	al	PROPN
ejpam-6266	216	16	.	.	PUNCT
ejpam-6266	216	17	/	/	SYM
ejpam-6266	216	18	eur	eur	PROPN
ejpam-6266	216	19	.	.	PUNCT
ejpam-6266	217	1	j.	j.	PROPN
ejpam-6266	217	2	pure	pure	PROPN
ejpam-6266	217	3	appl	appl	PROPN
ejpam-6266	217	4	.	.	PROPN
ejpam-6266	217	5	math	math	PROPN
ejpam-6266	217	6	,	,	PUNCT
ejpam-6266	217	7	18	18	NUM
ejpam-6266	217	8	(	(	PUNCT
ejpam-6266	217	9	4	4	NUM
ejpam-6266	217	10	)	)	PUNCT
ejpam-6266	217	11	(	(	PUNCT
ejpam-6266	217	12	2025	2025	NUM
ejpam-6266	217	13	)	)	PUNCT
ejpam-6266	217	14	,	,	PUNCT
ejpam-6266	217	15	6266	6266	NUM
ejpam-6266	217	16	11	11	NUM
ejpam-6266	217	17	of	of	ADP
ejpam-6266	217	18	24	24	NUM
ejpam-6266	217	19	.	.	PUNCT
ejpam-6266	218	1	(	(	PUNCT
ejpam-6266	218	2	1	1	NUM
ejpam-6266	218	3	+	+	NUM
ejpam-6266	218	4	s)−γ(p−1)(1−θj(p))(1	s)−γ(p−1)(1−θj(p))(1	PRON
ejpam-6266	218	5	+	+	CCONJ
ejpam-6266	218	6	s)−γ(p−1)θj(p)‖u‖p−1	s)−γ(p−1)θj(p)‖u‖p−1	PRON
ejpam-6266	218	7	x(t	x(t	PROPN
ejpam-6266	218	8	)	)	PUNCT
ejpam-6266	218	9	.	.	PUNCT
ejpam-6266	219	1	(	(	PUNCT
ejpam-6266	219	2	1	1	NUM
ejpam-6266	219	3	+	+	NUM
ejpam-6266	219	4	s)−γ(p−1)‖u‖p−1	s)−γ(p−1)‖u‖p−1	PROPN
ejpam-6266	219	5	x(t	x(t	PROPN
ejpam-6266	219	6	)	)	PUNCT
ejpam-6266	219	7	.	.	PUNCT
ejpam-6266	220	1	(	(	PUNCT
ejpam-6266	220	2	47	47	NUM
ejpam-6266	220	3	)	)	PUNCT
ejpam-6266	220	4	in	in	ADP
ejpam-6266	220	5	the	the	DET
ejpam-6266	220	6	same	same	ADJ
ejpam-6266	220	7	way	way	NOUN
ejpam-6266	220	8	we	we	PRON
ejpam-6266	220	9	derive	derive	VERB
ejpam-6266	220	10	‖vt(s	‖vt(s	NUM
ejpam-6266	220	11	,	,	PUNCT
ejpam-6266	220	12	·	·	PUNCT
ejpam-6266	220	13	)	)	PUNCT
ejpam-6266	220	14	‖p−1	‖p−1	PUNCT
ejpam-6266	220	15	ljp	ljp	NOUN
ejpam-6266	220	16	.	.	PUNCT
ejpam-6266	221	1	(	(	PUNCT
ejpam-6266	221	2	1	1	NUM
ejpam-6266	221	3	+	+	CCONJ
ejpam-6266	221	4	s)−γ(p−1)‖v‖p−1	s)−γ(p−1)‖v‖p−1	NOUN
ejpam-6266	221	5	x(t	x(t	PROPN
ejpam-6266	221	6	)	)	PUNCT
ejpam-6266	221	7	.	.	PUNCT
ejpam-6266	222	1	(	(	PUNCT
ejpam-6266	222	2	48	48	NUM
ejpam-6266	222	3	)	)	PUNCT
ejpam-6266	222	4	finally	finally	ADV
ejpam-6266	222	5	,	,	PUNCT
ejpam-6266	222	6	by	by	ADP
ejpam-6266	222	7	(	(	PUNCT
ejpam-6266	222	8	48	48	NUM
ejpam-6266	222	9	)	)	PUNCT
ejpam-6266	222	10	,	,	PUNCT
ejpam-6266	222	11	(	(	PUNCT
ejpam-6266	222	12	47	47	NUM
ejpam-6266	222	13	)	)	PUNCT
ejpam-6266	222	14	and	and	CCONJ
ejpam-6266	222	15	(	(	PUNCT
ejpam-6266	222	16	46	46	NUM
ejpam-6266	222	17	)	)	PUNCT
ejpam-6266	222	18	we	we	PRON
ejpam-6266	222	19	get	get	VERB
ejpam-6266	222	20	from	from	ADP
ejpam-6266	222	21	(	(	PUNCT
ejpam-6266	222	22	45	45	NUM
ejpam-6266	222	23	)	)	PUNCT
ejpam-6266	222	24	,	,	PUNCT
ejpam-6266	222	25	for	for	ADP
ejpam-6266	222	26	j	j	PROPN
ejpam-6266	222	27	=	=	SYM
ejpam-6266	222	28	1	1	NUM
ejpam-6266	222	29	,	,	PUNCT
ejpam-6266	222	30	2	2	NUM
ejpam-6266	222	31	the	the	DET
ejpam-6266	222	32	estimates	estimate	NOUN
ejpam-6266	222	33	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	222	34	,	,	PUNCT
ejpam-6266	222	35	·	·	PUNCT
ejpam-6266	222	36	)	)	PUNCT
ejpam-6266	222	37	|p	|p	NOUN
ejpam-6266	222	38	−	−	ADP
ejpam-6266	222	39	|vt(s	|vt(s	PROPN
ejpam-6266	222	40	,	,	PUNCT
ejpam-6266	222	41	·	·	PUNCT
ejpam-6266	222	42	)	)	PUNCT
ejpam-6266	222	43	|p‖lj	|p‖lj	NOUN
ejpam-6266	222	44	.	.	PUNCT
ejpam-6266	223	1	(	(	PUNCT
ejpam-6266	223	2	1	1	NUM
ejpam-6266	223	3	+	+	NUM
ejpam-6266	223	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	223	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	223	6	)	)	PUNCT
ejpam-6266	223	7	(	(	PUNCT
ejpam-6266	223	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	223	9	x(t	x(t	PROPN
ejpam-6266	223	10	)	)	PUNCT
ejpam-6266	224	1	+	+	CCONJ
ejpam-6266	224	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	224	3	x(t	x(t	PROPN
ejpam-6266	224	4	)	)	PUNCT
ejpam-6266	224	5	)	)	PUNCT
ejpam-6266	224	6	,	,	PUNCT
ejpam-6266	224	7	(	(	PUNCT
ejpam-6266	224	8	49	49	NUM
ejpam-6266	224	9	)	)	PUNCT
ejpam-6266	224	10	where	where	SCONJ
ejpam-6266	224	11	β	β	PROPN
ejpam-6266	224	12	is	be	AUX
ejpam-6266	224	13	given	give	VERB
ejpam-6266	224	14	by	by	ADP
ejpam-6266	224	15	(	(	PUNCT
ejpam-6266	224	16	36	36	NUM
ejpam-6266	224	17	)	)	PUNCT
ejpam-6266	224	18	.	.	PUNCT
ejpam-6266	225	1	as	as	ADP
ejpam-6266	225	2	a	a	DET
ejpam-6266	225	3	consequence	consequence	NOUN
ejpam-6266	225	4	,	,	PUNCT
ejpam-6266	225	5	it	it	PRON
ejpam-6266	225	6	follows	follow	VERB
ejpam-6266	225	7	from	from	ADP
ejpam-6266	225	8	(	(	PUNCT
ejpam-6266	225	9	49	49	NUM
ejpam-6266	225	10	)	)	PUNCT
ejpam-6266	225	11	that	that	SCONJ
ejpam-6266	225	12	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	225	13	,	,	PUNCT
ejpam-6266	225	14	·	·	PUNCT
ejpam-6266	225	15	)	)	PUNCT
ejpam-6266	225	16	|p	|p	NOUN
ejpam-6266	225	17	−	−	ADP
ejpam-6266	225	18	|vt(s	|vt(s	PROPN
ejpam-6266	225	19	,	,	PUNCT
ejpam-6266	225	20	·	·	PUNCT
ejpam-6266	225	21	)	)	PUNCT
ejpam-6266	225	22	|p‖l1∩l2	|p‖l1∩l2	NOUN
ejpam-6266	225	23	.	.	PUNCT
ejpam-6266	226	1	(	(	PUNCT
ejpam-6266	226	2	1	1	NUM
ejpam-6266	226	3	+	+	NUM
ejpam-6266	226	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	226	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	226	6	)	)	PUNCT
ejpam-6266	226	7	(	(	PUNCT
ejpam-6266	226	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	226	9	x(t	x(t	PROPN
ejpam-6266	226	10	)	)	PUNCT
ejpam-6266	227	1	+	+	CCONJ
ejpam-6266	227	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	227	3	x(t	x(t	PROPN
ejpam-6266	227	4	)	)	PUNCT
ejpam-6266	227	5	)	)	PUNCT
ejpam-6266	227	6	.	.	PUNCT
ejpam-6266	228	1	(	(	PUNCT
ejpam-6266	228	2	50	50	X
ejpam-6266	228	3	)	)	PUNCT
ejpam-6266	228	4	plugging	plug	VERB
ejpam-6266	228	5	the	the	DET
ejpam-6266	228	6	estimate	estimate	NOUN
ejpam-6266	228	7	(	(	PUNCT
ejpam-6266	228	8	50	50	NUM
ejpam-6266	228	9	)	)	PUNCT
ejpam-6266	228	10	in	in	ADP
ejpam-6266	228	11	(	(	PUNCT
ejpam-6266	228	12	44	44	NUM
ejpam-6266	228	13	)	)	PUNCT
ejpam-6266	228	14	we	we	PRON
ejpam-6266	228	15	find	find	VERB
ejpam-6266	228	16	‖(nu−nv)(t	‖(nu−nv)(t	PRON
ejpam-6266	228	17	,	,	PUNCT
ejpam-6266	228	18	·	·	PUNCT
ejpam-6266	228	19	)	)	PUNCT
ejpam-6266	228	20	‖l2	‖l2	VERB
ejpam-6266	228	21	.	.	PUNCT
ejpam-6266	229	1	j	j	PROPN
ejpam-6266	229	2	(	(	PUNCT
ejpam-6266	229	3	0,0	0,0	NUM
ejpam-6266	229	4	)	)	PUNCT
ejpam-6266	229	5	n	n	CCONJ
ejpam-6266	229	6	(	(	PUNCT
ejpam-6266	229	7	t)‖u−	t)‖u−	NOUN
ejpam-6266	229	8	v‖x(t	v‖x(t	PROPN
ejpam-6266	229	9	)	)	PUNCT
ejpam-6266	229	10	(	(	PUNCT
ejpam-6266	229	11	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	229	12	x(t	x(t	PROPN
ejpam-6266	229	13	)	)	PUNCT
ejpam-6266	230	1	+	+	CCONJ
ejpam-6266	230	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	230	3	x(t	x(t	PROPN
ejpam-6266	230	4	)	)	PUNCT
ejpam-6266	230	5	)	)	PUNCT
ejpam-6266	230	6	,	,	PUNCT
ejpam-6266	230	7	where	where	SCONJ
ejpam-6266	230	8	j	j	PROPN
ejpam-6266	230	9	(	(	PUNCT
ejpam-6266	230	10	0,0	0,0	NUM
ejpam-6266	230	11	)	)	PUNCT
ejpam-6266	230	12	n	n	CCONJ
ejpam-6266	230	13	(	(	PUNCT
ejpam-6266	230	14	t	t	NOUN
ejpam-6266	230	15	)	)	PUNCT
ejpam-6266	230	16	is	be	AUX
ejpam-6266	230	17	defined	define	VERB
ejpam-6266	230	18	by	by	ADP
ejpam-6266	230	19	(	(	PUNCT
ejpam-6266	230	20	18	18	NUM
ejpam-6266	230	21	)	)	PUNCT
ejpam-6266	230	22	(	(	PUNCT
ejpam-6266	230	23	case	case	NOUN
ejpam-6266	230	24	:	:	PUNCT
ejpam-6266	231	1	k	k	PROPN
ejpam-6266	231	2	=	=	PUNCT
ejpam-6266	231	3	j	j	PROPN
ejpam-6266	231	4	=	=	NOUN
ejpam-6266	231	5	0	0	NUM
ejpam-6266	231	6	)	)	PUNCT
ejpam-6266	231	7	.	.	PUNCT
ejpam-6266	232	1	then	then	ADV
ejpam-6266	232	2	,	,	PUNCT
ejpam-6266	232	3	using	use	VERB
ejpam-6266	232	4	the	the	DET
ejpam-6266	232	5	estimate	estimate	NOUN
ejpam-6266	232	6	(	(	PUNCT
ejpam-6266	232	7	39	39	NUM
ejpam-6266	232	8	)	)	PUNCT
ejpam-6266	232	9	we	we	PRON
ejpam-6266	232	10	may	may	AUX
ejpam-6266	232	11	conclude	conclude	VERB
ejpam-6266	232	12	that	that	SCONJ
ejpam-6266	232	13	‖(nu−nv)(t	‖(nu−nv)(t	PROPN
ejpam-6266	232	14	,	,	PUNCT
ejpam-6266	232	15	·	·	PUNCT
ejpam-6266	232	16	)	)	PUNCT
ejpam-6266	232	17	‖l2	‖l2	X
ejpam-6266	232	18	.	.	PUNCT
ejpam-6266	233	1	(	(	PUNCT
ejpam-6266	233	2	1	1	X
ejpam-6266	233	3	+	+	X
ejpam-6266	233	4	t)−	t)−	PROPN
ejpam-6266	233	5	n	n	PRON
ejpam-6266	233	6	4	4	NUM
ejpam-6266	233	7	+1−γ‖u−	+1−γ‖u−	PRON
ejpam-6266	233	8	v‖x(t	v‖x(t	PROPN
ejpam-6266	233	9	)	)	PUNCT
ejpam-6266	233	10	(	(	PUNCT
ejpam-6266	233	11	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	233	12	x(t	x(t	PROPN
ejpam-6266	233	13	)	)	PUNCT
ejpam-6266	234	1	+	+	CCONJ
ejpam-6266	234	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	234	3	x(t	x(t	PROPN
ejpam-6266	234	4	)	)	PUNCT
ejpam-6266	234	5	)	)	PUNCT
ejpam-6266	234	6	.	.	PUNCT
ejpam-6266	235	1	(	(	PUNCT
ejpam-6266	235	2	51	51	NUM
ejpam-6266	235	3	)	)	PUNCT
ejpam-6266	235	4	now	now	ADV
ejpam-6266	235	5	,	,	PUNCT
ejpam-6266	235	6	let	let	VERB
ejpam-6266	235	7	us	we	PRON
ejpam-6266	235	8	turn	turn	VERB
ejpam-6266	235	9	to	to	PART
ejpam-6266	235	10	estimate	estimate	VERB
ejpam-6266	235	11	the	the	DET
ejpam-6266	235	12	term	term	NOUN
ejpam-6266	235	13	‖∂j	‖∂j	VERB
ejpam-6266	236	1	t∇k(nu−nv)(t	t∇k(nu−nv)(t	PROPN
ejpam-6266	236	2	,	,	PUNCT
ejpam-6266	236	3	·	·	PUNCT
ejpam-6266	236	4	)	)	PUNCT
ejpam-6266	237	1	‖l2	‖l2	VERB
ejpam-6266	237	2	for	for	ADP
ejpam-6266	237	3	1	1	NUM
ejpam-6266	237	4	≤	≤	NOUN
ejpam-6266	237	5	k	k	PROPN
ejpam-6266	238	1	+	+	NUM
ejpam-6266	238	2	j	j	PROPN
ejpam-6266	238	3	≤	≤	ADV
ejpam-6266	238	4	2	2	NUM
ejpam-6266	238	5	.	.	PUNCT
ejpam-6266	239	1	as	as	SCONJ
ejpam-6266	239	2	we	we	PRON
ejpam-6266	239	3	did	do	VERB
ejpam-6266	239	4	above	above	ADV
ejpam-6266	239	5	we	we	PRON
ejpam-6266	239	6	have	have	VERB
ejpam-6266	239	7	after	after	ADP
ejpam-6266	239	8	using	use	VERB
ejpam-6266	239	9	the	the	DET
ejpam-6266	239	10	results	result	NOUN
ejpam-6266	239	11	of	of	ADP
ejpam-6266	239	12	corollary	corollary	ADJ
ejpam-6266	239	13	2	2	NUM
ejpam-6266	239	14	we	we	PRON
ejpam-6266	239	15	have	have	AUX
ejpam-6266	239	16	‖∂j	‖∂j	VERB
ejpam-6266	239	17	t∇k(nu−nv)(t	t∇k(nu−nv)(t	ADJ
ejpam-6266	239	18	,	,	PUNCT
ejpam-6266	239	19	·	·	PUNCT
ejpam-6266	239	20	)	)	PUNCT
ejpam-6266	239	21	∥∥	∥∥	X
ejpam-6266	239	22	l2	l2	NOUN
ejpam-6266	239	23	.	.	PUNCT
ejpam-6266	240	1	∫	∫	PROPN
ejpam-6266	240	2	t	t	PROPN
ejpam-6266	240	3	0	0	NUM
ejpam-6266	241	1	(	(	PUNCT
ejpam-6266	241	2	1	1	NUM
ejpam-6266	241	3	+	+	CCONJ
ejpam-6266	241	4	t−	t−	PROPN
ejpam-6266	241	5	τ)−	τ)−	PROPN
ejpam-6266	241	6	n	n	CCONJ
ejpam-6266	241	7	4	4	NUM
ejpam-6266	241	8	−	−	NOUN
ejpam-6266	241	9	k	k	SYM
ejpam-6266	241	10	2	2	NUM
ejpam-6266	241	11	−j	−j	NOUN
ejpam-6266	241	12	×	×	PROPN
ejpam-6266	241	13	∫	∫	PROPN
ejpam-6266	241	14	τ	τ	X
ejpam-6266	241	15	0	0	NUM
ejpam-6266	242	1	(	(	PUNCT
ejpam-6266	242	2	τ	τ	PROPN
ejpam-6266	242	3	−	−	PROPN
ejpam-6266	242	4	s)−γ‖|ut(s	s)−γ‖|ut(s	PROPN
ejpam-6266	242	5	,	,	PUNCT
ejpam-6266	242	6	·	·	PUNCT
ejpam-6266	242	7	)	)	PUNCT
ejpam-6266	242	8	|p	|p	NOUN
ejpam-6266	242	9	−	−	ADP
ejpam-6266	242	10	vt(s	vt(s	PROPN
ejpam-6266	242	11	,	,	PUNCT
ejpam-6266	242	12	·	·	PUNCT
ejpam-6266	242	13	)	)	PUNCT
ejpam-6266	242	14	|p‖l1∩l2	|p‖l1∩l2	NOUN
ejpam-6266	242	15	dsdτ	dsdτ	NOUN
ejpam-6266	242	16	.	.	PUNCT
ejpam-6266	242	17	(	(	PUNCT
ejpam-6266	242	18	52	52	NUM
ejpam-6266	242	19	)	)	PUNCT
ejpam-6266	242	20	including	include	VERB
ejpam-6266	242	21	the	the	DET
ejpam-6266	242	22	estimate	estimate	NOUN
ejpam-6266	242	23	(	(	PUNCT
ejpam-6266	242	24	50	50	NUM
ejpam-6266	242	25	)	)	PUNCT
ejpam-6266	242	26	into	into	ADP
ejpam-6266	242	27	(	(	PUNCT
ejpam-6266	242	28	52	52	NUM
ejpam-6266	242	29	)	)	PUNCT
ejpam-6266	242	30	we	we	PRON
ejpam-6266	242	31	find∥∥∇k∂j	find∥∥∇k∂j	PROPN
ejpam-6266	242	32	t	t	PROPN
ejpam-6266	242	33	(	(	PUNCT
ejpam-6266	242	34	nu−nv)(t	nu−nv)(t	PROPN
ejpam-6266	242	35	,	,	PUNCT
ejpam-6266	242	36	·	·	PUNCT
ejpam-6266	242	37	)	)	PUNCT
ejpam-6266	242	38	∥∥	∥∥	PRON
ejpam-6266	242	39	l2	l2	NOUN
ejpam-6266	242	40	.	.	PUNCT
ejpam-6266	243	1	j	j	PROPN
ejpam-6266	243	2	(	(	PUNCT
ejpam-6266	243	3	k	k	X
ejpam-6266	243	4	,	,	PUNCT
ejpam-6266	243	5	j	j	PROPN
ejpam-6266	243	6	)	)	PUNCT
ejpam-6266	243	7	n	n	PROPN
ejpam-6266	243	8	(	(	PUNCT
ejpam-6266	243	9	t)‖u−	t)‖u−	NOUN
ejpam-6266	243	10	v‖x(t	v‖x(t	PROPN
ejpam-6266	243	11	)	)	PUNCT
ejpam-6266	243	12	(	(	PUNCT
ejpam-6266	243	13	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	243	14	x(t	x(t	PROPN
ejpam-6266	243	15	)	)	PUNCT
ejpam-6266	244	1	+	+	CCONJ
ejpam-6266	244	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	244	3	x(t	x(t	PROPN
ejpam-6266	244	4	)	)	PUNCT
ejpam-6266	244	5	)	)	PUNCT
ejpam-6266	244	6	,	,	PUNCT
ejpam-6266	244	7	(	(	PUNCT
ejpam-6266	244	8	53	53	NUM
ejpam-6266	244	9	)	)	PUNCT
ejpam-6266	244	10	where	where	SCONJ
ejpam-6266	244	11	j	j	PROPN
ejpam-6266	244	12	(	(	PUNCT
ejpam-6266	244	13	k	k	PROPN
ejpam-6266	244	14	,	,	PUNCT
ejpam-6266	244	15	j	j	PROPN
ejpam-6266	244	16	)	)	PUNCT
ejpam-6266	244	17	n	n	PROPN
ejpam-6266	244	18	(	(	PUNCT
ejpam-6266	244	19	t	t	PROPN
ejpam-6266	244	20	)	)	PUNCT
ejpam-6266	244	21	is	be	AUX
ejpam-6266	244	22	defined	define	VERB
ejpam-6266	244	23	by	by	ADP
ejpam-6266	244	24	(	(	PUNCT
ejpam-6266	244	25	18	18	NUM
ejpam-6266	244	26	)	)	PUNCT
ejpam-6266	244	27	.	.	PUNCT
ejpam-6266	245	1	using	use	VERB
ejpam-6266	245	2	the	the	DET
ejpam-6266	245	3	estimate	estimate	NOUN
ejpam-6266	245	4	(	(	PUNCT
ejpam-6266	245	5	42	42	NUM
ejpam-6266	245	6	)	)	PUNCT
ejpam-6266	245	7	for	for	ADP
ejpam-6266	245	8	j	j	PROPN
ejpam-6266	245	9	(	(	PUNCT
ejpam-6266	245	10	k	k	PROPN
ejpam-6266	245	11	,	,	PUNCT
ejpam-6266	245	12	j	j	PROPN
ejpam-6266	245	13	)	)	PUNCT
ejpam-6266	245	14	n	n	PROPN
ejpam-6266	245	15	(	(	PUNCT
ejpam-6266	245	16	t	t	NOUN
ejpam-6266	245	17	)	)	PUNCT
ejpam-6266	245	18	we	we	PRON
ejpam-6266	245	19	find	find	VERB
ejpam-6266	245	20	from	from	ADP
ejpam-6266	245	21	(	(	PUNCT
ejpam-6266	245	22	53	53	NUM
ejpam-6266	245	23	)	)	PUNCT
ejpam-6266	245	24	the	the	DET
ejpam-6266	245	25	estimate∥∥∇k∂j	estimate∥∥∇k∂j	PROPN
ejpam-6266	245	26	t	t	PROPN
ejpam-6266	245	27	(	(	PUNCT
ejpam-6266	245	28	nu−nv)(t	nu−nv)(t	PROPN
ejpam-6266	245	29	,	,	PUNCT
ejpam-6266	245	30	·	·	PUNCT
ejpam-6266	245	31	)	)	PUNCT
ejpam-6266	245	32	∥∥	∥∥	X
ejpam-6266	245	33	l2	l2	NOUN
ejpam-6266	245	34	.	.	PUNCT
ejpam-6266	246	1			X
ejpam-6266	246	2	(	(	PUNCT
ejpam-6266	246	3	1	1	NUM
ejpam-6266	246	4	+	+	X
ejpam-6266	246	5	t)−	t)−	PROPN
ejpam-6266	246	6	3	3	NUM
ejpam-6266	246	7	4	4	NUM
ejpam-6266	246	8	‖u−	‖u−	ADP
ejpam-6266	246	9	v‖x(t	v‖x(t	PROPN
ejpam-6266	246	10	)	)	PUNCT
ejpam-6266	246	11	(	(	PUNCT
ejpam-6266	246	12	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	246	13	x(t	x(t	PROPN
ejpam-6266	246	14	)	)	PUNCT
ejpam-6266	247	1	+	+	CCONJ
ejpam-6266	247	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	247	3	x(t	x(t	PROPN
ejpam-6266	247	4	)	)	PUNCT
ejpam-6266	247	5	)	)	PUNCT
ejpam-6266	248	1	if	if	SCONJ
ejpam-6266	248	2	n	n	NOUN
ejpam-6266	248	3	=	=	SYM
ejpam-6266	248	4	k	k	NOUN
ejpam-6266	248	5	=	=	SYM
ejpam-6266	248	6	1	1	NUM
ejpam-6266	248	7	and	and	CCONJ
ejpam-6266	248	8	j	j	PROPN
ejpam-6266	248	9	=	=	SYM
ejpam-6266	248	10	0	0	PROPN
ejpam-6266	248	11	,	,	PUNCT
ejpam-6266	248	12	log(2+t	log(2+t	X
ejpam-6266	248	13	)	)	PUNCT
ejpam-6266	248	14	(	(	PUNCT
ejpam-6266	248	15	1+t)γ	1+t)γ	PROPN
ejpam-6266	248	16	‖u−	‖u−	PROPN
ejpam-6266	248	17	v‖x(t	v‖x(t	PROPN
ejpam-6266	248	18	)	)	PUNCT
ejpam-6266	248	19	(	(	PUNCT
ejpam-6266	248	20	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	248	21	x(t	x(t	PROPN
ejpam-6266	248	22	)	)	PUNCT
ejpam-6266	249	1	+	+	CCONJ
ejpam-6266	249	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	249	3	x(t	x(t	PROPN
ejpam-6266	249	4	)	)	PUNCT
ejpam-6266	249	5	)	)	PUNCT
ejpam-6266	250	1	if	if	SCONJ
ejpam-6266	250	2	n	n	NOUN
ejpam-6266	250	3	=	=	SYM
ejpam-6266	250	4	2	2	NUM
ejpam-6266	250	5	,	,	PUNCT
ejpam-6266	250	6	k	k	NOUN
ejpam-6266	250	7	=	=	SYM
ejpam-6266	250	8	1	1	NUM
ejpam-6266	250	9	and	and	CCONJ
ejpam-6266	250	10	j	j	PROPN
ejpam-6266	250	11	=	=	SYM
ejpam-6266	250	12	0	0	PROPN
ejpam-6266	250	13	,	,	PUNCT
ejpam-6266	250	14	(	(	PUNCT
ejpam-6266	250	15	1	1	NUM
ejpam-6266	250	16	+	+	NUM
ejpam-6266	250	17	t)−γ‖u−	t)−γ‖u−	X
ejpam-6266	250	18	v‖x(t	v‖x(t	PROPN
ejpam-6266	250	19	)	)	PUNCT
ejpam-6266	250	20	(	(	PUNCT
ejpam-6266	250	21	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	250	22	x(t	x(t	PROPN
ejpam-6266	250	23	)	)	PUNCT
ejpam-6266	251	1	+	+	CCONJ
ejpam-6266	251	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	251	3	x(t	x(t	PROPN
ejpam-6266	251	4	)	)	PUNCT
ejpam-6266	251	5	)	)	PUNCT
ejpam-6266	252	1	if	if	SCONJ
ejpam-6266	252	2	n	n	NOUN
ejpam-6266	252	3	=	=	SYM
ejpam-6266	252	4	1	1	NUM
ejpam-6266	252	5	,	,	PUNCT
ejpam-6266	252	6	2	2	NUM
ejpam-6266	252	7	and	and	CCONJ
ejpam-6266	252	8	1	1	NUM
ejpam-6266	252	9	≤	≤	NUM
ejpam-6266	253	1	k	k	PROPN
ejpam-6266	254	1	+	+	NUM
ejpam-6266	254	2	j	j	PROPN
ejpam-6266	254	3	≤	≤	ADV
ejpam-6266	254	4	2	2	NUM
ejpam-6266	254	5	.	.	PUNCT
ejpam-6266	254	6	(	(	PUNCT
ejpam-6266	254	7	54	54	NUM
ejpam-6266	254	8	)	)	PUNCT
ejpam-6266	254	9	finally	finally	ADV
ejpam-6266	254	10	,	,	PUNCT
ejpam-6266	254	11	the	the	DET
ejpam-6266	254	12	desired	desire	VERB
ejpam-6266	254	13	inequality	inequality	NOUN
ejpam-6266	254	14	(	(	PUNCT
ejpam-6266	254	15	16	16	NUM
ejpam-6266	254	16	)	)	PUNCT
ejpam-6266	254	17	is	be	AUX
ejpam-6266	254	18	concluded	conclude	VERB
ejpam-6266	254	19	from	from	ADP
ejpam-6266	254	20	the	the	DET
ejpam-6266	254	21	estimates	estimate	NOUN
ejpam-6266	254	22	(	(	PUNCT
ejpam-6266	254	23	54	54	NUM
ejpam-6266	254	24	)	)	PUNCT
ejpam-6266	254	25	,	,	PUNCT
ejpam-6266	254	26	(	(	PUNCT
ejpam-6266	254	27	51	51	NUM
ejpam-6266	254	28	)	)	PUNCT
ejpam-6266	254	29	and	and	CCONJ
ejpam-6266	254	30	the	the	DET
ejpam-6266	254	31	definition	definition	NOUN
ejpam-6266	254	32	(	(	PUNCT
ejpam-6266	254	33	30	30	NUM
ejpam-6266	254	34	)	)	PUNCT
ejpam-6266	254	35	for	for	ADP
ejpam-6266	254	36	the	the	DET
ejpam-6266	254	37	norm	norm	NOUN
ejpam-6266	254	38	in	in	ADP
ejpam-6266	254	39	x(t	x(t	PROPN
ejpam-6266	254	40	)	)	PUNCT
ejpam-6266	254	41	.	.	PUNCT
ejpam-6266	255	1	this	this	PRON
ejpam-6266	255	2	ends	end	VERB
ejpam-6266	255	3	the	the	DET
ejpam-6266	255	4	proof	proof	NOUN
ejpam-6266	255	5	of	of	ADP
ejpam-6266	255	6	theorem	theorem	NOUN
ejpam-6266	255	7	1	1	NUM
ejpam-6266	255	8	.	.	PUNCT
ejpam-6266	255	9	t.	t.	PROPN
ejpam-6266	255	10	hadj	hadj	PROPN
ejpam-6266	255	11	kaddour	kaddour	PROPN
ejpam-6266	255	12	et	et	PROPN
ejpam-6266	255	13	al	al	PROPN
ejpam-6266	255	14	.	.	PUNCT
ejpam-6266	255	15	/	/	SYM
ejpam-6266	255	16	eur	eur	PROPN
ejpam-6266	255	17	.	.	PUNCT
ejpam-6266	256	1	j.	j.	PROPN
ejpam-6266	256	2	pure	pure	PROPN
ejpam-6266	256	3	appl	appl	PROPN
ejpam-6266	256	4	.	.	PROPN
ejpam-6266	256	5	math	math	PROPN
ejpam-6266	256	6	,	,	PUNCT
ejpam-6266	256	7	18	18	NUM
ejpam-6266	256	8	(	(	PUNCT
ejpam-6266	256	9	4	4	NUM
ejpam-6266	256	10	)	)	PUNCT
ejpam-6266	256	11	(	(	PUNCT
ejpam-6266	256	12	2025	2025	NUM
ejpam-6266	256	13	)	)	PUNCT
ejpam-6266	256	14	,	,	PUNCT
ejpam-6266	256	15	6266	6266	NUM
ejpam-6266	256	16	12	12	NUM
ejpam-6266	256	17	of	of	ADP
ejpam-6266	256	18	24	24	NUM
ejpam-6266	256	19	4.1.2	4.1.2	NUM
ejpam-6266	256	20	.	.	PUNCT
ejpam-6266	257	1	proof	proof	NOUN
ejpam-6266	257	2	of	of	ADP
ejpam-6266	257	3	theorem	theorem	NOUN
ejpam-6266	257	4	2	2	NUM
ejpam-6266	257	5	the	the	DET
ejpam-6266	257	6	proof	proof	NOUN
ejpam-6266	257	7	of	of	ADP
ejpam-6266	257	8	theorem	theorem	ADJ
ejpam-6266	257	9	2	2	NUM
ejpam-6266	257	10	is	be	AUX
ejpam-6266	257	11	similar	similar	ADJ
ejpam-6266	257	12	to	to	ADP
ejpam-6266	257	13	that	that	PRON
ejpam-6266	257	14	of	of	ADP
ejpam-6266	257	15	theorem	theorem	NOUN
ejpam-6266	257	16	1	1	NUM
ejpam-6266	257	17	,	,	PUNCT
ejpam-6266	257	18	except	except	SCONJ
ejpam-6266	257	19	,	,	PUNCT
ejpam-6266	257	20	in	in	ADP
ejpam-6266	257	21	theorem	theorem	NOUN
ejpam-6266	257	22	2	2	NUM
ejpam-6266	257	23	an	an	DET
ejpam-6266	257	24	upper	upper	ADJ
ejpam-6266	257	25	bound	bind	VERB
ejpam-6266	257	26	appears	appear	VERB
ejpam-6266	257	27	for	for	SCONJ
ejpam-6266	257	28	the	the	DET
ejpam-6266	257	29	range	range	NOUN
ejpam-6266	257	30	of	of	ADP
ejpam-6266	257	31	admissible	admissible	ADJ
ejpam-6266	257	32	values	value	NOUN
ejpam-6266	257	33	of	of	ADP
ejpam-6266	257	34	p.	p.	NOUN
ejpam-6266	257	35	this	this	DET
ejpam-6266	257	36	upper	upper	ADJ
ejpam-6266	257	37	bound	bound	NOUN
ejpam-6266	257	38	is	be	AUX
ejpam-6266	257	39	caused	cause	VERB
ejpam-6266	257	40	by	by	ADP
ejpam-6266	257	41	the	the	DET
ejpam-6266	257	42	application	application	NOUN
ejpam-6266	257	43	of	of	ADP
ejpam-6266	257	44	gagliardo	gagliardo	NOUN
ejpam-6266	257	45	-	-	PUNCT
ejpam-6266	257	46	nirenberg	nirenberg	PROPN
ejpam-6266	257	47	inequality	inequality	NOUN
ejpam-6266	257	48	.	.	PUNCT
ejpam-6266	258	1	more	more	ADV
ejpam-6266	258	2	precisely	precisely	ADV
ejpam-6266	258	3	,	,	PUNCT
ejpam-6266	258	4	in	in	ADP
ejpam-6266	258	5	formula	formula	NOUN
ejpam-6266	258	6	(	(	PUNCT
ejpam-6266	258	7	35	35	NUM
ejpam-6266	258	8	)	)	PUNCT
ejpam-6266	258	9	,	,	PUNCT
ejpam-6266	258	10	the	the	DET
ejpam-6266	258	11	condition	condition	NOUN
ejpam-6266	258	12	θj(p	θj(p	VERB
ejpam-6266	258	13	)	)	PUNCT
ejpam-6266	258	14	∈	∈	PROPN
ejpam-6266	259	1	[	[	X
ejpam-6266	259	2	0	0	NUM
ejpam-6266	259	3	,	,	PUNCT
ejpam-6266	259	4	1	1	NUM
ejpam-6266	259	5	]	]	PUNCT
ejpam-6266	259	6	implies	imply	VERB
ejpam-6266	259	7	2	2	NUM
ejpam-6266	259	8	j	j	PROPN
ejpam-6266	259	9	≤	≤	PROPN
ejpam-6266	259	10	p	p	NOUN
ejpam-6266	259	11	≤	≤	ADJ
ejpam-6266	259	12	2n	2n	NUM
ejpam-6266	259	13	(	(	PUNCT
ejpam-6266	259	14	n−	n−	NOUN
ejpam-6266	259	15	2)j	2)j	NUM
ejpam-6266	259	16	,	,	PUNCT
ejpam-6266	259	17	(	(	PUNCT
ejpam-6266	259	18	55	55	NUM
ejpam-6266	259	19	)	)	PUNCT
ejpam-6266	259	20	according	accord	VERB
ejpam-6266	259	21	to	to	ADP
ejpam-6266	259	22	(	(	PUNCT
ejpam-6266	259	23	108	108	NUM
ejpam-6266	259	24	)	)	PUNCT
ejpam-6266	259	25	.	.	PUNCT
ejpam-6266	260	1	since	since	SCONJ
ejpam-6266	260	2	condition	condition	NOUN
ejpam-6266	260	3	(	(	PUNCT
ejpam-6266	260	4	55	55	NUM
ejpam-6266	260	5	)	)	PUNCT
ejpam-6266	260	6	must	must	AUX
ejpam-6266	260	7	hold	hold	VERB
ejpam-6266	260	8	simultaneously	simultaneously	ADV
ejpam-6266	260	9	for	for	ADP
ejpam-6266	260	10	j	j	PROPN
ejpam-6266	260	11	=	=	SYM
ejpam-6266	260	12	1	1	NUM
ejpam-6266	260	13	,	,	PUNCT
ejpam-6266	260	14	2	2	NUM
ejpam-6266	260	15	we	we	PRON
ejpam-6266	260	16	conclude	conclude	VERB
ejpam-6266	260	17	that	that	SCONJ
ejpam-6266	260	18	2	2	NUM
ejpam-6266	260	19	≤	≤	NOUN
ejpam-6266	260	20	p	p	NOUN
ejpam-6266	260	21	≤	≤	NOUN
ejpam-6266	260	22	n	n	DET
ejpam-6266	260	23	n−2	n−2	PROPN
ejpam-6266	260	24	.	.	PUNCT
ejpam-6266	261	1	the	the	DET
ejpam-6266	261	2	parameter	parameter	NOUN
ejpam-6266	261	3	n	n	PROPN
ejpam-6266	261	4	n−2	n−2	PROPN
ejpam-6266	261	5	is	be	AUX
ejpam-6266	261	6	called	call	VERB
ejpam-6266	261	7	gagliardo	gagliardo	NOUN
ejpam-6266	261	8	-	-	PUNCT
ejpam-6266	261	9	nirenberg	nirenberg	PROPN
ejpam-6266	261	10	exponent	exponent	NOUN
ejpam-6266	261	11	and	and	CCONJ
ejpam-6266	261	12	,	,	PUNCT
ejpam-6266	261	13	usually	usually	ADV
ejpam-6266	261	14	,	,	PUNCT
ejpam-6266	261	15	denoted	denote	VERB
ejpam-6266	261	16	by	by	ADP
ejpam-6266	261	17	pgn	pgn	PROPN
ejpam-6266	261	18	.	.	PUNCT
ejpam-6266	262	1	since	since	SCONJ
ejpam-6266	262	2	the	the	DET
ejpam-6266	262	3	proofs	proof	NOUN
ejpam-6266	262	4	are	be	AUX
ejpam-6266	262	5	essentially	essentially	ADV
ejpam-6266	262	6	the	the	DET
ejpam-6266	262	7	same	same	ADJ
ejpam-6266	262	8	we	we	PRON
ejpam-6266	262	9	omit	omit	VERB
ejpam-6266	262	10	the	the	DET
ejpam-6266	262	11	details	detail	NOUN
ejpam-6266	262	12	of	of	ADP
ejpam-6266	262	13	proof	proof	NOUN
ejpam-6266	262	14	of	of	ADP
ejpam-6266	262	15	theorem	theorem	ADJ
ejpam-6266	262	16	2	2	NUM
ejpam-6266	262	17	.	.	NOUN
ejpam-6266	262	18	4.2	4.2	NUM
ejpam-6266	262	19	.	.	PUNCT
ejpam-6266	263	1	proof	proof	NOUN
ejpam-6266	263	2	of	of	ADP
ejpam-6266	263	3	theorems	theorem	NOUN
ejpam-6266	263	4	3	3	NUM
ejpam-6266	263	5	and	and	CCONJ
ejpam-6266	263	6	4	4	NUM
ejpam-6266	263	7	4.2.1	4.2.1	NUM
ejpam-6266	263	8	.	.	PUNCT
ejpam-6266	264	1	proof	proof	NOUN
ejpam-6266	264	2	of	of	ADP
ejpam-6266	264	3	theorem	theorem	ADJ
ejpam-6266	264	4	3	3	NUM
ejpam-6266	264	5	let	let	VERB
ejpam-6266	264	6	us	we	PRON
ejpam-6266	264	7	introduce	introduce	VERB
ejpam-6266	264	8	,	,	PUNCT
ejpam-6266	264	9	for	for	ADP
ejpam-6266	264	10	t	t	PROPN
ejpam-6266	264	11	>	>	X
ejpam-6266	264	12	0	0	PROPN
ejpam-6266	264	13	,	,	PUNCT
ejpam-6266	264	14	the	the	DET
ejpam-6266	264	15	space	space	NOUN
ejpam-6266	264	16	of	of	ADP
ejpam-6266	264	17	energy	energy	NOUN
ejpam-6266	264	18	solutions	solution	NOUN
ejpam-6266	264	19	x(t	x(t	PROPN
ejpam-6266	264	20	)	)	PUNCT
ejpam-6266	265	1	=	=	PUNCT
ejpam-6266	266	1	c	c	NOUN
ejpam-6266	266	2	(	(	PUNCT
ejpam-6266	266	3	[	[	X
ejpam-6266	266	4	0	0	NUM
ejpam-6266	266	5	,	,	PUNCT
ejpam-6266	266	6	t	t	X
ejpam-6266	266	7	]	]	PUNCT
ejpam-6266	266	8	,	,	PUNCT
ejpam-6266	266	9	hs(r	hs(r	NUM
ejpam-6266	266	10	)	)	PUNCT
ejpam-6266	266	11	)	)	PUNCT
ejpam-6266	266	12	∩	∩	PROPN
ejpam-6266	266	13	c1	c1	NOUN
ejpam-6266	266	14	(	(	PUNCT
ejpam-6266	266	15	[	[	X
ejpam-6266	266	16	0	0	NUM
ejpam-6266	266	17	,	,	PUNCT
ejpam-6266	266	18	t	t	X
ejpam-6266	266	19	]	]	PUNCT
ejpam-6266	266	20	,	,	PUNCT
ejpam-6266	266	21	hs−1(r	hs−1(r	NOUN
ejpam-6266	266	22	)	)	PUNCT
ejpam-6266	266	23	)	)	PUNCT
ejpam-6266	266	24	(	(	PUNCT
ejpam-6266	266	25	56	56	NUM
ejpam-6266	266	26	)	)	PUNCT
ejpam-6266	266	27	with	with	ADP
ejpam-6266	266	28	the	the	DET
ejpam-6266	266	29	norm	norm	NOUN
ejpam-6266	266	30	‖u‖x(t	‖u‖x(t	PROPN
ejpam-6266	266	31	)	)	PUNCT
ejpam-6266	266	32	=	=	SYM
ejpam-6266	266	33	sup	sup	NOUN
ejpam-6266	266	34	0≤t≤t	0≤t≤t	NUM
ejpam-6266	266	35	{	{	PUNCT
ejpam-6266	266	36	(	(	PUNCT
ejpam-6266	266	37	1	1	NUM
ejpam-6266	266	38	+	+	NUM
ejpam-6266	266	39	t	t	PROPN
ejpam-6266	266	40	)	)	PUNCT
ejpam-6266	266	41	n	n	CCONJ
ejpam-6266	266	42	2	2	NUM
ejpam-6266	266	43	(	(	PUNCT
ejpam-6266	266	44	1	1	NUM
ejpam-6266	266	45	m	m	NOUN
ejpam-6266	266	46	−	−	NUM
ejpam-6266	266	47	1	1	NUM
ejpam-6266	266	48	2	2	NUM
ejpam-6266	266	49	)	)	PUNCT
ejpam-6266	266	50	+	+	NOUN
ejpam-6266	266	51	γ−1	γ−1	PROPN
ejpam-6266	266	52	(	(	PUNCT
ejpam-6266	266	53	‖u(t	‖u(t	X
ejpam-6266	266	54	,	,	PUNCT
ejpam-6266	266	55	·	·	PUNCT
ejpam-6266	266	56	)	)	PUNCT
ejpam-6266	266	57	‖l2	‖l2	VERB
ejpam-6266	266	58	+	+	PUNCT
ejpam-6266	266	59	(	(	PUNCT
ejpam-6266	266	60	1	1	NUM
ejpam-6266	266	61	+	+	NUM
ejpam-6266	266	62	t)γ‖|d|σu(t	t)γ‖|d|σu(t	PROPN
ejpam-6266	266	63	,	,	PUNCT
ejpam-6266	266	64	·	·	PUNCT
ejpam-6266	266	65	)	)	PUNCT
ejpam-6266	266	66	‖l2	‖l2	PRON
ejpam-6266	266	67	)	)	PUNCT
ejpam-6266	267	1	+	+	ADJ
ejpam-6266	267	2	(	(	PUNCT
ejpam-6266	267	3	1	1	NUM
ejpam-6266	267	4	+	+	NUM
ejpam-6266	267	5	t)γ‖ut(t	t)γ‖ut(t	NOUN
ejpam-6266	267	6	,	,	PUNCT
ejpam-6266	267	7	·	·	PUNCT
ejpam-6266	267	8	)	)	PUNCT
ejpam-6266	268	1	‖l2	‖l2	VERB
ejpam-6266	268	2	+	+	PUNCT
ejpam-6266	268	3	(	(	PUNCT
ejpam-6266	268	4	1	1	NUM
ejpam-6266	268	5	+	+	CCONJ
ejpam-6266	268	6	t)γ‖|d|σ−1ut(t	t)γ‖|d|σ−1ut(t	PROPN
ejpam-6266	268	7	,	,	PUNCT
ejpam-6266	268	8	·	·	PUNCT
ejpam-6266	268	9	)	)	PUNCT
ejpam-6266	268	10	‖l2	‖l2	VERB
ejpam-6266	268	11	}	}	PUNCT
ejpam-6266	268	12	.	.	PUNCT
ejpam-6266	269	1	(	(	PUNCT
ejpam-6266	269	2	57	57	NUM
ejpam-6266	269	3	)	)	PUNCT
ejpam-6266	269	4	as	as	ADP
ejpam-6266	269	5	usual	usual	ADJ
ejpam-6266	269	6	,	,	PUNCT
ejpam-6266	269	7	the	the	DET
ejpam-6266	269	8	aim	aim	NOUN
ejpam-6266	269	9	is	be	AUX
ejpam-6266	269	10	to	to	PART
ejpam-6266	269	11	prove	prove	VERB
ejpam-6266	269	12	the	the	DET
ejpam-6266	269	13	inequalities	inequality	NOUN
ejpam-6266	269	14	(	(	PUNCT
ejpam-6266	269	15	15	15	NUM
ejpam-6266	269	16	)	)	PUNCT
ejpam-6266	269	17	and	and	CCONJ
ejpam-6266	269	18	(	(	PUNCT
ejpam-6266	269	19	16	16	NUM
ejpam-6266	269	20	)	)	PUNCT
ejpam-6266	269	21	.	.	PUNCT
ejpam-6266	270	1	let	let	VERB
ejpam-6266	270	2	us	we	PRON
ejpam-6266	270	3	start	start	VERB
ejpam-6266	270	4	with	with	ADP
ejpam-6266	270	5	the	the	DET
ejpam-6266	270	6	first	first	ADJ
ejpam-6266	270	7	one	one	NUM
ejpam-6266	270	8	.	.	PUNCT
ejpam-6266	271	1	the	the	DET
ejpam-6266	271	2	inequality	inequality	NOUN
ejpam-6266	271	3	‖ulin‖x(t	‖ulin‖x(t	X
ejpam-6266	271	4	)	)	PUNCT
ejpam-6266	271	5	.	.	PUNCT
ejpam-6266	272	1	‖(u0	‖(u0	PROPN
ejpam-6266	272	2	,	,	PUNCT
ejpam-6266	272	3	u1)‖a1	u1)‖a1	PROPN
ejpam-6266	272	4	1,0	1,0	NUM
ejpam-6266	272	5	is	be	AUX
ejpam-6266	272	6	concluded	conclude	VERB
ejpam-6266	272	7	directly	directly	ADV
ejpam-6266	272	8	by	by	ADP
ejpam-6266	272	9	proposition	proposition	NOUN
ejpam-6266	272	10	2	2	NUM
ejpam-6266	272	11	from	from	ADP
ejpam-6266	272	12	[	[	X
ejpam-6266	272	13	11	11	NUM
ejpam-6266	272	14	]	]	PUNCT
ejpam-6266	272	15	and	and	CCONJ
ejpam-6266	272	16	corollary	corollary	ADJ
ejpam-6266	272	17	2	2	NUM
ejpam-6266	272	18	for	for	ADP
ejpam-6266	272	19	τ	τ	PROPN
ejpam-6266	272	20	=	=	SYM
ejpam-6266	272	21	0	0	PROPN
ejpam-6266	272	22	and	and	CCONJ
ejpam-6266	272	23	h(0	h(0	PROPN
ejpam-6266	272	24	,	,	PUNCT
ejpam-6266	272	25	u(x	u(x	NOUN
ejpam-6266	272	26	)	)	PUNCT
ejpam-6266	272	27	)	)	PUNCT
ejpam-6266	273	1	=	=	PUNCT
ejpam-6266	273	2	u1(x	u1(x	NOUN
ejpam-6266	273	3	)	)	PUNCT
ejpam-6266	273	4	.	.	PUNCT
ejpam-6266	274	1	it	it	PRON
ejpam-6266	274	2	remains	remain	VERB
ejpam-6266	274	3	to	to	PART
ejpam-6266	274	4	show	show	VERB
ejpam-6266	274	5	the	the	DET
ejpam-6266	274	6	inequality	inequality	NOUN
ejpam-6266	274	7	‖unl‖x(t	‖unl‖x(t	PRON
ejpam-6266	274	8	)	)	PUNCT
ejpam-6266	274	9	.	.	PUNCT
ejpam-6266	275	1	‖u‖px(t	‖u‖px(t	PROPN
ejpam-6266	275	2	)	)	PUNCT
ejpam-6266	275	3	.	.	PUNCT
ejpam-6266	276	1	(	(	PUNCT
ejpam-6266	276	2	58	58	X
ejpam-6266	276	3	)	)	PUNCT
ejpam-6266	276	4	thanks	thank	NOUN
ejpam-6266	276	5	to	to	ADP
ejpam-6266	276	6	the	the	DET
ejpam-6266	276	7	results	result	NOUN
ejpam-6266	276	8	of	of	ADP
ejpam-6266	276	9	proposition	proposition	NOUN
ejpam-6266	276	10	2	2	NUM
ejpam-6266	276	11	we	we	PRON
ejpam-6266	276	12	have	have	VERB
ejpam-6266	276	13	for	for	ADP
ejpam-6266	276	14	κ	κ	NOUN
ejpam-6266	276	15	=	=	SYM
ejpam-6266	276	16	0	0	PROPN
ejpam-6266	276	17	,	,	PUNCT
ejpam-6266	276	18	σ	σ	NOUN
ejpam-6266	276	19	(	(	PUNCT
ejpam-6266	276	20	with	with	ADP
ejpam-6266	276	21	the	the	DET
ejpam-6266	276	22	convention	convention	NOUN
ejpam-6266	276	23	|d|κ	|d|κ	X
ejpam-6266	277	1	=	=	PUNCT
ejpam-6266	277	2	i	i	PROPN
ejpam-6266	277	3	d	d	PROPN
ejpam-6266	277	4	if	if	SCONJ
ejpam-6266	277	5	κ	κ	X
ejpam-6266	277	6	=	=	NOUN
ejpam-6266	277	7	0	0	NUM
ejpam-6266	277	8	)	)	PUNCT
ejpam-6266	277	9	,	,	PUNCT
ejpam-6266	277	10	‖|d|κunl(t	‖|d|κunl(t	INTJ
ejpam-6266	277	11	,	,	PUNCT
ejpam-6266	277	12	·	·	PUNCT
ejpam-6266	277	13	)	)	PUNCT
ejpam-6266	277	14	‖l2	‖l2	VERB
ejpam-6266	277	15	.	.	PUNCT
ejpam-6266	278	1	∫	∫	PROPN
ejpam-6266	278	2	t	t	PROPN
ejpam-6266	278	3	0	0	NUM
ejpam-6266	279	1	(	(	PUNCT
ejpam-6266	279	2	1	1	NUM
ejpam-6266	279	3	+	+	CCONJ
ejpam-6266	279	4	t−	t−	PROPN
ejpam-6266	279	5	τ)−	τ)−	PROPN
ejpam-6266	279	6	n	n	CCONJ
ejpam-6266	279	7	2	2	NUM
ejpam-6266	279	8	(	(	PUNCT
ejpam-6266	279	9	1	1	NUM
ejpam-6266	279	10	m	m	NOUN
ejpam-6266	279	11	−	−	NUM
ejpam-6266	279	12	1	1	NUM
ejpam-6266	279	13	2	2	NUM
ejpam-6266	279	14	)	)	PUNCT
ejpam-6266	279	15	−κ	−κ	NOUN
ejpam-6266	279	16	2	2	NUM
ejpam-6266	279	17	×	×	NOUN
ejpam-6266	279	18	∫	∫	PROPN
ejpam-6266	279	19	τ	τ	X
ejpam-6266	279	20	0	0	NUM
ejpam-6266	280	1	(	(	PUNCT
ejpam-6266	280	2	τ	τ	X
ejpam-6266	280	3	−	−	PROPN
ejpam-6266	280	4	s)−γ	s)−γ	PROPN
ejpam-6266	280	5	∥∥|u(s	∥∥|u(s	PROPN
ejpam-6266	280	6	,	,	PUNCT
ejpam-6266	280	7	·	·	PUNCT
ejpam-6266	280	8	)	)	PUNCT
ejpam-6266	280	9	|p∥∥	|p∥∥	NUM
ejpam-6266	280	10	lm∩l2∩ḣσ−1	lm∩l2∩ḣσ−1	NUM
ejpam-6266	280	11	dsdτ	dsdτ	NOUN
ejpam-6266	280	12	.	.	PUNCT
ejpam-6266	281	1	(	(	PUNCT
ejpam-6266	281	2	59	59	NUM
ejpam-6266	281	3	)	)	PUNCT
ejpam-6266	281	4	for	for	ADP
ejpam-6266	281	5	this	this	DET
ejpam-6266	281	6	reason	reason	NOUN
ejpam-6266	281	7	we	we	PRON
ejpam-6266	281	8	shall	shall	AUX
ejpam-6266	281	9	estimate	estimate	VERB
ejpam-6266	281	10	the	the	DET
ejpam-6266	281	11	norms	norm	NOUN
ejpam-6266	281	12	‖|u(s	‖|u(s	NUM
ejpam-6266	281	13	,	,	PUNCT
ejpam-6266	281	14	·	·	PUNCT
ejpam-6266	281	15	)	)	PUNCT
ejpam-6266	281	16	|p‖lm	|p‖lm	ADJ
ejpam-6266	281	17	,	,	PUNCT
ejpam-6266	281	18	‖|u(s	‖|u(s	ADJ
ejpam-6266	281	19	,	,	PUNCT
ejpam-6266	281	20	·	·	PUNCT
ejpam-6266	281	21	)	)	PUNCT
ejpam-6266	281	22	|p‖l2	|p‖l2	ADJ
ejpam-6266	281	23	,	,	PUNCT
ejpam-6266	281	24	and	and	CCONJ
ejpam-6266	281	25	‖|u(s	‖|u(s	NUM
ejpam-6266	281	26	,	,	PUNCT
ejpam-6266	281	27	·	·	PUNCT
ejpam-6266	281	28	)	)	PUNCT
ejpam-6266	281	29	|p‖ḣσ−1	|p‖ḣσ−1	X
ejpam-6266	281	30	.	.	PUNCT
ejpam-6266	282	1	t.	t.	PROPN
ejpam-6266	282	2	hadj	hadj	PROPN
ejpam-6266	282	3	kaddour	kaddour	PROPN
ejpam-6266	282	4	et	et	PROPN
ejpam-6266	282	5	al	al	PROPN
ejpam-6266	282	6	.	.	PUNCT
ejpam-6266	282	7	/	/	SYM
ejpam-6266	282	8	eur	eur	PROPN
ejpam-6266	282	9	.	.	PUNCT
ejpam-6266	283	1	j.	j.	PROPN
ejpam-6266	283	2	pure	pure	PROPN
ejpam-6266	283	3	appl	appl	PROPN
ejpam-6266	283	4	.	.	PROPN
ejpam-6266	283	5	math	math	PROPN
ejpam-6266	283	6	,	,	PUNCT
ejpam-6266	283	7	18	18	NUM
ejpam-6266	283	8	(	(	PUNCT
ejpam-6266	283	9	4	4	NUM
ejpam-6266	283	10	)	)	PUNCT
ejpam-6266	283	11	(	(	PUNCT
ejpam-6266	283	12	2025	2025	NUM
ejpam-6266	283	13	)	)	PUNCT
ejpam-6266	283	14	,	,	PUNCT
ejpam-6266	283	15	6266	6266	NUM
ejpam-6266	283	16	13	13	NUM
ejpam-6266	283	17	of	of	ADP
ejpam-6266	283	18	24	24	NUM
ejpam-6266	283	19	first	first	ADJ
ejpam-6266	284	1	,	,	PUNCT
ejpam-6266	284	2	we	we	PRON
ejpam-6266	284	3	apply	apply	VERB
ejpam-6266	284	4	fractional	fractional	ADJ
ejpam-6266	284	5	gagliardo	gagliardo	NOUN
ejpam-6266	284	6	-	-	PUNCT
ejpam-6266	284	7	nirenberg	nirenberg	NOUN
ejpam-6266	284	8	inequality	inequality	NOUN
ejpam-6266	284	9	we	we	PRON
ejpam-6266	284	10	get	get	VERB
ejpam-6266	284	11	for	for	ADP
ejpam-6266	284	12	j	j	PROPN
ejpam-6266	284	13	=	=	SYM
ejpam-6266	284	14	m	m	PROPN
ejpam-6266	284	15	and	and	CCONJ
ejpam-6266	284	16	j	j	PROPN
ejpam-6266	284	17	=	=	SYM
ejpam-6266	284	18	2	2	NUM
ejpam-6266	284	19	the	the	DET
ejpam-6266	284	20	estimates	estimate	NOUN
ejpam-6266	284	21	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	284	22	,	,	PUNCT
ejpam-6266	284	23	·	·	PUNCT
ejpam-6266	284	24	)	)	PUNCT
ejpam-6266	285	1	|p‖lj	|p‖lj	ADP
ejpam-6266	285	2	=	=	SYM
ejpam-6266	285	3	‖ut(s	‖ut(s	PROPN
ejpam-6266	285	4	,	,	PUNCT
ejpam-6266	285	5	·	·	PUNCT
ejpam-6266	285	6	)	)	PUNCT
ejpam-6266	285	7	‖pljp	‖pljp	NOUN
ejpam-6266	285	8	.	.	PUNCT
ejpam-6266	286	1	‖ut(s	‖ut(s	PUNCT
ejpam-6266	286	2	,	,	PUNCT
ejpam-6266	286	3	·	·	PUNCT
ejpam-6266	286	4	)	)	PUNCT
ejpam-6266	287	1	‖	‖	PROPN
ejpam-6266	287	2	p(1−θσ	p(1−θσ	PROPN
ejpam-6266	287	3	,	,	PUNCT
ejpam-6266	287	4	j(p	j(p	PROPN
ejpam-6266	287	5	)	)	PUNCT
ejpam-6266	287	6	)	)	PUNCT
ejpam-6266	287	7	l2	l2	VERB
ejpam-6266	287	8	∥∥∣∣d∣∣σut(s	∥∥∣∣d∣∣σut(	NOUN
ejpam-6266	287	9	,	,	PUNCT
ejpam-6266	287	10	·	·	PUNCT
ejpam-6266	287	11	)	)	PUNCT
ejpam-6266	287	12	∥∥pθσ	∥∥pθσ	PROPN
ejpam-6266	287	13	,	,	PUNCT
ejpam-6266	287	14	j(p)l2	j(p)l2	VERB
ejpam-6266	287	15	.	.	PUNCT
ejpam-6266	288	1	(	(	PUNCT
ejpam-6266	288	2	1	1	X
ejpam-6266	288	3	+	+	CCONJ
ejpam-6266	288	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	288	5	)	)	PUNCT
ejpam-6266	288	6	,	,	PUNCT
ejpam-6266	288	7	(	(	PUNCT
ejpam-6266	288	8	60	60	NUM
ejpam-6266	288	9	)	)	PUNCT
ejpam-6266	288	10	where	where	SCONJ
ejpam-6266	288	11	β	β	X
ejpam-6266	288	12	=	=	SYM
ejpam-6266	288	13	γp	γp	PROPN
ejpam-6266	288	14	,	,	PUNCT
ejpam-6266	288	15	(	(	PUNCT
ejpam-6266	288	16	61	61	NUM
ejpam-6266	288	17	)	)	PUNCT
ejpam-6266	288	18	and	and	CCONJ
ejpam-6266	288	19	θσ	θσ	ADP
ejpam-6266	288	20	,	,	PUNCT
ejpam-6266	288	21	j(p	j(p	PROPN
ejpam-6266	288	22	)	)	PUNCT
ejpam-6266	289	1	=	=	SYM
ejpam-6266	289	2	n	n	PROPN
ejpam-6266	289	3	σ	σ	NOUN
ejpam-6266	289	4	(	(	PUNCT
ejpam-6266	289	5	1	1	NUM
ejpam-6266	289	6	2	2	NUM
ejpam-6266	289	7	−	−	NUM
ejpam-6266	289	8	1	1	NUM
ejpam-6266	289	9	jp	jp	NOUN
ejpam-6266	289	10	)	)	PUNCT
ejpam-6266	289	11	∈	∈	PROPN
ejpam-6266	290	1	[	[	X
ejpam-6266	290	2	0	0	NUM
ejpam-6266	290	3	,	,	PUNCT
ejpam-6266	290	4	1	1	NUM
ejpam-6266	290	5	]	]	PUNCT
ejpam-6266	291	1	if	if	SCONJ
ejpam-6266	291	2	and	and	CCONJ
ejpam-6266	291	3	only	only	ADV
ejpam-6266	291	4	if	if	SCONJ
ejpam-6266	291	5	{	{	PUNCT
ejpam-6266	291	6	2	2	NUM
ejpam-6266	291	7	j	j	NOUN
ejpam-6266	291	8	≤	≤	NUM
ejpam-6266	291	9	p	p	NOUN
ejpam-6266	291	10	if	if	SCONJ
ejpam-6266	291	11	n	n	NOUN
ejpam-6266	291	12	≤	≤	NOUN
ejpam-6266	291	13	2σ	2σ	NUM
ejpam-6266	291	14	,	,	PUNCT
ejpam-6266	291	15	2	2	NUM
ejpam-6266	291	16	j	j	PROPN
ejpam-6266	291	17	≤	≤	X
ejpam-6266	291	18	p	p	NOUN
ejpam-6266	291	19	≤	≤	ADJ
ejpam-6266	291	20	2n	2n	NUM
ejpam-6266	291	21	(	(	PUNCT
ejpam-6266	291	22	n−2σ)j	n−2σ)j	NOUN
ejpam-6266	291	23	if	if	SCONJ
ejpam-6266	291	24	n	n	PROPN
ejpam-6266	291	25	>	>	X
ejpam-6266	291	26	2σ	2σ	NUM
ejpam-6266	291	27	.	.	PUNCT
ejpam-6266	292	1	summarizing	summarizing	NOUN
ejpam-6266	292	2	,	,	PUNCT
ejpam-6266	292	3	we	we	PRON
ejpam-6266	292	4	have	have	VERB
ejpam-6266	292	5	‖|u(s	‖|u(s	NUM
ejpam-6266	292	6	,	,	PUNCT
ejpam-6266	292	7	·	·	PUNCT
ejpam-6266	292	8	)	)	PUNCT
ejpam-6266	292	9	|p‖lm∩l2	|p‖lm∩l2	NOUN
ejpam-6266	292	10	.	.	PUNCT
ejpam-6266	293	1	(	(	PUNCT
ejpam-6266	293	2	1	1	NUM
ejpam-6266	293	3	+	+	CCONJ
ejpam-6266	293	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	293	5	)	)	PUNCT
ejpam-6266	293	6	,	,	PUNCT
ejpam-6266	293	7	(	(	PUNCT
ejpam-6266	293	8	62	62	NUM
ejpam-6266	293	9	)	)	PUNCT
ejpam-6266	293	10	where	where	SCONJ
ejpam-6266	293	11	β	β	PROPN
ejpam-6266	293	12	is	be	AUX
ejpam-6266	293	13	given	give	VERB
ejpam-6266	293	14	by	by	ADP
ejpam-6266	293	15	(	(	PUNCT
ejpam-6266	293	16	61	61	NUM
ejpam-6266	293	17	)	)	PUNCT
ejpam-6266	293	18	and	and	CCONJ
ejpam-6266	293	19	{	{	PUNCT
ejpam-6266	293	20	2	2	NUM
ejpam-6266	293	21	≤	≤	NOUN
ejpam-6266	293	22	p	p	NOUN
ejpam-6266	293	23	if	if	SCONJ
ejpam-6266	293	24	n	n	NOUN
ejpam-6266	293	25	≤	≤	NOUN
ejpam-6266	293	26	2σ	2σ	NUM
ejpam-6266	293	27	,	,	PUNCT
ejpam-6266	293	28	2	2	NUM
ejpam-6266	293	29	≤	≤	NOUN
ejpam-6266	293	30	p	p	NOUN
ejpam-6266	293	31	≤	≤	NOUN
ejpam-6266	293	32	n	n	CCONJ
ejpam-6266	293	33	n−2σ	n−2σ	NOUN
ejpam-6266	293	34	if	if	SCONJ
ejpam-6266	293	35	n	n	X
ejpam-6266	293	36	>	>	X
ejpam-6266	293	37	2σ	2σ	NUM
ejpam-6266	293	38	.	.	PUNCT
ejpam-6266	294	1	(	(	PUNCT
ejpam-6266	294	2	63	63	NUM
ejpam-6266	294	3	)	)	PUNCT
ejpam-6266	294	4	to	to	PART
ejpam-6266	294	5	estimate	estimate	VERB
ejpam-6266	294	6	the	the	DET
ejpam-6266	294	7	norm	norm	NOUN
ejpam-6266	294	8	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	294	9	,	,	PUNCT
ejpam-6266	294	10	·	·	PUNCT
ejpam-6266	294	11	)	)	PUNCT
ejpam-6266	294	12	|p‖ḣσ−1	|p‖ḣσ−1	PROPN
ejpam-6266	294	13	we	we	PRON
ejpam-6266	294	14	apply	apply	VERB
ejpam-6266	294	15	the	the	DET
ejpam-6266	294	16	fractional	fractional	ADJ
ejpam-6266	294	17	chain	chain	NOUN
ejpam-6266	294	18	rule	rule	NOUN
ejpam-6266	294	19	(	(	PUNCT
ejpam-6266	294	20	110	110	NUM
ejpam-6266	294	21	)	)	PUNCT
ejpam-6266	294	22	as	as	SCONJ
ejpam-6266	294	23	follows	follow	VERB
ejpam-6266	294	24	:	:	PUNCT
ejpam-6266	294	25	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	294	26	,	,	PUNCT
ejpam-6266	294	27	·	·	PUNCT
ejpam-6266	294	28	)	)	PUNCT
ejpam-6266	294	29	|p‖ḣσ−1	|p‖ḣσ−1	PUNCT
ejpam-6266	294	30	=	=	SYM
ejpam-6266	294	31	‖|d|σ−1|ut(s	‖|d|σ−1|ut(s	X
ejpam-6266	294	32	,	,	PUNCT
ejpam-6266	294	33	·	·	PUNCT
ejpam-6266	294	34	)	)	PUNCT
ejpam-6266	294	35	|p‖l2	|p‖l2	VERB
ejpam-6266	294	36	.	.	PUNCT
ejpam-6266	295	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	295	2	,	,	PUNCT
ejpam-6266	295	3	·	·	PUNCT
ejpam-6266	295	4	)	)	PUNCT
ejpam-6266	295	5	‖p−1	‖p−1	NUM
ejpam-6266	296	1	lq1	lq1	PROPN
ejpam-6266	296	2	‖|d|σ−1ut(s	‖|d|σ−1ut(s	PROPN
ejpam-6266	296	3	,	,	PUNCT
ejpam-6266	296	4	·	·	PUNCT
ejpam-6266	296	5	)	)	PUNCT
ejpam-6266	296	6	‖lq2	‖lq2	PROPN
ejpam-6266	296	7	for	for	ADP
ejpam-6266	296	8	p	p	PROPN
ejpam-6266	296	9	>	>	X
ejpam-6266	296	10	dσ	dσ	PROPN
ejpam-6266	296	11	−	−	PROPN
ejpam-6266	296	12	1e	1e	NOUN
ejpam-6266	296	13	,	,	PUNCT
ejpam-6266	296	14	(	(	PUNCT
ejpam-6266	296	15	64	64	NUM
ejpam-6266	296	16	)	)	PUNCT
ejpam-6266	296	17	where	where	SCONJ
ejpam-6266	296	18	p−	p−	NOUN
ejpam-6266	296	19	1	1	NUM
ejpam-6266	296	20	q1	q1	NOUN
ejpam-6266	296	21	+	+	CCONJ
ejpam-6266	296	22	1	1	NUM
ejpam-6266	296	23	q2	q2	NOUN
ejpam-6266	296	24	=	=	SYM
ejpam-6266	296	25	1	1	NUM
ejpam-6266	296	26	2	2	NUM
ejpam-6266	296	27	.	.	PUNCT
ejpam-6266	297	1	(	(	PUNCT
ejpam-6266	297	2	65	65	NUM
ejpam-6266	297	3	)	)	PUNCT
ejpam-6266	297	4	a	a	DET
ejpam-6266	297	5	possible	possible	ADJ
ejpam-6266	297	6	choice	choice	NOUN
ejpam-6266	297	7	is	be	AUX
ejpam-6266	297	8	,	,	PUNCT
ejpam-6266	297	9	for	for	ADP
ejpam-6266	297	10	example	example	NOUN
ejpam-6266	297	11	,	,	PUNCT
ejpam-6266	297	12	q1	q1	PROPN
ejpam-6266	297	13	=	=	PUNCT
ejpam-6266	298	1	n(p	n(p	PROPN
ejpam-6266	298	2	−	−	NUM
ejpam-6266	298	3	1	1	NUM
ejpam-6266	298	4	)	)	PUNCT
ejpam-6266	298	5	and	and	CCONJ
ejpam-6266	298	6	q2	q2	NOUN
ejpam-6266	298	7	=	=	SYM
ejpam-6266	298	8	2n	2n	NUM
ejpam-6266	298	9	n−2	n−2	PROPN
ejpam-6266	298	10	for	for	ADP
ejpam-6266	298	11	n	n	X
ejpam-6266	298	12	≥	≥	NUM
ejpam-6266	298	13	3	3	NUM
ejpam-6266	298	14	.	.	PUNCT
ejpam-6266	299	1	the	the	DET
ejpam-6266	299	2	norm	norm	NOUN
ejpam-6266	299	3	‖ut(s	‖ut(s	PUNCT
ejpam-6266	299	4	,	,	PUNCT
ejpam-6266	299	5	·	·	PUNCT
ejpam-6266	299	6	)	)	PUNCT
ejpam-6266	299	7	‖p−1	‖p−1	PUNCT
ejpam-6266	299	8	lq1	lq1	PROPN
ejpam-6266	299	9	can	can	AUX
ejpam-6266	299	10	be	be	AUX
ejpam-6266	299	11	estimated	estimate	VERB
ejpam-6266	299	12	by	by	ADP
ejpam-6266	299	13	using	use	VERB
ejpam-6266	299	14	classical	classical	ADJ
ejpam-6266	299	15	gagliardo	gagliardo	NOUN
ejpam-6266	299	16	-	-	PUNCT
ejpam-6266	299	17	nirenberg	nirenberg	NOUN
ejpam-6266	299	18	inequality	inequality	NOUN
ejpam-6266	299	19	(	(	PUNCT
ejpam-6266	299	20	107	107	NUM
ejpam-6266	299	21	)	)	PUNCT
ejpam-6266	299	22	.	.	PUNCT
ejpam-6266	300	1	in	in	ADP
ejpam-6266	300	2	this	this	DET
ejpam-6266	300	3	way	way	NOUN
ejpam-6266	300	4	we	we	PRON
ejpam-6266	300	5	may	may	AUX
ejpam-6266	300	6	conclude	conclude	VERB
ejpam-6266	300	7	‖ut(s	‖ut(s	NUM
ejpam-6266	300	8	,	,	PUNCT
ejpam-6266	300	9	·	·	PUNCT
ejpam-6266	300	10	)	)	PUNCT
ejpam-6266	300	11	‖p−1	‖p−1	PUNCT
ejpam-6266	300	12	lq1	lq1	PROPN
ejpam-6266	300	13	.	.	PUNCT
ejpam-6266	301	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	301	2	,	,	PUNCT
ejpam-6266	301	3	·	·	PUNCT
ejpam-6266	301	4	)	)	PUNCT
ejpam-6266	301	5	‖	‖	PROPN
ejpam-6266	301	6	(	(	PUNCT
ejpam-6266	301	7	p−1)(1−θσ,3(q1	p−1)(1−θσ,3(q1	NOUN
ejpam-6266	301	8	)	)	PUNCT
ejpam-6266	301	9	)	)	PUNCT
ejpam-6266	302	1	l2	l2	NOUN
ejpam-6266	302	2	‖|d|σut(s	‖|d|σut(s	PROPN
ejpam-6266	302	3	,	,	PUNCT
ejpam-6266	302	4	·	·	PUNCT
ejpam-6266	302	5	)	)	PUNCT
ejpam-6266	302	6	‖	‖	PROPN
ejpam-6266	302	7	(	(	PUNCT
ejpam-6266	302	8	p−1)θσ,3(q1	p−1)θσ,3(q1	NOUN
ejpam-6266	302	9	)	)	PUNCT
ejpam-6266	302	10	l2	l2	NOUN
ejpam-6266	302	11	.	.	PUNCT
ejpam-6266	303	1	(	(	PUNCT
ejpam-6266	303	2	1	1	NUM
ejpam-6266	303	3	+	+	NUM
ejpam-6266	303	4	s)−γ(p−1)‖u‖p−1	s)−γ(p−1)‖u‖p−1	PROPN
ejpam-6266	303	5	x(t	x(t	PROPN
ejpam-6266	303	6	)	)	PUNCT
ejpam-6266	303	7	,	,	PUNCT
ejpam-6266	303	8	(	(	PUNCT
ejpam-6266	303	9	66	66	NUM
ejpam-6266	303	10	)	)	PUNCT
ejpam-6266	304	1	where	where	SCONJ
ejpam-6266	304	2	θσ,3(q1	θσ,3(q1	PROPN
ejpam-6266	304	3	)	)	PUNCT
ejpam-6266	304	4	=	=	SYM
ejpam-6266	305	1	n	n	PROPN
ejpam-6266	305	2	σ	σ	NOUN
ejpam-6266	305	3	(	(	PUNCT
ejpam-6266	305	4	1	1	NUM
ejpam-6266	305	5	2	2	NUM
ejpam-6266	305	6	−	−	NUM
ejpam-6266	305	7	1	1	NUM
ejpam-6266	305	8	q1	q1	PROPN
ejpam-6266	305	9	)	)	PUNCT
ejpam-6266	305	10	∈	∈	PROPN
ejpam-6266	306	1	[	[	X
ejpam-6266	306	2	0	0	NUM
ejpam-6266	306	3	,	,	PUNCT
ejpam-6266	306	4	1	1	NUM
ejpam-6266	306	5	]	]	PUNCT
ejpam-6266	307	1	if	if	SCONJ
ejpam-6266	307	2	and	and	CCONJ
ejpam-6266	307	3	only	only	ADV
ejpam-6266	307	4	if	if	SCONJ
ejpam-6266	307	5	2	2	NUM
ejpam-6266	307	6	≤	≤	NUM
ejpam-6266	307	7	q1	q1	PROPN
ejpam-6266	307	8	≤	≤	NUM
ejpam-6266	307	9	2n	2n	NUM
ejpam-6266	307	10	n−	n−	NOUN
ejpam-6266	307	11	2σ	2σ	X
ejpam-6266	307	12	if	if	SCONJ
ejpam-6266	307	13	n	n	X
ejpam-6266	307	14	>	>	X
ejpam-6266	307	15	2σ	2σ	NUM
ejpam-6266	307	16	.	.	PUNCT
ejpam-6266	308	1	on	on	ADP
ejpam-6266	308	2	the	the	DET
ejpam-6266	308	3	other	other	ADJ
ejpam-6266	308	4	hand	hand	NOUN
ejpam-6266	308	5	,	,	PUNCT
ejpam-6266	308	6	applying	apply	VERB
ejpam-6266	308	7	the	the	DET
ejpam-6266	308	8	fractional	fractional	ADJ
ejpam-6266	308	9	gagliardo	gagliardo	NOUN
ejpam-6266	308	10	-	-	PUNCT
ejpam-6266	308	11	nirenberg	nirenberg	NOUN
ejpam-6266	308	12	inequality	inequality	NOUN
ejpam-6266	308	13	(	(	PUNCT
ejpam-6266	308	14	106	106	NUM
ejpam-6266	308	15	)	)	PUNCT
ejpam-6266	308	16	gives	give	VERB
ejpam-6266	308	17	‖|d|σ−1ut(s	‖|d|σ−1ut(s	PRON
ejpam-6266	308	18	,	,	PUNCT
ejpam-6266	308	19	·	·	PUNCT
ejpam-6266	308	20	)	)	PUNCT
ejpam-6266	308	21	‖lq2	‖lq2	NOUN
ejpam-6266	308	22	.	.	PUNCT
ejpam-6266	309	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	309	2	,	,	PUNCT
ejpam-6266	309	3	·	·	PUNCT
ejpam-6266	309	4	)	)	PUNCT
ejpam-6266	310	1	‖	‖	PROPN
ejpam-6266	310	2	1−θσ	1−θσ	NUM
ejpam-6266	310	3	,	,	PUNCT
ejpam-6266	310	4	σ−1(q2	σ−1(q2	NOUN
ejpam-6266	310	5	)	)	PUNCT
ejpam-6266	310	6	l2	l2	NOUN
ejpam-6266	310	7	‖|d|σut(s	‖|d|σut(s	PROPN
ejpam-6266	310	8	,	,	PUNCT
ejpam-6266	310	9	·	·	PUNCT
ejpam-6266	310	10	)	)	PUNCT
ejpam-6266	310	11	‖	‖	PROPN
ejpam-6266	310	12	θσ	θσ	ADJ
ejpam-6266	310	13	,	,	PUNCT
ejpam-6266	310	14	σ−1(q2	σ−1(q2	NOUN
ejpam-6266	310	15	)	)	PUNCT
ejpam-6266	310	16	l2	l2	NOUN
ejpam-6266	310	17	t.	t.	PROPN
ejpam-6266	310	18	hadj	hadj	PROPN
ejpam-6266	310	19	kaddour	kaddour	PROPN
ejpam-6266	310	20	et	et	PROPN
ejpam-6266	310	21	al	al	PROPN
ejpam-6266	310	22	.	.	PUNCT
ejpam-6266	310	23	/	/	SYM
ejpam-6266	310	24	eur	eur	PROPN
ejpam-6266	310	25	.	.	PUNCT
ejpam-6266	311	1	j.	j.	PROPN
ejpam-6266	311	2	pure	pure	PROPN
ejpam-6266	311	3	appl	appl	PROPN
ejpam-6266	311	4	.	.	PROPN
ejpam-6266	311	5	math	math	PROPN
ejpam-6266	311	6	,	,	PUNCT
ejpam-6266	311	7	18	18	NUM
ejpam-6266	311	8	(	(	PUNCT
ejpam-6266	311	9	4	4	NUM
ejpam-6266	311	10	)	)	PUNCT
ejpam-6266	311	11	(	(	PUNCT
ejpam-6266	311	12	2025	2025	NUM
ejpam-6266	311	13	)	)	PUNCT
ejpam-6266	311	14	,	,	PUNCT
ejpam-6266	311	15	6266	6266	NUM
ejpam-6266	311	16	14	14	NUM
ejpam-6266	311	17	of	of	ADP
ejpam-6266	311	18	24	24	NUM
ejpam-6266	311	19	.	.	PUNCT
ejpam-6266	312	1	(	(	PUNCT
ejpam-6266	312	2	1	1	X
ejpam-6266	312	3	+	+	CCONJ
ejpam-6266	312	4	s)−γ‖u‖x(t	s)−γ‖u‖x(t	PROPN
ejpam-6266	312	5	)	)	PUNCT
ejpam-6266	312	6	,	,	PUNCT
ejpam-6266	312	7	(	(	PUNCT
ejpam-6266	312	8	67	67	NUM
ejpam-6266	312	9	)	)	PUNCT
ejpam-6266	312	10	where	where	SCONJ
ejpam-6266	312	11	θσ	θσ	NOUN
ejpam-6266	312	12	,	,	PUNCT
ejpam-6266	312	13	σ−1(q2	σ−1(q2	NOUN
ejpam-6266	312	14	)	)	PUNCT
ejpam-6266	312	15	=	=	SYM
ejpam-6266	312	16	n	n	PROPN
ejpam-6266	312	17	σ	σ	NOUN
ejpam-6266	312	18	(	(	PUNCT
ejpam-6266	312	19	1	1	NUM
ejpam-6266	312	20	2	2	NUM
ejpam-6266	312	21	−	−	NUM
ejpam-6266	312	22	1	1	NUM
ejpam-6266	312	23	q2	q2	NOUN
ejpam-6266	312	24	)	)	PUNCT
ejpam-6266	313	1	+	+	CCONJ
ejpam-6266	314	1	σ−1	σ−1	PROPN
ejpam-6266	314	2	σ	σ	NUM
ejpam-6266	314	3	∈	∈	PROPN
ejpam-6266	315	1	[	[	X
ejpam-6266	315	2	σ−1	σ−1	PROPN
ejpam-6266	315	3	σ	σ	PROPN
ejpam-6266	315	4	,	,	PUNCT
ejpam-6266	315	5	1	1	X
ejpam-6266	315	6	]	]	PUNCT
ejpam-6266	315	7	if	if	SCONJ
ejpam-6266	315	8	and	and	CCONJ
ejpam-6266	315	9	only	only	ADV
ejpam-6266	315	10	if	if	SCONJ
ejpam-6266	315	11	2	2	NUM
ejpam-6266	315	12	≤	≤	NUM
ejpam-6266	315	13	q2	q2	NOUN
ejpam-6266	315	14	≤	≤	NOUN
ejpam-6266	315	15	2n	2n	NUM
ejpam-6266	315	16	n−	n−	NOUN
ejpam-6266	315	17	2	2	NUM
ejpam-6266	315	18	if	if	SCONJ
ejpam-6266	315	19	n	n	PRON
ejpam-6266	315	20	≥	≥	NOUN
ejpam-6266	315	21	3	3	NUM
ejpam-6266	315	22	.	.	PUNCT
ejpam-6266	316	1	substituting	substitute	VERB
ejpam-6266	316	2	the	the	DET
ejpam-6266	316	3	estimates	estimate	NOUN
ejpam-6266	316	4	(	(	PUNCT
ejpam-6266	316	5	67	67	NUM
ejpam-6266	316	6	)	)	PUNCT
ejpam-6266	316	7	and	and	CCONJ
ejpam-6266	316	8	(	(	PUNCT
ejpam-6266	316	9	66	66	NUM
ejpam-6266	316	10	)	)	PUNCT
ejpam-6266	316	11	into	into	ADP
ejpam-6266	316	12	(	(	PUNCT
ejpam-6266	316	13	64	64	NUM
ejpam-6266	316	14	)	)	PUNCT
ejpam-6266	316	15	we	we	PRON
ejpam-6266	316	16	obtain	obtain	VERB
ejpam-6266	316	17	the	the	DET
ejpam-6266	316	18	estimate	estimate	NOUN
ejpam-6266	316	19	‖|u(s	‖|u(s	NUM
ejpam-6266	316	20	,	,	PUNCT
ejpam-6266	316	21	·	·	PUNCT
ejpam-6266	316	22	)	)	PUNCT
ejpam-6266	316	23	|p‖ḣσ−1	|p‖ḣσ−1	X
ejpam-6266	316	24	.	.	PUNCT
ejpam-6266	317	1	(	(	PUNCT
ejpam-6266	317	2	1	1	NUM
ejpam-6266	317	3	+	+	NUM
ejpam-6266	317	4	s)−γp‖u‖px(t	s)−γp‖u‖px(t	PROPN
ejpam-6266	317	5	)	)	PUNCT
ejpam-6266	317	6	=	=	PUNCT
ejpam-6266	318	1	(	(	PUNCT
ejpam-6266	318	2	1	1	NUM
ejpam-6266	318	3	+	+	CCONJ
ejpam-6266	318	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	318	5	)	)	PUNCT
ejpam-6266	318	6	,	,	PUNCT
ejpam-6266	318	7	(	(	PUNCT
ejpam-6266	318	8	68	68	NUM
ejpam-6266	318	9	)	)	PUNCT
ejpam-6266	318	10	where	where	SCONJ
ejpam-6266	318	11	β	β	PROPN
ejpam-6266	318	12	is	be	AUX
ejpam-6266	318	13	defined	define	VERB
ejpam-6266	318	14	by	by	ADP
ejpam-6266	318	15	(	(	PUNCT
ejpam-6266	318	16	61	61	NUM
ejpam-6266	318	17	)	)	PUNCT
ejpam-6266	318	18	.	.	PUNCT
ejpam-6266	319	1	consequently	consequently	ADV
ejpam-6266	319	2	,	,	PUNCT
ejpam-6266	319	3	from	from	ADP
ejpam-6266	319	4	the	the	DET
ejpam-6266	319	5	estimates	estimate	NOUN
ejpam-6266	319	6	(	(	PUNCT
ejpam-6266	319	7	68	68	NUM
ejpam-6266	319	8	)	)	PUNCT
ejpam-6266	319	9	and	and	CCONJ
ejpam-6266	319	10	(	(	PUNCT
ejpam-6266	319	11	62	62	NUM
ejpam-6266	319	12	)	)	PUNCT
ejpam-6266	319	13	we	we	PRON
ejpam-6266	319	14	conclude	conclude	VERB
ejpam-6266	319	15	the	the	DET
ejpam-6266	319	16	estimate	estimate	NOUN
ejpam-6266	319	17	‖|u(s	‖|u(s	NUM
ejpam-6266	319	18	,	,	PUNCT
ejpam-6266	319	19	·	·	PUNCT
ejpam-6266	319	20	)	)	PUNCT
ejpam-6266	319	21	|p‖lm∩l2∩ḣσ−1	|p‖lm∩l2∩ḣσ−1	PROPN
ejpam-6266	319	22	.	.	PUNCT
ejpam-6266	320	1	(	(	PUNCT
ejpam-6266	320	2	1	1	NUM
ejpam-6266	320	3	+	+	CCONJ
ejpam-6266	320	4	s)−β‖u‖px(t	s)−β‖u‖px(t	PROPN
ejpam-6266	320	5	)	)	PUNCT
ejpam-6266	320	6	,	,	PUNCT
ejpam-6266	320	7	(	(	PUNCT
ejpam-6266	320	8	69	69	NUM
ejpam-6266	320	9	)	)	PUNCT
ejpam-6266	320	10	where	where	SCONJ
ejpam-6266	320	11	β	β	PROPN
ejpam-6266	320	12	is	be	AUX
ejpam-6266	320	13	defined	define	VERB
ejpam-6266	320	14	by	by	ADP
ejpam-6266	320	15	(	(	PUNCT
ejpam-6266	320	16	61	61	NUM
ejpam-6266	320	17	)	)	PUNCT
ejpam-6266	320	18	.	.	PUNCT
ejpam-6266	320	19	notice	notice	VERB
ejpam-6266	320	20	that	that	SCONJ
ejpam-6266	320	21	β	β	NOUN
ejpam-6266	320	22	>	>	X
ejpam-6266	320	23	1	1	NUM
ejpam-6266	320	24	if	if	SCONJ
ejpam-6266	320	25	and	and	CCONJ
ejpam-6266	320	26	only	only	ADV
ejpam-6266	320	27	if	if	SCONJ
ejpam-6266	320	28	p	p	X
ejpam-6266	320	29	>	>	X
ejpam-6266	320	30	pγ	pγ	PROPN
ejpam-6266	320	31	,	,	PUNCT
ejpam-6266	320	32	m(n	m(n	PROPN
ejpam-6266	320	33	)	)	PUNCT
ejpam-6266	320	34	.	.	PUNCT
ejpam-6266	321	1	then	then	ADV
ejpam-6266	321	2	,	,	PUNCT
ejpam-6266	321	3	plugging	plug	VERB
ejpam-6266	321	4	(	(	PUNCT
ejpam-6266	321	5	69	69	NUM
ejpam-6266	321	6	)	)	PUNCT
ejpam-6266	321	7	into	into	ADP
ejpam-6266	321	8	(	(	PUNCT
ejpam-6266	321	9	59	59	NUM
ejpam-6266	321	10	)	)	PUNCT
ejpam-6266	321	11	we	we	PRON
ejpam-6266	321	12	get	get	VERB
ejpam-6266	321	13	‖|d|κunl(t	‖|d|κunl(t	INTJ
ejpam-6266	321	14	,	,	PUNCT
ejpam-6266	321	15	·	·	PUNCT
ejpam-6266	321	16	)	)	PUNCT
ejpam-6266	321	17	‖l2	‖l2	VERB
ejpam-6266	321	18	.	.	PUNCT
ejpam-6266	322	1	‖u‖px(t	‖u‖px(t	PROPN
ejpam-6266	322	2	)	)	PUNCT
ejpam-6266	323	1	∫	∫	PROPN
ejpam-6266	323	2	t	t	PROPN
ejpam-6266	323	3	0	0	NUM
ejpam-6266	323	4	(	(	PUNCT
ejpam-6266	323	5	1	1	NUM
ejpam-6266	323	6	+	+	ADP
ejpam-6266	323	7	t−	t−	PROPN
ejpam-6266	323	8	τ))−	τ))−	ADJ
ejpam-6266	323	9	n	n	ADV
ejpam-6266	323	10	2	2	NUM
ejpam-6266	323	11	(	(	PUNCT
ejpam-6266	323	12	1	1	NUM
ejpam-6266	323	13	m	m	NOUN
ejpam-6266	323	14	−	−	NUM
ejpam-6266	323	15	1	1	NUM
ejpam-6266	323	16	2	2	NUM
ejpam-6266	323	17	)	)	PUNCT
ejpam-6266	323	18	−κ	−κ	NOUN
ejpam-6266	323	19	2	2	NUM
ejpam-6266	323	20	×	×	NOUN
ejpam-6266	323	21	∫	∫	PROPN
ejpam-6266	323	22	τ	τ	X
ejpam-6266	323	23	0	0	NUM
ejpam-6266	324	1	(	(	PUNCT
ejpam-6266	324	2	τ	τ	X
ejpam-6266	324	3	−	−	NOUN
ejpam-6266	324	4	s)−γ(1	s)−γ(1	PROPN
ejpam-6266	325	1	+	+	CCONJ
ejpam-6266	325	2	s)−β	s)−β	ADJ
ejpam-6266	325	3	dsdτ	dsdτ	NOUN
ejpam-6266	325	4	.	.	PUNCT
ejpam-6266	326	1	jκ,0	jκ,0	PROPN
ejpam-6266	326	2	n	n	CCONJ
ejpam-6266	326	3	(	(	PUNCT
ejpam-6266	326	4	t)‖u‖px(t	t)‖u‖px(t	PROPN
ejpam-6266	326	5	)	)	PUNCT
ejpam-6266	326	6	,	,	PUNCT
ejpam-6266	326	7	(	(	PUNCT
ejpam-6266	326	8	70	70	NUM
ejpam-6266	326	9	)	)	PUNCT
ejpam-6266	326	10	where	where	SCONJ
ejpam-6266	326	11	jκ,0	jκ,0	PROPN
ejpam-6266	326	12	n	n	CCONJ
ejpam-6266	326	13	(	(	PUNCT
ejpam-6266	326	14	t	t	PROPN
ejpam-6266	326	15	)	)	PUNCT
ejpam-6266	326	16	is	be	AUX
ejpam-6266	326	17	defined	define	VERB
ejpam-6266	326	18	by	by	ADP
ejpam-6266	326	19	(	(	PUNCT
ejpam-6266	326	20	18	18	NUM
ejpam-6266	326	21	)	)	PUNCT
ejpam-6266	326	22	(	(	PUNCT
ejpam-6266	326	23	case	case	NOUN
ejpam-6266	326	24	(	(	PUNCT
ejpam-6266	326	25	k	k	X
ejpam-6266	326	26	,	,	PUNCT
ejpam-6266	326	27	j	j	NOUN
ejpam-6266	326	28	)	)	PUNCT
ejpam-6266	326	29	=	=	SYM
ejpam-6266	326	30	(	(	PUNCT
ejpam-6266	326	31	κ	κ	NOUN
ejpam-6266	326	32	,	,	PUNCT
ejpam-6266	326	33	0	0	NUM
ejpam-6266	326	34	)	)	PUNCT
ejpam-6266	326	35	)	)	PUNCT
ejpam-6266	326	36	.	.	PUNCT
ejpam-6266	327	1	so	so	ADV
ejpam-6266	327	2	,	,	PUNCT
ejpam-6266	327	3	due	due	ADP
ejpam-6266	327	4	to	to	ADP
ejpam-6266	327	5	lemma	lemma	PROPN
ejpam-6266	327	6	1	1	NUM
ejpam-6266	327	7	and	and	CCONJ
ejpam-6266	327	8	the	the	DET
ejpam-6266	327	9	assumptions	assumption	NOUN
ejpam-6266	327	10	of	of	ADP
ejpam-6266	327	11	theorem	theorem	NOUN
ejpam-6266	327	12	3	3	NUM
ejpam-6266	327	13	we	we	PRON
ejpam-6266	327	14	may	may	AUX
ejpam-6266	327	15	estimate	estimate	VERB
ejpam-6266	327	16	jκ,0	jκ,0	PROPN
ejpam-6266	327	17	n	n	CCONJ
ejpam-6266	327	18	(	(	PUNCT
ejpam-6266	327	19	t	t	PROPN
ejpam-6266	327	20	)	)	PUNCT
ejpam-6266	327	21	for	for	ADP
ejpam-6266	327	22	κ	κ	NOUN
ejpam-6266	327	23	=	=	SYM
ejpam-6266	327	24	0	0	NUM
ejpam-6266	327	25	or	or	CCONJ
ejpam-6266	327	26	κ	κ	X
ejpam-6266	327	27	=	=	PUNCT
ejpam-6266	327	28	σ	σ	NOUN
ejpam-6266	327	29	as	as	SCONJ
ejpam-6266	327	30	follows	follow	VERB
ejpam-6266	327	31	:	:	PUNCT
ejpam-6266	327	32	jκ,0	jκ,0	PROPN
ejpam-6266	327	33	n	n	CCONJ
ejpam-6266	327	34	(	(	PUNCT
ejpam-6266	327	35	t	t	PROPN
ejpam-6266	327	36	)	)	PUNCT
ejpam-6266	327	37	.	.	PUNCT
ejpam-6266	328	1	{	{	PUNCT
ejpam-6266	328	2	(	(	PUNCT
ejpam-6266	328	3	1	1	NUM
ejpam-6266	328	4	+	+	NUM
ejpam-6266	328	5	t)1−	t)1−	NOUN
ejpam-6266	328	6	n	n	ADP
ejpam-6266	328	7	2	2	NUM
ejpam-6266	328	8	(	(	PUNCT
ejpam-6266	328	9	1	1	NUM
ejpam-6266	328	10	m	m	NOUN
ejpam-6266	328	11	−	−	NUM
ejpam-6266	328	12	1	1	NUM
ejpam-6266	328	13	2	2	NUM
ejpam-6266	328	14	)	)	PUNCT
ejpam-6266	328	15	−γ	−γ	NOUN
ejpam-6266	328	16	if	if	SCONJ
ejpam-6266	328	17	κ	κ	NOUN
ejpam-6266	328	18	=	=	SYM
ejpam-6266	328	19	0	0	PROPN
ejpam-6266	328	20	,	,	PUNCT
ejpam-6266	328	21	(	(	PUNCT
ejpam-6266	328	22	1	1	NUM
ejpam-6266	328	23	+	+	SYM
ejpam-6266	328	24	t)−γ	t)−γ	PRON
ejpam-6266	328	25	if	if	SCONJ
ejpam-6266	328	26	κ	κ	X
ejpam-6266	328	27	=	=	PROPN
ejpam-6266	328	28	σ	σ	PROPN
ejpam-6266	328	29	.	.	PUNCT
ejpam-6266	329	1	(	(	PUNCT
ejpam-6266	329	2	71	71	NUM
ejpam-6266	329	3	)	)	PUNCT
ejpam-6266	329	4	the	the	DET
ejpam-6266	329	5	estimates	estimate	NOUN
ejpam-6266	329	6	(	(	PUNCT
ejpam-6266	329	7	71	71	NUM
ejpam-6266	329	8	)	)	PUNCT
ejpam-6266	329	9	lead	lead	NOUN
ejpam-6266	329	10	to	to	ADP
ejpam-6266	329	11	the	the	DET
ejpam-6266	329	12	following	follow	VERB
ejpam-6266	329	13	estimates	estimate	NOUN
ejpam-6266	329	14	:	:	PUNCT
ejpam-6266	329	15	‖unl(t	‖unl(t	NOUN
ejpam-6266	329	16	,	,	PUNCT
ejpam-6266	329	17	·	·	PUNCT
ejpam-6266	329	18	)	)	PUNCT
ejpam-6266	329	19	‖l2	‖l2	X
ejpam-6266	329	20	.	.	PUNCT
ejpam-6266	330	1	(	(	PUNCT
ejpam-6266	330	2	1	1	NUM
ejpam-6266	330	3	+	+	NUM
ejpam-6266	330	4	t)1−	t)1−	NOUN
ejpam-6266	330	5	n	n	ADP
ejpam-6266	330	6	2	2	NUM
ejpam-6266	330	7	(	(	PUNCT
ejpam-6266	330	8	1	1	NUM
ejpam-6266	330	9	m	m	NOUN
ejpam-6266	330	10	−	−	NUM
ejpam-6266	330	11	1	1	NUM
ejpam-6266	330	12	2	2	NUM
ejpam-6266	330	13	)	)	PUNCT
ejpam-6266	330	14	−γ‖u‖px(t	−γ‖u‖px(t	PROPN
ejpam-6266	330	15	)	)	PUNCT
ejpam-6266	330	16	,	,	PUNCT
ejpam-6266	330	17	(	(	PUNCT
ejpam-6266	330	18	72	72	NUM
ejpam-6266	330	19	)	)	PUNCT
ejpam-6266	330	20	and	and	CCONJ
ejpam-6266	330	21	∥∥|d|σunl(t	∥∥|d|σunl(t	PROPN
ejpam-6266	330	22	,	,	PUNCT
ejpam-6266	330	23	·	·	PUNCT
ejpam-6266	330	24	)	)	PUNCT
ejpam-6266	330	25	∥∥	∥∥	X
ejpam-6266	330	26	l2	l2	NOUN
ejpam-6266	330	27	.	.	PUNCT
ejpam-6266	331	1	(	(	PUNCT
ejpam-6266	331	2	1	1	X
ejpam-6266	331	3	+	+	NUM
ejpam-6266	331	4	t)−γ‖u‖px(t	t)−γ‖u‖px(t	PROPN
ejpam-6266	331	5	)	)	PUNCT
ejpam-6266	331	6	.	.	PUNCT
ejpam-6266	332	1	(	(	PUNCT
ejpam-6266	332	2	73	73	NUM
ejpam-6266	332	3	)	)	PUNCT
ejpam-6266	332	4	now	now	ADV
ejpam-6266	332	5	let	let	VERB
ejpam-6266	332	6	us	we	PRON
ejpam-6266	332	7	turn	turn	VERB
ejpam-6266	332	8	to	to	PART
ejpam-6266	332	9	estimate	estimate	VERB
ejpam-6266	332	10	the	the	DET
ejpam-6266	332	11	norms	norm	NOUN
ejpam-6266	332	12	‖unlt	‖unlt	PROPN
ejpam-6266	332	13	(	(	PUNCT
ejpam-6266	332	14	t	t	PROPN
ejpam-6266	332	15	,	,	PUNCT
ejpam-6266	332	16	·	·	PUNCT
ejpam-6266	332	17	)	)	PUNCT
ejpam-6266	332	18	‖l2	‖l2	ADJ
ejpam-6266	332	19	and	and	CCONJ
ejpam-6266	332	20	‖|d|σ−1unlt	‖|d|σ−1unlt	PROPN
ejpam-6266	332	21	(	(	PUNCT
ejpam-6266	332	22	t	t	PROPN
ejpam-6266	332	23	,	,	PUNCT
ejpam-6266	332	24	·	·	PUNCT
ejpam-6266	332	25	)	)	PUNCT
ejpam-6266	332	26	‖l2	‖l2	VERB
ejpam-6266	332	27	.	.	PUNCT
ejpam-6266	333	1	again	again	ADV
ejpam-6266	333	2	,	,	PUNCT
ejpam-6266	333	3	by	by	ADP
ejpam-6266	333	4	proposition	proposition	NOUN
ejpam-6266	333	5	2	2	NUM
ejpam-6266	333	6	,	,	PUNCT
ejpam-6266	333	7	we	we	PRON
ejpam-6266	333	8	have	have	VERB
ejpam-6266	333	9	for	for	ADP
ejpam-6266	333	10	κ	κ	NOUN
ejpam-6266	333	11	=	=	SYM
ejpam-6266	333	12	1	1	NUM
ejpam-6266	333	13	,	,	PUNCT
ejpam-6266	333	14	σ	σ	NOUN
ejpam-6266	333	15	the	the	DET
ejpam-6266	333	16	estimates	estimate	NOUN
ejpam-6266	333	17	‖|d|κ−1unlt	‖|d|κ−1unlt	PROPN
ejpam-6266	333	18	(	(	PUNCT
ejpam-6266	333	19	t	t	PROPN
ejpam-6266	333	20	,	,	PUNCT
ejpam-6266	333	21	·	·	PUNCT
ejpam-6266	333	22	)	)	PUNCT
ejpam-6266	333	23	‖l2	‖l2	VERB
ejpam-6266	333	24	.	.	PUNCT
ejpam-6266	334	1	∫	∫	PROPN
ejpam-6266	334	2	t	t	PROPN
ejpam-6266	334	3	0	0	NUM
ejpam-6266	335	1	(	(	PUNCT
ejpam-6266	335	2	1	1	NUM
ejpam-6266	335	3	+	+	CCONJ
ejpam-6266	335	4	t−	t−	PROPN
ejpam-6266	335	5	τ)−	τ)−	PROPN
ejpam-6266	335	6	n	n	CCONJ
ejpam-6266	335	7	2	2	NUM
ejpam-6266	335	8	(	(	PUNCT
ejpam-6266	335	9	1	1	NUM
ejpam-6266	335	10	m	m	NOUN
ejpam-6266	335	11	−	−	NUM
ejpam-6266	335	12	1	1	NUM
ejpam-6266	335	13	2	2	NUM
ejpam-6266	335	14	)	)	PUNCT
ejpam-6266	335	15	−κ−1	−κ−1	X
ejpam-6266	335	16	2	2	NUM
ejpam-6266	335	17	−1	−1	NOUN
ejpam-6266	335	18	×	×	NOUN
ejpam-6266	335	19	∫	∫	PROPN
ejpam-6266	335	20	τ	τ	X
ejpam-6266	335	21	0	0	NUM
ejpam-6266	335	22	(	(	PUNCT
ejpam-6266	335	23	τ	τ	X
ejpam-6266	335	24	−	−	PROPN
ejpam-6266	335	25	s)−γ	s)−γ	PROPN
ejpam-6266	335	26	∥∥|u(s	∥∥|u(s	PROPN
ejpam-6266	335	27	,	,	PUNCT
ejpam-6266	335	28	·	·	PUNCT
ejpam-6266	335	29	)	)	PUNCT
ejpam-6266	335	30	|p∥∥	|p∥∥	NUM
ejpam-6266	335	31	lm∩l2∩ḣσ−1	lm∩l2∩ḣσ−1	NUM
ejpam-6266	335	32	dsdτ	dsdτ	NOUN
ejpam-6266	335	33	.	.	PUNCT
ejpam-6266	336	1	(	(	PUNCT
ejpam-6266	336	2	74	74	X
ejpam-6266	336	3	)	)	PUNCT
ejpam-6266	336	4	t.	t.	NOUN
ejpam-6266	336	5	hadj	hadj	PROPN
ejpam-6266	336	6	kaddour	kaddour	PROPN
ejpam-6266	336	7	et	et	PROPN
ejpam-6266	336	8	al	al	PROPN
ejpam-6266	336	9	.	.	PUNCT
ejpam-6266	336	10	/	/	SYM
ejpam-6266	336	11	eur	eur	PROPN
ejpam-6266	336	12	.	.	PUNCT
ejpam-6266	337	1	j.	j.	PROPN
ejpam-6266	337	2	pure	pure	PROPN
ejpam-6266	337	3	appl	appl	PROPN
ejpam-6266	337	4	.	.	PROPN
ejpam-6266	337	5	math	math	PROPN
ejpam-6266	337	6	,	,	PUNCT
ejpam-6266	337	7	18	18	NUM
ejpam-6266	337	8	(	(	PUNCT
ejpam-6266	337	9	4	4	NUM
ejpam-6266	337	10	)	)	PUNCT
ejpam-6266	337	11	(	(	PUNCT
ejpam-6266	337	12	2025	2025	NUM
ejpam-6266	337	13	)	)	PUNCT
ejpam-6266	337	14	,	,	PUNCT
ejpam-6266	337	15	6266	6266	NUM
ejpam-6266	337	16	15	15	NUM
ejpam-6266	337	17	of	of	ADP
ejpam-6266	337	18	24	24	NUM
ejpam-6266	337	19	taking	take	VERB
ejpam-6266	337	20	into	into	ADP
ejpam-6266	337	21	account	account	NOUN
ejpam-6266	337	22	the	the	DET
ejpam-6266	337	23	estimate	estimate	NOUN
ejpam-6266	337	24	(	(	PUNCT
ejpam-6266	337	25	69	69	NUM
ejpam-6266	337	26	)	)	PUNCT
ejpam-6266	337	27	we	we	PRON
ejpam-6266	337	28	get	get	VERB
ejpam-6266	337	29	from	from	ADP
ejpam-6266	337	30	(	(	PUNCT
ejpam-6266	337	31	74	74	NUM
ejpam-6266	337	32	)	)	PUNCT
ejpam-6266	337	33	the	the	DET
ejpam-6266	337	34	estimates	estimate	NOUN
ejpam-6266	337	35	‖|d|κ−1unlt	‖|d|κ−1unlt	PROPN
ejpam-6266	337	36	(	(	PUNCT
ejpam-6266	337	37	t	t	PROPN
ejpam-6266	337	38	,	,	PUNCT
ejpam-6266	337	39	·	·	PUNCT
ejpam-6266	337	40	)	)	PUNCT
ejpam-6266	337	41	‖l2	‖l2	VERB
ejpam-6266	337	42	.	.	PUNCT
ejpam-6266	338	1	j	j	PROPN
ejpam-6266	338	2	(	(	PUNCT
ejpam-6266	338	3	κ−1,1	κ−1,1	NOUN
ejpam-6266	338	4	)	)	PUNCT
ejpam-6266	338	5	n	n	PROPN
ejpam-6266	338	6	(	(	PUNCT
ejpam-6266	338	7	t)‖u‖px(t	t)‖u‖px(t	PROPN
ejpam-6266	338	8	)	)	PUNCT
ejpam-6266	338	9	,	,	PUNCT
ejpam-6266	338	10	(	(	PUNCT
ejpam-6266	338	11	75	75	NUM
ejpam-6266	338	12	)	)	PUNCT
ejpam-6266	338	13	where	where	SCONJ
ejpam-6266	338	14	j	j	PROPN
ejpam-6266	338	15	(	(	PUNCT
ejpam-6266	338	16	κ−1,1	κ−1,1	NOUN
ejpam-6266	338	17	)	)	PUNCT
ejpam-6266	338	18	n	n	PROPN
ejpam-6266	338	19	(	(	PUNCT
ejpam-6266	338	20	t	t	NOUN
ejpam-6266	338	21	)	)	PUNCT
ejpam-6266	338	22	is	be	AUX
ejpam-6266	338	23	defined	define	VERB
ejpam-6266	338	24	by	by	ADP
ejpam-6266	338	25	(	(	PUNCT
ejpam-6266	338	26	18	18	NUM
ejpam-6266	338	27	)	)	PUNCT
ejpam-6266	338	28	(	(	PUNCT
ejpam-6266	338	29	case	case	NOUN
ejpam-6266	338	30	(	(	PUNCT
ejpam-6266	338	31	k	k	X
ejpam-6266	338	32	,	,	PUNCT
ejpam-6266	338	33	j	j	NOUN
ejpam-6266	338	34	)	)	PUNCT
ejpam-6266	338	35	=	=	PUNCT
ejpam-6266	338	36	(	(	PUNCT
ejpam-6266	338	37	κ	κ	X
ejpam-6266	338	38	−	−	PROPN
ejpam-6266	338	39	1	1	NUM
ejpam-6266	338	40	,	,	PUNCT
ejpam-6266	338	41	1	1	NUM
ejpam-6266	338	42	)	)	PUNCT
ejpam-6266	338	43	)	)	PUNCT
ejpam-6266	338	44	.	.	PUNCT
ejpam-6266	339	1	thanks	thank	NOUN
ejpam-6266	339	2	to	to	ADP
ejpam-6266	339	3	lemma	lemma	PROPN
ejpam-6266	339	4	1	1	NUM
ejpam-6266	339	5	,	,	PUNCT
ejpam-6266	339	6	the	the	DET
ejpam-6266	339	7	integral	integral	ADJ
ejpam-6266	339	8	j	j	PROPN
ejpam-6266	339	9	(	(	PUNCT
ejpam-6266	339	10	κ−1,1	κ−1,1	NOUN
ejpam-6266	339	11	)	)	PUNCT
ejpam-6266	339	12	n	n	PROPN
ejpam-6266	339	13	(	(	PUNCT
ejpam-6266	339	14	t	t	NOUN
ejpam-6266	339	15	)	)	PUNCT
ejpam-6266	339	16	is	be	AUX
ejpam-6266	339	17	estimated	estimate	VERB
ejpam-6266	339	18	in	in	ADP
ejpam-6266	339	19	both	both	DET
ejpam-6266	339	20	cases	case	NOUN
ejpam-6266	339	21	κ	κ	X
ejpam-6266	339	22	=	=	SYM
ejpam-6266	339	23	1	1	NUM
ejpam-6266	339	24	and	and	CCONJ
ejpam-6266	339	25	κ	κ	PROPN
ejpam-6266	339	26	=	=	SYM
ejpam-6266	339	27	σ	σ	PROPN
ejpam-6266	339	28	,	,	PUNCT
ejpam-6266	339	29	as	as	SCONJ
ejpam-6266	339	30	follows	follow	VERB
ejpam-6266	339	31	:	:	PUNCT
ejpam-6266	339	32	j	j	PROPN
ejpam-6266	339	33	(	(	PUNCT
ejpam-6266	339	34	κ−1,1	κ−1,1	NOUN
ejpam-6266	339	35	)	)	PUNCT
ejpam-6266	339	36	n	n	PROPN
ejpam-6266	339	37	(	(	PUNCT
ejpam-6266	339	38	t	t	PROPN
ejpam-6266	339	39	)	)	PUNCT
ejpam-6266	339	40	.	.	PUNCT
ejpam-6266	340	1	(	(	PUNCT
ejpam-6266	340	2	1	1	X
ejpam-6266	340	3	+	+	SYM
ejpam-6266	340	4	t)−γ	t)−γ	X
ejpam-6266	340	5	.	.	PUNCT
ejpam-6266	341	1	(	(	PUNCT
ejpam-6266	341	2	76	76	NUM
ejpam-6266	341	3	)	)	PUNCT
ejpam-6266	341	4	including	include	VERB
ejpam-6266	341	5	the	the	DET
ejpam-6266	341	6	estimate	estimate	NOUN
ejpam-6266	341	7	(	(	PUNCT
ejpam-6266	341	8	76	76	NUM
ejpam-6266	341	9	)	)	PUNCT
ejpam-6266	341	10	into	into	ADP
ejpam-6266	341	11	(	(	PUNCT
ejpam-6266	341	12	75	75	NUM
ejpam-6266	341	13	)	)	PUNCT
ejpam-6266	341	14	we	we	PRON
ejpam-6266	341	15	find	find	VERB
ejpam-6266	341	16	for	for	ADP
ejpam-6266	341	17	κ	κ	NOUN
ejpam-6266	341	18	=	=	SYM
ejpam-6266	341	19	1	1	NUM
ejpam-6266	341	20	‖unlt	‖unlt	X
ejpam-6266	341	21	(	(	PUNCT
ejpam-6266	341	22	t	t	PROPN
ejpam-6266	341	23	,	,	PUNCT
ejpam-6266	341	24	·	·	PUNCT
ejpam-6266	341	25	)	)	PUNCT
ejpam-6266	341	26	‖l2	‖l2	X
ejpam-6266	341	27	.	.	PUNCT
ejpam-6266	342	1	(	(	PUNCT
ejpam-6266	342	2	1	1	NUM
ejpam-6266	342	3	+	+	NUM
ejpam-6266	342	4	t)−γ‖u‖px(t	t)−γ‖u‖px(t	PROPN
ejpam-6266	342	5	)	)	PUNCT
ejpam-6266	342	6	,	,	PUNCT
ejpam-6266	342	7	(	(	PUNCT
ejpam-6266	342	8	77	77	NUM
ejpam-6266	342	9	)	)	PUNCT
ejpam-6266	342	10	and	and	CCONJ
ejpam-6266	342	11	for	for	ADP
ejpam-6266	342	12	κ	κ	NOUN
ejpam-6266	342	13	=	=	SYM
ejpam-6266	342	14	σ	σ	PROPN
ejpam-6266	342	15	‖|d|σ−1unlt	‖|d|σ−1unlt	PROPN
ejpam-6266	342	16	(	(	PUNCT
ejpam-6266	342	17	t	t	PROPN
ejpam-6266	342	18	,	,	PUNCT
ejpam-6266	342	19	·	·	PUNCT
ejpam-6266	342	20	)	)	PUNCT
ejpam-6266	342	21	‖l2	‖l2	X
ejpam-6266	342	22	.	.	PUNCT
ejpam-6266	343	1	(	(	PUNCT
ejpam-6266	343	2	1	1	NUM
ejpam-6266	343	3	+	+	NUM
ejpam-6266	343	4	t)−γ‖u‖px(t	t)−γ‖u‖px(t	PROPN
ejpam-6266	343	5	)	)	PUNCT
ejpam-6266	343	6	.	.	PUNCT
ejpam-6266	344	1	(	(	PUNCT
ejpam-6266	344	2	78	78	NUM
ejpam-6266	344	3	)	)	PUNCT
ejpam-6266	344	4	finally	finally	ADV
ejpam-6266	344	5	,	,	PUNCT
ejpam-6266	344	6	the	the	DET
ejpam-6266	344	7	desired	desire	VERB
ejpam-6266	344	8	inequality	inequality	NOUN
ejpam-6266	344	9	(	(	PUNCT
ejpam-6266	344	10	58	58	NUM
ejpam-6266	344	11	)	)	PUNCT
ejpam-6266	344	12	is	be	AUX
ejpam-6266	344	13	concluded	conclude	VERB
ejpam-6266	344	14	after	after	ADP
ejpam-6266	344	15	using	use	VERB
ejpam-6266	344	16	the	the	DET
ejpam-6266	344	17	estimates	estimate	NOUN
ejpam-6266	344	18	(	(	PUNCT
ejpam-6266	344	19	72	72	NUM
ejpam-6266	344	20	)	)	PUNCT
ejpam-6266	344	21	,	,	PUNCT
ejpam-6266	344	22	(	(	PUNCT
ejpam-6266	344	23	73	73	NUM
ejpam-6266	344	24	)	)	PUNCT
ejpam-6266	344	25	(	(	PUNCT
ejpam-6266	344	26	77	77	NUM
ejpam-6266	344	27	)	)	PUNCT
ejpam-6266	344	28	,	,	PUNCT
ejpam-6266	344	29	(	(	PUNCT
ejpam-6266	344	30	78	78	NUM
ejpam-6266	344	31	)	)	PUNCT
ejpam-6266	344	32	and	and	CCONJ
ejpam-6266	344	33	the	the	DET
ejpam-6266	344	34	definition	definition	NOUN
ejpam-6266	344	35	(	(	PUNCT
ejpam-6266	344	36	57	57	NUM
ejpam-6266	344	37	)	)	PUNCT
ejpam-6266	344	38	of	of	ADP
ejpam-6266	344	39	the	the	DET
ejpam-6266	344	40	norm	norm	NOUN
ejpam-6266	344	41	in	in	ADP
ejpam-6266	344	42	x(t	x(t	PROPN
ejpam-6266	344	43	)	)	PUNCT
ejpam-6266	344	44	.	.	PUNCT
ejpam-6266	345	1	summarizing	summarize	VERB
ejpam-6266	345	2	we	we	PRON
ejpam-6266	345	3	obtained	obtain	VERB
ejpam-6266	345	4	(	(	PUNCT
ejpam-6266	345	5	15	15	NUM
ejpam-6266	345	6	)	)	PUNCT
ejpam-6266	345	7	.	.	PUNCT
ejpam-6266	346	1	now	now	ADV
ejpam-6266	346	2	,	,	PUNCT
ejpam-6266	346	3	let	let	VERB
ejpam-6266	346	4	us	we	PRON
ejpam-6266	346	5	turn	turn	VERB
ejpam-6266	346	6	to	to	ADP
ejpam-6266	346	7	the	the	DET
ejpam-6266	346	8	inequality	inequality	NOUN
ejpam-6266	346	9	(	(	PUNCT
ejpam-6266	346	10	16	16	NUM
ejpam-6266	346	11	)	)	PUNCT
ejpam-6266	346	12	.	.	PUNCT
ejpam-6266	347	1	taking	take	VERB
ejpam-6266	347	2	into	into	ADP
ejpam-6266	347	3	account	account	NOUN
ejpam-6266	347	4	the	the	DET
ejpam-6266	347	5	definition	definition	NOUN
ejpam-6266	347	6	of	of	ADP
ejpam-6266	347	7	the	the	DET
ejpam-6266	347	8	aaplication	aaplication	NOUN
ejpam-6266	347	9	n	n	CCONJ
ejpam-6266	347	10	,	,	PUNCT
ejpam-6266	347	11	we	we	PRON
ejpam-6266	347	12	have	have	VERB
ejpam-6266	347	13	by	by	ADP
ejpam-6266	347	14	proposition	proposition	NOUN
ejpam-6266	347	15	2	2	NUM
ejpam-6266	347	16	for	for	ADP
ejpam-6266	347	17	κ	κ	NOUN
ejpam-6266	347	18	=	=	SYM
ejpam-6266	347	19	0	0	PROPN
ejpam-6266	347	20	and	and	CCONJ
ejpam-6266	347	21	σ	σ	NOUN
ejpam-6266	347	22	the	the	DET
ejpam-6266	347	23	estimates	estimate	NOUN
ejpam-6266	347	24	‖|d|κ(nu−nv)(t	‖|d|κ(nu−nv)(t	ADP
ejpam-6266	347	25	,	,	PUNCT
ejpam-6266	347	26	·	·	PUNCT
ejpam-6266	347	27	)	)	PUNCT
ejpam-6266	347	28	‖l2	‖l2	VERB
ejpam-6266	347	29	.	.	PUNCT
ejpam-6266	348	1	∫	∫	PROPN
ejpam-6266	348	2	t	t	PROPN
ejpam-6266	348	3	0	0	NUM
ejpam-6266	349	1	(	(	PUNCT
ejpam-6266	349	2	1	1	NUM
ejpam-6266	349	3	+	+	CCONJ
ejpam-6266	349	4	t−	t−	PROPN
ejpam-6266	349	5	τ)−	τ)−	PROPN
ejpam-6266	349	6	n	n	CCONJ
ejpam-6266	349	7	2	2	NUM
ejpam-6266	349	8	(	(	PUNCT
ejpam-6266	349	9	1	1	NUM
ejpam-6266	349	10	m	m	NOUN
ejpam-6266	349	11	−	−	NUM
ejpam-6266	349	12	1	1	NUM
ejpam-6266	349	13	2	2	NUM
ejpam-6266	349	14	)	)	PUNCT
ejpam-6266	349	15	−κ	−κ	NOUN
ejpam-6266	349	16	2	2	NUM
ejpam-6266	349	17	×	×	NOUN
ejpam-6266	349	18	∫	∫	PROPN
ejpam-6266	349	19	τ	τ	X
ejpam-6266	349	20	0	0	NUM
ejpam-6266	350	1	(	(	PUNCT
ejpam-6266	350	2	τ	τ	X
ejpam-6266	350	3	−	−	PROPN
ejpam-6266	350	4	s)−γ	s)−γ	PRON
ejpam-6266	350	5	∥∥|ut(s	∥∥|ut(s	PROPN
ejpam-6266	350	6	,	,	PUNCT
ejpam-6266	350	7	·	·	PUNCT
ejpam-6266	350	8	)	)	PUNCT
ejpam-6266	350	9	|p	|p	NOUN
ejpam-6266	350	10	−	−	ADP
ejpam-6266	350	11	|vt(s	|vt(s	PROPN
ejpam-6266	350	12	,	,	PUNCT
ejpam-6266	350	13	·	·	PUNCT
ejpam-6266	350	14	)	)	PUNCT
ejpam-6266	350	15	|p	|p	VERB
ejpam-6266	350	16	∥∥	∥∥	PUNCT
ejpam-6266	350	17	lm∩l2∩ḣσ−1	lm∩l2∩ḣσ−1	X
ejpam-6266	350	18	dsdτ	dsdτ	NOUN
ejpam-6266	350	19	.	.	PUNCT
ejpam-6266	351	1	(	(	PUNCT
ejpam-6266	351	2	79	79	NUM
ejpam-6266	351	3	)	)	PUNCT
ejpam-6266	351	4	then	then	ADV
ejpam-6266	351	5	,	,	PUNCT
ejpam-6266	351	6	we	we	PRON
ejpam-6266	351	7	have	have	VERB
ejpam-6266	351	8	to	to	PART
ejpam-6266	351	9	estimate	estimate	VERB
ejpam-6266	351	10	the	the	DET
ejpam-6266	351	11	norms∥∥|ut(s	norms∥∥|ut(s	PROPN
ejpam-6266	351	12	,	,	PUNCT
ejpam-6266	351	13	·	·	PUNCT
ejpam-6266	351	14	)	)	PUNCT
ejpam-6266	351	15	|p	|p	NOUN
ejpam-6266	351	16	−	−	ADP
ejpam-6266	351	17	|vt(s	|vt(s	PROPN
ejpam-6266	351	18	,	,	PUNCT
ejpam-6266	351	19	·	·	PUNCT
ejpam-6266	351	20	)	)	PUNCT
ejpam-6266	351	21	|p	|p	VERB
ejpam-6266	351	22	∥∥	∥∥	X
ejpam-6266	351	23	lm	lm	INTJ
ejpam-6266	351	24	,	,	PUNCT
ejpam-6266	351	25	∥∥|ut(s	∥∥|ut(s	PROPN
ejpam-6266	351	26	,	,	PUNCT
ejpam-6266	351	27	·	·	PUNCT
ejpam-6266	351	28	)	)	PUNCT
ejpam-6266	351	29	|p	|p	NOUN
ejpam-6266	351	30	−	−	ADP
ejpam-6266	351	31	|vt(s	|vt(s	PROPN
ejpam-6266	351	32	,	,	PUNCT
ejpam-6266	351	33	·	·	PUNCT
ejpam-6266	351	34	)	)	PUNCT
ejpam-6266	351	35	|p	|p	VERB
ejpam-6266	351	36	∥∥	∥∥	PRON
ejpam-6266	351	37	l2	l2	NOUN
ejpam-6266	351	38	,	,	PUNCT
ejpam-6266	351	39	and	and	CCONJ
ejpam-6266	351	40	∥∥|ut(s	∥∥|ut(s	PROPN
ejpam-6266	351	41	,	,	PUNCT
ejpam-6266	351	42	·	·	PUNCT
ejpam-6266	351	43	)	)	PUNCT
ejpam-6266	351	44	|p	|p	NOUN
ejpam-6266	351	45	−	−	ADP
ejpam-6266	351	46	|vt(s	|vt(s	PROPN
ejpam-6266	351	47	,	,	PUNCT
ejpam-6266	351	48	·	·	PUNCT
ejpam-6266	351	49	)	)	PUNCT
ejpam-6266	351	50	|p	|p	VERB
ejpam-6266	351	51	∥∥	∥∥	X
ejpam-6266	351	52	ḣσ−1	ḣσ−1	PROPN
ejpam-6266	351	53	.	.	PUNCT
ejpam-6266	352	1	following	follow	VERB
ejpam-6266	352	2	the	the	DET
ejpam-6266	352	3	steps	step	NOUN
ejpam-6266	352	4	of	of	ADP
ejpam-6266	352	5	proof	proof	NOUN
ejpam-6266	352	6	of	of	ADP
ejpam-6266	352	7	theorem	theorem	NOUN
ejpam-6266	352	8	1	1	NUM
ejpam-6266	352	9	,	,	PUNCT
ejpam-6266	352	10	we	we	PRON
ejpam-6266	352	11	show	show	VERB
ejpam-6266	352	12	immediately	immediately	ADV
ejpam-6266	352	13	that	that	SCONJ
ejpam-6266	352	14	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	352	15	,	,	PUNCT
ejpam-6266	352	16	·	·	PUNCT
ejpam-6266	352	17	)	)	PUNCT
ejpam-6266	352	18	|p	|p	NOUN
ejpam-6266	352	19	−	−	ADP
ejpam-6266	352	20	|vt(s	|vt(s	PROPN
ejpam-6266	352	21	,	,	PUNCT
ejpam-6266	352	22	·	·	PUNCT
ejpam-6266	352	23	)	)	PUNCT
ejpam-6266	352	24	|p‖lm∩l2	|p‖lm∩l2	NOUN
ejpam-6266	352	25	.	.	PUNCT
ejpam-6266	353	1	(	(	PUNCT
ejpam-6266	353	2	1	1	NUM
ejpam-6266	353	3	+	+	NUM
ejpam-6266	353	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	353	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	353	6	)	)	PUNCT
ejpam-6266	353	7	(	(	PUNCT
ejpam-6266	353	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	353	9	x(t	x(t	PROPN
ejpam-6266	353	10	)	)	PUNCT
ejpam-6266	354	1	+	+	CCONJ
ejpam-6266	354	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	354	3	x(t	x(t	PROPN
ejpam-6266	354	4	)	)	PUNCT
ejpam-6266	354	5	)	)	PUNCT
ejpam-6266	354	6	,	,	PUNCT
ejpam-6266	354	7	(	(	PUNCT
ejpam-6266	354	8	80	80	NUM
ejpam-6266	354	9	)	)	PUNCT
ejpam-6266	354	10	where	where	SCONJ
ejpam-6266	354	11	β	β	NOUN
ejpam-6266	354	12	is	be	AUX
ejpam-6266	354	13	as	as	ADP
ejpam-6266	354	14	in	in	ADP
ejpam-6266	354	15	(	(	PUNCT
ejpam-6266	354	16	61	61	NUM
ejpam-6266	354	17	)	)	PUNCT
ejpam-6266	354	18	.	.	PUNCT
ejpam-6266	355	1	then	then	ADV
ejpam-6266	355	2	,	,	PUNCT
ejpam-6266	355	3	it	it	PRON
ejpam-6266	355	4	remains	remain	VERB
ejpam-6266	355	5	to	to	PART
ejpam-6266	355	6	estimate	estimate	VERB
ejpam-6266	355	7	the	the	DET
ejpam-6266	355	8	norm	norm	NOUN
ejpam-6266	355	9	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	355	10	,	,	PUNCT
ejpam-6266	355	11	·	·	PUNCT
ejpam-6266	355	12	)	)	PUNCT
ejpam-6266	355	13	|p	|p	NOUN
ejpam-6266	355	14	−	−	ADP
ejpam-6266	355	15	|vt(s	|vt(s	PROPN
ejpam-6266	355	16	,	,	PUNCT
ejpam-6266	355	17	·	·	PUNCT
ejpam-6266	355	18	)	)	PUNCT
ejpam-6266	355	19	|p‖ḣσ−1	|p‖ḣσ−1	X
ejpam-6266	355	20	.	.	PUNCT
ejpam-6266	356	1	first	first	ADV
ejpam-6266	356	2	,	,	PUNCT
ejpam-6266	356	3	applying	apply	VERB
ejpam-6266	356	4	leibniz	leibniz	NOUN
ejpam-6266	356	5	formula	formula	NOUN
ejpam-6266	356	6	from	from	ADP
ejpam-6266	356	7	proposition	proposition	NOUN
ejpam-6266	356	8	3	3	NUM
ejpam-6266	356	9	allows	allow	VERB
ejpam-6266	356	10	us	we	PRON
ejpam-6266	356	11	to	to	PART
ejpam-6266	356	12	conclude	conclude	VERB
ejpam-6266	356	13	for	for	ADP
ejpam-6266	356	14	p	p	PROPN
ejpam-6266	356	15	>	>	X
ejpam-6266	356	16	dσe	dσe	NOUN
ejpam-6266	356	17	the	the	DET
ejpam-6266	356	18	estimate	estimate	NOUN
ejpam-6266	356	19	‖|ut(s	‖|ut(s	PROPN
ejpam-6266	356	20	,	,	PUNCT
ejpam-6266	356	21	·	·	PUNCT
ejpam-6266	356	22	)	)	PUNCT
ejpam-6266	356	23	|p	|p	NOUN
ejpam-6266	356	24	−	−	ADP
ejpam-6266	356	25	|vt(s	|vt(s	PROPN
ejpam-6266	356	26	,	,	PUNCT
ejpam-6266	356	27	·	·	PUNCT
ejpam-6266	356	28	)	)	PUNCT
ejpam-6266	356	29	|p‖ḣσ−1	|p‖ḣσ−1	PUNCT
ejpam-6266	356	30	=	=	PUNCT
ejpam-6266	356	31	‖|d|σ−1	‖|d|σ−1	X
ejpam-6266	356	32	(	(	PUNCT
ejpam-6266	356	33	|ut|p	|ut|p	X
ejpam-6266	356	34	−	−	PROPN
ejpam-6266	356	35	|vt|p	|vt|p	NUM
ejpam-6266	356	36	)	)	PUNCT
ejpam-6266	356	37	(	(	PUNCT
ejpam-6266	356	38	s	s	X
ejpam-6266	356	39	,	,	PUNCT
ejpam-6266	356	40	·	·	PUNCT
ejpam-6266	356	41	)	)	PUNCT
ejpam-6266	356	42	‖l2	‖l2	VERB
ejpam-6266	356	43	.	.	PUNCT
ejpam-6266	357	1	∫	∫	PROPN
ejpam-6266	357	2	1	1	NUM
ejpam-6266	357	3	0	0	NUM
ejpam-6266	358	1	∥∥|d|σ−1	∥∥|d|σ−1	NOUN
ejpam-6266	358	2	[	[	PUNCT
ejpam-6266	358	3	(	(	PUNCT
ejpam-6266	358	4	ut	ut	PROPN
ejpam-6266	358	5	−	−	PROPN
ejpam-6266	358	6	vt)(ut	vt)(ut	PROPN
ejpam-6266	358	7	−	−	PROPN
ejpam-6266	358	8	w(ut	w(ut	ADP
ejpam-6266	358	9	−	−	PROPN
ejpam-6266	358	10	vt))|ut	vt))|ut	ADJ
ejpam-6266	358	11	−	−	NOUN
ejpam-6266	358	12	w(ut	w(ut	ADP
ejpam-6266	358	13	−	−	PROPN
ejpam-6266	358	14	vt)|p−2	vt)|p−2	PROPN
ejpam-6266	358	15	]	]	PUNCT
ejpam-6266	358	16	(	(	PUNCT
ejpam-6266	358	17	s	s	X
ejpam-6266	358	18	,	,	PUNCT
ejpam-6266	358	19	·	·	PUNCT
ejpam-6266	358	20	)	)	PUNCT
ejpam-6266	358	21	∥∥	∥∥	X
ejpam-6266	358	22	l2	l2	VERB
ejpam-6266	358	23	dw	dw	PROPN
ejpam-6266	358	24	.	.	PUNCT
ejpam-6266	359	1	∫	∫	PROPN
ejpam-6266	359	2	1	1	NUM
ejpam-6266	359	3	0	0	NUM
ejpam-6266	359	4	‖|d|σ−1(ut	‖|d|σ−1(ut	NOUN
ejpam-6266	359	5	−	−	PROPN
ejpam-6266	359	6	vt)(s	vt)(s	PROPN
ejpam-6266	359	7	,	,	PUNCT
ejpam-6266	359	8	·	·	PUNCT
ejpam-6266	359	9	)	)	PUNCT
ejpam-6266	359	10	‖lr1	‖lr1	PROPN
ejpam-6266	359	11	∥∥(ut	∥∥(ut	PROPN
ejpam-6266	360	1	−	−	PROPN
ejpam-6266	360	2	w(ut	w(ut	ADP
ejpam-6266	360	3	−	−	PROPN
ejpam-6266	360	4	vt))|ut	vt))|ut	ADJ
ejpam-6266	360	5	−	−	NOUN
ejpam-6266	360	6	w(ut	w(ut	ADP
ejpam-6266	360	7	−	−	PROPN
ejpam-6266	360	8	vt)|p−2(s	vt)|p−2(s	NOUN
ejpam-6266	360	9	,	,	PUNCT
ejpam-6266	360	10	·	·	PUNCT
ejpam-6266	360	11	)	)	PUNCT
ejpam-6266	360	12	∥∥	∥∥	PROPN
ejpam-6266	361	1	lr2	lr2	PROPN
ejpam-6266	361	2	dw	dw	PROPN
ejpam-6266	361	3	+	+	CCONJ
ejpam-6266	361	4	∫	∫	PROPN
ejpam-6266	361	5	1	1	NUM
ejpam-6266	361	6	0	0	NUM
ejpam-6266	361	7	‖(ut	‖(ut	NOUN
ejpam-6266	361	8	−	−	PROPN
ejpam-6266	361	9	vt)(s	vt)(s	PROPN
ejpam-6266	361	10	,	,	PUNCT
ejpam-6266	361	11	·	·	PUNCT
ejpam-6266	361	12	)	)	PUNCT
ejpam-6266	361	13	‖lr3	‖lr3	VERB
ejpam-6266	361	14	∥∥|d|σ−1	∥∥|d|σ−1	PRON
ejpam-6266	361	15	[	[	PUNCT
ejpam-6266	361	16	(	(	PUNCT
ejpam-6266	361	17	ut	ut	INTJ
ejpam-6266	361	18	−	−	PROPN
ejpam-6266	361	19	w(ut	w(ut	ADP
ejpam-6266	361	20	−	−	PROPN
ejpam-6266	361	21	vt))|ut	vt))|ut	ADJ
ejpam-6266	361	22	−	−	NOUN
ejpam-6266	361	23	w(ut	w(ut	ADP
ejpam-6266	361	24	−	−	PROPN
ejpam-6266	361	25	vt)|p−2	vt)|p−2	PROPN
ejpam-6266	361	26	]	]	PUNCT
ejpam-6266	361	27	(	(	PUNCT
ejpam-6266	361	28	s	s	X
ejpam-6266	361	29	,	,	PUNCT
ejpam-6266	361	30	·	·	PUNCT
ejpam-6266	361	31	)	)	PUNCT
ejpam-6266	361	32	∥∥	∥∥	PROPN
ejpam-6266	361	33	lr4	lr4	NOUN
ejpam-6266	361	34	dw	dw	PROPN
ejpam-6266	361	35	t.	t.	PROPN
ejpam-6266	361	36	hadj	hadj	PROPN
ejpam-6266	361	37	kaddour	kaddour	PROPN
ejpam-6266	361	38	et	et	PROPN
ejpam-6266	361	39	al	al	PROPN
ejpam-6266	361	40	.	.	PUNCT
ejpam-6266	361	41	/	/	SYM
ejpam-6266	361	42	eur	eur	PROPN
ejpam-6266	361	43	.	.	PUNCT
ejpam-6266	362	1	j.	j.	PROPN
ejpam-6266	362	2	pure	pure	PROPN
ejpam-6266	362	3	appl	appl	PROPN
ejpam-6266	362	4	.	.	PROPN
ejpam-6266	362	5	math	math	PROPN
ejpam-6266	362	6	,	,	PUNCT
ejpam-6266	362	7	18	18	NUM
ejpam-6266	362	8	(	(	PUNCT
ejpam-6266	362	9	4	4	NUM
ejpam-6266	362	10	)	)	PUNCT
ejpam-6266	362	11	(	(	PUNCT
ejpam-6266	362	12	2025	2025	NUM
ejpam-6266	362	13	)	)	PUNCT
ejpam-6266	362	14	,	,	PUNCT
ejpam-6266	362	15	6266	6266	NUM
ejpam-6266	362	16	16	16	NUM
ejpam-6266	362	17	of	of	ADP
ejpam-6266	362	18	24	24	NUM
ejpam-6266	362	19	(	(	PUNCT
ejpam-6266	362	20	81	81	NUM
ejpam-6266	362	21	)	)	PUNCT
ejpam-6266	362	22	with	with	ADP
ejpam-6266	362	23	1	1	NUM
ejpam-6266	362	24	r1	r1	NOUN
ejpam-6266	362	25	+	+	CCONJ
ejpam-6266	362	26	1	1	NUM
ejpam-6266	362	27	r2	r2	NOUN
ejpam-6266	362	28	=	=	SYM
ejpam-6266	362	29	1	1	NUM
ejpam-6266	362	30	r3	r3	NOUN
ejpam-6266	362	31	+	+	CCONJ
ejpam-6266	362	32	1	1	NUM
ejpam-6266	362	33	r4	r4	NOUN
ejpam-6266	362	34	=	=	NOUN
ejpam-6266	362	35	1	1	NUM
ejpam-6266	362	36	2	2	NUM
ejpam-6266	362	37	.	.	PUNCT
ejpam-6266	363	1	(	(	PUNCT
ejpam-6266	363	2	82	82	NUM
ejpam-6266	363	3	)	)	PUNCT
ejpam-6266	363	4	the	the	DET
ejpam-6266	363	5	term	term	NOUN
ejpam-6266	363	6	‖|d|σ−1(ut	‖|d|σ−1(ut	NOUN
ejpam-6266	363	7	−	−	PROPN
ejpam-6266	363	8	vt)(s	vt)(s	PROPN
ejpam-6266	363	9	,	,	PUNCT
ejpam-6266	363	10	·	·	PUNCT
ejpam-6266	363	11	)	)	PUNCT
ejpam-6266	363	12	‖lr1	‖lr1	NOUN
ejpam-6266	363	13	can	can	AUX
ejpam-6266	363	14	be	be	AUX
ejpam-6266	363	15	estimated	estimate	VERB
ejpam-6266	363	16	by	by	ADP
ejpam-6266	363	17	using	use	VERB
ejpam-6266	363	18	the	the	DET
ejpam-6266	363	19	fractional	fractional	ADJ
ejpam-6266	363	20	gagliardonirenberg	gagliardonirenberg	NOUN
ejpam-6266	363	21	inequality	inequality	NOUN
ejpam-6266	363	22	(	(	PUNCT
ejpam-6266	363	23	106	106	NUM
ejpam-6266	363	24	)	)	PUNCT
ejpam-6266	363	25	in	in	ADP
ejpam-6266	363	26	the	the	DET
ejpam-6266	363	27	form	form	NOUN
ejpam-6266	363	28	‖|d|σ−1(ut	‖|d|σ−1(ut	NOUN
ejpam-6266	363	29	−	−	PROPN
ejpam-6266	363	30	vt)(s	vt)(s	PROPN
ejpam-6266	363	31	,	,	PUNCT
ejpam-6266	363	32	·	·	PUNCT
ejpam-6266	363	33	)	)	PUNCT
ejpam-6266	363	34	‖lr1	‖lr1	NOUN
ejpam-6266	363	35	.	.	PUNCT
ejpam-6266	364	1	‖ut(s	‖ut(s	PROPN
ejpam-6266	364	2	,	,	PUNCT
ejpam-6266	364	3	·	·	PUNCT
ejpam-6266	364	4	)	)	PUNCT
ejpam-6266	364	5	−	−	NOUN
ejpam-6266	365	1	vt(s	vt(s	PROPN
ejpam-6266	365	2	,	,	PUNCT
ejpam-6266	365	3	·	·	PUNCT
ejpam-6266	365	4	)	)	PUNCT
ejpam-6266	365	5	‖1−θ31(r1	‖1−θ31(r1	PROPN
ejpam-6266	365	6	)	)	PUNCT
ejpam-6266	365	7	l2	l2	NOUN
ejpam-6266	365	8	‖|d|σ(ut	‖|d|σ(ut	PROPN
ejpam-6266	365	9	−	−	PROPN
ejpam-6266	365	10	vt)(s	vt)(s	PROPN
ejpam-6266	365	11	,	,	PUNCT
ejpam-6266	365	12	·	·	PUNCT
ejpam-6266	365	13	)	)	PUNCT
ejpam-6266	365	14	‖θ31(r1)l2	‖θ31(r1)l2	VERB
ejpam-6266	365	15	.	.	PUNCT
ejpam-6266	366	1	(	(	PUNCT
ejpam-6266	366	2	1	1	NUM
ejpam-6266	366	3	+	+	CCONJ
ejpam-6266	366	4	s)−γ‖u−	s)−γ‖u−	PUNCT
ejpam-6266	366	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	366	6	)	)	PUNCT
ejpam-6266	366	7	(	(	PUNCT
ejpam-6266	366	8	83	83	NUM
ejpam-6266	366	9	)	)	PUNCT
ejpam-6266	366	10	with	with	ADP
ejpam-6266	366	11	θ31(r1	θ31(r1	NOUN
ejpam-6266	366	12	)	)	PUNCT
ejpam-6266	366	13	=	=	SYM
ejpam-6266	366	14	n	n	PROPN
ejpam-6266	366	15	σ	σ	NOUN
ejpam-6266	366	16	(	(	PUNCT
ejpam-6266	366	17	1	1	NUM
ejpam-6266	366	18	2	2	NUM
ejpam-6266	366	19	−	−	NUM
ejpam-6266	366	20	1	1	NUM
ejpam-6266	366	21	r1	r1	PROPN
ejpam-6266	366	22	)	)	PUNCT
ejpam-6266	367	1	+	+	CCONJ
ejpam-6266	368	1	σ−1	σ−1	PROPN
ejpam-6266	368	2	σ	σ	NUM
ejpam-6266	368	3	∈	∈	PROPN
ejpam-6266	369	1	[	[	X
ejpam-6266	369	2	σ−1	σ−1	PROPN
ejpam-6266	369	3	σ	σ	PROPN
ejpam-6266	369	4	,	,	PUNCT
ejpam-6266	369	5	1	1	NUM
ejpam-6266	369	6	]	]	X
ejpam-6266	369	7	∈	∈	PROPN
ejpam-6266	370	1	[	[	X
ejpam-6266	370	2	0	0	NUM
ejpam-6266	370	3	,	,	PUNCT
ejpam-6266	370	4	1	1	NUM
ejpam-6266	370	5	]	]	PUNCT
ejpam-6266	371	1	if	if	SCONJ
ejpam-6266	371	2	and	and	CCONJ
ejpam-6266	371	3	only	only	ADV
ejpam-6266	371	4	if	if	SCONJ
ejpam-6266	371	5	2	2	NUM
ejpam-6266	371	6	≤	≤	NOUN
ejpam-6266	371	7	r1	r1	NOUN
ejpam-6266	371	8	≤	≤	ADJ
ejpam-6266	371	9	2n	2n	NUM
ejpam-6266	371	10	n−	n−	NOUN
ejpam-6266	371	11	2	2	NUM
ejpam-6266	371	12	for	for	ADP
ejpam-6266	371	13	n	n	X
ejpam-6266	371	14	≥	≥	NOUN
ejpam-6266	371	15	3	3	NUM
ejpam-6266	371	16	.	.	PUNCT
ejpam-6266	372	1	in	in	ADP
ejpam-6266	372	2	the	the	DET
ejpam-6266	372	3	same	same	ADJ
ejpam-6266	372	4	way	way	NOUN
ejpam-6266	372	5	,	,	PUNCT
ejpam-6266	372	6	by	by	ADP
ejpam-6266	372	7	using	use	VERB
ejpam-6266	372	8	the	the	DET
ejpam-6266	372	9	classical	classical	ADJ
ejpam-6266	372	10	gagliardo	gagliardo	NOUN
ejpam-6266	372	11	-	-	PUNCT
ejpam-6266	372	12	norenberg	norenberg	PROPN
ejpam-6266	372	13	inequality	inequality	NOUN
ejpam-6266	372	14	,	,	PUNCT
ejpam-6266	372	15	we	we	PRON
ejpam-6266	372	16	estimate	estimate	VERB
ejpam-6266	372	17	the	the	DET
ejpam-6266	372	18	norm	norm	NOUN
ejpam-6266	372	19	∥∥(u−	∥∥(u−	ADJ
ejpam-6266	372	20	w(u−	w(u−	SYM
ejpam-6266	372	21	v))|ut	v))|ut	PROPN
ejpam-6266	372	22	−	−	NOUN
ejpam-6266	372	23	w(ut	w(ut	ADP
ejpam-6266	372	24	−	−	PROPN
ejpam-6266	372	25	vt)|p−2(s	vt)|p−2(s	NOUN
ejpam-6266	372	26	,	,	PUNCT
ejpam-6266	372	27	·	·	PUNCT
ejpam-6266	372	28	)	)	PUNCT
ejpam-6266	372	29	∥∥	∥∥	X
ejpam-6266	372	30	lr2	lr2	PROPN
ejpam-6266	372	31	as	as	ADP
ejpam-6266	372	32	follows:∥∥(ut	follows:∥∥(ut	PROPN
ejpam-6266	372	33	−	−	PROPN
ejpam-6266	372	34	w(ut	w(ut	ADP
ejpam-6266	372	35	−	−	PROPN
ejpam-6266	373	1	vt))|ut	vt))|ut	ADJ
ejpam-6266	373	2	−	−	NOUN
ejpam-6266	373	3	w(ut	w(ut	ADP
ejpam-6266	373	4	−	−	PROPN
ejpam-6266	373	5	vt)|p−2(s	vt)|p−2(s	NOUN
ejpam-6266	373	6	,	,	PUNCT
ejpam-6266	373	7	·	·	PUNCT
ejpam-6266	373	8	)	)	PUNCT
ejpam-6266	374	1	∥∥	∥∥	PROPN
ejpam-6266	374	2	lr2	lr2	PROPN
ejpam-6266	374	3	.	.	PUNCT
ejpam-6266	375	1	‖	‖	PROPN
ejpam-6266	376	1	(	(	PUNCT
ejpam-6266	376	2	ut	ut	PROPN
ejpam-6266	376	3	−	−	PROPN
ejpam-6266	376	4	w(ut	w(ut	ADP
ejpam-6266	376	5	−	−	PROPN
ejpam-6266	376	6	vt	vt	PROPN
ejpam-6266	376	7	)	)	PUNCT
ejpam-6266	376	8	)	)	PUNCT
ejpam-6266	377	1	(	(	PUNCT
ejpam-6266	377	2	s	s	X
ejpam-6266	377	3	,	,	PUNCT
ejpam-6266	377	4	·	·	PUNCT
ejpam-6266	377	5	)	)	PUNCT
ejpam-6266	377	6	‖p−1	‖p−1	X
ejpam-6266	377	7	l(p−1)r2	l(p−1)r2	VERB
ejpam-6266	377	8	.	.	PUNCT
ejpam-6266	378	1	‖ut	‖ut	PROPN
ejpam-6266	379	1	−	−	NOUN
ejpam-6266	379	2	w(ut	w(ut	ADP
ejpam-6266	379	3	−	−	NOUN
ejpam-6266	379	4	vt)‖(p−1)(1−θ32(r2	vt)‖(p−1)(1−θ32(r2	NOUN
ejpam-6266	379	5	)	)	PUNCT
ejpam-6266	379	6	)	)	PUNCT
ejpam-6266	379	7	l2	l2	NOUN
ejpam-6266	379	8	‖|d|σ	‖|d|σ	INTJ
ejpam-6266	379	9	(	(	PUNCT
ejpam-6266	379	10	ut	ut	PROPN
ejpam-6266	379	11	−	−	PROPN
ejpam-6266	379	12	w(ut	w(ut	ADP
ejpam-6266	379	13	−	−	PROPN
ejpam-6266	379	14	vt	vt	PROPN
ejpam-6266	379	15	)	)	PUNCT
ejpam-6266	379	16	)	)	PUNCT
ejpam-6266	379	17	‖(p−1)θ32(r2	‖(p−1)θ32(r2	PROPN
ejpam-6266	379	18	)	)	PUNCT
ejpam-6266	379	19	l2	l2	NOUN
ejpam-6266	379	20	.	.	PUNCT
ejpam-6266	380	1	(	(	PUNCT
ejpam-6266	380	2	1	1	X
ejpam-6266	380	3	+	+	CCONJ
ejpam-6266	380	4	s)−γ(p−1)‖u−	s)−γ(p−1)‖u−	VERB
ejpam-6266	380	5	w(u−	w(u−	PRON
ejpam-6266	380	6	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	380	7	x(t	x(t	PROPN
ejpam-6266	380	8	)	)	PUNCT
ejpam-6266	380	9	,	,	PUNCT
ejpam-6266	380	10	(	(	PUNCT
ejpam-6266	380	11	84	84	NUM
ejpam-6266	380	12	)	)	PUNCT
ejpam-6266	380	13	where	where	SCONJ
ejpam-6266	380	14	θ32(r2	θ32(r2	NOUN
ejpam-6266	380	15	)	)	PUNCT
ejpam-6266	380	16	=	=	SYM
ejpam-6266	380	17	n	n	PROPN
ejpam-6266	380	18	σ	σ	NOUN
ejpam-6266	380	19	(	(	PUNCT
ejpam-6266	380	20	1	1	NUM
ejpam-6266	380	21	2	2	NUM
ejpam-6266	380	22	−	−	NOUN
ejpam-6266	380	23	1	1	NUM
ejpam-6266	380	24	(	(	PUNCT
ejpam-6266	380	25	p−1)r2	p−1)r2	NUM
ejpam-6266	380	26	)	)	PUNCT
ejpam-6266	380	27	∈	∈	PROPN
ejpam-6266	381	1	[	[	X
ejpam-6266	381	2	0	0	NUM
ejpam-6266	381	3	,	,	PUNCT
ejpam-6266	381	4	1	1	NUM
ejpam-6266	381	5	]	]	PUNCT
ejpam-6266	382	1	if	if	SCONJ
ejpam-6266	382	2	and	and	CCONJ
ejpam-6266	382	3	only	only	ADV
ejpam-6266	382	4	if	if	SCONJ
ejpam-6266	382	5	2	2	NUM
ejpam-6266	382	6	p−	p−	NOUN
ejpam-6266	382	7	1	1	NUM
ejpam-6266	382	8	≤	≤	NUM
ejpam-6266	382	9	r2	r2	NOUN
ejpam-6266	382	10	≤	≤	NOUN
ejpam-6266	382	11	2n	2n	NUM
ejpam-6266	382	12	(	(	PUNCT
ejpam-6266	382	13	p−	p−	NOUN
ejpam-6266	382	14	1)(n−	1)(n−	PROPN
ejpam-6266	382	15	2σ	2σ	NUM
ejpam-6266	382	16	)	)	PUNCT
ejpam-6266	383	1	if	if	SCONJ
ejpam-6266	383	2	n	n	X
ejpam-6266	383	3	>	>	X
ejpam-6266	383	4	2σ	2σ	NUM
ejpam-6266	383	5	.	.	PUNCT
ejpam-6266	384	1	due	due	ADP
ejpam-6266	384	2	to	to	ADP
ejpam-6266	384	3	the	the	DET
ejpam-6266	384	4	estimates	estimate	NOUN
ejpam-6266	384	5	(	(	PUNCT
ejpam-6266	384	6	84	84	NUM
ejpam-6266	384	7	)	)	PUNCT
ejpam-6266	384	8	and	and	CCONJ
ejpam-6266	384	9	(	(	PUNCT
ejpam-6266	384	10	83	83	NUM
ejpam-6266	384	11	)	)	PUNCT
ejpam-6266	384	12	,	,	PUNCT
ejpam-6266	384	13	we	we	PRON
ejpam-6266	384	14	may	may	AUX
ejpam-6266	384	15	conclude	conclude	VERB
ejpam-6266	384	16	the	the	DET
ejpam-6266	384	17	estimate	estimate	NOUN
ejpam-6266	384	18	‖|d|σ−1(ut	‖|d|σ−1(ut	NOUN
ejpam-6266	384	19	−	−	PROPN
ejpam-6266	384	20	vt)(s	vt)(s	PROPN
ejpam-6266	384	21	,	,	PUNCT
ejpam-6266	384	22	·	·	PUNCT
ejpam-6266	384	23	)	)	PUNCT
ejpam-6266	384	24	‖lr1	‖lr1	PROPN
ejpam-6266	384	25	∥∥(ut	∥∥(ut	PROPN
ejpam-6266	384	26	−	−	PROPN
ejpam-6266	384	27	w(ut	w(ut	ADP
ejpam-6266	384	28	−	−	PROPN
ejpam-6266	384	29	vt))|ut	vt))|ut	ADJ
ejpam-6266	384	30	−	−	NOUN
ejpam-6266	384	31	w(ut	w(ut	ADP
ejpam-6266	384	32	−	−	PROPN
ejpam-6266	384	33	vt)|p−2(s	vt)|p−2(s	NOUN
ejpam-6266	384	34	,	,	PUNCT
ejpam-6266	384	35	·	·	PUNCT
ejpam-6266	384	36	)	)	PUNCT
ejpam-6266	384	37	∥∥	∥∥	PROPN
ejpam-6266	384	38	lr2	lr2	PROPN
ejpam-6266	384	39	.	.	PUNCT
ejpam-6266	385	1	(	(	PUNCT
ejpam-6266	385	2	1	1	X
ejpam-6266	385	3	+	+	CCONJ
ejpam-6266	385	4	s)−β−	s)−β−	ADJ
ejpam-6266	385	5	1	1	NUM
ejpam-6266	385	6	σ	σ	NOUN
ejpam-6266	385	7	(	(	PUNCT
ejpam-6266	385	8	1−am)(1−r)(2am+σ−1)‖u−	1−am)(1−r)(2am+σ−1)‖u−	ADJ
ejpam-6266	385	9	v‖x(t	v‖x(t	PROPN
ejpam-6266	385	10	)	)	PUNCT
ejpam-6266	386	1	‖u−	‖u−	PROPN
ejpam-6266	386	2	w(u−	w(u−	PRON
ejpam-6266	386	3	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	386	4	x(t	x(t	PROPN
ejpam-6266	386	5	)	)	PUNCT
ejpam-6266	386	6	.	.	PUNCT
ejpam-6266	387	1	(	(	PUNCT
ejpam-6266	387	2	1	1	NUM
ejpam-6266	387	3	+	+	NUM
ejpam-6266	387	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	387	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	387	6	)	)	PUNCT
ejpam-6266	388	1	‖u−	‖u−	PROPN
ejpam-6266	388	2	w(u−	w(u−	PRON
ejpam-6266	388	3	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	388	4	x(t	x(t	PROPN
ejpam-6266	388	5	)	)	PUNCT
ejpam-6266	388	6	,	,	PUNCT
ejpam-6266	388	7	(	(	PUNCT
ejpam-6266	388	8	85	85	NUM
ejpam-6266	388	9	)	)	PUNCT
ejpam-6266	388	10	where	where	SCONJ
ejpam-6266	388	11	β	β	NOUN
ejpam-6266	388	12	is	be	AUX
ejpam-6266	388	13	as	as	ADP
ejpam-6266	388	14	in	in	ADP
ejpam-6266	388	15	(	(	PUNCT
ejpam-6266	388	16	61	61	NUM
ejpam-6266	388	17	)	)	PUNCT
ejpam-6266	388	18	.	.	PUNCT
ejpam-6266	389	1	in	in	ADP
ejpam-6266	389	2	order	order	NOUN
ejpam-6266	389	3	to	to	PART
ejpam-6266	389	4	estimate	estimate	VERB
ejpam-6266	389	5	the	the	DET
ejpam-6266	389	6	norm	norm	NOUN
ejpam-6266	389	7	‖(ut	‖(ut	VERB
ejpam-6266	389	8	−	−	PROPN
ejpam-6266	389	9	vt)(s	vt)(s	PROPN
ejpam-6266	389	10	,	,	PUNCT
ejpam-6266	389	11	·	·	PUNCT
ejpam-6266	389	12	)	)	PUNCT
ejpam-6266	389	13	‖lr3	‖lr3	NOUN
ejpam-6266	389	14	we	we	PRON
ejpam-6266	389	15	apply	apply	VERB
ejpam-6266	389	16	the	the	DET
ejpam-6266	389	17	classical	classical	ADJ
ejpam-6266	389	18	gagliardo	gagliardo	NOUN
ejpam-6266	389	19	-	-	PUNCT
ejpam-6266	389	20	nirenberg	nirenberg	NOUN
ejpam-6266	389	21	inequality	inequality	NOUN
ejpam-6266	389	22	(	(	PUNCT
ejpam-6266	389	23	107	107	NUM
ejpam-6266	389	24	)	)	PUNCT
ejpam-6266	389	25	to	to	PART
ejpam-6266	389	26	obtain	obtain	VERB
ejpam-6266	389	27	‖(ut	‖(ut	NOUN
ejpam-6266	389	28	−	−	PROPN
ejpam-6266	389	29	vt)(s	vt)(s	NOUN
ejpam-6266	389	30	,	,	PUNCT
ejpam-6266	389	31	·	·	PUNCT
ejpam-6266	389	32	)	)	PUNCT
ejpam-6266	389	33	‖lr3	‖lr3	NOUN
ejpam-6266	389	34	.	.	PUNCT
ejpam-6266	390	1	‖(ut	‖(ut	NOUN
ejpam-6266	390	2	−	−	PROPN
ejpam-6266	390	3	vt)(s	vt)(s	PROPN
ejpam-6266	390	4	,	,	PUNCT
ejpam-6266	390	5	·	·	PUNCT
ejpam-6266	390	6	)	)	PUNCT
ejpam-6266	390	7	‖1−θ33(r3	‖1−θ33(r3	PROPN
ejpam-6266	390	8	)	)	PUNCT
ejpam-6266	390	9	l2	l2	NOUN
ejpam-6266	390	10	‖|d|σ(ut	‖|d|σ(ut	PROPN
ejpam-6266	390	11	−	−	PROPN
ejpam-6266	390	12	vt)(s	vt)(s	PROPN
ejpam-6266	390	13	,	,	PUNCT
ejpam-6266	390	14	·	·	PUNCT
ejpam-6266	390	15	)	)	PUNCT
ejpam-6266	390	16	‖θ33(r3)l2	‖θ33(r3)l2	VERB
ejpam-6266	390	17	.	.	PUNCT
ejpam-6266	391	1	(	(	PUNCT
ejpam-6266	391	2	1	1	NUM
ejpam-6266	391	3	+	+	CCONJ
ejpam-6266	391	4	s)−γ‖u−	s)−γ‖u−	PUNCT
ejpam-6266	391	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	391	6	)	)	PUNCT
ejpam-6266	391	7	,	,	PUNCT
ejpam-6266	391	8	(	(	PUNCT
ejpam-6266	391	9	86	86	NUM
ejpam-6266	391	10	)	)	PUNCT
ejpam-6266	391	11	where	where	SCONJ
ejpam-6266	391	12	θ33(r3	θ33(r3	NOUN
ejpam-6266	391	13	)	)	PUNCT
ejpam-6266	391	14	=	=	SYM
ejpam-6266	391	15	n	n	PROPN
ejpam-6266	391	16	σ	σ	NOUN
ejpam-6266	391	17	(	(	PUNCT
ejpam-6266	391	18	1	1	NUM
ejpam-6266	391	19	2	2	NUM
ejpam-6266	391	20	−	−	NUM
ejpam-6266	391	21	1	1	NUM
ejpam-6266	391	22	r3	r3	PROPN
ejpam-6266	391	23	)	)	PUNCT
ejpam-6266	391	24	∈	∈	PROPN
ejpam-6266	392	1	[	[	X
ejpam-6266	392	2	0	0	NUM
ejpam-6266	392	3	,	,	PUNCT
ejpam-6266	392	4	1	1	NUM
ejpam-6266	392	5	]	]	PUNCT
ejpam-6266	393	1	if	if	SCONJ
ejpam-6266	393	2	and	and	CCONJ
ejpam-6266	393	3	only	only	ADV
ejpam-6266	393	4	if	if	SCONJ
ejpam-6266	393	5	2	2	NUM
ejpam-6266	393	6	≤	≤	NUM
ejpam-6266	393	7	r3	r3	PROPN
ejpam-6266	393	8	≤	≤	NUM
ejpam-6266	393	9	2n	2n	NUM
ejpam-6266	393	10	n−	n−	NOUN
ejpam-6266	393	11	2σ	2σ	X
ejpam-6266	393	12	if	if	SCONJ
ejpam-6266	393	13	n	n	X
ejpam-6266	393	14	>	>	X
ejpam-6266	393	15	2σ	2σ	NUM
ejpam-6266	393	16	.	.	PUNCT
ejpam-6266	394	1	t.	t.	PROPN
ejpam-6266	394	2	hadj	hadj	PROPN
ejpam-6266	394	3	kaddour	kaddour	PROPN
ejpam-6266	394	4	et	et	PROPN
ejpam-6266	394	5	al	al	PROPN
ejpam-6266	394	6	.	.	PUNCT
ejpam-6266	394	7	/	/	SYM
ejpam-6266	394	8	eur	eur	PROPN
ejpam-6266	394	9	.	.	PUNCT
ejpam-6266	395	1	j.	j.	PROPN
ejpam-6266	395	2	pure	pure	PROPN
ejpam-6266	395	3	appl	appl	PROPN
ejpam-6266	395	4	.	.	PROPN
ejpam-6266	395	5	math	math	PROPN
ejpam-6266	395	6	,	,	PUNCT
ejpam-6266	395	7	18	18	NUM
ejpam-6266	395	8	(	(	PUNCT
ejpam-6266	395	9	4	4	NUM
ejpam-6266	395	10	)	)	PUNCT
ejpam-6266	395	11	(	(	PUNCT
ejpam-6266	395	12	2025	2025	NUM
ejpam-6266	395	13	)	)	PUNCT
ejpam-6266	395	14	,	,	PUNCT
ejpam-6266	395	15	6266	6266	NUM
ejpam-6266	395	16	17	17	NUM
ejpam-6266	395	17	of	of	ADP
ejpam-6266	395	18	24	24	NUM
ejpam-6266	395	19	now	now	ADV
ejpam-6266	395	20	,	,	PUNCT
ejpam-6266	395	21	we	we	PRON
ejpam-6266	395	22	turn	turn	VERB
ejpam-6266	395	23	to	to	PART
ejpam-6266	395	24	estimate	estimate	VERB
ejpam-6266	395	25	the	the	DET
ejpam-6266	395	26	norm	norm	NOUN
ejpam-6266	395	27	∥∥|d|σ−1	∥∥|d|σ−1	PROPN
ejpam-6266	395	28	(	(	PUNCT
ejpam-6266	395	29	(	(	PUNCT
ejpam-6266	395	30	ut	ut	PROPN
ejpam-6266	395	31	−	−	PROPN
ejpam-6266	395	32	w(ut	w(ut	ADP
ejpam-6266	395	33	−	−	PROPN
ejpam-6266	395	34	vt))|ut	vt))|ut	ADJ
ejpam-6266	395	35	−	−	NOUN
ejpam-6266	395	36	w(ut	w(ut	ADP
ejpam-6266	395	37	−	−	PROPN
ejpam-6266	395	38	vt)|p−2	vt)|p−2	NUM
ejpam-6266	395	39	)	)	PUNCT
ejpam-6266	395	40	∥∥	∥∥	PROPN
ejpam-6266	395	41	lr4	lr4	NOUN
ejpam-6266	395	42	.	.	PUNCT
ejpam-6266	396	1	we	we	PRON
ejpam-6266	396	2	can	can	AUX
ejpam-6266	396	3	do	do	VERB
ejpam-6266	396	4	this	this	PRON
ejpam-6266	396	5	by	by	ADP
ejpam-6266	396	6	applying	apply	VERB
ejpam-6266	396	7	the	the	DET
ejpam-6266	396	8	fractional	fractional	ADJ
ejpam-6266	396	9	chain	chain	NOUN
ejpam-6266	396	10	rule	rule	NOUN
ejpam-6266	396	11	(	(	PUNCT
ejpam-6266	396	12	110	110	NUM
ejpam-6266	396	13	)	)	PUNCT
ejpam-6266	396	14	.	.	PUNCT
ejpam-6266	397	1	in	in	ADP
ejpam-6266	397	2	this	this	DET
ejpam-6266	397	3	way	way	NOUN
ejpam-6266	397	4	we	we	PRON
ejpam-6266	397	5	get∥∥|d|σ−1	get∥∥|d|σ−1	PROPN
ejpam-6266	397	6	(	(	PUNCT
ejpam-6266	397	7	(	(	PUNCT
ejpam-6266	397	8	ut	ut	PROPN
ejpam-6266	397	9	−	−	PROPN
ejpam-6266	397	10	w(ut	w(ut	ADP
ejpam-6266	397	11	−	−	PROPN
ejpam-6266	397	12	vt))|ut	vt))|ut	ADJ
ejpam-6266	397	13	−	−	NOUN
ejpam-6266	397	14	w(ut	w(ut	ADP
ejpam-6266	397	15	−	−	PROPN
ejpam-6266	397	16	vt)|p−2	vt)|p−2	NUM
ejpam-6266	397	17	)	)	PUNCT
ejpam-6266	397	18	∥∥	∥∥	PROPN
ejpam-6266	397	19	lr4	lr4	NOUN
ejpam-6266	397	20	.	.	PUNCT
ejpam-6266	398	1	∥∥ut	∥∥ut	NUM
ejpam-6266	399	1	−	−	NOUN
ejpam-6266	399	2	w(ut	w(ut	ADP
ejpam-6266	399	3	−	−	PROPN
ejpam-6266	399	4	vt)‖p−2	vt)‖p−2	PROPN
ejpam-6266	399	5	lr5	lr5	PROPN
ejpam-6266	399	6	‖|d|σ−1(ut	‖|d|σ−1(ut	VERB
ejpam-6266	399	7	−	−	PROPN
ejpam-6266	399	8	w(ut	w(ut	ADP
ejpam-6266	399	9	−	−	PROPN
ejpam-6266	399	10	vt	vt	PROPN
ejpam-6266	399	11	)	)	PUNCT
ejpam-6266	399	12	)	)	PUNCT
ejpam-6266	400	1	∥∥	∥∥	X
ejpam-6266	400	2	lr6	lr6	PROPN
ejpam-6266	400	3	(	(	PUNCT
ejpam-6266	400	4	87	87	NUM
ejpam-6266	400	5	)	)	PUNCT
ejpam-6266	400	6	with	with	ADP
ejpam-6266	400	7	p−	p−	NOUN
ejpam-6266	400	8	2	2	NUM
ejpam-6266	400	9	r5	r5	PROPN
ejpam-6266	400	10	+	+	CCONJ
ejpam-6266	400	11	1	1	NUM
ejpam-6266	400	12	r6	r6	NOUN
ejpam-6266	400	13	=	=	SYM
ejpam-6266	400	14	1	1	NUM
ejpam-6266	400	15	r4	r4	NOUN
ejpam-6266	400	16	and	and	CCONJ
ejpam-6266	400	17	p	p	X
ejpam-6266	400	18	>	>	X
ejpam-6266	400	19	dσe	dσe	PROPN
ejpam-6266	400	20	.	.	PUNCT
ejpam-6266	401	1	(	(	PUNCT
ejpam-6266	401	2	88	88	NUM
ejpam-6266	401	3	)	)	PUNCT
ejpam-6266	401	4	in	in	ADP
ejpam-6266	401	5	one	one	NUM
ejpam-6266	401	6	hand	hand	NOUN
ejpam-6266	401	7	the	the	DET
ejpam-6266	401	8	classical	classical	ADJ
ejpam-6266	401	9	gagliardo	gagliardo	NOUN
ejpam-6266	401	10	-	-	PUNCT
ejpam-6266	401	11	nirenberg	nirenberg	NOUN
ejpam-6266	401	12	inequality	inequality	NOUN
ejpam-6266	401	13	(	(	PUNCT
ejpam-6266	401	14	107	107	NUM
ejpam-6266	401	15	)	)	PUNCT
ejpam-6266	401	16	allows	allow	VERB
ejpam-6266	401	17	us	we	PRON
ejpam-6266	401	18	to	to	PART
ejpam-6266	401	19	get	get	VERB
ejpam-6266	401	20	‖(ut	‖(ut	ADJ
ejpam-6266	401	21	−	−	NOUN
ejpam-6266	401	22	w(ut	w(ut	ADP
ejpam-6266	401	23	−	−	PROPN
ejpam-6266	401	24	vt))(s	vt))(s	ADJ
ejpam-6266	401	25	,	,	PUNCT
ejpam-6266	401	26	·	·	PUNCT
ejpam-6266	401	27	)	)	PUNCT
ejpam-6266	401	28	‖p−2	‖p−2	NUM
ejpam-6266	401	29	lr5	lr5	VERB
ejpam-6266	401	30	.	.	PUNCT
ejpam-6266	402	1	‖(ut	‖(ut	NOUN
ejpam-6266	402	2	−	−	PROPN
ejpam-6266	402	3	w(ut	w(ut	ADP
ejpam-6266	402	4	−	−	PROPN
ejpam-6266	402	5	vt))(s	vt))(s	ADJ
ejpam-6266	402	6	,	,	PUNCT
ejpam-6266	402	7	·	·	SYM
ejpam-6266	402	8	)	)	PUNCT
ejpam-6266	402	9	‖(p−2)(1−θ5(r5	‖(p−2)(1−θ5(r5	NOUN
ejpam-6266	402	10	)	)	PUNCT
ejpam-6266	402	11	)	)	PUNCT
ejpam-6266	403	1	l2	l2	NOUN
ejpam-6266	403	2	‖|d|σ	‖|d|σ	INTJ
ejpam-6266	403	3	(	(	PUNCT
ejpam-6266	403	4	ut	ut	PROPN
ejpam-6266	403	5	−	−	PROPN
ejpam-6266	403	6	w(ut	w(ut	ADP
ejpam-6266	403	7	−	−	PROPN
ejpam-6266	403	8	vt	vt	PROPN
ejpam-6266	403	9	)	)	PUNCT
ejpam-6266	403	10	)	)	PUNCT
ejpam-6266	404	1	(	(	PUNCT
ejpam-6266	404	2	s	s	X
ejpam-6266	404	3	,	,	PUNCT
ejpam-6266	404	4	·	·	PUNCT
ejpam-6266	404	5	)	)	PUNCT
ejpam-6266	404	6	‖(p−2)θ5(r5	‖(p−2)θ5(r5	NUM
ejpam-6266	404	7	)	)	PUNCT
ejpam-6266	404	8	l2	l2	NOUN
ejpam-6266	404	9	.	.	PUNCT
ejpam-6266	405	1	(	(	PUNCT
ejpam-6266	405	2	1	1	X
ejpam-6266	405	3	+	+	CCONJ
ejpam-6266	405	4	s)−γ(p−2)‖u−	s)−γ(p−2)‖u−	ADJ
ejpam-6266	405	5	w(u−	w(u−	PRON
ejpam-6266	405	6	v)‖p−2	v)‖p−2	NOUN
ejpam-6266	405	7	x(t	x(t	PROPN
ejpam-6266	405	8	)	)	PUNCT
ejpam-6266	405	9	(	(	PUNCT
ejpam-6266	405	10	89	89	NUM
ejpam-6266	405	11	)	)	PUNCT
ejpam-6266	405	12	with	with	ADP
ejpam-6266	405	13	θ5(r5	θ5(r5	NUM
ejpam-6266	405	14	)	)	PUNCT
ejpam-6266	405	15	=	=	SYM
ejpam-6266	405	16	n	n	PROPN
ejpam-6266	405	17	σ	σ	NOUN
ejpam-6266	405	18	(	(	PUNCT
ejpam-6266	405	19	1	1	NUM
ejpam-6266	405	20	2	2	NUM
ejpam-6266	405	21	−	−	PROPN
ejpam-6266	405	22	1	1	NUM
ejpam-6266	405	23	r5	r5	PROPN
ejpam-6266	405	24	)	)	PUNCT
ejpam-6266	405	25	∈	∈	PROPN
ejpam-6266	406	1	[	[	X
ejpam-6266	406	2	0	0	NUM
ejpam-6266	406	3	,	,	PUNCT
ejpam-6266	406	4	1	1	NUM
ejpam-6266	406	5	]	]	PUNCT
ejpam-6266	407	1	if	if	SCONJ
ejpam-6266	407	2	and	and	CCONJ
ejpam-6266	407	3	only	only	ADV
ejpam-6266	407	4	if	if	SCONJ
ejpam-6266	407	5	2	2	NUM
ejpam-6266	407	6	≤	≤	NUM
ejpam-6266	407	7	r5	r5	PROPN
ejpam-6266	407	8	≤	≤	ADV
ejpam-6266	407	9	2n	2n	NUM
ejpam-6266	407	10	n−	n−	NOUN
ejpam-6266	407	11	2σ	2σ	X
ejpam-6266	407	12	if	if	SCONJ
ejpam-6266	407	13	n	n	X
ejpam-6266	407	14	>	>	X
ejpam-6266	407	15	2σ	2σ	NUM
ejpam-6266	407	16	.	.	PUNCT
ejpam-6266	408	1	in	in	ADP
ejpam-6266	408	2	the	the	DET
ejpam-6266	408	3	other	other	ADJ
ejpam-6266	408	4	hand	hand	NOUN
ejpam-6266	408	5	,	,	PUNCT
ejpam-6266	408	6	by	by	ADP
ejpam-6266	408	7	applying	apply	VERB
ejpam-6266	408	8	the	the	DET
ejpam-6266	408	9	fractional	fractional	ADJ
ejpam-6266	408	10	chain	chain	NOUN
ejpam-6266	408	11	rule	rule	NOUN
ejpam-6266	408	12	(	(	PUNCT
ejpam-6266	408	13	110	110	NUM
ejpam-6266	408	14	)	)	PUNCT
ejpam-6266	408	15	we	we	PRON
ejpam-6266	408	16	may	may	AUX
ejpam-6266	408	17	estimate	estimate	VERB
ejpam-6266	408	18	the	the	DET
ejpam-6266	408	19	norm∥∥|d|σ−1(ut	norm∥∥|d|σ−1(ut	NOUN
ejpam-6266	408	20	−	−	PROPN
ejpam-6266	408	21	r(ut	r(ut	PROPN
ejpam-6266	408	22	−	−	PROPN
ejpam-6266	408	23	vt	vt	PROPN
ejpam-6266	408	24	)	)	PUNCT
ejpam-6266	408	25	)	)	PUNCT
ejpam-6266	408	26	∥∥	∥∥	X
ejpam-6266	408	27	lr6	lr6	VERB
ejpam-6266	408	28	as	as	ADP
ejpam-6266	408	29	follows:∥∥|d|σ−1(ut	follows:∥∥|d|σ−1(ut	PROPN
ejpam-6266	408	30	−	−	PROPN
ejpam-6266	408	31	w(ut	w(ut	ADP
ejpam-6266	408	32	−	−	PROPN
ejpam-6266	408	33	vt	vt	PROPN
ejpam-6266	408	34	)	)	PUNCT
ejpam-6266	408	35	)	)	PUNCT
ejpam-6266	409	1	∥∥	∥∥	PROPN
ejpam-6266	409	2	lr6	lr6	VERB
ejpam-6266	409	3	.	.	PUNCT
ejpam-6266	410	1	‖ut	‖ut	PROPN
ejpam-6266	411	1	−	−	NOUN
ejpam-6266	411	2	w(ut	w(ut	ADP
ejpam-6266	411	3	−	−	PROPN
ejpam-6266	411	4	vt)‖1−θ6(r6	vt)‖1−θ6(r6	NUM
ejpam-6266	411	5	)	)	PUNCT
ejpam-6266	411	6	l2	l2	NOUN
ejpam-6266	411	7	∥∥|d|σ(ut	∥∥|d|σ(ut	NUM
ejpam-6266	411	8	−	−	NOUN
ejpam-6266	411	9	w(ut	w(ut	ADP
ejpam-6266	411	10	−	−	PROPN
ejpam-6266	411	11	vt	vt	PROPN
ejpam-6266	411	12	)	)	PUNCT
ejpam-6266	411	13	)	)	PUNCT
ejpam-6266	411	14	∥∥θ6(r6	∥∥θ6(r6	ADJ
ejpam-6266	411	15	)	)	PUNCT
ejpam-6266	411	16	l2	l2	NOUN
ejpam-6266	411	17	.	.	PUNCT
ejpam-6266	412	1	(	(	PUNCT
ejpam-6266	412	2	1	1	X
ejpam-6266	412	3	+	+	CCONJ
ejpam-6266	412	4	s)−γ‖u−	s)−γ‖u−	PUNCT
ejpam-6266	412	5	w(u−	w(u−	X
ejpam-6266	412	6	v)‖x(t	v)‖x(t	NOUN
ejpam-6266	412	7	)	)	PUNCT
ejpam-6266	413	1	(	(	PUNCT
ejpam-6266	413	2	90	90	NUM
ejpam-6266	413	3	)	)	PUNCT
ejpam-6266	413	4	with	with	ADP
ejpam-6266	413	5	θ6	θ6	PROPN
ejpam-6266	413	6	=	=	PUNCT
ejpam-6266	413	7	n	n	PROPN
ejpam-6266	413	8	σ	σ	PROPN
ejpam-6266	413	9	(	(	PUNCT
ejpam-6266	413	10	1	1	NUM
ejpam-6266	413	11	2	2	NUM
ejpam-6266	413	12	−	−	NUM
ejpam-6266	413	13	1	1	NUM
ejpam-6266	413	14	r6	r6	NOUN
ejpam-6266	413	15	)	)	PUNCT
ejpam-6266	414	1	+	+	CCONJ
ejpam-6266	415	1	σ−1	σ−1	PROPN
ejpam-6266	415	2	σ	σ	NUM
ejpam-6266	415	3	∈	∈	PROPN
ejpam-6266	416	1	[	[	X
ejpam-6266	416	2	σ−1	σ−1	PROPN
ejpam-6266	416	3	σ	σ	PROPN
ejpam-6266	416	4	,	,	PUNCT
ejpam-6266	416	5	1	1	X
ejpam-6266	416	6	]	]	PUNCT
ejpam-6266	416	7	if	if	SCONJ
ejpam-6266	416	8	and	and	CCONJ
ejpam-6266	417	1	only	only	ADV
ejpam-6266	417	2	if	if	SCONJ
ejpam-6266	417	3	2	2	NUM
ejpam-6266	417	4	≤	≤	NOUN
ejpam-6266	417	5	r6	r6	NOUN
ejpam-6266	417	6	≤	≤	NUM
ejpam-6266	417	7	2n	2n	NUM
ejpam-6266	417	8	n−	n−	NOUN
ejpam-6266	417	9	2	2	NUM
ejpam-6266	417	10	for	for	ADP
ejpam-6266	417	11	n	n	X
ejpam-6266	417	12	≥	≥	NOUN
ejpam-6266	417	13	3	3	NUM
ejpam-6266	417	14	.	.	PUNCT
ejpam-6266	418	1	for	for	ADP
ejpam-6266	418	2	r1	r1	PROPN
ejpam-6266	418	3	and	and	CCONJ
ejpam-6266	418	4	r2	r2	NOUN
ejpam-6266	418	5	we	we	PRON
ejpam-6266	418	6	may	may	AUX
ejpam-6266	418	7	choose	choose	VERB
ejpam-6266	418	8	r1	r1	PROPN
ejpam-6266	418	9	=	=	SYM
ejpam-6266	418	10	2n	2n	NUM
ejpam-6266	418	11	n−2	n−2	PROPN
ejpam-6266	418	12	and	and	CCONJ
ejpam-6266	418	13	r2	r2	PROPN
ejpam-6266	418	14	=	=	SYM
ejpam-6266	418	15	n.	n.	PROPN
ejpam-6266	418	16	for	for	ADP
ejpam-6266	418	17	r3	r3	PROPN
ejpam-6266	418	18	,	,	PUNCT
ejpam-6266	418	19	·	·	PUNCT
ejpam-6266	418	20	·	·	PUNCT
ejpam-6266	418	21	·	·	PUNCT
ejpam-6266	418	22	,	,	PUNCT
ejpam-6266	418	23	r6	r6	NOUN
ejpam-6266	418	24	,	,	PUNCT
ejpam-6266	418	25	we	we	PRON
ejpam-6266	418	26	may	may	AUX
ejpam-6266	418	27	choose	choose	VERB
ejpam-6266	418	28	r3	r3	PROPN
ejpam-6266	418	29	=	=	SYM
ejpam-6266	418	30	r5	r5	PROPN
ejpam-6266	418	31	=	=	SYM
ejpam-6266	418	32	n(p−	n(p−	X
ejpam-6266	418	33	1	1	NUM
ejpam-6266	418	34	)	)	PUNCT
ejpam-6266	418	35	,	,	PUNCT
ejpam-6266	418	36	r6	r6	NOUN
ejpam-6266	418	37	=	=	SYM
ejpam-6266	418	38	2n	2n	NUM
ejpam-6266	418	39	n−2	n−2	PROPN
ejpam-6266	418	40	and	and	CCONJ
ejpam-6266	418	41	,	,	PUNCT
ejpam-6266	418	42	consequently	consequently	ADV
ejpam-6266	418	43	,	,	PUNCT
ejpam-6266	418	44	we	we	PRON
ejpam-6266	418	45	find	find	VERB
ejpam-6266	418	46	r4	r4	NOUN
ejpam-6266	418	47	=	=	SYM
ejpam-6266	418	48	2n(p−1	2n(p−1	NUM
ejpam-6266	418	49	)	)	PUNCT
ejpam-6266	418	50	n(p−1)−2	n(p−1)−2	PROPN
ejpam-6266	418	51	.	.	PUNCT
ejpam-6266	419	1	therefore	therefore	ADV
ejpam-6266	419	2	,	,	PUNCT
ejpam-6266	419	3	by	by	ADP
ejpam-6266	419	4	using	use	VERB
ejpam-6266	419	5	the	the	DET
ejpam-6266	419	6	estimates	estimate	NOUN
ejpam-6266	419	7	(	(	PUNCT
ejpam-6266	419	8	89	89	NUM
ejpam-6266	419	9	)	)	PUNCT
ejpam-6266	419	10	and	and	CCONJ
ejpam-6266	419	11	(	(	PUNCT
ejpam-6266	419	12	90	90	NUM
ejpam-6266	419	13	)	)	PUNCT
ejpam-6266	419	14	we	we	PRON
ejpam-6266	419	15	get	get	VERB
ejpam-6266	419	16	from	from	ADP
ejpam-6266	419	17	(	(	PUNCT
ejpam-6266	419	18	87	87	NUM
ejpam-6266	419	19	)	)	PUNCT
ejpam-6266	419	20	the	the	DET
ejpam-6266	419	21	estimate∥∥|d|σ−1	estimate∥∥|d|σ−1	PROPN
ejpam-6266	420	1	[	[	PUNCT
ejpam-6266	420	2	(	(	PUNCT
ejpam-6266	420	3	u−	u−	ADJ
ejpam-6266	420	4	w(u−	w(u−	NOUN
ejpam-6266	420	5	v))|u−	v))|u−	PROPN
ejpam-6266	420	6	w(u−	w(u−	PRON
ejpam-6266	420	7	v)|p−2	v)|p−2	X
ejpam-6266	420	8	]	]	X
ejpam-6266	420	9	∥∥	∥∥	X
ejpam-6266	420	10	lr4	lr4	NOUN
ejpam-6266	420	11	.	.	PUNCT
ejpam-6266	421	1	(	(	PUNCT
ejpam-6266	421	2	1	1	X
ejpam-6266	421	3	+	+	CCONJ
ejpam-6266	421	4	s)−γ(p−1)‖u−	s)−γ(p−1)‖u−	VERB
ejpam-6266	421	5	w(u−	w(u−	PRON
ejpam-6266	421	6	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	421	7	x(t	x(t	PROPN
ejpam-6266	421	8	)	)	PUNCT
ejpam-6266	421	9	.	.	PUNCT
ejpam-6266	422	1	(	(	PUNCT
ejpam-6266	422	2	91	91	NUM
ejpam-6266	422	3	)	)	PUNCT
ejpam-6266	422	4	hence	hence	ADV
ejpam-6266	422	5	,	,	PUNCT
ejpam-6266	422	6	both	both	DET
ejpam-6266	422	7	estimates	estimate	NOUN
ejpam-6266	422	8	(	(	PUNCT
ejpam-6266	422	9	91	91	NUM
ejpam-6266	422	10	)	)	PUNCT
ejpam-6266	422	11	and	and	CCONJ
ejpam-6266	422	12	(	(	PUNCT
ejpam-6266	422	13	86	86	NUM
ejpam-6266	422	14	)	)	PUNCT
ejpam-6266	422	15	imply	imply	VERB
ejpam-6266	422	16	the	the	DET
ejpam-6266	422	17	estimate	estimate	NOUN
ejpam-6266	422	18	‖u−	‖u−	VERB
ejpam-6266	422	19	v‖lr3	v‖lr3	PUNCT
ejpam-6266	422	20	∥∥|d|σ−1[(u−	∥∥|d|σ−1[(u−	PRON
ejpam-6266	422	21	w(u−	w(u−	PRON
ejpam-6266	422	22	v))|u−	v))|u−	PROPN
ejpam-6266	422	23	w(u−	w(u−	PRON
ejpam-6266	422	24	v)|p−2	v)|p−2	X
ejpam-6266	422	25	]	]	X
ejpam-6266	422	26	∥∥	∥∥	X
ejpam-6266	422	27	lr4	lr4	NOUN
ejpam-6266	422	28	.	.	PUNCT
ejpam-6266	423	1	(	(	PUNCT
ejpam-6266	423	2	1	1	NUM
ejpam-6266	423	3	+	+	CCONJ
ejpam-6266	423	4	s)−β−	s)−β−	ADJ
ejpam-6266	423	5	1	1	NUM
ejpam-6266	423	6	σ	σ	NOUN
ejpam-6266	423	7	(	(	PUNCT
ejpam-6266	423	8	2am+σ−1)(1−a)(1−r)‖u−	2am+σ−1)(1−a)(1−r)‖u−	NUM
ejpam-6266	423	9	v‖x(t	v‖x(t	PROPN
ejpam-6266	423	10	)	)	PUNCT
ejpam-6266	424	1	‖u−	‖u−	PROPN
ejpam-6266	424	2	w(u−	w(u−	PRON
ejpam-6266	424	3	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	424	4	x(t	x(t	PROPN
ejpam-6266	424	5	)	)	PUNCT
ejpam-6266	424	6	.	.	PUNCT
ejpam-6266	425	1	(	(	PUNCT
ejpam-6266	425	2	1	1	NUM
ejpam-6266	425	3	+	+	NUM
ejpam-6266	425	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	425	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	425	6	)	)	PUNCT
ejpam-6266	426	1	‖u−	‖u−	PROPN
ejpam-6266	426	2	w(u−	w(u−	PRON
ejpam-6266	426	3	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	426	4	x(t	x(t	PROPN
ejpam-6266	426	5	)	)	PUNCT
ejpam-6266	426	6	,	,	PUNCT
ejpam-6266	426	7	(	(	PUNCT
ejpam-6266	426	8	92	92	NUM
ejpam-6266	426	9	)	)	PUNCT
ejpam-6266	426	10	t.	t.	NOUN
ejpam-6266	426	11	hadj	hadj	PROPN
ejpam-6266	426	12	kaddour	kaddour	PROPN
ejpam-6266	426	13	et	et	PROPN
ejpam-6266	426	14	al	al	PROPN
ejpam-6266	426	15	.	.	PUNCT
ejpam-6266	426	16	/	/	SYM
ejpam-6266	426	17	eur	eur	PROPN
ejpam-6266	426	18	.	.	PUNCT
ejpam-6266	427	1	j.	j.	PROPN
ejpam-6266	427	2	pure	pure	PROPN
ejpam-6266	427	3	appl	appl	PROPN
ejpam-6266	427	4	.	.	PROPN
ejpam-6266	427	5	math	math	PROPN
ejpam-6266	427	6	,	,	PUNCT
ejpam-6266	427	7	18	18	NUM
ejpam-6266	427	8	(	(	PUNCT
ejpam-6266	427	9	4	4	NUM
ejpam-6266	427	10	)	)	PUNCT
ejpam-6266	427	11	(	(	PUNCT
ejpam-6266	427	12	2025	2025	NUM
ejpam-6266	427	13	)	)	PUNCT
ejpam-6266	427	14	,	,	PUNCT
ejpam-6266	427	15	6266	6266	NUM
ejpam-6266	427	16	18	18	NUM
ejpam-6266	427	17	of	of	ADP
ejpam-6266	427	18	24	24	NUM
ejpam-6266	427	19	where	where	SCONJ
ejpam-6266	427	20	β	β	PROPN
ejpam-6266	427	21	is	be	AUX
ejpam-6266	427	22	defined	define	VERB
ejpam-6266	427	23	by	by	ADP
ejpam-6266	427	24	(	(	PUNCT
ejpam-6266	427	25	61	61	NUM
ejpam-6266	427	26	)	)	PUNCT
ejpam-6266	427	27	.	.	PUNCT
ejpam-6266	428	1	then	then	ADV
ejpam-6266	428	2	,	,	PUNCT
ejpam-6266	428	3	plugging	plug	VERB
ejpam-6266	428	4	(	(	PUNCT
ejpam-6266	428	5	85	85	NUM
ejpam-6266	428	6	)	)	PUNCT
ejpam-6266	428	7	and	and	CCONJ
ejpam-6266	428	8	(	(	PUNCT
ejpam-6266	428	9	92	92	NUM
ejpam-6266	428	10	)	)	PUNCT
ejpam-6266	428	11	into	into	ADP
ejpam-6266	428	12	(	(	PUNCT
ejpam-6266	428	13	81	81	NUM
ejpam-6266	428	14	)	)	PUNCT
ejpam-6266	428	15	we	we	PRON
ejpam-6266	428	16	get∥∥|u(s	get∥∥|u(s	VERB
ejpam-6266	428	17	,	,	PUNCT
ejpam-6266	428	18	·	·	PUNCT
ejpam-6266	428	19	)	)	PUNCT
ejpam-6266	428	20	|p	|p	NOUN
ejpam-6266	428	21	−	−	PROPN
ejpam-6266	428	22	|v(s	|v(s	PROPN
ejpam-6266	428	23	,	,	PUNCT
ejpam-6266	428	24	·	·	PUNCT
ejpam-6266	428	25	)	)	PUNCT
ejpam-6266	428	26	|p)(s	|p)(s	NOUN
ejpam-6266	428	27	,	,	PUNCT
ejpam-6266	428	28	·	·	PUNCT
ejpam-6266	428	29	)	)	PUNCT
ejpam-6266	428	30	∥∥	∥∥	PROPN
ejpam-6266	428	31	ḣσ−1	ḣσ−1	PROPN
ejpam-6266	428	32	.	.	PUNCT
ejpam-6266	429	1	(	(	PUNCT
ejpam-6266	429	2	1	1	NUM
ejpam-6266	429	3	+	+	NUM
ejpam-6266	429	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	429	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	429	6	)	)	PUNCT
ejpam-6266	429	7	∫	∫	PROPN
ejpam-6266	429	8	1	1	NUM
ejpam-6266	429	9	0	0	NUM
ejpam-6266	430	1	‖u−	‖u−	NUM
ejpam-6266	430	2	w(u−	w(u−	PRON
ejpam-6266	430	3	v)‖p−1	v)‖p−1	NOUN
ejpam-6266	430	4	x(t	x(t	PROPN
ejpam-6266	430	5	)	)	PUNCT
ejpam-6266	430	6	dw	dw	PROPN
ejpam-6266	430	7	.	.	PUNCT
ejpam-6266	431	1	(	(	PUNCT
ejpam-6266	431	2	1	1	NUM
ejpam-6266	431	3	+	+	NUM
ejpam-6266	431	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	431	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	431	6	)	)	PUNCT
ejpam-6266	431	7	(	(	PUNCT
ejpam-6266	431	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	431	9	x(t	x(t	PROPN
ejpam-6266	431	10	)	)	PUNCT
ejpam-6266	432	1	+	+	CCONJ
ejpam-6266	432	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	432	3	x(t	x(t	PROPN
ejpam-6266	432	4	)	)	PUNCT
ejpam-6266	432	5	)	)	PUNCT
ejpam-6266	432	6	.	.	PUNCT
ejpam-6266	433	1	(	(	PUNCT
ejpam-6266	433	2	93	93	NUM
ejpam-6266	433	3	)	)	PUNCT
ejpam-6266	433	4	finally	finally	ADV
ejpam-6266	433	5	,	,	PUNCT
ejpam-6266	433	6	thanks	thank	NOUN
ejpam-6266	433	7	to	to	ADP
ejpam-6266	433	8	the	the	DET
ejpam-6266	433	9	estimates	estimate	NOUN
ejpam-6266	433	10	(	(	PUNCT
ejpam-6266	433	11	93	93	NUM
ejpam-6266	433	12	)	)	PUNCT
ejpam-6266	433	13	and	and	CCONJ
ejpam-6266	433	14	(	(	PUNCT
ejpam-6266	433	15	80	80	NUM
ejpam-6266	433	16	)	)	PUNCT
ejpam-6266	433	17	we	we	PRON
ejpam-6266	433	18	conclude	conclude	VERB
ejpam-6266	433	19	that∥∥|u(s	that∥∥|u(s	PROPN
ejpam-6266	433	20	,	,	PUNCT
ejpam-6266	433	21	·	·	PUNCT
ejpam-6266	433	22	)	)	PUNCT
ejpam-6266	433	23	|p	|p	NOUN
ejpam-6266	433	24	−	−	PROPN
ejpam-6266	433	25	|v(s	|v(s	PROPN
ejpam-6266	433	26	,	,	PUNCT
ejpam-6266	433	27	·	·	PUNCT
ejpam-6266	433	28	)	)	PUNCT
ejpam-6266	433	29	|p	|p	VERB
ejpam-6266	433	30	∥∥	∥∥	PUNCT
ejpam-6266	433	31	lm∩l2∩ḣσ−1	lm∩l2∩ḣσ−1	X
ejpam-6266	433	32	.	.	PUNCT
ejpam-6266	434	1	(	(	PUNCT
ejpam-6266	434	2	1	1	NUM
ejpam-6266	434	3	+	+	NUM
ejpam-6266	434	4	s)−β‖u−	s)−β‖u−	CCONJ
ejpam-6266	434	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	434	6	)	)	PUNCT
ejpam-6266	434	7	(	(	PUNCT
ejpam-6266	434	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	434	9	x(t	x(t	PROPN
ejpam-6266	434	10	)	)	PUNCT
ejpam-6266	435	1	+	+	CCONJ
ejpam-6266	435	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	435	3	x(t	x(t	PROPN
ejpam-6266	435	4	)	)	PUNCT
ejpam-6266	435	5	)	)	PUNCT
ejpam-6266	435	6	,	,	PUNCT
ejpam-6266	435	7	(	(	PUNCT
ejpam-6266	435	8	94	94	NUM
ejpam-6266	435	9	)	)	PUNCT
ejpam-6266	435	10	where	where	SCONJ
ejpam-6266	435	11	β	β	NOUN
ejpam-6266	435	12	is	be	AUX
ejpam-6266	435	13	as	as	ADP
ejpam-6266	435	14	(	(	PUNCT
ejpam-6266	435	15	61	61	NUM
ejpam-6266	435	16	)	)	PUNCT
ejpam-6266	435	17	.	.	PUNCT
ejpam-6266	436	1	next	next	ADV
ejpam-6266	436	2	,	,	PUNCT
ejpam-6266	436	3	including	include	VERB
ejpam-6266	436	4	the	the	DET
ejpam-6266	436	5	estimate	estimate	NOUN
ejpam-6266	436	6	(	(	PUNCT
ejpam-6266	436	7	94	94	NUM
ejpam-6266	436	8	)	)	PUNCT
ejpam-6266	436	9	into	into	ADP
ejpam-6266	436	10	(	(	PUNCT
ejpam-6266	436	11	79	79	NUM
ejpam-6266	436	12	)	)	PUNCT
ejpam-6266	436	13	we	we	PRON
ejpam-6266	436	14	get	get	VERB
ejpam-6266	436	15	‖|d|κ(nu−nv)(t	‖|d|κ(nu−nv)(t	ADP
ejpam-6266	436	16	,	,	PUNCT
ejpam-6266	436	17	·	·	PUNCT
ejpam-6266	436	18	)	)	PUNCT
ejpam-6266	436	19	‖l2	‖l2	VERB
ejpam-6266	436	20	.	.	PUNCT
ejpam-6266	437	1	jκ,0	jκ,0	PROPN
ejpam-6266	437	2	n	n	CCONJ
ejpam-6266	437	3	(	(	PUNCT
ejpam-6266	437	4	t)‖u−	t)‖u−	NOUN
ejpam-6266	437	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	437	6	)	)	PUNCT
ejpam-6266	437	7	(	(	PUNCT
ejpam-6266	437	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	437	9	x(t	x(t	PROPN
ejpam-6266	437	10	)	)	PUNCT
ejpam-6266	438	1	+	+	CCONJ
ejpam-6266	438	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	438	3	x(t	x(t	PROPN
ejpam-6266	438	4	)	)	PUNCT
ejpam-6266	438	5	)	)	PUNCT
ejpam-6266	438	6	,	,	PUNCT
ejpam-6266	438	7	where	where	SCONJ
ejpam-6266	438	8	jκ,0	jκ,0	PROPN
ejpam-6266	438	9	n	n	CCONJ
ejpam-6266	438	10	(	(	PUNCT
ejpam-6266	438	11	t	t	PROPN
ejpam-6266	438	12	)	)	PUNCT
ejpam-6266	438	13	is	be	AUX
ejpam-6266	438	14	given	give	VERB
ejpam-6266	438	15	by	by	ADP
ejpam-6266	438	16	(	(	PUNCT
ejpam-6266	438	17	18	18	NUM
ejpam-6266	438	18	)	)	PUNCT
ejpam-6266	438	19	.	.	PUNCT
ejpam-6266	439	1	hence	hence	ADV
ejpam-6266	439	2	,	,	PUNCT
ejpam-6266	439	3	due	due	ADP
ejpam-6266	439	4	to	to	ADP
ejpam-6266	439	5	the	the	DET
ejpam-6266	439	6	estimates	estimate	NOUN
ejpam-6266	439	7	(	(	PUNCT
ejpam-6266	439	8	71	71	NUM
ejpam-6266	439	9	)	)	PUNCT
ejpam-6266	439	10	we	we	PRON
ejpam-6266	439	11	find	find	VERB
ejpam-6266	439	12	‖(nu−nv)(t	‖(nu−nv)(t	PRON
ejpam-6266	439	13	,	,	PUNCT
ejpam-6266	439	14	·	·	PUNCT
ejpam-6266	439	15	)	)	PUNCT
ejpam-6266	439	16	‖l2	‖l2	X
ejpam-6266	439	17	.	.	PUNCT
ejpam-6266	440	1	(	(	PUNCT
ejpam-6266	440	2	1	1	NUM
ejpam-6266	440	3	+	+	NUM
ejpam-6266	440	4	t)1−	t)1−	NOUN
ejpam-6266	440	5	n	n	ADP
ejpam-6266	440	6	2	2	NUM
ejpam-6266	440	7	(	(	PUNCT
ejpam-6266	440	8	1	1	NUM
ejpam-6266	440	9	m	m	NOUN
ejpam-6266	440	10	−	−	NUM
ejpam-6266	440	11	1	1	NUM
ejpam-6266	440	12	2	2	NUM
ejpam-6266	440	13	)	)	PUNCT
ejpam-6266	440	14	−γ‖u−	−γ‖u−	NOUN
ejpam-6266	440	15	v‖x(t	v‖x(t	PROPN
ejpam-6266	440	16	)	)	PUNCT
ejpam-6266	440	17	(	(	PUNCT
ejpam-6266	440	18	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	440	19	x(t	x(t	PROPN
ejpam-6266	440	20	)	)	PUNCT
ejpam-6266	441	1	+	+	CCONJ
ejpam-6266	441	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	441	3	x(t	x(t	PROPN
ejpam-6266	441	4	)	)	PUNCT
ejpam-6266	441	5	)	)	PUNCT
ejpam-6266	442	1	,	,	PUNCT
ejpam-6266	442	2	(	(	PUNCT
ejpam-6266	442	3	95	95	NUM
ejpam-6266	442	4	)	)	PUNCT
ejpam-6266	442	5	and	and	CCONJ
ejpam-6266	442	6	‖|d|σ(nu−nv)(t	‖|d|σ(nu−nv)(t	NUM
ejpam-6266	442	7	,	,	PUNCT
ejpam-6266	442	8	·	·	PUNCT
ejpam-6266	442	9	)	)	PUNCT
ejpam-6266	442	10	‖l2	‖l2	X
ejpam-6266	442	11	.	.	PUNCT
ejpam-6266	443	1	(	(	PUNCT
ejpam-6266	443	2	1	1	NUM
ejpam-6266	443	3	+	+	NUM
ejpam-6266	443	4	t)−γ‖u−	t)−γ‖u−	X
ejpam-6266	443	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	443	6	)	)	PUNCT
ejpam-6266	443	7	(	(	PUNCT
ejpam-6266	443	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	443	9	x(t	x(t	PROPN
ejpam-6266	443	10	)	)	PUNCT
ejpam-6266	444	1	+	+	CCONJ
ejpam-6266	444	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	444	3	x(t	x(t	PROPN
ejpam-6266	444	4	)	)	PUNCT
ejpam-6266	444	5	)	)	PUNCT
ejpam-6266	444	6	,	,	PUNCT
ejpam-6266	444	7	(	(	PUNCT
ejpam-6266	444	8	96	96	NUM
ejpam-6266	444	9	)	)	PUNCT
ejpam-6266	444	10	respectively	respectively	ADV
ejpam-6266	444	11	.	.	PUNCT
ejpam-6266	445	1	now	now	ADV
ejpam-6266	445	2	,	,	PUNCT
ejpam-6266	445	3	we	we	PRON
ejpam-6266	445	4	turn	turn	VERB
ejpam-6266	445	5	to	to	PART
ejpam-6266	445	6	estimate	estimate	VERB
ejpam-6266	445	7	the	the	DET
ejpam-6266	445	8	norms	norm	NOUN
ejpam-6266	445	9	‖∂t(nu−nv)(t	‖∂t(nu−nv)(t	ADJ
ejpam-6266	445	10	,	,	PUNCT
ejpam-6266	445	11	·	·	PUNCT
ejpam-6266	445	12	)	)	PUNCT
ejpam-6266	445	13	‖l2	‖l2	ADJ
ejpam-6266	445	14	and	and	CCONJ
ejpam-6266	445	15	‖|d|σ−1∂t(nu−nv)(t	‖|d|σ−1∂t(nu−nv)(t	ADV
ejpam-6266	445	16	,	,	PUNCT
ejpam-6266	445	17	·	·	PUNCT
ejpam-6266	445	18	)	)	PUNCT
ejpam-6266	445	19	‖l2	‖l2	VERB
ejpam-6266	445	20	.	.	PUNCT
ejpam-6266	446	1	again	again	ADV
ejpam-6266	446	2	by	by	ADP
ejpam-6266	446	3	using	use	VERB
ejpam-6266	446	4	proposition	proposition	NOUN
ejpam-6266	446	5	2	2	NUM
ejpam-6266	446	6	we	we	PRON
ejpam-6266	446	7	have	have	VERB
ejpam-6266	446	8	for	for	ADP
ejpam-6266	446	9	κ	κ	NOUN
ejpam-6266	446	10	=	=	SYM
ejpam-6266	446	11	1	1	NUM
ejpam-6266	446	12	and	and	CCONJ
ejpam-6266	446	13	κ	κ	X
ejpam-6266	446	14	=	=	SYM
ejpam-6266	446	15	σ	σ	PROPN
ejpam-6266	446	16	the	the	DET
ejpam-6266	446	17	estimates	estimate	NOUN
ejpam-6266	446	18	‖|d|κ−1∂t(nu−nv)(t	‖|d|κ−1∂t(nu−nv)(t	PROPN
ejpam-6266	446	19	,	,	PUNCT
ejpam-6266	446	20	·	·	PUNCT
ejpam-6266	446	21	)	)	PUNCT
ejpam-6266	446	22	‖l2	‖l2	VERB
ejpam-6266	446	23	.	.	PUNCT
ejpam-6266	447	1	∫	∫	PROPN
ejpam-6266	447	2	t	t	PROPN
ejpam-6266	447	3	0	0	NUM
ejpam-6266	448	1	(	(	PUNCT
ejpam-6266	448	2	1	1	NUM
ejpam-6266	448	3	+	+	CCONJ
ejpam-6266	448	4	t−	t−	PROPN
ejpam-6266	448	5	τ)−	τ)−	PROPN
ejpam-6266	448	6	n	n	CCONJ
ejpam-6266	448	7	2	2	NUM
ejpam-6266	448	8	(	(	PUNCT
ejpam-6266	448	9	1	1	NUM
ejpam-6266	448	10	m	m	NOUN
ejpam-6266	448	11	−	−	NUM
ejpam-6266	448	12	1	1	NUM
ejpam-6266	448	13	2	2	NUM
ejpam-6266	448	14	)	)	PUNCT
ejpam-6266	448	15	−κ−1	−κ−1	X
ejpam-6266	448	16	2	2	NUM
ejpam-6266	448	17	−1	−1	NOUN
ejpam-6266	448	18	×	×	NOUN
ejpam-6266	448	19	∫	∫	PROPN
ejpam-6266	448	20	τ	τ	X
ejpam-6266	448	21	0	0	NUM
ejpam-6266	448	22	(	(	PUNCT
ejpam-6266	448	23	τ	τ	X
ejpam-6266	448	24	−	−	PROPN
ejpam-6266	448	25	s)−γ	s)−γ	PRON
ejpam-6266	448	26	∥∥|ut(s	∥∥|ut(s	PROPN
ejpam-6266	448	27	,	,	PUNCT
ejpam-6266	448	28	·	·	PUNCT
ejpam-6266	448	29	)	)	PUNCT
ejpam-6266	448	30	|p	|p	NOUN
ejpam-6266	448	31	−	−	ADP
ejpam-6266	448	32	|vt(s	|vt(s	PROPN
ejpam-6266	448	33	,	,	PUNCT
ejpam-6266	448	34	·	·	PUNCT
ejpam-6266	448	35	)	)	PUNCT
ejpam-6266	448	36	|p	|p	VERB
ejpam-6266	448	37	∥∥	∥∥	PUNCT
ejpam-6266	448	38	lm∩l2∩ḣσ−1	lm∩l2∩ḣσ−1	X
ejpam-6266	448	39	dsdτ	dsdτ	NOUN
ejpam-6266	448	40	.	.	PUNCT
ejpam-6266	449	1	(	(	PUNCT
ejpam-6266	449	2	97	97	NUM
ejpam-6266	449	3	)	)	PUNCT
ejpam-6266	449	4	including	include	VERB
ejpam-6266	449	5	the	the	DET
ejpam-6266	449	6	estimate	estimate	NOUN
ejpam-6266	449	7	(	(	PUNCT
ejpam-6266	449	8	94	94	NUM
ejpam-6266	449	9	)	)	PUNCT
ejpam-6266	449	10	into	into	ADP
ejpam-6266	449	11	(	(	PUNCT
ejpam-6266	449	12	97	97	NUM
ejpam-6266	449	13	)	)	PUNCT
ejpam-6266	449	14	we	we	PRON
ejpam-6266	449	15	get	get	VERB
ejpam-6266	449	16	‖|d|κ−1∂t(nu−nv)(t	‖|d|κ−1∂t(nu−nv)(t	PROPN
ejpam-6266	449	17	,	,	PUNCT
ejpam-6266	449	18	·	·	PUNCT
ejpam-6266	449	19	)	)	PUNCT
ejpam-6266	449	20	‖l2	‖l2	VERB
ejpam-6266	449	21	.	.	PUNCT
ejpam-6266	450	1	j	j	PROPN
ejpam-6266	450	2	(	(	PUNCT
ejpam-6266	450	3	κ−1,1	κ−1,1	NOUN
ejpam-6266	450	4	)	)	PUNCT
ejpam-6266	450	5	n	n	PROPN
ejpam-6266	450	6	(	(	PUNCT
ejpam-6266	450	7	t)‖u−	t)‖u−	NOUN
ejpam-6266	450	8	v‖x(t	v‖x(t	PROPN
ejpam-6266	450	9	)	)	PUNCT
ejpam-6266	450	10	(	(	PUNCT
ejpam-6266	450	11	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	450	12	x(t	x(t	PROPN
ejpam-6266	450	13	)	)	PUNCT
ejpam-6266	451	1	+	+	CCONJ
ejpam-6266	451	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	451	3	x(t	x(t	PROPN
ejpam-6266	451	4	)	)	PUNCT
ejpam-6266	451	5	)	)	PUNCT
ejpam-6266	452	1	,	,	PUNCT
ejpam-6266	452	2	(	(	PUNCT
ejpam-6266	452	3	98	98	NUM
ejpam-6266	452	4	)	)	PUNCT
ejpam-6266	452	5	where	where	SCONJ
ejpam-6266	452	6	j	j	PROPN
ejpam-6266	452	7	(	(	PUNCT
ejpam-6266	452	8	κ−1,1	κ−1,1	NOUN
ejpam-6266	452	9	)	)	PUNCT
ejpam-6266	452	10	n	n	PROPN
ejpam-6266	452	11	(	(	PUNCT
ejpam-6266	452	12	t	t	NOUN
ejpam-6266	452	13	)	)	PUNCT
ejpam-6266	452	14	is	be	AUX
ejpam-6266	452	15	defined	define	VERB
ejpam-6266	452	16	by	by	ADP
ejpam-6266	452	17	(	(	PUNCT
ejpam-6266	452	18	18	18	NUM
ejpam-6266	452	19	)	)	PUNCT
ejpam-6266	452	20	.	.	PUNCT
ejpam-6266	453	1	due	due	ADP
ejpam-6266	453	2	to	to	ADP
ejpam-6266	453	3	(	(	PUNCT
ejpam-6266	453	4	76	76	NUM
ejpam-6266	453	5	)	)	PUNCT
ejpam-6266	453	6	we	we	PRON
ejpam-6266	453	7	obtain	obtain	VERB
ejpam-6266	453	8	for	for	ADP
ejpam-6266	453	9	κ	κ	NOUN
ejpam-6266	453	10	=	=	SYM
ejpam-6266	453	11	0	0	PROPN
ejpam-6266	453	12	the	the	DET
ejpam-6266	453	13	estimate	estimate	NOUN
ejpam-6266	453	14	‖∂t(nu−nv)(t	‖∂t(nu−nv)(t	ADJ
ejpam-6266	453	15	,	,	PUNCT
ejpam-6266	453	16	·	·	PUNCT
ejpam-6266	453	17	)	)	PUNCT
ejpam-6266	453	18	‖l2	‖l2	X
ejpam-6266	453	19	.	.	PUNCT
ejpam-6266	454	1	(	(	PUNCT
ejpam-6266	454	2	1	1	NUM
ejpam-6266	454	3	+	+	NUM
ejpam-6266	454	4	t)−γ‖u−	t)−γ‖u−	X
ejpam-6266	454	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	454	6	)	)	PUNCT
ejpam-6266	454	7	(	(	PUNCT
ejpam-6266	454	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	454	9	x(t	x(t	PROPN
ejpam-6266	454	10	)	)	PUNCT
ejpam-6266	455	1	+	+	CCONJ
ejpam-6266	455	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	455	3	x(t	x(t	PROPN
ejpam-6266	455	4	)	)	PUNCT
ejpam-6266	455	5	)	)	PUNCT
ejpam-6266	455	6	,	,	PUNCT
ejpam-6266	455	7	(	(	PUNCT
ejpam-6266	455	8	99	99	NUM
ejpam-6266	455	9	)	)	PUNCT
ejpam-6266	455	10	and	and	CCONJ
ejpam-6266	455	11	for	for	ADP
ejpam-6266	455	12	κ	κ	NOUN
ejpam-6266	455	13	=	=	SYM
ejpam-6266	455	14	σ	σ	PROPN
ejpam-6266	455	15	the	the	DET
ejpam-6266	455	16	estimate∥∥|d|σ−1∂t(nu−nv)(t	estimate∥∥|d|σ−1∂t(nu−nv)(t	PROPN
ejpam-6266	455	17	,	,	PUNCT
ejpam-6266	455	18	·	·	PUNCT
ejpam-6266	455	19	)	)	PUNCT
ejpam-6266	455	20	∥∥	∥∥	X
ejpam-6266	455	21	l2	l2	NOUN
ejpam-6266	455	22	.	.	PUNCT
ejpam-6266	456	1	(	(	PUNCT
ejpam-6266	456	2	1	1	NUM
ejpam-6266	456	3	+	+	NUM
ejpam-6266	456	4	t)−γ‖u−	t)−γ‖u−	X
ejpam-6266	456	5	v‖x(t	v‖x(t	PROPN
ejpam-6266	456	6	)	)	PUNCT
ejpam-6266	456	7	(	(	PUNCT
ejpam-6266	456	8	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	456	9	x(t	x(t	PROPN
ejpam-6266	456	10	)	)	PUNCT
ejpam-6266	457	1	+	+	CCONJ
ejpam-6266	457	2	‖v‖p−1	‖v‖p−1	ADJ
ejpam-6266	457	3	x(t	x(t	PROPN
ejpam-6266	457	4	)	)	PUNCT
ejpam-6266	457	5	)	)	PUNCT
ejpam-6266	457	6	.	.	PUNCT
ejpam-6266	458	1	(	(	PUNCT
ejpam-6266	458	2	100	100	NUM
ejpam-6266	458	3	)	)	PUNCT
ejpam-6266	458	4	finally	finally	ADV
ejpam-6266	458	5	,	,	PUNCT
ejpam-6266	458	6	the	the	DET
ejpam-6266	458	7	estimates	estimate	NOUN
ejpam-6266	458	8	(	(	PUNCT
ejpam-6266	458	9	100	100	NUM
ejpam-6266	458	10	)	)	PUNCT
ejpam-6266	458	11	,	,	PUNCT
ejpam-6266	458	12	(	(	PUNCT
ejpam-6266	458	13	99	99	NUM
ejpam-6266	458	14	)	)	PUNCT
ejpam-6266	458	15	,	,	PUNCT
ejpam-6266	458	16	(	(	PUNCT
ejpam-6266	458	17	96	96	NUM
ejpam-6266	458	18	)	)	PUNCT
ejpam-6266	458	19	,	,	PUNCT
ejpam-6266	458	20	(	(	PUNCT
ejpam-6266	458	21	95	95	NUM
ejpam-6266	458	22	)	)	PUNCT
ejpam-6266	458	23	and	and	CCONJ
ejpam-6266	458	24	the	the	DET
ejpam-6266	458	25	definition	definition	NOUN
ejpam-6266	458	26	of	of	ADP
ejpam-6266	458	27	the	the	DET
ejpam-6266	458	28	norm	norm	NOUN
ejpam-6266	458	29	in	in	ADP
ejpam-6266	458	30	x(t	x(t	PROPN
ejpam-6266	458	31	)	)	PUNCT
ejpam-6266	458	32	yield	yield	VERB
ejpam-6266	458	33	the	the	DET
ejpam-6266	458	34	desired	desire	VERB
ejpam-6266	458	35	inequality	inequality	NOUN
ejpam-6266	458	36	(	(	PUNCT
ejpam-6266	458	37	16	16	NUM
ejpam-6266	458	38	)	)	PUNCT
ejpam-6266	458	39	.	.	PUNCT
ejpam-6266	459	1	this	this	PRON
ejpam-6266	459	2	ends	end	VERB
ejpam-6266	459	3	the	the	DET
ejpam-6266	459	4	proof	proof	NOUN
ejpam-6266	459	5	of	of	ADP
ejpam-6266	459	6	theorem	theorem	NOUN
ejpam-6266	459	7	3	3	NUM
ejpam-6266	459	8	.	.	PUNCT
ejpam-6266	460	1	t.	t.	PROPN
ejpam-6266	460	2	hadj	hadj	PROPN
ejpam-6266	460	3	kaddour	kaddour	PROPN
ejpam-6266	460	4	et	et	PROPN
ejpam-6266	460	5	al	al	PROPN
ejpam-6266	460	6	.	.	PUNCT
ejpam-6266	460	7	/	/	SYM
ejpam-6266	460	8	eur	eur	PROPN
ejpam-6266	460	9	.	.	PUNCT
ejpam-6266	461	1	j.	j.	PROPN
ejpam-6266	461	2	pure	pure	PROPN
ejpam-6266	461	3	appl	appl	PROPN
ejpam-6266	461	4	.	.	PROPN
ejpam-6266	461	5	math	math	PROPN
ejpam-6266	461	6	,	,	PUNCT
ejpam-6266	461	7	18	18	NUM
ejpam-6266	461	8	(	(	PUNCT
ejpam-6266	461	9	4	4	NUM
ejpam-6266	461	10	)	)	PUNCT
ejpam-6266	461	11	(	(	PUNCT
ejpam-6266	461	12	2025	2025	NUM
ejpam-6266	461	13	)	)	PUNCT
ejpam-6266	461	14	,	,	PUNCT
ejpam-6266	461	15	6266	6266	NUM
ejpam-6266	461	16	19	19	NUM
ejpam-6266	461	17	of	of	ADP
ejpam-6266	461	18	24	24	NUM
ejpam-6266	461	19	remark	remark	NOUN
ejpam-6266	461	20	1	1	NUM
ejpam-6266	461	21	.	.	PUNCT
ejpam-6266	462	1	let	let	VERB
ejpam-6266	462	2	us	we	PRON
ejpam-6266	462	3	explain	explain	VERB
ejpam-6266	462	4	how	how	SCONJ
ejpam-6266	462	5	to	to	PART
ejpam-6266	462	6	estimate	estimate	VERB
ejpam-6266	462	7	the	the	DET
ejpam-6266	462	8	norm	norm	NOUN
ejpam-6266	462	9	of	of	ADP
ejpam-6266	462	10	u	u	PROPN
ejpam-6266	462	11	in	in	ADP
ejpam-6266	462	12	ḣ1/2	ḣ1/2	NOUN
ejpam-6266	462	13	in	in	ADP
ejpam-6266	462	14	the	the	DET
ejpam-6266	462	15	case	case	NOUN
ejpam-6266	463	1	n	n	NOUN
ejpam-6266	463	2	=	=	SYM
ejpam-6266	463	3	3	3	NUM
ejpam-6266	464	1	and	and	CCONJ
ejpam-6266	464	2	why	why	SCONJ
ejpam-6266	464	3	the	the	DET
ejpam-6266	464	4	logarithmic	logarithmic	ADJ
ejpam-6266	464	5	term	term	NOUN
ejpam-6266	464	6	does	do	AUX
ejpam-6266	464	7	appear	appear	VERB
ejpam-6266	464	8	.	.	PUNCT
ejpam-6266	465	1	one	one	PRON
ejpam-6266	465	2	can	can	AUX
ejpam-6266	465	3	estimate	estimate	VERB
ejpam-6266	465	4	‖u‖ḣ1/2	‖u‖ḣ1/2	ADV
ejpam-6266	465	5	by	by	ADP
ejpam-6266	465	6	using	use	VERB
ejpam-6266	465	7	interpolation	interpolation	NOUN
ejpam-6266	465	8	argument	argument	NOUN
ejpam-6266	465	9	.	.	PUNCT
ejpam-6266	466	1	so	so	ADV
ejpam-6266	466	2	,	,	PUNCT
ejpam-6266	466	3	taking	take	VERB
ejpam-6266	466	4	in	in	ADP
ejpam-6266	466	5	(	(	PUNCT
ejpam-6266	466	6	109	109	NUM
ejpam-6266	466	7	)	)	PUNCT
ejpam-6266	466	8	)	)	PUNCT
ejpam-6266	467	1	σ	σ	NOUN
ejpam-6266	467	2	=	=	SYM
ejpam-6266	467	3	1	1	NUM
ejpam-6266	467	4	2	2	NUM
ejpam-6266	467	5	,	,	PUNCT
ejpam-6266	467	6	k1	k1	NOUN
ejpam-6266	467	7	=	=	SYM
ejpam-6266	467	8	0	0	NUM
ejpam-6266	467	9	,	,	PUNCT
ejpam-6266	467	10	k2	k2	NOUN
ejpam-6266	467	11	=	=	SYM
ejpam-6266	467	12	1	1	NUM
ejpam-6266	467	13	and	and	CCONJ
ejpam-6266	467	14	θ	θ	NOUN
ejpam-6266	467	15	=	=	SYM
ejpam-6266	467	16	1	1	NUM
ejpam-6266	467	17	2	2	NUM
ejpam-6266	467	18	we	we	PRON
ejpam-6266	467	19	get	get	VERB
ejpam-6266	467	20	‖u(t	‖u(t	NOUN
ejpam-6266	467	21	,	,	PUNCT
ejpam-6266	467	22	·	·	PUNCT
ejpam-6266	467	23	)	)	PUNCT
ejpam-6266	467	24	‖ḣ1/2	‖ḣ1/2	PROPN
ejpam-6266	467	25	.	.	PUNCT
ejpam-6266	468	1	‖u(t	‖u(t	X
ejpam-6266	468	2	,	,	PUNCT
ejpam-6266	468	3	·	·	PUNCT
ejpam-6266	468	4	)	)	PUNCT
ejpam-6266	468	5	‖	‖	PROPN
ejpam-6266	468	6	1	1	NUM
ejpam-6266	468	7	2	2	NUM
ejpam-6266	468	8	l2‖∇u(t	l2‖∇u(t	NOUN
ejpam-6266	468	9	,	,	PUNCT
ejpam-6266	468	10	·	·	PUNCT
ejpam-6266	468	11	)	)	PUNCT
ejpam-6266	468	12	‖	‖	PROPN
ejpam-6266	468	13	1	1	NUM
ejpam-6266	468	14	2	2	NUM
ejpam-6266	468	15	l2	l2	NOUN
ejpam-6266	468	16	.	.	PUNCT
ejpam-6266	469	1	(	(	PUNCT
ejpam-6266	469	2	1	1	NUM
ejpam-6266	469	3	+	+	NUM
ejpam-6266	469	4	t	t	NOUN
ejpam-6266	469	5	)	)	PUNCT
ejpam-6266	469	6	1	1	NUM
ejpam-6266	469	7	2	2	NUM
ejpam-6266	469	8	(	(	PUNCT
ejpam-6266	469	9	1	1	NUM
ejpam-6266	469	10	4	4	NUM
ejpam-6266	469	11	−γ)−	−γ)−	PROPN
ejpam-6266	469	12	γ	γ	PROPN
ejpam-6266	469	13	2	2	NUM
ejpam-6266	469	14	‖(u0	‖(u0	PROPN
ejpam-6266	469	15	,	,	PUNCT
ejpam-6266	469	16	u1)‖a1	u1)‖a1	PROPN
ejpam-6266	469	17	1,0	1,0	NUM
ejpam-6266	469	18	.	.	PUNCT
ejpam-6266	470	1	(	(	PUNCT
ejpam-6266	470	2	1	1	NUM
ejpam-6266	470	3	+	+	NUM
ejpam-6266	470	4	t	t	NOUN
ejpam-6266	470	5	)	)	PUNCT
ejpam-6266	470	6	1	1	NUM
ejpam-6266	470	7	8	8	NUM
ejpam-6266	470	8	−γ‖(u0	−γ‖(u0	PROPN
ejpam-6266	470	9	,	,	PUNCT
ejpam-6266	470	10	u1)‖a1	u1)‖a1	PROPN
ejpam-6266	470	11	1,0	1,0	NUM
ejpam-6266	470	12	.	.	PUNCT
ejpam-6266	471	1	(	(	PUNCT
ejpam-6266	471	2	101	101	NUM
ejpam-6266	471	3	)	)	PUNCT
ejpam-6266	471	4	in	in	ADP
ejpam-6266	471	5	the	the	DET
ejpam-6266	471	6	other	other	ADJ
ejpam-6266	471	7	hand	hand	NOUN
ejpam-6266	471	8	,	,	PUNCT
ejpam-6266	471	9	if	if	SCONJ
ejpam-6266	471	10	we	we	PRON
ejpam-6266	471	11	estimate	estimate	VERB
ejpam-6266	471	12	the	the	DET
ejpam-6266	471	13	norm	norm	NOUN
ejpam-6266	471	14	of	of	ADP
ejpam-6266	471	15	u	u	PROPN
ejpam-6266	471	16	in	in	ADP
ejpam-6266	471	17	ḣ1/2	ḣ1/2	NOUN
ejpam-6266	471	18	by	by	ADP
ejpam-6266	471	19	using	use	VERB
ejpam-6266	471	20	corollary	corollary	ADJ
ejpam-6266	471	21	1	1	NUM
ejpam-6266	471	22	and	and	CCONJ
ejpam-6266	471	23	lemma	lemma	PROPN
ejpam-6266	471	24	1	1	NUM
ejpam-6266	471	25	we	we	PRON
ejpam-6266	471	26	find	find	VERB
ejpam-6266	471	27	‖unl(t	‖unl(t	NOUN
ejpam-6266	471	28	,	,	PUNCT
ejpam-6266	471	29	·	·	PUNCT
ejpam-6266	471	30	)	)	PUNCT
ejpam-6266	471	31	‖ḣ1/2	‖ḣ1/2	PROPN
ejpam-6266	471	32	.	.	PUNCT
ejpam-6266	472	1	(	(	PUNCT
ejpam-6266	472	2	∫	∫	PROPN
ejpam-6266	472	3	t	t	PROPN
ejpam-6266	472	4	0	0	NUM
ejpam-6266	472	5	(	(	PUNCT
ejpam-6266	472	6	1	1	NUM
ejpam-6266	472	7	+	+	CCONJ
ejpam-6266	472	8	t−	t−	PROPN
ejpam-6266	472	9	τ)−	τ)−	PROPN
ejpam-6266	472	10	3	3	NUM
ejpam-6266	472	11	4	4	NUM
ejpam-6266	472	12	−	−	NOUN
ejpam-6266	472	13	1	1	NUM
ejpam-6266	472	14	4	4	NUM
ejpam-6266	472	15	∫	∫	PROPN
ejpam-6266	472	16	τ	τ	X
ejpam-6266	472	17	0	0	NUM
ejpam-6266	472	18	(	(	PUNCT
ejpam-6266	472	19	τ	τ	X
ejpam-6266	472	20	−	−	NOUN
ejpam-6266	472	21	s)−γ(1	s)−γ(1	PROPN
ejpam-6266	472	22	+	+	CCONJ
ejpam-6266	472	23	s)−βdsdτ	s)−βdsdτ	NOUN
ejpam-6266	472	24	)	)	PUNCT
ejpam-6266	472	25	‖u‖px(t	‖u‖px(t	PROPN
ejpam-6266	472	26	)	)	PUNCT
ejpam-6266	472	27	,	,	PUNCT
ejpam-6266	472	28	for	for	ADP
ejpam-6266	472	29	some	some	DET
ejpam-6266	472	30	β	β	X
ejpam-6266	472	31	>	>	X
ejpam-6266	472	32	1	1	NUM
ejpam-6266	472	33	.	.	PUNCT
ejpam-6266	473	1	since	since	SCONJ
ejpam-6266	473	2	β	β	PROPN
ejpam-6266	473	3	>	>	X
ejpam-6266	473	4	1	1	NUM
ejpam-6266	473	5	and	and	CCONJ
ejpam-6266	473	6	3	3	NUM
ejpam-6266	473	7	4	4	NUM
ejpam-6266	473	8	+	+	CCONJ
ejpam-6266	473	9	1	1	NUM
ejpam-6266	473	10	4	4	NUM
ejpam-6266	473	11	=	=	SYM
ejpam-6266	473	12	1	1	NUM
ejpam-6266	473	13	we	we	PRON
ejpam-6266	473	14	get	get	VERB
ejpam-6266	473	15	the	the	DET
ejpam-6266	473	16	estimate∫	estimate∫	ADJ
ejpam-6266	473	17	t	t	NOUN
ejpam-6266	473	18	0	0	NUM
ejpam-6266	474	1	(	(	PUNCT
ejpam-6266	474	2	1	1	NUM
ejpam-6266	474	3	+	+	CCONJ
ejpam-6266	474	4	t−	t−	PROPN
ejpam-6266	474	5	τ)−	τ)−	PROPN
ejpam-6266	474	6	3	3	NUM
ejpam-6266	474	7	4	4	NUM
ejpam-6266	474	8	−	−	NOUN
ejpam-6266	474	9	1	1	NUM
ejpam-6266	474	10	4	4	NUM
ejpam-6266	474	11	∫	∫	PROPN
ejpam-6266	474	12	τ	τ	X
ejpam-6266	474	13	0	0	NUM
ejpam-6266	474	14	(	(	PUNCT
ejpam-6266	474	15	τ	τ	X
ejpam-6266	474	16	−	−	NOUN
ejpam-6266	474	17	s)−γ(1	s)−γ(1	PROPN
ejpam-6266	474	18	+	+	CCONJ
ejpam-6266	474	19	s)−βdsdτ	s)−βdsdτ	PROPN
ejpam-6266	474	20	.	.	PUNCT
ejpam-6266	475	1	(	(	PUNCT
ejpam-6266	475	2	1	1	X
ejpam-6266	475	3	+	+	NUM
ejpam-6266	475	4	t)−γ	t)−γ	PRON
ejpam-6266	475	5	log(2	log(2	NOUN
ejpam-6266	475	6	+	+	CCONJ
ejpam-6266	475	7	t	t	PROPN
ejpam-6266	475	8	)	)	PUNCT
ejpam-6266	475	9	.	.	PUNCT
ejpam-6266	476	1	as	as	ADP
ejpam-6266	476	2	a	a	DET
ejpam-6266	476	3	consequence	consequence	NOUN
ejpam-6266	476	4	,	,	PUNCT
ejpam-6266	476	5	we	we	PRON
ejpam-6266	476	6	get	get	VERB
ejpam-6266	476	7	‖u(t	‖u(t	NOUN
ejpam-6266	476	8	,	,	PUNCT
ejpam-6266	476	9	·	·	PUNCT
ejpam-6266	476	10	)	)	PUNCT
ejpam-6266	476	11	‖ḣ1/2	‖ḣ1/2	PROPN
ejpam-6266	476	12	.	.	PUNCT
ejpam-6266	477	1	(	(	PUNCT
ejpam-6266	477	2	1	1	X
ejpam-6266	477	3	+	+	NUM
ejpam-6266	477	4	t)−γ	t)−γ	PRON
ejpam-6266	477	5	log(2	log(2	NOUN
ejpam-6266	478	1	+	+	CCONJ
ejpam-6266	478	2	t)‖(u0	t)‖(u0	ADJ
ejpam-6266	478	3	,	,	PUNCT
ejpam-6266	478	4	u1)‖a1,1	u1)‖a1,1	INTJ
ejpam-6266	478	5	.	.	PUNCT
ejpam-6266	479	1	(	(	PUNCT
ejpam-6266	479	2	102	102	NUM
ejpam-6266	479	3	)	)	PUNCT
ejpam-6266	479	4	in	in	ADP
ejpam-6266	479	5	term	term	NOUN
ejpam-6266	479	6	of	of	ADP
ejpam-6266	479	7	comparison	comparison	NOUN
ejpam-6266	479	8	,	,	PUNCT
ejpam-6266	479	9	the	the	DET
ejpam-6266	479	10	estimate	estimate	NOUN
ejpam-6266	479	11	(	(	PUNCT
ejpam-6266	479	12	102	102	NUM
ejpam-6266	479	13	)	)	PUNCT
ejpam-6266	479	14	is	be	AUX
ejpam-6266	479	15	more	more	ADV
ejpam-6266	479	16	precise	precise	ADJ
ejpam-6266	479	17	than	than	ADP
ejpam-6266	479	18	the	the	DET
ejpam-6266	479	19	estimate	estimate	NOUN
ejpam-6266	479	20	(	(	PUNCT
ejpam-6266	479	21	101	101	NUM
ejpam-6266	479	22	)	)	PUNCT
ejpam-6266	479	23	.	.	PUNCT
ejpam-6266	480	1	for	for	ADP
ejpam-6266	480	2	this	this	DET
ejpam-6266	480	3	reason	reason	NOUN
ejpam-6266	480	4	,	,	PUNCT
ejpam-6266	480	5	we	we	PRON
ejpam-6266	480	6	consider	consider	VERB
ejpam-6266	480	7	the	the	DET
ejpam-6266	480	8	estimate	estimate	NOUN
ejpam-6266	480	9	(	(	PUNCT
ejpam-6266	480	10	102	102	NUM
ejpam-6266	480	11	)	)	PUNCT
ejpam-6266	480	12	in	in	ADP
ejpam-6266	480	13	theorem	theorem	NOUN
ejpam-6266	480	14	3	3	NUM
ejpam-6266	480	15	.	.	X
ejpam-6266	481	1	4.2.2	4.2.2	NUM
ejpam-6266	481	2	.	.	PUNCT
ejpam-6266	482	1	proof	proof	NOUN
ejpam-6266	482	2	of	of	ADP
ejpam-6266	482	3	theorem	theorem	NOUN
ejpam-6266	482	4	4	4	NUM
ejpam-6266	482	5	the	the	DET
ejpam-6266	482	6	proof	proof	NOUN
ejpam-6266	482	7	of	of	ADP
ejpam-6266	482	8	theorem	theorem	ADJ
ejpam-6266	482	9	4	4	NUM
ejpam-6266	482	10	is	be	AUX
ejpam-6266	482	11	similar	similar	ADJ
ejpam-6266	482	12	to	to	ADP
ejpam-6266	482	13	the	the	DET
ejpam-6266	482	14	proof	proof	NOUN
ejpam-6266	482	15	of	of	ADP
ejpam-6266	482	16	theorem	theorem	ADJ
ejpam-6266	482	17	3	3	X
ejpam-6266	482	18	.	.	NUM
ejpam-6266	482	19	expect	expect	VERB
ejpam-6266	482	20	in	in	ADP
ejpam-6266	482	21	the	the	DET
ejpam-6266	482	22	case	case	NOUN
ejpam-6266	482	23	of	of	ADP
ejpam-6266	482	24	theorem	theorem	NOUN
ejpam-6266	482	25	4	4	NUM
ejpam-6266	482	26	we	we	PRON
ejpam-6266	482	27	have	have	VERB
ejpam-6266	482	28	n	n	ADV
ejpam-6266	482	29	2	2	NUM
ejpam-6266	482	30	(	(	PUNCT
ejpam-6266	482	31	1	1	NUM
ejpam-6266	482	32	m	m	NOUN
ejpam-6266	482	33	−	−	NUM
ejpam-6266	482	34	1	1	NUM
ejpam-6266	482	35	2	2	NUM
ejpam-6266	482	36	)	)	PUNCT
ejpam-6266	483	1	=	=	SYM
ejpam-6266	483	2	1	1	NUM
ejpam-6266	483	3	if	if	SCONJ
ejpam-6266	483	4	and	and	CCONJ
ejpam-6266	483	5	only	only	ADV
ejpam-6266	483	6	if	if	SCONJ
ejpam-6266	483	7	n	n	NUM
ejpam-6266	483	8	≥	≥	VERB
ejpam-6266	483	9	4	4	NUM
ejpam-6266	483	10	and	and	CCONJ
ejpam-6266	483	11	m	m	PROPN
ejpam-6266	483	12	=	=	ADJ
ejpam-6266	483	13	2n	2n	NUM
ejpam-6266	483	14	n+	n+	ADP
ejpam-6266	483	15	4	4	NUM
ejpam-6266	483	16	.	.	PUNCT
ejpam-6266	484	1	in	in	ADP
ejpam-6266	484	2	this	this	DET
ejpam-6266	484	3	case	case	NOUN
ejpam-6266	484	4	,	,	PUNCT
ejpam-6266	484	5	the	the	DET
ejpam-6266	484	6	integral	integral	ADJ
ejpam-6266	484	7	j	j	PROPN
ejpam-6266	484	8	(	(	PUNCT
ejpam-6266	484	9	k	k	X
ejpam-6266	484	10	,	,	PUNCT
ejpam-6266	484	11	j	j	PROPN
ejpam-6266	484	12	)	)	PUNCT
ejpam-6266	484	13	n	n	PROPN
ejpam-6266	484	14	(	(	PUNCT
ejpam-6266	484	15	t	t	PROPN
ejpam-6266	484	16	)	)	PUNCT
ejpam-6266	484	17	is	be	AUX
ejpam-6266	484	18	estimated	estimate	VERB
ejpam-6266	484	19	for	for	ADP
ejpam-6266	484	20	k	k	PROPN
ejpam-6266	484	21	=	=	PUNCT
ejpam-6266	484	22	j	j	PROPN
ejpam-6266	484	23	=	=	SYM
ejpam-6266	484	24	0	0	PUNCT
ejpam-6266	485	1	as	as	SCONJ
ejpam-6266	485	2	follows	follow	VERB
ejpam-6266	485	3	:	:	PUNCT
ejpam-6266	485	4	j	j	PROPN
ejpam-6266	485	5	(	(	PUNCT
ejpam-6266	485	6	0,0	0,0	NUM
ejpam-6266	485	7	)	)	PUNCT
ejpam-6266	485	8	n	n	CCONJ
ejpam-6266	485	9	(	(	PUNCT
ejpam-6266	485	10	t	t	NOUN
ejpam-6266	485	11	)	)	PUNCT
ejpam-6266	485	12	=	=	PRON
ejpam-6266	485	13	{	{	PUNCT
ejpam-6266	485	14	(	(	PUNCT
ejpam-6266	485	15	1	1	NUM
ejpam-6266	485	16	+	+	NUM
ejpam-6266	485	17	t)−γ	t)−γ	PRON
ejpam-6266	485	18	log(2	log(2	NOUN
ejpam-6266	486	1	+	+	CCONJ
ejpam-6266	486	2	t	t	X
ejpam-6266	486	3	)	)	PUNCT
ejpam-6266	486	4	if	if	SCONJ
ejpam-6266	486	5	n	n	NUM
ejpam-6266	486	6	≥	≥	VERB
ejpam-6266	486	7	4	4	NUM
ejpam-6266	486	8	and	and	CCONJ
ejpam-6266	486	9	m	m	PROPN
ejpam-6266	486	10	=	=	NOUN
ejpam-6266	486	11	2n	2n	NUM
ejpam-6266	486	12	n+4	n+4	NUM
ejpam-6266	486	13	,	,	PUNCT
ejpam-6266	486	14	(	(	PUNCT
ejpam-6266	486	15	1	1	NUM
ejpam-6266	486	16	+	+	SYM
ejpam-6266	486	17	t)−γ	t)−γ	X
ejpam-6266	486	18	else	else	ADV
ejpam-6266	486	19	.	.	PUNCT
ejpam-6266	487	1	remark	remark	NOUN
ejpam-6266	487	2	2	2	NUM
ejpam-6266	487	3	.	.	PUNCT
ejpam-6266	488	1	we	we	PRON
ejpam-6266	488	2	refer	refer	VERB
ejpam-6266	488	3	the	the	DET
ejpam-6266	488	4	curious	curious	ADJ
ejpam-6266	488	5	reader	reader	NOUN
ejpam-6266	488	6	asking	ask	VERB
ejpam-6266	488	7	for	for	ADP
ejpam-6266	488	8	the	the	DET
ejpam-6266	488	9	existence	existence	NOUN
ejpam-6266	488	10	of	of	ADP
ejpam-6266	488	11	the	the	DET
ejpam-6266	488	12	parameters	parameter	NOUN
ejpam-6266	488	13	qj	qj	PROPN
ejpam-6266	488	14	,	,	PUNCT
ejpam-6266	488	15	j	j	PROPN
ejpam-6266	488	16	=	=	SYM
ejpam-6266	488	17	1	1	NUM
ejpam-6266	488	18	,	,	PUNCT
ejpam-6266	488	19	2	2	NUM
ejpam-6266	488	20	and	and	CCONJ
ejpam-6266	488	21	ri	ri	NOUN
ejpam-6266	488	22	,	,	PUNCT
ejpam-6266	488	23	i	i	NOUN
ejpam-6266	488	24	=	=	NOUN
ejpam-6266	488	25	1	1	NUM
ejpam-6266	488	26	,	,	PUNCT
ejpam-6266	488	27	·	·	PUNCT
ejpam-6266	488	28	·	·	PUNCT
ejpam-6266	488	29	·	·	PUNCT
ejpam-6266	488	30	,	,	PUNCT
ejpam-6266	488	31	6	6	NUM
ejpam-6266	488	32	which	which	PRON
ejpam-6266	488	33	appears	appear	VERB
ejpam-6266	488	34	in	in	ADP
ejpam-6266	488	35	the	the	DET
ejpam-6266	488	36	proof	proof	NOUN
ejpam-6266	488	37	of	of	ADP
ejpam-6266	488	38	theorem	theorem	ADJ
ejpam-6266	488	39	3	3	NUM
ejpam-6266	488	40	and	and	CCONJ
ejpam-6266	488	41	theorem	theorem	VERB
ejpam-6266	488	42	4	4	NUM
ejpam-6266	488	43	to	to	PART
ejpam-6266	488	44	check	check	VERB
ejpam-6266	488	45	[	[	X
ejpam-6266	488	46	11	11	NUM
ejpam-6266	488	47	]	]	PUNCT
ejpam-6266	488	48	and	and	CCONJ
ejpam-6266	488	49	some	some	PRON
ejpam-6266	488	50	of	of	ADP
ejpam-6266	488	51	the	the	DET
ejpam-6266	488	52	references	reference	NOUN
ejpam-6266	488	53	therein	therein	ADV
ejpam-6266	488	54	.	.	PUNCT
ejpam-6266	489	1	t.	t.	PROPN
ejpam-6266	489	2	hadj	hadj	PROPN
ejpam-6266	489	3	kaddour	kaddour	PROPN
ejpam-6266	489	4	et	et	PROPN
ejpam-6266	489	5	al	al	PROPN
ejpam-6266	489	6	.	.	PUNCT
ejpam-6266	489	7	/	/	SYM
ejpam-6266	489	8	eur	eur	PROPN
ejpam-6266	489	9	.	.	PUNCT
ejpam-6266	490	1	j.	j.	PROPN
ejpam-6266	490	2	pure	pure	PROPN
ejpam-6266	490	3	appl	appl	PROPN
ejpam-6266	490	4	.	.	PROPN
ejpam-6266	490	5	math	math	PROPN
ejpam-6266	490	6	,	,	PUNCT
ejpam-6266	490	7	18	18	NUM
ejpam-6266	490	8	(	(	PUNCT
ejpam-6266	490	9	4	4	NUM
ejpam-6266	490	10	)	)	PUNCT
ejpam-6266	490	11	(	(	PUNCT
ejpam-6266	490	12	2025	2025	NUM
ejpam-6266	490	13	)	)	PUNCT
ejpam-6266	490	14	,	,	PUNCT
ejpam-6266	490	15	6266	6266	NUM
ejpam-6266	490	16	20	20	NUM
ejpam-6266	490	17	of	of	ADP
ejpam-6266	490	18	24	24	NUM
ejpam-6266	490	19	5	5	NUM
ejpam-6266	490	20	.	.	PUNCT
ejpam-6266	491	1	conclusion	conclusion	NOUN
ejpam-6266	491	2	we	we	PRON
ejpam-6266	491	3	showed	show	VERB
ejpam-6266	491	4	in	in	ADP
ejpam-6266	491	5	theorems	theorem	NOUN
ejpam-6266	491	6	1	1	NUM
ejpam-6266	491	7	,	,	PUNCT
ejpam-6266	491	8	3	3	NUM
ejpam-6266	491	9	and	and	CCONJ
ejpam-6266	491	10	4	4	NUM
ejpam-6266	491	11	the	the	DET
ejpam-6266	491	12	influence	influence	NOUN
ejpam-6266	491	13	of	of	ADP
ejpam-6266	491	14	the	the	DET
ejpam-6266	491	15	dissipative	dissipative	NOUN
ejpam-6266	491	16	memory	memory	NOUN
ejpam-6266	491	17	by	by	ADP
ejpam-6266	491	18	its	its	PRON
ejpam-6266	491	19	influence	influence	NOUN
ejpam-6266	491	20	on	on	ADP
ejpam-6266	491	21	the	the	DET
ejpam-6266	491	22	critical	critical	ADJ
ejpam-6266	491	23	exponent	exponent	NOUN
ejpam-6266	491	24	and	and	CCONJ
ejpam-6266	491	25	the	the	DET
ejpam-6266	491	26	estimates	estimate	NOUN
ejpam-6266	491	27	of	of	ADP
ejpam-6266	491	28	the	the	DET
ejpam-6266	491	29	norms	norm	NOUN
ejpam-6266	491	30	of	of	ADP
ejpam-6266	491	31	the	the	DET
ejpam-6266	491	32	solution	solution	NOUN
ejpam-6266	491	33	and	and	CCONJ
ejpam-6266	491	34	its	its	PRON
ejpam-6266	491	35	derivatives	derivative	NOUN
ejpam-6266	491	36	together	together	ADV
ejpam-6266	491	37	since	since	SCONJ
ejpam-6266	491	38	γ	γ	X
ejpam-6266	491	39	>	>	X
ejpam-6266	491	40	0	0	NUM
ejpam-6266	491	41	.	.	PUNCT
ejpam-6266	492	1	indeed	indeed	ADV
ejpam-6266	492	2	,	,	PUNCT
ejpam-6266	492	3	it	it	PRON
ejpam-6266	492	4	appears	appear	VERB
ejpam-6266	492	5	a	a	DET
ejpam-6266	492	6	loss	loss	NOUN
ejpam-6266	492	7	of	of	ADP
ejpam-6266	492	8	decay	decay	NOUN
ejpam-6266	492	9	in	in	ADP
ejpam-6266	492	10	the	the	DET
ejpam-6266	492	11	rate	rate	NOUN
ejpam-6266	492	12	of	of	ADP
ejpam-6266	492	13	the	the	DET
ejpam-6266	492	14	estimate	estimate	NOUN
ejpam-6266	492	15	of	of	ADP
ejpam-6266	492	16	these	these	DET
ejpam-6266	492	17	norms	norm	NOUN
ejpam-6266	492	18	.	.	PUNCT
ejpam-6266	493	1	in	in	ADP
ejpam-6266	493	2	the	the	DET
ejpam-6266	493	3	other	other	ADJ
ejpam-6266	493	4	hand	hand	NOUN
ejpam-6266	493	5	,	,	PUNCT
ejpam-6266	493	6	let	let	VERB
ejpam-6266	493	7	us	we	PRON
ejpam-6266	493	8	consider	consider	VERB
ejpam-6266	493	9	the	the	DET
ejpam-6266	493	10	following	follow	VERB
ejpam-6266	493	11	cauchy	cauchy	ADJ
ejpam-6266	493	12	problem	problem	NOUN
ejpam-6266	493	13	of	of	ADP
ejpam-6266	493	14	semi	semi	ADJ
ejpam-6266	493	15	-	-	ADJ
ejpam-6266	493	16	linear	linear	ADJ
ejpam-6266	493	17	dissipative	dissipative	ADJ
ejpam-6266	493	18	wave	wave	NOUN
ejpam-6266	493	19	equation:	equation:	PROPN
ejpam-6266	493	20	utt	utt	PROPN
ejpam-6266	494	1	−∆u+	−∆u+	NOUN
ejpam-6266	494	2	ut	ut	PROPN
ejpam-6266	494	3	=	=	SYM
ejpam-6266	494	4	|ut|p	|ut|p	PROPN
ejpam-6266	494	5	t	t	PROPN
ejpam-6266	494	6	>	>	X
ejpam-6266	494	7	0	0	PROPN
ejpam-6266	494	8	,	,	PUNCT
ejpam-6266	494	9	x	x	PROPN
ejpam-6266	494	10	∈	∈	PROPN
ejpam-6266	494	11	rn	rn	PROPN
ejpam-6266	494	12	,	,	PUNCT
ejpam-6266	494	13	u(0	u(0	PROPN
ejpam-6266	494	14	,	,	PUNCT
ejpam-6266	494	15	x	x	NOUN
ejpam-6266	494	16	)	)	PUNCT
ejpam-6266	494	17	=	=	SYM
ejpam-6266	494	18	u0(x	u0(x	NUM
ejpam-6266	494	19	)	)	PUNCT
ejpam-6266	494	20	,	,	PUNCT
ejpam-6266	494	21	x	x	PROPN
ejpam-6266	494	22	∈	∈	PROPN
ejpam-6266	494	23	rn	rn	PROPN
ejpam-6266	494	24	,	,	PUNCT
ejpam-6266	494	25	ut(0	ut(0	PROPN
ejpam-6266	494	26	,	,	PUNCT
ejpam-6266	494	27	x	x	NOUN
ejpam-6266	494	28	)	)	PUNCT
ejpam-6266	494	29	=	=	SYM
ejpam-6266	494	30	u1(x	u1(x	NOUN
ejpam-6266	494	31	)	)	PUNCT
ejpam-6266	494	32	,	,	PUNCT
ejpam-6266	494	33	x	x	PROPN
ejpam-6266	494	34	∈	∈	PROPN
ejpam-6266	494	35	rn	rn	PROPN
ejpam-6266	494	36	,	,	PUNCT
ejpam-6266	494	37	(	(	PUNCT
ejpam-6266	494	38	103	103	NUM
ejpam-6266	494	39	)	)	PUNCT
ejpam-6266	494	40	due	due	ADP
ejpam-6266	494	41	to	to	ADP
ejpam-6266	494	42	(	(	PUNCT
ejpam-6266	494	43	7	7	NUM
ejpam-6266	494	44	)	)	PUNCT
ejpam-6266	495	1	,	,	PUNCT
ejpam-6266	495	2	it	it	PRON
ejpam-6266	495	3	appears	appear	VERB
ejpam-6266	495	4	that	that	SCONJ
ejpam-6266	495	5	cauchy	cauchy	PROPN
ejpam-6266	495	6	problem	problem	NOUN
ejpam-6266	495	7	(	(	PUNCT
ejpam-6266	495	8	103	103	NUM
ejpam-6266	495	9	)	)	PUNCT
ejpam-6266	495	10	has	have	VERB
ejpam-6266	495	11	no	no	DET
ejpam-6266	495	12	critical	critical	ADJ
ejpam-6266	495	13	exponent	exponent	NOUN
ejpam-6266	495	14	in	in	ADP
ejpam-6266	495	15	fujita	fujita	PROPN
ejpam-6266	495	16	sense	sense	NOUN
ejpam-6266	495	17	since	since	SCONJ
ejpam-6266	495	18	lim	lim	PROPN
ejpam-6266	495	19	γ→1	γ→1	PROPN
ejpam-6266	495	20	1	1	NUM
ejpam-6266	495	21	γ	γ	X
ejpam-6266	495	22	=	=	SYM
ejpam-6266	495	23	1	1	NUM
ejpam-6266	495	24	.	.	X
ejpam-6266	495	25	one	one	PRON
ejpam-6266	495	26	can	can	AUX
ejpam-6266	495	27	interpret	interpret	VERB
ejpam-6266	495	28	this	this	DET
ejpam-6266	495	29	result	result	NOUN
ejpam-6266	495	30	by	by	ADP
ejpam-6266	495	31	concluding	conclude	VERB
ejpam-6266	495	32	that	that	SCONJ
ejpam-6266	495	33	the	the	DET
ejpam-6266	495	34	solutions	solution	NOUN
ejpam-6266	495	35	of	of	ADP
ejpam-6266	495	36	cauchy	cauchy	PROPN
ejpam-6266	495	37	problem	problem	NOUN
ejpam-6266	495	38	(	(	PUNCT
ejpam-6266	495	39	103	103	NUM
ejpam-6266	495	40	)	)	PUNCT
ejpam-6266	495	41	,	,	PUNCT
ejpam-6266	495	42	if	if	SCONJ
ejpam-6266	495	43	they	they	PRON
ejpam-6266	495	44	exist	exist	VERB
ejpam-6266	495	45	,	,	PUNCT
ejpam-6266	495	46	then	then	ADV
ejpam-6266	495	47	they	they	PRON
ejpam-6266	495	48	are	be	AUX
ejpam-6266	495	49	global	global	ADJ
ejpam-6266	495	50	in	in	ADP
ejpam-6266	495	51	time	time	NOUN
ejpam-6266	495	52	.	.	PUNCT
ejpam-6266	496	1	consequently	consequently	ADV
ejpam-6266	496	2	,	,	PUNCT
ejpam-6266	496	3	any	any	DET
ejpam-6266	496	4	solution	solution	NOUN
ejpam-6266	496	5	of	of	ADP
ejpam-6266	496	6	cauchy	cauchy	ADJ
ejpam-6266	496	7	problem	problem	NOUN
ejpam-6266	496	8	(	(	PUNCT
ejpam-6266	496	9	103	103	NUM
ejpam-6266	496	10	)	)	PUNCT
ejpam-6266	496	11	blows	blow	NOUN
ejpam-6266	496	12	-	-	PUNCT
ejpam-6266	496	13	up	up	NOUN
ejpam-6266	496	14	in	in	ADP
ejpam-6266	496	15	finite	finite	ADJ
ejpam-6266	496	16	time	time	NOUN
ejpam-6266	496	17	.	.	PUNCT
ejpam-6266	497	1	references	reference	NOUN
ejpam-6266	497	2	[	[	X
ejpam-6266	497	3	1	1	X
ejpam-6266	497	4	]	]	PUNCT
ejpam-6266	497	5	e.	e.	PROPN
ejpam-6266	497	6	a.	a.	PROPN
ejpam-6266	497	7	az	az	PROPN
ejpam-6266	497	8	-	-	PROPN
ejpam-6266	497	9	zo’bi	zo’bi	PROPN
ejpam-6266	497	10	.	.	PUNCT
ejpam-6266	498	1	new	new	ADJ
ejpam-6266	498	2	kink	kink	NOUN
ejpam-6266	498	3	solutions	solution	NOUN
ejpam-6266	498	4	for	for	ADP
ejpam-6266	498	5	the	the	DET
ejpam-6266	498	6	van	van	PROPN
ejpam-6266	498	7	der	der	NOUN
ejpam-6266	498	8	waals	waal	NOUN
ejpam-6266	498	9	p	p	NOUN
ejpam-6266	498	10	-	-	PUNCT
ejpam-6266	498	11	system	system	NOUN
ejpam-6266	498	12	.	.	PUNCT
ejpam-6266	499	1	math	math	NOUN
ejpam-6266	499	2	.	.	PUNCT
ejpam-6266	500	1	meth	meth	NOUN
ejpam-6266	500	2	.	.	PUNCT
ejpam-6266	501	1	app	app	PROPN
ejpam-6266	501	2	.	.	PUNCT
ejpam-6266	502	1	sci	sci	PROPN
ejpam-6266	502	2	,	,	PUNCT
ejpam-6266	502	3	42(18):6216–6226	42(18):6216–6226	PROPN
ejpam-6266	502	4	,	,	PUNCT
ejpam-6266	502	5	2019	2019	NUM
ejpam-6266	502	6	.	.	PUNCT
ejpam-6266	503	1	[	[	X
ejpam-6266	503	2	2	2	X
ejpam-6266	503	3	]	]	PUNCT
ejpam-6266	503	4	e.	e.	PROPN
ejpam-6266	503	5	a.	a.	PROPN
ejpam-6266	503	6	az	az	PROPN
ejpam-6266	503	7	-	-	PROPN
ejpam-6266	503	8	zo’bi	zo’bi	PROPN
ejpam-6266	503	9	.	.	PUNCT
ejpam-6266	504	1	numeric	numeric	ADJ
ejpam-6266	504	2	-	-	PUNCT
ejpam-6266	504	3	analytic	analytic	ADJ
ejpam-6266	504	4	solutions	solution	NOUN
ejpam-6266	504	5	of	of	ADP
ejpam-6266	504	6	mixed	mixed	ADJ
ejpam-6266	504	7	-	-	PUNCT
ejpam-6266	504	8	type	type	NOUN
ejpam-6266	504	9	systems	system	NOUN
ejpam-6266	504	10	of	of	ADP
ejpam-6266	504	11	balance	balance	NOUN
ejpam-6266	504	12	laws	law	NOUN
ejpam-6266	504	13	.	.	PUNCT
ejpam-6266	505	1	appl	appl	PROPN
ejpam-6266	505	2	.	.	PROPN
ejpam-6266	505	3	math	math	PROPN
ejpam-6266	505	4	.	.	PUNCT
ejpam-6266	506	1	comp	comp	PROPN
ejpam-6266	506	2	.	.	PUNCT
ejpam-6266	506	3	,	,	PUNCT
ejpam-6266	506	4	255:133–143	255:133–143	PROPN
ejpam-6266	506	5	,	,	PUNCT
ejpam-6266	506	6	2015	2015	NUM
ejpam-6266	506	7	.	.	PUNCT
ejpam-6266	507	1	[	[	X
ejpam-6266	507	2	3	3	X
ejpam-6266	507	3	]	]	X
ejpam-6266	507	4	e.	e.	PROPN
ejpam-6266	507	5	a.	a.	PROPN
ejpam-6266	507	6	az	az	PROPN
ejpam-6266	507	7	-	-	PROPN
ejpam-6266	507	8	zo’bi	zo’bi	PROPN
ejpam-6266	507	9	.	.	PUNCT
ejpam-6266	508	1	on	on	ADP
ejpam-6266	508	2	the	the	DET
ejpam-6266	508	3	reduced	reduce	VERB
ejpam-6266	508	4	differential	differential	NOUN
ejpam-6266	508	5	transform	transform	NOUN
ejpam-6266	508	6	method	method	NOUN
ejpam-6266	508	7	and	and	CCONJ
ejpam-6266	508	8	its	its	PRON
ejpam-6266	508	9	application	application	NOUN
ejpam-6266	508	10	to	to	ADP
ejpam-6266	508	11	the	the	DET
ejpam-6266	508	12	generalized	generalize	VERB
ejpam-6266	508	13	burgers	burger	NOUN
ejpam-6266	508	14	-	-	PUNCT
ejpam-6266	508	15	huxley	huxley	PROPN
ejpam-6266	508	16	equation	equation	NOUN
ejpam-6266	508	17	.	.	PUNCT
ejpam-6266	509	1	app	app	PROPN
ejpam-6266	509	2	.	.	PROPN
ejpam-6266	509	3	math	math	PROPN
ejpam-6266	509	4	.	.	PUNCT
ejpam-6266	510	1	sci	sci	PROPN
ejpam-6266	510	2	.	.	PROPN
ejpam-6266	510	3	,	,	PUNCT
ejpam-6266	510	4	8(177):8823–8831	8(177):8823–8831	NUM
ejpam-6266	510	5	,	,	PUNCT
ejpam-6266	510	6	2014	2014	NUM
ejpam-6266	510	7	.	.	PUNCT
ejpam-6266	511	1	[	[	X
ejpam-6266	511	2	4	4	X
ejpam-6266	511	3	]	]	PUNCT
ejpam-6266	511	4	e.	e.	PROPN
ejpam-6266	511	5	a.	a.	PROPN
ejpam-6266	511	6	az	az	PROPN
ejpam-6266	511	7	-	-	PROPN
ejpam-6266	511	8	zo’bi	zo’bi	PROPN
ejpam-6266	511	9	,	,	PUNCT
ejpam-6266	511	10	a.	a.	PROPN
ejpam-6266	511	11	yildirim	yildirim	PROPN
ejpam-6266	511	12	,	,	PUNCT
ejpam-6266	511	13	and	and	CCONJ
ejpam-6266	511	14	l.	l.	PROPN
ejpam-6266	511	15	akinyemi	akinyemi	PROPN
ejpam-6266	511	16	.	.	PUNCT
ejpam-6266	512	1	semi	semi	ADJ
ejpam-6266	512	2	-	-	ADJ
ejpam-6266	512	3	analytic	analytic	ADJ
ejpam-6266	512	4	treatment	treatment	NOUN
ejpam-6266	512	5	of	of	ADP
ejpam-6266	512	6	mixed	mixed	ADJ
ejpam-6266	512	7	hyperbolic	hyperbolic	ADJ
ejpam-6266	512	8	–	–	PUNCT
ejpam-6266	512	9	elliptic	elliptic	ADJ
ejpam-6266	512	10	cauchy	cauchy	NOUN
ejpam-6266	512	11	problem	problem	NOUN
ejpam-6266	512	12	modeling	model	VERB
ejpam-6266	512	13	three	three	NUM
ejpam-6266	512	14	-	-	PUNCT
ejpam-6266	512	15	phase	phase	NOUN
ejpam-6266	512	16	flow	flow	NOUN
ejpam-6266	512	17	in	in	ADP
ejpam-6266	512	18	porous	porous	ADJ
ejpam-6266	512	19	media	medium	NOUN
ejpam-6266	512	20	.	.	PUNCT
ejpam-6266	513	1	int	int	NOUN
ejpam-6266	513	2	.	.	PUNCT
ejpam-6266	514	1	journ	journ	PROPN
ejpam-6266	514	2	.	.	PUNCT
ejpam-6266	515	1	modern	modern	ADJ
ejpam-6266	515	2	phys	phy	NOUN
ejpam-6266	515	3	.	.	PUNCT
ejpam-6266	515	4	,	,	PUNCT
ejpam-6266	515	5	35(29	35(29	NUM
ejpam-6266	515	6	)	)	PUNCT
ejpam-6266	515	7	,	,	PUNCT
ejpam-6266	515	8	2021	2021	NUM
ejpam-6266	515	9	.	.	PUNCT
ejpam-6266	516	1	[	[	X
ejpam-6266	516	2	5	5	X
ejpam-6266	516	3	]	]	PUNCT
ejpam-6266	516	4	e.	e.	PROPN
ejpam-6266	516	5	a.	a.	PROPN
ejpam-6266	516	6	az	az	PROPN
ejpam-6266	516	7	-	-	PUNCT
ejpam-6266	516	8	zo’bi	zo’bi	PROPN
ejpam-6266	516	9	.	.	PUNCT
ejpam-6266	517	1	construction	construction	NOUN
ejpam-6266	517	2	of	of	ADP
ejpam-6266	517	3	solutions	solution	NOUN
ejpam-6266	517	4	for	for	ADP
ejpam-6266	517	5	mixed	mixed	ADJ
ejpam-6266	517	6	hyperbolic	hyperbolic	ADJ
ejpam-6266	517	7	elliptic	elliptic	ADJ
ejpam-6266	517	8	riemann	riemann	PROPN
ejpam-6266	517	9	initial	initial	ADJ
ejpam-6266	517	10	value	value	NOUN
ejpam-6266	517	11	system	system	NOUN
ejpam-6266	517	12	of	of	ADP
ejpam-6266	517	13	conservation	conservation	NOUN
ejpam-6266	517	14	laws	law	NOUN
ejpam-6266	517	15	.	.	PUNCT
ejpam-6266	518	1	37(8):6018–6024	37(8):6018–6024	NUM
ejpam-6266	518	2	,	,	PUNCT
ejpam-6266	518	3	2013	2013	NUM
ejpam-6266	518	4	.	.	PUNCT
ejpam-6266	519	1	[	[	X
ejpam-6266	519	2	6	6	NUM
ejpam-6266	519	3	]	]	PUNCT
ejpam-6266	519	4	a.	a.	NOUN
ejpam-6266	519	5	fino	fino	PROPN
ejpam-6266	519	6	.	.	PUNCT
ejpam-6266	520	1	critical	critical	ADJ
ejpam-6266	520	2	exponent	exponent	NOUN
ejpam-6266	520	3	for	for	ADP
ejpam-6266	520	4	damped	damped	ADJ
ejpam-6266	520	5	wave	wave	NOUN
ejpam-6266	520	6	equations	equation	NOUN
ejpam-6266	520	7	with	with	ADP
ejpam-6266	520	8	nonlinear	nonlinear	ADJ
ejpam-6266	520	9	memory	memory	NOUN
ejpam-6266	520	10	.	.	PUNCT
ejpam-6266	521	1	hal	hal	PROPN
ejpam-6266	521	2	arch	arch	PROPN
ejpam-6266	521	3	.	.	PUNCT
ejpam-6266	522	1	ouv	ouv	PROPN
ejpam-6266	522	2	.	.	PROPN
ejpam-6266	522	3	,	,	PUNCT
ejpam-6266	522	4	2010	2010	NUM
ejpam-6266	522	5	.	.	PUNCT
ejpam-6266	523	1	i	i	PRON
ejpam-6266	523	2	d	d	NOUN
ejpam-6266	523	3	:	:	PUNCT
ejpam-6266	523	4	00473941v2	00473941v2	NOUN
ejpam-6266	523	5	.	.	PUNCT
ejpam-6266	524	1	[	[	X
ejpam-6266	524	2	7	7	NUM
ejpam-6266	524	3	]	]	X
ejpam-6266	524	4	m.	m.	NOUN
ejpam-6266	524	5	d’abbicco	d’abbicco	NOUN
ejpam-6266	524	6	.	.	PUNCT
ejpam-6266	525	1	the	the	DET
ejpam-6266	525	2	influence	influence	NOUN
ejpam-6266	525	3	of	of	ADP
ejpam-6266	525	4	a	a	DET
ejpam-6266	525	5	nonlinear	nonlinear	ADJ
ejpam-6266	525	6	memory	memory	NOUN
ejpam-6266	525	7	on	on	ADP
ejpam-6266	525	8	the	the	DET
ejpam-6266	525	9	damped	damped	NOUN
ejpam-6266	525	10	wave	wave	NOUN
ejpam-6266	525	11	equation	equation	NOUN
ejpam-6266	525	12	.	.	PUNCT
ejpam-6266	526	1	nonlinear	nonlinear	ADJ
ejpam-6266	526	2	anal	anal	PROPN
ejpam-6266	526	3	.	.	PUNCT
ejpam-6266	526	4	,	,	PUNCT
ejpam-6266	526	5	95:130–145	95:130–145	PROPN
ejpam-6266	526	6	,	,	PUNCT
ejpam-6266	526	7	2014	2014	NUM
ejpam-6266	526	8	.	.	PUNCT
ejpam-6266	527	1	[	[	X
ejpam-6266	527	2	8	8	X
ejpam-6266	527	3	]	]	PUNCT
ejpam-6266	527	4	t.	t.	PROPN
ejpam-6266	527	5	cazenave	cazenave	PROPN
ejpam-6266	527	6	,	,	PUNCT
ejpam-6266	527	7	f.	f.	PROPN
ejpam-6266	527	8	dickstein	dickstein	PROPN
ejpam-6266	527	9	,	,	PUNCT
ejpam-6266	527	10	and	and	CCONJ
ejpam-6266	527	11	f.	f.	PROPN
ejpam-6266	527	12	d.	d.	PROPN
ejpam-6266	527	13	weissler	weissler	PROPN
ejpam-6266	527	14	.	.	PUNCT
ejpam-6266	528	1	an	an	DET
ejpam-6266	528	2	equation	equation	NOUN
ejpam-6266	528	3	whose	whose	DET
ejpam-6266	528	4	fujita	fujita	PROPN
ejpam-6266	528	5	critical	critical	ADJ
ejpam-6266	528	6	exponent	exponent	NOUN
ejpam-6266	528	7	is	be	AUX
ejpam-6266	528	8	not	not	PART
ejpam-6266	528	9	given	give	VERB
ejpam-6266	528	10	by	by	ADP
ejpam-6266	528	11	scaling	scale	VERB
ejpam-6266	528	12	.	.	PUNCT
ejpam-6266	529	1	nonlinear	nonlinear	ADJ
ejpam-6266	529	2	anal	anal	PROPN
ejpam-6266	529	3	.	.	PUNCT
ejpam-6266	529	4	,	,	PUNCT
ejpam-6266	529	5	68:862–874	68:862–874	PROPN
ejpam-6266	529	6	,	,	PUNCT
ejpam-6266	529	7	2008	2008	NUM
ejpam-6266	529	8	.	.	PUNCT
ejpam-6266	530	1	[	[	X
ejpam-6266	530	2	9	9	NUM
ejpam-6266	530	3	]	]	PUNCT
ejpam-6266	530	4	a.	a.	NOUN
ejpam-6266	530	5	matsumura	matsumura	NOUN
ejpam-6266	530	6	.	.	PUNCT
ejpam-6266	531	1	on	on	ADP
ejpam-6266	531	2	the	the	DET
ejpam-6266	531	3	asymptotic	asymptotic	ADJ
ejpam-6266	531	4	behavior	behavior	NOUN
ejpam-6266	531	5	of	of	ADP
ejpam-6266	531	6	solutions	solution	NOUN
ejpam-6266	531	7	of	of	ADP
ejpam-6266	531	8	semi	semi	ADJ
ejpam-6266	531	9	-	-	ADJ
ejpam-6266	531	10	linear	linear	ADJ
ejpam-6266	531	11	wave	wave	NOUN
ejpam-6266	531	12	equations	equation	NOUN
ejpam-6266	531	13	.	.	PUNCT
ejpam-6266	532	1	publ	publ	NOUN
ejpam-6266	532	2	.	.	PUNCT
ejpam-6266	533	1	res	re	NOUN
ejpam-6266	533	2	.	.	PROPN
ejpam-6266	533	3	inst	inst	PROPN
ejpam-6266	533	4	.	.	PUNCT
ejpam-6266	534	1	math	math	NOUN
ejpam-6266	534	2	.	.	PUNCT
ejpam-6266	535	1	sci	sci	PROPN
ejpam-6266	535	2	.	.	PROPN
ejpam-6266	535	3	,	,	PUNCT
ejpam-6266	535	4	12(1):169–189	12(1):169–189	NUM
ejpam-6266	535	5	,	,	PUNCT
ejpam-6266	535	6	1976	1976	NUM
ejpam-6266	535	7	.	.	PUNCT
ejpam-6266	536	1	[	[	X
ejpam-6266	536	2	10	10	NUM
ejpam-6266	536	3	]	]	X
ejpam-6266	536	4	r.	r.	PROPN
ejpam-6266	536	5	ikehata	ikehata	PROPN
ejpam-6266	536	6	and	and	CCONJ
ejpam-6266	536	7	k.	k.	PROPN
ejpam-6266	536	8	tanizawa	tanizawa	PROPN
ejpam-6266	536	9	.	.	PUNCT
ejpam-6266	537	1	global	global	ADJ
ejpam-6266	537	2	existence	existence	NOUN
ejpam-6266	537	3	of	of	ADP
ejpam-6266	537	4	solutions	solution	NOUN
ejpam-6266	537	5	for	for	ADP
ejpam-6266	537	6	semilinear	semilinear	NOUN
ejpam-6266	537	7	damped	damped	NOUN
ejpam-6266	537	8	wave	wave	NOUN
ejpam-6266	537	9	equations	equation	NOUN
ejpam-6266	537	10	in	in	ADP
ejpam-6266	537	11	rn	rn	PROPN
ejpam-6266	537	12	with	with	ADP
ejpam-6266	537	13	noncompactly	noncompactly	ADV
ejpam-6266	537	14	supported	support	VERB
ejpam-6266	537	15	initial	initial	ADJ
ejpam-6266	537	16	data	datum	NOUN
ejpam-6266	537	17	.	.	PUNCT
ejpam-6266	538	1	nonlinear	nonlinear	ADJ
ejpam-6266	538	2	analysis	analysis	NOUN
ejpam-6266	538	3	:	:	PUNCT
ejpam-6266	538	4	theory	theory	NOUN
ejpam-6266	538	5	,	,	PUNCT
ejpam-6266	538	6	methods	method	NOUN
ejpam-6266	538	7	&	&	CCONJ
ejpam-6266	538	8	applications	application	NOUN
ejpam-6266	538	9	,	,	PUNCT
ejpam-6266	538	10	61(7):1189–1208	61(7):1189–1208	NUM
ejpam-6266	538	11	,	,	PUNCT
ejpam-6266	538	12	2005	2005	NUM
ejpam-6266	538	13	.	.	PUNCT
ejpam-6266	539	1	t.	t.	PROPN
ejpam-6266	539	2	hadj	hadj	PROPN
ejpam-6266	539	3	kaddour	kaddour	PROPN
ejpam-6266	539	4	et	et	PROPN
ejpam-6266	539	5	al	al	PROPN
ejpam-6266	539	6	.	.	PUNCT
ejpam-6266	539	7	/	/	SYM
ejpam-6266	539	8	eur	eur	PROPN
ejpam-6266	539	9	.	.	PUNCT
ejpam-6266	540	1	j.	j.	PROPN
ejpam-6266	540	2	pure	pure	PROPN
ejpam-6266	540	3	appl	appl	PROPN
ejpam-6266	540	4	.	.	PROPN
ejpam-6266	540	5	math	math	PROPN
ejpam-6266	540	6	,	,	PUNCT
ejpam-6266	540	7	18	18	NUM
ejpam-6266	540	8	(	(	PUNCT
ejpam-6266	540	9	4	4	NUM
ejpam-6266	540	10	)	)	PUNCT
ejpam-6266	540	11	(	(	PUNCT
ejpam-6266	540	12	2025	2025	NUM
ejpam-6266	540	13	)	)	PUNCT
ejpam-6266	540	14	,	,	PUNCT
ejpam-6266	540	15	6266	6266	NUM
ejpam-6266	540	16	21	21	NUM
ejpam-6266	540	17	of	of	ADP
ejpam-6266	540	18	24	24	NUM
ejpam-6266	540	19	[	[	X
ejpam-6266	540	20	11	11	NUM
ejpam-6266	540	21	]	]	PUNCT
ejpam-6266	540	22	t.	t.	PROPN
ejpam-6266	540	23	hadj	hadj	PROPN
ejpam-6266	540	24	kaddour	kaddour	PROPN
ejpam-6266	540	25	and	and	CCONJ
ejpam-6266	540	26	m.	m.	NOUN
ejpam-6266	540	27	reissig	reissig	NOUN
ejpam-6266	540	28	.	.	PUNCT
ejpam-6266	541	1	global	global	ADJ
ejpam-6266	541	2	well	well	ADJ
ejpam-6266	541	3	posedness	posedness	NOUN
ejpam-6266	541	4	of	of	ADP
ejpam-6266	541	5	effectively	effectively	ADV
ejpam-6266	541	6	damped	damp	VERB
ejpam-6266	541	7	wave	wave	NOUN
ejpam-6266	541	8	models	model	NOUN
ejpam-6266	541	9	with	with	ADP
ejpam-6266	541	10	nonlinear	nonlinear	ADJ
ejpam-6266	541	11	memory	memory	NOUN
ejpam-6266	541	12	.	.	PUNCT
ejpam-6266	542	1	com	com	PROPN
ejpam-6266	542	2	.	.	PUNCT
ejpam-6266	542	3	pur	pur	PROPN
ejpam-6266	542	4	&	&	CCONJ
ejpam-6266	542	5	app	app	PROPN
ejpam-6266	542	6	.	.	PROPN
ejpam-6266	543	1	anal	anal	PROPN
ejpam-6266	543	2	.	.	PROPN
ejpam-6266	543	3	,	,	PUNCT
ejpam-6266	544	1	20(5):2039–2064	20(5):2039–2064	NOUN
ejpam-6266	544	2	,	,	PUNCT
ejpam-6266	544	3	2021	2021	NUM
ejpam-6266	544	4	.	.	PUNCT
ejpam-6266	545	1	[	[	X
ejpam-6266	545	2	12	12	NUM
ejpam-6266	545	3	]	]	X
ejpam-6266	545	4	s.	s.	PROPN
ejpam-6266	545	5	cui	cui	PROPN
ejpam-6266	545	6	.	.	PUNCT
ejpam-6266	546	1	local	local	ADJ
ejpam-6266	546	2	and	and	CCONJ
ejpam-6266	546	3	global	global	ADJ
ejpam-6266	546	4	existence	existence	NOUN
ejpam-6266	546	5	of	of	ADP
ejpam-6266	546	6	solutions	solution	NOUN
ejpam-6266	546	7	to	to	ADP
ejpam-6266	546	8	semilinear	semilinear	PROPN
ejpam-6266	546	9	parabolic	parabolic	PROPN
ejpam-6266	546	10	initial	initial	ADJ
ejpam-6266	546	11	value	value	NOUN
ejpam-6266	546	12	problems	problem	NOUN
ejpam-6266	546	13	.	.	PUNCT
ejpam-6266	547	1	nonlinear	nonlinear	ADJ
ejpam-6266	547	2	anal	anal	PROPN
ejpam-6266	547	3	.	.	PUNCT
ejpam-6266	547	4	,	,	PUNCT
ejpam-6266	547	5	43(3):293–323	43(3):293–323	PROPN
ejpam-6266	547	6	,	,	PUNCT
ejpam-6266	547	7	2001	2001	NUM
ejpam-6266	547	8	.	.	PUNCT
ejpam-6266	548	1	[	[	X
ejpam-6266	548	2	13	13	NUM
ejpam-6266	548	3	]	]	PUNCT
ejpam-6266	548	4	m.	m.	NOUN
ejpam-6266	548	5	d’abbicco	d’abbicco	PROPN
ejpam-6266	548	6	,	,	PUNCT
ejpam-6266	548	7	s.	s.	PROPN
ejpam-6266	548	8	lucente	lucente	NOUN
ejpam-6266	548	9	,	,	PUNCT
ejpam-6266	548	10	and	and	CCONJ
ejpam-6266	548	11	m.	m.	NOUN
ejpam-6266	548	12	reissig	reissig	PROPN
ejpam-6266	548	13	.	.	PUNCT
ejpam-6266	549	1	semilinear	semilinear	PROPN
ejpam-6266	549	2	wave	wave	PROPN
ejpam-6266	549	3	equations	equation	NOUN
ejpam-6266	549	4	with	with	ADP
ejpam-6266	549	5	effective	effective	ADJ
ejpam-6266	549	6	damping	damping	NOUN
ejpam-6266	549	7	.	.	PUNCT
ejpam-6266	550	1	chin	chin	PROPN
ejpam-6266	550	2	.	.	PUNCT
ejpam-6266	551	1	ann	ann	PROPN
ejpam-6266	551	2	.	.	PUNCT
ejpam-6266	551	3	math	math	PROPN
ejpam-6266	551	4	.	.	PUNCT
ejpam-6266	551	5	,	,	PUNCT
ejpam-6266	551	6	serie	serie	PROPN
ejpam-6266	551	7	b	b	PROPN
ejpam-6266	551	8	,	,	PUNCT
ejpam-6266	551	9	34:345–380	34:345–380	PROPN
ejpam-6266	551	10	,	,	PUNCT
ejpam-6266	551	11	2013	2013	NUM
ejpam-6266	551	12	.	.	PUNCT
ejpam-6266	552	1	[	[	X
ejpam-6266	552	2	14	14	NUM
ejpam-6266	552	3	]	]	PUNCT
ejpam-6266	552	4	m.	m.	PROPN
ejpam-6266	552	5	r.	r.	PROPN
ejpam-6266	552	6	ebert	ebert	PROPN
ejpam-6266	552	7	and	and	CCONJ
ejpam-6266	552	8	m.	m.	NOUN
ejpam-6266	552	9	reissig	reissig	NOUN
ejpam-6266	552	10	.	.	PUNCT
ejpam-6266	553	1	methods	method	NOUN
ejpam-6266	553	2	for	for	ADP
ejpam-6266	553	3	partial	partial	ADJ
ejpam-6266	553	4	differential	differential	ADJ
ejpam-6266	553	5	equations	equation	NOUN
ejpam-6266	553	6	.	.	PUNCT
ejpam-6266	554	1	qualitative	qualitative	ADJ
ejpam-6266	554	2	properties	property	NOUN
ejpam-6266	554	3	of	of	ADP
ejpam-6266	554	4	solutions	solution	NOUN
ejpam-6266	554	5	,	,	PUNCT
ejpam-6266	554	6	phase	phase	NOUN
ejpam-6266	554	7	space	space	NOUN
ejpam-6266	554	8	analysis	analysis	NOUN
ejpam-6266	554	9	,	,	PUNCT
ejpam-6266	554	10	semilinear	semilinear	NOUN
ejpam-6266	554	11	models	model	NOUN
ejpam-6266	554	12	.	.	PUNCT
ejpam-6266	555	1	birkhäuser	birkhäuser	PROPN
ejpam-6266	555	2	,	,	PUNCT
ejpam-6266	555	3	cham	cham	PROPN
ejpam-6266	555	4	,	,	PUNCT
ejpam-6266	555	5	2018	2018	NUM
ejpam-6266	555	6	.	.	PUNCT
ejpam-6266	556	1	[	[	X
ejpam-6266	556	2	15	15	X
ejpam-6266	556	3	]	]	X
ejpam-6266	556	4	t.	t.	NOUN
ejpam-6266	556	5	runst	runst	PROPN
ejpam-6266	556	6	and	and	CCONJ
ejpam-6266	556	7	w.	w.	PROPN
ejpam-6266	556	8	sickel	sickel	PROPN
ejpam-6266	556	9	.	.	PUNCT
ejpam-6266	557	1	sobolev	sobolev	PROPN
ejpam-6266	557	2	spaces	space	NOUN
ejpam-6266	557	3	of	of	ADP
ejpam-6266	557	4	fractional	fractional	ADJ
ejpam-6266	557	5	order	order	NOUN
ejpam-6266	557	6	,	,	PUNCT
ejpam-6266	557	7	nemytskij	nemytskij	NOUN
ejpam-6266	557	8	operators	operator	NOUN
ejpam-6266	557	9	,	,	PUNCT
ejpam-6266	557	10	and	and	CCONJ
ejpam-6266	557	11	nonlinear	nonlinear	ADJ
ejpam-6266	557	12	partial	partial	ADJ
ejpam-6266	557	13	differential	differential	NOUN
ejpam-6266	557	14	equations	equation	NOUN
ejpam-6266	557	15	.	.	PUNCT
ejpam-6266	558	1	de	de	X
ejpam-6266	558	2	gruyter	gruyter	PROPN
ejpam-6266	558	3	series	series	PROPN
ejpam-6266	558	4	in	in	ADP
ejpam-6266	558	5	nonlinear	nonlinear	ADJ
ejpam-6266	558	6	analysis	analysis	NOUN
ejpam-6266	558	7	and	and	CCONJ
ejpam-6266	558	8	applications	application	NOUN
ejpam-6266	558	9	.	.	PUNCT
ejpam-6266	559	1	walter	walter	PROPN
ejpam-6266	559	2	de	de	PROPN
ejpam-6266	559	3	gruyter	gruyter	PROPN
ejpam-6266	559	4	&	&	CCONJ
ejpam-6266	559	5	co.	co.	PROPN
ejpam-6266	559	6	,	,	PUNCT
ejpam-6266	559	7	berlin	berlin	PROPN
ejpam-6266	559	8	,	,	PUNCT
ejpam-6266	559	9	1996	1996	NUM
ejpam-6266	559	10	.	.	PUNCT
ejpam-6266	560	1	appendix	appendix	NOUN
ejpam-6266	560	2	5.1	5.1	NUM
ejpam-6266	560	3	.	.	PUNCT
ejpam-6266	561	1	some	some	DET
ejpam-6266	561	2	auxiliary	auxiliary	ADJ
ejpam-6266	561	3	estimates	estimate	NOUN
ejpam-6266	561	4	for	for	ADP
ejpam-6266	561	5	integrals	integral	NOUN
ejpam-6266	561	6	the	the	DET
ejpam-6266	561	7	following	follow	VERB
ejpam-6266	561	8	lemma	lemma	PROPN
ejpam-6266	561	9	is	be	AUX
ejpam-6266	561	10	the	the	DET
ejpam-6266	561	11	key	key	NOUN
ejpam-6266	561	12	to	to	PART
ejpam-6266	561	13	estimate	estimate	VERB
ejpam-6266	561	14	certain	certain	ADJ
ejpam-6266	561	15	integrals	integral	NOUN
ejpam-6266	561	16	that	that	PRON
ejpam-6266	561	17	appear	appear	VERB
ejpam-6266	561	18	in	in	ADP
ejpam-6266	561	19	the	the	DET
ejpam-6266	561	20	proof	proof	NOUN
ejpam-6266	561	21	of	of	ADP
ejpam-6266	561	22	the	the	DET
ejpam-6266	561	23	global	global	ADJ
ejpam-6266	561	24	existence	existence	NOUN
ejpam-6266	561	25	of	of	ADP
ejpam-6266	561	26	small	small	ADJ
ejpam-6266	561	27	data	datum	NOUN
ejpam-6266	561	28	solutions	solution	NOUN
ejpam-6266	561	29	(	(	PUNCT
ejpam-6266	561	30	section	section	NOUN
ejpam-6266	561	31	4	4	NUM
ejpam-6266	561	32	)	)	PUNCT
ejpam-6266	561	33	,	,	PUNCT
ejpam-6266	561	34	in	in	ADP
ejpam-6266	561	35	particular	particular	ADJ
ejpam-6266	561	36	those	those	PRON
ejpam-6266	561	37	arising	arise	VERB
ejpam-6266	561	38	from	from	ADP
ejpam-6266	561	39	the	the	DET
ejpam-6266	561	40	nonlinear	nonlinear	ADJ
ejpam-6266	561	41	terms	term	NOUN
ejpam-6266	561	42	.	.	PUNCT
ejpam-6266	562	1	lemma	lemma	PROPN
ejpam-6266	562	2	1	1	X
ejpam-6266	562	3	.	.	PUNCT
ejpam-6266	562	4	assume	assume	VERB
ejpam-6266	562	5	that	that	SCONJ
ejpam-6266	562	6	0	0	NUM
ejpam-6266	562	7	<	<	X
ejpam-6266	562	8	γ	γ	X
ejpam-6266	562	9	<	<	X
ejpam-6266	562	10	1	1	NUM
ejpam-6266	562	11	,	,	PUNCT
ejpam-6266	562	12	a	a	DET
ejpam-6266	562	13	≥	≥	NOUN
ejpam-6266	562	14	0	0	NUM
ejpam-6266	562	15	and	and	CCONJ
ejpam-6266	562	16	b	b	X
ejpam-6266	562	17	>	>	X
ejpam-6266	562	18	1	1	X
ejpam-6266	562	19	.	.	PUNCT
ejpam-6266	563	1	then	then	ADV
ejpam-6266	563	2	we	we	PRON
ejpam-6266	563	3	have∫	have∫	VERB
ejpam-6266	563	4	t	t	NOUN
ejpam-6266	563	5	0	0	NUM
ejpam-6266	563	6	(	(	PUNCT
ejpam-6266	563	7	1	1	NUM
ejpam-6266	563	8	+	+	CCONJ
ejpam-6266	563	9	t−	t−	PROPN
ejpam-6266	563	10	s)−a	s)−a	PROPN
ejpam-6266	563	11	∫	∫	PROPN
ejpam-6266	563	12	s	s	PART
ejpam-6266	563	13	0	0	NUM
ejpam-6266	563	14	(	(	PUNCT
ejpam-6266	563	15	s−	s−	PROPN
ejpam-6266	563	16	τ)−γ(1	τ)−γ(1	NOUN
ejpam-6266	564	1	+	+	CCONJ
ejpam-6266	564	2	τ)−b	τ)−b	NUM
ejpam-6266	564	3	dτds	dτd	VERB
ejpam-6266	564	4	≤	≤	NUM
ejpam-6266	564	5	c	c	NOUN
ejpam-6266	564	6			PUNCT
ejpam-6266	564	7	(	(	PUNCT
ejpam-6266	564	8	1	1	NUM
ejpam-6266	564	9	+	+	NUM
ejpam-6266	564	10	t)−γ	t)−γ	PRON
ejpam-6266	564	11	if	if	SCONJ
ejpam-6266	564	12	a	a	DET
ejpam-6266	564	13	>	>	X
ejpam-6266	564	14	1	1	NUM
ejpam-6266	564	15	,	,	PUNCT
ejpam-6266	564	16	(	(	PUNCT
ejpam-6266	564	17	1	1	NUM
ejpam-6266	564	18	+	+	NUM
ejpam-6266	564	19	t)−γ	t)−γ	PRON
ejpam-6266	564	20	log(2	log(2	NOUN
ejpam-6266	564	21	+	+	CCONJ
ejpam-6266	564	22	t	t	X
ejpam-6266	564	23	)	)	PUNCT
ejpam-6266	564	24	if	if	SCONJ
ejpam-6266	564	25	a	a	PRON
ejpam-6266	564	26	=	=	NOUN
ejpam-6266	564	27	1	1	NUM
ejpam-6266	564	28	,	,	PUNCT
ejpam-6266	564	29	(	(	PUNCT
ejpam-6266	564	30	1	1	NUM
ejpam-6266	564	31	+	+	NUM
ejpam-6266	564	32	t)1−a−γ	t)1−a−γ	NOUN
ejpam-6266	564	33	if	if	SCONJ
ejpam-6266	564	34	a	a	DET
ejpam-6266	564	35	<	<	X
ejpam-6266	564	36	1	1	NUM
ejpam-6266	564	37	.	.	PUNCT
ejpam-6266	564	38	proof	proof	NOUN
ejpam-6266	564	39	.	.	PUNCT
ejpam-6266	565	1	thanks	thank	NOUN
ejpam-6266	565	2	to	to	AUX
ejpam-6266	565	3	lemma	lemma	PROPN
ejpam-6266	565	4	4.1	4.1	NUM
ejpam-6266	565	5	from	from	ADP
ejpam-6266	565	6	[	[	X
ejpam-6266	565	7	12	12	NUM
ejpam-6266	565	8	]	]	PUNCT
ejpam-6266	565	9	and	and	CCONJ
ejpam-6266	565	10	the	the	DET
ejpam-6266	565	11	fact	fact	NOUN
ejpam-6266	565	12	that	that	SCONJ
ejpam-6266	565	13	γ	γ	X
ejpam-6266	565	14	<	<	X
ejpam-6266	565	15	1	1	NUM
ejpam-6266	565	16	,	,	PUNCT
ejpam-6266	565	17	the	the	DET
ejpam-6266	565	18	integral	integral	ADJ
ejpam-6266	565	19	with	with	ADP
ejpam-6266	565	20	respect	respect	NOUN
ejpam-6266	565	21	to	to	ADP
ejpam-6266	565	22	τ	τ	PROPN
ejpam-6266	565	23	on	on	ADP
ejpam-6266	565	24	[	[	X
ejpam-6266	565	25	0	0	NUM
ejpam-6266	565	26	,	,	PUNCT
ejpam-6266	565	27	s	s	AUX
ejpam-6266	565	28	]	]	X
ejpam-6266	565	29	is	be	AUX
ejpam-6266	565	30	estimated	estimate	VERB
ejpam-6266	565	31	as	as	ADP
ejpam-6266	565	32	follows:∫	follows:∫	NOUN
ejpam-6266	565	33	s	s	NOUN
ejpam-6266	565	34	0	0	NUM
ejpam-6266	565	35	(	(	PUNCT
ejpam-6266	565	36	s−	s−	PROPN
ejpam-6266	565	37	τ)−γ(1	τ)−γ(1	PRON
ejpam-6266	565	38	+	+	CCONJ
ejpam-6266	566	1	τ)−b	τ)−b	X
ejpam-6266	566	2	dτ	dτ	NOUN
ejpam-6266	566	3	.	.	PUNCT
ejpam-6266	567	1	(	(	PUNCT
ejpam-6266	567	2	1	1	NUM
ejpam-6266	567	3	+	+	CCONJ
ejpam-6266	567	4	s)−γ	s)−γ	ADJ
ejpam-6266	567	5	.	.	PUNCT
ejpam-6266	568	1	finally	finally	ADV
ejpam-6266	568	2	,	,	PUNCT
ejpam-6266	568	3	the	the	DET
ejpam-6266	568	4	statements	statement	NOUN
ejpam-6266	568	5	of	of	ADP
ejpam-6266	568	6	lemma	lemma	PROPN
ejpam-6266	568	7	1	1	NUM
ejpam-6266	568	8	are	be	AUX
ejpam-6266	568	9	concluded	conclude	VERB
ejpam-6266	568	10	after	after	ADP
ejpam-6266	568	11	applying	apply	VERB
ejpam-6266	568	12	lemma	lemma	PROPN
ejpam-6266	568	13	4.1	4.1	NUM
ejpam-6266	568	14	from	from	ADP
ejpam-6266	568	15	[	[	X
ejpam-6266	568	16	12	12	NUM
ejpam-6266	568	17	]	]	PUNCT
ejpam-6266	568	18	again	again	ADV
ejpam-6266	568	19	.	.	PUNCT
ejpam-6266	569	1	5.2	5.2	NUM
ejpam-6266	569	2	.	.	PUNCT
ejpam-6266	570	1	what	what	PRON
ejpam-6266	570	2	about	about	ADP
ejpam-6266	570	3	the	the	DET
ejpam-6266	570	4	condition	condition	NOUN
ejpam-6266	570	5	β	β	VERB
ejpam-6266	570	6	>	>	X
ejpam-6266	570	7	1	1	NUM
ejpam-6266	570	8	in	in	ADP
ejpam-6266	570	9	lemma	lemma	PROPN
ejpam-6266	570	10	1	1	NUM
ejpam-6266	570	11	?	?	PUNCT
ejpam-6266	571	1	the	the	DET
ejpam-6266	571	2	reader	reader	NOUN
ejpam-6266	571	3	may	may	AUX
ejpam-6266	571	4	ask	ask	VERB
ejpam-6266	571	5	for	for	ADP
ejpam-6266	571	6	a	a	DET
ejpam-6266	571	7	corresponding	corresponding	ADJ
ejpam-6266	571	8	result	result	NOUN
ejpam-6266	571	9	in	in	ADP
ejpam-6266	571	10	the	the	DET
ejpam-6266	571	11	case	case	NOUN
ejpam-6266	571	12	b	b	X
ejpam-6266	571	13	∈	∈	PROPN
ejpam-6266	571	14	(	(	PUNCT
ejpam-6266	571	15	0	0	NUM
ejpam-6266	571	16	,	,	PUNCT
ejpam-6266	571	17	1	1	NUM
ejpam-6266	571	18	]	]	PUNCT
ejpam-6266	571	19	and	and	CCONJ
ejpam-6266	571	20	how	how	SCONJ
ejpam-6266	571	21	about	about	ADP
ejpam-6266	571	22	the	the	DET
ejpam-6266	571	23	condition	condition	NOUN
ejpam-6266	571	24	β	β	X
ejpam-6266	571	25	>	>	X
ejpam-6266	571	26	1	1	X
ejpam-6266	571	27	.	.	PUNCT
ejpam-6266	572	1	we	we	PRON
ejpam-6266	572	2	confirm	confirm	VERB
ejpam-6266	572	3	that	that	SCONJ
ejpam-6266	572	4	the	the	DET
ejpam-6266	572	5	condition	condition	NOUN
ejpam-6266	572	6	β	β	VERB
ejpam-6266	572	7	>	>	X
ejpam-6266	572	8	1	1	NUM
ejpam-6266	572	9	allows	allow	VERB
ejpam-6266	572	10	to	to	PART
ejpam-6266	572	11	get	get	VERB
ejpam-6266	572	12	optimal	optimal	ADJ
ejpam-6266	572	13	estimate	estimate	NOUN
ejpam-6266	572	14	for	for	ADP
ejpam-6266	572	15	the	the	DET
ejpam-6266	572	16	integral	integral	NOUN
ejpam-6266	572	17	.	.	PUNCT
ejpam-6266	573	1	the	the	DET
ejpam-6266	573	2	curious	curious	ADJ
ejpam-6266	573	3	peoples	people	NOUN
ejpam-6266	573	4	are	be	AUX
ejpam-6266	573	5	advised	advise	VERB
ejpam-6266	573	6	to	to	PART
ejpam-6266	573	7	check	check	VERB
ejpam-6266	573	8	the	the	DET
ejpam-6266	573	9	discussion	discussion	NOUN
ejpam-6266	573	10	of	of	ADP
ejpam-6266	573	11	this	this	DET
ejpam-6266	573	12	point	point	NOUN
ejpam-6266	573	13	in	in	ADP
ejpam-6266	573	14	[	[	X
ejpam-6266	573	15	11	11	NUM
ejpam-6266	573	16	]	]	PUNCT
ejpam-6266	573	17	.	.	PUNCT
ejpam-6266	574	1	t.	t.	PROPN
ejpam-6266	574	2	hadj	hadj	PROPN
ejpam-6266	574	3	kaddour	kaddour	PROPN
ejpam-6266	574	4	et	et	PROPN
ejpam-6266	574	5	al	al	PROPN
ejpam-6266	574	6	.	.	PUNCT
ejpam-6266	574	7	/	/	SYM
ejpam-6266	574	8	eur	eur	PROPN
ejpam-6266	574	9	.	.	PUNCT
ejpam-6266	575	1	j.	j.	PROPN
ejpam-6266	575	2	pure	pure	PROPN
ejpam-6266	575	3	appl	appl	PROPN
ejpam-6266	575	4	.	.	PROPN
ejpam-6266	575	5	math	math	PROPN
ejpam-6266	575	6	,	,	PUNCT
ejpam-6266	575	7	18	18	NUM
ejpam-6266	575	8	(	(	PUNCT
ejpam-6266	575	9	4	4	NUM
ejpam-6266	575	10	)	)	PUNCT
ejpam-6266	575	11	(	(	PUNCT
ejpam-6266	575	12	2025	2025	NUM
ejpam-6266	575	13	)	)	PUNCT
ejpam-6266	575	14	,	,	PUNCT
ejpam-6266	575	15	6266	6266	NUM
ejpam-6266	575	16	22	22	NUM
ejpam-6266	575	17	of	of	ADP
ejpam-6266	575	18	24	24	NUM
ejpam-6266	575	19	5.3	5.3	NUM
ejpam-6266	575	20	.	.	PUNCT
ejpam-6266	576	1	decay	decay	NOUN
ejpam-6266	576	2	estimates	estimate	NOUN
ejpam-6266	576	3	for	for	ADP
ejpam-6266	576	4	solutions	solution	NOUN
ejpam-6266	576	5	to	to	ADP
ejpam-6266	576	6	auxiliary	auxiliary	ADJ
ejpam-6266	576	7	cauchy	cauchy	PROPN
ejpam-6266	576	8	problems	problem	NOUN
ejpam-6266	576	9	let	let	VERB
ejpam-6266	576	10	us	we	PRON
ejpam-6266	576	11	announce	announce	VERB
ejpam-6266	576	12	some	some	DET
ejpam-6266	576	13	results	result	NOUN
ejpam-6266	576	14	on	on	ADP
ejpam-6266	576	15	the	the	DET
ejpam-6266	576	16	decay	decay	NOUN
ejpam-6266	576	17	estimates	estimate	NOUN
ejpam-6266	576	18	for	for	ADP
ejpam-6266	576	19	cauchy	cauchy	NOUN
ejpam-6266	576	20	problems	problem	NOUN
ejpam-6266	576	21	(	(	PUNCT
ejpam-6266	576	22	9	9	NUM
ejpam-6266	576	23	)	)	PUNCT
ejpam-6266	576	24	and	and	CCONJ
ejpam-6266	576	25	(	(	PUNCT
ejpam-6266	576	26	10	10	NUM
ejpam-6266	576	27	)	)	PUNCT
ejpam-6266	576	28	.	.	PUNCT
ejpam-6266	577	1	first	first	ADV
ejpam-6266	577	2	,	,	PUNCT
ejpam-6266	577	3	for	for	ADP
ejpam-6266	577	4	problem	problem	NOUN
ejpam-6266	577	5	(	(	PUNCT
ejpam-6266	577	6	9	9	NUM
ejpam-6266	577	7	)	)	PUNCT
ejpam-6266	577	8	,	,	PUNCT
ejpam-6266	577	9	a.	a.	PROPN
ejpam-6266	577	10	matsumura	matsumura	PROPN
ejpam-6266	577	11	proved	prove	VERB
ejpam-6266	577	12	in	in	ADP
ejpam-6266	577	13	[	[	X
ejpam-6266	577	14	9	9	NUM
ejpam-6266	577	15	]	]	X
ejpam-6266	577	16	the	the	DET
ejpam-6266	577	17	following	follow	VERB
ejpam-6266	577	18	proposition	proposition	NOUN
ejpam-6266	577	19	proposition	proposition	NOUN
ejpam-6266	577	20	1	1	NUM
ejpam-6266	577	21	.	.	PUNCT
ejpam-6266	578	1	[	[	X
ejpam-6266	578	2	9	9	NUM
ejpam-6266	578	3	]	]	X
ejpam-6266	578	4	if	if	SCONJ
ejpam-6266	578	5	u	u	NOUN
ejpam-6266	578	6	is	be	AUX
ejpam-6266	578	7	solution	solution	NOUN
ejpam-6266	578	8	to	to	ADP
ejpam-6266	578	9	cauchy	cauchy	ADJ
ejpam-6266	578	10	problem	problem	NOUN
ejpam-6266	578	11	(	(	PUNCT
ejpam-6266	578	12	9	9	NUM
ejpam-6266	578	13	)	)	PUNCT
ejpam-6266	578	14	,	,	PUNCT
ejpam-6266	578	15	then	then	ADV
ejpam-6266	578	16	u	u	NOUN
ejpam-6266	578	17	and	and	CCONJ
ejpam-6266	578	18	its	its	PRON
ejpam-6266	578	19	derivatives	derivative	NOUN
ejpam-6266	578	20	∂j	∂j	NOUN
ejpam-6266	578	21	t∇κu	t∇κu	NOUN
ejpam-6266	578	22	satisfy	satisfy	VERB
ejpam-6266	578	23	for	for	ADP
ejpam-6266	578	24	all	all	DET
ejpam-6266	578	25	j	j	PROPN
ejpam-6266	578	26	∈	∈	PROPN
ejpam-6266	578	27	n	n	ADV
ejpam-6266	578	28	and	and	CCONJ
ejpam-6266	578	29	κ	κ	X
ejpam-6266	578	30	>	>	X
ejpam-6266	578	31	0	0	PUNCT
ejpam-6266	579	1	the	the	DET
ejpam-6266	579	2	following	follow	VERB
ejpam-6266	579	3	estimates	estimate	NOUN
ejpam-6266	579	4	:	:	PUNCT
ejpam-6266	579	5	‖u(t	‖u(t	NUM
ejpam-6266	579	6	,	,	PUNCT
ejpam-6266	579	7	·	·	PUNCT
ejpam-6266	579	8	)	)	PUNCT
ejpam-6266	579	9	‖	‖	PROPN
ejpam-6266	579	10	≤	≤	PROPN
ejpam-6266	579	11	c(1	c(1	PROPN
ejpam-6266	579	12	+	+	CCONJ
ejpam-6266	579	13	t)−	t)−	PROPN
ejpam-6266	579	14	n	n	PRON
ejpam-6266	579	15	4	4	NUM
ejpam-6266	579	16	−κ	−κ	NOUN
ejpam-6266	579	17	2	2	NUM
ejpam-6266	579	18	−j(‖(u0	−j(‖(u0	NOUN
ejpam-6266	579	19	,	,	PUNCT
ejpam-6266	579	20	u1)‖l1	u1)‖l1	PROPN
ejpam-6266	579	21	+	+	CCONJ
ejpam-6266	579	22	‖u0‖hκ+j	‖u0‖hκ+j	NUM
ejpam-6266	579	23	+	+	NUM
ejpam-6266	579	24	‖u1‖h[κ+j−1]+	‖u1‖h[κ+j−1]+	NUM
ejpam-6266	579	25	)	)	PUNCT
ejpam-6266	579	26	,	,	PUNCT
ejpam-6266	579	27	(	(	PUNCT
ejpam-6266	579	28	104	104	NUM
ejpam-6266	579	29	)	)	PUNCT
ejpam-6266	579	30	for	for	ADP
ejpam-6266	579	31	some	some	DET
ejpam-6266	579	32	constant	constant	ADJ
ejpam-6266	579	33	c	c	NOUN
ejpam-6266	579	34	>	>	X
ejpam-6266	579	35	0	0	X
ejpam-6266	579	36	.	.	PUNCT
ejpam-6266	580	1	the	the	DET
ejpam-6266	580	2	following	following	ADJ
ejpam-6266	580	3	result	result	NOUN
ejpam-6266	580	4	is	be	AUX
ejpam-6266	580	5	an	an	DET
ejpam-6266	580	6	immediate	immediate	ADJ
ejpam-6266	580	7	consequence	consequence	NOUN
ejpam-6266	580	8	of	of	ADP
ejpam-6266	580	9	proposition	proposition	NOUN
ejpam-6266	580	10	1	1	NUM
ejpam-6266	580	11	and	and	CCONJ
ejpam-6266	580	12	the	the	DET
ejpam-6266	580	13	fact	fact	NOUN
ejpam-6266	580	14	that	that	SCONJ
ejpam-6266	580	15	equation	equation	NOUN
ejpam-6266	580	16	utt	utt	PROPN
ejpam-6266	580	17	−∆u+	−∆u+	NOUN
ejpam-6266	580	18	ut	ut	PROPN
ejpam-6266	580	19	=	=	SYM
ejpam-6266	580	20	0	0	NUM
ejpam-6266	580	21	is	be	AUX
ejpam-6266	580	22	invariant	invariant	ADJ
ejpam-6266	580	23	by	by	ADP
ejpam-6266	580	24	translation	translation	NOUN
ejpam-6266	580	25	.	.	PUNCT
ejpam-6266	581	1	corollary	corollary	ADJ
ejpam-6266	581	2	1	1	NUM
ejpam-6266	581	3	.	.	PUNCT
ejpam-6266	582	1	if	if	SCONJ
ejpam-6266	582	2	v	v	NOUN
ejpam-6266	582	3	is	be	AUX
ejpam-6266	582	4	solution	solution	NOUN
ejpam-6266	582	5	to	to	ADP
ejpam-6266	582	6	cauchy	cauchy	ADJ
ejpam-6266	582	7	problem	problem	NOUN
ejpam-6266	582	8	(	(	PUNCT
ejpam-6266	582	9	10	10	NUM
ejpam-6266	582	10	)	)	PUNCT
ejpam-6266	582	11	,	,	PUNCT
ejpam-6266	582	12	then	then	ADV
ejpam-6266	582	13	v	v	NOUN
ejpam-6266	582	14	and	and	CCONJ
ejpam-6266	582	15	its	its	PRON
ejpam-6266	582	16	derivatives	derivative	NOUN
ejpam-6266	582	17	∂j	∂j	NOUN
ejpam-6266	582	18	t∇κv	t∇κv	NOUN
ejpam-6266	582	19	satisfy	satisfy	VERB
ejpam-6266	582	20	for	for	ADP
ejpam-6266	582	21	all	all	DET
ejpam-6266	582	22	j	j	PROPN
ejpam-6266	582	23	∈	∈	PROPN
ejpam-6266	582	24	n	n	ADV
ejpam-6266	582	25	and	and	CCONJ
ejpam-6266	582	26	κ	κ	X
ejpam-6266	582	27	>	>	X
ejpam-6266	582	28	0	0	PUNCT
ejpam-6266	583	1	the	the	DET
ejpam-6266	583	2	following	follow	VERB
ejpam-6266	583	3	estimates	estimate	NOUN
ejpam-6266	583	4	:	:	PUNCT
ejpam-6266	583	5	‖v(t	‖v(t	NUM
ejpam-6266	583	6	,	,	PUNCT
ejpam-6266	583	7	·	·	PUNCT
ejpam-6266	583	8	)	)	PUNCT
ejpam-6266	583	9	‖	‖	PROPN
ejpam-6266	583	10	≤	≤	PROPN
ejpam-6266	583	11	c(1	c(1	PROPN
ejpam-6266	583	12	+	+	CCONJ
ejpam-6266	583	13	t−	t−	PROPN
ejpam-6266	583	14	τ)−	τ)−	PROPN
ejpam-6266	583	15	n	n	CCONJ
ejpam-6266	583	16	4	4	NUM
ejpam-6266	583	17	−κ	−κ	NOUN
ejpam-6266	583	18	2	2	NUM
ejpam-6266	583	19	−j(‖h(τ	−j(‖h(τ	NOUN
ejpam-6266	583	20	,	,	PUNCT
ejpam-6266	583	21	·	·	PUNCT
ejpam-6266	583	22	)	)	PUNCT
ejpam-6266	583	23	‖l1	‖l1	PROPN
ejpam-6266	584	1	+	+	CCONJ
ejpam-6266	584	2	‖h(τ	‖h(τ	X
ejpam-6266	584	3	,	,	PUNCT
ejpam-6266	584	4	·	·	PUNCT
ejpam-6266	584	5	)	)	PUNCT
ejpam-6266	584	6	‖h[κ+j−1]+	‖h[κ+j−1]+	NUM
ejpam-6266	584	7	)	)	PUNCT
ejpam-6266	584	8	,	,	PUNCT
ejpam-6266	584	9	(	(	PUNCT
ejpam-6266	584	10	105	105	NUM
ejpam-6266	584	11	)	)	PUNCT
ejpam-6266	584	12	for	for	ADP
ejpam-6266	584	13	some	some	DET
ejpam-6266	584	14	constant	constant	ADJ
ejpam-6266	584	15	c	c	NOUN
ejpam-6266	584	16	>	>	X
ejpam-6266	584	17	0	0	X
ejpam-6266	584	18	.	.	PUNCT
ejpam-6266	585	1	the	the	DET
ejpam-6266	585	2	following	following	ADJ
ejpam-6266	585	3	result	result	NOUN
ejpam-6266	585	4	is	be	AUX
ejpam-6266	585	5	a	a	DET
ejpam-6266	585	6	particular	particular	ADJ
ejpam-6266	585	7	case	case	NOUN
ejpam-6266	585	8	of	of	ADP
ejpam-6266	585	9	proposition	proposition	NOUN
ejpam-6266	585	10	5.2	5.2	NUM
ejpam-6266	585	11	from	from	ADP
ejpam-6266	585	12	[	[	X
ejpam-6266	585	13	11	11	NUM
ejpam-6266	585	14	]	]	PUNCT
ejpam-6266	585	15	.	.	PUNCT
ejpam-6266	586	1	see	see	AUX
ejpam-6266	586	2	also	also	ADV
ejpam-6266	586	3	theorem	theorem	VERB
ejpam-6266	586	4	3	3	NUM
ejpam-6266	586	5	in	in	ADP
ejpam-6266	586	6	[	[	PUNCT
ejpam-6266	586	7	13	13	NUM
ejpam-6266	586	8	]	]	PUNCT
ejpam-6266	586	9	.	.	PUNCT
ejpam-6266	587	1	corollary	corollary	ADJ
ejpam-6266	587	2	2	2	NUM
ejpam-6266	587	3	.	.	PUNCT
ejpam-6266	588	1	[	[	X
ejpam-6266	588	2	proposition	proposition	NOUN
ejpam-6266	588	3	5.1	5.1	NUM
ejpam-6266	588	4	,	,	PUNCT
ejpam-6266	588	5	[	[	X
ejpam-6266	588	6	11	11	NUM
ejpam-6266	588	7	]	]	X
ejpam-6266	588	8	]	]	X
ejpam-6266	588	9	let	let	VERB
ejpam-6266	588	10	us	we	PRON
ejpam-6266	588	11	consider	consider	VERB
ejpam-6266	588	12	the	the	DET
ejpam-6266	588	13	cauchy	cauchy	ADJ
ejpam-6266	588	14	problem	problem	NOUN
ejpam-6266	588	15	(	(	PUNCT
ejpam-6266	588	16	10	10	NUM
ejpam-6266	588	17	)	)	PUNCT
ejpam-6266	588	18	with	with	ADP
ejpam-6266	588	19	h	h	NOUN
ejpam-6266	588	20	=	=	SYM
ejpam-6266	588	21	h(τ	h(τ	PROPN
ejpam-6266	588	22	,	,	PUNCT
ejpam-6266	588	23	·	·	PUNCT
ejpam-6266	588	24	)	)	PUNCT
ejpam-6266	589	1	∈	∈	PROPN
ejpam-6266	590	1	lm	lm	INTJ
ejpam-6266	590	2	∩hσ−1	∩hσ−1	INTJ
ejpam-6266	590	3	for	for	ADP
ejpam-6266	590	4	some	some	DET
ejpam-6266	590	5	m	m	NOUN
ejpam-6266	590	6	∈	∈	NOUN
ejpam-6266	591	1	[	[	X
ejpam-6266	591	2	1	1	NUM
ejpam-6266	591	3	,	,	PUNCT
ejpam-6266	591	4	2	2	NUM
ejpam-6266	591	5	)	)	PUNCT
ejpam-6266	591	6	and	and	CCONJ
ejpam-6266	591	7	σ	σ	X
ejpam-6266	591	8	>	>	X
ejpam-6266	592	1	1	1	X
ejpam-6266	592	2	.	.	PUNCT
ejpam-6266	593	1	then	then	ADV
ejpam-6266	593	2	the	the	DET
ejpam-6266	593	3	energy	energy	NOUN
ejpam-6266	593	4	solution	solution	NOUN
ejpam-6266	593	5	belongs	belong	VERB
ejpam-6266	593	6	to	to	ADP
ejpam-6266	593	7	c([τ,+∞),hσ	c([τ,+∞),hσ	PROPN
ejpam-6266	593	8	)	)	PUNCT
ejpam-6266	593	9	∩	∩	NOUN
ejpam-6266	593	10	c1([τ,+∞),hσ−1	c1([τ,+∞),hσ−1	NUM
ejpam-6266	593	11	)	)	PUNCT
ejpam-6266	593	12	,	,	PUNCT
ejpam-6266	593	13	and	and	CCONJ
ejpam-6266	593	14	satisfies	satisfy	VERB
ejpam-6266	593	15	the	the	DET
ejpam-6266	593	16	following	follow	VERB
ejpam-6266	593	17	matsumura	matsumura	ADJ
ejpam-6266	593	18	type	type	NOUN
ejpam-6266	593	19	decay	decay	NOUN
ejpam-6266	593	20	estimates	estimate	NOUN
ejpam-6266	593	21	:	:	PUNCT
ejpam-6266	593	22	‖v(t	‖v(t	NUM
ejpam-6266	593	23	,	,	PUNCT
ejpam-6266	593	24	·	·	PUNCT
ejpam-6266	593	25	)	)	PUNCT
ejpam-6266	593	26	‖l2	‖l2	ADJ
ejpam-6266	593	27	≤	≤	NUM
ejpam-6266	593	28	c(1	c(1	NOUN
ejpam-6266	593	29	+	+	CCONJ
ejpam-6266	593	30	t−	t−	PROPN
ejpam-6266	593	31	τ)−	τ)−	PROPN
ejpam-6266	593	32	n	n	CCONJ
ejpam-6266	593	33	2	2	NUM
ejpam-6266	593	34	(	(	PUNCT
ejpam-6266	593	35	1	1	NUM
ejpam-6266	593	36	m	m	NOUN
ejpam-6266	593	37	−	−	NUM
ejpam-6266	593	38	1	1	NUM
ejpam-6266	593	39	2	2	NUM
ejpam-6266	593	40	)	)	PUNCT
ejpam-6266	593	41	‖h(τ	‖h(τ	NOUN
ejpam-6266	593	42	,	,	PUNCT
ejpam-6266	593	43	·	·	PUNCT
ejpam-6266	593	44	)	)	PUNCT
ejpam-6266	593	45	‖lm∩hσ−1	‖lm∩hσ−1	NOUN
ejpam-6266	593	46	,	,	PUNCT
ejpam-6266	593	47	‖|d|σv(t	‖|d|σv(t	NOUN
ejpam-6266	593	48	,	,	PUNCT
ejpam-6266	593	49	·	·	PUNCT
ejpam-6266	593	50	)	)	PUNCT
ejpam-6266	593	51	‖l2	‖l2	ADJ
ejpam-6266	593	52	≤	≤	NUM
ejpam-6266	593	53	c(1	c(1	NOUN
ejpam-6266	593	54	+	+	CCONJ
ejpam-6266	593	55	t−	t−	PROPN
ejpam-6266	593	56	τ)−	τ)−	PROPN
ejpam-6266	593	57	n	n	CCONJ
ejpam-6266	593	58	2	2	NUM
ejpam-6266	593	59	(	(	PUNCT
ejpam-6266	593	60	1	1	NUM
ejpam-6266	593	61	m	m	NOUN
ejpam-6266	593	62	−	−	NUM
ejpam-6266	593	63	1	1	NUM
ejpam-6266	593	64	2	2	NUM
ejpam-6266	593	65	)	)	PUNCT
ejpam-6266	593	66	−σ	−σ	NOUN
ejpam-6266	593	67	2	2	NUM
ejpam-6266	593	68	‖h(τ	‖h(τ	NOUN
ejpam-6266	593	69	,	,	PUNCT
ejpam-6266	593	70	·	·	PUNCT
ejpam-6266	593	71	)	)	PUNCT
ejpam-6266	593	72	‖lm∩hσ−1	‖lm∩hσ−1	NOUN
ejpam-6266	593	73	,	,	PUNCT
ejpam-6266	593	74	‖vt(t	‖vt(t	PROPN
ejpam-6266	593	75	,	,	PUNCT
ejpam-6266	593	76	·	·	PUNCT
ejpam-6266	593	77	)	)	PUNCT
ejpam-6266	593	78	‖l2	‖l2	ADJ
ejpam-6266	593	79	≤	≤	NUM
ejpam-6266	593	80	c(1	c(1	NOUN
ejpam-6266	593	81	+	+	CCONJ
ejpam-6266	593	82	t−	t−	PROPN
ejpam-6266	593	83	τ)−	τ)−	PROPN
ejpam-6266	593	84	n	n	CCONJ
ejpam-6266	593	85	2	2	NUM
ejpam-6266	593	86	(	(	PUNCT
ejpam-6266	593	87	1	1	NUM
ejpam-6266	593	88	m	m	NOUN
ejpam-6266	593	89	−	−	NUM
ejpam-6266	593	90	1	1	NUM
ejpam-6266	593	91	2	2	NUM
ejpam-6266	593	92	)	)	PUNCT
ejpam-6266	593	93	−1‖h(τ	−1‖h(τ	NUM
ejpam-6266	593	94	,	,	PUNCT
ejpam-6266	593	95	·	·	PUNCT
ejpam-6266	593	96	)	)	PUNCT
ejpam-6266	593	97	‖lm∩hσ−1	‖lm∩hσ−1	NOUN
ejpam-6266	593	98	,	,	PUNCT
ejpam-6266	593	99	‖|d|σ−1vt(t	‖|d|σ−1vt(t	NOUN
ejpam-6266	593	100	,	,	PUNCT
ejpam-6266	593	101	·	·	PUNCT
ejpam-6266	593	102	)	)	PUNCT
ejpam-6266	593	103	‖l2	‖l2	ADJ
ejpam-6266	593	104	≤	≤	NUM
ejpam-6266	593	105	c(1	c(1	NOUN
ejpam-6266	593	106	+	+	CCONJ
ejpam-6266	593	107	t−	t−	PROPN
ejpam-6266	593	108	τ)−	τ)−	PROPN
ejpam-6266	593	109	n	n	CCONJ
ejpam-6266	593	110	2	2	NUM
ejpam-6266	593	111	(	(	PUNCT
ejpam-6266	593	112	1	1	NUM
ejpam-6266	593	113	m	m	NOUN
ejpam-6266	593	114	−	−	NUM
ejpam-6266	593	115	1	1	NUM
ejpam-6266	593	116	2	2	NUM
ejpam-6266	593	117	)	)	PUNCT
ejpam-6266	593	118	−σ−1	−σ−1	NUM
ejpam-6266	593	119	2	2	NUM
ejpam-6266	593	120	−1‖h(τ	−1‖h(τ	NUM
ejpam-6266	593	121	,	,	PUNCT
ejpam-6266	593	122	·	·	PUNCT
ejpam-6266	593	123	)	)	PUNCT
ejpam-6266	593	124	‖lm∩hσ−1	‖lm∩hσ−1	NOUN
ejpam-6266	593	125	.	.	PUNCT
ejpam-6266	594	1	5.4	5.4	NUM
ejpam-6266	594	2	.	.	PUNCT
ejpam-6266	594	3	main	main	ADJ
ejpam-6266	594	4	inequalities	inequality	NOUN
ejpam-6266	594	5	-	-	PUNCT
ejpam-6266	594	6	tools	tool	NOUN
ejpam-6266	594	7	from	from	ADP
ejpam-6266	594	8	harmonic	harmonic	ADJ
ejpam-6266	594	9	analysis	analysis	NOUN
ejpam-6266	594	10	the	the	DET
ejpam-6266	594	11	following	follow	VERB
ejpam-6266	594	12	results	result	NOUN
ejpam-6266	594	13	can	can	AUX
ejpam-6266	594	14	be	be	AUX
ejpam-6266	594	15	found	find	VERB
ejpam-6266	594	16	among	among	ADP
ejpam-6266	594	17	other	other	ADJ
ejpam-6266	594	18	things	thing	NOUN
ejpam-6266	594	19	in	in	ADP
ejpam-6266	594	20	[	[	X
ejpam-6266	594	21	14	14	NUM
ejpam-6266	594	22	]	]	PUNCT
ejpam-6266	594	23	or	or	CCONJ
ejpam-6266	594	24	[	[	X
ejpam-6266	594	25	15	15	NUM
ejpam-6266	594	26	]	]	PUNCT
ejpam-6266	594	27	.	.	PUNCT
ejpam-6266	595	1	5.4.1	5.4.1	X
ejpam-6266	595	2	.	.	PUNCT
ejpam-6266	595	3	fractional	fractional	ADJ
ejpam-6266	595	4	gagliardo	gagliardo	NOUN
ejpam-6266	595	5	-	-	PUNCT
ejpam-6266	595	6	nirenberg	nirenberg	PROPN
ejpam-6266	595	7	inequality	inequality	NOUN
ejpam-6266	595	8	proposition	proposition	NOUN
ejpam-6266	595	9	2	2	NUM
ejpam-6266	595	10	.	.	PUNCT
ejpam-6266	596	1	[	[	X
ejpam-6266	596	2	11	11	NUM
ejpam-6266	596	3	,	,	PUNCT
ejpam-6266	596	4	14	14	NUM
ejpam-6266	596	5	,	,	PUNCT
ejpam-6266	596	6	15	15	NUM
ejpam-6266	596	7	]	]	PUNCT
ejpam-6266	596	8	let	let	VERB
ejpam-6266	596	9	1	1	NUM
ejpam-6266	596	10	<	<	X
ejpam-6266	596	11	p	p	X
ejpam-6266	596	12	,	,	PUNCT
ejpam-6266	596	13	p0	p0	NOUN
ejpam-6266	596	14	,	,	PUNCT
ejpam-6266	596	15	p1	p1	NOUN
ejpam-6266	596	16	<	<	X
ejpam-6266	596	17	∞	∞	PROPN
ejpam-6266	596	18	and	and	CCONJ
ejpam-6266	596	19	κ	κ	NOUN
ejpam-6266	596	20	∈	∈	PROPN
ejpam-6266	597	1	[	[	X
ejpam-6266	597	2	0	0	NUM
ejpam-6266	597	3	,	,	PUNCT
ejpam-6266	597	4	σ	σ	PROPN
ejpam-6266	597	5	)	)	PUNCT
ejpam-6266	597	6	.	.	PUNCT
ejpam-6266	598	1	then	then	ADV
ejpam-6266	598	2	the	the	DET
ejpam-6266	598	3	following	follow	VERB
ejpam-6266	598	4	fractional	fractional	ADJ
ejpam-6266	598	5	gagliardo	gagliardo	NOUN
ejpam-6266	598	6	-	-	PUNCT
ejpam-6266	598	7	nirenberg	nirenberg	PROPN
ejpam-6266	598	8	inequality	inequality	NOUN
ejpam-6266	598	9	holds	hold	VERB
ejpam-6266	598	10	for	for	ADP
ejpam-6266	598	11	all	all	DET
ejpam-6266	598	12	u	u	PROPN
ejpam-6266	598	13	∈	∈	PROPN
ejpam-6266	598	14	lp0	lp0	NOUN
ejpam-6266	598	15	∩	∩	PROPN
ejpam-6266	598	16	ḣσ	ḣσ	PROPN
ejpam-6266	598	17	p1	p1	NOUN
ejpam-6266	598	18	:	:	PUNCT
ejpam-6266	598	19	‖u‖ḣκ	‖u‖ḣκ	PROPN
ejpam-6266	598	20	p	p	NOUN
ejpam-6266	598	21	.	.	PUNCT
ejpam-6266	599	1	‖u‖1−θ	‖u‖1−θ	PROPN
ejpam-6266	599	2	lp0	lp0	PROPN
ejpam-6266	599	3	‖u‖θḣσ	‖u‖θḣσ	PROPN
ejpam-6266	599	4	p1	p1	NOUN
ejpam-6266	599	5	for	for	ADP
ejpam-6266	599	6	κ	κ	PROPN
ejpam-6266	599	7	σ	σ	PROPN
ejpam-6266	599	8	≤	≤	NUM
ejpam-6266	599	9	θ	θ	PROPN
ejpam-6266	599	10	≤	≤	NUM
ejpam-6266	599	11	1	1	NUM
ejpam-6266	599	12	,	,	PUNCT
ejpam-6266	599	13	(	(	PUNCT
ejpam-6266	599	14	106	106	NUM
ejpam-6266	599	15	)	)	PUNCT
ejpam-6266	599	16	t.	t.	NOUN
ejpam-6266	599	17	hadj	hadj	PROPN
ejpam-6266	599	18	kaddour	kaddour	PROPN
ejpam-6266	599	19	et	et	PROPN
ejpam-6266	599	20	al	al	PROPN
ejpam-6266	599	21	.	.	PUNCT
ejpam-6266	599	22	/	/	SYM
ejpam-6266	599	23	eur	eur	PROPN
ejpam-6266	599	24	.	.	PUNCT
ejpam-6266	600	1	j.	j.	PROPN
ejpam-6266	600	2	pure	pure	PROPN
ejpam-6266	600	3	appl	appl	PROPN
ejpam-6266	600	4	.	.	PROPN
ejpam-6266	600	5	math	math	PROPN
ejpam-6266	600	6	,	,	PUNCT
ejpam-6266	600	7	18	18	NUM
ejpam-6266	600	8	(	(	PUNCT
ejpam-6266	600	9	4	4	NUM
ejpam-6266	600	10	)	)	PUNCT
ejpam-6266	600	11	(	(	PUNCT
ejpam-6266	600	12	2025	2025	NUM
ejpam-6266	600	13	)	)	PUNCT
ejpam-6266	600	14	,	,	PUNCT
ejpam-6266	600	15	6266	6266	NUM
ejpam-6266	600	16	23	23	NUM
ejpam-6266	600	17	of	of	ADP
ejpam-6266	600	18	24	24	NUM
ejpam-6266	600	19	where	where	SCONJ
ejpam-6266	600	20	θ	θ	NOUN
ejpam-6266	600	21	=	=	SYM
ejpam-6266	600	22	1	1	NUM
ejpam-6266	600	23	p0	p0	NOUN
ejpam-6266	600	24	−	−	ADP
ejpam-6266	600	25	1	1	NUM
ejpam-6266	600	26	p	p	NOUN
ejpam-6266	601	1	+	+	PROPN
ejpam-6266	601	2	κ	κ	PROPN
ejpam-6266	601	3	p	p	NOUN
ejpam-6266	601	4	1	1	NUM
ejpam-6266	601	5	p0	p0	NOUN
ejpam-6266	601	6	−	−	PROPN
ejpam-6266	601	7	1	1	NUM
ejpam-6266	601	8	p1	p1	PROPN
ejpam-6266	601	9	+	+	CCONJ
ejpam-6266	601	10	σ	σ	PROPN
ejpam-6266	601	11	n	n	PROPN
ejpam-6266	601	12	.	.	PUNCT
ejpam-6266	602	1	the	the	DET
ejpam-6266	602	2	following	follow	VERB
ejpam-6266	602	3	corollary	corollary	NOUN
ejpam-6266	602	4	is	be	AUX
ejpam-6266	602	5	a	a	DET
ejpam-6266	602	6	particular	particular	ADJ
ejpam-6266	602	7	case	case	NOUN
ejpam-6266	602	8	of	of	ADP
ejpam-6266	602	9	proposition	proposition	NOUN
ejpam-6266	602	10	2	2	NUM
ejpam-6266	602	11	.	.	PUNCT
ejpam-6266	602	12	corollary	corollary	ADJ
ejpam-6266	602	13	3	3	NUM
ejpam-6266	602	14	.	.	PUNCT
ejpam-6266	603	1	[	[	X
ejpam-6266	603	2	7	7	X
ejpam-6266	603	3	]	]	X
ejpam-6266	603	4	let	let	VERB
ejpam-6266	603	5	u	u	PRON
ejpam-6266	603	6	∈	∈	NOUN
ejpam-6266	603	7	l2	l2	NOUN
ejpam-6266	603	8	∩	∩	X
ejpam-6266	603	9	ḣk	ḣk	PROPN
ejpam-6266	603	10	2	2	NUM
ejpam-6266	603	11	.	.	PUNCT
ejpam-6266	604	1	then	then	ADV
ejpam-6266	604	2	the	the	DET
ejpam-6266	604	3	following	follow	VERB
ejpam-6266	604	4	inequality	inequality	NOUN
ejpam-6266	604	5	holds	hold	VERB
ejpam-6266	604	6	:	:	PUNCT
ejpam-6266	604	7	‖u‖lq	‖u‖lq	NUM
ejpam-6266	604	8	.	.	PUNCT
ejpam-6266	605	1	‖u‖1−θk(q	‖u‖1−θk(q	NUM
ejpam-6266	605	2	)	)	PUNCT
ejpam-6266	605	3	l2	l2	NOUN
ejpam-6266	605	4	‖u‖θk(q	‖u‖θk(q	ADJ
ejpam-6266	605	5	)	)	PUNCT
ejpam-6266	605	6	ḣk	ḣk	PROPN
ejpam-6266	605	7	2	2	NUM
ejpam-6266	605	8	,	,	PUNCT
ejpam-6266	605	9	θk(q	θk(q	NUM
ejpam-6266	605	10	)	)	PUNCT
ejpam-6266	605	11	=	=	SYM
ejpam-6266	606	1	n	n	CCONJ
ejpam-6266	606	2	k	k	NOUN
ejpam-6266	606	3	(	(	PUNCT
ejpam-6266	606	4	1	1	NUM
ejpam-6266	606	5	2	2	NUM
ejpam-6266	606	6	−	−	NUM
ejpam-6266	606	7	1	1	NUM
ejpam-6266	606	8	q	q	NOUN
ejpam-6266	606	9	)	)	PUNCT
ejpam-6266	606	10	(	(	PUNCT
ejpam-6266	606	11	107	107	NUM
ejpam-6266	606	12	)	)	PUNCT
ejpam-6266	606	13	for	for	ADP
ejpam-6266	606	14	any	any	DET
ejpam-6266	606	15	k	k	PROPN
ejpam-6266	606	16	∈	∈	PROPN
ejpam-6266	606	17	(	(	PUNCT
ejpam-6266	606	18	0	0	NUM
ejpam-6266	606	19	,	,	PUNCT
ejpam-6266	606	20	n2	n2	ADJ
ejpam-6266	606	21	)	)	PUNCT
ejpam-6266	606	22	and	and	CCONJ
ejpam-6266	606	23	any	any	DET
ejpam-6266	606	24	q	q	NOUN
ejpam-6266	606	25	such	such	ADJ
ejpam-6266	606	26	that	that	SCONJ
ejpam-6266	606	27	2	2	NUM
ejpam-6266	606	28	≤	≤	NOUN
ejpam-6266	606	29	q	q	ADJ
ejpam-6266	606	30	≤	≤	NUM
ejpam-6266	606	31	2n	2n	NUM
ejpam-6266	606	32	n−	n−	NOUN
ejpam-6266	606	33	2k	2k	NUM
ejpam-6266	606	34	.	.	PUNCT
ejpam-6266	607	1	(	(	PUNCT
ejpam-6266	607	2	108	108	NUM
ejpam-6266	607	3	)	)	PUNCT
ejpam-6266	607	4	the	the	DET
ejpam-6266	607	5	case	case	NOUN
ejpam-6266	607	6	q	q	X
ejpam-6266	608	1	=	=	SYM
ejpam-6266	608	2	2n	2n	NOUN
ejpam-6266	608	3	n−2k	n−2k	NOUN
ejpam-6266	608	4	reduces	reduce	VERB
ejpam-6266	608	5	the	the	DET
ejpam-6266	608	6	inequality	inequality	NOUN
ejpam-6266	608	7	(	(	PUNCT
ejpam-6266	608	8	107	107	NUM
ejpam-6266	608	9	)	)	PUNCT
ejpam-6266	608	10	to	to	ADP
ejpam-6266	608	11	a	a	DET
ejpam-6266	608	12	well	well	ADV
ejpam-6266	608	13	-	-	PUNCT
ejpam-6266	608	14	known	know	VERB
ejpam-6266	608	15	statement	statement	NOUN
ejpam-6266	608	16	in	in	ADP
ejpam-6266	608	17	the	the	DET
ejpam-6266	608	18	frame	frame	NOUN
ejpam-6266	608	19	of	of	ADP
ejpam-6266	608	20	sobolev	sobolev	NOUN
ejpam-6266	608	21	embeddings	embedding	NOUN
ejpam-6266	608	22	.	.	PUNCT
ejpam-6266	609	1	corollary	corollary	ADJ
ejpam-6266	609	2	4	4	NUM
ejpam-6266	609	3	.	.	PUNCT
ejpam-6266	610	1	[	[	X
ejpam-6266	610	2	11	11	NUM
ejpam-6266	610	3	,	,	PUNCT
ejpam-6266	610	4	14	14	NUM
ejpam-6266	610	5	,	,	PUNCT
ejpam-6266	610	6	15	15	NUM
ejpam-6266	610	7	]	]	PUNCT
ejpam-6266	610	8	for	for	ADP
ejpam-6266	610	9	u	u	PROPN
ejpam-6266	610	10	∈	∈	PROPN
ejpam-6266	610	11	ḣk	ḣk	PROPN
ejpam-6266	610	12	2	2	NUM
ejpam-6266	610	13	,	,	PUNCT
ejpam-6266	610	14	where	where	SCONJ
ejpam-6266	610	15	q	q	PROPN
ejpam-6266	610	16	∈	∈	PROPN
ejpam-6266	610	17	[	[	X
ejpam-6266	610	18	2,∞	2,∞	NUM
ejpam-6266	610	19	)	)	PUNCT
ejpam-6266	610	20	and	and	CCONJ
ejpam-6266	610	21	k	k	NOUN
ejpam-6266	610	22	=	=	SYM
ejpam-6266	610	23	n(12	n(12	ADJ
ejpam-6266	610	24	−	−	NUM
ejpam-6266	610	25	1	1	NUM
ejpam-6266	610	26	q	q	NOUN
ejpam-6266	610	27	)	)	PUNCT
ejpam-6266	610	28	,	,	PUNCT
ejpam-6266	610	29	the	the	DET
ejpam-6266	610	30	following	follow	VERB
ejpam-6266	610	31	inequality	inequality	NOUN
ejpam-6266	610	32	holds	hold	VERB
ejpam-6266	610	33	:	:	PUNCT
ejpam-6266	610	34	‖u‖lq	‖u‖lq	NUM
ejpam-6266	610	35	.	.	PUNCT
ejpam-6266	611	1	‖u‖ḣk	‖u‖ḣk	NOUN
ejpam-6266	612	1	2	2	X
ejpam-6266	612	2	.	.	PUNCT
ejpam-6266	613	1	interpolation	interpolation	NOUN
ejpam-6266	613	2	formulas	formula	NOUN
ejpam-6266	613	3	are	be	AUX
ejpam-6266	613	4	sometimes	sometimes	ADV
ejpam-6266	613	5	used	use	VERB
ejpam-6266	613	6	to	to	PART
ejpam-6266	613	7	obtain	obtain	VERB
ejpam-6266	613	8	suitable	suitable	ADJ
ejpam-6266	613	9	estimates	estimate	NOUN
ejpam-6266	613	10	.	.	PUNCT
ejpam-6266	614	1	here	here	ADV
ejpam-6266	614	2	we	we	PRON
ejpam-6266	614	3	recall	recall	VERB
ejpam-6266	614	4	the	the	DET
ejpam-6266	614	5	relation	relation	NOUN
ejpam-6266	614	6	‖u‖ḣσ	‖u‖ḣσ	VERB
ejpam-6266	614	7	2	2	NUM
ejpam-6266	614	8	≤	≤	NUM
ejpam-6266	614	9	‖u‖1−θ	‖u‖1−θ	PROPN
ejpam-6266	614	10	ḣ	ḣ	PROPN
ejpam-6266	614	11	k1	k1	PROPN
ejpam-6266	614	12	2	2	NUM
ejpam-6266	614	13	‖u‖θ	‖u‖θ	NOUN
ejpam-6266	614	14	ḣ	ḣ	PROPN
ejpam-6266	614	15	k2	k2	PROPN
ejpam-6266	614	16	2	2	NUM
ejpam-6266	614	17	for	for	ADP
ejpam-6266	614	18	some	some	DET
ejpam-6266	614	19	θ	θ	NOUN
ejpam-6266	614	20	∈	∈	PROPN
ejpam-6266	615	1	[	[	X
ejpam-6266	615	2	0	0	NUM
ejpam-6266	615	3	,	,	PUNCT
ejpam-6266	615	4	1	1	NUM
ejpam-6266	615	5	]	]	PUNCT
ejpam-6266	615	6	with	with	ADP
ejpam-6266	615	7	k1(1−	k1(1−	PROPN
ejpam-6266	615	8	θ	θ	PROPN
ejpam-6266	615	9	)	)	PUNCT
ejpam-6266	615	10	+	+	NUM
ejpam-6266	615	11	k2θ	k2θ	PROPN
ejpam-6266	615	12	=	=	SYM
ejpam-6266	615	13	σ	σ	PROPN
ejpam-6266	615	14	.	.	PUNCT
ejpam-6266	616	1	(	(	PUNCT
ejpam-6266	616	2	109	109	NUM
ejpam-6266	616	3	)	)	SYM
ejpam-6266	616	4	5.4.2	5.4.2	NUM
ejpam-6266	616	5	.	.	PUNCT
ejpam-6266	616	6	fractional	fractional	PROPN
ejpam-6266	616	7	leibniz	leibniz	PROPN
ejpam-6266	616	8	rule	rule	NOUN
ejpam-6266	616	9	proposition	proposition	NOUN
ejpam-6266	616	10	3	3	NUM
ejpam-6266	616	11	.	.	PUNCT
ejpam-6266	617	1	[	[	X
ejpam-6266	617	2	11	11	NUM
ejpam-6266	617	3	,	,	PUNCT
ejpam-6266	617	4	14	14	NUM
ejpam-6266	617	5	,	,	PUNCT
ejpam-6266	617	6	15	15	NUM
ejpam-6266	617	7	]	]	PUNCT
ejpam-6266	617	8	let	let	VERB
ejpam-6266	617	9	σ	σ	PROPN
ejpam-6266	617	10	>	>	X
ejpam-6266	617	11	0	0	PROPN
ejpam-6266	617	12	,	,	PUNCT
ejpam-6266	617	13	1	1	NUM
ejpam-6266	617	14	≤	≤	NOUN
ejpam-6266	617	15	r	r	NOUN
ejpam-6266	617	16	≤	≤	NUM
ejpam-6266	617	17	∞	∞	NUM
ejpam-6266	617	18	and	and	CCONJ
ejpam-6266	617	19	1	1	NUM
ejpam-6266	617	20	<	<	X
ejpam-6266	617	21	p1	p1	PROPN
ejpam-6266	617	22	,	,	PUNCT
ejpam-6266	617	23	p2	p2	NOUN
ejpam-6266	617	24	,	,	PUNCT
ejpam-6266	617	25	q1	q1	NOUN
ejpam-6266	617	26	,	,	PUNCT
ejpam-6266	617	27	q2	q2	NOUN
ejpam-6266	617	28	≤	≤	NOUN
ejpam-6266	617	29	∞	∞	NUM
ejpam-6266	617	30	satisfying	satisfy	VERB
ejpam-6266	617	31	1	1	NUM
ejpam-6266	617	32	r	r	NOUN
ejpam-6266	617	33	=	=	SYM
ejpam-6266	617	34	1	1	NUM
ejpam-6266	617	35	p1	p1	NOUN
ejpam-6266	617	36	+	+	CCONJ
ejpam-6266	617	37	1	1	NUM
ejpam-6266	617	38	p2	p2	NOUN
ejpam-6266	617	39	=	=	SYM
ejpam-6266	617	40	1	1	NUM
ejpam-6266	617	41	q1	q1	NOUN
ejpam-6266	617	42	+	+	CCONJ
ejpam-6266	617	43	1	1	NUM
ejpam-6266	617	44	q2	q2	NOUN
ejpam-6266	617	45	.	.	PUNCT
ejpam-6266	618	1	then	then	ADV
ejpam-6266	618	2	it	it	PRON
ejpam-6266	618	3	holds	hold	VERB
ejpam-6266	618	4	the	the	DET
ejpam-6266	618	5	following	follow	VERB
ejpam-6266	618	6	fractional	fractional	PROPN
ejpam-6266	618	7	leibniz	leibniz	PROPN
ejpam-6266	618	8	rule	rule	NOUN
ejpam-6266	618	9	:	:	PUNCT
ejpam-6266	618	10	‖|d|σ(fg)‖lr	‖|d|σ(fg)‖lr	PROPN
ejpam-6266	618	11	.	.	PUNCT
ejpam-6266	619	1	‖|d|σf‖lp1‖g‖lp2	‖|d|σf‖lp1‖g‖lp2	PROPN
ejpam-6266	620	1	+	+	CCONJ
ejpam-6266	620	2	‖f‖lq1‖|d|σg‖lq2	‖f‖lq1‖|d|σg‖lq2	INTJ
ejpam-6266	620	3	for	for	ADP
ejpam-6266	620	4	any	any	DET
ejpam-6266	620	5	f	f	PROPN
ejpam-6266	620	6	∈	∈	PROPN
ejpam-6266	620	7	ḣσ	ḣσ	NOUN
ejpam-6266	620	8	p1	p1	NOUN
ejpam-6266	620	9	∩	∩	NOUN
ejpam-6266	620	10	lq1	lq1	PROPN
ejpam-6266	620	11	and	and	CCONJ
ejpam-6266	620	12	g	g	PROPN
ejpam-6266	620	13	∈	∈	PROPN
ejpam-6266	620	14	ḣσ	ḣσ	PROPN
ejpam-6266	620	15	q2	q2	NOUN
ejpam-6266	620	16	∩	∩	PROPN
ejpam-6266	620	17	lp2	lp2	PROPN
ejpam-6266	620	18	.	.	PUNCT
ejpam-6266	621	1	5.4.3	5.4.3	X
ejpam-6266	621	2	.	.	PUNCT
ejpam-6266	621	3	fractional	fractional	ADJ
ejpam-6266	621	4	chain	chain	NOUN
ejpam-6266	621	5	rule	rule	NOUN
ejpam-6266	621	6	proposition	proposition	NOUN
ejpam-6266	621	7	4	4	NUM
ejpam-6266	621	8	.	.	PUNCT
ejpam-6266	622	1	[	[	X
ejpam-6266	622	2	11	11	NUM
ejpam-6266	622	3	,	,	PUNCT
ejpam-6266	622	4	14	14	NUM
ejpam-6266	622	5	,	,	PUNCT
ejpam-6266	622	6	15	15	NUM
ejpam-6266	622	7	]	]	PUNCT
ejpam-6266	622	8	let	let	VERB
ejpam-6266	622	9	σ	σ	X
ejpam-6266	622	10	∈	∈	PROPN
ejpam-6266	622	11	(	(	PUNCT
ejpam-6266	622	12	0	0	NUM
ejpam-6266	622	13	,	,	PUNCT
ejpam-6266	622	14	1	1	NUM
ejpam-6266	622	15	)	)	PUNCT
ejpam-6266	622	16	,	,	PUNCT
ejpam-6266	622	17	1	1	NUM
ejpam-6266	622	18	<	<	X
ejpam-6266	622	19	r	r	NOUN
ejpam-6266	622	20	,	,	PUNCT
ejpam-6266	622	21	r1	r1	NOUN
ejpam-6266	622	22	,	,	PUNCT
ejpam-6266	622	23	r2	r2	PROPN
ejpam-6266	622	24	<	<	X
ejpam-6266	622	25	∞	∞	PROPN
ejpam-6266	622	26	and	and	CCONJ
ejpam-6266	622	27	f	f	PROPN
ejpam-6266	622	28	a	a	DET
ejpam-6266	622	29	c1	c1	PROPN
ejpam-6266	622	30	function	function	VERB
ejpam-6266	622	31	satisfying	satisfy	VERB
ejpam-6266	622	32	for	for	ADP
ejpam-6266	622	33	any	any	DET
ejpam-6266	622	34	τ	τ	PROPN
ejpam-6266	622	35	∈	∈	PROPN
ejpam-6266	623	1	[	[	X
ejpam-6266	623	2	0	0	NUM
ejpam-6266	623	3	,	,	PUNCT
ejpam-6266	623	4	1	1	NUM
ejpam-6266	623	5	]	]	PUNCT
ejpam-6266	623	6	and	and	CCONJ
ejpam-6266	623	7	u	u	NOUN
ejpam-6266	623	8	,	,	PUNCT
ejpam-6266	623	9	v	v	NOUN
ejpam-6266	623	10	∈	∈	NOUN
ejpam-6266	623	11	r	r	NOUN
ejpam-6266	623	12	the	the	DET
ejpam-6266	623	13	inequality	inequality	NOUN
ejpam-6266	623	14	|f	|f	PROPN
ejpam-6266	623	15	′(τu+	′(τu+	PROPN
ejpam-6266	623	16	(	(	PUNCT
ejpam-6266	623	17	1−	1−	NUM
ejpam-6266	623	18	τ)v)|	τ)v)|	PROPN
ejpam-6266	623	19	≤	≤	NOUN
ejpam-6266	623	20	µ(τ)(g(u	µ(τ)(g(u	NOUN
ejpam-6266	623	21	)	)	PUNCT
ejpam-6266	623	22	+	+	ADJ
ejpam-6266	623	23	g(v	g(v	NOUN
ejpam-6266	623	24	)	)	PUNCT
ejpam-6266	623	25	)	)	PUNCT
ejpam-6266	623	26	)	)	PUNCT
ejpam-6266	623	27	,	,	PUNCT
ejpam-6266	623	28	t.	t.	PROPN
ejpam-6266	623	29	hadj	hadj	PROPN
ejpam-6266	623	30	kaddour	kaddour	PROPN
ejpam-6266	623	31	et	et	PROPN
ejpam-6266	623	32	al	al	PROPN
ejpam-6266	623	33	.	.	PUNCT
ejpam-6266	623	34	/	/	SYM
ejpam-6266	623	35	eur	eur	PROPN
ejpam-6266	623	36	.	.	PUNCT
ejpam-6266	624	1	j.	j.	PROPN
ejpam-6266	624	2	pure	pure	PROPN
ejpam-6266	624	3	appl	appl	PROPN
ejpam-6266	624	4	.	.	PROPN
ejpam-6266	624	5	math	math	PROPN
ejpam-6266	624	6	,	,	PUNCT
ejpam-6266	624	7	18	18	NUM
ejpam-6266	624	8	(	(	PUNCT
ejpam-6266	624	9	4	4	NUM
ejpam-6266	624	10	)	)	PUNCT
ejpam-6266	624	11	(	(	PUNCT
ejpam-6266	624	12	2025	2025	NUM
ejpam-6266	624	13	)	)	PUNCT
ejpam-6266	624	14	,	,	PUNCT
ejpam-6266	624	15	6266	6266	NUM
ejpam-6266	624	16	24	24	NUM
ejpam-6266	624	17	of	of	ADP
ejpam-6266	624	18	24	24	NUM
ejpam-6266	624	19	for	for	ADP
ejpam-6266	624	20	some	some	DET
ejpam-6266	624	21	continuous	continuous	ADJ
ejpam-6266	624	22	nonnegative	nonnegative	ADJ
ejpam-6266	624	23	function	function	NOUN
ejpam-6266	624	24	g	g	NOUN
ejpam-6266	624	25	and	and	CCONJ
ejpam-6266	624	26	µ	µ	PRON
ejpam-6266	624	27	∈	∈	PROPN
ejpam-6266	624	28	l1[0	l1[0	PROPN
ejpam-6266	624	29	,	,	PUNCT
ejpam-6266	624	30	1	1	NUM
ejpam-6266	624	31	]	]	PUNCT
ejpam-6266	624	32	.	.	PUNCT
ejpam-6266	625	1	then	then	ADV
ejpam-6266	625	2	,	,	PUNCT
ejpam-6266	625	3	‖f	‖f	ADP
ejpam-6266	625	4	(	(	PUNCT
ejpam-6266	625	5	u)‖ḣσ	u)‖ḣσ	NOUN
ejpam-6266	625	6	r	r	NOUN
ejpam-6266	625	7	.	.	PUNCT
ejpam-6266	626	1	‖g(u)‖lr1‖u‖ḣσ	‖g(u)‖lr1‖u‖ḣσ	NOUN
ejpam-6266	626	2	r2	r2	PROPN
ejpam-6266	626	3	,	,	PUNCT
ejpam-6266	626	4	for	for	ADP
ejpam-6266	626	5	any	any	DET
ejpam-6266	626	6	u	u	PROPN
ejpam-6266	626	7	∈	∈	PROPN
ejpam-6266	626	8	ḣσ	ḣσ	NOUN
ejpam-6266	626	9	r2	r2	NOUN
ejpam-6266	626	10	such	such	ADJ
ejpam-6266	626	11	that	that	SCONJ
ejpam-6266	626	12	g(u	g(u	PROPN
ejpam-6266	626	13	)	)	PUNCT
ejpam-6266	626	14	∈	∈	PROPN
ejpam-6266	626	15	lr1	lr1	NOUN
ejpam-6266	626	16	,	,	PUNCT
ejpam-6266	626	17	provided	provide	VERB
ejpam-6266	626	18	that	that	SCONJ
ejpam-6266	626	19	1	1	NUM
ejpam-6266	626	20	r	r	NOUN
ejpam-6266	626	21	=	=	SYM
ejpam-6266	626	22	1	1	NUM
ejpam-6266	626	23	r1	r1	NOUN
ejpam-6266	626	24	+	+	CCONJ
ejpam-6266	626	25	1	1	NUM
ejpam-6266	626	26	r2	r2	NOUN
ejpam-6266	626	27	.	.	PUNCT
ejpam-6266	627	1	in	in	ADP
ejpam-6266	627	2	particular	particular	ADJ
ejpam-6266	627	3	,	,	PUNCT
ejpam-6266	627	4	to	to	PART
ejpam-6266	627	5	estimate	estimate	VERB
ejpam-6266	627	6	norms	norm	NOUN
ejpam-6266	627	7	like	like	ADP
ejpam-6266	627	8	‖|u|p‖ḣs−1	‖|u|p‖ḣs−1	ADJ
ejpam-6266	627	9	r	r	NOUN
ejpam-6266	627	10	or	or	CCONJ
ejpam-6266	627	11	‖±u|u|p−1‖ḣs−1	‖±u|u|p−1‖ḣs−1	NOUN
ejpam-6266	627	12	r	r	NOUN
ejpam-6266	627	13	we	we	PRON
ejpam-6266	627	14	use	use	VERB
ejpam-6266	627	15	the	the	DET
ejpam-6266	627	16	fractional	fractional	ADJ
ejpam-6266	627	17	chain	chain	NOUN
ejpam-6266	627	18	rule	rule	NOUN
ejpam-6266	627	19	and	and	CCONJ
ejpam-6266	627	20	the	the	DET
ejpam-6266	627	21	gagliardo	gagliardo	NOUN
ejpam-6266	627	22	-	-	PUNCT
ejpam-6266	627	23	nirenberg	nirenberg	PROPN
ejpam-6266	627	24	inequality	inequality	NOUN
ejpam-6266	627	25	.	.	PUNCT
ejpam-6266	628	1	in	in	ADP
ejpam-6266	628	2	this	this	DET
ejpam-6266	628	3	way	way	NOUN
ejpam-6266	628	4	we	we	PRON
ejpam-6266	628	5	may	may	AUX
ejpam-6266	628	6	may	may	AUX
ejpam-6266	628	7	conclude	conclude	VERB
ejpam-6266	628	8	at	at	ADP
ejpam-6266	628	9	first	first	ADV
ejpam-6266	628	10	for	for	ADP
ejpam-6266	628	11	s	s	PROPN
ejpam-6266	628	12	∈	∈	PROPN
ejpam-6266	628	13	(	(	PUNCT
ejpam-6266	628	14	1	1	NUM
ejpam-6266	628	15	,	,	PUNCT
ejpam-6266	628	16	2	2	NUM
ejpam-6266	628	17	)	)	PUNCT
ejpam-6266	628	18	and	and	CCONJ
ejpam-6266	628	19	then	then	ADV
ejpam-6266	628	20	by	by	ADP
ejpam-6266	628	21	a	a	DET
ejpam-6266	628	22	straight	straight	ADJ
ejpam-6266	628	23	-	-	PUNCT
ejpam-6266	628	24	forward	forward	NOUN
ejpam-6266	628	25	step	step	NOUN
ejpam-6266	628	26	to	to	ADP
ejpam-6266	628	27	s	s	PRON
ejpam-6266	628	28	≥	≥	NUM
ejpam-6266	628	29	2	2	NUM
ejpam-6266	628	30	the	the	DET
ejpam-6266	628	31	estimate	estimate	NOUN
ejpam-6266	628	32	‖	‖	PROPN
ejpam-6266	628	33	±	±	NOUN
ejpam-6266	629	1	u|u|p−1‖ḣs−1	u|u|p−1‖ḣs−1	PROPN
ejpam-6266	629	2	r	r	NOUN
ejpam-6266	629	3	+	+	CCONJ
ejpam-6266	629	4	‖|u|p‖ḣs−1	‖|u|p‖ḣs−1	ADJ
ejpam-6266	629	5	r	r	NOUN
ejpam-6266	629	6	.	.	PUNCT
ejpam-6266	630	1	‖u‖p−1	‖u‖p−1	VERB
ejpam-6266	631	1	lq1	lq1	PROPN
ejpam-6266	631	2	‖|d|s−1u‖lq2	‖|d|s−1u‖lq2	NUM
ejpam-6266	631	3	,	,	PUNCT
ejpam-6266	631	4	(	(	PUNCT
ejpam-6266	631	5	110	110	NUM
ejpam-6266	631	6	)	)	PUNCT
ejpam-6266	631	7	where	where	SCONJ
ejpam-6266	631	8	p−	p−	NOUN
ejpam-6266	631	9	1	1	NUM
ejpam-6266	631	10	q1	q1	NOUN
ejpam-6266	631	11	+	+	CCONJ
ejpam-6266	631	12	1	1	NUM
ejpam-6266	631	13	q2	q2	NOUN
ejpam-6266	631	14	=	=	SYM
ejpam-6266	631	15	1	1	NUM
ejpam-6266	631	16	r	r	NOUN
ejpam-6266	631	17	,	,	PUNCT
ejpam-6266	631	18	s	s	NOUN
ejpam-6266	631	19	>	>	X
ejpam-6266	631	20	1	1	NUM
ejpam-6266	631	21	.	.	X
ejpam-6266	632	1	5.4.4	5.4.4	NUM
ejpam-6266	632	2	.	.	PUNCT
ejpam-6266	632	3	fractional	fractional	ADJ
ejpam-6266	632	4	powers	power	NOUN
ejpam-6266	632	5	the	the	DET
ejpam-6266	632	6	following	follow	VERB
ejpam-6266	632	7	tool	tool	NOUN
ejpam-6266	632	8	is	be	AUX
ejpam-6266	632	9	useful	useful	ADJ
ejpam-6266	632	10	to	to	PART
ejpam-6266	632	11	estimate	estimate	VERB
ejpam-6266	632	12	the	the	DET
ejpam-6266	632	13	p	p	NOUN
ejpam-6266	632	14	-	-	PUNCT
ejpam-6266	632	15	power	power	NOUN
ejpam-6266	632	16	of	of	ADP
ejpam-6266	632	17	a	a	DET
ejpam-6266	632	18	given	give	VERB
ejpam-6266	632	19	function	function	NOUN
ejpam-6266	632	20	and	and	CCONJ
ejpam-6266	632	21	the	the	DET
ejpam-6266	632	22	product	product	NOUN
ejpam-6266	632	23	of	of	ADP
ejpam-6266	632	24	two	two	NUM
ejpam-6266	632	25	functions	function	NOUN
ejpam-6266	632	26	in	in	ADP
ejpam-6266	632	27	hs(rn	hs(rn	NOUN
ejpam-6266	632	28	)	)	PUNCT
ejpam-6266	632	29	.	.	PUNCT
ejpam-6266	633	1	this	this	DET
ejpam-6266	633	2	tool	tool	NOUN
ejpam-6266	633	3	is	be	AUX
ejpam-6266	633	4	meaningful	meaningful	ADJ
ejpam-6266	633	5	in	in	ADP
ejpam-6266	633	6	the	the	DET
ejpam-6266	633	7	case	case	NOUN
ejpam-6266	633	8	in	in	ADP
ejpam-6266	633	9	which	which	PRON
ejpam-6266	633	10	we	we	PRON
ejpam-6266	633	11	have	have	VERB
ejpam-6266	633	12	the	the	DET
ejpam-6266	633	13	embedding	embed	VERB
ejpam-6266	633	14	l∞(rn	l∞(rn	PROPN
ejpam-6266	633	15	)	)	PUNCT
ejpam-6266	634	1	↪	↪	PROPN
ejpam-6266	634	2	→	→	SYM
ejpam-6266	634	3	hs	hs	PROPN
ejpam-6266	634	4	r	r	PROPN
ejpam-6266	634	5	(	(	PUNCT
ejpam-6266	634	6	rn	rn	NOUN
ejpam-6266	634	7	)	)	PUNCT
ejpam-6266	634	8	,	,	PUNCT
ejpam-6266	634	9	that	that	ADV
ejpam-6266	634	10	is	is	ADV
ejpam-6266	634	11	,	,	PUNCT
ejpam-6266	634	12	when	when	SCONJ
ejpam-6266	634	13	s	s	VERB
ejpam-6266	634	14	>	>	X
ejpam-6266	634	15	n	n	PRON
ejpam-6266	634	16	r	r	NOUN
ejpam-6266	634	17	.	.	PUNCT
ejpam-6266	635	1	proposition	proposition	NOUN
ejpam-6266	635	2	5	5	NUM
ejpam-6266	635	3	.	.	PUNCT
ejpam-6266	636	1	[	[	X
ejpam-6266	636	2	11	11	NUM
ejpam-6266	636	3	,	,	PUNCT
ejpam-6266	636	4	14	14	NUM
ejpam-6266	636	5	,	,	PUNCT
ejpam-6266	636	6	15	15	NUM
ejpam-6266	636	7	]	]	PUNCT
ejpam-6266	636	8	let	let	VERB
ejpam-6266	636	9	r	r	NOUN
ejpam-6266	636	10	∈	∈	PROPN
ejpam-6266	636	11	(	(	PUNCT
ejpam-6266	636	12	1,∞	1,∞	NUM
ejpam-6266	636	13	)	)	PUNCT
ejpam-6266	636	14	,	,	PUNCT
ejpam-6266	636	15	p	p	X
ejpam-6266	636	16	>	>	X
ejpam-6266	636	17	1	1	NUM
ejpam-6266	636	18	and	and	CCONJ
ejpam-6266	636	19	s	s	PROPN
ejpam-6266	636	20	∈	∈	PROPN
ejpam-6266	636	21	(	(	PUNCT
ejpam-6266	636	22	0	0	NUM
ejpam-6266	636	23	,	,	PUNCT
ejpam-6266	636	24	p	p	NOUN
ejpam-6266	636	25	)	)	PUNCT
ejpam-6266	636	26	.	.	PUNCT
ejpam-6266	637	1	let	let	VERB
ejpam-6266	637	2	f	f	PROPN
ejpam-6266	637	3	(	(	PUNCT
ejpam-6266	637	4	u	u	NOUN
ejpam-6266	637	5	)	)	PUNCT
ejpam-6266	637	6	denote	denote	VERB
ejpam-6266	637	7	one	one	NUM
ejpam-6266	637	8	of	of	ADP
ejpam-6266	637	9	the	the	DET
ejpam-6266	637	10	functions	function	NOUN
ejpam-6266	637	11	|u|p	|u|p	PROPN
ejpam-6266	637	12	or	or	CCONJ
ejpam-6266	637	13	±u|u|p−1	±u|u|p−1	NOUN
ejpam-6266	637	14	.	.	PUNCT
ejpam-6266	638	1	then	then	ADV
ejpam-6266	638	2	,	,	PUNCT
ejpam-6266	638	3	it	it	PRON
ejpam-6266	638	4	holds	hold	VERB
ejpam-6266	638	5	the	the	DET
ejpam-6266	638	6	following	follow	VERB
ejpam-6266	638	7	inequality	inequality	NOUN
ejpam-6266	638	8	:	:	PUNCT
ejpam-6266	638	9	‖f	‖f	ADP
ejpam-6266	638	10	(	(	PUNCT
ejpam-6266	638	11	u)‖hs	u)‖hs	PROPN
ejpam-6266	638	12	r	r	NOUN
ejpam-6266	638	13	.	.	PUNCT
ejpam-6266	639	1	‖u‖hs	‖u‖hs	INTJ
ejpam-6266	640	1	r	r	NOUN
ejpam-6266	640	2	‖u‖p−1	‖u‖p−1	NOUN
ejpam-6266	640	3	l∞	l∞	NOUN
ejpam-6266	640	4	for	for	ADP
ejpam-6266	640	5	any	any	DET
ejpam-6266	640	6	u	u	PROPN
ejpam-6266	640	7	∈	∈	PROPN
ejpam-6266	640	8	hs	hs	INTJ
ejpam-6266	640	9	r	r	PROPN
ejpam-6266	640	10	(	(	PUNCT
ejpam-6266	640	11	rn	rn	NOUN
ejpam-6266	640	12	)	)	PUNCT
ejpam-6266	640	13	∩	∩	ADJ
ejpam-6266	640	14	l∞(rn	l∞(rn	PROPN
ejpam-6266	640	15	)	)	PUNCT
ejpam-6266	640	16	.	.	PUNCT
ejpam-6266	641	1	the	the	DET
ejpam-6266	641	2	next	next	ADJ
ejpam-6266	641	3	result	result	NOUN
ejpam-6266	641	4	is	be	AUX
ejpam-6266	641	5	a	a	DET
ejpam-6266	641	6	direct	direct	ADJ
ejpam-6266	641	7	consequence	consequence	NOUN
ejpam-6266	641	8	of	of	ADP
ejpam-6266	641	9	the	the	DET
ejpam-6266	641	10	previous	previous	ADJ
ejpam-6266	641	11	one	one	NUM
ejpam-6266	641	12	for	for	ADP
ejpam-6266	641	13	the	the	DET
ejpam-6266	641	14	case	case	NOUN
ejpam-6266	641	15	of	of	ADP
ejpam-6266	641	16	homogeneous	homogeneous	ADJ
ejpam-6266	641	17	sobolev	sobolev	NOUN
ejpam-6266	641	18	spaces	space	NOUN
ejpam-6266	641	19	.	.	PUNCT
ejpam-6266	642	1	corollary	corollary	ADJ
ejpam-6266	642	2	5	5	NUM
ejpam-6266	642	3	.	.	PUNCT
ejpam-6266	643	1	let	let	VERB
ejpam-6266	643	2	r	r	NOUN
ejpam-6266	643	3	∈	∈	PROPN
ejpam-6266	643	4	(	(	PUNCT
ejpam-6266	643	5	1,∞	1,∞	NUM
ejpam-6266	643	6	)	)	PUNCT
ejpam-6266	643	7	,	,	PUNCT
ejpam-6266	643	8	p	p	X
ejpam-6266	643	9	>	>	X
ejpam-6266	643	10	1	1	NUM
ejpam-6266	643	11	and	and	CCONJ
ejpam-6266	643	12	s	s	PROPN
ejpam-6266	643	13	∈	∈	PROPN
ejpam-6266	643	14	(	(	PUNCT
ejpam-6266	643	15	0	0	NUM
ejpam-6266	643	16	,	,	PUNCT
ejpam-6266	643	17	p	p	NOUN
ejpam-6266	643	18	)	)	PUNCT
ejpam-6266	643	19	.	.	PUNCT
ejpam-6266	644	1	let	let	VERB
ejpam-6266	644	2	f	f	PROPN
ejpam-6266	644	3	(	(	PUNCT
ejpam-6266	644	4	u	u	NOUN
ejpam-6266	644	5	)	)	PUNCT
ejpam-6266	644	6	denote	denote	VERB
ejpam-6266	644	7	one	one	NUM
ejpam-6266	644	8	of	of	ADP
ejpam-6266	644	9	the	the	DET
ejpam-6266	644	10	functions	function	NOUN
ejpam-6266	644	11	|u|p	|u|p	PROPN
ejpam-6266	644	12	or	or	CCONJ
ejpam-6266	644	13	±u|u|p−1	±u|u|p−1	NOUN
ejpam-6266	644	14	.	.	PUNCT
ejpam-6266	645	1	then	then	ADV
ejpam-6266	645	2	,	,	PUNCT
ejpam-6266	645	3	it	it	PRON
ejpam-6266	645	4	holds	hold	VERB
ejpam-6266	645	5	the	the	DET
ejpam-6266	645	6	following	follow	VERB
ejpam-6266	645	7	inequality	inequality	NOUN
ejpam-6266	645	8	:	:	PUNCT
ejpam-6266	645	9	‖f	‖f	ADP
ejpam-6266	645	10	(	(	PUNCT
ejpam-6266	645	11	u)‖ḣs	u)‖ḣs	ADP
ejpam-6266	645	12	r	r	NOUN
ejpam-6266	645	13	.	.	PUNCT
ejpam-6266	646	1	‖u‖ḣs	‖u‖ḣs	NOUN
ejpam-6266	646	2	r	r	NOUN
ejpam-6266	646	3	‖u‖p−1	‖u‖p−1	NOUN
ejpam-6266	646	4	l∞	l∞	NOUN
ejpam-6266	646	5	for	for	ADP
ejpam-6266	646	6	any	any	DET
ejpam-6266	646	7	u	u	PROPN
ejpam-6266	646	8	∈	∈	PROPN
ejpam-6266	646	9	ḣs	ḣs	PROPN
ejpam-6266	646	10	r	r	X
ejpam-6266	646	11	(	(	PUNCT
ejpam-6266	646	12	rn	rn	NOUN
ejpam-6266	646	13	)	)	PUNCT
ejpam-6266	646	14	∩	∩	ADJ
ejpam-6266	646	15	l∞(rn	l∞(rn	PROPN
ejpam-6266	646	16	)	)	PUNCT
ejpam-6266	646	17	.	.	PUNCT