id	sid	tid	token	lemma	pos
ejpam-189	1	1	8_189_zhao.dvi	8_189_zhao.dvi	NUM
ejpam-189	1	2	european	european	ADJ
ejpam-189	1	3	journal	journal	NOUN
ejpam-189	1	4	of	of	ADP
ejpam-189	1	5	pure	pure	ADJ
ejpam-189	1	6	and	and	CCONJ
ejpam-189	1	7	applied	apply	VERB
ejpam-189	1	8	mathematics	mathematic	NOUN
ejpam-189	1	9	vol	vol	NOUN
ejpam-189	1	10	.	.	PUNCT
ejpam-189	2	1	3	3	NUM
ejpam-189	2	2	,	,	PUNCT
ejpam-189	2	3	no	no	INTJ
ejpam-189	2	4	.	.	NOUN
ejpam-189	2	5	2	2	NUM
ejpam-189	2	6	,	,	PUNCT
ejpam-189	2	7	2010	2010	NUM
ejpam-189	2	8	,	,	PUNCT
ejpam-189	2	9	227	227	NUM
ejpam-189	2	10	-	-	SYM
ejpam-189	2	11	234	234	NUM
ejpam-189	2	12	issn	issn	PROPN
ejpam-189	2	13	1307	1307	NUM
ejpam-189	2	14	-	-	SYM
ejpam-189	2	15	5543	5543	NUM
ejpam-189	2	16	–	–	PUNCT
ejpam-189	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-189	2	18	local	local	ADJ
ejpam-189	2	19	solvability	solvability	NOUN
ejpam-189	2	20	for	for	ADP
ejpam-189	2	21	the	the	DET
ejpam-189	2	22	2	2	NUM
ejpam-189	2	23	-	-	PUNCT
ejpam-189	2	24	coupled	couple	VERB
ejpam-189	2	25	system	system	NOUN
ejpam-189	2	26	of	of	ADP
ejpam-189	2	27	nonlinear	nonlinear	ADJ
ejpam-189	2	28	schrödinger	schrödinger	ADJ
ejpam-189	2	29	equations	equation	NOUN
ejpam-189	2	30	in	in	ADP
ejpam-189	2	31	a	a	DET
ejpam-189	2	32	banach	banach	NOUN
ejpam-189	2	33	algebra	algebra	NOUN
ejpam-189	2	34	e0	e0	PROPN
ejpam-189	2	35	2,1	2,1	NUM
ejpam-189	2	36	zaile	zaile	NOUN
ejpam-189	2	37	he	he	PRON
ejpam-189	2	38	and	and	CCONJ
ejpam-189	2	39	xiangqing	xiangqe	VERB
ejpam-189	2	40	zhao∗	zhao∗	PROPN
ejpam-189	2	41	school	school	NOUN
ejpam-189	2	42	of	of	ADP
ejpam-189	2	43	mathematics	mathematics	PROPN
ejpam-189	2	44	physics	physics	PROPN
ejpam-189	2	45	&	&	CCONJ
ejpam-189	2	46	information	information	PROPN
ejpam-189	2	47	science	science	PROPN
ejpam-189	2	48	,	,	PUNCT
ejpam-189	2	49	zhejiang	zhejiang	PROPN
ejpam-189	2	50	ocean	ocean	PROPN
ejpam-189	2	51	university	university	PROPN
ejpam-189	2	52	,	,	PUNCT
ejpam-189	2	53	zhoushan	zhoushan	PROPN
ejpam-189	2	54	,	,	PUNCT
ejpam-189	2	55	zhejiang	zhejiang	PROPN
ejpam-189	2	56	316000	316000	NUM
ejpam-189	2	57	.	.	PUNCT
ejpam-189	3	1	p.	p.	PROPN
ejpam-189	3	2	r.	r.	PROPN
ejpam-189	3	3	china	china	PROPN
ejpam-189	3	4	abstract	abstract	PROPN
ejpam-189	3	5	.	.	PUNCT
ejpam-189	4	1	this	this	DET
ejpam-189	4	2	paper	paper	NOUN
ejpam-189	4	3	is	be	AUX
ejpam-189	4	4	concerned	concern	VERB
ejpam-189	4	5	with	with	ADP
ejpam-189	4	6	initial	initial	ADJ
ejpam-189	4	7	value	value	NOUN
ejpam-189	4	8	problem	problem	NOUN
ejpam-189	4	9	of	of	ADP
ejpam-189	4	10	the	the	DET
ejpam-189	4	11	nonlinear	nonlinear	NOUN
ejpam-189	4	12	coupled	couple	VERB
ejpam-189	4	13	schrödinger	schrödinger	ADJ
ejpam-189	4	14	equations	equation	NOUN
ejpam-189	4	15	.	.	PUNCT
ejpam-189	5	1	we	we	PRON
ejpam-189	5	2	study	study	VERB
ejpam-189	5	3	local	local	ADJ
ejpam-189	5	4	well	well	ADJ
ejpam-189	5	5	posedness	posedness	NOUN
ejpam-189	5	6	in	in	ADP
ejpam-189	5	7	the	the	DET
ejpam-189	5	8	banach	banach	NOUN
ejpam-189	5	9	algebra	algebra	NOUN
ejpam-189	5	10	e0	e0	PROPN
ejpam-189	5	11	2,1	2,1	NUM
ejpam-189	5	12	(	(	PUNCT
ejpam-189	5	13	rn	rn	NOUN
ejpam-189	5	14	)	)	PUNCT
ejpam-189	5	15	which	which	PRON
ejpam-189	5	16	is	be	AUX
ejpam-189	5	17	the	the	DET
ejpam-189	5	18	extension	extension	NOUN
ejpam-189	5	19	of	of	ADP
ejpam-189	5	20	h	h	NOUN
ejpam-189	5	21	s(rn	s(rn	PROPN
ejpam-189	5	22	)	)	PUNCT
ejpam-189	5	23	when	when	SCONJ
ejpam-189	5	24	s	s	VERB
ejpam-189	5	25	≥	≥	NOUN
ejpam-189	5	26	n	n	PRON
ejpam-189	5	27	2	2	NUM
ejpam-189	5	28	.	.	PUNCT
ejpam-189	6	1	the	the	DET
ejpam-189	6	2	method	method	NOUN
ejpam-189	6	3	we	we	PRON
ejpam-189	6	4	use	use	VERB
ejpam-189	6	5	is	be	AUX
ejpam-189	6	6	similar	similar	ADJ
ejpam-189	6	7	to	to	ADP
ejpam-189	6	8	the	the	DET
ejpam-189	6	9	method	method	NOUN
ejpam-189	6	10	of	of	ADP
ejpam-189	6	11	semigroup	semigroup	PROPN
ejpam-189	6	12	.	.	PUNCT
ejpam-189	6	13	2000	2000	NUM
ejpam-189	6	14	mathematics	mathematic	NOUN
ejpam-189	6	15	subject	subject	NOUN
ejpam-189	6	16	classifications	classification	NOUN
ejpam-189	6	17	:	:	PUNCT
ejpam-189	6	18	35q53	35q53	NUM
ejpam-189	6	19	,	,	PUNCT
ejpam-189	6	20	35q35	35q35	NUM
ejpam-189	6	21	.	.	PUNCT
ejpam-189	7	1	key	key	ADJ
ejpam-189	7	2	words	word	NOUN
ejpam-189	7	3	and	and	CCONJ
ejpam-189	7	4	phrases	phrase	NOUN
ejpam-189	7	5	:	:	PUNCT
ejpam-189	7	6	nonlinear	nonlinear	ADJ
ejpam-189	7	7	,	,	PUNCT
ejpam-189	7	8	coupled	couple	VERB
ejpam-189	7	9	schrödinger	schrödinger	ADJ
ejpam-189	7	10	equations	equation	NOUN
ejpam-189	7	11	,	,	PUNCT
ejpam-189	7	12	banach	banach	NOUN
ejpam-189	7	13	algebra	algebra	NOUN
ejpam-189	7	14	,	,	PUNCT
ejpam-189	7	15	local	local	ADJ
ejpam-189	7	16	wellposedness	wellposedness	NOUN
ejpam-189	7	17	1	1	NUM
ejpam-189	7	18	.	.	PUNCT
ejpam-189	8	1	introduction	introduction	NOUN
ejpam-189	8	2	it	it	PRON
ejpam-189	8	3	is	be	AUX
ejpam-189	8	4	well	well	ADV
ejpam-189	8	5	-	-	PUNCT
ejpam-189	8	6	known	know	VERB
ejpam-189	8	7	that	that	SCONJ
ejpam-189	8	8	hs(rn	hs(rn	NOUN
ejpam-189	8	9	)	)	PUNCT
ejpam-189	8	10	is	be	AUX
ejpam-189	8	11	an	an	DET
ejpam-189	8	12	algebra	algebra	NOUN
ejpam-189	8	13	when	when	SCONJ
ejpam-189	8	14	s	s	VERB
ejpam-189	8	15	>	>	X
ejpam-189	8	16	n	n	PROPN
ejpam-189	8	17	2	2	NUM
ejpam-189	8	18	and	and	CCONJ
ejpam-189	8	19	the	the	DET
ejpam-189	8	20	schrödinger	schrödinger	ADJ
ejpam-189	8	21	operator	operator	NOUN
ejpam-189	8	22	generate	generate	VERB
ejpam-189	8	23	an	an	DET
ejpam-189	8	24	unitary	unitary	ADJ
ejpam-189	8	25	group	group	NOUN
ejpam-189	8	26	in	in	ADP
ejpam-189	8	27	hs(rn	hs(rn	PROPN
ejpam-189	8	28	)	)	PUNCT
ejpam-189	8	29	.	.	PUNCT
ejpam-189	9	1	the	the	DET
ejpam-189	9	2	well	well	ADV
ejpam-189	9	3	-	-	PUNCT
ejpam-189	9	4	posedness	posedness	NOUN
ejpam-189	9	5	in	in	ADP
ejpam-189	9	6	hs(s	hs(s	PUNCT
ejpam-189	9	7	≥	≥	NOUN
ejpam-189	9	8	n	n	PRON
ejpam-189	9	9	2	2	NUM
ejpam-189	9	10	)	)	PUNCT
ejpam-189	9	11	for	for	ADP
ejpam-189	9	12	the	the	DET
ejpam-189	9	13	cauchy	cauchy	ADJ
ejpam-189	9	14	problem	problem	NOUN
ejpam-189	9	15	of	of	ADP
ejpam-189	9	16	the	the	DET
ejpam-189	9	17	cubic	cubic	ADJ
ejpam-189	9	18	semi	semi	ADJ
ejpam-189	9	19	-	-	ADJ
ejpam-189	9	20	linear	linear	ADJ
ejpam-189	9	21	schrödinger	schrödinger	ADJ
ejpam-189	9	22	equation	equation	NOUN
ejpam-189	9	23	iut	iut	PROPN
ejpam-189	10	1	+	+	PROPN
ejpam-189	10	2	∆u=	∆u=	PROPN
ejpam-189	10	3	a|u|2u	a|u|2u	PROPN
ejpam-189	10	4	,	,	PUNCT
ejpam-189	10	5	x	x	PROPN
ejpam-189	10	6	∈	∈	PROPN
ejpam-189	10	7	rn	rn	PROPN
ejpam-189	10	8	,	,	PUNCT
ejpam-189	10	9	t	t	PROPN
ejpam-189	10	10	∈	∈	PROPN
ejpam-189	10	11	r.	r.	PROPN
ejpam-189	10	12	were	be	AUX
ejpam-189	10	13	treated	treat	VERB
ejpam-189	10	14	by	by	ADP
ejpam-189	10	15	using	use	VERB
ejpam-189	10	16	the	the	DET
ejpam-189	10	17	method	method	NOUN
ejpam-189	10	18	of	of	ADP
ejpam-189	10	19	semigroup	semigroup	PROPN
ejpam-189	10	20	[	[	X
ejpam-189	10	21	we	we	PRON
ejpam-189	10	22	refer	refer	VERB
ejpam-189	10	23	to	to	ADP
ejpam-189	10	24	6	6	NUM
ejpam-189	10	25	]	]	PUNCT
ejpam-189	10	26	.	.	PUNCT
ejpam-189	11	1	recently	recently	ADV
ejpam-189	11	2	,	,	PUNCT
ejpam-189	11	3	wang	wang	PROPN
ejpam-189	11	4	et	et	PROPN
ejpam-189	11	5	al	al	PROPN
ejpam-189	11	6	in	in	ADP
ejpam-189	11	7	[	[	X
ejpam-189	11	8	10	10	NUM
ejpam-189	11	9	]	]	PUNCT
ejpam-189	11	10	introduce	introduce	VERB
ejpam-189	11	11	a	a	DET
ejpam-189	11	12	new	new	ADJ
ejpam-189	11	13	banach	banach	NOUN
ejpam-189	11	14	algebra	algebra	NOUN
ejpam-189	11	15	e0	e0	PROPN
ejpam-189	11	16	2,1(r	2,1(r	PROPN
ejpam-189	11	17	n	n	CCONJ
ejpam-189	11	18	)	)	PUNCT
ejpam-189	11	19	which	which	PRON
ejpam-189	11	20	is	be	AUX
ejpam-189	11	21	the	the	DET
ejpam-189	11	22	extension	extension	NOUN
ejpam-189	11	23	of	of	ADP
ejpam-189	11	24	hs(rn	hs(rn	NOUN
ejpam-189	11	25	)	)	PUNCT
ejpam-189	11	26	when	when	SCONJ
ejpam-189	11	27	s	s	VERB
ejpam-189	11	28	≥	≥	NOUN
ejpam-189	11	29	n	n	CCONJ
ejpam-189	11	30	2	2	NUM
ejpam-189	11	31	and	and	CCONJ
ejpam-189	11	32	investigated	investigate	VERB
ejpam-189	11	33	the	the	DET
ejpam-189	11	34	cauchy	cauchy	ADJ
ejpam-189	11	35	problem	problem	NOUN
ejpam-189	11	36	of	of	ADP
ejpam-189	11	37	semi	semi	ADJ
ejpam-189	11	38	-	-	ADJ
ejpam-189	11	39	linear	linear	ADJ
ejpam-189	11	40	schrödinger	schrödinger	ADJ
ejpam-189	11	41	equation	equation	NOUN
ejpam-189	11	42	with	with	ADP
ejpam-189	11	43	nonlinear	nonlinear	ADJ
ejpam-189	11	44	term	term	NOUN
ejpam-189	11	45	|u|2ku	|u|2ku	ADJ
ejpam-189	11	46	,	,	PUNCT
ejpam-189	11	47	k	k	PROPN
ejpam-189	11	48	∈	∈	PROPN
ejpam-189	11	49	n	n	ADV
ejpam-189	11	50	.	.	PUNCT
ejpam-189	12	1	we	we	PRON
ejpam-189	12	2	shall	shall	AUX
ejpam-189	12	3	study	study	VERB
ejpam-189	12	4	a	a	DET
ejpam-189	12	5	coupled	couple	VERB
ejpam-189	12	6	system	system	NOUN
ejpam-189	12	7	by	by	ADP
ejpam-189	12	8	wang	wang	PROPN
ejpam-189	12	9	’s	’s	PART
ejpam-189	12	10	approach	approach	NOUN
ejpam-189	12	11	in	in	ADP
ejpam-189	12	12	this	this	DET
ejpam-189	12	13	paper	paper	NOUN
ejpam-189	12	14	.	.	PUNCT
ejpam-189	13	1	as	as	ADP
ejpam-189	13	2	a	a	DET
ejpam-189	13	3	natural	natural	ADJ
ejpam-189	13	4	extension	extension	NOUN
ejpam-189	13	5	of	of	ADP
ejpam-189	13	6	the	the	DET
ejpam-189	13	7	single	single	ADJ
ejpam-189	13	8	cubic	cubic	ADJ
ejpam-189	13	9	nonlinear	nonlinear	ADJ
ejpam-189	13	10	schrödinger	schrödinger	ADJ
ejpam-189	13	11	equation	equation	NOUN
ejpam-189	13	12	,	,	PUNCT
ejpam-189	13	13	the	the	DET
ejpam-189	13	14	2	2	NUM
ejpam-189	13	15	-	-	PUNCT
ejpam-189	13	16	coupled	couple	VERB
ejpam-189	13	17	nonlinear	nonlinear	ADJ
ejpam-189	13	18	schrödinger	schrödinger	ADJ
ejpam-189	13	19	equations	equation	NOUN
ejpam-189	13	20	:	:	PUNCT
ejpam-189	13	21	¨	¨	NOUN
ejpam-189	13	22	iut	iut	PROPN
ejpam-189	13	23	+	+	PROPN
ejpam-189	13	24	∆u=	∆u=	PROPN
ejpam-189	13	25	a|u|2u+	a|u|2u+	PROPN
ejpam-189	13	26	|v|2u	|v|2u	PROPN
ejpam-189	13	27	,	,	PUNCT
ejpam-189	13	28	x	x	X
ejpam-189	13	29	∈	∈	PROPN
ejpam-189	13	30	r	r	NOUN
ejpam-189	13	31	,	,	PUNCT
ejpam-189	13	32	t	t	PROPN
ejpam-189	13	33	∈	∈	PROPN
ejpam-189	13	34	r	r	PROPN
ejpam-189	13	35	,	,	PUNCT
ejpam-189	13	36	ivt	ivt	PROPN
ejpam-189	14	1	+	+	NOUN
ejpam-189	14	2	∆v	∆v	NOUN
ejpam-189	14	3	=	=	SYM
ejpam-189	14	4	|u|2v	|u|2v	PROPN
ejpam-189	14	5	+	+	CCONJ
ejpam-189	14	6	a|v|2v	a|v|2v	PROPN
ejpam-189	14	7	,	,	PUNCT
ejpam-189	14	8	x	x	X
ejpam-189	14	9	∈	∈	PROPN
ejpam-189	14	10	r	r	NOUN
ejpam-189	14	11	,	,	PUNCT
ejpam-189	14	12	t	t	PROPN
ejpam-189	14	13	∈	∈	PROPN
ejpam-189	14	14	r	r	PROPN
ejpam-189	14	15	,	,	PUNCT
ejpam-189	14	16	(	(	PUNCT
ejpam-189	14	17	1	1	X
ejpam-189	14	18	)	)	PUNCT
ejpam-189	14	19	∗corresponding	∗corresponde	VERB
ejpam-189	14	20	author	author	NOUN
ejpam-189	14	21	.	.	PUNCT
ejpam-189	15	1	email	email	NOUN
ejpam-189	15	2	address	address	NOUN
ejpam-189	15	3	:	:	PUNCT
ejpam-189	15	4	zhao	zhao	NOUN
ejpam-189	15	5	-	-	PUNCT
ejpam-189	15	6	xiangqing	xiangqe	VERB
ejpam-189	15	7	�	�	PROPN
ejpam-189	15	8	163	163	NUM
ejpam-189	15	9	.	.	PUNCT
ejpam-189	16	1	om	om	PROPN
ejpam-189	16	2	(	(	PUNCT
ejpam-189	16	3	x.	x.	PROPN
ejpam-189	16	4	zhao	zhao	PROPN
ejpam-189	16	5	)	)	PUNCT
ejpam-189	16	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-189	17	1	227	227	NUM
ejpam-189	17	2	c	c	X
ejpam-189	17	3	©	©	PROPN
ejpam-189	17	4	2010	2010	NUM
ejpam-189	17	5	ejpam	ejpam	NOUN
ejpam-189	17	6	all	all	DET
ejpam-189	17	7	rights	right	NOUN
ejpam-189	17	8	reserved	reserve	VERB
ejpam-189	17	9	.	.	PUNCT
ejpam-189	18	1	z.	z.	PROPN
ejpam-189	18	2	he	he	PRON
ejpam-189	18	3	and	and	CCONJ
ejpam-189	18	4	x.	x.	NOUN
ejpam-189	18	5	zhao	zhao	PROPN
ejpam-189	18	6	/	/	SYM
ejpam-189	18	7	eur	eur	PROPN
ejpam-189	18	8	.	.	PUNCT
ejpam-189	19	1	j.	j.	PROPN
ejpam-189	19	2	pure	pure	PROPN
ejpam-189	19	3	appl	appl	PROPN
ejpam-189	19	4	.	.	PROPN
ejpam-189	19	5	math	math	PROPN
ejpam-189	19	6	,	,	PUNCT
ejpam-189	19	7	3	3	NUM
ejpam-189	19	8	(	(	PUNCT
ejpam-189	19	9	2010	2010	NUM
ejpam-189	19	10	)	)	PUNCT
ejpam-189	19	11	,	,	PUNCT
ejpam-189	19	12	227	227	NUM
ejpam-189	19	13	-	-	SYM
ejpam-189	19	14	234	234	NUM
ejpam-189	19	15	228	228	NUM
ejpam-189	19	16	have	have	VERB
ejpam-189	19	17	many	many	ADJ
ejpam-189	19	18	applications	application	NOUN
ejpam-189	19	19	including	include	VERB
ejpam-189	19	20	,	,	PUNCT
ejpam-189	19	21	for	for	ADP
ejpam-189	19	22	example	example	NOUN
ejpam-189	19	23	,	,	PUNCT
ejpam-189	19	24	nonlinear	nonlinear	ADJ
ejpam-189	19	25	optics	optic	NOUN
ejpam-189	19	26	[	[	X
ejpam-189	19	27	cf	cf	NOUN
ejpam-189	19	28	.	.	NOUN
ejpam-189	19	29	2	2	NUM
ejpam-189	19	30	,	,	PUNCT
ejpam-189	19	31	4	4	NUM
ejpam-189	19	32	,	,	PUNCT
ejpam-189	19	33	5	5	NUM
ejpam-189	19	34	,	,	PUNCT
ejpam-189	19	35	9	9	NUM
ejpam-189	19	36	]	]	PUNCT
ejpam-189	19	37	and	and	CCONJ
ejpam-189	19	38	geophysical	geophysical	ADJ
ejpam-189	19	39	fluid	fluid	NOUN
ejpam-189	19	40	dynamics	dynamic	NOUN
ejpam-189	19	41	[	[	X
ejpam-189	19	42	cf	cf	NOUN
ejpam-189	19	43	.	.	NOUN
ejpam-189	19	44	7	7	NUM
ejpam-189	19	45	,	,	PUNCT
ejpam-189	19	46	8	8	NUM
ejpam-189	19	47	]	]	PUNCT
ejpam-189	19	48	.	.	PUNCT
ejpam-189	20	1	in	in	ADP
ejpam-189	20	2	the	the	DET
ejpam-189	20	3	above	above	ADJ
ejpam-189	20	4	equations	equation	NOUN
ejpam-189	20	5	,	,	PUNCT
ejpam-189	20	6	a	a	DET
ejpam-189	20	7	∈	∈	PROPN
ejpam-189	20	8	r	r	NOUN
ejpam-189	20	9	,	,	PUNCT
ejpam-189	20	10	the	the	DET
ejpam-189	20	11	unknowns	unknown	NOUN
ejpam-189	20	12	u(x	u(x	PROPN
ejpam-189	20	13	,	,	PUNCT
ejpam-189	20	14	t	t	PROPN
ejpam-189	20	15	)	)	PUNCT
ejpam-189	20	16	,	,	PUNCT
ejpam-189	20	17	v(x	v(x	PROPN
ejpam-189	20	18	,	,	PUNCT
ejpam-189	20	19	t	t	PROPN
ejpam-189	20	20	)	)	PUNCT
ejpam-189	20	21	are	be	AUX
ejpam-189	20	22	the	the	DET
ejpam-189	20	23	envelopes	envelope	NOUN
ejpam-189	20	24	of	of	ADP
ejpam-189	20	25	wave	wave	NOUN
ejpam-189	20	26	packets	packet	NOUN
ejpam-189	20	27	in	in	ADP
ejpam-189	20	28	two	two	NUM
ejpam-189	20	29	different	different	ADJ
ejpam-189	20	30	degrees	degree	NOUN
ejpam-189	20	31	of	of	ADP
ejpam-189	20	32	freedom	freedom	NOUN
ejpam-189	20	33	of	of	ADP
ejpam-189	20	34	the	the	DET
ejpam-189	20	35	underlying	underlying	ADJ
ejpam-189	20	36	physical	physical	ADJ
ejpam-189	20	37	systems	system	NOUN
ejpam-189	20	38	which	which	PRON
ejpam-189	20	39	we	we	PRON
ejpam-189	20	40	shall	shall	AUX
ejpam-189	20	41	call	call	VERB
ejpam-189	20	42	’	'	PUNCT
ejpam-189	20	43	modes	mode	NOUN
ejpam-189	20	44	’	'	PUNCT
ejpam-189	20	45	.	.	PUNCT
ejpam-189	21	1	the	the	DET
ejpam-189	21	2	system	system	NOUN
ejpam-189	21	3	is	be	AUX
ejpam-189	21	4	derived	derive	VERB
ejpam-189	21	5	as	as	ADP
ejpam-189	21	6	an	an	DET
ejpam-189	21	7	approximation	approximation	NOUN
ejpam-189	21	8	to	to	ADP
ejpam-189	21	9	a	a	DET
ejpam-189	21	10	more	more	ADV
ejpam-189	21	11	complex	complex	ADJ
ejpam-189	21	12	set	set	NOUN
ejpam-189	21	13	of	of	ADP
ejpam-189	21	14	equations	equation	NOUN
ejpam-189	21	15	by	by	ADP
ejpam-189	21	16	singular	singular	ADJ
ejpam-189	21	17	perturbation	perturbation	NOUN
ejpam-189	21	18	theory	theory	NOUN
ejpam-189	21	19	.	.	PUNCT
ejpam-189	22	1	instead	instead	ADV
ejpam-189	22	2	of	of	ADP
ejpam-189	22	3	studying	study	VERB
ejpam-189	22	4	(	(	PUNCT
ejpam-189	22	5	1	1	NUM
ejpam-189	22	6	)	)	PUNCT
ejpam-189	22	7	,	,	PUNCT
ejpam-189	22	8	this	this	DET
ejpam-189	22	9	paper	paper	NOUN
ejpam-189	22	10	is	be	AUX
ejpam-189	22	11	concerned	concern	VERB
ejpam-189	22	12	with	with	ADP
ejpam-189	22	13	the	the	DET
ejpam-189	22	14	following	follow	VERB
ejpam-189	22	15	general	general	ADJ
ejpam-189	22	16	schrödinger	schrödinger	ADJ
ejpam-189	22	17	system	system	NOUN
ejpam-189	22	18	:	:	PUNCT
ejpam-189	22	19			PROPN
ejpam-189	22	20			PRON
ejpam-189	22	21			NOUN
ejpam-189	22	22	iut	iut	PROPN
ejpam-189	22	23	+	+	PROPN
ejpam-189	22	24	∆u=	∆u=	ADV
ejpam-189	22	25	a|u|αu+	a|u|αu+	PUNCT
ejpam-189	23	1	|v|αu	|v|αu	PROPN
ejpam-189	23	2	,	,	PUNCT
ejpam-189	23	3	x	x	PROPN
ejpam-189	23	4	∈	∈	PROPN
ejpam-189	23	5	rn	rn	PROPN
ejpam-189	23	6	,	,	PUNCT
ejpam-189	23	7	t	t	PROPN
ejpam-189	23	8	∈	∈	PROPN
ejpam-189	23	9	r	r	PROPN
ejpam-189	23	10	,	,	PUNCT
ejpam-189	23	11	ivt	ivt	PROPN
ejpam-189	24	1	+	+	NOUN
ejpam-189	24	2	∆v	∆v	NOUN
ejpam-189	24	3	=	=	SYM
ejpam-189	24	4	|u|αv	|u|αv	NOUN
ejpam-189	24	5	+	+	CCONJ
ejpam-189	24	6	a|v|αv	a|v|αv	NOUN
ejpam-189	24	7	,	,	PUNCT
ejpam-189	24	8	x	x	PROPN
ejpam-189	24	9	∈	∈	PROPN
ejpam-189	24	10	rn	rn	PROPN
ejpam-189	24	11	,	,	PUNCT
ejpam-189	24	12	t	t	PROPN
ejpam-189	24	13	∈	∈	PROPN
ejpam-189	24	14	r	r	PROPN
ejpam-189	24	15	,	,	PUNCT
ejpam-189	24	16	u(0	u(0	PROPN
ejpam-189	24	17	,	,	PUNCT
ejpam-189	24	18	x	x	NOUN
ejpam-189	24	19	)	)	PUNCT
ejpam-189	24	20	=	=	SYM
ejpam-189	24	21	φ(x	φ(x	NOUN
ejpam-189	24	22	)	)	PUNCT
ejpam-189	24	23	,	,	PUNCT
ejpam-189	24	24	x	x	PROPN
ejpam-189	24	25	∈	∈	PROPN
ejpam-189	24	26	rn	rn	PROPN
ejpam-189	24	27	,	,	PUNCT
ejpam-189	24	28	v(0	v(0	PROPN
ejpam-189	24	29	,	,	PUNCT
ejpam-189	24	30	x	x	NOUN
ejpam-189	24	31	)	)	PUNCT
ejpam-189	24	32	=	=	NOUN
ejpam-189	24	33	ψ(x	ψ(x	NOUN
ejpam-189	24	34	)	)	PUNCT
ejpam-189	24	35	,	,	PUNCT
ejpam-189	24	36	x	x	PROPN
ejpam-189	24	37	∈	∈	PROPN
ejpam-189	24	38	rn	rn	PROPN
ejpam-189	24	39	.	.	PROPN
ejpam-189	25	1	(	(	PUNCT
ejpam-189	25	2	2	2	X
ejpam-189	25	3	)	)	PUNCT
ejpam-189	25	4	as	as	ADP
ejpam-189	25	5	in	in	ADP
ejpam-189	25	6	[	[	X
ejpam-189	25	7	10	10	NUM
ejpam-189	25	8	]	]	PUNCT
ejpam-189	25	9	,	,	PUNCT
ejpam-189	25	10	for	for	ADP
ejpam-189	25	11	technical	technical	ADJ
ejpam-189	25	12	reason	reason	NOUN
ejpam-189	25	13	,	,	PUNCT
ejpam-189	25	14	the	the	DET
ejpam-189	25	15	restriction	restriction	NOUN
ejpam-189	25	16	α	α	NOUN
ejpam-189	25	17	=	=	SYM
ejpam-189	25	18	2k	2k	NUM
ejpam-189	25	19	,	,	PUNCT
ejpam-189	25	20	k	k	PROPN
ejpam-189	25	21	∈	∈	PROPN
ejpam-189	25	22	n	n	PRON
ejpam-189	25	23	or	or	CCONJ
ejpam-189	25	24	|u|α	|u|α	PROPN
ejpam-189	25	25	=	=	SYM
ejpam-189	25	26	uα	uα	PROPN
ejpam-189	25	27	(	(	PUNCT
ejpam-189	25	28	or	or	CCONJ
ejpam-189	25	29	ūα	ūα	PROPN
ejpam-189	25	30	)	)	PUNCT
ejpam-189	25	31	and	and	CCONJ
ejpam-189	25	32	|v|α	|v|α	PROPN
ejpam-189	25	33	=	=	SYM
ejpam-189	25	34	vα	vα	PROPN
ejpam-189	25	35	(	(	PUNCT
ejpam-189	25	36	or	or	CCONJ
ejpam-189	25	37	v̄α	v̄α	PROPN
ejpam-189	25	38	)	)	PUNCT
ejpam-189	25	39	,	,	PUNCT
ejpam-189	25	40	α	α	PROPN
ejpam-189	25	41	∈	∈	PROPN
ejpam-189	25	42	n	n	PRON
ejpam-189	25	43	is	be	AUX
ejpam-189	25	44	required	require	VERB
ejpam-189	25	45	in	in	ADP
ejpam-189	25	46	the	the	DET
ejpam-189	25	47	nonlinear	nonlinear	ADJ
ejpam-189	25	48	coupled	couple	VERB
ejpam-189	25	49	terms	term	NOUN
ejpam-189	25	50	.	.	PUNCT
ejpam-189	26	1	by	by	ADP
ejpam-189	26	2	denoting	denote	VERB
ejpam-189	26	3	u	u	NOUN
ejpam-189	26	4	=	=	PUNCT
ejpam-189	26	5	�	�	PROPN
ejpam-189	26	6	u	u	PROPN
ejpam-189	26	7	v	v	PROPN
ejpam-189	26	8	�	�	PROPN
ejpam-189	26	9	,	,	PUNCT
ejpam-189	26	10	f(u	f(u	PROPN
ejpam-189	26	11	)	)	PUNCT
ejpam-189	26	12	=	=	PUNCT
ejpam-189	26	13	�	�	PROPN
ejpam-189	26	14	a|u|αu+|v|αu	a|u|αu+|v|αu	PROPN
ejpam-189	26	15	u|αv+a|v|αv	u|αv+a|v|αv	NUM
ejpam-189	26	16	�	�	PROPN
ejpam-189	26	17	and	and	CCONJ
ejpam-189	26	18	φ	φ	PROPN
ejpam-189	26	19	=	=	SYM
ejpam-189	26	20	�	�	PROPN
ejpam-189	26	21	φ	φ	PROPN
ejpam-189	26	22	ψ	ψ	X
ejpam-189	26	23	�	�	PROPN
ejpam-189	26	24	,	,	PUNCT
ejpam-189	26	25	we	we	PRON
ejpam-189	26	26	see	see	VERB
ejpam-189	26	27	readily	readily	ADV
ejpam-189	26	28	that	that	SCONJ
ejpam-189	26	29	(	(	PUNCT
ejpam-189	26	30	2	2	X
ejpam-189	26	31	)	)	PUNCT
ejpam-189	26	32	take	take	VERB
ejpam-189	26	33	the	the	DET
ejpam-189	26	34	following	follow	VERB
ejpam-189	26	35	form	form	NOUN
ejpam-189	26	36	:	:	PUNCT
ejpam-189	26	37	¨	¨	NOUN
ejpam-189	26	38	∂t	∂t	PROPN
ejpam-189	26	39	u	u	NOUN
ejpam-189	26	40	+	+	PROPN
ejpam-189	26	41	∆u	∆u	PROPN
ejpam-189	26	42	=	=	SYM
ejpam-189	26	43	f(u	f(u	PROPN
ejpam-189	26	44	)	)	PUNCT
ejpam-189	26	45	x	x	SYM
ejpam-189	26	46	∈	∈	PROPN
ejpam-189	26	47	rn	rn	PROPN
ejpam-189	26	48	,	,	PUNCT
ejpam-189	26	49	t	t	PROPN
ejpam-189	26	50	∈	∈	PROPN
ejpam-189	26	51	r.	r.	PROPN
ejpam-189	26	52	u(0	u(0	PROPN
ejpam-189	26	53	,	,	PUNCT
ejpam-189	26	54	x	x	NOUN
ejpam-189	26	55	)	)	PUNCT
ejpam-189	26	56	=	=	SYM
ejpam-189	26	57	φ(x	φ(x	NOUN
ejpam-189	26	58	)	)	PUNCT
ejpam-189	26	59	x	x	SYM
ejpam-189	26	60	∈	∈	PROPN
ejpam-189	26	61	rn	rn	PROPN
ejpam-189	26	62	.	.	PROPN
ejpam-189	27	1	(	(	PUNCT
ejpam-189	27	2	3	3	X
ejpam-189	27	3	)	)	PUNCT
ejpam-189	27	4	let	let	VERB
ejpam-189	27	5	λ(t	λ(t	PRON
ejpam-189	27	6	)	)	PUNCT
ejpam-189	27	7	=	=	SYM
ejpam-189	27	8	�	�	PROPN
ejpam-189	27	9	s(t	s(t	PROPN
ejpam-189	27	10	)	)	PUNCT
ejpam-189	27	11	0	0	NUM
ejpam-189	27	12	0	0	NUM
ejpam-189	27	13	s(t	s(t	PROPN
ejpam-189	27	14	)	)	PUNCT
ejpam-189	27	15	�	�	PROPN
ejpam-189	27	16	,	,	PUNCT
ejpam-189	27	17	where	where	SCONJ
ejpam-189	27	18	s(t	s(t	NOUN
ejpam-189	27	19	)	)	PUNCT
ejpam-189	27	20	=	=	PUNCT
ejpam-189	27	21	ei	ei	X
ejpam-189	27	22	t∆	t∆	PROPN
ejpam-189	27	23	is	be	AUX
ejpam-189	27	24	the	the	DET
ejpam-189	27	25	fundamental	fundamental	ADJ
ejpam-189	27	26	solution	solution	NOUN
ejpam-189	27	27	operator	operator	NOUN
ejpam-189	27	28	of	of	ADP
ejpam-189	27	29	the	the	DET
ejpam-189	27	30	schrödinger	schrödinger	ADJ
ejpam-189	27	31	equation	equation	NOUN
ejpam-189	27	32	and	and	CCONJ
ejpam-189	27	33	is	be	AUX
ejpam-189	27	34	given	give	VERB
ejpam-189	27	35	by	by	ADP
ejpam-189	27	36	s(t)φ	s(t)φ	NOUN
ejpam-189	27	37	=	=	SYM
ejpam-189	27	38	∫	∫	PROPN
ejpam-189	27	39	rn	rn	PROPN
ejpam-189	27	40	e−i	e−i	PROPN
ejpam-189	27	41	t|ξ|2+i	t|ξ|2+i	PROPN
ejpam-189	27	42	xξφ̂dξ	xξφ̂dξ	PROPN
ejpam-189	27	43	,	,	PUNCT
ejpam-189	27	44	∀	∀	X
ejpam-189	27	45	φ	φ	PROPN
ejpam-189	27	46	∈	∈	PROPN
ejpam-189	27	47	s(rn	s(rn	PROPN
ejpam-189	27	48	)	)	PUNCT
ejpam-189	27	49	.	.	PUNCT
ejpam-189	28	1	then	then	ADV
ejpam-189	28	2	by	by	ADP
ejpam-189	28	3	the	the	DET
ejpam-189	28	4	duhanmel	duhanmel	PROPN
ejpam-189	28	5	principle	principle	NOUN
ejpam-189	28	6	we	we	PRON
ejpam-189	28	7	see	see	VERB
ejpam-189	28	8	that	that	SCONJ
ejpam-189	28	9	the	the	DET
ejpam-189	28	10	cauchy	cauchy	PROPN
ejpam-189	28	11	problem	problem	NOUN
ejpam-189	28	12	(	(	PUNCT
ejpam-189	28	13	3	3	X
ejpam-189	28	14	)	)	PUNCT
ejpam-189	28	15	is	be	AUX
ejpam-189	28	16	equivalent	equivalent	ADJ
ejpam-189	28	17	to	to	ADP
ejpam-189	28	18	the	the	DET
ejpam-189	28	19	following	follow	VERB
ejpam-189	28	20	integral	integral	ADJ
ejpam-189	28	21	equation	equation	NOUN
ejpam-189	28	22	:	:	PUNCT
ejpam-189	28	23	u(t	u(t	NOUN
ejpam-189	28	24	)	)	PUNCT
ejpam-189	28	25	=	=	SYM
ejpam-189	29	1	λ(t)φ−	λ(t)φ−	NOUN
ejpam-189	30	1	i	i	PRON
ejpam-189	30	2	∫	∫	PROPN
ejpam-189	30	3	t	t	NOUN
ejpam-189	30	4	0	0	NUM
ejpam-189	31	1	λ(t	λ(t	NOUN
ejpam-189	31	2	−τ)f(u(τ))dτ	−τ)f(u(τ))dτ	PROPN
ejpam-189	31	3	.	.	PUNCT
ejpam-189	32	1	thus	thus	ADV
ejpam-189	32	2	,	,	PUNCT
ejpam-189	32	3	in	in	ADP
ejpam-189	32	4	the	the	DET
ejpam-189	32	5	sequel	sequel	NOUN
ejpam-189	32	6	we	we	PRON
ejpam-189	32	7	shall	shall	AUX
ejpam-189	32	8	solve	solve	VERB
ejpam-189	32	9	this	this	DET
ejpam-189	32	10	integral	integral	ADJ
ejpam-189	32	11	equation	equation	NOUN
ejpam-189	32	12	.	.	PUNCT
ejpam-189	33	1	we	we	PRON
ejpam-189	33	2	shall	shall	AUX
ejpam-189	33	3	use	use	VERB
ejpam-189	33	4	the	the	DET
ejpam-189	33	5	notation	notation	NOUN
ejpam-189	33	6	‖|	‖|	PROPN
ejpam-189	33	7	·	·	PUNCT
ejpam-189	33	8	‖|	‖|	NOUN
ejpam-189	33	9	to	to	PART
ejpam-189	33	10	denote	denote	VERB
ejpam-189	33	11	the	the	DET
ejpam-189	33	12	norm	norm	NOUN
ejpam-189	33	13	of	of	ADP
ejpam-189	33	14	2	2	NUM
ejpam-189	33	15	-	-	PUNCT
ejpam-189	33	16	dimensional	dimensional	ADJ
ejpam-189	33	17	vector	vector	NOUN
ejpam-189	33	18	functions	function	NOUN
ejpam-189	33	19	,	,	PUNCT
ejpam-189	33	20	and	and	CCONJ
ejpam-189	33	21	use	use	VERB
ejpam-189	33	22	‖	‖	PROPN
ejpam-189	33	23	·	·	PUNCT
ejpam-189	33	24	‖	‖	ADJ
ejpam-189	33	25	to	to	PART
ejpam-189	33	26	denote	denote	VERB
ejpam-189	33	27	the	the	DET
ejpam-189	33	28	norm	norm	NOUN
ejpam-189	33	29	of	of	ADP
ejpam-189	33	30	scale	scale	NOUN
ejpam-189	33	31	functions	function	NOUN
ejpam-189	33	32	,	,	PUNCT
ejpam-189	33	33	so	so	SCONJ
ejpam-189	33	34	that	that	SCONJ
ejpam-189	33	35	‖|u‖|	‖|u‖|	PRON
ejpam-189	33	36	=	=	PUNCT
ejpam-189	33	37	‖u‖+	‖u‖+	PROPN
ejpam-189	33	38	‖v‖	‖v‖	PROPN
ejpam-189	33	39	if	if	SCONJ
ejpam-189	33	40	u	u	NOUN
ejpam-189	33	41	=	=	SYM
ejpam-189	33	42	�	�	PROPN
ejpam-189	33	43	u	u	NOUN
ejpam-189	33	44	v	v	PROPN
ejpam-189	33	45	�	�	PROPN
ejpam-189	33	46	.	.	PUNCT
ejpam-189	34	1	the	the	DET
ejpam-189	34	2	main	main	ADJ
ejpam-189	34	3	result	result	NOUN
ejpam-189	34	4	of	of	ADP
ejpam-189	34	5	this	this	DET
ejpam-189	34	6	paper	paper	NOUN
ejpam-189	34	7	is	be	AUX
ejpam-189	34	8	theorem	theorem	VERB
ejpam-189	34	9	1	1	X
ejpam-189	34	10	.	.	PUNCT
ejpam-189	35	1	let	let	VERB
ejpam-189	35	2	φ	φ	PROPN
ejpam-189	35	3	∈	∈	PROPN
ejpam-189	35	4	e0	e0	PROPN
ejpam-189	35	5	2,1(r	2,1(r	NOUN
ejpam-189	35	6	n	n	CCONJ
ejpam-189	35	7	)	)	PUNCT
ejpam-189	35	8	.	.	PUNCT
ejpam-189	36	1	then	then	ADV
ejpam-189	36	2	there	there	PRON
ejpam-189	36	3	exists	exist	VERB
ejpam-189	36	4	t	t	PROPN
ejpam-189	36	5	∗	∗	PROPN
ejpam-189	36	6	≡	≡	PROPN
ejpam-189	36	7	t	t	PROPN
ejpam-189	36	8	∗(‖|φ‖|e0	∗(‖|φ‖|e0	PROPN
ejpam-189	36	9	2,1(r	2,1(r	PROPN
ejpam-189	36	10	n	n	CCONJ
ejpam-189	36	11	)	)	PUNCT
ejpam-189	36	12	>	>	X
ejpam-189	36	13	0	0	NUM
ejpam-189	37	1	such	such	ADJ
ejpam-189	37	2	that	that	SCONJ
ejpam-189	37	3	the	the	DET
ejpam-189	37	4	cauchy	cauchy	PROPN
ejpam-189	37	5	problem	problem	NOUN
ejpam-189	37	6	(	(	PUNCT
ejpam-189	37	7	3	3	X
ejpam-189	37	8	)	)	PUNCT
ejpam-189	37	9	has	have	VERB
ejpam-189	37	10	a	a	DET
ejpam-189	37	11	unique	unique	ADJ
ejpam-189	37	12	solution	solution	NOUN
ejpam-189	37	13	u	u	NOUN
ejpam-189	37	14	∈	∈	PROPN
ejpam-189	37	15	c([0	c([0	NOUN
ejpam-189	37	16	,	,	PUNCT
ejpam-189	37	17	t	t	PROPN
ejpam-189	37	18	∗	∗	NOUN
ejpam-189	37	19	)	)	PUNCT
ejpam-189	37	20	,	,	PUNCT
ejpam-189	37	21	e0	e0	PROPN
ejpam-189	37	22	2,1(r	2,1(r	NOUN
ejpam-189	37	23	n	n	CCONJ
ejpam-189	37	24	)	)	PUNCT
ejpam-189	37	25	)	)	PUNCT
ejpam-189	37	26	.	.	PUNCT
ejpam-189	38	1	z.	z.	PROPN
ejpam-189	38	2	he	he	PRON
ejpam-189	38	3	and	and	CCONJ
ejpam-189	38	4	x.	x.	NOUN
ejpam-189	38	5	zhao	zhao	PROPN
ejpam-189	38	6	/	/	SYM
ejpam-189	38	7	eur	eur	PROPN
ejpam-189	38	8	.	.	PUNCT
ejpam-189	39	1	j.	j.	PROPN
ejpam-189	39	2	pure	pure	PROPN
ejpam-189	39	3	appl	appl	PROPN
ejpam-189	39	4	.	.	PROPN
ejpam-189	39	5	math	math	PROPN
ejpam-189	39	6	,	,	PUNCT
ejpam-189	39	7	3	3	NUM
ejpam-189	39	8	(	(	PUNCT
ejpam-189	39	9	2010	2010	NUM
ejpam-189	39	10	)	)	PUNCT
ejpam-189	39	11	,	,	PUNCT
ejpam-189	39	12	227	227	NUM
ejpam-189	39	13	-	-	SYM
ejpam-189	39	14	234	234	NUM
ejpam-189	39	15	229	229	NUM
ejpam-189	40	1	moreover	moreover	ADV
ejpam-189	40	2	,	,	PUNCT
ejpam-189	40	3	if	if	SCONJ
ejpam-189	40	4	t	t	PROPN
ejpam-189	40	5	∗	∗	VERB
ejpam-189	40	6	<	<	X
ejpam-189	40	7	∞	∞	PROPN
ejpam-189	40	8	then	then	ADV
ejpam-189	40	9	lim	lim	PROPN
ejpam-189	40	10	t→t∗	t→t∗	PRON
ejpam-189	40	11	sup‖|u(t)‖|e0	sup‖|u(t)‖|e0	VERB
ejpam-189	40	12	2,1(r	2,1(r	NUM
ejpam-189	40	13	n	n	CCONJ
ejpam-189	40	14	)	)	PUNCT
ejpam-189	41	1	=	=	NOUN
ejpam-189	41	2	∞.	∞.	PROPN
ejpam-189	41	3	e0	e0	NOUN
ejpam-189	41	4	2,1(r	2,1(r	NOUN
ejpam-189	41	5	n	n	CCONJ
ejpam-189	41	6	)	)	PUNCT
ejpam-189	41	7	will	will	AUX
ejpam-189	41	8	be	be	AUX
ejpam-189	41	9	introduced	introduce	VERB
ejpam-189	41	10	in	in	ADP
ejpam-189	41	11	the	the	DET
ejpam-189	41	12	next	next	ADJ
ejpam-189	41	13	section	section	NOUN
ejpam-189	41	14	.	.	PUNCT
ejpam-189	42	1	in	in	ADP
ejpam-189	42	2	the	the	DET
ejpam-189	42	3	sequel	sequel	NOUN
ejpam-189	42	4	,	,	PUNCT
ejpam-189	42	5	c	c	PROPN
ejpam-189	42	6	will	will	AUX
ejpam-189	42	7	denote	denote	VERB
ejpam-189	42	8	a	a	DET
ejpam-189	42	9	constant	constant	ADJ
ejpam-189	42	10	which	which	PRON
ejpam-189	42	11	may	may	AUX
ejpam-189	42	12	differ	differ	VERB
ejpam-189	42	13	at	at	ADP
ejpam-189	42	14	each	each	DET
ejpam-189	42	15	appearance	appearance	NOUN
ejpam-189	42	16	,	,	PUNCT
ejpam-189	42	17	possibly	possibly	ADV
ejpam-189	42	18	depending	depend	VERB
ejpam-189	42	19	on	on	ADP
ejpam-189	42	20	the	the	DET
ejpam-189	42	21	dimension	dimension	NOUN
ejpam-189	42	22	or	or	CCONJ
ejpam-189	42	23	other	other	ADJ
ejpam-189	42	24	parameters	parameter	NOUN
ejpam-189	42	25	.	.	PUNCT
ejpam-189	43	1	for	for	ADP
ejpam-189	43	2	p	p	PRON
ejpam-189	43	3	≥	≥	NUM
ejpam-189	43	4	1	1	NUM
ejpam-189	43	5	we	we	PRON
ejpam-189	43	6	set	set	VERB
ejpam-189	43	7	p′	p′	NOUN
ejpam-189	43	8	=	=	PUNCT
ejpam-189	43	9	p	p	PROPN
ejpam-189	43	10	p−1	p−1	PROPN
ejpam-189	43	11	.	.	PUNCT
ejpam-189	44	1	2	2	X
ejpam-189	44	2	.	.	NUM
ejpam-189	44	3	preliminaries	preliminary	NOUN
ejpam-189	44	4	2.1	2.1	NUM
ejpam-189	44	5	.	.	PUNCT
ejpam-189	45	1	the	the	DET
ejpam-189	45	2	banach	banach	NOUN
ejpam-189	45	3	algebra	algebra	NOUN
ejpam-189	45	4	e0	e0	PROPN
ejpam-189	45	5	2,1	2,1	NUM
ejpam-189	45	6	we	we	PRON
ejpam-189	45	7	denote	denote	VERB
ejpam-189	45	8	by	by	ADP
ejpam-189	45	9	s(rn	s(rn	PROPN
ejpam-189	45	10	)	)	PUNCT
ejpam-189	45	11	and	and	CCONJ
ejpam-189	45	12	s′(rn	s′(rn	PROPN
ejpam-189	45	13	)	)	PUNCT
ejpam-189	45	14	the	the	DET
ejpam-189	45	15	schwartz	schwartz	PROPN
ejpam-189	45	16	space	space	NOUN
ejpam-189	45	17	and	and	CCONJ
ejpam-189	45	18	its	its	PRON
ejpam-189	45	19	dual	dual	ADJ
ejpam-189	45	20	space	space	NOUN
ejpam-189	45	21	,	,	PUNCT
ejpam-189	45	22	respectively	respectively	ADV
ejpam-189	45	23	.	.	PUNCT
ejpam-189	46	1	let	let	VERB
ejpam-189	46	2	ρ	ρ	PROPN
ejpam-189	46	3	∈	∈	PROPN
ejpam-189	46	4	s(rn	s(rn	PROPN
ejpam-189	46	5	)	)	PUNCT
ejpam-189	46	6	and	and	CCONJ
ejpam-189	46	7	ρ	ρ	PROPN
ejpam-189	46	8	:	:	PUNCT
ejpam-189	46	9	rn	rn	PROPN
ejpam-189	46	10	→	→	PUNCT
ejpam-189	47	1	[	[	X
ejpam-189	47	2	0,1	0,1	NUM
ejpam-189	47	3	]	]	PUNCT
ejpam-189	47	4	be	be	VERB
ejpam-189	47	5	a	a	DET
ejpam-189	47	6	smooth	smooth	ADJ
ejpam-189	47	7	radial	radial	ADJ
ejpam-189	47	8	bump	bump	NOUN
ejpam-189	47	9	function	function	NOUN
ejpam-189	47	10	adapted	adapt	VERB
ejpam-189	47	11	to	to	ADP
ejpam-189	47	12	the	the	DET
ejpam-189	47	13	ball	ball	NOUN
ejpam-189	47	14	b(0	b(0	NOUN
ejpam-189	47	15	,	,	PUNCT
ejpam-189	47	16	p	p	NOUN
ejpam-189	47	17	2n	2n	NUM
ejpam-189	47	18	)	)	PUNCT
ejpam-189	47	19	,	,	PUNCT
ejpam-189	47	20	say	say	VERB
ejpam-189	47	21	ρ(ξ	ρ(ξ	NOUN
ejpam-189	47	22	)	)	PUNCT
ejpam-189	47	23	=	=	SYM
ejpam-189	48	1	1	1	NUM
ejpam-189	48	2	as	as	ADP
ejpam-189	48	3	0≤	0≤	NUM
ejpam-189	48	4	|ξ|	|ξ|	PROPN
ejpam-189	48	5	≤p	≤p	PROPN
ejpam-189	48	6	n	n	ADV
ejpam-189	48	7	2	2	NUM
ejpam-189	48	8	,	,	PUNCT
ejpam-189	48	9	and	and	CCONJ
ejpam-189	48	10	ρ(ξ	ρ(ξ	NOUN
ejpam-189	48	11	)	)	PUNCT
ejpam-189	48	12	=	=	SYM
ejpam-189	48	13	0	0	PUNCT
ejpam-189	48	14	as	as	SCONJ
ejpam-189	48	15	|ξ|	|ξ|	PROPN
ejpam-189	48	16	≥	≥	PROPN
ejpam-189	48	17	p2n	p2n	PROPN
ejpam-189	48	18	.	.	PUNCT
ejpam-189	49	1	let	let	VERB
ejpam-189	49	2	ρk	ρk	PART
ejpam-189	49	3	be	be	AUX
ejpam-189	49	4	a	a	DET
ejpam-189	49	5	translation	translation	NOUN
ejpam-189	49	6	of	of	ADP
ejpam-189	49	7	ρ	ρ	PROPN
ejpam-189	49	8	:	:	PUNCT
ejpam-189	49	9	ρk(ξ	ρk(ξ	X
ejpam-189	49	10	)	)	PUNCT
ejpam-189	50	1	=	=	SYM
ejpam-189	50	2	ρ(ξ−	ρ(ξ−	PROPN
ejpam-189	50	3	k	k	NOUN
ejpam-189	50	4	)	)	PUNCT
ejpam-189	50	5	,	,	PUNCT
ejpam-189	50	6	k	k	PROPN
ejpam-189	50	7	∈	∈	PROPN
ejpam-189	50	8	zn	zn	PROPN
ejpam-189	50	9	,	,	PUNCT
ejpam-189	50	10	where	where	SCONJ
ejpam-189	50	11	k	k	PROPN
ejpam-189	50	12	∈	∈	PROPN
ejpam-189	50	13	zn	zn	PROPN
ejpam-189	50	14	means	mean	VERB
ejpam-189	50	15	that	that	SCONJ
ejpam-189	50	16	k	k	PROPN
ejpam-189	50	17	=	=	PRON
ejpam-189	50	18	(	(	PUNCT
ejpam-189	50	19	k1	k1	PROPN
ejpam-189	50	20	,	,	PUNCT
ejpam-189	50	21	k2	k2	NOUN
ejpam-189	50	22	,	,	PUNCT
ejpam-189	50	23	·	·	PUNCT
ejpam-189	50	24	·	·	PUNCT
ejpam-189	50	25	·	·	PUNCT
ejpam-189	50	26	,	,	PUNCT
ejpam-189	50	27	kn	kn	PROPN
ejpam-189	50	28	)	)	PUNCT
ejpam-189	50	29	,	,	PUNCT
ejpam-189	50	30	and	and	CCONJ
ejpam-189	50	31	k1	k1	NOUN
ejpam-189	50	32	,	,	PUNCT
ejpam-189	50	33	k2	k2	NOUN
ejpam-189	50	34	,	,	PUNCT
ejpam-189	50	35	·	·	PUNCT
ejpam-189	50	36	·	·	PUNCT
ejpam-189	50	37	·	·	PUNCT
ejpam-189	50	38	,	,	PUNCT
ejpam-189	50	39	kn	kn	PROPN
ejpam-189	50	40	are	be	AUX
ejpam-189	50	41	all	all	PRON
ejpam-189	50	42	integers	integer	NOUN
ejpam-189	50	43	.	.	PUNCT
ejpam-189	51	1	since	since	SCONJ
ejpam-189	51	2	ρ(ξ	ρ(ξ	NOUN
ejpam-189	51	3	)	)	PUNCT
ejpam-189	51	4	=	=	SYM
ejpam-189	51	5	1	1	NUM
ejpam-189	51	6	in	in	ADP
ejpam-189	51	7	the	the	DET
ejpam-189	51	8	unit	unit	NOUN
ejpam-189	51	9	closed	close	VERB
ejpam-189	51	10	cube	cube	NOUN
ejpam-189	51	11	qk	qk	NOUN
ejpam-189	51	12	with	with	ADP
ejpam-189	51	13	center	center	PROPN
ejpam-189	51	14	k	k	PROPN
ejpam-189	51	15	and	and	CCONJ
ejpam-189	51	16	{	{	PUNCT
ejpam-189	51	17	qk}k∈zn	qk}k∈zn	NOUN
ejpam-189	51	18	is	be	AUX
ejpam-189	51	19	a	a	DET
ejpam-189	51	20	covering	covering	NOUN
ejpam-189	51	21	of	of	ADP
ejpam-189	51	22	rn	rn	PROPN
ejpam-189	51	23	,	,	PUNCT
ejpam-189	51	24	one	one	PRON
ejpam-189	51	25	has	have	VERB
ejpam-189	51	26	that	that	PRON
ejpam-189	51	27	∑	∑	ADV
ejpam-189	51	28	k∈zn	k∈zn	ADJ
ejpam-189	51	29	ρk(ξ)≥	ρk(ξ)≥	PROPN
ejpam-189	51	30	1	1	NUM
ejpam-189	51	31	for	for	ADP
ejpam-189	51	32	all	all	DET
ejpam-189	51	33	ξ	ξ	PROPN
ejpam-189	51	34	∈	∈	PROPN
ejpam-189	51	35	rn	rn	PROPN
ejpam-189	51	36	.	.	PUNCT
ejpam-189	52	1	we	we	PRON
ejpam-189	52	2	write	write	VERB
ejpam-189	52	3	σk(ξ	σk(ξ	PUNCT
ejpam-189	52	4	)	)	PUNCT
ejpam-189	52	5	=	=	SYM
ejpam-189	52	6	ρk(ξ	ρk(ξ	X
ejpam-189	52	7	)	)	PUNCT
ejpam-189	52	8	�	�	PROPN
ejpam-189	52	9	∑	∑	ADP
ejpam-189	52	10	k∈zn	k∈zn	PROPN
ejpam-189	52	11	ρk(ξ	ρk(ξ	ADV
ejpam-189	52	12	)	)	PUNCT
ejpam-189	52	13	�	�	PROPN
ejpam-189	52	14	−1	−1	NOUN
ejpam-189	52	15	,	,	PUNCT
ejpam-189	52	16	k	k	PROPN
ejpam-189	52	17	∈	∈	PROPN
ejpam-189	53	1	zn	zn	X
ejpam-189	53	2	.	.	PUNCT
ejpam-189	54	1	it	it	PRON
ejpam-189	54	2	is	be	AUX
ejpam-189	54	3	easy	easy	ADJ
ejpam-189	54	4	to	to	PART
ejpam-189	54	5	see	see	VERB
ejpam-189	54	6	that	that	SCONJ
ejpam-189	54	7			NOUN
ejpam-189	54	8			VERB
ejpam-189	54	9			PRON
ejpam-189	54	10			ADJ
ejpam-189	54	11			ADJ
ejpam-189	54	12	|σk(ξ)|	|σk(ξ)|	ADJ
ejpam-189	54	13	≥	≥	NOUN
ejpam-189	54	14	c	c	NOUN
ejpam-189	54	15	,	,	PUNCT
ejpam-189	54	16	∀	∀	PUNCT
ejpam-189	54	17	ξ	ξ	X
ejpam-189	54	18	∈	∈	PROPN
ejpam-189	54	19	qk	qk	PROPN
ejpam-189	54	20	;	;	PUNCT
ejpam-189	54	21	suupσk(ξ)⊂	suupσk(ξ)⊂	X
ejpam-189	54	22	{	{	PUNCT
ejpam-189	54	23	ξ	ξ	NOUN
ejpam-189	54	24	:	:	PUNCT
ejpam-189	54	25	|ξ−	|ξ−	NOUN
ejpam-189	54	26	k|	k|	NOUN
ejpam-189	54	27	≤	≤	NUM
ejpam-189	54	28	p2n	p2n	VERB
ejpam-189	54	29	}	}	PUNCT
ejpam-189	54	30	;	;	PUNCT
ejpam-189	54	31	∑	∑	PUNCT
ejpam-189	54	32	k∈zn	k∈zn	NOUN
ejpam-189	54	33	σk(ξ	σk(ξ	X
ejpam-189	54	34	)	)	PUNCT
ejpam-189	54	35	=	=	SYM
ejpam-189	54	36	1	1	NUM
ejpam-189	54	37	,	,	PUNCT
ejpam-189	54	38	∀	∀	PUNCT
ejpam-189	54	39	ξ	ξ	PRON
ejpam-189	54	40	∈	∈	PROPN
ejpam-189	54	41	rn	rn	PROPN
ejpam-189	54	42	;	;	PUNCT
ejpam-189	54	43	|σ(m	|σ(m	PROPN
ejpam-189	54	44	)	)	PUNCT
ejpam-189	54	45	k	k	PROPN
ejpam-189	55	1	(	(	PUNCT
ejpam-189	55	2	ξ)|	ξ)|	INTJ
ejpam-189	55	3	≤	≤	ADJ
ejpam-189	55	4	cm	cm	NOUN
ejpam-189	55	5	,	,	PUNCT
ejpam-189	55	6	∀	∀	PUNCT
ejpam-189	55	7	ξ	ξ	PROPN
ejpam-189	55	8	∈	∈	PROPN
ejpam-189	55	9	rn	rn	PROPN
ejpam-189	55	10	.	.	PROPN
ejpam-189	55	11	(	(	PUNCT
ejpam-189	55	12	4	4	X
ejpam-189	55	13	)	)	PUNCT
ejpam-189	55	14	hence	hence	ADV
ejpam-189	55	15	,	,	PUNCT
ejpam-189	55	16	the	the	DET
ejpam-189	55	17	set	set	NOUN
ejpam-189	55	18	υ	υ	NOUN
ejpam-189	55	19	=	=	X
ejpam-189	55	20	{	{	PUNCT
ejpam-189	55	21	{	{	PUNCT
ejpam-189	55	22	σk}k∈zn	σk}k∈zn	PROPN
ejpam-189	55	23	:	:	PUNCT
ejpam-189	55	24	{	{	PUNCT
ejpam-189	55	25	σk}k∈zn	σk}k∈zn	NOUN
ejpam-189	55	26	satisfies	satisfie	NOUN
ejpam-189	55	27	(	(	PUNCT
ejpam-189	55	28	4	4	NUM
ejpam-189	55	29	)	)	PUNCT
ejpam-189	55	30	}	}	PUNCT
ejpam-189	55	31	is	be	AUX
ejpam-189	55	32	non	non	ADJ
ejpam-189	55	33	-	-	ADJ
ejpam-189	55	34	void	void	ADJ
ejpam-189	55	35	.	.	PUNCT
ejpam-189	56	1	let	let	VERB
ejpam-189	56	2	{	{	PUNCT
ejpam-189	56	3	σk}k∈zn	σk}k∈zn	VERB
ejpam-189	56	4	∈	∈	PROPN
ejpam-189	56	5	υ	υ	NOUN
ejpam-189	56	6	be	be	AUX
ejpam-189	56	7	a	a	DET
ejpam-189	56	8	function	function	NOUN
ejpam-189	56	9	sequence	sequence	NOUN
ejpam-189	56	10	.	.	PUNCT
ejpam-189	57	1	define	define	VERB
ejpam-189	57	2	operator	operator	NOUN
ejpam-189	57	3	:	:	PUNCT
ejpam-189	57	4	�	�	PROPN
ejpam-189	57	5	k	k	X
ejpam-189	57	6	≡f−1σkf	≡f−1σkf	PROPN
ejpam-189	57	7	,	,	PUNCT
ejpam-189	57	8	k	k	PROPN
ejpam-189	57	9	∈	∈	PROPN
ejpam-189	57	10	zn	zn	PROPN
ejpam-189	57	11	,	,	PUNCT
ejpam-189	57	12	where	where	SCONJ
ejpam-189	57	13	the	the	DET
ejpam-189	57	14	operator	operator	NOUN
ejpam-189	57	15	f	f	PROPN
ejpam-189	57	16	means	mean	VERB
ejpam-189	57	17	fourier	fouri	ADJ
ejpam-189	57	18	transformation	transformation	NOUN
ejpam-189	57	19	.	.	PUNCT
ejpam-189	58	1	for	for	ADP
ejpam-189	58	2	any	any	DET
ejpam-189	58	3	k	k	PROPN
ejpam-189	58	4	∈	∈	PROPN
ejpam-189	58	5	zn	zn	X
ejpam-189	58	6	,	,	PUNCT
ejpam-189	58	7	we	we	PRON
ejpam-189	58	8	write	write	VERB
ejpam-189	58	9	|k|	|k|	PROPN
ejpam-189	58	10	=	=	SYM
ejpam-189	58	11	|k1|+	|k1|+	X
ejpam-189	58	12	|k2|+	|k2|+	PROPN
ejpam-189	58	13	·	·	PUNCT
ejpam-189	58	14	·	·	PUNCT
ejpam-189	58	15	·	·	PUNCT
ejpam-189	59	1	+	+	CCONJ
ejpam-189	59	2	|kn|	|kn|	NUM
ejpam-189	59	3	.	.	PUNCT
ejpam-189	60	1	let	let	VERB
ejpam-189	60	2	0	0	NUM
ejpam-189	60	3	≤	≤	NUM
ejpam-189	61	1	λ	λ	X
ejpam-189	61	2	<	<	X
ejpam-189	61	3	∞	∞	PROPN
ejpam-189	61	4	,	,	PUNCT
ejpam-189	61	5	0	0	PUNCT
ejpam-189	61	6	<	<	X
ejpam-189	61	7	p	p	X
ejpam-189	61	8	,	,	PUNCT
ejpam-189	61	9	q	q	PROPN
ejpam-189	61	10	≤	≤	NUM
ejpam-189	61	11	∞	∞	PROPN
ejpam-189	61	12	,	,	PUNCT
ejpam-189	61	13	we	we	PRON
ejpam-189	61	14	introduce	introduce	VERB
ejpam-189	61	15	the	the	DET
ejpam-189	61	16	following	follow	VERB
ejpam-189	61	17	function	function	NOUN
ejpam-189	61	18	space	space	NOUN
ejpam-189	61	19	eλp	eλp	NOUN
ejpam-189	61	20	,	,	PUNCT
ejpam-189	61	21	q(r	q(r	PROPN
ejpam-189	61	22	n	n	CCONJ
ejpam-189	61	23	)	)	PUNCT
ejpam-189	61	24	=	=	SYM
ejpam-189	62	1	n	n	CCONJ
ejpam-189	62	2	f	f	PROPN
ejpam-189	62	3	∈	∈	PROPN
ejpam-189	62	4	s′(rn	s′(rn	PROPN
ejpam-189	62	5	)	)	PUNCT
ejpam-189	62	6	:	:	PUNCT
ejpam-189	63	1	‖	‖	PROPN
ejpam-189	63	2	f	f	PROPN
ejpam-189	63	3	‖eλp	‖eλp	PROPN
ejpam-189	63	4	,	,	PUNCT
ejpam-189	63	5	q	q	PROPN
ejpam-189	63	6	≡	≡	PROPN
ejpam-189	63	7	�	�	PROPN
ejpam-189	63	8	∑	∑	PUNCT
ejpam-189	63	9	k∈zn	k∈zn	PROPN
ejpam-189	64	1	[	[	X
ejpam-189	64	2	2λ|k|‖	2λ|k|‖	PROPN
ejpam-189	64	3	�	�	PROPN
ejpam-189	64	4	k	k	PROPN
ejpam-189	64	5	f	f	PROPN
ejpam-189	64	6	‖lp(rn	‖lp(rn	PROPN
ejpam-189	64	7	)	)	PUNCT
ejpam-189	64	8	]	]	PUNCT
ejpam-189	65	1	q	q	PUNCT
ejpam-189	65	2	�	�	PROPN
ejpam-189	65	3	1	1	NUM
ejpam-189	65	4	q	q	NOUN
ejpam-189	65	5	<	<	X
ejpam-189	65	6	∞	∞	NUM
ejpam-189	65	7	o	o	NOUN
ejpam-189	65	8	.	.	PUNCT
ejpam-189	66	1	z.	z.	PROPN
ejpam-189	66	2	he	he	PRON
ejpam-189	66	3	and	and	CCONJ
ejpam-189	66	4	x.	x.	NOUN
ejpam-189	66	5	zhao	zhao	PROPN
ejpam-189	66	6	/	/	SYM
ejpam-189	66	7	eur	eur	PROPN
ejpam-189	66	8	.	.	PUNCT
ejpam-189	67	1	j.	j.	PROPN
ejpam-189	67	2	pure	pure	PROPN
ejpam-189	67	3	appl	appl	PROPN
ejpam-189	67	4	.	.	PROPN
ejpam-189	67	5	math	math	PROPN
ejpam-189	67	6	,	,	PUNCT
ejpam-189	67	7	3	3	NUM
ejpam-189	67	8	(	(	PUNCT
ejpam-189	67	9	2010	2010	NUM
ejpam-189	67	10	)	)	PUNCT
ejpam-189	67	11	,	,	PUNCT
ejpam-189	67	12	227	227	NUM
ejpam-189	67	13	-	-	SYM
ejpam-189	67	14	234	234	NUM
ejpam-189	67	15	230	230	NUM
ejpam-189	67	16	obviously	obviously	ADV
ejpam-189	67	17	,	,	PUNCT
ejpam-189	67	18	the	the	DET
ejpam-189	67	19	function	function	NOUN
ejpam-189	67	20	space	space	NOUN
ejpam-189	67	21	eλp	eλp	NOUN
ejpam-189	67	22	,	,	PUNCT
ejpam-189	67	23	q(r	q(r	PROPN
ejpam-189	67	24	n	n	CCONJ
ejpam-189	67	25	)	)	PUNCT
ejpam-189	67	26	is	be	AUX
ejpam-189	67	27	modified	modify	VERB
ejpam-189	67	28	from	from	ADP
ejpam-189	67	29	the	the	DET
ejpam-189	67	30	besov	besov	NOUN
ejpam-189	67	31	space	space	NOUN
ejpam-189	67	32	bs	bs	X
ejpam-189	67	33	p	p	X
ejpam-189	67	34	,	,	PUNCT
ejpam-189	67	35	q(r	q(r	PROPN
ejpam-189	67	36	n	n	CCONJ
ejpam-189	67	37	)	)	PUNCT
ejpam-189	68	1	[	[	AUX
ejpam-189	68	2	see	see	VERB
ejpam-189	68	3	1	1	NUM
ejpam-189	68	4	]	]	PUNCT
ejpam-189	68	5	.	.	PUNCT
ejpam-189	69	1	since	since	SCONJ
ejpam-189	69	2	the	the	DET
ejpam-189	69	3	relation	relation	NOUN
ejpam-189	69	4	between	between	ADP
ejpam-189	69	5	eλp	eλp	NOUN
ejpam-189	69	6	,	,	PUNCT
ejpam-189	69	7	q(r	q(r	PROPN
ejpam-189	69	8	n	n	CCONJ
ejpam-189	69	9	)	)	PUNCT
ejpam-189	69	10	and	and	CCONJ
ejpam-189	69	11	the	the	DET
ejpam-189	69	12	besov	besov	NOUN
ejpam-189	69	13	space	space	NOUN
ejpam-189	69	14	bs	bs	X
ejpam-189	69	15	p	p	X
ejpam-189	69	16	,	,	PUNCT
ejpam-189	69	17	q(r	q(r	PROPN
ejpam-189	69	18	n	n	CCONJ
ejpam-189	69	19	)	)	PUNCT
ejpam-189	69	20	have	have	VERB
ejpam-189	69	21	nothing	nothing	PRON
ejpam-189	69	22	to	to	PART
ejpam-189	69	23	do	do	VERB
ejpam-189	69	24	with	with	ADP
ejpam-189	69	25	our	our	PRON
ejpam-189	69	26	result	result	NOUN
ejpam-189	69	27	,	,	PUNCT
ejpam-189	69	28	we	we	PRON
ejpam-189	69	29	omit	omit	VERB
ejpam-189	69	30	it	it	PRON
ejpam-189	69	31	here	here	ADV
ejpam-189	70	1	[	[	X
ejpam-189	70	2	for	for	ADP
ejpam-189	70	3	the	the	DET
ejpam-189	70	4	details	detail	NOUN
ejpam-189	70	5	,	,	PUNCT
ejpam-189	70	6	we	we	PRON
ejpam-189	70	7	refer	refer	VERB
ejpam-189	70	8	to	to	ADP
ejpam-189	70	9	10	10	NUM
ejpam-189	70	10	]	]	PUNCT
ejpam-189	70	11	.	.	PUNCT
ejpam-189	71	1	the	the	DET
ejpam-189	71	2	algebra	algebra	NOUN
ejpam-189	71	3	property	property	NOUN
ejpam-189	71	4	of	of	ADP
ejpam-189	71	5	e0	e0	PROPN
ejpam-189	71	6	2,1	2,1	NUM
ejpam-189	71	7	may	may	AUX
ejpam-189	71	8	deduce	deduce	VERB
ejpam-189	71	9	from	from	ADP
ejpam-189	71	10	the	the	DET
ejpam-189	71	11	following	follow	VERB
ejpam-189	71	12	embedding	embed	VERB
ejpam-189	71	13	property	property	NOUN
ejpam-189	71	14	and	and	CCONJ
ejpam-189	71	15	bilinear	bilinear	NOUN
ejpam-189	71	16	estimate	estimate	NOUN
ejpam-189	71	17	.	.	PUNCT
ejpam-189	72	1	lemma	lemma	PROPN
ejpam-189	72	2	1	1	X
ejpam-189	72	3	.	.	PUNCT
ejpam-189	73	1	let	let	VERB
ejpam-189	73	2	0≤	0≤	NUM
ejpam-189	73	3	λ	λ	VERB
ejpam-189	73	4	<	<	X
ejpam-189	73	5	∞	∞	PROPN
ejpam-189	73	6	,	,	PUNCT
ejpam-189	73	7	0	0	PUNCT
ejpam-189	73	8	<	<	X
ejpam-189	73	9	p1	p1	NOUN
ejpam-189	73	10	≤	≤	NUM
ejpam-189	73	11	p2	p2	PROPN
ejpam-189	73	12	≤∞	≤∞	PROPN
ejpam-189	73	13	,	,	PUNCT
ejpam-189	73	14	0	0	NUM
ejpam-189	73	15	<	<	X
ejpam-189	73	16	q1	q1	NOUN
ejpam-189	73	17	≤	≤	ADJ
ejpam-189	73	18	q2	q2	PROPN
ejpam-189	73	19	≤∞.	≤∞.	ADP
ejpam-189	73	20	then	then	ADV
ejpam-189	73	21	we	we	PRON
ejpam-189	73	22	have	have	VERB
ejpam-189	73	23	eλp1,q1	eλp1,q1	PROPN
ejpam-189	73	24	(	(	PUNCT
ejpam-189	73	25	rn)⊂	rn)⊂	PROPN
ejpam-189	73	26	eλp2,q2	eλp2,q2	PROPN
ejpam-189	73	27	(	(	PUNCT
ejpam-189	73	28	rn	rn	NOUN
ejpam-189	73	29	)	)	PUNCT
ejpam-189	73	30	.	.	PUNCT
ejpam-189	74	1	proof	proof	NOUN
ejpam-189	74	2	.	.	PUNCT
ejpam-189	75	1	see	see	VERB
ejpam-189	75	2	the	the	DET
ejpam-189	75	3	proof	proof	NOUN
ejpam-189	75	4	of	of	ADP
ejpam-189	75	5	proposition	proposition	NOUN
ejpam-189	75	6	3.5	3.5	NUM
ejpam-189	75	7	in	in	ADP
ejpam-189	75	8	[	[	X
ejpam-189	75	9	10	10	NUM
ejpam-189	75	10	]	]	PUNCT
ejpam-189	75	11	.	.	PUNCT
ejpam-189	76	1	lemma	lemma	PROPN
ejpam-189	76	2	2	2	X
ejpam-189	76	3	.	.	PUNCT
ejpam-189	77	1	let	let	VERB
ejpam-189	77	2	0≤	0≤	NUM
ejpam-189	77	3	λ	λ	VERB
ejpam-189	77	4	<	<	X
ejpam-189	77	5	∞	∞	PROPN
ejpam-189	77	6	,	,	PUNCT
ejpam-189	77	7	0	0	NUM
ejpam-189	77	8	<	<	X
ejpam-189	77	9	p	p	X
ejpam-189	77	10	≤	≤	PROPN
ejpam-189	77	11	p1	p1	NOUN
ejpam-189	77	12	,	,	PUNCT
ejpam-189	77	13	p2	p2	PROPN
ejpam-189	77	14	≤∞	≤∞	PROPN
ejpam-189	77	15	,	,	PUNCT
ejpam-189	77	16	0	0	PUNCT
ejpam-189	78	1	<	<	X
ejpam-189	78	2	q	q	X
ejpam-189	78	3	≤∞.	≤∞.	NOUN
ejpam-189	78	4	if	if	SCONJ
ejpam-189	78	5	1	1	NUM
ejpam-189	78	6	p	p	NOUN
ejpam-189	78	7	=	=	SYM
ejpam-189	78	8	1	1	NUM
ejpam-189	78	9	p1	p1	NOUN
ejpam-189	78	10	+	+	CCONJ
ejpam-189	78	11	1	1	NUM
ejpam-189	78	12	p2	p2	NOUN
ejpam-189	78	13	,	,	PUNCT
ejpam-189	78	14	then	then	ADV
ejpam-189	78	15	we	we	PRON
ejpam-189	78	16	have	have	VERB
ejpam-189	78	17	‖uv‖eλp	‖uv‖eλp	NOUN
ejpam-189	78	18	,	,	PUNCT
ejpam-189	78	19	q	q	PROPN
ejpam-189	78	20	≤	≤	NUM
ejpam-189	78	21	c2cqλ‖u‖eλ	c2cqλ‖u‖eλ	PUNCT
ejpam-189	78	22	p1,q∧1	p1,q∧1	PROPN
ejpam-189	78	23	‖v‖eλ	‖v‖eλ	PROPN
ejpam-189	78	24	p2,q∧1	p2,q∧1	PROPN
ejpam-189	78	25	,	,	PUNCT
ejpam-189	78	26	where	where	SCONJ
ejpam-189	78	27	a∧	a∧	PROPN
ejpam-189	78	28	b	b	PROPN
ejpam-189	78	29	=	=	SYM
ejpam-189	78	30	min{a	min{a	NOUN
ejpam-189	78	31	,	,	PUNCT
ejpam-189	78	32	b	b	NOUN
ejpam-189	78	33	}	}	PUNCT
ejpam-189	78	34	.	.	PUNCT
ejpam-189	79	1	c	c	PROPN
ejpam-189	79	2	is	be	AUX
ejpam-189	79	3	independent	independent	ADJ
ejpam-189	79	4	of	of	ADP
ejpam-189	79	5	λ	λ	PROPN
ejpam-189	79	6	,	,	PUNCT
ejpam-189	79	7	q	q	NOUN
ejpam-189	80	1	and	and	CCONJ
ejpam-189	80	2	if	if	SCONJ
ejpam-189	80	3	p	p	NOUN
ejpam-189	80	4	is	be	AUX
ejpam-189	80	5	fixed	fix	VERB
ejpam-189	80	6	,	,	PUNCT
ejpam-189	80	7	then	then	ADV
ejpam-189	80	8	c	c	PROPN
ejpam-189	80	9	is	be	AUX
ejpam-189	80	10	also	also	ADV
ejpam-189	80	11	independent	independent	ADJ
ejpam-189	80	12	of	of	ADP
ejpam-189	80	13	p1	p1	NOUN
ejpam-189	80	14	,	,	PUNCT
ejpam-189	80	15	p2	p2	NOUN
ejpam-189	80	16	.	.	PUNCT
ejpam-189	81	1	proof	proof	NOUN
ejpam-189	81	2	.	.	PUNCT
ejpam-189	82	1	see	see	VERB
ejpam-189	82	2	the	the	DET
ejpam-189	82	3	proof	proof	NOUN
ejpam-189	82	4	of	of	ADP
ejpam-189	82	5	lemma	lemma	PROPN
ejpam-189	82	6	4.1	4.1	NUM
ejpam-189	82	7	in	in	ADP
ejpam-189	82	8	[	[	X
ejpam-189	82	9	10	10	NUM
ejpam-189	82	10	]	]	PUNCT
ejpam-189	82	11	.	.	PUNCT
ejpam-189	83	1	as	as	ADP
ejpam-189	83	2	a	a	DET
ejpam-189	83	3	matter	matter	NOUN
ejpam-189	83	4	of	of	ADP
ejpam-189	83	5	fact	fact	NOUN
ejpam-189	83	6	,	,	PUNCT
ejpam-189	83	7	by	by	ADP
ejpam-189	83	8	lemma	lemma	PROPN
ejpam-189	83	9	1	1	NUM
ejpam-189	83	10	and	and	CCONJ
ejpam-189	83	11	lemma	lemma	PROPN
ejpam-189	83	12	2	2	NUM
ejpam-189	83	13	,	,	PUNCT
ejpam-189	83	14	we	we	PRON
ejpam-189	83	15	have	have	VERB
ejpam-189	83	16	‖uv‖e0	‖uv‖e0	VERB
ejpam-189	83	17	2,1	2,1	NUM
ejpam-189	83	18	≤	≤	NOUN
ejpam-189	83	19	c‖uv‖e0	c‖uv‖e0	VERB
ejpam-189	83	20	1,1	1,1	NUM
ejpam-189	83	21	≤	≤	NUM
ejpam-189	83	22	c‖u‖e0	c‖u‖e0	NOUN
ejpam-189	83	23	2,1	2,1	NUM
ejpam-189	83	24	‖v‖e0	‖v‖e0	NUM
ejpam-189	83	25	2,1	2,1	NUM
ejpam-189	83	26	.	.	PUNCT
ejpam-189	84	1	(	(	PUNCT
ejpam-189	84	2	5	5	NUM
ejpam-189	84	3	)	)	PUNCT
ejpam-189	84	4	which	which	PRON
ejpam-189	84	5	suggest	suggest	VERB
ejpam-189	84	6	that	that	SCONJ
ejpam-189	84	7	e0	e0	PROPN
ejpam-189	84	8	2,1	2,1	NUM
ejpam-189	84	9	is	be	AUX
ejpam-189	84	10	a	a	DET
ejpam-189	84	11	banach	banach	NOUN
ejpam-189	84	12	algebra	algebra	NOUN
ejpam-189	84	13	.	.	PUNCT
ejpam-189	85	1	from	from	ADP
ejpam-189	85	2	the	the	DET
ejpam-189	85	3	comparison	comparison	NOUN
ejpam-189	85	4	between	between	ADP
ejpam-189	85	5	e0	e0	PROPN
ejpam-189	85	6	2,q(r	2,q(r	NUM
ejpam-189	85	7	n	n	CCONJ
ejpam-189	85	8	)	)	PUNCT
ejpam-189	85	9	and	and	CCONJ
ejpam-189	85	10	hs(rn	hs(rn	PROPN
ejpam-189	85	11	)	)	PUNCT
ejpam-189	85	12	,	,	PUNCT
ejpam-189	85	13	we	we	PRON
ejpam-189	85	14	find	find	VERB
ejpam-189	85	15	that	that	SCONJ
ejpam-189	85	16	e0	e0	PROPN
ejpam-189	85	17	2,1(r	2,1(r	NOUN
ejpam-189	85	18	n	n	CCONJ
ejpam-189	85	19	)	)	PUNCT
ejpam-189	85	20	is	be	AUX
ejpam-189	85	21	the	the	DET
ejpam-189	85	22	extension	extension	NOUN
ejpam-189	85	23	of	of	ADP
ejpam-189	85	24	hs(rn	hs(rn	PROPN
ejpam-189	85	25	):	):	PUNCT
ejpam-189	85	26	hs(rn)⊂	hs(rn)⊂	PROPN
ejpam-189	85	27	e0	e0	PROPN
ejpam-189	85	28	2,1(r	2,1(r	NOUN
ejpam-189	85	29	n	n	CCONJ
ejpam-189	85	30	)	)	PUNCT
ejpam-189	85	31	for	for	ADP
ejpam-189	85	32	s	s	PROPN
ejpam-189	85	33	>	>	X
ejpam-189	85	34	n	n	NUM
ejpam-189	85	35	2	2	NUM
ejpam-189	85	36	,	,	PUNCT
ejpam-189	85	37	and	and	CCONJ
ejpam-189	85	38	hs(rn)⊂	hs(rn)⊂	PROPN
ejpam-189	85	39	e0	e0	PROPN
ejpam-189	85	40	2,1	2,1	NUM
ejpam-189	85	41	fails	fail	VERB
ejpam-189	85	42	,	,	PUNCT
ejpam-189	85	43	for	for	ADP
ejpam-189	85	44	s	s	PROPN
ejpam-189	85	45	≤	≤	NOUN
ejpam-189	85	46	n	n	DET
ejpam-189	85	47	2	2	NUM
ejpam-189	85	48	.	.	PUNCT
ejpam-189	86	1	indeed	indeed	ADV
ejpam-189	86	2	,	,	PUNCT
ejpam-189	86	3	we	we	PRON
ejpam-189	86	4	have	have	VERB
ejpam-189	86	5	lemma	lemma	PROPN
ejpam-189	86	6	3	3	X
ejpam-189	86	7	.	.	PUNCT
ejpam-189	87	1	we	we	PRON
ejpam-189	87	2	have	have	VERB
ejpam-189	87	3	hs(rn)⊂	hs(rn)⊂	PROPN
ejpam-189	87	4	e0	e0	PROPN
ejpam-189	87	5	2,q(r	2,q(r	NUM
ejpam-189	87	6	n	n	CCONJ
ejpam-189	87	7	)	)	PUNCT
ejpam-189	87	8	,	,	PUNCT
ejpam-189	87	9	s	s	VERB
ejpam-189	87	10	>	>	X
ejpam-189	87	11	n	n	CCONJ
ejpam-189	87	12	(	(	PUNCT
ejpam-189	87	13	1	1	NUM
ejpam-189	87	14	q	q	NOUN
ejpam-189	87	15	−	−	NUM
ejpam-189	87	16	1	1	NUM
ejpam-189	87	17	2	2	NUM
ejpam-189	87	18	)	)	PUNCT
ejpam-189	87	19	,	,	PUNCT
ejpam-189	88	1	0	0	PUNCT
ejpam-189	88	2	<	<	X
ejpam-189	88	3	q	q	X
ejpam-189	88	4	<	<	X
ejpam-189	88	5	2	2	NUM
ejpam-189	88	6	,	,	PUNCT
ejpam-189	88	7	l2(rn	l2(rn	PROPN
ejpam-189	88	8	)	)	PUNCT
ejpam-189	88	9	=	=	SYM
ejpam-189	88	10	e0	e0	PROPN
ejpam-189	88	11	2,2(r	2,2(r	NUM
ejpam-189	88	12	n	n	CCONJ
ejpam-189	88	13	)	)	PUNCT
ejpam-189	88	14	(	(	PUNCT
ejpam-189	88	15	equivalent	equivalent	ADJ
ejpam-189	88	16	norm	norm	NOUN
ejpam-189	88	17	)	)	PUNCT
ejpam-189	88	18	,	,	PUNCT
ejpam-189	88	19	e0	e0	PROPN
ejpam-189	88	20	2,q(r	2,q(r	NUM
ejpam-189	88	21	n)⊂	n)⊂	PROPN
ejpam-189	88	22	hs(rn	hs(rn	NUM
ejpam-189	88	23	)	)	PUNCT
ejpam-189	89	1	,	,	PUNCT
ejpam-189	89	2	s	s	VERB
ejpam-189	89	3	<	<	X
ejpam-189	89	4	n	n	X
ejpam-189	89	5	(	(	PUNCT
ejpam-189	89	6	1	1	NUM
ejpam-189	89	7	q	q	NOUN
ejpam-189	89	8	−	−	NUM
ejpam-189	89	9	1	1	NUM
ejpam-189	89	10	2	2	NUM
ejpam-189	89	11	)	)	PUNCT
ejpam-189	89	12	,	,	PUNCT
ejpam-189	89	13	2	2	NUM
ejpam-189	89	14	<	<	X
ejpam-189	89	15	q	q	X
ejpam-189	89	16	≤∞.	≤∞.	NOUN
ejpam-189	89	17	furthermore	furthermore	ADV
ejpam-189	89	18	,	,	PUNCT
ejpam-189	89	19	e0	e0	PROPN
ejpam-189	89	20	2,1	2,1	NUM
ejpam-189	89	21	is	be	AUX
ejpam-189	89	22	the	the	DET
ejpam-189	89	23	intermediate	intermediate	ADJ
ejpam-189	89	24	space	space	NOUN
ejpam-189	89	25	of	of	ADP
ejpam-189	89	26	hs(rn	hs(rn	PROPN
ejpam-189	89	27	)	)	PUNCT
ejpam-189	89	28	and	and	CCONJ
ejpam-189	89	29	l∞(rn	l∞(rn	PROPN
ejpam-189	89	30	)	)	PUNCT
ejpam-189	89	31	,	,	PUNCT
ejpam-189	89	32	that	that	PRON
ejpam-189	89	33	is	be	AUX
ejpam-189	89	34	hs(rn)⊂	hs(rn)⊂	PROPN
ejpam-189	89	35	e0	e0	PROPN
ejpam-189	89	36	2,1	2,1	NUM
ejpam-189	89	37	⊂	⊂	PROPN
ejpam-189	89	38	l∞(rn	l∞(rn	PROPN
ejpam-189	89	39	)	)	PUNCT
ejpam-189	89	40	,	,	PUNCT
ejpam-189	89	41	s	s	VERB
ejpam-189	89	42	>	>	X
ejpam-189	89	43	n/2	n/2	NOUN
ejpam-189	89	44	.	.	PUNCT
ejpam-189	90	1	[	[	X
ejpam-189	90	2	(	(	PUNCT
ejpam-189	90	3	3.43	3.43	NUM
ejpam-189	90	4	)	)	PUNCT
ejpam-189	90	5	in	in	ADP
ejpam-189	90	6	10	10	NUM
ejpam-189	90	7	]	]	PUNCT
ejpam-189	90	8	.	.	PUNCT
ejpam-189	91	1	proof	proof	NOUN
ejpam-189	91	2	.	.	PUNCT
ejpam-189	92	1	see	see	VERB
ejpam-189	92	2	the	the	DET
ejpam-189	92	3	proof	proof	NOUN
ejpam-189	92	4	of	of	ADP
ejpam-189	92	5	proposition	proposition	NOUN
ejpam-189	92	6	3.8	3.8	NUM
ejpam-189	92	7	in	in	ADP
ejpam-189	92	8	[	[	X
ejpam-189	92	9	10	10	NUM
ejpam-189	92	10	]	]	PUNCT
ejpam-189	92	11	.	.	PUNCT
ejpam-189	93	1	z.	z.	PROPN
ejpam-189	93	2	he	he	PRON
ejpam-189	93	3	and	and	CCONJ
ejpam-189	93	4	x.	x.	NOUN
ejpam-189	93	5	zhao	zhao	PROPN
ejpam-189	93	6	/	/	SYM
ejpam-189	93	7	eur	eur	PROPN
ejpam-189	93	8	.	.	PUNCT
ejpam-189	94	1	j.	j.	PROPN
ejpam-189	94	2	pure	pure	PROPN
ejpam-189	94	3	appl	appl	PROPN
ejpam-189	94	4	.	.	PROPN
ejpam-189	94	5	math	math	PROPN
ejpam-189	94	6	,	,	PUNCT
ejpam-189	94	7	3	3	NUM
ejpam-189	94	8	(	(	PUNCT
ejpam-189	94	9	2010	2010	NUM
ejpam-189	94	10	)	)	PUNCT
ejpam-189	94	11	,	,	PUNCT
ejpam-189	94	12	227	227	NUM
ejpam-189	94	13	-	-	SYM
ejpam-189	94	14	234	234	NUM
ejpam-189	94	15	231	231	NUM
ejpam-189	94	16	2.2	2.2	NUM
ejpam-189	94	17	.	.	PUNCT
ejpam-189	95	1	some	some	DET
ejpam-189	95	2	preliminary	preliminary	ADJ
ejpam-189	95	3	lemmas	lemmas	ADJ
ejpam-189	95	4	estimate	estimate	NOUN
ejpam-189	95	5	for	for	ADP
ejpam-189	95	6	the	the	DET
ejpam-189	95	7	schrödinger	schrödinger	ADJ
ejpam-189	95	8	group	group	NOUN
ejpam-189	95	9	lemma	lemma	PROPN
ejpam-189	95	10	4	4	X
ejpam-189	95	11	.	.	PUNCT
ejpam-189	96	1	let	let	VERB
ejpam-189	96	2	0	0	NUM
ejpam-189	96	3	<	<	X
ejpam-189	96	4	r	r	NOUN
ejpam-189	96	5	≤	≤	NUM
ejpam-189	96	6	2	2	NUM
ejpam-189	96	7	≤	≤	NOUN
ejpam-189	96	8	p	p	PRON
ejpam-189	96	9	≤∞	≤∞	PROPN
ejpam-189	96	10	,	,	PUNCT
ejpam-189	96	11	0	0	PUNCT
ejpam-189	96	12	<	<	X
ejpam-189	97	1	q	q	X
ejpam-189	97	2	≤∞.	≤∞.	NOUN
ejpam-189	97	3	then	then	ADV
ejpam-189	97	4	for	for	ADP
ejpam-189	97	5	the	the	DET
ejpam-189	97	6	schrödinger	schrödinger	ADJ
ejpam-189	97	7	group	group	NOUN
ejpam-189	97	8	s(t	s(t	PROPN
ejpam-189	97	9	)	)	PUNCT
ejpam-189	97	10	=	=	PUNCT
ejpam-189	97	11	ei	ei	ADP
ejpam-189	97	12	t∆	t∆	PROPN
ejpam-189	97	13	we	we	PRON
ejpam-189	97	14	have	have	VERB
ejpam-189	97	15	the	the	DET
ejpam-189	97	16	estimate	estimate	NOUN
ejpam-189	97	17	‖s(t)φ‖e0	‖s(t)φ‖e0	VERB
ejpam-189	97	18	p	p	X
ejpam-189	97	19	,	,	PUNCT
ejpam-189	97	20	q	q	PROPN
ejpam-189	97	21	≤	≤	NUM
ejpam-189	97	22	c‖φ‖e0	c‖φ‖e0	NOUN
ejpam-189	97	23	r	r	NOUN
ejpam-189	97	24	,	,	PUNCT
ejpam-189	97	25	q	q	NOUN
ejpam-189	97	26	.	.	PUNCT
ejpam-189	98	1	in	in	ADP
ejpam-189	98	2	particular	particular	ADJ
ejpam-189	98	3	,	,	PUNCT
ejpam-189	98	4	‖s(t)φ‖e0	‖s(t)φ‖e0	PROPN
ejpam-189	98	5	2,1	2,1	NUM
ejpam-189	98	6	≤	≤	NOUN
ejpam-189	98	7	c‖φ‖e0	c‖φ‖e0	NOUN
ejpam-189	98	8	2,1	2,1	NUM
ejpam-189	98	9	.	.	PUNCT
ejpam-189	99	1	proof	proof	NOUN
ejpam-189	99	2	.	.	PUNCT
ejpam-189	100	1	see	see	VERB
ejpam-189	100	2	the	the	DET
ejpam-189	100	3	proof	proof	NOUN
ejpam-189	100	4	of	of	ADP
ejpam-189	100	5	proposition	proposition	NOUN
ejpam-189	100	6	5.5	5.5	NUM
ejpam-189	100	7	in	in	ADP
ejpam-189	100	8	[	[	X
ejpam-189	100	9	10	10	NUM
ejpam-189	100	10	]	]	PUNCT
ejpam-189	100	11	.	.	PUNCT
ejpam-189	101	1	from	from	ADP
ejpam-189	101	2	lemma	lemma	PROPN
ejpam-189	101	3	4	4	NUM
ejpam-189	101	4	,	,	PUNCT
ejpam-189	101	5	we	we	PRON
ejpam-189	101	6	deduce	deduce	VERB
ejpam-189	101	7	that	that	SCONJ
ejpam-189	101	8	lemma	lemma	PROPN
ejpam-189	101	9	5	5	X
ejpam-189	101	10	.	.	PUNCT
ejpam-189	102	1	let	let	VERB
ejpam-189	102	2	0	0	NUM
ejpam-189	102	3	<	<	X
ejpam-189	102	4	r	r	NOUN
ejpam-189	102	5	≤	≤	NOUN
ejpam-189	102	6	2≤	2≤	NUM
ejpam-189	103	1	p	p	DET
ejpam-189	103	2	≤∞	≤∞	PROPN
ejpam-189	103	3	,	,	PUNCT
ejpam-189	103	4	0	0	PUNCT
ejpam-189	103	5	<	<	X
ejpam-189	103	6	q	q	X
ejpam-189	103	7	≤∞.	≤∞.	NOUN
ejpam-189	103	8	then	then	ADV
ejpam-189	103	9	for	for	ADP
ejpam-189	103	10	the	the	DET
ejpam-189	103	11	group	group	NOUN
ejpam-189	103	12	λ(t	λ(t	NOUN
ejpam-189	103	13	)	)	PUNCT
ejpam-189	103	14	we	we	PRON
ejpam-189	103	15	have	have	VERB
ejpam-189	103	16	the	the	DET
ejpam-189	103	17	estimate	estimate	NOUN
ejpam-189	103	18	‖|λ(t)φ‖|e0	‖|λ(t)φ‖|e0	PROPN
ejpam-189	103	19	p	p	NOUN
ejpam-189	103	20	,	,	PUNCT
ejpam-189	103	21	q	q	NOUN
ejpam-189	103	22	≤	≤	NUM
ejpam-189	103	23	c‖|φ‖|e0	c‖|φ‖|e0	X
ejpam-189	103	24	r	r	NOUN
ejpam-189	103	25	,	,	PUNCT
ejpam-189	103	26	q	q	NOUN
ejpam-189	103	27	.	.	PUNCT
ejpam-189	104	1	in	in	ADP
ejpam-189	104	2	particular	particular	ADJ
ejpam-189	104	3	,	,	PUNCT
ejpam-189	104	4	‖|λ(t)φ‖|e0	‖|λ(t)φ‖|e0	PROPN
ejpam-189	104	5	2,1	2,1	NUM
ejpam-189	104	6	≤	≤	NUM
ejpam-189	104	7	c‖|φ‖|e0	c‖|φ‖|e0	X
ejpam-189	104	8	2,1	2,1	NUM
ejpam-189	104	9	.	.	PUNCT
ejpam-189	105	1	with	with	ADP
ejpam-189	105	2	the	the	DET
ejpam-189	105	3	algebra	algebra	NOUN
ejpam-189	105	4	property	property	NOUN
ejpam-189	105	5	,	,	PUNCT
ejpam-189	105	6	we	we	PRON
ejpam-189	105	7	have	have	VERB
ejpam-189	105	8	the	the	DET
ejpam-189	105	9	estimates	estimate	NOUN
ejpam-189	105	10	for	for	ADP
ejpam-189	105	11	the	the	DET
ejpam-189	105	12	nonlinear	nonlinear	ADJ
ejpam-189	105	13	coupled	couple	VERB
ejpam-189	105	14	terms	term	NOUN
ejpam-189	105	15	lemma	lemma	PROPN
ejpam-189	105	16	6	6	NUM
ejpam-189	105	17	.	.	PUNCT
ejpam-189	106	1	‖|f(u)‖|e0	‖|f(u)‖|e0	NOUN
ejpam-189	106	2	2,1	2,1	NUM
ejpam-189	106	3	≤	≤	NOUN
ejpam-189	106	4	c‖|u‖|α+1	c‖|u‖|α+1	VERB
ejpam-189	106	5	e0	e0	PROPN
ejpam-189	106	6	2,1	2,1	NUM
ejpam-189	106	7	,	,	PUNCT
ejpam-189	106	8	and	and	CCONJ
ejpam-189	106	9	‖|f(u1)−	‖|f(u1)−	NUM
ejpam-189	106	10	f(u2)‖|e0	f(u2)‖|e0	PROPN
ejpam-189	106	11	2,1	2,1	NUM
ejpam-189	106	12	≤	≤	NOUN
ejpam-189	106	13	c‖|u1	c‖|u1	VERB
ejpam-189	106	14	−	−	PROPN
ejpam-189	106	15	u2‖|e0	u2‖|e0	ADJ
ejpam-189	106	16	2,1	2,1	NUM
ejpam-189	106	17	h	h	NOUN
ejpam-189	106	18	‖|u1‖|αe0	‖|u1‖|αe0	VERB
ejpam-189	106	19	2,1	2,1	NUM
ejpam-189	107	1	+	+	CCONJ
ejpam-189	107	2	‖|u2‖|αe0	‖|u2‖|αe0	NUM
ejpam-189	107	3	2,1	2,1	NUM
ejpam-189	107	4	i	i	PRON
ejpam-189	107	5	,	,	PUNCT
ejpam-189	107	6	where	where	SCONJ
ejpam-189	107	7	u	u	PROPN
ejpam-189	107	8	=	=	SYM
ejpam-189	107	9	�	�	PROPN
ejpam-189	107	10	u	u	NOUN
ejpam-189	107	11	v	v	PROPN
ejpam-189	107	12	�	�	PROPN
ejpam-189	107	13	,	,	PUNCT
ejpam-189	107	14	u1	u1	PROPN
ejpam-189	107	15	=	=	SYM
ejpam-189	107	16	�	�	PROPN
ejpam-189	107	17	u1	u1	PROPN
ejpam-189	107	18	v1	v1	PROPN
ejpam-189	107	19	�	�	PROPN
ejpam-189	107	20	,	,	PUNCT
ejpam-189	107	21	u2	u2	PROPN
ejpam-189	107	22	=	=	PUNCT
ejpam-189	107	23	�	�	PROPN
ejpam-189	107	24	u2	u2	PROPN
ejpam-189	107	25	v2	v2	PROPN
ejpam-189	107	26	�	�	PROPN
ejpam-189	107	27	.	.	PUNCT
ejpam-189	108	1	proof	proof	NOUN
ejpam-189	108	2	.	.	PUNCT
ejpam-189	109	1	by	by	ADP
ejpam-189	109	2	(	(	PUNCT
ejpam-189	109	3	5	5	NUM
ejpam-189	109	4	)	)	PUNCT
ejpam-189	109	5	,	,	PUNCT
ejpam-189	109	6	we	we	PRON
ejpam-189	109	7	have	have	VERB
ejpam-189	109	8	‖|f(u)‖|e0	‖|f(u)‖|e0	PROPN
ejpam-189	109	9	2,1	2,1	NUM
ejpam-189	109	10	=	=	SYM
ejpam-189	109	11	‖a|u|αu+	‖a|u|αu+	PROPN
ejpam-189	109	12	|v|αu‖e0	|v|αu‖e0	PROPN
ejpam-189	109	13	2,1	2,1	NUM
ejpam-189	109	14	+	+	NUM
ejpam-189	109	15	‖|u|αv	‖|u|αv	NOUN
ejpam-189	109	16	+	+	CCONJ
ejpam-189	109	17	a|v|αv‖e0	a|v|αv‖e0	PROPN
ejpam-189	109	18	2,1	2,1	NUM
ejpam-189	109	19	≤	≤	NOUN
ejpam-189	109	20	|a|‖|u|αu‖e0	|a|‖|u|αu‖e0	CCONJ
ejpam-189	109	21	2,1	2,1	NUM
ejpam-189	109	22	+	+	CCONJ
ejpam-189	109	23	‖|v|αu‖e0	‖|v|αu‖e0	NUM
ejpam-189	109	24	2,1	2,1	NUM
ejpam-189	109	25	+	+	CCONJ
ejpam-189	109	26	‖|u|αv‖e0	‖|u|αv‖e0	VERB
ejpam-189	109	27	2,1	2,1	NUM
ejpam-189	109	28	+	+	CCONJ
ejpam-189	109	29	|a|‖|v|αv‖e0	|a|‖|v|αv‖e0	ADJ
ejpam-189	109	30	2,1	2,1	NUM
ejpam-189	109	31	≤	≤	NUM
ejpam-189	109	32	|a|‖u‖α+1	|a|‖u‖α+1	NOUN
ejpam-189	109	33	e0	e0	PROPN
ejpam-189	109	34	2,1	2,1	NUM
ejpam-189	109	35	+	+	CCONJ
ejpam-189	109	36	‖|v|‖α	‖|v|‖α	PROPN
ejpam-189	109	37	e0	e0	PROPN
ejpam-189	109	38	2,1	2,1	NUM
ejpam-189	109	39	‖u‖e0	‖u‖e0	NUM
ejpam-189	109	40	2,1	2,1	NUM
ejpam-189	109	41	+	+	CCONJ
ejpam-189	109	42	‖u‖α	‖u‖α	PROPN
ejpam-189	109	43	e0	e0	PROPN
ejpam-189	109	44	2,1	2,1	NUM
ejpam-189	109	45	‖v‖e0	‖v‖e0	NUM
ejpam-189	109	46	2,1	2,1	NUM
ejpam-189	109	47	+	+	CCONJ
ejpam-189	109	48	|a|‖v‖α+1	|a|‖v‖α+1	NOUN
ejpam-189	109	49	e0	e0	PROPN
ejpam-189	109	50	2,1	2,1	NUM
ejpam-189	109	51	≤	≤	NUM
ejpam-189	109	52	‖u‖α	‖u‖α	NOUN
ejpam-189	109	53	e0	e0	PROPN
ejpam-189	109	54	2,1	2,1	NUM
ejpam-189	109	55	�	�	PROPN
ejpam-189	109	56	‖u‖e0	‖u‖e0	NUM
ejpam-189	109	57	2,1	2,1	NUM
ejpam-189	109	58	+	+	CCONJ
ejpam-189	109	59	‖v‖e0	‖v‖e0	NUM
ejpam-189	109	60	2,1	2,1	NUM
ejpam-189	109	61	�	�	NOUN
ejpam-189	109	62	+	+	NUM
ejpam-189	109	63	c‖v‖α	c‖v‖α	PROPN
ejpam-189	109	64	e0	e0	PROPN
ejpam-189	109	65	2,1	2,1	NUM
ejpam-189	109	66	�	�	PROPN
ejpam-189	109	67	‖u‖e0	‖u‖e0	NUM
ejpam-189	109	68	2,1	2,1	NUM
ejpam-189	109	69	+	+	CCONJ
ejpam-189	109	70	‖v‖e0	‖v‖e0	NUM
ejpam-189	109	71	2,1	2,1	NUM
ejpam-189	109	72	�	�	NOUN
ejpam-189	109	73	≤	≤	PROPN
ejpam-189	109	74	c‖|u‖|α+1	c‖|u‖|α+1	PROPN
ejpam-189	109	75	e0	e0	PROPN
ejpam-189	109	76	2,1	2,1	NUM
ejpam-189	109	77	by	by	ADP
ejpam-189	109	78	mean	mean	NOUN
ejpam-189	109	79	value	value	NOUN
ejpam-189	109	80	theorem	theorem	NOUN
ejpam-189	109	81	we	we	PRON
ejpam-189	109	82	obtain	obtain	VERB
ejpam-189	109	83	xα	xα	ADP
ejpam-189	109	84	−	−	PUNCT
ejpam-189	109	85	yα	yα	VERB
ejpam-189	110	1	=	=	SYM
ejpam-189	110	2	α(x	α(x	PROPN
ejpam-189	110	3	−	−	PROPN
ejpam-189	110	4	y)(x	y)(x	PROPN
ejpam-189	110	5	−	−	PROPN
ejpam-189	110	6	ηy)α−1	ηy)α−1	PROPN
ejpam-189	110	7	,	,	PUNCT
ejpam-189	110	8	(	(	PUNCT
ejpam-189	110	9	0	0	NUM
ejpam-189	110	10	≤	≤	NUM
ejpam-189	110	11	η	η	PROPN
ejpam-189	110	12	≤	≤	ADJ
ejpam-189	110	13	1	1	NUM
ejpam-189	110	14	)	)	PUNCT
ejpam-189	110	15	.	.	PUNCT
ejpam-189	111	1	using	use	VERB
ejpam-189	111	2	this	this	DET
ejpam-189	111	3	fact	fact	NOUN
ejpam-189	111	4	and	and	CCONJ
ejpam-189	111	5	(	(	PUNCT
ejpam-189	111	6	5	5	NUM
ejpam-189	111	7	)	)	PUNCT
ejpam-189	111	8	,	,	PUNCT
ejpam-189	111	9	young	young	PROPN
ejpam-189	111	10	’s	’s	PART
ejpam-189	111	11	inequality	inequality	NOUN
ejpam-189	111	12	(	(	PUNCT
ejpam-189	111	13	since	since	SCONJ
ejpam-189	111	14	α−1	α−1	PROPN
ejpam-189	111	15	α	α	NOUN
ejpam-189	111	16	+	+	NOUN
ejpam-189	111	17	1	1	NUM
ejpam-189	111	18	α	α	NOUN
ejpam-189	111	19	=	=	SYM
ejpam-189	111	20	1	1	NUM
ejpam-189	111	21	)	)	PUNCT
ejpam-189	111	22	,	,	PUNCT
ejpam-189	111	23	we	we	PRON
ejpam-189	111	24	have	have	VERB
ejpam-189	111	25	‖|f(u1)−	‖|f(u1)−	NUM
ejpam-189	111	26	f(u2)‖|e0	f(u2)‖|e0	PROPN
ejpam-189	111	27	2,1	2,1	NUM
ejpam-189	111	28	=	=	SYM
ejpam-189	111	29	‖a|u1|αu1	‖a|u1|αu1	PROPN
ejpam-189	111	30	+	+	CCONJ
ejpam-189	111	31	|v1|αu1	|v1|αu1	ADJ
ejpam-189	112	1	−	−	PROPN
ejpam-189	113	1	(	(	PUNCT
ejpam-189	113	2	a|u2|αu2	a|u2|αu2	ADP
ejpam-189	113	3	+	+	PROPN
ejpam-189	113	4	|v2|αu2)‖e0	|v2|αu2)‖e0	PROPN
ejpam-189	113	5	2,1	2,1	NUM
ejpam-189	113	6	z.	z.	X
ejpam-189	113	7	he	he	PRON
ejpam-189	113	8	and	and	CCONJ
ejpam-189	113	9	x.	x.	NOUN
ejpam-189	113	10	zhao	zhao	PROPN
ejpam-189	113	11	/	/	SYM
ejpam-189	113	12	eur	eur	PROPN
ejpam-189	113	13	.	.	PUNCT
ejpam-189	114	1	j.	j.	PROPN
ejpam-189	114	2	pure	pure	PROPN
ejpam-189	114	3	appl	appl	PROPN
ejpam-189	114	4	.	.	PROPN
ejpam-189	114	5	math	math	PROPN
ejpam-189	114	6	,	,	PUNCT
ejpam-189	114	7	3	3	NUM
ejpam-189	114	8	(	(	PUNCT
ejpam-189	114	9	2010	2010	NUM
ejpam-189	114	10	)	)	PUNCT
ejpam-189	114	11	,	,	PUNCT
ejpam-189	114	12	227	227	NUM
ejpam-189	114	13	-	-	SYM
ejpam-189	114	14	234	234	NUM
ejpam-189	114	15	232	232	NUM
ejpam-189	115	1	+	+	PUNCT
ejpam-189	115	2	‖|u1|αv1	‖|u1|αv1	VERB
ejpam-189	115	3	+	+	NOUN
ejpam-189	115	4	a|v1|αv1	a|v1|αv1	ADJ
ejpam-189	115	5	−	−	PROPN
ejpam-189	115	6	(	(	PUNCT
ejpam-189	115	7	|u2|αv2	|u2|αv2	PROPN
ejpam-189	115	8	+	+	CCONJ
ejpam-189	115	9	a|v2|αv2)‖e0	a|v2|αv2)‖e0	ADJ
ejpam-189	115	10	2,1	2,1	NUM
ejpam-189	115	11	=	=	SYM
ejpam-189	115	12	‖(a|u1|α+	‖(a|u1|α+	SYM
ejpam-189	115	13	|v1|α)(u1−	|v1|α)(u1−	PROPN
ejpam-189	115	14	u2	u2	NOUN
ejpam-189	115	15	)	)	PUNCT
ejpam-189	115	16	+	+	CCONJ
ejpam-189	115	17	(	(	PUNCT
ejpam-189	115	18	a(|u1|α−	a(|u1|α−	PRON
ejpam-189	115	19	|u2|α	|u2|α	NOUN
ejpam-189	115	20	)	)	PUNCT
ejpam-189	115	21	+	+	CCONJ
ejpam-189	115	22	(	(	PUNCT
ejpam-189	115	23	|v1|α−	|v1|α−	NOUN
ejpam-189	115	24	|v2|α))u2‖e0	|v2|α))u2‖e0	NUM
ejpam-189	115	25	2,1	2,1	NUM
ejpam-189	115	26	+	+	PROPN
ejpam-189	115	27	‖(|u1|α+	‖(|u1|α+	X
ejpam-189	115	28	a|v1|α)(v1−	a|v1|α)(v1−	PROPN
ejpam-189	115	29	v2	v2	PROPN
ejpam-189	115	30	)	)	PUNCT
ejpam-189	115	31	+	+	CCONJ
ejpam-189	115	32	(	(	PUNCT
ejpam-189	115	33	(	(	PUNCT
ejpam-189	115	34	|u1|α−	|u1|α−	PRON
ejpam-189	115	35	|u2|α	|u2|α	NOUN
ejpam-189	115	36	)	)	PUNCT
ejpam-189	116	1	+	+	CCONJ
ejpam-189	116	2	a(|v1|α−	a(|v1|α−	ADJ
ejpam-189	116	3	|v2|α))v2‖e0	|v2|α))v2‖e0	DET
ejpam-189	116	4	2,1	2,1	NUM
ejpam-189	116	5	≤	≤	NUM
ejpam-189	116	6	‖(a|u1|α+	‖(a|u1|α+	X
ejpam-189	116	7	|v1|α)(u1−	|v1|α)(u1−	PROPN
ejpam-189	116	8	u2)‖e0	u2)‖e0	PROPN
ejpam-189	116	9	2,1	2,1	NUM
ejpam-189	116	10	+	+	CCONJ
ejpam-189	116	11	‖(a(|u1|α−	‖(a(|u1|α−	PROPN
ejpam-189	116	12	|u2|α	|u2|α	NOUN
ejpam-189	116	13	)	)	PUNCT
ejpam-189	117	1	+	+	CCONJ
ejpam-189	117	2	‖(|v1|α−	‖(|v1|α−	NUM
ejpam-189	117	3	|v2|α))u2‖e0	|v2|α))u2‖e0	NUM
ejpam-189	117	4	2,1	2,1	NUM
ejpam-189	117	5	+	+	PROPN
ejpam-189	117	6	‖(|u1|α+	‖(|u1|α+	X
ejpam-189	117	7	a|v1|α)(v1−	a|v1|α)(v1−	PROPN
ejpam-189	117	8	v2)‖e0	v2)‖e0	PROPN
ejpam-189	117	9	2,1	2,1	NUM
ejpam-189	117	10	+	+	CCONJ
ejpam-189	117	11	‖((|u1|α−	‖((|u1|α−	PRON
ejpam-189	117	12	|u2|α	|u2|α	NOUN
ejpam-189	117	13	)	)	PUNCT
ejpam-189	118	1	+	+	CCONJ
ejpam-189	118	2	a(|v1|α−	a(|v1|α−	ADJ
ejpam-189	118	3	|v2|α))v2‖e0	|v2|α))v2‖e0	DET
ejpam-189	118	4	2,1	2,1	NUM
ejpam-189	118	5	≤	≤	NUM
ejpam-189	118	6	c	c	NOUN
ejpam-189	118	7	h	h	NOUN
ejpam-189	118	8	‖u1‖αe0	‖u1‖αe0	NOUN
ejpam-189	118	9	2,1	2,1	NUM
ejpam-189	119	1	+	+	CCONJ
ejpam-189	119	2	‖u2‖αe0	‖u2‖αe0	PROPN
ejpam-189	119	3	2,1	2,1	NUM
ejpam-189	119	4	+	+	CCONJ
ejpam-189	119	5	‖v1‖αe0	‖v1‖αe0	NOUN
ejpam-189	119	6	2,1	2,1	NUM
ejpam-189	119	7	+	+	CCONJ
ejpam-189	119	8	‖v2‖αe0	‖v2‖αe0	NOUN
ejpam-189	119	9	2,1	2,1	NUM
ejpam-189	119	10	i	i	PRON
ejpam-189	119	11	(	(	PUNCT
ejpam-189	119	12	‖u1	‖u1	ADV
ejpam-189	119	13	−	−	X
ejpam-189	119	14	u2‖e0	u2‖e0	PROPN
ejpam-189	119	15	2,1	2,1	NUM
ejpam-189	119	16	+	+	CCONJ
ejpam-189	119	17	‖v1	‖v1	X
ejpam-189	119	18	−	−	PROPN
ejpam-189	119	19	v2‖e0	v2‖e0	NUM
ejpam-189	119	20	2,1	2,1	NUM
ejpam-189	119	21	)	)	PUNCT
ejpam-189	119	22	≤	≤	NOUN
ejpam-189	119	23	c(‖|u1‖|αe0	c(‖|u1‖|αe0	NOUN
ejpam-189	119	24	2,1	2,1	NUM
ejpam-189	119	25	+	+	CCONJ
ejpam-189	119	26	‖|u2‖|αe0	‖|u2‖|αe0	NUM
ejpam-189	119	27	2,1	2,1	NUM
ejpam-189	119	28	)	)	PUNCT
ejpam-189	119	29	‖|u1−	‖|u1−	SYM
ejpam-189	119	30	u2‖|e0	u2‖|e0	NOUN
ejpam-189	119	31	2,1	2,1	NUM
ejpam-189	119	32	.	.	PUNCT
ejpam-189	120	1	3	3	X
ejpam-189	120	2	.	.	X
ejpam-189	120	3	proof	proof	NOUN
ejpam-189	120	4	of	of	ADP
ejpam-189	120	5	the	the	DET
ejpam-189	120	6	main	main	ADJ
ejpam-189	120	7	result	result	NOUN
ejpam-189	120	8	we	we	PRON
ejpam-189	120	9	shall	shall	AUX
ejpam-189	120	10	make	make	VERB
ejpam-189	120	11	use	use	NOUN
ejpam-189	120	12	of	of	ADP
ejpam-189	120	13	the	the	DET
ejpam-189	120	14	fixed	fix	VERB
ejpam-189	120	15	point	point	NOUN
ejpam-189	120	16	theorem	theorem	VERB
ejpam-189	120	17	to	to	PART
ejpam-189	120	18	solve	solve	VERB
ejpam-189	120	19	the	the	DET
ejpam-189	120	20	integral	integral	ADJ
ejpam-189	120	21	equation	equation	NOUN
ejpam-189	120	22	u	u	NOUN
ejpam-189	120	23	=	=	PROPN
ejpam-189	120	24	t	t	PROPN
ejpam-189	120	25	(	(	PUNCT
ejpam-189	120	26	u	u	NOUN
ejpam-189	120	27	)	)	PUNCT
ejpam-189	120	28	=	=	SYM
ejpam-189	121	1	λ(t)φ−	λ(t)φ−	NOUN
ejpam-189	122	1	i	i	PRON
ejpam-189	122	2	∫	∫	PROPN
ejpam-189	122	3	t	t	NOUN
ejpam-189	122	4	0	0	NUM
ejpam-189	123	1	λ(t	λ(t	NOUN
ejpam-189	123	2	−τ)f(u(τ))dτ	−τ)f(u(τ))dτ	PROPN
ejpam-189	123	3	.	.	PUNCT
ejpam-189	124	1	(	(	PUNCT
ejpam-189	124	2	6	6	X
ejpam-189	124	3	)	)	PUNCT
ejpam-189	124	4	define	define	VERB
ejpam-189	124	5	a	a	DET
ejpam-189	124	6	metric	metric	ADJ
ejpam-189	124	7	space	space	NOUN
ejpam-189	124	8	as	as	SCONJ
ejpam-189	124	9	follows	follow	VERB
ejpam-189	124	10	:	:	PUNCT
ejpam-189	124	11	d	d	X
ejpam-189	124	12	=	=	PUNCT
ejpam-189	124	13	{	{	PUNCT
ejpam-189	124	14	u	u	NOUN
ejpam-189	124	15	:	:	PUNCT
ejpam-189	124	16	‖|u‖|c(0,t	‖|u‖|c(0,t	NOUN
ejpam-189	124	17	;	;	PUNCT
ejpam-189	124	18	e0	e0	PROPN
ejpam-189	124	19	2,1	2,1	NUM
ejpam-189	124	20	)	)	PUNCT
ejpam-189	124	21	≤	≤	NUM
ejpam-189	124	22	m	m	ADP
ejpam-189	124	23	}	}	PUNCT
ejpam-189	124	24	,	,	PUNCT
ejpam-189	124	25	d(u	d(u	PROPN
ejpam-189	124	26	,	,	PUNCT
ejpam-189	124	27	v	v	NOUN
ejpam-189	124	28	)	)	PUNCT
ejpam-189	124	29	=	=	PUNCT
ejpam-189	124	30	‖|u	‖|u	NUM
ejpam-189	124	31	−	−	NUM
ejpam-189	124	32	v‖|c(0,t	v‖|c(0,t	NOUN
ejpam-189	124	33	;	;	PUNCT
ejpam-189	124	34	e0	e0	PROPN
ejpam-189	124	35	2,1	2,1	NUM
ejpam-189	124	36	)	)	PUNCT
ejpam-189	124	37	.	.	PUNCT
ejpam-189	125	1	by	by	ADP
ejpam-189	125	2	lemma	lemma	PROPN
ejpam-189	125	3	5	5	NUM
ejpam-189	125	4	,	,	PUNCT
ejpam-189	125	5	we	we	PRON
ejpam-189	125	6	have	have	VERB
ejpam-189	125	7	‖|λ(t)φ‖|c(0,t	‖|λ(t)φ‖|c(0,t	NOUN
ejpam-189	125	8	;	;	PUNCT
ejpam-189	125	9	e0	e0	PROPN
ejpam-189	125	10	2,1	2,1	NUM
ejpam-189	125	11	)	)	PUNCT
ejpam-189	125	12	≤	≤	NUM
ejpam-189	125	13	c‖|φ‖|e0	c‖|φ‖|e0	X
ejpam-189	125	14	2,1	2,1	NUM
ejpam-189	125	15	.	.	PUNCT
ejpam-189	126	1	(	(	PUNCT
ejpam-189	126	2	7	7	NUM
ejpam-189	126	3	)	)	PUNCT
ejpam-189	126	4	by	by	ADP
ejpam-189	126	5	lemma	lemma	PROPN
ejpam-189	126	6	5	5	NUM
ejpam-189	126	7	and	and	CCONJ
ejpam-189	126	8	the	the	DET
ejpam-189	126	9	first	first	ADJ
ejpam-189	126	10	inequality	inequality	NOUN
ejpam-189	126	11	of	of	ADP
ejpam-189	126	12	lemma	lemma	PROPN
ejpam-189	126	13	6	6	NUM
ejpam-189	126	14	,	,	PUNCT
ejpam-189	126	15	we	we	PRON
ejpam-189	126	16	obtain	obtain	VERB
ejpam-189	126	17	�	�	PROPN
ejpam-189	126	18	�	�	PROPN
ejpam-189	126	19	�	�	PROPN
ejpam-189	126	20	∫	∫	PROPN
ejpam-189	126	21	t	t	PROPN
ejpam-189	126	22	0	0	NUM
ejpam-189	127	1	λ(t	λ(t	NOUN
ejpam-189	127	2	−τ)f(u(τ))dτ	−τ)f(u(τ))dτ	PROPN
ejpam-189	127	3	�	�	PROPN
ejpam-189	127	4	�	�	PROPN
ejpam-189	127	5	�	�	PROPN
ejpam-189	127	6	c(0,t	c(0,t	PROPN
ejpam-189	127	7	;	;	PUNCT
ejpam-189	127	8	e0	e0	PROPN
ejpam-189	127	9	2,1	2,1	NUM
ejpam-189	127	10	)	)	PUNCT
ejpam-189	127	11	≤	≤	NUM
ejpam-189	127	12	c	c	NOUN
ejpam-189	127	13	t‖|u‖|α+1	t‖|u‖|α+1	PROPN
ejpam-189	127	14	c(0,t	c(0,t	NOUN
ejpam-189	127	15	;	;	PUNCT
ejpam-189	127	16	e0	e0	PROPN
ejpam-189	127	17	2,1	2,1	NUM
ejpam-189	127	18	)	)	PUNCT
ejpam-189	127	19	.	.	PUNCT
ejpam-189	128	1	(	(	PUNCT
ejpam-189	128	2	8)	8)	NUM
ejpam-189	128	3	let	let	VERB
ejpam-189	128	4	us	we	PRON
ejpam-189	128	5	consider	consider	VERB
ejpam-189	128	6	the	the	DET
ejpam-189	128	7	mapping	mapping	NOUN
ejpam-189	128	8	t	t	NOUN
ejpam-189	128	9	:	:	PUNCT
ejpam-189	128	10	u	u	NOUN
ejpam-189	128	11	→	→	SYM
ejpam-189	128	12	λ(t)φ	λ(t)φ	X
ejpam-189	128	13	−	−	NOUN
ejpam-189	129	1	i	i	PRON
ejpam-189	129	2	∫	∫	PROPN
ejpam-189	129	3	t	t	NOUN
ejpam-189	129	4	0	0	NUM
ejpam-189	130	1	λ(t	λ(t	NOUN
ejpam-189	130	2	−	−	PROPN
ejpam-189	130	3	τ)f(u(τ))dτ	τ)f(u(τ))dτ	PROPN
ejpam-189	130	4	.	.	PUNCT
ejpam-189	131	1	we	we	PRON
ejpam-189	131	2	show	show	VERB
ejpam-189	131	3	that	that	SCONJ
ejpam-189	131	4	t	t	NOUN
ejpam-189	131	5	:	:	PUNCT
ejpam-189	131	6	(	(	PUNCT
ejpam-189	131	7	d	d	X
ejpam-189	131	8	,	,	PUNCT
ejpam-189	131	9	d)→	d)→	X
ejpam-189	131	10	(	(	PUNCT
ejpam-189	131	11	d	d	NOUN
ejpam-189	131	12	,	,	PUNCT
ejpam-189	131	13	d	d	NOUN
ejpam-189	131	14	)	)	PUNCT
ejpam-189	131	15	is	be	AUX
ejpam-189	131	16	a	a	DET
ejpam-189	131	17	contraction	contraction	NOUN
ejpam-189	131	18	mapping	mapping	NOUN
ejpam-189	131	19	.	.	PUNCT
ejpam-189	132	1	indeed	indeed	ADV
ejpam-189	132	2	,	,	PUNCT
ejpam-189	132	3	for	for	ADP
ejpam-189	132	4	any	any	DET
ejpam-189	132	5	u	u	PROPN
ejpam-189	132	6	∈	∈	PROPN
ejpam-189	132	7	d	d	NOUN
ejpam-189	132	8	,	,	PUNCT
ejpam-189	132	9	by	by	ADP
ejpam-189	132	10	(	(	PUNCT
ejpam-189	132	11	7	7	NUM
ejpam-189	132	12	)	)	PUNCT
ejpam-189	132	13	and	and	CCONJ
ejpam-189	132	14	(	(	PUNCT
ejpam-189	132	15	8)	8)	NUM
ejpam-189	132	16	we	we	PRON
ejpam-189	132	17	have	have	AUX
ejpam-189	132	18	‖|t	‖|t	NOUN
ejpam-189	132	19	(	(	PUNCT
ejpam-189	132	20	u)‖|c(0,t	u)‖|c(0,t	NOUN
ejpam-189	132	21	;	;	PUNCT
ejpam-189	132	22	e0	e0	PROPN
ejpam-189	132	23	2,1	2,1	NUM
ejpam-189	132	24	)	)	PUNCT
ejpam-189	132	25	≤	≤	NUM
ejpam-189	132	26	c‖|φ‖|e0	c‖|φ‖|e0	X
ejpam-189	132	27	2,1	2,1	NUM
ejpam-189	133	1	+	+	CCONJ
ejpam-189	133	2	c	c	NOUN
ejpam-189	133	3	t‖|u‖|α+1	t‖|u‖|α+1	PROPN
ejpam-189	133	4	c(0,t	c(0,t	NOUN
ejpam-189	133	5	;	;	PUNCT
ejpam-189	133	6	e0	e0	PROPN
ejpam-189	133	7	2,1	2,1	NUM
ejpam-189	133	8	)	)	PUNCT
ejpam-189	133	9	.	.	PUNCT
ejpam-189	134	1	put	put	VERB
ejpam-189	134	2	m	m	PROPN
ejpam-189	134	3	=	=	NOUN
ejpam-189	134	4	2c‖|φ‖|e0	2c‖|φ‖|e0	NUM
ejpam-189	134	5	2,1	2,1	NUM
ejpam-189	134	6	,	,	PUNCT
ejpam-189	134	7	we	we	PRON
ejpam-189	134	8	have	have	VERB
ejpam-189	134	9	‖|t	‖|t	NOUN
ejpam-189	134	10	(	(	PUNCT
ejpam-189	134	11	u)‖|c(0,t	u)‖|c(0,t	NOUN
ejpam-189	134	12	;	;	PUNCT
ejpam-189	134	13	e0	e0	PROPN
ejpam-189	134	14	2,1	2,1	NUM
ejpam-189	134	15	)	)	PUNCT
ejpam-189	134	16	≤	≤	NUM
ejpam-189	134	17	m	m	VERB
ejpam-189	134	18	2	2	NUM
ejpam-189	134	19	+	+	NUM
ejpam-189	134	20	c	c	PROPN
ejpam-189	134	21	t	t	PROPN
ejpam-189	134	22	mα+1	mα+1	NUM
ejpam-189	134	23	.	.	PUNCT
ejpam-189	135	1	(	(	PUNCT
ejpam-189	135	2	9	9	X
ejpam-189	135	3	)	)	PUNCT
ejpam-189	135	4	let	let	VERB
ejpam-189	135	5	t	t	NOUN
ejpam-189	135	6	be	be	AUX
ejpam-189	135	7	small	small	ADJ
ejpam-189	135	8	enough	enough	ADV
ejpam-189	135	9	to	to	PART
ejpam-189	135	10	satisfies	satisfie	NOUN
ejpam-189	135	11	c	c	PROPN
ejpam-189	135	12	t	t	NOUN
ejpam-189	135	13	mα	mα	PROPN
ejpam-189	135	14	≤	≤	ADV
ejpam-189	135	15	1	1	NUM
ejpam-189	135	16	4	4	NUM
ejpam-189	135	17	.	.	PUNCT
ejpam-189	136	1	it	it	PRON
ejpam-189	136	2	follows	follow	VERB
ejpam-189	136	3	from	from	ADP
ejpam-189	136	4	(	(	PUNCT
ejpam-189	136	5	9	9	NUM
ejpam-189	136	6	)	)	PUNCT
ejpam-189	136	7	that	that	PRON
ejpam-189	136	8	t	t	PROPN
ejpam-189	136	9	(	(	PUNCT
ejpam-189	136	10	u	u	NOUN
ejpam-189	136	11	)	)	PUNCT
ejpam-189	136	12	∈	∈	PROPN
ejpam-189	136	13	d.	d.	NOUN
ejpam-189	136	14	references	reference	VERB
ejpam-189	136	15	233	233	NUM
ejpam-189	136	16	similarly	similarly	ADV
ejpam-189	136	17	,	,	PUNCT
ejpam-189	136	18	we	we	PRON
ejpam-189	136	19	have	have	VERB
ejpam-189	136	20	‖|t	‖|t	NOUN
ejpam-189	136	21	(	(	PUNCT
ejpam-189	136	22	u)−t	u)−t	PROPN
ejpam-189	136	23	(	(	PUNCT
ejpam-189	136	24	v	v	NOUN
ejpam-189	136	25	)	)	PUNCT
ejpam-189	136	26	‖|c(0,t	‖|c(0,t	PROPN
ejpam-189	136	27	;	;	PUNCT
ejpam-189	136	28	e0	e0	PROPN
ejpam-189	136	29	2,1	2,1	NUM
ejpam-189	136	30	)	)	PUNCT
ejpam-189	136	31	≤	≤	NUM
ejpam-189	136	32	1	1	NUM
ejpam-189	136	33	2	2	NUM
ejpam-189	136	34	‖|u	‖|u	NUM
ejpam-189	136	35	−	−	PROPN
ejpam-189	136	36	v‖|c(0,t	v‖|c(0,t	NOUN
ejpam-189	136	37	;	;	PUNCT
ejpam-189	136	38	e0	e0	PROPN
ejpam-189	136	39	2,1	2,1	NUM
ejpam-189	136	40	)	)	PUNCT
ejpam-189	136	41	.	.	PUNCT
ejpam-189	137	1	indeed	indeed	ADV
ejpam-189	137	2	,	,	PUNCT
ejpam-189	137	3	∀	∀	X
ejpam-189	137	4	u	u	NOUN
ejpam-189	137	5	,	,	PUNCT
ejpam-189	137	6	v	v	NOUN
ejpam-189	137	7	∈	∈	NOUN
ejpam-189	137	8	(	(	PUNCT
ejpam-189	137	9	d	d	NOUN
ejpam-189	137	10	,	,	PUNCT
ejpam-189	137	11	d	d	NOUN
ejpam-189	137	12	)	)	PUNCT
ejpam-189	137	13	,	,	PUNCT
ejpam-189	137	14	by	by	ADP
ejpam-189	137	15	lemma	lemma	PROPN
ejpam-189	137	16	5	5	NUM
ejpam-189	137	17	and	and	CCONJ
ejpam-189	137	18	the	the	DET
ejpam-189	137	19	second	second	ADJ
ejpam-189	137	20	inequality	inequality	NOUN
ejpam-189	137	21	of	of	ADP
ejpam-189	137	22	lemma	lemma	PROPN
ejpam-189	137	23	6	6	NUM
ejpam-189	137	24	,	,	PUNCT
ejpam-189	137	25	we	we	PRON
ejpam-189	137	26	obtain	obtain	VERB
ejpam-189	137	27	‖|t	‖|t	NOUN
ejpam-189	137	28	(	(	PUNCT
ejpam-189	137	29	u)−t	u)−t	PROPN
ejpam-189	137	30	(	(	PUNCT
ejpam-189	137	31	v	v	NOUN
ejpam-189	137	32	)	)	PUNCT
ejpam-189	138	1	‖|c(0,t	‖|c(0,t	PROPN
ejpam-189	138	2	;	;	PUNCT
ejpam-189	138	3	e0	e0	PROPN
ejpam-189	138	4	2,1	2,1	NUM
ejpam-189	138	5	)	)	PUNCT
ejpam-189	138	6	≤	≤	NUM
ejpam-189	138	7	�	�	PROPN
ejpam-189	138	8	�	�	PROPN
ejpam-189	138	9	�	�	PROPN
ejpam-189	138	10	∫	∫	PROPN
ejpam-189	138	11	t	t	PROPN
ejpam-189	138	12	0	0	NUM
ejpam-189	139	1	λ(t	λ(t	NOUN
ejpam-189	139	2	−τ)[f(u(τ))−	−τ)[f(u(τ))−	NUM
ejpam-189	139	3	f(v	f(v	NOUN
ejpam-189	139	4	)	)	PUNCT
ejpam-189	139	5	dτ	dτ	PROPN
ejpam-189	139	6	�	�	PROPN
ejpam-189	139	7	�	�	PROPN
ejpam-189	139	8	�	�	PROPN
ejpam-189	139	9	c(0,t	c(0,t	PROPN
ejpam-189	139	10	;	;	PUNCT
ejpam-189	139	11	e0	e0	PROPN
ejpam-189	139	12	2,1	2,1	NUM
ejpam-189	139	13	)	)	PUNCT
ejpam-189	139	14	≤	≤	NUM
ejpam-189	139	15	c	c	NOUN
ejpam-189	139	16	t‖|f(u)−	t‖|f(u)−	NOUN
ejpam-189	139	17	f(v	f(v	PROPN
ejpam-189	139	18	)	)	PUNCT
ejpam-189	140	1	‖|c(0,t	‖|c(0,t	PROPN
ejpam-189	140	2	;	;	PUNCT
ejpam-189	140	3	e0	e0	PROPN
ejpam-189	140	4	2,1	2,1	NUM
ejpam-189	140	5	)	)	PUNCT
ejpam-189	140	6	≤	≤	NUM
ejpam-189	140	7	c	c	NOUN
ejpam-189	140	8	t	t	PROPN
ejpam-189	140	9	h	h	NOUN
ejpam-189	140	10	‖|u‖|α	‖|u‖|α	NOUN
ejpam-189	140	11	c(0,t	c(0,t	NOUN
ejpam-189	140	12	;	;	PUNCT
ejpam-189	140	13	e0	e0	PROPN
ejpam-189	140	14	2,1	2,1	NUM
ejpam-189	140	15	)	)	PUNCT
ejpam-189	140	16	+	+	NUM
ejpam-189	140	17	‖|v‖|α	‖|v‖|α	NOUN
ejpam-189	140	18	c(0,t	c(0,t	NOUN
ejpam-189	140	19	;	;	PUNCT
ejpam-189	140	20	e0	e0	PROPN
ejpam-189	140	21	2,1	2,1	NUM
ejpam-189	140	22	)	)	PUNCT
ejpam-189	140	23	i	i	PRON
ejpam-189	140	24	‖|u	‖|u	VERB
ejpam-189	140	25	−	−	PROPN
ejpam-189	140	26	v‖|c(0,t	v‖|c(0,t	NOUN
ejpam-189	140	27	;	;	PUNCT
ejpam-189	140	28	e0	e0	PROPN
ejpam-189	140	29	2,1	2,1	NUM
ejpam-189	140	30	)	)	PUNCT
ejpam-189	140	31	≤	≤	NOUN
ejpam-189	140	32	2c	2c	NOUN
ejpam-189	140	33	t	t	NOUN
ejpam-189	140	34	mα‖|u	mα‖|u	NOUN
ejpam-189	140	35	−	−	PROPN
ejpam-189	140	36	v‖|c(0,t	v‖|c(0,t	NOUN
ejpam-189	140	37	;	;	PUNCT
ejpam-189	140	38	e0	e0	PROPN
ejpam-189	140	39	2,1	2,1	NUM
ejpam-189	140	40	)	)	PUNCT
ejpam-189	140	41	≤	≤	NUM
ejpam-189	140	42	1	1	NUM
ejpam-189	140	43	2	2	NUM
ejpam-189	140	44	‖|u	‖|u	NUM
ejpam-189	140	45	−	−	PROPN
ejpam-189	140	46	v‖|c(0,t	v‖|c(0,t	NOUN
ejpam-189	140	47	;	;	PUNCT
ejpam-189	140	48	e0	e0	PROPN
ejpam-189	140	49	2,1	2,1	NUM
ejpam-189	140	50	)	)	PUNCT
ejpam-189	140	51	.	.	PUNCT
ejpam-189	141	1	hence	hence	ADV
ejpam-189	141	2	,	,	PUNCT
ejpam-189	141	3	by	by	ADP
ejpam-189	141	4	banach	banach	ADV
ejpam-189	141	5	fixed	fix	VERB
ejpam-189	141	6	point	point	NOUN
ejpam-189	141	7	theorem	theorem	VERB
ejpam-189	141	8	,	,	PUNCT
ejpam-189	141	9	we	we	PRON
ejpam-189	141	10	see	see	VERB
ejpam-189	141	11	that	that	SCONJ
ejpam-189	141	12	t	t	PROPN
ejpam-189	141	13	has	have	VERB
ejpam-189	141	14	a	a	DET
ejpam-189	141	15	fixed	fix	VERB
ejpam-189	141	16	point	point	NOUN
ejpam-189	141	17	u	u	NOUN
ejpam-189	141	18	∈	∈	PROPN
ejpam-189	141	19	d	d	X
ejpam-189	141	20	which	which	PRON
ejpam-189	141	21	is	be	AUX
ejpam-189	141	22	a	a	DET
ejpam-189	141	23	solution	solution	NOUN
ejpam-189	141	24	of	of	ADP
ejpam-189	141	25	integral	integral	ADJ
ejpam-189	141	26	equation	equation	NOUN
ejpam-189	141	27	(	(	PUNCT
ejpam-189	141	28	6	6	NUM
ejpam-189	141	29	)	)	PUNCT
ejpam-189	141	30	.	.	PUNCT
ejpam-189	142	1	we	we	PRON
ejpam-189	142	2	can	can	AUX
ejpam-189	142	3	extend	extend	VERB
ejpam-189	142	4	this	this	DET
ejpam-189	142	5	solution	solution	NOUN
ejpam-189	142	6	step	step	NOUN
ejpam-189	142	7	by	by	ADP
ejpam-189	142	8	step	step	NOUN
ejpam-189	142	9	and	and	CCONJ
ejpam-189	142	10	finally	finally	ADV
ejpam-189	142	11	find	find	VERB
ejpam-189	142	12	a	a	DET
ejpam-189	142	13	maximal	maximal	ADJ
ejpam-189	142	14	t	t	NOUN
ejpam-189	142	15	∗	∗	NOUN
ejpam-189	142	16	>	>	X
ejpam-189	142	17	0	0	NUM
ejpam-189	142	18	such	such	ADJ
ejpam-189	142	19	that	that	SCONJ
ejpam-189	142	20	u	u	PROPN
ejpam-189	142	21	∈	∈	PROPN
ejpam-189	142	22	c([0	c([0	NOUN
ejpam-189	142	23	,	,	PUNCT
ejpam-189	142	24	t	t	PROPN
ejpam-189	142	25	∗	∗	NOUN
ejpam-189	142	26	)	)	PUNCT
ejpam-189	142	27	,	,	PUNCT
ejpam-189	142	28	e0	e0	PROPN
ejpam-189	142	29	2,1(r	2,1(r	NOUN
ejpam-189	142	30	n	n	CCONJ
ejpam-189	142	31	)	)	PUNCT
ejpam-189	142	32	)	)	PUNCT
ejpam-189	142	33	and	and	CCONJ
ejpam-189	142	34	lim	lim	PROPN
ejpam-189	142	35	t→t∗	t→t∗	PRON
ejpam-189	142	36	sup‖|u(t)‖|e0	sup‖|u(t)‖|e0	VERB
ejpam-189	142	37	2,1(r	2,1(r	NUM
ejpam-189	142	38	n	n	CCONJ
ejpam-189	142	39	)	)	PUNCT
ejpam-189	143	1	=	=	SYM
ejpam-189	143	2	∞.	∞.	PROPN
ejpam-189	143	3	the	the	DET
ejpam-189	143	4	uniqueness	uniqueness	NOUN
ejpam-189	143	5	of	of	ADP
ejpam-189	143	6	such	such	ADJ
ejpam-189	143	7	solutions	solution	NOUN
ejpam-189	143	8	can	can	AUX
ejpam-189	143	9	also	also	ADV
ejpam-189	143	10	be	be	AUX
ejpam-189	143	11	shown	show	VERB
ejpam-189	143	12	in	in	ADP
ejpam-189	143	13	a	a	DET
ejpam-189	143	14	standard	standard	ADJ
ejpam-189	143	15	way	way	NOUN
ejpam-189	143	16	.	.	PUNCT
ejpam-189	144	1	this	this	PRON
ejpam-189	144	2	finishes	finish	VERB
ejpam-189	144	3	the	the	DET
ejpam-189	144	4	proof	proof	NOUN
ejpam-189	144	5	of	of	ADP
ejpam-189	144	6	the	the	DET
ejpam-189	144	7	theorem	theorem	NOUN
ejpam-189	144	8	.	.	PUNCT
ejpam-189	145	1	acknowledgements	acknowledgement	NOUN
ejpam-189	145	2	this	this	DET
ejpam-189	145	3	work	work	NOUN
ejpam-189	145	4	is	be	AUX
ejpam-189	145	5	financially	financially	ADV
ejpam-189	145	6	supported	support	VERB
ejpam-189	145	7	by	by	ADP
ejpam-189	145	8	the	the	DET
ejpam-189	145	9	research	research	NOUN
ejpam-189	145	10	projects	project	NOUN
ejpam-189	145	11	of	of	ADP
ejpam-189	145	12	zhejiang	zhejiang	PROPN
ejpam-189	145	13	ocean	ocean	PROPN
ejpam-189	145	14	university	university	PROPN
ejpam-189	145	15	under	under	ADP
ejpam-189	145	16	the	the	DET
ejpam-189	145	17	grant	grant	NOUN
ejpam-189	145	18	numbers	number	NOUN
ejpam-189	145	19	x08m014	x08m014	PROPN
ejpam-189	145	20	and	and	CCONJ
ejpam-189	145	21	21065030608	21065030608	NUM
ejpam-189	145	22	.	.	PUNCT
ejpam-189	146	1	references	reference	NOUN
ejpam-189	146	2	[	[	X
ejpam-189	146	3	1	1	NUM
ejpam-189	146	4	]	]	X
ejpam-189	146	5	j	j	PROPN
ejpam-189	146	6	bergh	bergh	PROPN
ejpam-189	146	7	,	,	PUNCT
ejpam-189	146	8	j	j	PROPN
ejpam-189	146	9	löfström	löfström	NOUN
ejpam-189	146	10	.	.	PUNCT
ejpam-189	147	1	interpolation	interpolation	NOUN
ejpam-189	147	2	spaces	space	NOUN
ejpam-189	147	3	.	.	PUNCT
ejpam-189	148	1	springer	springer	NOUN
ejpam-189	148	2	-	-	PUNCT
ejpam-189	148	3	verlag	verlag	PROPN
ejpam-189	148	4	,	,	PUNCT
ejpam-189	148	5	berlin	berlin	PROPN
ejpam-189	148	6	,	,	PUNCT
ejpam-189	148	7	1974	1974	NUM
ejpam-189	148	8	.	.	PUNCT
ejpam-189	149	1	[	[	X
ejpam-189	149	2	2	2	NUM
ejpam-189	149	3	]	]	PUNCT
ejpam-189	149	4	a	a	DET
ejpam-189	149	5	l	l	NOUN
ejpam-189	149	6	berkhoer	berkhoer	NOUN
ejpam-189	149	7	,	,	PUNCT
ejpam-189	149	8	v	v	NOUN
ejpam-189	149	9	e	e	NOUN
ejpam-189	149	10	zakharov	zakharov	PROPN
ejpam-189	149	11	.	.	PUNCT
ejpam-189	150	1	self	self	NOUN
ejpam-189	150	2	excitation	excitation	NOUN
ejpam-189	150	3	of	of	ADP
ejpam-189	150	4	waves	wave	NOUN
ejpam-189	150	5	with	with	ADP
ejpam-189	150	6	diferent	diferent	NOUN
ejpam-189	150	7	polarizations	polarization	NOUN
ejpam-189	150	8	in	in	ADP
ejpam-189	150	9	nonlinear	nonlinear	ADJ
ejpam-189	150	10	media	medium	NOUN
ejpam-189	150	11	.	.	PUNCT
ejpam-189	151	1	sov	sov	NOUN
ejpam-189	151	2	.	.	PUNCT
ejpam-189	152	1	phys	phy	NOUN
ejpam-189	152	2	.	.	PUNCT
ejpam-189	153	1	jetp	jetp	PROPN
ejpam-189	153	2	,	,	PUNCT
ejpam-189	153	3	31:486–90	31:486–90	VERB
ejpam-189	153	4	,	,	PUNCT
ejpam-189	153	5	1970	1970	NUM
ejpam-189	153	6	.	.	PUNCT
ejpam-189	154	1	[	[	X
ejpam-189	154	2	3	3	X
ejpam-189	154	3	]	]	PUNCT
ejpam-189	154	4	t	t	NOUN
ejpam-189	154	5	cazenave.semilinear	cazenave.semilinear	NUM
ejpam-189	154	6	schrödinger	schrödinger	ADJ
ejpam-189	154	7	equations	equation	NOUN
ejpam-189	154	8	.	.	PUNCT
ejpam-189	155	1	amer	amer	PROPN
ejpam-189	155	2	.	.	PUNCT
ejpam-189	155	3	math	math	PROPN
ejpam-189	155	4	.	.	PUNCT
ejpam-189	156	1	soc	soc	PROPN
ejpam-189	156	2	.	.	PUNCT
ejpam-189	156	3	,	,	PUNCT
ejpam-189	156	4	providence	providence	NOUN
ejpam-189	156	5	,	,	PUNCT
ejpam-189	156	6	2003	2003	NUM
ejpam-189	156	7	.	.	PUNCT
ejpam-189	157	1	[	[	X
ejpam-189	157	2	4	4	X
ejpam-189	157	3	]	]	X
ejpam-189	157	4	c	c	PROPN
ejpam-189	157	5	j	j	PROPN
ejpam-189	157	6	chen	chen	PROPN
ejpam-189	157	7	,	,	PUNCT
ejpam-189	157	8	p	p	PROPN
ejpam-189	157	9	a	a	DET
ejpam-189	157	10	wai	wai	PROPN
ejpam-189	157	11	,	,	PUNCT
ejpam-189	157	12	c	c	PROPN
ejpam-189	157	13	r	r	NOUN
ejpam-189	157	14	menyuk	menyuk	NOUN
ejpam-189	157	15	.	.	PUNCT
ejpam-189	158	1	soliton	soliton	NOUN
ejpam-189	158	2	switch	switch	NOUN
ejpam-189	158	3	using	use	VERB
ejpam-189	158	4	birefringent	birefringent	NOUN
ejpam-189	158	5	optical	optical	ADJ
ejpam-189	158	6	fibers	fiber	NOUN
ejpam-189	158	7	.	.	PUNCT
ejpam-189	159	1	opt	opt	PROPN
ejpam-189	159	2	.	.	PUNCT
ejpam-189	160	1	lett	lett	PROPN
ejpam-189	160	2	.	.	PROPN
ejpam-189	160	3	,	,	PUNCT
ejpam-189	160	4	15	15	NUM
ejpam-189	160	5	:	:	PUNCT
ejpam-189	160	6	477–9	477–9	NUM
ejpam-189	160	7	,	,	PUNCT
ejpam-189	160	8	1990	1990	NUM
ejpam-189	160	9	.	.	PUNCT
ejpam-189	161	1	[	[	X
ejpam-189	161	2	5	5	NUM
ejpam-189	161	3	]	]	SYM
ejpam-189	161	4	s	s	NOUN
ejpam-189	161	5	v	v	NOUN
ejpam-189	161	6	manakov	manakov	NOUN
ejpam-189	161	7	.	.	PUNCT
ejpam-189	162	1	on	on	ADP
ejpam-189	162	2	the	the	DET
ejpam-189	162	3	theory	theory	NOUN
ejpam-189	162	4	of	of	ADP
ejpam-189	162	5	two	two	NUM
ejpam-189	162	6	-	-	PUNCT
ejpam-189	162	7	dimensional	dimensional	ADJ
ejpam-189	162	8	stationary	stationary	ADJ
ejpam-189	162	9	self	self	NOUN
ejpam-189	162	10	-	-	PUNCT
ejpam-189	162	11	focusing	focus	VERB
ejpam-189	162	12	of	of	ADP
ejpam-189	162	13	electromagnetic	electromagnetic	ADJ
ejpam-189	162	14	waves	wave	NOUN
ejpam-189	162	15	.	.	PUNCT
ejpam-189	163	1	sov	sov	NOUN
ejpam-189	163	2	.	.	PUNCT
ejpam-189	164	1	phys	phy	NOUN
ejpam-189	164	2	.	.	PUNCT
ejpam-189	165	1	jept	jept	PROPN
ejpam-189	165	2	,	,	PUNCT
ejpam-189	165	3	38	38	NUM
ejpam-189	165	4	:	:	SYM
ejpam-189	165	5	248–53	248–53	NUM
ejpam-189	165	6	,	,	PUNCT
ejpam-189	165	7	1974	1974	NUM
ejpam-189	165	8	.	.	PUNCT
ejpam-189	166	1	[	[	X
ejpam-189	166	2	6	6	NUM
ejpam-189	166	3	]	]	PUNCT
ejpam-189	166	4	a	a	DET
ejpam-189	166	5	pazy	pazy	NOUN
ejpam-189	166	6	.	.	PUNCT
ejpam-189	167	1	semigroups	semigroup	NOUN
ejpam-189	167	2	of	of	ADP
ejpam-189	167	3	linear	linear	PROPN
ejpam-189	167	4	operators	operator	NOUN
ejpam-189	167	5	and	and	CCONJ
ejpam-189	167	6	applications	application	NOUN
ejpam-189	167	7	to	to	ADP
ejpam-189	167	8	partial	partial	ADJ
ejpam-189	167	9	differential	differential	ADJ
ejpam-189	167	10	equations	equation	NOUN
ejpam-189	167	11	.	.	PUNCT
ejpam-189	168	1	springer	springer	NOUN
ejpam-189	168	2	-	-	PUNCT
ejpam-189	168	3	verlag	verlag	PROPN
ejpam-189	168	4	,	,	PUNCT
ejpam-189	168	5	berlin	berlin	PROPN
ejpam-189	168	6	,	,	PUNCT
ejpam-189	168	7	1983	1983	NUM
ejpam-189	168	8	.	.	PUNCT
ejpam-189	169	1	[	[	X
ejpam-189	169	2	7	7	NUM
ejpam-189	169	3	]	]	SYM
ejpam-189	169	4	b	b	NOUN
ejpam-189	169	5	tan	tan	PROPN
ejpam-189	169	6	,	,	PUNCT
ejpam-189	169	7	r	r	PROPN
ejpam-189	169	8	wu	wu	PROPN
ejpam-189	169	9	.	.	PUNCT
ejpam-189	170	1	nonlinear	nonlinear	ADJ
ejpam-189	170	2	rossby	rossby	ADJ
ejpam-189	170	3	waves	wave	NOUN
ejpam-189	170	4	and	and	CCONJ
ejpam-189	170	5	their	their	PRON
ejpam-189	170	6	interactions	interaction	NOUN
ejpam-189	170	7	.	.	PUNCT
ejpam-189	171	1	sci	sci	PROPN
ejpam-189	171	2	.	.	PUNCT
ejpam-189	172	1	china	china	PROPN
ejpam-189	172	2	b	b	PROPN
ejpam-189	172	3	,	,	PUNCT
ejpam-189	172	4	36:1367–80	36:1367–80	NUM
ejpam-189	172	5	,	,	PUNCT
ejpam-189	172	6	1993	1993	NUM
ejpam-189	172	7	.	.	PUNCT
ejpam-189	173	1	references	reference	NOUN
ejpam-189	173	2	234	234	NUM
ejpam-189	173	3	[	[	SYM
ejpam-189	173	4	8	8	NUM
ejpam-189	173	5	]	]	SYM
ejpam-189	173	6	b	b	NOUN
ejpam-189	173	7	tan	tan	PROPN
ejpam-189	173	8	,	,	PUNCT
ejpam-189	173	9	s	s	PART
ejpam-189	173	10	liu	liu	PROPN
ejpam-189	173	11	.	.	PUNCT
ejpam-189	174	1	collision	collision	NOUN
ejpam-189	174	2	interactions	interaction	NOUN
ejpam-189	174	3	of	of	ADP
ejpam-189	174	4	solitons	soliton	NOUN
ejpam-189	174	5	in	in	ADP
ejpam-189	174	6	a	a	DET
ejpam-189	174	7	baroclinic	baroclinic	ADJ
ejpam-189	174	8	atmosphere	atmosphere	NOUN
ejpam-189	174	9	.	.	PUNCT
ejpam-189	175	1	j.	j.	PROPN
ejpam-189	175	2	atmos	atmos	PROPN
ejpam-189	175	3	.	.	PUNCT
ejpam-189	176	1	sci	sci	PROPN
ejpam-189	176	2	.	.	PROPN
ejpam-189	176	3	,	,	PUNCT
ejpam-189	176	4	52	52	NUM
ejpam-189	176	5	:	:	PUNCT
ejpam-189	176	6	1501–12	1501–12	NUM
ejpam-189	176	7	,	,	PUNCT
ejpam-189	176	8	1995	1995	NUM
ejpam-189	176	9	.	.	PUNCT
ejpam-189	177	1	[	[	X
ejpam-189	177	2	9	9	NUM
ejpam-189	177	3	]	]	X
ejpam-189	177	4	s	s	X
ejpam-189	177	5	trillo	trillo	PROPN
ejpam-189	177	6	,	,	PUNCT
ejpam-189	177	7	s	s	PART
ejpam-189	177	8	wabnitz	wabnitz	NOUN
ejpam-189	177	9	.	.	PUNCT
ejpam-189	178	1	ultrashort	ultrashort	PROPN
ejpam-189	178	2	pulse	pulse	NOUN
ejpam-189	178	3	train	train	NOUN
ejpam-189	178	4	generation	generation	NOUN
ejpam-189	178	5	through	through	ADP
ejpam-189	178	6	induced	induce	VERB
ejpam-189	178	7	modulational	modulational	ADJ
ejpam-189	178	8	polarization	polarization	NOUN
ejpam-189	178	9	instability	instability	NOUN
ejpam-189	178	10	in	in	ADP
ejpam-189	178	11	a	a	DET
ejpam-189	178	12	birefringent	birefringent	NOUN
ejpam-189	178	13	kerr	kerr	NOUN
ejpam-189	178	14	-	-	PUNCT
ejpam-189	178	15	like	like	ADJ
ejpam-189	178	16	medium	medium	NOUN
ejpam-189	178	17	.	.	PUNCT
ejpam-189	179	1	j.	j.	PROPN
ejpam-189	179	2	opt	opt	PROPN
ejpam-189	179	3	.	.	PUNCT
ejpam-189	180	1	soc	soc	PROPN
ejpam-189	180	2	.	.	PUNCT
ejpam-189	181	1	am	be	AUX
ejpam-189	181	2	.	.	PROPN
ejpam-189	181	3	,	,	PUNCT
ejpam-189	181	4	b6	b6	NOUN
ejpam-189	181	5	:	:	PUNCT
ejpam-189	181	6	238–49	238–49	NUM
ejpam-189	181	7	,	,	PUNCT
ejpam-189	181	8	1989	1989	NUM
ejpam-189	181	9	.	.	PUNCT
ejpam-189	182	1	[	[	X
ejpam-189	182	2	10	10	NUM
ejpam-189	182	3	]	]	SYM
ejpam-189	182	4	b	b	NOUN
ejpam-189	182	5	x	x	SYM
ejpam-189	182	6	wang	wang	PROPN
ejpam-189	182	7	,	,	PUNCT
ejpam-189	182	8	l	l	PROPN
ejpam-189	182	9	f	f	PROPN
ejpam-189	182	10	zhao	zhao	PROPN
ejpam-189	182	11	,	,	PUNCT
ejpam-189	182	12	b	b	PROPN
ejpam-189	182	13	l	l	NOUN
ejpam-189	182	14	guo	guo	X
ejpam-189	182	15	.	.	PUNCT
ejpam-189	182	16	isometric	isometric	ADJ
ejpam-189	182	17	decomposition	decomposition	NOUN
ejpam-189	182	18	operators	operator	NOUN
ejpam-189	182	19	,	,	PUNCT
ejpam-189	182	20	function	function	NOUN
ejpam-189	182	21	spaces	space	NOUN
ejpam-189	182	22	eλp	eλp	VERB
ejpam-189	182	23	,	,	PUNCT
ejpam-189	182	24	q	q	NOUN
ejpam-189	182	25	and	and	CCONJ
ejpam-189	182	26	applications	application	NOUN
ejpam-189	182	27	to	to	PART
ejpam-189	182	28	nonlinear	nonlinear	ADJ
ejpam-189	182	29	evolution	evolution	NOUN
ejpam-189	182	30	equations	equation	NOUN
ejpam-189	182	31	.	.	PUNCT
ejpam-189	183	1	j.	j.	PROPN
ejpam-189	183	2	funct	funct	PROPN
ejpam-189	183	3	.	.	PUNCT
ejpam-189	184	1	anal	anal	PROPN
ejpam-189	184	2	.	.	PROPN
ejpam-189	184	3	,	,	PUNCT
ejpam-189	184	4	233:1–39	233:1–39	NUM
ejpam-189	184	5	,	,	PUNCT
ejpam-189	184	6	2006	2006	NUM
ejpam-189	184	7	.	.	PUNCT