id	sid	tid	token	lemma	pos
ejpam-8	1	1	european	european	PROPN
ejpam-8	1	2	journal	journal	PROPN
ejpam-8	1	3	of	of	ADP
ejpam-8	1	4	pure	pure	ADJ
ejpam-8	1	5	and	and	CCONJ
ejpam-8	1	6	applied	apply	VERB
ejpam-8	1	7	mathematics	mathematic	NOUN
ejpam-8	1	8	vol	vol	NOUN
ejpam-8	1	9	.	.	PROPN
ejpam-8	2	1	1	1	NUM
ejpam-8	2	2	,	,	PUNCT
ejpam-8	2	3	no	no	INTJ
ejpam-8	2	4	.	.	NOUN
ejpam-8	2	5	2	2	NUM
ejpam-8	2	6	,	,	PUNCT
ejpam-8	2	7	2008	2008	NUM
ejpam-8	2	8	,	,	PUNCT
ejpam-8	2	9	(	(	PUNCT
ejpam-8	2	10	3	3	NUM
ejpam-8	2	11	-	-	SYM
ejpam-8	2	12	10	10	NUM
ejpam-8	2	13	)	)	PUNCT
ejpam-8	2	14	issn	issn	PROPN
ejpam-8	2	15	1307	1307	NUM
ejpam-8	2	16	-	-	SYM
ejpam-8	2	17	5543	5543	NUM
ejpam-8	2	18	–	–	PUNCT
ejpam-8	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-8	2	20	asymptotic	asymptotic	ADJ
ejpam-8	2	21	attractors	attractor	NOUN
ejpam-8	2	22	of	of	ADP
ejpam-8	2	23	benjamin	benjamin	PROPN
ejpam-8	2	24	-	-	PUNCT
ejpam-8	2	25	bona	bona	ADJ
ejpam-8	2	26	-	-	PUNCT
ejpam-8	2	27	mahony	mahony	NOUN
ejpam-8	2	28	equations	equation	NOUN
ejpam-8	3	1	chaosheng	chaosheng	PROPN
ejpam-8	3	2	zhu∗†	zhu∗†	NOUN
ejpam-8	3	3	school	school	NOUN
ejpam-8	3	4	of	of	ADP
ejpam-8	3	5	mathematics	mathematic	NOUN
ejpam-8	3	6	and	and	CCONJ
ejpam-8	3	7	statistics	statistic	NOUN
ejpam-8	3	8	,	,	PUNCT
ejpam-8	3	9	southwest	southwest	PROPN
ejpam-8	3	10	university	university	NOUN
ejpam-8	3	11	,	,	PUNCT
ejpam-8	3	12	chongqing	chongqing	PROPN
ejpam-8	3	13	,	,	PUNCT
ejpam-8	3	14	400715	400715	NUM
ejpam-8	3	15	,	,	PUNCT
ejpam-8	4	1	p.	p.	PROPN
ejpam-8	4	2	r.	r.	PROPN
ejpam-8	4	3	china	china	PROPN
ejpam-8	4	4	abstract	abstract	PROPN
ejpam-8	4	5	.	.	PUNCT
ejpam-8	5	1	in	in	ADP
ejpam-8	5	2	this	this	DET
ejpam-8	5	3	paper	paper	NOUN
ejpam-8	5	4	,	,	PUNCT
ejpam-8	5	5	we	we	PRON
ejpam-8	5	6	consider	consider	VERB
ejpam-8	5	7	the	the	DET
ejpam-8	5	8	long	long	ADJ
ejpam-8	5	9	time	time	NOUN
ejpam-8	5	10	behavior	behavior	NOUN
ejpam-8	5	11	of	of	ADP
ejpam-8	5	12	solution	solution	NOUN
ejpam-8	5	13	for	for	ADP
ejpam-8	5	14	the	the	DET
ejpam-8	5	15	benjamin	benjamin	NOUN
ejpam-8	5	16	-	-	PUNCT
ejpam-8	5	17	bona	bona	ADJ
ejpam-8	5	18	-	-	PUNCT
ejpam-8	5	19	mahony	mahony	NOUN
ejpam-8	5	20	equations	equation	NOUN
ejpam-8	5	21	with	with	ADP
ejpam-8	5	22	periodic	periodic	ADJ
ejpam-8	5	23	boundary	boundary	ADJ
ejpam-8	5	24	conditions	condition	NOUN
ejpam-8	5	25	.	.	PUNCT
ejpam-8	6	1	by	by	ADP
ejpam-8	6	2	the	the	DET
ejpam-8	6	3	method	method	NOUN
ejpam-8	6	4	of	of	ADP
ejpam-8	6	5	orthogonal	orthogonal	ADJ
ejpam-8	6	6	decomposition	decomposition	NOUN
ejpam-8	6	7	,	,	PUNCT
ejpam-8	6	8	we	we	PRON
ejpam-8	6	9	show	show	VERB
ejpam-8	6	10	that	that	SCONJ
ejpam-8	6	11	the	the	DET
ejpam-8	6	12	existence	existence	NOUN
ejpam-8	6	13	of	of	ADP
ejpam-8	6	14	asymptotic	asymptotic	ADJ
ejpam-8	6	15	attractor	attractor	NOUN
ejpam-8	6	16	which	which	PRON
ejpam-8	6	17	overcome	overcome	VERB
ejpam-8	6	18	difficulty	difficulty	NOUN
ejpam-8	6	19	come	come	VERB
ejpam-8	6	20	from	from	ADP
ejpam-8	6	21	the	the	DET
ejpam-8	6	22	precision	precision	NOUN
ejpam-8	6	23	of	of	ADP
ejpam-8	6	24	approximate	approximate	ADJ
ejpam-8	6	25	inertial	inertial	ADJ
ejpam-8	6	26	manifolds	manifold	NOUN
ejpam-8	6	27	.	.	PUNCT
ejpam-8	7	1	moreover	moreover	ADV
ejpam-8	7	2	,	,	PUNCT
ejpam-8	7	3	the	the	DET
ejpam-8	7	4	dimensions	dimension	NOUN
ejpam-8	7	5	estimate	estimate	NOUN
ejpam-8	7	6	of	of	ADP
ejpam-8	7	7	the	the	DET
ejpam-8	7	8	asymptotic	asymptotic	ADJ
ejpam-8	7	9	attractor	attractor	NOUN
ejpam-8	7	10	is	be	AUX
ejpam-8	7	11	obtained	obtain	VERB
ejpam-8	7	12	.	.	PUNCT
ejpam-8	8	1	key	key	ADJ
ejpam-8	8	2	words	word	NOUN
ejpam-8	8	3	:	:	PUNCT
ejpam-8	8	4	benjamin	benjamin	NOUN
ejpam-8	8	5	-	-	PUNCT
ejpam-8	8	6	bona	bona	ADJ
ejpam-8	8	7	-	-	PUNCT
ejpam-8	8	8	mahony	mahony	NOUN
ejpam-8	8	9	equation	equation	NOUN
ejpam-8	8	10	,	,	PUNCT
ejpam-8	8	11	asymptotic	asymptotic	ADJ
ejpam-8	8	12	attractor	attractor	NOUN
ejpam-8	8	13	,	,	PUNCT
ejpam-8	8	14	dimensions	dimension	NOUN
ejpam-8	8	15	estimate	estimate	VERB
ejpam-8	8	16	,	,	PUNCT
ejpam-8	8	17	orthogonal	orthogonal	ADJ
ejpam-8	8	18	decomposition	decomposition	NOUN
ejpam-8	8	19	.	.	PUNCT
ejpam-8	9	1	1	1	X
ejpam-8	9	2	.	.	X
ejpam-8	9	3	introduction	introduction	NOUN
ejpam-8	9	4	it	it	PRON
ejpam-8	9	5	is	be	AUX
ejpam-8	9	6	well	well	ADV
ejpam-8	9	7	known	know	VERB
ejpam-8	9	8	that	that	SCONJ
ejpam-8	9	9	the	the	DET
ejpam-8	9	10	concept	concept	NOUN
ejpam-8	9	11	of	of	ADP
ejpam-8	9	12	an	an	DET
ejpam-8	9	13	inertial	inertial	ADJ
ejpam-8	9	14	manifold	manifold	NOUN
ejpam-8	9	15	plays	play	VERB
ejpam-8	9	16	an	an	DET
ejpam-8	9	17	important	important	ADJ
ejpam-8	9	18	role	role	NOUN
ejpam-8	9	19	in	in	ADP
ejpam-8	9	20	the	the	DET
ejpam-8	9	21	investigation	investigation	NOUN
ejpam-8	9	22	of	of	ADP
ejpam-8	9	23	the	the	DET
ejpam-8	9	24	long	long	ADJ
ejpam-8	9	25	-	-	PUNCT
ejpam-8	9	26	time	time	NOUN
ejpam-8	9	27	behavior	behavior	NOUN
ejpam-8	9	28	of	of	ADP
ejpam-8	9	29	infinite	infinite	ADJ
ejpam-8	9	30	dimensional	dimensional	ADJ
ejpam-8	9	31	dynamical	dynamical	ADJ
ejpam-8	9	32	systems	system	NOUN
ejpam-8	9	33	,	,	PUNCT
ejpam-8	9	34	see	see	VERB
ejpam-8	9	35	,	,	PUNCT
ejpam-8	9	36	for	for	ADP
ejpam-8	9	37	example	example	NOUN
ejpam-8	9	38	,	,	PUNCT
ejpam-8	9	39	[	[	X
ejpam-8	9	40	6	6	NUM
ejpam-8	9	41	,	,	PUNCT
ejpam-8	9	42	8	8	NUM
ejpam-8	9	43	]	]	PUNCT
ejpam-8	9	44	.	.	PUNCT
ejpam-8	10	1	inertial	inertial	ADJ
ejpam-8	10	2	manifold	manifold	NOUN
ejpam-8	10	3	is	be	AUX
ejpam-8	10	4	a	a	DET
ejpam-8	10	5	finite	finite	ADJ
ejpam-8	10	6	dimensional	dimensional	ADJ
ejpam-8	10	7	invariant	invariant	ADJ
ejpam-8	10	8	manifold	manifold	NOUN
ejpam-8	10	9	in	in	ADP
ejpam-8	10	10	the	the	DET
ejpam-8	10	11	phase	phase	NOUN
ejpam-8	10	12	space	space	NOUN
ejpam-8	10	13	h	h	NOUN
ejpam-8	10	14	of	of	ADP
ejpam-8	10	15	the	the	DET
ejpam-8	10	16	system	system	NOUN
ejpam-8	10	17	which	which	PRON
ejpam-8	10	18	attracts	attract	VERB
ejpam-8	10	19	exponentially	exponentially	ADV
ejpam-8	10	20	all	all	DET
ejpam-8	10	21	orbits	orbit	NOUN
ejpam-8	10	22	.	.	PUNCT
ejpam-8	11	1	it	it	PRON
ejpam-8	11	2	is	be	AUX
ejpam-8	11	3	constructed	construct	VERB
ejpam-8	11	4	as	as	ADP
ejpam-8	11	5	the	the	DET
ejpam-8	11	6	graph	graph	NOUN
ejpam-8	11	7	of	of	ADP
ejpam-8	11	8	a	a	DET
ejpam-8	11	9	mapping	mapping	NOUN
ejpam-8	11	10	from	from	ADP
ejpam-8	11	11	ph	ph	PROPN
ejpam-8	11	12	to	to	PART
ejpam-8	11	13	(	(	PUNCT
ejpam-8	11	14	i	i	PRON
ejpam-8	11	15	−	−	PROPN
ejpam-8	11	16	p)h	p)h	NOUN
ejpam-8	11	17	,	,	PUNCT
ejpam-8	11	18	where	where	SCONJ
ejpam-8	11	19	p	p	NOUN
ejpam-8	11	20	is	be	AUX
ejpam-8	11	21	a	a	DET
ejpam-8	11	22	projection	projection	NOUN
ejpam-8	11	23	of	of	ADP
ejpam-8	11	24	finite	finite	ADJ
ejpam-8	11	25	dimension	dimension	NOUN
ejpam-8	11	26	n	n	NOUN
ejpam-8	11	27	.	.	PUNCT
ejpam-8	12	1	however	however	ADV
ejpam-8	12	2	the	the	DET
ejpam-8	12	3	existence	existence	NOUN
ejpam-8	12	4	usually	usually	ADV
ejpam-8	12	5	holds	hold	VERB
ejpam-8	12	6	under	under	ADP
ejpam-8	12	7	a	a	DET
ejpam-8	12	8	restrictive	restrictive	ADJ
ejpam-8	12	9	spectral	spectral	ADJ
ejpam-8	12	10	gap	gap	NOUN
ejpam-8	12	11	condition	condition	NOUN
ejpam-8	12	12	.	.	PUNCT
ejpam-8	13	1	to	to	PART
ejpam-8	13	2	investigate	investigate	VERB
ejpam-8	13	3	the	the	DET
ejpam-8	13	4	case	case	NOUN
ejpam-8	13	5	when	when	SCONJ
ejpam-8	13	6	the	the	DET
ejpam-8	13	7	spectral	spectral	ADJ
ejpam-8	13	8	gap	gap	NOUN
ejpam-8	13	9	condition	condition	NOUN
ejpam-8	13	10	does	do	AUX
ejpam-8	13	11	not	not	PART
ejpam-8	13	12	hold	hold	VERB
ejpam-8	13	13	the	the	DET
ejpam-8	13	14	concepts	concept	NOUN
ejpam-8	13	15	of	of	ADP
ejpam-8	13	16	approximate	approximate	ADJ
ejpam-8	13	17	inertial	inertial	ADJ
ejpam-8	13	18	manifolds	manifold	NOUN
ejpam-8	14	1	[	[	X
ejpam-8	14	2	7	7	NUM
ejpam-8	14	3	]	]	PUNCT
ejpam-8	14	4	have	have	AUX
ejpam-8	14	5	been	be	AUX
ejpam-8	14	6	introduced	introduce	VERB
ejpam-8	14	7	.	.	PUNCT
ejpam-8	15	1	but	but	CCONJ
ejpam-8	15	2	the	the	DET
ejpam-8	15	3	precision	precision	NOUN
ejpam-8	15	4	of	of	ADP
ejpam-8	15	5	approximate	approximate	ADJ
ejpam-8	15	6	inertial	inertial	ADJ
ejpam-8	15	7	manifolds	manifold	NOUN
ejpam-8	15	8	is	be	AUX
ejpam-8	15	9	inextricable	inextricable	ADJ
ejpam-8	15	10	difficulty	difficulty	NOUN
ejpam-8	15	11	at	at	ADP
ejpam-8	15	12	all	all	DET
ejpam-8	15	13	times	time	NOUN
ejpam-8	15	14	.	.	PUNCT
ejpam-8	16	1	to	to	PART
ejpam-8	16	2	overcome	overcome	VERB
ejpam-8	16	3	this	this	DET
ejpam-8	16	4	difficulty	difficulty	NOUN
ejpam-8	16	5	,	,	PUNCT
ejpam-8	16	6	recently	recently	ADV
ejpam-8	16	7	,	,	PUNCT
ejpam-8	16	8	new	new	ADJ
ejpam-8	16	9	concept	concept	NOUN
ejpam-8	16	10	of	of	ADP
ejpam-8	16	11	asymptotic	asymptotic	ADJ
ejpam-8	16	12	attractor	attractor	NOUN
ejpam-8	16	13	has	have	AUX
ejpam-8	16	14	been	be	AUX
ejpam-8	16	15	introduced	introduce	VERB
ejpam-8	16	16	[	[	X
ejpam-8	16	17	12	12	NUM
ejpam-8	16	18	]	]	PUNCT
ejpam-8	16	19	.	.	PUNCT
ejpam-8	17	1	now	now	ADV
ejpam-8	17	2	let	let	VERB
ejpam-8	17	3	us	we	PRON
ejpam-8	17	4	recall	recall	VERB
ejpam-8	17	5	the	the	DET
ejpam-8	17	6	definition	definition	NOUN
ejpam-8	17	7	of	of	ADP
ejpam-8	17	8	asymptotic	asymptotic	ADJ
ejpam-8	17	9	attractor	attractor	NOUN
ejpam-8	17	10	.	.	PUNCT
ejpam-8	18	1	we	we	PRON
ejpam-8	18	2	consider	consider	VERB
ejpam-8	18	3	the	the	DET
ejpam-8	18	4	solution	solution	NOUN
ejpam-8	18	5	u(t	u(t	NOUN
ejpam-8	18	6	)	)	PUNCT
ejpam-8	18	7	of	of	ADP
ejpam-8	18	8	a	a	DET
ejpam-8	18	9	differential	differential	ADJ
ejpam-8	18	10	equation	equation	NOUN
ejpam-8	18	11	ut	ut	PROPN
ejpam-8	18	12	+	+	PROPN
ejpam-8	18	13	au=	au=	PROPN
ejpam-8	18	14	f(u	f(u	PROPN
ejpam-8	18	15	)	)	PUNCT
ejpam-8	18	16	,	,	PUNCT
ejpam-8	18	17	(	(	PUNCT
ejpam-8	18	18	1.1	1.1	NUM
ejpam-8	18	19	)	)	PUNCT
ejpam-8	18	20	with	with	ADP
ejpam-8	18	21	initial	initial	ADJ
ejpam-8	18	22	data	datum	NOUN
ejpam-8	18	23	u(0	u(0	PROPN
ejpam-8	18	24	)	)	PUNCT
ejpam-8	18	25	=	=	PUNCT
ejpam-8	19	1	u0	u0	ADJ
ejpam-8	19	2	.	.	PUNCT
ejpam-8	20	1	(	(	PUNCT
ejpam-8	20	2	1.2	1.2	NUM
ejpam-8	20	3	)	)	PUNCT
ejpam-8	20	4	the	the	DET
ejpam-8	20	5	variable	variable	ADJ
ejpam-8	20	6	u(t	u(t	NOUN
ejpam-8	20	7	)	)	PUNCT
ejpam-8	20	8	belongs	belong	VERB
ejpam-8	20	9	to	to	ADP
ejpam-8	20	10	a	a	DET
ejpam-8	20	11	linear	linear	ADJ
ejpam-8	20	12	space	space	NOUN
ejpam-8	20	13	e	e	NOUN
ejpam-8	20	14	called	call	VERB
ejpam-8	20	15	the	the	DET
ejpam-8	20	16	phase	phase	NOUN
ejpam-8	20	17	space	space	NOUN
ejpam-8	20	18	,	,	PUNCT
ejpam-8	20	19	and	and	CCONJ
ejpam-8	20	20	f	f	PROPN
ejpam-8	20	21	is	be	AUX
ejpam-8	20	22	a	a	DET
ejpam-8	20	23	mapping	mapping	NOUN
ejpam-8	20	24	of	of	ADP
ejpam-8	20	25	e	e	NOUN
ejpam-8	20	26	into	into	ADP
ejpam-8	20	27	itself	itself	PRON
ejpam-8	20	28	.	.	PUNCT
ejpam-8	21	1	the	the	DET
ejpam-8	21	2	semigroup	semigroup	PROPN
ejpam-8	21	3	n	n	PROPN
ejpam-8	21	4	s(t	s(t	PROPN
ejpam-8	21	5	)	)	PUNCT
ejpam-8	21	6	o	o	NOUN
ejpam-8	21	7	t≥0	t≥0	NOUN
ejpam-8	21	8	associated	associate	VERB
ejpam-8	21	9	to	to	ADP
ejpam-8	21	10	problems	problem	NOUN
ejpam-8	21	11	(	(	PUNCT
ejpam-8	21	12	1.1)-(1.2	1.1)-(1.2	NUM
ejpam-8	21	13	):	):	PUNCT
ejpam-8	21	14	s(t	s(t	PROPN
ejpam-8	21	15	)	)	PUNCT
ejpam-8	21	16	:	:	PUNCT
ejpam-8	21	17	u0	u0	PROPN
ejpam-8	21	18	∈	∈	PROPN
ejpam-8	21	19	e→	e→	PROPN
ejpam-8	21	20	u(t	u(t	PROPN
ejpam-8	21	21	)	)	PUNCT
ejpam-8	21	22	∈	∈	PROPN
ejpam-8	21	23	e.	e.	PROPN
ejpam-8	21	24	(	(	PUNCT
ejpam-8	21	25	1.3	1.3	NUM
ejpam-8	21	26	)	)	PUNCT
ejpam-8	21	27	∗corresponding	∗corresponde	VERB
ejpam-8	21	28	author	author	NOUN
ejpam-8	21	29	.	.	PUNCT
ejpam-8	22	1	email	email	NOUN
ejpam-8	22	2	address	address	NOUN
ejpam-8	22	3	:	:	PUNCT
ejpam-8	22	4	zhu.cauchy@yahoo.com.cn	zhu.cauchy@yahoo.com.cn	PROPN
ejpam-8	22	5	(	(	PUNCT
ejpam-8	22	6	chaosheng	chaosheng	PROPN
ejpam-8	22	7	zhu	zhu	PROPN
ejpam-8	22	8	)	)	PUNCT
ejpam-8	22	9	†this	†this	DET
ejpam-8	22	10	work	work	NOUN
ejpam-8	22	11	was	be	AUX
ejpam-8	22	12	supported	support	VERB
ejpam-8	22	13	by	by	ADP
ejpam-8	22	14	doctor	doctor	NOUN
ejpam-8	22	15	fund	fund	PROPN
ejpam-8	22	16	of	of	ADP
ejpam-8	22	17	southwest	southwest	PROPN
ejpam-8	22	18	university	university	PROPN
ejpam-8	22	19	(	(	PUNCT
ejpam-8	22	20	swub2008003	swub2008003	PROPN
ejpam-8	22	21	)	)	PUNCT
ejpam-8	22	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-8	23	1	3	3	NUM
ejpam-8	23	2	c	c	X
ejpam-8	23	3	©	©	PROPN
ejpam-8	23	4	2007	2007	NUM
ejpam-8	23	5	ejpam	ejpam	NOUN
ejpam-8	23	6	all	all	DET
ejpam-8	23	7	rights	right	NOUN
ejpam-8	23	8	reserved	reserve	VERB
ejpam-8	23	9	.	.	PUNCT
ejpam-8	24	1	chaosheng	chaosheng	PROPN
ejpam-8	24	2	zhu	zhu	PROPN
ejpam-8	24	3	/	/	SYM
ejpam-8	24	4	eur	eur	PROPN
ejpam-8	24	5	.	.	PUNCT
ejpam-8	25	1	j.	j.	PROPN
ejpam-8	25	2	pure	pure	PROPN
ejpam-8	25	3	appl	appl	PROPN
ejpam-8	25	4	.	.	PROPN
ejpam-8	25	5	math	math	PROPN
ejpam-8	25	6	,	,	PUNCT
ejpam-8	25	7	1	1	NUM
ejpam-8	25	8	(	(	PUNCT
ejpam-8	25	9	2008	2008	NUM
ejpam-8	25	10	)	)	PUNCT
ejpam-8	25	11	,	,	PUNCT
ejpam-8	25	12	(	(	PUNCT
ejpam-8	25	13	3	3	NUM
ejpam-8	25	14	-	-	SYM
ejpam-8	25	15	10	10	NUM
ejpam-8	25	16	)	)	PUNCT
ejpam-8	25	17	4	4	NUM
ejpam-8	25	18	if	if	SCONJ
ejpam-8	25	19	b	b	NOUN
ejpam-8	25	20	is	be	AUX
ejpam-8	25	21	a	a	DET
ejpam-8	25	22	bounded	bounded	ADJ
ejpam-8	25	23	absorbing	absorbing	NOUN
ejpam-8	25	24	set	set	NOUN
ejpam-8	25	25	,	,	PUNCT
ejpam-8	25	26	then	then	ADV
ejpam-8	25	27	a	a	DET
ejpam-8	25	28	=	=	SYM
ejpam-8	25	29	⋂	⋂	PROPN
ejpam-8	25	30	s≥0	s≥0	PROPN
ejpam-8	25	31	⋃	⋃	PROPN
ejpam-8	25	32	t≥s	t≥s	NOUN
ejpam-8	25	33	,	,	PUNCT
ejpam-8	25	34	u0∈b	u0∈b	ADV
ejpam-8	25	35	s(t)u0	s(t)u0	NOUN
ejpam-8	25	36	.	.	PUNCT
ejpam-8	26	1	(	(	PUNCT
ejpam-8	26	2	1.4	1.4	NUM
ejpam-8	26	3	)	)	PUNCT
ejpam-8	26	4	is	be	AUX
ejpam-8	26	5	global	global	ADJ
ejpam-8	26	6	attractor	attractor	NOUN
ejpam-8	26	7	for	for	ADP
ejpam-8	26	8	problems	problem	NOUN
ejpam-8	26	9	(	(	PUNCT
ejpam-8	26	10	1.1)-(1.2	1.1)-(1.2	NUM
ejpam-8	26	11	)	)	PUNCT
ejpam-8	26	12	.	.	PUNCT
ejpam-8	27	1	definition	definition	NOUN
ejpam-8	27	2	1.1	1.1	NUM
ejpam-8	27	3	.	.	PUNCT
ejpam-8	28	1	[	[	X
ejpam-8	28	2	12	12	NUM
ejpam-8	28	3	]	]	PUNCT
ejpam-8	28	4	.	.	PUNCT
ejpam-8	29	1	let	let	VERB
ejpam-8	29	2	e	e	PRON
ejpam-8	29	3	be	be	AUX
ejpam-8	29	4	a	a	DET
ejpam-8	29	5	finite	finite	ADJ
ejpam-8	29	6	-	-	ADJ
ejpam-8	29	7	dimensional	dimensional	ADJ
ejpam-8	29	8	subspace	subspace	NOUN
ejpam-8	29	9	of	of	ADP
ejpam-8	29	10	the	the	DET
ejpam-8	29	11	phase	phase	NOUN
ejpam-8	29	12	space	space	NOUN
ejpam-8	29	13	e	e	NOUN
ejpam-8	29	14	,	,	PUNCT
ejpam-8	29	15	and	and	CCONJ
ejpam-8	29	16	let	let	VERB
ejpam-8	29	17	b	b	X
ejpam-8	29	18	be	be	AUX
ejpam-8	29	19	a	a	DET
ejpam-8	29	20	bounded	bounded	ADJ
ejpam-8	29	21	absorbing	absorbing	NOUN
ejpam-8	29	22	set	set	NOUN
ejpam-8	29	23	in	in	ADP
ejpam-8	29	24	e.	e.	PROPN
ejpam-8	29	25	suppose	suppose	VERB
ejpam-8	29	26	there	there	PRON
ejpam-8	29	27	exists	exist	VERB
ejpam-8	29	28	a	a	DET
ejpam-8	29	29	number	number	NOUN
ejpam-8	29	30	t∗(b	t∗(b	NUM
ejpam-8	29	31	)	)	PUNCT
ejpam-8	29	32	>	>	X
ejpam-8	29	33	0	0	NUM
ejpam-8	29	34	such	such	ADJ
ejpam-8	29	35	that	that	PRON
ejpam-8	29	36	for	for	ADP
ejpam-8	29	37	all	all	DET
ejpam-8	29	38	u0	u0	PROPN
ejpam-8	29	39	∈	∈	PROPN
ejpam-8	29	40	b	b	PROPN
ejpam-8	29	41	and	and	CCONJ
ejpam-8	29	42	all	all	DET
ejpam-8	29	43	t	t	PROPN
ejpam-8	29	44	≥	≥	NOUN
ejpam-8	29	45	t∗(b	t∗(b	NUM
ejpam-8	29	46	)	)	PUNCT
ejpam-8	29	47	,	,	PUNCT
ejpam-8	29	48	there	there	PRON
ejpam-8	29	49	exists	exist	VERB
ejpam-8	29	50	a	a	DET
ejpam-8	29	51	sequence	sequence	NOUN
ejpam-8	29	52	{	{	PUNCT
ejpam-8	29	53	uk(t)}n	uk(t)}n	NUM
ejpam-8	29	54	⊂	⊂	PROPN
ejpam-8	29	55	e	e	NOUN
ejpam-8	29	56	such	such	ADJ
ejpam-8	29	57	that	that	DET
ejpam-8	29	58	‖uk(t)−	‖uk(t)−	PROPN
ejpam-8	29	59	s(t)u0‖e→	s(t)u0‖e→	PROPN
ejpam-8	29	60	0	0	NUM
ejpam-8	29	61	,	,	PUNCT
ejpam-8	29	62	k→∞.	k→∞.	NOUN
ejpam-8	29	63	(	(	PUNCT
ejpam-8	29	64	1.5	1.5	NUM
ejpam-8	29	65	)	)	PUNCT
ejpam-8	29	66	then	then	ADV
ejpam-8	29	67	the	the	DET
ejpam-8	29	68	sequence	sequence	NOUN
ejpam-8	29	69	of	of	ADP
ejpam-8	29	70	setsa	setsa	NOUN
ejpam-8	30	1	k	k	PROPN
ejpam-8	30	2	defined	define	VERB
ejpam-8	30	3	by	by	ADP
ejpam-8	30	4	a	a	DET
ejpam-8	30	5	k	k	PROPN
ejpam-8	30	6	=	=	SYM
ejpam-8	30	7	⋂	⋂	PROPN
ejpam-8	30	8	s≥0	s≥0	PROPN
ejpam-8	30	9	⋃	⋃	PROPN
ejpam-8	30	10	t≥s	t≥s	NOUN
ejpam-8	30	11	,	,	PUNCT
ejpam-8	30	12	u0∈b	u0∈b	NUM
ejpam-8	30	13	uk(t	uk(t	PUNCT
ejpam-8	30	14	)	)	PUNCT
ejpam-8	30	15	(	(	PUNCT
ejpam-8	30	16	1.6	1.6	NUM
ejpam-8	30	17	)	)	PUNCT
ejpam-8	30	18	is	be	AUX
ejpam-8	30	19	called	call	VERB
ejpam-8	30	20	an	an	DET
ejpam-8	30	21	asymptotic	asymptotic	ADJ
ejpam-8	30	22	attractor	attractor	NOUN
ejpam-8	30	23	of	of	ADP
ejpam-8	30	24	the	the	DET
ejpam-8	30	25	problem	problem	NOUN
ejpam-8	30	26	(	(	PUNCT
ejpam-8	30	27	1.1)-(1.2	1.1)-(1.2	NUM
ejpam-8	30	28	)	)	PUNCT
ejpam-8	30	29	.	.	PUNCT
ejpam-8	31	1	in	in	ADP
ejpam-8	31	2	this	this	DET
ejpam-8	31	3	paper	paper	NOUN
ejpam-8	31	4	,	,	PUNCT
ejpam-8	31	5	we	we	PRON
ejpam-8	31	6	will	will	AUX
ejpam-8	31	7	show	show	VERB
ejpam-8	31	8	that	that	SCONJ
ejpam-8	31	9	the	the	DET
ejpam-8	31	10	existence	existence	NOUN
ejpam-8	31	11	of	of	ADP
ejpam-8	31	12	the	the	DET
ejpam-8	31	13	asymptotic	asymptotic	ADJ
ejpam-8	31	14	attractor	attractor	NOUN
ejpam-8	31	15	for	for	ADP
ejpam-8	31	16	the	the	DET
ejpam-8	31	17	following	follow	VERB
ejpam-8	31	18	benjamin	benjamin	PROPN
ejpam-8	31	19	-	-	PUNCT
ejpam-8	31	20	bona	bona	ADJ
ejpam-8	31	21	-	-	PUNCT
ejpam-8	31	22	mahony	mahony	NOUN
ejpam-8	31	23	equations	equation	NOUN
ejpam-8	31	24	with	with	ADP
ejpam-8	31	25	periodic	periodic	ADJ
ejpam-8	31	26	boundary	boundary	ADJ
ejpam-8	31	27	conditions	condition	NOUN
ejpam-8	31	28	ut	ut	PROPN
ejpam-8	31	29	−δux	−δux	NOUN
ejpam-8	31	30	x	x	PROPN
ejpam-8	31	31	t	t	PROPN
ejpam-8	31	32	−µux	−µux	NUM
ejpam-8	31	33	x	x	PUNCT
ejpam-8	32	1	+	+	CCONJ
ejpam-8	32	2	uux	uux	PROPN
ejpam-8	32	3	=	=	SYM
ejpam-8	32	4	f	f	PROPN
ejpam-8	32	5	(	(	PUNCT
ejpam-8	32	6	x	x	NOUN
ejpam-8	32	7	)	)	PUNCT
ejpam-8	32	8	,	,	PUNCT
ejpam-8	32	9	(	(	PUNCT
ejpam-8	32	10	1.7	1.7	NUM
ejpam-8	32	11	)	)	PUNCT
ejpam-8	32	12	u(x	u(x	NOUN
ejpam-8	32	13	,	,	PUNCT
ejpam-8	32	14	0	0	NUM
ejpam-8	32	15	)	)	PUNCT
ejpam-8	32	16	=	=	SYM
ejpam-8	32	17	u0(x	u0(x	NUM
ejpam-8	32	18	)	)	PUNCT
ejpam-8	32	19	,	,	PUNCT
ejpam-8	32	20	(	(	PUNCT
ejpam-8	32	21	1.8	1.8	NUM
ejpam-8	32	22	)	)	PUNCT
ejpam-8	32	23	where	where	SCONJ
ejpam-8	32	24	u(x	u(x	PROPN
ejpam-8	32	25	,	,	PUNCT
ejpam-8	32	26	t	t	PROPN
ejpam-8	32	27	)	)	PUNCT
ejpam-8	32	28	=	=	PRON
ejpam-8	32	29	u(x	u(x	NOUN
ejpam-8	32	30	+	+	CCONJ
ejpam-8	32	31	2π	2π	NOUN
ejpam-8	32	32	,	,	PUNCT
ejpam-8	32	33	t	t	PROPN
ejpam-8	32	34	)	)	PUNCT
ejpam-8	32	35	,	,	PUNCT
ejpam-8	32	36	x	x	PROPN
ejpam-8	32	37	∈	∈	PROPN
ejpam-8	32	38	r1	r1	PROPN
ejpam-8	32	39	,	,	PUNCT
ejpam-8	32	40	∫	∫	PROPN
ejpam-8	32	41	2π	2π	PROPN
ejpam-8	32	42	0	0	NUM
ejpam-8	32	43	u(x	u(x	NOUN
ejpam-8	32	44	,	,	PUNCT
ejpam-8	32	45	t)d	t)d	ADJ
ejpam-8	32	46	x	x	X
ejpam-8	33	1	=	=	SYM
ejpam-8	33	2	0	0	NUM
ejpam-8	33	3	and	and	CCONJ
ejpam-8	33	4	δ	δ	PROPN
ejpam-8	33	5	,	,	PUNCT
ejpam-8	33	6	µ	µ	X
ejpam-8	33	7	are	be	AUX
ejpam-8	33	8	positive	positive	ADJ
ejpam-8	33	9	constants	constant	NOUN
ejpam-8	33	10	.	.	PUNCT
ejpam-8	34	1	the	the	DET
ejpam-8	34	2	benjamin	benjamin	PROPN
ejpam-8	34	3	-	-	PUNCT
ejpam-8	34	4	bona	bona	ADJ
ejpam-8	34	5	-	-	PUNCT
ejpam-8	34	6	mahony	mahony	NOUN
ejpam-8	34	7	equation	equation	NOUN
ejpam-8	34	8	was	be	AUX
ejpam-8	34	9	proposed	propose	VERB
ejpam-8	34	10	in	in	ADP
ejpam-8	34	11	[	[	X
ejpam-8	34	12	3	3	X
ejpam-8	34	13	]	]	PUNCT
ejpam-8	34	14	as	as	ADP
ejpam-8	34	15	a	a	DET
ejpam-8	34	16	model	model	NOUN
ejpam-8	34	17	for	for	ADP
ejpam-8	34	18	propagation	propagation	NOUN
ejpam-8	34	19	of	of	ADP
ejpam-8	34	20	long	long	ADJ
ejpam-8	34	21	waves	wave	NOUN
ejpam-8	34	22	which	which	PRON
ejpam-8	34	23	incorporates	incorporate	VERB
ejpam-8	34	24	nonlinear	nonlinear	ADJ
ejpam-8	34	25	dispersive	dispersive	ADJ
ejpam-8	34	26	and	and	CCONJ
ejpam-8	34	27	dissipative	dissipative	ADJ
ejpam-8	34	28	effects	effect	NOUN
ejpam-8	34	29	.	.	PUNCT
ejpam-8	35	1	the	the	DET
ejpam-8	35	2	existence	existence	NOUN
ejpam-8	35	3	and	and	CCONJ
ejpam-8	35	4	uniqueness	uniqueness	NOUN
ejpam-8	35	5	of	of	ADP
ejpam-8	35	6	solutions	solution	NOUN
ejpam-8	35	7	,	,	PUNCT
ejpam-8	35	8	as	as	ADV
ejpam-8	35	9	well	well	ADV
ejpam-8	35	10	as	as	ADP
ejpam-8	35	11	the	the	DET
ejpam-8	35	12	decay	decay	NOUN
ejpam-8	35	13	rates	rate	NOUN
ejpam-8	35	14	of	of	ADP
ejpam-8	35	15	solutions	solution	NOUN
ejpam-8	35	16	for	for	ADP
ejpam-8	35	17	this	this	DET
ejpam-8	35	18	equation	equation	NOUN
ejpam-8	35	19	were	be	AUX
ejpam-8	35	20	studied	study	VERB
ejpam-8	35	21	by	by	ADP
ejpam-8	35	22	many	many	ADJ
ejpam-8	35	23	authors	author	NOUN
ejpam-8	35	24	,	,	PUNCT
ejpam-8	35	25	see	see	VERB
ejpam-8	35	26	,	,	PUNCT
ejpam-8	35	27	for	for	ADP
ejpam-8	35	28	example	example	NOUN
ejpam-8	35	29	,	,	PUNCT
ejpam-8	35	30	[	[	X
ejpam-8	35	31	1	1	NUM
ejpam-8	35	32	,	,	PUNCT
ejpam-8	35	33	2	2	NUM
ejpam-8	35	34	,	,	PUNCT
ejpam-8	35	35	4	4	NUM
ejpam-8	35	36	]	]	PUNCT
ejpam-8	35	37	.	.	PUNCT
ejpam-8	36	1	on	on	ADP
ejpam-8	36	2	the	the	DET
ejpam-8	36	3	other	other	ADJ
ejpam-8	36	4	hand	hand	NOUN
ejpam-8	36	5	,	,	PUNCT
ejpam-8	36	6	the	the	DET
ejpam-8	36	7	long	long	ADJ
ejpam-8	36	8	-	-	PUNCT
ejpam-8	36	9	time	time	NOUN
ejpam-8	36	10	behavior	behavior	NOUN
ejpam-8	36	11	for	for	ADP
ejpam-8	36	12	this	this	DET
ejpam-8	36	13	equation	equation	NOUN
ejpam-8	36	14	were	be	AUX
ejpam-8	36	15	considered	consider	VERB
ejpam-8	36	16	also	also	ADV
ejpam-8	36	17	by	by	ADP
ejpam-8	36	18	many	many	ADJ
ejpam-8	36	19	authors	author	NOUN
ejpam-8	36	20	,	,	PUNCT
ejpam-8	36	21	see	see	VERB
ejpam-8	36	22	,	,	PUNCT
ejpam-8	36	23	for	for	ADP
ejpam-8	36	24	example	example	NOUN
ejpam-8	36	25	,	,	PUNCT
ejpam-8	36	26	[	[	X
ejpam-8	36	27	5,9–11,13–15	5,9–11,13–15	PROPN
ejpam-8	36	28	]	]	PUNCT
ejpam-8	36	29	.	.	PUNCT
ejpam-8	37	1	here	here	ADV
ejpam-8	37	2	,	,	PUNCT
ejpam-8	37	3	by	by	ADP
ejpam-8	37	4	the	the	DET
ejpam-8	37	5	method	method	NOUN
ejpam-8	37	6	of	of	ADP
ejpam-8	37	7	orthogonal	orthogonal	ADJ
ejpam-8	37	8	decomposition	decomposition	NOUN
ejpam-8	37	9	,	,	PUNCT
ejpam-8	37	10	we	we	PRON
ejpam-8	37	11	show	show	VERB
ejpam-8	37	12	that	that	SCONJ
ejpam-8	37	13	the	the	DET
ejpam-8	37	14	existence	existence	NOUN
ejpam-8	37	15	of	of	ADP
ejpam-8	37	16	asymptotic	asymptotic	ADJ
ejpam-8	37	17	attractor	attractor	NOUN
ejpam-8	37	18	for	for	ADP
ejpam-8	37	19	problems	problem	NOUN
ejpam-8	37	20	(	(	PUNCT
ejpam-8	37	21	1.7)-(1.8	1.7)-(1.8	NUM
ejpam-8	37	22	)	)	PUNCT
ejpam-8	37	23	.	.	PUNCT
ejpam-8	38	1	furthermore	furthermore	ADV
ejpam-8	38	2	,	,	PUNCT
ejpam-8	38	3	the	the	DET
ejpam-8	38	4	dimensions	dimension	NOUN
ejpam-8	38	5	estimate	estimate	NOUN
ejpam-8	38	6	of	of	ADP
ejpam-8	38	7	the	the	DET
ejpam-8	38	8	asymptotic	asymptotic	ADJ
ejpam-8	38	9	attractor	attractor	NOUN
ejpam-8	38	10	is	be	AUX
ejpam-8	38	11	obtained	obtain	VERB
ejpam-8	38	12	.	.	PUNCT
ejpam-8	39	1	throughout	throughout	ADP
ejpam-8	39	2	this	this	DET
ejpam-8	39	3	paper	paper	NOUN
ejpam-8	39	4	,	,	PUNCT
ejpam-8	39	5	we	we	PRON
ejpam-8	39	6	set	set	VERB
ejpam-8	39	7	ω=(0,2π	ω=(0,2π	NOUN
ejpam-8	39	8	)	)	PUNCT
ejpam-8	39	9	,	,	PUNCT
ejpam-8	39	10	‖u‖2	‖u‖2	PROPN
ejpam-8	39	11	=	=	SYM
ejpam-8	40	1	∫	∫	PROPN
ejpam-8	40	2	2π	2π	PROPN
ejpam-8	40	3	0	0	NUM
ejpam-8	40	4	|u|2d	|u|2d	NOUN
ejpam-8	40	5	x	x	X
ejpam-8	40	6	and	and	CCONJ
ejpam-8	40	7	ḣ1	ḣ1	PROPN
ejpam-8	40	8	per(ω	per(ω	PROPN
ejpam-8	40	9	)	)	PUNCT
ejpam-8	41	1	=	=	NOUN
ejpam-8	41	2	:	:	PUNCT
ejpam-8	41	3	¨	¨	ADJ
ejpam-8	41	4	u	u	ADJ
ejpam-8	41	5	�	�	PROPN
ejpam-8	41	6	�	�	PROPN
ejpam-8	41	7	�	�	PROPN
ejpam-8	41	8	�	�	PROPN
ejpam-8	41	9	�	�	PROPN
ejpam-8	41	10	u	u	PROPN
ejpam-8	41	11	∈	∈	PROPN
ejpam-8	41	12	l2(ω	l2(ω	PROPN
ejpam-8	41	13	)	)	PUNCT
ejpam-8	41	14	,	,	PUNCT
ejpam-8	41	15	ux	ux	PROPN
ejpam-8	41	16	∈	∈	PROPN
ejpam-8	41	17	l2(ω	l2(ω	PROPN
ejpam-8	41	18	)	)	PUNCT
ejpam-8	41	19	;	;	PUNCT
ejpam-8	41	20	∫	∫	PROPN
ejpam-8	41	21	2π	2π	PROPN
ejpam-8	41	22	0	0	NUM
ejpam-8	41	23	u(x	u(x	NOUN
ejpam-8	41	24	,	,	PUNCT
ejpam-8	41	25	t)d	t)d	ADJ
ejpam-8	41	26	x	x	X
ejpam-8	41	27	=	=	SYM
ejpam-8	41	28	0	0	NUM
ejpam-8	41	29	;	;	PUNCT
ejpam-8	41	30	u(x	u(x	PROPN
ejpam-8	41	31	,	,	PUNCT
ejpam-8	41	32	t	t	PROPN
ejpam-8	41	33	)	)	PUNCT
ejpam-8	41	34	=	=	PRON
ejpam-8	41	35	u(x	u(x	NOUN
ejpam-8	41	36	+	+	CCONJ
ejpam-8	41	37	2π	2π	NOUN
ejpam-8	41	38	,	,	PUNCT
ejpam-8	41	39	t	t	PROPN
ejpam-8	41	40	)	)	PUNCT
ejpam-8	41	41	,	,	PUNCT
ejpam-8	41	42	x	x	PUNCT
ejpam-8	41	43	∈	∈	PROPN
ejpam-8	41	44	r1	r1	NOUN
ejpam-8	41	45	«	«	PUNCT
ejpam-8	41	46	.	.	PUNCT
ejpam-8	42	1	applying	apply	VERB
ejpam-8	42	2	faedo	faedo	NOUN
ejpam-8	42	3	-	-	PUNCT
ejpam-8	42	4	galerkin	galerkin	ADJ
ejpam-8	42	5	method	method	NOUN
ejpam-8	42	6	,	,	PUNCT
ejpam-8	42	7	it	it	PRON
ejpam-8	42	8	is	be	AUX
ejpam-8	42	9	easy	easy	ADJ
ejpam-8	42	10	to	to	PART
ejpam-8	42	11	prove	prove	VERB
ejpam-8	42	12	that	that	SCONJ
ejpam-8	42	13	the	the	DET
ejpam-8	42	14	problems	problem	NOUN
ejpam-8	42	15	(	(	PUNCT
ejpam-8	42	16	1.7)-(1.8	1.7)-(1.8	NUM
ejpam-8	42	17	)	)	PUNCT
ejpam-8	42	18	exists	exist	VERB
ejpam-8	42	19	a	a	DET
ejpam-8	42	20	unique	unique	ADJ
ejpam-8	42	21	solution	solution	NOUN
ejpam-8	42	22	u(t	u(t	NOUN
ejpam-8	42	23	)	)	PUNCT
ejpam-8	42	24	∈	∈	PROPN
ejpam-8	42	25	ḣ1	ḣ1	PROPN
ejpam-8	42	26	per(ω	per(ω	PROPN
ejpam-8	42	27	)	)	PUNCT
ejpam-8	42	28	if	if	SCONJ
ejpam-8	42	29	u0(x	u0(x	NUM
ejpam-8	42	30	)	)	PUNCT
ejpam-8	42	31	∈	∈	PROPN
ejpam-8	42	32	ḣ1	ḣ1	PROPN
ejpam-8	42	33	per(ω	per(ω	PROPN
ejpam-8	42	34	)	)	PUNCT
ejpam-8	42	35	and	and	CCONJ
ejpam-8	42	36	f	f	PROPN
ejpam-8	42	37	(	(	PUNCT
ejpam-8	42	38	x	x	X
ejpam-8	42	39	)	)	PUNCT
ejpam-8	42	40	∈	∈	PROPN
ejpam-8	42	41	l2(ω	l2(ω	NOUN
ejpam-8	42	42	)	)	PUNCT
ejpam-8	42	43	.	.	PUNCT
ejpam-8	43	1	moreover	moreover	ADV
ejpam-8	43	2	,	,	PUNCT
ejpam-8	43	3	there	there	PRON
ejpam-8	43	4	are	be	VERB
ejpam-8	43	5	t0	t0	NOUN
ejpam-8	43	6	>	>	PUNCT
ejpam-8	43	7	0	0	PUNCT
ejpam-8	44	1	and	and	CCONJ
ejpam-8	44	2	ρ0	ρ0	X
ejpam-8	44	3	>	>	X
ejpam-8	44	4	0	0	NUM
ejpam-8	45	1	such	such	ADJ
ejpam-8	45	2	that	that	DET
ejpam-8	45	3	b	b	NOUN
ejpam-8	45	4	=	=	SYM
ejpam-8	45	5	n	n	PRON
ejpam-8	45	6	u(t	u(t	NOUN
ejpam-8	45	7	)	)	PUNCT
ejpam-8	45	8	∈	∈	PROPN
ejpam-8	45	9	ḣ1	ḣ1	PROPN
ejpam-8	45	10	per(ω	per(ω	PROPN
ejpam-8	45	11	)	)	PUNCT
ejpam-8	45	12	:	:	PUNCT
ejpam-8	45	13	‖u(t)‖2+δ‖ux(t)‖2	‖u(t)‖2+δ‖ux(t)‖2	PROPN
ejpam-8	45	14	≤	≤	PROPN
ejpam-8	45	15	ρ2	ρ2	NOUN
ejpam-8	45	16	0	0	NUM
ejpam-8	45	17	,	,	PUNCT
ejpam-8	45	18	t	t	PROPN
ejpam-8	45	19	≥	≥	NUM
ejpam-8	45	20	t0	t0	NOUN
ejpam-8	45	21	o	o	NOUN
ejpam-8	45	22	is	be	AUX
ejpam-8	45	23	a	a	DET
ejpam-8	45	24	bounded	bounded	ADJ
ejpam-8	45	25	absorbing	absorb	VERB
ejpam-8	45	26	set	set	NOUN
ejpam-8	45	27	.	.	PUNCT
ejpam-8	46	1	now	now	ADV
ejpam-8	46	2	we	we	PRON
ejpam-8	46	3	are	be	AUX
ejpam-8	46	4	in	in	ADP
ejpam-8	46	5	position	position	NOUN
ejpam-8	46	6	to	to	PART
ejpam-8	46	7	state	state	VERB
ejpam-8	46	8	our	our	PRON
ejpam-8	46	9	main	main	ADJ
ejpam-8	46	10	result	result	NOUN
ejpam-8	46	11	:	:	PUNCT
ejpam-8	46	12	chaosheng	chaosheng	PROPN
ejpam-8	46	13	zhu	zhu	PROPN
ejpam-8	46	14	/	/	SYM
ejpam-8	46	15	eur	eur	PROPN
ejpam-8	46	16	.	.	PUNCT
ejpam-8	47	1	j.	j.	PROPN
ejpam-8	47	2	pure	pure	PROPN
ejpam-8	47	3	appl	appl	PROPN
ejpam-8	47	4	.	.	PROPN
ejpam-8	47	5	math	math	PROPN
ejpam-8	47	6	,	,	PUNCT
ejpam-8	47	7	1	1	NUM
ejpam-8	47	8	(	(	PUNCT
ejpam-8	47	9	2008	2008	NUM
ejpam-8	47	10	)	)	PUNCT
ejpam-8	47	11	,	,	PUNCT
ejpam-8	47	12	(	(	PUNCT
ejpam-8	47	13	3	3	NUM
ejpam-8	47	14	-	-	SYM
ejpam-8	47	15	10	10	NUM
ejpam-8	47	16	)	)	PUNCT
ejpam-8	47	17	5	5	NUM
ejpam-8	47	18	theorem	theorem	VERB
ejpam-8	47	19	1.1	1.1	NUM
ejpam-8	47	20	.	.	PUNCT
ejpam-8	48	1	if	if	SCONJ
ejpam-8	48	2	u0(x	u0(x	NUM
ejpam-8	48	3	)	)	PUNCT
ejpam-8	48	4	∈	∈	PROPN
ejpam-8	48	5	ḣ1	ḣ1	PROPN
ejpam-8	48	6	per(ω	per(ω	PROPN
ejpam-8	48	7	)	)	PUNCT
ejpam-8	48	8	and	and	CCONJ
ejpam-8	48	9	f	f	PROPN
ejpam-8	48	10	(	(	PUNCT
ejpam-8	48	11	x	x	X
ejpam-8	48	12	)	)	PUNCT
ejpam-8	48	13	∈	∈	PROPN
ejpam-8	48	14	l2(ω	l2(ω	PROPN
ejpam-8	48	15	)	)	PUNCT
ejpam-8	48	16	,	,	PUNCT
ejpam-8	48	17	the	the	DET
ejpam-8	48	18	semigroup	semigroup	PROPN
ejpam-8	48	19	s(t	s(t	PROPN
ejpam-8	48	20	)	)	PUNCT
ejpam-8	48	21	associated	associate	VERB
ejpam-8	48	22	with	with	ADP
ejpam-8	48	23	problems	problem	NOUN
ejpam-8	48	24	(	(	PUNCT
ejpam-8	48	25	1.7)-(1.8	1.7)-(1.8	NUM
ejpam-8	48	26	)	)	PUNCT
ejpam-8	48	27	possesses	possess	VERB
ejpam-8	48	28	an	an	DET
ejpam-8	48	29	asymptotic	asymptotic	ADJ
ejpam-8	48	30	attractor	attractor	NOUN
ejpam-8	48	31	a	a	DET
ejpam-8	48	32	k	k	NOUN
ejpam-8	48	33	in	in	ADP
ejpam-8	48	34	ḣ1	ḣ1	PROPN
ejpam-8	48	35	per(ω	per(ω	PROPN
ejpam-8	48	36	)	)	PUNCT
ejpam-8	48	37	.	.	PUNCT
ejpam-8	49	1	moreover	moreover	ADV
ejpam-8	49	2	,	,	PUNCT
ejpam-8	49	3	the	the	DET
ejpam-8	49	4	dimensions	dimension	NOUN
ejpam-8	49	5	of	of	ADP
ejpam-8	49	6	a	a	DET
ejpam-8	49	7	k	k	PROPN
ejpam-8	49	8	satisfies	satisfie	NOUN
ejpam-8	49	9	na	na	ADP
ejpam-8	49	10	k	k	PROPN
ejpam-8	49	11	=	=	PUNCT
ejpam-8	49	12	min	min	PROPN
ejpam-8	49	13			PROPN
ejpam-8	49	14			NOUN
ejpam-8	49	15			NOUN
ejpam-8	49	16			NOUN
ejpam-8	49	17	n	n	ADP
ejpam-8	49	18	∈	∈	PROPN
ejpam-8	49	19	n	n	CCONJ
ejpam-8	49	20	�	�	PROPN
ejpam-8	49	21	�	�	PROPN
ejpam-8	49	22	�	�	PROPN
ejpam-8	49	23	�	�	PROPN
ejpam-8	49	24	�	�	PROPN
ejpam-8	49	25	�	�	PROPN
ejpam-8	49	26	2(4δ−	2(4δ−	PROPN
ejpam-8	49	27	3	3	NUM
ejpam-8	49	28	4ρ2	4ρ2	NUM
ejpam-8	49	29	0	0	NUM
ejpam-8	50	1	+	+	CCONJ
ejpam-8	50	2	‖	‖	PROPN
ejpam-8	50	3	f	f	PROPN
ejpam-8	50	4	‖	‖	PROPN
ejpam-8	50	5	)	)	PUNCT
ejpam-8	50	6	2	2	NUM
ejpam-8	50	7	ρ2	ρ2	NOUN
ejpam-8	50	8	0c1µ(n	0c1µ(n	PRON
ejpam-8	50	9	+	+	CCONJ
ejpam-8	50	10	1)2	1)2	NUM
ejpam-8	50	11	≤	≤	NUM
ejpam-8	50	12	1	1	NUM
ejpam-8	50	13	,	,	PUNCT
ejpam-8	50	14	2	2	NUM
ejpam-8	50	15	�	�	NOUN
ejpam-8	50	16	p	p	NOUN
ejpam-8	50	17	2ρ0δ	2ρ0δ	NOUN
ejpam-8	50	18	−	−	NUM
ejpam-8	50	19	1	1	NUM
ejpam-8	50	20	4	4	NUM
ejpam-8	50	21	+	+	CCONJ
ejpam-8	50	22	cρ0δ	cρ0δ	PROPN
ejpam-8	50	23	−	−	NUM
ejpam-8	50	24	1	1	NUM
ejpam-8	50	25	2	2	NUM
ejpam-8	50	26	�	�	SYM
ejpam-8	50	27	2	2	NUM
ejpam-8	50	28	c1µ(n	c1µ(n	PROPN
ejpam-8	50	29	+	+	CCONJ
ejpam-8	50	30	1)2	1)2	NUM
ejpam-8	50	31	<	<	X
ejpam-8	50	32	1	1	NUM
ejpam-8	50	33			NOUN
ejpam-8	50	34			NOUN
ejpam-8	50	35			VERB
ejpam-8	50	36			PUNCT
ejpam-8	50	37	,	,	PUNCT
ejpam-8	50	38	where	where	SCONJ
ejpam-8	50	39	c1	c1	PROPN
ejpam-8	50	40	=	=	SYM
ejpam-8	50	41	min	min	PROPN
ejpam-8	50	42	�	�	PROPN
ejpam-8	50	43	µ(n+1)2	µ(n+1)2	PROPN
ejpam-8	50	44	2	2	NUM
ejpam-8	50	45	,	,	PUNCT
ejpam-8	50	46	µ	µ	PRON
ejpam-8	50	47	2δ	2δ	NUM
ejpam-8	50	48	�	�	PROPN
ejpam-8	50	49	.	.	PUNCT
ejpam-8	51	1	2	2	X
ejpam-8	51	2	.	.	X
ejpam-8	51	3	asymptotic	asymptotic	ADJ
ejpam-8	51	4	attractor	attractor	NOUN
ejpam-8	51	5	in	in	ADP
ejpam-8	51	6	this	this	DET
ejpam-8	51	7	section	section	NOUN
ejpam-8	51	8	,	,	PUNCT
ejpam-8	51	9	we	we	PRON
ejpam-8	51	10	show	show	VERB
ejpam-8	51	11	that	that	SCONJ
ejpam-8	51	12	the	the	DET
ejpam-8	51	13	existence	existence	NOUN
ejpam-8	51	14	of	of	ADP
ejpam-8	51	15	asymptotic	asymptotic	ADJ
ejpam-8	51	16	attractor	attractor	NOUN
ejpam-8	51	17	for	for	ADP
ejpam-8	51	18	problems	problem	NOUN
ejpam-8	51	19	(	(	PUNCT
ejpam-8	51	20	1.7)(1.8	1.7)(1.8	NUM
ejpam-8	51	21	)	)	PUNCT
ejpam-8	51	22	by	by	ADP
ejpam-8	51	23	the	the	DET
ejpam-8	51	24	method	method	NOUN
ejpam-8	51	25	of	of	ADP
ejpam-8	51	26	orthogonal	orthogonal	ADJ
ejpam-8	51	27	decomposition	decomposition	NOUN
ejpam-8	51	28	.	.	PUNCT
ejpam-8	52	1	let	let	VERB
ejpam-8	52	2	{	{	PUNCT
ejpam-8	52	3	sin	sin	VERB
ejpam-8	52	4	kx	kx	PROPN
ejpam-8	52	5	,	,	PUNCT
ejpam-8	52	6	cos	cos	PROPN
ejpam-8	52	7	kx	kx	PROPN
ejpam-8	52	8	,	,	PUNCT
ejpam-8	52	9	k	k	PROPN
ejpam-8	53	1	=	=	SYM
ejpam-8	53	2	1	1	NUM
ejpam-8	53	3	,	,	PUNCT
ejpam-8	53	4	2	2	NUM
ejpam-8	53	5	,	,	PUNCT
ejpam-8	53	6	·	·	PUNCT
ejpam-8	53	7	·	·	PUNCT
ejpam-8	53	8	·	·	PUNCT
ejpam-8	53	9	}	}	PUNCT
ejpam-8	53	10	is	be	AUX
ejpam-8	53	11	an	an	DET
ejpam-8	53	12	orthonormal	orthonormal	ADJ
ejpam-8	53	13	basis	basis	NOUN
ejpam-8	53	14	of	of	ADP
ejpam-8	53	15	l̇2	l̇2	PROPN
ejpam-8	53	16	per([0,2π	per([0,2π	NOUN
ejpam-8	53	17	]	]	PUNCT
ejpam-8	53	18	)	)	PUNCT
ejpam-8	53	19	,	,	PUNCT
ejpam-8	53	20	denote	denote	VERB
ejpam-8	53	21	hn	hn	PROPN
ejpam-8	53	22	=	=	PUNCT
ejpam-8	53	23	span{sin	span{sin	PROPN
ejpam-8	53	24	kx	kx	PROPN
ejpam-8	53	25	,	,	PUNCT
ejpam-8	53	26	cos	cos	PROPN
ejpam-8	53	27	kx	kx	PROPN
ejpam-8	53	28	,	,	PUNCT
ejpam-8	53	29	k	k	PROPN
ejpam-8	53	30	=	=	SYM
ejpam-8	53	31	1	1	NUM
ejpam-8	53	32	,	,	PUNCT
ejpam-8	53	33	2	2	NUM
ejpam-8	53	34	,	,	PUNCT
ejpam-8	53	35	·	·	PUNCT
ejpam-8	53	36	·	·	PUNCT
ejpam-8	53	37	·	·	PUNCT
ejpam-8	53	38	,	,	PUNCT
ejpam-8	53	39	n	n	CCONJ
ejpam-8	53	40	}	}	PUNCT
ejpam-8	53	41	.	.	PUNCT
ejpam-8	54	1	let	let	VERB
ejpam-8	54	2	pn	pn	VERB
ejpam-8	54	3	:	:	PUNCT
ejpam-8	55	1	l̇2	l̇2	VERB
ejpam-8	55	2	per([0,2π])→	per([0,2π])→	NOUN
ejpam-8	55	3	hn	hn	PROPN
ejpam-8	55	4	,	,	PUNCT
ejpam-8	55	5	qn	qn	INTJ
ejpam-8	55	6	=	=	NOUN
ejpam-8	55	7	i	i	PRON
ejpam-8	55	8	−	−	PROPN
ejpam-8	55	9	pn	pn	INTJ
ejpam-8	55	10	.	.	PUNCT
ejpam-8	56	1	for	for	ADP
ejpam-8	56	2	any	any	DET
ejpam-8	56	3	u(x	u(x	PROPN
ejpam-8	56	4	,	,	PUNCT
ejpam-8	56	5	t	t	X
ejpam-8	56	6	)	)	PUNCT
ejpam-8	56	7	∈	∈	PROPN
ejpam-8	56	8	l̇2	l̇2	PROPN
ejpam-8	56	9	per([0,2π	per([0,2π	NOUN
ejpam-8	56	10	]	]	PUNCT
ejpam-8	56	11	)	)	PUNCT
ejpam-8	56	12	,	,	PUNCT
ejpam-8	56	13	we	we	PRON
ejpam-8	56	14	denote	denote	VERB
ejpam-8	56	15	p	p	X
ejpam-8	56	16	=	=	PUNCT
ejpam-8	56	17	pn	pn	PROPN
ejpam-8	56	18	u	u	PROPN
ejpam-8	56	19	,	,	PUNCT
ejpam-8	56	20	q	q	PROPN
ejpam-8	57	1	=	=	ADJ
ejpam-8	57	2	qn	qn	NOUN
ejpam-8	57	3	u.	u.	NOUN
ejpam-8	57	4	by	by	ADP
ejpam-8	57	5	projecting	project	VERB
ejpam-8	57	6	(	(	PUNCT
ejpam-8	57	7	1.7	1.7	NUM
ejpam-8	57	8	)	)	PUNCT
ejpam-8	57	9	on	on	ADP
ejpam-8	57	10	the	the	DET
ejpam-8	57	11	hn	hn	PROPN
ejpam-8	57	12	,	,	PUNCT
ejpam-8	57	13	we	we	PRON
ejpam-8	57	14	have	have	VERB
ejpam-8	57	15	pt	pt	NOUN
ejpam-8	57	16	−δpx	−δpx	NOUN
ejpam-8	58	1	x	x	SYM
ejpam-8	59	1	t	t	NOUN
ejpam-8	59	2	−µpx	−µpx	NOUN
ejpam-8	59	3	x	x	X
ejpam-8	60	1	+	+	CCONJ
ejpam-8	60	2	pn	pn	PROPN
ejpam-8	60	3	(	(	PUNCT
ejpam-8	60	4	uux	uux	PROPN
ejpam-8	60	5	)	)	PUNCT
ejpam-8	60	6	=	=	PUNCT
ejpam-8	61	1	pn	pn	PROPN
ejpam-8	61	2	f	f	PROPN
ejpam-8	61	3	,	,	PUNCT
ejpam-8	61	4	(	(	PUNCT
ejpam-8	61	5	2.1	2.1	NUM
ejpam-8	61	6	)	)	PUNCT
ejpam-8	61	7	and	and	CCONJ
ejpam-8	61	8	qt	qt	X
ejpam-8	61	9	−δqx	−δqx	X
ejpam-8	61	10	x	x	X
ejpam-8	62	1	t	t	PROPN
ejpam-8	62	2	−µqx	−µqx	NOUN
ejpam-8	62	3	x	x	PUNCT
ejpam-8	63	1	+	+	NOUN
ejpam-8	63	2	qn	qn	INTJ
ejpam-8	63	3	(	(	PUNCT
ejpam-8	63	4	uux	uux	PROPN
ejpam-8	63	5	)	)	PUNCT
ejpam-8	63	6	=	=	NOUN
ejpam-8	63	7	qn	qn	NOUN
ejpam-8	63	8	f	f	PROPN
ejpam-8	63	9	.	.	PUNCT
ejpam-8	64	1	(	(	PUNCT
ejpam-8	64	2	2.2	2.2	NUM
ejpam-8	64	3	)	)	PUNCT
ejpam-8	64	4	for	for	ADP
ejpam-8	64	5	any	any	DET
ejpam-8	64	6	u0(x	u0(x	NOUN
ejpam-8	64	7	)	)	PUNCT
ejpam-8	64	8	∈	∈	PROPN
ejpam-8	64	9	b	b	NOUN
ejpam-8	64	10	,	,	PUNCT
ejpam-8	64	11	we	we	PRON
ejpam-8	64	12	set	set	VERB
ejpam-8	64	13	uk	uk	PROPN
ejpam-8	64	14	=	=	SYM
ejpam-8	64	15	p+	p+	NOUN
ejpam-8	64	16	qk	qk	NOUN
ejpam-8	64	17	satisfies	satisfie	NOUN
ejpam-8	64	18	:	:	PUNCT
ejpam-8	64	19			PROPN
ejpam-8	64	20			ADP
ejpam-8	64	21			ADJ
ejpam-8	64	22	q0	q0	PROPN
ejpam-8	64	23	t	t	PROPN
ejpam-8	64	24	−δq0	−δq0	NOUN
ejpam-8	64	25	x	x	PUNCT
ejpam-8	64	26	x	x	SYM
ejpam-8	64	27	t	t	PROPN
ejpam-8	64	28	−µq0	−µq0	NOUN
ejpam-8	64	29	x	x	X
ejpam-8	64	30	x	x	X
ejpam-8	64	31	+	+	NOUN
ejpam-8	64	32	qn	qn	ADJ
ejpam-8	64	33	(	(	PUNCT
ejpam-8	64	34	ppx	ppx	NOUN
ejpam-8	64	35	)	)	PUNCT
ejpam-8	65	1	=	=	NOUN
ejpam-8	65	2	qn	qn	NOUN
ejpam-8	65	3	f	f	PROPN
ejpam-8	65	4	,	,	PUNCT
ejpam-8	65	5	q0(x	q0(x	PROPN
ejpam-8	65	6	,	,	PUNCT
ejpam-8	65	7	t	t	PROPN
ejpam-8	65	8	)	)	PUNCT
ejpam-8	65	9	=	=	PUNCT
ejpam-8	66	1	q0(x	q0(x	PROPN
ejpam-8	66	2	+	+	NUM
ejpam-8	66	3	2π	2π	NOUN
ejpam-8	66	4	,	,	PUNCT
ejpam-8	66	5	t	t	PROPN
ejpam-8	66	6	)	)	PUNCT
ejpam-8	66	7	,	,	PUNCT
ejpam-8	66	8	q0(x	q0(x	PROPN
ejpam-8	66	9	,	,	PUNCT
ejpam-8	66	10	0	0	NUM
ejpam-8	66	11	)	)	PUNCT
ejpam-8	67	1	=	=	NOUN
ejpam-8	67	2	qn	qn	X
ejpam-8	67	3	u0	u0	PROPN
ejpam-8	67	4	.	.	PUNCT
ejpam-8	68	1	(	(	PUNCT
ejpam-8	68	2	2.3	2.3	NUM
ejpam-8	68	3	)	)	PUNCT
ejpam-8	68	4			PROPN
ejpam-8	68	5			ADP
ejpam-8	68	6			PROPN
ejpam-8	68	7	qk	qk	PROPN
ejpam-8	68	8	t	t	PROPN
ejpam-8	68	9	−δqk	−δqk	NOUN
ejpam-8	68	10	x	x	PROPN
ejpam-8	69	1	x	x	X
ejpam-8	69	2	t	t	NOUN
ejpam-8	69	3	−µqk	−µqk	NOUN
ejpam-8	69	4	x	x	PUNCT
ejpam-8	70	1	x	x	X
ejpam-8	70	2	+	+	ADP
ejpam-8	70	3	qn	qn	INTJ
ejpam-8	70	4	(	(	PUNCT
ejpam-8	70	5	uk−1uk−1	uk−1uk−1	PROPN
ejpam-8	70	6	x	x	NOUN
ejpam-8	70	7	)	)	PUNCT
ejpam-8	70	8	=	=	NOUN
ejpam-8	70	9	qn	qn	X
ejpam-8	70	10	f	f	PROPN
ejpam-8	70	11	,	,	PUNCT
ejpam-8	70	12	qk(x	qk(x	X
ejpam-8	70	13	,	,	PUNCT
ejpam-8	70	14	t	t	PROPN
ejpam-8	70	15	)	)	PUNCT
ejpam-8	70	16	=	=	VERB
ejpam-8	70	17	qk(x	qk(x	NOUN
ejpam-8	70	18	+	+	CCONJ
ejpam-8	70	19	2π	2π	NOUN
ejpam-8	70	20	,	,	PUNCT
ejpam-8	70	21	t	t	PROPN
ejpam-8	70	22	)	)	PUNCT
ejpam-8	70	23	,	,	PUNCT
ejpam-8	70	24	qk(x	qk(x	VERB
ejpam-8	70	25	,	,	PUNCT
ejpam-8	70	26	0	0	X
ejpam-8	70	27	)	)	PUNCT
ejpam-8	70	28	=	=	NOUN
ejpam-8	70	29	qk	qk	NOUN
ejpam-8	70	30	n	n	X
ejpam-8	70	31	u0	u0	ADJ
ejpam-8	70	32	.	.	PUNCT
ejpam-8	71	1	(	(	PUNCT
ejpam-8	71	2	2.4	2.4	NUM
ejpam-8	71	3	)	)	PUNCT
ejpam-8	71	4	where	where	SCONJ
ejpam-8	71	5	qk	qk	NOUN
ejpam-8	71	6	n	n	NOUN
ejpam-8	71	7	=	=	X
ejpam-8	71	8	qn	qn	NOUN
ejpam-8	71	9	−q2k+1n	−q2k+1n	X
ejpam-8	71	10	,	,	PUNCT
ejpam-8	71	11	k	k	X
ejpam-8	71	12	=	=	SYM
ejpam-8	71	13	1,2	1,2	NUM
ejpam-8	71	14	,	,	PUNCT
ejpam-8	71	15	·	·	PUNCT
ejpam-8	71	16	·	·	PUNCT
ejpam-8	71	17	·	·	PUNCT
ejpam-8	71	18	.	.	PUNCT
ejpam-8	72	1	thus	thus	ADV
ejpam-8	72	2	by	by	ADP
ejpam-8	72	3	(	(	PUNCT
ejpam-8	72	4	2.3)-(2.4	2.3)-(2.4	NUM
ejpam-8	72	5	)	)	PUNCT
ejpam-8	72	6	,	,	PUNCT
ejpam-8	72	7	we	we	PRON
ejpam-8	72	8	can	can	AUX
ejpam-8	72	9	get	get	VERB
ejpam-8	72	10	a	a	DET
ejpam-8	72	11	sequence	sequence	NOUN
ejpam-8	72	12	{	{	PUNCT
ejpam-8	72	13	uk(t	uk(t	NOUN
ejpam-8	72	14	)	)	PUNCT
ejpam-8	72	15	}	}	PUNCT
ejpam-8	72	16	for	for	ADP
ejpam-8	72	17	problems	problem	NOUN
ejpam-8	72	18	(	(	PUNCT
ejpam-8	72	19	1.7)-(1.8	1.7)-(1.8	NUM
ejpam-8	72	20	)	)	PUNCT
ejpam-8	72	21	.	.	PUNCT
ejpam-8	73	1	to	to	PART
ejpam-8	73	2	prove	prove	VERB
ejpam-8	73	3	theorem	theorem	VERB
ejpam-8	73	4	1.2	1.2	NUM
ejpam-8	73	5	,	,	PUNCT
ejpam-8	73	6	we	we	PRON
ejpam-8	73	7	only	only	ADV
ejpam-8	73	8	to	to	PART
ejpam-8	73	9	check	check	VERB
ejpam-8	73	10	the	the	DET
ejpam-8	73	11	condition	condition	NOUN
ejpam-8	73	12	(	(	PUNCT
ejpam-8	73	13	1.5	1.5	NUM
ejpam-8	73	14	)	)	PUNCT
ejpam-8	73	15	,	,	PUNCT
ejpam-8	73	16	that	that	ADV
ejpam-8	73	17	is	is	ADV
ejpam-8	73	18	,	,	PUNCT
ejpam-8	73	19	we	we	PRON
ejpam-8	73	20	only	only	ADV
ejpam-8	73	21	prove	prove	VERB
ejpam-8	73	22	the	the	DET
ejpam-8	73	23	following	follow	VERB
ejpam-8	73	24	lemma	lemma	PROPN
ejpam-8	73	25	2.1	2.1	NUM
ejpam-8	73	26	and	and	CCONJ
ejpam-8	73	27	lemma	lemma	PROPN
ejpam-8	73	28	2.2	2.2	NUM
ejpam-8	73	29	.	.	PUNCT
ejpam-8	74	1	chaosheng	chaosheng	PROPN
ejpam-8	74	2	zhu	zhu	PROPN
ejpam-8	74	3	/	/	SYM
ejpam-8	74	4	eur	eur	PROPN
ejpam-8	74	5	.	.	PUNCT
ejpam-8	75	1	j.	j.	PROPN
ejpam-8	75	2	pure	pure	PROPN
ejpam-8	75	3	appl	appl	PROPN
ejpam-8	75	4	.	.	PROPN
ejpam-8	75	5	math	math	PROPN
ejpam-8	75	6	,	,	PUNCT
ejpam-8	75	7	1	1	NUM
ejpam-8	75	8	(	(	PUNCT
ejpam-8	75	9	2008	2008	NUM
ejpam-8	75	10	)	)	PUNCT
ejpam-8	75	11	,	,	PUNCT
ejpam-8	75	12	(	(	PUNCT
ejpam-8	75	13	3	3	NUM
ejpam-8	75	14	-	-	SYM
ejpam-8	75	15	10	10	NUM
ejpam-8	75	16	)	)	PUNCT
ejpam-8	75	17	6	6	NUM
ejpam-8	75	18	lemma	lemma	PROPN
ejpam-8	75	19	2.1	2.1	NUM
ejpam-8	75	20	.	.	PUNCT
ejpam-8	75	21	assume	assume	VERB
ejpam-8	75	22	that	that	SCONJ
ejpam-8	75	23	u(x	u(x	PROPN
ejpam-8	75	24	,	,	PUNCT
ejpam-8	75	25	t	t	PROPN
ejpam-8	75	26	)	)	PUNCT
ejpam-8	75	27	is	be	AUX
ejpam-8	75	28	solution	solution	NOUN
ejpam-8	75	29	for	for	ADP
ejpam-8	75	30	problems	problem	NOUN
ejpam-8	75	31	(	(	PUNCT
ejpam-8	75	32	1.7)-(1.8	1.7)-(1.8	NUM
ejpam-8	75	33	)	)	PUNCT
ejpam-8	75	34	with	with	ADP
ejpam-8	75	35	u0(x	u0(x	NOUN
ejpam-8	75	36	)	)	PUNCT
ejpam-8	75	37	∈	∈	PROPN
ejpam-8	75	38	b	b	NOUN
ejpam-8	75	39	,	,	PUNCT
ejpam-8	75	40	and	and	CCONJ
ejpam-8	76	1	qk	qk	X
ejpam-8	76	2	(	(	PUNCT
ejpam-8	76	3	k	k	NOUN
ejpam-8	76	4	=	=	SYM
ejpam-8	76	5	0,1	0,1	NUM
ejpam-8	76	6	,	,	PUNCT
ejpam-8	76	7	2	2	NUM
ejpam-8	76	8	,	,	PUNCT
ejpam-8	76	9	·	·	PUNCT
ejpam-8	76	10	·	·	PUNCT
ejpam-8	76	11	·	·	PUNCT
ejpam-8	76	12	)	)	PUNCT
ejpam-8	76	13	satisfy	satisfy	NOUN
ejpam-8	76	14	(	(	PUNCT
ejpam-8	76	15	2.3)-(2.4	2.3)-(2.4	NUM
ejpam-8	76	16	)	)	PUNCT
ejpam-8	76	17	,	,	PUNCT
ejpam-8	76	18	there	there	PRON
ejpam-8	76	19	are	be	VERB
ejpam-8	76	20	n0	n0	NUM
ejpam-8	76	21	∈	∈	PROPN
ejpam-8	76	22	n	n	PRON
ejpam-8	76	23	and	and	CCONJ
ejpam-8	76	24	t∗1(b	t∗1(b	PROPN
ejpam-8	76	25	)	)	PUNCT
ejpam-8	76	26	>	>	X
ejpam-8	76	27	0	0	NUM
ejpam-8	76	28	such	such	ADJ
ejpam-8	76	29	that	that	PRON
ejpam-8	76	30	for	for	ADP
ejpam-8	76	31	n	n	PRON
ejpam-8	76	32	≥	≥	NOUN
ejpam-8	76	33	n0	n0	NOUN
ejpam-8	76	34	we	we	PRON
ejpam-8	76	35	have	have	VERB
ejpam-8	76	36	‖uk‖2+δ‖uk	‖uk‖2+δ‖uk	PROPN
ejpam-8	76	37	x‖	x‖	PROPN
ejpam-8	76	38	2	2	NUM
ejpam-8	76	39	≤	≤	NUM
ejpam-8	76	40	2ρ2	2ρ2	NUM
ejpam-8	76	41	0	0	NUM
ejpam-8	76	42	,	,	PUNCT
ejpam-8	76	43	t	t	PROPN
ejpam-8	76	44	≥	≥	NOUN
ejpam-8	76	45	t∗1(b	t∗1(b	PROPN
ejpam-8	76	46	)	)	PUNCT
ejpam-8	76	47	,	,	PUNCT
ejpam-8	77	1	k	k	X
ejpam-8	77	2	=	=	SYM
ejpam-8	77	3	0,1	0,1	NUM
ejpam-8	77	4	,	,	PUNCT
ejpam-8	77	5	2	2	NUM
ejpam-8	77	6	,	,	PUNCT
ejpam-8	77	7	·	·	PUNCT
ejpam-8	77	8	·	·	PUNCT
ejpam-8	77	9	·	·	PUNCT
ejpam-8	77	10	.	.	PUNCT
ejpam-8	78	1	(	(	PUNCT
ejpam-8	78	2	2.5	2.5	NUM
ejpam-8	78	3	)	)	PUNCT
ejpam-8	78	4	proof	proof	NOUN
ejpam-8	78	5	:	:	PUNCT
ejpam-8	78	6	we	we	PRON
ejpam-8	78	7	only	only	ADV
ejpam-8	78	8	need	need	VERB
ejpam-8	78	9	to	to	PART
ejpam-8	78	10	prove	prove	VERB
ejpam-8	78	11	the	the	DET
ejpam-8	78	12	following	follow	VERB
ejpam-8	78	13	inequality	inequality	NOUN
ejpam-8	78	14	:	:	PUNCT
ejpam-8	78	15	‖qk‖2+δ‖qk	‖qk‖2+δ‖qk	PROPN
ejpam-8	78	16	x‖	x‖	PROPN
ejpam-8	78	17	2	2	NUM
ejpam-8	78	18	≤	≤	NOUN
ejpam-8	78	19	ρ2	ρ2	NOUN
ejpam-8	78	20	0	0	NUM
ejpam-8	78	21	.	.	PUNCT
ejpam-8	79	1	(	(	PUNCT
ejpam-8	79	2	2.6	2.6	NUM
ejpam-8	79	3	)	)	PUNCT
ejpam-8	79	4	here	here	ADV
ejpam-8	79	5	we	we	PRON
ejpam-8	79	6	verify	verify	VERB
ejpam-8	79	7	(	(	PUNCT
ejpam-8	79	8	2.6	2.6	NUM
ejpam-8	79	9	)	)	PUNCT
ejpam-8	79	10	by	by	ADP
ejpam-8	79	11	the	the	DET
ejpam-8	79	12	inductive	inductive	ADJ
ejpam-8	79	13	method	method	NOUN
ejpam-8	79	14	.	.	PUNCT
ejpam-8	80	1	firstly	firstly	ADV
ejpam-8	80	2	,	,	PUNCT
ejpam-8	80	3	multiplying	multiply	VERB
ejpam-8	80	4	(	(	PUNCT
ejpam-8	80	5	2.3	2.3	NUM
ejpam-8	80	6	)	)	PUNCT
ejpam-8	80	7	by	by	ADP
ejpam-8	80	8	q0	q0	PROPN
ejpam-8	80	9	,	,	PUNCT
ejpam-8	80	10	we	we	PRON
ejpam-8	80	11	have	have	VERB
ejpam-8	80	12	1	1	NUM
ejpam-8	80	13	2	2	NUM
ejpam-8	80	14	d	d	NOUN
ejpam-8	80	15	d	d	X
ejpam-8	80	16	t	t	PROPN
ejpam-8	80	17	(	(	PUNCT
ejpam-8	80	18	‖q0‖2+δ‖q0	‖q0‖2+δ‖q0	NOUN
ejpam-8	80	19	x‖	x‖	X
ejpam-8	80	20	2	2	NUM
ejpam-8	80	21	)	)	PUNCT
ejpam-8	81	1	+	+	PROPN
ejpam-8	81	2	µ‖q0	µ‖q0	X
ejpam-8	81	3	x‖	x‖	X
ejpam-8	81	4	2	2	NUM
ejpam-8	81	5	≤	≤	PROPN
ejpam-8	81	6	‖p‖	‖p‖	PROPN
ejpam-8	81	7	1	1	NUM
ejpam-8	81	8	2	2	NUM
ejpam-8	81	9	‖px‖	‖px‖	PROPN
ejpam-8	81	10	3	3	NUM
ejpam-8	81	11	2	2	NUM
ejpam-8	81	12	‖q0‖+	‖q0‖+	NUM
ejpam-8	81	13	‖	‖	PROPN
ejpam-8	81	14	f	f	PROPN
ejpam-8	81	15	‖‖q0‖	‖‖q0‖	PUNCT
ejpam-8	81	16	≤	≤	NUM
ejpam-8	81	17	ρ	ρ	NUM
ejpam-8	81	18	1	1	NUM
ejpam-8	81	19	2	2	NUM
ejpam-8	81	20	0	0	NUM
ejpam-8	81	21	δ	δ	NOUN
ejpam-8	81	22	−	−	NOUN
ejpam-8	81	23	3	3	NUM
ejpam-8	81	24	4ρ	4ρ	NOUN
ejpam-8	81	25	3	3	NUM
ejpam-8	81	26	2	2	NUM
ejpam-8	81	27	0	0	NUM
ejpam-8	81	28	‖q	‖q	NOUN
ejpam-8	81	29	0‖+	0‖+	NUM
ejpam-8	82	1	‖	‖	PROPN
ejpam-8	82	2	f	f	PROPN
ejpam-8	82	3	‖‖q0‖	‖‖q0‖	VERB
ejpam-8	82	4	≤	≤	NOUN
ejpam-8	82	5	(	(	PUNCT
ejpam-8	82	6	δ−	δ−	PROPN
ejpam-8	82	7	3	3	NUM
ejpam-8	82	8	4ρ2	4ρ2	NUM
ejpam-8	82	9	0	0	NUM
ejpam-8	83	1	+	+	CCONJ
ejpam-8	83	2	‖	‖	PROPN
ejpam-8	83	3	f	f	PROPN
ejpam-8	83	4	‖)‖q	‖)‖q	PUNCT
ejpam-8	84	1	0‖	0‖	NUM
ejpam-8	84	2	≤	≤	NOUN
ejpam-8	84	3	(	(	PUNCT
ejpam-8	84	4	δ−	δ−	PROPN
ejpam-8	84	5	3	3	NUM
ejpam-8	84	6	4ρ2	4ρ2	NUM
ejpam-8	84	7	0	0	NUM
ejpam-8	85	1	+	+	CCONJ
ejpam-8	86	1	‖	‖	PROPN
ejpam-8	86	2	f	f	PROPN
ejpam-8	86	3	‖	‖	PROPN
ejpam-8	86	4	)	)	PUNCT
ejpam-8	86	5	1	1	NUM
ejpam-8	86	6	n	n	NOUN
ejpam-8	86	7	+	+	CCONJ
ejpam-8	86	8	1	1	NUM
ejpam-8	86	9	‖q0	‖q0	NOUN
ejpam-8	86	10	x‖	x‖	NOUN
ejpam-8	86	11	≤	≤	NOUN
ejpam-8	86	12	µ	µ	PRON
ejpam-8	86	13	2	2	NUM
ejpam-8	86	14	‖q0	‖q0	NOUN
ejpam-8	86	15	x‖	x‖	PROPN
ejpam-8	86	16	2	2	NUM
ejpam-8	86	17	+	+	NUM
ejpam-8	86	18	1	1	NUM
ejpam-8	86	19	2µ(n	2µ(n	NUM
ejpam-8	87	1	+	+	CCONJ
ejpam-8	87	2	1)2	1)2	NUM
ejpam-8	87	3	(	(	PUNCT
ejpam-8	87	4	ρ2	ρ2	NOUN
ejpam-8	87	5	0δ	0δ	NOUN
ejpam-8	87	6	−	−	NUM
ejpam-8	87	7	3	3	NUM
ejpam-8	87	8	4	4	NUM
ejpam-8	87	9	+	+	CCONJ
ejpam-8	88	1	‖	‖	PROPN
ejpam-8	88	2	f	f	PROPN
ejpam-8	88	3	‖)2	‖)2	PROPN
ejpam-8	88	4	.	.	PUNCT
ejpam-8	89	1	it	it	PRON
ejpam-8	89	2	follows	follow	VERB
ejpam-8	89	3	that	that	SCONJ
ejpam-8	89	4	d	d	PROPN
ejpam-8	89	5	d	d	X
ejpam-8	89	6	t	t	PROPN
ejpam-8	89	7	(	(	PUNCT
ejpam-8	89	8	‖q0‖2+δ‖q0	‖q0‖2+δ‖q0	NOUN
ejpam-8	89	9	x‖	x‖	X
ejpam-8	89	10	2	2	NUM
ejpam-8	89	11	)	)	PUNCT
ejpam-8	90	1	+	+	PROPN
ejpam-8	90	2	µ‖q0	µ‖q0	X
ejpam-8	90	3	x‖	x‖	X
ejpam-8	90	4	2	2	NUM
ejpam-8	90	5	≤	≤	NOUN
ejpam-8	90	6	(	(	PUNCT
ejpam-8	90	7	ρ2	ρ2	NOUN
ejpam-8	90	8	0δ	0δ	NOUN
ejpam-8	90	9	−	−	NUM
ejpam-8	90	10	3	3	NUM
ejpam-8	90	11	4	4	NUM
ejpam-8	90	12	+	+	CCONJ
ejpam-8	90	13	‖	‖	PROPN
ejpam-8	90	14	f	f	PROPN
ejpam-8	90	15	‖)2	‖)2	PROPN
ejpam-8	90	16	µ(n	µ(n	PROPN
ejpam-8	90	17	+	+	PROPN
ejpam-8	90	18	1)2	1)2	NUM
ejpam-8	90	19	.	.	PUNCT
ejpam-8	91	1	noting	note	VERB
ejpam-8	91	2	that	that	SCONJ
ejpam-8	91	3	µ‖q0	µ‖q0	PROPN
ejpam-8	91	4	x‖	x‖	PROPN
ejpam-8	91	5	2	2	NUM
ejpam-8	91	6	=	=	SYM
ejpam-8	91	7	µ	µ	X
ejpam-8	91	8	2	2	NUM
ejpam-8	91	9	‖q0	‖q0	NOUN
ejpam-8	91	10	x‖	x‖	PROPN
ejpam-8	91	11	2	2	NUM
ejpam-8	91	12	+	+	SYM
ejpam-8	91	13	µ	µ	X
ejpam-8	91	14	2	2	NUM
ejpam-8	91	15	‖q0	‖q0	NOUN
ejpam-8	91	16	x‖	x‖	PROPN
ejpam-8	91	17	2	2	NUM
ejpam-8	91	18	≥	≥	NOUN
ejpam-8	91	19	�	�	PROPN
ejpam-8	91	20	µ(n	µ(n	PROPN
ejpam-8	91	21	+	+	CCONJ
ejpam-8	91	22	1)2	1)2	NUM
ejpam-8	91	23	2	2	NUM
ejpam-8	91	24	‖q0‖2	‖q0‖2	NOUN
ejpam-8	91	25	+	+	NOUN
ejpam-8	91	26	µ	µ	PRON
ejpam-8	91	27	2δ	2δ	NUM
ejpam-8	91	28	δ‖q0	δ‖q0	NOUN
ejpam-8	91	29	x‖	x‖	PROPN
ejpam-8	91	30	2	2	NUM
ejpam-8	91	31	�	�	PROPN
ejpam-8	91	32	≥	≥	NUM
ejpam-8	91	33	c1(‖q0‖2+δ‖q0	c1(‖q0‖2+δ‖q0	NOUN
ejpam-8	91	34	x‖	x‖	PROPN
ejpam-8	91	35	2	2	NUM
ejpam-8	91	36	)	)	PUNCT
ejpam-8	91	37	,	,	PUNCT
ejpam-8	91	38	we	we	PRON
ejpam-8	91	39	have	have	VERB
ejpam-8	91	40	d	d	PROPN
ejpam-8	91	41	d	d	X
ejpam-8	91	42	t	t	PROPN
ejpam-8	91	43	(	(	PUNCT
ejpam-8	91	44	‖q0‖2+δ‖q0	‖q0‖2+δ‖q0	NOUN
ejpam-8	91	45	x‖	x‖	X
ejpam-8	91	46	2	2	NUM
ejpam-8	91	47	)	)	PUNCT
ejpam-8	91	48	+	+	NUM
ejpam-8	91	49	c1(‖q0‖2+δ‖q0	c1(‖q0‖2+δ‖q0	NOUN
ejpam-8	91	50	x‖	x‖	X
ejpam-8	91	51	2)≤	2)≤	NOUN
ejpam-8	91	52	(	(	PUNCT
ejpam-8	91	53	ρ2	ρ2	VERB
ejpam-8	91	54	0δ	0δ	NOUN
ejpam-8	91	55	−	−	NUM
ejpam-8	91	56	3	3	NUM
ejpam-8	91	57	4	4	NUM
ejpam-8	91	58	+	+	CCONJ
ejpam-8	91	59	‖	‖	PROPN
ejpam-8	91	60	f	f	PROPN
ejpam-8	91	61	‖)2	‖)2	PROPN
ejpam-8	91	62	µ(n	µ(n	PROPN
ejpam-8	91	63	+	+	PROPN
ejpam-8	91	64	1)2	1)2	NUM
ejpam-8	91	65	.	.	PUNCT
ejpam-8	92	1	by	by	ADP
ejpam-8	92	2	gronwall	gronwall	PROPN
ejpam-8	92	3	’s	’s	PROPN
ejpam-8	92	4	lemma	lemma	PROPN
ejpam-8	92	5	,	,	PUNCT
ejpam-8	92	6	we	we	PRON
ejpam-8	92	7	have	have	VERB
ejpam-8	92	8	‖q0(t)‖2+δ‖q0	‖q0(t)‖2+δ‖q0	NUM
ejpam-8	92	9	x(t)‖	x(t)‖	NUM
ejpam-8	92	10	2	2	NUM
ejpam-8	92	11	≤	≤	NOUN
ejpam-8	92	12	(	(	PUNCT
ejpam-8	92	13	‖q0(0)‖2+δ‖q0	‖q0(0)‖2+δ‖q0	PUNCT
ejpam-8	92	14	x(0)‖	x(0)‖	PROPN
ejpam-8	92	15	2)e−c1	2)e−c1	PROPN
ejpam-8	92	16	t	t	PROPN
ejpam-8	93	1	+	+	CCONJ
ejpam-8	93	2	(	(	PUNCT
ejpam-8	93	3	ρ2	ρ2	NOUN
ejpam-8	93	4	0δ	0δ	NOUN
ejpam-8	93	5	−	−	NUM
ejpam-8	93	6	3	3	NUM
ejpam-8	93	7	4	4	NUM
ejpam-8	93	8	+	+	CCONJ
ejpam-8	93	9	‖	‖	PROPN
ejpam-8	93	10	f	f	PROPN
ejpam-8	93	11	‖)2	‖)2	PROPN
ejpam-8	93	12	c1µ(n	c1µ(n	PROPN
ejpam-8	93	13	+	+	CCONJ
ejpam-8	93	14	1)2	1)2	NUM
ejpam-8	93	15	(	(	PUNCT
ejpam-8	93	16	1−	1−	NUM
ejpam-8	93	17	e−c1	e−c1	PROPN
ejpam-8	93	18	t	t	PROPN
ejpam-8	93	19	)	)	PUNCT
ejpam-8	93	20	.	.	PUNCT
ejpam-8	94	1	chaosheng	chaosheng	PROPN
ejpam-8	94	2	zhu	zhu	PROPN
ejpam-8	94	3	/	/	SYM
ejpam-8	94	4	eur	eur	PROPN
ejpam-8	94	5	.	.	PUNCT
ejpam-8	95	1	j.	j.	PROPN
ejpam-8	95	2	pure	pure	PROPN
ejpam-8	95	3	appl	appl	PROPN
ejpam-8	95	4	.	.	PROPN
ejpam-8	95	5	math	math	PROPN
ejpam-8	95	6	,	,	PUNCT
ejpam-8	95	7	1	1	NUM
ejpam-8	95	8	(	(	PUNCT
ejpam-8	95	9	2008	2008	NUM
ejpam-8	95	10	)	)	PUNCT
ejpam-8	95	11	,	,	PUNCT
ejpam-8	95	12	(	(	PUNCT
ejpam-8	95	13	3	3	NUM
ejpam-8	95	14	-	-	SYM
ejpam-8	95	15	10	10	NUM
ejpam-8	95	16	)	)	PUNCT
ejpam-8	95	17	7	7	NUM
ejpam-8	95	18	there	there	PRON
ejpam-8	95	19	exists	exist	VERB
ejpam-8	95	20	a	a	DET
ejpam-8	95	21	t∗11(b	t∗11(b	NOUN
ejpam-8	95	22	)	)	PUNCT
ejpam-8	95	23	>	>	X
ejpam-8	95	24	0	0	NUM
ejpam-8	95	25	,	,	PUNCT
ejpam-8	95	26	such	such	ADJ
ejpam-8	95	27	that	that	PRON
ejpam-8	95	28	for	for	ADP
ejpam-8	95	29	∀t	∀t	PROPN
ejpam-8	95	30	≥	≥	NOUN
ejpam-8	95	31	t∗11(b	t∗11(b	ADJ
ejpam-8	95	32	)	)	PUNCT
ejpam-8	95	33	,	,	PUNCT
ejpam-8	95	34	we	we	PRON
ejpam-8	95	35	have	have	VERB
ejpam-8	95	36	‖q0(t)‖2+δ‖q0	‖q0(t)‖2+δ‖q0	NOUN
ejpam-8	95	37	x(t)‖	x(t)‖	NUM
ejpam-8	95	38	2	2	NUM
ejpam-8	95	39	≤	≤	NOUN
ejpam-8	95	40	2(ρ2	2(ρ2	NUM
ejpam-8	95	41	0δ	0δ	NUM
ejpam-8	96	1	−	−	NUM
ejpam-8	96	2	3	3	NUM
ejpam-8	96	3	4	4	NUM
ejpam-8	96	4	+	+	CCONJ
ejpam-8	96	5	‖	‖	PROPN
ejpam-8	96	6	f	f	PROPN
ejpam-8	96	7	‖)2	‖)2	PROPN
ejpam-8	96	8	c1µ(n	c1µ(n	PROPN
ejpam-8	96	9	+	+	CCONJ
ejpam-8	96	10	1)2	1)2	NUM
ejpam-8	96	11	.	.	PUNCT
ejpam-8	97	1	let	let	VERB
ejpam-8	97	2	n	n	PRON
ejpam-8	97	3	is	be	AUX
ejpam-8	97	4	large	large	ADJ
ejpam-8	97	5	enough	enough	ADV
ejpam-8	97	6	,	,	PUNCT
ejpam-8	97	7	such	such	ADJ
ejpam-8	97	8	that	that	SCONJ
ejpam-8	97	9	2(ρ2	2(ρ2	NUM
ejpam-8	97	10	0δ	0δ	NUM
ejpam-8	97	11	−	−	NUM
ejpam-8	97	12	3	3	NUM
ejpam-8	97	13	4	4	NUM
ejpam-8	97	14	+	+	CCONJ
ejpam-8	97	15	‖	‖	PROPN
ejpam-8	97	16	f	f	PROPN
ejpam-8	97	17	‖)2	‖)2	PROPN
ejpam-8	97	18	ρ2	ρ2	VERB
ejpam-8	97	19	0c1µ(n	0c1µ(n	PRON
ejpam-8	98	1	+	+	CCONJ
ejpam-8	98	2	1)2	1)2	NUM
ejpam-8	98	3	≤	≤	NUM
ejpam-8	98	4	1	1	NUM
ejpam-8	98	5	,	,	PUNCT
ejpam-8	98	6	(	(	PUNCT
ejpam-8	98	7	2.7	2.7	NUM
ejpam-8	98	8	)	)	PUNCT
ejpam-8	98	9	we	we	PRON
ejpam-8	98	10	have	have	VERB
ejpam-8	98	11	‖q0(t)‖2+δ‖q0	‖q0(t)‖2+δ‖q0	NUM
ejpam-8	98	12	x(t)‖	x(t)‖	NUM
ejpam-8	98	13	2	2	NUM
ejpam-8	98	14	≤	≤	NOUN
ejpam-8	98	15	ρ2	ρ2	NOUN
ejpam-8	98	16	0	0	NUM
ejpam-8	98	17	,	,	PUNCT
ejpam-8	98	18	t	t	PROPN
ejpam-8	98	19	≥	≥	NOUN
ejpam-8	98	20	t∗11(b	t∗11(b	PROPN
ejpam-8	98	21	)	)	PUNCT
ejpam-8	98	22	.	.	PUNCT
ejpam-8	99	1	(	(	PUNCT
ejpam-8	99	2	2.8	2.8	NUM
ejpam-8	99	3	)	)	PUNCT
ejpam-8	99	4	now	now	ADV
ejpam-8	99	5	assume	assume	VERB
ejpam-8	99	6	that	that	SCONJ
ejpam-8	99	7	‖qk−1‖2+δ‖qk−1	‖qk−1‖2+δ‖qk−1	PROPN
ejpam-8	99	8	x	x	SYM
ejpam-8	99	9	‖	‖	PROPN
ejpam-8	99	10	2	2	NUM
ejpam-8	99	11	≤	≤	NOUN
ejpam-8	99	12	ρ2	ρ2	NOUN
ejpam-8	99	13	0	0	NUM
ejpam-8	99	14	holds	hold	NOUN
ejpam-8	99	15	,	,	PUNCT
ejpam-8	99	16	we	we	PRON
ejpam-8	99	17	shall	shall	AUX
ejpam-8	99	18	prove	prove	VERB
ejpam-8	99	19	that	that	SCONJ
ejpam-8	99	20	for	for	ADP
ejpam-8	99	21	∀k	∀k	NOUN
ejpam-8	99	22	(	(	PUNCT
ejpam-8	99	23	2.6	2.6	NUM
ejpam-8	99	24	)	)	PUNCT
ejpam-8	99	25	is	be	AUX
ejpam-8	99	26	holds	hold	NOUN
ejpam-8	99	27	.	.	PUNCT
ejpam-8	100	1	multiplying	multiply	VERB
ejpam-8	100	2	(	(	PUNCT
ejpam-8	100	3	2.4	2.4	NUM
ejpam-8	100	4	)	)	PUNCT
ejpam-8	100	5	by	by	ADP
ejpam-8	100	6	qk	qk	NOUN
ejpam-8	100	7	,	,	PUNCT
ejpam-8	100	8	we	we	PRON
ejpam-8	100	9	have	have	VERB
ejpam-8	100	10	1	1	NUM
ejpam-8	100	11	2	2	NUM
ejpam-8	100	12	d	d	NOUN
ejpam-8	100	13	d	d	X
ejpam-8	100	14	t	t	PROPN
ejpam-8	100	15	(	(	PUNCT
ejpam-8	100	16	‖qk‖2+δ‖qk	‖qk‖2+δ‖qk	X
ejpam-8	100	17	x‖	x‖	PROPN
ejpam-8	100	18	2	2	NUM
ejpam-8	100	19	)	)	PUNCT
ejpam-8	101	1	+	+	PROPN
ejpam-8	101	2	µ‖qk	µ‖qk	PROPN
ejpam-8	101	3	x‖	x‖	PROPN
ejpam-8	101	4	2	2	NUM
ejpam-8	101	5	≤	≤	NOUN
ejpam-8	101	6	(	(	PUNCT
ejpam-8	101	7	4δ−	4δ−	NUM
ejpam-8	101	8	3	3	NUM
ejpam-8	101	9	4ρ2	4ρ2	NUM
ejpam-8	101	10	0	0	NUM
ejpam-8	102	1	+	+	CCONJ
ejpam-8	102	2	‖	‖	PROPN
ejpam-8	102	3	f	f	PROPN
ejpam-8	102	4	‖)‖q	‖)‖q	PUNCT
ejpam-8	102	5	k‖.	k‖.	NOUN
ejpam-8	102	6	by	by	ADP
ejpam-8	102	7	using	use	VERB
ejpam-8	102	8	similar	similar	ADJ
ejpam-8	102	9	argument	argument	NOUN
ejpam-8	102	10	as	as	ADP
ejpam-8	102	11	above	above	ADV
ejpam-8	102	12	,	,	PUNCT
ejpam-8	102	13	we	we	PRON
ejpam-8	102	14	can	can	AUX
ejpam-8	102	15	obtain	obtain	VERB
ejpam-8	102	16	d	d	PROPN
ejpam-8	102	17	d	d	X
ejpam-8	102	18	t	t	PROPN
ejpam-8	102	19	(	(	PUNCT
ejpam-8	102	20	‖qk‖2+δ‖qk	‖qk‖2+δ‖qk	X
ejpam-8	102	21	x‖	x‖	PROPN
ejpam-8	102	22	2	2	NUM
ejpam-8	102	23	)	)	PUNCT
ejpam-8	103	1	+	+	CCONJ
ejpam-8	103	2	c1(‖qk‖2+δ‖qk	c1(‖qk‖2+δ‖qk	PROPN
ejpam-8	103	3	x‖	x‖	PROPN
ejpam-8	103	4	2)≤	2)≤	PROPN
ejpam-8	103	5	(	(	PUNCT
ejpam-8	103	6	4ρ2	4ρ2	NUM
ejpam-8	103	7	0δ	0δ	NOUN
ejpam-8	103	8	−	−	NUM
ejpam-8	103	9	3	3	NUM
ejpam-8	103	10	4	4	NUM
ejpam-8	103	11	+	+	CCONJ
ejpam-8	103	12	‖	‖	PROPN
ejpam-8	103	13	f	f	PROPN
ejpam-8	103	14	‖)2	‖)2	PROPN
ejpam-8	103	15	µ(n	µ(n	PROPN
ejpam-8	103	16	+	+	PROPN
ejpam-8	103	17	1)2	1)2	NUM
ejpam-8	103	18	.	.	PUNCT
ejpam-8	104	1	by	by	ADP
ejpam-8	104	2	gronwall	gronwall	PROPN
ejpam-8	104	3	’s	’s	PROPN
ejpam-8	104	4	lemma	lemma	PROPN
ejpam-8	104	5	,	,	PUNCT
ejpam-8	104	6	there	there	PRON
ejpam-8	104	7	exists	exist	VERB
ejpam-8	104	8	a	a	DET
ejpam-8	104	9	t∗12(b	t∗12(b	NOUN
ejpam-8	104	10	)	)	PUNCT
ejpam-8	104	11	>	>	X
ejpam-8	104	12	0	0	NUM
ejpam-8	105	1	such	such	ADJ
ejpam-8	105	2	that	that	PRON
ejpam-8	105	3	for	for	SCONJ
ejpam-8	105	4	∀t	∀t	PROPN
ejpam-8	105	5	≥	≥	NOUN
ejpam-8	105	6	t∗12(b	t∗12(b	ADJ
ejpam-8	105	7	)	)	PUNCT
ejpam-8	105	8	we	we	PRON
ejpam-8	105	9	have	have	VERB
ejpam-8	105	10	‖qk(t)‖2+δ‖qk	‖qk(t)‖2+δ‖qk	PROPN
ejpam-8	105	11	x(t)‖	x(t)‖	NUM
ejpam-8	105	12	2	2	NUM
ejpam-8	105	13	≤	≤	NOUN
ejpam-8	105	14	2(4δ−	2(4δ−	NUM
ejpam-8	105	15	3	3	NUM
ejpam-8	105	16	4ρ2	4ρ2	NUM
ejpam-8	105	17	0	0	NUM
ejpam-8	106	1	+	+	CCONJ
ejpam-8	106	2	‖	‖	PROPN
ejpam-8	106	3	f	f	PROPN
ejpam-8	106	4	‖	‖	PROPN
ejpam-8	106	5	)	)	PUNCT
ejpam-8	106	6	2	2	NUM
ejpam-8	106	7	c1µ(n	c1µ(n	PROPN
ejpam-8	106	8	+	+	CCONJ
ejpam-8	106	9	1)2	1)2	NUM
ejpam-8	106	10	.	.	PUNCT
ejpam-8	107	1	let	let	VERB
ejpam-8	107	2	n	n	PRON
ejpam-8	107	3	is	be	AUX
ejpam-8	107	4	large	large	ADJ
ejpam-8	107	5	enough	enough	ADV
ejpam-8	107	6	,	,	PUNCT
ejpam-8	107	7	such	such	ADJ
ejpam-8	107	8	that	that	SCONJ
ejpam-8	107	9	2(4δ−	2(4δ−	NUM
ejpam-8	107	10	3	3	NUM
ejpam-8	107	11	4ρ2	4ρ2	NUM
ejpam-8	107	12	0	0	NUM
ejpam-8	108	1	+	+	CCONJ
ejpam-8	108	2	‖	‖	PROPN
ejpam-8	108	3	f	f	PROPN
ejpam-8	108	4	‖	‖	PROPN
ejpam-8	108	5	)	)	PUNCT
ejpam-8	108	6	2	2	NUM
ejpam-8	108	7	ρ2	ρ2	NOUN
ejpam-8	108	8	0c1µ(n	0c1µ(n	PRON
ejpam-8	108	9	+	+	CCONJ
ejpam-8	108	10	1)2	1)2	NUM
ejpam-8	108	11	≤	≤	NUM
ejpam-8	108	12	1	1	NUM
ejpam-8	108	13	,	,	PUNCT
ejpam-8	108	14	(	(	PUNCT
ejpam-8	108	15	2.9	2.9	NUM
ejpam-8	108	16	)	)	PUNCT
ejpam-8	108	17	we	we	PRON
ejpam-8	108	18	have	have	VERB
ejpam-8	108	19	‖qk(t)‖2+δ‖qk	‖qk(t)‖2+δ‖qk	PROPN
ejpam-8	108	20	x(t)‖	x(t)‖	NUM
ejpam-8	108	21	2	2	NUM
ejpam-8	108	22	≤	≤	NOUN
ejpam-8	108	23	ρ2	ρ2	NOUN
ejpam-8	108	24	0	0	NUM
ejpam-8	108	25	,	,	PUNCT
ejpam-8	108	26	t	t	PROPN
ejpam-8	108	27	≥	≥	NOUN
ejpam-8	108	28	t∗12(b	t∗12(b	PROPN
ejpam-8	108	29	)	)	PUNCT
ejpam-8	108	30	.	.	PUNCT
ejpam-8	109	1	(	(	PUNCT
ejpam-8	109	2	2.10	2.10	NUM
ejpam-8	109	3	)	)	PUNCT
ejpam-8	109	4	let	let	VERB
ejpam-8	109	5	t∗1(b	t∗1(b	PROPN
ejpam-8	109	6	)	)	PUNCT
ejpam-8	109	7	=	=	SYM
ejpam-8	110	1	max(t∗11(b	max(t∗11(b	PROPN
ejpam-8	110	2	)	)	PUNCT
ejpam-8	110	3	,	,	PUNCT
ejpam-8	110	4	t∗12(b	t∗12(b	NOUN
ejpam-8	110	5	)	)	PUNCT
ejpam-8	110	6	)	)	PUNCT
ejpam-8	110	7	,	,	PUNCT
ejpam-8	110	8	then	then	ADV
ejpam-8	110	9	(	(	PUNCT
ejpam-8	110	10	2.6	2.6	NUM
ejpam-8	110	11	)	)	PUNCT
ejpam-8	110	12	follows	follow	VERB
ejpam-8	110	13	from	from	ADP
ejpam-8	110	14	(	(	PUNCT
ejpam-8	110	15	2.8	2.8	NUM
ejpam-8	110	16	)	)	PUNCT
ejpam-8	110	17	and	and	CCONJ
ejpam-8	110	18	(	(	PUNCT
ejpam-8	110	19	2.10	2.10	NUM
ejpam-8	110	20	)	)	PUNCT
ejpam-8	110	21	.	.	PUNCT
ejpam-8	111	1	the	the	DET
ejpam-8	111	2	proof	proof	NOUN
ejpam-8	111	3	of	of	ADP
ejpam-8	111	4	lemma	lemma	PROPN
ejpam-8	111	5	2.1	2.1	NUM
ejpam-8	111	6	is	be	AUX
ejpam-8	111	7	completed	complete	VERB
ejpam-8	111	8	.	.	PUNCT
ejpam-8	112	1	lemma	lemma	PROPN
ejpam-8	112	2	2.2	2.2	NUM
ejpam-8	112	3	.	.	PUNCT
ejpam-8	113	1	under	under	ADP
ejpam-8	113	2	the	the	DET
ejpam-8	113	3	hypotheses	hypothesis	NOUN
ejpam-8	113	4	of	of	ADP
ejpam-8	113	5	lemma	lemma	PROPN
ejpam-8	113	6	2.1	2.1	NUM
ejpam-8	113	7	,	,	PUNCT
ejpam-8	113	8	there	there	PRON
ejpam-8	113	9	are	be	VERB
ejpam-8	113	10	n1	n1	PROPN
ejpam-8	113	11	∈	∈	PROPN
ejpam-8	113	12	n	n	PRON
ejpam-8	113	13	and	and	CCONJ
ejpam-8	113	14	t∗2(b	t∗2(b	PROPN
ejpam-8	113	15	)	)	PUNCT
ejpam-8	113	16	>	>	X
ejpam-8	113	17	0	0	NUM
ejpam-8	113	18	such	such	ADJ
ejpam-8	113	19	that	that	PRON
ejpam-8	113	20	for	for	ADP
ejpam-8	113	21	n	n	PRON
ejpam-8	113	22	≥	≥	NOUN
ejpam-8	113	23	n1	n1	NOUN
ejpam-8	113	24	we	we	PRON
ejpam-8	113	25	have	have	VERB
ejpam-8	113	26	‖qk	‖qk	NUM
ejpam-8	113	27	−	−	PROPN
ejpam-8	114	1	q‖2+δ‖qk	q‖2+δ‖qk	PROPN
ejpam-8	114	2	x	x	PUNCT
ejpam-8	114	3	−	−	PROPN
ejpam-8	114	4	qx‖2→	qx‖2→	PROPN
ejpam-8	114	5	0	0	NUM
ejpam-8	114	6	,	,	PUNCT
ejpam-8	114	7	k→∞	k→∞	NOUN
ejpam-8	114	8	,	,	PUNCT
ejpam-8	114	9	t	t	PROPN
ejpam-8	114	10	≥	≥	NOUN
ejpam-8	114	11	t∗2(b	t∗2(b	PROPN
ejpam-8	114	12	)	)	PUNCT
ejpam-8	114	13	.	.	PUNCT
ejpam-8	115	1	(	(	PUNCT
ejpam-8	115	2	2.11	2.11	NUM
ejpam-8	115	3	)	)	PUNCT
ejpam-8	115	4	chaosheng	chaosheng	PROPN
ejpam-8	115	5	zhu	zhu	PROPN
ejpam-8	115	6	/	/	SYM
ejpam-8	115	7	eur	eur	PROPN
ejpam-8	115	8	.	.	PUNCT
ejpam-8	116	1	j.	j.	PROPN
ejpam-8	116	2	pure	pure	PROPN
ejpam-8	116	3	appl	appl	PROPN
ejpam-8	116	4	.	.	PROPN
ejpam-8	116	5	math	math	PROPN
ejpam-8	116	6	,	,	PUNCT
ejpam-8	116	7	1	1	NUM
ejpam-8	116	8	(	(	PUNCT
ejpam-8	116	9	2008	2008	NUM
ejpam-8	116	10	)	)	PUNCT
ejpam-8	116	11	,	,	PUNCT
ejpam-8	116	12	(	(	PUNCT
ejpam-8	116	13	3	3	NUM
ejpam-8	116	14	-	-	SYM
ejpam-8	116	15	10	10	NUM
ejpam-8	116	16	)	)	PUNCT
ejpam-8	116	17	8	8	NUM
ejpam-8	116	18	proof	proof	NOUN
ejpam-8	116	19	:	:	PUNCT
ejpam-8	116	20	here	here	ADV
ejpam-8	116	21	we	we	PRON
ejpam-8	116	22	verify	verify	VERB
ejpam-8	116	23	(	(	PUNCT
ejpam-8	116	24	2.11	2.11	NUM
ejpam-8	116	25	)	)	PUNCT
ejpam-8	116	26	by	by	ADP
ejpam-8	116	27	the	the	DET
ejpam-8	116	28	inductive	inductive	ADJ
ejpam-8	116	29	method	method	NOUN
ejpam-8	116	30	.	.	PUNCT
ejpam-8	117	1	firstly	firstly	ADV
ejpam-8	117	2	,	,	PUNCT
ejpam-8	117	3	set	set	VERB
ejpam-8	117	4	w0	w0	PROPN
ejpam-8	117	5	=	=	PUNCT
ejpam-8	117	6	q0	q0	PROPN
ejpam-8	118	1	−	−	PROPN
ejpam-8	118	2	q	q	NOUN
ejpam-8	118	3	,	,	PUNCT
ejpam-8	118	4	by	by	ADP
ejpam-8	118	5	(	(	PUNCT
ejpam-8	118	6	2.2	2.2	NUM
ejpam-8	118	7	)	)	PUNCT
ejpam-8	118	8	and	and	CCONJ
ejpam-8	118	9	(	(	PUNCT
ejpam-8	118	10	2.3	2.3	NUM
ejpam-8	118	11	)	)	PUNCT
ejpam-8	119	1	we	we	PRON
ejpam-8	119	2	have	have	AUX
ejpam-8	119	3	w0	w0	PROPN
ejpam-8	119	4	t	t	PROPN
ejpam-8	119	5	−δw0	−δw0	PROPN
ejpam-8	119	6	x	x	SYM
ejpam-8	119	7	x	x	SYM
ejpam-8	119	8	t	t	NOUN
ejpam-8	120	1	−µw0	−µw0	NOUN
ejpam-8	120	2	x	x	PUNCT
ejpam-8	120	3	x	x	X
ejpam-8	120	4	+	+	NOUN
ejpam-8	120	5	qn	qn	INTJ
ejpam-8	120	6	(	(	PUNCT
ejpam-8	120	7	ppx	ppx	PROPN
ejpam-8	120	8	−	−	PROPN
ejpam-8	120	9	uux	uux	PROPN
ejpam-8	120	10	)	)	PUNCT
ejpam-8	120	11	=	=	NOUN
ejpam-8	121	1	0	0	X
ejpam-8	121	2	.	.	PUNCT
ejpam-8	122	1	(	(	PUNCT
ejpam-8	122	2	2.12	2.12	NUM
ejpam-8	122	3	)	)	PUNCT
ejpam-8	122	4	multiplying	multiplying	NOUN
ejpam-8	122	5	(	(	PUNCT
ejpam-8	122	6	2.12	2.12	NUM
ejpam-8	122	7	)	)	PUNCT
ejpam-8	122	8	by	by	ADP
ejpam-8	122	9	w0	w0	PROPN
ejpam-8	122	10	we	we	PRON
ejpam-8	122	11	obtain	obtain	VERB
ejpam-8	122	12	1	1	NUM
ejpam-8	122	13	2	2	NUM
ejpam-8	122	14	d	d	NOUN
ejpam-8	122	15	d	d	X
ejpam-8	122	16	t	t	PROPN
ejpam-8	122	17	(	(	PUNCT
ejpam-8	122	18	‖w0‖2+δ‖w0	‖w0‖2+δ‖w0	X
ejpam-8	122	19	x‖	x‖	X
ejpam-8	122	20	2	2	NUM
ejpam-8	122	21	)	)	PUNCT
ejpam-8	123	1	+	+	ADP
ejpam-8	123	2	µ‖w0	µ‖w0	VERB
ejpam-8	123	3	x‖	x‖	X
ejpam-8	123	4	2	2	NUM
ejpam-8	123	5	≤	≤	NOUN
ejpam-8	123	6	2‖u‖	2‖u‖	NUM
ejpam-8	123	7	1	1	NUM
ejpam-8	123	8	2	2	NUM
ejpam-8	123	9	‖ux‖	‖ux‖	NOUN
ejpam-8	123	10	3	3	NUM
ejpam-8	123	11	2	2	NUM
ejpam-8	123	12	‖w0‖	‖w0‖	NOUN
ejpam-8	123	13	≤	≤	NUM
ejpam-8	123	14	2ρ2	2ρ2	NUM
ejpam-8	123	15	0δ	0δ	NUM
ejpam-8	123	16	−	−	NUM
ejpam-8	123	17	3	3	NUM
ejpam-8	123	18	4	4	NUM
ejpam-8	123	19	‖w0‖.	‖w0‖.	X
ejpam-8	123	20	by	by	ADP
ejpam-8	123	21	using	use	VERB
ejpam-8	123	22	similar	similar	ADJ
ejpam-8	123	23	argument	argument	NOUN
ejpam-8	123	24	as	as	ADP
ejpam-8	123	25	above	above	ADV
ejpam-8	123	26	,	,	PUNCT
ejpam-8	123	27	we	we	PRON
ejpam-8	123	28	can	can	AUX
ejpam-8	123	29	obtain	obtain	VERB
ejpam-8	123	30	d	d	PROPN
ejpam-8	123	31	d	d	X
ejpam-8	123	32	t	t	PROPN
ejpam-8	123	33	(	(	PUNCT
ejpam-8	123	34	‖w0‖2+δ‖w0	‖w0‖2+δ‖w0	X
ejpam-8	123	35	x‖	x‖	X
ejpam-8	123	36	2	2	NUM
ejpam-8	123	37	)	)	PUNCT
ejpam-8	124	1	+	+	NUM
ejpam-8	124	2	c1(‖w0‖2+δ‖w0	c1(‖w0‖2+δ‖w0	X
ejpam-8	124	3	x‖	x‖	X
ejpam-8	124	4	2)≤	2)≤	NUM
ejpam-8	124	5	4ρ4	4ρ4	NUM
ejpam-8	124	6	0	0	NUM
ejpam-8	124	7	δ	δ	NOUN
ejpam-8	124	8	3	3	NUM
ejpam-8	124	9	2µ(n	2µ(n	NUM
ejpam-8	124	10	+	+	CCONJ
ejpam-8	124	11	1)2	1)2	NUM
ejpam-8	124	12	.	.	PUNCT
ejpam-8	125	1	(	(	PUNCT
ejpam-8	125	2	2.13	2.13	NUM
ejpam-8	125	3	)	)	PUNCT
ejpam-8	125	4	by	by	ADP
ejpam-8	125	5	gronwall	gronwall	PROPN
ejpam-8	125	6	’s	’s	PROPN
ejpam-8	125	7	lemma	lemma	PROPN
ejpam-8	125	8	,	,	PUNCT
ejpam-8	125	9	there	there	PRON
ejpam-8	125	10	exists	exist	VERB
ejpam-8	125	11	a	a	DET
ejpam-8	125	12	t∗20(b	t∗20(b	NOUN
ejpam-8	125	13	)	)	PUNCT
ejpam-8	125	14	>	>	X
ejpam-8	125	15	0	0	NUM
ejpam-8	125	16	,	,	PUNCT
ejpam-8	125	17	such	such	ADJ
ejpam-8	125	18	that	that	SCONJ
ejpam-8	125	19	‖w0(t)‖2+δ‖w0	‖w0(t)‖2+δ‖w0	NUM
ejpam-8	125	20	x(t)‖	x(t)‖	NUM
ejpam-8	125	21	2	2	NUM
ejpam-8	125	22	≤	≤	NUM
ejpam-8	125	23	8ρ4	8ρ4	NUM
ejpam-8	125	24	0	0	SYM
ejpam-8	125	25	c1δ	c1δ	NOUN
ejpam-8	125	26	3	3	NUM
ejpam-8	125	27	2µ(n	2µ(n	NUM
ejpam-8	125	28	+	+	CCONJ
ejpam-8	126	1	1)2	1)2	NUM
ejpam-8	126	2	,	,	PUNCT
ejpam-8	126	3	t	t	PROPN
ejpam-8	126	4	≥	≥	NOUN
ejpam-8	126	5	t∗20(b	t∗20(b	PROPN
ejpam-8	126	6	)	)	PUNCT
ejpam-8	126	7	.	.	PUNCT
ejpam-8	127	1	(	(	PUNCT
ejpam-8	127	2	2.14	2.14	NUM
ejpam-8	127	3	)	)	PUNCT
ejpam-8	127	4	denote	denote	NOUN
ejpam-8	127	5	wk	wk	NOUN
ejpam-8	128	1	=	=	PUNCT
ejpam-8	128	2	qk	qk	NOUN
ejpam-8	128	3	−	−	NOUN
ejpam-8	129	1	q	q	INTJ
ejpam-8	129	2	,	,	PUNCT
ejpam-8	129	3	by	by	ADP
ejpam-8	129	4	(	(	PUNCT
ejpam-8	129	5	2.2	2.2	NUM
ejpam-8	129	6	)	)	PUNCT
ejpam-8	129	7	and	and	CCONJ
ejpam-8	129	8	(	(	PUNCT
ejpam-8	129	9	2.4	2.4	NUM
ejpam-8	129	10	)	)	PUNCT
ejpam-8	129	11	,	,	PUNCT
ejpam-8	129	12	we	we	PRON
ejpam-8	129	13	have	have	VERB
ejpam-8	129	14	wk	wk	INTJ
ejpam-8	129	15	t	t	PROPN
ejpam-8	129	16	−δwk	−δwk	NOUN
ejpam-8	129	17	x	x	X
ejpam-8	130	1	x	x	SYM
ejpam-8	130	2	t	t	NOUN
ejpam-8	130	3	−µwk	−µwk	NUM
ejpam-8	130	4	x	x	X
ejpam-8	131	1	x	x	X
ejpam-8	131	2	+	+	NOUN
ejpam-8	131	3	qn	qn	INTJ
ejpam-8	131	4	(	(	PUNCT
ejpam-8	131	5	u	u	NOUN
ejpam-8	131	6	k−1uk−1	k−1uk−1	PROPN
ejpam-8	131	7	x	x	PUNCT
ejpam-8	131	8	−	−	PROPN
ejpam-8	131	9	uux	uux	PROPN
ejpam-8	131	10	)	)	PUNCT
ejpam-8	131	11	=	=	SYM
ejpam-8	131	12	0	0	NUM
ejpam-8	131	13	,	,	PUNCT
ejpam-8	131	14	(	(	PUNCT
ejpam-8	131	15	2.15	2.15	NUM
ejpam-8	131	16	)	)	PUNCT
ejpam-8	131	17	where	where	SCONJ
ejpam-8	131	18	k	k	NOUN
ejpam-8	131	19	=	=	SYM
ejpam-8	131	20	1,2	1,2	NUM
ejpam-8	131	21	,	,	PUNCT
ejpam-8	131	22	·	·	PUNCT
ejpam-8	131	23	·	·	PUNCT
ejpam-8	131	24	·	·	PUNCT
ejpam-8	131	25	.	.	PUNCT
ejpam-8	132	1	here	here	ADV
ejpam-8	132	2	we	we	PRON
ejpam-8	132	3	note	note	VERB
ejpam-8	132	4	that	that	SCONJ
ejpam-8	132	5	uk−1uk−1	uk−1uk−1	PROPN
ejpam-8	132	6	x	x	PUNCT
ejpam-8	132	7	−	−	PROPN
ejpam-8	133	1	uux	uux	PROPN
ejpam-8	133	2	=	=	PUNCT
ejpam-8	133	3	uk−1wk−1	uk−1wk−1	X
ejpam-8	133	4	x	x	PUNCT
ejpam-8	133	5	+	+	ADJ
ejpam-8	133	6	wk−1ux	wk−1ux	NUM
ejpam-8	133	7	.	.	PUNCT
ejpam-8	134	1	multiplying	multiply	VERB
ejpam-8	134	2	(	(	PUNCT
ejpam-8	134	3	2.15	2.15	NUM
ejpam-8	134	4	)	)	PUNCT
ejpam-8	134	5	by	by	ADP
ejpam-8	134	6	wk	wk	INTJ
ejpam-8	135	1	we	we	PRON
ejpam-8	135	2	have	have	VERB
ejpam-8	135	3	1	1	NUM
ejpam-8	135	4	2	2	NUM
ejpam-8	135	5	d	d	NOUN
ejpam-8	135	6	d	d	X
ejpam-8	135	7	t	t	PROPN
ejpam-8	135	8	(	(	PUNCT
ejpam-8	135	9	‖wk‖2+δ‖wk	‖wk‖2+δ‖wk	PROPN
ejpam-8	135	10	x‖	x‖	PROPN
ejpam-8	135	11	2	2	NUM
ejpam-8	135	12	)	)	PUNCT
ejpam-8	136	1	+	+	ADP
ejpam-8	136	2	µ‖wk	µ‖wk	NOUN
ejpam-8	136	3	x‖	x‖	ADP
ejpam-8	136	4	2	2	NUM
ejpam-8	136	5	≤	≤	NOUN
ejpam-8	136	6	p	p	PROPN
ejpam-8	136	7	2δ−	2δ−	PROPN
ejpam-8	136	8	1	1	NUM
ejpam-8	136	9	4ρ0‖wk−1	4ρ0‖wk−1	NUM
ejpam-8	136	10	x	x	PUNCT
ejpam-8	136	11	‖‖w	‖‖w	PROPN
ejpam-8	136	12	k‖+δ−	k‖+δ−	NOUN
ejpam-8	136	13	1	1	NUM
ejpam-8	136	14	2ρ0‖wk−1‖l∞‖wk‖	2ρ0‖wk−1‖l∞‖wk‖	PROPN
ejpam-8	136	15	≤	≤	NUM
ejpam-8	136	16	�	�	PROPN
ejpam-8	136	17	p	p	NOUN
ejpam-8	136	18	2ρ0δ	2ρ0δ	NOUN
ejpam-8	136	19	−	−	NUM
ejpam-8	136	20	1	1	NUM
ejpam-8	136	21	4	4	NUM
ejpam-8	136	22	+	+	CCONJ
ejpam-8	136	23	cρ0δ	cρ0δ	PROPN
ejpam-8	136	24	−	−	NUM
ejpam-8	136	25	1	1	NUM
ejpam-8	136	26	2	2	NUM
ejpam-8	136	27	�	�	PROPN
ejpam-8	136	28	‖wk−1	‖wk−1	NOUN
ejpam-8	136	29	x	x	X
ejpam-8	136	30	‖‖w	‖‖w	PRON
ejpam-8	136	31	k‖	k‖	X
ejpam-8	136	32	≤	≤	ADV
ejpam-8	136	33	1	1	NUM
ejpam-8	136	34	n	n	NOUN
ejpam-8	136	35	+	+	CCONJ
ejpam-8	136	36	1	1	NUM
ejpam-8	136	37	�	�	NOUN
ejpam-8	136	38	p	p	NOUN
ejpam-8	136	39	2ρ0δ	2ρ0δ	NOUN
ejpam-8	136	40	−	−	NUM
ejpam-8	136	41	1	1	NUM
ejpam-8	136	42	4	4	NUM
ejpam-8	136	43	+	+	CCONJ
ejpam-8	136	44	cρ0δ	cρ0δ	PROPN
ejpam-8	136	45	−	−	NUM
ejpam-8	136	46	1	1	NUM
ejpam-8	136	47	2	2	NUM
ejpam-8	136	48	�	�	PROPN
ejpam-8	136	49	‖wk−1	‖wk−1	NOUN
ejpam-8	136	50	x	x	X
ejpam-8	136	51	‖‖w	‖‖w	PROPN
ejpam-8	136	52	k	k	PROPN
ejpam-8	136	53	x‖	x‖	PROPN
ejpam-8	136	54	≤	≤	ADV
ejpam-8	136	55	1	1	NUM
ejpam-8	136	56	2µ(n	2µ(n	NUM
ejpam-8	136	57	+	+	CCONJ
ejpam-8	136	58	1)2	1)2	NUM
ejpam-8	136	59	�	�	NOUN
ejpam-8	136	60	p	p	NOUN
ejpam-8	136	61	2ρ0δ	2ρ0δ	NOUN
ejpam-8	136	62	−	−	NUM
ejpam-8	136	63	1	1	NUM
ejpam-8	136	64	4	4	NUM
ejpam-8	136	65	+	+	CCONJ
ejpam-8	136	66	cρ0δ	cρ0δ	PROPN
ejpam-8	136	67	−	−	NUM
ejpam-8	136	68	1	1	NUM
ejpam-8	136	69	2	2	NUM
ejpam-8	136	70	�	�	NOUN
ejpam-8	136	71	2	2	NUM
ejpam-8	136	72	‖wk−1	‖wk−1	NOUN
ejpam-8	136	73	x	x	X
ejpam-8	136	74	‖	‖	PROPN
ejpam-8	136	75	2	2	NUM
ejpam-8	136	76	+	+	NUM
ejpam-8	136	77	µ	µ	X
ejpam-8	136	78	2	2	NUM
ejpam-8	136	79	‖wk	‖wk	NUM
ejpam-8	136	80	x‖	x‖	PROPN
ejpam-8	136	81	2	2	NUM
ejpam-8	136	82	.	.	PUNCT
ejpam-8	137	1	it	it	PRON
ejpam-8	137	2	follows	follow	VERB
ejpam-8	137	3	that	that	SCONJ
ejpam-8	137	4	d	d	PROPN
ejpam-8	137	5	d	d	X
ejpam-8	137	6	t	t	PROPN
ejpam-8	137	7	(	(	PUNCT
ejpam-8	137	8	‖wk‖2+δ‖wk	‖wk‖2+δ‖wk	PROPN
ejpam-8	137	9	x‖	x‖	PROPN
ejpam-8	137	10	2	2	NUM
ejpam-8	137	11	)	)	PUNCT
ejpam-8	137	12	+	+	CCONJ
ejpam-8	137	13	c1(‖wk‖2+δ‖wk	c1(‖wk‖2+δ‖wk	VERB
ejpam-8	137	14	x‖	x‖	X
ejpam-8	137	15	2	2	NUM
ejpam-8	137	16	)	)	PUNCT
ejpam-8	137	17	≤	≤	NOUN
ejpam-8	137	18	1	1	NUM
ejpam-8	137	19	µ(n	µ(n	ADJ
ejpam-8	137	20	+	+	NUM
ejpam-8	137	21	1)2	1)2	NUM
ejpam-8	137	22	�	�	NOUN
ejpam-8	137	23	p	p	NOUN
ejpam-8	137	24	2ρ0δ	2ρ0δ	NOUN
ejpam-8	137	25	−	−	NUM
ejpam-8	137	26	1	1	NUM
ejpam-8	137	27	4	4	NUM
ejpam-8	137	28	+	+	CCONJ
ejpam-8	137	29	cρ0δ	cρ0δ	PROPN
ejpam-8	137	30	−	−	NUM
ejpam-8	137	31	1	1	NUM
ejpam-8	137	32	2	2	NUM
ejpam-8	137	33	�	�	NOUN
ejpam-8	137	34	2	2	NUM
ejpam-8	137	35	‖wk−1	‖wk−1	NOUN
ejpam-8	137	36	x	x	X
ejpam-8	137	37	‖	‖	PROPN
ejpam-8	137	38	2	2	X
ejpam-8	137	39	.	.	PUNCT
ejpam-8	137	40	(	(	PUNCT
ejpam-8	137	41	2.16	2.16	NUM
ejpam-8	137	42	)	)	PUNCT
ejpam-8	137	43	references	reference	NOUN
ejpam-8	137	44	9	9	NUM
ejpam-8	137	45	where	where	SCONJ
ejpam-8	137	46	k	k	NOUN
ejpam-8	137	47	=	=	SYM
ejpam-8	137	48	1	1	NUM
ejpam-8	137	49	,	,	PUNCT
ejpam-8	137	50	2	2	NUM
ejpam-8	137	51	,	,	PUNCT
ejpam-8	137	52	·	·	PUNCT
ejpam-8	137	53	·	·	PUNCT
ejpam-8	137	54	·	·	PUNCT
ejpam-8	137	55	.	.	PUNCT
ejpam-8	138	1	let	let	VERB
ejpam-8	138	2	k	k	NOUN
ejpam-8	138	3	=	=	SYM
ejpam-8	138	4	1	1	NUM
ejpam-8	138	5	in	in	ADP
ejpam-8	138	6	(	(	PUNCT
ejpam-8	138	7	2.16	2.16	NUM
ejpam-8	138	8	)	)	PUNCT
ejpam-8	138	9	,	,	PUNCT
ejpam-8	138	10	we	we	PRON
ejpam-8	138	11	have	have	VERB
ejpam-8	138	12	d	d	PROPN
ejpam-8	138	13	d	d	X
ejpam-8	138	14	t	t	PROPN
ejpam-8	138	15	(	(	PUNCT
ejpam-8	138	16	‖w1‖2+δ‖w1	‖w1‖2+δ‖w1	X
ejpam-8	138	17	x‖	x‖	X
ejpam-8	138	18	2	2	NUM
ejpam-8	138	19	)	)	PUNCT
ejpam-8	138	20	+	+	CCONJ
ejpam-8	138	21	c1(‖wk‖2+δ‖wk	c1(‖wk‖2+δ‖wk	VERB
ejpam-8	138	22	x‖	x‖	X
ejpam-8	138	23	2	2	NUM
ejpam-8	138	24	)	)	PUNCT
ejpam-8	138	25	≤	≤	NOUN
ejpam-8	138	26	1	1	NUM
ejpam-8	138	27	µ(n	µ(n	ADJ
ejpam-8	138	28	+	+	NUM
ejpam-8	138	29	1)2	1)2	NUM
ejpam-8	138	30	�	�	NOUN
ejpam-8	138	31	p	p	NOUN
ejpam-8	138	32	2ρ0δ	2ρ0δ	NOUN
ejpam-8	138	33	−	−	NUM
ejpam-8	138	34	1	1	NUM
ejpam-8	138	35	4	4	NUM
ejpam-8	138	36	+	+	CCONJ
ejpam-8	138	37	cρ0δ	cρ0δ	PROPN
ejpam-8	138	38	−	−	NUM
ejpam-8	138	39	1	1	NUM
ejpam-8	138	40	2	2	NUM
ejpam-8	138	41	�	�	PROPN
ejpam-8	138	42	2	2	NUM
ejpam-8	138	43	‖w0	‖w0	X
ejpam-8	138	44	x‖	x‖	PROPN
ejpam-8	138	45	2	2	NUM
ejpam-8	138	46	.	.	PUNCT
ejpam-8	138	47	(	(	PUNCT
ejpam-8	138	48	2.17	2.17	NUM
ejpam-8	138	49	)	)	PUNCT
ejpam-8	138	50	by	by	ADP
ejpam-8	138	51	gronwall	gronwall	PROPN
ejpam-8	138	52	’s	’s	PROPN
ejpam-8	138	53	lemma	lemma	PROPN
ejpam-8	138	54	,	,	PUNCT
ejpam-8	138	55	there	there	PRON
ejpam-8	138	56	is	be	VERB
ejpam-8	138	57	a	a	DET
ejpam-8	138	58	t∗21(b	t∗21(b	NOUN
ejpam-8	138	59	)	)	PUNCT
ejpam-8	138	60	>	>	X
ejpam-8	138	61	0	0	NUM
ejpam-8	139	1	such	such	ADJ
ejpam-8	139	2	that	that	SCONJ
ejpam-8	139	3	‖w1(t)‖2+δ‖w1	‖w1(t)‖2+δ‖w1	NOUN
ejpam-8	139	4	x(t)‖	x(t)‖	NUM
ejpam-8	139	5	2	2	NUM
ejpam-8	139	6	≤	≤	NUM
ejpam-8	139	7	2	2	NUM
ejpam-8	139	8	c1µ(n	c1µ(n	PROPN
ejpam-8	139	9	+	+	CCONJ
ejpam-8	139	10	1)2	1)2	NUM
ejpam-8	139	11	�	�	NOUN
ejpam-8	139	12	p	p	NOUN
ejpam-8	139	13	2ρ0δ	2ρ0δ	NOUN
ejpam-8	139	14	−	−	NUM
ejpam-8	139	15	1	1	NUM
ejpam-8	139	16	4	4	NUM
ejpam-8	139	17	+	+	CCONJ
ejpam-8	139	18	cρ0δ	cρ0δ	PROPN
ejpam-8	139	19	−	−	NUM
ejpam-8	139	20	1	1	NUM
ejpam-8	139	21	2	2	NUM
ejpam-8	139	22	�	�	NOUN
ejpam-8	139	23	2	2	NUM
ejpam-8	139	24	‖w0	‖w0	NOUN
ejpam-8	139	25	x(t)‖	x(t)‖	PROPN
ejpam-8	139	26	2	2	NUM
ejpam-8	139	27	,	,	PUNCT
ejpam-8	139	28	t	t	PROPN
ejpam-8	139	29	≥	≥	PROPN
ejpam-8	139	30	t∗21(b	t∗21(b	PROPN
ejpam-8	139	31	)	)	PUNCT
ejpam-8	139	32	.	.	PUNCT
ejpam-8	140	1	(	(	PUNCT
ejpam-8	140	2	2.18	2.18	NUM
ejpam-8	140	3	)	)	PUNCT
ejpam-8	140	4	by	by	ADP
ejpam-8	140	5	the	the	DET
ejpam-8	140	6	inductive	inductive	ADJ
ejpam-8	140	7	method	method	NOUN
ejpam-8	140	8	,	,	PUNCT
ejpam-8	140	9	there	there	PRON
ejpam-8	140	10	is	be	VERB
ejpam-8	140	11	a	a	DET
ejpam-8	140	12	t∗2k(b	t∗2k(b	NOUN
ejpam-8	140	13	)	)	PUNCT
ejpam-8	140	14	>	>	X
ejpam-8	140	15	0	0	PUNCT
ejpam-8	140	16	such	such	ADJ
ejpam-8	140	17	that	that	SCONJ
ejpam-8	140	18	‖wk‖2+δ‖wk	‖wk‖2+δ‖wk	NOUN
ejpam-8	140	19	x‖	x‖	PROPN
ejpam-8	140	20	2	2	NUM
ejpam-8	140	21	≤	≤	NOUN
ejpam-8	140	22	2k	2k	NUM
ejpam-8	140	23	ck	ck	PRON
ejpam-8	140	24	1µ	1µ	X
ejpam-8	140	25	k(n	k(n	X
ejpam-8	140	26	+	+	CCONJ
ejpam-8	140	27	1)2k	1)2k	NUM
ejpam-8	140	28	�	�	PROPN
ejpam-8	140	29	p	p	NOUN
ejpam-8	140	30	2ρ0δ	2ρ0δ	NOUN
ejpam-8	140	31	−	−	NUM
ejpam-8	140	32	1	1	NUM
ejpam-8	140	33	4	4	NUM
ejpam-8	140	34	+	+	CCONJ
ejpam-8	140	35	cρ0δ	cρ0δ	PROPN
ejpam-8	140	36	−	−	NUM
ejpam-8	140	37	1	1	NUM
ejpam-8	140	38	2	2	NUM
ejpam-8	140	39	�	�	NOUN
ejpam-8	140	40	2k	2k	NOUN
ejpam-8	140	41	‖w0	‖w0	NOUN
ejpam-8	140	42	x(t)‖	x(t)‖	PROPN
ejpam-8	140	43	2	2	NUM
ejpam-8	140	44	,	,	PUNCT
ejpam-8	140	45	t	t	PROPN
ejpam-8	140	46	≥	≥	NOUN
ejpam-8	140	47	t∗2k(b	t∗2k(b	NUM
ejpam-8	140	48	)	)	PUNCT
ejpam-8	140	49	(	(	PUNCT
ejpam-8	140	50	2.19	2.19	NUM
ejpam-8	140	51	)	)	PUNCT
ejpam-8	140	52	where	where	SCONJ
ejpam-8	140	53	k	k	NOUN
ejpam-8	140	54	=	=	SYM
ejpam-8	140	55	1	1	NUM
ejpam-8	140	56	,	,	PUNCT
ejpam-8	140	57	2	2	NUM
ejpam-8	140	58	,	,	PUNCT
ejpam-8	140	59	·	·	PUNCT
ejpam-8	140	60	·	·	PUNCT
ejpam-8	140	61	·	·	PUNCT
ejpam-8	140	62	.	.	PUNCT
ejpam-8	141	1	if	if	SCONJ
ejpam-8	141	2	n	n	PRON
ejpam-8	141	3	is	be	AUX
ejpam-8	141	4	large	large	ADJ
ejpam-8	141	5	enough	enough	ADV
ejpam-8	141	6	,	,	PUNCT
ejpam-8	141	7	such	such	ADJ
ejpam-8	141	8	that	that	SCONJ
ejpam-8	141	9	2	2	NUM
ejpam-8	141	10	�	�	PROPN
ejpam-8	141	11	p	p	NOUN
ejpam-8	141	12	2ρ0δ	2ρ0δ	NOUN
ejpam-8	141	13	−	−	NUM
ejpam-8	141	14	1	1	NUM
ejpam-8	141	15	4	4	NUM
ejpam-8	141	16	+	+	CCONJ
ejpam-8	141	17	cρ0δ	cρ0δ	PROPN
ejpam-8	141	18	−	−	NUM
ejpam-8	141	19	1	1	NUM
ejpam-8	141	20	2	2	NUM
ejpam-8	141	21	�	�	SYM
ejpam-8	141	22	2	2	NUM
ejpam-8	141	23	c1µ(n	c1µ(n	PROPN
ejpam-8	141	24	+	+	CCONJ
ejpam-8	141	25	1)2	1)2	NUM
ejpam-8	141	26	<	<	X
ejpam-8	141	27	1	1	NUM
ejpam-8	141	28	,	,	PUNCT
ejpam-8	141	29	(	(	PUNCT
ejpam-8	141	30	2.20	2.20	NUM
ejpam-8	141	31	)	)	PUNCT
ejpam-8	141	32	then	then	ADV
ejpam-8	141	33	(	(	PUNCT
ejpam-8	141	34	2.11	2.11	NUM
ejpam-8	141	35	)	)	PUNCT
ejpam-8	141	36	follows	follow	VERB
ejpam-8	141	37	from	from	ADP
ejpam-8	141	38	(	(	PUNCT
ejpam-8	141	39	2.14	2.14	NUM
ejpam-8	141	40	)	)	PUNCT
ejpam-8	141	41	and	and	CCONJ
ejpam-8	141	42	(	(	PUNCT
ejpam-8	141	43	2.19	2.19	NUM
ejpam-8	141	44	)	)	PUNCT
ejpam-8	141	45	.	.	PUNCT
ejpam-8	142	1	the	the	DET
ejpam-8	142	2	proof	proof	NOUN
ejpam-8	142	3	of	of	ADP
ejpam-8	142	4	lemma	lemma	PROPN
ejpam-8	142	5	2.2	2.2	NUM
ejpam-8	142	6	is	be	AUX
ejpam-8	142	7	completed	complete	VERB
ejpam-8	142	8	.	.	PUNCT
ejpam-8	143	1	references	reference	NOUN
ejpam-8	143	2	[	[	X
ejpam-8	143	3	1	1	X
ejpam-8	143	4	]	]	PUNCT
ejpam-8	143	5	j.	j.	PROPN
ejpam-8	143	6	albert	albert	PROPN
ejpam-8	143	7	,	,	PUNCT
ejpam-8	143	8	dispersion	dispersion	NOUN
ejpam-8	143	9	of	of	ADP
ejpam-8	143	10	low	low	ADJ
ejpam-8	143	11	-	-	PUNCT
ejpam-8	143	12	energy	energy	NOUN
ejpam-8	143	13	waves	wave	NOUN
ejpam-8	143	14	for	for	ADP
ejpam-8	143	15	the	the	DET
ejpam-8	143	16	generalized	generalize	VERB
ejpam-8	143	17	benjamin	benjamin	PROPN
ejpam-8	143	18	-	-	PUNCT
ejpam-8	143	19	bona	bona	ADJ
ejpam-8	143	20	-	-	PUNCT
ejpam-8	143	21	mahony	mahony	NOUN
ejpam-8	143	22	equation	equation	NOUN
ejpam-8	143	23	,	,	PUNCT
ejpam-8	143	24	j.	j.	PROPN
ejpam-8	143	25	diff	diff	PROPN
ejpam-8	143	26	.	.	PUNCT
ejpam-8	144	1	equ	equ	PROPN
ejpam-8	144	2	.	.	PROPN
ejpam-8	144	3	,	,	PUNCT
ejpam-8	144	4	63(1):117	63(1):117	PROPN
ejpam-8	144	5	-	-	PUNCT
ejpam-8	144	6	134	134	NUM
ejpam-8	144	7	,	,	PUNCT
ejpam-8	144	8	1986	1986	NUM
ejpam-8	144	9	.	.	PUNCT
ejpam-8	145	1	[	[	X
ejpam-8	145	2	2	2	X
ejpam-8	145	3	]	]	PUNCT
ejpam-8	145	4	j.	j.	PROPN
ejpam-8	145	5	avrin	avrin	PROPN
ejpam-8	145	6	,	,	PUNCT
ejpam-8	145	7	the	the	DET
ejpam-8	145	8	generalized	generalize	VERB
ejpam-8	145	9	benjamin	benjamin	NOUN
ejpam-8	145	10	-	-	PUNCT
ejpam-8	145	11	bona	bona	ADJ
ejpam-8	145	12	-	-	PUNCT
ejpam-8	145	13	mahony	mahony	NOUN
ejpam-8	145	14	equation	equation	NOUN
ejpam-8	145	15	in	in	ADP
ejpam-8	145	16	rn	rn	PROPN
ejpam-8	145	17	with	with	ADP
ejpam-8	145	18	singular	singular	PROPN
ejpam-8	145	19	initial	initial	ADJ
ejpam-8	145	20	data	datum	NOUN
ejpam-8	145	21	,	,	PUNCT
ejpam-8	145	22	nonlin	nonlin	PROPN
ejpam-8	145	23	.	.	PUNCT
ejpam-8	145	24	anal	anal	PROPN
ejpam-8	145	25	.	.	PROPN
ejpam-8	145	26	,	,	PUNCT
ejpam-8	145	27	11(1	11(1	NUM
ejpam-8	145	28	):	):	PUNCT
ejpam-8	145	29	139	139	NUM
ejpam-8	145	30	-	-	SYM
ejpam-8	145	31	147	147	NUM
ejpam-8	145	32	,	,	PUNCT
ejpam-8	145	33	1987	1987	NUM
ejpam-8	145	34	.	.	PUNCT
ejpam-8	146	1	[	[	X
ejpam-8	146	2	3	3	X
ejpam-8	146	3	]	]	PUNCT
ejpam-8	146	4	t.	t.	PROPN
ejpam-8	146	5	b.	b.	PROPN
ejpam-8	146	6	benjamin	benjamin	PROPN
ejpam-8	146	7	,	,	PUNCT
ejpam-8	146	8	j.	j.	PROPN
ejpam-8	146	9	l.	l.	PROPN
ejpam-8	146	10	bona	bona	PROPN
ejpam-8	146	11	and	and	CCONJ
ejpam-8	146	12	j.	j.	PROPN
ejpam-8	146	13	j.	j.	PROPN
ejpam-8	146	14	mahony	mahony	PROPN
ejpam-8	146	15	,	,	PUNCT
ejpam-8	146	16	model	model	NOUN
ejpam-8	146	17	equations	equation	NOUN
ejpam-8	146	18	for	for	ADP
ejpam-8	146	19	long	long	ADJ
ejpam-8	146	20	waves	wave	NOUN
ejpam-8	146	21	in	in	ADP
ejpam-8	146	22	nonlinear	nonlinear	ADJ
ejpam-8	146	23	dispersive	dispersive	ADJ
ejpam-8	146	24	systems	system	NOUN
ejpam-8	146	25	,	,	PUNCT
ejpam-8	146	26	philos	philos	PROPN
ejpam-8	146	27	.	.	PUNCT
ejpam-8	147	1	trans	trans	PROPN
ejpam-8	147	2	.	.	PUNCT
ejpam-8	148	1	roy	roy	PROPN
ejpam-8	148	2	.	.	PROPN
ejpam-8	148	3	soc	soc	PROPN
ejpam-8	148	4	.	.	PUNCT
ejpam-8	149	1	londan	londan	PROPN
ejpam-8	149	2	,	,	PUNCT
ejpam-8	149	3	272(1	272(1	NUM
ejpam-8	149	4	):	):	PUNCT
ejpam-8	149	5	47	47	NUM
ejpam-8	149	6	-	-	SYM
ejpam-8	149	7	78	78	NUM
ejpam-8	149	8	,	,	PUNCT
ejpam-8	149	9	1972	1972	NUM
ejpam-8	149	10	.	.	PUNCT
ejpam-8	150	1	[	[	X
ejpam-8	150	2	4	4	X
ejpam-8	150	3	]	]	X
ejpam-8	150	4	p.	p.	NOUN
ejpam-8	150	5	biler	biler	NOUN
ejpam-8	150	6	,	,	PUNCT
ejpam-8	150	7	long	long	ADJ
ejpam-8	150	8	time	time	NOUN
ejpam-8	150	9	behaviour	behaviour	NOUN
ejpam-8	150	10	of	of	ADP
ejpam-8	150	11	solutions	solution	NOUN
ejpam-8	150	12	of	of	ADP
ejpam-8	150	13	the	the	DET
ejpam-8	150	14	generalized	generalize	VERB
ejpam-8	150	15	benjamin	benjamin	NOUN
ejpam-8	150	16	-	-	PUNCT
ejpam-8	150	17	bona	bona	ADJ
ejpam-8	150	18	-	-	PUNCT
ejpam-8	150	19	mahony	mahony	NOUN
ejpam-8	150	20	equation	equation	NOUN
ejpam-8	150	21	in	in	ADP
ejpam-8	150	22	two	two	NUM
ejpam-8	150	23	-	-	PUNCT
ejpam-8	150	24	space	space	NOUN
ejpam-8	150	25	dimensions	dimension	NOUN
ejpam-8	150	26	,	,	PUNCT
ejpam-8	150	27	diff	diff	PROPN
ejpam-8	150	28	.	.	PUNCT
ejpam-8	151	1	integ	integ	PROPN
ejpam-8	151	2	.	.	PUNCT
ejpam-8	152	1	equ	equ	PROPN
ejpam-8	152	2	.	.	PROPN
ejpam-8	152	3	,	,	PUNCT
ejpam-8	152	4	5(4	5(4	NUM
ejpam-8	152	5	):	):	PUNCT
ejpam-8	152	6	891	891	NUM
ejpam-8	152	7	-	-	SYM
ejpam-8	152	8	901	901	NUM
ejpam-8	152	9	,	,	PUNCT
ejpam-8	152	10	1992	1992	NUM
ejpam-8	152	11	.	.	PUNCT
ejpam-8	153	1	[	[	X
ejpam-8	153	2	5	5	NUM
ejpam-8	153	3	]	]	PUNCT
ejpam-8	153	4	a.	a.	NOUN
ejpam-8	153	5	o.	o.	NOUN
ejpam-8	153	6	celebi	celebi	NOUN
ejpam-8	153	7	,	,	PUNCT
ejpam-8	153	8	v.	v.	PROPN
ejpam-8	153	9	k.	k.	PROPN
ejpam-8	154	1	kalantarov	kalantarov	PROPN
ejpam-8	154	2	and	and	CCONJ
ejpam-8	154	3	m.	m.	NOUN
ejpam-8	154	4	polat	polat	PROPN
ejpam-8	154	5	,	,	PUNCT
ejpam-8	154	6	attractors	attractor	NOUN
ejpam-8	154	7	for	for	ADP
ejpam-8	154	8	the	the	DET
ejpam-8	154	9	generalized	generalize	VERB
ejpam-8	154	10	benjamin	benjamin	PROPN
ejpam-8	154	11	-	-	PUNCT
ejpam-8	154	12	bona	bona	ADJ
ejpam-8	154	13	-	-	PUNCT
ejpam-8	154	14	mahony	mahony	NOUN
ejpam-8	154	15	equation	equation	NOUN
ejpam-8	154	16	,	,	PUNCT
ejpam-8	154	17	j.	j.	PROPN
ejpam-8	154	18	diff	diff	PROPN
ejpam-8	154	19	.	.	PUNCT
ejpam-8	155	1	equ	equ	PROPN
ejpam-8	155	2	.	.	PROPN
ejpam-8	155	3	,	,	PUNCT
ejpam-8	155	4	157(2	157(2	NUM
ejpam-8	155	5	):	):	PUNCT
ejpam-8	155	6	439	439	NUM
ejpam-8	155	7	-	-	SYM
ejpam-8	155	8	451	451	NUM
ejpam-8	155	9	,	,	PUNCT
ejpam-8	155	10	1999	1999	NUM
ejpam-8	155	11	.	.	PUNCT
ejpam-8	156	1	[	[	X
ejpam-8	156	2	6	6	NUM
ejpam-8	156	3	]	]	PUNCT
ejpam-8	156	4	s.	s.	PROPN
ejpam-8	156	5	n.	n.	PROPN
ejpam-8	156	6	chow	chow	PROPN
ejpam-8	156	7	and	and	CCONJ
ejpam-8	156	8	k.	k.	PROPN
ejpam-8	156	9	lu	lu	PROPN
ejpam-8	156	10	,	,	PUNCT
ejpam-8	156	11	inertial	inertial	NOUN
ejpam-8	156	12	manifolds	manifold	NOUN
ejpam-8	156	13	for	for	ADP
ejpam-8	156	14	flows	flow	NOUN
ejpam-8	156	15	in	in	ADP
ejpam-8	156	16	banach	banach	NOUN
ejpam-8	156	17	spaces	space	NOUN
ejpam-8	156	18	,	,	PUNCT
ejpam-8	156	19	j.	j.	PROPN
ejpam-8	156	20	diff	diff	PROPN
ejpam-8	156	21	.	.	PUNCT
ejpam-8	157	1	eqns	eqns	PROPN
ejpam-8	157	2	.	.	PUNCT
ejpam-8	157	3	,	,	PUNCT
ejpam-8	158	1	74(1	74(1	NOUN
ejpam-8	158	2	):	):	PUNCT
ejpam-8	158	3	285317	285317	NUM
ejpam-8	158	4	,	,	PUNCT
ejpam-8	158	5	1988	1988	NUM
ejpam-8	158	6	.	.	PUNCT
ejpam-8	159	1	[	[	X
ejpam-8	159	2	7	7	X
ejpam-8	159	3	]	]	X
ejpam-8	159	4	c.	c.	NOUN
ejpam-8	159	5	foias	foias	PROPN
ejpam-8	159	6	,	,	PUNCT
ejpam-8	159	7	o.	o.	PROPN
ejpam-8	159	8	manley	manley	PROPN
ejpam-8	159	9	and	and	CCONJ
ejpam-8	159	10	r.	r.	PROPN
ejpam-8	159	11	temam	temam	NOUN
ejpam-8	159	12	,	,	PUNCT
ejpam-8	159	13	sur	sur	PROPN
ejpam-8	159	14	l’interaction	l’interaction	PROPN
ejpam-8	159	15	des	des	PROPN
ejpam-8	159	16	petits	petits	PROPN
ejpam-8	159	17	et	et	PROPN
ejpam-8	159	18	grands	grand	VERB
ejpam-8	159	19	tourbillons	tourbillon	NOUN
ejpam-8	159	20	dans	dans	PROPN
ejpam-8	159	21	les	le	NOUN
ejpam-8	159	22	ecoulements	ecoulement	NOUN
ejpam-8	159	23	turbulents	turbulent	NOUN
ejpam-8	159	24	,	,	PUNCT
ejpam-8	159	25	c.	c.	PROPN
ejpam-8	159	26	r.	r.	PROPN
ejpam-8	159	27	acad	acad	PROPN
ejpam-8	159	28	.	.	PUNCT
ejpam-8	160	1	sci	sci	PROPN
ejpam-8	160	2	.	.	PROPN
ejpam-8	160	3	paris	paris	PROPN
ejpam-8	160	4	,	,	PUNCT
ejpam-8	160	5	serie	serie	VERB
ejpam-8	160	6	i	i	PRON
ejpam-8	160	7	,	,	PUNCT
ejpam-8	160	8	305	305	NUM
ejpam-8	160	9	:	:	PUNCT
ejpam-8	160	10	497	497	NUM
ejpam-8	160	11	-	-	SYM
ejpam-8	160	12	500	500	NUM
ejpam-8	160	13	,	,	PUNCT
ejpam-8	160	14	1987	1987	NUM
ejpam-8	160	15	.	.	PUNCT
ejpam-8	161	1	[	[	X
ejpam-8	161	2	8	8	NUM
ejpam-8	161	3	]	]	X
ejpam-8	161	4	c.	c.	NOUN
ejpam-8	161	5	foias	foias	PROPN
ejpam-8	161	6	,	,	PUNCT
ejpam-8	161	7	g.	g.	PROPN
ejpam-8	161	8	sell	sell	PROPN
ejpam-8	161	9	and	and	CCONJ
ejpam-8	161	10	r.	r.	PROPN
ejpam-8	161	11	temam	temam	NOUN
ejpam-8	161	12	,	,	PUNCT
ejpam-8	161	13	inertial	inertial	NOUN
ejpam-8	161	14	manifolds	manifold	NOUN
ejpam-8	161	15	for	for	ADP
ejpam-8	161	16	nonlinear	nonlinear	ADJ
ejpam-8	161	17	evolutionary	evolutionary	ADJ
ejpam-8	161	18	equations	equation	NOUN
ejpam-8	161	19	,	,	PUNCT
ejpam-8	161	20	j.	j.	PROPN
ejpam-8	161	21	diff	diff	PROPN
ejpam-8	161	22	.	.	PUNCT
ejpam-8	161	23	eqns	eqns	PROPN
ejpam-8	161	24	.	.	PUNCT
ejpam-8	161	25	,	,	PUNCT
ejpam-8	161	26	73(2	73(2	NUM
ejpam-8	161	27	):	):	PUNCT
ejpam-8	161	28	309	309	NUM
ejpam-8	161	29	-	-	SYM
ejpam-8	161	30	353	353	NUM
ejpam-8	161	31	,	,	PUNCT
ejpam-8	161	32	1988	1988	NUM
ejpam-8	161	33	.	.	PUNCT
ejpam-8	162	1	[	[	X
ejpam-8	162	2	9	9	NUM
ejpam-8	162	3	]	]	PUNCT
ejpam-8	162	4	m.	m.	NOUN
ejpam-8	162	5	stanislavova	stanislavova	PROPN
ejpam-8	162	6	,	,	PUNCT
ejpam-8	162	7	on	on	ADP
ejpam-8	162	8	the	the	DET
ejpam-8	162	9	global	global	ADJ
ejpam-8	162	10	attractor	attractor	NOUN
ejpam-8	162	11	for	for	ADP
ejpam-8	162	12	the	the	DET
ejpam-8	162	13	damped	damped	ADJ
ejpam-8	162	14	benjamin	benjamin	PROPN
ejpam-8	162	15	-	-	PUNCT
ejpam-8	162	16	bona	bona	ADJ
ejpam-8	162	17	-	-	PUNCT
ejpam-8	162	18	mahony	mahony	NOUN
ejpam-8	162	19	equation	equation	NOUN
ejpam-8	162	20	,	,	PUNCT
ejpam-8	162	21	proceedings	proceeding	NOUN
ejpam-8	162	22	of	of	ADP
ejpam-8	162	23	the	the	DET
ejpam-8	162	24	fifth	fifth	ADJ
ejpam-8	162	25	international	international	ADJ
ejpam-8	162	26	conference	conference	NOUN
ejpam-8	162	27	on	on	ADP
ejpam-8	162	28	dynamical	dynamical	ADJ
ejpam-8	162	29	systems	system	NOUN
ejpam-8	162	30	and	and	CCONJ
ejpam-8	162	31	differential	differential	ADJ
ejpam-8	162	32	equations	equation	NOUN
ejpam-8	162	33	,	,	PUNCT
ejpam-8	162	34	june	june	PROPN
ejpam-8	162	35	16	16	NUM
ejpam-8	162	36	-	-	SYM
ejpam-8	162	37	19	19	NUM
ejpam-8	162	38	,	,	PUNCT
ejpam-8	162	39	2004	2004	NUM
ejpam-8	162	40	,	,	PUNCT
ejpam-8	162	41	pomona	pomona	PROPN
ejpam-8	162	42	,	,	PUNCT
ejpam-8	162	43	ca	ca	PROPN
ejpam-8	162	44	,	,	PUNCT
ejpam-8	162	45	usa	usa	PROPN
ejpam-8	162	46	references	reference	VERB
ejpam-8	162	47	10	10	NUM
ejpam-8	162	48	[	[	SYM
ejpam-8	162	49	10	10	NUM
ejpam-8	162	50	]	]	PUNCT
ejpam-8	162	51	m.	m.	NOUN
ejpam-8	162	52	stanislavova	stanislavova	PROPN
ejpam-8	162	53	,	,	PUNCT
ejpam-8	162	54	a.	a.	NOUN
ejpam-8	162	55	stefanov	stefanov	PROPN
ejpam-8	162	56	and	and	CCONJ
ejpam-8	162	57	b.	b.	PROPN
ejpam-8	162	58	wang	wang	PROPN
ejpam-8	162	59	,	,	PUNCT
ejpam-8	162	60	asymptotic	asymptotic	ADJ
ejpam-8	162	61	smoothing	smoothing	NOUN
ejpam-8	162	62	and	and	CCONJ
ejpam-8	162	63	attractors	attractor	NOUN
ejpam-8	162	64	for	for	ADP
ejpam-8	162	65	the	the	DET
ejpam-8	162	66	generalized	generalize	VERB
ejpam-8	162	67	benjamin	benjamin	PROPN
ejpam-8	162	68	-	-	PUNCT
ejpam-8	162	69	bona	bona	ADJ
ejpam-8	162	70	-	-	PUNCT
ejpam-8	162	71	mahony	mahony	NOUN
ejpam-8	162	72	equation	equation	NOUN
ejpam-8	162	73	on	on	ADP
ejpam-8	162	74	r3	r3	PROPN
ejpam-8	162	75	,	,	PUNCT
ejpam-8	162	76	j.	j.	PROPN
ejpam-8	162	77	diff	diff	PROPN
ejpam-8	162	78	.	.	PUNCT
ejpam-8	163	1	equ	equ	PROPN
ejpam-8	163	2	.	.	PROPN
ejpam-8	163	3	,	,	PUNCT
ejpam-8	163	4	219(2	219(2	NUM
ejpam-8	163	5	):	):	PUNCT
ejpam-8	163	6	451	451	NUM
ejpam-8	163	7	-	-	SYM
ejpam-8	163	8	483	483	NUM
ejpam-8	163	9	,	,	PUNCT
ejpam-8	163	10	2005	2005	NUM
ejpam-8	163	11	.	.	PUNCT
ejpam-8	164	1	[	[	X
ejpam-8	164	2	11	11	NUM
ejpam-8	164	3	]	]	PUNCT
ejpam-8	164	4	b.	b.	PROPN
ejpam-8	164	5	wang	wang	PROPN
ejpam-8	164	6	,	,	PUNCT
ejpam-8	164	7	strong	strong	ADJ
ejpam-8	164	8	attracrors	attracror	NOUN
ejpam-8	164	9	for	for	ADP
ejpam-8	164	10	the	the	DET
ejpam-8	164	11	benjamin	benjamin	PROPN
ejpam-8	164	12	-	-	PUNCT
ejpam-8	164	13	bona	bona	ADJ
ejpam-8	164	14	-	-	PUNCT
ejpam-8	164	15	mahony	mahony	NOUN
ejpam-8	164	16	equation	equation	NOUN
ejpam-8	164	17	,	,	PUNCT
ejpam-8	164	18	appl	appl	PROPN
ejpam-8	164	19	.	.	PROPN
ejpam-8	164	20	math	math	PROPN
ejpam-8	164	21	.	.	PUNCT
ejpam-8	165	1	lett	lett	PROPN
ejpam-8	165	2	.	.	PROPN
ejpam-8	165	3	,	,	PUNCT
ejpam-8	166	1	10(1	10(1	NUM
ejpam-8	166	2	):	):	PUNCT
ejpam-8	166	3	23	23	NUM
ejpam-8	166	4	-	-	SYM
ejpam-8	166	5	28	28	NUM
ejpam-8	166	6	,	,	PUNCT
ejpam-8	166	7	1997	1997	NUM
ejpam-8	166	8	.	.	PUNCT
ejpam-8	167	1	[	[	X
ejpam-8	167	2	12	12	NUM
ejpam-8	167	3	]	]	X
ejpam-8	167	4	g.	g.	PROPN
ejpam-8	167	5	x.	x.	PROPN
ejpam-8	167	6	wang	wang	PROPN
ejpam-8	167	7	,	,	PUNCT
ejpam-8	167	8	z.	z.	PROPN
ejpam-8	167	9	r.	r.	PROPN
ejpam-8	167	10	liu	liu	PROPN
ejpam-8	167	11	,	,	PUNCT
ejpam-8	167	12	the	the	DET
ejpam-8	167	13	asymptotic	asymptotic	ADJ
ejpam-8	167	14	attractors	attractor	NOUN
ejpam-8	167	15	of	of	ADP
ejpam-8	167	16	kuramoto	kuramoto	NOUN
ejpam-8	167	17	-	-	PUNCT
ejpam-8	167	18	sivashinsky	sivashinsky	NOUN
ejpam-8	167	19	equation	equation	NOUN
ejpam-8	167	20	,	,	PUNCT
ejpam-8	167	21	acta	acta	PROPN
ejpam-8	167	22	math	math	PROPN
ejpam-8	167	23	.	.	PUNCT
ejpam-8	168	1	appl	appl	PROPN
ejpam-8	168	2	.	.	PUNCT
ejpam-8	169	1	sinica(in	sinica(in	PROPN
ejpam-8	169	2	chinese	chinese	PROPN
ejpam-8	169	3	)	)	PUNCT
ejpam-8	169	4	,	,	PUNCT
ejpam-8	169	5	23(2	23(2	NUM
ejpam-8	169	6	):	):	PUNCT
ejpam-8	169	7	329	329	NUM
ejpam-8	169	8	-	-	SYM
ejpam-8	169	9	336	336	NUM
ejpam-8	169	10	,	,	PUNCT
ejpam-8	169	11	2000	2000	NUM
ejpam-8	169	12	.	.	PUNCT
ejpam-8	170	1	[	[	X
ejpam-8	170	2	13	13	NUM
ejpam-8	170	3	]	]	PUNCT
ejpam-8	170	4	b.	b.	PROPN
ejpam-8	170	5	wang	wang	PROPN
ejpam-8	170	6	,	,	PUNCT
ejpam-8	170	7	w.	w.	PROPN
ejpam-8	170	8	yang	yang	PROPN
ejpam-8	170	9	,	,	PUNCT
ejpam-8	170	10	finite	finite	VERB
ejpam-8	170	11	dimensional	dimensional	ADJ
ejpam-8	170	12	behaviour	behaviour	NOUN
ejpam-8	170	13	for	for	ADP
ejpam-8	170	14	the	the	DET
ejpam-8	170	15	benjamin	benjamin	NOUN
ejpam-8	170	16	-	-	PUNCT
ejpam-8	170	17	bona	bona	ADJ
ejpam-8	170	18	-	-	PUNCT
ejpam-8	170	19	mahony	mahony	NOUN
ejpam-8	170	20	equation	equation	NOUN
ejpam-8	170	21	,	,	PUNCT
ejpam-8	170	22	j.	j.	PROPN
ejpam-8	170	23	phys	phys	PROPN
ejpam-8	170	24	.	.	PUNCT
ejpam-8	171	1	a	a	DET
ejpam-8	171	2	,	,	PUNCT
ejpam-8	171	3	math	math	NOUN
ejpam-8	171	4	.	.	PUNCT
ejpam-8	172	1	gen	gen	PROPN
ejpam-8	172	2	.	.	PROPN
ejpam-8	172	3	,	,	PUNCT
ejpam-8	172	4	30(12):4877	30(12):4877	NUM
ejpam-8	172	5	-	-	SYM
ejpam-8	172	6	4885	4885	NUM
ejpam-8	172	7	,	,	PUNCT
ejpam-8	172	8	1997	1997	NUM
ejpam-8	172	9	.	.	PUNCT
ejpam-8	173	1	[	[	X
ejpam-8	173	2	14	14	NUM
ejpam-8	173	3	]	]	X
ejpam-8	173	4	c.	c.	PROPN
ejpam-8	173	5	s.	s.	PROPN
ejpam-8	173	6	zhu	zhu	PROPN
ejpam-8	173	7	,	,	PUNCT
ejpam-8	173	8	global	global	ADJ
ejpam-8	173	9	attractor	attractor	NOUN
ejpam-8	173	10	for	for	ADP
ejpam-8	173	11	the	the	DET
ejpam-8	173	12	damped	damped	ADJ
ejpam-8	173	13	benjamin	benjamin	PROPN
ejpam-8	173	14	-	-	PUNCT
ejpam-8	173	15	bona	bona	ADJ
ejpam-8	173	16	-	-	PUNCT
ejpam-8	173	17	mahony	mahony	NOUN
ejpam-8	173	18	equations	equation	NOUN
ejpam-8	173	19	on	on	ADP
ejpam-8	173	20	r1	r1	PROPN
ejpam-8	173	21	,	,	PUNCT
ejpam-8	173	22	appl	appl	PROPN
ejpam-8	173	23	.	.	PROPN
ejpam-8	173	24	anal	anal	PROPN
ejpam-8	173	25	.	.	PROPN
ejpam-8	173	26	,	,	PUNCT
ejpam-8	173	27	86(1):59	86(1):59	PROPN
ejpam-8	173	28	-	-	SYM
ejpam-8	173	29	65	65	NUM
ejpam-8	173	30	,	,	PUNCT
ejpam-8	173	31	2007	2007	NUM
ejpam-8	173	32	.	.	PUNCT
ejpam-8	174	1	[	[	X
ejpam-8	174	2	15	15	NUM
ejpam-8	174	3	]	]	X
ejpam-8	174	4	c.	c.	PROPN
ejpam-8	174	5	s.	s.	PROPN
ejpam-8	174	6	zhu	zhu	PROPN
ejpam-8	174	7	,	,	PUNCT
ejpam-8	174	8	c.	c.	PROPN
ejpam-8	174	9	l.	l.	PROPN
ejpam-8	174	10	mu	mu	PROPN
ejpam-8	174	11	,	,	PUNCT
ejpam-8	174	12	exponential	exponential	ADJ
ejpam-8	174	13	decay	decay	NOUN
ejpam-8	174	14	estimates	estimate	NOUN
ejpam-8	174	15	for	for	ADP
ejpam-8	174	16	time	time	NOUN
ejpam-8	174	17	-	-	PUNCT
ejpam-8	174	18	delayed	delay	VERB
ejpam-8	174	19	benjamin	benjamin	NOUN
ejpam-8	174	20	-	-	PUNCT
ejpam-8	174	21	bona	bona	ADJ
ejpam-8	174	22	-	-	PUNCT
ejpam-8	174	23	mahony	mahony	NOUN
ejpam-8	174	24	equations	equation	NOUN
ejpam-8	174	25	,	,	PUNCT
ejpam-8	174	26	appl	appl	PROPN
ejpam-8	174	27	.	.	PROPN
ejpam-8	175	1	anal	anal	PROPN
ejpam-8	175	2	.	.	PROPN
ejpam-8	175	3	,	,	PUNCT
ejpam-8	175	4	87(4):401	87(4):401	NUM
ejpam-8	175	5	-	-	SYM
ejpam-8	175	6	07	07	NUM
ejpam-8	175	7	,	,	PUNCT
ejpam-8	175	8	2008	2008	NUM
ejpam-8	175	9	.	.	PUNCT