id	sid	tid	token	lemma	pos
ejpam-371	1	1	9_371_gopal.dvi	9_371_gopal.dvi	NUM
ejpam-371	1	2	european	european	ADJ
ejpam-371	1	3	journal	journal	NOUN
ejpam-371	1	4	of	of	ADP
ejpam-371	1	5	pure	pure	ADJ
ejpam-371	1	6	and	and	CCONJ
ejpam-371	1	7	applied	apply	VERB
ejpam-371	1	8	mathematics	mathematic	NOUN
ejpam-371	1	9	vol	vol	NOUN
ejpam-371	1	10	.	.	PUNCT
ejpam-371	2	1	3	3	NUM
ejpam-371	2	2	,	,	PUNCT
ejpam-371	2	3	no	no	INTJ
ejpam-371	2	4	.	.	NOUN
ejpam-371	2	5	2	2	NUM
ejpam-371	2	6	,	,	PUNCT
ejpam-371	2	7	2010	2010	NUM
ejpam-371	2	8	,	,	PUNCT
ejpam-371	2	9	235	235	NUM
ejpam-371	2	10	-	-	SYM
ejpam-371	2	11	253	253	NUM
ejpam-371	2	12	issn	issn	PROPN
ejpam-371	2	13	1307	1307	NUM
ejpam-371	2	14	-	-	SYM
ejpam-371	2	15	5543	5543	NUM
ejpam-371	2	16	–	–	PUNCT
ejpam-371	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-371	2	18	identification	identification	NOUN
ejpam-371	2	19	of	of	ADP
ejpam-371	2	20	the	the	DET
ejpam-371	2	21	memory	memory	NOUN
ejpam-371	2	22	kernels	kernel	NOUN
ejpam-371	2	23	and	and	CCONJ
ejpam-371	2	24	controllability	controllability	NOUN
ejpam-371	2	25	for	for	ADP
ejpam-371	2	26	parabolic	parabolic	ADJ
ejpam-371	2	27	equations	equation	NOUN
ejpam-371	2	28	r.	r.	PROPN
ejpam-371	2	29	lavanya	lavanya	PROPN
ejpam-371	2	30	adithya	adithya	PROPN
ejpam-371	2	31	institute	institute	PROPN
ejpam-371	2	32	of	of	ADP
ejpam-371	2	33	technology	technology	PROPN
ejpam-371	2	34	,	,	PUNCT
ejpam-371	2	35	coimbatore	coimbatore	PROPN
ejpam-371	2	36	,	,	PUNCT
ejpam-371	2	37	india	india	PROPN
ejpam-371	2	38	abstract	abstract	NOUN
ejpam-371	2	39	.	.	PUNCT
ejpam-371	3	1	this	this	DET
ejpam-371	3	2	paper	paper	NOUN
ejpam-371	3	3	deals	deal	NOUN
ejpam-371	3	4	with	with	ADP
ejpam-371	3	5	the	the	DET
ejpam-371	3	6	controllability	controllability	NOUN
ejpam-371	3	7	and	and	CCONJ
ejpam-371	3	8	observability	observability	NOUN
ejpam-371	3	9	properties	property	NOUN
ejpam-371	3	10	of	of	ADP
ejpam-371	3	11	the	the	DET
ejpam-371	3	12	mathematical	mathematical	ADJ
ejpam-371	3	13	models	model	NOUN
ejpam-371	3	14	(	(	PUNCT
ejpam-371	3	15	describing	describe	VERB
ejpam-371	3	16	systems	system	NOUN
ejpam-371	3	17	with	with	ADP
ejpam-371	3	18	thermal	thermal	ADJ
ejpam-371	3	19	memory	memory	NOUN
ejpam-371	3	20	)	)	PUNCT
ejpam-371	3	21	consisting	consist	VERB
ejpam-371	3	22	of	of	ADP
ejpam-371	3	23	boundary	boundary	ADJ
ejpam-371	3	24	value	value	NOUN
ejpam-371	3	25	problems	problem	NOUN
ejpam-371	3	26	of	of	ADP
ejpam-371	3	27	parabolic	parabolic	ADJ
ejpam-371	3	28	type	type	NOUN
ejpam-371	3	29	,	,	PUNCT
ejpam-371	3	30	where	where	SCONJ
ejpam-371	3	31	the	the	DET
ejpam-371	3	32	differential	differential	ADJ
ejpam-371	3	33	equation	equation	NOUN
ejpam-371	3	34	contains	contain	VERB
ejpam-371	3	35	additional	additional	ADJ
ejpam-371	3	36	integral	integral	ADJ
ejpam-371	3	37	expressions	expression	NOUN
ejpam-371	3	38	including	include	VERB
ejpam-371	3	39	“	"	PUNCT
ejpam-371	3	40	memory	memory	NOUN
ejpam-371	3	41	functions	function	NOUN
ejpam-371	3	42	”	"	PUNCT
ejpam-371	3	43	which	which	PRON
ejpam-371	3	44	describe	describe	VERB
ejpam-371	3	45	the	the	DET
ejpam-371	3	46	memory	memory	NOUN
ejpam-371	3	47	property	property	NOUN
ejpam-371	3	48	of	of	ADP
ejpam-371	3	49	the	the	DET
ejpam-371	3	50	material	material	NOUN
ejpam-371	3	51	.	.	PUNCT
ejpam-371	4	1	the	the	DET
ejpam-371	4	2	proof	proof	NOUN
ejpam-371	4	3	of	of	ADP
ejpam-371	4	4	controllability	controllability	NOUN
ejpam-371	4	5	relies	rely	VERB
ejpam-371	4	6	on	on	ADP
ejpam-371	4	7	a	a	DET
ejpam-371	4	8	carleman	carleman	ADJ
ejpam-371	4	9	type	type	NOUN
ejpam-371	4	10	estimate	estimate	NOUN
ejpam-371	4	11	and	and	CCONJ
ejpam-371	4	12	duality	duality	NOUN
ejpam-371	4	13	arguments	argument	NOUN
ejpam-371	4	14	.	.	PUNCT
ejpam-371	5	1	2000	2000	NUM
ejpam-371	5	2	mathematics	mathematic	NOUN
ejpam-371	5	3	subject	subject	NOUN
ejpam-371	5	4	classifications	classification	NOUN
ejpam-371	5	5	:	:	PUNCT
ejpam-371	5	6	93b05	93b05	NUM
ejpam-371	5	7	,	,	PUNCT
ejpam-371	5	8	93c20	93c20	NUM
ejpam-371	5	9	,	,	PUNCT
ejpam-371	5	10	45k05	45k05	NOUN
ejpam-371	5	11	,	,	PUNCT
ejpam-371	5	12	35k50	35k50	NUM
ejpam-371	5	13	.	.	PUNCT
ejpam-371	6	1	key	key	ADJ
ejpam-371	6	2	words	word	NOUN
ejpam-371	6	3	and	and	CCONJ
ejpam-371	6	4	phrases	phrase	NOUN
ejpam-371	6	5	:	:	PUNCT
ejpam-371	6	6	controllability	controllability	NOUN
ejpam-371	6	7	,	,	PUNCT
ejpam-371	6	8	observability	observability	NOUN
ejpam-371	6	9	,	,	PUNCT
ejpam-371	6	10	memory	memory	NOUN
ejpam-371	6	11	kernels	kernel	NOUN
ejpam-371	6	12	,	,	PUNCT
ejpam-371	6	13	carleman	carleman	ADJ
ejpam-371	6	14	estimate	estimate	NOUN
ejpam-371	6	15	.	.	PUNCT
ejpam-371	7	1	1	1	X
ejpam-371	7	2	.	.	X
ejpam-371	7	3	introduction	introduction	NOUN
ejpam-371	7	4	in	in	ADP
ejpam-371	7	5	many	many	ADJ
ejpam-371	7	6	of	of	ADP
ejpam-371	7	7	the	the	DET
ejpam-371	7	8	applications	application	NOUN
ejpam-371	7	9	[	[	X
ejpam-371	7	10	4	4	X
ejpam-371	7	11	]	]	PUNCT
ejpam-371	7	12	we	we	PRON
ejpam-371	7	13	begin	begin	VERB
ejpam-371	7	14	with	with	ADP
ejpam-371	7	15	a	a	DET
ejpam-371	7	16	partial	partial	ADJ
ejpam-371	7	17	differential	differential	NOUN
ejpam-371	7	18	equation	equation	NOUN
ejpam-371	7	19	and	and	CCONJ
ejpam-371	7	20	,	,	PUNCT
ejpam-371	7	21	through	through	ADP
ejpam-371	7	22	simplifying	simplifying	NOUN
ejpam-371	7	23	assumptions	assumption	NOUN
ejpam-371	7	24	,	,	PUNCT
ejpam-371	7	25	arrive	arrive	VERB
ejpam-371	7	26	at	at	ADP
ejpam-371	7	27	an	an	DET
ejpam-371	7	28	integral	integral	ADJ
ejpam-371	7	29	or	or	CCONJ
ejpam-371	7	30	integrodifferential	integrodifferential	ADJ
ejpam-371	7	31	equation	equation	NOUN
ejpam-371	7	32	which	which	PRON
ejpam-371	7	33	takes	take	VERB
ejpam-371	7	34	the	the	DET
ejpam-371	7	35	whole	whole	ADJ
ejpam-371	7	36	history	history	NOUN
ejpam-371	7	37	into	into	ADP
ejpam-371	7	38	account	account	NOUN
ejpam-371	7	39	.	.	PUNCT
ejpam-371	8	1	lunardi	lunardi	NOUN
ejpam-371	9	1	[	[	X
ejpam-371	9	2	11	11	NUM
ejpam-371	9	3	]	]	PUNCT
ejpam-371	9	4	and	and	CCONJ
ejpam-371	9	5	unger	unger	PROPN
ejpam-371	9	6	et	et	PROPN
ejpam-371	9	7	al	al	PROPN
ejpam-371	10	1	[	[	X
ejpam-371	10	2	14	14	NUM
ejpam-371	10	3	]	]	PUNCT
ejpam-371	10	4	,	,	PUNCT
ejpam-371	10	5	for	for	ADP
ejpam-371	10	6	example	example	NOUN
ejpam-371	10	7	,	,	PUNCT
ejpam-371	10	8	studied	study	VERB
ejpam-371	10	9	the	the	DET
ejpam-371	10	10	problem	problem	NOUN
ejpam-371	10	11	concerned	concern	VERB
ejpam-371	10	12	with	with	ADP
ejpam-371	10	13	materials	material	NOUN
ejpam-371	10	14	with	with	ADP
ejpam-371	10	15	memory	memory	NOUN
ejpam-371	10	16	having	have	VERB
ejpam-371	10	17	the	the	DET
ejpam-371	10	18	property	property	NOUN
ejpam-371	10	19	that	that	PRON
ejpam-371	10	20	the	the	DET
ejpam-371	10	21	mathematicalphysical	mathematicalphysical	ADJ
ejpam-371	10	22	description	description	NOUN
ejpam-371	10	23	of	of	ADP
ejpam-371	10	24	their	their	PRON
ejpam-371	10	25	state	state	NOUN
ejpam-371	10	26	at	at	ADP
ejpam-371	10	27	a	a	DET
ejpam-371	10	28	given	give	VERB
ejpam-371	10	29	point	point	NOUN
ejpam-371	10	30	of	of	ADP
ejpam-371	10	31	time	time	NOUN
ejpam-371	10	32	includes	include	VERB
ejpam-371	10	33	such	such	ADJ
ejpam-371	10	34	states	state	NOUN
ejpam-371	10	35	in	in	ADP
ejpam-371	10	36	which	which	PRON
ejpam-371	10	37	the	the	DET
ejpam-371	10	38	materials	material	NOUN
ejpam-371	10	39	have	have	AUX
ejpam-371	10	40	been	be	AUX
ejpam-371	10	41	at	at	ADP
ejpam-371	10	42	earlier	early	ADJ
ejpam-371	10	43	points	point	NOUN
ejpam-371	10	44	of	of	ADP
ejpam-371	10	45	time	time	NOUN
ejpam-371	10	46	.	.	PUNCT
ejpam-371	11	1	in	in	ADP
ejpam-371	11	2	the	the	DET
ejpam-371	11	3	linear	linear	PROPN
ejpam-371	11	4	theory	theory	NOUN
ejpam-371	11	5	of	of	ADP
ejpam-371	11	6	heat	heat	NOUN
ejpam-371	11	7	flow	flow	NOUN
ejpam-371	11	8	in	in	ADP
ejpam-371	11	9	a	a	DET
ejpam-371	11	10	rigid	rigid	ADJ
ejpam-371	11	11	homogeneous	homogeneous	ADJ
ejpam-371	11	12	isotropic	isotropic	NOUN
ejpam-371	11	13	body	body	NOUN
ejpam-371	11	14	consisting	consist	VERB
ejpam-371	11	15	of	of	ADP
ejpam-371	11	16	material	material	NOUN
ejpam-371	11	17	with	with	ADP
ejpam-371	11	18	thermal	thermal	ADJ
ejpam-371	11	19	memory	memory	NOUN
ejpam-371	11	20	,	,	PUNCT
ejpam-371	11	21	the	the	DET
ejpam-371	11	22	following	follow	VERB
ejpam-371	11	23	system	system	NOUN
ejpam-371	11	24	of	of	ADP
ejpam-371	11	25	constitutive	constitutive	ADJ
ejpam-371	11	26	relationships	relationship	NOUN
ejpam-371	11	27	hold	hold	VERB
ejpam-371	11	28	(	(	PUNCT
ejpam-371	11	29	see	see	VERB
ejpam-371	11	30	[	[	X
ejpam-371	11	31	9,14	9,14	NUM
ejpam-371	11	32	]	]	SYM
ejpam-371	11	33	)	)	PUNCT
ejpam-371	11	34	e(t	e(t	NOUN
ejpam-371	11	35	,	,	PUNCT
ejpam-371	11	36	x	x	NOUN
ejpam-371	11	37	)	)	PUNCT
ejpam-371	11	38	=	=	PUNCT
ejpam-371	12	1	β	β	X
ejpam-371	12	2	y(t	y(t	PROPN
ejpam-371	12	3	,	,	PUNCT
ejpam-371	12	4	x	x	PRON
ejpam-371	12	5	)	)	PUNCT
ejpam-371	13	1	+	+	CCONJ
ejpam-371	13	2	∫	∫	PROPN
ejpam-371	13	3	t	t	PROPN
ejpam-371	13	4	−∞	−∞	ADP
ejpam-371	13	5	n(t	n(t	PROPN
ejpam-371	13	6	,	,	PUNCT
ejpam-371	13	7	τ)y(τ	τ)y(τ	PROPN
ejpam-371	13	8	,	,	PUNCT
ejpam-371	13	9	x)dτ	x)dτ	PROPN
ejpam-371	13	10	,	,	PUNCT
ejpam-371	13	11	(	(	PUNCT
ejpam-371	13	12	1	1	X
ejpam-371	13	13	)	)	PUNCT
ejpam-371	13	14	s(t	s(t	PROPN
ejpam-371	13	15	,	,	PUNCT
ejpam-371	13	16	x	x	X
ejpam-371	13	17	)	)	PUNCT
ejpam-371	13	18	=	=	SYM
ejpam-371	13	19	−ζ∇y(t	−ζ∇y(t	PROPN
ejpam-371	13	20	,	,	PUNCT
ejpam-371	13	21	x)−	x)−	PROPN
ejpam-371	13	22	∫	∫	PROPN
ejpam-371	13	23	t	t	PROPN
ejpam-371	13	24	−∞	−∞	ADP
ejpam-371	13	25	m(t	m(t	PROPN
ejpam-371	13	26	,	,	PUNCT
ejpam-371	13	27	τ)∇y(τ	τ)∇y(τ	NOUN
ejpam-371	13	28	,	,	PUNCT
ejpam-371	13	29	x)dτ	x)dτ	PROPN
ejpam-371	13	30	,	,	PUNCT
ejpam-371	13	31	(	(	PUNCT
ejpam-371	13	32	2	2	NUM
ejpam-371	13	33	)	)	PUNCT
ejpam-371	13	34	together	together	ADV
ejpam-371	13	35	with	with	ADP
ejpam-371	13	36	the	the	DET
ejpam-371	13	37	heat	heat	NOUN
ejpam-371	13	38	-	-	PUNCT
ejpam-371	13	39	balance	balance	NOUN
ejpam-371	13	40	equation	equation	NOUN
ejpam-371	13	41	:	:	PUNCT
ejpam-371	13	42	et(t	et(t	NOUN
ejpam-371	13	43	,	,	PUNCT
ejpam-371	13	44	x	x	PRON
ejpam-371	13	45	)	)	PUNCT
ejpam-371	14	1	+	+	CCONJ
ejpam-371	14	2	divs(t	divs(t	PROPN
ejpam-371	14	3	,	,	PUNCT
ejpam-371	14	4	x	x	NOUN
ejpam-371	14	5	)	)	PUNCT
ejpam-371	15	1	=	=	SYM
ejpam-371	15	2	f	f	PROPN
ejpam-371	15	3	(	(	PUNCT
ejpam-371	15	4	t	t	PROPN
ejpam-371	15	5	,	,	PUNCT
ejpam-371	15	6	x	x	NOUN
ejpam-371	15	7	)	)	PUNCT
ejpam-371	15	8	,	,	PUNCT
ejpam-371	15	9	(	(	PUNCT
ejpam-371	15	10	3	3	X
ejpam-371	15	11	)	)	PUNCT
ejpam-371	15	12	email	email	NOUN
ejpam-371	15	13	address	address	NOUN
ejpam-371	15	14	:	:	PUNCT
ejpam-371	15	15	lavnya.gopal	lavnya.gopal	NUM
ejpam-371	15	16	�	�	NOUN
ejpam-371	15	17	gmail	gmail	NOUN
ejpam-371	15	18	.	.	PUNCT
ejpam-371	16	1	om	om	PROPN
ejpam-371	16	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-371	16	3	235	235	NUM
ejpam-371	17	1	c	c	X
ejpam-371	17	2	©	©	PROPN
ejpam-371	17	3	2010	2010	NUM
ejpam-371	17	4	ejpam	ejpam	NOUN
ejpam-371	17	5	all	all	DET
ejpam-371	17	6	rights	right	NOUN
ejpam-371	17	7	reserved	reserve	VERB
ejpam-371	17	8	.	.	PUNCT
ejpam-371	18	1	r.	r.	PROPN
ejpam-371	18	2	lavanya	lavanya	PROPN
ejpam-371	18	3	/	/	SYM
ejpam-371	18	4	eur	eur	PROPN
ejpam-371	18	5	.	.	PUNCT
ejpam-371	19	1	j.	j.	PROPN
ejpam-371	19	2	pure	pure	PROPN
ejpam-371	19	3	appl	appl	PROPN
ejpam-371	19	4	.	.	PROPN
ejpam-371	19	5	math	math	PROPN
ejpam-371	19	6	,	,	PUNCT
ejpam-371	19	7	3	3	NUM
ejpam-371	19	8	(	(	PUNCT
ejpam-371	19	9	2010	2010	NUM
ejpam-371	19	10	)	)	PUNCT
ejpam-371	19	11	,	,	PUNCT
ejpam-371	19	12	235	235	NUM
ejpam-371	19	13	-	-	SYM
ejpam-371	19	14	253	253	NUM
ejpam-371	19	15	236	236	NUM
ejpam-371	19	16	where	where	SCONJ
ejpam-371	19	17	e(t	e(t	NOUN
ejpam-371	19	18	,	,	PUNCT
ejpam-371	19	19	x	x	PRON
ejpam-371	19	20	)	)	PUNCT
ejpam-371	19	21	is	be	AUX
ejpam-371	19	22	the	the	DET
ejpam-371	19	23	internal	internal	ADJ
ejpam-371	19	24	energy	energy	NOUN
ejpam-371	19	25	,	,	PUNCT
ejpam-371	19	26	s(t	s(t	PROPN
ejpam-371	19	27	,	,	PUNCT
ejpam-371	19	28	x	x	PRON
ejpam-371	19	29	)	)	PUNCT
ejpam-371	19	30	is	be	AUX
ejpam-371	19	31	the	the	DET
ejpam-371	19	32	heat	heat	NOUN
ejpam-371	19	33	flux	flux	NOUN
ejpam-371	19	34	,	,	PUNCT
ejpam-371	19	35	y(t	y(t	PROPN
ejpam-371	19	36	,	,	PUNCT
ejpam-371	19	37	x	x	X
ejpam-371	19	38	)	)	PUNCT
ejpam-371	19	39	is	be	AUX
ejpam-371	19	40	the	the	DET
ejpam-371	19	41	body	body	NOUN
ejpam-371	19	42	temperature	temperature	NOUN
ejpam-371	19	43	with	with	ADP
ejpam-371	19	44	time	time	NOUN
ejpam-371	19	45	t	t	PROPN
ejpam-371	19	46	∈	∈	PROPN
ejpam-371	20	1	[	[	X
ejpam-371	20	2	0	0	NUM
ejpam-371	20	3	,	,	PUNCT
ejpam-371	20	4	t	t	PROPN
ejpam-371	20	5	]	]	PUNCT
ejpam-371	20	6	for	for	ADP
ejpam-371	20	7	fixed	fix	VERB
ejpam-371	20	8	t	t	NOUN
ejpam-371	20	9	,	,	PUNCT
ejpam-371	20	10	x	x	PUNCT
ejpam-371	20	11	∈	∈	PROPN
ejpam-371	20	12	ω	ω	NUM
ejpam-371	20	13	where	where	SCONJ
ejpam-371	20	14	ω	ω	PROPN
ejpam-371	20	15	⊂	⊂	PROPN
ejpam-371	20	16	r3	r3	PROPN
ejpam-371	20	17	is	be	AUX
ejpam-371	20	18	an	an	DET
ejpam-371	20	19	open	open	ADJ
ejpam-371	20	20	bounded	bounded	ADJ
ejpam-371	20	21	domain	domain	NOUN
ejpam-371	20	22	with	with	ADP
ejpam-371	20	23	a	a	DET
ejpam-371	20	24	smooth	smooth	ADJ
ejpam-371	20	25	boundary	boundary	ADJ
ejpam-371	20	26	∂ω	∂ω	PROPN
ejpam-371	20	27	of	of	ADP
ejpam-371	20	28	class	class	NOUN
ejpam-371	20	29	c1	c1	PROPN
ejpam-371	20	30	,	,	PUNCT
ejpam-371	20	31	f	f	PROPN
ejpam-371	20	32	(	(	PUNCT
ejpam-371	20	33	t	t	PROPN
ejpam-371	20	34	,	,	PUNCT
ejpam-371	20	35	x	x	X
ejpam-371	20	36	)	)	PUNCT
ejpam-371	20	37	is	be	AUX
ejpam-371	20	38	the	the	DET
ejpam-371	20	39	given	give	VERB
ejpam-371	20	40	heat	heat	NOUN
ejpam-371	20	41	source	source	NOUN
ejpam-371	20	42	,	,	PUNCT
ejpam-371	20	43	β	β	X
ejpam-371	20	44	=	=	SYM
ejpam-371	20	45	cρ	cρ	PROPN
ejpam-371	20	46	(	(	PUNCT
ejpam-371	20	47	c	c	NOUN
ejpam-371	20	48	is	be	AUX
ejpam-371	20	49	the	the	DET
ejpam-371	20	50	specific	specific	ADJ
ejpam-371	20	51	caloric	caloric	NOUN
ejpam-371	20	52	constant	constant	ADJ
ejpam-371	20	53	;	;	PUNCT
ejpam-371	20	54	ρ	ρ	PROPN
ejpam-371	20	55	is	be	AUX
ejpam-371	20	56	the	the	DET
ejpam-371	20	57	density	density	NOUN
ejpam-371	20	58	)	)	PUNCT
ejpam-371	20	59	and	and	CCONJ
ejpam-371	20	60	ζ	ζ	NOUN
ejpam-371	20	61	is	be	AUX
ejpam-371	20	62	the	the	DET
ejpam-371	20	63	heat	heat	NOUN
ejpam-371	20	64	-	-	PUNCT
ejpam-371	20	65	conduction	conduction	NOUN
ejpam-371	20	66	coefficient	coefficient	NOUN
ejpam-371	20	67	.	.	PUNCT
ejpam-371	21	1	if	if	SCONJ
ejpam-371	21	2	we	we	PRON
ejpam-371	21	3	assume	assume	VERB
ejpam-371	21	4	that	that	SCONJ
ejpam-371	21	5	y(t	y(t	PROPN
ejpam-371	21	6	,	,	PUNCT
ejpam-371	21	7	x	x	X
ejpam-371	21	8	)	)	PUNCT
ejpam-371	21	9	≡	≡	PROPN
ejpam-371	21	10	0	0	PUNCT
ejpam-371	22	1	for	for	ADP
ejpam-371	22	2	−∞	−∞	X
ejpam-371	22	3	<	<	X
ejpam-371	22	4	t	t	X
ejpam-371	22	5	<	<	X
ejpam-371	22	6	0	0	NUM
ejpam-371	22	7	,	,	PUNCT
ejpam-371	22	8	it	it	PRON
ejpam-371	22	9	can	can	AUX
ejpam-371	22	10	be	be	AUX
ejpam-371	22	11	immediately	immediately	ADV
ejpam-371	22	12	seen	see	VERB
ejpam-371	22	13	that	that	SCONJ
ejpam-371	22	14	the	the	DET
ejpam-371	22	15	relations	relation	NOUN
ejpam-371	22	16	(	(	PUNCT
ejpam-371	22	17	1)-(3	1)-(3	NOUN
ejpam-371	22	18	)	)	PUNCT
ejpam-371	22	19	lead	lead	VERB
ejpam-371	22	20	to	to	ADP
ejpam-371	22	21	the	the	DET
ejpam-371	22	22	system	system	NOUN
ejpam-371	22	23	of	of	ADP
ejpam-371	22	24	the	the	DET
ejpam-371	22	25	form	form	NOUN
ejpam-371	22	26	,	,	PUNCT
ejpam-371	22	27	β	β	X
ejpam-371	22	28	yt(t	yt(t	NOUN
ejpam-371	22	29	,	,	PUNCT
ejpam-371	22	30	x	x	NOUN
ejpam-371	22	31	)	)	PUNCT
ejpam-371	22	32	−	−	PROPN
ejpam-371	22	33	ζ∆y(t	ζ∆y(t	PROPN
ejpam-371	22	34	,	,	PUNCT
ejpam-371	22	35	x)−	x)−	PROPN
ejpam-371	22	36	∫	∫	PROPN
ejpam-371	23	1	t	t	PROPN
ejpam-371	23	2	0	0	NUM
ejpam-371	23	3	m(t	m(t	PROPN
ejpam-371	23	4	,	,	PUNCT
ejpam-371	23	5	τ)∆y(τ	τ)∆y(τ	PROPN
ejpam-371	23	6	,	,	PUNCT
ejpam-371	23	7	x)dτ	x)dτ	PROPN
ejpam-371	23	8	+	+	NUM
ejpam-371	23	9	∂	∂	NUM
ejpam-371	23	10	∂	∂	NUM
ejpam-371	23	11	t	t	PROPN
ejpam-371	23	12	�	�	PROPN
ejpam-371	23	13	∫	∫	PROPN
ejpam-371	23	14	t	t	PROPN
ejpam-371	23	15	0	0	NUM
ejpam-371	23	16	n(t	n(t	PROPN
ejpam-371	23	17	,	,	PUNCT
ejpam-371	23	18	τ)y(τ	τ)y(τ	PROPN
ejpam-371	23	19	,	,	PUNCT
ejpam-371	24	1	x)dτ	x)dτ	PROPN
ejpam-371	24	2	�	�	PROPN
ejpam-371	24	3	=	=	SYM
ejpam-371	24	4	f	f	PROPN
ejpam-371	24	5	(	(	PUNCT
ejpam-371	24	6	t	t	PROPN
ejpam-371	24	7	,	,	PUNCT
ejpam-371	24	8	x	x	NOUN
ejpam-371	24	9	)	)	PUNCT
ejpam-371	24	10	in	in	ADP
ejpam-371	24	11	(	(	PUNCT
ejpam-371	24	12	0	0	NUM
ejpam-371	24	13	,	,	PUNCT
ejpam-371	24	14	t	t	NOUN
ejpam-371	24	15	)	)	PUNCT
ejpam-371	24	16	×ω	×ω	PROPN
ejpam-371	24	17	,	,	PUNCT
ejpam-371	24	18	y(0	y(0	PROPN
ejpam-371	24	19	,	,	PUNCT
ejpam-371	24	20	x	x	NOUN
ejpam-371	24	21	)	)	PUNCT
ejpam-371	24	22	=	=	SYM
ejpam-371	24	23	y0(x	y0(x	NOUN
ejpam-371	24	24	)	)	PUNCT
ejpam-371	24	25	in	in	ADP
ejpam-371	24	26	ω	ω	PROPN
ejpam-371	24	27	,	,	PUNCT
ejpam-371	24	28	y(t	y(t	PROPN
ejpam-371	24	29	,	,	PUNCT
ejpam-371	24	30	x	x	NOUN
ejpam-371	24	31	)	)	PUNCT
ejpam-371	24	32	=	=	SYM
ejpam-371	24	33	0	0	NUM
ejpam-371	24	34	on	on	ADP
ejpam-371	24	35	(	(	PUNCT
ejpam-371	24	36	0	0	NUM
ejpam-371	24	37	,	,	PUNCT
ejpam-371	24	38	t	t	NOUN
ejpam-371	24	39	)	)	PUNCT
ejpam-371	24	40	×	×	PROPN
ejpam-371	24	41	∂ω	∂ω	PROPN
ejpam-371	24	42	,	,	PUNCT
ejpam-371	24	43	where	where	SCONJ
ejpam-371	24	44	y0(x	y0(x	X
ejpam-371	24	45	)	)	PUNCT
ejpam-371	24	46	is	be	AUX
ejpam-371	24	47	the	the	DET
ejpam-371	24	48	given	give	VERB
ejpam-371	24	49	initial	initial	ADJ
ejpam-371	24	50	temperature	temperature	NOUN
ejpam-371	24	51	distribution	distribution	NOUN
ejpam-371	24	52	.	.	PUNCT
ejpam-371	25	1	the	the	DET
ejpam-371	25	2	memory	memory	NOUN
ejpam-371	25	3	kernels	kernel	NOUN
ejpam-371	25	4	n	n	PROPN
ejpam-371	25	5	and	and	CCONJ
ejpam-371	25	6	m	m	PROPN
ejpam-371	25	7	are	be	AUX
ejpam-371	25	8	sufficiently	sufficiently	ADV
ejpam-371	25	9	smooth	smooth	ADJ
ejpam-371	25	10	and	and	CCONJ
ejpam-371	25	11	have	have	VERB
ejpam-371	25	12	support	support	NOUN
ejpam-371	25	13	in	in	ADP
ejpam-371	25	14	(	(	PUNCT
ejpam-371	25	15	t0	t0	PROPN
ejpam-371	25	16	,	,	PUNCT
ejpam-371	25	17	t1	t1	PROPN
ejpam-371	25	18	)	)	PUNCT
ejpam-371	25	19	,	,	PUNCT
ejpam-371	25	20	where	where	SCONJ
ejpam-371	25	21	0	0	X
ejpam-371	25	22	<	<	X
ejpam-371	25	23	t0	t0	X
ejpam-371	25	24	<	<	X
ejpam-371	25	25	t1	t1	NOUN
ejpam-371	25	26	<	<	X
ejpam-371	25	27	t	t	X
ejpam-371	25	28	satisfying	satisfy	VERB
ejpam-371	25	29	m(t	m(t	PROPN
ejpam-371	25	30	,	,	PUNCT
ejpam-371	25	31	t	t	PROPN
ejpam-371	25	32	)	)	PUNCT
ejpam-371	25	33	=	=	SYM
ejpam-371	26	1	n(t	n(t	PROPN
ejpam-371	26	2	,	,	PUNCT
ejpam-371	26	3	t	t	PROPN
ejpam-371	26	4	)	)	PUNCT
ejpam-371	26	5	=	=	SYM
ejpam-371	26	6	0	0	PUNCT
ejpam-371	26	7	and	and	CCONJ
ejpam-371	26	8	represent	represent	VERB
ejpam-371	26	9	the	the	DET
ejpam-371	26	10	derivatives	derivative	NOUN
ejpam-371	26	11	of	of	ADP
ejpam-371	26	12	the	the	DET
ejpam-371	26	13	relaxation	relaxation	NOUN
ejpam-371	26	14	function	function	NOUN
ejpam-371	26	15	of	of	ADP
ejpam-371	26	16	internal	internal	ADJ
ejpam-371	26	17	energy	energy	NOUN
ejpam-371	26	18	and	and	CCONJ
ejpam-371	26	19	heat	heat	NOUN
ejpam-371	26	20	flux	flux	NOUN
ejpam-371	26	21	respectively	respectively	ADV
ejpam-371	26	22	.	.	PUNCT
ejpam-371	27	1	hereafter	hereafter	ADV
ejpam-371	27	2	,	,	PUNCT
ejpam-371	27	3	for	for	ADP
ejpam-371	27	4	our	our	PRON
ejpam-371	27	5	convenience	convenience	NOUN
ejpam-371	27	6	,	,	PUNCT
ejpam-371	27	7	assume	assume	VERB
ejpam-371	27	8	that	that	SCONJ
ejpam-371	27	9	β	β	NOUN
ejpam-371	27	10	=	=	SYM
ejpam-371	27	11	1	1	NUM
ejpam-371	27	12	and	and	CCONJ
ejpam-371	27	13	ζ	ζ	NOUN
ejpam-371	27	14	=	=	SYM
ejpam-371	27	15	1	1	NUM
ejpam-371	27	16	and	and	CCONJ
ejpam-371	27	17	set	set	VERB
ejpam-371	27	18	q	q	PROPN
ejpam-371	27	19	=	=	SYM
ejpam-371	27	20	(	(	PUNCT
ejpam-371	27	21	0	0	NUM
ejpam-371	27	22	,	,	PUNCT
ejpam-371	27	23	t	t	NOUN
ejpam-371	27	24	)	)	PUNCT
ejpam-371	27	25	×ω	×ω	NOUN
ejpam-371	27	26	and	and	CCONJ
ejpam-371	27	27	σ	σ	X
ejpam-371	27	28	=	=	SYM
ejpam-371	27	29	(	(	PUNCT
ejpam-371	27	30	0	0	NUM
ejpam-371	27	31	,	,	PUNCT
ejpam-371	27	32	t	t	NOUN
ejpam-371	27	33	)	)	PUNCT
ejpam-371	27	34	×	×	PROPN
ejpam-371	27	35	∂ω	∂ω	PROPN
ejpam-371	27	36	.	.	PUNCT
ejpam-371	28	1	we	we	PRON
ejpam-371	28	2	now	now	ADV
ejpam-371	28	3	consider	consider	VERB
ejpam-371	28	4	the	the	DET
ejpam-371	28	5	corresponding	corresponding	ADJ
ejpam-371	28	6	controlled	control	VERB
ejpam-371	28	7	parabolic	parabolic	NOUN
ejpam-371	28	8	system	system	NOUN
ejpam-371	28	9	with	with	ADP
ejpam-371	28	10	memory	memory	NOUN
ejpam-371	28	11	kernels	kernel	NOUN
ejpam-371	28	12	yt	yt	PROPN
ejpam-371	28	13	−∆y(t	−∆y(t	PROPN
ejpam-371	28	14	,	,	PUNCT
ejpam-371	28	15	x)−m	x)−m	X
ejpam-371	28	16	t	t	PROPN
ejpam-371	28	17	0	0	NUM
ejpam-371	28	18	∗∆y(t	∗∆y(t	NOUN
ejpam-371	28	19	)	)	PUNCT
ejpam-371	29	1	+	+	CCONJ
ejpam-371	29	2	(	(	PUNCT
ejpam-371	29	3	n	n	PRON
ejpam-371	29	4	t	t	NOUN
ejpam-371	29	5	0	0	NUM
ejpam-371	29	6	∗	∗	NOUN
ejpam-371	29	7	y(t))t	y(t))t	PROPN
ejpam-371	30	1	=	=	SYM
ejpam-371	30	2	f	f	PROPN
ejpam-371	30	3	(	(	PUNCT
ejpam-371	30	4	t	t	PROPN
ejpam-371	30	5	,	,	PUNCT
ejpam-371	30	6	x	x	NOUN
ejpam-371	30	7	)	)	PUNCT
ejpam-371	30	8	+	+	SYM
ejpam-371	30	9	χωu(t	χωu(t	PROPN
ejpam-371	30	10	,	,	PUNCT
ejpam-371	30	11	x	x	NOUN
ejpam-371	30	12	)	)	PUNCT
ejpam-371	30	13	in	in	ADP
ejpam-371	30	14	q	q	PROPN
ejpam-371	30	15	y(0	y(0	PROPN
ejpam-371	30	16	,	,	PUNCT
ejpam-371	30	17	x	x	NOUN
ejpam-371	30	18	)	)	PUNCT
ejpam-371	30	19	=	=	SYM
ejpam-371	30	20	y0(x	y0(x	NOUN
ejpam-371	30	21	)	)	PUNCT
ejpam-371	30	22	in	in	ADP
ejpam-371	30	23	ω	ω	PROPN
ejpam-371	30	24	y(t	y(t	PROPN
ejpam-371	30	25	,	,	PUNCT
ejpam-371	30	26	x	x	X
ejpam-371	30	27	)	)	PUNCT
ejpam-371	31	1	=	=	SYM
ejpam-371	31	2	0	0	NUM
ejpam-371	31	3	on	on	ADP
ejpam-371	31	4	σ	σ	PROPN
ejpam-371	31	5	,	,	PUNCT
ejpam-371	31	6			PROPN
ejpam-371	31	7			PROPN
ejpam-371	31	8			NOUN
ejpam-371	31	9	(	(	PUNCT
ejpam-371	31	10	4	4	NUM
ejpam-371	31	11	)	)	PUNCT
ejpam-371	31	12	where	where	SCONJ
ejpam-371	31	13	χω	χω	ADV
ejpam-371	31	14	is	be	AUX
ejpam-371	31	15	the	the	DET
ejpam-371	31	16	characteristic	characteristic	ADJ
ejpam-371	31	17	function	function	NOUN
ejpam-371	31	18	of	of	ADP
ejpam-371	31	19	the	the	DET
ejpam-371	31	20	open	open	ADJ
ejpam-371	31	21	set	set	NOUN
ejpam-371	31	22	ω	ω	PROPN
ejpam-371	31	23	⊂	⊂	PROPN
ejpam-371	31	24	ω	ω	PROPN
ejpam-371	31	25	,	,	PUNCT
ejpam-371	31	26	u	u	NOUN
ejpam-371	31	27	=	=	SYM
ejpam-371	31	28	u(t	u(t	NOUN
ejpam-371	31	29	,	,	PUNCT
ejpam-371	31	30	x	x	X
ejpam-371	31	31	)	)	PUNCT
ejpam-371	31	32	is	be	AUX
ejpam-371	31	33	the	the	DET
ejpam-371	31	34	control	control	NOUN
ejpam-371	31	35	function	function	NOUN
ejpam-371	31	36	to	to	PART
ejpam-371	31	37	be	be	AUX
ejpam-371	31	38	determined	determine	VERB
ejpam-371	31	39	which	which	PRON
ejpam-371	31	40	acts	act	VERB
ejpam-371	31	41	on	on	ADP
ejpam-371	31	42	the	the	DET
ejpam-371	31	43	system	system	NOUN
ejpam-371	31	44	through	through	ADP
ejpam-371	31	45	ω	ω	NUM
ejpam-371	31	46	while	while	SCONJ
ejpam-371	31	47	f	f	PROPN
ejpam-371	31	48	∈	∈	PROPN
ejpam-371	31	49	l2(q	l2(q	PROPN
ejpam-371	31	50	)	)	PUNCT
ejpam-371	31	51	is	be	AUX
ejpam-371	31	52	the	the	DET
ejpam-371	31	53	given	give	VERB
ejpam-371	31	54	source	source	NOUN
ejpam-371	31	55	term	term	NOUN
ejpam-371	31	56	.	.	PUNCT
ejpam-371	32	1	the	the	DET
ejpam-371	32	2	notations	notation	NOUN
ejpam-371	32	3	m	m	VERB
ejpam-371	32	4	t	t	NOUN
ejpam-371	32	5	0	0	NUM
ejpam-371	32	6	∗∆y	∗∆y	NOUN
ejpam-371	32	7	and	and	CCONJ
ejpam-371	32	8	n	n	PRON
ejpam-371	32	9	t	t	PROPN
ejpam-371	32	10	0	0	NUM
ejpam-371	32	11	∗	∗	NOUN
ejpam-371	32	12	y	y	PROPN
ejpam-371	32	13	respectively	respectively	ADV
ejpam-371	32	14	stand	stand	VERB
ejpam-371	32	15	for	for	ADP
ejpam-371	32	16	memory	memory	NOUN
ejpam-371	32	17	integrals	integral	NOUN
ejpam-371	32	18	from	from	ADP
ejpam-371	32	19	0	0	NUM
ejpam-371	32	20	to	to	ADP
ejpam-371	32	21	t	t	PROPN
ejpam-371	32	22	,	,	PUNCT
ejpam-371	32	23	that	that	ADV
ejpam-371	32	24	is	is	ADV
ejpam-371	32	25	,	,	PUNCT
ejpam-371	32	26	m	m	VERB
ejpam-371	32	27	t	t	NOUN
ejpam-371	32	28	0	0	NUM
ejpam-371	32	29	∗∆y(t	∗∆y(t	NOUN
ejpam-371	32	30	)	)	PUNCT
ejpam-371	33	1	=	=	SYM
ejpam-371	33	2	∫	∫	PROPN
ejpam-371	33	3	t	t	PROPN
ejpam-371	33	4	0	0	SYM
ejpam-371	33	5	m(t	m(t	PROPN
ejpam-371	33	6	,	,	PUNCT
ejpam-371	33	7	τ)∆y(τ)dτ	τ)∆y(τ)dτ	PROPN
ejpam-371	33	8	,	,	PUNCT
ejpam-371	33	9	n	n	PROPN
ejpam-371	33	10	t	t	NOUN
ejpam-371	33	11	0	0	NUM
ejpam-371	33	12	∗	∗	NOUN
ejpam-371	33	13	y(t	y(t	NUM
ejpam-371	33	14	)	)	PUNCT
ejpam-371	34	1	=	=	SYM
ejpam-371	35	1	∫	∫	PROPN
ejpam-371	35	2	t	t	PROPN
ejpam-371	35	3	0	0	NUM
ejpam-371	36	1	n(t	n(t	PROPN
ejpam-371	36	2	,	,	PUNCT
ejpam-371	36	3	τ)y(τ)dτ	τ)y(τ)dτ	NOUN
ejpam-371	36	4	.	.	PUNCT
ejpam-371	37	1	the	the	DET
ejpam-371	37	2	system	system	NOUN
ejpam-371	37	3	is	be	AUX
ejpam-371	37	4	null	null	ADJ
ejpam-371	37	5	controllable	controllable	ADJ
ejpam-371	37	6	at	at	ADP
ejpam-371	37	7	time	time	NOUN
ejpam-371	37	8	t	t	NOUN
ejpam-371	37	9	if	if	SCONJ
ejpam-371	37	10	,	,	PUNCT
ejpam-371	37	11	for	for	ADP
ejpam-371	37	12	each	each	DET
ejpam-371	37	13	y0	y0	PROPN
ejpam-371	37	14	∈	∈	NOUN
ejpam-371	37	15	h1	h1	NOUN
ejpam-371	37	16	0(ω	0(ω	NUM
ejpam-371	37	17	)	)	PUNCT
ejpam-371	37	18	,	,	PUNCT
ejpam-371	37	19	there	there	PRON
ejpam-371	37	20	exists	exist	VERB
ejpam-371	37	21	a	a	DET
ejpam-371	37	22	control	control	NOUN
ejpam-371	37	23	u	u	NOUN
ejpam-371	37	24	∈	∈	PROPN
ejpam-371	37	25	l2(ω×	l2(ω×	NOUN
ejpam-371	37	26	(	(	PUNCT
ejpam-371	37	27	0	0	NUM
ejpam-371	37	28	,	,	PUNCT
ejpam-371	37	29	t	t	NOUN
ejpam-371	37	30	)	)	PUNCT
ejpam-371	37	31	)	)	PUNCT
ejpam-371	37	32	such	such	ADJ
ejpam-371	37	33	that	that	SCONJ
ejpam-371	37	34	the	the	DET
ejpam-371	37	35	associated	associated	ADJ
ejpam-371	37	36	solution	solution	NOUN
ejpam-371	37	37	satisfies	satisfy	VERB
ejpam-371	37	38	y(t	y(t	PROPN
ejpam-371	37	39	,	,	PUNCT
ejpam-371	37	40	x	x	X
ejpam-371	37	41	)	)	PUNCT
ejpam-371	37	42	=	=	SYM
ejpam-371	37	43	0	0	NUM
ejpam-371	38	1	a.e	a.e	PROPN
ejpam-371	38	2	.	.	PUNCT
ejpam-371	38	3	x	x	SYM
ejpam-371	38	4	∈	∈	PROPN
ejpam-371	38	5	ω	ω	PROPN
ejpam-371	38	6	.	.	PUNCT
ejpam-371	39	1	the	the	DET
ejpam-371	39	2	null	null	ADJ
ejpam-371	39	3	controllability	controllability	NOUN
ejpam-371	39	4	of	of	ADP
ejpam-371	39	5	linear	linear	PROPN
ejpam-371	39	6	parabolic	parabolic	ADJ
ejpam-371	39	7	equations	equation	NOUN
ejpam-371	39	8	without	without	ADP
ejpam-371	39	9	the	the	DET
ejpam-371	39	10	memory	memory	NOUN
ejpam-371	39	11	kernels	kernel	NOUN
ejpam-371	39	12	has	have	AUX
ejpam-371	39	13	been	be	AUX
ejpam-371	39	14	intensively	intensively	ADV
ejpam-371	39	15	studied	study	VERB
ejpam-371	39	16	by	by	ADP
ejpam-371	39	17	several	several	ADJ
ejpam-371	39	18	authors	author	NOUN
ejpam-371	39	19	;	;	PUNCT
ejpam-371	39	20	for	for	ADP
ejpam-371	39	21	instance	instance	NOUN
ejpam-371	39	22	see	see	VERB
ejpam-371	39	23	barbu	barbu	PROPN
ejpam-371	39	24	[	[	X
ejpam-371	39	25	2	2	NUM
ejpam-371	39	26	]	]	PUNCT
ejpam-371	39	27	,	,	PUNCT
ejpam-371	39	28	fernandez	fernandez	PROPN
ejpam-371	39	29	-	-	PUNCT
ejpam-371	39	30	cara	cara	PROPN
ejpam-371	39	31	et	et	NOUN
ejpam-371	39	32	al	al	PROPN
ejpam-371	40	1	[	[	X
ejpam-371	40	2	6	6	NUM
ejpam-371	40	3	]	]	PUNCT
ejpam-371	40	4	,	,	PUNCT
ejpam-371	40	5	fursikov	fursikov	NOUN
ejpam-371	40	6	and	and	CCONJ
ejpam-371	40	7	imanuvilov	imanuvilov	NOUN
ejpam-371	41	1	[	[	X
ejpam-371	41	2	7	7	NUM
ejpam-371	41	3	]	]	PUNCT
ejpam-371	41	4	,	,	PUNCT
ejpam-371	41	5	imanuvilov	imanuvilov	NOUN
ejpam-371	42	1	[	[	X
ejpam-371	42	2	8	8	NUM
ejpam-371	42	3	]	]	PUNCT
ejpam-371	42	4	and	and	CCONJ
ejpam-371	42	5	the	the	DET
ejpam-371	42	6	references	reference	NOUN
ejpam-371	42	7	cited	cite	VERB
ejpam-371	42	8	therein	therein	ADV
ejpam-371	42	9	.	.	PUNCT
ejpam-371	43	1	fernandezcara	fernandezcara	NOUN
ejpam-371	43	2	and	and	CCONJ
ejpam-371	43	3	zuazua	zuazua	NOUN
ejpam-371	43	4	[	[	X
ejpam-371	43	5	5	5	NUM
ejpam-371	43	6	]	]	PUNCT
ejpam-371	43	7	studied	study	VERB
ejpam-371	43	8	the	the	DET
ejpam-371	43	9	approximate	approximate	ADJ
ejpam-371	43	10	controllability	controllability	NOUN
ejpam-371	43	11	for	for	ADP
ejpam-371	43	12	heat	heat	NOUN
ejpam-371	43	13	equations	equation	NOUN
ejpam-371	43	14	and	and	CCONJ
ejpam-371	43	15	barbu	barbu	PROPN
ejpam-371	43	16	r.	r.	PROPN
ejpam-371	43	17	lavanya	lavanya	PROPN
ejpam-371	43	18	/	/	SYM
ejpam-371	43	19	eur	eur	PROPN
ejpam-371	43	20	.	.	PUNCT
ejpam-371	44	1	j.	j.	PROPN
ejpam-371	44	2	pure	pure	PROPN
ejpam-371	44	3	appl	appl	PROPN
ejpam-371	44	4	.	.	PROPN
ejpam-371	44	5	math	math	PROPN
ejpam-371	44	6	,	,	PUNCT
ejpam-371	44	7	3	3	NUM
ejpam-371	44	8	(	(	PUNCT
ejpam-371	44	9	2010	2010	NUM
ejpam-371	44	10	)	)	PUNCT
ejpam-371	44	11	,	,	PUNCT
ejpam-371	44	12	235	235	NUM
ejpam-371	44	13	-	-	SYM
ejpam-371	44	14	253	253	NUM
ejpam-371	44	15	237	237	NUM
ejpam-371	44	16	and	and	CCONJ
ejpam-371	44	17	iannelli	iannelli	ADV
ejpam-371	45	1	[	[	X
ejpam-371	45	2	3	3	X
ejpam-371	45	3	]	]	PUNCT
ejpam-371	45	4	discussed	discuss	VERB
ejpam-371	45	5	the	the	DET
ejpam-371	45	6	approximate	approximate	ADJ
ejpam-371	45	7	controllability	controllability	NOUN
ejpam-371	45	8	for	for	ADP
ejpam-371	45	9	the	the	DET
ejpam-371	45	10	system	system	NOUN
ejpam-371	45	11	of	of	ADP
ejpam-371	45	12	the	the	DET
ejpam-371	45	13	form	form	NOUN
ejpam-371	45	14	(	(	PUNCT
ejpam-371	45	15	4	4	NUM
ejpam-371	45	16	)	)	PUNCT
ejpam-371	45	17	with	with	ADP
ejpam-371	45	18	the	the	DET
ejpam-371	45	19	kernel	kernel	PROPN
ejpam-371	45	20	n	n	CCONJ
ejpam-371	45	21	(	(	PUNCT
ejpam-371	45	22	·	·	PUNCT
ejpam-371	45	23	)	)	PUNCT
ejpam-371	46	1	=	=	SYM
ejpam-371	46	2	0	0	X
ejpam-371	46	3	.	.	X
ejpam-371	46	4	sakthivel	sakthivel	NOUN
ejpam-371	46	5	et	et	PROPN
ejpam-371	46	6	al	al	PROPN
ejpam-371	47	1	[	[	X
ejpam-371	47	2	12	12	NUM
ejpam-371	47	3	]	]	PUNCT
ejpam-371	47	4	obtained	obtain	VERB
ejpam-371	47	5	the	the	DET
ejpam-371	47	6	exact	exact	ADJ
ejpam-371	47	7	null	null	ADJ
ejpam-371	47	8	controllability	controllability	NOUN
ejpam-371	47	9	result	result	NOUN
ejpam-371	47	10	by	by	ADP
ejpam-371	47	11	establishing	establish	VERB
ejpam-371	47	12	a	a	DET
ejpam-371	47	13	carleman	carleman	ADJ
ejpam-371	47	14	type	type	NOUN
ejpam-371	47	15	inequality	inequality	NOUN
ejpam-371	47	16	for	for	ADP
ejpam-371	47	17	the	the	DET
ejpam-371	47	18	linear	linear	ADJ
ejpam-371	47	19	parabolic	parabolic	NOUN
ejpam-371	47	20	equation	equation	NOUN
ejpam-371	47	21	(	(	PUNCT
ejpam-371	47	22	taking	take	VERB
ejpam-371	47	23	the	the	DET
ejpam-371	47	24	history	history	NOUN
ejpam-371	47	25	into	into	ADP
ejpam-371	47	26	account	account	NOUN
ejpam-371	47	27	)	)	PUNCT
ejpam-371	47	28	,	,	PUNCT
ejpam-371	47	29	yt	yt	VERB
ejpam-371	47	30	−∆y	−∆y	X
ejpam-371	47	31	+	+	CCONJ
ejpam-371	47	32	∫	∫	PROPN
ejpam-371	47	33	t	t	NOUN
ejpam-371	47	34	0	0	NUM
ejpam-371	47	35	a(t	a(t	PROPN
ejpam-371	47	36	−τ)y(τ	−τ)y(τ	NUM
ejpam-371	47	37	,	,	PUNCT
ejpam-371	47	38	x)dτ	x)dτ	PROPN
ejpam-371	47	39	=	=	NOUN
ejpam-371	47	40	u(t	u(t	NOUN
ejpam-371	47	41	,	,	PUNCT
ejpam-371	47	42	x)+	x)+	NUM
ejpam-371	47	43	l(t	l(t	PROPN
ejpam-371	47	44	,	,	PUNCT
ejpam-371	47	45	x	x	X
ejpam-371	47	46	)	)	PUNCT
ejpam-371	47	47	in	in	ADP
ejpam-371	47	48	q	q	NOUN
ejpam-371	47	49	,	,	PUNCT
ejpam-371	47	50	y(0	y(0	PROPN
ejpam-371	47	51	,	,	PUNCT
ejpam-371	47	52	x	x	NOUN
ejpam-371	47	53	)	)	PUNCT
ejpam-371	47	54	=	=	SYM
ejpam-371	47	55	y0(x	y0(x	NOUN
ejpam-371	47	56	)	)	PUNCT
ejpam-371	47	57	in	in	ADP
ejpam-371	47	58	ω	ω	PROPN
ejpam-371	47	59	,	,	PUNCT
ejpam-371	47	60	α1	α1	PROPN
ejpam-371	47	61	∂	∂	NUM
ejpam-371	47	62	y	y	PROPN
ejpam-371	47	63	∂	∂	NOUN
ejpam-371	47	64	ν	ν	X
ejpam-371	47	65	+	+	CCONJ
ejpam-371	47	66	α2	α2	ADJ
ejpam-371	47	67	y	y	NOUN
ejpam-371	47	68	=	=	NOUN
ejpam-371	47	69	0	0	NUM
ejpam-371	47	70	on	on	ADP
ejpam-371	47	71	σ	σ	PROPN
ejpam-371	47	72	,	,	PUNCT
ejpam-371	47	73	where	where	SCONJ
ejpam-371	47	74	ω⊂	ω⊂	PROPN
ejpam-371	47	75	rn	rn	PROPN
ejpam-371	47	76	is	be	AUX
ejpam-371	47	77	a	a	DET
ejpam-371	47	78	bounded	bounded	ADJ
ejpam-371	47	79	domain	domain	NOUN
ejpam-371	47	80	with	with	ADP
ejpam-371	47	81	boundary	boundary	ADJ
ejpam-371	47	82	∂ω	∂ω	PROPN
ejpam-371	47	83	∈	∈	PROPN
ejpam-371	47	84	c1	c1	NOUN
ejpam-371	47	85	,	,	PUNCT
ejpam-371	47	86	the	the	DET
ejpam-371	47	87	kernel	kernel	PROPN
ejpam-371	47	88	a	a	PRON
ejpam-371	47	89	∈	∈	PROPN
ejpam-371	47	90	c1[0	c1[0	PROPN
ejpam-371	47	91	,	,	PUNCT
ejpam-371	47	92	t	t	X
ejpam-371	47	93	]	]	PUNCT
ejpam-371	47	94	,	,	PUNCT
ejpam-371	47	95	a(0	a(0	PROPN
ejpam-371	47	96	)	)	PUNCT
ejpam-371	47	97	=	=	SYM
ejpam-371	47	98	0	0	NUM
ejpam-371	47	99	and	and	CCONJ
ejpam-371	47	100	α1	α1	PROPN
ejpam-371	47	101	≥	≥	NUM
ejpam-371	47	102	0	0	NUM
ejpam-371	47	103	is	be	AUX
ejpam-371	47	104	a	a	DET
ejpam-371	47	105	constant	constant	ADJ
ejpam-371	47	106	and	and	CCONJ
ejpam-371	47	107	α2	α2	PROPN
ejpam-371	47	108	∈	∈	PROPN
ejpam-371	47	109	c1(σ	c1(σ	NOUN
ejpam-371	47	110	)	)	PUNCT
ejpam-371	47	111	,	,	PUNCT
ejpam-371	47	112	α2	α2	PROPN
ejpam-371	47	113	≥	≥	NOUN
ejpam-371	47	114	0	0	NUM
ejpam-371	47	115	,	,	PUNCT
ejpam-371	47	116	while	while	SCONJ
ejpam-371	47	117	fernandez	fernandez	PROPN
ejpam-371	47	118	-	-	PUNCT
ejpam-371	47	119	cara	cara	PROPN
ejpam-371	47	120	et	et	NOUN
ejpam-371	47	121	al	al	PROPN
ejpam-371	48	1	[	[	X
ejpam-371	48	2	6	6	NUM
ejpam-371	48	3	]	]	PUNCT
ejpam-371	48	4	studied	study	VERB
ejpam-371	48	5	the	the	DET
ejpam-371	48	6	exact	exact	ADJ
ejpam-371	48	7	controllability	controllability	NOUN
ejpam-371	48	8	of	of	ADP
ejpam-371	48	9	the	the	DET
ejpam-371	48	10	parabolic	parabolic	ADJ
ejpam-371	48	11	equation	equation	NOUN
ejpam-371	48	12	of	of	ADP
ejpam-371	48	13	the	the	DET
ejpam-371	48	14	form	form	NOUN
ejpam-371	48	15	,	,	PUNCT
ejpam-371	48	16	yt	yt	VERB
ejpam-371	48	17	−∆y	−∆y	NOUN
ejpam-371	48	18	+	+	CCONJ
ejpam-371	49	1	b(t	b(t	PROPN
ejpam-371	49	2	,	,	PUNCT
ejpam-371	49	3	x)∇y	x)∇y	ADJ
ejpam-371	49	4	+	+	CCONJ
ejpam-371	49	5	a(t	a(t	PROPN
ejpam-371	49	6	,	,	PUNCT
ejpam-371	49	7	x)y	x)y	PUNCT
ejpam-371	50	1	=	=	SYM
ejpam-371	50	2	v(t	v(t	X
ejpam-371	50	3	,	,	PUNCT
ejpam-371	50	4	x)χω	x)χω	PROPN
ejpam-371	50	5	in	in	ADP
ejpam-371	50	6	q	q	NOUN
ejpam-371	50	7	with	with	ADP
ejpam-371	50	8	fourier	fouri	ADJ
ejpam-371	50	9	boundary	boundary	ADJ
ejpam-371	50	10	conditions	condition	NOUN
ejpam-371	50	11	when	when	SCONJ
ejpam-371	50	12	the	the	DET
ejpam-371	50	13	coefficients	coefficient	NOUN
ejpam-371	50	14	a	a	PRON
ejpam-371	50	15	,	,	PUNCT
ejpam-371	50	16	b	b	NOUN
ejpam-371	50	17	and	and	CCONJ
ejpam-371	50	18	α2	α2	PROPN
ejpam-371	50	19	satisfy	satisfy	VERB
ejpam-371	50	20	a	a	DET
ejpam-371	50	21	∈	∈	PROPN
ejpam-371	50	22	l∞(q	l∞(q	NOUN
ejpam-371	50	23	)	)	PUNCT
ejpam-371	50	24	,	,	PUNCT
ejpam-371	50	25	b	b	X
ejpam-371	50	26	∈	∈	PROPN
ejpam-371	50	27	l∞(q	l∞(q	NOUN
ejpam-371	50	28	)	)	PUNCT
ejpam-371	50	29	,	,	PUNCT
ejpam-371	50	30	and	and	CCONJ
ejpam-371	50	31	α2	α2	PROPN
ejpam-371	50	32	∈	∈	PROPN
ejpam-371	50	33	l∞(σ	l∞(σ	NOUN
ejpam-371	50	34	)	)	PUNCT
ejpam-371	50	35	.	.	PUNCT
ejpam-371	51	1	the	the	DET
ejpam-371	51	2	problem	problem	NOUN
ejpam-371	51	3	under	under	ADP
ejpam-371	51	4	consideration	consideration	NOUN
ejpam-371	51	5	is	be	AUX
ejpam-371	51	6	interesting	interesting	ADJ
ejpam-371	51	7	and	and	CCONJ
ejpam-371	51	8	different	different	ADJ
ejpam-371	51	9	from	from	ADP
ejpam-371	51	10	the	the	DET
ejpam-371	51	11	previous	previous	ADJ
ejpam-371	51	12	works	work	NOUN
ejpam-371	51	13	(	(	PUNCT
ejpam-371	51	14	see	see	VERB
ejpam-371	51	15	[	[	X
ejpam-371	51	16	9,10	9,10	NUM
ejpam-371	51	17	]	]	PUNCT
ejpam-371	51	18	)	)	PUNCT
ejpam-371	51	19	because	because	SCONJ
ejpam-371	51	20	the	the	DET
ejpam-371	51	21	derivation	derivation	NOUN
ejpam-371	51	22	of	of	ADP
ejpam-371	51	23	carleman	carleman	ADJ
ejpam-371	51	24	estimate	estimate	NOUN
ejpam-371	51	25	containing	contain	VERB
ejpam-371	51	26	a	a	DET
ejpam-371	51	27	special	special	ADJ
ejpam-371	51	28	type	type	NOUN
ejpam-371	51	29	of	of	ADP
ejpam-371	51	30	integral	integral	ADJ
ejpam-371	51	31	term	term	NOUN
ejpam-371	51	32	for	for	ADP
ejpam-371	51	33	the	the	DET
ejpam-371	51	34	backward	backward	ADJ
ejpam-371	51	35	adjoint	adjoint	PROPN
ejpam-371	51	36	problem	problem	NOUN
ejpam-371	51	37	of	of	ADP
ejpam-371	51	38	(	(	PUNCT
ejpam-371	51	39	4	4	X
ejpam-371	51	40	)	)	PUNCT
ejpam-371	51	41	stated	state	VERB
ejpam-371	51	42	in	in	ADP
ejpam-371	51	43	(	(	PUNCT
ejpam-371	51	44	5	5	NUM
ejpam-371	51	45	)	)	PUNCT
ejpam-371	51	46	require	require	VERB
ejpam-371	51	47	a	a	DET
ejpam-371	51	48	careful	careful	ADJ
ejpam-371	51	49	treatment	treatment	NOUN
ejpam-371	51	50	of	of	ADP
ejpam-371	51	51	the	the	DET
ejpam-371	51	52	surface	surface	NOUN
ejpam-371	51	53	integrals	integral	NOUN
ejpam-371	51	54	to	to	PART
ejpam-371	51	55	guarantee	guarantee	VERB
ejpam-371	51	56	the	the	DET
ejpam-371	51	57	existence	existence	NOUN
ejpam-371	51	58	(	(	PUNCT
ejpam-371	51	59	ie	ie	X
ejpam-371	51	60	.	.	NOUN
ejpam-371	51	61	,	,	PUNCT
ejpam-371	51	62	to	to	PART
ejpam-371	51	63	settle	settle	VERB
ejpam-371	51	64	the	the	DET
ejpam-371	51	65	integral	integral	ADJ
ejpam-371	51	66	term	term	NOUN
ejpam-371	51	67	properly	properly	ADV
ejpam-371	51	68	so	so	SCONJ
ejpam-371	51	69	as	as	SCONJ
ejpam-371	51	70	to	to	PART
ejpam-371	51	71	get	get	VERB
ejpam-371	51	72	the	the	DET
ejpam-371	51	73	same	same	ADJ
ejpam-371	51	74	upper	upper	ADJ
ejpam-371	51	75	bound	bound	NOUN
ejpam-371	51	76	)	)	PUNCT
ejpam-371	51	77	of	of	ADP
ejpam-371	51	78	this	this	DET
ejpam-371	51	79	estimate	estimate	NOUN
ejpam-371	51	80	for	for	ADP
ejpam-371	51	81	the	the	DET
ejpam-371	51	82	parabolic	parabolic	ADJ
ejpam-371	51	83	integrodifferential	integrodifferential	ADJ
ejpam-371	51	84	equations	equation	NOUN
ejpam-371	51	85	.	.	PUNCT
ejpam-371	52	1	throughout	throughout	ADP
ejpam-371	52	2	this	this	DET
ejpam-371	52	3	paper	paper	NOUN
ejpam-371	52	4	we	we	PRON
ejpam-371	52	5	shall	shall	AUX
ejpam-371	52	6	use	use	VERB
ejpam-371	52	7	the	the	DET
ejpam-371	52	8	following	follow	VERB
ejpam-371	52	9	notations	notation	NOUN
ejpam-371	52	10	for	for	ADP
ejpam-371	52	11	general	general	ADJ
ejpam-371	52	12	function	function	NOUN
ejpam-371	52	13	spaces	space	NOUN
ejpam-371	52	14	.	.	PUNCT
ejpam-371	53	1	for	for	ADP
ejpam-371	53	2	each	each	DET
ejpam-371	53	3	positive	positive	ADJ
ejpam-371	53	4	integer	integer	NOUN
ejpam-371	53	5	m	m	NOUN
ejpam-371	53	6	,	,	PUNCT
ejpam-371	53	7	we	we	PRON
ejpam-371	53	8	denote	denote	VERB
ejpam-371	53	9	,	,	PUNCT
ejpam-371	53	10	by	by	ADP
ejpam-371	53	11	hm(ω	hm(ω	NOUN
ejpam-371	53	12	)	)	PUNCT
ejpam-371	53	13	,	,	PUNCT
ejpam-371	53	14	the	the	DET
ejpam-371	53	15	sobolev	sobolev	NOUN
ejpam-371	53	16	spaces	space	NOUN
ejpam-371	53	17	of	of	ADP
ejpam-371	53	18	functions	function	NOUN
ejpam-371	53	19	in	in	ADP
ejpam-371	53	20	l2(ω	l2(ω	NOUN
ejpam-371	53	21	)	)	PUNCT
ejpam-371	53	22	whose	whose	DET
ejpam-371	53	23	weak	weak	ADJ
ejpam-371	53	24	derivatives	derivative	NOUN
ejpam-371	53	25	of	of	ADP
ejpam-371	53	26	order	order	NOUN
ejpam-371	53	27	less	less	ADJ
ejpam-371	53	28	than	than	ADP
ejpam-371	53	29	or	or	CCONJ
ejpam-371	53	30	equal	equal	ADJ
ejpam-371	53	31	to	to	ADP
ejpam-371	53	32	m	m	PROPN
ejpam-371	53	33	are	be	AUX
ejpam-371	53	34	also	also	ADV
ejpam-371	53	35	in	in	ADP
ejpam-371	53	36	l2(ω	l2(ω	NOUN
ejpam-371	53	37	)	)	PUNCT
ejpam-371	53	38	.	.	PUNCT
ejpam-371	54	1	we	we	PRON
ejpam-371	54	2	define	define	VERB
ejpam-371	54	3	l2(0	l2(0	NOUN
ejpam-371	54	4	,	,	PUNCT
ejpam-371	54	5	t	t	NOUN
ejpam-371	54	6	;	;	PUNCT
ejpam-371	54	7	h1(ω	h1(ω	PROPN
ejpam-371	54	8	)	)	PUNCT
ejpam-371	54	9	)	)	PUNCT
ejpam-371	54	10	,	,	PUNCT
ejpam-371	54	11	the	the	DET
ejpam-371	54	12	space	space	NOUN
ejpam-371	54	13	of	of	ADP
ejpam-371	54	14	all	all	DET
ejpam-371	54	15	equivalence	equivalence	NOUN
ejpam-371	54	16	classes	class	NOUN
ejpam-371	54	17	of	of	ADP
ejpam-371	54	18	square	square	ADJ
ejpam-371	54	19	integrable	integrable	ADJ
ejpam-371	54	20	functions	function	NOUN
ejpam-371	54	21	from	from	ADP
ejpam-371	54	22	(	(	PUNCT
ejpam-371	54	23	0	0	NUM
ejpam-371	54	24	,	,	PUNCT
ejpam-371	54	25	t	t	NOUN
ejpam-371	54	26	)	)	PUNCT
ejpam-371	54	27	to	to	ADP
ejpam-371	54	28	h1(ω	h1(ω	PROPN
ejpam-371	54	29	)	)	PUNCT
ejpam-371	54	30	.	.	PUNCT
ejpam-371	55	1	the	the	DET
ejpam-371	55	2	space	space	NOUN
ejpam-371	55	3	l2(0	l2(0	NOUN
ejpam-371	55	4	,	,	PUNCT
ejpam-371	55	5	t	t	NOUN
ejpam-371	55	6	;	;	PUNCT
ejpam-371	55	7	l2(ω	l2(ω	X
ejpam-371	55	8	)	)	PUNCT
ejpam-371	55	9	)	)	PUNCT
ejpam-371	55	10	is	be	AUX
ejpam-371	55	11	analogously	analogously	ADV
ejpam-371	55	12	defined	define	VERB
ejpam-371	55	13	.	.	PUNCT
ejpam-371	56	1	moreover	moreover	ADV
ejpam-371	56	2	,	,	PUNCT
ejpam-371	56	3	we	we	PRON
ejpam-371	56	4	set	set	VERB
ejpam-371	56	5	h1(0	h1(0	PROPN
ejpam-371	56	6	,	,	PUNCT
ejpam-371	56	7	t	t	PROPN
ejpam-371	56	8	;	;	PUNCT
ejpam-371	56	9	l2(ω	l2(ω	X
ejpam-371	56	10	)	)	PUNCT
ejpam-371	56	11	)	)	PUNCT
ejpam-371	57	1	=	=	PRON
ejpam-371	57	2	{	{	PUNCT
ejpam-371	57	3	y	y	PROPN
ejpam-371	57	4	∈	∈	PROPN
ejpam-371	57	5	l2(0	l2(0	NOUN
ejpam-371	57	6	,	,	PUNCT
ejpam-371	57	7	t	t	NOUN
ejpam-371	57	8	;	;	PUNCT
ejpam-371	57	9	l2(ω	l2(ω	X
ejpam-371	57	10	)	)	PUNCT
ejpam-371	57	11	)	)	PUNCT
ejpam-371	57	12	:	:	PUNCT
ejpam-371	58	1	d	d	X
ejpam-371	58	2	y	y	PROPN
ejpam-371	58	3	d	d	X
ejpam-371	58	4	t	t	PROPN
ejpam-371	58	5	∈	∈	PROPN
ejpam-371	58	6	l2(0	l2(0	PROPN
ejpam-371	58	7	,	,	PUNCT
ejpam-371	58	8	t	t	NOUN
ejpam-371	58	9	;	;	PUNCT
ejpam-371	58	10	l2(ω	l2(ω	NOUN
ejpam-371	58	11	)	)	PUNCT
ejpam-371	58	12	)	)	PUNCT
ejpam-371	58	13	}	}	PUNCT
ejpam-371	58	14	,	,	PUNCT
ejpam-371	58	15	h2,1(q	h2,1(q	NOUN
ejpam-371	58	16	)	)	PUNCT
ejpam-371	58	17	=	=	PRON
ejpam-371	58	18	{	{	PUNCT
ejpam-371	58	19	y	y	PROPN
ejpam-371	58	20	∈	∈	PROPN
ejpam-371	58	21	l2(0	l2(0	NOUN
ejpam-371	58	22	,	,	PUNCT
ejpam-371	58	23	t	t	PROPN
ejpam-371	58	24	;	;	PUNCT
ejpam-371	58	25	h1	h1	PROPN
ejpam-371	58	26	0(ω)∩h2(ω	0(ω)∩h2(ω	NUM
ejpam-371	58	27	)	)	PUNCT
ejpam-371	58	28	)	)	PUNCT
ejpam-371	58	29	,	,	PUNCT
ejpam-371	59	1	d	d	NOUN
ejpam-371	59	2	y	y	PROPN
ejpam-371	59	3	d	d	PROPN
ejpam-371	59	4	t	t	PROPN
ejpam-371	59	5	∈	∈	PROPN
ejpam-371	59	6	l2(0	l2(0	PROPN
ejpam-371	59	7	,	,	PUNCT
ejpam-371	59	8	t	t	NOUN
ejpam-371	59	9	;	;	PUNCT
ejpam-371	59	10	l2(ω	l2(ω	NOUN
ejpam-371	59	11	)	)	PUNCT
ejpam-371	59	12	)	)	PUNCT
ejpam-371	59	13	}	}	PUNCT
ejpam-371	59	14	,	,	PUNCT
ejpam-371	59	15	where	where	SCONJ
ejpam-371	59	16	d	d	PROPN
ejpam-371	59	17	y	y	PROPN
ejpam-371	59	18	d	d	PROPN
ejpam-371	59	19	t	t	PROPN
ejpam-371	59	20	is	be	AUX
ejpam-371	59	21	taken	take	VERB
ejpam-371	59	22	in	in	ADP
ejpam-371	59	23	the	the	DET
ejpam-371	59	24	sense	sense	NOUN
ejpam-371	59	25	of	of	ADP
ejpam-371	59	26	distributions	distribution	NOUN
ejpam-371	59	27	.	.	PUNCT
ejpam-371	60	1	for	for	ADP
ejpam-371	60	2	the	the	DET
ejpam-371	60	3	definition	definition	NOUN
ejpam-371	60	4	and	and	CCONJ
ejpam-371	60	5	detailed	detailed	ADJ
ejpam-371	60	6	discussion	discussion	NOUN
ejpam-371	60	7	on	on	ADP
ejpam-371	60	8	these	these	DET
ejpam-371	60	9	spaces	space	NOUN
ejpam-371	60	10	one	one	PRON
ejpam-371	60	11	can	can	AUX
ejpam-371	60	12	refer	refer	VERB
ejpam-371	60	13	[	[	PRON
ejpam-371	60	14	1,13	1,13	NUM
ejpam-371	60	15	]	]	PUNCT
ejpam-371	60	16	.	.	PUNCT
ejpam-371	61	1	the	the	DET
ejpam-371	61	2	paper	paper	NOUN
ejpam-371	61	3	is	be	AUX
ejpam-371	61	4	organized	organize	VERB
ejpam-371	61	5	as	as	SCONJ
ejpam-371	61	6	follows	follow	VERB
ejpam-371	61	7	:	:	PUNCT
ejpam-371	61	8	in	in	ADP
ejpam-371	61	9	section	section	NOUN
ejpam-371	61	10	2	2	NUM
ejpam-371	61	11	we	we	PRON
ejpam-371	61	12	establish	establish	VERB
ejpam-371	61	13	a	a	DET
ejpam-371	61	14	carleman	carleman	ADJ
ejpam-371	61	15	estimate	estimate	NOUN
ejpam-371	61	16	for	for	ADP
ejpam-371	61	17	the	the	DET
ejpam-371	61	18	dual	dual	ADJ
ejpam-371	61	19	problem	problem	NOUN
ejpam-371	61	20	stated	state	VERB
ejpam-371	61	21	in	in	ADP
ejpam-371	61	22	(	(	PUNCT
ejpam-371	61	23	5	5	NUM
ejpam-371	61	24	)	)	PUNCT
ejpam-371	61	25	and	and	CCONJ
ejpam-371	61	26	we	we	PRON
ejpam-371	61	27	deduce	deduce	VERB
ejpam-371	61	28	an	an	DET
ejpam-371	61	29	observability	observability	NOUN
ejpam-371	61	30	inequality	inequality	NOUN
ejpam-371	61	31	.	.	PUNCT
ejpam-371	62	1	in	in	ADP
ejpam-371	62	2	section	section	NOUN
ejpam-371	62	3	3	3	NUM
ejpam-371	62	4	,	,	PUNCT
ejpam-371	62	5	we	we	PRON
ejpam-371	62	6	prove	prove	VERB
ejpam-371	62	7	the	the	DET
ejpam-371	62	8	null	null	ADJ
ejpam-371	62	9	controllability	controllability	NOUN
ejpam-371	62	10	of	of	ADP
ejpam-371	62	11	the	the	DET
ejpam-371	62	12	system	system	NOUN
ejpam-371	62	13	(	(	PUNCT
ejpam-371	62	14	4	4	X
ejpam-371	62	15	)	)	PUNCT
ejpam-371	62	16	making	make	VERB
ejpam-371	62	17	use	use	NOUN
ejpam-371	62	18	of	of	ADP
ejpam-371	62	19	observability	observability	NOUN
ejpam-371	62	20	inequality	inequality	NOUN
ejpam-371	62	21	and	and	CCONJ
ejpam-371	62	22	an	an	DET
ejpam-371	62	23	a	a	DET
ejpam-371	62	24	priori	priori	ADJ
ejpam-371	62	25	estimate	estimate	NOUN
ejpam-371	62	26	for	for	ADP
ejpam-371	62	27	the	the	DET
ejpam-371	62	28	solution	solution	NOUN
ejpam-371	62	29	of	of	ADP
ejpam-371	62	30	the	the	DET
ejpam-371	62	31	system	system	NOUN
ejpam-371	62	32	(	(	PUNCT
ejpam-371	62	33	4	4	NUM
ejpam-371	62	34	)	)	PUNCT
ejpam-371	62	35	.	.	PUNCT
ejpam-371	63	1	r.	r.	PROPN
ejpam-371	63	2	lavanya	lavanya	PROPN
ejpam-371	63	3	/	/	SYM
ejpam-371	63	4	eur	eur	PROPN
ejpam-371	63	5	.	.	PUNCT
ejpam-371	64	1	j.	j.	PROPN
ejpam-371	64	2	pure	pure	PROPN
ejpam-371	64	3	appl	appl	PROPN
ejpam-371	64	4	.	.	PROPN
ejpam-371	64	5	math	math	PROPN
ejpam-371	64	6	,	,	PUNCT
ejpam-371	64	7	3	3	NUM
ejpam-371	64	8	(	(	PUNCT
ejpam-371	64	9	2010	2010	NUM
ejpam-371	64	10	)	)	PUNCT
ejpam-371	64	11	,	,	PUNCT
ejpam-371	64	12	235	235	NUM
ejpam-371	64	13	-	-	SYM
ejpam-371	64	14	253	253	NUM
ejpam-371	64	15	238	238	NUM
ejpam-371	64	16	2	2	NUM
ejpam-371	64	17	.	.	PUNCT
ejpam-371	64	18	carleman	carleman	ADJ
ejpam-371	64	19	and	and	CCONJ
ejpam-371	64	20	observability	observability	NOUN
ejpam-371	64	21	inequalities	inequality	NOUN
ejpam-371	64	22	in	in	ADP
ejpam-371	64	23	this	this	DET
ejpam-371	64	24	section	section	NOUN
ejpam-371	64	25	we	we	PRON
ejpam-371	64	26	shall	shall	AUX
ejpam-371	64	27	obtain	obtain	VERB
ejpam-371	64	28	a	a	DET
ejpam-371	64	29	carleman	carleman	ADJ
ejpam-371	64	30	inequality	inequality	NOUN
ejpam-371	64	31	and	and	CCONJ
ejpam-371	64	32	an	an	DET
ejpam-371	64	33	observability	observability	NOUN
ejpam-371	64	34	estimate	estimate	NOUN
ejpam-371	64	35	for	for	ADP
ejpam-371	64	36	the	the	DET
ejpam-371	64	37	following	follow	VERB
ejpam-371	64	38	adjoint	adjoint	NOUN
ejpam-371	64	39	system	system	NOUN
ejpam-371	64	40	associated	associate	VERB
ejpam-371	64	41	with	with	ADP
ejpam-371	64	42	(	(	PUNCT
ejpam-371	64	43	4	4	NUM
ejpam-371	64	44	)	)	PUNCT
ejpam-371	64	45	,	,	PUNCT
ejpam-371	64	46	qt	qt	ADP
ejpam-371	64	47	+	+	NOUN
ejpam-371	64	48	∆q+m	∆q+m	PROPN
ejpam-371	64	49	t	t	PROPN
ejpam-371	64	50	t	t	PROPN
ejpam-371	64	51	∗∆q(t	∗∆q(t	ADV
ejpam-371	64	52	)	)	PUNCT
ejpam-371	65	1	+	+	CCONJ
ejpam-371	65	2	n	n	NUM
ejpam-371	65	3	t	t	NOUN
ejpam-371	65	4	t	t	NOUN
ejpam-371	65	5	∗	∗	NOUN
ejpam-371	65	6	qt(t	qt(t	NUM
ejpam-371	65	7	)	)	PUNCT
ejpam-371	66	1	=	=	SYM
ejpam-371	66	2	g	g	NOUN
ejpam-371	66	3	in	in	ADP
ejpam-371	66	4	q	q	PROPN
ejpam-371	66	5	q(t	q(t	PROPN
ejpam-371	66	6	,	,	PUNCT
ejpam-371	66	7	x	x	NOUN
ejpam-371	66	8	)	)	PUNCT
ejpam-371	66	9	=	=	SYM
ejpam-371	66	10	qt	qt	NOUN
ejpam-371	66	11	(	(	PUNCT
ejpam-371	66	12	x	x	NOUN
ejpam-371	66	13	)	)	PUNCT
ejpam-371	66	14	in	in	ADP
ejpam-371	66	15	ω	ω	PROPN
ejpam-371	66	16	q(t	q(t	PROPN
ejpam-371	66	17	,	,	PUNCT
ejpam-371	66	18	x	x	NOUN
ejpam-371	66	19	)	)	PUNCT
ejpam-371	66	20	=	=	SYM
ejpam-371	66	21	0	0	NUM
ejpam-371	67	1	on	on	ADP
ejpam-371	67	2	σ	σ	PROPN
ejpam-371	67	3	,	,	PUNCT
ejpam-371	67	4			PROPN
ejpam-371	67	5			PROPN
ejpam-371	67	6			NOUN
ejpam-371	67	7	(	(	PUNCT
ejpam-371	67	8	5	5	NUM
ejpam-371	67	9	)	)	PUNCT
ejpam-371	67	10	where	where	SCONJ
ejpam-371	67	11	qt	qt	ADP
ejpam-371	67	12	∈	∈	PROPN
ejpam-371	67	13	l2(ω	l2(ω	PROPN
ejpam-371	67	14	)	)	PUNCT
ejpam-371	67	15	,	,	PUNCT
ejpam-371	67	16	g	g	PROPN
ejpam-371	67	17	∈	∈	PROPN
ejpam-371	67	18	l2(q	l2(q	PROPN
ejpam-371	67	19	)	)	PUNCT
ejpam-371	67	20	and	and	CCONJ
ejpam-371	67	21	m	m	PROPN
ejpam-371	67	22	t	t	NOUN
ejpam-371	67	23	t	t	PROPN
ejpam-371	67	24	∗∆q	∗∆q	PROPN
ejpam-371	67	25	,	,	PUNCT
ejpam-371	67	26	n	n	PROPN
ejpam-371	67	27	t	t	NOUN
ejpam-371	67	28	t	t	PROPN
ejpam-371	67	29	∗	∗	NOUN
ejpam-371	67	30	qt	qt	NOUN
ejpam-371	67	31	are	be	AUX
ejpam-371	67	32	the	the	DET
ejpam-371	67	33	corresponding	corresponding	ADJ
ejpam-371	67	34	adjoint	adjoint	NOUN
ejpam-371	67	35	integrals	integral	NOUN
ejpam-371	67	36	,	,	PUNCT
ejpam-371	67	37	that	that	ADV
ejpam-371	67	38	is	is	ADV
ejpam-371	67	39	,	,	PUNCT
ejpam-371	67	40	m	m	VERB
ejpam-371	67	41	t	t	NOUN
ejpam-371	67	42	t	t	PROPN
ejpam-371	67	43	∗∆q(t	∗∆q(t	ADJ
ejpam-371	67	44	)	)	PUNCT
ejpam-371	68	1	=	=	SYM
ejpam-371	69	1	∫	∫	PROPN
ejpam-371	69	2	t	t	PROPN
ejpam-371	69	3	t	t	PROPN
ejpam-371	69	4	m(τ	m(τ	PROPN
ejpam-371	69	5	,	,	PUNCT
ejpam-371	69	6	t)∆q(τ)dτ	t)∆q(τ)dτ	PROPN
ejpam-371	69	7	,	,	PUNCT
ejpam-371	69	8	n	n	PROPN
ejpam-371	69	9	t	t	NOUN
ejpam-371	69	10	t	t	NOUN
ejpam-371	69	11	∗	∗	NOUN
ejpam-371	69	12	qt(t	qt(t	NUM
ejpam-371	69	13	)	)	PUNCT
ejpam-371	70	1	=	=	SYM
ejpam-371	70	2	∫	∫	PROPN
ejpam-371	70	3	t	t	PROPN
ejpam-371	70	4	t	t	PROPN
ejpam-371	70	5	n(τ	n(τ	PROPN
ejpam-371	70	6	,	,	PUNCT
ejpam-371	70	7	t)qτ(τ)dτ	t)qτ(τ)dτ	PROPN
ejpam-371	70	8	.	.	PUNCT
ejpam-371	71	1	to	to	PART
ejpam-371	71	2	formulate	formulate	VERB
ejpam-371	71	3	our	our	PRON
ejpam-371	71	4	results	result	NOUN
ejpam-371	71	5	,	,	PUNCT
ejpam-371	71	6	we	we	PRON
ejpam-371	71	7	give	give	VERB
ejpam-371	71	8	some	some	PRON
ejpam-371	71	9	of	of	ADP
ejpam-371	71	10	the	the	DET
ejpam-371	71	11	frequently	frequently	ADV
ejpam-371	71	12	used	use	VERB
ejpam-371	71	13	notations	notation	NOUN
ejpam-371	71	14	,	,	PUNCT
ejpam-371	71	15	following	follow	VERB
ejpam-371	71	16	the	the	DET
ejpam-371	71	17	idea	idea	NOUN
ejpam-371	71	18	used	use	VERB
ejpam-371	71	19	in	in	ADP
ejpam-371	71	20	[	[	X
ejpam-371	71	21	7	7	NUM
ejpam-371	71	22	]	]	PUNCT
ejpam-371	71	23	,	,	PUNCT
ejpam-371	71	24	which	which	PRON
ejpam-371	71	25	provide	provide	VERB
ejpam-371	71	26	a	a	DET
ejpam-371	71	27	fundamental	fundamental	ADJ
ejpam-371	71	28	tool	tool	NOUN
ejpam-371	71	29	in	in	ADP
ejpam-371	71	30	proving	prove	VERB
ejpam-371	71	31	the	the	DET
ejpam-371	71	32	carleman	carleman	ADJ
ejpam-371	71	33	type	type	NOUN
ejpam-371	71	34	estimates	estimate	NOUN
ejpam-371	71	35	.	.	PUNCT
ejpam-371	72	1	let	let	VERB
ejpam-371	72	2	ω0	ω0	PRON
ejpam-371	72	3	⋐ω	⋐ω	NOUN
ejpam-371	72	4	be	be	AUX
ejpam-371	72	5	a	a	DET
ejpam-371	72	6	suitably	suitably	ADV
ejpam-371	72	7	fixed	fix	VERB
ejpam-371	72	8	sub	sub	NOUN
ejpam-371	72	9	domain	domain	NOUN
ejpam-371	72	10	.	.	PUNCT
ejpam-371	73	1	then	then	ADV
ejpam-371	73	2	there	there	PRON
ejpam-371	73	3	exists	exist	VERB
ejpam-371	73	4	a	a	DET
ejpam-371	73	5	function	function	NOUN
ejpam-371	73	6	ψ	ψ	X
ejpam-371	73	7	∈	∈	PROPN
ejpam-371	73	8	c2(ω	c2(ω	NUM
ejpam-371	73	9	)	)	PUNCT
ejpam-371	73	10	such	such	ADJ
ejpam-371	73	11	that	that	DET
ejpam-371	73	12	ψ(x	ψ(x	NOUN
ejpam-371	73	13	)	)	PUNCT
ejpam-371	73	14	>	>	X
ejpam-371	73	15	0	0	NUM
ejpam-371	73	16	∀	∀	NOUN
ejpam-371	73	17	x	x	X
ejpam-371	73	18	∈	∈	PROPN
ejpam-371	73	19	ω	ω	PROPN
ejpam-371	73	20	,	,	PUNCT
ejpam-371	73	21	ψ|∂ω	ψ|∂ω	NOUN
ejpam-371	73	22	=	=	SYM
ejpam-371	73	23	0	0	NUM
ejpam-371	73	24	,	,	PUNCT
ejpam-371	73	25	|∇ψ(x)|	|∇ψ(x)|	VERB
ejpam-371	73	26	>	>	X
ejpam-371	73	27	0	0	NUM
ejpam-371	73	28	∀	∀	NOUN
ejpam-371	73	29	x	x	SYM
ejpam-371	73	30	∈	∈	NOUN
ejpam-371	73	31	ω\ω0	ω\ω0	VERB
ejpam-371	73	32	.	.	PUNCT
ejpam-371	74	1	we	we	PRON
ejpam-371	74	2	define	define	VERB
ejpam-371	74	3	two	two	NUM
ejpam-371	74	4	weight	weight	NOUN
ejpam-371	74	5	functions	function	NOUN
ejpam-371	74	6	that	that	PRON
ejpam-371	74	7	will	will	AUX
ejpam-371	74	8	be	be	AUX
ejpam-371	74	9	used	use	VERB
ejpam-371	74	10	throughout	throughout	ADP
ejpam-371	74	11	this	this	DET
ejpam-371	74	12	paper	paper	NOUN
ejpam-371	74	13	as	as	SCONJ
ejpam-371	74	14	follows	follow	VERB
ejpam-371	74	15	:	:	PUNCT
ejpam-371	74	16	for	for	ADP
ejpam-371	74	17	fixed	fixed	ADJ
ejpam-371	74	18	λ	λ	PROPN
ejpam-371	74	19	>	>	X
ejpam-371	74	20	0	0	PUNCT
ejpam-371	74	21	and	and	CCONJ
ejpam-371	74	22	the	the	DET
ejpam-371	74	23	function	function	NOUN
ejpam-371	74	24	ψ	ψ	NOUN
ejpam-371	74	25	defined	define	VERB
ejpam-371	74	26	above	above	ADV
ejpam-371	74	27	,	,	PUNCT
ejpam-371	74	28	we	we	PRON
ejpam-371	74	29	introduce	introduce	VERB
ejpam-371	74	30	functions	function	NOUN
ejpam-371	74	31	φ	φ	NOUN
ejpam-371	74	32	,	,	PUNCT
ejpam-371	74	33	α	α	X
ejpam-371	74	34	:	:	PUNCT
ejpam-371	74	35	q→	q→	NUM
ejpam-371	74	36	r	r	NOUN
ejpam-371	74	37	defined	define	VERB
ejpam-371	74	38	by	by	ADP
ejpam-371	74	39	the	the	DET
ejpam-371	74	40	formulas	formula	NOUN
ejpam-371	74	41	φ(t	φ(t	PROPN
ejpam-371	74	42	,	,	PUNCT
ejpam-371	74	43	x	x	X
ejpam-371	74	44	)	)	PUNCT
ejpam-371	74	45	=	=	SYM
ejpam-371	74	46	eλψ(x	eλψ(x	NOUN
ejpam-371	74	47	)	)	PUNCT
ejpam-371	74	48	ξ(t	ξ(t	NOUN
ejpam-371	74	49	)	)	PUNCT
ejpam-371	74	50	,	,	PUNCT
ejpam-371	74	51	α(t	α(t	PROPN
ejpam-371	74	52	,	,	PUNCT
ejpam-371	74	53	x	x	NOUN
ejpam-371	74	54	)	)	PUNCT
ejpam-371	74	55	=	=	SYM
ejpam-371	74	56	e2λψ(x	e2λψ(x	PROPN
ejpam-371	74	57	)	)	PUNCT
ejpam-371	74	58	−	−	NOUN
ejpam-371	74	59	eλψ	eλψ	VERB
ejpam-371	74	60	ξ(t	ξ(t	NOUN
ejpam-371	74	61	)	)	PUNCT
ejpam-371	74	62	,	,	PUNCT
ejpam-371	74	63	where	where	SCONJ
ejpam-371	74	64	ξ(t	ξ(t	NOUN
ejpam-371	74	65	)	)	PUNCT
ejpam-371	74	66	=	=	SYM
ejpam-371	75	1	t(t	t(t	NOUN
ejpam-371	75	2	−	−	PROPN
ejpam-371	75	3	t	t	PROPN
ejpam-371	75	4	)	)	PUNCT
ejpam-371	75	5	and	and	CCONJ
ejpam-371	75	6	ψ	ψ	X
ejpam-371	75	7	=	=	SYM
ejpam-371	75	8	‖ψ(x)‖c(ω	‖ψ(x)‖c(ω	X
ejpam-371	75	9	)	)	PUNCT
ejpam-371	75	10	.	.	PUNCT
ejpam-371	76	1	moreover	moreover	ADV
ejpam-371	76	2	,	,	PUNCT
ejpam-371	76	3	in	in	ADP
ejpam-371	76	4	proving	prove	VERB
ejpam-371	76	5	the	the	DET
ejpam-371	76	6	main	main	ADJ
ejpam-371	76	7	inequality	inequality	NOUN
ejpam-371	76	8	,	,	PUNCT
ejpam-371	76	9	we	we	PRON
ejpam-371	76	10	need	need	VERB
ejpam-371	76	11	the	the	DET
ejpam-371	76	12	following	follow	VERB
ejpam-371	76	13	estimates	estimate	NOUN
ejpam-371	76	14	for	for	ADP
ejpam-371	76	15	the	the	DET
ejpam-371	76	16	functions	function	NOUN
ejpam-371	76	17	φ	φ	PROPN
ejpam-371	76	18	and	and	CCONJ
ejpam-371	76	19	α	α	NOUN
ejpam-371	76	20	:	:	PUNCT
ejpam-371	76	21	�	�	PROPN
ejpam-371	76	22	�	�	PROPN
ejpam-371	76	23	∂	∂	NUM
ejpam-371	76	24	φ	φ	PROPN
ejpam-371	76	25	∂	∂	PROPN
ejpam-371	76	26	t	t	PROPN
ejpam-371	76	27	�	�	PROPN
ejpam-371	76	28	�	�	PROPN
ejpam-371	76	29	=	=	SYM
ejpam-371	76	30	|t−2t|	|t−2t|	PROPN
ejpam-371	76	31	t2(t−t)2	t2(t−t)2	ADV
ejpam-371	76	32	eλψ	eλψ	VERB
ejpam-371	76	33	≤	≤	PROPN
ejpam-371	76	34	c(ω	c(ω	PROPN
ejpam-371	76	35	,	,	PUNCT
ejpam-371	76	36	ω)tφ2	ω)tφ2	NUM
ejpam-371	76	37	�	�	PROPN
ejpam-371	76	38	�	�	PROPN
ejpam-371	76	39	∂	∂	NUM
ejpam-371	76	40	α	α	PROPN
ejpam-371	76	41	∂	∂	NOUN
ejpam-371	76	42	t	t	PROPN
ejpam-371	76	43	�	�	PROPN
ejpam-371	76	44	�	�	PROPN
ejpam-371	76	45	=	=	SYM
ejpam-371	76	46	|t−2t|	|t−2t|	PROPN
ejpam-371	76	47	t2(t−t)2	t2(t−t)2	ADP
ejpam-371	76	48	|e2λψ	|e2λψ	PROPN
ejpam-371	76	49	−	−	PROPN
ejpam-371	76	50	eλψ|	eλψ|	NOUN
ejpam-371	76	51	≤	≤	PROPN
ejpam-371	76	52	c(ω	c(ω	PROPN
ejpam-371	76	53	,	,	PUNCT
ejpam-371	76	54	ω	ω	NOUN
ejpam-371	76	55	)	)	PUNCT
ejpam-371	76	56	teλψ	teλψ	NOUN
ejpam-371	76	57	t2(t−t)2	t2(t−t)2	ADJ
ejpam-371	76	58	)	)	PUNCT
ejpam-371	76	59	≤	≤	NOUN
ejpam-371	77	1	c(ω	c(ω	PROPN
ejpam-371	77	2	,	,	PUNCT
ejpam-371	77	3	ω)tφ2	ω)tφ2	NUM
ejpam-371	77	4	�	�	PROPN
ejpam-371	77	5	�	�	PROPN
ejpam-371	77	6	∂	∂	NUM
ejpam-371	77	7	2α	2α	PROPN
ejpam-371	77	8	∂	∂	NUM
ejpam-371	77	9	t2	t2	PROPN
ejpam-371	77	10	�	�	PROPN
ejpam-371	77	11	�	�	PROPN
ejpam-371	77	12	=	=	PUNCT
ejpam-371	77	13	|2t2−6	|2t2−6	PROPN
ejpam-371	77	14	t	t	NOUN
ejpam-371	77	15	t+6t2	t+6t2	NOUN
ejpam-371	77	16	|	|	ADV
ejpam-371	77	17	t3(t−t)3	t3(t−t)3	NOUN
ejpam-371	77	18	|e2λψ	|e2λψ	PUNCT
ejpam-371	77	19	−	−	NOUN
ejpam-371	77	20	eλψ|	eλψ|	NOUN
ejpam-371	77	21	≤	≤	PROPN
ejpam-371	77	22	c(ω	c(ω	PROPN
ejpam-371	77	23	,	,	PUNCT
ejpam-371	77	24	ω)t	ω)t	NOUN
ejpam-371	77	25	2φ3	2φ3	PROPN
ejpam-371	77	26			PROPN
ejpam-371	77	27			PROPN
ejpam-371	77	28			NOUN
ejpam-371	77	29	(	(	PUNCT
ejpam-371	77	30	6	6	NUM
ejpam-371	77	31	)	)	PUNCT
ejpam-371	77	32	where	where	SCONJ
ejpam-371	77	33	c(ω	c(ω	PROPN
ejpam-371	77	34	,	,	PUNCT
ejpam-371	77	35	ω	ω	NOUN
ejpam-371	77	36	)	)	PUNCT
ejpam-371	77	37	is	be	AUX
ejpam-371	77	38	a	a	DET
ejpam-371	77	39	generic	generic	ADJ
ejpam-371	77	40	constant	constant	ADJ
ejpam-371	77	41	.	.	PUNCT
ejpam-371	78	1	throughout	throughout	ADP
ejpam-371	78	2	the	the	DET
ejpam-371	78	3	proof	proof	NOUN
ejpam-371	78	4	of	of	ADP
ejpam-371	78	5	the	the	DET
ejpam-371	78	6	estimate	estimate	NOUN
ejpam-371	78	7	,	,	PUNCT
ejpam-371	78	8	we	we	PRON
ejpam-371	78	9	use	use	VERB
ejpam-371	78	10	c(ω	c(ω	PROPN
ejpam-371	78	11	,	,	PUNCT
ejpam-371	78	12	ω	ω	NOUN
ejpam-371	78	13	)	)	PUNCT
ejpam-371	78	14	,	,	PUNCT
ejpam-371	78	15	the	the	DET
ejpam-371	78	16	generic	generic	ADJ
ejpam-371	78	17	constant	constant	NOUN
ejpam-371	78	18	for	for	ADP
ejpam-371	78	19	all	all	DET
ejpam-371	78	20	the	the	DET
ejpam-371	78	21	space	space	NOUN
ejpam-371	78	22	derivatives	derivative	NOUN
ejpam-371	78	23	of	of	ADP
ejpam-371	78	24	ψ	ψ	PROPN
ejpam-371	78	25	.	.	PUNCT
ejpam-371	79	1	one	one	PRON
ejpam-371	79	2	can	can	AUX
ejpam-371	79	3	also	also	ADV
ejpam-371	79	4	easily	easily	ADV
ejpam-371	79	5	verify	verify	VERB
ejpam-371	79	6	the	the	DET
ejpam-371	79	7	identities	identity	NOUN
ejpam-371	79	8	which	which	PRON
ejpam-371	79	9	will	will	AUX
ejpam-371	79	10	be	be	AUX
ejpam-371	79	11	used	use	VERB
ejpam-371	79	12	in	in	ADP
ejpam-371	79	13	the	the	DET
ejpam-371	79	14	sequel	sequel	NOUN
ejpam-371	79	15	are	be	AUX
ejpam-371	79	16	∇φ	∇φ	PROPN
ejpam-371	79	17	=	=	SYM
ejpam-371	79	18	λφ∇ψ	λφ∇ψ	PROPN
ejpam-371	79	19	,	,	PUNCT
ejpam-371	79	20	∇α=	∇α=	PROPN
ejpam-371	79	21	−λφ∇ψ	−λφ∇ψ	PROPN
ejpam-371	79	22	.	.	PUNCT
ejpam-371	80	1	r.	r.	PROPN
ejpam-371	80	2	lavanya	lavanya	PROPN
ejpam-371	80	3	/	/	SYM
ejpam-371	80	4	eur	eur	PROPN
ejpam-371	80	5	.	.	PUNCT
ejpam-371	81	1	j.	j.	PROPN
ejpam-371	81	2	pure	pure	PROPN
ejpam-371	81	3	appl	appl	PROPN
ejpam-371	81	4	.	.	PROPN
ejpam-371	81	5	math	math	PROPN
ejpam-371	81	6	,	,	PUNCT
ejpam-371	81	7	3	3	NUM
ejpam-371	81	8	(	(	PUNCT
ejpam-371	81	9	2010	2010	NUM
ejpam-371	81	10	)	)	PUNCT
ejpam-371	81	11	,	,	PUNCT
ejpam-371	81	12	235	235	NUM
ejpam-371	81	13	-	-	SYM
ejpam-371	81	14	253	253	NUM
ejpam-371	81	15	239	239	NUM
ejpam-371	81	16	now	now	ADV
ejpam-371	81	17	we	we	PRON
ejpam-371	81	18	are	be	AUX
ejpam-371	81	19	ready	ready	ADJ
ejpam-371	81	20	to	to	PART
ejpam-371	81	21	state	state	VERB
ejpam-371	81	22	and	and	CCONJ
ejpam-371	81	23	prove	prove	VERB
ejpam-371	81	24	the	the	DET
ejpam-371	81	25	main	main	ADJ
ejpam-371	81	26	estimate	estimate	NOUN
ejpam-371	81	27	of	of	ADP
ejpam-371	81	28	this	this	DET
ejpam-371	81	29	section	section	NOUN
ejpam-371	81	30	.	.	PUNCT
ejpam-371	82	1	though	though	SCONJ
ejpam-371	82	2	the	the	DET
ejpam-371	82	3	proof	proof	NOUN
ejpam-371	82	4	of	of	ADP
ejpam-371	82	5	this	this	DET
ejpam-371	82	6	estimate	estimate	NOUN
ejpam-371	82	7	follows	follow	VERB
ejpam-371	82	8	standard	standard	ADJ
ejpam-371	82	9	technique	technique	NOUN
ejpam-371	82	10	for	for	ADP
ejpam-371	82	11	general	general	ADJ
ejpam-371	82	12	parabolic	parabolic	NOUN
ejpam-371	82	13	equations	equation	NOUN
ejpam-371	82	14	without	without	ADP
ejpam-371	82	15	memory	memory	NOUN
ejpam-371	82	16	,	,	PUNCT
ejpam-371	82	17	we	we	PRON
ejpam-371	82	18	have	have	VERB
ejpam-371	82	19	to	to	PART
ejpam-371	82	20	do	do	VERB
ejpam-371	82	21	careful	careful	ADJ
ejpam-371	82	22	calculations	calculation	NOUN
ejpam-371	82	23	on	on	ADP
ejpam-371	82	24	the	the	DET
ejpam-371	82	25	memory	memory	NOUN
ejpam-371	82	26	integrals	integral	NOUN
ejpam-371	82	27	which	which	PRON
ejpam-371	82	28	involves	involve	VERB
ejpam-371	82	29	second	second	ADJ
ejpam-371	82	30	derivative	derivative	NOUN
ejpam-371	82	31	in	in	ADP
ejpam-371	82	32	spatial	spatial	ADJ
ejpam-371	82	33	variable	variable	NOUN
ejpam-371	82	34	as	as	ADV
ejpam-371	82	35	well	well	ADV
ejpam-371	82	36	as	as	ADP
ejpam-371	82	37	first	first	ADJ
ejpam-371	82	38	derivative	derivative	NOUN
ejpam-371	82	39	in	in	ADP
ejpam-371	82	40	time	time	NOUN
ejpam-371	82	41	variable	variable	NOUN
ejpam-371	82	42	.	.	PUNCT
ejpam-371	83	1	theorem	theorem	NOUN
ejpam-371	83	2	1	1	NUM
ejpam-371	83	3	.	.	X
ejpam-371	84	1	for	for	ADP
ejpam-371	84	2	any	any	DET
ejpam-371	84	3	solution	solution	NOUN
ejpam-371	84	4	q	q	PROPN
ejpam-371	84	5	of	of	ADP
ejpam-371	84	6	the	the	DET
ejpam-371	84	7	dual	dual	ADJ
ejpam-371	84	8	problem	problem	NOUN
ejpam-371	84	9	(	(	PUNCT
ejpam-371	84	10	5	5	NUM
ejpam-371	84	11	)	)	PUNCT
ejpam-371	84	12	with	with	ADP
ejpam-371	84	13	the	the	DET
ejpam-371	84	14	kernels	kernels	PROPN
ejpam-371	84	15	m	m	PROPN
ejpam-371	84	16	(	(	PUNCT
ejpam-371	84	17	·	·	PUNCT
ejpam-371	84	18	,	,	PUNCT
ejpam-371	84	19	·	·	PUNCT
ejpam-371	84	20	)	)	PUNCT
ejpam-371	84	21	and	and	CCONJ
ejpam-371	84	22	n	n	CCONJ
ejpam-371	84	23	(	(	PUNCT
ejpam-371	84	24	·	·	PUNCT
ejpam-371	84	25	,	,	PUNCT
ejpam-371	84	26	·	·	PUNCT
ejpam-371	84	27	)	)	PUNCT
ejpam-371	84	28	have	have	VERB
ejpam-371	84	29	support	support	NOUN
ejpam-371	84	30	in	in	ADP
ejpam-371	84	31	(	(	PUNCT
ejpam-371	84	32	t0	t0	PROPN
ejpam-371	84	33	,	,	PUNCT
ejpam-371	84	34	t1	t1	PROPN
ejpam-371	84	35	)	)	PUNCT
ejpam-371	84	36	,	,	PUNCT
ejpam-371	84	37	where	where	SCONJ
ejpam-371	84	38	0	0	X
ejpam-371	84	39	<	<	X
ejpam-371	84	40	t0	t0	X
ejpam-371	84	41	<	<	X
ejpam-371	84	42	t1	t1	PROPN
ejpam-371	84	43	<	<	X
ejpam-371	84	44	t	t	PROPN
ejpam-371	84	45	,	,	PUNCT
ejpam-371	84	46	there	there	PRON
ejpam-371	84	47	exist	exist	VERB
ejpam-371	84	48	λ0	λ0	NOUN
ejpam-371	84	49	,	,	PUNCT
ejpam-371	84	50	s0	s0	NOUN
ejpam-371	84	51	and	and	CCONJ
ejpam-371	84	52	c	c	NOUN
ejpam-371	84	53	,	,	PUNCT
ejpam-371	84	54	the	the	DET
ejpam-371	84	55	constant	constant	ADJ
ejpam-371	84	56	depending	depend	VERB
ejpam-371	84	57	on	on	ADP
ejpam-371	84	58	ω	ω	PROPN
ejpam-371	84	59	,	,	PUNCT
ejpam-371	84	60	ω	ω	PROPN
ejpam-371	84	61	,	,	PUNCT
ejpam-371	84	62	λ	λ	PROPN
ejpam-371	84	63	and	and	CCONJ
ejpam-371	84	64	t	t	PROPN
ejpam-371	84	65	such	such	ADJ
ejpam-371	84	66	that	that	PRON
ejpam-371	84	67	for	for	ADP
ejpam-371	84	68	every	every	DET
ejpam-371	84	69	λ≥	λ≥	ADJ
ejpam-371	84	70	λ0	λ0	NOUN
ejpam-371	84	71	,	,	PUNCT
ejpam-371	84	72	s	s	PART
ejpam-371	84	73	≥	≥	NOUN
ejpam-371	84	74	s0	s0	NOUN
ejpam-371	84	75	the	the	DET
ejpam-371	84	76	following	follow	VERB
ejpam-371	84	77	inequality	inequality	NOUN
ejpam-371	84	78	holds	hold	VERB
ejpam-371	84	79	:	:	PUNCT
ejpam-371	84	80	lq	lq	PROPN
ejpam-371	84	81	,	,	PUNCT
ejpam-371	84	82	s	s	NOUN
ejpam-371	84	83	,	,	PUNCT
ejpam-371	84	84	φ(q)≤	φ(q)≤	NOUN
ejpam-371	85	1	c	c	VERB
ejpam-371	85	2	�	�	PROPN
ejpam-371	86	1	∫∫	∫∫	ADV
ejpam-371	86	2	(	(	PUNCT
ejpam-371	86	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	86	4	e−2sαs3φ3|q|2d	e−2sαs3φ3|q|2d	VERB
ejpam-371	86	5	xd	xd	INTJ
ejpam-371	86	6	t	t	NOUN
ejpam-371	86	7	+	+	CCONJ
ejpam-371	87	1	∫∫	∫∫	ADV
ejpam-371	87	2	q	q	PROPN
ejpam-371	88	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	88	2	xd	xd	PROPN
ejpam-371	88	3	t	t	PROPN
ejpam-371	88	4	�	�	PROPN
ejpam-371	88	5	,	,	PUNCT
ejpam-371	88	6	(	(	PUNCT
ejpam-371	88	7	7	7	X
ejpam-371	88	8	)	)	PUNCT
ejpam-371	88	9	where	where	SCONJ
ejpam-371	88	10	we	we	PRON
ejpam-371	88	11	used	use	VERB
ejpam-371	88	12	the	the	DET
ejpam-371	88	13	notation	notation	NOUN
ejpam-371	88	14	lq	lq	NOUN
ejpam-371	88	15	,	,	PUNCT
ejpam-371	88	16	s	s	NOUN
ejpam-371	88	17	,	,	PUNCT
ejpam-371	88	18	φ(q	φ(q	NUM
ejpam-371	88	19	)	)	PUNCT
ejpam-371	88	20	=	=	PUNCT
ejpam-371	89	1	∫∫	∫∫	ADV
ejpam-371	89	2	q	q	NOUN
ejpam-371	89	3	(	(	PUNCT
ejpam-371	89	4	sφ)−1	sφ)−1	ADP
ejpam-371	89	5	�	�	PROPN
ejpam-371	89	6	|qt	|qt	NUM
ejpam-371	89	7	|2	|2	NUM
ejpam-371	89	8	+	+	NUM
ejpam-371	89	9	|∆q|2	|∆q|2	NOUN
ejpam-371	89	10	+	+	SYM
ejpam-371	89	11	�	�	PROPN
ejpam-371	89	12	�	�	PROPN
ejpam-371	89	13	m	m	PROPN
ejpam-371	89	14	t	t	PROPN
ejpam-371	89	15	t	t	PROPN
ejpam-371	89	16	∗∆q(t	∗∆q(t	ADJ
ejpam-371	89	17	)	)	PUNCT
ejpam-371	89	18	�	�	PROPN
ejpam-371	89	19	�	�	PROPN
ejpam-371	89	20	2	2	NUM
ejpam-371	89	21	+	+	NUM
ejpam-371	89	22	�	�	PROPN
ejpam-371	89	23	�	�	PROPN
ejpam-371	89	24	n	n	ADP
ejpam-371	89	25	t	t	NOUN
ejpam-371	89	26	t	t	PROPN
ejpam-371	89	27	∗	∗	NOUN
ejpam-371	89	28	qt(t	qt(t	NOUN
ejpam-371	89	29	)	)	PUNCT
ejpam-371	89	30	�	�	PROPN
ejpam-371	89	31	�	�	PROPN
ejpam-371	89	32	2	2	NUM
ejpam-371	89	33	�	�	NOUN
ejpam-371	89	34	e−2sαd	e−2sαd	NOUN
ejpam-371	89	35	xd	xd	NOUN
ejpam-371	89	36	t	t	NOUN
ejpam-371	90	1	+	+	CCONJ
ejpam-371	91	1	∫∫	∫∫	ADV
ejpam-371	91	2	q	q	X
ejpam-371	91	3	(	(	PUNCT
ejpam-371	91	4	s3φ3|q|2	s3φ3|q|2	NOUN
ejpam-371	91	5	+	+	X
ejpam-371	91	6	sφ|∇q|2)e−2sαd	sφ|∇q|2)e−2sαd	NUM
ejpam-371	91	7	xd	xd	ADP
ejpam-371	91	8	t.	t.	PROPN
ejpam-371	91	9	moreover	moreover	ADV
ejpam-371	91	10	,	,	PUNCT
ejpam-371	91	11	the	the	DET
ejpam-371	91	12	constants	constant	NOUN
ejpam-371	91	13	λ0	λ0	NOUN
ejpam-371	91	14	,	,	PUNCT
ejpam-371	91	15	s0	s0	PROPN
ejpam-371	91	16	take	take	VERB
ejpam-371	91	17	the	the	DET
ejpam-371	91	18	form	form	NOUN
ejpam-371	91	19	λ0	λ0	NOUN
ejpam-371	91	20	=	=	PUNCT
ejpam-371	91	21	c(ω	c(ω	NOUN
ejpam-371	91	22	,	,	PUNCT
ejpam-371	91	23	ω)[1	ω)[1	PROPN
ejpam-371	91	24	+	+	NOUN
ejpam-371	91	25	p	p	X
ejpam-371	91	26	t	t	PROPN
ejpam-371	91	27	+	+	CCONJ
ejpam-371	91	28	t	t	PROPN
ejpam-371	91	29	2	2	NUM
ejpam-371	91	30	+	+	CCONJ
ejpam-371	91	31	t	t	PROPN
ejpam-371	91	32	4	4	NUM
ejpam-371	91	33	]	]	PUNCT
ejpam-371	91	34	and	and	CCONJ
ejpam-371	91	35	s0	s0	PROPN
ejpam-371	91	36	=	=	SYM
ejpam-371	91	37	c(ω	c(ω	PROPN
ejpam-371	91	38	,	,	PUNCT
ejpam-371	91	39	ω)[t	ω)[t	PROPN
ejpam-371	92	1	+	+	CCONJ
ejpam-371	92	2	t	t	PROPN
ejpam-371	92	3	p	p	X
ejpam-371	92	4	t	t	PROPN
ejpam-371	92	5	+	+	CCONJ
ejpam-371	92	6	t	t	PROPN
ejpam-371	92	7	2	2	NUM
ejpam-371	92	8	+	+	CCONJ
ejpam-371	92	9	t	t	PROPN
ejpam-371	92	10	4	4	NUM
ejpam-371	92	11	]	]	PUNCT
ejpam-371	92	12	.	.	PUNCT
ejpam-371	93	1	to	to	PART
ejpam-371	93	2	prove	prove	VERB
ejpam-371	93	3	this	this	DET
ejpam-371	93	4	theorem	theorem	NOUN
ejpam-371	93	5	we	we	PRON
ejpam-371	93	6	need	need	VERB
ejpam-371	93	7	the	the	DET
ejpam-371	93	8	following	follow	VERB
ejpam-371	93	9	lemma	lemma	PROPN
ejpam-371	93	10	in	in	ADP
ejpam-371	93	11	terms	term	NOUN
ejpam-371	93	12	of	of	ADP
ejpam-371	93	13	the	the	DET
ejpam-371	93	14	new	new	ADJ
ejpam-371	93	15	transformed	transform	VERB
ejpam-371	93	16	variable	variable	NOUN
ejpam-371	93	17	p	p	NOUN
ejpam-371	93	18	=	=	NOUN
ejpam-371	93	19	e−sαq	e−sαq	NOUN
ejpam-371	93	20	which	which	PRON
ejpam-371	93	21	essentially	essentially	ADV
ejpam-371	93	22	completes	complete	VERB
ejpam-371	93	23	the	the	DET
ejpam-371	93	24	first	first	ADJ
ejpam-371	93	25	part	part	NOUN
ejpam-371	93	26	of	of	ADP
ejpam-371	93	27	theorem	theorem	NOUN
ejpam-371	93	28	1	1	NUM
ejpam-371	93	29	.	.	PUNCT
ejpam-371	94	1	lemma	lemma	PROPN
ejpam-371	94	2	1	1	X
ejpam-371	94	3	.	.	PUNCT
ejpam-371	95	1	let	let	VERB
ejpam-371	95	2	the	the	DET
ejpam-371	95	3	kernels	kernel	NOUN
ejpam-371	95	4	m	m	PROPN
ejpam-371	95	5	(	(	PUNCT
ejpam-371	95	6	·	·	PUNCT
ejpam-371	95	7	,	,	PUNCT
ejpam-371	95	8	·	·	PUNCT
ejpam-371	95	9	)	)	PUNCT
ejpam-371	95	10	and	and	CCONJ
ejpam-371	95	11	n	n	CCONJ
ejpam-371	95	12	(	(	PUNCT
ejpam-371	95	13	·	·	PUNCT
ejpam-371	95	14	,	,	PUNCT
ejpam-371	95	15	·	·	PUNCT
ejpam-371	95	16	)	)	PUNCT
ejpam-371	95	17	have	have	VERB
ejpam-371	95	18	support	support	NOUN
ejpam-371	95	19	in	in	ADP
ejpam-371	95	20	(	(	PUNCT
ejpam-371	95	21	t0	t0	PROPN
ejpam-371	95	22	,	,	PUNCT
ejpam-371	95	23	t1	t1	PROPN
ejpam-371	95	24	)	)	PUNCT
ejpam-371	95	25	,	,	PUNCT
ejpam-371	95	26	where	where	SCONJ
ejpam-371	95	27	0	0	X
ejpam-371	95	28	<	<	X
ejpam-371	95	29	t0	t0	X
ejpam-371	95	30	<	<	X
ejpam-371	95	31	t1	t1	NOUN
ejpam-371	95	32	<	<	X
ejpam-371	95	33	t	t	PROPN
ejpam-371	95	34	and	and	CCONJ
ejpam-371	95	35	g	g	PROPN
ejpam-371	95	36	∈	∈	PROPN
ejpam-371	95	37	l2(q	l2(q	PROPN
ejpam-371	95	38	)	)	PUNCT
ejpam-371	95	39	be	be	AUX
ejpam-371	95	40	given	give	VERB
ejpam-371	95	41	.	.	PUNCT
ejpam-371	96	1	there	there	PRON
ejpam-371	96	2	exist	exist	VERB
ejpam-371	96	3	eλ0,es0	eλ0,es0	NOUN
ejpam-371	96	4	and	and	CCONJ
ejpam-371	96	5	c	c	X
ejpam-371	96	6	only	only	ADV
ejpam-371	96	7	depending	depend	VERB
ejpam-371	96	8	on	on	ADP
ejpam-371	96	9	ω	ω	PROPN
ejpam-371	96	10	,	,	PUNCT
ejpam-371	96	11	ω	ω	PROPN
ejpam-371	96	12	and	and	CCONJ
ejpam-371	96	13	t	t	NOUN
ejpam-371	96	14	such	such	ADJ
ejpam-371	96	15	that	that	SCONJ
ejpam-371	96	16	,	,	PUNCT
ejpam-371	96	17	for	for	ADP
ejpam-371	96	18	any	any	DET
ejpam-371	96	19	λ	λ	PROPN
ejpam-371	96	20	≥	≥	NOUN
ejpam-371	96	21	eλ0	eλ0	NOUN
ejpam-371	96	22	=	=	SYM
ejpam-371	96	23	c(ω	c(ω	PROPN
ejpam-371	96	24	,	,	PUNCT
ejpam-371	96	25	ω)(1	ω)(1	NUM
ejpam-371	96	26	+	+	SYM
ejpam-371	96	27	t	t	NOUN
ejpam-371	96	28	4	4	NUM
ejpam-371	96	29	)	)	PUNCT
ejpam-371	96	30	,	,	PUNCT
ejpam-371	96	31	any	any	PRON
ejpam-371	96	32	s	s	NOUN
ejpam-371	96	33	≥	≥	NOUN
ejpam-371	96	34	es0	es0	NOUN
ejpam-371	96	35	=	=	SYM
ejpam-371	96	36	c(ω	c(ω	PROPN
ejpam-371	96	37	,	,	PUNCT
ejpam-371	96	38	ω)(t	ω)(t	X
ejpam-371	96	39	+	+	CCONJ
ejpam-371	96	40	t	t	PROPN
ejpam-371	96	41	2	2	NUM
ejpam-371	96	42	+	+	CCONJ
ejpam-371	96	43	t	t	PROPN
ejpam-371	96	44	4	4	NUM
ejpam-371	96	45	)	)	PUNCT
ejpam-371	96	46	,	,	PUNCT
ejpam-371	96	47	the	the	DET
ejpam-371	96	48	weak	weak	ADJ
ejpam-371	96	49	solution	solution	NOUN
ejpam-371	96	50	of	of	ADP
ejpam-371	96	51	(	(	PUNCT
ejpam-371	96	52	5	5	NUM
ejpam-371	96	53	)	)	PUNCT
ejpam-371	96	54	satisfies	satisfie	NOUN
ejpam-371	96	55	elq	elq	PROPN
ejpam-371	96	56	,	,	PUNCT
ejpam-371	96	57	s	s	X
ejpam-371	96	58	,	,	PUNCT
ejpam-371	96	59	λ(p	λ(p	PROPN
ejpam-371	96	60	)	)	PUNCT
ejpam-371	96	61	≤	≤	NUM
ejpam-371	96	62	c	c	PROPN
ejpam-371	96	63	�	�	PROPN
ejpam-371	96	64	‖e−sαg‖2	‖e−sαg‖2	PROPN
ejpam-371	96	65	l2(q	l2(q	PROPN
ejpam-371	96	66	)	)	PUNCT
ejpam-371	97	1	+	+	CCONJ
ejpam-371	97	2	elqω0	elqω0	X
ejpam-371	97	3	,	,	PUNCT
ejpam-371	97	4	s	s	X
ejpam-371	97	5	,	,	PUNCT
ejpam-371	97	6	λ(p	λ(p	PROPN
ejpam-371	97	7	)	)	PUNCT
ejpam-371	98	1	+	+	NUM
ejpam-371	98	2	mq	mq	PROPN
ejpam-371	98	3	,	,	PUNCT
ejpam-371	98	4	s	s	PROPN
ejpam-371	98	5	,	,	PUNCT
ejpam-371	98	6	λ(m	λ(m	PROPN
ejpam-371	98	7	;	;	PUNCT
ejpam-371	98	8	p	p	X
ejpam-371	98	9	)	)	PUNCT
ejpam-371	98	10	+	+	CCONJ
ejpam-371	98	11	nq	nq	PROPN
ejpam-371	98	12	,	,	PUNCT
ejpam-371	98	13	s	s	X
ejpam-371	98	14	,	,	PUNCT
ejpam-371	98	15	λ(n	λ(n	PROPN
ejpam-371	98	16	;	;	PUNCT
ejpam-371	98	17	p	p	X
ejpam-371	98	18	)	)	PUNCT
ejpam-371	98	19	(	(	PUNCT
ejpam-371	98	20	8)	8)	NUM
ejpam-371	98	21	+	+	CCONJ
ejpam-371	98	22	mq	mq	PROPN
ejpam-371	98	23	,	,	PUNCT
ejpam-371	98	24	s	s	NOUN
ejpam-371	98	25	,	,	PUNCT
ejpam-371	98	26	λ(mt	λ(mt	X
ejpam-371	98	27	;	;	PUNCT
ejpam-371	98	28	p	p	X
ejpam-371	98	29	)	)	PUNCT
ejpam-371	98	30	+	+	CCONJ
ejpam-371	98	31	nq	nq	PROPN
ejpam-371	98	32	,	,	PUNCT
ejpam-371	98	33	s	s	X
ejpam-371	98	34	,	,	PUNCT
ejpam-371	98	35	λ(nt	λ(nt	PRON
ejpam-371	98	36	;	;	PUNCT
ejpam-371	98	37	p	p	X
ejpam-371	98	38	)	)	PUNCT
ejpam-371	98	39	�	�	PROPN
ejpam-371	98	40	,	,	PUNCT
ejpam-371	98	41	where	where	SCONJ
ejpam-371	98	42	elq	elq	PROPN
ejpam-371	98	43	,	,	PUNCT
ejpam-371	98	44	s	s	X
ejpam-371	98	45	,	,	PUNCT
ejpam-371	98	46	λ(p	λ(p	PROPN
ejpam-371	98	47	)	)	PUNCT
ejpam-371	99	1	=	=	PUNCT
ejpam-371	100	1	∫∫	∫∫	ADV
ejpam-371	100	2	q	q	ADJ
ejpam-371	100	3	s3λ4φ3|p|2d	s3λ4φ3|p|2d	NOUN
ejpam-371	100	4	xd	xd	INTJ
ejpam-371	100	5	t	t	NOUN
ejpam-371	100	6	+	+	CCONJ
ejpam-371	101	1	∫∫	∫∫	ADV
ejpam-371	101	2	q	q	VERB
ejpam-371	102	1	sλ2φ|∇p|2d	sλ2φ|∇p|2d	ADV
ejpam-371	102	2	xd	xd	INTJ
ejpam-371	102	3	t	t	PROPN
ejpam-371	102	4	,	,	PUNCT
ejpam-371	102	5	mq	mq	PROPN
ejpam-371	102	6	,	,	PUNCT
ejpam-371	102	7	s	s	PROPN
ejpam-371	102	8	,	,	PUNCT
ejpam-371	102	9	λ(m	λ(m	PROPN
ejpam-371	102	10	;	;	PUNCT
ejpam-371	102	11	p	p	X
ejpam-371	102	12	)	)	PUNCT
ejpam-371	102	13	=	=	PUNCT
ejpam-371	103	1	∫∫	∫∫	ADV
ejpam-371	103	2	q	q	PROPN
ejpam-371	103	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	103	4	�	�	PROPN
ejpam-371	103	5	�	�	PROPN
ejpam-371	103	6	m	m	PROPN
ejpam-371	103	7	t	t	PROPN
ejpam-371	103	8	t	t	PROPN
ejpam-371	103	9	∗∆(esαp)(t	∗∆(esαp)(t	PROPN
ejpam-371	103	10	)	)	PUNCT
ejpam-371	103	11	�	�	PROPN
ejpam-371	103	12	�	�	PROPN
ejpam-371	103	13	2d	2d	PROPN
ejpam-371	103	14	xd	xd	ADP
ejpam-371	103	15	t	t	PROPN
ejpam-371	103	16	,	,	PUNCT
ejpam-371	103	17	nq	nq	PROPN
ejpam-371	103	18	,	,	PUNCT
ejpam-371	103	19	s	s	X
ejpam-371	103	20	,	,	PUNCT
ejpam-371	103	21	λ(n	λ(n	PROPN
ejpam-371	103	22	;	;	PUNCT
ejpam-371	103	23	p	p	X
ejpam-371	103	24	)	)	PUNCT
ejpam-371	103	25	=	=	PUNCT
ejpam-371	104	1	∫∫	∫∫	ADV
ejpam-371	104	2	q	q	PROPN
ejpam-371	104	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	104	4	�	�	PROPN
ejpam-371	104	5	�	�	PROPN
ejpam-371	104	6	n	n	ADP
ejpam-371	104	7	t	t	PROPN
ejpam-371	104	8	t	t	PROPN
ejpam-371	104	9	∗	∗	NOUN
ejpam-371	104	10	(	(	PUNCT
ejpam-371	104	11	esαp)t(t	esαp)t(t	PROPN
ejpam-371	104	12	)	)	PUNCT
ejpam-371	104	13	�	�	PROPN
ejpam-371	104	14	�	�	PROPN
ejpam-371	104	15	2d	2d	PROPN
ejpam-371	104	16	xd	xd	ADP
ejpam-371	104	17	t	t	PROPN
ejpam-371	104	18	,	,	PUNCT
ejpam-371	104	19	r.	r.	PROPN
ejpam-371	104	20	lavanya	lavanya	PROPN
ejpam-371	104	21	/	/	SYM
ejpam-371	104	22	eur	eur	PROPN
ejpam-371	104	23	.	.	PUNCT
ejpam-371	105	1	j.	j.	PROPN
ejpam-371	105	2	pure	pure	PROPN
ejpam-371	105	3	appl	appl	PROPN
ejpam-371	105	4	.	.	PROPN
ejpam-371	105	5	math	math	PROPN
ejpam-371	105	6	,	,	PUNCT
ejpam-371	105	7	3	3	NUM
ejpam-371	105	8	(	(	PUNCT
ejpam-371	105	9	2010	2010	NUM
ejpam-371	105	10	)	)	PUNCT
ejpam-371	105	11	,	,	PUNCT
ejpam-371	105	12	235	235	NUM
ejpam-371	105	13	-	-	SYM
ejpam-371	105	14	253	253	NUM
ejpam-371	105	15	240	240	NUM
ejpam-371	105	16	and	and	CCONJ
ejpam-371	105	17	the	the	DET
ejpam-371	105	18	notations	notation	NOUN
ejpam-371	105	19	mq	mq	PROPN
ejpam-371	105	20	,	,	PUNCT
ejpam-371	105	21	s	s	PART
ejpam-371	105	22	,	,	PUNCT
ejpam-371	105	23	λ(mt	λ(mt	X
ejpam-371	105	24	;	;	PUNCT
ejpam-371	105	25	p	p	X
ejpam-371	105	26	)	)	PUNCT
ejpam-371	105	27	,	,	PUNCT
ejpam-371	105	28	nq	nq	PROPN
ejpam-371	105	29	,	,	PUNCT
ejpam-371	105	30	s	s	PROPN
ejpam-371	105	31	,	,	PUNCT
ejpam-371	105	32	λ(nt	λ(nt	PRON
ejpam-371	105	33	;	;	PUNCT
ejpam-371	105	34	p	p	X
ejpam-371	105	35	)	)	PUNCT
ejpam-371	105	36	denote	denote	VERB
ejpam-371	105	37	the	the	DET
ejpam-371	105	38	time	time	NOUN
ejpam-371	105	39	derivative	derivative	NOUN
ejpam-371	105	40	of	of	ADP
ejpam-371	105	41	the	the	DET
ejpam-371	105	42	kernels	kernel	NOUN
ejpam-371	105	43	respectively	respectively	ADV
ejpam-371	105	44	in	in	ADP
ejpam-371	105	45	mq	mq	PROPN
ejpam-371	105	46	,	,	PUNCT
ejpam-371	105	47	s	s	PROPN
ejpam-371	105	48	,	,	PUNCT
ejpam-371	105	49	λ(m	λ(m	PROPN
ejpam-371	105	50	;	;	PUNCT
ejpam-371	105	51	p	p	X
ejpam-371	105	52	)	)	PUNCT
ejpam-371	105	53	,	,	PUNCT
ejpam-371	105	54	nq	nq	PROPN
ejpam-371	105	55	,	,	PUNCT
ejpam-371	105	56	s	s	X
ejpam-371	105	57	,	,	PUNCT
ejpam-371	105	58	λ(n	λ(n	PROPN
ejpam-371	105	59	;	;	PUNCT
ejpam-371	105	60	p	p	X
ejpam-371	105	61	)	)	PUNCT
ejpam-371	105	62	and	and	CCONJ
ejpam-371	105	63	qω0	qω0	NOUN
ejpam-371	105	64	=	=	SYM
ejpam-371	105	65	(	(	PUNCT
ejpam-371	105	66	0	0	NUM
ejpam-371	105	67	,	,	PUNCT
ejpam-371	105	68	t	t	NOUN
ejpam-371	105	69	)	)	PUNCT
ejpam-371	105	70	×ω0	×ω0	PROPN
ejpam-371	105	71	.	.	PUNCT
ejpam-371	106	1	the	the	DET
ejpam-371	106	2	proof	proof	NOUN
ejpam-371	106	3	of	of	ADP
ejpam-371	106	4	lemma	lemma	PROPN
ejpam-371	106	5	1	1	NUM
ejpam-371	106	6	is	be	AUX
ejpam-371	106	7	quite	quite	ADV
ejpam-371	106	8	similar	similar	ADJ
ejpam-371	106	9	to	to	ADP
ejpam-371	106	10	the	the	DET
ejpam-371	106	11	detailed	detailed	ADJ
ejpam-371	106	12	proof	proof	NOUN
ejpam-371	106	13	given	give	VERB
ejpam-371	106	14	in	in	ADP
ejpam-371	106	15	[	[	X
ejpam-371	106	16	9],[10	9],[10	NUM
ejpam-371	106	17	]	]	X
ejpam-371	106	18	.	.	PUNCT
ejpam-371	107	1	the	the	DET
ejpam-371	107	2	explicit	explicit	ADJ
ejpam-371	107	3	dependence	dependence	NOUN
ejpam-371	107	4	of	of	ADP
ejpam-371	107	5	the	the	DET
ejpam-371	107	6	constant	constant	ADJ
ejpam-371	107	7	on	on	ADP
ejpam-371	107	8	time	time	NOUN
ejpam-371	107	9	and	and	CCONJ
ejpam-371	107	10	space	space	NOUN
ejpam-371	107	11	is	be	AUX
ejpam-371	107	12	not	not	PART
ejpam-371	107	13	obtained	obtain	VERB
ejpam-371	107	14	in	in	ADP
ejpam-371	107	15	[	[	X
ejpam-371	107	16	12	12	NUM
ejpam-371	107	17	]	]	PUNCT
ejpam-371	107	18	and	and	CCONJ
ejpam-371	107	19	we	we	PRON
ejpam-371	107	20	refer	refer	VERB
ejpam-371	107	21	to	to	ADP
ejpam-371	107	22	[	[	X
ejpam-371	107	23	10],[6	10],[6	NOUN
ejpam-371	107	24	]	]	PUNCT
ejpam-371	107	25	where	where	SCONJ
ejpam-371	107	26	the	the	DET
ejpam-371	107	27	explicit	explicit	ADJ
ejpam-371	107	28	dependence	dependence	NOUN
ejpam-371	107	29	has	have	AUX
ejpam-371	107	30	been	be	AUX
ejpam-371	107	31	computed	compute	VERB
ejpam-371	107	32	.	.	PUNCT
ejpam-371	108	1	now	now	ADV
ejpam-371	108	2	we	we	PRON
ejpam-371	108	3	need	need	VERB
ejpam-371	108	4	to	to	PART
ejpam-371	108	5	estimate	estimate	VERB
ejpam-371	108	6	the	the	DET
ejpam-371	108	7	memory	memory	NOUN
ejpam-371	108	8	integrals	integral	NOUN
ejpam-371	108	9	appearing	appear	VERB
ejpam-371	108	10	on	on	ADP
ejpam-371	108	11	the	the	DET
ejpam-371	108	12	right	right	ADJ
ejpam-371	108	13	hand	hand	NOUN
ejpam-371	108	14	side	side	NOUN
ejpam-371	108	15	of	of	ADP
ejpam-371	108	16	the	the	DET
ejpam-371	108	17	estimate	estimate	NOUN
ejpam-371	108	18	(	(	PUNCT
ejpam-371	108	19	8)	8)	NUM
ejpam-371	108	20	and	and	CCONJ
ejpam-371	108	21	in	in	ADP
ejpam-371	108	22	fact	fact	NOUN
ejpam-371	108	23	this	this	PRON
ejpam-371	108	24	will	will	AUX
ejpam-371	108	25	complete	complete	VERB
ejpam-371	108	26	the	the	DET
ejpam-371	108	27	proof	proof	NOUN
ejpam-371	108	28	of	of	ADP
ejpam-371	108	29	theorem	theorem	NOUN
ejpam-371	108	30	1	1	NUM
ejpam-371	108	31	.	.	PUNCT
ejpam-371	109	1	proof	proof	NOUN
ejpam-371	109	2	.	.	PUNCT
ejpam-371	110	1	first	first	ADV
ejpam-371	110	2	we	we	PRON
ejpam-371	110	3	write	write	VERB
ejpam-371	110	4	the	the	DET
ejpam-371	110	5	inequality	inequality	NOUN
ejpam-371	110	6	(	(	PUNCT
ejpam-371	110	7	8)	8)	NUM
ejpam-371	110	8	in	in	ADP
ejpam-371	110	9	terms	term	NOUN
ejpam-371	110	10	of	of	ADP
ejpam-371	110	11	the	the	DET
ejpam-371	110	12	original	original	ADJ
ejpam-371	110	13	variable	variable	NOUN
ejpam-371	110	14	by	by	ADP
ejpam-371	110	15	substituting	substitute	VERB
ejpam-371	110	16	p	p	NOUN
ejpam-371	110	17	=	=	NOUN
ejpam-371	110	18	e−sαq	e−sαq	NOUN
ejpam-371	110	19	to	to	PART
ejpam-371	110	20	have	have	VERB
ejpam-371	110	21	∫∫	∫∫	ADV
ejpam-371	110	22	q	q	NOUN
ejpam-371	110	23	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	ADJ
ejpam-371	110	24	xd	xd	INTJ
ejpam-371	110	25	t	t	PROPN
ejpam-371	110	26	+	+	CCONJ
ejpam-371	111	1	∫∫	∫∫	ADV
ejpam-371	111	2	q	q	NOUN
ejpam-371	112	1	sλ2φ|∇(e−sαq)|2d	sλ2φ|∇(e−sαq)|2d	NOUN
ejpam-371	112	2	xd	xd	ADP
ejpam-371	112	3	t	t	PROPN
ejpam-371	112	4	≤	≤	NUM
ejpam-371	112	5	c	c	SYM
ejpam-371	112	6	�	�	PROPN
ejpam-371	113	1	∫∫	∫∫	ADV
ejpam-371	113	2	q	q	NOUN
ejpam-371	114	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	114	2	xd	xd	INTJ
ejpam-371	114	3	t	t	NOUN
ejpam-371	114	4	+	+	CCONJ
ejpam-371	115	1	∫∫	∫∫	ADV
ejpam-371	115	2	qω0	qω0	ADV
ejpam-371	115	3	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	ADJ
ejpam-371	115	4	xd	xd	ADP
ejpam-371	115	5	t	t	PROPN
ejpam-371	115	6	+	+	PUNCT
ejpam-371	116	1	∫∫	∫∫	ADV
ejpam-371	116	2	qω0	qω0	ADJ
ejpam-371	116	3	sλ2φ|∇(e−sαq)|2d	sλ2φ|∇(e−sαq)|2d	NOUN
ejpam-371	116	4	xd	xd	INTJ
ejpam-371	116	5	t	t	PROPN
ejpam-371	116	6	+	+	PROPN
ejpam-371	116	7	mq	mq	PROPN
ejpam-371	116	8	,	,	PUNCT
ejpam-371	116	9	s	s	PROPN
ejpam-371	116	10	,	,	PUNCT
ejpam-371	116	11	λ(m	λ(m	PROPN
ejpam-371	116	12	;	;	PUNCT
ejpam-371	116	13	q	q	X
ejpam-371	116	14	)	)	PUNCT
ejpam-371	116	15	+	+	NOUN
ejpam-371	116	16	mq	mq	NOUN
ejpam-371	116	17	,	,	PUNCT
ejpam-371	116	18	s	s	NOUN
ejpam-371	116	19	,	,	PUNCT
ejpam-371	116	20	λ(mt	λ(mt	X
ejpam-371	116	21	;	;	PUNCT
ejpam-371	116	22	q	q	X
ejpam-371	116	23	)	)	PUNCT
ejpam-371	116	24	+	+	CCONJ
ejpam-371	116	25	nq	nq	PROPN
ejpam-371	116	26	,	,	PUNCT
ejpam-371	116	27	s	s	X
ejpam-371	116	28	,	,	PUNCT
ejpam-371	116	29	λ(n	λ(n	PROPN
ejpam-371	116	30	;	;	PUNCT
ejpam-371	116	31	q)+	q)+	PROPN
ejpam-371	116	32	nq	nq	PROPN
ejpam-371	116	33	,	,	PUNCT
ejpam-371	116	34	s	s	PROPN
ejpam-371	116	35	,	,	PUNCT
ejpam-371	116	36	λ(nt	λ(nt	NUM
ejpam-371	116	37	;	;	PUNCT
ejpam-371	116	38	q	q	X
ejpam-371	116	39	)	)	PUNCT
ejpam-371	116	40	�	�	PROPN
ejpam-371	116	41	.	.	PUNCT
ejpam-371	117	1	note	note	VERB
ejpam-371	117	2	that	that	SCONJ
ejpam-371	117	3	∇(e−sαq	∇(e−sαq	PROPN
ejpam-371	117	4	)	)	PUNCT
ejpam-371	117	5	=	=	PUNCT
ejpam-371	118	1	e−sαsλφ∇ψq+	e−sαsλφ∇ψq+	NOUN
ejpam-371	118	2	e−sα∇q	e−sα∇q	NUM
ejpam-371	118	3	and	and	CCONJ
ejpam-371	118	4	2	2	NUM
ejpam-371	119	1	∫∫	∫∫	ADV
ejpam-371	119	2	q	q	NOUN
ejpam-371	119	3	e−2sαs2λ3φ2∇ψq∇qd	e−2sαs2λ3φ2∇ψq∇qd	NOUN
ejpam-371	119	4	xd	xd	INTJ
ejpam-371	119	5	t	t	PROPN
ejpam-371	119	6	≥	≥	NOUN
ejpam-371	119	7	−ρ	−ρ	NOUN
ejpam-371	120	1	∫∫	∫∫	ADV
ejpam-371	120	2	q	q	PROPN
ejpam-371	120	3	e−2sαsλ2φ|∇q|2d	e−2sαsλ2φ|∇q|2d	NOUN
ejpam-371	121	1	xd	xd	INTJ
ejpam-371	121	2	t	t	PROPN
ejpam-371	121	3	−	−	NUM
ejpam-371	121	4	1	1	NUM
ejpam-371	121	5	ρ	ρ	PROPN
ejpam-371	122	1	∫∫	∫∫	PROPN
ejpam-371	122	2	q	q	NOUN
ejpam-371	122	3	e−2sαs3λ4φ3|∇ψ|2|q|2d	e−2sαs3λ4φ3|∇ψ|2|q|2d	NOUN
ejpam-371	122	4	xd	xd	INTJ
ejpam-371	122	5	t	t	PROPN
ejpam-371	122	6	,	,	PUNCT
ejpam-371	122	7	where	where	SCONJ
ejpam-371	122	8	the	the	DET
ejpam-371	122	9	parameter	parameter	NOUN
ejpam-371	122	10	ρ	ρ	PROPN
ejpam-371	122	11	∈	∈	PROPN
ejpam-371	122	12	(	(	PUNCT
ejpam-371	122	13	0,1	0,1	NUM
ejpam-371	122	14	)	)	PUNCT
ejpam-371	122	15	.	.	PUNCT
ejpam-371	123	1	choose	choose	VERB
ejpam-371	123	2	‖∇ψ‖c(ω̄	‖∇ψ‖c(ω̄	NOUN
ejpam-371	123	3	)	)	PUNCT
ejpam-371	123	4	≤	≤	NOUN
ejpam-371	123	5	ρ	ρ	NOUN
ejpam-371	123	6	to	to	PART
ejpam-371	123	7	obtain	obtain	VERB
ejpam-371	123	8	elq	elq	PROPN
ejpam-371	123	9	,	,	PUNCT
ejpam-371	123	10	s	s	NOUN
ejpam-371	123	11	,	,	PUNCT
ejpam-371	123	12	λ(q)≤	λ(q)≤	NOUN
ejpam-371	123	13	c	c	NOUN
ejpam-371	123	14	�	�	PROPN
ejpam-371	124	1	∫∫	∫∫	PROPN
ejpam-371	124	2	q	q	NOUN
ejpam-371	125	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	125	2	xd	xd	INTJ
ejpam-371	125	3	t	t	PROPN
ejpam-371	125	4	+	+	CCONJ
ejpam-371	125	5	elqω0	elqω0	X
ejpam-371	125	6	,	,	PUNCT
ejpam-371	125	7	s	s	NOUN
ejpam-371	125	8	,	,	PUNCT
ejpam-371	125	9	λ(q)+mq	λ(q)+mq	ADJ
ejpam-371	125	10	,	,	PUNCT
ejpam-371	125	11	s	s	X
ejpam-371	125	12	,	,	PUNCT
ejpam-371	125	13	λ(m	λ(m	PROPN
ejpam-371	125	14	;	;	PUNCT
ejpam-371	125	15	q	q	X
ejpam-371	125	16	)	)	PUNCT
ejpam-371	125	17	(	(	PUNCT
ejpam-371	125	18	9	9	X
ejpam-371	125	19	)	)	PUNCT
ejpam-371	125	20	+	+	NOUN
ejpam-371	125	21	mq	mq	NOUN
ejpam-371	125	22	,	,	PUNCT
ejpam-371	125	23	s	s	NOUN
ejpam-371	125	24	,	,	PUNCT
ejpam-371	125	25	λ(mt	λ(mt	X
ejpam-371	125	26	;	;	PUNCT
ejpam-371	125	27	q	q	X
ejpam-371	125	28	)	)	PUNCT
ejpam-371	125	29	+	+	CCONJ
ejpam-371	125	30	nq	nq	PROPN
ejpam-371	125	31	,	,	PUNCT
ejpam-371	125	32	s	s	X
ejpam-371	125	33	,	,	PUNCT
ejpam-371	125	34	λ(n	λ(n	PROPN
ejpam-371	125	35	;	;	PUNCT
ejpam-371	125	36	q)+	q)+	PROPN
ejpam-371	125	37	nq	nq	PROPN
ejpam-371	125	38	,	,	PUNCT
ejpam-371	125	39	s	s	PROPN
ejpam-371	125	40	,	,	PUNCT
ejpam-371	125	41	λ(nt	λ(nt	NUM
ejpam-371	125	42	;	;	PUNCT
ejpam-371	125	43	q	q	X
ejpam-371	125	44	)	)	PUNCT
ejpam-371	125	45	�	�	PROPN
ejpam-371	125	46	,	,	PUNCT
ejpam-371	125	47	since	since	SCONJ
ejpam-371	125	48	we	we	PRON
ejpam-371	125	49	have	have	AUX
ejpam-371	125	50	redefined	redefine	VERB
ejpam-371	125	51	the	the	DET
ejpam-371	125	52	notations	notation	NOUN
ejpam-371	125	53	el	el	PROPN
ejpam-371	125	54	,	,	PUNCT
ejpam-371	125	55	m	m	PROPN
ejpam-371	125	56	,	,	PUNCT
ejpam-371	125	57	n	n	CCONJ
ejpam-371	125	58	as	as	SCONJ
ejpam-371	125	59	follows	follow	VERB
ejpam-371	125	60	:	:	PUNCT
ejpam-371	125	61	elq	elq	PROPN
ejpam-371	125	62	,	,	PUNCT
ejpam-371	125	63	s	s	PROPN
ejpam-371	125	64	,	,	PUNCT
ejpam-371	125	65	λ(q	λ(q	NOUN
ejpam-371	125	66	)	)	PUNCT
ejpam-371	125	67	=	=	PUNCT
ejpam-371	126	1	∫∫	∫∫	ADV
ejpam-371	126	2	q	q	NOUN
ejpam-371	126	3	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	ADJ
ejpam-371	126	4	xd	xd	INTJ
ejpam-371	126	5	t	t	PROPN
ejpam-371	126	6	+	+	CCONJ
ejpam-371	127	1	∫∫	∫∫	ADV
ejpam-371	127	2	q	q	PROPN
ejpam-371	127	3	e−2sαsλ2φ|∇q|2d	e−2sαsλ2φ|∇q|2d	PROPN
ejpam-371	127	4	xd	xd	INTJ
ejpam-371	127	5	t	t	PROPN
ejpam-371	127	6	,	,	PUNCT
ejpam-371	127	7	mq	mq	PROPN
ejpam-371	127	8	,	,	PUNCT
ejpam-371	127	9	s	s	PROPN
ejpam-371	127	10	,	,	PUNCT
ejpam-371	127	11	λ(m	λ(m	PROPN
ejpam-371	127	12	;	;	PUNCT
ejpam-371	127	13	q	q	X
ejpam-371	127	14	)	)	PUNCT
ejpam-371	127	15	=	=	PUNCT
ejpam-371	128	1	∫∫	∫∫	ADV
ejpam-371	128	2	q	q	PROPN
ejpam-371	128	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	128	4	�	�	PROPN
ejpam-371	128	5	�	�	PROPN
ejpam-371	128	6	m	m	PROPN
ejpam-371	128	7	t	t	PROPN
ejpam-371	128	8	t	t	PROPN
ejpam-371	128	9	∗∆q(t	∗∆q(t	ADJ
ejpam-371	128	10	)	)	PUNCT
ejpam-371	128	11	�	�	PROPN
ejpam-371	128	12	�	�	PROPN
ejpam-371	128	13	2d	2d	PROPN
ejpam-371	128	14	xd	xd	ADP
ejpam-371	128	15	t	t	PROPN
ejpam-371	128	16	,	,	PUNCT
ejpam-371	128	17	r.	r.	PROPN
ejpam-371	128	18	lavanya	lavanya	PROPN
ejpam-371	128	19	/	/	SYM
ejpam-371	128	20	eur	eur	PROPN
ejpam-371	128	21	.	.	PUNCT
ejpam-371	129	1	j.	j.	PROPN
ejpam-371	129	2	pure	pure	PROPN
ejpam-371	129	3	appl	appl	PROPN
ejpam-371	129	4	.	.	PROPN
ejpam-371	129	5	math	math	PROPN
ejpam-371	129	6	,	,	PUNCT
ejpam-371	129	7	3	3	NUM
ejpam-371	129	8	(	(	PUNCT
ejpam-371	129	9	2010	2010	NUM
ejpam-371	129	10	)	)	PUNCT
ejpam-371	129	11	,	,	PUNCT
ejpam-371	129	12	235	235	NUM
ejpam-371	129	13	-	-	SYM
ejpam-371	129	14	253	253	NUM
ejpam-371	129	15	241	241	NUM
ejpam-371	129	16	nq	nq	PROPN
ejpam-371	129	17	,	,	PUNCT
ejpam-371	129	18	s	s	X
ejpam-371	129	19	,	,	PUNCT
ejpam-371	129	20	λ(n	λ(n	PROPN
ejpam-371	129	21	;	;	PUNCT
ejpam-371	129	22	q	q	X
ejpam-371	129	23	)	)	PUNCT
ejpam-371	129	24	=	=	PUNCT
ejpam-371	130	1	∫∫	∫∫	ADV
ejpam-371	130	2	q	q	PROPN
ejpam-371	130	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	130	4	�	�	PROPN
ejpam-371	130	5	�	�	PROPN
ejpam-371	130	6	n	n	ADP
ejpam-371	130	7	t	t	PROPN
ejpam-371	130	8	t	t	PROPN
ejpam-371	130	9	∗	∗	NOUN
ejpam-371	130	10	qt(t	qt(t	NOUN
ejpam-371	130	11	)	)	PUNCT
ejpam-371	130	12	�	�	PROPN
ejpam-371	130	13	�	�	NOUN
ejpam-371	130	14	2d	2d	NOUN
ejpam-371	130	15	xd	xd	INTJ
ejpam-371	131	1	t.	t.	PROPN
ejpam-371	131	2	next	next	ADV
ejpam-371	131	3	we	we	PRON
ejpam-371	131	4	shall	shall	AUX
ejpam-371	131	5	express	express	VERB
ejpam-371	131	6	the	the	DET
ejpam-371	131	7	term	term	NOUN
ejpam-371	131	8	|∇q|2	|∇q|2	PUNCT
ejpam-371	131	9	over	over	ADP
ejpam-371	131	10	qω0	qω0	NOUN
ejpam-371	131	11	on	on	ADP
ejpam-371	131	12	the	the	DET
ejpam-371	131	13	right	right	ADJ
ejpam-371	131	14	hand	hand	NOUN
ejpam-371	131	15	side	side	NOUN
ejpam-371	131	16	of	of	ADP
ejpam-371	131	17	(	(	PUNCT
ejpam-371	131	18	9	9	NUM
ejpam-371	131	19	)	)	PUNCT
ejpam-371	131	20	,	,	PUNCT
ejpam-371	131	21	in	in	ADP
ejpam-371	131	22	terms	term	NOUN
ejpam-371	131	23	of	of	ADP
ejpam-371	131	24	|q|2	|q|2	PROPN
ejpam-371	131	25	in	in	ADP
ejpam-371	131	26	the	the	DET
ejpam-371	131	27	larger	large	ADJ
ejpam-371	131	28	domain	domain	NOUN
ejpam-371	131	29	ω(since	ω(since	NOUN
ejpam-371	131	30	ω0	ω0	ADV
ejpam-371	131	31	⋐ω⊂	⋐ω⊂	VERB
ejpam-371	131	32	ω	ω	NOUN
ejpam-371	131	33	)	)	PUNCT
ejpam-371	131	34	.	.	PUNCT
ejpam-371	132	1	to	to	PART
ejpam-371	132	2	attain	attain	VERB
ejpam-371	132	3	this	this	PRON
ejpam-371	132	4	,	,	PUNCT
ejpam-371	132	5	let	let	VERB
ejpam-371	132	6	us	we	PRON
ejpam-371	132	7	introduce	introduce	VERB
ejpam-371	132	8	a	a	DET
ejpam-371	132	9	truncating	truncating	NOUN
ejpam-371	132	10	function	function	NOUN
ejpam-371	132	11	θ	θ	NOUN
ejpam-371	132	12	=	=	SYM
ejpam-371	132	13	θ(x	θ(x	PROPN
ejpam-371	132	14	)	)	PUNCT
ejpam-371	132	15	,	,	PUNCT
ejpam-371	132	16	0≤	0≤	NUM
ejpam-371	132	17	θ	θ	NOUN
ejpam-371	132	18	≤	≤	NOUN
ejpam-371	132	19	1	1	NUM
ejpam-371	132	20	satisfying	satisfy	VERB
ejpam-371	132	21	θ	θ	PROPN
ejpam-371	132	22	∈	∈	PROPN
ejpam-371	132	23	c2	c2	PROPN
ejpam-371	132	24	0	0	NUM
ejpam-371	132	25	(	(	PUNCT
ejpam-371	132	26	ω	ω	NOUN
ejpam-371	132	27	)	)	PUNCT
ejpam-371	132	28	,	,	PUNCT
ejpam-371	132	29	θ	θ	X
ejpam-371	132	30	=	=	PUNCT
ejpam-371	132	31	1	1	NUM
ejpam-371	132	32	in	in	ADP
ejpam-371	132	33	ω̄0	ω̄0	NUM
ejpam-371	132	34	and	and	CCONJ
ejpam-371	132	35	θ	θ	PROPN
ejpam-371	132	36	=	=	SYM
ejpam-371	132	37	0	0	NUM
ejpam-371	132	38	in	in	ADP
ejpam-371	132	39	ω\ω	ω\ω	PROPN
ejpam-371	132	40	.	.	PUNCT
ejpam-371	133	1	multiplying	multiply	VERB
ejpam-371	133	2	(	(	PUNCT
ejpam-371	133	3	5	5	NUM
ejpam-371	133	4	)	)	PUNCT
ejpam-371	133	5	by	by	ADP
ejpam-371	133	6	e−2sαθ	e−2sαθ	ADV
ejpam-371	133	7	sλ2φq	sλ2φq	ADV
ejpam-371	133	8	and	and	CCONJ
ejpam-371	133	9	integrating	integrate	VERB
ejpam-371	133	10	over	over	ADP
ejpam-371	133	11	q	q	NOUN
ejpam-371	133	12	,	,	PUNCT
ejpam-371	133	13	we	we	PRON
ejpam-371	133	14	obtain	obtain	VERB
ejpam-371	133	15	that	that	PRON
ejpam-371	134	1	∫∫	∫∫	ADV
ejpam-371	134	2	q	q	PUNCT
ejpam-371	134	3	e−2sαθ	e−2sαθ	ADJ
ejpam-371	134	4	sλ2φ|∇q|2d	sλ2φ|∇q|2d	NOUN
ejpam-371	135	1	xd	xd	INTJ
ejpam-371	135	2	t	t	NOUN
ejpam-371	135	3	≤	≤	NUM
ejpam-371	135	4	1	1	NUM
ejpam-371	135	5	4	4	NUM
ejpam-371	136	1	∫∫	∫∫	ADV
ejpam-371	136	2	q	q	PROPN
ejpam-371	137	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	138	1	xd	xd	INTJ
ejpam-371	138	2	t	t	PROPN
ejpam-371	138	3	+	+	CCONJ
ejpam-371	138	4	1	1	NUM
ejpam-371	138	5	4	4	NUM
ejpam-371	138	6	mqω	mqω	NOUN
ejpam-371	138	7	,	,	PUNCT
ejpam-371	138	8	s	s	X
ejpam-371	138	9	,	,	PUNCT
ejpam-371	138	10	λ(m	λ(m	PROPN
ejpam-371	138	11	;	;	PUNCT
ejpam-371	138	12	q	q	X
ejpam-371	138	13	)	)	PUNCT
ejpam-371	139	1	+	+	CCONJ
ejpam-371	139	2	1	1	NUM
ejpam-371	139	3	4	4	NUM
ejpam-371	139	4	nqω	nqω	NOUN
ejpam-371	139	5	,	,	PUNCT
ejpam-371	139	6	s	s	PART
ejpam-371	139	7	,	,	PUNCT
ejpam-371	139	8	λ(n	λ(n	PROPN
ejpam-371	139	9	;	;	PUNCT
ejpam-371	139	10	q)−	q)−	PROPN
ejpam-371	139	11	∫∫	∫∫	PROPN
ejpam-371	139	12	q	q	VERB
ejpam-371	139	13	sλ2∇(e−2sαθφ)q∇qd	sλ2∇(e−2sαθφ)q∇qd	NOUN
ejpam-371	139	14	xd	xd	ADP
ejpam-371	139	15	t	t	NOUN
ejpam-371	140	1	+	+	CCONJ
ejpam-371	140	2	∫∫	∫∫	ADV
ejpam-371	140	3	qω	qω	VERB
ejpam-371	140	4	e−2sα(s2λ4φ2	e−2sα(s2λ4φ2	NOUN
ejpam-371	140	5	+	+	CCONJ
ejpam-371	140	6	2sλ3φ)|q|2d	2sλ3φ)|q|2d	NUM
ejpam-371	141	1	xd	xd	INTJ
ejpam-371	141	2	t	t	PROPN
ejpam-371	142	1	−	−	NOUN
ejpam-371	143	1	1	1	NUM
ejpam-371	143	2	2	2	X
ejpam-371	143	3	∫∫	∫∫	ADV
ejpam-371	143	4	qω	qω	VERB
ejpam-371	143	5	sλ2(e−2sαφ)t	sλ2(e−2sαφ)t	ADV
ejpam-371	143	6	|q|2d	|q|2d	NOUN
ejpam-371	143	7	xd	xd	ADV
ejpam-371	143	8	t	t	NOUN
ejpam-371	143	9	=	=	PUNCT
ejpam-371	143	10	6∑	6∑	NUM
ejpam-371	143	11	i=1	i=1	PROPN
ejpam-371	143	12	ii	ii	PROPN
ejpam-371	143	13	.	.	PUNCT
ejpam-371	144	1	(	(	PUNCT
ejpam-371	144	2	10	10	NUM
ejpam-371	144	3	)	)	PUNCT
ejpam-371	144	4	now	now	ADV
ejpam-371	144	5	a	a	DET
ejpam-371	144	6	simple	simple	ADJ
ejpam-371	144	7	computation	computation	NOUN
ejpam-371	144	8	yields	yield	VERB
ejpam-371	144	9	the	the	DET
ejpam-371	144	10	following	follow	VERB
ejpam-371	144	11	estimates	estimate	NOUN
ejpam-371	144	12	:	:	PUNCT
ejpam-371	144	13	the	the	DET
ejpam-371	144	14	integral	integral	ADJ
ejpam-371	144	15	i4	i4	PROPN
ejpam-371	144	16	can	can	AUX
ejpam-371	144	17	be	be	AUX
ejpam-371	144	18	estimated	estimate	VERB
ejpam-371	144	19	by	by	ADP
ejpam-371	144	20	c(ω	c(ω	PROPN
ejpam-371	144	21	,	,	PUNCT
ejpam-371	144	22	ω	ω	NOUN
ejpam-371	144	23	)	)	PUNCT
ejpam-371	145	1	∫∫	∫∫	ADV
ejpam-371	145	2	qω0	qω0	ADJ
ejpam-371	145	3	e−2sα(s3λ4φ3	e−2sα(s3λ4φ3	NOUN
ejpam-371	145	4	+	+	CCONJ
ejpam-371	145	5	sφ(λ4	sφ(λ4	VERB
ejpam-371	145	6	+	+	NOUN
ejpam-371	145	7	λ2))|q|2d	λ2))|q|2d	NOUN
ejpam-371	145	8	xd	xd	ADP
ejpam-371	145	9	t	t	PROPN
ejpam-371	145	10	+	+	CCONJ
ejpam-371	145	11	1	1	NUM
ejpam-371	145	12	4	4	NUM
ejpam-371	145	13	∫∫	∫∫	ADV
ejpam-371	145	14	qω0	qω0	ADJ
ejpam-371	145	15	e−2sαsλ2φ|∇q|2d	e−2sαsλ2φ|∇q|2d	INTJ
ejpam-371	145	16	xd	xd	INTJ
ejpam-371	145	17	t	t	PROPN
ejpam-371	145	18	,	,	PUNCT
ejpam-371	145	19	where	where	SCONJ
ejpam-371	145	20	the	the	DET
ejpam-371	145	21	first	first	ADJ
ejpam-371	145	22	integral	integral	NOUN
ejpam-371	145	23	can	can	AUX
ejpam-371	145	24	be	be	AUX
ejpam-371	145	25	bounded	bound	VERB
ejpam-371	145	26	by	by	ADP
ejpam-371	145	27	∫∫	∫∫	ADV
ejpam-371	145	28	qω	qω	VERB
ejpam-371	145	29	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	PROPN
ejpam-371	145	30	xd	xd	ADP
ejpam-371	145	31	t	t	PROPN
ejpam-371	145	32	,	,	PUNCT
ejpam-371	145	33	if	if	SCONJ
ejpam-371	145	34	λ	λ	PROPN
ejpam-371	145	35	≥	≥	X
ejpam-371	145	36	c(ω	c(ω	PROPN
ejpam-371	145	37	,	,	PUNCT
ejpam-371	145	38	ω)t	ω)t	NOUN
ejpam-371	145	39	2	2	NUM
ejpam-371	145	40	,	,	PUNCT
ejpam-371	145	41	s	s	VERB
ejpam-371	145	42	≥	≥	NOUN
ejpam-371	145	43	1	1	NUM
ejpam-371	145	44	.	.	PUNCT
ejpam-371	146	1	the	the	DET
ejpam-371	146	2	integral	integral	ADJ
ejpam-371	146	3	i6	i6	NOUN
ejpam-371	146	4	has	have	VERB
ejpam-371	146	5	also	also	ADV
ejpam-371	146	6	the	the	DET
ejpam-371	146	7	same	same	ADJ
ejpam-371	146	8	bound	bind	VERB
ejpam-371	146	9	,	,	PUNCT
ejpam-371	146	10	i6	i6	NOUN
ejpam-371	146	11	≤	≤	PUNCT
ejpam-371	146	12	c(ω	c(ω	PROPN
ejpam-371	146	13	,	,	PUNCT
ejpam-371	146	14	ω)t	ω)t	PUNCT
ejpam-371	147	1	∫∫	∫∫	ADV
ejpam-371	147	2	qω	qω	VERB
ejpam-371	147	3	e−2sα(s2λ2φ3	e−2sα(s2λ2φ3	PRON
ejpam-371	147	4	+	+	CCONJ
ejpam-371	147	5	sλ2φ2)|q|2d	sλ2φ2)|q|2d	ADV
ejpam-371	147	6	xd	xd	ADP
ejpam-371	147	7	t	t	NOUN
ejpam-371	147	8	≤	≤	NOUN
ejpam-371	148	1	∫∫	∫∫	ADV
ejpam-371	148	2	qω	qω	VERB
ejpam-371	148	3	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	PROPN
ejpam-371	148	4	xd	xd	INTJ
ejpam-371	148	5	t	t	PROPN
ejpam-371	148	6	for	for	ADP
ejpam-371	148	7	the	the	DET
ejpam-371	148	8	choice	choice	NOUN
ejpam-371	148	9	of	of	ADP
ejpam-371	148	10	λ	λ	PROPN
ejpam-371	148	11	≥	≥	NUM
ejpam-371	148	12	1	1	NUM
ejpam-371	148	13	,	,	PUNCT
ejpam-371	148	14	s	s	VERB
ejpam-371	148	15	≥	≥	NOUN
ejpam-371	148	16	c(ω	c(ω	PROPN
ejpam-371	148	17	,	,	PUNCT
ejpam-371	148	18	ω)(t	ω)(t	X
ejpam-371	148	19	+	+	NUM
ejpam-371	148	20	t	t	NOUN
ejpam-371	148	21	3/2	3/2	NUM
ejpam-371	148	22	)	)	PUNCT
ejpam-371	148	23	.	.	PUNCT
ejpam-371	149	1	thus	thus	ADV
ejpam-371	149	2	,	,	PUNCT
ejpam-371	149	3	combining	combine	VERB
ejpam-371	149	4	all	all	DET
ejpam-371	149	5	the	the	DET
ejpam-371	149	6	preceding	precede	VERB
ejpam-371	149	7	inequality	inequality	NOUN
ejpam-371	149	8	,	,	PUNCT
ejpam-371	149	9	we	we	PRON
ejpam-371	149	10	obtain	obtain	VERB
ejpam-371	149	11	∫∫	∫∫	ADV
ejpam-371	149	12	qω0	qω0	VERB
ejpam-371	149	13	e−2sαsλ2φ|∇q|2d	e−2sαsλ2φ|∇q|2d	NOUN
ejpam-371	149	14	xd	xd	ADP
ejpam-371	149	15	t	t	PROPN
ejpam-371	149	16	≤	≤	NUM
ejpam-371	149	17	c	c	NOUN
ejpam-371	149	18	�	�	PROPN
ejpam-371	150	1	∫∫	∫∫	ADV
ejpam-371	150	2	q	q	NOUN
ejpam-371	151	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	151	2	xd	xd	INTJ
ejpam-371	151	3	t	t	NOUN
ejpam-371	152	1	+	+	CCONJ
ejpam-371	153	1	∫∫	∫∫	ADV
ejpam-371	153	2	qω	qω	VERB
ejpam-371	153	3	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	PROPN
ejpam-371	153	4	xd	xd	ADP
ejpam-371	153	5	t	t	PROPN
ejpam-371	153	6	(	(	PUNCT
ejpam-371	153	7	11	11	NUM
ejpam-371	153	8	)	)	PUNCT
ejpam-371	153	9	+	+	CCONJ
ejpam-371	153	10	mqω	mqω	X
ejpam-371	153	11	,	,	PUNCT
ejpam-371	153	12	s	s	X
ejpam-371	153	13	,	,	PUNCT
ejpam-371	153	14	λ(m	λ(m	PROPN
ejpam-371	153	15	;	;	PUNCT
ejpam-371	153	16	q	q	X
ejpam-371	153	17	)	)	PUNCT
ejpam-371	153	18	+	+	CCONJ
ejpam-371	153	19	nqω	nqω	PROPN
ejpam-371	153	20	,	,	PUNCT
ejpam-371	153	21	s	s	PART
ejpam-371	153	22	,	,	PUNCT
ejpam-371	153	23	λ(n	λ(n	PROPN
ejpam-371	153	24	;	;	PUNCT
ejpam-371	153	25	q	q	X
ejpam-371	153	26	)	)	PUNCT
ejpam-371	153	27	�	�	PROPN
ejpam-371	153	28	.	.	PUNCT
ejpam-371	154	1	using	use	VERB
ejpam-371	154	2	(	(	PUNCT
ejpam-371	154	3	11	11	NUM
ejpam-371	154	4	)	)	PUNCT
ejpam-371	154	5	,	,	PUNCT
ejpam-371	154	6	the	the	DET
ejpam-371	154	7	inequality	inequality	NOUN
ejpam-371	154	8	(	(	PUNCT
ejpam-371	154	9	9	9	NUM
ejpam-371	154	10	)	)	PUNCT
ejpam-371	154	11	can	can	AUX
ejpam-371	154	12	be	be	AUX
ejpam-371	154	13	re	re	VERB
ejpam-371	154	14	-	-	VERB
ejpam-371	154	15	estimated	estimate	VERB
ejpam-371	154	16	as	as	ADP
ejpam-371	154	17	elq	elq	PROPN
ejpam-371	154	18	,	,	PUNCT
ejpam-371	154	19	s	s	NOUN
ejpam-371	154	20	,	,	PUNCT
ejpam-371	154	21	λ(q)≤	λ(q)≤	NOUN
ejpam-371	154	22	c	c	NOUN
ejpam-371	154	23	�	�	PROPN
ejpam-371	155	1	∫∫	∫∫	PROPN
ejpam-371	155	2	q	q	NOUN
ejpam-371	156	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	156	2	xd	xd	INTJ
ejpam-371	156	3	t	t	NOUN
ejpam-371	156	4	+	+	CCONJ
ejpam-371	157	1	∫∫	∫∫	ADV
ejpam-371	157	2	(	(	PUNCT
ejpam-371	157	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	157	4	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	PROPN
ejpam-371	157	5	xd	xd	INTJ
ejpam-371	157	6	t	t	PROPN
ejpam-371	157	7	r.	r.	PROPN
ejpam-371	157	8	lavanya	lavanya	PROPN
ejpam-371	157	9	/	/	SYM
ejpam-371	157	10	eur	eur	PROPN
ejpam-371	157	11	.	.	PUNCT
ejpam-371	158	1	j.	j.	PROPN
ejpam-371	158	2	pure	pure	PROPN
ejpam-371	158	3	appl	appl	PROPN
ejpam-371	158	4	.	.	PROPN
ejpam-371	158	5	math	math	PROPN
ejpam-371	158	6	,	,	PUNCT
ejpam-371	158	7	3	3	NUM
ejpam-371	158	8	(	(	PUNCT
ejpam-371	158	9	2010	2010	NUM
ejpam-371	158	10	)	)	PUNCT
ejpam-371	158	11	,	,	PUNCT
ejpam-371	158	12	235	235	NUM
ejpam-371	158	13	-	-	SYM
ejpam-371	158	14	253	253	NUM
ejpam-371	158	15	242	242	NUM
ejpam-371	158	16	+	+	SYM
ejpam-371	158	17	mq	mq	NOUN
ejpam-371	158	18	,	,	PUNCT
ejpam-371	158	19	s	s	PROPN
ejpam-371	158	20	,	,	PUNCT
ejpam-371	158	21	λ(m	λ(m	PROPN
ejpam-371	158	22	;	;	PUNCT
ejpam-371	158	23	q	q	X
ejpam-371	158	24	)	)	PUNCT
ejpam-371	159	1	+	+	NOUN
ejpam-371	159	2	mq	mq	NOUN
ejpam-371	159	3	,	,	PUNCT
ejpam-371	159	4	s	s	NOUN
ejpam-371	159	5	,	,	PUNCT
ejpam-371	159	6	λ(mt	λ(mt	X
ejpam-371	159	7	;	;	PUNCT
ejpam-371	159	8	q	q	X
ejpam-371	159	9	)	)	PUNCT
ejpam-371	159	10	+	+	CCONJ
ejpam-371	159	11	nq	nq	PROPN
ejpam-371	159	12	,	,	PUNCT
ejpam-371	159	13	s	s	X
ejpam-371	159	14	,	,	PUNCT
ejpam-371	159	15	λ(n	λ(n	PROPN
ejpam-371	159	16	;	;	PUNCT
ejpam-371	159	17	q)+	q)+	PROPN
ejpam-371	159	18	nq	nq	PROPN
ejpam-371	159	19	,	,	PUNCT
ejpam-371	159	20	s	s	PROPN
ejpam-371	159	21	,	,	PUNCT
ejpam-371	159	22	λ(nt	λ(nt	NUM
ejpam-371	159	23	;	;	PUNCT
ejpam-371	159	24	q	q	X
ejpam-371	159	25	)	)	PUNCT
ejpam-371	159	26	�	�	PROPN
ejpam-371	159	27	,	,	PUNCT
ejpam-371	159	28	(	(	PUNCT
ejpam-371	159	29	12	12	NUM
ejpam-371	159	30	)	)	PUNCT
ejpam-371	159	31	for	for	ADP
ejpam-371	159	32	any	any	DET
ejpam-371	159	33	λ	λ	PROPN
ejpam-371	159	34	≥	≥	NOUN
ejpam-371	159	35	λ0	λ0	NOUN
ejpam-371	159	36	=	=	SYM
ejpam-371	159	37	c(ω	c(ω	X
ejpam-371	159	38	,	,	PUNCT
ejpam-371	159	39	ω)[1	ω)[1	PROPN
ejpam-371	159	40	+	+	X
ejpam-371	159	41	p	p	X
ejpam-371	159	42	t	t	NOUN
ejpam-371	159	43	+	+	CCONJ
ejpam-371	159	44	t	t	PROPN
ejpam-371	159	45	2	2	NUM
ejpam-371	160	1	+	+	CCONJ
ejpam-371	160	2	t	t	PROPN
ejpam-371	160	3	4	4	NUM
ejpam-371	160	4	]	]	PUNCT
ejpam-371	160	5	and	and	CCONJ
ejpam-371	160	6	s	s	PRON
ejpam-371	160	7	≥	≥	NOUN
ejpam-371	160	8	s̃0	s̃0	PROPN
ejpam-371	160	9	=	=	SYM
ejpam-371	160	10	c(ω	c(ω	PROPN
ejpam-371	160	11	,	,	PUNCT
ejpam-371	160	12	ω)[t	ω)[t	PROPN
ejpam-371	160	13	+	+	CCONJ
ejpam-371	160	14	t	t	PROPN
ejpam-371	160	15	2	2	NUM
ejpam-371	161	1	+	+	CCONJ
ejpam-371	161	2	t	t	PROPN
ejpam-371	161	3	p	p	X
ejpam-371	161	4	t	t	PROPN
ejpam-371	161	5	+	+	CCONJ
ejpam-371	161	6	t	t	PROPN
ejpam-371	161	7	4	4	NUM
ejpam-371	161	8	]	]	PUNCT
ejpam-371	161	9	.	.	PUNCT
ejpam-371	162	1	making	make	VERB
ejpam-371	162	2	use	use	NOUN
ejpam-371	162	3	of	of	ADP
ejpam-371	162	4	the	the	DET
ejpam-371	162	5	assumptions	assumption	NOUN
ejpam-371	162	6	on	on	ADP
ejpam-371	162	7	the	the	DET
ejpam-371	162	8	kernel	kernel	NOUN
ejpam-371	162	9	,	,	PUNCT
ejpam-371	162	10	hölder	hölder	PROPN
ejpam-371	162	11	’s	’s	PART
ejpam-371	162	12	inequality	inequality	NOUN
ejpam-371	162	13	and	and	CCONJ
ejpam-371	162	14	changing	change	VERB
ejpam-371	162	15	the	the	DET
ejpam-371	162	16	order	order	NOUN
ejpam-371	162	17	of	of	ADP
ejpam-371	162	18	integration	integration	NOUN
ejpam-371	162	19	,	,	PUNCT
ejpam-371	162	20	we	we	PRON
ejpam-371	162	21	have	have	VERB
ejpam-371	162	22	mq	mq	PROPN
ejpam-371	162	23	,	,	PUNCT
ejpam-371	162	24	s	s	PROPN
ejpam-371	162	25	,	,	PUNCT
ejpam-371	162	26	λ(m	λ(m	PROPN
ejpam-371	162	27	;	;	PUNCT
ejpam-371	162	28	q	q	X
ejpam-371	162	29	)	)	PUNCT
ejpam-371	162	30	=	=	PUNCT
ejpam-371	163	1	∫∫	∫∫	ADV
ejpam-371	163	2	q	q	PROPN
ejpam-371	163	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	163	4	�	�	PROPN
ejpam-371	163	5	�	�	PROPN
ejpam-371	163	6	m	m	PROPN
ejpam-371	163	7	t	t	PROPN
ejpam-371	163	8	t	t	PROPN
ejpam-371	163	9	∗∆q(t	∗∆q(t	ADJ
ejpam-371	163	10	)	)	PUNCT
ejpam-371	163	11	�	�	PROPN
ejpam-371	163	12	�	�	PROPN
ejpam-371	163	13	2d	2d	PROPN
ejpam-371	163	14	xd	xd	ADP
ejpam-371	163	15	t	t	NOUN
ejpam-371	163	16	≤	≤	NOUN
ejpam-371	164	1	∫∫	∫∫	ADV
ejpam-371	164	2	q	q	PROPN
ejpam-371	164	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	164	4	�	�	PROPN
ejpam-371	164	5	�	�	PROPN
ejpam-371	164	6	m	m	PROPN
ejpam-371	164	7	t	t	PROPN
ejpam-371	164	8	0	0	NUM
ejpam-371	164	9	∗∆q(t	∗∆q(t	ADJ
ejpam-371	164	10	)	)	PUNCT
ejpam-371	164	11	�	�	PROPN
ejpam-371	164	12	�	�	PROPN
ejpam-371	164	13	2d	2d	PROPN
ejpam-371	164	14	xd	xd	ADP
ejpam-371	164	15	t	t	NOUN
ejpam-371	164	16	≤	≤	NOUN
ejpam-371	165	1	∫∫	∫∫	ADV
ejpam-371	165	2	q	q	PROPN
ejpam-371	165	3	e−2sαλφ	e−2sαλφ	PROPN
ejpam-371	165	4	�	�	PROPN
ejpam-371	165	5	∫	∫	PROPN
ejpam-371	165	6	t1	t1	PROPN
ejpam-371	165	7	t0	t0	PROPN
ejpam-371	165	8	|m(τ	|m(τ	PROPN
ejpam-371	165	9	,	,	PUNCT
ejpam-371	165	10	t)|2e(s	t)|2e(s	X
ejpam-371	165	11	2	2	NUM
ejpam-371	165	12	+	+	ADJ
ejpam-371	165	13	2sα)φ(τ)dτ	2sα)φ(τ)dτ	PROPN
ejpam-371	165	14	�	�	PROPN
ejpam-371	165	15	�	�	PROPN
ejpam-371	165	16	∫	∫	PROPN
ejpam-371	165	17	t1	t1	PROPN
ejpam-371	165	18	t0	t0	PROPN
ejpam-371	165	19	e−2sαs−1φ−1(τ)|∆q(τ)|2dτ	e−2sαs−1φ−1(τ)|∆q(τ)|2dτ	PUNCT
ejpam-371	165	20	�	�	PROPN
ejpam-371	165	21	d	d	PROPN
ejpam-371	165	22	xd	xd	PROPN
ejpam-371	165	23	t	t	PROPN
ejpam-371	165	24	≤	≤	X
ejpam-371	166	1	c‖m‖2l∞	c‖m‖2l∞	PROPN
ejpam-371	166	2	∫∫	∫∫	PROPN
ejpam-371	166	3	(	(	PUNCT
ejpam-371	166	4	t0	t0	PROPN
ejpam-371	166	5	,	,	PUNCT
ejpam-371	166	6	t1)×ω	t1)×ω	PROPN
ejpam-371	166	7	e−2sα(sφ)−1λ|∆q|2	e−2sα(sφ)−1λ|∆q|2	PROPN
ejpam-371	166	8	�	�	PROPN
ejpam-371	166	9	∫	∫	PROPN
ejpam-371	166	10	t	t	PROPN
ejpam-371	166	11	0	0	NUM
ejpam-371	166	12	e−2sαφ(τ)dτ	e−2sαφ(τ)dτ	PROPN
ejpam-371	166	13	�	�	PROPN
ejpam-371	167	1	d	d	NOUN
ejpam-371	167	2	xd	xd	NOUN
ejpam-371	167	3	t	t	X
ejpam-371	167	4	≤	≤	NOUN
ejpam-371	167	5	c	c	X
ejpam-371	168	1	∫∫	∫∫	ADV
ejpam-371	168	2	(	(	PUNCT
ejpam-371	168	3	t0,t1)×ω	t0,t1)×ω	PROPN
ejpam-371	168	4	e−2sαλ(sφ)−1|∆q|2d	e−2sαλ(sφ)−1|∆q|2d	INTJ
ejpam-371	168	5	xd	xd	INTJ
ejpam-371	168	6	t	t	NOUN
ejpam-371	168	7	≤	≤	NOUN
ejpam-371	168	8	c	c	X
ejpam-371	169	1	∫∫	∫∫	ADV
ejpam-371	169	2	q	q	PUNCT
ejpam-371	170	1	e−2sαλ(sφ)−1|∆q|2d	e−2sαλ(sφ)−1|∆q|2d	ADV
ejpam-371	171	1	xd	xd	INTJ
ejpam-371	171	2	t	t	PROPN
ejpam-371	171	3	,	,	PUNCT
ejpam-371	171	4	(	(	PUNCT
ejpam-371	171	5	13	13	NUM
ejpam-371	171	6	)	)	PUNCT
ejpam-371	171	7	where	where	SCONJ
ejpam-371	171	8	c	c	NOUN
ejpam-371	171	9	depends	depend	VERB
ejpam-371	171	10	on	on	ADP
ejpam-371	171	11	ω	ω	PROPN
ejpam-371	171	12	,	,	PUNCT
ejpam-371	171	13	ω	ω	PROPN
ejpam-371	171	14	,	,	PUNCT
ejpam-371	171	15	t0	t0	PROPN
ejpam-371	171	16	,	,	PUNCT
ejpam-371	171	17	t1	t1	PROPN
ejpam-371	171	18	,	,	PUNCT
ejpam-371	171	19	t	t	NOUN
ejpam-371	171	20	,	,	PUNCT
ejpam-371	171	21	and	and	CCONJ
ejpam-371	171	22	m.	m.	NOUN
ejpam-371	171	23	similarly	similarly	ADV
ejpam-371	171	24	,	,	PUNCT
ejpam-371	171	25	estimating	estimate	VERB
ejpam-371	171	26	the	the	DET
ejpam-371	171	27	integral	integral	ADJ
ejpam-371	171	28	nq	nq	PROPN
ejpam-371	171	29	,	,	PUNCT
ejpam-371	171	30	s	s	X
ejpam-371	171	31	,	,	PUNCT
ejpam-371	171	32	λ(n	λ(n	PROPN
ejpam-371	171	33	;	;	PUNCT
ejpam-371	171	34	q	q	X
ejpam-371	171	35	)	)	PUNCT
ejpam-371	171	36	,	,	PUNCT
ejpam-371	171	37	one	one	PRON
ejpam-371	171	38	can	can	AUX
ejpam-371	171	39	have	have	VERB
ejpam-371	171	40	nq	nq	PROPN
ejpam-371	171	41	,	,	PUNCT
ejpam-371	171	42	s	s	PART
ejpam-371	171	43	,	,	PUNCT
ejpam-371	171	44	λ(n	λ(n	PROPN
ejpam-371	171	45	;	;	PUNCT
ejpam-371	171	46	q	q	X
ejpam-371	171	47	)	)	PUNCT
ejpam-371	171	48	=	=	PUNCT
ejpam-371	172	1	∫∫	∫∫	ADV
ejpam-371	172	2	q	q	PROPN
ejpam-371	172	3	e−2sαsλφ	e−2sαsλφ	PROPN
ejpam-371	172	4	�	�	PROPN
ejpam-371	172	5	�	�	PROPN
ejpam-371	172	6	n	n	ADP
ejpam-371	172	7	t	t	PROPN
ejpam-371	172	8	t	t	PROPN
ejpam-371	172	9	∗	∗	NOUN
ejpam-371	172	10	qt(t	qt(t	NOUN
ejpam-371	172	11	)	)	PUNCT
ejpam-371	172	12	�	�	PROPN
ejpam-371	172	13	�	�	PROPN
ejpam-371	172	14	2d	2d	PROPN
ejpam-371	172	15	xd	xd	ADP
ejpam-371	172	16	t	t	PROPN
ejpam-371	172	17	≤	≤	NOUN
ejpam-371	172	18	c	c	X
ejpam-371	173	1	∫∫	∫∫	ADV
ejpam-371	173	2	q	q	ADJ
ejpam-371	173	3	e−2sαλ(sφ)−1|qt	e−2sαλ(sφ)−1|qt	ADJ
ejpam-371	173	4	|2d	|2d	NOUN
ejpam-371	173	5	xd	xd	ADP
ejpam-371	173	6	t	t	PROPN
ejpam-371	173	7	,	,	PUNCT
ejpam-371	173	8	(	(	PUNCT
ejpam-371	173	9	14	14	NUM
ejpam-371	173	10	)	)	PUNCT
ejpam-371	173	11	where	where	SCONJ
ejpam-371	173	12	c	c	NOUN
ejpam-371	173	13	depends	depend	VERB
ejpam-371	173	14	on	on	ADP
ejpam-371	173	15	ω	ω	PROPN
ejpam-371	173	16	,	,	PUNCT
ejpam-371	173	17	ω	ω	PROPN
ejpam-371	173	18	,	,	PUNCT
ejpam-371	173	19	t0	t0	PROPN
ejpam-371	173	20	,	,	PUNCT
ejpam-371	173	21	t1	t1	PROPN
ejpam-371	173	22	,	,	PUNCT
ejpam-371	173	23	t	t	NOUN
ejpam-371	173	24	,	,	PUNCT
ejpam-371	173	25	and	and	CCONJ
ejpam-371	173	26	n.	n.	VERB
ejpam-371	173	27	the	the	DET
ejpam-371	173	28	similar	similar	ADJ
ejpam-371	173	29	estimates	estimate	NOUN
ejpam-371	173	30	holds	hold	VERB
ejpam-371	173	31	true	true	ADJ
ejpam-371	173	32	for	for	ADP
ejpam-371	173	33	mq	mq	PROPN
ejpam-371	173	34	,	,	PUNCT
ejpam-371	173	35	s	s	X
ejpam-371	173	36	,	,	PUNCT
ejpam-371	173	37	λ(mt	λ(mt	X
ejpam-371	173	38	;	;	PUNCT
ejpam-371	173	39	q	q	X
ejpam-371	173	40	)	)	PUNCT
ejpam-371	173	41	and	and	CCONJ
ejpam-371	173	42	nq	nq	PROPN
ejpam-371	173	43	,	,	PUNCT
ejpam-371	173	44	s	s	PROPN
ejpam-371	173	45	,	,	PUNCT
ejpam-371	173	46	λ(nt	λ(nt	PRON
ejpam-371	173	47	;	;	PUNCT
ejpam-371	173	48	q	q	X
ejpam-371	173	49	)	)	PUNCT
ejpam-371	173	50	.	.	PUNCT
ejpam-371	174	1	indeed	indeed	ADV
ejpam-371	174	2	one	one	PRON
ejpam-371	174	3	can	can	AUX
ejpam-371	174	4	obtain	obtain	VERB
ejpam-371	174	5	a	a	DET
ejpam-371	174	6	sharp	sharp	ADJ
ejpam-371	174	7	estimate	estimate	NOUN
ejpam-371	174	8	for	for	ADP
ejpam-371	174	9	the	the	DET
ejpam-371	174	10	weight	weight	NOUN
ejpam-371	174	11	functions	function	NOUN
ejpam-371	174	12	(	(	PUNCT
ejpam-371	174	13	used	use	VERB
ejpam-371	174	14	above	above	ADV
ejpam-371	174	15	)	)	PUNCT
ejpam-371	174	16	as	as	SCONJ
ejpam-371	174	17	follows	follow	VERB
ejpam-371	174	18	:	:	PUNCT
ejpam-371	174	19	following	follow	VERB
ejpam-371	174	20	certain	certain	ADJ
ejpam-371	174	21	standard	standard	ADJ
ejpam-371	174	22	analysis	analysis	NOUN
ejpam-371	174	23	used	use	VERB
ejpam-371	174	24	in	in	ADP
ejpam-371	174	25	[	[	X
ejpam-371	174	26	5	5	NUM
ejpam-371	174	27	]	]	PUNCT
ejpam-371	174	28	,	,	PUNCT
ejpam-371	174	29	we	we	PRON
ejpam-371	174	30	obtain	obtain	VERB
ejpam-371	174	31	esαφ	esαφ	NOUN
ejpam-371	174	32	≤	≤	PROPN
ejpam-371	174	33	c(ω	c(ω	PROPN
ejpam-371	174	34	,	,	PUNCT
ejpam-371	174	35	ω)(t(t	ω)(t(t	PUNCT
ejpam-371	174	36	−	−	PROPN
ejpam-371	174	37	t	t	NOUN
ejpam-371	174	38	)	)	PUNCT
ejpam-371	174	39	)	)	PUNCT
ejpam-371	174	40	−1e−sα̃/t(t−t	−1e−sα̃/t(t−t	NUM
ejpam-371	174	41	)	)	PUNCT
ejpam-371	174	42	≤	≤	NUM
ejpam-371	174	43	4t−2e−σ(ω	4t−2e−σ(ω	NOUN
ejpam-371	174	44	,	,	PUNCT
ejpam-371	174	45	ω)st−2	ω)st−2	NOUN
ejpam-371	174	46	,	,	PUNCT
ejpam-371	174	47	where	where	SCONJ
ejpam-371	174	48	eα=	eα=	NOUN
ejpam-371	174	49	e2λψ	e2λψ	PUNCT
ejpam-371	174	50	−	−	NOUN
ejpam-371	174	51	eλψ	eλψ	NOUN
ejpam-371	174	52	and	and	CCONJ
ejpam-371	174	53	σ	σ	NUM
ejpam-371	174	54	=	=	SYM
ejpam-371	174	55	4	4	NUM
ejpam-371	174	56	min	min	NOUN
ejpam-371	174	57	x∈ω	x∈ω	X
ejpam-371	174	58	eα	eα	VERB
ejpam-371	174	59	for	for	ADP
ejpam-371	174	60	s	s	PRON
ejpam-371	174	61	≥	≥	NOUN
ejpam-371	174	62	s0	s0	NOUN
ejpam-371	174	63	=	=	SYM
ejpam-371	174	64	max(s̃0	max(s̃0	PROPN
ejpam-371	174	65	,	,	PUNCT
ejpam-371	174	66	(	(	PUNCT
ejpam-371	174	67	σ(ω	σ(ω	PROPN
ejpam-371	174	68	,	,	PUNCT
ejpam-371	174	69	ω))−1	ω))−1	PROPN
ejpam-371	174	70	t	t	PROPN
ejpam-371	174	71	2	2	NUM
ejpam-371	174	72	)	)	PUNCT
ejpam-371	174	73	.	.	PUNCT
ejpam-371	175	1	in	in	ADP
ejpam-371	175	2	order	order	NOUN
ejpam-371	175	3	to	to	PART
ejpam-371	175	4	complete	complete	VERB
ejpam-371	175	5	the	the	DET
ejpam-371	175	6	theorem	theorem	NOUN
ejpam-371	175	7	,	,	PUNCT
ejpam-371	175	8	it	it	PRON
ejpam-371	175	9	remains	remain	VERB
ejpam-371	175	10	to	to	PART
ejpam-371	175	11	obtain	obtain	VERB
ejpam-371	175	12	an	an	DET
ejpam-371	175	13	estimate	estimate	NOUN
ejpam-371	175	14	for	for	ADP
ejpam-371	175	15	the	the	DET
ejpam-371	175	16	terms	term	NOUN
ejpam-371	175	17	involving	involve	VERB
ejpam-371	175	18	first	first	ADJ
ejpam-371	175	19	order	order	NOUN
ejpam-371	175	20	derivative	derivative	NOUN
ejpam-371	175	21	in	in	ADP
ejpam-371	175	22	time	time	NOUN
ejpam-371	175	23	and	and	CCONJ
ejpam-371	175	24	second	second	ADJ
ejpam-371	175	25	in	in	ADP
ejpam-371	175	26	space	space	NOUN
ejpam-371	175	27	variable	variable	NOUN
ejpam-371	175	28	.	.	PUNCT
ejpam-371	176	1	to	to	PART
ejpam-371	176	2	obtain	obtain	VERB
ejpam-371	176	3	this	this	PRON
ejpam-371	176	4	,	,	PUNCT
ejpam-371	176	5	first	first	ADV
ejpam-371	176	6	of	of	ADP
ejpam-371	176	7	all	all	DET
ejpam-371	176	8	multiplying	multiply	VERB
ejpam-371	176	9	(	(	PUNCT
ejpam-371	176	10	5	5	NUM
ejpam-371	176	11	)	)	PUNCT
ejpam-371	176	12	by	by	ADP
ejpam-371	176	13	e	e	X
ejpam-371	176	14	p−2sαλ	p−2sαλ	PROPN
ejpam-371	176	15	p	p	X
ejpam-371	176	16	(	(	PUNCT
ejpam-371	176	17	sφ)−1	sφ)−1	NOUN
ejpam-371	176	18	,	,	PUNCT
ejpam-371	176	19	squaring	square	VERB
ejpam-371	176	20	and	and	CCONJ
ejpam-371	176	21	then	then	ADV
ejpam-371	176	22	integrating	integrate	VERB
ejpam-371	176	23	on	on	ADP
ejpam-371	176	24	q	q	NOUN
ejpam-371	176	25	,	,	PUNCT
ejpam-371	176	26	we	we	PRON
ejpam-371	176	27	get	get	VERB
ejpam-371	176	28	blq	blq	PROPN
ejpam-371	176	29	,	,	PUNCT
ejpam-371	176	30	s	s	X
ejpam-371	176	31	,	,	PUNCT
ejpam-371	176	32	λ(q	λ(q	NOUN
ejpam-371	176	33	)	)	PUNCT
ejpam-371	176	34	=	=	PUNCT
ejpam-371	177	1	∫∫	∫∫	ADV
ejpam-371	177	2	q	q	NOUN
ejpam-371	178	1	e−2sα(sφ)−1λ2|g|2d	e−2sα(sφ)−1λ2|g|2d	NOUN
ejpam-371	179	1	xd	xd	INTJ
ejpam-371	179	2	t	t	NOUN
ejpam-371	179	3	+	+	CCONJ
ejpam-371	179	4	2(d+	2(d+	NUM
ejpam-371	179	5	e	e	X
ejpam-371	179	6	)	)	PUNCT
ejpam-371	180	1	+	+	CCONJ
ejpam-371	180	2	2(f	2(f	NUM
ejpam-371	180	3	+	+	CCONJ
ejpam-371	180	4	g	g	NOUN
ejpam-371	180	5	)	)	PUNCT
ejpam-371	181	1	+	+	NUM
ejpam-371	181	2	2h	2h	NUM
ejpam-371	181	3	−2	−2	NOUN
ejpam-371	182	1	∫∫	∫∫	ADV
ejpam-371	182	2	q	q	PUNCT
ejpam-371	182	3	e−2sα(sφ)−1λ2qt∆qd	e−2sα(sφ)−1λ2qt∆qd	PROPN
ejpam-371	182	4	xd	xd	PROPN
ejpam-371	182	5	t	t	PROPN
ejpam-371	182	6	,	,	PUNCT
ejpam-371	182	7	(	(	PUNCT
ejpam-371	182	8	15	15	X
ejpam-371	182	9	)	)	PUNCT
ejpam-371	182	10	r.	r.	PROPN
ejpam-371	182	11	lavanya	lavanya	PROPN
ejpam-371	182	12	/	/	SYM
ejpam-371	182	13	eur	eur	PROPN
ejpam-371	182	14	.	.	PUNCT
ejpam-371	183	1	j.	j.	PROPN
ejpam-371	183	2	pure	pure	PROPN
ejpam-371	183	3	appl	appl	PROPN
ejpam-371	183	4	.	.	PROPN
ejpam-371	183	5	math	math	PROPN
ejpam-371	183	6	,	,	PUNCT
ejpam-371	183	7	3	3	NUM
ejpam-371	183	8	(	(	PUNCT
ejpam-371	183	9	2010	2010	NUM
ejpam-371	183	10	)	)	PUNCT
ejpam-371	183	11	,	,	PUNCT
ejpam-371	183	12	235	235	NUM
ejpam-371	183	13	-	-	SYM
ejpam-371	183	14	253	253	NUM
ejpam-371	183	15	243	243	NUM
ejpam-371	183	16	where	where	SCONJ
ejpam-371	183	17	blq	blq	PROPN
ejpam-371	183	18	,	,	PUNCT
ejpam-371	183	19	s	s	X
ejpam-371	183	20	,	,	PUNCT
ejpam-371	183	21	λ(q	λ(q	NOUN
ejpam-371	183	22	)	)	PUNCT
ejpam-371	183	23	=	=	PUNCT
ejpam-371	184	1	∫∫	∫∫	ADV
ejpam-371	184	2	q	q	PUNCT
ejpam-371	184	3	e−2sα(sφ)−1λ2	e−2sα(sφ)−1λ2	NUM
ejpam-371	184	4	�	�	PROPN
ejpam-371	184	5	|qt	|qt	NUM
ejpam-371	184	6	|2	|2	NUM
ejpam-371	184	7	+	+	CCONJ
ejpam-371	184	8	|∆q|2	|∆q|2	ADJ
ejpam-371	184	9	+	+	SYM
ejpam-371	184	10	�	�	PROPN
ejpam-371	184	11	�	�	PROPN
ejpam-371	184	12	m	m	PROPN
ejpam-371	184	13	t	t	PROPN
ejpam-371	184	14	t	t	PROPN
ejpam-371	184	15	∗∆q(t	∗∆q(t	ADJ
ejpam-371	184	16	)	)	PUNCT
ejpam-371	184	17	�	�	PROPN
ejpam-371	184	18	�	�	PROPN
ejpam-371	184	19	2	2	NUM
ejpam-371	184	20	+	+	NUM
ejpam-371	184	21	�	�	PROPN
ejpam-371	184	22	�	�	PROPN
ejpam-371	184	23	n	n	ADP
ejpam-371	184	24	t	t	NOUN
ejpam-371	184	25	t	t	PROPN
ejpam-371	184	26	∗	∗	NOUN
ejpam-371	184	27	qt(t	qt(t	NOUN
ejpam-371	184	28	)	)	PUNCT
ejpam-371	184	29	�	�	PROPN
ejpam-371	184	30	�	�	PROPN
ejpam-371	184	31	2	2	NUM
ejpam-371	184	32	�	�	PROPN
ejpam-371	184	33	d	d	NOUN
ejpam-371	184	34	xd	xd	NOUN
ejpam-371	184	35	t	t	PROPN
ejpam-371	184	36	,	,	PUNCT
ejpam-371	184	37	(	(	PUNCT
ejpam-371	184	38	d+	d+	X
ejpam-371	184	39	e	e	X
ejpam-371	184	40	)	)	PUNCT
ejpam-371	184	41	=	=	PUNCT
ejpam-371	185	1	−	−	PROPN
ejpam-371	186	1	∫∫	∫∫	ADV
ejpam-371	186	2	q	q	NOUN
ejpam-371	186	3	e−2sα(sφ)−1λ2qt	e−2sα(sφ)−1λ2qt	PROPN
ejpam-371	186	4	�	�	PROPN
ejpam-371	186	5	m	m	PROPN
ejpam-371	186	6	t	t	PROPN
ejpam-371	186	7	t	t	PROPN
ejpam-371	186	8	∗∆q(t	∗∆q(t	ADV
ejpam-371	186	9	)	)	PUNCT
ejpam-371	187	1	+	+	CCONJ
ejpam-371	187	2	n	n	NUM
ejpam-371	187	3	t	t	NOUN
ejpam-371	187	4	t	t	NOUN
ejpam-371	187	5	∗	∗	NOUN
ejpam-371	187	6	qt(t	qt(t	NOUN
ejpam-371	187	7	)	)	PUNCT
ejpam-371	187	8	�	�	PROPN
ejpam-371	188	1	d	d	PROPN
ejpam-371	188	2	xd	xd	PROPN
ejpam-371	188	3	t	t	PROPN
ejpam-371	188	4	,	,	PUNCT
ejpam-371	188	5	(	(	PUNCT
ejpam-371	188	6	f	f	X
ejpam-371	189	1	+	+	CCONJ
ejpam-371	189	2	g	g	NOUN
ejpam-371	189	3	)	)	PUNCT
ejpam-371	189	4	=	=	PUNCT
ejpam-371	190	1	−	−	PROPN
ejpam-371	191	1	∫∫	∫∫	ADV
ejpam-371	191	2	q	q	PUNCT
ejpam-371	191	3	e−2sα(sφ)−1λ2∆q	e−2sα(sφ)−1λ2∆q	NOUN
ejpam-371	191	4	�	�	PROPN
ejpam-371	191	5	m	m	PROPN
ejpam-371	191	6	t	t	PROPN
ejpam-371	191	7	t	t	PROPN
ejpam-371	191	8	∗∆q(t	∗∆q(t	ADV
ejpam-371	191	9	)	)	PUNCT
ejpam-371	192	1	+	+	ADP
ejpam-371	192	2	n	n	PROPN
ejpam-371	192	3	t	t	NOUN
ejpam-371	192	4	t	t	NOUN
ejpam-371	192	5	∗	∗	NOUN
ejpam-371	192	6	qt(t	qt(t	NOUN
ejpam-371	192	7	)	)	PUNCT
ejpam-371	192	8	�	�	PROPN
ejpam-371	193	1	d	d	PROPN
ejpam-371	193	2	xd	xd	PROPN
ejpam-371	193	3	t	t	PROPN
ejpam-371	193	4	,	,	PUNCT
ejpam-371	193	5	h	h	NOUN
ejpam-371	193	6	=	=	PUNCT
ejpam-371	194	1	−	−	PROPN
ejpam-371	195	1	∫∫	∫∫	ADV
ejpam-371	195	2	q	q	PUNCT
ejpam-371	195	3	e−2sα(sφ)−1λ2	e−2sα(sφ)−1λ2	NOUN
ejpam-371	195	4	�	�	PROPN
ejpam-371	195	5	m	m	PROPN
ejpam-371	195	6	t	t	PROPN
ejpam-371	195	7	t	t	PROPN
ejpam-371	195	8	∗∆q(t	∗∆q(t	ADJ
ejpam-371	195	9	)	)	PUNCT
ejpam-371	195	10	�	�	PROPN
ejpam-371	195	11	�	�	PROPN
ejpam-371	195	12	n	n	ADP
ejpam-371	195	13	t	t	NOUN
ejpam-371	195	14	t	t	PROPN
ejpam-371	195	15	∗	∗	NOUN
ejpam-371	195	16	qt(t	qt(t	NOUN
ejpam-371	195	17	)	)	PUNCT
ejpam-371	195	18	�	�	PROPN
ejpam-371	196	1	d	d	NOUN
ejpam-371	196	2	xd	xd	INTJ
ejpam-371	197	1	t.	t.	PROPN
ejpam-371	197	2	now	now	ADV
ejpam-371	197	3	we	we	PRON
ejpam-371	197	4	have	have	VERB
ejpam-371	197	5	the	the	DET
ejpam-371	197	6	following	follow	VERB
ejpam-371	197	7	estimates	estimate	NOUN
ejpam-371	197	8	by	by	ADP
ejpam-371	197	9	choosing	choose	VERB
ejpam-371	197	10	the	the	DET
ejpam-371	197	11	constants	constant	NOUN
ejpam-371	197	12	carefully	carefully	ADV
ejpam-371	197	13	and	and	CCONJ
ejpam-371	197	14	applying	apply	VERB
ejpam-371	197	15	young	young	PROPN
ejpam-371	197	16	’s	’s	PART
ejpam-371	197	17	inequality	inequality	NOUN
ejpam-371	197	18	followed	follow	VERB
ejpam-371	197	19	by	by	ADP
ejpam-371	197	20	green	green	PROPN
ejpam-371	197	21	’s	’s	PART
ejpam-371	197	22	theorem	theorem	NOUN
ejpam-371	197	23	and	and	CCONJ
ejpam-371	197	24	integration	integration	NOUN
ejpam-371	197	25	by	by	ADP
ejpam-371	197	26	parts	part	NOUN
ejpam-371	197	27	.	.	PUNCT
ejpam-371	198	1	integrating	integrate	VERB
ejpam-371	198	2	by	by	ADP
ejpam-371	198	3	parts	part	NOUN
ejpam-371	198	4	with	with	ADP
ejpam-371	198	5	respect	respect	NOUN
ejpam-371	198	6	to	to	ADP
ejpam-371	198	7	time	time	NOUN
ejpam-371	198	8	in	in	ADP
ejpam-371	198	9	d+	d+	NOUN
ejpam-371	198	10	e	e	NOUN
ejpam-371	198	11	,	,	PUNCT
ejpam-371	198	12	we	we	PRON
ejpam-371	198	13	obtain	obtain	VERB
ejpam-371	198	14	2(d+	2(d+	NUM
ejpam-371	198	15	e	e	NOUN
ejpam-371	198	16	)	)	PUNCT
ejpam-371	198	17	=	=	PUNCT
ejpam-371	199	1	−	−	PROPN
ejpam-371	200	1	∫∫	∫∫	ADV
ejpam-371	200	2	q	q	NOUN
ejpam-371	200	3	e−2sαλ2(4αtφ	e−2sαλ2(4αtφ	NOUN
ejpam-371	200	4	−1	−1	NOUN
ejpam-371	201	1	+	+	CCONJ
ejpam-371	201	2	2s−1φ−2φt)q	2s−1φ−2φt)q	NUM
ejpam-371	201	3	�	�	PROPN
ejpam-371	202	1	m	m	ADP
ejpam-371	203	1	t	t	PROPN
ejpam-371	203	2	t	t	PROPN
ejpam-371	203	3	∗∆q(t	∗∆q(t	ADV
ejpam-371	203	4	)	)	PUNCT
ejpam-371	204	1	+	+	CCONJ
ejpam-371	204	2	n	n	NUM
ejpam-371	204	3	t	t	NOUN
ejpam-371	204	4	t	t	NOUN
ejpam-371	204	5	∗	∗	NOUN
ejpam-371	204	6	qt(t	qt(t	NOUN
ejpam-371	204	7	)	)	PUNCT
ejpam-371	204	8	�	�	PROPN
ejpam-371	205	1	d	d	NOUN
ejpam-371	205	2	xd	xd	INTJ
ejpam-371	205	3	t	t	NOUN
ejpam-371	205	4	+2	+2	PROPN
ejpam-371	206	1	∫∫	∫∫	ADV
ejpam-371	206	2	q	q	PROPN
ejpam-371	206	3	e−2sαλ2(sφ)−1q	e−2sαλ2(sφ)−1q	PROPN
ejpam-371	206	4	�	�	PROPN
ejpam-371	206	5	∫	∫	PROPN
ejpam-371	206	6	t	t	PROPN
ejpam-371	206	7	t	t	PROPN
ejpam-371	206	8	mt(τ	mt(τ	PROPN
ejpam-371	206	9	,	,	PUNCT
ejpam-371	206	10	t)∆q(τ)dτ+	t)∆q(τ)dτ+	PUNCT
ejpam-371	206	11	∫	∫	PROPN
ejpam-371	206	12	t	t	PROPN
ejpam-371	206	13	t	t	PROPN
ejpam-371	206	14	nt(τ	nt(τ	PUNCT
ejpam-371	206	15	,	,	PUNCT
ejpam-371	206	16	t)qτ(τ)dτ	t)qτ(τ)dτ	PROPN
ejpam-371	206	17	�	�	PROPN
ejpam-371	207	1	d	d	NOUN
ejpam-371	207	2	xd	xd	NOUN
ejpam-371	207	3	t	t	NOUN
ejpam-371	207	4	=	=	SYM
ejpam-371	207	5	d1	d1	PROPN
ejpam-371	207	6	+	+	CCONJ
ejpam-371	207	7	d2	d2	PROPN
ejpam-371	207	8	,	,	PUNCT
ejpam-371	207	9	(	(	PUNCT
ejpam-371	207	10	16	16	NUM
ejpam-371	207	11	)	)	PUNCT
ejpam-371	207	12	where	where	SCONJ
ejpam-371	207	13	we	we	PRON
ejpam-371	207	14	used	use	VERB
ejpam-371	207	15	the	the	DET
ejpam-371	207	16	assumption	assumption	NOUN
ejpam-371	207	17	m(t	m(t	PROPN
ejpam-371	207	18	,	,	PUNCT
ejpam-371	207	19	t	t	PROPN
ejpam-371	207	20	)	)	PUNCT
ejpam-371	207	21	=	=	SYM
ejpam-371	208	1	n(t	n(t	PROPN
ejpam-371	208	2	,	,	PUNCT
ejpam-371	208	3	t	t	PROPN
ejpam-371	208	4	)	)	PUNCT
ejpam-371	208	5	=	=	NOUN
ejpam-371	208	6	0	0	X
ejpam-371	208	7	.	.	PUNCT
ejpam-371	209	1	since	since	SCONJ
ejpam-371	209	2	we	we	PRON
ejpam-371	209	3	observe	observe	VERB
ejpam-371	209	4	that	that	SCONJ
ejpam-371	209	5	d1	d1	PROPN
ejpam-371	209	6	≤	≤	PUNCT
ejpam-371	210	1	∫∫	∫∫	ADV
ejpam-371	210	2	q	q	NOUN
ejpam-371	211	1	e−2sαs3λ4φ3|q|2d	e−2sαs3λ4φ3|q|2d	ADJ
ejpam-371	211	2	xd	xd	INTJ
ejpam-371	211	3	t	t	PROPN
ejpam-371	212	1	+	+	CCONJ
ejpam-371	212	2	1	1	NUM
ejpam-371	212	3	2	2	NUM
ejpam-371	212	4	∫∫	∫∫	ADV
ejpam-371	212	5	q	q	PART
ejpam-371	212	6	e−2sαλ2(sφ)−1	e−2sαλ2(sφ)−1	PROPN
ejpam-371	212	7	�	�	PROPN
ejpam-371	212	8	�	�	PROPN
ejpam-371	212	9	�	�	PROPN
ejpam-371	212	10	m	m	PROPN
ejpam-371	212	11	t	t	PROPN
ejpam-371	212	12	t	t	PROPN
ejpam-371	212	13	∗∆q(t	∗∆q(t	ADJ
ejpam-371	212	14	)	)	PUNCT
ejpam-371	212	15	�	�	PROPN
ejpam-371	212	16	�	�	PROPN
ejpam-371	212	17	2	2	NUM
ejpam-371	212	18	+	+	NUM
ejpam-371	212	19	�	�	PROPN
ejpam-371	212	20	�	�	PROPN
ejpam-371	212	21	n	n	ADP
ejpam-371	212	22	t	t	NOUN
ejpam-371	212	23	t	t	PROPN
ejpam-371	212	24	∗	∗	NOUN
ejpam-371	212	25	qt(t	qt(t	NOUN
ejpam-371	212	26	)	)	PUNCT
ejpam-371	212	27	�	�	PROPN
ejpam-371	212	28	�	�	PROPN
ejpam-371	212	29	2	2	NUM
ejpam-371	212	30	�	�	PROPN
ejpam-371	212	31	d	d	NOUN
ejpam-371	212	32	xd	xd	NOUN
ejpam-371	212	33	t	t	PROPN
ejpam-371	212	34	for	for	ADP
ejpam-371	212	35	any	any	DET
ejpam-371	212	36	λ≥	λ≥	ADJ
ejpam-371	212	37	1	1	NUM
ejpam-371	212	38	and	and	CCONJ
ejpam-371	212	39	s	s	PRON
ejpam-371	212	40	≥	≥	NOUN
ejpam-371	212	41	c(ω	c(ω	PROPN
ejpam-371	212	42	,	,	PUNCT
ejpam-371	212	43	ω)(t	ω)(t	X
ejpam-371	213	1	+	+	NUM
ejpam-371	213	2	t	t	PROPN
ejpam-371	213	3	p	p	X
ejpam-371	213	4	t	t	PROPN
ejpam-371	213	5	)	)	PUNCT
ejpam-371	213	6	.	.	PUNCT
ejpam-371	214	1	the	the	DET
ejpam-371	214	2	integral	integral	ADJ
ejpam-371	214	3	d2	d2	NOUN
ejpam-371	214	4	can	can	AUX
ejpam-371	214	5	be	be	AUX
ejpam-371	214	6	bounded	bound	VERB
ejpam-371	214	7	by	by	ADP
ejpam-371	214	8	d2	d2	PROPN
ejpam-371	214	9	≤	≤	PUNCT
ejpam-371	215	1	∫∫	∫∫	ADV
ejpam-371	215	2	q	q	NOUN
ejpam-371	215	3	e−2sαs3λ3φ3|q|2d	e−2sαs3λ3φ3|q|2d	PROPN
ejpam-371	215	4	xd	xd	INTJ
ejpam-371	215	5	t	t	NOUN
ejpam-371	215	6	+	+	CCONJ
ejpam-371	216	1	∫∫	∫∫	ADV
ejpam-371	216	2	q	q	VERB
ejpam-371	216	3	e−2sαλ(sφ)−1	e−2sαλ(sφ)−1	X
ejpam-371	216	4	�	�	PROPN
ejpam-371	216	5	�	�	PROPN
ejpam-371	216	6	�	�	PROPN
ejpam-371	216	7	�	�	PROPN
ejpam-371	216	8	∫	∫	PROPN
ejpam-371	216	9	t	t	PROPN
ejpam-371	216	10	t	t	PROPN
ejpam-371	216	11	mt(τ	mt(τ	PROPN
ejpam-371	216	12	,	,	PUNCT
ejpam-371	216	13	t)∆q(τ)dτ	t)∆q(τ)dτ	PROPN
ejpam-371	216	14	�	�	PROPN
ejpam-371	216	15	�	�	PROPN
ejpam-371	216	16	�	�	PROPN
ejpam-371	216	17	2	2	NUM
ejpam-371	216	18	+	+	NUM
ejpam-371	216	19	�	�	PROPN
ejpam-371	216	20	�	�	PROPN
ejpam-371	216	21	�	�	PROPN
ejpam-371	216	22	∫	∫	PROPN
ejpam-371	216	23	t	t	PROPN
ejpam-371	216	24	t	t	PROPN
ejpam-371	216	25	nt(τ	nt(τ	PUNCT
ejpam-371	216	26	,	,	PUNCT
ejpam-371	216	27	t)qτ(τ)dτ	t)qτ(τ)dτ	PROPN
ejpam-371	216	28	�	�	PROPN
ejpam-371	216	29	�	�	PROPN
ejpam-371	216	30	�	�	PROPN
ejpam-371	216	31	2	2	NUM
ejpam-371	216	32	�	�	PROPN
ejpam-371	216	33	d	d	NOUN
ejpam-371	216	34	xd	xd	NOUN
ejpam-371	216	35	t	t	PROPN
ejpam-371	216	36	=	=	SYM
ejpam-371	216	37	d21	d21	PROPN
ejpam-371	216	38	+	+	CCONJ
ejpam-371	216	39	d22	d22	PROPN
ejpam-371	216	40	(	(	PUNCT
ejpam-371	216	41	17	17	NUM
ejpam-371	216	42	)	)	PUNCT
ejpam-371	216	43	r.	r.	PROPN
ejpam-371	216	44	lavanya	lavanya	PROPN
ejpam-371	216	45	/	/	SYM
ejpam-371	216	46	eur	eur	PROPN
ejpam-371	216	47	.	.	PUNCT
ejpam-371	217	1	j.	j.	PROPN
ejpam-371	217	2	pure	pure	PROPN
ejpam-371	217	3	appl	appl	PROPN
ejpam-371	217	4	.	.	PROPN
ejpam-371	217	5	math	math	PROPN
ejpam-371	217	6	,	,	PUNCT
ejpam-371	217	7	3	3	NUM
ejpam-371	217	8	(	(	PUNCT
ejpam-371	217	9	2010	2010	NUM
ejpam-371	217	10	)	)	PUNCT
ejpam-371	217	11	,	,	PUNCT
ejpam-371	217	12	235	235	NUM
ejpam-371	217	13	-	-	SYM
ejpam-371	217	14	253	253	NUM
ejpam-371	217	15	244	244	NUM
ejpam-371	217	16	for	for	ADP
ejpam-371	217	17	s	s	PROPN
ejpam-371	217	18	≥	≥	NOUN
ejpam-371	217	19	c(ω	c(ω	PROPN
ejpam-371	217	20	,	,	PUNCT
ejpam-371	217	21	ω)t	ω)t	NOUN
ejpam-371	217	22	2	2	NUM
ejpam-371	217	23	.	.	X
ejpam-371	217	24	computation	computation	NOUN
ejpam-371	217	25	similar	similar	ADJ
ejpam-371	217	26	to	to	ADP
ejpam-371	217	27	(	(	PUNCT
ejpam-371	217	28	13	13	NUM
ejpam-371	217	29	)	)	PUNCT
ejpam-371	217	30	gives	give	VERB
ejpam-371	217	31	further	far	ADV
ejpam-371	217	32	that	that	SCONJ
ejpam-371	217	33	,	,	PUNCT
ejpam-371	217	34	d22	d22	NOUN
ejpam-371	217	35	≤	≤	PUNCT
ejpam-371	218	1	∫∫	∫∫	ADV
ejpam-371	218	2	q	q	NOUN
ejpam-371	218	3	e−2sαλ(sφ)−1	e−2sαλ(sφ)−1	NOUN
ejpam-371	218	4	h	h	PROPN
ejpam-371	218	5	�	�	PROPN
ejpam-371	218	6	∫	∫	PROPN
ejpam-371	218	7	t1	t1	PROPN
ejpam-371	218	8	t0	t0	PROPN
ejpam-371	218	9	|mt(τ	|mt(τ	NOUN
ejpam-371	218	10	,	,	PUNCT
ejpam-371	218	11	t)|2e2sαφdτ	t)|2e2sαφdτ	PROPN
ejpam-371	218	12	�	�	PROPN
ejpam-371	218	13	�	�	PROPN
ejpam-371	218	14	∫	∫	PROPN
ejpam-371	218	15	t1	t1	PROPN
ejpam-371	218	16	t0	t0	PROPN
ejpam-371	218	17	e−2sαφ−1|∆q(τ)|2dτ	e−2sαφ−1|∆q(τ)|2dτ	ADP
ejpam-371	218	18	�	�	PROPN
ejpam-371	218	19	+	+	CCONJ
ejpam-371	218	20	�	�	PROPN
ejpam-371	218	21	∫	∫	PROPN
ejpam-371	218	22	t1	t1	PROPN
ejpam-371	218	23	t0	t0	PROPN
ejpam-371	218	24	|nt(τ	|nt(τ	PROPN
ejpam-371	218	25	,	,	PUNCT
ejpam-371	218	26	t)|2e2sαφdτ	t)|2e2sαφdτ	PROPN
ejpam-371	218	27	�	�	PROPN
ejpam-371	218	28	�	�	PROPN
ejpam-371	218	29	∫	∫	PROPN
ejpam-371	218	30	t1	t1	PROPN
ejpam-371	218	31	t0	t0	PROPN
ejpam-371	218	32	e−2sαφ−1|qτ(τ)|2dτ	e−2sαφ−1|qτ(τ)|2dτ	PROPN
ejpam-371	218	33	�	�	PROPN
ejpam-371	218	34	i	i	NOUN
ejpam-371	219	1	d	d	NOUN
ejpam-371	219	2	xd	xd	ADP
ejpam-371	219	3	t	t	PROPN
ejpam-371	219	4	≤	≤	NOUN
ejpam-371	219	5	c‖mt‖2l∞	c‖mt‖2l∞	VERB
ejpam-371	220	1	∫∫	∫∫	ADV
ejpam-371	220	2	q	q	NOUN
ejpam-371	221	1	e−2sαλ(sφ)−1|∆q|2d	e−2sαλ(sφ)−1|∆q|2d	ADV
ejpam-371	222	1	xd	xd	INTJ
ejpam-371	222	2	t	t	NOUN
ejpam-371	222	3	+	+	CCONJ
ejpam-371	222	4	c‖nt‖2l∞	c‖nt‖2l∞	X
ejpam-371	223	1	∫∫	∫∫	ADV
ejpam-371	223	2	q	q	ADJ
ejpam-371	223	3	e−2sαλ(sφ)−1|qt	e−2sαλ(sφ)−1|qt	ADJ
ejpam-371	223	4	|2d	|2d	NOUN
ejpam-371	223	5	xd	xd	NOUN
ejpam-371	223	6	t.	t.	PROPN
ejpam-371	223	7	here	here	ADV
ejpam-371	223	8	we	we	PRON
ejpam-371	223	9	abserve	abserve	VERB
ejpam-371	223	10	that	that	PRON
ejpam-371	223	11	for	for	ADP
ejpam-371	223	12	any	any	DET
ejpam-371	223	13	λ	λ	PROPN
ejpam-371	223	14	≥	≥	NOUN
ejpam-371	223	15	λ0	λ0	NOUN
ejpam-371	223	16	sufficiently	sufficiently	ADV
ejpam-371	223	17	large	large	ADJ
ejpam-371	223	18	,	,	PUNCT
ejpam-371	223	19	the	the	DET
ejpam-371	223	20	last	last	ADJ
ejpam-371	223	21	two	two	NUM
ejpam-371	223	22	integrals	integral	NOUN
ejpam-371	223	23	can	can	AUX
ejpam-371	223	24	be	be	AUX
ejpam-371	223	25	absorbed	absorb	VERB
ejpam-371	223	26	in	in	ADP
ejpam-371	223	27	blq	blq	PROPN
ejpam-371	223	28	,	,	PUNCT
ejpam-371	223	29	s	s	X
ejpam-371	223	30	,	,	PUNCT
ejpam-371	223	31	λ(q	λ(q	PROPN
ejpam-371	223	32	)	)	PUNCT
ejpam-371	223	33	.	.	PUNCT
ejpam-371	224	1	now	now	ADV
ejpam-371	224	2	the	the	DET
ejpam-371	224	3	simple	simple	ADJ
ejpam-371	224	4	calculation	calculation	NOUN
ejpam-371	224	5	using	use	VERB
ejpam-371	224	6	green	green	PROPN
ejpam-371	224	7	’s	’s	PART
ejpam-371	224	8	formula	formula	NOUN
ejpam-371	224	9	yields	yield	VERB
ejpam-371	224	10	−2	−2	NOUN
ejpam-371	225	1	∫∫	∫∫	ADV
ejpam-371	225	2	q	q	PUNCT
ejpam-371	225	3	e−2sα(sφ)−1λ2qt∆qd	e−2sα(sφ)−1λ2qt∆qd	NOUN
ejpam-371	225	4	xd	xd	INTJ
ejpam-371	225	5	t	t	NOUN
ejpam-371	225	6	=	=	PUNCT
ejpam-371	226	1	∫∫	∫∫	ADV
ejpam-371	226	2	q	q	PUNCT
ejpam-371	226	3	e−2sαλ3(4−	e−2sαλ3(4−	PUNCT
ejpam-371	226	4	2(sφ)−1)qt(∇ψ	2(sφ)−1)qt(∇ψ	PROPN
ejpam-371	226	5	·	·	PUNCT
ejpam-371	226	6	∇q)d	∇q)d	PROPN
ejpam-371	227	1	xd	xd	ADP
ejpam-371	227	2	t	t	NOUN
ejpam-371	228	1	+	+	CCONJ
ejpam-371	229	1	∫∫	∫∫	ADV
ejpam-371	229	2	q	q	NOUN
ejpam-371	229	3	e−2sαλ2(s−1φ−2φt	e−2sαλ2(s−1φ−2φt	NOUN
ejpam-371	230	1	+	+	CCONJ
ejpam-371	231	1	2φ−1αt)|∇q|2d	2φ−1αt)|∇q|2d	NUM
ejpam-371	231	2	xd	xd	INTJ
ejpam-371	231	3	t	t	X
ejpam-371	231	4	≤	≤	NUM
ejpam-371	231	5	1	1	NUM
ejpam-371	231	6	4	4	NUM
ejpam-371	232	1	∫∫	∫∫	ADV
ejpam-371	232	2	q	q	NOUN
ejpam-371	232	3	e−2sα(sφ)−1λ2|qt	e−2sα(sφ)−1λ2|qt	NUM
ejpam-371	232	4	|2d	|2d	ADP
ejpam-371	232	5	xd	xd	ADV
ejpam-371	232	6	t	t	NOUN
ejpam-371	232	7	+	+	CCONJ
ejpam-371	233	1	∫∫	∫∫	ADV
ejpam-371	233	2	q	q	PROPN
ejpam-371	233	3	e−2sαsλ2φ|∇q|2d	e−2sαsλ2φ|∇q|2d	PROPN
ejpam-371	233	4	xd	xd	INTJ
ejpam-371	233	5	t	t	PROPN
ejpam-371	233	6	,	,	PUNCT
ejpam-371	233	7	(	(	PUNCT
ejpam-371	233	8	18	18	NUM
ejpam-371	233	9	)	)	PUNCT
ejpam-371	233	10	for	for	ADP
ejpam-371	233	11	any	any	DET
ejpam-371	233	12	s	s	PART
ejpam-371	233	13	≥	≥	NOUN
ejpam-371	233	14	c(ω	c(ω	PROPN
ejpam-371	233	15	,	,	PUNCT
ejpam-371	233	16	ω)(t	ω)(t	X
ejpam-371	234	1	+	+	CCONJ
ejpam-371	234	2	t	t	PROPN
ejpam-371	234	3	2	2	NUM
ejpam-371	235	1	+	+	CCONJ
ejpam-371	235	2	t	t	PROPN
ejpam-371	235	3	p	p	X
ejpam-371	235	4	t	t	PROPN
ejpam-371	235	5	)	)	PUNCT
ejpam-371	235	6	.	.	PUNCT
ejpam-371	236	1	since	since	SCONJ
ejpam-371	236	2	we	we	PRON
ejpam-371	236	3	have	have	AUX
ejpam-371	236	4	chosen	choose	VERB
ejpam-371	236	5	(	(	PUNCT
ejpam-371	236	6	if	if	SCONJ
ejpam-371	236	7	necessarily	necessarily	ADV
ejpam-371	236	8	by	by	ADP
ejpam-371	236	9	normalizing	normalize	VERB
ejpam-371	236	10	)	)	PUNCT
ejpam-371	236	11	that	that	SCONJ
ejpam-371	236	12	‖∇ψ‖c(ω̄	‖∇ψ‖c(ω̄	NOUN
ejpam-371	236	13	)	)	PUNCT
ejpam-371	236	14	≤	≤	NOUN
ejpam-371	236	15	1	1	NUM
ejpam-371	236	16	/	/	SYM
ejpam-371	236	17	λ	λ	NOUN
ejpam-371	236	18	and	and	CCONJ
ejpam-371	236	19	used	use	VERB
ejpam-371	236	20	the	the	DET
ejpam-371	236	21	fact	fact	NOUN
ejpam-371	236	22	that	that	SCONJ
ejpam-371	236	23	α(0	α(0	NOUN
ejpam-371	236	24	)	)	PUNCT
ejpam-371	236	25	=	=	SYM
ejpam-371	236	26	α(t	α(t	X
ejpam-371	236	27	)	)	PUNCT
ejpam-371	237	1	=	=	PUNCT
ejpam-371	238	1	+	+	NUM
ejpam-371	238	2	∞.	∞.	PROPN
ejpam-371	238	3	moreover	moreover	ADV
ejpam-371	238	4	,	,	PUNCT
ejpam-371	238	5	we	we	PRON
ejpam-371	238	6	have	have	VERB
ejpam-371	238	7	2h	2h	NUM
ejpam-371	238	8	≤	≤	NUM
ejpam-371	239	1	∫∫	∫∫	ADV
ejpam-371	239	2	q	q	ADJ
ejpam-371	239	3	e−2sα(sφ)−1λ2	e−2sα(sφ)−1λ2	NUM
ejpam-371	239	4	�	�	PROPN
ejpam-371	239	5	�	�	PROPN
ejpam-371	239	6	�	�	PROPN
ejpam-371	239	7	m	m	PROPN
ejpam-371	239	8	t	t	PROPN
ejpam-371	239	9	0	0	NUM
ejpam-371	239	10	∗∆q(t	∗∆q(t	ADJ
ejpam-371	239	11	)	)	PUNCT
ejpam-371	239	12	�	�	PROPN
ejpam-371	239	13	�	�	PROPN
ejpam-371	239	14	2	2	NUM
ejpam-371	239	15	+	+	NUM
ejpam-371	239	16	�	�	PROPN
ejpam-371	239	17	�	�	PROPN
ejpam-371	239	18	n	n	ADP
ejpam-371	239	19	t	t	NOUN
ejpam-371	239	20	0	0	NUM
ejpam-371	239	21	∗	∗	NOUN
ejpam-371	239	22	qt(t	qt(t	NOUN
ejpam-371	239	23	)	)	PUNCT
ejpam-371	239	24	�	�	PROPN
ejpam-371	239	25	�	�	PROPN
ejpam-371	239	26	2	2	NUM
ejpam-371	239	27	�	�	PROPN
ejpam-371	239	28	d	d	NOUN
ejpam-371	239	29	xd	xd	NOUN
ejpam-371	239	30	t	t	PROPN
ejpam-371	239	31	,	,	PUNCT
ejpam-371	239	32	(	(	PUNCT
ejpam-371	239	33	19	19	NUM
ejpam-371	239	34	)	)	PUNCT
ejpam-371	239	35	and	and	CCONJ
ejpam-371	239	36	2(f	2(f	NUM
ejpam-371	239	37	+	+	CCONJ
ejpam-371	239	38	g	g	NOUN
ejpam-371	239	39	)	)	PUNCT
ejpam-371	239	40	≤	≤	NUM
ejpam-371	239	41	1	1	NUM
ejpam-371	239	42	4	4	NUM
ejpam-371	239	43	∫∫	∫∫	ADV
ejpam-371	239	44	q	q	NOUN
ejpam-371	239	45	e−2sα(sφ)−1λ2|∆q|2d	e−2sα(sφ)−1λ2|∆q|2d	NOUN
ejpam-371	239	46	xd	xd	INTJ
ejpam-371	239	47	t	t	NOUN
ejpam-371	239	48	+8	+8	PROPN
ejpam-371	240	1	∫∫	∫∫	ADV
ejpam-371	240	2	q	q	PROPN
ejpam-371	240	3	e−2sα(sφ)−1λ2	e−2sα(sφ)−1λ2	NUM
ejpam-371	240	4	�	�	PROPN
ejpam-371	240	5	�	�	PROPN
ejpam-371	240	6	�	�	PROPN
ejpam-371	240	7	m	m	PROPN
ejpam-371	240	8	t	t	PROPN
ejpam-371	240	9	0	0	NUM
ejpam-371	240	10	∗∆q(t	∗∆q(t	ADJ
ejpam-371	240	11	)	)	PUNCT
ejpam-371	240	12	�	�	NOUN
ejpam-371	240	13	�	�	PROPN
ejpam-371	240	14	2	2	NUM
ejpam-371	240	15	+	+	NUM
ejpam-371	240	16	�	�	PROPN
ejpam-371	240	17	�	�	PROPN
ejpam-371	240	18	n	n	ADP
ejpam-371	240	19	t	t	NOUN
ejpam-371	240	20	0	0	NUM
ejpam-371	240	21	∗	∗	NOUN
ejpam-371	240	22	qt(t	qt(t	NOUN
ejpam-371	240	23	)	)	PUNCT
ejpam-371	240	24	�	�	PROPN
ejpam-371	240	25	�	�	PROPN
ejpam-371	240	26	2	2	NUM
ejpam-371	240	27	�	�	PROPN
ejpam-371	240	28	d	d	NOUN
ejpam-371	240	29	xd	xd	NOUN
ejpam-371	240	30	t.	t.	PROPN
ejpam-371	240	31	(	(	PUNCT
ejpam-371	240	32	20	20	NUM
ejpam-371	240	33	)	)	PUNCT
ejpam-371	240	34	proceeding	proceeding	NOUN
ejpam-371	240	35	calculations	calculation	NOUN
ejpam-371	240	36	similar	similar	ADJ
ejpam-371	240	37	to	to	ADP
ejpam-371	240	38	(	(	PUNCT
ejpam-371	240	39	13	13	NUM
ejpam-371	240	40	)	)	PUNCT
ejpam-371	240	41	and	and	CCONJ
ejpam-371	240	42	(	(	PUNCT
ejpam-371	240	43	14	14	NUM
ejpam-371	240	44	)	)	PUNCT
ejpam-371	240	45	,	,	PUNCT
ejpam-371	240	46	we	we	PRON
ejpam-371	240	47	note	note	VERB
ejpam-371	240	48	that	that	SCONJ
ejpam-371	240	49	the	the	DET
ejpam-371	240	50	integrals	integral	NOUN
ejpam-371	240	51	in	in	ADP
ejpam-371	240	52	(	(	PUNCT
ejpam-371	240	53	19	19	NUM
ejpam-371	240	54	)	)	PUNCT
ejpam-371	240	55	and	and	CCONJ
ejpam-371	240	56	the	the	DET
ejpam-371	240	57	last	last	ADJ
ejpam-371	240	58	integral	integral	NOUN
ejpam-371	240	59	in	in	ADP
ejpam-371	240	60	(	(	PUNCT
ejpam-371	240	61	20	20	NUM
ejpam-371	240	62	)	)	PUNCT
ejpam-371	240	63	can	can	AUX
ejpam-371	240	64	further	far	ADV
ejpam-371	240	65	be	be	AUX
ejpam-371	240	66	estimated	estimate	VERB
ejpam-371	240	67	as	as	ADP
ejpam-371	240	68	c‖m‖2l∞	c‖m‖2l∞	PROPN
ejpam-371	240	69	∫∫	∫∫	ADV
ejpam-371	240	70	q	q	X
ejpam-371	240	71	e−2sα(sφ)−1λ2|∆q|2d	e−2sα(sφ)−1λ2|∆q|2d	NOUN
ejpam-371	241	1	xd	xd	INTJ
ejpam-371	241	2	t	t	PROPN
ejpam-371	241	3	+	+	CCONJ
ejpam-371	241	4	c‖n‖2l∞	c‖n‖2l∞	PROPN
ejpam-371	241	5	∫∫	∫∫	PROPN
ejpam-371	241	6	q	q	NOUN
ejpam-371	241	7	e−2sα(sφ)−1λ2|qt	e−2sα(sφ)−1λ2|qt	NUM
ejpam-371	241	8	|2d	|2d	NOUN
ejpam-371	241	9	xd	xd	PROPN
ejpam-371	241	10	t.	t.	PROPN
ejpam-371	241	11	(	(	PUNCT
ejpam-371	241	12	21	21	NUM
ejpam-371	241	13	)	)	PUNCT
ejpam-371	241	14	r.	r.	PROPN
ejpam-371	241	15	lavanya	lavanya	PROPN
ejpam-371	241	16	/	/	SYM
ejpam-371	241	17	eur	eur	PROPN
ejpam-371	241	18	.	.	PUNCT
ejpam-371	242	1	j.	j.	PROPN
ejpam-371	242	2	pure	pure	PROPN
ejpam-371	242	3	appl	appl	PROPN
ejpam-371	242	4	.	.	PROPN
ejpam-371	242	5	math	math	PROPN
ejpam-371	242	6	,	,	PUNCT
ejpam-371	242	7	3	3	NUM
ejpam-371	242	8	(	(	PUNCT
ejpam-371	242	9	2010	2010	NUM
ejpam-371	242	10	)	)	PUNCT
ejpam-371	242	11	,	,	PUNCT
ejpam-371	242	12	235	235	NUM
ejpam-371	242	13	-	-	SYM
ejpam-371	242	14	253	253	NUM
ejpam-371	242	15	245	245	NUM
ejpam-371	242	16	consequently	consequently	ADV
ejpam-371	242	17	,	,	PUNCT
ejpam-371	242	18	if	if	SCONJ
ejpam-371	242	19	c‖m‖2	c‖m‖2	PROPN
ejpam-371	242	20	l∞	l∞	VERB
ejpam-371	242	21	≤	≤	NUM
ejpam-371	242	22	1	1	NUM
ejpam-371	242	23	4	4	NUM
ejpam-371	242	24	and	and	CCONJ
ejpam-371	242	25	c‖n‖2	c‖n‖2	PROPN
ejpam-371	242	26	l∞	l∞	NOUN
ejpam-371	242	27	≤	≤	NOUN
ejpam-371	242	28	1	1	NUM
ejpam-371	242	29	4	4	NUM
ejpam-371	242	30	,	,	PUNCT
ejpam-371	242	31	the	the	DET
ejpam-371	242	32	estimations	estimation	NOUN
ejpam-371	242	33	(	(	PUNCT
ejpam-371	242	34	16)-(21	16)-(21	NUM
ejpam-371	242	35	)	)	PUNCT
ejpam-371	242	36	yield	yield	VERB
ejpam-371	242	37	blq	blq	PROPN
ejpam-371	242	38	,	,	PUNCT
ejpam-371	242	39	s	s	PROPN
ejpam-371	242	40	,	,	PUNCT
ejpam-371	242	41	λ(q)≤	λ(q)≤	VERB
ejpam-371	242	42	c	c	ADP
ejpam-371	242	43	�	�	PROPN
ejpam-371	243	1	∫∫	∫∫	ADV
ejpam-371	243	2	q	q	PROPN
ejpam-371	244	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	244	2	xd	xd	INTJ
ejpam-371	244	3	t	t	PROPN
ejpam-371	244	4	+	+	CCONJ
ejpam-371	244	5	elq	elq	PROPN
ejpam-371	244	6	,	,	PUNCT
ejpam-371	244	7	s	s	PROPN
ejpam-371	244	8	,	,	PUNCT
ejpam-371	244	9	λ(q	λ(q	PROPN
ejpam-371	244	10	)	)	PUNCT
ejpam-371	244	11	�	�	PROPN
ejpam-371	244	12	.	.	PUNCT
ejpam-371	245	1	(	(	PUNCT
ejpam-371	245	2	22	22	NUM
ejpam-371	245	3	)	)	PUNCT
ejpam-371	245	4	eventually	eventually	ADV
ejpam-371	245	5	,	,	PUNCT
ejpam-371	245	6	making	make	VERB
ejpam-371	245	7	use	use	NOUN
ejpam-371	245	8	of	of	ADP
ejpam-371	245	9	the	the	DET
ejpam-371	245	10	estimations	estimation	NOUN
ejpam-371	245	11	(	(	PUNCT
ejpam-371	245	12	13	13	NUM
ejpam-371	245	13	)	)	PUNCT
ejpam-371	245	14	,	,	PUNCT
ejpam-371	245	15	(	(	PUNCT
ejpam-371	245	16	14	14	NUM
ejpam-371	245	17	)	)	PUNCT
ejpam-371	245	18	and	and	CCONJ
ejpam-371	245	19	choosing	choose	VERB
ejpam-371	245	20	λ≥	λ≥	ADJ
ejpam-371	245	21	λ0	λ0	NOUN
ejpam-371	245	22	,	,	PUNCT
ejpam-371	245	23	s	s	PART
ejpam-371	245	24	≥	≥	NOUN
ejpam-371	245	25	s0	s0	X
ejpam-371	245	26	large	large	ADJ
ejpam-371	245	27	enough	enough	ADV
ejpam-371	245	28	,	,	PUNCT
ejpam-371	245	29	recall	recall	VERB
ejpam-371	245	30	that	that	SCONJ
ejpam-371	245	31	the	the	DET
ejpam-371	245	32	powers	power	NOUN
ejpam-371	245	33	of	of	ADP
ejpam-371	245	34	λ	λ	PROPN
ejpam-371	245	35	in	in	ADP
ejpam-371	245	36	blq	blq	PROPN
ejpam-371	245	37	,	,	PUNCT
ejpam-371	245	38	s	s	X
ejpam-371	245	39	,	,	PUNCT
ejpam-371	245	40	λ(q	λ(q	PROPN
ejpam-371	245	41	)	)	PUNCT
ejpam-371	245	42	,	,	PUNCT
ejpam-371	245	43	dominates	dominate	VERB
ejpam-371	245	44	the	the	DET
ejpam-371	245	45	powers	power	NOUN
ejpam-371	245	46	in	in	ADP
ejpam-371	245	47	(	(	PUNCT
ejpam-371	245	48	13),(14	13),(14	NOUN
ejpam-371	245	49	)	)	PUNCT
ejpam-371	245	50	)	)	PUNCT
ejpam-371	245	51	,	,	PUNCT
ejpam-371	245	52	we	we	PRON
ejpam-371	245	53	get	get	VERB
ejpam-371	245	54	blq	blq	PROPN
ejpam-371	245	55	,	,	PUNCT
ejpam-371	245	56	s	s	X
ejpam-371	245	57	,	,	PUNCT
ejpam-371	245	58	λ(q)+	λ(q)+	PROPN
ejpam-371	245	59	elq	elq	PROPN
ejpam-371	245	60	,	,	PUNCT
ejpam-371	245	61	s	s	PROPN
ejpam-371	245	62	,	,	PUNCT
ejpam-371	245	63	λ(q	λ(q	NOUN
ejpam-371	245	64	)	)	PUNCT
ejpam-371	245	65	≤	≤	NUM
ejpam-371	245	66	c	c	X
ejpam-371	245	67	�	�	PROPN
ejpam-371	246	1	∫∫	∫∫	ADV
ejpam-371	246	2	q	q	NOUN
ejpam-371	247	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	247	2	xd	xd	INTJ
ejpam-371	247	3	t	t	NOUN
ejpam-371	247	4	+	+	CCONJ
ejpam-371	248	1	∫∫	∫∫	PROPN
ejpam-371	248	2	(	(	PUNCT
ejpam-371	248	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	248	4	e−2sα(sφ)3λ4|q|2d	e−2sα(sφ)3λ4|q|2d	NOUN
ejpam-371	248	5	xd	xd	PROPN
ejpam-371	248	6	t	t	PROPN
ejpam-371	248	7	�	�	PROPN
ejpam-371	248	8	.	.	PUNCT
ejpam-371	249	1	(	(	PUNCT
ejpam-371	249	2	23	23	NUM
ejpam-371	249	3	)	)	PUNCT
ejpam-371	249	4	this	this	PRON
ejpam-371	249	5	completes	complete	VERB
ejpam-371	249	6	the	the	DET
ejpam-371	249	7	proof	proof	NOUN
ejpam-371	249	8	of	of	ADP
ejpam-371	249	9	the	the	DET
ejpam-371	249	10	theorem	theorem	PROPN
ejpam-371	249	11	.	.	PROPN
ejpam-371	249	12	remark	remark	PROPN
ejpam-371	249	13	1	1	NUM
ejpam-371	249	14	.	.	PUNCT
ejpam-371	250	1	smallness	smallness	NOUN
ejpam-371	250	2	condition	condition	NOUN
ejpam-371	250	3	on	on	ADP
ejpam-371	250	4	the	the	DET
ejpam-371	250	5	memory	memory	NOUN
ejpam-371	250	6	kernels	kernels	PROPN
ejpam-371	250	7	m	m	PROPN
ejpam-371	250	8	(	(	PUNCT
ejpam-371	250	9	·	·	PUNCT
ejpam-371	250	10	,	,	PUNCT
ejpam-371	250	11	·	·	PUNCT
ejpam-371	250	12	)	)	PUNCT
ejpam-371	250	13	and	and	CCONJ
ejpam-371	250	14	n	n	CCONJ
ejpam-371	250	15	(	(	PUNCT
ejpam-371	250	16	·	·	PUNCT
ejpam-371	250	17	,	,	PUNCT
ejpam-371	250	18	·	·	PUNCT
ejpam-371	250	19	)	)	PUNCT
ejpam-371	250	20	imposed	impose	VERB
ejpam-371	250	21	in	in	ADP
ejpam-371	250	22	the	the	DET
ejpam-371	250	23	estimate	estimate	NOUN
ejpam-371	250	24	(	(	PUNCT
ejpam-371	250	25	22	22	NUM
ejpam-371	250	26	)	)	PUNCT
ejpam-371	250	27	is	be	AUX
ejpam-371	250	28	indeed	indeed	ADV
ejpam-371	250	29	necessary	necessary	ADJ
ejpam-371	250	30	to	to	PART
ejpam-371	250	31	arrive	arrive	VERB
ejpam-371	250	32	at	at	ADP
ejpam-371	250	33	such	such	DET
ejpam-371	250	34	an	an	DET
ejpam-371	250	35	estimate	estimate	NOUN
ejpam-371	250	36	as	as	SCONJ
ejpam-371	250	37	the	the	DET
ejpam-371	250	38	integral	integral	ADJ
ejpam-371	250	39	involves	involve	VERB
ejpam-371	250	40	the	the	DET
ejpam-371	250	41	second	second	ADJ
ejpam-371	250	42	spatial	spatial	ADJ
ejpam-371	250	43	derivative	derivative	NOUN
ejpam-371	250	44	as	as	SCONJ
ejpam-371	250	45	the	the	DET
ejpam-371	250	46	absorption	absorption	NOUN
ejpam-371	250	47	is	be	AUX
ejpam-371	250	48	not	not	PART
ejpam-371	250	49	possible	possible	ADJ
ejpam-371	250	50	otherwise	otherwise	ADV
ejpam-371	250	51	.	.	PUNCT
ejpam-371	251	1	in	in	ADP
ejpam-371	251	2	practice	practice	NOUN
ejpam-371	251	3	the	the	DET
ejpam-371	251	4	memory	memory	NOUN
ejpam-371	251	5	kernels	kernel	NOUN
ejpam-371	251	6	are	be	AUX
ejpam-371	251	7	exponential	exponential	ADJ
ejpam-371	251	8	functions	function	NOUN
ejpam-371	251	9	(	(	PUNCT
ejpam-371	251	10	with	with	ADP
ejpam-371	251	11	negative	negative	ADJ
ejpam-371	251	12	exponents	exponent	NOUN
ejpam-371	251	13	,	,	PUNCT
ejpam-371	251	14	in	in	ADP
ejpam-371	251	15	general	general	ADJ
ejpam-371	251	16	)	)	PUNCT
ejpam-371	251	17	and	and	CCONJ
ejpam-371	251	18	so	so	ADV
ejpam-371	251	19	the	the	DET
ejpam-371	251	20	assumption	assumption	NOUN
ejpam-371	251	21	is	be	AUX
ejpam-371	251	22	valid	valid	ADJ
ejpam-371	251	23	for	for	ADP
ejpam-371	251	24	appropriate	appropriate	ADJ
ejpam-371	251	25	weights	weight	NOUN
ejpam-371	251	26	.	.	PUNCT
ejpam-371	252	1	an	an	DET
ejpam-371	252	2	important	important	ADJ
ejpam-371	252	3	consequence	consequence	NOUN
ejpam-371	252	4	of	of	ADP
ejpam-371	252	5	theorem	theorem	NOUN
ejpam-371	252	6	1	1	NUM
ejpam-371	252	7	is	be	AUX
ejpam-371	252	8	the	the	DET
ejpam-371	252	9	following	follow	VERB
ejpam-371	252	10	observability	observability	NOUN
ejpam-371	252	11	estimate	estimate	NOUN
ejpam-371	252	12	.	.	PUNCT
ejpam-371	253	1	the	the	DET
ejpam-371	253	2	proof	proof	NOUN
ejpam-371	253	3	of	of	ADP
ejpam-371	253	4	this	this	DET
ejpam-371	253	5	estimate	estimate	NOUN
ejpam-371	253	6	is	be	AUX
ejpam-371	253	7	similar	similar	ADJ
ejpam-371	253	8	to	to	ADP
ejpam-371	253	9	that	that	PRON
ejpam-371	253	10	of	of	ADP
ejpam-371	253	11	the	the	DET
ejpam-371	253	12	estimate	estimate	NOUN
ejpam-371	253	13	derived	derive	VERB
ejpam-371	253	14	for	for	ADP
ejpam-371	253	15	various	various	ADJ
ejpam-371	253	16	problems	problem	NOUN
ejpam-371	253	17	in	in	ADP
ejpam-371	253	18	fursikov	fursikov	PROPN
ejpam-371	253	19	et	et	PROPN
ejpam-371	253	20	al	al	PROPN
ejpam-371	254	1	[	[	X
ejpam-371	254	2	7	7	NUM
ejpam-371	254	3	]	]	PUNCT
ejpam-371	254	4	and	and	CCONJ
ejpam-371	254	5	fernandez	fernandez	PROPN
ejpam-371	254	6	-	-	PUNCT
ejpam-371	254	7	cara	cara	PROPN
ejpam-371	254	8	et	et	NOUN
ejpam-371	254	9	al	al	PROPN
ejpam-371	255	1	[	[	X
ejpam-371	255	2	5	5	NUM
ejpam-371	255	3	]	]	PUNCT
ejpam-371	255	4	.	.	PUNCT
ejpam-371	256	1	this	this	DET
ejpam-371	256	2	estimate	estimate	NOUN
ejpam-371	256	3	essentially	essentially	ADV
ejpam-371	256	4	gives	give	VERB
ejpam-371	256	5	the	the	DET
ejpam-371	256	6	unique	unique	ADJ
ejpam-371	256	7	continuation	continuation	NOUN
ejpam-371	256	8	property	property	NOUN
ejpam-371	256	9	for	for	ADP
ejpam-371	256	10	the	the	DET
ejpam-371	256	11	solutions	solution	NOUN
ejpam-371	256	12	of	of	ADP
ejpam-371	256	13	the	the	DET
ejpam-371	256	14	system	system	NOUN
ejpam-371	256	15	(	(	PUNCT
ejpam-371	256	16	5	5	NUM
ejpam-371	256	17	)	)	PUNCT
ejpam-371	256	18	,	,	PUNCT
ejpam-371	256	19	precisely	precisely	ADV
ejpam-371	256	20	,	,	PUNCT
ejpam-371	256	21	q	q	NOUN
ejpam-371	257	1	=	=	SYM
ejpam-371	257	2	0	0	NUM
ejpam-371	257	3	in	in	ADP
ejpam-371	257	4	(	(	PUNCT
ejpam-371	257	5	0	0	NUM
ejpam-371	257	6	,	,	PUNCT
ejpam-371	257	7	t	t	NOUN
ejpam-371	257	8	)	)	PUNCT
ejpam-371	257	9	×ω	×ω	PRON
ejpam-371	257	10	implies	imply	VERB
ejpam-371	257	11	q	q	PROPN
ejpam-371	257	12	≡	≡	PROPN
ejpam-371	257	13	0	0	PUNCT
ejpam-371	258	1	in	in	ADP
ejpam-371	258	2	(	(	PUNCT
ejpam-371	258	3	0	0	NUM
ejpam-371	258	4	,	,	PUNCT
ejpam-371	258	5	t	t	NOUN
ejpam-371	258	6	)	)	PUNCT
ejpam-371	258	7	×ω	×ω	ADV
ejpam-371	258	8	;	;	PUNCT
ejpam-371	258	9	in	in	ADP
ejpam-371	258	10	particular	particular	ADJ
ejpam-371	258	11	q(0	q(0	PROPN
ejpam-371	258	12	)	)	PUNCT
ejpam-371	258	13	=	=	SYM
ejpam-371	258	14	0	0	NUM
ejpam-371	258	15	in	in	ADP
ejpam-371	258	16	ω	ω	PROPN
ejpam-371	258	17	.	.	PUNCT
ejpam-371	259	1	now	now	ADV
ejpam-371	259	2	we	we	PRON
ejpam-371	259	3	state	state	VERB
ejpam-371	259	4	the	the	DET
ejpam-371	259	5	observability	observability	NOUN
ejpam-371	259	6	inequality	inequality	NOUN
ejpam-371	259	7	for	for	ADP
ejpam-371	259	8	the	the	DET
ejpam-371	259	9	adjoint	adjoint	NOUN
ejpam-371	259	10	system	system	NOUN
ejpam-371	259	11	(	(	PUNCT
ejpam-371	259	12	5	5	NUM
ejpam-371	259	13	)	)	PUNCT
ejpam-371	259	14	.	.	PUNCT
ejpam-371	260	1	corollary	corollary	ADJ
ejpam-371	260	2	1	1	NUM
ejpam-371	260	3	.	.	PUNCT
ejpam-371	261	1	under	under	ADP
ejpam-371	261	2	the	the	DET
ejpam-371	261	3	assumptions	assumption	NOUN
ejpam-371	261	4	of	of	ADP
ejpam-371	261	5	theorem	theorem	NOUN
ejpam-371	261	6	1	1	NUM
ejpam-371	261	7	,	,	PUNCT
ejpam-371	261	8	there	there	PRON
ejpam-371	261	9	exists	exist	VERB
ejpam-371	261	10	a	a	DET
ejpam-371	261	11	positive	positive	ADJ
ejpam-371	261	12	constant	constant	ADJ
ejpam-371	261	13	w	w	NOUN
ejpam-371	261	14	depending	depend	VERB
ejpam-371	261	15	on	on	ADP
ejpam-371	261	16	ω	ω	PROPN
ejpam-371	261	17	,	,	PUNCT
ejpam-371	261	18	ω	ω	PROPN
ejpam-371	261	19	,	,	PUNCT
ejpam-371	261	20	m	m	PROPN
ejpam-371	261	21	,	,	PUNCT
ejpam-371	261	22	n	n	PROPN
ejpam-371	261	23	and	and	CCONJ
ejpam-371	261	24	t	t	PROPN
ejpam-371	261	25	such	such	ADJ
ejpam-371	261	26	that	that	SCONJ
ejpam-371	261	27	‖q(0)‖2	‖q(0)‖2	PROPN
ejpam-371	261	28	l2(ω	l2(ω	NOUN
ejpam-371	261	29	)	)	PUNCT
ejpam-371	261	30	≤w	≤w	NOUN
ejpam-371	261	31	(	(	PUNCT
ejpam-371	261	32	ω	ω	PROPN
ejpam-371	261	33	,	,	PUNCT
ejpam-371	261	34	ω	ω	PROPN
ejpam-371	261	35	,	,	PUNCT
ejpam-371	261	36	t	t	PROPN
ejpam-371	261	37	)	)	PUNCT
ejpam-371	261	38	�	�	PROPN
ejpam-371	262	1	∫∫	∫∫	PROPN
ejpam-371	262	2	(	(	PUNCT
ejpam-371	262	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	262	4	|q|2d	|q|2d	NOUN
ejpam-371	262	5	xd	xd	INTJ
ejpam-371	262	6	t	t	NOUN
ejpam-371	262	7	+	+	CCONJ
ejpam-371	263	1	∫∫	∫∫	ADV
ejpam-371	263	2	q	q	ADJ
ejpam-371	263	3	|g|2d	|g|2d	ADJ
ejpam-371	263	4	xd	xd	PROPN
ejpam-371	263	5	t	t	PROPN
ejpam-371	263	6	�	�	PROPN
ejpam-371	263	7	(	(	PUNCT
ejpam-371	263	8	24	24	NUM
ejpam-371	263	9	)	)	PUNCT
ejpam-371	263	10	where	where	SCONJ
ejpam-371	263	11	w	w	X
ejpam-371	263	12	(	(	PUNCT
ejpam-371	263	13	·	·	PUNCT
ejpam-371	263	14	)	)	PUNCT
ejpam-371	263	15	=	=	SYM
ejpam-371	263	16	exp	exp	NOUN
ejpam-371	263	17	�	�	PROPN
ejpam-371	263	18	c(1	c(1	PROPN
ejpam-371	263	19	+	+	PROPN
ejpam-371	263	20	1	1	NUM
ejpam-371	263	21	t	t	NOUN
ejpam-371	263	22	+	+	CCONJ
ejpam-371	263	23	1p	1p	NUM
ejpam-371	263	24	t	t	NOUN
ejpam-371	263	25	+	+	X
ejpam-371	263	26	t	t	PROPN
ejpam-371	263	27	+	+	CCONJ
ejpam-371	263	28	t	t	PROPN
ejpam-371	263	29	2	2	NUM
ejpam-371	263	30	+	+	NUM
ejpam-371	263	31	t	t	PROPN
ejpam-371	263	32	2(‖m‖2	2(‖m‖2	NUM
ejpam-371	263	33	l∞	l∞	NOUN
ejpam-371	263	34	+	+	NUM
ejpam-371	263	35	‖n‖2l∞	‖n‖2l∞	NOUN
ejpam-371	263	36	)	)	PUNCT
ejpam-371	263	37	�	�	PROPN
ejpam-371	263	38	and	and	CCONJ
ejpam-371	263	39	q	q	NOUN
ejpam-371	263	40	is	be	AUX
ejpam-371	263	41	the	the	DET
ejpam-371	263	42	weak	weak	ADJ
ejpam-371	263	43	solution	solution	NOUN
ejpam-371	263	44	of	of	ADP
ejpam-371	263	45	the	the	DET
ejpam-371	263	46	problem	problem	NOUN
ejpam-371	263	47	(	(	PUNCT
ejpam-371	263	48	5	5	NUM
ejpam-371	263	49	)	)	PUNCT
ejpam-371	263	50	.	.	PUNCT
ejpam-371	264	1	proof	proof	NOUN
ejpam-371	264	2	.	.	PUNCT
ejpam-371	265	1	let	let	VERB
ejpam-371	265	2	q	q	PRON
ejpam-371	265	3	be	be	AUX
ejpam-371	265	4	the	the	DET
ejpam-371	265	5	solution	solution	NOUN
ejpam-371	265	6	of	of	ADP
ejpam-371	265	7	(	(	PUNCT
ejpam-371	265	8	5	5	NUM
ejpam-371	265	9	)	)	PUNCT
ejpam-371	265	10	and	and	CCONJ
ejpam-371	265	11	g	g	PROPN
ejpam-371	265	12	∈	∈	PROPN
ejpam-371	265	13	l2(q	l2(q	PROPN
ejpam-371	265	14	)	)	PUNCT
ejpam-371	265	15	.	.	PUNCT
ejpam-371	266	1	we	we	PRON
ejpam-371	266	2	shall	shall	AUX
ejpam-371	266	3	first	first	ADV
ejpam-371	266	4	prove	prove	VERB
ejpam-371	266	5	the	the	DET
ejpam-371	266	6	variant	variant	NOUN
ejpam-371	266	7	of	of	ADP
ejpam-371	266	8	the	the	DET
ejpam-371	266	9	inequality	inequality	NOUN
ejpam-371	266	10	(	(	PUNCT
ejpam-371	266	11	24	24	NUM
ejpam-371	266	12	)	)	PUNCT
ejpam-371	266	13	,	,	PUNCT
ejpam-371	266	14	namely	namely	ADV
ejpam-371	266	15	,	,	PUNCT
ejpam-371	266	16	‖q(0)‖2	‖q(0)‖2	PROPN
ejpam-371	266	17	l2(ω	l2(ω	NOUN
ejpam-371	266	18	)	)	PUNCT
ejpam-371	266	19	≤w	≤w	ADJ
ejpam-371	266	20	∗(t	∗(t	PROPN
ejpam-371	266	21	)	)	PUNCT
ejpam-371	266	22	�	�	PROPN
ejpam-371	267	1	∫∫	∫∫	ADV
ejpam-371	267	2	(	(	PUNCT
ejpam-371	267	3	t/4,3t/4)×ω	t/4,3t/4)×ω	PROPN
ejpam-371	267	4	|q|2d	|q|2d	NOUN
ejpam-371	267	5	xd	xd	INTJ
ejpam-371	267	6	t	t	NOUN
ejpam-371	267	7	+	+	CCONJ
ejpam-371	268	1	∫∫	∫∫	ADV
ejpam-371	268	2	q	q	NOUN
ejpam-371	268	3	|g|2d	|g|2d	NOUN
ejpam-371	268	4	xd	xd	INTJ
ejpam-371	268	5	t	t	PROPN
ejpam-371	268	6	r.	r.	PROPN
ejpam-371	268	7	lavanya	lavanya	PROPN
ejpam-371	268	8	/	/	SYM
ejpam-371	268	9	eur	eur	PROPN
ejpam-371	268	10	.	.	PUNCT
ejpam-371	269	1	j.	j.	PROPN
ejpam-371	269	2	pure	pure	PROPN
ejpam-371	269	3	appl	appl	PROPN
ejpam-371	269	4	.	.	PROPN
ejpam-371	269	5	math	math	PROPN
ejpam-371	269	6	,	,	PUNCT
ejpam-371	269	7	3	3	NUM
ejpam-371	269	8	(	(	PUNCT
ejpam-371	269	9	2010	2010	NUM
ejpam-371	269	10	)	)	PUNCT
ejpam-371	269	11	,	,	PUNCT
ejpam-371	269	12	235	235	NUM
ejpam-371	269	13	-	-	SYM
ejpam-371	269	14	253	253	NUM
ejpam-371	269	15	246	246	NUM
ejpam-371	269	16	+	+	CCONJ
ejpam-371	270	1	∫∫	∫∫	ADV
ejpam-371	270	2	(	(	PUNCT
ejpam-371	270	3	t0,t1)×ω	t0,t1)×ω	PROPN
ejpam-371	270	4	e−2sα(sφ)−1(|∆q|2	e−2sα(sφ)−1(|∆q|2	VERB
ejpam-371	270	5	+	+	CCONJ
ejpam-371	270	6	|qt	|qt	PRON
ejpam-371	270	7	|2)d	|2)d	PUNCT
ejpam-371	270	8	xd	xd	INTJ
ejpam-371	270	9	t	t	PROPN
ejpam-371	270	10	�	�	PROPN
ejpam-371	270	11	(	(	PUNCT
ejpam-371	270	12	25	25	NUM
ejpam-371	270	13	)	)	PUNCT
ejpam-371	270	14	where	where	SCONJ
ejpam-371	270	15	w	w	NOUN
ejpam-371	270	16	∗	∗	X
ejpam-371	270	17	(	(	PUNCT
ejpam-371	270	18	·	·	PUNCT
ejpam-371	270	19	)	)	PUNCT
ejpam-371	270	20	=	=	PUNCT
ejpam-371	271	1	exp[c	exp[c	ADJ
ejpam-371	271	2	(	(	PUNCT
ejpam-371	271	3	1	1	NUM
ejpam-371	271	4	t	t	NOUN
ejpam-371	271	5	+	+	NUM
ejpam-371	271	6	t	t	PROPN
ejpam-371	271	7	+	+	X
ejpam-371	271	8	t	t	PROPN
ejpam-371	271	9	2(‖m‖2	2(‖m‖2	NUM
ejpam-371	271	10	l∞	l∞	NOUN
ejpam-371	271	11	+	+	CCONJ
ejpam-371	271	12	‖n‖2l∞	‖n‖2l∞	NOUN
ejpam-371	271	13	)	)	PUNCT
ejpam-371	271	14	]	]	PUNCT
ejpam-371	271	15	.	.	PUNCT
ejpam-371	272	1	multiplying	multiply	VERB
ejpam-371	272	2	(	(	PUNCT
ejpam-371	272	3	5	5	NUM
ejpam-371	272	4	)	)	PUNCT
ejpam-371	272	5	by	by	ADP
ejpam-371	272	6	q	q	NOUN
ejpam-371	272	7	and	and	CCONJ
ejpam-371	272	8	integrating	integrate	VERB
ejpam-371	272	9	on	on	ADP
ejpam-371	272	10	ω	ω	PROPN
ejpam-371	272	11	,	,	PUNCT
ejpam-371	272	12	we	we	PRON
ejpam-371	272	13	get	get	VERB
ejpam-371	272	14	−1	−1	ADV
ejpam-371	272	15	2	2	NUM
ejpam-371	273	1	d	d	NOUN
ejpam-371	274	1	d	d	NOUN
ejpam-371	275	1	t	t	PROPN
ejpam-371	276	1	∫	∫	PROPN
ejpam-371	277	1	ω	ω	NUM
ejpam-371	277	2	|q|2d	|q|2d	NOUN
ejpam-371	277	3	x	x	SYM
ejpam-371	278	1	+	+	NUM
ejpam-371	278	2	∫	∫	PROPN
ejpam-371	278	3	ω	ω	NUM
ejpam-371	278	4	|∇q|2d	|∇q|2d	NOUN
ejpam-371	278	5	x	x	SYM
ejpam-371	278	6	≤	≤	NUM
ejpam-371	278	7	3	3	NUM
ejpam-371	278	8	2	2	NUM
ejpam-371	278	9	∫	∫	PROPN
ejpam-371	278	10	ω	ω	NUM
ejpam-371	278	11	|q|2d	|q|2d	NOUN
ejpam-371	278	12	x	x	X
ejpam-371	279	1	+	+	CCONJ
ejpam-371	279	2	1	1	NUM
ejpam-371	279	3	2	2	NUM
ejpam-371	279	4	∫	∫	PROPN
ejpam-371	279	5	ω	ω	PROPN
ejpam-371	279	6	�	�	PROPN
ejpam-371	279	7	|g|2	|g|2	PROPN
ejpam-371	279	8	+	+	PROPN
ejpam-371	279	9	�	�	PROPN
ejpam-371	279	10	�	�	PROPN
ejpam-371	279	11	m	m	PROPN
ejpam-371	279	12	t	t	PROPN
ejpam-371	279	13	t	t	PROPN
ejpam-371	279	14	∗∆q(t	∗∆q(t	ADJ
ejpam-371	279	15	)	)	PUNCT
ejpam-371	279	16	�	�	PROPN
ejpam-371	279	17	�	�	PROPN
ejpam-371	279	18	2	2	NUM
ejpam-371	279	19	+	+	NUM
ejpam-371	279	20	�	�	PROPN
ejpam-371	279	21	�	�	PROPN
ejpam-371	279	22	n	n	ADP
ejpam-371	279	23	t	t	NOUN
ejpam-371	279	24	t	t	PROPN
ejpam-371	279	25	∗	∗	NOUN
ejpam-371	279	26	qt(t	qt(t	NOUN
ejpam-371	279	27	)	)	PUNCT
ejpam-371	279	28	�	�	PROPN
ejpam-371	279	29	�	�	PROPN
ejpam-371	279	30	2	2	NUM
ejpam-371	279	31	�	�	PROPN
ejpam-371	279	32	d	d	NOUN
ejpam-371	279	33	x	x	NOUN
ejpam-371	279	34	.	.	PUNCT
ejpam-371	280	1	it	it	PRON
ejpam-371	280	2	follows	follow	VERB
ejpam-371	280	3	that	that	SCONJ
ejpam-371	280	4	−	−	PROPN
ejpam-371	281	1	d	d	X
ejpam-371	281	2	d	d	PROPN
ejpam-371	281	3	t	t	PROPN
ejpam-371	281	4	�	�	PROPN
ejpam-371	281	5	exp[3	exp[3	PROPN
ejpam-371	281	6	t	t	PROPN
ejpam-371	281	7	]	]	PUNCT
ejpam-371	281	8	∫	∫	PROPN
ejpam-371	281	9	ω	ω	NUM
ejpam-371	281	10	|q|2d	|q|2d	NOUN
ejpam-371	281	11	x	x	SYM
ejpam-371	281	12	�	�	PROPN
ejpam-371	281	13	≤	≤	PROPN
ejpam-371	281	14	exp[3	exp[3	NOUN
ejpam-371	281	15	t	t	X
ejpam-371	281	16	]	]	X
ejpam-371	281	17	∫	∫	PROPN
ejpam-371	281	18	ω	ω	PROPN
ejpam-371	281	19	�	�	PROPN
ejpam-371	281	20	|g|2	|g|2	PROPN
ejpam-371	281	21	+	+	PROPN
ejpam-371	281	22	�	�	PROPN
ejpam-371	281	23	�	�	PROPN
ejpam-371	281	24	m	m	PROPN
ejpam-371	281	25	t	t	PROPN
ejpam-371	281	26	t	t	PROPN
ejpam-371	281	27	∗∆q(t	∗∆q(t	ADJ
ejpam-371	281	28	)	)	PUNCT
ejpam-371	281	29	�	�	PROPN
ejpam-371	281	30	�	�	PROPN
ejpam-371	281	31	2	2	NUM
ejpam-371	281	32	+	+	NUM
ejpam-371	281	33	�	�	PROPN
ejpam-371	281	34	�	�	PROPN
ejpam-371	281	35	n	n	ADP
ejpam-371	281	36	t	t	NOUN
ejpam-371	281	37	t	t	PROPN
ejpam-371	281	38	∗	∗	NOUN
ejpam-371	281	39	qt(t	qt(t	NOUN
ejpam-371	281	40	)	)	PUNCT
ejpam-371	281	41	�	�	PROPN
ejpam-371	281	42	�	�	PROPN
ejpam-371	281	43	2	2	NUM
ejpam-371	281	44	�	�	PROPN
ejpam-371	281	45	d	d	NOUN
ejpam-371	281	46	x	x	X
ejpam-371	281	47	.	.	PUNCT
ejpam-371	282	1	(	(	PUNCT
ejpam-371	282	2	26	26	NUM
ejpam-371	282	3	)	)	PUNCT
ejpam-371	282	4	integrating	integrating	NOUN
ejpam-371	282	5	(	(	PUNCT
ejpam-371	282	6	26	26	NUM
ejpam-371	282	7	)	)	PUNCT
ejpam-371	282	8	with	with	ADP
ejpam-371	282	9	respect	respect	NOUN
ejpam-371	282	10	to	to	ADP
ejpam-371	282	11	time	time	NOUN
ejpam-371	282	12	in	in	ADP
ejpam-371	282	13	0≤	0≤	NUM
ejpam-371	282	14	t	t	NOUN
ejpam-371	282	15	≤	≤	NOUN
ejpam-371	282	16	t/4	t/4	PROPN
ejpam-371	282	17	,	,	PUNCT
ejpam-371	282	18	we	we	PRON
ejpam-371	282	19	have	have	VERB
ejpam-371	282	20	∫	∫	PROPN
ejpam-371	282	21	ω	ω	NUM
ejpam-371	282	22	|q(0)|2d	|q(0)|2d	PROPN
ejpam-371	282	23	x	x	SYM
ejpam-371	282	24	≤	≤	NOUN
ejpam-371	282	25	exp[3t/4	exp[3t/4	NOUN
ejpam-371	282	26	]	]	PUNCT
ejpam-371	282	27	∫	∫	PROPN
ejpam-371	282	28	ω	ω	NUM
ejpam-371	282	29	|q(t/4	|q(t/4	NUM
ejpam-371	282	30	,	,	PUNCT
ejpam-371	282	31	x)|2d	x)|2d	PROPN
ejpam-371	282	32	x	x	PUNCT
ejpam-371	283	1	+	+	NOUN
ejpam-371	283	2	exp[3	exp[3	NOUN
ejpam-371	283	3	t	t	X
ejpam-371	283	4	]	]	X
ejpam-371	283	5	∫	∫	PROPN
ejpam-371	283	6	t/4	t/4	PROPN
ejpam-371	283	7	0	0	NUM
ejpam-371	284	1	∫	∫	PROPN
ejpam-371	284	2	ω	ω	PROPN
ejpam-371	284	3	�	�	PROPN
ejpam-371	284	4	|g|2	|g|2	PROPN
ejpam-371	284	5	+	+	PROPN
ejpam-371	284	6	�	�	PROPN
ejpam-371	284	7	�	�	PROPN
ejpam-371	284	8	m	m	PROPN
ejpam-371	284	9	t	t	PROPN
ejpam-371	284	10	t	t	PROPN
ejpam-371	284	11	∗∆q(t	∗∆q(t	ADJ
ejpam-371	284	12	)	)	PUNCT
ejpam-371	284	13	�	�	PROPN
ejpam-371	284	14	�	�	PROPN
ejpam-371	284	15	2	2	NUM
ejpam-371	284	16	+	+	NUM
ejpam-371	284	17	�	�	PROPN
ejpam-371	284	18	�	�	PROPN
ejpam-371	284	19	n	n	ADP
ejpam-371	284	20	t	t	NOUN
ejpam-371	284	21	t	t	PROPN
ejpam-371	284	22	∗	∗	NOUN
ejpam-371	284	23	qt(t	qt(t	NOUN
ejpam-371	284	24	)	)	PUNCT
ejpam-371	284	25	�	�	PROPN
ejpam-371	284	26	�	�	PROPN
ejpam-371	284	27	2	2	NUM
ejpam-371	284	28	�	�	PROPN
ejpam-371	284	29	d	d	PROPN
ejpam-371	284	30	xdτ	xdτ	PROPN
ejpam-371	284	31	.	.	PUNCT
ejpam-371	285	1	again	again	ADV
ejpam-371	285	2	integrating	integrate	VERB
ejpam-371	285	3	(	(	PUNCT
ejpam-371	285	4	26	26	NUM
ejpam-371	285	5	)	)	PUNCT
ejpam-371	285	6	from	from	ADP
ejpam-371	285	7	t/4	t/4	PROPN
ejpam-371	285	8	to	to	ADP
ejpam-371	285	9	t	t	PROPN
ejpam-371	285	10	,	,	PUNCT
ejpam-371	285	11	we	we	PRON
ejpam-371	285	12	get	get	AUX
ejpam-371	285	13	exp[3t/4	exp[3t/4	NOUN
ejpam-371	285	14	]	]	X
ejpam-371	285	15	∫	∫	PROPN
ejpam-371	285	16	ω	ω	NUM
ejpam-371	285	17	|q(t/4	|q(t/4	NUM
ejpam-371	285	18	,	,	PUNCT
ejpam-371	285	19	x)|2d	x)|2d	PROPN
ejpam-371	286	1	x	x	SYM
ejpam-371	286	2	≤	≤	NUM
ejpam-371	286	3	exp[3	exp[3	NOUN
ejpam-371	286	4	t	t	X
ejpam-371	286	5	]	]	PUNCT
ejpam-371	286	6	∫	∫	PROPN
ejpam-371	286	7	ω	ω	NUM
ejpam-371	286	8	|q|2d	|q|2d	NOUN
ejpam-371	286	9	x	x	SYM
ejpam-371	287	1	+	+	NOUN
ejpam-371	287	2	exp[3	exp[3	NOUN
ejpam-371	287	3	t	t	X
ejpam-371	287	4	]	]	X
ejpam-371	287	5	∫	∫	PROPN
ejpam-371	287	6	t	t	PROPN
ejpam-371	287	7	t/4	t/4	PROPN
ejpam-371	287	8	∫	∫	PROPN
ejpam-371	287	9	ω	ω	PROPN
ejpam-371	287	10	�	�	PROPN
ejpam-371	287	11	|g|2	|g|2	PROPN
ejpam-371	287	12	+	+	PROPN
ejpam-371	287	13	�	�	PROPN
ejpam-371	287	14	�	�	PROPN
ejpam-371	287	15	m	m	PROPN
ejpam-371	287	16	t	t	PROPN
ejpam-371	287	17	t	t	PROPN
ejpam-371	287	18	∗∆q(t	∗∆q(t	ADJ
ejpam-371	287	19	)	)	PUNCT
ejpam-371	287	20	�	�	PROPN
ejpam-371	287	21	�	�	PROPN
ejpam-371	287	22	2	2	NUM
ejpam-371	287	23	+	+	NUM
ejpam-371	287	24	�	�	PROPN
ejpam-371	287	25	�	�	PROPN
ejpam-371	287	26	n	n	ADP
ejpam-371	287	27	t	t	NOUN
ejpam-371	287	28	t	t	PROPN
ejpam-371	287	29	∗	∗	NOUN
ejpam-371	287	30	qt(t	qt(t	NOUN
ejpam-371	287	31	)	)	PUNCT
ejpam-371	287	32	�	�	PROPN
ejpam-371	287	33	�	�	PROPN
ejpam-371	287	34	2	2	NUM
ejpam-371	287	35	�	�	PROPN
ejpam-371	287	36	d	d	NOUN
ejpam-371	287	37	xdτ	xdτ	NOUN
ejpam-371	287	38	for	for	ADP
ejpam-371	287	39	all	all	DET
ejpam-371	287	40	t	t	PROPN
ejpam-371	287	41	∈	∈	PROPN
ejpam-371	287	42	�	�	PROPN
ejpam-371	287	43	t/4,3t/4	t/4,3t/4	PROPN
ejpam-371	287	44	�	�	PROPN
ejpam-371	287	45	.	.	PUNCT
ejpam-371	288	1	thus	thus	ADV
ejpam-371	288	2	we	we	PRON
ejpam-371	288	3	have	have	VERB
ejpam-371	288	4	∫	∫	PROPN
ejpam-371	288	5	ω	ω	NUM
ejpam-371	288	6	|q(0)|2d	|q(0)|2d	PROPN
ejpam-371	288	7	x	x	SYM
ejpam-371	288	8	≤	≤	PROPN
ejpam-371	288	9	c	c	NOUN
ejpam-371	288	10	�	�	PROPN
ejpam-371	288	11	∫	∫	PROPN
ejpam-371	288	12	ω	ω	PROPN
ejpam-371	288	13	|q|2d	|q|2d	NOUN
ejpam-371	288	14	x	x	SYM
ejpam-371	289	1	+	+	NUM
ejpam-371	289	2	∫	∫	PROPN
ejpam-371	289	3	t	t	PROPN
ejpam-371	289	4	0	0	NUM
ejpam-371	289	5	∫	∫	PROPN
ejpam-371	289	6	ω	ω	PROPN
ejpam-371	289	7	�	�	PROPN
ejpam-371	289	8	|g|2	|g|2	PROPN
ejpam-371	289	9	+	+	PROPN
ejpam-371	289	10	�	�	PROPN
ejpam-371	289	11	�	�	PROPN
ejpam-371	289	12	m	m	PROPN
ejpam-371	289	13	t	t	PROPN
ejpam-371	289	14	t	t	PROPN
ejpam-371	289	15	∗∆q(t	∗∆q(t	ADJ
ejpam-371	289	16	)	)	PUNCT
ejpam-371	289	17	�	�	PROPN
ejpam-371	289	18	�	�	PROPN
ejpam-371	289	19	2	2	NUM
ejpam-371	289	20	+	+	NUM
ejpam-371	289	21	�	�	PROPN
ejpam-371	289	22	�	�	PROPN
ejpam-371	289	23	n	n	ADP
ejpam-371	289	24	t	t	NOUN
ejpam-371	289	25	t	t	PROPN
ejpam-371	289	26	∗	∗	NOUN
ejpam-371	289	27	qt(t	qt(t	NOUN
ejpam-371	289	28	)	)	PUNCT
ejpam-371	289	29	�	�	PROPN
ejpam-371	289	30	�	�	PROPN
ejpam-371	289	31	2	2	NUM
ejpam-371	289	32	�	�	PROPN
ejpam-371	289	33	d	d	PROPN
ejpam-371	289	34	xdτ	xdτ	PROPN
ejpam-371	289	35	�	�	PROPN
ejpam-371	289	36	,	,	PUNCT
ejpam-371	289	37	(	(	PUNCT
ejpam-371	289	38	27	27	NUM
ejpam-371	289	39	)	)	PUNCT
ejpam-371	290	1	where	where	SCONJ
ejpam-371	290	2	c	c	NOUN
ejpam-371	290	3	=	=	SYM
ejpam-371	290	4	exp[3	exp[3	PROPN
ejpam-371	290	5	t	t	PROPN
ejpam-371	290	6	]	]	PUNCT
ejpam-371	290	7	.	.	PUNCT
ejpam-371	291	1	by	by	ADP
ejpam-371	291	2	the	the	DET
ejpam-371	291	3	assumption	assumption	NOUN
ejpam-371	291	4	on	on	ADP
ejpam-371	291	5	the	the	DET
ejpam-371	291	6	kernel	kernel	NOUN
ejpam-371	291	7	,	,	PUNCT
ejpam-371	291	8	we	we	PRON
ejpam-371	291	9	have	have	VERB
ejpam-371	291	10	∫	∫	PROPN
ejpam-371	291	11	t	t	PROPN
ejpam-371	291	12	0	0	NUM
ejpam-371	292	1	∫	∫	PROPN
ejpam-371	292	2	ω	ω	PROPN
ejpam-371	292	3	�	�	PROPN
ejpam-371	292	4	�	�	PROPN
ejpam-371	292	5	�	�	PROPN
ejpam-371	292	6	m	m	PROPN
ejpam-371	292	7	t	t	PROPN
ejpam-371	292	8	t	t	PROPN
ejpam-371	292	9	∗∆q(t	∗∆q(t	ADJ
ejpam-371	292	10	)	)	PUNCT
ejpam-371	292	11	�	�	PROPN
ejpam-371	292	12	�	�	PROPN
ejpam-371	292	13	�	�	PROPN
ejpam-371	292	14	2	2	NUM
ejpam-371	292	15	d	d	NOUN
ejpam-371	292	16	xdτ	xdτ	PROPN
ejpam-371	292	17	≤	≤	NUM
ejpam-371	292	18	∫	∫	PROPN
ejpam-371	292	19	t	t	PROPN
ejpam-371	292	20	0	0	NUM
ejpam-371	292	21	∫	∫	PROPN
ejpam-371	292	22	ω	ω	PROPN
ejpam-371	292	23	�	�	PROPN
ejpam-371	292	24	∫	∫	PROPN
ejpam-371	292	25	t1	t1	PROPN
ejpam-371	292	26	t0	t0	PROPN
ejpam-371	292	27	|m(τ	|m(τ	PROPN
ejpam-371	292	28	,	,	PUNCT
ejpam-371	292	29	t)|2es(1	t)|2es(1	PROPN
ejpam-371	292	30	+	+	PROPN
ejpam-371	292	31	2α(τ))φ(τ)dτ	2α(τ))φ(τ)dτ	PROPN
ejpam-371	292	32	�	�	PROPN
ejpam-371	292	33	�	�	PROPN
ejpam-371	292	34	∫	∫	PROPN
ejpam-371	292	35	t1	t1	PROPN
ejpam-371	292	36	t0	t0	PROPN
ejpam-371	292	37	e−2sα(τ)s−1φ−1(τ)|∆q(τ)|2dτ	e−2sα(τ)s−1φ−1(τ)|∆q(τ)|2dτ	PROPN
ejpam-371	292	38	�	�	PROPN
ejpam-371	293	1	d	d	PROPN
ejpam-371	293	2	xd	xd	PROPN
ejpam-371	293	3	t	t	PROPN
ejpam-371	293	4	≤	≤	NUM
ejpam-371	293	5	c	c	NOUN
ejpam-371	293	6	t‖m‖2l∞	t‖m‖2l∞	NOUN
ejpam-371	293	7	∫∫	∫∫	PROPN
ejpam-371	293	8	(	(	PUNCT
ejpam-371	293	9	t0	t0	PROPN
ejpam-371	293	10	,	,	PUNCT
ejpam-371	293	11	t1)×ω	t1)×ω	NOUN
ejpam-371	293	12	e−2sα(sφ)−1|∆q|2d	e−2sα(sφ)−1|∆q|2d	NOUN
ejpam-371	293	13	xd	xd	PUNCT
ejpam-371	293	14	t.	t.	PROPN
ejpam-371	293	15	(	(	PUNCT
ejpam-371	293	16	28	28	NUM
ejpam-371	293	17	)	)	PUNCT
ejpam-371	293	18	r.	r.	PROPN
ejpam-371	293	19	lavanya	lavanya	PROPN
ejpam-371	293	20	/	/	SYM
ejpam-371	293	21	eur	eur	PROPN
ejpam-371	293	22	.	.	PUNCT
ejpam-371	294	1	j.	j.	PROPN
ejpam-371	294	2	pure	pure	PROPN
ejpam-371	294	3	appl	appl	PROPN
ejpam-371	294	4	.	.	PROPN
ejpam-371	294	5	math	math	PROPN
ejpam-371	294	6	,	,	PUNCT
ejpam-371	294	7	3	3	NUM
ejpam-371	294	8	(	(	PUNCT
ejpam-371	294	9	2010	2010	NUM
ejpam-371	294	10	)	)	PUNCT
ejpam-371	294	11	,	,	PUNCT
ejpam-371	294	12	235	235	NUM
ejpam-371	294	13	-	-	SYM
ejpam-371	294	14	253	253	NUM
ejpam-371	294	15	247	247	NUM
ejpam-371	294	16	now	now	ADV
ejpam-371	294	17	estimating	estimate	VERB
ejpam-371	294	18	the	the	DET
ejpam-371	294	19	integral	integral	ADJ
ejpam-371	294	20	∫	∫	PROPN
ejpam-371	294	21	t	t	PROPN
ejpam-371	294	22	0	0	NUM
ejpam-371	294	23	∫	∫	PROPN
ejpam-371	294	24	ω	ω	PROPN
ejpam-371	294	25	�	�	PROPN
ejpam-371	294	26	�	�	PROPN
ejpam-371	294	27	n	n	ADP
ejpam-371	294	28	t	t	PROPN
ejpam-371	294	29	t	t	PROPN
ejpam-371	294	30	∗	∗	NOUN
ejpam-371	294	31	qt(t	qt(t	NOUN
ejpam-371	294	32	)	)	PUNCT
ejpam-371	294	33	�	�	PROPN
ejpam-371	294	34	�	�	PROPN
ejpam-371	294	35	2d	2d	NUM
ejpam-371	294	36	xdτ	xdτ	NOUN
ejpam-371	294	37	similar	similar	ADJ
ejpam-371	294	38	to	to	ADP
ejpam-371	294	39	the	the	DET
ejpam-371	294	40	above	above	NOUN
ejpam-371	294	41	and	and	CCONJ
ejpam-371	294	42	substituting	substitute	VERB
ejpam-371	294	43	the	the	DET
ejpam-371	294	44	preceding	precede	VERB
ejpam-371	294	45	estimates	estimate	NOUN
ejpam-371	294	46	into	into	ADP
ejpam-371	294	47	(	(	PUNCT
ejpam-371	294	48	27	27	NUM
ejpam-371	294	49	)	)	PUNCT
ejpam-371	294	50	and	and	CCONJ
ejpam-371	294	51	integrating	integrate	VERB
ejpam-371	294	52	the	the	DET
ejpam-371	294	53	resulting	result	VERB
ejpam-371	294	54	inequality	inequality	NOUN
ejpam-371	294	55	with	with	ADP
ejpam-371	294	56	respect	respect	NOUN
ejpam-371	294	57	to	to	ADP
ejpam-371	294	58	time	time	NOUN
ejpam-371	294	59	in	in	ADP
ejpam-371	294	60	(	(	PUNCT
ejpam-371	294	61	t/4,3t/4	t/4,3t/4	PROPN
ejpam-371	294	62	)	)	PUNCT
ejpam-371	294	63	,	,	PUNCT
ejpam-371	294	64	one	one	PRON
ejpam-371	294	65	can	can	AUX
ejpam-371	294	66	obtain	obtain	VERB
ejpam-371	294	67	the	the	DET
ejpam-371	294	68	inequality	inequality	NOUN
ejpam-371	294	69	(	(	PUNCT
ejpam-371	294	70	25	25	NUM
ejpam-371	294	71	)	)	PUNCT
ejpam-371	294	72	.	.	PUNCT
ejpam-371	295	1	to	to	PART
ejpam-371	295	2	complete	complete	VERB
ejpam-371	295	3	the	the	DET
ejpam-371	295	4	proof	proof	NOUN
ejpam-371	295	5	it	it	PRON
ejpam-371	295	6	suffices	suffice	VERB
ejpam-371	295	7	to	to	PART
ejpam-371	295	8	obtain	obtain	VERB
ejpam-371	295	9	an	an	DET
ejpam-371	295	10	estimate	estimate	NOUN
ejpam-371	295	11	for	for	ADP
ejpam-371	295	12	the	the	DET
ejpam-371	295	13	right	right	ADJ
ejpam-371	295	14	hand	hand	NOUN
ejpam-371	295	15	side	side	NOUN
ejpam-371	295	16	integrals	integral	NOUN
ejpam-371	295	17	of	of	ADP
ejpam-371	295	18	(	(	PUNCT
ejpam-371	295	19	25	25	NUM
ejpam-371	295	20	)	)	PUNCT
ejpam-371	295	21	in	in	ADP
ejpam-371	295	22	terms	term	NOUN
ejpam-371	295	23	of	of	ADP
ejpam-371	295	24	the	the	DET
ejpam-371	295	25	l2	l2	NOUN
ejpam-371	295	26	integral	integral	ADJ
ejpam-371	295	27	of	of	ADP
ejpam-371	295	28	q	q	NOUN
ejpam-371	295	29	over	over	ADP
ejpam-371	295	30	(	(	PUNCT
ejpam-371	295	31	0	0	NUM
ejpam-371	295	32	,	,	PUNCT
ejpam-371	295	33	t	t	NOUN
ejpam-371	295	34	)	)	PUNCT
ejpam-371	295	35	×ω	×ω	NOUN
ejpam-371	295	36	.	.	PUNCT
ejpam-371	296	1	from	from	ADP
ejpam-371	296	2	the	the	DET
ejpam-371	296	3	carleman	carleman	ADJ
ejpam-371	296	4	estimate	estimate	NOUN
ejpam-371	296	5	for	for	ADP
ejpam-371	296	6	the	the	DET
ejpam-371	296	7	adjoint	adjoint	NOUN
ejpam-371	296	8	system	system	NOUN
ejpam-371	296	9	(	(	PUNCT
ejpam-371	296	10	5	5	NUM
ejpam-371	296	11	)	)	PUNCT
ejpam-371	296	12	,	,	PUNCT
ejpam-371	296	13	we	we	PRON
ejpam-371	296	14	obtain	obtain	VERB
ejpam-371	296	15	lq	lq	NOUN
ejpam-371	296	16	,	,	PUNCT
ejpam-371	296	17	s,1(q	s,1(q	ADJ
ejpam-371	296	18	)	)	PUNCT
ejpam-371	296	19	≤	≤	NUM
ejpam-371	296	20	c	c	NOUN
ejpam-371	296	21	�	�	PROPN
ejpam-371	297	1	∫∫	∫∫	ADV
ejpam-371	297	2	q	q	NOUN
ejpam-371	298	1	e−2sα|g|2d	e−2sα|g|2d	NOUN
ejpam-371	298	2	xd	xd	INTJ
ejpam-371	298	3	t	t	NOUN
ejpam-371	298	4	+	+	CCONJ
ejpam-371	299	1	∫∫	∫∫	ADV
ejpam-371	299	2	(	(	PUNCT
ejpam-371	299	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	299	4	e−2sαs3φ3|q|2d	e−2sαs3φ3|q|2d	PROPN
ejpam-371	299	5	xd	xd	PROPN
ejpam-371	299	6	t	t	PROPN
ejpam-371	299	7	�	�	PROPN
ejpam-371	299	8	.	.	PUNCT
ejpam-371	300	1	(	(	PUNCT
ejpam-371	300	2	29	29	NUM
ejpam-371	300	3	)	)	PUNCT
ejpam-371	300	4	here	here	ADV
ejpam-371	300	5	one	one	PRON
ejpam-371	300	6	can	can	AUX
ejpam-371	300	7	easily	easily	ADV
ejpam-371	300	8	verify	verify	VERB
ejpam-371	300	9	the	the	DET
ejpam-371	300	10	following	follow	VERB
ejpam-371	300	11	weight	weight	NOUN
ejpam-371	300	12	function	function	NOUN
ejpam-371	300	13	estimates	estimate	NOUN
ejpam-371	300	14	using	use	VERB
ejpam-371	300	15	certain	certain	ADJ
ejpam-371	300	16	standard	standard	ADJ
ejpam-371	300	17	analysis	analysis	NOUN
ejpam-371	300	18	(	(	PUNCT
ejpam-371	300	19	see	see	VERB
ejpam-371	300	20	[	[	X
ejpam-371	300	21	5	5	NUM
ejpam-371	300	22	]	]	PUNCT
ejpam-371	300	23	):	):	PUNCT
ejpam-371	300	24	e−2sαφ3	e−2sαφ3	PROPN
ejpam-371	300	25	≤	≤	PROPN
ejpam-371	300	26	c(ω	c(ω	PROPN
ejpam-371	300	27	,	,	PUNCT
ejpam-371	300	28	ω	ω	NOUN
ejpam-371	300	29	)	)	PUNCT
ejpam-371	300	30	1	1	NUM
ejpam-371	300	31	(	(	PUNCT
ejpam-371	300	32	t(t	t(t	NOUN
ejpam-371	300	33	−	−	NOUN
ejpam-371	300	34	t))3	t))3	NOUN
ejpam-371	300	35	e2sα̃/t(t−t	e2sα̃/t(t−t	NOUN
ejpam-371	300	36	)	)	PUNCT
ejpam-371	300	37	≤	≤	PUNCT
ejpam-371	300	38	c(ω	c(ω	PROPN
ejpam-371	300	39	,	,	PUNCT
ejpam-371	300	40	ω	ω	NUM
ejpam-371	300	41	)	)	PUNCT
ejpam-371	300	42	�	�	PROPN
ejpam-371	300	43	2	2	NUM
ejpam-371	300	44	t	t	NOUN
ejpam-371	300	45	�	�	PROPN
ejpam-371	300	46	6	6	NUM
ejpam-371	300	47	e−σ(ω	e−σ(ω	ADJ
ejpam-371	300	48	,	,	PUNCT
ejpam-371	300	49	ω)st−2	ω)st−2	NOUN
ejpam-371	300	50	∀	∀	X
ejpam-371	300	51	(	(	PUNCT
ejpam-371	300	52	t	t	PROPN
ejpam-371	300	53	,	,	PUNCT
ejpam-371	300	54	x	x	NOUN
ejpam-371	300	55	)	)	PUNCT
ejpam-371	300	56	∈	∈	PROPN
ejpam-371	300	57	q̄	q̄	NOUN
ejpam-371	300	58	,	,	PUNCT
ejpam-371	300	59	provided	provide	VERB
ejpam-371	300	60	s	s	PRON
ejpam-371	300	61	≥	≥	NOUN
ejpam-371	300	62	s1	s1	NOUN
ejpam-371	300	63	=	=	SYM
ejpam-371	300	64	max(s0	max(s0	PROPN
ejpam-371	300	65	,	,	PUNCT
ejpam-371	300	66	3(σ(ω	3(σ(ω	NUM
ejpam-371	300	67	,	,	PUNCT
ejpam-371	300	68	ω))−1	ω))−1	PROPN
ejpam-371	300	69	t	t	PROPN
ejpam-371	300	70	2	2	NUM
ejpam-371	300	71	)	)	PUNCT
ejpam-371	300	72	,	,	PUNCT
ejpam-371	300	73	where	where	SCONJ
ejpam-371	300	74	the	the	DET
ejpam-371	300	75	constant	constant	ADJ
ejpam-371	300	76	σ(ω	σ(ω	PROPN
ejpam-371	300	77	,	,	PUNCT
ejpam-371	300	78	ω	ω	NOUN
ejpam-371	300	79	)	)	PUNCT
ejpam-371	300	80	=	=	SYM
ejpam-371	300	81	8	8	NUM
ejpam-371	300	82	min	min	NOUN
ejpam-371	300	83	eα	eα	NOUN
ejpam-371	300	84	.	.	PUNCT
ejpam-371	300	85	if	if	SCONJ
ejpam-371	300	86	we	we	PRON
ejpam-371	300	87	look	look	VERB
ejpam-371	300	88	at	at	ADP
ejpam-371	300	89	the	the	DET
ejpam-371	300	90	constants	constant	NOUN
ejpam-371	300	91	s0	s0	NOUN
ejpam-371	300	92	and	and	CCONJ
ejpam-371	300	93	s1	s1	NOUN
ejpam-371	300	94	,	,	PUNCT
ejpam-371	300	95	then	then	ADV
ejpam-371	300	96	we	we	PRON
ejpam-371	300	97	get	get	VERB
ejpam-371	300	98	s1	s1	NOUN
ejpam-371	300	99	≤	≤	NUM
ejpam-371	300	100	s2	s2	NOUN
ejpam-371	300	101	=	=	SYM
ejpam-371	300	102	c(ω	c(ω	PROPN
ejpam-371	300	103	,	,	PUNCT
ejpam-371	300	104	ω	ω	NUM
ejpam-371	300	105	)	)	PUNCT
ejpam-371	300	106	�	�	PROPN
ejpam-371	300	107	t	t	PROPN
ejpam-371	300	108	+	+	CCONJ
ejpam-371	300	109	t	t	PROPN
ejpam-371	300	110	2	2	NUM
ejpam-371	301	1	+	+	CCONJ
ejpam-371	301	2	t	t	PROPN
ejpam-371	301	3	p	p	X
ejpam-371	301	4	t	t	PROPN
ejpam-371	301	5	+	+	CCONJ
ejpam-371	301	6	t	t	PROPN
ejpam-371	301	7	4	4	NUM
ejpam-371	301	8	�	�	PROPN
ejpam-371	301	9	.	.	PUNCT
ejpam-371	302	1	for	for	ADP
ejpam-371	302	2	s	s	PROPN
ejpam-371	302	3	≥	≥	NOUN
ejpam-371	302	4	s2	s2	NOUN
ejpam-371	302	5	,	,	PUNCT
ejpam-371	302	6	we	we	PRON
ejpam-371	302	7	have	have	VERB
ejpam-371	302	8	e−2sαφ3	e−2sαφ3	PROPN
ejpam-371	302	9	≥	≥	NUM
ejpam-371	302	10	c(ω	c(ω	PROPN
ejpam-371	302	11	,	,	PUNCT
ejpam-371	302	12	ω	ω	NOUN
ejpam-371	302	13	)	)	PUNCT
ejpam-371	302	14	�	�	PROPN
ejpam-371	302	15	16	16	NUM
ejpam-371	302	16	3	3	NUM
ejpam-371	302	17	t	t	PROPN
ejpam-371	302	18	2	2	NUM
ejpam-371	302	19	�	�	PROPN
ejpam-371	302	20	3	3	NUM
ejpam-371	302	21	e−c(ω	e−c(ω	NOUN
ejpam-371	302	22	,	,	PUNCT
ejpam-371	302	23	ω)st−2	ω)st−2	NOUN
ejpam-371	302	24	∀	∀	X
ejpam-371	302	25	(	(	PUNCT
ejpam-371	302	26	t	t	PROPN
ejpam-371	302	27	,	,	PUNCT
ejpam-371	302	28	x	x	NOUN
ejpam-371	302	29	)	)	PUNCT
ejpam-371	302	30	∈	∈	PROPN
ejpam-371	303	1	[	[	X
ejpam-371	303	2	t/4,3t/4]×	t/4,3t/4]×	PROPN
ejpam-371	303	3	ω̄.	ω̄.	PUNCT
ejpam-371	303	4	let	let	VERB
ejpam-371	303	5	us	we	PRON
ejpam-371	303	6	fix	fix	VERB
ejpam-371	303	7	the	the	DET
ejpam-371	303	8	constant	constant	ADJ
ejpam-371	303	9	s	s	PART
ejpam-371	303	10	=	=	X
ejpam-371	303	11	s2	s2	NOUN
ejpam-371	303	12	and	and	CCONJ
ejpam-371	303	13	making	make	VERB
ejpam-371	303	14	use	use	NOUN
ejpam-371	303	15	of	of	ADP
ejpam-371	303	16	the	the	DET
ejpam-371	303	17	above	above	ADJ
ejpam-371	303	18	weight	weight	NOUN
ejpam-371	303	19	function	function	NOUN
ejpam-371	303	20	estimates	estimate	NOUN
ejpam-371	303	21	,	,	PUNCT
ejpam-371	303	22	and	and	CCONJ
ejpam-371	303	23	from	from	ADP
ejpam-371	303	24	(	(	PUNCT
ejpam-371	303	25	29	29	NUM
ejpam-371	303	26	)	)	PUNCT
ejpam-371	303	27	,	,	PUNCT
ejpam-371	303	28	we	we	PRON
ejpam-371	303	29	deduce	deduce	VERB
ejpam-371	303	30	the	the	DET
ejpam-371	303	31	following	follow	VERB
ejpam-371	303	32	estimate	estimate	NOUN
ejpam-371	303	33	∫∫	∫∫	PROPN
ejpam-371	303	34	(	(	PUNCT
ejpam-371	303	35	t/4,3t/4)×ω	t/4,3t/4)×ω	PROPN
ejpam-371	303	36	|q|2d	|q|2d	NOUN
ejpam-371	303	37	xd	xd	INTJ
ejpam-371	303	38	t	t	NOUN
ejpam-371	303	39	+	+	CCONJ
ejpam-371	304	1	∫∫	∫∫	ADV
ejpam-371	304	2	(	(	PUNCT
ejpam-371	304	3	t0,t1)×ω	t0,t1)×ω	PROPN
ejpam-371	304	4	e−2sα(sφ)−1(|∆q|2	e−2sα(sφ)−1(|∆q|2	VERB
ejpam-371	304	5	+	+	CCONJ
ejpam-371	304	6	|qt	|qt	PRON
ejpam-371	304	7	|2)d	|2)d	X
ejpam-371	304	8	xd	xd	INTJ
ejpam-371	304	9	t	t	PROPN
ejpam-371	304	10	≤fw	≤fw	PROPN
ejpam-371	304	11	(	(	PUNCT
ejpam-371	304	12	·	·	PUNCT
ejpam-371	304	13	)	)	PUNCT
ejpam-371	304	14	�	�	PROPN
ejpam-371	305	1	∫∫	∫∫	ADV
ejpam-371	305	2	(	(	PUNCT
ejpam-371	305	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	305	4	|q|2d	|q|2d	NOUN
ejpam-371	305	5	xd	xd	INTJ
ejpam-371	305	6	t	t	NOUN
ejpam-371	305	7	+	+	CCONJ
ejpam-371	306	1	∫∫	∫∫	ADV
ejpam-371	306	2	q	q	ADJ
ejpam-371	306	3	|g|2d	|g|2d	ADJ
ejpam-371	306	4	xd	xd	PROPN
ejpam-371	306	5	t	t	PROPN
ejpam-371	306	6	�	�	PROPN
ejpam-371	306	7	,	,	PUNCT
ejpam-371	306	8	where	where	SCONJ
ejpam-371	306	9	fw	fw	PROPN
ejpam-371	306	10	(	(	PUNCT
ejpam-371	306	11	·	·	PUNCT
ejpam-371	306	12	)	)	PUNCT
ejpam-371	306	13	=	=	SYM
ejpam-371	306	14	exp	exp	NOUN
ejpam-371	306	15	�	�	PROPN
ejpam-371	306	16	c(1	c(1	PROPN
ejpam-371	306	17	+	+	PROPN
ejpam-371	306	18	1	1	NUM
ejpam-371	306	19	t	t	NOUN
ejpam-371	306	20	+	+	CCONJ
ejpam-371	306	21	1p	1p	NUM
ejpam-371	306	22	t	t	NOUN
ejpam-371	306	23	+	+	X
ejpam-371	306	24	t	t	PROPN
ejpam-371	306	25	2	2	NUM
ejpam-371	306	26	)	)	PUNCT
ejpam-371	306	27	�	�	PROPN
ejpam-371	306	28	.	.	PUNCT
ejpam-371	307	1	coupling	couple	VERB
ejpam-371	307	2	the	the	DET
ejpam-371	307	3	above	above	ADJ
ejpam-371	307	4	estimate	estimate	NOUN
ejpam-371	307	5	with	with	ADP
ejpam-371	307	6	(	(	PUNCT
ejpam-371	307	7	25	25	NUM
ejpam-371	307	8	)	)	PUNCT
ejpam-371	307	9	,	,	PUNCT
ejpam-371	307	10	one	one	PRON
ejpam-371	307	11	can	can	AUX
ejpam-371	307	12	obtain	obtain	VERB
ejpam-371	307	13	the	the	DET
ejpam-371	307	14	observability	observability	NOUN
ejpam-371	307	15	estimate	estimate	NOUN
ejpam-371	307	16	(	(	PUNCT
ejpam-371	307	17	24	24	NUM
ejpam-371	307	18	)	)	PUNCT
ejpam-371	307	19	.	.	PUNCT
ejpam-371	308	1	3	3	X
ejpam-371	308	2	.	.	X
ejpam-371	308	3	controllability	controllability	NOUN
ejpam-371	308	4	results	result	NOUN
ejpam-371	308	5	in	in	ADP
ejpam-371	308	6	this	this	DET
ejpam-371	308	7	section	section	NOUN
ejpam-371	308	8	,	,	PUNCT
ejpam-371	308	9	we	we	PRON
ejpam-371	308	10	prove	prove	VERB
ejpam-371	308	11	a	a	DET
ejpam-371	308	12	null	null	ADJ
ejpam-371	308	13	controllability	controllability	NOUN
ejpam-371	308	14	result	result	NOUN
ejpam-371	308	15	for	for	ADP
ejpam-371	308	16	the	the	DET
ejpam-371	308	17	problem	problem	NOUN
ejpam-371	308	18	stated	state	VERB
ejpam-371	308	19	in	in	ADP
ejpam-371	308	20	(	(	PUNCT
ejpam-371	308	21	4	4	NUM
ejpam-371	308	22	)	)	PUNCT
ejpam-371	308	23	.	.	PUNCT
ejpam-371	309	1	we	we	PRON
ejpam-371	309	2	shall	shall	AUX
ejpam-371	309	3	obtain	obtain	VERB
ejpam-371	309	4	a	a	DET
ejpam-371	309	5	solution	solution	NOUN
ejpam-371	309	6	to	to	ADP
ejpam-371	309	7	the	the	DET
ejpam-371	309	8	global	global	ADJ
ejpam-371	309	9	controllability	controllability	NOUN
ejpam-371	309	10	problem	problem	NOUN
ejpam-371	309	11	for	for	ADP
ejpam-371	309	12	the	the	DET
ejpam-371	309	13	equation	equation	NOUN
ejpam-371	309	14	(	(	PUNCT
ejpam-371	309	15	4	4	NUM
ejpam-371	309	16	)	)	PUNCT
ejpam-371	309	17	as	as	ADP
ejpam-371	309	18	a	a	DET
ejpam-371	309	19	limit	limit	NOUN
ejpam-371	309	20	of	of	ADP
ejpam-371	309	21	an	an	DET
ejpam-371	309	22	approximation	approximation	NOUN
ejpam-371	309	23	process	process	NOUN
ejpam-371	309	24	with	with	ADP
ejpam-371	309	25	the	the	DET
ejpam-371	309	26	aid	aid	NOUN
ejpam-371	309	27	of	of	ADP
ejpam-371	309	28	certain	certain	ADJ
ejpam-371	309	29	suitably	suitably	ADV
ejpam-371	309	30	defined	define	VERB
ejpam-371	309	31	optimal	optimal	ADJ
ejpam-371	309	32	control	control	NOUN
ejpam-371	309	33	problem	problem	NOUN
ejpam-371	309	34	.	.	PUNCT
ejpam-371	310	1	to	to	PART
ejpam-371	310	2	r.	r.	PROPN
ejpam-371	310	3	lavanya	lavanya	PROPN
ejpam-371	310	4	/	/	SYM
ejpam-371	310	5	eur	eur	PROPN
ejpam-371	310	6	.	.	PUNCT
ejpam-371	311	1	j.	j.	PROPN
ejpam-371	311	2	pure	pure	PROPN
ejpam-371	311	3	appl	appl	PROPN
ejpam-371	311	4	.	.	PROPN
ejpam-371	311	5	math	math	PROPN
ejpam-371	311	6	,	,	PUNCT
ejpam-371	311	7	3	3	NUM
ejpam-371	311	8	(	(	PUNCT
ejpam-371	311	9	2010	2010	NUM
ejpam-371	311	10	)	)	PUNCT
ejpam-371	311	11	,	,	PUNCT
ejpam-371	311	12	235	235	NUM
ejpam-371	311	13	-	-	SYM
ejpam-371	311	14	253	253	NUM
ejpam-371	311	15	248	248	NUM
ejpam-371	311	16	derive	derive	ADJ
ejpam-371	311	17	the	the	DET
ejpam-371	311	18	estimate	estimate	NOUN
ejpam-371	311	19	,	,	PUNCT
ejpam-371	311	20	we	we	PRON
ejpam-371	311	21	use	use	VERB
ejpam-371	311	22	the	the	DET
ejpam-371	311	23	maximum	maximum	ADJ
ejpam-371	311	24	principle	principle	NOUN
ejpam-371	311	25	and	and	CCONJ
ejpam-371	311	26	the	the	DET
ejpam-371	311	27	observability	observability	NOUN
ejpam-371	311	28	inequality	inequality	NOUN
ejpam-371	311	29	which	which	PRON
ejpam-371	311	30	is	be	AUX
ejpam-371	311	31	derived	derive	VERB
ejpam-371	311	32	in	in	ADP
ejpam-371	311	33	the	the	DET
ejpam-371	311	34	previous	previous	ADJ
ejpam-371	311	35	section	section	NOUN
ejpam-371	311	36	for	for	ADP
ejpam-371	311	37	the	the	DET
ejpam-371	311	38	dual	dual	ADJ
ejpam-371	311	39	problem	problem	NOUN
ejpam-371	311	40	(	(	PUNCT
ejpam-371	311	41	5	5	NUM
ejpam-371	311	42	)	)	PUNCT
ejpam-371	311	43	.	.	PUNCT
ejpam-371	312	1	we	we	PRON
ejpam-371	312	2	first	first	ADV
ejpam-371	312	3	obtain	obtain	VERB
ejpam-371	312	4	an	an	DET
ejpam-371	312	5	explicit	explicit	ADJ
ejpam-371	312	6	bound	bind	VERB
ejpam-371	312	7	for	for	ADP
ejpam-371	312	8	the	the	DET
ejpam-371	312	9	weak	weak	ADJ
ejpam-371	312	10	solution	solution	NOUN
ejpam-371	312	11	of	of	ADP
ejpam-371	312	12	the	the	DET
ejpam-371	312	13	system	system	NOUN
ejpam-371	312	14	yt	yt	VERB
ejpam-371	312	15	−∆y	−∆y	PRON
ejpam-371	312	16	−m	−m	NOUN
ejpam-371	312	17	t	t	PROPN
ejpam-371	312	18	0	0	NUM
ejpam-371	312	19	∗∆y(t	∗∆y(t	NOUN
ejpam-371	312	20	)	)	PUNCT
ejpam-371	313	1	+	+	CCONJ
ejpam-371	313	2	(	(	PUNCT
ejpam-371	313	3	n	n	PRON
ejpam-371	313	4	t	t	NOUN
ejpam-371	313	5	0	0	NUM
ejpam-371	313	6	∗	∗	NOUN
ejpam-371	313	7	y(t))t	y(t))t	X
ejpam-371	314	1	=	=	SYM
ejpam-371	314	2	f	f	PROPN
ejpam-371	314	3	in	in	ADP
ejpam-371	314	4	q	q	PROPN
ejpam-371	314	5	y(0	y(0	PROPN
ejpam-371	314	6	,	,	PUNCT
ejpam-371	314	7	x	x	NOUN
ejpam-371	314	8	)	)	PUNCT
ejpam-371	314	9	=	=	SYM
ejpam-371	314	10	y0(x	y0(x	NOUN
ejpam-371	314	11	)	)	PUNCT
ejpam-371	314	12	in	in	ADP
ejpam-371	314	13	ω	ω	PROPN
ejpam-371	314	14	y(t	y(t	PROPN
ejpam-371	314	15	,	,	PUNCT
ejpam-371	314	16	x	x	X
ejpam-371	314	17	)	)	PUNCT
ejpam-371	314	18	=	=	SYM
ejpam-371	314	19	0	0	NUM
ejpam-371	314	20	on	on	ADP
ejpam-371	314	21	σ	σ	PROPN
ejpam-371	314	22	,	,	PUNCT
ejpam-371	314	23			PROPN
ejpam-371	314	24			PROPN
ejpam-371	314	25			NOUN
ejpam-371	314	26	(	(	PUNCT
ejpam-371	314	27	30	30	NUM
ejpam-371	314	28	)	)	PUNCT
ejpam-371	314	29	where	where	SCONJ
ejpam-371	314	30	f	f	PROPN
ejpam-371	314	31	∈	∈	PROPN
ejpam-371	314	32	l2(q	l2(q	PROPN
ejpam-371	314	33	)	)	PUNCT
ejpam-371	314	34	,	,	PUNCT
ejpam-371	314	35	y0	y0	PROPN
ejpam-371	314	36	∈	∈	NOUN
ejpam-371	314	37	h1	h1	NOUN
ejpam-371	314	38	0(ω	0(ω	ADV
ejpam-371	314	39	)	)	PUNCT
ejpam-371	314	40	are	be	AUX
ejpam-371	314	41	given	give	VERB
ejpam-371	314	42	.	.	PUNCT
ejpam-371	315	1	the	the	DET
ejpam-371	315	2	above	above	ADJ
ejpam-371	315	3	problem	problem	NOUN
ejpam-371	315	4	has	have	VERB
ejpam-371	315	5	a	a	DET
ejpam-371	315	6	unique	unique	ADJ
ejpam-371	315	7	solution	solution	NOUN
ejpam-371	315	8	y	y	PROPN
ejpam-371	315	9	∈	∈	PROPN
ejpam-371	315	10	l2(0	l2(0	NOUN
ejpam-371	315	11	,	,	PUNCT
ejpam-371	315	12	t	t	PROPN
ejpam-371	315	13	;	;	PUNCT
ejpam-371	315	14	h1	h1	PROPN
ejpam-371	315	15	0(ω)∩h2(ω))∩h1([0	0(ω)∩h2(ω))∩h1([0	PROPN
ejpam-371	315	16	,	,	PUNCT
ejpam-371	315	17	t	t	PROPN
ejpam-371	315	18	]	]	X
ejpam-371	315	19	;	;	PUNCT
ejpam-371	315	20	l2(ω	l2(ω	X
ejpam-371	315	21	)	)	PUNCT
ejpam-371	315	22	)	)	PUNCT
ejpam-371	316	1	whenever	whenever	SCONJ
ejpam-371	316	2	y0	y0	PROPN
ejpam-371	316	3	∈	∈	NOUN
ejpam-371	316	4	h1	h1	NOUN
ejpam-371	316	5	0(ω	0(ω	NUM
ejpam-371	316	6	)	)	PUNCT
ejpam-371	316	7	.	.	PUNCT
ejpam-371	317	1	the	the	DET
ejpam-371	317	2	existence	existence	NOUN
ejpam-371	317	3	and	and	CCONJ
ejpam-371	317	4	uniqueness	uniqueness	NOUN
ejpam-371	317	5	of	of	ADP
ejpam-371	317	6	a	a	DET
ejpam-371	317	7	solution	solution	NOUN
ejpam-371	317	8	to	to	ADP
ejpam-371	317	9	this	this	DET
ejpam-371	317	10	problem	problem	NOUN
ejpam-371	317	11	is	be	AUX
ejpam-371	317	12	well	well	ADV
ejpam-371	317	13	known	know	VERB
ejpam-371	317	14	,	,	PUNCT
ejpam-371	317	15	see	see	VERB
ejpam-371	317	16	for	for	ADP
ejpam-371	317	17	example	example	NOUN
ejpam-371	317	18	[	[	X
ejpam-371	317	19	9	9	NUM
ejpam-371	317	20	]	]	PUNCT
ejpam-371	317	21	.	.	PUNCT
ejpam-371	318	1	the	the	DET
ejpam-371	318	2	following	follow	VERB
ejpam-371	318	3	proposition	proposition	NOUN
ejpam-371	318	4	gives	give	VERB
ejpam-371	318	5	an	an	DET
ejpam-371	318	6	a	a	DET
ejpam-371	318	7	priori	priori	ADJ
ejpam-371	318	8	estimate	estimate	NOUN
ejpam-371	318	9	for	for	ADP
ejpam-371	318	10	the	the	DET
ejpam-371	318	11	solution	solution	NOUN
ejpam-371	318	12	of	of	ADP
ejpam-371	318	13	the	the	DET
ejpam-371	318	14	system	system	NOUN
ejpam-371	318	15	(	(	PUNCT
ejpam-371	318	16	30	30	NUM
ejpam-371	318	17	)	)	PUNCT
ejpam-371	318	18	.	.	PUNCT
ejpam-371	319	1	proposition	proposition	NOUN
ejpam-371	319	2	1	1	NUM
ejpam-371	319	3	.	.	PUNCT
ejpam-371	320	1	let	let	VERB
ejpam-371	320	2	f	f	PROPN
ejpam-371	320	3	∈	∈	PROPN
ejpam-371	320	4	l2(q	l2(q	PROPN
ejpam-371	320	5	)	)	PUNCT
ejpam-371	320	6	and	and	CCONJ
ejpam-371	320	7	y0	y0	PROPN
ejpam-371	320	8	∈	∈	NOUN
ejpam-371	320	9	h1	h1	NOUN
ejpam-371	320	10	0(ω	0(ω	ADV
ejpam-371	320	11	)	)	PUNCT
ejpam-371	320	12	be	be	AUX
ejpam-371	320	13	given	give	VERB
ejpam-371	320	14	.	.	PUNCT
ejpam-371	321	1	then	then	ADV
ejpam-371	321	2	the	the	DET
ejpam-371	321	3	weak	weak	ADJ
ejpam-371	321	4	solution	solution	NOUN
ejpam-371	321	5	y	y	PROPN
ejpam-371	321	6	∈	∈	PROPN
ejpam-371	321	7	h2,1(q	h2,1(q	PROPN
ejpam-371	321	8	)	)	PUNCT
ejpam-371	321	9	of	of	ADP
ejpam-371	321	10	the	the	DET
ejpam-371	321	11	problem	problem	NOUN
ejpam-371	321	12	(	(	PUNCT
ejpam-371	321	13	30	30	NUM
ejpam-371	321	14	)	)	PUNCT
ejpam-371	321	15	satisfies	satisfie	NOUN
ejpam-371	321	16	the	the	DET
ejpam-371	321	17	estimate	estimate	NOUN
ejpam-371	321	18	‖y‖2	‖y‖2	PROPN
ejpam-371	321	19	h2,1(q	h2,1(q	NOUN
ejpam-371	321	20	)	)	PUNCT
ejpam-371	322	1	≤	≤	NOUN
ejpam-371	322	2	v	v	X
ejpam-371	322	3	(	(	PUNCT
ejpam-371	322	4	·	·	PUNCT
ejpam-371	322	5	)	)	PUNCT
ejpam-371	322	6	�	�	NOUN
ejpam-371	322	7	‖y0‖2h1	‖y0‖2h1	NUM
ejpam-371	322	8	0(ω	0(ω	NUM
ejpam-371	322	9	)	)	PUNCT
ejpam-371	323	1	+	+	CCONJ
ejpam-371	323	2	‖	‖	PROPN
ejpam-371	323	3	f	f	PROPN
ejpam-371	323	4	‖2	‖2	NOUN
ejpam-371	323	5	l2(q	l2(q	NOUN
ejpam-371	323	6	)	)	PUNCT
ejpam-371	323	7	�	�	PROPN
ejpam-371	323	8	,	,	PUNCT
ejpam-371	323	9	(	(	PUNCT
ejpam-371	323	10	31	31	NUM
ejpam-371	323	11	)	)	PUNCT
ejpam-371	323	12	where	where	SCONJ
ejpam-371	323	13	v	v	X
ejpam-371	323	14	(	(	PUNCT
ejpam-371	323	15	·	·	PUNCT
ejpam-371	323	16	)	)	PUNCT
ejpam-371	323	17	=	=	SYM
ejpam-371	324	1	exp[c(1	exp[c(1	PROPN
ejpam-371	324	2	+	+	CCONJ
ejpam-371	324	3	t	t	NOUN
ejpam-371	324	4	+	+	NUM
ejpam-371	324	5	‖nt‖l∞	‖nt‖l∞	NOUN
ejpam-371	324	6	+	+	X
ejpam-371	324	7	t	t	PROPN
ejpam-371	324	8	2(‖n‖2	2(‖n‖2	NUM
ejpam-371	324	9	l∞	l∞	NOUN
ejpam-371	324	10	+	+	CCONJ
ejpam-371	324	11	‖nt‖2l∞	‖nt‖2l∞	NOUN
ejpam-371	324	12	+	+	CCONJ
ejpam-371	324	13	‖nt	‖nt	NUM
ejpam-371	324	14	t‖2l∞	t‖2l∞	NOUN
ejpam-371	324	15	)	)	PUNCT
ejpam-371	324	16	)	)	PUNCT
ejpam-371	324	17	]	]	PUNCT
ejpam-371	324	18	.	.	PUNCT
ejpam-371	325	1	proof	proof	NOUN
ejpam-371	325	2	.	.	PUNCT
ejpam-371	326	1	the	the	DET
ejpam-371	326	2	proof	proof	NOUN
ejpam-371	326	3	follows	follow	VERB
ejpam-371	326	4	the	the	DET
ejpam-371	326	5	standard	standard	ADJ
ejpam-371	326	6	technique	technique	NOUN
ejpam-371	326	7	.	.	PUNCT
ejpam-371	327	1	first	first	ADJ
ejpam-371	327	2	multiplying	multiply	VERB
ejpam-371	327	3	(	(	PUNCT
ejpam-371	327	4	30	30	NUM
ejpam-371	327	5	)	)	PUNCT
ejpam-371	327	6	by	by	ADP
ejpam-371	327	7	y	y	PROPN
ejpam-371	327	8	and	and	CCONJ
ejpam-371	327	9	integrating	integrate	VERB
ejpam-371	327	10	on	on	ADP
ejpam-371	327	11	ω	ω	PROPN
ejpam-371	327	12	,	,	PUNCT
ejpam-371	327	13	we	we	PRON
ejpam-371	327	14	obtain	obtain	VERB
ejpam-371	327	15	that	that	PRON
ejpam-371	327	16	1	1	NUM
ejpam-371	327	17	2	2	NUM
ejpam-371	327	18	d	d	NOUN
ejpam-371	327	19	d	d	NOUN
ejpam-371	327	20	t	t	PROPN
ejpam-371	327	21	∫	∫	PROPN
ejpam-371	327	22	ω	ω	PROPN
ejpam-371	327	23	|y|2d	|y|2d	PROPN
ejpam-371	327	24	x	x	PROPN
ejpam-371	328	1	+	+	NUM
ejpam-371	328	2	∫	∫	PROPN
ejpam-371	328	3	ω	ω	NUM
ejpam-371	328	4	|∇y|2d	|∇y|2d	NOUN
ejpam-371	328	5	x	x	SYM
ejpam-371	328	6	≤	≤	NUM
ejpam-371	328	7	3	3	NUM
ejpam-371	328	8	2	2	NUM
ejpam-371	328	9	∫	∫	PROPN
ejpam-371	328	10	ω	ω	NUM
ejpam-371	328	11	|y|2d	|y|2d	NOUN
ejpam-371	328	12	x+	x+	SYM
ejpam-371	328	13	1	1	NUM
ejpam-371	328	14	2	2	NUM
ejpam-371	328	15	∫	∫	PROPN
ejpam-371	328	16	ω	ω	PROPN
ejpam-371	328	17	�	�	PROPN
ejpam-371	328	18	|	|	PROPN
ejpam-371	328	19	f	f	PROPN
ejpam-371	328	20	|2	|2	NUM
ejpam-371	328	21	+	+	X
ejpam-371	328	22	�	�	PROPN
ejpam-371	328	23	�	�	PROPN
ejpam-371	328	24	m	m	PROPN
ejpam-371	328	25	t	t	PROPN
ejpam-371	328	26	0	0	NUM
ejpam-371	328	27	∗∆y(t	∗∆y(t	NOUN
ejpam-371	328	28	)	)	PUNCT
ejpam-371	328	29	�	�	PROPN
ejpam-371	328	30	�	�	PROPN
ejpam-371	328	31	2	2	NUM
ejpam-371	328	32	+	+	NUM
ejpam-371	328	33	�	�	PROPN
ejpam-371	328	34	�	�	PROPN
ejpam-371	328	35	(	(	PUNCT
ejpam-371	328	36	n	n	NOUN
ejpam-371	328	37	t	t	NOUN
ejpam-371	328	38	0	0	NUM
ejpam-371	328	39	∗	∗	NOUN
ejpam-371	328	40	y(t))t	y(t))t	PROPN
ejpam-371	328	41	�	�	PROPN
ejpam-371	328	42	�	�	PROPN
ejpam-371	328	43	2	2	NUM
ejpam-371	328	44	�	�	PROPN
ejpam-371	328	45	d	d	NOUN
ejpam-371	328	46	x	x	X
ejpam-371	328	47	.	.	PUNCT
ejpam-371	329	1	applying	apply	VERB
ejpam-371	329	2	the	the	DET
ejpam-371	329	3	differential	differential	ADJ
ejpam-371	329	4	version	version	NOUN
ejpam-371	329	5	of	of	ADP
ejpam-371	329	6	gronwall	gronwall	PROPN
ejpam-371	329	7	’s	’s	PART
ejpam-371	329	8	inequality	inequality	NOUN
ejpam-371	329	9	in	in	ADP
ejpam-371	329	10	the	the	DET
ejpam-371	329	11	interval	interval	NOUN
ejpam-371	329	12	0	0	NUM
ejpam-371	329	13	to	to	ADP
ejpam-371	329	14	t	t	PROPN
ejpam-371	329	15	with	with	ADP
ejpam-371	329	16	0≤	0≤	NUM
ejpam-371	329	17	t	t	PROPN
ejpam-371	329	18	≤	≤	NUM
ejpam-371	329	19	t1	t1	NOUN
ejpam-371	329	20	for	for	ADP
ejpam-371	329	21	some	some	DET
ejpam-371	329	22	fixed	fix	VERB
ejpam-371	329	23	t1	t1	NOUN
ejpam-371	329	24	∈	∈	PROPN
ejpam-371	329	25	(	(	PUNCT
ejpam-371	329	26	0	0	NUM
ejpam-371	329	27	,	,	PUNCT
ejpam-371	329	28	t	t	PROPN
ejpam-371	329	29	)	)	PUNCT
ejpam-371	329	30	,	,	PUNCT
ejpam-371	329	31	we	we	PRON
ejpam-371	329	32	have	have	VERB
ejpam-371	329	33	∫∫	∫∫	PROPN
ejpam-371	329	34	(	(	PUNCT
ejpam-371	329	35	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	329	36	|∇y|2d	|∇y|2d	NOUN
ejpam-371	329	37	xd	xd	INTJ
ejpam-371	329	38	t	t	PROPN
ejpam-371	330	1	+	+	CCONJ
ejpam-371	330	2	∫	∫	PROPN
ejpam-371	330	3	ω	ω	NUM
ejpam-371	330	4	|y(t1)|2d	|y(t1)|2d	PROPN
ejpam-371	330	5	x	x	SYM
ejpam-371	330	6	≤	≤	NUM
ejpam-371	330	7	exp[3t1	exp[3t1	NOUN
ejpam-371	330	8	]	]	PUNCT
ejpam-371	330	9	�	�	PROPN
ejpam-371	330	10	∫	∫	PROPN
ejpam-371	330	11	ω	ω	PROPN
ejpam-371	330	12	|y0|2d	|y0|2d	PROPN
ejpam-371	330	13	x	x	X
ejpam-371	330	14	+	+	CCONJ
ejpam-371	331	1	∫∫	∫∫	PROPN
ejpam-371	331	2	(	(	PUNCT
ejpam-371	331	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	331	4	�	�	PROPN
ejpam-371	331	5	|	|	PROPN
ejpam-371	331	6	f	f	PROPN
ejpam-371	331	7	|2	|2	NUM
ejpam-371	331	8	+	+	X
ejpam-371	331	9	�	�	PROPN
ejpam-371	331	10	�	�	PROPN
ejpam-371	331	11	m	m	PROPN
ejpam-371	331	12	t	t	PROPN
ejpam-371	331	13	0	0	NUM
ejpam-371	331	14	∗∆y(t	∗∆y(t	NOUN
ejpam-371	331	15	)	)	PUNCT
ejpam-371	331	16	�	�	PROPN
ejpam-371	331	17	�	�	PROPN
ejpam-371	331	18	2	2	NUM
ejpam-371	331	19	+	+	NUM
ejpam-371	331	20	�	�	PROPN
ejpam-371	331	21	�	�	PROPN
ejpam-371	331	22	(	(	PUNCT
ejpam-371	331	23	n	n	NOUN
ejpam-371	331	24	t	t	NOUN
ejpam-371	331	25	0	0	NUM
ejpam-371	331	26	∗	∗	NOUN
ejpam-371	331	27	y(t))t	y(t))t	PROPN
ejpam-371	331	28	�	�	PROPN
ejpam-371	331	29	�	�	PROPN
ejpam-371	331	30	2	2	NUM
ejpam-371	331	31	�	�	PROPN
ejpam-371	331	32	d	d	NOUN
ejpam-371	331	33	xd	xd	PROPN
ejpam-371	331	34	t	t	PROPN
ejpam-371	331	35	�	�	PROPN
ejpam-371	331	36	.	.	PUNCT
ejpam-371	332	1	(	(	PUNCT
ejpam-371	332	2	32	32	NUM
ejpam-371	332	3	)	)	PUNCT
ejpam-371	332	4	squaring	square	VERB
ejpam-371	332	5	both	both	DET
ejpam-371	332	6	sides	side	NOUN
ejpam-371	332	7	of	of	ADP
ejpam-371	332	8	the	the	DET
ejpam-371	332	9	equation	equation	NOUN
ejpam-371	332	10	(	(	PUNCT
ejpam-371	332	11	30	30	NUM
ejpam-371	332	12	)	)	PUNCT
ejpam-371	332	13	,	,	PUNCT
ejpam-371	332	14	and	and	CCONJ
ejpam-371	332	15	integrating	integrate	VERB
ejpam-371	332	16	on	on	ADP
ejpam-371	332	17	ω	ω	PROPN
ejpam-371	332	18	,	,	PUNCT
ejpam-371	332	19	we	we	PRON
ejpam-371	332	20	obtain	obtain	VERB
ejpam-371	332	21	d	d	PROPN
ejpam-371	332	22	d	d	NOUN
ejpam-371	332	23	t	t	PROPN
ejpam-371	332	24	∫	∫	PROPN
ejpam-371	332	25	ω	ω	X
ejpam-371	332	26	|∇y|2	|∇y|2	X
ejpam-371	332	27	+	+	CCONJ
ejpam-371	332	28	∫	∫	PROPN
ejpam-371	332	29	ω	ω	PROPN
ejpam-371	332	30	�	�	PROPN
ejpam-371	332	31	|yt	|yt	NUM
ejpam-371	332	32	|2	|2	NUM
ejpam-371	332	33	+	+	CCONJ
ejpam-371	332	34	|∆y|2	|∆y|2	ADJ
ejpam-371	332	35	+	+	ADJ
ejpam-371	332	36	�	�	PROPN
ejpam-371	332	37	�	�	PROPN
ejpam-371	332	38	m	m	PROPN
ejpam-371	332	39	t	t	PROPN
ejpam-371	332	40	0	0	NUM
ejpam-371	332	41	∗∆y(t	∗∆y(t	NOUN
ejpam-371	332	42	)	)	PUNCT
ejpam-371	332	43	�	�	PROPN
ejpam-371	332	44	�	�	PROPN
ejpam-371	332	45	2	2	NUM
ejpam-371	332	46	+	+	NUM
ejpam-371	332	47	�	�	PROPN
ejpam-371	332	48	�	�	PROPN
ejpam-371	332	49	(	(	PUNCT
ejpam-371	332	50	n	n	NOUN
ejpam-371	332	51	t	t	NOUN
ejpam-371	332	52	0	0	NUM
ejpam-371	332	53	∗	∗	NOUN
ejpam-371	332	54	y(t))t	y(t))t	PROPN
ejpam-371	332	55	�	�	PROPN
ejpam-371	332	56	�	�	PROPN
ejpam-371	332	57	2	2	NUM
ejpam-371	332	58	�	�	PROPN
ejpam-371	332	59	d	d	NOUN
ejpam-371	332	60	x	x	SYM
ejpam-371	332	61	=	=	SYM
ejpam-371	332	62	‖	‖	PROPN
ejpam-371	332	63	f	f	PROPN
ejpam-371	332	64	‖2	‖2	NOUN
ejpam-371	332	65	l2(ω	l2(ω	NOUN
ejpam-371	332	66	)	)	PUNCT
ejpam-371	332	67	(	(	PUNCT
ejpam-371	332	68	33	33	NUM
ejpam-371	332	69	)	)	PUNCT
ejpam-371	333	1	+2	+2	PROPN
ejpam-371	333	2	∫	∫	PROPN
ejpam-371	333	3	ω	ω	NUM
ejpam-371	333	4	∆y	∆y	PROPN
ejpam-371	333	5	�	�	PROPN
ejpam-371	333	6	(	(	PUNCT
ejpam-371	333	7	n	n	NOUN
ejpam-371	333	8	t	t	PROPN
ejpam-371	333	9	0	0	NUM
ejpam-371	333	10	∗	∗	NOUN
ejpam-371	333	11	y(t))t	y(t))t	PROPN
ejpam-371	333	12	−m	−m	PROPN
ejpam-371	333	13	t	t	PROPN
ejpam-371	333	14	0	0	NUM
ejpam-371	333	15	∗∆y(t	∗∆y(t	ADJ
ejpam-371	333	16	)	)	PUNCT
ejpam-371	333	17	�	�	PROPN
ejpam-371	334	1	d	d	NOUN
ejpam-371	334	2	x	x	SYM
ejpam-371	334	3	−	−	PROPN
ejpam-371	334	4	2	2	NUM
ejpam-371	334	5	∫	∫	PROPN
ejpam-371	334	6	ω	ω	PROPN
ejpam-371	334	7	yt	yt	PROPN
ejpam-371	334	8	�	�	PROPN
ejpam-371	334	9	(	(	PUNCT
ejpam-371	334	10	n	n	NOUN
ejpam-371	334	11	t	t	PROPN
ejpam-371	334	12	0	0	NUM
ejpam-371	334	13	∗	∗	NOUN
ejpam-371	334	14	y(t))t	y(t))t	PROPN
ejpam-371	334	15	−m	−m	PROPN
ejpam-371	334	16	t	t	PROPN
ejpam-371	334	17	0	0	NUM
ejpam-371	334	18	∗∆y(t	∗∆y(t	ADJ
ejpam-371	334	19	)	)	PUNCT
ejpam-371	334	20	�	�	PROPN
ejpam-371	335	1	d	d	NOUN
ejpam-371	335	2	x	x	SYM
ejpam-371	336	1	+2	+2	PROPN
ejpam-371	336	2	∫	∫	PROPN
ejpam-371	336	3	ω	ω	NUM
ejpam-371	336	4	�	�	PROPN
ejpam-371	336	5	m	m	PROPN
ejpam-371	336	6	t	t	PROPN
ejpam-371	336	7	0	0	NUM
ejpam-371	336	8	∗∆y(t	∗∆y(t	ADJ
ejpam-371	336	9	)	)	PUNCT
ejpam-371	336	10	�	�	PROPN
ejpam-371	336	11	(	(	PUNCT
ejpam-371	336	12	n	n	NOUN
ejpam-371	336	13	t	t	PROPN
ejpam-371	336	14	0	0	NUM
ejpam-371	336	15	∗	∗	NOUN
ejpam-371	336	16	y(t))t	y(t))t	PROPN
ejpam-371	336	17	d	d	NOUN
ejpam-371	336	18	x	x	SYM
ejpam-371	336	19	=	=	SYM
ejpam-371	336	20	4∑	4∑	NUM
ejpam-371	336	21	i=1	i=1	PROPN
ejpam-371	336	22	ii	ii	PROPN
ejpam-371	336	23	r.	r.	PROPN
ejpam-371	336	24	lavanya	lavanya	PROPN
ejpam-371	336	25	/	/	SYM
ejpam-371	336	26	eur	eur	PROPN
ejpam-371	336	27	.	.	PUNCT
ejpam-371	337	1	j.	j.	PROPN
ejpam-371	337	2	pure	pure	PROPN
ejpam-371	337	3	appl	appl	PROPN
ejpam-371	337	4	.	.	PROPN
ejpam-371	337	5	math	math	PROPN
ejpam-371	337	6	,	,	PUNCT
ejpam-371	337	7	3	3	NUM
ejpam-371	337	8	(	(	PUNCT
ejpam-371	337	9	2010	2010	NUM
ejpam-371	337	10	)	)	PUNCT
ejpam-371	337	11	,	,	PUNCT
ejpam-371	337	12	235	235	NUM
ejpam-371	337	13	-	-	SYM
ejpam-371	337	14	253	253	NUM
ejpam-371	337	15	249	249	NUM
ejpam-371	337	16	for	for	ADP
ejpam-371	337	17	all	all	DET
ejpam-371	337	18	t	t	NOUN
ejpam-371	337	19	∈	∈	PROPN
ejpam-371	337	20	(	(	PUNCT
ejpam-371	337	21	0	0	NUM
ejpam-371	337	22	,	,	PUNCT
ejpam-371	337	23	t	t	NOUN
ejpam-371	337	24	)	)	PUNCT
ejpam-371	337	25	.	.	PUNCT
ejpam-371	338	1	using	use	VERB
ejpam-371	338	2	cauchy	cauchy	ADJ
ejpam-371	338	3	inequality	inequality	NOUN
ejpam-371	338	4	one	one	PRON
ejpam-371	338	5	can	can	AUX
ejpam-371	338	6	easily	easily	ADV
ejpam-371	338	7	see	see	VERB
ejpam-371	338	8	that	that	DET
ejpam-371	338	9	∫	∫	PROPN
ejpam-371	338	10	t1	t1	NOUN
ejpam-371	338	11	0	0	NUM
ejpam-371	339	1	i2d	i2d	PROPN
ejpam-371	339	2	t	t	VERB
ejpam-371	339	3	≤	≤	NUM
ejpam-371	339	4	1	1	NUM
ejpam-371	339	5	4	4	NUM
ejpam-371	339	6	∫∫	∫∫	PROPN
ejpam-371	339	7	(	(	PUNCT
ejpam-371	339	8	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	340	1	|∆y|2d	|∆y|2d	ADP
ejpam-371	340	2	xd	xd	INTJ
ejpam-371	340	3	t	t	NOUN
ejpam-371	340	4	+	+	CCONJ
ejpam-371	340	5	8	8	NUM
ejpam-371	340	6	∫∫	∫∫	PROPN
ejpam-371	340	7	(	(	PUNCT
ejpam-371	340	8	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	340	9	�	�	PROPN
ejpam-371	340	10	�	�	PROPN
ejpam-371	340	11	�	�	PROPN
ejpam-371	340	12	m	m	PROPN
ejpam-371	340	13	t	t	PROPN
ejpam-371	340	14	0	0	NUM
ejpam-371	340	15	∗∆y(t	∗∆y(t	NOUN
ejpam-371	340	16	)	)	PUNCT
ejpam-371	340	17	�	�	PROPN
ejpam-371	340	18	�	�	PROPN
ejpam-371	340	19	2	2	NUM
ejpam-371	340	20	+	+	NUM
ejpam-371	340	21	�	�	PROPN
ejpam-371	340	22	�	�	PROPN
ejpam-371	340	23	�	�	PROPN
ejpam-371	340	24	∫	∫	PROPN
ejpam-371	340	25	t	t	PROPN
ejpam-371	340	26	0	0	NUM
ejpam-371	340	27	nt(t	nt(t	PROPN
ejpam-371	340	28	,	,	PUNCT
ejpam-371	340	29	τ)y(τ)dτ	τ)y(τ)dτ	PROPN
ejpam-371	340	30	�	�	PROPN
ejpam-371	340	31	�	�	PROPN
ejpam-371	340	32	�	�	PROPN
ejpam-371	340	33	2	2	NUM
ejpam-371	340	34	�	�	PROPN
ejpam-371	340	35	d	d	NOUN
ejpam-371	340	36	xd	xd	ADJ
ejpam-371	340	37	t.(34	t.(34	NOUN
ejpam-371	340	38	)	)	PUNCT
ejpam-371	340	39	applying	apply	VERB
ejpam-371	340	40	hölder	hölder	NOUN
ejpam-371	340	41	’s	’s	PART
ejpam-371	340	42	inequality	inequality	NOUN
ejpam-371	340	43	,	,	PUNCT
ejpam-371	340	44	the	the	DET
ejpam-371	340	45	last	last	ADJ
ejpam-371	340	46	integral	integral	NOUN
ejpam-371	340	47	can	can	AUX
ejpam-371	340	48	further	far	ADV
ejpam-371	340	49	be	be	AUX
ejpam-371	340	50	estimated	estimate	VERB
ejpam-371	340	51	as	as	ADP
ejpam-371	340	52	‖m‖2l∞	‖m‖2l∞	NOUN
ejpam-371	340	53	t2	t2	NOUN
ejpam-371	340	54	1	1	NUM
ejpam-371	340	55	∫∫	∫∫	PROPN
ejpam-371	340	56	(	(	PUNCT
ejpam-371	340	57	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	340	58	|∆y|2d	|∆y|2d	ADP
ejpam-371	340	59	xd	xd	INTJ
ejpam-371	340	60	t	t	NOUN
ejpam-371	340	61	+	+	CCONJ
ejpam-371	340	62	‖nt‖2l∞	‖nt‖2l∞	NOUN
ejpam-371	340	63	t2	t2	NOUN
ejpam-371	340	64	1	1	NUM
ejpam-371	341	1	∫∫	∫∫	PROPN
ejpam-371	341	2	(	(	PUNCT
ejpam-371	341	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	341	4	|y|2d	|y|2d	NOUN
ejpam-371	341	5	xd	xd	INTJ
ejpam-371	341	6	t.	t.	NOUN
ejpam-371	341	7	integration	integration	NOUN
ejpam-371	341	8	by	by	ADP
ejpam-371	341	9	parts	part	NOUN
ejpam-371	341	10	in	in	ADP
ejpam-371	341	11	time	time	NOUN
ejpam-371	341	12	together	together	ADV
ejpam-371	341	13	with	with	ADP
ejpam-371	341	14	the	the	DET
ejpam-371	341	15	assumptions	assumption	NOUN
ejpam-371	341	16	on	on	ADP
ejpam-371	341	17	the	the	DET
ejpam-371	341	18	kernel	kernel	NOUN
ejpam-371	341	19	yields	yield	NOUN
ejpam-371	341	20	,	,	PUNCT
ejpam-371	341	21	∫	∫	PROPN
ejpam-371	341	22	t1	t1	NOUN
ejpam-371	341	23	0	0	NUM
ejpam-371	342	1	i3d	i3d	NOUN
ejpam-371	342	2	t	t	NOUN
ejpam-371	342	3	=	=	SYM
ejpam-371	342	4	2	2	NUM
ejpam-371	343	1	∫∫	∫∫	PROPN
ejpam-371	343	2	(	(	PUNCT
ejpam-371	343	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	343	4	y	y	PROPN
ejpam-371	343	5	�	�	PROPN
ejpam-371	343	6	∫	∫	PROPN
ejpam-371	343	7	t	t	PROPN
ejpam-371	343	8	0	0	PUNCT
ejpam-371	343	9	nt	not	PART
ejpam-371	343	10	t(t	t(t	NOUN
ejpam-371	343	11	,	,	PUNCT
ejpam-371	343	12	τ)y(τ)dτ+	τ)y(τ)dτ+	NOUN
ejpam-371	343	13	nt(t	nt(t	NUM
ejpam-371	343	14	,	,	PUNCT
ejpam-371	343	15	t)y(t	t)y(t	NOUN
ejpam-371	343	16	)	)	PUNCT
ejpam-371	343	17	�	�	PROPN
ejpam-371	344	1	d	d	NOUN
ejpam-371	344	2	xd	xd	INTJ
ejpam-371	344	3	t	t	PROPN
ejpam-371	344	4	−2	−2	NOUN
ejpam-371	345	1	∫∫	∫∫	PROPN
ejpam-371	345	2	(	(	PUNCT
ejpam-371	345	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	345	4	y	y	PROPN
ejpam-371	345	5	�	�	PROPN
ejpam-371	345	6	∫	∫	PROPN
ejpam-371	345	7	t	t	PROPN
ejpam-371	345	8	0	0	NUM
ejpam-371	345	9	mt(t	mt(t	PROPN
ejpam-371	345	10	,	,	PUNCT
ejpam-371	345	11	τ)∆y(τ)dτ	τ)∆y(τ)dτ	PROPN
ejpam-371	345	12	�	�	PROPN
ejpam-371	346	1	d	d	NOUN
ejpam-371	346	2	xd	xd	NOUN
ejpam-371	346	3	t	t	NOUN
ejpam-371	346	4	=	=	NOUN
ejpam-371	346	5	i31	i31	PROPN
ejpam-371	346	6	+	+	CCONJ
ejpam-371	346	7	i32	i32	NOUN
ejpam-371	346	8	.	.	PUNCT
ejpam-371	347	1	(	(	PUNCT
ejpam-371	347	2	35	35	NUM
ejpam-371	347	3	)	)	PUNCT
ejpam-371	347	4	since	since	SCONJ
ejpam-371	347	5	using	use	VERB
ejpam-371	347	6	young	young	PROPN
ejpam-371	347	7	’s	’s	PART
ejpam-371	347	8	and	and	CCONJ
ejpam-371	347	9	hölder	hölder	PROPN
ejpam-371	347	10	’s	’s	PART
ejpam-371	347	11	inequality	inequality	NOUN
ejpam-371	347	12	,	,	PUNCT
ejpam-371	347	13	we	we	PRON
ejpam-371	347	14	further	far	ADV
ejpam-371	347	15	obtain	obtain	VERB
ejpam-371	347	16	that	that	DET
ejpam-371	347	17	i31	i31	NOUN
ejpam-371	347	18	≤	≤	NOUN
ejpam-371	347	19	(	(	PUNCT
ejpam-371	347	20	1	1	NUM
ejpam-371	347	21	+	+	NUM
ejpam-371	347	22	2‖nt‖l∞	2‖nt‖l∞	NUM
ejpam-371	347	23	)	)	PUNCT
ejpam-371	348	1	∫∫	∫∫	PROPN
ejpam-371	348	2	(	(	PUNCT
ejpam-371	348	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	348	4	|y|2d	|y|2d	NOUN
ejpam-371	349	1	xd	xd	INTJ
ejpam-371	349	2	t	t	PROPN
ejpam-371	349	3	+	+	CCONJ
ejpam-371	349	4	‖nt	‖nt	NUM
ejpam-371	349	5	t‖2l∞	t‖2l∞	PROPN
ejpam-371	349	6	t2	t2	NOUN
ejpam-371	349	7	1	1	NUM
ejpam-371	349	8	∫∫	∫∫	PROPN
ejpam-371	349	9	(	(	PUNCT
ejpam-371	349	10	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	349	11	|y|2d	|y|2d	NOUN
ejpam-371	349	12	xd	xd	INTJ
ejpam-371	349	13	t	t	PROPN
ejpam-371	349	14	and	and	CCONJ
ejpam-371	349	15	i32	i32	PROPN
ejpam-371	349	16	≤	≤	PROPN
ejpam-371	349	17	ηt2	ηt2	NOUN
ejpam-371	349	18	1‖mt‖2l∞	1‖mt‖2l∞	NUM
ejpam-371	349	19	∫∫	∫∫	PROPN
ejpam-371	349	20	(	(	PUNCT
ejpam-371	349	21	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	350	1	|∆y|2d	|∆y|2d	ADP
ejpam-371	350	2	xd	xd	INTJ
ejpam-371	350	3	t	t	NOUN
ejpam-371	350	4	+	+	CCONJ
ejpam-371	350	5	1	1	NUM
ejpam-371	350	6	η	η	X
ejpam-371	350	7	∫∫	∫∫	PROPN
ejpam-371	350	8	(	(	PUNCT
ejpam-371	350	9	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	350	10	|y|2d	|y|2d	NOUN
ejpam-371	350	11	xd	xd	INTJ
ejpam-371	350	12	t.	t.	PROPN
ejpam-371	350	13	finally	finally	ADV
ejpam-371	350	14	,	,	PUNCT
ejpam-371	350	15	we	we	PRON
ejpam-371	350	16	note	note	VERB
ejpam-371	350	17	that	that	SCONJ
ejpam-371	350	18	the	the	DET
ejpam-371	350	19	estimation	estimation	NOUN
ejpam-371	350	20	similar	similar	ADJ
ejpam-371	350	21	to	to	ADP
ejpam-371	350	22	i32	i32	PROPN
ejpam-371	350	23	yields	yield	NOUN
ejpam-371	350	24	∫	∫	PROPN
ejpam-371	350	25	t1	t1	NOUN
ejpam-371	350	26	0	0	NUM
ejpam-371	351	1	i4d	i4d	X
ejpam-371	351	2	t	t	VERB
ejpam-371	351	3	≤	≤	NUM
ejpam-371	351	4	ηt2	ηt2	NOUN
ejpam-371	351	5	1‖mt‖2l∞	1‖mt‖2l∞	NUM
ejpam-371	352	1	∫∫	∫∫	PROPN
ejpam-371	352	2	(	(	PUNCT
ejpam-371	352	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	352	4	|∆y|2d	|∆y|2d	ADP
ejpam-371	352	5	xd	xd	INTJ
ejpam-371	352	6	t	t	NOUN
ejpam-371	352	7	+	+	CCONJ
ejpam-371	352	8	1	1	NUM
ejpam-371	352	9	η	η	PROPN
ejpam-371	352	10	‖n‖2l∞	‖n‖2l∞	NOUN
ejpam-371	352	11	t2	t2	NOUN
ejpam-371	352	12	1	1	NUM
ejpam-371	352	13	∫∫	∫∫	PROPN
ejpam-371	352	14	(	(	PUNCT
ejpam-371	352	15	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	352	16	|y|2d	|y|2d	NOUN
ejpam-371	352	17	xd	xd	INTJ
ejpam-371	352	18	t.	t.	PROPN
ejpam-371	352	19	(	(	PUNCT
ejpam-371	352	20	36	36	NUM
ejpam-371	352	21	)	)	PUNCT
ejpam-371	352	22	if	if	SCONJ
ejpam-371	352	23	‖m‖2	‖m‖2	NOUN
ejpam-371	352	24	l∞(0,t	l∞(0,t	ADJ
ejpam-371	352	25	)	)	PUNCT
ejpam-371	352	26	t2	t2	NOUN
ejpam-371	352	27	1	1	NUM
ejpam-371	352	28	≤	≤	NUM
ejpam-371	352	29	1	1	NUM
ejpam-371	352	30	16	16	NUM
ejpam-371	352	31	,	,	PUNCT
ejpam-371	352	32	integrating	integrate	VERB
ejpam-371	352	33	(	(	PUNCT
ejpam-371	352	34	33	33	NUM
ejpam-371	352	35	)	)	PUNCT
ejpam-371	352	36	in	in	ADP
ejpam-371	352	37	the	the	DET
ejpam-371	352	38	interval	interval	NOUN
ejpam-371	352	39	(	(	PUNCT
ejpam-371	352	40	0,t	0,t	PROPN
ejpam-371	352	41	)	)	PUNCT
ejpam-371	352	42	and	and	CCONJ
ejpam-371	352	43	substituting	substitute	VERB
ejpam-371	352	44	(	(	PUNCT
ejpam-371	352	45	34)-(36	34)-(36	NUM
ejpam-371	352	46	)	)	PUNCT
ejpam-371	352	47	and	and	CCONJ
ejpam-371	352	48	using	use	VERB
ejpam-371	352	49	the	the	DET
ejpam-371	352	50	poincaré	poincaré	PROPN
ejpam-371	352	51	inequality	inequality	PROPN
ejpam-371	352	52	∫	∫	PROPN
ejpam-371	352	53	ω	ω	PROPN
ejpam-371	352	54	|y|2d	|y|2d	PROPN
ejpam-371	352	55	x	x	SYM
ejpam-371	352	56	≤	≤	PROPN
ejpam-371	352	57	c(ω	c(ω	PROPN
ejpam-371	352	58	)	)	PUNCT
ejpam-371	352	59	∫	∫	PROPN
ejpam-371	353	1	ω	ω	NUM
ejpam-371	353	2	|∇y|2d	|∇y|2d	PROPN
ejpam-371	353	3	x	x	X
ejpam-371	353	4	,	,	PUNCT
ejpam-371	353	5	one	one	PRON
ejpam-371	353	6	can	can	AUX
ejpam-371	353	7	have	have	VERB
ejpam-371	353	8	the	the	DET
ejpam-371	353	9	following	following	ADJ
ejpam-371	353	10	‖y(t1)‖2h1	‖y(t1)‖2h1	NOUN
ejpam-371	353	11	0(ω	0(ω	ADV
ejpam-371	353	12	)	)	PUNCT
ejpam-371	354	1	+	+	CCONJ
ejpam-371	355	1	∫∫	∫∫	ADV
ejpam-371	355	2	(	(	PUNCT
ejpam-371	355	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	355	4	�	�	PROPN
ejpam-371	355	5	|yt	|yt	NUM
ejpam-371	355	6	|2	|2	NUM
ejpam-371	355	7	+	+	CCONJ
ejpam-371	355	8	|∆y|2	|∆y|2	ADJ
ejpam-371	355	9	+	+	SYM
ejpam-371	355	10	�	�	PROPN
ejpam-371	355	11	�	�	PROPN
ejpam-371	355	12	m	m	PROPN
ejpam-371	355	13	t	t	PROPN
ejpam-371	355	14	0	0	NUM
ejpam-371	355	15	∗∆y(t	∗∆y(t	NOUN
ejpam-371	355	16	)	)	PUNCT
ejpam-371	355	17	�	�	PROPN
ejpam-371	355	18	�	�	PROPN
ejpam-371	355	19	2	2	NUM
ejpam-371	355	20	+	+	NUM
ejpam-371	355	21	�	�	PROPN
ejpam-371	355	22	�	�	PROPN
ejpam-371	355	23	(	(	PUNCT
ejpam-371	355	24	n	n	NOUN
ejpam-371	355	25	t	t	NOUN
ejpam-371	355	26	0	0	NUM
ejpam-371	355	27	∗	∗	NOUN
ejpam-371	355	28	y(t))t	y(t))t	PROPN
ejpam-371	355	29	�	�	PROPN
ejpam-371	355	30	�	�	PROPN
ejpam-371	355	31	2	2	NUM
ejpam-371	355	32	�	�	PROPN
ejpam-371	355	33	d	d	NOUN
ejpam-371	355	34	xd	xd	NOUN
ejpam-371	355	35	t	t	PROPN
ejpam-371	355	36	≤	≤	NUM
ejpam-371	355	37	m(·)	m(·)	NOUN
ejpam-371	355	38	�	�	NOUN
ejpam-371	355	39	‖y0‖2h1	‖y0‖2h1	NUM
ejpam-371	355	40	0(ω	0(ω	NUM
ejpam-371	355	41	)	)	PUNCT
ejpam-371	356	1	+	+	X
ejpam-371	357	1	∫∫	∫∫	ADV
ejpam-371	357	2	(	(	PUNCT
ejpam-371	357	3	0,t1)×ω	0,t1)×ω	PROPN
ejpam-371	357	4	|	|	ADV
ejpam-371	357	5	f	f	PROPN
ejpam-371	357	6	|2d	|2d	NOUN
ejpam-371	357	7	xd	xd	PROPN
ejpam-371	357	8	t	t	PROPN
ejpam-371	357	9	�	�	PROPN
ejpam-371	357	10	,	,	PUNCT
ejpam-371	357	11	(	(	PUNCT
ejpam-371	357	12	37	37	NUM
ejpam-371	357	13	)	)	PUNCT
ejpam-371	357	14	r.	r.	PROPN
ejpam-371	357	15	lavanya	lavanya	PROPN
ejpam-371	357	16	/	/	SYM
ejpam-371	357	17	eur	eur	PROPN
ejpam-371	357	18	.	.	PUNCT
ejpam-371	358	1	j.	j.	PROPN
ejpam-371	358	2	pure	pure	PROPN
ejpam-371	358	3	appl	appl	PROPN
ejpam-371	358	4	.	.	PROPN
ejpam-371	358	5	math	math	PROPN
ejpam-371	358	6	,	,	PUNCT
ejpam-371	358	7	3	3	NUM
ejpam-371	358	8	(	(	PUNCT
ejpam-371	358	9	2010	2010	NUM
ejpam-371	358	10	)	)	PUNCT
ejpam-371	358	11	,	,	PUNCT
ejpam-371	358	12	235	235	NUM
ejpam-371	358	13	-	-	SYM
ejpam-371	358	14	253	253	NUM
ejpam-371	358	15	250	250	NUM
ejpam-371	358	16	where	where	SCONJ
ejpam-371	358	17	m	m	VERB
ejpam-371	358	18	(	(	PUNCT
ejpam-371	358	19	·	·	PUNCT
ejpam-371	358	20	)	)	PUNCT
ejpam-371	358	21	=	=	PUNCT
ejpam-371	359	1	exp[c(1+‖nt‖l∞+	exp[c(1+‖nt‖l∞+	PROPN
ejpam-371	359	2	t2	t2	PROPN
ejpam-371	359	3	1(‖n‖2l∞+‖nt‖2l∞+‖nt	1(‖n‖2l∞+‖nt‖2l∞+‖nt	PROPN
ejpam-371	359	4	t‖2l∞	t‖2l∞	PROPN
ejpam-371	359	5	)	)	PUNCT
ejpam-371	359	6	)	)	PUNCT
ejpam-371	359	7	]	]	PUNCT
ejpam-371	359	8	.	.	PUNCT
ejpam-371	360	1	since	since	SCONJ
ejpam-371	360	2	we	we	PRON
ejpam-371	360	3	have	have	AUX
ejpam-371	360	4	also	also	ADV
ejpam-371	360	5	chosen	choose	VERB
ejpam-371	360	6	that	that	SCONJ
ejpam-371	360	7	η	η	PROPN
ejpam-371	360	8	≤	≤	PROPN
ejpam-371	360	9	1	1	NUM
ejpam-371	360	10	16t2	16t2	NUM
ejpam-371	360	11	1‖mt‖2l∞	1‖mt‖2l∞	NUM
ejpam-371	360	12	.	.	PUNCT
ejpam-371	361	1	with	with	ADP
ejpam-371	361	2	the	the	DET
ejpam-371	361	3	estimate	estimate	NOUN
ejpam-371	361	4	(	(	PUNCT
ejpam-371	361	5	37	37	NUM
ejpam-371	361	6	)	)	PUNCT
ejpam-371	361	7	together	together	ADV
ejpam-371	361	8	with	with	ADP
ejpam-371	361	9	(	(	PUNCT
ejpam-371	361	10	32	32	NUM
ejpam-371	361	11	)	)	PUNCT
ejpam-371	361	12	and	and	CCONJ
ejpam-371	361	13	the	the	DET
ejpam-371	361	14	sobolev	sobolev	ADJ
ejpam-371	361	15	estimate	estimate	NOUN
ejpam-371	361	16	,	,	PUNCT
ejpam-371	361	17	one	one	PRON
ejpam-371	361	18	can	can	AUX
ejpam-371	361	19	conclude	conclude	VERB
ejpam-371	361	20	the	the	DET
ejpam-371	361	21	proof	proof	NOUN
ejpam-371	361	22	.	.	PUNCT
ejpam-371	362	1	now	now	ADV
ejpam-371	362	2	we	we	PRON
ejpam-371	362	3	prove	prove	VERB
ejpam-371	362	4	the	the	DET
ejpam-371	362	5	main	main	ADJ
ejpam-371	362	6	result	result	NOUN
ejpam-371	362	7	of	of	ADP
ejpam-371	362	8	this	this	DET
ejpam-371	362	9	work	work	NOUN
ejpam-371	362	10	.	.	PUNCT
ejpam-371	363	1	theorem	theorem	NOUN
ejpam-371	363	2	2	2	NUM
ejpam-371	363	3	.	.	X
ejpam-371	363	4	assume	assume	VERB
ejpam-371	363	5	that	that	SCONJ
ejpam-371	363	6	t	t	PROPN
ejpam-371	363	7	>	>	X
ejpam-371	363	8	0	0	NUM
ejpam-371	363	9	is	be	AUX
ejpam-371	363	10	fixed	fix	VERB
ejpam-371	363	11	and	and	CCONJ
ejpam-371	363	12	y0	y0	PROPN
ejpam-371	363	13	∈	∈	NOUN
ejpam-371	363	14	h1	h1	NOUN
ejpam-371	363	15	0(ω	0(ω	ADV
ejpam-371	363	16	)	)	PUNCT
ejpam-371	363	17	is	be	AUX
ejpam-371	363	18	given	give	VERB
ejpam-371	363	19	and	and	CCONJ
ejpam-371	363	20	the	the	DET
ejpam-371	363	21	kernels	kernels	PROPN
ejpam-371	363	22	m	m	PROPN
ejpam-371	363	23	(	(	PUNCT
ejpam-371	363	24	·	·	PUNCT
ejpam-371	363	25	,	,	PUNCT
ejpam-371	363	26	·	·	PUNCT
ejpam-371	363	27	)	)	PUNCT
ejpam-371	363	28	and	and	CCONJ
ejpam-371	363	29	n	n	CCONJ
ejpam-371	363	30	(	(	PUNCT
ejpam-371	363	31	·	·	PUNCT
ejpam-371	363	32	,	,	PUNCT
ejpam-371	363	33	·	·	PUNCT
ejpam-371	363	34	)	)	PUNCT
ejpam-371	363	35	have	have	VERB
ejpam-371	363	36	support	support	NOUN
ejpam-371	363	37	in	in	ADP
ejpam-371	363	38	(	(	PUNCT
ejpam-371	363	39	t0	t0	PROPN
ejpam-371	363	40	,	,	PUNCT
ejpam-371	363	41	t1	t1	PROPN
ejpam-371	363	42	)	)	PUNCT
ejpam-371	363	43	where	where	SCONJ
ejpam-371	363	44	0	0	NUM
ejpam-371	363	45	<	<	X
ejpam-371	363	46	t0	t0	X
ejpam-371	363	47	<	<	X
ejpam-371	363	48	t1	t1	NOUN
ejpam-371	363	49	<	<	X
ejpam-371	363	50	t.	t.	X
ejpam-371	363	51	then	then	ADV
ejpam-371	363	52	there	there	PRON
ejpam-371	363	53	exists	exist	VERB
ejpam-371	363	54	a	a	DET
ejpam-371	363	55	control	control	NOUN
ejpam-371	363	56	u	u	PROPN
ejpam-371	363	57	∈	∈	PROPN
ejpam-371	363	58	l2(0	l2(0	NOUN
ejpam-371	363	59	,	,	PUNCT
ejpam-371	363	60	t	t	NOUN
ejpam-371	363	61	;	;	PUNCT
ejpam-371	363	62	l2(ω	l2(ω	X
ejpam-371	363	63	)	)	PUNCT
ejpam-371	363	64	)	)	PUNCT
ejpam-371	364	1	such	such	ADJ
ejpam-371	364	2	that	that	SCONJ
ejpam-371	364	3	the	the	DET
ejpam-371	364	4	corresponding	corresponding	ADJ
ejpam-371	364	5	solution	solution	NOUN
ejpam-371	364	6	of	of	ADP
ejpam-371	364	7	(	(	PUNCT
ejpam-371	364	8	4	4	X
ejpam-371	364	9	)	)	PUNCT
ejpam-371	364	10	satisfies	satisfie	NOUN
ejpam-371	364	11	y(t	y(t	NUM
ejpam-371	364	12	,	,	PUNCT
ejpam-371	364	13	x	x	X
ejpam-371	364	14	)	)	PUNCT
ejpam-371	364	15	=	=	SYM
ejpam-371	364	16	0	0	NUM
ejpam-371	364	17	a.e	a.e	PROPN
ejpam-371	364	18	.	.	PUNCT
ejpam-371	364	19	x	x	SYM
ejpam-371	364	20	∈	∈	PROPN
ejpam-371	364	21	ω	ω	X
ejpam-371	364	22	.	.	PUNCT
ejpam-371	365	1	moreover	moreover	ADV
ejpam-371	365	2	,	,	PUNCT
ejpam-371	365	3	the	the	DET
ejpam-371	365	4	control	control	NOUN
ejpam-371	365	5	u	u	PROPN
ejpam-371	365	6	can	can	AUX
ejpam-371	365	7	be	be	AUX
ejpam-371	365	8	chosen	choose	VERB
ejpam-371	365	9	in	in	ADP
ejpam-371	365	10	such	such	DET
ejpam-371	365	11	a	a	DET
ejpam-371	365	12	way	way	NOUN
ejpam-371	365	13	that	that	SCONJ
ejpam-371	365	14	||u||2	||u||2	ADJ
ejpam-371	365	15	l2(0,t	l2(0,t	NOUN
ejpam-371	365	16	;	;	PUNCT
ejpam-371	365	17	l2(ω	l2(ω	NUM
ejpam-371	365	18	)	)	PUNCT
ejpam-371	365	19	)	)	PUNCT
ejpam-371	365	20	≤w	≤w	NOUN
ejpam-371	365	21	(	(	PUNCT
ejpam-371	365	22	ω	ω	PROPN
ejpam-371	365	23	,	,	PUNCT
ejpam-371	365	24	ω	ω	PROPN
ejpam-371	365	25	,	,	PUNCT
ejpam-371	365	26	t	t	NOUN
ejpam-371	365	27	)	)	PUNCT
ejpam-371	365	28	||y0||2l2(ω	||y0||2l2(ω	NUM
ejpam-371	365	29	)	)	PUNCT
ejpam-371	365	30	,	,	PUNCT
ejpam-371	365	31	where	where	SCONJ
ejpam-371	365	32	the	the	DET
ejpam-371	365	33	constant	constant	ADJ
ejpam-371	365	34	w	w	PROPN
ejpam-371	365	35	(	(	PUNCT
ejpam-371	365	36	·	·	PUNCT
ejpam-371	365	37	)	)	PUNCT
ejpam-371	365	38	is	be	AUX
ejpam-371	365	39	explicitly	explicitly	ADV
ejpam-371	365	40	given	give	VERB
ejpam-371	365	41	in	in	ADP
ejpam-371	365	42	(	(	PUNCT
ejpam-371	365	43	24	24	NUM
ejpam-371	365	44	)	)	PUNCT
ejpam-371	365	45	.	.	PUNCT
ejpam-371	366	1	proof	proof	NOUN
ejpam-371	366	2	.	.	PUNCT
ejpam-371	367	1	let	let	VERB
ejpam-371	367	2	us	we	PRON
ejpam-371	367	3	fix	fix	VERB
ejpam-371	367	4	t	t	PROPN
ejpam-371	367	5	>	>	X
ejpam-371	367	6	0	0	PUNCT
ejpam-371	368	1	and	and	CCONJ
ejpam-371	368	2	y0	y0	PROPN
ejpam-371	368	3	∈	∈	NOUN
ejpam-371	368	4	h1	h1	NOUN
ejpam-371	368	5	0(ω	0(ω	NUM
ejpam-371	368	6	)	)	PUNCT
ejpam-371	368	7	.	.	PUNCT
ejpam-371	369	1	for	for	ADP
ejpam-371	369	2	every	every	DET
ejpam-371	369	3	ε	ε	PROPN
ejpam-371	369	4	>	>	X
ejpam-371	369	5	0	0	PROPN
ejpam-371	369	6	,	,	PUNCT
ejpam-371	369	7	let	let	VERB
ejpam-371	369	8	us	we	PRON
ejpam-371	369	9	consider	consider	VERB
ejpam-371	369	10	the	the	DET
ejpam-371	369	11	problem	problem	NOUN
ejpam-371	369	12	min	min	PROPN
ejpam-371	369	13	n	n	NOUN
ejpam-371	369	14	jε(u	jε(u	NUM
ejpam-371	369	15	)	)	PUNCT
ejpam-371	369	16	:	:	PUNCT
ejpam-371	369	17	u	u	PROPN
ejpam-371	369	18	∈	∈	PROPN
ejpam-371	369	19	l2(0	l2(0	NOUN
ejpam-371	369	20	,	,	PUNCT
ejpam-371	369	21	t	t	NOUN
ejpam-371	369	22	;	;	PUNCT
ejpam-371	369	23	l2(ω	l2(ω	X
ejpam-371	369	24	)	)	PUNCT
ejpam-371	369	25	)	)	PUNCT
ejpam-371	370	1	o	o	NOUN
ejpam-371	370	2	,	,	PUNCT
ejpam-371	370	3	where	where	SCONJ
ejpam-371	370	4	the	the	DET
ejpam-371	370	5	functional	functional	ADJ
ejpam-371	370	6	jε	jε	NOUN
ejpam-371	370	7	is	be	AUX
ejpam-371	370	8	defined	define	VERB
ejpam-371	370	9	by	by	ADP
ejpam-371	370	10	jε(u	jε(u	NOUN
ejpam-371	370	11	)	)	PUNCT
ejpam-371	370	12	=	=	SYM
ejpam-371	371	1	1	1	NUM
ejpam-371	371	2	2	2	NUM
ejpam-371	371	3	∫∫	∫∫	PROPN
ejpam-371	371	4	(	(	PUNCT
ejpam-371	371	5	0,t)×ω	0,t)×ω	NUM
ejpam-371	371	6	|u|2d	|u|2d	NOUN
ejpam-371	371	7	xd	xd	INTJ
ejpam-371	371	8	t	t	PROPN
ejpam-371	372	1	+	+	CCONJ
ejpam-371	373	1	1	1	NUM
ejpam-371	373	2	2ε	2ε	NUM
ejpam-371	373	3	∫	∫	PROPN
ejpam-371	373	4	ω	ω	PROPN
ejpam-371	373	5	|y(t	|y(t	PROPN
ejpam-371	373	6	,	,	PUNCT
ejpam-371	373	7	x)|2d	x)|2d	PROPN
ejpam-371	373	8	x	x	SYM
ejpam-371	373	9	,	,	PUNCT
ejpam-371	373	10	(	(	PUNCT
ejpam-371	373	11	38	38	NUM
ejpam-371	373	12	)	)	PUNCT
ejpam-371	373	13	where	where	SCONJ
ejpam-371	373	14	y	y	PROPN
ejpam-371	373	15	is	be	AUX
ejpam-371	373	16	the	the	DET
ejpam-371	373	17	solution	solution	NOUN
ejpam-371	373	18	of	of	ADP
ejpam-371	373	19	(	(	PUNCT
ejpam-371	373	20	4	4	NUM
ejpam-371	373	21	)	)	PUNCT
ejpam-371	373	22	associated	associate	VERB
ejpam-371	373	23	with	with	ADP
ejpam-371	373	24	the	the	DET
ejpam-371	373	25	control	control	NOUN
ejpam-371	373	26	u.	u.	VERB
ejpam-371	373	27	in	in	ADP
ejpam-371	373	28	order	order	NOUN
ejpam-371	373	29	to	to	PART
ejpam-371	373	30	solve	solve	VERB
ejpam-371	373	31	this	this	DET
ejpam-371	373	32	control	control	NOUN
ejpam-371	373	33	problem	problem	NOUN
ejpam-371	373	34	,	,	PUNCT
ejpam-371	373	35	it	it	PRON
ejpam-371	373	36	is	be	AUX
ejpam-371	373	37	enough	enough	ADJ
ejpam-371	373	38	to	to	PART
ejpam-371	373	39	prove	prove	VERB
ejpam-371	373	40	that	that	SCONJ
ejpam-371	373	41	the	the	DET
ejpam-371	373	42	functional	functional	ADJ
ejpam-371	373	43	jε	jε	AUX
ejpam-371	373	44	has	have	VERB
ejpam-371	373	45	a	a	DET
ejpam-371	373	46	unique	unique	ADJ
ejpam-371	373	47	solution	solution	NOUN
ejpam-371	373	48	(	(	PUNCT
ejpam-371	373	49	see	see	VERB
ejpam-371	373	50	fernandezcara	fernandezcara	NOUN
ejpam-371	373	51	et	et	PROPN
ejpam-371	373	52	al	al	PROPN
ejpam-371	374	1	[	[	X
ejpam-371	374	2	5	5	NUM
ejpam-371	374	3	]	]	PUNCT
ejpam-371	374	4	)	)	PUNCT
ejpam-371	374	5	.	.	PUNCT
ejpam-371	375	1	since	since	SCONJ
ejpam-371	375	2	,	,	PUNCT
ejpam-371	375	3	jε	jε	X
ejpam-371	375	4	is	be	AUX
ejpam-371	375	5	a	a	DET
ejpam-371	375	6	continuous	continuous	ADJ
ejpam-371	375	7	strictly	strictly	ADV
ejpam-371	375	8	convex	convex	ADJ
ejpam-371	375	9	functional	functional	ADJ
ejpam-371	375	10	in	in	ADP
ejpam-371	375	11	l2(q	l2(q	PROPN
ejpam-371	375	12	)	)	PUNCT
ejpam-371	375	13	and	and	CCONJ
ejpam-371	375	14	coercive	coercive	ADJ
ejpam-371	375	15	,	,	PUNCT
ejpam-371	375	16	that	that	ADV
ejpam-371	375	17	is	is	ADV
ejpam-371	375	18	,	,	PUNCT
ejpam-371	375	19	lim	lim	PROPN
ejpam-371	375	20	inf	inf	PROPN
ejpam-371	375	21	||u||	||u||	PROPN
ejpam-371	375	22	l2((0,t	l2((0,t	PROPN
ejpam-371	375	23	)	)	PUNCT
ejpam-371	375	24	×ω→∞	×ω→∞	PROPN
ejpam-371	375	25	jε(u	jε(u	NOUN
ejpam-371	375	26	)	)	PUNCT
ejpam-371	376	1	=	=	SYM
ejpam-371	376	2	∞	∞	PROPN
ejpam-371	376	3	,	,	PUNCT
ejpam-371	376	4	jε	jε	AUX
ejpam-371	376	5	has	have	VERB
ejpam-371	376	6	a	a	DET
ejpam-371	376	7	unique	unique	ADJ
ejpam-371	376	8	solution	solution	NOUN
ejpam-371	376	9	(	(	PUNCT
ejpam-371	376	10	uε	uε	NOUN
ejpam-371	376	11	,	,	PUNCT
ejpam-371	376	12	yε	yε	PROPN
ejpam-371	376	13	)	)	PUNCT
ejpam-371	376	14	for	for	ADP
ejpam-371	376	15	every	every	DET
ejpam-371	376	16	ε	ε	PROPN
ejpam-371	376	17	>	>	X
ejpam-371	376	18	0	0	PROPN
ejpam-371	376	19	.	.	PUNCT
ejpam-371	377	1	next	next	ADV
ejpam-371	377	2	,	,	PUNCT
ejpam-371	377	3	we	we	PRON
ejpam-371	377	4	shall	shall	AUX
ejpam-371	377	5	obtain	obtain	VERB
ejpam-371	377	6	the	the	DET
ejpam-371	377	7	necessary	necessary	ADJ
ejpam-371	377	8	condition	condition	NOUN
ejpam-371	377	9	for	for	ADP
ejpam-371	377	10	optimality	optimality	NOUN
ejpam-371	377	11	via	via	ADP
ejpam-371	377	12	maximum	maximum	ADJ
ejpam-371	377	13	principle	principle	NOUN
ejpam-371	377	14	.	.	PUNCT
ejpam-371	378	1	we	we	PRON
ejpam-371	378	2	can	can	AUX
ejpam-371	378	3	verify	verify	VERB
ejpam-371	378	4	that	that	SCONJ
ejpam-371	378	5	it	it	PRON
ejpam-371	378	6	is	be	AUX
ejpam-371	378	7	characterized	characterize	VERB
ejpam-371	378	8	by	by	ADP
ejpam-371	378	9	uε	uε	PROPN
ejpam-371	378	10	=	=	PUNCT
ejpam-371	378	11	−χωqε	−χωqε	PROPN
ejpam-371	378	12	(	(	PUNCT
ejpam-371	378	13	39	39	NUM
ejpam-371	378	14	)	)	PUNCT
ejpam-371	378	15	where	where	SCONJ
ejpam-371	378	16	qε	qε	ADV
ejpam-371	378	17	is	be	VERB
ejpam-371	378	18	the	the	DET
ejpam-371	378	19	solution	solution	NOUN
ejpam-371	378	20	to	to	ADP
ejpam-371	378	21	the	the	DET
ejpam-371	378	22	adjoint	adjoint	NOUN
ejpam-371	378	23	problem	problem	NOUN
ejpam-371	378	24	(	(	PUNCT
ejpam-371	378	25	qε)t	qε)t	NOUN
ejpam-371	378	26	+	+	NOUN
ejpam-371	378	27	∆qε+m	∆qε+m	NOUN
ejpam-371	378	28	t	t	NOUN
ejpam-371	378	29	0	0	NUM
ejpam-371	378	30	∗∆qε(t	∗∆qε(t	PUNCT
ejpam-371	378	31	)	)	PUNCT
ejpam-371	379	1	+	+	CCONJ
ejpam-371	379	2	(	(	PUNCT
ejpam-371	379	3	n	n	PRON
ejpam-371	379	4	t	t	PROPN
ejpam-371	379	5	0	0	NUM
ejpam-371	379	6	∗	∗	NOUN
ejpam-371	379	7	qε(t))t	qε(t))t	PUNCT
ejpam-371	380	1	=	=	SYM
ejpam-371	380	2	0	0	NUM
ejpam-371	380	3	in	in	ADP
ejpam-371	380	4	q	q	PROPN
ejpam-371	380	5	qε(t	qε(t	NOUN
ejpam-371	380	6	,	,	PUNCT
ejpam-371	380	7	x	x	X
ejpam-371	380	8	)	)	PUNCT
ejpam-371	380	9	=	=	SYM
ejpam-371	380	10	1	1	NUM
ejpam-371	380	11	ε	ε	PROPN
ejpam-371	380	12	yε(t	yε(t	X
ejpam-371	380	13	,	,	PUNCT
ejpam-371	380	14	x	x	X
ejpam-371	380	15	)	)	PUNCT
ejpam-371	380	16	in	in	ADP
ejpam-371	380	17	ω	ω	PROPN
ejpam-371	380	18	qε(t	qε(t	NOUN
ejpam-371	380	19	,	,	PUNCT
ejpam-371	380	20	x	x	X
ejpam-371	380	21	)	)	PUNCT
ejpam-371	380	22	=	=	SYM
ejpam-371	380	23	0	0	NUM
ejpam-371	380	24	on	on	ADP
ejpam-371	380	25	σ	σ	PROPN
ejpam-371	380	26	.	.	PUNCT
ejpam-371	380	27			PROPN
ejpam-371	380	28			PROPN
ejpam-371	380	29			NOUN
ejpam-371	380	30	(	(	PUNCT
ejpam-371	380	31	40	40	NUM
ejpam-371	380	32	)	)	PUNCT
ejpam-371	380	33	r.	r.	PROPN
ejpam-371	380	34	lavanya	lavanya	PROPN
ejpam-371	380	35	/	/	SYM
ejpam-371	380	36	eur	eur	PROPN
ejpam-371	380	37	.	.	PUNCT
ejpam-371	381	1	j.	j.	PROPN
ejpam-371	381	2	pure	pure	PROPN
ejpam-371	381	3	appl	appl	PROPN
ejpam-371	381	4	.	.	PROPN
ejpam-371	381	5	math	math	PROPN
ejpam-371	381	6	,	,	PUNCT
ejpam-371	381	7	3	3	NUM
ejpam-371	381	8	(	(	PUNCT
ejpam-371	381	9	2010	2010	NUM
ejpam-371	381	10	)	)	PUNCT
ejpam-371	381	11	,	,	PUNCT
ejpam-371	381	12	235	235	NUM
ejpam-371	381	13	-	-	SYM
ejpam-371	381	14	253	253	NUM
ejpam-371	381	15	251	251	NUM
ejpam-371	381	16	let	let	VERB
ejpam-371	381	17	us	we	PRON
ejpam-371	381	18	put	put	VERB
ejpam-371	381	19	y	y	PROPN
ejpam-371	381	20	=	=	NOUN
ejpam-371	381	21	w+ϕ.	w+ϕ.	NOUN
ejpam-371	381	22	if	if	SCONJ
ejpam-371	381	23	y	y	PROPN
ejpam-371	381	24	is	be	AUX
ejpam-371	381	25	the	the	DET
ejpam-371	381	26	solution	solution	NOUN
ejpam-371	381	27	of	of	ADP
ejpam-371	381	28	(	(	PUNCT
ejpam-371	381	29	4	4	NUM
ejpam-371	381	30	)	)	PUNCT
ejpam-371	381	31	associated	associate	VERB
ejpam-371	381	32	with	with	ADP
ejpam-371	381	33	u	u	PROPN
ejpam-371	381	34	,	,	PUNCT
ejpam-371	381	35	and	and	CCONJ
ejpam-371	381	36	w	w	NOUN
ejpam-371	381	37	is	be	AUX
ejpam-371	381	38	the	the	DET
ejpam-371	381	39	weak	weak	ADJ
ejpam-371	381	40	solution	solution	NOUN
ejpam-371	381	41	of	of	ADP
ejpam-371	381	42	the	the	DET
ejpam-371	381	43	homogeneous	homogeneous	ADJ
ejpam-371	381	44	problem	problem	NOUN
ejpam-371	381	45	corresponding	correspond	VERB
ejpam-371	381	46	to	to	ADP
ejpam-371	381	47	(	(	PUNCT
ejpam-371	381	48	30	30	NUM
ejpam-371	381	49	)	)	PUNCT
ejpam-371	381	50	,	,	PUNCT
ejpam-371	381	51	then	then	ADV
ejpam-371	381	52	ϕ	ϕ	PROPN
ejpam-371	381	53	satisfies	satisfie	NOUN
ejpam-371	381	54	ϕt	ϕt	ADP
ejpam-371	381	55	−∆ϕ−m	−∆ϕ−m	PROPN
ejpam-371	381	56	t	t	PROPN
ejpam-371	381	57	0	0	PUNCT
ejpam-371	381	58	∗∆φε(t	∗∆φε(t	PUNCT
ejpam-371	381	59	)	)	PUNCT
ejpam-371	382	1	+	+	CCONJ
ejpam-371	382	2	(	(	PUNCT
ejpam-371	382	3	n	n	PRON
ejpam-371	382	4	t	t	PROPN
ejpam-371	382	5	0	0	NUM
ejpam-371	382	6	∗φε(t))t	∗φε(t))t	PROPN
ejpam-371	382	7	=	=	PUNCT
ejpam-371	382	8	χωu	χωu	PROPN
ejpam-371	382	9	in	in	ADP
ejpam-371	382	10	q	q	PROPN
ejpam-371	382	11	ϕ(0	ϕ(0	PROPN
ejpam-371	382	12	,	,	PUNCT
ejpam-371	382	13	x	x	NOUN
ejpam-371	382	14	)	)	PUNCT
ejpam-371	382	15	=	=	SYM
ejpam-371	382	16	0	0	NUM
ejpam-371	382	17	in	in	ADP
ejpam-371	382	18	ω	ω	NUM
ejpam-371	382	19	ϕ(t	ϕ(t	PROPN
ejpam-371	382	20	,	,	PUNCT
ejpam-371	382	21	x	x	NOUN
ejpam-371	382	22	)	)	PUNCT
ejpam-371	382	23	=	=	SYM
ejpam-371	382	24	0	0	NUM
ejpam-371	382	25	on	on	ADP
ejpam-371	382	26	σ	σ	PROPN
ejpam-371	382	27	.	.	PUNCT
ejpam-371	383	1			PROPN
ejpam-371	383	2			PROPN
ejpam-371	383	3			NOUN
ejpam-371	383	4	(	(	PUNCT
ejpam-371	383	5	41	41	NUM
ejpam-371	383	6	)	)	PUNCT
ejpam-371	383	7	now	now	ADV
ejpam-371	383	8	the	the	DET
ejpam-371	383	9	functional	functional	ADJ
ejpam-371	383	10	jε	jε	NOUN
ejpam-371	383	11	is	be	AUX
ejpam-371	383	12	differentiable	differentiable	ADJ
ejpam-371	383	13	at	at	ADP
ejpam-371	383	14	the	the	DET
ejpam-371	383	15	point	point	NOUN
ejpam-371	383	16	u.	u.	NOUN
ejpam-371	383	17	for	for	ADP
ejpam-371	383	18	u	u	NOUN
ejpam-371	383	19	,	,	PUNCT
ejpam-371	383	20	v	v	PROPN
ejpam-371	383	21	∈	∈	PROPN
ejpam-371	383	22	l2(0	l2(0	NOUN
ejpam-371	383	23	,	,	PUNCT
ejpam-371	383	24	t	t	NOUN
ejpam-371	383	25	;	;	PUNCT
ejpam-371	383	26	l2(ω	l2(ω	NOUN
ejpam-371	383	27	)	)	PUNCT
ejpam-371	383	28	)	)	PUNCT
ejpam-371	383	29	,	,	PUNCT
ejpam-371	383	30	we	we	PRON
ejpam-371	383	31	obtain	obtain	VERB
ejpam-371	383	32	〈	〈	PRON
ejpam-371	383	33	j	j	NOUN
ejpam-371	383	34	′ε(uε	′ε(uε	NUM
ejpam-371	383	35	)	)	PUNCT
ejpam-371	383	36	,	,	PUNCT
ejpam-371	383	37	v〉l2(q	v〉l2(q	NOUN
ejpam-371	383	38	)	)	PUNCT
ejpam-371	383	39	=	=	PUNCT
ejpam-371	384	1	∫∫	∫∫	ADV
ejpam-371	384	2	(	(	PUNCT
ejpam-371	384	3	0,t)×ω	0,t)×ω	NUM
ejpam-371	384	4	uεvd	uεvd	NOUN
ejpam-371	384	5	xd	xd	INTJ
ejpam-371	384	6	t+	t+	NUM
ejpam-371	384	7	1	1	NUM
ejpam-371	384	8	ε	ε	PROPN
ejpam-371	384	9	∫	∫	PROPN
ejpam-371	384	10	ω	ω	PROPN
ejpam-371	384	11	y(t	y(t	PROPN
ejpam-371	384	12	)	)	PUNCT
ejpam-371	384	13	ϕ(t	ϕ(t	NUM
ejpam-371	384	14	)	)	PUNCT
ejpam-371	385	1	d	d	NOUN
ejpam-371	385	2	x	x	X
ejpam-371	385	3	,	,	PUNCT
ejpam-371	385	4	(	(	PUNCT
ejpam-371	385	5	42	42	NUM
ejpam-371	385	6	)	)	PUNCT
ejpam-371	385	7	where	where	SCONJ
ejpam-371	385	8	ϕ	ϕ	NOUN
ejpam-371	385	9	is	be	AUX
ejpam-371	385	10	the	the	DET
ejpam-371	385	11	solution	solution	NOUN
ejpam-371	385	12	to	to	ADP
ejpam-371	385	13	(	(	PUNCT
ejpam-371	385	14	41	41	NUM
ejpam-371	385	15	)	)	PUNCT
ejpam-371	385	16	associated	associate	VERB
ejpam-371	385	17	with	with	ADP
ejpam-371	385	18	the	the	DET
ejpam-371	385	19	control	control	NOUN
ejpam-371	385	20	v.	v.	CCONJ
ejpam-371	385	21	for	for	ADP
ejpam-371	385	22	the	the	DET
ejpam-371	385	23	pair	pair	NOUN
ejpam-371	385	24	(	(	PUNCT
ejpam-371	385	25	uε	uε	NOUN
ejpam-371	385	26	,	,	PUNCT
ejpam-371	385	27	yε	yε	PROPN
ejpam-371	385	28	)	)	PUNCT
ejpam-371	385	29	to	to	PART
ejpam-371	385	30	be	be	AUX
ejpam-371	385	31	a	a	DET
ejpam-371	385	32	unique	unique	ADJ
ejpam-371	385	33	solution	solution	NOUN
ejpam-371	385	34	of	of	ADP
ejpam-371	385	35	jε	jε	PROPN
ejpam-371	385	36	,	,	PUNCT
ejpam-371	385	37	we	we	PRON
ejpam-371	385	38	must	must	AUX
ejpam-371	385	39	have	have	VERB
ejpam-371	385	40	〈	〈	PROPN
ejpam-371	385	41	j	j	PROPN
ejpam-371	385	42	′ε(uε	′ε(uε	NUM
ejpam-371	385	43	)	)	PUNCT
ejpam-371	385	44	,	,	PUNCT
ejpam-371	385	45	v〉l2(q	v〉l2(q	NOUN
ejpam-371	385	46	)	)	PUNCT
ejpam-371	385	47	=	=	SYM
ejpam-371	386	1	0	0	X
ejpam-371	386	2	.	.	PUNCT
ejpam-371	387	1	the	the	DET
ejpam-371	387	2	duality	duality	NOUN
ejpam-371	387	3	between	between	ADP
ejpam-371	387	4	ϕ	ϕ	PROPN
ejpam-371	387	5	and	and	CCONJ
ejpam-371	387	6	q	q	PROPN
ejpam-371	387	7	gives	give	VERB
ejpam-371	387	8	the	the	DET
ejpam-371	387	9	following	follow	VERB
ejpam-371	387	10	∫∫	∫∫	PROPN
ejpam-371	387	11	(	(	PUNCT
ejpam-371	387	12	0,t)×ω	0,t)×ω	NUM
ejpam-371	387	13	qεvd	qεvd	NOUN
ejpam-371	387	14	xd	xd	INTJ
ejpam-371	387	15	t	t	PROPN
ejpam-371	387	16	=	=	SYM
ejpam-371	387	17	∫	∫	PROPN
ejpam-371	387	18	ω	ω	PROPN
ejpam-371	387	19	qε(t	qε(t	PUNCT
ejpam-371	387	20	)	)	PUNCT
ejpam-371	387	21	ϕ(t	ϕ(t	NUM
ejpam-371	387	22	)	)	PUNCT
ejpam-371	388	1	d	d	NOUN
ejpam-371	388	2	x	x	SYM
ejpam-371	388	3	=	=	SYM
ejpam-371	388	4	1	1	NUM
ejpam-371	388	5	ε	ε	PROPN
ejpam-371	388	6	∫	∫	PROPN
ejpam-371	388	7	ω	ω	PROPN
ejpam-371	388	8	yε(t	yε(t	NUM
ejpam-371	388	9	)	)	PUNCT
ejpam-371	388	10	ϕ(t	ϕ(t	NUM
ejpam-371	388	11	)	)	PUNCT
ejpam-371	389	1	d	d	NOUN
ejpam-371	389	2	x	x	X
ejpam-371	389	3	.	.	PUNCT
ejpam-371	390	1	(	(	PUNCT
ejpam-371	390	2	43	43	NUM
ejpam-371	390	3	)	)	PUNCT
ejpam-371	390	4	in	in	ADP
ejpam-371	390	5	view	view	NOUN
ejpam-371	390	6	of	of	ADP
ejpam-371	390	7	(	(	PUNCT
ejpam-371	390	8	42	42	NUM
ejpam-371	390	9	)	)	PUNCT
ejpam-371	390	10	and	and	CCONJ
ejpam-371	390	11	(	(	PUNCT
ejpam-371	390	12	43	43	NUM
ejpam-371	390	13	)	)	PUNCT
ejpam-371	390	14	,	,	PUNCT
ejpam-371	390	15	we	we	PRON
ejpam-371	390	16	can	can	AUX
ejpam-371	390	17	identify	identify	VERB
ejpam-371	390	18	uε	uε	ADP
ejpam-371	390	19	=	=	NOUN
ejpam-371	390	20	−χωqε	−χωqε	PROPN
ejpam-371	390	21	,	,	PUNCT
ejpam-371	390	22	the	the	DET
ejpam-371	390	23	optimal	optimal	ADJ
ejpam-371	390	24	control	control	NOUN
ejpam-371	390	25	stated	state	VERB
ejpam-371	390	26	in	in	ADP
ejpam-371	390	27	(	(	PUNCT
ejpam-371	390	28	39	39	NUM
ejpam-371	390	29	)	)	PUNCT
ejpam-371	390	30	.	.	PUNCT
ejpam-371	391	1	next	next	ADV
ejpam-371	391	2	we	we	PRON
ejpam-371	391	3	shall	shall	AUX
ejpam-371	391	4	show	show	VERB
ejpam-371	391	5	that	that	SCONJ
ejpam-371	391	6	(	(	PUNCT
ejpam-371	391	7	uε	uε	PROPN
ejpam-371	391	8	,	,	PUNCT
ejpam-371	391	9	yε	yε	ADJ
ejpam-371	391	10	)	)	PUNCT
ejpam-371	391	11	converges	converge	NOUN
ejpam-371	391	12	along	along	ADP
ejpam-371	391	13	a	a	DET
ejpam-371	391	14	subsequence	subsequence	NOUN
ejpam-371	391	15	of	of	ADP
ejpam-371	391	16	ε	ε	PROPN
ejpam-371	391	17	in	in	ADP
ejpam-371	391	18	a	a	DET
ejpam-371	391	19	certain	certain	ADJ
ejpam-371	391	20	topology	topology	NOUN
ejpam-371	391	21	.	.	PUNCT
ejpam-371	392	1	in	in	ADP
ejpam-371	392	2	order	order	NOUN
ejpam-371	392	3	to	to	PART
ejpam-371	392	4	prove	prove	VERB
ejpam-371	392	5	this	this	PRON
ejpam-371	392	6	,	,	PUNCT
ejpam-371	392	7	we	we	PRON
ejpam-371	392	8	need	need	VERB
ejpam-371	392	9	a	a	DET
ejpam-371	392	10	suitable	suitable	ADJ
ejpam-371	392	11	estimate	estimate	NOUN
ejpam-371	392	12	for	for	ADP
ejpam-371	392	13	(	(	PUNCT
ejpam-371	392	14	uε	uε	PROPN
ejpam-371	392	15	,	,	PUNCT
ejpam-371	392	16	yε	yε	NOUN
ejpam-371	392	17	)	)	PUNCT
ejpam-371	392	18	.	.	PUNCT
ejpam-371	393	1	in	in	ADP
ejpam-371	393	2	particular	particular	ADJ
ejpam-371	393	3	,	,	PUNCT
ejpam-371	393	4	we	we	PRON
ejpam-371	393	5	get	get	VERB
ejpam-371	393	6	l2	l2	NOUN
ejpam-371	393	7	estimate	estimate	NOUN
ejpam-371	393	8	for	for	ADP
ejpam-371	393	9	uε	uε	PROPN
ejpam-371	393	10	.	.	PUNCT
ejpam-371	394	1	multiplying	multiplying	NOUN
ejpam-371	394	2	(	(	PUNCT
ejpam-371	394	3	4	4	NUM
ejpam-371	394	4	)	)	PUNCT
ejpam-371	394	5	by	by	ADP
ejpam-371	394	6	qε(replace	qε(replace	PROPN
ejpam-371	394	7	y	y	PROPN
ejpam-371	394	8	by	by	ADP
ejpam-371	394	9	yε	yε	PROPN
ejpam-371	394	10	)	)	PUNCT
ejpam-371	394	11	and	and	CCONJ
ejpam-371	394	12	(	(	PUNCT
ejpam-371	394	13	40	40	NUM
ejpam-371	394	14	)	)	PUNCT
ejpam-371	394	15	by	by	ADP
ejpam-371	394	16	yε	yε	NOUN
ejpam-371	394	17	and	and	CCONJ
ejpam-371	394	18	adding	add	VERB
ejpam-371	394	19	and	and	CCONJ
ejpam-371	394	20	then	then	ADV
ejpam-371	394	21	integrating	integrate	VERB
ejpam-371	394	22	on	on	ADP
ejpam-371	394	23	(	(	PUNCT
ejpam-371	394	24	0	0	NUM
ejpam-371	394	25	,	,	PUNCT
ejpam-371	394	26	t	t	NOUN
ejpam-371	394	27	)	)	PUNCT
ejpam-371	394	28	×ω	×ω	ADV
ejpam-371	394	29	,	,	PUNCT
ejpam-371	394	30	we	we	PRON
ejpam-371	394	31	have	have	VERB
ejpam-371	394	32	∫	∫	PROPN
ejpam-371	394	33	ω	ω	PROPN
ejpam-371	394	34	qε(t	qε(t	PUNCT
ejpam-371	394	35	)	)	PUNCT
ejpam-371	394	36	yε(t	yε(t	X
ejpam-371	394	37	)	)	PUNCT
ejpam-371	395	1	d	d	X
ejpam-371	395	2	x	x	X
ejpam-371	395	3	=	=	SYM
ejpam-371	395	4	∫	∫	PROPN
ejpam-371	395	5	ω	ω	NUM
ejpam-371	395	6	y0(x)qε(0)d	y0(x)qε(0)d	PROPN
ejpam-371	395	7	x	x	X
ejpam-371	396	1	+	+	CCONJ
ejpam-371	396	2	∫∫	∫∫	PROPN
ejpam-371	396	3	(	(	PUNCT
ejpam-371	396	4	0,t)×ω	0,t)×ω	NUM
ejpam-371	396	5	uεqεd	uεqεd	NOUN
ejpam-371	396	6	xd	xd	INTJ
ejpam-371	396	7	t.	t.	NOUN
ejpam-371	396	8	making	make	VERB
ejpam-371	396	9	use	use	NOUN
ejpam-371	396	10	of	of	ADP
ejpam-371	396	11	the	the	DET
ejpam-371	396	12	optimality	optimality	NOUN
ejpam-371	396	13	condition	condition	NOUN
ejpam-371	396	14	qε(t	qε(t	NOUN
ejpam-371	396	15	,	,	PUNCT
ejpam-371	396	16	x	x	X
ejpam-371	396	17	)	)	PUNCT
ejpam-371	396	18	=	=	SYM
ejpam-371	396	19	1	1	NUM
ejpam-371	396	20	ε	ε	PROPN
ejpam-371	396	21	yε(t	yε(t	X
ejpam-371	396	22	,	,	PUNCT
ejpam-371	396	23	x	x	X
ejpam-371	396	24	)	)	PUNCT
ejpam-371	396	25	and	and	CCONJ
ejpam-371	396	26	the	the	DET
ejpam-371	396	27	young	young	PROPN
ejpam-371	396	28	’s	’s	PART
ejpam-371	396	29	inequality	inequality	NOUN
ejpam-371	396	30	,	,	PUNCT
ejpam-371	396	31	we	we	PRON
ejpam-371	396	32	obtain	obtain	VERB
ejpam-371	396	33	∫∫	∫∫	PROPN
ejpam-371	396	34	(	(	PUNCT
ejpam-371	396	35	0,t)×ω	0,t)×ω	NUM
ejpam-371	397	1	|uε|2d	|uε|2d	NOUN
ejpam-371	397	2	xd	xd	INTJ
ejpam-371	397	3	t	t	PROPN
ejpam-371	397	4	+	+	CCONJ
ejpam-371	397	5	1	1	NUM
ejpam-371	397	6	ε	ε	PROPN
ejpam-371	397	7	∫	∫	PROPN
ejpam-371	397	8	ω	ω	PROPN
ejpam-371	397	9	|yε(t	|yε(t	PROPN
ejpam-371	397	10	,	,	PUNCT
ejpam-371	397	11	x)|2d	x)|2d	PROPN
ejpam-371	397	12	x	x	SYM
ejpam-371	397	13	≤	≤	NUM
ejpam-371	397	14	η	η	X
ejpam-371	397	15	2	2	NUM
ejpam-371	397	16	||y0||2l2(ω	||y0||2l2(ω	NUM
ejpam-371	397	17	)	)	PUNCT
ejpam-371	397	18	+	+	CCONJ
ejpam-371	397	19	1	1	NUM
ejpam-371	397	20	2η	2η	NUM
ejpam-371	397	21	||qε(0)||2l2(ω	||qε(0)||2l2(ω	NUM
ejpam-371	397	22	)	)	PUNCT
ejpam-371	397	23	∀	∀	PUNCT
ejpam-371	397	24	η	η	X
ejpam-371	397	25	>	>	X
ejpam-371	397	26	0	0	NUM
ejpam-371	397	27	.	.	PUNCT
ejpam-371	398	1	using	use	VERB
ejpam-371	398	2	corollary	corollary	ADJ
ejpam-371	398	3	1	1	NUM
ejpam-371	398	4	,	,	PUNCT
ejpam-371	398	5	we	we	PRON
ejpam-371	398	6	can	can	AUX
ejpam-371	398	7	choose	choose	VERB
ejpam-371	398	8	η	η	PROPN
ejpam-371	398	9	appropriately	appropriately	ADV
ejpam-371	398	10	,	,	PUNCT
ejpam-371	398	11	for	for	ADP
ejpam-371	398	12	instance	instance	NOUN
ejpam-371	398	13	η	η	PROPN
ejpam-371	398	14	=	=	PROPN
ejpam-371	398	15	w	w	PROPN
ejpam-371	398	16	(	(	PUNCT
ejpam-371	398	17	ω	ω	PROPN
ejpam-371	398	18	,	,	PUNCT
ejpam-371	398	19	ω	ω	PROPN
ejpam-371	398	20	,	,	PUNCT
ejpam-371	398	21	t	t	PROPN
ejpam-371	398	22	)	)	PUNCT
ejpam-371	398	23	;	;	PUNCT
ejpam-371	398	24	then	then	ADV
ejpam-371	398	25	we	we	PRON
ejpam-371	398	26	have	have	VERB
ejpam-371	398	27	1	1	NUM
ejpam-371	398	28	2	2	NUM
ejpam-371	398	29	∫∫	∫∫	PROPN
ejpam-371	398	30	(	(	PUNCT
ejpam-371	398	31	0,t)×ω	0,t)×ω	NUM
ejpam-371	398	32	|uε|2d	|uε|2d	NOUN
ejpam-371	398	33	xd	xd	INTJ
ejpam-371	398	34	t	t	PROPN
ejpam-371	398	35	+	+	CCONJ
ejpam-371	398	36	1	1	NUM
ejpam-371	398	37	ε	ε	PROPN
ejpam-371	398	38	∫	∫	PROPN
ejpam-371	398	39	ω	ω	PROPN
ejpam-371	398	40	|yε(t	|yε(t	PROPN
ejpam-371	398	41	,	,	PUNCT
ejpam-371	398	42	x)|2d	x)|2d	PROPN
ejpam-371	399	1	x	x	SYM
ejpam-371	399	2	≤w	≤w	INTJ
ejpam-371	399	3	(	(	PUNCT
ejpam-371	399	4	ω	ω	PROPN
ejpam-371	399	5	,	,	PUNCT
ejpam-371	399	6	ω	ω	PROPN
ejpam-371	399	7	,	,	PUNCT
ejpam-371	399	8	t	t	NOUN
ejpam-371	399	9	)	)	PUNCT
ejpam-371	399	10	||y0||2l2(ω	||y0||2l2(ω	NUM
ejpam-371	399	11	)	)	PUNCT
ejpam-371	399	12	,	,	PUNCT
ejpam-371	399	13	(	(	PUNCT
ejpam-371	399	14	44	44	NUM
ejpam-371	399	15	)	)	PUNCT
ejpam-371	399	16	references	reference	NOUN
ejpam-371	399	17	252	252	NUM
ejpam-371	399	18	where	where	SCONJ
ejpam-371	399	19	the	the	DET
ejpam-371	399	20	constant	constant	ADJ
ejpam-371	399	21	w	w	PROPN
ejpam-371	399	22	(	(	PUNCT
ejpam-371	399	23	·	·	PUNCT
ejpam-371	399	24	)	)	PUNCT
ejpam-371	399	25	is	be	AUX
ejpam-371	399	26	given	give	VERB
ejpam-371	399	27	by	by	ADP
ejpam-371	399	28	(	(	PUNCT
ejpam-371	399	29	24	24	NUM
ejpam-371	399	30	)	)	PUNCT
ejpam-371	399	31	.	.	PUNCT
ejpam-371	400	1	the	the	DET
ejpam-371	400	2	proposition	proposition	NOUN
ejpam-371	400	3	1	1	NUM
ejpam-371	400	4	and	and	CCONJ
ejpam-371	400	5	the	the	DET
ejpam-371	400	6	estimate	estimate	NOUN
ejpam-371	400	7	(	(	PUNCT
ejpam-371	400	8	44	44	NUM
ejpam-371	400	9	)	)	PUNCT
ejpam-371	400	10	allow	allow	VERB
ejpam-371	400	11	us	we	PRON
ejpam-371	400	12	to	to	PART
ejpam-371	400	13	pass	pass	VERB
ejpam-371	400	14	to	to	ADP
ejpam-371	400	15	the	the	DET
ejpam-371	400	16	weak	weak	ADJ
ejpam-371	400	17	limit	limit	NOUN
ejpam-371	400	18	in	in	ADP
ejpam-371	400	19	(	(	PUNCT
ejpam-371	400	20	4	4	NUM
ejpam-371	400	21	)	)	PUNCT
ejpam-371	400	22	(	(	PUNCT
ejpam-371	400	23	after	after	ADP
ejpam-371	400	24	replacing	replace	VERB
ejpam-371	400	25	(	(	PUNCT
ejpam-371	400	26	u	u	NOUN
ejpam-371	400	27	,	,	PUNCT
ejpam-371	400	28	y	y	PROPN
ejpam-371	400	29	)	)	PUNCT
ejpam-371	400	30	by	by	ADP
ejpam-371	400	31	(	(	PUNCT
ejpam-371	400	32	uε	uε	PROPN
ejpam-371	400	33	,	,	PUNCT
ejpam-371	400	34	yε	yε	NOUN
ejpam-371	400	35	)	)	PUNCT
ejpam-371	400	36	)	)	PUNCT
ejpam-371	401	1	as	as	ADP
ejpam-371	401	2	ε→	ε→	NUM
ejpam-371	401	3	0	0	NUM
ejpam-371	401	4	,	,	PUNCT
ejpam-371	401	5	which	which	PRON
ejpam-371	401	6	gives	give	VERB
ejpam-371	401	7	the	the	DET
ejpam-371	401	8	solution	solution	NOUN
ejpam-371	401	9	of	of	ADP
ejpam-371	401	10	the	the	DET
ejpam-371	401	11	null	null	ADJ
ejpam-371	401	12	controllability	controllability	NOUN
ejpam-371	401	13	problem	problem	NOUN
ejpam-371	401	14	(	(	PUNCT
ejpam-371	401	15	4	4	NUM
ejpam-371	401	16	)	)	PUNCT
ejpam-371	401	17	.	.	PUNCT
ejpam-371	402	1	since	since	SCONJ
ejpam-371	402	2	uε	uε	PROPN
ejpam-371	402	3	is	be	AUX
ejpam-371	402	4	bounded	bound	VERB
ejpam-371	402	5	in	in	ADP
ejpam-371	402	6	l2(0	l2(0	PROPN
ejpam-371	402	7	,	,	PUNCT
ejpam-371	402	8	t	t	NOUN
ejpam-371	402	9	;	;	PUNCT
ejpam-371	402	10	l2(ω	l2(ω	NOUN
ejpam-371	402	11	)	)	PUNCT
ejpam-371	402	12	)	)	PUNCT
ejpam-371	402	13	,	,	PUNCT
ejpam-371	402	14	there	there	PRON
ejpam-371	402	15	exists	exist	VERB
ejpam-371	402	16	a	a	DET
ejpam-371	402	17	subsequence	subsequence	NOUN
ejpam-371	402	18	of	of	ADP
ejpam-371	402	19	ε	ε	PROPN
ejpam-371	402	20	still	still	ADV
ejpam-371	402	21	indexed	index	VERB
ejpam-371	402	22	by	by	ADP
ejpam-371	402	23	ε	ε	PROPN
ejpam-371	402	24	such	such	ADJ
ejpam-371	402	25	that	that	DET
ejpam-371	402	26	uε→	uε→	PROPN
ejpam-371	402	27	u	u	NOUN
ejpam-371	402	28	weakly	weakly	ADJ
ejpam-371	402	29	in	in	ADP
ejpam-371	402	30	l2(0	l2(0	NOUN
ejpam-371	402	31	,	,	PUNCT
ejpam-371	402	32	t	t	NOUN
ejpam-371	402	33	;	;	PUNCT
ejpam-371	402	34	l2(ω	l2(ω	NOUN
ejpam-371	402	35	)	)	PUNCT
ejpam-371	402	36	)	)	PUNCT
ejpam-371	402	37	,	,	PUNCT
ejpam-371	402	38	yε→	yε→	NOUN
ejpam-371	403	1	y	y	PROPN
ejpam-371	403	2	weakly	weakly	ADV
ejpam-371	403	3	in	in	ADP
ejpam-371	403	4	h2,1(q	h2,1(q	NOUN
ejpam-371	403	5	)	)	PUNCT
ejpam-371	403	6	as	as	ADP
ejpam-371	403	7	ε→	ε→	X
ejpam-371	403	8	0	0	NUM
ejpam-371	403	9	.	.	PUNCT
ejpam-371	404	1	from	from	ADP
ejpam-371	404	2	(	(	PUNCT
ejpam-371	404	3	44	44	NUM
ejpam-371	404	4	)	)	PUNCT
ejpam-371	404	5	and	and	CCONJ
ejpam-371	404	6	fatou	fatou	PROPN
ejpam-371	404	7	’s	’s	PART
ejpam-371	404	8	lemma	lemma	PROPN
ejpam-371	404	9	for	for	ADP
ejpam-371	404	10	any	any	DET
ejpam-371	404	11	constant	constant	ADJ
ejpam-371	404	12	c	c	NOUN
ejpam-371	404	13	independent	independent	NOUN
ejpam-371	404	14	of	of	ADP
ejpam-371	404	15	ε	ε	PROPN
ejpam-371	404	16	,	,	PUNCT
ejpam-371	404	17	we	we	PRON
ejpam-371	404	18	have	have	VERB
ejpam-371	404	19	||y(t	||y(t	PROPN
ejpam-371	404	20	,	,	PUNCT
ejpam-371	404	21	x)||2	x)||2	PROPN
ejpam-371	404	22	l2(ω	l2(ω	NOUN
ejpam-371	404	23	)	)	PUNCT
ejpam-371	404	24	≤	≤	NOUN
ejpam-371	404	25	lim	lim	PROPN
ejpam-371	404	26	inf	inf	PROPN
ejpam-371	404	27	ε→0	ε→0	NOUN
ejpam-371	404	28	∫	∫	PROPN
ejpam-371	404	29	ω	ω	NUM
ejpam-371	404	30	|yε(t	|yε(t	PROPN
ejpam-371	404	31	,	,	PUNCT
ejpam-371	404	32	x)|2d	x)|2d	PROPN
ejpam-371	404	33	x	x	SYM
ejpam-371	404	34	≤	≤	ADJ
ejpam-371	404	35	lim	lim	PROPN
ejpam-371	404	36	inf	inf	PROPN
ejpam-371	404	37	ε→0	ε→0	NOUN
ejpam-371	404	38	cε	cε	VERB
ejpam-371	404	39	=	=	SYM
ejpam-371	404	40	0	0	PROPN
ejpam-371	404	41	.	.	PUNCT
ejpam-371	405	1	it	it	PRON
ejpam-371	405	2	follows	follow	VERB
ejpam-371	405	3	that	that	SCONJ
ejpam-371	405	4	y(t	y(t	PROPN
ejpam-371	405	5	,	,	PUNCT
ejpam-371	405	6	x	x	X
ejpam-371	405	7	)	)	PUNCT
ejpam-371	405	8	≡	≡	PROPN
ejpam-371	405	9	0	0	NUM
ejpam-371	406	1	a.e	a.e	PROPN
ejpam-371	406	2	.	.	PUNCT
ejpam-371	406	3	x	x	SYM
ejpam-371	406	4	∈	∈	PROPN
ejpam-371	406	5	ω	ω	NOUN
ejpam-371	406	6	.	.	PUNCT
ejpam-371	407	1	the	the	DET
ejpam-371	407	2	estimate	estimate	NOUN
ejpam-371	407	3	for	for	ADP
ejpam-371	407	4	the	the	DET
ejpam-371	407	5	control	control	NOUN
ejpam-371	407	6	u	u	NOUN
ejpam-371	407	7	follows	follow	VERB
ejpam-371	407	8	from	from	ADP
ejpam-371	407	9	(	(	PUNCT
ejpam-371	407	10	44	44	NUM
ejpam-371	407	11	)	)	PUNCT
ejpam-371	407	12	and	and	CCONJ
ejpam-371	407	13	the	the	DET
ejpam-371	407	14	proof	proof	NOUN
ejpam-371	407	15	is	be	AUX
ejpam-371	407	16	thus	thus	ADV
ejpam-371	407	17	completed	complete	VERB
ejpam-371	407	18	.	.	PUNCT
ejpam-371	408	1	references	reference	NOUN
ejpam-371	408	2	[	[	X
ejpam-371	408	3	1	1	NUM
ejpam-371	408	4	]	]	X
ejpam-371	408	5	r.a	r.a	PROPN
ejpam-371	408	6	.	.	PROPN
ejpam-371	408	7	adams	adams	PROPN
ejpam-371	408	8	and	and	CCONJ
ejpam-371	408	9	j.f	j.f	PROPN
ejpam-371	408	10	.	.	PROPN
ejpam-371	408	11	fournier	fournier	PROPN
ejpam-371	408	12	,	,	PUNCT
ejpam-371	408	13	sobolev	sobolev	NOUN
ejpam-371	408	14	spaces	space	NOUN
ejpam-371	408	15	,	,	PUNCT
ejpam-371	408	16	second	second	ADJ
ejpam-371	408	17	edition	edition	NOUN
ejpam-371	408	18	,	,	PUNCT
ejpam-371	408	19	new	new	PROPN
ejpam-371	408	20	york	york	PROPN
ejpam-371	408	21	,	,	PUNCT
ejpam-371	408	22	academic	academic	ADJ
ejpam-371	408	23	press	press	NOUN
ejpam-371	408	24	,	,	PUNCT
ejpam-371	408	25	2003	2003	NUM
ejpam-371	408	26	.	.	PUNCT
ejpam-371	409	1	[	[	X
ejpam-371	409	2	2	2	X
ejpam-371	409	3	]	]	X
ejpam-371	409	4	v.	v.	CCONJ
ejpam-371	409	5	barbu	barbu	PROPN
ejpam-371	409	6	,	,	PUNCT
ejpam-371	409	7	"	"	PUNCT
ejpam-371	409	8	controllability	controllability	NOUN
ejpam-371	409	9	of	of	ADP
ejpam-371	409	10	parabolic	parabolic	ADJ
ejpam-371	409	11	and	and	CCONJ
ejpam-371	409	12	navier	navier	NOUN
ejpam-371	409	13	-	-	PUNCT
ejpam-371	409	14	stokes	stokes	PROPN
ejpam-371	409	15	equations	equation	NOUN
ejpam-371	409	16	"	"	PUNCT
ejpam-371	409	17	,	,	PUNCT
ejpam-371	409	18	scientiae	scientiae	NOUN
ejpam-371	409	19	mathematicae	mathematicae	PROPN
ejpam-371	409	20	japonicae	japonicae	PROPN
ejpam-371	409	21	,	,	PUNCT
ejpam-371	409	22	56(2002	56(2002	NUM
ejpam-371	409	23	)	)	PUNCT
ejpam-371	409	24	,	,	PUNCT
ejpam-371	409	25	143	143	NUM
ejpam-371	409	26	-	-	SYM
ejpam-371	409	27	211	211	NUM
ejpam-371	409	28	.	.	PUNCT
ejpam-371	410	1	[	[	X
ejpam-371	410	2	3	3	X
ejpam-371	410	3	]	]	X
ejpam-371	410	4	v.	v.	CCONJ
ejpam-371	410	5	barbu	barbu	PROPN
ejpam-371	410	6	and	and	CCONJ
ejpam-371	410	7	m.	m.	NOUN
ejpam-371	410	8	iannelli	iannelli	ADV
ejpam-371	410	9	,	,	PUNCT
ejpam-371	410	10	"	"	PUNCT
ejpam-371	410	11	controllability	controllability	NOUN
ejpam-371	410	12	of	of	ADP
ejpam-371	410	13	the	the	DET
ejpam-371	410	14	heat	heat	NOUN
ejpam-371	410	15	equation	equation	NOUN
ejpam-371	410	16	with	with	ADP
ejpam-371	410	17	memory	memory	NOUN
ejpam-371	410	18	"	"	PUNCT
ejpam-371	410	19	,	,	PUNCT
ejpam-371	410	20	differential	differential	ADJ
ejpam-371	410	21	and	and	CCONJ
ejpam-371	410	22	integral	integral	ADJ
ejpam-371	410	23	equations	equation	NOUN
ejpam-371	410	24	,	,	PUNCT
ejpam-371	410	25	13(2000	13(2000	NUM
ejpam-371	410	26	)	)	PUNCT
ejpam-371	410	27	,	,	PUNCT
ejpam-371	410	28	1393	1393	NUM
ejpam-371	410	29	-	-	SYM
ejpam-371	410	30	1412	1412	NUM
ejpam-371	410	31	.	.	PUNCT
ejpam-371	411	1	[	[	X
ejpam-371	411	2	4	4	X
ejpam-371	411	3	]	]	PUNCT
ejpam-371	411	4	t.	t.	PROPN
ejpam-371	411	5	a.	a.	PROPN
ejpam-371	411	6	burton	burton	PROPN
ejpam-371	411	7	,	,	PUNCT
ejpam-371	411	8	volterra	volterra	PROPN
ejpam-371	411	9	integral	integral	ADJ
ejpam-371	411	10	and	and	CCONJ
ejpam-371	411	11	differential	differential	ADJ
ejpam-371	411	12	equations	equation	NOUN
ejpam-371	411	13	,	,	PUNCT
ejpam-371	411	14	new	new	PROPN
ejpam-371	411	15	york	york	PROPN
ejpam-371	411	16	,	,	PUNCT
ejpam-371	411	17	academic	academic	ADJ
ejpam-371	411	18	press	press	NOUN
ejpam-371	411	19	,	,	PUNCT
ejpam-371	411	20	1983	1983	NUM
ejpam-371	411	21	.	.	PUNCT
ejpam-371	412	1	[	[	X
ejpam-371	412	2	5	5	X
ejpam-371	412	3	]	]	PUNCT
ejpam-371	412	4	e.	e.	PROPN
ejpam-371	412	5	fernandez	fernandez	PROPN
ejpam-371	412	6	-	-	PUNCT
ejpam-371	412	7	cara	cara	PROPN
ejpam-371	412	8	and	and	CCONJ
ejpam-371	412	9	e.	e.	PROPN
ejpam-371	412	10	zuazua	zuazua	PROPN
ejpam-371	412	11	,	,	PUNCT
ejpam-371	412	12	"	"	PUNCT
ejpam-371	412	13	the	the	DET
ejpam-371	412	14	cost	cost	NOUN
ejpam-371	412	15	of	of	ADP
ejpam-371	412	16	approximate	approximate	ADJ
ejpam-371	412	17	controllability	controllability	NOUN
ejpam-371	412	18	for	for	ADP
ejpam-371	412	19	heat	heat	NOUN
ejpam-371	412	20	equations	equation	NOUN
ejpam-371	412	21	:	:	PUNCT
ejpam-371	412	22	the	the	DET
ejpam-371	412	23	linear	linear	ADJ
ejpam-371	412	24	case	case	NOUN
ejpam-371	412	25	"	"	PUNCT
ejpam-371	412	26	,	,	PUNCT
ejpam-371	412	27	advances	advance	NOUN
ejpam-371	412	28	in	in	ADP
ejpam-371	412	29	differential	differential	ADJ
ejpam-371	412	30	equations	equation	NOUN
ejpam-371	412	31	,	,	PUNCT
ejpam-371	412	32	5(2000	5(2000	NUM
ejpam-371	412	33	)	)	PUNCT
ejpam-371	412	34	,	,	PUNCT
ejpam-371	412	35	465	465	NUM
ejpam-371	412	36	-	-	SYM
ejpam-371	412	37	514	514	NUM
ejpam-371	412	38	.	.	PUNCT
ejpam-371	413	1	[	[	X
ejpam-371	413	2	6	6	NUM
ejpam-371	413	3	]	]	PUNCT
ejpam-371	413	4	e.	e.	PROPN
ejpam-371	413	5	fernandez	fernandez	PROPN
ejpam-371	413	6	-	-	PUNCT
ejpam-371	413	7	cara	cara	PROPN
ejpam-371	413	8	,	,	PUNCT
ejpam-371	413	9	m.	m.	NOUN
ejpam-371	413	10	gonzalez	gonzalez	PROPN
ejpam-371	413	11	-	-	PUNCT
ejpam-371	413	12	burgos	burgos	PROPN
ejpam-371	413	13	,	,	PUNCT
ejpam-371	413	14	s.	s.	PROPN
ejpam-371	413	15	guerrero	guerrero	PROPN
ejpam-371	413	16	and	and	CCONJ
ejpam-371	413	17	j.	j.	PROPN
ejpam-371	413	18	p.	p.	PROPN
ejpam-371	413	19	puel	puel	PROPN
ejpam-371	413	20	,	,	PUNCT
ejpam-371	413	21	"	"	PUNCT
ejpam-371	413	22	null	null	ADJ
ejpam-371	413	23	controllability	controllability	NOUN
ejpam-371	413	24	of	of	ADP
ejpam-371	413	25	the	the	DET
ejpam-371	413	26	heat	heat	NOUN
ejpam-371	413	27	equation	equation	NOUN
ejpam-371	413	28	with	with	ADP
ejpam-371	413	29	boundary	boundary	ADJ
ejpam-371	413	30	fourier	fourier	NOUN
ejpam-371	413	31	conditions	condition	NOUN
ejpam-371	413	32	:	:	PUNCT
ejpam-371	413	33	the	the	DET
ejpam-371	413	34	linear	linear	ADJ
ejpam-371	413	35	case	case	NOUN
ejpam-371	413	36	"	"	PUNCT
ejpam-371	413	37	,	,	PUNCT
ejpam-371	413	38	esaim	esaim	VERB
ejpam-371	413	39	:	:	PUNCT
ejpam-371	413	40	control	control	NOUN
ejpam-371	413	41	,	,	PUNCT
ejpam-371	413	42	optimization	optimization	NOUN
ejpam-371	413	43	and	and	CCONJ
ejpam-371	413	44	calculus	calculus	NOUN
ejpam-371	413	45	of	of	ADP
ejpam-371	413	46	variations	variation	NOUN
ejpam-371	413	47	,	,	PUNCT
ejpam-371	413	48	12(2006	12(2006	NUM
ejpam-371	413	49	)	)	PUNCT
ejpam-371	413	50	,	,	PUNCT
ejpam-371	413	51	442	442	NUM
ejpam-371	413	52	-	-	SYM
ejpam-371	413	53	465	465	NUM
ejpam-371	413	54	.	.	PUNCT
ejpam-371	414	1	[	[	X
ejpam-371	414	2	7	7	NUM
ejpam-371	414	3	]	]	X
ejpam-371	414	4	a.	a.	NOUN
ejpam-371	414	5	v.	v.	ADP
ejpam-371	414	6	fursikov	fursikov	PROPN
ejpam-371	414	7	and	and	CCONJ
ejpam-371	414	8	o.	o.	PROPN
ejpam-371	414	9	yu	yu	PROPN
ejpam-371	414	10	.	.	PROPN
ejpam-371	414	11	imanuvilov	imanuvilov	PROPN
ejpam-371	414	12	,	,	PUNCT
ejpam-371	414	13	controllability	controllability	NOUN
ejpam-371	414	14	of	of	ADP
ejpam-371	414	15	evolution	evolution	NOUN
ejpam-371	414	16	equations	equation	NOUN
ejpam-371	414	17	,	,	PUNCT
ejpam-371	414	18	lecture	lecture	NOUN
ejpam-371	414	19	notes	note	NOUN
ejpam-371	414	20	series	series	PROPN
ejpam-371	414	21	34	34	NUM
ejpam-371	414	22	,	,	PUNCT
ejpam-371	414	23	seoul	seoul	PROPN
ejpam-371	414	24	national	national	PROPN
ejpam-371	414	25	university	university	PROPN
ejpam-371	414	26	,	,	PUNCT
ejpam-371	414	27	rim	rim	PROPN
ejpam-371	414	28	,	,	PUNCT
ejpam-371	414	29	seoul	seoul	PROPN
ejpam-371	414	30	,	,	PUNCT
ejpam-371	414	31	1996	1996	NUM
ejpam-371	414	32	.	.	PUNCT
ejpam-371	415	1	[	[	X
ejpam-371	415	2	8	8	NUM
ejpam-371	415	3	]	]	X
ejpam-371	415	4	o.	o.	PROPN
ejpam-371	415	5	yu	yu	PROPN
ejpam-371	415	6	.	.	PROPN
ejpam-371	415	7	imanuvilov	imanuvilov	PROPN
ejpam-371	415	8	,	,	PUNCT
ejpam-371	415	9	"	"	PUNCT
ejpam-371	415	10	boundary	boundary	ADJ
ejpam-371	415	11	controllability	controllability	NOUN
ejpam-371	415	12	of	of	ADP
ejpam-371	415	13	parabolic	parabolic	ADJ
ejpam-371	415	14	equations	equation	NOUN
ejpam-371	415	15	"	"	PUNCT
ejpam-371	415	16	,	,	PUNCT
ejpam-371	415	17	sbornik	sbornik	ADJ
ejpam-371	415	18	mathematics	mathematic	NOUN
ejpam-371	415	19	,	,	PUNCT
ejpam-371	415	20	186(1995	186(1995	NUM
ejpam-371	415	21	)	)	PUNCT
ejpam-371	415	22	,	,	PUNCT
ejpam-371	415	23	879	879	NUM
ejpam-371	415	24	-	-	SYM
ejpam-371	415	25	900	900	NUM
ejpam-371	415	26	.	.	PUNCT
ejpam-371	416	1	[	[	X
ejpam-371	416	2	9	9	NUM
ejpam-371	416	3	]	]	X
ejpam-371	416	4	r.	r.	NOUN
ejpam-371	416	5	lavanya	lavanya	PROPN
ejpam-371	416	6	and	and	CCONJ
ejpam-371	416	7	k.	k.	PROPN
ejpam-371	416	8	balachandran	balachandran	PROPN
ejpam-371	416	9	,	,	PUNCT
ejpam-371	416	10	"	"	PUNCT
ejpam-371	416	11	controllability	controllability	NOUN
ejpam-371	416	12	results	result	NOUN
ejpam-371	416	13	of	of	ADP
ejpam-371	416	14	linear	linear	ADJ
ejpam-371	416	15	parabolic	parabolic	ADJ
ejpam-371	416	16	integrodifferential	integrodifferential	ADJ
ejpam-371	416	17	equations	equation	NOUN
ejpam-371	416	18	"	"	PUNCT
ejpam-371	416	19	,	,	PUNCT
ejpam-371	416	20	differential	differential	ADJ
ejpam-371	416	21	and	and	CCONJ
ejpam-371	416	22	integral	integral	ADJ
ejpam-371	416	23	equations	equation	NOUN
ejpam-371	416	24	,	,	PUNCT
ejpam-371	416	25	21(2008	21(2008	NUM
ejpam-371	416	26	)	)	PUNCT
ejpam-371	416	27	,	,	PUNCT
ejpam-371	416	28	801	801	NUM
ejpam-371	416	29	-	-	SYM
ejpam-371	416	30	819	819	NUM
ejpam-371	416	31	.	.	PUNCT
ejpam-371	417	1	[	[	X
ejpam-371	417	2	10	10	NUM
ejpam-371	417	3	]	]	X
ejpam-371	417	4	r.	r.	PROPN
ejpam-371	417	5	lavanya	lavanya	PROPN
ejpam-371	417	6	,	,	PUNCT
ejpam-371	417	7	"	"	PUNCT
ejpam-371	417	8	controllability	controllability	NOUN
ejpam-371	417	9	and	and	CCONJ
ejpam-371	417	10	influence	influence	NOUN
ejpam-371	417	11	of	of	ADP
ejpam-371	417	12	spatial	spatial	ADJ
ejpam-371	417	13	discretization	discretization	NOUN
ejpam-371	417	14	of	of	ADP
ejpam-371	417	15	the	the	DET
ejpam-371	417	16	beam	beam	NOUN
ejpam-371	417	17	equation	equation	NOUN
ejpam-371	417	18	"	"	PUNCT
ejpam-371	417	19	,	,	PUNCT
ejpam-371	417	20	nonlinear	nonlinear	ADJ
ejpam-371	417	21	analysis	analysis	NOUN
ejpam-371	417	22	:	:	PUNCT
ejpam-371	417	23	hybrid	hybrid	ADJ
ejpam-371	417	24	systems	system	NOUN
ejpam-371	417	25	,	,	PUNCT
ejpam-371	417	26	3(2010	3(2010	NUM
ejpam-371	417	27	)	)	PUNCT
ejpam-371	417	28	,	,	PUNCT
ejpam-371	417	29	in	in	ADP
ejpam-371	417	30	press	press	NOUN
ejpam-371	417	31	.	.	PUNCT
ejpam-371	418	1	references	reference	NOUN
ejpam-371	418	2	253	253	NUM
ejpam-371	419	1	[	[	X
ejpam-371	419	2	11	11	NUM
ejpam-371	419	3	]	]	PUNCT
ejpam-371	419	4	a.	a.	NOUN
ejpam-371	419	5	lunardi	lunardi	NOUN
ejpam-371	419	6	,	,	PUNCT
ejpam-371	419	7	"	"	PUNCT
ejpam-371	419	8	on	on	ADP
ejpam-371	419	9	the	the	DET
ejpam-371	419	10	linear	linear	ADJ
ejpam-371	419	11	heat	heat	NOUN
ejpam-371	419	12	equation	equation	NOUN
ejpam-371	419	13	with	with	ADP
ejpam-371	419	14	fading	fade	VERB
ejpam-371	419	15	memory	memory	NOUN
ejpam-371	419	16	"	"	PUNCT
ejpam-371	419	17	,	,	PUNCT
ejpam-371	419	18	siam	siam	PROPN
ejpam-371	419	19	journal	journal	NOUN
ejpam-371	419	20	on	on	ADP
ejpam-371	419	21	mathematical	mathematical	ADJ
ejpam-371	419	22	analysis	analysis	NOUN
ejpam-371	419	23	,	,	PUNCT
ejpam-371	419	24	21(1990	21(1990	NUM
ejpam-371	419	25	)	)	PUNCT
ejpam-371	419	26	,	,	PUNCT
ejpam-371	419	27	1213	1213	NUM
ejpam-371	419	28	-	-	SYM
ejpam-371	419	29	1224	1224	NUM
ejpam-371	419	30	.	.	PUNCT
ejpam-371	420	1	[	[	X
ejpam-371	420	2	12	12	NUM
ejpam-371	420	3	]	]	PUNCT
ejpam-371	420	4	k.	k.	NOUN
ejpam-371	420	5	sakthivel	sakthivel	PROPN
ejpam-371	420	6	,	,	PUNCT
ejpam-371	420	7	k.	k.	PROPN
ejpam-371	420	8	balachandran	balachandran	PROPN
ejpam-371	420	9	and	and	CCONJ
ejpam-371	420	10	r.	r.	PROPN
ejpam-371	420	11	lavanya	lavanya	PROPN
ejpam-371	420	12	,	,	PUNCT
ejpam-371	420	13	"	"	PUNCT
ejpam-371	420	14	exact	exact	ADJ
ejpam-371	420	15	controllability	controllability	NOUN
ejpam-371	420	16	of	of	ADP
ejpam-371	420	17	partial	partial	ADJ
ejpam-371	420	18	integrodifferential	integrodifferential	ADJ
ejpam-371	420	19	equations	equation	NOUN
ejpam-371	420	20	with	with	ADP
ejpam-371	420	21	mixed	mixed	ADJ
ejpam-371	420	22	boundary	boundary	ADJ
ejpam-371	420	23	conditions	condition	NOUN
ejpam-371	420	24	"	"	PUNCT
ejpam-371	420	25	,	,	PUNCT
ejpam-371	420	26	journal	journal	NOUN
ejpam-371	420	27	of	of	ADP
ejpam-371	420	28	mathematical	mathematical	ADJ
ejpam-371	420	29	analysis	analysis	NOUN
ejpam-371	420	30	and	and	CCONJ
ejpam-371	420	31	applications	application	NOUN
ejpam-371	420	32	,	,	PUNCT
ejpam-371	420	33	325(2007	325(2007	NUM
ejpam-371	420	34	)	)	PUNCT
ejpam-371	420	35	,	,	PUNCT
ejpam-371	420	36	1257	1257	NUM
ejpam-371	420	37	-	-	SYM
ejpam-371	420	38	1279	1279	NUM
ejpam-371	420	39	.	.	PUNCT
ejpam-371	421	1	[	[	X
ejpam-371	421	2	13	13	NUM
ejpam-371	421	3	]	]	PUNCT
ejpam-371	421	4	r.	r.	NOUN
ejpam-371	421	5	temam	temam	NOUN
ejpam-371	421	6	,	,	PUNCT
ejpam-371	421	7	"	"	PUNCT
ejpam-371	421	8	navierstokes	navierstoke	NOUN
ejpam-371	421	9	equations	equation	NOUN
ejpam-371	421	10	and	and	CCONJ
ejpam-371	421	11	nonlinear	nonlinear	ADJ
ejpam-371	421	12	functional	functional	ADJ
ejpam-371	421	13	analysis	analysis	NOUN
ejpam-371	421	14	"	"	PUNCT
ejpam-371	421	15	,	,	PUNCT
ejpam-371	421	16	siam	siam	PROPN
ejpam-371	421	17	,	,	PUNCT
ejpam-371	421	18	philadelphia	philadelphia	PROPN
ejpam-371	421	19	,	,	PUNCT
ejpam-371	421	20	1983	1983	NUM
ejpam-371	421	21	.	.	PUNCT
ejpam-371	422	1	[	[	X
ejpam-371	422	2	14	14	NUM
ejpam-371	422	3	]	]	X
ejpam-371	422	4	f.	f.	PROPN
ejpam-371	422	5	unger	unger	PROPN
ejpam-371	422	6	,	,	PUNCT
ejpam-371	422	7	l.	l.	PROPN
ejpam-371	422	8	v.	v.	PROPN
ejpam-371	422	9	wolfersdorf	wolfersdorf	PROPN
ejpam-371	422	10	,	,	PUNCT
ejpam-371	422	11	"	"	PUNCT
ejpam-371	422	12	identification	identification	NOUN
ejpam-371	422	13	of	of	ADP
ejpam-371	422	14	memory	memory	NOUN
ejpam-371	422	15	kernels	kernel	NOUN
ejpam-371	422	16	for	for	ADP
ejpam-371	422	17	materials	material	NOUN
ejpam-371	422	18	with	with	ADP
ejpam-371	422	19	memory	memory	NOUN
ejpam-371	422	20	"	"	PUNCT
ejpam-371	422	21	,	,	PUNCT
ejpam-371	422	22	journal	journal	NOUN
ejpam-371	422	23	of	of	ADP
ejpam-371	422	24	materials	material	NOUN
ejpam-371	422	25	processing	processing	NOUN
ejpam-371	422	26	technology	technology	NOUN
ejpam-371	422	27	,	,	PUNCT
ejpam-371	422	28	67(1997	67(1997	PROPN
ejpam-371	422	29	)	)	PUNCT
ejpam-371	422	30	,	,	PUNCT
ejpam-371	422	31	173	173	NUM
ejpam-371	422	32	-	-	SYM
ejpam-371	422	33	176	176	NUM
ejpam-371	422	34	.	.	PUNCT