id	sid	tid	token	lemma	pos
ejpam-3768	1	1	european	european	PROPN
ejpam-3768	1	2	journal	journal	PROPN
ejpam-3768	1	3	of	of	ADP
ejpam-3768	1	4	pure	pure	ADJ
ejpam-3768	1	5	and	and	CCONJ
ejpam-3768	1	6	applied	apply	VERB
ejpam-3768	1	7	mathematics	mathematic	NOUN
ejpam-3768	1	8	vol	vol	NOUN
ejpam-3768	1	9	.	.	PROPN
ejpam-3768	2	1	13	13	NUM
ejpam-3768	2	2	,	,	PUNCT
ejpam-3768	2	3	no	no	INTJ
ejpam-3768	2	4	.	.	NOUN
ejpam-3768	2	5	3	3	NUM
ejpam-3768	2	6	,	,	PUNCT
ejpam-3768	2	7	2020	2020	NUM
ejpam-3768	2	8	,	,	PUNCT
ejpam-3768	2	9	645	645	NUM
ejpam-3768	2	10	-	-	SYM
ejpam-3768	2	11	662	662	NUM
ejpam-3768	2	12	issn	issn	PROPN
ejpam-3768	2	13	1307	1307	NUM
ejpam-3768	2	14	-	-	SYM
ejpam-3768	2	15	5543	5543	NUM
ejpam-3768	2	16	–	–	PUNCT
ejpam-3768	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3768	2	18	published	publish	VERB
ejpam-3768	2	19	by	by	ADP
ejpam-3768	2	20	new	new	PROPN
ejpam-3768	2	21	york	york	PROPN
ejpam-3768	2	22	business	business	PROPN
ejpam-3768	2	23	global	global	PROPN
ejpam-3768	2	24	some	some	DET
ejpam-3768	2	25	results	result	NOUN
ejpam-3768	2	26	on	on	ADP
ejpam-3768	2	27	blow	blow	NOUN
ejpam-3768	2	28	-	-	PUNCT
ejpam-3768	2	29	up	up	ADP
ejpam-3768	2	30	phenomenon	phenomenon	NOUN
ejpam-3768	2	31	for	for	ADP
ejpam-3768	2	32	nonlinear	nonlinear	ADJ
ejpam-3768	2	33	porous	porous	ADJ
ejpam-3768	2	34	medium	medium	ADJ
ejpam-3768	2	35	equations	equation	NOUN
ejpam-3768	2	36	with	with	ADP
ejpam-3768	2	37	weighted	weight	VERB
ejpam-3768	2	38	source	source	NOUN
ejpam-3768	2	39	huafei	huafei	PROPN
ejpam-3768	2	40	di1,∗	di1,∗	PROPN
ejpam-3768	2	41	,	,	PUNCT
ejpam-3768	2	42	lin	lin	PROPN
ejpam-3768	2	43	chen2	chen2	PROPN
ejpam-3768	2	44	,	,	PUNCT
ejpam-3768	2	45	zefang	zefang	PROPN
ejpam-3768	2	46	song3	song3	PROPN
ejpam-3768	2	47	1	1	NUM
ejpam-3768	2	48	school	school	NOUN
ejpam-3768	2	49	of	of	ADP
ejpam-3768	2	50	mathematics	mathematic	NOUN
ejpam-3768	2	51	and	and	CCONJ
ejpam-3768	2	52	information	information	NOUN
ejpam-3768	2	53	science	science	NOUN
ejpam-3768	2	54	,	,	PUNCT
ejpam-3768	2	55	guangzhou	guangzhou	PROPN
ejpam-3768	2	56	university	university	PROPN
ejpam-3768	2	57	,	,	PUNCT
ejpam-3768	2	58	guangzhou	guangzhou	PROPN
ejpam-3768	2	59	510006	510006	NUM
ejpam-3768	2	60	,	,	PUNCT
ejpam-3768	2	61	p	p	PROPN
ejpam-3768	2	62	r	r	PROPN
ejpam-3768	2	63	china	china	PROPN
ejpam-3768	2	64	2	2	NUM
ejpam-3768	2	65	college	college	NOUN
ejpam-3768	2	66	of	of	ADP
ejpam-3768	2	67	management	management	NOUN
ejpam-3768	2	68	and	and	CCONJ
ejpam-3768	2	69	economics	economic	NOUN
ejpam-3768	2	70	,	,	PUNCT
ejpam-3768	2	71	tianjin	tianjin	PROPN
ejpam-3768	2	72	university	university	PROPN
ejpam-3768	2	73	,	,	PUNCT
ejpam-3768	2	74	tianjin	tianjin	PROPN
ejpam-3768	2	75	300072	300072	NUM
ejpam-3768	2	76	,	,	PUNCT
ejpam-3768	2	77	p	p	PROPN
ejpam-3768	2	78	r	r	PROPN
ejpam-3768	2	79	china	china	PROPN
ejpam-3768	2	80	3	3	NUM
ejpam-3768	2	81	school	school	NOUN
ejpam-3768	2	82	of	of	ADP
ejpam-3768	2	83	economics	economic	NOUN
ejpam-3768	2	84	and	and	CCONJ
ejpam-3768	2	85	statistics	statistic	NOUN
ejpam-3768	2	86	,	,	PUNCT
ejpam-3768	2	87	guangzhou	guangzhou	PROPN
ejpam-3768	2	88	university	university	PROPN
ejpam-3768	2	89	,	,	PUNCT
ejpam-3768	2	90	guangzhou	guangzhou	PROPN
ejpam-3768	2	91	510006	510006	NUM
ejpam-3768	2	92	,	,	PUNCT
ejpam-3768	2	93	p	p	PROPN
ejpam-3768	2	94	r	r	PROPN
ejpam-3768	2	95	china	china	PROPN
ejpam-3768	2	96	abstract	abstract	NOUN
ejpam-3768	2	97	.	.	PUNCT
ejpam-3768	3	1	this	this	DET
ejpam-3768	3	2	paper	paper	NOUN
ejpam-3768	3	3	deals	deal	NOUN
ejpam-3768	3	4	with	with	ADP
ejpam-3768	3	5	the	the	DET
ejpam-3768	3	6	blow	blow	NOUN
ejpam-3768	3	7	-	-	PUNCT
ejpam-3768	3	8	up	up	ADP
ejpam-3768	3	9	phenomena	phenomenon	NOUN
ejpam-3768	3	10	for	for	ADP
ejpam-3768	3	11	a	a	DET
ejpam-3768	3	12	type	type	NOUN
ejpam-3768	3	13	of	of	ADP
ejpam-3768	3	14	nonlinear	nonlinear	ADJ
ejpam-3768	3	15	porous	porous	ADJ
ejpam-3768	3	16	medium	medium	ADJ
ejpam-3768	3	17	equations	equation	NOUN
ejpam-3768	3	18	with	with	ADP
ejpam-3768	3	19	weighted	weighted	ADJ
ejpam-3768	3	20	source	source	NOUN
ejpam-3768	3	21	ut−4um	ut−4um	NUM
ejpam-3768	3	22	=	=	SYM
ejpam-3768	3	23	a(x)f(u	a(x)f(u	NUM
ejpam-3768	3	24	)	)	PUNCT
ejpam-3768	3	25	subject	subject	NOUN
ejpam-3768	3	26	to	to	ADP
ejpam-3768	3	27	dirichlet	dirichlet	PROPN
ejpam-3768	3	28	(	(	PUNCT
ejpam-3768	3	29	or	or	CCONJ
ejpam-3768	3	30	neumann	neumann	PROPN
ejpam-3768	3	31	)	)	PUNCT
ejpam-3768	3	32	boundary	boundary	ADJ
ejpam-3768	3	33	conditions	condition	NOUN
ejpam-3768	3	34	.	.	PUNCT
ejpam-3768	4	1	based	base	VERB
ejpam-3768	4	2	on	on	ADP
ejpam-3768	4	3	the	the	DET
ejpam-3768	4	4	auxiliary	auxiliary	ADJ
ejpam-3768	4	5	functions	function	NOUN
ejpam-3768	4	6	and	and	CCONJ
ejpam-3768	4	7	differential	differential	ADJ
ejpam-3768	4	8	-	-	PUNCT
ejpam-3768	4	9	integral	integral	ADJ
ejpam-3768	4	10	inequalities	inequality	NOUN
ejpam-3768	4	11	,	,	PUNCT
ejpam-3768	4	12	the	the	DET
ejpam-3768	4	13	blow	blow	NOUN
ejpam-3768	4	14	-	-	PUNCT
ejpam-3768	4	15	up	up	ADP
ejpam-3768	4	16	criterions	criterion	NOUN
ejpam-3768	4	17	which	which	PRON
ejpam-3768	4	18	ensure	ensure	VERB
ejpam-3768	4	19	that	that	SCONJ
ejpam-3768	4	20	u	u	PRON
ejpam-3768	4	21	can	can	AUX
ejpam-3768	4	22	not	not	PART
ejpam-3768	4	23	exist	exist	VERB
ejpam-3768	4	24	all	all	DET
ejpam-3768	4	25	time	time	NOUN
ejpam-3768	4	26	are	be	AUX
ejpam-3768	4	27	given	give	VERB
ejpam-3768	4	28	under	under	ADP
ejpam-3768	4	29	two	two	NUM
ejpam-3768	4	30	different	different	ADJ
ejpam-3768	4	31	assumptions	assumption	NOUN
ejpam-3768	4	32	,	,	PUNCT
ejpam-3768	4	33	and	and	CCONJ
ejpam-3768	4	34	the	the	DET
ejpam-3768	4	35	corresponding	corresponding	ADJ
ejpam-3768	4	36	estimates	estimate	NOUN
ejpam-3768	4	37	on	on	ADP
ejpam-3768	4	38	the	the	DET
ejpam-3768	4	39	upper	upper	ADJ
ejpam-3768	4	40	bounds	bound	NOUN
ejpam-3768	4	41	for	for	ADP
ejpam-3768	4	42	blow	blow	NOUN
ejpam-3768	4	43	-	-	PUNCT
ejpam-3768	4	44	up	up	ADP
ejpam-3768	4	45	time	time	NOUN
ejpam-3768	4	46	and	and	CCONJ
ejpam-3768	4	47	blow	blow	NOUN
ejpam-3768	4	48	-	-	PUNCT
ejpam-3768	4	49	up	up	ADP
ejpam-3768	4	50	rate	rate	NOUN
ejpam-3768	4	51	are	be	AUX
ejpam-3768	4	52	derived	derive	VERB
ejpam-3768	4	53	respectively	respectively	ADV
ejpam-3768	4	54	.	.	PUNCT
ejpam-3768	5	1	moreover	moreover	ADV
ejpam-3768	5	2	,	,	PUNCT
ejpam-3768	5	3	we	we	PRON
ejpam-3768	5	4	use	use	VERB
ejpam-3768	5	5	three	three	NUM
ejpam-3768	5	6	different	different	ADJ
ejpam-3768	5	7	methods	method	NOUN
ejpam-3768	5	8	to	to	PART
ejpam-3768	5	9	determine	determine	VERB
ejpam-3768	5	10	the	the	DET
ejpam-3768	5	11	lower	low	ADJ
ejpam-3768	5	12	bounds	bound	NOUN
ejpam-3768	5	13	for	for	ADP
ejpam-3768	5	14	blow	blow	NOUN
ejpam-3768	5	15	-	-	PUNCT
ejpam-3768	5	16	up	up	ADP
ejpam-3768	5	17	time	time	NOUN
ejpam-3768	5	18	and	and	CCONJ
ejpam-3768	5	19	blow	blow	NOUN
ejpam-3768	5	20	-	-	PUNCT
ejpam-3768	5	21	up	up	ADP
ejpam-3768	5	22	rate	rate	NOUN
ejpam-3768	5	23	estimates	estimate	NOUN
ejpam-3768	5	24	if	if	SCONJ
ejpam-3768	5	25	blow	blow	NOUN
ejpam-3768	5	26	-	-	PUNCT
ejpam-3768	5	27	up	up	NOUN
ejpam-3768	5	28	does	do	AUX
ejpam-3768	5	29	occurs	occur	VERB
ejpam-3768	5	30	.	.	PUNCT
ejpam-3768	6	1	2020	2020	NUM
ejpam-3768	6	2	mathematics	mathematic	NOUN
ejpam-3768	6	3	subject	subject	NOUN
ejpam-3768	6	4	classifications	classification	NOUN
ejpam-3768	6	5	:	:	PUNCT
ejpam-3768	6	6	35a01	35a01	NUM
ejpam-3768	6	7	,	,	PUNCT
ejpam-3768	6	8	35b44	35b44	NUM
ejpam-3768	6	9	,	,	PUNCT
ejpam-3768	6	10	35k20	35k20	NUM
ejpam-3768	6	11	,	,	PUNCT
ejpam-3768	6	12	35k61	35k61	NUM
ejpam-3768	6	13	key	key	ADJ
ejpam-3768	6	14	words	word	NOUN
ejpam-3768	6	15	and	and	CCONJ
ejpam-3768	6	16	phrases	phrase	NOUN
ejpam-3768	6	17	:	:	PUNCT
ejpam-3768	6	18	porous	porous	ADJ
ejpam-3768	6	19	medium	medium	ADJ
ejpam-3768	6	20	equation	equation	NOUN
ejpam-3768	6	21	,	,	PUNCT
ejpam-3768	6	22	upper	upper	ADJ
ejpam-3768	6	23	and	and	CCONJ
ejpam-3768	6	24	lower	low	ADJ
ejpam-3768	6	25	bounds	bound	NOUN
ejpam-3768	6	26	,	,	PUNCT
ejpam-3768	6	27	blow	blow	NOUN
ejpam-3768	6	28	-	-	PUNCT
ejpam-3768	6	29	up	up	ADP
ejpam-3768	6	30	rate	rate	NOUN
ejpam-3768	6	31	,	,	PUNCT
ejpam-3768	6	32	weighted	weight	VERB
ejpam-3768	6	33	source	source	NOUN
ejpam-3768	6	34	1	1	NUM
ejpam-3768	6	35	.	.	PUNCT
ejpam-3768	6	36	introduction	introduction	NOUN
ejpam-3768	6	37	in	in	ADP
ejpam-3768	6	38	this	this	DET
ejpam-3768	6	39	paper	paper	NOUN
ejpam-3768	6	40	,	,	PUNCT
ejpam-3768	6	41	we	we	PRON
ejpam-3768	6	42	deal	deal	VERB
ejpam-3768	6	43	with	with	ADP
ejpam-3768	6	44	the	the	DET
ejpam-3768	6	45	blow	blow	NOUN
ejpam-3768	6	46	-	-	PUNCT
ejpam-3768	6	47	up	up	ADP
ejpam-3768	6	48	time	time	NOUN
ejpam-3768	6	49	and	and	CCONJ
ejpam-3768	6	50	blow	blow	NOUN
ejpam-3768	6	51	-	-	PUNCT
ejpam-3768	6	52	up	up	ADP
ejpam-3768	6	53	rate	rate	NOUN
ejpam-3768	6	54	estimates	estimate	NOUN
ejpam-3768	6	55	of	of	ADP
ejpam-3768	6	56	the	the	DET
ejpam-3768	6	57	solutions	solution	NOUN
ejpam-3768	6	58	to	to	ADP
ejpam-3768	6	59	the	the	DET
ejpam-3768	6	60	following	following	ADJ
ejpam-3768	6	61	problem	problem	NOUN
ejpam-3768	6	62	:	:	PUNCT
ejpam-3768	7	1	ut	ut	PROPN
ejpam-3768	7	2	−4um	−4um	PROPN
ejpam-3768	7	3	=	=	PUNCT
ejpam-3768	7	4	a(x)f(u	a(x)f(u	NUM
ejpam-3768	7	5	)	)	PUNCT
ejpam-3768	7	6	,	,	PUNCT
ejpam-3768	7	7	x	x	PUNCT
ejpam-3768	7	8	∈	∈	PROPN
ejpam-3768	7	9	ω	ω	PROPN
ejpam-3768	7	10	,	,	PUNCT
ejpam-3768	7	11	t	t	X
ejpam-3768	7	12	>	>	X
ejpam-3768	7	13	0	0	NUM
ejpam-3768	7	14	,	,	PUNCT
ejpam-3768	7	15	(	(	PUNCT
ejpam-3768	7	16	1.1	1.1	NUM
ejpam-3768	7	17	)	)	PUNCT
ejpam-3768	7	18	u(x	u(x	NOUN
ejpam-3768	7	19	,	,	PUNCT
ejpam-3768	7	20	t	t	NOUN
ejpam-3768	7	21	)	)	PUNCT
ejpam-3768	7	22	=	=	SYM
ejpam-3768	7	23	0	0	NUM
ejpam-3768	7	24	or	or	CCONJ
ejpam-3768	7	25	∂u	∂u	PROPN
ejpam-3768	7	26	∂ν	∂ν	X
ejpam-3768	8	1	=	=	PUNCT
ejpam-3768	8	2	0	0	PROPN
ejpam-3768	8	3	,	,	PUNCT
ejpam-3768	8	4	x	x	X
ejpam-3768	8	5	∈	∈	PROPN
ejpam-3768	8	6	∂ω	∂ω	PROPN
ejpam-3768	8	7	,	,	PUNCT
ejpam-3768	8	8	t	t	PROPN
ejpam-3768	8	9	>	>	X
ejpam-3768	8	10	0	0	NUM
ejpam-3768	8	11	,	,	PUNCT
ejpam-3768	8	12	(	(	PUNCT
ejpam-3768	8	13	1.2	1.2	NUM
ejpam-3768	8	14	)	)	PUNCT
ejpam-3768	8	15	u(x	u(x	NOUN
ejpam-3768	8	16	,	,	PUNCT
ejpam-3768	8	17	0	0	NUM
ejpam-3768	8	18	)	)	PUNCT
ejpam-3768	8	19	=	=	SYM
ejpam-3768	8	20	g(x	g(x	NOUN
ejpam-3768	8	21	)	)	PUNCT
ejpam-3768	8	22	≥	≥	NOUN
ejpam-3768	8	23	0	0	NUM
ejpam-3768	8	24	,	,	PUNCT
ejpam-3768	8	25	x	x	X
ejpam-3768	8	26	∈	∈	PROPN
ejpam-3768	8	27	ω	ω	PROPN
ejpam-3768	8	28	,	,	PUNCT
ejpam-3768	8	29	(	(	PUNCT
ejpam-3768	8	30	1.3	1.3	NUM
ejpam-3768	8	31	)	)	PUNCT
ejpam-3768	8	32	where	where	SCONJ
ejpam-3768	8	33	m	m	VERB
ejpam-3768	8	34	>	>	X
ejpam-3768	8	35	1	1	NUM
ejpam-3768	8	36	and	and	CCONJ
ejpam-3768	8	37	ω	ω	NUM
ejpam-3768	8	38	⊂	⊂	PROPN
ejpam-3768	8	39	rn	rn	PROPN
ejpam-3768	8	40	(	(	PUNCT
ejpam-3768	8	41	n	n	CCONJ
ejpam-3768	8	42	≥	≥	NOUN
ejpam-3768	8	43	3	3	NUM
ejpam-3768	8	44	)	)	PUNCT
ejpam-3768	8	45	is	be	AUX
ejpam-3768	8	46	a	a	DET
ejpam-3768	8	47	smooth	smooth	ADJ
ejpam-3768	8	48	bounded	bounded	ADJ
ejpam-3768	8	49	domain	domain	NOUN
ejpam-3768	8	50	,	,	PUNCT
ejpam-3768	8	51	ν	ν	X
ejpam-3768	8	52	is	be	AUX
ejpam-3768	8	53	the	the	DET
ejpam-3768	8	54	outward	outward	ADJ
ejpam-3768	8	55	normal	normal	ADJ
ejpam-3768	8	56	vector	vector	NOUN
ejpam-3768	8	57	,	,	PUNCT
ejpam-3768	8	58	g(x	g(x	NOUN
ejpam-3768	8	59	)	)	PUNCT
ejpam-3768	8	60	is	be	AUX
ejpam-3768	8	61	a	a	DET
ejpam-3768	8	62	continuous	continuous	ADJ
ejpam-3768	8	63	nonnegative	nonnegative	ADJ
ejpam-3768	8	64	function	function	NOUN
ejpam-3768	8	65	and	and	CCONJ
ejpam-3768	8	66	satisfies	satisfy	VERB
ejpam-3768	8	67	the	the	DET
ejpam-3768	8	68	compatible	compatible	ADJ
ejpam-3768	8	69	condition	condition	NOUN
ejpam-3768	8	70	.	.	PUNCT
ejpam-3768	9	1	here	here	ADV
ejpam-3768	9	2	,	,	PUNCT
ejpam-3768	9	3	the	the	DET
ejpam-3768	9	4	nonlinear	nonlinear	ADJ
ejpam-3768	9	5	function	function	NOUN
ejpam-3768	9	6	f	f	PROPN
ejpam-3768	9	7	satisfies	satisfy	VERB
ejpam-3768	9	8	∗corresponding	∗corresponde	VERB
ejpam-3768	9	9	author	author	NOUN
ejpam-3768	9	10	.	.	PUNCT
ejpam-3768	10	1	doi	doi	NOUN
ejpam-3768	10	2	:	:	PUNCT
ejpam-3768	10	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3768	https://doi.org/10.29020/nybg.ejpam.v13i3.3768	PROPN
ejpam-3768	10	4	email	email	NOUN
ejpam-3768	10	5	addresses	address	VERB
ejpam-3768	10	6	:	:	PUNCT
ejpam-3768	10	7	dihuafei@yeah.net	dihuafei@yeah.net	PROPN
ejpam-3768	10	8	(	(	PUNCT
ejpam-3768	10	9	h.f	h.f	PROPN
ejpam-3768	10	10	.	.	PROPN
ejpam-3768	10	11	di	di	PROPN
ejpam-3768	10	12	)	)	PUNCT
ejpam-3768	10	13	,	,	PUNCT
ejpam-3768	10	14	chenlinalbert@126.com	chenlinalbert@126.com	PROPN
ejpam-3768	10	15	(	(	PUNCT
ejpam-3768	10	16	l.	l.	PROPN
ejpam-3768	10	17	chen	chen	PROPN
ejpam-3768	10	18	)	)	PUNCT
ejpam-3768	10	19	,	,	PUNCT
ejpam-3768	10	20	song−zefang@163.com	song−zefang@163.com	PROPN
ejpam-3768	10	21	(	(	PUNCT
ejpam-3768	10	22	z.f	z.f	PROPN
ejpam-3768	10	23	.	.	PROPN
ejpam-3768	10	24	song	song	PROPN
ejpam-3768	10	25	)	)	PUNCT
ejpam-3768	10	26	.	.	PUNCT
ejpam-3768	11	1	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3768	12	1	645	645	NUM
ejpam-3768	12	2	c	c	X
ejpam-3768	12	3	©	©	PROPN
ejpam-3768	12	4	2020	2020	NUM
ejpam-3768	12	5	ejpam	ejpam	VERB
ejpam-3768	12	6	all	all	DET
ejpam-3768	12	7	rights	right	NOUN
ejpam-3768	12	8	reserved	reserve	VERB
ejpam-3768	12	9	.	.	PUNCT
ejpam-3768	13	1	h.f	h.f	PROPN
ejpam-3768	13	2	.	.	PROPN
ejpam-3768	13	3	di	di	PROPN
ejpam-3768	13	4	,	,	PUNCT
ejpam-3768	13	5	l.	l.	PROPN
ejpam-3768	13	6	chen	chen	PROPN
ejpam-3768	13	7	and	and	CCONJ
ejpam-3768	13	8	z.f	z.f	PROPN
ejpam-3768	13	9	.	.	PROPN
ejpam-3768	13	10	song	song	PROPN
ejpam-3768	13	11	/	/	SYM
ejpam-3768	13	12	eur	eur	PROPN
ejpam-3768	13	13	.	.	PUNCT
ejpam-3768	14	1	j.	j.	PROPN
ejpam-3768	14	2	pure	pure	PROPN
ejpam-3768	14	3	appl	appl	PROPN
ejpam-3768	14	4	.	.	PROPN
ejpam-3768	14	5	math	math	PROPN
ejpam-3768	14	6	,	,	PUNCT
ejpam-3768	14	7	13	13	NUM
ejpam-3768	14	8	(	(	PUNCT
ejpam-3768	14	9	3	3	NUM
ejpam-3768	14	10	)	)	PUNCT
ejpam-3768	14	11	(	(	PUNCT
ejpam-3768	14	12	2020	2020	NUM
ejpam-3768	14	13	)	)	PUNCT
ejpam-3768	14	14	,	,	PUNCT
ejpam-3768	14	15	645	645	NUM
ejpam-3768	14	16	-	-	SYM
ejpam-3768	14	17	662	662	NUM
ejpam-3768	14	18	646	646	NUM
ejpam-3768	14	19	(	(	PUNCT
ejpam-3768	14	20	f1	f1	NOUN
ejpam-3768	14	21	):	):	PUNCT
ejpam-3768	14	22	f(s	f(s	PROPN
ejpam-3768	14	23	)	)	PUNCT
ejpam-3768	14	24	≥	≥	X
ejpam-3768	14	25	0	0	NUM
ejpam-3768	14	26	for	for	ADP
ejpam-3768	14	27	all	all	PRON
ejpam-3768	14	28	s	s	PART
ejpam-3768	14	29	≥	≥	NOUN
ejpam-3768	14	30	0	0	NUM
ejpam-3768	14	31	;	;	PUNCT
ejpam-3768	14	32	and	and	CCONJ
ejpam-3768	14	33	the	the	DET
ejpam-3768	14	34	weighted	weight	VERB
ejpam-3768	14	35	function	function	NOUN
ejpam-3768	14	36	a(x	a(x	NOUN
ejpam-3768	14	37	)	)	PUNCT
ejpam-3768	14	38	∈	∈	PROPN
ejpam-3768	14	39	c1(ω	c1(ω	NOUN
ejpam-3768	14	40	)	)	PUNCT
ejpam-3768	14	41	∩	∩	NOUN
ejpam-3768	14	42	c0(ω̄	c0(ω̄	NUM
ejpam-3768	14	43	)	)	PUNCT
ejpam-3768	14	44	satisfies	satisfie	NOUN
ejpam-3768	14	45	(	(	PUNCT
ejpam-3768	14	46	a1	a1	NOUN
ejpam-3768	14	47	):	):	PUNCT
ejpam-3768	14	48	a(x	a(x	PROPN
ejpam-3768	14	49	)	)	PUNCT
ejpam-3768	14	50	≥	≥	NOUN
ejpam-3768	14	51	c	c	NOUN
ejpam-3768	14	52	>	>	X
ejpam-3768	14	53	0	0	PUNCT
ejpam-3768	15	1	on	on	ADP
ejpam-3768	15	2	ω̄	ω̄	ADP
ejpam-3768	15	3	for	for	ADP
ejpam-3768	15	4	some	some	DET
ejpam-3768	15	5	constant	constant	ADJ
ejpam-3768	15	6	c	c	NOUN
ejpam-3768	15	7	or	or	CCONJ
ejpam-3768	15	8	(	(	PUNCT
ejpam-3768	15	9	a2	a2	PROPN
ejpam-3768	15	10	):	):	PUNCT
ejpam-3768	15	11	a(x	a(x	NOUN
ejpam-3768	15	12	)	)	PUNCT
ejpam-3768	15	13	>	>	X
ejpam-3768	15	14	0	0	PUNCT
ejpam-3768	16	1	in	in	ADP
ejpam-3768	16	2	ω	ω	PROPN
ejpam-3768	16	3	and	and	CCONJ
ejpam-3768	16	4	a(x	a(x	PROPN
ejpam-3768	16	5	)	)	PUNCT
ejpam-3768	16	6	=	=	SYM
ejpam-3768	16	7	0	0	NUM
ejpam-3768	17	1	on	on	ADP
ejpam-3768	17	2	∂ω	∂ω	PROPN
ejpam-3768	17	3	.	.	PUNCT
ejpam-3768	18	1	it	it	PRON
ejpam-3768	18	2	is	be	AUX
ejpam-3768	18	3	well	well	ADV
ejpam-3768	18	4	known	know	VERB
ejpam-3768	18	5	that	that	SCONJ
ejpam-3768	18	6	the	the	DET
ejpam-3768	18	7	porous	porous	ADJ
ejpam-3768	18	8	medium	medium	ADJ
ejpam-3768	18	9	equations	equation	NOUN
ejpam-3768	18	10	have	have	VERB
ejpam-3768	18	11	extensive	extensive	ADJ
ejpam-3768	18	12	physical	physical	ADJ
ejpam-3768	18	13	background	background	NOUN
ejpam-3768	18	14	and	and	CCONJ
ejpam-3768	18	15	rich	rich	ADJ
ejpam-3768	18	16	theoretical	theoretical	ADJ
ejpam-3768	18	17	connotation	connotation	NOUN
ejpam-3768	18	18	.	.	PUNCT
ejpam-3768	19	1	they	they	PRON
ejpam-3768	19	2	have	have	AUX
ejpam-3768	19	3	been	be	AUX
ejpam-3768	19	4	used	use	VERB
ejpam-3768	19	5	to	to	PART
ejpam-3768	19	6	model	model	VERB
ejpam-3768	19	7	the	the	DET
ejpam-3768	19	8	processes	process	NOUN
ejpam-3768	19	9	involving	involve	VERB
ejpam-3768	19	10	the	the	DET
ejpam-3768	19	11	chemical	chemical	NOUN
ejpam-3768	19	12	reaction	reaction	NOUN
ejpam-3768	19	13	,	,	PUNCT
ejpam-3768	19	14	heat	heat	NOUN
ejpam-3768	19	15	transfer	transfer	NOUN
ejpam-3768	19	16	or	or	CCONJ
ejpam-3768	19	17	diffusion	diffusion	NOUN
ejpam-3768	19	18	,	,	PUNCT
ejpam-3768	19	19	population	population	NOUN
ejpam-3768	19	20	dynamics	dynamic	NOUN
ejpam-3768	19	21	and	and	CCONJ
ejpam-3768	19	22	so	so	ADV
ejpam-3768	19	23	on	on	ADV
ejpam-3768	19	24	.	.	PUNCT
ejpam-3768	20	1	we	we	PRON
ejpam-3768	20	2	refer	refer	VERB
ejpam-3768	20	3	readers	reader	NOUN
ejpam-3768	20	4	to	to	PART
ejpam-3768	20	5	see	see	VERB
ejpam-3768	20	6	[	[	X
ejpam-3768	20	7	1	1	NUM
ejpam-3768	20	8	,	,	PUNCT
ejpam-3768	20	9	26	26	NUM
ejpam-3768	20	10	]	]	PUNCT
ejpam-3768	20	11	and	and	CCONJ
ejpam-3768	20	12	references	reference	NOUN
ejpam-3768	20	13	therein	therein	ADV
ejpam-3768	20	14	,	,	PUNCT
ejpam-3768	20	15	where	where	SCONJ
ejpam-3768	20	16	a	a	DET
ejpam-3768	20	17	series	series	NOUN
ejpam-3768	20	18	of	of	ADP
ejpam-3768	20	19	physical	physical	ADJ
ejpam-3768	20	20	application	application	NOUN
ejpam-3768	20	21	of	of	ADP
ejpam-3768	20	22	eq.(1.1	eq.(1.1	PROPN
ejpam-3768	20	23	)	)	PUNCT
ejpam-3768	20	24	are	be	AUX
ejpam-3768	20	25	also	also	ADV
ejpam-3768	20	26	summarized	summarize	VERB
ejpam-3768	20	27	.	.	PUNCT
ejpam-3768	21	1	for	for	ADP
ejpam-3768	21	2	instance	instance	NOUN
ejpam-3768	21	3	,	,	PUNCT
ejpam-3768	21	4	the	the	DET
ejpam-3768	21	5	nonlinear	nonlinear	ADJ
ejpam-3768	21	6	term	term	NOUN
ejpam-3768	21	7	f(u	f(u	PROPN
ejpam-3768	21	8	)	)	PUNCT
ejpam-3768	21	9	of	of	ADP
ejpam-3768	21	10	eq.(1.1	eq.(1.1	NOUN
ejpam-3768	21	11	)	)	PUNCT
ejpam-3768	21	12	describes	describe	VERB
ejpam-3768	21	13	the	the	DET
ejpam-3768	21	14	nonlinear	nonlinear	ADJ
ejpam-3768	21	15	source	source	NOUN
ejpam-3768	21	16	in	in	ADP
ejpam-3768	21	17	the	the	DET
ejpam-3768	21	18	diffusion	diffusion	NOUN
ejpam-3768	21	19	phenomena	phenomenon	NOUN
ejpam-3768	21	20	,	,	PUNCT
ejpam-3768	21	21	and	and	CCONJ
ejpam-3768	21	22	it	it	PRON
ejpam-3768	21	23	is	be	AUX
ejpam-3768	21	24	called	call	VERB
ejpam-3768	21	25	to	to	PART
ejpam-3768	21	26	be	be	AUX
ejpam-3768	21	27	“	"	PUNCT
ejpam-3768	21	28	heat	heat	NOUN
ejpam-3768	21	29	source	source	NOUN
ejpam-3768	21	30	”	"	PUNCT
ejpam-3768	21	31	.	.	PUNCT
ejpam-3768	22	1	if	if	SCONJ
ejpam-3768	22	2	the	the	DET
ejpam-3768	22	3	“	"	PUNCT
ejpam-3768	22	4	heat	heat	NOUN
ejpam-3768	22	5	source	source	NOUN
ejpam-3768	22	6	”	"	PUNCT
ejpam-3768	22	7	occurs	occur	VERB
ejpam-3768	22	8	,	,	PUNCT
ejpam-3768	22	9	the	the	DET
ejpam-3768	22	10	solutions	solution	NOUN
ejpam-3768	22	11	of	of	ADP
ejpam-3768	22	12	eq.(1.1	eq.(1.1	NOUN
ejpam-3768	22	13	)	)	PUNCT
ejpam-3768	22	14	might	might	AUX
ejpam-3768	22	15	be	be	AUX
ejpam-3768	22	16	unbounded	unbounded	ADJ
ejpam-3768	22	17	at	at	ADP
ejpam-3768	22	18	finite	finite	ADJ
ejpam-3768	22	19	time	time	NOUN
ejpam-3768	22	20	,	,	PUNCT
ejpam-3768	22	21	namely	namely	ADV
ejpam-3768	22	22	,	,	PUNCT
ejpam-3768	22	23	the	the	DET
ejpam-3768	22	24	solutions	solution	NOUN
ejpam-3768	22	25	might	might	AUX
ejpam-3768	22	26	be	be	AUX
ejpam-3768	22	27	blowing	blow	VERB
ejpam-3768	22	28	up	up	ADP
ejpam-3768	22	29	in	in	ADP
ejpam-3768	22	30	finite	finite	ADJ
ejpam-3768	22	31	time	time	NOUN
ejpam-3768	22	32	.	.	PUNCT
ejpam-3768	23	1	the	the	DET
ejpam-3768	23	2	eq.(1.1	eq.(1.1	NOUN
ejpam-3768	23	3	)	)	PUNCT
ejpam-3768	23	4	includes	include	VERB
ejpam-3768	23	5	many	many	ADJ
ejpam-3768	23	6	important	important	ADJ
ejpam-3768	23	7	physical	physical	ADJ
ejpam-3768	23	8	models	model	NOUN
ejpam-3768	23	9	.	.	PUNCT
ejpam-3768	24	1	if	if	SCONJ
ejpam-3768	24	2	the	the	DET
ejpam-3768	24	3	exponent	exponent	NOUN
ejpam-3768	24	4	m	m	NOUN
ejpam-3768	24	5	=	=	NOUN
ejpam-3768	24	6	1	1	NUM
ejpam-3768	24	7	and	and	CCONJ
ejpam-3768	24	8	weighted	weight	VERB
ejpam-3768	24	9	function	function	NOUN
ejpam-3768	24	10	a(x	a(x	NOUN
ejpam-3768	24	11	)	)	PUNCT
ejpam-3768	24	12	≡	≡	PROPN
ejpam-3768	24	13	1	1	NUM
ejpam-3768	24	14	,	,	PUNCT
ejpam-3768	24	15	the	the	DET
ejpam-3768	24	16	model	model	NOUN
ejpam-3768	24	17	(	(	PUNCT
ejpam-3768	24	18	1.1	1.1	NUM
ejpam-3768	24	19	)	)	PUNCT
ejpam-3768	24	20	reduces	reduce	VERB
ejpam-3768	24	21	to	to	ADP
ejpam-3768	24	22	the	the	DET
ejpam-3768	24	23	semilinear	semilinear	ADJ
ejpam-3768	24	24	heat	heat	PROPN
ejpam-3768	24	25	equations	equation	NOUN
ejpam-3768	24	26	ut	ut	PROPN
ejpam-3768	24	27	−4u	−4u	PROPN
ejpam-3768	24	28	=	=	SYM
ejpam-3768	24	29	f(u	f(u	PROPN
ejpam-3768	24	30	)	)	PUNCT
ejpam-3768	24	31	,	,	PUNCT
ejpam-3768	24	32	x	x	PUNCT
ejpam-3768	24	33	∈	∈	PROPN
ejpam-3768	24	34	ω	ω	PROPN
ejpam-3768	24	35	,	,	PUNCT
ejpam-3768	24	36	t	t	X
ejpam-3768	24	37	>	>	X
ejpam-3768	24	38	0	0	NUM
ejpam-3768	24	39	.	.	PUNCT
ejpam-3768	25	1	(	(	PUNCT
ejpam-3768	25	2	1.4	1.4	NUM
ejpam-3768	25	3	)	)	PUNCT
ejpam-3768	25	4	about	about	ADP
ejpam-3768	25	5	this	this	DET
ejpam-3768	25	6	model	model	NOUN
ejpam-3768	25	7	,	,	PUNCT
ejpam-3768	25	8	many	many	ADJ
ejpam-3768	25	9	results	result	NOUN
ejpam-3768	25	10	about	about	ADP
ejpam-3768	25	11	the	the	DET
ejpam-3768	25	12	blow	blow	NOUN
ejpam-3768	25	13	-	-	PUNCT
ejpam-3768	25	14	up	up	ADP
ejpam-3768	25	15	phenomenon	phenomenon	NOUN
ejpam-3768	25	16	of	of	ADP
ejpam-3768	25	17	the	the	DET
ejpam-3768	25	18	solutions	solution	NOUN
ejpam-3768	25	19	have	have	AUX
ejpam-3768	25	20	been	be	AUX
ejpam-3768	25	21	obtained	obtain	VERB
ejpam-3768	25	22	,	,	PUNCT
ejpam-3768	25	23	we	we	PRON
ejpam-3768	25	24	refer	refer	VERB
ejpam-3768	25	25	to	to	PART
ejpam-3768	25	26	see	see	VERB
ejpam-3768	25	27	[	[	X
ejpam-3768	25	28	13	13	NUM
ejpam-3768	25	29	,	,	PUNCT
ejpam-3768	25	30	16–19	16–19	NUM
ejpam-3768	25	31	,	,	PUNCT
ejpam-3768	25	32	23	23	NUM
ejpam-3768	25	33	,	,	PUNCT
ejpam-3768	25	34	25	25	NUM
ejpam-3768	25	35	]	]	PUNCT
ejpam-3768	25	36	and	and	CCONJ
ejpam-3768	25	37	references	reference	NOUN
ejpam-3768	25	38	therein	therein	ADV
ejpam-3768	25	39	.	.	PUNCT
ejpam-3768	26	1	in	in	ADP
ejpam-3768	26	2	[	[	X
ejpam-3768	26	3	18	18	NUM
ejpam-3768	26	4	,	,	PUNCT
ejpam-3768	26	5	19	19	NUM
ejpam-3768	26	6	]	]	PUNCT
ejpam-3768	26	7	,	,	PUNCT
ejpam-3768	26	8	payne	payne	PROPN
ejpam-3768	26	9	and	and	CCONJ
ejpam-3768	26	10	schaefer	schaefer	PROPN
ejpam-3768	26	11	obtained	obtain	VERB
ejpam-3768	26	12	a	a	DET
ejpam-3768	26	13	lower	low	ADJ
ejpam-3768	26	14	bound	bind	VERB
ejpam-3768	26	15	on	on	ADP
ejpam-3768	26	16	blow	blow	NOUN
ejpam-3768	26	17	-	-	PUNCT
ejpam-3768	26	18	up	up	ADP
ejpam-3768	26	19	time	time	NOUN
ejpam-3768	26	20	of	of	ADP
ejpam-3768	26	21	the	the	DET
ejpam-3768	26	22	solutions	solution	NOUN
ejpam-3768	26	23	to	to	ADP
ejpam-3768	26	24	the	the	DET
ejpam-3768	26	25	eq.(1.4	eq.(1.4	PROPN
ejpam-3768	26	26	)	)	PUNCT
ejpam-3768	26	27	under	under	ADP
ejpam-3768	26	28	null	null	ADJ
ejpam-3768	26	29	dirichlet	dirichlet	PROPN
ejpam-3768	26	30	boundary	boundary	ADJ
ejpam-3768	26	31	condition	condition	NOUN
ejpam-3768	26	32	and	and	CCONJ
ejpam-3768	26	33	homogeneous	homogeneous	ADJ
ejpam-3768	26	34	neumann	neumann	PROPN
ejpam-3768	26	35	boundary	boundary	PROPN
ejpam-3768	26	36	condition	condition	NOUN
ejpam-3768	26	37	,	,	PUNCT
ejpam-3768	26	38	respectively	respectively	ADV
ejpam-3768	26	39	.	.	PUNCT
ejpam-3768	27	1	later	later	ADV
ejpam-3768	27	2	,	,	PUNCT
ejpam-3768	27	3	payne	payne	PROPN
ejpam-3768	27	4	et	et	PROPN
ejpam-3768	27	5	al	al	PROPN
ejpam-3768	27	6	.	.	PUNCT
ejpam-3768	28	1	[	[	X
ejpam-3768	28	2	16	16	NUM
ejpam-3768	28	3	,	,	PUNCT
ejpam-3768	28	4	17	17	NUM
ejpam-3768	28	5	]	]	PUNCT
ejpam-3768	28	6	studied	study	VERB
ejpam-3768	28	7	the	the	DET
ejpam-3768	28	8	blow	blow	NOUN
ejpam-3768	28	9	-	-	PUNCT
ejpam-3768	28	10	up	up	ADP
ejpam-3768	28	11	phenomenon	phenomenon	NOUN
ejpam-3768	28	12	of	of	ADP
ejpam-3768	28	13	the	the	DET
ejpam-3768	28	14	solutions	solution	NOUN
ejpam-3768	28	15	for	for	ADP
ejpam-3768	28	16	eq.(1.4	eq.(1.4	PROPN
ejpam-3768	28	17	)	)	PUNCT
ejpam-3768	28	18	with	with	ADP
ejpam-3768	28	19	nonlinear	nonlinear	ADJ
ejpam-3768	28	20	boundary	boundary	ADJ
ejpam-3768	28	21	conditions	condition	NOUN
ejpam-3768	28	22	.	.	PUNCT
ejpam-3768	29	1	when	when	SCONJ
ejpam-3768	29	2	the	the	DET
ejpam-3768	29	3	nonlinear	nonlinear	ADJ
ejpam-3768	29	4	source	source	NOUN
ejpam-3768	29	5	term	term	NOUN
ejpam-3768	29	6	f(u	f(u	PROPN
ejpam-3768	29	7	)	)	PUNCT
ejpam-3768	29	8	=	=	SYM
ejpam-3768	30	1	∫	∫	PROPN
ejpam-3768	30	2	ω	ω	NUM
ejpam-3768	30	3	u	u	PROPN
ejpam-3768	30	4	qdx−	qdx−	PROPN
ejpam-3768	30	5	kus	kus	PROPN
ejpam-3768	30	6	,	,	PUNCT
ejpam-3768	30	7	song	song	NOUN
ejpam-3768	30	8	[	[	X
ejpam-3768	30	9	23	23	NUM
ejpam-3768	30	10	]	]	PUNCT
ejpam-3768	30	11	obtained	obtain	VERB
ejpam-3768	30	12	the	the	DET
ejpam-3768	30	13	lower	low	ADJ
ejpam-3768	30	14	bounds	bound	NOUN
ejpam-3768	30	15	for	for	ADP
ejpam-3768	30	16	blow	blow	NOUN
ejpam-3768	30	17	-	-	PUNCT
ejpam-3768	30	18	up	up	ADP
ejpam-3768	30	19	time	time	NOUN
ejpam-3768	30	20	of	of	ADP
ejpam-3768	30	21	the	the	DET
ejpam-3768	30	22	solutions	solution	NOUN
ejpam-3768	30	23	with	with	ADP
ejpam-3768	30	24	either	either	CCONJ
ejpam-3768	30	25	homogeneous	homogeneous	ADJ
ejpam-3768	30	26	dirichlet	dirichlet	NOUN
ejpam-3768	30	27	or	or	CCONJ
ejpam-3768	30	28	homogeneous	homogeneous	ADJ
ejpam-3768	30	29	neumann	neumann	PROPN
ejpam-3768	30	30	boundary	boundary	ADJ
ejpam-3768	30	31	conditions	condition	NOUN
ejpam-3768	30	32	in	in	ADP
ejpam-3768	30	33	three	three	NUM
ejpam-3768	30	34	dimensional	dimensional	ADJ
ejpam-3768	30	35	space	space	NOUN
ejpam-3768	30	36	.	.	PUNCT
ejpam-3768	31	1	afterwards	afterwards	ADV
ejpam-3768	31	2	,	,	PUNCT
ejpam-3768	31	3	liu	liu	PROPN
ejpam-3768	31	4	[	[	X
ejpam-3768	31	5	13	13	NUM
ejpam-3768	31	6	]	]	PUNCT
ejpam-3768	31	7	studied	study	VERB
ejpam-3768	31	8	the	the	DET
ejpam-3768	31	9	lower	low	ADJ
ejpam-3768	31	10	bounds	bound	NOUN
ejpam-3768	31	11	for	for	ADP
ejpam-3768	31	12	blow	blow	NOUN
ejpam-3768	31	13	-	-	PUNCT
ejpam-3768	31	14	up	up	ADP
ejpam-3768	31	15	time	time	NOUN
ejpam-3768	31	16	under	under	ADP
ejpam-3768	31	17	nonlinear	nonlinear	ADJ
ejpam-3768	31	18	boundary	boundary	ADJ
ejpam-3768	31	19	conditions	condition	NOUN
ejpam-3768	31	20	in	in	ADP
ejpam-3768	31	21	three	three	NUM
ejpam-3768	31	22	dimensional	dimensional	ADJ
ejpam-3768	31	23	space	space	NOUN
ejpam-3768	31	24	.	.	PUNCT
ejpam-3768	32	1	in	in	ADP
ejpam-3768	32	2	[	[	X
ejpam-3768	32	3	25	25	NUM
ejpam-3768	32	4	]	]	PUNCT
ejpam-3768	32	5	,	,	PUNCT
ejpam-3768	32	6	tang	tang	X
ejpam-3768	32	7	et	et	PROPN
ejpam-3768	32	8	al	al	PROPN
ejpam-3768	32	9	.	.	PROPN
ejpam-3768	32	10	extended	extend	VERB
ejpam-3768	32	11	the	the	DET
ejpam-3768	32	12	results	result	NOUN
ejpam-3768	32	13	of	of	ADP
ejpam-3768	32	14	literature	literature	NOUN
ejpam-3768	32	15	[	[	X
ejpam-3768	32	16	13	13	NUM
ejpam-3768	32	17	]	]	PUNCT
ejpam-3768	32	18	in	in	ADP
ejpam-3768	32	19	higher	high	ADJ
ejpam-3768	32	20	dimensional	dimensional	ADJ
ejpam-3768	32	21	space	space	NOUN
ejpam-3768	32	22	.	.	PUNCT
ejpam-3768	33	1	when	when	SCONJ
ejpam-3768	33	2	the	the	DET
ejpam-3768	33	3	exponent	exponent	NOUN
ejpam-3768	33	4	m	m	VERB
ejpam-3768	33	5	6=	6=	NUM
ejpam-3768	33	6	1	1	NUM
ejpam-3768	33	7	and	and	CCONJ
ejpam-3768	33	8	weighted	weight	VERB
ejpam-3768	33	9	function	function	NOUN
ejpam-3768	33	10	a(x	a(x	NOUN
ejpam-3768	33	11	)	)	PUNCT
ejpam-3768	33	12	≡	≡	PROPN
ejpam-3768	33	13	1	1	NUM
ejpam-3768	33	14	,	,	PUNCT
ejpam-3768	33	15	the	the	DET
ejpam-3768	33	16	model	model	NOUN
ejpam-3768	33	17	(	(	PUNCT
ejpam-3768	33	18	1.1	1.1	NUM
ejpam-3768	33	19	)	)	PUNCT
ejpam-3768	33	20	becomes	become	VERB
ejpam-3768	33	21	the	the	DET
ejpam-3768	33	22	following	follow	VERB
ejpam-3768	33	23	porous	porous	ADJ
ejpam-3768	33	24	medium	medium	ADJ
ejpam-3768	33	25	equations	equation	NOUN
ejpam-3768	33	26	ut	ut	PROPN
ejpam-3768	33	27	−4um	−4um	PROPN
ejpam-3768	33	28	=	=	PROPN
ejpam-3768	33	29	f(u	f(u	PROPN
ejpam-3768	33	30	)	)	PUNCT
ejpam-3768	33	31	,	,	PUNCT
ejpam-3768	33	32	x	x	PUNCT
ejpam-3768	33	33	∈	∈	PROPN
ejpam-3768	33	34	ω	ω	PROPN
ejpam-3768	33	35	,	,	PUNCT
ejpam-3768	33	36	t	t	X
ejpam-3768	33	37	>	>	X
ejpam-3768	33	38	0	0	NUM
ejpam-3768	33	39	.	.	PUNCT
ejpam-3768	33	40	(	(	PUNCT
ejpam-3768	33	41	1.5	1.5	NUM
ejpam-3768	33	42	)	)	PUNCT
ejpam-3768	33	43	this	this	DET
ejpam-3768	33	44	type	type	NOUN
ejpam-3768	33	45	of	of	ADP
ejpam-3768	33	46	equations	equation	NOUN
ejpam-3768	33	47	appears	appear	VERB
ejpam-3768	33	48	in	in	ADP
ejpam-3768	33	49	several	several	ADJ
ejpam-3768	33	50	branches	branch	NOUN
ejpam-3768	33	51	of	of	ADP
ejpam-3768	33	52	applied	apply	VERB
ejpam-3768	33	53	mathematics	mathematic	NOUN
ejpam-3768	33	54	[	[	X
ejpam-3768	33	55	10	10	NUM
ejpam-3768	33	56	,	,	PUNCT
ejpam-3768	33	57	12	12	NUM
ejpam-3768	33	58	]	]	PUNCT
ejpam-3768	33	59	.	.	PUNCT
ejpam-3768	34	1	there	there	PRON
ejpam-3768	34	2	is	be	VERB
ejpam-3768	34	3	large	large	ADJ
ejpam-3768	34	4	body	body	NOUN
ejpam-3768	34	5	of	of	ADP
ejpam-3768	34	6	literature	literature	NOUN
ejpam-3768	34	7	on	on	ADP
ejpam-3768	34	8	the	the	DET
ejpam-3768	34	9	study	study	NOUN
ejpam-3768	34	10	of	of	ADP
ejpam-3768	34	11	the	the	DET
ejpam-3768	34	12	eq.(1.5	eq.(1.5	NOUN
ejpam-3768	34	13	)	)	PUNCT
ejpam-3768	34	14	,	,	PUNCT
ejpam-3768	34	15	such	such	ADJ
ejpam-3768	34	16	as	as	ADP
ejpam-3768	34	17	the	the	DET
ejpam-3768	34	18	existence	existence	NOUN
ejpam-3768	34	19	and	and	CCONJ
ejpam-3768	34	20	uniqueness	uniqueness	NOUN
ejpam-3768	34	21	in	in	ADP
ejpam-3768	34	22	[	[	X
ejpam-3768	34	23	4	4	NUM
ejpam-3768	34	24	,	,	PUNCT
ejpam-3768	34	25	5	5	NUM
ejpam-3768	34	26	,	,	PUNCT
ejpam-3768	34	27	9	9	NUM
ejpam-3768	34	28	,	,	PUNCT
ejpam-3768	34	29	11	11	NUM
ejpam-3768	34	30	,	,	PUNCT
ejpam-3768	34	31	26	26	NUM
ejpam-3768	34	32	]	]	PUNCT
ejpam-3768	34	33	,	,	PUNCT
ejpam-3768	34	34	blow	blow	NOUN
ejpam-3768	34	35	-	-	PUNCT
ejpam-3768	34	36	up	up	NOUN
ejpam-3768	34	37	in	in	ADP
ejpam-3768	34	38	[	[	X
ejpam-3768	34	39	5	5	NUM
ejpam-3768	34	40	,	,	PUNCT
ejpam-3768	34	41	7–10	7–10	NUM
ejpam-3768	34	42	,	,	PUNCT
ejpam-3768	34	43	26	26	NUM
ejpam-3768	34	44	]	]	PUNCT
ejpam-3768	34	45	,	,	PUNCT
ejpam-3768	34	46	asymptotic	asymptotic	ADJ
ejpam-3768	34	47	behavior	behavior	NOUN
ejpam-3768	34	48	in	in	ADP
ejpam-3768	34	49	[	[	X
ejpam-3768	34	50	3	3	NUM
ejpam-3768	34	51	,	,	PUNCT
ejpam-3768	34	52	20	20	NUM
ejpam-3768	34	53	,	,	PUNCT
ejpam-3768	34	54	21	21	NUM
ejpam-3768	34	55	,	,	PUNCT
ejpam-3768	34	56	26	26	NUM
ejpam-3768	34	57	]	]	PUNCT
ejpam-3768	34	58	and	and	CCONJ
ejpam-3768	34	59	other	other	ADJ
ejpam-3768	34	60	interesting	interesting	ADJ
ejpam-3768	34	61	results	result	NOUN
ejpam-3768	34	62	in	in	ADP
ejpam-3768	34	63	[	[	X
ejpam-3768	34	64	2	2	NUM
ejpam-3768	34	65	,	,	PUNCT
ejpam-3768	34	66	4	4	NUM
ejpam-3768	34	67	,	,	PUNCT
ejpam-3768	34	68	12	12	NUM
ejpam-3768	34	69	,	,	PUNCT
ejpam-3768	34	70	26	26	NUM
ejpam-3768	34	71	]	]	PUNCT
ejpam-3768	34	72	and	and	CCONJ
ejpam-3768	34	73	references	reference	NOUN
ejpam-3768	34	74	therein	therein	ADV
ejpam-3768	34	75	.	.	PUNCT
ejpam-3768	35	1	for	for	ADP
ejpam-3768	35	2	instance	instance	NOUN
ejpam-3768	35	3	,	,	PUNCT
ejpam-3768	35	4	in	in	ADP
ejpam-3768	35	5	the	the	DET
ejpam-3768	35	6	case	case	NOUN
ejpam-3768	35	7	of	of	ADP
ejpam-3768	35	8	nonlinear	nonlinear	ADJ
ejpam-3768	35	9	source	source	NOUN
ejpam-3768	35	10	f(u	f(u	PROPN
ejpam-3768	35	11	)	)	PUNCT
ejpam-3768	35	12	=	=	PUNCT
ejpam-3768	36	1	up	up	ADV
ejpam-3768	36	2	,	,	PUNCT
ejpam-3768	36	3	galaktionov	galaktionov	PROPN
ejpam-3768	36	4	et	et	PROPN
ejpam-3768	36	5	al	al	PROPN
ejpam-3768	36	6	.	.	PUNCT
ejpam-3768	37	1	[	[	X
ejpam-3768	37	2	5	5	NUM
ejpam-3768	37	3	]	]	PUNCT
ejpam-3768	37	4	obtained	obtain	VERB
ejpam-3768	37	5	the	the	DET
ejpam-3768	37	6	finite	finite	ADJ
ejpam-3768	37	7	time	time	NOUN
ejpam-3768	37	8	blow	blow	NOUN
ejpam-3768	37	9	-	-	PUNCT
ejpam-3768	37	10	up	up	NOUN
ejpam-3768	37	11	of	of	ADP
ejpam-3768	37	12	the	the	DET
ejpam-3768	37	13	solutions	solution	NOUN
ejpam-3768	37	14	for	for	ADP
ejpam-3768	37	15	1	1	NUM
ejpam-3768	37	16	<	<	X
ejpam-3768	37	17	p	p	X
ejpam-3768	37	18	<	<	X
ejpam-3768	37	19	m	m	PROPN
ejpam-3768	37	20	+	+	ADJ
ejpam-3768	37	21	2	2	NUM
ejpam-3768	37	22	n	n	NOUN
ejpam-3768	37	23	,	,	PUNCT
ejpam-3768	37	24	and	and	CCONJ
ejpam-3768	37	25	proved	prove	VERB
ejpam-3768	37	26	the	the	DET
ejpam-3768	37	27	global	global	ADJ
ejpam-3768	37	28	existence	existence	NOUN
ejpam-3768	37	29	of	of	ADP
ejpam-3768	37	30	the	the	DET
ejpam-3768	37	31	solutions	solution	NOUN
ejpam-3768	37	32	for	for	ADP
ejpam-3768	37	33	p	p	PROPN
ejpam-3768	37	34	>	>	X
ejpam-3768	37	35	m+	m+	NUM
ejpam-3768	37	36	2	2	NUM
ejpam-3768	37	37	n	n	NOUN
ejpam-3768	37	38	.	.	PUNCT
ejpam-3768	38	1	for	for	ADP
ejpam-3768	38	2	the	the	DET
ejpam-3768	38	3	critical	critical	ADJ
ejpam-3768	38	4	case	case	NOUN
ejpam-3768	38	5	,	,	PUNCT
ejpam-3768	38	6	galaktionov	galaktionov	PROPN
ejpam-3768	38	7	and	and	CCONJ
ejpam-3768	38	8	levine	levine	PROPN
ejpam-3768	38	9	[	[	X
ejpam-3768	38	10	6	6	NUM
ejpam-3768	38	11	]	]	PUNCT
ejpam-3768	38	12	,	,	PUNCT
ejpam-3768	38	13	kawanago	kawanago	X
ejpam-3768	39	1	[	[	X
ejpam-3768	39	2	9	9	X
ejpam-3768	39	3	]	]	PUNCT
ejpam-3768	39	4	revealed	reveal	VERB
ejpam-3768	39	5	that	that	SCONJ
ejpam-3768	39	6	all	all	DET
ejpam-3768	39	7	nonnegative	nonnegative	ADJ
ejpam-3768	39	8	nontrivial	nontrivial	ADJ
ejpam-3768	39	9	mild	mild	ADJ
ejpam-3768	39	10	solutions	solution	NOUN
ejpam-3768	39	11	blow	blow	VERB
ejpam-3768	39	12	up	up	ADP
ejpam-3768	39	13	in	in	ADP
ejpam-3768	39	14	finite	finite	ADJ
ejpam-3768	39	15	time	time	NOUN
ejpam-3768	39	16	.	.	PUNCT
ejpam-3768	40	1	jiang	jiang	PROPN
ejpam-3768	40	2	,	,	PUNCT
ejpam-3768	40	3	zheng	zheng	PROPN
ejpam-3768	40	4	and	and	CCONJ
ejpam-3768	40	5	song	song	NOUN
ejpam-3768	40	6	[	[	X
ejpam-3768	40	7	8	8	NUM
ejpam-3768	40	8	]	]	PUNCT
ejpam-3768	40	9	gave	give	VERB
ejpam-3768	40	10	some	some	DET
ejpam-3768	40	11	sufficient	sufficient	ADJ
ejpam-3768	40	12	or	or	CCONJ
ejpam-3768	40	13	necessary	necessary	ADJ
ejpam-3768	40	14	blow	blow	NOUN
ejpam-3768	40	15	-	-	PUNCT
ejpam-3768	40	16	up	up	ADP
ejpam-3768	40	17	conditions	condition	NOUN
ejpam-3768	40	18	,	,	PUNCT
ejpam-3768	40	19	and	and	CCONJ
ejpam-3768	40	20	the	the	DET
ejpam-3768	40	21	blow	blow	NOUN
ejpam-3768	40	22	-	-	PUNCT
ejpam-3768	40	23	up	up	ADP
ejpam-3768	40	24	rate	rate	NOUN
ejpam-3768	40	25	estimates	estimate	NOUN
ejpam-3768	40	26	,	,	PUNCT
ejpam-3768	40	27	where	where	SCONJ
ejpam-3768	40	28	f(u	f(u	PROPN
ejpam-3768	40	29	)	)	PUNCT
ejpam-3768	40	30	=	=	PUNCT
ejpam-3768	41	1	up	up	ADV
ejpam-3768	41	2	,	,	PUNCT
ejpam-3768	41	3	m	m	VERB
ejpam-3768	41	4	>	>	X
ejpam-3768	41	5	1	1	NUM
ejpam-3768	41	6	,	,	PUNCT
ejpam-3768	41	7	p	p	X
ejpam-3768	41	8	>	>	X
ejpam-3768	41	9	1	1	X
ejpam-3768	41	10	.	.	PUNCT
ejpam-3768	42	1	h.f	h.f	PROPN
ejpam-3768	42	2	.	.	PROPN
ejpam-3768	42	3	di	di	PROPN
ejpam-3768	42	4	,	,	PUNCT
ejpam-3768	42	5	l.	l.	PROPN
ejpam-3768	42	6	chen	chen	PROPN
ejpam-3768	42	7	and	and	CCONJ
ejpam-3768	42	8	z.f	z.f	PROPN
ejpam-3768	42	9	.	.	PROPN
ejpam-3768	42	10	song	song	PROPN
ejpam-3768	42	11	/	/	SYM
ejpam-3768	42	12	eur	eur	PROPN
ejpam-3768	42	13	.	.	PUNCT
ejpam-3768	43	1	j.	j.	PROPN
ejpam-3768	43	2	pure	pure	PROPN
ejpam-3768	43	3	appl	appl	PROPN
ejpam-3768	43	4	.	.	PROPN
ejpam-3768	43	5	math	math	PROPN
ejpam-3768	43	6	,	,	PUNCT
ejpam-3768	43	7	13	13	NUM
ejpam-3768	43	8	(	(	PUNCT
ejpam-3768	43	9	3	3	NUM
ejpam-3768	43	10	)	)	PUNCT
ejpam-3768	43	11	(	(	PUNCT
ejpam-3768	43	12	2020	2020	NUM
ejpam-3768	43	13	)	)	PUNCT
ejpam-3768	43	14	,	,	PUNCT
ejpam-3768	43	15	645	645	NUM
ejpam-3768	43	16	-	-	SYM
ejpam-3768	43	17	662	662	NUM
ejpam-3768	43	18	647	647	NUM
ejpam-3768	43	19	if	if	SCONJ
ejpam-3768	43	20	the	the	DET
ejpam-3768	43	21	exponent	exponent	NOUN
ejpam-3768	43	22	m	m	NOUN
ejpam-3768	43	23	=	=	NOUN
ejpam-3768	43	24	1	1	NUM
ejpam-3768	43	25	and	and	CCONJ
ejpam-3768	43	26	weighted	weight	VERB
ejpam-3768	43	27	function	function	NOUN
ejpam-3768	43	28	a(x	a(x	NOUN
ejpam-3768	43	29	)	)	PUNCT
ejpam-3768	43	30	6≡	6≡	NUM
ejpam-3768	43	31	1	1	NUM
ejpam-3768	43	32	,	,	PUNCT
ejpam-3768	43	33	the	the	DET
ejpam-3768	43	34	model	model	NOUN
ejpam-3768	43	35	(	(	PUNCT
ejpam-3768	43	36	1.1	1.1	NUM
ejpam-3768	43	37	)	)	PUNCT
ejpam-3768	43	38	reduces	reduce	VERB
ejpam-3768	43	39	to	to	ADP
ejpam-3768	43	40	the	the	DET
ejpam-3768	43	41	semilinear	semilinear	PROPN
ejpam-3768	43	42	parabolic	parabolic	PROPN
ejpam-3768	43	43	equations	equation	NOUN
ejpam-3768	43	44	with	with	ADP
ejpam-3768	43	45	weighted	weight	VERB
ejpam-3768	43	46	source	source	NOUN
ejpam-3768	43	47	ut	ut	PROPN
ejpam-3768	43	48	−4u	−4u	PROPN
ejpam-3768	43	49	=	=	SYM
ejpam-3768	43	50	a(x)f(u	a(x)f(u	NUM
ejpam-3768	43	51	)	)	PUNCT
ejpam-3768	43	52	,	,	PUNCT
ejpam-3768	43	53	x	x	PUNCT
ejpam-3768	43	54	∈	∈	PROPN
ejpam-3768	43	55	ω	ω	PROPN
ejpam-3768	43	56	,	,	PUNCT
ejpam-3768	43	57	t	t	X
ejpam-3768	43	58	>	>	X
ejpam-3768	43	59	0	0	NUM
ejpam-3768	43	60	.	.	PUNCT
ejpam-3768	43	61	(	(	PUNCT
ejpam-3768	43	62	1.6	1.6	NUM
ejpam-3768	43	63	)	)	PUNCT
ejpam-3768	43	64	recently	recently	ADV
ejpam-3768	43	65	,	,	PUNCT
ejpam-3768	43	66	the	the	DET
ejpam-3768	43	67	studying	studying	NOUN
ejpam-3768	43	68	on	on	ADP
ejpam-3768	43	69	the	the	DET
ejpam-3768	43	70	blow	blow	NOUN
ejpam-3768	43	71	-	-	PUNCT
ejpam-3768	43	72	up	up	ADP
ejpam-3768	43	73	phenomenon	phenomenon	NOUN
ejpam-3768	43	74	had	have	VERB
ejpam-3768	43	75	some	some	DET
ejpam-3768	43	76	new	new	ADJ
ejpam-3768	43	77	development	development	NOUN
ejpam-3768	43	78	,	,	PUNCT
ejpam-3768	43	79	where	where	SCONJ
ejpam-3768	43	80	more	more	ADJ
ejpam-3768	43	81	attention	attention	NOUN
ejpam-3768	43	82	was	be	AUX
ejpam-3768	43	83	paid	pay	VERB
ejpam-3768	43	84	on	on	ADP
ejpam-3768	43	85	the	the	DET
ejpam-3768	43	86	parabolic	parabolic	ADJ
ejpam-3768	43	87	equations	equation	NOUN
ejpam-3768	43	88	with	with	ADP
ejpam-3768	43	89	weighted	weighted	ADJ
ejpam-3768	43	90	source	source	NOUN
ejpam-3768	43	91	.	.	PUNCT
ejpam-3768	44	1	these	these	DET
ejpam-3768	44	2	models	model	NOUN
ejpam-3768	44	3	can	can	AUX
ejpam-3768	44	4	be	be	AUX
ejpam-3768	44	5	used	use	VERB
ejpam-3768	44	6	to	to	PART
ejpam-3768	44	7	illustrate	illustrate	VERB
ejpam-3768	44	8	the	the	DET
ejpam-3768	44	9	processes	process	NOUN
ejpam-3768	44	10	of	of	ADP
ejpam-3768	44	11	heat	heat	NOUN
ejpam-3768	44	12	transfer	transfer	NOUN
ejpam-3768	44	13	arising	arise	VERB
ejpam-3768	44	14	in	in	ADP
ejpam-3768	44	15	physical	physical	ADJ
ejpam-3768	44	16	and	and	CCONJ
ejpam-3768	44	17	engineering	engineering	NOUN
ejpam-3768	44	18	applications	application	NOUN
ejpam-3768	44	19	,	,	PUNCT
ejpam-3768	44	20	such	such	ADJ
ejpam-3768	44	21	as	as	ADP
ejpam-3768	44	22	a	a	DET
ejpam-3768	44	23	model	model	NOUN
ejpam-3768	44	24	of	of	ADP
ejpam-3768	44	25	phase	phase	NOUN
ejpam-3768	44	26	separation	separation	NOUN
ejpam-3768	44	27	in	in	ADP
ejpam-3768	44	28	binary	binary	ADJ
ejpam-3768	44	29	alloys	alloy	NOUN
ejpam-3768	44	30	[	[	X
ejpam-3768	44	31	22	22	NUM
ejpam-3768	44	32	]	]	PUNCT
ejpam-3768	44	33	.	.	PUNCT
ejpam-3768	45	1	the	the	DET
ejpam-3768	45	2	existence	existence	NOUN
ejpam-3768	45	3	and	and	CCONJ
ejpam-3768	45	4	nonexistence	nonexistence	NOUN
ejpam-3768	45	5	of	of	ADP
ejpam-3768	45	6	global	global	ADJ
ejpam-3768	45	7	solutions	solution	NOUN
ejpam-3768	45	8	,	,	PUNCT
ejpam-3768	45	9	bounds	bound	VERB
ejpam-3768	45	10	for	for	ADP
ejpam-3768	45	11	blow	blow	NOUN
ejpam-3768	45	12	-	-	PUNCT
ejpam-3768	45	13	up	up	ADP
ejpam-3768	45	14	time	time	NOUN
ejpam-3768	45	15	,	,	PUNCT
ejpam-3768	45	16	blow	blow	NOUN
ejpam-3768	45	17	-	-	PUNCT
ejpam-3768	45	18	up	up	ADP
ejpam-3768	45	19	rate	rate	NOUN
ejpam-3768	45	20	,	,	PUNCT
ejpam-3768	45	21	blow	blow	NOUN
ejpam-3768	45	22	-	-	PUNCT
ejpam-3768	45	23	up	up	ADP
ejpam-3768	45	24	sets	set	NOUN
ejpam-3768	45	25	and	and	CCONJ
ejpam-3768	45	26	asymptotic	asymptotic	ADJ
ejpam-3768	45	27	behavior	behavior	NOUN
ejpam-3768	45	28	for	for	ADP
ejpam-3768	45	29	this	this	DET
ejpam-3768	45	30	type	type	NOUN
ejpam-3768	45	31	of	of	ADP
ejpam-3768	45	32	equations	equation	NOUN
ejpam-3768	45	33	were	be	AUX
ejpam-3768	45	34	investigated	investigate	VERB
ejpam-3768	45	35	by	by	ADP
ejpam-3768	45	36	many	many	ADJ
ejpam-3768	45	37	authors	author	NOUN
ejpam-3768	45	38	.	.	PUNCT
ejpam-3768	46	1	we	we	PRON
ejpam-3768	46	2	refer	refer	VERB
ejpam-3768	46	3	the	the	DET
ejpam-3768	46	4	reader	reader	NOUN
ejpam-3768	46	5	to	to	PART
ejpam-3768	46	6	see	see	VERB
ejpam-3768	46	7	[	[	X
ejpam-3768	46	8	14	14	NUM
ejpam-3768	46	9	,	,	PUNCT
ejpam-3768	46	10	15	15	NUM
ejpam-3768	46	11	,	,	PUNCT
ejpam-3768	46	12	24	24	NUM
ejpam-3768	46	13	]	]	PUNCT
ejpam-3768	46	14	and	and	CCONJ
ejpam-3768	46	15	papers	paper	NOUN
ejpam-3768	46	16	cited	cite	VERB
ejpam-3768	46	17	therein	therein	ADV
ejpam-3768	46	18	.	.	PUNCT
ejpam-3768	47	1	for	for	ADP
ejpam-3768	47	2	example	example	NOUN
ejpam-3768	47	3	,	,	PUNCT
ejpam-3768	47	4	song	song	NOUN
ejpam-3768	47	5	and	and	CCONJ
ejpam-3768	47	6	lv	lv	PROPN
ejpam-3768	48	1	[	[	X
ejpam-3768	48	2	14	14	NUM
ejpam-3768	48	3	,	,	PUNCT
ejpam-3768	48	4	24	24	NUM
ejpam-3768	48	5	]	]	PUNCT
ejpam-3768	48	6	studied	study	VERB
ejpam-3768	48	7	the	the	DET
ejpam-3768	48	8	initial	initial	ADJ
ejpam-3768	48	9	boundary	boundary	ADJ
ejpam-3768	48	10	value	value	NOUN
ejpam-3768	48	11	problem	problem	NOUN
ejpam-3768	48	12	for	for	ADP
ejpam-3768	48	13	the	the	DET
ejpam-3768	48	14	above	above	ADJ
ejpam-3768	48	15	equations	equation	NOUN
ejpam-3768	48	16	with	with	ADP
ejpam-3768	48	17	nonlinear	nonlinear	PROPN
ejpam-3768	48	18	neumann	neumann	PROPN
ejpam-3768	48	19	boundary	boundary	PROPN
ejpam-3768	48	20	condition	condition	NOUN
ejpam-3768	48	21	,	,	PUNCT
ejpam-3768	48	22	and	and	CCONJ
ejpam-3768	48	23	they	they	PRON
ejpam-3768	48	24	derived	derive	VERB
ejpam-3768	48	25	the	the	DET
ejpam-3768	48	26	upper	upper	ADJ
ejpam-3768	48	27	and	and	CCONJ
ejpam-3768	48	28	lower	low	ADJ
ejpam-3768	48	29	bounds	bound	NOUN
ejpam-3768	48	30	for	for	ADP
ejpam-3768	48	31	blow	blow	NOUN
ejpam-3768	48	32	-	-	PUNCT
ejpam-3768	48	33	up	up	ADP
ejpam-3768	48	34	time	time	NOUN
ejpam-3768	48	35	in	in	ADP
ejpam-3768	48	36	three	three	NUM
ejpam-3768	48	37	dimensional	dimensional	ADJ
ejpam-3768	48	38	space	space	NOUN
ejpam-3768	48	39	[	[	X
ejpam-3768	48	40	14	14	NUM
ejpam-3768	48	41	]	]	PUNCT
ejpam-3768	48	42	.	.	PUNCT
ejpam-3768	49	1	in	in	ADP
ejpam-3768	49	2	[	[	X
ejpam-3768	49	3	24	24	NUM
ejpam-3768	49	4	]	]	PUNCT
ejpam-3768	49	5	,	,	PUNCT
ejpam-3768	49	6	they	they	PRON
ejpam-3768	49	7	further	far	ADV
ejpam-3768	49	8	investigated	investigate	VERB
ejpam-3768	49	9	the	the	DET
ejpam-3768	49	10	estimates	estimate	NOUN
ejpam-3768	49	11	of	of	ADP
ejpam-3768	49	12	blow	blow	NOUN
ejpam-3768	49	13	-	-	PUNCT
ejpam-3768	49	14	up	up	ADP
ejpam-3768	49	15	rate	rate	NOUN
ejpam-3768	49	16	and	and	CCONJ
ejpam-3768	49	17	the	the	DET
ejpam-3768	49	18	bounds	bound	NOUN
ejpam-3768	49	19	for	for	ADP
ejpam-3768	49	20	blow	blow	NOUN
ejpam-3768	49	21	-	-	PUNCT
ejpam-3768	49	22	up	up	ADP
ejpam-3768	49	23	time	time	NOUN
ejpam-3768	49	24	in	in	ADP
ejpam-3768	49	25	higher	high	ADJ
ejpam-3768	49	26	dimensional	dimensional	ADJ
ejpam-3768	49	27	space	space	NOUN
ejpam-3768	49	28	.	.	PUNCT
ejpam-3768	50	1	ma	ma	PROPN
ejpam-3768	50	2	and	and	CCONJ
ejpam-3768	50	3	fang	fang	X
ejpam-3768	51	1	[	[	X
ejpam-3768	51	2	15	15	NUM
ejpam-3768	51	3	]	]	PUNCT
ejpam-3768	51	4	changed	change	VERB
ejpam-3768	51	5	the	the	DET
ejpam-3768	51	6	diffusion	diffusion	NOUN
ejpam-3768	51	7	term	term	NOUN
ejpam-3768	51	8	4u	4u	NOUN
ejpam-3768	51	9	into	into	ADP
ejpam-3768	51	10	∑n	∑n	PROPN
ejpam-3768	51	11	i	i	PROPN
ejpam-3768	51	12	,	,	PUNCT
ejpam-3768	51	13	j=1	j=1	PROPN
ejpam-3768	51	14	(	(	PUNCT
ejpam-3768	51	15	ai	ai	PROPN
ejpam-3768	51	16	,	,	PUNCT
ejpam-3768	51	17	j(x)uxi	j(x)uxi	PROPN
ejpam-3768	51	18	)	)	PUNCT
ejpam-3768	51	19	xj	xj	PROPN
ejpam-3768	51	20	in	in	ADP
ejpam-3768	51	21	eq.(1.6	eq.(1.6	PROPN
ejpam-3768	51	22	)	)	PUNCT
ejpam-3768	51	23	,	,	PUNCT
ejpam-3768	51	24	where	where	SCONJ
ejpam-3768	51	25	the	the	DET
ejpam-3768	51	26	upper	upper	ADJ
ejpam-3768	51	27	and	and	CCONJ
ejpam-3768	51	28	lower	low	ADJ
ejpam-3768	51	29	bounds	bound	NOUN
ejpam-3768	51	30	for	for	ADP
ejpam-3768	51	31	the	the	DET
ejpam-3768	51	32	blow	blow	NOUN
ejpam-3768	51	33	-	-	PUNCT
ejpam-3768	51	34	up	up	ADP
ejpam-3768	51	35	time	time	NOUN
ejpam-3768	51	36	were	be	AUX
ejpam-3768	51	37	derived	derive	VERB
ejpam-3768	51	38	in	in	ADP
ejpam-3768	51	39	higher	high	ADJ
ejpam-3768	51	40	dimensional	dimensional	ADJ
ejpam-3768	51	41	space	space	NOUN
ejpam-3768	51	42	.	.	PUNCT
ejpam-3768	52	1	in	in	ADP
ejpam-3768	52	2	the	the	DET
ejpam-3768	52	3	present	present	ADJ
ejpam-3768	52	4	work	work	NOUN
ejpam-3768	52	5	,	,	PUNCT
ejpam-3768	52	6	we	we	PRON
ejpam-3768	52	7	main	main	ADJ
ejpam-3768	52	8	study	study	NOUN
ejpam-3768	52	9	the	the	DET
ejpam-3768	52	10	blow	blow	VERB
ejpam-3768	52	11	-	-	PUNCT
ejpam-3768	52	12	up	up	ADP
ejpam-3768	52	13	phenomena	phenomenon	NOUN
ejpam-3768	52	14	for	for	ADP
ejpam-3768	52	15	the	the	DET
ejpam-3768	52	16	porous	porous	ADJ
ejpam-3768	52	17	medium	medium	ADJ
ejpam-3768	52	18	equations	equation	NOUN
ejpam-3768	52	19	with	with	ADP
ejpam-3768	52	20	weighted	weight	VERB
ejpam-3768	52	21	nonlinear	nonlinear	ADJ
ejpam-3768	52	22	source	source	NOUN
ejpam-3768	52	23	.	.	PUNCT
ejpam-3768	53	1	as	as	ADV
ejpam-3768	53	2	far	far	ADV
ejpam-3768	53	3	as	as	SCONJ
ejpam-3768	53	4	we	we	PRON
ejpam-3768	53	5	known	know	VERB
ejpam-3768	53	6	,	,	PUNCT
ejpam-3768	53	7	there	there	PRON
ejpam-3768	53	8	is	be	VERB
ejpam-3768	53	9	little	little	ADJ
ejpam-3768	53	10	information	information	NOUN
ejpam-3768	53	11	on	on	ADP
ejpam-3768	53	12	the	the	DET
ejpam-3768	53	13	blow	blow	NOUN
ejpam-3768	53	14	-	-	PUNCT
ejpam-3768	53	15	up	up	ADP
ejpam-3768	53	16	results	result	NOUN
ejpam-3768	53	17	of	of	ADP
ejpam-3768	53	18	the	the	DET
ejpam-3768	53	19	solutions	solution	NOUN
ejpam-3768	53	20	for	for	ADP
ejpam-3768	53	21	problem	problem	NOUN
ejpam-3768	53	22	(	(	PUNCT
ejpam-3768	53	23	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	53	24	)	)	PUNCT
ejpam-3768	53	25	.	.	PUNCT
ejpam-3768	54	1	obviously	obviously	ADV
ejpam-3768	54	2	,	,	PUNCT
ejpam-3768	54	3	the	the	DET
ejpam-3768	54	4	existence	existence	NOUN
ejpam-3768	54	5	and	and	CCONJ
ejpam-3768	54	6	uniqueness	uniqueness	NOUN
ejpam-3768	54	7	of	of	ADP
ejpam-3768	54	8	local	local	ADJ
ejpam-3768	54	9	solutions	solution	NOUN
ejpam-3768	54	10	for	for	ADP
ejpam-3768	54	11	this	this	DET
ejpam-3768	54	12	problem	problem	NOUN
ejpam-3768	54	13	can	can	AUX
ejpam-3768	54	14	be	be	AUX
ejpam-3768	54	15	obtained	obtain	VERB
ejpam-3768	54	16	by	by	ADP
ejpam-3768	54	17	applying	apply	VERB
ejpam-3768	54	18	the	the	DET
ejpam-3768	54	19	classical	classical	ADJ
ejpam-3768	54	20	faedo	faedo	NOUN
ejpam-3768	54	21	-	-	PUNCT
ejpam-3768	54	22	galerkin	galerkin	ADJ
ejpam-3768	54	23	method	method	NOUN
ejpam-3768	54	24	or	or	CCONJ
ejpam-3768	54	25	contraction	contraction	NOUN
ejpam-3768	54	26	mapping	mapping	NOUN
ejpam-3768	54	27	principle	principle	NOUN
ejpam-3768	54	28	.	.	PUNCT
ejpam-3768	55	1	naturally	naturally	ADV
ejpam-3768	55	2	,	,	PUNCT
ejpam-3768	55	3	we	we	PRON
ejpam-3768	55	4	would	would	AUX
ejpam-3768	55	5	like	like	VERB
ejpam-3768	55	6	to	to	PART
ejpam-3768	55	7	study	study	VERB
ejpam-3768	55	8	the	the	DET
ejpam-3768	55	9	estimates	estimate	NOUN
ejpam-3768	55	10	of	of	ADP
ejpam-3768	55	11	blow	blow	NOUN
ejpam-3768	55	12	-	-	PUNCT
ejpam-3768	55	13	up	up	ADP
ejpam-3768	55	14	rate	rate	NOUN
ejpam-3768	55	15	and	and	CCONJ
ejpam-3768	55	16	the	the	DET
ejpam-3768	55	17	bounds	bound	NOUN
ejpam-3768	55	18	for	for	ADP
ejpam-3768	55	19	blow	blow	NOUN
ejpam-3768	55	20	-	-	PUNCT
ejpam-3768	55	21	up	up	ADP
ejpam-3768	55	22	time	time	NOUN
ejpam-3768	55	23	of	of	ADP
ejpam-3768	55	24	the	the	DET
ejpam-3768	55	25	solutions	solution	NOUN
ejpam-3768	55	26	in	in	ADP
ejpam-3768	55	27	any	any	DET
ejpam-3768	55	28	smooth	smooth	ADJ
ejpam-3768	55	29	bounded	bounded	ADJ
ejpam-3768	55	30	domain	domain	NOUN
ejpam-3768	55	31	ω	ω	PROPN
ejpam-3768	55	32	⊂	⊂	PROPN
ejpam-3768	55	33	rn	rn	PROPN
ejpam-3768	55	34	(	(	PUNCT
ejpam-3768	55	35	n	n	CCONJ
ejpam-3768	55	36	≥	≥	NOUN
ejpam-3768	55	37	3	3	NUM
ejpam-3768	55	38	)	)	PUNCT
ejpam-3768	55	39	.	.	PUNCT
ejpam-3768	56	1	here	here	ADV
ejpam-3768	56	2	,	,	PUNCT
ejpam-3768	56	3	the	the	DET
ejpam-3768	56	4	appearance	appearance	NOUN
ejpam-3768	56	5	of	of	ADP
ejpam-3768	56	6	the	the	DET
ejpam-3768	56	7	diffusion	diffusion	NOUN
ejpam-3768	56	8	term	term	NOUN
ejpam-3768	56	9	4um	4um	NOUN
ejpam-3768	56	10	and	and	CCONJ
ejpam-3768	56	11	weighted	weight	VERB
ejpam-3768	56	12	nonlinear	nonlinear	ADJ
ejpam-3768	56	13	source	source	NOUN
ejpam-3768	56	14	a(x)f(u	a(x)f(u	NUM
ejpam-3768	56	15	)	)	PUNCT
ejpam-3768	56	16	cause	cause	VERB
ejpam-3768	56	17	some	some	DET
ejpam-3768	56	18	difficulties	difficulty	NOUN
ejpam-3768	56	19	in	in	ADP
ejpam-3768	56	20	dealing	deal	VERB
ejpam-3768	56	21	with	with	ADP
ejpam-3768	56	22	the	the	DET
ejpam-3768	56	23	qualitative	qualitative	ADJ
ejpam-3768	56	24	properties	property	NOUN
ejpam-3768	56	25	of	of	ADP
ejpam-3768	56	26	problem	problem	NOUN
ejpam-3768	56	27	(	(	PUNCT
ejpam-3768	56	28	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	56	29	)	)	PUNCT
ejpam-3768	56	30	.	.	PUNCT
ejpam-3768	57	1	hence	hence	ADV
ejpam-3768	57	2	,	,	PUNCT
ejpam-3768	57	3	we	we	PRON
ejpam-3768	57	4	shall	shall	AUX
ejpam-3768	57	5	use	use	VERB
ejpam-3768	57	6	some	some	DET
ejpam-3768	57	7	modified	modify	VERB
ejpam-3768	57	8	auxiliary	auxiliary	ADJ
ejpam-3768	57	9	functions	function	NOUN
ejpam-3768	57	10	and	and	CCONJ
ejpam-3768	57	11	differential	differential	ADJ
ejpam-3768	57	12	-	-	PUNCT
ejpam-3768	57	13	integral	integral	ADJ
ejpam-3768	57	14	inequality	inequality	NOUN
ejpam-3768	57	15	skills	skill	NOUN
ejpam-3768	57	16	to	to	ADP
ejpam-3768	57	17	over	over	ADP
ejpam-3768	57	18	these	these	DET
ejpam-3768	57	19	difficulties	difficulty	NOUN
ejpam-3768	57	20	.	.	PUNCT
ejpam-3768	58	1	in	in	ADP
ejpam-3768	58	2	detail	detail	NOUN
ejpam-3768	58	3	,	,	PUNCT
ejpam-3768	58	4	this	this	DET
ejpam-3768	58	5	paper	paper	NOUN
ejpam-3768	58	6	is	be	AUX
ejpam-3768	58	7	organized	organize	VERB
ejpam-3768	58	8	as	as	SCONJ
ejpam-3768	58	9	follows	follow	VERB
ejpam-3768	58	10	:	:	PUNCT
ejpam-3768	58	11	the	the	DET
ejpam-3768	58	12	blow	blow	VERB
ejpam-3768	58	13	-	-	PUNCT
ejpam-3768	58	14	up	up	ADP
ejpam-3768	58	15	criterions	criterion	NOUN
ejpam-3768	58	16	are	be	AUX
ejpam-3768	58	17	given	give	VERB
ejpam-3768	58	18	under	under	ADP
ejpam-3768	58	19	two	two	NUM
ejpam-3768	58	20	different	different	ADJ
ejpam-3768	58	21	assumptions	assumption	NOUN
ejpam-3768	58	22	,	,	PUNCT
ejpam-3768	58	23	and	and	CCONJ
ejpam-3768	58	24	the	the	DET
ejpam-3768	58	25	corresponding	corresponding	ADJ
ejpam-3768	58	26	estimates	estimate	NOUN
ejpam-3768	58	27	on	on	ADP
ejpam-3768	58	28	the	the	DET
ejpam-3768	58	29	upper	upper	ADJ
ejpam-3768	58	30	bounds	bound	NOUN
ejpam-3768	58	31	for	for	ADP
ejpam-3768	58	32	blow	blow	NOUN
ejpam-3768	58	33	-	-	PUNCT
ejpam-3768	58	34	up	up	ADP
ejpam-3768	58	35	time	time	NOUN
ejpam-3768	58	36	and	and	CCONJ
ejpam-3768	58	37	blow	blow	NOUN
ejpam-3768	58	38	-	-	PUNCT
ejpam-3768	58	39	up	up	ADP
ejpam-3768	58	40	rate	rate	NOUN
ejpam-3768	58	41	are	be	AUX
ejpam-3768	58	42	derived	derive	VERB
ejpam-3768	58	43	in	in	ADP
ejpam-3768	58	44	subsection	subsection	NOUN
ejpam-3768	58	45	2.1	2.1	NUM
ejpam-3768	58	46	and	and	CCONJ
ejpam-3768	58	47	2.2	2.2	NUM
ejpam-3768	58	48	.	.	PUNCT
ejpam-3768	59	1	in	in	ADP
ejpam-3768	59	2	section	section	NOUN
ejpam-3768	59	3	3	3	NUM
ejpam-3768	59	4	,	,	PUNCT
ejpam-3768	59	5	we	we	PRON
ejpam-3768	59	6	will	will	AUX
ejpam-3768	59	7	use	use	VERB
ejpam-3768	59	8	three	three	NUM
ejpam-3768	59	9	methods	method	NOUN
ejpam-3768	59	10	to	to	PART
ejpam-3768	59	11	give	give	VERB
ejpam-3768	59	12	the	the	DET
ejpam-3768	59	13	lower	low	ADJ
ejpam-3768	59	14	bounds	bound	NOUN
ejpam-3768	59	15	for	for	ADP
ejpam-3768	59	16	blow	blow	NOUN
ejpam-3768	59	17	-	-	PUNCT
ejpam-3768	59	18	up	up	ADP
ejpam-3768	59	19	time	time	NOUN
ejpam-3768	59	20	and	and	CCONJ
ejpam-3768	59	21	blow	blow	NOUN
ejpam-3768	59	22	-	-	PUNCT
ejpam-3768	59	23	up	up	ADP
ejpam-3768	59	24	rate	rate	NOUN
ejpam-3768	59	25	of	of	ADP
ejpam-3768	59	26	the	the	DET
ejpam-3768	59	27	solutions	solution	NOUN
ejpam-3768	59	28	if	if	SCONJ
ejpam-3768	59	29	the	the	DET
ejpam-3768	59	30	blow	blow	NOUN
ejpam-3768	59	31	-	-	PUNCT
ejpam-3768	59	32	up	up	NOUN
ejpam-3768	59	33	does	do	AUX
ejpam-3768	59	34	occurs	occur	VERB
ejpam-3768	59	35	.	.	PUNCT
ejpam-3768	60	1	2	2	X
ejpam-3768	60	2	.	.	X
ejpam-3768	60	3	upper	upper	ADJ
ejpam-3768	60	4	estimates	estimate	NOUN
ejpam-3768	60	5	for	for	ADP
ejpam-3768	60	6	blow	blow	NOUN
ejpam-3768	60	7	-	-	PUNCT
ejpam-3768	60	8	up	up	ADP
ejpam-3768	60	9	time	time	NOUN
ejpam-3768	60	10	and	and	CCONJ
ejpam-3768	60	11	blow	blow	NOUN
ejpam-3768	60	12	-	-	PUNCT
ejpam-3768	60	13	up	up	ADP
ejpam-3768	60	14	rate	rate	NOUN
ejpam-3768	60	15	the	the	DET
ejpam-3768	60	16	purpose	purpose	NOUN
ejpam-3768	60	17	of	of	ADP
ejpam-3768	60	18	this	this	DET
ejpam-3768	60	19	section	section	NOUN
ejpam-3768	60	20	is	be	AUX
ejpam-3768	60	21	to	to	PART
ejpam-3768	60	22	establish	establish	VERB
ejpam-3768	60	23	some	some	DET
ejpam-3768	60	24	estimates	estimate	NOUN
ejpam-3768	60	25	about	about	ADP
ejpam-3768	60	26	the	the	DET
ejpam-3768	60	27	upper	upper	ADJ
ejpam-3768	60	28	bounds	bound	NOUN
ejpam-3768	60	29	for	for	ADP
ejpam-3768	60	30	blow	blow	NOUN
ejpam-3768	60	31	-	-	PUNCT
ejpam-3768	60	32	up	up	ADP
ejpam-3768	60	33	time	time	NOUN
ejpam-3768	60	34	and	and	CCONJ
ejpam-3768	60	35	blow	blow	NOUN
ejpam-3768	60	36	-	-	PUNCT
ejpam-3768	60	37	up	up	ADP
ejpam-3768	60	38	rate	rate	NOUN
ejpam-3768	60	39	of	of	ADP
ejpam-3768	60	40	the	the	DET
ejpam-3768	60	41	solutions	solution	NOUN
ejpam-3768	60	42	to	to	ADP
ejpam-3768	60	43	problem	problem	NOUN
ejpam-3768	60	44	(	(	PUNCT
ejpam-3768	60	45	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	60	46	)	)	PUNCT
ejpam-3768	60	47	under	under	ADP
ejpam-3768	60	48	two	two	NUM
ejpam-3768	60	49	different	different	ADJ
ejpam-3768	60	50	assumptions	assumption	NOUN
ejpam-3768	60	51	,	,	PUNCT
ejpam-3768	60	52	respectively	respectively	ADV
ejpam-3768	60	53	.	.	PUNCT
ejpam-3768	61	1	2.1	2.1	NUM
ejpam-3768	61	2	.	.	PUNCT
ejpam-3768	62	1	the	the	DET
ejpam-3768	62	2	first	first	ADJ
ejpam-3768	62	3	method	method	NOUN
ejpam-3768	62	4	to	to	PART
ejpam-3768	62	5	obtain	obtain	VERB
ejpam-3768	62	6	the	the	DET
ejpam-3768	62	7	results	result	NOUN
ejpam-3768	62	8	of	of	ADP
ejpam-3768	62	9	this	this	DET
ejpam-3768	62	10	subsection	subsection	NOUN
ejpam-3768	62	11	,	,	PUNCT
ejpam-3768	62	12	we	we	PRON
ejpam-3768	62	13	first	first	ADV
ejpam-3768	62	14	assume	assume	VERB
ejpam-3768	62	15	that	that	SCONJ
ejpam-3768	62	16	h.f	h.f	PROPN
ejpam-3768	62	17	.	.	PROPN
ejpam-3768	62	18	di	di	PROPN
ejpam-3768	62	19	,	,	PUNCT
ejpam-3768	62	20	l.	l.	PROPN
ejpam-3768	62	21	chen	chen	PROPN
ejpam-3768	62	22	and	and	CCONJ
ejpam-3768	62	23	z.f	z.f	PROPN
ejpam-3768	62	24	.	.	PROPN
ejpam-3768	62	25	song	song	PROPN
ejpam-3768	62	26	/	/	SYM
ejpam-3768	62	27	eur	eur	PROPN
ejpam-3768	62	28	.	.	PUNCT
ejpam-3768	63	1	j.	j.	PROPN
ejpam-3768	63	2	pure	pure	PROPN
ejpam-3768	63	3	appl	appl	PROPN
ejpam-3768	63	4	.	.	PROPN
ejpam-3768	63	5	math	math	PROPN
ejpam-3768	63	6	,	,	PUNCT
ejpam-3768	63	7	13	13	NUM
ejpam-3768	63	8	(	(	PUNCT
ejpam-3768	63	9	3	3	NUM
ejpam-3768	63	10	)	)	PUNCT
ejpam-3768	63	11	(	(	PUNCT
ejpam-3768	63	12	2020	2020	NUM
ejpam-3768	63	13	)	)	PUNCT
ejpam-3768	63	14	,	,	PUNCT
ejpam-3768	63	15	645	645	NUM
ejpam-3768	63	16	-	-	SYM
ejpam-3768	63	17	662	662	NUM
ejpam-3768	63	18	648	648	NUM
ejpam-3768	63	19	(	(	PUNCT
ejpam-3768	63	20	f2	f2	PROPN
ejpam-3768	63	21	):	):	PUNCT
ejpam-3768	63	22	there	there	PRON
ejpam-3768	63	23	exists	exist	VERB
ejpam-3768	63	24	a	a	DET
ejpam-3768	63	25	positive	positive	ADJ
ejpam-3768	63	26	constant	constant	ADJ
ejpam-3768	63	27	c1	c1	NOUN
ejpam-3768	63	28	>	>	X
ejpam-3768	63	29	2	2	NUM
ejpam-3768	63	30	such	such	ADJ
ejpam-3768	63	31	that∫	that∫	NOUN
ejpam-3768	63	32	ω	ω	PROPN
ejpam-3768	63	33	a(x)smf(s)dx	a(x)smf(s)dx	PROPN
ejpam-3768	63	34	≥	≥	PROPN
ejpam-3768	63	35	c1	c1	PROPN
ejpam-3768	63	36	∫	∫	PROPN
ejpam-3768	63	37	ω	ω	PROPN
ejpam-3768	63	38	a(x)f	a(x)f	PROPN
ejpam-3768	63	39	(	(	PUNCT
ejpam-3768	63	40	s)dx	s)dx	PROPN
ejpam-3768	63	41	,	,	PUNCT
ejpam-3768	63	42	for	for	ADP
ejpam-3768	63	43	any	any	DET
ejpam-3768	63	44	function	function	NOUN
ejpam-3768	63	45	s(x	s(x	PROPN
ejpam-3768	63	46	)	)	PUNCT
ejpam-3768	63	47	≥	≥	NOUN
ejpam-3768	63	48	0	0	NUM
ejpam-3768	63	49	,	,	PUNCT
ejpam-3768	63	50	where	where	SCONJ
ejpam-3768	63	51	f	f	PROPN
ejpam-3768	63	52	(	(	PUNCT
ejpam-3768	63	53	s	s	X
ejpam-3768	63	54	)	)	PUNCT
ejpam-3768	63	55	=	=	PUNCT
ejpam-3768	64	1	m	m	VERB
ejpam-3768	64	2	∫	∫	PROPN
ejpam-3768	64	3	s	s	PART
ejpam-3768	64	4	0	0	NUM
ejpam-3768	64	5	θ	θ	PROPN
ejpam-3768	64	6	m−1f(θ)dθ	m−1f(θ)dθ	NOUN
ejpam-3768	64	7	;	;	PUNCT
ejpam-3768	64	8	(	(	PUNCT
ejpam-3768	64	9	g1	g1	PROPN
ejpam-3768	64	10	):	):	PUNCT
ejpam-3768	64	11	the	the	DET
ejpam-3768	64	12	initial	initial	ADJ
ejpam-3768	64	13	data	datum	NOUN
ejpam-3768	64	14	g(x	g(x	NOUN
ejpam-3768	64	15	)	)	PUNCT
ejpam-3768	64	16	satisfies∫	satisfies∫	PUNCT
ejpam-3768	64	17	ω	ω	NUM
ejpam-3768	64	18	|∇gm|2dx	|∇gm|2dx	CCONJ
ejpam-3768	64	19	<	<	X
ejpam-3768	64	20	2	2	NUM
ejpam-3768	64	21	∫	∫	PROPN
ejpam-3768	64	22	ω	ω	NUM
ejpam-3768	64	23	a(x)f	a(x)f	PROPN
ejpam-3768	64	24	(	(	PUNCT
ejpam-3768	64	25	g)dx	g)dx	PROPN
ejpam-3768	64	26	.	.	PUNCT
ejpam-3768	65	1	then	then	ADV
ejpam-3768	65	2	,	,	PUNCT
ejpam-3768	65	3	inspired	inspire	VERB
ejpam-3768	65	4	by	by	ADP
ejpam-3768	65	5	payne	payne	PROPN
ejpam-3768	65	6	et	et	PROPN
ejpam-3768	65	7	al	al	PROPN
ejpam-3768	65	8	.	.	PUNCT
ejpam-3768	66	1	[	[	X
ejpam-3768	66	2	16	16	NUM
ejpam-3768	66	3	,	,	PUNCT
ejpam-3768	66	4	17	17	NUM
ejpam-3768	66	5	]	]	PUNCT
ejpam-3768	66	6	,	,	PUNCT
ejpam-3768	66	7	we	we	PRON
ejpam-3768	66	8	further	far	ADV
ejpam-3768	66	9	define	define	VERB
ejpam-3768	66	10	the	the	DET
ejpam-3768	66	11	following	follow	VERB
ejpam-3768	66	12	auxiliary	auxiliary	ADJ
ejpam-3768	66	13	function	function	NOUN
ejpam-3768	66	14	ϕ(t	ϕ(t	NUM
ejpam-3768	66	15	)	)	PUNCT
ejpam-3768	67	1	=	=	SYM
ejpam-3768	67	2	∫	∫	PROPN
ejpam-3768	67	3	ω	ω	NUM
ejpam-3768	67	4	um+1dx	um+1dx	PROPN
ejpam-3768	67	5	.	.	PUNCT
ejpam-3768	68	1	(	(	PUNCT
ejpam-3768	68	2	2.1	2.1	NUM
ejpam-3768	68	3	)	)	PUNCT
ejpam-3768	68	4	theorem	theorem	NOUN
ejpam-3768	68	5	1	1	NUM
ejpam-3768	68	6	.	.	PUNCT
ejpam-3768	68	7	assume	assume	VERB
ejpam-3768	68	8	that	that	SCONJ
ejpam-3768	68	9	the	the	DET
ejpam-3768	68	10	conditions	condition	NOUN
ejpam-3768	68	11	(	(	PUNCT
ejpam-3768	68	12	f1	f1	NOUN
ejpam-3768	68	13	)	)	PUNCT
ejpam-3768	68	14	,	,	PUNCT
ejpam-3768	68	15	(	(	PUNCT
ejpam-3768	68	16	f2	f2	PROPN
ejpam-3768	68	17	)	)	PUNCT
ejpam-3768	68	18	,	,	PUNCT
ejpam-3768	68	19	(	(	PUNCT
ejpam-3768	68	20	g1	g1	PROPN
ejpam-3768	68	21	)	)	PUNCT
ejpam-3768	68	22	,	,	PUNCT
ejpam-3768	68	23	(	(	PUNCT
ejpam-3768	68	24	a1	a1	NOUN
ejpam-3768	68	25	)	)	PUNCT
ejpam-3768	68	26	,	,	PUNCT
ejpam-3768	68	27	(	(	PUNCT
ejpam-3768	68	28	a2	a2	NOUN
ejpam-3768	68	29	)	)	PUNCT
ejpam-3768	68	30	hold	hold	NOUN
ejpam-3768	68	31	,	,	PUNCT
ejpam-3768	68	32	and	and	CCONJ
ejpam-3768	68	33	u	u	NOUN
ejpam-3768	68	34	is	be	AUX
ejpam-3768	68	35	a	a	DET
ejpam-3768	68	36	nonnegative	nonnegative	ADJ
ejpam-3768	68	37	solution	solution	NOUN
ejpam-3768	68	38	of	of	ADP
ejpam-3768	68	39	problem	problem	NOUN
ejpam-3768	68	40	(	(	PUNCT
ejpam-3768	68	41	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	68	42	)	)	PUNCT
ejpam-3768	68	43	.	.	PUNCT
ejpam-3768	69	1	then	then	ADV
ejpam-3768	69	2	,	,	PUNCT
ejpam-3768	69	3	we	we	PRON
ejpam-3768	69	4	conclude	conclude	VERB
ejpam-3768	69	5	that	that	SCONJ
ejpam-3768	69	6	the	the	DET
ejpam-3768	69	7	solution	solution	NOUN
ejpam-3768	69	8	u	u	NOUN
ejpam-3768	69	9	becomes	become	VERB
ejpam-3768	69	10	unbounded	unbounded	ADJ
ejpam-3768	69	11	in	in	ADP
ejpam-3768	69	12	lm+1−norm	lm+1−norm	PROPN
ejpam-3768	69	13	at	at	ADP
ejpam-3768	69	14	t	t	NOUN
ejpam-3768	69	15	=	=	SYM
ejpam-3768	69	16	t∗.	t∗.	PROPN
ejpam-3768	69	17	moreover	moreover	ADV
ejpam-3768	69	18	,	,	PUNCT
ejpam-3768	69	19	an	an	DET
ejpam-3768	69	20	upper	upper	ADJ
ejpam-3768	69	21	bound	bind	VERB
ejpam-3768	69	22	for	for	ADP
ejpam-3768	69	23	blow	blow	NOUN
ejpam-3768	69	24	-	-	PUNCT
ejpam-3768	69	25	up	up	ADP
ejpam-3768	69	26	time	time	NOUN
ejpam-3768	69	27	t∗	t∗	NOUN
ejpam-3768	69	28	is	be	AUX
ejpam-3768	69	29	given	give	VERB
ejpam-3768	69	30	by	by	ADP
ejpam-3768	69	31	t∗	t∗	NOUN
ejpam-3768	69	32	≤	≤	NOUN
ejpam-3768	69	33	(	(	PUNCT
ejpam-3768	69	34	m+	m+	NUM
ejpam-3768	69	35	1)ϕ(0	1)ϕ(0	NOUN
ejpam-3768	69	36	)	)	PUNCT
ejpam-3768	69	37	(	(	PUNCT
ejpam-3768	69	38	m−	m−	PROPN
ejpam-3768	69	39	1)φ(0	1)φ(0	NOUN
ejpam-3768	69	40	)	)	PUNCT
ejpam-3768	69	41	,	,	PUNCT
ejpam-3768	69	42	(	(	PUNCT
ejpam-3768	69	43	2.2	2.2	NUM
ejpam-3768	69	44	)	)	PUNCT
ejpam-3768	69	45	and	and	CCONJ
ejpam-3768	69	46	the	the	DET
ejpam-3768	69	47	upper	upper	ADJ
ejpam-3768	69	48	estimate	estimate	NOUN
ejpam-3768	69	49	of	of	ADP
ejpam-3768	69	50	blow	blow	NOUN
ejpam-3768	69	51	-	-	PUNCT
ejpam-3768	69	52	up	up	ADP
ejpam-3768	69	53	rate	rate	NOUN
ejpam-3768	69	54	can	can	AUX
ejpam-3768	69	55	be	be	AUX
ejpam-3768	69	56	given	give	VERB
ejpam-3768	69	57	by	by	ADP
ejpam-3768	69	58	‖u‖m+1	‖u‖m+1	PROPN
ejpam-3768	69	59	≤	≤	PROPN
ejpam-3768	69	60	(	(	PUNCT
ejpam-3768	69	61	(	(	PUNCT
ejpam-3768	69	62	m+	m+	NUM
ejpam-3768	69	63	1)ϕ(0	1)ϕ(0	NOUN
ejpam-3768	69	64	)	)	PUNCT
ejpam-3768	69	65	2	2	NUM
ejpam-3768	69	66	m	m	NOUN
ejpam-3768	69	67	m+1	m+1	NUM
ejpam-3768	69	68	(	(	PUNCT
ejpam-3768	69	69	m−	m−	PROPN
ejpam-3768	69	70	1)φ(0	1)φ(0	NOUN
ejpam-3768	69	71	)	)	PUNCT
ejpam-3768	69	72	)	)	PUNCT
ejpam-3768	70	1	1	1	NUM
ejpam-3768	70	2	m−1	m−1	PROPN
ejpam-3768	70	3	(	(	PUNCT
ejpam-3768	70	4	t∗	t∗	PROPN
ejpam-3768	70	5	−	−	PROPN
ejpam-3768	70	6	t)−	t)−	PROPN
ejpam-3768	70	7	1	1	NUM
ejpam-3768	70	8	m−1	m−1	PROPN
ejpam-3768	70	9	,	,	PUNCT
ejpam-3768	70	10	(	(	PUNCT
ejpam-3768	70	11	2.3	2.3	NUM
ejpam-3768	70	12	)	)	PUNCT
ejpam-3768	70	13	where	where	SCONJ
ejpam-3768	70	14	ϕ(0	ϕ(0	NOUN
ejpam-3768	70	15	)	)	PUNCT
ejpam-3768	70	16	=	=	PUNCT
ejpam-3768	71	1	‖g‖m+1	‖g‖m+1	PROPN
ejpam-3768	71	2	m+1	m+1	NUM
ejpam-3768	71	3	and	and	CCONJ
ejpam-3768	71	4	φ(0	φ(0	ADJ
ejpam-3768	71	5	)	)	PUNCT
ejpam-3768	71	6	=	=	SYM
ejpam-3768	71	7	−(m+	−(m+	NUM
ejpam-3768	71	8	1	1	X
ejpam-3768	71	9	)	)	PUNCT
ejpam-3768	71	10	∫	∫	PROPN
ejpam-3768	72	1	ω	ω	PROPN
ejpam-3768	72	2	|∇g	|∇g	PROPN
ejpam-3768	72	3	m|2dx+	m|2dx+	NOUN
ejpam-3768	72	4	2(m+	2(m+	NUM
ejpam-3768	72	5	1	1	NUM
ejpam-3768	72	6	)	)	PUNCT
ejpam-3768	72	7	∫	∫	PROPN
ejpam-3768	73	1	ω	ω	PROPN
ejpam-3768	73	2	a(x)f	a(x)f	PROPN
ejpam-3768	73	3	(	(	PUNCT
ejpam-3768	73	4	g)dx	g)dx	PROPN
ejpam-3768	73	5	>	>	X
ejpam-3768	73	6	0	0	X
ejpam-3768	73	7	.	.	PUNCT
ejpam-3768	73	8	proof	proof	NOUN
ejpam-3768	73	9	.	.	PUNCT
ejpam-3768	74	1	firstly	firstly	ADV
ejpam-3768	74	2	,	,	PUNCT
ejpam-3768	74	3	differentiating	differentiate	VERB
ejpam-3768	74	4	(	(	PUNCT
ejpam-3768	74	5	2.1	2.1	NUM
ejpam-3768	74	6	)	)	PUNCT
ejpam-3768	74	7	with	with	ADP
ejpam-3768	74	8	respect	respect	NOUN
ejpam-3768	74	9	to	to	ADP
ejpam-3768	74	10	t	t	NOUN
ejpam-3768	74	11	and	and	CCONJ
ejpam-3768	74	12	using	use	VERB
ejpam-3768	74	13	eq.(1.1	eq.(1.1	NOUN
ejpam-3768	74	14	)	)	PUNCT
ejpam-3768	74	15	,	,	PUNCT
ejpam-3768	74	16	then	then	ADV
ejpam-3768	74	17	we	we	PRON
ejpam-3768	74	18	have	have	VERB
ejpam-3768	74	19	ϕ′(t	ϕ′(t	VERB
ejpam-3768	74	20	)	)	PUNCT
ejpam-3768	74	21	=	=	PRON
ejpam-3768	75	1	(	(	PUNCT
ejpam-3768	75	2	m+	m+	NOUN
ejpam-3768	75	3	1	1	NUM
ejpam-3768	75	4	)	)	PUNCT
ejpam-3768	75	5	∫	∫	PROPN
ejpam-3768	76	1	ω	ω	NUM
ejpam-3768	76	2	umutdx	umutdx	PROPN
ejpam-3768	76	3	=	=	PRON
ejpam-3768	76	4	(	(	PUNCT
ejpam-3768	76	5	m+	m+	NOUN
ejpam-3768	76	6	1	1	NUM
ejpam-3768	76	7	)	)	PUNCT
ejpam-3768	76	8	∫	∫	PROPN
ejpam-3768	77	1	ω	ω	INTJ
ejpam-3768	77	2	um	um	INTJ
ejpam-3768	77	3	(	(	PUNCT
ejpam-3768	77	4	4um	4um	NOUN
ejpam-3768	77	5	+	+	X
ejpam-3768	77	6	a(x)f(u	a(x)f(u	NUM
ejpam-3768	77	7	)	)	PUNCT
ejpam-3768	77	8	)	)	PUNCT
ejpam-3768	78	1	dx	dx	PROPN
ejpam-3768	79	1	=	=	PUNCT
ejpam-3768	79	2	−(m+	−(m+	NUM
ejpam-3768	79	3	1	1	X
ejpam-3768	79	4	)	)	PUNCT
ejpam-3768	79	5	∫	∫	PROPN
ejpam-3768	79	6	ω	ω	NUM
ejpam-3768	79	7	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	79	8	(	(	PUNCT
ejpam-3768	79	9	m+	m+	NOUN
ejpam-3768	79	10	1	1	NUM
ejpam-3768	79	11	)	)	PUNCT
ejpam-3768	79	12	∫	∫	PROPN
ejpam-3768	79	13	ω	ω	PROPN
ejpam-3768	79	14	a(x)umf(u)dx	a(x)umf(u)dx	PROPN
ejpam-3768	79	15	.	.	PUNCT
ejpam-3768	80	1	(	(	PUNCT
ejpam-3768	80	2	2.4	2.4	NUM
ejpam-3768	80	3	)	)	PUNCT
ejpam-3768	80	4	by	by	ADP
ejpam-3768	80	5	the	the	DET
ejpam-3768	80	6	combination	combination	NOUN
ejpam-3768	80	7	of	of	ADP
ejpam-3768	80	8	(	(	PUNCT
ejpam-3768	80	9	2.4	2.4	NUM
ejpam-3768	80	10	)	)	PUNCT
ejpam-3768	80	11	and	and	CCONJ
ejpam-3768	80	12	condition	condition	NOUN
ejpam-3768	80	13	(	(	PUNCT
ejpam-3768	80	14	f2	f2	PROPN
ejpam-3768	80	15	)	)	PUNCT
ejpam-3768	80	16	,	,	PUNCT
ejpam-3768	80	17	we	we	PRON
ejpam-3768	80	18	obtain	obtain	VERB
ejpam-3768	80	19	ϕ′(t	ϕ′(t	SYM
ejpam-3768	80	20	)	)	PUNCT
ejpam-3768	80	21	≥	≥	NOUN
ejpam-3768	80	22	−(m+	−(m+	NUM
ejpam-3768	80	23	1	1	NUM
ejpam-3768	80	24	)	)	PUNCT
ejpam-3768	80	25	∫	∫	PROPN
ejpam-3768	81	1	ω	ω	NUM
ejpam-3768	81	2	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	81	3	c1(m+	c1(m+	PROPN
ejpam-3768	81	4	1	1	NUM
ejpam-3768	81	5	)	)	PUNCT
ejpam-3768	81	6	∫	∫	PROPN
ejpam-3768	81	7	ω	ω	NUM
ejpam-3768	81	8	a(x)f	a(x)f	PROPN
ejpam-3768	81	9	(	(	PUNCT
ejpam-3768	81	10	u)dx	u)dx	PROPN
ejpam-3768	81	11	>	>	X
ejpam-3768	81	12	φ(t	φ(t	PROPN
ejpam-3768	81	13	)	)	PUNCT
ejpam-3768	81	14	,	,	PUNCT
ejpam-3768	81	15	(	(	PUNCT
ejpam-3768	81	16	2.5	2.5	NUM
ejpam-3768	81	17	)	)	PUNCT
ejpam-3768	81	18	where	where	SCONJ
ejpam-3768	81	19	φ(t	φ(t	NOUN
ejpam-3768	81	20	)	)	PUNCT
ejpam-3768	81	21	=	=	PUNCT
ejpam-3768	81	22	−(m+	−(m+	NUM
ejpam-3768	81	23	1	1	X
ejpam-3768	81	24	)	)	PUNCT
ejpam-3768	81	25	∫	∫	PROPN
ejpam-3768	81	26	ω	ω	NUM
ejpam-3768	81	27	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	81	28	2(m+	2(m+	NUM
ejpam-3768	81	29	1	1	NUM
ejpam-3768	81	30	)	)	PUNCT
ejpam-3768	81	31	∫	∫	PROPN
ejpam-3768	81	32	ω	ω	NUM
ejpam-3768	81	33	a(x)f	a(x)f	PROPN
ejpam-3768	81	34	(	(	PUNCT
ejpam-3768	81	35	u)dx	u)dx	PROPN
ejpam-3768	81	36	.	.	PUNCT
ejpam-3768	82	1	(	(	PUNCT
ejpam-3768	82	2	2.6	2.6	NUM
ejpam-3768	82	3	)	)	PUNCT
ejpam-3768	82	4	h.f	h.f	PROPN
ejpam-3768	82	5	.	.	PROPN
ejpam-3768	82	6	di	di	PROPN
ejpam-3768	82	7	,	,	PUNCT
ejpam-3768	82	8	l.	l.	PROPN
ejpam-3768	82	9	chen	chen	PROPN
ejpam-3768	82	10	and	and	CCONJ
ejpam-3768	82	11	z.f	z.f	PROPN
ejpam-3768	82	12	.	.	PROPN
ejpam-3768	82	13	song	song	PROPN
ejpam-3768	82	14	/	/	SYM
ejpam-3768	82	15	eur	eur	PROPN
ejpam-3768	82	16	.	.	PUNCT
ejpam-3768	83	1	j.	j.	PROPN
ejpam-3768	83	2	pure	pure	PROPN
ejpam-3768	83	3	appl	appl	PROPN
ejpam-3768	83	4	.	.	PROPN
ejpam-3768	83	5	math	math	PROPN
ejpam-3768	83	6	,	,	PUNCT
ejpam-3768	83	7	13	13	NUM
ejpam-3768	83	8	(	(	PUNCT
ejpam-3768	83	9	3	3	NUM
ejpam-3768	83	10	)	)	PUNCT
ejpam-3768	83	11	(	(	PUNCT
ejpam-3768	83	12	2020	2020	NUM
ejpam-3768	83	13	)	)	PUNCT
ejpam-3768	83	14	,	,	PUNCT
ejpam-3768	83	15	645	645	NUM
ejpam-3768	83	16	-	-	SYM
ejpam-3768	83	17	662	662	NUM
ejpam-3768	83	18	649	649	NUM
ejpam-3768	83	19	on	on	ADP
ejpam-3768	83	20	the	the	DET
ejpam-3768	83	21	other	other	ADJ
ejpam-3768	83	22	hand	hand	NOUN
ejpam-3768	83	23	,	,	PUNCT
ejpam-3768	83	24	a	a	DET
ejpam-3768	83	25	simple	simple	ADJ
ejpam-3768	83	26	computation	computation	NOUN
ejpam-3768	83	27	yields	yield	NOUN
ejpam-3768	83	28	φ′(t	φ′(t	NOUN
ejpam-3768	83	29	)	)	PUNCT
ejpam-3768	83	30	=	=	SYM
ejpam-3768	83	31	−2(m+	−2(m+	X
ejpam-3768	83	32	1	1	X
ejpam-3768	83	33	)	)	PUNCT
ejpam-3768	83	34	∫	∫	PROPN
ejpam-3768	84	1	ω	ω	PROPN
ejpam-3768	84	2	∇um	∇um	PROPN
ejpam-3768	84	3	·	·	PUNCT
ejpam-3768	84	4	(	(	PUNCT
ejpam-3768	84	5	∇um)tdx	∇um)tdx	NOUN
ejpam-3768	84	6	+	+	X
ejpam-3768	84	7	2m(m+	2m(m+	NUM
ejpam-3768	84	8	1	1	NUM
ejpam-3768	84	9	)	)	PUNCT
ejpam-3768	84	10	∫	∫	PROPN
ejpam-3768	84	11	ω	ω	PROPN
ejpam-3768	84	12	a(x)um−1utf(u)dx	a(x)um−1utf(u)dx	PUNCT
ejpam-3768	84	13	=	=	SYM
ejpam-3768	85	1	2m(m+	2m(m+	NUM
ejpam-3768	85	2	1	1	NUM
ejpam-3768	85	3	)	)	PUNCT
ejpam-3768	85	4	∫	∫	PROPN
ejpam-3768	86	1	ω	ω	NUM
ejpam-3768	86	2	um−1ut	um−1ut	PROPN
ejpam-3768	86	3	(	(	PUNCT
ejpam-3768	86	4	4um	4um	NOUN
ejpam-3768	86	5	+	+	X
ejpam-3768	86	6	a(x)f(u	a(x)f(u	NUM
ejpam-3768	86	7	)	)	PUNCT
ejpam-3768	86	8	)	)	PUNCT
ejpam-3768	87	1	dx	dx	PROPN
ejpam-3768	88	1	=	=	PUNCT
ejpam-3768	88	2	2m(m+	2m(m+	NUM
ejpam-3768	88	3	1	1	NUM
ejpam-3768	88	4	)	)	PUNCT
ejpam-3768	88	5	∫	∫	PROPN
ejpam-3768	88	6	ω	ω	PROPN
ejpam-3768	88	7	um−1u2	um−1u2	PROPN
ejpam-3768	88	8	tdx	tdx	PROPN
ejpam-3768	88	9	≥	≥	PROPN
ejpam-3768	88	10	0	0	NUM
ejpam-3768	88	11	.	.	PUNCT
ejpam-3768	88	12	(	(	PUNCT
ejpam-3768	88	13	2.7	2.7	NUM
ejpam-3768	88	14	)	)	PUNCT
ejpam-3768	88	15	here	here	ADV
ejpam-3768	88	16	,	,	PUNCT
ejpam-3768	88	17	we	we	PRON
ejpam-3768	88	18	have	have	AUX
ejpam-3768	88	19	used	use	VERB
ejpam-3768	88	20	the	the	DET
ejpam-3768	88	21	fact	fact	NOUN
ejpam-3768	88	22	that	that	SCONJ
ejpam-3768	88	23	u(x	u(x	NOUN
ejpam-3768	88	24	,	,	PUNCT
ejpam-3768	88	25	t	t	PROPN
ejpam-3768	88	26	)	)	PUNCT
ejpam-3768	88	27	=	=	SYM
ejpam-3768	88	28	0	0	PUNCT
ejpam-3768	89	1	(	(	PUNCT
ejpam-3768	89	2	or	or	CCONJ
ejpam-3768	89	3	∂u	∂u	PROPN
ejpam-3768	89	4	∂ν	∂ν	X
ejpam-3768	89	5	=	=	PUNCT
ejpam-3768	89	6	0	0	NUM
ejpam-3768	89	7	)	)	PUNCT
ejpam-3768	89	8	on	on	ADP
ejpam-3768	89	9	∂ω	∂ω	PROPN
ejpam-3768	89	10	.	.	PUNCT
ejpam-3768	90	1	using	use	VERB
ejpam-3768	90	2	schwarz	schwarz	PROPN
ejpam-3768	90	3	’s	’s	PART
ejpam-3768	90	4	inequality	inequality	NOUN
ejpam-3768	90	5	,	,	PUNCT
ejpam-3768	90	6	we	we	PRON
ejpam-3768	90	7	get	get	VERB
ejpam-3768	90	8	(	(	PUNCT
ejpam-3768	90	9	∫	∫	PROPN
ejpam-3768	90	10	ω	ω	PROPN
ejpam-3768	90	11	umutdx	umutdx	PROPN
ejpam-3768	90	12	)	)	PUNCT
ejpam-3768	90	13	2	2	NUM
ejpam-3768	90	14	≤	≤	NUM
ejpam-3768	90	15	∫	∫	PROPN
ejpam-3768	90	16	ω	ω	PROPN
ejpam-3768	91	1	um+1dx	um+1dx	PROPN
ejpam-3768	91	2	∫	∫	PROPN
ejpam-3768	91	3	ω	ω	PROPN
ejpam-3768	91	4	um−1u2	um−1u2	PROPN
ejpam-3768	91	5	tdx	tdx	PROPN
ejpam-3768	91	6	.	.	PUNCT
ejpam-3768	92	1	(	(	PUNCT
ejpam-3768	92	2	2.8	2.8	NUM
ejpam-3768	92	3	)	)	PUNCT
ejpam-3768	92	4	hence	hence	ADV
ejpam-3768	92	5	,	,	PUNCT
ejpam-3768	92	6	multiplying	multiply	VERB
ejpam-3768	92	7	ϕ(t	ϕ(t	NUM
ejpam-3768	92	8	)	)	PUNCT
ejpam-3768	92	9	by	by	ADP
ejpam-3768	92	10	φ′(t	φ′(t	NOUN
ejpam-3768	92	11	)	)	PUNCT
ejpam-3768	92	12	,	,	PUNCT
ejpam-3768	92	13	it	it	PRON
ejpam-3768	92	14	follows	follow	VERB
ejpam-3768	92	15	from	from	ADP
ejpam-3768	92	16	(	(	PUNCT
ejpam-3768	92	17	2.5	2.5	NUM
ejpam-3768	92	18	)	)	PUNCT
ejpam-3768	92	19	that	that	SCONJ
ejpam-3768	92	20	ϕ(t)φ′(t	ϕ(t)φ′(t	PROPN
ejpam-3768	92	21	)	)	PUNCT
ejpam-3768	93	1	=	=	PUNCT
ejpam-3768	94	1	2m(m+	2m(m+	NUM
ejpam-3768	94	2	1	1	NUM
ejpam-3768	94	3	)	)	PUNCT
ejpam-3768	94	4	∫	∫	PROPN
ejpam-3768	95	1	ω	ω	PROPN
ejpam-3768	95	2	um+1dx	um+1dx	NOUN
ejpam-3768	95	3	∫	∫	PROPN
ejpam-3768	95	4	ω	ω	PROPN
ejpam-3768	95	5	um−1u2	um−1u2	PROPN
ejpam-3768	95	6	tdx	tdx	PROPN
ejpam-3768	95	7	≥	≥	NOUN
ejpam-3768	95	8	2m(m+	2m(m+	NUM
ejpam-3768	95	9	1	1	NUM
ejpam-3768	95	10	)	)	PUNCT
ejpam-3768	95	11	(	(	PUNCT
ejpam-3768	95	12	∫	∫	PROPN
ejpam-3768	95	13	ω	ω	PROPN
ejpam-3768	95	14	umutdx	umutdx	PROPN
ejpam-3768	95	15	)	)	PUNCT
ejpam-3768	95	16	2	2	NUM
ejpam-3768	95	17	=	=	SYM
ejpam-3768	95	18	2	2	NUM
ejpam-3768	95	19	m	m	NOUN
ejpam-3768	95	20	m+	m+	NUM
ejpam-3768	95	21	1	1	NUM
ejpam-3768	96	1	[	[	X
ejpam-3768	96	2	ϕ′(t)]2	ϕ′(t)]2	NOUN
ejpam-3768	96	3	≥	≥	NUM
ejpam-3768	96	4	2	2	NUM
ejpam-3768	96	5	m	m	NOUN
ejpam-3768	96	6	m+	m+	NUM
ejpam-3768	96	7	1	1	NUM
ejpam-3768	96	8	ϕ′(t)φ(t	ϕ′(t)φ(t	NOUN
ejpam-3768	96	9	)	)	PUNCT
ejpam-3768	96	10	.	.	PUNCT
ejpam-3768	97	1	(	(	PUNCT
ejpam-3768	97	2	2.9	2.9	NUM
ejpam-3768	97	3	)	)	PUNCT
ejpam-3768	97	4	thus	thus	ADV
ejpam-3768	97	5	,	,	PUNCT
ejpam-3768	97	6	the	the	DET
ejpam-3768	97	7	above	above	ADJ
ejpam-3768	97	8	inequality	inequality	NOUN
ejpam-3768	97	9	implies	imply	VERB
ejpam-3768	97	10	that	that	SCONJ
ejpam-3768	97	11	(	(	PUNCT
ejpam-3768	97	12	φ(t	φ(t	PROPN
ejpam-3768	97	13	)	)	PUNCT
ejpam-3768	98	1	[	[	X
ejpam-3768	98	2	ϕ(t)]−	ϕ(t)]−	PROPN
ejpam-3768	98	3	2	2	NUM
ejpam-3768	98	4	m	m	NOUN
ejpam-3768	98	5	m+1	m+1	NUM
ejpam-3768	98	6	)	)	PUNCT
ejpam-3768	98	7	′	′	NUM
ejpam-3768	99	1	=	=	PUNCT
ejpam-3768	100	1	[	[	X
ejpam-3768	100	2	ϕ(t)]−	ϕ(t)]−	PROPN
ejpam-3768	100	3	3m+1	3m+1	NUM
ejpam-3768	100	4	m+1	m+1	NUM
ejpam-3768	100	5	{	{	PUNCT
ejpam-3768	100	6	ϕ(t)φ′(t)−	ϕ(t)φ′(t)−	PROPN
ejpam-3768	100	7	2	2	NUM
ejpam-3768	100	8	m	m	NOUN
ejpam-3768	100	9	m+	m+	NUM
ejpam-3768	100	10	1	1	NUM
ejpam-3768	100	11	ϕ′(t)φ(t	ϕ′(t)φ(t	NOUN
ejpam-3768	100	12	)	)	PUNCT
ejpam-3768	100	13	}	}	PUNCT
ejpam-3768	100	14	≥	≥	NOUN
ejpam-3768	100	15	0	0	NUM
ejpam-3768	100	16	.	.	PUNCT
ejpam-3768	101	1	(	(	PUNCT
ejpam-3768	101	2	2.10	2.10	NUM
ejpam-3768	101	3	)	)	PUNCT
ejpam-3768	101	4	utilizing	utilize	VERB
ejpam-3768	101	5	the	the	DET
ejpam-3768	101	6	assumption	assumption	NOUN
ejpam-3768	101	7	(	(	PUNCT
ejpam-3768	101	8	g1	g1	PROPN
ejpam-3768	101	9	)	)	PUNCT
ejpam-3768	101	10	and	and	CCONJ
ejpam-3768	101	11	(	(	PUNCT
ejpam-3768	101	12	2.1	2.1	NUM
ejpam-3768	101	13	)	)	PUNCT
ejpam-3768	101	14	,	,	PUNCT
ejpam-3768	101	15	(	(	PUNCT
ejpam-3768	101	16	2.7	2.7	NUM
ejpam-3768	101	17	)	)	PUNCT
ejpam-3768	101	18	,	,	PUNCT
ejpam-3768	101	19	we	we	PRON
ejpam-3768	101	20	know	know	VERB
ejpam-3768	101	21	that	that	SCONJ
ejpam-3768	101	22	ϕ(0	ϕ(0	PRON
ejpam-3768	101	23	)	)	PUNCT
ejpam-3768	102	1	=	=	PUNCT
ejpam-3768	103	1	‖g‖m+1	‖g‖m+1	PROPN
ejpam-3768	103	2	m+1	m+1	X
ejpam-3768	103	3	>	>	X
ejpam-3768	103	4	0	0	NUM
ejpam-3768	103	5	,	,	PUNCT
ejpam-3768	103	6	(	(	PUNCT
ejpam-3768	103	7	2.11	2.11	NUM
ejpam-3768	103	8	)	)	PUNCT
ejpam-3768	103	9	and	and	CCONJ
ejpam-3768	103	10	φ(t	φ(t	PROPN
ejpam-3768	103	11	)	)	PUNCT
ejpam-3768	103	12	≥	≥	NOUN
ejpam-3768	103	13	φ(0	φ(0	ADJ
ejpam-3768	103	14	)	)	PUNCT
ejpam-3768	103	15	=	=	SYM
ejpam-3768	103	16	−(m+	−(m+	NUM
ejpam-3768	103	17	1	1	X
ejpam-3768	103	18	)	)	PUNCT
ejpam-3768	103	19	∫	∫	PROPN
ejpam-3768	104	1	ω	ω	NUM
ejpam-3768	104	2	|∇gm|2dx+	|∇gm|2dx+	NOUN
ejpam-3768	104	3	2(m+	2(m+	NUM
ejpam-3768	104	4	1	1	NUM
ejpam-3768	104	5	)	)	PUNCT
ejpam-3768	104	6	∫	∫	PROPN
ejpam-3768	104	7	ω	ω	PROPN
ejpam-3768	104	8	a(x)f	a(x)f	PROPN
ejpam-3768	104	9	(	(	PUNCT
ejpam-3768	104	10	g)dx	g)dx	PROPN
ejpam-3768	104	11	>	>	X
ejpam-3768	104	12	0	0	NUM
ejpam-3768	104	13	.	.	PUNCT
ejpam-3768	105	1	(	(	PUNCT
ejpam-3768	105	2	2.12	2.12	NUM
ejpam-3768	105	3	)	)	PUNCT
ejpam-3768	105	4	integrating	integrating	NOUN
ejpam-3768	105	5	(	(	PUNCT
ejpam-3768	105	6	2.10	2.10	NUM
ejpam-3768	105	7	)	)	PUNCT
ejpam-3768	105	8	from	from	ADP
ejpam-3768	105	9	0	0	NUM
ejpam-3768	105	10	to	to	ADP
ejpam-3768	105	11	t	t	PROPN
ejpam-3768	105	12	,	,	PUNCT
ejpam-3768	105	13	we	we	PRON
ejpam-3768	105	14	obtain	obtain	VERB
ejpam-3768	105	15	φ(t	φ(t	NUM
ejpam-3768	105	16	)	)	PUNCT
ejpam-3768	106	1	[	[	X
ejpam-3768	106	2	ϕ(t)]−	ϕ(t)]−	PROPN
ejpam-3768	106	3	2	2	NUM
ejpam-3768	106	4	m	m	NOUN
ejpam-3768	106	5	m+1	m+1	NUM
ejpam-3768	106	6	≥	≥	NOUN
ejpam-3768	106	7	φ(0	φ(0	PROPN
ejpam-3768	106	8	)	)	PUNCT
ejpam-3768	107	1	[	[	X
ejpam-3768	107	2	ϕ(0)]−	ϕ(0)]−	PROPN
ejpam-3768	107	3	2	2	NUM
ejpam-3768	107	4	m	m	NOUN
ejpam-3768	107	5	m+1	m+1	NUM
ejpam-3768	107	6	=	=	PUNCT
ejpam-3768	107	7	m	m	NOUN
ejpam-3768	107	8	>	>	X
ejpam-3768	107	9	0	0	NUM
ejpam-3768	107	10	.	.	PUNCT
ejpam-3768	107	11	(	(	PUNCT
ejpam-3768	107	12	2.13	2.13	NUM
ejpam-3768	107	13	)	)	PUNCT
ejpam-3768	107	14	by	by	ADP
ejpam-3768	107	15	(	(	PUNCT
ejpam-3768	107	16	2.5	2.5	NUM
ejpam-3768	107	17	)	)	PUNCT
ejpam-3768	107	18	and	and	CCONJ
ejpam-3768	107	19	(	(	PUNCT
ejpam-3768	107	20	2.13	2.13	NUM
ejpam-3768	107	21	)	)	PUNCT
ejpam-3768	107	22	,	,	PUNCT
ejpam-3768	107	23	we	we	PRON
ejpam-3768	107	24	get	get	VERB
ejpam-3768	107	25	m+	m+	NUM
ejpam-3768	107	26	1	1	NUM
ejpam-3768	107	27	1−m	1−m	NUM
ejpam-3768	107	28	(	(	PUNCT
ejpam-3768	107	29	[	[	X
ejpam-3768	107	30	ϕ(t	ϕ(t	NUM
ejpam-3768	107	31	)	)	PUNCT
ejpam-3768	107	32	]	]	PUNCT
ejpam-3768	108	1	1−m	1−m	NUM
ejpam-3768	108	2	m+1	m+1	NUM
ejpam-3768	108	3	)	)	PUNCT
ejpam-3768	108	4	′	′	NUM
ejpam-3768	108	5	=	=	PUNCT
ejpam-3768	108	6	ϕ′(t	ϕ′(t	NOUN
ejpam-3768	108	7	)	)	PUNCT
ejpam-3768	109	1	[	[	X
ejpam-3768	109	2	ϕ(t)]−	ϕ(t)]−	PROPN
ejpam-3768	109	3	2	2	NUM
ejpam-3768	109	4	m	m	NOUN
ejpam-3768	109	5	m+1	m+1	NUM
ejpam-3768	109	6	≥	≥	NOUN
ejpam-3768	109	7	φ(t	φ(t	NUM
ejpam-3768	109	8	)	)	PUNCT
ejpam-3768	110	1	[	[	X
ejpam-3768	110	2	ϕ(t)]−	ϕ(t)]−	PROPN
ejpam-3768	110	3	2	2	NUM
ejpam-3768	110	4	m	m	NOUN
ejpam-3768	110	5	m+1	m+1	NUM
ejpam-3768	110	6	>	>	X
ejpam-3768	110	7	0	0	NUM
ejpam-3768	110	8	.	.	PUNCT
ejpam-3768	110	9	(	(	PUNCT
ejpam-3768	110	10	2.14	2.14	NUM
ejpam-3768	110	11	)	)	PUNCT
ejpam-3768	110	12	h.f	h.f	PROPN
ejpam-3768	110	13	.	.	PROPN
ejpam-3768	110	14	di	di	PROPN
ejpam-3768	110	15	,	,	PUNCT
ejpam-3768	110	16	l.	l.	PROPN
ejpam-3768	110	17	chen	chen	PROPN
ejpam-3768	110	18	and	and	CCONJ
ejpam-3768	110	19	z.f	z.f	PROPN
ejpam-3768	110	20	.	.	PROPN
ejpam-3768	110	21	song	song	PROPN
ejpam-3768	110	22	/	/	SYM
ejpam-3768	110	23	eur	eur	PROPN
ejpam-3768	110	24	.	.	PUNCT
ejpam-3768	111	1	j.	j.	PROPN
ejpam-3768	111	2	pure	pure	PROPN
ejpam-3768	111	3	appl	appl	PROPN
ejpam-3768	111	4	.	.	PROPN
ejpam-3768	111	5	math	math	PROPN
ejpam-3768	111	6	,	,	PUNCT
ejpam-3768	111	7	13	13	NUM
ejpam-3768	111	8	(	(	PUNCT
ejpam-3768	111	9	3	3	NUM
ejpam-3768	111	10	)	)	PUNCT
ejpam-3768	111	11	(	(	PUNCT
ejpam-3768	111	12	2020	2020	NUM
ejpam-3768	111	13	)	)	PUNCT
ejpam-3768	111	14	,	,	PUNCT
ejpam-3768	111	15	645	645	NUM
ejpam-3768	111	16	-	-	SYM
ejpam-3768	111	17	662	662	NUM
ejpam-3768	111	18	650	650	NUM
ejpam-3768	111	19	integrating	integrating	NOUN
ejpam-3768	111	20	(	(	PUNCT
ejpam-3768	111	21	2.14	2.14	NUM
ejpam-3768	111	22	)	)	PUNCT
ejpam-3768	111	23	from	from	ADP
ejpam-3768	111	24	0	0	NUM
ejpam-3768	111	25	to	to	ADP
ejpam-3768	111	26	t	t	PROPN
ejpam-3768	111	27	,	,	PUNCT
ejpam-3768	111	28	we	we	PRON
ejpam-3768	111	29	have	have	AUX
ejpam-3768	111	30	[	[	X
ejpam-3768	111	31	ϕ(t	ϕ(t	NUM
ejpam-3768	111	32	)	)	PUNCT
ejpam-3768	111	33	]	]	PUNCT
ejpam-3768	112	1	1−m	1−m	NUM
ejpam-3768	112	2	m+1	m+1	PRON
ejpam-3768	112	3	≤	≤	PUNCT
ejpam-3768	113	1	[	[	X
ejpam-3768	113	2	ϕ(0	ϕ(0	NOUN
ejpam-3768	113	3	)	)	PUNCT
ejpam-3768	113	4	]	]	PUNCT
ejpam-3768	114	1	1−m	1−m	NUM
ejpam-3768	114	2	m+1	m+1	NUM
ejpam-3768	114	3	−	−	NOUN
ejpam-3768	114	4	m−	m−	PROPN
ejpam-3768	114	5	1	1	NUM
ejpam-3768	114	6	m+	m+	NUM
ejpam-3768	114	7	1	1	NUM
ejpam-3768	114	8	mt	mt	PROPN
ejpam-3768	114	9	.	.	PROPN
ejpam-3768	115	1	(	(	PUNCT
ejpam-3768	115	2	2.15	2.15	NUM
ejpam-3768	115	3	)	)	PUNCT
ejpam-3768	115	4	clearly	clearly	ADV
ejpam-3768	115	5	,	,	PUNCT
ejpam-3768	115	6	the	the	DET
ejpam-3768	115	7	above	above	ADJ
ejpam-3768	115	8	inequality	inequality	NOUN
ejpam-3768	115	9	can	can	AUX
ejpam-3768	115	10	not	not	PART
ejpam-3768	115	11	hold	hold	VERB
ejpam-3768	115	12	for	for	ADP
ejpam-3768	115	13	all	all	DET
ejpam-3768	115	14	t	t	NOUN
ejpam-3768	115	15	>	>	X
ejpam-3768	115	16	0	0	X
ejpam-3768	115	17	.	.	PUNCT
ejpam-3768	116	1	consequently	consequently	ADV
ejpam-3768	116	2	,	,	PUNCT
ejpam-3768	116	3	u	u	PRON
ejpam-3768	116	4	blows	blow	VERB
ejpam-3768	116	5	up	up	ADP
ejpam-3768	116	6	at	at	ADP
ejpam-3768	116	7	some	some	DET
ejpam-3768	116	8	finite	finite	ADJ
ejpam-3768	116	9	time	time	NOUN
ejpam-3768	116	10	t∗	t∗	NOUN
ejpam-3768	116	11	and	and	CCONJ
ejpam-3768	116	12	t∗	t∗	NOUN
ejpam-3768	116	13	≤	≤	NUM
ejpam-3768	116	14	m+	m+	NUM
ejpam-3768	116	15	1ϕ(0	1ϕ(0	NUM
ejpam-3768	116	16	)	)	PUNCT
ejpam-3768	116	17	(	(	PUNCT
ejpam-3768	116	18	m−	m−	PROPN
ejpam-3768	116	19	1)φ(0	1)φ(0	NOUN
ejpam-3768	116	20	)	)	PUNCT
ejpam-3768	116	21	.	.	PUNCT
ejpam-3768	117	1	furthermore	furthermore	ADV
ejpam-3768	117	2	,	,	PUNCT
ejpam-3768	117	3	from	from	ADP
ejpam-3768	117	4	(	(	PUNCT
ejpam-3768	117	5	2.5	2.5	NUM
ejpam-3768	117	6	)	)	PUNCT
ejpam-3768	117	7	and	and	CCONJ
ejpam-3768	117	8	(	(	PUNCT
ejpam-3768	117	9	2.13	2.13	NUM
ejpam-3768	117	10	)	)	PUNCT
ejpam-3768	117	11	again	again	ADV
ejpam-3768	117	12	,	,	PUNCT
ejpam-3768	117	13	we	we	PRON
ejpam-3768	117	14	have	have	VERB
ejpam-3768	117	15	ϕ′(t	ϕ′(t	NOUN
ejpam-3768	117	16	)	)	PUNCT
ejpam-3768	117	17	≥	≥	NOUN
ejpam-3768	117	18	φ(t	φ(t	PROPN
ejpam-3768	117	19	)	)	PUNCT
ejpam-3768	117	20	≥	≥	NOUN
ejpam-3768	118	1	φ(0	φ(0	ADJ
ejpam-3768	118	2	)	)	PUNCT
ejpam-3768	119	1	[	[	X
ejpam-3768	119	2	ϕ(0)]−	ϕ(0)]−	PROPN
ejpam-3768	119	3	2	2	NUM
ejpam-3768	119	4	m	m	NOUN
ejpam-3768	119	5	m+1	m+1	X
ejpam-3768	119	6	[	[	X
ejpam-3768	119	7	ϕ(t	ϕ(t	NUM
ejpam-3768	119	8	)	)	PUNCT
ejpam-3768	119	9	]	]	PUNCT
ejpam-3768	120	1	2	2	NUM
ejpam-3768	120	2	m	m	NOUN
ejpam-3768	120	3	m+1	m+1	NUM
ejpam-3768	120	4	.	.	PUNCT
ejpam-3768	121	1	(	(	PUNCT
ejpam-3768	121	2	2.16	2.16	NUM
ejpam-3768	121	3	)	)	PUNCT
ejpam-3768	121	4	integrating	integrating	NOUN
ejpam-3768	121	5	(	(	PUNCT
ejpam-3768	121	6	2.16	2.16	NUM
ejpam-3768	121	7	)	)	PUNCT
ejpam-3768	121	8	from	from	ADP
ejpam-3768	121	9	t	t	PROPN
ejpam-3768	121	10	to	to	ADP
ejpam-3768	121	11	t∗	t∗	PROPN
ejpam-3768	121	12	,	,	PUNCT
ejpam-3768	121	13	we	we	PRON
ejpam-3768	121	14	obtain	obtain	VERB
ejpam-3768	121	15	ϕ(t	ϕ(t	NUM
ejpam-3768	121	16	)	)	PUNCT
ejpam-3768	121	17	≤	≤	NOUN
ejpam-3768	121	18	(	(	PUNCT
ejpam-3768	121	19	(	(	PUNCT
ejpam-3768	121	20	m+	m+	NUM
ejpam-3768	121	21	1)ϕ(0	1)ϕ(0	NOUN
ejpam-3768	121	22	)	)	PUNCT
ejpam-3768	121	23	2	2	NUM
ejpam-3768	121	24	m	m	NOUN
ejpam-3768	121	25	m+1	m+1	NUM
ejpam-3768	121	26	(	(	PUNCT
ejpam-3768	121	27	m−	m−	PROPN
ejpam-3768	121	28	1)φ(0	1)φ(0	NOUN
ejpam-3768	121	29	)	)	PUNCT
ejpam-3768	121	30	)	)	PUNCT
ejpam-3768	122	1	m+1	m+1	PROPN
ejpam-3768	122	2	m−1	m−1	PROPN
ejpam-3768	122	3	(	(	PUNCT
ejpam-3768	122	4	t∗	t∗	NOUN
ejpam-3768	122	5	−	−	PROPN
ejpam-3768	123	1	t)−	t)−	PROPN
ejpam-3768	123	2	m+1	m+1	X
ejpam-3768	123	3	m−1	m−1	PROPN
ejpam-3768	123	4	,	,	PUNCT
ejpam-3768	123	5	(	(	PUNCT
ejpam-3768	123	6	2.17	2.17	NUM
ejpam-3768	123	7	)	)	PUNCT
ejpam-3768	123	8	which	which	PRON
ejpam-3768	123	9	implies	imply	VERB
ejpam-3768	123	10	that	that	SCONJ
ejpam-3768	123	11	the	the	DET
ejpam-3768	123	12	upper	upper	ADJ
ejpam-3768	123	13	estimate	estimate	NOUN
ejpam-3768	123	14	of	of	ADP
ejpam-3768	123	15	blow	blow	NOUN
ejpam-3768	123	16	-	-	PUNCT
ejpam-3768	123	17	up	up	ADP
ejpam-3768	123	18	rate	rate	NOUN
ejpam-3768	123	19	is	be	AUX
ejpam-3768	123	20	given	give	VERB
ejpam-3768	123	21	by	by	ADP
ejpam-3768	123	22	(	(	PUNCT
ejpam-3768	123	23	2.3	2.3	NUM
ejpam-3768	123	24	)	)	PUNCT
ejpam-3768	123	25	.	.	PUNCT
ejpam-3768	124	1	2.2	2.2	NUM
ejpam-3768	124	2	.	.	PUNCT
ejpam-3768	125	1	the	the	DET
ejpam-3768	125	2	second	second	ADJ
ejpam-3768	125	3	method	method	NOUN
ejpam-3768	125	4	we	we	PRON
ejpam-3768	125	5	first	first	ADV
ejpam-3768	125	6	assume	assume	VERB
ejpam-3768	125	7	that	that	SCONJ
ejpam-3768	125	8	(	(	PUNCT
ejpam-3768	125	9	f3	f3	ADJ
ejpam-3768	125	10	):	):	PUNCT
ejpam-3768	125	11	there	there	PRON
ejpam-3768	125	12	exists	exist	VERB
ejpam-3768	125	13	a	a	DET
ejpam-3768	125	14	positive	positive	ADJ
ejpam-3768	125	15	function	function	NOUN
ejpam-3768	125	16	g(θ	g(θ	VERB
ejpam-3768	125	17	)	)	PUNCT
ejpam-3768	125	18	such	such	ADJ
ejpam-3768	125	19	that∫	that∫	PROPN
ejpam-3768	125	20	ω	ω	PROPN
ejpam-3768	125	21	a(x)f(s)dx	a(x)f(s)dx	VERB
ejpam-3768	125	22	≥	≥	PROPN
ejpam-3768	125	23	c2	c2	PROPN
ejpam-3768	125	24	g	g	PROPN
ejpam-3768	126	1	[	[	X
ejpam-3768	126	2	∫	∫	PROPN
ejpam-3768	126	3	ω	ω	PROPN
ejpam-3768	126	4	sdx	sdx	PROPN
ejpam-3768	126	5	]	]	PUNCT
ejpam-3768	126	6	with	with	ADP
ejpam-3768	126	7	∫	∫	PROPN
ejpam-3768	127	1	+	+	PROPN
ejpam-3768	127	2	∞	∞	PROPN
ejpam-3768	127	3	0	0	NUM
ejpam-3768	127	4	dθ	dθ	PROPN
ejpam-3768	127	5	g(θ	g(θ	PROPN
ejpam-3768	127	6	)	)	PUNCT
ejpam-3768	127	7	<	<	X
ejpam-3768	128	1	+	+	PROPN
ejpam-3768	128	2	∞	∞	PROPN
ejpam-3768	128	3	,	,	PUNCT
ejpam-3768	128	4	for	for	ADP
ejpam-3768	128	5	any	any	DET
ejpam-3768	128	6	function	function	NOUN
ejpam-3768	128	7	s(x	s(x	PROPN
ejpam-3768	128	8	)	)	PUNCT
ejpam-3768	128	9	≥	≥	NOUN
ejpam-3768	128	10	0	0	NUM
ejpam-3768	128	11	.	.	PUNCT
ejpam-3768	129	1	then	then	ADV
ejpam-3768	129	2	,	,	PUNCT
ejpam-3768	129	3	we	we	PRON
ejpam-3768	129	4	define	define	VERB
ejpam-3768	129	5	the	the	DET
ejpam-3768	129	6	following	follow	VERB
ejpam-3768	129	7	auxiliary	auxiliary	ADJ
ejpam-3768	129	8	function	function	NOUN
ejpam-3768	129	9	ϕ1(t	ϕ1(t	PRON
ejpam-3768	129	10	)	)	PUNCT
ejpam-3768	129	11	=	=	SYM
ejpam-3768	129	12	∫	∫	PROPN
ejpam-3768	129	13	ω	ω	NUM
ejpam-3768	129	14	udx	udx	NOUN
ejpam-3768	129	15	.	.	PUNCT
ejpam-3768	130	1	(	(	PUNCT
ejpam-3768	130	2	2.18	2.18	NUM
ejpam-3768	130	3	)	)	PUNCT
ejpam-3768	130	4	theorem	theorem	NOUN
ejpam-3768	130	5	2	2	NUM
ejpam-3768	130	6	.	.	X
ejpam-3768	130	7	assume	assume	VERB
ejpam-3768	130	8	that	that	SCONJ
ejpam-3768	130	9	the	the	DET
ejpam-3768	130	10	conditions	condition	NOUN
ejpam-3768	130	11	(	(	PUNCT
ejpam-3768	130	12	f1	f1	NOUN
ejpam-3768	130	13	)	)	PUNCT
ejpam-3768	130	14	,	,	PUNCT
ejpam-3768	130	15	(	(	PUNCT
ejpam-3768	130	16	f3	f3	ADJ
ejpam-3768	130	17	)	)	PUNCT
ejpam-3768	130	18	,	,	PUNCT
ejpam-3768	130	19	(	(	PUNCT
ejpam-3768	130	20	a1	a1	NOUN
ejpam-3768	130	21	)	)	PUNCT
ejpam-3768	130	22	,	,	PUNCT
ejpam-3768	130	23	(	(	PUNCT
ejpam-3768	130	24	a2	a2	NOUN
ejpam-3768	130	25	)	)	PUNCT
ejpam-3768	130	26	hold	hold	NOUN
ejpam-3768	130	27	,	,	PUNCT
ejpam-3768	130	28	and	and	CCONJ
ejpam-3768	130	29	u	u	NOUN
ejpam-3768	130	30	is	be	AUX
ejpam-3768	130	31	a	a	DET
ejpam-3768	130	32	nonnegative	nonnegative	ADJ
ejpam-3768	130	33	solution	solution	NOUN
ejpam-3768	130	34	of	of	ADP
ejpam-3768	130	35	problem	problem	NOUN
ejpam-3768	130	36	(	(	PUNCT
ejpam-3768	130	37	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	130	38	)	)	PUNCT
ejpam-3768	130	39	.	.	PUNCT
ejpam-3768	131	1	then	then	ADV
ejpam-3768	131	2	,	,	PUNCT
ejpam-3768	131	3	we	we	PRON
ejpam-3768	131	4	conclude	conclude	VERB
ejpam-3768	131	5	that	that	SCONJ
ejpam-3768	131	6	the	the	DET
ejpam-3768	131	7	solution	solution	NOUN
ejpam-3768	131	8	u	u	NOUN
ejpam-3768	131	9	becomes	become	VERB
ejpam-3768	131	10	unbounded	unbounded	ADJ
ejpam-3768	131	11	in	in	ADP
ejpam-3768	131	12	l1−norm	l1−norm	NOUN
ejpam-3768	131	13	at	at	ADP
ejpam-3768	131	14	t	t	PROPN
ejpam-3768	131	15	=	=	SYM
ejpam-3768	131	16	t∗.	t∗.	PROPN
ejpam-3768	131	17	moreover	moreover	ADV
ejpam-3768	131	18	,	,	PUNCT
ejpam-3768	131	19	an	an	DET
ejpam-3768	131	20	upper	upper	ADJ
ejpam-3768	131	21	bound	bind	VERB
ejpam-3768	131	22	for	for	ADP
ejpam-3768	131	23	blow	blow	NOUN
ejpam-3768	131	24	-	-	PUNCT
ejpam-3768	131	25	up	up	ADP
ejpam-3768	131	26	time	time	NOUN
ejpam-3768	131	27	t∗	t∗	NOUN
ejpam-3768	131	28	is	be	AUX
ejpam-3768	131	29	given	give	VERB
ejpam-3768	131	30	by	by	ADP
ejpam-3768	131	31	t∗	t∗	NOUN
ejpam-3768	131	32	≤	≤	NUM
ejpam-3768	131	33	∫	∫	PROPN
ejpam-3768	132	1	+	+	NUM
ejpam-3768	132	2	∞	∞	PROPN
ejpam-3768	132	3	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	132	4	)	)	PUNCT
ejpam-3768	132	5	dθ	dθ	PROPN
ejpam-3768	132	6	g(θ	g(θ	PROPN
ejpam-3768	132	7	)	)	PUNCT
ejpam-3768	132	8	<	<	X
ejpam-3768	133	1	+	+	PROPN
ejpam-3768	133	2	∞	∞	PROPN
ejpam-3768	133	3	,	,	PUNCT
ejpam-3768	133	4	(	(	PUNCT
ejpam-3768	133	5	2.19	2.19	NUM
ejpam-3768	133	6	)	)	PUNCT
ejpam-3768	133	7	and	and	CCONJ
ejpam-3768	133	8	the	the	DET
ejpam-3768	133	9	upper	upper	ADJ
ejpam-3768	133	10	estimate	estimate	NOUN
ejpam-3768	133	11	of	of	ADP
ejpam-3768	133	12	blow	blow	NOUN
ejpam-3768	133	13	-	-	PUNCT
ejpam-3768	133	14	up	up	ADP
ejpam-3768	133	15	rate	rate	NOUN
ejpam-3768	133	16	can	can	AUX
ejpam-3768	133	17	be	be	AUX
ejpam-3768	133	18	given	give	VERB
ejpam-3768	133	19	by	by	ADP
ejpam-3768	133	20	‖u‖l1	‖u‖l1	NUM
ejpam-3768	133	21	≤	≤	NUM
ejpam-3768	133	22	y	y	PROPN
ejpam-3768	133	23	−1(t∗	−1(t∗	PROPN
ejpam-3768	133	24	−	−	PROPN
ejpam-3768	133	25	t	t	PROPN
ejpam-3768	133	26	)	)	PUNCT
ejpam-3768	133	27	,	,	PUNCT
ejpam-3768	133	28	(	(	PUNCT
ejpam-3768	133	29	2.20	2.20	NUM
ejpam-3768	133	30	)	)	PUNCT
ejpam-3768	133	31	where	where	SCONJ
ejpam-3768	133	32	the	the	DET
ejpam-3768	133	33	function	function	NOUN
ejpam-3768	133	34	y	y	PROPN
ejpam-3768	133	35	(	(	PUNCT
ejpam-3768	133	36	s	s	NOUN
ejpam-3768	133	37	)	)	PUNCT
ejpam-3768	133	38	:	:	PUNCT
ejpam-3768	134	1	=	=	PUNCT
ejpam-3768	134	2	∫	∫	PROPN
ejpam-3768	135	1	+	+	NUM
ejpam-3768	135	2	∞	∞	PROPN
ejpam-3768	135	3	s	s	PART
ejpam-3768	135	4	dθ	dθ	PROPN
ejpam-3768	135	5	g(θ	g(θ	PROPN
ejpam-3768	135	6	)	)	PUNCT
ejpam-3768	135	7	for	for	ADP
ejpam-3768	135	8	any	any	DET
ejpam-3768	135	9	function	function	NOUN
ejpam-3768	135	10	s(x	s(x	PROPN
ejpam-3768	135	11	)	)	PUNCT
ejpam-3768	135	12	≥	≥	NOUN
ejpam-3768	135	13	0	0	NUM
ejpam-3768	135	14	,	,	PUNCT
ejpam-3768	135	15	and	and	CCONJ
ejpam-3768	135	16	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	135	17	)	)	PUNCT
ejpam-3768	136	1	=	=	SYM
ejpam-3768	136	2	∫	∫	PROPN
ejpam-3768	136	3	ω	ω	NUM
ejpam-3768	136	4	gdx	gdx	PROPN
ejpam-3768	136	5	.	.	PUNCT
ejpam-3768	137	1	h.f	h.f	PROPN
ejpam-3768	137	2	.	.	PROPN
ejpam-3768	137	3	di	di	PROPN
ejpam-3768	137	4	,	,	PUNCT
ejpam-3768	137	5	l.	l.	PROPN
ejpam-3768	137	6	chen	chen	PROPN
ejpam-3768	137	7	and	and	CCONJ
ejpam-3768	137	8	z.f	z.f	PROPN
ejpam-3768	137	9	.	.	PROPN
ejpam-3768	137	10	song	song	PROPN
ejpam-3768	137	11	/	/	SYM
ejpam-3768	137	12	eur	eur	PROPN
ejpam-3768	137	13	.	.	PUNCT
ejpam-3768	138	1	j.	j.	PROPN
ejpam-3768	138	2	pure	pure	PROPN
ejpam-3768	138	3	appl	appl	PROPN
ejpam-3768	138	4	.	.	PROPN
ejpam-3768	138	5	math	math	PROPN
ejpam-3768	138	6	,	,	PUNCT
ejpam-3768	138	7	13	13	NUM
ejpam-3768	138	8	(	(	PUNCT
ejpam-3768	138	9	3	3	NUM
ejpam-3768	138	10	)	)	PUNCT
ejpam-3768	138	11	(	(	PUNCT
ejpam-3768	138	12	2020	2020	NUM
ejpam-3768	138	13	)	)	PUNCT
ejpam-3768	138	14	,	,	PUNCT
ejpam-3768	138	15	645	645	NUM
ejpam-3768	138	16	-	-	SYM
ejpam-3768	138	17	662	662	NUM
ejpam-3768	138	18	651	651	NUM
ejpam-3768	138	19	proof	proof	NOUN
ejpam-3768	138	20	.	.	PUNCT
ejpam-3768	139	1	integrating	integrate	VERB
ejpam-3768	139	2	the	the	DET
ejpam-3768	139	3	eq.(1.1	eq.(1.1	NOUN
ejpam-3768	139	4	)	)	PUNCT
ejpam-3768	139	5	by	by	ADP
ejpam-3768	139	6	parts	part	NOUN
ejpam-3768	139	7	,	,	PUNCT
ejpam-3768	139	8	from	from	ADP
ejpam-3768	139	9	the	the	DET
ejpam-3768	139	10	condition	condition	NOUN
ejpam-3768	139	11	(	(	PUNCT
ejpam-3768	139	12	f3	f3	ADJ
ejpam-3768	139	13	)	)	PUNCT
ejpam-3768	139	14	and	and	CCONJ
ejpam-3768	139	15	(	(	PUNCT
ejpam-3768	139	16	2.18	2.18	NUM
ejpam-3768	139	17	)	)	PUNCT
ejpam-3768	139	18	we	we	PRON
ejpam-3768	139	19	have∫	have∫	VERB
ejpam-3768	139	20	ω	ω	NUM
ejpam-3768	139	21	utdx	utdx	NOUN
ejpam-3768	139	22	=	=	SYM
ejpam-3768	139	23	∫	∫	PROPN
ejpam-3768	139	24	ω	ω	PROPN
ejpam-3768	139	25	a(x)f(u)dx	a(x)f(u)dx	PROPN
ejpam-3768	139	26	≥	≥	PROPN
ejpam-3768	139	27	c2	c2	PROPN
ejpam-3768	139	28	g	g	PROPN
ejpam-3768	140	1	[	[	X
ejpam-3768	140	2	∫	∫	PROPN
ejpam-3768	140	3	ω	ω	PROPN
ejpam-3768	140	4	udx	udx	PROPN
ejpam-3768	140	5	]	]	PUNCT
ejpam-3768	140	6	,	,	PUNCT
ejpam-3768	140	7	(	(	PUNCT
ejpam-3768	140	8	2.21	2.21	NUM
ejpam-3768	140	9	)	)	PUNCT
ejpam-3768	140	10	which	which	PRON
ejpam-3768	140	11	means	mean	VERB
ejpam-3768	140	12	that	that	SCONJ
ejpam-3768	140	13	ϕ′1(t	ϕ′1(t	PROPN
ejpam-3768	140	14	)	)	PUNCT
ejpam-3768	140	15	≥	≥	PROPN
ejpam-3768	141	1	c2	c2	PROPN
ejpam-3768	141	2	g	g	PROPN
ejpam-3768	141	3	[	[	X
ejpam-3768	141	4	ϕ1(t	ϕ1(t	X
ejpam-3768	141	5	)	)	PUNCT
ejpam-3768	141	6	]	]	PUNCT
ejpam-3768	142	1	>	>	X
ejpam-3768	142	2	0	0	X
ejpam-3768	142	3	.	.	PUNCT
ejpam-3768	143	1	(	(	PUNCT
ejpam-3768	143	2	2.22	2.22	NUM
ejpam-3768	143	3	)	)	PUNCT
ejpam-3768	143	4	here	here	ADV
ejpam-3768	143	5	,	,	PUNCT
ejpam-3768	143	6	we	we	PRON
ejpam-3768	143	7	have	have	AUX
ejpam-3768	143	8	used	use	VERB
ejpam-3768	143	9	the	the	DET
ejpam-3768	143	10	fact	fact	NOUN
ejpam-3768	143	11	that	that	SCONJ
ejpam-3768	143	12	u(x	u(x	NOUN
ejpam-3768	143	13	,	,	PUNCT
ejpam-3768	143	14	t	t	PROPN
ejpam-3768	143	15	)	)	PUNCT
ejpam-3768	143	16	=	=	SYM
ejpam-3768	143	17	0	0	PUNCT
ejpam-3768	144	1	(	(	PUNCT
ejpam-3768	144	2	or	or	CCONJ
ejpam-3768	144	3	∂u	∂u	PROPN
ejpam-3768	144	4	∂ν	∂ν	X
ejpam-3768	144	5	=	=	PUNCT
ejpam-3768	144	6	0	0	NUM
ejpam-3768	144	7	)	)	PUNCT
ejpam-3768	144	8	on	on	ADP
ejpam-3768	144	9	∂ω	∂ω	PROPN
ejpam-3768	144	10	.	.	PUNCT
ejpam-3768	145	1	it	it	PRON
ejpam-3768	145	2	then	then	ADV
ejpam-3768	145	3	follows	follow	VERB
ejpam-3768	145	4	from	from	ADP
ejpam-3768	145	5	(	(	PUNCT
ejpam-3768	145	6	2.22	2.22	NUM
ejpam-3768	145	7	)	)	PUNCT
ejpam-3768	145	8	that	that	PRON
ejpam-3768	145	9	ϕ1(t	ϕ1(t	X
ejpam-3768	145	10	)	)	PUNCT
ejpam-3768	145	11	is	be	AUX
ejpam-3768	145	12	a	a	DET
ejpam-3768	145	13	increasing	increase	VERB
ejpam-3768	145	14	function	function	NOUN
ejpam-3768	145	15	,	,	PUNCT
ejpam-3768	145	16	so	so	ADV
ejpam-3768	145	17	we	we	PRON
ejpam-3768	145	18	have	have	VERB
ejpam-3768	145	19	ϕ1(t	ϕ1(t	NUM
ejpam-3768	145	20	)	)	PUNCT
ejpam-3768	145	21	>	>	PUNCT
ejpam-3768	145	22	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	145	23	)	)	PUNCT
ejpam-3768	146	1	=	=	SYM
ejpam-3768	146	2	∫	∫	PROPN
ejpam-3768	146	3	ω	ω	PROPN
ejpam-3768	146	4	g(x)dx	g(x)dx	VERB
ejpam-3768	146	5	≥	≥	NOUN
ejpam-3768	146	6	0	0	NUM
ejpam-3768	146	7	.	.	PUNCT
ejpam-3768	147	1	(	(	PUNCT
ejpam-3768	147	2	2.23	2.23	NUM
ejpam-3768	147	3	)	)	PUNCT
ejpam-3768	147	4	integrating	integrating	NOUN
ejpam-3768	147	5	(	(	PUNCT
ejpam-3768	147	6	2.22	2.22	NUM
ejpam-3768	147	7	)	)	PUNCT
ejpam-3768	147	8	from	from	ADP
ejpam-3768	147	9	0	0	NUM
ejpam-3768	147	10	to	to	ADP
ejpam-3768	147	11	t	t	NOUN
ejpam-3768	147	12	and	and	CCONJ
ejpam-3768	147	13	using	use	VERB
ejpam-3768	147	14	(	(	PUNCT
ejpam-3768	147	15	2.23	2.23	NUM
ejpam-3768	147	16	)	)	PUNCT
ejpam-3768	147	17	,	,	PUNCT
ejpam-3768	147	18	(	(	PUNCT
ejpam-3768	147	19	f3	f3	ADJ
ejpam-3768	147	20	)	)	PUNCT
ejpam-3768	147	21	,	,	PUNCT
ejpam-3768	147	22	we	we	PRON
ejpam-3768	147	23	discover	discover	VERB
ejpam-3768	147	24	t	t	PROPN
ejpam-3768	147	25	≤	≤	NUM
ejpam-3768	148	1	∫	∫	PROPN
ejpam-3768	149	1	ϕ1(t	ϕ1(t	PART
ejpam-3768	150	1	)	)	PUNCT
ejpam-3768	150	2	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	150	3	)	)	PUNCT
ejpam-3768	151	1	dθ	dθ	PROPN
ejpam-3768	151	2	g(θ	g(θ	PROPN
ejpam-3768	151	3	)	)	PUNCT
ejpam-3768	151	4	≤	≤	NUM
ejpam-3768	151	5	∫	∫	PROPN
ejpam-3768	152	1	+	+	NUM
ejpam-3768	152	2	∞	∞	PROPN
ejpam-3768	152	3	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	152	4	)	)	PUNCT
ejpam-3768	152	5	dθ	dθ	PROPN
ejpam-3768	152	6	g(θ	g(θ	PROPN
ejpam-3768	152	7	)	)	PUNCT
ejpam-3768	152	8	<	<	X
ejpam-3768	153	1	+	+	PROPN
ejpam-3768	153	2	∞.	∞.	PROPN
ejpam-3768	153	3	(	(	PUNCT
ejpam-3768	153	4	2.24	2.24	NUM
ejpam-3768	153	5	)	)	PUNCT
ejpam-3768	153	6	obviously	obviously	ADV
ejpam-3768	153	7	,	,	PUNCT
ejpam-3768	153	8	(	(	PUNCT
ejpam-3768	153	9	2.24	2.24	NUM
ejpam-3768	153	10	)	)	PUNCT
ejpam-3768	153	11	can	can	AUX
ejpam-3768	153	12	not	not	PART
ejpam-3768	153	13	hold	hold	VERB
ejpam-3768	153	14	for	for	ADP
ejpam-3768	153	15	all	all	DET
ejpam-3768	153	16	time	time	NOUN
ejpam-3768	153	17	t.	t.	PROPN
ejpam-3768	153	18	consequently	consequently	ADV
ejpam-3768	153	19	,	,	PUNCT
ejpam-3768	153	20	we	we	PRON
ejpam-3768	153	21	can	can	AUX
ejpam-3768	153	22	derive	derive	VERB
ejpam-3768	153	23	an	an	DET
ejpam-3768	153	24	upper	upper	ADJ
ejpam-3768	153	25	bound	bind	VERB
ejpam-3768	153	26	t∗	t∗	NOUN
ejpam-3768	153	27	such	such	ADJ
ejpam-3768	153	28	that	that	DET
ejpam-3768	153	29	t∗	t∗	PROPN
ejpam-3768	153	30	≤	≤	X
ejpam-3768	153	31	∫	∫	PROPN
ejpam-3768	154	1	+	+	NUM
ejpam-3768	154	2	∞	∞	PROPN
ejpam-3768	154	3	ϕ1(0	ϕ1(0	PROPN
ejpam-3768	154	4	)	)	PUNCT
ejpam-3768	154	5	dθ	dθ	PROPN
ejpam-3768	154	6	g(θ	g(θ	PROPN
ejpam-3768	154	7	)	)	PUNCT
ejpam-3768	154	8	<	<	X
ejpam-3768	155	1	+	+	PROPN
ejpam-3768	155	2	∞	∞	PROPN
ejpam-3768	155	3	,	,	PUNCT
ejpam-3768	155	4	and	and	CCONJ
ejpam-3768	155	5	lim	lim	PROPN
ejpam-3768	155	6	t→t∗	t→t∗	PRON
ejpam-3768	155	7	ϕ1(t	ϕ1(t	X
ejpam-3768	155	8	)	)	PUNCT
ejpam-3768	156	1	=	=	PUNCT
ejpam-3768	157	1	+	+	NUM
ejpam-3768	157	2	∞	∞	PROPN
ejpam-3768	157	3	,	,	PUNCT
ejpam-3768	157	4	(	(	PUNCT
ejpam-3768	157	5	2.25	2.25	NUM
ejpam-3768	157	6	)	)	PUNCT
ejpam-3768	157	7	where	where	SCONJ
ejpam-3768	157	8	(	(	PUNCT
ejpam-3768	157	9	0	0	NUM
ejpam-3768	157	10	,	,	PUNCT
ejpam-3768	157	11	t∗	t∗	PROPN
ejpam-3768	157	12	)	)	PUNCT
ejpam-3768	157	13	is	be	AUX
ejpam-3768	157	14	the	the	DET
ejpam-3768	157	15	interval	interval	NOUN
ejpam-3768	157	16	of	of	ADP
ejpam-3768	157	17	existence	existence	NOUN
ejpam-3768	157	18	of	of	ADP
ejpam-3768	157	19	the	the	DET
ejpam-3768	157	20	solutions	solution	NOUN
ejpam-3768	157	21	u	u	NOUN
ejpam-3768	157	22	in	in	ADP
ejpam-3768	157	23	l1−norm	l1−norm	PROPN
ejpam-3768	157	24	.	.	PUNCT
ejpam-3768	158	1	in	in	ADP
ejpam-3768	158	2	fact	fact	NOUN
ejpam-3768	158	3	,	,	PUNCT
ejpam-3768	158	4	if	if	SCONJ
ejpam-3768	158	5	the	the	DET
ejpam-3768	158	6	equality	equality	NOUN
ejpam-3768	158	7	(	(	PUNCT
ejpam-3768	158	8	2.25	2.25	NUM
ejpam-3768	158	9	)	)	PUNCT
ejpam-3768	158	10	does	do	AUX
ejpam-3768	158	11	n’t	not	PART
ejpam-3768	158	12	hold	hold	VERB
ejpam-3768	158	13	,	,	PUNCT
ejpam-3768	158	14	then	then	ADV
ejpam-3768	158	15	there	there	PRON
ejpam-3768	158	16	exists	exist	VERB
ejpam-3768	158	17	a	a	DET
ejpam-3768	158	18	time	time	NOUN
ejpam-3768	158	19	t1	t1	NOUN
ejpam-3768	158	20	>	>	X
ejpam-3768	158	21	t∗	t∗	NOUN
ejpam-3768	159	1	such	such	ADJ
ejpam-3768	159	2	that	that	DET
ejpam-3768	159	3	ϕ1(t∗	ϕ1(t∗	NUM
ejpam-3768	159	4	)	)	PUNCT
ejpam-3768	159	5	<	<	X
ejpam-3768	159	6	ϕ1(t1	ϕ1(t1	INTJ
ejpam-3768	159	7	)	)	PUNCT
ejpam-3768	159	8	<	<	X
ejpam-3768	160	1	+	+	X
ejpam-3768	160	2	∞	∞	NUM
ejpam-3768	160	3	and	and	CCONJ
ejpam-3768	160	4	t1	t1	NOUN
ejpam-3768	160	5	satisfies	satisfy	VERB
ejpam-3768	160	6	the	the	DET
ejpam-3768	160	7	inequality	inequality	NOUN
ejpam-3768	160	8	(	(	PUNCT
ejpam-3768	160	9	2.23),(2.24	2.23),(2.24	NUM
ejpam-3768	160	10	)	)	PUNCT
ejpam-3768	160	11	,	,	PUNCT
ejpam-3768	160	12	which	which	PRON
ejpam-3768	160	13	contradict	contradict	VERB
ejpam-3768	160	14	the	the	DET
ejpam-3768	160	15	maximum	maximum	ADJ
ejpam-3768	160	16	existence	existence	NOUN
ejpam-3768	160	17	of	of	ADP
ejpam-3768	160	18	t∗.	t∗.	PROPN
ejpam-3768	160	19	furthermore	furthermore	ADV
ejpam-3768	160	20	,	,	PUNCT
ejpam-3768	160	21	integrating	integrate	VERB
ejpam-3768	160	22	(	(	PUNCT
ejpam-3768	160	23	2.22	2.22	NUM
ejpam-3768	160	24	)	)	PUNCT
ejpam-3768	160	25	from	from	ADP
ejpam-3768	160	26	t	t	PROPN
ejpam-3768	160	27	to	to	ADP
ejpam-3768	160	28	t∗	t∗	PROPN
ejpam-3768	160	29	,	,	PUNCT
ejpam-3768	160	30	it	it	PRON
ejpam-3768	160	31	follows	follow	VERB
ejpam-3768	160	32	that	that	DET
ejpam-3768	160	33	t∗	t∗	NOUN
ejpam-3768	161	1	−	−	PROPN
ejpam-3768	161	2	t	t	PROPN
ejpam-3768	161	3	≤	≤	NUM
ejpam-3768	161	4	∫	∫	PROPN
ejpam-3768	162	1	+	+	NUM
ejpam-3768	162	2	∞	∞	PROPN
ejpam-3768	162	3	ϕ1(t	ϕ1(t	NUM
ejpam-3768	162	4	)	)	PUNCT
ejpam-3768	162	5	dθ	dθ	PROPN
ejpam-3768	162	6	g(θ	g(θ	PROPN
ejpam-3768	162	7	)	)	PUNCT
ejpam-3768	162	8	:	:	PUNCT
ejpam-3768	162	9	=	=	SYM
ejpam-3768	162	10	y	y	PROPN
ejpam-3768	162	11	(	(	PUNCT
ejpam-3768	162	12	ϕ1(t	ϕ1(t	NOUN
ejpam-3768	162	13	)	)	PUNCT
ejpam-3768	162	14	)	)	PUNCT
ejpam-3768	162	15	.	.	PUNCT
ejpam-3768	163	1	(	(	PUNCT
ejpam-3768	163	2	2.26	2.26	NUM
ejpam-3768	163	3	)	)	PUNCT
ejpam-3768	163	4	we	we	PRON
ejpam-3768	163	5	note	note	VERB
ejpam-3768	163	6	that	that	SCONJ
ejpam-3768	163	7	y	y	PROPN
ejpam-3768	163	8	is	be	AUX
ejpam-3768	163	9	a	a	DET
ejpam-3768	163	10	decreasing	decrease	VERB
ejpam-3768	163	11	function	function	NOUN
ejpam-3768	163	12	,	,	PUNCT
ejpam-3768	163	13	which	which	PRON
ejpam-3768	163	14	means	mean	VERB
ejpam-3768	163	15	its	its	PRON
ejpam-3768	163	16	inverse	inverse	NOUN
ejpam-3768	163	17	function	function	NOUN
ejpam-3768	163	18	y	y	PROPN
ejpam-3768	163	19	−1	−1	NOUN
ejpam-3768	163	20	exists	exist	VERB
ejpam-3768	163	21	and	and	CCONJ
ejpam-3768	163	22	is	be	AUX
ejpam-3768	163	23	also	also	ADV
ejpam-3768	163	24	a	a	DET
ejpam-3768	163	25	decreasing	decrease	VERB
ejpam-3768	163	26	function	function	NOUN
ejpam-3768	163	27	.	.	PUNCT
ejpam-3768	164	1	therefore	therefore	ADV
ejpam-3768	164	2	,	,	PUNCT
ejpam-3768	164	3	we	we	PRON
ejpam-3768	164	4	have	have	VERB
ejpam-3768	164	5	ϕ1(t	ϕ1(t	NUM
ejpam-3768	164	6	)	)	PUNCT
ejpam-3768	164	7	≤	≤	NUM
ejpam-3768	164	8	y	y	PROPN
ejpam-3768	164	9	−1(t∗	−1(t∗	PROPN
ejpam-3768	164	10	−	−	PROPN
ejpam-3768	164	11	t	t	PROPN
ejpam-3768	164	12	)	)	PUNCT
ejpam-3768	164	13	,	,	PUNCT
ejpam-3768	164	14	(	(	PUNCT
ejpam-3768	164	15	2.27	2.27	NUM
ejpam-3768	164	16	)	)	PUNCT
ejpam-3768	164	17	which	which	PRON
ejpam-3768	164	18	implies	imply	VERB
ejpam-3768	164	19	that	that	SCONJ
ejpam-3768	164	20	the	the	DET
ejpam-3768	164	21	estimate	estimate	NOUN
ejpam-3768	164	22	(	(	PUNCT
ejpam-3768	164	23	2.20	2.20	NUM
ejpam-3768	164	24	)	)	PUNCT
ejpam-3768	164	25	of	of	ADP
ejpam-3768	164	26	blow	blow	NOUN
ejpam-3768	164	27	-	-	PUNCT
ejpam-3768	164	28	up	up	ADP
ejpam-3768	164	29	rate	rate	NOUN
ejpam-3768	164	30	holds	hold	NOUN
ejpam-3768	164	31	.	.	PUNCT
ejpam-3768	165	1	remark	remark	PROPN
ejpam-3768	165	2	1	1	NUM
ejpam-3768	165	3	.	.	PUNCT
ejpam-3768	166	1	this	this	DET
ejpam-3768	166	2	result	result	NOUN
ejpam-3768	166	3	can	can	AUX
ejpam-3768	166	4	be	be	AUX
ejpam-3768	166	5	generalized	generalize	VERB
ejpam-3768	166	6	to	to	ADP
ejpam-3768	166	7	the	the	DET
ejpam-3768	166	8	case	case	NOUN
ejpam-3768	166	9	of	of	ADP
ejpam-3768	166	10	problem	problem	NOUN
ejpam-3768	166	11	(	(	PUNCT
ejpam-3768	166	12	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	166	13	)	)	PUNCT
ejpam-3768	166	14	subject	subject	NOUN
ejpam-3768	166	15	to	to	ADP
ejpam-3768	166	16	∂u	∂u	PROPN
ejpam-3768	166	17	∂ν	∂ν	X
ejpam-3768	167	1	=	=	PUNCT
ejpam-3768	167	2	b(x	b(x	PROPN
ejpam-3768	167	3	,	,	PUNCT
ejpam-3768	167	4	t	t	PROPN
ejpam-3768	167	5	)	)	PUNCT
ejpam-3768	167	6	≥	≥	NOUN
ejpam-3768	167	7	0	0	NUM
ejpam-3768	167	8	.	.	PUNCT
ejpam-3768	168	1	in	in	ADP
ejpam-3768	168	2	this	this	DET
ejpam-3768	168	3	case	case	NOUN
ejpam-3768	168	4	,	,	PUNCT
ejpam-3768	168	5	it	it	PRON
ejpam-3768	168	6	follows	follow	VERB
ejpam-3768	168	7	that	that	SCONJ
ejpam-3768	168	8	ϕ′1(t	ϕ′1(t	PROPN
ejpam-3768	168	9	)	)	PUNCT
ejpam-3768	168	10	≥	≥	PROPN
ejpam-3768	169	1	m	m	VERB
ejpam-3768	169	2	∫	∫	PROPN
ejpam-3768	169	3	∂ω	∂ω	PROPN
ejpam-3768	169	4	um−1b(x	um−1b(x	NOUN
ejpam-3768	169	5	,	,	PUNCT
ejpam-3768	169	6	t)ds+	t)ds+	PROPN
ejpam-3768	169	7	c2	c2	PROPN
ejpam-3768	169	8	g	g	PROPN
ejpam-3768	169	9	[	[	X
ejpam-3768	169	10	ϕ1(t	ϕ1(t	X
ejpam-3768	169	11	)	)	PUNCT
ejpam-3768	169	12	]	]	PUNCT
ejpam-3768	170	1	>	>	X
ejpam-3768	170	2	0	0	X
ejpam-3768	170	3	.	.	PUNCT
ejpam-3768	171	1	(	(	PUNCT
ejpam-3768	171	2	2.28	2.28	NUM
ejpam-3768	171	3	)	)	PUNCT
ejpam-3768	171	4	we	we	PRON
ejpam-3768	171	5	also	also	ADV
ejpam-3768	171	6	can	can	AUX
ejpam-3768	171	7	obtain	obtain	VERB
ejpam-3768	171	8	the	the	DET
ejpam-3768	171	9	inequalities	inequality	NOUN
ejpam-3768	171	10	(	(	PUNCT
ejpam-3768	171	11	2.19	2.19	NUM
ejpam-3768	171	12	)	)	PUNCT
ejpam-3768	171	13	and	and	CCONJ
ejpam-3768	171	14	(	(	PUNCT
ejpam-3768	171	15	2.20	2.20	NUM
ejpam-3768	171	16	)	)	PUNCT
ejpam-3768	171	17	.	.	PUNCT
ejpam-3768	172	1	h.f	h.f	PROPN
ejpam-3768	172	2	.	.	PROPN
ejpam-3768	172	3	di	di	PROPN
ejpam-3768	172	4	,	,	PUNCT
ejpam-3768	172	5	l.	l.	PROPN
ejpam-3768	172	6	chen	chen	PROPN
ejpam-3768	172	7	and	and	CCONJ
ejpam-3768	172	8	z.f	z.f	PROPN
ejpam-3768	172	9	.	.	PROPN
ejpam-3768	172	10	song	song	PROPN
ejpam-3768	172	11	/	/	SYM
ejpam-3768	172	12	eur	eur	PROPN
ejpam-3768	172	13	.	.	PUNCT
ejpam-3768	173	1	j.	j.	PROPN
ejpam-3768	173	2	pure	pure	PROPN
ejpam-3768	173	3	appl	appl	PROPN
ejpam-3768	173	4	.	.	PROPN
ejpam-3768	173	5	math	math	PROPN
ejpam-3768	173	6	,	,	PUNCT
ejpam-3768	173	7	13	13	NUM
ejpam-3768	173	8	(	(	PUNCT
ejpam-3768	173	9	3	3	NUM
ejpam-3768	173	10	)	)	PUNCT
ejpam-3768	173	11	(	(	PUNCT
ejpam-3768	173	12	2020	2020	NUM
ejpam-3768	173	13	)	)	PUNCT
ejpam-3768	173	14	,	,	PUNCT
ejpam-3768	173	15	645	645	NUM
ejpam-3768	173	16	-	-	SYM
ejpam-3768	173	17	662	662	NUM
ejpam-3768	173	18	652	652	NUM
ejpam-3768	173	19	3	3	NUM
ejpam-3768	173	20	.	.	PUNCT
ejpam-3768	174	1	lower	low	ADJ
ejpam-3768	174	2	estimates	estimate	NOUN
ejpam-3768	174	3	for	for	ADP
ejpam-3768	174	4	blow	blow	NOUN
ejpam-3768	174	5	-	-	PUNCT
ejpam-3768	174	6	up	up	ADP
ejpam-3768	174	7	time	time	NOUN
ejpam-3768	174	8	and	and	CCONJ
ejpam-3768	174	9	blow	blow	NOUN
ejpam-3768	174	10	-	-	PUNCT
ejpam-3768	174	11	up	up	ADP
ejpam-3768	174	12	rate	rate	NOUN
ejpam-3768	174	13	in	in	ADP
ejpam-3768	174	14	this	this	DET
ejpam-3768	174	15	section	section	NOUN
ejpam-3768	174	16	,	,	PUNCT
ejpam-3768	174	17	we	we	PRON
ejpam-3768	174	18	will	will	AUX
ejpam-3768	174	19	give	give	VERB
ejpam-3768	174	20	three	three	NUM
ejpam-3768	174	21	methods	method	NOUN
ejpam-3768	174	22	to	to	PART
ejpam-3768	174	23	establish	establish	VERB
ejpam-3768	174	24	the	the	DET
ejpam-3768	174	25	lower	low	ADJ
ejpam-3768	174	26	bounds	bound	NOUN
ejpam-3768	174	27	for	for	ADP
ejpam-3768	174	28	blow	blow	NOUN
ejpam-3768	174	29	-	-	PUNCT
ejpam-3768	174	30	up	up	ADP
ejpam-3768	174	31	time	time	NOUN
ejpam-3768	174	32	and	and	CCONJ
ejpam-3768	174	33	blow	blow	NOUN
ejpam-3768	174	34	-	-	PUNCT
ejpam-3768	174	35	up	up	ADP
ejpam-3768	174	36	rate	rate	NOUN
ejpam-3768	174	37	of	of	ADP
ejpam-3768	174	38	the	the	DET
ejpam-3768	174	39	solution	solution	NOUN
ejpam-3768	174	40	to	to	ADP
ejpam-3768	174	41	problem	problem	NOUN
ejpam-3768	174	42	(	(	PUNCT
ejpam-3768	174	43	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	174	44	)	)	PUNCT
ejpam-3768	174	45	.	.	PUNCT
ejpam-3768	175	1	3.1	3.1	NUM
ejpam-3768	175	2	.	.	PUNCT
ejpam-3768	176	1	the	the	DET
ejpam-3768	176	2	first	first	ADJ
ejpam-3768	176	3	method	method	NOUN
ejpam-3768	176	4	firstly	firstly	ADV
ejpam-3768	176	5	,	,	PUNCT
ejpam-3768	176	6	let	let	VERB
ejpam-3768	176	7	us	we	PRON
ejpam-3768	176	8	assume	assume	VERB
ejpam-3768	176	9	that	that	SCONJ
ejpam-3768	176	10	(	(	PUNCT
ejpam-3768	176	11	f4	f4	NUM
ejpam-3768	176	12	):	):	PUNCT
ejpam-3768	176	13	there	there	PRON
ejpam-3768	176	14	exists	exist	VERB
ejpam-3768	176	15	positive	positive	ADJ
ejpam-3768	176	16	constants	constant	NOUN
ejpam-3768	176	17	c3	c3	PROPN
ejpam-3768	176	18	,	,	PUNCT
ejpam-3768	176	19	c4	c4	VERB
ejpam-3768	176	20	such	such	ADJ
ejpam-3768	176	21	that	that	SCONJ
ejpam-3768	176	22	a(x)f(s	a(x)f(	NOUN
ejpam-3768	176	23	)	)	PUNCT
ejpam-3768	176	24	≤	≤	NOUN
ejpam-3768	176	25	c3	c3	NOUN
ejpam-3768	176	26	+	+	CCONJ
ejpam-3768	176	27	c4s	c4s	PROPN
ejpam-3768	176	28	l+1	l+1	ADV
ejpam-3768	176	29	,	,	PUNCT
ejpam-3768	176	30	for	for	ADP
ejpam-3768	176	31	any	any	DET
ejpam-3768	176	32	function	function	NOUN
ejpam-3768	176	33	s(x	s(x	PROPN
ejpam-3768	176	34	)	)	PUNCT
ejpam-3768	176	35	≥	≥	NOUN
ejpam-3768	176	36	0	0	NUM
ejpam-3768	176	37	,	,	PUNCT
ejpam-3768	176	38	where	where	SCONJ
ejpam-3768	176	39	0	0	NUM
ejpam-3768	176	40	<	<	X
ejpam-3768	176	41	l	l	X
ejpam-3768	176	42	≤	≤	NUM
ejpam-3768	176	43	2nm−(n−2)(m+1	2nm−(n−2)(m+1	NUM
ejpam-3768	176	44	)	)	PUNCT
ejpam-3768	176	45	n	n	NOUN
ejpam-3768	176	46	.	.	PUNCT
ejpam-3768	177	1	and	and	CCONJ
ejpam-3768	177	2	then	then	ADV
ejpam-3768	177	3	we	we	PRON
ejpam-3768	177	4	introduce	introduce	VERB
ejpam-3768	177	5	the	the	DET
ejpam-3768	177	6	auxiliary	auxiliary	ADJ
ejpam-3768	177	7	function	function	NOUN
ejpam-3768	177	8	ϕ(t	ϕ(t	NUM
ejpam-3768	177	9	)	)	PUNCT
ejpam-3768	178	1	=	=	SYM
ejpam-3768	179	1	∫	∫	PROPN
ejpam-3768	179	2	ω	ω	NUM
ejpam-3768	179	3	u	u	NOUN
ejpam-3768	179	4	m+1dx	m+1dx	PROPN
ejpam-3768	179	5	as	as	ADP
ejpam-3768	179	6	(	(	PUNCT
ejpam-3768	179	7	2.1	2.1	NUM
ejpam-3768	179	8	)	)	PUNCT
ejpam-3768	179	9	.	.	PUNCT
ejpam-3768	180	1	next	next	ADV
ejpam-3768	180	2	,	,	PUNCT
ejpam-3768	180	3	we	we	PRON
ejpam-3768	180	4	shall	shall	AUX
ejpam-3768	180	5	state	state	NOUN
ejpam-3768	180	6	and	and	CCONJ
ejpam-3768	180	7	prove	prove	VERB
ejpam-3768	180	8	the	the	DET
ejpam-3768	180	9	main	main	ADJ
ejpam-3768	180	10	results	result	NOUN
ejpam-3768	180	11	of	of	ADP
ejpam-3768	180	12	this	this	DET
ejpam-3768	180	13	subsection	subsection	NOUN
ejpam-3768	180	14	as	as	SCONJ
ejpam-3768	180	15	follows	follow	VERB
ejpam-3768	180	16	:	:	PUNCT
ejpam-3768	180	17	theorem	theorem	NOUN
ejpam-3768	180	18	3	3	X
ejpam-3768	180	19	.	.	PUNCT
ejpam-3768	180	20	assume	assume	VERB
ejpam-3768	180	21	that	that	SCONJ
ejpam-3768	180	22	the	the	DET
ejpam-3768	180	23	conditions	condition	NOUN
ejpam-3768	180	24	(	(	PUNCT
ejpam-3768	180	25	f1	f1	NOUN
ejpam-3768	180	26	)	)	PUNCT
ejpam-3768	180	27	,	,	PUNCT
ejpam-3768	180	28	(	(	PUNCT
ejpam-3768	180	29	f4	f4	NOUN
ejpam-3768	180	30	)	)	PUNCT
ejpam-3768	180	31	,	,	PUNCT
ejpam-3768	180	32	(	(	PUNCT
ejpam-3768	180	33	a1	a1	NOUN
ejpam-3768	180	34	)	)	PUNCT
ejpam-3768	180	35	,	,	PUNCT
ejpam-3768	180	36	(	(	PUNCT
ejpam-3768	180	37	a2	a2	NOUN
ejpam-3768	180	38	)	)	PUNCT
ejpam-3768	180	39	hold	hold	NOUN
ejpam-3768	180	40	,	,	PUNCT
ejpam-3768	180	41	and	and	CCONJ
ejpam-3768	180	42	u	u	NOUN
ejpam-3768	180	43	is	be	AUX
ejpam-3768	180	44	a	a	DET
ejpam-3768	180	45	nonnegative	nonnegative	ADJ
ejpam-3768	180	46	solution	solution	NOUN
ejpam-3768	180	47	of	of	ADP
ejpam-3768	180	48	problem	problem	NOUN
ejpam-3768	180	49	(	(	PUNCT
ejpam-3768	180	50	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	180	51	)	)	PUNCT
ejpam-3768	180	52	which	which	PRON
ejpam-3768	180	53	becomes	become	VERB
ejpam-3768	180	54	unbounded	unbounded	ADJ
ejpam-3768	180	55	in	in	ADP
ejpam-3768	180	56	lm+1−norm	lm+1−norm	PROPN
ejpam-3768	180	57	at	at	ADP
ejpam-3768	180	58	t	t	PROPN
ejpam-3768	180	59	=	=	SYM
ejpam-3768	180	60	t∗.	t∗.	PROPN
ejpam-3768	180	61	then	then	ADV
ejpam-3768	180	62	,	,	PUNCT
ejpam-3768	180	63	we	we	PRON
ejpam-3768	180	64	conclude	conclude	VERB
ejpam-3768	180	65	that	that	SCONJ
ejpam-3768	180	66	a	a	PRON
ejpam-3768	180	67	lower	lower	ADV
ejpam-3768	180	68	bound	bind	VERB
ejpam-3768	180	69	for	for	ADP
ejpam-3768	180	70	blow	blow	NOUN
ejpam-3768	180	71	-	-	PUNCT
ejpam-3768	180	72	up	up	ADP
ejpam-3768	180	73	time	time	NOUN
ejpam-3768	180	74	t∗	t∗	NOUN
ejpam-3768	180	75	is	be	AUX
ejpam-3768	180	76	given	give	VERB
ejpam-3768	180	77	by	by	ADP
ejpam-3768	180	78	t∗	t∗	PROPN
ejpam-3768	180	79	≥	≥	NUM
ejpam-3768	180	80	∫	∫	PROPN
ejpam-3768	181	1	+	+	NUM
ejpam-3768	181	2	∞	∞	PROPN
ejpam-3768	181	3	ϕ(0	ϕ(0	PROPN
ejpam-3768	181	4	)	)	PUNCT
ejpam-3768	181	5	dη	dη	PART
ejpam-3768	182	1	k1η	k1η	NOUN
ejpam-3768	182	2	+	+	CCONJ
ejpam-3768	182	3	k2η	k2η	PROPN
ejpam-3768	182	4	1	1	NUM
ejpam-3768	182	5	+	+	NUM
ejpam-3768	182	6	2	2	NUM
ejpam-3768	182	7	nε2	nε2	X
ejpam-3768	182	8	.	.	PUNCT
ejpam-3768	183	1	(	(	PUNCT
ejpam-3768	183	2	3.1	3.1	NUM
ejpam-3768	183	3	)	)	PUNCT
ejpam-3768	183	4	and	and	CCONJ
ejpam-3768	183	5	the	the	DET
ejpam-3768	183	6	lower	low	ADJ
ejpam-3768	183	7	estimate	estimate	NOUN
ejpam-3768	183	8	of	of	ADP
ejpam-3768	183	9	blow	blow	NOUN
ejpam-3768	183	10	-	-	PUNCT
ejpam-3768	183	11	up	up	ADP
ejpam-3768	183	12	rate	rate	NOUN
ejpam-3768	183	13	is	be	AUX
ejpam-3768	183	14	‖u‖m+1	‖u‖m+1	PROPN
ejpam-3768	183	15	≥	≥	NUM
ejpam-3768	183	16	(	(	PUNCT
ejpam-3768	183	17	4k2	4k2	NUM
ejpam-3768	183	18	nε2	nε2	NOUN
ejpam-3768	183	19	)	)	PUNCT
ejpam-3768	183	20	−	−	PROPN
ejpam-3768	183	21	nε2	nε2	PROPN
ejpam-3768	183	22	2(m+1	2(m+1	NUM
ejpam-3768	183	23	)	)	PUNCT
ejpam-3768	183	24	(	(	PUNCT
ejpam-3768	183	25	t∗	t∗	NOUN
ejpam-3768	183	26	−	−	PROPN
ejpam-3768	184	1	t)−	t)−	PROPN
ejpam-3768	184	2	nε2	nε2	PROPN
ejpam-3768	184	3	2(m+1	2(m+1	NUM
ejpam-3768	184	4	)	)	PUNCT
ejpam-3768	184	5	,	,	PUNCT
ejpam-3768	184	6	(	(	PUNCT
ejpam-3768	184	7	3.2	3.2	NUM
ejpam-3768	184	8	)	)	PUNCT
ejpam-3768	184	9	where	where	SCONJ
ejpam-3768	184	10	k1	k1	NOUN
ejpam-3768	184	11	,	,	PUNCT
ejpam-3768	184	12	k2	k2	NOUN
ejpam-3768	184	13	and	and	CCONJ
ejpam-3768	184	14	ε2	ε2	NOUN
ejpam-3768	184	15	are	be	AUX
ejpam-3768	184	16	positive	positive	ADJ
ejpam-3768	184	17	constants	constant	NOUN
ejpam-3768	184	18	which	which	PRON
ejpam-3768	184	19	will	will	AUX
ejpam-3768	184	20	be	be	AUX
ejpam-3768	184	21	given	give	VERB
ejpam-3768	184	22	later	later	ADV
ejpam-3768	184	23	.	.	PUNCT
ejpam-3768	185	1	proof	proof	NOUN
ejpam-3768	185	2	.	.	PUNCT
ejpam-3768	186	1	differentiating	differentiate	VERB
ejpam-3768	186	2	(	(	PUNCT
ejpam-3768	186	3	2.1	2.1	NUM
ejpam-3768	186	4	)	)	PUNCT
ejpam-3768	186	5	with	with	ADP
ejpam-3768	186	6	respect	respect	NOUN
ejpam-3768	186	7	to	to	ADP
ejpam-3768	186	8	t	t	NOUN
ejpam-3768	186	9	and	and	CCONJ
ejpam-3768	186	10	using	use	VERB
ejpam-3768	186	11	the	the	DET
ejpam-3768	186	12	condition	condition	NOUN
ejpam-3768	186	13	(	(	PUNCT
ejpam-3768	186	14	f4	f4	PROPN
ejpam-3768	186	15	)	)	PUNCT
ejpam-3768	186	16	and	and	CCONJ
ejpam-3768	186	17	(	(	PUNCT
ejpam-3768	186	18	1.1	1.1	NUM
ejpam-3768	186	19	)	)	PUNCT
ejpam-3768	186	20	,	,	PUNCT
ejpam-3768	186	21	we	we	PRON
ejpam-3768	186	22	have	have	VERB
ejpam-3768	186	23	ϕ′(t	ϕ′(t	VERB
ejpam-3768	186	24	)	)	PUNCT
ejpam-3768	186	25	=	=	PRON
ejpam-3768	187	1	(	(	PUNCT
ejpam-3768	187	2	m+	m+	NOUN
ejpam-3768	187	3	1	1	NUM
ejpam-3768	187	4	)	)	PUNCT
ejpam-3768	187	5	∫	∫	PROPN
ejpam-3768	188	1	ω	ω	NUM
ejpam-3768	188	2	umutdx	umutdx	PROPN
ejpam-3768	188	3	=	=	PRON
ejpam-3768	188	4	(	(	PUNCT
ejpam-3768	188	5	m+	m+	NOUN
ejpam-3768	188	6	1	1	NUM
ejpam-3768	188	7	)	)	PUNCT
ejpam-3768	188	8	∫	∫	PROPN
ejpam-3768	189	1	ω	ω	INTJ
ejpam-3768	189	2	um	um	INTJ
ejpam-3768	189	3	(	(	PUNCT
ejpam-3768	189	4	4um	4um	NOUN
ejpam-3768	189	5	+	+	X
ejpam-3768	189	6	a(x)f(u	a(x)f(u	NUM
ejpam-3768	189	7	)	)	PUNCT
ejpam-3768	189	8	)	)	PUNCT
ejpam-3768	190	1	dx	dx	PROPN
ejpam-3768	191	1	=	=	PUNCT
ejpam-3768	191	2	−(m+	−(m+	NUM
ejpam-3768	191	3	1	1	X
ejpam-3768	191	4	)	)	PUNCT
ejpam-3768	191	5	∫	∫	PROPN
ejpam-3768	191	6	ω	ω	NUM
ejpam-3768	191	7	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	191	8	(	(	PUNCT
ejpam-3768	191	9	m+	m+	NOUN
ejpam-3768	191	10	1	1	NUM
ejpam-3768	191	11	)	)	PUNCT
ejpam-3768	191	12	∫	∫	PROPN
ejpam-3768	192	1	ω	ω	PROPN
ejpam-3768	192	2	a(x)umf(u)dx	a(x)umf(u)dx	PART
ejpam-3768	192	3	≤	≤	NUM
ejpam-3768	192	4	−(m+	−(m+	NUM
ejpam-3768	192	5	1	1	NUM
ejpam-3768	192	6	)	)	PUNCT
ejpam-3768	192	7	∫	∫	PROPN
ejpam-3768	192	8	ω	ω	NUM
ejpam-3768	192	9	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	192	10	(	(	PUNCT
ejpam-3768	192	11	m+	m+	NOUN
ejpam-3768	192	12	1)c3	1)c3	NUM
ejpam-3768	192	13	∫	∫	PROPN
ejpam-3768	192	14	ω	ω	NUM
ejpam-3768	192	15	umdx	umdx	NOUN
ejpam-3768	192	16	+	+	CCONJ
ejpam-3768	192	17	(	(	PUNCT
ejpam-3768	192	18	m+	m+	NUM
ejpam-3768	192	19	1)c4	1)c4	NUM
ejpam-3768	192	20	∫	∫	PROPN
ejpam-3768	192	21	ω	ω	NUM
ejpam-3768	192	22	um+l+1dx	um+l+1dx	X
ejpam-3768	192	23	.	.	PUNCT
ejpam-3768	193	1	(	(	PUNCT
ejpam-3768	193	2	3.3	3.3	NUM
ejpam-3768	193	3	)	)	PUNCT
ejpam-3768	193	4	from	from	ADP
ejpam-3768	193	5	hölder	hölder	PROPN
ejpam-3768	193	6	’s	’s	PART
ejpam-3768	193	7	inequality	inequality	NOUN
ejpam-3768	193	8	,	,	PUNCT
ejpam-3768	193	9	young	young	ADJ
ejpam-3768	193	10	’s	’s	PART
ejpam-3768	193	11	inequality	inequality	NOUN
ejpam-3768	193	12	and	and	CCONJ
ejpam-3768	193	13	condition	condition	NOUN
ejpam-3768	193	14	(	(	PUNCT
ejpam-3768	193	15	f4	f4	PROPN
ejpam-3768	193	16	)	)	PUNCT
ejpam-3768	193	17	,	,	PUNCT
ejpam-3768	193	18	we	we	PRON
ejpam-3768	193	19	have∫	have∫	VERB
ejpam-3768	193	20	ω	ω	NUM
ejpam-3768	193	21	umdx	umdx	NOUN
ejpam-3768	194	1	≤	≤	PROPN
ejpam-3768	195	1	m	m	VERB
ejpam-3768	196	1	m+	m+	NUM
ejpam-3768	197	1	l	l	NOUN
ejpam-3768	198	1	+	+	CCONJ
ejpam-3768	198	2	1	1	NUM
ejpam-3768	198	3	∫	∫	PROPN
ejpam-3768	198	4	ω	ω	PROPN
ejpam-3768	198	5	um+l+1dx+	um+l+1dx+	PROPN
ejpam-3768	198	6	l	l	PROPN
ejpam-3768	199	1	+	+	CCONJ
ejpam-3768	199	2	1	1	NUM
ejpam-3768	199	3	m+	m+	NUM
ejpam-3768	199	4	l	l	NOUN
ejpam-3768	199	5	+	+	CCONJ
ejpam-3768	199	6	1	1	NUM
ejpam-3768	199	7	|ω|	|ω|	NOUN
ejpam-3768	199	8	,	,	PUNCT
ejpam-3768	199	9	(	(	PUNCT
ejpam-3768	199	10	3.4	3.4	NUM
ejpam-3768	199	11	)	)	PUNCT
ejpam-3768	199	12	h.f	h.f	PROPN
ejpam-3768	199	13	.	.	PROPN
ejpam-3768	199	14	di	di	PROPN
ejpam-3768	199	15	,	,	PUNCT
ejpam-3768	199	16	l.	l.	PROPN
ejpam-3768	199	17	chen	chen	PROPN
ejpam-3768	199	18	and	and	CCONJ
ejpam-3768	199	19	z.f	z.f	PROPN
ejpam-3768	199	20	.	.	PROPN
ejpam-3768	199	21	song	song	PROPN
ejpam-3768	199	22	/	/	SYM
ejpam-3768	199	23	eur	eur	PROPN
ejpam-3768	199	24	.	.	PUNCT
ejpam-3768	200	1	j.	j.	PROPN
ejpam-3768	200	2	pure	pure	PROPN
ejpam-3768	200	3	appl	appl	PROPN
ejpam-3768	200	4	.	.	PROPN
ejpam-3768	200	5	math	math	PROPN
ejpam-3768	200	6	,	,	PUNCT
ejpam-3768	200	7	13	13	NUM
ejpam-3768	200	8	(	(	PUNCT
ejpam-3768	200	9	3	3	NUM
ejpam-3768	200	10	)	)	PUNCT
ejpam-3768	200	11	(	(	PUNCT
ejpam-3768	200	12	2020	2020	NUM
ejpam-3768	200	13	)	)	PUNCT
ejpam-3768	200	14	,	,	PUNCT
ejpam-3768	200	15	645	645	NUM
ejpam-3768	200	16	-	-	SYM
ejpam-3768	200	17	662	662	NUM
ejpam-3768	200	18	653	653	NUM
ejpam-3768	200	19	and	and	CCONJ
ejpam-3768	200	20	∫	∫	PROPN
ejpam-3768	200	21	ω	ω	PROPN
ejpam-3768	200	22	um+l+1dx	um+l+1dx	NUM
ejpam-3768	201	1	=	=	SYM
ejpam-3768	201	2	∫	∫	PROPN
ejpam-3768	201	3	ω	ω	PROPN
ejpam-3768	201	4	um+1−ε1ul−ε1dx	um+1−ε1ul−ε1dx	PROPN
ejpam-3768	201	5	≤	≤	PROPN
ejpam-3768	201	6	(	(	PUNCT
ejpam-3768	201	7	∫	∫	PROPN
ejpam-3768	201	8	ω	ω	NUM
ejpam-3768	201	9	um+1dx	um+1dx	NOUN
ejpam-3768	201	10	)	)	PUNCT
ejpam-3768	201	11	m+1−ε1	m+1−ε1	PROPN
ejpam-3768	201	12	m+1	m+1	X
ejpam-3768	201	13	(	(	PUNCT
ejpam-3768	201	14	∫	∫	PROPN
ejpam-3768	201	15	ω	ω	NUM
ejpam-3768	201	16	u	u	PROPN
ejpam-3768	201	17	(	(	PUNCT
ejpam-3768	201	18	l+ε1)(m+1	l+ε1)(m+1	X
ejpam-3768	201	19	)	)	PUNCT
ejpam-3768	201	20	ε1	ε1	AUX
ejpam-3768	201	21	dx	dx	PROPN
ejpam-3768	201	22	)	)	PUNCT
ejpam-3768	201	23	ε1	ε1	VERB
ejpam-3768	201	24	m+1	m+1	PRON
ejpam-3768	201	25	=	=	SYM
ejpam-3768	201	26	(	(	PUNCT
ejpam-3768	201	27	∫	∫	PROPN
ejpam-3768	201	28	ω	ω	PROPN
ejpam-3768	201	29	um+1dx	um+1dx	NOUN
ejpam-3768	201	30	)	)	PUNCT
ejpam-3768	201	31	m+1−ε1	m+1−ε1	PROPN
ejpam-3768	201	32	m+1	m+1	X
ejpam-3768	201	33	(	(	PUNCT
ejpam-3768	201	34	∫	∫	PROPN
ejpam-3768	201	35	ω	ω	PROPN
ejpam-3768	201	36	u	u	NOUN
ejpam-3768	201	37	2	2	NUM
ejpam-3768	201	38	nm	nm	VERB
ejpam-3768	201	39	n−2	n−2	PROPN
ejpam-3768	201	40	dx	dx	PROPN
ejpam-3768	201	41	)	)	PUNCT
ejpam-3768	201	42	ε1	ε1	VERB
ejpam-3768	201	43	m+1	m+1	NUM
ejpam-3768	201	44	≤	≤	NUM
ejpam-3768	201	45	ε2c(ε	ε2c(ε	NOUN
ejpam-3768	201	46	)	)	PUNCT
ejpam-3768	201	47	1	1	NUM
ejpam-3768	202	1	+	+	CCONJ
ejpam-3768	202	2	ε2	ε2	ADJ
ejpam-3768	202	3	(	(	PUNCT
ejpam-3768	202	4	∫	∫	PROPN
ejpam-3768	202	5	ω	ω	NUM
ejpam-3768	202	6	um+1dx	um+1dx	PROPN
ejpam-3768	202	7	)	)	PUNCT
ejpam-3768	202	8	(	(	PUNCT
ejpam-3768	202	9	m+1−ε1)(ε2	m+1−ε1)(ε2	NOUN
ejpam-3768	202	10	+	+	NOUN
ejpam-3768	202	11	1	1	NUM
ejpam-3768	202	12	)	)	PUNCT
ejpam-3768	202	13	(	(	PUNCT
ejpam-3768	202	14	m+1)ε2	m+1)ε2	NOUN
ejpam-3768	202	15	+	+	CCONJ
ejpam-3768	202	16	ε	ε	PROPN
ejpam-3768	202	17	1	1	NUM
ejpam-3768	202	18	+	+	CCONJ
ejpam-3768	202	19	ε2	ε2	ADJ
ejpam-3768	202	20	(	(	PUNCT
ejpam-3768	202	21	∫	∫	PROPN
ejpam-3768	202	22	ω	ω	PROPN
ejpam-3768	202	23	u	u	NOUN
ejpam-3768	202	24	2	2	NUM
ejpam-3768	202	25	nm	nm	VERB
ejpam-3768	202	26	n−2	n−2	PROPN
ejpam-3768	202	27	dx	dx	PROPN
ejpam-3768	202	28	)	)	PUNCT
ejpam-3768	202	29	ε1(1+ε2	ε1(1+ε2	PROPN
ejpam-3768	202	30	)	)	PUNCT
ejpam-3768	202	31	m+1	m+1	NUM
ejpam-3768	202	32	,	,	PUNCT
ejpam-3768	202	33	(	(	PUNCT
ejpam-3768	202	34	3.5	3.5	NUM
ejpam-3768	202	35	)	)	PUNCT
ejpam-3768	202	36	where	where	SCONJ
ejpam-3768	202	37	ε1	ε1	PROPN
ejpam-3768	202	38	=	=	PUNCT
ejpam-3768	202	39	(	(	PUNCT
ejpam-3768	202	40	n−2)(m+1)l	n−2)(m+1)l	NOUN
ejpam-3768	202	41	2nm−(n−2)(m+1	2nm−(n−2)(m+1	NUM
ejpam-3768	202	42	)	)	PUNCT
ejpam-3768	202	43	>	>	X
ejpam-3768	202	44	0	0	NUM
ejpam-3768	202	45	,	,	PUNCT
ejpam-3768	202	46	ε2	ε2	NOUN
ejpam-3768	202	47	=	=	SYM
ejpam-3768	202	48	n(2m−l)−(n−2)(m+1	n(2m−l)−(n−2)(m+1	NOUN
ejpam-3768	202	49	)	)	PUNCT
ejpam-3768	202	50	nl	nl	NOUN
ejpam-3768	202	51	>	>	X
ejpam-3768	202	52	0	0	NUM
ejpam-3768	202	53	,	,	PUNCT
ejpam-3768	202	54	and	and	CCONJ
ejpam-3768	202	55	ε	ε	PROPN
ejpam-3768	202	56	will	will	AUX
ejpam-3768	202	57	be	be	AUX
ejpam-3768	202	58	determined	determine	VERB
ejpam-3768	202	59	later	later	ADV
ejpam-3768	202	60	.	.	PUNCT
ejpam-3768	203	1	noting	note	VERB
ejpam-3768	203	2	that	that	SCONJ
ejpam-3768	203	3	∫	∫	PROPN
ejpam-3768	203	4	ω	ω	NUM
ejpam-3768	203	5	u	u	PROPN
ejpam-3768	203	6	2	2	NUM
ejpam-3768	203	7	nm	nm	NOUN
ejpam-3768	203	8	n−2	n−2	PROPN
ejpam-3768	203	9	dx	dx	PROPN
ejpam-3768	203	10	≤	≤	PROPN
ejpam-3768	203	11	c	c	NOUN
ejpam-3768	203	12	2n	2n	NUM
ejpam-3768	203	13	n−2	n−2	PROPN
ejpam-3768	203	14	5	5	NUM
ejpam-3768	203	15	(	(	PUNCT
ejpam-3768	203	16	∫	∫	PROPN
ejpam-3768	203	17	ω	ω	PROPN
ejpam-3768	203	18	|∇um|2	|∇um|2	NOUN
ejpam-3768	203	19	)	)	PUNCT
ejpam-3768	204	1	n	n	PROPN
ejpam-3768	204	2	n−2	n−2	PROPN
ejpam-3768	204	3	,	,	PUNCT
ejpam-3768	204	4	(	(	PUNCT
ejpam-3768	204	5	3.6	3.6	NUM
ejpam-3768	204	6	)	)	PUNCT
ejpam-3768	204	7	where	where	SCONJ
ejpam-3768	204	8	c5	c5	PROPN
ejpam-3768	204	9	is	be	AUX
ejpam-3768	204	10	the	the	DET
ejpam-3768	204	11	optimal	optimal	ADJ
ejpam-3768	204	12	constant	constant	NOUN
ejpam-3768	204	13	of	of	ADP
ejpam-3768	204	14	the	the	DET
ejpam-3768	204	15	sobolev	sobolev	NOUN
ejpam-3768	204	16	embedding	embed	VERB
ejpam-3768	204	17	h1(ω	h1(ω	PROPN
ejpam-3768	204	18	)	)	PUNCT
ejpam-3768	204	19	↪	↪	PROPN
ejpam-3768	204	20	→	→	SYM
ejpam-3768	204	21	l	l	NOUN
ejpam-3768	204	22	2n	2n	X
ejpam-3768	204	23	n−2	n−2	PROPN
ejpam-3768	204	24	(	(	PUNCT
ejpam-3768	204	25	ω	ω	NOUN
ejpam-3768	204	26	)	)	PUNCT
ejpam-3768	204	27	.	.	PUNCT
ejpam-3768	205	1	furthermore	furthermore	ADV
ejpam-3768	205	2	,	,	PUNCT
ejpam-3768	205	3	from	from	ADP
ejpam-3768	205	4	the	the	DET
ejpam-3768	205	5	choice	choice	NOUN
ejpam-3768	205	6	of	of	ADP
ejpam-3768	205	7	ε1	ε1	PROPN
ejpam-3768	205	8	and	and	CCONJ
ejpam-3768	205	9	ε2	ε2	ADJ
ejpam-3768	205	10	,	,	PUNCT
ejpam-3768	205	11	it	it	PRON
ejpam-3768	205	12	is	be	AUX
ejpam-3768	205	13	easy	easy	ADJ
ejpam-3768	205	14	to	to	PART
ejpam-3768	205	15	see	see	VERB
ejpam-3768	205	16	that	that	SCONJ
ejpam-3768	205	17	ε1(1+ε2)n	ε1(1+ε2)n	PROPN
ejpam-3768	205	18	(	(	PUNCT
ejpam-3768	205	19	m+1)(n−2	m+1)(n−2	PROPN
ejpam-3768	205	20	)	)	PUNCT
ejpam-3768	205	21	=	=	SYM
ejpam-3768	205	22	1	1	X
ejpam-3768	205	23	.	.	X
ejpam-3768	205	24	inserting	insert	VERB
ejpam-3768	205	25	(	(	PUNCT
ejpam-3768	205	26	3.4)-(3.6	3.4)-(3.6	NUM
ejpam-3768	205	27	)	)	PUNCT
ejpam-3768	205	28	into	into	ADP
ejpam-3768	205	29	(	(	PUNCT
ejpam-3768	205	30	3.3	3.3	NUM
ejpam-3768	205	31	)	)	PUNCT
ejpam-3768	205	32	,	,	PUNCT
ejpam-3768	205	33	it	it	PRON
ejpam-3768	205	34	follows	follow	VERB
ejpam-3768	205	35	that	that	SCONJ
ejpam-3768	205	36	ϕ′(t	ϕ′(t	NOUN
ejpam-3768	205	37	)	)	PUNCT
ejpam-3768	205	38	≤	≤	NUM
ejpam-3768	205	39	−(m+	−(m+	NUM
ejpam-3768	205	40	1	1	NUM
ejpam-3768	205	41	)	)	PUNCT
ejpam-3768	205	42	∫	∫	PROPN
ejpam-3768	206	1	ω	ω	NUM
ejpam-3768	206	2	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	206	3	(	(	PUNCT
ejpam-3768	206	4	m+	m+	NUM
ejpam-3768	206	5	1)c3(l	1)c3(l	NUM
ejpam-3768	206	6	+	+	CCONJ
ejpam-3768	206	7	1	1	NUM
ejpam-3768	206	8	)	)	PUNCT
ejpam-3768	206	9	m+	m+	NUM
ejpam-3768	206	10	l	l	NOUN
ejpam-3768	206	11	+	+	CCONJ
ejpam-3768	206	12	1	1	NUM
ejpam-3768	206	13	|ω|	|ω|	NOUN
ejpam-3768	206	14	+	+	CCONJ
ejpam-3768	206	15	[	[	X
ejpam-3768	206	16	m(m+	m(m+	X
ejpam-3768	206	17	1)c3	1)c3	NUM
ejpam-3768	206	18	m+	m+	NUM
ejpam-3768	206	19	l	l	NOUN
ejpam-3768	206	20	+	+	CCONJ
ejpam-3768	206	21	1	1	NUM
ejpam-3768	206	22	+	+	CCONJ
ejpam-3768	206	23	(	(	PUNCT
ejpam-3768	206	24	m+	m+	NUM
ejpam-3768	206	25	1)c4	1)c4	PROPN
ejpam-3768	206	26	]	]	PUNCT
ejpam-3768	206	27	∫	∫	PROPN
ejpam-3768	206	28	ω	ω	PROPN
ejpam-3768	206	29	um+l+1dx	um+l+1dx	X
ejpam-3768	206	30	≤	≤	NUM
ejpam-3768	206	31	−	−	PROPN
ejpam-3768	207	1	[	[	PUNCT
ejpam-3768	207	2	m+	m+	NUM
ejpam-3768	207	3	1−	1−	NUM
ejpam-3768	207	4	(	(	PUNCT
ejpam-3768	207	5	m+	m+	NUM
ejpam-3768	207	6	1)(mc3	1)(mc3	NUM
ejpam-3768	207	7	+	+	PROPN
ejpam-3768	207	8	mc4	mc4	PROPN
ejpam-3768	207	9	+	+	CCONJ
ejpam-3768	207	10	lc4	lc4	PROPN
ejpam-3768	207	11	+	+	CCONJ
ejpam-3768	207	12	c4)c2	c4)c2	PROPN
ejpam-3768	207	13	5ε	5ε	NUM
ejpam-3768	207	14	(	(	PUNCT
ejpam-3768	207	15	1	1	NUM
ejpam-3768	207	16	+	+	NUM
ejpam-3768	207	17	ε2)(m+	ε2)(m+	NOUN
ejpam-3768	207	18	l	l	NOUN
ejpam-3768	207	19	+	+	NOUN
ejpam-3768	207	20	1	1	NUM
ejpam-3768	207	21	)	)	PUNCT
ejpam-3768	207	22	]	]	PUNCT
ejpam-3768	207	23	∫	∫	PROPN
ejpam-3768	208	1	ω	ω	NUM
ejpam-3768	208	2	|∇um|2dx	|∇um|2dx	X
ejpam-3768	208	3	+	+	CCONJ
ejpam-3768	208	4	(	(	PUNCT
ejpam-3768	208	5	m+	m+	NUM
ejpam-3768	208	6	1)(mc3	1)(mc3	NUM
ejpam-3768	208	7	+	+	PROPN
ejpam-3768	208	8	mc4	mc4	PROPN
ejpam-3768	208	9	+	+	CCONJ
ejpam-3768	208	10	lc4	lc4	PROPN
ejpam-3768	208	11	+	+	CCONJ
ejpam-3768	208	12	c4)ε2c(ε	c4)ε2c(ε	NOUN
ejpam-3768	208	13	)	)	PUNCT
ejpam-3768	208	14	(	(	PUNCT
ejpam-3768	208	15	1	1	NUM
ejpam-3768	208	16	+	+	NUM
ejpam-3768	208	17	ε2)(m+	ε2)(m+	NOUN
ejpam-3768	208	18	l	l	NOUN
ejpam-3768	208	19	+	+	NOUN
ejpam-3768	208	20	1	1	X
ejpam-3768	208	21	)	)	PUNCT
ejpam-3768	208	22	(	(	PUNCT
ejpam-3768	208	23	∫	∫	PROPN
ejpam-3768	208	24	ω	ω	NUM
ejpam-3768	208	25	um+1dx	um+1dx	PROPN
ejpam-3768	208	26	)	)	PUNCT
ejpam-3768	208	27	(	(	PUNCT
ejpam-3768	208	28	m+1−ε1)(ε2	m+1−ε1)(ε2	NOUN
ejpam-3768	208	29	+	+	NOUN
ejpam-3768	208	30	1	1	NUM
ejpam-3768	208	31	)	)	PUNCT
ejpam-3768	208	32	(	(	PUNCT
ejpam-3768	208	33	m+1)ε2	m+1)ε2	NOUN
ejpam-3768	208	34	+	+	CCONJ
ejpam-3768	208	35	(	(	PUNCT
ejpam-3768	208	36	m+	m+	NUM
ejpam-3768	208	37	1)c3(l	1)c3(l	NUM
ejpam-3768	208	38	+	+	CCONJ
ejpam-3768	208	39	1	1	NUM
ejpam-3768	208	40	)	)	PUNCT
ejpam-3768	208	41	m+	m+	NUM
ejpam-3768	208	42	l	l	NOUN
ejpam-3768	209	1	+	+	CCONJ
ejpam-3768	209	2	1	1	NUM
ejpam-3768	209	3	|ω|	|ω|	PROPN
ejpam-3768	209	4	.	.	PUNCT
ejpam-3768	209	5	(	(	PUNCT
ejpam-3768	209	6	3.7	3.7	NUM
ejpam-3768	209	7	)	)	PUNCT
ejpam-3768	209	8	taking	take	VERB
ejpam-3768	209	9	ε	ε	PROPN
ejpam-3768	209	10	small	small	ADJ
ejpam-3768	209	11	enough	enough	ADV
ejpam-3768	209	12	such	such	ADJ
ejpam-3768	209	13	that	that	DET
ejpam-3768	209	14	m+	m+	NOUN
ejpam-3768	209	15	1−	1−	NUM
ejpam-3768	210	1	(	(	PUNCT
ejpam-3768	210	2	m+	m+	NUM
ejpam-3768	210	3	1)(mc3	1)(mc3	NUM
ejpam-3768	210	4	+	+	PROPN
ejpam-3768	210	5	mc4	mc4	PROPN
ejpam-3768	210	6	+	+	CCONJ
ejpam-3768	210	7	lc4	lc4	PROPN
ejpam-3768	210	8	+	+	CCONJ
ejpam-3768	210	9	c4)c2	c4)c2	PROPN
ejpam-3768	210	10	5ε	5ε	NUM
ejpam-3768	210	11	(	(	PUNCT
ejpam-3768	210	12	1	1	NUM
ejpam-3768	210	13	+	+	NUM
ejpam-3768	210	14	ε2)(m+	ε2)(m+	NOUN
ejpam-3768	210	15	l	l	NOUN
ejpam-3768	210	16	+	+	CCONJ
ejpam-3768	210	17	1	1	X
ejpam-3768	210	18	)	)	PUNCT
ejpam-3768	210	19	>	>	X
ejpam-3768	210	20	0	0	X
ejpam-3768	210	21	.	.	PUNCT
ejpam-3768	211	1	(	(	PUNCT
ejpam-3768	211	2	3.8	3.8	NUM
ejpam-3768	211	3	)	)	PUNCT
ejpam-3768	211	4	hence	hence	ADV
ejpam-3768	211	5	,	,	PUNCT
ejpam-3768	211	6	we	we	PRON
ejpam-3768	211	7	have	have	VERB
ejpam-3768	211	8	ϕ′(t	ϕ′(t	NOUN
ejpam-3768	211	9	)	)	PUNCT
ejpam-3768	211	10	≤	≤	NOUN
ejpam-3768	211	11	k1	k1	NOUN
ejpam-3768	211	12	+	+	CCONJ
ejpam-3768	211	13	k2[ϕ(t	k2[ϕ(t	PROPN
ejpam-3768	211	14	)	)	PUNCT
ejpam-3768	211	15	]	]	PUNCT
ejpam-3768	212	1	(	(	PUNCT
ejpam-3768	212	2	m+1−ε1)(1+ε2	m+1−ε1)(1+ε2	PROPN
ejpam-3768	212	3	)	)	PUNCT
ejpam-3768	212	4	(	(	PUNCT
ejpam-3768	212	5	m+1)ε2	m+1)ε2	NOUN
ejpam-3768	212	6	=	=	SYM
ejpam-3768	212	7	k1	k1	PROPN
ejpam-3768	212	8	+	+	CCONJ
ejpam-3768	212	9	k2[ϕ(t	k2[ϕ(t	PROPN
ejpam-3768	212	10	)	)	PUNCT
ejpam-3768	212	11	]	]	PUNCT
ejpam-3768	213	1	1	1	NUM
ejpam-3768	213	2	+	+	SYM
ejpam-3768	213	3	2	2	NUM
ejpam-3768	213	4	nε2	nε2	NOUN
ejpam-3768	213	5	,	,	PUNCT
ejpam-3768	213	6	(	(	PUNCT
ejpam-3768	213	7	3.9	3.9	NUM
ejpam-3768	213	8	)	)	PUNCT
ejpam-3768	213	9	where	where	SCONJ
ejpam-3768	213	10	k1	k1	NOUN
ejpam-3768	213	11	=	=	SYM
ejpam-3768	213	12	(	(	PUNCT
ejpam-3768	213	13	m+1)c3(l+1	m+1)c3(l+1	PROPN
ejpam-3768	213	14	)	)	PUNCT
ejpam-3768	213	15	m+l+1	m+l+1	PROPN
ejpam-3768	213	16	|ω|	|ω|	PROPN
ejpam-3768	213	17	and	and	CCONJ
ejpam-3768	213	18	k2	k2	PROPN
ejpam-3768	213	19	=	=	SYM
ejpam-3768	213	20	(	(	PUNCT
ejpam-3768	213	21	m+1)(mc3+mc4+lc4+c4)ε2c(ε	m+1)(mc3+mc4+lc4+c4)ε2c(ε	PROPN
ejpam-3768	213	22	)	)	PUNCT
ejpam-3768	213	23	(	(	PUNCT
ejpam-3768	213	24	1+ε2)(m+l+1	1+ε2)(m+l+1	NUM
ejpam-3768	213	25	)	)	PUNCT
ejpam-3768	213	26	.	.	PUNCT
ejpam-3768	214	1	h.f	h.f	PROPN
ejpam-3768	214	2	.	.	PROPN
ejpam-3768	214	3	di	di	PROPN
ejpam-3768	214	4	,	,	PUNCT
ejpam-3768	214	5	l.	l.	PROPN
ejpam-3768	214	6	chen	chen	PROPN
ejpam-3768	214	7	and	and	CCONJ
ejpam-3768	214	8	z.f	z.f	PROPN
ejpam-3768	214	9	.	.	PROPN
ejpam-3768	214	10	song	song	PROPN
ejpam-3768	214	11	/	/	SYM
ejpam-3768	214	12	eur	eur	PROPN
ejpam-3768	214	13	.	.	PUNCT
ejpam-3768	215	1	j.	j.	PROPN
ejpam-3768	215	2	pure	pure	PROPN
ejpam-3768	215	3	appl	appl	PROPN
ejpam-3768	215	4	.	.	PROPN
ejpam-3768	215	5	math	math	PROPN
ejpam-3768	215	6	,	,	PUNCT
ejpam-3768	215	7	13	13	NUM
ejpam-3768	215	8	(	(	PUNCT
ejpam-3768	215	9	3	3	NUM
ejpam-3768	215	10	)	)	PUNCT
ejpam-3768	215	11	(	(	PUNCT
ejpam-3768	215	12	2020	2020	NUM
ejpam-3768	215	13	)	)	PUNCT
ejpam-3768	215	14	,	,	PUNCT
ejpam-3768	215	15	645	645	NUM
ejpam-3768	215	16	-	-	SYM
ejpam-3768	215	17	662	662	NUM
ejpam-3768	215	18	654	654	NUM
ejpam-3768	215	19	integrating	integrating	NOUN
ejpam-3768	215	20	(	(	PUNCT
ejpam-3768	215	21	3.9	3.9	NUM
ejpam-3768	215	22	)	)	PUNCT
ejpam-3768	215	23	from	from	ADP
ejpam-3768	215	24	0	0	NUM
ejpam-3768	215	25	to	to	ADP
ejpam-3768	215	26	t	t	PROPN
ejpam-3768	215	27	,	,	PUNCT
ejpam-3768	215	28	we	we	PRON
ejpam-3768	215	29	get∫	get∫	VERB
ejpam-3768	215	30	ϕ(t	ϕ(t	NUM
ejpam-3768	215	31	)	)	PUNCT
ejpam-3768	216	1	ϕ(0	ϕ(0	PROPN
ejpam-3768	216	2	)	)	PUNCT
ejpam-3768	217	1	dη	dη	PART
ejpam-3768	218	1	k1η	k1η	NOUN
ejpam-3768	218	2	+	+	CCONJ
ejpam-3768	218	3	k2η	k2η	PROPN
ejpam-3768	218	4	1	1	NUM
ejpam-3768	218	5	+	+	NUM
ejpam-3768	218	6	2	2	NUM
ejpam-3768	218	7	nε2	nε2	NUM
ejpam-3768	218	8	≤	≤	NOUN
ejpam-3768	218	9	t.	t.	NOUN
ejpam-3768	218	10	(	(	PUNCT
ejpam-3768	218	11	3.10	3.10	NUM
ejpam-3768	218	12	)	)	PUNCT
ejpam-3768	218	13	if	if	SCONJ
ejpam-3768	218	14	u	u	PRON
ejpam-3768	218	15	blows	blow	VERB
ejpam-3768	218	16	up	up	ADP
ejpam-3768	218	17	in	in	ADP
ejpam-3768	218	18	the	the	DET
ejpam-3768	218	19	measure	measure	NOUN
ejpam-3768	218	20	ϕ(t	ϕ(t	NUM
ejpam-3768	218	21	)	)	PUNCT
ejpam-3768	218	22	as	as	ADP
ejpam-3768	218	23	t→	t→	DET
ejpam-3768	218	24	t∗	t∗	PROPN
ejpam-3768	218	25	,	,	PUNCT
ejpam-3768	218	26	then	then	ADV
ejpam-3768	218	27	we	we	PRON
ejpam-3768	218	28	can	can	AUX
ejpam-3768	218	29	obtain	obtain	VERB
ejpam-3768	218	30	the	the	DET
ejpam-3768	218	31	lower	low	ADJ
ejpam-3768	218	32	bound	bind	VERB
ejpam-3768	218	33	t∗	t∗	PROPN
ejpam-3768	218	34	≥	≥	PUNCT
ejpam-3768	218	35	∫	∫	PROPN
ejpam-3768	219	1	+	+	NUM
ejpam-3768	219	2	∞	∞	PROPN
ejpam-3768	219	3	ϕ(0	ϕ(0	PROPN
ejpam-3768	219	4	)	)	PUNCT
ejpam-3768	219	5	dη	dη	PART
ejpam-3768	220	1	k1η	k1η	NOUN
ejpam-3768	220	2	+	+	CCONJ
ejpam-3768	220	3	k2η	k2η	PROPN
ejpam-3768	220	4	1	1	NUM
ejpam-3768	220	5	+	+	NUM
ejpam-3768	220	6	2	2	NUM
ejpam-3768	220	7	nε2	nε2	NOUN
ejpam-3768	220	8	.	.	PUNCT
ejpam-3768	221	1	moreover	moreover	ADV
ejpam-3768	221	2	,	,	PUNCT
ejpam-3768	221	3	integrating	integrate	VERB
ejpam-3768	221	4	the	the	DET
ejpam-3768	221	5	inequality	inequality	NOUN
ejpam-3768	221	6	(	(	PUNCT
ejpam-3768	221	7	3.9	3.9	NUM
ejpam-3768	221	8	)	)	PUNCT
ejpam-3768	221	9	from	from	ADP
ejpam-3768	221	10	t	t	PROPN
ejpam-3768	221	11	to	to	ADP
ejpam-3768	221	12	t∗	t∗	PROPN
ejpam-3768	221	13	,	,	PUNCT
ejpam-3768	221	14	we	we	PRON
ejpam-3768	221	15	obtain	obtain	VERB
ejpam-3768	221	16	t∗	t∗	NOUN
ejpam-3768	221	17	−	−	PROPN
ejpam-3768	222	1	t	t	PROPN
ejpam-3768	223	1	≥	≥	X
ejpam-3768	224	1	∫	∫	PROPN
ejpam-3768	225	1	+	+	X
ejpam-3768	225	2	∞	∞	PROPN
ejpam-3768	225	3	ϕ(t	ϕ(t	NUM
ejpam-3768	225	4	)	)	PUNCT
ejpam-3768	226	1	dη	dη	X
ejpam-3768	227	1	k1η	k1η	NOUN
ejpam-3768	227	2	+	+	CCONJ
ejpam-3768	227	3	k2η	k2η	PROPN
ejpam-3768	227	4	1	1	NUM
ejpam-3768	227	5	+	+	NUM
ejpam-3768	227	6	2	2	NUM
ejpam-3768	227	7	nε2	nε2	X
ejpam-3768	227	8	:	:	PUNCT
ejpam-3768	227	9	=	=	NOUN
ejpam-3768	227	10	y1(ϕ(t	y1(ϕ(t	NOUN
ejpam-3768	227	11	)	)	PUNCT
ejpam-3768	227	12	)	)	PUNCT
ejpam-3768	227	13	.	.	PUNCT
ejpam-3768	228	1	(	(	PUNCT
ejpam-3768	228	2	3.11	3.11	NUM
ejpam-3768	228	3	)	)	PUNCT
ejpam-3768	228	4	we	we	PRON
ejpam-3768	228	5	note	note	VERB
ejpam-3768	228	6	that	that	SCONJ
ejpam-3768	228	7	y1	y1	NOUN
ejpam-3768	228	8	is	be	AUX
ejpam-3768	228	9	a	a	DET
ejpam-3768	228	10	decreasing	decrease	VERB
ejpam-3768	228	11	function	function	NOUN
ejpam-3768	228	12	,	,	PUNCT
ejpam-3768	228	13	which	which	PRON
ejpam-3768	228	14	means	mean	VERB
ejpam-3768	228	15	its	its	PRON
ejpam-3768	228	16	inverse	inverse	NOUN
ejpam-3768	228	17	function	function	NOUN
ejpam-3768	228	18	y	y	PROPN
ejpam-3768	228	19	−1	−1	NOUN
ejpam-3768	228	20	1	1	NUM
ejpam-3768	228	21	exists	exist	VERB
ejpam-3768	228	22	and	and	CCONJ
ejpam-3768	228	23	is	be	AUX
ejpam-3768	228	24	also	also	ADV
ejpam-3768	228	25	a	a	DET
ejpam-3768	228	26	decreasing	decrease	VERB
ejpam-3768	228	27	function	function	NOUN
ejpam-3768	228	28	.	.	PUNCT
ejpam-3768	229	1	therefore	therefore	ADV
ejpam-3768	229	2	,	,	PUNCT
ejpam-3768	229	3	we	we	PRON
ejpam-3768	229	4	have	have	VERB
ejpam-3768	229	5	ϕ(t	ϕ(t	NUM
ejpam-3768	229	6	)	)	PUNCT
ejpam-3768	229	7	≥	≥	NOUN
ejpam-3768	229	8	y	y	PROPN
ejpam-3768	229	9	−1	−1	NOUN
ejpam-3768	229	10	1	1	NUM
ejpam-3768	229	11	(	(	PUNCT
ejpam-3768	229	12	t∗	t∗	NOUN
ejpam-3768	229	13	−	−	PROPN
ejpam-3768	229	14	t	t	PROPN
ejpam-3768	229	15	)	)	PUNCT
ejpam-3768	229	16	,	,	PUNCT
ejpam-3768	229	17	(	(	PUNCT
ejpam-3768	229	18	3.12	3.12	NUM
ejpam-3768	229	19	)	)	PUNCT
ejpam-3768	229	20	which	which	PRON
ejpam-3768	229	21	gives	give	VERB
ejpam-3768	229	22	the	the	DET
ejpam-3768	229	23	lower	low	ADJ
ejpam-3768	229	24	estimate	estimate	NOUN
ejpam-3768	229	25	of	of	ADP
ejpam-3768	229	26	blow	blow	NOUN
ejpam-3768	229	27	-	-	PUNCT
ejpam-3768	229	28	up	up	ADP
ejpam-3768	229	29	rate	rate	NOUN
ejpam-3768	229	30	.	.	PUNCT
ejpam-3768	230	1	in	in	ADP
ejpam-3768	230	2	fact	fact	NOUN
ejpam-3768	230	3	,	,	PUNCT
ejpam-3768	230	4	if	if	SCONJ
ejpam-3768	230	5	t	t	PROPN
ejpam-3768	230	6	closes	close	VERB
ejpam-3768	230	7	t∗	t∗	NOUN
ejpam-3768	230	8	enough	enough	ADJ
ejpam-3768	230	9	such	such	ADJ
ejpam-3768	230	10	that	that	SCONJ
ejpam-3768	230	11	ϕ(t	ϕ(t	PROPN
ejpam-3768	230	12	)	)	PUNCT
ejpam-3768	230	13	�	�	PROPN
ejpam-3768	230	14	1	1	NUM
ejpam-3768	230	15	and	and	CCONJ
ejpam-3768	230	16	k2η	k2η	PROPN
ejpam-3768	230	17	1	1	NUM
ejpam-3768	230	18	+	+	NUM
ejpam-3768	230	19	2	2	NUM
ejpam-3768	230	20	nε2	nε2	X
ejpam-3768	230	21	>	>	X
ejpam-3768	230	22	k1η	k1η	NOUN
ejpam-3768	230	23	in	in	ADP
ejpam-3768	230	24	the	the	DET
ejpam-3768	230	25	inequality	inequality	NOUN
ejpam-3768	230	26	(	(	PUNCT
ejpam-3768	230	27	3.11	3.11	NUM
ejpam-3768	230	28	)	)	PUNCT
ejpam-3768	230	29	,	,	PUNCT
ejpam-3768	230	30	then	then	ADV
ejpam-3768	230	31	we	we	PRON
ejpam-3768	230	32	have	have	VERB
ejpam-3768	230	33	t∗	t∗	NOUN
ejpam-3768	230	34	−	−	PROPN
ejpam-3768	230	35	t	t	PROPN
ejpam-3768	230	36	≥	≥	NOUN
ejpam-3768	230	37	nε2	nε2	X
ejpam-3768	230	38	4k2	4k2	NUM
ejpam-3768	231	1	[	[	PUNCT
ejpam-3768	232	1	ϕ(t	ϕ(t	NUM
ejpam-3768	232	2	)	)	PUNCT
ejpam-3768	232	3	]	]	PUNCT
ejpam-3768	232	4	−	−	PROPN
ejpam-3768	232	5	2	2	NUM
ejpam-3768	232	6	nε2	nε2	X
ejpam-3768	232	7	,	,	PUNCT
ejpam-3768	232	8	(	(	PUNCT
ejpam-3768	232	9	3.13	3.13	NUM
ejpam-3768	232	10	)	)	PUNCT
ejpam-3768	232	11	which	which	PRON
ejpam-3768	232	12	means	mean	VERB
ejpam-3768	232	13	that	that	SCONJ
ejpam-3768	232	14	ϕ(t	ϕ(t	NUM
ejpam-3768	232	15	)	)	PUNCT
ejpam-3768	232	16	≥	≥	NUM
ejpam-3768	232	17	(	(	PUNCT
ejpam-3768	232	18	4k2	4k2	NUM
ejpam-3768	232	19	nε2	nε2	NOUN
ejpam-3768	232	20	)	)	PUNCT
ejpam-3768	233	1	−nε2	−nε2	PROPN
ejpam-3768	233	2	2	2	NUM
ejpam-3768	233	3	(	(	PUNCT
ejpam-3768	233	4	t∗	t∗	NOUN
ejpam-3768	233	5	−	−	PROPN
ejpam-3768	233	6	t)−	t)−	PROPN
ejpam-3768	233	7	nε2	nε2	PROPN
ejpam-3768	233	8	2	2	NUM
ejpam-3768	233	9	.	.	PUNCT
ejpam-3768	234	1	(	(	PUNCT
ejpam-3768	234	2	3.14	3.14	NUM
ejpam-3768	234	3	)	)	PUNCT
ejpam-3768	234	4	thus	thus	ADV
ejpam-3768	234	5	,	,	PUNCT
ejpam-3768	234	6	the	the	DET
ejpam-3768	234	7	estimate	estimate	NOUN
ejpam-3768	234	8	(	(	PUNCT
ejpam-3768	234	9	3.2	3.2	NUM
ejpam-3768	234	10	)	)	PUNCT
ejpam-3768	234	11	of	of	ADP
ejpam-3768	234	12	blow	blow	NOUN
ejpam-3768	234	13	-	-	PUNCT
ejpam-3768	234	14	up	up	ADP
ejpam-3768	234	15	rate	rate	NOUN
ejpam-3768	234	16	also	also	ADV
ejpam-3768	234	17	holds	hold	VERB
ejpam-3768	234	18	.	.	PUNCT
ejpam-3768	235	1	3.2	3.2	NUM
ejpam-3768	235	2	.	.	PUNCT
ejpam-3768	236	1	the	the	DET
ejpam-3768	236	2	second	second	ADJ
ejpam-3768	236	3	method	method	NOUN
ejpam-3768	236	4	firstly	firstly	ADV
ejpam-3768	236	5	,	,	PUNCT
ejpam-3768	236	6	we	we	PRON
ejpam-3768	236	7	need	need	VERB
ejpam-3768	236	8	the	the	DET
ejpam-3768	236	9	following	following	ADJ
ejpam-3768	236	10	assumption	assumption	NOUN
ejpam-3768	236	11	:	:	PUNCT
ejpam-3768	236	12	(	(	PUNCT
ejpam-3768	236	13	f5	f5	NOUN
ejpam-3768	236	14	):	):	PUNCT
ejpam-3768	236	15	there	there	PRON
ejpam-3768	236	16	exists	exist	VERB
ejpam-3768	236	17	positive	positive	ADJ
ejpam-3768	236	18	constants	constant	NOUN
ejpam-3768	236	19	c6	c6	PROPN
ejpam-3768	236	20	,	,	PUNCT
ejpam-3768	236	21	c7	c7	PROPN
ejpam-3768	236	22	,	,	PUNCT
ejpam-3768	236	23	q	q	PROPN
ejpam-3768	236	24	and	and	CCONJ
ejpam-3768	236	25	q	q	NOUN
ejpam-3768	236	26	such	such	ADJ
ejpam-3768	236	27	that	that	SCONJ
ejpam-3768	236	28	a(x)f(s	a(x)f(	NOUN
ejpam-3768	236	29	)	)	PUNCT
ejpam-3768	236	30	≤	≤	NOUN
ejpam-3768	236	31	c6	c6	PROPN
ejpam-3768	236	32	+	+	CCONJ
ejpam-3768	236	33	c7s	c7s	PROPN
ejpam-3768	236	34	p	p	X
ejpam-3768	236	35	(	(	PUNCT
ejpam-3768	236	36	∫	∫	PROPN
ejpam-3768	236	37	ω	ω	PROPN
ejpam-3768	236	38	sq+1dx	sq+1dx	PROPN
ejpam-3768	236	39	)	)	PUNCT
ejpam-3768	236	40	q	q	NOUN
ejpam-3768	236	41	,	,	PUNCT
ejpam-3768	236	42	for	for	ADP
ejpam-3768	236	43	any	any	DET
ejpam-3768	236	44	function	function	NOUN
ejpam-3768	236	45	s(x	s(x	PROPN
ejpam-3768	236	46	)	)	PUNCT
ejpam-3768	236	47	≥	≥	NOUN
ejpam-3768	236	48	0	0	NUM
ejpam-3768	236	49	.	.	PUNCT
ejpam-3768	237	1	(	(	PUNCT
ejpam-3768	237	2	e1	e1	NOUN
ejpam-3768	237	3	):	):	PUNCT
ejpam-3768	237	4	we	we	PRON
ejpam-3768	237	5	also	also	ADV
ejpam-3768	237	6	assume	assume	VERB
ejpam-3768	237	7	that	that	SCONJ
ejpam-3768	237	8	0	0	NUM
ejpam-3768	237	9	≤	≤	NOUN
ejpam-3768	237	10	p	p	X
ejpam-3768	237	11	≤	≤	NUM
ejpam-3768	237	12	1	1	NUM
ejpam-3768	237	13	,	,	PUNCT
ejpam-3768	237	14	0	0	NUM
ejpam-3768	237	15	≤	≤	NUM
ejpam-3768	237	16	q	q	PROPN
ejpam-3768	237	17	≤	≤	NUM
ejpam-3768	237	18	m	m	PROPN
ejpam-3768	237	19	,	,	PUNCT
ejpam-3768	237	20	and	and	CCONJ
ejpam-3768	237	21	(	(	PUNCT
ejpam-3768	237	22	q	q	PROPN
ejpam-3768	238	1	+	+	NUM
ejpam-3768	238	2	1)q+	1)q+	NUM
ejpam-3768	238	3	p	p	X
ejpam-3768	238	4	>	>	X
ejpam-3768	238	5	1	1	NUM
ejpam-3768	238	6	.	.	PUNCT
ejpam-3768	238	7	to	to	PART
ejpam-3768	238	8	obtain	obtain	VERB
ejpam-3768	238	9	the	the	DET
ejpam-3768	238	10	main	main	ADJ
ejpam-3768	238	11	results	result	NOUN
ejpam-3768	238	12	,	,	PUNCT
ejpam-3768	238	13	we	we	PRON
ejpam-3768	238	14	define	define	VERB
ejpam-3768	238	15	the	the	DET
ejpam-3768	238	16	auxiliary	auxiliary	ADJ
ejpam-3768	238	17	function	function	NOUN
ejpam-3768	238	18	ϕ(t	ϕ(t	NUM
ejpam-3768	238	19	)	)	PUNCT
ejpam-3768	239	1	=	=	SYM
ejpam-3768	239	2	∫	∫	PROPN
ejpam-3768	239	3	ω	ω	NUM
ejpam-3768	239	4	u	u	NOUN
ejpam-3768	239	5	m+1dx	m+1dx	PROPN
ejpam-3768	239	6	again	again	ADV
ejpam-3768	239	7	.	.	PUNCT
ejpam-3768	240	1	next	next	ADV
ejpam-3768	240	2	,	,	PUNCT
ejpam-3768	240	3	we	we	PRON
ejpam-3768	240	4	will	will	AUX
ejpam-3768	240	5	state	state	VERB
ejpam-3768	240	6	our	our	PRON
ejpam-3768	240	7	results	result	NOUN
ejpam-3768	240	8	below	below	ADP
ejpam-3768	240	9	:	:	PUNCT
ejpam-3768	240	10	h.f	h.f	PROPN
ejpam-3768	240	11	.	.	PROPN
ejpam-3768	240	12	di	di	PROPN
ejpam-3768	240	13	,	,	PUNCT
ejpam-3768	240	14	l.	l.	PROPN
ejpam-3768	240	15	chen	chen	PROPN
ejpam-3768	240	16	and	and	CCONJ
ejpam-3768	240	17	z.f	z.f	PROPN
ejpam-3768	240	18	.	.	PROPN
ejpam-3768	240	19	song	song	PROPN
ejpam-3768	240	20	/	/	SYM
ejpam-3768	240	21	eur	eur	PROPN
ejpam-3768	240	22	.	.	PUNCT
ejpam-3768	241	1	j.	j.	PROPN
ejpam-3768	241	2	pure	pure	PROPN
ejpam-3768	241	3	appl	appl	PROPN
ejpam-3768	241	4	.	.	PROPN
ejpam-3768	241	5	math	math	PROPN
ejpam-3768	241	6	,	,	PUNCT
ejpam-3768	241	7	13	13	NUM
ejpam-3768	241	8	(	(	PUNCT
ejpam-3768	241	9	3	3	NUM
ejpam-3768	241	10	)	)	PUNCT
ejpam-3768	241	11	(	(	PUNCT
ejpam-3768	241	12	2020	2020	NUM
ejpam-3768	241	13	)	)	PUNCT
ejpam-3768	241	14	,	,	PUNCT
ejpam-3768	241	15	645	645	NUM
ejpam-3768	241	16	-	-	SYM
ejpam-3768	241	17	662	662	NUM
ejpam-3768	241	18	655	655	NUM
ejpam-3768	241	19	theorem	theorem	NOUN
ejpam-3768	241	20	4	4	NUM
ejpam-3768	241	21	.	.	PUNCT
ejpam-3768	241	22	assume	assume	VERB
ejpam-3768	241	23	that	that	SCONJ
ejpam-3768	241	24	the	the	DET
ejpam-3768	241	25	conditions	condition	NOUN
ejpam-3768	241	26	(	(	PUNCT
ejpam-3768	241	27	f1	f1	NOUN
ejpam-3768	241	28	)	)	PUNCT
ejpam-3768	241	29	,	,	PUNCT
ejpam-3768	241	30	(	(	PUNCT
ejpam-3768	241	31	f5	f5	PROPN
ejpam-3768	241	32	)	)	PUNCT
ejpam-3768	241	33	,	,	PUNCT
ejpam-3768	241	34	(	(	PUNCT
ejpam-3768	241	35	e1	e1	NOUN
ejpam-3768	241	36	)	)	PUNCT
ejpam-3768	241	37	,	,	PUNCT
ejpam-3768	241	38	(	(	PUNCT
ejpam-3768	241	39	a1	a1	NOUN
ejpam-3768	241	40	)	)	PUNCT
ejpam-3768	241	41	,	,	PUNCT
ejpam-3768	241	42	(	(	PUNCT
ejpam-3768	241	43	a2	a2	NOUN
ejpam-3768	241	44	)	)	PUNCT
ejpam-3768	241	45	hold	hold	NOUN
ejpam-3768	241	46	,	,	PUNCT
ejpam-3768	241	47	and	and	CCONJ
ejpam-3768	241	48	u	u	NOUN
ejpam-3768	241	49	is	be	AUX
ejpam-3768	241	50	a	a	DET
ejpam-3768	241	51	nonnegative	nonnegative	ADJ
ejpam-3768	241	52	solution	solution	NOUN
ejpam-3768	241	53	of	of	ADP
ejpam-3768	241	54	problem	problem	NOUN
ejpam-3768	241	55	(	(	PUNCT
ejpam-3768	241	56	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	241	57	)	)	PUNCT
ejpam-3768	241	58	which	which	PRON
ejpam-3768	241	59	becomes	become	VERB
ejpam-3768	241	60	unbounded	unbounded	ADJ
ejpam-3768	241	61	in	in	ADP
ejpam-3768	241	62	lm+1−norm	lm+1−norm	PROPN
ejpam-3768	241	63	at	at	ADP
ejpam-3768	241	64	t	t	PROPN
ejpam-3768	241	65	=	=	SYM
ejpam-3768	241	66	t∗.	t∗.	PROPN
ejpam-3768	241	67	then	then	ADV
ejpam-3768	241	68	,	,	PUNCT
ejpam-3768	241	69	we	we	PRON
ejpam-3768	241	70	conclude	conclude	VERB
ejpam-3768	241	71	that	that	SCONJ
ejpam-3768	241	72	a	a	PRON
ejpam-3768	241	73	lower	lower	ADV
ejpam-3768	241	74	bound	bind	VERB
ejpam-3768	241	75	for	for	ADP
ejpam-3768	241	76	blow	blow	NOUN
ejpam-3768	241	77	-	-	PUNCT
ejpam-3768	241	78	up	up	ADP
ejpam-3768	241	79	time	time	NOUN
ejpam-3768	241	80	t∗	t∗	NOUN
ejpam-3768	241	81	is	be	AUX
ejpam-3768	241	82	given	give	VERB
ejpam-3768	241	83	by	by	ADP
ejpam-3768	241	84	t∗	t∗	PROPN
ejpam-3768	241	85	≥	≥	NUM
ejpam-3768	241	86	∫	∫	PROPN
ejpam-3768	242	1	+	+	NUM
ejpam-3768	242	2	∞	∞	PROPN
ejpam-3768	242	3	ϕ(0	ϕ(0	PROPN
ejpam-3768	242	4	)	)	PUNCT
ejpam-3768	242	5	dη	dη	ADP
ejpam-3768	243	1	k3η	k3η	PROPN
ejpam-3768	243	2	m	m	VERB
ejpam-3768	243	3	m+1	m+1	PROPN
ejpam-3768	243	4	+	+	CCONJ
ejpam-3768	243	5	k4η	k4η	NOUN
ejpam-3768	243	6	m+p+(q+1)q	m+p+(q+1)q	NOUN
ejpam-3768	243	7	m+1	m+1	PRON
ejpam-3768	243	8	,	,	PUNCT
ejpam-3768	243	9	(	(	PUNCT
ejpam-3768	243	10	3.15	3.15	NUM
ejpam-3768	243	11	)	)	PUNCT
ejpam-3768	243	12	and	and	CCONJ
ejpam-3768	243	13	the	the	DET
ejpam-3768	243	14	lower	low	ADJ
ejpam-3768	243	15	estimate	estimate	NOUN
ejpam-3768	243	16	of	of	ADP
ejpam-3768	243	17	blow	blow	NOUN
ejpam-3768	243	18	-	-	PUNCT
ejpam-3768	243	19	up	up	ADP
ejpam-3768	243	20	rate	rate	NOUN
ejpam-3768	243	21	is	be	AUX
ejpam-3768	243	22	‖u‖m+1	‖u‖m+1	PROPN
ejpam-3768	243	23	≥	≥	NUM
ejpam-3768	244	1	[	[	X
ejpam-3768	244	2	2k4((q	2k4((q	NUM
ejpam-3768	244	3	+	+	NUM
ejpam-3768	244	4	1)q+	1)q+	NUM
ejpam-3768	244	5	p−	p−	NOUN
ejpam-3768	244	6	1	1	NUM
ejpam-3768	244	7	)	)	PUNCT
ejpam-3768	244	8	m+	m+	NOUN
ejpam-3768	244	9	1	1	NUM
ejpam-3768	244	10	]	]	SYM
ejpam-3768	244	11	−	−	PROPN
ejpam-3768	244	12	1	1	NUM
ejpam-3768	244	13	(	(	PUNCT
ejpam-3768	244	14	q+1)q+p−1	q+1)q+p−1	NOUN
ejpam-3768	244	15	(	(	PUNCT
ejpam-3768	244	16	t∗	t∗	PROPN
ejpam-3768	244	17	−	−	PROPN
ejpam-3768	244	18	t)−	t)−	PROPN
ejpam-3768	244	19	1	1	NUM
ejpam-3768	244	20	(	(	PUNCT
ejpam-3768	244	21	q+1)q+p−1	q+1)q+p−1	NOUN
ejpam-3768	244	22	,	,	PUNCT
ejpam-3768	244	23	(	(	PUNCT
ejpam-3768	244	24	3.16	3.16	NUM
ejpam-3768	244	25	)	)	PUNCT
ejpam-3768	244	26	where	where	SCONJ
ejpam-3768	244	27	k3	k3	VERB
ejpam-3768	244	28	=	=	SYM
ejpam-3768	244	29	c6(m+	c6(m+	NOUN
ejpam-3768	244	30	1)|ω|	1)|ω|	NUM
ejpam-3768	244	31	1	1	NUM
ejpam-3768	244	32	m+1	m+1	NUM
ejpam-3768	244	33	,	,	PUNCT
ejpam-3768	244	34	k4	k4	NOUN
ejpam-3768	244	35	=	=	SYM
ejpam-3768	244	36	c7(m+	c7(m+	PROPN
ejpam-3768	244	37	1)|ω|	1)|ω|	NUM
ejpam-3768	244	38	1−p+(m−q)q	1−p+(m−q)q	NUM
ejpam-3768	244	39	m+1	m+1	NUM
ejpam-3768	244	40	.	.	PUNCT
ejpam-3768	245	1	proof	proof	NOUN
ejpam-3768	245	2	.	.	PUNCT
ejpam-3768	246	1	under	under	ADP
ejpam-3768	246	2	the	the	DET
ejpam-3768	246	3	assumption	assumption	NOUN
ejpam-3768	246	4	condition	condition	NOUN
ejpam-3768	246	5	(	(	PUNCT
ejpam-3768	246	6	f5	f5	PROPN
ejpam-3768	246	7	)	)	PUNCT
ejpam-3768	246	8	,	,	PUNCT
ejpam-3768	246	9	we	we	PRON
ejpam-3768	246	10	have	have	VERB
ejpam-3768	246	11	from	from	ADP
ejpam-3768	246	12	(	(	PUNCT
ejpam-3768	246	13	1.1	1.1	NUM
ejpam-3768	246	14	)	)	PUNCT
ejpam-3768	246	15	and	and	CCONJ
ejpam-3768	246	16	(	(	PUNCT
ejpam-3768	246	17	2.1	2.1	NUM
ejpam-3768	246	18	)	)	PUNCT
ejpam-3768	246	19	that	that	PRON
ejpam-3768	246	20	ϕ′(t	ϕ′(t	VERB
ejpam-3768	246	21	)	)	PUNCT
ejpam-3768	246	22	=	=	PRON
ejpam-3768	246	23	(	(	PUNCT
ejpam-3768	246	24	m+	m+	NOUN
ejpam-3768	246	25	1	1	NUM
ejpam-3768	246	26	)	)	PUNCT
ejpam-3768	247	1	∫	∫	PROPN
ejpam-3768	248	1	ω	ω	NUM
ejpam-3768	248	2	umutdx	umutdx	PROPN
ejpam-3768	248	3	=	=	PRON
ejpam-3768	248	4	(	(	PUNCT
ejpam-3768	248	5	m+	m+	NOUN
ejpam-3768	248	6	1	1	NUM
ejpam-3768	248	7	)	)	PUNCT
ejpam-3768	248	8	∫	∫	PROPN
ejpam-3768	249	1	ω	ω	INTJ
ejpam-3768	249	2	um	um	INTJ
ejpam-3768	249	3	(	(	PUNCT
ejpam-3768	249	4	4um	4um	NOUN
ejpam-3768	249	5	+	+	X
ejpam-3768	249	6	a(x)f(u	a(x)f(u	NUM
ejpam-3768	249	7	)	)	PUNCT
ejpam-3768	249	8	)	)	PUNCT
ejpam-3768	250	1	dx	dx	PROPN
ejpam-3768	251	1	=	=	PUNCT
ejpam-3768	251	2	−(m+	−(m+	NUM
ejpam-3768	251	3	1	1	X
ejpam-3768	251	4	)	)	PUNCT
ejpam-3768	251	5	∫	∫	PROPN
ejpam-3768	251	6	ω	ω	NUM
ejpam-3768	251	7	|∇um|2dx+	|∇um|2dx+	NOUN
ejpam-3768	251	8	(	(	PUNCT
ejpam-3768	251	9	m+	m+	NOUN
ejpam-3768	251	10	1	1	NUM
ejpam-3768	251	11	)	)	PUNCT
ejpam-3768	251	12	∫	∫	PROPN
ejpam-3768	251	13	ω	ω	PROPN
ejpam-3768	251	14	a(x)umf(u)dx	a(x)umf(u)dx	PART
ejpam-3768	251	15	≤	≤	PRON
ejpam-3768	251	16	c6(m+	c6(m+	PROPN
ejpam-3768	251	17	1	1	NUM
ejpam-3768	251	18	)	)	PUNCT
ejpam-3768	251	19	∫	∫	PROPN
ejpam-3768	251	20	ω	ω	PROPN
ejpam-3768	251	21	umdx+	umdx+	X
ejpam-3768	251	22	c7(m+	c7(m+	PROPN
ejpam-3768	251	23	1	1	NUM
ejpam-3768	251	24	)	)	PUNCT
ejpam-3768	251	25	∫	∫	PROPN
ejpam-3768	251	26	ω	ω	NUM
ejpam-3768	251	27	um+pdx	um+pdx	PROPN
ejpam-3768	251	28	(	(	PUNCT
ejpam-3768	251	29	∫	∫	PROPN
ejpam-3768	251	30	ω	ω	PROPN
ejpam-3768	251	31	uq+1dx	uq+1dx	PROPN
ejpam-3768	251	32	)	)	PUNCT
ejpam-3768	251	33	q	q	NOUN
ejpam-3768	251	34	.	.	PUNCT
ejpam-3768	252	1	(	(	PUNCT
ejpam-3768	252	2	3.17	3.17	NUM
ejpam-3768	252	3	)	)	PUNCT
ejpam-3768	252	4	applying	apply	VERB
ejpam-3768	252	5	hölder	hölder	NOUN
ejpam-3768	252	6	’s	’s	PART
ejpam-3768	252	7	inequality	inequality	NOUN
ejpam-3768	252	8	and	and	CCONJ
ejpam-3768	252	9	condition	condition	NOUN
ejpam-3768	252	10	(	(	PUNCT
ejpam-3768	252	11	e1	e1	PROPN
ejpam-3768	252	12	)	)	PUNCT
ejpam-3768	252	13	,	,	PUNCT
ejpam-3768	252	14	we	we	PRON
ejpam-3768	252	15	know	know	VERB
ejpam-3768	252	16	that∫	that∫	PROPN
ejpam-3768	252	17	ω	ω	PROPN
ejpam-3768	252	18	umdx	umdx	NOUN
ejpam-3768	252	19	≤	≤	PROPN
ejpam-3768	252	20	(	(	PUNCT
ejpam-3768	252	21	∫	∫	PROPN
ejpam-3768	252	22	ω	ω	PROPN
ejpam-3768	252	23	um+1dx	um+1dx	PROPN
ejpam-3768	252	24	)	)	PUNCT
ejpam-3768	252	25	m	m	VERB
ejpam-3768	252	26	m+1	m+1	NUM
ejpam-3768	252	27	|ω|	|ω|	ADP
ejpam-3768	252	28	1	1	NUM
ejpam-3768	252	29	m+1	m+1	NUM
ejpam-3768	252	30	,	,	PUNCT
ejpam-3768	252	31	(	(	PUNCT
ejpam-3768	252	32	3.18	3.18	NUM
ejpam-3768	252	33	)	)	PUNCT
ejpam-3768	252	34	∫	∫	PROPN
ejpam-3768	253	1	ω	ω	PROPN
ejpam-3768	253	2	um+pdx	um+pdx	PROPN
ejpam-3768	253	3	≤	≤	PROPN
ejpam-3768	253	4	(	(	PUNCT
ejpam-3768	253	5	∫	∫	PROPN
ejpam-3768	253	6	ω	ω	NUM
ejpam-3768	253	7	um+1dx	um+1dx	NOUN
ejpam-3768	253	8	)	)	PUNCT
ejpam-3768	253	9	m+p	m+p	NOUN
ejpam-3768	253	10	m+1	m+1	NUM
ejpam-3768	253	11	|ω|	|ω|	PROPN
ejpam-3768	253	12	1−p	1−p	NUM
ejpam-3768	253	13	m+1	m+1	NUM
ejpam-3768	253	14	,	,	PUNCT
ejpam-3768	253	15	(	(	PUNCT
ejpam-3768	253	16	3.19	3.19	NUM
ejpam-3768	253	17	)	)	PUNCT
ejpam-3768	253	18	and	and	CCONJ
ejpam-3768	253	19	∫	∫	PROPN
ejpam-3768	253	20	ω	ω	PROPN
ejpam-3768	253	21	uq+1dx	uq+1dx	PROPN
ejpam-3768	253	22	≤	≤	PROPN
ejpam-3768	253	23	(	(	PUNCT
ejpam-3768	253	24	∫	∫	PROPN
ejpam-3768	253	25	ω	ω	NUM
ejpam-3768	253	26	um+1dx	um+1dx	PROPN
ejpam-3768	253	27	)	)	PUNCT
ejpam-3768	254	1	q+1	q+1	NOUN
ejpam-3768	254	2	m+1	m+1	NUM
ejpam-3768	254	3	|ω|	|ω|	PROPN
ejpam-3768	254	4	m−q	m−q	PROPN
ejpam-3768	254	5	m+1	m+1	NUM
ejpam-3768	254	6	.	.	PUNCT
ejpam-3768	255	1	(	(	PUNCT
ejpam-3768	255	2	3.20	3.20	NUM
ejpam-3768	255	3	)	)	PUNCT
ejpam-3768	255	4	inserting	insert	VERB
ejpam-3768	255	5	(	(	PUNCT
ejpam-3768	255	6	3.18)-(3.20	3.18)-(3.20	NUM
ejpam-3768	255	7	)	)	PUNCT
ejpam-3768	255	8	into	into	ADP
ejpam-3768	255	9	(	(	PUNCT
ejpam-3768	255	10	3.17	3.17	NUM
ejpam-3768	255	11	)	)	PUNCT
ejpam-3768	255	12	,	,	PUNCT
ejpam-3768	255	13	it	it	PRON
ejpam-3768	255	14	follows	follow	VERB
ejpam-3768	255	15	that	that	SCONJ
ejpam-3768	255	16	ϕ′(t	ϕ′(t	NOUN
ejpam-3768	255	17	)	)	PUNCT
ejpam-3768	255	18	≤	≤	NOUN
ejpam-3768	256	1	c6(m+	c6(m+	NOUN
ejpam-3768	256	2	1)|ω|	1)|ω|	NUM
ejpam-3768	256	3	1	1	NUM
ejpam-3768	256	4	m+1	m+1	NUM
ejpam-3768	256	5	(	(	PUNCT
ejpam-3768	256	6	∫	∫	PROPN
ejpam-3768	256	7	ω	ω	PROPN
ejpam-3768	256	8	um+1dx	um+1dx	PROPN
ejpam-3768	256	9	)	)	PUNCT
ejpam-3768	256	10	m	m	VERB
ejpam-3768	256	11	m+1	m+1	PRON
ejpam-3768	256	12	+	+	CCONJ
ejpam-3768	257	1	c7(m+	c7(m+	PROPN
ejpam-3768	257	2	1)|ω|	1)|ω|	NUM
ejpam-3768	257	3	1−p+(m−q)q	1−p+(m−q)q	NUM
ejpam-3768	257	4	m+1	m+1	NUM
ejpam-3768	257	5	(	(	PUNCT
ejpam-3768	257	6	∫	∫	PROPN
ejpam-3768	257	7	ω	ω	PROPN
ejpam-3768	257	8	um+1dx	um+1dx	NOUN
ejpam-3768	257	9	)	)	PUNCT
ejpam-3768	257	10	m+p+(q+1)q	m+p+(q+1)q	NOUN
ejpam-3768	257	11	m+1	m+1	NUM
ejpam-3768	257	12	,	,	PUNCT
ejpam-3768	257	13	(	(	PUNCT
ejpam-3768	257	14	3.21	3.21	NUM
ejpam-3768	257	15	)	)	PUNCT
ejpam-3768	257	16	h.f	h.f	PROPN
ejpam-3768	257	17	.	.	PROPN
ejpam-3768	257	18	di	di	PROPN
ejpam-3768	257	19	,	,	PUNCT
ejpam-3768	257	20	l.	l.	PROPN
ejpam-3768	257	21	chen	chen	PROPN
ejpam-3768	257	22	and	and	CCONJ
ejpam-3768	257	23	z.f	z.f	PROPN
ejpam-3768	257	24	.	.	PROPN
ejpam-3768	257	25	song	song	PROPN
ejpam-3768	257	26	/	/	SYM
ejpam-3768	257	27	eur	eur	PROPN
ejpam-3768	257	28	.	.	PUNCT
ejpam-3768	258	1	j.	j.	PROPN
ejpam-3768	258	2	pure	pure	PROPN
ejpam-3768	258	3	appl	appl	PROPN
ejpam-3768	258	4	.	.	PROPN
ejpam-3768	258	5	math	math	PROPN
ejpam-3768	258	6	,	,	PUNCT
ejpam-3768	258	7	13	13	NUM
ejpam-3768	258	8	(	(	PUNCT
ejpam-3768	258	9	3	3	NUM
ejpam-3768	258	10	)	)	PUNCT
ejpam-3768	258	11	(	(	PUNCT
ejpam-3768	258	12	2020	2020	NUM
ejpam-3768	258	13	)	)	PUNCT
ejpam-3768	258	14	,	,	PUNCT
ejpam-3768	258	15	645	645	NUM
ejpam-3768	258	16	-	-	SYM
ejpam-3768	258	17	662	662	NUM
ejpam-3768	258	18	656	656	NUM
ejpam-3768	258	19	where	where	SCONJ
ejpam-3768	258	20	from	from	ADP
ejpam-3768	258	21	the	the	DET
ejpam-3768	258	22	condition	condition	NOUN
ejpam-3768	258	23	(	(	PUNCT
ejpam-3768	258	24	e1	e1	PROPN
ejpam-3768	258	25	)	)	PUNCT
ejpam-3768	258	26	,	,	PUNCT
ejpam-3768	258	27	it	it	PRON
ejpam-3768	258	28	is	be	AUX
ejpam-3768	258	29	easy	easy	ADJ
ejpam-3768	258	30	to	to	PART
ejpam-3768	258	31	see	see	VERB
ejpam-3768	258	32	that	that	SCONJ
ejpam-3768	258	33	m+p+(q+1)q	m+p+(q+1)q	VERB
ejpam-3768	258	34	m+1	m+1	PRON
ejpam-3768	258	35	>	>	X
ejpam-3768	258	36	1	1	NUM
ejpam-3768	258	37	.	.	PUNCT
ejpam-3768	259	1	then	then	ADV
ejpam-3768	259	2	,	,	PUNCT
ejpam-3768	259	3	integrating	integrate	VERB
ejpam-3768	259	4	the	the	DET
ejpam-3768	259	5	above	above	ADJ
ejpam-3768	259	6	inequality	inequality	NOUN
ejpam-3768	259	7	from	from	ADP
ejpam-3768	259	8	0	0	NUM
ejpam-3768	259	9	to	to	ADP
ejpam-3768	259	10	t	t	PROPN
ejpam-3768	259	11	yields	yield	NOUN
ejpam-3768	259	12	that∫	that∫	PROPN
ejpam-3768	259	13	ϕ(t	ϕ(t	NUM
ejpam-3768	259	14	)	)	PUNCT
ejpam-3768	260	1	ϕ(0	ϕ(0	PROPN
ejpam-3768	260	2	)	)	PUNCT
ejpam-3768	261	1	dη	dη	ADP
ejpam-3768	262	1	k3η	k3η	PROPN
ejpam-3768	262	2	m	m	VERB
ejpam-3768	262	3	m+1	m+1	PROPN
ejpam-3768	262	4	+	+	CCONJ
ejpam-3768	262	5	k4η	k4η	NOUN
ejpam-3768	262	6	m+p+(q+1)q	m+p+(q+1)q	NOUN
ejpam-3768	262	7	m+1	m+1	PRON
ejpam-3768	262	8	≤	≤	NUM
ejpam-3768	262	9	t	t	PROPN
ejpam-3768	262	10	,	,	PUNCT
ejpam-3768	262	11	where	where	SCONJ
ejpam-3768	262	12	k3	k3	VERB
ejpam-3768	262	13	=	=	SYM
ejpam-3768	262	14	c6(m+	c6(m+	NOUN
ejpam-3768	262	15	1)|ω|	1)|ω|	NUM
ejpam-3768	262	16	1	1	NUM
ejpam-3768	262	17	m+1	m+1	NUM
ejpam-3768	262	18	,	,	PUNCT
ejpam-3768	262	19	k4	k4	NOUN
ejpam-3768	262	20	=	=	SYM
ejpam-3768	262	21	c7(m+	c7(m+	PROPN
ejpam-3768	262	22	1)|ω|	1)|ω|	NUM
ejpam-3768	262	23	1−p+(m−q)q	1−p+(m−q)q	NUM
ejpam-3768	262	24	m+1	m+1	NUM
ejpam-3768	262	25	.	.	PUNCT
ejpam-3768	263	1	if	if	SCONJ
ejpam-3768	263	2	u	u	PRON
ejpam-3768	263	3	blows	blow	VERB
ejpam-3768	263	4	up	up	ADP
ejpam-3768	263	5	in	in	ADP
ejpam-3768	263	6	the	the	DET
ejpam-3768	263	7	measure	measure	NOUN
ejpam-3768	263	8	ϕ(t	ϕ(t	NUM
ejpam-3768	263	9	)	)	PUNCT
ejpam-3768	263	10	as	as	ADP
ejpam-3768	263	11	t→	t→	DET
ejpam-3768	263	12	t∗	t∗	PROPN
ejpam-3768	263	13	,	,	PUNCT
ejpam-3768	263	14	then	then	ADV
ejpam-3768	263	15	we	we	PRON
ejpam-3768	263	16	can	can	AUX
ejpam-3768	263	17	obtain	obtain	VERB
ejpam-3768	263	18	the	the	DET
ejpam-3768	263	19	lower	low	ADJ
ejpam-3768	263	20	bound	bind	VERB
ejpam-3768	263	21	t∗	t∗	PROPN
ejpam-3768	263	22	≥	≥	PUNCT
ejpam-3768	263	23	∫	∫	PROPN
ejpam-3768	264	1	+	+	NUM
ejpam-3768	264	2	∞	∞	PROPN
ejpam-3768	264	3	ϕ(0	ϕ(0	PROPN
ejpam-3768	264	4	)	)	PUNCT
ejpam-3768	264	5	dη	dη	ADP
ejpam-3768	265	1	k3η	k3η	PROPN
ejpam-3768	265	2	m	m	VERB
ejpam-3768	265	3	m+1	m+1	PROPN
ejpam-3768	265	4	+	+	CCONJ
ejpam-3768	265	5	k4η	k4η	NOUN
ejpam-3768	265	6	m+p+(q+1)q	m+p+(q+1)q	NOUN
ejpam-3768	265	7	m+1	m+1	PRON
ejpam-3768	265	8	.	.	PUNCT
ejpam-3768	266	1	furthermore	furthermore	ADV
ejpam-3768	266	2	,	,	PUNCT
ejpam-3768	266	3	integrating	integrate	VERB
ejpam-3768	266	4	the	the	DET
ejpam-3768	266	5	inequality	inequality	NOUN
ejpam-3768	266	6	(	(	PUNCT
ejpam-3768	266	7	3.21	3.21	NUM
ejpam-3768	266	8	)	)	PUNCT
ejpam-3768	266	9	from	from	ADP
ejpam-3768	266	10	t	t	PROPN
ejpam-3768	266	11	to	to	ADP
ejpam-3768	266	12	t∗	t∗	PROPN
ejpam-3768	266	13	,	,	PUNCT
ejpam-3768	266	14	we	we	PRON
ejpam-3768	266	15	obtain	obtain	VERB
ejpam-3768	266	16	t∗	t∗	NOUN
ejpam-3768	266	17	−	−	PROPN
ejpam-3768	266	18	t	t	PROPN
ejpam-3768	266	19	≥	≥	X
ejpam-3768	266	20	∫	∫	PROPN
ejpam-3768	267	1	+	+	X
ejpam-3768	267	2	∞	∞	PROPN
ejpam-3768	267	3	ϕ(t	ϕ(t	NUM
ejpam-3768	267	4	)	)	PUNCT
ejpam-3768	267	5	dη	dη	ADP
ejpam-3768	268	1	k3η	k3η	PROPN
ejpam-3768	268	2	m	m	VERB
ejpam-3768	268	3	m+1	m+1	PROPN
ejpam-3768	268	4	+	+	CCONJ
ejpam-3768	268	5	k4η	k4η	NOUN
ejpam-3768	268	6	m+p+(q+1)q	m+p+(q+1)q	NOUN
ejpam-3768	268	7	m+1	m+1	PRON
ejpam-3768	268	8	:	:	PUNCT
ejpam-3768	268	9	=	=	PUNCT
ejpam-3768	268	10	y2(ϕ(t	y2(ϕ(t	NUM
ejpam-3768	268	11	)	)	PUNCT
ejpam-3768	268	12	)	)	PUNCT
ejpam-3768	268	13	.	.	PUNCT
ejpam-3768	269	1	(	(	PUNCT
ejpam-3768	269	2	3.22	3.22	NUM
ejpam-3768	269	3	)	)	PUNCT
ejpam-3768	269	4	we	we	PRON
ejpam-3768	269	5	note	note	VERB
ejpam-3768	269	6	that	that	SCONJ
ejpam-3768	269	7	y2	y2	PROPN
ejpam-3768	269	8	is	be	AUX
ejpam-3768	269	9	a	a	DET
ejpam-3768	269	10	decreasing	decrease	VERB
ejpam-3768	269	11	function	function	NOUN
ejpam-3768	269	12	,	,	PUNCT
ejpam-3768	269	13	which	which	PRON
ejpam-3768	269	14	means	mean	VERB
ejpam-3768	269	15	its	its	PRON
ejpam-3768	269	16	inverse	inverse	NOUN
ejpam-3768	269	17	function	function	NOUN
ejpam-3768	269	18	y	y	PROPN
ejpam-3768	269	19	−1	−1	NOUN
ejpam-3768	269	20	2	2	NUM
ejpam-3768	269	21	exists	exist	VERB
ejpam-3768	269	22	and	and	CCONJ
ejpam-3768	269	23	it	it	PRON
ejpam-3768	269	24	is	be	AUX
ejpam-3768	269	25	also	also	ADV
ejpam-3768	269	26	a	a	DET
ejpam-3768	269	27	decreasing	decrease	VERB
ejpam-3768	269	28	function	function	NOUN
ejpam-3768	269	29	.	.	PUNCT
ejpam-3768	270	1	therefore	therefore	ADV
ejpam-3768	270	2	,	,	PUNCT
ejpam-3768	270	3	we	we	PRON
ejpam-3768	270	4	have	have	VERB
ejpam-3768	270	5	ϕ(t	ϕ(t	NUM
ejpam-3768	270	6	)	)	PUNCT
ejpam-3768	270	7	≥	≥	NOUN
ejpam-3768	270	8	y	y	PROPN
ejpam-3768	270	9	−1	−1	NOUN
ejpam-3768	270	10	2	2	NUM
ejpam-3768	270	11	(	(	PUNCT
ejpam-3768	270	12	t∗	t∗	NOUN
ejpam-3768	270	13	−	−	PROPN
ejpam-3768	270	14	t	t	PROPN
ejpam-3768	270	15	)	)	PUNCT
ejpam-3768	270	16	,	,	PUNCT
ejpam-3768	270	17	(	(	PUNCT
ejpam-3768	270	18	3.23	3.23	NUM
ejpam-3768	270	19	)	)	PUNCT
ejpam-3768	270	20	which	which	PRON
ejpam-3768	270	21	gives	give	VERB
ejpam-3768	270	22	the	the	DET
ejpam-3768	270	23	lower	low	ADJ
ejpam-3768	270	24	estimate	estimate	NOUN
ejpam-3768	270	25	of	of	ADP
ejpam-3768	270	26	blow	blow	NOUN
ejpam-3768	270	27	-	-	PUNCT
ejpam-3768	270	28	up	up	ADP
ejpam-3768	270	29	rate	rate	NOUN
ejpam-3768	270	30	.	.	PUNCT
ejpam-3768	271	1	in	in	ADP
ejpam-3768	271	2	fact	fact	NOUN
ejpam-3768	271	3	,	,	PUNCT
ejpam-3768	271	4	the	the	DET
ejpam-3768	271	5	auxiliary	auxiliary	ADJ
ejpam-3768	271	6	function	function	NOUN
ejpam-3768	271	7	ϕ(t	ϕ(t	NUM
ejpam-3768	271	8	)	)	PUNCT
ejpam-3768	271	9	becomes	become	VERB
ejpam-3768	271	10	unbounded	unbounded	ADJ
ejpam-3768	271	11	at	at	ADP
ejpam-3768	271	12	time	time	NOUN
ejpam-3768	271	13	t	t	NOUN
ejpam-3768	271	14	=	=	SYM
ejpam-3768	271	15	t∗	t∗	PROPN
ejpam-3768	271	16	,	,	PUNCT
ejpam-3768	271	17	so	so	SCONJ
ejpam-3768	271	18	we	we	PRON
ejpam-3768	271	19	know	know	VERB
ejpam-3768	271	20	that	that	SCONJ
ejpam-3768	271	21	ϕ(t	ϕ(t	NUM
ejpam-3768	271	22	)	)	PUNCT
ejpam-3768	271	23	�	�	PROPN
ejpam-3768	271	24	1	1	NUM
ejpam-3768	271	25	and	and	CCONJ
ejpam-3768	271	26	the	the	DET
ejpam-3768	271	27	inequality	inequality	NOUN
ejpam-3768	271	28	k4η	k4η	NOUN
ejpam-3768	271	29	m+p+(q+1)q	m+p+(q+1)q	VERB
ejpam-3768	271	30	m+1	m+1	PRON
ejpam-3768	271	31	>	>	X
ejpam-3768	271	32	k3η	k3η	PROPN
ejpam-3768	271	33	m	m	NOUN
ejpam-3768	271	34	m+1	m+1	NUM
ejpam-3768	271	35	as	as	ADP
ejpam-3768	271	36	t→	t→	PRON
ejpam-3768	271	37	t∗−.	t∗−.	PROPN
ejpam-3768	271	38	hence	hence	ADV
ejpam-3768	271	39	,	,	PUNCT
ejpam-3768	271	40	when	when	SCONJ
ejpam-3768	271	41	t	t	PROPN
ejpam-3768	271	42	is	be	AUX
ejpam-3768	271	43	close	close	ADJ
ejpam-3768	271	44	to	to	ADP
ejpam-3768	271	45	t∗	t∗	NOUN
ejpam-3768	271	46	,	,	PUNCT
ejpam-3768	271	47	inserting	insert	VERB
ejpam-3768	271	48	the	the	DET
ejpam-3768	271	49	above	above	ADJ
ejpam-3768	271	50	inequality	inequality	NOUN
ejpam-3768	271	51	into	into	ADP
ejpam-3768	271	52	(	(	PUNCT
ejpam-3768	271	53	3.22	3.22	NUM
ejpam-3768	271	54	)	)	PUNCT
ejpam-3768	271	55	and	and	CCONJ
ejpam-3768	271	56	then	then	ADV
ejpam-3768	271	57	a	a	DET
ejpam-3768	271	58	direct	direct	ADJ
ejpam-3768	271	59	calculation	calculation	NOUN
ejpam-3768	271	60	yields	yield	NOUN
ejpam-3768	271	61	that	that	PRON
ejpam-3768	271	62	t∗	t∗	VERB
ejpam-3768	271	63	−	−	PROPN
ejpam-3768	271	64	t	t	PROPN
ejpam-3768	271	65	≥	≥	NUM
ejpam-3768	271	66	m+	m+	NUM
ejpam-3768	271	67	1	1	NUM
ejpam-3768	271	68	2k4[(q	2k4[(q	NUM
ejpam-3768	271	69	+	+	NUM
ejpam-3768	271	70	1)q+	1)q+	NUM
ejpam-3768	271	71	p−	p−	NOUN
ejpam-3768	271	72	1	1	NUM
ejpam-3768	271	73	]	]	X
ejpam-3768	271	74	[	[	PUNCT
ejpam-3768	271	75	ϕ(t	ϕ(t	NUM
ejpam-3768	271	76	)	)	PUNCT
ejpam-3768	271	77	]	]	PUNCT
ejpam-3768	271	78	−	−	PROPN
ejpam-3768	271	79	(	(	PUNCT
ejpam-3768	271	80	q+1)q+p−1	q+1)q+p−1	NOUN
ejpam-3768	271	81	m+1	m+1	X
ejpam-3768	271	82	,	,	PUNCT
ejpam-3768	271	83	(	(	PUNCT
ejpam-3768	271	84	3.24	3.24	NUM
ejpam-3768	271	85	)	)	PUNCT
ejpam-3768	271	86	which	which	PRON
ejpam-3768	271	87	means	mean	VERB
ejpam-3768	271	88	that	that	SCONJ
ejpam-3768	271	89	ϕ(t	ϕ(t	NUM
ejpam-3768	271	90	)	)	PUNCT
ejpam-3768	271	91	≥	≥	PRON
ejpam-3768	272	1	[	[	X
ejpam-3768	272	2	2k4((q	2k4((q	NUM
ejpam-3768	272	3	+	+	NUM
ejpam-3768	272	4	1)q+	1)q+	NUM
ejpam-3768	272	5	p−	p−	NOUN
ejpam-3768	272	6	1	1	NUM
ejpam-3768	272	7	)	)	PUNCT
ejpam-3768	272	8	m+	m+	NOUN
ejpam-3768	272	9	1	1	NUM
ejpam-3768	272	10	]	]	SYM
ejpam-3768	272	11	−	−	PROPN
ejpam-3768	272	12	m+1	m+1	NUM
ejpam-3768	272	13	(	(	PUNCT
ejpam-3768	272	14	q+1)q+p−1	q+1)q+p−1	X
ejpam-3768	272	15	(	(	PUNCT
ejpam-3768	272	16	t∗	t∗	NOUN
ejpam-3768	272	17	−	−	PROPN
ejpam-3768	272	18	t)−	t)−	PROPN
ejpam-3768	272	19	m+1	m+1	X
ejpam-3768	272	20	(	(	PUNCT
ejpam-3768	272	21	q+1)q+p−1	q+1)q+p−1	NOUN
ejpam-3768	272	22	.	.	PUNCT
ejpam-3768	273	1	(	(	PUNCT
ejpam-3768	273	2	3.25	3.25	NUM
ejpam-3768	273	3	)	)	PUNCT
ejpam-3768	273	4	hence	hence	ADV
ejpam-3768	273	5	,	,	PUNCT
ejpam-3768	273	6	the	the	DET
ejpam-3768	273	7	estimate	estimate	NOUN
ejpam-3768	273	8	(	(	PUNCT
ejpam-3768	273	9	3.16	3.16	NUM
ejpam-3768	273	10	)	)	PUNCT
ejpam-3768	273	11	of	of	ADP
ejpam-3768	273	12	blow	blow	NOUN
ejpam-3768	273	13	-	-	PUNCT
ejpam-3768	273	14	up	up	ADP
ejpam-3768	273	15	rate	rate	NOUN
ejpam-3768	273	16	holds	hold	NOUN
ejpam-3768	273	17	.	.	PUNCT
ejpam-3768	273	18	3.3	3.3	NUM
ejpam-3768	273	19	.	.	PUNCT
ejpam-3768	274	1	the	the	DET
ejpam-3768	274	2	third	third	ADJ
ejpam-3768	274	3	method	method	NOUN
ejpam-3768	274	4	this	this	DET
ejpam-3768	274	5	subsection	subsection	NOUN
ejpam-3768	274	6	is	be	AUX
ejpam-3768	274	7	devoted	devote	VERB
ejpam-3768	274	8	to	to	ADP
ejpam-3768	274	9	the	the	DET
ejpam-3768	274	10	estimates	estimate	NOUN
ejpam-3768	274	11	of	of	ADP
ejpam-3768	274	12	the	the	DET
ejpam-3768	274	13	lower	low	ADJ
ejpam-3768	274	14	bounds	bound	NOUN
ejpam-3768	274	15	for	for	ADP
ejpam-3768	274	16	blow	blow	NOUN
ejpam-3768	274	17	-	-	PUNCT
ejpam-3768	274	18	up	up	ADP
ejpam-3768	274	19	time	time	NOUN
ejpam-3768	274	20	and	and	CCONJ
ejpam-3768	274	21	blow	blow	NOUN
ejpam-3768	274	22	-	-	PUNCT
ejpam-3768	274	23	up	up	ADP
ejpam-3768	274	24	rate	rate	NOUN
ejpam-3768	274	25	of	of	ADP
ejpam-3768	274	26	the	the	DET
ejpam-3768	274	27	solutions	solution	NOUN
ejpam-3768	274	28	to	to	ADP
ejpam-3768	274	29	problem	problem	NOUN
ejpam-3768	274	30	(	(	PUNCT
ejpam-3768	274	31	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	274	32	)	)	PUNCT
ejpam-3768	274	33	by	by	ADP
ejpam-3768	274	34	utilizing	utilize	VERB
ejpam-3768	274	35	the	the	DET
ejpam-3768	274	36	method	method	NOUN
ejpam-3768	274	37	appearing	appear	VERB
ejpam-3768	274	38	in	in	ADP
ejpam-3768	274	39	[	[	X
ejpam-3768	274	40	18	18	NUM
ejpam-3768	274	41	,	,	PUNCT
ejpam-3768	274	42	19	19	NUM
ejpam-3768	274	43	]	]	PUNCT
ejpam-3768	274	44	.	.	PUNCT
ejpam-3768	275	1	for	for	ADP
ejpam-3768	275	2	this	this	DET
ejpam-3768	275	3	purpose	purpose	NOUN
ejpam-3768	275	4	,	,	PUNCT
ejpam-3768	275	5	we	we	PRON
ejpam-3768	275	6	need	need	VERB
ejpam-3768	275	7	to	to	PART
ejpam-3768	275	8	assume	assume	VERB
ejpam-3768	275	9	that	that	SCONJ
ejpam-3768	275	10	(	(	PUNCT
ejpam-3768	275	11	f6	f6	PROPN
ejpam-3768	275	12	):	):	PUNCT
ejpam-3768	275	13	sm−1	sm−1	NOUN
ejpam-3768	275	14	≥	≥	NUM
ejpam-3768	275	15	α	α	PROPN
ejpam-3768	275	16	(	(	PUNCT
ejpam-3768	275	17	∫	∫	PROPN
ejpam-3768	275	18	+	+	NUM
ejpam-3768	275	19	∞	∞	PROPN
ejpam-3768	275	20	s	s	NOUN
ejpam-3768	275	21	dη	dη	NOUN
ejpam-3768	275	22	f(η	f(η	NOUN
ejpam-3768	275	23	)	)	PUNCT
ejpam-3768	275	24	)	)	PUNCT
ejpam-3768	275	25	−γ	−γ	NOUN
ejpam-3768	275	26	,	,	PUNCT
ejpam-3768	275	27	for	for	ADP
ejpam-3768	275	28	any	any	DET
ejpam-3768	275	29	function	function	NOUN
ejpam-3768	275	30	s(x	s(x	PROPN
ejpam-3768	275	31	)	)	PUNCT
ejpam-3768	275	32	≥	≥	NOUN
ejpam-3768	275	33	0	0	NUM
ejpam-3768	275	34	,	,	PUNCT
ejpam-3768	275	35	where	where	SCONJ
ejpam-3768	275	36	α	α	X
ejpam-3768	275	37	,	,	PUNCT
ejpam-3768	275	38	γ	γ	NOUN
ejpam-3768	275	39	are	be	AUX
ejpam-3768	275	40	positive	positive	ADJ
ejpam-3768	275	41	constants	constant	NOUN
ejpam-3768	275	42	and	and	CCONJ
ejpam-3768	275	43	0	0	NUM
ejpam-3768	275	44	<	<	X
ejpam-3768	275	45	γ	γ	X
ejpam-3768	275	46	<	<	X
ejpam-3768	275	47	1	1	NUM
ejpam-3768	275	48	;	;	PUNCT
ejpam-3768	275	49	h.f	h.f	PROPN
ejpam-3768	275	50	.	.	PROPN
ejpam-3768	275	51	di	di	PROPN
ejpam-3768	275	52	,	,	PUNCT
ejpam-3768	275	53	l.	l.	PROPN
ejpam-3768	275	54	chen	chen	PROPN
ejpam-3768	275	55	and	and	CCONJ
ejpam-3768	275	56	z.f	z.f	PROPN
ejpam-3768	275	57	.	.	PROPN
ejpam-3768	275	58	song	song	PROPN
ejpam-3768	275	59	/	/	SYM
ejpam-3768	275	60	eur	eur	PROPN
ejpam-3768	275	61	.	.	PUNCT
ejpam-3768	276	1	j.	j.	PROPN
ejpam-3768	276	2	pure	pure	PROPN
ejpam-3768	276	3	appl	appl	PROPN
ejpam-3768	276	4	.	.	PROPN
ejpam-3768	276	5	math	math	PROPN
ejpam-3768	276	6	,	,	PUNCT
ejpam-3768	276	7	13	13	NUM
ejpam-3768	276	8	(	(	PUNCT
ejpam-3768	276	9	3	3	NUM
ejpam-3768	276	10	)	)	PUNCT
ejpam-3768	276	11	(	(	PUNCT
ejpam-3768	276	12	2020	2020	NUM
ejpam-3768	276	13	)	)	PUNCT
ejpam-3768	276	14	,	,	PUNCT
ejpam-3768	276	15	645	645	NUM
ejpam-3768	276	16	-	-	SYM
ejpam-3768	276	17	662	662	NUM
ejpam-3768	276	18	657	657	NUM
ejpam-3768	276	19	(	(	PUNCT
ejpam-3768	276	20	f7	f7	PROPN
ejpam-3768	276	21	):	):	PUNCT
ejpam-3768	276	22	there	there	PRON
ejpam-3768	276	23	exist	exist	VERB
ejpam-3768	276	24	positive	positive	ADJ
ejpam-3768	276	25	constants	constant	NOUN
ejpam-3768	276	26	k	k	PROPN
ejpam-3768	276	27	and	and	CCONJ
ejpam-3768	276	28	β	β	PRON
ejpam-3768	276	29	such	such	ADJ
ejpam-3768	276	30	that	that	SCONJ
ejpam-3768	276	31	k	k	PROPN
ejpam-3768	276	32	>	>	X
ejpam-3768	276	33	4(n−2)−nγ	4(n−2)−nγ	PROPN
ejpam-3768	276	34	2n	2n	NUM
ejpam-3768	276	35	,	,	PUNCT
ejpam-3768	276	36	f(s	f(s	PROPN
ejpam-3768	276	37	)	)	PUNCT
ejpam-3768	277	1	(	(	PUNCT
ejpam-3768	277	2	∫	∫	PROPN
ejpam-3768	277	3	+	+	NUM
ejpam-3768	277	4	∞	∞	PROPN
ejpam-3768	277	5	s	s	NOUN
ejpam-3768	277	6	dη	dη	NOUN
ejpam-3768	277	7	f(η	f(η	NOUN
ejpam-3768	277	8	)	)	PUNCT
ejpam-3768	277	9	)	)	PUNCT
ejpam-3768	277	10	nk+1	nk+1	X
ejpam-3768	277	11	→	→	SYM
ejpam-3768	277	12	+	+	NOUN
ejpam-3768	277	13	∞	∞	PROPN
ejpam-3768	277	14	,	,	PUNCT
ejpam-3768	277	15	as	as	ADP
ejpam-3768	277	16	s→	s→	X
ejpam-3768	277	17	0	0	NUM
ejpam-3768	277	18	+	+	ADJ
ejpam-3768	277	19	,	,	PUNCT
ejpam-3768	277	20	and	and	CCONJ
ejpam-3768	277	21	f	f	PROPN
ejpam-3768	277	22	′(s	′(s	PROPN
ejpam-3768	277	23	)	)	PUNCT
ejpam-3768	277	24	∫	∫	PROPN
ejpam-3768	278	1	+	+	NUM
ejpam-3768	278	2	∞	∞	PROPN
ejpam-3768	278	3	s	s	NOUN
ejpam-3768	278	4	dη	dη	NOUN
ejpam-3768	278	5	f(η	f(η	NOUN
ejpam-3768	278	6	)	)	PUNCT
ejpam-3768	278	7	≤	≤	PUNCT
ejpam-3768	278	8	nk	nk	PROPN
ejpam-3768	279	1	+	+	NUM
ejpam-3768	279	2	1−	1−	NUM
ejpam-3768	279	3	β	β	NOUN
ejpam-3768	279	4	,	,	PUNCT
ejpam-3768	279	5	for	for	ADP
ejpam-3768	279	6	any	any	DET
ejpam-3768	279	7	function	function	NOUN
ejpam-3768	279	8	s(x	s(x	PROPN
ejpam-3768	279	9	)	)	PUNCT
ejpam-3768	279	10	≥	≥	NOUN
ejpam-3768	279	11	0	0	NUM
ejpam-3768	279	12	.	.	PUNCT
ejpam-3768	280	1	then	then	ADV
ejpam-3768	280	2	,	,	PUNCT
ejpam-3768	280	3	we	we	PRON
ejpam-3768	280	4	define	define	VERB
ejpam-3768	280	5	the	the	DET
ejpam-3768	280	6	following	follow	VERB
ejpam-3768	280	7	auxiliary	auxiliary	ADJ
ejpam-3768	280	8	function	function	NOUN
ejpam-3768	280	9	ϕ2(t	ϕ2(t	PROPN
ejpam-3768	280	10	)	)	PUNCT
ejpam-3768	280	11	=	=	SYM
ejpam-3768	281	1	∫	∫	PROPN
ejpam-3768	281	2	ω	ω	NUM
ejpam-3768	281	3	v	v	ADP
ejpam-3768	281	4	nk(u)dx	nk(u)dx	ADJ
ejpam-3768	281	5	,	,	PUNCT
ejpam-3768	281	6	v	v	NOUN
ejpam-3768	281	7	(	(	PUNCT
ejpam-3768	281	8	u	u	NOUN
ejpam-3768	281	9	)	)	PUNCT
ejpam-3768	281	10	=	=	SYM
ejpam-3768	281	11	(	(	PUNCT
ejpam-3768	281	12	∫	∫	PROPN
ejpam-3768	282	1	+	+	NUM
ejpam-3768	282	2	∞	∞	PROPN
ejpam-3768	282	3	u	u	NOUN
ejpam-3768	282	4	dη	dη	X
ejpam-3768	282	5	f(η	f(η	NOUN
ejpam-3768	282	6	)	)	PUNCT
ejpam-3768	282	7	)	)	PUNCT
ejpam-3768	283	1	−1	−1	NOUN
ejpam-3768	283	2	.	.	PUNCT
ejpam-3768	284	1	(	(	PUNCT
ejpam-3768	284	2	3.26	3.26	NUM
ejpam-3768	284	3	)	)	PUNCT
ejpam-3768	284	4	next	next	ADV
ejpam-3768	284	5	,	,	PUNCT
ejpam-3768	284	6	we	we	PRON
ejpam-3768	284	7	will	will	AUX
ejpam-3768	284	8	state	state	VERB
ejpam-3768	284	9	our	our	PRON
ejpam-3768	284	10	results	result	NOUN
ejpam-3768	284	11	below	below	ADV
ejpam-3768	284	12	:	:	PUNCT
ejpam-3768	284	13	theorem	theorem	NOUN
ejpam-3768	284	14	5	5	NUM
ejpam-3768	284	15	.	.	PUNCT
ejpam-3768	284	16	assume	assume	VERB
ejpam-3768	284	17	that	that	SCONJ
ejpam-3768	284	18	the	the	DET
ejpam-3768	284	19	conditions	condition	NOUN
ejpam-3768	284	20	(	(	PUNCT
ejpam-3768	284	21	f1	f1	NOUN
ejpam-3768	284	22	)	)	PUNCT
ejpam-3768	284	23	,	,	PUNCT
ejpam-3768	284	24	(	(	PUNCT
ejpam-3768	284	25	f6	f6	PROPN
ejpam-3768	284	26	)	)	PUNCT
ejpam-3768	284	27	,	,	PUNCT
ejpam-3768	284	28	(	(	PUNCT
ejpam-3768	284	29	f7	f7	PROPN
ejpam-3768	284	30	)	)	PUNCT
ejpam-3768	284	31	,	,	PUNCT
ejpam-3768	284	32	(	(	PUNCT
ejpam-3768	284	33	a1	a1	NOUN
ejpam-3768	284	34	)	)	PUNCT
ejpam-3768	284	35	,	,	PUNCT
ejpam-3768	284	36	(	(	PUNCT
ejpam-3768	284	37	a2	a2	NOUN
ejpam-3768	284	38	)	)	PUNCT
ejpam-3768	284	39	hold	hold	NOUN
ejpam-3768	284	40	,	,	PUNCT
ejpam-3768	284	41	and	and	CCONJ
ejpam-3768	284	42	u	u	NOUN
ejpam-3768	284	43	is	be	AUX
ejpam-3768	284	44	a	a	DET
ejpam-3768	284	45	nonnegative	nonnegative	ADJ
ejpam-3768	284	46	solution	solution	NOUN
ejpam-3768	284	47	of	of	ADP
ejpam-3768	284	48	problem	problem	NOUN
ejpam-3768	284	49	(	(	PUNCT
ejpam-3768	284	50	1.1)-(1.3	1.1)-(1.3	NUM
ejpam-3768	284	51	)	)	PUNCT
ejpam-3768	284	52	which	which	PRON
ejpam-3768	284	53	becomes	become	VERB
ejpam-3768	284	54	unbounded	unbounded	ADJ
ejpam-3768	284	55	in	in	ADP
ejpam-3768	284	56	ϕ2(t)-form	ϕ2(t)-form	NOUN
ejpam-3768	284	57	at	at	ADP
ejpam-3768	284	58	t	t	PROPN
ejpam-3768	284	59	=	=	SYM
ejpam-3768	284	60	t∗.	t∗.	PROPN
ejpam-3768	284	61	then	then	ADV
ejpam-3768	284	62	,	,	PUNCT
ejpam-3768	284	63	we	we	PRON
ejpam-3768	284	64	conclude	conclude	VERB
ejpam-3768	284	65	that	that	SCONJ
ejpam-3768	284	66	a	a	PRON
ejpam-3768	284	67	lower	lower	ADV
ejpam-3768	284	68	bound	bind	VERB
ejpam-3768	284	69	for	for	ADP
ejpam-3768	284	70	blow	blow	NOUN
ejpam-3768	284	71	-	-	PUNCT
ejpam-3768	284	72	up	up	ADP
ejpam-3768	284	73	time	time	NOUN
ejpam-3768	284	74	t∗	t∗	NOUN
ejpam-3768	284	75	is	be	AUX
ejpam-3768	284	76	given	give	VERB
ejpam-3768	284	77	by	by	ADP
ejpam-3768	284	78	t∗	t∗	PROPN
ejpam-3768	284	79	≥	≥	NUM
ejpam-3768	284	80	∫	∫	PROPN
ejpam-3768	285	1	+	+	CCONJ
ejpam-3768	285	2	∞	∞	PROPN
ejpam-3768	285	3	ϕ2(0	ϕ2(0	NOUN
ejpam-3768	285	4	)	)	PUNCT
ejpam-3768	286	1	dη	dη	ADP
ejpam-3768	286	2	k5	k5	PROPN
ejpam-3768	286	3	+	+	CCONJ
ejpam-3768	286	4	k6η	k6η	PROPN
ejpam-3768	286	5	3n−6	3n−6	NUM
ejpam-3768	286	6	3n−8	3n−8	NUM
ejpam-3768	286	7	,	,	PUNCT
ejpam-3768	286	8	(	(	PUNCT
ejpam-3768	286	9	3.27	3.27	NUM
ejpam-3768	286	10	)	)	PUNCT
ejpam-3768	286	11	and	and	CCONJ
ejpam-3768	286	12	the	the	DET
ejpam-3768	286	13	lower	low	ADJ
ejpam-3768	286	14	estimate	estimate	NOUN
ejpam-3768	286	15	of	of	ADP
ejpam-3768	286	16	blow	blow	NOUN
ejpam-3768	286	17	-	-	PUNCT
ejpam-3768	286	18	up	up	ADP
ejpam-3768	286	19	rate	rate	NOUN
ejpam-3768	286	20	can	can	AUX
ejpam-3768	286	21	be	be	AUX
ejpam-3768	286	22	given	give	VERB
ejpam-3768	286	23	by	by	ADP
ejpam-3768	286	24	ϕ2(t	ϕ2(t	PROPN
ejpam-3768	286	25	)	)	PUNCT
ejpam-3768	286	26	≥	≥	NOUN
ejpam-3768	286	27	(	(	PUNCT
ejpam-3768	286	28	4k6	4k6	NUM
ejpam-3768	286	29	3n−	3n−	NUM
ejpam-3768	286	30	8	8	NUM
ejpam-3768	286	31	)	)	PUNCT
ejpam-3768	286	32	−	−	PROPN
ejpam-3768	286	33	3n−8	3n−8	NUM
ejpam-3768	286	34	2	2	NUM
ejpam-3768	286	35	(	(	PUNCT
ejpam-3768	286	36	t∗	t∗	NOUN
ejpam-3768	286	37	−	−	PROPN
ejpam-3768	286	38	t)−	t)−	PROPN
ejpam-3768	286	39	3n−8	3n−8	NUM
ejpam-3768	286	40	2	2	NUM
ejpam-3768	286	41	,	,	PUNCT
ejpam-3768	286	42	(	(	PUNCT
ejpam-3768	286	43	3.28	3.28	NUM
ejpam-3768	286	44	)	)	PUNCT
ejpam-3768	286	45	where	where	SCONJ
ejpam-3768	286	46	k5	k5	PROPN
ejpam-3768	286	47	,	,	PUNCT
ejpam-3768	286	48	k6	k6	PROPN
ejpam-3768	286	49	will	will	AUX
ejpam-3768	286	50	be	be	AUX
ejpam-3768	286	51	given	give	VERB
ejpam-3768	286	52	later	later	ADV
ejpam-3768	286	53	,	,	PUNCT
ejpam-3768	286	54	and	and	CCONJ
ejpam-3768	286	55	ϕ2(0	ϕ2(0	NOUN
ejpam-3768	286	56	)	)	PUNCT
ejpam-3768	287	1	=	=	SYM
ejpam-3768	288	1	∫	∫	PROPN
ejpam-3768	288	2	ω	ω	PROPN
ejpam-3768	289	1	[	[	X
ejpam-3768	289	2	∫	∫	X
ejpam-3768	289	3	+	+	NOUN
ejpam-3768	289	4	∞	∞	PROPN
ejpam-3768	289	5	g	g	NOUN
ejpam-3768	289	6	dη	dη	NOUN
ejpam-3768	289	7	f(η	f(η	NOUN
ejpam-3768	289	8	)	)	PUNCT
ejpam-3768	290	1	]	]	PUNCT
ejpam-3768	290	2	−nk	−nk	X
ejpam-3768	290	3	dx	dx	PROPN
ejpam-3768	290	4	.	.	PUNCT
ejpam-3768	290	5	proof	proof	NOUN
ejpam-3768	290	6	.	.	PUNCT
ejpam-3768	291	1	under	under	ADP
ejpam-3768	291	2	the	the	DET
ejpam-3768	291	3	assumptions	assumption	NOUN
ejpam-3768	291	4	(	(	PUNCT
ejpam-3768	291	5	f7	f7	PROPN
ejpam-3768	291	6	)	)	PUNCT
ejpam-3768	291	7	,	,	PUNCT
ejpam-3768	291	8	we	we	PRON
ejpam-3768	291	9	have	have	VERB
ejpam-3768	291	10	from	from	ADP
ejpam-3768	291	11	(	(	PUNCT
ejpam-3768	291	12	1.1	1.1	NUM
ejpam-3768	291	13	)	)	PUNCT
ejpam-3768	291	14	and	and	CCONJ
ejpam-3768	291	15	(	(	PUNCT
ejpam-3768	291	16	3.26	3.26	NUM
ejpam-3768	291	17	)	)	PUNCT
ejpam-3768	291	18	that	that	PRON
ejpam-3768	291	19	ϕ′2(t	ϕ′2(t	PROPN
ejpam-3768	291	20	)	)	PUNCT
ejpam-3768	292	1	=	=	SYM
ejpam-3768	292	2	nk	nk	PROPN
ejpam-3768	292	3	∫	∫	PROPN
ejpam-3768	292	4	ω	ω	PROPN
ejpam-3768	292	5	v	v	ADP
ejpam-3768	292	6	nk+1[f(u)]−1utdx	nk+1[f(u)]−1utdx	PROPN
ejpam-3768	292	7	=	=	PROPN
ejpam-3768	293	1	nk	nk	PROPN
ejpam-3768	293	2	∫	∫	PROPN
ejpam-3768	293	3	ω	ω	PROPN
ejpam-3768	293	4	v	v	ADP
ejpam-3768	293	5	nk+1[f(u)]−1[4um	nk+1[f(u)]−1[4um	PROPN
ejpam-3768	294	1	+	+	CCONJ
ejpam-3768	294	2	a(x)f(u)]dx	a(x)f(u)]dx	NOUN
ejpam-3768	294	3	=	=	SYM
ejpam-3768	294	4	−mnk(nk	−mnk(nk	X
ejpam-3768	294	5	+	+	CCONJ
ejpam-3768	294	6	1	1	X
ejpam-3768	294	7	)	)	PUNCT
ejpam-3768	294	8	∫	∫	PROPN
ejpam-3768	295	1	ω	ω	PROPN
ejpam-3768	295	2	v	v	X
ejpam-3768	295	3	nk+2[f(u)]−2|∇u|2um−1dx+	nk+2[f(u)]−2|∇u|2um−1dx+	ADV
ejpam-3768	295	4	nk	nk	NOUN
ejpam-3768	295	5	∫	∫	PROPN
ejpam-3768	295	6	ω	ω	PROPN
ejpam-3768	295	7	v	v	ADP
ejpam-3768	295	8	nk+1a(x)dx	nk+1a(x)dx	NOUN
ejpam-3768	296	1	+	+	ADP
ejpam-3768	296	2	mnk	mnk	PROPN
ejpam-3768	296	3	∫	∫	PROPN
ejpam-3768	296	4	ω	ω	PROPN
ejpam-3768	296	5	v	v	ADP
ejpam-3768	296	6	nk+1[f(u)]−2f	nk+1[f(u)]−2f	PROPN
ejpam-3768	296	7	′(u)um−1|∇u|2dx	′(u)um−1|∇u|2dx	NUM
ejpam-3768	296	8	.	.	PUNCT
ejpam-3768	297	1	≤	≤	NOUN
ejpam-3768	298	1	−mnk(nk	−mnk(nk	NUM
ejpam-3768	298	2	+	+	CCONJ
ejpam-3768	298	3	1	1	NUM
ejpam-3768	298	4	)	)	PUNCT
ejpam-3768	298	5	∫	∫	PROPN
ejpam-3768	299	1	ω	ω	PROPN
ejpam-3768	299	2	v	v	X
ejpam-3768	299	3	nk+2[f(u)]−2|∇u|2um−1dx+	nk+2[f(u)]−2|∇u|2um−1dx+	ADV
ejpam-3768	299	4	nk	nk	NOUN
ejpam-3768	299	5	∫	∫	PROPN
ejpam-3768	299	6	ω	ω	PROPN
ejpam-3768	299	7	v	v	ADP
ejpam-3768	299	8	nk+1a(x)dx	nk+1a(x)dx	NOUN
ejpam-3768	300	1	+	+	CCONJ
ejpam-3768	300	2	mnk(nk	mnk(nk	X
ejpam-3768	300	3	+	+	X
ejpam-3768	300	4	1−	1−	NUM
ejpam-3768	300	5	β	β	NOUN
ejpam-3768	300	6	)	)	PUNCT
ejpam-3768	300	7	∫	∫	PROPN
ejpam-3768	300	8	ω	ω	NUM
ejpam-3768	300	9	v	v	ADP
ejpam-3768	300	10	nk+2[f(u)]−2um−1|∇u|2dx	nk+2[f(u)]−2um−1|∇u|2dx	PROPN
ejpam-3768	300	11	h.f	h.f	PROPN
ejpam-3768	300	12	.	.	PROPN
ejpam-3768	300	13	di	di	PROPN
ejpam-3768	300	14	,	,	PUNCT
ejpam-3768	300	15	l.	l.	PROPN
ejpam-3768	300	16	chen	chen	PROPN
ejpam-3768	300	17	and	and	CCONJ
ejpam-3768	300	18	z.f	z.f	PROPN
ejpam-3768	300	19	.	.	PROPN
ejpam-3768	300	20	song	song	PROPN
ejpam-3768	300	21	/	/	SYM
ejpam-3768	300	22	eur	eur	PROPN
ejpam-3768	300	23	.	.	PUNCT
ejpam-3768	301	1	j.	j.	PROPN
ejpam-3768	301	2	pure	pure	PROPN
ejpam-3768	301	3	appl	appl	PROPN
ejpam-3768	301	4	.	.	PROPN
ejpam-3768	301	5	math	math	PROPN
ejpam-3768	301	6	,	,	PUNCT
ejpam-3768	301	7	13	13	NUM
ejpam-3768	301	8	(	(	PUNCT
ejpam-3768	301	9	3	3	NUM
ejpam-3768	301	10	)	)	PUNCT
ejpam-3768	301	11	(	(	PUNCT
ejpam-3768	301	12	2020	2020	NUM
ejpam-3768	301	13	)	)	PUNCT
ejpam-3768	301	14	,	,	PUNCT
ejpam-3768	301	15	645	645	NUM
ejpam-3768	301	16	-	-	SYM
ejpam-3768	301	17	662	662	NUM
ejpam-3768	301	18	658	658	NUM
ejpam-3768	301	19	=	=	SYM
ejpam-3768	302	1	nk	nk	PROPN
ejpam-3768	302	2	∫	∫	PROPN
ejpam-3768	302	3	ω	ω	PROPN
ejpam-3768	302	4	v	v	PROPN
ejpam-3768	302	5	nk+1a(x)dx−mnkβ	nk+1a(x)dx−mnkβ	PROPN
ejpam-3768	302	6	∫	∫	PROPN
ejpam-3768	302	7	ω	ω	PROPN
ejpam-3768	302	8	v	v	PROPN
ejpam-3768	302	9	nk+2[f(u)]−2um−1|∇u|2dx	nk+2[f(u)]−2um−1|∇u|2dx	ADV
ejpam-3768	302	10	.	.	PUNCT
ejpam-3768	303	1	(	(	PUNCT
ejpam-3768	303	2	3.29	3.29	NUM
ejpam-3768	303	3	)	)	PUNCT
ejpam-3768	303	4	since	since	SCONJ
ejpam-3768	303	5	|∇v	|∇v	NOUN
ejpam-3768	303	6	nk+γ	nk+γ	NOUN
ejpam-3768	303	7	2	2	NUM
ejpam-3768	303	8	|2	|2	NUM
ejpam-3768	303	9	=	=	PUNCT
ejpam-3768	303	10	(	(	PUNCT
ejpam-3768	303	11	nk	nk	PROPN
ejpam-3768	303	12	+	+	CCONJ
ejpam-3768	303	13	γ	γ	X
ejpam-3768	303	14	2	2	NUM
ejpam-3768	303	15	)	)	SYM
ejpam-3768	303	16	2	2	NUM
ejpam-3768	303	17	v	v	ADP
ejpam-3768	303	18	nk+γ+2[f(u)]−2|∇u|2	nk+γ+2[f(u)]−2|∇u|2	PROPN
ejpam-3768	303	19	.	.	PUNCT
ejpam-3768	304	1	(	(	PUNCT
ejpam-3768	304	2	3.30	3.30	NUM
ejpam-3768	304	3	)	)	PUNCT
ejpam-3768	304	4	in	in	ADP
ejpam-3768	304	5	view	view	NOUN
ejpam-3768	304	6	of	of	ADP
ejpam-3768	304	7	assumptions	assumption	NOUN
ejpam-3768	304	8	(	(	PUNCT
ejpam-3768	304	9	f6	f6	PROPN
ejpam-3768	304	10	)	)	PUNCT
ejpam-3768	304	11	,	,	PUNCT
ejpam-3768	304	12	(	(	PUNCT
ejpam-3768	304	13	3.29	3.29	NUM
ejpam-3768	304	14	)	)	PUNCT
ejpam-3768	304	15	and	and	CCONJ
ejpam-3768	304	16	(	(	PUNCT
ejpam-3768	304	17	3.30	3.30	NUM
ejpam-3768	304	18	)	)	PUNCT
ejpam-3768	304	19	,	,	PUNCT
ejpam-3768	304	20	we	we	PRON
ejpam-3768	304	21	discover	discover	VERB
ejpam-3768	304	22	that	that	SCONJ
ejpam-3768	304	23	ϕ′2(t	ϕ′2(t	NOUN
ejpam-3768	304	24	)	)	PUNCT
ejpam-3768	304	25	≤	≤	PUNCT
ejpam-3768	305	1	nk	nk	PROPN
ejpam-3768	305	2	∫	∫	PROPN
ejpam-3768	305	3	ω	ω	PROPN
ejpam-3768	305	4	v	v	ADP
ejpam-3768	305	5	nk+1a(x)dx−	nk+1a(x)dx−	PROPN
ejpam-3768	305	6	4nkαβ	4nkαβ	NUM
ejpam-3768	305	7	(	(	PUNCT
ejpam-3768	305	8	nk	nk	PROPN
ejpam-3768	305	9	+	+	PROPN
ejpam-3768	305	10	γ)2	γ)2	PROPN
ejpam-3768	305	11	∫	∫	PROPN
ejpam-3768	305	12	ω	ω	NUM
ejpam-3768	305	13	|∇v	|∇v	NOUN
ejpam-3768	305	14	nk+γ	nk+γ	NOUN
ejpam-3768	305	15	2	2	NUM
ejpam-3768	305	16	|2dx	|2dx	X
ejpam-3768	305	17	.	.	PUNCT
ejpam-3768	305	18	(	(	PUNCT
ejpam-3768	305	19	3.31	3.31	NUM
ejpam-3768	305	20	)	)	PUNCT
ejpam-3768	305	21	for	for	ADP
ejpam-3768	305	22	convenience	convenience	NOUN
ejpam-3768	305	23	,	,	PUNCT
ejpam-3768	305	24	we	we	PRON
ejpam-3768	305	25	denote	denote	VERB
ejpam-3768	305	26	ε3	ε3	PROPN
ejpam-3768	305	27	=	=	SYM
ejpam-3768	305	28	3nk(n−	3nk(n−	NUM
ejpam-3768	305	29	2	2	NUM
ejpam-3768	305	30	)	)	PUNCT
ejpam-3768	306	1	+	+	CCONJ
ejpam-3768	306	2	n(nk	n(nk	PROPN
ejpam-3768	306	3	+	+	NUM
ejpam-3768	306	4	γ)−	γ)−	PROPN
ejpam-3768	306	5	4(n−	4(n−	NUM
ejpam-3768	306	6	2)(nk	2)(nk	NUM
ejpam-3768	306	7	+	+	CCONJ
ejpam-3768	306	8	1	1	NUM
ejpam-3768	306	9	)	)	PUNCT
ejpam-3768	306	10	3nk(n−	3nk(n−	NUM
ejpam-3768	306	11	2	2	NUM
ejpam-3768	306	12	)	)	PUNCT
ejpam-3768	306	13	+	+	CCONJ
ejpam-3768	306	14	n(nk	n(nk	PRON
ejpam-3768	306	15	+	+	CCONJ
ejpam-3768	306	16	γ	γ	X
ejpam-3768	306	17	)	)	PUNCT
ejpam-3768	306	18	,	,	PUNCT
ejpam-3768	306	19	ε4	ε4	NOUN
ejpam-3768	306	20	=	=	SYM
ejpam-3768	306	21	4(n−	4(n−	NUM
ejpam-3768	306	22	2)(nk	2)(nk	NUM
ejpam-3768	306	23	+	+	CCONJ
ejpam-3768	306	24	1	1	NUM
ejpam-3768	306	25	)	)	PUNCT
ejpam-3768	306	26	3nk(n−	3nk(n−	NUM
ejpam-3768	306	27	2	2	NUM
ejpam-3768	306	28	)	)	PUNCT
ejpam-3768	307	1	+	+	CCONJ
ejpam-3768	307	2	n(nk	n(nk	PRON
ejpam-3768	307	3	+	+	CCONJ
ejpam-3768	307	4	γ	γ	X
ejpam-3768	307	5	)	)	PUNCT
ejpam-3768	307	6	,	,	PUNCT
ejpam-3768	307	7	where	where	SCONJ
ejpam-3768	307	8	the	the	DET
ejpam-3768	307	9	assumptions	assumption	NOUN
ejpam-3768	307	10	(	(	PUNCT
ejpam-3768	307	11	f7	f7	PROPN
ejpam-3768	307	12	)	)	PUNCT
ejpam-3768	307	13	implies	imply	VERB
ejpam-3768	307	14	that	that	PRON
ejpam-3768	307	15	ε3	ε3	VERB
ejpam-3768	307	16	>	>	X
ejpam-3768	307	17	0	0	PROPN
ejpam-3768	307	18	,	,	PUNCT
ejpam-3768	307	19	ε4	ε4	NOUN
ejpam-3768	307	20	>	>	X
ejpam-3768	307	21	0	0	PUNCT
ejpam-3768	308	1	and	and	CCONJ
ejpam-3768	308	2	ε3	ε3	PROPN
ejpam-3768	308	3	+	+	CCONJ
ejpam-3768	308	4	ε4	ε4	NOUN
ejpam-3768	308	5	=	=	SYM
ejpam-3768	308	6	1	1	X
ejpam-3768	308	7	.	.	PUNCT
ejpam-3768	309	1	so	so	ADV
ejpam-3768	309	2	by	by	ADP
ejpam-3768	309	3	hölder	hölder	PROPN
ejpam-3768	309	4	’s	’s	PART
ejpam-3768	309	5	inequality	inequality	NOUN
ejpam-3768	309	6	,	,	PUNCT
ejpam-3768	309	7	we	we	PRON
ejpam-3768	309	8	have∫	have∫	VERB
ejpam-3768	309	9	ω	ω	PROPN
ejpam-3768	309	10	v	v	ADP
ejpam-3768	309	11	nk+1a(x)dx	nk+1a(x)dx	ADJ
ejpam-3768	309	12	≤	≤	NUM
ejpam-3768	309	13	(	(	PUNCT
ejpam-3768	309	14	∫	∫	PROPN
ejpam-3768	309	15	ω	ω	PROPN
ejpam-3768	309	16	v	v	ADP
ejpam-3768	309	17	3nk(n−2)+n(nk+γ	3nk(n−2)+n(nk+γ	NUM
ejpam-3768	309	18	)	)	PUNCT
ejpam-3768	309	19	4(n−2	4(n−2	NOUN
ejpam-3768	309	20	)	)	PUNCT
ejpam-3768	309	21	dx	dx	PROPN
ejpam-3768	309	22	)	)	PUNCT
ejpam-3768	310	1	ε4	ε4	PROPN
ejpam-3768	310	2	(	(	PUNCT
ejpam-3768	310	3	∫	∫	PROPN
ejpam-3768	310	4	ω	ω	PROPN
ejpam-3768	310	5	a(x	a(x	PROPN
ejpam-3768	310	6	)	)	PUNCT
ejpam-3768	310	7	1	1	NUM
ejpam-3768	310	8	ε3	ε3	PROPN
ejpam-3768	310	9	dx	dx	PROPN
ejpam-3768	310	10	)	)	PUNCT
ejpam-3768	310	11	ε3	ε3	PROPN
ejpam-3768	310	12	.	.	PUNCT
ejpam-3768	311	1	(	(	PUNCT
ejpam-3768	311	2	3.32	3.32	NUM
ejpam-3768	311	3	)	)	PUNCT
ejpam-3768	311	4	using	use	VERB
ejpam-3768	311	5	hölder	hölder	NOUN
ejpam-3768	311	6	’s	’s	PART
ejpam-3768	311	7	inequality	inequality	NOUN
ejpam-3768	311	8	again	again	ADV
ejpam-3768	311	9	,	,	PUNCT
ejpam-3768	311	10	it	it	PRON
ejpam-3768	311	11	follows	follow	VERB
ejpam-3768	311	12	that∫	that∫	PROPN
ejpam-3768	311	13	ω	ω	PROPN
ejpam-3768	311	14	v	v	ADP
ejpam-3768	311	15	3nk(n−2)+n(nk+γ	3nk(n−2)+n(nk+γ	NUM
ejpam-3768	311	16	)	)	PUNCT
ejpam-3768	311	17	4(n−2	4(n−2	NOUN
ejpam-3768	311	18	)	)	PUNCT
ejpam-3768	311	19	dx	dx	PROPN
ejpam-3768	311	20	≤	≤	NUM
ejpam-3768	311	21	(	(	PUNCT
ejpam-3768	311	22	∫	∫	PROPN
ejpam-3768	311	23	ω	ω	PROPN
ejpam-3768	311	24	v	v	PROPN
ejpam-3768	311	25	nkdx	nkdx	PROPN
ejpam-3768	311	26	)	)	PUNCT
ejpam-3768	311	27	3	3	NUM
ejpam-3768	311	28	4	4	NUM
ejpam-3768	311	29	(	(	PUNCT
ejpam-3768	311	30	∫	∫	PROPN
ejpam-3768	311	31	ω	ω	PROPN
ejpam-3768	311	32	v	v	PROPN
ejpam-3768	311	33	n(nk+γ	n(nk+γ	PROPN
ejpam-3768	311	34	)	)	PUNCT
ejpam-3768	311	35	n−2	n−2	PROPN
ejpam-3768	311	36	dx	dx	PROPN
ejpam-3768	311	37	)	)	PUNCT
ejpam-3768	311	38	1	1	NUM
ejpam-3768	311	39	4	4	NUM
ejpam-3768	311	40	.	.	PUNCT
ejpam-3768	312	1	(	(	PUNCT
ejpam-3768	312	2	3.33	3.33	NUM
ejpam-3768	312	3	)	)	PUNCT
ejpam-3768	312	4	furthermore	furthermore	ADV
ejpam-3768	312	5	,	,	PUNCT
ejpam-3768	312	6	applying	apply	VERB
ejpam-3768	312	7	the	the	DET
ejpam-3768	312	8	sobolev	sobolev	NOUN
ejpam-3768	312	9	’s	’s	PART
ejpam-3768	312	10	inequality	inequality	NOUN
ejpam-3768	312	11	,	,	PUNCT
ejpam-3768	312	12	we	we	PRON
ejpam-3768	312	13	obtain	obtain	VERB
ejpam-3768	312	14	that(∫	that(∫	DET
ejpam-3768	312	15	ω	ω	PROPN
ejpam-3768	312	16	v	v	NOUN
ejpam-3768	312	17	n(nk+γ	n(nk+γ	PROPN
ejpam-3768	312	18	)	)	PUNCT
ejpam-3768	312	19	n−2	n−2	PROPN
ejpam-3768	312	20	dx	dx	PROPN
ejpam-3768	312	21	)	)	PUNCT
ejpam-3768	313	1	n−2	n−2	PROPN
ejpam-3768	313	2	2n	2n	NUM
ejpam-3768	313	3	=	=	SYM
ejpam-3768	313	4	(	(	PUNCT
ejpam-3768	313	5	∫	∫	PROPN
ejpam-3768	313	6	ω	ω	PROPN
ejpam-3768	313	7	(	(	PUNCT
ejpam-3768	313	8	v	v	NOUN
ejpam-3768	313	9	nk+γ	nk+γ	PROPN
ejpam-3768	313	10	2	2	NUM
ejpam-3768	313	11	)	)	PUNCT
ejpam-3768	313	12	2n	2n	NUM
ejpam-3768	313	13	n−2dx	n−2dx	ADV
ejpam-3768	313	14	)	)	PUNCT
ejpam-3768	313	15	n−2	n−2	PROPN
ejpam-3768	313	16	2n	2n	ADJ
ejpam-3768	313	17	≤	≤	ADV
ejpam-3768	314	1	c5	c5	PROPN
ejpam-3768	314	2	(	(	PUNCT
ejpam-3768	314	3	∫	∫	PROPN
ejpam-3768	314	4	ω	ω	PROPN
ejpam-3768	314	5	|∇v	|∇v	NOUN
ejpam-3768	314	6	nk+γ	nk+γ	NOUN
ejpam-3768	314	7	2	2	NUM
ejpam-3768	314	8	|2dx	|2dx	X
ejpam-3768	314	9	)	)	PUNCT
ejpam-3768	314	10	1	1	NUM
ejpam-3768	314	11	2	2	NUM
ejpam-3768	314	12	,	,	PUNCT
ejpam-3768	314	13	(	(	PUNCT
ejpam-3768	314	14	3.34	3.34	NUM
ejpam-3768	314	15	)	)	PUNCT
ejpam-3768	314	16	where	where	SCONJ
ejpam-3768	314	17	c5	c5	PROPN
ejpam-3768	314	18	is	be	AUX
ejpam-3768	314	19	the	the	DET
ejpam-3768	314	20	optimal	optimal	ADJ
ejpam-3768	314	21	sobolev	sobolev	NOUN
ejpam-3768	314	22	’s	’s	PART
ejpam-3768	314	23	embedding	embed	VERB
ejpam-3768	314	24	constant	constant	ADJ
ejpam-3768	314	25	defined	define	VERB
ejpam-3768	314	26	as	as	ADP
ejpam-3768	314	27	(	(	PUNCT
ejpam-3768	314	28	3.6	3.6	NUM
ejpam-3768	314	29	)	)	PUNCT
ejpam-3768	314	30	.	.	PUNCT
ejpam-3768	315	1	substituting	substitute	VERB
ejpam-3768	315	2	(	(	PUNCT
ejpam-3768	315	3	3.34	3.34	NUM
ejpam-3768	315	4	)	)	PUNCT
ejpam-3768	315	5	into	into	ADP
ejpam-3768	315	6	(	(	PUNCT
ejpam-3768	315	7	3.33	3.33	NUM
ejpam-3768	315	8	)	)	PUNCT
ejpam-3768	315	9	yields	yield	NOUN
ejpam-3768	315	10	that∫	that∫	PROPN
ejpam-3768	315	11	ω	ω	NUM
ejpam-3768	315	12	v	v	ADP
ejpam-3768	315	13	3nk(n−2)+n(nk+γ	3nk(n−2)+n(nk+γ	NUM
ejpam-3768	315	14	)	)	PUNCT
ejpam-3768	315	15	4(n−2	4(n−2	NOUN
ejpam-3768	315	16	)	)	PUNCT
ejpam-3768	315	17	dx	dx	PROPN
ejpam-3768	315	18	≤	≤	PROPN
ejpam-3768	315	19	c	c	PROPN
ejpam-3768	315	20	n	n	NUM
ejpam-3768	315	21	2(n−2	2(n−2	NOUN
ejpam-3768	315	22	)	)	PUNCT
ejpam-3768	315	23	5	5	NUM
ejpam-3768	315	24	(	(	PUNCT
ejpam-3768	315	25	∫	∫	PROPN
ejpam-3768	315	26	ω	ω	PROPN
ejpam-3768	315	27	v	v	PROPN
ejpam-3768	315	28	nkdx	nkdx	PROPN
ejpam-3768	315	29	)	)	PUNCT
ejpam-3768	315	30	3	3	NUM
ejpam-3768	315	31	4	4	NUM
ejpam-3768	315	32	(	(	PUNCT
ejpam-3768	315	33	∫	∫	PROPN
ejpam-3768	315	34	ω	ω	PROPN
ejpam-3768	315	35	|∇v	|∇v	NOUN
ejpam-3768	315	36	nk+γ	nk+γ	NOUN
ejpam-3768	315	37	2	2	NUM
ejpam-3768	315	38	|2dx	|2dx	X
ejpam-3768	315	39	)	)	PUNCT
ejpam-3768	315	40	n	n	NUM
ejpam-3768	315	41	4(n−2	4(n−2	NOUN
ejpam-3768	315	42	)	)	PUNCT
ejpam-3768	315	43	.	.	PUNCT
ejpam-3768	316	1	(	(	PUNCT
ejpam-3768	316	2	3.35	3.35	NUM
ejpam-3768	316	3	)	)	PUNCT
ejpam-3768	316	4	by	by	ADP
ejpam-3768	316	5	young	young	PROPN
ejpam-3768	316	6	’s	’s	PART
ejpam-3768	316	7	inequality	inequality	NOUN
ejpam-3768	316	8	,	,	PUNCT
ejpam-3768	316	9	(	(	PUNCT
ejpam-3768	316	10	3.32	3.32	NUM
ejpam-3768	316	11	)	)	PUNCT
ejpam-3768	316	12	and	and	CCONJ
ejpam-3768	316	13	(	(	PUNCT
ejpam-3768	316	14	3.35	3.35	NUM
ejpam-3768	316	15	)	)	PUNCT
ejpam-3768	316	16	,	,	PUNCT
ejpam-3768	316	17	we	we	PRON
ejpam-3768	316	18	obtain∫	obtain∫	VERB
ejpam-3768	316	19	ω	ω	PROPN
ejpam-3768	316	20	v	v	ADP
ejpam-3768	316	21	nk+1a(x)dx	nk+1a(x)dx	ADJ
ejpam-3768	316	22	h.f	h.f	PROPN
ejpam-3768	316	23	.	.	PROPN
ejpam-3768	316	24	di	di	PROPN
ejpam-3768	316	25	,	,	PUNCT
ejpam-3768	316	26	l.	l.	PROPN
ejpam-3768	316	27	chen	chen	PROPN
ejpam-3768	316	28	and	and	CCONJ
ejpam-3768	316	29	z.f	z.f	PROPN
ejpam-3768	316	30	.	.	PROPN
ejpam-3768	316	31	song	song	PROPN
ejpam-3768	316	32	/	/	SYM
ejpam-3768	316	33	eur	eur	PROPN
ejpam-3768	316	34	.	.	PUNCT
ejpam-3768	317	1	j.	j.	PROPN
ejpam-3768	317	2	pure	pure	PROPN
ejpam-3768	317	3	appl	appl	PROPN
ejpam-3768	317	4	.	.	PROPN
ejpam-3768	317	5	math	math	PROPN
ejpam-3768	317	6	,	,	PUNCT
ejpam-3768	317	7	13	13	NUM
ejpam-3768	317	8	(	(	PUNCT
ejpam-3768	317	9	3	3	NUM
ejpam-3768	317	10	)	)	PUNCT
ejpam-3768	317	11	(	(	PUNCT
ejpam-3768	317	12	2020	2020	NUM
ejpam-3768	317	13	)	)	PUNCT
ejpam-3768	317	14	,	,	PUNCT
ejpam-3768	317	15	645	645	NUM
ejpam-3768	317	16	-	-	SYM
ejpam-3768	317	17	662	662	NUM
ejpam-3768	317	18	659	659	NUM
ejpam-3768	317	19	≤	≤	NOUN
ejpam-3768	317	20	(	(	PUNCT
ejpam-3768	317	21	c	c	NOUN
ejpam-3768	317	22	n	n	PRON
ejpam-3768	317	23	2(n−2	2(n−2	NOUN
ejpam-3768	317	24	)	)	PUNCT
ejpam-3768	317	25	5	5	NUM
ejpam-3768	317	26	(	(	PUNCT
ejpam-3768	317	27	∫	∫	PROPN
ejpam-3768	317	28	ω	ω	PROPN
ejpam-3768	317	29	v	v	PROPN
ejpam-3768	317	30	nkdx	nkdx	PROPN
ejpam-3768	317	31	)	)	PUNCT
ejpam-3768	317	32	3	3	NUM
ejpam-3768	317	33	4	4	NUM
ejpam-3768	317	34	(	(	PUNCT
ejpam-3768	317	35	∫	∫	PROPN
ejpam-3768	317	36	ω	ω	PROPN
ejpam-3768	317	37	|∇v	|∇v	NOUN
ejpam-3768	317	38	nk+γ	nk+γ	NOUN
ejpam-3768	317	39	2	2	NUM
ejpam-3768	317	40	|2dx	|2dx	X
ejpam-3768	317	41	)	)	PUNCT
ejpam-3768	317	42	n	n	NUM
ejpam-3768	317	43	4(n−2	4(n−2	NOUN
ejpam-3768	317	44	)	)	PUNCT
ejpam-3768	317	45	)	)	PUNCT
ejpam-3768	318	1	ε4	ε4	NOUN
ejpam-3768	318	2	(	(	PUNCT
ejpam-3768	318	3	∫	∫	PROPN
ejpam-3768	318	4	ω	ω	PROPN
ejpam-3768	318	5	a(x	a(x	PROPN
ejpam-3768	318	6	)	)	PUNCT
ejpam-3768	318	7	1	1	NUM
ejpam-3768	318	8	ε3	ε3	PROPN
ejpam-3768	318	9	dx	dx	PROPN
ejpam-3768	318	10	)	)	PUNCT
ejpam-3768	318	11	ε3	ε3	VERB
ejpam-3768	318	12	≤	≤	PROPN
ejpam-3768	318	13	ε4c	ε4c	PROPN
ejpam-3768	318	14	n	n	PRON
ejpam-3768	318	15	2(n−2	2(n−2	NOUN
ejpam-3768	318	16	)	)	PUNCT
ejpam-3768	318	17	5	5	NUM
ejpam-3768	318	18	(	(	PUNCT
ejpam-3768	318	19	∫	∫	PROPN
ejpam-3768	318	20	ω	ω	PROPN
ejpam-3768	318	21	v	v	PROPN
ejpam-3768	318	22	nkdx	nkdx	PROPN
ejpam-3768	318	23	)	)	PUNCT
ejpam-3768	318	24	3	3	NUM
ejpam-3768	318	25	4	4	NUM
ejpam-3768	318	26	(	(	PUNCT
ejpam-3768	318	27	∫	∫	PROPN
ejpam-3768	318	28	ω	ω	PROPN
ejpam-3768	318	29	|∇v	|∇v	NOUN
ejpam-3768	318	30	nk+γ	nk+γ	NOUN
ejpam-3768	318	31	2	2	NUM
ejpam-3768	318	32	|2dx	|2dx	X
ejpam-3768	318	33	)	)	PUNCT
ejpam-3768	318	34	n	n	NUM
ejpam-3768	318	35	4(n−2	4(n−2	NOUN
ejpam-3768	318	36	)	)	PUNCT
ejpam-3768	318	37	+	+	CCONJ
ejpam-3768	318	38	ε3	ε3	PROPN
ejpam-3768	318	39	∫	∫	PROPN
ejpam-3768	318	40	ω	ω	PROPN
ejpam-3768	318	41	a(x	a(x	PROPN
ejpam-3768	318	42	)	)	PUNCT
ejpam-3768	318	43	1	1	NUM
ejpam-3768	318	44	ε3	ε3	PROPN
ejpam-3768	318	45	dx	dx	PROPN
ejpam-3768	318	46	.	.	PUNCT
ejpam-3768	319	1	(	(	PUNCT
ejpam-3768	319	2	3.36	3.36	NUM
ejpam-3768	319	3	)	)	PUNCT
ejpam-3768	319	4	applying	apply	VERB
ejpam-3768	319	5	young	young	PROPN
ejpam-3768	319	6	’s	’s	PART
ejpam-3768	319	7	inequality	inequality	NOUN
ejpam-3768	319	8	again	again	ADV
ejpam-3768	319	9	,	,	PUNCT
ejpam-3768	319	10	we	we	PRON
ejpam-3768	319	11	have(∫	have(∫	VERB
ejpam-3768	319	12	ω	ω	NUM
ejpam-3768	319	13	v	v	X
ejpam-3768	319	14	nkdx	nkdx	PROPN
ejpam-3768	319	15	)	)	PUNCT
ejpam-3768	319	16	3	3	NUM
ejpam-3768	319	17	4	4	NUM
ejpam-3768	319	18	(	(	PUNCT
ejpam-3768	319	19	∫	∫	PROPN
ejpam-3768	319	20	ω	ω	PROPN
ejpam-3768	319	21	|∇v	|∇v	NOUN
ejpam-3768	319	22	nk+γ	nk+γ	NOUN
ejpam-3768	319	23	2	2	NUM
ejpam-3768	319	24	|2dx	|2dx	X
ejpam-3768	319	25	)	)	PUNCT
ejpam-3768	319	26	n	n	CCONJ
ejpam-3768	319	27	4(n−2	4(n−2	NOUN
ejpam-3768	319	28	)	)	PUNCT
ejpam-3768	319	29	≤	≤	NOUN
ejpam-3768	319	30	nδ	nδ	ADP
ejpam-3768	319	31	4(n−	4(n−	PROPN
ejpam-3768	319	32	2	2	NUM
ejpam-3768	319	33	)	)	PUNCT
ejpam-3768	319	34	∫	∫	PROPN
ejpam-3768	320	1	ω	ω	NUM
ejpam-3768	320	2	|∇v	|∇v	NOUN
ejpam-3768	320	3	nk+γ	nk+γ	NOUN
ejpam-3768	320	4	2	2	NUM
ejpam-3768	320	5	|2dx+	|2dx+	ADJ
ejpam-3768	320	6	(	(	PUNCT
ejpam-3768	320	7	3n−	3n−	PROPN
ejpam-3768	320	8	8)c(δ	8)c(δ	NUM
ejpam-3768	320	9	)	)	PUNCT
ejpam-3768	320	10	4(n−	4(n−	PROPN
ejpam-3768	320	11	2	2	NUM
ejpam-3768	320	12	)	)	PUNCT
ejpam-3768	320	13	(	(	PUNCT
ejpam-3768	320	14	∫	∫	PROPN
ejpam-3768	320	15	ω	ω	PROPN
ejpam-3768	320	16	v	v	PROPN
ejpam-3768	320	17	nkdx	nkdx	PROPN
ejpam-3768	320	18	)	)	PUNCT
ejpam-3768	320	19	3n−6	3n−6	NUM
ejpam-3768	320	20	3n−8	3n−8	NUM
ejpam-3768	320	21	,	,	PUNCT
ejpam-3768	320	22	(	(	PUNCT
ejpam-3768	320	23	3.37	3.37	NUM
ejpam-3768	320	24	)	)	PUNCT
ejpam-3768	320	25	where	where	SCONJ
ejpam-3768	320	26	n	n	NUM
ejpam-3768	320	27	4(n−2	4(n−2	NOUN
ejpam-3768	320	28	)	)	PUNCT
ejpam-3768	320	29	>	>	X
ejpam-3768	320	30	1	1	NUM
ejpam-3768	320	31	,	,	PUNCT
ejpam-3768	320	32	3n−8	3n−8	NUM
ejpam-3768	320	33	4(n−2	4(n−2	NOUN
ejpam-3768	320	34	)	)	PUNCT
ejpam-3768	320	35	>	>	X
ejpam-3768	320	36	1	1	NUM
ejpam-3768	320	37	with	with	ADP
ejpam-3768	320	38	n	n	PROPN
ejpam-3768	320	39	4(n−2	4(n−2	NOUN
ejpam-3768	320	40	)	)	PUNCT
ejpam-3768	321	1	+	+	NUM
ejpam-3768	321	2	3n−8	3n−8	NUM
ejpam-3768	321	3	4(n−2	4(n−2	NOUN
ejpam-3768	321	4	)	)	PUNCT
ejpam-3768	322	1	=	=	SYM
ejpam-3768	322	2	1	1	X
ejpam-3768	322	3	.	.	PUNCT
ejpam-3768	322	4	consequently	consequently	ADV
ejpam-3768	322	5	,	,	PUNCT
ejpam-3768	322	6	it	it	PRON
ejpam-3768	322	7	follows	follow	VERB
ejpam-3768	322	8	that∫	that∫	PROPN
ejpam-3768	322	9	ω	ω	PROPN
ejpam-3768	322	10	v	v	ADP
ejpam-3768	322	11	nk+1a(x)dx	nk+1a(x)dx	ADJ
ejpam-3768	322	12	≤	≤	PROPN
ejpam-3768	322	13	ε3	ε3	PROPN
ejpam-3768	322	14	∫	∫	PROPN
ejpam-3768	322	15	ω	ω	PROPN
ejpam-3768	322	16	a(x	a(x	PROPN
ejpam-3768	322	17	)	)	PUNCT
ejpam-3768	322	18	1	1	NUM
ejpam-3768	322	19	ε3	ε3	PROPN
ejpam-3768	322	20	dx+	dx+	NOUN
ejpam-3768	322	21	ε4nδ	ε4nδ	PUNCT
ejpam-3768	322	22	4(n−	4(n−	NUM
ejpam-3768	322	23	2	2	NUM
ejpam-3768	322	24	)	)	PUNCT
ejpam-3768	322	25	∫	∫	PROPN
ejpam-3768	323	1	ω	ω	NUM
ejpam-3768	323	2	|∇v	|∇v	NOUN
ejpam-3768	323	3	nk+γ	nk+γ	NOUN
ejpam-3768	323	4	2	2	NUM
ejpam-3768	323	5	|2dx	|2dx	ADJ
ejpam-3768	323	6	+	+	NUM
ejpam-3768	323	7	ε4(3n−	ε4(3n−	NOUN
ejpam-3768	323	8	8)c(δ	8)c(δ	NUM
ejpam-3768	323	9	)	)	PUNCT
ejpam-3768	323	10	4(n−	4(n−	PROPN
ejpam-3768	323	11	2	2	NUM
ejpam-3768	323	12	)	)	PUNCT
ejpam-3768	323	13	(	(	PUNCT
ejpam-3768	323	14	∫	∫	PROPN
ejpam-3768	323	15	ω	ω	PROPN
ejpam-3768	323	16	v	v	PROPN
ejpam-3768	323	17	nkdx	nkdx	PROPN
ejpam-3768	323	18	)	)	PUNCT
ejpam-3768	323	19	3n−6	3n−6	NUM
ejpam-3768	323	20	3n−8	3n−8	NUM
ejpam-3768	323	21	.	.	PUNCT
ejpam-3768	324	1	(	(	PUNCT
ejpam-3768	324	2	3.38	3.38	NUM
ejpam-3768	324	3	)	)	PUNCT
ejpam-3768	324	4	substituting	substitute	VERB
ejpam-3768	324	5	(	(	PUNCT
ejpam-3768	324	6	3.38	3.38	NUM
ejpam-3768	324	7	)	)	PUNCT
ejpam-3768	324	8	into	into	ADP
ejpam-3768	324	9	(	(	PUNCT
ejpam-3768	324	10	3.29	3.29	NUM
ejpam-3768	324	11	)	)	PUNCT
ejpam-3768	324	12	,	,	PUNCT
ejpam-3768	324	13	we	we	PRON
ejpam-3768	324	14	get	get	VERB
ejpam-3768	324	15	ϕ′2(t	ϕ′2(t	NOUN
ejpam-3768	324	16	)	)	PUNCT
ejpam-3768	324	17	≤	≤	PUNCT
ejpam-3768	325	1	ε3	ε3	PROPN
ejpam-3768	325	2	∫	∫	PROPN
ejpam-3768	325	3	ω	ω	PROPN
ejpam-3768	325	4	a(x	a(x	PROPN
ejpam-3768	325	5	)	)	PUNCT
ejpam-3768	325	6	1	1	NUM
ejpam-3768	325	7	ε3	ε3	PROPN
ejpam-3768	325	8	dx+	dx+	NOUN
ejpam-3768	325	9	ε4nk(3n−	ε4nk(3n−	X
ejpam-3768	325	10	8)c(δ	8)c(δ	NUM
ejpam-3768	325	11	)	)	PUNCT
ejpam-3768	325	12	4(n−	4(n−	PROPN
ejpam-3768	325	13	2	2	NUM
ejpam-3768	325	14	)	)	PUNCT
ejpam-3768	325	15	(	(	PUNCT
ejpam-3768	325	16	∫	∫	PROPN
ejpam-3768	325	17	ω	ω	PROPN
ejpam-3768	325	18	v	v	PROPN
ejpam-3768	325	19	nkdx	nkdx	PROPN
ejpam-3768	325	20	)	)	PUNCT
ejpam-3768	325	21	3n−6	3n−6	NUM
ejpam-3768	325	22	3n−8	3n−8	NUM
ejpam-3768	325	23	−	−	NOUN
ejpam-3768	325	24	[	[	PUNCT
ejpam-3768	325	25	4nkαβ	4nkαβ	NUM
ejpam-3768	325	26	(	(	PUNCT
ejpam-3768	325	27	nk	nk	PROPN
ejpam-3768	325	28	+	+	PROPN
ejpam-3768	325	29	γ)2	γ)2	PROPN
ejpam-3768	325	30	−	−	NOUN
ejpam-3768	325	31	ε4n	ε4n	NOUN
ejpam-3768	325	32	2kδ	2kδ	NOUN
ejpam-3768	325	33	4(n−	4(n−	NUM
ejpam-3768	325	34	2	2	NUM
ejpam-3768	325	35	)	)	PUNCT
ejpam-3768	325	36	]	]	PUNCT
ejpam-3768	326	1	∫	∫	PROPN
ejpam-3768	326	2	ω	ω	NUM
ejpam-3768	326	3	|∇v	|∇v	NOUN
ejpam-3768	326	4	nk+γ	nk+γ	NOUN
ejpam-3768	326	5	2	2	NUM
ejpam-3768	326	6	|2dx	|2dx	X
ejpam-3768	326	7	.	.	PUNCT
ejpam-3768	327	1	(	(	PUNCT
ejpam-3768	327	2	3.39	3.39	NUM
ejpam-3768	327	3	)	)	PUNCT
ejpam-3768	327	4	now	now	ADV
ejpam-3768	327	5	,	,	PUNCT
ejpam-3768	327	6	we	we	PRON
ejpam-3768	327	7	can	can	AUX
ejpam-3768	327	8	choose	choose	VERB
ejpam-3768	327	9	δ	δ	PROPN
ejpam-3768	327	10	small	small	ADJ
ejpam-3768	327	11	enough	enough	ADV
ejpam-3768	327	12	to	to	PART
ejpam-3768	327	13	make	make	VERB
ejpam-3768	327	14	the	the	DET
ejpam-3768	327	15	coefficient	coefficient	NOUN
ejpam-3768	327	16	4nkαβ	4nkαβ	NUM
ejpam-3768	327	17	(	(	PUNCT
ejpam-3768	327	18	nk+γ)2	nk+γ)2	NOUN
ejpam-3768	327	19	−	−	NOUN
ejpam-3768	327	20	ε4n2kδ	ε4n2kδ	NOUN
ejpam-3768	327	21	4(n−2	4(n−2	NOUN
ejpam-3768	327	22	)	)	PUNCT
ejpam-3768	327	23	>	>	X
ejpam-3768	328	1	0	0	X
ejpam-3768	328	2	.	.	PUNCT
ejpam-3768	329	1	hence	hence	ADV
ejpam-3768	329	2	,	,	PUNCT
ejpam-3768	329	3	we	we	PRON
ejpam-3768	329	4	have	have	VERB
ejpam-3768	329	5	ϕ′2(t	ϕ′2(t	NOUN
ejpam-3768	329	6	)	)	PUNCT
ejpam-3768	329	7	≤	≤	PUNCT
ejpam-3768	330	1	k5	k5	PROPN
ejpam-3768	330	2	+	+	CCONJ
ejpam-3768	330	3	k	k	PROPN
ejpam-3768	330	4	3n−6	3n−6	NUM
ejpam-3768	330	5	3n−8	3n−8	NUM
ejpam-3768	330	6	6	6	NUM
ejpam-3768	330	7	,	,	PUNCT
ejpam-3768	330	8	(	(	PUNCT
ejpam-3768	330	9	3.40	3.40	NUM
ejpam-3768	330	10	)	)	PUNCT
ejpam-3768	330	11	where	where	SCONJ
ejpam-3768	330	12	k5	k5	PROPN
ejpam-3768	330	13	=	=	PROPN
ejpam-3768	330	14	ε3	ε3	PROPN
ejpam-3768	330	15	∫	∫	PROPN
ejpam-3768	330	16	ω	ω	PROPN
ejpam-3768	330	17	a(x	a(x	PROPN
ejpam-3768	330	18	)	)	PUNCT
ejpam-3768	330	19	1	1	NUM
ejpam-3768	330	20	ε3	ε3	PROPN
ejpam-3768	330	21	dx	dx	PROPN
ejpam-3768	330	22	and	and	CCONJ
ejpam-3768	330	23	k6	k6	PROPN
ejpam-3768	330	24	=	=	SYM
ejpam-3768	330	25	ε4nk(3n−8)c(δ	ε4nk(3n−8)c(δ	PROPN
ejpam-3768	330	26	)	)	PUNCT
ejpam-3768	330	27	4(n−2	4(n−2	NOUN
ejpam-3768	330	28	)	)	PUNCT
ejpam-3768	330	29	.	.	PUNCT
ejpam-3768	331	1	then	then	ADV
ejpam-3768	331	2	,	,	PUNCT
ejpam-3768	331	3	integrating	integrate	VERB
ejpam-3768	331	4	(	(	PUNCT
ejpam-3768	331	5	3.40	3.40	NUM
ejpam-3768	331	6	)	)	PUNCT
ejpam-3768	331	7	from	from	ADP
ejpam-3768	331	8	0	0	NUM
ejpam-3768	331	9	to	to	ADP
ejpam-3768	331	10	t	t	PROPN
ejpam-3768	331	11	yields	yield	NOUN
ejpam-3768	331	12	that∫	that∫	PROPN
ejpam-3768	331	13	ϕ2(t	ϕ2(t	PROPN
ejpam-3768	331	14	)	)	PUNCT
ejpam-3768	331	15	ϕ2(0	ϕ2(0	PROPN
ejpam-3768	331	16	)	)	PUNCT
ejpam-3768	332	1	dη	dη	ADP
ejpam-3768	332	2	k5	k5	PROPN
ejpam-3768	332	3	+	+	CCONJ
ejpam-3768	332	4	k6η	k6η	PROPN
ejpam-3768	333	1	3n−6	3n−6	NUM
ejpam-3768	333	2	3n−8	3n−8	NUM
ejpam-3768	333	3	≤	≤	NOUN
ejpam-3768	333	4	t.	t.	NOUN
ejpam-3768	333	5	(	(	PUNCT
ejpam-3768	333	6	3.41	3.41	NUM
ejpam-3768	333	7	)	)	PUNCT
ejpam-3768	333	8	if	if	SCONJ
ejpam-3768	333	9	u	u	PRON
ejpam-3768	333	10	blows	blow	VERB
ejpam-3768	333	11	up	up	ADP
ejpam-3768	333	12	in	in	ADP
ejpam-3768	333	13	the	the	DET
ejpam-3768	333	14	measure	measure	NOUN
ejpam-3768	333	15	ϕ2(t	ϕ2(t	NUM
ejpam-3768	333	16	)	)	PUNCT
ejpam-3768	333	17	as	as	ADP
ejpam-3768	333	18	t→	t→	DET
ejpam-3768	333	19	t∗	t∗	PROPN
ejpam-3768	333	20	,	,	PUNCT
ejpam-3768	333	21	then	then	ADV
ejpam-3768	333	22	we	we	PRON
ejpam-3768	333	23	can	can	AUX
ejpam-3768	333	24	obtain	obtain	VERB
ejpam-3768	333	25	the	the	DET
ejpam-3768	333	26	lower	low	ADJ
ejpam-3768	333	27	bound	bind	VERB
ejpam-3768	333	28	t∗	t∗	PROPN
ejpam-3768	333	29	≥	≥	X
ejpam-3768	333	30	∫	∫	PROPN
ejpam-3768	334	1	+	+	CCONJ
ejpam-3768	334	2	∞	∞	PROPN
ejpam-3768	334	3	ϕ2(0	ϕ2(0	NOUN
ejpam-3768	334	4	)	)	PUNCT
ejpam-3768	335	1	dη	dη	ADP
ejpam-3768	335	2	k5	k5	PROPN
ejpam-3768	335	3	+	+	CCONJ
ejpam-3768	335	4	k6η	k6η	PROPN
ejpam-3768	335	5	3n−6	3n−6	NUM
ejpam-3768	335	6	3n−8	3n−8	NUM
ejpam-3768	335	7	.	.	PUNCT
ejpam-3768	336	1	references	reference	NOUN
ejpam-3768	336	2	660	660	NUM
ejpam-3768	336	3	similar	similar	ADJ
ejpam-3768	336	4	to	to	ADP
ejpam-3768	336	5	the	the	DET
ejpam-3768	336	6	above	above	ADJ
ejpam-3768	336	7	derivation	derivation	NOUN
ejpam-3768	336	8	of	of	ADP
ejpam-3768	336	9	(	(	PUNCT
ejpam-3768	336	10	3.14	3.14	NUM
ejpam-3768	336	11	)	)	PUNCT
ejpam-3768	336	12	and	and	CCONJ
ejpam-3768	336	13	(	(	PUNCT
ejpam-3768	336	14	3.25	3.25	NUM
ejpam-3768	336	15	)	)	PUNCT
ejpam-3768	336	16	,	,	PUNCT
ejpam-3768	336	17	it	it	PRON
ejpam-3768	336	18	is	be	AUX
ejpam-3768	336	19	easy	easy	ADJ
ejpam-3768	336	20	to	to	PART
ejpam-3768	336	21	get	get	VERB
ejpam-3768	336	22	ϕ2(t	ϕ2(t	NUM
ejpam-3768	336	23	)	)	PUNCT
ejpam-3768	336	24	≥	≥	NOUN
ejpam-3768	336	25	(	(	PUNCT
ejpam-3768	336	26	4k6	4k6	NUM
ejpam-3768	336	27	3n−	3n−	NUM
ejpam-3768	336	28	8	8	NUM
ejpam-3768	336	29	)	)	PUNCT
ejpam-3768	336	30	−	−	PROPN
ejpam-3768	337	1	3n−8	3n−8	NUM
ejpam-3768	337	2	2	2	NUM
ejpam-3768	337	3	(	(	PUNCT
ejpam-3768	337	4	t∗	t∗	NOUN
ejpam-3768	337	5	−	−	PROPN
ejpam-3768	337	6	t)−	t)−	PROPN
ejpam-3768	337	7	3n−8	3n−8	NUM
ejpam-3768	337	8	2	2	NUM
ejpam-3768	337	9	.	.	PUNCT
ejpam-3768	338	1	this	this	PRON
ejpam-3768	338	2	completes	complete	VERB
ejpam-3768	338	3	the	the	DET
ejpam-3768	338	4	proof	proof	NOUN
ejpam-3768	338	5	of	of	ADP
ejpam-3768	338	6	theorem	theorem	ADJ
ejpam-3768	338	7	5	5	NUM
ejpam-3768	338	8	.	.	PUNCT
ejpam-3768	338	9	acknowledgements	acknowledgement	NOUN
ejpam-3768	338	10	the	the	DET
ejpam-3768	338	11	authors	author	NOUN
ejpam-3768	338	12	would	would	AUX
ejpam-3768	338	13	like	like	VERB
ejpam-3768	338	14	to	to	PART
ejpam-3768	338	15	express	express	VERB
ejpam-3768	338	16	their	their	PRON
ejpam-3768	338	17	thanks	thank	NOUN
ejpam-3768	338	18	to	to	ADP
ejpam-3768	338	19	the	the	DET
ejpam-3768	338	20	editor	editor	NOUN
ejpam-3768	338	21	and	and	CCONJ
ejpam-3768	338	22	the	the	DET
ejpam-3768	338	23	referees	referee	NOUN
ejpam-3768	338	24	for	for	ADP
ejpam-3768	338	25	their	their	PRON
ejpam-3768	338	26	helpful	helpful	ADJ
ejpam-3768	338	27	comments	comment	NOUN
ejpam-3768	338	28	.	.	PUNCT
ejpam-3768	339	1	this	this	DET
ejpam-3768	339	2	work	work	NOUN
ejpam-3768	339	3	is	be	AUX
ejpam-3768	339	4	supported	support	VERB
ejpam-3768	339	5	by	by	ADP
ejpam-3768	339	6	the	the	DET
ejpam-3768	339	7	nsf	nsf	PROPN
ejpam-3768	339	8	of	of	ADP
ejpam-3768	339	9	china	china	PROPN
ejpam-3768	339	10	(	(	PUNCT
ejpam-3768	339	11	11801108	11801108	NUM
ejpam-3768	339	12	,	,	PUNCT
ejpam-3768	339	13	11701116	11701116	NUM
ejpam-3768	339	14	)	)	PUNCT
ejpam-3768	339	15	,	,	PUNCT
ejpam-3768	339	16	the	the	DET
ejpam-3768	339	17	scientific	scientific	ADJ
ejpam-3768	339	18	program	program	NOUN
ejpam-3768	339	19	(	(	PUNCT
ejpam-3768	339	20	2016a030310262	2016a030310262	NUM
ejpam-3768	339	21	)	)	PUNCT
ejpam-3768	339	22	of	of	ADP
ejpam-3768	339	23	guangdong	guangdong	PROPN
ejpam-3768	339	24	province	province	PROPN
ejpam-3768	339	25	,	,	PUNCT
ejpam-3768	339	26	and	and	CCONJ
ejpam-3768	339	27	the	the	DET
ejpam-3768	339	28	college	college	NOUN
ejpam-3768	339	29	scientific	scientific	ADJ
ejpam-3768	339	30	research	research	NOUN
ejpam-3768	339	31	project	project	NOUN
ejpam-3768	339	32	(	(	PUNCT
ejpam-3768	339	33	yg2020005	yg2020005	PROPN
ejpam-3768	339	34	)	)	PUNCT
ejpam-3768	339	35	of	of	ADP
ejpam-3768	339	36	guangzhou	guangzhou	PROPN
ejpam-3768	339	37	university	university	PROPN
ejpam-3768	339	38	.	.	PUNCT
ejpam-3768	340	1	dr.huafei	dr.huafei	PROPN
ejpam-3768	340	2	di	di	PROPN
ejpam-3768	340	3	also	also	ADV
ejpam-3768	340	4	specially	specially	ADV
ejpam-3768	340	5	appreciates	appreciate	VERB
ejpam-3768	340	6	prof.yue	prof.yue	NOUN
ejpam-3768	340	7	liu	liu	PROPN
ejpam-3768	340	8	for	for	ADP
ejpam-3768	340	9	his	his	PRON
ejpam-3768	340	10	invitation	invitation	NOUN
ejpam-3768	340	11	of	of	ADP
ejpam-3768	340	12	visiting	visit	VERB
ejpam-3768	340	13	to	to	ADP
ejpam-3768	340	14	the	the	DET
ejpam-3768	340	15	university	university	PROPN
ejpam-3768	340	16	of	of	ADP
ejpam-3768	340	17	texas	texas	PROPN
ejpam-3768	340	18	at	at	ADP
ejpam-3768	340	19	arlington	arlington	PROPN
ejpam-3768	340	20	.	.	PUNCT
ejpam-3768	341	1	references	reference	NOUN
ejpam-3768	341	2	[	[	X
ejpam-3768	341	3	1	1	NUM
ejpam-3768	341	4	]	]	PUNCT
ejpam-3768	341	5	a.	a.	PROPN
ejpam-3768	341	6	b.	b.	PROPN
ejpam-3768	341	7	al’shin	al’shin	PROPN
ejpam-3768	341	8	and	and	CCONJ
ejpam-3768	341	9	a.	a.	PROPN
ejpam-3768	341	10	g.	g.	PROPN
ejpam-3768	341	11	sveshnikov	sveshnikov	PROPN
ejpam-3768	341	12	m.	m.	PROPN
ejpam-3768	341	13	o.	o.	PROPN
ejpam-3768	341	14	korpusov	korpusov	PROPN
ejpam-3768	341	15	.	.	PUNCT
ejpam-3768	342	1	blow	blow	NOUN
ejpam-3768	342	2	-	-	PUNCT
ejpam-3768	342	3	up	up	NOUN
ejpam-3768	342	4	in	in	ADP
ejpam-3768	342	5	nonlinear	nonlinear	ADJ
ejpam-3768	342	6	sobolev	sobolev	ADJ
ejpam-3768	342	7	type	type	NOUN
ejpam-3768	342	8	equations	equation	NOUN
ejpam-3768	342	9	.	.	PUNCT
ejpam-3768	343	1	de	de	X
ejpam-3768	343	2	gruyter	gruyter	PROPN
ejpam-3768	343	3	series	series	PROPN
ejpam-3768	343	4	in	in	ADP
ejpam-3768	343	5	nonlinear	nonlinear	ADJ
ejpam-3768	343	6	analysis	analysis	NOUN
ejpam-3768	343	7	and	and	CCONJ
ejpam-3768	343	8	applications	application	NOUN
ejpam-3768	343	9	,	,	PUNCT
ejpam-3768	343	10	15	15	NUM
ejpam-3768	343	11	,	,	PUNCT
ejpam-3768	343	12	walter	walter	PROPN
ejpam-3768	343	13	de	de	PROPN
ejpam-3768	343	14	gruyter	gruyter	PROPN
ejpam-3768	343	15	&	&	CCONJ
ejpam-3768	343	16	co.	co.	PROPN
ejpam-3768	343	17	,	,	PUNCT
ejpam-3768	343	18	berlin	berlin	PROPN
ejpam-3768	343	19	,	,	PUNCT
ejpam-3768	343	20	2011	2011	NUM
ejpam-3768	343	21	.	.	PUNCT
ejpam-3768	344	1	[	[	X
ejpam-3768	344	2	2	2	X
ejpam-3768	344	3	]	]	PUNCT
ejpam-3768	344	4	d.	d.	PROPN
ejpam-3768	344	5	g.	g.	PROPN
ejpam-3768	344	6	aronson	aronson	PROPN
ejpam-3768	344	7	.	.	PUNCT
ejpam-3768	345	1	the	the	DET
ejpam-3768	345	2	porous	porous	ADJ
ejpam-3768	345	3	medium	medium	ADJ
ejpam-3768	345	4	equation	equation	NOUN
ejpam-3768	345	5	.	.	PUNCT
ejpam-3768	346	1	nonlinear	nonlinear	ADJ
ejpam-3768	346	2	diffusion	diffusion	NOUN
ejpam-3768	346	3	problems	problem	NOUN
ejpam-3768	346	4	.	.	PUNCT
ejpam-3768	347	1	springer	springer	NOUN
ejpam-3768	347	2	,	,	PUNCT
ejpam-3768	347	3	heidelberg	heidelberg	PROPN
ejpam-3768	347	4	,	,	PUNCT
ejpam-3768	347	5	berlin	berlin	PROPN
ejpam-3768	347	6	,	,	PUNCT
ejpam-3768	347	7	1986	1986	NUM
ejpam-3768	347	8	.	.	PUNCT
ejpam-3768	348	1	[	[	X
ejpam-3768	348	2	3	3	X
ejpam-3768	348	3	]	]	X
ejpam-3768	348	4	d.	d.	PROPN
ejpam-3768	348	5	g.	g.	PROPN
ejpam-3768	348	6	aronson	aronson	PROPN
ejpam-3768	348	7	and	and	CCONJ
ejpam-3768	348	8	l.	l.	PROPN
ejpam-3768	348	9	a.	a.	PROPN
ejpam-3768	348	10	peletier	peletier	PROPN
ejpam-3768	348	11	.	.	PUNCT
ejpam-3768	349	1	large	large	ADJ
ejpam-3768	349	2	time	time	NOUN
ejpam-3768	349	3	behaviour	behaviour	NOUN
ejpam-3768	349	4	of	of	ADP
ejpam-3768	349	5	solutions	solution	NOUN
ejpam-3768	349	6	of	of	ADP
ejpam-3768	349	7	the	the	DET
ejpam-3768	349	8	porous	porous	ADJ
ejpam-3768	349	9	medium	medium	ADJ
ejpam-3768	349	10	equation	equation	NOUN
ejpam-3768	349	11	in	in	ADP
ejpam-3768	349	12	bounded	bounded	ADJ
ejpam-3768	349	13	domains	domain	NOUN
ejpam-3768	349	14	.	.	PUNCT
ejpam-3768	350	1	j.	j.	PROPN
ejpam-3768	350	2	differ	differ	VERB
ejpam-3768	350	3	.	.	PUNCT
ejpam-3768	351	1	equations	equation	NOUN
ejpam-3768	351	2	,	,	PUNCT
ejpam-3768	351	3	39(3):378–412	39(3):378–412	PROPN
ejpam-3768	351	4	,	,	PUNCT
ejpam-3768	351	5	1981	1981	NUM
ejpam-3768	351	6	.	.	PUNCT
ejpam-3768	352	1	[	[	X
ejpam-3768	352	2	4	4	X
ejpam-3768	352	3	]	]	PUNCT
ejpam-3768	352	4	p.	p.	NOUN
ejpam-3768	352	5	biler	biler	PROPN
ejpam-3768	352	6	and	and	CCONJ
ejpam-3768	352	7	g.	g.	PROPN
ejpam-3768	352	8	karch	karch	PROPN
ejpam-3768	352	9	c.	c.	PROPN
ejpam-3768	352	10	imbert	imbert	PROPN
ejpam-3768	352	11	.	.	PUNCT
ejpam-3768	353	1	the	the	DET
ejpam-3768	353	2	nonlocal	nonlocal	ADJ
ejpam-3768	353	3	porous	porous	ADJ
ejpam-3768	353	4	medium	medium	ADJ
ejpam-3768	353	5	equation	equation	NOUN
ejpam-3768	353	6	:	:	PUNCT
ejpam-3768	353	7	barenblatt	barenblatt	NOUN
ejpam-3768	353	8	profiles	profile	NOUN
ejpam-3768	353	9	and	and	CCONJ
ejpam-3768	353	10	other	other	ADJ
ejpam-3768	353	11	weak	weak	ADJ
ejpam-3768	353	12	solutions	solution	NOUN
ejpam-3768	353	13	.	.	PUNCT
ejpam-3768	354	1	arch	arch	NOUN
ejpam-3768	354	2	.	.	PUNCT
ejpam-3768	355	1	ration	ration	NOUN
ejpam-3768	355	2	.	.	PUNCT
ejpam-3768	356	1	mech	mech	PROPN
ejpam-3768	356	2	.	.	PUNCT
ejpam-3768	357	1	anal	anal	PROPN
ejpam-3768	357	2	.	.	PROPN
ejpam-3768	357	3	,	,	PUNCT
ejpam-3768	357	4	215(2):497–529	215(2):497–529	NUM
ejpam-3768	357	5	,	,	PUNCT
ejpam-3768	357	6	2015	2015	NUM
ejpam-3768	357	7	.	.	PUNCT
ejpam-3768	358	1	[	[	X
ejpam-3768	358	2	5	5	X
ejpam-3768	358	3	]	]	PUNCT
ejpam-3768	358	4	v.	v.	ADP
ejpam-3768	358	5	a.	a.	PROPN
ejpam-3768	358	6	galaktionov	galaktionov	PROPN
ejpam-3768	358	7	et	et	PROPN
ejpam-3768	358	8	al	al	PROPN
ejpam-3768	358	9	.	.	PROPN
ejpam-3768	358	10	on	on	ADP
ejpam-3768	358	11	unbounded	unbounded	ADJ
ejpam-3768	358	12	solutions	solution	NOUN
ejpam-3768	358	13	of	of	ADP
ejpam-3768	358	14	the	the	DET
ejpam-3768	358	15	cauchy	cauchy	ADJ
ejpam-3768	358	16	problem	problem	NOUN
ejpam-3768	358	17	for	for	ADP
ejpam-3768	358	18	the	the	DET
ejpam-3768	358	19	parabolic	parabolic	ADJ
ejpam-3768	358	20	equation	equation	NOUN
ejpam-3768	358	21	ut	ut	PROPN
ejpam-3768	358	22	=	=	PUNCT
ejpam-3768	358	23	∇(uσ∇u	∇(uσ∇u	NOUN
ejpam-3768	358	24	)	)	PUNCT
ejpam-3768	359	1	+	+	CCONJ
ejpam-3768	359	2	uβ	uβ	PROPN
ejpam-3768	359	3	.	.	PROPN
ejpam-3768	359	4	dokl	dokl	PROPN
ejpam-3768	359	5	.	.	PUNCT
ejpam-3768	360	1	akad	akad	PROPN
ejpam-3768	360	2	.	.	PUNCT
ejpam-3768	361	1	nauk	nauk	PROPN
ejpam-3768	361	2	sssr	sssr	PROPN
ejpam-3768	361	3	.	.	PUNCT
ejpam-3768	361	4	,	,	PUNCT
ejpam-3768	362	1	252(6):1362–1364	252(6):1362–1364	PROPN
ejpam-3768	362	2	,	,	PUNCT
ejpam-3768	362	3	1980	1980	NUM
ejpam-3768	362	4	.	.	PUNCT
ejpam-3768	363	1	[	[	X
ejpam-3768	363	2	6	6	NUM
ejpam-3768	363	3	]	]	PUNCT
ejpam-3768	363	4	v.	v.	ADP
ejpam-3768	363	5	a.	a.	NOUN
ejpam-3768	363	6	galaktionov	galaktionov	PROPN
ejpam-3768	363	7	and	and	CCONJ
ejpam-3768	363	8	h.	h.	PROPN
ejpam-3768	363	9	a.	a.	PROPN
ejpam-3768	363	10	levine	levine	PROPN
ejpam-3768	363	11	.	.	PUNCT
ejpam-3768	364	1	a	a	DET
ejpam-3768	364	2	general	general	ADJ
ejpam-3768	364	3	approach	approach	NOUN
ejpam-3768	364	4	to	to	ADP
ejpam-3768	364	5	critical	critical	ADJ
ejpam-3768	364	6	fujita	fujita	NOUN
ejpam-3768	364	7	exponents	exponent	NOUN
ejpam-3768	364	8	in	in	ADP
ejpam-3768	364	9	nonlinear	nonlinear	ADJ
ejpam-3768	364	10	parabolic	parabolic	ADJ
ejpam-3768	364	11	problems	problem	NOUN
ejpam-3768	364	12	.	.	PUNCT
ejpam-3768	365	1	nonlinear	nonlinear	ADJ
ejpam-3768	365	2	anal	anal	PROPN
ejpam-3768	365	3	.	.	PUNCT
ejpam-3768	365	4	,	,	PUNCT
ejpam-3768	365	5	34(7):1005–1027	34(7):1005–1027	NUM
ejpam-3768	365	6	,	,	PUNCT
ejpam-3768	365	7	1998	1998	NUM
ejpam-3768	365	8	.	.	PUNCT
ejpam-3768	366	1	[	[	X
ejpam-3768	366	2	7	7	X
ejpam-3768	366	3	]	]	X
ejpam-3768	366	4	y.	y.	PROPN
ejpam-3768	366	5	hu	hu	PROPN
ejpam-3768	367	1	and	and	CCONJ
ejpam-3768	367	2	x.	x.	PROPN
ejpam-3768	367	3	c.	c.	PROPN
ejpam-3768	367	4	chen	chen	PROPN
ejpam-3768	367	5	l.	l.	PROPN
ejpam-3768	367	6	w.	w.	PROPN
ejpam-3768	367	7	wang	wang	PROPN
ejpam-3768	367	8	.	.	PUNCT
ejpam-3768	368	1	lower	low	ADJ
ejpam-3768	368	2	bounds	bound	NOUN
ejpam-3768	368	3	for	for	ADP
ejpam-3768	368	4	blow	blow	NOUN
ejpam-3768	368	5	-	-	PUNCT
ejpam-3768	368	6	up	up	ADP
ejpam-3768	368	7	time	time	NOUN
ejpam-3768	368	8	of	of	ADP
ejpam-3768	368	9	porous	porous	ADJ
ejpam-3768	368	10	medium	medium	ADJ
ejpam-3768	368	11	equation	equation	NOUN
ejpam-3768	368	12	with	with	ADP
ejpam-3768	368	13	nonlinear	nonlinear	ADJ
ejpam-3768	368	14	flux	flux	NOUN
ejpam-3768	368	15	on	on	ADP
ejpam-3768	368	16	boundary	boundary	NOUN
ejpam-3768	368	17	.	.	PUNCT
ejpam-3768	369	1	int	int	NOUN
ejpam-3768	369	2	.	.	PUNCT
ejpam-3768	370	1	j.	j.	PROPN
ejpam-3768	370	2	math	math	PROPN
ejpam-3768	370	3	.	.	PUNCT
ejpam-3768	371	1	anal	anal	PROPN
ejpam-3768	371	2	.	.	PUNCT
ejpam-3768	372	1	(	(	PUNCT
ejpam-3768	372	2	ruse	ruse	NOUN
ejpam-3768	372	3	)	)	PUNCT
ejpam-3768	372	4	,	,	PUNCT
ejpam-3768	372	5	7(53	7(53	NUM
ejpam-3768	372	6	-	-	SYM
ejpam-3768	372	7	56):2671	56):2671	NUM
ejpam-3768	372	8	–	–	PUNCT
ejpam-3768	372	9	2676	2676	NUM
ejpam-3768	372	10	,	,	PUNCT
ejpam-3768	372	11	2013	2013	NUM
ejpam-3768	372	12	.	.	PUNCT
ejpam-3768	373	1	[	[	X
ejpam-3768	373	2	8	8	NUM
ejpam-3768	373	3	]	]	PUNCT
ejpam-3768	373	4	z.	z.	PROPN
ejpam-3768	373	5	x.	x.	PROPN
ejpam-3768	373	6	jiang	jiang	PROPN
ejpam-3768	373	7	and	and	CCONJ
ejpam-3768	373	8	x.	x.	PROPN
ejpam-3768	373	9	f.	f.	PROPN
ejpam-3768	373	10	song	song	PROPN
ejpam-3768	373	11	s.	s.	PROPN
ejpam-3768	373	12	n.	n.	PROPN
ejpam-3768	373	13	zheng	zheng	PROPN
ejpam-3768	373	14	.	.	PUNCT
ejpam-3768	374	1	blow	blow	VERB
ejpam-3768	374	2	-	-	PUNCT
ejpam-3768	374	3	up	up	ADP
ejpam-3768	374	4	analysis	analysis	NOUN
ejpam-3768	374	5	for	for	ADP
ejpam-3768	374	6	a	a	DET
ejpam-3768	374	7	nonlinear	nonlinear	ADJ
ejpam-3768	374	8	diffusion	diffusion	NOUN
ejpam-3768	374	9	equation	equation	NOUN
ejpam-3768	374	10	with	with	ADP
ejpam-3768	374	11	nonlinear	nonlinear	ADJ
ejpam-3768	374	12	boundary	boundary	ADJ
ejpam-3768	374	13	conditions	condition	NOUN
ejpam-3768	374	14	.	.	PUNCT
ejpam-3768	375	1	appl	appl	PROPN
ejpam-3768	375	2	.	.	PROPN
ejpam-3768	375	3	math	math	PROPN
ejpam-3768	375	4	.	.	PUNCT
ejpam-3768	376	1	lett	lett	PROPN
ejpam-3768	376	2	.	.	PROPN
ejpam-3768	376	3	,	,	PUNCT
ejpam-3768	376	4	17(2):193–199	17(2):193–199	NUM
ejpam-3768	376	5	,	,	PUNCT
ejpam-3768	376	6	2004	2004	NUM
ejpam-3768	376	7	.	.	PUNCT
ejpam-3768	377	1	[	[	X
ejpam-3768	377	2	9	9	NUM
ejpam-3768	377	3	]	]	PUNCT
ejpam-3768	377	4	t.	t.	NOUN
ejpam-3768	377	5	kawanago	kawanago	PROPN
ejpam-3768	377	6	.	.	PUNCT
ejpam-3768	378	1	existence	existence	NOUN
ejpam-3768	378	2	and	and	CCONJ
ejpam-3768	378	3	behaviour	behaviour	NOUN
ejpam-3768	378	4	of	of	ADP
ejpam-3768	378	5	solutions	solution	NOUN
ejpam-3768	378	6	for	for	ADP
ejpam-3768	378	7	ut	ut	PROPN
ejpam-3768	378	8	=	=	PUNCT
ejpam-3768	378	9	∆(um	∆(um	NOUN
ejpam-3768	378	10	)	)	PUNCT
ejpam-3768	379	1	+	+	NOUN
ejpam-3768	379	2	ul	ul	INTJ
ejpam-3768	379	3	.	.	PUNCT
ejpam-3768	379	4	adv	adv	PROPN
ejpam-3768	379	5	.	.	PUNCT
ejpam-3768	379	6	math	math	PROPN
ejpam-3768	379	7	.	.	PUNCT
ejpam-3768	380	1	sci	sci	PROPN
ejpam-3768	380	2	.	.	PUNCT
ejpam-3768	380	3	appl	appl	PROPN
ejpam-3768	380	4	.	.	PROPN
ejpam-3768	380	5	,	,	PUNCT
ejpam-3768	380	6	7(1):367–400	7(1):367–400	NUM
ejpam-3768	380	7	,	,	PUNCT
ejpam-3768	380	8	1997	1997	NUM
ejpam-3768	380	9	.	.	PUNCT
ejpam-3768	381	1	references	reference	NOUN
ejpam-3768	381	2	661	661	NUM
ejpam-3768	381	3	[	[	SYM
ejpam-3768	381	4	10	10	NUM
ejpam-3768	381	5	]	]	PUNCT
ejpam-3768	381	6	h.	h.	PROPN
ejpam-3768	381	7	a.	a.	PROPN
ejpam-3768	381	8	levine	levine	PROPN
ejpam-3768	381	9	.	.	PUNCT
ejpam-3768	382	1	the	the	DET
ejpam-3768	382	2	role	role	NOUN
ejpam-3768	382	3	of	of	ADP
ejpam-3768	382	4	critical	critical	ADJ
ejpam-3768	382	5	exponents	exponent	NOUN
ejpam-3768	382	6	in	in	ADP
ejpam-3768	382	7	blowup	blowup	ADJ
ejpam-3768	382	8	theorems	theorem	NOUN
ejpam-3768	382	9	.	.	PUNCT
ejpam-3768	383	1	siam	siam	PROPN
ejpam-3768	383	2	rev	rev	PROPN
ejpam-3768	383	3	.	.	PROPN
ejpam-3768	383	4	,	,	PUNCT
ejpam-3768	383	5	32(2):262–288	32(2):262–288	PROPN
ejpam-3768	383	6	,	,	PUNCT
ejpam-3768	383	7	1990	1990	NUM
ejpam-3768	383	8	.	.	PUNCT
ejpam-3768	384	1	[	[	X
ejpam-3768	384	2	11	11	NUM
ejpam-3768	384	3	]	]	PUNCT
ejpam-3768	384	4	s.	s.	PROPN
ejpam-3768	384	5	z.	z.	PROPN
ejpam-3768	384	6	lian	lian	PROPN
ejpam-3768	384	7	and	and	CCONJ
ejpam-3768	384	8	c.	c.	PROPN
ejpam-3768	384	9	c.	c.	PROPN
ejpam-3768	384	10	liu	liu	PROPN
ejpam-3768	384	11	.	.	PUNCT
ejpam-3768	385	1	on	on	ADP
ejpam-3768	385	2	the	the	DET
ejpam-3768	385	3	existence	existence	NOUN
ejpam-3768	385	4	and	and	CCONJ
ejpam-3768	385	5	nonexistence	nonexistence	NOUN
ejpam-3768	385	6	of	of	ADP
ejpam-3768	385	7	global	global	ADJ
ejpam-3768	385	8	solutions	solution	NOUN
ejpam-3768	385	9	for	for	ADP
ejpam-3768	385	10	the	the	DET
ejpam-3768	385	11	porous	porous	ADJ
ejpam-3768	385	12	medium	medium	ADJ
ejpam-3768	385	13	equation	equation	NOUN
ejpam-3768	385	14	with	with	ADP
ejpam-3768	385	15	strongly	strongly	ADV
ejpam-3768	385	16	nonlinear	nonlinear	ADJ
ejpam-3768	385	17	sources	source	NOUN
ejpam-3768	385	18	in	in	ADP
ejpam-3768	385	19	a	a	DET
ejpam-3768	385	20	cone	cone	NOUN
ejpam-3768	385	21	.	.	PUNCT
ejpam-3768	386	1	arch	arch	PROPN
ejpam-3768	386	2	.	.	PUNCT
ejpam-3768	387	1	math	math	NOUN
ejpam-3768	387	2	.	.	PUNCT
ejpam-3768	388	1	(	(	PUNCT
ejpam-3768	388	2	basel	basel	PROPN
ejpam-3768	388	3	)	)	PUNCT
ejpam-3768	388	4	,	,	PUNCT
ejpam-3768	389	1	94(3):245–253	94(3):245–253	PROPN
ejpam-3768	389	2	,	,	PUNCT
ejpam-3768	389	3	2010	2010	NUM
ejpam-3768	389	4	.	.	PUNCT
ejpam-3768	390	1	[	[	X
ejpam-3768	390	2	12	12	NUM
ejpam-3768	390	3	]	]	X
ejpam-3768	390	4	g.	g.	PROPN
ejpam-3768	390	5	m.	m.	PROPN
ejpam-3768	390	6	lieberman	lieberman	PROPN
ejpam-3768	390	7	.	.	PUNCT
ejpam-3768	391	1	second	second	ADJ
ejpam-3768	391	2	order	order	NOUN
ejpam-3768	391	3	parabolic	parabolic	PROPN
ejpam-3768	391	4	differential	differential	NOUN
ejpam-3768	391	5	equations	equation	NOUN
ejpam-3768	391	6	.	.	PUNCT
ejpam-3768	392	1	world	world	NOUN
ejpam-3768	392	2	scientific	scientific	PROPN
ejpam-3768	392	3	publishing	publishing	PROPN
ejpam-3768	392	4	co.	co.	PROPN
ejpam-3768	392	5	,	,	PUNCT
ejpam-3768	392	6	inc	inc	PROPN
ejpam-3768	392	7	,	,	PUNCT
ejpam-3768	392	8	river	river	NOUN
ejpam-3768	392	9	edge	edge	NOUN
ejpam-3768	392	10	,	,	PUNCT
ejpam-3768	392	11	new	new	PROPN
ejpam-3768	392	12	jersey	jersey	PROPN
ejpam-3768	392	13	,	,	PUNCT
ejpam-3768	392	14	1996	1996	NUM
ejpam-3768	392	15	.	.	PUNCT
ejpam-3768	393	1	[	[	X
ejpam-3768	393	2	13	13	NUM
ejpam-3768	393	3	]	]	X
ejpam-3768	393	4	y.	y.	PROPN
ejpam-3768	393	5	liu	liu	PROPN
ejpam-3768	393	6	.	.	PUNCT
ejpam-3768	394	1	lower	low	ADJ
ejpam-3768	394	2	bounds	bound	NOUN
ejpam-3768	394	3	for	for	ADP
ejpam-3768	394	4	the	the	DET
ejpam-3768	394	5	blow	blow	NOUN
ejpam-3768	394	6	-	-	PUNCT
ejpam-3768	394	7	up	up	ADP
ejpam-3768	394	8	time	time	NOUN
ejpam-3768	394	9	in	in	ADP
ejpam-3768	394	10	a	a	DET
ejpam-3768	394	11	non	non	ADJ
ejpam-3768	394	12	-	-	ADJ
ejpam-3768	394	13	local	local	ADJ
ejpam-3768	394	14	reaction	reaction	NOUN
ejpam-3768	394	15	diffusion	diffusion	NOUN
ejpam-3768	394	16	problem	problem	NOUN
ejpam-3768	394	17	under	under	ADP
ejpam-3768	394	18	nonlinear	nonlinear	ADJ
ejpam-3768	394	19	boundary	boundary	ADJ
ejpam-3768	394	20	conditions	condition	NOUN
ejpam-3768	394	21	.	.	PUNCT
ejpam-3768	395	1	math	math	NOUN
ejpam-3768	395	2	.	.	PUNCT
ejpam-3768	396	1	comput	comput	NOUN
ejpam-3768	396	2	.	.	PUNCT
ejpam-3768	397	1	modelling	modelling	NOUN
ejpam-3768	397	2	,	,	PUNCT
ejpam-3768	397	3	57(3	57(3	NUM
ejpam-3768	397	4	-	-	PUNCT
ejpam-3768	397	5	4):926–931	4):926–931	NOUN
ejpam-3768	397	6	,	,	PUNCT
ejpam-3768	397	7	2013	2013	NUM
ejpam-3768	397	8	.	.	PUNCT
ejpam-3768	398	1	[	[	X
ejpam-3768	398	2	14	14	NUM
ejpam-3768	398	3	]	]	PUNCT
ejpam-3768	398	4	x.	x.	NOUN
ejpam-3768	398	5	s.	s.	PROPN
ejpam-3768	398	6	lv	lv	PROPN
ejpam-3768	398	7	and	and	CCONJ
ejpam-3768	398	8	x.	x.	PROPN
ejpam-3768	398	9	f.	f.	PROPN
ejpam-3768	398	10	song	song	PROPN
ejpam-3768	398	11	.	.	PUNCT
ejpam-3768	399	1	bounds	bound	NOUN
ejpam-3768	399	2	of	of	ADP
ejpam-3768	399	3	the	the	DET
ejpam-3768	399	4	blowup	blowup	ADJ
ejpam-3768	399	5	time	time	NOUN
ejpam-3768	399	6	in	in	ADP
ejpam-3768	399	7	parabolic	parabolic	ADJ
ejpam-3768	399	8	equations	equation	NOUN
ejpam-3768	399	9	with	with	ADP
ejpam-3768	399	10	weighted	weighted	ADJ
ejpam-3768	399	11	source	source	NOUN
ejpam-3768	399	12	under	under	ADP
ejpam-3768	399	13	nonhomogeneous	nonhomogeneous	ADJ
ejpam-3768	399	14	neumann	neumann	PROPN
ejpam-3768	399	15	boundary	boundary	ADJ
ejpam-3768	399	16	condition	condition	NOUN
ejpam-3768	399	17	.	.	PUNCT
ejpam-3768	400	1	math	math	NOUN
ejpam-3768	400	2	.	.	PUNCT
ejpam-3768	401	1	methods	method	NOUN
ejpam-3768	401	2	appl	appl	PROPN
ejpam-3768	401	3	.	.	PUNCT
ejpam-3768	402	1	sci	sci	PROPN
ejpam-3768	402	2	.	.	PROPN
ejpam-3768	402	3	,	,	PUNCT
ejpam-3768	402	4	37(7):1019–1028	37(7):1019–1028	NUM
ejpam-3768	402	5	,	,	PUNCT
ejpam-3768	402	6	2014	2014	NUM
ejpam-3768	402	7	.	.	PUNCT
ejpam-3768	403	1	[	[	X
ejpam-3768	403	2	15	15	NUM
ejpam-3768	403	3	]	]	X
ejpam-3768	403	4	l.	l.	PROPN
ejpam-3768	403	5	ma	ma	PROPN
ejpam-3768	403	6	and	and	CCONJ
ejpam-3768	403	7	z.	z.	PROPN
ejpam-3768	403	8	b.	b.	PROPN
ejpam-3768	403	9	fang	fang	PROPN
ejpam-3768	403	10	.	.	PUNCT
ejpam-3768	404	1	blow	blow	NOUN
ejpam-3768	404	2	-	-	PUNCT
ejpam-3768	404	3	up	up	ADP
ejpam-3768	404	4	analysis	analysis	NOUN
ejpam-3768	404	5	for	for	ADP
ejpam-3768	404	6	a	a	DET
ejpam-3768	404	7	reaction	reaction	NOUN
ejpam-3768	404	8	-	-	PUNCT
ejpam-3768	404	9	diffusion	diffusion	NOUN
ejpam-3768	404	10	equation	equation	NOUN
ejpam-3768	404	11	with	with	ADP
ejpam-3768	404	12	weighted	weight	VERB
ejpam-3768	404	13	nonlocal	nonlocal	ADJ
ejpam-3768	404	14	inner	inner	ADJ
ejpam-3768	404	15	absorptions	absorption	NOUN
ejpam-3768	404	16	under	under	ADP
ejpam-3768	404	17	nonlinear	nonlinear	ADJ
ejpam-3768	404	18	boundary	boundary	ADJ
ejpam-3768	404	19	flux	flux	NOUN
ejpam-3768	404	20	.	.	PUNCT
ejpam-3768	405	1	nonlinear	nonlinear	ADJ
ejpam-3768	405	2	anal	anal	PROPN
ejpam-3768	405	3	.	.	PUNCT
ejpam-3768	406	1	real	real	ADJ
ejpam-3768	406	2	world	world	NOUN
ejpam-3768	406	3	appl	appl	PROPN
ejpam-3768	406	4	.	.	PROPN
ejpam-3768	406	5	,	,	PUNCT
ejpam-3768	406	6	32:338–354	32:338–354	PROPN
ejpam-3768	406	7	,	,	PUNCT
ejpam-3768	406	8	2016	2016	NUM
ejpam-3768	406	9	.	.	PUNCT
ejpam-3768	407	1	[	[	X
ejpam-3768	407	2	16	16	NUM
ejpam-3768	407	3	]	]	PUNCT
ejpam-3768	407	4	l.	l.	PROPN
ejpam-3768	407	5	e.	e.	PROPN
ejpam-3768	407	6	payne	payne	PROPN
ejpam-3768	407	7	and	and	CCONJ
ejpam-3768	407	8	s.	s.	PROPN
ejpam-3768	407	9	vernier	vernier	PROPN
ejpam-3768	407	10	piro	piro	PROPN
ejpam-3768	407	11	g.	g.	PROPN
ejpam-3768	407	12	a.	a.	NOUN
ejpam-3768	407	13	philippin	philippin	PROPN
ejpam-3768	407	14	.	.	PUNCT
ejpam-3768	408	1	blow	blow	VERB
ejpam-3768	408	2	-	-	PUNCT
ejpam-3768	408	3	up	up	ADP
ejpam-3768	408	4	phenomena	phenomenon	NOUN
ejpam-3768	408	5	for	for	ADP
ejpam-3768	408	6	a	a	DET
ejpam-3768	408	7	semilinear	semilinear	ADJ
ejpam-3768	408	8	heat	heat	NOUN
ejpam-3768	408	9	equation	equation	NOUN
ejpam-3768	408	10	with	with	ADP
ejpam-3768	408	11	nonlinear	nonlinear	ADJ
ejpam-3768	408	12	boundary	boundary	ADJ
ejpam-3768	408	13	condition	condition	NOUN
ejpam-3768	408	14	,	,	PUNCT
ejpam-3768	408	15	i.	i.	PROPN
ejpam-3768	408	16	z.	z.	PROPN
ejpam-3768	408	17	angew	angew	PROPN
ejpam-3768	408	18	.	.	PUNCT
ejpam-3768	409	1	math	math	NOUN
ejpam-3768	409	2	.	.	PUNCT
ejpam-3768	410	1	phys	phy	NOUN
ejpam-3768	410	2	.	.	PUNCT
ejpam-3768	410	3	,	,	PUNCT
ejpam-3768	410	4	61(6):999–1007	61(6):999–1007	NUM
ejpam-3768	410	5	,	,	PUNCT
ejpam-3768	410	6	2010	2010	NUM
ejpam-3768	410	7	.	.	PUNCT
ejpam-3768	411	1	[	[	X
ejpam-3768	411	2	17	17	NUM
ejpam-3768	411	3	]	]	X
ejpam-3768	411	4	l.	l.	PROPN
ejpam-3768	411	5	e.	e.	PROPN
ejpam-3768	411	6	payne	payne	PROPN
ejpam-3768	411	7	and	and	CCONJ
ejpam-3768	411	8	s.	s.	PROPN
ejpam-3768	411	9	vernier	vernier	PROPN
ejpam-3768	411	10	piro	piro	PROPN
ejpam-3768	411	11	g.	g.	PROPN
ejpam-3768	411	12	a.	a.	NOUN
ejpam-3768	411	13	philippin	philippin	PROPN
ejpam-3768	411	14	.	.	PUNCT
ejpam-3768	412	1	blow	blow	VERB
ejpam-3768	412	2	-	-	PUNCT
ejpam-3768	412	3	up	up	ADP
ejpam-3768	412	4	phenomena	phenomenon	NOUN
ejpam-3768	412	5	for	for	ADP
ejpam-3768	412	6	a	a	DET
ejpam-3768	412	7	semilinear	semilinear	ADJ
ejpam-3768	412	8	heat	heat	NOUN
ejpam-3768	412	9	equation	equation	NOUN
ejpam-3768	412	10	with	with	ADP
ejpam-3768	412	11	nonlinear	nonlinear	ADJ
ejpam-3768	412	12	boundary	boundary	ADJ
ejpam-3768	412	13	condition	condition	NOUN
ejpam-3768	412	14	,	,	PUNCT
ejpam-3768	412	15	ii	ii	PROPN
ejpam-3768	412	16	.	.	PUNCT
ejpam-3768	413	1	nonlinear	nonlinear	PROPN
ejpam-3768	413	2	anal	anal	PROPN
ejpam-3768	413	3	.	.	PUNCT
ejpam-3768	413	4	,	,	PUNCT
ejpam-3768	413	5	73(4):971–978	73(4):971–978	PROPN
ejpam-3768	413	6	,	,	PUNCT
ejpam-3768	413	7	2010	2010	NUM
ejpam-3768	413	8	.	.	PUNCT
ejpam-3768	414	1	[	[	X
ejpam-3768	414	2	18	18	NUM
ejpam-3768	414	3	]	]	X
ejpam-3768	414	4	l.	l.	PROPN
ejpam-3768	414	5	e.	e.	PROPN
ejpam-3768	414	6	payne	payne	PROPN
ejpam-3768	414	7	and	and	CCONJ
ejpam-3768	414	8	p.	p.	PROPN
ejpam-3768	414	9	w.	w.	PROPN
ejpam-3768	414	10	schaefer	schaefer	PROPN
ejpam-3768	414	11	.	.	PUNCT
ejpam-3768	415	1	lower	low	ADJ
ejpam-3768	415	2	bounds	bound	NOUN
ejpam-3768	415	3	for	for	ADP
ejpam-3768	415	4	blow	blow	NOUN
ejpam-3768	415	5	-	-	PUNCT
ejpam-3768	415	6	up	up	ADP
ejpam-3768	415	7	time	time	NOUN
ejpam-3768	415	8	in	in	ADP
ejpam-3768	415	9	parabolic	parabolic	ADJ
ejpam-3768	415	10	problems	problem	NOUN
ejpam-3768	415	11	under	under	ADP
ejpam-3768	415	12	neumann	neumann	PROPN
ejpam-3768	415	13	conditions	condition	NOUN
ejpam-3768	415	14	.	.	PUNCT
ejpam-3768	416	1	appl	appl	PROPN
ejpam-3768	416	2	.	.	PUNCT
ejpam-3768	417	1	anal	anal	PROPN
ejpam-3768	417	2	.	.	PROPN
ejpam-3768	417	3	,	,	PUNCT
ejpam-3768	417	4	85(10):1301–1311	85(10):1301–1311	NUM
ejpam-3768	417	5	,	,	PUNCT
ejpam-3768	417	6	2006	2006	NUM
ejpam-3768	417	7	.	.	PUNCT
ejpam-3768	418	1	[	[	X
ejpam-3768	418	2	19	19	NUM
ejpam-3768	418	3	]	]	PUNCT
ejpam-3768	418	4	l.	l.	PROPN
ejpam-3768	418	5	e.	e.	PROPN
ejpam-3768	418	6	payne	payne	PROPN
ejpam-3768	418	7	and	and	CCONJ
ejpam-3768	418	8	p.	p.	PROPN
ejpam-3768	418	9	w.	w.	PROPN
ejpam-3768	418	10	schaefer	schaefer	PROPN
ejpam-3768	418	11	.	.	PUNCT
ejpam-3768	419	1	lower	low	ADJ
ejpam-3768	419	2	bounds	bound	NOUN
ejpam-3768	419	3	for	for	ADP
ejpam-3768	419	4	blow	blow	NOUN
ejpam-3768	419	5	-	-	PUNCT
ejpam-3768	419	6	up	up	ADP
ejpam-3768	419	7	time	time	NOUN
ejpam-3768	419	8	in	in	ADP
ejpam-3768	419	9	parabolic	parabolic	ADJ
ejpam-3768	419	10	problems	problem	NOUN
ejpam-3768	419	11	under	under	ADP
ejpam-3768	419	12	dirichlet	dirichlet	PROPN
ejpam-3768	419	13	conditions	condition	NOUN
ejpam-3768	419	14	.	.	PUNCT
ejpam-3768	420	1	j.	j.	PROPN
ejpam-3768	420	2	math	math	PROPN
ejpam-3768	420	3	.	.	PUNCT
ejpam-3768	421	1	anal	anal	PROPN
ejpam-3768	421	2	.	.	PUNCT
ejpam-3768	422	1	appl	appl	PROPN
ejpam-3768	422	2	.	.	PROPN
ejpam-3768	422	3	,	,	PUNCT
ejpam-3768	422	4	328(2):1196–1205	328(2):1196–1205	NUM
ejpam-3768	422	5	,	,	PUNCT
ejpam-3768	422	6	2007	2007	NUM
ejpam-3768	422	7	.	.	PUNCT
ejpam-3768	423	1	[	[	X
ejpam-3768	423	2	20	20	NUM
ejpam-3768	423	3	]	]	PUNCT
ejpam-3768	423	4	l.	l.	PROPN
ejpam-3768	423	5	a.	a.	NOUN
ejpam-3768	423	6	peletier	peletier	PROPN
ejpam-3768	423	7	.	.	PUNCT
ejpam-3768	424	1	asymptotic	asymptotic	ADJ
ejpam-3768	424	2	behavior	behavior	NOUN
ejpam-3768	424	3	of	of	ADP
ejpam-3768	424	4	solutions	solution	NOUN
ejpam-3768	424	5	of	of	ADP
ejpam-3768	424	6	the	the	DET
ejpam-3768	424	7	porous	porous	ADJ
ejpam-3768	424	8	media	medium	NOUN
ejpam-3768	424	9	equation	equation	NOUN
ejpam-3768	424	10	.	.	PUNCT
ejpam-3768	425	1	siam	siam	PROPN
ejpam-3768	425	2	j.	j.	PROPN
ejpam-3768	425	3	appl	appl	PROPN
ejpam-3768	425	4	.	.	PROPN
ejpam-3768	425	5	math	math	PROPN
ejpam-3768	425	6	.	.	PUNCT
ejpam-3768	425	7	,	,	PUNCT
ejpam-3768	425	8	21:542–551	21:542–551	NUM
ejpam-3768	425	9	,	,	PUNCT
ejpam-3768	425	10	1971	1971	NUM
ejpam-3768	425	11	.	.	PUNCT
ejpam-3768	426	1	[	[	X
ejpam-3768	426	2	21	21	NUM
ejpam-3768	426	3	]	]	X
ejpam-3768	426	4	f.	f.	PROPN
ejpam-3768	426	5	quirós	quirós	PROPN
ejpam-3768	426	6	and	and	CCONJ
ejpam-3768	426	7	j.	j.	PROPN
ejpam-3768	426	8	l.	l.	PROPN
ejpam-3768	426	9	vázquez	vázquez	PROPN
ejpam-3768	426	10	.	.	PROPN
ejpam-3768	426	11	asymptotic	asymptotic	ADJ
ejpam-3768	426	12	behaviour	behaviour	NOUN
ejpam-3768	426	13	of	of	ADP
ejpam-3768	426	14	the	the	DET
ejpam-3768	426	15	porous	porous	ADJ
ejpam-3768	426	16	media	medium	NOUN
ejpam-3768	426	17	equation	equation	NOUN
ejpam-3768	426	18	in	in	ADP
ejpam-3768	426	19	an	an	DET
ejpam-3768	426	20	exterior	exterior	ADJ
ejpam-3768	426	21	domain	domain	NOUN
ejpam-3768	426	22	.	.	PUNCT
ejpam-3768	427	1	annali	annali	PROPN
ejpam-3768	427	2	della	della	PROPN
ejpam-3768	427	3	scuola	scuola	PROPN
ejpam-3768	427	4	normale	normale	PROPN
ejpam-3768	427	5	superiore	superiore	PROPN
ejpam-3768	427	6	di	di	PROPN
ejpam-3768	427	7	pisa	pisa	PROPN
ejpam-3768	427	8	-	-	PROPN
ejpam-3768	427	9	classe	classe	PROPN
ejpam-3768	427	10	di	di	X
ejpam-3768	427	11	scienze	scienze	PROPN
ejpam-3768	427	12	,	,	PUNCT
ejpam-3768	427	13	28(2):183–227	28(2):183–227	PROPN
ejpam-3768	427	14	,	,	PUNCT
ejpam-3768	427	15	1998	1998	NUM
ejpam-3768	427	16	.	.	PUNCT
ejpam-3768	428	1	[	[	X
ejpam-3768	428	2	22	22	NUM
ejpam-3768	428	3	]	]	PUNCT
ejpam-3768	428	4	j.	j.	PROPN
ejpam-3768	428	5	rubinstein	rubinstein	PROPN
ejpam-3768	428	6	and	and	CCONJ
ejpam-3768	428	7	p.	p.	PROPN
ejpam-3768	428	8	sternberg	sternberg	PROPN
ejpam-3768	428	9	.	.	PUNCT
ejpam-3768	429	1	nonlocal	nonlocal	ADJ
ejpam-3768	429	2	reaction	reaction	NOUN
ejpam-3768	429	3	-	-	PUNCT
ejpam-3768	429	4	diffusion	diffusion	NOUN
ejpam-3768	429	5	equations	equation	NOUN
ejpam-3768	429	6	and	and	CCONJ
ejpam-3768	429	7	nucleation	nucleation	NOUN
ejpam-3768	429	8	.	.	PUNCT
ejpam-3768	430	1	i	i	PRON
ejpam-3768	430	2	m	m	VERB
ejpam-3768	430	3	a	a	PROPN
ejpam-3768	430	4	j.	j.	PROPN
ejpam-3768	430	5	appl	appl	PROPN
ejpam-3768	430	6	.	.	PROPN
ejpam-3768	430	7	math	math	PROPN
ejpam-3768	430	8	.	.	PUNCT
ejpam-3768	430	9	,	,	PUNCT
ejpam-3768	430	10	48(3):249–264	48(3):249–264	NOUN
ejpam-3768	430	11	,	,	PUNCT
ejpam-3768	430	12	1992	1992	NUM
ejpam-3768	430	13	.	.	PUNCT
ejpam-3768	431	1	[	[	X
ejpam-3768	431	2	23	23	NUM
ejpam-3768	431	3	]	]	PUNCT
ejpam-3768	431	4	j.	j.	PROPN
ejpam-3768	431	5	c.	c.	PROPN
ejpam-3768	431	6	song	song	PROPN
ejpam-3768	431	7	.	.	PUNCT
ejpam-3768	432	1	lower	low	ADJ
ejpam-3768	432	2	bounds	bound	NOUN
ejpam-3768	432	3	for	for	ADP
ejpam-3768	432	4	the	the	DET
ejpam-3768	432	5	blow	blow	NOUN
ejpam-3768	432	6	-	-	PUNCT
ejpam-3768	432	7	up	up	ADP
ejpam-3768	432	8	time	time	NOUN
ejpam-3768	432	9	in	in	ADP
ejpam-3768	432	10	a	a	DET
ejpam-3768	432	11	non	non	ADJ
ejpam-3768	432	12	-	-	ADJ
ejpam-3768	432	13	local	local	ADJ
ejpam-3768	432	14	reaction	reaction	NOUN
ejpam-3768	432	15	-	-	PUNCT
ejpam-3768	432	16	diffusion	diffusion	NOUN
ejpam-3768	432	17	problem	problem	NOUN
ejpam-3768	432	18	.	.	PUNCT
ejpam-3768	433	1	appl	appl	PROPN
ejpam-3768	433	2	.	.	PROPN
ejpam-3768	433	3	math	math	PROPN
ejpam-3768	433	4	.	.	PUNCT
ejpam-3768	434	1	lett	lett	PROPN
ejpam-3768	434	2	.	.	PROPN
ejpam-3768	434	3	,	,	PUNCT
ejpam-3768	434	4	24(5):793–796	24(5):793–796	NUM
ejpam-3768	434	5	,	,	PUNCT
ejpam-3768	434	6	2011	2011	NUM
ejpam-3768	434	7	.	.	PUNCT
ejpam-3768	435	1	references	reference	NOUN
ejpam-3768	435	2	662	662	NUM
ejpam-3768	435	3	[	[	X
ejpam-3768	435	4	24	24	NUM
ejpam-3768	435	5	]	]	PUNCT
ejpam-3768	435	6	x.	x.	PROPN
ejpam-3768	435	7	f.	f.	PROPN
ejpam-3768	435	8	song	song	PROPN
ejpam-3768	435	9	and	and	CCONJ
ejpam-3768	435	10	x.	x.	PROPN
ejpam-3768	435	11	s.	s.	PROPN
ejpam-3768	435	12	lv	lv	PROPN
ejpam-3768	435	13	.	.	PROPN
ejpam-3768	435	14	bounds	bound	VERB
ejpam-3768	435	15	for	for	ADP
ejpam-3768	435	16	the	the	DET
ejpam-3768	435	17	blow	blow	NOUN
ejpam-3768	435	18	-	-	PUNCT
ejpam-3768	435	19	up	up	ADP
ejpam-3768	435	20	time	time	NOUN
ejpam-3768	435	21	and	and	CCONJ
ejpam-3768	435	22	blow	blow	NOUN
ejpam-3768	435	23	-	-	PUNCT
ejpam-3768	435	24	up	up	ADP
ejpam-3768	435	25	rate	rate	NOUN
ejpam-3768	435	26	estimates	estimate	NOUN
ejpam-3768	435	27	for	for	ADP
ejpam-3768	435	28	a	a	DET
ejpam-3768	435	29	type	type	NOUN
ejpam-3768	435	30	of	of	ADP
ejpam-3768	435	31	parabolic	parabolic	ADJ
ejpam-3768	435	32	equations	equation	NOUN
ejpam-3768	435	33	with	with	ADP
ejpam-3768	435	34	weighted	weighted	ADJ
ejpam-3768	435	35	source	source	NOUN
ejpam-3768	435	36	.	.	PUNCT
ejpam-3768	436	1	appl	appl	PROPN
ejpam-3768	436	2	.	.	PROPN
ejpam-3768	436	3	math	math	PROPN
ejpam-3768	436	4	.	.	PUNCT
ejpam-3768	437	1	comput	comput	NOUN
ejpam-3768	437	2	.	.	PUNCT
ejpam-3768	437	3	,	,	PUNCT
ejpam-3768	437	4	236:78–92	236:78–92	NUM
ejpam-3768	437	5	,	,	PUNCT
ejpam-3768	437	6	2014	2014	NUM
ejpam-3768	437	7	.	.	PUNCT
ejpam-3768	438	1	[	[	X
ejpam-3768	438	2	25	25	NUM
ejpam-3768	438	3	]	]	X
ejpam-3768	438	4	g.	g.	PROPN
ejpam-3768	438	5	s.	s.	PROPN
ejpam-3768	438	6	tang	tang	PROPN
ejpam-3768	438	7	and	and	CCONJ
ejpam-3768	438	8	x.	x.	NOUN
ejpam-3768	438	9	t.	t.	PROPN
ejpam-3768	438	10	yang	yang	PROPN
ejpam-3768	438	11	y.	y.	PROPN
ejpam-3768	438	12	f.	f.	PROPN
ejpam-3768	438	13	li	li	PROPN
ejpam-3768	438	14	.	.	PROPN
ejpam-3768	439	1	lower	low	ADJ
ejpam-3768	439	2	bounds	bound	NOUN
ejpam-3768	439	3	for	for	ADP
ejpam-3768	439	4	the	the	DET
ejpam-3768	439	5	blow	blow	NOUN
ejpam-3768	439	6	-	-	PUNCT
ejpam-3768	439	7	up	up	ADP
ejpam-3768	439	8	time	time	NOUN
ejpam-3768	439	9	of	of	ADP
ejpam-3768	439	10	the	the	DET
ejpam-3768	439	11	nonlinear	nonlinear	ADJ
ejpam-3768	439	12	non	non	ADJ
ejpam-3768	439	13	-	-	ADJ
ejpam-3768	439	14	local	local	ADJ
ejpam-3768	439	15	reaction	reaction	NOUN
ejpam-3768	439	16	diffusion	diffusion	NOUN
ejpam-3768	439	17	problems	problem	NOUN
ejpam-3768	439	18	in	in	ADP
ejpam-3768	439	19	rn	rn	PROPN
ejpam-3768	439	20	(	(	PUNCT
ejpam-3768	439	21	n	n	CCONJ
ejpam-3768	439	22	≥	≥	NOUN
ejpam-3768	439	23	3	3	NUM
ejpam-3768	439	24	)	)	PUNCT
ejpam-3768	439	25	.	.	PUNCT
ejpam-3768	440	1	bound	bind	VERB
ejpam-3768	440	2	.	.	PUNCT
ejpam-3768	441	1	value	value	PROPN
ejpam-3768	441	2	probl	probl	NOUN
ejpam-3768	441	3	.	.	PUNCT
ejpam-3768	441	4	,	,	PUNCT
ejpam-3768	441	5	265:1–5	265:1–5	NUM
ejpam-3768	441	6	,	,	PUNCT
ejpam-3768	441	7	2014	2014	NUM
ejpam-3768	441	8	.	.	PUNCT
ejpam-3768	442	1	[	[	X
ejpam-3768	442	2	26	26	NUM
ejpam-3768	442	3	]	]	PUNCT
ejpam-3768	442	4	j.	j.	PROPN
ejpam-3768	442	5	l.	l.	PROPN
ejpam-3768	442	6	vázquez	vázquez	PROPN
ejpam-3768	442	7	.	.	PROPN
ejpam-3768	443	1	the	the	DET
ejpam-3768	443	2	porous	porous	ADJ
ejpam-3768	443	3	medium	medium	ADJ
ejpam-3768	443	4	equation	equation	NOUN
ejpam-3768	443	5	.	.	PUNCT
ejpam-3768	444	1	oxford	oxford	PROPN
ejpam-3768	444	2	mathematical	mathematical	PROPN
ejpam-3768	444	3	monographs	monograph	NOUN
ejpam-3768	444	4	,	,	PUNCT
ejpam-3768	444	5	oxford	oxford	PROPN
ejpam-3768	444	6	university	university	PROPN
ejpam-3768	444	7	press	press	NOUN
ejpam-3768	444	8	,	,	PUNCT
ejpam-3768	444	9	oxford	oxford	PROPN
ejpam-3768	444	10	,	,	PUNCT
ejpam-3768	444	11	2007	2007	NUM
ejpam-3768	444	12	.	.	PUNCT