id	sid	tid	token	lemma	pos
ejpam-3498	1	1	european	european	PROPN
ejpam-3498	1	2	journal	journal	PROPN
ejpam-3498	1	3	of	of	ADP
ejpam-3498	1	4	pure	pure	ADJ
ejpam-3498	1	5	and	and	CCONJ
ejpam-3498	1	6	applied	apply	VERB
ejpam-3498	1	7	mathematics	mathematic	NOUN
ejpam-3498	1	8	vol	vol	NOUN
ejpam-3498	1	9	.	.	PROPN
ejpam-3498	2	1	12	12	NUM
ejpam-3498	2	2	,	,	PUNCT
ejpam-3498	2	3	no	no	INTJ
ejpam-3498	2	4	.	.	NOUN
ejpam-3498	2	5	3	3	NUM
ejpam-3498	2	6	,	,	PUNCT
ejpam-3498	2	7	2019	2019	NUM
ejpam-3498	2	8	,	,	PUNCT
ejpam-3498	2	9	1297	1297	NUM
ejpam-3498	2	10	-	-	SYM
ejpam-3498	2	11	1314	1314	NUM
ejpam-3498	2	12	issn	issn	PROPN
ejpam-3498	2	13	1307	1307	NUM
ejpam-3498	2	14	-	-	SYM
ejpam-3498	2	15	5543	5543	NUM
ejpam-3498	2	16	–	–	PUNCT
ejpam-3498	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3498	2	18	published	publish	VERB
ejpam-3498	2	19	by	by	ADP
ejpam-3498	2	20	new	new	PROPN
ejpam-3498	2	21	york	york	PROPN
ejpam-3498	2	22	business	business	PROPN
ejpam-3498	2	23	global	global	PROPN
ejpam-3498	2	24	on	on	ADP
ejpam-3498	2	25	a	a	DET
ejpam-3498	2	26	system	system	NOUN
ejpam-3498	2	27	of	of	ADP
ejpam-3498	2	28	linear	linear	PROPN
ejpam-3498	2	29	singular	singular	ADJ
ejpam-3498	2	30	partial	partial	ADJ
ejpam-3498	2	31	differential	differential	NOUN
ejpam-3498	2	32	equations	equation	NOUN
ejpam-3498	2	33	with	with	ADP
ejpam-3498	2	34	weight	weight	NOUN
ejpam-3498	2	35	functions	function	NOUN
ejpam-3498	2	36	euler	euler	PROPN
ejpam-3498	2	37	yoland	yoland	PROPN
ejpam-3498	2	38	b.	b.	PROPN
ejpam-3498	2	39	guerrero	guerrero	PROPN
ejpam-3498	2	40	1	1	NUM
ejpam-3498	2	41	department	department	NOUN
ejpam-3498	2	42	of	of	ADP
ejpam-3498	2	43	mathematics	mathematic	NOUN
ejpam-3498	2	44	and	and	CCONJ
ejpam-3498	2	45	statistics	statistic	NOUN
ejpam-3498	2	46	,	,	PUNCT
ejpam-3498	2	47	college	college	NOUN
ejpam-3498	2	48	of	of	ADP
ejpam-3498	2	49	science	science	NOUN
ejpam-3498	2	50	and	and	CCONJ
ejpam-3498	2	51	mathematics	mathematic	NOUN
ejpam-3498	2	52	,	,	PUNCT
ejpam-3498	2	53	msu	msu	PROPN
ejpam-3498	2	54	-	-	PUNCT
ejpam-3498	2	55	iligan	iligan	PROPN
ejpam-3498	2	56	institute	institute	PROPN
ejpam-3498	2	57	of	of	ADP
ejpam-3498	2	58	technology	technology	PROPN
ejpam-3498	2	59	,	,	PUNCT
ejpam-3498	2	60	iligan	iligan	PROPN
ejpam-3498	2	61	city	city	PROPN
ejpam-3498	2	62	,	,	PUNCT
ejpam-3498	2	63	philippines	philippine	NOUN
ejpam-3498	2	64	abstract	abstract	ADJ
ejpam-3498	2	65	.	.	PUNCT
ejpam-3498	3	1	let	let	VERB
ejpam-3498	3	2	x	x	PRON
ejpam-3498	3	3	be	be	AUX
ejpam-3498	3	4	a	a	DET
ejpam-3498	3	5	banach	banach	NOUN
ejpam-3498	3	6	space	space	NOUN
ejpam-3498	3	7	,	,	PUNCT
ejpam-3498	3	8	ω	ω	X
ejpam-3498	3	9	an	an	DET
ejpam-3498	3	10	open	open	ADJ
ejpam-3498	3	11	bounded	bounded	ADJ
ejpam-3498	3	12	subset	subset	NOUN
ejpam-3498	3	13	of	of	ADP
ejpam-3498	3	14	x	x	X
ejpam-3498	3	15	,	,	PUNCT
ejpam-3498	3	16	and	and	CCONJ
ejpam-3498	3	17	y	y	PROPN
ejpam-3498	3	18	a	a	DET
ejpam-3498	3	19	complex	complex	ADJ
ejpam-3498	3	20	banach	banach	NOUN
ejpam-3498	3	21	space	space	NOUN
ejpam-3498	3	22	.	.	PUNCT
ejpam-3498	4	1	we	we	PRON
ejpam-3498	4	2	consider	consider	VERB
ejpam-3498	4	3	a	a	DET
ejpam-3498	4	4	volevič	volevič	NOUN
ejpam-3498	4	5	system	system	NOUN
ejpam-3498	4	6	of	of	ADP
ejpam-3498	4	7	singular	singular	ADJ
ejpam-3498	4	8	linear	linear	PROPN
ejpam-3498	4	9	partial	partial	ADJ
ejpam-3498	4	10	differential	differential	ADJ
ejpam-3498	4	11	equations	equation	NOUN
ejpam-3498	4	12	of	of	ADP
ejpam-3498	4	13	the	the	DET
ejpam-3498	4	14	form	form	NOUN
ejpam-3498	4	15	t	t	X
ejpam-3498	4	16	∂ui	∂ui	PROPN
ejpam-3498	5	1	∂t	∂t	PROPN
ejpam-3498	5	2	=	=	PUNCT
ejpam-3498	5	3	n∑	n∑	PROPN
ejpam-3498	5	4	j=1	j=1	PROPN
ejpam-3498	5	5	aij(t	aij(t	PROPN
ejpam-3498	5	6	,	,	PUNCT
ejpam-3498	5	7	x)uj(t	x)uj(t	PROPN
ejpam-3498	5	8	,	,	PUNCT
ejpam-3498	5	9	x	x	X
ejpam-3498	5	10	)	)	PUNCT
ejpam-3498	6	1	+	+	CCONJ
ejpam-3498	6	2	∑	∑	PROPN
ejpam-3498	6	3	(	(	PUNCT
ejpam-3498	6	4	j	j	PROPN
ejpam-3498	6	5	,	,	PUNCT
ejpam-3498	6	6	k)∈n	k)∈n	X
ejpam-3498	6	7	(	(	PUNCT
ejpam-3498	6	8	i	i	NOUN
ejpam-3498	6	9	)	)	PUNCT
ejpam-3498	6	10	bjk(t	bjk(t	PROPN
ejpam-3498	6	11	,	,	PUNCT
ejpam-3498	6	12	x)((µ0(t)d)kuj(t	x)((µ0(t)d)kuj(t	PROPN
ejpam-3498	6	13	,	,	PUNCT
ejpam-3498	6	14	x	x	X
ejpam-3498	6	15	)	)	PUNCT
ejpam-3498	6	16	·	·	PUNCT
ejpam-3498	6	17	x(k)k	x(k)k	NUM
ejpam-3498	6	18	)	)	PUNCT
ejpam-3498	7	1	(	(	PUNCT
ejpam-3498	7	2	j	j	NOUN
ejpam-3498	7	3	,	,	PUNCT
ejpam-3498	7	4	k	k	PROPN
ejpam-3498	7	5	)	)	PUNCT
ejpam-3498	7	6	+	+	CCONJ
ejpam-3498	7	7	gi(t	gi(t	NOUN
ejpam-3498	7	8	,	,	PUNCT
ejpam-3498	7	9	x	x	NOUN
ejpam-3498	7	10	)	)	PUNCT
ejpam-3498	7	11	,	,	PUNCT
ejpam-3498	7	12	(	(	PUNCT
ejpam-3498	7	13	1	1	X
ejpam-3498	7	14	)	)	SYM
ejpam-3498	7	15	1	1	NUM
ejpam-3498	7	16	≤	≤	NUM
ejpam-3498	7	17	i	i	PRON
ejpam-3498	8	1	≤	≤	ADJ
ejpam-3498	8	2	n	n	CCONJ
ejpam-3498	8	3	,	,	PUNCT
ejpam-3498	8	4	in	in	ADP
ejpam-3498	8	5	the	the	DET
ejpam-3498	8	6	unknown	unknown	ADJ
ejpam-3498	8	7	function	function	NOUN
ejpam-3498	8	8	u	u	NOUN
ejpam-3498	8	9	=	=	PUNCT
ejpam-3498	8	10	(	(	PUNCT
ejpam-3498	8	11	u1	u1	PROPN
ejpam-3498	8	12	,	,	PUNCT
ejpam-3498	8	13	u2	u2	PROPN
ejpam-3498	8	14	,	,	PUNCT
ejpam-3498	8	15	...	...	PUNCT
ejpam-3498	9	1	,	,	PUNCT
ejpam-3498	9	2	un	un	PROPN
ejpam-3498	9	3	)	)	PUNCT
ejpam-3498	9	4	∈	∈	PROPN
ejpam-3498	9	5	y	y	PROPN
ejpam-3498	9	6	n	n	PROPN
ejpam-3498	9	7	of	of	ADP
ejpam-3498	9	8	t	t	PROPN
ejpam-3498	9	9	≥	≥	NOUN
ejpam-3498	9	10	0	0	PUNCT
ejpam-3498	9	11	and	and	CCONJ
ejpam-3498	9	12	x	x	PUNCT
ejpam-3498	9	13	∈	∈	PROPN
ejpam-3498	9	14	ω	ω	PROPN
ejpam-3498	9	15	,	,	PUNCT
ejpam-3498	9	16	where	where	SCONJ
ejpam-3498	9	17	aij	aij	PROPN
ejpam-3498	9	18	,	,	PUNCT
ejpam-3498	9	19	bjk	bjk	PROPN
ejpam-3498	9	20	∈	∈	PROPN
ejpam-3498	9	21	c	c	X
ejpam-3498	9	22	,	,	PUNCT
ejpam-3498	9	23	xk	xk	X
ejpam-3498	9	24	=	=	PUNCT
ejpam-3498	9	25	(	(	PUNCT
ejpam-3498	9	26	x	x	X
ejpam-3498	9	27	,	,	PUNCT
ejpam-3498	9	28	...	...	PUNCT
ejpam-3498	9	29	,	,	PUNCT
ejpam-3498	9	30	x	x	X
ejpam-3498	9	31	)	)	PUNCT
ejpam-3498	9	32	(	(	PUNCT
ejpam-3498	9	33	x	x	X
ejpam-3498	9	34	is	be	AUX
ejpam-3498	9	35	k	k	PROPN
ejpam-3498	9	36	times	times	PROPN
ejpam-3498	9	37	)	)	PUNCT
ejpam-3498	10	1	d	d	PROPN
ejpam-3498	10	2	denotes	denote	VERB
ejpam-3498	10	3	the	the	DET
ejpam-3498	10	4	frechet	frechet	NOUN
ejpam-3498	10	5	differentiation	differentiation	NOUN
ejpam-3498	10	6	with	with	ADP
ejpam-3498	10	7	respect	respect	NOUN
ejpam-3498	10	8	to	to	ADP
ejpam-3498	10	9	x	x	PRON
ejpam-3498	10	10	,	,	PUNCT
ejpam-3498	10	11	and	and	CCONJ
ejpam-3498	10	12	n	n	CCONJ
ejpam-3498	10	13	(	(	PUNCT
ejpam-3498	10	14	i	i	NOUN
ejpam-3498	10	15	)	)	PUNCT
ejpam-3498	10	16	=	=	PRON
ejpam-3498	10	17	{	{	PUNCT
ejpam-3498	10	18	(	(	PUNCT
ejpam-3498	10	19	j	j	PROPN
ejpam-3498	10	20	,	,	PUNCT
ejpam-3498	10	21	k	k	PROPN
ejpam-3498	10	22	)	)	PUNCT
ejpam-3498	10	23	:	:	PUNCT
ejpam-3498	11	1	j	j	PROPN
ejpam-3498	11	2	and	and	CCONJ
ejpam-3498	11	3	k	k	PROPN
ejpam-3498	11	4	are	be	AUX
ejpam-3498	11	5	integers	integer	NOUN
ejpam-3498	11	6	,	,	PUNCT
ejpam-3498	11	7	1	1	NUM
ejpam-3498	11	8	≤	≤	NUM
ejpam-3498	11	9	j	j	PROPN
ejpam-3498	11	10	≤	≤	NUM
ejpam-3498	11	11	n	n	CCONJ
ejpam-3498	11	12	,	,	PUNCT
ejpam-3498	11	13	0	0	PUNCT
ejpam-3498	11	14	<	<	X
ejpam-3498	11	15	k	k	PROPN
ejpam-3498	11	16	≤	≤	PROPN
ejpam-3498	11	17	n(i	n(i	PROPN
ejpam-3498	11	18	,	,	PUNCT
ejpam-3498	11	19	j	j	NOUN
ejpam-3498	11	20	)	)	PUNCT
ejpam-3498	11	21	}	}	PUNCT
ejpam-3498	11	22	,	,	PUNCT
ejpam-3498	11	23	(	(	PUNCT
ejpam-3498	11	24	2	2	X
ejpam-3498	11	25	)	)	PUNCT
ejpam-3498	11	26	n(i	n(i	PROPN
ejpam-3498	11	27	,	,	PUNCT
ejpam-3498	11	28	j	j	NOUN
ejpam-3498	11	29	)	)	PUNCT
ejpam-3498	11	30	=	=	SYM
ejpam-3498	11	31	n(i)−	n(i)−	PROPN
ejpam-3498	11	32	n(j	n(j	NOUN
ejpam-3498	11	33	)	)	PUNCT
ejpam-3498	11	34	+	+	CCONJ
ejpam-3498	11	35	1	1	NUM
ejpam-3498	11	36	,	,	PUNCT
ejpam-3498	11	37	where	where	SCONJ
ejpam-3498	11	38	n(i	n(i	PROPN
ejpam-3498	11	39	)	)	PUNCT
ejpam-3498	11	40	,	,	PUNCT
ejpam-3498	11	41	i	i	PRON
ejpam-3498	11	42	=	=	NOUN
ejpam-3498	11	43	1	1	NUM
ejpam-3498	11	44	,	,	PUNCT
ejpam-3498	11	45	2	2	NUM
ejpam-3498	11	46	,	,	PUNCT
ejpam-3498	11	47	...	...	PUNCT
ejpam-3498	11	48	,	,	PUNCT
ejpam-3498	11	49	n	n	CCONJ
ejpam-3498	11	50	,	,	PUNCT
ejpam-3498	11	51	are	be	AUX
ejpam-3498	11	52	nonnegative	nonnegative	ADJ
ejpam-3498	11	53	integers	integer	NOUN
ejpam-3498	11	54	.	.	PUNCT
ejpam-3498	12	1	the	the	DET
ejpam-3498	12	2	map	map	NOUN
ejpam-3498	12	3	µ0	µ0	NOUN
ejpam-3498	12	4	belongs	belong	VERB
ejpam-3498	12	5	to	to	ADP
ejpam-3498	12	6	c0([0	c0([0	PROPN
ejpam-3498	12	7	,	,	PUNCT
ejpam-3498	12	8	t	t	X
ejpam-3498	12	9	]	]	PUNCT
ejpam-3498	12	10	,	,	PUNCT
ejpam-3498	12	11	c	c	NOUN
ejpam-3498	12	12	)	)	PUNCT
ejpam-3498	12	13	.	.	PUNCT
ejpam-3498	13	1	we	we	PRON
ejpam-3498	13	2	express	express	VERB
ejpam-3498	13	3	growth	growth	NOUN
ejpam-3498	13	4	estimates	estimate	NOUN
ejpam-3498	13	5	in	in	ADP
ejpam-3498	13	6	terms	term	NOUN
ejpam-3498	13	7	of	of	ADP
ejpam-3498	13	8	weight	weight	NOUN
ejpam-3498	13	9	functions	function	NOUN
ejpam-3498	13	10	and	and	CCONJ
ejpam-3498	13	11	we	we	PRON
ejpam-3498	13	12	establish	establish	VERB
ejpam-3498	13	13	an	an	DET
ejpam-3498	13	14	existence	existence	NOUN
ejpam-3498	13	15	and	and	CCONJ
ejpam-3498	13	16	uniqueness	uniqueness	NOUN
ejpam-3498	13	17	theorem	theorem	VERB
ejpam-3498	13	18	for	for	ADP
ejpam-3498	13	19	our	our	PRON
ejpam-3498	13	20	system	system	NOUN
ejpam-3498	13	21	in	in	ADP
ejpam-3498	13	22	the	the	DET
ejpam-3498	13	23	class	class	NOUN
ejpam-3498	13	24	of	of	ADP
ejpam-3498	13	25	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	13	26	maps	map	NOUN
ejpam-3498	13	27	with	with	ADP
ejpam-3498	13	28	respect	respect	NOUN
ejpam-3498	13	29	to	to	ADP
ejpam-3498	13	30	the	the	DET
ejpam-3498	13	31	space	space	NOUN
ejpam-3498	13	32	variable	variable	NOUN
ejpam-3498	13	33	x.	x.	NOUN
ejpam-3498	13	34	2010	2010	NUM
ejpam-3498	13	35	mathematics	mathematic	NOUN
ejpam-3498	13	36	subject	subject	NOUN
ejpam-3498	13	37	classifications	classification	NOUN
ejpam-3498	13	38	:	:	PUNCT
ejpam-3498	13	39	35a01	35a01	NUM
ejpam-3498	13	40	,	,	PUNCT
ejpam-3498	13	41	35a02	35a02	NUM
ejpam-3498	13	42	,	,	PUNCT
ejpam-3498	13	43	35a10	35a10	NUM
ejpam-3498	13	44	key	key	ADJ
ejpam-3498	13	45	words	word	NOUN
ejpam-3498	13	46	and	and	CCONJ
ejpam-3498	13	47	phrases	phrase	NOUN
ejpam-3498	13	48	:	:	PUNCT
ejpam-3498	13	49	system	system	NOUN
ejpam-3498	13	50	of	of	ADP
ejpam-3498	13	51	partial	partial	ADJ
ejpam-3498	13	52	differential	differential	NOUN
ejpam-3498	13	53	equations	equation	NOUN
ejpam-3498	13	54	,	,	PUNCT
ejpam-3498	13	55	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	13	56	,	,	PUNCT
ejpam-3498	13	57	weight	weight	NOUN
ejpam-3498	13	58	functions	function	NOUN
ejpam-3498	13	59	1	1	NUM
ejpam-3498	13	60	.	.	PUNCT
ejpam-3498	14	1	introduction	introduction	NOUN
ejpam-3498	14	2	the	the	DET
ejpam-3498	14	3	study	study	NOUN
ejpam-3498	14	4	of	of	ADP
ejpam-3498	14	5	partial	partial	ADJ
ejpam-3498	14	6	differential	differential	NOUN
ejpam-3498	14	7	equations	equation	NOUN
ejpam-3498	14	8	have	have	AUX
ejpam-3498	14	9	been	be	AUX
ejpam-3498	14	10	a	a	DET
ejpam-3498	14	11	very	very	ADV
ejpam-3498	14	12	fruitful	fruitful	ADJ
ejpam-3498	14	13	endeavor	endeavor	NOUN
ejpam-3498	14	14	both	both	CCONJ
ejpam-3498	14	15	in	in	ADP
ejpam-3498	14	16	pure	pure	ADJ
ejpam-3498	14	17	and	and	CCONJ
ejpam-3498	14	18	applied	applied	ADJ
ejpam-3498	14	19	mathematics	mathematic	NOUN
ejpam-3498	14	20	.	.	PUNCT
ejpam-3498	15	1	its	its	PRON
ejpam-3498	15	2	practical	practical	ADJ
ejpam-3498	15	3	use	use	NOUN
ejpam-3498	15	4	can	can	AUX
ejpam-3498	15	5	not	not	PART
ejpam-3498	15	6	be	be	AUX
ejpam-3498	15	7	underestimated	underestimate	VERB
ejpam-3498	15	8	as	as	ADV
ejpam-3498	15	9	many	many	ADJ
ejpam-3498	15	10	recent	recent	ADJ
ejpam-3498	15	11	scientific	scientific	ADJ
ejpam-3498	15	12	and	and	CCONJ
ejpam-3498	15	13	engineering	engineering	NOUN
ejpam-3498	15	14	works	work	NOUN
ejpam-3498	15	15	such	such	ADJ
ejpam-3498	15	16	as	as	ADP
ejpam-3498	15	17	in	in	ADP
ejpam-3498	15	18	[	[	NOUN
ejpam-3498	15	19	8	8	NUM
ejpam-3498	15	20	]	]	PUNCT
ejpam-3498	15	21	uses	use	VERB
ejpam-3498	15	22	partial	partial	ADJ
ejpam-3498	15	23	differential	differential	ADJ
ejpam-3498	15	24	equations	equation	NOUN
ejpam-3498	15	25	to	to	PART
ejpam-3498	15	26	model	model	VERB
ejpam-3498	15	27	real	real	ADJ
ejpam-3498	15	28	-	-	PUNCT
ejpam-3498	15	29	world	world	NOUN
ejpam-3498	15	30	problems	problem	NOUN
ejpam-3498	15	31	.	.	PUNCT
ejpam-3498	16	1	gerard	gerard	NOUN
ejpam-3498	16	2	and	and	CCONJ
ejpam-3498	16	3	tahara	tahara	NOUN
ejpam-3498	17	1	[	[	X
ejpam-3498	17	2	2	2	NUM
ejpam-3498	17	3	]	]	PUNCT
ejpam-3498	17	4	,	,	PUNCT
ejpam-3498	17	5	and	and	CCONJ
ejpam-3498	17	6	baouendi	baouendi	NOUN
ejpam-3498	17	7	and	and	CCONJ
ejpam-3498	17	8	goulaouic	goulaouic	ADJ
ejpam-3498	17	9	[	[	X
ejpam-3498	17	10	1	1	NUM
ejpam-3498	17	11	]	]	PUNCT
ejpam-3498	17	12	were	be	AUX
ejpam-3498	17	13	some	some	PRON
ejpam-3498	17	14	of	of	ADP
ejpam-3498	17	15	the	the	DET
ejpam-3498	17	16	authors	author	NOUN
ejpam-3498	17	17	who	who	PRON
ejpam-3498	17	18	worked	work	VERB
ejpam-3498	17	19	on	on	ADP
ejpam-3498	17	20	nonlinear	nonlinear	ADJ
ejpam-3498	17	21	or	or	CCONJ
ejpam-3498	17	22	linear	linear	ADJ
ejpam-3498	17	23	differential	differential	ADJ
ejpam-3498	17	24	equations	equation	NOUN
ejpam-3498	17	25	with	with	ADP
ejpam-3498	17	26	singularity	singularity	NOUN
ejpam-3498	17	27	.	.	PUNCT
ejpam-3498	18	1	lope	lope	X
ejpam-3498	19	1	[	[	X
ejpam-3498	19	2	5	5	NUM
ejpam-3498	19	3	]	]	PUNCT
ejpam-3498	19	4	,	,	PUNCT
ejpam-3498	19	5	extended	extended	ADJ
ejpam-3498	19	6	doi	doi	NOUN
ejpam-3498	19	7	:	:	PUNCT
ejpam-3498	19	8	https://doi.org/10.29020/nybg.ejpam.v12i3.3498	https://doi.org/10.29020/nybg.ejpam.v12i3.3498	NOUN
ejpam-3498	19	9	email	email	NOUN
ejpam-3498	19	10	addresses	address	NOUN
ejpam-3498	19	11	:	:	PUNCT
ejpam-3498	19	12	euleryoland.guerrero@g.msuiit.edu.ph	euleryoland.guerrero@g.msuiit.edu.ph	PROPN
ejpam-3498	19	13	(	(	PUNCT
ejpam-3498	19	14	ey	ey	X
ejpam-3498	19	15	guerrero	guerrero	NOUN
ejpam-3498	19	16	)	)	PUNCT
ejpam-3498	19	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3498	20	1	1297	1297	NUM
ejpam-3498	21	1	c	c	X
ejpam-3498	21	2	©	©	PROPN
ejpam-3498	21	3	2019	2019	NUM
ejpam-3498	21	4	ejpam	ejpam	NOUN
ejpam-3498	21	5	all	all	DET
ejpam-3498	21	6	rights	right	NOUN
ejpam-3498	21	7	reserved	reserve	VERB
ejpam-3498	21	8	.	.	PUNCT
ejpam-3498	22	1	e.	e.	PROPN
ejpam-3498	22	2	y.	y.	PROPN
ejpam-3498	22	3	guerrero	guerrero	PROPN
ejpam-3498	22	4	/	/	SYM
ejpam-3498	22	5	eur	eur	PROPN
ejpam-3498	22	6	.	.	PUNCT
ejpam-3498	23	1	j.	j.	PROPN
ejpam-3498	23	2	pure	pure	PROPN
ejpam-3498	23	3	appl	appl	PROPN
ejpam-3498	23	4	.	.	PROPN
ejpam-3498	23	5	math	math	PROPN
ejpam-3498	23	6	,	,	PUNCT
ejpam-3498	23	7	12	12	NUM
ejpam-3498	23	8	(	(	PUNCT
ejpam-3498	23	9	3	3	NUM
ejpam-3498	23	10	)	)	PUNCT
ejpam-3498	23	11	(	(	PUNCT
ejpam-3498	23	12	2019	2019	NUM
ejpam-3498	23	13	)	)	PUNCT
ejpam-3498	23	14	,	,	PUNCT
ejpam-3498	23	15	1297	1297	NUM
ejpam-3498	23	16	-	-	SYM
ejpam-3498	23	17	1314	1314	NUM
ejpam-3498	23	18	1298	1298	NUM
ejpam-3498	23	19	the	the	DET
ejpam-3498	23	20	work	work	NOUN
ejpam-3498	23	21	of	of	ADP
ejpam-3498	23	22	baouendi	baouendi	PROPN
ejpam-3498	23	23	and	and	CCONJ
ejpam-3498	23	24	galaouic	galaouic	NOUN
ejpam-3498	23	25	using	use	VERB
ejpam-3498	23	26	the	the	DET
ejpam-3498	23	27	concept	concept	NOUN
ejpam-3498	23	28	of	of	ADP
ejpam-3498	23	29	weight	weight	NOUN
ejpam-3498	23	30	functions	function	NOUN
ejpam-3498	23	31	.	.	PUNCT
ejpam-3498	24	1	these	these	DET
ejpam-3498	24	2	weight	weight	NOUN
ejpam-3498	24	3	functions	function	NOUN
ejpam-3498	24	4	are	be	AUX
ejpam-3498	24	5	used	use	VERB
ejpam-3498	24	6	to	to	PART
ejpam-3498	24	7	describe	describe	VERB
ejpam-3498	24	8	growth	growth	NOUN
ejpam-3498	24	9	estimates	estimate	NOUN
ejpam-3498	24	10	on	on	ADP
ejpam-3498	24	11	the	the	DET
ejpam-3498	24	12	coefficients	coefficient	NOUN
ejpam-3498	24	13	of	of	ADP
ejpam-3498	24	14	the	the	DET
ejpam-3498	24	15	partial	partial	ADJ
ejpam-3498	24	16	taylor	taylor	PROPN
ejpam-3498	24	17	expansion	expansion	NOUN
ejpam-3498	24	18	of	of	ADP
ejpam-3498	24	19	a	a	DET
ejpam-3498	24	20	function	function	NOUN
ejpam-3498	24	21	.	.	PUNCT
ejpam-3498	25	1	in	in	ADP
ejpam-3498	25	2	[	[	X
ejpam-3498	25	3	3	3	NUM
ejpam-3498	25	4	]	]	PUNCT
ejpam-3498	25	5	,	,	PUNCT
ejpam-3498	25	6	koike	koike	NOUN
ejpam-3498	25	7	considered	consider	VERB
ejpam-3498	25	8	a	a	DET
ejpam-3498	25	9	volevič	volevič	NOUN
ejpam-3498	25	10	system	system	NOUN
ejpam-3498	25	11	of	of	ADP
ejpam-3498	25	12	singular	singular	PROPN
ejpam-3498	25	13	nonlinear	nonlinear	ADJ
ejpam-3498	25	14	partial	partial	ADJ
ejpam-3498	25	15	differential	differential	NOUN
ejpam-3498	25	16	equations	equation	NOUN
ejpam-3498	25	17	with	with	ADP
ejpam-3498	25	18	general	general	ADJ
ejpam-3498	25	19	singularity	singularity	NOUN
ejpam-3498	25	20	.	.	PUNCT
ejpam-3498	26	1	he	he	PRON
ejpam-3498	26	2	established	establish	VERB
ejpam-3498	26	3	the	the	DET
ejpam-3498	26	4	existence	existence	NOUN
ejpam-3498	26	5	and	and	CCONJ
ejpam-3498	26	6	uniqueness	uniqueness	NOUN
ejpam-3498	26	7	theorem	theorem	NOUN
ejpam-3498	26	8	of	of	ADP
ejpam-3498	26	9	the	the	DET
ejpam-3498	26	10	solution	solution	NOUN
ejpam-3498	26	11	in	in	ADP
ejpam-3498	26	12	the	the	DET
ejpam-3498	26	13	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	26	14	class	class	NOUN
ejpam-3498	26	15	using	use	VERB
ejpam-3498	26	16	the	the	DET
ejpam-3498	26	17	banach	banach	ADV
ejpam-3498	26	18	fixed	fix	VERB
ejpam-3498	26	19	point	point	NOUN
ejpam-3498	26	20	theorem	theorem	NOUN
ejpam-3498	26	21	and	and	CCONJ
ejpam-3498	26	22	nirenberg	nirenberg	PROPN
ejpam-3498	26	23	-	-	PUNCT
ejpam-3498	26	24	nishida	nishida	PROPN
ejpam-3498	27	1	[	[	X
ejpam-3498	27	2	6	6	NUM
ejpam-3498	27	3	,	,	PUNCT
ejpam-3498	27	4	7	7	NUM
ejpam-3498	27	5	]	]	ADJ
ejpam-3498	27	6	iteration	iteration	NOUN
ejpam-3498	27	7	method	method	NOUN
ejpam-3498	27	8	.	.	PUNCT
ejpam-3498	28	1	this	this	DET
ejpam-3498	28	2	method	method	NOUN
ejpam-3498	28	3	was	be	AUX
ejpam-3498	28	4	also	also	ADV
ejpam-3498	28	5	used	use	VERB
ejpam-3498	28	6	in	in	ADP
ejpam-3498	28	7	[	[	X
ejpam-3498	28	8	4	4	NUM
ejpam-3498	28	9	]	]	PUNCT
ejpam-3498	28	10	.	.	PUNCT
ejpam-3498	29	1	in	in	ADP
ejpam-3498	29	2	this	this	DET
ejpam-3498	29	3	paper	paper	NOUN
ejpam-3498	29	4	,	,	PUNCT
ejpam-3498	29	5	we	we	PRON
ejpam-3498	29	6	will	will	AUX
ejpam-3498	29	7	establish	establish	VERB
ejpam-3498	29	8	an	an	DET
ejpam-3498	29	9	existence	existence	NOUN
ejpam-3498	29	10	and	and	CCONJ
ejpam-3498	29	11	uniqueness	uniqueness	NOUN
ejpam-3498	29	12	theorem	theorem	VERB
ejpam-3498	29	13	on	on	ADP
ejpam-3498	29	14	(	(	PUNCT
ejpam-3498	29	15	1	1	NUM
ejpam-3498	29	16	)	)	PUNCT
ejpam-3498	29	17	in	in	ADP
ejpam-3498	29	18	the	the	DET
ejpam-3498	29	19	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	29	20	class	class	NOUN
ejpam-3498	29	21	with	with	ADP
ejpam-3498	29	22	growth	growth	NOUN
ejpam-3498	29	23	estimates	estimate	NOUN
ejpam-3498	29	24	in	in	ADP
ejpam-3498	29	25	terms	term	NOUN
ejpam-3498	29	26	of	of	ADP
ejpam-3498	29	27	weight	weight	NOUN
ejpam-3498	29	28	functions	function	NOUN
ejpam-3498	29	29	.	.	PUNCT
ejpam-3498	30	1	2	2	X
ejpam-3498	30	2	.	.	X
ejpam-3498	30	3	preliminaries	preliminary	NOUN
ejpam-3498	30	4	we	we	PRON
ejpam-3498	30	5	first	first	ADV
ejpam-3498	30	6	give	give	VERB
ejpam-3498	30	7	the	the	DET
ejpam-3498	30	8	definition	definition	NOUN
ejpam-3498	30	9	of	of	ADP
ejpam-3498	30	10	a	a	DET
ejpam-3498	30	11	weight	weight	NOUN
ejpam-3498	30	12	function	function	NOUN
ejpam-3498	30	13	as	as	SCONJ
ejpam-3498	30	14	defined	define	VERB
ejpam-3498	30	15	by	by	ADP
ejpam-3498	30	16	tahara	tahara	NOUN
ejpam-3498	31	1	[	[	X
ejpam-3498	31	2	9	9	NUM
ejpam-3498	31	3	]	]	PUNCT
ejpam-3498	31	4	.	.	PUNCT
ejpam-3498	32	1	we	we	PRON
ejpam-3498	32	2	then	then	ADV
ejpam-3498	32	3	give	give	VERB
ejpam-3498	32	4	the	the	DET
ejpam-3498	32	5	definitions	definition	NOUN
ejpam-3498	32	6	and	and	CCONJ
ejpam-3498	32	7	basic	basic	ADJ
ejpam-3498	32	8	results	result	NOUN
ejpam-3498	32	9	about	about	ADP
ejpam-3498	32	10	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	32	11	maps	map	NOUN
ejpam-3498	32	12	as	as	SCONJ
ejpam-3498	32	13	proved	prove	VERB
ejpam-3498	32	14	by	by	ADP
ejpam-3498	32	15	koike	koike	NOUN
ejpam-3498	32	16	[	[	X
ejpam-3498	32	17	3	3	NUM
ejpam-3498	32	18	]	]	PUNCT
ejpam-3498	32	19	.	.	PUNCT
ejpam-3498	33	1	definition	definition	NOUN
ejpam-3498	33	2	1	1	NUM
ejpam-3498	33	3	.	.	PUNCT
ejpam-3498	34	1	let	let	VERB
ejpam-3498	34	2	t	t	PROPN
ejpam-3498	34	3	>	>	X
ejpam-3498	34	4	0	0	X
ejpam-3498	34	5	.	.	PUNCT
ejpam-3498	35	1	we	we	PRON
ejpam-3498	35	2	say	say	VERB
ejpam-3498	35	3	that	that	SCONJ
ejpam-3498	35	4	µ(t	µ(t	ADJ
ejpam-3498	35	5	)	)	PUNCT
ejpam-3498	35	6	is	be	AUX
ejpam-3498	35	7	a	a	DET
ejpam-3498	35	8	weight	weight	NOUN
ejpam-3498	35	9	function	function	NOUN
ejpam-3498	35	10	on	on	ADP
ejpam-3498	35	11	[	[	X
ejpam-3498	35	12	0	0	NUM
ejpam-3498	35	13	,	,	PUNCT
ejpam-3498	35	14	t	t	X
ejpam-3498	35	15	]	]	PUNCT
ejpam-3498	35	16	if	if	SCONJ
ejpam-3498	35	17	it	it	PRON
ejpam-3498	35	18	is	be	AUX
ejpam-3498	35	19	continuous	continuous	ADJ
ejpam-3498	35	20	,	,	PUNCT
ejpam-3498	35	21	nonnegative	nonnegative	ADJ
ejpam-3498	35	22	,	,	PUNCT
ejpam-3498	35	23	increasing	increase	VERB
ejpam-3498	35	24	function	function	NOUN
ejpam-3498	35	25	on	on	ADP
ejpam-3498	35	26	(	(	PUNCT
ejpam-3498	35	27	0	0	NUM
ejpam-3498	35	28	,	,	PUNCT
ejpam-3498	35	29	t	t	X
ejpam-3498	35	30	]	]	PUNCT
ejpam-3498	36	1	such	such	ADJ
ejpam-3498	36	2	that∫	that∫	NOUN
ejpam-3498	36	3	t	t	NOUN
ejpam-3498	36	4	0	0	PUNCT
ejpam-3498	36	5	µ(t	µ(t	ADJ
ejpam-3498	36	6	)	)	PUNCT
ejpam-3498	36	7	t	t	NOUN
ejpam-3498	37	1	dt	dt	X
ejpam-3498	38	1	<	<	X
ejpam-3498	39	1	+	+	NOUN
ejpam-3498	39	2	∞.	∞.	PROPN
ejpam-3498	39	3	let	let	VERB
ejpam-3498	39	4	v	v	NOUN
ejpam-3498	39	5	and	and	CCONJ
ejpam-3498	39	6	w	w	NOUN
ejpam-3498	39	7	be	be	AUX
ejpam-3498	39	8	banach	banach	ADV
ejpam-3498	39	9	spaces	space	NOUN
ejpam-3498	39	10	,	,	PUNCT
ejpam-3498	39	11	and	and	CCONJ
ejpam-3498	39	12	u	u	PRON
ejpam-3498	39	13	be	be	VERB
ejpam-3498	39	14	an	an	DET
ejpam-3498	39	15	open	open	ADJ
ejpam-3498	39	16	subset	subset	NOUN
ejpam-3498	39	17	of	of	ADP
ejpam-3498	39	18	v	v	NOUN
ejpam-3498	39	19	.	.	PUNCT
ejpam-3498	40	1	we	we	PRON
ejpam-3498	40	2	denote	denote	VERB
ejpam-3498	40	3	by	by	ADP
ejpam-3498	40	4	c0(v	c0(v	PROPN
ejpam-3498	40	5	,	,	PUNCT
ejpam-3498	40	6	w	w	PROPN
ejpam-3498	40	7	)	)	PUNCT
ejpam-3498	40	8	the	the	DET
ejpam-3498	40	9	set	set	NOUN
ejpam-3498	40	10	of	of	ADP
ejpam-3498	40	11	all	all	DET
ejpam-3498	40	12	continuous	continuous	ADJ
ejpam-3498	40	13	mappings	mapping	NOUN
ejpam-3498	40	14	from	from	ADP
ejpam-3498	40	15	v	v	NUM
ejpam-3498	40	16	to	to	ADP
ejpam-3498	40	17	w	w	PROPN
ejpam-3498	40	18	and	and	CCONJ
ejpam-3498	40	19	l(v	l(v	PROPN
ejpam-3498	40	20	,	,	PUNCT
ejpam-3498	40	21	w	w	PROPN
ejpam-3498	40	22	)	)	PUNCT
ejpam-3498	40	23	the	the	DET
ejpam-3498	40	24	banach	banach	NOUN
ejpam-3498	40	25	space	space	NOUN
ejpam-3498	40	26	of	of	ADP
ejpam-3498	40	27	all	all	DET
ejpam-3498	40	28	bounded	bounded	ADJ
ejpam-3498	40	29	(	(	PUNCT
ejpam-3498	40	30	continuous	continuous	ADJ
ejpam-3498	40	31	)	)	PUNCT
ejpam-3498	40	32	linear	linear	ADJ
ejpam-3498	40	33	mappings	mapping	NOUN
ejpam-3498	40	34	from	from	ADP
ejpam-3498	40	35	v	v	NUM
ejpam-3498	40	36	to	to	ADP
ejpam-3498	40	37	w	w	PROPN
ejpam-3498	40	38	.	.	PUNCT
ejpam-3498	41	1	moreover	moreover	ADV
ejpam-3498	41	2	,	,	PUNCT
ejpam-3498	41	3	we	we	PRON
ejpam-3498	41	4	let	let	VERB
ejpam-3498	41	5	lp(u	lp(u	NOUN
ejpam-3498	41	6	,	,	PUNCT
ejpam-3498	41	7	w	w	NOUN
ejpam-3498	41	8	)	)	PUNCT
ejpam-3498	41	9	to	to	PART
ejpam-3498	41	10	be	be	AUX
ejpam-3498	41	11	the	the	DET
ejpam-3498	41	12	space	space	NOUN
ejpam-3498	41	13	of	of	ADP
ejpam-3498	41	14	all	all	DET
ejpam-3498	41	15	p	p	ADJ
ejpam-3498	41	16	-	-	PUNCT
ejpam-3498	41	17	linear	linear	ADJ
ejpam-3498	41	18	continuous	continuous	ADJ
ejpam-3498	41	19	mappings	mapping	NOUN
ejpam-3498	41	20	of	of	ADP
ejpam-3498	41	21	up	up	NOUN
ejpam-3498	41	22	into	into	ADP
ejpam-3498	41	23	w	w	PROPN
ejpam-3498	41	24	.	.	PUNCT
ejpam-3498	42	1	definition	definition	NOUN
ejpam-3498	42	2	2	2	NUM
ejpam-3498	42	3	.	.	PUNCT
ejpam-3498	43	1	let	let	VERB
ejpam-3498	43	2	mj	mj	VERB
ejpam-3498	43	3	,	,	PUNCT
ejpam-3498	43	4	j	j	PROPN
ejpam-3498	43	5	=	=	SYM
ejpam-3498	43	6	0	0	NUM
ejpam-3498	43	7	,	,	PUNCT
ejpam-3498	43	8	1	1	NUM
ejpam-3498	43	9	,	,	PUNCT
ejpam-3498	43	10	...	...	PUNCT
ejpam-3498	43	11	,	,	PUNCT
ejpam-3498	43	12	be	be	AUX
ejpam-3498	43	13	a	a	DET
ejpam-3498	43	14	sequence	sequence	NOUN
ejpam-3498	43	15	of	of	ADP
ejpam-3498	43	16	positive	positive	ADJ
ejpam-3498	43	17	numbers	number	NOUN
ejpam-3498	43	18	with	with	ADP
ejpam-3498	43	19	m0	m0	NOUN
ejpam-3498	43	20	=	=	SYM
ejpam-3498	43	21	m1	m1	PROPN
ejpam-3498	43	22	=	=	SYM
ejpam-3498	44	1	1	1	X
ejpam-3498	44	2	.	.	PUNCT
ejpam-3498	44	3	a	a	DET
ejpam-3498	44	4	map	map	NOUN
ejpam-3498	44	5	v	v	ADP
ejpam-3498	44	6	∈	∈	PROPN
ejpam-3498	44	7	c∞(ω	c∞(ω	NOUN
ejpam-3498	44	8	,	,	PUNCT
ejpam-3498	44	9	y	y	PROPN
ejpam-3498	44	10	)	)	PUNCT
ejpam-3498	44	11	is	be	AUX
ejpam-3498	44	12	said	say	VERB
ejpam-3498	44	13	to	to	PART
ejpam-3498	44	14	belong	belong	VERB
ejpam-3498	44	15	to	to	ADP
ejpam-3498	44	16	the	the	DET
ejpam-3498	44	17	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	44	18	class	class	NOUN
ejpam-3498	44	19	{	{	PUNCT
ejpam-3498	44	20	mp}(ω	mp}(ω	PROPN
ejpam-3498	44	21	,	,	PUNCT
ejpam-3498	44	22	y	y	PROPN
ejpam-3498	44	23	)	)	PUNCT
ejpam-3498	44	24	(	(	PUNCT
ejpam-3498	44	25	or	or	CCONJ
ejpam-3498	44	26	{	{	PUNCT
ejpam-3498	44	27	mp	mp	NOUN
ejpam-3498	44	28	}	}	PUNCT
ejpam-3498	44	29	for	for	ADP
ejpam-3498	44	30	short	short	ADJ
ejpam-3498	44	31	)	)	PUNCT
ejpam-3498	44	32	if	if	SCONJ
ejpam-3498	44	33	‖djv(x)‖	‖djv(x)‖	ADJ
ejpam-3498	44	34	≤	≤	ADJ
ejpam-3498	44	35	c1+jmj	c1+jmj	NOUN
ejpam-3498	44	36	x	x	SYM
ejpam-3498	44	37	∈	∈	PROPN
ejpam-3498	44	38	ω	ω	PROPN
ejpam-3498	44	39	,	,	PUNCT
ejpam-3498	44	40	j	j	PROPN
ejpam-3498	44	41	=	=	SYM
ejpam-3498	44	42	0	0	NUM
ejpam-3498	44	43	,	,	PUNCT
ejpam-3498	44	44	1	1	NUM
ejpam-3498	44	45	,	,	PUNCT
ejpam-3498	44	46	2	2	NUM
ejpam-3498	44	47	,	,	PUNCT
ejpam-3498	44	48	...	...	PUNCT
ejpam-3498	44	49	,	,	PUNCT
ejpam-3498	44	50	and	and	CCONJ
ejpam-3498	44	51	constant	constant	ADJ
ejpam-3498	44	52	c.	c.	NOUN
ejpam-3498	44	53	as	as	SCONJ
ejpam-3498	44	54	was	be	AUX
ejpam-3498	44	55	done	do	VERB
ejpam-3498	44	56	in	in	ADP
ejpam-3498	44	57	koike	koike	NOUN
ejpam-3498	44	58	’s	’s	PART
ejpam-3498	44	59	paper	paper	NOUN
ejpam-3498	44	60	,	,	PUNCT
ejpam-3498	44	61	in	in	ADP
ejpam-3498	44	62	our	our	PRON
ejpam-3498	44	63	problem	problem	NOUN
ejpam-3498	44	64	,	,	PUNCT
ejpam-3498	44	65	we	we	PRON
ejpam-3498	44	66	impose	impose	VERB
ejpam-3498	44	67	on	on	ADP
ejpam-3498	44	68	the	the	DET
ejpam-3498	44	69	sequence	sequence	NOUN
ejpam-3498	44	70	{	{	PUNCT
ejpam-3498	44	71	mp	mp	PROPN
ejpam-3498	44	72	}	}	PUNCT
ejpam-3498	44	73	the	the	DET
ejpam-3498	44	74	following	follow	VERB
ejpam-3498	44	75	conditions	condition	NOUN
ejpam-3498	44	76	:	:	PUNCT
ejpam-3498	44	77	(	(	PUNCT
ejpam-3498	44	78	c1	c1	NOUN
ejpam-3498	44	79	)	)	PUNCT
ejpam-3498	45	1	if	if	SCONJ
ejpam-3498	45	2	n∑	n∑	PROPN
ejpam-3498	45	3	i=1	i=1	PROPN
ejpam-3498	45	4	ki	ki	PROPN
ejpam-3498	45	5	=	=	SYM
ejpam-3498	46	1	n	n	CCONJ
ejpam-3498	46	2	,	,	PUNCT
ejpam-3498	46	3	ki	ki	PROPN
ejpam-3498	46	4	≥	≥	PROPN
ejpam-3498	46	5	0	0	NUM
ejpam-3498	46	6	,	,	PUNCT
ejpam-3498	46	7	n	n	NOUN
ejpam-3498	46	8	=	=	SYM
ejpam-3498	46	9	1	1	NUM
ejpam-3498	46	10	,	,	PUNCT
ejpam-3498	46	11	2	2	NUM
ejpam-3498	46	12	,	,	PUNCT
ejpam-3498	46	13	...	...	PUNCT
ejpam-3498	46	14	,	,	PUNCT
ejpam-3498	46	15	then	then	ADV
ejpam-3498	46	16	n∏	n∏	PROPN
ejpam-3498	46	17	i=1	i=1	PROPN
ejpam-3498	46	18	nki+1	nki+1	PROPN
ejpam-3498	46	19	≤	≤	PROPN
ejpam-3498	46	20	nn+1	nn+1	PROPN
ejpam-3498	46	21	,	,	PUNCT
ejpam-3498	46	22	where	where	SCONJ
ejpam-3498	46	23	np	np	ADV
ejpam-3498	46	24	=	=	SYM
ejpam-3498	46	25	mp	mp	PROPN
ejpam-3498	47	1	p	p	X
ejpam-3498	47	2	!	!	PUNCT
ejpam-3498	47	3	.	.	PUNCT
ejpam-3498	48	1	(	(	PUNCT
ejpam-3498	48	2	c2	c2	PROPN
ejpam-3498	48	3	)	)	PUNCT
ejpam-3498	48	4	there	there	PRON
ejpam-3498	48	5	is	be	VERB
ejpam-3498	48	6	a	a	DET
ejpam-3498	48	7	constant	constant	ADJ
ejpam-3498	48	8	k	k	NOUN
ejpam-3498	49	1	such	such	ADJ
ejpam-3498	49	2	that	that	SCONJ
ejpam-3498	49	3	mj+1	mj+1	ADJ
ejpam-3498	49	4	≤	≤	NOUN
ejpam-3498	49	5	k(j	k(j	PROPN
ejpam-3498	49	6	+	+	SYM
ejpam-3498	49	7	1)mj	1)mj	PROPN
ejpam-3498	49	8	,	,	PUNCT
ejpam-3498	49	9	j	j	X
ejpam-3498	49	10	=	=	SYM
ejpam-3498	49	11	0	0	NUM
ejpam-3498	49	12	,	,	PUNCT
ejpam-3498	49	13	1	1	NUM
ejpam-3498	49	14	,	,	PUNCT
ejpam-3498	49	15	2	2	NUM
ejpam-3498	49	16	,	,	PUNCT
ejpam-3498	49	17	....	....	PUNCT
ejpam-3498	49	18	e.	e.	PROPN
ejpam-3498	49	19	y.	y.	PROPN
ejpam-3498	49	20	guerrero	guerrero	PROPN
ejpam-3498	49	21	/	/	SYM
ejpam-3498	49	22	eur	eur	PROPN
ejpam-3498	49	23	.	.	PUNCT
ejpam-3498	50	1	j.	j.	PROPN
ejpam-3498	50	2	pure	pure	PROPN
ejpam-3498	50	3	appl	appl	PROPN
ejpam-3498	50	4	.	.	PROPN
ejpam-3498	50	5	math	math	PROPN
ejpam-3498	50	6	,	,	PUNCT
ejpam-3498	50	7	12	12	NUM
ejpam-3498	50	8	(	(	PUNCT
ejpam-3498	50	9	3	3	NUM
ejpam-3498	50	10	)	)	PUNCT
ejpam-3498	50	11	(	(	PUNCT
ejpam-3498	50	12	2019	2019	NUM
ejpam-3498	50	13	)	)	PUNCT
ejpam-3498	50	14	,	,	PUNCT
ejpam-3498	50	15	1297	1297	NUM
ejpam-3498	50	16	-	-	SYM
ejpam-3498	50	17	1314	1314	NUM
ejpam-3498	50	18	1299	1299	NUM
ejpam-3498	50	19	for	for	ADP
ejpam-3498	50	20	s	s	PROPN
ejpam-3498	50	21	>	>	X
ejpam-3498	50	22	0	0	NUM
ejpam-3498	50	23	,	,	PUNCT
ejpam-3498	50	24	we	we	PRON
ejpam-3498	50	25	write	write	VERB
ejpam-3498	50	26	‖u‖s	‖u‖s	NOUN
ejpam-3498	50	27	=	=	SYM
ejpam-3498	50	28	‖u‖s(u	‖u‖s(u	X
ejpam-3498	50	29	)	)	PUNCT
ejpam-3498	50	30	=	=	PUNCT
ejpam-3498	51	1	sup	sup	NOUN
ejpam-3498	51	2	x∈u	x∈u	NOUN
ejpam-3498	52	1	∞∑	∞∑	NUM
ejpam-3498	52	2	j=0	j=0	PROPN
ejpam-3498	52	3	‖dju(x)‖sj	‖dju(x)‖sj	PROPN
ejpam-3498	52	4	mj	mj	PROPN
ejpam-3498	52	5	,	,	PUNCT
ejpam-3498	52	6	‖u‖′s	‖u‖′s	PROPN
ejpam-3498	52	7	=	=	PUNCT
ejpam-3498	52	8	‖u‖′s(u	‖u‖′s(u	PROPN
ejpam-3498	52	9	)	)	PUNCT
ejpam-3498	53	1	=	=	PUNCT
ejpam-3498	53	2	sup	sup	NOUN
ejpam-3498	53	3	x∈u	x∈u	NOUN
ejpam-3498	54	1	∞∑	∞∑	NUM
ejpam-3498	54	2	j=1	j=1	NOUN
ejpam-3498	54	3	‖dju(x)‖sj	‖dju(x)‖sj	PROPN
ejpam-3498	55	1	mj	mj	INTJ
ejpam-3498	55	2	,	,	PUNCT
ejpam-3498	55	3	and	and	CCONJ
ejpam-3498	55	4	bs(u	bs(u	NOUN
ejpam-3498	55	5	,	,	PUNCT
ejpam-3498	55	6	v	v	NOUN
ejpam-3498	55	7	)	)	PUNCT
ejpam-3498	55	8	=	=	PUNCT
ejpam-3498	56	1	{	{	PUNCT
ejpam-3498	56	2	u	u	NOUN
ejpam-3498	56	3	∈	∈	PROPN
ejpam-3498	56	4	c∞(u	c∞(u	NOUN
ejpam-3498	56	5	,	,	PUNCT
ejpam-3498	56	6	v	v	NOUN
ejpam-3498	56	7	)	)	PUNCT
ejpam-3498	56	8	:	:	PUNCT
ejpam-3498	57	1	‖u‖s(u	‖u‖s(u	X
ejpam-3498	57	2	)	)	PUNCT
ejpam-3498	57	3	<	<	X
ejpam-3498	57	4	∞	∞	NUM
ejpam-3498	57	5	}	}	PUNCT
ejpam-3498	57	6	,	,	PUNCT
ejpam-3498	57	7	where	where	SCONJ
ejpam-3498	57	8	v	v	NOUN
ejpam-3498	57	9	is	be	AUX
ejpam-3498	57	10	a	a	DET
ejpam-3498	57	11	subset	subset	NOUN
ejpam-3498	57	12	of	of	ADP
ejpam-3498	57	13	a	a	DET
ejpam-3498	57	14	banach	banach	NOUN
ejpam-3498	57	15	space	space	NOUN
ejpam-3498	57	16	.	.	PUNCT
ejpam-3498	58	1	remark	remark	NOUN
ejpam-3498	58	2	1	1	NUM
ejpam-3498	58	3	.	.	PUNCT
ejpam-3498	59	1	it	it	PRON
ejpam-3498	59	2	is	be	AUX
ejpam-3498	59	3	not	not	PART
ejpam-3498	59	4	difficult	difficult	ADJ
ejpam-3498	59	5	to	to	PART
ejpam-3498	59	6	show	show	VERB
ejpam-3498	59	7	that	that	SCONJ
ejpam-3498	59	8	u	u	PRON
ejpam-3498	59	9	∈	∈	PROPN
ejpam-3498	59	10	{	{	PUNCT
ejpam-3498	59	11	mp}(u	mp}(u	NOUN
ejpam-3498	59	12	,	,	PUNCT
ejpam-3498	59	13	v	v	NOUN
ejpam-3498	59	14	)	)	PUNCT
ejpam-3498	59	15	if	if	SCONJ
ejpam-3498	60	1	and	and	CCONJ
ejpam-3498	60	2	only	only	ADV
ejpam-3498	60	3	if	if	SCONJ
ejpam-3498	60	4	u	u	PROPN
ejpam-3498	60	5	∈	∈	PROPN
ejpam-3498	60	6	bs(u	bs(u	NOUN
ejpam-3498	60	7	,	,	PUNCT
ejpam-3498	60	8	v	v	NOUN
ejpam-3498	60	9	)	)	PUNCT
ejpam-3498	60	10	for	for	ADP
ejpam-3498	60	11	some	some	PRON
ejpam-3498	60	12	s	s	VERB
ejpam-3498	60	13	>	>	X
ejpam-3498	60	14	0	0	X
ejpam-3498	60	15	.	.	PUNCT
ejpam-3498	61	1	let	let	VERB
ejpam-3498	61	2	x	x	SYM
ejpam-3498	61	3	,	,	PUNCT
ejpam-3498	61	4	y	y	PROPN
ejpam-3498	61	5	,	,	PUNCT
ejpam-3498	61	6	and	and	CCONJ
ejpam-3498	61	7	z	z	NOUN
ejpam-3498	61	8	be	be	VERB
ejpam-3498	61	9	banach	banach	NOUN
ejpam-3498	61	10	spaces	space	NOUN
ejpam-3498	61	11	,	,	PUNCT
ejpam-3498	61	12	u	u	NOUN
ejpam-3498	61	13	an	an	DET
ejpam-3498	61	14	open	open	ADJ
ejpam-3498	61	15	subset	subset	NOUN
ejpam-3498	61	16	of	of	ADP
ejpam-3498	61	17	x	x	X
ejpam-3498	61	18	,	,	PUNCT
ejpam-3498	61	19	and	and	CCONJ
ejpam-3498	61	20	v	v	ADP
ejpam-3498	61	21	an	an	DET
ejpam-3498	61	22	open	open	ADJ
ejpam-3498	61	23	subset	subset	NOUN
ejpam-3498	61	24	of	of	ADP
ejpam-3498	61	25	y.	y.	PROPN
ejpam-3498	61	26	the	the	DET
ejpam-3498	61	27	next	next	ADJ
ejpam-3498	61	28	theorem	theorem	NOUN
ejpam-3498	61	29	states	state	VERB
ejpam-3498	61	30	the	the	DET
ejpam-3498	61	31	multiplication	multiplication	NOUN
ejpam-3498	61	32	-	-	PUNCT
ejpam-3498	61	33	closedness	closedness	NOUN
ejpam-3498	61	34	of	of	ADP
ejpam-3498	61	35	the	the	DET
ejpam-3498	61	36	{	{	PUNCT
ejpam-3498	61	37	mp	mp	NOUN
ejpam-3498	61	38	}	}	PUNCT
ejpam-3498	61	39	class	class	NOUN
ejpam-3498	61	40	.	.	PUNCT
ejpam-3498	62	1	theorem	theorem	NOUN
ejpam-3498	62	2	1	1	NUM
ejpam-3498	62	3	.	.	PUNCT
ejpam-3498	63	1	let	let	VERB
ejpam-3498	63	2	g	g	PROPN
ejpam-3498	63	3	∈	∈	PROPN
ejpam-3498	63	4	c∞(u	c∞(u	NOUN
ejpam-3498	63	5	,	,	PUNCT
ejpam-3498	63	6	lm(y	lm(y	NOUN
ejpam-3498	63	7	,	,	PUNCT
ejpam-3498	63	8	z	z	NOUN
ejpam-3498	63	9	)	)	PUNCT
ejpam-3498	63	10	)	)	PUNCT
ejpam-3498	64	1	,	,	PUNCT
ejpam-3498	64	2	ui	ui	PROPN
ejpam-3498	64	3	∈	∈	PROPN
ejpam-3498	64	4	c∞(u	c∞(u	PROPN
ejpam-3498	64	5	,	,	PUNCT
ejpam-3498	64	6	y	y	NOUN
ejpam-3498	64	7	)	)	PUNCT
ejpam-3498	64	8	,	,	PUNCT
ejpam-3498	64	9	i	i	PRON
ejpam-3498	64	10	=	=	NOUN
ejpam-3498	64	11	1	1	NUM
ejpam-3498	64	12	,	,	PUNCT
ejpam-3498	64	13	2	2	NUM
ejpam-3498	64	14	,	,	PUNCT
ejpam-3498	64	15	...	...	PUNCT
ejpam-3498	64	16	,	,	PUNCT
ejpam-3498	64	17	m(m	m(m	NOUN
ejpam-3498	64	18	=	=	SYM
ejpam-3498	64	19	1	1	NUM
ejpam-3498	64	20	,	,	PUNCT
ejpam-3498	64	21	2	2	NUM
ejpam-3498	64	22	,	,	PUNCT
ejpam-3498	64	23	...	...	PUNCT
ejpam-3498	64	24	)	)	PUNCT
ejpam-3498	64	25	.	.	PUNCT
ejpam-3498	65	1	then	then	ADV
ejpam-3498	65	2	‖gu1	‖gu1	PROPN
ejpam-3498	65	3	,	,	PUNCT
ejpam-3498	65	4	...	...	PUNCT
ejpam-3498	65	5	,	,	PUNCT
ejpam-3498	65	6	um‖s	um‖s	PROPN
ejpam-3498	65	7	/	/	SYM
ejpam-3498	65	8	h(u	h(u	PROPN
ejpam-3498	65	9	)	)	PUNCT
ejpam-3498	65	10	≤	≤	PROPN
ejpam-3498	65	11	cm1	cm1	X
ejpam-3498	65	12	‖g‖s(u	‖g‖s(u	PROPN
ejpam-3498	65	13	)	)	PUNCT
ejpam-3498	65	14	m∏	m∏	PROPN
ejpam-3498	65	15	i=1	i=1	PRON
ejpam-3498	65	16	‖ui‖s(u	‖ui‖s(u	NOUN
ejpam-3498	65	17	)	)	PUNCT
ejpam-3498	65	18	,	,	PUNCT
ejpam-3498	65	19	where	where	SCONJ
ejpam-3498	65	20	(	(	PUNCT
ejpam-3498	65	21	gu1	gu1	ADJ
ejpam-3498	65	22	,	,	PUNCT
ejpam-3498	65	23	...	...	PUNCT
ejpam-3498	65	24	,	,	PUNCT
ejpam-3498	65	25	um)(x	um)(x	NUM
ejpam-3498	65	26	)	)	PUNCT
ejpam-3498	65	27	=	=	SYM
ejpam-3498	65	28	g(x)u1(x	g(x)u1(x	NOUN
ejpam-3498	65	29	)	)	PUNCT
ejpam-3498	65	30	,	,	PUNCT
ejpam-3498	65	31	....	....	PUNCT
ejpam-3498	65	32	,	,	PUNCT
ejpam-3498	65	33	um(x	um(x	NOUN
ejpam-3498	65	34	)	)	PUNCT
ejpam-3498	65	35	and	and	CCONJ
ejpam-3498	65	36	c1	c1	PROPN
ejpam-3498	65	37	=	=	PROPN
ejpam-3498	65	38	max	max	PROPN
ejpam-3498	65	39	{	{	PUNCT
ejpam-3498	65	40	1	1	NUM
ejpam-3498	65	41	n2	n2	NOUN
ejpam-3498	65	42	,	,	PUNCT
ejpam-3498	65	43	1	1	NUM
ejpam-3498	65	44	}	}	PUNCT
ejpam-3498	65	45	.	.	PUNCT
ejpam-3498	66	1	theorem	theorem	NOUN
ejpam-3498	66	2	2	2	NUM
ejpam-3498	66	3	.	.	PUNCT
ejpam-3498	67	1	let	let	VERB
ejpam-3498	67	2	f	f	PROPN
ejpam-3498	67	3	∈	∈	PROPN
ejpam-3498	67	4	c∞(v	c∞(v	NOUN
ejpam-3498	67	5	,	,	PUNCT
ejpam-3498	67	6	z	z	NOUN
ejpam-3498	67	7	)	)	PUNCT
ejpam-3498	67	8	and	and	CCONJ
ejpam-3498	67	9	u	u	PROPN
ejpam-3498	67	10	∈	∈	PROPN
ejpam-3498	67	11	c∞(u	c∞(u	NOUN
ejpam-3498	67	12	,	,	PUNCT
ejpam-3498	67	13	v	v	NOUN
ejpam-3498	67	14	)	)	PUNCT
ejpam-3498	67	15	.	.	PUNCT
ejpam-3498	68	1	if	if	SCONJ
ejpam-3498	68	2	‖u‖s′(u	‖u‖s′(u	NOUN
ejpam-3498	68	3	)	)	PUNCT
ejpam-3498	68	4	≤	≤	NOUN
ejpam-3498	68	5	r	r	NOUN
ejpam-3498	68	6	for	for	ADP
ejpam-3498	68	7	some	some	DET
ejpam-3498	68	8	s	s	VERB
ejpam-3498	68	9	>	>	X
ejpam-3498	68	10	0	0	PUNCT
ejpam-3498	69	1	and	and	CCONJ
ejpam-3498	69	2	r	r	X
ejpam-3498	69	3	>	>	X
ejpam-3498	69	4	0	0	NUM
ejpam-3498	69	5	,	,	PUNCT
ejpam-3498	69	6	then	then	ADV
ejpam-3498	69	7	‖f	‖f	ADJ
ejpam-3498	69	8	◦	◦	NOUN
ejpam-3498	69	9	u‖s	u‖s	PROPN
ejpam-3498	69	10	/	/	SYM
ejpam-3498	69	11	h(u	h(u	PROPN
ejpam-3498	69	12	)	)	PUNCT
ejpam-3498	69	13	≤	≤	NOUN
ejpam-3498	70	1	‖f‖r(v	‖f‖r(v	X
ejpam-3498	70	2	)	)	PUNCT
ejpam-3498	70	3	.	.	PUNCT
ejpam-3498	71	1	corollary	corollary	ADJ
ejpam-3498	71	2	1	1	NUM
ejpam-3498	71	3	.	.	PUNCT
ejpam-3498	72	1	let	let	VERB
ejpam-3498	72	2	f	f	PROPN
ejpam-3498	72	3	∈	∈	PROPN
ejpam-3498	72	4	c∞(v	c∞(v	NOUN
ejpam-3498	72	5	,	,	PUNCT
ejpam-3498	72	6	z	z	NOUN
ejpam-3498	72	7	)	)	PUNCT
ejpam-3498	72	8	,	,	PUNCT
ejpam-3498	72	9	and	and	CCONJ
ejpam-3498	72	10	u	u	NOUN
ejpam-3498	72	11	,	,	PUNCT
ejpam-3498	72	12	v	v	PROPN
ejpam-3498	72	13	∈	∈	PROPN
ejpam-3498	72	14	c∞(u	c∞(u	NOUN
ejpam-3498	72	15	,	,	PUNCT
ejpam-3498	72	16	v	v	NOUN
ejpam-3498	72	17	)	)	PUNCT
ejpam-3498	72	18	.	.	PUNCT
ejpam-3498	73	1	then	then	ADV
ejpam-3498	73	2	‖f	‖f	DET
ejpam-3498	73	3	◦	◦	NOUN
ejpam-3498	73	4	u−	u−	PROPN
ejpam-3498	73	5	f	f	NOUN
ejpam-3498	73	6	◦	◦	NOUN
ejpam-3498	73	7	v‖s	v‖s	NOUN
ejpam-3498	73	8	/	/	SYM
ejpam-3498	73	9	h2(u	h2(u	NOUN
ejpam-3498	73	10	)	)	PUNCT
ejpam-3498	73	11	≤	≤	NOUN
ejpam-3498	73	12	c1‖df‖r(v	c1‖df‖r(v	NOUN
ejpam-3498	73	13	)	)	PUNCT
ejpam-3498	73	14	‖u−	‖u−	PROPN
ejpam-3498	73	15	v‖s	v‖s	NOUN
ejpam-3498	73	16	/	/	SYM
ejpam-3498	73	17	h(u	h(u	PROPN
ejpam-3498	73	18	)	)	PUNCT
ejpam-3498	73	19	if	if	SCONJ
ejpam-3498	73	20	‖u‖′s(u	‖u‖′s(u	NOUN
ejpam-3498	73	21	)	)	PUNCT
ejpam-3498	73	22	≤	≤	NOUN
ejpam-3498	73	23	r	r	NOUN
ejpam-3498	73	24	and	and	CCONJ
ejpam-3498	73	25	‖v‖′s(u	‖v‖′s(u	NOUN
ejpam-3498	73	26	)	)	PUNCT
ejpam-3498	73	27	≤	≤	PROPN
ejpam-3498	73	28	r.	r.	PROPN
ejpam-3498	73	29	theorem	theorem	VERB
ejpam-3498	73	30	3	3	X
ejpam-3498	73	31	.	.	X
ejpam-3498	74	1	assume	assume	VERB
ejpam-3498	74	2	(	(	PUNCT
ejpam-3498	74	3	c2	c2	PROPN
ejpam-3498	74	4	)	)	PUNCT
ejpam-3498	74	5	.	.	PUNCT
ejpam-3498	75	1	then	then	ADV
ejpam-3498	75	2	there	there	PRON
ejpam-3498	75	3	exists	exist	VERB
ejpam-3498	75	4	kn	kn	PROPN
ejpam-3498	75	5	>	>	X
ejpam-3498	75	6	0	0	NUM
ejpam-3498	75	7	such	such	ADJ
ejpam-3498	75	8	that	that	SCONJ
ejpam-3498	75	9	‖dnu‖r	‖dnu‖r	VERB
ejpam-3498	75	10	≤	≤	NUM
ejpam-3498	75	11	kn(s−	kn(s−	PROPN
ejpam-3498	75	12	r)−n‖u‖s	r)−n‖u‖s	X
ejpam-3498	75	13	(	(	PUNCT
ejpam-3498	75	14	3	3	NUM
ejpam-3498	75	15	)	)	PUNCT
ejpam-3498	75	16	0	0	PUNCT
ejpam-3498	76	1	<	<	X
ejpam-3498	76	2	r	r	X
ejpam-3498	76	3	<	<	X
ejpam-3498	76	4	s	s	PART
ejpam-3498	76	5	≤	≤	NUM
ejpam-3498	76	6	s1	s1	NOUN
ejpam-3498	76	7	,	,	PUNCT
ejpam-3498	76	8	where	where	SCONJ
ejpam-3498	76	9	kn	kn	PROPN
ejpam-3498	76	10	is	be	AUX
ejpam-3498	76	11	independent	independent	ADJ
ejpam-3498	76	12	of	of	ADP
ejpam-3498	76	13	u	u	PROPN
ejpam-3498	76	14	,	,	PUNCT
ejpam-3498	76	15	r	r	NOUN
ejpam-3498	76	16	and	and	CCONJ
ejpam-3498	76	17	s.	s.	PROPN
ejpam-3498	76	18	remark	remark	PROPN
ejpam-3498	76	19	2	2	NUM
ejpam-3498	76	20	.	.	PUNCT
ejpam-3498	77	1	the	the	DET
ejpam-3498	77	2	preceding	precede	VERB
ejpam-3498	77	3	theorem	theorem	NOUN
ejpam-3498	77	4	implies	imply	VERB
ejpam-3498	77	5	that	that	SCONJ
ejpam-3498	77	6	if	if	SCONJ
ejpam-3498	77	7	u	u	PROPN
ejpam-3498	77	8	∈	∈	PROPN
ejpam-3498	77	9	{	{	PUNCT
ejpam-3498	77	10	mp	mp	NOUN
ejpam-3498	77	11	}	}	PUNCT
ejpam-3498	77	12	,	,	PUNCT
ejpam-3498	77	13	then	then	ADV
ejpam-3498	77	14	du	du	PROPN
ejpam-3498	77	15	∈	∈	PROPN
ejpam-3498	77	16	{	{	PUNCT
ejpam-3498	77	17	mp	mp	NOUN
ejpam-3498	77	18	}	}	PUNCT
ejpam-3498	77	19	.	.	PUNCT
ejpam-3498	78	1	e.	e.	PROPN
ejpam-3498	78	2	y.	y.	PROPN
ejpam-3498	78	3	guerrero	guerrero	PROPN
ejpam-3498	78	4	/	/	SYM
ejpam-3498	78	5	eur	eur	PROPN
ejpam-3498	78	6	.	.	PUNCT
ejpam-3498	79	1	j.	j.	PROPN
ejpam-3498	79	2	pure	pure	PROPN
ejpam-3498	79	3	appl	appl	PROPN
ejpam-3498	79	4	.	.	PROPN
ejpam-3498	79	5	math	math	PROPN
ejpam-3498	79	6	,	,	PUNCT
ejpam-3498	79	7	12	12	NUM
ejpam-3498	79	8	(	(	PUNCT
ejpam-3498	79	9	3	3	NUM
ejpam-3498	79	10	)	)	PUNCT
ejpam-3498	79	11	(	(	PUNCT
ejpam-3498	79	12	2019	2019	NUM
ejpam-3498	79	13	)	)	PUNCT
ejpam-3498	79	14	,	,	PUNCT
ejpam-3498	79	15	1297	1297	NUM
ejpam-3498	79	16	-	-	SYM
ejpam-3498	79	17	1314	1314	NUM
ejpam-3498	79	18	1300	1300	NUM
ejpam-3498	79	19	we	we	PRON
ejpam-3498	79	20	will	will	AUX
ejpam-3498	79	21	now	now	ADV
ejpam-3498	79	22	give	give	VERB
ejpam-3498	79	23	our	our	PRON
ejpam-3498	79	24	assumptions	assumption	NOUN
ejpam-3498	79	25	for	for	ADP
ejpam-3498	79	26	(	(	PUNCT
ejpam-3498	79	27	1	1	NUM
ejpam-3498	79	28	)	)	PUNCT
ejpam-3498	79	29	.	.	PUNCT
ejpam-3498	80	1	let	let	VERB
ejpam-3498	80	2	y	y	PRON
ejpam-3498	80	3	be	be	AUX
ejpam-3498	80	4	a	a	DET
ejpam-3498	80	5	complex	complex	ADJ
ejpam-3498	80	6	banach	banach	NOUN
ejpam-3498	80	7	space	space	NOUN
ejpam-3498	80	8	and	and	CCONJ
ejpam-3498	80	9	lk(x	lk(x	NOUN
ejpam-3498	80	10	,	,	PUNCT
ejpam-3498	80	11	y	y	PROPN
ejpam-3498	80	12	)	)	PUNCT
ejpam-3498	80	13	the	the	DET
ejpam-3498	80	14	banach	banach	NOUN
ejpam-3498	80	15	space	space	NOUN
ejpam-3498	80	16	of	of	ADP
ejpam-3498	80	17	all	all	DET
ejpam-3498	80	18	bounded	bounded	ADJ
ejpam-3498	80	19	multi	multi	ADJ
ejpam-3498	80	20	-	-	ADJ
ejpam-3498	80	21	k	k	ADJ
ejpam-3498	80	22	-	-	PUNCT
ejpam-3498	80	23	linear	linear	ADJ
ejpam-3498	80	24	maps	map	NOUN
ejpam-3498	80	25	from	from	ADP
ejpam-3498	80	26	xk	xk	PROPN
ejpam-3498	80	27	to	to	ADP
ejpam-3498	80	28	y	y	PROPN
ejpam-3498	80	29	,	,	PUNCT
ejpam-3498	80	30	while	while	SCONJ
ejpam-3498	80	31	l0(x	l0(x	ADP
ejpam-3498	80	32	,	,	PUNCT
ejpam-3498	80	33	y	y	PROPN
ejpam-3498	80	34	)	)	PUNCT
ejpam-3498	80	35	denotes	denote	VERB
ejpam-3498	80	36	y	y	PROPN
ejpam-3498	80	37	.	.	PUNCT
ejpam-3498	81	1	let	let	VERB
ejpam-3498	81	2	ω	ω	PRON
ejpam-3498	81	3	be	be	AUX
ejpam-3498	81	4	an	an	DET
ejpam-3498	81	5	open	open	ADJ
ejpam-3498	81	6	subset	subset	NOUN
ejpam-3498	81	7	of	of	ADP
ejpam-3498	81	8	x	x	PUNCT
ejpam-3498	81	9	and	and	CCONJ
ejpam-3498	81	10	ui	ui	PROPN
ejpam-3498	81	11	a	a	DET
ejpam-3498	81	12	neighborhood	neighborhood	NOUN
ejpam-3498	81	13	of	of	ADP
ejpam-3498	81	14	the	the	DET
ejpam-3498	81	15	origin	origin	NOUN
ejpam-3498	81	16	in	in	ADP
ejpam-3498	81	17	the	the	DET
ejpam-3498	81	18	banach	banach	NOUN
ejpam-3498	81	19	space	space	NOUN
ejpam-3498	81	20	{	{	PUNCT
ejpam-3498	81	21	(	(	PUNCT
ejpam-3498	81	22	ξjk)(j	ξjk)(j	ADJ
ejpam-3498	81	23	,	,	PUNCT
ejpam-3498	81	24	k)∈n	k)∈n	X
ejpam-3498	81	25	(	(	PUNCT
ejpam-3498	81	26	i	i	NOUN
ejpam-3498	81	27	)	)	PUNCT
ejpam-3498	81	28	:	:	PUNCT
ejpam-3498	81	29	ξjk	ξjk	VERB
ejpam-3498	81	30	∈	∈	PROPN
ejpam-3498	81	31	lk(x	lk(x	NOUN
ejpam-3498	81	32	,	,	PUNCT
ejpam-3498	81	33	y	y	PROPN
ejpam-3498	81	34	)	)	PUNCT
ejpam-3498	81	35	}	}	PUNCT
ejpam-3498	81	36	,	,	PUNCT
ejpam-3498	81	37	where	where	SCONJ
ejpam-3498	81	38	n	n	X
ejpam-3498	81	39	(	(	PUNCT
ejpam-3498	81	40	i	i	NOUN
ejpam-3498	81	41	)	)	PUNCT
ejpam-3498	81	42	is	be	AUX
ejpam-3498	81	43	the	the	DET
ejpam-3498	81	44	set	set	NOUN
ejpam-3498	81	45	defined	define	VERB
ejpam-3498	81	46	in	in	ADP
ejpam-3498	81	47	(	(	PUNCT
ejpam-3498	81	48	2	2	NUM
ejpam-3498	81	49	)	)	PUNCT
ejpam-3498	81	50	.	.	PUNCT
ejpam-3498	82	1	let	let	VERB
ejpam-3498	82	2	fi(u	fi(u	NOUN
ejpam-3498	82	3	,	,	PUNCT
ejpam-3498	82	4	w)(t	w)(t	PROPN
ejpam-3498	82	5	,	,	PUNCT
ejpam-3498	82	6	x	x	NOUN
ejpam-3498	82	7	)	)	PUNCT
ejpam-3498	82	8	=	=	SYM
ejpam-3498	83	1	n∑	n∑	NOUN
ejpam-3498	83	2	j=1	j=1	PROPN
ejpam-3498	83	3	aij(t	aij(t	PROPN
ejpam-3498	83	4	,	,	PUNCT
ejpam-3498	83	5	x)uj(t	x)uj(t	PROPN
ejpam-3498	83	6	,	,	PUNCT
ejpam-3498	83	7	x	x	X
ejpam-3498	83	8	)	)	PUNCT
ejpam-3498	84	1	+	+	CCONJ
ejpam-3498	84	2	∑	∑	PROPN
ejpam-3498	84	3	(	(	PUNCT
ejpam-3498	84	4	j	j	PROPN
ejpam-3498	84	5	,	,	PUNCT
ejpam-3498	84	6	k)∈n	k)∈n	X
ejpam-3498	84	7	(	(	PUNCT
ejpam-3498	84	8	i	i	NOUN
ejpam-3498	84	9	)	)	PUNCT
ejpam-3498	84	10	bjk(t	bjk(t	PROPN
ejpam-3498	84	11	,	,	PUNCT
ejpam-3498	84	12	x)((µ0(t)d)kuj(t	x)((µ0(t)d)kuj(t	PROPN
ejpam-3498	84	13	,	,	PUNCT
ejpam-3498	84	14	x	x	X
ejpam-3498	84	15	)	)	PUNCT
ejpam-3498	84	16	·	·	PUNCT
ejpam-3498	84	17	x(k)k	x(k)k	NUM
ejpam-3498	84	18	)	)	PUNCT
ejpam-3498	85	1	(	(	PUNCT
ejpam-3498	85	2	j	j	NOUN
ejpam-3498	85	3	,	,	PUNCT
ejpam-3498	85	4	k	k	NOUN
ejpam-3498	85	5	)	)	PUNCT
ejpam-3498	85	6	.	.	PUNCT
ejpam-3498	86	1	we	we	PRON
ejpam-3498	86	2	work	work	VERB
ejpam-3498	86	3	on	on	ADP
ejpam-3498	86	4	(	(	PUNCT
ejpam-3498	86	5	1	1	NUM
ejpam-3498	86	6	)	)	PUNCT
ejpam-3498	86	7	under	under	ADP
ejpam-3498	86	8	the	the	DET
ejpam-3498	86	9	following	following	ADJ
ejpam-3498	86	10	assumptions	assumption	NOUN
ejpam-3498	86	11	:	:	PUNCT
ejpam-3498	86	12	(	(	PUNCT
ejpam-3498	86	13	a1	a1	NOUN
ejpam-3498	86	14	)	)	PUNCT
ejpam-3498	86	15	µ0	µ0	NOUN
ejpam-3498	86	16	belong	belong	VERB
ejpam-3498	86	17	to	to	ADP
ejpam-3498	86	18	c0([0	c0([0	PROPN
ejpam-3498	86	19	,	,	PUNCT
ejpam-3498	86	20	t	t	X
ejpam-3498	86	21	]	]	PUNCT
ejpam-3498	86	22	,	,	PUNCT
ejpam-3498	86	23	c	c	X
ejpam-3498	86	24	)	)	PUNCT
ejpam-3498	86	25	for	for	ADP
ejpam-3498	86	26	a	a	DET
ejpam-3498	86	27	t	t	NOUN
ejpam-3498	86	28	>	>	X
ejpam-3498	86	29	0	0	PUNCT
ejpam-3498	86	30	and	and	CCONJ
ejpam-3498	86	31	fi	fi	NOUN
ejpam-3498	86	32	∈	∈	PROPN
ejpam-3498	86	33	c0([0	c0([0	PROPN
ejpam-3498	86	34	,	,	PUNCT
ejpam-3498	86	35	t	t	X
ejpam-3498	86	36	]	]	PUNCT
ejpam-3498	86	37	,	,	PUNCT
ejpam-3498	86	38	bs1(ω×	bs1(ω×	PROPN
ejpam-3498	86	39	ui	ui	PROPN
ejpam-3498	86	40	,	,	PUNCT
ejpam-3498	86	41	y	y	PROPN
ejpam-3498	86	42	)	)	PUNCT
ejpam-3498	86	43	)	)	PUNCT
ejpam-3498	86	44	,	,	PUNCT
ejpam-3498	86	45	for	for	ADP
ejpam-3498	86	46	some	some	DET
ejpam-3498	86	47	s1	s1	PROPN
ejpam-3498	86	48	>	>	X
ejpam-3498	86	49	0	0	NUM
ejpam-3498	86	50	.	.	PUNCT
ejpam-3498	87	1	(	(	PUNCT
ejpam-3498	87	2	a2	a2	PROPN
ejpam-3498	87	3	)	)	PUNCT
ejpam-3498	87	4	fi(0	fi(0	PROPN
ejpam-3498	87	5	,	,	PUNCT
ejpam-3498	87	6	0)(0	0)(0	NUM
ejpam-3498	87	7	,	,	PUNCT
ejpam-3498	87	8	x	x	NOUN
ejpam-3498	87	9	)	)	PUNCT
ejpam-3498	87	10	=	=	SYM
ejpam-3498	87	11	0	0	NUM
ejpam-3498	87	12	,	,	PUNCT
ejpam-3498	87	13	for	for	ADP
ejpam-3498	87	14	all	all	DET
ejpam-3498	87	15	x	x	SYM
ejpam-3498	87	16	∈	∈	PROPN
ejpam-3498	87	17	ω	ω	PROPN
ejpam-3498	87	18	,	,	PUNCT
ejpam-3498	87	19	1	1	NUM
ejpam-3498	87	20	≤	≤	NUM
ejpam-3498	87	21	i	i	PRON
ejpam-3498	87	22	≤	≤	ADJ
ejpam-3498	87	23	n	n	CCONJ
ejpam-3498	87	24	(	(	PUNCT
ejpam-3498	87	25	a3	a3	NOUN
ejpam-3498	87	26	)	)	PUNCT
ejpam-3498	87	27	the	the	DET
ejpam-3498	87	28	spectrum	spectrum	NOUN
ejpam-3498	87	29	of	of	ADP
ejpam-3498	87	30	the	the	DET
ejpam-3498	87	31	n	n	ADV
ejpam-3498	87	32	×n	×n	PRON
ejpam-3498	87	33	matrix	matrix	NOUN
ejpam-3498	87	34	a(x	a(x	NOUN
ejpam-3498	87	35	)	)	PUNCT
ejpam-3498	87	36	=	=	PUNCT
ejpam-3498	87	37	(	(	PUNCT
ejpam-3498	87	38	aij(x	aij(x	PROPN
ejpam-3498	87	39	)	)	PUNCT
ejpam-3498	87	40	)	)	PUNCT
ejpam-3498	88	1	∈	∈	PROPN
ejpam-3498	88	2	l(y	l(y	PROPN
ejpam-3498	88	3	n	n	CCONJ
ejpam-3498	88	4	)	)	PUNCT
ejpam-3498	88	5	,	,	PUNCT
ejpam-3498	88	6	where	where	SCONJ
ejpam-3498	88	7	aij	aij	PROPN
ejpam-3498	88	8	=	=	SYM
ejpam-3498	88	9	−dujfi(u	−dujfi(u	PROPN
ejpam-3498	88	10	,	,	PUNCT
ejpam-3498	88	11	w)(0	w)(0	NUM
ejpam-3498	88	12	,	,	PUNCT
ejpam-3498	88	13	x)|(u	x)|(u	NOUN
ejpam-3498	88	14	,	,	PUNCT
ejpam-3498	88	15	w)=(0,0	w)=(0,0	NOUN
ejpam-3498	88	16	)	)	PUNCT
ejpam-3498	88	17	is	be	AUX
ejpam-3498	88	18	contained	contain	VERB
ejpam-3498	88	19	in	in	ADP
ejpam-3498	88	20	the	the	DET
ejpam-3498	88	21	half	half	ADJ
ejpam-3498	88	22	plane{z	plane{z	PROPN
ejpam-3498	88	23	∈	∈	PROPN
ejpam-3498	89	1	c	c	NOUN
ejpam-3498	89	2	:	:	PUNCT
ejpam-3498	89	3	rez	rez	PROPN
ejpam-3498	89	4	>	>	X
ejpam-3498	89	5	b0	b0	NOUN
ejpam-3498	89	6	}	}	PUNCT
ejpam-3498	89	7	for	for	ADP
ejpam-3498	89	8	a	a	DET
ejpam-3498	89	9	positive	positive	ADJ
ejpam-3498	89	10	number	number	NOUN
ejpam-3498	89	11	b0	b0	NOUN
ejpam-3498	89	12	.	.	PUNCT
ejpam-3498	90	1	(	(	PUNCT
ejpam-3498	90	2	a4	a4	NOUN
ejpam-3498	90	3	)	)	PUNCT
ejpam-3498	90	4	for	for	ADP
ejpam-3498	90	5	some	some	DET
ejpam-3498	90	6	κ	κ	X
ejpam-3498	90	7	∈	∈	PROPN
ejpam-3498	90	8	(	(	PUNCT
ejpam-3498	90	9	0	0	NUM
ejpam-3498	90	10	,	,	PUNCT
ejpam-3498	90	11	1	1	NUM
ejpam-3498	90	12	)	)	PUNCT
ejpam-3498	90	13	,	,	PUNCT
ejpam-3498	90	14	∫	∫	PROPN
ejpam-3498	90	15	t	t	PROPN
ejpam-3498	90	16	0	0	NUM
ejpam-3498	91	1	(	(	PUNCT
ejpam-3498	91	2	µ(t))κ	µ(t))κ	PROPN
ejpam-3498	91	3	t	t	PROPN
ejpam-3498	91	4	dt	dt	X
ejpam-3498	91	5	<	<	X
ejpam-3498	91	6	∞	∞	PROPN
ejpam-3498	91	7	,	,	PUNCT
ejpam-3498	91	8	where	where	SCONJ
ejpam-3498	91	9	µ(t	µ(t	ADJ
ejpam-3498	91	10	)	)	PUNCT
ejpam-3498	91	11	=	=	PRON
ejpam-3498	91	12	sup0≤τ≤t	sup0≤τ≤t	PROPN
ejpam-3498	91	13	|µ0(τ)|	|µ0(τ)|	PRON
ejpam-3498	91	14	.	.	PUNCT
ejpam-3498	92	1	condition	condition	NOUN
ejpam-3498	92	2	(	(	PUNCT
ejpam-3498	92	3	a1	a1	NOUN
ejpam-3498	92	4	)	)	PUNCT
ejpam-3498	92	5	states	state	NOUN
ejpam-3498	92	6	that	that	SCONJ
ejpam-3498	92	7	fi	fi	NOUN
ejpam-3498	92	8	is	be	AUX
ejpam-3498	92	9	continuous	continuous	ADJ
ejpam-3498	92	10	in	in	ADP
ejpam-3498	92	11	t	t	PROPN
ejpam-3498	92	12	and	and	CCONJ
ejpam-3498	92	13	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	92	14	in	in	ADP
ejpam-3498	92	15	the	the	DET
ejpam-3498	92	16	other	other	ADJ
ejpam-3498	92	17	variables	variable	NOUN
ejpam-3498	92	18	.	.	PUNCT
ejpam-3498	93	1	the	the	DET
ejpam-3498	93	2	next	next	ADJ
ejpam-3498	93	3	results	result	NOUN
ejpam-3498	93	4	are	be	AUX
ejpam-3498	93	5	proved	prove	VERB
ejpam-3498	93	6	in	in	ADP
ejpam-3498	93	7	[	[	X
ejpam-3498	93	8	3	3	X
ejpam-3498	93	9	]	]	PUNCT
ejpam-3498	93	10	assuming	assume	VERB
ejpam-3498	93	11	(	(	PUNCT
ejpam-3498	93	12	c1	c1	NOUN
ejpam-3498	93	13	)	)	PUNCT
ejpam-3498	93	14	,	,	PUNCT
ejpam-3498	93	15	(	(	PUNCT
ejpam-3498	93	16	c2	c2	PROPN
ejpam-3498	93	17	)	)	PUNCT
ejpam-3498	93	18	,	,	PUNCT
ejpam-3498	93	19	and	and	CCONJ
ejpam-3498	93	20	(	(	PUNCT
ejpam-3498	93	21	a1)-(a4	a1)-(a4	PROPN
ejpam-3498	93	22	)	)	PUNCT
ejpam-3498	93	23	.	.	PUNCT
ejpam-3498	94	1	let	let	VERB
ejpam-3498	94	2	κ	κ	PRON
ejpam-3498	94	3	be	be	AUX
ejpam-3498	94	4	the	the	DET
ejpam-3498	94	5	number	number	NOUN
ejpam-3498	94	6	as	as	ADP
ejpam-3498	94	7	in	in	ADP
ejpam-3498	94	8	(	(	PUNCT
ejpam-3498	94	9	a2	a2	NOUN
ejpam-3498	94	10	)	)	PUNCT
ejpam-3498	94	11	and	and	CCONJ
ejpam-3498	94	12	c	c	X
ejpam-3498	94	13	=	=	SYM
ejpam-3498	94	14	max	max	PROPN
ejpam-3498	94	15	1≤i≤n	1≤i≤n	NUM
ejpam-3498	94	16	{	{	PUNCT
ejpam-3498	94	17	n(i)}+	n(i)}+	NOUN
ejpam-3498	94	18	1	1	NUM
ejpam-3498	94	19	+	+	SYM
ejpam-3498	94	20	κ	κ	X
ejpam-3498	94	21	1−	1−	NUM
ejpam-3498	94	22	κ	κ	NOUN
ejpam-3498	94	23	d	d	NOUN
ejpam-3498	94	24	=	=	SYM
ejpam-3498	94	25	max	max	PROPN
ejpam-3498	94	26	1≤i	1≤i	PROPN
ejpam-3498	94	27	,	,	PUNCT
ejpam-3498	94	28	j≤n	j≤n	NOUN
ejpam-3498	94	29	{	{	PUNCT
ejpam-3498	94	30	n(i	n(i	PROPN
ejpam-3498	94	31	,	,	PUNCT
ejpam-3498	94	32	j	j	NOUN
ejpam-3498	94	33	)	)	PUNCT
ejpam-3498	94	34	}	}	PUNCT
ejpam-3498	94	35	.	.	PUNCT
ejpam-3498	95	1	(	(	PUNCT
ejpam-3498	95	2	4	4	X
ejpam-3498	95	3	)	)	PUNCT
ejpam-3498	95	4	then	then	ADV
ejpam-3498	95	5	c	c	X
ejpam-3498	95	6	≥	≥	PROPN
ejpam-3498	96	1	d	d	NOUN
ejpam-3498	96	2	+	+	CCONJ
ejpam-3498	96	3	1	1	NUM
ejpam-3498	96	4	and	and	CCONJ
ejpam-3498	96	5	d	d	NOUN
ejpam-3498	96	6	≥	≥	NUM
ejpam-3498	96	7	1	1	NUM
ejpam-3498	96	8	.	.	PUNCT
ejpam-3498	97	1	the	the	DET
ejpam-3498	97	2	function	function	NOUN
ejpam-3498	97	3	ω	ω	PROPN
ejpam-3498	97	4	in	in	ADP
ejpam-3498	97	5	the	the	DET
ejpam-3498	97	6	following	follow	VERB
ejpam-3498	97	7	lemma	lemma	PROPN
ejpam-3498	97	8	plays	play	VERB
ejpam-3498	97	9	an	an	DET
ejpam-3498	97	10	important	important	ADJ
ejpam-3498	97	11	role	role	NOUN
ejpam-3498	97	12	.	.	PUNCT
ejpam-3498	98	1	lemma	lemma	PROPN
ejpam-3498	98	2	1	1	NUM
ejpam-3498	98	3	.	.	PUNCT
ejpam-3498	99	1	there	there	PRON
ejpam-3498	99	2	exists	exist	VERB
ejpam-3498	99	3	a	a	DET
ejpam-3498	99	4	function	function	NOUN
ejpam-3498	99	5	ω	ω	PROPN
ejpam-3498	99	6	∈	∈	PROPN
ejpam-3498	99	7	c0([0	c0([0	PROPN
ejpam-3498	99	8	,	,	PUNCT
ejpam-3498	99	9	t	t	X
ejpam-3498	99	10	]	]	PUNCT
ejpam-3498	99	11	,	,	PUNCT
ejpam-3498	99	12	r	r	NOUN
ejpam-3498	99	13	)	)	PUNCT
ejpam-3498	99	14	∩	∩	ADJ
ejpam-3498	99	15	c1((0	c1((0	PROPN
ejpam-3498	99	16	,	,	PUNCT
ejpam-3498	99	17	t	t	X
ejpam-3498	99	18	]	]	PUNCT
ejpam-3498	99	19	,	,	PUNCT
ejpam-3498	99	20	r	r	NOUN
ejpam-3498	99	21	)	)	PUNCT
ejpam-3498	99	22	such	such	ADJ
ejpam-3498	99	23	that	that	DET
ejpam-3498	99	24	ω(0	ω(0	PROPN
ejpam-3498	99	25	)	)	PUNCT
ejpam-3498	99	26	=	=	SYM
ejpam-3498	99	27	0	0	NUM
ejpam-3498	99	28	,	,	PUNCT
ejpam-3498	99	29	ω(t)cω′(t	ω(t)cω′(t	NOUN
ejpam-3498	99	30	)	)	PUNCT
ejpam-3498	99	31	≥	≥	NOUN
ejpam-3498	99	32	µ(t	µ(t	ADJ
ejpam-3498	99	33	)	)	PUNCT
ejpam-3498	99	34	κ	κ	PROPN
ejpam-3498	99	35	t	t	PROPN
ejpam-3498	99	36	(	(	PUNCT
ejpam-3498	99	37	5	5	NUM
ejpam-3498	99	38	)	)	PUNCT
ejpam-3498	99	39	and	and	CCONJ
ejpam-3498	99	40	ω(t)c	ω(t)c	NOUN
ejpam-3498	99	41	≥	≥	NOUN
ejpam-3498	99	42	µ(t)κ	µ(t)κ	PROPN
ejpam-3498	99	43	(	(	PUNCT
ejpam-3498	99	44	6	6	NUM
ejpam-3498	99	45	)	)	PUNCT
ejpam-3498	99	46	for	for	ADP
ejpam-3498	99	47	t	t	PROPN
ejpam-3498	99	48	∈	∈	PROPN
ejpam-3498	99	49	(	(	PUNCT
ejpam-3498	99	50	0	0	NUM
ejpam-3498	99	51	,	,	PUNCT
ejpam-3498	99	52	t	t	X
ejpam-3498	99	53	]	]	PUNCT
ejpam-3498	99	54	.	.	PUNCT
ejpam-3498	100	1	e.	e.	PROPN
ejpam-3498	100	2	y.	y.	PROPN
ejpam-3498	100	3	guerrero	guerrero	PROPN
ejpam-3498	100	4	/	/	SYM
ejpam-3498	100	5	eur	eur	PROPN
ejpam-3498	100	6	.	.	PUNCT
ejpam-3498	101	1	j.	j.	PROPN
ejpam-3498	101	2	pure	pure	PROPN
ejpam-3498	101	3	appl	appl	PROPN
ejpam-3498	101	4	.	.	PROPN
ejpam-3498	101	5	math	math	PROPN
ejpam-3498	101	6	,	,	PUNCT
ejpam-3498	101	7	12	12	NUM
ejpam-3498	101	8	(	(	PUNCT
ejpam-3498	101	9	3	3	NUM
ejpam-3498	101	10	)	)	PUNCT
ejpam-3498	101	11	(	(	PUNCT
ejpam-3498	101	12	2019	2019	NUM
ejpam-3498	101	13	)	)	PUNCT
ejpam-3498	101	14	,	,	PUNCT
ejpam-3498	101	15	1297	1297	NUM
ejpam-3498	101	16	-	-	SYM
ejpam-3498	101	17	1314	1314	NUM
ejpam-3498	101	18	1301	1301	NUM
ejpam-3498	101	19	now	now	ADV
ejpam-3498	101	20	put	put	VERB
ejpam-3498	101	21	ρ(i	ρ(i	PROPN
ejpam-3498	101	22	,	,	PUNCT
ejpam-3498	101	23	j	j	PROPN
ejpam-3498	101	24	)	)	PUNCT
ejpam-3498	101	25	=	=	SYM
ejpam-3498	101	26	max{n(j	max{n(j	NOUN
ejpam-3498	101	27	,	,	PUNCT
ejpam-3498	101	28	i	i	NOUN
ejpam-3498	101	29	)	)	PUNCT
ejpam-3498	101	30	,	,	PUNCT
ejpam-3498	101	31	1	1	X
ejpam-3498	101	32	}	}	PUNCT
ejpam-3498	101	33	ν(τ	ν(τ	PROPN
ejpam-3498	101	34	,	,	PUNCT
ejpam-3498	101	35	t	t	PROPN
ejpam-3498	101	36	)	)	PUNCT
ejpam-3498	101	37	=	=	SYM
ejpam-3498	102	1	ln	ln	ADJ
ejpam-3498	102	2	(	(	PUNCT
ejpam-3498	102	3	t	t	PROPN
ejpam-3498	102	4	τ	τ	PROPN
ejpam-3498	102	5	)	)	PUNCT
ejpam-3498	102	6	and	and	CCONJ
ejpam-3498	102	7	e(τ	e(τ	PROPN
ejpam-3498	102	8	,	,	PUNCT
ejpam-3498	102	9	t)(x	t)(x	PROPN
ejpam-3498	102	10	)	)	PUNCT
ejpam-3498	102	11	=	=	SYM
ejpam-3498	102	12	(	(	PUNCT
ejpam-3498	102	13	eij(τ	eij(τ	PROPN
ejpam-3498	102	14	,	,	PUNCT
ejpam-3498	102	15	t)(x	t)(x	PROPN
ejpam-3498	102	16	)	)	PUNCT
ejpam-3498	102	17	)	)	PUNCT
ejpam-3498	103	1	=	=	SYM
ejpam-3498	103	2	exp	exp	NOUN
ejpam-3498	103	3	[	[	PUNCT
ejpam-3498	103	4	ln	ln	X
ejpam-3498	103	5	τ	τ	PROPN
ejpam-3498	103	6	t	t	NOUN
ejpam-3498	103	7	a(x	a(x	PROPN
ejpam-3498	103	8	)	)	PUNCT
ejpam-3498	103	9	]	]	PUNCT
ejpam-3498	104	1	∈	∈	PROPN
ejpam-3498	104	2	l(y	l(y	PROPN
ejpam-3498	104	3	n	n	CCONJ
ejpam-3498	104	4	)	)	PUNCT
ejpam-3498	104	5	for	for	ADP
ejpam-3498	104	6	(	(	PUNCT
ejpam-3498	104	7	τ	τ	PROPN
ejpam-3498	104	8	,	,	PUNCT
ejpam-3498	104	9	t	t	PROPN
ejpam-3498	104	10	)	)	PUNCT
ejpam-3498	104	11	∈	∈	PROPN
ejpam-3498	104	12	∆	∆	PROPN
ejpam-3498	104	13	,	,	PUNCT
ejpam-3498	104	14	where	where	SCONJ
ejpam-3498	104	15	a(x	a(x	NOUN
ejpam-3498	104	16	)	)	PUNCT
ejpam-3498	104	17	=	=	SYM
ejpam-3498	104	18	(	(	PUNCT
ejpam-3498	104	19	aij(x	aij(x	PROPN
ejpam-3498	104	20	)	)	PUNCT
ejpam-3498	104	21	)	)	PUNCT
ejpam-3498	104	22	is	be	AUX
ejpam-3498	104	23	the	the	DET
ejpam-3498	104	24	matrix	matrix	NOUN
ejpam-3498	104	25	operaton	operaton	NOUN
ejpam-3498	104	26	as	as	ADP
ejpam-3498	104	27	in	in	ADP
ejpam-3498	104	28	(	(	PUNCT
ejpam-3498	104	29	a3	a3	NOUN
ejpam-3498	104	30	)	)	PUNCT
ejpam-3498	104	31	and	and	CCONJ
ejpam-3498	104	32	∆	∆	PROPN
ejpam-3498	104	33	=	=	PRON
ejpam-3498	104	34	{	{	PUNCT
ejpam-3498	104	35	(	(	PUNCT
ejpam-3498	104	36	τ	τ	PROPN
ejpam-3498	104	37	,	,	PUNCT
ejpam-3498	104	38	t	t	PROPN
ejpam-3498	104	39	)	)	PUNCT
ejpam-3498	104	40	:	:	PUNCT
ejpam-3498	104	41	0	0	NUM
ejpam-3498	105	1	=	=	SYM
ejpam-3498	105	2	τ	τ	X
ejpam-3498	105	3	<	<	X
ejpam-3498	105	4	t	t	X
ejpam-3498	105	5	≤	≤	X
ejpam-3498	105	6	t	t	NOUN
ejpam-3498	105	7	or	or	CCONJ
ejpam-3498	105	8	0	0	NUM
ejpam-3498	105	9	<	<	X
ejpam-3498	105	10	τ	τ	PROPN
ejpam-3498	105	11	≤	≤	X
ejpam-3498	105	12	t	t	PROPN
ejpam-3498	105	13	≤	≤	NUM
ejpam-3498	105	14	t	t	PROPN
ejpam-3498	105	15	}	}	PUNCT
ejpam-3498	105	16	.	.	PUNCT
ejpam-3498	106	1	lemma	lemma	PROPN
ejpam-3498	106	2	2	2	NUM
ejpam-3498	106	3	.	.	PUNCT
ejpam-3498	107	1	there	there	PRON
ejpam-3498	107	2	exists	exist	VERB
ejpam-3498	107	3	a	a	DET
ejpam-3498	107	4	positive	positive	ADJ
ejpam-3498	107	5	number	number	NOUN
ejpam-3498	107	6	b	b	NOUN
ejpam-3498	107	7	such	such	ADJ
ejpam-3498	107	8	that	that	PRON
ejpam-3498	107	9	for	for	ADP
ejpam-3498	107	10	every	every	DET
ejpam-3498	107	11	x0	x0	PROPN
ejpam-3498	107	12	∈	∈	PROPN
ejpam-3498	107	13	ω	ω	NOUN
ejpam-3498	107	14	there	there	PRON
ejpam-3498	107	15	are	be	VERB
ejpam-3498	107	16	positive	positive	ADJ
ejpam-3498	107	17	numbers	number	NOUN
ejpam-3498	107	18	s0(s0	s0(s0	VERB
ejpam-3498	107	19	<	<	X
ejpam-3498	107	20	s1	s1	NOUN
ejpam-3498	107	21	)	)	PUNCT
ejpam-3498	107	22	,	,	PUNCT
ejpam-3498	107	23	c0	c0	NOUN
ejpam-3498	107	24	and	and	CCONJ
ejpam-3498	107	25	an	an	DET
ejpam-3498	107	26	open	open	ADJ
ejpam-3498	107	27	neighborhood	neighborhood	NOUN
ejpam-3498	107	28	u	u	NOUN
ejpam-3498	107	29	⊂	⊂	PROPN
ejpam-3498	107	30	ω	ω	PROPN
ejpam-3498	107	31	of	of	ADP
ejpam-3498	107	32	x0	x0	PROPN
ejpam-3498	108	1	such	such	ADJ
ejpam-3498	108	2	that	that	SCONJ
ejpam-3498	108	3	e	e	PROPN
ejpam-3498	108	4	∈	∈	PROPN
ejpam-3498	108	5	c0(∆	c0(∆	PROPN
ejpam-3498	108	6	,	,	PUNCT
ejpam-3498	108	7	bs0(u	bs0(u	PROPN
ejpam-3498	108	8	,	,	PUNCT
ejpam-3498	108	9	l(y	l(y	PROPN
ejpam-3498	108	10	n	n	NOUN
ejpam-3498	108	11	)	)	PUNCT
ejpam-3498	108	12	)	)	PUNCT
ejpam-3498	108	13	)	)	PUNCT
ejpam-3498	108	14	,	,	PUNCT
ejpam-3498	108	15	‖e(τ	‖e(τ	NOUN
ejpam-3498	108	16	,	,	PUNCT
ejpam-3498	108	17	t)‖s0(u	t)‖s0(u	ADJ
ejpam-3498	108	18	)	)	PUNCT
ejpam-3498	108	19	≤	≤	NOUN
ejpam-3498	108	20	c0	c0	NOUN
ejpam-3498	108	21	(	(	PUNCT
ejpam-3498	108	22	τ	τ	PROPN
ejpam-3498	108	23	t	t	PROPN
ejpam-3498	108	24	)	)	PUNCT
ejpam-3498	108	25	b	b	PROPN
ejpam-3498	108	26	(	(	PUNCT
ejpam-3498	108	27	7	7	NUM
ejpam-3498	108	28	)	)	PUNCT
ejpam-3498	108	29	and	and	CCONJ
ejpam-3498	108	30	‖eij(τ	‖eij(τ	ADV
ejpam-3498	108	31	,	,	PUNCT
ejpam-3498	108	32	t)‖s0(u	t)‖s0(u	ADJ
ejpam-3498	108	33	)	)	PUNCT
ejpam-3498	108	34	≤	≤	NOUN
ejpam-3498	108	35	c0eρ(i	c0eρ(i	PROPN
ejpam-3498	108	36	,	,	PUNCT
ejpam-3498	108	37	j)(τ	j)(τ	PROPN
ejpam-3498	108	38	,	,	PUNCT
ejpam-3498	108	39	t	t	PROPN
ejpam-3498	108	40	)	)	PUNCT
ejpam-3498	108	41	,	,	PUNCT
ejpam-3498	108	42	(	(	PUNCT
ejpam-3498	108	43	8)	8)	NUM
ejpam-3498	108	44	where	where	SCONJ
ejpam-3498	108	45	eρ(i	eρ(i	NOUN
ejpam-3498	108	46	,	,	PUNCT
ejpam-3498	108	47	j)(τ	j)(τ	PROPN
ejpam-3498	108	48	,	,	PUNCT
ejpam-3498	108	49	t	t	PROPN
ejpam-3498	108	50	)	)	PUNCT
ejpam-3498	108	51	=	=	PUNCT
ejpam-3498	108	52	(	(	PUNCT
ejpam-3498	108	53	τ	τ	PROPN
ejpam-3498	108	54	t	t	PROPN
ejpam-3498	108	55	)	)	PUNCT
ejpam-3498	108	56	b	b	PROPN
ejpam-3498	109	1	ν(τ	ν(τ	PROPN
ejpam-3498	109	2	,	,	PUNCT
ejpam-3498	109	3	t)ρ(i	t)ρ(i	NOUN
ejpam-3498	109	4	,	,	PUNCT
ejpam-3498	109	5	j)−1	j)−1	NOUN
ejpam-3498	109	6	(	(	PUNCT
ejpam-3498	109	7	ρ(i	ρ(i	PROPN
ejpam-3498	109	8	,	,	PUNCT
ejpam-3498	109	9	j)−	j)−	PROPN
ejpam-3498	109	10	1	1	NUM
ejpam-3498	109	11	)	)	PUNCT
ejpam-3498	109	12	!	!	PUNCT
ejpam-3498	109	13	.	.	PUNCT
ejpam-3498	110	1	note	note	VERB
ejpam-3498	110	2	that	that	SCONJ
ejpam-3498	110	3	0	0	NUM
ejpam-3498	110	4	does	do	AUX
ejpam-3498	110	5	not	not	PART
ejpam-3498	110	6	belong	belong	VERB
ejpam-3498	110	7	to	to	ADP
ejpam-3498	110	8	the	the	DET
ejpam-3498	110	9	spectrum	spectrum	NOUN
ejpam-3498	110	10	of	of	ADP
ejpam-3498	110	11	a(x	a(x	NOUN
ejpam-3498	110	12	)	)	PUNCT
ejpam-3498	110	13	,	,	PUNCT
ejpam-3498	110	14	thus	thus	ADV
ejpam-3498	110	15	the	the	DET
ejpam-3498	110	16	map	map	NOUN
ejpam-3498	110	17	a	a	PRON
ejpam-3498	110	18	:	:	PUNCT
ejpam-3498	110	19	x	x	SYM
ejpam-3498	110	20	→	→	SYM
ejpam-3498	110	21	a(x)−1	a(x)−1	NOUN
ejpam-3498	110	22	is	be	AUX
ejpam-3498	110	23	well	well	ADV
ejpam-3498	110	24	-	-	PUNCT
ejpam-3498	110	25	defined	define	VERB
ejpam-3498	110	26	and	and	CCONJ
ejpam-3498	110	27	ultradifferentiable	ultradifferentiable	ADJ
ejpam-3498	110	28	with	with	ADP
ejpam-3498	110	29	respect	respect	NOUN
ejpam-3498	110	30	to	to	ADP
ejpam-3498	110	31	x	x	PRON
ejpam-3498	110	32	,	,	PUNCT
ejpam-3498	110	33	that	that	ADV
ejpam-3498	110	34	is	is	ADV
ejpam-3498	110	35	,	,	PUNCT
ejpam-3498	110	36	we	we	PRON
ejpam-3498	110	37	can	can	AUX
ejpam-3498	110	38	assume	assume	VERB
ejpam-3498	110	39	that	that	SCONJ
ejpam-3498	110	40	a	a	DET
ejpam-3498	110	41	∈	∈	PROPN
ejpam-3498	110	42	bs0(ω	bs0(ω	NOUN
ejpam-3498	110	43	,	,	PUNCT
ejpam-3498	110	44	l(y	l(y	PROPN
ejpam-3498	110	45	n	n	NOUN
ejpam-3498	110	46	)	)	PUNCT
ejpam-3498	110	47	)	)	PUNCT
ejpam-3498	110	48	,	,	PUNCT
ejpam-3498	110	49	for	for	ADP
ejpam-3498	110	50	some	some	DET
ejpam-3498	110	51	s0	s0	PROPN
ejpam-3498	110	52	>	>	X
ejpam-3498	111	1	0	0	X
ejpam-3498	111	2	.	.	PUNCT
ejpam-3498	112	1	lemma	lemma	PROPN
ejpam-3498	112	2	3	3	X
ejpam-3498	112	3	.	.	PUNCT
ejpam-3498	113	1	let	let	VERB
ejpam-3498	113	2	s	s	PRON
ejpam-3498	113	3	∈	∈	PROPN
ejpam-3498	113	4	(	(	PUNCT
ejpam-3498	113	5	0	0	NUM
ejpam-3498	113	6	,	,	PUNCT
ejpam-3498	113	7	s0	s0	PROPN
ejpam-3498	113	8	]	]	PUNCT
ejpam-3498	113	9	,	,	PUNCT
ejpam-3498	113	10	δ	δ	PROPN
ejpam-3498	113	11	∈	∈	PROPN
ejpam-3498	113	12	(	(	PUNCT
ejpam-3498	113	13	0	0	NUM
ejpam-3498	113	14	,	,	PUNCT
ejpam-3498	113	15	t	t	NOUN
ejpam-3498	113	16	]	]	PUNCT
ejpam-3498	113	17	and	and	CCONJ
ejpam-3498	113	18	v	v	ADP
ejpam-3498	113	19	∈	∈	PROPN
ejpam-3498	113	20	c0([0	c0([0	PROPN
ejpam-3498	113	21	,	,	PUNCT
ejpam-3498	113	22	δ	δ	PROPN
ejpam-3498	113	23	)	)	PUNCT
ejpam-3498	113	24	,	,	PUNCT
ejpam-3498	113	25	bs(u	bs(u	PROPN
ejpam-3498	113	26	,	,	PUNCT
ejpam-3498	113	27	y	y	PROPN
ejpam-3498	113	28	n	n	PROPN
ejpam-3498	113	29	)	)	PUNCT
ejpam-3498	113	30	)	)	PUNCT
ejpam-3498	113	31	.	.	PUNCT
ejpam-3498	114	1	then	then	ADV
ejpam-3498	114	2	u(0	u(0	PROPN
ejpam-3498	114	3	)	)	PUNCT
ejpam-3498	114	4	=	=	SYM
ejpam-3498	114	5	av(0	av(0	NOUN
ejpam-3498	114	6	)	)	PUNCT
ejpam-3498	114	7	and	and	CCONJ
ejpam-3498	114	8	u(t	u(t	NOUN
ejpam-3498	114	9	)	)	PUNCT
ejpam-3498	114	10	=	=	SYM
ejpam-3498	115	1	∫	∫	PROPN
ejpam-3498	115	2	t	t	NOUN
ejpam-3498	115	3	0	0	NUM
ejpam-3498	115	4	1	1	NUM
ejpam-3498	115	5	τ	τ	X
ejpam-3498	115	6	e(τ	e(τ	PROPN
ejpam-3498	115	7	,	,	PUNCT
ejpam-3498	115	8	t)v(τ)dτ	t)v(τ)dτ	NOUN
ejpam-3498	115	9	for	for	ADP
ejpam-3498	115	10	t	t	PROPN
ejpam-3498	115	11	∈	∈	PROPN
ejpam-3498	115	12	(	(	PUNCT
ejpam-3498	115	13	0	0	NUM
ejpam-3498	115	14	,	,	PUNCT
ejpam-3498	115	15	δ	δ	PROPN
ejpam-3498	115	16	)	)	PUNCT
ejpam-3498	115	17	,	,	PUNCT
ejpam-3498	115	18	if	if	SCONJ
ejpam-3498	115	19	and	and	CCONJ
ejpam-3498	115	20	only	only	ADV
ejpam-3498	116	1	if	if	SCONJ
ejpam-3498	116	2	u	u	PROPN
ejpam-3498	116	3	∈	∈	PROPN
ejpam-3498	116	4	c0([0	c0([0	PROPN
ejpam-3498	116	5	,	,	PUNCT
ejpam-3498	116	6	δ	δ	PROPN
ejpam-3498	116	7	)	)	PUNCT
ejpam-3498	116	8	,	,	PUNCT
ejpam-3498	116	9	bs(u	bs(u	PROPN
ejpam-3498	116	10	,	,	PUNCT
ejpam-3498	116	11	y	y	PROPN
ejpam-3498	116	12	n	n	PROPN
ejpam-3498	116	13	)	)	PUNCT
ejpam-3498	116	14	)	)	PUNCT
ejpam-3498	116	15	and	and	CCONJ
ejpam-3498	116	16	t	t	X
ejpam-3498	116	17	∂u	∂u	PROPN
ejpam-3498	116	18	∂t	∂t	PROPN
ejpam-3498	116	19	(	(	PUNCT
ejpam-3498	116	20	t	t	PROPN
ejpam-3498	116	21	)	)	PUNCT
ejpam-3498	116	22	+	+	NOUN
ejpam-3498	116	23	au(t	au(t	NUM
ejpam-3498	116	24	)	)	PUNCT
ejpam-3498	116	25	=	=	SYM
ejpam-3498	116	26	v(t	v(t	NOUN
ejpam-3498	116	27	)	)	PUNCT
ejpam-3498	116	28	for	for	ADP
ejpam-3498	116	29	t	t	PROPN
ejpam-3498	116	30	∈	∈	PROPN
ejpam-3498	116	31	(	(	PUNCT
ejpam-3498	116	32	0	0	NUM
ejpam-3498	116	33	,	,	PUNCT
ejpam-3498	116	34	δ	δ	PROPN
ejpam-3498	116	35	)	)	PUNCT
ejpam-3498	116	36	.	.	PUNCT
ejpam-3498	117	1	e.	e.	PROPN
ejpam-3498	117	2	y.	y.	PROPN
ejpam-3498	117	3	guerrero	guerrero	PROPN
ejpam-3498	117	4	/	/	SYM
ejpam-3498	117	5	eur	eur	PROPN
ejpam-3498	117	6	.	.	PUNCT
ejpam-3498	118	1	j.	j.	PROPN
ejpam-3498	118	2	pure	pure	PROPN
ejpam-3498	118	3	appl	appl	PROPN
ejpam-3498	118	4	.	.	PROPN
ejpam-3498	118	5	math	math	PROPN
ejpam-3498	118	6	,	,	PUNCT
ejpam-3498	118	7	12	12	NUM
ejpam-3498	118	8	(	(	PUNCT
ejpam-3498	118	9	3	3	NUM
ejpam-3498	118	10	)	)	PUNCT
ejpam-3498	118	11	(	(	PUNCT
ejpam-3498	118	12	2019	2019	NUM
ejpam-3498	118	13	)	)	PUNCT
ejpam-3498	118	14	,	,	PUNCT
ejpam-3498	118	15	1297	1297	NUM
ejpam-3498	118	16	-	-	SYM
ejpam-3498	118	17	1314	1314	NUM
ejpam-3498	118	18	1302	1302	NUM
ejpam-3498	118	19	we	we	PRON
ejpam-3498	118	20	write	write	VERB
ejpam-3498	118	21	,	,	PUNCT
ejpam-3498	118	22	for	for	ADP
ejpam-3498	118	23	t	t	PROPN
ejpam-3498	118	24	>	>	X
ejpam-3498	118	25	0	0	NUM
ejpam-3498	118	26	,	,	PUNCT
ejpam-3498	118	27	h[h](t	h[h](t	ADJ
ejpam-3498	118	28	)	)	PUNCT
ejpam-3498	118	29	=	=	SYM
ejpam-3498	119	1	∫	∫	PROPN
ejpam-3498	119	2	t	t	NOUN
ejpam-3498	119	3	0	0	NUM
ejpam-3498	120	1	τ	τ	X
ejpam-3498	120	2	b−1	b−1	PROPN
ejpam-3498	120	3	tb	tb	ADP
ejpam-3498	120	4	h(τ)dτ	h(τ)dτ	PROPN
ejpam-3498	120	5	.	.	PROPN
ejpam-3498	120	6	note	note	VERB
ejpam-3498	120	7	that	that	SCONJ
ejpam-3498	120	8	h[h](0	h[h](0	NOUN
ejpam-3498	121	1	)	)	PUNCT
ejpam-3498	121	2	=	=	SYM
ejpam-3498	121	3	h(0)/b	h(0)/b	PROPN
ejpam-3498	121	4	.	.	PUNCT
ejpam-3498	122	1	we	we	PRON
ejpam-3498	122	2	may	may	AUX
ejpam-3498	122	3	assume	assume	VERB
ejpam-3498	122	4	b	b	NUM
ejpam-3498	122	5	≤	≤	ADV
ejpam-3498	122	6	1	1	NUM
ejpam-3498	122	7	without	without	ADP
ejpam-3498	122	8	loss	loss	NOUN
ejpam-3498	122	9	of	of	ADP
ejpam-3498	122	10	generality	generality	NOUN
ejpam-3498	122	11	.	.	PUNCT
ejpam-3498	123	1	note	note	VERB
ejpam-3498	123	2	that	that	SCONJ
ejpam-3498	123	3	h[1](t	h[1](t	ADJ
ejpam-3498	123	4	)	)	PUNCT
ejpam-3498	123	5	=	=	SYM
ejpam-3498	123	6	1	1	X
ejpam-3498	123	7	/	/	SYM
ejpam-3498	123	8	b.	b.	PROPN
ejpam-3498	123	9	lemma	lemma	PROPN
ejpam-3498	123	10	4	4	X
ejpam-3498	123	11	.	.	PUNCT
ejpam-3498	124	1	let	let	VERB
ejpam-3498	124	2	δ	δ	PROPN
ejpam-3498	124	3	∈	∈	PROPN
ejpam-3498	124	4	(	(	PUNCT
ejpam-3498	124	5	0	0	NUM
ejpam-3498	124	6	,	,	PUNCT
ejpam-3498	124	7	t	t	X
ejpam-3498	124	8	]	]	PUNCT
ejpam-3498	124	9	,	,	PUNCT
ejpam-3498	124	10	a	a	DET
ejpam-3498	124	11	>	>	X
ejpam-3498	124	12	0	0	NUM
ejpam-3498	124	13	,	,	PUNCT
ejpam-3498	124	14	β	β	X
ejpam-3498	124	15	≥	≥	NOUN
ejpam-3498	124	16	0and	0and	PROPN
ejpam-3498	124	17	γ	γ	X
ejpam-3498	124	18	≥	≥	PROPN
ejpam-3498	124	19	1	1	NUM
ejpam-3498	124	20	,	,	PUNCT
ejpam-3498	124	21	and	and	CCONJ
ejpam-3498	124	22	let	let	VERB
ejpam-3498	124	23	m	m	VERB
ejpam-3498	124	24	=	=	SYM
ejpam-3498	124	25	0	0	NUM
ejpam-3498	124	26	or	or	CCONJ
ejpam-3498	124	27	m	m	VERB
ejpam-3498	124	28	=	=	NOUN
ejpam-3498	124	29	1	1	X
ejpam-3498	124	30	.	.	PUNCT
ejpam-3498	125	1	if	if	SCONJ
ejpam-3498	125	2	α	α	PRON
ejpam-3498	125	3	≥	≥	X
ejpam-3498	125	4	κm	κm	PROPN
ejpam-3498	125	5	,	,	PUNCT
ejpam-3498	125	6	ω(t	ω(t	NOUN
ejpam-3498	125	7	)	)	PUNCT
ejpam-3498	125	8	<	<	X
ejpam-3498	125	9	a	a	PRON
ejpam-3498	125	10	and	and	CCONJ
ejpam-3498	125	11	h(t	h(t	NUM
ejpam-3498	125	12	)	)	PUNCT
ejpam-3498	125	13	≤	≤	NOUN
ejpam-3498	125	14	µ(t)αω(t)β(1−	µ(t)αω(t)β(1−	ADP
ejpam-3498	125	15	ω(t)/a))−γ	ω(t)/a))−γ	X
ejpam-3498	125	16	for	for	ADP
ejpam-3498	125	17	t	t	PROPN
ejpam-3498	125	18	∈	∈	PROPN
ejpam-3498	126	1	[	[	X
ejpam-3498	126	2	0	0	NUM
ejpam-3498	126	3	,	,	PUNCT
ejpam-3498	126	4	δ	δ	PROPN
ejpam-3498	126	5	)	)	PUNCT
ejpam-3498	126	6	,	,	PUNCT
ejpam-3498	126	7	then	then	ADV
ejpam-3498	126	8	h[h](t	h[h](t	NOUN
ejpam-3498	126	9	)	)	PUNCT
ejpam-3498	126	10	≤	≤	NUM
ejpam-3498	126	11	cγamµ(t)α−κmω(t)β+cm	cγamµ(t)α−κmω(t)β+cm	NOUN
ejpam-3498	126	12	(	(	PUNCT
ejpam-3498	126	13	1−	1−	NUM
ejpam-3498	126	14	ω(t	ω(t	NOUN
ejpam-3498	126	15	)	)	PUNCT
ejpam-3498	126	16	a	a	DET
ejpam-3498	126	17	)	)	PUNCT
ejpam-3498	126	18	−max{1,γ−m	−max{1,γ−m	NOUN
ejpam-3498	126	19	}	}	PUNCT
ejpam-3498	126	20	for	for	ADP
ejpam-3498	126	21	t	t	PROPN
ejpam-3498	126	22	∈	∈	PROPN
ejpam-3498	127	1	[	[	X
ejpam-3498	127	2	0	0	NUM
ejpam-3498	127	3	,	,	PUNCT
ejpam-3498	127	4	δ	δ	PROPN
ejpam-3498	127	5	)	)	PUNCT
ejpam-3498	127	6	,	,	PUNCT
ejpam-3498	127	7	where	where	SCONJ
ejpam-3498	127	8	cγ	cγ	NOUN
ejpam-3498	127	9	=	=	SYM
ejpam-3498	127	10	max	max	PROPN
ejpam-3498	127	11	{	{	PUNCT
ejpam-3498	127	12	1	1	NUM
ejpam-3498	127	13	γ	γ	NOUN
ejpam-3498	127	14	−	−	PROPN
ejpam-3498	127	15	1	1	NUM
ejpam-3498	127	16	,	,	PUNCT
ejpam-3498	127	17	1	1	NUM
ejpam-3498	127	18	b	b	X
ejpam-3498	127	19	}	}	PUNCT
ejpam-3498	127	20	if	if	SCONJ
ejpam-3498	127	21	γ	γ	X
ejpam-3498	127	22	>	>	X
ejpam-3498	127	23	1	1	NUM
ejpam-3498	127	24	and	and	CCONJ
ejpam-3498	127	25	cγ	cγ	X
ejpam-3498	127	26	=	=	SYM
ejpam-3498	127	27	1	1	NUM
ejpam-3498	127	28	b	b	NOUN
ejpam-3498	127	29	if	if	SCONJ
ejpam-3498	127	30	γ	γ	X
ejpam-3498	127	31	=	=	SYM
ejpam-3498	127	32	1	1	X
ejpam-3498	127	33	.	.	PUNCT
ejpam-3498	127	34	lemma	lemma	PROPN
ejpam-3498	127	35	5	5	X
ejpam-3498	127	36	.	.	PUNCT
ejpam-3498	127	37	let	let	VERB
ejpam-3498	127	38	h	h	NOUN
ejpam-3498	127	39	∈	∈	PROPN
ejpam-3498	127	40	c0([0	c0([0	PROPN
ejpam-3498	127	41	,	,	PUNCT
ejpam-3498	127	42	δ),r	δ),r	PROPN
ejpam-3498	127	43	)	)	PUNCT
ejpam-3498	127	44	,	,	PUNCT
ejpam-3498	127	45	δ	δ	PROPN
ejpam-3498	127	46	∈	∈	PROPN
ejpam-3498	127	47	(	(	PUNCT
ejpam-3498	127	48	0	0	NUM
ejpam-3498	127	49	,	,	PUNCT
ejpam-3498	127	50	t	t	X
ejpam-3498	127	51	]	]	PUNCT
ejpam-3498	127	52	.	.	PUNCT
ejpam-3498	128	1	then	then	ADV
ejpam-3498	128	2	it	it	PRON
ejpam-3498	128	3	holds	hold	VERB
ejpam-3498	128	4	that∫	that∫	PROPN
ejpam-3498	128	5	t	t	NOUN
ejpam-3498	128	6	0	0	NUM
ejpam-3498	128	7	1	1	NUM
ejpam-3498	128	8	τ	τ	PROPN
ejpam-3498	128	9	ep(τ	ep(τ	PROPN
ejpam-3498	128	10	,	,	PUNCT
ejpam-3498	128	11	t)h(τ)dτ	t)h(τ)dτ	NOUN
ejpam-3498	128	12	=	=	SYM
ejpam-3498	128	13	hp[h](t	hp[h](t	PROPN
ejpam-3498	128	14	)	)	PUNCT
ejpam-3498	128	15	for	for	ADP
ejpam-3498	128	16	t	t	PROPN
ejpam-3498	128	17	∈	∈	PROPN
ejpam-3498	128	18	(	(	PUNCT
ejpam-3498	128	19	0	0	NUM
ejpam-3498	128	20	,	,	PUNCT
ejpam-3498	128	21	δ	δ	PROPN
ejpam-3498	128	22	)	)	PUNCT
ejpam-3498	128	23	and	and	CCONJ
ejpam-3498	128	24	p	p	NOUN
ejpam-3498	128	25	=	=	PROPN
ejpam-3498	128	26	1	1	NUM
ejpam-3498	128	27	,	,	PUNCT
ejpam-3498	128	28	2	2	NUM
ejpam-3498	128	29	,	,	PUNCT
ejpam-3498	128	30	.	.	PUNCT
ejpam-3498	128	31	.	.	PUNCT
ejpam-3498	128	32	.	.	PUNCT
ejpam-3498	128	33	.	.	PUNCT
ejpam-3498	129	1	3	3	X
ejpam-3498	129	2	.	.	X
ejpam-3498	129	3	existence	existence	NOUN
ejpam-3498	129	4	and	and	CCONJ
ejpam-3498	129	5	uniqueness	uniqueness	NOUN
ejpam-3498	129	6	theorem	theorem	VERB
ejpam-3498	129	7	we	we	PRON
ejpam-3498	129	8	first	first	ADV
ejpam-3498	129	9	state	state	VERB
ejpam-3498	129	10	our	our	PRON
ejpam-3498	129	11	main	main	ADJ
ejpam-3498	129	12	theorem	theorem	NOUN
ejpam-3498	129	13	and	and	CCONJ
ejpam-3498	129	14	then	then	ADV
ejpam-3498	129	15	prove	prove	VERB
ejpam-3498	129	16	the	the	DET
ejpam-3498	129	17	existence	existence	NOUN
ejpam-3498	129	18	and	and	CCONJ
ejpam-3498	129	19	uniqueness	uniqueness	ADJ
ejpam-3498	129	20	parts	part	NOUN
ejpam-3498	129	21	in	in	ADP
ejpam-3498	129	22	two	two	NUM
ejpam-3498	129	23	sections	section	NOUN
ejpam-3498	129	24	.	.	PUNCT
ejpam-3498	130	1	theorem	theorem	ADJ
ejpam-3498	130	2	4	4	NUM
ejpam-3498	130	3	(	(	PUNCT
ejpam-3498	130	4	main	main	ADJ
ejpam-3498	130	5	theorem	theorem	NOUN
ejpam-3498	130	6	)	)	PUNCT
ejpam-3498	130	7	.	.	PUNCT
ejpam-3498	131	1	let	let	VERB
ejpam-3498	131	2	c1	c1	PROPN
ejpam-3498	131	3	,	,	PUNCT
ejpam-3498	131	4	c2	c2	PROPN
ejpam-3498	131	5	,	,	PUNCT
ejpam-3498	131	6	anda1	anda1	NOUN
ejpam-3498	131	7	−	−	ADP
ejpam-3498	131	8	a4	a4	NOUN
ejpam-3498	131	9	hold	hold	VERB
ejpam-3498	131	10	and	and	CCONJ
ejpam-3498	131	11	α	α	PRON
ejpam-3498	131	12	∈	∈	PROPN
ejpam-3498	131	13	(	(	PUNCT
ejpam-3498	131	14	0	0	NUM
ejpam-3498	131	15	,	,	PUNCT
ejpam-3498	131	16	1	1	NUM
ejpam-3498	131	17	]	]	PUNCT
ejpam-3498	131	18	.	.	PUNCT
ejpam-3498	132	1	for	for	ADP
ejpam-3498	132	2	every	every	DET
ejpam-3498	132	3	x0	x0	PROPN
ejpam-3498	132	4	∈	∈	PROPN
ejpam-3498	132	5	ω	ω	PROPN
ejpam-3498	132	6	,	,	PUNCT
ejpam-3498	132	7	there	there	PRON
ejpam-3498	132	8	exists	exist	VERB
ejpam-3498	132	9	a	a	DET
ejpam-3498	132	10	positive	positive	ADJ
ejpam-3498	132	11	number	number	NOUN
ejpam-3498	132	12	r	r	NOUN
ejpam-3498	132	13	small	small	ADJ
ejpam-3498	132	14	enough	enough	ADV
ejpam-3498	132	15	and	and	CCONJ
ejpam-3498	132	16	a	a	DET
ejpam-3498	132	17	neighborhood	neighborhood	NOUN
ejpam-3498	132	18	u	u	NOUN
ejpam-3498	132	19	⊂	⊂	PROPN
ejpam-3498	132	20	ω	ω	NUM
ejpam-3498	132	21	such	such	ADJ
ejpam-3498	132	22	that	that	SCONJ
ejpam-3498	132	23	if	if	SCONJ
ejpam-3498	132	24	the	the	DET
ejpam-3498	132	25	map	map	NOUN
ejpam-3498	132	26	gi	gi	INTJ
ejpam-3498	132	27	:	:	PUNCT
ejpam-3498	132	28	t→	t→	X
ejpam-3498	132	29	(	(	PUNCT
ejpam-3498	132	30	x	x	SYM
ejpam-3498	132	31	7→	7→	NUM
ejpam-3498	132	32	gi(t	gi(t	NOUN
ejpam-3498	132	33	,	,	PUNCT
ejpam-3498	132	34	x	x	NOUN
ejpam-3498	132	35	)	)	PUNCT
ejpam-3498	132	36	)	)	PUNCT
ejpam-3498	132	37	belongs	belong	VERB
ejpam-3498	132	38	to	to	ADP
ejpam-3498	132	39	c0([0	c0([0	PROPN
ejpam-3498	132	40	,	,	PUNCT
ejpam-3498	132	41	t	t	X
ejpam-3498	132	42	]	]	PUNCT
ejpam-3498	132	43	,	,	PUNCT
ejpam-3498	132	44	bs1(ω	bs1(ω	PROPN
ejpam-3498	132	45	,	,	PUNCT
ejpam-3498	132	46	y	y	PROPN
ejpam-3498	132	47	)	)	PUNCT
ejpam-3498	132	48	for	for	ADP
ejpam-3498	132	49	some	some	DET
ejpam-3498	132	50	s1	s1	PROPN
ejpam-3498	132	51	>	>	X
ejpam-3498	132	52	0	0	PUNCT
ejpam-3498	132	53	with	with	ADP
ejpam-3498	132	54	‖gi(t	‖gi(t	PROPN
ejpam-3498	132	55	,	,	PUNCT
ejpam-3498	132	56	x)‖s1(ω	x)‖s1(ω	NUM
ejpam-3498	132	57	)	)	PUNCT
ejpam-3498	132	58	≤	≤	NUM
ejpam-3498	132	59	crµ(t)α	crµ(t)α	NOUN
ejpam-3498	132	60	,	,	PUNCT
ejpam-3498	132	61	(	(	PUNCT
ejpam-3498	132	62	t	t	PROPN
ejpam-3498	132	63	,	,	PUNCT
ejpam-3498	132	64	x	x	NOUN
ejpam-3498	132	65	)	)	PUNCT
ejpam-3498	132	66	∈	∈	PROPN
ejpam-3498	133	1	[	[	X
ejpam-3498	133	2	0	0	NUM
ejpam-3498	133	3	,	,	PUNCT
ejpam-3498	133	4	t	t	X
ejpam-3498	133	5	]	]	X
ejpam-3498	133	6	×	×	PROPN
ejpam-3498	133	7	ω	ω	PROPN
ejpam-3498	133	8	,	,	PUNCT
ejpam-3498	133	9	1	1	NUM
ejpam-3498	133	10	≤	≤	NUM
ejpam-3498	133	11	i	i	PRON
ejpam-3498	133	12	≤	≤	ADJ
ejpam-3498	133	13	n	n	CCONJ
ejpam-3498	133	14	for	for	ADP
ejpam-3498	133	15	some	some	DET
ejpam-3498	133	16	constant	constant	ADJ
ejpam-3498	133	17	c	c	NOUN
ejpam-3498	133	18	>	>	X
ejpam-3498	133	19	0	0	PROPN
ejpam-3498	133	20	,	,	PUNCT
ejpam-3498	133	21	then	then	ADV
ejpam-3498	133	22	(	(	PUNCT
ejpam-3498	133	23	1	1	X
ejpam-3498	133	24	)	)	PUNCT
ejpam-3498	133	25	has	have	VERB
ejpam-3498	133	26	a	a	DET
ejpam-3498	133	27	unique	unique	ADJ
ejpam-3498	133	28	solution	solution	NOUN
ejpam-3498	133	29	u	u	NOUN
ejpam-3498	133	30	=	=	PUNCT
ejpam-3498	133	31	(	(	PUNCT
ejpam-3498	133	32	u1	u1	PROPN
ejpam-3498	133	33	,	,	PUNCT
ejpam-3498	133	34	...	...	PUNCT
ejpam-3498	133	35	,	,	PUNCT
ejpam-3498	133	36	un	un	PROPN
ejpam-3498	133	37	)	)	PUNCT
ejpam-3498	133	38	in	in	ADP
ejpam-3498	133	39	[	[	X
ejpam-3498	133	40	0	0	NUM
ejpam-3498	133	41	,	,	PUNCT
ejpam-3498	133	42	t0)×u	t0)×u	VERB
ejpam-3498	133	43	for	for	ADP
ejpam-3498	133	44	a	a	DET
ejpam-3498	133	45	positive	positive	ADJ
ejpam-3498	133	46	number	number	NOUN
ejpam-3498	133	47	t0	t0	PROPN
ejpam-3498	133	48	≤	≤	PROPN
ejpam-3498	133	49	t	t	PROPN
ejpam-3498	133	50	and	and	CCONJ
ejpam-3498	133	51	a	a	DET
ejpam-3498	133	52	neighborhood	neighborhood	NOUN
ejpam-3498	133	53	u	u	NOUN
ejpam-3498	133	54	⊂	⊂	PROPN
ejpam-3498	133	55	ω	ω	PROPN
ejpam-3498	133	56	of	of	ADP
ejpam-3498	133	57	x0	x0	PROPN
ejpam-3498	133	58	,	,	PUNCT
ejpam-3498	133	59	satisfying	satisfy	VERB
ejpam-3498	133	60	uj	uj	PROPN
ejpam-3498	133	61	∈	∈	PROPN
ejpam-3498	133	62	c0([0	c0([0	PROPN
ejpam-3498	133	63	,	,	PUNCT
ejpam-3498	133	64	t0	t0	PROPN
ejpam-3498	133	65	)	)	PUNCT
ejpam-3498	133	66	,	,	PUNCT
ejpam-3498	133	67	bs(u	bs(u	X
ejpam-3498	133	68	,	,	PUNCT
ejpam-3498	133	69	y	y	NOUN
ejpam-3498	133	70	)	)	PUNCT
ejpam-3498	133	71	)	)	PUNCT
ejpam-3498	133	72	∩	∩	ADJ
ejpam-3498	133	73	c1((0	c1((0	PROPN
ejpam-3498	133	74	,	,	PUNCT
ejpam-3498	133	75	t0	t0	PROPN
ejpam-3498	133	76	)	)	PUNCT
ejpam-3498	133	77	,	,	PUNCT
ejpam-3498	133	78	bs(u	bs(u	X
ejpam-3498	133	79	,	,	PUNCT
ejpam-3498	133	80	y	y	PROPN
ejpam-3498	133	81	)	)	PUNCT
ejpam-3498	133	82	)	)	PUNCT
ejpam-3498	133	83	,	,	PUNCT
ejpam-3498	133	84	1	1	NUM
ejpam-3498	133	85	≤	≤	NUM
ejpam-3498	133	86	j	j	PROPN
ejpam-3498	133	87	≤	≤	PROPN
ejpam-3498	133	88	n	n	CCONJ
ejpam-3498	133	89	and	and	CCONJ
ejpam-3498	133	90	‖uj(t	‖uj(t	NUM
ejpam-3498	133	91	,	,	PUNCT
ejpam-3498	133	92	x)‖s(u	x)‖s(u	X
ejpam-3498	133	93	)	)	PUNCT
ejpam-3498	133	94	≤	≤	NOUN
ejpam-3498	133	95	rµ(t)α	rµ(t)α	PUNCT
ejpam-3498	133	96	and	and	CCONJ
ejpam-3498	133	97	‖((µ0d)kuj(t	‖((µ0d)kuj(t	PROPN
ejpam-3498	133	98	,	,	PUNCT
ejpam-3498	133	99	x))(j	x))(j	PROPN
ejpam-3498	133	100	,	,	PUNCT
ejpam-3498	133	101	k)∈n	k)∈n	X
ejpam-3498	133	102	(	(	PUNCT
ejpam-3498	133	103	i)‖s(u	i)‖s(u	NOUN
ejpam-3498	133	104	)	)	PUNCT
ejpam-3498	133	105	≤	≤	NOUN
ejpam-3498	133	106	rµ(t)α	rµ(t)α	NOUN
ejpam-3498	133	107	,	,	PUNCT
ejpam-3498	133	108	for	for	ADP
ejpam-3498	133	109	all	all	DET
ejpam-3498	133	110	t	t	NOUN
ejpam-3498	133	111	∈	∈	PROPN
ejpam-3498	134	1	[	[	X
ejpam-3498	134	2	0	0	NUM
ejpam-3498	134	3	,	,	PUNCT
ejpam-3498	134	4	δ	δ	PROPN
ejpam-3498	134	5	)	)	PUNCT
ejpam-3498	134	6	and	and	CCONJ
ejpam-3498	134	7	some	some	PRON
ejpam-3498	134	8	s	s	VERB
ejpam-3498	134	9	>	>	X
ejpam-3498	134	10	0	0	NUM
ejpam-3498	134	11	.	.	PUNCT
ejpam-3498	135	1	e.	e.	PROPN
ejpam-3498	135	2	y.	y.	PROPN
ejpam-3498	135	3	guerrero	guerrero	PROPN
ejpam-3498	135	4	/	/	SYM
ejpam-3498	135	5	eur	eur	PROPN
ejpam-3498	135	6	.	.	PUNCT
ejpam-3498	136	1	j.	j.	PROPN
ejpam-3498	136	2	pure	pure	PROPN
ejpam-3498	136	3	appl	appl	PROPN
ejpam-3498	136	4	.	.	PROPN
ejpam-3498	136	5	math	math	PROPN
ejpam-3498	136	6	,	,	PUNCT
ejpam-3498	136	7	12	12	NUM
ejpam-3498	136	8	(	(	PUNCT
ejpam-3498	136	9	3	3	NUM
ejpam-3498	136	10	)	)	PUNCT
ejpam-3498	136	11	(	(	PUNCT
ejpam-3498	136	12	2019	2019	NUM
ejpam-3498	136	13	)	)	PUNCT
ejpam-3498	136	14	,	,	PUNCT
ejpam-3498	136	15	1297	1297	NUM
ejpam-3498	136	16	-	-	SYM
ejpam-3498	136	17	1314	1314	NUM
ejpam-3498	136	18	1303	1303	NUM
ejpam-3498	136	19	3.1	3.1	NUM
ejpam-3498	136	20	.	.	PUNCT
ejpam-3498	137	1	existence	existence	NOUN
ejpam-3498	137	2	let	let	VERB
ejpam-3498	137	3	α	α	PRON
ejpam-3498	137	4	∈	∈	PROPN
ejpam-3498	138	1	[	[	X
ejpam-3498	138	2	0	0	NUM
ejpam-3498	138	3	,	,	PUNCT
ejpam-3498	138	4	1	1	NUM
ejpam-3498	138	5	]	]	PUNCT
ejpam-3498	138	6	,	,	PUNCT
ejpam-3498	138	7	µ(t	µ(t	ADJ
ejpam-3498	138	8	)	)	PUNCT
ejpam-3498	138	9	be	be	VERB
ejpam-3498	138	10	a	a	DET
ejpam-3498	138	11	weight	weight	NOUN
ejpam-3498	138	12	function	function	NOUN
ejpam-3498	138	13	,	,	PUNCT
ejpam-3498	138	14	and	and	CCONJ
ejpam-3498	139	1	x0	x0	PROPN
ejpam-3498	139	2	∈	∈	PROPN
ejpam-3498	139	3	ω	ω	X
ejpam-3498	139	4	.	.	PUNCT
ejpam-3498	140	1	let	let	VERB
ejpam-3498	140	2	u	u	PRON
ejpam-3498	140	3	be	be	AUX
ejpam-3498	140	4	the	the	DET
ejpam-3498	140	5	set	set	NOUN
ejpam-3498	140	6	obtained	obtain	VERB
ejpam-3498	140	7	by	by	ADP
ejpam-3498	140	8	lemma	lemma	PROPN
ejpam-3498	140	9	2	2	NUM
ejpam-3498	140	10	.	.	PUNCT
ejpam-3498	141	1	for	for	ADP
ejpam-3498	141	2	brevity	brevity	NOUN
ejpam-3498	141	3	,	,	PUNCT
ejpam-3498	141	4	we	we	PRON
ejpam-3498	141	5	abbreviate	abbreviate	VERB
ejpam-3498	141	6	‖	‖	PROPN
ejpam-3498	141	7	·	·	PUNCT
ejpam-3498	141	8	‖s(u	‖s(u	X
ejpam-3498	141	9	)	)	PUNCT
ejpam-3498	141	10	to	to	ADP
ejpam-3498	141	11	‖	‖	PROPN
ejpam-3498	141	12	·	·	PUNCT
ejpam-3498	142	1	‖s	‖s	ADV
ejpam-3498	142	2	,	,	PUNCT
ejpam-3498	142	3	and	and	CCONJ
ejpam-3498	142	4	(	(	PUNCT
ejpam-3498	142	5	t	t	PROPN
ejpam-3498	142	6	,	,	PUNCT
ejpam-3498	142	7	x	x	NOUN
ejpam-3498	142	8	)	)	PUNCT
ejpam-3498	142	9	to	to	ADP
ejpam-3498	142	10	(	(	PUNCT
ejpam-3498	142	11	t	t	PROPN
ejpam-3498	142	12	)	)	PUNCT
ejpam-3498	142	13	if	if	SCONJ
ejpam-3498	142	14	t	t	PROPN
ejpam-3498	142	15	is	be	AUX
ejpam-3498	142	16	the	the	DET
ejpam-3498	142	17	only	only	ADJ
ejpam-3498	142	18	variable	variable	NOUN
ejpam-3498	142	19	needed	need	VERB
ejpam-3498	142	20	in	in	ADP
ejpam-3498	142	21	our	our	PRON
ejpam-3498	142	22	analysis	analysis	NOUN
ejpam-3498	142	23	.	.	PUNCT
ejpam-3498	143	1	we	we	PRON
ejpam-3498	143	2	let	let	VERB
ejpam-3498	143	3	wjk(t	wjk(t	PROPN
ejpam-3498	143	4	,	,	PUNCT
ejpam-3498	143	5	x	x	X
ejpam-3498	143	6	)	)	PUNCT
ejpam-3498	143	7	=	=	SYM
ejpam-3498	143	8	(	(	PUNCT
ejpam-3498	143	9	(	(	PUNCT
ejpam-3498	143	10	µ0d)kuj(t	µ0d)kuj(t	NOUN
ejpam-3498	143	11	,	,	PUNCT
ejpam-3498	143	12	x))(j	x))(j	PROPN
ejpam-3498	143	13	,	,	PUNCT
ejpam-3498	143	14	k	k	NOUN
ejpam-3498	143	15	)	)	PUNCT
ejpam-3498	143	16	then	then	ADV
ejpam-3498	143	17	fi(u	fi(u	NOUN
ejpam-3498	143	18	,	,	PUNCT
ejpam-3498	143	19	w)(t	w)(t	PROPN
ejpam-3498	143	20	,	,	PUNCT
ejpam-3498	143	21	x	x	NOUN
ejpam-3498	143	22	)	)	PUNCT
ejpam-3498	143	23	=	=	SYM
ejpam-3498	143	24	n∑	n∑	PROPN
ejpam-3498	143	25	j=1	j=1	PROPN
ejpam-3498	143	26	aij(t)uj(t	aij(t)uj(t	PROPN
ejpam-3498	143	27	,	,	PUNCT
ejpam-3498	143	28	x	x	X
ejpam-3498	143	29	)	)	PUNCT
ejpam-3498	143	30	+	+	CCONJ
ejpam-3498	143	31	∑	∑	PROPN
ejpam-3498	143	32	(	(	PUNCT
ejpam-3498	143	33	j	j	PROPN
ejpam-3498	143	34	,	,	PUNCT
ejpam-3498	143	35	k)∈n	k)∈n	X
ejpam-3498	143	36	(	(	PUNCT
ejpam-3498	143	37	i	i	NOUN
ejpam-3498	143	38	)	)	PUNCT
ejpam-3498	143	39	bjkw(j	bjkw(j	PROPN
ejpam-3498	143	40	,	,	PUNCT
ejpam-3498	143	41	k)(t	k)(t	PROPN
ejpam-3498	143	42	,	,	PUNCT
ejpam-3498	143	43	x	x	NOUN
ejpam-3498	143	44	)	)	PUNCT
ejpam-3498	143	45	,	,	PUNCT
ejpam-3498	143	46	and	and	CCONJ
ejpam-3498	143	47	write	write	VERB
ejpam-3498	143	48	fi(u	fi(u	NOUN
ejpam-3498	143	49	,	,	PUNCT
ejpam-3498	143	50	w)(t	w)(t	PROPN
ejpam-3498	143	51	,	,	PUNCT
ejpam-3498	143	52	x	x	NOUN
ejpam-3498	143	53	)	)	PUNCT
ejpam-3498	143	54	=	=	SYM
ejpam-3498	143	55	fi(t	fi(t	NOUN
ejpam-3498	143	56	,	,	PUNCT
ejpam-3498	143	57	x	x	X
ejpam-3498	143	58	,	,	PUNCT
ejpam-3498	143	59	uj(t	uj(t	PROPN
ejpam-3498	143	60	,	,	PUNCT
ejpam-3498	143	61	x	x	X
ejpam-3498	143	62	)	)	PUNCT
ejpam-3498	143	63	,	,	PUNCT
ejpam-3498	143	64	wjk(t	wjk(t	PROPN
ejpam-3498	143	65	,	,	PUNCT
ejpam-3498	143	66	x	x	NOUN
ejpam-3498	143	67	)	)	PUNCT
ejpam-3498	143	68	)	)	PUNCT
ejpam-3498	143	69	for	for	ADP
ejpam-3498	143	70	u	u	NOUN
ejpam-3498	143	71	=	=	SYM
ejpam-3498	143	72	(	(	PUNCT
ejpam-3498	143	73	uj)1≤j≤n	uj)1≤j≤n	PROPN
ejpam-3498	143	74	and	and	CCONJ
ejpam-3498	143	75	w	w	NOUN
ejpam-3498	143	76	=	=	PUNCT
ejpam-3498	143	77	(	(	PUNCT
ejpam-3498	143	78	wjk)(j	wjk)(j	X
ejpam-3498	143	79	,	,	PUNCT
ejpam-3498	143	80	k)∈n	k)∈n	X
ejpam-3498	143	81	(	(	PUNCT
ejpam-3498	143	82	i	i	NOUN
ejpam-3498	143	83	)	)	PUNCT
ejpam-3498	143	84	,	,	PUNCT
ejpam-3498	143	85	where	where	SCONJ
ejpam-3498	143	86	the	the	DET
ejpam-3498	143	87	values	value	NOUN
ejpam-3498	143	88	of	of	ADP
ejpam-3498	143	89	uj	uj	PROPN
ejpam-3498	143	90	and	and	CCONJ
ejpam-3498	143	91	wjk	wjk	NOUN
ejpam-3498	143	92	belong	belong	VERB
ejpam-3498	143	93	to	to	ADP
ejpam-3498	143	94	y	y	PROPN
ejpam-3498	143	95	and	and	CCONJ
ejpam-3498	143	96	lk(x	lk(x	PROPN
ejpam-3498	143	97	,	,	PUNCT
ejpam-3498	143	98	y	y	PROPN
ejpam-3498	143	99	)	)	PUNCT
ejpam-3498	143	100	,	,	PUNCT
ejpam-3498	143	101	respectively	respectively	ADV
ejpam-3498	143	102	.	.	PUNCT
ejpam-3498	144	1	further	far	ADV
ejpam-3498	144	2	,	,	PUNCT
ejpam-3498	144	3	we	we	PRON
ejpam-3498	144	4	set	set	VERB
ejpam-3498	144	5	f	f	PROPN
ejpam-3498	144	6	=	=	PRON
ejpam-3498	144	7	(	(	PUNCT
ejpam-3498	144	8	fi)1≤i≤n	fi)1≤i≤n	PROPN
ejpam-3498	144	9	and	and	CCONJ
ejpam-3498	144	10	ψ(u	ψ(u	PROPN
ejpam-3498	144	11	,	,	PUNCT
ejpam-3498	144	12	w)(t	w)(t	PROPN
ejpam-3498	144	13	)	)	PUNCT
ejpam-3498	144	14	=	=	SYM
ejpam-3498	145	1	∫	∫	PROPN
ejpam-3498	145	2	t	t	NOUN
ejpam-3498	145	3	0	0	NUM
ejpam-3498	145	4	e(τ	e(τ	PROPN
ejpam-3498	145	5	,	,	PUNCT
ejpam-3498	145	6	t	t	PROPN
ejpam-3498	145	7	)	)	PUNCT
ejpam-3498	145	8	τ	τ	PROPN
ejpam-3498	145	9	(	(	PUNCT
ejpam-3498	145	10	f	f	PROPN
ejpam-3498	145	11	(	(	PUNCT
ejpam-3498	145	12	u	u	NOUN
ejpam-3498	145	13	,	,	PUNCT
ejpam-3498	145	14	w)(τ	w)(τ	PUNCT
ejpam-3498	145	15	)	)	PUNCT
ejpam-3498	146	1	+	+	ADJ
ejpam-3498	146	2	au(τ	au(τ	NUM
ejpam-3498	146	3	)	)	PUNCT
ejpam-3498	147	1	+	+	CCONJ
ejpam-3498	147	2	g(τ))dτ	g(τ))dτ	NOUN
ejpam-3498	147	3	.	.	PUNCT
ejpam-3498	148	1	we	we	PRON
ejpam-3498	148	2	need	need	VERB
ejpam-3498	148	3	to	to	PART
ejpam-3498	148	4	show	show	VERB
ejpam-3498	148	5	that	that	SCONJ
ejpam-3498	148	6	for	for	ADP
ejpam-3498	148	7	a	a	DET
ejpam-3498	148	8	fixed	fixed	ADJ
ejpam-3498	148	9	w	w	NOUN
ejpam-3498	148	10	,	,	PUNCT
ejpam-3498	148	11	the	the	DET
ejpam-3498	148	12	operator	operator	NOUN
ejpam-3498	148	13	ψ	ψ	X
ejpam-3498	148	14	(	(	PUNCT
ejpam-3498	148	15	·	·	PUNCT
ejpam-3498	148	16	,	,	PUNCT
ejpam-3498	148	17	w	w	NOUN
ejpam-3498	148	18	)	)	PUNCT
ejpam-3498	148	19	is	be	AUX
ejpam-3498	148	20	a	a	DET
ejpam-3498	148	21	contraction	contraction	NOUN
ejpam-3498	148	22	mapping	mapping	NOUN
ejpam-3498	148	23	from	from	ADP
ejpam-3498	148	24	a	a	DET
ejpam-3498	148	25	function	function	NOUN
ejpam-3498	148	26	space	space	NOUN
ejpam-3498	148	27	to	to	ADP
ejpam-3498	148	28	itself	itself	PRON
ejpam-3498	148	29	.	.	PUNCT
ejpam-3498	149	1	let	let	VERB
ejpam-3498	149	2	u	u	PRON
ejpam-3498	149	3	=	=	PUNCT
ejpam-3498	149	4	(	(	PUNCT
ejpam-3498	149	5	u1	u1	PROPN
ejpam-3498	149	6	,	,	PUNCT
ejpam-3498	149	7	...	...	PUNCT
ejpam-3498	149	8	,	,	PUNCT
ejpam-3498	149	9	un	un	PROPN
ejpam-3498	149	10	)	)	PUNCT
ejpam-3498	149	11	and	and	CCONJ
ejpam-3498	149	12	wt	wt	AUX
ejpam-3498	149	13	be	be	AUX
ejpam-3498	149	14	the	the	DET
ejpam-3498	149	15	set	set	NOUN
ejpam-3498	149	16	wt	wt	NOUN
ejpam-3498	149	17	=	=	SYM
ejpam-3498	149	18	{	{	PUNCT
ejpam-3498	149	19	u	u	NOUN
ejpam-3498	149	20	∈	∈	PROPN
ejpam-3498	149	21	c0([0	c0([0	PROPN
ejpam-3498	149	22	,	,	PUNCT
ejpam-3498	149	23	t	t	PROPN
ejpam-3498	149	24	)	)	PUNCT
ejpam-3498	149	25	,	,	PUNCT
ejpam-3498	149	26	(	(	PUNCT
ejpam-3498	149	27	bs(u	bs(u	X
ejpam-3498	149	28	,	,	PUNCT
ejpam-3498	149	29	y	y	NOUN
ejpam-3498	149	30	)	)	PUNCT
ejpam-3498	149	31	)	)	PUNCT
ejpam-3498	149	32	n	n	X
ejpam-3498	149	33	)	)	PUNCT
ejpam-3498	149	34	:	:	PUNCT
ejpam-3498	149	35	‖u(t)‖s	‖u(t)‖s	ADP
ejpam-3498	149	36	≤	≤	NOUN
ejpam-3498	149	37	cµ(t)α	cµ(t)α	PROPN
ejpam-3498	149	38	for	for	ADP
ejpam-3498	149	39	some	some	DET
ejpam-3498	149	40	c	c	PROPN
ejpam-3498	149	41	>	>	X
ejpam-3498	149	42	0	0	NUM
ejpam-3498	149	43	}	}	PUNCT
ejpam-3498	149	44	.	.	PUNCT
ejpam-3498	150	1	for	for	ADP
ejpam-3498	150	2	a	a	DET
ejpam-3498	150	3	u	u	NOUN
ejpam-3498	150	4	∈wt	∈wt	PROPN
ejpam-3498	150	5	we	we	PRON
ejpam-3498	150	6	define	define	VERB
ejpam-3498	150	7	the	the	DET
ejpam-3498	150	8	norm	norm	NOUN
ejpam-3498	150	9	‖u‖w	‖u‖w	NOUN
ejpam-3498	150	10	as	as	ADP
ejpam-3498	150	11	‖u(t)‖w	‖u(t)‖w	PROPN
ejpam-3498	150	12	=	=	SYM
ejpam-3498	150	13	max	max	PROPN
ejpam-3498	150	14	1≤j≤n	1≤j≤n	NUM
ejpam-3498	150	15	‖uj(t)‖s	‖uj(t)‖s	PROPN
ejpam-3498	150	16	.	.	PUNCT
ejpam-3498	151	1	then	then	ADV
ejpam-3498	151	2	(	(	PUNCT
ejpam-3498	151	3	wt	wt	INTJ
ejpam-3498	151	4	,	,	PUNCT
ejpam-3498	151	5	‖	‖	PROPN
ejpam-3498	151	6	·	·	PUNCT
ejpam-3498	151	7	‖w	‖w	NOUN
ejpam-3498	151	8	)	)	PUNCT
ejpam-3498	151	9	is	be	AUX
ejpam-3498	151	10	a	a	DET
ejpam-3498	151	11	banach	banach	NOUN
ejpam-3498	151	12	space	space	NOUN
ejpam-3498	151	13	.	.	PUNCT
ejpam-3498	152	1	for	for	ADP
ejpam-3498	152	2	r	r	NOUN
ejpam-3498	152	3	>	>	X
ejpam-3498	152	4	0	0	NUM
ejpam-3498	152	5	,	,	PUNCT
ejpam-3498	152	6	we	we	PRON
ejpam-3498	152	7	set	set	VERB
ejpam-3498	152	8	wt	wt	NOUN
ejpam-3498	152	9	,	,	PUNCT
ejpam-3498	152	10	r	r	NOUN
ejpam-3498	152	11	=	=	PUNCT
ejpam-3498	152	12	{	{	PUNCT
ejpam-3498	152	13	u	u	NOUN
ejpam-3498	152	14	∈wt	∈wt	PROPN
ejpam-3498	152	15	:	:	PUNCT
ejpam-3498	152	16	‖u‖w	‖u‖w	NOUN
ejpam-3498	152	17	≤	≤	NOUN
ejpam-3498	152	18	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	152	19	}	}	PUNCT
ejpam-3498	152	20	.	.	PUNCT
ejpam-3498	153	1	this	this	PRON
ejpam-3498	153	2	is	be	AUX
ejpam-3498	153	3	a	a	DET
ejpam-3498	153	4	closed	closed	ADJ
ejpam-3498	153	5	subset	subset	NOUN
ejpam-3498	153	6	of	of	ADP
ejpam-3498	153	7	wt	wt	NOUN
ejpam-3498	154	1	and	and	CCONJ
ejpam-3498	154	2	so	so	ADV
ejpam-3498	154	3	it	it	PRON
ejpam-3498	154	4	is	be	AUX
ejpam-3498	154	5	a	a	DET
ejpam-3498	154	6	complete	complete	ADJ
ejpam-3498	154	7	metric	metric	ADJ
ejpam-3498	154	8	space	space	NOUN
ejpam-3498	154	9	.	.	PUNCT
ejpam-3498	155	1	wt	wt	NOUN
ejpam-3498	155	2	,	,	PUNCT
ejpam-3498	155	3	r	r	NOUN
ejpam-3498	155	4	will	will	AUX
ejpam-3498	155	5	be	be	AUX
ejpam-3498	155	6	the	the	DET
ejpam-3498	155	7	form	form	NOUN
ejpam-3498	155	8	of	of	ADP
ejpam-3498	155	9	our	our	PRON
ejpam-3498	155	10	function	function	NOUN
ejpam-3498	155	11	space	space	NOUN
ejpam-3498	155	12	.	.	PUNCT
ejpam-3498	156	1	we	we	PRON
ejpam-3498	156	2	note	note	VERB
ejpam-3498	156	3	that	that	SCONJ
ejpam-3498	156	4	if	if	SCONJ
ejpam-3498	156	5	u	u	PROPN
ejpam-3498	156	6	∈wt	∈wt	PROPN
ejpam-3498	156	7	,	,	PUNCT
ejpam-3498	156	8	r	r	NOUN
ejpam-3498	156	9	,	,	PUNCT
ejpam-3498	156	10	then	then	ADV
ejpam-3498	156	11	‖u(t)‖s	‖u(t)‖s	ADP
ejpam-3498	156	12	≤	≤	ADJ
ejpam-3498	156	13	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	156	14	.	.	PUNCT
ejpam-3498	157	1	similarly	similarly	ADV
ejpam-3498	157	2	,	,	PUNCT
ejpam-3498	157	3	we	we	PRON
ejpam-3498	157	4	define	define	VERB
ejpam-3498	157	5	w	w	ADJ
ejpam-3498	157	6	′t	′t	NOUN
ejpam-3498	157	7	,	,	PUNCT
ejpam-3498	157	8	r	r	NOUN
ejpam-3498	157	9	by	by	ADP
ejpam-3498	157	10	just	just	ADV
ejpam-3498	157	11	replacing	replace	VERB
ejpam-3498	157	12	(	(	PUNCT
ejpam-3498	157	13	bs(u	bs(u	X
ejpam-3498	157	14	,	,	PUNCT
ejpam-3498	157	15	y	y	NOUN
ejpam-3498	157	16	)	)	PUNCT
ejpam-3498	157	17	)	)	PUNCT
ejpam-3498	158	1	n	n	X
ejpam-3498	158	2	in	in	ADP
ejpam-3498	158	3	our	our	PRON
ejpam-3498	158	4	definition	definition	NOUN
ejpam-3498	158	5	of	of	ADP
ejpam-3498	158	6	wt	wt	X
ejpam-3498	158	7	by	by	ADP
ejpam-3498	158	8	bs(u	bs(u	NOUN
ejpam-3498	158	9	,	,	PUNCT
ejpam-3498	158	10	l	l	PROPN
ejpam-3498	158	11	k(x	k(x	PROPN
ejpam-3498	158	12	,	,	PUNCT
ejpam-3498	158	13	y	y	PROPN
ejpam-3498	158	14	)	)	PUNCT
ejpam-3498	158	15	)	)	PUNCT
ejpam-3498	158	16	.	.	PUNCT
ejpam-3498	159	1	let	let	VERB
ejpam-3498	159	2	c2	c2	PROPN
ejpam-3498	159	3	=	=	SYM
ejpam-3498	159	4	sup0≤t≤t	sup0≤t≤t	PROPN
ejpam-3498	160	1	‖dwfi(t)‖s	‖dwfi(t)‖s	NOUN
ejpam-3498	160	2	(	(	PUNCT
ejpam-3498	160	3	ω	ω	NUM
ejpam-3498	160	4	×	×	NOUN
ejpam-3498	160	5	y	y	PROPN
ejpam-3498	160	6	n	n	CCONJ
ejpam-3498	160	7	×	×	PROPN
ejpam-3498	160	8	∏	∏	PROPN
ejpam-3498	160	9	(	(	PUNCT
ejpam-3498	160	10	j	j	PROPN
ejpam-3498	160	11	,	,	PUNCT
ejpam-3498	160	12	k)∈n	k)∈n	X
ejpam-3498	160	13	(	(	PUNCT
ejpam-3498	160	14	i),k>0	i),k>0	NOUN
ejpam-3498	160	15	lk(x	lk(x	NOUN
ejpam-3498	160	16	,	,	PUNCT
ejpam-3498	160	17	y	y	PROPN
ejpam-3498	160	18	)	)	PUNCT
ejpam-3498	160	19	)	)	PUNCT
ejpam-3498	160	20	.	.	PUNCT
ejpam-3498	161	1	this	this	PRON
ejpam-3498	161	2	is	be	AUX
ejpam-3498	161	3	finite	finite	ADJ
ejpam-3498	161	4	by	by	ADP
ejpam-3498	161	5	(	(	PUNCT
ejpam-3498	161	6	a1	a1	NOUN
ejpam-3498	161	7	)	)	PUNCT
ejpam-3498	161	8	and	and	CCONJ
ejpam-3498	161	9	remark	remark	VERB
ejpam-3498	161	10	2.10	2.10	NUM
ejpam-3498	161	11	.	.	PUNCT
ejpam-3498	162	1	further	far	ADV
ejpam-3498	162	2	,	,	PUNCT
ejpam-3498	162	3	we	we	PRON
ejpam-3498	162	4	let	let	VERB
ejpam-3498	162	5	c	c	NOUN
ejpam-3498	162	6	′	′	VERB
ejpam-3498	162	7	=	=	PUNCT
ejpam-3498	163	1	n2c2	n2c2	PROPN
ejpam-3498	163	2	1c0c2	1c0c2	NUM
ejpam-3498	163	3	,	,	PUNCT
ejpam-3498	163	4	where	where	SCONJ
ejpam-3498	163	5	c1	c1	PROPN
ejpam-3498	163	6	and	and	CCONJ
ejpam-3498	163	7	c0	c0	PROPN
ejpam-3498	163	8	are	be	AUX
ejpam-3498	163	9	the	the	DET
ejpam-3498	163	10	constants	constant	NOUN
ejpam-3498	163	11	in	in	ADP
ejpam-3498	163	12	theorem	theorem	ADJ
ejpam-3498	163	13	2.6	2.6	NUM
ejpam-3498	163	14	and	and	CCONJ
ejpam-3498	163	15	lemma	lemma	PROPN
ejpam-3498	163	16	2.12	2.12	NUM
ejpam-3498	163	17	,	,	PUNCT
ejpam-3498	163	18	respectively	respectively	ADV
ejpam-3498	163	19	.	.	PUNCT
ejpam-3498	164	1	set	set	VERB
ejpam-3498	164	2	r0	r0	NOUN
ejpam-3498	164	3	=	=	PUNCT
ejpam-3498	164	4	min{bd	min{bd	PUNCT
ejpam-3498	164	5	/	/	SYM
ejpam-3498	164	6	c	c	NOUN
ejpam-3498	164	7	′	′	NOUN
ejpam-3498	164	8	,	,	PUNCT
ejpam-3498	164	9	1	1	NUM
ejpam-3498	164	10	}	}	PUNCT
ejpam-3498	164	11	and	and	CCONJ
ejpam-3498	164	12	b	b	NOUN
ejpam-3498	164	13	is	be	AUX
ejpam-3498	164	14	the	the	DET
ejpam-3498	164	15	positive	positive	ADJ
ejpam-3498	164	16	constant	constant	NOUN
ejpam-3498	164	17	obtained	obtain	VERB
ejpam-3498	164	18	in	in	ADP
ejpam-3498	164	19	lemma	lemma	PROPN
ejpam-3498	164	20	2	2	NUM
ejpam-3498	164	21	.	.	PUNCT
ejpam-3498	164	22	proposition	proposition	NOUN
ejpam-3498	164	23	1	1	NUM
ejpam-3498	164	24	.	.	PUNCT
ejpam-3498	165	1	there	there	PRON
ejpam-3498	165	2	exists	exist	VERB
ejpam-3498	165	3	t0	t0	PROPN
ejpam-3498	165	4	∈	∈	PROPN
ejpam-3498	165	5	(	(	PUNCT
ejpam-3498	165	6	0	0	NUM
ejpam-3498	165	7	,	,	PUNCT
ejpam-3498	165	8	t	t	NOUN
ejpam-3498	165	9	]	]	PUNCT
ejpam-3498	165	10	and	and	CCONJ
ejpam-3498	165	11	r	r	NOUN
ejpam-3498	165	12	<	<	X
ejpam-3498	165	13	s1	s1	NOUN
ejpam-3498	165	14	such	such	ADJ
ejpam-3498	165	15	that	that	SCONJ
ejpam-3498	165	16	if	if	SCONJ
ejpam-3498	165	17	‖gi(t)‖s(ω	‖gi(t)‖s(ω	NOUN
ejpam-3498	165	18	)	)	PUNCT
ejpam-3498	165	19	≤	≤	NOUN
ejpam-3498	165	20	br2(1−	br2(1−	PUNCT
ejpam-3498	165	21	r	r	NOUN
ejpam-3498	165	22	)	)	PUNCT
ejpam-3498	165	23	c0	c0	NOUN
ejpam-3498	165	24	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	165	25	,	,	PUNCT
ejpam-3498	165	26	t	t	PROPN
ejpam-3498	165	27	∈	∈	PROPN
ejpam-3498	166	1	[	[	X
ejpam-3498	166	2	0	0	NUM
ejpam-3498	166	3	,	,	PUNCT
ejpam-3498	166	4	t	t	X
ejpam-3498	166	5	]	]	PUNCT
ejpam-3498	166	6	,	,	PUNCT
ejpam-3498	166	7	‖x(k)k	‖x(k)k	NUM
ejpam-3498	166	8	‖	‖	ADJ
ejpam-3498	166	9	≤	≤	PROPN
ejpam-3498	166	10	1	1	NUM
ejpam-3498	166	11	e.	e.	PROPN
ejpam-3498	166	12	y.	y.	PROPN
ejpam-3498	166	13	guerrero	guerrero	PROPN
ejpam-3498	166	14	/	/	SYM
ejpam-3498	166	15	eur	eur	PROPN
ejpam-3498	166	16	.	.	PUNCT
ejpam-3498	167	1	j.	j.	PROPN
ejpam-3498	167	2	pure	pure	PROPN
ejpam-3498	167	3	appl	appl	PROPN
ejpam-3498	167	4	.	.	PROPN
ejpam-3498	167	5	math	math	PROPN
ejpam-3498	167	6	,	,	PUNCT
ejpam-3498	167	7	12	12	NUM
ejpam-3498	167	8	(	(	PUNCT
ejpam-3498	167	9	3	3	NUM
ejpam-3498	167	10	)	)	PUNCT
ejpam-3498	167	11	(	(	PUNCT
ejpam-3498	167	12	2019	2019	NUM
ejpam-3498	167	13	)	)	PUNCT
ejpam-3498	167	14	,	,	PUNCT
ejpam-3498	167	15	1297	1297	NUM
ejpam-3498	167	16	-	-	SYM
ejpam-3498	167	17	1314	1314	NUM
ejpam-3498	167	18	1304	1304	NUM
ejpam-3498	167	19	and	and	CCONJ
ejpam-3498	167	20	fixed	fix	VERB
ejpam-3498	167	21	w	w	PROPN
ejpam-3498	167	22	∈w	∈w	NOUN
ejpam-3498	167	23	′t0,r	′t0,r	NOUN
ejpam-3498	167	24	with	with	ADP
ejpam-3498	167	25	‖wjk(t)‖s	‖wjk(t)‖s	PROPN
ejpam-3498	167	26	≤	≤	NUM
ejpam-3498	167	27	r0rrµ(t)α	r0rrµ(t)α	NOUN
ejpam-3498	167	28	,	,	PUNCT
ejpam-3498	167	29	t	t	PROPN
ejpam-3498	167	30	∈	∈	PROPN
ejpam-3498	168	1	[	[	X
ejpam-3498	168	2	0	0	NUM
ejpam-3498	168	3	,	,	PUNCT
ejpam-3498	168	4	t0	t0	PROPN
ejpam-3498	168	5	)	)	PUNCT
ejpam-3498	168	6	,	,	PUNCT
ejpam-3498	168	7	(	(	PUNCT
ejpam-3498	168	8	9	9	X
ejpam-3498	168	9	)	)	PUNCT
ejpam-3498	168	10	then	then	ADV
ejpam-3498	168	11	the	the	DET
ejpam-3498	168	12	following	follow	VERB
ejpam-3498	168	13	are	be	AUX
ejpam-3498	168	14	true	true	ADJ
ejpam-3498	168	15	:	:	PUNCT
ejpam-3498	168	16	(	(	PUNCT
ejpam-3498	168	17	a	a	X
ejpam-3498	168	18	)	)	PUNCT
ejpam-3498	168	19	ψ	ψ	SYM
ejpam-3498	168	20	[	[	X
ejpam-3498	168	21	·	·	PUNCT
ejpam-3498	168	22	,	,	PUNCT
ejpam-3498	168	23	w	w	PROPN
ejpam-3498	168	24	]	]	X
ejpam-3498	168	25	is	be	AUX
ejpam-3498	168	26	a	a	DET
ejpam-3498	168	27	mapping	mapping	NOUN
ejpam-3498	168	28	from	from	ADP
ejpam-3498	168	29	wt0,r	wt0,r	NUM
ejpam-3498	168	30	to	to	ADP
ejpam-3498	168	31	itself	itself	PRON
ejpam-3498	168	32	.	.	PUNCT
ejpam-3498	169	1	(	(	PUNCT
ejpam-3498	169	2	b	b	X
ejpam-3498	169	3	)	)	PUNCT
ejpam-3498	169	4	ψ	ψ	X
ejpam-3498	169	5	[	[	X
ejpam-3498	169	6	·	·	PUNCT
ejpam-3498	169	7	,	,	PUNCT
ejpam-3498	169	8	w	w	PROPN
ejpam-3498	169	9	]	]	X
ejpam-3498	169	10	is	be	AUX
ejpam-3498	169	11	a	a	DET
ejpam-3498	169	12	contraction	contraction	NOUN
ejpam-3498	169	13	map	map	NOUN
ejpam-3498	169	14	.	.	PUNCT
ejpam-3498	170	1	proof	proof	NOUN
ejpam-3498	170	2	.	.	PUNCT
ejpam-3498	171	1	by	by	ADP
ejpam-3498	171	2	remark	remark	NOUN
ejpam-3498	171	3	2	2	NUM
ejpam-3498	171	4	and	and	CCONJ
ejpam-3498	171	5	(	(	PUNCT
ejpam-3498	171	6	a1	a1	NOUN
ejpam-3498	171	7	)	)	PUNCT
ejpam-3498	171	8	,	,	PUNCT
ejpam-3498	171	9	dufi	dufi	NOUN
ejpam-3498	171	10	∈	∈	PROPN
ejpam-3498	171	11	{	{	PUNCT
ejpam-3498	171	12	mp	mp	NOUN
ejpam-3498	171	13	}	}	PUNCT
ejpam-3498	171	14	.	.	PUNCT
ejpam-3498	172	1	hence	hence	ADV
ejpam-3498	172	2	,	,	PUNCT
ejpam-3498	172	3	fi	fi	NOUN
ejpam-3498	172	4	is	be	AUX
ejpam-3498	172	5	continuous	continuous	ADJ
ejpam-3498	172	6	with	with	ADP
ejpam-3498	172	7	respect	respect	NOUN
ejpam-3498	172	8	to	to	ADP
ejpam-3498	172	9	t	t	PROPN
ejpam-3498	172	10	,	,	PUNCT
ejpam-3498	172	11	u	u	NOUN
ejpam-3498	172	12	,	,	PUNCT
ejpam-3498	172	13	and	and	CCONJ
ejpam-3498	172	14	w.	w.	PROPN
ejpam-3498	172	15	thus	thus	ADV
ejpam-3498	172	16	,	,	PUNCT
ejpam-3498	172	17	we	we	PRON
ejpam-3498	172	18	can	can	AUX
ejpam-3498	172	19	find	find	VERB
ejpam-3498	172	20	t0	t0	PRON
ejpam-3498	172	21	∈	∈	PROPN
ejpam-3498	173	1	[	[	X
ejpam-3498	173	2	0	0	NUM
ejpam-3498	173	3	,	,	PUNCT
ejpam-3498	173	4	t	t	NOUN
ejpam-3498	173	5	]	]	PUNCT
ejpam-3498	173	6	and	and	CCONJ
ejpam-3498	173	7	r	r	NOUN
ejpam-3498	173	8	<	<	X
ejpam-3498	173	9	s1	s1	NOUN
ejpam-3498	173	10	such	such	ADJ
ejpam-3498	173	11	that	that	SCONJ
ejpam-3498	173	12	if	if	SCONJ
ejpam-3498	173	13	u	u	PROPN
ejpam-3498	173	14	,	,	PUNCT
ejpam-3498	173	15	v	v	NOUN
ejpam-3498	173	16	∈	∈	NOUN
ejpam-3498	173	17	wt0,r	wt0,r	NOUN
ejpam-3498	173	18	and	and	CCONJ
ejpam-3498	173	19	w	w	NOUN
ejpam-3498	173	20	,	,	PUNCT
ejpam-3498	173	21	w	w	PROPN
ejpam-3498	173	22	∈w	∈w	NOUN
ejpam-3498	173	23	′t0,r	′t0,r	NUM
ejpam-3498	173	24	,	,	PUNCT
ejpam-3498	173	25	then	then	ADV
ejpam-3498	173	26	n2c2	n2c2	PROPN
ejpam-3498	173	27	1c0‖dufi(τ	1c0‖dufi(τ	NUM
ejpam-3498	173	28	,	,	PUNCT
ejpam-3498	173	29	p	p	X
ejpam-3498	173	30	,	,	PUNCT
ejpam-3498	173	31	q)−dufi(0	q)−dufi(0	PROPN
ejpam-3498	173	32	,	,	PUNCT
ejpam-3498	173	33	0	0	NUM
ejpam-3498	173	34	,	,	PUNCT
ejpam-3498	173	35	0)‖s	0)‖s	NUM
ejpam-3498	173	36	≤	≤	NUM
ejpam-3498	173	37	rbd	rbd	X
ejpam-3498	173	38	(	(	PUNCT
ejpam-3498	173	39	10	10	NUM
ejpam-3498	173	40	)	)	PUNCT
ejpam-3498	173	41	where	where	SCONJ
ejpam-3498	173	42	p	p	NOUN
ejpam-3498	173	43	=	=	X
ejpam-3498	173	44	θu+	θu+	NOUN
ejpam-3498	173	45	(	(	PUNCT
ejpam-3498	173	46	1−	1−	NUM
ejpam-3498	173	47	θ)v	θ)v	NOUN
ejpam-3498	173	48	,	,	PUNCT
ejpam-3498	173	49	q	q	NOUN
ejpam-3498	173	50	=	=	PRON
ejpam-3498	173	51	θw	θw	NOUN
ejpam-3498	173	52	+	+	X
ejpam-3498	173	53	(	(	PUNCT
ejpam-3498	173	54	1−	1−	NUM
ejpam-3498	173	55	θ)w	θ)w	X
ejpam-3498	173	56	.	.	PUNCT
ejpam-3498	174	1	now	now	ADV
ejpam-3498	174	2	,	,	PUNCT
ejpam-3498	174	3	since	since	SCONJ
ejpam-3498	174	4	fi(0	fi(0	PROPN
ejpam-3498	174	5	,	,	PUNCT
ejpam-3498	174	6	0	0	NUM
ejpam-3498	174	7	,	,	PUNCT
ejpam-3498	174	8	0	0	NUM
ejpam-3498	174	9	)	)	PUNCT
ejpam-3498	174	10	=	=	SYM
ejpam-3498	174	11	0	0	NUM
ejpam-3498	174	12	fi(u	fi(u	NOUN
ejpam-3498	174	13	,	,	PUNCT
ejpam-3498	174	14	w)(t	w)(t	ADJ
ejpam-3498	174	15	)	)	PUNCT
ejpam-3498	174	16	=	=	SYM
ejpam-3498	174	17	fi(u	fi(u	NOUN
ejpam-3498	174	18	,	,	PUNCT
ejpam-3498	174	19	v)(t)−	v)(t)−	PROPN
ejpam-3498	174	20	fi(0	fi(0	PROPN
ejpam-3498	174	21	,	,	PUNCT
ejpam-3498	174	22	0)(t	0)(t	X
ejpam-3498	174	23	)	)	PUNCT
ejpam-3498	174	24	=	=	SYM
ejpam-3498	174	25	n∑	n∑	NOUN
ejpam-3498	174	26	j=1	j=1	NOUN
ejpam-3498	174	27	∫	∫	PROPN
ejpam-3498	174	28	1	1	NUM
ejpam-3498	174	29	0	0	NUM
ejpam-3498	175	1	dufi(t	dufi(t	PROPN
ejpam-3498	175	2	,	,	PUNCT
ejpam-3498	175	3	θu	θu	ADP
ejpam-3498	175	4	,	,	PUNCT
ejpam-3498	175	5	θw)uj(t)dθ	θw)uj(t)dθ	PROPN
ejpam-3498	175	6	+	+	CCONJ
ejpam-3498	175	7	∑	∑	PROPN
ejpam-3498	175	8	(	(	PUNCT
ejpam-3498	175	9	j	j	PROPN
ejpam-3498	175	10	,	,	PUNCT
ejpam-3498	175	11	k)∈n	k)∈n	X
ejpam-3498	175	12	(	(	PUNCT
ejpam-3498	175	13	i	i	NOUN
ejpam-3498	175	14	)	)	PUNCT
ejpam-3498	175	15	∫	∫	PROPN
ejpam-3498	176	1	1	1	NUM
ejpam-3498	176	2	0	0	NUM
ejpam-3498	176	3	dwfi(t	dwfi(t	NOUN
ejpam-3498	176	4	,	,	PUNCT
ejpam-3498	176	5	θu	θu	NOUN
ejpam-3498	176	6	,	,	PUNCT
ejpam-3498	176	7	θw)wjk(t	θw)wjk(t	NOUN
ejpam-3498	176	8	)	)	PUNCT
ejpam-3498	176	9	·	·	PUNCT
ejpam-3498	176	10	x	x	X
ejpam-3498	176	11	(	(	PUNCT
ejpam-3498	176	12	k	k	NOUN
ejpam-3498	176	13	)	)	PUNCT
ejpam-3498	176	14	k	k	PROPN
ejpam-3498	176	15	dθ	dθ	PROPN
ejpam-3498	176	16	.	.	PUNCT
ejpam-3498	177	1	using	use	VERB
ejpam-3498	177	2	the	the	DET
ejpam-3498	177	3	definition	definition	NOUN
ejpam-3498	177	4	of	of	ADP
ejpam-3498	177	5	a	a	PRON
ejpam-3498	177	6	we	we	PRON
ejpam-3498	177	7	may	may	AUX
ejpam-3498	177	8	rewrite	rewrite	VERB
ejpam-3498	177	9	aijuj(t	aijuj(t	PROPN
ejpam-3498	177	10	)	)	PUNCT
ejpam-3498	177	11	as	as	ADP
ejpam-3498	177	12	aijuj(t	aijuj(t	PROPN
ejpam-3498	177	13	)	)	PUNCT
ejpam-3498	177	14	=	=	PUNCT
ejpam-3498	178	1	−	−	PROPN
ejpam-3498	178	2	∫	∫	NOUN
ejpam-3498	178	3	1	1	NUM
ejpam-3498	178	4	0	0	NUM
ejpam-3498	178	5	dufi(0	dufi(0	PROPN
ejpam-3498	178	6	,	,	PUNCT
ejpam-3498	178	7	0	0	NUM
ejpam-3498	178	8	,	,	PUNCT
ejpam-3498	178	9	0	0	NUM
ejpam-3498	178	10	)	)	PUNCT
ejpam-3498	178	11	·	·	PUNCT
ejpam-3498	179	1	uj(t)dθ	uj(t)dθ	ADJ
ejpam-3498	179	2	.	.	PUNCT
ejpam-3498	180	1	hence	hence	ADV
ejpam-3498	180	2	,	,	PUNCT
ejpam-3498	180	3	fi(u	fi(u	NOUN
ejpam-3498	180	4	,	,	PUNCT
ejpam-3498	180	5	w)(t	w)(t	ADJ
ejpam-3498	180	6	)	)	PUNCT
ejpam-3498	181	1	+	+	CCONJ
ejpam-3498	181	2	n∑	n∑	PROPN
ejpam-3498	181	3	j=1	j=1	PROPN
ejpam-3498	181	4	aijuj(t	aijuj(t	PROPN
ejpam-3498	181	5	)	)	PUNCT
ejpam-3498	181	6	+	+	NOUN
ejpam-3498	181	7	gi(t	gi(t	NOUN
ejpam-3498	181	8	)	)	PUNCT
ejpam-3498	181	9	=	=	SYM
ejpam-3498	182	1	n∑	n∑	NOUN
ejpam-3498	182	2	j=1	j=1	NOUN
ejpam-3498	182	3	∫	∫	PROPN
ejpam-3498	183	1	1	1	NUM
ejpam-3498	183	2	0	0	NUM
ejpam-3498	184	1	[	[	X
ejpam-3498	184	2	dufi(t	dufi(t	PROPN
ejpam-3498	184	3	,	,	PUNCT
ejpam-3498	184	4	θu	θu	ADP
ejpam-3498	184	5	,	,	PUNCT
ejpam-3498	184	6	θw)−dufi(0	θw)−dufi(0	PROPN
ejpam-3498	184	7	,	,	PUNCT
ejpam-3498	184	8	0	0	NUM
ejpam-3498	184	9	,	,	PUNCT
ejpam-3498	184	10	0)]uj(t)dθ	0)]uj(t)dθ	NOUN
ejpam-3498	184	11	+	+	CCONJ
ejpam-3498	184	12	∑	∑	PROPN
ejpam-3498	184	13	(	(	PUNCT
ejpam-3498	184	14	j	j	PROPN
ejpam-3498	184	15	,	,	PUNCT
ejpam-3498	184	16	k)∈n	k)∈n	X
ejpam-3498	184	17	(	(	PUNCT
ejpam-3498	184	18	i	i	NOUN
ejpam-3498	184	19	)	)	PUNCT
ejpam-3498	184	20	∫	∫	PROPN
ejpam-3498	184	21	1	1	NUM
ejpam-3498	184	22	0	0	NUM
ejpam-3498	184	23	dwfi(t	dwfi(t	NOUN
ejpam-3498	184	24	,	,	PUNCT
ejpam-3498	184	25	θu	θu	NOUN
ejpam-3498	184	26	,	,	PUNCT
ejpam-3498	184	27	θw)wjk(t	θw)wjk(t	NOUN
ejpam-3498	184	28	)	)	PUNCT
ejpam-3498	184	29	·	·	PUNCT
ejpam-3498	184	30	x	x	X
ejpam-3498	184	31	(	(	PUNCT
ejpam-3498	184	32	k	k	NOUN
ejpam-3498	184	33	)	)	PUNCT
ejpam-3498	184	34	k	k	PROPN
ejpam-3498	184	35	dθ	dθ	PROPN
ejpam-3498	184	36	+	+	PROPN
ejpam-3498	184	37	gi(t	gi(t	NOUN
ejpam-3498	184	38	)	)	PUNCT
ejpam-3498	184	39	.	.	PUNCT
ejpam-3498	185	1	thus,∥∥∥∥∥fi(u	thus,∥∥∥∥∥fi(u	NOUN
ejpam-3498	185	2	,	,	PUNCT
ejpam-3498	185	3	w)(t	w)(t	PROPN
ejpam-3498	185	4	)	)	PUNCT
ejpam-3498	186	1	+	+	CCONJ
ejpam-3498	186	2	n∑	n∑	PROPN
ejpam-3498	186	3	j=1	j=1	PROPN
ejpam-3498	186	4	aijuj(t	aijuj(t	PROPN
ejpam-3498	186	5	)	)	PUNCT
ejpam-3498	186	6	+	+	SYM
ejpam-3498	186	7	gi(t	gi(t	NOUN
ejpam-3498	186	8	)	)	PUNCT
ejpam-3498	186	9	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	186	10	s	s	PART
ejpam-3498	186	11	≤	≤	NUM
ejpam-3498	186	12	n∑	n∑	PROPN
ejpam-3498	186	13	j=1	j=1	NOUN
ejpam-3498	186	14	c1‖dufi(t	c1‖dufi(t	PROPN
ejpam-3498	186	15	,	,	PUNCT
ejpam-3498	186	16	θu	θu	ADP
ejpam-3498	186	17	,	,	PUNCT
ejpam-3498	186	18	θw)−dufi(0	θw)−dufi(0	PROPN
ejpam-3498	186	19	,	,	PUNCT
ejpam-3498	186	20	0	0	NUM
ejpam-3498	186	21	,	,	PUNCT
ejpam-3498	186	22	0)]‖s‖uj(t)‖s	0)]‖s‖uj(t)‖s	PUNCT
ejpam-3498	187	1	+	+	CCONJ
ejpam-3498	187	2	∑	∑	PROPN
ejpam-3498	187	3	(	(	PUNCT
ejpam-3498	187	4	j	j	PROPN
ejpam-3498	187	5	,	,	PUNCT
ejpam-3498	187	6	k)∈n	k)∈n	X
ejpam-3498	187	7	(	(	PUNCT
ejpam-3498	187	8	i	i	NOUN
ejpam-3498	187	9	)	)	PUNCT
ejpam-3498	187	10	c1‖dwfi(t	c1‖dwfi(t	PROPN
ejpam-3498	187	11	,	,	PUNCT
ejpam-3498	187	12	θu	θu	X
ejpam-3498	187	13	,	,	PUNCT
ejpam-3498	187	14	θw)‖s‖wjk(t	θw)‖s‖wjk(t	NOUN
ejpam-3498	187	15	)	)	PUNCT
ejpam-3498	187	16	·	·	PUNCT
ejpam-3498	188	1	x	x	X
ejpam-3498	188	2	(	(	PUNCT
ejpam-3498	188	3	k	k	NOUN
ejpam-3498	188	4	)	)	PUNCT
ejpam-3498	188	5	k	k	NOUN
ejpam-3498	188	6	‖s	‖s	NOUN
ejpam-3498	189	1	+	+	PROPN
ejpam-3498	189	2	‖gi(t)‖s	‖gi(t)‖s	ADV
ejpam-3498	189	3	.	.	PUNCT
ejpam-3498	189	4	using	use	VERB
ejpam-3498	189	5	lemma	lemma	PROPN
ejpam-3498	189	6	2	2	NUM
ejpam-3498	189	7	,	,	PUNCT
ejpam-3498	189	8	we	we	PRON
ejpam-3498	189	9	have	have	VERB
ejpam-3498	189	10	‖ψi(u	‖ψi(u	NOUN
ejpam-3498	189	11	,	,	PUNCT
ejpam-3498	189	12	w)(t)‖s	w)(t)‖s	ADP
ejpam-3498	189	13	≤	≤	NUM
ejpam-3498	190	1	∫	∫	PROPN
ejpam-3498	190	2	t	t	X
ejpam-3498	190	3	0	0	NUM
ejpam-3498	190	4	∥∥∥∥∥e(τ	∥∥∥∥∥e(τ	PROPN
ejpam-3498	190	5	,	,	PUNCT
ejpam-3498	190	6	t	t	PROPN
ejpam-3498	190	7	)	)	PUNCT
ejpam-3498	190	8	(	(	PUNCT
ejpam-3498	190	9	fi(u	fi(u	NOUN
ejpam-3498	190	10	,	,	PUNCT
ejpam-3498	190	11	w)(τ	w)(τ	PUNCT
ejpam-3498	190	12	)	)	PUNCT
ejpam-3498	191	1	+	+	CCONJ
ejpam-3498	191	2	n∑	n∑	ADJ
ejpam-3498	191	3	j=1	j=1	PROPN
ejpam-3498	191	4	aijuj(τ	aijuj(τ	PROPN
ejpam-3498	191	5	)	)	PUNCT
ejpam-3498	192	1	+	+	CCONJ
ejpam-3498	193	1	gi(τ	gi(τ	NUM
ejpam-3498	193	2	)	)	PUNCT
ejpam-3498	193	3	)	)	PUNCT
ejpam-3498	194	1	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	194	2	s	s	PART
ejpam-3498	194	3	dτ	dτ	X
ejpam-3498	194	4	τ	τ	PROPN
ejpam-3498	194	5	.	.	PUNCT
ejpam-3498	195	1	e.	e.	PROPN
ejpam-3498	195	2	y.	y.	PROPN
ejpam-3498	195	3	guerrero	guerrero	PROPN
ejpam-3498	195	4	/	/	SYM
ejpam-3498	195	5	eur	eur	PROPN
ejpam-3498	195	6	.	.	PUNCT
ejpam-3498	196	1	j.	j.	PROPN
ejpam-3498	196	2	pure	pure	PROPN
ejpam-3498	196	3	appl	appl	PROPN
ejpam-3498	196	4	.	.	PROPN
ejpam-3498	196	5	math	math	PROPN
ejpam-3498	196	6	,	,	PUNCT
ejpam-3498	196	7	12	12	NUM
ejpam-3498	196	8	(	(	PUNCT
ejpam-3498	196	9	3	3	NUM
ejpam-3498	196	10	)	)	PUNCT
ejpam-3498	196	11	(	(	PUNCT
ejpam-3498	196	12	2019	2019	NUM
ejpam-3498	196	13	)	)	PUNCT
ejpam-3498	196	14	,	,	PUNCT
ejpam-3498	196	15	1297	1297	NUM
ejpam-3498	196	16	-	-	SYM
ejpam-3498	196	17	1314	1314	NUM
ejpam-3498	196	18	1305	1305	NUM
ejpam-3498	196	19	≤	≤	NUM
ejpam-3498	196	20	∫	∫	PROPN
ejpam-3498	196	21	t	t	PROPN
ejpam-3498	196	22	0	0	NUM
ejpam-3498	196	23	{	{	PUNCT
ejpam-3498	196	24	c0	c0	PROPN
ejpam-3498	196	25	τ	τ	X
ejpam-3498	196	26	b−1	b−1	PROPN
ejpam-3498	196	27	tb	tb	X
ejpam-3498	196	28	(	(	PUNCT
ejpam-3498	196	29	n∑	n∑	INTJ
ejpam-3498	196	30	j=1	j=1	PROPN
ejpam-3498	196	31	c1‖dufi(t	c1‖dufi(t	PROPN
ejpam-3498	196	32	,	,	PUNCT
ejpam-3498	196	33	θu	θu	ADP
ejpam-3498	196	34	,	,	PUNCT
ejpam-3498	196	35	θw)−dufi(0	θw)−dufi(0	PROPN
ejpam-3498	196	36	,	,	PUNCT
ejpam-3498	196	37	0	0	NUM
ejpam-3498	196	38	,	,	PUNCT
ejpam-3498	196	39	0)]‖s‖uj(τ)‖s	0)]‖s‖uj(τ)‖s	X
ejpam-3498	197	1	+	+	CCONJ
ejpam-3498	197	2	∑	∑	PROPN
ejpam-3498	197	3	(	(	PUNCT
ejpam-3498	197	4	j	j	PROPN
ejpam-3498	197	5	,	,	PUNCT
ejpam-3498	197	6	k)∈n	k)∈n	X
ejpam-3498	197	7	(	(	PUNCT
ejpam-3498	197	8	i	i	NOUN
ejpam-3498	197	9	)	)	PUNCT
ejpam-3498	197	10	c1‖dwfi(t	c1‖dwfi(t	PROPN
ejpam-3498	197	11	,	,	PUNCT
ejpam-3498	197	12	θu	θu	X
ejpam-3498	197	13	,	,	PUNCT
ejpam-3498	197	14	θw)‖s‖wjk(τ	θw)‖s‖wjk(τ	NOUN
ejpam-3498	197	15	)	)	PUNCT
ejpam-3498	197	16	·	·	PUNCT
ejpam-3498	197	17	x(k)k	x(k)k	NUM
ejpam-3498	198	1	‖s	‖s	PROPN
ejpam-3498	199	1	+	+	CCONJ
ejpam-3498	199	2	‖gi(τ)‖s	‖gi(τ)‖s	PROPN
ejpam-3498	199	3	)	)	PUNCT
ejpam-3498	199	4	}	}	PUNCT
ejpam-3498	199	5	dτ	dτ	NOUN
ejpam-3498	199	6	=	=	SYM
ejpam-3498	199	7	(	(	PUNCT
ejpam-3498	199	8	n∑	n∑	INTJ
ejpam-3498	199	9	j=1	j=1	PROPN
ejpam-3498	199	10	c0c1‖dufi(t	c0c1‖dufi(t	PROPN
ejpam-3498	199	11	,	,	PUNCT
ejpam-3498	199	12	θu	θu	ADP
ejpam-3498	199	13	,	,	PUNCT
ejpam-3498	199	14	θw)−dufi(0	θw)−dufi(0	PROPN
ejpam-3498	199	15	,	,	PUNCT
ejpam-3498	199	16	0	0	NUM
ejpam-3498	199	17	,	,	PUNCT
ejpam-3498	199	18	0)]‖s‖uj(t)‖s	0)]‖s‖uj(t)‖s	PUNCT
ejpam-3498	200	1	+	+	CCONJ
ejpam-3498	200	2	∑	∑	PROPN
ejpam-3498	200	3	(	(	PUNCT
ejpam-3498	200	4	j	j	PROPN
ejpam-3498	200	5	,	,	PUNCT
ejpam-3498	200	6	k)∈n	k)∈n	X
ejpam-3498	200	7	(	(	PUNCT
ejpam-3498	200	8	i	i	NOUN
ejpam-3498	200	9	)	)	PUNCT
ejpam-3498	200	10	c0c1‖dwfi(t	c0c1‖dwfi(t	NOUN
ejpam-3498	200	11	,	,	PUNCT
ejpam-3498	200	12	θu	θu	ADP
ejpam-3498	200	13	,	,	PUNCT
ejpam-3498	200	14	θw)‖s‖wjk(t)‖s‖x	θw)‖s‖wjk(t)‖s‖x	PROPN
ejpam-3498	200	15	(	(	PUNCT
ejpam-3498	200	16	k	k	NOUN
ejpam-3498	200	17	)	)	PUNCT
ejpam-3498	200	18	k	k	NOUN
ejpam-3498	200	19	‖s	‖s	NOUN
ejpam-3498	201	1	+	+	CCONJ
ejpam-3498	201	2	c0‖gi(t)‖s	c0‖gi(t)‖s	ADV
ejpam-3498	201	3	)	)	PUNCT
ejpam-3498	201	4	1	1	NUM
ejpam-3498	201	5	b	b	NOUN
ejpam-3498	201	6	.	.	PUNCT
ejpam-3498	202	1	note	note	NOUN
ejpam-3498	202	2	also	also	ADV
ejpam-3498	202	3	that	that	SCONJ
ejpam-3498	202	4	bd	bd	PROPN
ejpam-3498	202	5	<	<	X
ejpam-3498	202	6	b	b	X
ejpam-3498	202	7	≤	≤	ADV
ejpam-3498	202	8	1	1	NUM
ejpam-3498	203	1	and	and	CCONJ
ejpam-3498	203	2	d	d	X
ejpam-3498	203	3	>	>	X
ejpam-3498	203	4	1	1	NUM
ejpam-3498	203	5	.	.	PUNCT
ejpam-3498	204	1	thus	thus	ADV
ejpam-3498	204	2	,	,	PUNCT
ejpam-3498	204	3	by	by	ADP
ejpam-3498	204	4	our	our	PRON
ejpam-3498	204	5	assumptions	assumption	NOUN
ejpam-3498	204	6	,	,	PUNCT
ejpam-3498	204	7	(	(	PUNCT
ejpam-3498	204	8	10	10	NUM
ejpam-3498	204	9	)	)	PUNCT
ejpam-3498	204	10	and	and	CCONJ
ejpam-3498	204	11	our	our	PRON
ejpam-3498	204	12	defined	define	VERB
ejpam-3498	204	13	constant	constant	ADJ
ejpam-3498	204	14	c	c	NOUN
ejpam-3498	204	15	′	′	NOUN
ejpam-3498	204	16	,	,	PUNCT
ejpam-3498	204	17	‖ψi(u	‖ψi(u	NOUN
ejpam-3498	204	18	,	,	PUNCT
ejpam-3498	204	19	w)(t)‖s	w)(t)‖s	ADP
ejpam-3498	204	20	≤	≤	NOUN
ejpam-3498	204	21	(	(	PUNCT
ejpam-3498	204	22	nc0c1‖dufi(t	nc0c1‖dufi(t	NOUN
ejpam-3498	204	23	,	,	PUNCT
ejpam-3498	204	24	θu	θu	ADP
ejpam-3498	204	25	,	,	PUNCT
ejpam-3498	204	26	θw)−dufi(0	θw)−dufi(0	PROPN
ejpam-3498	204	27	,	,	PUNCT
ejpam-3498	204	28	0	0	NUM
ejpam-3498	204	29	,	,	PUNCT
ejpam-3498	204	30	0)]‖s	0)]‖s	NOUN
ejpam-3498	204	31	max	max	PROPN
ejpam-3498	204	32	1≤j≤n	1≤j≤n	NUM
ejpam-3498	204	33	‖uj(t)‖s	‖uj(t)‖s	PROPN
ejpam-3498	204	34	+	+	PROPN
ejpam-3498	204	35	nc0c1‖dwfi(t	nc0c1‖dwfi(t	ADJ
ejpam-3498	204	36	,	,	PUNCT
ejpam-3498	204	37	θu	θu	X
ejpam-3498	204	38	,	,	PUNCT
ejpam-3498	204	39	θw)‖s	θw)‖s	PROPN
ejpam-3498	204	40	max	max	PROPN
ejpam-3498	204	41	(	(	PUNCT
ejpam-3498	204	42	j	j	PROPN
ejpam-3498	204	43	,	,	PUNCT
ejpam-3498	204	44	k)∈n(i	k)∈n(i	PROPN
ejpam-3498	204	45	)	)	PUNCT
ejpam-3498	204	46	‖wjk(t)‖s	‖wjk(t)‖s	PROPN
ejpam-3498	205	1	+	+	CCONJ
ejpam-3498	205	2	c0‖gi(t)‖s	c0‖gi(t)‖s	ADV
ejpam-3498	205	3	)	)	PUNCT
ejpam-3498	205	4	1	1	NUM
ejpam-3498	205	5	b	b	X
ejpam-3498	205	6	≤	≤	X
ejpam-3498	205	7	(	(	PUNCT
ejpam-3498	205	8	rb	rb	PROPN
ejpam-3498	205	9	max	max	PROPN
ejpam-3498	205	10	1≤j≤n	1≤j≤n	NUM
ejpam-3498	205	11	‖uj(t)‖s	‖uj(t)‖s	PROPN
ejpam-3498	206	1	+	+	PUNCT
ejpam-3498	206	2	c	c	NOUN
ejpam-3498	206	3	′	′	NUM
ejpam-3498	207	1	max	max	PROPN
ejpam-3498	207	2	(	(	PUNCT
ejpam-3498	207	3	j	j	PROPN
ejpam-3498	207	4	,	,	PUNCT
ejpam-3498	207	5	k)∈n(i	k)∈n(i	PROPN
ejpam-3498	207	6	)	)	PUNCT
ejpam-3498	207	7	‖wjk(t)‖s	‖wjk(t)‖s	PROPN
ejpam-3498	208	1	+	+	CCONJ
ejpam-3498	208	2	c0	c0	PROPN
ejpam-3498	208	3	br2(1−	br2(1−	X
ejpam-3498	208	4	r	r	PROPN
ejpam-3498	208	5	)	)	PUNCT
ejpam-3498	208	6	c0	c0	NOUN
ejpam-3498	208	7	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	208	8	)	)	PUNCT
ejpam-3498	208	9	1	1	NUM
ejpam-3498	208	10	b	b	NOUN
ejpam-3498	208	11	≤	≤	NUM
ejpam-3498	208	12	r	r	NOUN
ejpam-3498	208	13	max	max	PROPN
ejpam-3498	208	14	1≤j≤n	1≤j≤n	NUM
ejpam-3498	208	15	‖uj(t)‖s	‖uj(t)‖s	PROPN
ejpam-3498	209	1	+	+	PUNCT
ejpam-3498	209	2	c	c	NOUN
ejpam-3498	209	3	′	′	NUM
ejpam-3498	209	4	b	b	NOUN
ejpam-3498	209	5	max	max	PROPN
ejpam-3498	209	6	(	(	PUNCT
ejpam-3498	209	7	j	j	PROPN
ejpam-3498	209	8	,	,	PUNCT
ejpam-3498	209	9	k)∈n(i	k)∈n(i	PROPN
ejpam-3498	209	10	)	)	PUNCT
ejpam-3498	209	11	‖wjk(t)‖s	‖wjk(t)‖s	PROPN
ejpam-3498	210	1	+	+	CCONJ
ejpam-3498	210	2	r2(1−	r2(1−	VERB
ejpam-3498	210	3	r)rµ(t)α	r)rµ(t)α	NOUN
ejpam-3498	210	4	≤	≤	NUM
ejpam-3498	210	5	sup	sup	NOUN
ejpam-3498	210	6	0≤τ≤t	0≤τ≤t	NUM
ejpam-3498	210	7	{	{	PUNCT
ejpam-3498	210	8	r	r	NOUN
ejpam-3498	210	9	max	max	PROPN
ejpam-3498	210	10	1≤j≤n	1≤j≤n	NUM
ejpam-3498	210	11	‖uj(t)‖s	‖uj(t)‖s	PROPN
ejpam-3498	211	1	+	+	PUNCT
ejpam-3498	211	2	c	c	NOUN
ejpam-3498	211	3	′	′	NUM
ejpam-3498	211	4	b	b	NOUN
ejpam-3498	211	5	max	max	PROPN
ejpam-3498	211	6	(	(	PUNCT
ejpam-3498	211	7	j	j	PROPN
ejpam-3498	211	8	,	,	PUNCT
ejpam-3498	211	9	k)∈n(i	k)∈n(i	PROPN
ejpam-3498	211	10	)	)	PUNCT
ejpam-3498	211	11	‖wjk(t)‖s	‖wjk(t)‖s	NOUN
ejpam-3498	211	12	}	}	PUNCT
ejpam-3498	212	1	+	+	CCONJ
ejpam-3498	212	2	r2(1−	r2(1−	NOUN
ejpam-3498	212	3	r)rµ(t)α	r)rµ(t)α	NOUN
ejpam-3498	212	4	.	.	PUNCT
ejpam-3498	213	1	thus	thus	ADV
ejpam-3498	213	2	,	,	PUNCT
ejpam-3498	213	3	using	use	VERB
ejpam-3498	213	4	the	the	DET
ejpam-3498	213	5	definition	definition	NOUN
ejpam-3498	213	6	of	of	ADP
ejpam-3498	213	7	r0	r0	NOUN
ejpam-3498	213	8	and	and	CCONJ
ejpam-3498	213	9	with	with	ADP
ejpam-3498	213	10	r	r	NOUN
ejpam-3498	213	11	≤	≤	NUM
ejpam-3498	213	12	1	1	NUM
ejpam-3498	213	13	3	3	NUM
ejpam-3498	213	14	,	,	PUNCT
ejpam-3498	213	15	we	we	PRON
ejpam-3498	213	16	have	have	VERB
ejpam-3498	213	17	‖ψi(u	‖ψi(u	NOUN
ejpam-3498	213	18	,	,	PUNCT
ejpam-3498	213	19	w)(t)‖	w)(t)‖	ADJ
ejpam-3498	213	20	≤	≤	NUM
ejpam-3498	213	21	rrµ(t)α	rrµ(t)α	NOUN
ejpam-3498	213	22	+	+	CCONJ
ejpam-3498	213	23	c	c	NOUN
ejpam-3498	213	24	′	′	NUM
ejpam-3498	213	25	b	b	X
ejpam-3498	213	26	rr0rµ(t)α	rr0rµ(t)α	NOUN
ejpam-3498	213	27	+	+	CCONJ
ejpam-3498	213	28	r2(1−	r2(1−	NOUN
ejpam-3498	213	29	r)rµ(t)α	r)rµ(t)α	NOUN
ejpam-3498	213	30	≤	≤	NUM
ejpam-3498	213	31	1	1	NUM
ejpam-3498	213	32	3	3	NUM
ejpam-3498	213	33	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	213	34	+	+	CCONJ
ejpam-3498	213	35	c	c	NOUN
ejpam-3498	213	36	′	′	NUM
ejpam-3498	213	37	b	b	PROPN
ejpam-3498	213	38	·	·	PUNCT
ejpam-3498	213	39	b	b	X
ejpam-3498	214	1	d	d	NOUN
ejpam-3498	214	2	c	c	NOUN
ejpam-3498	214	3	′	′	NUM
ejpam-3498	214	4	1	1	NUM
ejpam-3498	214	5	3	3	NUM
ejpam-3498	214	6	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	214	7	+	+	CCONJ
ejpam-3498	214	8	1	1	NUM
ejpam-3498	214	9	3	3	NUM
ejpam-3498	214	10	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	214	11	≤	≤	NOUN
ejpam-3498	214	12	(	(	PUNCT
ejpam-3498	214	13	1	1	NUM
ejpam-3498	214	14	3	3	NUM
ejpam-3498	214	15	+	+	CCONJ
ejpam-3498	214	16	c	c	NOUN
ejpam-3498	214	17	′	′	NUM
ejpam-3498	214	18	b	b	PROPN
ejpam-3498	214	19	·	·	PUNCT
ejpam-3498	214	20	b	b	X
ejpam-3498	215	1	d	d	NOUN
ejpam-3498	215	2	3c	3c	NUM
ejpam-3498	215	3	′	′	NUM
ejpam-3498	216	1	+	+	CCONJ
ejpam-3498	216	2	1	1	NUM
ejpam-3498	216	3	3	3	NUM
ejpam-3498	216	4	)	)	PUNCT
ejpam-3498	216	5	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	216	6	=	=	SYM
ejpam-3498	216	7	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	216	8	proving	prove	VERB
ejpam-3498	216	9	(	(	PUNCT
ejpam-3498	216	10	a	a	NOUN
ejpam-3498	216	11	)	)	PUNCT
ejpam-3498	216	12	.	.	PUNCT
ejpam-3498	217	1	furthermore	furthermore	ADV
ejpam-3498	217	2	,	,	PUNCT
ejpam-3498	217	3	note	note	VERB
ejpam-3498	217	4	that	that	SCONJ
ejpam-3498	217	5	fj(u	fj(u	NOUN
ejpam-3498	217	6	,	,	PUNCT
ejpam-3498	217	7	w)(t	w)(t	ADJ
ejpam-3498	217	8	)	)	PUNCT
ejpam-3498	217	9	−	−	NOUN
ejpam-3498	217	10	fj(v	fj(v	ADJ
ejpam-3498	217	11	,	,	PUNCT
ejpam-3498	217	12	w)(t	w)(t	ADJ
ejpam-3498	217	13	)	)	PUNCT
ejpam-3498	217	14	=	=	SYM
ejpam-3498	218	1	n∑	n∑	NOUN
ejpam-3498	218	2	k=1	k=1	PUNCT
ejpam-3498	219	1	∫	∫	PROPN
ejpam-3498	219	2	1	1	NUM
ejpam-3498	219	3	0	0	NUM
ejpam-3498	220	1	[	[	PUNCT
ejpam-3498	220	2	dufj(t	dufj(t	PROPN
ejpam-3498	220	3	,	,	PUNCT
ejpam-3498	220	4	p	p	X
ejpam-3498	220	5	,	,	PUNCT
ejpam-3498	220	6	q	q	NOUN
ejpam-3498	220	7	)	)	PUNCT
ejpam-3498	220	8	·	·	PUNCT
ejpam-3498	220	9	(	(	PUNCT
ejpam-3498	220	10	uk	uk	PROPN
ejpam-3498	220	11	−	−	PROPN
ejpam-3498	220	12	vk)(t	vk)(t	PROPN
ejpam-3498	220	13	)	)	PUNCT
ejpam-3498	220	14	+	+	NOUN
ejpam-3498	220	15	dwfj(t	dwfj(t	PROPN
ejpam-3498	220	16	,	,	PUNCT
ejpam-3498	220	17	p	p	X
ejpam-3498	220	18	,	,	PUNCT
ejpam-3498	220	19	q)(wkη	q)(wkη	NOUN
ejpam-3498	220	20	−	−	PROPN
ejpam-3498	220	21	wkη	wkη	NOUN
ejpam-3498	220	22	)	)	PUNCT
ejpam-3498	220	23	]	]	PUNCT
ejpam-3498	221	1	dθ	dθ	PROPN
ejpam-3498	221	2	.	.	PROPN
ejpam-3498	221	3	e.	e.	PROPN
ejpam-3498	221	4	y.	y.	PROPN
ejpam-3498	221	5	guerrero	guerrero	PROPN
ejpam-3498	221	6	/	/	SYM
ejpam-3498	221	7	eur	eur	PROPN
ejpam-3498	221	8	.	.	PUNCT
ejpam-3498	222	1	j.	j.	PROPN
ejpam-3498	222	2	pure	pure	PROPN
ejpam-3498	222	3	appl	appl	PROPN
ejpam-3498	222	4	.	.	PROPN
ejpam-3498	222	5	math	math	PROPN
ejpam-3498	222	6	,	,	PUNCT
ejpam-3498	222	7	12	12	NUM
ejpam-3498	222	8	(	(	PUNCT
ejpam-3498	222	9	3	3	NUM
ejpam-3498	222	10	)	)	PUNCT
ejpam-3498	222	11	(	(	PUNCT
ejpam-3498	222	12	2019	2019	NUM
ejpam-3498	222	13	)	)	PUNCT
ejpam-3498	222	14	,	,	PUNCT
ejpam-3498	222	15	1297	1297	NUM
ejpam-3498	222	16	-	-	SYM
ejpam-3498	222	17	1314	1314	NUM
ejpam-3498	222	18	1306	1306	NUM
ejpam-3498	222	19	hence	hence	ADV
ejpam-3498	222	20	,	,	PUNCT
ejpam-3498	222	21	similar	similar	ADJ
ejpam-3498	222	22	to	to	ADP
ejpam-3498	222	23	the	the	DET
ejpam-3498	222	24	previous	previous	ADJ
ejpam-3498	222	25	approach	approach	NOUN
ejpam-3498	222	26	,	,	PUNCT
ejpam-3498	222	27	fj(u	fj(u	NUM
ejpam-3498	222	28	,	,	PUNCT
ejpam-3498	222	29	w)(t	w)(t	ADJ
ejpam-3498	222	30	)	)	PUNCT
ejpam-3498	222	31	−	−	NOUN
ejpam-3498	222	32	fj(v	fj(v	ADJ
ejpam-3498	222	33	,	,	PUNCT
ejpam-3498	222	34	w)(t	w)(t	ADJ
ejpam-3498	222	35	)	)	PUNCT
ejpam-3498	223	1	+	+	NUM
ejpam-3498	223	2	n∑	n∑	INTJ
ejpam-3498	223	3	k=1	k=1	PUNCT
ejpam-3498	223	4	ajk(uk(t)−	ajk(uk(t)−	PROPN
ejpam-3498	223	5	vk(t	vk(t	NOUN
ejpam-3498	223	6	)	)	PUNCT
ejpam-3498	223	7	)	)	PUNCT
ejpam-3498	224	1	=	=	PUNCT
ejpam-3498	224	2	n∑	n∑	INTJ
ejpam-3498	224	3	k=1	k=1	PUNCT
ejpam-3498	225	1	∫	∫	PROPN
ejpam-3498	225	2	1	1	NUM
ejpam-3498	225	3	0	0	NUM
ejpam-3498	226	1	[	[	PUNCT
ejpam-3498	226	2	dufj(t	dufj(t	PROPN
ejpam-3498	226	3	,	,	PUNCT
ejpam-3498	226	4	p	p	X
ejpam-3498	226	5	,	,	PUNCT
ejpam-3498	226	6	q)−dufj(0	q)−dufj(0	PROPN
ejpam-3498	226	7	,	,	PUNCT
ejpam-3498	226	8	0	0	NUM
ejpam-3498	226	9	,	,	PUNCT
ejpam-3498	226	10	0)](uk	0)](uk	NUM
ejpam-3498	226	11	−	−	PROPN
ejpam-3498	227	1	vk)(τ)]dθ	vk)(τ)]dθ	ADP
ejpam-3498	227	2	+	+	PROPN
ejpam-3498	227	3	∑	∑	PROPN
ejpam-3498	227	4	(	(	PUNCT
ejpam-3498	227	5	k	k	X
ejpam-3498	227	6	,	,	PUNCT
ejpam-3498	227	7	η	η	NOUN
ejpam-3498	227	8	)	)	PUNCT
ejpam-3498	227	9	dwfj(t	dwfj(t	PROPN
ejpam-3498	227	10	,	,	PUNCT
ejpam-3498	227	11	p	p	X
ejpam-3498	227	12	,	,	PUNCT
ejpam-3498	227	13	q)(wkη	q)(wkη	NOUN
ejpam-3498	227	14	−	−	PROPN
ejpam-3498	227	15	wkη)(τ)dθ	wkη)(τ)dθ	PROPN
ejpam-3498	227	16	thus	thus	ADV
ejpam-3498	227	17	,	,	PUNCT
ejpam-3498	227	18	by	by	ADP
ejpam-3498	227	19	lemma	lemma	PROPN
ejpam-3498	227	20	2	2	PROPN
ejpam-3498	227	21	and	and	CCONJ
ejpam-3498	227	22	(	(	PUNCT
ejpam-3498	227	23	10	10	NUM
ejpam-3498	227	24	)	)	PUNCT
ejpam-3498	227	25	we	we	PRON
ejpam-3498	227	26	have∥∥∥∥∥	have∥∥∥∥∥	PROPN
ejpam-3498	227	27	n∑	n∑	PROPN
ejpam-3498	228	1	j=1	j=1	PROPN
ejpam-3498	228	2	eij	eij	PROPN
ejpam-3498	228	3	[	[	PUNCT
ejpam-3498	228	4	fj(u	fj(u	NUM
ejpam-3498	228	5	,	,	PUNCT
ejpam-3498	228	6	w)(t)−	w)(t)−	NOUN
ejpam-3498	228	7	fj(v	fj(v	ADJ
ejpam-3498	228	8	,	,	PUNCT
ejpam-3498	228	9	w)(t	w)(t	ADJ
ejpam-3498	228	10	)	)	PUNCT
ejpam-3498	229	1	+	+	NUM
ejpam-3498	229	2	n∑	n∑	INTJ
ejpam-3498	229	3	k=1	k=1	PUNCT
ejpam-3498	229	4	ajk(uk(t)−	ajk(uk(t)−	PROPN
ejpam-3498	229	5	vk(t	vk(t	NOUN
ejpam-3498	229	6	)	)	PUNCT
ejpam-3498	229	7	)	)	PUNCT
ejpam-3498	230	1	]	]	PUNCT
ejpam-3498	230	2	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-3498	230	3	s	s	PART
ejpam-3498	230	4	≤	≤	NUM
ejpam-3498	230	5	n∑	n∑	PROPN
ejpam-3498	230	6	j=1	j=1	PROPN
ejpam-3498	230	7	c0eρ(i	c0eρ(i	PROPN
ejpam-3498	230	8	,	,	PUNCT
ejpam-3498	230	9	j)(τ	j)(τ	PROPN
ejpam-3498	230	10	,	,	PUNCT
ejpam-3498	230	11	t	t	PROPN
ejpam-3498	230	12	)	)	PUNCT
ejpam-3498	231	1	[	[	PUNCT
ejpam-3498	231	2	n∑	n∑	NOUN
ejpam-3498	231	3	k=1	k=1	PROPN
ejpam-3498	231	4	c1‖dufj(t	c1‖dufj(t	PROPN
ejpam-3498	231	5	,	,	PUNCT
ejpam-3498	231	6	p	p	X
ejpam-3498	231	7	,	,	PUNCT
ejpam-3498	231	8	q)−dufj(0	q)−dufj(0	PROPN
ejpam-3498	231	9	,	,	PUNCT
ejpam-3498	231	10	0	0	NUM
ejpam-3498	231	11	,	,	PUNCT
ejpam-3498	231	12	0)‖s‖(uk	0)‖s‖(uk	NUM
ejpam-3498	231	13	−	−	PUNCT
ejpam-3498	231	14	vk)(t)‖s	vk)(t)‖s	ADV
ejpam-3498	232	1	+	+	CCONJ
ejpam-3498	232	2	∑	∑	PROPN
ejpam-3498	232	3	(	(	PUNCT
ejpam-3498	232	4	k	k	X
ejpam-3498	232	5	,	,	PUNCT
ejpam-3498	232	6	η	η	NOUN
ejpam-3498	232	7	)	)	PUNCT
ejpam-3498	232	8	c1‖dwfj(t	c1‖dwfj(t	PROPN
ejpam-3498	232	9	,	,	PUNCT
ejpam-3498	232	10	p	p	X
ejpam-3498	232	11	,	,	PUNCT
ejpam-3498	232	12	q)‖s‖(wkη	q)‖s‖(wkη	NOUN
ejpam-3498	232	13	−	−	NOUN
ejpam-3498	232	14	wkη)(t)‖s	wkη)(t)‖s	NOUN
ejpam-3498	232	15	]	]	PUNCT
ejpam-3498	232	16	≤	≤	NUM
ejpam-3498	232	17	n	n	PRON
ejpam-3498	232	18	max	max	PROPN
ejpam-3498	232	19	1≤j≤n	1≤j≤n	NUM
ejpam-3498	232	20	eρ(i	eρ(i	NUM
ejpam-3498	232	21	,	,	PUNCT
ejpam-3498	232	22	j)(τ	j)(τ	PROPN
ejpam-3498	232	23	,	,	PUNCT
ejpam-3498	232	24	t	t	PROPN
ejpam-3498	232	25	)	)	PUNCT
ejpam-3498	232	26	[	[	PUNCT
ejpam-3498	232	27	nc1c0‖dufj(t	nc1c0‖dufj(t	X
ejpam-3498	232	28	,	,	PUNCT
ejpam-3498	232	29	p	p	X
ejpam-3498	232	30	,	,	PUNCT
ejpam-3498	232	31	q)−dufj(0	q)−dufj(0	PROPN
ejpam-3498	232	32	,	,	PUNCT
ejpam-3498	232	33	0	0	NUM
ejpam-3498	232	34	,	,	PUNCT
ejpam-3498	232	35	0)‖s	0)‖s	NUM
ejpam-3498	232	36	×	×	PROPN
ejpam-3498	232	37	max	max	PROPN
ejpam-3498	233	1	1≤k≤n	1≤k≤n	NUM
ejpam-3498	233	2	‖(uk	‖(uk	ADJ
ejpam-3498	233	3	−	−	NOUN
ejpam-3498	233	4	vk)(t)‖s	vk)(t)‖s	ADV
ejpam-3498	234	1	+	+	PROPN
ejpam-3498	234	2	nc1c0‖dwfj(t	nc1c0‖dwfj(t	ADJ
ejpam-3498	234	3	,	,	PUNCT
ejpam-3498	234	4	p	p	X
ejpam-3498	234	5	,	,	PUNCT
ejpam-3498	234	6	q)‖s	q)‖s	ADV
ejpam-3498	234	7	×	×	PROPN
ejpam-3498	234	8	max	max	PROPN
ejpam-3498	234	9	(	(	PUNCT
ejpam-3498	234	10	k	k	NOUN
ejpam-3498	234	11	,	,	PUNCT
ejpam-3498	234	12	η)∈n	η)∈n	NUM
ejpam-3498	234	13	(	(	PUNCT
ejpam-3498	234	14	i	i	NOUN
ejpam-3498	234	15	)	)	PUNCT
ejpam-3498	234	16	‖(wkη	‖(wkη	VERB
ejpam-3498	234	17	−	−	PROPN
ejpam-3498	234	18	wkη)(t)‖s	wkη)(t)‖s	PROPN
ejpam-3498	234	19	]	]	PUNCT
ejpam-3498	234	20	≤	≤	NUM
ejpam-3498	234	21	rbd	rbd	PROPN
ejpam-3498	234	22	max	max	PROPN
ejpam-3498	234	23	1≤j	1≤j	PROPN
ejpam-3498	234	24	,	,	PUNCT
ejpam-3498	234	25	k≤n	k≤n	PROPN
ejpam-3498	234	26	eρ(i	eρ(i	SYM
ejpam-3498	234	27	,	,	PUNCT
ejpam-3498	234	28	j)(τ	j)(τ	PROPN
ejpam-3498	234	29	,	,	PUNCT
ejpam-3498	234	30	t)‖(uk	t)‖(uk	VERB
ejpam-3498	234	31	−	−	NOUN
ejpam-3498	234	32	vk)(t)‖s	vk)(t)‖s	ADV
ejpam-3498	235	1	+	+	CCONJ
ejpam-3498	235	2	c	c	NOUN
ejpam-3498	235	3	′	′	NOUN
ejpam-3498	236	1	max	max	PROPN
ejpam-3498	236	2	1≤j≤n	1≤j≤n	NUM
ejpam-3498	236	3	(	(	PUNCT
ejpam-3498	236	4	k	k	NOUN
ejpam-3498	236	5	,	,	PUNCT
ejpam-3498	236	6	η)∈n	η)∈n	NUM
ejpam-3498	236	7	(	(	PUNCT
ejpam-3498	236	8	i	i	NOUN
ejpam-3498	236	9	)	)	PUNCT
ejpam-3498	236	10	[	[	PUNCT
ejpam-3498	236	11	eρ(i	eρ(i	NOUN
ejpam-3498	236	12	,	,	PUNCT
ejpam-3498	236	13	j)(τ	j)(τ	PROPN
ejpam-3498	236	14	,	,	PUNCT
ejpam-3498	236	15	t	t	PROPN
ejpam-3498	236	16	)	)	PUNCT
ejpam-3498	236	17	×‖(wkη	×‖(wkη	NOUN
ejpam-3498	236	18	−	−	NOUN
ejpam-3498	236	19	wkη)(t)‖s	wkη)(t)‖s	NOUN
ejpam-3498	236	20	]	]	PUNCT
ejpam-3498	236	21	by	by	ADP
ejpam-3498	236	22	lemma	lemma	PROPN
ejpam-3498	236	23	5	5	NUM
ejpam-3498	236	24	,	,	PUNCT
ejpam-3498	236	25	‖ψi(u	‖ψi(u	NOUN
ejpam-3498	236	26	,	,	PUNCT
ejpam-3498	236	27	w)(t)−ψi(v	w)(t)−ψi(v	PROPN
ejpam-3498	236	28	,	,	PUNCT
ejpam-3498	236	29	w)(t)‖	w)(t)‖	PROPN
ejpam-3498	236	30	≤	≤	NUM
ejpam-3498	236	31	rbd	rbd	NOUN
ejpam-3498	236	32	max	max	PROPN
ejpam-3498	236	33	1≤j	1≤j	PROPN
ejpam-3498	236	34	,	,	PUNCT
ejpam-3498	236	35	k≤n	k≤n	PROPN
ejpam-3498	236	36	hρ(i	hρ(i	NOUN
ejpam-3498	236	37	,	,	PUNCT
ejpam-3498	236	38	j)[‖uk	j)[‖uk	PROPN
ejpam-3498	236	39	−	−	PROPN
ejpam-3498	236	40	vk‖s](t	vk‖s](t	PROPN
ejpam-3498	236	41	)	)	PUNCT
ejpam-3498	237	1	+	+	NOUN
ejpam-3498	237	2	c	c	NOUN
ejpam-3498	237	3	′	′	NOUN
ejpam-3498	237	4	max	max	PROPN
ejpam-3498	237	5	1≤j≤n	1≤j≤n	NUM
ejpam-3498	237	6	(	(	PUNCT
ejpam-3498	237	7	k	k	NOUN
ejpam-3498	237	8	,	,	PUNCT
ejpam-3498	237	9	η)∈n	η)∈n	NUM
ejpam-3498	237	10	(	(	PUNCT
ejpam-3498	237	11	i	i	NOUN
ejpam-3498	237	12	)	)	PUNCT
ejpam-3498	237	13	hρ(i	hρ(i	PUNCT
ejpam-3498	237	14	,	,	PUNCT
ejpam-3498	237	15	j)[‖wlη	j)[‖wlη	ADJ
ejpam-3498	237	16	−	−	NOUN
ejpam-3498	237	17	wlη‖s](t	wlη‖s](t	ADV
ejpam-3498	237	18	)	)	PUNCT
ejpam-3498	237	19	.	.	PUNCT
ejpam-3498	238	1	(	(	PUNCT
ejpam-3498	238	2	11	11	NUM
ejpam-3498	238	3	)	)	PUNCT
ejpam-3498	238	4	hence	hence	ADV
ejpam-3498	238	5	,	,	PUNCT
ejpam-3498	238	6	when	when	SCONJ
ejpam-3498	238	7	w	w	PROPN
ejpam-3498	238	8	=	=	SYM
ejpam-3498	238	9	w	w	PROPN
ejpam-3498	238	10	,	,	PUNCT
ejpam-3498	238	11	we	we	PRON
ejpam-3498	238	12	have	have	VERB
ejpam-3498	238	13	‖ψi(u	‖ψi(u	NOUN
ejpam-3498	238	14	,	,	PUNCT
ejpam-3498	238	15	w)(t)−ψi(v	w)(t)−ψi(v	PROPN
ejpam-3498	238	16	,	,	PUNCT
ejpam-3498	238	17	w)‖	w)‖	VERB
ejpam-3498	238	18	≤	≤	NUM
ejpam-3498	238	19	rbd	rbd	NOUN
ejpam-3498	238	20	max	max	PROPN
ejpam-3498	238	21	1≤j≤n	1≤j≤n	NUM
ejpam-3498	238	22	hρ(i	hρ(i	PROPN
ejpam-3498	238	23	,	,	PUNCT
ejpam-3498	238	24	j)[‖uk	j)[‖uk	PROPN
ejpam-3498	238	25	−	−	PROPN
ejpam-3498	238	26	vk‖s](t	vk‖s](t	PROPN
ejpam-3498	238	27	)	)	PUNCT
ejpam-3498	238	28	,	,	PUNCT
ejpam-3498	238	29	e.	e.	PROPN
ejpam-3498	238	30	y.	y.	PROPN
ejpam-3498	238	31	guerrero	guerrero	PROPN
ejpam-3498	238	32	/	/	SYM
ejpam-3498	238	33	eur	eur	PROPN
ejpam-3498	238	34	.	.	PUNCT
ejpam-3498	239	1	j.	j.	PROPN
ejpam-3498	239	2	pure	pure	PROPN
ejpam-3498	239	3	appl	appl	PROPN
ejpam-3498	239	4	.	.	PROPN
ejpam-3498	239	5	math	math	PROPN
ejpam-3498	239	6	,	,	PUNCT
ejpam-3498	239	7	12	12	NUM
ejpam-3498	239	8	(	(	PUNCT
ejpam-3498	239	9	3	3	NUM
ejpam-3498	239	10	)	)	PUNCT
ejpam-3498	239	11	(	(	PUNCT
ejpam-3498	239	12	2019	2019	NUM
ejpam-3498	239	13	)	)	PUNCT
ejpam-3498	239	14	,	,	PUNCT
ejpam-3498	239	15	1297	1297	NUM
ejpam-3498	239	16	-	-	SYM
ejpam-3498	239	17	1314	1314	NUM
ejpam-3498	239	18	1307	1307	NUM
ejpam-3498	239	19	proving	prove	VERB
ejpam-3498	239	20	(	(	PUNCT
ejpam-3498	239	21	b	b	NOUN
ejpam-3498	239	22	)	)	PUNCT
ejpam-3498	239	23	.	.	PUNCT
ejpam-3498	240	1	it	it	PRON
ejpam-3498	240	2	follows	follow	VERB
ejpam-3498	240	3	from	from	ADP
ejpam-3498	240	4	the	the	DET
ejpam-3498	240	5	banach	banach	ADV
ejpam-3498	240	6	fixed	fix	VERB
ejpam-3498	240	7	point	point	NOUN
ejpam-3498	240	8	theorem	theorem	VERB
ejpam-3498	240	9	that	that	SCONJ
ejpam-3498	240	10	there	there	PRON
ejpam-3498	240	11	exists	exist	VERB
ejpam-3498	240	12	a	a	DET
ejpam-3498	240	13	unique	unique	ADJ
ejpam-3498	240	14	u	u	NOUN
ejpam-3498	240	15	∈	∈	NOUN
ejpam-3498	240	16	wt0,r	wt0,r	NOUN
ejpam-3498	240	17	such	such	ADJ
ejpam-3498	240	18	that	that	PRON
ejpam-3498	240	19	u	u	NOUN
ejpam-3498	240	20	=	=	PROPN
ejpam-3498	240	21	ψ(u	ψ(u	PROPN
ejpam-3498	240	22	,	,	PUNCT
ejpam-3498	240	23	w	w	NOUN
ejpam-3498	240	24	)	)	PUNCT
ejpam-3498	240	25	.	.	PUNCT
ejpam-3498	241	1	denote	denote	VERB
ejpam-3498	241	2	this	this	DET
ejpam-3498	241	3	u	u	NOUN
ejpam-3498	241	4	by	by	ADP
ejpam-3498	241	5	s[w	s[w	NOUN
ejpam-3498	241	6	]	]	PUNCT
ejpam-3498	241	7	.	.	PUNCT
ejpam-3498	242	1	we	we	PRON
ejpam-3498	242	2	have	have	VERB
ejpam-3498	242	3	by	by	ADP
ejpam-3498	242	4	(	(	PUNCT
ejpam-3498	242	5	11	11	NUM
ejpam-3498	242	6	)	)	PUNCT
ejpam-3498	242	7	,	,	PUNCT
ejpam-3498	242	8	‖si[w](t)−	‖si[w](t)−	X
ejpam-3498	242	9	si[w(t)]‖s‖	si[w(t)]‖s‖	ADV
ejpam-3498	242	10	=	=	SYM
ejpam-3498	242	11	‖ψi(s[w	‖ψi(s[w	PROPN
ejpam-3498	242	12	]	]	X
ejpam-3498	242	13	,	,	PUNCT
ejpam-3498	242	14	w)(t)−ψi(s[w	w)(t)−ψi(s[w	PROPN
ejpam-3498	242	15	]	]	X
ejpam-3498	242	16	,	,	PUNCT
ejpam-3498	242	17	w)(t)‖	w)(t)‖	PROPN
ejpam-3498	242	18	≤	≤	NUM
ejpam-3498	242	19	rbd	rbd	NOUN
ejpam-3498	242	20	max	max	PROPN
ejpam-3498	242	21	1≤j≤n	1≤j≤n	NUM
ejpam-3498	242	22	hρ(i	hρ(i	PROPN
ejpam-3498	242	23	,	,	PUNCT
ejpam-3498	242	24	j)[‖sk[w]−	j)[‖sk[w]−	PROPN
ejpam-3498	242	25	sk[w]‖s](t	sk[w]‖s](t	PUNCT
ejpam-3498	242	26	)	)	PUNCT
ejpam-3498	243	1	+	+	ADP
ejpam-3498	243	2	c	c	NOUN
ejpam-3498	243	3	′	′	NUM
ejpam-3498	243	4	max	max	PROPN
ejpam-3498	243	5	(	(	PUNCT
ejpam-3498	243	6	k	k	NOUN
ejpam-3498	243	7	,	,	PUNCT
ejpam-3498	243	8	η)∈n	η)∈n	NUM
ejpam-3498	243	9	(	(	PUNCT
ejpam-3498	243	10	i	i	NOUN
ejpam-3498	243	11	)	)	PUNCT
ejpam-3498	243	12	hρ(i	hρ(i	PUNCT
ejpam-3498	243	13	,	,	PUNCT
ejpam-3498	243	14	j)[‖wkη	j)[‖wkη	PROPN
ejpam-3498	243	15	−	−	PROPN
ejpam-3498	243	16	wkη‖s](t	wkη‖s](t	PROPN
ejpam-3498	243	17	)	)	PUNCT
ejpam-3498	243	18	.	.	PUNCT
ejpam-3498	244	1	using	use	VERB
ejpam-3498	244	2	(	(	PUNCT
ejpam-3498	244	3	11	11	NUM
ejpam-3498	244	4	)	)	PUNCT
ejpam-3498	244	5	n	n	CCONJ
ejpam-3498	244	6	-	-	PUNCT
ejpam-3498	244	7	times	time	NOUN
ejpam-3498	244	8	,	,	PUNCT
ejpam-3498	244	9	we	we	PRON
ejpam-3498	244	10	get	get	VERB
ejpam-3498	244	11	‖si[w](t)−	‖si[w](t)−	NOUN
ejpam-3498	244	12	si[w(t)]‖s‖	si[w(t)]‖s‖	ADV
ejpam-3498	244	13	≤	≤	NUM
ejpam-3498	244	14	rn+1bd	rn+1bd	NOUN
ejpam-3498	244	15	max	max	PROPN
ejpam-3498	244	16	1≤j≤n	1≤j≤n	NUM
ejpam-3498	244	17	sup	sup	NOUN
ejpam-3498	244	18	0≤τ≤t	0≤τ≤t	NUM
ejpam-3498	244	19	hρ(i	hρ(i	PUNCT
ejpam-3498	244	20	,	,	PUNCT
ejpam-3498	244	21	j)[‖sk[w]−	j)[‖sk[w]−	PROPN
ejpam-3498	244	22	sk[w]‖s](τ	sk[w]‖s](τ	PUNCT
ejpam-3498	244	23	)	)	PUNCT
ejpam-3498	245	1	+	+	CCONJ
ejpam-3498	245	2	n∑	n∑	ADJ
ejpam-3498	245	3	p=0	p=0	PROPN
ejpam-3498	245	4	rpc	rpc	VERB
ejpam-3498	245	5	′	′	NUM
ejpam-3498	245	6	max	max	PROPN
ejpam-3498	245	7	(	(	PUNCT
ejpam-3498	245	8	k	k	NOUN
ejpam-3498	245	9	,	,	PUNCT
ejpam-3498	245	10	η)∈n	η)∈n	NUM
ejpam-3498	245	11	(	(	PUNCT
ejpam-3498	245	12	i	i	NOUN
ejpam-3498	245	13	)	)	PUNCT
ejpam-3498	245	14	sup	sup	NOUN
ejpam-3498	245	15	0≤τ≤t	0≤τ≤t	NUM
ejpam-3498	245	16	hρ(i	hρ(i	ADP
ejpam-3498	245	17	,	,	PUNCT
ejpam-3498	245	18	j)[‖wkη	j)[‖wkη	VERB
ejpam-3498	245	19	−	−	PROPN
ejpam-3498	245	20	wkη‖s](τ	wkη‖s](τ	NOUN
ejpam-3498	245	21	)	)	PUNCT
ejpam-3498	245	22	.	.	PUNCT
ejpam-3498	246	1	as	as	ADP
ejpam-3498	246	2	n→∞	n→∞	NUM
ejpam-3498	246	3	,	,	PUNCT
ejpam-3498	246	4	we	we	PRON
ejpam-3498	246	5	have	have	VERB
ejpam-3498	246	6	the	the	DET
ejpam-3498	246	7	following	follow	VERB
ejpam-3498	246	8	proposition	proposition	NOUN
ejpam-3498	246	9	:	:	PUNCT
ejpam-3498	246	10	proposition	proposition	NOUN
ejpam-3498	246	11	2	2	NUM
ejpam-3498	246	12	.	.	X
ejpam-3498	246	13	for	for	ADP
ejpam-3498	246	14	w	w	PROPN
ejpam-3498	246	15	,	,	PUNCT
ejpam-3498	246	16	w	w	NOUN
ejpam-3498	246	17	∈wt0,r	∈wt0,r	NOUN
ejpam-3498	246	18	satisfying	satisfying	ADJ
ejpam-3498	246	19	(	(	PUNCT
ejpam-3498	246	20	9	9	NUM
ejpam-3498	246	21	)	)	PUNCT
ejpam-3498	246	22	,	,	PUNCT
ejpam-3498	246	23	we	we	PRON
ejpam-3498	246	24	have	have	VERB
ejpam-3498	246	25	‖si[w](t)−	‖si[w](t)−	NOUN
ejpam-3498	246	26	si[w(t)]‖s‖	si[w(t)]‖s‖	ADV
ejpam-3498	246	27	≤	≤	PROPN
ejpam-3498	246	28	c	c	PROPN
ejpam-3498	246	29	max	max	PROPN
ejpam-3498	246	30	(	(	PUNCT
ejpam-3498	246	31	k	k	NOUN
ejpam-3498	246	32	,	,	PUNCT
ejpam-3498	246	33	η)∈n	η)∈n	NUM
ejpam-3498	246	34	(	(	PUNCT
ejpam-3498	246	35	i	i	NOUN
ejpam-3498	246	36	)	)	PUNCT
ejpam-3498	246	37	sup	sup	NOUN
ejpam-3498	246	38	0≤τ≤t	0≤τ≤t	NUM
ejpam-3498	246	39	hρ(i	hρ(i	ADP
ejpam-3498	246	40	,	,	PUNCT
ejpam-3498	246	41	j)[‖wkη	j)[‖wkη	VERB
ejpam-3498	246	42	−	−	PROPN
ejpam-3498	246	43	wkη‖s](τ	wkη‖s](τ	NOUN
ejpam-3498	246	44	)	)	PUNCT
ejpam-3498	246	45	,	,	PUNCT
ejpam-3498	246	46	(	(	PUNCT
ejpam-3498	246	47	12	12	NUM
ejpam-3498	246	48	)	)	PUNCT
ejpam-3498	246	49	where	where	SCONJ
ejpam-3498	246	50	c	c	NOUN
ejpam-3498	246	51	=	=	PUNCT
ejpam-3498	247	1	c	c	X
ejpam-3498	247	2	′/(1−	′/(1−	PROPN
ejpam-3498	247	3	r	r	NOUN
ejpam-3498	247	4	)	)	PUNCT
ejpam-3498	247	5	.	.	PUNCT
ejpam-3498	248	1	from	from	ADP
ejpam-3498	248	2	(	(	PUNCT
ejpam-3498	248	3	11	11	NUM
ejpam-3498	248	4	)	)	PUNCT
ejpam-3498	248	5	,	,	PUNCT
ejpam-3498	248	6	when	when	SCONJ
ejpam-3498	248	7	w	w	PROPN
ejpam-3498	248	8	=	=	NOUN
ejpam-3498	248	9	0	0	NUM
ejpam-3498	248	10	and	and	CCONJ
ejpam-3498	248	11	u	u	PROPN
ejpam-3498	248	12	∈wt0,r	∈wt0,r	NOUN
ejpam-3498	248	13	,	,	PUNCT
ejpam-3498	248	14	we	we	PRON
ejpam-3498	248	15	have	have	VERB
ejpam-3498	248	16	‖si[0](t)‖s	‖si[0](t)‖	VERB
ejpam-3498	248	17	=	=	SYM
ejpam-3498	248	18	‖ψi(s[0	‖ψi(s[0	NOUN
ejpam-3498	248	19	]	]	X
ejpam-3498	248	20	,	,	PUNCT
ejpam-3498	248	21	0)(t)‖s	0)(t)‖s	DET
ejpam-3498	248	22	≤	≤	PUNCT
ejpam-3498	248	23	r‖si[0](t)‖s	r‖si[0](t)‖s	PROPN
ejpam-3498	248	24	+	+	CCONJ
ejpam-3498	248	25	r2(1−	r2(1−	NOUN
ejpam-3498	248	26	r)rµ(t)α	r)rµ(t)α	NOUN
ejpam-3498	248	27	.	.	PUNCT
ejpam-3498	249	1	hence	hence	ADV
ejpam-3498	249	2	,	,	PUNCT
ejpam-3498	249	3	since	since	SCONJ
ejpam-3498	249	4	r	r	NOUN
ejpam-3498	249	5	∈	∈	PROPN
ejpam-3498	249	6	(	(	PUNCT
ejpam-3498	249	7	0	0	NUM
ejpam-3498	249	8	,	,	PUNCT
ejpam-3498	249	9	1	1	NUM
ejpam-3498	249	10	)	)	PUNCT
ejpam-3498	249	11	,	,	PUNCT
ejpam-3498	249	12	we	we	PRON
ejpam-3498	249	13	have	have	VERB
ejpam-3498	249	14	(	(	PUNCT
ejpam-3498	249	15	1−	1−	NUM
ejpam-3498	249	16	r)‖si[0](t)‖s	r)‖si[0](t)‖s	NOUN
ejpam-3498	249	17	≤	≤	NUM
ejpam-3498	249	18	r2(1−	r2(1−	VERB
ejpam-3498	249	19	r)rµ(t)α	r)rµ(t)α	NOUN
ejpam-3498	249	20	‖si[0]‖s	‖si[0]‖s	ADJ
ejpam-3498	249	21	≤	≤	NUM
ejpam-3498	249	22	r2rµ(t)α	r2rµ(t)α	NOUN
ejpam-3498	249	23	.	.	PUNCT
ejpam-3498	250	1	(	(	PUNCT
ejpam-3498	250	2	13	13	NUM
ejpam-3498	250	3	)	)	PUNCT
ejpam-3498	250	4	to	to	PART
ejpam-3498	250	5	solve	solve	VERB
ejpam-3498	250	6	the	the	DET
ejpam-3498	250	7	equation	equation	NOUN
ejpam-3498	250	8	u	u	NOUN
ejpam-3498	250	9	=	=	PROPN
ejpam-3498	250	10	s[((µ0d)ηuk)(k	s[((µ0d)ηuk)(k	PROPN
ejpam-3498	250	11	,	,	PUNCT
ejpam-3498	250	12	η)∈m	η)∈m	PROPN
ejpam-3498	250	13	]	]	PUNCT
ejpam-3498	250	14	we	we	PRON
ejpam-3498	250	15	use	use	VERB
ejpam-3498	250	16	the	the	DET
ejpam-3498	250	17	method	method	NOUN
ejpam-3498	250	18	of	of	ADP
ejpam-3498	250	19	nirenbergnishida	nirenbergnishida	PROPN
ejpam-3498	250	20	.	.	PUNCT
ejpam-3498	251	1	we	we	PRON
ejpam-3498	251	2	define	define	VERB
ejpam-3498	251	3	un	un	PROPN
ejpam-3498	251	4	=	=	SYM
ejpam-3498	251	5	(	(	PUNCT
ejpam-3498	251	6	un,1	un,1	PROPN
ejpam-3498	251	7	,	,	PUNCT
ejpam-3498	251	8	un,2	un,2	ADJ
ejpam-3498	251	9	...	...	PUNCT
ejpam-3498	251	10	,	,	PUNCT
ejpam-3498	251	11	un	un	PROPN
ejpam-3498	251	12	,	,	PUNCT
ejpam-3498	251	13	n	n	NOUN
ejpam-3498	251	14	)	)	PUNCT
ejpam-3498	251	15	,	,	PUNCT
ejpam-3498	251	16	n	n	NOUN
ejpam-3498	251	17	=	=	SYM
ejpam-3498	251	18	0	0	NUM
ejpam-3498	251	19	,	,	PUNCT
ejpam-3498	251	20	1	1	NUM
ejpam-3498	251	21	,	,	PUNCT
ejpam-3498	251	22	...	...	PUNCT
ejpam-3498	251	23	,	,	PUNCT
ejpam-3498	251	24	recursively	recursively	ADV
ejpam-3498	251	25	by	by	ADP
ejpam-3498	251	26	u0	u0	ADJ
ejpam-3498	251	27	=	=	PROPN
ejpam-3498	251	28	0	0	NUM
ejpam-3498	251	29	,	,	PUNCT
ejpam-3498	251	30	un+1	un+1	NOUN
ejpam-3498	251	31	=	=	SYM
ejpam-3498	251	32	s[((µ0d)ηun	s[((µ0d)ηun	NOUN
ejpam-3498	251	33	,	,	PUNCT
ejpam-3498	251	34	k)(k	k)(k	PROPN
ejpam-3498	251	35	,	,	PUNCT
ejpam-3498	251	36	η)∈n	η)∈n	X
ejpam-3498	251	37	(	(	PUNCT
ejpam-3498	251	38	i	i	NOUN
ejpam-3498	251	39	)	)	PUNCT
ejpam-3498	251	40	]	]	PUNCT
ejpam-3498	252	1	(	(	PUNCT
ejpam-3498	252	2	n	n	NOUN
ejpam-3498	252	3	=	=	SYM
ejpam-3498	252	4	0	0	NUM
ejpam-3498	252	5	,	,	PUNCT
ejpam-3498	252	6	1	1	NUM
ejpam-3498	252	7	,	,	PUNCT
ejpam-3498	252	8	...	...	PUNCT
ejpam-3498	252	9	)	)	PUNCT
ejpam-3498	252	10	.	.	PUNCT
ejpam-3498	253	1	we	we	PRON
ejpam-3498	253	2	write	write	VERB
ejpam-3498	253	3	vn	vn	PROPN
ejpam-3498	253	4	=	=	SYM
ejpam-3498	253	5	un+1	un+1	PROPN
ejpam-3498	253	6	−	−	PROPN
ejpam-3498	253	7	un	un	PROPN
ejpam-3498	253	8	.	.	PROPN
ejpam-3498	254	1	let	let	VERB
ejpam-3498	254	2	a0	a0	PROPN
ejpam-3498	254	3	∈	∈	PROPN
ejpam-3498	254	4	(	(	PUNCT
ejpam-3498	254	5	0	0	NUM
ejpam-3498	254	6	,	,	PUNCT
ejpam-3498	254	7	1	1	NUM
ejpam-3498	254	8	)	)	PUNCT
ejpam-3498	254	9	be	be	AUX
ejpam-3498	254	10	a	a	DET
ejpam-3498	254	11	small	small	ADJ
ejpam-3498	254	12	number	number	NOUN
ejpam-3498	254	13	to	to	PART
ejpam-3498	254	14	be	be	AUX
ejpam-3498	254	15	determined	determine	VERB
ejpam-3498	254	16	later	later	ADV
ejpam-3498	254	17	and	and	CCONJ
ejpam-3498	254	18	an	an	DET
ejpam-3498	254	19	=	=	PROPN
ejpam-3498	254	20	a0	a0	PROPN
ejpam-3498	254	21	n∏	n∏	PROPN
ejpam-3498	254	22	j=1	j=1	PROPN
ejpam-3498	254	23	(	(	PUNCT
ejpam-3498	254	24	1	1	NUM
ejpam-3498	254	25	+	+	NUM
ejpam-3498	254	26	j−2)−1	j−2)−1	NOUN
ejpam-3498	254	27	.	.	PUNCT
ejpam-3498	255	1	e.	e.	PROPN
ejpam-3498	255	2	y.	y.	PROPN
ejpam-3498	255	3	guerrero	guerrero	PROPN
ejpam-3498	255	4	/	/	SYM
ejpam-3498	255	5	eur	eur	PROPN
ejpam-3498	255	6	.	.	PUNCT
ejpam-3498	256	1	j.	j.	PROPN
ejpam-3498	256	2	pure	pure	PROPN
ejpam-3498	256	3	appl	appl	PROPN
ejpam-3498	256	4	.	.	PROPN
ejpam-3498	256	5	math	math	PROPN
ejpam-3498	256	6	,	,	PUNCT
ejpam-3498	256	7	12	12	NUM
ejpam-3498	256	8	(	(	PUNCT
ejpam-3498	256	9	3	3	NUM
ejpam-3498	256	10	)	)	PUNCT
ejpam-3498	256	11	(	(	PUNCT
ejpam-3498	256	12	2019	2019	NUM
ejpam-3498	256	13	)	)	PUNCT
ejpam-3498	256	14	,	,	PUNCT
ejpam-3498	256	15	1297	1297	NUM
ejpam-3498	256	16	-	-	SYM
ejpam-3498	256	17	1314	1314	NUM
ejpam-3498	256	18	1308	1308	NUM
ejpam-3498	256	19	then	then	ADV
ejpam-3498	256	20	,	,	PUNCT
ejpam-3498	256	21	{	{	PUNCT
ejpam-3498	256	22	an}n≥0	an}n≥0	NOUN
ejpam-3498	256	23	is	be	AUX
ejpam-3498	256	24	a	a	DET
ejpam-3498	256	25	decreasing	decrease	VERB
ejpam-3498	256	26	sequence	sequence	NOUN
ejpam-3498	256	27	of	of	ADP
ejpam-3498	256	28	positive	positive	ADJ
ejpam-3498	256	29	numbers	number	NOUN
ejpam-3498	256	30	tending	tend	VERB
ejpam-3498	256	31	to	to	ADP
ejpam-3498	256	32	a	a	DET
ejpam-3498	256	33	positive	positive	ADJ
ejpam-3498	256	34	limit	limit	NOUN
ejpam-3498	256	35	a∞.	a∞.	PROPN
ejpam-3498	256	36	observe	observe	VERB
ejpam-3498	256	37	that	that	SCONJ
ejpam-3498	256	38	a∞	a∞	PROPN
ejpam-3498	256	39	=	=	SYM
ejpam-3498	256	40	a0	a0	PROPN
ejpam-3498	256	41	∞∏	∞∏	PROPN
ejpam-3498	256	42	j=1	j=1	PROPN
ejpam-3498	256	43	(	(	PUNCT
ejpam-3498	256	44	1	1	NUM
ejpam-3498	256	45	+	+	NUM
ejpam-3498	256	46	j−2)−1	j−2)−1	NOUN
ejpam-3498	256	47	=	=	SYM
ejpam-3498	256	48	a0	a0	PROPN
ejpam-3498	256	49	(	(	PUNCT
ejpam-3498	256	50	∞∏	∞∏	X
ejpam-3498	256	51	j=1	j=1	NOUN
ejpam-3498	256	52	(	(	PUNCT
ejpam-3498	256	53	1	1	NUM
ejpam-3498	256	54	+	+	CCONJ
ejpam-3498	256	55	j−2	j−2	PROPN
ejpam-3498	256	56	)	)	PUNCT
ejpam-3498	256	57	)	)	PUNCT
ejpam-3498	256	58	−1	−1	NOUN
ejpam-3498	256	59	.	.	PUNCT
ejpam-3498	257	1	since	since	SCONJ
ejpam-3498	257	2	∑∞	∑∞	NOUN
ejpam-3498	257	3	j=1	j=1	PROPN
ejpam-3498	257	4	j	j	PROPN
ejpam-3498	257	5	−2	−2	PROPN
ejpam-3498	257	6	is	be	AUX
ejpam-3498	257	7	convergent	convergent	ADJ
ejpam-3498	257	8	,	,	PUNCT
ejpam-3498	257	9	a∞	a∞	PROPN
ejpam-3498	257	10	is	be	AUX
ejpam-3498	257	11	convergent	convergent	NOUN
ejpam-3498	257	12	.	.	PUNCT
ejpam-3498	258	1	corresponding	correspond	VERB
ejpam-3498	258	2	to	to	ADP
ejpam-3498	258	3	each	each	DET
ejpam-3498	258	4	an	an	NOUN
ejpam-3498	258	5	,	,	PUNCT
ejpam-3498	258	6	we	we	PRON
ejpam-3498	258	7	have	have	VERB
ejpam-3498	258	8	the	the	DET
ejpam-3498	258	9	t	t	NOUN
ejpam-3498	258	10	-	-	PUNCT
ejpam-3498	258	11	interval	interval	NOUN
ejpam-3498	258	12	in(s	in(s	NOUN
ejpam-3498	258	13	)	)	PUNCT
ejpam-3498	258	14	=	=	PRON
ejpam-3498	258	15	{	{	PUNCT
ejpam-3498	258	16	t	t	X
ejpam-3498	258	17	≥	≥	NOUN
ejpam-3498	258	18	0	0	NUM
ejpam-3498	258	19	:	:	PUNCT
ejpam-3498	258	20	ω(t	ω(t	NOUN
ejpam-3498	258	21	)	)	PUNCT
ejpam-3498	258	22	<	<	X
ejpam-3498	258	23	an(s0	an(s0	X
ejpam-3498	258	24	−	−	PROPN
ejpam-3498	258	25	s	s	NOUN
ejpam-3498	258	26	)	)	PUNCT
ejpam-3498	258	27	}	}	PUNCT
ejpam-3498	258	28	(	(	PUNCT
ejpam-3498	258	29	0	0	PUNCT
ejpam-3498	258	30	<	<	X
ejpam-3498	258	31	s	s	X
ejpam-3498	258	32	<	<	X
ejpam-3498	258	33	s0	s0	PROPN
ejpam-3498	258	34	)	)	PUNCT
ejpam-3498	258	35	,	,	PUNCT
ejpam-3498	258	36	and	and	CCONJ
ejpam-3498	258	37	σn	σn	NOUN
ejpam-3498	258	38	,	,	PUNCT
ejpam-3498	258	39	s(t	s(t	PROPN
ejpam-3498	258	40	)	)	PUNCT
ejpam-3498	258	41	=	=	PRON
ejpam-3498	258	42	(	(	PUNCT
ejpam-3498	258	43	1−	1−	NUM
ejpam-3498	258	44	ω(t	ω(t	NOUN
ejpam-3498	258	45	)	)	PUNCT
ejpam-3498	258	46	an(s0	an(s0	X
ejpam-3498	259	1	−	−	PROPN
ejpam-3498	259	2	s	s	PROPN
ejpam-3498	259	3	)	)	PUNCT
ejpam-3498	259	4	)	)	PUNCT
ejpam-3498	260	1	−1	−1	NOUN
ejpam-3498	260	2	.	.	PUNCT
ejpam-3498	261	1	note	note	VERB
ejpam-3498	261	2	that	that	SCONJ
ejpam-3498	261	3	for	for	ADP
ejpam-3498	261	4	all	all	DET
ejpam-3498	261	5	n	n	CCONJ
ejpam-3498	261	6	,	,	PUNCT
ejpam-3498	261	7	σn	σn	NOUN
ejpam-3498	261	8	,	,	PUNCT
ejpam-3498	261	9	s(t	s(t	PROPN
ejpam-3498	261	10	)	)	PUNCT
ejpam-3498	261	11	≥	≥	NOUN
ejpam-3498	261	12	1	1	NUM
ejpam-3498	261	13	and	and	CCONJ
ejpam-3498	261	14	in+1(s	in+1(s	PROPN
ejpam-3498	261	15	)	)	PUNCT
ejpam-3498	261	16	⊂	⊂	PROPN
ejpam-3498	261	17	in(s	in(	NOUN
ejpam-3498	261	18	)	)	PUNCT
ejpam-3498	261	19	.	.	PUNCT
ejpam-3498	262	1	let	let	VERB
ejpam-3498	262	2	a0s0	a0s0	VERB
ejpam-3498	262	3	≤	≤	ADV
ejpam-3498	262	4	w(t0	w(t0	NOUN
ejpam-3498	262	5	)	)	PUNCT
ejpam-3498	262	6	.	.	PUNCT
ejpam-3498	263	1	then	then	ADV
ejpam-3498	263	2	i0(s	i0(s	X
ejpam-3498	263	3	)	)	PUNCT
ejpam-3498	263	4	⊂	⊂	PROPN
ejpam-3498	264	1	[	[	X
ejpam-3498	264	2	0	0	NUM
ejpam-3498	264	3	,	,	PUNCT
ejpam-3498	264	4	t0	t0	PROPN
ejpam-3498	264	5	)	)	PUNCT
ejpam-3498	264	6	.	.	PUNCT
ejpam-3498	265	1	put	put	VERB
ejpam-3498	265	2	s(t	s(t	PROPN
ejpam-3498	265	3	)	)	PUNCT
ejpam-3498	265	4	=	=	PUNCT
ejpam-3498	266	1	(	(	PUNCT
ejpam-3498	266	2	s0	s0	PROPN
ejpam-3498	266	3	+	+	CCONJ
ejpam-3498	266	4	s	s	PART
ejpam-3498	266	5	−	−	PROPN
ejpam-3498	266	6	ω(t	ω(t	NOUN
ejpam-3498	266	7	)	)	PUNCT
ejpam-3498	266	8	an	an	PRON
ejpam-3498	266	9	)	)	PUNCT
ejpam-3498	266	10	/2	/2	PUNCT
ejpam-3498	266	11	.	.	PUNCT
ejpam-3498	267	1	then	then	ADV
ejpam-3498	267	2	,	,	PUNCT
ejpam-3498	267	3	for	for	ADP
ejpam-3498	267	4	0	0	NUM
ejpam-3498	267	5	<	<	X
ejpam-3498	267	6	s	s	X
ejpam-3498	267	7	<	<	X
ejpam-3498	267	8	s(t	s(t	PROPN
ejpam-3498	267	9	)	)	PUNCT
ejpam-3498	267	10	<	<	X
ejpam-3498	267	11	s0	s0	PROPN
ejpam-3498	267	12	,	,	PUNCT
ejpam-3498	267	13	we	we	PRON
ejpam-3498	267	14	have	have	VERB
ejpam-3498	267	15	the	the	DET
ejpam-3498	267	16	following	follow	VERB
ejpam-3498	267	17	remark	remark	NOUN
ejpam-3498	267	18	.	.	PUNCT
ejpam-3498	268	1	remark	remark	PROPN
ejpam-3498	268	2	3	3	NUM
ejpam-3498	268	3	.	.	PUNCT
ejpam-3498	269	1	if	if	SCONJ
ejpam-3498	269	2	t	t	PROPN
ejpam-3498	269	3	∈	∈	PROPN
ejpam-3498	269	4	in(s	in(s	NOUN
ejpam-3498	269	5	)	)	PUNCT
ejpam-3498	269	6	,	,	PUNCT
ejpam-3498	269	7	then	then	ADV
ejpam-3498	269	8	(	(	PUNCT
ejpam-3498	269	9	1	1	X
ejpam-3498	269	10	)	)	PUNCT
ejpam-3498	269	11	t	t	PROPN
ejpam-3498	269	12	∈	∈	PROPN
ejpam-3498	269	13	in(s(t	in(s(t	NOUN
ejpam-3498	269	14	)	)	PUNCT
ejpam-3498	269	15	)	)	PUNCT
ejpam-3498	269	16	(	(	PUNCT
ejpam-3498	269	17	2	2	X
ejpam-3498	269	18	)	)	PUNCT
ejpam-3498	269	19	σn	σn	NOUN
ejpam-3498	269	20	,	,	PUNCT
ejpam-3498	269	21	s(t	s(t	PROPN
ejpam-3498	269	22	)	)	PUNCT
ejpam-3498	269	23	≤	≤	NOUN
ejpam-3498	269	24	2σn	2σn	ADJ
ejpam-3498	269	25	,	,	PUNCT
ejpam-3498	269	26	s(t	s(t	PROPN
ejpam-3498	269	27	)	)	PUNCT
ejpam-3498	269	28	(	(	PUNCT
ejpam-3498	269	29	3	3	X
ejpam-3498	269	30	)	)	PUNCT
ejpam-3498	269	31	(	(	PUNCT
ejpam-3498	269	32	s(t)−	s(t)−	PROPN
ejpam-3498	269	33	s)−η	s)−η	NOUN
ejpam-3498	269	34	=	=	SYM
ejpam-3498	269	35	2η(s0	2η(s0	NUM
ejpam-3498	269	36	−	−	PROPN
ejpam-3498	269	37	s)−ησn	s)−ησn	PROPN
ejpam-3498	269	38	,	,	PUNCT
ejpam-3498	269	39	s(t)η	s(t)η	PROPN
ejpam-3498	269	40	(	(	PUNCT
ejpam-3498	269	41	4	4	NUM
ejpam-3498	269	42	)	)	SYM
ejpam-3498	269	43	1	1	NUM
ejpam-3498	269	44	≤	≤	NUM
ejpam-3498	269	45	σn	σn	NOUN
ejpam-3498	269	46	,	,	PUNCT
ejpam-3498	269	47	s(t	s(t	PROPN
ejpam-3498	269	48	)	)	PUNCT
ejpam-3498	269	49	≤	≤	NOUN
ejpam-3498	269	50	(	(	PUNCT
ejpam-3498	269	51	n+	n+	NUM
ejpam-3498	269	52	1)2	1)2	NUM
ejpam-3498	269	53	+	+	CCONJ
ejpam-3498	269	54	1	1	X
ejpam-3498	269	55	.	.	PUNCT
ejpam-3498	269	56	(	(	PUNCT
ejpam-3498	269	57	5	5	NUM
ejpam-3498	269	58	)	)	PUNCT
ejpam-3498	269	59	(	(	PUNCT
ejpam-3498	269	60	s0	s0	PROPN
ejpam-3498	269	61	−	−	PROPN
ejpam-3498	269	62	s)−η	s)−η	PROPN
ejpam-3498	269	63	≤	≤	ADV
ejpam-3498	269	64	a0ω(t)cη	a0ω(t)cη	PRON
ejpam-3498	269	65	ω(t)ηµ(t)κη	ω(t)ηµ(t)κη	PUNCT
ejpam-3498	269	66	we	we	PRON
ejpam-3498	269	67	now	now	ADV
ejpam-3498	269	68	prove	prove	VERB
ejpam-3498	269	69	the	the	DET
ejpam-3498	269	70	following	follow	VERB
ejpam-3498	269	71	proposition	proposition	NOUN
ejpam-3498	269	72	.	.	PUNCT
ejpam-3498	270	1	proving	prove	VERB
ejpam-3498	270	2	it	it	PRON
ejpam-3498	270	3	means	mean	VERB
ejpam-3498	270	4	proving	prove	VERB
ejpam-3498	270	5	the	the	DET
ejpam-3498	270	6	convergence	convergence	NOUN
ejpam-3498	270	7	of	of	ADP
ejpam-3498	270	8	our	our	PRON
ejpam-3498	270	9	solution	solution	NOUN
ejpam-3498	270	10	u(t	u(t	NOUN
ejpam-3498	270	11	,	,	PUNCT
ejpam-3498	270	12	x	x	NOUN
ejpam-3498	270	13	)	)	PUNCT
ejpam-3498	270	14	=	=	SYM
ejpam-3498	270	15	lim	lim	PROPN
ejpam-3498	270	16	n→∞	n→∞	NUM
ejpam-3498	270	17	un(t	un(t	NOUN
ejpam-3498	270	18	,	,	PUNCT
ejpam-3498	270	19	x	x	NOUN
ejpam-3498	270	20	)	)	PUNCT
ejpam-3498	270	21	,	,	PUNCT
ejpam-3498	270	22	for	for	ADP
ejpam-3498	270	23	x	x	PROPN
ejpam-3498	270	24	∈	∈	PROPN
ejpam-3498	270	25	u	u	NOUN
ejpam-3498	270	26	and	and	CCONJ
ejpam-3498	270	27	t	t	NOUN
ejpam-3498	270	28	∈	∈	PROPN
ejpam-3498	270	29	i∞(s	i∞(	NOUN
ejpam-3498	270	30	)	)	PUNCT
ejpam-3498	270	31	=	=	SYM
ejpam-3498	270	32	{	{	PUNCT
ejpam-3498	270	33	t	t	X
ejpam-3498	270	34	≥	≥	NOUN
ejpam-3498	270	35	0	0	NUM
ejpam-3498	270	36	:	:	PUNCT
ejpam-3498	270	37	ω(t	ω(t	NOUN
ejpam-3498	270	38	)	)	PUNCT
ejpam-3498	270	39	<	<	X
ejpam-3498	270	40	a0(s0	a0(s0	CCONJ
ejpam-3498	270	41	−	−	PROPN
ejpam-3498	270	42	s	s	NOUN
ejpam-3498	270	43	)	)	PUNCT
ejpam-3498	270	44	}	}	PUNCT
ejpam-3498	270	45	(	(	PUNCT
ejpam-3498	270	46	0	0	PUNCT
ejpam-3498	270	47	<	<	X
ejpam-3498	270	48	s	s	X
ejpam-3498	270	49	<	<	X
ejpam-3498	270	50	s0	s0	PROPN
ejpam-3498	270	51	)	)	PUNCT
ejpam-3498	270	52	.	.	PUNCT
ejpam-3498	271	1	proposition	proposition	NOUN
ejpam-3498	271	2	3	3	X
ejpam-3498	271	3	.	.	PUNCT
ejpam-3498	272	1	let	let	VERB
ejpam-3498	272	2	vn	vn	VERB
ejpam-3498	272	3	,	,	PUNCT
ejpam-3498	272	4	i	i	PRON
ejpam-3498	272	5	=	=	PUNCT
ejpam-3498	272	6	un+1,i	un+1,i	PROPN
ejpam-3498	272	7	−	−	PROPN
ejpam-3498	272	8	un	un	PROPN
ejpam-3498	272	9	,	,	PUNCT
ejpam-3498	272	10	i.	i.	NOUN
ejpam-3498	272	11	for	for	ADP
ejpam-3498	272	12	n	n	PROPN
ejpam-3498	272	13	≥	≥	NOUN
ejpam-3498	272	14	0	0	NUM
ejpam-3498	272	15	the	the	DET
ejpam-3498	272	16	following	follow	VERB
ejpam-3498	272	17	hold	hold	NOUN
ejpam-3498	272	18	:	:	PUNCT
ejpam-3498	272	19	(	(	PUNCT
ejpam-3498	272	20	a	a	X
ejpam-3498	272	21	)	)	PUNCT
ejpam-3498	272	22	un+1,i	un+1,i	NOUN
ejpam-3498	272	23	:	:	PUNCT
ejpam-3498	272	24	=	=	SYM
ejpam-3498	272	25	si[(µ0d)ηun	si[(µ0d)ηun	PROPN
ejpam-3498	272	26	,	,	PUNCT
ejpam-3498	272	27	k](k	k](k	X
ejpam-3498	272	28	,	,	PUNCT
ejpam-3498	272	29	η)∈n	η)∈n	X
ejpam-3498	272	30	(	(	PUNCT
ejpam-3498	272	31	i	i	NOUN
ejpam-3498	272	32	)	)	PUNCT
ejpam-3498	272	33	exists	exist	VERB
ejpam-3498	272	34	on	on	ADP
ejpam-3498	272	35	in(s)×	in(s)×	PROPN
ejpam-3498	272	36	ui	ui	PROPN
ejpam-3498	272	37	.	.	PUNCT
ejpam-3498	273	1	(	(	PUNCT
ejpam-3498	273	2	b	b	X
ejpam-3498	273	3	)	)	PUNCT
ejpam-3498	273	4	for	for	ADP
ejpam-3498	273	5	t	t	PROPN
ejpam-3498	273	6	∈	∈	PROPN
ejpam-3498	273	7	in(s	in(s	NOUN
ejpam-3498	273	8	)	)	PUNCT
ejpam-3498	273	9	,	,	PUNCT
ejpam-3498	273	10	‖vn	‖vn	PROPN
ejpam-3498	273	11	,	,	PUNCT
ejpam-3498	273	12	i(t)‖s	i(t)‖s	ADJ
ejpam-3498	273	13	≤	≤	NUM
ejpam-3498	273	14	rrn+2µ(t)(1−κ)nω(t)nσn	rrn+2µ(t)(1−κ)nω(t)nσn	NOUN
ejpam-3498	273	15	,	,	PUNCT
ejpam-3498	273	16	s(t	s(t	PROPN
ejpam-3498	273	17	)	)	PUNCT
ejpam-3498	273	18	dnµ(t)α	dnµ(t)α	PROPN
ejpam-3498	273	19	.	.	PUNCT
ejpam-3498	274	1	e.	e.	PROPN
ejpam-3498	274	2	y.	y.	PROPN
ejpam-3498	274	3	guerrero	guerrero	PROPN
ejpam-3498	274	4	/	/	SYM
ejpam-3498	274	5	eur	eur	PROPN
ejpam-3498	274	6	.	.	PUNCT
ejpam-3498	275	1	j.	j.	PROPN
ejpam-3498	275	2	pure	pure	PROPN
ejpam-3498	275	3	appl	appl	PROPN
ejpam-3498	275	4	.	.	PROPN
ejpam-3498	275	5	math	math	PROPN
ejpam-3498	275	6	,	,	PUNCT
ejpam-3498	275	7	12	12	NUM
ejpam-3498	275	8	(	(	PUNCT
ejpam-3498	275	9	3	3	NUM
ejpam-3498	275	10	)	)	PUNCT
ejpam-3498	275	11	(	(	PUNCT
ejpam-3498	275	12	2019	2019	NUM
ejpam-3498	275	13	)	)	PUNCT
ejpam-3498	275	14	,	,	PUNCT
ejpam-3498	275	15	1297	1297	NUM
ejpam-3498	275	16	-	-	SYM
ejpam-3498	275	17	1314	1314	NUM
ejpam-3498	275	18	1309	1309	NUM
ejpam-3498	275	19	(	(	PUNCT
ejpam-3498	275	20	c	c	NOUN
ejpam-3498	275	21	)	)	PUNCT
ejpam-3498	275	22	for	for	ADP
ejpam-3498	275	23	t	t	PROPN
ejpam-3498	275	24	∈	∈	PROPN
ejpam-3498	275	25	in(s	in(s	NOUN
ejpam-3498	275	26	)	)	PUNCT
ejpam-3498	275	27	,	,	PUNCT
ejpam-3498	275	28	‖(µ0(t)d)ηvn	‖(µ0(t)d)ηvn	NOUN
ejpam-3498	275	29	,	,	PUNCT
ejpam-3498	275	30	i(t)‖s	i(t)‖s	ADJ
ejpam-3498	275	31	≤	≤	NUM
ejpam-3498	275	32	rrn+22dn+ηkη(s0	rrn+22dn+ηkη(s0	NOUN
ejpam-3498	275	33	−	−	PROPN
ejpam-3498	275	34	s)−ηµ(t)(1−κ)n+ηω(t)nσn	s)−ηµ(t)(1−κ)n+ηω(t)nσn	PROPN
ejpam-3498	275	35	,	,	PUNCT
ejpam-3498	275	36	s(t	s(t	PROPN
ejpam-3498	275	37	)	)	PUNCT
ejpam-3498	275	38	dn+ηµ(t)α	dn+ηµ(t)α	PROPN
ejpam-3498	275	39	.	.	PUNCT
ejpam-3498	276	1	implying	imply	VERB
ejpam-3498	276	2	that	that	PRON
ejpam-3498	276	3	for	for	ADP
ejpam-3498	276	4	t	t	PROPN
ejpam-3498	276	5	∈	∈	PROPN
ejpam-3498	276	6	in+1	in+1	NOUN
ejpam-3498	276	7	,	,	PUNCT
ejpam-3498	276	8	‖(µ0(t)d)ηvn	‖(µ0(t)d)ηvn	NOUN
ejpam-3498	276	9	,	,	PUNCT
ejpam-3498	276	10	i(t)‖s	i(t)‖s	ADJ
ejpam-3498	276	11	≤	≤	PROPN
ejpam-3498	276	12	rrn+22dn+ηkηa0µ(t)(1−κ)n+(1−κ)ηωn+(c−1)ησn	rrn+22dn+ηkηa0µ(t)(1−κ)n+(1−κ)ηωn+(c−1)ησn	PROPN
ejpam-3498	276	13	,	,	PUNCT
ejpam-3498	276	14	s(t	s(t	PROPN
ejpam-3498	276	15	)	)	PUNCT
ejpam-3498	276	16	dn+ηµ(t)α	dn+ηµ(t)α	PROPN
ejpam-3498	276	17	and	and	CCONJ
ejpam-3498	276	18	thus	thus	ADV
ejpam-3498	276	19	,	,	PUNCT
ejpam-3498	276	20	‖(µ0(t)d)ηun+1,i‖s	‖(µ0(t)d)ηun+1,i‖s	PROPN
ejpam-3498	276	21	≤	≤	PROPN
ejpam-3498	276	22	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	276	23	.	.	PUNCT
ejpam-3498	276	24	proof	proof	NOUN
ejpam-3498	276	25	.	.	PUNCT
ejpam-3498	277	1	since	since	SCONJ
ejpam-3498	277	2	u0,i	u0,i	PROPN
ejpam-3498	277	3	=	=	SYM
ejpam-3498	277	4	0	0	NUM
ejpam-3498	277	5	,	,	PUNCT
ejpam-3498	277	6	proposition	proposition	NOUN
ejpam-3498	277	7	1	1	NUM
ejpam-3498	277	8	assures	assure	VERB
ejpam-3498	277	9	us	we	PRON
ejpam-3498	277	10	that	that	PRON
ejpam-3498	277	11	u1,i	u1,i	NOUN
ejpam-3498	277	12	=	=	SYM
ejpam-3498	277	13	si[0	si[0	NOUN
ejpam-3498	277	14	]	]	PUNCT
ejpam-3498	277	15	exists	exist	VERB
ejpam-3498	277	16	for	for	ADP
ejpam-3498	277	17	t	t	PROPN
ejpam-3498	277	18	∈	∈	PROPN
ejpam-3498	277	19	i0(s	i0(s	PROPN
ejpam-3498	277	20	)	)	PUNCT
ejpam-3498	277	21	.	.	PUNCT
ejpam-3498	278	1	by	by	ADP
ejpam-3498	278	2	(	(	PUNCT
ejpam-3498	278	3	13	13	NUM
ejpam-3498	278	4	)	)	PUNCT
ejpam-3498	278	5	,	,	PUNCT
ejpam-3498	278	6	‖v0,i(t)‖s	‖v0,i(t)‖s	ADV
ejpam-3498	278	7	=	=	PUNCT
ejpam-3498	278	8	‖u1,i(t)−	‖u1,i(t)−	PUNCT
ejpam-3498	278	9	u0,i(t)‖s	u0,i(t)‖s	PROPN
ejpam-3498	278	10	=	=	SYM
ejpam-3498	278	11	‖u1,i(t)‖s	‖u1,i(t)‖s	NUM
ejpam-3498	278	12	=	=	NOUN
ejpam-3498	278	13	‖si[0](t)‖s	‖si[0](t)‖s	X
ejpam-3498	278	14	≤	≤	ADJ
ejpam-3498	278	15	rr2µ(t)α	rr2µ(t)α	NOUN
ejpam-3498	278	16	.	.	PUNCT
ejpam-3498	279	1	by	by	ADP
ejpam-3498	279	2	(	(	PUNCT
ejpam-3498	279	3	3	3	NUM
ejpam-3498	279	4	)	)	PUNCT
ejpam-3498	279	5	and	and	CCONJ
ejpam-3498	279	6	remark	remark	VERB
ejpam-3498	279	7	3	3	NUM
ejpam-3498	279	8	(	(	PUNCT
ejpam-3498	279	9	3	3	X
ejpam-3498	279	10	)	)	PUNCT
ejpam-3498	279	11	we	we	PRON
ejpam-3498	279	12	have	have	VERB
ejpam-3498	279	13	‖(µ0d)ηv0,i(t)‖s	‖(µ0d)ηv0,i(t)‖s	ADJ
ejpam-3498	279	14	≤	≤	ADJ
ejpam-3498	279	15	µ(t)ηkη(s(t)−	µ(t)ηkη(s(t)−	PROPN
ejpam-3498	279	16	s)−η‖v0,i(t)‖s(t	s)−η‖v0,i(t)‖s(t	PROPN
ejpam-3498	279	17	)	)	PUNCT
ejpam-3498	279	18	≤	≤	NUM
ejpam-3498	279	19	µ(t)ηkη2	µ(t)ηkη2	PROPN
ejpam-3498	279	20	η(s0	η(s0	NOUN
ejpam-3498	279	21	−	−	NOUN
ejpam-3498	279	22	s)−ησ0,s(t)ηrr2µ(t)α	s)−ησ0,s(t)ηrr2µ(t)α	NOUN
ejpam-3498	279	23	=	=	SYM
ejpam-3498	279	24	rr22ηkη(s0	rr22ηkη(s0	PROPN
ejpam-3498	279	25	−	−	PROPN
ejpam-3498	279	26	s)−ηµ(t)ηση0,sµ(t)α	s)−ηµ(t)ηση0,sµ(t)α	PROPN
ejpam-3498	279	27	.	.	PUNCT
ejpam-3498	280	1	hence	hence	ADV
ejpam-3498	280	2	,	,	PUNCT
ejpam-3498	280	3	by	by	ADP
ejpam-3498	280	4	remark	remark	NOUN
ejpam-3498	280	5	3	3	NUM
ejpam-3498	280	6	(	(	PUNCT
ejpam-3498	280	7	5	5	NUM
ejpam-3498	280	8	)	)	PUNCT
ejpam-3498	280	9	,	,	PUNCT
ejpam-3498	280	10	for	for	ADP
ejpam-3498	280	11	t	t	PROPN
ejpam-3498	280	12	∈	∈	PROPN
ejpam-3498	280	13	i1(s	i1(s	PROPN
ejpam-3498	280	14	)	)	PUNCT
ejpam-3498	280	15	,	,	PUNCT
ejpam-3498	280	16	we	we	PRON
ejpam-3498	280	17	have	have	VERB
ejpam-3498	280	18	‖(µ0d)ηv0,i(t)‖s	‖(µ0d)ηv0,i(t)‖s	ADJ
ejpam-3498	280	19	=	=	SYM
ejpam-3498	280	20	‖(µ0d)ηu1,i(t)‖	‖(µ0d)ηu1,i(t)‖	PROPN
ejpam-3498	280	21	≤	≤	PROPN
ejpam-3498	280	22	rr22ηkη(s0	rr22ηkη(s0	NOUN
ejpam-3498	280	23	−	−	PROPN
ejpam-3498	280	24	s)−ηµ(t)ηση0,sµ(t)α	s)−ηµ(t)ηση0,sµ(t)α	VERB
ejpam-3498	280	25	≤	≤	PUNCT
ejpam-3498	280	26	rr22ηkη	rr22ηkη	PRON
ejpam-3498	280	27	aη0ω(t)cη	aη0ω(t)cη	NOUN
ejpam-3498	280	28	ω(t)ηµ(t)κη	ω(t)ηµ(t)κη	PRON
ejpam-3498	280	29	µ(t)ηση0,sµ(t)α	µ(t)ηση0,sµ(t)α	VERB
ejpam-3498	280	30	≤	≤	NUM
ejpam-3498	280	31	rr22ηkηa0µ(t)(1−κ)ηω(t)(c−1)ηση0,sµ(t)α	rr22ηkηa0µ(t)(1−κ)ηω(t)(c−1)ηση0,sµ(t)α	NUM
ejpam-3498	280	32	≤	≤	NUM
ejpam-3498	280	33	rµ(t)α	rµ(t)α	NOUN
ejpam-3498	280	34	,	,	PUNCT
ejpam-3498	280	35	provided	provide	VERB
ejpam-3498	280	36	a0	a0	PROPN
ejpam-3498	280	37	is	be	AUX
ejpam-3498	280	38	small	small	ADJ
ejpam-3498	280	39	enough	enough	ADV
ejpam-3498	280	40	.	.	PUNCT
ejpam-3498	281	1	suppose	suppose	VERB
ejpam-3498	281	2	(	(	PUNCT
ejpam-3498	281	3	a)-(c	a)-(c	NUM
ejpam-3498	281	4	)	)	PUNCT
ejpam-3498	281	5	hold	hold	VERB
ejpam-3498	281	6	for	for	ADP
ejpam-3498	281	7	n	n	NOUN
ejpam-3498	281	8	=	=	SYM
ejpam-3498	281	9	0	0	NUM
ejpam-3498	281	10	,	,	PUNCT
ejpam-3498	281	11	1	1	NUM
ejpam-3498	281	12	,	,	PUNCT
ejpam-3498	281	13	...	...	PUNCT
ejpam-3498	281	14	,	,	PUNCT
ejpam-3498	281	15	p	p	NOUN
ejpam-3498	281	16	with	with	ADP
ejpam-3498	281	17	n	n	PRON
ejpam-3498	281	18	≤	≤	NOUN
ejpam-3498	281	19	l.	l.	NOUN
ejpam-3498	281	20	proposition	proposition	NOUN
ejpam-3498	281	21	1	1	NUM
ejpam-3498	281	22	and	and	CCONJ
ejpam-3498	281	23	(	(	PUNCT
ejpam-3498	281	24	c	c	NOUN
ejpam-3498	281	25	)	)	PUNCT
ejpam-3498	281	26	imply	imply	VERB
ejpam-3498	281	27	that	that	PRON
ejpam-3498	281	28	up+2,i	up+2,i	PROPN
ejpam-3498	281	29	=	=	SYM
ejpam-3498	281	30	s[(µ0d)ηup+1,k	s[(µ0d)ηup+1,k	PROPN
ejpam-3498	281	31	]	]	PUNCT
ejpam-3498	281	32	exists	exist	VERB
ejpam-3498	281	33	for	for	ADP
ejpam-3498	281	34	t	t	PROPN
ejpam-3498	281	35	∈	∈	PROPN
ejpam-3498	281	36	ip+1(s	ip+1(s	PROPN
ejpam-3498	281	37	)	)	PUNCT
ejpam-3498	281	38	,	,	PUNCT
ejpam-3498	281	39	showing	show	VERB
ejpam-3498	281	40	(	(	PUNCT
ejpam-3498	281	41	a	a	NOUN
ejpam-3498	281	42	)	)	PUNCT
ejpam-3498	281	43	for	for	ADP
ejpam-3498	281	44	n	n	NOUN
ejpam-3498	281	45	=	=	SYM
ejpam-3498	281	46	p	p	NOUN
ejpam-3498	282	1	+	+	NOUN
ejpam-3498	282	2	1	1	X
ejpam-3498	282	3	.	.	PUNCT
ejpam-3498	282	4	now	now	ADV
ejpam-3498	282	5	,	,	PUNCT
ejpam-3498	282	6	for	for	ADP
ejpam-3498	282	7	t	t	PROPN
ejpam-3498	282	8	∈	∈	PROPN
ejpam-3498	282	9	ip+1(s	ip+1(s	PROPN
ejpam-3498	282	10	)	)	PUNCT
ejpam-3498	282	11	and	and	CCONJ
ejpam-3498	282	12	proposition	proposition	NOUN
ejpam-3498	282	13	2	2	NUM
ejpam-3498	282	14	,	,	PUNCT
ejpam-3498	282	15	‖vp+1,i(t)‖s	‖vp+1,i(t)‖s	NOUN
ejpam-3498	282	16	=	=	SYM
ejpam-3498	282	17	‖si[((µ0d)ηup+1,k)](t)−	‖si[((µ0d)ηup+1,k)](t)−	PROPN
ejpam-3498	282	18	si[((µ0d)ηup	si[((µ0d)ηup	PROPN
ejpam-3498	282	19	,	,	PUNCT
ejpam-3498	282	20	k)](t)‖s	k)](t)‖	NOUN
ejpam-3498	282	21	≤	≤	NUM
ejpam-3498	282	22	c	c	X
ejpam-3498	282	23	max	max	PROPN
ejpam-3498	282	24	(	(	PUNCT
ejpam-3498	282	25	k	k	NOUN
ejpam-3498	282	26	,	,	PUNCT
ejpam-3498	282	27	η)∈n	η)∈n	NUM
ejpam-3498	282	28	(	(	PUNCT
ejpam-3498	282	29	i	i	NOUN
ejpam-3498	282	30	)	)	PUNCT
ejpam-3498	282	31	sup	sup	NOUN
ejpam-3498	282	32	0≤τ≤t	0≤τ≤t	NUM
ejpam-3498	282	33	hρ(i.j)[‖((µ0d)ηvp	hρ(i.j)[‖((µ0d)ηvp	NOUN
ejpam-3498	282	34	,	,	PUNCT
ejpam-3498	282	35	k)‖s](τ	k)‖s](τ	PROPN
ejpam-3498	282	36	)	)	PUNCT
ejpam-3498	282	37	.	.	PUNCT
ejpam-3498	283	1	e.	e.	PROPN
ejpam-3498	283	2	y.	y.	PROPN
ejpam-3498	283	3	guerrero	guerrero	PROPN
ejpam-3498	283	4	/	/	SYM
ejpam-3498	283	5	eur	eur	PROPN
ejpam-3498	283	6	.	.	PUNCT
ejpam-3498	284	1	j.	j.	PROPN
ejpam-3498	284	2	pure	pure	PROPN
ejpam-3498	284	3	appl	appl	PROPN
ejpam-3498	284	4	.	.	PROPN
ejpam-3498	284	5	math	math	PROPN
ejpam-3498	284	6	,	,	PUNCT
ejpam-3498	284	7	12	12	NUM
ejpam-3498	284	8	(	(	PUNCT
ejpam-3498	284	9	3	3	NUM
ejpam-3498	284	10	)	)	PUNCT
ejpam-3498	284	11	(	(	PUNCT
ejpam-3498	284	12	2019	2019	NUM
ejpam-3498	284	13	)	)	PUNCT
ejpam-3498	284	14	,	,	PUNCT
ejpam-3498	284	15	1297	1297	NUM
ejpam-3498	284	16	-	-	SYM
ejpam-3498	284	17	1314	1314	NUM
ejpam-3498	284	18	1310	1310	NUM
ejpam-3498	284	19	using	use	VERB
ejpam-3498	284	20	lemma	lemma	PROPN
ejpam-3498	284	21	4	4	NUM
ejpam-3498	284	22	ρ(i	ρ(i	PROPN
ejpam-3498	284	23	,	,	PUNCT
ejpam-3498	284	24	j)-times	j)-time	NOUN
ejpam-3498	284	25	,	,	PUNCT
ejpam-3498	284	26	we	we	PRON
ejpam-3498	284	27	have	have	VERB
ejpam-3498	284	28	by	by	ADP
ejpam-3498	284	29	proposition	proposition	NOUN
ejpam-3498	284	30	2	2	NUM
ejpam-3498	284	31	and	and	CCONJ
ejpam-3498	284	32	(	(	PUNCT
ejpam-3498	284	33	c	c	NOUN
ejpam-3498	284	34	)	)	PUNCT
ejpam-3498	284	35	that	that	PRON
ejpam-3498	284	36	‖vp+1,i(t)‖s	‖vp+1,i(t)‖s	PROPN
ejpam-3498	284	37	≤	≤	NUM
ejpam-3498	284	38	max	max	PROPN
ejpam-3498	284	39	(	(	PUNCT
ejpam-3498	284	40	k	k	NOUN
ejpam-3498	284	41	,	,	PUNCT
ejpam-3498	284	42	η)∈n	η)∈n	NUM
ejpam-3498	284	43	(	(	PUNCT
ejpam-3498	284	44	i	i	NOUN
ejpam-3498	284	45	)	)	PUNCT
ejpam-3498	284	46	(	(	PUNCT
ejpam-3498	284	47	i	i	PROPN
ejpam-3498	284	48	,	,	PUNCT
ejpam-3498	284	49	j	j	PROPN
ejpam-3498	284	50	)	)	PUNCT
ejpam-3498	284	51	min	min	PROPN
ejpam-3498	284	52	m	m	VERB
ejpam-3498	284	53	hc(γ)(s0	hc(γ)(s0	NOUN
ejpam-3498	284	54	−	−	NOUN
ejpam-3498	284	55	s)−η(ap+1(s0	s)−η(ap+1(s0	NOUN
ejpam-3498	284	56	−	−	PROPN
ejpam-3498	284	57	s))mµ(t)(1−κ)p+η−κm	s))mµ(t)(1−κ)p+η−κm	ADJ
ejpam-3498	284	58	×ω(t)p+cmσp+1,s(t	×ω(t)p+cmσp+1,s(t	NOUN
ejpam-3498	284	59	)	)	PUNCT
ejpam-3498	284	60	max{1,dp+η−m}µ(t)α	max{1,dp+η−m}µ(t)α	NOUN
ejpam-3498	284	61	,	,	PUNCT
ejpam-3498	284	62	where	where	SCONJ
ejpam-3498	284	63	(	(	PUNCT
ejpam-3498	284	64	i	i	PROPN
ejpam-3498	284	65	,	,	PUNCT
ejpam-3498	284	66	j	j	PROPN
ejpam-3498	284	67	)	)	PUNCT
ejpam-3498	284	68	min	min	PROPN
ejpam-3498	284	69	m	m	PROPN
ejpam-3498	284	70	=	=	SYM
ejpam-3498	284	71	min	min	PROPN
ejpam-3498	285	1	0≤m≤min{ρ(i	0≤m≤min{ρ(i	PROPN
ejpam-3498	285	2	,	,	PUNCT
ejpam-3498	285	3	j),α+η	j),α+η	PROPN
ejpam-3498	285	4	κ	κ	X
ejpam-3498	285	5	}	}	PUNCT
ejpam-3498	285	6	m	m	VERB
ejpam-3498	285	7	an	an	DET
ejpam-3498	285	8	integer	integer	NOUN
ejpam-3498	285	9	,	,	PUNCT
ejpam-3498	285	10	and	and	CCONJ
ejpam-3498	285	11	c(γ	c(γ	NOUN
ejpam-3498	285	12	)	)	PUNCT
ejpam-3498	285	13	depends	depend	VERB
ejpam-3498	285	14	only	only	ADV
ejpam-3498	285	15	on	on	ADP
ejpam-3498	285	16	γ	γ	PROPN
ejpam-3498	285	17	.	.	PUNCT
ejpam-3498	285	18	thus	thus	ADV
ejpam-3498	285	19	,	,	PUNCT
ejpam-3498	285	20	since	since	SCONJ
ejpam-3498	285	21	w(t	w(t	PROPN
ejpam-3498	285	22	)	)	PUNCT
ejpam-3498	285	23	<	<	X
ejpam-3498	285	24	a0(s0	a0(s0	CCONJ
ejpam-3498	285	25	−	−	PROPN
ejpam-3498	285	26	s	s	PART
ejpam-3498	285	27	)	)	PUNCT
ejpam-3498	285	28	and	and	CCONJ
ejpam-3498	285	29	ap+1(s0	ap+1(s0	VERB
ejpam-3498	285	30	−	−	PROPN
ejpam-3498	285	31	s	s	PART
ejpam-3498	285	32	)	)	PUNCT
ejpam-3498	285	33	<	<	X
ejpam-3498	285	34	1	1	NUM
ejpam-3498	285	35	,	,	PUNCT
ejpam-3498	285	36	we	we	PRON
ejpam-3498	285	37	have	have	VERB
ejpam-3498	285	38	‖vp+1,i(t)‖s	‖vp+1,i(t)‖s	PROPN
ejpam-3498	285	39	≤	≤	NUM
ejpam-3498	285	40	max	max	PROPN
ejpam-3498	285	41	(	(	PUNCT
ejpam-3498	285	42	k	k	NOUN
ejpam-3498	285	43	,	,	PUNCT
ejpam-3498	285	44	η)∈n	η)∈n	NUM
ejpam-3498	285	45	(	(	PUNCT
ejpam-3498	285	46	i	i	NOUN
ejpam-3498	285	47	)	)	PUNCT
ejpam-3498	285	48	(	(	PUNCT
ejpam-3498	285	49	i	i	PROPN
ejpam-3498	285	50	,	,	PUNCT
ejpam-3498	285	51	j	j	PROPN
ejpam-3498	285	52	)	)	PUNCT
ejpam-3498	285	53	min	min	PROPN
ejpam-3498	285	54	m	m	PROPN
ejpam-3498	285	55	hc(γ)a0µ(t)(1−κ)p+η−κm	hc(γ)a0µ(t)(1−κ)p+η−κm	PROPN
ejpam-3498	285	56	×ω(t)p+cm−ησp+1,s(t	×ω(t)p+cm−ησp+1,s(t	NOUN
ejpam-3498	285	57	)	)	PUNCT
ejpam-3498	285	58	max{1,dp+η−m}µ(t)α	max{1,dp+η−m}µ(t)α	NOUN
ejpam-3498	285	59	.	.	PUNCT
ejpam-3498	286	1	if	if	SCONJ
ejpam-3498	286	2	m	m	NOUN
ejpam-3498	286	3	=	=	NOUN
ejpam-3498	286	4	1	1	NUM
ejpam-3498	286	5	,	,	PUNCT
ejpam-3498	286	6	then	then	ADV
ejpam-3498	286	7	‖vp+1,i(t)‖s	‖vp+1,i(t)‖s	PROPN
ejpam-3498	286	8	≤	≤	NUM
ejpam-3498	286	9	rrp+3µ(t)(1−κ)p+1−κω(t)p+1σp+1,s(t	rrp+3µ(t)(1−κ)p+1−κω(t)p+1σp+1,s(t	ADJ
ejpam-3498	286	10	)	)	PUNCT
ejpam-3498	286	11	d(p+1)µ(t)α	d(p+1)µ(t)α	NOUN
ejpam-3498	286	12	,	,	PUNCT
ejpam-3498	286	13	where	where	SCONJ
ejpam-3498	286	14	h	h	PROPN
ejpam-3498	286	15	=	=	SYM
ejpam-3498	286	16	rr2	rr2	PROPN
ejpam-3498	286	17	,	,	PUNCT
ejpam-3498	286	18	c(γ)a0	c(γ)a0	VERB
ejpam-3498	286	19	≤	≤	NOUN
ejpam-3498	286	20	rp+1	rp+1	NOUN
ejpam-3498	286	21	,	,	PUNCT
ejpam-3498	286	22	since	since	SCONJ
ejpam-3498	286	23	σp+1,s	σp+1,s	PROPN
ejpam-3498	286	24	≥	≥	NUM
ejpam-3498	286	25	1	1	NUM
ejpam-3498	286	26	and	and	CCONJ
ejpam-3498	286	27	dp	dp	ADJ
ejpam-3498	286	28	≤	≤	NUM
ejpam-3498	286	29	d(p+	d(p+	PROPN
ejpam-3498	286	30	1	1	NUM
ejpam-3498	286	31	)	)	PUNCT
ejpam-3498	286	32	.	.	PUNCT
ejpam-3498	287	1	thus	thus	ADV
ejpam-3498	287	2	,	,	PUNCT
ejpam-3498	287	3	‖vp+1,i(t)‖s	‖vp+1,i(t)‖s	PROPN
ejpam-3498	287	4	≤	≤	NUM
ejpam-3498	287	5	rrq+3µ(t)(1−κ)(p+1)ω(t)p+1σp+1,s(t	rrq+3µ(t)(1−κ)(p+1)ω(t)p+1σp+1,s(t	PROPN
ejpam-3498	287	6	)	)	PUNCT
ejpam-3498	287	7	d(p+1)µ(t)α	d(p+1)µ(t)α	NOUN
ejpam-3498	287	8	.	.	PUNCT
ejpam-3498	288	1	hence	hence	ADV
ejpam-3498	288	2	,	,	PUNCT
ejpam-3498	288	3	by	by	ADP
ejpam-3498	288	4	(	(	PUNCT
ejpam-3498	288	5	3	3	X
ejpam-3498	288	6	)	)	PUNCT
ejpam-3498	288	7	we	we	PRON
ejpam-3498	288	8	have	have	VERB
ejpam-3498	288	9	‖(µ(t)d)ηvp+1,i‖s	‖(µ(t)d)ηvp+1,i‖s	NOUN
ejpam-3498	288	10	≤	≤	X
ejpam-3498	288	11	µ(t)ηkη(s(t)−	µ(t)ηkη(s(t)−	PROPN
ejpam-3498	288	12	s)−η‖vp+1,i‖s(t	s)−η‖vp+1,i‖s(t	PROPN
ejpam-3498	288	13	)	)	PUNCT
ejpam-3498	288	14	≤	≤	NOUN
ejpam-3498	288	15	rrp+3kη2	rrp+3kη2	VERB
ejpam-3498	288	16	d(p+1)+ηa0µ(t)(1−κ)(p+1)+(1−κ)η	d(p+1)+ηa0µ(t)(1−κ)(p+1)+(1−κ)η	PROPN
ejpam-3498	288	17	×ω(t)(p+1)+(c−1)ησp+1,s(t	×ω(t)(p+1)+(c−1)ησp+1,s(t	NOUN
ejpam-3498	288	18	)	)	PUNCT
ejpam-3498	288	19	d(p+1)+ηµ(t)α	d(p+1)+ηµ(t)α	NOUN
ejpam-3498	288	20	.	.	PUNCT
ejpam-3498	289	1	then	then	ADV
ejpam-3498	289	2	,	,	PUNCT
ejpam-3498	289	3	by	by	ADP
ejpam-3498	289	4	(	(	PUNCT
ejpam-3498	289	5	3	3	NUM
ejpam-3498	289	6	)	)	PUNCT
ejpam-3498	289	7	and	and	CCONJ
ejpam-3498	289	8	remark	remark	NOUN
ejpam-3498	289	9	3.1.3	3.1.3	NUM
ejpam-3498	289	10	,	,	PUNCT
ejpam-3498	289	11	we	we	PRON
ejpam-3498	289	12	have	have	VERB
ejpam-3498	289	13	for	for	ADP
ejpam-3498	289	14	t	t	PROPN
ejpam-3498	289	15	∈	∈	PROPN
ejpam-3498	289	16	ip(s	ip(s	NOUN
ejpam-3498	289	17	)	)	PUNCT
ejpam-3498	289	18	(	(	PUNCT
ejpam-3498	289	19	n	n	X
ejpam-3498	289	20	<	<	X
ejpam-3498	289	21	p	p	X
ejpam-3498	289	22	≤	≤	PROPN
ejpam-3498	289	23	l	l	NOUN
ejpam-3498	289	24	)	)	PUNCT
ejpam-3498	289	25	‖(µ0d)ηup	‖(µ0d)ηup	NOUN
ejpam-3498	289	26	,	,	PUNCT
ejpam-3498	289	27	i(t)‖s	i(t)‖s	X
ejpam-3498	289	28	=	=	SYM
ejpam-3498	289	29	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	289	30	p−1∑	p−1∑	NOUN
ejpam-3498	289	31	n=0	n=0	NUM
ejpam-3498	289	32	(	(	PUNCT
ejpam-3498	289	33	µ0d)ηvn	µ0d)ηvn	PROPN
ejpam-3498	289	34	,	,	PUNCT
ejpam-3498	289	35	i	i	PRON
ejpam-3498	289	36	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	289	37	s	s	PART
ejpam-3498	289	38	≤	≤	NUM
ejpam-3498	289	39	p−1∑	p−1∑	NOUN
ejpam-3498	289	40	n=0	n=0	X
ejpam-3498	289	41	rrn+2kn2dn+ηa0µ(t)(1−k)n+(1−k)ηω(t)n+(c−1)ησn	rrn+2kn2dn+ηa0µ(t)(1−k)n+(1−k)ηω(t)n+(c−1)ησn	NOUN
ejpam-3498	289	42	,	,	PUNCT
ejpam-3498	289	43	s(t	s(t	PROPN
ejpam-3498	289	44	)	)	PUNCT
ejpam-3498	289	45	dn+ηµ(t)α	dn+ηµ(t)α	PROPN
ejpam-3498	289	46	.	.	PUNCT
ejpam-3498	290	1	thus	thus	ADV
ejpam-3498	290	2	,	,	PUNCT
ejpam-3498	290	3	by	by	ADP
ejpam-3498	290	4	remark	remark	NOUN
ejpam-3498	290	5	3.1.3(4	3.1.3(4	NUM
ejpam-3498	290	6	)	)	PUNCT
ejpam-3498	290	7	,	,	PUNCT
ejpam-3498	290	8	‖(µ0d)ηup	‖(µ0d)ηup	PROPN
ejpam-3498	290	9	,	,	PUNCT
ejpam-3498	290	10	i(t)‖s	i(t)‖	VERB
ejpam-3498	290	11	≤	≤	NUM
ejpam-3498	290	12	rr2a02	rr2a02	NOUN
ejpam-3498	290	13	dl+d((l	dl+d((l	NOUN
ejpam-3498	290	14	+	+	X
ejpam-3498	291	1	1)2	1)2	NUM
ejpam-3498	291	2	+	+	NUM
ejpam-3498	291	3	1)dl+dkηµ(t)α	1)dl+dkηµ(t)α	NUM
ejpam-3498	291	4	p−1∑	p−1∑	NOUN
ejpam-3498	291	5	n=0	n=0	SYM
ejpam-3498	291	6	rn	rn	PROPN
ejpam-3498	291	7	e.	e.	PROPN
ejpam-3498	291	8	y.	y.	PROPN
ejpam-3498	291	9	guerrero	guerrero	PROPN
ejpam-3498	291	10	/	/	SYM
ejpam-3498	291	11	eur	eur	PROPN
ejpam-3498	291	12	.	.	PUNCT
ejpam-3498	292	1	j.	j.	PROPN
ejpam-3498	292	2	pure	pure	PROPN
ejpam-3498	292	3	appl	appl	PROPN
ejpam-3498	292	4	.	.	PROPN
ejpam-3498	292	5	math	math	PROPN
ejpam-3498	292	6	,	,	PUNCT
ejpam-3498	292	7	12	12	NUM
ejpam-3498	292	8	(	(	PUNCT
ejpam-3498	292	9	3	3	NUM
ejpam-3498	292	10	)	)	PUNCT
ejpam-3498	292	11	(	(	PUNCT
ejpam-3498	292	12	2019	2019	NUM
ejpam-3498	292	13	)	)	PUNCT
ejpam-3498	292	14	,	,	PUNCT
ejpam-3498	292	15	1297	1297	NUM
ejpam-3498	292	16	-	-	SYM
ejpam-3498	292	17	1314	1314	NUM
ejpam-3498	292	18	1311	1311	NUM
ejpam-3498	292	19	≤	≤	NOUN
ejpam-3498	292	20	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	292	21	,	,	PUNCT
ejpam-3498	292	22	provided	provide	VERB
ejpam-3498	292	23	r	r	NOUN
ejpam-3498	292	24	and	and	CCONJ
ejpam-3498	292	25	a0	a0	NOUN
ejpam-3498	292	26	are	be	AUX
ejpam-3498	292	27	small	small	ADJ
ejpam-3498	292	28	enough	enough	ADV
ejpam-3498	292	29	.	.	PUNCT
ejpam-3498	293	1	now	now	ADV
ejpam-3498	293	2	let	let	VERB
ejpam-3498	293	3	l	l	NOUN
ejpam-3498	293	4	be	be	AUX
ejpam-3498	293	5	an	an	DET
ejpam-3498	293	6	arbitrary	arbitrary	ADJ
ejpam-3498	293	7	integer	integer	NOUN
ejpam-3498	293	8	satisfying	satisfy	VERB
ejpam-3498	293	9	l	l	PROPN
ejpam-3498	293	10	≥	≥	X
ejpam-3498	293	11	cd+c	cd+c	PROPN
ejpam-3498	293	12	1−κ	1−κ	PROPN
ejpam-3498	293	13	.	.	PUNCT
ejpam-3498	294	1	we	we	PRON
ejpam-3498	294	2	prove	prove	VERB
ejpam-3498	294	3	by	by	ADP
ejpam-3498	294	4	induction	induction	NOUN
ejpam-3498	294	5	on	on	ADP
ejpam-3498	294	6	(	(	PUNCT
ejpam-3498	294	7	p	p	X
ejpam-3498	294	8	,	,	PUNCT
ejpam-3498	294	9	q	q	NOUN
ejpam-3498	294	10	)	)	PUNCT
ejpam-3498	294	11	(	(	PUNCT
ejpam-3498	294	12	p	p	NOUN
ejpam-3498	294	13	≥	≥	NOUN
ejpam-3498	294	14	0	0	NUM
ejpam-3498	294	15	,	,	PUNCT
ejpam-3498	294	16	0	0	NUM
ejpam-3498	294	17	≤	≤	NUM
ejpam-3498	294	18	q	q	ADJ
ejpam-3498	294	19	≤	≤	NUM
ejpam-3498	294	20	c	c	NOUN
ejpam-3498	294	21	)	)	PUNCT
ejpam-3498	294	22	that	that	SCONJ
ejpam-3498	294	23	the	the	DET
ejpam-3498	294	24	estimation	estimation	NOUN
ejpam-3498	294	25	‖vl+pc+q	‖vl+pc+q	PROPN
ejpam-3498	294	26	,	,	PUNCT
ejpam-3498	294	27	i(t)‖s	i(t)‖s	NOUN
ejpam-3498	294	28	≤	≤	NUM
ejpam-3498	294	29	rrl+pc+q+2	rrl+pc+q+2	VERB
ejpam-3498	294	30	(	(	PUNCT
ejpam-3498	294	31	q	q	X
ejpam-3498	294	32	,	,	PUNCT
ejpam-3498	294	33	i	i	NOUN
ejpam-3498	294	34	)	)	PUNCT
ejpam-3498	294	35	max	max	PROPN
ejpam-3498	294	36	g	g	PROPN
ejpam-3498	294	37	,	,	PUNCT
ejpam-3498	294	38	φ	φ	PROPN
ejpam-3498	294	39	min	min	PROPN
ejpam-3498	294	40	0≤l≤g	0≤l≤g	NUM
ejpam-3498	294	41	µ(t)α(φ	µ(t)α(φ	NUM
ejpam-3498	294	42	,	,	PUNCT
ejpam-3498	294	43	l)ω(t)β(φ	l)ω(t)β(φ	PROPN
ejpam-3498	294	44	,	,	PUNCT
ejpam-3498	294	45	l)σl+pc+q	l)σl+pc+q	PROPN
ejpam-3498	294	46	,	,	PUNCT
ejpam-3498	294	47	s(t	s(t	PROPN
ejpam-3498	294	48	)	)	PUNCT
ejpam-3498	294	49	γ(φ	γ(φ	PROPN
ejpam-3498	294	50	,	,	PUNCT
ejpam-3498	294	51	l)µ(t)α	l)µ(t)α	NOUN
ejpam-3498	294	52	(	(	PUNCT
ejpam-3498	294	53	14	14	NUM
ejpam-3498	294	54	)	)	PUNCT
ejpam-3498	294	55	holds	hold	VERB
ejpam-3498	294	56	for	for	ADP
ejpam-3498	294	57	t	t	PROPN
ejpam-3498	294	58	∈	∈	PROPN
ejpam-3498	294	59	il+pc+q(s	il+pc+q(s	NOUN
ejpam-3498	294	60	)	)	PUNCT
ejpam-3498	294	61	,	,	PUNCT
ejpam-3498	294	62	where	where	SCONJ
ejpam-3498	294	63	α(φ	α(φ	NUM
ejpam-3498	294	64	,	,	PUNCT
ejpam-3498	294	65	l	l	NOUN
ejpam-3498	294	66	)	)	PUNCT
ejpam-3498	294	67	=	=	PRON
ejpam-3498	294	68	cd+	cd+	VERB
ejpam-3498	294	69	φ−	φ−	PROPN
ejpam-3498	294	70	κl	κl	PROPN
ejpam-3498	294	71	,	,	PUNCT
ejpam-3498	294	72	β(φ	β(φ	PROPN
ejpam-3498	294	73	,	,	PUNCT
ejpam-3498	294	74	l	l	NOUN
ejpam-3498	294	75	)	)	PUNCT
ejpam-3498	295	1	=	=	PRON
ejpam-3498	295	2	cd+	cd+	VERB
ejpam-3498	295	3	c−	c−	ADJ
ejpam-3498	295	4	φ+	φ+	NOUN
ejpam-3498	295	5	l	l	NOUN
ejpam-3498	295	6	,	,	PUNCT
ejpam-3498	295	7	γ(φ	γ(φ	NOUN
ejpam-3498	295	8	,	,	PUNCT
ejpam-3498	295	9	l	l	NOUN
ejpam-3498	295	10	)	)	PUNCT
ejpam-3498	295	11	=	=	SYM
ejpam-3498	295	12	ld+	ld+	NOUN
ejpam-3498	295	13	φ−	φ−	PROPN
ejpam-3498	295	14	l	l	PROPN
ejpam-3498	295	15	,	,	PUNCT
ejpam-3498	295	16	and	and	CCONJ
ejpam-3498	295	17	(	(	PUNCT
ejpam-3498	295	18	q	q	X
ejpam-3498	295	19	,	,	PUNCT
ejpam-3498	295	20	i	i	NOUN
ejpam-3498	295	21	)	)	PUNCT
ejpam-3498	295	22	max	max	PROPN
ejpam-3498	295	23	g	g	PROPN
ejpam-3498	295	24	,	,	PUNCT
ejpam-3498	295	25	φ	φ	PROPN
ejpam-3498	295	26	=	=	SYM
ejpam-3498	295	27	max	max	PROPN
ejpam-3498	295	28	q≤g≤qd	q≤g≤qd	PROPN
ejpam-3498	295	29	,	,	PUNCT
ejpam-3498	295	30	q≤φ≤n(i)+g	q≤φ≤n(i)+g	PROPN
ejpam-3498	295	31	,	,	PUNCT
ejpam-3498	295	32	with	with	ADP
ejpam-3498	295	33	g	g	NOUN
ejpam-3498	295	34	,	,	PUNCT
ejpam-3498	295	35	l	l	NOUN
ejpam-3498	295	36	denoting	denote	VERB
ejpam-3498	295	37	integers	integer	NOUN
ejpam-3498	295	38	and	and	CCONJ
ejpam-3498	295	39	φ	φ	X
ejpam-3498	295	40	a	a	DET
ejpam-3498	295	41	real	real	ADJ
ejpam-3498	295	42	number	number	NOUN
ejpam-3498	295	43	.	.	PUNCT
ejpam-3498	296	1	when	when	SCONJ
ejpam-3498	296	2	(	(	PUNCT
ejpam-3498	296	3	p	p	X
ejpam-3498	296	4	,	,	PUNCT
ejpam-3498	296	5	q)=(0,0	q)=(0,0	NOUN
ejpam-3498	296	6	)	)	PUNCT
ejpam-3498	296	7	,	,	PUNCT
ejpam-3498	296	8	‖vl	‖vl	NUM
ejpam-3498	296	9	,	,	PUNCT
ejpam-3498	296	10	i(t)‖s	i(t)‖s	NOUN
ejpam-3498	296	11	≤	≤	NUM
ejpam-3498	296	12	rrl+2µ(t)cdω(t)cd+cσl	rrl+2µ(t)cdω(t)cd+cσl	NOUN
ejpam-3498	296	13	,	,	PUNCT
ejpam-3498	296	14	s(t	s(t	PROPN
ejpam-3498	296	15	)	)	PUNCT
ejpam-3498	296	16	ldµ(t)α	ldµ(t)α	NOUN
ejpam-3498	296	17	,	,	PUNCT
ejpam-3498	296	18	where	where	SCONJ
ejpam-3498	296	19	g	g	NOUN
ejpam-3498	296	20	=	=	SYM
ejpam-3498	296	21	0	0	PUNCT
ejpam-3498	296	22	=	=	SYM
ejpam-3498	296	23	l	l	NOUN
ejpam-3498	296	24	and	and	CCONJ
ejpam-3498	296	25	φ	φ	NUM
ejpam-3498	296	26	=	=	SYM
ejpam-3498	296	27	0	0	PROPN
ejpam-3498	296	28	.	.	PUNCT
ejpam-3498	297	1	thus	thus	ADV
ejpam-3498	297	2	,	,	PUNCT
ejpam-3498	297	3	‖vl	‖vl	NUM
ejpam-3498	297	4	,	,	PUNCT
ejpam-3498	297	5	i(t)‖s	i(t)‖s	NOUN
ejpam-3498	297	6	≤	≤	NUM
ejpam-3498	297	7	rr1	rr1	ADP
ejpam-3498	297	8	+	+	PROPN
ejpam-3498	297	9	2µ(t)(1−κ)lω(t)lσl	2µ(t)(1−κ)lω(t)lσl	PROPN
ejpam-3498	297	10	,	,	PUNCT
ejpam-3498	297	11	s(t	s(t	PROPN
ejpam-3498	297	12	)	)	PUNCT
ejpam-3498	297	13	ldµ(t)α	ldµ(t)α	NOUN
ejpam-3498	297	14	,	,	PUNCT
ejpam-3498	297	15	since	since	SCONJ
ejpam-3498	297	16	l(1	l(1	PROPN
ejpam-3498	297	17	−	−	PROPN
ejpam-3498	297	18	κ	κ	NOUN
ejpam-3498	297	19	)	)	PUNCT
ejpam-3498	297	20	≥	≥	PROPN
ejpam-3498	297	21	cd	cd	PROPN
ejpam-3498	297	22	+	+	CCONJ
ejpam-3498	297	23	c	c	PROPN
ejpam-3498	297	24	≥	≥	PROPN
ejpam-3498	297	25	cd	cd	PROPN
ejpam-3498	297	26	and	and	CCONJ
ejpam-3498	297	27	l	l	PROPN
ejpam-3498	297	28	≥	≥	X
ejpam-3498	297	29	cd+c	cd+c	PROPN
ejpam-3498	297	30	1−k	1−k	NUM
ejpam-3498	297	31	≥	≥	NOUN
ejpam-3498	297	32	cd	cd	PROPN
ejpam-3498	297	33	+	+	CCONJ
ejpam-3498	297	34	c.	c.	PROPN
ejpam-3498	297	35	hence	hence	ADV
ejpam-3498	297	36	,	,	PUNCT
ejpam-3498	297	37	(	(	PUNCT
ejpam-3498	297	38	b	b	X
ejpam-3498	297	39	)	)	PUNCT
ejpam-3498	297	40	shows	show	VERB
ejpam-3498	297	41	that	that	SCONJ
ejpam-3498	297	42	(	(	PUNCT
ejpam-3498	297	43	14	14	NUM
ejpam-3498	297	44	)	)	PUNCT
ejpam-3498	297	45	holds	hold	VERB
ejpam-3498	297	46	.	.	PUNCT
ejpam-3498	298	1	assume	assume	VERB
ejpam-3498	298	2	that	that	SCONJ
ejpam-3498	298	3	(	(	PUNCT
ejpam-3498	298	4	14	14	NUM
ejpam-3498	298	5	)	)	PUNCT
ejpam-3498	298	6	holds	hold	VERB
ejpam-3498	298	7	for	for	ADP
ejpam-3498	298	8	some	some	PRON
ejpam-3498	298	9	(	(	PUNCT
ejpam-3498	298	10	p	p	X
ejpam-3498	298	11	,	,	PUNCT
ejpam-3498	298	12	q	q	NOUN
ejpam-3498	298	13	)	)	PUNCT
ejpam-3498	298	14	with	with	ADP
ejpam-3498	298	15	q	q	NOUN
ejpam-3498	298	16	<	<	X
ejpam-3498	298	17	c.	c.	NOUN
ejpam-3498	298	18	if	if	SCONJ
ejpam-3498	298	19	a0	a0	PROPN
ejpam-3498	298	20	max{c(γ(φ	max{c(γ(φ	PROPN
ejpam-3498	298	21	,	,	PUNCT
ejpam-3498	298	22	l	l	NOUN
ejpam-3498	298	23	)	)	PUNCT
ejpam-3498	298	24	)	)	PUNCT
ejpam-3498	298	25	:	:	PUNCT
ejpam-3498	298	26	0	0	NUM
ejpam-3498	298	27	≤	≤	NUM
ejpam-3498	298	28	φ	φ	PROPN
ejpam-3498	298	29	≤	≤	NUM
ejpam-3498	298	30	cd+	cd+	NOUN
ejpam-3498	298	31	c	c	NOUN
ejpam-3498	298	32	,	,	PUNCT
ejpam-3498	298	33	0	0	NUM
ejpam-3498	298	34	≤	≤	NUM
ejpam-3498	298	35	l	l	NOUN
ejpam-3498	298	36	≤	≤	PROPN
ejpam-3498	298	37	cd	cd	PROPN
ejpam-3498	298	38	}	}	PUNCT
ejpam-3498	298	39	≤	≤	NOUN
ejpam-3498	298	40	r	r	NOUN
ejpam-3498	298	41	,	,	PUNCT
ejpam-3498	298	42	then	then	ADV
ejpam-3498	298	43	,	,	PUNCT
ejpam-3498	298	44	applying	apply	VERB
ejpam-3498	298	45	lemma	lemma	PROPN
ejpam-3498	298	46	4	4	NUM
ejpam-3498	298	47	ρ(i	ρ(i	PROPN
ejpam-3498	298	48	,	,	PUNCT
ejpam-3498	298	49	j)-times	j)-time	NOUN
ejpam-3498	298	50	,	,	PUNCT
ejpam-3498	298	51	we	we	PRON
ejpam-3498	298	52	have	have	VERB
ejpam-3498	298	53	‖vl+pc+q+1,i(t)‖s	‖vl+pc+q+1,i(t)‖s	NOUN
ejpam-3498	298	54	≤	≤	NUM
ejpam-3498	299	1	rrl+pc+q+3	rrl+pc+q+3	PROPN
ejpam-3498	299	2	max	max	PROPN
ejpam-3498	299	3	(	(	PUNCT
ejpam-3498	299	4	k	k	X
ejpam-3498	299	5	,	,	PUNCT
ejpam-3498	299	6	η)∈m(j	η)∈m(j	PROPN
ejpam-3498	299	7	)	)	PUNCT
ejpam-3498	299	8	,	,	PUNCT
ejpam-3498	299	9	1≤j≤n	1≤j≤n	NUM
ejpam-3498	299	10	(	(	PUNCT
ejpam-3498	299	11	q	q	NOUN
ejpam-3498	299	12	,	,	PUNCT
ejpam-3498	299	13	k	k	NOUN
ejpam-3498	299	14	)	)	PUNCT
ejpam-3498	299	15	max	max	PROPN
ejpam-3498	299	16	g	g	PROPN
ejpam-3498	299	17	,	,	PUNCT
ejpam-3498	299	18	φ	φ	PROPN
ejpam-3498	299	19	(	(	PUNCT
ejpam-3498	299	20	i	i	PROPN
ejpam-3498	299	21	,	,	PUNCT
ejpam-3498	299	22	j	j	PROPN
ejpam-3498	299	23	)	)	PUNCT
ejpam-3498	299	24	min	min	PROPN
ejpam-3498	299	25	m	m	PROPN
ejpam-3498	299	26	min	min	PROPN
ejpam-3498	299	27	0≤l≤g	0≤l≤g	NUM
ejpam-3498	299	28	µ(t)α(φ+η	µ(t)α(φ+η	ADP
ejpam-3498	299	29	,	,	PUNCT
ejpam-3498	299	30	l+m	l+m	X
ejpam-3498	299	31	)	)	PUNCT
ejpam-3498	299	32	×ω(t)β(φ+η	×ω(t)β(φ+η	NOUN
ejpam-3498	299	33	,	,	PUNCT
ejpam-3498	299	34	l+m)σ1+pc+q	l+m)σ1+pc+q	NOUN
ejpam-3498	299	35	,	,	PUNCT
ejpam-3498	299	36	s(t	s(t	PROPN
ejpam-3498	299	37	)	)	PUNCT
ejpam-3498	299	38	γ(φ+η	γ(φ+η	NOUN
ejpam-3498	299	39	,	,	PUNCT
ejpam-3498	299	40	l+m)µ(t)α	l+m)µ(t)α	NOUN
ejpam-3498	299	41	,	,	PUNCT
ejpam-3498	299	42	and	and	CCONJ
ejpam-3498	299	43	(	(	PUNCT
ejpam-3498	299	44	q	q	X
ejpam-3498	299	45	,	,	PUNCT
ejpam-3498	299	46	i	i	NOUN
ejpam-3498	299	47	)	)	PUNCT
ejpam-3498	299	48	max	max	PROPN
ejpam-3498	299	49	g	g	PROPN
ejpam-3498	299	50	,	,	PUNCT
ejpam-3498	299	51	φ	φ	PROPN
ejpam-3498	299	52	=	=	SYM
ejpam-3498	299	53	max	max	PROPN
ejpam-3498	299	54	q+1≤g+ρ(i	q+1≤g+ρ(i	PROPN
ejpam-3498	299	55	,	,	PUNCT
ejpam-3498	299	56	j)≤qd+d	j)≤qd+d	PROPN
ejpam-3498	299	57	,	,	PUNCT
ejpam-3498	299	58	q+1≤φ+η≤n(i)+(g+ρ(i	q+1≤φ+η≤n(i)+(g+ρ(i	PROPN
ejpam-3498	299	59	,	,	PUNCT
ejpam-3498	299	60	j	j	PROPN
ejpam-3498	299	61	)	)	PUNCT
ejpam-3498	299	62	)	)	PUNCT
ejpam-3498	299	63	,	,	PUNCT
ejpam-3498	299	64	which	which	PRON
ejpam-3498	299	65	implies	imply	VERB
ejpam-3498	299	66	(	(	PUNCT
ejpam-3498	299	67	14	14	NUM
ejpam-3498	299	68	)	)	PUNCT
ejpam-3498	299	69	for	for	ADP
ejpam-3498	299	70	(	(	PUNCT
ejpam-3498	299	71	p	p	X
ejpam-3498	299	72	,	,	PUNCT
ejpam-3498	299	73	q	q	NOUN
ejpam-3498	299	74	+	+	NOUN
ejpam-3498	299	75	1	1	NUM
ejpam-3498	299	76	)	)	PUNCT
ejpam-3498	299	77	,	,	PUNCT
ejpam-3498	299	78	since	since	SCONJ
ejpam-3498	299	79	the	the	DET
ejpam-3498	299	80	conditions	condition	NOUN
ejpam-3498	299	81	(	(	PUNCT
ejpam-3498	299	82	k	k	X
ejpam-3498	299	83	,	,	PUNCT
ejpam-3498	299	84	η	η	NOUN
ejpam-3498	299	85	)	)	PUNCT
ejpam-3498	299	86	∈	∈	PROPN
ejpam-3498	299	87	m(j	m(j	PROPN
ejpam-3498	299	88	)	)	PUNCT
ejpam-3498	299	89	and	and	CCONJ
ejpam-3498	299	90	m	m	PROPN
ejpam-3498	299	91	≤	≤	ADJ
ejpam-3498	299	92	ρ(i	ρ(i	PROPN
ejpam-3498	299	93	,	,	PUNCT
ejpam-3498	299	94	j	j	NOUN
ejpam-3498	299	95	)	)	PUNCT
ejpam-3498	299	96	yield	yield	VERB
ejpam-3498	299	97	that	that	PRON
ejpam-3498	299	98	q	q	PROPN
ejpam-3498	300	1	+	+	NUM
ejpam-3498	300	2	1	1	NUM
ejpam-3498	300	3	≤	≤	NOUN
ejpam-3498	300	4	φ+	φ+	X
ejpam-3498	300	5	η	η	PROPN
ejpam-3498	300	6	,	,	PUNCT
ejpam-3498	300	7	φ+	φ+	X
ejpam-3498	300	8	η	η	PROPN
ejpam-3498	300	9	≤	≤	X
ejpam-3498	300	10	(	(	PUNCT
ejpam-3498	300	11	n(k	n(k	PROPN
ejpam-3498	300	12	)	)	PUNCT
ejpam-3498	300	13	+	+	NOUN
ejpam-3498	300	14	g	g	NOUN
ejpam-3498	300	15	)	)	PUNCT
ejpam-3498	300	16	+	+	CCONJ
ejpam-3498	300	17	n(j	n(j	PROPN
ejpam-3498	300	18	,	,	PUNCT
ejpam-3498	300	19	k	k	NOUN
ejpam-3498	300	20	)	)	PUNCT
ejpam-3498	300	21	=	=	SYM
ejpam-3498	300	22	n(k	n(k	PROPN
ejpam-3498	300	23	)	)	PUNCT
ejpam-3498	301	1	+	+	NOUN
ejpam-3498	301	2	g+	g+	NOUN
ejpam-3498	301	3	n(j)−	n(j)−	PROPN
ejpam-3498	301	4	n(k	n(k	PROPN
ejpam-3498	301	5	)	)	PUNCT
ejpam-3498	301	6	+	+	CCONJ
ejpam-3498	301	7	1	1	NUM
ejpam-3498	301	8	=	=	SYM
ejpam-3498	301	9	g+	g+	NOUN
ejpam-3498	301	10	n(j	n(j	NOUN
ejpam-3498	301	11	)	)	PUNCT
ejpam-3498	301	12	+	+	CCONJ
ejpam-3498	301	13	1	1	NUM
ejpam-3498	301	14	e.	e.	PROPN
ejpam-3498	301	15	y.	y.	PROPN
ejpam-3498	301	16	guerrero	guerrero	PROPN
ejpam-3498	301	17	/	/	SYM
ejpam-3498	301	18	eur	eur	PROPN
ejpam-3498	301	19	.	.	PUNCT
ejpam-3498	302	1	j.	j.	PROPN
ejpam-3498	302	2	pure	pure	PROPN
ejpam-3498	302	3	appl	appl	PROPN
ejpam-3498	302	4	.	.	PROPN
ejpam-3498	302	5	math	math	PROPN
ejpam-3498	302	6	,	,	PUNCT
ejpam-3498	302	7	12	12	NUM
ejpam-3498	302	8	(	(	PUNCT
ejpam-3498	302	9	3	3	NUM
ejpam-3498	302	10	)	)	PUNCT
ejpam-3498	302	11	(	(	PUNCT
ejpam-3498	302	12	2019	2019	NUM
ejpam-3498	302	13	)	)	PUNCT
ejpam-3498	302	14	,	,	PUNCT
ejpam-3498	302	15	1297	1297	NUM
ejpam-3498	302	16	-	-	SYM
ejpam-3498	302	17	1314	1314	NUM
ejpam-3498	302	18	1312	1312	NUM
ejpam-3498	302	19	=	=	SYM
ejpam-3498	302	20	n(i	n(i	PROPN
ejpam-3498	302	21	)	)	PUNCT
ejpam-3498	303	1	+	+	NOUN
ejpam-3498	303	2	g+	g+	NOUN
ejpam-3498	303	3	n(j)−	n(j)−	PROPN
ejpam-3498	303	4	n(i	n(i	PROPN
ejpam-3498	303	5	)	)	PUNCT
ejpam-3498	304	1	+	+	CCONJ
ejpam-3498	304	2	1	1	NUM
ejpam-3498	304	3	=	=	SYM
ejpam-3498	304	4	n(i	n(i	PROPN
ejpam-3498	304	5	)	)	PUNCT
ejpam-3498	305	1	+	+	NOUN
ejpam-3498	305	2	g+	g+	NOUN
ejpam-3498	305	3	n(j	n(j	PROPN
ejpam-3498	305	4	,	,	PUNCT
ejpam-3498	305	5	i	i	NOUN
ejpam-3498	305	6	)	)	PUNCT
ejpam-3498	305	7	≤	≤	NUM
ejpam-3498	305	8	n(i	n(i	PROPN
ejpam-3498	305	9	)	)	PUNCT
ejpam-3498	306	1	+	+	CCONJ
ejpam-3498	306	2	(	(	PUNCT
ejpam-3498	306	3	g+	g+	ADP
ejpam-3498	306	4	ρ(i	ρ(i	PROPN
ejpam-3498	306	5	,	,	PUNCT
ejpam-3498	306	6	j	j	PROPN
ejpam-3498	306	7	)	)	PUNCT
ejpam-3498	306	8	)	)	PUNCT
ejpam-3498	307	1	,	,	PUNCT
ejpam-3498	307	2	l+m	l+m	X
ejpam-3498	307	3	≤	≤	NUM
ejpam-3498	307	4	g+	g+	VERB
ejpam-3498	307	5	ρ(i	ρ(i	PROPN
ejpam-3498	307	6	,	,	PUNCT
ejpam-3498	307	7	j	j	PROPN
ejpam-3498	307	8	)	)	PUNCT
ejpam-3498	307	9	and	and	CCONJ
ejpam-3498	307	10	q	q	PROPN
ejpam-3498	308	1	+	+	NOUN
ejpam-3498	308	2	1	1	NUM
ejpam-3498	308	3	≤	≤	NUM
ejpam-3498	308	4	g+	g+	VERB
ejpam-3498	308	5	ρ(i	ρ(i	PROPN
ejpam-3498	308	6	,	,	PUNCT
ejpam-3498	308	7	j	j	PROPN
ejpam-3498	308	8	)	)	PUNCT
ejpam-3498	308	9	≤	≤	NUM
ejpam-3498	308	10	qd+	qd+	PROPN
ejpam-3498	308	11	d.	d.	PROPN
ejpam-3498	308	12	now	now	ADV
ejpam-3498	308	13	,	,	PUNCT
ejpam-3498	308	14	assume	assume	VERB
ejpam-3498	308	15	that	that	SCONJ
ejpam-3498	308	16	(	(	PUNCT
ejpam-3498	308	17	14	14	NUM
ejpam-3498	308	18	)	)	PUNCT
ejpam-3498	308	19	holds	hold	VERB
ejpam-3498	308	20	for	for	ADP
ejpam-3498	308	21	(	(	PUNCT
ejpam-3498	308	22	p	p	X
ejpam-3498	308	23	,	,	PUNCT
ejpam-3498	308	24	c	c	NOUN
ejpam-3498	308	25	)	)	PUNCT
ejpam-3498	308	26	(	(	PUNCT
ejpam-3498	308	27	i.e.	i.e.	X
ejpam-3498	308	28	,	,	PUNCT
ejpam-3498	308	29	c	c	NOUN
ejpam-3498	308	30	=	=	SYM
ejpam-3498	308	31	q	q	NOUN
ejpam-3498	308	32	)	)	PUNCT
ejpam-3498	308	33	with	with	ADP
ejpam-3498	308	34	some	some	DET
ejpam-3498	308	35	p.	p.	NOUN
ejpam-3498	308	36	then	then	ADV
ejpam-3498	308	37	0	0	NUM
ejpam-3498	308	38	≤	≤	NUM
ejpam-3498	308	39	c−	c−	NOUN
ejpam-3498	308	40	n(i	n(i	PROPN
ejpam-3498	308	41	)	)	PUNCT
ejpam-3498	308	42	≤	≤	NUM
ejpam-3498	308	43	φ−	φ−	PROPN
ejpam-3498	308	44	n(i	n(i	PROPN
ejpam-3498	308	45	)	)	PUNCT
ejpam-3498	308	46	≤	≤	NOUN
ejpam-3498	308	47	g	g	NOUN
ejpam-3498	308	48	,	,	PUNCT
ejpam-3498	308	49	so	so	SCONJ
ejpam-3498	308	50	we	we	PRON
ejpam-3498	308	51	can	can	AUX
ejpam-3498	308	52	put	put	VERB
ejpam-3498	308	53	l	l	NOUN
ejpam-3498	308	54	=	=	PUNCT
ejpam-3498	308	55	φ−	φ−	PROPN
ejpam-3498	308	56	n(i	n(i	PROPN
ejpam-3498	308	57	)	)	PUNCT
ejpam-3498	308	58	(	(	PUNCT
ejpam-3498	308	59	−[−z	−[−z	PROPN
ejpam-3498	308	60	]	]	PUNCT
ejpam-3498	308	61	)	)	PUNCT
ejpam-3498	308	62	is	be	AUX
ejpam-3498	308	63	the	the	DET
ejpam-3498	308	64	smallest	small	ADJ
ejpam-3498	308	65	integer	integer	NOUN
ejpam-3498	308	66	which	which	PRON
ejpam-3498	308	67	is	be	AUX
ejpam-3498	308	68	not	not	PART
ejpam-3498	308	69	less	less	ADJ
ejpam-3498	308	70	than	than	SCONJ
ejpam-3498	308	71	z.	z.	PROPN
ejpam-3498	308	72	we	we	PRON
ejpam-3498	308	73	have	have	VERB
ejpam-3498	308	74	then	then	ADV
ejpam-3498	308	75	α(φ	α(φ	NUM
ejpam-3498	308	76	,	,	PUNCT
ejpam-3498	308	77	l	l	NOUN
ejpam-3498	308	78	)	)	PUNCT
ejpam-3498	308	79	≥	≥	PRON
ejpam-3498	308	80	cd+	cd+	VERB
ejpam-3498	308	81	φ−	φ−	PROPN
ejpam-3498	308	82	κ(φ+	κ(φ+	NOUN
ejpam-3498	308	83	1−	1−	NUM
ejpam-3498	308	84	n(i	n(i	PROPN
ejpam-3498	308	85	)	)	PUNCT
ejpam-3498	308	86	)	)	PUNCT
ejpam-3498	309	1	=	=	PRON
ejpam-3498	309	2	cd+	cd+	VERB
ejpam-3498	309	3	n(i	n(i	PROPN
ejpam-3498	309	4	)	)	PUNCT
ejpam-3498	310	1	+	+	CCONJ
ejpam-3498	310	2	(	(	PUNCT
ejpam-3498	310	3	1−	1−	NUM
ejpam-3498	310	4	κ	κ	NOUN
ejpam-3498	310	5	)	)	PUNCT
ejpam-3498	310	6	(	(	PUNCT
ejpam-3498	310	7	φ−	φ−	PROPN
ejpam-3498	310	8	n(i)−	n(i)−	PROPN
ejpam-3498	310	9	κ	κ	PROPN
ejpam-3498	310	10	1−	1−	NUM
ejpam-3498	310	11	κ	κ	NOUN
ejpam-3498	310	12	)	)	PUNCT
ejpam-3498	310	13	≥	≥	NOUN
ejpam-3498	310	14	α(n(i	α(n(i	PROPN
ejpam-3498	310	15	)	)	PUNCT
ejpam-3498	310	16	,	,	PUNCT
ejpam-3498	310	17	0	0	NUM
ejpam-3498	310	18	)	)	PUNCT
ejpam-3498	311	1	+	+	CCONJ
ejpam-3498	311	2	(	(	PUNCT
ejpam-3498	311	3	1−	1−	NUM
ejpam-3498	311	4	κ	κ	NOUN
ejpam-3498	311	5	)	)	PUNCT
ejpam-3498	311	6	(	(	PUNCT
ejpam-3498	311	7	c−	c−	X
ejpam-3498	311	8	n(i)−	n(i)−	PROPN
ejpam-3498	311	9	κ	κ	X
ejpam-3498	311	10	1−	1−	NUM
ejpam-3498	311	11	κ	κ	NOUN
ejpam-3498	311	12	)	)	PUNCT
ejpam-3498	311	13	≥	≥	NOUN
ejpam-3498	311	14	α(n(i	α(n(i	PROPN
ejpam-3498	311	15	)	)	PUNCT
ejpam-3498	311	16	,	,	PUNCT
ejpam-3498	311	17	0	0	NUM
ejpam-3498	311	18	)	)	PUNCT
ejpam-3498	311	19	,	,	PUNCT
ejpam-3498	311	20	β(φ	β(φ	PROPN
ejpam-3498	311	21	,	,	PUNCT
ejpam-3498	311	22	l	l	NOUN
ejpam-3498	311	23	)	)	PUNCT
ejpam-3498	311	24	≥	≥	PRON
ejpam-3498	311	25	cd+	cd+	VERB
ejpam-3498	311	26	c−	c−	NOUN
ejpam-3498	311	27	φ+	φ+	NOUN
ejpam-3498	311	28	(	(	PUNCT
ejpam-3498	311	29	φ−	φ−	PROPN
ejpam-3498	311	30	n(i	n(i	PROPN
ejpam-3498	311	31	)	)	PUNCT
ejpam-3498	311	32	)	)	PUNCT
ejpam-3498	312	1	=	=	PUNCT
ejpam-3498	312	2	β(n(i	β(n(i	ADJ
ejpam-3498	312	3	)	)	PUNCT
ejpam-3498	312	4	,	,	PUNCT
ejpam-3498	312	5	0	0	NUM
ejpam-3498	312	6	)	)	PUNCT
ejpam-3498	312	7	and	and	CCONJ
ejpam-3498	312	8	γ(φ	γ(φ	PROPN
ejpam-3498	312	9	,	,	PUNCT
ejpam-3498	312	10	l	l	NOUN
ejpam-3498	312	11	)	)	PUNCT
ejpam-3498	312	12	≤	≤	NOUN
ejpam-3498	312	13	γ(n(i	γ(n(i	PROPN
ejpam-3498	312	14	)	)	PUNCT
ejpam-3498	312	15	,	,	PUNCT
ejpam-3498	312	16	0	0	NUM
ejpam-3498	312	17	)	)	PUNCT
ejpam-3498	312	18	.	.	PUNCT
ejpam-3498	313	1	therefore	therefore	ADV
ejpam-3498	313	2	,	,	PUNCT
ejpam-3498	313	3	(	(	PUNCT
ejpam-3498	313	4	14	14	NUM
ejpam-3498	313	5	)	)	PUNCT
ejpam-3498	313	6	holds	hold	VERB
ejpam-3498	313	7	for	for	ADP
ejpam-3498	313	8	(	(	PUNCT
ejpam-3498	313	9	p+1	p+1	NOUN
ejpam-3498	313	10	,	,	PUNCT
ejpam-3498	313	11	0	0	NUM
ejpam-3498	313	12	)	)	PUNCT
ejpam-3498	313	13	.	.	PUNCT
ejpam-3498	314	1	this	this	PRON
ejpam-3498	314	2	completes	complete	VERB
ejpam-3498	314	3	the	the	DET
ejpam-3498	314	4	proof	proof	NOUN
ejpam-3498	314	5	of	of	ADP
ejpam-3498	314	6	(	(	PUNCT
ejpam-3498	314	7	14	14	NUM
ejpam-3498	314	8	)	)	PUNCT
ejpam-3498	314	9	.	.	PUNCT
ejpam-3498	315	1	note	note	VERB
ejpam-3498	315	2	that	that	SCONJ
ejpam-3498	315	3	α(φ	α(φ	NUM
ejpam-3498	315	4	,	,	PUNCT
ejpam-3498	315	5	l	l	NOUN
ejpam-3498	315	6	)	)	PUNCT
ejpam-3498	315	7	≥	≥	NOUN
ejpam-3498	315	8	0	0	NUM
ejpam-3498	315	9	,	,	PUNCT
ejpam-3498	315	10	β(φ	β(φ	PROPN
ejpam-3498	315	11	,	,	PUNCT
ejpam-3498	315	12	l	l	NOUN
ejpam-3498	315	13	)	)	PUNCT
ejpam-3498	315	14	≥	≥	NOUN
ejpam-3498	315	15	0	0	NUM
ejpam-3498	315	16	and	and	CCONJ
ejpam-3498	315	17	γ(φ	γ(φ	PROPN
ejpam-3498	315	18	,	,	PUNCT
ejpam-3498	315	19	l	l	NOUN
ejpam-3498	315	20	)	)	PUNCT
ejpam-3498	315	21	is	be	AUX
ejpam-3498	315	22	bounded	bound	VERB
ejpam-3498	315	23	(	(	PUNCT
ejpam-3498	315	24	indeed	indeed	ADV
ejpam-3498	315	25	γ(φ	γ(φ	PROPN
ejpam-3498	315	26	,	,	PUNCT
ejpam-3498	315	27	l	l	NOUN
ejpam-3498	315	28	)	)	PUNCT
ejpam-3498	315	29	≤	≤	PROPN
ejpam-3498	315	30	ld+	ld+	NOUN
ejpam-3498	315	31	cd+	cd+	NOUN
ejpam-3498	315	32	c	c	NOUN
ejpam-3498	315	33	)	)	PUNCT
ejpam-3498	315	34	.	.	PUNCT
ejpam-3498	316	1	hence	hence	ADV
ejpam-3498	316	2	,	,	PUNCT
ejpam-3498	316	3	for	for	ADP
ejpam-3498	316	4	n	n	PRON
ejpam-3498	316	5	≥	≥	NOUN
ejpam-3498	316	6	l	l	NOUN
ejpam-3498	316	7	,	,	PUNCT
ejpam-3498	316	8	‖(µ0d)ηun+1,i(t)‖s	‖(µ0d)ηun+1,i(t)‖s	NOUN
ejpam-3498	316	9	=	=	SYM
ejpam-3498	316	10	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	316	11	n∑	n∑	PROPN
ejpam-3498	316	12	x=0	x=0	PROPN
ejpam-3498	316	13	(	(	PUNCT
ejpam-3498	316	14	µ0d)ηvx	µ0d)ηvx	PROPN
ejpam-3498	316	15	,	,	PUNCT
ejpam-3498	316	16	i(t	i(t	PROPN
ejpam-3498	316	17	)	)	PUNCT
ejpam-3498	316	18	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3498	316	19	s	s	PART
ejpam-3498	316	20	≤	≤	NUM
ejpam-3498	316	21	n∑	n∑	NOUN
ejpam-3498	316	22	x=0	x=0	PROPN
ejpam-3498	316	23	µ(t)η‖dηvx	µ(t)η‖dηvx	NOUN
ejpam-3498	316	24	,	,	PUNCT
ejpam-3498	316	25	i‖s	i‖s	PROPN
ejpam-3498	316	26	e.	e.	PROPN
ejpam-3498	316	27	y.	y.	PROPN
ejpam-3498	316	28	guerrero	guerrero	PROPN
ejpam-3498	316	29	/	/	SYM
ejpam-3498	316	30	eur	eur	PROPN
ejpam-3498	316	31	.	.	PUNCT
ejpam-3498	317	1	j.	j.	PROPN
ejpam-3498	317	2	pure	pure	PROPN
ejpam-3498	317	3	appl	appl	PROPN
ejpam-3498	317	4	.	.	PROPN
ejpam-3498	317	5	math	math	PROPN
ejpam-3498	317	6	,	,	PUNCT
ejpam-3498	317	7	12	12	NUM
ejpam-3498	317	8	(	(	PUNCT
ejpam-3498	317	9	3	3	NUM
ejpam-3498	317	10	)	)	PUNCT
ejpam-3498	317	11	(	(	PUNCT
ejpam-3498	317	12	2019	2019	NUM
ejpam-3498	317	13	)	)	PUNCT
ejpam-3498	317	14	,	,	PUNCT
ejpam-3498	317	15	1297	1297	NUM
ejpam-3498	317	16	-	-	SYM
ejpam-3498	317	17	1314	1314	NUM
ejpam-3498	317	18	1313	1313	NUM
ejpam-3498	317	19	≤	≤	NUM
ejpam-3498	317	20	n∑	n∑	PROPN
ejpam-3498	317	21	x=0	x=0	PROPN
ejpam-3498	318	1	µ(t)ηkη(s(t)−	µ(t)ηkη(s(t)−	PROPN
ejpam-3498	318	2	s)−η‖vx	s)−η‖vx	PROPN
ejpam-3498	318	3	,	,	PUNCT
ejpam-3498	318	4	i(t)‖s(t)µ(t)α	i(t)‖s(t)µ(t)α	ADJ
ejpam-3498	318	5	≤	≤	NUM
ejpam-3498	318	6	n∑	n∑	NOUN
ejpam-3498	318	7	x=0	x=0	PROPN
ejpam-3498	318	8	kη2	kη2	NOUN
ejpam-3498	318	9	ηa0µ(t)(1−κ)ηω(t)(c−1)ησx	ηa0µ(t)(1−κ)ηω(t)(c−1)ησx	NOUN
ejpam-3498	318	10	,	,	PUNCT
ejpam-3498	318	11	s(t	s(t	PROPN
ejpam-3498	318	12	)	)	PUNCT
ejpam-3498	318	13	η	η	PROPN
ejpam-3498	318	14	×rrx+2	×rrx+2	PROPN
ejpam-3498	318	15	(	(	PUNCT
ejpam-3498	318	16	q	q	X
ejpam-3498	318	17	,	,	PUNCT
ejpam-3498	318	18	i	i	NOUN
ejpam-3498	318	19	)	)	PUNCT
ejpam-3498	318	20	max	max	PROPN
ejpam-3498	318	21	g	g	PROPN
ejpam-3498	318	22	,	,	PUNCT
ejpam-3498	318	23	φ	φ	PROPN
ejpam-3498	318	24	min	min	PROPN
ejpam-3498	318	25	0≤l≤g	0≤l≤g	NUM
ejpam-3498	318	26	µ(t)α(φ	µ(t)α(φ	NUM
ejpam-3498	318	27	,	,	PUNCT
ejpam-3498	318	28	l)ω(t)β(φ	l)ω(t)β(φ	PROPN
ejpam-3498	318	29	,	,	PUNCT
ejpam-3498	318	30	l)σx	l)σx	PROPN
ejpam-3498	318	31	,	,	PUNCT
ejpam-3498	318	32	s(t)(t	s(t)(t	NUM
ejpam-3498	318	33	)	)	PUNCT
ejpam-3498	318	34	γ(φ	γ(φ	NOUN
ejpam-3498	318	35	,	,	PUNCT
ejpam-3498	318	36	l)µ(t)α	l)µ(t)α	VERB
ejpam-3498	318	37	≤	≤	NUM
ejpam-3498	318	38	n∑	n∑	NOUN
ejpam-3498	318	39	x=0	x=0	PROPN
ejpam-3498	318	40	kη2	kη2	NOUN
ejpam-3498	318	41	ηa0µ(t)(1−κ)ηω(t)(c−1)ησx	ηa0µ(t)(1−κ)ηω(t)(c−1)ησx	NOUN
ejpam-3498	318	42	,	,	PUNCT
ejpam-3498	318	43	s(t	s(t	PROPN
ejpam-3498	318	44	)	)	PUNCT
ejpam-3498	318	45	η	η	PROPN
ejpam-3498	318	46	×rrx+2	×rrx+2	PROPN
ejpam-3498	318	47	(	(	PUNCT
ejpam-3498	318	48	q	q	X
ejpam-3498	318	49	,	,	PUNCT
ejpam-3498	318	50	i	i	NOUN
ejpam-3498	318	51	)	)	PUNCT
ejpam-3498	318	52	max	max	PROPN
ejpam-3498	318	53	g	g	PROPN
ejpam-3498	318	54	,	,	PUNCT
ejpam-3498	318	55	φ	φ	PROPN
ejpam-3498	318	56	min	min	PROPN
ejpam-3498	318	57	0≤l≤g	0≤l≤g	NUM
ejpam-3498	318	58	µ(t)α(φ	µ(t)α(φ	NUM
ejpam-3498	318	59	,	,	PUNCT
ejpam-3498	318	60	l)ω(t)β(φ	l)ω(t)β(φ	PROPN
ejpam-3498	318	61	,	,	PUNCT
ejpam-3498	318	62	l)2γ(φ	l)2γ(φ	NOUN
ejpam-3498	318	63	,	,	PUNCT
ejpam-3498	318	64	l)σx	l)σx	PROPN
ejpam-3498	318	65	,	,	PUNCT
ejpam-3498	318	66	s(t	s(t	PROPN
ejpam-3498	318	67	)	)	PUNCT
ejpam-3498	318	68	γ(φ	γ(φ	PROPN
ejpam-3498	318	69	,	,	PUNCT
ejpam-3498	318	70	l)µ(t)α	l)µ(t)α	PROPN
ejpam-3498	318	71	.	.	PUNCT
ejpam-3498	319	1	thus	thus	ADV
ejpam-3498	319	2	,	,	PUNCT
ejpam-3498	319	3	‖(µ0d)ηun+1	‖(µ0d)ηun+1	VERB
ejpam-3498	319	4	i	i	PRON
ejpam-3498	319	5	(	(	PUNCT
ejpam-3498	319	6	t)‖s	t)‖s	ADJ
ejpam-3498	319	7	≤	≤	NUM
ejpam-3498	319	8	rr2a0kη2	rr2a0kη2	NOUN
ejpam-3498	319	9	d+ld+φ((x+	d+ld+φ((x+	PRON
ejpam-3498	319	10	1)2	1)2	NUM
ejpam-3498	319	11	+	+	CCONJ
ejpam-3498	319	12	1)d+ld+φ	1)d+ld+φ	NUM
ejpam-3498	319	13	n∑	n∑	NOUN
ejpam-3498	319	14	x=0	x=0	PROPN
ejpam-3498	319	15	rx	rx	VERB
ejpam-3498	319	16	≤	≤	NUM
ejpam-3498	319	17	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	319	18	.	.	PUNCT
ejpam-3498	320	1	therefore	therefore	ADV
ejpam-3498	320	2	,	,	PUNCT
ejpam-3498	320	3	we	we	PRON
ejpam-3498	320	4	have	have	AUX
ejpam-3498	320	5	shown	show	VERB
ejpam-3498	320	6	the	the	DET
ejpam-3498	320	7	well	well	NOUN
ejpam-3498	320	8	-	-	PUNCT
ejpam-3498	320	9	definedness	definedness	NOUN
ejpam-3498	320	10	of	of	ADP
ejpam-3498	320	11	un+1(t	un+1(t	PROPN
ejpam-3498	320	12	)	)	PUNCT
ejpam-3498	320	13	for	for	ADP
ejpam-3498	320	14	n	n	PRON
ejpam-3498	320	15	≥	≥	NOUN
ejpam-3498	320	16	l	l	NOUN
ejpam-3498	320	17	and	and	CCONJ
ejpam-3498	320	18	un(t	un(t	NOUN
ejpam-3498	320	19	)	)	PUNCT
ejpam-3498	320	20	converges	converge	VERB
ejpam-3498	320	21	to	to	ADP
ejpam-3498	320	22	u(t	u(t	NOUN
ejpam-3498	320	23	)	)	PUNCT
ejpam-3498	320	24	∈	∈	NOUN
ejpam-3498	321	1	bs	b	NOUN
ejpam-3498	321	2	uniformly	uniformly	ADV
ejpam-3498	321	3	in	in	ADP
ejpam-3498	321	4	i(s	i(s	NOUN
ejpam-3498	321	5	)	)	PUNCT
ejpam-3498	321	6	=	=	PRON
ejpam-3498	321	7	{	{	PUNCT
ejpam-3498	321	8	t	t	X
ejpam-3498	321	9	≥	≥	NOUN
ejpam-3498	321	10	0	0	NUM
ejpam-3498	321	11	:	:	PUNCT
ejpam-3498	321	12	ω(t	ω(t	NOUN
ejpam-3498	321	13	)	)	PUNCT
ejpam-3498	321	14	<	<	X
ejpam-3498	321	15	limn→∞	limn→∞	PROPN
ejpam-3498	321	16	an(s0	an(s0	X
ejpam-3498	321	17	−	−	PROPN
ejpam-3498	321	18	s	s	NOUN
ejpam-3498	321	19	)	)	PUNCT
ejpam-3498	321	20	}	}	PUNCT
ejpam-3498	321	21	.	.	PUNCT
ejpam-3498	322	1	this	this	DET
ejpam-3498	322	2	u	u	PROPN
ejpam-3498	322	3	∈	∈	PROPN
ejpam-3498	322	4	c0(i(s	c0(i(s	NOUN
ejpam-3498	322	5	)	)	PUNCT
ejpam-3498	322	6	,	,	PUNCT
ejpam-3498	322	7	bs	bs	PROPN
ejpam-3498	322	8	)	)	PUNCT
ejpam-3498	322	9	is	be	AUX
ejpam-3498	322	10	the	the	DET
ejpam-3498	322	11	solution	solution	NOUN
ejpam-3498	322	12	of	of	ADP
ejpam-3498	322	13	(	(	PUNCT
ejpam-3498	322	14	1	1	NUM
ejpam-3498	322	15	)	)	PUNCT
ejpam-3498	322	16	.	.	PUNCT
ejpam-3498	323	1	3.2	3.2	NUM
ejpam-3498	323	2	.	.	PUNCT
ejpam-3498	323	3	uniqueness	uniqueness	NOUN
ejpam-3498	323	4	of	of	ADP
ejpam-3498	323	5	the	the	DET
ejpam-3498	323	6	solution	solution	NOUN
ejpam-3498	323	7	the	the	DET
ejpam-3498	323	8	next	next	ADJ
ejpam-3498	323	9	proposition	proposition	NOUN
ejpam-3498	323	10	implies	imply	VERB
ejpam-3498	323	11	the	the	DET
ejpam-3498	323	12	uniqueness	uniqueness	NOUN
ejpam-3498	323	13	of	of	ADP
ejpam-3498	323	14	our	our	PRON
ejpam-3498	323	15	solution	solution	NOUN
ejpam-3498	323	16	,	,	PUNCT
ejpam-3498	323	17	but	but	CCONJ
ejpam-3498	323	18	the	the	DET
ejpam-3498	323	19	proof	proof	NOUN
ejpam-3498	323	20	is	be	AUX
ejpam-3498	323	21	similar	similar	ADJ
ejpam-3498	323	22	to	to	ADP
ejpam-3498	323	23	that	that	PRON
ejpam-3498	323	24	of	of	ADP
ejpam-3498	323	25	proposition	proposition	NOUN
ejpam-3498	323	26	3	3	NUM
ejpam-3498	324	1	and	and	CCONJ
ejpam-3498	324	2	so	so	ADV
ejpam-3498	324	3	we	we	PRON
ejpam-3498	324	4	omit	omit	VERB
ejpam-3498	324	5	it	it	PRON
ejpam-3498	324	6	here	here	ADV
ejpam-3498	324	7	.	.	PUNCT
ejpam-3498	325	1	proposition	proposition	NOUN
ejpam-3498	325	2	4	4	NUM
ejpam-3498	325	3	.	.	PUNCT
ejpam-3498	325	4	suppose	suppose	VERB
ejpam-3498	325	5	un	un	PROPN
ejpam-3498	325	6	=	=	SYM
ejpam-3498	325	7	(	(	PUNCT
ejpam-3498	325	8	un	un	PROPN
ejpam-3498	325	9	,	,	PUNCT
ejpam-3498	325	10	i)1≤n≤n	i)1≤n≤n	PROPN
ejpam-3498	325	11	and	and	CCONJ
ejpam-3498	325	12	vn	vn	PROPN
ejpam-3498	325	13	=	=	SYM
ejpam-3498	325	14	(	(	PUNCT
ejpam-3498	325	15	vn	vn	PROPN
ejpam-3498	325	16	,	,	PUNCT
ejpam-3498	325	17	i)1≤n≤n	i)1≤n≤n	PROPN
ejpam-3498	325	18	are	be	AUX
ejpam-3498	325	19	two	two	NUM
ejpam-3498	325	20	solutions	solution	NOUN
ejpam-3498	325	21	of	of	ADP
ejpam-3498	325	22	(	(	PUNCT
ejpam-3498	325	23	1	1	NUM
ejpam-3498	325	24	)	)	PUNCT
ejpam-3498	325	25	in	in	ADP
ejpam-3498	325	26	c0(i∞	c0(i∞	ADJ
ejpam-3498	325	27	,	,	PUNCT
ejpam-3498	325	28	(	(	PUNCT
ejpam-3498	325	29	bs(u	bs(u	X
ejpam-3498	325	30	,	,	PUNCT
ejpam-3498	325	31	y	y	NOUN
ejpam-3498	325	32	)	)	PUNCT
ejpam-3498	325	33	)	)	PUNCT
ejpam-3498	326	1	n	n	X
ejpam-3498	326	2	)	)	PUNCT
ejpam-3498	326	3	with	with	ADP
ejpam-3498	326	4	estimate	estimate	NOUN
ejpam-3498	326	5	{	{	PUNCT
ejpam-3498	326	6	‖un	‖un	PROPN
ejpam-3498	326	7	,	,	PUNCT
ejpam-3498	326	8	i‖s	i‖s	NOUN
ejpam-3498	326	9	,	,	PUNCT
ejpam-3498	326	10	‖vn	‖vn	NUM
ejpam-3498	326	11	,	,	PUNCT
ejpam-3498	326	12	i‖s	i‖s	NOUN
ejpam-3498	326	13	}	}	PUNCT
ejpam-3498	326	14	≤	≤	NOUN
ejpam-3498	326	15	rµ(t)α	rµ(t)α	PROPN
ejpam-3498	326	16	for	for	ADP
ejpam-3498	326	17	all	all	DET
ejpam-3498	326	18	t	t	NOUN
ejpam-3498	326	19	∈	∈	PROPN
ejpam-3498	326	20	i∞(s	i∞(	NOUN
ejpam-3498	326	21	)	)	PUNCT
ejpam-3498	326	22	.	.	PUNCT
ejpam-3498	327	1	then	then	ADV
ejpam-3498	327	2	,	,	PUNCT
ejpam-3498	327	3	for	for	ADP
ejpam-3498	327	4	t	t	PROPN
ejpam-3498	327	5	∈	∈	PROPN
ejpam-3498	327	6	i∞(s	i∞(	NOUN
ejpam-3498	327	7	)	)	PUNCT
ejpam-3498	327	8	,	,	PUNCT
ejpam-3498	327	9	n	n	NOUN
ejpam-3498	327	10	=	=	SYM
ejpam-3498	327	11	0	0	NUM
ejpam-3498	327	12	,	,	PUNCT
ejpam-3498	327	13	1	1	NUM
ejpam-3498	327	14	,	,	PUNCT
ejpam-3498	327	15	2	2	NUM
ejpam-3498	327	16	,	,	PUNCT
ejpam-3498	327	17	.	.	PUNCT
ejpam-3498	327	18	.	.	PUNCT
ejpam-3498	327	19	.	.	PUNCT
ejpam-3498	328	1	,	,	PUNCT
ejpam-3498	328	2	we	we	PRON
ejpam-3498	328	3	have	have	VERB
ejpam-3498	328	4	‖(un	‖(un	NOUN
ejpam-3498	328	5	,	,	PUNCT
ejpam-3498	328	6	i	i	PRON
ejpam-3498	328	7	−	−	PROPN
ejpam-3498	328	8	vn	vn	PROPN
ejpam-3498	328	9	,	,	PUNCT
ejpam-3498	328	10	i)(t)‖s	i)(t)‖s	PROPN
ejpam-3498	328	11	≤	≤	NOUN
ejpam-3498	328	12	2rrn+2µ(t)(1−κ)nω(t)nσn	2rrn+2µ(t)(1−κ)nω(t)nσn	NUM
ejpam-3498	328	13	,	,	PUNCT
ejpam-3498	328	14	s(t	s(t	PROPN
ejpam-3498	328	15	)	)	PUNCT
ejpam-3498	328	16	dnµ(t)α	dnµ(t)α	NOUN
ejpam-3498	328	17	and	and	CCONJ
ejpam-3498	328	18	‖(µ0(t)d)η(un	‖(µ0(t)d)η(un	PROPN
ejpam-3498	328	19	,	,	PUNCT
ejpam-3498	328	20	i	i	PRON
ejpam-3498	328	21	−	−	PROPN
ejpam-3498	328	22	vn	vn	PROPN
ejpam-3498	328	23	,	,	PUNCT
ejpam-3498	328	24	i)(t)‖s	i)(t)‖s	PROPN
ejpam-3498	328	25	≤	≤	NUM
ejpam-3498	328	26	rrn+22dn+η+1kηa0µ(t)(1−κ)n+(1−κ)η	rrn+22dn+η+1kηa0µ(t)(1−κ)n+(1−κ)η	NOUN
ejpam-3498	328	27	×ω(t)n(c−1)ησn	×ω(t)n(c−1)ησn	NOUN
ejpam-3498	328	28	,	,	PUNCT
ejpam-3498	328	29	s(t	s(t	PROPN
ejpam-3498	328	30	)	)	PUNCT
ejpam-3498	328	31	dn+ηµ(t)α	dn+ηµ(t)α	PROPN
ejpam-3498	328	32	.	.	PUNCT
ejpam-3498	329	1	references	reference	NOUN
ejpam-3498	329	2	1314	1314	NUM
ejpam-3498	329	3	acknowledgements	acknowledgement	NOUN
ejpam-3498	329	4	the	the	DET
ejpam-3498	329	5	author	author	NOUN
ejpam-3498	329	6	is	be	AUX
ejpam-3498	329	7	supported	support	VERB
ejpam-3498	329	8	by	by	ADP
ejpam-3498	329	9	the	the	DET
ejpam-3498	329	10	commission	commission	NOUN
ejpam-3498	329	11	on	on	ADP
ejpam-3498	329	12	higher	high	ADJ
ejpam-3498	329	13	education	education	NOUN
ejpam-3498	329	14	(	(	PUNCT
ejpam-3498	329	15	ched	che	VERB
ejpam-3498	329	16	)	)	PUNCT
ejpam-3498	329	17	of	of	ADP
ejpam-3498	329	18	the	the	DET
ejpam-3498	329	19	philippines	philippine	NOUN
ejpam-3498	329	20	.	.	PUNCT
ejpam-3498	330	1	references	reference	NOUN
ejpam-3498	330	2	[	[	X
ejpam-3498	330	3	1	1	NUM
ejpam-3498	330	4	]	]	X
ejpam-3498	330	5	m.s	m.s	PROPN
ejpam-3498	330	6	.	.	PROPN
ejpam-3498	330	7	baouendi	baouendi	PROPN
ejpam-3498	330	8	and	and	CCONJ
ejpam-3498	330	9	c.	c.	PROPN
ejpam-3498	330	10	guolaonic	guolaonic	PROPN
ejpam-3498	330	11	.	.	PUNCT
ejpam-3498	331	1	singular	singular	PROPN
ejpam-3498	331	2	nonlinear	nonlinear	PROPN
ejpam-3498	331	3	cauchy	cauchy	PROPN
ejpam-3498	331	4	problems	problem	NOUN
ejpam-3498	331	5	.	.	PUNCT
ejpam-3498	332	1	j.	j.	PROPN
ejpam-3498	332	2	differential	differential	PROPN
ejpam-3498	332	3	equations	equations	PROPN
ejpam-3498	332	4	,	,	PUNCT
ejpam-3498	332	5	22:455–475	22:455–475	PROPN
ejpam-3498	332	6	,	,	PUNCT
ejpam-3498	332	7	1973	1973	NUM
ejpam-3498	332	8	.	.	PUNCT
ejpam-3498	333	1	[	[	X
ejpam-3498	333	2	2	2	NUM
ejpam-3498	333	3	]	]	PUNCT
ejpam-3498	333	4	r.	r.	PROPN
ejpam-3498	333	5	gerard	gerard	PROPN
ejpam-3498	333	6	and	and	CCONJ
ejpam-3498	333	7	h.	h.	PROPN
ejpam-3498	333	8	tahara	tahara	PROPN
ejpam-3498	333	9	.	.	PUNCT
ejpam-3498	334	1	singular	singular	PROPN
ejpam-3498	334	2	nonlinear	nonlinear	ADJ
ejpam-3498	334	3	partial	partial	ADJ
ejpam-3498	334	4	differential	differential	NOUN
ejpam-3498	334	5	equations	equation	NOUN
ejpam-3498	334	6	.	.	PUNCT
ejpam-3498	335	1	friedr	friedr	PROPN
ejpam-3498	335	2	.	.	PUNCT
ejpam-3498	335	3	vieweg	vieweg	PROPN
ejpam-3498	335	4	&	&	CCONJ
ejpam-3498	335	5	sohn	sohn	PROPN
ejpam-3498	335	6	,	,	PUNCT
ejpam-3498	335	7	pages	page	NOUN
ejpam-3498	335	8	viii–269	viii–269	NOUN
ejpam-3498	335	9	,	,	PUNCT
ejpam-3498	335	10	1996	1996	NUM
ejpam-3498	335	11	.	.	PUNCT
ejpam-3498	336	1	[	[	X
ejpam-3498	336	2	3	3	NUM
ejpam-3498	336	3	]	]	X
ejpam-3498	336	4	m.	m.	NOUN
ejpam-3498	336	5	koike	koike	NOUN
ejpam-3498	336	6	.	.	PUNCT
ejpam-3498	337	1	volevič	volevič	NOUN
ejpam-3498	337	2	systems	system	NOUN
ejpam-3498	337	3	of	of	ADP
ejpam-3498	337	4	singular	singular	PROPN
ejpam-3498	337	5	nonlinear	nonlinear	ADJ
ejpam-3498	337	6	partial	partial	ADJ
ejpam-3498	337	7	differential	differential	NOUN
ejpam-3498	337	8	equations	equation	NOUN
ejpam-3498	337	9	.	.	PUNCT
ejpam-3498	338	1	nonlinear	nonlinear	ADJ
ejpam-3498	338	2	anal	anal	PROPN
ejpam-3498	338	3	.	.	PUNCT
ejpam-3498	338	4	,	,	PUNCT
ejpam-3498	338	5	24:997–1009	24:997–1009	NUM
ejpam-3498	338	6	,	,	PUNCT
ejpam-3498	338	7	1995	1995	NUM
ejpam-3498	338	8	.	.	PUNCT
ejpam-3498	339	1	[	[	X
ejpam-3498	339	2	4	4	X
ejpam-3498	339	3	]	]	PUNCT
ejpam-3498	339	4	j.	j.	PROPN
ejpam-3498	339	5	e.	e.	PROPN
ejpam-3498	339	6	c.	c.	PROPN
ejpam-3498	339	7	lope	lope	PROPN
ejpam-3498	339	8	and	and	CCONJ
ejpam-3498	339	9	r.	r.	PROPN
ejpam-3498	339	10	l.	l.	PROPN
ejpam-3498	339	11	caga	caga	PROPN
ejpam-3498	339	12	-	-	PUNCT
ejpam-3498	339	13	anan	anan	PROPN
ejpam-3498	339	14	.	.	PUNCT
ejpam-3498	340	1	fixed	fix	VERB
ejpam-3498	340	2	-	-	PUNCT
ejpam-3498	340	3	point	point	NOUN
ejpam-3498	340	4	theorem	theorem	NOUN
ejpam-3498	340	5	and	and	CCONJ
ejpam-3498	340	6	the	the	DET
ejpam-3498	340	7	nishida	nishida	ADJ
ejpam-3498	340	8	-	-	PUNCT
ejpam-3498	340	9	nirenberg	nirenberg	PROPN
ejpam-3498	340	10	method	method	NOUN
ejpam-3498	340	11	in	in	ADP
ejpam-3498	340	12	solving	solve	VERB
ejpam-3498	340	13	certain	certain	ADJ
ejpam-3498	340	14	nonlinear	nonlinear	ADJ
ejpam-3498	340	15	singular	singular	ADJ
ejpam-3498	340	16	partial	partial	ADJ
ejpam-3498	340	17	differential	differential	NOUN
ejpam-3498	340	18	equations	equation	NOUN
ejpam-3498	340	19	.	.	PUNCT
ejpam-3498	341	1	science	science	PROPN
ejpam-3498	341	2	diliman	diliman	PROPN
ejpam-3498	341	3	,	,	PUNCT
ejpam-3498	341	4	25(2):34–50	25(2):34–50	NUM
ejpam-3498	341	5	,	,	PUNCT
ejpam-3498	341	6	2013	2013	NUM
ejpam-3498	341	7	.	.	PUNCT
ejpam-3498	342	1	[	[	X
ejpam-3498	342	2	5	5	NUM
ejpam-3498	342	3	]	]	X
ejpam-3498	342	4	j.e.c	j.e.c	NOUN
ejpam-3498	342	5	.	.	PUNCT
ejpam-3498	343	1	lope	lope	PROPN
ejpam-3498	343	2	.	.	PUNCT
ejpam-3498	344	1	existence	existence	NOUN
ejpam-3498	344	2	and	and	CCONJ
ejpam-3498	344	3	uniqueness	uniqueness	ADJ
ejpam-3498	344	4	theorems	theorem	NOUN
ejpam-3498	344	5	for	for	ADP
ejpam-3498	344	6	a	a	DET
ejpam-3498	344	7	class	class	NOUN
ejpam-3498	344	8	of	of	ADP
ejpam-3498	344	9	linear	linear	ADJ
ejpam-3498	344	10	fushian	fushian	ADJ
ejpam-3498	344	11	partial	partial	ADJ
ejpam-3498	344	12	differential	differential	NOUN
ejpam-3498	344	13	equations	equation	NOUN
ejpam-3498	344	14	.	.	PUNCT
ejpam-3498	345	1	j.	j.	PROPN
ejpam-3498	345	2	math	math	PROPN
ejpam-3498	345	3	.	.	PUNCT
ejpam-3498	346	1	sci	sci	PROPN
ejpam-3498	346	2	.	.	PROPN
ejpam-3498	346	3	univ	univ	PROPN
ejpam-3498	346	4	.	.	PUNCT
ejpam-3498	347	1	tokyo	tokyo	PROPN
ejpam-3498	347	2	,	,	PUNCT
ejpam-3498	347	3	6:527–538	6:527–538	NOUN
ejpam-3498	347	4	,	,	PUNCT
ejpam-3498	347	5	1999	1999	NUM
ejpam-3498	347	6	.	.	PUNCT
ejpam-3498	348	1	[	[	X
ejpam-3498	348	2	6	6	NUM
ejpam-3498	348	3	]	]	PUNCT
ejpam-3498	348	4	l.	l.	PROPN
ejpam-3498	348	5	nirenberg	nirenberg	PROPN
ejpam-3498	348	6	.	.	PUNCT
ejpam-3498	349	1	an	an	DET
ejpam-3498	349	2	abstract	abstract	ADJ
ejpam-3498	349	3	form	form	NOUN
ejpam-3498	349	4	of	of	ADP
ejpam-3498	349	5	the	the	DET
ejpam-3498	349	6	nonlinear	nonlinear	ADJ
ejpam-3498	349	7	cauchy	cauchy	PROPN
ejpam-3498	349	8	-	-	PUNCT
ejpam-3498	349	9	kowalewski	kowalewski	PROPN
ejpam-3498	349	10	theorem	theorem	PROPN
ejpam-3498	349	11	.	.	PUNCT
ejpam-3498	350	1	j.	j.	PROPN
ejpam-3498	350	2	diff	diff	PROPN
ejpam-3498	350	3	.	.	PUNCT
ejpam-3498	351	1	geom	geom	PROPN
ejpam-3498	351	2	.	.	PROPN
ejpam-3498	351	3	,	,	PUNCT
ejpam-3498	351	4	6:561–576	6:561–576	PROPN
ejpam-3498	351	5	,	,	PUNCT
ejpam-3498	351	6	1972	1972	NUM
ejpam-3498	351	7	.	.	PUNCT
ejpam-3498	352	1	[	[	X
ejpam-3498	352	2	7	7	X
ejpam-3498	352	3	]	]	PUNCT
ejpam-3498	352	4	t.	t.	PROPN
ejpam-3498	352	5	nishida	nishida	PROPN
ejpam-3498	352	6	.	.	PUNCT
ejpam-3498	353	1	a	a	DET
ejpam-3498	353	2	note	note	NOUN
ejpam-3498	353	3	on	on	ADP
ejpam-3498	353	4	a	a	DET
ejpam-3498	353	5	theorem	theorem	NOUN
ejpam-3498	353	6	of	of	ADP
ejpam-3498	353	7	nirenberg	nirenberg	PROPN
ejpam-3498	353	8	.	.	PUNCT
ejpam-3498	354	1	j.	j.	PROPN
ejpam-3498	354	2	diff	diff	PROPN
ejpam-3498	354	3	.	.	PUNCT
ejpam-3498	355	1	geom	geom	PROPN
ejpam-3498	355	2	.	.	PROPN
ejpam-3498	355	3	,	,	PUNCT
ejpam-3498	355	4	12:629–633	12:629–633	NUM
ejpam-3498	355	5	,	,	PUNCT
ejpam-3498	355	6	1977	1977	NUM
ejpam-3498	355	7	.	.	PUNCT
ejpam-3498	356	1	[	[	X
ejpam-3498	356	2	8	8	X
ejpam-3498	356	3	]	]	PUNCT
ejpam-3498	356	4	j.	j.	PROPN
ejpam-3498	356	5	raza	raza	PROPN
ejpam-3498	356	6	,	,	PUNCT
ejpam-3498	356	7	f.	f.	PROPN
ejpam-3498	356	8	mebarek	mebarek	PROPN
ejpam-3498	356	9	-	-	PUNCT
ejpam-3498	356	10	oudina	oudina	PROPN
ejpam-3498	356	11	,	,	PUNCT
ejpam-3498	356	12	and	and	CCONJ
ejpam-3498	356	13	a.	a.	PROPN
ejpam-3498	356	14	j.	j.	PROPN
ejpam-3498	356	15	chamkha	chamkha	PROPN
ejpam-3498	356	16	.	.	PUNCT
ejpam-3498	357	1	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-3498	357	2	flow	flow	NOUN
ejpam-3498	357	3	of	of	ADP
ejpam-3498	357	4	molybdenum	molybdenum	NOUN
ejpam-3498	357	5	disulfide	disulfide	NOUN
ejpam-3498	357	6	nanofluid	nanofluid	NOUN
ejpam-3498	357	7	in	in	ADP
ejpam-3498	357	8	a	a	DET
ejpam-3498	357	9	channel	channel	NOUN
ejpam-3498	357	10	with	with	ADP
ejpam-3498	357	11	shape	shape	NOUN
ejpam-3498	357	12	effects	effect	NOUN
ejpam-3498	357	13	.	.	PUNCT
ejpam-3498	358	1	multidiscipline	multidiscipline	NOUN
ejpam-3498	358	2	modeling	modeling	NOUN
ejpam-3498	358	3	in	in	ADP
ejpam-3498	358	4	materials	material	NOUN
ejpam-3498	358	5	and	and	CCONJ
ejpam-3498	358	6	structures	structure	NOUN
ejpam-3498	358	7	,	,	PUNCT
ejpam-3498	358	8	15(4):737–757	15(4):737–757	PROPN
ejpam-3498	358	9	,	,	PUNCT
ejpam-3498	358	10	2019	2019	NUM
ejpam-3498	358	11	.	.	PUNCT
ejpam-3498	359	1	[	[	X
ejpam-3498	359	2	9	9	NUM
ejpam-3498	359	3	]	]	X
ejpam-3498	359	4	h.	h.	NOUN
ejpam-3498	359	5	tahara	tahara	PROPN
ejpam-3498	359	6	.	.	PUNCT
ejpam-3498	360	1	on	on	ADP
ejpam-3498	360	2	the	the	DET
ejpam-3498	360	3	uniqueness	uniqueness	NOUN
ejpam-3498	360	4	theorem	theorem	VERB
ejpam-3498	360	5	for	for	ADP
ejpam-3498	360	6	nonlinear	nonlinear	ADJ
ejpam-3498	360	7	singular	singular	ADJ
ejpam-3498	360	8	partial	partial	ADJ
ejpam-3498	360	9	differential	differential	NOUN
ejpam-3498	360	10	equations	equation	NOUN
ejpam-3498	360	11	.	.	PUNCT
ejpam-3498	361	1	j.	j.	PROPN
ejpam-3498	361	2	math	math	PROPN
ejpam-3498	361	3	.	.	PUNCT
ejpam-3498	362	1	sci	sci	PROPN
ejpam-3498	362	2	.	.	PROPN
ejpam-3498	362	3	univ	univ	PROPN
ejpam-3498	362	4	.	.	PUNCT
ejpam-3498	363	1	tokyo	tokyo	PROPN
ejpam-3498	363	2	,	,	PUNCT
ejpam-3498	363	3	5:477–506	5:477–506	NOUN
ejpam-3498	363	4	,	,	PUNCT
ejpam-3498	363	5	1998	1998	NUM
ejpam-3498	363	6	.	.	PUNCT