id	sid	tid	token	lemma	pos
ejpam-5714	1	1	european	european	PROPN
ejpam-5714	1	2	journal	journal	PROPN
ejpam-5714	1	3	of	of	ADP
ejpam-5714	1	4	pure	pure	ADJ
ejpam-5714	1	5	and	and	CCONJ
ejpam-5714	1	6	applied	applied	ADJ
ejpam-5714	1	7	mathematics	mathematic	NOUN
ejpam-5714	1	8	2025	2025	NUM
ejpam-5714	1	9	,	,	PUNCT
ejpam-5714	1	10	vol	vol	NOUN
ejpam-5714	1	11	.	.	PROPN
ejpam-5714	1	12	18	18	NUM
ejpam-5714	1	13	,	,	PUNCT
ejpam-5714	1	14	issue	issue	NOUN
ejpam-5714	1	15	1	1	NUM
ejpam-5714	1	16	,	,	PUNCT
ejpam-5714	1	17	article	article	NOUN
ejpam-5714	1	18	number	number	NOUN
ejpam-5714	1	19	5714	5714	NUM
ejpam-5714	1	20	issn	issn	PROPN
ejpam-5714	1	21	1307	1307	NUM
ejpam-5714	1	22	-	-	SYM
ejpam-5714	1	23	5543	5543	NUM
ejpam-5714	1	24	–	–	PUNCT
ejpam-5714	1	25	ejpam.com	ejpam.com	X
ejpam-5714	1	26	published	publish	VERB
ejpam-5714	1	27	by	by	ADP
ejpam-5714	1	28	new	new	PROPN
ejpam-5714	1	29	york	york	PROPN
ejpam-5714	1	30	business	business	PROPN
ejpam-5714	1	31	global	global	ADJ
ejpam-5714	1	32	new	new	ADJ
ejpam-5714	1	33	criteria	criterion	NOUN
ejpam-5714	1	34	for	for	ADP
ejpam-5714	1	35	guaranteeing	guarantee	VERB
ejpam-5714	1	36	oscillation	oscillation	NOUN
ejpam-5714	1	37	of	of	ADP
ejpam-5714	1	38	second	second	ADJ
ejpam-5714	1	39	-	-	PUNCT
ejpam-5714	1	40	order	order	NOUN
ejpam-5714	1	41	differential	differential	ADJ
ejpam-5714	1	42	equations	equation	NOUN
ejpam-5714	1	43	with	with	ADP
ejpam-5714	1	44	several	several	ADJ
ejpam-5714	1	45	delays	delay	NOUN
ejpam-5714	1	46	faten	faten	VERB
ejpam-5714	1	47	aldosari	aldosari	ADJ
ejpam-5714	1	48	department	department	NOUN
ejpam-5714	1	49	of	of	ADP
ejpam-5714	1	50	mathematics	mathematics	PROPN
ejpam-5714	1	51	,	,	PUNCT
ejpam-5714	1	52	college	college	NOUN
ejpam-5714	1	53	of	of	ADP
ejpam-5714	1	54	science	science	PROPN
ejpam-5714	1	55	,	,	PUNCT
ejpam-5714	1	56	shaqra	shaqra	PROPN
ejpam-5714	1	57	university	university	PROPN
ejpam-5714	1	58	,	,	PUNCT
ejpam-5714	1	59	p.o	p.o	PROPN
ejpam-5714	1	60	.	.	PROPN
ejpam-5714	1	61	box	box	PROPN
ejpam-5714	1	62	15572	15572	NUM
ejpam-5714	1	63	,	,	PUNCT
ejpam-5714	1	64	shaqra	shaqra	NOUN
ejpam-5714	1	65	11961	11961	NUM
ejpam-5714	1	66	,	,	PUNCT
ejpam-5714	1	67	saudi	saudi	PROPN
ejpam-5714	1	68	arabia	arabia	PROPN
ejpam-5714	1	69	abstract	abstract	NOUN
ejpam-5714	1	70	.	.	PUNCT
ejpam-5714	2	1	the	the	DET
ejpam-5714	2	2	primary	primary	ADJ
ejpam-5714	2	3	objective	objective	NOUN
ejpam-5714	2	4	of	of	ADP
ejpam-5714	2	5	this	this	DET
ejpam-5714	2	6	work	work	NOUN
ejpam-5714	2	7	is	be	AUX
ejpam-5714	2	8	to	to	PART
ejpam-5714	2	9	establish	establish	VERB
ejpam-5714	2	10	new	new	ADJ
ejpam-5714	2	11	criteria	criterion	NOUN
ejpam-5714	2	12	to	to	PART
ejpam-5714	2	13	guarantee	guarantee	VERB
ejpam-5714	2	14	the	the	DET
ejpam-5714	2	15	oscillation	oscillation	NOUN
ejpam-5714	2	16	of	of	ADP
ejpam-5714	2	17	solutions	solution	NOUN
ejpam-5714	2	18	for	for	ADP
ejpam-5714	2	19	second	second	ADJ
ejpam-5714	2	20	-	-	PUNCT
ejpam-5714	2	21	order	order	NOUN
ejpam-5714	2	22	differential	differential	ADJ
ejpam-5714	2	23	equations	equation	NOUN
ejpam-5714	2	24	with	with	ADP
ejpam-5714	2	25	p	p	ADJ
ejpam-5714	2	26	-	-	PUNCT
ejpam-5714	2	27	laplace	laplace	NOUN
ejpam-5714	2	28	type	type	NOUN
ejpam-5714	2	29	operator	operator	NOUN
ejpam-5714	2	30	.	.	PUNCT
ejpam-5714	3	1	new	new	ADJ
ejpam-5714	3	2	prerequisites	prerequisite	NOUN
ejpam-5714	3	3	are	be	AUX
ejpam-5714	3	4	presented	present	VERB
ejpam-5714	3	5	in	in	ADP
ejpam-5714	3	6	order	order	NOUN
ejpam-5714	3	7	to	to	PART
ejpam-5714	3	8	analyze	analyze	VERB
ejpam-5714	3	9	the	the	DET
ejpam-5714	3	10	oscillatory	oscillatory	ADJ
ejpam-5714	3	11	features	feature	NOUN
ejpam-5714	3	12	of	of	ADP
ejpam-5714	3	13	the	the	DET
ejpam-5714	3	14	analyzed	analyze	VERB
ejpam-5714	3	15	equations	equation	NOUN
ejpam-5714	3	16	.	.	PUNCT
ejpam-5714	4	1	to	to	PART
ejpam-5714	4	2	support	support	VERB
ejpam-5714	4	3	these	these	DET
ejpam-5714	4	4	findings	finding	NOUN
ejpam-5714	4	5	,	,	PUNCT
ejpam-5714	4	6	we	we	PRON
ejpam-5714	4	7	employ	employ	VERB
ejpam-5714	4	8	a	a	DET
ejpam-5714	4	9	range	range	NOUN
ejpam-5714	4	10	of	of	ADP
ejpam-5714	4	11	analysis	analysis	NOUN
ejpam-5714	4	12	tools	tool	NOUN
ejpam-5714	4	13	,	,	PUNCT
ejpam-5714	4	14	establishing	establish	VERB
ejpam-5714	4	15	new	new	ADJ
ejpam-5714	4	16	conditions	condition	NOUN
ejpam-5714	4	17	to	to	PART
ejpam-5714	4	18	address	address	VERB
ejpam-5714	4	19	specific	specific	ADJ
ejpam-5714	4	20	the	the	DET
ejpam-5714	4	21	problems	problem	NOUN
ejpam-5714	4	22	that	that	PRON
ejpam-5714	4	23	have	have	AUX
ejpam-5714	4	24	hindered	hinder	VERB
ejpam-5714	4	25	previous	previous	ADJ
ejpam-5714	4	26	researches	research	NOUN
ejpam-5714	4	27	.	.	PUNCT
ejpam-5714	5	1	more	more	ADV
ejpam-5714	5	2	specifically	specifically	ADV
ejpam-5714	5	3	,	,	PUNCT
ejpam-5714	5	4	we	we	PRON
ejpam-5714	5	5	obtain	obtain	VERB
ejpam-5714	5	6	results	result	NOUN
ejpam-5714	5	7	that	that	SCONJ
ejpam-5714	5	8	both	both	PRON
ejpam-5714	5	9	build	build	VERB
ejpam-5714	5	10	upon	upon	SCONJ
ejpam-5714	5	11	and	and	CCONJ
ejpam-5714	5	12	extend	extend	VERB
ejpam-5714	5	13	those	those	PRON
ejpam-5714	5	14	discovered	discover	VERB
ejpam-5714	5	15	in	in	ADP
ejpam-5714	5	16	earlier	early	ADJ
ejpam-5714	5	17	studies	study	NOUN
ejpam-5714	5	18	by	by	ADP
ejpam-5714	5	19	applying	apply	VERB
ejpam-5714	5	20	the	the	DET
ejpam-5714	5	21	riccati	riccati	NOUN
ejpam-5714	5	22	transformation	transformation	NOUN
ejpam-5714	5	23	and	and	CCONJ
ejpam-5714	5	24	the	the	DET
ejpam-5714	5	25	principles	principle	NOUN
ejpam-5714	5	26	of	of	ADP
ejpam-5714	5	27	comparison	comparison	NOUN
ejpam-5714	5	28	.	.	PUNCT
ejpam-5714	6	1	several	several	ADJ
ejpam-5714	6	2	examples	example	NOUN
ejpam-5714	6	3	are	be	AUX
ejpam-5714	6	4	given	give	VERB
ejpam-5714	6	5	to	to	PART
ejpam-5714	6	6	illustrate	illustrate	VERB
ejpam-5714	6	7	the	the	DET
ejpam-5714	6	8	significance	significance	NOUN
ejpam-5714	6	9	of	of	ADP
ejpam-5714	6	10	our	our	PRON
ejpam-5714	6	11	results	result	NOUN
ejpam-5714	6	12	.	.	PUNCT
ejpam-5714	7	1	2020	2020	NUM
ejpam-5714	7	2	mathematics	mathematic	NOUN
ejpam-5714	7	3	subject	subject	NOUN
ejpam-5714	7	4	classifications	classification	NOUN
ejpam-5714	7	5	:	:	PUNCT
ejpam-5714	7	6	34c10	34c10	NUM
ejpam-5714	7	7	,	,	PUNCT
ejpam-5714	7	8	34k11	34k11	NUM
ejpam-5714	7	9	key	key	ADJ
ejpam-5714	7	10	words	word	NOUN
ejpam-5714	7	11	and	and	CCONJ
ejpam-5714	7	12	phrases	phrase	NOUN
ejpam-5714	7	13	:	:	PUNCT
ejpam-5714	7	14	differential	differential	ADJ
ejpam-5714	7	15	equations	equation	NOUN
ejpam-5714	7	16	,	,	PUNCT
ejpam-5714	7	17	oscillation	oscillation	NOUN
ejpam-5714	7	18	theorems	theorem	NOUN
ejpam-5714	7	19	,	,	PUNCT
ejpam-5714	7	20	second	second	ADJ
ejpam-5714	7	21	-	-	PUNCT
ejpam-5714	7	22	order	order	NOUN
ejpam-5714	7	23	,	,	PUNCT
ejpam-5714	7	24	delay	delay	VERB
ejpam-5714	7	25	terms	term	NOUN
ejpam-5714	7	26	1	1	NUM
ejpam-5714	7	27	.	.	X
ejpam-5714	8	1	introduction	introduction	NOUN
ejpam-5714	8	2	in	in	ADP
ejpam-5714	8	3	this	this	DET
ejpam-5714	8	4	article	article	NOUN
ejpam-5714	8	5	,	,	PUNCT
ejpam-5714	8	6	we	we	PRON
ejpam-5714	8	7	examine	examine	VERB
ejpam-5714	8	8	the	the	DET
ejpam-5714	8	9	p	p	ADJ
ejpam-5714	8	10	-	-	PUNCT
ejpam-5714	8	11	laplace	laplace	NOUN
ejpam-5714	8	12	type	type	NOUN
ejpam-5714	8	13	operator	operator	NOUN
ejpam-5714	8	14	oscillation	oscillation	NOUN
ejpam-5714	8	15	problem	problem	NOUN
ejpam-5714	8	16	for	for	ADP
ejpam-5714	8	17	secondorder	secondorder	ADJ
ejpam-5714	8	18	differential	differential	NOUN
ejpam-5714	8	19	equations	equation	NOUN
ejpam-5714	8	20	(	(	PUNCT
ejpam-5714	8	21	b	b	X
ejpam-5714	8	22	(	(	PUNCT
ejpam-5714	8	23	t	t	NOUN
ejpam-5714	8	24	)	)	PUNCT
ejpam-5714	8	25	|ϖ′(t)|p−2ϖ′(t	|ϖ′(t)|p−2ϖ′(t	NOUN
ejpam-5714	8	26	)	)	PUNCT
ejpam-5714	8	27	)	)	PUNCT
ejpam-5714	9	1	′	′	NUM
ejpam-5714	10	1	+	+	CCONJ
ejpam-5714	11	1	n∑	n∑	ADJ
ejpam-5714	11	2	i=1	i=1	ADP
ejpam-5714	11	3	qi	qi	PROPN
ejpam-5714	11	4	∣∣κp−2	∣∣κp−2	PROPN
ejpam-5714	11	5	(	(	PUNCT
ejpam-5714	11	6	πi	πi	PROPN
ejpam-5714	11	7	(	(	PUNCT
ejpam-5714	11	8	t	t	NOUN
ejpam-5714	11	9	)	)	PUNCT
ejpam-5714	11	10	)	)	PUNCT
ejpam-5714	11	11	∣∣κ	∣∣κ	NOUN
ejpam-5714	11	12	(	(	PUNCT
ejpam-5714	11	13	πi	πi	X
ejpam-5714	11	14	(	(	PUNCT
ejpam-5714	11	15	t	t	NOUN
ejpam-5714	11	16	)	)	PUNCT
ejpam-5714	11	17	)	)	PUNCT
ejpam-5714	12	1	=	=	PUNCT
ejpam-5714	12	2	0	0	NUM
ejpam-5714	12	3	,	,	PUNCT
ejpam-5714	12	4	t	t	PROPN
ejpam-5714	12	5	≥	≥	PROPN
ejpam-5714	12	6	t0	t0	PROPN
ejpam-5714	12	7	,	,	PUNCT
ejpam-5714	12	8	(	(	PUNCT
ejpam-5714	12	9	1	1	X
ejpam-5714	12	10	)	)	PUNCT
ejpam-5714	12	11	where	where	SCONJ
ejpam-5714	12	12	p	p	X
ejpam-5714	12	13	>	>	X
ejpam-5714	12	14	1	1	NUM
ejpam-5714	12	15	,	,	PUNCT
ejpam-5714	12	16	ϖ	ϖ	PROPN
ejpam-5714	12	17	(	(	PUNCT
ejpam-5714	12	18	t	t	PROPN
ejpam-5714	12	19	)	)	PUNCT
ejpam-5714	12	20	:	:	PUNCT
ejpam-5714	12	21	=	=	SYM
ejpam-5714	12	22	κ	κ	X
ejpam-5714	12	23	(	(	PUNCT
ejpam-5714	12	24	t	t	PROPN
ejpam-5714	12	25	)	)	PUNCT
ejpam-5714	13	1	+	+	NOUN
ejpam-5714	13	2	y	y	PROPN
ejpam-5714	13	3	(	(	PUNCT
ejpam-5714	13	4	t)κ	t)κ	X
ejpam-5714	13	5	(	(	PUNCT
ejpam-5714	13	6	ζ	ζ	NOUN
ejpam-5714	13	7	(	(	PUNCT
ejpam-5714	13	8	t	t	NOUN
ejpam-5714	13	9	)	)	PUNCT
ejpam-5714	13	10	)	)	PUNCT
ejpam-5714	13	11	,	,	PUNCT
ejpam-5714	14	1	b	b	X
ejpam-5714	14	2	∈	∈	PROPN
ejpam-5714	14	3	c	c	X
ejpam-5714	14	4	(	(	PUNCT
ejpam-5714	14	5	[	[	X
ejpam-5714	14	6	t,∞	t,∞	NUM
ejpam-5714	14	7	)	)	PUNCT
ejpam-5714	14	8	,	,	PUNCT
ejpam-5714	14	9	(	(	PUNCT
ejpam-5714	14	10	0,∞	0,∞	NOUN
ejpam-5714	14	11	)	)	PUNCT
ejpam-5714	14	12	)	)	PUNCT
ejpam-5714	14	13	,	,	PUNCT
ejpam-5714	14	14	y	y	PROPN
ejpam-5714	14	15	∈	∈	PROPN
ejpam-5714	14	16	c	c	X
ejpam-5714	14	17	(	(	PUNCT
ejpam-5714	14	18	[	[	X
ejpam-5714	14	19	t,∞	t,∞	NUM
ejpam-5714	14	20	)	)	PUNCT
ejpam-5714	14	21	,	,	PUNCT
ejpam-5714	15	1	[	[	X
ejpam-5714	15	2	0,∞	0,∞	NOUN
ejpam-5714	15	3	)	)	PUNCT
ejpam-5714	15	4	)	)	PUNCT
ejpam-5714	15	5	,	,	PUNCT
ejpam-5714	15	6	qi	qi	PROPN
ejpam-5714	15	7	∈	∈	PROPN
ejpam-5714	15	8	c	c	X
ejpam-5714	15	9	(	(	PUNCT
ejpam-5714	16	1	[	[	X
ejpam-5714	16	2	t,∞	t,∞	NUM
ejpam-5714	16	3	)	)	PUNCT
ejpam-5714	16	4	,	,	PUNCT
ejpam-5714	17	1	[	[	X
ejpam-5714	17	2	0,∞	0,∞	NOUN
ejpam-5714	17	3	)	)	PUNCT
ejpam-5714	17	4	)	)	PUNCT
ejpam-5714	18	1	,	,	PUNCT
ejpam-5714	18	2	ζ	ζ	NOUN
ejpam-5714	18	3	,	,	PUNCT
ejpam-5714	18	4	πi	πi	ADV
ejpam-5714	18	5	∈	∈	PROPN
ejpam-5714	18	6	c	c	NOUN
ejpam-5714	18	7	(	(	PUNCT
ejpam-5714	18	8	[	[	X
ejpam-5714	18	9	t,∞),r	t,∞),r	NOUN
ejpam-5714	18	10	)	)	PUNCT
ejpam-5714	18	11	,	,	PUNCT
ejpam-5714	18	12	ζ	ζ	PROPN
ejpam-5714	18	13	(	(	PUNCT
ejpam-5714	18	14	t	t	NOUN
ejpam-5714	18	15	)	)	PUNCT
ejpam-5714	18	16	≤	≤	NOUN
ejpam-5714	18	17	t	t	PROPN
ejpam-5714	18	18	,	,	PUNCT
ejpam-5714	18	19	πi	πi	PROPN
ejpam-5714	18	20	(	(	PUNCT
ejpam-5714	18	21	t	t	NOUN
ejpam-5714	18	22	)	)	PUNCT
ejpam-5714	18	23	≤	≤	NOUN
ejpam-5714	18	24	t	t	PROPN
ejpam-5714	18	25	,	,	PUNCT
ejpam-5714	18	26	limt→∞	limt→∞	ADP
ejpam-5714	18	27	ζ	ζ	NOUN
ejpam-5714	18	28	(	(	PUNCT
ejpam-5714	18	29	t	t	NOUN
ejpam-5714	18	30	)	)	PUNCT
ejpam-5714	18	31	=	=	PUNCT
ejpam-5714	19	1	limt→∞	limt→∞	PROPN
ejpam-5714	19	2	πi	πi	CCONJ
ejpam-5714	19	3	(	(	PUNCT
ejpam-5714	19	4	t	t	NOUN
ejpam-5714	19	5	)	)	PUNCT
ejpam-5714	19	6	=	=	SYM
ejpam-5714	19	7	∞	∞	PROPN
ejpam-5714	19	8	,	,	PUNCT
ejpam-5714	19	9	qi	qi	PROPN
ejpam-5714	19	10	(	(	PUNCT
ejpam-5714	19	11	t	t	PROPN
ejpam-5714	19	12	)	)	PUNCT
ejpam-5714	19	13	does	do	AUX
ejpam-5714	19	14	not	not	PART
ejpam-5714	19	15	vanish	vanish	VERB
ejpam-5714	19	16	identically	identically	ADV
ejpam-5714	19	17	,	,	PUNCT
ejpam-5714	19	18	i	i	PRON
ejpam-5714	19	19	=	=	NOUN
ejpam-5714	19	20	1	1	NUM
ejpam-5714	19	21	,	,	PUNCT
ejpam-5714	19	22	2	2	NUM
ejpam-5714	19	23	,	,	PUNCT
ejpam-5714	19	24	...	...	PUNCT
ejpam-5714	19	25	,	,	PUNCT
ejpam-5714	19	26	n	n	CCONJ
ejpam-5714	19	27	,	,	PUNCT
ejpam-5714	19	28	y	y	PROPN
ejpam-5714	19	29	(	(	PUNCT
ejpam-5714	19	30	t	t	PROPN
ejpam-5714	19	31	)	)	PUNCT
ejpam-5714	19	32	<	<	X
ejpam-5714	19	33	1	1	NUM
ejpam-5714	19	34	and∫	and∫	NOUN
ejpam-5714	19	35	∞	∞	NUM
ejpam-5714	19	36	t0	t0	PROPN
ejpam-5714	19	37	b−1/(p−1	b−1/(p−1	NOUN
ejpam-5714	19	38	)	)	PUNCT
ejpam-5714	19	39	(	(	PUNCT
ejpam-5714	19	40	s	s	X
ejpam-5714	19	41	)	)	PUNCT
ejpam-5714	19	42	ds	ds	PROPN
ejpam-5714	19	43	=	=	SYM
ejpam-5714	19	44	∞.	∞.	PROPN
ejpam-5714	19	45	(	(	PUNCT
ejpam-5714	19	46	2	2	NUM
ejpam-5714	19	47	)	)	PUNCT
ejpam-5714	19	48	doi	doi	NOUN
ejpam-5714	19	49	:	:	PUNCT
ejpam-5714	19	50	https://doi.org/10.29020/nybg.ejpam.v18i1.5714	https://doi.org/10.29020/nybg.ejpam.v18i1.5714	PROPN
ejpam-5714	19	51	email	email	NOUN
ejpam-5714	19	52	address	address	NOUN
ejpam-5714	19	53	:	:	PUNCT
ejpam-5714	19	54	faldosari@su.edu.sa	faldosari@su.edu.sa	PROPN
ejpam-5714	19	55	(	(	PUNCT
ejpam-5714	19	56	f.	f.	PROPN
ejpam-5714	19	57	aldosari	aldosari	PROPN
ejpam-5714	19	58	)	)	PUNCT
ejpam-5714	19	59	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5714	20	1	1	1	NUM
ejpam-5714	20	2	copyright	copyright	NOUN
ejpam-5714	20	3	:	:	PUNCT
ejpam-5714	20	4	©	©	PROPN
ejpam-5714	20	5	2025	2025	NUM
ejpam-5714	20	6	the	the	DET
ejpam-5714	20	7	author(s	author(s	NOUN
ejpam-5714	20	8	)	)	PUNCT
ejpam-5714	20	9	.	.	PUNCT
ejpam-5714	21	1	(	(	PUNCT
ejpam-5714	21	2	cc	cc	NOUN
ejpam-5714	21	3	by	by	ADP
ejpam-5714	21	4	-	-	PUNCT
ejpam-5714	21	5	nc	nc	PROPN
ejpam-5714	21	6	4.0	4.0	NUM
ejpam-5714	21	7	)	)	PUNCT
ejpam-5714	21	8	f.	f.	NOUN
ejpam-5714	21	9	aldosari	aldosari	PROPN
ejpam-5714	21	10	/	/	SYM
ejpam-5714	21	11	eur	eur	PROPN
ejpam-5714	21	12	.	.	PUNCT
ejpam-5714	22	1	j.	j.	PROPN
ejpam-5714	22	2	pure	pure	PROPN
ejpam-5714	22	3	appl	appl	PROPN
ejpam-5714	22	4	.	.	PROPN
ejpam-5714	22	5	math	math	PROPN
ejpam-5714	22	6	,	,	PUNCT
ejpam-5714	22	7	18	18	NUM
ejpam-5714	22	8	(	(	PUNCT
ejpam-5714	22	9	1	1	NUM
ejpam-5714	22	10	)	)	PUNCT
ejpam-5714	22	11	(	(	PUNCT
ejpam-5714	22	12	2025	2025	NUM
ejpam-5714	22	13	)	)	PUNCT
ejpam-5714	22	14	,	,	PUNCT
ejpam-5714	22	15	5714	5714	NUM
ejpam-5714	22	16	2	2	NUM
ejpam-5714	22	17	of	of	ADP
ejpam-5714	22	18	16	16	NUM
ejpam-5714	22	19	definition	definition	NOUN
ejpam-5714	22	20	1	1	NUM
ejpam-5714	22	21	.	.	PUNCT
ejpam-5714	23	1	by	by	ADP
ejpam-5714	23	2	a	a	DET
ejpam-5714	23	3	solution	solution	NOUN
ejpam-5714	23	4	of	of	ADP
ejpam-5714	23	5	(	(	PUNCT
ejpam-5714	23	6	1	1	NUM
ejpam-5714	23	7	)	)	PUNCT
ejpam-5714	23	8	,	,	PUNCT
ejpam-5714	23	9	we	we	PRON
ejpam-5714	23	10	mean	mean	VERB
ejpam-5714	23	11	a	a	DET
ejpam-5714	23	12	function	function	NOUN
ejpam-5714	23	13	κ	κ	PROPN
ejpam-5714	23	14	∈	∈	PROPN
ejpam-5714	23	15	c1	c1	PROPN
ejpam-5714	23	16	(	(	PUNCT
ejpam-5714	23	17	[	[	X
ejpam-5714	23	18	t,∞),r	t,∞),r	NOUN
ejpam-5714	23	19	)	)	PUNCT
ejpam-5714	23	20	,	,	PUNCT
ejpam-5714	23	21	tκ	tκ	ADP
ejpam-5714	23	22	≥	≥	PROPN
ejpam-5714	23	23	t0	t0	PROPN
ejpam-5714	23	24	,	,	PUNCT
ejpam-5714	23	25	which	which	PRON
ejpam-5714	23	26	has	have	VERB
ejpam-5714	23	27	the	the	DET
ejpam-5714	23	28	property	property	NOUN
ejpam-5714	23	29	b	b	PROPN
ejpam-5714	23	30	(	(	PUNCT
ejpam-5714	23	31	t	t	PROPN
ejpam-5714	23	32	)	)	PUNCT
ejpam-5714	23	33	(	(	PUNCT
ejpam-5714	23	34	ϖ′	ϖ′	X
ejpam-5714	23	35	(	(	PUNCT
ejpam-5714	23	36	t))(p−1	t))(p−1	NOUN
ejpam-5714	23	37	)	)	PUNCT
ejpam-5714	23	38	∈	∈	PROPN
ejpam-5714	23	39	c1	c1	NOUN
ejpam-5714	23	40	(	(	PUNCT
ejpam-5714	23	41	[	[	X
ejpam-5714	23	42	t0,∞),r	t0,∞),r	NOUN
ejpam-5714	23	43	)	)	PUNCT
ejpam-5714	23	44	,	,	PUNCT
ejpam-5714	23	45	p	p	X
ejpam-5714	23	46	>	>	X
ejpam-5714	23	47	1	1	NUM
ejpam-5714	23	48	,	,	PUNCT
ejpam-5714	23	49	and	and	CCONJ
ejpam-5714	23	50	satisfies	satisfie	NOUN
ejpam-5714	23	51	(	(	PUNCT
ejpam-5714	23	52	1	1	NUM
ejpam-5714	23	53	)	)	PUNCT
ejpam-5714	23	54	on	on	ADP
ejpam-5714	23	55	[	[	NOUN
ejpam-5714	23	56	tκ,∞	tκ,∞	NOUN
ejpam-5714	23	57	)	)	PUNCT
ejpam-5714	23	58	.	.	PUNCT
ejpam-5714	24	1	we	we	PRON
ejpam-5714	24	2	consider	consider	VERB
ejpam-5714	24	3	only	only	ADV
ejpam-5714	24	4	those	those	DET
ejpam-5714	24	5	solutions	solution	NOUN
ejpam-5714	24	6	κ	κ	X
ejpam-5714	24	7	of	of	ADP
ejpam-5714	24	8	(	(	PUNCT
ejpam-5714	24	9	1	1	NUM
ejpam-5714	24	10	)	)	PUNCT
ejpam-5714	24	11	which	which	PRON
ejpam-5714	24	12	satisfy	satisfy	VERB
ejpam-5714	24	13	sup{|κ	sup{|κ	NOUN
ejpam-5714	24	14	(	(	PUNCT
ejpam-5714	24	15	t)|	t)|	NOUN
ejpam-5714	24	16	:	:	PUNCT
ejpam-5714	24	17	t	t	PROPN
ejpam-5714	24	18	≥	≥	NOUN
ejpam-5714	24	19	tκ	tκ	ADP
ejpam-5714	24	20	}	}	PUNCT
ejpam-5714	24	21	>	>	X
ejpam-5714	24	22	0	0	NUM
ejpam-5714	24	23	,	,	PUNCT
ejpam-5714	24	24	for	for	ADP
ejpam-5714	24	25	all	all	DET
ejpam-5714	24	26	t	t	PROPN
ejpam-5714	24	27	>	>	X
ejpam-5714	24	28	tκ	tκ	ADP
ejpam-5714	24	29	.	.	PUNCT
ejpam-5714	25	1	definition	definition	NOUN
ejpam-5714	25	2	2	2	NUM
ejpam-5714	25	3	.	.	PUNCT
ejpam-5714	26	1	κ	κ	PROPN
ejpam-5714	26	2	is	be	AUX
ejpam-5714	26	3	referred	refer	VERB
ejpam-5714	26	4	to	to	ADP
ejpam-5714	26	5	as	as	ADP
ejpam-5714	26	6	oscillatory	oscillatory	ADJ
ejpam-5714	26	7	if	if	SCONJ
ejpam-5714	26	8	it	it	PRON
ejpam-5714	26	9	is	be	AUX
ejpam-5714	26	10	neither	neither	CCONJ
ejpam-5714	26	11	finally	finally	ADV
ejpam-5714	26	12	positive	positive	ADJ
ejpam-5714	26	13	nor	nor	CCONJ
ejpam-5714	26	14	eventually	eventually	ADV
ejpam-5714	26	15	negative	negative	ADJ
ejpam-5714	26	16	.	.	PUNCT
ejpam-5714	27	1	otherwise	otherwise	ADV
ejpam-5714	27	2	it	it	PRON
ejpam-5714	27	3	is	be	AUX
ejpam-5714	27	4	referred	refer	VERB
ejpam-5714	27	5	to	to	ADP
ejpam-5714	27	6	as	as	ADP
ejpam-5714	27	7	non	non	ADJ
ejpam-5714	27	8	-	-	ADJ
ejpam-5714	27	9	oscillatory	oscillatory	ADJ
ejpam-5714	27	10	.	.	PUNCT
ejpam-5714	28	1	if	if	SCONJ
ejpam-5714	28	2	every	every	DET
ejpam-5714	28	3	solution	solution	NOUN
ejpam-5714	28	4	to	to	ADP
ejpam-5714	28	5	the	the	DET
ejpam-5714	28	6	equation	equation	NOUN
ejpam-5714	28	7	oscillates	oscillate	NOUN
ejpam-5714	28	8	,	,	PUNCT
ejpam-5714	28	9	then	then	ADV
ejpam-5714	28	10	the	the	DET
ejpam-5714	28	11	equation	equation	NOUN
ejpam-5714	28	12	is	be	AUX
ejpam-5714	28	13	said	say	VERB
ejpam-5714	28	14	to	to	PART
ejpam-5714	28	15	be	be	AUX
ejpam-5714	28	16	oscillatory	oscillatory	ADJ
ejpam-5714	28	17	.	.	PUNCT
ejpam-5714	29	1	in	in	ADP
ejpam-5714	29	2	differential	differential	ADJ
ejpam-5714	29	3	equations	equation	NOUN
ejpam-5714	29	4	(	(	PUNCT
ejpam-5714	29	5	des	des	PROPN
ejpam-5714	29	6	)	)	PUNCT
ejpam-5714	29	7	,	,	PUNCT
ejpam-5714	29	8	which	which	PRON
ejpam-5714	29	9	are	be	AUX
ejpam-5714	29	10	the	the	DET
ejpam-5714	29	11	most	most	ADV
ejpam-5714	29	12	successful	successful	ADJ
ejpam-5714	29	13	models	model	NOUN
ejpam-5714	29	14	for	for	ADP
ejpam-5714	29	15	studying	study	VERB
ejpam-5714	29	16	natural	natural	ADJ
ejpam-5714	29	17	events	event	NOUN
ejpam-5714	29	18	,	,	PUNCT
ejpam-5714	29	19	each	each	DET
ejpam-5714	29	20	dependant	dependant	ADJ
ejpam-5714	29	21	variable	variable	NOUN
ejpam-5714	29	22	represents	represent	VERB
ejpam-5714	29	23	a	a	DET
ejpam-5714	29	24	quantity	quantity	NOUN
ejpam-5714	29	25	in	in	ADP
ejpam-5714	29	26	the	the	DET
ejpam-5714	29	27	modeled	model	VERB
ejpam-5714	29	28	phenomenon	phenomenon	NOUN
ejpam-5714	29	29	.	.	PUNCT
ejpam-5714	30	1	des	des	PROPN
ejpam-5714	30	2	have	have	AUX
ejpam-5714	30	3	helped	help	VERB
ejpam-5714	30	4	us	we	PRON
ejpam-5714	30	5	understand	understand	VERB
ejpam-5714	30	6	a	a	DET
ejpam-5714	30	7	variety	variety	NOUN
ejpam-5714	30	8	of	of	ADP
ejpam-5714	30	9	complex	complex	ADJ
ejpam-5714	30	10	events	event	NOUN
ejpam-5714	30	11	in	in	ADP
ejpam-5714	30	12	our	our	PRON
ejpam-5714	30	13	daily	daily	ADJ
ejpam-5714	30	14	lives	life	NOUN
ejpam-5714	30	15	and	and	CCONJ
ejpam-5714	30	16	are	be	AUX
ejpam-5714	30	17	crucial	crucial	ADJ
ejpam-5714	30	18	to	to	ADP
ejpam-5714	30	19	many	many	ADJ
ejpam-5714	30	20	technical	technical	ADJ
ejpam-5714	30	21	applications	application	NOUN
ejpam-5714	30	22	.	.	PUNCT
ejpam-5714	31	1	these	these	DET
ejpam-5714	31	2	days	day	NOUN
ejpam-5714	31	3	,	,	PUNCT
ejpam-5714	31	4	they	they	PRON
ejpam-5714	31	5	are	be	AUX
ejpam-5714	31	6	essential	essential	ADJ
ejpam-5714	31	7	tools	tool	NOUN
ejpam-5714	31	8	in	in	ADP
ejpam-5714	31	9	applied	applied	ADJ
ejpam-5714	31	10	sciences	science	NOUN
ejpam-5714	31	11	and	and	CCONJ
ejpam-5714	31	12	technology	technology	NOUN
ejpam-5714	31	13	,	,	PUNCT
ejpam-5714	31	14	used	use	VERB
ejpam-5714	31	15	to	to	PART
ejpam-5714	31	16	study	study	VERB
ejpam-5714	31	17	media	medium	NOUN
ejpam-5714	31	18	,	,	PUNCT
ejpam-5714	31	19	conversations	conversation	NOUN
ejpam-5714	31	20	,	,	PUNCT
ejpam-5714	31	21	phone	phone	NOUN
ejpam-5714	31	22	signals	signal	NOUN
ejpam-5714	31	23	,	,	PUNCT
ejpam-5714	31	24	and	and	CCONJ
ejpam-5714	31	25	online	online	ADJ
ejpam-5714	31	26	purchasing	purchase	VERB
ejpam-5714	31	27	data	datum	NOUN
ejpam-5714	31	28	.	.	PUNCT
ejpam-5714	32	1	in	in	ADP
ejpam-5714	32	2	a	a	DET
ejpam-5714	32	3	more	more	ADV
ejpam-5714	32	4	traditional	traditional	ADJ
ejpam-5714	32	5	sense	sense	NOUN
ejpam-5714	32	6	,	,	PUNCT
ejpam-5714	32	7	astronomers	astronomer	NOUN
ejpam-5714	32	8	used	use	VERB
ejpam-5714	32	9	them	they	PRON
ejpam-5714	32	10	to	to	PART
ejpam-5714	32	11	describe	describe	VERB
ejpam-5714	32	12	the	the	DET
ejpam-5714	32	13	motion	motion	NOUN
ejpam-5714	32	14	of	of	ADP
ejpam-5714	32	15	stars	star	NOUN
ejpam-5714	32	16	and	and	CCONJ
ejpam-5714	32	17	the	the	DET
ejpam-5714	32	18	orbits	orbit	NOUN
ejpam-5714	32	19	of	of	ADP
ejpam-5714	32	20	planets	planet	NOUN
ejpam-5714	32	21	.	.	PUNCT
ejpam-5714	33	1	they	they	PRON
ejpam-5714	33	2	also	also	ADV
ejpam-5714	33	3	serve	serve	VERB
ejpam-5714	33	4	a	a	DET
ejpam-5714	33	5	variety	variety	NOUN
ejpam-5714	33	6	of	of	ADP
ejpam-5714	33	7	purposes	purpose	NOUN
ejpam-5714	33	8	in	in	ADP
ejpam-5714	33	9	biology	biology	NOUN
ejpam-5714	33	10	and	and	CCONJ
ejpam-5714	33	11	medicine	medicine	NOUN
ejpam-5714	33	12	,	,	PUNCT
ejpam-5714	33	13	see	see	VERB
ejpam-5714	33	14	[	[	X
ejpam-5714	33	15	11	11	NUM
ejpam-5714	33	16	]	]	PUNCT
ejpam-5714	33	17	.	.	PUNCT
ejpam-5714	34	1	neutral	neutral	ADJ
ejpam-5714	34	2	differential	differential	ADJ
ejpam-5714	34	3	equations	equation	NOUN
ejpam-5714	34	4	(	(	PUNCT
ejpam-5714	34	5	ndes	nde	NOUN
ejpam-5714	34	6	)	)	PUNCT
ejpam-5714	34	7	,	,	PUNCT
ejpam-5714	34	8	a	a	DET
ejpam-5714	34	9	specific	specific	ADJ
ejpam-5714	34	10	subset	subset	NOUN
ejpam-5714	34	11	of	of	ADP
ejpam-5714	34	12	functional	functional	ADJ
ejpam-5714	34	13	differential	differential	ADJ
ejpam-5714	34	14	equations	equation	NOUN
ejpam-5714	34	15	,	,	PUNCT
ejpam-5714	34	16	have	have	VERB
ejpam-5714	34	17	derivatives	derivative	NOUN
ejpam-5714	34	18	that	that	PRON
ejpam-5714	34	19	depend	depend	VERB
ejpam-5714	34	20	on	on	ADP
ejpam-5714	34	21	both	both	CCONJ
ejpam-5714	34	22	the	the	DET
ejpam-5714	34	23	function	function	NOUN
ejpam-5714	34	24	’s	’s	PART
ejpam-5714	34	25	derivatives	derivative	NOUN
ejpam-5714	34	26	from	from	ADP
ejpam-5714	34	27	earlier	early	ADJ
ejpam-5714	34	28	periods	period	NOUN
ejpam-5714	34	29	and	and	CCONJ
ejpam-5714	34	30	its	its	PRON
ejpam-5714	34	31	current	current	ADJ
ejpam-5714	34	32	values	value	NOUN
ejpam-5714	34	33	.	.	PUNCT
ejpam-5714	35	1	this	this	DET
ejpam-5714	35	2	unique	unique	ADJ
ejpam-5714	35	3	characteristic	characteristic	ADJ
ejpam-5714	35	4	distinguishes	distinguish	VERB
ejpam-5714	35	5	ndes	nde	NOUN
ejpam-5714	35	6	from	from	ADP
ejpam-5714	35	7	traditional	traditional	ADJ
ejpam-5714	35	8	differential	differential	ADJ
ejpam-5714	35	9	equations	equation	NOUN
ejpam-5714	35	10	and	and	CCONJ
ejpam-5714	35	11	establishes	establish	VERB
ejpam-5714	35	12	a	a	DET
ejpam-5714	35	13	distinct	distinct	ADJ
ejpam-5714	35	14	analytical	analytical	ADJ
ejpam-5714	35	15	framework	framework	NOUN
ejpam-5714	35	16	.	.	PUNCT
ejpam-5714	36	1	the	the	DET
ejpam-5714	36	2	relationship	relationship	NOUN
ejpam-5714	36	3	between	between	ADP
ejpam-5714	36	4	ndes	nde	NOUN
ejpam-5714	36	5	and	and	CCONJ
ejpam-5714	36	6	fdes	fde	NOUN
ejpam-5714	36	7	is	be	AUX
ejpam-5714	36	8	essential	essential	ADJ
ejpam-5714	36	9	because	because	SCONJ
ejpam-5714	36	10	they	they	PRON
ejpam-5714	36	11	often	often	ADV
ejpam-5714	36	12	arise	arise	VERB
ejpam-5714	36	13	in	in	ADP
ejpam-5714	36	14	systems	system	NOUN
ejpam-5714	36	15	where	where	SCONJ
ejpam-5714	36	16	past	past	ADJ
ejpam-5714	36	17	values	value	NOUN
ejpam-5714	36	18	and	and	CCONJ
ejpam-5714	36	19	rates	rate	NOUN
ejpam-5714	36	20	of	of	ADP
ejpam-5714	36	21	change	change	NOUN
ejpam-5714	36	22	influence	influence	NOUN
ejpam-5714	36	23	future	future	ADJ
ejpam-5714	36	24	states	state	NOUN
ejpam-5714	36	25	.	.	PUNCT
ejpam-5714	37	1	ndes	nde	NOUN
ejpam-5714	37	2	’	'	PUNCT
ejpam-5714	37	3	significance	significance	NOUN
ejpam-5714	37	4	is	be	AUX
ejpam-5714	37	5	particularly	particularly	ADV
ejpam-5714	37	6	evident	evident	ADJ
ejpam-5714	37	7	in	in	ADP
ejpam-5714	37	8	fields	field	NOUN
ejpam-5714	37	9	like	like	ADP
ejpam-5714	37	10	control	control	NOUN
ejpam-5714	37	11	theory	theory	NOUN
ejpam-5714	37	12	and	and	CCONJ
ejpam-5714	37	13	signal	signal	NOUN
ejpam-5714	37	14	processing	processing	NOUN
ejpam-5714	37	15	since	since	SCONJ
ejpam-5714	37	16	they	they	PRON
ejpam-5714	37	17	represent	represent	VERB
ejpam-5714	37	18	systems	system	NOUN
ejpam-5714	37	19	with	with	ADP
ejpam-5714	37	20	memory	memory	NOUN
ejpam-5714	37	21	effects	effect	NOUN
ejpam-5714	37	22	.	.	PUNCT
ejpam-5714	38	1	for	for	ADP
ejpam-5714	38	2	instance	instance	NOUN
ejpam-5714	38	3	,	,	PUNCT
ejpam-5714	38	4	in	in	ADP
ejpam-5714	38	5	mechanical	mechanical	ADJ
ejpam-5714	38	6	systems	system	NOUN
ejpam-5714	38	7	with	with	ADP
ejpam-5714	38	8	inertia	inertia	NOUN
ejpam-5714	38	9	,	,	PUNCT
ejpam-5714	38	10	acceleration	acceleration	NOUN
ejpam-5714	38	11	may	may	AUX
ejpam-5714	38	12	be	be	AUX
ejpam-5714	38	13	affected	affect	VERB
ejpam-5714	38	14	by	by	ADP
ejpam-5714	38	15	both	both	DET
ejpam-5714	38	16	velocity	velocity	NOUN
ejpam-5714	38	17	and	and	CCONJ
ejpam-5714	38	18	current	current	ADJ
ejpam-5714	38	19	position	position	NOUN
ejpam-5714	38	20	.	.	PUNCT
ejpam-5714	39	1	this	this	DET
ejpam-5714	39	2	association	association	NOUN
ejpam-5714	39	3	emphasizes	emphasize	VERB
ejpam-5714	39	4	the	the	DET
ejpam-5714	39	5	importance	importance	NOUN
ejpam-5714	39	6	of	of	ADP
ejpam-5714	39	7	ndes	nde	NOUN
ejpam-5714	39	8	in	in	ADP
ejpam-5714	39	9	accurately	accurately	ADV
ejpam-5714	39	10	modeling	model	VERB
ejpam-5714	39	11	and	and	CCONJ
ejpam-5714	39	12	simulating	simulate	VERB
ejpam-5714	39	13	dynamic	dynamic	ADJ
ejpam-5714	39	14	systems	system	NOUN
ejpam-5714	39	15	.	.	PUNCT
ejpam-5714	40	1	moreover	moreover	ADV
ejpam-5714	40	2	,	,	PUNCT
ejpam-5714	40	3	the	the	DET
ejpam-5714	40	4	research	research	NOUN
ejpam-5714	40	5	of	of	ADP
ejpam-5714	40	6	ndes	nde	NOUN
ejpam-5714	40	7	complements	complement	NOUN
ejpam-5714	40	8	that	that	PRON
ejpam-5714	40	9	of	of	ADP
ejpam-5714	40	10	ddes	dde	NOUN
ejpam-5714	40	11	because	because	SCONJ
ejpam-5714	40	12	understanding	understand	VERB
ejpam-5714	40	13	one	one	NOUN
ejpam-5714	40	14	usually	usually	ADV
ejpam-5714	40	15	provides	provide	VERB
ejpam-5714	40	16	significant	significant	ADJ
ejpam-5714	40	17	insights	insight	NOUN
ejpam-5714	40	18	into	into	ADP
ejpam-5714	40	19	the	the	DET
ejpam-5714	40	20	other	other	ADJ
ejpam-5714	40	21	[	[	X
ejpam-5714	40	22	2	2	NUM
ejpam-5714	40	23	,	,	PUNCT
ejpam-5714	40	24	7	7	NUM
ejpam-5714	40	25	,	,	PUNCT
ejpam-5714	40	26	9	9	NUM
ejpam-5714	40	27	,	,	PUNCT
ejpam-5714	40	28	14	14	NUM
ejpam-5714	40	29	]	]	PUNCT
ejpam-5714	40	30	.	.	PUNCT
ejpam-5714	41	1	these	these	DET
ejpam-5714	41	2	equations	equation	NOUN
ejpam-5714	41	3	find	find	VERB
ejpam-5714	41	4	use	use	NOUN
ejpam-5714	41	5	in	in	ADP
ejpam-5714	41	6	a	a	DET
ejpam-5714	41	7	wide	wide	ADJ
ejpam-5714	41	8	range	range	NOUN
ejpam-5714	41	9	of	of	ADP
ejpam-5714	41	10	fields	field	NOUN
ejpam-5714	41	11	,	,	PUNCT
ejpam-5714	41	12	including	include	VERB
ejpam-5714	41	13	problems	problem	NOUN
ejpam-5714	41	14	requiring	require	VERB
ejpam-5714	41	15	masses	masse	NOUN
ejpam-5714	41	16	connected	connect	VERB
ejpam-5714	41	17	to	to	ADP
ejpam-5714	41	18	a	a	DET
ejpam-5714	41	19	flexible	flexible	ADJ
ejpam-5714	41	20	,	,	PUNCT
ejpam-5714	41	21	shaky	shaky	ADJ
ejpam-5714	41	22	rod	rod	NOUN
ejpam-5714	41	23	[	[	X
ejpam-5714	41	24	10	10	NUM
ejpam-5714	41	25	,	,	PUNCT
ejpam-5714	41	26	13	13	NUM
ejpam-5714	41	27	,	,	PUNCT
ejpam-5714	41	28	16	16	NUM
ejpam-5714	41	29	]	]	PUNCT
ejpam-5714	41	30	.	.	PUNCT
ejpam-5714	42	1	the	the	DET
ejpam-5714	42	2	ordinary	ordinary	ADJ
ejpam-5714	42	3	differential	differential	ADJ
ejpam-5714	42	4	equation	equation	NOUN
ejpam-5714	42	5	(	(	PUNCT
ejpam-5714	42	6	ode	ode	PROPN
ejpam-5714	42	7	)	)	PUNCT
ejpam-5714	42	8	is	be	AUX
ejpam-5714	42	9	a	a	DET
ejpam-5714	42	10	crucial	crucial	ADJ
ejpam-5714	42	11	tool	tool	NOUN
ejpam-5714	42	12	for	for	ADP
ejpam-5714	42	13	understanding	understanding	NOUN
ejpam-5714	42	14	and	and	CCONJ
ejpam-5714	42	15	modeling	model	VERB
ejpam-5714	42	16	a	a	DET
ejpam-5714	42	17	wide	wide	ADJ
ejpam-5714	42	18	range	range	NOUN
ejpam-5714	42	19	of	of	ADP
ejpam-5714	42	20	technical	technical	ADJ
ejpam-5714	42	21	and	and	CCONJ
ejpam-5714	42	22	natural	natural	ADJ
ejpam-5714	42	23	systems	system	NOUN
ejpam-5714	42	24	.	.	PUNCT
ejpam-5714	43	1	the	the	DET
ejpam-5714	43	2	complexity	complexity	NOUN
ejpam-5714	43	3	and	and	CCONJ
ejpam-5714	43	4	diversity	diversity	NOUN
ejpam-5714	43	5	of	of	ADP
ejpam-5714	43	6	real	real	ADJ
ejpam-5714	43	7	-	-	PUNCT
ejpam-5714	43	8	world	world	NOUN
ejpam-5714	43	9	events	event	NOUN
ejpam-5714	43	10	often	often	ADV
ejpam-5714	43	11	necessitate	necessitate	VERB
ejpam-5714	43	12	the	the	DET
ejpam-5714	43	13	use	use	NOUN
ejpam-5714	43	14	of	of	ADP
ejpam-5714	43	15	sophisticated	sophisticated	ADJ
ejpam-5714	43	16	arguments	argument	NOUN
ejpam-5714	43	17	to	to	PART
ejpam-5714	43	18	obtain	obtain	VERB
ejpam-5714	43	19	more	more	ADV
ejpam-5714	43	20	comprehensive	comprehensive	ADJ
ejpam-5714	43	21	and	and	CCONJ
ejpam-5714	43	22	correct	correct	ADJ
ejpam-5714	43	23	solutions	solution	NOUN
ejpam-5714	43	24	,	,	PUNCT
ejpam-5714	43	25	despite	despite	SCONJ
ejpam-5714	43	26	the	the	DET
ejpam-5714	43	27	widespread	widespread	ADJ
ejpam-5714	43	28	use	use	NOUN
ejpam-5714	43	29	of	of	ADP
ejpam-5714	43	30	odes	ode	NOUN
ejpam-5714	43	31	(	(	PUNCT
ejpam-5714	43	32	see	see	VERB
ejpam-5714	43	33	[	[	X
ejpam-5714	43	34	15	15	NUM
ejpam-5714	43	35	,	,	PUNCT
ejpam-5714	43	36	17	17	NUM
ejpam-5714	43	37	]	]	PUNCT
ejpam-5714	43	38	)	)	PUNCT
ejpam-5714	43	39	.	.	PUNCT
ejpam-5714	44	1	the	the	DET
ejpam-5714	44	2	behavior	behavior	NOUN
ejpam-5714	44	3	of	of	ADP
ejpam-5714	44	4	many	many	ADJ
ejpam-5714	44	5	nonlinear	nonlinear	ADJ
ejpam-5714	44	6	systems	system	NOUN
ejpam-5714	44	7	is	be	AUX
ejpam-5714	44	8	not	not	PART
ejpam-5714	44	9	well	well	ADV
ejpam-5714	44	10	described	describe	VERB
ejpam-5714	44	11	by	by	ADP
ejpam-5714	44	12	conventional	conventional	ADJ
ejpam-5714	44	13	linear	linear	PROPN
ejpam-5714	44	14	differential	differential	NOUN
ejpam-5714	44	15	equations	equation	NOUN
ejpam-5714	44	16	,	,	PUNCT
ejpam-5714	44	17	which	which	PRON
ejpam-5714	44	18	emphasizes	emphasize	VERB
ejpam-5714	44	19	the	the	DET
ejpam-5714	44	20	importance	importance	NOUN
ejpam-5714	44	21	of	of	ADP
ejpam-5714	44	22	including	include	VERB
ejpam-5714	44	23	complex	complex	ADJ
ejpam-5714	44	24	arguments	argument	NOUN
ejpam-5714	44	25	into	into	ADP
ejpam-5714	44	26	odes	ode	NOUN
ejpam-5714	44	27	.	.	PUNCT
ejpam-5714	45	1	advanced	advanced	ADJ
ejpam-5714	45	2	nonlinear	nonlinear	ADJ
ejpam-5714	45	3	dynamics	dynamic	NOUN
ejpam-5714	45	4	may	may	AUX
ejpam-5714	45	5	make	make	VERB
ejpam-5714	45	6	these	these	DET
ejpam-5714	45	7	systems	system	NOUN
ejpam-5714	45	8	more	more	ADV
ejpam-5714	45	9	realistically	realistically	ADV
ejpam-5714	45	10	represented	represent	VERB
ejpam-5714	45	11	,	,	PUNCT
ejpam-5714	45	12	improving	improve	VERB
ejpam-5714	45	13	insights	insight	NOUN
ejpam-5714	45	14	and	and	CCONJ
ejpam-5714	45	15	predictions	prediction	NOUN
ejpam-5714	45	16	.	.	PUNCT
ejpam-5714	46	1	furthermore	furthermore	ADV
ejpam-5714	46	2	,	,	PUNCT
ejpam-5714	46	3	perturbation	perturbation	NOUN
ejpam-5714	46	4	methods	method	NOUN
ejpam-5714	46	5	can	can	AUX
ejpam-5714	46	6	be	be	AUX
ejpam-5714	46	7	used	use	VERB
ejpam-5714	46	8	to	to	PART
ejpam-5714	46	9	analyze	analyze	VERB
ejpam-5714	46	10	systems	system	NOUN
ejpam-5714	46	11	that	that	PRON
ejpam-5714	46	12	are	be	AUX
ejpam-5714	46	13	subject	subject	ADJ
ejpam-5714	46	14	to	to	ADP
ejpam-5714	46	15	small	small	ADJ
ejpam-5714	46	16	perturbations	perturbation	NOUN
ejpam-5714	46	17	,	,	PUNCT
ejpam-5714	46	18	providing	provide	VERB
ejpam-5714	46	19	a	a	DET
ejpam-5714	46	20	means	means	NOUN
ejpam-5714	46	21	of	of	ADP
ejpam-5714	46	22	understanding	understand	VERB
ejpam-5714	46	23	how	how	SCONJ
ejpam-5714	46	24	complex	complex	ADJ
ejpam-5714	46	25	systems	system	NOUN
ejpam-5714	46	26	react	react	VERB
ejpam-5714	46	27	in	in	ADP
ejpam-5714	46	28	different	different	ADJ
ejpam-5714	46	29	contexts	contexts	NOUN
ejpam-5714	46	30	.	.	PUNCT
ejpam-5714	47	1	furthermore	furthermore	ADV
ejpam-5714	47	2	,	,	PUNCT
ejpam-5714	47	3	stability	stability	NOUN
ejpam-5714	47	4	analysis	analysis	NOUN
ejpam-5714	47	5	is	be	AUX
ejpam-5714	47	6	essential	essential	ADJ
ejpam-5714	47	7	for	for	ADP
ejpam-5714	47	8	determining	determine	VERB
ejpam-5714	47	9	the	the	DET
ejpam-5714	47	10	long	long	ADJ
ejpam-5714	47	11	-	-	PUNCT
ejpam-5714	47	12	term	term	NOUN
ejpam-5714	47	13	behavior	behavior	NOUN
ejpam-5714	47	14	of	of	ADP
ejpam-5714	47	15	ode	ode	ADJ
ejpam-5714	47	16	solutions	solution	NOUN
ejpam-5714	47	17	,	,	PUNCT
ejpam-5714	47	18	which	which	PRON
ejpam-5714	47	19	is	be	AUX
ejpam-5714	47	20	important	important	ADJ
ejpam-5714	47	21	in	in	ADP
ejpam-5714	47	22	fields	field	NOUN
ejpam-5714	47	23	such	such	ADJ
ejpam-5714	47	24	as	as	ADP
ejpam-5714	47	25	control	control	NOUN
ejpam-5714	47	26	theory	theory	NOUN
ejpam-5714	47	27	and	and	CCONJ
ejpam-5714	47	28	epidemiology	epidemiology	NOUN
ejpam-5714	47	29	(	(	PUNCT
ejpam-5714	47	30	see	see	VERB
ejpam-5714	47	31	[	[	X
ejpam-5714	47	32	12	12	NUM
ejpam-5714	47	33	]	]	PUNCT
ejpam-5714	47	34	)	)	PUNCT
ejpam-5714	47	35	.	.	PUNCT
ejpam-5714	48	1	in	in	ADP
ejpam-5714	48	2	recent	recent	ADJ
ejpam-5714	48	3	years	year	NOUN
ejpam-5714	48	4	,	,	PUNCT
ejpam-5714	48	5	there	there	PRON
ejpam-5714	48	6	has	have	AUX
ejpam-5714	48	7	been	be	AUX
ejpam-5714	48	8	a	a	DET
ejpam-5714	48	9	substantial	substantial	ADJ
ejpam-5714	48	10	advancement	advancement	NOUN
ejpam-5714	48	11	in	in	ADP
ejpam-5714	48	12	the	the	DET
ejpam-5714	48	13	study	study	NOUN
ejpam-5714	48	14	of	of	ADP
ejpam-5714	48	15	oscillation	oscillation	NOUN
ejpam-5714	48	16	conditions	condition	NOUN
ejpam-5714	48	17	for	for	ADP
ejpam-5714	48	18	higher	high	ADJ
ejpam-5714	48	19	-	-	PUNCT
ejpam-5714	48	20	order	order	NOUN
ejpam-5714	48	21	equations	equation	NOUN
ejpam-5714	48	22	,	,	PUNCT
ejpam-5714	48	23	particularly	particularly	ADV
ejpam-5714	48	24	second	second	ADJ
ejpam-5714	48	25	-	-	PUNCT
ejpam-5714	48	26	order	order	NOUN
ejpam-5714	48	27	differential	differential	ADJ
ejpam-5714	48	28	equations	equation	NOUN
ejpam-5714	48	29	with	with	ADP
ejpam-5714	48	30	f.	f.	PROPN
ejpam-5714	48	31	aldosari	aldosari	PROPN
ejpam-5714	48	32	/	/	SYM
ejpam-5714	48	33	eur	eur	PROPN
ejpam-5714	48	34	.	.	PUNCT
ejpam-5714	49	1	j.	j.	PROPN
ejpam-5714	49	2	pure	pure	PROPN
ejpam-5714	49	3	appl	appl	PROPN
ejpam-5714	49	4	.	.	PROPN
ejpam-5714	49	5	math	math	PROPN
ejpam-5714	49	6	,	,	PUNCT
ejpam-5714	49	7	18	18	NUM
ejpam-5714	49	8	(	(	PUNCT
ejpam-5714	49	9	1	1	NUM
ejpam-5714	49	10	)	)	PUNCT
ejpam-5714	49	11	(	(	PUNCT
ejpam-5714	49	12	2025	2025	NUM
ejpam-5714	49	13	)	)	PUNCT
ejpam-5714	49	14	,	,	PUNCT
ejpam-5714	49	15	5714	5714	NUM
ejpam-5714	49	16	3	3	NUM
ejpam-5714	49	17	of	of	ADP
ejpam-5714	49	18	16	16	NUM
ejpam-5714	49	19	delays	delay	NOUN
ejpam-5714	49	20	[	[	X
ejpam-5714	49	21	1	1	NUM
ejpam-5714	49	22	,	,	PUNCT
ejpam-5714	49	23	3	3	NUM
ejpam-5714	49	24	]	]	PUNCT
ejpam-5714	49	25	.	.	PUNCT
ejpam-5714	50	1	this	this	PRON
ejpam-5714	50	2	explains	explain	VERB
ejpam-5714	50	3	why	why	SCONJ
ejpam-5714	50	4	the	the	DET
ejpam-5714	50	5	qualitative	qualitative	ADJ
ejpam-5714	50	6	aspects	aspect	NOUN
ejpam-5714	50	7	of	of	ADP
ejpam-5714	50	8	these	these	DET
ejpam-5714	50	9	equations	equation	NOUN
ejpam-5714	50	10	are	be	AUX
ejpam-5714	50	11	so	so	ADV
ejpam-5714	50	12	fascinating	fascinating	ADJ
ejpam-5714	50	13	.	.	PUNCT
ejpam-5714	51	1	oscillation	oscillation	NOUN
ejpam-5714	51	2	phenomena	phenomenon	NOUN
ejpam-5714	51	3	are	be	AUX
ejpam-5714	51	4	present	present	ADJ
ejpam-5714	51	5	in	in	ADP
ejpam-5714	51	6	many	many	ADJ
ejpam-5714	51	7	real	real	ADJ
ejpam-5714	51	8	-	-	PUNCT
ejpam-5714	51	9	world	world	NOUN
ejpam-5714	51	10	models	model	NOUN
ejpam-5714	51	11	;	;	PUNCT
ejpam-5714	51	12	for	for	ADP
ejpam-5714	51	13	instance	instance	NOUN
ejpam-5714	51	14	,	,	PUNCT
ejpam-5714	51	15	mathematical	mathematical	ADJ
ejpam-5714	51	16	biology	biology	NOUN
ejpam-5714	51	17	models	model	NOUN
ejpam-5714	51	18	that	that	PRON
ejpam-5714	51	19	use	use	VERB
ejpam-5714	51	20	cross	cross	ADJ
ejpam-5714	51	21	-	-	ADJ
ejpam-5714	51	22	diffusion	diffusion	NOUN
ejpam-5714	51	23	terms	term	NOUN
ejpam-5714	51	24	to	to	PART
ejpam-5714	51	25	construct	construct	VERB
ejpam-5714	51	26	oscillation	oscillation	NOUN
ejpam-5714	51	27	and/or	and/or	CCONJ
ejpam-5714	51	28	delay	delay	NOUN
ejpam-5714	51	29	actions	action	NOUN
ejpam-5714	51	30	are	be	AUX
ejpam-5714	51	31	discussed	discuss	VERB
ejpam-5714	51	32	in	in	ADP
ejpam-5714	51	33	the	the	DET
ejpam-5714	51	34	publications	publication	NOUN
ejpam-5714	52	1	[	[	X
ejpam-5714	52	2	5	5	NUM
ejpam-5714	52	3	,	,	PUNCT
ejpam-5714	52	4	6	6	NUM
ejpam-5714	52	5	]	]	PUNCT
ejpam-5714	52	6	.	.	PUNCT
ejpam-5714	53	1	this	this	DET
ejpam-5714	53	2	methodology	methodology	NOUN
ejpam-5714	53	3	includes	include	VERB
ejpam-5714	53	4	a	a	DET
ejpam-5714	53	5	detailed	detailed	ADJ
ejpam-5714	53	6	development	development	NOUN
ejpam-5714	53	7	of	of	ADP
ejpam-5714	53	8	the	the	DET
ejpam-5714	53	9	oscillation	oscillation	NOUN
ejpam-5714	53	10	theory	theory	NOUN
ejpam-5714	53	11	of	of	ADP
ejpam-5714	53	12	this	this	DET
ejpam-5714	53	13	type	type	NOUN
ejpam-5714	53	14	of	of	ADP
ejpam-5714	53	15	equation	equation	NOUN
ejpam-5714	53	16	.	.	PUNCT
ejpam-5714	54	1	alqahtani	alqahtani	PROPN
ejpam-5714	54	2	et	et	PROPN
ejpam-5714	54	3	al	al	PROPN
ejpam-5714	54	4	.	.	PUNCT
ejpam-5714	55	1	[	[	X
ejpam-5714	55	2	22	22	NUM
ejpam-5714	55	3	]	]	PUNCT
ejpam-5714	55	4	established	establish	VERB
ejpam-5714	55	5	asymptotic	asymptotic	ADJ
ejpam-5714	55	6	behavior	behavior	NOUN
ejpam-5714	55	7	for	for	ADP
ejpam-5714	55	8	equations	equation	NOUN
ejpam-5714	55	9	with	with	ADP
ejpam-5714	55	10	several	several	ADJ
ejpam-5714	55	11	delays	delay	NOUN
ejpam-5714	55	12	(	(	PUNCT
ejpam-5714	55	13	b	b	X
ejpam-5714	55	14	(	(	PUNCT
ejpam-5714	55	15	t	t	PROPN
ejpam-5714	55	16	)	)	PUNCT
ejpam-5714	55	17	(	(	PUNCT
ejpam-5714	55	18	κ′	κ′	X
ejpam-5714	55	19	(	(	PUNCT
ejpam-5714	55	20	t	t	PROPN
ejpam-5714	55	21	)	)	PUNCT
ejpam-5714	55	22	)	)	PUNCT
ejpam-5714	55	23	α)′	α)′	PROPN
ejpam-5714	56	1	+	+	NUM
ejpam-5714	56	2	n∑	n∑	NOUN
ejpam-5714	56	3	i=1	i=1	ADP
ejpam-5714	56	4	qi	qi	PROPN
ejpam-5714	56	5	(	(	PUNCT
ejpam-5714	56	6	t)κα	t)κα	PROPN
ejpam-5714	56	7	(	(	PUNCT
ejpam-5714	56	8	πi	πi	PROPN
ejpam-5714	56	9	(	(	PUNCT
ejpam-5714	56	10	t	t	NOUN
ejpam-5714	56	11	)	)	PUNCT
ejpam-5714	56	12	)	)	PUNCT
ejpam-5714	57	1	=	=	SYM
ejpam-5714	57	2	0	0	NUM
ejpam-5714	57	3	,	,	PUNCT
ejpam-5714	57	4	α	α	NOUN
ejpam-5714	57	5	>	>	X
ejpam-5714	57	6	0	0	X
ejpam-5714	57	7	.	.	PUNCT
ejpam-5714	58	1	in	in	ADP
ejpam-5714	58	2	[	[	X
ejpam-5714	58	3	8	8	NUM
ejpam-5714	58	4	]	]	PUNCT
ejpam-5714	58	5	,	,	PUNCT
ejpam-5714	58	6	the	the	DET
ejpam-5714	58	7	authors	author	NOUN
ejpam-5714	58	8	was	be	AUX
ejpam-5714	58	9	able	able	ADJ
ejpam-5714	58	10	to	to	PART
ejpam-5714	58	11	provide	provide	VERB
ejpam-5714	58	12	some	some	DET
ejpam-5714	58	13	oscillation	oscillation	NOUN
ejpam-5714	58	14	conditions	condition	NOUN
ejpam-5714	58	15	for	for	ADP
ejpam-5714	58	16	(	(	PUNCT
ejpam-5714	58	17	b(t)|κ′(t)|α−1κ′(t))′	b(t)|κ′(t)|α−1κ′(t))′	PROPN
ejpam-5714	58	18	+	+	NUM
ejpam-5714	58	19	q(t)|κ[π(t)]|α−1κ[π(t	q(t)|κ[π(t)]|α−1κ[π(t	PROPN
ejpam-5714	58	20	)	)	PUNCT
ejpam-5714	58	21	]	]	PUNCT
ejpam-5714	59	1	=	=	PUNCT
ejpam-5714	59	2	0	0	X
ejpam-5714	59	3	.	.	PUNCT
ejpam-5714	60	1	(	(	PUNCT
ejpam-5714	60	2	3	3	X
ejpam-5714	60	3	)	)	PUNCT
ejpam-5714	60	4	later	later	ADJ
ejpam-5714	60	5	contributions	contribution	NOUN
ejpam-5714	60	6	include	include	VERB
ejpam-5714	60	7	studies	study	NOUN
ejpam-5714	60	8	by	by	ADP
ejpam-5714	60	9	sahiner	sahiner	NOUN
ejpam-5714	60	10	and	and	CCONJ
ejpam-5714	60	11	wang	wang	PROPN
ejpam-5714	61	1	[	[	X
ejpam-5714	61	2	18	18	NUM
ejpam-5714	61	3	,	,	PUNCT
ejpam-5714	61	4	20	20	NUM
ejpam-5714	61	5	]	]	PUNCT
ejpam-5714	61	6	,	,	PUNCT
ejpam-5714	61	7	zhao	zhao	PROPN
ejpam-5714	61	8	and	and	CCONJ
ejpam-5714	61	9	meng	meng	PROPN
ejpam-5714	62	1	[	[	X
ejpam-5714	62	2	23	23	NUM
ejpam-5714	62	3	]	]	PUNCT
ejpam-5714	62	4	and	and	CCONJ
ejpam-5714	62	5	xu	xu	PROPN
ejpam-5714	62	6	and	and	CCONJ
ejpam-5714	62	7	weng	weng	PROPN
ejpam-5714	63	1	[	[	X
ejpam-5714	63	2	21	21	NUM
ejpam-5714	63	3	]	]	PUNCT
ejpam-5714	63	4	that	that	PRON
ejpam-5714	63	5	focus	focus	VERB
ejpam-5714	63	6	on	on	ADP
ejpam-5714	63	7	oscillation	oscillation	NOUN
ejpam-5714	63	8	criteria	criterion	NOUN
ejpam-5714	63	9	and	and	CCONJ
ejpam-5714	63	10	asymptotic	asymptotic	ADJ
ejpam-5714	63	11	behavior	behavior	NOUN
ejpam-5714	63	12	.	.	PUNCT
ejpam-5714	64	1	baculikova	baculikova	PROPN
ejpam-5714	64	2	and	and	CCONJ
ejpam-5714	64	3	dzurina	dzurina	PROPN
ejpam-5714	64	4	’s	’s	PART
ejpam-5714	64	5	recent	recent	ADJ
ejpam-5714	64	6	study	study	NOUN
ejpam-5714	64	7	[	[	X
ejpam-5714	64	8	4	4	X
ejpam-5714	64	9	]	]	PUNCT
ejpam-5714	64	10	is	be	AUX
ejpam-5714	64	11	significant	significant	ADJ
ejpam-5714	64	12	because	because	SCONJ
ejpam-5714	64	13	it	it	PRON
ejpam-5714	64	14	provides	provide	VERB
ejpam-5714	64	15	crucial	crucial	ADJ
ejpam-5714	64	16	new	new	ADJ
ejpam-5714	64	17	details	detail	NOUN
ejpam-5714	64	18	on	on	ADP
ejpam-5714	64	19	oscillation	oscillation	NOUN
ejpam-5714	64	20	conditions	condition	NOUN
ejpam-5714	64	21	for	for	ADP
ejpam-5714	64	22	second	second	ADJ
ejpam-5714	64	23	-	-	PUNCT
ejpam-5714	64	24	order	order	NOUN
ejpam-5714	64	25	delay	delay	NOUN
ejpam-5714	64	26	differential	differential	ADJ
ejpam-5714	64	27	equations	equation	NOUN
ejpam-5714	64	28	of	of	ADP
ejpam-5714	64	29	type	type	NOUN
ejpam-5714	64	30	(	(	PUNCT
ejpam-5714	64	31	b	b	PROPN
ejpam-5714	64	32	(	(	PUNCT
ejpam-5714	64	33	t	t	NOUN
ejpam-5714	64	34	)	)	PUNCT
ejpam-5714	64	35	(	(	PUNCT
ejpam-5714	64	36	(	(	PUNCT
ejpam-5714	64	37	κ	κ	X
ejpam-5714	64	38	(	(	PUNCT
ejpam-5714	64	39	t	t	PROPN
ejpam-5714	64	40	)	)	PUNCT
ejpam-5714	65	1	+	+	NOUN
ejpam-5714	65	2	y	y	PROPN
ejpam-5714	65	3	(	(	PUNCT
ejpam-5714	65	4	t)κ	t)κ	X
ejpam-5714	65	5	(	(	PUNCT
ejpam-5714	65	6	ζ	ζ	NOUN
ejpam-5714	65	7	(	(	PUNCT
ejpam-5714	65	8	t)))′	t)))′	NOUN
ejpam-5714	65	9	)	)	PUNCT
ejpam-5714	65	10	α)′	α)′	PROPN
ejpam-5714	65	11	+	+	CCONJ
ejpam-5714	65	12	q	q	X
ejpam-5714	66	1	(	(	PUNCT
ejpam-5714	66	2	t)κα	t)κα	PROPN
ejpam-5714	66	3	(	(	PUNCT
ejpam-5714	66	4	π	π	PROPN
ejpam-5714	66	5	(	(	PUNCT
ejpam-5714	66	6	t	t	PROPN
ejpam-5714	66	7	)	)	PUNCT
ejpam-5714	66	8	)	)	PUNCT
ejpam-5714	66	9	=	=	PUNCT
ejpam-5714	67	1	0	0	X
ejpam-5714	67	2	.	.	PUNCT
ejpam-5714	68	1	(	(	PUNCT
ejpam-5714	68	2	4	4	NUM
ejpam-5714	68	3	)	)	PUNCT
ejpam-5714	68	4	lastly	lastly	ADV
ejpam-5714	68	5	,	,	PUNCT
ejpam-5714	68	6	recent	recent	ADJ
ejpam-5714	68	7	publications	publication	NOUN
ejpam-5714	68	8	by	by	ADP
ejpam-5714	68	9	al	al	PROPN
ejpam-5714	68	10	-	-	PUNCT
ejpam-5714	68	11	jaser	jaser	NOUN
ejpam-5714	68	12	et	et	PROPN
ejpam-5714	68	13	al	al	PROPN
ejpam-5714	68	14	.	.	PUNCT
ejpam-5714	69	1	[	[	X
ejpam-5714	69	2	3	3	NUM
ejpam-5714	69	3	]	]	PUNCT
ejpam-5714	69	4	give	give	VERB
ejpam-5714	69	5	additional	additional	ADJ
ejpam-5714	69	6	helpful	helpful	ADJ
ejpam-5714	69	7	criteria	criterion	NOUN
ejpam-5714	69	8	for	for	ADP
ejpam-5714	69	9	assessing	assess	VERB
ejpam-5714	69	10	the	the	DET
ejpam-5714	69	11	asymptotic	asymptotic	ADJ
ejpam-5714	69	12	and	and	CCONJ
ejpam-5714	69	13	oscillatory	oscillatory	ADJ
ejpam-5714	69	14	behavior	behavior	NOUN
ejpam-5714	69	15	of	of	ADP
ejpam-5714	69	16	solutions	solution	NOUN
ejpam-5714	69	17	.	.	PUNCT
ejpam-5714	70	1	the	the	DET
ejpam-5714	70	2	first	first	ADJ
ejpam-5714	70	3	-	-	PUNCT
ejpam-5714	70	4	order	order	NOUN
ejpam-5714	70	5	differential	differential	ADJ
ejpam-5714	70	6	equations	equation	NOUN
ejpam-5714	70	7	and	and	CCONJ
ejpam-5714	70	8	the	the	DET
ejpam-5714	70	9	second	second	ADJ
ejpam-5714	70	10	-	-	PUNCT
ejpam-5714	70	11	order	order	NOUN
ejpam-5714	70	12	(	(	PUNCT
ejpam-5714	70	13	4	4	NUM
ejpam-5714	70	14	)	)	PUNCT
ejpam-5714	70	15	differential	differential	NOUN
ejpam-5714	70	16	equations	equation	NOUN
ejpam-5714	70	17	are	be	AUX
ejpam-5714	70	18	compared	compare	VERB
ejpam-5714	70	19	using	use	VERB
ejpam-5714	70	20	established	establish	VERB
ejpam-5714	70	21	comparison	comparison	NOUN
ejpam-5714	70	22	theorems	theorem	NOUN
ejpam-5714	70	23	.	.	PUNCT
ejpam-5714	71	1	in	in	ADP
ejpam-5714	71	2	this	this	DET
ejpam-5714	71	3	research	research	NOUN
ejpam-5714	71	4	,	,	PUNCT
ejpam-5714	71	5	we	we	PRON
ejpam-5714	71	6	use	use	VERB
ejpam-5714	71	7	comparison	comparison	NOUN
ejpam-5714	71	8	principles	principle	NOUN
ejpam-5714	71	9	and	and	CCONJ
ejpam-5714	71	10	riccati	riccati	NOUN
ejpam-5714	71	11	transformations	transformation	NOUN
ejpam-5714	71	12	to	to	PART
ejpam-5714	71	13	obtain	obtain	VERB
ejpam-5714	71	14	the	the	DET
ejpam-5714	71	15	different	different	ADJ
ejpam-5714	71	16	conditions	condition	NOUN
ejpam-5714	71	17	for	for	ADP
ejpam-5714	71	18	oscillation	oscillation	NOUN
ejpam-5714	71	19	of	of	ADP
ejpam-5714	71	20	(	(	PUNCT
ejpam-5714	71	21	1	1	NUM
ejpam-5714	71	22	)	)	PUNCT
ejpam-5714	71	23	.	.	PUNCT
ejpam-5714	72	1	examples	example	NOUN
ejpam-5714	72	2	are	be	AUX
ejpam-5714	72	3	provided	provide	VERB
ejpam-5714	72	4	to	to	PART
ejpam-5714	72	5	illustrate	illustrate	VERB
ejpam-5714	72	6	the	the	DET
ejpam-5714	72	7	main	main	ADJ
ejpam-5714	72	8	findings	finding	NOUN
ejpam-5714	72	9	.	.	PUNCT
ejpam-5714	73	1	the	the	DET
ejpam-5714	73	2	format	format	NOUN
ejpam-5714	73	3	of	of	ADP
ejpam-5714	73	4	this	this	DET
ejpam-5714	73	5	document	document	NOUN
ejpam-5714	73	6	is	be	AUX
ejpam-5714	73	7	as	as	SCONJ
ejpam-5714	73	8	follows	follow	VERB
ejpam-5714	73	9	.	.	PUNCT
ejpam-5714	74	1	in	in	ADP
ejpam-5714	74	2	the	the	DET
ejpam-5714	74	3	first	first	ADJ
ejpam-5714	74	4	section	section	NOUN
ejpam-5714	74	5	(	(	PUNCT
ejpam-5714	74	6	introduction	introduction	NOUN
ejpam-5714	74	7	)	)	PUNCT
ejpam-5714	74	8	,	,	PUNCT
ejpam-5714	74	9	we	we	PRON
ejpam-5714	74	10	present	present	VERB
ejpam-5714	74	11	the	the	DET
ejpam-5714	74	12	studied	studied	ADJ
ejpam-5714	74	13	equation	equation	NOUN
ejpam-5714	74	14	and	and	CCONJ
ejpam-5714	74	15	the	the	DET
ejpam-5714	74	16	general	general	ADJ
ejpam-5714	74	17	conditions	condition	NOUN
ejpam-5714	74	18	needed	need	VERB
ejpam-5714	74	19	to	to	PART
ejpam-5714	74	20	reach	reach	VERB
ejpam-5714	74	21	the	the	DET
ejpam-5714	74	22	main	main	ADJ
ejpam-5714	74	23	results	result	NOUN
ejpam-5714	74	24	of	of	ADP
ejpam-5714	74	25	the	the	DET
ejpam-5714	74	26	paper	paper	NOUN
ejpam-5714	74	27	.	.	PUNCT
ejpam-5714	75	1	we	we	PRON
ejpam-5714	75	2	also	also	ADV
ejpam-5714	75	3	provide	provide	VERB
ejpam-5714	75	4	an	an	DET
ejpam-5714	75	5	overview	overview	NOUN
ejpam-5714	75	6	of	of	ADP
ejpam-5714	75	7	pertinent	pertinent	ADJ
ejpam-5714	75	8	topics	topic	NOUN
ejpam-5714	75	9	and	and	CCONJ
ejpam-5714	75	10	the	the	DET
ejpam-5714	75	11	goal	goal	NOUN
ejpam-5714	75	12	of	of	ADP
ejpam-5714	75	13	this	this	DET
ejpam-5714	75	14	study	study	NOUN
ejpam-5714	75	15	.	.	PUNCT
ejpam-5714	76	1	the	the	DET
ejpam-5714	76	2	oscillation	oscillation	NOUN
ejpam-5714	76	3	results	result	NOUN
ejpam-5714	76	4	discussed	discuss	VERB
ejpam-5714	76	5	in	in	ADP
ejpam-5714	76	6	the	the	DET
ejpam-5714	76	7	”	"	PUNCT
ejpam-5714	76	8	oscillation	oscillation	NOUN
ejpam-5714	76	9	results	result	NOUN
ejpam-5714	76	10	”	"	PUNCT
ejpam-5714	76	11	part	part	NOUN
ejpam-5714	76	12	will	will	AUX
ejpam-5714	76	13	be	be	AUX
ejpam-5714	76	14	derived	derive	VERB
ejpam-5714	76	15	using	use	VERB
ejpam-5714	76	16	a	a	DET
ejpam-5714	76	17	few	few	ADJ
ejpam-5714	76	18	relationships	relationship	NOUN
ejpam-5714	76	19	and	and	CCONJ
ejpam-5714	76	20	findings	finding	NOUN
ejpam-5714	76	21	that	that	PRON
ejpam-5714	76	22	we	we	PRON
ejpam-5714	76	23	present	present	VERB
ejpam-5714	76	24	in	in	ADP
ejpam-5714	76	25	section	section	NOUN
ejpam-5714	76	26	2	2	NUM
ejpam-5714	76	27	.	.	PUNCT
ejpam-5714	77	1	in	in	ADP
ejpam-5714	77	2	section	section	NOUN
ejpam-5714	77	3	3	3	NUM
ejpam-5714	77	4	,	,	PUNCT
ejpam-5714	77	5	we	we	PRON
ejpam-5714	77	6	provide	provide	VERB
ejpam-5714	77	7	several	several	ADJ
ejpam-5714	77	8	examples	example	NOUN
ejpam-5714	77	9	to	to	PART
ejpam-5714	77	10	illustrate	illustrate	VERB
ejpam-5714	77	11	the	the	DET
ejpam-5714	77	12	significance	significance	NOUN
ejpam-5714	77	13	of	of	ADP
ejpam-5714	77	14	the	the	DET
ejpam-5714	77	15	obtained	obtain	VERB
ejpam-5714	77	16	results	result	NOUN
ejpam-5714	77	17	.	.	PUNCT
ejpam-5714	78	1	we	we	PRON
ejpam-5714	78	2	summarize	summarize	VERB
ejpam-5714	78	3	the	the	DET
ejpam-5714	78	4	main	main	ADJ
ejpam-5714	78	5	conclusions	conclusion	NOUN
ejpam-5714	78	6	of	of	ADP
ejpam-5714	78	7	the	the	DET
ejpam-5714	78	8	paper	paper	NOUN
ejpam-5714	78	9	in	in	ADP
ejpam-5714	78	10	section	section	NOUN
ejpam-5714	78	11	4	4	NUM
ejpam-5714	78	12	and	and	CCONJ
ejpam-5714	78	13	draw	draw	VERB
ejpam-5714	78	14	attention	attention	NOUN
ejpam-5714	78	15	to	to	ADP
ejpam-5714	78	16	an	an	DET
ejpam-5714	78	17	open	open	ADJ
ejpam-5714	78	18	question	question	NOUN
ejpam-5714	78	19	that	that	PRON
ejpam-5714	78	20	may	may	AUX
ejpam-5714	78	21	be	be	AUX
ejpam-5714	78	22	of	of	ADP
ejpam-5714	78	23	interest	interest	NOUN
ejpam-5714	78	24	to	to	ADP
ejpam-5714	78	25	researchers	researcher	NOUN
ejpam-5714	78	26	in	in	ADP
ejpam-5714	78	27	the	the	DET
ejpam-5714	78	28	considered	consider	VERB
ejpam-5714	78	29	field	field	NOUN
ejpam-5714	78	30	.	.	PUNCT
ejpam-5714	79	1	2	2	X
ejpam-5714	79	2	.	.	X
ejpam-5714	79	3	oscillation	oscillation	NOUN
ejpam-5714	79	4	results	result	NOUN
ejpam-5714	79	5	we	we	PRON
ejpam-5714	79	6	start	start	VERB
ejpam-5714	79	7	by	by	ADP
ejpam-5714	79	8	listing	list	VERB
ejpam-5714	79	9	a	a	DET
ejpam-5714	79	10	number	number	NOUN
ejpam-5714	79	11	of	of	ADP
ejpam-5714	79	12	auxiliary	auxiliary	ADJ
ejpam-5714	79	13	lemmas	lemma	NOUN
ejpam-5714	79	14	and	and	CCONJ
ejpam-5714	79	15	conditions	condition	NOUN
ejpam-5714	79	16	that	that	PRON
ejpam-5714	79	17	we	we	PRON
ejpam-5714	79	18	will	will	AUX
ejpam-5714	79	19	employ	employ	VERB
ejpam-5714	79	20	in	in	ADP
ejpam-5714	79	21	order	order	NOUN
ejpam-5714	79	22	to	to	PART
ejpam-5714	79	23	accomplish	accomplish	VERB
ejpam-5714	79	24	the	the	DET
ejpam-5714	79	25	primary	primary	ADJ
ejpam-5714	79	26	findings	finding	NOUN
ejpam-5714	79	27	.	.	PUNCT
ejpam-5714	80	1	for	for	ADP
ejpam-5714	80	2	ease	ease	NOUN
ejpam-5714	80	3	of	of	ADP
ejpam-5714	80	4	use	use	NOUN
ejpam-5714	80	5	,	,	PUNCT
ejpam-5714	80	6	we	we	PRON
ejpam-5714	80	7	set	set	VERB
ejpam-5714	80	8	the	the	DET
ejpam-5714	80	9	following	following	ADJ
ejpam-5714	80	10	notation	notation	NOUN
ejpam-5714	80	11	:	:	PUNCT
ejpam-5714	80	12	bt0	bt0	PROPN
ejpam-5714	80	13	(	(	PUNCT
ejpam-5714	80	14	t	t	PROPN
ejpam-5714	80	15	)	)	PUNCT
ejpam-5714	80	16	:	:	PUNCT
ejpam-5714	81	1	=	=	PUNCT
ejpam-5714	81	2	∫	∫	PROPN
ejpam-5714	81	3	t	t	PROPN
ejpam-5714	81	4	t0	t0	PROPN
ejpam-5714	81	5	b−1/(p−1	b−1/(p−1	PROPN
ejpam-5714	81	6	)	)	PUNCT
ejpam-5714	81	7	(	(	PUNCT
ejpam-5714	81	8	t	t	NOUN
ejpam-5714	81	9	)	)	PUNCT
ejpam-5714	81	10	dt	dt	PROPN
ejpam-5714	81	11	,	,	PUNCT
ejpam-5714	81	12	p	p	X
ejpam-5714	81	13	>	>	X
ejpam-5714	81	14	1	1	NUM
ejpam-5714	81	15	,	,	PUNCT
ejpam-5714	81	16	f.	f.	PROPN
ejpam-5714	81	17	aldosari	aldosari	PROPN
ejpam-5714	81	18	/	/	SYM
ejpam-5714	81	19	eur	eur	PROPN
ejpam-5714	81	20	.	.	PUNCT
ejpam-5714	82	1	j.	j.	PROPN
ejpam-5714	82	2	pure	pure	PROPN
ejpam-5714	82	3	appl	appl	PROPN
ejpam-5714	82	4	.	.	PROPN
ejpam-5714	82	5	math	math	PROPN
ejpam-5714	82	6	,	,	PUNCT
ejpam-5714	82	7	18	18	NUM
ejpam-5714	82	8	(	(	PUNCT
ejpam-5714	82	9	1	1	NUM
ejpam-5714	82	10	)	)	PUNCT
ejpam-5714	82	11	(	(	PUNCT
ejpam-5714	82	12	2025	2025	NUM
ejpam-5714	82	13	)	)	PUNCT
ejpam-5714	82	14	,	,	PUNCT
ejpam-5714	82	15	5714	5714	NUM
ejpam-5714	82	16	4	4	NUM
ejpam-5714	82	17	of	of	ADP
ejpam-5714	82	18	16	16	NUM
ejpam-5714	82	19	b̃t0(t	b̃t0(t	PROPN
ejpam-5714	82	20	)	)	PUNCT
ejpam-5714	82	21	:	:	PUNCT
ejpam-5714	83	1	=	=	PUNCT
ejpam-5714	83	2	bt0	bt0	PROPN
ejpam-5714	83	3	(	(	PUNCT
ejpam-5714	83	4	t	t	PROPN
ejpam-5714	83	5	)	)	PUNCT
ejpam-5714	83	6	+	+	CCONJ
ejpam-5714	83	7	1	1	NUM
ejpam-5714	83	8	(	(	PUNCT
ejpam-5714	83	9	p−	p−	NOUN
ejpam-5714	83	10	1	1	NUM
ejpam-5714	83	11	)	)	PUNCT
ejpam-5714	83	12	∫	∫	PROPN
ejpam-5714	83	13	t	t	PROPN
ejpam-5714	83	14	t0	t0	PROPN
ejpam-5714	83	15	bt1	bt1	PROPN
ejpam-5714	83	16	(	(	PUNCT
ejpam-5714	83	17	t)b	t)b	NOUN
ejpam-5714	83	18	p−1	p−1	PROPN
ejpam-5714	83	19	t0	t0	PROPN
ejpam-5714	83	20	(	(	PUNCT
ejpam-5714	83	21	πi(t	πi(t	NUM
ejpam-5714	83	22	)	)	PUNCT
ejpam-5714	83	23	)	)	PUNCT
ejpam-5714	84	1	n∑	n∑	PROPN
ejpam-5714	84	2	i=1	i=1	PROPN
ejpam-5714	85	1	qi	qi	PROPN
ejpam-5714	85	2	(	(	PUNCT
ejpam-5714	85	3	t	t	PROPN
ejpam-5714	85	4	)	)	PUNCT
ejpam-5714	85	5	(	(	PUNCT
ejpam-5714	85	6	1−	1−	NUM
ejpam-5714	85	7	y	y	PROPN
ejpam-5714	85	8	(	(	PUNCT
ejpam-5714	85	9	πi	πi	PROPN
ejpam-5714	85	10	(	(	PUNCT
ejpam-5714	85	11	t	t	NOUN
ejpam-5714	85	12	)	)	PUNCT
ejpam-5714	85	13	)	)	PUNCT
ejpam-5714	85	14	)	)	PUNCT
ejpam-5714	86	1	(	(	PUNCT
ejpam-5714	86	2	p−1	p−1	PROPN
ejpam-5714	86	3	)	)	PUNCT
ejpam-5714	86	4	dt	dt	PROPN
ejpam-5714	86	5	,	,	PUNCT
ejpam-5714	86	6	and	and	CCONJ
ejpam-5714	86	7	b̂	b̂	NOUN
ejpam-5714	86	8	(	(	PUNCT
ejpam-5714	86	9	t	t	PROPN
ejpam-5714	86	10	)	)	PUNCT
ejpam-5714	86	11	:	:	PUNCT
ejpam-5714	86	12	=	=	SYM
ejpam-5714	86	13	exp	exp	NOUN
ejpam-5714	86	14	(	(	PUNCT
ejpam-5714	86	15	−	−	PROPN
ejpam-5714	86	16	(	(	PUNCT
ejpam-5714	86	17	p−	p−	NOUN
ejpam-5714	86	18	1	1	NUM
ejpam-5714	86	19	)	)	PUNCT
ejpam-5714	86	20	∫	∫	PROPN
ejpam-5714	86	21	t	t	PROPN
ejpam-5714	86	22	πi(t	πi(t	NUM
ejpam-5714	86	23	)	)	PUNCT
ejpam-5714	86	24	dt	dt	X
ejpam-5714	86	25	b̃t0(t)b	b̃t0(t)b	PROPN
ejpam-5714	86	26	1/(p−1	1/(p−1	NUM
ejpam-5714	86	27	)	)	PUNCT
ejpam-5714	86	28	(	(	PUNCT
ejpam-5714	86	29	t	t	PROPN
ejpam-5714	86	30	)	)	PUNCT
ejpam-5714	86	31	)	)	PUNCT
ejpam-5714	86	32	.	.	PUNCT
ejpam-5714	87	1	lemma	lemma	PROPN
ejpam-5714	87	2	1	1	NUM
ejpam-5714	87	3	.	.	PUNCT
ejpam-5714	88	1	[	[	X
ejpam-5714	88	2	4	4	X
ejpam-5714	88	3	]	]	X
ejpam-5714	88	4	if	if	SCONJ
ejpam-5714	88	5	κ	κ	NOUN
ejpam-5714	88	6	be	be	AUX
ejpam-5714	88	7	an	an	DET
ejpam-5714	88	8	eventually	eventually	ADV
ejpam-5714	88	9	positive	positive	ADJ
ejpam-5714	88	10	solution	solution	NOUN
ejpam-5714	88	11	of	of	ADP
ejpam-5714	88	12	(	(	PUNCT
ejpam-5714	88	13	1	1	NUM
ejpam-5714	88	14	)	)	PUNCT
ejpam-5714	88	15	,	,	PUNCT
ejpam-5714	88	16	then	then	ADV
ejpam-5714	88	17	ϖ	ϖ	X
ejpam-5714	88	18	(	(	PUNCT
ejpam-5714	88	19	t	t	PROPN
ejpam-5714	88	20	)	)	PUNCT
ejpam-5714	88	21	>	>	X
ejpam-5714	88	22	0	0	NUM
ejpam-5714	88	23	,	,	PUNCT
ejpam-5714	88	24	ϖ′	ϖ′	X
ejpam-5714	88	25	(	(	PUNCT
ejpam-5714	88	26	t	t	NOUN
ejpam-5714	88	27	)	)	PUNCT
ejpam-5714	88	28	>	>	X
ejpam-5714	88	29	0	0	NUM
ejpam-5714	88	30	,	,	PUNCT
ejpam-5714	88	31	(	(	PUNCT
ejpam-5714	88	32	b	b	X
ejpam-5714	88	33	(	(	PUNCT
ejpam-5714	88	34	t	t	NOUN
ejpam-5714	88	35	)	)	PUNCT
ejpam-5714	88	36	(	(	PUNCT
ejpam-5714	88	37	ϖ′	ϖ′	X
ejpam-5714	88	38	(	(	PUNCT
ejpam-5714	88	39	t	t	NOUN
ejpam-5714	88	40	)	)	PUNCT
ejpam-5714	88	41	)	)	PUNCT
ejpam-5714	88	42	(	(	PUNCT
ejpam-5714	88	43	p−1	p−1	PROPN
ejpam-5714	88	44	)	)	PUNCT
ejpam-5714	88	45	)	)	PUNCT
ejpam-5714	88	46	′	′	NUM
ejpam-5714	88	47	≤	≤	NUM
ejpam-5714	88	48	0	0	NUM
ejpam-5714	88	49	,	,	PUNCT
ejpam-5714	88	50	(	(	PUNCT
ejpam-5714	88	51	5	5	NUM
ejpam-5714	88	52	)	)	PUNCT
ejpam-5714	88	53	for	for	ADP
ejpam-5714	88	54	t	t	PROPN
ejpam-5714	88	55	≥	≥	NUM
ejpam-5714	88	56	t1	t1	PROPN
ejpam-5714	88	57	.	.	PUNCT
ejpam-5714	89	1	lemma	lemma	PROPN
ejpam-5714	89	2	2	2	NUM
ejpam-5714	89	3	.	.	PUNCT
ejpam-5714	90	1	[	[	X
ejpam-5714	90	2	19	19	NUM
ejpam-5714	90	3	]	]	PUNCT
ejpam-5714	90	4	let	let	VERB
ejpam-5714	90	5	g	g	NOUN
ejpam-5714	90	6	,	,	PUNCT
ejpam-5714	90	7	w	w	ADP
ejpam-5714	90	8	>	>	X
ejpam-5714	90	9	0	0	NUM
ejpam-5714	90	10	be	be	NOUN
ejpam-5714	90	11	constants	constant	NOUN
ejpam-5714	90	12	and	and	CCONJ
ejpam-5714	90	13	max	max	PROPN
ejpam-5714	90	14	κ∈b	κ∈b	PROPN
ejpam-5714	90	15	f	f	PROPN
ejpam-5714	90	16	=	=	SYM
ejpam-5714	90	17	f	f	PROPN
ejpam-5714	90	18	(	(	PUNCT
ejpam-5714	90	19	κ∗	κ∗	PROPN
ejpam-5714	90	20	)	)	PUNCT
ejpam-5714	90	21	=	=	SYM
ejpam-5714	91	1	αα	αα	X
ejpam-5714	91	2	(	(	PUNCT
ejpam-5714	91	3	α+	α+	X
ejpam-5714	91	4	1)−(α+1	1)−(α+1	NUM
ejpam-5714	91	5	)	)	PUNCT
ejpam-5714	91	6	g	g	NOUN
ejpam-5714	91	7	α+1	α+1	NUM
ejpam-5714	91	8	wα	wα	NOUN
ejpam-5714	91	9	,	,	PUNCT
ejpam-5714	91	10	α	α	PRON
ejpam-5714	91	11	≥	≥	NOUN
ejpam-5714	91	12	1	1	NUM
ejpam-5714	91	13	,	,	PUNCT
ejpam-5714	91	14	(	(	PUNCT
ejpam-5714	91	15	6	6	NUM
ejpam-5714	91	16	)	)	PUNCT
ejpam-5714	91	17	where	where	SCONJ
ejpam-5714	91	18	κ∗	κ∗	NOUN
ejpam-5714	91	19	=	=	SYM
ejpam-5714	91	20	(	(	PUNCT
ejpam-5714	91	21	αg/	αg/	NOUN
ejpam-5714	91	22	(	(	PUNCT
ejpam-5714	91	23	(	(	PUNCT
ejpam-5714	91	24	α+	α+	PROPN
ejpam-5714	91	25	1)w	1)w	NUM
ejpam-5714	91	26	)	)	PUNCT
ejpam-5714	91	27	)	)	PUNCT
ejpam-5714	92	1	α	α	PROPN
ejpam-5714	92	2	and	and	CCONJ
ejpam-5714	92	3	f	f	PROPN
ejpam-5714	92	4	(	(	PUNCT
ejpam-5714	92	5	κ	κ	NOUN
ejpam-5714	92	6	)	)	PUNCT
ejpam-5714	92	7	=	=	VERB
ejpam-5714	92	8	gκ	gκ	VERB
ejpam-5714	92	9	−wκ(α+1)/α	−wκ(α+1)/α	PRON
ejpam-5714	92	10	.	.	PUNCT
ejpam-5714	93	1	lemma	lemma	PROPN
ejpam-5714	93	2	3	3	X
ejpam-5714	93	3	.	.	PUNCT
ejpam-5714	94	1	let	let	VERB
ejpam-5714	94	2	κ	κ	PRON
ejpam-5714	94	3	be	be	AUX
ejpam-5714	94	4	an	an	DET
ejpam-5714	94	5	eventually	eventually	ADV
ejpam-5714	94	6	positive	positive	ADJ
ejpam-5714	94	7	solution	solution	NOUN
ejpam-5714	94	8	of	of	ADP
ejpam-5714	94	9	(	(	PUNCT
ejpam-5714	94	10	1	1	NUM
ejpam-5714	94	11	)	)	PUNCT
ejpam-5714	94	12	.	.	PUNCT
ejpam-5714	95	1	then	then	ADV
ejpam-5714	95	2	(	(	PUNCT
ejpam-5714	95	3	b	b	X
ejpam-5714	95	4	(	(	PUNCT
ejpam-5714	95	5	t	t	NOUN
ejpam-5714	95	6	)	)	PUNCT
ejpam-5714	95	7	(	(	PUNCT
ejpam-5714	95	8	ϖ′	ϖ′	X
ejpam-5714	95	9	(	(	PUNCT
ejpam-5714	95	10	t	t	NOUN
ejpam-5714	95	11	)	)	PUNCT
ejpam-5714	95	12	)	)	PUNCT
ejpam-5714	95	13	(	(	PUNCT
ejpam-5714	95	14	p−1	p−1	PROPN
ejpam-5714	95	15	)	)	PUNCT
ejpam-5714	95	16	)	)	PUNCT
ejpam-5714	95	17	′	′	NUM
ejpam-5714	95	18	≤	≤	NUM
ejpam-5714	96	1	−	−	PUNCT
ejpam-5714	97	1	n∑	n∑	NOUN
ejpam-5714	97	2	i=1	i=1	PROPN
ejpam-5714	98	1	qi	qi	PROPN
ejpam-5714	98	2	(	(	PUNCT
ejpam-5714	98	3	t	t	PROPN
ejpam-5714	98	4	)	)	PUNCT
ejpam-5714	98	5	(	(	PUNCT
ejpam-5714	98	6	1−	1−	NUM
ejpam-5714	98	7	y	y	PROPN
ejpam-5714	98	8	(	(	PUNCT
ejpam-5714	98	9	πi	πi	PROPN
ejpam-5714	98	10	(	(	PUNCT
ejpam-5714	98	11	t	t	NOUN
ejpam-5714	98	12	)	)	PUNCT
ejpam-5714	98	13	)	)	PUNCT
ejpam-5714	98	14	)	)	PUNCT
ejpam-5714	99	1	(	(	PUNCT
ejpam-5714	99	2	p−1)ϖ(p−1	p−1)ϖ(p−1	X
ejpam-5714	99	3	)	)	PUNCT
ejpam-5714	99	4	(	(	PUNCT
ejpam-5714	99	5	πi	πi	PROPN
ejpam-5714	99	6	(	(	PUNCT
ejpam-5714	99	7	t	t	NOUN
ejpam-5714	99	8	)	)	PUNCT
ejpam-5714	99	9	)	)	PUNCT
ejpam-5714	99	10	,	,	PUNCT
ejpam-5714	99	11	(	(	PUNCT
ejpam-5714	99	12	7	7	X
ejpam-5714	99	13	)	)	PUNCT
ejpam-5714	99	14	and	and	CCONJ
ejpam-5714	99	15	ϖ	ϖ	INTJ
ejpam-5714	99	16	(	(	PUNCT
ejpam-5714	99	17	t	t	PROPN
ejpam-5714	99	18	)	)	PUNCT
ejpam-5714	99	19	≥	≥	NOUN
ejpam-5714	99	20	b̃t1	b̃t1	PROPN
ejpam-5714	99	21	(	(	PUNCT
ejpam-5714	99	22	t	t	PROPN
ejpam-5714	99	23	)	)	PUNCT
ejpam-5714	99	24	b	b	NOUN
ejpam-5714	99	25	1/(p−1	1/(p−1	NUM
ejpam-5714	99	26	)	)	PUNCT
ejpam-5714	99	27	(	(	PUNCT
ejpam-5714	99	28	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	99	29	(	(	PUNCT
ejpam-5714	99	30	t	t	PROPN
ejpam-5714	99	31	)	)	PUNCT
ejpam-5714	99	32	,	,	PUNCT
ejpam-5714	99	33	(	(	PUNCT
ejpam-5714	99	34	8)	8)	NUM
ejpam-5714	99	35	also	also	ADV
ejpam-5714	99	36	,	,	PUNCT
ejpam-5714	99	37	(	(	PUNCT
ejpam-5714	99	38	b	b	X
ejpam-5714	99	39	(	(	PUNCT
ejpam-5714	99	40	t	t	NOUN
ejpam-5714	99	41	)	)	PUNCT
ejpam-5714	99	42	(	(	PUNCT
ejpam-5714	99	43	ϖ′	ϖ′	X
ejpam-5714	99	44	(	(	PUNCT
ejpam-5714	99	45	t	t	NOUN
ejpam-5714	99	46	)	)	PUNCT
ejpam-5714	99	47	)	)	PUNCT
ejpam-5714	99	48	(	(	PUNCT
ejpam-5714	99	49	p−1	p−1	PROPN
ejpam-5714	99	50	)	)	PUNCT
ejpam-5714	99	51	)	)	PUNCT
ejpam-5714	100	1	′	′	NUM
ejpam-5714	100	2	≤	≤	NUM
ejpam-5714	101	1	−	−	PUNCT
ejpam-5714	102	1	n∑	n∑	NOUN
ejpam-5714	102	2	i=1	i=1	PROPN
ejpam-5714	103	1	qi	qi	PROPN
ejpam-5714	103	2	(	(	PUNCT
ejpam-5714	103	3	t	t	PROPN
ejpam-5714	103	4	)	)	PUNCT
ejpam-5714	103	5	(	(	PUNCT
ejpam-5714	103	6	1−	1−	NUM
ejpam-5714	103	7	y	y	PROPN
ejpam-5714	103	8	(	(	PUNCT
ejpam-5714	103	9	πi	πi	PROPN
ejpam-5714	103	10	(	(	PUNCT
ejpam-5714	103	11	t	t	NOUN
ejpam-5714	103	12	)	)	PUNCT
ejpam-5714	103	13	)	)	PUNCT
ejpam-5714	103	14	)	)	PUNCT
ejpam-5714	104	1	(	(	PUNCT
ejpam-5714	104	2	p−1	p−1	PROPN
ejpam-5714	104	3	)	)	PUNCT
ejpam-5714	104	4	b̂	b̂	NOUN
ejpam-5714	104	5	(	(	PUNCT
ejpam-5714	104	6	t)ϖ(p−1	t)ϖ(p−1	NOUN
ejpam-5714	104	7	)	)	PUNCT
ejpam-5714	104	8	(	(	PUNCT
ejpam-5714	104	9	t	t	PROPN
ejpam-5714	104	10	)	)	PUNCT
ejpam-5714	104	11	.	.	PUNCT
ejpam-5714	105	1	(	(	PUNCT
ejpam-5714	105	2	9	9	X
ejpam-5714	105	3	)	)	PUNCT
ejpam-5714	105	4	proof	proof	NOUN
ejpam-5714	105	5	.	.	PUNCT
ejpam-5714	106	1	let	let	VERB
ejpam-5714	106	2	κ	κ	PRON
ejpam-5714	106	3	be	be	AUX
ejpam-5714	106	4	an	an	DET
ejpam-5714	106	5	eventually	eventually	ADV
ejpam-5714	106	6	positive	positive	ADJ
ejpam-5714	106	7	solution	solution	NOUN
ejpam-5714	106	8	of	of	ADP
ejpam-5714	106	9	(	(	PUNCT
ejpam-5714	106	10	1	1	NUM
ejpam-5714	106	11	)	)	PUNCT
ejpam-5714	106	12	.	.	PUNCT
ejpam-5714	107	1	(	(	PUNCT
ejpam-5714	107	2	5	5	X
ejpam-5714	107	3	)	)	PUNCT
ejpam-5714	107	4	holds	hold	VERB
ejpam-5714	107	5	according	accord	VERB
ejpam-5714	107	6	to	to	ADP
ejpam-5714	107	7	lemma	lemma	PROPN
ejpam-5714	107	8	1	1	NUM
ejpam-5714	107	9	.	.	PUNCT
ejpam-5714	108	1	therefore	therefore	ADV
ejpam-5714	108	2	,	,	PUNCT
ejpam-5714	108	3	using	use	VERB
ejpam-5714	108	4	the	the	DET
ejpam-5714	108	5	definition	definition	NOUN
ejpam-5714	108	6	ofϖ	ofϖ	NOUN
ejpam-5714	108	7	(	(	PUNCT
ejpam-5714	108	8	t	t	PROPN
ejpam-5714	108	9	)	)	PUNCT
ejpam-5714	108	10	,	,	PUNCT
ejpam-5714	108	11	we	we	PRON
ejpam-5714	108	12	get	get	VERB
ejpam-5714	108	13	κ	κ	PRON
ejpam-5714	108	14	(	(	PUNCT
ejpam-5714	108	15	t	t	NOUN
ejpam-5714	108	16	)	)	PUNCT
ejpam-5714	108	17	=	=	SYM
ejpam-5714	109	1	ϖ	ϖ	INTJ
ejpam-5714	109	2	(	(	PUNCT
ejpam-5714	109	3	t)−	t)−	PROPN
ejpam-5714	109	4	y	y	PROPN
ejpam-5714	109	5	(	(	PUNCT
ejpam-5714	109	6	t)κ	t)κ	X
ejpam-5714	109	7	(	(	PUNCT
ejpam-5714	109	8	ζ	ζ	NOUN
ejpam-5714	109	9	(	(	PUNCT
ejpam-5714	109	10	t	t	NOUN
ejpam-5714	109	11	)	)	PUNCT
ejpam-5714	109	12	)	)	PUNCT
ejpam-5714	109	13	≥	≥	NUM
ejpam-5714	110	1	ϖ	ϖ	INTJ
ejpam-5714	110	2	(	(	PUNCT
ejpam-5714	110	3	t)−	t)−	PROPN
ejpam-5714	110	4	y	y	PROPN
ejpam-5714	110	5	(	(	PUNCT
ejpam-5714	110	6	t)ϖ	t)ϖ	X
ejpam-5714	110	7	(	(	PUNCT
ejpam-5714	110	8	ζ	ζ	PROPN
ejpam-5714	110	9	(	(	PUNCT
ejpam-5714	110	10	t	t	NOUN
ejpam-5714	110	11	)	)	PUNCT
ejpam-5714	110	12	)	)	PUNCT
ejpam-5714	110	13	≥	≥	NUM
ejpam-5714	110	14	ϖ	ϖ	X
ejpam-5714	110	15	(	(	PUNCT
ejpam-5714	110	16	t	t	NOUN
ejpam-5714	110	17	)	)	PUNCT
ejpam-5714	110	18	(	(	PUNCT
ejpam-5714	110	19	1−	1−	NUM
ejpam-5714	110	20	y	y	PROPN
ejpam-5714	110	21	(	(	PUNCT
ejpam-5714	110	22	t	t	PROPN
ejpam-5714	110	23	)	)	PUNCT
ejpam-5714	110	24	)	)	PUNCT
ejpam-5714	110	25	.	.	PUNCT
ejpam-5714	111	1	this	this	PRON
ejpam-5714	111	2	suggests	suggest	VERB
ejpam-5714	111	3	that	that	SCONJ
ejpam-5714	111	4	(	(	PUNCT
ejpam-5714	111	5	1	1	X
ejpam-5714	111	6	)	)	PUNCT
ejpam-5714	111	7	(	(	PUNCT
ejpam-5714	111	8	b	b	X
ejpam-5714	111	9	(	(	PUNCT
ejpam-5714	111	10	t	t	NOUN
ejpam-5714	111	11	)	)	PUNCT
ejpam-5714	111	12	(	(	PUNCT
ejpam-5714	111	13	ϖ′	ϖ′	X
ejpam-5714	111	14	(	(	PUNCT
ejpam-5714	111	15	t	t	NOUN
ejpam-5714	111	16	)	)	PUNCT
ejpam-5714	111	17	)	)	PUNCT
ejpam-5714	111	18	(	(	PUNCT
ejpam-5714	111	19	p−1	p−1	PROPN
ejpam-5714	111	20	)	)	PUNCT
ejpam-5714	111	21	)	)	PUNCT
ejpam-5714	111	22	′	′	NUM
ejpam-5714	111	23	≤	≤	NUM
ejpam-5714	112	1	−	−	PUNCT
ejpam-5714	113	1	n∑	n∑	NOUN
ejpam-5714	113	2	i=1	i=1	PROPN
ejpam-5714	113	3	qi	qi	PROPN
ejpam-5714	113	4	(	(	PUNCT
ejpam-5714	113	5	t)ϖ	t)ϖ	X
ejpam-5714	113	6	(	(	PUNCT
ejpam-5714	113	7	p−1	p−1	PROPN
ejpam-5714	113	8	)	)	PUNCT
ejpam-5714	113	9	(	(	PUNCT
ejpam-5714	113	10	πi	πi	CCONJ
ejpam-5714	113	11	(	(	PUNCT
ejpam-5714	113	12	t	t	NOUN
ejpam-5714	113	13	)	)	PUNCT
ejpam-5714	113	14	)	)	PUNCT
ejpam-5714	114	1	(	(	PUNCT
ejpam-5714	114	2	1−	1−	NUM
ejpam-5714	114	3	y	y	PROPN
ejpam-5714	114	4	(	(	PUNCT
ejpam-5714	114	5	πi	πi	PROPN
ejpam-5714	114	6	(	(	PUNCT
ejpam-5714	114	7	t	t	NOUN
ejpam-5714	114	8	)	)	PUNCT
ejpam-5714	114	9	)	)	PUNCT
ejpam-5714	114	10	)	)	PUNCT
ejpam-5714	115	1	(	(	PUNCT
ejpam-5714	115	2	p−1	p−1	PROPN
ejpam-5714	115	3	)	)	PUNCT
ejpam-5714	115	4	.	.	PUNCT
ejpam-5714	116	1	f.	f.	PROPN
ejpam-5714	116	2	aldosari	aldosari	PROPN
ejpam-5714	116	3	/	/	SYM
ejpam-5714	116	4	eur	eur	PROPN
ejpam-5714	116	5	.	.	PUNCT
ejpam-5714	117	1	j.	j.	PROPN
ejpam-5714	117	2	pure	pure	PROPN
ejpam-5714	117	3	appl	appl	PROPN
ejpam-5714	117	4	.	.	PROPN
ejpam-5714	117	5	math	math	PROPN
ejpam-5714	117	6	,	,	PUNCT
ejpam-5714	117	7	18	18	NUM
ejpam-5714	117	8	(	(	PUNCT
ejpam-5714	117	9	1	1	NUM
ejpam-5714	117	10	)	)	PUNCT
ejpam-5714	117	11	(	(	PUNCT
ejpam-5714	117	12	2025	2025	NUM
ejpam-5714	117	13	)	)	PUNCT
ejpam-5714	117	14	,	,	PUNCT
ejpam-5714	117	15	5714	5714	NUM
ejpam-5714	117	16	5	5	NUM
ejpam-5714	117	17	of	of	ADP
ejpam-5714	117	18	16	16	NUM
ejpam-5714	117	19	since	since	SCONJ
ejpam-5714	117	20	ϖ′	ϖ′	NUM
ejpam-5714	117	21	(	(	PUNCT
ejpam-5714	117	22	t	t	NOUN
ejpam-5714	117	23	)	)	PUNCT
ejpam-5714	117	24	>	>	X
ejpam-5714	117	25	0	0	NUM
ejpam-5714	117	26	and	and	CCONJ
ejpam-5714	117	27	∂	∂	NUM
ejpam-5714	117	28	∂sπi	∂sπi	NUM
ejpam-5714	117	29	(	(	PUNCT
ejpam-5714	117	30	t	t	PROPN
ejpam-5714	117	31	)	)	PUNCT
ejpam-5714	117	32	>	>	X
ejpam-5714	118	1	0	0	NUM
ejpam-5714	118	2	,	,	PUNCT
ejpam-5714	118	3	we	we	PRON
ejpam-5714	118	4	obtain	obtain	VERB
ejpam-5714	118	5	ϖ	ϖ	INTJ
ejpam-5714	118	6	(	(	PUNCT
ejpam-5714	118	7	πi	πi	PROPN
ejpam-5714	118	8	(	(	PUNCT
ejpam-5714	118	9	t	t	NOUN
ejpam-5714	118	10	)	)	PUNCT
ejpam-5714	118	11	)	)	PUNCT
ejpam-5714	119	1	>	>	PUNCT
ejpam-5714	120	1	ϖ	ϖ	INTJ
ejpam-5714	120	2	(	(	PUNCT
ejpam-5714	120	3	πi	πi	PROPN
ejpam-5714	120	4	(	(	PUNCT
ejpam-5714	120	5	t	t	NOUN
ejpam-5714	120	6	)	)	PUNCT
ejpam-5714	120	7	)	)	PUNCT
ejpam-5714	121	1	and	and	CCONJ
ejpam-5714	121	2	so	so	ADV
ejpam-5714	121	3	(	(	PUNCT
ejpam-5714	121	4	b	b	X
ejpam-5714	121	5	(	(	PUNCT
ejpam-5714	121	6	t	t	NOUN
ejpam-5714	121	7	)	)	PUNCT
ejpam-5714	121	8	(	(	PUNCT
ejpam-5714	121	9	ϖ′	ϖ′	X
ejpam-5714	121	10	(	(	PUNCT
ejpam-5714	121	11	t	t	NOUN
ejpam-5714	121	12	)	)	PUNCT
ejpam-5714	121	13	)	)	PUNCT
ejpam-5714	121	14	(	(	PUNCT
ejpam-5714	121	15	p−1	p−1	PROPN
ejpam-5714	121	16	)	)	PUNCT
ejpam-5714	121	17	)	)	PUNCT
ejpam-5714	122	1	′	′	NUM
ejpam-5714	122	2	≤	≤	NUM
ejpam-5714	123	1	−	−	PUNCT
ejpam-5714	124	1	n∑	n∑	NOUN
ejpam-5714	124	2	i=1	i=1	PROPN
ejpam-5714	125	1	qi	qi	PROPN
ejpam-5714	125	2	(	(	PUNCT
ejpam-5714	125	3	t	t	PROPN
ejpam-5714	125	4	)	)	PUNCT
ejpam-5714	125	5	(	(	PUNCT
ejpam-5714	125	6	1−	1−	NUM
ejpam-5714	125	7	y	y	PROPN
ejpam-5714	125	8	(	(	PUNCT
ejpam-5714	125	9	πi	πi	PROPN
ejpam-5714	125	10	(	(	PUNCT
ejpam-5714	125	11	t	t	NOUN
ejpam-5714	125	12	)	)	PUNCT
ejpam-5714	125	13	)	)	PUNCT
ejpam-5714	125	14	)	)	PUNCT
ejpam-5714	126	1	(	(	PUNCT
ejpam-5714	126	2	p−1)ϖ(p−1	p−1)ϖ(p−1	X
ejpam-5714	126	3	)	)	PUNCT
ejpam-5714	126	4	(	(	PUNCT
ejpam-5714	126	5	πi	πi	PROPN
ejpam-5714	126	6	(	(	PUNCT
ejpam-5714	126	7	t	t	NOUN
ejpam-5714	126	8	)	)	PUNCT
ejpam-5714	126	9	)	)	PUNCT
ejpam-5714	126	10	.	.	PUNCT
ejpam-5714	127	1	using	use	VERB
ejpam-5714	127	2	basic	basic	ADJ
ejpam-5714	127	3	computation	computation	NOUN
ejpam-5714	127	4	and	and	CCONJ
ejpam-5714	127	5	the	the	DET
ejpam-5714	127	6	chain	chain	NOUN
ejpam-5714	127	7	rule	rule	NOUN
ejpam-5714	127	8	,	,	PUNCT
ejpam-5714	127	9	it	it	PRON
ejpam-5714	127	10	is	be	AUX
ejpam-5714	127	11	evident	evident	ADJ
ejpam-5714	127	12	that	that	SCONJ
ejpam-5714	127	13	bt1	bt1	PROPN
ejpam-5714	127	14	(	(	PUNCT
ejpam-5714	127	15	t	t	PROPN
ejpam-5714	127	16	)	)	PUNCT
ejpam-5714	127	17	(	(	PUNCT
ejpam-5714	127	18	b	b	X
ejpam-5714	127	19	(	(	PUNCT
ejpam-5714	127	20	t	t	NOUN
ejpam-5714	127	21	)	)	PUNCT
ejpam-5714	127	22	(	(	PUNCT
ejpam-5714	127	23	ϖ′	ϖ′	X
ejpam-5714	127	24	(	(	PUNCT
ejpam-5714	127	25	t	t	NOUN
ejpam-5714	127	26	)	)	PUNCT
ejpam-5714	127	27	)	)	PUNCT
ejpam-5714	127	28	(	(	PUNCT
ejpam-5714	127	29	p−1	p−1	PROPN
ejpam-5714	127	30	)	)	PUNCT
ejpam-5714	127	31	)	)	PUNCT
ejpam-5714	127	32	′	′	NUM
ejpam-5714	128	1	=	=	PUNCT
ejpam-5714	128	2	(	(	PUNCT
ejpam-5714	128	3	p−	p−	NOUN
ejpam-5714	128	4	1	1	NUM
ejpam-5714	128	5	)	)	PUNCT
ejpam-5714	128	6	(	(	PUNCT
ejpam-5714	128	7	b1/(p−1	b1/(p−1	NUM
ejpam-5714	128	8	)	)	PUNCT
ejpam-5714	128	9	(	(	PUNCT
ejpam-5714	128	10	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	128	11	(	(	PUNCT
ejpam-5714	128	12	t	t	PROPN
ejpam-5714	128	13	)	)	PUNCT
ejpam-5714	128	14	)	)	PUNCT
ejpam-5714	128	15	(	(	PUNCT
ejpam-5714	128	16	p−1)−1	p−1)−1	NOUN
ejpam-5714	128	17	bt1	bt1	NOUN
ejpam-5714	128	18	(	(	PUNCT
ejpam-5714	128	19	t	t	PROPN
ejpam-5714	128	20	)	)	PUNCT
ejpam-5714	128	21	(	(	PUNCT
ejpam-5714	128	22	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	128	23	)	)	PUNCT
ejpam-5714	128	24	(	(	PUNCT
ejpam-5714	128	25	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	128	26	(	(	PUNCT
ejpam-5714	128	27	t	t	PROPN
ejpam-5714	128	28	)	)	PUNCT
ejpam-5714	128	29	)	)	PUNCT
ejpam-5714	128	30	′	′	NUM
ejpam-5714	129	1	=	=	PUNCT
ejpam-5714	129	2	−	−	PROPN
ejpam-5714	129	3	(	(	PUNCT
ejpam-5714	129	4	p−	p−	NOUN
ejpam-5714	129	5	1	1	NUM
ejpam-5714	129	6	)	)	PUNCT
ejpam-5714	129	7	(	(	PUNCT
ejpam-5714	129	8	b1/(p−1	b1/(p−1	NUM
ejpam-5714	129	9	)	)	PUNCT
ejpam-5714	129	10	(	(	PUNCT
ejpam-5714	129	11	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	129	12	(	(	PUNCT
ejpam-5714	129	13	t	t	PROPN
ejpam-5714	129	14	)	)	PUNCT
ejpam-5714	129	15	)	)	PUNCT
ejpam-5714	129	16	(	(	PUNCT
ejpam-5714	129	17	p−1)−1	p−1)−1	NOUN
ejpam-5714	129	18	d	d	NOUN
ejpam-5714	129	19	dt	dt	X
ejpam-5714	129	20	(	(	PUNCT
ejpam-5714	129	21	ϖ	ϖ	X
ejpam-5714	129	22	(	(	PUNCT
ejpam-5714	129	23	t)−bt1	t)−bt1	PROPN
ejpam-5714	129	24	(	(	PUNCT
ejpam-5714	129	25	t	t	PROPN
ejpam-5714	129	26	)	)	PUNCT
ejpam-5714	129	27	b	b	NOUN
ejpam-5714	129	28	1/(p−1	1/(p−1	NUM
ejpam-5714	129	29	)	)	PUNCT
ejpam-5714	129	30	(	(	PUNCT
ejpam-5714	129	31	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	129	32	(	(	PUNCT
ejpam-5714	129	33	t	t	PROPN
ejpam-5714	129	34	)	)	PUNCT
ejpam-5714	129	35	)	)	PUNCT
ejpam-5714	129	36	.(10	.(10	X
ejpam-5714	129	37	)	)	PUNCT
ejpam-5714	130	1	combining	combine	VERB
ejpam-5714	130	2	(	(	PUNCT
ejpam-5714	130	3	7	7	NUM
ejpam-5714	130	4	)	)	PUNCT
ejpam-5714	130	5	and	and	CCONJ
ejpam-5714	130	6	(	(	PUNCT
ejpam-5714	130	7	10	10	NUM
ejpam-5714	130	8	)	)	PUNCT
ejpam-5714	130	9	,	,	PUNCT
ejpam-5714	130	10	we	we	PRON
ejpam-5714	130	11	obtain	obtain	VERB
ejpam-5714	130	12	d	d	X
ejpam-5714	130	13	dt	dt	X
ejpam-5714	130	14	(	(	PUNCT
ejpam-5714	130	15	ϖ	ϖ	X
ejpam-5714	130	16	(	(	PUNCT
ejpam-5714	130	17	t)−bt1	t)−bt1	PROPN
ejpam-5714	130	18	(	(	PUNCT
ejpam-5714	130	19	t	t	PROPN
ejpam-5714	130	20	)	)	PUNCT
ejpam-5714	130	21	b	b	NOUN
ejpam-5714	130	22	1/(p−1	1/(p−1	NUM
ejpam-5714	130	23	)	)	PUNCT
ejpam-5714	130	24	(	(	PUNCT
ejpam-5714	130	25	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	130	26	(	(	PUNCT
ejpam-5714	130	27	t	t	PROPN
ejpam-5714	130	28	)	)	PUNCT
ejpam-5714	130	29	)	)	PUNCT
ejpam-5714	130	30	≥	≥	X
ejpam-5714	130	31	(	(	PUNCT
ejpam-5714	130	32	1	1	NUM
ejpam-5714	130	33	(	(	PUNCT
ejpam-5714	130	34	p−	p−	NOUN
ejpam-5714	130	35	1	1	NUM
ejpam-5714	130	36	)	)	PUNCT
ejpam-5714	130	37	bt1	bt1	NOUN
ejpam-5714	130	38	(	(	PUNCT
ejpam-5714	130	39	t	t	PROPN
ejpam-5714	130	40	)	)	PUNCT
ejpam-5714	130	41	(	(	PUNCT
ejpam-5714	130	42	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	130	43	)	)	PUNCT
ejpam-5714	130	44	(	(	PUNCT
ejpam-5714	130	45	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	130	46	(	(	PUNCT
ejpam-5714	130	47	t	t	PROPN
ejpam-5714	130	48	)	)	PUNCT
ejpam-5714	130	49	)	)	PUNCT
ejpam-5714	130	50	2−p	2−p	NUM
ejpam-5714	130	51	)	)	PUNCT
ejpam-5714	131	1	(	(	PUNCT
ejpam-5714	131	2	n∑	n∑	NOUN
ejpam-5714	131	3	i=1	i=1	PROPN
ejpam-5714	131	4	qi	qi	PROPN
ejpam-5714	131	5	(	(	PUNCT
ejpam-5714	131	6	t	t	PROPN
ejpam-5714	131	7	)	)	PUNCT
ejpam-5714	131	8	(	(	PUNCT
ejpam-5714	131	9	1−	1−	NUM
ejpam-5714	131	10	y	y	PROPN
ejpam-5714	131	11	(	(	PUNCT
ejpam-5714	131	12	πi	πi	PROPN
ejpam-5714	131	13	(	(	PUNCT
ejpam-5714	131	14	t	t	NOUN
ejpam-5714	131	15	)	)	PUNCT
ejpam-5714	131	16	)	)	PUNCT
ejpam-5714	131	17	)	)	PUNCT
ejpam-5714	132	1	p−1ϖp−1	p−1ϖp−1	NOUN
ejpam-5714	132	2	(	(	PUNCT
ejpam-5714	132	3	πi	πi	PROPN
ejpam-5714	132	4	(	(	PUNCT
ejpam-5714	132	5	t	t	NOUN
ejpam-5714	132	6	)	)	PUNCT
ejpam-5714	132	7	)	)	PUNCT
ejpam-5714	132	8	)	)	PUNCT
ejpam-5714	132	9	.	.	PUNCT
ejpam-5714	133	1	integrating	integrate	VERB
ejpam-5714	133	2	this	this	DET
ejpam-5714	133	3	inequality	inequality	NOUN
ejpam-5714	133	4	from	from	ADP
ejpam-5714	133	5	t1	t1	PROPN
ejpam-5714	133	6	to	to	ADP
ejpam-5714	133	7	t	t	PROPN
ejpam-5714	133	8	,	,	PUNCT
ejpam-5714	133	9	we	we	PRON
ejpam-5714	133	10	have	have	VERB
ejpam-5714	133	11	ϖ	ϖ	PROPN
ejpam-5714	133	12	(	(	PUNCT
ejpam-5714	133	13	t	t	PROPN
ejpam-5714	133	14	)	)	PUNCT
ejpam-5714	133	15	≥	≥	NOUN
ejpam-5714	133	16	bt1	bt1	PROPN
ejpam-5714	133	17	(	(	PUNCT
ejpam-5714	133	18	t	t	PROPN
ejpam-5714	133	19	)	)	PUNCT
ejpam-5714	133	20	b	b	NOUN
ejpam-5714	133	21	1/(p−1	1/(p−1	NUM
ejpam-5714	133	22	)	)	PUNCT
ejpam-5714	133	23	(	(	PUNCT
ejpam-5714	133	24	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	133	25	(	(	PUNCT
ejpam-5714	133	26	t	t	PROPN
ejpam-5714	133	27	)	)	PUNCT
ejpam-5714	134	1	+	+	CCONJ
ejpam-5714	134	2	1	1	NUM
ejpam-5714	134	3	(	(	PUNCT
ejpam-5714	134	4	p−	p−	NOUN
ejpam-5714	134	5	1	1	NUM
ejpam-5714	134	6	)	)	PUNCT
ejpam-5714	134	7	∫	∫	PROPN
ejpam-5714	134	8	t	t	PROPN
ejpam-5714	134	9	t1	t1	PROPN
ejpam-5714	134	10	bt1	bt1	PROPN
ejpam-5714	134	11	(	(	PUNCT
ejpam-5714	134	12	t	t	PROPN
ejpam-5714	134	13	)	)	PUNCT
ejpam-5714	135	1	n∑	n∑	PROPN
ejpam-5714	135	2	i=1	i=1	PROPN
ejpam-5714	136	1	qi	qi	PROPN
ejpam-5714	136	2	(	(	PUNCT
ejpam-5714	136	3	t	t	PROPN
ejpam-5714	136	4	)	)	PUNCT
ejpam-5714	136	5	(	(	PUNCT
ejpam-5714	136	6	1−	1−	NUM
ejpam-5714	136	7	y	y	PROPN
ejpam-5714	136	8	(	(	PUNCT
ejpam-5714	136	9	πi	πi	PROPN
ejpam-5714	136	10	(	(	PUNCT
ejpam-5714	136	11	t	t	NOUN
ejpam-5714	136	12	)	)	PUNCT
ejpam-5714	136	13	)	)	PUNCT
ejpam-5714	136	14	)	)	PUNCT
ejpam-5714	137	1	(	(	PUNCT
ejpam-5714	137	2	p−1	p−1	PROPN
ejpam-5714	137	3	)	)	PUNCT
ejpam-5714	137	4	(	(	PUNCT
ejpam-5714	137	5	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	137	6	)	)	PUNCT
ejpam-5714	137	7	(	(	PUNCT
ejpam-5714	137	8	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	137	9	(	(	PUNCT
ejpam-5714	137	10	t	t	PROPN
ejpam-5714	137	11	)	)	PUNCT
ejpam-5714	137	12	)	)	PUNCT
ejpam-5714	137	13	2−p	2−p	NUM
ejpam-5714	137	14	ϖ(p−1	ϖ(p−1	NOUN
ejpam-5714	137	15	)	)	PUNCT
ejpam-5714	137	16	(	(	PUNCT
ejpam-5714	137	17	πi(t	πi(t	NUM
ejpam-5714	137	18	)	)	PUNCT
ejpam-5714	137	19	)	)	PUNCT
ejpam-5714	137	20	dt.(11	dt.(11	NUM
ejpam-5714	137	21	)	)	PUNCT
ejpam-5714	137	22	from	from	ADP
ejpam-5714	137	23	the	the	DET
ejpam-5714	137	24	monotonicity	monotonicity	NOUN
ejpam-5714	137	25	of	of	ADP
ejpam-5714	137	26	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	137	27	)	)	PUNCT
ejpam-5714	137	28	(	(	PUNCT
ejpam-5714	137	29	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	137	30	(	(	PUNCT
ejpam-5714	137	31	t	t	PROPN
ejpam-5714	137	32	)	)	PUNCT
ejpam-5714	137	33	,	,	PUNCT
ejpam-5714	137	34	we	we	PRON
ejpam-5714	137	35	have	have	VERB
ejpam-5714	137	36	ϖ	ϖ	X
ejpam-5714	137	37	(	(	PUNCT
ejpam-5714	137	38	t	t	NOUN
ejpam-5714	137	39	)	)	PUNCT
ejpam-5714	137	40	=	=	SYM
ejpam-5714	138	1	ϖ	ϖ	PROPN
ejpam-5714	138	2	(	(	PUNCT
ejpam-5714	138	3	t1	t1	NOUN
ejpam-5714	138	4	)	)	PUNCT
ejpam-5714	139	1	+	+	CCONJ
ejpam-5714	139	2	∫	∫	PROPN
ejpam-5714	139	3	t	t	PROPN
ejpam-5714	139	4	t1	t1	NOUN
ejpam-5714	139	5	1	1	NUM
ejpam-5714	139	6	b1/(p−1	b1/(p−1	NUM
ejpam-5714	139	7	)	)	PUNCT
ejpam-5714	139	8	(	(	PUNCT
ejpam-5714	139	9	t	t	NOUN
ejpam-5714	139	10	)	)	PUNCT
ejpam-5714	139	11	(	(	PUNCT
ejpam-5714	139	12	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	139	13	)	)	PUNCT
ejpam-5714	139	14	(	(	PUNCT
ejpam-5714	139	15	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	139	16	(	(	PUNCT
ejpam-5714	139	17	t	t	PROPN
ejpam-5714	139	18	)	)	PUNCT
ejpam-5714	139	19	)	)	PUNCT
ejpam-5714	140	1	dt	dt	X
ejpam-5714	141	1	≥	≥	PROPN
ejpam-5714	141	2	bt1	bt1	PROPN
ejpam-5714	141	3	(	(	PUNCT
ejpam-5714	141	4	t	t	PROPN
ejpam-5714	141	5	)	)	PUNCT
ejpam-5714	141	6	b	b	NOUN
ejpam-5714	141	7	1/(p−1	1/(p−1	NUM
ejpam-5714	141	8	)	)	PUNCT
ejpam-5714	141	9	(	(	PUNCT
ejpam-5714	141	10	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	141	11	(	(	PUNCT
ejpam-5714	141	12	t	t	PROPN
ejpam-5714	141	13	)	)	PUNCT
ejpam-5714	141	14	.	.	PUNCT
ejpam-5714	142	1	so	so	ADV
ejpam-5714	142	2	,	,	PUNCT
ejpam-5714	142	3	by	by	ADP
ejpam-5714	142	4	(	(	PUNCT
ejpam-5714	142	5	b1/(p−1	b1/(p−1	NUM
ejpam-5714	142	6	)	)	PUNCT
ejpam-5714	142	7	(	(	PUNCT
ejpam-5714	142	8	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	142	9	(	(	PUNCT
ejpam-5714	142	10	t	t	PROPN
ejpam-5714	142	11	)	)	PUNCT
ejpam-5714	142	12	)	)	PUNCT
ejpam-5714	142	13	′	′	NUM
ejpam-5714	142	14	≤	≤	NUM
ejpam-5714	142	15	0	0	NUM
ejpam-5714	142	16	,	,	PUNCT
ejpam-5714	142	17	(	(	PUNCT
ejpam-5714	142	18	11	11	NUM
ejpam-5714	142	19	)	)	PUNCT
ejpam-5714	142	20	becomes	become	VERB
ejpam-5714	142	21	ϖ	ϖ	INTJ
ejpam-5714	142	22	(	(	PUNCT
ejpam-5714	142	23	t	t	PROPN
ejpam-5714	142	24	)	)	PUNCT
ejpam-5714	142	25	≥	≥	NOUN
ejpam-5714	142	26	bt1	bt1	PROPN
ejpam-5714	142	27	(	(	PUNCT
ejpam-5714	142	28	t	t	PROPN
ejpam-5714	142	29	)	)	PUNCT
ejpam-5714	142	30	b	b	NOUN
ejpam-5714	142	31	1/(p−1	1/(p−1	NUM
ejpam-5714	142	32	)	)	PUNCT
ejpam-5714	142	33	(	(	PUNCT
ejpam-5714	142	34	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	142	35	(	(	PUNCT
ejpam-5714	142	36	t	t	PROPN
ejpam-5714	142	37	)	)	PUNCT
ejpam-5714	143	1	+	+	CCONJ
ejpam-5714	143	2	1	1	NUM
ejpam-5714	143	3	(	(	PUNCT
ejpam-5714	143	4	p−	p−	NOUN
ejpam-5714	143	5	1	1	NUM
ejpam-5714	143	6	)	)	PUNCT
ejpam-5714	143	7	∫	∫	PROPN
ejpam-5714	143	8	t	t	PROPN
ejpam-5714	143	9	t1	t1	PROPN
ejpam-5714	143	10	(	(	PUNCT
ejpam-5714	143	11	bt1	bt1	PROPN
ejpam-5714	143	12	(	(	PUNCT
ejpam-5714	143	13	t	t	PROPN
ejpam-5714	143	14	)	)	PUNCT
ejpam-5714	144	1	n∑	n∑	PROPN
ejpam-5714	144	2	i=1	i=1	PROPN
ejpam-5714	145	1	qi	qi	PROPN
ejpam-5714	145	2	(	(	PUNCT
ejpam-5714	145	3	t	t	PROPN
ejpam-5714	145	4	)	)	PUNCT
ejpam-5714	145	5	(	(	PUNCT
ejpam-5714	145	6	1−	1−	NUM
ejpam-5714	145	7	y	y	PROPN
ejpam-5714	145	8	(	(	PUNCT
ejpam-5714	145	9	πi	πi	PROPN
ejpam-5714	145	10	(	(	PUNCT
ejpam-5714	145	11	t	t	NOUN
ejpam-5714	145	12	)	)	PUNCT
ejpam-5714	145	13	)	)	PUNCT
ejpam-5714	145	14	)	)	PUNCT
ejpam-5714	146	1	(	(	PUNCT
ejpam-5714	146	2	p−1	p−1	PROPN
ejpam-5714	146	3	)	)	PUNCT
ejpam-5714	146	4	(	(	PUNCT
ejpam-5714	146	5	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	146	6	)	)	PUNCT
ejpam-5714	146	7	(	(	PUNCT
ejpam-5714	146	8	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	146	9	(	(	PUNCT
ejpam-5714	146	10	t	t	PROPN
ejpam-5714	146	11	)	)	PUNCT
ejpam-5714	146	12	)	)	PUNCT
ejpam-5714	146	13	1−(p−1	1−(p−1	NUM
ejpam-5714	146	14	)	)	PUNCT
ejpam-5714	146	15	b	b	NOUN
ejpam-5714	146	16	(	(	PUNCT
ejpam-5714	146	17	p−1	p−1	PROPN
ejpam-5714	146	18	)	)	PUNCT
ejpam-5714	146	19	t1	t1	NOUN
ejpam-5714	146	20	(	(	PUNCT
ejpam-5714	146	21	πi(t	πi(t	NUM
ejpam-5714	146	22	)	)	PUNCT
ejpam-5714	146	23	)	)	PUNCT
ejpam-5714	147	1	[	[	PUNCT
ejpam-5714	147	2	b	b	X
ejpam-5714	147	3	(	(	PUNCT
ejpam-5714	147	4	πi(t	πi(t	NUM
ejpam-5714	147	5	)	)	PUNCT
ejpam-5714	147	6	)	)	PUNCT
ejpam-5714	147	7	(	(	PUNCT
ejpam-5714	147	8	ϖ′	ϖ′	X
ejpam-5714	147	9	(	(	PUNCT
ejpam-5714	147	10	πi(t	πi(t	NUM
ejpam-5714	147	11	)	)	PUNCT
ejpam-5714	147	12	)	)	PUNCT
ejpam-5714	147	13	)	)	PUNCT
ejpam-5714	147	14	(	(	PUNCT
ejpam-5714	147	15	p−1	p−1	PROPN
ejpam-5714	147	16	)	)	PUNCT
ejpam-5714	147	17	]	]	PUNCT
ejpam-5714	147	18	)	)	PUNCT
ejpam-5714	147	19	dt	dt	X
ejpam-5714	148	1	≥	≥	PROPN
ejpam-5714	148	2	bt1	bt1	PROPN
ejpam-5714	148	3	(	(	PUNCT
ejpam-5714	148	4	t	t	PROPN
ejpam-5714	148	5	)	)	PUNCT
ejpam-5714	148	6	b	b	NOUN
ejpam-5714	148	7	1/(p−1	1/(p−1	NUM
ejpam-5714	148	8	)	)	PUNCT
ejpam-5714	148	9	(	(	PUNCT
ejpam-5714	148	10	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	148	11	(	(	PUNCT
ejpam-5714	148	12	t	t	PROPN
ejpam-5714	148	13	)	)	PUNCT
ejpam-5714	148	14	+	+	CCONJ
ejpam-5714	148	15	1	1	NUM
ejpam-5714	148	16	(	(	PUNCT
ejpam-5714	148	17	p−	p−	NOUN
ejpam-5714	148	18	1	1	NUM
ejpam-5714	148	19	)	)	PUNCT
ejpam-5714	148	20	∫	∫	PROPN
ejpam-5714	149	1	t	t	PROPN
ejpam-5714	149	2	t1	t1	PROPN
ejpam-5714	149	3	(	(	PUNCT
ejpam-5714	149	4	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	149	5	)	)	PUNCT
ejpam-5714	149	6	(	(	PUNCT
ejpam-5714	149	7	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	149	8	(	(	PUNCT
ejpam-5714	149	9	t	t	PROPN
ejpam-5714	149	10	)	)	PUNCT
ejpam-5714	149	11	)	)	PUNCT
ejpam-5714	150	1	2−p	2−p	NUM
ejpam-5714	150	2	bt1	bt1	NOUN
ejpam-5714	150	3	(	(	PUNCT
ejpam-5714	150	4	t)b	t)b	NOUN
ejpam-5714	150	5	(	(	PUNCT
ejpam-5714	150	6	p−1	p−1	PROPN
ejpam-5714	150	7	)	)	PUNCT
ejpam-5714	150	8	t1	t1	NOUN
ejpam-5714	150	9	πi(t	πi(t	NUM
ejpam-5714	150	10	)	)	PUNCT
ejpam-5714	150	11	n∑	n∑	PROPN
ejpam-5714	150	12	i=1	i=1	PROPN
ejpam-5714	150	13	qi	qi	PROPN
ejpam-5714	150	14	(	(	PUNCT
ejpam-5714	150	15	t	t	PROPN
ejpam-5714	150	16	)	)	PUNCT
ejpam-5714	150	17	(	(	PUNCT
ejpam-5714	150	18	1−	1−	NUM
ejpam-5714	150	19	y	y	PROPN
ejpam-5714	150	20	(	(	PUNCT
ejpam-5714	150	21	πi	πi	PROPN
ejpam-5714	150	22	(	(	PUNCT
ejpam-5714	150	23	t	t	NOUN
ejpam-5714	150	24	)	)	PUNCT
ejpam-5714	150	25	)	)	PUNCT
ejpam-5714	150	26	)	)	PUNCT
ejpam-5714	151	1	(	(	PUNCT
ejpam-5714	151	2	p−1	p−1	PROPN
ejpam-5714	151	3	)	)	PUNCT
ejpam-5714	151	4	[	[	PUNCT
ejpam-5714	151	5	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	151	6	)	)	PUNCT
ejpam-5714	151	7	(	(	PUNCT
ejpam-5714	151	8	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	151	9	(	(	PUNCT
ejpam-5714	151	10	t	t	PROPN
ejpam-5714	151	11	)	)	PUNCT
ejpam-5714	151	12	]	]	PUNCT
ejpam-5714	151	13	(	(	PUNCT
ejpam-5714	151	14	p−1	p−1	PROPN
ejpam-5714	151	15	)	)	PUNCT
ejpam-5714	151	16	dt	dt	PART
ejpam-5714	151	17	≥	≥	PROPN
ejpam-5714	151	18	b1/(p−1	b1/(p−1	NUM
ejpam-5714	151	19	)	)	PUNCT
ejpam-5714	151	20	(	(	PUNCT
ejpam-5714	151	21	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	151	22	(	(	PUNCT
ejpam-5714	151	23	t	t	PROPN
ejpam-5714	151	24	)	)	PUNCT
ejpam-5714	151	25	[	[	PUNCT
ejpam-5714	151	26	bt1	bt1	NOUN
ejpam-5714	151	27	(	(	PUNCT
ejpam-5714	151	28	t	t	PROPN
ejpam-5714	151	29	)	)	PUNCT
ejpam-5714	152	1	+	+	CCONJ
ejpam-5714	152	2	1	1	NUM
ejpam-5714	152	3	(	(	PUNCT
ejpam-5714	152	4	p−	p−	NOUN
ejpam-5714	152	5	1	1	NUM
ejpam-5714	152	6	)	)	PUNCT
ejpam-5714	152	7	∫	∫	PROPN
ejpam-5714	152	8	t	t	PROPN
ejpam-5714	152	9	t1	t1	PROPN
ejpam-5714	152	10	bt1	bt1	PROPN
ejpam-5714	152	11	(	(	PUNCT
ejpam-5714	152	12	t)b	t)b	NOUN
ejpam-5714	152	13	p−1	p−1	PROPN
ejpam-5714	152	14	t1	t1	PROPN
ejpam-5714	152	15	(	(	PUNCT
ejpam-5714	152	16	πi(t	πi(t	NUM
ejpam-5714	152	17	)	)	PUNCT
ejpam-5714	152	18	)	)	PUNCT
ejpam-5714	153	1	n∑	n∑	PROPN
ejpam-5714	153	2	i=1	i=1	PROPN
ejpam-5714	154	1	qi	qi	PROPN
ejpam-5714	154	2	(	(	PUNCT
ejpam-5714	154	3	t	t	PROPN
ejpam-5714	154	4	)	)	PUNCT
ejpam-5714	154	5	(	(	PUNCT
ejpam-5714	154	6	1−	1−	NUM
ejpam-5714	154	7	y	y	PROPN
ejpam-5714	154	8	(	(	PUNCT
ejpam-5714	154	9	πi	πi	PROPN
ejpam-5714	154	10	(	(	PUNCT
ejpam-5714	154	11	t	t	NOUN
ejpam-5714	154	12	)	)	PUNCT
ejpam-5714	154	13	)	)	PUNCT
ejpam-5714	154	14	)	)	PUNCT
ejpam-5714	155	1	p−1	p−1	PROPN
ejpam-5714	155	2	dt	dt	X
ejpam-5714	155	3	]	]	PUNCT
ejpam-5714	155	4	.	.	PUNCT
ejpam-5714	156	1	f.	f.	PROPN
ejpam-5714	156	2	aldosari	aldosari	PROPN
ejpam-5714	156	3	/	/	SYM
ejpam-5714	156	4	eur	eur	PROPN
ejpam-5714	156	5	.	.	PUNCT
ejpam-5714	157	1	j.	j.	PROPN
ejpam-5714	157	2	pure	pure	PROPN
ejpam-5714	157	3	appl	appl	PROPN
ejpam-5714	157	4	.	.	PROPN
ejpam-5714	157	5	math	math	PROPN
ejpam-5714	157	6	,	,	PUNCT
ejpam-5714	157	7	18	18	NUM
ejpam-5714	157	8	(	(	PUNCT
ejpam-5714	157	9	1	1	NUM
ejpam-5714	157	10	)	)	PUNCT
ejpam-5714	157	11	(	(	PUNCT
ejpam-5714	157	12	2025	2025	NUM
ejpam-5714	157	13	)	)	PUNCT
ejpam-5714	157	14	,	,	PUNCT
ejpam-5714	157	15	5714	5714	NUM
ejpam-5714	157	16	6	6	NUM
ejpam-5714	157	17	of	of	ADP
ejpam-5714	157	18	16	16	NUM
ejpam-5714	157	19	≥	≥	NOUN
ejpam-5714	157	20	b̃t1(t)b	b̃t1(t)b	NOUN
ejpam-5714	157	21	1/(p−1	1/(p−1	NUM
ejpam-5714	157	22	)	)	PUNCT
ejpam-5714	157	23	(	(	PUNCT
ejpam-5714	157	24	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	157	25	(	(	PUNCT
ejpam-5714	157	26	t	t	PROPN
ejpam-5714	157	27	)	)	PUNCT
ejpam-5714	157	28	,	,	PUNCT
ejpam-5714	157	29	or	or	CCONJ
ejpam-5714	157	30	ϖ′	ϖ′	X
ejpam-5714	157	31	(	(	PUNCT
ejpam-5714	157	32	t	t	NOUN
ejpam-5714	157	33	)	)	PUNCT
ejpam-5714	157	34	ϖ(t	ϖ(t	PROPN
ejpam-5714	157	35	)	)	PUNCT
ejpam-5714	157	36	≤	≤	NUM
ejpam-5714	157	37	1	1	NUM
ejpam-5714	157	38	b̃t1(t)b	b̃t1(t)b	NUM
ejpam-5714	157	39	1/(p−1	1/(p−1	NUM
ejpam-5714	157	40	)	)	PUNCT
ejpam-5714	157	41	(	(	PUNCT
ejpam-5714	157	42	t	t	PROPN
ejpam-5714	157	43	)	)	PUNCT
ejpam-5714	157	44	.	.	PUNCT
ejpam-5714	158	1	integrating	integrate	VERB
ejpam-5714	158	2	from	from	ADP
ejpam-5714	158	3	πi	πi	PROPN
ejpam-5714	158	4	(	(	PUNCT
ejpam-5714	158	5	t	t	NOUN
ejpam-5714	158	6	)	)	PUNCT
ejpam-5714	158	7	to	to	ADP
ejpam-5714	158	8	t	t	PROPN
ejpam-5714	158	9	,	,	PUNCT
ejpam-5714	158	10	we	we	PRON
ejpam-5714	158	11	find	find	VERB
ejpam-5714	158	12	that	that	SCONJ
ejpam-5714	159	1	ϖ	ϖ	INTJ
ejpam-5714	159	2	(	(	PUNCT
ejpam-5714	159	3	πi	πi	PROPN
ejpam-5714	159	4	(	(	PUNCT
ejpam-5714	159	5	t	t	NOUN
ejpam-5714	159	6	)	)	PUNCT
ejpam-5714	159	7	)	)	PUNCT
ejpam-5714	160	1	ϖ	ϖ	X
ejpam-5714	160	2	(	(	PUNCT
ejpam-5714	160	3	t	t	PROPN
ejpam-5714	160	4	)	)	PUNCT
ejpam-5714	160	5	≥	≥	NOUN
ejpam-5714	160	6	exp	exp	NOUN
ejpam-5714	160	7	(	(	PUNCT
ejpam-5714	160	8	−	−	PROPN
ejpam-5714	160	9	∫	∫	PROPN
ejpam-5714	160	10	t	t	PROPN
ejpam-5714	160	11	πi(t	πi(t	NUM
ejpam-5714	160	12	)	)	PUNCT
ejpam-5714	160	13	dt	dt	ADP
ejpam-5714	160	14	b̃t1(t)b	b̃t1(t)b	NOUN
ejpam-5714	160	15	1/(p−1	1/(p−1	NUM
ejpam-5714	160	16	)	)	PUNCT
ejpam-5714	160	17	(	(	PUNCT
ejpam-5714	160	18	t	t	PROPN
ejpam-5714	160	19	)	)	PUNCT
ejpam-5714	160	20	)	)	PUNCT
ejpam-5714	160	21	,	,	PUNCT
ejpam-5714	160	22	which	which	PRON
ejpam-5714	160	23	with	with	ADP
ejpam-5714	160	24	(	(	PUNCT
ejpam-5714	160	25	7	7	NUM
ejpam-5714	160	26	)	)	PUNCT
ejpam-5714	160	27	,	,	PUNCT
ejpam-5714	160	28	gives	give	VERB
ejpam-5714	160	29	(	(	PUNCT
ejpam-5714	160	30	b	b	PROPN
ejpam-5714	160	31	(	(	PUNCT
ejpam-5714	160	32	t	t	PROPN
ejpam-5714	160	33	)	)	PUNCT
ejpam-5714	160	34	(	(	PUNCT
ejpam-5714	160	35	ϖ′	ϖ′	X
ejpam-5714	160	36	(	(	PUNCT
ejpam-5714	160	37	t))(p−1	t))(p−1	NOUN
ejpam-5714	160	38	)	)	PUNCT
ejpam-5714	160	39	)	)	PUNCT
ejpam-5714	161	1	′	′	NUM
ejpam-5714	161	2	ϖ(p−1	ϖ(p−1	NOUN
ejpam-5714	161	3	)	)	PUNCT
ejpam-5714	161	4	(	(	PUNCT
ejpam-5714	161	5	t	t	NOUN
ejpam-5714	161	6	)	)	PUNCT
ejpam-5714	161	7	≤	≤	NOUN
ejpam-5714	162	1	−	−	PROPN
ejpam-5714	162	2	n∑	n∑	PROPN
ejpam-5714	162	3	i=1	i=1	PROPN
ejpam-5714	163	1	qi	qi	PROPN
ejpam-5714	163	2	(	(	PUNCT
ejpam-5714	163	3	t	t	PROPN
ejpam-5714	163	4	)	)	PUNCT
ejpam-5714	163	5	(	(	PUNCT
ejpam-5714	163	6	1−	1−	NUM
ejpam-5714	163	7	y	y	PROPN
ejpam-5714	163	8	(	(	PUNCT
ejpam-5714	163	9	πi	πi	PROPN
ejpam-5714	163	10	(	(	PUNCT
ejpam-5714	163	11	t	t	NOUN
ejpam-5714	163	12	)	)	PUNCT
ejpam-5714	163	13	)	)	PUNCT
ejpam-5714	163	14	)	)	PUNCT
ejpam-5714	164	1	(	(	PUNCT
ejpam-5714	164	2	p−1	p−1	PROPN
ejpam-5714	164	3	)	)	PUNCT
ejpam-5714	164	4	(	(	PUNCT
ejpam-5714	164	5	ϖ	ϖ	X
ejpam-5714	164	6	(	(	PUNCT
ejpam-5714	164	7	πi	πi	PROPN
ejpam-5714	164	8	(	(	PUNCT
ejpam-5714	164	9	t	t	NOUN
ejpam-5714	164	10	)	)	PUNCT
ejpam-5714	164	11	)	)	PUNCT
ejpam-5714	165	1	ϖ	ϖ	X
ejpam-5714	165	2	(	(	PUNCT
ejpam-5714	165	3	t	t	PROPN
ejpam-5714	165	4	)	)	PUNCT
ejpam-5714	165	5	)	)	PUNCT
ejpam-5714	166	1	(	(	PUNCT
ejpam-5714	166	2	p−1	p−1	NOUN
ejpam-5714	166	3	)	)	PUNCT
ejpam-5714	166	4	≤	≤	NOUN
ejpam-5714	167	1	−	−	PROPN
ejpam-5714	167	2	n∑	n∑	PROPN
ejpam-5714	167	3	i=1	i=1	PROPN
ejpam-5714	168	1	qi	qi	PROPN
ejpam-5714	168	2	(	(	PUNCT
ejpam-5714	168	3	t	t	PROPN
ejpam-5714	168	4	)	)	PUNCT
ejpam-5714	168	5	(	(	PUNCT
ejpam-5714	168	6	1−	1−	NUM
ejpam-5714	168	7	y	y	PROPN
ejpam-5714	168	8	(	(	PUNCT
ejpam-5714	168	9	πi	πi	PROPN
ejpam-5714	168	10	(	(	PUNCT
ejpam-5714	168	11	t	t	NOUN
ejpam-5714	168	12	)	)	PUNCT
ejpam-5714	168	13	)	)	PUNCT
ejpam-5714	168	14	)	)	PUNCT
ejpam-5714	169	1	(	(	PUNCT
ejpam-5714	169	2	p−1	p−1	PROPN
ejpam-5714	169	3	)	)	PUNCT
ejpam-5714	169	4	b̂	b̂	NOUN
ejpam-5714	169	5	(	(	PUNCT
ejpam-5714	169	6	t	t	PROPN
ejpam-5714	169	7	)	)	PUNCT
ejpam-5714	169	8	.	.	PUNCT
ejpam-5714	170	1	the	the	DET
ejpam-5714	170	2	proof	proof	NOUN
ejpam-5714	170	3	is	be	AUX
ejpam-5714	170	4	complete	complete	ADJ
ejpam-5714	170	5	.	.	PUNCT
ejpam-5714	171	1	lemma	lemma	PROPN
ejpam-5714	171	2	4	4	X
ejpam-5714	171	3	.	.	PUNCT
ejpam-5714	172	1	let	let	AUX
ejpam-5714	172	2	(	(	PUNCT
ejpam-5714	172	3	1	1	X
ejpam-5714	172	4	)	)	PUNCT
ejpam-5714	172	5	have	have	VERB
ejpam-5714	172	6	a	a	DET
ejpam-5714	172	7	positive	positive	ADJ
ejpam-5714	172	8	solution	solution	NOUN
ejpam-5714	172	9	.	.	PUNCT
ejpam-5714	173	1	if	if	SCONJ
ejpam-5714	173	2	ξ	ξ	PROPN
ejpam-5714	173	3	(	(	PUNCT
ejpam-5714	173	4	t	t	NOUN
ejpam-5714	173	5	)	)	PUNCT
ejpam-5714	173	6	=	=	SYM
ejpam-5714	173	7	x	x	X
ejpam-5714	173	8	(	(	PUNCT
ejpam-5714	173	9	t	t	PROPN
ejpam-5714	173	10	)	)	PUNCT
ejpam-5714	173	11	b	b	PROPN
ejpam-5714	173	12	(	(	PUNCT
ejpam-5714	173	13	t	t	PROPN
ejpam-5714	173	14	)	)	PUNCT
ejpam-5714	173	15	(	(	PUNCT
ejpam-5714	173	16	ϖ′	ϖ′	X
ejpam-5714	173	17	(	(	PUNCT
ejpam-5714	173	18	t	t	NOUN
ejpam-5714	173	19	)	)	PUNCT
ejpam-5714	173	20	ϖ	ϖ	PROPN
ejpam-5714	173	21	(	(	PUNCT
ejpam-5714	173	22	t	t	PROPN
ejpam-5714	173	23	)	)	PUNCT
ejpam-5714	173	24	)	)	PUNCT
ejpam-5714	174	1	p−1	p−1	PROPN
ejpam-5714	174	2	>	>	X
ejpam-5714	174	3	0	0	PROPN
ejpam-5714	174	4	,	,	PUNCT
ejpam-5714	174	5	(	(	PUNCT
ejpam-5714	174	6	12	12	NUM
ejpam-5714	174	7	)	)	PUNCT
ejpam-5714	174	8	then	then	ADV
ejpam-5714	174	9	ξ′	ξ′	PROPN
ejpam-5714	174	10	(	(	PUNCT
ejpam-5714	174	11	t	t	NOUN
ejpam-5714	174	12	)	)	PUNCT
ejpam-5714	174	13	≤	≤	NUM
ejpam-5714	174	14	x′+	x′+	PUNCT
ejpam-5714	174	15	(	(	PUNCT
ejpam-5714	174	16	t	t	PROPN
ejpam-5714	174	17	)	)	PUNCT
ejpam-5714	174	18	x	x	X
ejpam-5714	174	19	(	(	PUNCT
ejpam-5714	174	20	t	t	PROPN
ejpam-5714	174	21	)	)	PUNCT
ejpam-5714	174	22	ξ(t)−	ξ(t)−	PROPN
ejpam-5714	174	23	x(t	x(t	PROPN
ejpam-5714	174	24	)	)	PUNCT
ejpam-5714	174	25	n∑	n∑	PROPN
ejpam-5714	174	26	i=1	i=1	PROPN
ejpam-5714	175	1	qi	qi	PROPN
ejpam-5714	175	2	(	(	PUNCT
ejpam-5714	175	3	t	t	PROPN
ejpam-5714	175	4	)	)	PUNCT
ejpam-5714	175	5	(	(	PUNCT
ejpam-5714	175	6	1−	1−	NUM
ejpam-5714	175	7	y	y	PROPN
ejpam-5714	175	8	(	(	PUNCT
ejpam-5714	175	9	πi	πi	PROPN
ejpam-5714	175	10	(	(	PUNCT
ejpam-5714	175	11	t	t	NOUN
ejpam-5714	175	12	)	)	PUNCT
ejpam-5714	175	13	)	)	PUNCT
ejpam-5714	175	14	)	)	PUNCT
ejpam-5714	175	15	p−1	p−1	NOUN
ejpam-5714	175	16	b̂	b̂	NOUN
ejpam-5714	176	1	(	(	PUNCT
ejpam-5714	176	2	t)−	t)−	PROPN
ejpam-5714	176	3	(	(	PUNCT
ejpam-5714	176	4	p−	p−	NOUN
ejpam-5714	176	5	1	1	NUM
ejpam-5714	176	6	)	)	PUNCT
ejpam-5714	176	7	(	(	PUNCT
ejpam-5714	176	8	x	x	X
ejpam-5714	176	9	(	(	PUNCT
ejpam-5714	176	10	t	t	PROPN
ejpam-5714	176	11	)	)	PUNCT
ejpam-5714	176	12	b	b	PROPN
ejpam-5714	176	13	(	(	PUNCT
ejpam-5714	176	14	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	176	15	)	)	PUNCT
ejpam-5714	176	16	ξp/(p−1	ξp/(p−1	NUM
ejpam-5714	176	17	)	)	PUNCT
ejpam-5714	176	18	(	(	PUNCT
ejpam-5714	176	19	t	t	NOUN
ejpam-5714	176	20	)	)	PUNCT
ejpam-5714	176	21	.	.	PUNCT
ejpam-5714	177	1	(	(	PUNCT
ejpam-5714	177	2	13	13	NUM
ejpam-5714	177	3	)	)	PUNCT
ejpam-5714	177	4	proof	proof	NOUN
ejpam-5714	177	5	.	.	PUNCT
ejpam-5714	178	1	let	let	VERB
ejpam-5714	178	2	κ	κ	PRON
ejpam-5714	178	3	be	be	AUX
ejpam-5714	178	4	a	a	DET
ejpam-5714	178	5	positive	positive	ADJ
ejpam-5714	178	6	solution	solution	NOUN
ejpam-5714	178	7	of	of	ADP
ejpam-5714	178	8	equation	equation	NOUN
ejpam-5714	178	9	(	(	PUNCT
ejpam-5714	178	10	1	1	NUM
ejpam-5714	178	11	)	)	PUNCT
ejpam-5714	178	12	.	.	PUNCT
ejpam-5714	179	1	from	from	ADP
ejpam-5714	179	2	lemma	lemma	PROPN
ejpam-5714	179	3	3	3	NUM
ejpam-5714	179	4	,	,	PUNCT
ejpam-5714	179	5	we	we	PRON
ejpam-5714	179	6	have	have	VERB
ejpam-5714	179	7	(	(	PUNCT
ejpam-5714	179	8	9	9	X
ejpam-5714	179	9	)	)	PUNCT
ejpam-5714	179	10	holds	hold	NOUN
ejpam-5714	179	11	.	.	PUNCT
ejpam-5714	180	1	thus	thus	ADV
ejpam-5714	180	2	,	,	PUNCT
ejpam-5714	180	3	when	when	SCONJ
ejpam-5714	180	4	we	we	PRON
ejpam-5714	180	5	differentiate	differentiate	VERB
ejpam-5714	180	6	ξ	ξ	PROPN
ejpam-5714	180	7	(	(	PUNCT
ejpam-5714	180	8	t	t	NOUN
ejpam-5714	180	9	)	)	PUNCT
ejpam-5714	180	10	we	we	PRON
ejpam-5714	180	11	get	get	VERB
ejpam-5714	180	12	ξ′	ξ′	NOUN
ejpam-5714	180	13	(	(	PUNCT
ejpam-5714	180	14	t	t	NOUN
ejpam-5714	180	15	)	)	PUNCT
ejpam-5714	180	16	=	=	SYM
ejpam-5714	180	17	x′	x′	PROPN
ejpam-5714	180	18	(	(	PUNCT
ejpam-5714	180	19	t	t	PROPN
ejpam-5714	180	20	)	)	PUNCT
ejpam-5714	181	1	x	x	X
ejpam-5714	181	2	(	(	PUNCT
ejpam-5714	181	3	t	t	PROPN
ejpam-5714	181	4	)	)	PUNCT
ejpam-5714	181	5	ξ	ξ	PROPN
ejpam-5714	181	6	(	(	PUNCT
ejpam-5714	181	7	t	t	PROPN
ejpam-5714	181	8	)	)	PUNCT
ejpam-5714	182	1	+	+	NOUN
ejpam-5714	182	2	x	x	SYM
ejpam-5714	182	3	(	(	PUNCT
ejpam-5714	182	4	t	t	NOUN
ejpam-5714	182	5	)	)	PUNCT
ejpam-5714	182	6	(	(	PUNCT
ejpam-5714	182	7	b	b	X
ejpam-5714	182	8	(	(	PUNCT
ejpam-5714	182	9	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	182	10	(	(	PUNCT
ejpam-5714	182	11	t))′	t))′	SYM
ejpam-5714	182	12	ϖ(p−1	ϖ(p−1	PROPN
ejpam-5714	182	13	)	)	PUNCT
ejpam-5714	182	14	(	(	PUNCT
ejpam-5714	182	15	t	t	NOUN
ejpam-5714	182	16	)	)	PUNCT
ejpam-5714	182	17	−	−	PROPN
ejpam-5714	182	18	(	(	PUNCT
ejpam-5714	182	19	p−	p−	NOUN
ejpam-5714	182	20	1)x	1)x	NUM
ejpam-5714	182	21	(	(	PUNCT
ejpam-5714	182	22	t	t	PROPN
ejpam-5714	182	23	)	)	PUNCT
ejpam-5714	182	24	b	b	PROPN
ejpam-5714	182	25	(	(	PUNCT
ejpam-5714	182	26	t	t	PROPN
ejpam-5714	182	27	)	)	PUNCT
ejpam-5714	182	28	(	(	PUNCT
ejpam-5714	182	29	ϖ′	ϖ′	X
ejpam-5714	182	30	(	(	PUNCT
ejpam-5714	182	31	t	t	NOUN
ejpam-5714	182	32	)	)	PUNCT
ejpam-5714	182	33	ϖ(t	ϖ(t	PROPN
ejpam-5714	182	34	)	)	PUNCT
ejpam-5714	182	35	)	)	PUNCT
ejpam-5714	183	1	p	p	NOUN
ejpam-5714	183	2	.	.	PUNCT
ejpam-5714	184	1	from	from	ADP
ejpam-5714	184	2	(	(	PUNCT
ejpam-5714	184	3	9	9	NUM
ejpam-5714	184	4	)	)	PUNCT
ejpam-5714	184	5	and	and	CCONJ
ejpam-5714	184	6	(	(	PUNCT
ejpam-5714	184	7	12	12	NUM
ejpam-5714	184	8	)	)	PUNCT
ejpam-5714	184	9	,	,	PUNCT
ejpam-5714	184	10	we	we	PRON
ejpam-5714	184	11	see	see	VERB
ejpam-5714	184	12	that	that	SCONJ
ejpam-5714	184	13	ξ′	ξ′	NOUN
ejpam-5714	184	14	(	(	PUNCT
ejpam-5714	184	15	t	t	NOUN
ejpam-5714	184	16	)	)	PUNCT
ejpam-5714	184	17	≤	≤	NUM
ejpam-5714	184	18	x′+	x′+	PUNCT
ejpam-5714	185	1	(	(	PUNCT
ejpam-5714	185	2	t	t	PROPN
ejpam-5714	185	3	)	)	PUNCT
ejpam-5714	185	4	x	x	X
ejpam-5714	185	5	(	(	PUNCT
ejpam-5714	185	6	t	t	NOUN
ejpam-5714	185	7	)	)	PUNCT
ejpam-5714	185	8	ξ(t)−1x(t	ξ(t)−1x(t	PROPN
ejpam-5714	185	9	)	)	PUNCT
ejpam-5714	186	1	n∑	n∑	NOUN
ejpam-5714	186	2	i=1	i=1	PROPN
ejpam-5714	187	1	qi	qi	PROPN
ejpam-5714	187	2	(	(	PUNCT
ejpam-5714	187	3	t	t	PROPN
ejpam-5714	187	4	)	)	PUNCT
ejpam-5714	187	5	(	(	PUNCT
ejpam-5714	187	6	1−	1−	NUM
ejpam-5714	187	7	y	y	PROPN
ejpam-5714	187	8	(	(	PUNCT
ejpam-5714	187	9	πi	πi	PROPN
ejpam-5714	187	10	(	(	PUNCT
ejpam-5714	187	11	t	t	NOUN
ejpam-5714	187	12	)	)	PUNCT
ejpam-5714	187	13	)	)	PUNCT
ejpam-5714	187	14	)	)	PUNCT
ejpam-5714	188	1	(	(	PUNCT
ejpam-5714	188	2	p−1	p−1	PROPN
ejpam-5714	188	3	)	)	PUNCT
ejpam-5714	188	4	b̂	b̂	NOUN
ejpam-5714	189	1	(	(	PUNCT
ejpam-5714	189	2	t)−	t)−	PROPN
ejpam-5714	189	3	(	(	PUNCT
ejpam-5714	189	4	p−	p−	NOUN
ejpam-5714	189	5	1	1	NUM
ejpam-5714	189	6	)	)	PUNCT
ejpam-5714	189	7	(	(	PUNCT
ejpam-5714	189	8	x	x	X
ejpam-5714	189	9	(	(	PUNCT
ejpam-5714	189	10	t	t	PROPN
ejpam-5714	189	11	)	)	PUNCT
ejpam-5714	189	12	b	b	PROPN
ejpam-5714	189	13	(	(	PUNCT
ejpam-5714	189	14	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	189	15	)	)	PUNCT
ejpam-5714	189	16	ξp/(p−1	ξp/(p−1	NUM
ejpam-5714	189	17	)	)	PUNCT
ejpam-5714	189	18	(	(	PUNCT
ejpam-5714	189	19	t	t	NOUN
ejpam-5714	189	20	)	)	PUNCT
ejpam-5714	189	21	.	.	PUNCT
ejpam-5714	190	1	the	the	DET
ejpam-5714	190	2	proof	proof	NOUN
ejpam-5714	190	3	is	be	AUX
ejpam-5714	190	4	complete	complete	ADJ
ejpam-5714	190	5	.	.	PUNCT
ejpam-5714	191	1	f.	f.	PROPN
ejpam-5714	191	2	aldosari	aldosari	PROPN
ejpam-5714	191	3	/	/	SYM
ejpam-5714	191	4	eur	eur	PROPN
ejpam-5714	191	5	.	.	PUNCT
ejpam-5714	192	1	j.	j.	PROPN
ejpam-5714	192	2	pure	pure	PROPN
ejpam-5714	192	3	appl	appl	PROPN
ejpam-5714	192	4	.	.	PROPN
ejpam-5714	192	5	math	math	PROPN
ejpam-5714	192	6	,	,	PUNCT
ejpam-5714	192	7	18	18	NUM
ejpam-5714	192	8	(	(	PUNCT
ejpam-5714	192	9	1	1	NUM
ejpam-5714	192	10	)	)	PUNCT
ejpam-5714	192	11	(	(	PUNCT
ejpam-5714	192	12	2025	2025	NUM
ejpam-5714	192	13	)	)	PUNCT
ejpam-5714	192	14	,	,	PUNCT
ejpam-5714	192	15	5714	5714	NUM
ejpam-5714	192	16	7	7	NUM
ejpam-5714	192	17	of	of	ADP
ejpam-5714	192	18	16	16	NUM
ejpam-5714	192	19	theorem	theorem	NOUN
ejpam-5714	192	20	1	1	NUM
ejpam-5714	192	21	.	.	PUNCT
ejpam-5714	193	1	if	if	SCONJ
ejpam-5714	193	2	the	the	DET
ejpam-5714	193	3	equation	equation	NOUN
ejpam-5714	193	4	ω′	ω′	X
ejpam-5714	193	5	(	(	PUNCT
ejpam-5714	193	6	t	t	PROPN
ejpam-5714	193	7	)	)	PUNCT
ejpam-5714	193	8	+	+	CCONJ
ejpam-5714	193	9	b̃	b̃	PROPN
ejpam-5714	193	10	(	(	PUNCT
ejpam-5714	193	11	p−1	p−1	PROPN
ejpam-5714	193	12	)	)	PUNCT
ejpam-5714	193	13	t1	t1	NOUN
ejpam-5714	193	14	(	(	PUNCT
ejpam-5714	193	15	πi	πi	PROPN
ejpam-5714	193	16	(	(	PUNCT
ejpam-5714	193	17	t	t	NOUN
ejpam-5714	193	18	)	)	PUNCT
ejpam-5714	193	19	)	)	PUNCT
ejpam-5714	194	1	n∑	n∑	PROPN
ejpam-5714	194	2	i=1	i=1	PROPN
ejpam-5714	195	1	qi	qi	PROPN
ejpam-5714	195	2	(	(	PUNCT
ejpam-5714	195	3	t	t	PROPN
ejpam-5714	195	4	)	)	PUNCT
ejpam-5714	195	5	(	(	PUNCT
ejpam-5714	195	6	1−	1−	NUM
ejpam-5714	195	7	y	y	PROPN
ejpam-5714	195	8	(	(	PUNCT
ejpam-5714	195	9	πi	πi	PROPN
ejpam-5714	195	10	(	(	PUNCT
ejpam-5714	195	11	t	t	NOUN
ejpam-5714	195	12	)	)	PUNCT
ejpam-5714	195	13	)	)	PUNCT
ejpam-5714	195	14	)	)	PUNCT
ejpam-5714	196	1	(	(	PUNCT
ejpam-5714	196	2	p−1	p−1	PROPN
ejpam-5714	196	3	)	)	PUNCT
ejpam-5714	196	4	ω	ω	PROPN
ejpam-5714	196	5	(	(	PUNCT
ejpam-5714	196	6	πi	πi	PROPN
ejpam-5714	196	7	(	(	PUNCT
ejpam-5714	196	8	t	t	NOUN
ejpam-5714	196	9	)	)	PUNCT
ejpam-5714	196	10	)	)	PUNCT
ejpam-5714	197	1	=	=	PUNCT
ejpam-5714	197	2	0	0	NUM
ejpam-5714	197	3	,	,	PUNCT
ejpam-5714	197	4	(	(	PUNCT
ejpam-5714	197	5	14	14	NUM
ejpam-5714	197	6	)	)	PUNCT
ejpam-5714	197	7	is	be	AUX
ejpam-5714	197	8	oscillatory	oscillatory	ADJ
ejpam-5714	197	9	,	,	PUNCT
ejpam-5714	197	10	then	then	ADV
ejpam-5714	197	11	(	(	PUNCT
ejpam-5714	197	12	1	1	X
ejpam-5714	197	13	)	)	PUNCT
ejpam-5714	197	14	is	be	AUX
ejpam-5714	197	15	oscillatory	oscillatory	ADJ
ejpam-5714	197	16	.	.	PUNCT
ejpam-5714	198	1	proof	proof	NOUN
ejpam-5714	198	2	.	.	PUNCT
ejpam-5714	199	1	let	let	VERB
ejpam-5714	199	2	κ	κ	PROPN
ejpam-5714	199	3	(	(	PUNCT
ejpam-5714	199	4	t	t	PROPN
ejpam-5714	199	5	)	)	PUNCT
ejpam-5714	199	6	>	>	X
ejpam-5714	199	7	0	0	NUM
ejpam-5714	199	8	,	,	PUNCT
ejpam-5714	199	9	that	that	PRON
ejpam-5714	199	10	is	be	AUX
ejpam-5714	199	11	κ	κ	NOUN
ejpam-5714	199	12	(	(	PUNCT
ejpam-5714	199	13	ζ	ζ	X
ejpam-5714	199	14	(	(	PUNCT
ejpam-5714	199	15	t	t	NOUN
ejpam-5714	199	16	)	)	PUNCT
ejpam-5714	199	17	)	)	PUNCT
ejpam-5714	200	1	>	>	X
ejpam-5714	200	2	0	0	PUNCT
ejpam-5714	201	1	and	and	CCONJ
ejpam-5714	201	2	κ	κ	PROPN
ejpam-5714	201	3	(	(	PUNCT
ejpam-5714	201	4	πi	πi	PROPN
ejpam-5714	201	5	(	(	PUNCT
ejpam-5714	201	6	t	t	NOUN
ejpam-5714	201	7	)	)	PUNCT
ejpam-5714	201	8	)	)	PUNCT
ejpam-5714	202	1	>	>	X
ejpam-5714	202	2	0	0	X
ejpam-5714	202	3	.	.	PUNCT
ejpam-5714	203	1	from	from	ADP
ejpam-5714	203	2	lemma	lemma	PROPN
ejpam-5714	203	3	3	3	NUM
ejpam-5714	203	4	,	,	PUNCT
ejpam-5714	203	5	we	we	PRON
ejpam-5714	203	6	have	have	VERB
ejpam-5714	203	7	(	(	PUNCT
ejpam-5714	203	8	7	7	NUM
ejpam-5714	203	9	)	)	PUNCT
ejpam-5714	203	10	and	and	CCONJ
ejpam-5714	203	11	(	(	PUNCT
ejpam-5714	203	12	8)	8)	NUM
ejpam-5714	203	13	hold	hold	NOUN
ejpam-5714	203	14	.	.	PUNCT
ejpam-5714	204	1	using	use	VERB
ejpam-5714	204	2	(	(	PUNCT
ejpam-5714	204	3	7	7	NUM
ejpam-5714	204	4	)	)	PUNCT
ejpam-5714	204	5	and	and	CCONJ
ejpam-5714	204	6	(	(	PUNCT
ejpam-5714	204	7	8)	8)	NUM
ejpam-5714	204	8	,	,	PUNCT
ejpam-5714	204	9	we	we	PRON
ejpam-5714	204	10	find	find	VERB
ejpam-5714	204	11	ω	ω	PROPN
ejpam-5714	204	12	(	(	PUNCT
ejpam-5714	204	13	t	t	PROPN
ejpam-5714	204	14	)	)	PUNCT
ejpam-5714	204	15	=	=	SYM
ejpam-5714	204	16	b	b	PROPN
ejpam-5714	204	17	(	(	PUNCT
ejpam-5714	204	18	t	t	PROPN
ejpam-5714	204	19	)	)	PUNCT
ejpam-5714	204	20	(	(	PUNCT
ejpam-5714	204	21	ϖ′	ϖ′	X
ejpam-5714	204	22	(	(	PUNCT
ejpam-5714	204	23	t))(p−1	t))(p−1	NOUN
ejpam-5714	204	24	)	)	PUNCT
ejpam-5714	204	25	is	be	AUX
ejpam-5714	204	26	a	a	DET
ejpam-5714	204	27	positive	positive	ADJ
ejpam-5714	204	28	solution	solution	NOUN
ejpam-5714	204	29	of	of	ADP
ejpam-5714	204	30	ω′	ω′	PROPN
ejpam-5714	204	31	(	(	PUNCT
ejpam-5714	204	32	t	t	PROPN
ejpam-5714	204	33	)	)	PUNCT
ejpam-5714	205	1	+	+	CCONJ
ejpam-5714	206	1	b̃	b̃	PROPN
ejpam-5714	206	2	(	(	PUNCT
ejpam-5714	206	3	p−1	p−1	PROPN
ejpam-5714	206	4	)	)	PUNCT
ejpam-5714	206	5	t1	t1	NOUN
ejpam-5714	206	6	(	(	PUNCT
ejpam-5714	206	7	πi	πi	PROPN
ejpam-5714	206	8	(	(	PUNCT
ejpam-5714	206	9	t	t	NOUN
ejpam-5714	206	10	)	)	PUNCT
ejpam-5714	206	11	)	)	PUNCT
ejpam-5714	207	1	n∑	n∑	PROPN
ejpam-5714	207	2	i=1	i=1	PROPN
ejpam-5714	208	1	qi	qi	PROPN
ejpam-5714	208	2	(	(	PUNCT
ejpam-5714	208	3	t	t	PROPN
ejpam-5714	208	4	)	)	PUNCT
ejpam-5714	208	5	(	(	PUNCT
ejpam-5714	208	6	1−	1−	NUM
ejpam-5714	208	7	y	y	PROPN
ejpam-5714	208	8	(	(	PUNCT
ejpam-5714	208	9	πi	πi	PROPN
ejpam-5714	208	10	(	(	PUNCT
ejpam-5714	208	11	t	t	NOUN
ejpam-5714	208	12	)	)	PUNCT
ejpam-5714	208	13	)	)	PUNCT
ejpam-5714	208	14	)	)	PUNCT
ejpam-5714	209	1	(	(	PUNCT
ejpam-5714	209	2	p−1	p−1	PROPN
ejpam-5714	209	3	)	)	PUNCT
ejpam-5714	209	4	ω	ω	PROPN
ejpam-5714	209	5	(	(	PUNCT
ejpam-5714	209	6	πi	πi	PROPN
ejpam-5714	209	7	(	(	PUNCT
ejpam-5714	209	8	t	t	NOUN
ejpam-5714	209	9	)	)	PUNCT
ejpam-5714	209	10	)	)	PUNCT
ejpam-5714	210	1	≤	≤	ADV
ejpam-5714	210	2	0	0	X
ejpam-5714	210	3	.	.	PUNCT
ejpam-5714	211	1	by	by	ADP
ejpam-5714	211	2	[	[	X
ejpam-5714	211	3	12	12	NUM
ejpam-5714	211	4	,	,	PUNCT
ejpam-5714	211	5	theorem	theorem	VERB
ejpam-5714	211	6	1	1	NUM
ejpam-5714	211	7	]	]	PUNCT
ejpam-5714	211	8	,	,	PUNCT
ejpam-5714	211	9	then	then	ADV
ejpam-5714	211	10	also	also	ADV
ejpam-5714	211	11	,	,	PUNCT
ejpam-5714	211	12	the	the	DET
ejpam-5714	211	13	solution	solution	NOUN
ejpam-5714	211	14	of	of	ADP
ejpam-5714	211	15	the	the	DET
ejpam-5714	211	16	associated	associated	ADJ
ejpam-5714	211	17	equation	equation	NOUN
ejpam-5714	211	18	(	(	PUNCT
ejpam-5714	211	19	14	14	NUM
ejpam-5714	211	20	)	)	PUNCT
ejpam-5714	211	21	is	be	AUX
ejpam-5714	211	22	a	a	DET
ejpam-5714	211	23	positive	positive	ADJ
ejpam-5714	211	24	,	,	PUNCT
ejpam-5714	211	25	and	and	CCONJ
ejpam-5714	211	26	this	this	DET
ejpam-5714	211	27	a	a	DET
ejpam-5714	211	28	contradiction	contradiction	NOUN
ejpam-5714	211	29	.	.	PUNCT
ejpam-5714	212	1	the	the	DET
ejpam-5714	212	2	proof	proof	NOUN
ejpam-5714	212	3	is	be	AUX
ejpam-5714	212	4	complete	complete	ADJ
ejpam-5714	212	5	.	.	PUNCT
ejpam-5714	213	1	corollary	corollary	ADJ
ejpam-5714	213	2	1	1	NUM
ejpam-5714	213	3	.	.	PUNCT
ejpam-5714	214	1	let	let	VERB
ejpam-5714	214	2	lim	lim	PROPN
ejpam-5714	214	3	sup	sup	PROPN
ejpam-5714	214	4	t→∞	t→∞	NUM
ejpam-5714	214	5	∫	∫	PROPN
ejpam-5714	214	6	t	t	PROPN
ejpam-5714	214	7	πi(t	πi(t	PUNCT
ejpam-5714	214	8	)	)	PUNCT
ejpam-5714	215	1	b̃	b̃	PROPN
ejpam-5714	215	2	(	(	PUNCT
ejpam-5714	215	3	p−1	p−1	PROPN
ejpam-5714	215	4	)	)	PUNCT
ejpam-5714	215	5	t1	t1	NOUN
ejpam-5714	215	6	(	(	PUNCT
ejpam-5714	215	7	πi	πi	PROPN
ejpam-5714	215	8	(	(	PUNCT
ejpam-5714	215	9	t	t	NOUN
ejpam-5714	215	10	)	)	PUNCT
ejpam-5714	215	11	)	)	PUNCT
ejpam-5714	216	1	n∑	n∑	PROPN
ejpam-5714	216	2	i=1	i=1	PROPN
ejpam-5714	217	1	qi	qi	PROPN
ejpam-5714	217	2	(	(	PUNCT
ejpam-5714	217	3	t	t	PROPN
ejpam-5714	217	4	)	)	PUNCT
ejpam-5714	217	5	(	(	PUNCT
ejpam-5714	217	6	1−	1−	NUM
ejpam-5714	217	7	y	y	PROPN
ejpam-5714	217	8	(	(	PUNCT
ejpam-5714	217	9	πi	πi	PROPN
ejpam-5714	217	10	(	(	PUNCT
ejpam-5714	217	11	t	t	NOUN
ejpam-5714	217	12	)	)	PUNCT
ejpam-5714	217	13	)	)	PUNCT
ejpam-5714	217	14	)	)	PUNCT
ejpam-5714	218	1	(	(	PUNCT
ejpam-5714	218	2	p−1	p−1	PROPN
ejpam-5714	218	3	)	)	PUNCT
ejpam-5714	218	4	dt	dt	X
ejpam-5714	218	5	>	>	X
ejpam-5714	218	6	1	1	NUM
ejpam-5714	218	7	,	,	PUNCT
ejpam-5714	218	8	∂	∂	NOUN
ejpam-5714	218	9	∂t	∂t	PROPN
ejpam-5714	218	10	πi	πi	PROPN
ejpam-5714	218	11	(	(	PUNCT
ejpam-5714	218	12	t	t	PROPN
ejpam-5714	218	13	)	)	PUNCT
ejpam-5714	218	14	≥	≥	NOUN
ejpam-5714	218	15	0	0	NUM
ejpam-5714	218	16	,	,	PUNCT
ejpam-5714	218	17	(	(	PUNCT
ejpam-5714	218	18	15	15	NUM
ejpam-5714	218	19	)	)	PUNCT
ejpam-5714	218	20	or	or	CCONJ
ejpam-5714	218	21	lim	lim	PROPN
ejpam-5714	218	22	inf	inf	PROPN
ejpam-5714	218	23	t→∞	t→∞	NUM
ejpam-5714	218	24	∫	∫	PROPN
ejpam-5714	218	25	t	t	PROPN
ejpam-5714	218	26	πi(t	πi(t	PUNCT
ejpam-5714	218	27	)	)	PUNCT
ejpam-5714	219	1	b̃	b̃	PROPN
ejpam-5714	219	2	(	(	PUNCT
ejpam-5714	219	3	p−1	p−1	PROPN
ejpam-5714	219	4	)	)	PUNCT
ejpam-5714	219	5	t1	t1	NOUN
ejpam-5714	219	6	(	(	PUNCT
ejpam-5714	219	7	πi	πi	PROPN
ejpam-5714	219	8	(	(	PUNCT
ejpam-5714	219	9	t	t	NOUN
ejpam-5714	219	10	)	)	PUNCT
ejpam-5714	219	11	)	)	PUNCT
ejpam-5714	220	1	n∑	n∑	PROPN
ejpam-5714	220	2	i=1	i=1	PROPN
ejpam-5714	221	1	qi	qi	PROPN
ejpam-5714	221	2	(	(	PUNCT
ejpam-5714	221	3	t	t	PROPN
ejpam-5714	221	4	)	)	PUNCT
ejpam-5714	221	5	(	(	PUNCT
ejpam-5714	221	6	1−	1−	NUM
ejpam-5714	221	7	y	y	PROPN
ejpam-5714	221	8	(	(	PUNCT
ejpam-5714	221	9	πi	πi	PROPN
ejpam-5714	221	10	(	(	PUNCT
ejpam-5714	221	11	t	t	NOUN
ejpam-5714	221	12	)	)	PUNCT
ejpam-5714	221	13	)	)	PUNCT
ejpam-5714	221	14	)	)	PUNCT
ejpam-5714	222	1	p−1	p−1	PROPN
ejpam-5714	222	2	dt	dt	X
ejpam-5714	222	3	>	>	X
ejpam-5714	222	4	1	1	NUM
ejpam-5714	222	5	e	e	NOUN
ejpam-5714	222	6	,	,	PUNCT
ejpam-5714	222	7	(	(	PUNCT
ejpam-5714	222	8	16	16	NUM
ejpam-5714	222	9	)	)	PUNCT
ejpam-5714	222	10	then	then	ADV
ejpam-5714	222	11	all	all	DET
ejpam-5714	222	12	solutions	solution	NOUN
ejpam-5714	222	13	of	of	ADP
ejpam-5714	222	14	(	(	PUNCT
ejpam-5714	222	15	1	1	X
ejpam-5714	222	16	)	)	PUNCT
ejpam-5714	222	17	is	be	AUX
ejpam-5714	222	18	oscillatory	oscillatory	ADJ
ejpam-5714	222	19	.	.	PUNCT
ejpam-5714	223	1	proof	proof	NOUN
ejpam-5714	223	2	.	.	PUNCT
ejpam-5714	224	1	as	as	SCONJ
ejpam-5714	224	2	may	may	AUX
ejpam-5714	224	3	be	be	AUX
ejpam-5714	224	4	shown	show	VERB
ejpam-5714	224	5	from	from	ADP
ejpam-5714	224	6	[	[	X
ejpam-5714	224	7	10	10	NUM
ejpam-5714	224	8	,	,	PUNCT
ejpam-5714	224	9	theorem	theorem	VERB
ejpam-5714	224	10	2.1.1	2.1.1	NUM
ejpam-5714	224	11	]	]	PUNCT
ejpam-5714	224	12	,	,	PUNCT
ejpam-5714	224	13	(	(	PUNCT
ejpam-5714	224	14	15	15	NUM
ejpam-5714	224	15	)	)	PUNCT
ejpam-5714	224	16	or	or	CCONJ
ejpam-5714	224	17	(	(	PUNCT
ejpam-5714	224	18	16	16	NUM
ejpam-5714	224	19	)	)	PUNCT
ejpam-5714	224	20	guarantee	guarantee	VERB
ejpam-5714	224	21	oscillation	oscillation	NOUN
ejpam-5714	224	22	of	of	ADP
ejpam-5714	224	23	(	(	PUNCT
ejpam-5714	224	24	14	14	NUM
ejpam-5714	224	25	)	)	PUNCT
ejpam-5714	224	26	.	.	PUNCT
ejpam-5714	225	1	lemma	lemma	PROPN
ejpam-5714	225	2	5	5	X
ejpam-5714	225	3	.	.	PUNCT
ejpam-5714	225	4	suppose	suppose	VERB
ejpam-5714	225	5	πi	πi	ADP
ejpam-5714	225	6	is	be	AUX
ejpam-5714	225	7	strictly	strictly	ADV
ejpam-5714	225	8	growing	grow	VERB
ejpam-5714	225	9	in	in	ADP
ejpam-5714	225	10	relation	relation	NOUN
ejpam-5714	225	11	to	to	ADP
ejpam-5714	225	12	t	t	PROPN
ejpam-5714	225	13	and	and	CCONJ
ejpam-5714	225	14	lim	lim	PROPN
ejpam-5714	225	15	inf	inf	PROPN
ejpam-5714	225	16	t→∞	t→∞	NUM
ejpam-5714	225	17	∫	∫	PROPN
ejpam-5714	225	18	t	t	PROPN
ejpam-5714	225	19	πi(t	πi(t	PUNCT
ejpam-5714	225	20	)	)	PUNCT
ejpam-5714	226	1	b̃	b̃	PROPN
ejpam-5714	226	2	(	(	PUNCT
ejpam-5714	226	3	p−1	p−1	PROPN
ejpam-5714	226	4	)	)	PUNCT
ejpam-5714	226	5	t1	t1	NOUN
ejpam-5714	226	6	(	(	PUNCT
ejpam-5714	226	7	πi	πi	PROPN
ejpam-5714	226	8	(	(	PUNCT
ejpam-5714	226	9	t	t	NOUN
ejpam-5714	226	10	)	)	PUNCT
ejpam-5714	226	11	)	)	PUNCT
ejpam-5714	227	1	n∑	n∑	PROPN
ejpam-5714	227	2	i=1	i=1	PROPN
ejpam-5714	228	1	qi	qi	PROPN
ejpam-5714	228	2	(	(	PUNCT
ejpam-5714	228	3	t	t	PROPN
ejpam-5714	228	4	)	)	PUNCT
ejpam-5714	228	5	(	(	PUNCT
ejpam-5714	228	6	1−	1−	NUM
ejpam-5714	228	7	y	y	PROPN
ejpam-5714	228	8	(	(	PUNCT
ejpam-5714	228	9	πi	πi	PROPN
ejpam-5714	228	10	(	(	PUNCT
ejpam-5714	228	11	t	t	NOUN
ejpam-5714	228	12	)	)	PUNCT
ejpam-5714	228	13	)	)	PUNCT
ejpam-5714	228	14	)	)	PUNCT
ejpam-5714	229	1	p−1	p−1	PROPN
ejpam-5714	229	2	dt	dt	X
ejpam-5714	229	3	≥	≥	PROPN
ejpam-5714	229	4	δ	δ	PROPN
ejpam-5714	229	5	,	,	PUNCT
ejpam-5714	229	6	(	(	PUNCT
ejpam-5714	229	7	17	17	NUM
ejpam-5714	229	8	)	)	PUNCT
ejpam-5714	229	9	for	for	ADP
ejpam-5714	229	10	some	some	DET
ejpam-5714	229	11	δ	δ	PROPN
ejpam-5714	229	12	>	>	X
ejpam-5714	229	13	0	0	NUM
ejpam-5714	229	14	,	,	PUNCT
ejpam-5714	229	15	and	and	CCONJ
ejpam-5714	229	16	(	(	PUNCT
ejpam-5714	229	17	1	1	X
ejpam-5714	229	18	)	)	PUNCT
ejpam-5714	229	19	has	have	VERB
ejpam-5714	229	20	an	an	DET
ejpam-5714	229	21	eventually	eventually	ADV
ejpam-5714	229	22	positive	positive	ADJ
ejpam-5714	229	23	solution	solution	NOUN
ejpam-5714	229	24	κ	κ	NOUN
ejpam-5714	229	25	.	.	PUNCT
ejpam-5714	230	1	then	then	ADV
ejpam-5714	230	2	,	,	PUNCT
ejpam-5714	230	3	h	h	PROPN
ejpam-5714	230	4	(	(	PUNCT
ejpam-5714	230	5	πi	πi	PROPN
ejpam-5714	230	6	(	(	PUNCT
ejpam-5714	230	7	t	t	NOUN
ejpam-5714	230	8	)	)	PUNCT
ejpam-5714	230	9	)	)	PUNCT
ejpam-5714	230	10	h	h	NOUN
ejpam-5714	230	11	(	(	PUNCT
ejpam-5714	230	12	t	t	PROPN
ejpam-5714	230	13	)	)	PUNCT
ejpam-5714	230	14	≥	≥	PROPN
ejpam-5714	230	15	zn	zn	PROPN
ejpam-5714	230	16	(	(	PUNCT
ejpam-5714	230	17	δ	δ	PROPN
ejpam-5714	230	18	)	)	PUNCT
ejpam-5714	230	19	,	,	PUNCT
ejpam-5714	230	20	n	n	X
ejpam-5714	230	21	≥	≥	NOUN
ejpam-5714	230	22	0	0	NUM
ejpam-5714	230	23	,	,	PUNCT
ejpam-5714	230	24	(	(	PUNCT
ejpam-5714	230	25	18	18	NUM
ejpam-5714	230	26	)	)	PUNCT
ejpam-5714	230	27	where	where	SCONJ
ejpam-5714	230	28	h	h	PROPN
ejpam-5714	230	29	(	(	PUNCT
ejpam-5714	230	30	t	t	PROPN
ejpam-5714	230	31	)	)	PUNCT
ejpam-5714	230	32	:	:	PUNCT
ejpam-5714	231	1	=	=	SYM
ejpam-5714	231	2	b	b	PROPN
ejpam-5714	231	3	(	(	PUNCT
ejpam-5714	231	4	t	t	PROPN
ejpam-5714	231	5	)	)	PUNCT
ejpam-5714	231	6	(	(	PUNCT
ejpam-5714	231	7	ϖ′	ϖ′	X
ejpam-5714	231	8	(	(	PUNCT
ejpam-5714	231	9	t))(p−1	t))(p−1	NOUN
ejpam-5714	231	10	)	)	PUNCT
ejpam-5714	231	11	,	,	PUNCT
ejpam-5714	231	12	and	and	CCONJ
ejpam-5714	231	13	z0	z0	PROPN
ejpam-5714	231	14	(	(	PUNCT
ejpam-5714	231	15	t	t	PROPN
ejpam-5714	231	16	)	)	PUNCT
ejpam-5714	231	17	:	:	PUNCT
ejpam-5714	232	1	=	=	SYM
ejpam-5714	232	2	1	1	NUM
ejpam-5714	232	3	and	and	CCONJ
ejpam-5714	232	4	zn	zn	PROPN
ejpam-5714	232	5	(	(	PUNCT
ejpam-5714	232	6	t	t	PROPN
ejpam-5714	232	7	)	)	PUNCT
ejpam-5714	232	8	:	:	PUNCT
ejpam-5714	232	9	=	=	SYM
ejpam-5714	232	10	exp	exp	X
ejpam-5714	232	11	(	(	PUNCT
ejpam-5714	232	12	ρzn−1	ρzn−1	PROPN
ejpam-5714	232	13	(	(	PUNCT
ejpam-5714	232	14	t	t	PROPN
ejpam-5714	232	15	)	)	PUNCT
ejpam-5714	232	16	)	)	PUNCT
ejpam-5714	232	17	.	.	PUNCT
ejpam-5714	233	1	(	(	PUNCT
ejpam-5714	233	2	19	19	NUM
ejpam-5714	233	3	)	)	PUNCT
ejpam-5714	233	4	proof	proof	NOUN
ejpam-5714	233	5	.	.	PUNCT
ejpam-5714	234	1	let	let	VERB
ejpam-5714	234	2	κ	κ	PROPN
ejpam-5714	234	3	(	(	PUNCT
ejpam-5714	234	4	t	t	PROPN
ejpam-5714	234	5	)	)	PUNCT
ejpam-5714	234	6	>	>	X
ejpam-5714	234	7	0	0	NUM
ejpam-5714	234	8	,	,	PUNCT
ejpam-5714	234	9	κ	κ	X
ejpam-5714	234	10	(	(	PUNCT
ejpam-5714	234	11	ζ	ζ	PROPN
ejpam-5714	234	12	(	(	PUNCT
ejpam-5714	234	13	t	t	NOUN
ejpam-5714	234	14	)	)	PUNCT
ejpam-5714	234	15	)	)	PUNCT
ejpam-5714	234	16	>	>	X
ejpam-5714	234	17	0	0	PUNCT
ejpam-5714	235	1	and	and	CCONJ
ejpam-5714	235	2	κ	κ	PROPN
ejpam-5714	235	3	(	(	PUNCT
ejpam-5714	235	4	πi	πi	PROPN
ejpam-5714	235	5	(	(	PUNCT
ejpam-5714	235	6	t	t	NOUN
ejpam-5714	235	7	)	)	PUNCT
ejpam-5714	235	8	)	)	PUNCT
ejpam-5714	236	1	>	>	X
ejpam-5714	236	2	0	0	PUNCT
ejpam-5714	237	1	for	for	ADP
ejpam-5714	237	2	t	t	PROPN
ejpam-5714	237	3	≥	≥	NUM
ejpam-5714	237	4	t1	t1	NOUN
ejpam-5714	237	5	.	.	PUNCT
ejpam-5714	238	1	we	we	PRON
ejpam-5714	238	2	conclude	conclude	VERB
ejpam-5714	238	3	that	that	SCONJ
ejpam-5714	238	4	ω	ω	PROPN
ejpam-5714	238	5	is	be	AUX
ejpam-5714	238	6	a	a	DET
ejpam-5714	238	7	positive	positive	ADJ
ejpam-5714	238	8	solution	solution	NOUN
ejpam-5714	238	9	of	of	ADP
ejpam-5714	238	10	(	(	PUNCT
ejpam-5714	238	11	14	14	NUM
ejpam-5714	238	12	)	)	PUNCT
ejpam-5714	238	13	by	by	ADP
ejpam-5714	238	14	following	follow	VERB
ejpam-5714	238	15	the	the	DET
ejpam-5714	238	16	same	same	ADJ
ejpam-5714	238	17	procedure	procedure	NOUN
ejpam-5714	238	18	as	as	ADP
ejpam-5714	238	19	in	in	ADP
ejpam-5714	238	20	the	the	DET
ejpam-5714	238	21	proof	proof	NOUN
ejpam-5714	238	22	of	of	ADP
ejpam-5714	238	23	theorem	theorem	NOUN
ejpam-5714	238	24	1	1	X
ejpam-5714	238	25	.	.	PUNCT
ejpam-5714	239	1	we	we	PRON
ejpam-5714	239	2	can	can	AUX
ejpam-5714	239	3	demonstrate	demonstrate	VERB
ejpam-5714	239	4	that	that	SCONJ
ejpam-5714	239	5	(	(	PUNCT
ejpam-5714	239	6	18	18	NUM
ejpam-5714	239	7	)	)	PUNCT
ejpam-5714	239	8	holds	hold	VERB
ejpam-5714	239	9	in	in	ADP
ejpam-5714	239	10	a	a	DET
ejpam-5714	239	11	manner	manner	NOUN
ejpam-5714	239	12	akin	akin	ADJ
ejpam-5714	239	13	to	to	ADP
ejpam-5714	239	14	that	that	PRON
ejpam-5714	239	15	used	use	VERB
ejpam-5714	239	16	in	in	ADP
ejpam-5714	239	17	the	the	DET
ejpam-5714	239	18	proof	proof	NOUN
ejpam-5714	239	19	of	of	ADP
ejpam-5714	239	20	lemma	lemma	PROPN
ejpam-5714	239	21	1	1	NUM
ejpam-5714	239	22	in	in	ADP
ejpam-5714	239	23	[	[	X
ejpam-5714	239	24	19	19	NUM
ejpam-5714	239	25	]	]	PUNCT
ejpam-5714	239	26	.	.	PUNCT
ejpam-5714	240	1	f.	f.	PROPN
ejpam-5714	240	2	aldosari	aldosari	PROPN
ejpam-5714	240	3	/	/	SYM
ejpam-5714	240	4	eur	eur	PROPN
ejpam-5714	240	5	.	.	PUNCT
ejpam-5714	241	1	j.	j.	PROPN
ejpam-5714	241	2	pure	pure	PROPN
ejpam-5714	241	3	appl	appl	PROPN
ejpam-5714	241	4	.	.	PROPN
ejpam-5714	241	5	math	math	PROPN
ejpam-5714	241	6	,	,	PUNCT
ejpam-5714	241	7	18	18	NUM
ejpam-5714	241	8	(	(	PUNCT
ejpam-5714	241	9	1	1	NUM
ejpam-5714	241	10	)	)	PUNCT
ejpam-5714	241	11	(	(	PUNCT
ejpam-5714	241	12	2025	2025	NUM
ejpam-5714	241	13	)	)	PUNCT
ejpam-5714	241	14	,	,	PUNCT
ejpam-5714	241	15	5714	5714	NUM
ejpam-5714	241	16	8	8	NUM
ejpam-5714	241	17	of	of	ADP
ejpam-5714	241	18	16	16	NUM
ejpam-5714	241	19	lemma	lemma	PROPN
ejpam-5714	241	20	6	6	NUM
ejpam-5714	241	21	.	.	PUNCT
ejpam-5714	242	1	let	let	AUX
ejpam-5714	242	2	(	(	PUNCT
ejpam-5714	242	3	1	1	X
ejpam-5714	242	4	)	)	PUNCT
ejpam-5714	242	5	have	have	VERB
ejpam-5714	242	6	a	a	DET
ejpam-5714	242	7	positive	positive	ADJ
ejpam-5714	242	8	solution	solution	NOUN
ejpam-5714	242	9	.	.	PUNCT
ejpam-5714	243	1	if	if	SCONJ
ejpam-5714	243	2	σ(t	σ(t	PROPN
ejpam-5714	243	3	)	)	PUNCT
ejpam-5714	243	4	:	:	PUNCT
ejpam-5714	243	5	=	=	SYM
ejpam-5714	243	6	ς(t)b(t	ς(t)b(t	X
ejpam-5714	243	7	)	)	PUNCT
ejpam-5714	243	8	(	(	PUNCT
ejpam-5714	243	9	ϖ′(t	ϖ′(t	NOUN
ejpam-5714	243	10	)	)	PUNCT
ejpam-5714	243	11	ϖ	ϖ	NOUN
ejpam-5714	243	12	(	(	PUNCT
ejpam-5714	243	13	πi	πi	PROPN
ejpam-5714	243	14	(	(	PUNCT
ejpam-5714	243	15	t	t	NOUN
ejpam-5714	243	16	)	)	PUNCT
ejpam-5714	243	17	)	)	PUNCT
ejpam-5714	243	18	)	)	PUNCT
ejpam-5714	244	1	p−1	p−1	PROPN
ejpam-5714	244	2	>	>	X
ejpam-5714	244	3	0	0	PROPN
ejpam-5714	244	4	,	,	PUNCT
ejpam-5714	244	5	(	(	PUNCT
ejpam-5714	244	6	20	20	NUM
ejpam-5714	244	7	)	)	PUNCT
ejpam-5714	244	8	then	then	ADV
ejpam-5714	244	9	σ′	σ′	PROPN
ejpam-5714	244	10	(	(	PUNCT
ejpam-5714	244	11	t	t	NOUN
ejpam-5714	244	12	)	)	PUNCT
ejpam-5714	244	13	≤	≤	NUM
ejpam-5714	244	14	−ς	−ς	PROPN
ejpam-5714	244	15	(	(	PUNCT
ejpam-5714	244	16	t	t	PROPN
ejpam-5714	244	17	)	)	PUNCT
ejpam-5714	244	18	n∑	n∑	PROPN
ejpam-5714	244	19	i=1	i=1	PROPN
ejpam-5714	245	1	qi	qi	PROPN
ejpam-5714	245	2	(	(	PUNCT
ejpam-5714	245	3	t	t	PROPN
ejpam-5714	245	4	)	)	PUNCT
ejpam-5714	245	5	(	(	PUNCT
ejpam-5714	245	6	1−	1−	NUM
ejpam-5714	245	7	y	y	PROPN
ejpam-5714	245	8	(	(	PUNCT
ejpam-5714	245	9	πi	πi	PROPN
ejpam-5714	245	10	(	(	PUNCT
ejpam-5714	245	11	t	t	NOUN
ejpam-5714	245	12	)	)	PUNCT
ejpam-5714	245	13	)	)	PUNCT
ejpam-5714	245	14	)	)	PUNCT
ejpam-5714	246	1	p−1	p−1	PROPN
ejpam-5714	246	2	+	+	CCONJ
ejpam-5714	246	3	ς	ς	PROPN
ejpam-5714	246	4	′+	′+	PUNCT
ejpam-5714	246	5	(	(	PUNCT
ejpam-5714	246	6	t	t	NOUN
ejpam-5714	246	7	)	)	PUNCT
ejpam-5714	246	8	ς(t	ς(t	PROPN
ejpam-5714	246	9	)	)	PUNCT
ejpam-5714	246	10	σ	σ	PROPN
ejpam-5714	246	11	(	(	PUNCT
ejpam-5714	246	12	t)−(p−	t)−(p−	PROPN
ejpam-5714	246	13	1	1	NUM
ejpam-5714	246	14	)	)	PUNCT
ejpam-5714	246	15	z	z	NOUN
ejpam-5714	246	16	1/(p−1	1/(p−1	NUM
ejpam-5714	246	17	)	)	PUNCT
ejpam-5714	246	18	n	n	CCONJ
ejpam-5714	246	19	(	(	PUNCT
ejpam-5714	246	20	δ)π′i	δ)π′i	PROPN
ejpam-5714	246	21	(	(	PUNCT
ejpam-5714	246	22	t	t	NOUN
ejpam-5714	246	23	)	)	PUNCT
ejpam-5714	246	24	(	(	PUNCT
ejpam-5714	246	25	ς	ς	PROPN
ejpam-5714	246	26	(	(	PUNCT
ejpam-5714	246	27	t	t	PROPN
ejpam-5714	246	28	)	)	PUNCT
ejpam-5714	246	29	b	b	PROPN
ejpam-5714	246	30	(	(	PUNCT
ejpam-5714	246	31	πi	πi	PROPN
ejpam-5714	246	32	(	(	PUNCT
ejpam-5714	246	33	t	t	NOUN
ejpam-5714	246	34	)	)	PUNCT
ejpam-5714	246	35	)	)	PUNCT
ejpam-5714	246	36	)	)	PUNCT
ejpam-5714	247	1	1/(p−1	1/(p−1	NUM
ejpam-5714	247	2	)	)	PUNCT
ejpam-5714	247	3	σp/(p−1	σp/(p−1	NOUN
ejpam-5714	247	4	)	)	PUNCT
ejpam-5714	247	5	(	(	PUNCT
ejpam-5714	247	6	t	t	PROPN
ejpam-5714	247	7	)	)	PUNCT
ejpam-5714	247	8	.	.	PUNCT
ejpam-5714	248	1	(	(	PUNCT
ejpam-5714	248	2	21	21	NUM
ejpam-5714	248	3	)	)	PUNCT
ejpam-5714	248	4	proof	proof	NOUN
ejpam-5714	248	5	.	.	PUNCT
ejpam-5714	249	1	let	let	VERB
ejpam-5714	249	2	κ	κ	PRON
ejpam-5714	249	3	be	be	AUX
ejpam-5714	249	4	a	a	DET
ejpam-5714	249	5	positive	positive	ADJ
ejpam-5714	249	6	solution	solution	NOUN
ejpam-5714	249	7	of	of	ADP
ejpam-5714	249	8	equation	equation	NOUN
ejpam-5714	249	9	(	(	PUNCT
ejpam-5714	249	10	1	1	NUM
ejpam-5714	249	11	)	)	PUNCT
ejpam-5714	249	12	.	.	PUNCT
ejpam-5714	250	1	from	from	ADP
ejpam-5714	250	2	lemma	lemma	PROPN
ejpam-5714	250	3	3	3	NUM
ejpam-5714	250	4	,	,	PUNCT
ejpam-5714	250	5	we	we	PRON
ejpam-5714	250	6	obtain	obtain	VERB
ejpam-5714	250	7	(	(	PUNCT
ejpam-5714	250	8	7	7	X
ejpam-5714	250	9	)	)	PUNCT
ejpam-5714	250	10	holds	hold	NOUN
ejpam-5714	250	11	.	.	PUNCT
ejpam-5714	251	1	by	by	ADP
ejpam-5714	251	2	lemma	lemma	PROPN
ejpam-5714	251	3	5	5	NUM
ejpam-5714	251	4	,	,	PUNCT
ejpam-5714	251	5	we	we	PRON
ejpam-5714	251	6	find	find	VERB
ejpam-5714	251	7	ϖ′	ϖ′	X
ejpam-5714	251	8	(	(	PUNCT
ejpam-5714	251	9	πi	πi	X
ejpam-5714	251	10	(	(	PUNCT
ejpam-5714	251	11	t	t	NOUN
ejpam-5714	251	12	)	)	PUNCT
ejpam-5714	251	13	)	)	PUNCT
ejpam-5714	251	14	ϖ′	ϖ′	NUM
ejpam-5714	251	15	(	(	PUNCT
ejpam-5714	251	16	t	t	NOUN
ejpam-5714	251	17	)	)	PUNCT
ejpam-5714	251	18	≥	≥	PROPN
ejpam-5714	251	19	(	(	PUNCT
ejpam-5714	251	20	zn	zn	PROPN
ejpam-5714	251	21	(	(	PUNCT
ejpam-5714	251	22	δ	δ	PROPN
ejpam-5714	251	23	)	)	PUNCT
ejpam-5714	251	24	b	b	PROPN
ejpam-5714	251	25	(	(	PUNCT
ejpam-5714	251	26	t	t	PROPN
ejpam-5714	251	27	)	)	PUNCT
ejpam-5714	251	28	b	b	PROPN
ejpam-5714	251	29	(	(	PUNCT
ejpam-5714	251	30	πi	πi	PROPN
ejpam-5714	251	31	(	(	PUNCT
ejpam-5714	251	32	t	t	NOUN
ejpam-5714	251	33	)	)	PUNCT
ejpam-5714	251	34	)	)	PUNCT
ejpam-5714	251	35	)	)	PUNCT
ejpam-5714	252	1	1/(p−1	1/(p−1	NUM
ejpam-5714	252	2	)	)	PUNCT
ejpam-5714	252	3	.	.	PUNCT
ejpam-5714	253	1	(	(	PUNCT
ejpam-5714	253	2	22	22	NUM
ejpam-5714	253	3	)	)	PUNCT
ejpam-5714	253	4	now	now	ADV
ejpam-5714	253	5	,	,	PUNCT
ejpam-5714	253	6	we	we	PRON
ejpam-5714	253	7	differentiate	differentiate	VERB
ejpam-5714	253	8	σ	σ	PROPN
ejpam-5714	253	9	(	(	PUNCT
ejpam-5714	253	10	t	t	PROPN
ejpam-5714	253	11	)	)	PUNCT
ejpam-5714	253	12	,	,	PUNCT
ejpam-5714	253	13	we	we	PRON
ejpam-5714	253	14	get	get	VERB
ejpam-5714	253	15	σ′(t	σ′(t	VERB
ejpam-5714	253	16	)	)	PUNCT
ejpam-5714	253	17	=	=	SYM
ejpam-5714	253	18	ς	ς	PROPN
ejpam-5714	253	19	′(t	′(t	PROPN
ejpam-5714	253	20	)	)	PUNCT
ejpam-5714	253	21	ς(t	ς(t	PROPN
ejpam-5714	253	22	)	)	PUNCT
ejpam-5714	253	23	σ(t)+ς(t	σ(t)+ς(t	PROPN
ejpam-5714	253	24	)	)	PUNCT
ejpam-5714	253	25	(	(	PUNCT
ejpam-5714	253	26	b(t)(ϖ′(t))p−1)′	b(t)(ϖ′(t))p−1)′	NOUN
ejpam-5714	253	27	ϖ(p−1	ϖ(p−1	NOUN
ejpam-5714	253	28	)	)	PUNCT
ejpam-5714	253	29	(	(	PUNCT
ejpam-5714	253	30	πi	πi	PROPN
ejpam-5714	253	31	(	(	PUNCT
ejpam-5714	253	32	t	t	NOUN
ejpam-5714	253	33	)	)	PUNCT
ejpam-5714	253	34	)	)	PUNCT
ejpam-5714	253	35	−(p−	−(p−	VERB
ejpam-5714	253	36	1	1	NUM
ejpam-5714	253	37	)	)	PUNCT
ejpam-5714	253	38	ς(t)b(t	ς(t)b(t	NOUN
ejpam-5714	253	39	)	)	PUNCT
ejpam-5714	253	40	(	(	PUNCT
ejpam-5714	254	1	ϖ′(t	ϖ′(t	NOUN
ejpam-5714	254	2	)	)	PUNCT
ejpam-5714	254	3	ϖ	ϖ	NOUN
ejpam-5714	254	4	(	(	PUNCT
ejpam-5714	254	5	πi	πi	PROPN
ejpam-5714	254	6	(	(	PUNCT
ejpam-5714	254	7	t	t	NOUN
ejpam-5714	254	8	)	)	PUNCT
ejpam-5714	254	9	)	)	PUNCT
ejpam-5714	254	10	)	)	PUNCT
ejpam-5714	255	1	(	(	PUNCT
ejpam-5714	255	2	p−1)(ϖ′	p−1)(ϖ′	NOUN
ejpam-5714	255	3	(	(	PUNCT
ejpam-5714	255	4	πi	πi	PROPN
ejpam-5714	255	5	(	(	PUNCT
ejpam-5714	255	6	t	t	NOUN
ejpam-5714	255	7	)	)	PUNCT
ejpam-5714	255	8	)	)	PUNCT
ejpam-5714	256	1	ϖ	ϖ	X
ejpam-5714	256	2	(	(	PUNCT
ejpam-5714	256	3	πi	πi	PROPN
ejpam-5714	256	4	(	(	PUNCT
ejpam-5714	256	5	t	t	NOUN
ejpam-5714	256	6	)	)	PUNCT
ejpam-5714	256	7	)	)	PUNCT
ejpam-5714	256	8	)	)	PUNCT
ejpam-5714	257	1	π′i	π′i	NOUN
ejpam-5714	257	2	(	(	PUNCT
ejpam-5714	257	3	t	t	PROPN
ejpam-5714	257	4	)	)	PUNCT
ejpam-5714	257	5	.	.	PUNCT
ejpam-5714	258	1	from	from	ADP
ejpam-5714	258	2	(	(	PUNCT
ejpam-5714	258	3	7	7	NUM
ejpam-5714	258	4	)	)	PUNCT
ejpam-5714	258	5	,	,	PUNCT
ejpam-5714	258	6	(	(	PUNCT
ejpam-5714	258	7	20	20	NUM
ejpam-5714	258	8	)	)	PUNCT
ejpam-5714	258	9	and	and	CCONJ
ejpam-5714	258	10	(	(	PUNCT
ejpam-5714	258	11	22	22	NUM
ejpam-5714	258	12	)	)	PUNCT
ejpam-5714	258	13	,	,	PUNCT
ejpam-5714	258	14	we	we	PRON
ejpam-5714	258	15	obtain	obtain	VERB
ejpam-5714	258	16	σ′	σ′	PROPN
ejpam-5714	258	17	(	(	PUNCT
ejpam-5714	258	18	t	t	NOUN
ejpam-5714	258	19	)	)	PUNCT
ejpam-5714	258	20	≤	≤	NUM
ejpam-5714	258	21	−ς	−ς	PROPN
ejpam-5714	258	22	(	(	PUNCT
ejpam-5714	258	23	t	t	PROPN
ejpam-5714	258	24	)	)	PUNCT
ejpam-5714	258	25	n∑	n∑	PROPN
ejpam-5714	258	26	i=1	i=1	PROPN
ejpam-5714	259	1	qi	qi	PROPN
ejpam-5714	259	2	(	(	PUNCT
ejpam-5714	259	3	t	t	PROPN
ejpam-5714	259	4	)	)	PUNCT
ejpam-5714	259	5	(	(	PUNCT
ejpam-5714	259	6	1−	1−	NUM
ejpam-5714	259	7	y	y	PROPN
ejpam-5714	259	8	(	(	PUNCT
ejpam-5714	259	9	πi	πi	PROPN
ejpam-5714	259	10	(	(	PUNCT
ejpam-5714	259	11	t	t	NOUN
ejpam-5714	259	12	)	)	PUNCT
ejpam-5714	259	13	)	)	PUNCT
ejpam-5714	259	14	)	)	PUNCT
ejpam-5714	260	1	p−1	p−1	PROPN
ejpam-5714	260	2	+	+	CCONJ
ejpam-5714	260	3	ς	ς	PROPN
ejpam-5714	260	4	′+	′+	PUNCT
ejpam-5714	260	5	(	(	PUNCT
ejpam-5714	260	6	t	t	NOUN
ejpam-5714	260	7	)	)	PUNCT
ejpam-5714	260	8	ς(t	ς(t	PROPN
ejpam-5714	260	9	)	)	PUNCT
ejpam-5714	260	10	σ	σ	PROPN
ejpam-5714	260	11	(	(	PUNCT
ejpam-5714	260	12	t)−(p−	t)−(p−	PROPN
ejpam-5714	260	13	1	1	NUM
ejpam-5714	260	14	)	)	PUNCT
ejpam-5714	260	15	z	z	NOUN
ejpam-5714	260	16	1/(p−1	1/(p−1	NUM
ejpam-5714	260	17	)	)	PUNCT
ejpam-5714	260	18	n	n	CCONJ
ejpam-5714	260	19	(	(	PUNCT
ejpam-5714	260	20	δ)π′i	δ)π′i	PROPN
ejpam-5714	260	21	(	(	PUNCT
ejpam-5714	260	22	t	t	NOUN
ejpam-5714	260	23	)	)	PUNCT
ejpam-5714	260	24	(	(	PUNCT
ejpam-5714	260	25	ς	ς	PROPN
ejpam-5714	260	26	(	(	PUNCT
ejpam-5714	260	27	t	t	PROPN
ejpam-5714	260	28	)	)	PUNCT
ejpam-5714	260	29	b	b	PROPN
ejpam-5714	260	30	(	(	PUNCT
ejpam-5714	260	31	πi	πi	PROPN
ejpam-5714	260	32	(	(	PUNCT
ejpam-5714	260	33	t	t	NOUN
ejpam-5714	260	34	)	)	PUNCT
ejpam-5714	260	35	)	)	PUNCT
ejpam-5714	260	36	)	)	PUNCT
ejpam-5714	261	1	1/(p−1	1/(p−1	NUM
ejpam-5714	261	2	)	)	PUNCT
ejpam-5714	261	3	σp/(p−1	σp/(p−1	NOUN
ejpam-5714	261	4	)	)	PUNCT
ejpam-5714	261	5	(	(	PUNCT
ejpam-5714	261	6	t	t	PROPN
ejpam-5714	261	7	)	)	PUNCT
ejpam-5714	261	8	.	.	PUNCT
ejpam-5714	262	1	the	the	DET
ejpam-5714	262	2	proof	proof	NOUN
ejpam-5714	262	3	is	be	AUX
ejpam-5714	262	4	complete	complete	ADJ
ejpam-5714	262	5	.	.	PUNCT
ejpam-5714	263	1	theorem	theorem	NOUN
ejpam-5714	263	2	2	2	NUM
ejpam-5714	264	1	.	.	PUNCT
ejpam-5714	264	2	suppose	suppose	VERB
ejpam-5714	264	3	πi	πi	ADP
ejpam-5714	264	4	is	be	AUX
ejpam-5714	264	5	strictly	strictly	ADV
ejpam-5714	264	6	growing	grow	VERB
ejpam-5714	264	7	in	in	ADP
ejpam-5714	264	8	relation	relation	NOUN
ejpam-5714	264	9	to	to	ADP
ejpam-5714	264	10	t	t	PROPN
ejpam-5714	264	11	and	and	CCONJ
ejpam-5714	264	12	(	(	PUNCT
ejpam-5714	264	13	17	17	NUM
ejpam-5714	264	14	)	)	PUNCT
ejpam-5714	264	15	holds	hold	VERB
ejpam-5714	264	16	.	.	PUNCT
ejpam-5714	265	1	if	if	SCONJ
ejpam-5714	265	2	ς	ς	PROPN
ejpam-5714	265	3	∈	∈	PROPN
ejpam-5714	265	4	c1(i	c1(i	NOUN
ejpam-5714	265	5	,	,	PUNCT
ejpam-5714	265	6	(	(	PUNCT
ejpam-5714	265	7	0,∞	0,∞	NOUN
ejpam-5714	265	8	)	)	PUNCT
ejpam-5714	265	9	)	)	PUNCT
ejpam-5714	266	1	such	such	ADJ
ejpam-5714	266	2	that	that	SCONJ
ejpam-5714	266	3	lim	lim	PROPN
ejpam-5714	266	4	t→∞	t→∞	PRON
ejpam-5714	266	5	sup	sup	NOUN
ejpam-5714	266	6	∫	∫	PROPN
ejpam-5714	266	7	t	t	PROPN
ejpam-5714	266	8	t1	t1	PROPN
ejpam-5714	266	9	(	(	PUNCT
ejpam-5714	266	10	ς	ς	PROPN
ejpam-5714	266	11	(	(	PUNCT
ejpam-5714	266	12	t	t	PROPN
ejpam-5714	266	13	)	)	PUNCT
ejpam-5714	266	14	n∑	n∑	PROPN
ejpam-5714	266	15	i=1	i=1	PROPN
ejpam-5714	266	16	qi	qi	PROPN
ejpam-5714	266	17	(	(	PUNCT
ejpam-5714	266	18	t	t	PROPN
ejpam-5714	266	19	)	)	PUNCT
ejpam-5714	266	20	(	(	PUNCT
ejpam-5714	266	21	1−	1−	NUM
ejpam-5714	266	22	y	y	PROPN
ejpam-5714	266	23	(	(	PUNCT
ejpam-5714	266	24	πi	πi	PROPN
ejpam-5714	266	25	(	(	PUNCT
ejpam-5714	266	26	t	t	NOUN
ejpam-5714	266	27	)	)	PUNCT
ejpam-5714	266	28	)	)	PUNCT
ejpam-5714	266	29	)	)	PUNCT
ejpam-5714	267	1	p−1	p−1	PROPN
ejpam-5714	267	2	−	−	PROPN
ejpam-5714	267	3	(	(	PUNCT
ejpam-5714	267	4	ς	ς	PROPN
ejpam-5714	267	5	′+	′+	PUNCT
ejpam-5714	267	6	(	(	PUNCT
ejpam-5714	267	7	t	t	PROPN
ejpam-5714	267	8	)	)	PUNCT
ejpam-5714	267	9	)	)	PUNCT
ejpam-5714	268	1	p	p	NOUN
ejpam-5714	268	2	b	b	PROPN
ejpam-5714	268	3	(	(	PUNCT
ejpam-5714	268	4	πi	πi	PROPN
ejpam-5714	268	5	(	(	PUNCT
ejpam-5714	268	6	t	t	NOUN
ejpam-5714	268	7	)	)	PUNCT
ejpam-5714	268	8	)	)	PUNCT
ejpam-5714	268	9	ppzn	ppzn	NOUN
ejpam-5714	268	10	(	(	PUNCT
ejpam-5714	268	11	δ	δ	PROPN
ejpam-5714	268	12	)	)	PUNCT
ejpam-5714	268	13	ς(p−1	ς(p−1	NOUN
ejpam-5714	268	14	)	)	PUNCT
ejpam-5714	268	15	(	(	PUNCT
ejpam-5714	268	16	t	t	NOUN
ejpam-5714	268	17	)	)	PUNCT
ejpam-5714	268	18	(	(	PUNCT
ejpam-5714	268	19	π′i(t	π′i(t	NOUN
ejpam-5714	268	20	)	)	PUNCT
ejpam-5714	268	21	)	)	PUNCT
ejpam-5714	269	1	p−1	p−1	NOUN
ejpam-5714	269	2	)	)	PUNCT
ejpam-5714	270	1	=	=	PUNCT
ejpam-5714	270	2	∞	∞	PROPN
ejpam-5714	270	3	,	,	PUNCT
ejpam-5714	270	4	(	(	PUNCT
ejpam-5714	270	5	23	23	NUM
ejpam-5714	270	6	)	)	PUNCT
ejpam-5714	270	7	for	for	ADP
ejpam-5714	270	8	some	some	DET
ejpam-5714	270	9	δ	δ	PROPN
ejpam-5714	270	10	<	<	X
ejpam-5714	270	11	0	0	PUNCT
ejpam-5714	270	12	and	and	CCONJ
ejpam-5714	270	13	n	n	PRON
ejpam-5714	270	14	≥	≥	NOUN
ejpam-5714	270	15	0	0	NUM
ejpam-5714	270	16	,	,	PUNCT
ejpam-5714	270	17	where	where	SCONJ
ejpam-5714	270	18	ς	ς	PROPN
ejpam-5714	270	19	′+(t	′+(t	PROPN
ejpam-5714	270	20	)	)	PUNCT
ejpam-5714	270	21	=	=	SYM
ejpam-5714	270	22	max	max	PROPN
ejpam-5714	270	23	{	{	PUNCT
ejpam-5714	270	24	0	0	NUM
ejpam-5714	270	25	,	,	PUNCT
ejpam-5714	270	26	ς	ς	PROPN
ejpam-5714	270	27	′(t	′(t	NOUN
ejpam-5714	270	28	)	)	PUNCT
ejpam-5714	270	29	}	}	PUNCT
ejpam-5714	270	30	and	and	CCONJ
ejpam-5714	270	31	zn(δ	zn(δ	NUM
ejpam-5714	270	32	)	)	PUNCT
ejpam-5714	270	33	is	be	AUX
ejpam-5714	270	34	defined	define	VERB
ejpam-5714	270	35	as	as	ADP
ejpam-5714	270	36	(	(	PUNCT
ejpam-5714	270	37	19	19	NUM
ejpam-5714	270	38	)	)	PUNCT
ejpam-5714	270	39	,	,	PUNCT
ejpam-5714	270	40	then	then	ADV
ejpam-5714	270	41	all	all	DET
ejpam-5714	270	42	solutions	solution	NOUN
ejpam-5714	270	43	of	of	ADP
ejpam-5714	270	44	(	(	PUNCT
ejpam-5714	270	45	1	1	X
ejpam-5714	270	46	)	)	PUNCT
ejpam-5714	270	47	is	be	AUX
ejpam-5714	270	48	oscillatory	oscillatory	ADJ
ejpam-5714	270	49	.	.	PUNCT
ejpam-5714	271	1	proof	proof	NOUN
ejpam-5714	271	2	.	.	PUNCT
ejpam-5714	272	1	suppose	suppose	VERB
ejpam-5714	272	2	κ	κ	X
ejpam-5714	272	3	(	(	PUNCT
ejpam-5714	272	4	t	t	PROPN
ejpam-5714	272	5	)	)	PUNCT
ejpam-5714	272	6	>	>	X
ejpam-5714	272	7	0	0	NUM
ejpam-5714	272	8	,	,	PUNCT
ejpam-5714	272	9	κ	κ	X
ejpam-5714	272	10	(	(	PUNCT
ejpam-5714	272	11	ζ	ζ	PROPN
ejpam-5714	272	12	(	(	PUNCT
ejpam-5714	272	13	t	t	NOUN
ejpam-5714	272	14	)	)	PUNCT
ejpam-5714	272	15	)	)	PUNCT
ejpam-5714	272	16	>	>	X
ejpam-5714	272	17	0	0	PUNCT
ejpam-5714	273	1	and	and	CCONJ
ejpam-5714	273	2	κ	κ	PROPN
ejpam-5714	273	3	(	(	PUNCT
ejpam-5714	273	4	πi	πi	PROPN
ejpam-5714	273	5	(	(	PUNCT
ejpam-5714	273	6	t	t	NOUN
ejpam-5714	273	7	)	)	PUNCT
ejpam-5714	273	8	)	)	PUNCT
ejpam-5714	274	1	>	>	X
ejpam-5714	274	2	0	0	X
ejpam-5714	274	3	.	.	PUNCT
ejpam-5714	275	1	from	from	ADP
ejpam-5714	275	2	lemma	lemma	PROPN
ejpam-5714	275	3	6	6	NUM
ejpam-5714	275	4	,	,	PUNCT
ejpam-5714	275	5	we	we	PRON
ejpam-5714	275	6	have	have	AUX
ejpam-5714	275	7	(	(	PUNCT
ejpam-5714	275	8	21	21	NUM
ejpam-5714	275	9	)	)	PUNCT
ejpam-5714	275	10	holds	hold	VERB
ejpam-5714	275	11	.	.	PUNCT
ejpam-5714	276	1	using	use	VERB
ejpam-5714	276	2	lemma	lemma	PROPN
ejpam-5714	276	3	2	2	NUM
ejpam-5714	276	4	with	with	ADP
ejpam-5714	276	5	w	w	NOUN
ejpam-5714	276	6	=	=	PUNCT
ejpam-5714	276	7	(	(	PUNCT
ejpam-5714	276	8	p−	p−	NOUN
ejpam-5714	276	9	1	1	NUM
ejpam-5714	276	10	)	)	PUNCT
ejpam-5714	276	11	z	z	NOUN
ejpam-5714	276	12	1/(p−1	1/(p−1	NUM
ejpam-5714	276	13	)	)	PUNCT
ejpam-5714	276	14	n	n	PROPN
ejpam-5714	276	15	(	(	PUNCT
ejpam-5714	276	16	δ	δ	NOUN
ejpam-5714	276	17	)	)	PUNCT
ejpam-5714	276	18	/	/	PUNCT
ejpam-5714	276	19	(	(	PUNCT
ejpam-5714	276	20	ς	ς	PROPN
ejpam-5714	276	21	(	(	PUNCT
ejpam-5714	276	22	t	t	PROPN
ejpam-5714	276	23	)	)	PUNCT
ejpam-5714	276	24	b	b	PROPN
ejpam-5714	276	25	(	(	PUNCT
ejpam-5714	276	26	πi	πi	PROPN
ejpam-5714	276	27	(	(	PUNCT
ejpam-5714	276	28	t	t	NOUN
ejpam-5714	276	29	)	)	PUNCT
ejpam-5714	276	30	)	)	PUNCT
ejpam-5714	276	31	)	)	PUNCT
ejpam-5714	277	1	−1/(p−1	−1/(p−1	NOUN
ejpam-5714	277	2	)	)	PUNCT
ejpam-5714	277	3	and	and	CCONJ
ejpam-5714	277	4	g	g	NOUN
ejpam-5714	277	5	=	=	SYM
ejpam-5714	277	6	ς	ς	PROPN
ejpam-5714	277	7	′+	′+	PUNCT
ejpam-5714	277	8	(	(	PUNCT
ejpam-5714	277	9	t	t	NOUN
ejpam-5714	277	10	)	)	PUNCT
ejpam-5714	277	11	/ς	/ς	PUNCT
ejpam-5714	277	12	(	(	PUNCT
ejpam-5714	277	13	t	t	NOUN
ejpam-5714	277	14	)	)	PUNCT
ejpam-5714	277	15	,	,	PUNCT
ejpam-5714	277	16	(	(	PUNCT
ejpam-5714	277	17	21	21	NUM
ejpam-5714	277	18	)	)	PUNCT
ejpam-5714	277	19	yield	yield	NOUN
ejpam-5714	277	20	σ′	σ′	PROPN
ejpam-5714	277	21	(	(	PUNCT
ejpam-5714	277	22	t	t	NOUN
ejpam-5714	277	23	)	)	PUNCT
ejpam-5714	277	24	≤	≤	NUM
ejpam-5714	278	1	−ς	−ς	PROPN
ejpam-5714	278	2	(	(	PUNCT
ejpam-5714	278	3	t	t	PROPN
ejpam-5714	278	4	)	)	PUNCT
ejpam-5714	278	5	n∑	n∑	PROPN
ejpam-5714	278	6	i=1	i=1	PROPN
ejpam-5714	279	1	qi	qi	PROPN
ejpam-5714	279	2	(	(	PUNCT
ejpam-5714	279	3	t	t	PROPN
ejpam-5714	279	4	)	)	PUNCT
ejpam-5714	279	5	(	(	PUNCT
ejpam-5714	279	6	1−	1−	NUM
ejpam-5714	279	7	y	y	PROPN
ejpam-5714	279	8	(	(	PUNCT
ejpam-5714	279	9	πi	πi	PROPN
ejpam-5714	279	10	(	(	PUNCT
ejpam-5714	279	11	t	t	NOUN
ejpam-5714	279	12	)	)	PUNCT
ejpam-5714	279	13	)	)	PUNCT
ejpam-5714	279	14	)	)	PUNCT
ejpam-5714	280	1	(	(	PUNCT
ejpam-5714	280	2	p−1	p−1	PROPN
ejpam-5714	280	3	)	)	PUNCT
ejpam-5714	281	1	+	+	NUM
ejpam-5714	281	2	ς	ς	PROPN
ejpam-5714	281	3	′+	′+	PUNCT
ejpam-5714	281	4	(	(	PUNCT
ejpam-5714	281	5	t)p	t)p	X
ejpam-5714	281	6	b	b	NOUN
ejpam-5714	281	7	(	(	PUNCT
ejpam-5714	281	8	πi	πi	PROPN
ejpam-5714	281	9	(	(	PUNCT
ejpam-5714	281	10	t	t	NOUN
ejpam-5714	281	11	)	)	PUNCT
ejpam-5714	281	12	)	)	PUNCT
ejpam-5714	281	13	ppzn	ppzn	NOUN
ejpam-5714	281	14	(	(	PUNCT
ejpam-5714	281	15	δ	δ	PROPN
ejpam-5714	281	16	)	)	PUNCT
ejpam-5714	281	17	ςp−1	ςp−1	PROPN
ejpam-5714	281	18	(	(	PUNCT
ejpam-5714	281	19	t	t	NOUN
ejpam-5714	281	20	)	)	PUNCT
ejpam-5714	281	21	(	(	PUNCT
ejpam-5714	281	22	π′i	π′i	NOUN
ejpam-5714	281	23	(	(	PUNCT
ejpam-5714	281	24	t	t	NOUN
ejpam-5714	281	25	)	)	PUNCT
ejpam-5714	281	26	)	)	PUNCT
ejpam-5714	282	1	p−1	p−1	PROPN
ejpam-5714	282	2	.	.	PUNCT
ejpam-5714	283	1	f.	f.	PROPN
ejpam-5714	283	2	aldosari	aldosari	PROPN
ejpam-5714	283	3	/	/	SYM
ejpam-5714	283	4	eur	eur	PROPN
ejpam-5714	283	5	.	.	PUNCT
ejpam-5714	284	1	j.	j.	PROPN
ejpam-5714	284	2	pure	pure	PROPN
ejpam-5714	284	3	appl	appl	PROPN
ejpam-5714	284	4	.	.	PROPN
ejpam-5714	284	5	math	math	PROPN
ejpam-5714	284	6	,	,	PUNCT
ejpam-5714	284	7	18	18	NUM
ejpam-5714	284	8	(	(	PUNCT
ejpam-5714	284	9	1	1	NUM
ejpam-5714	284	10	)	)	PUNCT
ejpam-5714	284	11	(	(	PUNCT
ejpam-5714	284	12	2025	2025	NUM
ejpam-5714	284	13	)	)	PUNCT
ejpam-5714	284	14	,	,	PUNCT
ejpam-5714	284	15	5714	5714	NUM
ejpam-5714	284	16	9	9	NUM
ejpam-5714	284	17	of	of	ADP
ejpam-5714	284	18	16	16	NUM
ejpam-5714	284	19	integrating	integrate	VERB
ejpam-5714	284	20	this	this	DET
ejpam-5714	284	21	inequality	inequality	NOUN
ejpam-5714	284	22	from	from	ADP
ejpam-5714	284	23	t1	t1	PROPN
ejpam-5714	284	24	to	to	ADP
ejpam-5714	284	25	t	t	PROPN
ejpam-5714	284	26	,	,	PUNCT
ejpam-5714	284	27	we	we	PRON
ejpam-5714	284	28	find∫	find∫	VERB
ejpam-5714	284	29	t	t	PROPN
ejpam-5714	284	30	t1	t1	NOUN
ejpam-5714	284	31	(	(	PUNCT
ejpam-5714	284	32	ς	ς	PROPN
ejpam-5714	284	33	(	(	PUNCT
ejpam-5714	284	34	t	t	PROPN
ejpam-5714	284	35	)	)	PUNCT
ejpam-5714	284	36	n∑	n∑	PROPN
ejpam-5714	284	37	i=1	i=1	PROPN
ejpam-5714	285	1	qi	qi	PROPN
ejpam-5714	285	2	(	(	PUNCT
ejpam-5714	285	3	t	t	PROPN
ejpam-5714	285	4	)	)	PUNCT
ejpam-5714	285	5	(	(	PUNCT
ejpam-5714	285	6	1−	1−	NUM
ejpam-5714	285	7	y	y	PROPN
ejpam-5714	285	8	(	(	PUNCT
ejpam-5714	285	9	πi	πi	PROPN
ejpam-5714	285	10	(	(	PUNCT
ejpam-5714	285	11	t	t	NOUN
ejpam-5714	285	12	)	)	PUNCT
ejpam-5714	285	13	)	)	PUNCT
ejpam-5714	285	14	)	)	PUNCT
ejpam-5714	286	1	(	(	PUNCT
ejpam-5714	286	2	p−1	p−1	PROPN
ejpam-5714	286	3	)	)	PUNCT
ejpam-5714	286	4	−	−	PROPN
ejpam-5714	287	1	(	(	PUNCT
ejpam-5714	287	2	ς	ς	PROPN
ejpam-5714	287	3	′+	′+	PUNCT
ejpam-5714	287	4	(	(	PUNCT
ejpam-5714	287	5	t	t	PROPN
ejpam-5714	287	6	)	)	PUNCT
ejpam-5714	287	7	)	)	PUNCT
ejpam-5714	288	1	p	p	NOUN
ejpam-5714	288	2	b	b	PROPN
ejpam-5714	288	3	(	(	PUNCT
ejpam-5714	288	4	πi	πi	PROPN
ejpam-5714	288	5	(	(	PUNCT
ejpam-5714	288	6	t	t	NOUN
ejpam-5714	288	7	)	)	PUNCT
ejpam-5714	288	8	)	)	PUNCT
ejpam-5714	288	9	ppzn	ppzn	NOUN
ejpam-5714	288	10	(	(	PUNCT
ejpam-5714	288	11	δ	δ	PROPN
ejpam-5714	288	12	)	)	PUNCT
ejpam-5714	288	13	ςp−1	ςp−1	PROPN
ejpam-5714	288	14	(	(	PUNCT
ejpam-5714	288	15	t	t	NOUN
ejpam-5714	288	16	)	)	PUNCT
ejpam-5714	288	17	(	(	PUNCT
ejpam-5714	288	18	π′i	π′i	NOUN
ejpam-5714	288	19	(	(	PUNCT
ejpam-5714	288	20	t	t	NOUN
ejpam-5714	288	21	)	)	PUNCT
ejpam-5714	288	22	)	)	PUNCT
ejpam-5714	288	23	p−1	p−1	PROPN
ejpam-5714	288	24	)	)	PUNCT
ejpam-5714	289	1	dt	dt	PROPN
ejpam-5714	289	2	≤	≤	PROPN
ejpam-5714	289	3	σ	σ	PROPN
ejpam-5714	289	4	(	(	PUNCT
ejpam-5714	289	5	t	t	PROPN
ejpam-5714	289	6	)	)	PUNCT
ejpam-5714	289	7	.	.	PUNCT
ejpam-5714	290	1	a	a	DET
ejpam-5714	290	2	contradiction	contradiction	NOUN
ejpam-5714	290	3	with	with	ADP
ejpam-5714	290	4	condition	condition	NOUN
ejpam-5714	290	5	(	(	PUNCT
ejpam-5714	290	6	23	23	NUM
ejpam-5714	290	7	)	)	PUNCT
ejpam-5714	290	8	is	be	AUX
ejpam-5714	290	9	then	then	ADV
ejpam-5714	290	10	discovered	discover	VERB
ejpam-5714	290	11	.	.	PUNCT
ejpam-5714	291	1	the	the	DET
ejpam-5714	291	2	proof	proof	NOUN
ejpam-5714	291	3	is	be	AUX
ejpam-5714	291	4	finished	finish	VERB
ejpam-5714	291	5	.	.	PUNCT
ejpam-5714	292	1	theorem	theorem	NOUN
ejpam-5714	292	2	3	3	X
ejpam-5714	292	3	.	.	PUNCT
ejpam-5714	293	1	if	if	SCONJ
ejpam-5714	293	2	lim	lim	PROPN
ejpam-5714	293	3	t→∞	t→∞	DET
ejpam-5714	293	4	sup	sup	NOUN
ejpam-5714	293	5	∫	∫	PROPN
ejpam-5714	293	6	t	t	PROPN
ejpam-5714	293	7	t1	t1	PROPN
ejpam-5714	293	8	(	(	PUNCT
ejpam-5714	293	9	x	x	X
ejpam-5714	293	10	(	(	PUNCT
ejpam-5714	293	11	t	t	PROPN
ejpam-5714	293	12	)	)	PUNCT
ejpam-5714	293	13	n∑	n∑	PROPN
ejpam-5714	293	14	i=1	i=1	PROPN
ejpam-5714	294	1	qi	qi	PROPN
ejpam-5714	294	2	(	(	PUNCT
ejpam-5714	294	3	t	t	PROPN
ejpam-5714	294	4	)	)	PUNCT
ejpam-5714	294	5	(	(	PUNCT
ejpam-5714	294	6	1−	1−	NUM
ejpam-5714	294	7	y	y	PROPN
ejpam-5714	294	8	(	(	PUNCT
ejpam-5714	294	9	πi	πi	PROPN
ejpam-5714	294	10	(	(	PUNCT
ejpam-5714	294	11	t	t	NOUN
ejpam-5714	294	12	)	)	PUNCT
ejpam-5714	294	13	)	)	PUNCT
ejpam-5714	294	14	)	)	PUNCT
ejpam-5714	294	15	p−1	p−1	NOUN
ejpam-5714	294	16	b̂	b̂	NOUN
ejpam-5714	295	1	(	(	PUNCT
ejpam-5714	295	2	t)−	t)−	PROPN
ejpam-5714	295	3	b	b	PROPN
ejpam-5714	295	4	(	(	PUNCT
ejpam-5714	295	5	t	t	PROPN
ejpam-5714	295	6	)	)	PUNCT
ejpam-5714	295	7	(	(	PUNCT
ejpam-5714	295	8	x′+	x′+	X
ejpam-5714	295	9	(	(	PUNCT
ejpam-5714	295	10	t	t	PROPN
ejpam-5714	295	11	)	)	PUNCT
ejpam-5714	295	12	)	)	PUNCT
ejpam-5714	296	1	p	p	NOUN
ejpam-5714	296	2	ppxp−1	ppxp−1	PROPN
ejpam-5714	296	3	(	(	PUNCT
ejpam-5714	296	4	t	t	PROPN
ejpam-5714	296	5	)	)	PUNCT
ejpam-5714	296	6	)	)	PUNCT
ejpam-5714	297	1	dt	dt	X
ejpam-5714	298	1	=	=	SYM
ejpam-5714	298	2	∞	∞	PROPN
ejpam-5714	298	3	,	,	PUNCT
ejpam-5714	298	4	(	(	PUNCT
ejpam-5714	298	5	24	24	NUM
ejpam-5714	298	6	)	)	PUNCT
ejpam-5714	298	7	where	where	SCONJ
ejpam-5714	298	8	x	x	SYM
ejpam-5714	298	9	∈	∈	PROPN
ejpam-5714	298	10	c1	c1	NOUN
ejpam-5714	298	11	(	(	PUNCT
ejpam-5714	298	12	i	i	PROPN
ejpam-5714	298	13	,	,	PUNCT
ejpam-5714	298	14	(	(	PUNCT
ejpam-5714	298	15	0,∞	0,∞	NOUN
ejpam-5714	298	16	)	)	PUNCT
ejpam-5714	298	17	)	)	PUNCT
ejpam-5714	298	18	and	and	CCONJ
ejpam-5714	298	19	x′+	x′+	PROPN
ejpam-5714	298	20	(	(	PUNCT
ejpam-5714	298	21	t	t	PROPN
ejpam-5714	298	22	)	)	PUNCT
ejpam-5714	298	23	=	=	SYM
ejpam-5714	298	24	max	max	PROPN
ejpam-5714	298	25	{	{	PUNCT
ejpam-5714	298	26	0	0	NUM
ejpam-5714	298	27	,	,	PUNCT
ejpam-5714	298	28	ψ′	ψ′	PUNCT
ejpam-5714	298	29	(	(	PUNCT
ejpam-5714	298	30	t	t	NOUN
ejpam-5714	298	31	)	)	PUNCT
ejpam-5714	298	32	}	}	PUNCT
ejpam-5714	298	33	,	,	PUNCT
ejpam-5714	298	34	then	then	ADV
ejpam-5714	298	35	(	(	PUNCT
ejpam-5714	298	36	1	1	X
ejpam-5714	298	37	)	)	PUNCT
ejpam-5714	298	38	is	be	AUX
ejpam-5714	298	39	oscillatory	oscillatory	ADJ
ejpam-5714	298	40	.	.	PUNCT
ejpam-5714	299	1	proof	proof	NOUN
ejpam-5714	299	2	.	.	PUNCT
ejpam-5714	300	1	let	let	VERB
ejpam-5714	300	2	κ	κ	PROPN
ejpam-5714	300	3	(	(	PUNCT
ejpam-5714	300	4	t	t	PROPN
ejpam-5714	300	5	)	)	PUNCT
ejpam-5714	300	6	>	>	X
ejpam-5714	300	7	0	0	NUM
ejpam-5714	300	8	,	,	PUNCT
ejpam-5714	300	9	that	that	PRON
ejpam-5714	300	10	is	be	AUX
ejpam-5714	300	11	κ	κ	NOUN
ejpam-5714	300	12	(	(	PUNCT
ejpam-5714	300	13	ζ	ζ	X
ejpam-5714	300	14	(	(	PUNCT
ejpam-5714	300	15	t	t	NOUN
ejpam-5714	300	16	)	)	PUNCT
ejpam-5714	300	17	)	)	PUNCT
ejpam-5714	300	18	and	and	CCONJ
ejpam-5714	300	19	κ	κ	X
ejpam-5714	300	20	(	(	PUNCT
ejpam-5714	300	21	πi	πi	PROPN
ejpam-5714	300	22	(	(	PUNCT
ejpam-5714	300	23	t	t	NOUN
ejpam-5714	300	24	)	)	PUNCT
ejpam-5714	300	25	)	)	PUNCT
ejpam-5714	300	26	are	be	AUX
ejpam-5714	300	27	positive	positive	ADJ
ejpam-5714	300	28	on	on	ADP
ejpam-5714	300	29	[	[	X
ejpam-5714	300	30	t0,∞	t0,∞	NUM
ejpam-5714	300	31	)	)	PUNCT
ejpam-5714	300	32	.	.	PUNCT
ejpam-5714	301	1	from	from	ADP
ejpam-5714	301	2	lemma	lemma	PROPN
ejpam-5714	301	3	3	3	NUM
ejpam-5714	301	4	,	,	PUNCT
ejpam-5714	301	5	we	we	PRON
ejpam-5714	301	6	have	have	VERB
ejpam-5714	301	7	(	(	PUNCT
ejpam-5714	301	8	7)-(9	7)-(9	NOUN
ejpam-5714	301	9	)	)	PUNCT
ejpam-5714	301	10	hold	hold	NOUN
ejpam-5714	301	11	.	.	PUNCT
ejpam-5714	302	1	next	next	ADV
ejpam-5714	302	2	,	,	PUNCT
ejpam-5714	302	3	we	we	PRON
ejpam-5714	302	4	arrive	arrive	VERB
ejpam-5714	302	5	at	at	ADP
ejpam-5714	302	6	(	(	PUNCT
ejpam-5714	302	7	13	13	NUM
ejpam-5714	302	8	)	)	PUNCT
ejpam-5714	302	9	using	use	VERB
ejpam-5714	302	10	lemma	lemma	PROPN
ejpam-5714	302	11	2	2	NUM
ejpam-5714	302	12	with	with	ADP
ejpam-5714	302	13	g	g	PROPN
ejpam-5714	302	14	=	=	SYM
ejpam-5714	302	15	x′+	x′+	PROPN
ejpam-5714	302	16	(	(	PUNCT
ejpam-5714	302	17	t	t	PROPN
ejpam-5714	302	18	)	)	PUNCT
ejpam-5714	302	19	/x	/x	PUNCT
ejpam-5714	303	1	(	(	PUNCT
ejpam-5714	303	2	t	t	NOUN
ejpam-5714	303	3	)	)	PUNCT
ejpam-5714	303	4	and	and	CCONJ
ejpam-5714	303	5	w	w	NOUN
ejpam-5714	303	6	=	=	PUNCT
ejpam-5714	303	7	(	(	PUNCT
ejpam-5714	303	8	p−	p−	NOUN
ejpam-5714	303	9	1	1	NUM
ejpam-5714	303	10	)	)	PUNCT
ejpam-5714	303	11	(	(	PUNCT
ejpam-5714	303	12	x	x	X
ejpam-5714	303	13	(	(	PUNCT
ejpam-5714	303	14	t	t	PROPN
ejpam-5714	303	15	)	)	PUNCT
ejpam-5714	303	16	b	b	PROPN
ejpam-5714	303	17	(	(	PUNCT
ejpam-5714	303	18	t))−1/(p−1	t))−1/(p−1	NOUN
ejpam-5714	303	19	)	)	PUNCT
ejpam-5714	303	20	(	(	PUNCT
ejpam-5714	303	21	lemma	lemma	PROPN
ejpam-5714	303	22	4	4	NUM
ejpam-5714	303	23	)	)	PUNCT
ejpam-5714	303	24	,	,	PUNCT
ejpam-5714	303	25	the	the	DET
ejpam-5714	303	26	inequality(13	inequality(13	NOUN
ejpam-5714	303	27	)	)	PUNCT
ejpam-5714	303	28	becomes	become	VERB
ejpam-5714	303	29	ξ′	ξ′	NOUN
ejpam-5714	303	30	(	(	PUNCT
ejpam-5714	303	31	t	t	NOUN
ejpam-5714	303	32	)	)	PUNCT
ejpam-5714	303	33	≤	≤	NOUN
ejpam-5714	303	34	−x(t	−x(t	PROPN
ejpam-5714	303	35	)	)	PUNCT
ejpam-5714	304	1	n∑	n∑	PROPN
ejpam-5714	304	2	i=1	i=1	PROPN
ejpam-5714	305	1	qi	qi	PROPN
ejpam-5714	305	2	(	(	PUNCT
ejpam-5714	305	3	t	t	PROPN
ejpam-5714	305	4	)	)	PUNCT
ejpam-5714	305	5	(	(	PUNCT
ejpam-5714	305	6	1−	1−	NUM
ejpam-5714	305	7	y	y	PROPN
ejpam-5714	305	8	(	(	PUNCT
ejpam-5714	305	9	πi	πi	PROPN
ejpam-5714	305	10	(	(	PUNCT
ejpam-5714	305	11	t	t	NOUN
ejpam-5714	305	12	)	)	PUNCT
ejpam-5714	305	13	)	)	PUNCT
ejpam-5714	305	14	)	)	PUNCT
ejpam-5714	305	15	p−1	p−1	NOUN
ejpam-5714	305	16	b̂	b̂	NOUN
ejpam-5714	305	17	(	(	PUNCT
ejpam-5714	305	18	t	t	PROPN
ejpam-5714	305	19	)	)	PUNCT
ejpam-5714	306	1	+	+	SYM
ejpam-5714	306	2	b	b	X
ejpam-5714	306	3	(	(	PUNCT
ejpam-5714	306	4	t	t	PROPN
ejpam-5714	306	5	)	)	PUNCT
ejpam-5714	306	6	(	(	PUNCT
ejpam-5714	306	7	x′+	x′+	X
ejpam-5714	306	8	(	(	PUNCT
ejpam-5714	306	9	t	t	PROPN
ejpam-5714	306	10	)	)	PUNCT
ejpam-5714	306	11	)	)	PUNCT
ejpam-5714	307	1	p	p	NOUN
ejpam-5714	307	2	ppxp−1	ppxp−1	PROPN
ejpam-5714	307	3	(	(	PUNCT
ejpam-5714	307	4	t	t	PROPN
ejpam-5714	307	5	)	)	PUNCT
ejpam-5714	307	6	.	.	PUNCT
ejpam-5714	308	1	integrating	integrate	VERB
ejpam-5714	308	2	this	this	DET
ejpam-5714	308	3	inequality	inequality	NOUN
ejpam-5714	308	4	from	from	ADP
ejpam-5714	308	5	t1	t1	PROPN
ejpam-5714	308	6	to	to	ADP
ejpam-5714	308	7	t	t	PROPN
ejpam-5714	308	8	,	,	PUNCT
ejpam-5714	308	9	we	we	PRON
ejpam-5714	308	10	have∫	have∫	VERB
ejpam-5714	308	11	t	t	PROPN
ejpam-5714	308	12	t1	t1	NOUN
ejpam-5714	308	13	(	(	PUNCT
ejpam-5714	308	14	x	x	X
ejpam-5714	308	15	(	(	PUNCT
ejpam-5714	308	16	t	t	PROPN
ejpam-5714	308	17	)	)	PUNCT
ejpam-5714	308	18	n∑	n∑	PROPN
ejpam-5714	308	19	i=1	i=1	PROPN
ejpam-5714	309	1	qi	qi	PROPN
ejpam-5714	309	2	(	(	PUNCT
ejpam-5714	309	3	t	t	PROPN
ejpam-5714	309	4	)	)	PUNCT
ejpam-5714	309	5	(	(	PUNCT
ejpam-5714	309	6	1−	1−	NUM
ejpam-5714	309	7	y	y	PROPN
ejpam-5714	309	8	(	(	PUNCT
ejpam-5714	309	9	πi	πi	PROPN
ejpam-5714	309	10	(	(	PUNCT
ejpam-5714	309	11	t	t	NOUN
ejpam-5714	309	12	)	)	PUNCT
ejpam-5714	309	13	)	)	PUNCT
ejpam-5714	309	14	)	)	PUNCT
ejpam-5714	309	15	p−1	p−1	NOUN
ejpam-5714	309	16	b̂	b̂	NOUN
ejpam-5714	310	1	(	(	PUNCT
ejpam-5714	310	2	t)−	t)−	PROPN
ejpam-5714	310	3	b	b	PROPN
ejpam-5714	310	4	(	(	PUNCT
ejpam-5714	310	5	t	t	PROPN
ejpam-5714	310	6	)	)	PUNCT
ejpam-5714	310	7	(	(	PUNCT
ejpam-5714	310	8	x′+	x′+	X
ejpam-5714	310	9	(	(	PUNCT
ejpam-5714	310	10	t)p	t)p	X
ejpam-5714	310	11	)	)	PUNCT
ejpam-5714	310	12	ppxp−1	ppxp−1	PROPN
ejpam-5714	310	13	(	(	PUNCT
ejpam-5714	310	14	t	t	PROPN
ejpam-5714	310	15	)	)	PUNCT
ejpam-5714	310	16	)	)	PUNCT
ejpam-5714	310	17	dt	dt	X
ejpam-5714	310	18	≤	≤	PROPN
ejpam-5714	310	19	ξ	ξ	X
ejpam-5714	310	20	(	(	PUNCT
ejpam-5714	310	21	t	t	PROPN
ejpam-5714	310	22	)	)	PUNCT
ejpam-5714	310	23	.	.	PUNCT
ejpam-5714	311	1	this	this	PRON
ejpam-5714	311	2	contradicts	contradict	VERB
ejpam-5714	311	3	the	the	DET
ejpam-5714	311	4	condition	condition	NOUN
ejpam-5714	311	5	(	(	PUNCT
ejpam-5714	311	6	24	24	NUM
ejpam-5714	311	7	)	)	PUNCT
ejpam-5714	311	8	.	.	PUNCT
ejpam-5714	312	1	the	the	DET
ejpam-5714	312	2	proof	proof	NOUN
ejpam-5714	312	3	is	be	AUX
ejpam-5714	312	4	finished	finish	VERB
ejpam-5714	312	5	.	.	PUNCT
ejpam-5714	313	1	now	now	ADV
ejpam-5714	313	2	,	,	PUNCT
ejpam-5714	313	3	we	we	PRON
ejpam-5714	313	4	obtain	obtain	VERB
ejpam-5714	313	5	some	some	DET
ejpam-5714	313	6	oscillation	oscillation	NOUN
ejpam-5714	313	7	results	result	NOUN
ejpam-5714	313	8	for	for	ADP
ejpam-5714	313	9	equation	equation	NOUN
ejpam-5714	313	10	(	(	PUNCT
ejpam-5714	313	11	1	1	X
ejpam-5714	313	12	)	)	PUNCT
ejpam-5714	313	13	using	use	VERB
ejpam-5714	313	14	other	other	ADJ
ejpam-5714	313	15	methods	method	NOUN
ejpam-5714	313	16	.	.	PUNCT
ejpam-5714	314	1	theorem	theorem	NOUN
ejpam-5714	314	2	4	4	NUM
ejpam-5714	314	3	.	.	PUNCT
ejpam-5714	315	1	let	let	VERB
ejpam-5714	315	2	∫	∫	PROPN
ejpam-5714	315	3	∞	∞	PROPN
ejpam-5714	315	4	t0	t0	PROPN
ejpam-5714	315	5	n∑	n∑	PROPN
ejpam-5714	315	6	i=1	i=1	PROPN
ejpam-5714	316	1	qi	qi	PROPN
ejpam-5714	316	2	(	(	PUNCT
ejpam-5714	316	3	t	t	PROPN
ejpam-5714	316	4	)	)	PUNCT
ejpam-5714	316	5	(	(	PUNCT
ejpam-5714	316	6	1−	1−	NUM
ejpam-5714	316	7	y	y	PROPN
ejpam-5714	316	8	(	(	PUNCT
ejpam-5714	316	9	πi	πi	PROPN
ejpam-5714	316	10	(	(	PUNCT
ejpam-5714	316	11	t	t	NOUN
ejpam-5714	316	12	)	)	PUNCT
ejpam-5714	316	13	)	)	PUNCT
ejpam-5714	316	14	)	)	PUNCT
ejpam-5714	317	1	(	(	PUNCT
ejpam-5714	317	2	p−1	p−1	PROPN
ejpam-5714	317	3	)	)	PUNCT
ejpam-5714	317	4	b̂	b̂	NOUN
ejpam-5714	317	5	(	(	PUNCT
ejpam-5714	317	6	t	t	NOUN
ejpam-5714	317	7	)	)	PUNCT
ejpam-5714	317	8	dt	dt	NOUN
ejpam-5714	318	1	=	=	SYM
ejpam-5714	318	2	∞	∞	PROPN
ejpam-5714	318	3	,	,	PUNCT
ejpam-5714	318	4	(	(	PUNCT
ejpam-5714	318	5	25	25	NUM
ejpam-5714	318	6	)	)	PUNCT
ejpam-5714	318	7	then	then	ADV
ejpam-5714	318	8	,	,	PUNCT
ejpam-5714	318	9	equation	equation	NOUN
ejpam-5714	318	10	(	(	PUNCT
ejpam-5714	318	11	1	1	X
ejpam-5714	318	12	)	)	PUNCT
ejpam-5714	318	13	is	be	AUX
ejpam-5714	318	14	oscillatory	oscillatory	ADJ
ejpam-5714	318	15	.	.	PUNCT
ejpam-5714	319	1	proof	proof	NOUN
ejpam-5714	319	2	.	.	PUNCT
ejpam-5714	320	1	suppose	suppose	VERB
ejpam-5714	320	2	κ	κ	X
ejpam-5714	320	3	(	(	PUNCT
ejpam-5714	320	4	t	t	PROPN
ejpam-5714	320	5	)	)	PUNCT
ejpam-5714	320	6	>	>	X
ejpam-5714	320	7	0	0	NUM
ejpam-5714	320	8	,	,	PUNCT
ejpam-5714	320	9	κ	κ	X
ejpam-5714	320	10	(	(	PUNCT
ejpam-5714	320	11	ζ	ζ	PROPN
ejpam-5714	320	12	(	(	PUNCT
ejpam-5714	320	13	t	t	NOUN
ejpam-5714	320	14	)	)	PUNCT
ejpam-5714	320	15	)	)	PUNCT
ejpam-5714	320	16	>	>	X
ejpam-5714	320	17	0	0	PUNCT
ejpam-5714	321	1	and	and	CCONJ
ejpam-5714	321	2	κ	κ	PROPN
ejpam-5714	321	3	(	(	PUNCT
ejpam-5714	321	4	πi	πi	PROPN
ejpam-5714	321	5	(	(	PUNCT
ejpam-5714	321	6	t	t	NOUN
ejpam-5714	321	7	)	)	PUNCT
ejpam-5714	321	8	)	)	PUNCT
ejpam-5714	322	1	>	>	X
ejpam-5714	322	2	0	0	NUM
ejpam-5714	322	3	,	,	PUNCT
ejpam-5714	322	4	we	we	PRON
ejpam-5714	322	5	can	can	AUX
ejpam-5714	322	6	infer	infer	VERB
ejpam-5714	322	7	from	from	ADP
ejpam-5714	322	8	lemma	lemma	PROPN
ejpam-5714	322	9	4	4	NUM
ejpam-5714	322	10	that	that	PRON
ejpam-5714	322	11	(	(	PUNCT
ejpam-5714	322	12	13	13	NUM
ejpam-5714	322	13	)	)	PUNCT
ejpam-5714	322	14	holds	hold	VERB
ejpam-5714	322	15	.	.	PUNCT
ejpam-5714	323	1	if	if	SCONJ
ejpam-5714	323	2	we	we	PRON
ejpam-5714	323	3	set	set	VERB
ejpam-5714	323	4	x	x	SYM
ejpam-5714	323	5	(	(	PUNCT
ejpam-5714	323	6	t	t	PROPN
ejpam-5714	323	7	)	)	PUNCT
ejpam-5714	323	8	:	:	PUNCT
ejpam-5714	324	1	=	=	SYM
ejpam-5714	324	2	1	1	NUM
ejpam-5714	324	3	,	,	PUNCT
ejpam-5714	324	4	then	then	ADV
ejpam-5714	324	5	(	(	PUNCT
ejpam-5714	324	6	13	13	NUM
ejpam-5714	324	7	)	)	PUNCT
ejpam-5714	324	8	becomes	become	VERB
ejpam-5714	324	9	ξ′	ξ′	NOUN
ejpam-5714	324	10	(	(	PUNCT
ejpam-5714	324	11	t	t	PROPN
ejpam-5714	324	12	)	)	PUNCT
ejpam-5714	325	1	+	+	CCONJ
ejpam-5714	325	2	n∑	n∑	X
ejpam-5714	325	3	i=1	i=1	ADP
ejpam-5714	325	4	qi	qi	PROPN
ejpam-5714	325	5	(	(	PUNCT
ejpam-5714	325	6	t	t	PROPN
ejpam-5714	325	7	)	)	PUNCT
ejpam-5714	325	8	(	(	PUNCT
ejpam-5714	325	9	1−	1−	NUM
ejpam-5714	325	10	y	y	PROPN
ejpam-5714	325	11	(	(	PUNCT
ejpam-5714	325	12	πi	πi	PROPN
ejpam-5714	325	13	(	(	PUNCT
ejpam-5714	325	14	t	t	NOUN
ejpam-5714	325	15	)	)	PUNCT
ejpam-5714	325	16	)	)	PUNCT
ejpam-5714	325	17	)	)	PUNCT
ejpam-5714	326	1	(	(	PUNCT
ejpam-5714	326	2	p−1	p−1	PROPN
ejpam-5714	326	3	)	)	PUNCT
ejpam-5714	326	4	b̂	b̂	NOUN
ejpam-5714	326	5	(	(	PUNCT
ejpam-5714	326	6	t	t	NOUN
ejpam-5714	326	7	)	)	PUNCT
ejpam-5714	327	1	+	+	CCONJ
ejpam-5714	327	2	(	(	PUNCT
ejpam-5714	327	3	p−	p−	NOUN
ejpam-5714	327	4	1	1	NUM
ejpam-5714	327	5	)	)	PUNCT
ejpam-5714	327	6	/	/	PUNCT
ejpam-5714	327	7	(	(	PUNCT
ejpam-5714	327	8	b	b	X
ejpam-5714	327	9	(	(	PUNCT
ejpam-5714	327	10	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	327	11	)	)	PUNCT
ejpam-5714	327	12	ξ	ξ	PROPN
ejpam-5714	327	13	p	p	X
ejpam-5714	327	14	(	(	PUNCT
ejpam-5714	327	15	p−1	p−1	PROPN
ejpam-5714	327	16	)	)	PUNCT
ejpam-5714	327	17	(	(	PUNCT
ejpam-5714	327	18	t	t	NOUN
ejpam-5714	327	19	)	)	PUNCT
ejpam-5714	327	20	≤	≤	NOUN
ejpam-5714	327	21	0	0	NUM
ejpam-5714	327	22	,	,	PUNCT
ejpam-5714	327	23	(	(	PUNCT
ejpam-5714	327	24	26	26	NUM
ejpam-5714	327	25	)	)	PUNCT
ejpam-5714	327	26	or	or	CCONJ
ejpam-5714	327	27	ξ′	ξ′	PROPN
ejpam-5714	327	28	(	(	PUNCT
ejpam-5714	327	29	t	t	PROPN
ejpam-5714	327	30	)	)	PUNCT
ejpam-5714	328	1	+	+	CCONJ
ejpam-5714	328	2	n∑	n∑	X
ejpam-5714	328	3	i=1	i=1	ADP
ejpam-5714	328	4	qi	qi	PROPN
ejpam-5714	328	5	(	(	PUNCT
ejpam-5714	328	6	t	t	PROPN
ejpam-5714	328	7	)	)	PUNCT
ejpam-5714	328	8	(	(	PUNCT
ejpam-5714	328	9	1−	1−	NUM
ejpam-5714	328	10	y	y	PROPN
ejpam-5714	328	11	(	(	PUNCT
ejpam-5714	328	12	πi	πi	PROPN
ejpam-5714	328	13	(	(	PUNCT
ejpam-5714	328	14	t	t	NOUN
ejpam-5714	328	15	)	)	PUNCT
ejpam-5714	328	16	)	)	PUNCT
ejpam-5714	328	17	)	)	PUNCT
ejpam-5714	329	1	(	(	PUNCT
ejpam-5714	329	2	p−1	p−1	PROPN
ejpam-5714	329	3	)	)	PUNCT
ejpam-5714	329	4	b̂	b̂	NOUN
ejpam-5714	329	5	(	(	PUNCT
ejpam-5714	329	6	t	t	NOUN
ejpam-5714	329	7	)	)	PUNCT
ejpam-5714	329	8	≤	≤	NOUN
ejpam-5714	329	9	0	0	NUM
ejpam-5714	329	10	.	.	PUNCT
ejpam-5714	330	1	(	(	PUNCT
ejpam-5714	330	2	27	27	NUM
ejpam-5714	330	3	)	)	PUNCT
ejpam-5714	330	4	f.	f.	NOUN
ejpam-5714	330	5	aldosari	aldosari	PROPN
ejpam-5714	330	6	/	/	SYM
ejpam-5714	330	7	eur	eur	PROPN
ejpam-5714	330	8	.	.	PUNCT
ejpam-5714	331	1	j.	j.	PROPN
ejpam-5714	331	2	pure	pure	PROPN
ejpam-5714	331	3	appl	appl	PROPN
ejpam-5714	331	4	.	.	PROPN
ejpam-5714	331	5	math	math	PROPN
ejpam-5714	331	6	,	,	PUNCT
ejpam-5714	331	7	18	18	NUM
ejpam-5714	331	8	(	(	PUNCT
ejpam-5714	331	9	1	1	NUM
ejpam-5714	331	10	)	)	PUNCT
ejpam-5714	331	11	(	(	PUNCT
ejpam-5714	331	12	2025	2025	NUM
ejpam-5714	331	13	)	)	PUNCT
ejpam-5714	331	14	,	,	PUNCT
ejpam-5714	331	15	5714	5714	NUM
ejpam-5714	331	16	10	10	NUM
ejpam-5714	331	17	of	of	ADP
ejpam-5714	331	18	16	16	NUM
ejpam-5714	331	19	integrating	integrating	NOUN
ejpam-5714	331	20	(	(	PUNCT
ejpam-5714	331	21	27	27	NUM
ejpam-5714	331	22	)	)	PUNCT
ejpam-5714	331	23	from	from	ADP
ejpam-5714	331	24	t3	t3	PROPN
ejpam-5714	331	25	to	to	ADP
ejpam-5714	331	26	t	t	PROPN
ejpam-5714	331	27	and	and	CCONJ
ejpam-5714	331	28	using	use	VERB
ejpam-5714	331	29	(	(	PUNCT
ejpam-5714	331	30	25	25	NUM
ejpam-5714	331	31	)	)	PUNCT
ejpam-5714	331	32	,	,	PUNCT
ejpam-5714	331	33	we	we	PRON
ejpam-5714	331	34	arrive	arrive	VERB
ejpam-5714	331	35	at	at	ADP
ejpam-5714	331	36	ξ	ξ	PROPN
ejpam-5714	331	37	(	(	PUNCT
ejpam-5714	331	38	t	t	NOUN
ejpam-5714	331	39	)	)	PUNCT
ejpam-5714	331	40	≤	≤	NOUN
ejpam-5714	331	41	ξ	ξ	X
ejpam-5714	331	42	(	(	PUNCT
ejpam-5714	331	43	t3)−	t3)−	PROPN
ejpam-5714	331	44	∫	∫	PROPN
ejpam-5714	331	45	t	t	PROPN
ejpam-5714	331	46	t3	t3	PROPN
ejpam-5714	331	47	n∑	n∑	PROPN
ejpam-5714	331	48	i=1	i=1	PROPN
ejpam-5714	332	1	qi	qi	PROPN
ejpam-5714	332	2	(	(	PUNCT
ejpam-5714	332	3	t	t	PROPN
ejpam-5714	332	4	)	)	PUNCT
ejpam-5714	332	5	(	(	PUNCT
ejpam-5714	332	6	1−	1−	NUM
ejpam-5714	332	7	y	y	PROPN
ejpam-5714	332	8	(	(	PUNCT
ejpam-5714	332	9	πi	πi	PROPN
ejpam-5714	332	10	(	(	PUNCT
ejpam-5714	332	11	t	t	NOUN
ejpam-5714	332	12	)	)	PUNCT
ejpam-5714	332	13	)	)	PUNCT
ejpam-5714	332	14	)	)	PUNCT
ejpam-5714	333	1	(	(	PUNCT
ejpam-5714	333	2	p−1	p−1	PROPN
ejpam-5714	333	3	)	)	PUNCT
ejpam-5714	333	4	b̂	b̂	NOUN
ejpam-5714	333	5	(	(	PUNCT
ejpam-5714	333	6	t	t	NOUN
ejpam-5714	333	7	)	)	PUNCT
ejpam-5714	333	8	ds→	ds→	VERB
ejpam-5714	333	9	∞	∞	NUM
ejpam-5714	333	10	as	as	SCONJ
ejpam-5714	333	11	t→	t→	DET
ejpam-5714	333	12	∞.	∞.	PROPN
ejpam-5714	333	13	this	this	PRON
ejpam-5714	333	14	contradicts	contradict	VERB
ejpam-5714	333	15	the	the	DET
ejpam-5714	333	16	conclusion	conclusion	NOUN
ejpam-5714	333	17	that	that	SCONJ
ejpam-5714	333	18	the	the	DET
ejpam-5714	333	19	evidence	evidence	NOUN
ejpam-5714	333	20	is	be	AUX
ejpam-5714	333	21	complete	complete	ADJ
ejpam-5714	334	1	because	because	SCONJ
ejpam-5714	334	2	ξ	ξ	PROPN
ejpam-5714	334	3	(	(	PUNCT
ejpam-5714	334	4	t	t	PROPN
ejpam-5714	334	5	)	)	PUNCT
ejpam-5714	334	6	>	>	X
ejpam-5714	334	7	0	0	X
ejpam-5714	334	8	.	.	PUNCT
ejpam-5714	335	1	definition	definition	NOUN
ejpam-5714	335	2	3	3	NUM
ejpam-5714	335	3	.	.	PUNCT
ejpam-5714	335	4	assume	assume	VERB
ejpam-5714	335	5	that	that	SCONJ
ejpam-5714	335	6	the	the	DET
ejpam-5714	335	7	series	series	NOUN
ejpam-5714	335	8	of	of	ADP
ejpam-5714	335	9	functions	function	NOUN
ejpam-5714	335	10	{	{	PUNCT
ejpam-5714	335	11	ϑn	ϑn	NOUN
ejpam-5714	335	12	(	(	PUNCT
ejpam-5714	335	13	t)}∞n=0	t)}∞n=0	NOUN
ejpam-5714	335	14	is	be	AUX
ejpam-5714	335	15	defined	define	VERB
ejpam-5714	335	16	as	as	ADP
ejpam-5714	335	17	ϑn	ϑn	NOUN
ejpam-5714	335	18	(	(	PUNCT
ejpam-5714	335	19	t	t	NOUN
ejpam-5714	335	20	)	)	PUNCT
ejpam-5714	335	21	=	=	SYM
ejpam-5714	336	1	∫	∫	PROPN
ejpam-5714	336	2	∞	∞	PROPN
ejpam-5714	336	3	t	t	PROPN
ejpam-5714	336	4	(	(	PUNCT
ejpam-5714	336	5	p−	p−	NOUN
ejpam-5714	336	6	1	1	NUM
ejpam-5714	336	7	)	)	PUNCT
ejpam-5714	336	8	/	/	PUNCT
ejpam-5714	336	9	(	(	PUNCT
ejpam-5714	336	10	b	b	X
ejpam-5714	336	11	(	(	PUNCT
ejpam-5714	336	12	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	336	13	)	)	PUNCT
ejpam-5714	336	14	ϑ	ϑ	X
ejpam-5714	336	15	p	p	X
ejpam-5714	336	16	(	(	PUNCT
ejpam-5714	336	17	p−1	p−1	PROPN
ejpam-5714	336	18	)	)	PUNCT
ejpam-5714	336	19	n−1	n−1	PROPN
ejpam-5714	336	20	(	(	PUNCT
ejpam-5714	336	21	s	s	NOUN
ejpam-5714	336	22	)	)	PUNCT
ejpam-5714	336	23	ds+	ds+	ADJ
ejpam-5714	336	24	ϑ0	ϑ0	PROPN
ejpam-5714	336	25	(	(	PUNCT
ejpam-5714	336	26	t	t	PROPN
ejpam-5714	336	27	)	)	PUNCT
ejpam-5714	336	28	,	,	PUNCT
ejpam-5714	336	29	t	t	PROPN
ejpam-5714	336	30	≥	≥	PROPN
ejpam-5714	336	31	t0	t0	PROPN
ejpam-5714	336	32	,	,	PUNCT
ejpam-5714	336	33	n	n	NOUN
ejpam-5714	336	34	=	=	SYM
ejpam-5714	336	35	1	1	NUM
ejpam-5714	336	36	,	,	PUNCT
ejpam-5714	336	37	2	2	NUM
ejpam-5714	336	38	,	,	PUNCT
ejpam-5714	336	39	3	3	NUM
ejpam-5714	336	40	,	,	PUNCT
ejpam-5714	336	41	...	...	PUNCT
ejpam-5714	336	42	,	,	PUNCT
ejpam-5714	336	43	(	(	PUNCT
ejpam-5714	336	44	28	28	NUM
ejpam-5714	336	45	)	)	PUNCT
ejpam-5714	336	46	and	and	CCONJ
ejpam-5714	336	47	ϑ0	ϑ0	PROPN
ejpam-5714	336	48	(	(	PUNCT
ejpam-5714	336	49	t	t	NOUN
ejpam-5714	336	50	)	)	PUNCT
ejpam-5714	336	51	=	=	SYM
ejpam-5714	337	1	∫	∫	PROPN
ejpam-5714	338	1	∞	∞	PROPN
ejpam-5714	338	2	t	t	PROPN
ejpam-5714	338	3	n∑	n∑	PROPN
ejpam-5714	338	4	i=1	i=1	PROPN
ejpam-5714	339	1	qi	qi	PROPN
ejpam-5714	339	2	(	(	PUNCT
ejpam-5714	339	3	t	t	PROPN
ejpam-5714	339	4	)	)	PUNCT
ejpam-5714	339	5	(	(	PUNCT
ejpam-5714	339	6	1−	1−	NUM
ejpam-5714	339	7	y	y	PROPN
ejpam-5714	339	8	(	(	PUNCT
ejpam-5714	339	9	πi	πi	PROPN
ejpam-5714	339	10	(	(	PUNCT
ejpam-5714	339	11	t	t	NOUN
ejpam-5714	339	12	)	)	PUNCT
ejpam-5714	339	13	)	)	PUNCT
ejpam-5714	339	14	)	)	PUNCT
ejpam-5714	340	1	(	(	PUNCT
ejpam-5714	340	2	p−1	p−1	PROPN
ejpam-5714	340	3	)	)	PUNCT
ejpam-5714	340	4	b̂	b̂	NOUN
ejpam-5714	340	5	(	(	PUNCT
ejpam-5714	340	6	t	t	NOUN
ejpam-5714	340	7	)	)	PUNCT
ejpam-5714	340	8	dt	dt	PROPN
ejpam-5714	340	9	,	,	PUNCT
ejpam-5714	340	10	t	t	PROPN
ejpam-5714	340	11	≥	≥	PROPN
ejpam-5714	340	12	t0	t0	PROPN
ejpam-5714	340	13	,	,	PUNCT
ejpam-5714	340	14	where	where	SCONJ
ejpam-5714	340	15	ϑn	ϑn	NOUN
ejpam-5714	340	16	(	(	PUNCT
ejpam-5714	340	17	t	t	NOUN
ejpam-5714	340	18	)	)	PUNCT
ejpam-5714	340	19	≤	≤	X
ejpam-5714	340	20	ϑn+1	ϑn+1	X
ejpam-5714	340	21	(	(	PUNCT
ejpam-5714	340	22	t	t	PROPN
ejpam-5714	340	23	)	)	PUNCT
ejpam-5714	340	24	,	,	PUNCT
ejpam-5714	340	25	t	t	PROPN
ejpam-5714	340	26	≥	≥	PROPN
ejpam-5714	340	27	t0	t0	PROPN
ejpam-5714	340	28	.	.	PUNCT
ejpam-5714	341	1	lemma	lemma	PROPN
ejpam-5714	341	2	7	7	X
ejpam-5714	341	3	.	.	PUNCT
ejpam-5714	342	1	let	let	VERB
ejpam-5714	342	2	κ	κ	PRON
ejpam-5714	342	3	be	be	AUX
ejpam-5714	342	4	a	a	DET
ejpam-5714	342	5	solution	solution	NOUN
ejpam-5714	342	6	of	of	ADP
ejpam-5714	342	7	equation	equation	NOUN
ejpam-5714	342	8	(	(	PUNCT
ejpam-5714	342	9	1	1	NUM
ejpam-5714	342	10	)	)	PUNCT
ejpam-5714	342	11	that	that	PRON
ejpam-5714	342	12	becomes	become	VERB
ejpam-5714	342	13	positive	positive	ADJ
ejpam-5714	342	14	for	for	ADP
ejpam-5714	342	15	suffciently	suffciently	ADV
ejpam-5714	342	16	large	large	ADJ
ejpam-5714	342	17	t.	t.	NOUN
ejpam-5714	342	18	then	then	ADV
ejpam-5714	342	19	ξ	ξ	PROPN
ejpam-5714	342	20	(	(	PUNCT
ejpam-5714	342	21	t	t	PROPN
ejpam-5714	342	22	)	)	PUNCT
ejpam-5714	342	23	≥	≥	NOUN
ejpam-5714	342	24	ϑn	ϑn	NOUN
ejpam-5714	342	25	(	(	PUNCT
ejpam-5714	342	26	t	t	PROPN
ejpam-5714	342	27	)	)	PUNCT
ejpam-5714	342	28	where	where	SCONJ
ejpam-5714	342	29	limn→∞	limn→∞	PROPN
ejpam-5714	342	30	ϑn	ϑn	NOUN
ejpam-5714	342	31	(	(	PUNCT
ejpam-5714	342	32	t	t	NOUN
ejpam-5714	342	33	)	)	PUNCT
ejpam-5714	342	34	=	=	SYM
ejpam-5714	342	35	ϑ	ϑ	X
ejpam-5714	342	36	(	(	PUNCT
ejpam-5714	342	37	t	t	PROPN
ejpam-5714	342	38	)	)	PUNCT
ejpam-5714	342	39	for	for	ADP
ejpam-5714	342	40	t	t	PROPN
ejpam-5714	342	41	≥	≥	PROPN
ejpam-5714	342	42	t	t	PROPN
ejpam-5714	342	43	≥	≥	PROPN
ejpam-5714	342	44	t0	t0	PROPN
ejpam-5714	342	45	when	when	SCONJ
ejpam-5714	342	46	ϑ	ϑ	X
ejpam-5714	342	47	(	(	PUNCT
ejpam-5714	342	48	t	t	NOUN
ejpam-5714	342	49	)	)	PUNCT
ejpam-5714	342	50	on	on	ADP
ejpam-5714	342	51	[	[	X
ejpam-5714	342	52	t,∞	t,∞	NUM
ejpam-5714	342	53	)	)	PUNCT
ejpam-5714	342	54	and	and	CCONJ
ejpam-5714	342	55	ϑ	ϑ	X
ejpam-5714	342	56	(	(	PUNCT
ejpam-5714	342	57	t	t	PROPN
ejpam-5714	342	58	)	)	PUNCT
ejpam-5714	342	59	=	=	SYM
ejpam-5714	343	1	∫	∫	PROPN
ejpam-5714	343	2	∞	∞	PROPN
ejpam-5714	343	3	t	t	PROPN
ejpam-5714	343	4	(	(	PUNCT
ejpam-5714	343	5	p−	p−	NOUN
ejpam-5714	343	6	1	1	NUM
ejpam-5714	343	7	)	)	PUNCT
ejpam-5714	343	8	/	/	PUNCT
ejpam-5714	343	9	(	(	PUNCT
ejpam-5714	343	10	b	b	X
ejpam-5714	343	11	(	(	PUNCT
ejpam-5714	343	12	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	343	13	)	)	PUNCT
ejpam-5714	343	14	ϑ	ϑ	X
ejpam-5714	343	15	p	p	X
ejpam-5714	343	16	(	(	PUNCT
ejpam-5714	343	17	p−1	p−1	PROPN
ejpam-5714	343	18	)	)	PUNCT
ejpam-5714	343	19	(	(	PUNCT
ejpam-5714	343	20	s	s	NOUN
ejpam-5714	343	21	)	)	PUNCT
ejpam-5714	343	22	ds+	ds+	ADJ
ejpam-5714	343	23	ϑ0	ϑ0	PROPN
ejpam-5714	343	24	(	(	PUNCT
ejpam-5714	343	25	t	t	PROPN
ejpam-5714	343	26	)	)	PUNCT
ejpam-5714	343	27	,	,	PUNCT
ejpam-5714	343	28	t	t	PROPN
ejpam-5714	343	29	≥	≥	NOUN
ejpam-5714	343	30	t.	t.	PROPN
ejpam-5714	343	31	(	(	PUNCT
ejpam-5714	343	32	29	29	NUM
ejpam-5714	343	33	)	)	PUNCT
ejpam-5714	343	34	proof	proof	NOUN
ejpam-5714	343	35	.	.	PUNCT
ejpam-5714	344	1	let	let	VERB
ejpam-5714	344	2	κ	κ	PRON
ejpam-5714	344	3	be	be	AUX
ejpam-5714	344	4	a	a	DET
ejpam-5714	344	5	solution	solution	NOUN
ejpam-5714	344	6	of	of	ADP
ejpam-5714	344	7	equation	equation	NOUN
ejpam-5714	344	8	(	(	PUNCT
ejpam-5714	344	9	1	1	NUM
ejpam-5714	344	10	)	)	PUNCT
ejpam-5714	344	11	that	that	PRON
ejpam-5714	344	12	becomes	become	VERB
ejpam-5714	344	13	positive	positive	ADJ
ejpam-5714	344	14	for	for	ADP
ejpam-5714	344	15	suffciently	suffciently	ADV
ejpam-5714	344	16	large	large	ADJ
ejpam-5714	344	17	t.	t.	NOUN
ejpam-5714	344	18	we	we	PRON
ejpam-5714	344	19	get	get	VERB
ejpam-5714	344	20	to	to	ADP
ejpam-5714	344	21	(	(	PUNCT
ejpam-5714	344	22	26	26	NUM
ejpam-5714	344	23	)	)	PUNCT
ejpam-5714	344	24	by	by	ADP
ejpam-5714	344	25	using	use	VERB
ejpam-5714	344	26	the	the	DET
ejpam-5714	344	27	same	same	ADJ
ejpam-5714	344	28	steps	step	NOUN
ejpam-5714	344	29	as	as	ADP
ejpam-5714	344	30	in	in	ADP
ejpam-5714	344	31	the	the	DET
ejpam-5714	344	32	proof	proof	NOUN
ejpam-5714	344	33	of	of	ADP
ejpam-5714	344	34	theorem	theorem	ADJ
ejpam-5714	344	35	4	4	NUM
ejpam-5714	344	36	.	.	PUNCT
ejpam-5714	345	1	the	the	DET
ejpam-5714	345	2	result	result	NOUN
ejpam-5714	345	3	of	of	ADP
ejpam-5714	345	4	integrating	integrating	NOUN
ejpam-5714	345	5	(	(	PUNCT
ejpam-5714	345	6	26	26	NUM
ejpam-5714	345	7	)	)	PUNCT
ejpam-5714	345	8	from	from	ADP
ejpam-5714	345	9	t	t	PROPN
ejpam-5714	345	10	to	to	ADP
ejpam-5714	345	11	t′	t′	PROPN
ejpam-5714	345	12	is	be	AUX
ejpam-5714	345	13	ξ	ξ	X
ejpam-5714	345	14	(	(	PUNCT
ejpam-5714	345	15	t′	t′	NUM
ejpam-5714	345	16	)	)	PUNCT
ejpam-5714	345	17	−ξ	−ξ	NOUN
ejpam-5714	345	18	(	(	PUNCT
ejpam-5714	345	19	t)+	t)+	NOUN
ejpam-5714	345	20	∫	∫	PROPN
ejpam-5714	345	21	t′	t′	PROPN
ejpam-5714	346	1	t	t	PROPN
ejpam-5714	346	2	n∑	n∑	PROPN
ejpam-5714	346	3	i=1	i=1	PROPN
ejpam-5714	347	1	qi	qi	PROPN
ejpam-5714	347	2	(	(	PUNCT
ejpam-5714	347	3	s	s	NOUN
ejpam-5714	347	4	)	)	PUNCT
ejpam-5714	347	5	(	(	PUNCT
ejpam-5714	347	6	1−	1−	NUM
ejpam-5714	347	7	y	y	PROPN
ejpam-5714	347	8	(	(	PUNCT
ejpam-5714	347	9	πi	πi	PROPN
ejpam-5714	347	10	(	(	PUNCT
ejpam-5714	347	11	s	s	NOUN
ejpam-5714	347	12	)	)	PUNCT
ejpam-5714	347	13	)	)	PUNCT
ejpam-5714	347	14	)	)	PUNCT
ejpam-5714	348	1	(	(	PUNCT
ejpam-5714	348	2	p−1	p−1	PROPN
ejpam-5714	348	3	)	)	PUNCT
ejpam-5714	348	4	b̂	b̂	NOUN
ejpam-5714	348	5	(	(	PUNCT
ejpam-5714	348	6	s	s	NOUN
ejpam-5714	348	7	)	)	PUNCT
ejpam-5714	348	8	ds+	ds+	PROPN
ejpam-5714	348	9	∫	∫	PROPN
ejpam-5714	349	1	t′	t′	NUM
ejpam-5714	349	2	t	t	PROPN
ejpam-5714	349	3	ξ	ξ	X
ejpam-5714	349	4	p	p	X
ejpam-5714	349	5	(	(	PUNCT
ejpam-5714	349	6	p−1	p−1	PROPN
ejpam-5714	349	7	)	)	PUNCT
ejpam-5714	349	8	(	(	PUNCT
ejpam-5714	349	9	s	s	X
ejpam-5714	349	10	)	)	PUNCT
ejpam-5714	349	11	(	(	PUNCT
ejpam-5714	349	12	p−	p−	NOUN
ejpam-5714	349	13	1	1	NUM
ejpam-5714	349	14	)	)	PUNCT
ejpam-5714	349	15	/	/	PUNCT
ejpam-5714	349	16	(	(	PUNCT
ejpam-5714	349	17	b	b	X
ejpam-5714	349	18	(	(	PUNCT
ejpam-5714	349	19	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	349	20	)	)	PUNCT
ejpam-5714	349	21	ds	ds	ADJ
ejpam-5714	349	22	≤	≤	NOUN
ejpam-5714	349	23	0	0	NUM
ejpam-5714	349	24	.	.	PUNCT
ejpam-5714	350	1	this	this	PRON
ejpam-5714	350	2	implies	imply	VERB
ejpam-5714	350	3	ξ	ξ	PROPN
ejpam-5714	350	4	(	(	PUNCT
ejpam-5714	350	5	t′	t′	NUM
ejpam-5714	350	6	)	)	PUNCT
ejpam-5714	351	1	−	−	PROPN
ejpam-5714	351	2	ξ	ξ	PROPN
ejpam-5714	351	3	(	(	PUNCT
ejpam-5714	351	4	t	t	PROPN
ejpam-5714	351	5	)	)	PUNCT
ejpam-5714	351	6	+	+	NUM
ejpam-5714	351	7	∫	∫	PROPN
ejpam-5714	351	8	t′	t′	NUM
ejpam-5714	351	9	t	t	PROPN
ejpam-5714	351	10	ξ	ξ	X
ejpam-5714	351	11	p	p	X
ejpam-5714	351	12	(	(	PUNCT
ejpam-5714	351	13	p−1	p−1	PROPN
ejpam-5714	351	14	)	)	PUNCT
ejpam-5714	351	15	(	(	PUNCT
ejpam-5714	351	16	s	s	X
ejpam-5714	351	17	)	)	PUNCT
ejpam-5714	351	18	(	(	PUNCT
ejpam-5714	351	19	p−	p−	NOUN
ejpam-5714	351	20	1	1	NUM
ejpam-5714	351	21	)	)	PUNCT
ejpam-5714	351	22	/	/	PUNCT
ejpam-5714	351	23	(	(	PUNCT
ejpam-5714	351	24	b	b	X
ejpam-5714	351	25	(	(	PUNCT
ejpam-5714	351	26	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	351	27	)	)	PUNCT
ejpam-5714	351	28	ds	ds	ADJ
ejpam-5714	351	29	≤	≤	NOUN
ejpam-5714	351	30	0	0	NUM
ejpam-5714	351	31	.	.	PUNCT
ejpam-5714	352	1	then	then	ADV
ejpam-5714	352	2	,	,	PUNCT
ejpam-5714	352	3	we	we	PRON
ejpam-5714	352	4	conclude	conclude	VERB
ejpam-5714	352	5	that∫	that∫	PROPN
ejpam-5714	353	1	∞	∞	PROPN
ejpam-5714	353	2	t	t	PROPN
ejpam-5714	354	1	ξ	ξ	X
ejpam-5714	354	2	p	p	X
ejpam-5714	354	3	(	(	PUNCT
ejpam-5714	354	4	p−1	p−1	PROPN
ejpam-5714	354	5	)	)	PUNCT
ejpam-5714	354	6	(	(	PUNCT
ejpam-5714	354	7	s	s	X
ejpam-5714	354	8	)	)	PUNCT
ejpam-5714	354	9	(	(	PUNCT
ejpam-5714	354	10	p−	p−	NOUN
ejpam-5714	354	11	1	1	NUM
ejpam-5714	354	12	)	)	PUNCT
ejpam-5714	354	13	/	/	PUNCT
ejpam-5714	354	14	(	(	PUNCT
ejpam-5714	354	15	b	b	X
ejpam-5714	354	16	(	(	PUNCT
ejpam-5714	354	17	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	354	18	)	)	PUNCT
ejpam-5714	354	19	ds	ds	ADJ
ejpam-5714	354	20	<	<	X
ejpam-5714	354	21	∞	∞	PROPN
ejpam-5714	354	22	for	for	ADP
ejpam-5714	354	23	t	t	PROPN
ejpam-5714	354	24	≥	≥	PROPN
ejpam-5714	354	25	t	t	PROPN
ejpam-5714	354	26	,	,	PUNCT
ejpam-5714	354	27	(	(	PUNCT
ejpam-5714	354	28	30	30	NUM
ejpam-5714	354	29	)	)	PUNCT
ejpam-5714	354	30	otherwise	otherwise	ADV
ejpam-5714	354	31	,	,	PUNCT
ejpam-5714	354	32	when	when	SCONJ
ejpam-5714	354	33	t′	t′	NUM
ejpam-5714	354	34	→	→	SYM
ejpam-5714	354	35	∞	∞	PROPN
ejpam-5714	354	36	,	,	PUNCT
ejpam-5714	354	37	ξ(t′	ξ(t′	NUM
ejpam-5714	354	38	)	)	PUNCT
ejpam-5714	354	39	≤	≤	NUM
ejpam-5714	354	40	ξ(t	ξ(t	NOUN
ejpam-5714	354	41	)	)	PUNCT
ejpam-5714	354	42	−	−	NUM
ejpam-5714	354	43	∫	∫	PROPN
ejpam-5714	354	44	t′	t′	NUM
ejpam-5714	354	45	t	t	NOUN
ejpam-5714	354	46	ξ	ξ	X
ejpam-5714	354	47	p	p	X
ejpam-5714	354	48	(	(	PUNCT
ejpam-5714	354	49	p−1	p−1	PROPN
ejpam-5714	354	50	)	)	PUNCT
ejpam-5714	354	51	(	(	PUNCT
ejpam-5714	354	52	s	s	X
ejpam-5714	354	53	)	)	PUNCT
ejpam-5714	354	54	(	(	PUNCT
ejpam-5714	354	55	p−	p−	NOUN
ejpam-5714	354	56	1	1	NUM
ejpam-5714	354	57	)	)	PUNCT
ejpam-5714	354	58	/	/	PUNCT
ejpam-5714	354	59	(	(	PUNCT
ejpam-5714	354	60	b	b	X
ejpam-5714	354	61	(	(	PUNCT
ejpam-5714	354	62	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	354	63	)	)	PUNCT
ejpam-5714	354	64	ds	ds	PROPN
ejpam-5714	354	65	→	→	SYM
ejpam-5714	354	66	−∞	−∞	NOUN
ejpam-5714	354	67	,	,	PUNCT
ejpam-5714	354	68	which	which	PRON
ejpam-5714	354	69	contradicts	contradict	VERB
ejpam-5714	354	70	ξ(t	ξ(t	NOUN
ejpam-5714	354	71	)	)	PUNCT
ejpam-5714	354	72	>	>	X
ejpam-5714	354	73	0	0	X
ejpam-5714	354	74	.	.	PUNCT
ejpam-5714	355	1	given	give	VERB
ejpam-5714	355	2	that	that	PRON
ejpam-5714	355	3	ξ(t	ξ(t	NOUN
ejpam-5714	355	4	)	)	PUNCT
ejpam-5714	355	5	>	>	X
ejpam-5714	355	6	0	0	NUM
ejpam-5714	355	7	and	and	CCONJ
ejpam-5714	355	8	ξ′(t	ξ′(t	NOUN
ejpam-5714	355	9	)	)	PUNCT
ejpam-5714	355	10	>	>	X
ejpam-5714	355	11	0	0	NUM
ejpam-5714	355	12	,	,	PUNCT
ejpam-5714	355	13	(	(	PUNCT
ejpam-5714	355	14	26	26	NUM
ejpam-5714	355	15	)	)	PUNCT
ejpam-5714	355	16	indicates	indicate	VERB
ejpam-5714	355	17	that	that	SCONJ
ejpam-5714	355	18	ξ	ξ	PROPN
ejpam-5714	355	19	(	(	PUNCT
ejpam-5714	355	20	t	t	PROPN
ejpam-5714	355	21	)	)	PUNCT
ejpam-5714	355	22	≥	≥	NOUN
ejpam-5714	356	1	∫	∫	PROPN
ejpam-5714	357	1	∞	∞	PROPN
ejpam-5714	357	2	t	t	PROPN
ejpam-5714	357	3	n∑	n∑	PROPN
ejpam-5714	357	4	i=1	i=1	PROPN
ejpam-5714	358	1	qi	qi	PROPN
ejpam-5714	358	2	(	(	PUNCT
ejpam-5714	358	3	t	t	PROPN
ejpam-5714	358	4	)	)	PUNCT
ejpam-5714	358	5	(	(	PUNCT
ejpam-5714	358	6	1−	1−	NUM
ejpam-5714	358	7	y	y	PROPN
ejpam-5714	358	8	(	(	PUNCT
ejpam-5714	358	9	πi	πi	PROPN
ejpam-5714	358	10	(	(	PUNCT
ejpam-5714	358	11	t	t	NOUN
ejpam-5714	358	12	)	)	PUNCT
ejpam-5714	358	13	)	)	PUNCT
ejpam-5714	358	14	)	)	PUNCT
ejpam-5714	359	1	(	(	PUNCT
ejpam-5714	359	2	p−1	p−1	PROPN
ejpam-5714	359	3	)	)	PUNCT
ejpam-5714	359	4	b̂	b̂	NOUN
ejpam-5714	359	5	(	(	PUNCT
ejpam-5714	359	6	t	t	NOUN
ejpam-5714	359	7	)	)	PUNCT
ejpam-5714	359	8	dt+	dt+	NOUN
ejpam-5714	359	9	∫	∫	PROPN
ejpam-5714	360	1	∞	∞	PROPN
ejpam-5714	360	2	t	t	PROPN
ejpam-5714	361	1	ξ	ξ	X
ejpam-5714	361	2	p	p	X
ejpam-5714	361	3	(	(	PUNCT
ejpam-5714	361	4	p−1	p−1	PROPN
ejpam-5714	361	5	)	)	PUNCT
ejpam-5714	361	6	(	(	PUNCT
ejpam-5714	361	7	s	s	X
ejpam-5714	361	8	)	)	PUNCT
ejpam-5714	361	9	(	(	PUNCT
ejpam-5714	361	10	p−	p−	NOUN
ejpam-5714	361	11	1	1	NUM
ejpam-5714	361	12	)	)	PUNCT
ejpam-5714	361	13	/	/	PUNCT
ejpam-5714	361	14	(	(	PUNCT
ejpam-5714	361	15	b	b	X
ejpam-5714	361	16	(	(	PUNCT
ejpam-5714	361	17	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	361	18	)	)	PUNCT
ejpam-5714	361	19	ds	ds	PROPN
ejpam-5714	361	20	f.	f.	NOUN
ejpam-5714	361	21	aldosari	aldosari	PROPN
ejpam-5714	361	22	/	/	SYM
ejpam-5714	361	23	eur	eur	PROPN
ejpam-5714	361	24	.	.	PUNCT
ejpam-5714	362	1	j.	j.	PROPN
ejpam-5714	362	2	pure	pure	PROPN
ejpam-5714	362	3	appl	appl	PROPN
ejpam-5714	362	4	.	.	PROPN
ejpam-5714	362	5	math	math	PROPN
ejpam-5714	362	6	,	,	PUNCT
ejpam-5714	362	7	18	18	NUM
ejpam-5714	362	8	(	(	PUNCT
ejpam-5714	362	9	1	1	NUM
ejpam-5714	362	10	)	)	PUNCT
ejpam-5714	362	11	(	(	PUNCT
ejpam-5714	362	12	2025	2025	NUM
ejpam-5714	362	13	)	)	PUNCT
ejpam-5714	362	14	,	,	PUNCT
ejpam-5714	362	15	5714	5714	NUM
ejpam-5714	362	16	11	11	NUM
ejpam-5714	362	17	of	of	ADP
ejpam-5714	362	18	16	16	NUM
ejpam-5714	362	19	=	=	SYM
ejpam-5714	362	20	ϑ0	ϑ0	PROPN
ejpam-5714	362	21	(	(	PUNCT
ejpam-5714	362	22	t	t	PROPN
ejpam-5714	362	23	)	)	PUNCT
ejpam-5714	362	24	+	+	NUM
ejpam-5714	363	1	∫	∫	PROPN
ejpam-5714	363	2	∞	∞	PROPN
ejpam-5714	363	3	t	t	PROPN
ejpam-5714	364	1	ξ	ξ	X
ejpam-5714	364	2	p	p	X
ejpam-5714	364	3	(	(	PUNCT
ejpam-5714	364	4	p−1	p−1	PROPN
ejpam-5714	364	5	)	)	PUNCT
ejpam-5714	364	6	(	(	PUNCT
ejpam-5714	364	7	s	s	X
ejpam-5714	364	8	)	)	PUNCT
ejpam-5714	364	9	(	(	PUNCT
ejpam-5714	364	10	p−	p−	NOUN
ejpam-5714	364	11	1	1	NUM
ejpam-5714	364	12	)	)	PUNCT
ejpam-5714	364	13	/	/	PUNCT
ejpam-5714	364	14	(	(	PUNCT
ejpam-5714	364	15	b	b	X
ejpam-5714	364	16	(	(	PUNCT
ejpam-5714	364	17	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	364	18	)	)	PUNCT
ejpam-5714	364	19	ds	ds	NOUN
ejpam-5714	364	20	,	,	PUNCT
ejpam-5714	364	21	(	(	PUNCT
ejpam-5714	364	22	31	31	NUM
ejpam-5714	364	23	)	)	PUNCT
ejpam-5714	364	24	or	or	CCONJ
ejpam-5714	364	25	ξ	ξ	PROPN
ejpam-5714	364	26	(	(	PUNCT
ejpam-5714	364	27	t	t	PROPN
ejpam-5714	364	28	)	)	PUNCT
ejpam-5714	364	29	≥	≥	NOUN
ejpam-5714	365	1	∫	∫	PROPN
ejpam-5714	366	1	∞	∞	PROPN
ejpam-5714	366	2	t	t	PROPN
ejpam-5714	366	3	n∑	n∑	PROPN
ejpam-5714	366	4	i=1	i=1	PROPN
ejpam-5714	367	1	qi	qi	PROPN
ejpam-5714	367	2	(	(	PUNCT
ejpam-5714	367	3	t	t	PROPN
ejpam-5714	367	4	)	)	PUNCT
ejpam-5714	367	5	(	(	PUNCT
ejpam-5714	367	6	1−	1−	NUM
ejpam-5714	367	7	y	y	PROPN
ejpam-5714	367	8	(	(	PUNCT
ejpam-5714	367	9	πi	πi	PROPN
ejpam-5714	367	10	(	(	PUNCT
ejpam-5714	367	11	t	t	NOUN
ejpam-5714	367	12	)	)	PUNCT
ejpam-5714	367	13	)	)	PUNCT
ejpam-5714	367	14	)	)	PUNCT
ejpam-5714	368	1	(	(	PUNCT
ejpam-5714	368	2	p−1	p−1	PROPN
ejpam-5714	368	3	)	)	PUNCT
ejpam-5714	368	4	b̂	b̂	NOUN
ejpam-5714	368	5	(	(	PUNCT
ejpam-5714	368	6	t	t	NOUN
ejpam-5714	368	7	)	)	PUNCT
ejpam-5714	368	8	dt	dt	PUNCT
ejpam-5714	368	9	:	:	PUNCT
ejpam-5714	369	1	=	=	SYM
ejpam-5714	369	2	ϑ0	ϑ0	PROPN
ejpam-5714	369	3	(	(	PUNCT
ejpam-5714	369	4	t	t	PROPN
ejpam-5714	369	5	)	)	PUNCT
ejpam-5714	369	6	.	.	PUNCT
ejpam-5714	370	1	consequently	consequently	ADV
ejpam-5714	370	2	,	,	PUNCT
ejpam-5714	370	3	ξ(t	ξ(t	PROPN
ejpam-5714	370	4	)	)	PUNCT
ejpam-5714	370	5	≥	≥	NOUN
ejpam-5714	370	6	ϑn(t	ϑn(t	NUM
ejpam-5714	370	7	)	)	PUNCT
ejpam-5714	370	8	,	,	PUNCT
ejpam-5714	370	9	where	where	SCONJ
ejpam-5714	370	10	n	n	NOUN
ejpam-5714	370	11	=	=	SYM
ejpam-5714	370	12	1	1	NUM
ejpam-5714	370	13	,	,	PUNCT
ejpam-5714	370	14	2	2	NUM
ejpam-5714	370	15	,	,	PUNCT
ejpam-5714	370	16	3	3	NUM
ejpam-5714	370	17	,	,	PUNCT
ejpam-5714	370	18	....	....	PUNCT
ejpam-5714	371	1	we	we	PRON
ejpam-5714	371	2	obtain	obtain	VERB
ejpam-5714	371	3	that	that	DET
ejpam-5714	371	4	ϑn	ϑn	NOUN
ejpam-5714	371	5	→	→	SYM
ejpam-5714	371	6	ϑ	ϑ	X
ejpam-5714	371	7	as	as	ADP
ejpam-5714	371	8	n	n	PROPN
ejpam-5714	371	9	→	→	SYM
ejpam-5714	371	10	∞	∞	PROPN
ejpam-5714	371	11	since	since	SCONJ
ejpam-5714	371	12	{	{	PUNCT
ejpam-5714	371	13	ϑn(t)}∞n=0	ϑn(t)}∞n=0	NOUN
ejpam-5714	371	14	is	be	AUX
ejpam-5714	371	15	growing	grow	VERB
ejpam-5714	371	16	and	and	CCONJ
ejpam-5714	371	17	bounded	bound	VERB
ejpam-5714	371	18	above	above	ADV
ejpam-5714	371	19	.	.	PUNCT
ejpam-5714	372	1	the	the	DET
ejpam-5714	372	2	monotone	monotone	ADJ
ejpam-5714	372	3	convergence	convergence	NOUN
ejpam-5714	372	4	theorem	theorem	NOUN
ejpam-5714	372	5	of	of	ADP
ejpam-5714	372	6	lebesgue	lebesgue	NOUN
ejpam-5714	372	7	shows	show	VERB
ejpam-5714	372	8	that	that	SCONJ
ejpam-5714	372	9	when	when	SCONJ
ejpam-5714	372	10	n→	n→	PROPN
ejpam-5714	372	11	∞	∞	PROPN
ejpam-5714	372	12	,	,	PUNCT
ejpam-5714	372	13	(	(	PUNCT
ejpam-5714	372	14	28	28	NUM
ejpam-5714	372	15	)	)	PUNCT
ejpam-5714	372	16	becomes	become	VERB
ejpam-5714	372	17	(	(	PUNCT
ejpam-5714	372	18	29	29	NUM
ejpam-5714	372	19	)	)	PUNCT
ejpam-5714	372	20	.	.	PUNCT
ejpam-5714	373	1	theorem	theorem	NOUN
ejpam-5714	373	2	5	5	NUM
ejpam-5714	373	3	.	.	PUNCT
ejpam-5714	374	1	if	if	SCONJ
ejpam-5714	374	2	lim	lim	PROPN
ejpam-5714	374	3	inf	inf	VERB
ejpam-5714	374	4	t→∞	t→∞	PRON
ejpam-5714	374	5	1	1	NUM
ejpam-5714	374	6	ϑ0	ϑ0	NOUN
ejpam-5714	374	7	(	(	PUNCT
ejpam-5714	374	8	t	t	PROPN
ejpam-5714	374	9	)	)	PUNCT
ejpam-5714	374	10	∫	∫	PROPN
ejpam-5714	375	1	∞	∞	PROPN
ejpam-5714	375	2	t	t	PROPN
ejpam-5714	375	3	ϑ	ϑ	X
ejpam-5714	375	4	p	p	X
ejpam-5714	375	5	(	(	PUNCT
ejpam-5714	375	6	p−1	p−1	PROPN
ejpam-5714	375	7	)	)	PUNCT
ejpam-5714	375	8	0	0	PUNCT
ejpam-5714	376	1	(	(	PUNCT
ejpam-5714	376	2	s	s	NOUN
ejpam-5714	376	3	)	)	PUNCT
ejpam-5714	376	4	(	(	PUNCT
ejpam-5714	376	5	p−	p−	NOUN
ejpam-5714	376	6	1	1	NUM
ejpam-5714	376	7	)	)	PUNCT
ejpam-5714	376	8	/	/	PUNCT
ejpam-5714	376	9	(	(	PUNCT
ejpam-5714	376	10	b	b	X
ejpam-5714	376	11	(	(	PUNCT
ejpam-5714	376	12	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	376	13	)	)	PUNCT
ejpam-5714	376	14	ds	ds	NOUN
ejpam-5714	376	15	>	>	PUNCT
ejpam-5714	376	16	p−	p−	NOUN
ejpam-5714	376	17	1	1	NUM
ejpam-5714	376	18	p	p	NOUN
ejpam-5714	376	19	p	p	PROPN
ejpam-5714	376	20	p−1	p−1	PROPN
ejpam-5714	376	21	,	,	PUNCT
ejpam-5714	376	22	(	(	PUNCT
ejpam-5714	376	23	32	32	NUM
ejpam-5714	376	24	)	)	PUNCT
ejpam-5714	376	25	then	then	ADV
ejpam-5714	376	26	all	all	DET
ejpam-5714	376	27	solutions	solution	NOUN
ejpam-5714	376	28	(	(	PUNCT
ejpam-5714	376	29	1	1	X
ejpam-5714	376	30	)	)	PUNCT
ejpam-5714	376	31	are	be	AUX
ejpam-5714	376	32	oscillatory	oscillatory	ADJ
ejpam-5714	376	33	.	.	PUNCT
ejpam-5714	377	1	proof	proof	NOUN
ejpam-5714	377	2	.	.	PUNCT
ejpam-5714	378	1	assume	assume	VERB
ejpam-5714	378	2	that	that	SCONJ
ejpam-5714	378	3	κ	κ	PROPN
ejpam-5714	378	4	(	(	PUNCT
ejpam-5714	378	5	t	t	PROPN
ejpam-5714	378	6	)	)	PUNCT
ejpam-5714	378	7	>	>	X
ejpam-5714	378	8	0	0	NUM
ejpam-5714	378	9	,	,	PUNCT
ejpam-5714	378	10	meaning	mean	VERB
ejpam-5714	378	11	that	that	SCONJ
ejpam-5714	378	12	both	both	PRON
ejpam-5714	378	13	κ	κ	X
ejpam-5714	378	14	(	(	PUNCT
ejpam-5714	378	15	ζ	ζ	NOUN
ejpam-5714	378	16	(	(	PUNCT
ejpam-5714	378	17	t	t	NOUN
ejpam-5714	378	18	)	)	PUNCT
ejpam-5714	378	19	)	)	PUNCT
ejpam-5714	378	20	and	and	CCONJ
ejpam-5714	378	21	κ	κ	X
ejpam-5714	378	22	(	(	PUNCT
ejpam-5714	378	23	πi	πi	PROPN
ejpam-5714	378	24	(	(	PUNCT
ejpam-5714	378	25	t	t	NOUN
ejpam-5714	378	26	)	)	PUNCT
ejpam-5714	378	27	)	)	PUNCT
ejpam-5714	378	28	are	be	AUX
ejpam-5714	378	29	positive	positive	ADJ
ejpam-5714	378	30	.	.	PUNCT
ejpam-5714	379	1	following	follow	VERB
ejpam-5714	379	2	the	the	DET
ejpam-5714	379	3	same	same	ADJ
ejpam-5714	379	4	steps	step	NOUN
ejpam-5714	379	5	as	as	ADP
ejpam-5714	379	6	in	in	ADP
ejpam-5714	379	7	the	the	DET
ejpam-5714	379	8	lemma	lemma	PROPN
ejpam-5714	379	9	7	7	NUM
ejpam-5714	379	10	proof	proof	NOUN
ejpam-5714	379	11	,	,	PUNCT
ejpam-5714	379	12	we	we	PRON
ejpam-5714	379	13	get	get	VERB
ejpam-5714	379	14	(	(	PUNCT
ejpam-5714	379	15	31	31	NUM
ejpam-5714	379	16	)	)	PUNCT
ejpam-5714	379	17	.	.	PUNCT
ejpam-5714	380	1	using	use	VERB
ejpam-5714	380	2	(	(	PUNCT
ejpam-5714	380	3	31	31	NUM
ejpam-5714	380	4	)	)	PUNCT
ejpam-5714	380	5	,	,	PUNCT
ejpam-5714	380	6	we	we	PRON
ejpam-5714	380	7	discover	discover	VERB
ejpam-5714	380	8	ξ(t	ξ(t	NOUN
ejpam-5714	380	9	)	)	PUNCT
ejpam-5714	380	10	ϑ0(t	ϑ0(t	NOUN
ejpam-5714	380	11	)	)	PUNCT
ejpam-5714	380	12	≥	≥	NOUN
ejpam-5714	380	13	1	1	NUM
ejpam-5714	381	1	+	+	CCONJ
ejpam-5714	381	2	1	1	NUM
ejpam-5714	381	3	ϑ0(t	ϑ0(t	NOUN
ejpam-5714	381	4	)	)	PUNCT
ejpam-5714	381	5	∫	∫	PROPN
ejpam-5714	382	1	∞	∞	PROPN
ejpam-5714	382	2	t	t	PROPN
ejpam-5714	382	3	ϑ	ϑ	X
ejpam-5714	382	4	p−	p−	PROPN
ejpam-5714	382	5	p−1	p−1	PROPN
ejpam-5714	382	6	0	0	NUM
ejpam-5714	382	7	(	(	PUNCT
ejpam-5714	382	8	s	s	NOUN
ejpam-5714	382	9	)	)	PUNCT
ejpam-5714	382	10	(	(	PUNCT
ejpam-5714	382	11	p−	p−	NOUN
ejpam-5714	382	12	1	1	NUM
ejpam-5714	382	13	)	)	PUNCT
ejpam-5714	382	14	/	/	PUNCT
ejpam-5714	382	15	(	(	PUNCT
ejpam-5714	382	16	b	b	X
ejpam-5714	382	17	(	(	PUNCT
ejpam-5714	382	18	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	382	19	)	)	PUNCT
ejpam-5714	382	20	(	(	PUNCT
ejpam-5714	382	21	ξ(s	ξ(s	PROPN
ejpam-5714	382	22	)	)	PUNCT
ejpam-5714	382	23	ϑ0(s	ϑ0(s	PROPN
ejpam-5714	382	24	)	)	PUNCT
ejpam-5714	382	25	)	)	PUNCT
ejpam-5714	383	1	p	p	X
ejpam-5714	383	2	p−1	p−1	PROPN
ejpam-5714	383	3	ds	ds	PROPN
ejpam-5714	383	4	.	.	PUNCT
ejpam-5714	384	1	(	(	PUNCT
ejpam-5714	384	2	33	33	NUM
ejpam-5714	384	3	)	)	PUNCT
ejpam-5714	384	4	if	if	SCONJ
ejpam-5714	384	5	we	we	PRON
ejpam-5714	384	6	consider	consider	VERB
ejpam-5714	384	7	µ	µ	X
ejpam-5714	384	8	=	=	SYM
ejpam-5714	384	9	inft≥t	inft≥t	PROPN
ejpam-5714	384	10	(	(	PUNCT
ejpam-5714	384	11	ξ(t)/ϑ0(t	ξ(t)/ϑ0(t	PROPN
ejpam-5714	384	12	)	)	PUNCT
ejpam-5714	384	13	)	)	PUNCT
ejpam-5714	384	14	,	,	PUNCT
ejpam-5714	384	15	then	then	ADV
ejpam-5714	384	16	µ	µ	X
ejpam-5714	384	17	≥	≥	NOUN
ejpam-5714	384	18	1	1	NUM
ejpam-5714	384	19	of	of	ADP
ejpam-5714	384	20	course	course	NOUN
ejpam-5714	384	21	.	.	PUNCT
ejpam-5714	385	1	we	we	PRON
ejpam-5714	385	2	can	can	AUX
ejpam-5714	385	3	observe	observe	VERB
ejpam-5714	385	4	using(32	using(32	NOUN
ejpam-5714	385	5	)	)	PUNCT
ejpam-5714	385	6	and	and	CCONJ
ejpam-5714	385	7	(	(	PUNCT
ejpam-5714	385	8	33	33	NUM
ejpam-5714	385	9	)	)	PUNCT
ejpam-5714	386	1	that	that	PRON
ejpam-5714	386	2	µ	µ	PRON
ejpam-5714	386	3	≥	≥	NOUN
ejpam-5714	386	4	p	p	X
ejpam-5714	386	5	(	(	PUNCT
ejpam-5714	386	6	µ	µ	X
ejpam-5714	386	7	p	p	NOUN
ejpam-5714	386	8	)	)	PUNCT
ejpam-5714	386	9	p	p	PROPN
ejpam-5714	386	10	p−1	p−1	PROPN
ejpam-5714	386	11	,	,	PUNCT
ejpam-5714	386	12	or	or	CCONJ
ejpam-5714	386	13	p−	p−	NOUN
ejpam-5714	386	14	1	1	NUM
ejpam-5714	386	15	p	p	NOUN
ejpam-5714	386	16	(	(	PUNCT
ejpam-5714	386	17	µ	µ	X
ejpam-5714	386	18	p	p	NOUN
ejpam-5714	386	19	)	)	PUNCT
ejpam-5714	386	20	p	p	PROPN
ejpam-5714	386	21	p−1	p−1	PROPN
ejpam-5714	386	22	+	+	CCONJ
ejpam-5714	386	23	1	1	NUM
ejpam-5714	386	24	p	p	NOUN
ejpam-5714	386	25	≤	≤	NUM
ejpam-5714	386	26	µ	µ	X
ejpam-5714	386	27	p	p	NOUN
ejpam-5714	386	28	.	.	PUNCT
ejpam-5714	387	1	it	it	PRON
ejpam-5714	387	2	defies	defy	VERB
ejpam-5714	387	3	the	the	DET
ejpam-5714	387	4	predicted	predict	VERB
ejpam-5714	387	5	value	value	NOUN
ejpam-5714	387	6	of	of	ADP
ejpam-5714	387	7	µ	µ	NOUN
ejpam-5714	387	8	and	and	CCONJ
ejpam-5714	387	9	p	p	X
ejpam-5714	387	10	,	,	PUNCT
ejpam-5714	387	11	hence	hence	ADV
ejpam-5714	387	12	,	,	PUNCT
ejpam-5714	387	13	the	the	DET
ejpam-5714	387	14	proof	proof	NOUN
ejpam-5714	387	15	is	be	AUX
ejpam-5714	387	16	finished	finish	VERB
ejpam-5714	387	17	.	.	PUNCT
ejpam-5714	388	1	theorem	theorem	ADJ
ejpam-5714	388	2	6	6	NUM
ejpam-5714	388	3	.	.	PUNCT
ejpam-5714	389	1	let	let	VERB
ejpam-5714	389	2	lim	lim	PROPN
ejpam-5714	389	3	sup	sup	VERB
ejpam-5714	389	4	t→∞	t→∞	NUM
ejpam-5714	389	5	ϑn(t	ϑn(t	NOUN
ejpam-5714	389	6	)	)	PUNCT
ejpam-5714	390	1	(	(	PUNCT
ejpam-5714	390	2	∫	∫	PROPN
ejpam-5714	390	3	t	t	PROPN
ejpam-5714	390	4	t0	t0	PROPN
ejpam-5714	390	5	b	b	PROPN
ejpam-5714	390	6	−	−	PROPN
ejpam-5714	390	7	1	1	NUM
ejpam-5714	390	8	(	(	PUNCT
ejpam-5714	390	9	p−1	p−1	PROPN
ejpam-5714	390	10	)	)	PUNCT
ejpam-5714	390	11	(	(	PUNCT
ejpam-5714	390	12	s)ds	s)ds	PROPN
ejpam-5714	390	13	)	)	PUNCT
ejpam-5714	390	14	(	(	PUNCT
ejpam-5714	390	15	p−1	p−1	PROPN
ejpam-5714	390	16	)	)	PUNCT
ejpam-5714	390	17	>	>	X
ejpam-5714	390	18	1	1	NUM
ejpam-5714	390	19	,	,	PUNCT
ejpam-5714	390	20	(	(	PUNCT
ejpam-5714	390	21	34	34	NUM
ejpam-5714	390	22	)	)	PUNCT
ejpam-5714	390	23	then	then	ADV
ejpam-5714	390	24	every	every	DET
ejpam-5714	390	25	solutions	solution	NOUN
ejpam-5714	390	26	of	of	ADP
ejpam-5714	390	27	(	(	PUNCT
ejpam-5714	390	28	1	1	X
ejpam-5714	390	29	)	)	PUNCT
ejpam-5714	390	30	are	be	AUX
ejpam-5714	390	31	oscillatory	oscillatory	ADJ
ejpam-5714	390	32	.	.	PUNCT
ejpam-5714	391	1	proof	proof	NOUN
ejpam-5714	391	2	.	.	PUNCT
ejpam-5714	392	1	assume	assume	VERB
ejpam-5714	392	2	that	that	SCONJ
ejpam-5714	392	3	κ	κ	PROPN
ejpam-5714	392	4	(	(	PUNCT
ejpam-5714	392	5	t	t	PROPN
ejpam-5714	392	6	)	)	PUNCT
ejpam-5714	392	7	>	>	X
ejpam-5714	392	8	0	0	NUM
ejpam-5714	392	9	,	,	PUNCT
ejpam-5714	392	10	meaning	mean	VERB
ejpam-5714	392	11	that	that	SCONJ
ejpam-5714	392	12	both	both	PRON
ejpam-5714	392	13	κ	κ	X
ejpam-5714	392	14	(	(	PUNCT
ejpam-5714	392	15	ζ	ζ	NOUN
ejpam-5714	392	16	(	(	PUNCT
ejpam-5714	392	17	t	t	NOUN
ejpam-5714	392	18	)	)	PUNCT
ejpam-5714	392	19	)	)	PUNCT
ejpam-5714	392	20	and	and	CCONJ
ejpam-5714	392	21	κ	κ	X
ejpam-5714	392	22	(	(	PUNCT
ejpam-5714	392	23	πi	πi	PROPN
ejpam-5714	392	24	(	(	PUNCT
ejpam-5714	392	25	t	t	NOUN
ejpam-5714	392	26	)	)	PUNCT
ejpam-5714	392	27	)	)	PUNCT
ejpam-5714	392	28	are	be	AUX
ejpam-5714	392	29	positive	positive	ADJ
ejpam-5714	392	30	.	.	PUNCT
ejpam-5714	393	1	from	from	ADP
ejpam-5714	393	2	(	(	PUNCT
ejpam-5714	393	3	12	12	NUM
ejpam-5714	393	4	)	)	PUNCT
ejpam-5714	393	5	,	,	PUNCT
ejpam-5714	393	6	we	we	PRON
ejpam-5714	393	7	obtain	obtain	VERB
ejpam-5714	393	8	1	1	NUM
ejpam-5714	393	9	ξ	ξ	PROPN
ejpam-5714	393	10	(	(	PUNCT
ejpam-5714	393	11	t	t	NOUN
ejpam-5714	393	12	)	)	PUNCT
ejpam-5714	393	13	=	=	SYM
ejpam-5714	393	14	1	1	NUM
ejpam-5714	393	15	b	b	X
ejpam-5714	393	16	(	(	PUNCT
ejpam-5714	393	17	t	t	PROPN
ejpam-5714	393	18	)	)	PUNCT
ejpam-5714	393	19	(	(	PUNCT
ejpam-5714	393	20	ϖ	ϖ	X
ejpam-5714	393	21	(	(	PUNCT
ejpam-5714	393	22	t	t	NOUN
ejpam-5714	393	23	)	)	PUNCT
ejpam-5714	393	24	ϖ′	ϖ′	NUM
ejpam-5714	393	25	(	(	PUNCT
ejpam-5714	393	26	t	t	NOUN
ejpam-5714	393	27	)	)	PUNCT
ejpam-5714	393	28	)	)	PUNCT
ejpam-5714	393	29	(	(	PUNCT
ejpam-5714	393	30	p−1	p−1	PROPN
ejpam-5714	393	31	)	)	PUNCT
ejpam-5714	393	32	=	=	PUNCT
ejpam-5714	393	33	1	1	NUM
ejpam-5714	393	34	b	b	X
ejpam-5714	393	35	(	(	PUNCT
ejpam-5714	393	36	t	t	PROPN
ejpam-5714	393	37	)	)	PUNCT
ejpam-5714	393	38	(	(	PUNCT
ejpam-5714	393	39	ϖ	ϖ	X
ejpam-5714	393	40	(	(	PUNCT
ejpam-5714	393	41	t	t	PROPN
ejpam-5714	393	42	)	)	PUNCT
ejpam-5714	394	1	+	+	CCONJ
ejpam-5714	395	1	∫	∫	PROPN
ejpam-5714	395	2	t	t	PROPN
ejpam-5714	395	3	t	t	PROPN
ejpam-5714	395	4	b	b	X
ejpam-5714	395	5	−1/(p−1	−1/(p−1	NOUN
ejpam-5714	395	6	)	)	PUNCT
ejpam-5714	395	7	(	(	PUNCT
ejpam-5714	395	8	s	s	NOUN
ejpam-5714	395	9	)	)	PUNCT
ejpam-5714	395	10	b1/(p−1	b1/(p−1	NUM
ejpam-5714	395	11	)	)	PUNCT
ejpam-5714	395	12	(	(	PUNCT
ejpam-5714	395	13	s)ϖ′	s)ϖ′	PROPN
ejpam-5714	395	14	(	(	PUNCT
ejpam-5714	395	15	s	s	X
ejpam-5714	395	16	)	)	PUNCT
ejpam-5714	395	17	ds	ds	ADJ
ejpam-5714	395	18	ϖ′	ϖ′	X
ejpam-5714	395	19	(	(	PUNCT
ejpam-5714	395	20	t	t	NOUN
ejpam-5714	395	21	)	)	PUNCT
ejpam-5714	395	22	)	)	PUNCT
ejpam-5714	395	23	(	(	PUNCT
ejpam-5714	395	24	p−1	p−1	PROPN
ejpam-5714	395	25	)	)	PUNCT
ejpam-5714	395	26	f.	f.	PROPN
ejpam-5714	395	27	aldosari	aldosari	PROPN
ejpam-5714	395	28	/	/	SYM
ejpam-5714	395	29	eur	eur	PROPN
ejpam-5714	395	30	.	.	PUNCT
ejpam-5714	396	1	j.	j.	PROPN
ejpam-5714	396	2	pure	pure	PROPN
ejpam-5714	396	3	appl	appl	PROPN
ejpam-5714	396	4	.	.	PROPN
ejpam-5714	396	5	math	math	PROPN
ejpam-5714	396	6	,	,	PUNCT
ejpam-5714	396	7	18	18	NUM
ejpam-5714	396	8	(	(	PUNCT
ejpam-5714	396	9	1	1	NUM
ejpam-5714	396	10	)	)	PUNCT
ejpam-5714	396	11	(	(	PUNCT
ejpam-5714	396	12	2025	2025	NUM
ejpam-5714	396	13	)	)	PUNCT
ejpam-5714	396	14	,	,	PUNCT
ejpam-5714	396	15	5714	5714	NUM
ejpam-5714	396	16	12	12	NUM
ejpam-5714	396	17	of	of	ADP
ejpam-5714	396	18	16	16	NUM
ejpam-5714	396	19	≥	≥	NOUN
ejpam-5714	396	20	1	1	NUM
ejpam-5714	396	21	b	b	PROPN
ejpam-5714	396	22	(	(	PUNCT
ejpam-5714	396	23	t	t	PROPN
ejpam-5714	396	24	)	)	PUNCT
ejpam-5714	396	25	(	(	PUNCT
ejpam-5714	396	26	b1/(p−1	b1/(p−1	NOUN
ejpam-5714	396	27	)	)	PUNCT
ejpam-5714	396	28	(	(	PUNCT
ejpam-5714	396	29	t)ϖ′	t)ϖ′	PROPN
ejpam-5714	396	30	(	(	PUNCT
ejpam-5714	396	31	t	t	PROPN
ejpam-5714	396	32	)	)	PUNCT
ejpam-5714	396	33	∫	∫	PROPN
ejpam-5714	397	1	t	t	PROPN
ejpam-5714	397	2	t	t	PROPN
ejpam-5714	397	3	b	b	X
ejpam-5714	397	4	−1/(p−1	−1/(p−1	NOUN
ejpam-5714	397	5	)	)	PUNCT
ejpam-5714	397	6	(	(	PUNCT
ejpam-5714	397	7	s	s	X
ejpam-5714	397	8	)	)	PUNCT
ejpam-5714	397	9	ds	ds	X
ejpam-5714	397	10	ϖ′	ϖ′	X
ejpam-5714	397	11	(	(	PUNCT
ejpam-5714	397	12	t	t	NOUN
ejpam-5714	397	13	)	)	PUNCT
ejpam-5714	397	14	)	)	PUNCT
ejpam-5714	398	1	(	(	PUNCT
ejpam-5714	398	2	p−1	p−1	PROPN
ejpam-5714	398	3	)	)	PUNCT
ejpam-5714	398	4	=	=	PUNCT
ejpam-5714	399	1	(	(	PUNCT
ejpam-5714	399	2	∫	∫	PROPN
ejpam-5714	399	3	t	t	PROPN
ejpam-5714	399	4	t	t	PROPN
ejpam-5714	399	5	b−1/(p−1	b−1/(p−1	PROPN
ejpam-5714	399	6	)	)	PUNCT
ejpam-5714	399	7	(	(	PUNCT
ejpam-5714	399	8	s	s	X
ejpam-5714	399	9	)	)	PUNCT
ejpam-5714	399	10	ds	ds	NOUN
ejpam-5714	399	11	)	)	PUNCT
ejpam-5714	399	12	(	(	PUNCT
ejpam-5714	399	13	p−1	p−1	PROPN
ejpam-5714	399	14	)	)	PUNCT
ejpam-5714	399	15	,	,	PUNCT
ejpam-5714	399	16	(	(	PUNCT
ejpam-5714	399	17	35	35	NUM
ejpam-5714	399	18	)	)	PUNCT
ejpam-5714	399	19	for	for	ADP
ejpam-5714	399	20	t	t	PROPN
ejpam-5714	399	21	≥	≥	PROPN
ejpam-5714	399	22	t	t	PROPN
ejpam-5714	399	23	.	.	PUNCT
ejpam-5714	400	1	so	so	ADV
ejpam-5714	400	2	,	,	PUNCT
ejpam-5714	400	3	from	from	ADP
ejpam-5714	400	4	(	(	PUNCT
ejpam-5714	400	5	35	35	NUM
ejpam-5714	400	6	)	)	PUNCT
ejpam-5714	400	7	we	we	PRON
ejpam-5714	400	8	find	find	VERB
ejpam-5714	400	9	ξ	ξ	PROPN
ejpam-5714	400	10	(	(	PUNCT
ejpam-5714	400	11	t	t	PROPN
ejpam-5714	400	12	)	)	PUNCT
ejpam-5714	400	13	(	(	PUNCT
ejpam-5714	400	14	∫	∫	PROPN
ejpam-5714	400	15	t	t	PROPN
ejpam-5714	400	16	t0	t0	PROPN
ejpam-5714	400	17	b−1/(p−1	b−1/(p−1	PROPN
ejpam-5714	400	18	)	)	PUNCT
ejpam-5714	400	19	(	(	PUNCT
ejpam-5714	400	20	s	s	X
ejpam-5714	400	21	)	)	PUNCT
ejpam-5714	400	22	ds	ds	NOUN
ejpam-5714	400	23	)	)	PUNCT
ejpam-5714	400	24	(	(	PUNCT
ejpam-5714	400	25	p−1	p−1	PROPN
ejpam-5714	400	26	)	)	PUNCT
ejpam-5714	400	27	≤	≤	NOUN
ejpam-5714	400	28	(	(	PUNCT
ejpam-5714	400	29	∫	∫	PROPN
ejpam-5714	400	30	t	t	PROPN
ejpam-5714	400	31	t0	t0	PROPN
ejpam-5714	400	32	b−1/(p−1	b−1/(p−1	PROPN
ejpam-5714	400	33	)	)	PUNCT
ejpam-5714	400	34	(	(	PUNCT
ejpam-5714	400	35	s	s	X
ejpam-5714	400	36	)	)	PUNCT
ejpam-5714	400	37	ds∫	ds∫	NOUN
ejpam-5714	400	38	t	t	PROPN
ejpam-5714	400	39	t	t	NOUN
ejpam-5714	401	1	b	b	X
ejpam-5714	401	2	−1/(p−1	−1/(p−1	NOUN
ejpam-5714	401	3	)	)	PUNCT
ejpam-5714	401	4	(	(	PUNCT
ejpam-5714	401	5	s	s	X
ejpam-5714	401	6	)	)	PUNCT
ejpam-5714	401	7	ds	ds	NOUN
ejpam-5714	401	8	)	)	PUNCT
ejpam-5714	401	9	(	(	PUNCT
ejpam-5714	401	10	p−1	p−1	PROPN
ejpam-5714	401	11	)	)	PUNCT
ejpam-5714	401	12	,	,	PUNCT
ejpam-5714	401	13	and	and	CCONJ
ejpam-5714	401	14	so	so	ADV
ejpam-5714	401	15	lim	lim	PROPN
ejpam-5714	401	16	sup	sup	PROPN
ejpam-5714	401	17	t→∞	t→∞	NUM
ejpam-5714	401	18	ξ	ξ	PROPN
ejpam-5714	401	19	(	(	PUNCT
ejpam-5714	401	20	t	t	PROPN
ejpam-5714	401	21	)	)	PUNCT
ejpam-5714	401	22	(	(	PUNCT
ejpam-5714	401	23	∫	∫	PROPN
ejpam-5714	401	24	t	t	PROPN
ejpam-5714	401	25	t0	t0	PROPN
ejpam-5714	401	26	b	b	PROPN
ejpam-5714	401	27	−	−	PROPN
ejpam-5714	401	28	1	1	NUM
ejpam-5714	401	29	(	(	PUNCT
ejpam-5714	401	30	p−1	p−1	PROPN
ejpam-5714	401	31	)	)	PUNCT
ejpam-5714	401	32	(	(	PUNCT
ejpam-5714	401	33	s)ds	s)ds	PROPN
ejpam-5714	401	34	)	)	PUNCT
ejpam-5714	401	35	(	(	PUNCT
ejpam-5714	401	36	p−1	p−1	PROPN
ejpam-5714	401	37	)	)	PUNCT
ejpam-5714	401	38	≤	≤	NOUN
ejpam-5714	401	39	1	1	NUM
ejpam-5714	401	40	,	,	PUNCT
ejpam-5714	401	41	which	which	PRON
ejpam-5714	401	42	contradicts	contradict	VERB
ejpam-5714	401	43	(	(	PUNCT
ejpam-5714	401	44	34	34	NUM
ejpam-5714	401	45	)	)	PUNCT
ejpam-5714	401	46	.	.	PUNCT
ejpam-5714	402	1	hence	hence	ADV
ejpam-5714	402	2	,	,	PUNCT
ejpam-5714	402	3	the	the	DET
ejpam-5714	402	4	proof	proof	NOUN
ejpam-5714	402	5	is	be	AUX
ejpam-5714	402	6	finished	finish	VERB
ejpam-5714	402	7	.	.	PUNCT
ejpam-5714	403	1	corollary	corollary	ADJ
ejpam-5714	403	2	2	2	NUM
ejpam-5714	403	3	.	.	PUNCT
ejpam-5714	404	1	if∫	if∫	PROPN
ejpam-5714	404	2	∞	∞	PROPN
ejpam-5714	404	3	t0	t0	PROPN
ejpam-5714	404	4	n∑	n∑	PROPN
ejpam-5714	405	1	i=1	i=1	PROPN
ejpam-5714	405	2	qi	qi	PROPN
ejpam-5714	405	3	(	(	PUNCT
ejpam-5714	405	4	t	t	PROPN
ejpam-5714	405	5	)	)	PUNCT
ejpam-5714	406	1	(	(	PUNCT
ejpam-5714	406	2	1−	1−	NUM
ejpam-5714	406	3	y	y	PROPN
ejpam-5714	406	4	(	(	PUNCT
ejpam-5714	406	5	πi	πi	PROPN
ejpam-5714	406	6	(	(	PUNCT
ejpam-5714	406	7	t	t	NOUN
ejpam-5714	406	8	)	)	PUNCT
ejpam-5714	406	9	)	)	PUNCT
ejpam-5714	406	10	)	)	PUNCT
ejpam-5714	407	1	(	(	PUNCT
ejpam-5714	407	2	p−1	p−1	PROPN
ejpam-5714	407	3	)	)	PUNCT
ejpam-5714	407	4	b̂	b̂	NOUN
ejpam-5714	407	5	(	(	PUNCT
ejpam-5714	407	6	t	t	NOUN
ejpam-5714	407	7	)	)	PUNCT
ejpam-5714	407	8	exp	exp	NOUN
ejpam-5714	407	9	(	(	PUNCT
ejpam-5714	407	10	∫	∫	PROPN
ejpam-5714	407	11	t	t	PROPN
ejpam-5714	407	12	t0	t0	PROPN
ejpam-5714	407	13	ϑ	ϑ	X
ejpam-5714	407	14	1	1	NUM
ejpam-5714	407	15	(	(	PUNCT
ejpam-5714	407	16	p−1	p−1	PROPN
ejpam-5714	407	17	)	)	PUNCT
ejpam-5714	407	18	n	n	CCONJ
ejpam-5714	407	19	(	(	PUNCT
ejpam-5714	407	20	s	s	X
ejpam-5714	407	21	)	)	PUNCT
ejpam-5714	407	22	(	(	PUNCT
ejpam-5714	407	23	p−	p−	NOUN
ejpam-5714	407	24	1	1	NUM
ejpam-5714	407	25	)	)	PUNCT
ejpam-5714	407	26	/	/	PUNCT
ejpam-5714	408	1	(	(	PUNCT
ejpam-5714	408	2	b	b	X
ejpam-5714	408	3	(	(	PUNCT
ejpam-5714	408	4	s))1/(p−1	s))1/(p−1	ADJ
ejpam-5714	408	5	)	)	PUNCT
ejpam-5714	408	6	ds	ds	ADJ
ejpam-5714	408	7	)	)	PUNCT
ejpam-5714	408	8	dt	dt	NOUN
ejpam-5714	408	9	=	=	SYM
ejpam-5714	408	10	∞	∞	PROPN
ejpam-5714	408	11	,	,	PUNCT
ejpam-5714	408	12	(	(	PUNCT
ejpam-5714	408	13	36	36	NUM
ejpam-5714	408	14	)	)	PUNCT
ejpam-5714	408	15	or∫	or∫	PROPN
ejpam-5714	408	16	∞	∞	PROPN
ejpam-5714	408	17	t0	t0	PROPN
ejpam-5714	408	18	(	(	PUNCT
ejpam-5714	408	19	p−	p−	NOUN
ejpam-5714	408	20	1	1	NUM
ejpam-5714	408	21	)	)	PUNCT
ejpam-5714	408	22	/	/	PUNCT
ejpam-5714	408	23	(	(	PUNCT
ejpam-5714	408	24	b	b	X
ejpam-5714	408	25	(	(	PUNCT
ejpam-5714	408	26	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	408	27	)	)	PUNCT
ejpam-5714	408	28	ϑ	ϑ	X
ejpam-5714	408	29	1	1	NUM
ejpam-5714	408	30	(	(	PUNCT
ejpam-5714	408	31	p−1	p−1	PROPN
ejpam-5714	408	32	)	)	PUNCT
ejpam-5714	408	33	n	n	CCONJ
ejpam-5714	408	34	(	(	PUNCT
ejpam-5714	408	35	t)ϑ0(t	t)ϑ0(t	NOUN
ejpam-5714	408	36	)	)	PUNCT
ejpam-5714	408	37	exp	exp	NOUN
ejpam-5714	408	38	(	(	PUNCT
ejpam-5714	408	39	∫	∫	PROPN
ejpam-5714	408	40	t	t	PROPN
ejpam-5714	408	41	t0	t0	PROPN
ejpam-5714	408	42	(	(	PUNCT
ejpam-5714	408	43	p−	p−	NOUN
ejpam-5714	408	44	1	1	NUM
ejpam-5714	408	45	)	)	PUNCT
ejpam-5714	408	46	/	/	PUNCT
ejpam-5714	408	47	(	(	PUNCT
ejpam-5714	408	48	b	b	X
ejpam-5714	408	49	(	(	PUNCT
ejpam-5714	408	50	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	408	51	)	)	PUNCT
ejpam-5714	408	52	ϑ	ϑ	X
ejpam-5714	408	53	1	1	NUM
ejpam-5714	408	54	(	(	PUNCT
ejpam-5714	408	55	p−1	p−1	PROPN
ejpam-5714	408	56	)	)	PUNCT
ejpam-5714	408	57	n	n	PROPN
ejpam-5714	408	58	(	(	PUNCT
ejpam-5714	408	59	s)ds	s)ds	PROPN
ejpam-5714	408	60	)	)	PUNCT
ejpam-5714	408	61	dt	dt	NOUN
ejpam-5714	408	62	=	=	SYM
ejpam-5714	408	63	∞	∞	PROPN
ejpam-5714	408	64	,	,	PUNCT
ejpam-5714	408	65	(	(	PUNCT
ejpam-5714	408	66	37	37	NUM
ejpam-5714	408	67	)	)	PUNCT
ejpam-5714	408	68	then	then	ADV
ejpam-5714	408	69	all	all	DET
ejpam-5714	408	70	solutions	solution	NOUN
ejpam-5714	408	71	(	(	PUNCT
ejpam-5714	408	72	1	1	X
ejpam-5714	408	73	)	)	PUNCT
ejpam-5714	408	74	are	be	AUX
ejpam-5714	408	75	oscillatory	oscillatory	ADJ
ejpam-5714	408	76	.	.	PUNCT
ejpam-5714	409	1	proof	proof	NOUN
ejpam-5714	409	2	.	.	PUNCT
ejpam-5714	410	1	suppose	suppose	VERB
ejpam-5714	410	2	that	that	SCONJ
ejpam-5714	410	3	κ	κ	PROPN
ejpam-5714	410	4	(	(	PUNCT
ejpam-5714	410	5	t	t	PROPN
ejpam-5714	410	6	)	)	PUNCT
ejpam-5714	410	7	>	>	X
ejpam-5714	410	8	0	0	NUM
ejpam-5714	410	9	,	,	PUNCT
ejpam-5714	410	10	meaning	mean	VERB
ejpam-5714	410	11	that	that	SCONJ
ejpam-5714	410	12	both	both	PRON
ejpam-5714	410	13	κ	κ	X
ejpam-5714	410	14	(	(	PUNCT
ejpam-5714	410	15	ζ	ζ	NOUN
ejpam-5714	410	16	(	(	PUNCT
ejpam-5714	410	17	t	t	NOUN
ejpam-5714	410	18	)	)	PUNCT
ejpam-5714	410	19	)	)	PUNCT
ejpam-5714	410	20	and	and	CCONJ
ejpam-5714	410	21	κ	κ	X
ejpam-5714	410	22	(	(	PUNCT
ejpam-5714	410	23	πi	πi	PROPN
ejpam-5714	410	24	(	(	PUNCT
ejpam-5714	410	25	t	t	NOUN
ejpam-5714	410	26	)	)	PUNCT
ejpam-5714	410	27	)	)	PUNCT
ejpam-5714	410	28	are	be	AUX
ejpam-5714	410	29	positive	positive	ADJ
ejpam-5714	410	30	on	on	ADP
ejpam-5714	410	31	[	[	X
ejpam-5714	410	32	t0,∞	t0,∞	NUM
ejpam-5714	410	33	)	)	PUNCT
ejpam-5714	410	34	.	.	PUNCT
ejpam-5714	411	1	(	(	PUNCT
ejpam-5714	411	2	29	29	NUM
ejpam-5714	411	3	)	)	PUNCT
ejpam-5714	411	4	holds	hold	VERB
ejpam-5714	411	5	according	accord	VERB
ejpam-5714	411	6	to	to	ADP
ejpam-5714	411	7	lemma	lemma	PROPN
ejpam-5714	411	8	7	7	NUM
ejpam-5714	411	9	.	.	PUNCT
ejpam-5714	412	1	(	(	PUNCT
ejpam-5714	412	2	29	29	NUM
ejpam-5714	412	3	)	)	PUNCT
ejpam-5714	412	4	gives	give	VERB
ejpam-5714	412	5	us	we	PRON
ejpam-5714	412	6	ϑ′	ϑ′	X
ejpam-5714	412	7	(	(	PUNCT
ejpam-5714	412	8	t	t	NOUN
ejpam-5714	412	9	)	)	PUNCT
ejpam-5714	412	10	=	=	SYM
ejpam-5714	413	1	−	−	PROPN
ejpam-5714	413	2	(	(	PUNCT
ejpam-5714	413	3	p−	p−	NOUN
ejpam-5714	413	4	1	1	NUM
ejpam-5714	413	5	)	)	PUNCT
ejpam-5714	413	6	/	/	PUNCT
ejpam-5714	413	7	(	(	PUNCT
ejpam-5714	413	8	b	b	X
ejpam-5714	413	9	(	(	PUNCT
ejpam-5714	413	10	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	413	11	)	)	PUNCT
ejpam-5714	413	12	ϑ	ϑ	X
ejpam-5714	413	13	p−	p−	NOUN
ejpam-5714	413	14	p−1	p−1	NOUN
ejpam-5714	413	15	(	(	PUNCT
ejpam-5714	413	16	t)−	t)−	PROPN
ejpam-5714	413	17	n∑	n∑	PROPN
ejpam-5714	413	18	i=1	i=1	PROPN
ejpam-5714	413	19	qi	qi	PROPN
ejpam-5714	413	20	(	(	PUNCT
ejpam-5714	413	21	t	t	PROPN
ejpam-5714	413	22	)	)	PUNCT
ejpam-5714	413	23	(	(	PUNCT
ejpam-5714	413	24	1−	1−	NUM
ejpam-5714	413	25	y	y	PROPN
ejpam-5714	413	26	(	(	PUNCT
ejpam-5714	413	27	πi	πi	PROPN
ejpam-5714	413	28	(	(	PUNCT
ejpam-5714	413	29	t	t	NOUN
ejpam-5714	413	30	)	)	PUNCT
ejpam-5714	413	31	)	)	PUNCT
ejpam-5714	413	32	)	)	PUNCT
ejpam-5714	414	1	p−1	p−1	NOUN
ejpam-5714	414	2	b̂	b̂	NOUN
ejpam-5714	414	3	(	(	PUNCT
ejpam-5714	414	4	t	t	NOUN
ejpam-5714	414	5	)	)	PUNCT
ejpam-5714	414	6	≤	≤	NOUN
ejpam-5714	414	7	−	−	PROPN
ejpam-5714	414	8	(	(	PUNCT
ejpam-5714	414	9	p−	p−	NOUN
ejpam-5714	414	10	1	1	NUM
ejpam-5714	414	11	)	)	PUNCT
ejpam-5714	414	12	/	/	PUNCT
ejpam-5714	414	13	(	(	PUNCT
ejpam-5714	414	14	b	b	X
ejpam-5714	414	15	(	(	PUNCT
ejpam-5714	414	16	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	414	17	)	)	PUNCT
ejpam-5714	414	18	ϑ	ϑ	PROPN
ejpam-5714	414	19	1	1	NUM
ejpam-5714	414	20	p−1	p−1	PROPN
ejpam-5714	414	21	n	n	PROPN
ejpam-5714	414	22	(	(	PUNCT
ejpam-5714	414	23	t)ϑ	t)ϑ	X
ejpam-5714	414	24	(	(	PUNCT
ejpam-5714	414	25	t)−	t)−	PROPN
ejpam-5714	414	26	n∑	n∑	PROPN
ejpam-5714	414	27	i=1	i=1	PROPN
ejpam-5714	415	1	qi	qi	PROPN
ejpam-5714	415	2	(	(	PUNCT
ejpam-5714	415	3	t	t	PROPN
ejpam-5714	415	4	)	)	PUNCT
ejpam-5714	415	5	(	(	PUNCT
ejpam-5714	415	6	1−	1−	NUM
ejpam-5714	415	7	y	y	PROPN
ejpam-5714	415	8	(	(	PUNCT
ejpam-5714	415	9	πi	πi	PROPN
ejpam-5714	415	10	(	(	PUNCT
ejpam-5714	415	11	t	t	NOUN
ejpam-5714	415	12	)	)	PUNCT
ejpam-5714	415	13	)	)	PUNCT
ejpam-5714	415	14	)	)	PUNCT
ejpam-5714	416	1	p−1	p−1	NOUN
ejpam-5714	416	2	b̂	b̂	NOUN
ejpam-5714	416	3	(	(	PUNCT
ejpam-5714	416	4	t	t	PROPN
ejpam-5714	416	5	)	)	PUNCT
ejpam-5714	416	6	.(38	.(38	PUNCT
ejpam-5714	416	7	)	)	PUNCT
ejpam-5714	416	8	hence,∫	hence,∫	X
ejpam-5714	417	1	t	t	PROPN
ejpam-5714	417	2	t	t	PROPN
ejpam-5714	417	3	n∑	n∑	PROPN
ejpam-5714	417	4	i=1	i=1	PROPN
ejpam-5714	418	1	qi	qi	PROPN
ejpam-5714	418	2	(	(	PUNCT
ejpam-5714	418	3	s	s	NOUN
ejpam-5714	418	4	)	)	PUNCT
ejpam-5714	418	5	(	(	PUNCT
ejpam-5714	418	6	1−	1−	NUM
ejpam-5714	418	7	y	y	PROPN
ejpam-5714	418	8	(	(	PUNCT
ejpam-5714	418	9	πi	πi	PROPN
ejpam-5714	418	10	(	(	PUNCT
ejpam-5714	418	11	s	s	NOUN
ejpam-5714	418	12	)	)	PUNCT
ejpam-5714	418	13	)	)	PUNCT
ejpam-5714	418	14	)	)	PUNCT
ejpam-5714	418	15	p−1	p−1	NOUN
ejpam-5714	418	16	b̂	b̂	NOUN
ejpam-5714	418	17	(	(	PUNCT
ejpam-5714	418	18	s	s	NOUN
ejpam-5714	418	19	)	)	PUNCT
ejpam-5714	418	20	exp	exp	NOUN
ejpam-5714	418	21	(	(	PUNCT
ejpam-5714	418	22	∫	∫	PROPN
ejpam-5714	418	23	s	s	PROPN
ejpam-5714	418	24	t	t	PROPN
ejpam-5714	418	25	ϑ	ϑ	X
ejpam-5714	418	26	1	1	NUM
ejpam-5714	418	27	(	(	PUNCT
ejpam-5714	418	28	p−1	p−1	PROPN
ejpam-5714	418	29	)	)	PUNCT
ejpam-5714	418	30	n	n	PROPN
ejpam-5714	418	31	(	(	PUNCT
ejpam-5714	418	32	t	t	NOUN
ejpam-5714	418	33	)	)	PUNCT
ejpam-5714	418	34	(	(	PUNCT
ejpam-5714	418	35	p−	p−	NOUN
ejpam-5714	418	36	1	1	NUM
ejpam-5714	418	37	)	)	PUNCT
ejpam-5714	418	38	/	/	PUNCT
ejpam-5714	418	39	(	(	PUNCT
ejpam-5714	418	40	b	b	X
ejpam-5714	418	41	(	(	PUNCT
ejpam-5714	418	42	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	418	43	)	)	PUNCT
ejpam-5714	418	44	dt	dt	NOUN
ejpam-5714	418	45	)	)	PUNCT
ejpam-5714	419	1	ds	ds	ADJ
ejpam-5714	419	2	≤	≤	NUM
ejpam-5714	419	3	ϑ	ϑ	X
ejpam-5714	419	4	(	(	PUNCT
ejpam-5714	419	5	t	t	PROPN
ejpam-5714	419	6	)	)	PUNCT
ejpam-5714	419	7	<	<	X
ejpam-5714	419	8	∞	∞	PROPN
ejpam-5714	419	9	,	,	PUNCT
ejpam-5714	419	10	which	which	PRON
ejpam-5714	419	11	contradicts	contradict	VERB
ejpam-5714	419	12	(	(	PUNCT
ejpam-5714	419	13	36	36	NUM
ejpam-5714	419	14	)	)	PUNCT
ejpam-5714	419	15	.	.	PUNCT
ejpam-5714	420	1	next	next	ADV
ejpam-5714	420	2	,	,	PUNCT
ejpam-5714	420	3	let	let	VERB
ejpam-5714	420	4	m	m	PROPN
ejpam-5714	420	5	(	(	PUNCT
ejpam-5714	420	6	t	t	PROPN
ejpam-5714	420	7	)	)	PUNCT
ejpam-5714	420	8	=	=	SYM
ejpam-5714	421	1	∫∞	∫∞	PROPN
ejpam-5714	421	2	t	t	PROPN
ejpam-5714	421	3	(	(	PUNCT
ejpam-5714	421	4	p−	p−	NOUN
ejpam-5714	421	5	1	1	NUM
ejpam-5714	421	6	)	)	PUNCT
ejpam-5714	421	7	/	/	PUNCT
ejpam-5714	421	8	(	(	PUNCT
ejpam-5714	421	9	b	b	X
ejpam-5714	421	10	(	(	PUNCT
ejpam-5714	421	11	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	421	12	)	)	PUNCT
ejpam-5714	421	13	ϑ	ϑ	PROPN
ejpam-5714	421	14	p	p	X
ejpam-5714	421	15	p−1	p−1	PROPN
ejpam-5714	421	16	(	(	PUNCT
ejpam-5714	421	17	s	s	NOUN
ejpam-5714	421	18	)	)	PUNCT
ejpam-5714	421	19	ds	ds	NOUN
ejpam-5714	421	20	.	.	PUNCT
ejpam-5714	422	1	then	then	ADV
ejpam-5714	422	2	,	,	PUNCT
ejpam-5714	422	3	we	we	PRON
ejpam-5714	422	4	obtain	obtain	VERB
ejpam-5714	422	5	m	m	VERB
ejpam-5714	422	6	′	′	NUM
ejpam-5714	422	7	(	(	PUNCT
ejpam-5714	422	8	t	t	NOUN
ejpam-5714	422	9	)	)	PUNCT
ejpam-5714	422	10	=	=	SYM
ejpam-5714	423	1	−	−	PROPN
ejpam-5714	423	2	(	(	PUNCT
ejpam-5714	423	3	p−	p−	NOUN
ejpam-5714	423	4	1	1	NUM
ejpam-5714	423	5	)	)	PUNCT
ejpam-5714	423	6	/	/	PUNCT
ejpam-5714	423	7	(	(	PUNCT
ejpam-5714	423	8	b	b	X
ejpam-5714	423	9	(	(	PUNCT
ejpam-5714	423	10	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	423	11	)	)	PUNCT
ejpam-5714	423	12	ϑ	ϑ	PROPN
ejpam-5714	423	13	p	p	X
ejpam-5714	423	14	p−1	p−1	PROPN
ejpam-5714	423	15	(	(	PUNCT
ejpam-5714	423	16	t	t	PROPN
ejpam-5714	423	17	)	)	PUNCT
ejpam-5714	423	18	f.	f.	NOUN
ejpam-5714	423	19	aldosari	aldosari	PROPN
ejpam-5714	423	20	/	/	SYM
ejpam-5714	423	21	eur	eur	PROPN
ejpam-5714	423	22	.	.	PUNCT
ejpam-5714	424	1	j.	j.	PROPN
ejpam-5714	424	2	pure	pure	PROPN
ejpam-5714	424	3	appl	appl	PROPN
ejpam-5714	424	4	.	.	PROPN
ejpam-5714	424	5	math	math	PROPN
ejpam-5714	424	6	,	,	PUNCT
ejpam-5714	424	7	18	18	NUM
ejpam-5714	424	8	(	(	PUNCT
ejpam-5714	424	9	1	1	NUM
ejpam-5714	424	10	)	)	PUNCT
ejpam-5714	424	11	(	(	PUNCT
ejpam-5714	424	12	2025	2025	NUM
ejpam-5714	424	13	)	)	PUNCT
ejpam-5714	424	14	,	,	PUNCT
ejpam-5714	424	15	5714	5714	NUM
ejpam-5714	424	16	13	13	NUM
ejpam-5714	424	17	of	of	ADP
ejpam-5714	424	18	16	16	NUM
ejpam-5714	424	19	≤	≤	NUM
ejpam-5714	424	20	−	−	PROPN
ejpam-5714	424	21	(	(	PUNCT
ejpam-5714	424	22	p−	p−	NOUN
ejpam-5714	424	23	1	1	NUM
ejpam-5714	424	24	)	)	PUNCT
ejpam-5714	424	25	/	/	PUNCT
ejpam-5714	425	1	(	(	PUNCT
ejpam-5714	425	2	b	b	X
ejpam-5714	425	3	(	(	PUNCT
ejpam-5714	425	4	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	425	5	)	)	PUNCT
ejpam-5714	425	6	ϑ	ϑ	PROPN
ejpam-5714	425	7	1	1	NUM
ejpam-5714	425	8	p−1	p−1	PROPN
ejpam-5714	425	9	n	n	PROPN
ejpam-5714	425	10	(	(	PUNCT
ejpam-5714	425	11	t)ϑ	t)ϑ	X
ejpam-5714	425	12	(	(	PUNCT
ejpam-5714	425	13	t	t	NOUN
ejpam-5714	425	14	)	)	PUNCT
ejpam-5714	425	15	=	=	SYM
ejpam-5714	426	1	−	−	PROPN
ejpam-5714	426	2	(	(	PUNCT
ejpam-5714	426	3	p−	p−	NOUN
ejpam-5714	426	4	1	1	NUM
ejpam-5714	426	5	)	)	PUNCT
ejpam-5714	426	6	/	/	PUNCT
ejpam-5714	426	7	(	(	PUNCT
ejpam-5714	426	8	b	b	X
ejpam-5714	426	9	(	(	PUNCT
ejpam-5714	426	10	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	426	11	)	)	PUNCT
ejpam-5714	426	12	ϑ	ϑ	PROPN
ejpam-5714	426	13	1	1	NUM
ejpam-5714	426	14	p−1	p−1	PROPN
ejpam-5714	426	15	n	n	PROPN
ejpam-5714	426	16	(	(	PUNCT
ejpam-5714	426	17	t	t	PROPN
ejpam-5714	426	18	)	)	PUNCT
ejpam-5714	426	19	(	(	PUNCT
ejpam-5714	426	20	m	m	PROPN
ejpam-5714	426	21	(	(	PUNCT
ejpam-5714	426	22	t	t	PROPN
ejpam-5714	426	23	)	)	PUNCT
ejpam-5714	426	24	+	+	CCONJ
ejpam-5714	426	25	ϑ0	ϑ0	PROPN
ejpam-5714	426	26	(	(	PUNCT
ejpam-5714	426	27	t	t	NOUN
ejpam-5714	426	28	)	)	PUNCT
ejpam-5714	426	29	)	)	PUNCT
ejpam-5714	426	30	.	.	PUNCT
ejpam-5714	427	1	consequently	consequently	ADV
ejpam-5714	427	2	,	,	PUNCT
ejpam-5714	427	3	we	we	PRON
ejpam-5714	427	4	discover∫	discover∫	VERB
ejpam-5714	427	5	∞	∞	PROPN
ejpam-5714	427	6	t	t	NOUN
ejpam-5714	427	7	(	(	PUNCT
ejpam-5714	427	8	p−	p−	NOUN
ejpam-5714	427	9	1	1	NUM
ejpam-5714	427	10	)	)	PUNCT
ejpam-5714	427	11	/	/	PUNCT
ejpam-5714	428	1	(	(	PUNCT
ejpam-5714	428	2	b	b	X
ejpam-5714	428	3	(	(	PUNCT
ejpam-5714	428	4	t))1/(p−1	t))1/(p−1	ADJ
ejpam-5714	428	5	)	)	PUNCT
ejpam-5714	428	6	ϑ	ϑ	PROPN
ejpam-5714	428	7	1	1	NUM
ejpam-5714	428	8	p−1	p−1	PROPN
ejpam-5714	428	9	n	n	PROPN
ejpam-5714	428	10	(	(	PUNCT
ejpam-5714	428	11	t)ϑ0(t	t)ϑ0(t	PROPN
ejpam-5714	428	12	)	)	PUNCT
ejpam-5714	428	13	exp	exp	NOUN
ejpam-5714	428	14	(	(	PUNCT
ejpam-5714	428	15	∫	∫	PROPN
ejpam-5714	428	16	t	t	PROPN
ejpam-5714	428	17	t	t	PROPN
ejpam-5714	428	18	(	(	PUNCT
ejpam-5714	428	19	p−	p−	NOUN
ejpam-5714	428	20	1	1	NUM
ejpam-5714	428	21	)	)	PUNCT
ejpam-5714	428	22	/	/	PUNCT
ejpam-5714	428	23	(	(	PUNCT
ejpam-5714	428	24	b	b	X
ejpam-5714	428	25	(	(	PUNCT
ejpam-5714	428	26	s))1/(p−1	s))1/(p−1	NOUN
ejpam-5714	428	27	)	)	PUNCT
ejpam-5714	428	28	ϑ	ϑ	PROPN
ejpam-5714	428	29	1	1	NUM
ejpam-5714	428	30	p−1	p−1	PROPN
ejpam-5714	428	31	n	n	PROPN
ejpam-5714	428	32	(	(	PUNCT
ejpam-5714	428	33	s)ds	s)ds	PROPN
ejpam-5714	428	34	)	)	PUNCT
ejpam-5714	428	35	dt	dt	X
ejpam-5714	429	1	<	<	X
ejpam-5714	429	2	∞.	∞.	PROPN
ejpam-5714	429	3	this	this	DET
ejpam-5714	429	4	runs	run	VERB
ejpam-5714	429	5	counter	counter	ADV
ejpam-5714	429	6	to	to	ADP
ejpam-5714	429	7	(	(	PUNCT
ejpam-5714	429	8	37	37	NUM
ejpam-5714	429	9	)	)	PUNCT
ejpam-5714	429	10	.	.	PUNCT
ejpam-5714	430	1	the	the	DET
ejpam-5714	430	2	proof	proof	NOUN
ejpam-5714	430	3	is	be	AUX
ejpam-5714	430	4	finished	finish	VERB
ejpam-5714	430	5	.	.	PUNCT
ejpam-5714	431	1	3	3	X
ejpam-5714	431	2	.	.	X
ejpam-5714	431	3	examples	example	NOUN
ejpam-5714	431	4	and	and	CCONJ
ejpam-5714	431	5	discussion	discussion	NOUN
ejpam-5714	431	6	example	example	NOUN
ejpam-5714	431	7	1	1	X
ejpam-5714	431	8	.	.	PUNCT
ejpam-5714	432	1	let	let	VERB
ejpam-5714	432	2	the	the	DET
ejpam-5714	432	3	equation	equation	NOUN
ejpam-5714	432	4	(	(	PUNCT
ejpam-5714	432	5	(	(	PUNCT
ejpam-5714	432	6	(	(	PUNCT
ejpam-5714	432	7	κ	κ	X
ejpam-5714	432	8	(	(	PUNCT
ejpam-5714	432	9	t	t	PROPN
ejpam-5714	432	10	)	)	PUNCT
ejpam-5714	432	11	+	+	CCONJ
ejpam-5714	433	1	y0κ	y0κ	PRON
ejpam-5714	433	2	(	(	PUNCT
ejpam-5714	433	3	ζ0	ζ0	PROPN
ejpam-5714	433	4	t	t	PROPN
ejpam-5714	433	5	)	)	PUNCT
ejpam-5714	433	6	)	)	PUNCT
ejpam-5714	433	7	′)(p−1	′)(p−1	PROPN
ejpam-5714	433	8	)	)	PUNCT
ejpam-5714	433	9	)	)	PUNCT
ejpam-5714	433	10	′	′	NOUN
ejpam-5714	434	1	+	+	CCONJ
ejpam-5714	434	2	q0	q0	PROPN
ejpam-5714	434	3	t	t	PROPN
ejpam-5714	434	4	p−1	p−1	PROPN
ejpam-5714	434	5	−	−	PROPN
ejpam-5714	434	6	ptp	ptp	PROPN
ejpam-5714	434	7	t2p−1	t2p−1	PROPN
ejpam-5714	434	8	κ(p−1	κ(p−1	PROPN
ejpam-5714	434	9	)	)	PUNCT
ejpam-5714	434	10	(	(	PUNCT
ejpam-5714	434	11	εt	εt	X
ejpam-5714	434	12	)	)	PUNCT
ejpam-5714	434	13	+	+	CCONJ
ejpam-5714	434	14	p	p	DET
ejpam-5714	434	15	tp−1	tp−1	PROPN
ejpam-5714	434	16	κ(p−1	κ(p−1	PROPN
ejpam-5714	434	17	)	)	PUNCT
ejpam-5714	434	18	(	(	PUNCT
ejpam-5714	434	19	εt	εt	PROPN
ejpam-5714	434	20	)	)	PUNCT
ejpam-5714	434	21	=	=	SYM
ejpam-5714	434	22	0	0	NUM
ejpam-5714	434	23	,	,	PUNCT
ejpam-5714	434	24	(	(	PUNCT
ejpam-5714	434	25	39	39	NUM
ejpam-5714	434	26	)	)	PUNCT
ejpam-5714	434	27	let	let	VERB
ejpam-5714	434	28	b	b	X
ejpam-5714	434	29	(	(	PUNCT
ejpam-5714	434	30	t	t	PROPN
ejpam-5714	434	31	)	)	PUNCT
ejpam-5714	434	32	=	=	SYM
ejpam-5714	435	1	1	1	NUM
ejpam-5714	435	2	,	,	PUNCT
ejpam-5714	435	3	y	y	PROPN
ejpam-5714	435	4	(	(	PUNCT
ejpam-5714	435	5	t	t	PROPN
ejpam-5714	435	6	)	)	PUNCT
ejpam-5714	435	7	=	=	SYM
ejpam-5714	435	8	y0	y0	NOUN
ejpam-5714	435	9	,	,	PUNCT
ejpam-5714	435	10	ζ	ζ	PROPN
ejpam-5714	435	11	(	(	PUNCT
ejpam-5714	435	12	t	t	NOUN
ejpam-5714	435	13	)	)	PUNCT
ejpam-5714	435	14	=	=	PUNCT
ejpam-5714	435	15	ζ0	ζ0	PROPN
ejpam-5714	435	16	t	t	PROPN
ejpam-5714	435	17	,	,	PUNCT
ejpam-5714	435	18	∑n	∑n	PROPN
ejpam-5714	435	19	i=1	i=1	PROPN
ejpam-5714	435	20	qi	qi	PROPN
ejpam-5714	435	21	(	(	PUNCT
ejpam-5714	435	22	t	t	PROPN
ejpam-5714	435	23	)	)	PUNCT
ejpam-5714	435	24	=	=	PUNCT
ejpam-5714	436	1	q0tp−1−ptp	q0tp−1−ptp	NOUN
ejpam-5714	437	1	t2p−1	t2p−1	PROPN
ejpam-5714	438	1	+	+	CCONJ
ejpam-5714	438	2	p	p	X
ejpam-5714	438	3	tp−1	tp−1	PROPN
ejpam-5714	438	4	and	and	CCONJ
ejpam-5714	438	5	πi	πi	PROPN
ejpam-5714	438	6	(	(	PUNCT
ejpam-5714	438	7	t	t	NOUN
ejpam-5714	438	8	)	)	PUNCT
ejpam-5714	439	1	=	=	SYM
ejpam-5714	439	2	εt	εt	PROPN
ejpam-5714	439	3	,	,	PUNCT
ejpam-5714	439	4	where	where	SCONJ
ejpam-5714	439	5	ε	ε	PROPN
ejpam-5714	439	6	,	,	PUNCT
ejpam-5714	439	7	ζ0	ζ0	PROPN
ejpam-5714	439	8	∈	∈	PROPN
ejpam-5714	439	9	(	(	PUNCT
ejpam-5714	439	10	0	0	NUM
ejpam-5714	439	11	,	,	PUNCT
ejpam-5714	439	12	1	1	NUM
ejpam-5714	439	13	)	)	PUNCT
ejpam-5714	439	14	.	.	PUNCT
ejpam-5714	440	1	it	it	PRON
ejpam-5714	440	2	is	be	AUX
ejpam-5714	440	3	easy	easy	ADJ
ejpam-5714	440	4	to	to	PART
ejpam-5714	440	5	verify	verify	VERB
ejpam-5714	440	6	that	that	SCONJ
ejpam-5714	441	1	n∑	n∑	PROPN
ejpam-5714	441	2	i=1	i=1	PROPN
ejpam-5714	441	3	qi	qi	PROPN
ejpam-5714	441	4	(	(	PUNCT
ejpam-5714	441	5	t	t	PROPN
ejpam-5714	441	6	)	)	PUNCT
ejpam-5714	441	7	(	(	PUNCT
ejpam-5714	441	8	1−	1−	NUM
ejpam-5714	441	9	y	y	PROPN
ejpam-5714	441	10	(	(	PUNCT
ejpam-5714	441	11	πi	πi	PROPN
ejpam-5714	441	12	(	(	PUNCT
ejpam-5714	441	13	t	t	NOUN
ejpam-5714	441	14	)	)	PUNCT
ejpam-5714	441	15	)	)	PUNCT
ejpam-5714	441	16	)	)	PUNCT
ejpam-5714	442	1	p−1	p−1	PROPN
ejpam-5714	442	2	=	=	NOUN
ejpam-5714	442	3	q0	q0	PROPN
ejpam-5714	442	4	tp	tp	X
ejpam-5714	442	5	(	(	PUNCT
ejpam-5714	442	6	1−	1−	NUM
ejpam-5714	442	7	ε	ε	PROPN
ejpam-5714	442	8	)	)	PUNCT
ejpam-5714	443	1	[	[	X
ejpam-5714	443	2	1−	1−	NUM
ejpam-5714	443	3	y0	y0	NOUN
ejpam-5714	443	4	]	]	X
ejpam-5714	443	5	p−1	p−1	PROPN
ejpam-5714	443	6	,	,	PUNCT
ejpam-5714	443	7	bt0	bt0	PROPN
ejpam-5714	443	8	(	(	PUNCT
ejpam-5714	443	9	t	t	NOUN
ejpam-5714	443	10	)	)	PUNCT
ejpam-5714	443	11	=	=	NOUN
ejpam-5714	443	12	t	t	NOUN
ejpam-5714	443	13	and	and	CCONJ
ejpam-5714	443	14	b̃t0(t	b̃t0(t	PROPN
ejpam-5714	443	15	)	)	PUNCT
ejpam-5714	443	16	=	=	PROPN
ejpam-5714	443	17	mt	mt	PROPN
ejpam-5714	443	18	,	,	PUNCT
ejpam-5714	443	19	where	where	SCONJ
ejpam-5714	443	20	m	m	VERB
ejpam-5714	443	21	:	:	PUNCT
ejpam-5714	443	22	=	=	SYM
ejpam-5714	443	23	1	1	NUM
ejpam-5714	443	24	+	+	CCONJ
ejpam-5714	443	25	ε(p−1	ε(p−1	ADJ
ejpam-5714	443	26	)	)	PUNCT
ejpam-5714	443	27	q0	q0	NOUN
ejpam-5714	443	28	(	(	PUNCT
ejpam-5714	443	29	p−	p−	NOUN
ejpam-5714	443	30	1	1	NUM
ejpam-5714	443	31	)	)	PUNCT
ejpam-5714	443	32	(	(	PUNCT
ejpam-5714	443	33	1−	1−	NUM
ejpam-5714	443	34	ε	ε	PROPN
ejpam-5714	443	35	)	)	PUNCT
ejpam-5714	444	1	[	[	X
ejpam-5714	444	2	1−	1−	NUM
ejpam-5714	444	3	y0	y0	NOUN
ejpam-5714	444	4	]	]	PUNCT
ejpam-5714	444	5	(	(	PUNCT
ejpam-5714	444	6	p−1	p−1	PROPN
ejpam-5714	444	7	)	)	PUNCT
ejpam-5714	444	8	.	.	PUNCT
ejpam-5714	445	1	by	by	ADP
ejpam-5714	445	2	corollary	corollary	ADJ
ejpam-5714	445	3	1	1	NUM
ejpam-5714	445	4	,	,	PUNCT
ejpam-5714	445	5	we	we	PRON
ejpam-5714	445	6	find	find	VERB
ejpam-5714	445	7	(	(	PUNCT
ejpam-5714	445	8	39	39	NUM
ejpam-5714	445	9	)	)	PUNCT
ejpam-5714	445	10	is	be	AUX
ejpam-5714	445	11	oscillatory	oscillatory	ADJ
ejpam-5714	445	12	if	if	SCONJ
ejpam-5714	445	13	(	(	PUNCT
ejpam-5714	445	14	m	m	PROPN
ejpam-5714	445	15	(	(	PUNCT
ejpam-5714	445	16	p−1)ε(p−1)q0	p−1)ε(p−1)q0	NOUN
ejpam-5714	445	17	(	(	PUNCT
ejpam-5714	445	18	1−	1−	NUM
ejpam-5714	445	19	ε	ε	PROPN
ejpam-5714	445	20	)	)	PUNCT
ejpam-5714	446	1	[	[	X
ejpam-5714	446	2	1−	1−	NUM
ejpam-5714	446	3	y0	y0	NOUN
ejpam-5714	446	4	]	]	PUNCT
ejpam-5714	446	5	(	(	PUNCT
ejpam-5714	446	6	p−1	p−1	PROPN
ejpam-5714	446	7	)	)	PUNCT
ejpam-5714	446	8	)	)	PUNCT
ejpam-5714	447	1	ln	ln	ADV
ejpam-5714	447	2	1	1	NUM
ejpam-5714	447	3	ε	ε	X
ejpam-5714	447	4	>	>	X
ejpam-5714	447	5	1	1	NUM
ejpam-5714	447	6	e	e	NOUN
ejpam-5714	447	7	,	,	PUNCT
ejpam-5714	447	8	or	or	CCONJ
ejpam-5714	447	9	(	(	PUNCT
ejpam-5714	447	10	p−	p−	NOUN
ejpam-5714	447	11	1	1	NUM
ejpam-5714	447	12	)	)	PUNCT
ejpam-5714	447	13	(	(	PUNCT
ejpam-5714	447	14	m	m	VERB
ejpam-5714	447	15	−	−	PROPN
ejpam-5714	447	16	1)m	1)m	NUM
ejpam-5714	447	17	(	(	PUNCT
ejpam-5714	447	18	p−1	p−1	PROPN
ejpam-5714	447	19	)	)	PUNCT
ejpam-5714	447	20	ln	ln	PROPN
ejpam-5714	447	21	1	1	NUM
ejpam-5714	447	22	ε	ε	X
ejpam-5714	447	23	>	>	X
ejpam-5714	447	24	1	1	NUM
ejpam-5714	447	25	e	e	NOUN
ejpam-5714	447	26	.	.	PUNCT
ejpam-5714	448	1	(	(	PUNCT
ejpam-5714	448	2	40	40	NUM
ejpam-5714	448	3	)	)	PUNCT
ejpam-5714	448	4	also	also	ADV
ejpam-5714	448	5	,	,	PUNCT
ejpam-5714	448	6	we	we	PRON
ejpam-5714	448	7	find	find	VERB
ejpam-5714	448	8	that	that	DET
ejpam-5714	448	9	b̂t1	b̂t1	NOUN
ejpam-5714	448	10	(	(	PUNCT
ejpam-5714	448	11	t	t	NOUN
ejpam-5714	448	12	)	)	PUNCT
ejpam-5714	448	13	=	=	SYM
ejpam-5714	449	1	ε1	ε1	PROPN
ejpam-5714	449	2	/	/	SYM
ejpam-5714	449	3	m	m	PROPN
ejpam-5714	449	4	,	,	PUNCT
ejpam-5714	449	5	n∑	n∑	PROPN
ejpam-5714	449	6	i=1	i=1	PROPN
ejpam-5714	450	1	qi	qi	PROPN
ejpam-5714	450	2	(	(	PUNCT
ejpam-5714	450	3	t	t	PROPN
ejpam-5714	450	4	)	)	PUNCT
ejpam-5714	450	5	(	(	PUNCT
ejpam-5714	450	6	1−	1−	NUM
ejpam-5714	450	7	y	y	PROPN
ejpam-5714	450	8	(	(	PUNCT
ejpam-5714	450	9	πi	πi	PROPN
ejpam-5714	450	10	(	(	PUNCT
ejpam-5714	450	11	t	t	NOUN
ejpam-5714	450	12	)	)	PUNCT
ejpam-5714	450	13	)	)	PUNCT
ejpam-5714	450	14	)	)	PUNCT
ejpam-5714	451	1	(	(	PUNCT
ejpam-5714	451	2	p−1	p−1	PROPN
ejpam-5714	451	3	)	)	PUNCT
ejpam-5714	451	4	b̂	b̂	NOUN
ejpam-5714	451	5	(	(	PUNCT
ejpam-5714	451	6	t	t	NOUN
ejpam-5714	451	7	)	)	PUNCT
ejpam-5714	451	8	=	=	VERB
ejpam-5714	452	1	q0	q0	PROPN
ejpam-5714	452	2	(	(	PUNCT
ejpam-5714	452	3	1−	1−	NUM
ejpam-5714	452	4	y0	y0	NOUN
ejpam-5714	452	5	)	)	PUNCT
ejpam-5714	452	6	(	(	PUNCT
ejpam-5714	452	7	p−1	p−1	PROPN
ejpam-5714	452	8	)	)	PUNCT
ejpam-5714	452	9	(	(	PUNCT
ejpam-5714	452	10	1−	1−	NUM
ejpam-5714	452	11	ε	ε	PROPN
ejpam-5714	452	12	)	)	PUNCT
ejpam-5714	452	13	tp	tp	ADP
ejpam-5714	452	14	ε(p−1)/m	ε(p−1)/m	PROPN
ejpam-5714	452	15	,	,	PUNCT
ejpam-5714	452	16	and∫	and∫	PROPN
ejpam-5714	453	1	∞	∞	PROPN
ejpam-5714	453	2	t	t	PROPN
ejpam-5714	453	3	n∑	n∑	NOUN
ejpam-5714	453	4	i=1	i=1	PROPN
ejpam-5714	454	1	qi	qi	PROPN
ejpam-5714	454	2	(	(	PUNCT
ejpam-5714	454	3	s	s	NOUN
ejpam-5714	454	4	)	)	PUNCT
ejpam-5714	454	5	(	(	PUNCT
ejpam-5714	454	6	1−	1−	NUM
ejpam-5714	454	7	y	y	PROPN
ejpam-5714	454	8	(	(	PUNCT
ejpam-5714	454	9	πi	πi	PROPN
ejpam-5714	454	10	(	(	PUNCT
ejpam-5714	454	11	s	s	NOUN
ejpam-5714	454	12	)	)	PUNCT
ejpam-5714	454	13	)	)	PUNCT
ejpam-5714	454	14	)	)	PUNCT
ejpam-5714	454	15	p−1	p−1	NOUN
ejpam-5714	454	16	b̂	b̂	NOUN
ejpam-5714	454	17	(	(	PUNCT
ejpam-5714	454	18	s	s	X
ejpam-5714	454	19	)	)	PUNCT
ejpam-5714	454	20	ds	ds	NOUN
ejpam-5714	454	21	=	=	PUNCT
ejpam-5714	454	22	q0	q0	PROPN
ejpam-5714	454	23	(	(	PUNCT
ejpam-5714	454	24	1−	1−	NUM
ejpam-5714	454	25	y0	y0	NOUN
ejpam-5714	454	26	)	)	PUNCT
ejpam-5714	454	27	p−1	p−1	PROPN
ejpam-5714	454	28	(	(	PUNCT
ejpam-5714	454	29	1−	1−	NUM
ejpam-5714	454	30	ε	ε	PROPN
ejpam-5714	454	31	)	)	PUNCT
ejpam-5714	454	32	ε(p−1)/m	ε(p−1)/m	NOUN
ejpam-5714	454	33	(	(	PUNCT
ejpam-5714	454	34	p−	p−	NOUN
ejpam-5714	454	35	1)−1	1)−1	NUM
ejpam-5714	454	36	t−p	t−p	NUM
ejpam-5714	454	37	.	.	PUNCT
ejpam-5714	455	1	f.	f.	PROPN
ejpam-5714	455	2	aldosari	aldosari	PROPN
ejpam-5714	455	3	/	/	SYM
ejpam-5714	455	4	eur	eur	PROPN
ejpam-5714	455	5	.	.	PUNCT
ejpam-5714	456	1	j.	j.	PROPN
ejpam-5714	456	2	pure	pure	PROPN
ejpam-5714	456	3	appl	appl	PROPN
ejpam-5714	456	4	.	.	PROPN
ejpam-5714	456	5	math	math	PROPN
ejpam-5714	456	6	,	,	PUNCT
ejpam-5714	456	7	18	18	NUM
ejpam-5714	456	8	(	(	PUNCT
ejpam-5714	456	9	1	1	NUM
ejpam-5714	456	10	)	)	PUNCT
ejpam-5714	456	11	(	(	PUNCT
ejpam-5714	456	12	2025	2025	NUM
ejpam-5714	456	13	)	)	PUNCT
ejpam-5714	456	14	,	,	PUNCT
ejpam-5714	456	15	5714	5714	NUM
ejpam-5714	456	16	14	14	NUM
ejpam-5714	456	17	of	of	ADP
ejpam-5714	456	18	16	16	NUM
ejpam-5714	456	19	from	from	ADP
ejpam-5714	456	20	theorem	theorem	ADJ
ejpam-5714	456	21	5	5	NUM
ejpam-5714	456	22	,	,	PUNCT
ejpam-5714	456	23	(	(	PUNCT
ejpam-5714	456	24	39	39	NUM
ejpam-5714	456	25	)	)	PUNCT
ejpam-5714	456	26	is	be	AUX
ejpam-5714	456	27	oscillatory	oscillatory	ADJ
ejpam-5714	456	28	if	if	SCONJ
ejpam-5714	456	29	(	(	PUNCT
ejpam-5714	456	30	q0	q0	PROPN
ejpam-5714	456	31	(	(	PUNCT
ejpam-5714	456	32	1−	1−	NUM
ejpam-5714	456	33	y0	y0	NOUN
ejpam-5714	456	34	)	)	PUNCT
ejpam-5714	456	35	p−1	p−1	PROPN
ejpam-5714	456	36	(	(	PUNCT
ejpam-5714	456	37	1−	1−	NUM
ejpam-5714	456	38	ε	ε	PROPN
ejpam-5714	456	39	)	)	PUNCT
ejpam-5714	456	40	p−	p−	NOUN
ejpam-5714	456	41	1	1	NUM
ejpam-5714	456	42	ε(p−1)/m	ε(p−1)/m	NOUN
ejpam-5714	456	43	)	)	PUNCT
ejpam-5714	456	44	1/(p−1	1/(p−1	NUM
ejpam-5714	456	45	)	)	PUNCT
ejpam-5714	456	46	>	>	X
ejpam-5714	457	1	(	(	PUNCT
ejpam-5714	457	2	p−	p−	NOUN
ejpam-5714	457	3	1	1	NUM
ejpam-5714	457	4	)	)	PUNCT
ejpam-5714	457	5	p−p/(p−1	p−p/(p−1	NOUN
ejpam-5714	457	6	)	)	PUNCT
ejpam-5714	457	7	.	.	PUNCT
ejpam-5714	458	1	example	example	NOUN
ejpam-5714	459	1	2	2	NUM
ejpam-5714	459	2	.	.	X
ejpam-5714	459	3	consider	consider	VERB
ejpam-5714	459	4	the	the	DET
ejpam-5714	459	5	differential	differential	ADJ
ejpam-5714	459	6	equation	equation	NOUN
ejpam-5714	459	7	(	(	PUNCT
ejpam-5714	459	8	κ	κ	X
ejpam-5714	459	9	(	(	PUNCT
ejpam-5714	459	10	t	t	PROPN
ejpam-5714	459	11	)	)	PUNCT
ejpam-5714	459	12	+	+	CCONJ
ejpam-5714	459	13	1	1	NUM
ejpam-5714	459	14	2	2	NUM
ejpam-5714	459	15	κ	κ	NOUN
ejpam-5714	459	16	(	(	PUNCT
ejpam-5714	459	17	ζ0	ζ0	PROPN
ejpam-5714	459	18	t	t	PROPN
ejpam-5714	459	19	)	)	PUNCT
ejpam-5714	459	20	)	)	PUNCT
ejpam-5714	460	1	′′	′′	PROPN
ejpam-5714	460	2	+	+	CCONJ
ejpam-5714	460	3	q0t−	q0t−	PROPN
ejpam-5714	460	4	2	2	NUM
ejpam-5714	460	5	t3	t3	NOUN
ejpam-5714	460	6	κ	κ	PROPN
ejpam-5714	460	7	(	(	PUNCT
ejpam-5714	460	8	1/3	1/3	PROPN
ejpam-5714	460	9	t	t	NOUN
ejpam-5714	460	10	)	)	PUNCT
ejpam-5714	460	11	+	+	CCONJ
ejpam-5714	460	12	2	2	NUM
ejpam-5714	460	13	t3	t3	NOUN
ejpam-5714	460	14	κ	κ	PROPN
ejpam-5714	460	15	(	(	PUNCT
ejpam-5714	460	16	1/3	1/3	NUM
ejpam-5714	460	17	t	t	NOUN
ejpam-5714	460	18	)	)	PUNCT
ejpam-5714	460	19	=	=	SYM
ejpam-5714	460	20	0	0	NUM
ejpam-5714	460	21	,	,	PUNCT
ejpam-5714	460	22	(	(	PUNCT
ejpam-5714	460	23	41	41	NUM
ejpam-5714	460	24	)	)	PUNCT
ejpam-5714	460	25	where	where	SCONJ
ejpam-5714	460	26	ζ0	ζ0	PROPN
ejpam-5714	460	27	∈	∈	PROPN
ejpam-5714	460	28	(	(	PUNCT
ejpam-5714	460	29	0	0	NUM
ejpam-5714	460	30	,	,	PUNCT
ejpam-5714	460	31	1	1	NUM
ejpam-5714	460	32	)	)	PUNCT
ejpam-5714	460	33	.	.	PUNCT
ejpam-5714	461	1	let	let	VERB
ejpam-5714	461	2	b	b	X
ejpam-5714	461	3	(	(	PUNCT
ejpam-5714	461	4	t	t	PROPN
ejpam-5714	461	5	)	)	PUNCT
ejpam-5714	461	6	=	=	SYM
ejpam-5714	462	1	1	1	NUM
ejpam-5714	462	2	,	,	PUNCT
ejpam-5714	462	3	y	y	PROPN
ejpam-5714	462	4	(	(	PUNCT
ejpam-5714	462	5	t	t	PROPN
ejpam-5714	462	6	)	)	PUNCT
ejpam-5714	462	7	=	=	SYM
ejpam-5714	462	8	1	1	NUM
ejpam-5714	462	9	2	2	NUM
ejpam-5714	462	10	,	,	PUNCT
ejpam-5714	462	11	ζ	ζ	NOUN
ejpam-5714	462	12	(	(	PUNCT
ejpam-5714	462	13	t	t	NOUN
ejpam-5714	462	14	)	)	PUNCT
ejpam-5714	462	15	=	=	PUNCT
ejpam-5714	463	1	ζ0	ζ0	PROPN
ejpam-5714	463	2	t	t	PROPN
ejpam-5714	463	3	,	,	PUNCT
ejpam-5714	463	4	qi	qi	PROPN
ejpam-5714	463	5	(	(	PUNCT
ejpam-5714	463	6	t	t	PROPN
ejpam-5714	463	7	)	)	PUNCT
ejpam-5714	463	8	=	=	SYM
ejpam-5714	463	9	q0t−2	q0t−2	PROPN
ejpam-5714	463	10	t3	t3	NOUN
ejpam-5714	463	11	+	+	CCONJ
ejpam-5714	463	12	2	2	NUM
ejpam-5714	463	13	t3	t3	NOUN
ejpam-5714	463	14	and	and	CCONJ
ejpam-5714	463	15	πi	πi	ADV
ejpam-5714	463	16	(	(	PUNCT
ejpam-5714	463	17	t	t	NOUN
ejpam-5714	463	18	)	)	PUNCT
ejpam-5714	463	19	=	=	SYM
ejpam-5714	464	1	1/3	1/3	NUM
ejpam-5714	464	2	t.	t.	NOUN
ejpam-5714	464	3	from	from	ADP
ejpam-5714	464	4	theorem	theorem	ADJ
ejpam-5714	464	5	5	5	NUM
ejpam-5714	464	6	,	,	PUNCT
ejpam-5714	464	7	we	we	PRON
ejpam-5714	464	8	find	find	VERB
ejpam-5714	464	9	the	the	DET
ejpam-5714	464	10	equation	equation	NOUN
ejpam-5714	464	11	(	(	PUNCT
ejpam-5714	464	12	41	41	NUM
ejpam-5714	464	13	)	)	PUNCT
ejpam-5714	464	14	is	be	AUX
ejpam-5714	464	15	oscillatory	oscillatory	ADJ
ejpam-5714	464	16	if	if	SCONJ
ejpam-5714	464	17	q0	q0	PROPN
ejpam-5714	464	18	6	6	NUM
ejpam-5714	464	19	(	(	PUNCT
ejpam-5714	464	20	1	1	NUM
ejpam-5714	464	21	+	+	NUM
ejpam-5714	464	22	1	1	NUM
ejpam-5714	464	23	6	6	NUM
ejpam-5714	464	24	q0	q0	NOUN
ejpam-5714	464	25	)	)	PUNCT
ejpam-5714	465	1	ln	ln	ADV
ejpam-5714	465	2	3	3	NUM
ejpam-5714	465	3	>	>	SYM
ejpam-5714	465	4	1	1	NUM
ejpam-5714	465	5	e	e	NOUN
ejpam-5714	465	6	,	,	PUNCT
ejpam-5714	465	7	(	(	PUNCT
ejpam-5714	465	8	42	42	NUM
ejpam-5714	465	9	)	)	PUNCT
ejpam-5714	465	10	thus	thus	ADV
ejpam-5714	465	11	,	,	PUNCT
ejpam-5714	465	12	he	he	PRON
ejpam-5714	465	13	equation	equation	NOUN
ejpam-5714	465	14	(	(	PUNCT
ejpam-5714	465	15	41	41	NUM
ejpam-5714	465	16	)	)	PUNCT
ejpam-5714	465	17	is	be	AUX
ejpam-5714	465	18	oscillatory	oscillatory	ADJ
ejpam-5714	465	19	if	if	SCONJ
ejpam-5714	465	20	q0	q0	PROPN
ejpam-5714	465	21	>	>	X
ejpam-5714	465	22	1.588	1.588	NUM
ejpam-5714	465	23	.	.	PUNCT
ejpam-5714	465	24	example	example	NOUN
ejpam-5714	466	1	3	3	X
ejpam-5714	466	2	.	.	PUNCT
ejpam-5714	467	1	let	let	VERB
ejpam-5714	467	2	equation	equation	NOUN
ejpam-5714	467	3	(	(	PUNCT
ejpam-5714	467	4	κ	κ	X
ejpam-5714	467	5	(	(	PUNCT
ejpam-5714	467	6	t	t	PROPN
ejpam-5714	467	7	)	)	PUNCT
ejpam-5714	468	1	+	+	CCONJ
ejpam-5714	468	2	1	1	NUM
ejpam-5714	468	3	2	2	NUM
ejpam-5714	468	4	κ	κ	NOUN
ejpam-5714	468	5	(	(	PUNCT
ejpam-5714	468	6	t	t	PROPN
ejpam-5714	468	7	3	3	NUM
ejpam-5714	468	8	)	)	PUNCT
ejpam-5714	468	9	)	)	PUNCT
ejpam-5714	469	1	′′	′′	PROPN
ejpam-5714	469	2	+	+	CCONJ
ejpam-5714	469	3	q0	q0	PROPN
ejpam-5714	469	4	t2	t2	PROPN
ejpam-5714	469	5	κ	κ	PROPN
ejpam-5714	469	6	(	(	PUNCT
ejpam-5714	469	7	t	t	PROPN
ejpam-5714	469	8	2	2	NUM
ejpam-5714	469	9	)	)	PUNCT
ejpam-5714	469	10	=	=	SYM
ejpam-5714	469	11	0	0	NUM
ejpam-5714	469	12	,	,	PUNCT
ejpam-5714	469	13	q0	q0	VERB
ejpam-5714	469	14	>	>	X
ejpam-5714	469	15	0	0	X
ejpam-5714	469	16	.	.	PUNCT
ejpam-5714	470	1	(	(	PUNCT
ejpam-5714	470	2	43	43	X
ejpam-5714	470	3	)	)	PUNCT
ejpam-5714	470	4	let	let	VERB
ejpam-5714	470	5	b	b	X
ejpam-5714	470	6	(	(	PUNCT
ejpam-5714	470	7	t	t	PROPN
ejpam-5714	470	8	)	)	PUNCT
ejpam-5714	470	9	=	=	SYM
ejpam-5714	471	1	1	1	NUM
ejpam-5714	471	2	,	,	PUNCT
ejpam-5714	471	3	y	y	PROPN
ejpam-5714	471	4	(	(	PUNCT
ejpam-5714	471	5	t	t	PROPN
ejpam-5714	471	6	)	)	PUNCT
ejpam-5714	471	7	=	=	SYM
ejpam-5714	471	8	1	1	NUM
ejpam-5714	471	9	2	2	NUM
ejpam-5714	471	10	,	,	PUNCT
ejpam-5714	471	11	ζ	ζ	NOUN
ejpam-5714	471	12	(	(	PUNCT
ejpam-5714	471	13	t	t	NOUN
ejpam-5714	471	14	)	)	PUNCT
ejpam-5714	471	15	=	=	SYM
ejpam-5714	472	1	t	t	PROPN
ejpam-5714	472	2	3	3	NUM
ejpam-5714	472	3	,	,	PUNCT
ejpam-5714	472	4	qi	qi	PROPN
ejpam-5714	472	5	(	(	PUNCT
ejpam-5714	472	6	t	t	PROPN
ejpam-5714	472	7	)	)	PUNCT
ejpam-5714	472	8	=	=	VERB
ejpam-5714	473	1	q0	q0	PROPN
ejpam-5714	473	2	t2	t2	NOUN
ejpam-5714	473	3	and	and	CCONJ
ejpam-5714	473	4	πi	πi	ADV
ejpam-5714	473	5	(	(	PUNCT
ejpam-5714	473	6	t	t	NOUN
ejpam-5714	473	7	)	)	PUNCT
ejpam-5714	473	8	=	=	SYM
ejpam-5714	474	1	t	t	PROPN
ejpam-5714	474	2	2	2	NUM
ejpam-5714	474	3	.	.	PUNCT
ejpam-5714	475	1	it	it	PRON
ejpam-5714	475	2	is	be	AUX
ejpam-5714	475	3	easy	easy	ADJ
ejpam-5714	475	4	to	to	PART
ejpam-5714	475	5	verify	verify	VERB
ejpam-5714	475	6	that	that	PRON
ejpam-5714	475	7	bt0	bt0	PROPN
ejpam-5714	475	8	(	(	PUNCT
ejpam-5714	475	9	t	t	PROPN
ejpam-5714	475	10	)	)	PUNCT
ejpam-5714	475	11	=	=	SYM
ejpam-5714	475	12	t	t	PROPN
ejpam-5714	475	13	,	,	PUNCT
ejpam-5714	475	14	and	and	CCONJ
ejpam-5714	475	15	b̃t0	b̃t0	PROPN
ejpam-5714	475	16	=	=	SYM
ejpam-5714	475	17	t+	t+	PUNCT
ejpam-5714	475	18	q0	q0	PROPN
ejpam-5714	476	1	4	4	NUM
ejpam-5714	476	2	∫	∫	NOUN
ejpam-5714	476	3	t	t	PROPN
ejpam-5714	476	4	t0	t0	PROPN
ejpam-5714	476	5	dκ	dκ	PROPN
ejpam-5714	476	6	=	=	PROPN
ejpam-5714	476	7	t	t	PROPN
ejpam-5714	476	8	(	(	PUNCT
ejpam-5714	476	9	1	1	NUM
ejpam-5714	476	10	+	+	X
ejpam-5714	476	11	qi0	qi0	NOUN
ejpam-5714	476	12	4	4	NUM
ejpam-5714	476	13	)	)	PUNCT
ejpam-5714	476	14	.	.	PUNCT
ejpam-5714	477	1	using	use	VERB
ejpam-5714	477	2	corollary	corollary	ADJ
ejpam-5714	477	3	1	1	NUM
ejpam-5714	477	4	,	,	PUNCT
ejpam-5714	477	5	if	if	SCONJ
ejpam-5714	477	6	q0	q0	PROPN
ejpam-5714	477	7	+	+	CCONJ
ejpam-5714	477	8	q20	q20	NOUN
ejpam-5714	477	9	4	4	NUM
ejpam-5714	477	10	>	>	SYM
ejpam-5714	477	11	4	4	NUM
ejpam-5714	477	12	ln	ln	ADJ
ejpam-5714	477	13	2e	2e	NOUN
ejpam-5714	477	14	,	,	PUNCT
ejpam-5714	477	15	then	then	ADV
ejpam-5714	477	16	(	(	PUNCT
ejpam-5714	477	17	43	43	NUM
ejpam-5714	477	18	)	)	PUNCT
ejpam-5714	477	19	is	be	AUX
ejpam-5714	477	20	oscillatory	oscillatory	ADJ
ejpam-5714	477	21	.	.	PUNCT
ejpam-5714	478	1	4	4	X
ejpam-5714	478	2	.	.	X
ejpam-5714	478	3	conclusion	conclusion	NOUN
ejpam-5714	478	4	the	the	DET
ejpam-5714	478	5	oscillatory	oscillatory	ADJ
ejpam-5714	478	6	properties	property	NOUN
ejpam-5714	478	7	of	of	ADP
ejpam-5714	478	8	neutral	neutral	ADJ
ejpam-5714	478	9	second	second	ADJ
ejpam-5714	478	10	-	-	PUNCT
ejpam-5714	478	11	order	order	NOUN
ejpam-5714	478	12	differential	differential	ADJ
ejpam-5714	478	13	equations	equation	NOUN
ejpam-5714	478	14	with	with	ADP
ejpam-5714	478	15	p	p	ADJ
ejpam-5714	478	16	-	-	PUNCT
ejpam-5714	478	17	laplace	laplace	NOUN
ejpam-5714	478	18	type	type	NOUN
ejpam-5714	478	19	operator	operator	NOUN
ejpam-5714	478	20	is	be	AUX
ejpam-5714	478	21	thoroughly	thoroughly	ADV
ejpam-5714	478	22	examined	examine	VERB
ejpam-5714	478	23	in	in	ADP
ejpam-5714	478	24	this	this	DET
ejpam-5714	478	25	work	work	NOUN
ejpam-5714	478	26	.	.	PUNCT
ejpam-5714	479	1	the	the	DET
ejpam-5714	479	2	analytical	analytical	ADJ
ejpam-5714	479	3	process	process	NOUN
ejpam-5714	479	4	is	be	AUX
ejpam-5714	479	5	greatly	greatly	ADV
ejpam-5714	479	6	simplified	simplify	VERB
ejpam-5714	479	7	by	by	ADP
ejpam-5714	479	8	this	this	DET
ejpam-5714	479	9	modification	modification	NOUN
ejpam-5714	479	10	.	.	PUNCT
ejpam-5714	480	1	under	under	ADP
ejpam-5714	480	2	certain	certain	ADJ
ejpam-5714	480	3	limits	limit	NOUN
ejpam-5714	480	4	,	,	PUNCT
ejpam-5714	480	5	we	we	PRON
ejpam-5714	480	6	have	have	AUX
ejpam-5714	480	7	defined	define	VERB
ejpam-5714	480	8	some	some	DET
ejpam-5714	480	9	conditions	condition	NOUN
ejpam-5714	480	10	that	that	PRON
ejpam-5714	480	11	effectively	effectively	ADV
ejpam-5714	480	12	exclude	exclude	VERB
ejpam-5714	480	13	the	the	DET
ejpam-5714	480	14	existence	existence	NOUN
ejpam-5714	480	15	of	of	ADP
ejpam-5714	480	16	positive	positive	ADJ
ejpam-5714	480	17	solutions	solution	NOUN
ejpam-5714	480	18	.	.	PUNCT
ejpam-5714	481	1	building	build	VERB
ejpam-5714	481	2	on	on	ADP
ejpam-5714	481	3	these	these	DET
ejpam-5714	481	4	discoveries	discovery	NOUN
ejpam-5714	481	5	,	,	PUNCT
ejpam-5714	481	6	we	we	PRON
ejpam-5714	481	7	created	create	VERB
ejpam-5714	481	8	new	new	ADJ
ejpam-5714	481	9	standards	standard	NOUN
ejpam-5714	481	10	that	that	PRON
ejpam-5714	481	11	ensure	ensure	VERB
ejpam-5714	481	12	all	all	DET
ejpam-5714	481	13	solutions	solution	NOUN
ejpam-5714	481	14	to	to	ADP
ejpam-5714	481	15	the	the	DET
ejpam-5714	481	16	examined	examine	VERB
ejpam-5714	481	17	equations	equation	NOUN
ejpam-5714	481	18	oscillate	oscillate	VERB
ejpam-5714	481	19	.	.	PUNCT
ejpam-5714	482	1	this	this	DET
ejpam-5714	482	2	contribution	contribution	NOUN
ejpam-5714	482	3	offers	offer	VERB
ejpam-5714	482	4	a	a	DET
ejpam-5714	482	5	strong	strong	ADJ
ejpam-5714	482	6	basis	basis	NOUN
ejpam-5714	482	7	for	for	ADP
ejpam-5714	482	8	upcoming	upcoming	ADJ
ejpam-5714	482	9	investigations	investigation	NOUN
ejpam-5714	482	10	and	and	CCONJ
ejpam-5714	482	11	is	be	AUX
ejpam-5714	482	12	essential	essential	ADJ
ejpam-5714	482	13	for	for	ADP
ejpam-5714	482	14	developing	develop	VERB
ejpam-5714	482	15	the	the	DET
ejpam-5714	482	16	theoretical	theoretical	ADJ
ejpam-5714	482	17	framework	framework	NOUN
ejpam-5714	482	18	of	of	ADP
ejpam-5714	482	19	neutral	neutral	ADJ
ejpam-5714	482	20	differential	differential	ADJ
ejpam-5714	482	21	equations	equation	NOUN
ejpam-5714	482	22	.	.	PUNCT
ejpam-5714	483	1	furthermore	furthermore	ADV
ejpam-5714	483	2	,	,	PUNCT
ejpam-5714	483	3	we	we	PRON
ejpam-5714	483	4	included	include	VERB
ejpam-5714	483	5	illustrated	illustrate	VERB
ejpam-5714	483	6	instances	instance	NOUN
ejpam-5714	483	7	that	that	PRON
ejpam-5714	483	8	show	show	VERB
ejpam-5714	483	9	the	the	DET
ejpam-5714	483	10	theoretical	theoretical	ADJ
ejpam-5714	483	11	significance	significance	NOUN
ejpam-5714	483	12	and	and	CCONJ
ejpam-5714	483	13	practical	practical	ADJ
ejpam-5714	483	14	implementation	implementation	NOUN
ejpam-5714	483	15	f.	f.	NOUN
ejpam-5714	483	16	aldosari	aldosari	PROPN
ejpam-5714	483	17	/	/	SYM
ejpam-5714	483	18	eur	eur	PROPN
ejpam-5714	483	19	.	.	PUNCT
ejpam-5714	484	1	j.	j.	PROPN
ejpam-5714	484	2	pure	pure	PROPN
ejpam-5714	484	3	appl	appl	PROPN
ejpam-5714	484	4	.	.	PROPN
ejpam-5714	484	5	math	math	PROPN
ejpam-5714	484	6	,	,	PUNCT
ejpam-5714	484	7	18	18	NUM
ejpam-5714	484	8	(	(	PUNCT
ejpam-5714	484	9	1	1	NUM
ejpam-5714	484	10	)	)	PUNCT
ejpam-5714	484	11	(	(	PUNCT
ejpam-5714	484	12	2025	2025	NUM
ejpam-5714	484	13	)	)	PUNCT
ejpam-5714	484	14	,	,	PUNCT
ejpam-5714	484	15	5714	5714	NUM
ejpam-5714	484	16	15	15	NUM
ejpam-5714	484	17	of	of	ADP
ejpam-5714	484	18	16	16	NUM
ejpam-5714	484	19	of	of	ADP
ejpam-5714	484	20	our	our	PRON
ejpam-5714	484	21	criteria	criterion	NOUN
ejpam-5714	484	22	.	.	PUNCT
ejpam-5714	485	1	these	these	DET
ejpam-5714	485	2	illustrations	illustration	NOUN
ejpam-5714	485	3	demonstrate	demonstrate	VERB
ejpam-5714	485	4	how	how	SCONJ
ejpam-5714	485	5	well	well	ADV
ejpam-5714	485	6	our	our	PRON
ejpam-5714	485	7	method	method	NOUN
ejpam-5714	485	8	works	work	VERB
ejpam-5714	485	9	to	to	PART
ejpam-5714	485	10	solve	solve	VERB
ejpam-5714	485	11	challenging	challenge	VERB
ejpam-5714	485	12	neutral	neutral	ADJ
ejpam-5714	485	13	differential	differential	ADJ
ejpam-5714	485	14	equation	equation	NOUN
ejpam-5714	485	15	situations	situation	NOUN
ejpam-5714	485	16	.	.	PUNCT
ejpam-5714	486	1	the	the	DET
ejpam-5714	486	2	study	study	NOUN
ejpam-5714	486	3	’s	’s	PART
ejpam-5714	486	4	findings	finding	NOUN
ejpam-5714	486	5	broaden	broaden	VERB
ejpam-5714	486	6	the	the	DET
ejpam-5714	486	7	field	field	NOUN
ejpam-5714	486	8	’s	’s	PART
ejpam-5714	486	9	current	current	ADJ
ejpam-5714	486	10	theoretical	theoretical	ADJ
ejpam-5714	486	11	frameworks	framework	NOUN
ejpam-5714	486	12	and	and	CCONJ
ejpam-5714	486	13	create	create	VERB
ejpam-5714	486	14	new	new	ADJ
ejpam-5714	486	15	research	research	NOUN
ejpam-5714	486	16	opportunities	opportunity	NOUN
ejpam-5714	486	17	.	.	PUNCT
ejpam-5714	487	1	we	we	PRON
ejpam-5714	487	2	suggest	suggest	VERB
ejpam-5714	487	3	that	that	SCONJ
ejpam-5714	487	4	future	future	ADJ
ejpam-5714	487	5	research	research	NOUN
ejpam-5714	487	6	investigate	investigate	VERB
ejpam-5714	487	7	the	the	DET
ejpam-5714	487	8	use	use	NOUN
ejpam-5714	487	9	of	of	ADP
ejpam-5714	487	10	our	our	PRON
ejpam-5714	487	11	techniques	technique	NOUN
ejpam-5714	487	12	for	for	ADP
ejpam-5714	487	13	higher	high	ADJ
ejpam-5714	487	14	-	-	PUNCT
ejpam-5714	487	15	order	order	NOUN
ejpam-5714	487	16	equations	equation	NOUN
ejpam-5714	487	17	,	,	PUNCT
ejpam-5714	487	18	especially	especially	ADV
ejpam-5714	487	19	odd	odd	ADJ
ejpam-5714	487	20	-	-	PUNCT
ejpam-5714	487	21	order	order	NOUN
ejpam-5714	487	22	ones.b	ones.b	SYM
ejpam-5714	487	23	(	(	PUNCT
ejpam-5714	487	24	t	t	PROPN
ejpam-5714	487	25	)	)	PUNCT
ejpam-5714	487	26	(κ	(κ	PROPN
ejpam-5714	487	27	(	(	PUNCT
ejpam-5714	487	28	t	t	PROPN
ejpam-5714	487	29	)	)	PUNCT
ejpam-5714	488	1	+	+	CCONJ
ejpam-5714	488	2	n∑	n∑	PROPN
ejpam-5714	488	3	i=1	i=1	PROPN
ejpam-5714	488	4	yi	yi	PROPN
ejpam-5714	488	5	(	(	PUNCT
ejpam-5714	488	6	t)κ	t)κ	X
ejpam-5714	488	7	(	(	PUNCT
ejpam-5714	488	8	ζi	ζi	PROPN
ejpam-5714	488	9	(	(	PUNCT
ejpam-5714	488	10	t	t	PROPN
ejpam-5714	488	11	)	)	PUNCT
ejpam-5714	488	12	)	)	PUNCT
ejpam-5714	488	13	)	)	PUNCT
ejpam-5714	489	1	(	(	PUNCT
ejpam-5714	489	2	n−1	n−1	PROPN
ejpam-5714	489	3	)	)	PUNCT
ejpam-5714	489	4	(p−1	(p−1	PROPN
ejpam-5714	489	5	)	)	PUNCT
ejpam-5714	489	6			NOUN
ejpam-5714	489	7	′	′	NUM
ejpam-5714	490	1	+	+	CCONJ
ejpam-5714	490	2	n∑	n∑	PROPN
ejpam-5714	490	3	i=1	i=1	ADP
ejpam-5714	490	4	qi	qi	PROPN
ejpam-5714	490	5	(	(	PUNCT
ejpam-5714	490	6	t)κ(p−1	t)κ(p−1	PROPN
ejpam-5714	490	7	)	)	PUNCT
ejpam-5714	490	8	(	(	PUNCT
ejpam-5714	490	9	πi	πi	X
ejpam-5714	490	10	(	(	PUNCT
ejpam-5714	490	11	t	t	NOUN
ejpam-5714	490	12	)	)	PUNCT
ejpam-5714	490	13	)	)	PUNCT
ejpam-5714	491	1	=	=	PUNCT
ejpam-5714	491	2	0	0	X
ejpam-5714	491	3	.	.	PUNCT
ejpam-5714	492	1	acknowledgements	acknowledgement	VERB
ejpam-5714	492	2	the	the	DET
ejpam-5714	492	3	author	author	NOUN
ejpam-5714	492	4	would	would	AUX
ejpam-5714	492	5	like	like	VERB
ejpam-5714	492	6	to	to	PART
ejpam-5714	492	7	thank	thank	VERB
ejpam-5714	492	8	the	the	DET
ejpam-5714	492	9	deanship	deanship	NOUN
ejpam-5714	492	10	of	of	ADP
ejpam-5714	492	11	scientific	scientific	ADJ
ejpam-5714	492	12	research	research	NOUN
ejpam-5714	492	13	at	at	ADP
ejpam-5714	492	14	shagra	shagra	PROPN
ejpam-5714	492	15	university	university	PROPN
ejpam-5714	492	16	for	for	ADP
ejpam-5714	492	17	supporting	support	VERB
ejpam-5714	492	18	this	this	DET
ejpam-5714	492	19	work	work	NOUN
ejpam-5714	492	20	.	.	PUNCT
ejpam-5714	493	1	references	reference	NOUN
ejpam-5714	493	2	[	[	X
ejpam-5714	493	3	1	1	NUM
ejpam-5714	493	4	]	]	SYM
ejpam-5714	493	5	b	b	X
ejpam-5714	493	6	qaraad	qaraad	NOUN
ejpam-5714	493	7	l	l	PROPN
ejpam-5714	493	8	f	f	PROPN
ejpam-5714	493	9	iambor	iambor	VERB
ejpam-5714	493	10	a	a	DET
ejpam-5714	493	11	al	al	PROPN
ejpam-5714	493	12	-	-	PUNCT
ejpam-5714	493	13	jaser	jaser	NOUN
ejpam-5714	493	14	,	,	PUNCT
ejpam-5714	493	15	c	c	PROPN
ejpam-5714	493	16	cesarano	cesarano	PROPN
ejpam-5714	493	17	.	.	PUNCT
ejpam-5714	494	1	second	second	ADJ
ejpam-5714	494	2	-	-	PUNCT
ejpam-5714	494	3	order	order	NOUN
ejpam-5714	494	4	damped	damped	NOUN
ejpam-5714	494	5	differential	differential	ADJ
ejpam-5714	494	6	equations	equation	NOUN
ejpam-5714	494	7	with	with	ADP
ejpam-5714	494	8	superlinear	superlinear	ADJ
ejpam-5714	494	9	neutral	neutral	ADJ
ejpam-5714	494	10	term	term	NOUN
ejpam-5714	494	11	:	:	PUNCT
ejpam-5714	494	12	new	new	ADJ
ejpam-5714	494	13	criteria	criterion	NOUN
ejpam-5714	494	14	for	for	ADP
ejpam-5714	494	15	oscillation	oscillation	NOUN
ejpam-5714	494	16	.	.	PUNCT
ejpam-5714	495	1	axioms	axiom	NOUN
ejpam-5714	495	2	,	,	PUNCT
ejpam-5714	495	3	13:234	13:234	NUM
ejpam-5714	495	4	,	,	PUNCT
ejpam-5714	495	5	2024	2024	NUM
ejpam-5714	495	6	.	.	PUNCT
ejpam-5714	496	1	[	[	X
ejpam-5714	496	2	2	2	NUM
ejpam-5714	496	3	]	]	AUX
ejpam-5714	496	4	h	h	PROPN
ejpam-5714	496	5	ramos	ramos	PROPN
ejpam-5714	496	6	s	s	PART
ejpam-5714	496	7	serra	serra	PROPN
ejpam-5714	496	8	-	-	PUNCT
ejpam-5714	496	9	capizzano	capizzano	PROPN
ejpam-5714	496	10	a	a	DET
ejpam-5714	496	11	al	al	PROPN
ejpam-5714	496	12	-	-	PUNCT
ejpam-5714	496	13	jaser	jaser	NOUN
ejpam-5714	496	14	,	,	PUNCT
ejpam-5714	496	15	b	b	PROPN
ejpam-5714	496	16	qaraad	qaraad	NOUN
ejpam-5714	496	17	.	.	PUNCT
ejpam-5714	497	1	new	new	ADJ
ejpam-5714	497	2	conditions	condition	NOUN
ejpam-5714	497	3	for	for	ADP
ejpam-5714	497	4	testing	test	VERB
ejpam-5714	497	5	the	the	DET
ejpam-5714	497	6	oscillation	oscillation	NOUN
ejpam-5714	497	7	of	of	ADP
ejpam-5714	497	8	solutions	solution	NOUN
ejpam-5714	497	9	of	of	ADP
ejpam-5714	497	10	second	second	ADJ
ejpam-5714	497	11	-	-	PUNCT
ejpam-5714	497	12	order	order	NOUN
ejpam-5714	497	13	nonlinear	nonlinear	ADJ
ejpam-5714	497	14	differential	differential	ADJ
ejpam-5714	497	15	equations	equation	NOUN
ejpam-5714	497	16	with	with	ADP
ejpam-5714	497	17	damped	damped	ADJ
ejpam-5714	497	18	term	term	NOUN
ejpam-5714	497	19	.	.	PUNCT
ejpam-5714	498	1	axioms	axiom	NOUN
ejpam-5714	498	2	,	,	PUNCT
ejpam-5714	498	3	13:105	13:105	NUM
ejpam-5714	498	4	,	,	PUNCT
ejpam-5714	498	5	2024	2024	NUM
ejpam-5714	498	6	.	.	PUNCT
ejpam-5714	499	1	[	[	X
ejpam-5714	499	2	3	3	X
ejpam-5714	499	3	]	]	X
ejpam-5714	499	4	o	o	NOUN
ejpam-5714	499	5	bazighifan	bazighifan	NOUN
ejpam-5714	499	6	f	f	PROPN
ejpam-5714	499	7	masood	masood	PROPN
ejpam-5714	499	8	b	b	PROPN
ejpam-5714	499	9	almarri	almarri	PROPN
ejpam-5714	499	10	,	,	PUNCT
ejpam-5714	499	11	b	b	NOUN
ejpam-5714	499	12	batiha	batiha	NOUN
ejpam-5714	499	13	.	.	PUNCT
ejpam-5714	500	1	third	third	ADJ
ejpam-5714	500	2	-	-	PUNCT
ejpam-5714	500	3	order	order	NOUN
ejpam-5714	500	4	neutral	neutral	ADJ
ejpam-5714	500	5	differential	differential	NOUN
ejpam-5714	500	6	equations	equation	NOUN
ejpam-5714	500	7	with	with	ADP
ejpam-5714	500	8	non	non	ADJ
ejpam-5714	500	9	-	-	ADJ
ejpam-5714	500	10	canonical	canonical	ADJ
ejpam-5714	500	11	forms	form	NOUN
ejpam-5714	500	12	:	:	PUNCT
ejpam-5714	500	13	novel	novel	ADJ
ejpam-5714	500	14	oscillation	oscillation	NOUN
ejpam-5714	500	15	theorems	theorem	NOUN
ejpam-5714	500	16	.	.	PUNCT
ejpam-5714	501	1	axioms	axiom	NOUN
ejpam-5714	501	2	,	,	PUNCT
ejpam-5714	501	3	13:755	13:755	NUM
ejpam-5714	501	4	,	,	PUNCT
ejpam-5714	501	5	2024	2024	NUM
ejpam-5714	501	6	.	.	PUNCT
ejpam-5714	502	1	[	[	X
ejpam-5714	502	2	4	4	NUM
ejpam-5714	502	3	]	]	SYM
ejpam-5714	502	4	b	b	X
ejpam-5714	502	5	baculikova	baculikova	NOUN
ejpam-5714	502	6	and	and	CCONJ
ejpam-5714	502	7	j	j	PROPN
ejpam-5714	502	8	dzurina	dzurina	PROPN
ejpam-5714	502	9	.	.	PUNCT
ejpam-5714	503	1	oscillation	oscillation	NOUN
ejpam-5714	503	2	theorems	theorem	NOUN
ejpam-5714	503	3	for	for	ADP
ejpam-5714	503	4	second	second	ADJ
ejpam-5714	503	5	order	order	NOUN
ejpam-5714	503	6	nonlinear	nonlinear	ADJ
ejpam-5714	503	7	neutral	neutral	ADJ
ejpam-5714	503	8	differential	differential	NOUN
ejpam-5714	503	9	equations	equation	NOUN
ejpam-5714	503	10	.	.	PUNCT
ejpam-5714	504	1	comput	comput	NOUN
ejpam-5714	504	2	.	.	PUNCT
ejpam-5714	505	1	math	math	NOUN
ejpam-5714	505	2	.	.	PUNCT
ejpam-5714	506	1	appl	appl	PROPN
ejpam-5714	506	2	.	.	PROPN
ejpam-5714	506	3	,	,	PUNCT
ejpam-5714	506	4	62:4472–4478	62:4472–4478	PROPN
ejpam-5714	506	5	,	,	PUNCT
ejpam-5714	506	6	2011	2011	NUM
ejpam-5714	506	7	.	.	PUNCT
ejpam-5714	507	1	[	[	X
ejpam-5714	507	2	5	5	NUM
ejpam-5714	507	3	]	]	PUNCT
ejpam-5714	507	4	o	o	X
ejpam-5714	507	5	bazighifan	bazighifan	NOUN
ejpam-5714	507	6	.	.	PUNCT
ejpam-5714	508	1	an	an	DET
ejpam-5714	508	2	approach	approach	NOUN
ejpam-5714	508	3	for	for	ADP
ejpam-5714	508	4	studying	study	VERB
ejpam-5714	508	5	asymptotic	asymptotic	ADJ
ejpam-5714	508	6	properties	property	NOUN
ejpam-5714	508	7	of	of	ADP
ejpam-5714	508	8	solutions	solution	NOUN
ejpam-5714	508	9	of	of	ADP
ejpam-5714	508	10	neutral	neutral	ADJ
ejpam-5714	508	11	differential	differential	ADJ
ejpam-5714	508	12	equations	equation	NOUN
ejpam-5714	508	13	.	.	PUNCT
ejpam-5714	509	1	symmetry	symmetry	PROPN
ejpam-5714	509	2	,	,	PUNCT
ejpam-5714	509	3	12:555	12:555	NUM
ejpam-5714	509	4	,	,	PUNCT
ejpam-5714	509	5	2020	2020	NUM
ejpam-5714	509	6	.	.	PUNCT
ejpam-5714	510	1	[	[	X
ejpam-5714	510	2	6	6	NUM
ejpam-5714	510	3	]	]	PUNCT
ejpam-5714	510	4	o	o	X
ejpam-5714	510	5	bazighifan	bazighifan	NOUN
ejpam-5714	510	6	.	.	PUNCT
ejpam-5714	511	1	on	on	ADP
ejpam-5714	511	2	the	the	DET
ejpam-5714	511	3	oscillation	oscillation	NOUN
ejpam-5714	511	4	of	of	ADP
ejpam-5714	511	5	certain	certain	ADJ
ejpam-5714	511	6	fourth	fourth	ADJ
ejpam-5714	511	7	-	-	PUNCT
ejpam-5714	511	8	order	order	NOUN
ejpam-5714	511	9	differential	differential	ADJ
ejpam-5714	511	10	equations	equation	NOUN
ejpam-5714	511	11	with	with	ADP
ejpam-5714	511	12	p	p	NOUN
ejpam-5714	511	13	-	-	PUNCT
ejpam-5714	511	14	laplacian	laplacian	ADJ
ejpam-5714	511	15	like	like	ADP
ejpam-5714	511	16	operator	operator	NOUN
ejpam-5714	511	17	.	.	PUNCT
ejpam-5714	512	1	appl	appl	PROPN
ejpam-5714	512	2	.	.	PROPN
ejpam-5714	512	3	math	math	PROPN
ejpam-5714	512	4	.	.	PUNCT
ejpam-5714	513	1	comput	comput	NOUN
ejpam-5714	513	2	.	.	PUNCT
ejpam-5714	513	3	,	,	PUNCT
ejpam-5714	513	4	386:125475	386:125475	NUM
ejpam-5714	513	5	,	,	PUNCT
ejpam-5714	513	6	2020	2020	NUM
ejpam-5714	513	7	.	.	PUNCT
ejpam-5714	514	1	[	[	X
ejpam-5714	514	2	7	7	NUM
ejpam-5714	514	3	]	]	X
ejpam-5714	514	4	t	t	X
ejpam-5714	514	5	candan	candan	PROPN
ejpam-5714	514	6	.	.	PUNCT
ejpam-5714	515	1	oscillatory	oscillatory	ADJ
ejpam-5714	515	2	behavior	behavior	NOUN
ejpam-5714	515	3	of	of	ADP
ejpam-5714	515	4	second	second	ADJ
ejpam-5714	515	5	order	order	NOUN
ejpam-5714	515	6	nonlinear	nonlinear	ADJ
ejpam-5714	515	7	neutral	neutral	ADJ
ejpam-5714	515	8	differential	differential	ADJ
ejpam-5714	515	9	equations	equation	NOUN
ejpam-5714	515	10	with	with	ADP
ejpam-5714	515	11	distributed	distribute	VERB
ejpam-5714	515	12	deviating	deviate	VERB
ejpam-5714	515	13	arguments	argument	NOUN
ejpam-5714	515	14	.	.	PUNCT
ejpam-5714	516	1	appl	appl	PROPN
ejpam-5714	516	2	.	.	PROPN
ejpam-5714	516	3	math	math	PROPN
ejpam-5714	516	4	.	.	PUNCT
ejpam-5714	517	1	comput	comput	NOUN
ejpam-5714	517	2	.	.	PUNCT
ejpam-5714	517	3	,	,	PUNCT
ejpam-5714	517	4	262:199–203	262:199–203	NUM
ejpam-5714	517	5	,	,	PUNCT
ejpam-5714	517	6	2015	2015	NUM
ejpam-5714	517	7	.	.	PUNCT
ejpam-5714	518	1	[	[	X
ejpam-5714	518	2	8	8	NUM
ejpam-5714	518	3	]	]	X
ejpam-5714	518	4	j	j	PROPN
ejpam-5714	518	5	dzurina	dzurina	NOUN
ejpam-5714	518	6	and	and	CCONJ
ejpam-5714	518	7	i	i	PRON
ejpam-5714	518	8	p	p	NOUN
ejpam-5714	518	9	stavroulakis	stavroulakis	PROPN
ejpam-5714	518	10	.	.	PUNCT
ejpam-5714	519	1	oscillation	oscillation	NOUN
ejpam-5714	519	2	criteria	criterion	NOUN
ejpam-5714	519	3	for	for	ADP
ejpam-5714	519	4	second	second	ADJ
ejpam-5714	519	5	-	-	PUNCT
ejpam-5714	519	6	order	order	NOUN
ejpam-5714	519	7	delay	delay	NOUN
ejpam-5714	519	8	differential	differential	ADJ
ejpam-5714	519	9	equations	equation	NOUN
ejpam-5714	519	10	.	.	PUNCT
ejpam-5714	520	1	appl	appl	PROPN
ejpam-5714	520	2	.	.	PROPN
ejpam-5714	520	3	math	math	PROPN
ejpam-5714	520	4	.	.	PUNCT
ejpam-5714	521	1	comput	comput	NOUN
ejpam-5714	521	2	.	.	PUNCT
ejpam-5714	521	3	,	,	PUNCT
ejpam-5714	521	4	140:445–453	140:445–453	NUM
ejpam-5714	521	5	,	,	PUNCT
ejpam-5714	521	6	2003	2003	NUM
ejpam-5714	521	7	.	.	PUNCT
ejpam-5714	522	1	[	[	X
ejpam-5714	522	2	9	9	NUM
ejpam-5714	522	3	]	]	PUNCT
ejpam-5714	522	4	a	a	DET
ejpam-5714	522	5	kaymaz	kaymaz	PROPN
ejpam-5714	522	6	e	e	NOUN
ejpam-5714	522	7	tunç.	tunç.	NOUN
ejpam-5714	522	8	on	on	ADP
ejpam-5714	522	9	oscillation	oscillation	NOUN
ejpam-5714	522	10	of	of	ADP
ejpam-5714	522	11	second	second	ADJ
ejpam-5714	522	12	-	-	PUNCT
ejpam-5714	522	13	order	order	NOUN
ejpam-5714	522	14	linear	linear	ADJ
ejpam-5714	522	15	neutral	neutral	ADJ
ejpam-5714	522	16	differential	differential	ADJ
ejpam-5714	522	17	equations	equation	NOUN
ejpam-5714	522	18	with	with	ADP
ejpam-5714	522	19	damping	damp	VERB
ejpam-5714	522	20	term	term	NOUN
ejpam-5714	522	21	.	.	PUNCT
ejpam-5714	523	1	dynam	dynam	PROPN
ejpam-5714	523	2	.	.	PUNCT
ejpam-5714	524	1	syst	syst	PROPN
ejpam-5714	524	2	.	.	PUNCT
ejpam-5714	524	3	appl	appl	PROPN
ejpam-5714	524	4	.	.	PROPN
ejpam-5714	524	5	,	,	PUNCT
ejpam-5714	524	6	28:289–301	28:289–301	PROPN
ejpam-5714	524	7	,	,	PUNCT
ejpam-5714	524	8	2019	2019	NUM
ejpam-5714	524	9	.	.	PUNCT
ejpam-5714	525	1	[	[	X
ejpam-5714	525	2	10	10	NUM
ejpam-5714	525	3	]	]	SYM
ejpam-5714	525	4	b	b	PROPN
ejpam-5714	525	5	zhang	zhang	PROPN
ejpam-5714	525	6	g	g	PROPN
ejpam-5714	525	7	ladde	ladde	PROPN
ejpam-5714	525	8	,	,	PUNCT
ejpam-5714	525	9	v	v	ADP
ejpam-5714	525	10	lakshmikantham	lakshmikantham	NOUN
ejpam-5714	525	11	.	.	PUNCT
ejpam-5714	526	1	oscillation	oscillation	NOUN
ejpam-5714	526	2	theory	theory	NOUN
ejpam-5714	526	3	of	of	ADP
ejpam-5714	526	4	differential	differential	NOUN
ejpam-5714	526	5	equationswith	equationswith	NOUN
ejpam-5714	526	6	deviating	deviate	VERB
ejpam-5714	526	7	arguments	argument	NOUN
ejpam-5714	526	8	.	.	PUNCT
ejpam-5714	527	1	marcel	marcel	PROPN
ejpam-5714	527	2	dekker	dekker	PROPN
ejpam-5714	527	3	,	,	PUNCT
ejpam-5714	527	4	newyork	newyork	PROPN
ejpam-5714	527	5	,	,	PUNCT
ejpam-5714	527	6	1987	1987	NUM
ejpam-5714	527	7	.	.	PUNCT
ejpam-5714	528	1	[	[	X
ejpam-5714	528	2	11	11	NUM
ejpam-5714	528	3	]	]	X
ejpam-5714	528	4	i	i	PRON
ejpam-5714	528	5	gyori	gyori	VERB
ejpam-5714	528	6	and	and	CCONJ
ejpam-5714	528	7	g	g	PROPN
ejpam-5714	528	8	ladas	ladas	PROPN
ejpam-5714	528	9	.	.	PUNCT
ejpam-5714	529	1	oscillation	oscillation	NOUN
ejpam-5714	529	2	theory	theory	NOUN
ejpam-5714	529	3	of	of	ADP
ejpam-5714	529	4	delay	delay	NOUN
ejpam-5714	529	5	differential	differential	ADJ
ejpam-5714	529	6	equations	equation	NOUN
ejpam-5714	529	7	with	with	ADP
ejpam-5714	529	8	applications	application	NOUN
ejpam-5714	529	9	.	.	PUNCT
ejpam-5714	530	1	oxford	oxford	PROPN
ejpam-5714	530	2	university	university	PROPN
ejpam-5714	530	3	press	press	NOUN
ejpam-5714	530	4	,	,	PUNCT
ejpam-5714	530	5	new	new	PROPN
ejpam-5714	530	6	york	york	PROPN
ejpam-5714	530	7	,	,	PUNCT
ejpam-5714	530	8	us	we	PRON
ejpam-5714	530	9	,	,	PUNCT
ejpam-5714	530	10	1991	1991	NUM
ejpam-5714	530	11	.	.	PUNCT
ejpam-5714	531	1	f.	f.	PROPN
ejpam-5714	531	2	aldosari	aldosari	PROPN
ejpam-5714	531	3	/	/	SYM
ejpam-5714	531	4	eur	eur	PROPN
ejpam-5714	531	5	.	.	PUNCT
ejpam-5714	532	1	j.	j.	PROPN
ejpam-5714	532	2	pure	pure	PROPN
ejpam-5714	532	3	appl	appl	PROPN
ejpam-5714	532	4	.	.	PROPN
ejpam-5714	532	5	math	math	PROPN
ejpam-5714	532	6	,	,	PUNCT
ejpam-5714	532	7	18	18	NUM
ejpam-5714	532	8	(	(	PUNCT
ejpam-5714	532	9	1	1	NUM
ejpam-5714	532	10	)	)	PUNCT
ejpam-5714	532	11	(	(	PUNCT
ejpam-5714	532	12	2025	2025	NUM
ejpam-5714	532	13	)	)	PUNCT
ejpam-5714	532	14	,	,	PUNCT
ejpam-5714	532	15	5714	5714	NUM
ejpam-5714	532	16	16	16	NUM
ejpam-5714	532	17	of	of	ADP
ejpam-5714	532	18	16	16	NUM
ejpam-5714	533	1	[	[	X
ejpam-5714	533	2	12	12	NUM
ejpam-5714	533	3	]	]	X
ejpam-5714	533	4	j	j	PROPN
ejpam-5714	533	5	k	k	PROPN
ejpam-5714	533	6	hale	hale	PROPN
ejpam-5714	533	7	.	.	PUNCT
ejpam-5714	534	1	theory	theory	NOUN
ejpam-5714	534	2	of	of	ADP
ejpam-5714	534	3	functional	functional	ADJ
ejpam-5714	534	4	differential	differential	ADJ
ejpam-5714	534	5	equations	equation	NOUN
ejpam-5714	534	6	.	.	PUNCT
ejpam-5714	535	1	springer	springer	NOUN
ejpam-5714	535	2	,	,	PUNCT
ejpam-5714	535	3	new	new	PROPN
ejpam-5714	535	4	york	york	PROPN
ejpam-5714	535	5	,	,	PUNCT
ejpam-5714	535	6	1977	1977	NUM
ejpam-5714	535	7	.	.	PUNCT
ejpam-5714	536	1	[	[	X
ejpam-5714	536	2	13	13	NUM
ejpam-5714	536	3	]	]	PUNCT
ejpam-5714	536	4	l	l	PROPN
ejpam-5714	536	5	liu	liu	PROPN
ejpam-5714	536	6	and	and	CCONJ
ejpam-5714	536	7	y	y	PROPN
ejpam-5714	536	8	bai	bai	PROPN
ejpam-5714	536	9	.	.	PUNCT
ejpam-5714	537	1	new	new	ADJ
ejpam-5714	537	2	oscillation	oscillation	NOUN
ejpam-5714	537	3	criteria	criterion	NOUN
ejpam-5714	537	4	for	for	ADP
ejpam-5714	537	5	second	second	ADJ
ejpam-5714	537	6	-	-	PUNCT
ejpam-5714	537	7	order	order	NOUN
ejpam-5714	537	8	nonlinear	nonlinear	ADJ
ejpam-5714	537	9	neutral	neutral	ADJ
ejpam-5714	537	10	delay	delay	NOUN
ejpam-5714	537	11	differential	differential	NOUN
ejpam-5714	537	12	equations	equation	NOUN
ejpam-5714	537	13	.	.	PUNCT
ejpam-5714	538	1	j.	j.	PROPN
ejpam-5714	538	2	comput	comput	PROPN
ejpam-5714	538	3	.	.	PUNCT
ejpam-5714	539	1	appl	appl	PROPN
ejpam-5714	539	2	.	.	PROPN
ejpam-5714	539	3	math	math	PROPN
ejpam-5714	539	4	.	.	PUNCT
ejpam-5714	539	5	,	,	PUNCT
ejpam-5714	540	1	231:657–663	231:657–663	NUM
ejpam-5714	540	2	,	,	PUNCT
ejpam-5714	540	3	2009	2009	NUM
ejpam-5714	540	4	.	.	PUNCT
ejpam-5714	541	1	[	[	X
ejpam-5714	541	2	14	14	NUM
ejpam-5714	541	3	]	]	X
ejpam-5714	541	4	l	l	NOUN
ejpam-5714	541	5	f	f	PROPN
ejpam-5714	541	6	lambor	lambor	PROPN
ejpam-5714	541	7	e	e	PROPN
ejpam-5714	541	8	m	m	PROPN
ejpam-5714	541	9	elabbasy	elabbasy	PROPN
ejpam-5714	541	10	m.	m.	PROPN
ejpam-5714	541	11	aldiaiji	aldiaiji	PROPN
ejpam-5714	541	12	,	,	PUNCT
ejpam-5714	541	13	b	b	PROPN
ejpam-5714	541	14	qaraad	qaraad	NOUN
ejpam-5714	541	15	.	.	PUNCT
ejpam-5714	542	1	new	new	ADJ
ejpam-5714	542	2	oscillation	oscillation	NOUN
ejpam-5714	542	3	theorems	theorem	NOUN
ejpam-5714	542	4	for	for	ADP
ejpam-5714	542	5	second	second	ADJ
ejpam-5714	542	6	-	-	PUNCT
ejpam-5714	542	7	order	order	NOUN
ejpam-5714	542	8	superlinear	superlinear	ADJ
ejpam-5714	542	9	neutral	neutral	ADJ
ejpam-5714	542	10	differential	differential	ADJ
ejpam-5714	542	11	equations	equation	NOUN
ejpam-5714	542	12	with	with	ADP
ejpam-5714	542	13	variable	variable	ADJ
ejpam-5714	542	14	damping	damp	VERB
ejpam-5714	542	15	terms	term	NOUN
ejpam-5714	542	16	.	.	PUNCT
ejpam-5714	543	1	symmetry	symmetry	NOUN
ejpam-5714	543	2	,	,	PUNCT
ejpam-5714	543	3	15:1630	15:1630	NOUN
ejpam-5714	543	4	,	,	PUNCT
ejpam-5714	543	5	2023	2023	NUM
ejpam-5714	543	6	.	.	PUNCT
ejpam-5714	544	1	[	[	X
ejpam-5714	544	2	15	15	NUM
ejpam-5714	544	3	]	]	X
ejpam-5714	544	4	s	s	PART
ejpam-5714	544	5	h	h	NOUN
ejpam-5714	544	6	saker	saker	PROPN
ejpam-5714	544	7	m	m	PROPN
ejpam-5714	544	8	bohner	bohner	NOUN
ejpam-5714	544	9	.	.	PUNCT
ejpam-5714	545	1	oscillation	oscillation	NOUN
ejpam-5714	545	2	of	of	ADP
ejpam-5714	545	3	damped	damped	ADJ
ejpam-5714	545	4	second	second	ADJ
ejpam-5714	545	5	order	order	NOUN
ejpam-5714	545	6	nonlinear	nonlinear	ADJ
ejpam-5714	545	7	delay	delay	NOUN
ejpam-5714	545	8	differential	differential	ADJ
ejpam-5714	545	9	equations	equation	NOUN
ejpam-5714	545	10	of	of	ADP
ejpam-5714	545	11	emden	emden	ADJ
ejpam-5714	545	12	-	-	PUNCT
ejpam-5714	545	13	fowler	fowler	PROPN
ejpam-5714	545	14	type	type	NOUN
ejpam-5714	545	15	.	.	PUNCT
ejpam-5714	546	1	adv	adv	PROPN
ejpam-5714	546	2	.	.	PUNCT
ejpam-5714	547	1	dyn	dyn	PROPN
ejpam-5714	547	2	.	.	PUNCT
ejpam-5714	548	1	syst	syst	PROPN
ejpam-5714	548	2	.	.	PUNCT
ejpam-5714	549	1	appl	appl	PROPN
ejpam-5714	549	2	.	.	PROPN
ejpam-5714	549	3	,	,	PUNCT
ejpam-5714	549	4	1:163–182	1:163–182	NOUN
ejpam-5714	549	5	,	,	PUNCT
ejpam-5714	549	6	2006	2006	NUM
ejpam-5714	549	7	.	.	PUNCT
ejpam-5714	550	1	[	[	X
ejpam-5714	550	2	16	16	NUM
ejpam-5714	550	3	]	]	X
ejpam-5714	550	4	c	c	PROPN
ejpam-5714	550	5	philos	philos	PROPN
ejpam-5714	550	6	.	.	PUNCT
ejpam-5714	551	1	on	on	ADP
ejpam-5714	551	2	the	the	DET
ejpam-5714	551	3	existence	existence	NOUN
ejpam-5714	551	4	of	of	ADP
ejpam-5714	551	5	nonoscillatory	nonoscillatory	ADJ
ejpam-5714	551	6	solutions	solution	NOUN
ejpam-5714	551	7	tending	tend	VERB
ejpam-5714	551	8	to	to	ADP
ejpam-5714	551	9	zero	zero	NUM
ejpam-5714	551	10	at	at	ADP
ejpam-5714	551	11	∞	∞	PROPN
ejpam-5714	551	12	for	for	ADP
ejpam-5714	551	13	differential	differential	ADJ
ejpam-5714	551	14	equations	equation	NOUN
ejpam-5714	551	15	with	with	ADP
ejpam-5714	551	16	positive	positive	ADJ
ejpam-5714	551	17	delay	delay	NOUN
ejpam-5714	551	18	.	.	PUNCT
ejpam-5714	552	1	arch	arch	PROPN
ejpam-5714	552	2	.	.	PUNCT
ejpam-5714	553	1	math	math	NOUN
ejpam-5714	553	2	.	.	PUNCT
ejpam-5714	554	1	(	(	PUNCT
ejpam-5714	554	2	basel	basel	PROPN
ejpam-5714	554	3	)	)	PUNCT
ejpam-5714	554	4	,	,	PUNCT
ejpam-5714	554	5	36:168–178	36:168–178	NUM
ejpam-5714	554	6	,	,	PUNCT
ejpam-5714	554	7	1981	1981	NUM
ejpam-5714	554	8	.	.	PUNCT
ejpam-5714	555	1	[	[	X
ejpam-5714	555	2	17	17	NUM
ejpam-5714	555	3	]	]	X
ejpam-5714	555	4	l	l	NOUN
ejpam-5714	555	5	f	f	PROPN
ejpam-5714	555	6	iambor	iambor	NOUN
ejpam-5714	555	7	o	o	PROPN
ejpam-5714	555	8	bazighifan	bazighifan	NOUN
ejpam-5714	555	9	s	s	PART
ejpam-5714	555	10	k	k	PROPN
ejpam-5714	555	11	marappan	marappan	NOUN
ejpam-5714	555	12	,	,	PUNCT
ejpam-5714	555	13	a	a	DET
ejpam-5714	555	14	almutairi	almutairi	NOUN
ejpam-5714	555	15	.	.	PUNCT
ejpam-5714	556	1	oscillation	oscillation	NOUN
ejpam-5714	556	2	of	of	ADP
ejpam-5714	556	3	emden	emden	ADJ
ejpam-5714	556	4	–	–	PUNCT
ejpam-5714	556	5	fowlertype	fowlertype	NOUN
ejpam-5714	556	6	differential	differential	ADJ
ejpam-5714	556	7	equations	equation	NOUN
ejpam-5714	556	8	with	with	ADP
ejpam-5714	556	9	non	non	ADJ
ejpam-5714	556	10	-	-	ADJ
ejpam-5714	556	11	canonical	canonical	ADJ
ejpam-5714	556	12	operators	operator	NOUN
ejpam-5714	556	13	and	and	CCONJ
ejpam-5714	556	14	mixed	mixed	ADJ
ejpam-5714	556	15	neutral	neutral	ADJ
ejpam-5714	556	16	terms	term	NOUN
ejpam-5714	556	17	.	.	PUNCT
ejpam-5714	557	1	symmetry	symmetry	NOUN
ejpam-5714	557	2	,	,	PUNCT
ejpam-5714	557	3	15:553	15:553	NUM
ejpam-5714	557	4	,	,	PUNCT
ejpam-5714	557	5	2023	2023	NUM
ejpam-5714	557	6	.	.	PUNCT
ejpam-5714	558	1	[	[	X
ejpam-5714	558	2	18	18	NUM
ejpam-5714	558	3	]	]	X
ejpam-5714	558	4	y	y	PROPN
ejpam-5714	558	5	sahiner	sahiner	NOUN
ejpam-5714	558	6	.	.	PUNCT
ejpam-5714	559	1	on	on	ADP
ejpam-5714	559	2	oscillation	oscillation	NOUN
ejpam-5714	559	3	of	of	ADP
ejpam-5714	559	4	second	second	ADJ
ejpam-5714	559	5	-	-	PUNCT
ejpam-5714	559	6	order	order	NOUN
ejpam-5714	559	7	neutral	neutral	ADJ
ejpam-5714	559	8	type	type	NOUN
ejpam-5714	559	9	delay	delay	NOUN
ejpam-5714	559	10	differential	differential	NOUN
ejpam-5714	559	11	equations	equation	NOUN
ejpam-5714	559	12	.	.	PUNCT
ejpam-5714	560	1	appl	appl	PROPN
ejpam-5714	560	2	.	.	PROPN
ejpam-5714	560	3	math	math	PROPN
ejpam-5714	560	4	.	.	PUNCT
ejpam-5714	561	1	comput	comput	NOUN
ejpam-5714	561	2	.	.	PUNCT
ejpam-5714	561	3	,	,	PUNCT
ejpam-5714	561	4	150:697–706	150:697–706	PROPN
ejpam-5714	561	5	,	,	PUNCT
ejpam-5714	561	6	2004	2004	NUM
ejpam-5714	561	7	.	.	PUNCT
ejpam-5714	562	1	[	[	X
ejpam-5714	562	2	19	19	NUM
ejpam-5714	562	3	]	]	X
ejpam-5714	562	4	y	y	PROPN
ejpam-5714	562	5	v	v	NUM
ejpam-5714	562	6	rogovchenko	rogovchenko	PROPN
ejpam-5714	562	7	t	t	PROPN
ejpam-5714	562	8	li	li	PROPN
ejpam-5714	562	9	.	.	PUNCT
ejpam-5714	562	10	oscillation	oscillation	NOUN
ejpam-5714	562	11	of	of	ADP
ejpam-5714	562	12	second	second	ADJ
ejpam-5714	562	13	-	-	PUNCT
ejpam-5714	562	14	order	order	NOUN
ejpam-5714	562	15	neutral	neutral	ADJ
ejpam-5714	562	16	differential	differential	NOUN
ejpam-5714	562	17	equations	equation	NOUN
ejpam-5714	562	18	.	.	PUNCT
ejpam-5714	563	1	math	math	NOUN
ejpam-5714	563	2	.	.	PUNCT
ejpam-5714	564	1	nachr	nachr	PROPN
ejpam-5714	564	2	.	.	PUNCT
ejpam-5714	564	3	,	,	PUNCT
ejpam-5714	564	4	288:1150–1162	288:1150–1162	NUM
ejpam-5714	564	5	,	,	PUNCT
ejpam-5714	564	6	2015	2015	NUM
ejpam-5714	564	7	.	.	PUNCT
ejpam-5714	565	1	[	[	X
ejpam-5714	565	2	20	20	NUM
ejpam-5714	565	3	]	]	X
ejpam-5714	565	4	p	p	X
ejpam-5714	565	5	g	g	PROPN
ejpam-5714	565	6	wang	wang	PROPN
ejpam-5714	565	7	.	.	PUNCT
ejpam-5714	566	1	oscillation	oscillation	NOUN
ejpam-5714	566	2	criteria	criterion	NOUN
ejpam-5714	566	3	for	for	ADP
ejpam-5714	566	4	second	second	ADJ
ejpam-5714	566	5	-	-	PUNCT
ejpam-5714	566	6	order	order	NOUN
ejpam-5714	566	7	neutral	neutral	ADJ
ejpam-5714	566	8	equations	equation	NOUN
ejpam-5714	566	9	with	with	ADP
ejpam-5714	566	10	distributed	distribute	VERB
ejpam-5714	566	11	deviating	deviate	VERB
ejpam-5714	566	12	arguments	argument	NOUN
ejpam-5714	566	13	.	.	PUNCT
ejpam-5714	567	1	comput	comput	NOUN
ejpam-5714	567	2	.	.	PUNCT
ejpam-5714	568	1	math	math	NOUN
ejpam-5714	568	2	.	.	PUNCT
ejpam-5714	569	1	appl	appl	PROPN
ejpam-5714	569	2	.	.	PROPN
ejpam-5714	569	3	,	,	PUNCT
ejpam-5714	569	4	47:1935–1946	47:1935–1946	PROPN
ejpam-5714	569	5	,	,	PUNCT
ejpam-5714	569	6	2004	2004	NUM
ejpam-5714	569	7	.	.	PUNCT
ejpam-5714	570	1	[	[	X
ejpam-5714	570	2	21	21	NUM
ejpam-5714	570	3	]	]	X
ejpam-5714	571	1	z	z	NOUN
ejpam-5714	571	2	t	t	PROPN
ejpam-5714	572	1	xu	xu	PROPN
ejpam-5714	572	2	and	and	CCONJ
ejpam-5714	572	3	p	p	X
ejpam-5714	572	4	x	x	PROPN
ejpam-5714	572	5	weng	weng	PROPN
ejpam-5714	572	6	.	.	PUNCT
ejpam-5714	573	1	oscillation	oscillation	NOUN
ejpam-5714	573	2	of	of	ADP
ejpam-5714	573	3	second	second	ADJ
ejpam-5714	573	4	-	-	PUNCT
ejpam-5714	573	5	order	order	NOUN
ejpam-5714	573	6	neutral	neutral	ADJ
ejpam-5714	573	7	equations	equation	NOUN
ejpam-5714	573	8	with	with	ADP
ejpam-5714	573	9	distributed	distribute	VERB
ejpam-5714	573	10	deviating	deviate	VERB
ejpam-5714	573	11	arguments	argument	NOUN
ejpam-5714	573	12	.	.	PUNCT
ejpam-5714	574	1	j.	j.	PROPN
ejpam-5714	574	2	comput	comput	PROPN
ejpam-5714	574	3	.	.	PUNCT
ejpam-5714	575	1	appl	appl	PROPN
ejpam-5714	575	2	.	.	PROPN
ejpam-5714	575	3	math	math	PROPN
ejpam-5714	575	4	.	.	PUNCT
ejpam-5714	575	5	,	,	PUNCT
ejpam-5714	575	6	202:460–477	202:460–477	NUM
ejpam-5714	575	7	,	,	PUNCT
ejpam-5714	575	8	2007	2007	NUM
ejpam-5714	575	9	.	.	PUNCT
ejpam-5714	576	1	[	[	X
ejpam-5714	576	2	22	22	NUM
ejpam-5714	576	3	]	]	PUNCT
ejpam-5714	576	4	a	a	DET
ejpam-5714	576	5	almuneef	almuneef	PROPN
ejpam-5714	576	6	f	f	PROPN
ejpam-5714	576	7	alharbi	alharbi	PROPN
ejpam-5714	576	8	z	z	PROPN
ejpam-5714	576	9	alqahtani	alqahtani	PROPN
ejpam-5714	576	10	,	,	PUNCT
ejpam-5714	576	11	b	b	NOUN
ejpam-5714	576	12	qaraad	qaraad	NOUN
ejpam-5714	576	13	.	.	PUNCT
ejpam-5714	577	1	oscillatory	oscillatory	ADJ
ejpam-5714	577	2	properties	property	NOUN
ejpam-5714	577	3	of	of	ADP
ejpam-5714	577	4	second	second	ADJ
ejpam-5714	577	5	-	-	PUNCT
ejpam-5714	577	6	order	order	NOUN
ejpam-5714	577	7	differential	differential	ADJ
ejpam-5714	577	8	equations	equation	NOUN
ejpam-5714	577	9	with	with	ADP
ejpam-5714	577	10	advanced	advanced	ADJ
ejpam-5714	577	11	arguments	argument	NOUN
ejpam-5714	577	12	in	in	ADP
ejpam-5714	577	13	the	the	DET
ejpam-5714	577	14	noncanonical	noncanonical	ADJ
ejpam-5714	577	15	case	case	NOUN
ejpam-5714	577	16	.	.	PUNCT
ejpam-5714	578	1	symmetry	symmetry	NOUN
ejpam-5714	578	2	,	,	PUNCT
ejpam-5714	578	3	16:1018	16:1018	NOUN
ejpam-5714	578	4	,	,	PUNCT
ejpam-5714	578	5	2024	2024	NUM
ejpam-5714	578	6	.	.	PUNCT
ejpam-5714	579	1	[	[	X
ejpam-5714	579	2	23	23	NUM
ejpam-5714	579	3	]	]	X
ejpam-5714	579	4	j	j	PROPN
ejpam-5714	579	5	zhao	zhao	PROPN
ejpam-5714	579	6	and	and	CCONJ
ejpam-5714	579	7	f	f	PROPN
ejpam-5714	579	8	meng	meng	PROPN
ejpam-5714	579	9	.	.	PUNCT
ejpam-5714	580	1	oscillation	oscillation	NOUN
ejpam-5714	580	2	criteria	criterion	NOUN
ejpam-5714	580	3	for	for	ADP
ejpam-5714	580	4	second	second	ADJ
ejpam-5714	580	5	-	-	PUNCT
ejpam-5714	580	6	order	order	NOUN
ejpam-5714	580	7	neutral	neutral	ADJ
ejpam-5714	580	8	equations	equation	NOUN
ejpam-5714	580	9	with	with	ADP
ejpam-5714	580	10	distributed	distribute	VERB
ejpam-5714	580	11	deviating	deviate	VERB
ejpam-5714	580	12	argument	argument	NOUN
ejpam-5714	580	13	.	.	PUNCT
ejpam-5714	581	1	applied	apply	VERB
ejpam-5714	581	2	mathematics	mathematic	NOUN
ejpam-5714	581	3	and	and	CCONJ
ejpam-5714	581	4	computation	computation	NOUN
ejpam-5714	581	5	,	,	PUNCT
ejpam-5714	581	6	206:485	206:485	NOUN
ejpam-5714	581	7	–	–	PUNCT
ejpam-5714	581	8	493	493	NUM
ejpam-5714	581	9	,	,	PUNCT
ejpam-5714	581	10	2008	2008	NUM
ejpam-5714	581	11	.	.	PUNCT