id	sid	tid	token	lemma	pos
ejpam-3654	1	1	european	european	PROPN
ejpam-3654	1	2	journal	journal	PROPN
ejpam-3654	1	3	of	of	ADP
ejpam-3654	1	4	pure	pure	ADJ
ejpam-3654	1	5	and	and	CCONJ
ejpam-3654	1	6	applied	apply	VERB
ejpam-3654	1	7	mathematics	mathematic	NOUN
ejpam-3654	1	8	vol	vol	NOUN
ejpam-3654	1	9	.	.	PROPN
ejpam-3654	2	1	13	13	NUM
ejpam-3654	2	2	,	,	PUNCT
ejpam-3654	2	3	no	no	INTJ
ejpam-3654	2	4	.	.	NOUN
ejpam-3654	2	5	2	2	NUM
ejpam-3654	2	6	,	,	PUNCT
ejpam-3654	2	7	2020	2020	NUM
ejpam-3654	2	8	,	,	PUNCT
ejpam-3654	2	9	185	185	NUM
ejpam-3654	2	10	-	-	SYM
ejpam-3654	2	11	199	199	NUM
ejpam-3654	2	12	issn	issn	PROPN
ejpam-3654	2	13	1307	1307	NUM
ejpam-3654	2	14	-	-	SYM
ejpam-3654	2	15	5543	5543	NUM
ejpam-3654	2	16	–	–	PUNCT
ejpam-3654	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3654	2	18	published	publish	VERB
ejpam-3654	2	19	by	by	ADP
ejpam-3654	2	20	new	new	PROPN
ejpam-3654	2	21	york	york	PROPN
ejpam-3654	2	22	business	business	NOUN
ejpam-3654	2	23	global	global	PROPN
ejpam-3654	2	24	some	some	DET
ejpam-3654	2	25	new	new	ADJ
ejpam-3654	2	26	oscillation	oscillation	NOUN
ejpam-3654	2	27	results	result	NOUN
ejpam-3654	2	28	for	for	ADP
ejpam-3654	2	29	fourth	fourth	ADJ
ejpam-3654	2	30	-	-	PUNCT
ejpam-3654	2	31	order	order	NOUN
ejpam-3654	2	32	neutral	neutral	ADJ
ejpam-3654	2	33	differential	differential	ADJ
ejpam-3654	2	34	equations	equation	NOUN
ejpam-3654	2	35	osama	osama	PROPN
ejpam-3654	2	36	moaaz1	moaaz1	PROPN
ejpam-3654	2	37	,	,	PUNCT
ejpam-3654	2	38	clemente	clemente	PROPN
ejpam-3654	2	39	cesarano2,∗	cesarano2,∗	PROPN
ejpam-3654	2	40	,	,	PUNCT
ejpam-3654	2	41	ali	ali	PROPN
ejpam-3654	2	42	muhib3	muhib3	PROPN
ejpam-3654	2	43	1	1	NUM
ejpam-3654	2	44	department	department	NOUN
ejpam-3654	2	45	of	of	ADP
ejpam-3654	2	46	mathematics	mathematic	NOUN
ejpam-3654	2	47	,	,	PUNCT
ejpam-3654	2	48	faculty	faculty	NOUN
ejpam-3654	2	49	of	of	ADP
ejpam-3654	2	50	science	science	NOUN
ejpam-3654	2	51	,	,	PUNCT
ejpam-3654	2	52	mansoura	mansoura	PROPN
ejpam-3654	2	53	university	university	NOUN
ejpam-3654	2	54	,	,	PUNCT
ejpam-3654	2	55	35516	35516	NUM
ejpam-3654	2	56	mansoura	mansoura	PROPN
ejpam-3654	2	57	,	,	PUNCT
ejpam-3654	2	58	egypt	egypt	PROPN
ejpam-3654	2	59	2	2	NUM
ejpam-3654	2	60	section	section	NOUN
ejpam-3654	2	61	of	of	ADP
ejpam-3654	2	62	mathematics	mathematic	NOUN
ejpam-3654	2	63	,	,	PUNCT
ejpam-3654	2	64	international	international	ADJ
ejpam-3654	2	65	telematic	telematic	ADJ
ejpam-3654	2	66	university	university	NOUN
ejpam-3654	2	67	uninettuno	uninettuno	NOUN
ejpam-3654	2	68	,	,	PUNCT
ejpam-3654	2	69	corsovittorio	corsovittorio	NOUN
ejpam-3654	2	70	emanuele	emanuele	PROPN
ejpam-3654	2	71	ii	ii	PROPN
ejpam-3654	2	72	,	,	PUNCT
ejpam-3654	2	73	39	39	NUM
ejpam-3654	2	74	,	,	PUNCT
ejpam-3654	2	75	00186	00186	NUM
ejpam-3654	2	76	roma	roma	PROPN
ejpam-3654	2	77	,	,	PUNCT
ejpam-3654	2	78	italy	italy	PROPN
ejpam-3654	2	79	3	3	NUM
ejpam-3654	2	80	department	department	PROPN
ejpam-3654	2	81	of	of	ADP
ejpam-3654	2	82	mathematics	mathematic	NOUN
ejpam-3654	2	83	,	,	PUNCT
ejpam-3654	2	84	faculty	faculty	NOUN
ejpam-3654	2	85	of	of	ADP
ejpam-3654	2	86	education	education	NOUN
ejpam-3654	2	87	–	–	PUNCT
ejpam-3654	2	88	al	al	PROPN
ejpam-3654	2	89	-	-	PUNCT
ejpam-3654	2	90	nadirah	nadirah	PROPN
ejpam-3654	2	91	,	,	PUNCT
ejpam-3654	2	92	ibb	ibb	PROPN
ejpam-3654	2	93	university	university	NOUN
ejpam-3654	2	94	,	,	PUNCT
ejpam-3654	2	95	ibb	ibb	NOUN
ejpam-3654	2	96	,	,	PUNCT
ejpam-3654	2	97	yemen	yemen	PROPN
ejpam-3654	2	98	abstract	abstract	NOUN
ejpam-3654	2	99	.	.	PUNCT
ejpam-3654	3	1	by	by	ADP
ejpam-3654	3	2	employing	employ	VERB
ejpam-3654	3	3	the	the	DET
ejpam-3654	3	4	riccati	riccati	PROPN
ejpam-3654	3	5	substitution	substitution	NOUN
ejpam-3654	3	6	technique	technique	NOUN
ejpam-3654	3	7	,	,	PUNCT
ejpam-3654	3	8	we	we	PRON
ejpam-3654	3	9	establish	establish	VERB
ejpam-3654	3	10	new	new	ADJ
ejpam-3654	3	11	oscillation	oscillation	NOUN
ejpam-3654	3	12	criteria	criterion	NOUN
ejpam-3654	3	13	for	for	ADP
ejpam-3654	3	14	a	a	DET
ejpam-3654	3	15	class	class	NOUN
ejpam-3654	3	16	of	of	ADP
ejpam-3654	3	17	fourth	fourth	ADJ
ejpam-3654	3	18	-	-	PUNCT
ejpam-3654	3	19	order	order	NOUN
ejpam-3654	3	20	neutral	neutral	ADJ
ejpam-3654	3	21	differential	differential	NOUN
ejpam-3654	3	22	equations	equation	NOUN
ejpam-3654	3	23	.	.	PUNCT
ejpam-3654	4	1	our	our	PRON
ejpam-3654	4	2	new	new	ADJ
ejpam-3654	4	3	criteria	criterion	NOUN
ejpam-3654	4	4	complement	complement	VERB
ejpam-3654	4	5	a	a	DET
ejpam-3654	4	6	number	number	NOUN
ejpam-3654	4	7	of	of	ADP
ejpam-3654	4	8	existing	exist	VERB
ejpam-3654	4	9	ones	one	NOUN
ejpam-3654	4	10	.	.	PUNCT
ejpam-3654	5	1	an	an	DET
ejpam-3654	5	2	illustrative	illustrative	ADJ
ejpam-3654	5	3	example	example	NOUN
ejpam-3654	5	4	is	be	AUX
ejpam-3654	5	5	provided	provide	VERB
ejpam-3654	5	6	.	.	PUNCT
ejpam-3654	6	1	2020	2020	NUM
ejpam-3654	6	2	mathematics	mathematic	NOUN
ejpam-3654	6	3	subject	subject	NOUN
ejpam-3654	6	4	classifications	classification	NOUN
ejpam-3654	6	5	:	:	PUNCT
ejpam-3654	6	6	34k10	34k10	NUM
ejpam-3654	6	7	,	,	PUNCT
ejpam-3654	6	8	34k11	34k11	NUM
ejpam-3654	6	9	key	key	ADJ
ejpam-3654	6	10	words	word	NOUN
ejpam-3654	6	11	and	and	CCONJ
ejpam-3654	6	12	phrases	phrase	NOUN
ejpam-3654	6	13	:	:	PUNCT
ejpam-3654	6	14	fourth	fourth	ADJ
ejpam-3654	6	15	-	-	PUNCT
ejpam-3654	6	16	order	order	NOUN
ejpam-3654	6	17	differential	differential	ADJ
ejpam-3654	6	18	equations	equation	NOUN
ejpam-3654	6	19	,	,	PUNCT
ejpam-3654	6	20	neutral	neutral	ADJ
ejpam-3654	6	21	delay	delay	NOUN
ejpam-3654	6	22	,	,	PUNCT
ejpam-3654	6	23	oscillation	oscillation	NOUN
ejpam-3654	6	24	1	1	NUM
ejpam-3654	6	25	.	.	PUNCT
ejpam-3654	7	1	introduction	introduction	NOUN
ejpam-3654	7	2	for	for	ADP
ejpam-3654	7	3	several	several	ADJ
ejpam-3654	7	4	decades	decade	NOUN
ejpam-3654	7	5	,	,	PUNCT
ejpam-3654	7	6	an	an	DET
ejpam-3654	7	7	increasing	increase	VERB
ejpam-3654	7	8	interest	interest	NOUN
ejpam-3654	7	9	in	in	ADP
ejpam-3654	7	10	obtaining	obtain	VERB
ejpam-3654	7	11	sufficient	sufficient	ADJ
ejpam-3654	7	12	conditions	condition	NOUN
ejpam-3654	7	13	for	for	ADP
ejpam-3654	7	14	oscillatory	oscillatory	ADJ
ejpam-3654	7	15	and	and	CCONJ
ejpam-3654	7	16	nonoscillatory	nonoscillatory	ADJ
ejpam-3654	7	17	behavior	behavior	NOUN
ejpam-3654	7	18	of	of	ADP
ejpam-3654	7	19	different	different	ADJ
ejpam-3654	7	20	classes	class	NOUN
ejpam-3654	7	21	of	of	ADP
ejpam-3654	7	22	differential	differential	ADJ
ejpam-3654	7	23	equations	equation	NOUN
ejpam-3654	7	24	has	have	AUX
ejpam-3654	7	25	been	be	AUX
ejpam-3654	7	26	observed	observe	VERB
ejpam-3654	7	27	;	;	PUNCT
ejpam-3654	7	28	see	see	VERB
ejpam-3654	7	29	,	,	PUNCT
ejpam-3654	7	30	for	for	ADP
ejpam-3654	7	31	instance	instance	NOUN
ejpam-3654	7	32	,	,	PUNCT
ejpam-3654	7	33	the	the	DET
ejpam-3654	7	34	monographs	monograph	NOUN
ejpam-3654	8	1	[	[	X
ejpam-3654	8	2	1]-[5	1]-[5	X
ejpam-3654	8	3	]	]	X
ejpam-3654	8	4	,	,	PUNCT
ejpam-3654	8	5	the	the	DET
ejpam-3654	8	6	papers	paper	NOUN
ejpam-3654	8	7	[	[	X
ejpam-3654	8	8	6]-[20	6]-[20	X
ejpam-3654	8	9	]	]	X
ejpam-3654	8	10	,	,	PUNCT
ejpam-3654	8	11	and	and	CCONJ
ejpam-3654	8	12	the	the	DET
ejpam-3654	8	13	references	reference	NOUN
ejpam-3654	8	14	cited	cite	VERB
ejpam-3654	8	15	therein	therein	ADV
ejpam-3654	8	16	.	.	PUNCT
ejpam-3654	9	1	neutral	neutral	ADJ
ejpam-3654	9	2	differential	differential	ADJ
ejpam-3654	9	3	equations	equation	NOUN
ejpam-3654	9	4	are	be	AUX
ejpam-3654	9	5	used	use	VERB
ejpam-3654	9	6	in	in	ADP
ejpam-3654	9	7	numerous	numerous	ADJ
ejpam-3654	9	8	applications	application	NOUN
ejpam-3654	9	9	in	in	ADP
ejpam-3654	9	10	technology	technology	NOUN
ejpam-3654	9	11	and	and	CCONJ
ejpam-3654	9	12	natural	natural	ADJ
ejpam-3654	9	13	science	science	NOUN
ejpam-3654	9	14	.	.	PUNCT
ejpam-3654	10	1	for	for	ADP
ejpam-3654	10	2	instance	instance	NOUN
ejpam-3654	10	3	,	,	PUNCT
ejpam-3654	10	4	they	they	PRON
ejpam-3654	10	5	are	be	AUX
ejpam-3654	10	6	frequently	frequently	ADV
ejpam-3654	10	7	used	use	VERB
ejpam-3654	10	8	for	for	ADP
ejpam-3654	10	9	the	the	DET
ejpam-3654	10	10	study	study	NOUN
ejpam-3654	10	11	of	of	ADP
ejpam-3654	10	12	distributed	distribute	VERB
ejpam-3654	10	13	networks	network	NOUN
ejpam-3654	10	14	containing	contain	VERB
ejpam-3654	10	15	lossless	lossless	NOUN
ejpam-3654	10	16	transmission	transmission	NOUN
ejpam-3654	10	17	lines	line	NOUN
ejpam-3654	10	18	;	;	PUNCT
ejpam-3654	10	19	see	see	VERB
ejpam-3654	10	20	hale	hale	PROPN
ejpam-3654	10	21	[	[	X
ejpam-3654	10	22	22	22	NUM
ejpam-3654	10	23	]	]	PUNCT
ejpam-3654	10	24	,	,	PUNCT
ejpam-3654	10	25	and	and	CCONJ
ejpam-3654	10	26	therefore	therefore	ADV
ejpam-3654	10	27	their	their	PRON
ejpam-3654	10	28	qualitative	qualitative	ADJ
ejpam-3654	10	29	properties	property	NOUN
ejpam-3654	10	30	are	be	AUX
ejpam-3654	10	31	important	important	ADJ
ejpam-3654	10	32	.	.	PUNCT
ejpam-3654	11	1	in	in	ADP
ejpam-3654	11	2	this	this	DET
ejpam-3654	11	3	paper	paper	NOUN
ejpam-3654	11	4	,	,	PUNCT
ejpam-3654	11	5	we	we	PRON
ejpam-3654	11	6	are	be	AUX
ejpam-3654	11	7	concerned	concerned	ADJ
ejpam-3654	11	8	with	with	ADP
ejpam-3654	11	9	the	the	DET
ejpam-3654	11	10	oscillation	oscillation	NOUN
ejpam-3654	11	11	of	of	ADP
ejpam-3654	11	12	solutions	solution	NOUN
ejpam-3654	11	13	of	of	ADP
ejpam-3654	11	14	the	the	DET
ejpam-3654	11	15	fourth	fourth	ADJ
ejpam-3654	11	16	-	-	PUNCT
ejpam-3654	11	17	order	order	NOUN
ejpam-3654	11	18	neutral	neutral	ADJ
ejpam-3654	11	19	differential	differential	NOUN
ejpam-3654	11	20	equation	equation	NOUN
ejpam-3654	11	21	(	(	PUNCT
ejpam-3654	11	22	r	r	NOUN
ejpam-3654	11	23	(	(	PUNCT
ejpam-3654	11	24	t	t	NOUN
ejpam-3654	11	25	)	)	PUNCT
ejpam-3654	11	26	(	(	PUNCT
ejpam-3654	11	27	(	(	PUNCT
ejpam-3654	11	28	x	x	X
ejpam-3654	11	29	(	(	PUNCT
ejpam-3654	11	30	t	t	NOUN
ejpam-3654	11	31	)	)	PUNCT
ejpam-3654	12	1	+	+	NOUN
ejpam-3654	12	2	p	p	X
ejpam-3654	12	3	(	(	PUNCT
ejpam-3654	12	4	t)x	t)x	X
ejpam-3654	12	5	(	(	PUNCT
ejpam-3654	12	6	τ	τ	X
ejpam-3654	12	7	(	(	PUNCT
ejpam-3654	12	8	t)))′′′	t)))′′′	NUM
ejpam-3654	12	9	)	)	PUNCT
ejpam-3654	12	10	α)′	α)′	PROPN
ejpam-3654	12	11	+	+	NUM
ejpam-3654	12	12	q	q	X
ejpam-3654	12	13	(	(	PUNCT
ejpam-3654	12	14	t)xβ	t)xβ	PROPN
ejpam-3654	12	15	(	(	PUNCT
ejpam-3654	12	16	σ	σ	PROPN
ejpam-3654	12	17	(	(	PUNCT
ejpam-3654	12	18	t	t	PROPN
ejpam-3654	12	19	)	)	PUNCT
ejpam-3654	12	20	)	)	PUNCT
ejpam-3654	13	1	=	=	PUNCT
ejpam-3654	13	2	0	0	NUM
ejpam-3654	13	3	,	,	PUNCT
ejpam-3654	13	4	(	(	PUNCT
ejpam-3654	13	5	1	1	X
ejpam-3654	13	6	)	)	PUNCT
ejpam-3654	13	7	where	where	SCONJ
ejpam-3654	13	8	t	t	PROPN
ejpam-3654	13	9	≥	≥	PROPN
ejpam-3654	13	10	t0	t0	PROPN
ejpam-3654	13	11	.	.	PUNCT
ejpam-3654	14	1	in	in	ADP
ejpam-3654	14	2	this	this	DET
ejpam-3654	14	3	work	work	NOUN
ejpam-3654	14	4	,	,	PUNCT
ejpam-3654	14	5	we	we	PRON
ejpam-3654	14	6	assume	assume	VERB
ejpam-3654	14	7	that	that	SCONJ
ejpam-3654	14	8	α	α	PROPN
ejpam-3654	14	9	and	and	CCONJ
ejpam-3654	14	10	β	β	X
ejpam-3654	14	11	are	be	AUX
ejpam-3654	14	12	quotients	quotient	NOUN
ejpam-3654	14	13	of	of	ADP
ejpam-3654	14	14	odd	odd	ADJ
ejpam-3654	14	15	positive	positive	ADJ
ejpam-3654	14	16	integers	integer	NOUN
ejpam-3654	14	17	,	,	PUNCT
ejpam-3654	14	18	r	r	NOUN
ejpam-3654	14	19	,	,	PUNCT
ejpam-3654	14	20	p	p	X
ejpam-3654	14	21	,	,	PUNCT
ejpam-3654	14	22	q	q	PROPN
ejpam-3654	14	23	∈	∈	PROPN
ejpam-3654	14	24	c[t0,∞	c[t0,∞	NOUN
ejpam-3654	14	25	)	)	PUNCT
ejpam-3654	14	26	,	,	PUNCT
ejpam-3654	14	27	r	r	NOUN
ejpam-3654	14	28	(	(	PUNCT
ejpam-3654	14	29	t	t	PROPN
ejpam-3654	14	30	)	)	PUNCT
ejpam-3654	14	31	>	>	X
ejpam-3654	14	32	0	0	NUM
ejpam-3654	14	33	,	,	PUNCT
ejpam-3654	14	34	r′	r′	PROPN
ejpam-3654	14	35	(	(	PUNCT
ejpam-3654	14	36	t	t	PROPN
ejpam-3654	14	37	)	)	PUNCT
ejpam-3654	14	38	≥	≥	NOUN
ejpam-3654	14	39	0	0	NUM
ejpam-3654	14	40	,	,	PUNCT
ejpam-3654	14	41	q	q	X
ejpam-3654	14	42	(	(	PUNCT
ejpam-3654	14	43	t	t	PROPN
ejpam-3654	14	44	)	)	PUNCT
ejpam-3654	14	45	>	>	X
ejpam-3654	14	46	0	0	NUM
ejpam-3654	14	47	,	,	PUNCT
ejpam-3654	14	48	0	0	NUM
ejpam-3654	14	49	≤	≤	NOUN
ejpam-3654	14	50	p	p	NOUN
ejpam-3654	14	51	(	(	PUNCT
ejpam-3654	14	52	t	t	PROPN
ejpam-3654	14	53	)	)	PUNCT
ejpam-3654	14	54	<	<	X
ejpam-3654	14	55	p0	p0	NOUN
ejpam-3654	14	56	<	<	X
ejpam-3654	14	57	∞	∞	PROPN
ejpam-3654	14	58	,	,	PUNCT
ejpam-3654	14	59	τ	τ	PROPN
ejpam-3654	14	60	,	,	PUNCT
ejpam-3654	14	61	σ	σ	PROPN
ejpam-3654	14	62	∈	∈	PROPN
ejpam-3654	14	63	c[t0,∞	c[t0,∞	NOUN
ejpam-3654	14	64	)	)	PUNCT
ejpam-3654	14	65	,	,	PUNCT
ejpam-3654	14	66	∗corresponding	∗corresponde	VERB
ejpam-3654	14	67	author	author	NOUN
ejpam-3654	14	68	.	.	PUNCT
ejpam-3654	15	1	doi	doi	NOUN
ejpam-3654	15	2	:	:	PUNCT
ejpam-3654	15	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3654	https://doi.org/10.29020/nybg.ejpam.v13i2.3654	ADJ
ejpam-3654	15	4	email	email	NOUN
ejpam-3654	15	5	addresses	address	NOUN
ejpam-3654	15	6	:	:	PUNCT
ejpam-3654	15	7	o	o	NOUN
ejpam-3654	15	8	moaaz@mans.edu.eg	moaaz@mans.edu.eg	NOUN
ejpam-3654	15	9	(	(	PUNCT
ejpam-3654	15	10	o.	o.	NOUN
ejpam-3654	15	11	moaaz	moaaz	PROPN
ejpam-3654	15	12	)	)	PUNCT
ejpam-3654	15	13	,	,	PUNCT
ejpam-3654	15	14	c.cesarano@uninettunouniversity.net	c.cesarano@uninettunouniversity.net	PROPN
ejpam-3654	15	15	(	(	PUNCT
ejpam-3654	15	16	c.	c.	PROPN
ejpam-3654	15	17	cesarano),muhib39@students.mans.edu.eg	cesarano),muhib39@students.mans.edu.eg	PROPN
ejpam-3654	15	18	(	(	PUNCT
ejpam-3654	15	19	a.	a.	NOUN
ejpam-3654	15	20	muhib	muhib	NOUN
ejpam-3654	15	21	)	)	PUNCT
ejpam-3654	15	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3654	16	1	185	185	NUM
ejpam-3654	16	2	c	c	NOUN
ejpam-3654	16	3	©	©	NOUN
ejpam-3654	16	4	2020	2020	NUM
ejpam-3654	16	5	ejpam	ejpam	VERB
ejpam-3654	16	6	all	all	DET
ejpam-3654	16	7	rights	right	NOUN
ejpam-3654	16	8	reserved	reserve	VERB
ejpam-3654	16	9	.	.	PUNCT
ejpam-3654	17	1	o.	o.	PROPN
ejpam-3654	17	2	moaaz	moaaz	PROPN
ejpam-3654	17	3	,	,	PUNCT
ejpam-3654	17	4	c.	c.	PROPN
ejpam-3654	17	5	cesarano	cesarano	PROPN
ejpam-3654	17	6	,	,	PUNCT
ejpam-3654	17	7	a.	a.	NOUN
ejpam-3654	17	8	muhib	muhib	NOUN
ejpam-3654	17	9	/	/	SYM
ejpam-3654	17	10	eur	eur	PROPN
ejpam-3654	17	11	.	.	PUNCT
ejpam-3654	18	1	j.	j.	PROPN
ejpam-3654	18	2	pure	pure	PROPN
ejpam-3654	18	3	appl	appl	PROPN
ejpam-3654	18	4	.	.	PROPN
ejpam-3654	18	5	math	math	PROPN
ejpam-3654	18	6	,	,	PUNCT
ejpam-3654	18	7	13	13	NUM
ejpam-3654	18	8	(	(	PUNCT
ejpam-3654	18	9	2	2	NUM
ejpam-3654	18	10	)	)	PUNCT
ejpam-3654	18	11	(	(	PUNCT
ejpam-3654	18	12	2020	2020	NUM
ejpam-3654	18	13	)	)	PUNCT
ejpam-3654	18	14	,	,	PUNCT
ejpam-3654	18	15	185	185	NUM
ejpam-3654	18	16	-	-	SYM
ejpam-3654	18	17	199	199	NUM
ejpam-3654	18	18	186	186	NUM
ejpam-3654	18	19	τ	τ	X
ejpam-3654	18	20	(	(	PUNCT
ejpam-3654	18	21	t	t	PROPN
ejpam-3654	18	22	)	)	PUNCT
ejpam-3654	18	23	≤	≤	NOUN
ejpam-3654	18	24	t	t	PROPN
ejpam-3654	18	25	,	,	PUNCT
ejpam-3654	18	26	limt→∞	limt→∞	PROPN
ejpam-3654	18	27	τ	τ	PROPN
ejpam-3654	18	28	(	(	PUNCT
ejpam-3654	18	29	t	t	PROPN
ejpam-3654	18	30	)	)	PUNCT
ejpam-3654	18	31	=	=	SYM
ejpam-3654	19	1	limt→∞	limt→∞	PROPN
ejpam-3654	19	2	σ	σ	PROPN
ejpam-3654	19	3	(	(	PUNCT
ejpam-3654	19	4	t	t	PROPN
ejpam-3654	19	5	)	)	PUNCT
ejpam-3654	20	1	=	=	SYM
ejpam-3654	20	2	∞.	∞.	PROPN
ejpam-3654	20	3	moreover	moreover	ADV
ejpam-3654	20	4	,	,	PUNCT
ejpam-3654	20	5	we	we	PRON
ejpam-3654	20	6	study	study	VERB
ejpam-3654	20	7	(	(	PUNCT
ejpam-3654	20	8	1	1	NUM
ejpam-3654	20	9	)	)	PUNCT
ejpam-3654	20	10	under	under	ADP
ejpam-3654	20	11	the	the	DET
ejpam-3654	20	12	condition	condition	NOUN
ejpam-3654	20	13	that	that	SCONJ
ejpam-3654	20	14	∫	∫	PROPN
ejpam-3654	20	15	∞	∞	PROPN
ejpam-3654	20	16	t0	t0	PROPN
ejpam-3654	20	17	1	1	NUM
ejpam-3654	20	18	r1	r1	PROPN
ejpam-3654	20	19	/	/	SYM
ejpam-3654	20	20	α	α	PROPN
ejpam-3654	20	21	(	(	PUNCT
ejpam-3654	20	22	s	s	NOUN
ejpam-3654	20	23	)	)	PUNCT
ejpam-3654	20	24	ds	ds	ADJ
ejpam-3654	20	25	=	=	NOUN
ejpam-3654	20	26	∞	∞	PROPN
ejpam-3654	20	27	,	,	PUNCT
ejpam-3654	20	28	(	(	PUNCT
ejpam-3654	20	29	2	2	NUM
ejpam-3654	20	30	)	)	PUNCT
ejpam-3654	20	31	and	and	CCONJ
ejpam-3654	20	32	we	we	PRON
ejpam-3654	20	33	define	define	VERB
ejpam-3654	20	34	the	the	DET
ejpam-3654	20	35	function	function	NOUN
ejpam-3654	20	36	z	z	NOUN
ejpam-3654	20	37	(	(	PUNCT
ejpam-3654	20	38	t	t	PROPN
ejpam-3654	20	39	)	)	PUNCT
ejpam-3654	20	40	:	:	PUNCT
ejpam-3654	21	1	=	=	SYM
ejpam-3654	21	2	x	x	X
ejpam-3654	21	3	(	(	PUNCT
ejpam-3654	21	4	t	t	PROPN
ejpam-3654	21	5	)	)	PUNCT
ejpam-3654	21	6	+	+	NOUN
ejpam-3654	21	7	p	p	X
ejpam-3654	21	8	(	(	PUNCT
ejpam-3654	21	9	t)x	t)x	X
ejpam-3654	21	10	(	(	PUNCT
ejpam-3654	21	11	τ	τ	X
ejpam-3654	21	12	(	(	PUNCT
ejpam-3654	21	13	t	t	PROPN
ejpam-3654	21	14	)	)	PUNCT
ejpam-3654	21	15	)	)	PUNCT
ejpam-3654	21	16	.	.	PUNCT
ejpam-3654	22	1	by	by	ADP
ejpam-3654	22	2	a	a	DET
ejpam-3654	22	3	solution	solution	NOUN
ejpam-3654	22	4	of	of	ADP
ejpam-3654	22	5	(	(	PUNCT
ejpam-3654	22	6	1	1	X
ejpam-3654	22	7	)	)	PUNCT
ejpam-3654	22	8	we	we	PRON
ejpam-3654	22	9	mean	mean	VERB
ejpam-3654	22	10	a	a	DET
ejpam-3654	22	11	function	function	NOUN
ejpam-3654	22	12	x	x	SYM
ejpam-3654	22	13	∈	∈	NOUN
ejpam-3654	22	14	c3[tx,∞	c3[tx,∞	NOUN
ejpam-3654	22	15	)	)	PUNCT
ejpam-3654	22	16	,	,	PUNCT
ejpam-3654	22	17	tx	tx	PROPN
ejpam-3654	22	18	≥	≥	NUM
ejpam-3654	22	19	t0	t0	PROPN
ejpam-3654	22	20	,	,	PUNCT
ejpam-3654	22	21	which	which	PRON
ejpam-3654	22	22	has	have	VERB
ejpam-3654	22	23	the	the	DET
ejpam-3654	22	24	property	property	NOUN
ejpam-3654	22	25	r	r	NOUN
ejpam-3654	22	26	(	(	PUNCT
ejpam-3654	22	27	t	t	NOUN
ejpam-3654	22	28	)	)	PUNCT
ejpam-3654	22	29	(	(	PUNCT
ejpam-3654	22	30	z′′′	z′′′	PROPN
ejpam-3654	22	31	(	(	PUNCT
ejpam-3654	22	32	t))α	t))α	NOUN
ejpam-3654	22	33	∈	∈	PROPN
ejpam-3654	22	34	c1[tx,∞	c1[tx,∞	NOUN
ejpam-3654	22	35	)	)	PUNCT
ejpam-3654	22	36	,	,	PUNCT
ejpam-3654	22	37	and	and	CCONJ
ejpam-3654	22	38	satisfies	satisfie	NOUN
ejpam-3654	22	39	(	(	PUNCT
ejpam-3654	22	40	1	1	NUM
ejpam-3654	22	41	)	)	PUNCT
ejpam-3654	22	42	on	on	ADP
ejpam-3654	22	43	[	[	X
ejpam-3654	22	44	tx,∞	tx,∞	NOUN
ejpam-3654	22	45	)	)	PUNCT
ejpam-3654	22	46	.	.	PUNCT
ejpam-3654	23	1	we	we	PRON
ejpam-3654	23	2	consider	consider	VERB
ejpam-3654	23	3	only	only	ADV
ejpam-3654	23	4	those	those	DET
ejpam-3654	23	5	solutions	solution	NOUN
ejpam-3654	23	6	x	x	X
ejpam-3654	23	7	of	of	ADP
ejpam-3654	23	8	(	(	PUNCT
ejpam-3654	23	9	1	1	NUM
ejpam-3654	23	10	)	)	PUNCT
ejpam-3654	23	11	which	which	PRON
ejpam-3654	23	12	satisfy	satisfy	VERB
ejpam-3654	23	13	sup{|x	sup{|x	PROPN
ejpam-3654	23	14	(	(	PUNCT
ejpam-3654	23	15	t)|	t)|	NOUN
ejpam-3654	23	16	:	:	PUNCT
ejpam-3654	23	17	t	t	PROPN
ejpam-3654	23	18	≥	≥	PROPN
ejpam-3654	23	19	t	t	PROPN
ejpam-3654	23	20	}	}	PUNCT
ejpam-3654	23	21	>	>	X
ejpam-3654	23	22	0	0	NUM
ejpam-3654	23	23	,	,	PUNCT
ejpam-3654	23	24	for	for	ADP
ejpam-3654	23	25	all	all	DET
ejpam-3654	23	26	t	t	PROPN
ejpam-3654	23	27	≥	≥	NOUN
ejpam-3654	23	28	tx	tx	PROPN
ejpam-3654	23	29	.	.	PUNCT
ejpam-3654	24	1	definition	definition	NOUN
ejpam-3654	24	2	1	1	NUM
ejpam-3654	24	3	.	.	PUNCT
ejpam-3654	25	1	a	a	DET
ejpam-3654	25	2	solution	solution	NOUN
ejpam-3654	25	3	x	x	X
ejpam-3654	25	4	of	of	ADP
ejpam-3654	25	5	(	(	PUNCT
ejpam-3654	25	6	1	1	NUM
ejpam-3654	25	7	)	)	PUNCT
ejpam-3654	25	8	is	be	AUX
ejpam-3654	25	9	said	say	VERB
ejpam-3654	25	10	to	to	PART
ejpam-3654	25	11	be	be	AUX
ejpam-3654	25	12	non	non	ADJ
ejpam-3654	25	13	-	-	ADJ
ejpam-3654	25	14	oscillatory	oscillatory	ADJ
ejpam-3654	25	15	if	if	SCONJ
ejpam-3654	25	16	it	it	PRON
ejpam-3654	25	17	is	be	AUX
ejpam-3654	25	18	positive	positive	ADJ
ejpam-3654	25	19	or	or	CCONJ
ejpam-3654	25	20	negative	negative	ADJ
ejpam-3654	25	21	,	,	PUNCT
ejpam-3654	25	22	ultimately	ultimately	ADV
ejpam-3654	25	23	;	;	PUNCT
ejpam-3654	25	24	otherwise	otherwise	ADV
ejpam-3654	25	25	,	,	PUNCT
ejpam-3654	25	26	it	it	PRON
ejpam-3654	25	27	is	be	AUX
ejpam-3654	25	28	said	say	VERB
ejpam-3654	25	29	to	to	PART
ejpam-3654	25	30	be	be	AUX
ejpam-3654	25	31	oscillatory	oscillatory	ADJ
ejpam-3654	25	32	.	.	PUNCT
ejpam-3654	26	1	the	the	DET
ejpam-3654	26	2	equation	equation	NOUN
ejpam-3654	26	3	itself	itself	PRON
ejpam-3654	26	4	is	be	AUX
ejpam-3654	26	5	termed	term	VERB
ejpam-3654	26	6	oscillatory	oscillatory	ADJ
ejpam-3654	26	7	if	if	SCONJ
ejpam-3654	26	8	all	all	DET
ejpam-3654	26	9	its	its	PRON
ejpam-3654	26	10	solutions	solution	NOUN
ejpam-3654	26	11	oscillate	oscillate	VERB
ejpam-3654	26	12	.	.	PUNCT
ejpam-3654	27	1	let	let	VERB
ejpam-3654	27	2	us	we	PRON
ejpam-3654	27	3	briefly	briefly	ADV
ejpam-3654	27	4	comment	comment	VERB
ejpam-3654	27	5	on	on	ADP
ejpam-3654	27	6	a	a	DET
ejpam-3654	27	7	number	number	NOUN
ejpam-3654	27	8	of	of	ADP
ejpam-3654	27	9	related	relate	VERB
ejpam-3654	27	10	results	result	NOUN
ejpam-3654	27	11	which	which	PRON
ejpam-3654	27	12	motivated	motivate	VERB
ejpam-3654	27	13	our	our	PRON
ejpam-3654	27	14	study	study	NOUN
ejpam-3654	27	15	.	.	PUNCT
ejpam-3654	28	1	a	a	DET
ejpam-3654	28	2	number	number	NOUN
ejpam-3654	28	3	of	of	ADP
ejpam-3654	28	4	oscillation	oscillation	NOUN
ejpam-3654	28	5	results	result	NOUN
ejpam-3654	28	6	for	for	ADP
ejpam-3654	28	7	differential	differential	ADJ
ejpam-3654	28	8	equation	equation	NOUN
ejpam-3654	28	9	(	(	PUNCT
ejpam-3654	28	10	r	r	NOUN
ejpam-3654	28	11	(	(	PUNCT
ejpam-3654	28	12	t	t	NOUN
ejpam-3654	28	13	)	)	PUNCT
ejpam-3654	28	14	(	(	PUNCT
ejpam-3654	28	15	x(n−1	x(n−1	PROPN
ejpam-3654	28	16	)	)	PUNCT
ejpam-3654	28	17	(	(	PUNCT
ejpam-3654	28	18	t	t	PROPN
ejpam-3654	28	19	)	)	PUNCT
ejpam-3654	28	20	)	)	PUNCT
ejpam-3654	28	21	α)′	α)′	PROPN
ejpam-3654	29	1	+	+	NUM
ejpam-3654	29	2	q	q	X
ejpam-3654	29	3	(	(	PUNCT
ejpam-3654	29	4	t	t	PROPN
ejpam-3654	29	5	)	)	PUNCT
ejpam-3654	29	6	f	f	NOUN
ejpam-3654	29	7	(	(	PUNCT
ejpam-3654	29	8	x	x	X
ejpam-3654	29	9	(	(	PUNCT
ejpam-3654	29	10	τ	τ	X
ejpam-3654	29	11	(	(	PUNCT
ejpam-3654	29	12	t	t	PROPN
ejpam-3654	29	13	)	)	PUNCT
ejpam-3654	29	14	)	)	PUNCT
ejpam-3654	29	15	)	)	PUNCT
ejpam-3654	30	1	=	=	SYM
ejpam-3654	30	2	0	0	NUM
ejpam-3654	30	3	,	,	PUNCT
ejpam-3654	30	4	have	have	AUX
ejpam-3654	30	5	been	be	AUX
ejpam-3654	30	6	established	establish	VERB
ejpam-3654	30	7	by	by	ADP
ejpam-3654	30	8	baculikova	baculikova	X
ejpam-3654	30	9	et	et	PROPN
ejpam-3654	30	10	al	al	PROPN
ejpam-3654	30	11	.	.	PUNCT
ejpam-3654	31	1	[	[	X
ejpam-3654	31	2	16	16	NUM
ejpam-3654	31	3	]	]	PUNCT
ejpam-3654	31	4	under	under	ADP
ejpam-3654	31	5	the	the	DET
ejpam-3654	31	6	conditions	condition	NOUN
ejpam-3654	31	7	(	(	PUNCT
ejpam-3654	31	8	2	2	NUM
ejpam-3654	31	9	)	)	PUNCT
ejpam-3654	31	10	and∫	and∫	NOUN
ejpam-3654	31	11	∞	∞	PROPN
ejpam-3654	31	12	r−1	r−1	PROPN
ejpam-3654	31	13	/	/	SYM
ejpam-3654	31	14	α	α	PROPN
ejpam-3654	31	15	(	(	PUNCT
ejpam-3654	31	16	t	t	PROPN
ejpam-3654	31	17	)	)	PUNCT
ejpam-3654	31	18	dt	dt	PUNCT
ejpam-3654	32	1	<	<	X
ejpam-3654	32	2	∞.	∞.	ADJ
ejpam-3654	32	3	asymptotic	asymptotic	ADJ
ejpam-3654	32	4	behavior	behavior	NOUN
ejpam-3654	32	5	of	of	ADP
ejpam-3654	32	6	higher	high	ADJ
ejpam-3654	32	7	-	-	PUNCT
ejpam-3654	32	8	order	order	NOUN
ejpam-3654	32	9	quasilinear	quasilinear	NOUN
ejpam-3654	32	10	neutral	neutral	ADJ
ejpam-3654	32	11	differential	differential	ADJ
ejpam-3654	32	12	equations	equation	NOUN
ejpam-3654	32	13	of	of	ADP
ejpam-3654	32	14	the	the	DET
ejpam-3654	32	15	form	form	NOUN
ejpam-3654	32	16	(	(	PUNCT
ejpam-3654	32	17	r	r	NOUN
ejpam-3654	32	18	(	(	PUNCT
ejpam-3654	32	19	t	t	NOUN
ejpam-3654	32	20	)	)	PUNCT
ejpam-3654	32	21	(	(	PUNCT
ejpam-3654	32	22	z(n−1	z(n−1	PROPN
ejpam-3654	32	23	)	)	PUNCT
ejpam-3654	32	24	(	(	PUNCT
ejpam-3654	32	25	t	t	PROPN
ejpam-3654	32	26	)	)	PUNCT
ejpam-3654	32	27	)	)	PUNCT
ejpam-3654	32	28	α)′	α)′	PROPN
ejpam-3654	32	29	+	+	NUM
ejpam-3654	32	30	q	q	X
ejpam-3654	32	31	(	(	PUNCT
ejpam-3654	32	32	t)xβ	t)xβ	PROPN
ejpam-3654	32	33	(	(	PUNCT
ejpam-3654	32	34	σ	σ	PROPN
ejpam-3654	32	35	(	(	PUNCT
ejpam-3654	32	36	t	t	PROPN
ejpam-3654	32	37	)	)	PUNCT
ejpam-3654	32	38	)	)	PUNCT
ejpam-3654	33	1	=	=	SYM
ejpam-3654	33	2	0	0	PUNCT
ejpam-3654	33	3	have	have	AUX
ejpam-3654	33	4	been	be	AUX
ejpam-3654	33	5	studied	study	VERB
ejpam-3654	33	6	by	by	ADP
ejpam-3654	33	7	li	li	PROPN
ejpam-3654	33	8	and	and	CCONJ
ejpam-3654	33	9	rogovchenko	rogovchenko	PROPN
ejpam-3654	34	1	[	[	X
ejpam-3654	34	2	21	21	NUM
ejpam-3654	34	3	]	]	PUNCT
ejpam-3654	34	4	.	.	PUNCT
ejpam-3654	35	1	agarwal	agarwal	PROPN
ejpam-3654	35	2	et	et	PROPN
ejpam-3654	35	3	al	al	PROPN
ejpam-3654	35	4	.	.	PUNCT
ejpam-3654	36	1	[	[	X
ejpam-3654	36	2	6	6	NUM
ejpam-3654	36	3	]	]	PUNCT
ejpam-3654	36	4	investigated	investigate	VERB
ejpam-3654	36	5	the	the	DET
ejpam-3654	36	6	oscillatory	oscillatory	ADJ
ejpam-3654	36	7	behavior	behavior	NOUN
ejpam-3654	36	8	of	of	ADP
ejpam-3654	36	9	a	a	DET
ejpam-3654	36	10	higher	high	ADJ
ejpam-3654	36	11	-	-	PUNCT
ejpam-3654	36	12	order	order	NOUN
ejpam-3654	36	13	differential	differential	ADJ
ejpam-3654	36	14	equation	equation	NOUN
ejpam-3654	36	15	(	(	PUNCT
ejpam-3654	36	16	r	r	NOUN
ejpam-3654	36	17	(	(	PUNCT
ejpam-3654	36	18	t	t	NOUN
ejpam-3654	36	19	)	)	PUNCT
ejpam-3654	36	20	(	(	PUNCT
ejpam-3654	36	21	x(n−1	x(n−1	PROPN
ejpam-3654	36	22	)	)	PUNCT
ejpam-3654	36	23	(	(	PUNCT
ejpam-3654	36	24	t	t	PROPN
ejpam-3654	36	25	)	)	PUNCT
ejpam-3654	36	26	)	)	PUNCT
ejpam-3654	37	1	α)′	α)′	PROPN
ejpam-3654	37	2	+	+	NUM
ejpam-3654	37	3	q	q	X
ejpam-3654	37	4	(	(	PUNCT
ejpam-3654	37	5	t)xβ	t)xβ	PROPN
ejpam-3654	37	6	(	(	PUNCT
ejpam-3654	37	7	τ	τ	X
ejpam-3654	37	8	(	(	PUNCT
ejpam-3654	37	9	t	t	PROPN
ejpam-3654	37	10	)	)	PUNCT
ejpam-3654	37	11	)	)	PUNCT
ejpam-3654	38	1	=	=	PUNCT
ejpam-3654	38	2	0	0	NUM
ejpam-3654	38	3	,	,	PUNCT
ejpam-3654	38	4	under	under	ADP
ejpam-3654	38	5	the	the	DET
ejpam-3654	38	6	condition	condition	NOUN
ejpam-3654	38	7	(	(	PUNCT
ejpam-3654	38	8	2	2	NUM
ejpam-3654	38	9	)	)	PUNCT
ejpam-3654	38	10	.	.	PUNCT
ejpam-3654	39	1	the	the	DET
ejpam-3654	39	2	purpose	purpose	NOUN
ejpam-3654	39	3	of	of	ADP
ejpam-3654	39	4	this	this	DET
ejpam-3654	39	5	article	article	NOUN
ejpam-3654	39	6	is	be	AUX
ejpam-3654	39	7	to	to	PART
ejpam-3654	39	8	give	give	VERB
ejpam-3654	39	9	sufficient	sufficient	ADJ
ejpam-3654	39	10	conditions	condition	NOUN
ejpam-3654	39	11	for	for	ADP
ejpam-3654	39	12	the	the	DET
ejpam-3654	39	13	oscillatory	oscillatory	ADJ
ejpam-3654	39	14	behavior	behavior	NOUN
ejpam-3654	39	15	of	of	ADP
ejpam-3654	39	16	(	(	PUNCT
ejpam-3654	39	17	1	1	NUM
ejpam-3654	39	18	)	)	PUNCT
ejpam-3654	39	19	.	.	PUNCT
ejpam-3654	40	1	under	under	ADP
ejpam-3654	40	2	the	the	DET
ejpam-3654	40	3	condition	condition	NOUN
ejpam-3654	40	4	that	that	SCONJ
ejpam-3654	40	5	(	(	PUNCT
ejpam-3654	40	6	2	2	X
ejpam-3654	40	7	)	)	PUNCT
ejpam-3654	40	8	in	in	ADP
ejpam-3654	40	9	order	order	NOUN
ejpam-3654	40	10	to	to	PART
ejpam-3654	40	11	discuss	discuss	VERB
ejpam-3654	40	12	our	our	PRON
ejpam-3654	40	13	main	main	ADJ
ejpam-3654	40	14	results	result	NOUN
ejpam-3654	40	15	,	,	PUNCT
ejpam-3654	40	16	we	we	PRON
ejpam-3654	40	17	need	need	VERB
ejpam-3654	40	18	the	the	DET
ejpam-3654	40	19	following	follow	VERB
ejpam-3654	40	20	lemmas	lemmas	NOUN
ejpam-3654	40	21	:	:	PUNCT
ejpam-3654	40	22	lemma	lemma	PROPN
ejpam-3654	40	23	1	1	NUM
ejpam-3654	40	24	.	.	PUNCT
ejpam-3654	41	1	[	[	X
ejpam-3654	41	2	5]if	5]if	NUM
ejpam-3654	41	3	the	the	DET
ejpam-3654	41	4	function	function	NOUN
ejpam-3654	41	5	x	x	PUNCT
ejpam-3654	41	6	satisfies	satisfy	VERB
ejpam-3654	41	7	x(i	x(i	PROPN
ejpam-3654	41	8	)	)	PUNCT
ejpam-3654	41	9	(	(	PUNCT
ejpam-3654	41	10	t	t	PROPN
ejpam-3654	41	11	)	)	PUNCT
ejpam-3654	41	12	>	>	X
ejpam-3654	42	1	0	0	NUM
ejpam-3654	42	2	,	,	PUNCT
ejpam-3654	42	3	i	i	PRON
ejpam-3654	42	4	=	=	NOUN
ejpam-3654	42	5	0	0	NUM
ejpam-3654	42	6	,	,	PUNCT
ejpam-3654	42	7	1	1	NUM
ejpam-3654	42	8	,	,	PUNCT
ejpam-3654	42	9	...	...	PUNCT
ejpam-3654	42	10	,	,	PUNCT
ejpam-3654	42	11	n	n	CCONJ
ejpam-3654	42	12	,	,	PUNCT
ejpam-3654	42	13	and	and	CCONJ
ejpam-3654	42	14	x(n+1	x(n+1	NUM
ejpam-3654	42	15	)	)	PUNCT
ejpam-3654	42	16	(	(	PUNCT
ejpam-3654	42	17	t	t	NOUN
ejpam-3654	42	18	)	)	PUNCT
ejpam-3654	42	19	<	<	X
ejpam-3654	42	20	0	0	NUM
ejpam-3654	42	21	,	,	PUNCT
ejpam-3654	42	22	then	then	ADV
ejpam-3654	42	23	x	x	X
ejpam-3654	42	24	(	(	PUNCT
ejpam-3654	42	25	t	t	PROPN
ejpam-3654	42	26	)	)	PUNCT
ejpam-3654	42	27	tn	tn	PROPN
ejpam-3654	42	28	/	/	SYM
ejpam-3654	42	29	n	n	CCONJ
ejpam-3654	42	30	!	!	X
ejpam-3654	42	31	≥	≥	PROPN
ejpam-3654	42	32	x′	x′	PROPN
ejpam-3654	42	33	(	(	PUNCT
ejpam-3654	42	34	t	t	PROPN
ejpam-3654	42	35	)	)	PUNCT
ejpam-3654	42	36	tn−1/	tn−1/	PUNCT
ejpam-3654	42	37	(	(	PUNCT
ejpam-3654	42	38	n−	n−	NOUN
ejpam-3654	42	39	1	1	NUM
ejpam-3654	42	40	)	)	PUNCT
ejpam-3654	42	41	!	!	PUNCT
ejpam-3654	42	42	.	.	PUNCT
ejpam-3654	43	1	o.	o.	PROPN
ejpam-3654	43	2	moaaz	moaaz	PROPN
ejpam-3654	43	3	,	,	PUNCT
ejpam-3654	43	4	c.	c.	PROPN
ejpam-3654	43	5	cesarano	cesarano	PROPN
ejpam-3654	43	6	,	,	PUNCT
ejpam-3654	43	7	a.	a.	NOUN
ejpam-3654	43	8	muhib	muhib	NOUN
ejpam-3654	43	9	/	/	SYM
ejpam-3654	43	10	eur	eur	PROPN
ejpam-3654	43	11	.	.	PUNCT
ejpam-3654	44	1	j.	j.	PROPN
ejpam-3654	44	2	pure	pure	PROPN
ejpam-3654	44	3	appl	appl	PROPN
ejpam-3654	44	4	.	.	PROPN
ejpam-3654	44	5	math	math	PROPN
ejpam-3654	44	6	,	,	PUNCT
ejpam-3654	44	7	13	13	NUM
ejpam-3654	44	8	(	(	PUNCT
ejpam-3654	44	9	2	2	NUM
ejpam-3654	44	10	)	)	PUNCT
ejpam-3654	44	11	(	(	PUNCT
ejpam-3654	44	12	2020	2020	NUM
ejpam-3654	44	13	)	)	PUNCT
ejpam-3654	44	14	,	,	PUNCT
ejpam-3654	44	15	185	185	NUM
ejpam-3654	44	16	-	-	SYM
ejpam-3654	44	17	199	199	NUM
ejpam-3654	44	18	187	187	NUM
ejpam-3654	44	19	lemma	lemma	PROPN
ejpam-3654	44	20	2	2	NUM
ejpam-3654	44	21	.	.	PUNCT
ejpam-3654	45	1	[	[	X
ejpam-3654	45	2	3	3	NUM
ejpam-3654	45	3	,	,	PUNCT
ejpam-3654	45	4	lemma	lemma	PROPN
ejpam-3654	45	5	2.2.3]let	2.2.3]let	PROPN
ejpam-3654	45	6	x	x	SYM
ejpam-3654	45	7	∈	∈	PROPN
ejpam-3654	45	8	cn	cn	X
ejpam-3654	45	9	(	(	PUNCT
ejpam-3654	45	10	[	[	X
ejpam-3654	45	11	t0,∞	t0,∞	NUM
ejpam-3654	45	12	)	)	PUNCT
ejpam-3654	45	13	,	,	PUNCT
ejpam-3654	45	14	(	(	PUNCT
ejpam-3654	45	15	0,∞	0,∞	NOUN
ejpam-3654	45	16	)	)	PUNCT
ejpam-3654	45	17	)	)	PUNCT
ejpam-3654	45	18	.	.	PUNCT
ejpam-3654	46	1	assume	assume	VERB
ejpam-3654	46	2	that	that	SCONJ
ejpam-3654	46	3	x(n	x(n	NOUN
ejpam-3654	46	4	)	)	PUNCT
ejpam-3654	46	5	(	(	PUNCT
ejpam-3654	46	6	t	t	NOUN
ejpam-3654	46	7	)	)	PUNCT
ejpam-3654	46	8	is	be	AUX
ejpam-3654	46	9	of	of	ADP
ejpam-3654	46	10	fixed	fix	VERB
ejpam-3654	46	11	sign	sign	NOUN
ejpam-3654	46	12	and	and	CCONJ
ejpam-3654	46	13	not	not	PART
ejpam-3654	46	14	identically	identically	ADV
ejpam-3654	46	15	zero	zero	NUM
ejpam-3654	46	16	on	on	ADP
ejpam-3654	46	17	[	[	X
ejpam-3654	46	18	t0,∞	t0,∞	NUM
ejpam-3654	46	19	)	)	PUNCT
ejpam-3654	46	20	and	and	CCONJ
ejpam-3654	46	21	that	that	SCONJ
ejpam-3654	46	22	there	there	PRON
ejpam-3654	46	23	exists	exist	VERB
ejpam-3654	46	24	a	a	DET
ejpam-3654	46	25	t1	t1	NOUN
ejpam-3654	46	26	≥	≥	NOUN
ejpam-3654	46	27	t0	t0	NOUN
ejpam-3654	46	28	such	such	ADJ
ejpam-3654	46	29	that	that	DET
ejpam-3654	46	30	x(n−1	x(n−1	NOUN
ejpam-3654	46	31	)	)	PUNCT
ejpam-3654	46	32	(	(	PUNCT
ejpam-3654	46	33	t)x(n	t)x(n	PROPN
ejpam-3654	46	34	)	)	PUNCT
ejpam-3654	46	35	(	(	PUNCT
ejpam-3654	46	36	t	t	NOUN
ejpam-3654	46	37	)	)	PUNCT
ejpam-3654	46	38	≤	≤	NOUN
ejpam-3654	46	39	0	0	NUM
ejpam-3654	46	40	for	for	SCONJ
ejpam-3654	46	41	all	all	DET
ejpam-3654	46	42	t	t	PROPN
ejpam-3654	46	43	≥	≥	NOUN
ejpam-3654	46	44	t1	t1	NOUN
ejpam-3654	46	45	.	.	PUNCT
ejpam-3654	47	1	if	if	SCONJ
ejpam-3654	47	2	limt→∞	limt→∞	PROPN
ejpam-3654	47	3	x	x	SYM
ejpam-3654	47	4	(	(	PUNCT
ejpam-3654	47	5	t	t	PROPN
ejpam-3654	47	6	)	)	PUNCT
ejpam-3654	47	7	6=	6=	ADP
ejpam-3654	47	8	0	0	NUM
ejpam-3654	47	9	,	,	PUNCT
ejpam-3654	47	10	then	then	ADV
ejpam-3654	47	11	for	for	ADP
ejpam-3654	47	12	every	every	DET
ejpam-3654	47	13	µ	µ	PROPN
ejpam-3654	47	14	∈	∈	NOUN
ejpam-3654	47	15	(	(	PUNCT
ejpam-3654	47	16	0	0	NUM
ejpam-3654	47	17	,	,	PUNCT
ejpam-3654	47	18	1	1	NUM
ejpam-3654	47	19	)	)	PUNCT
ejpam-3654	47	20	there	there	PRON
ejpam-3654	47	21	exists	exist	VERB
ejpam-3654	47	22	tµ	tµ	PRON
ejpam-3654	47	23	≥	≥	NOUN
ejpam-3654	47	24	t1	t1	NOUN
ejpam-3654	47	25	such	such	ADJ
ejpam-3654	47	26	that	that	SCONJ
ejpam-3654	47	27	x	x	X
ejpam-3654	47	28	(	(	PUNCT
ejpam-3654	47	29	t	t	PROPN
ejpam-3654	47	30	)	)	PUNCT
ejpam-3654	47	31	≥	≥	NOUN
ejpam-3654	47	32	µ	µ	X
ejpam-3654	47	33	(	(	PUNCT
ejpam-3654	47	34	n−	n−	NOUN
ejpam-3654	47	35	1	1	NUM
ejpam-3654	47	36	)	)	PUNCT
ejpam-3654	47	37	!	!	PUNCT
ejpam-3654	48	1	tn−1	tn−1	PROPN
ejpam-3654	48	2	∣∣∣x(n−1	∣∣∣x(n−1	PROPN
ejpam-3654	48	3	)	)	PUNCT
ejpam-3654	48	4	(	(	PUNCT
ejpam-3654	48	5	t	t	NOUN
ejpam-3654	48	6	)	)	PUNCT
ejpam-3654	48	7	∣∣∣	∣∣∣	NOUN
ejpam-3654	48	8	for	for	ADP
ejpam-3654	48	9	t	t	PROPN
ejpam-3654	48	10	≥	≥	PROPN
ejpam-3654	48	11	tµ.	tµ.	NOUN
ejpam-3654	48	12	lemma	lemma	PROPN
ejpam-3654	49	1	3	3	X
ejpam-3654	49	2	.	.	PUNCT
ejpam-3654	50	1	[	[	X
ejpam-3654	50	2	23]let	23]let	NUM
ejpam-3654	50	3	x	x	SYM
ejpam-3654	50	4	(	(	PUNCT
ejpam-3654	50	5	t	t	NOUN
ejpam-3654	50	6	)	)	PUNCT
ejpam-3654	50	7	be	be	AUX
ejpam-3654	50	8	a	a	DET
ejpam-3654	50	9	positive	positive	ADJ
ejpam-3654	50	10	and	and	CCONJ
ejpam-3654	50	11	n	n	CCONJ
ejpam-3654	50	12	-	-	PUNCT
ejpam-3654	50	13	times	time	NOUN
ejpam-3654	50	14	differentiable	differentiable	ADJ
ejpam-3654	50	15	function	function	NOUN
ejpam-3654	50	16	on	on	ADP
ejpam-3654	50	17	an	an	DET
ejpam-3654	50	18	interval	interval	NOUN
ejpam-3654	50	19	[	[	X
ejpam-3654	50	20	t,∞	t,∞	NUM
ejpam-3654	50	21	)	)	PUNCT
ejpam-3654	50	22	with	with	ADP
ejpam-3654	50	23	its	its	PRON
ejpam-3654	50	24	nth	nth	NOUN
ejpam-3654	50	25	derivative	derivative	ADJ
ejpam-3654	50	26	x(n	x(n	NOUN
ejpam-3654	50	27	)	)	PUNCT
ejpam-3654	50	28	(	(	PUNCT
ejpam-3654	50	29	t	t	NOUN
ejpam-3654	50	30	)	)	PUNCT
ejpam-3654	50	31	non	non	ADJ
ejpam-3654	50	32	-	-	ADJ
ejpam-3654	50	33	positive	positive	ADJ
ejpam-3654	50	34	on	on	ADP
ejpam-3654	50	35	[	[	X
ejpam-3654	50	36	t,∞	t,∞	NUM
ejpam-3654	50	37	)	)	PUNCT
ejpam-3654	50	38	and	and	CCONJ
ejpam-3654	50	39	not	not	PART
ejpam-3654	50	40	identically	identically	ADV
ejpam-3654	50	41	zero	zero	NUM
ejpam-3654	50	42	on	on	ADP
ejpam-3654	50	43	any	any	DET
ejpam-3654	50	44	interval	interval	NOUN
ejpam-3654	50	45	of	of	ADP
ejpam-3654	50	46	the	the	DET
ejpam-3654	50	47	form	form	NOUN
ejpam-3654	50	48	[	[	X
ejpam-3654	50	49	t	t	NOUN
ejpam-3654	50	50	′,∞	′,∞	NUM
ejpam-3654	50	51	)	)	PUNCT
ejpam-3654	50	52	,	,	PUNCT
ejpam-3654	50	53	t	t	PROPN
ejpam-3654	50	54	′	′	NUM
ejpam-3654	50	55	≥	≥	PROPN
ejpam-3654	50	56	t	t	PROPN
ejpam-3654	50	57	and	and	CCONJ
ejpam-3654	50	58	x(n−1	x(n−1	NUM
ejpam-3654	50	59	)	)	PUNCT
ejpam-3654	50	60	(	(	PUNCT
ejpam-3654	50	61	t)x(n	t)x(n	PROPN
ejpam-3654	50	62	)	)	PUNCT
ejpam-3654	50	63	(	(	PUNCT
ejpam-3654	50	64	t	t	NOUN
ejpam-3654	50	65	)	)	PUNCT
ejpam-3654	50	66	≤	≤	NOUN
ejpam-3654	50	67	0	0	NUM
ejpam-3654	50	68	,	,	PUNCT
ejpam-3654	50	69	t	t	PROPN
ejpam-3654	50	70	≥	≥	NUM
ejpam-3654	50	71	tx	tx	INTJ
ejpam-3654	50	72	then	then	ADV
ejpam-3654	50	73	there	there	PRON
ejpam-3654	50	74	exist	exist	VERB
ejpam-3654	50	75	constants	constant	NOUN
ejpam-3654	50	76	θ	θ	NOUN
ejpam-3654	50	77	,	,	PUNCT
ejpam-3654	50	78	0	0	NUM
ejpam-3654	50	79	<	<	X
ejpam-3654	50	80	θ	θ	X
ejpam-3654	50	81	<	<	X
ejpam-3654	50	82	1	1	NUM
ejpam-3654	50	83	and	and	CCONJ
ejpam-3654	50	84	n	n	NOUN
ejpam-3654	50	85	>	>	X
ejpam-3654	50	86	0	0	NUM
ejpam-3654	50	87	such	such	ADJ
ejpam-3654	50	88	that	that	SCONJ
ejpam-3654	50	89	x′	x′	PROPN
ejpam-3654	50	90	(	(	PUNCT
ejpam-3654	50	91	θt	θt	PROPN
ejpam-3654	50	92	)	)	PUNCT
ejpam-3654	50	93	≥	≥	NOUN
ejpam-3654	50	94	ntn−2x(n−1	ntn−2x(n−1	PROPN
ejpam-3654	50	95	)	)	PUNCT
ejpam-3654	50	96	(	(	PUNCT
ejpam-3654	50	97	t	t	PROPN
ejpam-3654	50	98	)	)	PUNCT
ejpam-3654	50	99	,	,	PUNCT
ejpam-3654	50	100	for	for	ADP
ejpam-3654	50	101	all	all	DET
ejpam-3654	50	102	sufficient	sufficient	ADJ
ejpam-3654	50	103	large	large	ADJ
ejpam-3654	50	104	t.	t.	NOUN
ejpam-3654	50	105	in	in	ADP
ejpam-3654	50	106	this	this	DET
ejpam-3654	50	107	section	section	NOUN
ejpam-3654	50	108	we	we	PRON
ejpam-3654	50	109	will	will	AUX
ejpam-3654	50	110	find	find	VERB
ejpam-3654	50	111	one	one	NUM
ejpam-3654	50	112	condition	condition	NOUN
ejpam-3654	50	113	to	to	PART
ejpam-3654	50	114	ensure	ensure	VERB
ejpam-3654	50	115	the	the	DET
ejpam-3654	50	116	oscillation	oscillation	NOUN
ejpam-3654	50	117	of	of	ADP
ejpam-3654	50	118	solutions	solution	NOUN
ejpam-3654	50	119	of	of	ADP
ejpam-3654	50	120	(	(	PUNCT
ejpam-3654	50	121	1	1	NUM
ejpam-3654	50	122	)	)	PUNCT
ejpam-3654	50	123	in	in	ADP
ejpam-3654	50	124	the	the	DET
ejpam-3654	50	125	case	case	NOUN
ejpam-3654	50	126	p0	p0	NOUN
ejpam-3654	50	127	<	<	X
ejpam-3654	50	128	1	1	NUM
ejpam-3654	50	129	.	.	NOUN
ejpam-3654	50	130	2	2	NUM
ejpam-3654	50	131	.	.	X
ejpam-3654	50	132	one	one	NUM
ejpam-3654	50	133	-	-	PUNCT
ejpam-3654	50	134	condition	condition	NOUN
ejpam-3654	50	135	theorems	theorem	NOUN
ejpam-3654	50	136	lemma	lemma	PROPN
ejpam-3654	50	137	4	4	X
ejpam-3654	50	138	.	.	PUNCT
ejpam-3654	50	139	assume	assume	VERB
ejpam-3654	50	140	that	that	SCONJ
ejpam-3654	50	141	x	x	PRON
ejpam-3654	50	142	is	be	AUX
ejpam-3654	50	143	an	an	DET
ejpam-3654	50	144	eventually	eventually	ADV
ejpam-3654	50	145	positive	positive	ADJ
ejpam-3654	50	146	solution	solution	NOUN
ejpam-3654	50	147	of	of	ADP
ejpam-3654	50	148	(	(	PUNCT
ejpam-3654	50	149	1	1	NUM
ejpam-3654	50	150	)	)	PUNCT
ejpam-3654	50	151	.	.	PUNCT
ejpam-3654	51	1	then	then	ADV
ejpam-3654	51	2	(	(	PUNCT
ejpam-3654	51	3	r	r	NOUN
ejpam-3654	51	4	(	(	PUNCT
ejpam-3654	51	5	t	t	NOUN
ejpam-3654	51	6	)	)	PUNCT
ejpam-3654	51	7	(	(	PUNCT
ejpam-3654	51	8	z′′′	z′′′	PROPN
ejpam-3654	51	9	(	(	PUNCT
ejpam-3654	51	10	t	t	PROPN
ejpam-3654	51	11	)	)	PUNCT
ejpam-3654	51	12	)	)	PUNCT
ejpam-3654	51	13	α)′	α)′	VERB
ejpam-3654	51	14	≤	≤	NUM
ejpam-3654	51	15	−q	−q	NOUN
ejpam-3654	51	16	(	(	PUNCT
ejpam-3654	51	17	t	t	NOUN
ejpam-3654	51	18	)	)	PUNCT
ejpam-3654	51	19	(	(	PUNCT
ejpam-3654	51	20	1−	1−	NUM
ejpam-3654	51	21	p0)β	p0)β	NOUN
ejpam-3654	51	22	zβ	zβ	PROPN
ejpam-3654	51	23	(	(	PUNCT
ejpam-3654	51	24	σ	σ	PROPN
ejpam-3654	51	25	(	(	PUNCT
ejpam-3654	51	26	t	t	PROPN
ejpam-3654	51	27	)	)	PUNCT
ejpam-3654	51	28	)	)	PUNCT
ejpam-3654	51	29	.	.	PUNCT
ejpam-3654	52	1	(	(	PUNCT
ejpam-3654	52	2	3	3	X
ejpam-3654	52	3	)	)	PUNCT
ejpam-3654	52	4	proof	proof	NOUN
ejpam-3654	52	5	.	.	PUNCT
ejpam-3654	53	1	assume	assume	VERB
ejpam-3654	53	2	that	that	SCONJ
ejpam-3654	53	3	x	x	PRON
ejpam-3654	53	4	is	be	AUX
ejpam-3654	53	5	an	an	DET
ejpam-3654	53	6	eventually	eventually	ADV
ejpam-3654	53	7	positive	positive	ADJ
ejpam-3654	53	8	solution	solution	NOUN
ejpam-3654	53	9	of	of	ADP
ejpam-3654	53	10	(	(	PUNCT
ejpam-3654	53	11	1	1	NUM
ejpam-3654	53	12	)	)	PUNCT
ejpam-3654	53	13	.	.	PUNCT
ejpam-3654	54	1	then	then	ADV
ejpam-3654	54	2	,	,	PUNCT
ejpam-3654	54	3	there	there	PRON
ejpam-3654	54	4	exists	exist	VERB
ejpam-3654	54	5	a	a	DET
ejpam-3654	54	6	t1	t1	NOUN
ejpam-3654	54	7	≥	≥	NOUN
ejpam-3654	54	8	t0	t0	NOUN
ejpam-3654	54	9	such	such	ADJ
ejpam-3654	54	10	that	that	SCONJ
ejpam-3654	54	11	x	x	X
ejpam-3654	54	12	(	(	PUNCT
ejpam-3654	54	13	t	t	PROPN
ejpam-3654	54	14	)	)	PUNCT
ejpam-3654	54	15	>	>	X
ejpam-3654	54	16	0	0	NUM
ejpam-3654	54	17	,	,	PUNCT
ejpam-3654	54	18	x	x	X
ejpam-3654	54	19	(	(	PUNCT
ejpam-3654	54	20	τ	τ	X
ejpam-3654	54	21	(	(	PUNCT
ejpam-3654	54	22	t	t	PROPN
ejpam-3654	54	23	)	)	PUNCT
ejpam-3654	54	24	)	)	PUNCT
ejpam-3654	54	25	>	>	X
ejpam-3654	54	26	0	0	PUNCT
ejpam-3654	55	1	and	and	CCONJ
ejpam-3654	55	2	x	x	SYM
ejpam-3654	55	3	(	(	PUNCT
ejpam-3654	55	4	σ	σ	PROPN
ejpam-3654	55	5	(	(	PUNCT
ejpam-3654	55	6	t	t	PROPN
ejpam-3654	55	7	)	)	PUNCT
ejpam-3654	55	8	)	)	PUNCT
ejpam-3654	55	9	>	>	X
ejpam-3654	55	10	0	0	PUNCT
ejpam-3654	56	1	for	for	ADP
ejpam-3654	56	2	t	t	PROPN
ejpam-3654	56	3	≥	≥	NUM
ejpam-3654	56	4	t1	t1	NOUN
ejpam-3654	56	5	.	.	PUNCT
ejpam-3654	57	1	since	since	SCONJ
ejpam-3654	57	2	r′	r′	PROPN
ejpam-3654	57	3	(	(	PUNCT
ejpam-3654	57	4	t	t	PROPN
ejpam-3654	57	5	)	)	PUNCT
ejpam-3654	57	6	>	>	X
ejpam-3654	57	7	0	0	NUM
ejpam-3654	57	8	,	,	PUNCT
ejpam-3654	57	9	we	we	PRON
ejpam-3654	57	10	have	have	VERB
ejpam-3654	57	11	z	z	NOUN
ejpam-3654	57	12	(	(	PUNCT
ejpam-3654	57	13	t	t	PROPN
ejpam-3654	57	14	)	)	PUNCT
ejpam-3654	57	15	>	>	X
ejpam-3654	57	16	0	0	NUM
ejpam-3654	57	17	,	,	PUNCT
ejpam-3654	57	18	z′	z′	NUM
ejpam-3654	57	19	(	(	PUNCT
ejpam-3654	57	20	t	t	PROPN
ejpam-3654	57	21	)	)	PUNCT
ejpam-3654	57	22	>	>	X
ejpam-3654	57	23	0	0	NUM
ejpam-3654	57	24	,	,	PUNCT
ejpam-3654	57	25	z′′′	z′′′	PROPN
ejpam-3654	57	26	(	(	PUNCT
ejpam-3654	57	27	t	t	PROPN
ejpam-3654	57	28	)	)	PUNCT
ejpam-3654	57	29	>	>	X
ejpam-3654	58	1	0	0	NUM
ejpam-3654	58	2	,	,	PUNCT
ejpam-3654	58	3	z(4	z(4	PROPN
ejpam-3654	58	4	)	)	PUNCT
ejpam-3654	58	5	(	(	PUNCT
ejpam-3654	58	6	t	t	NOUN
ejpam-3654	58	7	)	)	PUNCT
ejpam-3654	58	8	<	<	X
ejpam-3654	58	9	0	0	PUNCT
ejpam-3654	59	1	and	and	CCONJ
ejpam-3654	59	2	(	(	PUNCT
ejpam-3654	59	3	r	r	NOUN
ejpam-3654	59	4	(	(	PUNCT
ejpam-3654	59	5	t	t	NOUN
ejpam-3654	59	6	)	)	PUNCT
ejpam-3654	59	7	(	(	PUNCT
ejpam-3654	59	8	z′′′	z′′′	PROPN
ejpam-3654	59	9	(	(	PUNCT
ejpam-3654	59	10	t	t	PROPN
ejpam-3654	59	11	)	)	PUNCT
ejpam-3654	59	12	)	)	PUNCT
ejpam-3654	59	13	α)′	α)′	NOUN
ejpam-3654	59	14	≤	≤	NUM
ejpam-3654	59	15	0	0	NUM
ejpam-3654	59	16	,	,	PUNCT
ejpam-3654	59	17	(	(	PUNCT
ejpam-3654	59	18	4	4	NUM
ejpam-3654	59	19	)	)	PUNCT
ejpam-3654	59	20	for	for	ADP
ejpam-3654	59	21	t	t	PROPN
ejpam-3654	59	22	≥	≥	NUM
ejpam-3654	59	23	t1	t1	NOUN
ejpam-3654	59	24	.	.	PUNCT
ejpam-3654	60	1	from	from	ADP
ejpam-3654	60	2	definition	definition	NOUN
ejpam-3654	60	3	of	of	ADP
ejpam-3654	60	4	z	z	PROPN
ejpam-3654	60	5	,	,	PUNCT
ejpam-3654	60	6	we	we	PRON
ejpam-3654	60	7	get	get	VERB
ejpam-3654	60	8	x	x	X
ejpam-3654	60	9	(	(	PUNCT
ejpam-3654	60	10	t	t	PROPN
ejpam-3654	60	11	)	)	PUNCT
ejpam-3654	60	12	≥	≥	NOUN
ejpam-3654	60	13	z	z	NOUN
ejpam-3654	60	14	(	(	PUNCT
ejpam-3654	60	15	t)−	t)−	PROPN
ejpam-3654	60	16	p0x	p0x	NOUN
ejpam-3654	60	17	(	(	PUNCT
ejpam-3654	60	18	τ	τ	X
ejpam-3654	60	19	(	(	PUNCT
ejpam-3654	60	20	t	t	PROPN
ejpam-3654	60	21	)	)	PUNCT
ejpam-3654	60	22	)	)	PUNCT
ejpam-3654	60	23	≥	≥	PROPN
ejpam-3654	61	1	z	z	NOUN
ejpam-3654	61	2	(	(	PUNCT
ejpam-3654	61	3	t)−	t)−	PROPN
ejpam-3654	61	4	p0z	p0z	PROPN
ejpam-3654	61	5	(	(	PUNCT
ejpam-3654	61	6	τ	τ	PROPN
ejpam-3654	61	7	(	(	PUNCT
ejpam-3654	61	8	t	t	PROPN
ejpam-3654	61	9	)	)	PUNCT
ejpam-3654	61	10	)	)	PUNCT
ejpam-3654	61	11	≥	≥	NOUN
ejpam-3654	61	12	(	(	PUNCT
ejpam-3654	61	13	1−	1−	NUM
ejpam-3654	61	14	p0	p0	NOUN
ejpam-3654	61	15	)	)	PUNCT
ejpam-3654	61	16	z	z	NOUN
ejpam-3654	61	17	(	(	PUNCT
ejpam-3654	61	18	t	t	PROPN
ejpam-3654	61	19	)	)	PUNCT
ejpam-3654	61	20	,	,	PUNCT
ejpam-3654	61	21	which	which	PRON
ejpam-3654	61	22	with	with	ADP
ejpam-3654	61	23	(	(	PUNCT
ejpam-3654	61	24	1	1	X
ejpam-3654	61	25	)	)	PUNCT
ejpam-3654	61	26	gives	give	VERB
ejpam-3654	61	27	(	(	PUNCT
ejpam-3654	61	28	r	r	NOUN
ejpam-3654	61	29	(	(	PUNCT
ejpam-3654	61	30	t	t	NOUN
ejpam-3654	61	31	)	)	PUNCT
ejpam-3654	61	32	(	(	PUNCT
ejpam-3654	61	33	z′′′	z′′′	PROPN
ejpam-3654	61	34	(	(	PUNCT
ejpam-3654	61	35	t	t	PROPN
ejpam-3654	61	36	)	)	PUNCT
ejpam-3654	61	37	)	)	PUNCT
ejpam-3654	61	38	α)′	α)′	PROPN
ejpam-3654	61	39	+	+	NUM
ejpam-3654	61	40	q	q	X
ejpam-3654	61	41	(	(	PUNCT
ejpam-3654	61	42	t	t	NOUN
ejpam-3654	61	43	)	)	PUNCT
ejpam-3654	61	44	(	(	PUNCT
ejpam-3654	61	45	1−	1−	NUM
ejpam-3654	61	46	p0)β	p0)β	NOUN
ejpam-3654	61	47	zβ	zβ	PROPN
ejpam-3654	61	48	(	(	PUNCT
ejpam-3654	61	49	σ	σ	PROPN
ejpam-3654	61	50	(	(	PUNCT
ejpam-3654	61	51	t	t	PROPN
ejpam-3654	61	52	)	)	PUNCT
ejpam-3654	61	53	)	)	PUNCT
ejpam-3654	61	54	≤	≤	ADV
ejpam-3654	61	55	0	0	X
ejpam-3654	61	56	.	.	PUNCT
ejpam-3654	62	1	the	the	DET
ejpam-3654	62	2	proof	proof	NOUN
ejpam-3654	62	3	is	be	AUX
ejpam-3654	62	4	complete	complete	ADJ
ejpam-3654	62	5	.	.	PUNCT
ejpam-3654	63	1	theorem	theorem	NOUN
ejpam-3654	63	2	1	1	NUM
ejpam-3654	63	3	.	.	PUNCT
ejpam-3654	63	4	assume	assume	VERB
ejpam-3654	63	5	that	that	SCONJ
ejpam-3654	63	6	lim	lim	PROPN
ejpam-3654	63	7	inf	inf	PROPN
ejpam-3654	63	8	t→∞	t→∞	DET
ejpam-3654	63	9	1	1	NUM
ejpam-3654	63	10	ψ̃1	ψ̃1	PROPN
ejpam-3654	63	11	(	(	PUNCT
ejpam-3654	63	12	t	t	PROPN
ejpam-3654	63	13	)	)	PUNCT
ejpam-3654	63	14	∫	∫	PROPN
ejpam-3654	64	1	∞	∞	PROPN
ejpam-3654	64	2	t	t	PROPN
ejpam-3654	64	3	ψ2	ψ2	NOUN
ejpam-3654	64	4	(	(	PUNCT
ejpam-3654	64	5	s	s	X
ejpam-3654	64	6	)	)	PUNCT
ejpam-3654	64	7	ψ̃	ψ̃	PROPN
ejpam-3654	64	8	α+1	α+1	NUM
ejpam-3654	64	9	α	α	NOUN
ejpam-3654	64	10	1	1	NUM
ejpam-3654	64	11	(	(	PUNCT
ejpam-3654	64	12	s	s	X
ejpam-3654	64	13	)	)	PUNCT
ejpam-3654	64	14	ds	ds	VERB
ejpam-3654	64	15	>	>	PUNCT
ejpam-3654	64	16	α	α	PROPN
ejpam-3654	64	17	(	(	PUNCT
ejpam-3654	64	18	α+	α+	NOUN
ejpam-3654	64	19	1	1	NUM
ejpam-3654	64	20	)	)	PUNCT
ejpam-3654	64	21	α+1	α+1	NUM
ejpam-3654	64	22	α	α	NOUN
ejpam-3654	64	23	,	,	PUNCT
ejpam-3654	64	24	(	(	PUNCT
ejpam-3654	64	25	5	5	X
ejpam-3654	64	26	)	)	PUNCT
ejpam-3654	64	27	o.	o.	NOUN
ejpam-3654	64	28	moaaz	moaaz	PROPN
ejpam-3654	64	29	,	,	PUNCT
ejpam-3654	64	30	c.	c.	PROPN
ejpam-3654	64	31	cesarano	cesarano	PROPN
ejpam-3654	64	32	,	,	PUNCT
ejpam-3654	64	33	a.	a.	NOUN
ejpam-3654	64	34	muhib	muhib	NOUN
ejpam-3654	64	35	/	/	SYM
ejpam-3654	64	36	eur	eur	PROPN
ejpam-3654	64	37	.	.	PUNCT
ejpam-3654	65	1	j.	j.	PROPN
ejpam-3654	65	2	pure	pure	PROPN
ejpam-3654	65	3	appl	appl	PROPN
ejpam-3654	65	4	.	.	PROPN
ejpam-3654	65	5	math	math	PROPN
ejpam-3654	65	6	,	,	PUNCT
ejpam-3654	65	7	13	13	NUM
ejpam-3654	65	8	(	(	PUNCT
ejpam-3654	65	9	2	2	NUM
ejpam-3654	65	10	)	)	PUNCT
ejpam-3654	65	11	(	(	PUNCT
ejpam-3654	65	12	2020	2020	NUM
ejpam-3654	65	13	)	)	PUNCT
ejpam-3654	65	14	,	,	PUNCT
ejpam-3654	65	15	185	185	NUM
ejpam-3654	65	16	-	-	SYM
ejpam-3654	65	17	199	199	NUM
ejpam-3654	65	18	188	188	NUM
ejpam-3654	65	19	where	where	SCONJ
ejpam-3654	65	20	ψ1	ψ1	NOUN
ejpam-3654	65	21	(	(	PUNCT
ejpam-3654	65	22	t	t	NOUN
ejpam-3654	65	23	)	)	PUNCT
ejpam-3654	65	24	=	=	SYM
ejpam-3654	66	1	q	q	X
ejpam-3654	66	2	(	(	PUNCT
ejpam-3654	66	3	t	t	NOUN
ejpam-3654	66	4	)	)	PUNCT
ejpam-3654	66	5	(	(	PUNCT
ejpam-3654	66	6	1−	1−	NUM
ejpam-3654	66	7	p0)βmβ−α	p0)βmβ−α	NOUN
ejpam-3654	66	8	(	(	PUNCT
ejpam-3654	66	9	σ	σ	PROPN
ejpam-3654	66	10	(	(	PUNCT
ejpam-3654	66	11	t	t	PROPN
ejpam-3654	66	12	)	)	PUNCT
ejpam-3654	66	13	)	)	PUNCT
ejpam-3654	66	14	,	,	PUNCT
ejpam-3654	66	15	ψ2	ψ2	NOUN
ejpam-3654	66	16	(	(	PUNCT
ejpam-3654	66	17	t	t	NOUN
ejpam-3654	66	18	)	)	PUNCT
ejpam-3654	66	19	=	=	PROPN
ejpam-3654	67	1	αε	αε	ADP
ejpam-3654	67	2	σ2	σ2	PROPN
ejpam-3654	67	3	(	(	PUNCT
ejpam-3654	67	4	t	t	PROPN
ejpam-3654	67	5	)	)	PUNCT
ejpam-3654	67	6	ζσ′	ζσ′	VERB
ejpam-3654	67	7	(	(	PUNCT
ejpam-3654	67	8	t	t	NOUN
ejpam-3654	67	9	)	)	PUNCT
ejpam-3654	67	10	r1	r1	PROPN
ejpam-3654	67	11	/	/	SYM
ejpam-3654	67	12	α	α	PROPN
ejpam-3654	67	13	(	(	PUNCT
ejpam-3654	67	14	t	t	PROPN
ejpam-3654	67	15	)	)	PUNCT
ejpam-3654	67	16	and	and	CCONJ
ejpam-3654	67	17	ψ̃1	ψ̃1	PROPN
ejpam-3654	67	18	(	(	PUNCT
ejpam-3654	67	19	t	t	PROPN
ejpam-3654	67	20	)	)	PUNCT
ejpam-3654	67	21	=	=	SYM
ejpam-3654	68	1	∫	∫	PROPN
ejpam-3654	68	2	∞	∞	PROPN
ejpam-3654	68	3	t	t	PROPN
ejpam-3654	68	4	ψ1	ψ1	NOUN
ejpam-3654	68	5	(	(	PUNCT
ejpam-3654	68	6	s	s	NOUN
ejpam-3654	68	7	)	)	PUNCT
ejpam-3654	68	8	ds	ds	NOUN
ejpam-3654	68	9	.	.	PUNCT
ejpam-3654	69	1	then	then	ADV
ejpam-3654	69	2	,	,	PUNCT
ejpam-3654	69	3	(	(	PUNCT
ejpam-3654	69	4	1	1	X
ejpam-3654	69	5	)	)	PUNCT
ejpam-3654	69	6	is	be	AUX
ejpam-3654	69	7	oscillatory	oscillatory	ADJ
ejpam-3654	69	8	.	.	PUNCT
ejpam-3654	70	1	proof	proof	NOUN
ejpam-3654	70	2	.	.	PUNCT
ejpam-3654	71	1	assume	assume	VERB
ejpam-3654	71	2	that	that	SCONJ
ejpam-3654	71	3	x	x	PRON
ejpam-3654	71	4	is	be	AUX
ejpam-3654	71	5	an	an	DET
ejpam-3654	71	6	eventually	eventually	ADV
ejpam-3654	71	7	positive	positive	ADJ
ejpam-3654	71	8	solution	solution	NOUN
ejpam-3654	71	9	of	of	ADP
ejpam-3654	71	10	(	(	PUNCT
ejpam-3654	71	11	1	1	NUM
ejpam-3654	71	12	)	)	PUNCT
ejpam-3654	71	13	.	.	PUNCT
ejpam-3654	72	1	then	then	ADV
ejpam-3654	72	2	,	,	PUNCT
ejpam-3654	72	3	there	there	PRON
ejpam-3654	72	4	exists	exist	VERB
ejpam-3654	72	5	a	a	DET
ejpam-3654	72	6	t1	t1	NOUN
ejpam-3654	72	7	≥	≥	NOUN
ejpam-3654	72	8	t0	t0	NOUN
ejpam-3654	72	9	such	such	ADJ
ejpam-3654	72	10	that	that	SCONJ
ejpam-3654	72	11	x	x	X
ejpam-3654	72	12	(	(	PUNCT
ejpam-3654	72	13	t	t	PROPN
ejpam-3654	72	14	)	)	PUNCT
ejpam-3654	72	15	>	>	X
ejpam-3654	72	16	0	0	NUM
ejpam-3654	72	17	,	,	PUNCT
ejpam-3654	72	18	x	x	X
ejpam-3654	72	19	(	(	PUNCT
ejpam-3654	72	20	τ	τ	X
ejpam-3654	72	21	(	(	PUNCT
ejpam-3654	72	22	t	t	PROPN
ejpam-3654	72	23	)	)	PUNCT
ejpam-3654	72	24	)	)	PUNCT
ejpam-3654	72	25	>	>	X
ejpam-3654	72	26	0	0	PUNCT
ejpam-3654	73	1	and	and	CCONJ
ejpam-3654	73	2	x	x	SYM
ejpam-3654	73	3	(	(	PUNCT
ejpam-3654	73	4	σ	σ	PROPN
ejpam-3654	73	5	(	(	PUNCT
ejpam-3654	73	6	t	t	PROPN
ejpam-3654	73	7	)	)	PUNCT
ejpam-3654	73	8	)	)	PUNCT
ejpam-3654	73	9	>	>	X
ejpam-3654	73	10	0	0	PUNCT
ejpam-3654	74	1	for	for	ADP
ejpam-3654	74	2	t	t	PROPN
ejpam-3654	74	3	≥	≥	NOUN
ejpam-3654	74	4	t1	t1	NOUN
ejpam-3654	74	5	.	.	PUNCT
ejpam-3654	75	1	using	use	VERB
ejpam-3654	75	2	lemma	lemma	PROPN
ejpam-3654	75	3	4	4	NUM
ejpam-3654	75	4	,	,	PUNCT
ejpam-3654	75	5	we	we	PRON
ejpam-3654	75	6	obtain	obtain	VERB
ejpam-3654	75	7	that	that	SCONJ
ejpam-3654	75	8	(	(	PUNCT
ejpam-3654	75	9	3	3	X
ejpam-3654	75	10	)	)	PUNCT
ejpam-3654	75	11	holds	hold	VERB
ejpam-3654	75	12	.	.	PUNCT
ejpam-3654	76	1	define	define	VERB
ejpam-3654	76	2	ω	ω	PROPN
ejpam-3654	76	3	as	as	SCONJ
ejpam-3654	76	4	follows	follow	VERB
ejpam-3654	76	5	ω	ω	PROPN
ejpam-3654	76	6	(	(	PUNCT
ejpam-3654	76	7	t	t	PROPN
ejpam-3654	76	8	)	)	PUNCT
ejpam-3654	76	9	:	:	PUNCT
ejpam-3654	77	1	=	=	SYM
ejpam-3654	77	2	r	r	NOUN
ejpam-3654	77	3	(	(	PUNCT
ejpam-3654	77	4	t	t	PROPN
ejpam-3654	77	5	)	)	PUNCT
ejpam-3654	77	6	(	(	PUNCT
ejpam-3654	77	7	z′′′	z′′′	PROPN
ejpam-3654	77	8	(	(	PUNCT
ejpam-3654	77	9	t))α	t))α	NOUN
ejpam-3654	77	10	zα	zα	PROPN
ejpam-3654	77	11	(	(	PUNCT
ejpam-3654	77	12	ζσ	ζσ	PROPN
ejpam-3654	77	13	(	(	PUNCT
ejpam-3654	77	14	t	t	PROPN
ejpam-3654	77	15	)	)	PUNCT
ejpam-3654	77	16	)	)	PUNCT
ejpam-3654	77	17	.	.	PUNCT
ejpam-3654	78	1	(	(	PUNCT
ejpam-3654	78	2	6	6	NUM
ejpam-3654	78	3	)	)	PUNCT
ejpam-3654	78	4	by	by	ADP
ejpam-3654	78	5	differentiating	differentiate	VERB
ejpam-3654	78	6	and	and	CCONJ
ejpam-3654	78	7	using	use	VERB
ejpam-3654	78	8	(	(	PUNCT
ejpam-3654	78	9	3	3	NUM
ejpam-3654	78	10	)	)	PUNCT
ejpam-3654	78	11	,	,	PUNCT
ejpam-3654	78	12	we	we	PRON
ejpam-3654	78	13	obtain	obtain	VERB
ejpam-3654	78	14	ω′	ω′	PROPN
ejpam-3654	78	15	(	(	PUNCT
ejpam-3654	78	16	t	t	NOUN
ejpam-3654	78	17	)	)	PUNCT
ejpam-3654	78	18	≤	≤	NUM
ejpam-3654	79	1	−q	−q	NOUN
ejpam-3654	79	2	(	(	PUNCT
ejpam-3654	79	3	t	t	NOUN
ejpam-3654	79	4	)	)	PUNCT
ejpam-3654	79	5	(	(	PUNCT
ejpam-3654	79	6	1−	1−	NUM
ejpam-3654	79	7	p0)β	p0)β	NOUN
ejpam-3654	79	8	zβ	zβ	PROPN
ejpam-3654	79	9	(	(	PUNCT
ejpam-3654	79	10	σ	σ	PROPN
ejpam-3654	79	11	(	(	PUNCT
ejpam-3654	79	12	t	t	PROPN
ejpam-3654	79	13	)	)	PUNCT
ejpam-3654	79	14	)	)	PUNCT
ejpam-3654	79	15	.	.	PUNCT
ejpam-3654	80	1	zα	zα	INTJ
ejpam-3654	80	2	(	(	PUNCT
ejpam-3654	80	3	ζσ	ζσ	INTJ
ejpam-3654	80	4	(	(	PUNCT
ejpam-3654	80	5	t	t	PROPN
ejpam-3654	80	6	)	)	PUNCT
ejpam-3654	80	7	)	)	PUNCT
ejpam-3654	81	1	−	−	PROPN
ejpam-3654	82	1	αr	αr	PROPN
ejpam-3654	82	2	(	(	PUNCT
ejpam-3654	82	3	t	t	PROPN
ejpam-3654	82	4	)	)	PUNCT
ejpam-3654	82	5	(	(	PUNCT
ejpam-3654	82	6	z′′′	z′′′	PROPN
ejpam-3654	82	7	(	(	PUNCT
ejpam-3654	82	8	t))α	t))α	NOUN
ejpam-3654	82	9	z′	z′	NUM
ejpam-3654	82	10	(	(	PUNCT
ejpam-3654	82	11	ζσ	ζσ	PROPN
ejpam-3654	82	12	(	(	PUNCT
ejpam-3654	82	13	t	t	PROPN
ejpam-3654	82	14	)	)	PUNCT
ejpam-3654	82	15	)	)	PUNCT
ejpam-3654	83	1	ζσ′	ζσ′	VERB
ejpam-3654	83	2	(	(	PUNCT
ejpam-3654	83	3	t	t	NOUN
ejpam-3654	83	4	)	)	PUNCT
ejpam-3654	83	5	zα+1	zα+1	NOUN
ejpam-3654	83	6	(	(	PUNCT
ejpam-3654	83	7	ζσ	ζσ	PROPN
ejpam-3654	83	8	(	(	PUNCT
ejpam-3654	83	9	t	t	PROPN
ejpam-3654	83	10	)	)	PUNCT
ejpam-3654	83	11	)	)	PUNCT
ejpam-3654	83	12	.	.	PUNCT
ejpam-3654	84	1	from	from	ADP
ejpam-3654	84	2	lemma	lemma	PROPN
ejpam-3654	84	3	3	3	NUM
ejpam-3654	84	4	,	,	PUNCT
ejpam-3654	84	5	we	we	PRON
ejpam-3654	84	6	have	have	VERB
ejpam-3654	84	7	ω′	ω′	PROPN
ejpam-3654	84	8	(	(	PUNCT
ejpam-3654	84	9	t	t	NOUN
ejpam-3654	84	10	)	)	PUNCT
ejpam-3654	84	11	≤	≤	NUM
ejpam-3654	85	1	−q	−q	NOUN
ejpam-3654	85	2	(	(	PUNCT
ejpam-3654	85	3	t	t	NOUN
ejpam-3654	85	4	)	)	PUNCT
ejpam-3654	85	5	(	(	PUNCT
ejpam-3654	85	6	1−	1−	NUM
ejpam-3654	85	7	p0)β	p0)β	NOUN
ejpam-3654	85	8	zβ−α	zβ−α	NOUN
ejpam-3654	85	9	(	(	PUNCT
ejpam-3654	85	10	σ	σ	PROPN
ejpam-3654	85	11	(	(	PUNCT
ejpam-3654	85	12	t))−	t))−	NOUN
ejpam-3654	85	13	αr	αr	PROPN
ejpam-3654	85	14	(	(	PUNCT
ejpam-3654	85	15	t	t	PROPN
ejpam-3654	85	16	)	)	PUNCT
ejpam-3654	85	17	(	(	PUNCT
ejpam-3654	85	18	z′′′	z′′′	PROPN
ejpam-3654	85	19	(	(	PUNCT
ejpam-3654	85	20	t))α	t))α	NOUN
ejpam-3654	85	21	εσ2	εσ2	NOUN
ejpam-3654	85	22	(	(	PUNCT
ejpam-3654	85	23	t	t	NOUN
ejpam-3654	85	24	)	)	PUNCT
ejpam-3654	85	25	z′′′	z′′′	PROPN
ejpam-3654	85	26	(	(	PUNCT
ejpam-3654	85	27	σ	σ	PROPN
ejpam-3654	85	28	(	(	PUNCT
ejpam-3654	85	29	t	t	PROPN
ejpam-3654	85	30	)	)	PUNCT
ejpam-3654	85	31	)	)	PUNCT
ejpam-3654	86	1	ζσ′	ζσ′	VERB
ejpam-3654	86	2	(	(	PUNCT
ejpam-3654	86	3	t	t	NOUN
ejpam-3654	86	4	)	)	PUNCT
ejpam-3654	86	5	zα+1	zα+1	NOUN
ejpam-3654	86	6	(	(	PUNCT
ejpam-3654	86	7	ζσ	ζσ	PROPN
ejpam-3654	86	8	(	(	PUNCT
ejpam-3654	86	9	t	t	PROPN
ejpam-3654	86	10	)	)	PUNCT
ejpam-3654	86	11	)	)	PUNCT
ejpam-3654	86	12	,	,	PUNCT
ejpam-3654	86	13	which	which	PRON
ejpam-3654	86	14	is	be	AUX
ejpam-3654	86	15	ω′	ω′	PROPN
ejpam-3654	86	16	(	(	PUNCT
ejpam-3654	86	17	t	t	NOUN
ejpam-3654	86	18	)	)	PUNCT
ejpam-3654	86	19	≤	≤	NUM
ejpam-3654	86	20	−q	−q	NOUN
ejpam-3654	86	21	(	(	PUNCT
ejpam-3654	86	22	t	t	NOUN
ejpam-3654	86	23	)	)	PUNCT
ejpam-3654	86	24	(	(	PUNCT
ejpam-3654	86	25	1−	1−	NUM
ejpam-3654	86	26	p0)β	p0)β	NOUN
ejpam-3654	86	27	zβ−α	zβ−α	NOUN
ejpam-3654	86	28	(	(	PUNCT
ejpam-3654	86	29	σ	σ	PROPN
ejpam-3654	86	30	(	(	PUNCT
ejpam-3654	86	31	t))−	t))−	NOUN
ejpam-3654	86	32	αεr	αεr	NOUN
ejpam-3654	86	33	(	(	PUNCT
ejpam-3654	86	34	t)σ2	t)σ2	PROPN
ejpam-3654	86	35	(	(	PUNCT
ejpam-3654	86	36	t	t	NOUN
ejpam-3654	86	37	)	)	PUNCT
ejpam-3654	86	38	ζσ′	ζσ′	X
ejpam-3654	86	39	(	(	PUNCT
ejpam-3654	86	40	t	t	NOUN
ejpam-3654	86	41	)	)	PUNCT
ejpam-3654	86	42	(	(	PUNCT
ejpam-3654	86	43	z′′′	z′′′	X
ejpam-3654	86	44	(	(	PUNCT
ejpam-3654	86	45	t))α+1	t))α+1	NOUN
ejpam-3654	86	46	zα+1	zα+1	PROPN
ejpam-3654	86	47	(	(	PUNCT
ejpam-3654	86	48	ζσ	ζσ	PROPN
ejpam-3654	86	49	(	(	PUNCT
ejpam-3654	86	50	t	t	PROPN
ejpam-3654	86	51	)	)	PUNCT
ejpam-3654	86	52	)	)	PUNCT
ejpam-3654	86	53	,	,	PUNCT
ejpam-3654	86	54	by	by	ADP
ejpam-3654	86	55	using	use	VERB
ejpam-3654	86	56	(	(	PUNCT
ejpam-3654	86	57	6	6	NUM
ejpam-3654	86	58	)	)	PUNCT
ejpam-3654	86	59	we	we	PRON
ejpam-3654	86	60	have	have	VERB
ejpam-3654	86	61	ω′	ω′	PROPN
ejpam-3654	86	62	(	(	PUNCT
ejpam-3654	86	63	t	t	NOUN
ejpam-3654	86	64	)	)	PUNCT
ejpam-3654	86	65	≤	≤	NUM
ejpam-3654	87	1	−q	−q	NOUN
ejpam-3654	87	2	(	(	PUNCT
ejpam-3654	87	3	t	t	NOUN
ejpam-3654	87	4	)	)	PUNCT
ejpam-3654	87	5	(	(	PUNCT
ejpam-3654	87	6	1−	1−	NUM
ejpam-3654	87	7	p0)β	p0)β	NOUN
ejpam-3654	87	8	zβ−α	zβ−α	NOUN
ejpam-3654	87	9	(	(	PUNCT
ejpam-3654	87	10	σ	σ	PROPN
ejpam-3654	87	11	(	(	PUNCT
ejpam-3654	87	12	t))−	t))−	NOUN
ejpam-3654	87	13	αεσ	αεσ	DET
ejpam-3654	87	14	2	2	NUM
ejpam-3654	87	15	(	(	PUNCT
ejpam-3654	87	16	t	t	NOUN
ejpam-3654	87	17	)	)	PUNCT
ejpam-3654	87	18	ζσ′	ζσ′	VERB
ejpam-3654	87	19	(	(	PUNCT
ejpam-3654	87	20	t	t	NOUN
ejpam-3654	87	21	)	)	PUNCT
ejpam-3654	87	22	r1	r1	PROPN
ejpam-3654	87	23	/	/	SYM
ejpam-3654	87	24	α	α	PROPN
ejpam-3654	87	25	(	(	PUNCT
ejpam-3654	87	26	t	t	NOUN
ejpam-3654	87	27	)	)	PUNCT
ejpam-3654	87	28	ω(α+1)/α	ω(α+1)/α	NOUN
ejpam-3654	87	29	(	(	PUNCT
ejpam-3654	87	30	t	t	PROPN
ejpam-3654	87	31	)	)	PUNCT
ejpam-3654	87	32	,	,	PUNCT
ejpam-3654	87	33	(	(	PUNCT
ejpam-3654	87	34	7	7	X
ejpam-3654	87	35	)	)	PUNCT
ejpam-3654	87	36	since	since	SCONJ
ejpam-3654	87	37	z′	z′	NUM
ejpam-3654	87	38	(	(	PUNCT
ejpam-3654	87	39	t	t	PROPN
ejpam-3654	87	40	)	)	PUNCT
ejpam-3654	87	41	>	>	X
ejpam-3654	87	42	0	0	NUM
ejpam-3654	87	43	,	,	PUNCT
ejpam-3654	87	44	there	there	PRON
ejpam-3654	87	45	exist	exist	VERB
ejpam-3654	87	46	a	a	DET
ejpam-3654	87	47	t2	t2	NOUN
ejpam-3654	87	48	≥	≥	NOUN
ejpam-3654	87	49	t1	t1	NOUN
ejpam-3654	87	50	and	and	CCONJ
ejpam-3654	87	51	a	a	DET
ejpam-3654	87	52	constant	constant	ADJ
ejpam-3654	87	53	m	m	NOUN
ejpam-3654	87	54	>	>	X
ejpam-3654	87	55	0	0	NUM
ejpam-3654	87	56	such	such	ADJ
ejpam-3654	87	57	that	that	SCONJ
ejpam-3654	87	58	z	z	NOUN
ejpam-3654	87	59	(	(	PUNCT
ejpam-3654	87	60	t	t	PROPN
ejpam-3654	87	61	)	)	PUNCT
ejpam-3654	87	62	>	>	X
ejpam-3654	88	1	m.	m.	NOUN
ejpam-3654	88	2	then	then	ADV
ejpam-3654	88	3	,	,	PUNCT
ejpam-3654	88	4	(	(	PUNCT
ejpam-3654	88	5	7	7	NUM
ejpam-3654	88	6	)	)	PUNCT
ejpam-3654	88	7	,	,	PUNCT
ejpam-3654	88	8	turn	turn	VERB
ejpam-3654	88	9	to	to	ADP
ejpam-3654	88	10	ω′	ω′	PROPN
ejpam-3654	88	11	(	(	PUNCT
ejpam-3654	88	12	t	t	NOUN
ejpam-3654	88	13	)	)	PUNCT
ejpam-3654	88	14	≤	≤	NUM
ejpam-3654	88	15	−q	−q	NOUN
ejpam-3654	88	16	(	(	PUNCT
ejpam-3654	88	17	t	t	NOUN
ejpam-3654	88	18	)	)	PUNCT
ejpam-3654	88	19	(	(	PUNCT
ejpam-3654	88	20	1−	1−	NUM
ejpam-3654	88	21	p0)βmβ−α	p0)βmβ−α	NOUN
ejpam-3654	88	22	(	(	PUNCT
ejpam-3654	88	23	σ	σ	X
ejpam-3654	88	24	(	(	PUNCT
ejpam-3654	88	25	t))−	t))−	NOUN
ejpam-3654	88	26	αεσ	αεσ	DET
ejpam-3654	88	27	2	2	NUM
ejpam-3654	88	28	(	(	PUNCT
ejpam-3654	88	29	t	t	NOUN
ejpam-3654	88	30	)	)	PUNCT
ejpam-3654	88	31	ζσ′	ζσ′	VERB
ejpam-3654	88	32	(	(	PUNCT
ejpam-3654	88	33	t	t	NOUN
ejpam-3654	88	34	)	)	PUNCT
ejpam-3654	88	35	r1	r1	PROPN
ejpam-3654	88	36	/	/	SYM
ejpam-3654	88	37	α	α	PROPN
ejpam-3654	88	38	(	(	PUNCT
ejpam-3654	88	39	t	t	NOUN
ejpam-3654	88	40	)	)	PUNCT
ejpam-3654	88	41	ω(α+1)/α	ω(α+1)/α	NOUN
ejpam-3654	88	42	(	(	PUNCT
ejpam-3654	88	43	t	t	PROPN
ejpam-3654	88	44	)	)	PUNCT
ejpam-3654	88	45	,	,	PUNCT
ejpam-3654	88	46	that	that	ADV
ejpam-3654	88	47	is	is	ADV
ejpam-3654	88	48	,	,	PUNCT
ejpam-3654	88	49	ω′	ω′	PROPN
ejpam-3654	88	50	(	(	PUNCT
ejpam-3654	88	51	t	t	PROPN
ejpam-3654	88	52	)	)	PUNCT
ejpam-3654	88	53	+	+	CCONJ
ejpam-3654	88	54	ψ1	ψ1	ADJ
ejpam-3654	88	55	(	(	PUNCT
ejpam-3654	88	56	t	t	NOUN
ejpam-3654	88	57	)	)	PUNCT
ejpam-3654	88	58	+	+	NUM
ejpam-3654	88	59	ψ2	ψ2	NOUN
ejpam-3654	88	60	(	(	PUNCT
ejpam-3654	88	61	t)ω(α+1)/α	t)ω(α+1)/α	NOUN
ejpam-3654	88	62	(	(	PUNCT
ejpam-3654	88	63	t	t	PROPN
ejpam-3654	88	64	)	)	PUNCT
ejpam-3654	88	65	≤	≤	NOUN
ejpam-3654	88	66	0	0	NUM
ejpam-3654	88	67	.	.	PUNCT
ejpam-3654	89	1	o.	o.	PROPN
ejpam-3654	89	2	moaaz	moaaz	PROPN
ejpam-3654	89	3	,	,	PUNCT
ejpam-3654	89	4	c.	c.	PROPN
ejpam-3654	89	5	cesarano	cesarano	PROPN
ejpam-3654	89	6	,	,	PUNCT
ejpam-3654	89	7	a.	a.	NOUN
ejpam-3654	89	8	muhib	muhib	NOUN
ejpam-3654	89	9	/	/	SYM
ejpam-3654	89	10	eur	eur	PROPN
ejpam-3654	89	11	.	.	PUNCT
ejpam-3654	90	1	j.	j.	PROPN
ejpam-3654	90	2	pure	pure	PROPN
ejpam-3654	90	3	appl	appl	PROPN
ejpam-3654	90	4	.	.	PROPN
ejpam-3654	90	5	math	math	PROPN
ejpam-3654	90	6	,	,	PUNCT
ejpam-3654	90	7	13	13	NUM
ejpam-3654	90	8	(	(	PUNCT
ejpam-3654	90	9	2	2	NUM
ejpam-3654	90	10	)	)	PUNCT
ejpam-3654	90	11	(	(	PUNCT
ejpam-3654	90	12	2020	2020	NUM
ejpam-3654	90	13	)	)	PUNCT
ejpam-3654	90	14	,	,	PUNCT
ejpam-3654	90	15	185	185	NUM
ejpam-3654	90	16	-	-	SYM
ejpam-3654	90	17	199	199	NUM
ejpam-3654	90	18	189	189	NUM
ejpam-3654	90	19	integrating	integrate	VERB
ejpam-3654	90	20	the	the	DET
ejpam-3654	90	21	above	above	ADJ
ejpam-3654	90	22	inequality	inequality	NOUN
ejpam-3654	90	23	from	from	ADP
ejpam-3654	90	24	t	t	PROPN
ejpam-3654	90	25	to	to	ADP
ejpam-3654	90	26	l	l	NOUN
ejpam-3654	90	27	,	,	PUNCT
ejpam-3654	90	28	we	we	PRON
ejpam-3654	90	29	get	get	VERB
ejpam-3654	90	30	ω	ω	PROPN
ejpam-3654	90	31	(	(	PUNCT
ejpam-3654	90	32	l)−	l)−	PROPN
ejpam-3654	90	33	ω	ω	PROPN
ejpam-3654	90	34	(	(	PUNCT
ejpam-3654	90	35	t	t	PROPN
ejpam-3654	90	36	)	)	PUNCT
ejpam-3654	91	1	+	+	NUM
ejpam-3654	91	2	∫	∫	PROPN
ejpam-3654	91	3	l	l	PROPN
ejpam-3654	91	4	t	t	PROPN
ejpam-3654	91	5	ψ1	ψ1	NOUN
ejpam-3654	91	6	(	(	PUNCT
ejpam-3654	91	7	s	s	NOUN
ejpam-3654	91	8	)	)	PUNCT
ejpam-3654	91	9	ds+	ds+	ADJ
ejpam-3654	91	10	∫	∫	PROPN
ejpam-3654	91	11	l	l	PROPN
ejpam-3654	91	12	t	t	PROPN
ejpam-3654	91	13	ψ2	ψ2	NOUN
ejpam-3654	91	14	(	(	PUNCT
ejpam-3654	91	15	s)ω	s)ω	X
ejpam-3654	91	16	α+1	α+1	NUM
ejpam-3654	91	17	α	α	NOUN
ejpam-3654	91	18	(	(	PUNCT
ejpam-3654	91	19	s	s	NOUN
ejpam-3654	91	20	)	)	PUNCT
ejpam-3654	91	21	ds	ds	ADJ
ejpam-3654	91	22	≤	≤	NOUN
ejpam-3654	91	23	0	0	NUM
ejpam-3654	91	24	.	.	PUNCT
ejpam-3654	92	1	letting	let	VERB
ejpam-3654	92	2	l→∞	l→∞	NUM
ejpam-3654	92	3	and	and	CCONJ
ejpam-3654	92	4	using	use	VERB
ejpam-3654	92	5	ω	ω	PROPN
ejpam-3654	92	6	>	>	X
ejpam-3654	92	7	0	0	PROPN
ejpam-3654	92	8	and	and	CCONJ
ejpam-3654	92	9	ω′	ω′	X
ejpam-3654	92	10	<	<	X
ejpam-3654	92	11	0	0	PROPN
ejpam-3654	92	12	,	,	PUNCT
ejpam-3654	92	13	we	we	PRON
ejpam-3654	92	14	have	have	VERB
ejpam-3654	92	15	ω	ω	NUM
ejpam-3654	92	16	(	(	PUNCT
ejpam-3654	92	17	t	t	PROPN
ejpam-3654	92	18	)	)	PUNCT
ejpam-3654	92	19	≥	≥	NOUN
ejpam-3654	93	1	ψ̃1	ψ̃1	PROPN
ejpam-3654	93	2	(	(	PUNCT
ejpam-3654	93	3	t	t	PROPN
ejpam-3654	93	4	)	)	PUNCT
ejpam-3654	94	1	+	+	NUM
ejpam-3654	94	2	∫	∫	PROPN
ejpam-3654	94	3	∞	∞	PROPN
ejpam-3654	94	4	t	t	PROPN
ejpam-3654	94	5	ψ2	ψ2	NOUN
ejpam-3654	94	6	(	(	PUNCT
ejpam-3654	94	7	s)ω	s)ω	X
ejpam-3654	94	8	α+1	α+1	NUM
ejpam-3654	94	9	α	α	NOUN
ejpam-3654	94	10	(	(	PUNCT
ejpam-3654	94	11	s	s	NOUN
ejpam-3654	94	12	)	)	PUNCT
ejpam-3654	94	13	ds	ds	NOUN
ejpam-3654	94	14	.	.	PUNCT
ejpam-3654	95	1	this	this	PRON
ejpam-3654	95	2	implies	imply	VERB
ejpam-3654	95	3	ω	ω	PROPN
ejpam-3654	95	4	(	(	PUNCT
ejpam-3654	95	5	t	t	PROPN
ejpam-3654	95	6	)	)	PUNCT
ejpam-3654	95	7	ψ̃1	ψ̃1	PROPN
ejpam-3654	95	8	(	(	PUNCT
ejpam-3654	95	9	t	t	PROPN
ejpam-3654	95	10	)	)	PUNCT
ejpam-3654	95	11	≥	≥	NOUN
ejpam-3654	96	1	1	1	NUM
ejpam-3654	96	2	+	+	SYM
ejpam-3654	96	3	1	1	NUM
ejpam-3654	96	4	ψ̃1	ψ̃1	PROPN
ejpam-3654	96	5	(	(	PUNCT
ejpam-3654	96	6	t	t	PROPN
ejpam-3654	96	7	)	)	PUNCT
ejpam-3654	96	8	∫	∫	PROPN
ejpam-3654	97	1	∞	∞	PROPN
ejpam-3654	97	2	t	t	PROPN
ejpam-3654	97	3	ψ2	ψ2	NOUN
ejpam-3654	97	4	(	(	PUNCT
ejpam-3654	97	5	s	s	X
ejpam-3654	97	6	)	)	PUNCT
ejpam-3654	97	7	ψ̃	ψ̃	PROPN
ejpam-3654	97	8	α+1	α+1	NUM
ejpam-3654	97	9	α	α	NOUN
ejpam-3654	97	10	1	1	NUM
ejpam-3654	97	11	(	(	PUNCT
ejpam-3654	97	12	s	s	NOUN
ejpam-3654	97	13	)	)	PUNCT
ejpam-3654	97	14	(	(	PUNCT
ejpam-3654	97	15	ω	ω	X
ejpam-3654	97	16	(	(	PUNCT
ejpam-3654	97	17	s	s	NOUN
ejpam-3654	97	18	)	)	PUNCT
ejpam-3654	97	19	ψ̃1	ψ̃1	PROPN
ejpam-3654	97	20	(	(	PUNCT
ejpam-3654	97	21	s	s	NOUN
ejpam-3654	97	22	)	)	PUNCT
ejpam-3654	97	23	)	)	PUNCT
ejpam-3654	98	1	α+1	α+1	NUM
ejpam-3654	98	2	α	α	PRON
ejpam-3654	98	3	ds	ds	NOUN
ejpam-3654	98	4	.	.	PUNCT
ejpam-3654	99	1	(	(	PUNCT
ejpam-3654	99	2	8)	8)	NUM
ejpam-3654	99	3	let	let	VERB
ejpam-3654	99	4	λ	λ	X
ejpam-3654	99	5	=	=	PRON
ejpam-3654	99	6	inft≥t	inft≥t	PROPN
ejpam-3654	99	7	ω	ω	X
ejpam-3654	99	8	(	(	PUNCT
ejpam-3654	99	9	t	t	PROPN
ejpam-3654	99	10	)	)	PUNCT
ejpam-3654	99	11	/ψ̃1	/ψ̃1	PROPN
ejpam-3654	99	12	(	(	PUNCT
ejpam-3654	99	13	t	t	PROPN
ejpam-3654	99	14	)	)	PUNCT
ejpam-3654	99	15	.	.	PUNCT
ejpam-3654	100	1	then	then	ADV
ejpam-3654	100	2	obviously	obviously	ADV
ejpam-3654	100	3	λ	λ	X
ejpam-3654	100	4	≥	≥	NUM
ejpam-3654	100	5	1	1	NUM
ejpam-3654	100	6	.	.	PUNCT
ejpam-3654	101	1	thus	thus	ADV
ejpam-3654	101	2	,	,	PUNCT
ejpam-3654	101	3	from	from	ADP
ejpam-3654	101	4	(	(	PUNCT
ejpam-3654	101	5	5	5	NUM
ejpam-3654	101	6	)	)	PUNCT
ejpam-3654	101	7	and	and	CCONJ
ejpam-3654	101	8	(	(	PUNCT
ejpam-3654	101	9	8)	8)	NUM
ejpam-3654	101	10	we	we	PRON
ejpam-3654	101	11	see	see	VERB
ejpam-3654	101	12	that	that	SCONJ
ejpam-3654	101	13	λ	λ	PROPN
ejpam-3654	101	14	≥	≥	PRON
ejpam-3654	101	15	1	1	NUM
ejpam-3654	101	16	+	+	CCONJ
ejpam-3654	101	17	α	α	PROPN
ejpam-3654	101	18	(	(	PUNCT
ejpam-3654	101	19	λ	λ	X
ejpam-3654	101	20	α+	α+	PUNCT
ejpam-3654	101	21	1	1	NUM
ejpam-3654	101	22	)	)	PUNCT
ejpam-3654	101	23	(	(	PUNCT
ejpam-3654	101	24	α+1)/α	α+1)/α	NOUN
ejpam-3654	101	25	or	or	CCONJ
ejpam-3654	101	26	λ	λ	X
ejpam-3654	101	27	α+	α+	PUNCT
ejpam-3654	101	28	1	1	NUM
ejpam-3654	101	29	≥	≥	NOUN
ejpam-3654	101	30	1	1	NUM
ejpam-3654	101	31	α+	α+	SYM
ejpam-3654	101	32	1	1	NUM
ejpam-3654	101	33	+	+	NUM
ejpam-3654	101	34	α	α	NOUN
ejpam-3654	101	35	α+	α+	PUNCT
ejpam-3654	101	36	1	1	NUM
ejpam-3654	101	37	(	(	PUNCT
ejpam-3654	101	38	λ	λ	X
ejpam-3654	101	39	α+	α+	X
ejpam-3654	101	40	1	1	NUM
ejpam-3654	101	41	)	)	PUNCT
ejpam-3654	101	42	(	(	PUNCT
ejpam-3654	101	43	α+1)/α	α+1)/α	PROPN
ejpam-3654	101	44	,	,	PUNCT
ejpam-3654	101	45	which	which	PRON
ejpam-3654	101	46	contradicts	contradict	VERB
ejpam-3654	101	47	the	the	DET
ejpam-3654	101	48	admissible	admissible	ADJ
ejpam-3654	101	49	value	value	NOUN
ejpam-3654	101	50	of	of	ADP
ejpam-3654	101	51	λ	λ	PROPN
ejpam-3654	101	52	≥	≥	NOUN
ejpam-3654	101	53	1	1	NUM
ejpam-3654	101	54	and	and	CCONJ
ejpam-3654	101	55	α	α	PRON
ejpam-3654	101	56	>	>	X
ejpam-3654	101	57	0	0	PROPN
ejpam-3654	101	58	.	.	PUNCT
ejpam-3654	102	1	therefore	therefore	ADV
ejpam-3654	102	2	,	,	PUNCT
ejpam-3654	102	3	the	the	DET
ejpam-3654	102	4	proof	proof	NOUN
ejpam-3654	102	5	is	be	AUX
ejpam-3654	102	6	complete	complete	ADJ
ejpam-3654	102	7	.	.	PUNCT
ejpam-3654	103	1	in	in	ADP
ejpam-3654	103	2	this	this	DET
ejpam-3654	103	3	section	section	NOUN
ejpam-3654	103	4	we	we	PRON
ejpam-3654	103	5	will	will	AUX
ejpam-3654	103	6	find	find	VERB
ejpam-3654	103	7	two	two	NUM
ejpam-3654	103	8	independent	independent	ADJ
ejpam-3654	103	9	conditions	condition	NOUN
ejpam-3654	103	10	to	to	PART
ejpam-3654	103	11	ensure	ensure	VERB
ejpam-3654	103	12	the	the	DET
ejpam-3654	103	13	oscillation	oscillation	NOUN
ejpam-3654	103	14	of	of	ADP
ejpam-3654	103	15	solutions	solution	NOUN
ejpam-3654	103	16	of	of	ADP
ejpam-3654	103	17	(	(	PUNCT
ejpam-3654	103	18	1	1	NUM
ejpam-3654	103	19	)	)	PUNCT
ejpam-3654	103	20	in	in	ADP
ejpam-3654	103	21	the	the	DET
ejpam-3654	103	22	case	case	NOUN
ejpam-3654	103	23	p0	p0	NOUN
ejpam-3654	103	24	<	<	X
ejpam-3654	103	25	1	1	NUM
ejpam-3654	103	26	3	3	NUM
ejpam-3654	103	27	.	.	PUNCT
ejpam-3654	104	1	two	two	NUM
ejpam-3654	104	2	independent	independent	ADJ
ejpam-3654	104	3	conditions	condition	NOUN
ejpam-3654	104	4	theorems	theorem	NOUN
ejpam-3654	104	5	here	here	ADV
ejpam-3654	104	6	,	,	PUNCT
ejpam-3654	104	7	we	we	PRON
ejpam-3654	104	8	introduce	introduce	VERB
ejpam-3654	104	9	riccati	riccati	NOUN
ejpam-3654	104	10	substitutions	substitution	NOUN
ejpam-3654	104	11	ω	ω	X
ejpam-3654	104	12	(	(	PUNCT
ejpam-3654	104	13	t	t	PROPN
ejpam-3654	104	14	)	)	PUNCT
ejpam-3654	104	15	:	:	PUNCT
ejpam-3654	105	1	=	=	SYM
ejpam-3654	105	2	r	r	NOUN
ejpam-3654	105	3	(	(	PUNCT
ejpam-3654	105	4	t	t	PROPN
ejpam-3654	105	5	)	)	PUNCT
ejpam-3654	105	6	(	(	PUNCT
ejpam-3654	105	7	z′′′	z′′′	PROPN
ejpam-3654	105	8	(	(	PUNCT
ejpam-3654	105	9	t))α	t))α	NOUN
ejpam-3654	105	10	zα	zα	PROPN
ejpam-3654	105	11	(	(	PUNCT
ejpam-3654	105	12	t	t	PROPN
ejpam-3654	105	13	)	)	PUNCT
ejpam-3654	105	14	and	and	CCONJ
ejpam-3654	105	15	w	w	PROPN
ejpam-3654	105	16	(	(	PUNCT
ejpam-3654	105	17	t	t	PROPN
ejpam-3654	105	18	)	)	PUNCT
ejpam-3654	105	19	:	:	PUNCT
ejpam-3654	105	20	=	=	SYM
ejpam-3654	105	21	z′	z′	NUM
ejpam-3654	105	22	(	(	PUNCT
ejpam-3654	105	23	t	t	PROPN
ejpam-3654	105	24	)	)	PUNCT
ejpam-3654	105	25	z	z	PROPN
ejpam-3654	105	26	(	(	PUNCT
ejpam-3654	105	27	t	t	PROPN
ejpam-3654	105	28	)	)	PUNCT
ejpam-3654	105	29	.	.	PUNCT
ejpam-3654	106	1	(	(	PUNCT
ejpam-3654	106	2	9	9	X
ejpam-3654	106	3	)	)	PUNCT
ejpam-3654	106	4	also	also	ADV
ejpam-3654	106	5	,	,	PUNCT
ejpam-3654	106	6	for	for	ADP
ejpam-3654	106	7	convenience	convenience	NOUN
ejpam-3654	106	8	,	,	PUNCT
ejpam-3654	106	9	we	we	PRON
ejpam-3654	106	10	denote	denote	VERB
ejpam-3654	106	11	that	that	SCONJ
ejpam-3654	106	12	:	:	PUNCT
ejpam-3654	106	13	r1	r1	PROPN
ejpam-3654	106	14	(	(	PUNCT
ejpam-3654	106	15	t	t	PROPN
ejpam-3654	106	16	)	)	PUNCT
ejpam-3654	106	17	:	:	PUNCT
ejpam-3654	107	1	=	=	PUNCT
ejpam-3654	107	2	αµ	αµ	ADP
ejpam-3654	107	3	t2	t2	NOUN
ejpam-3654	107	4	2r1	2r1	NUM
ejpam-3654	107	5	/	/	SYM
ejpam-3654	107	6	α	α	PROPN
ejpam-3654	107	7	(	(	PUNCT
ejpam-3654	107	8	t	t	PROPN
ejpam-3654	107	9	)	)	PUNCT
ejpam-3654	107	10	,	,	PUNCT
ejpam-3654	107	11	q1	q1	PROPN
ejpam-3654	107	12	(	(	PUNCT
ejpam-3654	107	13	t	t	PROPN
ejpam-3654	107	14	)	)	PUNCT
ejpam-3654	107	15	:	:	PUNCT
ejpam-3654	108	1	=	=	PUNCT
ejpam-3654	108	2	q	q	X
ejpam-3654	108	3	(	(	PUNCT
ejpam-3654	108	4	t	t	NOUN
ejpam-3654	108	5	)	)	PUNCT
ejpam-3654	108	6	(	(	PUNCT
ejpam-3654	108	7	1−	1−	NUM
ejpam-3654	108	8	p0)βmβ−α	p0)βmβ−α	NOUN
ejpam-3654	108	9	1	1	NUM
ejpam-3654	108	10	(	(	PUNCT
ejpam-3654	108	11	σ	σ	PROPN
ejpam-3654	108	12	(	(	PUNCT
ejpam-3654	108	13	t	t	PROPN
ejpam-3654	108	14	)	)	PUNCT
ejpam-3654	108	15	t	t	PROPN
ejpam-3654	108	16	)	)	PUNCT
ejpam-3654	108	17	3β	3β	NUM
ejpam-3654	108	18	and	and	CCONJ
ejpam-3654	108	19	q2	q2	PROPN
ejpam-3654	108	20	(	(	PUNCT
ejpam-3654	108	21	t	t	PROPN
ejpam-3654	108	22	)	)	PUNCT
ejpam-3654	108	23	:	:	PUNCT
ejpam-3654	108	24	=	=	SYM
ejpam-3654	108	25	(	(	PUNCT
ejpam-3654	108	26	1−	1−	NUM
ejpam-3654	108	27	p0)β	p0)β	NOUN
ejpam-3654	108	28	/	/	SYM
ejpam-3654	108	29	αmβ	αmβ	PROPN
ejpam-3654	108	30	/	/	SYM
ejpam-3654	108	31	α−1	α−1	PROPN
ejpam-3654	108	32	2	2	NUM
ejpam-3654	108	33	∫	∫	NOUN
ejpam-3654	108	34	∞	∞	PROPN
ejpam-3654	108	35	t	t	PROPN
ejpam-3654	108	36	(	(	PUNCT
ejpam-3654	108	37	1	1	NUM
ejpam-3654	108	38	r	r	NOUN
ejpam-3654	108	39	(	(	PUNCT
ejpam-3654	108	40	u	u	NOUN
ejpam-3654	108	41	)	)	PUNCT
ejpam-3654	108	42	∫	∫	PROPN
ejpam-3654	108	43	∞	∞	NUM
ejpam-3654	108	44	u	u	PROPN
ejpam-3654	108	45	q	q	X
ejpam-3654	108	46	(	(	PUNCT
ejpam-3654	108	47	s	s	NOUN
ejpam-3654	108	48	)	)	PUNCT
ejpam-3654	108	49	σβ	σβ	NOUN
ejpam-3654	108	50	(	(	PUNCT
ejpam-3654	108	51	s	s	X
ejpam-3654	108	52	)	)	PUNCT
ejpam-3654	108	53	sβ	sβ	NOUN
ejpam-3654	108	54	ds	ds	ADJ
ejpam-3654	108	55	)	)	PUNCT
ejpam-3654	108	56	1	1	PROPN
ejpam-3654	108	57	/	/	SYM
ejpam-3654	108	58	α	α	PRON
ejpam-3654	108	59	du	du	PROPN
ejpam-3654	108	60	,	,	PUNCT
ejpam-3654	108	61	o.	o.	PROPN
ejpam-3654	108	62	moaaz	moaaz	PROPN
ejpam-3654	108	63	,	,	PUNCT
ejpam-3654	108	64	c.	c.	PROPN
ejpam-3654	108	65	cesarano	cesarano	PROPN
ejpam-3654	108	66	,	,	PUNCT
ejpam-3654	108	67	a.	a.	NOUN
ejpam-3654	108	68	muhib	muhib	NOUN
ejpam-3654	108	69	/	/	SYM
ejpam-3654	108	70	eur	eur	PROPN
ejpam-3654	108	71	.	.	PUNCT
ejpam-3654	109	1	j.	j.	PROPN
ejpam-3654	109	2	pure	pure	PROPN
ejpam-3654	109	3	appl	appl	PROPN
ejpam-3654	109	4	.	.	PROPN
ejpam-3654	109	5	math	math	PROPN
ejpam-3654	109	6	,	,	PUNCT
ejpam-3654	109	7	13	13	NUM
ejpam-3654	109	8	(	(	PUNCT
ejpam-3654	109	9	2	2	NUM
ejpam-3654	109	10	)	)	PUNCT
ejpam-3654	109	11	(	(	PUNCT
ejpam-3654	109	12	2020	2020	NUM
ejpam-3654	109	13	)	)	PUNCT
ejpam-3654	109	14	,	,	PUNCT
ejpam-3654	109	15	185	185	NUM
ejpam-3654	109	16	-	-	SYM
ejpam-3654	109	17	199	199	NUM
ejpam-3654	109	18	190	190	NUM
ejpam-3654	109	19	for	for	ADP
ejpam-3654	109	20	some	some	DET
ejpam-3654	109	21	µ	µ	PRON
ejpam-3654	109	22	∈	∈	NOUN
ejpam-3654	109	23	(	(	PUNCT
ejpam-3654	109	24	0	0	NUM
ejpam-3654	109	25	,	,	PUNCT
ejpam-3654	109	26	1	1	NUM
ejpam-3654	109	27	)	)	PUNCT
ejpam-3654	109	28	and	and	CCONJ
ejpam-3654	109	29	every	every	DET
ejpam-3654	109	30	m1,m2	m1,m2	PROPN
ejpam-3654	109	31	are	be	AUX
ejpam-3654	109	32	positive	positive	ADJ
ejpam-3654	109	33	constants	constant	NOUN
ejpam-3654	109	34	.	.	PUNCT
ejpam-3654	110	1	all	all	DET
ejpam-3654	110	2	functional	functional	ADJ
ejpam-3654	110	3	inequalities	inequality	NOUN
ejpam-3654	110	4	are	be	AUX
ejpam-3654	110	5	assumed	assume	VERB
ejpam-3654	110	6	to	to	PART
ejpam-3654	110	7	hold	hold	VERB
ejpam-3654	110	8	eventually	eventually	ADV
ejpam-3654	110	9	,	,	PUNCT
ejpam-3654	110	10	that	that	ADV
ejpam-3654	110	11	is	is	ADV
ejpam-3654	110	12	,	,	PUNCT
ejpam-3654	110	13	they	they	PRON
ejpam-3654	110	14	are	be	AUX
ejpam-3654	110	15	assumed	assume	VERB
ejpam-3654	110	16	to	to	PART
ejpam-3654	110	17	be	be	AUX
ejpam-3654	110	18	satisfied	satisfied	ADJ
ejpam-3654	110	19	for	for	SCONJ
ejpam-3654	110	20	all	all	DET
ejpam-3654	110	21	t	t	NOUN
ejpam-3654	110	22	sufficiently	sufficiently	ADV
ejpam-3654	110	23	large	large	ADJ
ejpam-3654	110	24	.	.	PUNCT
ejpam-3654	111	1	the	the	DET
ejpam-3654	111	2	proof	proof	NOUN
ejpam-3654	111	3	of	of	ADP
ejpam-3654	111	4	the	the	DET
ejpam-3654	111	5	next	next	ADJ
ejpam-3654	111	6	lemma	lemma	PROPN
ejpam-3654	111	7	is	be	AUX
ejpam-3654	111	8	immediate	immediate	ADJ
ejpam-3654	111	9	from	from	ADP
ejpam-3654	111	10	[	[	X
ejpam-3654	111	11	23	23	NUM
ejpam-3654	111	12	]	]	PUNCT
ejpam-3654	111	13	and	and	CCONJ
ejpam-3654	111	14	hence	hence	ADV
ejpam-3654	111	15	is	be	AUX
ejpam-3654	111	16	omitted	omit	VERB
ejpam-3654	111	17	.	.	PUNCT
ejpam-3654	112	1	lemma	lemma	PROPN
ejpam-3654	112	2	5	5	X
ejpam-3654	112	3	.	.	PUNCT
ejpam-3654	112	4	assume	assume	VERB
ejpam-3654	112	5	that	that	SCONJ
ejpam-3654	112	6	(	(	PUNCT
ejpam-3654	112	7	2	2	X
ejpam-3654	112	8	)	)	PUNCT
ejpam-3654	112	9	holds	hold	VERB
ejpam-3654	112	10	and	and	CCONJ
ejpam-3654	112	11	x	x	X
ejpam-3654	112	12	is	be	AUX
ejpam-3654	112	13	an	an	DET
ejpam-3654	112	14	eventually	eventually	ADV
ejpam-3654	112	15	positive	positive	ADJ
ejpam-3654	112	16	solution	solution	NOUN
ejpam-3654	112	17	of	of	ADP
ejpam-3654	112	18	(	(	PUNCT
ejpam-3654	112	19	1	1	NUM
ejpam-3654	112	20	)	)	PUNCT
ejpam-3654	112	21	.	.	PUNCT
ejpam-3654	113	1	then	then	ADV
ejpam-3654	113	2	,	,	PUNCT
ejpam-3654	113	3	(	(	PUNCT
ejpam-3654	113	4	r	r	NOUN
ejpam-3654	113	5	(	(	PUNCT
ejpam-3654	113	6	t	t	NOUN
ejpam-3654	113	7	)	)	PUNCT
ejpam-3654	113	8	(	(	PUNCT
ejpam-3654	113	9	z′′′	z′′′	PROPN
ejpam-3654	113	10	(	(	PUNCT
ejpam-3654	113	11	t))α	t))α	NOUN
ejpam-3654	113	12	)	)	PUNCT
ejpam-3654	113	13	′	′	PUNCT
ejpam-3654	114	1	<	<	X
ejpam-3654	114	2	0	0	PUNCT
ejpam-3654	115	1	and	and	CCONJ
ejpam-3654	115	2	there	there	PRON
ejpam-3654	115	3	are	be	VERB
ejpam-3654	115	4	the	the	DET
ejpam-3654	115	5	following	follow	VERB
ejpam-3654	115	6	two	two	NUM
ejpam-3654	115	7	possible	possible	ADJ
ejpam-3654	115	8	cases	case	NOUN
ejpam-3654	115	9	eventually	eventually	ADV
ejpam-3654	115	10	:	:	PUNCT
ejpam-3654	115	11	(	(	PUNCT
ejpam-3654	115	12	c1	c1	NOUN
ejpam-3654	115	13	)	)	PUNCT
ejpam-3654	115	14	z	z	PROPN
ejpam-3654	115	15	(	(	PUNCT
ejpam-3654	115	16	t	t	PROPN
ejpam-3654	115	17	)	)	PUNCT
ejpam-3654	115	18	>	>	X
ejpam-3654	115	19	0	0	NUM
ejpam-3654	115	20	,	,	PUNCT
ejpam-3654	115	21	z′	z′	NUM
ejpam-3654	115	22	(	(	PUNCT
ejpam-3654	115	23	t	t	PROPN
ejpam-3654	115	24	)	)	PUNCT
ejpam-3654	115	25	>	>	X
ejpam-3654	115	26	0	0	NUM
ejpam-3654	115	27	,	,	PUNCT
ejpam-3654	115	28	z′′	z′′	NOUN
ejpam-3654	115	29	(	(	PUNCT
ejpam-3654	115	30	t	t	PROPN
ejpam-3654	115	31	)	)	PUNCT
ejpam-3654	115	32	>	>	X
ejpam-3654	115	33	0	0	NUM
ejpam-3654	115	34	,	,	PUNCT
ejpam-3654	115	35	z′′′	z′′′	PROPN
ejpam-3654	115	36	(	(	PUNCT
ejpam-3654	115	37	t	t	PROPN
ejpam-3654	115	38	)	)	PUNCT
ejpam-3654	115	39	>	>	X
ejpam-3654	115	40	0	0	NUM
ejpam-3654	115	41	,	,	PUNCT
ejpam-3654	115	42	z(4	z(4	PROPN
ejpam-3654	115	43	)	)	PUNCT
ejpam-3654	115	44	(	(	PUNCT
ejpam-3654	115	45	t	t	NOUN
ejpam-3654	115	46	)	)	PUNCT
ejpam-3654	115	47	<	<	X
ejpam-3654	115	48	0	0	NUM
ejpam-3654	115	49	,	,	PUNCT
ejpam-3654	115	50	(	(	PUNCT
ejpam-3654	115	51	c2	c2	PROPN
ejpam-3654	115	52	)	)	PUNCT
ejpam-3654	115	53	z	z	PROPN
ejpam-3654	115	54	(	(	PUNCT
ejpam-3654	115	55	t	t	PROPN
ejpam-3654	115	56	)	)	PUNCT
ejpam-3654	115	57	>	>	X
ejpam-3654	115	58	0	0	NUM
ejpam-3654	115	59	,	,	PUNCT
ejpam-3654	115	60	z′	z′	NUM
ejpam-3654	115	61	(	(	PUNCT
ejpam-3654	115	62	t	t	PROPN
ejpam-3654	115	63	)	)	PUNCT
ejpam-3654	115	64	>	>	X
ejpam-3654	115	65	0	0	NUM
ejpam-3654	115	66	,	,	PUNCT
ejpam-3654	115	67	z′′	z′′	NOUN
ejpam-3654	115	68	(	(	PUNCT
ejpam-3654	115	69	t	t	PROPN
ejpam-3654	115	70	)	)	PUNCT
ejpam-3654	115	71	<	<	X
ejpam-3654	115	72	0	0	NUM
ejpam-3654	115	73	,	,	PUNCT
ejpam-3654	115	74	z′′′	z′′′	PROPN
ejpam-3654	115	75	(	(	PUNCT
ejpam-3654	115	76	t	t	PROPN
ejpam-3654	115	77	)	)	PUNCT
ejpam-3654	115	78	>	>	X
ejpam-3654	115	79	0	0	X
ejpam-3654	115	80	.	.	PUNCT
ejpam-3654	116	1	lemma	lemma	PROPN
ejpam-3654	116	2	6	6	NUM
ejpam-3654	116	3	.	.	PUNCT
ejpam-3654	117	1	let	let	VERB
ejpam-3654	117	2	x	x	PRON
ejpam-3654	117	3	be	be	AUX
ejpam-3654	117	4	an	an	DET
ejpam-3654	117	5	eventually	eventually	ADV
ejpam-3654	117	6	positive	positive	ADJ
ejpam-3654	117	7	solution	solution	NOUN
ejpam-3654	117	8	of	of	ADP
ejpam-3654	117	9	(	(	PUNCT
ejpam-3654	117	10	1	1	NUM
ejpam-3654	117	11	)	)	PUNCT
ejpam-3654	117	12	and	and	CCONJ
ejpam-3654	117	13	the	the	DET
ejpam-3654	117	14	functions	function	NOUN
ejpam-3654	117	15	ω	ω	PROPN
ejpam-3654	117	16	and	and	CCONJ
ejpam-3654	117	17	w	w	NOUN
ejpam-3654	117	18	are	be	AUX
ejpam-3654	117	19	defined	define	VERB
ejpam-3654	117	20	as	as	ADP
ejpam-3654	117	21	in	in	ADP
ejpam-3654	117	22	(	(	PUNCT
ejpam-3654	117	23	9	9	NUM
ejpam-3654	117	24	)	)	PUNCT
ejpam-3654	117	25	.	.	PUNCT
ejpam-3654	118	1	(	(	PUNCT
ejpam-3654	118	2	i1	i1	PROPN
ejpam-3654	118	3	)	)	PUNCT
ejpam-3654	118	4	if	if	SCONJ
ejpam-3654	118	5	x	x	PRON
ejpam-3654	118	6	satisfies	satisfie	NOUN
ejpam-3654	118	7	(	(	PUNCT
ejpam-3654	118	8	c1	c1	PROPN
ejpam-3654	118	9	)	)	PUNCT
ejpam-3654	118	10	,	,	PUNCT
ejpam-3654	118	11	then	then	ADV
ejpam-3654	118	12	ω′	ω′	PROPN
ejpam-3654	118	13	(	(	PUNCT
ejpam-3654	118	14	t	t	PROPN
ejpam-3654	118	15	)	)	PUNCT
ejpam-3654	118	16	+	+	PROPN
ejpam-3654	118	17	q1	q1	PROPN
ejpam-3654	118	18	(	(	PUNCT
ejpam-3654	118	19	t	t	PROPN
ejpam-3654	118	20	)	)	PUNCT
ejpam-3654	118	21	+	+	NOUN
ejpam-3654	118	22	r1	r1	PROPN
ejpam-3654	118	23	(	(	PUNCT
ejpam-3654	118	24	t)ω	t)ω	X
ejpam-3654	118	25	α+1	α+1	NUM
ejpam-3654	118	26	α	α	PROPN
ejpam-3654	118	27	(	(	PUNCT
ejpam-3654	118	28	t	t	PROPN
ejpam-3654	118	29	)	)	PUNCT
ejpam-3654	118	30	≤	≤	NOUN
ejpam-3654	118	31	0	0	NUM
ejpam-3654	118	32	;	;	PUNCT
ejpam-3654	118	33	(	(	PUNCT
ejpam-3654	118	34	10	10	NUM
ejpam-3654	118	35	)	)	PUNCT
ejpam-3654	118	36	(	(	PUNCT
ejpam-3654	118	37	i2	i2	PROPN
ejpam-3654	118	38	)	)	PUNCT
ejpam-3654	118	39	if	if	SCONJ
ejpam-3654	118	40	x	x	PRON
ejpam-3654	118	41	satisfies	satisfie	NOUN
ejpam-3654	118	42	(	(	PUNCT
ejpam-3654	118	43	c2	c2	PROPN
ejpam-3654	118	44	)	)	PUNCT
ejpam-3654	118	45	,	,	PUNCT
ejpam-3654	118	46	then	then	ADV
ejpam-3654	118	47	w′	w′	PROPN
ejpam-3654	118	48	(	(	PUNCT
ejpam-3654	118	49	t	t	PROPN
ejpam-3654	118	50	)	)	PUNCT
ejpam-3654	118	51	+	+	PROPN
ejpam-3654	118	52	q2	q2	NOUN
ejpam-3654	118	53	(	(	PUNCT
ejpam-3654	118	54	t	t	PROPN
ejpam-3654	118	55	)	)	PUNCT
ejpam-3654	118	56	+	+	NUM
ejpam-3654	118	57	w2	w2	NOUN
ejpam-3654	118	58	(	(	PUNCT
ejpam-3654	118	59	t	t	PROPN
ejpam-3654	118	60	)	)	PUNCT
ejpam-3654	118	61	≤	≤	NOUN
ejpam-3654	118	62	0	0	NUM
ejpam-3654	118	63	.	.	PUNCT
ejpam-3654	119	1	(	(	PUNCT
ejpam-3654	119	2	11	11	NUM
ejpam-3654	119	3	)	)	PUNCT
ejpam-3654	119	4	proof	proof	NOUN
ejpam-3654	119	5	.	.	PUNCT
ejpam-3654	120	1	assume	assume	VERB
ejpam-3654	120	2	that	that	SCONJ
ejpam-3654	120	3	x	x	PRON
ejpam-3654	120	4	is	be	AUX
ejpam-3654	120	5	an	an	DET
ejpam-3654	120	6	eventually	eventually	ADV
ejpam-3654	120	7	positive	positive	ADJ
ejpam-3654	120	8	solution	solution	NOUN
ejpam-3654	120	9	of	of	ADP
ejpam-3654	120	10	(	(	PUNCT
ejpam-3654	120	11	1	1	NUM
ejpam-3654	120	12	)	)	PUNCT
ejpam-3654	120	13	.	.	PUNCT
ejpam-3654	121	1	then	then	ADV
ejpam-3654	121	2	,	,	PUNCT
ejpam-3654	121	3	there	there	PRON
ejpam-3654	121	4	exists	exist	VERB
ejpam-3654	121	5	a	a	DET
ejpam-3654	121	6	t1	t1	NOUN
ejpam-3654	121	7	≥	≥	NOUN
ejpam-3654	121	8	t0	t0	NOUN
ejpam-3654	121	9	such	such	ADJ
ejpam-3654	121	10	that	that	SCONJ
ejpam-3654	121	11	x	x	X
ejpam-3654	121	12	(	(	PUNCT
ejpam-3654	121	13	t	t	PROPN
ejpam-3654	121	14	)	)	PUNCT
ejpam-3654	121	15	>	>	X
ejpam-3654	121	16	0	0	NUM
ejpam-3654	121	17	,	,	PUNCT
ejpam-3654	121	18	x	x	X
ejpam-3654	121	19	(	(	PUNCT
ejpam-3654	121	20	τ	τ	X
ejpam-3654	121	21	(	(	PUNCT
ejpam-3654	121	22	t	t	PROPN
ejpam-3654	121	23	)	)	PUNCT
ejpam-3654	121	24	)	)	PUNCT
ejpam-3654	121	25	>	>	X
ejpam-3654	121	26	0	0	PUNCT
ejpam-3654	122	1	and	and	CCONJ
ejpam-3654	122	2	x	x	SYM
ejpam-3654	122	3	(	(	PUNCT
ejpam-3654	122	4	σ	σ	PROPN
ejpam-3654	122	5	(	(	PUNCT
ejpam-3654	122	6	t	t	PROPN
ejpam-3654	122	7	)	)	PUNCT
ejpam-3654	122	8	)	)	PUNCT
ejpam-3654	122	9	>	>	X
ejpam-3654	122	10	0	0	PUNCT
ejpam-3654	123	1	for	for	ADP
ejpam-3654	123	2	t	t	PROPN
ejpam-3654	123	3	≥	≥	NOUN
ejpam-3654	123	4	t1	t1	NOUN
ejpam-3654	123	5	.	.	PUNCT
ejpam-3654	124	1	using	use	VERB
ejpam-3654	124	2	lemma	lemma	PROPN
ejpam-3654	124	3	4	4	NUM
ejpam-3654	124	4	,	,	PUNCT
ejpam-3654	124	5	we	we	PRON
ejpam-3654	124	6	obtain	obtain	VERB
ejpam-3654	124	7	that	that	SCONJ
ejpam-3654	124	8	(	(	PUNCT
ejpam-3654	124	9	3	3	X
ejpam-3654	124	10	)	)	PUNCT
ejpam-3654	124	11	holds	hold	VERB
ejpam-3654	124	12	.	.	PUNCT
ejpam-3654	125	1	in	in	ADP
ejpam-3654	125	2	the	the	DET
ejpam-3654	125	3	case	case	NOUN
ejpam-3654	125	4	(	(	PUNCT
ejpam-3654	125	5	c1	c1	NOUN
ejpam-3654	125	6	)	)	PUNCT
ejpam-3654	125	7	,	,	PUNCT
ejpam-3654	125	8	by	by	ADP
ejpam-3654	125	9	differentiating	differentiate	VERB
ejpam-3654	125	10	ω	ω	PROPN
ejpam-3654	125	11	and	and	CCONJ
ejpam-3654	125	12	using	use	VERB
ejpam-3654	125	13	(	(	PUNCT
ejpam-3654	125	14	3	3	NUM
ejpam-3654	125	15	)	)	PUNCT
ejpam-3654	125	16	,	,	PUNCT
ejpam-3654	125	17	we	we	PRON
ejpam-3654	125	18	obtain	obtain	VERB
ejpam-3654	125	19	ω′	ω′	PROPN
ejpam-3654	125	20	(	(	PUNCT
ejpam-3654	125	21	t	t	NOUN
ejpam-3654	125	22	)	)	PUNCT
ejpam-3654	125	23	≤	≤	NUM
ejpam-3654	126	1	−q	−q	NOUN
ejpam-3654	126	2	(	(	PUNCT
ejpam-3654	126	3	t	t	NOUN
ejpam-3654	126	4	)	)	PUNCT
ejpam-3654	126	5	(	(	PUNCT
ejpam-3654	126	6	1−	1−	NUM
ejpam-3654	126	7	p0)β	p0)β	NOUN
ejpam-3654	126	8	zβ	zβ	PROPN
ejpam-3654	126	9	(	(	PUNCT
ejpam-3654	126	10	σ	σ	PROPN
ejpam-3654	126	11	(	(	PUNCT
ejpam-3654	126	12	t	t	PROPN
ejpam-3654	126	13	)	)	PUNCT
ejpam-3654	126	14	)	)	PUNCT
ejpam-3654	127	1	zα	zα	PROPN
ejpam-3654	127	2	(	(	PUNCT
ejpam-3654	127	3	t	t	PROPN
ejpam-3654	127	4	)	)	PUNCT
ejpam-3654	127	5	−	−	PROPN
ejpam-3654	128	1	αr	αr	PROPN
ejpam-3654	128	2	(	(	PUNCT
ejpam-3654	128	3	t	t	PROPN
ejpam-3654	128	4	)	)	PUNCT
ejpam-3654	128	5	(	(	PUNCT
ejpam-3654	128	6	z′′′	z′′′	PROPN
ejpam-3654	128	7	(	(	PUNCT
ejpam-3654	128	8	t))α	t))α	NOUN
ejpam-3654	128	9	zα+1	zα+1	PROPN
ejpam-3654	128	10	(	(	PUNCT
ejpam-3654	128	11	t	t	NOUN
ejpam-3654	128	12	)	)	PUNCT
ejpam-3654	128	13	z′	z′	PROPN
ejpam-3654	128	14	(	(	PUNCT
ejpam-3654	128	15	t	t	PROPN
ejpam-3654	128	16	)	)	PUNCT
ejpam-3654	128	17	.	.	PUNCT
ejpam-3654	129	1	(	(	PUNCT
ejpam-3654	129	2	12	12	NUM
ejpam-3654	129	3	)	)	PUNCT
ejpam-3654	129	4	from	from	ADP
ejpam-3654	129	5	lemma	lemma	PROPN
ejpam-3654	129	6	1	1	NUM
ejpam-3654	129	7	,	,	PUNCT
ejpam-3654	129	8	we	we	PRON
ejpam-3654	129	9	have	have	VERB
ejpam-3654	129	10	that	that	DET
ejpam-3654	129	11	z	z	PROPN
ejpam-3654	129	12	(	(	PUNCT
ejpam-3654	129	13	t	t	PROPN
ejpam-3654	129	14	)	)	PUNCT
ejpam-3654	129	15	≥	≥	NOUN
ejpam-3654	129	16	t	t	PROPN
ejpam-3654	129	17	3	3	NUM
ejpam-3654	129	18	z′	z′	NUM
ejpam-3654	129	19	(	(	PUNCT
ejpam-3654	129	20	t	t	PROPN
ejpam-3654	129	21	)	)	PUNCT
ejpam-3654	129	22	and	and	CCONJ
ejpam-3654	129	23	hence	hence	ADV
ejpam-3654	129	24	z	z	PROPN
ejpam-3654	129	25	(	(	PUNCT
ejpam-3654	129	26	σ	σ	PROPN
ejpam-3654	129	27	(	(	PUNCT
ejpam-3654	129	28	t	t	PROPN
ejpam-3654	129	29	)	)	PUNCT
ejpam-3654	129	30	)	)	PUNCT
ejpam-3654	130	1	z	z	NOUN
ejpam-3654	130	2	(	(	PUNCT
ejpam-3654	130	3	t	t	PROPN
ejpam-3654	130	4	)	)	PUNCT
ejpam-3654	130	5	≥	≥	NOUN
ejpam-3654	130	6	σ3	σ3	PROPN
ejpam-3654	130	7	(	(	PUNCT
ejpam-3654	130	8	t	t	PROPN
ejpam-3654	130	9	)	)	PUNCT
ejpam-3654	130	10	t3	t3	PROPN
ejpam-3654	130	11	.	.	PUNCT
ejpam-3654	131	1	(	(	PUNCT
ejpam-3654	131	2	13	13	NUM
ejpam-3654	131	3	)	)	PUNCT
ejpam-3654	131	4	it	it	PRON
ejpam-3654	131	5	follows	follow	VERB
ejpam-3654	131	6	from	from	ADP
ejpam-3654	131	7	lemma	lemma	PROPN
ejpam-3654	131	8	2	2	NUM
ejpam-3654	131	9	that	that	SCONJ
ejpam-3654	131	10	z′	z′	NUM
ejpam-3654	131	11	(	(	PUNCT
ejpam-3654	131	12	t	t	PROPN
ejpam-3654	131	13	)	)	PUNCT
ejpam-3654	131	14	≥	≥	NOUN
ejpam-3654	131	15	µ1	µ1	PROPN
ejpam-3654	131	16	2	2	NUM
ejpam-3654	131	17	t2z′′′	t2z′′′	PROPN
ejpam-3654	131	18	(	(	PUNCT
ejpam-3654	131	19	t	t	PROPN
ejpam-3654	131	20	)	)	PUNCT
ejpam-3654	131	21	,	,	PUNCT
ejpam-3654	131	22	(	(	PUNCT
ejpam-3654	131	23	14	14	NUM
ejpam-3654	131	24	)	)	PUNCT
ejpam-3654	131	25	for	for	ADP
ejpam-3654	131	26	all	all	DET
ejpam-3654	131	27	µ1	µ1	PROPN
ejpam-3654	131	28	∈	∈	PROPN
ejpam-3654	131	29	(	(	PUNCT
ejpam-3654	131	30	0	0	NUM
ejpam-3654	131	31	,	,	PUNCT
ejpam-3654	131	32	1	1	NUM
ejpam-3654	131	33	)	)	PUNCT
ejpam-3654	131	34	and	and	CCONJ
ejpam-3654	131	35	every	every	DET
ejpam-3654	131	36	sufficiently	sufficiently	ADV
ejpam-3654	131	37	large	large	ADJ
ejpam-3654	131	38	t.	t.	NOUN
ejpam-3654	131	39	since	since	SCONJ
ejpam-3654	131	40	z′	z′	PROPN
ejpam-3654	131	41	(	(	PUNCT
ejpam-3654	131	42	t	t	PROPN
ejpam-3654	131	43	)	)	PUNCT
ejpam-3654	131	44	>	>	X
ejpam-3654	132	1	0	0	NUM
ejpam-3654	132	2	,	,	PUNCT
ejpam-3654	132	3	there	there	PRON
ejpam-3654	132	4	exist	exist	VERB
ejpam-3654	132	5	a	a	DET
ejpam-3654	132	6	t2	t2	NOUN
ejpam-3654	132	7	≥	≥	NOUN
ejpam-3654	132	8	t1	t1	NOUN
ejpam-3654	132	9	and	and	CCONJ
ejpam-3654	132	10	a	a	DET
ejpam-3654	132	11	constant	constant	ADJ
ejpam-3654	132	12	m	m	NOUN
ejpam-3654	132	13	>	>	X
ejpam-3654	132	14	0	0	NUM
ejpam-3654	132	15	such	such	ADJ
ejpam-3654	132	16	that	that	SCONJ
ejpam-3654	132	17	z	z	NOUN
ejpam-3654	132	18	(	(	PUNCT
ejpam-3654	132	19	t	t	PROPN
ejpam-3654	132	20	)	)	PUNCT
ejpam-3654	132	21	>	>	X
ejpam-3654	133	1	m	m	PROPN
ejpam-3654	133	2	,	,	PUNCT
ejpam-3654	133	3	(	(	PUNCT
ejpam-3654	133	4	15	15	NUM
ejpam-3654	133	5	)	)	PUNCT
ejpam-3654	133	6	for	for	ADP
ejpam-3654	133	7	t	t	PROPN
ejpam-3654	133	8	≥	≥	PROPN
ejpam-3654	133	9	t2	t2	PROPN
ejpam-3654	133	10	.	.	PUNCT
ejpam-3654	134	1	thus	thus	ADV
ejpam-3654	134	2	,	,	PUNCT
ejpam-3654	134	3	by	by	ADP
ejpam-3654	134	4	(	(	PUNCT
ejpam-3654	134	5	12	12	NUM
ejpam-3654	134	6	)	)	PUNCT
ejpam-3654	134	7	,	,	PUNCT
ejpam-3654	134	8	(	(	PUNCT
ejpam-3654	134	9	13	13	NUM
ejpam-3654	134	10	)	)	PUNCT
ejpam-3654	134	11	,	,	PUNCT
ejpam-3654	134	12	(	(	PUNCT
ejpam-3654	134	13	14	14	NUM
ejpam-3654	134	14	)	)	PUNCT
ejpam-3654	134	15	and	and	CCONJ
ejpam-3654	134	16	(	(	PUNCT
ejpam-3654	134	17	15	15	NUM
ejpam-3654	134	18	)	)	PUNCT
ejpam-3654	134	19	,	,	PUNCT
ejpam-3654	134	20	we	we	PRON
ejpam-3654	134	21	get	get	VERB
ejpam-3654	134	22	ω′	ω′	PROPN
ejpam-3654	134	23	(	(	PUNCT
ejpam-3654	134	24	t	t	PROPN
ejpam-3654	134	25	)	)	PUNCT
ejpam-3654	135	1	+	+	PROPN
ejpam-3654	135	2	q1	q1	PROPN
ejpam-3654	135	3	(	(	PUNCT
ejpam-3654	135	4	t	t	PROPN
ejpam-3654	135	5	)	)	PUNCT
ejpam-3654	136	1	+	+	NOUN
ejpam-3654	136	2	r1	r1	PROPN
ejpam-3654	136	3	(	(	PUNCT
ejpam-3654	136	4	t)ω	t)ω	X
ejpam-3654	136	5	α+1	α+1	NUM
ejpam-3654	136	6	α	α	PROPN
ejpam-3654	136	7	(	(	PUNCT
ejpam-3654	136	8	t	t	PROPN
ejpam-3654	136	9	)	)	PUNCT
ejpam-3654	136	10	≤	≤	NOUN
ejpam-3654	136	11	0	0	NUM
ejpam-3654	136	12	.	.	PUNCT
ejpam-3654	137	1	in	in	ADP
ejpam-3654	137	2	the	the	DET
ejpam-3654	137	3	case	case	NOUN
ejpam-3654	137	4	(	(	PUNCT
ejpam-3654	137	5	c2	c2	PROPN
ejpam-3654	137	6	)	)	PUNCT
ejpam-3654	137	7	,	,	PUNCT
ejpam-3654	137	8	integrating	integrate	VERB
ejpam-3654	137	9	(	(	PUNCT
ejpam-3654	137	10	3	3	NUM
ejpam-3654	137	11	)	)	PUNCT
ejpam-3654	137	12	from	from	ADP
ejpam-3654	137	13	t	t	PROPN
ejpam-3654	137	14	to	to	ADP
ejpam-3654	137	15	u	u	NOUN
ejpam-3654	137	16	,	,	PUNCT
ejpam-3654	137	17	we	we	PRON
ejpam-3654	137	18	obtain	obtain	VERB
ejpam-3654	137	19	r	r	NOUN
ejpam-3654	137	20	(	(	PUNCT
ejpam-3654	137	21	u	u	NOUN
ejpam-3654	137	22	)	)	PUNCT
ejpam-3654	137	23	(	(	PUNCT
ejpam-3654	137	24	z′′′	z′′′	PROPN
ejpam-3654	137	25	(	(	PUNCT
ejpam-3654	137	26	u	u	NOUN
ejpam-3654	137	27	)	)	PUNCT
ejpam-3654	137	28	)	)	PUNCT
ejpam-3654	138	1	α	α	PRON
ejpam-3654	138	2	−	−	NOUN
ejpam-3654	139	1	r	r	NOUN
ejpam-3654	139	2	(	(	PUNCT
ejpam-3654	139	3	t	t	NOUN
ejpam-3654	139	4	)	)	PUNCT
ejpam-3654	139	5	(	(	PUNCT
ejpam-3654	139	6	z′′′	z′′′	PROPN
ejpam-3654	139	7	(	(	PUNCT
ejpam-3654	139	8	t	t	PROPN
ejpam-3654	139	9	)	)	PUNCT
ejpam-3654	139	10	)	)	PUNCT
ejpam-3654	140	1	α	α	PROPN
ejpam-3654	140	2	≤	≤	PUNCT
ejpam-3654	140	3	−∫	−∫	X
ejpam-3654	140	4	u	u	NOUN
ejpam-3654	140	5	t	t	PROPN
ejpam-3654	140	6	q	q	PROPN
ejpam-3654	140	7	(	(	PUNCT
ejpam-3654	140	8	s	s	NOUN
ejpam-3654	140	9	)	)	PUNCT
ejpam-3654	140	10	(	(	PUNCT
ejpam-3654	140	11	1−	1−	NUM
ejpam-3654	140	12	p0)β	p0)β	NOUN
ejpam-3654	140	13	zβ	zβ	PROPN
ejpam-3654	140	14	(	(	PUNCT
ejpam-3654	140	15	σ	σ	X
ejpam-3654	140	16	(	(	PUNCT
ejpam-3654	140	17	s	s	NOUN
ejpam-3654	140	18	)	)	PUNCT
ejpam-3654	140	19	)	)	PUNCT
ejpam-3654	140	20	ds	ds	PROPN
ejpam-3654	140	21	.	.	PUNCT
ejpam-3654	140	22	(	(	PUNCT
ejpam-3654	140	23	16	16	NUM
ejpam-3654	140	24	)	)	PUNCT
ejpam-3654	140	25	o.	o.	NOUN
ejpam-3654	140	26	moaaz	moaaz	PROPN
ejpam-3654	140	27	,	,	PUNCT
ejpam-3654	140	28	c.	c.	PROPN
ejpam-3654	140	29	cesarano	cesarano	PROPN
ejpam-3654	140	30	,	,	PUNCT
ejpam-3654	140	31	a.	a.	NOUN
ejpam-3654	140	32	muhib	muhib	NOUN
ejpam-3654	140	33	/	/	SYM
ejpam-3654	140	34	eur	eur	PROPN
ejpam-3654	140	35	.	.	PUNCT
ejpam-3654	141	1	j.	j.	PROPN
ejpam-3654	141	2	pure	pure	PROPN
ejpam-3654	141	3	appl	appl	PROPN
ejpam-3654	141	4	.	.	PROPN
ejpam-3654	141	5	math	math	PROPN
ejpam-3654	141	6	,	,	PUNCT
ejpam-3654	141	7	13	13	NUM
ejpam-3654	141	8	(	(	PUNCT
ejpam-3654	141	9	2	2	NUM
ejpam-3654	141	10	)	)	PUNCT
ejpam-3654	141	11	(	(	PUNCT
ejpam-3654	141	12	2020	2020	NUM
ejpam-3654	141	13	)	)	PUNCT
ejpam-3654	141	14	,	,	PUNCT
ejpam-3654	141	15	185	185	NUM
ejpam-3654	141	16	-	-	SYM
ejpam-3654	141	17	199	199	NUM
ejpam-3654	141	18	191	191	NUM
ejpam-3654	141	19	from	from	ADP
ejpam-3654	141	20	lemma	lemma	PROPN
ejpam-3654	141	21	1	1	NUM
ejpam-3654	141	22	,	,	PUNCT
ejpam-3654	141	23	we	we	PRON
ejpam-3654	141	24	get	get	VERB
ejpam-3654	141	25	that	that	PRON
ejpam-3654	141	26	z	z	NOUN
ejpam-3654	141	27	(	(	PUNCT
ejpam-3654	141	28	t	t	PROPN
ejpam-3654	141	29	)	)	PUNCT
ejpam-3654	141	30	≥	≥	NOUN
ejpam-3654	141	31	tz′	tz′	NOUN
ejpam-3654	141	32	(	(	PUNCT
ejpam-3654	141	33	t	t	NOUN
ejpam-3654	141	34	)	)	PUNCT
ejpam-3654	141	35	and	and	CCONJ
ejpam-3654	141	36	hence	hence	ADV
ejpam-3654	141	37	z	z	PROPN
ejpam-3654	141	38	(	(	PUNCT
ejpam-3654	141	39	σ	σ	PROPN
ejpam-3654	141	40	(	(	PUNCT
ejpam-3654	141	41	t	t	PROPN
ejpam-3654	141	42	)	)	PUNCT
ejpam-3654	141	43	)	)	PUNCT
ejpam-3654	141	44	≥	≥	PROPN
ejpam-3654	142	1	σ	σ	PROPN
ejpam-3654	142	2	(	(	PUNCT
ejpam-3654	142	3	t	t	PROPN
ejpam-3654	142	4	)	)	PUNCT
ejpam-3654	142	5	t	t	PROPN
ejpam-3654	142	6	z	z	PROPN
ejpam-3654	142	7	(	(	PUNCT
ejpam-3654	142	8	t	t	PROPN
ejpam-3654	142	9	)	)	PUNCT
ejpam-3654	142	10	.	.	PUNCT
ejpam-3654	143	1	(	(	PUNCT
ejpam-3654	143	2	17	17	NUM
ejpam-3654	143	3	)	)	PUNCT
ejpam-3654	143	4	for	for	ADP
ejpam-3654	143	5	(	(	PUNCT
ejpam-3654	143	6	16	16	NUM
ejpam-3654	143	7	)	)	PUNCT
ejpam-3654	143	8	,	,	PUNCT
ejpam-3654	143	9	letting	let	VERB
ejpam-3654	143	10	u→∞	u→∞	NUM
ejpam-3654	143	11	and	and	CCONJ
ejpam-3654	143	12	using	use	VERB
ejpam-3654	143	13	(	(	PUNCT
ejpam-3654	143	14	17	17	NUM
ejpam-3654	143	15	)	)	PUNCT
ejpam-3654	143	16	,	,	PUNCT
ejpam-3654	143	17	we	we	PRON
ejpam-3654	143	18	see	see	VERB
ejpam-3654	143	19	that	that	SCONJ
ejpam-3654	144	1	r	r	NOUN
ejpam-3654	144	2	(	(	PUNCT
ejpam-3654	144	3	t	t	NOUN
ejpam-3654	144	4	)	)	PUNCT
ejpam-3654	144	5	(	(	PUNCT
ejpam-3654	144	6	z′′′	z′′′	PROPN
ejpam-3654	144	7	(	(	PUNCT
ejpam-3654	144	8	t	t	PROPN
ejpam-3654	144	9	)	)	PUNCT
ejpam-3654	144	10	)	)	PUNCT
ejpam-3654	145	1	α	α	PRON
ejpam-3654	145	2	≥	≥	NUM
ejpam-3654	145	3	(	(	PUNCT
ejpam-3654	145	4	1−	1−	NUM
ejpam-3654	145	5	p0)β	p0)β	NOUN
ejpam-3654	145	6	zβ	zβ	PROPN
ejpam-3654	145	7	(	(	PUNCT
ejpam-3654	145	8	t	t	PROPN
ejpam-3654	145	9	)	)	PUNCT
ejpam-3654	145	10	∫	∫	PROPN
ejpam-3654	146	1	∞	∞	PROPN
ejpam-3654	146	2	t	t	PROPN
ejpam-3654	146	3	q	q	X
ejpam-3654	146	4	(	(	PUNCT
ejpam-3654	146	5	s	s	NOUN
ejpam-3654	146	6	)	)	PUNCT
ejpam-3654	146	7	σβ	σβ	NOUN
ejpam-3654	146	8	(	(	PUNCT
ejpam-3654	146	9	s	s	X
ejpam-3654	146	10	)	)	PUNCT
ejpam-3654	146	11	sβ	sβ	NOUN
ejpam-3654	146	12	ds	ds	PROPN
ejpam-3654	146	13	.	.	NOUN
ejpam-3654	146	14	integrating	integrate	VERB
ejpam-3654	146	15	this	this	DET
ejpam-3654	146	16	inequality	inequality	NOUN
ejpam-3654	146	17	again	again	ADV
ejpam-3654	146	18	from	from	ADP
ejpam-3654	146	19	t	t	PROPN
ejpam-3654	146	20	to	to	ADP
ejpam-3654	146	21	∞	∞	PROPN
ejpam-3654	146	22	,	,	PUNCT
ejpam-3654	146	23	we	we	PRON
ejpam-3654	146	24	get	get	VERB
ejpam-3654	146	25	z′′	z′′	NOUN
ejpam-3654	146	26	(	(	PUNCT
ejpam-3654	146	27	t	t	PROPN
ejpam-3654	146	28	)	)	PUNCT
ejpam-3654	146	29	≤	≤	NOUN
ejpam-3654	146	30	−	−	PROPN
ejpam-3654	146	31	(	(	PUNCT
ejpam-3654	146	32	1−	1−	NUM
ejpam-3654	146	33	p0)β	p0)β	NOUN
ejpam-3654	146	34	/	/	SYM
ejpam-3654	146	35	α	α	PROPN
ejpam-3654	146	36	zβ	zβ	PROPN
ejpam-3654	146	37	/	/	SYM
ejpam-3654	146	38	α	α	PROPN
ejpam-3654	146	39	(	(	PUNCT
ejpam-3654	146	40	t	t	PROPN
ejpam-3654	146	41	)	)	PUNCT
ejpam-3654	146	42	∫	∫	PROPN
ejpam-3654	147	1	∞	∞	PROPN
ejpam-3654	147	2	t	t	PROPN
ejpam-3654	147	3	(	(	PUNCT
ejpam-3654	147	4	1	1	NUM
ejpam-3654	147	5	r	r	NOUN
ejpam-3654	147	6	(	(	PUNCT
ejpam-3654	147	7	u	u	NOUN
ejpam-3654	147	8	)	)	PUNCT
ejpam-3654	147	9	∫	∫	PROPN
ejpam-3654	147	10	∞	∞	NUM
ejpam-3654	147	11	u	u	PROPN
ejpam-3654	147	12	q	q	X
ejpam-3654	147	13	(	(	PUNCT
ejpam-3654	147	14	s	s	NOUN
ejpam-3654	147	15	)	)	PUNCT
ejpam-3654	147	16	σβ	σβ	NOUN
ejpam-3654	147	17	(	(	PUNCT
ejpam-3654	147	18	s	s	X
ejpam-3654	147	19	)	)	PUNCT
ejpam-3654	147	20	sβ	sβ	NOUN
ejpam-3654	147	21	ds	ds	ADJ
ejpam-3654	147	22	)	)	PUNCT
ejpam-3654	147	23	1	1	PROPN
ejpam-3654	147	24	/	/	SYM
ejpam-3654	147	25	α	α	PRON
ejpam-3654	147	26	du	du	PROPN
ejpam-3654	147	27	,	,	PUNCT
ejpam-3654	147	28	(	(	PUNCT
ejpam-3654	147	29	18	18	NUM
ejpam-3654	147	30	)	)	PUNCT
ejpam-3654	147	31	for	for	ADP
ejpam-3654	147	32	all	all	DET
ejpam-3654	147	33	µ2	µ2	PROPN
ejpam-3654	147	34	∈	∈	PROPN
ejpam-3654	147	35	(	(	PUNCT
ejpam-3654	147	36	0	0	NUM
ejpam-3654	147	37	,	,	PUNCT
ejpam-3654	147	38	1	1	NUM
ejpam-3654	147	39	)	)	PUNCT
ejpam-3654	147	40	.	.	PUNCT
ejpam-3654	148	1	by	by	ADP
ejpam-3654	148	2	differentiating	differentiate	VERB
ejpam-3654	148	3	w	w	PROPN
ejpam-3654	148	4	and	and	CCONJ
ejpam-3654	148	5	using	use	VERB
ejpam-3654	148	6	(	(	PUNCT
ejpam-3654	148	7	15	15	NUM
ejpam-3654	148	8	)	)	PUNCT
ejpam-3654	148	9	and	and	CCONJ
ejpam-3654	148	10	(	(	PUNCT
ejpam-3654	148	11	18	18	NUM
ejpam-3654	148	12	)	)	PUNCT
ejpam-3654	148	13	,	,	PUNCT
ejpam-3654	148	14	we	we	PRON
ejpam-3654	148	15	find	find	VERB
ejpam-3654	148	16	w′	w′	PROPN
ejpam-3654	148	17	(	(	PUNCT
ejpam-3654	148	18	t	t	NOUN
ejpam-3654	148	19	)	)	PUNCT
ejpam-3654	148	20	=	=	NOUN
ejpam-3654	148	21	z′′	z′′	NOUN
ejpam-3654	148	22	(	(	PUNCT
ejpam-3654	148	23	t	t	PROPN
ejpam-3654	148	24	)	)	PUNCT
ejpam-3654	148	25	z	z	PROPN
ejpam-3654	148	26	(	(	PUNCT
ejpam-3654	148	27	t	t	PROPN
ejpam-3654	148	28	)	)	PUNCT
ejpam-3654	148	29	−	−	PROPN
ejpam-3654	149	1	(	(	PUNCT
ejpam-3654	149	2	z′	z′	NUM
ejpam-3654	149	3	(	(	PUNCT
ejpam-3654	149	4	t	t	PROPN
ejpam-3654	149	5	)	)	PUNCT
ejpam-3654	149	6	z	z	PROPN
ejpam-3654	149	7	(	(	PUNCT
ejpam-3654	149	8	t	t	PROPN
ejpam-3654	149	9	)	)	PUNCT
ejpam-3654	149	10	)	)	PUNCT
ejpam-3654	149	11	2	2	NUM
ejpam-3654	149	12	≤	≤	NOUN
ejpam-3654	149	13	−w2	−w2	PROPN
ejpam-3654	149	14	(	(	PUNCT
ejpam-3654	149	15	t)−	t)−	PROPN
ejpam-3654	149	16	(	(	PUNCT
ejpam-3654	149	17	1−	1−	NUM
ejpam-3654	149	18	p0)β	p0)β	NOUN
ejpam-3654	149	19	/	/	SYM
ejpam-3654	149	20	αm	αm	NOUN
ejpam-3654	149	21	(	(	PUNCT
ejpam-3654	149	22	β	β	NOUN
ejpam-3654	149	23	/	/	SYM
ejpam-3654	149	24	α)−1	α)−1	NOUN
ejpam-3654	149	25	∫	∫	NOUN
ejpam-3654	149	26	∞	∞	PROPN
ejpam-3654	149	27	t	t	PROPN
ejpam-3654	149	28	(	(	PUNCT
ejpam-3654	149	29	1	1	NUM
ejpam-3654	149	30	r	r	NOUN
ejpam-3654	149	31	(	(	PUNCT
ejpam-3654	149	32	u	u	NOUN
ejpam-3654	149	33	)	)	PUNCT
ejpam-3654	149	34	∫	∫	PROPN
ejpam-3654	150	1	∞	∞	NUM
ejpam-3654	151	1	u	u	PROPN
ejpam-3654	151	2	q	q	X
ejpam-3654	151	3	(	(	PUNCT
ejpam-3654	151	4	s	s	NOUN
ejpam-3654	151	5	)	)	PUNCT
ejpam-3654	151	6	σβ	σβ	NOUN
ejpam-3654	151	7	(	(	PUNCT
ejpam-3654	151	8	s	s	X
ejpam-3654	151	9	)	)	PUNCT
ejpam-3654	151	10	sβ	sβ	NOUN
ejpam-3654	151	11	ds	ds	ADJ
ejpam-3654	151	12	)	)	PUNCT
ejpam-3654	151	13	1	1	PROPN
ejpam-3654	151	14	/	/	SYM
ejpam-3654	151	15	α	α	PRON
ejpam-3654	151	16	du	du	PROPN
ejpam-3654	151	17	,	,	PUNCT
ejpam-3654	151	18	(	(	PUNCT
ejpam-3654	151	19	19	19	NUM
ejpam-3654	151	20	)	)	PUNCT
ejpam-3654	151	21	hence	hence	ADV
ejpam-3654	151	22	w′	w′	PROPN
ejpam-3654	151	23	(	(	PUNCT
ejpam-3654	151	24	t	t	PROPN
ejpam-3654	151	25	)	)	PUNCT
ejpam-3654	151	26	+	+	PROPN
ejpam-3654	151	27	q2	q2	NOUN
ejpam-3654	151	28	(	(	PUNCT
ejpam-3654	151	29	t	t	PROPN
ejpam-3654	151	30	)	)	PUNCT
ejpam-3654	151	31	+	+	NUM
ejpam-3654	151	32	w2	w2	NOUN
ejpam-3654	151	33	(	(	PUNCT
ejpam-3654	151	34	t	t	PROPN
ejpam-3654	151	35	)	)	PUNCT
ejpam-3654	151	36	≤	≤	NOUN
ejpam-3654	151	37	0	0	NUM
ejpam-3654	151	38	.	.	PUNCT
ejpam-3654	152	1	the	the	DET
ejpam-3654	152	2	proof	proof	NOUN
ejpam-3654	152	3	is	be	AUX
ejpam-3654	152	4	complete	complete	ADJ
ejpam-3654	152	5	.	.	PUNCT
ejpam-3654	153	1	theorem	theorem	NOUN
ejpam-3654	153	2	2	2	NUM
ejpam-3654	153	3	.	.	X
ejpam-3654	153	4	assume	assume	VERB
ejpam-3654	153	5	that	that	SCONJ
ejpam-3654	153	6	lim	lim	PROPN
ejpam-3654	153	7	inf	inf	PROPN
ejpam-3654	153	8	t→∞	t→∞	ADP
ejpam-3654	153	9	1	1	NUM
ejpam-3654	153	10	q̃1	q̃1	PROPN
ejpam-3654	153	11	(	(	PUNCT
ejpam-3654	153	12	t	t	PROPN
ejpam-3654	153	13	)	)	PUNCT
ejpam-3654	153	14	∫	∫	PROPN
ejpam-3654	153	15	∞	∞	PROPN
ejpam-3654	153	16	t	t	PROPN
ejpam-3654	153	17	r1	r1	PROPN
ejpam-3654	153	18	(	(	PUNCT
ejpam-3654	153	19	s	s	X
ejpam-3654	153	20	)	)	PUNCT
ejpam-3654	153	21	q̃	q̃	PROPN
ejpam-3654	153	22	α+1	α+1	NUM
ejpam-3654	153	23	α	α	NOUN
ejpam-3654	153	24	1	1	NUM
ejpam-3654	153	25	(	(	PUNCT
ejpam-3654	153	26	s	s	X
ejpam-3654	153	27	)	)	PUNCT
ejpam-3654	153	28	ds	ds	VERB
ejpam-3654	153	29	>	>	PUNCT
ejpam-3654	153	30	α	α	PROPN
ejpam-3654	153	31	(	(	PUNCT
ejpam-3654	153	32	α+	α+	NOUN
ejpam-3654	153	33	1	1	NUM
ejpam-3654	153	34	)	)	PUNCT
ejpam-3654	153	35	α+1	α+1	NUM
ejpam-3654	153	36	α	α	PROPN
ejpam-3654	153	37	(	(	PUNCT
ejpam-3654	153	38	20	20	NUM
ejpam-3654	153	39	)	)	PUNCT
ejpam-3654	153	40	and	and	CCONJ
ejpam-3654	153	41	lim	lim	PROPN
ejpam-3654	153	42	inf	inf	PROPN
ejpam-3654	153	43	t→∞	t→∞	PRON
ejpam-3654	153	44	1	1	NUM
ejpam-3654	153	45	q̃2	q̃2	PROPN
ejpam-3654	153	46	(	(	PUNCT
ejpam-3654	153	47	t	t	PROPN
ejpam-3654	153	48	)	)	PUNCT
ejpam-3654	154	1	∫	∫	PROPN
ejpam-3654	155	1	∞	∞	NUM
ejpam-3654	155	2	t0	t0	PROPN
ejpam-3654	155	3	q̃2	q̃2	NOUN
ejpam-3654	155	4	2	2	NUM
ejpam-3654	155	5	(	(	PUNCT
ejpam-3654	155	6	s	s	X
ejpam-3654	155	7	)	)	PUNCT
ejpam-3654	155	8	ds	ds	X
ejpam-3654	155	9	>	>	X
ejpam-3654	155	10	1	1	NUM
ejpam-3654	155	11	4	4	NUM
ejpam-3654	155	12	,	,	PUNCT
ejpam-3654	155	13	(	(	PUNCT
ejpam-3654	155	14	21	21	NUM
ejpam-3654	155	15	)	)	PUNCT
ejpam-3654	155	16	where	where	SCONJ
ejpam-3654	155	17	q̃1	q̃1	PROPN
ejpam-3654	155	18	(	(	PUNCT
ejpam-3654	155	19	t	t	PROPN
ejpam-3654	155	20	)	)	PUNCT
ejpam-3654	155	21	=	=	SYM
ejpam-3654	155	22	∫	∫	PROPN
ejpam-3654	156	1	∞	∞	PROPN
ejpam-3654	156	2	t	t	PROPN
ejpam-3654	156	3	q1	q1	PROPN
ejpam-3654	156	4	(	(	PUNCT
ejpam-3654	156	5	s	s	NOUN
ejpam-3654	156	6	)	)	PUNCT
ejpam-3654	156	7	ds	ds	ADJ
ejpam-3654	156	8	and	and	CCONJ
ejpam-3654	156	9	q̃2	q̃2	PROPN
ejpam-3654	156	10	(	(	PUNCT
ejpam-3654	156	11	t	t	NOUN
ejpam-3654	156	12	)	)	PUNCT
ejpam-3654	156	13	=	=	SYM
ejpam-3654	157	1	∫	∫	PROPN
ejpam-3654	157	2	∞	∞	PROPN
ejpam-3654	157	3	t	t	PROPN
ejpam-3654	157	4	q2	q2	NOUN
ejpam-3654	157	5	(	(	PUNCT
ejpam-3654	157	6	s	s	NOUN
ejpam-3654	157	7	)	)	PUNCT
ejpam-3654	157	8	ds	ds	NOUN
ejpam-3654	157	9	.	.	PUNCT
ejpam-3654	158	1	(	(	PUNCT
ejpam-3654	158	2	22	22	NUM
ejpam-3654	158	3	)	)	PUNCT
ejpam-3654	158	4	then	then	ADV
ejpam-3654	158	5	,	,	PUNCT
ejpam-3654	158	6	(	(	PUNCT
ejpam-3654	158	7	1	1	X
ejpam-3654	158	8	)	)	PUNCT
ejpam-3654	158	9	is	be	AUX
ejpam-3654	158	10	oscillatory	oscillatory	ADJ
ejpam-3654	158	11	.	.	PUNCT
ejpam-3654	159	1	proof	proof	NOUN
ejpam-3654	159	2	.	.	PUNCT
ejpam-3654	160	1	assume	assume	VERB
ejpam-3654	160	2	to	to	ADP
ejpam-3654	160	3	the	the	DET
ejpam-3654	160	4	contrary	contrary	NOUN
ejpam-3654	160	5	that	that	SCONJ
ejpam-3654	160	6	(	(	PUNCT
ejpam-3654	160	7	1	1	X
ejpam-3654	160	8	)	)	PUNCT
ejpam-3654	160	9	has	have	VERB
ejpam-3654	160	10	a	a	DET
ejpam-3654	160	11	nonoscillatory	nonoscillatory	ADJ
ejpam-3654	160	12	solution	solution	NOUN
ejpam-3654	160	13	in	in	ADP
ejpam-3654	160	14	[	[	X
ejpam-3654	160	15	t0,∞	t0,∞	NUM
ejpam-3654	160	16	)	)	PUNCT
ejpam-3654	160	17	.	.	PUNCT
ejpam-3654	161	1	without	without	ADP
ejpam-3654	161	2	loss	loss	NOUN
ejpam-3654	161	3	of	of	ADP
ejpam-3654	161	4	generality	generality	NOUN
ejpam-3654	161	5	,	,	PUNCT
ejpam-3654	161	6	we	we	PRON
ejpam-3654	161	7	let	let	VERB
ejpam-3654	161	8	x	x	PART
ejpam-3654	161	9	be	be	AUX
ejpam-3654	161	10	an	an	DET
ejpam-3654	161	11	eventually	eventually	ADV
ejpam-3654	161	12	positive	positive	ADJ
ejpam-3654	161	13	solution	solution	NOUN
ejpam-3654	161	14	of	of	ADP
ejpam-3654	161	15	(	(	PUNCT
ejpam-3654	161	16	1	1	NUM
ejpam-3654	161	17	)	)	PUNCT
ejpam-3654	161	18	.	.	PUNCT
ejpam-3654	162	1	then	then	ADV
ejpam-3654	162	2	,	,	PUNCT
ejpam-3654	162	3	there	there	PRON
ejpam-3654	162	4	exists	exist	VERB
ejpam-3654	162	5	a	a	DET
ejpam-3654	162	6	t1	t1	NOUN
ejpam-3654	162	7	≥	≥	NOUN
ejpam-3654	162	8	t0	t0	NOUN
ejpam-3654	162	9	such	such	ADJ
ejpam-3654	162	10	that	that	SCONJ
ejpam-3654	162	11	x	x	X
ejpam-3654	162	12	(	(	PUNCT
ejpam-3654	162	13	t	t	PROPN
ejpam-3654	162	14	)	)	PUNCT
ejpam-3654	162	15	>	>	X
ejpam-3654	162	16	0	0	NUM
ejpam-3654	162	17	,	,	PUNCT
ejpam-3654	162	18	x	x	X
ejpam-3654	162	19	(	(	PUNCT
ejpam-3654	162	20	τ	τ	X
ejpam-3654	162	21	(	(	PUNCT
ejpam-3654	162	22	t	t	PROPN
ejpam-3654	162	23	)	)	PUNCT
ejpam-3654	162	24	)	)	PUNCT
ejpam-3654	162	25	>	>	X
ejpam-3654	162	26	0	0	PUNCT
ejpam-3654	163	1	and	and	CCONJ
ejpam-3654	163	2	x	x	SYM
ejpam-3654	163	3	(	(	PUNCT
ejpam-3654	163	4	σ	σ	PROPN
ejpam-3654	163	5	(	(	PUNCT
ejpam-3654	163	6	t	t	PROPN
ejpam-3654	163	7	)	)	PUNCT
ejpam-3654	163	8	)	)	PUNCT
ejpam-3654	163	9	>	>	X
ejpam-3654	163	10	0	0	PUNCT
ejpam-3654	164	1	for	for	ADP
ejpam-3654	164	2	t	t	PROPN
ejpam-3654	164	3	≥	≥	NUM
ejpam-3654	164	4	t1	t1	NOUN
ejpam-3654	164	5	.	.	PUNCT
ejpam-3654	165	1	from	from	ADP
ejpam-3654	165	2	lemma	lemma	PROPN
ejpam-3654	165	3	5	5	NUM
ejpam-3654	165	4	o.	o.	NOUN
ejpam-3654	165	5	moaaz	moaaz	PROPN
ejpam-3654	165	6	,	,	PUNCT
ejpam-3654	165	7	c.	c.	PROPN
ejpam-3654	165	8	cesarano	cesarano	PROPN
ejpam-3654	165	9	,	,	PUNCT
ejpam-3654	165	10	a.	a.	NOUN
ejpam-3654	165	11	muhib	muhib	NOUN
ejpam-3654	165	12	/	/	SYM
ejpam-3654	165	13	eur	eur	PROPN
ejpam-3654	165	14	.	.	PUNCT
ejpam-3654	166	1	j.	j.	PROPN
ejpam-3654	166	2	pure	pure	PROPN
ejpam-3654	166	3	appl	appl	PROPN
ejpam-3654	166	4	.	.	PROPN
ejpam-3654	166	5	math	math	PROPN
ejpam-3654	166	6	,	,	PUNCT
ejpam-3654	166	7	13	13	NUM
ejpam-3654	166	8	(	(	PUNCT
ejpam-3654	166	9	2	2	NUM
ejpam-3654	166	10	)	)	PUNCT
ejpam-3654	166	11	(	(	PUNCT
ejpam-3654	166	12	2020	2020	NUM
ejpam-3654	166	13	)	)	PUNCT
ejpam-3654	166	14	,	,	PUNCT
ejpam-3654	166	15	185	185	NUM
ejpam-3654	166	16	-	-	SYM
ejpam-3654	166	17	199	199	NUM
ejpam-3654	166	18	192	192	NUM
ejpam-3654	166	19	there	there	PRON
ejpam-3654	166	20	is	be	VERB
ejpam-3654	166	21	two	two	NUM
ejpam-3654	166	22	cases	case	NOUN
ejpam-3654	166	23	.	.	PUNCT
ejpam-3654	167	1	for	for	ADP
ejpam-3654	167	2	case	case	NOUN
ejpam-3654	167	3	(	(	PUNCT
ejpam-3654	167	4	c1	c1	NOUN
ejpam-3654	167	5	)	)	PUNCT
ejpam-3654	167	6	.	.	PUNCT
ejpam-3654	168	1	using	use	VERB
ejpam-3654	168	2	lemma	lemma	PROPN
ejpam-3654	168	3	6	6	NUM
ejpam-3654	168	4	,	,	PUNCT
ejpam-3654	168	5	we	we	PRON
ejpam-3654	168	6	obtain	obtain	VERB
ejpam-3654	168	7	(	(	PUNCT
ejpam-3654	168	8	10	10	NUM
ejpam-3654	168	9	)	)	PUNCT
ejpam-3654	168	10	holds	hold	NOUN
ejpam-3654	168	11	.	.	PUNCT
ejpam-3654	169	1	integrating	integrate	VERB
ejpam-3654	169	2	(	(	PUNCT
ejpam-3654	169	3	10	10	NUM
ejpam-3654	169	4	)	)	PUNCT
ejpam-3654	169	5	from	from	ADP
ejpam-3654	169	6	t	t	PROPN
ejpam-3654	169	7	to	to	ADP
ejpam-3654	169	8	l	l	NOUN
ejpam-3654	169	9	,	,	PUNCT
ejpam-3654	169	10	we	we	PRON
ejpam-3654	169	11	get	get	VERB
ejpam-3654	169	12	ω	ω	PROPN
ejpam-3654	169	13	(	(	PUNCT
ejpam-3654	169	14	l)−	l)−	PROPN
ejpam-3654	169	15	ω	ω	PROPN
ejpam-3654	169	16	(	(	PUNCT
ejpam-3654	169	17	t	t	PROPN
ejpam-3654	169	18	)	)	PUNCT
ejpam-3654	170	1	+	+	NUM
ejpam-3654	170	2	∫	∫	PROPN
ejpam-3654	170	3	l	l	PROPN
ejpam-3654	170	4	t	t	PROPN
ejpam-3654	170	5	q1	q1	PROPN
ejpam-3654	170	6	(	(	PUNCT
ejpam-3654	170	7	s	s	NOUN
ejpam-3654	170	8	)	)	PUNCT
ejpam-3654	170	9	ds+	ds+	ADJ
ejpam-3654	170	10	∫	∫	PROPN
ejpam-3654	170	11	l	l	PROPN
ejpam-3654	170	12	t	t	PROPN
ejpam-3654	170	13	r1	r1	PROPN
ejpam-3654	170	14	(	(	PUNCT
ejpam-3654	170	15	s)ω	s)ω	X
ejpam-3654	170	16	α+1	α+1	NUM
ejpam-3654	170	17	α	α	NOUN
ejpam-3654	170	18	(	(	PUNCT
ejpam-3654	170	19	s	s	NOUN
ejpam-3654	170	20	)	)	PUNCT
ejpam-3654	170	21	ds	ds	ADJ
ejpam-3654	170	22	≤	≤	NOUN
ejpam-3654	170	23	0	0	NUM
ejpam-3654	170	24	.	.	PUNCT
ejpam-3654	171	1	letting	let	VERB
ejpam-3654	171	2	l→∞	l→∞	NUM
ejpam-3654	171	3	and	and	CCONJ
ejpam-3654	171	4	using	use	VERB
ejpam-3654	171	5	ω	ω	PROPN
ejpam-3654	171	6	>	>	X
ejpam-3654	171	7	0	0	PROPN
ejpam-3654	171	8	and	and	CCONJ
ejpam-3654	171	9	ω′	ω′	X
ejpam-3654	171	10	<	<	X
ejpam-3654	171	11	0	0	PROPN
ejpam-3654	171	12	,	,	PUNCT
ejpam-3654	171	13	we	we	PRON
ejpam-3654	171	14	have	have	VERB
ejpam-3654	171	15	ω	ω	NUM
ejpam-3654	171	16	(	(	PUNCT
ejpam-3654	171	17	t	t	PROPN
ejpam-3654	171	18	)	)	PUNCT
ejpam-3654	171	19	≥	≥	NOUN
ejpam-3654	172	1	q̃1	q̃1	INTJ
ejpam-3654	172	2	(	(	PUNCT
ejpam-3654	172	3	t	t	PROPN
ejpam-3654	172	4	)	)	PUNCT
ejpam-3654	172	5	+	+	NUM
ejpam-3654	172	6	∫	∫	PROPN
ejpam-3654	172	7	∞	∞	PROPN
ejpam-3654	172	8	t	t	PROPN
ejpam-3654	172	9	r1	r1	PROPN
ejpam-3654	172	10	(	(	PUNCT
ejpam-3654	172	11	s)ω	s)ω	X
ejpam-3654	172	12	α+1	α+1	NUM
ejpam-3654	172	13	α	α	NOUN
ejpam-3654	172	14	(	(	PUNCT
ejpam-3654	172	15	s	s	NOUN
ejpam-3654	172	16	)	)	PUNCT
ejpam-3654	172	17	ds	ds	NOUN
ejpam-3654	172	18	.	.	PUNCT
ejpam-3654	173	1	(	(	PUNCT
ejpam-3654	173	2	23	23	NUM
ejpam-3654	173	3	)	)	PUNCT
ejpam-3654	173	4	this	this	PRON
ejpam-3654	173	5	implies	imply	VERB
ejpam-3654	173	6	ω	ω	PROPN
ejpam-3654	173	7	(	(	PUNCT
ejpam-3654	173	8	t	t	NOUN
ejpam-3654	173	9	)	)	PUNCT
ejpam-3654	173	10	q̃1	q̃1	PROPN
ejpam-3654	173	11	(	(	PUNCT
ejpam-3654	173	12	t	t	PROPN
ejpam-3654	173	13	)	)	PUNCT
ejpam-3654	173	14	≥	≥	NOUN
ejpam-3654	173	15	1	1	NUM
ejpam-3654	173	16	+	+	CCONJ
ejpam-3654	173	17	1	1	NUM
ejpam-3654	173	18	q̃1	q̃1	PROPN
ejpam-3654	173	19	(	(	PUNCT
ejpam-3654	173	20	t	t	PROPN
ejpam-3654	173	21	)	)	PUNCT
ejpam-3654	173	22	∫	∫	PROPN
ejpam-3654	173	23	∞	∞	PROPN
ejpam-3654	173	24	t	t	PROPN
ejpam-3654	173	25	r1	r1	PROPN
ejpam-3654	173	26	(	(	PUNCT
ejpam-3654	173	27	s	s	X
ejpam-3654	173	28	)	)	PUNCT
ejpam-3654	173	29	q̃	q̃	PROPN
ejpam-3654	173	30	α+1	α+1	NUM
ejpam-3654	173	31	α	α	NOUN
ejpam-3654	173	32	1	1	NUM
ejpam-3654	173	33	(	(	PUNCT
ejpam-3654	173	34	s	s	NOUN
ejpam-3654	173	35	)	)	PUNCT
ejpam-3654	173	36	(	(	PUNCT
ejpam-3654	173	37	ω	ω	X
ejpam-3654	173	38	(	(	PUNCT
ejpam-3654	173	39	s	s	NOUN
ejpam-3654	173	40	)	)	PUNCT
ejpam-3654	173	41	q̃1	q̃1	PROPN
ejpam-3654	173	42	(	(	PUNCT
ejpam-3654	173	43	s	s	NOUN
ejpam-3654	173	44	)	)	PUNCT
ejpam-3654	173	45	)	)	PUNCT
ejpam-3654	174	1	α+1	α+1	NUM
ejpam-3654	174	2	α	α	PRON
ejpam-3654	174	3	ds	ds	NOUN
ejpam-3654	174	4	.	.	PUNCT
ejpam-3654	174	5	(	(	PUNCT
ejpam-3654	174	6	24	24	NUM
ejpam-3654	174	7	)	)	PUNCT
ejpam-3654	174	8	let	let	VERB
ejpam-3654	174	9	λ	λ	X
ejpam-3654	174	10	=	=	PRON
ejpam-3654	174	11	inft≥t	inft≥t	PROPN
ejpam-3654	174	12	ω	ω	X
ejpam-3654	174	13	(	(	PUNCT
ejpam-3654	174	14	t	t	PROPN
ejpam-3654	174	15	)	)	PUNCT
ejpam-3654	174	16	/q̃1	/q̃1	PUNCT
ejpam-3654	174	17	(	(	PUNCT
ejpam-3654	174	18	t	t	PROPN
ejpam-3654	174	19	)	)	PUNCT
ejpam-3654	174	20	.	.	PUNCT
ejpam-3654	175	1	then	then	ADV
ejpam-3654	175	2	obviously	obviously	ADV
ejpam-3654	175	3	λ	λ	X
ejpam-3654	175	4	≥	≥	NUM
ejpam-3654	175	5	1	1	NUM
ejpam-3654	175	6	.	.	PUNCT
ejpam-3654	176	1	thus	thus	ADV
ejpam-3654	176	2	,	,	PUNCT
ejpam-3654	176	3	from	from	ADP
ejpam-3654	176	4	(	(	PUNCT
ejpam-3654	176	5	20	20	NUM
ejpam-3654	176	6	)	)	PUNCT
ejpam-3654	176	7	and	and	CCONJ
ejpam-3654	176	8	(	(	PUNCT
ejpam-3654	176	9	24	24	NUM
ejpam-3654	176	10	)	)	PUNCT
ejpam-3654	176	11	we	we	PRON
ejpam-3654	176	12	see	see	VERB
ejpam-3654	176	13	that	that	SCONJ
ejpam-3654	176	14	λ	λ	PROPN
ejpam-3654	176	15	≥	≥	PRON
ejpam-3654	176	16	1	1	NUM
ejpam-3654	176	17	+	+	CCONJ
ejpam-3654	176	18	α	α	PROPN
ejpam-3654	176	19	(	(	PUNCT
ejpam-3654	176	20	λ	λ	X
ejpam-3654	176	21	α+	α+	PUNCT
ejpam-3654	176	22	1	1	NUM
ejpam-3654	176	23	)	)	PUNCT
ejpam-3654	176	24	(	(	PUNCT
ejpam-3654	176	25	α+1)/α	α+1)/α	NOUN
ejpam-3654	176	26	or	or	CCONJ
ejpam-3654	176	27	λ	λ	X
ejpam-3654	176	28	α+	α+	PUNCT
ejpam-3654	176	29	1	1	NUM
ejpam-3654	176	30	≥	≥	NOUN
ejpam-3654	176	31	1	1	NUM
ejpam-3654	176	32	α+	α+	SYM
ejpam-3654	176	33	1	1	NUM
ejpam-3654	176	34	+	+	NUM
ejpam-3654	176	35	α	α	NOUN
ejpam-3654	176	36	α+	α+	PUNCT
ejpam-3654	176	37	1	1	NUM
ejpam-3654	176	38	(	(	PUNCT
ejpam-3654	176	39	λ	λ	X
ejpam-3654	176	40	α+	α+	X
ejpam-3654	176	41	1	1	NUM
ejpam-3654	176	42	)	)	PUNCT
ejpam-3654	176	43	(	(	PUNCT
ejpam-3654	176	44	α+1)/α	α+1)/α	PROPN
ejpam-3654	176	45	,	,	PUNCT
ejpam-3654	176	46	which	which	PRON
ejpam-3654	176	47	contradicts	contradict	VERB
ejpam-3654	176	48	the	the	DET
ejpam-3654	176	49	admissible	admissible	ADJ
ejpam-3654	176	50	value	value	NOUN
ejpam-3654	176	51	of	of	ADP
ejpam-3654	176	52	λ	λ	PROPN
ejpam-3654	176	53	≥	≥	NOUN
ejpam-3654	176	54	1	1	NUM
ejpam-3654	176	55	and	and	CCONJ
ejpam-3654	176	56	α	α	PRON
ejpam-3654	176	57	>	>	X
ejpam-3654	176	58	0	0	PROPN
ejpam-3654	176	59	.	.	PUNCT
ejpam-3654	177	1	the	the	DET
ejpam-3654	177	2	proof	proof	NOUN
ejpam-3654	177	3	of	of	ADP
ejpam-3654	177	4	the	the	DET
ejpam-3654	177	5	case	case	NOUN
ejpam-3654	177	6	where	where	SCONJ
ejpam-3654	177	7	(	(	PUNCT
ejpam-3654	177	8	c2	c2	PROPN
ejpam-3654	177	9	)	)	PUNCT
ejpam-3654	177	10	holds	hold	VERB
ejpam-3654	177	11	is	be	AUX
ejpam-3654	177	12	the	the	DET
ejpam-3654	177	13	same	same	ADJ
ejpam-3654	177	14	as	as	ADP
ejpam-3654	177	15	that	that	PRON
ejpam-3654	177	16	of	of	ADP
ejpam-3654	177	17	case	case	NOUN
ejpam-3654	177	18	(	(	PUNCT
ejpam-3654	177	19	c1	c1	NOUN
ejpam-3654	177	20	)	)	PUNCT
ejpam-3654	177	21	.	.	PUNCT
ejpam-3654	178	1	therefore	therefore	ADV
ejpam-3654	178	2	,	,	PUNCT
ejpam-3654	178	3	the	the	DET
ejpam-3654	178	4	proof	proof	NOUN
ejpam-3654	178	5	is	be	AUX
ejpam-3654	178	6	complete	complete	ADJ
ejpam-3654	178	7	.	.	PUNCT
ejpam-3654	179	1	define	define	VERB
ejpam-3654	179	2	a	a	DET
ejpam-3654	179	3	sequence	sequence	NOUN
ejpam-3654	179	4	of	of	ADP
ejpam-3654	179	5	functions	function	NOUN
ejpam-3654	179	6	{	{	PUNCT
ejpam-3654	179	7	un	un	PROPN
ejpam-3654	179	8	(	(	PUNCT
ejpam-3654	179	9	t)}∞n=0	t)}∞n=0	NUM
ejpam-3654	179	10	and	and	CCONJ
ejpam-3654	179	11	{	{	PUNCT
ejpam-3654	179	12	vn	vn	X
ejpam-3654	179	13	(	(	PUNCT
ejpam-3654	179	14	t)}∞n=0	t)}∞n=0	NOUN
ejpam-3654	179	15	as	as	ADP
ejpam-3654	179	16	u0	u0	ADJ
ejpam-3654	179	17	(	(	PUNCT
ejpam-3654	179	18	t	t	NOUN
ejpam-3654	179	19	)	)	PUNCT
ejpam-3654	180	1	=	=	SYM
ejpam-3654	180	2	q̃1	q̃1	PROPN
ejpam-3654	180	3	(	(	PUNCT
ejpam-3654	180	4	t	t	NOUN
ejpam-3654	180	5	)	)	PUNCT
ejpam-3654	180	6	,	,	PUNCT
ejpam-3654	180	7	and	and	CCONJ
ejpam-3654	180	8	v0	v0	PROPN
ejpam-3654	180	9	(	(	PUNCT
ejpam-3654	180	10	t	t	PROPN
ejpam-3654	180	11	)	)	PUNCT
ejpam-3654	180	12	=	=	SYM
ejpam-3654	180	13	q̃2	q̃2	PROPN
ejpam-3654	180	14	(	(	PUNCT
ejpam-3654	180	15	t	t	PROPN
ejpam-3654	180	16	)	)	PUNCT
ejpam-3654	180	17	,	,	PUNCT
ejpam-3654	180	18	un	un	PROPN
ejpam-3654	180	19	(	(	PUNCT
ejpam-3654	180	20	t	t	PROPN
ejpam-3654	180	21	)	)	PUNCT
ejpam-3654	180	22	=	=	PRON
ejpam-3654	180	23	u0	u0	ADJ
ejpam-3654	180	24	(	(	PUNCT
ejpam-3654	180	25	t	t	PROPN
ejpam-3654	180	26	)	)	PUNCT
ejpam-3654	180	27	+	+	NUM
ejpam-3654	180	28	∫∞	∫∞	NOUN
ejpam-3654	180	29	t	t	PROPN
ejpam-3654	180	30	r1	r1	PROPN
ejpam-3654	180	31	(	(	PUNCT
ejpam-3654	180	32	t)u	t)u	X
ejpam-3654	180	33	(	(	PUNCT
ejpam-3654	180	34	α+1)/α	α+1)/α	PROPN
ejpam-3654	180	35	n−1	n−1	PROPN
ejpam-3654	180	36	(	(	PUNCT
ejpam-3654	180	37	s	s	NOUN
ejpam-3654	180	38	)	)	PUNCT
ejpam-3654	180	39	ds	ds	ADJ
ejpam-3654	180	40	,	,	PUNCT
ejpam-3654	180	41	n	n	CCONJ
ejpam-3654	180	42	>	>	X
ejpam-3654	180	43	1	1	NUM
ejpam-3654	180	44	,	,	PUNCT
ejpam-3654	180	45	vn	vn	X
ejpam-3654	180	46	(	(	PUNCT
ejpam-3654	180	47	t	t	PROPN
ejpam-3654	180	48	)	)	PUNCT
ejpam-3654	180	49	=	=	SYM
ejpam-3654	180	50	v0	v0	NOUN
ejpam-3654	180	51	(	(	PUNCT
ejpam-3654	180	52	t	t	PROPN
ejpam-3654	180	53	)	)	PUNCT
ejpam-3654	181	1	+	+	NUM
ejpam-3654	181	2	∫∞	∫∞	NOUN
ejpam-3654	181	3	t	t	PROPN
ejpam-3654	181	4	v	v	PROPN
ejpam-3654	181	5	(	(	PUNCT
ejpam-3654	181	6	α+1)/α	α+1)/α	PROPN
ejpam-3654	181	7	n−1	n−1	PROPN
ejpam-3654	181	8	(	(	PUNCT
ejpam-3654	181	9	s	s	NOUN
ejpam-3654	181	10	)	)	PUNCT
ejpam-3654	181	11	ds	ds	ADJ
ejpam-3654	181	12	,	,	PUNCT
ejpam-3654	181	13	n	n	CCONJ
ejpam-3654	181	14	>	>	X
ejpam-3654	181	15	1	1	NUM
ejpam-3654	181	16	,	,	PUNCT
ejpam-3654	181	17	(	(	PUNCT
ejpam-3654	181	18	25	25	NUM
ejpam-3654	181	19	)	)	PUNCT
ejpam-3654	181	20	where	where	SCONJ
ejpam-3654	181	21	q̃1	q̃1	PROPN
ejpam-3654	181	22	and	and	CCONJ
ejpam-3654	181	23	q̃2	q̃2	PROPN
ejpam-3654	181	24	defined	define	VERB
ejpam-3654	181	25	as	as	ADP
ejpam-3654	181	26	in	in	ADP
ejpam-3654	181	27	(	(	PUNCT
ejpam-3654	181	28	22	22	NUM
ejpam-3654	181	29	)	)	PUNCT
ejpam-3654	181	30	.	.	PUNCT
ejpam-3654	182	1	we	we	PRON
ejpam-3654	182	2	see	see	VERB
ejpam-3654	182	3	by	by	ADP
ejpam-3654	182	4	induction	induction	NOUN
ejpam-3654	182	5	that	that	PRON
ejpam-3654	182	6	un	un	PROPN
ejpam-3654	182	7	(	(	PUNCT
ejpam-3654	182	8	t	t	PROPN
ejpam-3654	182	9	)	)	PUNCT
ejpam-3654	182	10	≤	≤	NUM
ejpam-3654	182	11	un+1	un+1	PROPN
ejpam-3654	182	12	(	(	PUNCT
ejpam-3654	182	13	t	t	PROPN
ejpam-3654	182	14	)	)	PUNCT
ejpam-3654	182	15	and	and	CCONJ
ejpam-3654	182	16	vn	vn	PROPN
ejpam-3654	182	17	(	(	PUNCT
ejpam-3654	182	18	t	t	PROPN
ejpam-3654	182	19	)	)	PUNCT
ejpam-3654	182	20	≤	≤	NUM
ejpam-3654	182	21	vn+1	vn+1	PROPN
ejpam-3654	182	22	(	(	PUNCT
ejpam-3654	182	23	t	t	PROPN
ejpam-3654	182	24	)	)	PUNCT
ejpam-3654	182	25	for	for	ADP
ejpam-3654	182	26	t	t	PROPN
ejpam-3654	182	27	≥	≥	PROPN
ejpam-3654	182	28	t0	t0	PROPN
ejpam-3654	182	29	,	,	PUNCT
ejpam-3654	182	30	n	n	PROPN
ejpam-3654	182	31	>	>	X
ejpam-3654	182	32	1	1	X
ejpam-3654	182	33	.	.	PUNCT
ejpam-3654	182	34	theorem	theorem	NOUN
ejpam-3654	182	35	3	3	X
ejpam-3654	182	36	.	.	PUNCT
ejpam-3654	183	1	let	let	VERB
ejpam-3654	183	2	un	un	PROPN
ejpam-3654	183	3	(	(	PUNCT
ejpam-3654	183	4	t	t	PROPN
ejpam-3654	183	5	)	)	PUNCT
ejpam-3654	183	6	and	and	CCONJ
ejpam-3654	183	7	vn	vn	PROPN
ejpam-3654	183	8	(	(	PUNCT
ejpam-3654	183	9	t	t	PROPN
ejpam-3654	183	10	)	)	PUNCT
ejpam-3654	183	11	be	be	AUX
ejpam-3654	183	12	defined	define	VERB
ejpam-3654	183	13	as	as	ADP
ejpam-3654	183	14	in	in	ADP
ejpam-3654	183	15	(	(	PUNCT
ejpam-3654	183	16	25	25	NUM
ejpam-3654	183	17	)	)	PUNCT
ejpam-3654	183	18	.	.	PUNCT
ejpam-3654	184	1	if	if	SCONJ
ejpam-3654	184	2	lim	lim	PROPN
ejpam-3654	184	3	sup	sup	NOUN
ejpam-3654	184	4	t→∞	t→∞	NUM
ejpam-3654	184	5	(	(	PUNCT
ejpam-3654	184	6	µ1	µ1	PROPN
ejpam-3654	184	7	t	t	PROPN
ejpam-3654	184	8	3	3	NUM
ejpam-3654	184	9	6r1	6r1	NUM
ejpam-3654	184	10	/	/	SYM
ejpam-3654	184	11	α	α	PROPN
ejpam-3654	184	12	(	(	PUNCT
ejpam-3654	184	13	t	t	PROPN
ejpam-3654	184	14	)	)	PUNCT
ejpam-3654	184	15	)	)	PUNCT
ejpam-3654	185	1	α	α	PROPN
ejpam-3654	185	2	un	un	PROPN
ejpam-3654	185	3	(	(	PUNCT
ejpam-3654	185	4	t	t	PROPN
ejpam-3654	185	5	)	)	PUNCT
ejpam-3654	185	6	>	>	X
ejpam-3654	185	7	1	1	NUM
ejpam-3654	185	8	(	(	PUNCT
ejpam-3654	185	9	26	26	NUM
ejpam-3654	185	10	)	)	PUNCT
ejpam-3654	185	11	and	and	CCONJ
ejpam-3654	185	12	lim	lim	PROPN
ejpam-3654	185	13	sup	sup	NOUN
ejpam-3654	185	14	t→∞	t→∞	PRON
ejpam-3654	185	15	λtvn	λtvn	NOUN
ejpam-3654	185	16	(	(	PUNCT
ejpam-3654	185	17	t	t	NOUN
ejpam-3654	185	18	)	)	PUNCT
ejpam-3654	185	19	>	>	X
ejpam-3654	186	1	1	1	NUM
ejpam-3654	186	2	,	,	PUNCT
ejpam-3654	186	3	(	(	PUNCT
ejpam-3654	186	4	27	27	NUM
ejpam-3654	186	5	)	)	PUNCT
ejpam-3654	186	6	for	for	ADP
ejpam-3654	186	7	some	some	DET
ejpam-3654	186	8	n	n	CCONJ
ejpam-3654	186	9	,	,	PUNCT
ejpam-3654	186	10	then	then	ADV
ejpam-3654	186	11	(	(	PUNCT
ejpam-3654	186	12	1)is	1)is	NUM
ejpam-3654	186	13	oscillatory	oscillatory	NOUN
ejpam-3654	186	14	.	.	PUNCT
ejpam-3654	187	1	o.	o.	PROPN
ejpam-3654	187	2	moaaz	moaaz	PROPN
ejpam-3654	187	3	,	,	PUNCT
ejpam-3654	187	4	c.	c.	PROPN
ejpam-3654	187	5	cesarano	cesarano	PROPN
ejpam-3654	187	6	,	,	PUNCT
ejpam-3654	187	7	a.	a.	NOUN
ejpam-3654	187	8	muhib	muhib	NOUN
ejpam-3654	187	9	/	/	SYM
ejpam-3654	187	10	eur	eur	PROPN
ejpam-3654	187	11	.	.	PUNCT
ejpam-3654	188	1	j.	j.	PROPN
ejpam-3654	188	2	pure	pure	PROPN
ejpam-3654	188	3	appl	appl	PROPN
ejpam-3654	188	4	.	.	PROPN
ejpam-3654	188	5	math	math	PROPN
ejpam-3654	188	6	,	,	PUNCT
ejpam-3654	188	7	13	13	NUM
ejpam-3654	188	8	(	(	PUNCT
ejpam-3654	188	9	2	2	NUM
ejpam-3654	188	10	)	)	PUNCT
ejpam-3654	188	11	(	(	PUNCT
ejpam-3654	188	12	2020	2020	NUM
ejpam-3654	188	13	)	)	PUNCT
ejpam-3654	188	14	,	,	PUNCT
ejpam-3654	188	15	185	185	NUM
ejpam-3654	188	16	-	-	SYM
ejpam-3654	188	17	199	199	NUM
ejpam-3654	188	18	193	193	NUM
ejpam-3654	188	19	proof	proof	NOUN
ejpam-3654	188	20	.	.	PUNCT
ejpam-3654	189	1	assume	assume	VERB
ejpam-3654	189	2	to	to	ADP
ejpam-3654	189	3	the	the	DET
ejpam-3654	189	4	contrary	contrary	NOUN
ejpam-3654	189	5	that	that	SCONJ
ejpam-3654	189	6	(	(	PUNCT
ejpam-3654	189	7	1	1	X
ejpam-3654	189	8	)	)	PUNCT
ejpam-3654	189	9	has	have	VERB
ejpam-3654	189	10	a	a	DET
ejpam-3654	189	11	nonoscillatory	nonoscillatory	ADJ
ejpam-3654	189	12	solution	solution	NOUN
ejpam-3654	189	13	in	in	ADP
ejpam-3654	189	14	[	[	X
ejpam-3654	189	15	t0,∞	t0,∞	NUM
ejpam-3654	189	16	)	)	PUNCT
ejpam-3654	189	17	.	.	PUNCT
ejpam-3654	190	1	without	without	ADP
ejpam-3654	190	2	loss	loss	NOUN
ejpam-3654	190	3	of	of	ADP
ejpam-3654	190	4	generality	generality	NOUN
ejpam-3654	190	5	,	,	PUNCT
ejpam-3654	190	6	we	we	PRON
ejpam-3654	190	7	let	let	VERB
ejpam-3654	190	8	x	x	PART
ejpam-3654	190	9	be	be	AUX
ejpam-3654	190	10	an	an	DET
ejpam-3654	190	11	eventually	eventually	ADV
ejpam-3654	190	12	positive	positive	ADJ
ejpam-3654	190	13	solution	solution	NOUN
ejpam-3654	190	14	of	of	ADP
ejpam-3654	190	15	(	(	PUNCT
ejpam-3654	190	16	1	1	NUM
ejpam-3654	190	17	)	)	PUNCT
ejpam-3654	190	18	.	.	PUNCT
ejpam-3654	191	1	then	then	ADV
ejpam-3654	191	2	,	,	PUNCT
ejpam-3654	191	3	there	there	PRON
ejpam-3654	191	4	exists	exist	VERB
ejpam-3654	191	5	a	a	DET
ejpam-3654	191	6	t1	t1	NOUN
ejpam-3654	191	7	≥	≥	NOUN
ejpam-3654	191	8	t0	t0	NOUN
ejpam-3654	191	9	such	such	ADJ
ejpam-3654	191	10	that	that	SCONJ
ejpam-3654	191	11	x	x	X
ejpam-3654	191	12	(	(	PUNCT
ejpam-3654	191	13	t	t	PROPN
ejpam-3654	191	14	)	)	PUNCT
ejpam-3654	191	15	>	>	X
ejpam-3654	191	16	0	0	NUM
ejpam-3654	191	17	,	,	PUNCT
ejpam-3654	191	18	x	x	X
ejpam-3654	191	19	(	(	PUNCT
ejpam-3654	191	20	τ	τ	X
ejpam-3654	191	21	(	(	PUNCT
ejpam-3654	191	22	t	t	PROPN
ejpam-3654	191	23	)	)	PUNCT
ejpam-3654	191	24	)	)	PUNCT
ejpam-3654	191	25	>	>	X
ejpam-3654	191	26	0	0	PUNCT
ejpam-3654	192	1	and	and	CCONJ
ejpam-3654	192	2	x	x	SYM
ejpam-3654	192	3	(	(	PUNCT
ejpam-3654	192	4	σ	σ	PROPN
ejpam-3654	192	5	(	(	PUNCT
ejpam-3654	192	6	t	t	PROPN
ejpam-3654	192	7	)	)	PUNCT
ejpam-3654	192	8	)	)	PUNCT
ejpam-3654	192	9	>	>	X
ejpam-3654	192	10	0	0	PUNCT
ejpam-3654	193	1	for	for	ADP
ejpam-3654	193	2	t	t	PROPN
ejpam-3654	193	3	≥	≥	NUM
ejpam-3654	193	4	t1	t1	NOUN
ejpam-3654	193	5	.	.	PUNCT
ejpam-3654	194	1	from	from	ADP
ejpam-3654	194	2	lemma	lemma	PROPN
ejpam-3654	194	3	5	5	NUM
ejpam-3654	194	4	there	there	PRON
ejpam-3654	194	5	is	be	VERB
ejpam-3654	194	6	two	two	NUM
ejpam-3654	194	7	cases	case	NOUN
ejpam-3654	194	8	.	.	PUNCT
ejpam-3654	195	1	in	in	ADP
ejpam-3654	195	2	the	the	DET
ejpam-3654	195	3	case	case	NOUN
ejpam-3654	195	4	(	(	PUNCT
ejpam-3654	195	5	c1	c1	PROPN
ejpam-3654	195	6	)	)	PUNCT
ejpam-3654	195	7	,	,	PUNCT
ejpam-3654	195	8	proceeding	proceed	VERB
ejpam-3654	195	9	as	as	ADP
ejpam-3654	195	10	in	in	ADP
ejpam-3654	195	11	the	the	DET
ejpam-3654	195	12	proof	proof	NOUN
ejpam-3654	195	13	of	of	ADP
ejpam-3654	195	14	lemma	lemma	PROPN
ejpam-3654	195	15	6	6	NUM
ejpam-3654	195	16	,	,	PUNCT
ejpam-3654	195	17	we	we	PRON
ejpam-3654	195	18	get	get	VERB
ejpam-3654	195	19	that	that	PRON
ejpam-3654	195	20	(	(	PUNCT
ejpam-3654	195	21	14	14	NUM
ejpam-3654	195	22	)	)	PUNCT
ejpam-3654	195	23	holds	hold	VERB
ejpam-3654	195	24	.	.	PUNCT
ejpam-3654	196	1	it	it	PRON
ejpam-3654	196	2	follows	follow	VERB
ejpam-3654	196	3	from	from	ADP
ejpam-3654	196	4	lemma	lemma	PROPN
ejpam-3654	196	5	2	2	NUM
ejpam-3654	196	6	that	that	PRON
ejpam-3654	196	7	z	z	NOUN
ejpam-3654	196	8	(	(	PUNCT
ejpam-3654	196	9	t	t	PROPN
ejpam-3654	196	10	)	)	PUNCT
ejpam-3654	196	11	≥	≥	NOUN
ejpam-3654	196	12	µ1	µ1	PROPN
ejpam-3654	196	13	6	6	NUM
ejpam-3654	196	14	t3z′′′	t3z′′′	NOUN
ejpam-3654	196	15	(	(	PUNCT
ejpam-3654	196	16	t	t	PROPN
ejpam-3654	196	17	)	)	PUNCT
ejpam-3654	196	18	.	.	PUNCT
ejpam-3654	197	1	(	(	PUNCT
ejpam-3654	197	2	28	28	NUM
ejpam-3654	197	3	)	)	PUNCT
ejpam-3654	197	4	from	from	ADP
ejpam-3654	197	5	definition	definition	NOUN
ejpam-3654	197	6	of	of	ADP
ejpam-3654	197	7	ω	ω	PROPN
ejpam-3654	197	8	(	(	PUNCT
ejpam-3654	197	9	t	t	PROPN
ejpam-3654	197	10	)	)	PUNCT
ejpam-3654	197	11	and	and	CCONJ
ejpam-3654	197	12	(	(	PUNCT
ejpam-3654	197	13	28	28	NUM
ejpam-3654	197	14	)	)	PUNCT
ejpam-3654	197	15	,	,	PUNCT
ejpam-3654	197	16	we	we	PRON
ejpam-3654	197	17	have	have	VERB
ejpam-3654	197	18	1	1	NUM
ejpam-3654	197	19	ω	ω	NUM
ejpam-3654	197	20	(	(	PUNCT
ejpam-3654	197	21	t	t	PROPN
ejpam-3654	197	22	)	)	PUNCT
ejpam-3654	197	23	=	=	SYM
ejpam-3654	197	24	1	1	NUM
ejpam-3654	197	25	r	r	NOUN
ejpam-3654	197	26	(	(	PUNCT
ejpam-3654	197	27	t	t	NOUN
ejpam-3654	197	28	)	)	PUNCT
ejpam-3654	197	29	(	(	PUNCT
ejpam-3654	197	30	z	z	NOUN
ejpam-3654	197	31	(	(	PUNCT
ejpam-3654	197	32	t	t	NOUN
ejpam-3654	197	33	)	)	PUNCT
ejpam-3654	197	34	z′′′	z′′′	PROPN
ejpam-3654	197	35	(	(	PUNCT
ejpam-3654	197	36	t	t	PROPN
ejpam-3654	197	37	)	)	PUNCT
ejpam-3654	197	38	)	)	PUNCT
ejpam-3654	198	1	α	α	PRON
ejpam-3654	198	2	≥	≥	NUM
ejpam-3654	198	3	1	1	NUM
ejpam-3654	198	4	r	r	NOUN
ejpam-3654	198	5	(	(	PUNCT
ejpam-3654	198	6	t	t	NOUN
ejpam-3654	198	7	)	)	PUNCT
ejpam-3654	198	8	(	(	PUNCT
ejpam-3654	198	9	µ1	µ1	PROPN
ejpam-3654	198	10	6	6	NUM
ejpam-3654	198	11	t3	t3	PROPN
ejpam-3654	198	12	)	)	PUNCT
ejpam-3654	198	13	α	α	PROPN
ejpam-3654	198	14	.	.	PUNCT
ejpam-3654	199	1	thus	thus	ADV
ejpam-3654	199	2	,	,	PUNCT
ejpam-3654	199	3	ω	ω	PROPN
ejpam-3654	199	4	(	(	PUNCT
ejpam-3654	199	5	t	t	PROPN
ejpam-3654	199	6	)	)	PUNCT
ejpam-3654	199	7	(	(	PUNCT
ejpam-3654	199	8	µ1	µ1	PROPN
ejpam-3654	199	9	t	t	NOUN
ejpam-3654	199	10	3	3	NUM
ejpam-3654	199	11	6r1	6r1	NUM
ejpam-3654	199	12	/	/	SYM
ejpam-3654	199	13	α	α	PROPN
ejpam-3654	199	14	(	(	PUNCT
ejpam-3654	199	15	t	t	PROPN
ejpam-3654	199	16	)	)	PUNCT
ejpam-3654	199	17	)	)	PUNCT
ejpam-3654	199	18	α	α	PROPN
ejpam-3654	199	19	≤	≤	NUM
ejpam-3654	199	20	1	1	NUM
ejpam-3654	199	21	.	.	PUNCT
ejpam-3654	200	1	therefore	therefore	ADV
ejpam-3654	200	2	,	,	PUNCT
ejpam-3654	200	3	lim	lim	PROPN
ejpam-3654	200	4	sup	sup	PROPN
ejpam-3654	200	5	t→∞	t→∞	NUM
ejpam-3654	200	6	ω	ω	PROPN
ejpam-3654	200	7	(	(	PUNCT
ejpam-3654	200	8	t	t	PROPN
ejpam-3654	200	9	)	)	PUNCT
ejpam-3654	200	10	(	(	PUNCT
ejpam-3654	200	11	µ1	µ1	PROPN
ejpam-3654	200	12	t	t	NOUN
ejpam-3654	200	13	3	3	NUM
ejpam-3654	200	14	6r1	6r1	NUM
ejpam-3654	200	15	/	/	SYM
ejpam-3654	200	16	α	α	PROPN
ejpam-3654	200	17	(	(	PUNCT
ejpam-3654	200	18	t	t	PROPN
ejpam-3654	200	19	)	)	PUNCT
ejpam-3654	200	20	)	)	PUNCT
ejpam-3654	201	1	α	α	PROPN
ejpam-3654	201	2	≤	≤	NUM
ejpam-3654	201	3	1	1	NUM
ejpam-3654	201	4	,	,	PUNCT
ejpam-3654	201	5	which	which	PRON
ejpam-3654	201	6	contradicts	contradict	VERB
ejpam-3654	201	7	(	(	PUNCT
ejpam-3654	201	8	26	26	NUM
ejpam-3654	201	9	)	)	PUNCT
ejpam-3654	201	10	.	.	PUNCT
ejpam-3654	202	1	the	the	DET
ejpam-3654	202	2	proof	proof	NOUN
ejpam-3654	202	3	of	of	ADP
ejpam-3654	202	4	the	the	DET
ejpam-3654	202	5	case	case	NOUN
ejpam-3654	202	6	where	where	SCONJ
ejpam-3654	202	7	(	(	PUNCT
ejpam-3654	202	8	c2	c2	PROPN
ejpam-3654	202	9	)	)	PUNCT
ejpam-3654	202	10	holds	hold	VERB
ejpam-3654	202	11	is	be	AUX
ejpam-3654	202	12	the	the	DET
ejpam-3654	202	13	same	same	ADJ
ejpam-3654	202	14	as	as	ADP
ejpam-3654	202	15	that	that	PRON
ejpam-3654	202	16	of	of	ADP
ejpam-3654	202	17	case	case	NOUN
ejpam-3654	202	18	(	(	PUNCT
ejpam-3654	202	19	c1	c1	NOUN
ejpam-3654	202	20	)	)	PUNCT
ejpam-3654	202	21	.	.	PUNCT
ejpam-3654	203	1	therefore	therefore	ADV
ejpam-3654	203	2	,	,	PUNCT
ejpam-3654	203	3	the	the	DET
ejpam-3654	203	4	proof	proof	NOUN
ejpam-3654	203	5	is	be	AUX
ejpam-3654	203	6	complete	complete	ADJ
ejpam-3654	203	7	.	.	PUNCT
ejpam-3654	204	1	corollary	corollary	ADJ
ejpam-3654	204	2	1	1	NUM
ejpam-3654	204	3	.	.	PUNCT
ejpam-3654	205	1	let	let	VERB
ejpam-3654	205	2	un	un	PROPN
ejpam-3654	205	3	(	(	PUNCT
ejpam-3654	205	4	t	t	PROPN
ejpam-3654	205	5	)	)	PUNCT
ejpam-3654	205	6	and	and	CCONJ
ejpam-3654	205	7	vn	vn	PROPN
ejpam-3654	205	8	(	(	PUNCT
ejpam-3654	205	9	t	t	PROPN
ejpam-3654	205	10	)	)	PUNCT
ejpam-3654	205	11	be	be	AUX
ejpam-3654	205	12	defined	define	VERB
ejpam-3654	205	13	as	as	ADP
ejpam-3654	205	14	in	in	ADP
ejpam-3654	205	15	(	(	PUNCT
ejpam-3654	205	16	25	25	NUM
ejpam-3654	205	17	)	)	PUNCT
ejpam-3654	205	18	.	.	PUNCT
ejpam-3654	206	1	if∫	if∫	PROPN
ejpam-3654	206	2	∞	∞	PROPN
ejpam-3654	206	3	t0	t0	PROPN
ejpam-3654	206	4	q1	q1	PROPN
ejpam-3654	206	5	(	(	PUNCT
ejpam-3654	206	6	t	t	PROPN
ejpam-3654	206	7	)	)	PUNCT
ejpam-3654	206	8	exp	exp	NOUN
ejpam-3654	206	9	(	(	PUNCT
ejpam-3654	206	10	∫	∫	PROPN
ejpam-3654	206	11	t	t	PROPN
ejpam-3654	206	12	t0	t0	PROPN
ejpam-3654	206	13	r1	r1	PROPN
ejpam-3654	206	14	(	(	PUNCT
ejpam-3654	206	15	s)u1	s)u1	PROPN
ejpam-3654	206	16	/	/	SYM
ejpam-3654	206	17	αn	αn	NOUN
ejpam-3654	206	18	(	(	PUNCT
ejpam-3654	206	19	s	s	NOUN
ejpam-3654	206	20	)	)	PUNCT
ejpam-3654	206	21	ds	ds	ADJ
ejpam-3654	206	22	)	)	PUNCT
ejpam-3654	206	23	dt	dt	X
ejpam-3654	207	1	=	=	SYM
ejpam-3654	207	2	∞	∞	PROPN
ejpam-3654	207	3	(	(	PUNCT
ejpam-3654	207	4	29	29	NUM
ejpam-3654	207	5	)	)	PUNCT
ejpam-3654	207	6	and	and	CCONJ
ejpam-3654	207	7	∫	∫	PROPN
ejpam-3654	207	8	∞	∞	PROPN
ejpam-3654	207	9	t0	t0	PROPN
ejpam-3654	207	10	q2	q2	NOUN
ejpam-3654	207	11	(	(	PUNCT
ejpam-3654	207	12	t	t	PROPN
ejpam-3654	207	13	)	)	PUNCT
ejpam-3654	207	14	exp	exp	NOUN
ejpam-3654	207	15	(	(	PUNCT
ejpam-3654	207	16	∫	∫	PROPN
ejpam-3654	207	17	t	t	PROPN
ejpam-3654	207	18	t0	t0	PROPN
ejpam-3654	207	19	v1	v1	PROPN
ejpam-3654	207	20	/	/	SYM
ejpam-3654	207	21	αn	αn	NOUN
ejpam-3654	207	22	(	(	PUNCT
ejpam-3654	207	23	s	s	NOUN
ejpam-3654	207	24	)	)	PUNCT
ejpam-3654	207	25	ds	ds	ADJ
ejpam-3654	207	26	)	)	PUNCT
ejpam-3654	207	27	dt	dt	X
ejpam-3654	208	1	=	=	NOUN
ejpam-3654	208	2	∞	∞	PROPN
ejpam-3654	208	3	,	,	PUNCT
ejpam-3654	208	4	(	(	PUNCT
ejpam-3654	208	5	30	30	NUM
ejpam-3654	208	6	)	)	PUNCT
ejpam-3654	208	7	for	for	ADP
ejpam-3654	208	8	some	some	DET
ejpam-3654	208	9	n	n	CCONJ
ejpam-3654	208	10	,	,	PUNCT
ejpam-3654	208	11	then	then	ADV
ejpam-3654	208	12	(	(	PUNCT
ejpam-3654	208	13	1	1	X
ejpam-3654	208	14	)	)	PUNCT
ejpam-3654	208	15	is	be	AUX
ejpam-3654	208	16	oscillatory	oscillatory	ADJ
ejpam-3654	208	17	.	.	PUNCT
ejpam-3654	209	1	proof	proof	NOUN
ejpam-3654	209	2	.	.	PUNCT
ejpam-3654	210	1	assume	assume	VERB
ejpam-3654	210	2	to	to	ADP
ejpam-3654	210	3	the	the	DET
ejpam-3654	210	4	contrary	contrary	NOUN
ejpam-3654	210	5	that	that	SCONJ
ejpam-3654	210	6	(	(	PUNCT
ejpam-3654	210	7	1	1	X
ejpam-3654	210	8	)	)	PUNCT
ejpam-3654	210	9	has	have	VERB
ejpam-3654	210	10	a	a	DET
ejpam-3654	210	11	nonoscillatory	nonoscillatory	ADJ
ejpam-3654	210	12	solution	solution	NOUN
ejpam-3654	210	13	in	in	ADP
ejpam-3654	210	14	[	[	X
ejpam-3654	210	15	t0,∞	t0,∞	NUM
ejpam-3654	210	16	)	)	PUNCT
ejpam-3654	210	17	.	.	PUNCT
ejpam-3654	211	1	without	without	ADP
ejpam-3654	211	2	loss	loss	NOUN
ejpam-3654	211	3	of	of	ADP
ejpam-3654	211	4	generality	generality	NOUN
ejpam-3654	211	5	,	,	PUNCT
ejpam-3654	211	6	we	we	PRON
ejpam-3654	211	7	let	let	VERB
ejpam-3654	211	8	x	x	PART
ejpam-3654	211	9	be	be	AUX
ejpam-3654	211	10	an	an	DET
ejpam-3654	211	11	eventually	eventually	ADV
ejpam-3654	211	12	positive	positive	ADJ
ejpam-3654	211	13	solution	solution	NOUN
ejpam-3654	211	14	of	of	ADP
ejpam-3654	211	15	(	(	PUNCT
ejpam-3654	211	16	1	1	NUM
ejpam-3654	211	17	)	)	PUNCT
ejpam-3654	211	18	.	.	PUNCT
ejpam-3654	212	1	then	then	ADV
ejpam-3654	212	2	,	,	PUNCT
ejpam-3654	212	3	there	there	PRON
ejpam-3654	212	4	exists	exist	VERB
ejpam-3654	212	5	a	a	DET
ejpam-3654	212	6	t1	t1	NOUN
ejpam-3654	212	7	≥	≥	NOUN
ejpam-3654	212	8	t0	t0	NOUN
ejpam-3654	212	9	such	such	ADJ
ejpam-3654	212	10	that	that	SCONJ
ejpam-3654	212	11	x	x	X
ejpam-3654	212	12	(	(	PUNCT
ejpam-3654	212	13	t	t	PROPN
ejpam-3654	212	14	)	)	PUNCT
ejpam-3654	212	15	>	>	X
ejpam-3654	212	16	0	0	NUM
ejpam-3654	212	17	,	,	PUNCT
ejpam-3654	212	18	x	x	X
ejpam-3654	212	19	(	(	PUNCT
ejpam-3654	212	20	τ	τ	X
ejpam-3654	212	21	(	(	PUNCT
ejpam-3654	212	22	t	t	PROPN
ejpam-3654	212	23	)	)	PUNCT
ejpam-3654	212	24	)	)	PUNCT
ejpam-3654	212	25	>	>	X
ejpam-3654	212	26	0	0	PUNCT
ejpam-3654	213	1	and	and	CCONJ
ejpam-3654	213	2	x	x	SYM
ejpam-3654	213	3	(	(	PUNCT
ejpam-3654	213	4	σ	σ	PROPN
ejpam-3654	213	5	(	(	PUNCT
ejpam-3654	213	6	t	t	PROPN
ejpam-3654	213	7	)	)	PUNCT
ejpam-3654	213	8	)	)	PUNCT
ejpam-3654	213	9	>	>	X
ejpam-3654	213	10	0	0	PUNCT
ejpam-3654	214	1	for	for	ADP
ejpam-3654	214	2	t	t	PROPN
ejpam-3654	214	3	≥	≥	NUM
ejpam-3654	214	4	t1	t1	NOUN
ejpam-3654	214	5	.	.	PUNCT
ejpam-3654	215	1	from	from	ADP
ejpam-3654	215	2	lemma	lemma	PROPN
ejpam-3654	215	3	5	5	NUM
ejpam-3654	215	4	there	there	PRON
ejpam-3654	215	5	is	be	VERB
ejpam-3654	215	6	two	two	NUM
ejpam-3654	215	7	cases	case	NOUN
ejpam-3654	215	8	.	.	PUNCT
ejpam-3654	216	1	in	in	ADP
ejpam-3654	216	2	the	the	DET
ejpam-3654	216	3	case	case	NOUN
ejpam-3654	216	4	(	(	PUNCT
ejpam-3654	216	5	c1	c1	PROPN
ejpam-3654	216	6	)	)	PUNCT
ejpam-3654	216	7	,	,	PUNCT
ejpam-3654	216	8	proceeding	proceed	VERB
ejpam-3654	216	9	as	as	ADP
ejpam-3654	216	10	in	in	ADP
ejpam-3654	216	11	the	the	DET
ejpam-3654	216	12	proof	proof	NOUN
ejpam-3654	216	13	of	of	ADP
ejpam-3654	216	14	theorem	theorem	NOUN
ejpam-3654	216	15	2	2	NUM
ejpam-3654	216	16	,	,	PUNCT
ejpam-3654	216	17	we	we	PRON
ejpam-3654	216	18	get	get	VERB
ejpam-3654	216	19	that	that	PRON
ejpam-3654	216	20	(	(	PUNCT
ejpam-3654	216	21	23	23	NUM
ejpam-3654	216	22	)	)	PUNCT
ejpam-3654	216	23	holds	hold	VERB
ejpam-3654	216	24	.	.	PUNCT
ejpam-3654	217	1	it	it	PRON
ejpam-3654	217	2	follows	follow	VERB
ejpam-3654	217	3	from	from	ADP
ejpam-3654	217	4	(	(	PUNCT
ejpam-3654	217	5	23	23	NUM
ejpam-3654	217	6	)	)	PUNCT
ejpam-3654	217	7	that	that	SCONJ
ejpam-3654	218	1	ω	ω	PROPN
ejpam-3654	218	2	(	(	PUNCT
ejpam-3654	218	3	t	t	PROPN
ejpam-3654	218	4	)	)	PUNCT
ejpam-3654	218	5	≥	≥	NOUN
ejpam-3654	218	6	u0	u0	PROPN
ejpam-3654	218	7	(	(	PUNCT
ejpam-3654	218	8	t	t	PROPN
ejpam-3654	218	9	)	)	PUNCT
ejpam-3654	218	10	.	.	PUNCT
ejpam-3654	219	1	moreover	moreover	ADV
ejpam-3654	219	2	,	,	PUNCT
ejpam-3654	219	3	by	by	ADP
ejpam-3654	219	4	induction	induction	NOUN
ejpam-3654	219	5	we	we	PRON
ejpam-3654	219	6	can	can	AUX
ejpam-3654	219	7	also	also	ADV
ejpam-3654	219	8	see	see	VERB
ejpam-3654	219	9	that	that	SCONJ
ejpam-3654	219	10	ω	ω	PROPN
ejpam-3654	219	11	(	(	PUNCT
ejpam-3654	219	12	t	t	PROPN
ejpam-3654	219	13	)	)	PUNCT
ejpam-3654	219	14	≥	≥	NOUN
ejpam-3654	219	15	un	un	PROPN
ejpam-3654	219	16	(	(	PUNCT
ejpam-3654	219	17	t	t	PROPN
ejpam-3654	219	18	)	)	PUNCT
ejpam-3654	219	19	for	for	ADP
ejpam-3654	219	20	t	t	PROPN
ejpam-3654	219	21	≥	≥	PROPN
ejpam-3654	219	22	t0	t0	PROPN
ejpam-3654	219	23	,	,	PUNCT
ejpam-3654	219	24	n	n	PROPN
ejpam-3654	219	25	>	>	X
ejpam-3654	219	26	1	1	X
ejpam-3654	219	27	.	.	PUNCT
ejpam-3654	220	1	since	since	SCONJ
ejpam-3654	220	2	the	the	DET
ejpam-3654	220	3	sequence	sequence	NOUN
ejpam-3654	220	4	{	{	PUNCT
ejpam-3654	220	5	un	un	PROPN
ejpam-3654	220	6	(	(	PUNCT
ejpam-3654	220	7	t)}∞n=0	t)}∞n=0	NUM
ejpam-3654	220	8	monotone	monotone	NOUN
ejpam-3654	220	9	increasing	increasing	NOUN
ejpam-3654	220	10	and	and	CCONJ
ejpam-3654	220	11	bounded	bound	VERB
ejpam-3654	220	12	above	above	ADV
ejpam-3654	220	13	,	,	PUNCT
ejpam-3654	220	14	it	it	PRON
ejpam-3654	220	15	converges	converge	VERB
ejpam-3654	220	16	to	to	ADP
ejpam-3654	220	17	u	u	PROPN
ejpam-3654	220	18	(	(	PUNCT
ejpam-3654	220	19	t	t	PROPN
ejpam-3654	220	20	)	)	PUNCT
ejpam-3654	220	21	.	.	PUNCT
ejpam-3654	221	1	thus	thus	ADV
ejpam-3654	221	2	,	,	PUNCT
ejpam-3654	221	3	by	by	ADP
ejpam-3654	221	4	using	use	VERB
ejpam-3654	221	5	lebesgue	lebesgue	NOUN
ejpam-3654	221	6	’s	’s	PART
ejpam-3654	221	7	monotone	monotone	ADJ
ejpam-3654	221	8	convergence	convergence	NOUN
ejpam-3654	221	9	theorem	theorem	NOUN
ejpam-3654	221	10	,	,	PUNCT
ejpam-3654	221	11	we	we	PRON
ejpam-3654	221	12	see	see	VERB
ejpam-3654	221	13	that	that	SCONJ
ejpam-3654	221	14	u	u	PROPN
ejpam-3654	221	15	(	(	PUNCT
ejpam-3654	221	16	t	t	PROPN
ejpam-3654	221	17	)	)	PUNCT
ejpam-3654	221	18	=	=	PROPN
ejpam-3654	222	1	lim	lim	PROPN
ejpam-3654	222	2	n→∞	n→∞	NUM
ejpam-3654	222	3	un	un	PROPN
ejpam-3654	222	4	(	(	PUNCT
ejpam-3654	222	5	t	t	PROPN
ejpam-3654	222	6	)	)	PUNCT
ejpam-3654	222	7	=	=	SYM
ejpam-3654	223	1	∫	∫	PROPN
ejpam-3654	223	2	∞	∞	PROPN
ejpam-3654	223	3	t	t	PROPN
ejpam-3654	223	4	r1	r1	NOUN
ejpam-3654	223	5	(	(	PUNCT
ejpam-3654	223	6	t)u(α+1)/α	t)u(α+1)/α	NOUN
ejpam-3654	223	7	(	(	PUNCT
ejpam-3654	223	8	s	s	NOUN
ejpam-3654	223	9	)	)	PUNCT
ejpam-3654	223	10	ds+	ds+	ADJ
ejpam-3654	223	11	u0	u0	PROPN
ejpam-3654	223	12	(	(	PUNCT
ejpam-3654	223	13	t	t	PROPN
ejpam-3654	223	14	)	)	PUNCT
ejpam-3654	223	15	o.	o.	NOUN
ejpam-3654	223	16	moaaz	moaaz	PROPN
ejpam-3654	223	17	,	,	PUNCT
ejpam-3654	223	18	c.	c.	PROPN
ejpam-3654	223	19	cesarano	cesarano	PROPN
ejpam-3654	223	20	,	,	PUNCT
ejpam-3654	223	21	a.	a.	NOUN
ejpam-3654	223	22	muhib	muhib	NOUN
ejpam-3654	223	23	/	/	SYM
ejpam-3654	223	24	eur	eur	PROPN
ejpam-3654	223	25	.	.	PUNCT
ejpam-3654	224	1	j.	j.	PROPN
ejpam-3654	224	2	pure	pure	PROPN
ejpam-3654	224	3	appl	appl	PROPN
ejpam-3654	224	4	.	.	PROPN
ejpam-3654	224	5	math	math	PROPN
ejpam-3654	224	6	,	,	PUNCT
ejpam-3654	224	7	13	13	NUM
ejpam-3654	224	8	(	(	PUNCT
ejpam-3654	224	9	2	2	NUM
ejpam-3654	224	10	)	)	PUNCT
ejpam-3654	224	11	(	(	PUNCT
ejpam-3654	224	12	2020	2020	NUM
ejpam-3654	224	13	)	)	PUNCT
ejpam-3654	224	14	,	,	PUNCT
ejpam-3654	224	15	185	185	NUM
ejpam-3654	224	16	-	-	SYM
ejpam-3654	224	17	199	199	NUM
ejpam-3654	224	18	194	194	NUM
ejpam-3654	224	19	and	and	CCONJ
ejpam-3654	224	20	u′	u′	PROPN
ejpam-3654	224	21	(	(	PUNCT
ejpam-3654	224	22	t	t	NOUN
ejpam-3654	224	23	)	)	PUNCT
ejpam-3654	224	24	=	=	SYM
ejpam-3654	225	1	−r1	−r1	PROPN
ejpam-3654	225	2	(	(	PUNCT
ejpam-3654	225	3	t)u(α+1)/α	t)u(α+1)/α	NOUN
ejpam-3654	225	4	(	(	PUNCT
ejpam-3654	225	5	t)−q1	t)−q1	PROPN
ejpam-3654	225	6	(	(	PUNCT
ejpam-3654	225	7	t	t	PROPN
ejpam-3654	225	8	)	)	PUNCT
ejpam-3654	225	9	.	.	PUNCT
ejpam-3654	226	1	(	(	PUNCT
ejpam-3654	226	2	31	31	NUM
ejpam-3654	226	3	)	)	PUNCT
ejpam-3654	226	4	since	since	SCONJ
ejpam-3654	226	5	un	un	PROPN
ejpam-3654	226	6	(	(	PUNCT
ejpam-3654	226	7	t	t	PROPN
ejpam-3654	226	8	)	)	PUNCT
ejpam-3654	226	9	≤	≤	NOUN
ejpam-3654	226	10	u	u	PROPN
ejpam-3654	226	11	(	(	PUNCT
ejpam-3654	226	12	t	t	PROPN
ejpam-3654	226	13	)	)	PUNCT
ejpam-3654	226	14	,	,	PUNCT
ejpam-3654	226	15	it	it	PRON
ejpam-3654	226	16	follows	follow	VERB
ejpam-3654	226	17	from	from	ADP
ejpam-3654	226	18	(	(	PUNCT
ejpam-3654	226	19	31	31	NUM
ejpam-3654	226	20	)	)	PUNCT
ejpam-3654	226	21	that	that	PRON
ejpam-3654	226	22	u′	u′	PROPN
ejpam-3654	226	23	(	(	PUNCT
ejpam-3654	226	24	t	t	NOUN
ejpam-3654	226	25	)	)	PUNCT
ejpam-3654	226	26	≤	≤	NOUN
ejpam-3654	226	27	−r1	−r1	PROPN
ejpam-3654	226	28	(	(	PUNCT
ejpam-3654	226	29	t)u1	t)u1	PROPN
ejpam-3654	226	30	/	/	SYM
ejpam-3654	226	31	αn	αn	NOUN
ejpam-3654	226	32	(	(	PUNCT
ejpam-3654	226	33	t)u	t)u	X
ejpam-3654	226	34	(	(	PUNCT
ejpam-3654	226	35	t)−q1	t)−q1	PROPN
ejpam-3654	226	36	(	(	PUNCT
ejpam-3654	226	37	t	t	PROPN
ejpam-3654	226	38	)	)	PUNCT
ejpam-3654	226	39	.	.	PUNCT
ejpam-3654	227	1	hence	hence	ADV
ejpam-3654	227	2	,	,	PUNCT
ejpam-3654	227	3	we	we	PRON
ejpam-3654	227	4	get	get	VERB
ejpam-3654	227	5	u	u	NOUN
ejpam-3654	227	6	(	(	PUNCT
ejpam-3654	227	7	t	t	NOUN
ejpam-3654	227	8	)	)	PUNCT
ejpam-3654	227	9	≤	≤	NOUN
ejpam-3654	227	10	exp	exp	NOUN
ejpam-3654	227	11	(	(	PUNCT
ejpam-3654	227	12	−	−	PROPN
ejpam-3654	227	13	∫	∫	PROPN
ejpam-3654	227	14	t	t	PROPN
ejpam-3654	227	15	t	t	PROPN
ejpam-3654	227	16	r1	r1	PROPN
ejpam-3654	227	17	(	(	PUNCT
ejpam-3654	227	18	s)u1	s)u1	PROPN
ejpam-3654	227	19	/	/	SYM
ejpam-3654	227	20	αn	αn	NOUN
ejpam-3654	227	21	(	(	PUNCT
ejpam-3654	227	22	s	s	NOUN
ejpam-3654	227	23	)	)	PUNCT
ejpam-3654	227	24	ds	ds	NOUN
ejpam-3654	227	25	)	)	PUNCT
ejpam-3654	227	26	(	(	PUNCT
ejpam-3654	227	27	u	u	NOUN
ejpam-3654	227	28	(	(	PUNCT
ejpam-3654	227	29	t	t	PROPN
ejpam-3654	227	30	)	)	PUNCT
ejpam-3654	227	31	−	−	PROPN
ejpam-3654	228	1	∫	∫	PROPN
ejpam-3654	228	2	t	t	PROPN
ejpam-3654	228	3	t	t	PROPN
ejpam-3654	228	4	q1	q1	PROPN
ejpam-3654	228	5	(	(	PUNCT
ejpam-3654	228	6	s	s	NOUN
ejpam-3654	228	7	)	)	PUNCT
ejpam-3654	228	8	exp	exp	NOUN
ejpam-3654	228	9	(	(	PUNCT
ejpam-3654	228	10	∫	∫	PROPN
ejpam-3654	228	11	s	s	PROPN
ejpam-3654	228	12	t	t	PROPN
ejpam-3654	228	13	r1	r1	PROPN
ejpam-3654	228	14	(	(	PUNCT
ejpam-3654	228	15	u)u1	u)u1	PROPN
ejpam-3654	228	16	/	/	SYM
ejpam-3654	228	17	αn	αn	NOUN
ejpam-3654	228	18	(	(	PUNCT
ejpam-3654	228	19	u	u	NOUN
ejpam-3654	228	20	)	)	PUNCT
ejpam-3654	228	21	du	du	NOUN
ejpam-3654	228	22	)	)	PUNCT
ejpam-3654	228	23	ds	ds	PROPN
ejpam-3654	228	24	)	)	PUNCT
ejpam-3654	228	25	.	.	PUNCT
ejpam-3654	229	1	this	this	PRON
ejpam-3654	229	2	implies	imply	VERB
ejpam-3654	229	3	∫	∫	PROPN
ejpam-3654	229	4	t	t	PROPN
ejpam-3654	229	5	t	t	PROPN
ejpam-3654	229	6	q1	q1	PROPN
ejpam-3654	229	7	(	(	PUNCT
ejpam-3654	229	8	s	s	NOUN
ejpam-3654	229	9	)	)	PUNCT
ejpam-3654	229	10	exp	exp	NOUN
ejpam-3654	229	11	(	(	PUNCT
ejpam-3654	229	12	∫	∫	PROPN
ejpam-3654	229	13	s	s	PROPN
ejpam-3654	229	14	t	t	PROPN
ejpam-3654	229	15	r1	r1	PROPN
ejpam-3654	229	16	(	(	PUNCT
ejpam-3654	229	17	u)u1	u)u1	PROPN
ejpam-3654	229	18	/	/	SYM
ejpam-3654	229	19	αn	αn	NOUN
ejpam-3654	229	20	(	(	PUNCT
ejpam-3654	229	21	u	u	NOUN
ejpam-3654	229	22	)	)	PUNCT
ejpam-3654	229	23	du	du	X
ejpam-3654	229	24	)	)	PUNCT
ejpam-3654	229	25	ds	ds	ADJ
ejpam-3654	229	26	≤	≤	NUM
ejpam-3654	229	27	u	u	NOUN
ejpam-3654	229	28	(	(	PUNCT
ejpam-3654	229	29	t	t	PROPN
ejpam-3654	229	30	)	)	PUNCT
ejpam-3654	229	31	<	<	X
ejpam-3654	229	32	∞	∞	PROPN
ejpam-3654	229	33	,	,	PUNCT
ejpam-3654	229	34	which	which	PRON
ejpam-3654	229	35	contradicts	contradict	VERB
ejpam-3654	229	36	(	(	PUNCT
ejpam-3654	229	37	29	29	NUM
ejpam-3654	229	38	)	)	PUNCT
ejpam-3654	229	39	.	.	PUNCT
ejpam-3654	230	1	the	the	DET
ejpam-3654	230	2	proof	proof	NOUN
ejpam-3654	230	3	of	of	ADP
ejpam-3654	230	4	the	the	DET
ejpam-3654	230	5	case	case	NOUN
ejpam-3654	230	6	where	where	SCONJ
ejpam-3654	230	7	(	(	PUNCT
ejpam-3654	230	8	c2	c2	PROPN
ejpam-3654	230	9	)	)	PUNCT
ejpam-3654	230	10	holds	hold	VERB
ejpam-3654	230	11	is	be	AUX
ejpam-3654	230	12	the	the	DET
ejpam-3654	230	13	same	same	ADJ
ejpam-3654	230	14	as	as	ADP
ejpam-3654	230	15	that	that	PRON
ejpam-3654	230	16	of	of	ADP
ejpam-3654	230	17	case	case	NOUN
ejpam-3654	230	18	(	(	PUNCT
ejpam-3654	230	19	c1	c1	NOUN
ejpam-3654	230	20	)	)	PUNCT
ejpam-3654	230	21	.	.	PUNCT
ejpam-3654	231	1	therefore	therefore	ADV
ejpam-3654	231	2	,	,	PUNCT
ejpam-3654	231	3	the	the	DET
ejpam-3654	231	4	proof	proof	NOUN
ejpam-3654	231	5	is	be	AUX
ejpam-3654	231	6	complete	complete	ADJ
ejpam-3654	231	7	.	.	PUNCT
ejpam-3654	232	1	4	4	X
ejpam-3654	232	2	.	.	X
ejpam-3654	232	3	further	further	ADJ
ejpam-3654	232	4	results	result	NOUN
ejpam-3654	232	5	lemma	lemma	PROPN
ejpam-3654	232	6	7	7	X
ejpam-3654	232	7	.	.	PUNCT
ejpam-3654	232	8	assume	assume	VERB
ejpam-3654	232	9	that	that	SCONJ
ejpam-3654	232	10	x	x	PRON
ejpam-3654	232	11	is	be	AUX
ejpam-3654	232	12	an	an	DET
ejpam-3654	232	13	eventually	eventually	ADV
ejpam-3654	232	14	positive	positive	ADJ
ejpam-3654	232	15	solution	solution	NOUN
ejpam-3654	232	16	of	of	ADP
ejpam-3654	232	17	(	(	PUNCT
ejpam-3654	232	18	1	1	NUM
ejpam-3654	232	19	)	)	PUNCT
ejpam-3654	232	20	and	and	CCONJ
ejpam-3654	232	21	p	p	X
ejpam-3654	232	22	(	(	PUNCT
ejpam-3654	232	23	τ−1	τ−1	PROPN
ejpam-3654	232	24	(	(	PUNCT
ejpam-3654	232	25	τ−1	τ−1	PROPN
ejpam-3654	232	26	(	(	PUNCT
ejpam-3654	232	27	t	t	PROPN
ejpam-3654	232	28	)	)	PUNCT
ejpam-3654	232	29	)	)	PUNCT
ejpam-3654	232	30	)	)	PUNCT
ejpam-3654	232	31	≥	≥	X
ejpam-3654	232	32	(	(	PUNCT
ejpam-3654	232	33	τ−1	τ−1	PROPN
ejpam-3654	232	34	(	(	PUNCT
ejpam-3654	232	35	τ−1	τ−1	PROPN
ejpam-3654	232	36	(	(	PUNCT
ejpam-3654	232	37	t	t	PROPN
ejpam-3654	232	38	)	)	PUNCT
ejpam-3654	232	39	)	)	PUNCT
ejpam-3654	233	1	τ−1	τ−1	PROPN
ejpam-3654	233	2	(	(	PUNCT
ejpam-3654	233	3	t	t	PROPN
ejpam-3654	233	4	)	)	PUNCT
ejpam-3654	233	5	)	)	PUNCT
ejpam-3654	233	6	3	3	X
ejpam-3654	233	7	.	.	PUNCT
ejpam-3654	234	1	(	(	PUNCT
ejpam-3654	234	2	32	32	NUM
ejpam-3654	234	3	)	)	PUNCT
ejpam-3654	234	4	then	then	ADV
ejpam-3654	234	5	(	(	PUNCT
ejpam-3654	234	6	r	r	NOUN
ejpam-3654	234	7	(	(	PUNCT
ejpam-3654	234	8	t	t	NOUN
ejpam-3654	234	9	)	)	PUNCT
ejpam-3654	234	10	(	(	PUNCT
ejpam-3654	234	11	z′′′	z′′′	PROPN
ejpam-3654	234	12	(	(	PUNCT
ejpam-3654	234	13	t	t	PROPN
ejpam-3654	234	14	)	)	PUNCT
ejpam-3654	234	15	)	)	PUNCT
ejpam-3654	235	1	α)′	α)′	PROPN
ejpam-3654	235	2	+	+	NUM
ejpam-3654	235	3	q	q	X
ejpam-3654	235	4	(	(	PUNCT
ejpam-3654	235	5	t	t	NOUN
ejpam-3654	235	6	)	)	PUNCT
ejpam-3654	235	7	p̃β	p̃β	NOUN
ejpam-3654	235	8	(	(	PUNCT
ejpam-3654	235	9	σ	σ	PROPN
ejpam-3654	235	10	(	(	PUNCT
ejpam-3654	235	11	t	t	PROPN
ejpam-3654	235	12	)	)	PUNCT
ejpam-3654	235	13	)	)	PUNCT
ejpam-3654	236	1	zβ	zβ	PROPN
ejpam-3654	236	2	(	(	PUNCT
ejpam-3654	236	3	τ−1	τ−1	PROPN
ejpam-3654	236	4	(	(	PUNCT
ejpam-3654	236	5	σ	σ	PROPN
ejpam-3654	236	6	(	(	PUNCT
ejpam-3654	236	7	t	t	PROPN
ejpam-3654	236	8	)	)	PUNCT
ejpam-3654	236	9	)	)	PUNCT
ejpam-3654	236	10	)	)	PUNCT
ejpam-3654	237	1	≤	≤	ADV
ejpam-3654	237	2	0	0	NUM
ejpam-3654	237	3	,	,	PUNCT
ejpam-3654	237	4	(	(	PUNCT
ejpam-3654	237	5	33	33	NUM
ejpam-3654	237	6	)	)	PUNCT
ejpam-3654	237	7	where	where	SCONJ
ejpam-3654	237	8	p̃	p̃	PROPN
ejpam-3654	237	9	(	(	PUNCT
ejpam-3654	237	10	t	t	PROPN
ejpam-3654	237	11	)	)	PUNCT
ejpam-3654	237	12	:	:	PUNCT
ejpam-3654	237	13	=	=	PUNCT
ejpam-3654	237	14			NUM
ejpam-3654	237	15	1	1	NUM
ejpam-3654	237	16	p(τ−1(t	p(τ−1(t	PROPN
ejpam-3654	237	17	)	)	PUNCT
ejpam-3654	237	18	)	)	PUNCT
ejpam-3654	238	1	(	(	PUNCT
ejpam-3654	238	2	1−	1−	NUM
ejpam-3654	238	3	(	(	PUNCT
ejpam-3654	238	4	τ−1(τ−1(t	τ−1(τ−1(t	PROPN
ejpam-3654	238	5	)	)	PUNCT
ejpam-3654	238	6	)	)	PUNCT
ejpam-3654	238	7	)	)	PUNCT
ejpam-3654	238	8	3	3	NUM
ejpam-3654	238	9	(	(	PUNCT
ejpam-3654	238	10	τ−1(t))3p(τ−1(τ−1(t	τ−1(t))3p(τ−1(τ−1(t	PROPN
ejpam-3654	238	11	)	)	PUNCT
ejpam-3654	238	12	)	)	PUNCT
ejpam-3654	238	13	)	)	PUNCT
ejpam-3654	238	14	)	)	PUNCT
ejpam-3654	239	1	for	for	ADP
ejpam-3654	239	2	case	case	NOUN
ejpam-3654	239	3	(	(	PUNCT
ejpam-3654	239	4	c1	c1	PROPN
ejpam-3654	239	5	)	)	PUNCT
ejpam-3654	239	6	;	;	PUNCT
ejpam-3654	239	7	1	1	NUM
ejpam-3654	239	8	p(τ−1(t	p(τ−1(t	PROPN
ejpam-3654	239	9	)	)	PUNCT
ejpam-3654	239	10	)	)	PUNCT
ejpam-3654	239	11	(	(	PUNCT
ejpam-3654	239	12	1−	1−	NUM
ejpam-3654	239	13	(	(	PUNCT
ejpam-3654	239	14	τ−1(τ−1(t	τ−1(τ−1(t	PROPN
ejpam-3654	239	15	)	)	PUNCT
ejpam-3654	239	16	)	)	PUNCT
ejpam-3654	239	17	)	)	PUNCT
ejpam-3654	239	18	(	(	PUNCT
ejpam-3654	239	19	τ−1(t))p(τ−1(τ−1(t	τ−1(t))p(τ−1(τ−1(t	ADV
ejpam-3654	239	20	)	)	PUNCT
ejpam-3654	239	21	)	)	PUNCT
ejpam-3654	239	22	)	)	PUNCT
ejpam-3654	239	23	)	)	PUNCT
ejpam-3654	239	24	for	for	ADP
ejpam-3654	239	25	case	case	NOUN
ejpam-3654	239	26	(	(	PUNCT
ejpam-3654	239	27	c2	c2	PROPN
ejpam-3654	239	28	)	)	PUNCT
ejpam-3654	239	29	.	.	PUNCT
ejpam-3654	240	1	(	(	PUNCT
ejpam-3654	240	2	34	34	NUM
ejpam-3654	240	3	)	)	PUNCT
ejpam-3654	240	4	proof	proof	NOUN
ejpam-3654	240	5	.	.	PUNCT
ejpam-3654	241	1	proceeding	proceed	VERB
ejpam-3654	241	2	as	as	ADP
ejpam-3654	241	3	in	in	ADP
ejpam-3654	241	4	the	the	DET
ejpam-3654	241	5	proof	proof	NOUN
ejpam-3654	241	6	of	of	ADP
ejpam-3654	241	7	lemma	lemma	PROPN
ejpam-3654	241	8	4	4	NUM
ejpam-3654	241	9	,	,	PUNCT
ejpam-3654	241	10	we	we	PRON
ejpam-3654	241	11	get	get	VERB
ejpam-3654	241	12	that	that	PRON
ejpam-3654	241	13	(	(	PUNCT
ejpam-3654	241	14	4	4	X
ejpam-3654	241	15	)	)	PUNCT
ejpam-3654	241	16	holds	hold	VERB
ejpam-3654	241	17	.	.	PUNCT
ejpam-3654	242	1	it	it	PRON
ejpam-3654	242	2	follows	follow	VERB
ejpam-3654	242	3	from	from	ADP
ejpam-3654	242	4	lemma	lemma	PROPN
ejpam-3654	242	5	5	5	NUM
ejpam-3654	242	6	that	that	SCONJ
ejpam-3654	242	7	there	there	PRON
ejpam-3654	242	8	exist	exist	VERB
ejpam-3654	242	9	two	two	NUM
ejpam-3654	242	10	possible	possible	ADJ
ejpam-3654	242	11	cases	case	NOUN
ejpam-3654	242	12	(	(	PUNCT
ejpam-3654	242	13	c1	c1	NOUN
ejpam-3654	242	14	)	)	PUNCT
ejpam-3654	242	15	and	and	CCONJ
ejpam-3654	242	16	(	(	PUNCT
ejpam-3654	242	17	c2	c2	PROPN
ejpam-3654	242	18	)	)	PUNCT
ejpam-3654	242	19	.	.	PUNCT
ejpam-3654	243	1	from	from	ADP
ejpam-3654	243	2	the	the	DET
ejpam-3654	243	3	definition	definition	NOUN
ejpam-3654	243	4	of	of	ADP
ejpam-3654	243	5	z	z	PROPN
ejpam-3654	243	6	(	(	PUNCT
ejpam-3654	243	7	t	t	PROPN
ejpam-3654	243	8	)	)	PUNCT
ejpam-3654	243	9	,	,	PUNCT
ejpam-3654	243	10	we	we	PRON
ejpam-3654	243	11	see	see	VERB
ejpam-3654	243	12	that	that	SCONJ
ejpam-3654	243	13	x	x	X
ejpam-3654	243	14	(	(	PUNCT
ejpam-3654	243	15	t	t	NOUN
ejpam-3654	243	16	)	)	PUNCT
ejpam-3654	243	17	=	=	SYM
ejpam-3654	243	18	1	1	NUM
ejpam-3654	243	19	p	p	NOUN
ejpam-3654	243	20	(	(	PUNCT
ejpam-3654	243	21	τ−1	τ−1	PROPN
ejpam-3654	243	22	(	(	PUNCT
ejpam-3654	243	23	t	t	PROPN
ejpam-3654	243	24	)	)	PUNCT
ejpam-3654	243	25	)	)	PUNCT
ejpam-3654	244	1	(	(	PUNCT
ejpam-3654	244	2	z	z	NOUN
ejpam-3654	244	3	(	(	PUNCT
ejpam-3654	244	4	τ−1	τ−1	PROPN
ejpam-3654	244	5	(	(	PUNCT
ejpam-3654	244	6	t	t	PROPN
ejpam-3654	244	7	)	)	PUNCT
ejpam-3654	244	8	)	)	PUNCT
ejpam-3654	245	1	−	−	NOUN
ejpam-3654	245	2	x	x	SYM
ejpam-3654	245	3	(	(	PUNCT
ejpam-3654	245	4	τ−1	τ−1	PROPN
ejpam-3654	245	5	(	(	PUNCT
ejpam-3654	245	6	t	t	PROPN
ejpam-3654	245	7	)	)	PUNCT
ejpam-3654	245	8	)	)	PUNCT
ejpam-3654	245	9	)	)	PUNCT
ejpam-3654	245	10	.	.	PUNCT
ejpam-3654	246	1	by	by	ADP
ejpam-3654	246	2	repeating	repeat	VERB
ejpam-3654	246	3	the	the	DET
ejpam-3654	246	4	same	same	ADJ
ejpam-3654	246	5	process	process	NOUN
ejpam-3654	246	6	,	,	PUNCT
ejpam-3654	246	7	we	we	PRON
ejpam-3654	246	8	find	find	VERB
ejpam-3654	246	9	that	that	SCONJ
ejpam-3654	246	10	x	x	X
ejpam-3654	246	11	(	(	PUNCT
ejpam-3654	246	12	t	t	NOUN
ejpam-3654	246	13	)	)	PUNCT
ejpam-3654	246	14	=	=	SYM
ejpam-3654	246	15	z	z	NOUN
ejpam-3654	246	16	(	(	PUNCT
ejpam-3654	246	17	τ−1	τ−1	PROPN
ejpam-3654	246	18	(	(	PUNCT
ejpam-3654	246	19	t	t	PROPN
ejpam-3654	246	20	)	)	PUNCT
ejpam-3654	246	21	)	)	PUNCT
ejpam-3654	247	1	p	p	X
ejpam-3654	247	2	(	(	PUNCT
ejpam-3654	247	3	τ−1	τ−1	PROPN
ejpam-3654	247	4	(	(	PUNCT
ejpam-3654	247	5	t	t	PROPN
ejpam-3654	247	6	)	)	PUNCT
ejpam-3654	247	7	)	)	PUNCT
ejpam-3654	248	1	−	−	PROPN
ejpam-3654	248	2	1	1	NUM
ejpam-3654	248	3	p	p	NOUN
ejpam-3654	248	4	(	(	PUNCT
ejpam-3654	248	5	τ−1	τ−1	PROPN
ejpam-3654	248	6	(	(	PUNCT
ejpam-3654	248	7	t	t	PROPN
ejpam-3654	248	8	)	)	PUNCT
ejpam-3654	248	9	)	)	PUNCT
ejpam-3654	249	1	(	(	PUNCT
ejpam-3654	249	2	z	z	NOUN
ejpam-3654	249	3	(	(	PUNCT
ejpam-3654	249	4	τ−1	τ−1	PROPN
ejpam-3654	249	5	(	(	PUNCT
ejpam-3654	249	6	τ−1	τ−1	PROPN
ejpam-3654	249	7	(	(	PUNCT
ejpam-3654	249	8	t	t	PROPN
ejpam-3654	249	9	)	)	PUNCT
ejpam-3654	249	10	)	)	PUNCT
ejpam-3654	249	11	)	)	PUNCT
ejpam-3654	249	12	p	p	X
ejpam-3654	249	13	(	(	PUNCT
ejpam-3654	249	14	τ−1	τ−1	PROPN
ejpam-3654	249	15	(	(	PUNCT
ejpam-3654	249	16	τ−1	τ−1	PROPN
ejpam-3654	249	17	(	(	PUNCT
ejpam-3654	249	18	t	t	PROPN
ejpam-3654	249	19	)	)	PUNCT
ejpam-3654	249	20	)	)	PUNCT
ejpam-3654	249	21	)	)	PUNCT
ejpam-3654	250	1	−	−	NOUN
ejpam-3654	250	2	x	x	SYM
ejpam-3654	250	3	(	(	PUNCT
ejpam-3654	250	4	τ−1	τ−1	PROPN
ejpam-3654	250	5	(	(	PUNCT
ejpam-3654	250	6	τ−1	τ−1	PROPN
ejpam-3654	250	7	(	(	PUNCT
ejpam-3654	250	8	t	t	PROPN
ejpam-3654	250	9	)	)	PUNCT
ejpam-3654	250	10	)	)	PUNCT
ejpam-3654	250	11	)	)	PUNCT
ejpam-3654	251	1	p	p	X
ejpam-3654	251	2	(	(	PUNCT
ejpam-3654	251	3	τ−1	τ−1	PROPN
ejpam-3654	251	4	(	(	PUNCT
ejpam-3654	251	5	τ−1	τ−1	PROPN
ejpam-3654	251	6	(	(	PUNCT
ejpam-3654	251	7	t	t	PROPN
ejpam-3654	251	8	)	)	PUNCT
ejpam-3654	251	9	)	)	PUNCT
ejpam-3654	251	10	)	)	PUNCT
ejpam-3654	251	11	)	)	PUNCT
ejpam-3654	252	1	o.	o.	PROPN
ejpam-3654	252	2	moaaz	moaaz	PROPN
ejpam-3654	252	3	,	,	PUNCT
ejpam-3654	252	4	c.	c.	PROPN
ejpam-3654	252	5	cesarano	cesarano	PROPN
ejpam-3654	252	6	,	,	PUNCT
ejpam-3654	252	7	a.	a.	NOUN
ejpam-3654	252	8	muhib	muhib	NOUN
ejpam-3654	252	9	/	/	SYM
ejpam-3654	252	10	eur	eur	PROPN
ejpam-3654	252	11	.	.	PUNCT
ejpam-3654	253	1	j.	j.	PROPN
ejpam-3654	253	2	pure	pure	PROPN
ejpam-3654	253	3	appl	appl	PROPN
ejpam-3654	253	4	.	.	PROPN
ejpam-3654	253	5	math	math	PROPN
ejpam-3654	253	6	,	,	PUNCT
ejpam-3654	253	7	13	13	NUM
ejpam-3654	253	8	(	(	PUNCT
ejpam-3654	253	9	2	2	NUM
ejpam-3654	253	10	)	)	PUNCT
ejpam-3654	253	11	(	(	PUNCT
ejpam-3654	253	12	2020	2020	NUM
ejpam-3654	253	13	)	)	PUNCT
ejpam-3654	253	14	,	,	PUNCT
ejpam-3654	253	15	185	185	NUM
ejpam-3654	253	16	-	-	SYM
ejpam-3654	253	17	199	199	NUM
ejpam-3654	253	18	195	195	NUM
ejpam-3654	253	19	≥	≥	NOUN
ejpam-3654	253	20	z	z	NOUN
ejpam-3654	253	21	(	(	PUNCT
ejpam-3654	253	22	τ−1	τ−1	PROPN
ejpam-3654	253	23	(	(	PUNCT
ejpam-3654	253	24	t	t	PROPN
ejpam-3654	253	25	)	)	PUNCT
ejpam-3654	253	26	)	)	PUNCT
ejpam-3654	254	1	p	p	X
ejpam-3654	254	2	(	(	PUNCT
ejpam-3654	254	3	τ−1	τ−1	PROPN
ejpam-3654	254	4	(	(	PUNCT
ejpam-3654	254	5	t	t	PROPN
ejpam-3654	254	6	)	)	PUNCT
ejpam-3654	254	7	)	)	PUNCT
ejpam-3654	255	1	−	−	PROPN
ejpam-3654	255	2	1	1	NUM
ejpam-3654	255	3	p	p	NOUN
ejpam-3654	255	4	(	(	PUNCT
ejpam-3654	255	5	τ−1	τ−1	PROPN
ejpam-3654	255	6	(	(	PUNCT
ejpam-3654	255	7	t	t	PROPN
ejpam-3654	255	8	)	)	PUNCT
ejpam-3654	255	9	)	)	PUNCT
ejpam-3654	256	1	z	z	NOUN
ejpam-3654	256	2	(	(	PUNCT
ejpam-3654	256	3	τ−1	τ−1	PROPN
ejpam-3654	256	4	(	(	PUNCT
ejpam-3654	256	5	τ−1	τ−1	PROPN
ejpam-3654	256	6	(	(	PUNCT
ejpam-3654	256	7	t	t	PROPN
ejpam-3654	256	8	)	)	PUNCT
ejpam-3654	256	9	)	)	PUNCT
ejpam-3654	256	10	)	)	PUNCT
ejpam-3654	257	1	p	p	X
ejpam-3654	257	2	(	(	PUNCT
ejpam-3654	257	3	τ−1	τ−1	PROPN
ejpam-3654	257	4	(	(	PUNCT
ejpam-3654	257	5	τ−1	τ−1	PROPN
ejpam-3654	257	6	(	(	PUNCT
ejpam-3654	257	7	t	t	PROPN
ejpam-3654	257	8	)	)	PUNCT
ejpam-3654	257	9	)	)	PUNCT
ejpam-3654	257	10	)	)	PUNCT
ejpam-3654	257	11	.	.	PUNCT
ejpam-3654	258	1	(	(	PUNCT
ejpam-3654	258	2	35	35	NUM
ejpam-3654	258	3	)	)	PUNCT
ejpam-3654	258	4	assume	assume	VERB
ejpam-3654	258	5	that	that	SCONJ
ejpam-3654	258	6	case	case	NOUN
ejpam-3654	258	7	(	(	PUNCT
ejpam-3654	258	8	c1	c1	NOUN
ejpam-3654	258	9	)	)	PUNCT
ejpam-3654	258	10	holds	hold	VERB
ejpam-3654	258	11	.	.	PUNCT
ejpam-3654	259	1	proceeding	proceed	VERB
ejpam-3654	259	2	as	as	ADP
ejpam-3654	259	3	in	in	ADP
ejpam-3654	259	4	the	the	DET
ejpam-3654	259	5	proof	proof	NOUN
ejpam-3654	259	6	of	of	ADP
ejpam-3654	259	7	lemma	lemma	PROPN
ejpam-3654	259	8	6	6	NUM
ejpam-3654	259	9	,	,	PUNCT
ejpam-3654	259	10	we	we	PRON
ejpam-3654	259	11	get	get	VERB
ejpam-3654	259	12	that	that	PRON
ejpam-3654	259	13	(	(	PUNCT
ejpam-3654	259	14	13	13	NUM
ejpam-3654	259	15	)	)	PUNCT
ejpam-3654	259	16	holds	hold	NOUN
ejpam-3654	259	17	,	,	PUNCT
ejpam-3654	260	1	which	which	PRON
ejpam-3654	260	2	with	with	ADP
ejpam-3654	260	3	the	the	DET
ejpam-3654	260	4	fact	fact	NOUN
ejpam-3654	260	5	that	that	SCONJ
ejpam-3654	260	6	τ	τ	PROPN
ejpam-3654	260	7	(	(	PUNCT
ejpam-3654	260	8	t	t	PROPN
ejpam-3654	260	9	)	)	PUNCT
ejpam-3654	260	10	≤	≤	NOUN
ejpam-3654	260	11	t	t	PROPN
ejpam-3654	260	12	gives	give	VERB
ejpam-3654	260	13	z	z	NOUN
ejpam-3654	260	14	(	(	PUNCT
ejpam-3654	260	15	τ−1	τ−1	PROPN
ejpam-3654	260	16	(	(	PUNCT
ejpam-3654	260	17	τ−1	τ−1	PROPN
ejpam-3654	260	18	(	(	PUNCT
ejpam-3654	260	19	t	t	PROPN
ejpam-3654	260	20	)	)	PUNCT
ejpam-3654	260	21	)	)	PUNCT
ejpam-3654	260	22	)	)	PUNCT
ejpam-3654	260	23	≤	≤	NOUN
ejpam-3654	260	24	(	(	PUNCT
ejpam-3654	260	25	τ−1	τ−1	PROPN
ejpam-3654	260	26	(	(	PUNCT
ejpam-3654	260	27	τ−1	τ−1	PROPN
ejpam-3654	260	28	(	(	PUNCT
ejpam-3654	260	29	t	t	PROPN
ejpam-3654	260	30	)	)	PUNCT
ejpam-3654	260	31	)	)	PUNCT
ejpam-3654	261	1	τ−1	τ−1	PROPN
ejpam-3654	261	2	(	(	PUNCT
ejpam-3654	261	3	t	t	PROPN
ejpam-3654	261	4	)	)	PUNCT
ejpam-3654	261	5	)	)	PUNCT
ejpam-3654	261	6	3	3	NUM
ejpam-3654	261	7	z	z	NOUN
ejpam-3654	261	8	(	(	PUNCT
ejpam-3654	261	9	τ−1	τ−1	PROPN
ejpam-3654	261	10	(	(	PUNCT
ejpam-3654	261	11	t	t	PROPN
ejpam-3654	261	12	)	)	PUNCT
ejpam-3654	261	13	)	)	PUNCT
ejpam-3654	261	14	.	.	PUNCT
ejpam-3654	262	1	(	(	PUNCT
ejpam-3654	262	2	36	36	NUM
ejpam-3654	262	3	)	)	PUNCT
ejpam-3654	262	4	from	from	ADP
ejpam-3654	262	5	(	(	PUNCT
ejpam-3654	262	6	35	35	NUM
ejpam-3654	262	7	)	)	PUNCT
ejpam-3654	262	8	and	and	CCONJ
ejpam-3654	262	9	(	(	PUNCT
ejpam-3654	262	10	36	36	NUM
ejpam-3654	262	11	)	)	PUNCT
ejpam-3654	262	12	,	,	PUNCT
ejpam-3654	262	13	we	we	PRON
ejpam-3654	262	14	find	find	VERB
ejpam-3654	262	15	that	that	SCONJ
ejpam-3654	262	16	x	x	X
ejpam-3654	262	17	(	(	PUNCT
ejpam-3654	262	18	t	t	PROPN
ejpam-3654	262	19	)	)	PUNCT
ejpam-3654	262	20	≥	≥	NOUN
ejpam-3654	262	21	1	1	NUM
ejpam-3654	262	22	p	p	NOUN
ejpam-3654	262	23	(	(	PUNCT
ejpam-3654	262	24	τ−1	τ−1	PROPN
ejpam-3654	262	25	(	(	PUNCT
ejpam-3654	262	26	t	t	PROPN
ejpam-3654	262	27	)	)	PUNCT
ejpam-3654	262	28	)	)	PUNCT
ejpam-3654	262	29	(	(	PUNCT
ejpam-3654	262	30	1−	1−	NUM
ejpam-3654	262	31	(	(	PUNCT
ejpam-3654	262	32	τ−1	τ−1	PROPN
ejpam-3654	262	33	(	(	PUNCT
ejpam-3654	262	34	τ−1	τ−1	PROPN
ejpam-3654	262	35	(	(	PUNCT
ejpam-3654	262	36	t	t	PROPN
ejpam-3654	262	37	)	)	PUNCT
ejpam-3654	262	38	)	)	PUNCT
ejpam-3654	262	39	)	)	PUNCT
ejpam-3654	262	40	3	3	NUM
ejpam-3654	262	41	(	(	PUNCT
ejpam-3654	262	42	τ−1	τ−1	PROPN
ejpam-3654	262	43	(	(	PUNCT
ejpam-3654	262	44	t))3	t))3	NOUN
ejpam-3654	262	45	p	p	NOUN
ejpam-3654	262	46	(	(	PUNCT
ejpam-3654	262	47	τ−1	τ−1	PROPN
ejpam-3654	262	48	(	(	PUNCT
ejpam-3654	262	49	τ−1	τ−1	PROPN
ejpam-3654	262	50	(	(	PUNCT
ejpam-3654	262	51	t	t	PROPN
ejpam-3654	262	52	)	)	PUNCT
ejpam-3654	262	53	)	)	PUNCT
ejpam-3654	262	54	)	)	PUNCT
ejpam-3654	262	55	)	)	PUNCT
ejpam-3654	263	1	z	z	NOUN
ejpam-3654	263	2	(	(	PUNCT
ejpam-3654	263	3	τ−1	τ−1	PROPN
ejpam-3654	263	4	(	(	PUNCT
ejpam-3654	263	5	t	t	PROPN
ejpam-3654	263	6	)	)	PUNCT
ejpam-3654	263	7	)	)	PUNCT
ejpam-3654	263	8	.	.	PUNCT
ejpam-3654	264	1	(	(	PUNCT
ejpam-3654	264	2	37	37	NUM
ejpam-3654	264	3	)	)	PUNCT
ejpam-3654	264	4	assume	assume	VERB
ejpam-3654	264	5	that	that	SCONJ
ejpam-3654	264	6	case	case	NOUN
ejpam-3654	264	7	(	(	PUNCT
ejpam-3654	264	8	c2	c2	PROPN
ejpam-3654	264	9	)	)	PUNCT
ejpam-3654	264	10	holds	hold	VERB
ejpam-3654	264	11	.	.	PUNCT
ejpam-3654	265	1	proceeding	proceed	VERB
ejpam-3654	265	2	as	as	ADP
ejpam-3654	265	3	in	in	ADP
ejpam-3654	265	4	the	the	DET
ejpam-3654	265	5	proof	proof	NOUN
ejpam-3654	265	6	of	of	ADP
ejpam-3654	265	7	(	(	PUNCT
ejpam-3654	265	8	c2	c2	PROPN
ejpam-3654	265	9	)	)	PUNCT
ejpam-3654	265	10	in	in	ADP
ejpam-3654	265	11	lemma	lemma	PROPN
ejpam-3654	265	12	6	6	NUM
ejpam-3654	265	13	,	,	PUNCT
ejpam-3654	265	14	we	we	PRON
ejpam-3654	265	15	get	get	VERB
ejpam-3654	265	16	that	that	PRON
ejpam-3654	265	17	(	(	PUNCT
ejpam-3654	265	18	17	17	NUM
ejpam-3654	265	19	)	)	PUNCT
ejpam-3654	265	20	holds	hold	VERB
ejpam-3654	265	21	.	.	PUNCT
ejpam-3654	266	1	since	since	SCONJ
ejpam-3654	266	2	τ−1	τ−1	PROPN
ejpam-3654	266	3	(	(	PUNCT
ejpam-3654	266	4	t	t	PROPN
ejpam-3654	266	5	)	)	PUNCT
ejpam-3654	266	6	≤	≤	NOUN
ejpam-3654	266	7	τ−1	τ−1	PROPN
ejpam-3654	266	8	(	(	PUNCT
ejpam-3654	266	9	τ−1	τ−1	PROPN
ejpam-3654	266	10	(	(	PUNCT
ejpam-3654	266	11	t	t	PROPN
ejpam-3654	266	12	)	)	PUNCT
ejpam-3654	266	13	)	)	PUNCT
ejpam-3654	266	14	,	,	PUNCT
ejpam-3654	266	15	we	we	PRON
ejpam-3654	266	16	obtain	obtain	VERB
ejpam-3654	266	17	τ−1	τ−1	PROPN
ejpam-3654	266	18	(	(	PUNCT
ejpam-3654	266	19	t	t	NOUN
ejpam-3654	266	20	)	)	PUNCT
ejpam-3654	266	21	z	z	NOUN
ejpam-3654	266	22	(	(	PUNCT
ejpam-3654	266	23	τ−1	τ−1	PROPN
ejpam-3654	266	24	(	(	PUNCT
ejpam-3654	266	25	τ−1	τ−1	PROPN
ejpam-3654	266	26	(	(	PUNCT
ejpam-3654	266	27	t	t	PROPN
ejpam-3654	266	28	)	)	PUNCT
ejpam-3654	266	29	)	)	PUNCT
ejpam-3654	266	30	)	)	PUNCT
ejpam-3654	267	1	≤	≤	NUM
ejpam-3654	267	2	τ−1	τ−1	PROPN
ejpam-3654	267	3	(	(	PUNCT
ejpam-3654	267	4	τ−1	τ−1	PROPN
ejpam-3654	267	5	(	(	PUNCT
ejpam-3654	267	6	t	t	PROPN
ejpam-3654	267	7	)	)	PUNCT
ejpam-3654	267	8	)	)	PUNCT
ejpam-3654	268	1	z	z	NOUN
ejpam-3654	268	2	(	(	PUNCT
ejpam-3654	268	3	τ−1	τ−1	PROPN
ejpam-3654	268	4	(	(	PUNCT
ejpam-3654	268	5	t	t	PROPN
ejpam-3654	268	6	)	)	PUNCT
ejpam-3654	268	7	)	)	PUNCT
ejpam-3654	268	8	.	.	PUNCT
ejpam-3654	269	1	(	(	PUNCT
ejpam-3654	269	2	38	38	NUM
ejpam-3654	269	3	)	)	PUNCT
ejpam-3654	269	4	from	from	ADP
ejpam-3654	269	5	(	(	PUNCT
ejpam-3654	269	6	35	35	NUM
ejpam-3654	269	7	)	)	PUNCT
ejpam-3654	269	8	and	and	CCONJ
ejpam-3654	269	9	(	(	PUNCT
ejpam-3654	269	10	38	38	NUM
ejpam-3654	269	11	)	)	PUNCT
ejpam-3654	269	12	,	,	PUNCT
ejpam-3654	269	13	we	we	PRON
ejpam-3654	269	14	find	find	VERB
ejpam-3654	269	15	x	x	X
ejpam-3654	269	16	(	(	PUNCT
ejpam-3654	269	17	t	t	PROPN
ejpam-3654	269	18	)	)	PUNCT
ejpam-3654	269	19	≥	≥	NOUN
ejpam-3654	269	20	1	1	NUM
ejpam-3654	269	21	p	p	NOUN
ejpam-3654	269	22	(	(	PUNCT
ejpam-3654	269	23	τ−1	τ−1	PROPN
ejpam-3654	269	24	(	(	PUNCT
ejpam-3654	269	25	t	t	PROPN
ejpam-3654	269	26	)	)	PUNCT
ejpam-3654	269	27	)	)	PUNCT
ejpam-3654	270	1	(	(	PUNCT
ejpam-3654	270	2	1−	1−	NUM
ejpam-3654	270	3	(	(	PUNCT
ejpam-3654	270	4	τ−1	τ−1	PROPN
ejpam-3654	270	5	(	(	PUNCT
ejpam-3654	270	6	τ−1	τ−1	PROPN
ejpam-3654	270	7	(	(	PUNCT
ejpam-3654	270	8	t	t	PROPN
ejpam-3654	270	9	)	)	PUNCT
ejpam-3654	270	10	)	)	PUNCT
ejpam-3654	270	11	)	)	PUNCT
ejpam-3654	271	1	(	(	PUNCT
ejpam-3654	271	2	τ−1	τ−1	PROPN
ejpam-3654	271	3	(	(	PUNCT
ejpam-3654	271	4	t	t	PROPN
ejpam-3654	271	5	)	)	PUNCT
ejpam-3654	271	6	)	)	PUNCT
ejpam-3654	272	1	p	p	X
ejpam-3654	272	2	(	(	PUNCT
ejpam-3654	272	3	τ−1	τ−1	PROPN
ejpam-3654	272	4	(	(	PUNCT
ejpam-3654	272	5	τ−1	τ−1	PROPN
ejpam-3654	272	6	(	(	PUNCT
ejpam-3654	272	7	t	t	PROPN
ejpam-3654	272	8	)	)	PUNCT
ejpam-3654	272	9	)	)	PUNCT
ejpam-3654	272	10	)	)	PUNCT
ejpam-3654	272	11	)	)	PUNCT
ejpam-3654	273	1	z	z	NOUN
ejpam-3654	273	2	(	(	PUNCT
ejpam-3654	273	3	τ−1	τ−1	PROPN
ejpam-3654	273	4	(	(	PUNCT
ejpam-3654	273	5	t	t	PROPN
ejpam-3654	273	6	)	)	PUNCT
ejpam-3654	273	7	)	)	PUNCT
ejpam-3654	273	8	.	.	PUNCT
ejpam-3654	274	1	(	(	PUNCT
ejpam-3654	274	2	39	39	NUM
ejpam-3654	274	3	)	)	PUNCT
ejpam-3654	274	4	next	next	ADV
ejpam-3654	274	5	,	,	PUNCT
ejpam-3654	274	6	from	from	ADP
ejpam-3654	274	7	(	(	PUNCT
ejpam-3654	274	8	37	37	NUM
ejpam-3654	274	9	)	)	PUNCT
ejpam-3654	274	10	and	and	CCONJ
ejpam-3654	274	11	(	(	PUNCT
ejpam-3654	274	12	39	39	NUM
ejpam-3654	274	13	)	)	PUNCT
ejpam-3654	274	14	,	,	PUNCT
ejpam-3654	274	15	we	we	PRON
ejpam-3654	274	16	get	get	VERB
ejpam-3654	274	17	that	that	PRON
ejpam-3654	274	18	x	x	X
ejpam-3654	274	19	(	(	PUNCT
ejpam-3654	274	20	t	t	PROPN
ejpam-3654	274	21	)	)	PUNCT
ejpam-3654	274	22	≥	≥	NOUN
ejpam-3654	275	1	p̃	p̃	PROPN
ejpam-3654	275	2	(	(	PUNCT
ejpam-3654	275	3	t	t	PROPN
ejpam-3654	275	4	)	)	PUNCT
ejpam-3654	275	5	z	z	NOUN
ejpam-3654	275	6	(	(	PUNCT
ejpam-3654	275	7	τ−1	τ−1	PROPN
ejpam-3654	275	8	(	(	PUNCT
ejpam-3654	275	9	t	t	PROPN
ejpam-3654	275	10	)	)	PUNCT
ejpam-3654	275	11	)	)	PUNCT
ejpam-3654	275	12	,	,	PUNCT
ejpam-3654	275	13	which	which	PRON
ejpam-3654	275	14	with	with	ADP
ejpam-3654	275	15	(	(	PUNCT
ejpam-3654	275	16	1	1	X
ejpam-3654	275	17	)	)	PUNCT
ejpam-3654	275	18	yields	yield	NOUN
ejpam-3654	275	19	(	(	PUNCT
ejpam-3654	275	20	33	33	NUM
ejpam-3654	275	21	)	)	PUNCT
ejpam-3654	275	22	.	.	PUNCT
ejpam-3654	276	1	therefore	therefore	ADV
ejpam-3654	276	2	,	,	PUNCT
ejpam-3654	276	3	the	the	DET
ejpam-3654	276	4	proof	proof	NOUN
ejpam-3654	276	5	is	be	AUX
ejpam-3654	276	6	complete	complete	ADJ
ejpam-3654	276	7	.	.	PUNCT
ejpam-3654	277	1	lemma	lemma	PROPN
ejpam-3654	277	2	8	8	NUM
ejpam-3654	277	3	.	.	PUNCT
ejpam-3654	278	1	assume	assume	VERB
ejpam-3654	278	2	that	that	SCONJ
ejpam-3654	278	3	σ	σ	PROPN
ejpam-3654	278	4	(	(	PUNCT
ejpam-3654	278	5	t	t	PROPN
ejpam-3654	278	6	)	)	PUNCT
ejpam-3654	278	7	≤	≤	NUM
ejpam-3654	278	8	τ	τ	X
ejpam-3654	278	9	(	(	PUNCT
ejpam-3654	278	10	t	t	PROPN
ejpam-3654	278	11	)	)	PUNCT
ejpam-3654	278	12	,	,	PUNCT
ejpam-3654	278	13	x	x	X
ejpam-3654	278	14	is	be	AUX
ejpam-3654	278	15	an	an	DET
ejpam-3654	278	16	eventually	eventually	ADV
ejpam-3654	278	17	positive	positive	ADJ
ejpam-3654	278	18	solution	solution	NOUN
ejpam-3654	278	19	of	of	ADP
ejpam-3654	278	20	(	(	PUNCT
ejpam-3654	278	21	1	1	NUM
ejpam-3654	278	22	)	)	PUNCT
ejpam-3654	278	23	and	and	CCONJ
ejpam-3654	278	24	the	the	DET
ejpam-3654	278	25	functions	function	NOUN
ejpam-3654	278	26	ω	ω	PROPN
ejpam-3654	278	27	and	and	CCONJ
ejpam-3654	278	28	w	w	NOUN
ejpam-3654	278	29	are	be	AUX
ejpam-3654	278	30	defined	define	VERB
ejpam-3654	278	31	as	as	ADP
ejpam-3654	278	32	in	in	ADP
ejpam-3654	278	33	(	(	PUNCT
ejpam-3654	278	34	9	9	NUM
ejpam-3654	278	35	)	)	PUNCT
ejpam-3654	278	36	.	.	PUNCT
ejpam-3654	279	1	(	(	PUNCT
ejpam-3654	279	2	i3	i3	NOUN
ejpam-3654	279	3	)	)	PUNCT
ejpam-3654	279	4	if	if	SCONJ
ejpam-3654	279	5	x	x	PRON
ejpam-3654	279	6	satisfies	satisfie	NOUN
ejpam-3654	279	7	(	(	PUNCT
ejpam-3654	279	8	c1	c1	PROPN
ejpam-3654	279	9	)	)	PUNCT
ejpam-3654	279	10	,	,	PUNCT
ejpam-3654	279	11	then	then	ADV
ejpam-3654	279	12	ω′	ω′	PROPN
ejpam-3654	279	13	(	(	PUNCT
ejpam-3654	279	14	t	t	PROPN
ejpam-3654	279	15	)	)	PUNCT
ejpam-3654	280	1	+	+	NOUN
ejpam-3654	280	2	q3	q3	PROPN
ejpam-3654	280	3	(	(	PUNCT
ejpam-3654	280	4	t	t	PROPN
ejpam-3654	280	5	)	)	PUNCT
ejpam-3654	281	1	+	+	NOUN
ejpam-3654	281	2	r1	r1	PROPN
ejpam-3654	281	3	(	(	PUNCT
ejpam-3654	281	4	t)ω	t)ω	X
ejpam-3654	281	5	α+1	α+1	NUM
ejpam-3654	281	6	α	α	PROPN
ejpam-3654	281	7	(	(	PUNCT
ejpam-3654	281	8	t	t	PROPN
ejpam-3654	281	9	)	)	PUNCT
ejpam-3654	281	10	≤	≤	NOUN
ejpam-3654	281	11	0	0	NUM
ejpam-3654	281	12	;	;	PUNCT
ejpam-3654	281	13	(	(	PUNCT
ejpam-3654	281	14	i4	i4	PROPN
ejpam-3654	281	15	)	)	PUNCT
ejpam-3654	281	16	if	if	SCONJ
ejpam-3654	281	17	x	x	PRON
ejpam-3654	281	18	satisfies	satisfie	NOUN
ejpam-3654	281	19	(	(	PUNCT
ejpam-3654	281	20	c2	c2	PROPN
ejpam-3654	281	21	)	)	PUNCT
ejpam-3654	281	22	,	,	PUNCT
ejpam-3654	281	23	then	then	ADV
ejpam-3654	281	24	w′	w′	PROPN
ejpam-3654	281	25	(	(	PUNCT
ejpam-3654	281	26	t	t	PROPN
ejpam-3654	281	27	)	)	PUNCT
ejpam-3654	281	28	+	+	PROPN
ejpam-3654	281	29	q4	q4	PROPN
ejpam-3654	281	30	(	(	PUNCT
ejpam-3654	281	31	t	t	PROPN
ejpam-3654	281	32	)	)	PUNCT
ejpam-3654	281	33	+	+	NUM
ejpam-3654	281	34	w2	w2	NOUN
ejpam-3654	281	35	(	(	PUNCT
ejpam-3654	281	36	t	t	PROPN
ejpam-3654	281	37	)	)	PUNCT
ejpam-3654	281	38	≤	≤	NOUN
ejpam-3654	281	39	0	0	NUM
ejpam-3654	281	40	,	,	PUNCT
ejpam-3654	281	41	where	where	SCONJ
ejpam-3654	281	42	q3	q3	PROPN
ejpam-3654	281	43	(	(	PUNCT
ejpam-3654	281	44	t	t	PROPN
ejpam-3654	281	45	)	)	PUNCT
ejpam-3654	281	46	=	=	SYM
ejpam-3654	281	47	q	q	X
ejpam-3654	281	48	(	(	PUNCT
ejpam-3654	281	49	t	t	NOUN
ejpam-3654	281	50	)	)	PUNCT
ejpam-3654	281	51	p̃β	p̃β	NOUN
ejpam-3654	281	52	(	(	PUNCT
ejpam-3654	281	53	σ	σ	PROPN
ejpam-3654	281	54	(	(	PUNCT
ejpam-3654	281	55	t))mβ−α	t))mβ−α	NOUN
ejpam-3654	281	56	3	3	NUM
ejpam-3654	281	57	(	(	PUNCT
ejpam-3654	281	58	τ−1	τ−1	PROPN
ejpam-3654	281	59	(	(	PUNCT
ejpam-3654	281	60	σ	σ	PROPN
ejpam-3654	281	61	(	(	PUNCT
ejpam-3654	281	62	t	t	PROPN
ejpam-3654	281	63	)	)	PUNCT
ejpam-3654	281	64	)	)	PUNCT
ejpam-3654	282	1	t	t	NOUN
ejpam-3654	282	2	)	)	PUNCT
ejpam-3654	282	3	3α	3α	PROPN
ejpam-3654	282	4	and	and	CCONJ
ejpam-3654	282	5	q4	q4	PROPN
ejpam-3654	282	6	(	(	PUNCT
ejpam-3654	282	7	t	t	PROPN
ejpam-3654	282	8	)	)	PUNCT
ejpam-3654	282	9	=	=	PUNCT
ejpam-3654	283	1	p̃β	p̃β	NOUN
ejpam-3654	283	2	/	/	SYM
ejpam-3654	283	3	α	α	PROPN
ejpam-3654	283	4	(	(	PUNCT
ejpam-3654	283	5	σ	σ	PROPN
ejpam-3654	283	6	(	(	PUNCT
ejpam-3654	283	7	s))m	s))m	NOUN
ejpam-3654	283	8	(	(	PUNCT
ejpam-3654	283	9	β	β	X
ejpam-3654	283	10	/	/	SYM
ejpam-3654	283	11	α)−1	α)−1	NOUN
ejpam-3654	283	12	4	4	NUM
ejpam-3654	283	13	∫	∫	NOUN
ejpam-3654	283	14	∞	∞	PROPN
ejpam-3654	283	15	t	t	PROPN
ejpam-3654	283	16	(	(	PUNCT
ejpam-3654	283	17	1	1	NUM
ejpam-3654	283	18	r	r	NOUN
ejpam-3654	283	19	(	(	PUNCT
ejpam-3654	283	20	u	u	NOUN
ejpam-3654	283	21	)	)	PUNCT
ejpam-3654	283	22	∫	∫	PROPN
ejpam-3654	284	1	∞	∞	NUM
ejpam-3654	284	2	u	u	PROPN
ejpam-3654	284	3	q	q	X
ejpam-3654	284	4	(	(	PUNCT
ejpam-3654	284	5	s	s	NOUN
ejpam-3654	284	6	)	)	PUNCT
ejpam-3654	284	7	(	(	PUNCT
ejpam-3654	284	8	τ−1	τ−1	PROPN
ejpam-3654	284	9	(	(	PUNCT
ejpam-3654	284	10	σ	σ	PROPN
ejpam-3654	284	11	(	(	PUNCT
ejpam-3654	284	12	s	s	NOUN
ejpam-3654	284	13	)	)	PUNCT
ejpam-3654	284	14	)	)	PUNCT
ejpam-3654	284	15	s	s	PART
ejpam-3654	284	16	)	)	PUNCT
ejpam-3654	284	17	β	β	X
ejpam-3654	284	18	ds	ds	X
ejpam-3654	284	19	)	)	PUNCT
ejpam-3654	284	20	1	1	PROPN
ejpam-3654	284	21	/	/	SYM
ejpam-3654	284	22	α	α	DET
ejpam-3654	284	23	du	du	PROPN
ejpam-3654	284	24	.	.	PUNCT
ejpam-3654	284	25	o.	o.	PROPN
ejpam-3654	284	26	moaaz	moaaz	PROPN
ejpam-3654	284	27	,	,	PUNCT
ejpam-3654	284	28	c.	c.	PROPN
ejpam-3654	284	29	cesarano	cesarano	PROPN
ejpam-3654	284	30	,	,	PUNCT
ejpam-3654	284	31	a.	a.	NOUN
ejpam-3654	284	32	muhib	muhib	NOUN
ejpam-3654	284	33	/	/	SYM
ejpam-3654	284	34	eur	eur	PROPN
ejpam-3654	284	35	.	.	PUNCT
ejpam-3654	285	1	j.	j.	PROPN
ejpam-3654	285	2	pure	pure	PROPN
ejpam-3654	285	3	appl	appl	PROPN
ejpam-3654	285	4	.	.	PROPN
ejpam-3654	285	5	math	math	PROPN
ejpam-3654	285	6	,	,	PUNCT
ejpam-3654	285	7	13	13	NUM
ejpam-3654	285	8	(	(	PUNCT
ejpam-3654	285	9	2	2	NUM
ejpam-3654	285	10	)	)	PUNCT
ejpam-3654	285	11	(	(	PUNCT
ejpam-3654	285	12	2020	2020	NUM
ejpam-3654	285	13	)	)	PUNCT
ejpam-3654	285	14	,	,	PUNCT
ejpam-3654	285	15	185	185	NUM
ejpam-3654	285	16	-	-	SYM
ejpam-3654	285	17	199	199	NUM
ejpam-3654	285	18	196	196	NUM
ejpam-3654	285	19	proof	proof	NOUN
ejpam-3654	285	20	.	.	PUNCT
ejpam-3654	286	1	assume	assume	VERB
ejpam-3654	286	2	that	that	SCONJ
ejpam-3654	286	3	x	x	PRON
ejpam-3654	286	4	is	be	AUX
ejpam-3654	286	5	an	an	DET
ejpam-3654	286	6	eventually	eventually	ADV
ejpam-3654	286	7	positive	positive	ADJ
ejpam-3654	286	8	solution	solution	NOUN
ejpam-3654	286	9	of	of	ADP
ejpam-3654	286	10	(	(	PUNCT
ejpam-3654	286	11	1	1	NUM
ejpam-3654	286	12	)	)	PUNCT
ejpam-3654	286	13	.	.	PUNCT
ejpam-3654	287	1	then	then	ADV
ejpam-3654	287	2	,	,	PUNCT
ejpam-3654	287	3	there	there	PRON
ejpam-3654	287	4	exists	exist	VERB
ejpam-3654	287	5	a	a	DET
ejpam-3654	287	6	t1	t1	NOUN
ejpam-3654	287	7	≥	≥	NOUN
ejpam-3654	287	8	t0	t0	NOUN
ejpam-3654	287	9	such	such	ADJ
ejpam-3654	287	10	that	that	SCONJ
ejpam-3654	287	11	x	x	X
ejpam-3654	287	12	(	(	PUNCT
ejpam-3654	287	13	t	t	PROPN
ejpam-3654	287	14	)	)	PUNCT
ejpam-3654	287	15	>	>	X
ejpam-3654	287	16	0	0	NUM
ejpam-3654	287	17	,	,	PUNCT
ejpam-3654	287	18	x	x	X
ejpam-3654	287	19	(	(	PUNCT
ejpam-3654	287	20	τ	τ	X
ejpam-3654	287	21	(	(	PUNCT
ejpam-3654	287	22	t	t	PROPN
ejpam-3654	287	23	)	)	PUNCT
ejpam-3654	287	24	)	)	PUNCT
ejpam-3654	287	25	>	>	X
ejpam-3654	287	26	0	0	PUNCT
ejpam-3654	288	1	and	and	CCONJ
ejpam-3654	288	2	x	x	SYM
ejpam-3654	288	3	(	(	PUNCT
ejpam-3654	288	4	σ	σ	PROPN
ejpam-3654	288	5	(	(	PUNCT
ejpam-3654	288	6	t	t	PROPN
ejpam-3654	288	7	)	)	PUNCT
ejpam-3654	288	8	)	)	PUNCT
ejpam-3654	288	9	>	>	X
ejpam-3654	288	10	0	0	PUNCT
ejpam-3654	289	1	for	for	ADP
ejpam-3654	289	2	t	t	PROPN
ejpam-3654	289	3	≥	≥	NOUN
ejpam-3654	289	4	t1	t1	NOUN
ejpam-3654	289	5	.	.	PUNCT
ejpam-3654	290	1	using	use	VERB
ejpam-3654	290	2	lemma	lemma	PROPN
ejpam-3654	290	3	7	7	NUM
ejpam-3654	290	4	,	,	PUNCT
ejpam-3654	290	5	we	we	PRON
ejpam-3654	290	6	obtain	obtain	VERB
ejpam-3654	290	7	that	that	SCONJ
ejpam-3654	290	8	(	(	PUNCT
ejpam-3654	290	9	33	33	NUM
ejpam-3654	290	10	)	)	PUNCT
ejpam-3654	290	11	holds	hold	VERB
ejpam-3654	290	12	.	.	PUNCT
ejpam-3654	291	1	in	in	ADP
ejpam-3654	291	2	the	the	DET
ejpam-3654	291	3	case	case	NOUN
ejpam-3654	291	4	(	(	PUNCT
ejpam-3654	291	5	c1	c1	NOUN
ejpam-3654	291	6	)	)	PUNCT
ejpam-3654	291	7	,	,	PUNCT
ejpam-3654	291	8	by	by	ADP
ejpam-3654	291	9	differentiating	differentiate	VERB
ejpam-3654	291	10	ω	ω	PROPN
ejpam-3654	291	11	and	and	CCONJ
ejpam-3654	291	12	using	use	VERB
ejpam-3654	291	13	(	(	PUNCT
ejpam-3654	291	14	33	33	NUM
ejpam-3654	291	15	)	)	PUNCT
ejpam-3654	291	16	,	,	PUNCT
ejpam-3654	291	17	we	we	PRON
ejpam-3654	291	18	obtain	obtain	VERB
ejpam-3654	291	19	ω′	ω′	PROPN
ejpam-3654	291	20	(	(	PUNCT
ejpam-3654	291	21	t	t	PROPN
ejpam-3654	291	22	)	)	PUNCT
ejpam-3654	291	23	≤	≤	NOUN
ejpam-3654	291	24	−	−	ADP
ejpam-3654	291	25	q	q	NOUN
ejpam-3654	291	26	(	(	PUNCT
ejpam-3654	291	27	t	t	NOUN
ejpam-3654	291	28	)	)	PUNCT
ejpam-3654	291	29	p̃β	p̃β	NOUN
ejpam-3654	291	30	(	(	PUNCT
ejpam-3654	291	31	σ	σ	PROPN
ejpam-3654	291	32	(	(	PUNCT
ejpam-3654	291	33	t	t	PROPN
ejpam-3654	291	34	)	)	PUNCT
ejpam-3654	291	35	)	)	PUNCT
ejpam-3654	292	1	zβ	zβ	PROPN
ejpam-3654	292	2	(	(	PUNCT
ejpam-3654	292	3	τ−1	τ−1	PROPN
ejpam-3654	292	4	(	(	PUNCT
ejpam-3654	292	5	σ	σ	PROPN
ejpam-3654	292	6	(	(	PUNCT
ejpam-3654	292	7	t	t	PROPN
ejpam-3654	292	8	)	)	PUNCT
ejpam-3654	292	9	)	)	PUNCT
ejpam-3654	292	10	)	)	PUNCT
ejpam-3654	293	1	zα	zα	PROPN
ejpam-3654	293	2	(	(	PUNCT
ejpam-3654	293	3	t	t	PROPN
ejpam-3654	293	4	)	)	PUNCT
ejpam-3654	293	5	−	−	PROPN
ejpam-3654	294	1	αr	αr	PROPN
ejpam-3654	294	2	(	(	PUNCT
ejpam-3654	294	3	t	t	PROPN
ejpam-3654	294	4	)	)	PUNCT
ejpam-3654	294	5	(	(	PUNCT
ejpam-3654	294	6	z′′′	z′′′	PROPN
ejpam-3654	294	7	(	(	PUNCT
ejpam-3654	294	8	t))α	t))α	NOUN
ejpam-3654	294	9	zα+1	zα+1	PROPN
ejpam-3654	294	10	(	(	PUNCT
ejpam-3654	294	11	t	t	NOUN
ejpam-3654	294	12	)	)	PUNCT
ejpam-3654	294	13	z′	z′	PROPN
ejpam-3654	294	14	(	(	PUNCT
ejpam-3654	294	15	t	t	PROPN
ejpam-3654	294	16	)	)	PUNCT
ejpam-3654	294	17	.	.	PUNCT
ejpam-3654	295	1	(	(	PUNCT
ejpam-3654	295	2	40	40	NUM
ejpam-3654	295	3	)	)	PUNCT
ejpam-3654	295	4	from	from	ADP
ejpam-3654	295	5	lemma	lemma	PROPN
ejpam-3654	295	6	1	1	NUM
ejpam-3654	295	7	,	,	PUNCT
ejpam-3654	295	8	we	we	PRON
ejpam-3654	295	9	have	have	VERB
ejpam-3654	295	10	that	that	DET
ejpam-3654	295	11	z	z	PROPN
ejpam-3654	295	12	(	(	PUNCT
ejpam-3654	295	13	t	t	PROPN
ejpam-3654	295	14	)	)	PUNCT
ejpam-3654	295	15	≥	≥	NOUN
ejpam-3654	295	16	t	t	PROPN
ejpam-3654	295	17	3	3	NUM
ejpam-3654	295	18	z′	z′	NUM
ejpam-3654	295	19	(	(	PUNCT
ejpam-3654	295	20	t	t	PROPN
ejpam-3654	295	21	)	)	PUNCT
ejpam-3654	295	22	and	and	CCONJ
ejpam-3654	295	23	hence	hence	ADV
ejpam-3654	295	24	z	z	PROPN
ejpam-3654	295	25	(	(	PUNCT
ejpam-3654	295	26	τ−1	τ−1	PROPN
ejpam-3654	295	27	(	(	PUNCT
ejpam-3654	295	28	σ	σ	PROPN
ejpam-3654	295	29	(	(	PUNCT
ejpam-3654	295	30	t	t	PROPN
ejpam-3654	295	31	)	)	PUNCT
ejpam-3654	295	32	)	)	PUNCT
ejpam-3654	295	33	)	)	PUNCT
ejpam-3654	296	1	z	z	NOUN
ejpam-3654	296	2	(	(	PUNCT
ejpam-3654	296	3	t	t	PROPN
ejpam-3654	296	4	)	)	PUNCT
ejpam-3654	296	5	≥	≥	PROPN
ejpam-3654	296	6	(	(	PUNCT
ejpam-3654	296	7	τ−1	τ−1	PROPN
ejpam-3654	296	8	(	(	PUNCT
ejpam-3654	296	9	σ	σ	PROPN
ejpam-3654	296	10	(	(	PUNCT
ejpam-3654	296	11	t	t	PROPN
ejpam-3654	296	12	)	)	PUNCT
ejpam-3654	296	13	)	)	PUNCT
ejpam-3654	296	14	)	)	PUNCT
ejpam-3654	297	1	3	3	NUM
ejpam-3654	297	2	t3	t3	NOUN
ejpam-3654	297	3	.	.	PUNCT
ejpam-3654	298	1	(	(	PUNCT
ejpam-3654	298	2	41	41	NUM
ejpam-3654	298	3	)	)	PUNCT
ejpam-3654	298	4	it	it	PRON
ejpam-3654	298	5	follows	follow	VERB
ejpam-3654	298	6	from	from	ADP
ejpam-3654	298	7	lemma	lemma	PROPN
ejpam-3654	298	8	2	2	NUM
ejpam-3654	298	9	that	that	SCONJ
ejpam-3654	298	10	z′	z′	NUM
ejpam-3654	298	11	(	(	PUNCT
ejpam-3654	298	12	t	t	PROPN
ejpam-3654	298	13	)	)	PUNCT
ejpam-3654	298	14	≥	≥	NOUN
ejpam-3654	298	15	µ1	µ1	PROPN
ejpam-3654	298	16	2	2	NUM
ejpam-3654	298	17	t2z′′′	t2z′′′	PROPN
ejpam-3654	298	18	(	(	PUNCT
ejpam-3654	298	19	t	t	PROPN
ejpam-3654	298	20	)	)	PUNCT
ejpam-3654	298	21	,	,	PUNCT
ejpam-3654	298	22	(	(	PUNCT
ejpam-3654	298	23	42	42	NUM
ejpam-3654	298	24	)	)	PUNCT
ejpam-3654	298	25	for	for	ADP
ejpam-3654	298	26	all	all	DET
ejpam-3654	298	27	µ1	µ1	PROPN
ejpam-3654	298	28	∈	∈	PROPN
ejpam-3654	298	29	(	(	PUNCT
ejpam-3654	298	30	0	0	NUM
ejpam-3654	298	31	,	,	PUNCT
ejpam-3654	298	32	1	1	NUM
ejpam-3654	298	33	)	)	PUNCT
ejpam-3654	298	34	and	and	CCONJ
ejpam-3654	298	35	every	every	DET
ejpam-3654	298	36	sufficiently	sufficiently	ADV
ejpam-3654	298	37	large	large	ADJ
ejpam-3654	298	38	t.	t.	NOUN
ejpam-3654	298	39	since	since	SCONJ
ejpam-3654	298	40	z′	z′	PROPN
ejpam-3654	298	41	(	(	PUNCT
ejpam-3654	298	42	t	t	PROPN
ejpam-3654	298	43	)	)	PUNCT
ejpam-3654	298	44	>	>	X
ejpam-3654	299	1	0	0	NUM
ejpam-3654	299	2	,	,	PUNCT
ejpam-3654	299	3	there	there	PRON
ejpam-3654	299	4	exist	exist	VERB
ejpam-3654	299	5	a	a	DET
ejpam-3654	299	6	t2	t2	NOUN
ejpam-3654	299	7	≥	≥	NOUN
ejpam-3654	299	8	t1	t1	NOUN
ejpam-3654	299	9	and	and	CCONJ
ejpam-3654	299	10	a	a	DET
ejpam-3654	299	11	constant	constant	ADJ
ejpam-3654	299	12	m	m	NOUN
ejpam-3654	299	13	>	>	X
ejpam-3654	299	14	0	0	NUM
ejpam-3654	299	15	such	such	ADJ
ejpam-3654	299	16	that	that	SCONJ
ejpam-3654	299	17	z	z	NOUN
ejpam-3654	299	18	(	(	PUNCT
ejpam-3654	299	19	t	t	PROPN
ejpam-3654	299	20	)	)	PUNCT
ejpam-3654	299	21	>	>	X
ejpam-3654	300	1	m	m	PROPN
ejpam-3654	300	2	,	,	PUNCT
ejpam-3654	300	3	(	(	PUNCT
ejpam-3654	300	4	43	43	NUM
ejpam-3654	300	5	)	)	PUNCT
ejpam-3654	300	6	for	for	ADP
ejpam-3654	300	7	t	t	PROPN
ejpam-3654	300	8	≥	≥	PROPN
ejpam-3654	300	9	t2	t2	PROPN
ejpam-3654	300	10	.	.	PUNCT
ejpam-3654	301	1	thus	thus	ADV
ejpam-3654	301	2	,	,	PUNCT
ejpam-3654	301	3	by	by	ADP
ejpam-3654	301	4	(	(	PUNCT
ejpam-3654	301	5	40	40	NUM
ejpam-3654	301	6	)	)	PUNCT
ejpam-3654	301	7	,	,	PUNCT
ejpam-3654	301	8	(	(	PUNCT
ejpam-3654	301	9	41	41	NUM
ejpam-3654	301	10	)	)	PUNCT
ejpam-3654	301	11	,	,	PUNCT
ejpam-3654	301	12	(	(	PUNCT
ejpam-3654	301	13	42	42	NUM
ejpam-3654	301	14	)	)	PUNCT
ejpam-3654	301	15	and	and	CCONJ
ejpam-3654	301	16	(	(	PUNCT
ejpam-3654	301	17	43	43	NUM
ejpam-3654	301	18	)	)	PUNCT
ejpam-3654	301	19	,	,	PUNCT
ejpam-3654	301	20	we	we	PRON
ejpam-3654	301	21	get	get	VERB
ejpam-3654	301	22	ω′	ω′	PROPN
ejpam-3654	301	23	(	(	PUNCT
ejpam-3654	301	24	t	t	PROPN
ejpam-3654	301	25	)	)	PUNCT
ejpam-3654	302	1	+	+	NOUN
ejpam-3654	302	2	q3	q3	PROPN
ejpam-3654	302	3	(	(	PUNCT
ejpam-3654	302	4	t	t	PROPN
ejpam-3654	302	5	)	)	PUNCT
ejpam-3654	303	1	+	+	NOUN
ejpam-3654	303	2	r1	r1	PROPN
ejpam-3654	303	3	(	(	PUNCT
ejpam-3654	303	4	t)ω	t)ω	X
ejpam-3654	303	5	α+1	α+1	NUM
ejpam-3654	303	6	α	α	PROPN
ejpam-3654	303	7	(	(	PUNCT
ejpam-3654	303	8	t	t	PROPN
ejpam-3654	303	9	)	)	PUNCT
ejpam-3654	303	10	≤	≤	NOUN
ejpam-3654	303	11	0	0	NUM
ejpam-3654	303	12	.	.	PUNCT
ejpam-3654	304	1	in	in	ADP
ejpam-3654	304	2	the	the	DET
ejpam-3654	304	3	case	case	NOUN
ejpam-3654	304	4	(	(	PUNCT
ejpam-3654	304	5	c2	c2	PROPN
ejpam-3654	304	6	)	)	PUNCT
ejpam-3654	304	7	,	,	PUNCT
ejpam-3654	304	8	integrating	integrate	VERB
ejpam-3654	304	9	(	(	PUNCT
ejpam-3654	304	10	33	33	NUM
ejpam-3654	304	11	)	)	PUNCT
ejpam-3654	304	12	from	from	ADP
ejpam-3654	304	13	t	t	PROPN
ejpam-3654	304	14	to	to	ADP
ejpam-3654	304	15	u	u	NOUN
ejpam-3654	304	16	,	,	PUNCT
ejpam-3654	304	17	we	we	PRON
ejpam-3654	304	18	obtain	obtain	VERB
ejpam-3654	304	19	r	r	NOUN
ejpam-3654	304	20	(	(	PUNCT
ejpam-3654	304	21	u	u	NOUN
ejpam-3654	304	22	)	)	PUNCT
ejpam-3654	304	23	(	(	PUNCT
ejpam-3654	304	24	z′′′	z′′′	PROPN
ejpam-3654	304	25	(	(	PUNCT
ejpam-3654	304	26	u	u	NOUN
ejpam-3654	304	27	)	)	PUNCT
ejpam-3654	304	28	)	)	PUNCT
ejpam-3654	305	1	α	α	PRON
ejpam-3654	305	2	−	−	NOUN
ejpam-3654	306	1	r	r	NOUN
ejpam-3654	306	2	(	(	PUNCT
ejpam-3654	306	3	t	t	NOUN
ejpam-3654	306	4	)	)	PUNCT
ejpam-3654	306	5	(	(	PUNCT
ejpam-3654	306	6	z′′′	z′′′	PROPN
ejpam-3654	306	7	(	(	PUNCT
ejpam-3654	306	8	t	t	PROPN
ejpam-3654	306	9	)	)	PUNCT
ejpam-3654	306	10	)	)	PUNCT
ejpam-3654	307	1	α	α	PROPN
ejpam-3654	307	2	≤	≤	PUNCT
ejpam-3654	307	3	−∫	−∫	X
ejpam-3654	307	4	u	u	NOUN
ejpam-3654	307	5	t	t	PROPN
ejpam-3654	307	6	q	q	PROPN
ejpam-3654	307	7	(	(	PUNCT
ejpam-3654	307	8	s	s	NOUN
ejpam-3654	307	9	)	)	PUNCT
ejpam-3654	307	10	p̃β	p̃β	NOUN
ejpam-3654	307	11	(	(	PUNCT
ejpam-3654	307	12	σ	σ	X
ejpam-3654	307	13	(	(	PUNCT
ejpam-3654	307	14	s	s	NOUN
ejpam-3654	307	15	)	)	PUNCT
ejpam-3654	307	16	)	)	PUNCT
ejpam-3654	307	17	zβ	zβ	PROPN
ejpam-3654	307	18	(	(	PUNCT
ejpam-3654	307	19	τ−1	τ−1	PROPN
ejpam-3654	307	20	(	(	PUNCT
ejpam-3654	307	21	σ	σ	PROPN
ejpam-3654	307	22	(	(	PUNCT
ejpam-3654	307	23	s	s	NOUN
ejpam-3654	307	24	)	)	PUNCT
ejpam-3654	307	25	)	)	PUNCT
ejpam-3654	307	26	)	)	PUNCT
ejpam-3654	308	1	ds	ds	ADJ
ejpam-3654	308	2	≤	≤	NUM
ejpam-3654	308	3	0	0	NUM
ejpam-3654	308	4	.	.	PUNCT
ejpam-3654	309	1	(	(	PUNCT
ejpam-3654	309	2	44	44	NUM
ejpam-3654	309	3	)	)	PUNCT
ejpam-3654	309	4	from	from	ADP
ejpam-3654	309	5	lemma	lemma	PROPN
ejpam-3654	309	6	1	1	NUM
ejpam-3654	309	7	,	,	PUNCT
ejpam-3654	309	8	we	we	PRON
ejpam-3654	309	9	get	get	VERB
ejpam-3654	309	10	that	that	DET
ejpam-3654	309	11	z	z	NOUN
ejpam-3654	309	12	(	(	PUNCT
ejpam-3654	309	13	t	t	PROPN
ejpam-3654	309	14	)	)	PUNCT
ejpam-3654	309	15	≥	≥	NOUN
ejpam-3654	309	16	tz′	tz′	NOUN
ejpam-3654	309	17	(	(	PUNCT
ejpam-3654	309	18	t	t	NOUN
ejpam-3654	309	19	)	)	PUNCT
ejpam-3654	309	20	and	and	CCONJ
ejpam-3654	309	21	hence	hence	ADV
ejpam-3654	309	22	z	z	PROPN
ejpam-3654	309	23	(	(	PUNCT
ejpam-3654	309	24	τ−1	τ−1	PROPN
ejpam-3654	309	25	(	(	PUNCT
ejpam-3654	309	26	σ	σ	PROPN
ejpam-3654	309	27	(	(	PUNCT
ejpam-3654	309	28	t	t	PROPN
ejpam-3654	309	29	)	)	PUNCT
ejpam-3654	309	30	)	)	PUNCT
ejpam-3654	309	31	)	)	PUNCT
ejpam-3654	310	1	≥	≥	PROPN
ejpam-3654	311	1	τ−1	τ−1	PROPN
ejpam-3654	311	2	(	(	PUNCT
ejpam-3654	311	3	σ	σ	PROPN
ejpam-3654	311	4	(	(	PUNCT
ejpam-3654	311	5	t	t	PROPN
ejpam-3654	311	6	)	)	PUNCT
ejpam-3654	311	7	)	)	PUNCT
ejpam-3654	312	1	t	t	PROPN
ejpam-3654	312	2	z	z	PROPN
ejpam-3654	312	3	(	(	PUNCT
ejpam-3654	312	4	t	t	PROPN
ejpam-3654	312	5	)	)	PUNCT
ejpam-3654	312	6	.	.	PUNCT
ejpam-3654	313	1	(	(	PUNCT
ejpam-3654	313	2	45	45	NUM
ejpam-3654	313	3	)	)	PUNCT
ejpam-3654	313	4	for	for	ADP
ejpam-3654	313	5	(	(	PUNCT
ejpam-3654	313	6	44	44	NUM
ejpam-3654	313	7	)	)	PUNCT
ejpam-3654	313	8	,	,	PUNCT
ejpam-3654	313	9	letting	let	VERB
ejpam-3654	313	10	u→∞	u→∞	NUM
ejpam-3654	313	11	and	and	CCONJ
ejpam-3654	313	12	using	use	VERB
ejpam-3654	313	13	(	(	PUNCT
ejpam-3654	313	14	45	45	NUM
ejpam-3654	313	15	)	)	PUNCT
ejpam-3654	313	16	,	,	PUNCT
ejpam-3654	313	17	we	we	PRON
ejpam-3654	313	18	see	see	VERB
ejpam-3654	313	19	that	that	SCONJ
ejpam-3654	314	1	r	r	NOUN
ejpam-3654	314	2	(	(	PUNCT
ejpam-3654	314	3	t	t	NOUN
ejpam-3654	314	4	)	)	PUNCT
ejpam-3654	314	5	(	(	PUNCT
ejpam-3654	314	6	z′′′	z′′′	PROPN
ejpam-3654	314	7	(	(	PUNCT
ejpam-3654	314	8	t	t	PROPN
ejpam-3654	314	9	)	)	PUNCT
ejpam-3654	314	10	)	)	PUNCT
ejpam-3654	315	1	α	α	PRON
ejpam-3654	315	2	≥	≥	NOUN
ejpam-3654	315	3	p̃β	p̃β	NOUN
ejpam-3654	315	4	(	(	PUNCT
ejpam-3654	315	5	σ	σ	X
ejpam-3654	315	6	(	(	PUNCT
ejpam-3654	315	7	s	s	NOUN
ejpam-3654	315	8	)	)	PUNCT
ejpam-3654	315	9	)	)	PUNCT
ejpam-3654	315	10	zβ	zβ	PROPN
ejpam-3654	315	11	(	(	PUNCT
ejpam-3654	315	12	t	t	PROPN
ejpam-3654	315	13	)	)	PUNCT
ejpam-3654	315	14	∫	∫	PROPN
ejpam-3654	316	1	∞	∞	PROPN
ejpam-3654	316	2	t	t	PROPN
ejpam-3654	316	3	q	q	X
ejpam-3654	316	4	(	(	PUNCT
ejpam-3654	316	5	s	s	NOUN
ejpam-3654	316	6	)	)	PUNCT
ejpam-3654	316	7	(	(	PUNCT
ejpam-3654	316	8	τ−1	τ−1	PROPN
ejpam-3654	316	9	(	(	PUNCT
ejpam-3654	316	10	σ	σ	PROPN
ejpam-3654	316	11	(	(	PUNCT
ejpam-3654	316	12	s	s	NOUN
ejpam-3654	316	13	)	)	PUNCT
ejpam-3654	316	14	)	)	PUNCT
ejpam-3654	316	15	s	s	PART
ejpam-3654	316	16	)	)	PUNCT
ejpam-3654	316	17	β	β	X
ejpam-3654	316	18	ds	ds	X
ejpam-3654	316	19	.	.	NOUN
ejpam-3654	316	20	integrating	integrate	VERB
ejpam-3654	316	21	this	this	DET
ejpam-3654	316	22	inequality	inequality	NOUN
ejpam-3654	316	23	again	again	ADV
ejpam-3654	316	24	from	from	ADP
ejpam-3654	316	25	t	t	PROPN
ejpam-3654	316	26	to	to	ADP
ejpam-3654	316	27	∞	∞	PROPN
ejpam-3654	316	28	,	,	PUNCT
ejpam-3654	316	29	we	we	PRON
ejpam-3654	316	30	get	get	VERB
ejpam-3654	316	31	z′′	z′′	NOUN
ejpam-3654	316	32	(	(	PUNCT
ejpam-3654	316	33	t	t	PROPN
ejpam-3654	316	34	)	)	PUNCT
ejpam-3654	316	35	≤	≤	NOUN
ejpam-3654	316	36	−p̃β	−p̃β	PROPN
ejpam-3654	316	37	/	/	SYM
ejpam-3654	316	38	α	α	PROPN
ejpam-3654	316	39	(	(	PUNCT
ejpam-3654	316	40	σ	σ	X
ejpam-3654	316	41	(	(	PUNCT
ejpam-3654	316	42	s	s	NOUN
ejpam-3654	316	43	)	)	PUNCT
ejpam-3654	316	44	)	)	PUNCT
ejpam-3654	317	1	zβ	zβ	PROPN
ejpam-3654	317	2	/	/	SYM
ejpam-3654	317	3	α	α	PROPN
ejpam-3654	317	4	(	(	PUNCT
ejpam-3654	317	5	t	t	PROPN
ejpam-3654	317	6	)	)	PUNCT
ejpam-3654	317	7	∫	∫	PROPN
ejpam-3654	318	1	∞	∞	PROPN
ejpam-3654	318	2	t	t	PROPN
ejpam-3654	318	3	(	(	PUNCT
ejpam-3654	318	4	1	1	NUM
ejpam-3654	318	5	r	r	NOUN
ejpam-3654	318	6	(	(	PUNCT
ejpam-3654	318	7	u	u	NOUN
ejpam-3654	318	8	)	)	PUNCT
ejpam-3654	318	9	∫	∫	PROPN
ejpam-3654	318	10	∞	∞	NUM
ejpam-3654	318	11	u	u	PROPN
ejpam-3654	318	12	q	q	X
ejpam-3654	318	13	(	(	PUNCT
ejpam-3654	318	14	s	s	NOUN
ejpam-3654	318	15	)	)	PUNCT
ejpam-3654	318	16	(	(	PUNCT
ejpam-3654	318	17	τ−1	τ−1	PROPN
ejpam-3654	318	18	(	(	PUNCT
ejpam-3654	318	19	σ	σ	PROPN
ejpam-3654	318	20	(	(	PUNCT
ejpam-3654	318	21	s	s	NOUN
ejpam-3654	318	22	)	)	PUNCT
ejpam-3654	318	23	)	)	PUNCT
ejpam-3654	318	24	s	s	PART
ejpam-3654	318	25	)	)	PUNCT
ejpam-3654	318	26	β	β	X
ejpam-3654	318	27	ds	ds	X
ejpam-3654	318	28	)	)	PUNCT
ejpam-3654	318	29	1	1	PROPN
ejpam-3654	318	30	/	/	SYM
ejpam-3654	318	31	α	α	PRON
ejpam-3654	318	32	du	du	PROPN
ejpam-3654	318	33	,	,	PUNCT
ejpam-3654	318	34	(	(	PUNCT
ejpam-3654	318	35	46	46	NUM
ejpam-3654	318	36	)	)	PUNCT
ejpam-3654	318	37	for	for	ADP
ejpam-3654	318	38	all	all	DET
ejpam-3654	318	39	µ2	µ2	PROPN
ejpam-3654	318	40	∈	∈	PROPN
ejpam-3654	318	41	(	(	PUNCT
ejpam-3654	318	42	0	0	NUM
ejpam-3654	318	43	,	,	PUNCT
ejpam-3654	318	44	1	1	NUM
ejpam-3654	318	45	)	)	PUNCT
ejpam-3654	318	46	.	.	PUNCT
ejpam-3654	319	1	by	by	ADP
ejpam-3654	319	2	differentiating	differentiate	VERB
ejpam-3654	319	3	w	w	PROPN
ejpam-3654	319	4	and	and	CCONJ
ejpam-3654	319	5	using	use	VERB
ejpam-3654	319	6	(	(	PUNCT
ejpam-3654	319	7	15	15	NUM
ejpam-3654	319	8	)	)	PUNCT
ejpam-3654	319	9	and	and	CCONJ
ejpam-3654	319	10	(	(	PUNCT
ejpam-3654	319	11	46	46	NUM
ejpam-3654	319	12	)	)	PUNCT
ejpam-3654	319	13	,	,	PUNCT
ejpam-3654	319	14	we	we	PRON
ejpam-3654	319	15	find	find	VERB
ejpam-3654	319	16	w′	w′	PROPN
ejpam-3654	319	17	(	(	PUNCT
ejpam-3654	319	18	t	t	NOUN
ejpam-3654	319	19	)	)	PUNCT
ejpam-3654	319	20	=	=	NOUN
ejpam-3654	319	21	z′′	z′′	NOUN
ejpam-3654	319	22	(	(	PUNCT
ejpam-3654	319	23	t	t	PROPN
ejpam-3654	319	24	)	)	PUNCT
ejpam-3654	319	25	z	z	PROPN
ejpam-3654	319	26	(	(	PUNCT
ejpam-3654	319	27	t	t	PROPN
ejpam-3654	319	28	)	)	PUNCT
ejpam-3654	319	29	−	−	PROPN
ejpam-3654	320	1	(	(	PUNCT
ejpam-3654	320	2	z′	z′	NUM
ejpam-3654	320	3	(	(	PUNCT
ejpam-3654	320	4	t	t	PROPN
ejpam-3654	320	5	)	)	PUNCT
ejpam-3654	320	6	z	z	PROPN
ejpam-3654	320	7	(	(	PUNCT
ejpam-3654	320	8	t	t	PROPN
ejpam-3654	320	9	)	)	PUNCT
ejpam-3654	320	10	)	)	PUNCT
ejpam-3654	320	11	2	2	NUM
ejpam-3654	320	12	o.	o.	NOUN
ejpam-3654	320	13	moaaz	moaaz	PROPN
ejpam-3654	320	14	,	,	PUNCT
ejpam-3654	320	15	c.	c.	PROPN
ejpam-3654	320	16	cesarano	cesarano	PROPN
ejpam-3654	320	17	,	,	PUNCT
ejpam-3654	320	18	a.	a.	NOUN
ejpam-3654	320	19	muhib	muhib	NOUN
ejpam-3654	320	20	/	/	SYM
ejpam-3654	320	21	eur	eur	PROPN
ejpam-3654	320	22	.	.	PUNCT
ejpam-3654	321	1	j.	j.	PROPN
ejpam-3654	321	2	pure	pure	PROPN
ejpam-3654	321	3	appl	appl	PROPN
ejpam-3654	321	4	.	.	PROPN
ejpam-3654	321	5	math	math	PROPN
ejpam-3654	321	6	,	,	PUNCT
ejpam-3654	321	7	13	13	NUM
ejpam-3654	321	8	(	(	PUNCT
ejpam-3654	321	9	2	2	NUM
ejpam-3654	321	10	)	)	PUNCT
ejpam-3654	321	11	(	(	PUNCT
ejpam-3654	321	12	2020	2020	NUM
ejpam-3654	321	13	)	)	PUNCT
ejpam-3654	321	14	,	,	PUNCT
ejpam-3654	321	15	185	185	NUM
ejpam-3654	321	16	-	-	SYM
ejpam-3654	321	17	199	199	NUM
ejpam-3654	321	18	197	197	NUM
ejpam-3654	321	19	≤	≤	NOUN
ejpam-3654	321	20	−w2	−w2	PROPN
ejpam-3654	321	21	(	(	PUNCT
ejpam-3654	321	22	t)−	t)−	PROPN
ejpam-3654	321	23	p̃β	p̃β	PROPN
ejpam-3654	321	24	/	/	SYM
ejpam-3654	321	25	α	α	PROPN
ejpam-3654	321	26	(	(	PUNCT
ejpam-3654	321	27	σ	σ	PROPN
ejpam-3654	321	28	(	(	PUNCT
ejpam-3654	321	29	s))m	s))m	NOUN
ejpam-3654	321	30	(	(	PUNCT
ejpam-3654	321	31	β	β	NOUN
ejpam-3654	321	32	/	/	SYM
ejpam-3654	321	33	α)−1	α)−1	NOUN
ejpam-3654	321	34	∫	∫	NOUN
ejpam-3654	321	35	∞	∞	PROPN
ejpam-3654	321	36	t	t	PROPN
ejpam-3654	321	37	(	(	PUNCT
ejpam-3654	321	38	1	1	NUM
ejpam-3654	321	39	r	r	NOUN
ejpam-3654	321	40	(	(	PUNCT
ejpam-3654	321	41	u	u	NOUN
ejpam-3654	321	42	)	)	PUNCT
ejpam-3654	321	43	∫	∫	PROPN
ejpam-3654	321	44	∞	∞	NUM
ejpam-3654	321	45	u	u	PROPN
ejpam-3654	321	46	q	q	X
ejpam-3654	321	47	(	(	PUNCT
ejpam-3654	321	48	s	s	NOUN
ejpam-3654	321	49	)	)	PUNCT
ejpam-3654	321	50	(	(	PUNCT
ejpam-3654	321	51	τ−1	τ−1	PROPN
ejpam-3654	321	52	(	(	PUNCT
ejpam-3654	321	53	σ	σ	PROPN
ejpam-3654	321	54	(	(	PUNCT
ejpam-3654	321	55	s	s	NOUN
ejpam-3654	321	56	)	)	PUNCT
ejpam-3654	321	57	)	)	PUNCT
ejpam-3654	321	58	s	s	PART
ejpam-3654	321	59	)	)	PUNCT
ejpam-3654	321	60	β	β	X
ejpam-3654	321	61	ds	ds	X
ejpam-3654	321	62	)	)	PUNCT
ejpam-3654	321	63	1	1	PROPN
ejpam-3654	321	64	/	/	SYM
ejpam-3654	321	65	α	α	PRON
ejpam-3654	321	66	du	du	PROPN
ejpam-3654	321	67	,	,	PUNCT
ejpam-3654	321	68	(	(	PUNCT
ejpam-3654	321	69	47	47	NUM
ejpam-3654	321	70	)	)	PUNCT
ejpam-3654	321	71	hence	hence	ADV
ejpam-3654	321	72	w′	w′	PROPN
ejpam-3654	321	73	(	(	PUNCT
ejpam-3654	321	74	t	t	PROPN
ejpam-3654	321	75	)	)	PUNCT
ejpam-3654	322	1	+	+	PROPN
ejpam-3654	322	2	q4	q4	PROPN
ejpam-3654	322	3	(	(	PUNCT
ejpam-3654	322	4	t	t	PROPN
ejpam-3654	322	5	)	)	PUNCT
ejpam-3654	322	6	+	+	NUM
ejpam-3654	322	7	w2	w2	NOUN
ejpam-3654	322	8	(	(	PUNCT
ejpam-3654	322	9	t	t	PROPN
ejpam-3654	322	10	)	)	PUNCT
ejpam-3654	322	11	≤	≤	NOUN
ejpam-3654	322	12	0	0	NUM
ejpam-3654	322	13	.	.	PUNCT
ejpam-3654	323	1	the	the	DET
ejpam-3654	323	2	proof	proof	NOUN
ejpam-3654	323	3	is	be	AUX
ejpam-3654	323	4	complete	complete	ADJ
ejpam-3654	323	5	.	.	PUNCT
ejpam-3654	324	1	theorem	theorem	ADJ
ejpam-3654	324	2	4	4	NUM
ejpam-3654	324	3	.	.	PUNCT
ejpam-3654	325	1	assume	assume	VERB
ejpam-3654	325	2	that	that	SCONJ
ejpam-3654	325	3	lim	lim	PROPN
ejpam-3654	325	4	inf	inf	PROPN
ejpam-3654	325	5	t→∞	t→∞	ADV
ejpam-3654	325	6	1	1	NUM
ejpam-3654	325	7	q̃3	q̃3	PROPN
ejpam-3654	325	8	(	(	PUNCT
ejpam-3654	325	9	t	t	PROPN
ejpam-3654	325	10	)	)	PUNCT
ejpam-3654	325	11	∫	∫	PROPN
ejpam-3654	325	12	∞	∞	PROPN
ejpam-3654	325	13	t	t	PROPN
ejpam-3654	325	14	r1	r1	PROPN
ejpam-3654	325	15	(	(	PUNCT
ejpam-3654	325	16	s	s	X
ejpam-3654	325	17	)	)	PUNCT
ejpam-3654	325	18	q̃	q̃	PROPN
ejpam-3654	325	19	α+1	α+1	NUM
ejpam-3654	325	20	α	α	NOUN
ejpam-3654	325	21	3	3	NUM
ejpam-3654	325	22	(	(	PUNCT
ejpam-3654	325	23	s	s	X
ejpam-3654	325	24	)	)	PUNCT
ejpam-3654	325	25	ds	ds	VERB
ejpam-3654	325	26	>	>	PUNCT
ejpam-3654	325	27	α	α	PROPN
ejpam-3654	325	28	(	(	PUNCT
ejpam-3654	325	29	α+	α+	NOUN
ejpam-3654	325	30	1	1	NUM
ejpam-3654	325	31	)	)	PUNCT
ejpam-3654	325	32	α+1	α+1	NUM
ejpam-3654	325	33	α	α	PROPN
ejpam-3654	325	34	(	(	PUNCT
ejpam-3654	325	35	48	48	NUM
ejpam-3654	325	36	)	)	PUNCT
ejpam-3654	325	37	and	and	CCONJ
ejpam-3654	325	38	lim	lim	PROPN
ejpam-3654	325	39	inf	inf	PROPN
ejpam-3654	325	40	t→∞	t→∞	ADP
ejpam-3654	325	41	1	1	NUM
ejpam-3654	325	42	q̃4	q̃4	PROPN
ejpam-3654	325	43	(	(	PUNCT
ejpam-3654	325	44	t	t	PROPN
ejpam-3654	325	45	)	)	PUNCT
ejpam-3654	325	46	∫	∫	PROPN
ejpam-3654	326	1	∞	∞	PROPN
ejpam-3654	326	2	t	t	PROPN
ejpam-3654	326	3	q̃2	q̃2	NOUN
ejpam-3654	326	4	4	4	NUM
ejpam-3654	326	5	(	(	PUNCT
ejpam-3654	326	6	s	s	X
ejpam-3654	326	7	)	)	PUNCT
ejpam-3654	326	8	ds	ds	X
ejpam-3654	326	9	>	>	X
ejpam-3654	326	10	1	1	NUM
ejpam-3654	326	11	4	4	NUM
ejpam-3654	326	12	,	,	PUNCT
ejpam-3654	326	13	(	(	PUNCT
ejpam-3654	326	14	49	49	NUM
ejpam-3654	326	15	)	)	PUNCT
ejpam-3654	327	1	where	where	SCONJ
ejpam-3654	327	2	q̃3	q̃3	PROPN
ejpam-3654	327	3	(	(	PUNCT
ejpam-3654	327	4	t	t	PROPN
ejpam-3654	327	5	)	)	PUNCT
ejpam-3654	327	6	=	=	SYM
ejpam-3654	328	1	∫	∫	PROPN
ejpam-3654	328	2	∞	∞	PROPN
ejpam-3654	328	3	t	t	PROPN
ejpam-3654	328	4	q3	q3	PROPN
ejpam-3654	328	5	(	(	PUNCT
ejpam-3654	328	6	s	s	NOUN
ejpam-3654	328	7	)	)	PUNCT
ejpam-3654	328	8	ds	ds	NOUN
ejpam-3654	328	9	and	and	CCONJ
ejpam-3654	328	10	q̃4	q̃4	PROPN
ejpam-3654	328	11	(	(	PUNCT
ejpam-3654	328	12	t	t	PROPN
ejpam-3654	328	13	)	)	PUNCT
ejpam-3654	329	1	=	=	SYM
ejpam-3654	330	1	∫	∫	PROPN
ejpam-3654	331	1	∞	∞	PROPN
ejpam-3654	331	2	t	t	PROPN
ejpam-3654	331	3	q4	q4	PROPN
ejpam-3654	331	4	(	(	PUNCT
ejpam-3654	331	5	s	s	NOUN
ejpam-3654	331	6	)	)	PUNCT
ejpam-3654	331	7	ds	ds	NOUN
ejpam-3654	331	8	.	.	PUNCT
ejpam-3654	331	9	then	then	ADV
ejpam-3654	331	10	,	,	PUNCT
ejpam-3654	331	11	(	(	PUNCT
ejpam-3654	331	12	1	1	X
ejpam-3654	331	13	)	)	PUNCT
ejpam-3654	331	14	is	be	AUX
ejpam-3654	331	15	oscillatory	oscillatory	ADJ
ejpam-3654	331	16	.	.	PUNCT
ejpam-3654	332	1	proof	proof	NOUN
ejpam-3654	332	2	.	.	PUNCT
ejpam-3654	333	1	proceeding	proceed	VERB
ejpam-3654	333	2	as	as	ADP
ejpam-3654	333	3	in	in	ADP
ejpam-3654	333	4	the	the	DET
ejpam-3654	333	5	proof	proof	NOUN
ejpam-3654	333	6	of	of	ADP
ejpam-3654	333	7	theorem	theorem	ADJ
ejpam-3654	333	8	2	2	NUM
ejpam-3654	333	9	,	,	PUNCT
ejpam-3654	333	10	example	example	NOUN
ejpam-3654	333	11	1	1	NUM
ejpam-3654	333	12	.	.	PUNCT
ejpam-3654	334	1	consider	consider	VERB
ejpam-3654	334	2	the	the	DET
ejpam-3654	334	3	differential	differential	ADJ
ejpam-3654	334	4	equation	equation	NOUN
ejpam-3654	334	5	(	(	PUNCT
ejpam-3654	334	6	x	x	X
ejpam-3654	334	7	(	(	PUNCT
ejpam-3654	334	8	t	t	NOUN
ejpam-3654	334	9	)	)	PUNCT
ejpam-3654	334	10	+	+	NUM
ejpam-3654	334	11	16x	16x	NOUN
ejpam-3654	334	12	(	(	PUNCT
ejpam-3654	334	13	t	t	PROPN
ejpam-3654	334	14	2	2	NUM
ejpam-3654	334	15	)	)	PUNCT
ejpam-3654	334	16	)	)	PUNCT
ejpam-3654	334	17	(	(	PUNCT
ejpam-3654	334	18	4	4	X
ejpam-3654	334	19	)	)	PUNCT
ejpam-3654	334	20	+	+	CCONJ
ejpam-3654	335	1	q0	q0	PROPN
ejpam-3654	335	2	t4	t4	PROPN
ejpam-3654	335	3	x	x	X
ejpam-3654	335	4	(	(	PUNCT
ejpam-3654	335	5	t	t	PROPN
ejpam-3654	335	6	6	6	NUM
ejpam-3654	335	7	)	)	PUNCT
ejpam-3654	335	8	=	=	SYM
ejpam-3654	335	9	0	0	X
ejpam-3654	335	10	.	.	PUNCT
ejpam-3654	336	1	(	(	PUNCT
ejpam-3654	336	2	50	50	NUM
ejpam-3654	336	3	)	)	PUNCT
ejpam-3654	336	4	we	we	PRON
ejpam-3654	336	5	note	note	VERB
ejpam-3654	336	6	that	that	SCONJ
ejpam-3654	336	7	α	α	PRON
ejpam-3654	336	8	=	=	X
ejpam-3654	336	9	β	β	X
ejpam-3654	336	10	=	=	SYM
ejpam-3654	336	11	1	1	NUM
ejpam-3654	336	12	,	,	PUNCT
ejpam-3654	336	13	r	r	NOUN
ejpam-3654	336	14	(	(	PUNCT
ejpam-3654	336	15	t	t	NOUN
ejpam-3654	336	16	)	)	PUNCT
ejpam-3654	336	17	=	=	SYM
ejpam-3654	337	1	1	1	NUM
ejpam-3654	337	2	,	,	PUNCT
ejpam-3654	337	3	p	p	X
ejpam-3654	337	4	(	(	PUNCT
ejpam-3654	337	5	t	t	NOUN
ejpam-3654	337	6	)	)	PUNCT
ejpam-3654	337	7	=	=	SYM
ejpam-3654	338	1	16	16	NUM
ejpam-3654	338	2	,	,	PUNCT
ejpam-3654	338	3	τ	τ	PROPN
ejpam-3654	338	4	(	(	PUNCT
ejpam-3654	338	5	t	t	PROPN
ejpam-3654	338	6	)	)	PUNCT
ejpam-3654	338	7	=	=	SYM
ejpam-3654	339	1	t/2	t/2	PROPN
ejpam-3654	339	2	,	,	PUNCT
ejpam-3654	339	3	σ	σ	PROPN
ejpam-3654	339	4	(	(	PUNCT
ejpam-3654	339	5	t	t	PROPN
ejpam-3654	339	6	)	)	PUNCT
ejpam-3654	339	7	=	=	PUNCT
ejpam-3654	339	8	t/6	t/6	X
ejpam-3654	339	9	and	and	CCONJ
ejpam-3654	339	10	q	q	PROPN
ejpam-3654	339	11	(	(	PUNCT
ejpam-3654	339	12	t	t	NOUN
ejpam-3654	339	13	)	)	PUNCT
ejpam-3654	339	14	=	=	VERB
ejpam-3654	340	1	q0	q0	PROPN
ejpam-3654	340	2	/	/	SYM
ejpam-3654	340	3	t	t	PROPN
ejpam-3654	340	4	4	4	NUM
ejpam-3654	340	5	.	.	PUNCT
ejpam-3654	341	1	hence	hence	ADV
ejpam-3654	341	2	,	,	PUNCT
ejpam-3654	341	3	it	it	PRON
ejpam-3654	341	4	is	be	AUX
ejpam-3654	341	5	easy	easy	ADJ
ejpam-3654	341	6	to	to	PART
ejpam-3654	341	7	see	see	VERB
ejpam-3654	342	1	that	that	SCONJ
ejpam-3654	342	2	q̃3	q̃3	PROPN
ejpam-3654	342	3	(	(	PUNCT
ejpam-3654	342	4	t	t	NOUN
ejpam-3654	342	5	)	)	PUNCT
ejpam-3654	342	6	=	=	VERB
ejpam-3654	342	7	q0	q0	VERB
ejpam-3654	342	8	34	34	NUM
ejpam-3654	342	9	(	(	PUNCT
ejpam-3654	342	10	32	32	NUM
ejpam-3654	342	11	)	)	PUNCT
ejpam-3654	342	12	t3	t3	PROPN
ejpam-3654	342	13	and	and	CCONJ
ejpam-3654	342	14	q̃4	q̃4	PROPN
ejpam-3654	342	15	(	(	PUNCT
ejpam-3654	342	16	t	t	PROPN
ejpam-3654	342	17	)	)	PUNCT
ejpam-3654	342	18	=	=	PUNCT
ejpam-3654	343	1	7q0	7q0	NUM
ejpam-3654	343	2	32	32	NUM
ejpam-3654	343	3	(	(	PUNCT
ejpam-3654	343	4	256	256	NUM
ejpam-3654	343	5	)	)	PUNCT
ejpam-3654	343	6	t	t	NOUN
ejpam-3654	343	7	.	.	PUNCT
ejpam-3654	344	1	using	use	VERB
ejpam-3654	344	2	conditions	condition	NOUN
ejpam-3654	344	3	(	(	PUNCT
ejpam-3654	344	4	48	48	NUM
ejpam-3654	344	5	)	)	PUNCT
ejpam-3654	344	6	and	and	CCONJ
ejpam-3654	344	7	(	(	PUNCT
ejpam-3654	344	8	49	49	NUM
ejpam-3654	344	9	)	)	PUNCT
ejpam-3654	344	10	,	,	PUNCT
ejpam-3654	344	11	we	we	PRON
ejpam-3654	344	12	see	see	VERB
ejpam-3654	344	13	that	that	DET
ejpam-3654	344	14	equation	equation	NOUN
ejpam-3654	344	15	(	(	PUNCT
ejpam-3654	344	16	50	50	NUM
ejpam-3654	344	17	)	)	PUNCT
ejpam-3654	344	18	is	be	AUX
ejpam-3654	344	19	oscillatory	oscillatory	ADJ
ejpam-3654	344	20	if	if	SCONJ
ejpam-3654	344	21	q0	q0	PROPN
ejpam-3654	344	22	>	>	X
ejpam-3654	344	23	3888	3888	NUM
ejpam-3654	344	24	.	.	PUNCT
ejpam-3654	345	1	5	5	NUM
ejpam-3654	345	2	.	.	X
ejpam-3654	345	3	conclusion	conclusion	NOUN
ejpam-3654	345	4	in	in	ADP
ejpam-3654	345	5	this	this	DET
ejpam-3654	345	6	work	work	NOUN
ejpam-3654	345	7	,	,	PUNCT
ejpam-3654	345	8	we	we	PRON
ejpam-3654	345	9	offer	offer	VERB
ejpam-3654	345	10	some	some	DET
ejpam-3654	345	11	new	new	ADJ
ejpam-3654	345	12	sufficient	sufficient	ADJ
ejpam-3654	345	13	conditions	condition	NOUN
ejpam-3654	345	14	which	which	PRON
ejpam-3654	345	15	ensure	ensure	VERB
ejpam-3654	345	16	that	that	SCONJ
ejpam-3654	345	17	any	any	DET
ejpam-3654	345	18	solution	solution	NOUN
ejpam-3654	345	19	of	of	ADP
ejpam-3654	345	20	(	(	PUNCT
ejpam-3654	345	21	1	1	X
ejpam-3654	345	22	)	)	PUNCT
ejpam-3654	345	23	oscillates	oscillate	NOUN
ejpam-3654	345	24	under	under	ADP
ejpam-3654	345	25	the	the	DET
ejpam-3654	345	26	condition	condition	NOUN
ejpam-3654	345	27	∫∞	∫∞	NOUN
ejpam-3654	345	28	t0	t0	PROPN
ejpam-3654	345	29	1	1	NUM
ejpam-3654	345	30	r1	r1	PROPN
ejpam-3654	345	31	/	/	SYM
ejpam-3654	345	32	α(s	α(s	PROPN
ejpam-3654	345	33	)	)	PUNCT
ejpam-3654	345	34	ds	ds	PROPN
ejpam-3654	345	35	=	=	SYM
ejpam-3654	345	36	∞.	∞.	PROPN
ejpam-3654	345	37	and	and	CCONJ
ejpam-3654	345	38	we	we	PRON
ejpam-3654	345	39	can	can	AUX
ejpam-3654	345	40	try	try	VERB
ejpam-3654	345	41	to	to	PART
ejpam-3654	345	42	get	get	VERB
ejpam-3654	345	43	some	some	DET
ejpam-3654	345	44	oscillation	oscillation	NOUN
ejpam-3654	345	45	criteria	criterion	NOUN
ejpam-3654	345	46	of	of	ADP
ejpam-3654	345	47	(	(	PUNCT
ejpam-3654	345	48	1	1	NUM
ejpam-3654	345	49	)	)	PUNCT
ejpam-3654	345	50	under	under	ADP
ejpam-3654	345	51	the	the	DET
ejpam-3654	345	52	condition	condition	NOUN
ejpam-3654	345	53	∫∞	∫∞	NOUN
ejpam-3654	345	54	t0	t0	PROPN
ejpam-3654	345	55	1	1	NUM
ejpam-3654	345	56	r1	r1	PROPN
ejpam-3654	345	57	/	/	SYM
ejpam-3654	345	58	α(s	α(s	PROPN
ejpam-3654	345	59	)	)	PUNCT
ejpam-3654	345	60	ds	ds	ADP
ejpam-3654	345	61	<	<	X
ejpam-3654	345	62	∞	∞	PROPN
ejpam-3654	345	63	,	,	PUNCT
ejpam-3654	345	64	in	in	ADP
ejpam-3654	345	65	the	the	DET
ejpam-3654	345	66	future	future	ADJ
ejpam-3654	345	67	work	work	NOUN
ejpam-3654	345	68	.	.	PUNCT
ejpam-3654	346	1	references	reference	NOUN
ejpam-3654	346	2	198	198	NUM
ejpam-3654	346	3	references	reference	NOUN
ejpam-3654	346	4	[	[	X
ejpam-3654	346	5	1	1	NUM
ejpam-3654	346	6	]	]	PUNCT
ejpam-3654	346	7	r.	r.	PROPN
ejpam-3654	346	8	p.	p.	PROPN
ejpam-3654	346	9	agarwal	agarwal	PROPN
ejpam-3654	346	10	,	,	PUNCT
ejpam-3654	346	11	l.	l.	PROPN
ejpam-3654	346	12	berezansky	berezansky	PROPN
ejpam-3654	346	13	,	,	PUNCT
ejpam-3654	346	14	e.braverman	e.braverman	NOUN
ejpam-3654	346	15	,	,	PUNCT
ejpam-3654	346	16	anda	anda	PROPN
ejpam-3654	346	17	.	.	PUNCT
ejpam-3654	347	1	domoshnitsky	domoshnitsky	PROPN
ejpam-3654	347	2	,	,	PUNCT
ejpam-3654	347	3	nonoscillation	nonoscillation	NOUN
ejpam-3654	347	4	theory	theory	NOUN
ejpam-3654	347	5	of	of	ADP
ejpam-3654	347	6	functional	functional	ADJ
ejpam-3654	347	7	differential	differential	ADJ
ejpam-3654	347	8	equations	equation	NOUN
ejpam-3654	347	9	with	with	ADP
ejpam-3654	347	10	applications	application	NOUN
ejpam-3654	347	11	,	,	PUNCT
ejpam-3654	347	12	springer	springer	NOUN
ejpam-3654	347	13	,	,	PUNCT
ejpam-3654	347	14	new	new	PROPN
ejpam-3654	347	15	york	york	PROPN
ejpam-3654	347	16	,	,	PUNCT
ejpam-3654	347	17	ny	ny	PROPN
ejpam-3654	347	18	,	,	PUNCT
ejpam-3654	347	19	usa	usa	PROPN
ejpam-3654	347	20	,	,	PUNCT
ejpam-3654	347	21	2012	2012	NUM
ejpam-3654	347	22	.	.	PUNCT
ejpam-3654	348	1	[	[	X
ejpam-3654	348	2	2	2	NUM
ejpam-3654	348	3	]	]	PUNCT
ejpam-3654	348	4	r.	r.	PROPN
ejpam-3654	348	5	p.	p.	PROPN
ejpam-3654	348	6	agarwal	agarwal	PROPN
ejpam-3654	348	7	,	,	PUNCT
ejpam-3654	348	8	m.	m.	NOUN
ejpam-3654	348	9	bohner	bohner	NOUN
ejpam-3654	348	10	,	,	PUNCT
ejpam-3654	348	11	and	and	CCONJ
ejpam-3654	348	12	w.-t	w.-t	NOUN
ejpam-3654	348	13	.	.	PUNCT
ejpam-3654	349	1	li	li	PROPN
ejpam-3654	349	2	,	,	PUNCT
ejpam-3654	349	3	nonoscillation	nonoscillation	NOUN
ejpam-3654	349	4	and	and	CCONJ
ejpam-3654	349	5	oscillation	oscillation	NOUN
ejpam-3654	349	6	:	:	PUNCT
ejpam-3654	349	7	theory	theory	NOUN
ejpam-3654	349	8	for	for	ADP
ejpam-3654	349	9	functional	functional	ADJ
ejpam-3654	349	10	differential	differential	ADJ
ejpam-3654	349	11	equations	equation	NOUN
ejpam-3654	349	12	,	,	PUNCT
ejpam-3654	349	13	vol	vol	NOUN
ejpam-3654	349	14	.	.	PROPN
ejpam-3654	349	15	267,marcel	267,marcel	NUM
ejpam-3654	349	16	dekker	dekker	NOUN
ejpam-3654	349	17	,	,	PUNCT
ejpam-3654	349	18	newyork	newyork	PROPN
ejpam-3654	349	19	,	,	PUNCT
ejpam-3654	349	20	ny	ny	PROPN
ejpam-3654	349	21	,	,	PUNCT
ejpam-3654	349	22	usa	usa	PROPN
ejpam-3654	349	23	,	,	PUNCT
ejpam-3654	349	24	2004	2004	NUM
ejpam-3654	349	25	.	.	PUNCT
ejpam-3654	350	1	[	[	X
ejpam-3654	350	2	3	3	NUM
ejpam-3654	350	3	]	]	X
ejpam-3654	350	4	r.	r.	PROPN
ejpam-3654	350	5	agarwal	agarwal	PROPN
ejpam-3654	350	6	,	,	PUNCT
ejpam-3654	350	7	s.	s.	PROPN
ejpam-3654	350	8	grace	grace	PROPN
ejpam-3654	350	9	,	,	PUNCT
ejpam-3654	350	10	d.	d.	PROPN
ejpam-3654	350	11	o’regan	o’regan	PROPN
ejpam-3654	350	12	,	,	PUNCT
ejpam-3654	350	13	oscillation	oscillation	NOUN
ejpam-3654	350	14	theory	theory	NOUN
ejpam-3654	350	15	for	for	ADP
ejpam-3654	350	16	difference	difference	NOUN
ejpam-3654	350	17	and	and	CCONJ
ejpam-3654	350	18	functional	functional	ADJ
ejpam-3654	350	19	differential	differential	NOUN
ejpam-3654	350	20	equations	equation	NOUN
ejpam-3654	350	21	,	,	PUNCT
ejpam-3654	350	22	kluwer	kluwer	NOUN
ejpam-3654	350	23	acad	acad	PROPN
ejpam-3654	350	24	.	.	PUNCT
ejpam-3654	351	1	publ	publ	PROPN
ejpam-3654	351	2	.	.	PUNCT
ejpam-3654	351	3	,	,	PUNCT
ejpam-3654	351	4	dordrecht	dordrecht	PROPN
ejpam-3654	351	5	(	(	PUNCT
ejpam-3654	351	6	2000	2000	NUM
ejpam-3654	351	7	)	)	PUNCT
ejpam-3654	351	8	.	.	PUNCT
ejpam-3654	352	1	[	[	X
ejpam-3654	352	2	4	4	X
ejpam-3654	352	3	]	]	X
ejpam-3654	352	4	g.	g.	PROPN
ejpam-3654	352	5	s.	s.	PROPN
ejpam-3654	352	6	ladde	ladde	PROPN
ejpam-3654	352	7	,	,	PUNCT
ejpam-3654	352	8	v.	v.	ADP
ejpam-3654	352	9	lakshmikantham	lakshmikantham	NOUN
ejpam-3654	352	10	,	,	PUNCT
ejpam-3654	352	11	and	and	CCONJ
ejpam-3654	352	12	b.	b.	PROPN
ejpam-3654	352	13	g.	g.	PROPN
ejpam-3654	352	14	zhang	zhang	PROPN
ejpam-3654	352	15	,	,	PUNCT
ejpam-3654	352	16	oscillation	oscillation	NOUN
ejpam-3654	352	17	theory	theory	NOUN
ejpam-3654	352	18	of	of	ADP
ejpam-3654	352	19	differential	differential	ADJ
ejpam-3654	352	20	equations	equation	NOUN
ejpam-3654	352	21	with	with	ADP
ejpam-3654	352	22	deviating	deviate	VERB
ejpam-3654	352	23	arguments	argument	NOUN
ejpam-3654	352	24	,	,	PUNCT
ejpam-3654	352	25	vol	vol	NOUN
ejpam-3654	352	26	.	.	PROPN
ejpam-3654	352	27	110	110	NUM
ejpam-3654	352	28	,	,	PUNCT
ejpam-3654	352	29	marcel	marcel	PROPN
ejpam-3654	352	30	dekker	dekker	PROPN
ejpam-3654	352	31	,	,	PUNCT
ejpam-3654	352	32	new	new	PROPN
ejpam-3654	352	33	york	york	PROPN
ejpam-3654	352	34	,	,	PUNCT
ejpam-3654	352	35	ny	ny	PROPN
ejpam-3654	352	36	,	,	PUNCT
ejpam-3654	352	37	usa	usa	PROPN
ejpam-3654	352	38	,	,	PUNCT
ejpam-3654	352	39	1987	1987	NUM
ejpam-3654	352	40	.	.	PUNCT
ejpam-3654	353	1	[	[	X
ejpam-3654	353	2	5	5	NUM
ejpam-3654	353	3	]	]	X
ejpam-3654	353	4	i.	i.	NOUN
ejpam-3654	353	5	t.	t.	PROPN
ejpam-3654	353	6	kiguradze	kiguradze	PROPN
ejpam-3654	353	7	and	and	CCONJ
ejpam-3654	353	8	t.	t.	PROPN
ejpam-3654	353	9	a.	a.	PROPN
ejpam-3654	353	10	chanturiya	chanturiya	PROPN
ejpam-3654	353	11	,	,	PUNCT
ejpam-3654	353	12	asymptotic	asymptotic	ADJ
ejpam-3654	353	13	properties	property	NOUN
ejpam-3654	353	14	of	of	ADP
ejpam-3654	353	15	solutions	solution	NOUN
ejpam-3654	353	16	of	of	ADP
ejpam-3654	353	17	nonautonomous	nonautonomous	ADJ
ejpam-3654	353	18	ordinary	ordinary	ADJ
ejpam-3654	353	19	differential	differential	ADJ
ejpam-3654	353	20	equations	equation	NOUN
ejpam-3654	353	21	,	,	PUNCT
ejpam-3654	353	22	kluwer	kluwer	NOUN
ejpam-3654	353	23	acad	acad	PROPN
ejpam-3654	353	24	.	.	PUNCT
ejpam-3654	353	25	publ	publ	PROPN
ejpam-3654	353	26	.	.	PUNCT
ejpam-3654	353	27	,	,	PUNCT
ejpam-3654	353	28	dordrecht	dordrecht	PROPN
ejpam-3654	353	29	(	(	PUNCT
ejpam-3654	353	30	1993	1993	NUM
ejpam-3654	353	31	)	)	PUNCT
ejpam-3654	353	32	.	.	PUNCT
ejpam-3654	354	1	[	[	X
ejpam-3654	354	2	6	6	NUM
ejpam-3654	354	3	]	]	X
ejpam-3654	354	4	r.	r.	PROPN
ejpam-3654	354	5	agarwal	agarwal	PROPN
ejpam-3654	354	6	,	,	PUNCT
ejpam-3654	354	7	s.	s.	PROPN
ejpam-3654	354	8	grace	grace	PROPN
ejpam-3654	354	9	,	,	PUNCT
ejpam-3654	354	10	d.	d.	PROPN
ejpam-3654	354	11	o’regan	o’regan	PROPN
ejpam-3654	354	12	,	,	PUNCT
ejpam-3654	354	13	oscillation	oscillation	NOUN
ejpam-3654	354	14	criteria	criterion	NOUN
ejpam-3654	354	15	for	for	ADP
ejpam-3654	354	16	certain	certain	ADJ
ejpam-3654	354	17	nth	nth	NOUN
ejpam-3654	354	18	order	order	NOUN
ejpam-3654	354	19	differential	differential	ADJ
ejpam-3654	354	20	equations	equation	NOUN
ejpam-3654	354	21	with	with	ADP
ejpam-3654	354	22	deviating	deviate	VERB
ejpam-3654	354	23	arguments	argument	NOUN
ejpam-3654	354	24	,	,	PUNCT
ejpam-3654	354	25	j.	j.	PROPN
ejpam-3654	354	26	math	math	PROPN
ejpam-3654	354	27	.	.	PUNCT
ejpam-3654	355	1	appl	appl	PROPN
ejpam-3654	355	2	.	.	PUNCT
ejpam-3654	356	1	anal	anal	PROPN
ejpam-3654	356	2	.	.	PROPN
ejpam-3654	356	3	,	,	PUNCT
ejpam-3654	356	4	262	262	NUM
ejpam-3654	356	5	(	(	PUNCT
ejpam-3654	356	6	2001	2001	NUM
ejpam-3654	356	7	)	)	PUNCT
ejpam-3654	356	8	,	,	PUNCT
ejpam-3654	356	9	601–622	601–622	NUM
ejpam-3654	356	10	.	.	PUNCT
ejpam-3654	357	1	[	[	X
ejpam-3654	357	2	7	7	X
ejpam-3654	357	3	]	]	PUNCT
ejpam-3654	357	4	t.	t.	PROPN
ejpam-3654	357	5	li	li	PROPN
ejpam-3654	357	6	and	and	CCONJ
ejpam-3654	357	7	yu	yu	PROPN
ejpam-3654	357	8	.	.	PUNCT
ejpam-3654	358	1	v.	v.	PROPN
ejpam-3654	358	2	rogovchenko	rogovchenko	PROPN
ejpam-3654	358	3	,	,	PUNCT
ejpam-3654	358	4	on	on	ADP
ejpam-3654	358	5	asymptotic	asymptotic	ADJ
ejpam-3654	358	6	behavior	behavior	NOUN
ejpam-3654	358	7	of	of	ADP
ejpam-3654	358	8	solutions	solution	NOUN
ejpam-3654	358	9	to	to	ADP
ejpam-3654	358	10	higher	high	ADJ
ejpam-3654	358	11	-	-	PUNCT
ejpam-3654	358	12	order	order	NOUN
ejpam-3654	358	13	sublinear	sublinear	NOUN
ejpam-3654	358	14	emden	emden	ADJ
ejpam-3654	358	15	–	–	PUNCT
ejpam-3654	358	16	fowler	fowler	PROPN
ejpam-3654	358	17	delay	delay	PROPN
ejpam-3654	358	18	differential	differential	ADJ
ejpam-3654	358	19	equations	equation	NOUN
ejpam-3654	358	20	,	,	PUNCT
ejpam-3654	358	21	appl	appl	PROPN
ejpam-3654	358	22	.	.	PROPN
ejpam-3654	358	23	math	math	PROPN
ejpam-3654	358	24	.	.	PUNCT
ejpam-3654	359	1	lett	lett	PROPN
ejpam-3654	359	2	.	.	PUNCT
ejpam-3654	360	1	67	67	NUM
ejpam-3654	360	2	(	(	PUNCT
ejpam-3654	360	3	2017	2017	NUM
ejpam-3654	360	4	)	)	PUNCT
ejpam-3654	360	5	,	,	PUNCT
ejpam-3654	360	6	53–59	53–59	NUM
ejpam-3654	360	7	.	.	PUNCT
ejpam-3654	361	1	[	[	X
ejpam-3654	361	2	8	8	NUM
ejpam-3654	361	3	]	]	X
ejpam-3654	361	4	g.	g.	PROPN
ejpam-3654	361	5	e.	e.	PROPN
ejpam-3654	361	6	chatzarakis	chatzarakis	PROPN
ejpam-3654	361	7	,	,	PUNCT
ejpam-3654	361	8	s.	s.	PROPN
ejpam-3654	361	9	r.	r.	PROPN
ejpam-3654	361	10	grace	grace	PROPN
ejpam-3654	361	11	,	,	PUNCT
ejpam-3654	361	12	i.	i.	PROPN
ejpam-3654	361	13	jadlovska	jadlovska	PROPN
ejpam-3654	361	14	,	,	PUNCT
ejpam-3654	361	15	t.	t.	PROPN
ejpam-3654	361	16	li	li	PROPN
ejpam-3654	361	17	,	,	PUNCT
ejpam-3654	361	18	and	and	CCONJ
ejpam-3654	361	19	e.	e.	PROPN
ejpam-3654	361	20	tuņc	tuņc	PROPN
ejpam-3654	361	21	,	,	PUNCT
ejpam-3654	361	22	oscillation	oscillation	NOUN
ejpam-3654	361	23	criteria	criterion	NOUN
ejpam-3654	361	24	for	for	ADP
ejpam-3654	361	25	third	third	ADJ
ejpam-3654	361	26	-	-	PUNCT
ejpam-3654	361	27	order	order	NOUN
ejpam-3654	361	28	emden	emden	ADJ
ejpam-3654	361	29	–	–	PUNCT
ejpam-3654	361	30	fowler	fowler	PROPN
ejpam-3654	361	31	differential	differential	ADJ
ejpam-3654	361	32	equations	equation	NOUN
ejpam-3654	361	33	with	with	ADP
ejpam-3654	361	34	unbounded	unbounded	ADJ
ejpam-3654	361	35	neutral	neutral	ADJ
ejpam-3654	361	36	coefficients	coefficient	NOUN
ejpam-3654	361	37	,	,	PUNCT
ejpam-3654	361	38	complexity	complexity	NOUN
ejpam-3654	361	39	,	,	PUNCT
ejpam-3654	361	40	2019	2019	NUM
ejpam-3654	361	41	(	(	PUNCT
ejpam-3654	361	42	2019	2019	NUM
ejpam-3654	361	43	)	)	PUNCT
ejpam-3654	361	44	,	,	PUNCT
ejpam-3654	361	45	1–7	1–7	X
ejpam-3654	361	46	.	.	PUNCT
ejpam-3654	362	1	[	[	X
ejpam-3654	362	2	9	9	NUM
ejpam-3654	362	3	]	]	PUNCT
ejpam-3654	362	4	c.	c.	PROPN
ejpam-3654	362	5	zhang	zhang	PROPN
ejpam-3654	362	6	,	,	PUNCT
ejpam-3654	362	7	r.	r.	PROPN
ejpam-3654	362	8	p.	p.	PROPN
ejpam-3654	362	9	agarwal	agarwal	PROPN
ejpam-3654	362	10	,	,	PUNCT
ejpam-3654	362	11	m.	m.	NOUN
ejpam-3654	362	12	bohner	bohner	NOUN
ejpam-3654	362	13	,	,	PUNCT
ejpam-3654	362	14	and	and	CCONJ
ejpam-3654	362	15	t.	t.	PROPN
ejpam-3654	362	16	li	li	PROPN
ejpam-3654	362	17	,	,	PUNCT
ejpam-3654	362	18	new	new	ADJ
ejpam-3654	362	19	results	result	NOUN
ejpam-3654	362	20	for	for	ADP
ejpam-3654	362	21	oscillatory	oscillatory	ADJ
ejpam-3654	362	22	behavior	behavior	NOUN
ejpam-3654	362	23	of	of	ADP
ejpam-3654	362	24	even	even	ADJ
ejpam-3654	362	25	-	-	PUNCT
ejpam-3654	362	26	order	order	NOUN
ejpam-3654	362	27	half	half	ADJ
ejpam-3654	362	28	-	-	PUNCT
ejpam-3654	362	29	linear	linear	NOUN
ejpam-3654	362	30	delay	delay	NOUN
ejpam-3654	362	31	differential	differential	ADJ
ejpam-3654	362	32	equations	equation	NOUN
ejpam-3654	362	33	,	,	PUNCT
ejpam-3654	362	34	appl	appl	PROPN
ejpam-3654	362	35	.	.	PROPN
ejpam-3654	362	36	math	math	PROPN
ejpam-3654	362	37	.	.	PUNCT
ejpam-3654	363	1	lett	lett	PROPN
ejpam-3654	363	2	.	.	PUNCT
ejpam-3654	364	1	26	26	NUM
ejpam-3654	364	2	(	(	PUNCT
ejpam-3654	364	3	2013	2013	NUM
ejpam-3654	364	4	)	)	PUNCT
ejpam-3654	364	5	,	,	PUNCT
ejpam-3654	364	6	179–183	179–183	NUM
ejpam-3654	364	7	.	.	PUNCT
ejpam-3654	365	1	[	[	X
ejpam-3654	365	2	10	10	NUM
ejpam-3654	365	3	]	]	X
ejpam-3654	365	4	b.	b.	PROPN
ejpam-3654	365	5	baculikova	baculikova	PROPN
ejpam-3654	365	6	,	,	PUNCT
ejpam-3654	365	7	j.	j.	PROPN
ejpam-3654	365	8	dzurina	dzurina	PROPN
ejpam-3654	365	9	,	,	PUNCT
ejpam-3654	365	10	oscillation	oscillation	NOUN
ejpam-3654	365	11	theorems	theorem	NOUN
ejpam-3654	365	12	for	for	ADP
ejpam-3654	365	13	second	second	ADJ
ejpam-3654	365	14	-	-	PUNCT
ejpam-3654	365	15	order	order	NOUN
ejpam-3654	365	16	nonlinear	nonlinear	ADJ
ejpam-3654	365	17	neutral	neutral	ADJ
ejpam-3654	365	18	differential	differential	NOUN
ejpam-3654	365	19	equations	equation	NOUN
ejpam-3654	365	20	,	,	PUNCT
ejpam-3654	365	21	comput	comput	NOUN
ejpam-3654	365	22	.	.	PUNCT
ejpam-3654	366	1	math	math	NOUN
ejpam-3654	366	2	.	.	PUNCT
ejpam-3654	367	1	appl	appl	PROPN
ejpam-3654	367	2	.	.	PUNCT
ejpam-3654	368	1	62	62	NUM
ejpam-3654	368	2	(	(	PUNCT
ejpam-3654	368	3	2011	2011	NUM
ejpam-3654	368	4	)	)	PUNCT
ejpam-3654	368	5	4472–4478	4472–4478	NUM
ejpam-3654	368	6	.	.	PUNCT
ejpam-3654	369	1	[	[	X
ejpam-3654	369	2	11	11	NUM
ejpam-3654	369	3	]	]	PUNCT
ejpam-3654	369	4	r.	r.	PROPN
ejpam-3654	369	5	p.	p.	PROPN
ejpam-3654	369	6	agarwal	agarwal	PROPN
ejpam-3654	369	7	,	,	PUNCT
ejpam-3654	369	8	m.	m.	NOUN
ejpam-3654	369	9	bohner	bohner	NOUN
ejpam-3654	369	10	,	,	PUNCT
ejpam-3654	369	11	t.	t.	PROPN
ejpam-3654	369	12	li	li	PROPN
ejpam-3654	369	13	,	,	PUNCT
ejpam-3654	369	14	and	and	CCONJ
ejpam-3654	369	15	c.	c.	PROPN
ejpam-3654	369	16	zhang	zhang	PROPN
ejpam-3654	369	17	,	,	PUNCT
ejpam-3654	369	18	a	a	DET
ejpam-3654	369	19	new	new	ADJ
ejpam-3654	369	20	approach	approach	NOUN
ejpam-3654	369	21	in	in	ADP
ejpam-3654	369	22	the	the	DET
ejpam-3654	369	23	study	study	NOUN
ejpam-3654	369	24	of	of	ADP
ejpam-3654	369	25	oscillatory	oscillatory	ADJ
ejpam-3654	369	26	behavior	behavior	NOUN
ejpam-3654	369	27	of	of	ADP
ejpam-3654	369	28	even	even	ADJ
ejpam-3654	369	29	-	-	PUNCT
ejpam-3654	369	30	order	order	NOUN
ejpam-3654	369	31	neutral	neutral	ADJ
ejpam-3654	369	32	delay	delay	NOUN
ejpam-3654	369	33	differential	differential	PROPN
ejpam-3654	369	34	equations	equation	NOUN
ejpam-3654	369	35	,	,	PUNCT
ejpam-3654	369	36	appl	appl	PROPN
ejpam-3654	369	37	.	.	PROPN
ejpam-3654	369	38	math	math	PROPN
ejpam-3654	369	39	.	.	PUNCT
ejpam-3654	370	1	comput	comput	NOUN
ejpam-3654	370	2	.	.	PUNCT
ejpam-3654	371	1	225	225	NUM
ejpam-3654	371	2	(	(	PUNCT
ejpam-3654	371	3	2013	2013	NUM
ejpam-3654	371	4	)	)	PUNCT
ejpam-3654	371	5	,	,	PUNCT
ejpam-3654	372	1	787–794	787–794	NUM
ejpam-3654	372	2	.	.	PUNCT
ejpam-3654	373	1	[	[	X
ejpam-3654	373	2	12	12	NUM
ejpam-3654	373	3	]	]	X
ejpam-3654	373	4	s.	s.	PROPN
ejpam-3654	373	5	r.	r.	PROPN
ejpam-3654	373	6	grace	grace	PROPN
ejpam-3654	373	7	,	,	PUNCT
ejpam-3654	373	8	j.	j.	PROPN
ejpam-3654	373	9	dzurina	dzurina	PROPN
ejpam-3654	373	10	,	,	PUNCT
ejpam-3654	373	11	i.	i.	PROPN
ejpam-3654	373	12	jadlovska	jadlovska	PROPN
ejpam-3654	373	13	,	,	PUNCT
ejpam-3654	373	14	and	and	CCONJ
ejpam-3654	373	15	t.	t.	PROPN
ejpam-3654	373	16	li	li	PROPN
ejpam-3654	373	17	,	,	PUNCT
ejpam-3654	373	18	on	on	ADP
ejpam-3654	373	19	the	the	DET
ejpam-3654	373	20	oscillation	oscillation	NOUN
ejpam-3654	373	21	of	of	ADP
ejpam-3654	373	22	fourth	fourth	ADJ
ejpam-3654	373	23	-	-	PUNCT
ejpam-3654	373	24	order	order	NOUN
ejpam-3654	373	25	delay	delay	NOUN
ejpam-3654	373	26	differential	differential	ADJ
ejpam-3654	373	27	equations	equation	NOUN
ejpam-3654	373	28	,	,	PUNCT
ejpam-3654	373	29	adv	adv	PROPN
ejpam-3654	373	30	.	.	PUNCT
ejpam-3654	373	31	difference	difference	PROPN
ejpam-3654	373	32	equ	equ	PROPN
ejpam-3654	373	33	.	.	PROPN
ejpam-3654	373	34	2019	2019	NUM
ejpam-3654	373	35	(	(	PUNCT
ejpam-3654	373	36	2019	2019	NUM
ejpam-3654	373	37	)	)	PUNCT
ejpam-3654	373	38	,	,	PUNCT
ejpam-3654	373	39	1–15	1–15	NUM
ejpam-3654	373	40	.	.	PUNCT
ejpam-3654	374	1	[	[	X
ejpam-3654	374	2	13	13	NUM
ejpam-3654	374	3	]	]	PUNCT
ejpam-3654	374	4	t.	t.	PROPN
ejpam-3654	374	5	li	li	PROPN
ejpam-3654	374	6	,	,	PUNCT
ejpam-3654	374	7	b.	b.	PROPN
ejpam-3654	374	8	baculikova	baculikova	PROPN
ejpam-3654	374	9	,	,	PUNCT
ejpam-3654	374	10	j.	j.	PROPN
ejpam-3654	374	11	dzurina	dzurina	PROPN
ejpam-3654	374	12	,	,	PUNCT
ejpam-3654	374	13	and	and	CCONJ
ejpam-3654	374	14	c.	c.	PROPN
ejpam-3654	374	15	zhang	zhang	PROPN
ejpam-3654	374	16	,	,	PUNCT
ejpam-3654	374	17	oscillation	oscillation	NOUN
ejpam-3654	374	18	of	of	ADP
ejpam-3654	374	19	fourth	fourth	ADJ
ejpam-3654	374	20	-	-	PUNCT
ejpam-3654	374	21	order	order	NOUN
ejpam-3654	374	22	neutral	neutral	ADJ
ejpam-3654	374	23	differential	differential	ADJ
ejpam-3654	374	24	equations	equation	NOUN
ejpam-3654	374	25	with	with	ADP
ejpam-3654	374	26	p	p	NOUN
ejpam-3654	374	27	-	-	PUNCT
ejpam-3654	374	28	laplacian	laplacian	ADJ
ejpam-3654	374	29	like	like	ADP
ejpam-3654	374	30	operators	operator	NOUN
ejpam-3654	374	31	,	,	PUNCT
ejpam-3654	374	32	bound	bind	VERB
ejpam-3654	374	33	.	.	PUNCT
ejpam-3654	375	1	value	value	PROPN
ejpam-3654	375	2	probl	probl	NOUN
ejpam-3654	375	3	.	.	PUNCT
ejpam-3654	376	1	2014	2014	NUM
ejpam-3654	376	2	(	(	PUNCT
ejpam-3654	376	3	2014	2014	NUM
ejpam-3654	376	4	)	)	PUNCT
ejpam-3654	377	1	,	,	PUNCT
ejpam-3654	377	2	1–9	1–9	PROPN
ejpam-3654	377	3	.	.	NOUN
ejpam-3654	377	4	references	reference	NOUN
ejpam-3654	377	5	199	199	NUM
ejpam-3654	377	6	[	[	X
ejpam-3654	377	7	14	14	NUM
ejpam-3654	377	8	]	]	PUNCT
ejpam-3654	377	9	t.	t.	PROPN
ejpam-3654	377	10	li	li	PROPN
ejpam-3654	377	11	and	and	CCONJ
ejpam-3654	377	12	yu	yu	PROPN
ejpam-3654	377	13	.	.	PUNCT
ejpam-3654	378	1	v.	v.	PROPN
ejpam-3654	378	2	rogovchenko	rogovchenko	PROPN
ejpam-3654	378	3	,	,	PUNCT
ejpam-3654	378	4	oscillation	oscillation	NOUN
ejpam-3654	378	5	criteria	criterion	NOUN
ejpam-3654	378	6	for	for	ADP
ejpam-3654	378	7	even	even	ADV
ejpam-3654	378	8	-	-	PUNCT
ejpam-3654	378	9	order	order	NOUN
ejpam-3654	378	10	neutral	neutral	ADJ
ejpam-3654	378	11	differential	differential	NOUN
ejpam-3654	378	12	equations	equation	NOUN
ejpam-3654	378	13	,	,	PUNCT
ejpam-3654	378	14	appl	appl	PROPN
ejpam-3654	378	15	.	.	PROPN
ejpam-3654	378	16	math	math	PROPN
ejpam-3654	378	17	.	.	PUNCT
ejpam-3654	379	1	lett	lett	PROPN
ejpam-3654	379	2	.	.	PUNCT
ejpam-3654	380	1	61	61	NUM
ejpam-3654	380	2	(	(	PUNCT
ejpam-3654	380	3	2016	2016	NUM
ejpam-3654	380	4	)	)	PUNCT
ejpam-3654	380	5	,	,	PUNCT
ejpam-3654	380	6	35–41	35–41	NUM
ejpam-3654	380	7	.	.	PUNCT
ejpam-3654	381	1	[	[	X
ejpam-3654	381	2	15	15	NUM
ejpam-3654	381	3	]	]	PUNCT
ejpam-3654	381	4	t.	t.	PROPN
ejpam-3654	381	5	li	li	PROPN
ejpam-3654	381	6	,	,	PUNCT
ejpam-3654	381	7	yu	yu	PROPN
ejpam-3654	381	8	.	.	PUNCT
ejpam-3654	382	1	v.	v.	PROPN
ejpam-3654	382	2	rogovchenko	rogovchenko	PROPN
ejpam-3654	382	3	,	,	PUNCT
ejpam-3654	382	4	and	and	CCONJ
ejpam-3654	382	5	c.	c.	PROPN
ejpam-3654	382	6	zhang	zhang	PROPN
ejpam-3654	382	7	,	,	PUNCT
ejpam-3654	382	8	oscillation	oscillation	NOUN
ejpam-3654	382	9	of	of	ADP
ejpam-3654	382	10	fourth	fourth	ADJ
ejpam-3654	382	11	-	-	PUNCT
ejpam-3654	382	12	order	order	NOUN
ejpam-3654	382	13	quasilinear	quasilinear	NOUN
ejpam-3654	382	14	differential	differential	PROPN
ejpam-3654	382	15	equations	equation	NOUN
ejpam-3654	382	16	,	,	PUNCT
ejpam-3654	382	17	math	math	NOUN
ejpam-3654	382	18	.	.	PUNCT
ejpam-3654	382	19	bohem	bohem	PROPN
ejpam-3654	382	20	.	.	PUNCT
ejpam-3654	383	1	140	140	NUM
ejpam-3654	383	2	(	(	PUNCT
ejpam-3654	383	3	2015	2015	NUM
ejpam-3654	383	4	)	)	PUNCT
ejpam-3654	383	5	,	,	PUNCT
ejpam-3654	383	6	405–418	405–418	NUM
ejpam-3654	383	7	.	.	PUNCT
ejpam-3654	384	1	[	[	X
ejpam-3654	384	2	16	16	NUM
ejpam-3654	384	3	]	]	X
ejpam-3654	384	4	b.	b.	PROPN
ejpam-3654	384	5	baculikova	baculikova	PROPN
ejpam-3654	384	6	,	,	PUNCT
ejpam-3654	384	7	j.	j.	PROPN
ejpam-3654	384	8	dzurina	dzurina	PROPN
ejpam-3654	384	9	,	,	PUNCT
ejpam-3654	384	10	j.	j.	PROPN
ejpam-3654	384	11	r.	r.	PROPN
ejpam-3654	384	12	graef	graef	PROPN
ejpam-3654	384	13	,	,	PUNCT
ejpam-3654	384	14	on	on	ADP
ejpam-3654	384	15	the	the	DET
ejpam-3654	384	16	oscillation	oscillation	NOUN
ejpam-3654	384	17	of	of	ADP
ejpam-3654	384	18	higher	high	ADJ
ejpam-3654	384	19	-	-	PUNCT
ejpam-3654	384	20	order	order	NOUN
ejpam-3654	384	21	delay	delay	NOUN
ejpam-3654	384	22	differential	differential	ADJ
ejpam-3654	384	23	equations	equation	NOUN
ejpam-3654	384	24	,	,	PUNCT
ejpam-3654	384	25	journal	journal	NOUN
ejpam-3654	384	26	of	of	ADP
ejpam-3654	384	27	mathematical	mathematical	ADJ
ejpam-3654	384	28	sciences	sciences	PROPN
ejpam-3654	384	29	,	,	PUNCT
ejpam-3654	384	30	vol	vol	NOUN
ejpam-3654	384	31	.	.	PROPN
ejpam-3654	384	32	187	187	NUM
ejpam-3654	384	33	,	,	PUNCT
ejpam-3654	384	34	no	no	INTJ
ejpam-3654	384	35	.	.	NOUN
ejpam-3654	384	36	4	4	NUM
ejpam-3654	384	37	,	,	PUNCT
ejpam-3654	384	38	2012	2012	NUM
ejpam-3654	384	39	.	.	PUNCT
ejpam-3654	385	1	[	[	X
ejpam-3654	385	2	17	17	NUM
ejpam-3654	385	3	]	]	X
ejpam-3654	385	4	s.r	s.r	PROPN
ejpam-3654	385	5	.	.	PROPN
ejpam-3654	385	6	grace	grace	NOUN
ejpam-3654	385	7	,	,	PUNCT
ejpam-3654	385	8	oscillation	oscillation	NOUN
ejpam-3654	385	9	theorems	theorem	NOUN
ejpam-3654	385	10	for	for	ADP
ejpam-3654	385	11	nth	nth	NOUN
ejpam-3654	385	12	-	-	PUNCT
ejpam-3654	385	13	order	order	NOUN
ejpam-3654	385	14	differential	differential	ADJ
ejpam-3654	385	15	equations	equation	NOUN
ejpam-3654	385	16	with	with	ADP
ejpam-3654	385	17	deviating	deviate	VERB
ejpam-3654	385	18	arguments	argument	NOUN
ejpam-3654	385	19	,	,	PUNCT
ejpam-3654	385	20	j.	j.	PROPN
ejpam-3654	385	21	math	math	PROPN
ejpam-3654	385	22	.	.	PUNCT
ejpam-3654	386	1	appl	appl	PROPN
ejpam-3654	386	2	.	.	PUNCT
ejpam-3654	387	1	anal	anal	PROPN
ejpam-3654	387	2	.	.	PUNCT
ejpam-3654	388	1	101	101	NUM
ejpam-3654	388	2	(	(	PUNCT
ejpam-3654	388	3	1984	1984	NUM
ejpam-3654	388	4	)	)	PUNCT
ejpam-3654	388	5	268–296	268–296	NUM
ejpam-3654	388	6	.	.	PUNCT
ejpam-3654	389	1	[	[	X
ejpam-3654	389	2	18	18	NUM
ejpam-3654	389	3	]	]	X
ejpam-3654	389	4	o.	o.	NOUN
ejpam-3654	389	5	moaaz	moaaz	PROPN
ejpam-3654	389	6	,	,	PUNCT
ejpam-3654	389	7	new	new	ADJ
ejpam-3654	389	8	criteria	criterion	NOUN
ejpam-3654	389	9	for	for	ADP
ejpam-3654	389	10	oscillation	oscillation	NOUN
ejpam-3654	389	11	of	of	ADP
ejpam-3654	389	12	nonlinear	nonlinear	ADJ
ejpam-3654	389	13	neutral	neutral	ADJ
ejpam-3654	389	14	differential	differential	NOUN
ejpam-3654	389	15	equations	equation	NOUN
ejpam-3654	389	16	,	,	PUNCT
ejpam-3654	389	17	adv	adv	PROPN
ejpam-3654	389	18	.	.	PUNCT
ejpam-3654	389	19	difference	difference	PROPN
ejpam-3654	389	20	eqs	eqs	PROPN
ejpam-3654	389	21	.	.	PUNCT
ejpam-3654	389	22	(	(	PUNCT
ejpam-3654	389	23	2019	2019	NUM
ejpam-3654	389	24	)	)	PUNCT
ejpam-3654	389	25	2019:484	2019:484	NOUN
ejpam-3654	389	26	.	.	PUNCT
ejpam-3654	390	1	[	[	X
ejpam-3654	390	2	19	19	NUM
ejpam-3654	390	3	]	]	X
ejpam-3654	390	4	o	o	X
ejpam-3654	390	5	moaaz	moaaz	PROPN
ejpam-3654	390	6	,	,	PUNCT
ejpam-3654	390	7	e.m	e.m	PROPN
ejpam-3654	390	8	.	.	PROPN
ejpam-3654	390	9	elabbasy	elabbasy	PROPN
ejpam-3654	390	10	,	,	PUNCT
ejpam-3654	390	11	o.	o.	PROPN
ejpam-3654	390	12	bazighifan	bazighifan	PROPN
ejpam-3654	390	13	,	,	PUNCT
ejpam-3654	390	14	on	on	ADP
ejpam-3654	390	15	the	the	DET
ejpam-3654	390	16	asymptotic	asymptotic	ADJ
ejpam-3654	390	17	behavior	behavior	NOUN
ejpam-3654	390	18	of	of	ADP
ejpam-3654	390	19	fourth	fourth	ADJ
ejpam-3654	390	20	-	-	PUNCT
ejpam-3654	390	21	order	order	NOUN
ejpam-3654	390	22	functional	functional	ADJ
ejpam-3654	390	23	differential	differential	NOUN
ejpam-3654	390	24	equations	equation	NOUN
ejpam-3654	390	25	.	.	PUNCT
ejpam-3654	391	1	adv	adv	PROPN
ejpam-3654	391	2	.	.	PUNCT
ejpam-3654	391	3	difference	difference	PROPN
ejpam-3654	391	4	equ	equ	PROPN
ejpam-3654	391	5	.	.	PROPN
ejpam-3654	391	6	2017	2017	NUM
ejpam-3654	391	7	,	,	PUNCT
ejpam-3654	391	8	261	261	NUM
ejpam-3654	391	9	(	(	PUNCT
ejpam-3654	391	10	2017	2017	NUM
ejpam-3654	391	11	)	)	PUNCT
ejpam-3654	392	1	[	[	X
ejpam-3654	392	2	20	20	NUM
ejpam-3654	392	3	]	]	PUNCT
ejpam-3654	392	4	o.	o.	PROPN
ejpam-3654	392	5	moaaz	moaaz	PROPN
ejpam-3654	392	6	,	,	PUNCT
ejpam-3654	392	7	e.m	e.m	PROPN
ejpam-3654	392	8	.	.	PROPN
ejpam-3654	392	9	elabbasy	elabbasy	PROPN
ejpam-3654	392	10	,	,	PUNCT
ejpam-3654	392	11	a.	a.	NOUN
ejpam-3654	392	12	muhib	muhib	NOUN
ejpam-3654	392	13	,	,	PUNCT
ejpam-3654	392	14	oscillation	oscillation	NOUN
ejpam-3654	392	15	criteria	criterion	NOUN
ejpam-3654	392	16	for	for	ADP
ejpam-3654	392	17	even	even	ADV
ejpam-3654	392	18	-	-	PUNCT
ejpam-3654	392	19	order	order	NOUN
ejpam-3654	392	20	neutral	neutral	ADJ
ejpam-3654	392	21	differential	differential	ADJ
ejpam-3654	392	22	equations	equation	NOUN
ejpam-3654	392	23	with	with	ADP
ejpam-3654	392	24	distributed	distribute	VERB
ejpam-3654	392	25	deviating	deviate	VERB
ejpam-3654	392	26	arguments	argument	NOUN
ejpam-3654	392	27	,	,	PUNCT
ejpam-3654	392	28	adv	adv	PROPN
ejpam-3654	392	29	.	.	PUNCT
ejpam-3654	392	30	difference	difference	PROPN
ejpam-3654	392	31	equ	equ	PROPN
ejpam-3654	392	32	.	.	PUNCT
ejpam-3654	393	1	(	(	PUNCT
ejpam-3654	393	2	2019	2019	NUM
ejpam-3654	393	3	)	)	PUNCT
ejpam-3654	393	4	2019:297	2019:297	NUM
ejpam-3654	393	5	.	.	PUNCT
ejpam-3654	394	1	[	[	X
ejpam-3654	394	2	21	21	NUM
ejpam-3654	394	3	]	]	PUNCT
ejpam-3654	394	4	t.	t.	PROPN
ejpam-3654	394	5	li	li	PROPN
ejpam-3654	394	6	,	,	PUNCT
ejpam-3654	394	7	y.v	y.v	PROPN
ejpam-3654	394	8	.	.	PROPN
ejpam-3654	394	9	rogovchenko	rogovchenko	PROPN
ejpam-3654	394	10	,	,	PUNCT
ejpam-3654	394	11	asymptotic	asymptotic	ADJ
ejpam-3654	394	12	behavior	behavior	NOUN
ejpam-3654	394	13	of	of	ADP
ejpam-3654	394	14	higher	high	ADJ
ejpam-3654	394	15	-	-	PUNCT
ejpam-3654	394	16	order	order	NOUN
ejpam-3654	394	17	quasilinear	quasilinear	NOUN
ejpam-3654	394	18	neutral	neutral	ADJ
ejpam-3654	394	19	differential	differential	NOUN
ejpam-3654	394	20	equations	equation	NOUN
ejpam-3654	394	21	,	,	PUNCT
ejpam-3654	394	22	hindawi	hindawi	ADJ
ejpam-3654	394	23	publishing	publishing	NOUN
ejpam-3654	394	24	corporation	corporation	NOUN
ejpam-3654	394	25	,	,	PUNCT
ejpam-3654	394	26	2014	2014	NUM
ejpam-3654	394	27	,	,	PUNCT
ejpam-3654	394	28	11	11	NUM
ejpam-3654	394	29	pages	page	NOUN
ejpam-3654	394	30	[	[	X
ejpam-3654	394	31	22	22	NUM
ejpam-3654	394	32	]	]	X
ejpam-3654	394	33	j.k	j.k	PROPN
ejpam-3654	394	34	.	.	PROPN
ejpam-3654	394	35	hale	hale	PROPN
ejpam-3654	394	36	,	,	PUNCT
ejpam-3654	394	37	theory	theory	NOUN
ejpam-3654	394	38	of	of	ADP
ejpam-3654	394	39	functional	functional	ADJ
ejpam-3654	394	40	differential	differential	ADJ
ejpam-3654	394	41	equations	equation	NOUN
ejpam-3654	394	42	,	,	PUNCT
ejpam-3654	394	43	springer	springer	NOUN
ejpam-3654	394	44	-	-	PUNCT
ejpam-3654	394	45	verlag	verlag	PROPN
ejpam-3654	394	46	,	,	PUNCT
ejpam-3654	394	47	new	new	PROPN
ejpam-3654	394	48	york	york	PROPN
ejpam-3654	394	49	(	(	PUNCT
ejpam-3654	394	50	1977	1977	NUM
ejpam-3654	394	51	)	)	PUNCT
ejpam-3654	395	1	[	[	X
ejpam-3654	395	2	23	23	NUM
ejpam-3654	395	3	]	]	PUNCT
ejpam-3654	395	4	ch.g	ch.g	X
ejpam-3654	395	5	.	.	PUNCT
ejpam-3654	396	1	philos	philos	PROPN
ejpam-3654	396	2	,	,	PUNCT
ejpam-3654	396	3	a	a	DET
ejpam-3654	396	4	new	new	ADJ
ejpam-3654	396	5	criterion	criterion	NOUN
ejpam-3654	396	6	for	for	ADP
ejpam-3654	396	7	the	the	DET
ejpam-3654	396	8	oscillatory	oscillatory	ADJ
ejpam-3654	396	9	and	and	CCONJ
ejpam-3654	396	10	asymptotic	asymptotic	ADJ
ejpam-3654	396	11	behavior	behavior	NOUN
ejpam-3654	396	12	of	of	ADP
ejpam-3654	396	13	delay	delay	NOUN
ejpam-3654	396	14	differential	differential	PROPN
ejpam-3654	396	15	equations	equation	NOUN
ejpam-3654	396	16	,	,	PUNCT
ejpam-3654	396	17	bull	bull	NOUN
ejpam-3654	396	18	.	.	PUNCT
ejpam-3654	397	1	acad	acad	PROPN
ejpam-3654	397	2	.	.	PUNCT
ejpam-3654	398	1	pol	pol	PROPN
ejpam-3654	398	2	.	.	PUNCT
ejpam-3654	399	1	sci	sci	PROPN
ejpam-3654	399	2	.	.	PROPN
ejpam-3654	399	3	,	,	PUNCT
ejpam-3654	399	4	ser	ser	PROPN
ejpam-3654	399	5	.	.	PUNCT
ejpam-3654	400	1	sci	sci	PROPN
ejpam-3654	400	2	.	.	PUNCT
ejpam-3654	400	3	math	math	PROPN
ejpam-3654	400	4	.	.	PUNCT
ejpam-3654	401	1	39	39	NUM
ejpam-3654	401	2	(	(	PUNCT
ejpam-3654	401	3	1981	1981	NUM
ejpam-3654	401	4	)	)	PUNCT
ejpam-3654	401	5	61–64	61–64	NUM
ejpam-3654	401	6	.	.	PUNCT