id	sid	tid	token	lemma	pos
ejpam-4945	1	1	european	european	PROPN
ejpam-4945	1	2	journal	journal	PROPN
ejpam-4945	1	3	of	of	ADP
ejpam-4945	1	4	pure	pure	ADJ
ejpam-4945	1	5	and	and	CCONJ
ejpam-4945	1	6	applied	apply	VERB
ejpam-4945	1	7	mathematics	mathematic	NOUN
ejpam-4945	1	8	vol	vol	NOUN
ejpam-4945	1	9	.	.	PUNCT
ejpam-4945	2	1	16	16	NUM
ejpam-4945	2	2	,	,	PUNCT
ejpam-4945	2	3	no	no	INTJ
ejpam-4945	2	4	.	.	NOUN
ejpam-4945	2	5	4	4	NUM
ejpam-4945	2	6	,	,	PUNCT
ejpam-4945	2	7	2023	2023	NUM
ejpam-4945	2	8	,	,	PUNCT
ejpam-4945	2	9	2499	2499	NUM
ejpam-4945	2	10	-	-	SYM
ejpam-4945	2	11	2508	2508	NUM
ejpam-4945	2	12	issn	issn	PROPN
ejpam-4945	2	13	1307	1307	NUM
ejpam-4945	2	14	-	-	SYM
ejpam-4945	2	15	5543	5543	NUM
ejpam-4945	2	16	–	–	PUNCT
ejpam-4945	2	17	ejpam.com	ejpam.com	X
ejpam-4945	2	18	published	publish	VERB
ejpam-4945	2	19	by	by	ADP
ejpam-4945	2	20	new	new	PROPN
ejpam-4945	2	21	york	york	PROPN
ejpam-4945	2	22	business	business	PROPN
ejpam-4945	2	23	global	global	ADJ
ejpam-4945	2	24	oscillatory	oscillatory	ADJ
ejpam-4945	2	25	properties	property	NOUN
ejpam-4945	2	26	test	test	VERB
ejpam-4945	2	27	for	for	ADP
ejpam-4945	2	28	even	even	ADV
ejpam-4945	2	29	-	-	PUNCT
ejpam-4945	2	30	order	order	NOUN
ejpam-4945	2	31	differential	differential	ADJ
ejpam-4945	2	32	equations	equation	NOUN
ejpam-4945	2	33	of	of	ADP
ejpam-4945	2	34	neutral	neutral	ADJ
ejpam-4945	2	35	type	type	NOUN
ejpam-4945	2	36	alanoud	alanoud	PROPN
ejpam-4945	2	37	almutairi	almutairi	NOUN
ejpam-4945	2	38	1	1	NUM
ejpam-4945	2	39	department	department	NOUN
ejpam-4945	2	40	of	of	ADP
ejpam-4945	2	41	mathematics	mathematic	NOUN
ejpam-4945	2	42	,	,	PUNCT
ejpam-4945	2	43	faculty	faculty	NOUN
ejpam-4945	2	44	of	of	ADP
ejpam-4945	2	45	science	science	NOUN
ejpam-4945	2	46	,	,	PUNCT
ejpam-4945	2	47	university	university	NOUN
ejpam-4945	2	48	of	of	ADP
ejpam-4945	2	49	hafr	hafr	PROPN
ejpam-4945	2	50	al	al	PROPN
ejpam-4945	2	51	batin	batin	PROPN
ejpam-4945	2	52	,	,	PUNCT
ejpam-4945	2	53	p.o	p.o	PROPN
ejpam-4945	2	54	.	.	PROPN
ejpam-4945	2	55	box	box	PROPN
ejpam-4945	2	56	1803	1803	NUM
ejpam-4945	2	57	,	,	PUNCT
ejpam-4945	2	58	hafar	hafar	ADV
ejpam-4945	2	59	al	al	PROPN
ejpam-4945	2	60	batin	batin	PROPN
ejpam-4945	2	61	31991	31991	NUM
ejpam-4945	2	62	,	,	PUNCT
ejpam-4945	2	63	saudi	saudi	PROPN
ejpam-4945	2	64	arabia	arabia	PROPN
ejpam-4945	2	65	abstract	abstract	NOUN
ejpam-4945	2	66	.	.	PUNCT
ejpam-4945	3	1	this	this	DET
ejpam-4945	3	2	paper	paper	NOUN
ejpam-4945	3	3	presents	present	VERB
ejpam-4945	3	4	a	a	DET
ejpam-4945	3	5	study	study	NOUN
ejpam-4945	3	6	on	on	ADP
ejpam-4945	3	7	the	the	DET
ejpam-4945	3	8	oscillatory	oscillatory	ADJ
ejpam-4945	3	9	behavior	behavior	NOUN
ejpam-4945	3	10	of	of	ADP
ejpam-4945	3	11	solutions	solution	NOUN
ejpam-4945	3	12	to	to	ADP
ejpam-4945	3	13	even	even	ADV
ejpam-4945	3	14	-	-	PUNCT
ejpam-4945	3	15	order	order	NOUN
ejpam-4945	3	16	neutral	neutral	ADJ
ejpam-4945	3	17	differential	differential	NOUN
ejpam-4945	3	18	equations	equation	NOUN
ejpam-4945	3	19	involving	involve	VERB
ejpam-4945	3	20	p	p	NOUN
ejpam-4945	3	21	-	-	PUNCT
ejpam-4945	3	22	laplacian	laplacian	ADJ
ejpam-4945	3	23	-	-	PUNCT
ejpam-4945	3	24	like	like	ADJ
ejpam-4945	3	25	operator	operator	NOUN
ejpam-4945	3	26	.	.	PUNCT
ejpam-4945	4	1	we	we	PRON
ejpam-4945	4	2	obtain	obtain	VERB
ejpam-4945	4	3	oscillation	oscillation	NOUN
ejpam-4945	4	4	criteria	criterion	NOUN
ejpam-4945	4	5	using	use	VERB
ejpam-4945	4	6	techniques	technique	NOUN
ejpam-4945	4	7	from	from	ADP
ejpam-4945	4	8	first	first	ADJ
ejpam-4945	4	9	-	-	PUNCT
ejpam-4945	4	10	order	order	NOUN
ejpam-4945	4	11	delay	delay	NOUN
ejpam-4945	4	12	differential	differential	ADJ
ejpam-4945	4	13	equations	equation	NOUN
ejpam-4945	4	14	,	,	PUNCT
ejpam-4945	4	15	riccati	riccati	NOUN
ejpam-4945	4	16	technique	technique	NOUN
ejpam-4945	4	17	and	and	CCONJ
ejpam-4945	4	18	integral	integral	ADJ
ejpam-4945	4	19	averages	average	NOUN
ejpam-4945	4	20	technique	technique	NOUN
ejpam-4945	4	21	.	.	PUNCT
ejpam-4945	5	1	the	the	DET
ejpam-4945	5	2	results	result	NOUN
ejpam-4945	5	3	of	of	ADP
ejpam-4945	5	4	this	this	DET
ejpam-4945	5	5	work	work	NOUN
ejpam-4945	5	6	contribute	contribute	VERB
ejpam-4945	5	7	to	to	ADP
ejpam-4945	5	8	a	a	DET
ejpam-4945	5	9	deeper	deep	ADJ
ejpam-4945	5	10	understanding	understanding	NOUN
ejpam-4945	5	11	of	of	ADP
ejpam-4945	5	12	even	even	ADJ
ejpam-4945	5	13	-	-	PUNCT
ejpam-4945	5	14	order	order	NOUN
ejpam-4945	5	15	differential	differential	ADJ
ejpam-4945	5	16	equations	equation	NOUN
ejpam-4945	5	17	and	and	CCONJ
ejpam-4945	5	18	their	their	PRON
ejpam-4945	5	19	connections	connection	NOUN
ejpam-4945	5	20	to	to	ADP
ejpam-4945	5	21	various	various	ADJ
ejpam-4945	5	22	branches	branch	NOUN
ejpam-4945	5	23	of	of	ADP
ejpam-4945	5	24	mathematics	mathematic	NOUN
ejpam-4945	5	25	and	and	CCONJ
ejpam-4945	5	26	practical	practical	ADJ
ejpam-4945	5	27	sciences	science	NOUN
ejpam-4945	5	28	.	.	PUNCT
ejpam-4945	6	1	the	the	DET
ejpam-4945	6	2	findings	finding	NOUN
ejpam-4945	6	3	emphasize	emphasize	VERB
ejpam-4945	6	4	the	the	DET
ejpam-4945	6	5	importance	importance	NOUN
ejpam-4945	6	6	of	of	ADP
ejpam-4945	6	7	continued	continue	VERB
ejpam-4945	6	8	research	research	NOUN
ejpam-4945	6	9	in	in	ADP
ejpam-4945	6	10	this	this	DET
ejpam-4945	6	11	area	area	NOUN
ejpam-4945	6	12	.	.	PUNCT
ejpam-4945	7	1	2020	2020	NUM
ejpam-4945	7	2	mathematics	mathematic	NOUN
ejpam-4945	7	3	subject	subject	NOUN
ejpam-4945	7	4	classifications	classification	NOUN
ejpam-4945	7	5	:	:	PUNCT
ejpam-4945	7	6	34k10	34k10	NUM
ejpam-4945	7	7	,	,	PUNCT
ejpam-4945	7	8	34k11	34k11	NUM
ejpam-4945	7	9	key	key	ADJ
ejpam-4945	7	10	words	word	NOUN
ejpam-4945	7	11	and	and	CCONJ
ejpam-4945	7	12	phrases	phrase	NOUN
ejpam-4945	7	13	:	:	PUNCT
ejpam-4945	7	14	oscillation	oscillation	NOUN
ejpam-4945	7	15	conditions	condition	NOUN
ejpam-4945	7	16	,	,	PUNCT
ejpam-4945	7	17	neutral	neutral	ADJ
ejpam-4945	7	18	,	,	PUNCT
ejpam-4945	7	19	even	even	ADJ
ejpam-4945	7	20	-	-	PUNCT
ejpam-4945	7	21	order	order	NOUN
ejpam-4945	7	22	,	,	PUNCT
ejpam-4945	7	23	differential	differential	ADJ
ejpam-4945	7	24	equation	equation	NOUN
ejpam-4945	7	25	1	1	NUM
ejpam-4945	7	26	.	.	PUNCT
ejpam-4945	8	1	introduction	introduction	NOUN
ejpam-4945	8	2	differential	differential	NOUN
ejpam-4945	8	3	equations	equation	NOUN
ejpam-4945	8	4	are	be	AUX
ejpam-4945	8	5	characterized	characterize	VERB
ejpam-4945	8	6	by	by	ADP
ejpam-4945	8	7	many	many	ADJ
ejpam-4945	8	8	important	important	ADJ
ejpam-4945	8	9	advantages	advantage	NOUN
ejpam-4945	8	10	that	that	PRON
ejpam-4945	8	11	contribute	contribute	VERB
ejpam-4945	8	12	to	to	ADP
ejpam-4945	8	13	many	many	ADJ
ejpam-4945	8	14	practical	practical	ADJ
ejpam-4945	8	15	applications	application	NOUN
ejpam-4945	8	16	in	in	ADP
ejpam-4945	8	17	this	this	DET
ejpam-4945	8	18	life	life	NOUN
ejpam-4945	8	19	.	.	PUNCT
ejpam-4945	9	1	it	it	PRON
ejpam-4945	9	2	is	be	AUX
ejpam-4945	9	3	involved	involve	VERB
ejpam-4945	9	4	in	in	ADP
ejpam-4945	9	5	the	the	DET
ejpam-4945	9	6	aviation	aviation	NOUN
ejpam-4945	9	7	industry	industry	NOUN
ejpam-4945	9	8	,	,	PUNCT
ejpam-4945	9	9	especially	especially	ADV
ejpam-4945	9	10	in	in	ADP
ejpam-4945	9	11	controlling	control	VERB
ejpam-4945	9	12	vibrational	vibrational	ADJ
ejpam-4945	9	13	motion	motion	NOUN
ejpam-4945	9	14	,	,	PUNCT
ejpam-4945	9	15	in	in	ADP
ejpam-4945	9	16	medicine	medicine	NOUN
ejpam-4945	9	17	and	and	CCONJ
ejpam-4945	9	18	in	in	ADP
ejpam-4945	9	19	civil	civil	ADJ
ejpam-4945	9	20	engineering	engineering	NOUN
ejpam-4945	9	21	in	in	ADP
ejpam-4945	9	22	building	building	NOUN
ejpam-4945	9	23	bridges	bridge	NOUN
ejpam-4945	9	24	;	;	PUNCT
ejpam-4945	9	25	see	see	VERB
ejpam-4945	9	26	[	[	X
ejpam-4945	9	27	2	2	NUM
ejpam-4945	9	28	,	,	PUNCT
ejpam-4945	9	29	3	3	NUM
ejpam-4945	9	30	,	,	PUNCT
ejpam-4945	9	31	5–7	5–7	NOUN
ejpam-4945	9	32	]	]	PUNCT
ejpam-4945	9	33	.	.	PUNCT
ejpam-4945	10	1	the	the	DET
ejpam-4945	10	2	p	p	PROPN
ejpam-4945	10	3	-laplace	-laplace	PROPN
ejpam-4945	10	4	equations	equation	NOUN
ejpam-4945	10	5	have	have	VERB
ejpam-4945	10	6	some	some	DET
ejpam-4945	10	7	significant	significant	ADJ
ejpam-4945	10	8	applications	application	NOUN
ejpam-4945	10	9	in	in	ADP
ejpam-4945	10	10	elasticity	elasticity	NOUN
ejpam-4945	10	11	theory	theory	NOUN
ejpam-4945	10	12	and	and	CCONJ
ejpam-4945	10	13	continuum	continuum	ADJ
ejpam-4945	10	14	mechanics	mechanic	NOUN
ejpam-4945	10	15	.	.	PUNCT
ejpam-4945	11	1	the	the	DET
ejpam-4945	11	2	oscillation	oscillation	NOUN
ejpam-4945	11	3	theory	theory	NOUN
ejpam-4945	11	4	of	of	ADP
ejpam-4945	11	5	equations	equation	NOUN
ejpam-4945	11	6	has	have	AUX
ejpam-4945	11	7	undergone	undergo	VERB
ejpam-4945	11	8	many	many	ADJ
ejpam-4945	11	9	research	research	NOUN
ejpam-4945	11	10	contributions	contribution	NOUN
ejpam-4945	11	11	by	by	ADP
ejpam-4945	11	12	many	many	ADJ
ejpam-4945	11	13	researchers	researcher	NOUN
ejpam-4945	11	14	,	,	PUNCT
ejpam-4945	11	15	especially	especially	ADV
ejpam-4945	11	16	the	the	DET
ejpam-4945	11	17	study	study	NOUN
ejpam-4945	11	18	of	of	ADP
ejpam-4945	11	19	approximate	approximate	ADJ
ejpam-4945	11	20	and	and	CCONJ
ejpam-4945	11	21	oscillatory	oscillatory	ADJ
ejpam-4945	11	22	behavior	behavior	NOUN
ejpam-4945	11	23	;	;	PUNCT
ejpam-4945	11	24	see	see	VERB
ejpam-4945	11	25	[	[	X
ejpam-4945	11	26	1	1	NUM
ejpam-4945	11	27	,	,	PUNCT
ejpam-4945	11	28	4	4	NUM
ejpam-4945	11	29	,	,	PUNCT
ejpam-4945	11	30	8	8	NUM
ejpam-4945	11	31	,	,	PUNCT
ejpam-4945	11	32	10	10	NUM
ejpam-4945	11	33	,	,	PUNCT
ejpam-4945	11	34	10	10	NUM
ejpam-4945	11	35	,	,	PUNCT
ejpam-4945	11	36	11	11	NUM
ejpam-4945	11	37	,	,	PUNCT
ejpam-4945	11	38	16	16	NUM
ejpam-4945	11	39	,	,	PUNCT
ejpam-4945	11	40	17	17	NUM
ejpam-4945	11	41	]	]	PUNCT
ejpam-4945	11	42	.	.	PUNCT
ejpam-4945	12	1	the	the	DET
ejpam-4945	12	2	aim	aim	NOUN
ejpam-4945	12	3	of	of	ADP
ejpam-4945	12	4	this	this	DET
ejpam-4945	12	5	work	work	NOUN
ejpam-4945	12	6	is	be	AUX
ejpam-4945	12	7	to	to	PART
ejpam-4945	12	8	study	study	VERB
ejpam-4945	12	9	the	the	DET
ejpam-4945	12	10	oscillatory	oscillatory	ADJ
ejpam-4945	12	11	properties	property	NOUN
ejpam-4945	12	12	of	of	ADP
ejpam-4945	12	13	the	the	DET
ejpam-4945	12	14	solutions	solution	NOUN
ejpam-4945	12	15	of	of	ADP
ejpam-4945	12	16	even	even	ADJ
ejpam-4945	12	17	-	-	PUNCT
ejpam-4945	12	18	order	order	NOUN
ejpam-4945	12	19	delay	delay	NOUN
ejpam-4945	12	20	differential	differential	ADJ
ejpam-4945	12	21	equations	equation	NOUN
ejpam-4945	12	22	(	(	PUNCT
ejpam-4945	12	23	a	a	DET
ejpam-4945	12	24	(	(	PUNCT
ejpam-4945	12	25	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	12	26	)	)	PUNCT
ejpam-4945	12	27	(	(	PUNCT
ejpam-4945	12	28	ι	ι	NOUN
ejpam-4945	12	29	)	)	PUNCT
ejpam-4945	12	30	)	)	PUNCT
ejpam-4945	13	1	′	′	NOUN
ejpam-4945	14	1	+	+	CCONJ
ejpam-4945	14	2	r∑	r∑	X
ejpam-4945	14	3	i=1	i=1	PROPN
ejpam-4945	14	4	bi	bi	NOUN
ejpam-4945	14	5	(	(	PUNCT
ejpam-4945	14	6	ι)φ	ι)φ	X
ejpam-4945	14	7	(	(	PUNCT
ejpam-4945	14	8	ξ	ξ	X
ejpam-4945	14	9	(	(	PUNCT
ejpam-4945	14	10	zi	zi	X
ejpam-4945	14	11	(	(	PUNCT
ejpam-4945	14	12	ι	ι	NOUN
ejpam-4945	14	13	)	)	PUNCT
ejpam-4945	14	14	)	)	PUNCT
ejpam-4945	14	15	)	)	PUNCT
ejpam-4945	15	1	=	=	PUNCT
ejpam-4945	15	2	0	0	NUM
ejpam-4945	15	3	,	,	PUNCT
ejpam-4945	15	4	(	(	PUNCT
ejpam-4945	15	5	1	1	X
ejpam-4945	15	6	)	)	PUNCT
ejpam-4945	15	7	where	where	SCONJ
ejpam-4945	15	8	β	β	X
ejpam-4945	15	9	≥	≥	NOUN
ejpam-4945	15	10	2	2	NUM
ejpam-4945	15	11	and	and	CCONJ
ejpam-4945	15	12	w	w	PROPN
ejpam-4945	15	13	(	(	PUNCT
ejpam-4945	15	14	ι	ι	NOUN
ejpam-4945	15	15	)	)	PUNCT
ejpam-4945	15	16	=	=	PUNCT
ejpam-4945	15	17	|ξ	|ξ	NOUN
ejpam-4945	15	18	(	(	PUNCT
ejpam-4945	15	19	ι)|p−2	ι)|p−2	PUNCT
ejpam-4945	15	20	ξ	ξ	X
ejpam-4945	15	21	(	(	PUNCT
ejpam-4945	15	22	ι	ι	NOUN
ejpam-4945	15	23	)	)	PUNCT
ejpam-4945	16	1	+	+	CCONJ
ejpam-4945	16	2	ς	ς	PROPN
ejpam-4945	16	3	(	(	PUNCT
ejpam-4945	16	4	ι	ι	NOUN
ejpam-4945	16	5	)	)	PUNCT
ejpam-4945	16	6	ξ	ξ	PROPN
ejpam-4945	16	7	(	(	PUNCT
ejpam-4945	16	8	γ	γ	X
ejpam-4945	16	9	(	(	PUNCT
ejpam-4945	16	10	ι	ι	PROPN
ejpam-4945	16	11	)	)	PUNCT
ejpam-4945	16	12	)	)	PUNCT
ejpam-4945	16	13	(	(	PUNCT
ejpam-4945	16	14	2	2	X
ejpam-4945	16	15	)	)	PUNCT
ejpam-4945	16	16	doi	doi	NOUN
ejpam-4945	16	17	:	:	PUNCT
ejpam-4945	16	18	https://doi.org/10.29020/nybg.ejpam.v16i4.4945	https://doi.org/10.29020/nybg.ejpam.v16i4.4945	ADV
ejpam-4945	16	19	email	email	NOUN
ejpam-4945	16	20	address	address	NOUN
ejpam-4945	16	21	:	:	PUNCT
ejpam-4945	16	22	amalmutairi@uhb.edu.sa	amalmutairi@uhb.edu.sa	PROPN
ejpam-4945	16	23	(	(	PUNCT
ejpam-4945	16	24	a.	a.	NOUN
ejpam-4945	16	25	almutairi	almutairi	PROPN
ejpam-4945	16	26	)	)	PUNCT
ejpam-4945	16	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4945	16	28	2499	2499	NUM
ejpam-4945	17	1	©	©	ADP
ejpam-4945	17	2	2023	2023	NUM
ejpam-4945	17	3	ejpam	ejpam	NOUN
ejpam-4945	17	4	all	all	DET
ejpam-4945	17	5	rights	right	NOUN
ejpam-4945	17	6	reserved	reserve	VERB
ejpam-4945	17	7	.	.	PUNCT
ejpam-4945	18	1	a.	a.	NOUN
ejpam-4945	18	2	almutairi	almutairi	PROPN
ejpam-4945	18	3	/	/	SYM
ejpam-4945	18	4	eur	eur	PROPN
ejpam-4945	18	5	.	.	PUNCT
ejpam-4945	19	1	j.	j.	PROPN
ejpam-4945	19	2	pure	pure	PROPN
ejpam-4945	19	3	appl	appl	PROPN
ejpam-4945	19	4	.	.	PROPN
ejpam-4945	19	5	math	math	PROPN
ejpam-4945	19	6	,	,	PUNCT
ejpam-4945	19	7	16	16	NUM
ejpam-4945	19	8	(	(	PUNCT
ejpam-4945	19	9	4	4	NUM
ejpam-4945	19	10	)	)	PUNCT
ejpam-4945	19	11	(	(	PUNCT
ejpam-4945	19	12	2023	2023	NUM
ejpam-4945	19	13	)	)	PUNCT
ejpam-4945	19	14	,	,	PUNCT
ejpam-4945	19	15	2499	2499	NUM
ejpam-4945	19	16	-	-	SYM
ejpam-4945	19	17	2508	2508	NUM
ejpam-4945	19	18	2500	2500	NUM
ejpam-4945	19	19	also	also	ADV
ejpam-4945	19	20	∫	∫	PROPN
ejpam-4945	20	1	∞	∞	PROPN
ejpam-4945	20	2	ι0	ι0	PROPN
ejpam-4945	20	3	1	1	NUM
ejpam-4945	20	4	a	a	DET
ejpam-4945	20	5	(	(	PUNCT
ejpam-4945	20	6	s	s	NOUN
ejpam-4945	20	7	)	)	PUNCT
ejpam-4945	20	8	ds	ds	PROPN
ejpam-4945	20	9	=	=	SYM
ejpam-4945	20	10	∞.	∞.	PROPN
ejpam-4945	20	11	(	(	PUNCT
ejpam-4945	20	12	3	3	X
ejpam-4945	20	13	)	)	PUNCT
ejpam-4945	20	14	we	we	PRON
ejpam-4945	20	15	also	also	ADV
ejpam-4945	20	16	suppose	suppose	VERB
ejpam-4945	20	17	the	the	DET
ejpam-4945	20	18	following	follow	VERB
ejpam-4945	20	19	conditions:	conditions:	PROPN
ejpam-4945	20	20	(	(	PUNCT
ejpam-4945	20	21	h1)a	h1)a	PROPN
ejpam-4945	20	22	,	,	PUNCT
ejpam-4945	20	23	ς	ς	PROPN
ejpam-4945	20	24	∈	∈	PROPN
ejpam-4945	20	25	c	c	X
ejpam-4945	20	26	(	(	PUNCT
ejpam-4945	20	27	[	[	X
ejpam-4945	20	28	ι0,∞	ι0,∞	X
ejpam-4945	20	29	)	)	PUNCT
ejpam-4945	20	30	,	,	PUNCT
ejpam-4945	21	1	[	[	X
ejpam-4945	21	2	0,∞	0,∞	NOUN
ejpam-4945	21	3	)	)	PUNCT
ejpam-4945	21	4	)	)	PUNCT
ejpam-4945	22	1	,	,	PUNCT
ejpam-4945	22	2	bi	bi	NOUN
ejpam-4945	22	3	∈	∈	PROPN
ejpam-4945	22	4	c	c	PROPN
ejpam-4945	22	5	(	(	PUNCT
ejpam-4945	22	6	[	[	X
ejpam-4945	22	7	ι0,∞	ι0,∞	NOUN
ejpam-4945	22	8	)	)	PUNCT
ejpam-4945	22	9	,	,	PUNCT
ejpam-4945	22	10	r+	r+	X
ejpam-4945	22	11	)	)	PUNCT
ejpam-4945	22	12	,	,	PUNCT
ejpam-4945	22	13	a	a	DET
ejpam-4945	22	14	(	(	PUNCT
ejpam-4945	22	15	ι	ι	NOUN
ejpam-4945	22	16	)	)	PUNCT
ejpam-4945	22	17	>	>	X
ejpam-4945	22	18	0	0	NUM
ejpam-4945	22	19	,	,	PUNCT
ejpam-4945	22	20	a′	a′	PROPN
ejpam-4945	22	21	(	(	PUNCT
ejpam-4945	22	22	ι	ι	PROPN
ejpam-4945	22	23	)	)	PUNCT
ejpam-4945	22	24	≥	≥	NOUN
ejpam-4945	22	25	0	0	NUM
ejpam-4945	22	26	,	,	PUNCT
ejpam-4945	22	27	0	0	NUM
ejpam-4945	22	28	≤	≤	NUM
ejpam-4945	22	29	ς	ς	PROPN
ejpam-4945	22	30	(	(	PUNCT
ejpam-4945	22	31	ι	ι	PROPN
ejpam-4945	22	32	)	)	PUNCT
ejpam-4945	22	33	<	<	X
ejpam-4945	22	34	1	1	NUM
ejpam-4945	22	35	,	,	PUNCT
ejpam-4945	22	36	(	(	PUNCT
ejpam-4945	22	37	h2)γ	h2)γ	VERB
ejpam-4945	22	38	∈	∈	PROPN
ejpam-4945	22	39	c	c	X
ejpam-4945	22	40	(	(	PUNCT
ejpam-4945	22	41	[	[	X
ejpam-4945	22	42	ι0,∞	ι0,∞	NOUN
ejpam-4945	22	43	)	)	PUNCT
ejpam-4945	22	44	,	,	PUNCT
ejpam-4945	22	45	(	(	PUNCT
ejpam-4945	22	46	0,∞	0,∞	NOUN
ejpam-4945	22	47	)	)	PUNCT
ejpam-4945	22	48	)	)	PUNCT
ejpam-4945	22	49	,	,	PUNCT
ejpam-4945	22	50	γ	γ	X
ejpam-4945	22	51	(	(	PUNCT
ejpam-4945	22	52	ι	ι	PROPN
ejpam-4945	22	53	)	)	PUNCT
ejpam-4945	22	54	≤	≤	NOUN
ejpam-4945	22	55	ι	ι	PROPN
ejpam-4945	22	56	,	,	PUNCT
ejpam-4945	22	57	limι→∞	limι→∞	PROPN
ejpam-4945	22	58	γ	γ	X
ejpam-4945	22	59	(	(	PUNCT
ejpam-4945	22	60	ι	ι	PROPN
ejpam-4945	22	61	)	)	PUNCT
ejpam-4945	22	62	=	=	SYM
ejpam-4945	22	63	∞	∞	PROPN
ejpam-4945	22	64	;	;	PUNCT
ejpam-4945	22	65	zi	zi	PROPN
ejpam-4945	22	66	∈	∈	PROPN
ejpam-4945	22	67	c	c	X
ejpam-4945	22	68	(	(	PUNCT
ejpam-4945	22	69	[	[	X
ejpam-4945	22	70	ι0,∞	ι0,∞	NOUN
ejpam-4945	22	71	)	)	PUNCT
ejpam-4945	22	72	,	,	PUNCT
ejpam-4945	22	73	r	r	NOUN
ejpam-4945	22	74	)	)	PUNCT
ejpam-4945	22	75	,	,	PUNCT
ejpam-4945	22	76	i	i	PRON
ejpam-4945	22	77	=	=	NOUN
ejpam-4945	22	78	1	1	NUM
ejpam-4945	22	79	,	,	PUNCT
ejpam-4945	22	80	2	2	NUM
ejpam-4945	22	81	,	,	PUNCT
ejpam-4945	22	82	...	...	PUNCT
ejpam-4945	22	83	,	,	PUNCT
ejpam-4945	22	84	r	r	NOUN
ejpam-4945	22	85	(	(	PUNCT
ejpam-4945	22	86	h3)φ	h3)φ	NOUN
ejpam-4945	22	87	∈	∈	PROPN
ejpam-4945	22	88	c	c	X
ejpam-4945	22	89	(	(	PUNCT
ejpam-4945	22	90	r	r	NOUN
ejpam-4945	22	91	,	,	PUNCT
ejpam-4945	22	92	r	r	NOUN
ejpam-4945	22	93	)	)	PUNCT
ejpam-4945	22	94	,	,	PUNCT
ejpam-4945	22	95	φ	φ	X
ejpam-4945	22	96	(	(	PUNCT
ejpam-4945	22	97	ξ	ξ	PROPN
ejpam-4945	22	98	)	)	PUNCT
ejpam-4945	22	99	≥	≥	NOUN
ejpam-4945	22	100	|ξ|p−2	|ξ|p−2	X
ejpam-4945	22	101	ξ	ξ	X
ejpam-4945	22	102	for	for	ADP
ejpam-4945	22	103	ξ	ξ	X
ejpam-4945	22	104	̸=	̸=	PROPN
ejpam-4945	22	105	0	0	NUM
ejpam-4945	22	106	,	,	PUNCT
ejpam-4945	22	107	zi	zi	NOUN
ejpam-4945	22	108	(	(	PUNCT
ejpam-4945	22	109	ι	ι	NOUN
ejpam-4945	22	110	)	)	PUNCT
ejpam-4945	22	111	≤	≤	NOUN
ejpam-4945	22	112	ι	ι	PROPN
ejpam-4945	22	113	,	,	PUNCT
ejpam-4945	22	114	z′i	z′i	X
ejpam-4945	22	115	(	(	PUNCT
ejpam-4945	22	116	ι	ι	PROPN
ejpam-4945	22	117	)	)	PUNCT
ejpam-4945	22	118	>	>	X
ejpam-4945	22	119	0	0	PROPN
ejpam-4945	22	120	,	,	PUNCT
ejpam-4945	22	121	limι→∞	limι→∞	PROPN
ejpam-4945	22	122	zi	zi	PROPN
ejpam-4945	22	123	(	(	PUNCT
ejpam-4945	22	124	ι	ι	X
ejpam-4945	22	125	)	)	PUNCT
ejpam-4945	22	126	=	=	SYM
ejpam-4945	22	127	∞.	∞.	PROPN
ejpam-4945	22	128	(	(	PUNCT
ejpam-4945	22	129	h4)β	h4)β	NOUN
ejpam-4945	22	130	and	and	CCONJ
ejpam-4945	22	131	p	p	NOUN
ejpam-4945	22	132	are	be	AUX
ejpam-4945	22	133	positive	positive	ADJ
ejpam-4945	22	134	integers	integer	NOUN
ejpam-4945	22	135	,	,	PUNCT
ejpam-4945	22	136	β	β	X
ejpam-4945	22	137	is	be	AUX
ejpam-4945	22	138	even	even	ADV
ejpam-4945	22	139	,	,	PUNCT
ejpam-4945	22	140	p	p	X
ejpam-4945	22	141	>	>	X
ejpam-4945	22	142	1	1	NUM
ejpam-4945	22	143	.	.	PUNCT
ejpam-4945	23	1	k	k	NOUN
ejpam-4945	23	2	definition	definition	NOUN
ejpam-4945	23	3	1	1	NUM
ejpam-4945	23	4	.	.	PUNCT
ejpam-4945	24	1	a	a	DET
ejpam-4945	24	2	solution	solution	NOUN
ejpam-4945	24	3	of	of	ADP
ejpam-4945	24	4	(	(	PUNCT
ejpam-4945	24	5	1	1	NUM
ejpam-4945	24	6	)	)	PUNCT
ejpam-4945	24	7	is	be	AUX
ejpam-4945	24	8	said	say	VERB
ejpam-4945	24	9	oscillatory	oscillatory	ADJ
ejpam-4945	24	10	if	if	SCONJ
ejpam-4945	24	11	it	it	PRON
ejpam-4945	24	12	has	have	VERB
ejpam-4945	24	13	arbitrarily	arbitrarily	ADV
ejpam-4945	24	14	large	large	ADJ
ejpam-4945	24	15	zeros	zero	NOUN
ejpam-4945	24	16	on	on	ADP
ejpam-4945	24	17	[	[	X
ejpam-4945	24	18	ιξ,∞	ιξ,∞	NOUN
ejpam-4945	24	19	)	)	PUNCT
ejpam-4945	24	20	,	,	PUNCT
ejpam-4945	24	21	and	and	CCONJ
ejpam-4945	24	22	otherwise	otherwise	ADV
ejpam-4945	24	23	is	be	AUX
ejpam-4945	24	24	called	call	VERB
ejpam-4945	24	25	to	to	PART
ejpam-4945	24	26	be	be	AUX
ejpam-4945	24	27	nonoscillatory	nonoscillatory	ADJ
ejpam-4945	24	28	.	.	PUNCT
ejpam-4945	25	1	definition	definition	NOUN
ejpam-4945	25	2	2	2	NUM
ejpam-4945	25	3	.	.	PUNCT
ejpam-4945	26	1	eq	eq	NOUN
ejpam-4945	26	2	.	.	PUNCT
ejpam-4945	27	1	(	(	PUNCT
ejpam-4945	27	2	1	1	X
ejpam-4945	27	3	)	)	PUNCT
ejpam-4945	27	4	is	be	AUX
ejpam-4945	27	5	called	call	VERB
ejpam-4945	27	6	to	to	PART
ejpam-4945	27	7	be	be	AUX
ejpam-4945	27	8	oscillatory	oscillatory	ADJ
ejpam-4945	27	9	if	if	SCONJ
ejpam-4945	27	10	all	all	DET
ejpam-4945	27	11	its	its	PRON
ejpam-4945	27	12	solutions	solution	NOUN
ejpam-4945	27	13	are	be	AUX
ejpam-4945	27	14	oscillatory	oscillatory	ADJ
ejpam-4945	27	15	.	.	PUNCT
ejpam-4945	28	1	definition	definition	NOUN
ejpam-4945	28	2	3	3	NUM
ejpam-4945	28	3	.	.	PUNCT
ejpam-4945	29	1	[	[	X
ejpam-4945	29	2	14	14	NUM
ejpam-4945	29	3	]	]	PUNCT
ejpam-4945	29	4	let	let	VERB
ejpam-4945	29	5	l0	l0	NOUN
ejpam-4945	29	6	=	=	PRON
ejpam-4945	29	7	{	{	PUNCT
ejpam-4945	29	8	(	(	PUNCT
ejpam-4945	29	9	ι	ι	PROPN
ejpam-4945	29	10	,	,	PUNCT
ejpam-4945	29	11	s	s	NOUN
ejpam-4945	29	12	)	)	PUNCT
ejpam-4945	29	13	:	:	PUNCT
ejpam-4945	29	14	ι	ι	X
ejpam-4945	29	15	>	>	X
ejpam-4945	29	16	s	s	X
ejpam-4945	29	17	>	>	X
ejpam-4945	29	18	ι0	ι0	NOUN
ejpam-4945	29	19	}	}	PUNCT
ejpam-4945	29	20	and	and	CCONJ
ejpam-4945	29	21	l	l	NOUN
ejpam-4945	30	1	=	=	SYM
ejpam-4945	30	2	{	{	PUNCT
ejpam-4945	30	3	(	(	PUNCT
ejpam-4945	30	4	ι	ι	PROPN
ejpam-4945	30	5	,	,	PUNCT
ejpam-4945	30	6	s	s	NOUN
ejpam-4945	30	7	)	)	PUNCT
ejpam-4945	30	8	:	:	PUNCT
ejpam-4945	30	9	ι	ι	X
ejpam-4945	30	10	≥	≥	NOUN
ejpam-4945	30	11	s	s	PART
ejpam-4945	30	12	≥	≥	NOUN
ejpam-4945	30	13	ι0	ι0	NOUN
ejpam-4945	30	14	}	}	PUNCT
ejpam-4945	30	15	.	.	PUNCT
ejpam-4945	31	1	a	a	DET
ejpam-4945	31	2	function	function	NOUN
ejpam-4945	31	3	w	w	PROPN
ejpam-4945	31	4	∈	∈	PROPN
ejpam-4945	31	5	c	c	X
ejpam-4945	31	6	(	(	PUNCT
ejpam-4945	31	7	l	l	NOUN
ejpam-4945	31	8	,	,	PUNCT
ejpam-4945	31	9	r	r	NOUN
ejpam-4945	31	10	)	)	PUNCT
ejpam-4945	31	11	is	be	AUX
ejpam-4945	31	12	said	say	VERB
ejpam-4945	31	13	to	to	PART
ejpam-4945	31	14	belong	belong	VERB
ejpam-4945	31	15	to	to	ADP
ejpam-4945	31	16	the	the	DET
ejpam-4945	31	17	function	function	NOUN
ejpam-4945	31	18	class	class	NOUN
ejpam-4945	31	19	ς	ς	PROPN
ejpam-4945	31	20	,	,	PUNCT
ejpam-4945	31	21	written	write	VERB
ejpam-4945	31	22	by	by	ADP
ejpam-4945	31	23	w	w	PROPN
ejpam-4945	31	24	∈	∈	PROPN
ejpam-4945	31	25	ς	ς	PROPN
ejpam-4945	31	26	,	,	PUNCT
ejpam-4945	31	27	if	if	SCONJ
ejpam-4945	31	28	(	(	PUNCT
ejpam-4945	31	29	i	i	NOUN
ejpam-4945	31	30	)	)	PUNCT
ejpam-4945	31	31	w	w	PROPN
ejpam-4945	31	32	(	(	PUNCT
ejpam-4945	31	33	ι	ι	PROPN
ejpam-4945	31	34	,	,	PUNCT
ejpam-4945	31	35	s	s	NOUN
ejpam-4945	31	36	)	)	PUNCT
ejpam-4945	31	37	>	>	X
ejpam-4945	31	38	0	0	PUNCT
ejpam-4945	32	1	on	on	ADP
ejpam-4945	32	2	l0	l0	PROPN
ejpam-4945	32	3	and	and	CCONJ
ejpam-4945	32	4	w	w	PROPN
ejpam-4945	32	5	(	(	PUNCT
ejpam-4945	32	6	ι	ι	PROPN
ejpam-4945	32	7	,	,	PUNCT
ejpam-4945	32	8	s	s	NOUN
ejpam-4945	32	9	)	)	PUNCT
ejpam-4945	32	10	=	=	SYM
ejpam-4945	32	11	0	0	NUM
ejpam-4945	33	1	for	for	ADP
ejpam-4945	33	2	ι	ι	PROPN
ejpam-4945	33	3	≥	≥	NOUN
ejpam-4945	33	4	ι0	ι0	NOUN
ejpam-4945	33	5	with	with	ADP
ejpam-4945	33	6	(	(	PUNCT
ejpam-4945	33	7	ι	ι	PROPN
ejpam-4945	33	8	,	,	PUNCT
ejpam-4945	33	9	s	s	NOUN
ejpam-4945	33	10	)	)	PUNCT
ejpam-4945	33	11	/∈	/∈	PUNCT
ejpam-4945	34	1	l0	l0	NOUN
ejpam-4945	34	2	;	;	PUNCT
ejpam-4945	34	3	w	w	X
ejpam-4945	34	4	(	(	PUNCT
ejpam-4945	34	5	ι	ι	PROPN
ejpam-4945	34	6	,	,	PUNCT
ejpam-4945	34	7	s	s	PART
ejpam-4945	34	8	)	)	PUNCT
ejpam-4945	34	9	has	have	VERB
ejpam-4945	34	10	a	a	DET
ejpam-4945	34	11	continuous	continuous	ADJ
ejpam-4945	34	12	and	and	CCONJ
ejpam-4945	34	13	nonpositive	nonpositive	ADJ
ejpam-4945	34	14	partial	partial	ADJ
ejpam-4945	34	15	derivative	derivative	ADJ
ejpam-4945	34	16	∂w/∂s	∂w/∂s	PROPN
ejpam-4945	34	17	on	on	ADP
ejpam-4945	34	18	l0	l0	PROPN
ejpam-4945	34	19	and	and	CCONJ
ejpam-4945	35	1	ςi	ςi	NUM
ejpam-4945	35	2	∈	∈	PROPN
ejpam-4945	35	3	c	c	X
ejpam-4945	35	4	(	(	PUNCT
ejpam-4945	35	5	l0,r	l0,r	NOUN
ejpam-4945	35	6	)	)	PUNCT
ejpam-4945	35	7	such	such	ADJ
ejpam-4945	35	8	that	that	DET
ejpam-4945	35	9	∂w	∂w	PROPN
ejpam-4945	35	10	(	(	PUNCT
ejpam-4945	35	11	ι	ι	PROPN
ejpam-4945	35	12	,	,	PUNCT
ejpam-4945	35	13	s	s	NOUN
ejpam-4945	35	14	)	)	PUNCT
ejpam-4945	35	15	∂s	∂s	PROPN
ejpam-4945	35	16	=	=	SYM
ejpam-4945	35	17	−g(ι	−g(ι	PROPN
ejpam-4945	35	18	,	,	PUNCT
ejpam-4945	35	19	s	s	NOUN
ejpam-4945	35	20	)	)	PUNCT
ejpam-4945	35	21	√	√	PROPN
ejpam-4945	35	22	w	w	PROPN
ejpam-4945	35	23	(	(	PUNCT
ejpam-4945	35	24	ι	ι	PROPN
ejpam-4945	35	25	,	,	PUNCT
ejpam-4945	35	26	s	s	NOUN
ejpam-4945	35	27	)	)	PUNCT
ejpam-4945	35	28	.	.	PUNCT
ejpam-4945	36	1	in	in	ADP
ejpam-4945	36	2	recent	recent	ADJ
ejpam-4945	36	3	times	time	NOUN
ejpam-4945	36	4	,	,	PUNCT
ejpam-4945	36	5	some	some	DET
ejpam-4945	36	6	conditions	condition	NOUN
ejpam-4945	36	7	and	and	CCONJ
ejpam-4945	36	8	properties	property	NOUN
ejpam-4945	36	9	have	have	AUX
ejpam-4945	36	10	been	be	AUX
ejpam-4945	36	11	found	find	VERB
ejpam-4945	36	12	for	for	ADP
ejpam-4945	36	13	delay	delay	NOUN
ejpam-4945	36	14	and	and	CCONJ
ejpam-4945	36	15	neutral	neutral	ADJ
ejpam-4945	36	16	differential	differential	ADJ
ejpam-4945	36	17	equations	equation	NOUN
ejpam-4945	36	18	of	of	ADP
ejpam-4945	36	19	different	different	ADJ
ejpam-4945	36	20	orders	order	NOUN
ejpam-4945	36	21	;	;	PUNCT
ejpam-4945	36	22	see	see	VERB
ejpam-4945	36	23	[	[	X
ejpam-4945	36	24	9	9	NUM
ejpam-4945	36	25	,	,	PUNCT
ejpam-4945	36	26	11–15	11–15	NUM
ejpam-4945	36	27	,	,	PUNCT
ejpam-4945	36	28	18	18	NUM
ejpam-4945	36	29	]	]	PUNCT
ejpam-4945	36	30	.	.	PUNCT
ejpam-4945	37	1	agarwal	agarwal	PROPN
ejpam-4945	37	2	et	et	PROPN
ejpam-4945	37	3	al	al	PROPN
ejpam-4945	37	4	.	.	PUNCT
ejpam-4945	38	1	[	[	X
ejpam-4945	38	2	2	2	NUM
ejpam-4945	38	3	]	]	PUNCT
ejpam-4945	38	4	used	use	VERB
ejpam-4945	38	5	the	the	DET
ejpam-4945	38	6	riccati	riccati	PROPN
ejpam-4945	38	7	method	method	NOUN
ejpam-4945	38	8	to	to	PART
ejpam-4945	38	9	obtain	obtain	VERB
ejpam-4945	38	10	conditions	condition	NOUN
ejpam-4945	38	11	for	for	ADP
ejpam-4945	38	12	the	the	DET
ejpam-4945	38	13	oscillation	oscillation	NOUN
ejpam-4945	38	14	of	of	ADP
ejpam-4945	38	15	equation	equation	NOUN
ejpam-4945	38	16	[	[	X
ejpam-4945	38	17	∣∣∣ξ(β−1	∣∣∣ξ(β−1	NOUN
ejpam-4945	38	18	)	)	PUNCT
ejpam-4945	38	19	(	(	PUNCT
ejpam-4945	38	20	ι	ι	X
ejpam-4945	38	21	)	)	PUNCT
ejpam-4945	38	22	∣∣∣α−1	∣∣∣α−1	NOUN
ejpam-4945	38	23	ξ(β−1	ξ(β−1	NOUN
ejpam-4945	38	24	)	)	PUNCT
ejpam-4945	38	25	(	(	PUNCT
ejpam-4945	38	26	ι	ι	PROPN
ejpam-4945	38	27	)	)	PUNCT
ejpam-4945	38	28	]	]	PUNCT
ejpam-4945	38	29	′	′	NUM
ejpam-4945	39	1	+	+	CCONJ
ejpam-4945	39	2	b	b	X
ejpam-4945	39	3	(	(	PUNCT
ejpam-4945	39	4	ι	ι	NOUN
ejpam-4945	39	5	)	)	PUNCT
ejpam-4945	39	6	|ξ	|ξ	NOUN
ejpam-4945	39	7	(	(	PUNCT
ejpam-4945	39	8	γ	γ	X
ejpam-4945	39	9	(	(	PUNCT
ejpam-4945	39	10	ι))|α−1	ι))|α−1	PROPN
ejpam-4945	39	11	ξ	ξ	PROPN
ejpam-4945	39	12	(	(	PUNCT
ejpam-4945	39	13	γ	γ	X
ejpam-4945	39	14	(	(	PUNCT
ejpam-4945	39	15	ι	ι	NOUN
ejpam-4945	39	16	)	)	PUNCT
ejpam-4945	39	17	)	)	PUNCT
ejpam-4945	40	1	=	=	SYM
ejpam-4945	40	2	0	0	X
ejpam-4945	40	3	.	.	X
ejpam-4945	40	4	elabbasy	elabbasy	PROPN
ejpam-4945	40	5	et	et	PROPN
ejpam-4945	40	6	al	al	PROPN
ejpam-4945	40	7	.	.	PUNCT
ejpam-4945	41	1	[	[	X
ejpam-4945	41	2	8	8	NUM
ejpam-4945	41	3	]	]	PUNCT
ejpam-4945	41	4	used	use	VERB
ejpam-4945	41	5	the	the	DET
ejpam-4945	41	6	comparison	comparison	NOUN
ejpam-4945	41	7	method	method	NOUN
ejpam-4945	41	8	to	to	PART
ejpam-4945	41	9	obtain	obtain	VERB
ejpam-4945	41	10	comparison	comparison	NOUN
ejpam-4945	41	11	for	for	ADP
ejpam-4945	41	12	the	the	DET
ejpam-4945	41	13	oscillation	oscillation	NOUN
ejpam-4945	41	14	of	of	ADP
ejpam-4945	41	15	equation	equation	NOUN
ejpam-4945	41	16	[	[	PUNCT
ejpam-4945	41	17	a	a	DET
ejpam-4945	41	18	(	(	PUNCT
ejpam-4945	41	19	ι	ι	NOUN
ejpam-4945	41	20	)	)	PUNCT
ejpam-4945	41	21	∣∣∣(ξ(β−1	∣∣∣(ξ(β−1	NOUN
ejpam-4945	41	22	)	)	PUNCT
ejpam-4945	41	23	(	(	PUNCT
ejpam-4945	41	24	ι	ι	NOUN
ejpam-4945	41	25	)	)	PUNCT
ejpam-4945	41	26	)	)	PUNCT
ejpam-4945	42	1	∣∣∣p−2	∣∣∣p−2	NUM
ejpam-4945	42	2	ξ(β−1	ξ(β−1	NOUN
ejpam-4945	42	3	)	)	PUNCT
ejpam-4945	42	4	(	(	PUNCT
ejpam-4945	42	5	ι	ι	PROPN
ejpam-4945	42	6	)	)	PUNCT
ejpam-4945	42	7	]	]	PUNCT
ejpam-4945	42	8	′	′	NUM
ejpam-4945	43	1	+	+	CCONJ
ejpam-4945	43	2	b	b	X
ejpam-4945	43	3	(	(	PUNCT
ejpam-4945	43	4	ι)φ	ι)φ	X
ejpam-4945	43	5	(	(	PUNCT
ejpam-4945	43	6	ξ	ξ	X
ejpam-4945	43	7	(	(	PUNCT
ejpam-4945	43	8	γ	γ	X
ejpam-4945	43	9	(	(	PUNCT
ejpam-4945	43	10	ι	ι	PROPN
ejpam-4945	43	11	)	)	PUNCT
ejpam-4945	43	12	)	)	PUNCT
ejpam-4945	43	13	)	)	PUNCT
ejpam-4945	44	1	=	=	PUNCT
ejpam-4945	44	2	0	0	NUM
ejpam-4945	44	3	,	,	PUNCT
ejpam-4945	44	4	p	p	X
ejpam-4945	44	5	>	>	X
ejpam-4945	44	6	1	1	NUM
ejpam-4945	44	7	,	,	PUNCT
ejpam-4945	44	8	under	under	ADP
ejpam-4945	44	9	∫	∫	PROPN
ejpam-4945	44	10	∞	∞	PROPN
ejpam-4945	44	11	ι0	ι0	PROPN
ejpam-4945	44	12	1	1	NUM
ejpam-4945	44	13	a1/(p−1	a1/(p−1	NOUN
ejpam-4945	44	14	)	)	PUNCT
ejpam-4945	44	15	(	(	PUNCT
ejpam-4945	44	16	s	s	X
ejpam-4945	44	17	)	)	PUNCT
ejpam-4945	44	18	ds	ds	ADJ
ejpam-4945	44	19	=	=	SYM
ejpam-4945	44	20	∞	∞	NUM
ejpam-4945	44	21	a.	a.	NOUN
ejpam-4945	44	22	almutairi	almutairi	PROPN
ejpam-4945	44	23	/	/	SYM
ejpam-4945	44	24	eur	eur	PROPN
ejpam-4945	44	25	.	.	PUNCT
ejpam-4945	45	1	j.	j.	PROPN
ejpam-4945	45	2	pure	pure	PROPN
ejpam-4945	45	3	appl	appl	PROPN
ejpam-4945	45	4	.	.	PROPN
ejpam-4945	45	5	math	math	PROPN
ejpam-4945	45	6	,	,	PUNCT
ejpam-4945	45	7	16	16	NUM
ejpam-4945	45	8	(	(	PUNCT
ejpam-4945	45	9	4	4	NUM
ejpam-4945	45	10	)	)	PUNCT
ejpam-4945	45	11	(	(	PUNCT
ejpam-4945	45	12	2023	2023	NUM
ejpam-4945	45	13	)	)	PUNCT
ejpam-4945	45	14	,	,	PUNCT
ejpam-4945	45	15	2499	2499	NUM
ejpam-4945	45	16	-	-	SYM
ejpam-4945	45	17	2508	2508	NUM
ejpam-4945	45	18	2501	2501	NUM
ejpam-4945	45	19	bazighifan	bazighifan	NOUN
ejpam-4945	45	20	et	et	PROPN
ejpam-4945	45	21	al	al	PROPN
ejpam-4945	45	22	.	.	PUNCT
ejpam-4945	46	1	in	in	ADP
ejpam-4945	46	2	[	[	X
ejpam-4945	46	3	13	13	NUM
ejpam-4945	46	4	]	]	PUNCT
ejpam-4945	46	5	considered	consider	VERB
ejpam-4945	46	6	the	the	DET
ejpam-4945	46	7	equation	equation	NOUN
ejpam-4945	46	8	(	(	PUNCT
ejpam-4945	46	9	a	a	DET
ejpam-4945	46	10	(	(	PUNCT
ejpam-4945	46	11	ι)φ	ι)φ	X
ejpam-4945	46	12	(	(	PUNCT
ejpam-4945	46	13	ξ(β−1	ξ(β−1	NOUN
ejpam-4945	46	14	)	)	PUNCT
ejpam-4945	46	15	(	(	PUNCT
ejpam-4945	46	16	ι	ι	NOUN
ejpam-4945	46	17	)	)	PUNCT
ejpam-4945	46	18	)	)	PUNCT
ejpam-4945	46	19	)	)	PUNCT
ejpam-4945	46	20	′	′	NUM
ejpam-4945	47	1	+	+	CCONJ
ejpam-4945	47	2	b	b	X
ejpam-4945	47	3	(	(	PUNCT
ejpam-4945	47	4	ι)φ	ι)φ	X
ejpam-4945	47	5	(	(	PUNCT
ejpam-4945	47	6	ξ	ξ	X
ejpam-4945	47	7	(	(	PUNCT
ejpam-4945	47	8	γ	γ	X
ejpam-4945	47	9	(	(	PUNCT
ejpam-4945	47	10	ι	ι	PROPN
ejpam-4945	47	11	)	)	PUNCT
ejpam-4945	47	12	)	)	PUNCT
ejpam-4945	47	13	)	)	PUNCT
ejpam-4945	48	1	=	=	PUNCT
ejpam-4945	48	2	0	0	NUM
ejpam-4945	48	3	,	,	PUNCT
ejpam-4945	48	4	(	(	PUNCT
ejpam-4945	48	5	4	4	X
ejpam-4945	48	6	)	)	PUNCT
ejpam-4945	48	7	where	where	SCONJ
ejpam-4945	48	8	φ	φ	PROPN
ejpam-4945	48	9	(	(	PUNCT
ejpam-4945	48	10	s	s	NOUN
ejpam-4945	48	11	)	)	PUNCT
ejpam-4945	48	12	=	=	PUNCT
ejpam-4945	48	13	|s|p−2	|s|p−2	NOUN
ejpam-4945	48	14	s	s	PART
ejpam-4945	48	15	and	and	CCONJ
ejpam-4945	48	16	obtained	obtain	VERB
ejpam-4945	48	17	properties	property	NOUN
ejpam-4945	48	18	for	for	ADP
ejpam-4945	48	19	oscillation	oscillation	NOUN
ejpam-4945	48	20	of	of	ADP
ejpam-4945	48	21	(	(	PUNCT
ejpam-4945	48	22	4	4	NUM
ejpam-4945	48	23	)	)	PUNCT
ejpam-4945	48	24	.	.	PUNCT
ejpam-4945	49	1	in	in	ADP
ejpam-4945	49	2	[	[	X
ejpam-4945	49	3	18	18	NUM
ejpam-4945	49	4	]	]	PUNCT
ejpam-4945	49	5	.	.	PUNCT
ejpam-4945	50	1	zhang	zhang	PROPN
ejpam-4945	50	2	et	et	PROPN
ejpam-4945	50	3	al	al	PROPN
ejpam-4945	50	4	.	.	PROPN
ejpam-4945	50	5	studied	study	VERB
ejpam-4945	50	6	the	the	DET
ejpam-4945	50	7	oscillation	oscillation	NOUN
ejpam-4945	50	8	of	of	ADP
ejpam-4945	50	9	the	the	DET
ejpam-4945	50	10	solutions	solution	NOUN
ejpam-4945	50	11	of	of	ADP
ejpam-4945	50	12	equation	equation	NOUN
ejpam-4945	50	13	(	(	PUNCT
ejpam-4945	50	14	a	a	DET
ejpam-4945	50	15	(	(	PUNCT
ejpam-4945	50	16	ι	ι	NOUN
ejpam-4945	50	17	)	)	PUNCT
ejpam-4945	50	18	(	(	PUNCT
ejpam-4945	50	19	ξ(β−1	ξ(β−1	NOUN
ejpam-4945	50	20	)	)	PUNCT
ejpam-4945	50	21	(	(	PUNCT
ejpam-4945	50	22	ι	ι	NOUN
ejpam-4945	50	23	)	)	PUNCT
ejpam-4945	50	24	)	)	PUNCT
ejpam-4945	51	1	α)′	α)′	PROPN
ejpam-4945	51	2	+	+	NUM
ejpam-4945	51	3	b	b	PROPN
ejpam-4945	51	4	(	(	PUNCT
ejpam-4945	51	5	ι	ι	NOUN
ejpam-4945	51	6	)	)	PUNCT
ejpam-4945	51	7	ξγ	ξγ	NOUN
ejpam-4945	51	8	(	(	PUNCT
ejpam-4945	51	9	γ	γ	X
ejpam-4945	51	10	(	(	PUNCT
ejpam-4945	51	11	ι	ι	NOUN
ejpam-4945	51	12	)	)	PUNCT
ejpam-4945	51	13	)	)	PUNCT
ejpam-4945	52	1	=	=	SYM
ejpam-4945	52	2	0	0	NUM
ejpam-4945	52	3	,	,	PUNCT
ejpam-4945	52	4	under	under	ADP
ejpam-4945	52	5	∫∞	∫∞	NOUN
ejpam-4945	52	6	ι0	ι0	PROPN
ejpam-4945	52	7	a−1	a−1	PROPN
ejpam-4945	52	8	/	/	SYM
ejpam-4945	52	9	α	α	PROPN
ejpam-4945	52	10	(	(	PUNCT
ejpam-4945	52	11	s	s	X
ejpam-4945	52	12	)	)	PUNCT
ejpam-4945	52	13	ds	ds	NOUN
ejpam-4945	52	14	<	<	X
ejpam-4945	52	15	∞.	∞.	PROPN
ejpam-4945	52	16	in	in	ADP
ejpam-4945	52	17	our	our	PRON
ejpam-4945	52	18	current	current	ADJ
ejpam-4945	52	19	research	research	NOUN
ejpam-4945	52	20	,	,	PUNCT
ejpam-4945	52	21	we	we	PRON
ejpam-4945	52	22	applied	apply	VERB
ejpam-4945	52	23	three	three	NUM
ejpam-4945	52	24	techniques	technique	NOUN
ejpam-4945	52	25	with	with	ADP
ejpam-4945	52	26	some	some	DET
ejpam-4945	52	27	auxiliary	auxiliary	NOUN
ejpam-4945	52	28	lemmas	lemma	VERB
ejpam-4945	52	29	to	to	PART
ejpam-4945	52	30	obtain	obtain	VERB
ejpam-4945	52	31	several	several	ADJ
ejpam-4945	52	32	conditions	condition	NOUN
ejpam-4945	52	33	and	and	CCONJ
ejpam-4945	52	34	properties	property	NOUN
ejpam-4945	52	35	of	of	ADP
ejpam-4945	52	36	the	the	DET
ejpam-4945	52	37	approximate	approximate	ADJ
ejpam-4945	52	38	and	and	CCONJ
ejpam-4945	52	39	oscillatory	oscillatory	ADJ
ejpam-4945	52	40	behavior	behavior	NOUN
ejpam-4945	52	41	of	of	ADP
ejpam-4945	52	42	the	the	DET
ejpam-4945	52	43	studied	study	VERB
ejpam-4945	52	44	equation	equation	NOUN
ejpam-4945	52	45	.	.	PUNCT
ejpam-4945	53	1	these	these	DET
ejpam-4945	53	2	techniques	technique	NOUN
ejpam-4945	53	3	are	be	AUX
ejpam-4945	53	4	the	the	DET
ejpam-4945	53	5	comparison	comparison	NOUN
ejpam-4945	53	6	method	method	NOUN
ejpam-4945	53	7	,	,	PUNCT
ejpam-4945	53	8	riccati	riccati	NOUN
ejpam-4945	53	9	method	method	NOUN
ejpam-4945	53	10	and	and	CCONJ
ejpam-4945	53	11	integral	integral	ADJ
ejpam-4945	53	12	averages	average	NOUN
ejpam-4945	53	13	method	method	NOUN
ejpam-4945	53	14	.	.	PUNCT
ejpam-4945	54	1	2	2	X
ejpam-4945	54	2	.	.	X
ejpam-4945	54	3	oscillation	oscillation	NOUN
ejpam-4945	54	4	results	result	NOUN
ejpam-4945	54	5	now	now	ADV
ejpam-4945	54	6	,	,	PUNCT
ejpam-4945	54	7	we	we	PRON
ejpam-4945	54	8	present	present	VERB
ejpam-4945	54	9	some	some	PRON
ejpam-4945	54	10	the	the	DET
ejpam-4945	54	11	lemmas	lemma	NOUN
ejpam-4945	54	12	:	:	PUNCT
ejpam-4945	54	13	lemma	lemma	PROPN
ejpam-4945	54	14	1	1	NUM
ejpam-4945	54	15	.	.	PUNCT
ejpam-4945	55	1	[	[	X
ejpam-4945	55	2	7	7	X
ejpam-4945	55	3	]	]	X
ejpam-4945	55	4	if	if	SCONJ
ejpam-4945	55	5	w	w	PROPN
ejpam-4945	55	6	∈	∈	PROPN
ejpam-4945	55	7	cβ	cβ	NOUN
ejpam-4945	55	8	(	(	PUNCT
ejpam-4945	55	9	[	[	X
ejpam-4945	55	10	ι0,∞	ι0,∞	NOUN
ejpam-4945	55	11	)	)	PUNCT
ejpam-4945	55	12	,	,	PUNCT
ejpam-4945	55	13	(	(	PUNCT
ejpam-4945	55	14	0,∞	0,∞	NOUN
ejpam-4945	55	15	)	)	PUNCT
ejpam-4945	55	16	)	)	PUNCT
ejpam-4945	55	17	and	and	CCONJ
ejpam-4945	55	18	w(β−1	w(β−1	X
ejpam-4945	55	19	)	)	PUNCT
ejpam-4945	55	20	(	(	PUNCT
ejpam-4945	55	21	ι)w(β	ι)w(β	PROPN
ejpam-4945	55	22	)	)	PUNCT
ejpam-4945	55	23	(	(	PUNCT
ejpam-4945	55	24	ι	ι	X
ejpam-4945	55	25	)	)	PUNCT
ejpam-4945	55	26	≤	≤	NOUN
ejpam-4945	55	27	0	0	NUM
ejpam-4945	55	28	for	for	ADP
ejpam-4945	55	29	ι	ι	PROPN
ejpam-4945	55	30	≥	≥	PROPN
ejpam-4945	55	31	ι0	ι0	NOUN
ejpam-4945	55	32	,	,	PUNCT
ejpam-4945	55	33	then	then	ADV
ejpam-4945	55	34	for	for	ADP
ejpam-4945	55	35	every	every	DET
ejpam-4945	55	36	ν	ν	X
ejpam-4945	55	37	∈	∈	PROPN
ejpam-4945	55	38	(	(	PUNCT
ejpam-4945	55	39	0	0	NUM
ejpam-4945	55	40	,	,	PUNCT
ejpam-4945	55	41	1	1	NUM
ejpam-4945	55	42	)	)	PUNCT
ejpam-4945	55	43	there	there	PRON
ejpam-4945	55	44	exists	exist	VERB
ejpam-4945	55	45	a	a	DET
ejpam-4945	55	46	constant	constant	ADJ
ejpam-4945	55	47	j	j	NOUN
ejpam-4945	55	48	>	>	X
ejpam-4945	55	49	0	0	NUM
ejpam-4945	55	50	such	such	ADJ
ejpam-4945	55	51	that	that	SCONJ
ejpam-4945	55	52	|w	|w	NOUN
ejpam-4945	55	53	(	(	PUNCT
ejpam-4945	55	54	νι)|	νι)|	PROPN
ejpam-4945	55	55	≥	≥	AUX
ejpam-4945	55	56	jιβ−1	jιβ−1	PROPN
ejpam-4945	55	57	∣∣∣w(β−1	∣∣∣w(β−1	PROPN
ejpam-4945	55	58	)	)	PUNCT
ejpam-4945	55	59	(	(	PUNCT
ejpam-4945	55	60	ι	ι	NOUN
ejpam-4945	55	61	)	)	PUNCT
ejpam-4945	55	62	∣∣∣	∣∣∣	NOUN
ejpam-4945	55	63	,	,	PUNCT
ejpam-4945	55	64	for	for	ADP
ejpam-4945	55	65	all	all	DET
ejpam-4945	55	66	large	large	ADJ
ejpam-4945	55	67	t.	t.	NOUN
ejpam-4945	55	68	lemma	lemma	PROPN
ejpam-4945	56	1	2	2	NUM
ejpam-4945	56	2	.	.	PUNCT
ejpam-4945	57	1	[	[	X
ejpam-4945	57	2	4	4	X
ejpam-4945	57	3	]	]	PUNCT
ejpam-4945	57	4	let	let	VERB
ejpam-4945	57	5	w	w	PROPN
ejpam-4945	57	6	∈	∈	PROPN
ejpam-4945	57	7	cβ	cβ	NOUN
ejpam-4945	57	8	(	(	PUNCT
ejpam-4945	57	9	[	[	X
ejpam-4945	57	10	ι0,∞	ι0,∞	NOUN
ejpam-4945	57	11	)	)	PUNCT
ejpam-4945	57	12	,	,	PUNCT
ejpam-4945	57	13	(	(	PUNCT
ejpam-4945	57	14	0,∞	0,∞	NOUN
ejpam-4945	57	15	)	)	PUNCT
ejpam-4945	57	16	)	)	PUNCT
ejpam-4945	57	17	and	and	CCONJ
ejpam-4945	57	18	w(β−1	w(β−1	X
ejpam-4945	57	19	)	)	PUNCT
ejpam-4945	57	20	(	(	PUNCT
ejpam-4945	57	21	ι)w(β	ι)w(β	PROPN
ejpam-4945	57	22	)	)	PUNCT
ejpam-4945	57	23	(	(	PUNCT
ejpam-4945	57	24	ι	ι	X
ejpam-4945	57	25	)	)	PUNCT
ejpam-4945	57	26	≤	≤	NOUN
ejpam-4945	57	27	0	0	NUM
ejpam-4945	57	28	.	.	PUNCT
ejpam-4945	58	1	if	if	SCONJ
ejpam-4945	58	2	limι→∞w	limι→∞w	PROPN
ejpam-4945	58	3	(	(	PUNCT
ejpam-4945	58	4	ι	ι	NOUN
ejpam-4945	58	5	)	)	PUNCT
ejpam-4945	58	6	̸=	̸=	PROPN
ejpam-4945	58	7	0	0	NUM
ejpam-4945	58	8	,	,	PUNCT
ejpam-4945	58	9	then	then	ADV
ejpam-4945	58	10	for	for	ADP
ejpam-4945	58	11	every	every	DET
ejpam-4945	58	12	µ	µ	PROPN
ejpam-4945	58	13	∈	∈	NOUN
ejpam-4945	58	14	(	(	PUNCT
ejpam-4945	58	15	0	0	NUM
ejpam-4945	58	16	,	,	PUNCT
ejpam-4945	58	17	1	1	NUM
ejpam-4945	58	18	)	)	PUNCT
ejpam-4945	58	19	there	there	PRON
ejpam-4945	58	20	exists	exist	VERB
ejpam-4945	58	21	a	a	DET
ejpam-4945	58	22	ιµ	ιµ	ADJ
ejpam-4945	58	23	≥	≥	NOUN
ejpam-4945	58	24	ι0	ι0	VERB
ejpam-4945	58	25	such	such	ADJ
ejpam-4945	58	26	that	that	DET
ejpam-4945	58	27	|w	|w	NOUN
ejpam-4945	58	28	(	(	PUNCT
ejpam-4945	58	29	ι)|	ι)|	INTJ
ejpam-4945	58	30	≥	≥	X
ejpam-4945	58	31	µ	µ	X
ejpam-4945	58	32	(	(	PUNCT
ejpam-4945	58	33	β	β	NOUN
ejpam-4945	58	34	−	−	NOUN
ejpam-4945	58	35	1	1	NUM
ejpam-4945	58	36	)	)	PUNCT
ejpam-4945	58	37	!	!	PUNCT
ejpam-4945	59	1	ιβ−1	ιβ−1	PUNCT
ejpam-4945	59	2	∣∣∣w(β−1	∣∣∣w(β−1	NOUN
ejpam-4945	59	3	)	)	PUNCT
ejpam-4945	59	4	(	(	PUNCT
ejpam-4945	59	5	ι	ι	NOUN
ejpam-4945	59	6	)	)	PUNCT
ejpam-4945	59	7	∣∣∣	∣∣∣	NOUN
ejpam-4945	59	8	,	,	PUNCT
ejpam-4945	59	9	for	for	ADP
ejpam-4945	59	10	all	all	PRON
ejpam-4945	59	11	ι	ι	DET
ejpam-4945	59	12	≥	≥	NOUN
ejpam-4945	59	13	ιµ.	ιµ.	VERB
ejpam-4945	59	14	lemma	lemma	PROPN
ejpam-4945	59	15	3	3	X
ejpam-4945	59	16	.	.	PUNCT
ejpam-4945	60	1	[	[	X
ejpam-4945	60	2	3	3	X
ejpam-4945	60	3	]	]	PUNCT
ejpam-4945	60	4	let	let	VERB
ejpam-4945	60	5	w(ι	w(ι	PROPN
ejpam-4945	60	6	)	)	PUNCT
ejpam-4945	60	7	be	be	AUX
ejpam-4945	60	8	an	an	DET
ejpam-4945	60	9	β	β	NOUN
ejpam-4945	60	10	times	time	NOUN
ejpam-4945	60	11	differentiable	differentiable	ADJ
ejpam-4945	60	12	function	function	NOUN
ejpam-4945	60	13	on	on	ADP
ejpam-4945	60	14	[	[	X
ejpam-4945	60	15	ι0,∞	ι0,∞	NOUN
ejpam-4945	60	16	)	)	PUNCT
ejpam-4945	60	17	of	of	ADP
ejpam-4945	60	18	constant	constant	ADJ
ejpam-4945	60	19	sign	sign	NOUN
ejpam-4945	60	20	and	and	CCONJ
ejpam-4945	60	21	w(β	w(β	NOUN
ejpam-4945	60	22	)	)	PUNCT
ejpam-4945	60	23	(	(	PUNCT
ejpam-4945	60	24	ι	ι	X
ejpam-4945	60	25	)	)	PUNCT
ejpam-4945	60	26	̸=	̸=	NOUN
ejpam-4945	60	27	0	0	NUM
ejpam-4945	60	28	on	on	ADP
ejpam-4945	60	29	[	[	X
ejpam-4945	60	30	ι0,∞	ι0,∞	NOUN
ejpam-4945	60	31	)	)	PUNCT
ejpam-4945	60	32	which	which	PRON
ejpam-4945	60	33	satisfies	satisfy	VERB
ejpam-4945	60	34	w	w	PROPN
ejpam-4945	60	35	(	(	PUNCT
ejpam-4945	60	36	ι)w(β	ι)w(β	PROPN
ejpam-4945	60	37	)	)	PUNCT
ejpam-4945	60	38	(	(	PUNCT
ejpam-4945	60	39	ι	ι	X
ejpam-4945	60	40	)	)	PUNCT
ejpam-4945	60	41	≤	≤	NOUN
ejpam-4945	60	42	0	0	NUM
ejpam-4945	60	43	.	.	PUNCT
ejpam-4945	61	1	then	then	ADV
ejpam-4945	61	2	,	,	PUNCT
ejpam-4945	61	3	(	(	PUNCT
ejpam-4945	61	4	i	i	NOUN
ejpam-4945	61	5	)	)	PUNCT
ejpam-4945	61	6	there	there	PRON
ejpam-4945	61	7	exists	exist	VERB
ejpam-4945	61	8	a	a	DET
ejpam-4945	61	9	ι1	ι1	ADJ
ejpam-4945	61	10	≥	≥	NOUN
ejpam-4945	61	11	ι0	ι0	NOUN
ejpam-4945	61	12	such	such	ADJ
ejpam-4945	61	13	that	that	SCONJ
ejpam-4945	61	14	the	the	DET
ejpam-4945	61	15	functions	function	NOUN
ejpam-4945	61	16	w(i	w(i	PROPN
ejpam-4945	61	17	)	)	PUNCT
ejpam-4945	61	18	(	(	PUNCT
ejpam-4945	61	19	ι	ι	X
ejpam-4945	61	20	)	)	PUNCT
ejpam-4945	61	21	,	,	PUNCT
ejpam-4945	61	22	i	i	PRON
ejpam-4945	61	23	=	=	NOUN
ejpam-4945	61	24	1	1	NUM
ejpam-4945	61	25	,	,	PUNCT
ejpam-4945	61	26	2	2	NUM
ejpam-4945	61	27	,	,	PUNCT
ejpam-4945	61	28	...	...	PUNCT
ejpam-4945	61	29	,	,	PUNCT
ejpam-4945	61	30	β−1	β−1	X
ejpam-4945	61	31	are	be	AUX
ejpam-4945	61	32	of	of	ADP
ejpam-4945	61	33	constant	constant	ADJ
ejpam-4945	61	34	sign	sign	NOUN
ejpam-4945	61	35	on	on	ADP
ejpam-4945	61	36	[	[	X
ejpam-4945	61	37	ι0,∞	ι0,∞	NOUN
ejpam-4945	61	38	)	)	PUNCT
ejpam-4945	61	39	;	;	PUNCT
ejpam-4945	61	40	(	(	PUNCT
ejpam-4945	61	41	ii	ii	NOUN
ejpam-4945	61	42	)	)	PUNCT
ejpam-4945	61	43	there	there	PRON
ejpam-4945	61	44	exists	exist	VERB
ejpam-4945	61	45	a	a	DET
ejpam-4945	61	46	number	number	NOUN
ejpam-4945	61	47	l	l	NOUN
ejpam-4945	61	48	∈	∈	PROPN
ejpam-4945	61	49	{	{	PUNCT
ejpam-4945	61	50	1	1	NUM
ejpam-4945	61	51	,	,	PUNCT
ejpam-4945	61	52	3	3	NUM
ejpam-4945	61	53	,	,	PUNCT
ejpam-4945	61	54	5	5	NUM
ejpam-4945	61	55	,	,	PUNCT
ejpam-4945	61	56	...	...	PUNCT
ejpam-4945	61	57	,	,	PUNCT
ejpam-4945	61	58	β	β	X
ejpam-4945	61	59	−	−	NOUN
ejpam-4945	61	60	1	1	X
ejpam-4945	61	61	}	}	PUNCT
ejpam-4945	61	62	when	when	SCONJ
ejpam-4945	61	63	β	β	X
ejpam-4945	61	64	is	be	AUX
ejpam-4945	61	65	even	even	ADV
ejpam-4945	61	66	,	,	PUNCT
ejpam-4945	61	67	l	l	PROPN
ejpam-4945	61	68	∈	∈	PROPN
ejpam-4945	61	69	{	{	PUNCT
ejpam-4945	61	70	0	0	NUM
ejpam-4945	61	71	,	,	PUNCT
ejpam-4945	61	72	2	2	NUM
ejpam-4945	61	73	,	,	PUNCT
ejpam-4945	61	74	4	4	NUM
ejpam-4945	61	75	,	,	PUNCT
ejpam-4945	61	76	...	...	PUNCT
ejpam-4945	61	77	,	,	PUNCT
ejpam-4945	61	78	β	β	X
ejpam-4945	61	79	−	−	NOUN
ejpam-4945	61	80	1	1	X
ejpam-4945	61	81	}	}	PUNCT
ejpam-4945	61	82	when	when	SCONJ
ejpam-4945	61	83	β	β	X
ejpam-4945	61	84	is	be	AUX
ejpam-4945	61	85	odd	odd	ADJ
ejpam-4945	61	86	,	,	PUNCT
ejpam-4945	61	87	such	such	ADJ
ejpam-4945	61	88	that	that	SCONJ
ejpam-4945	61	89	,	,	PUNCT
ejpam-4945	61	90	for	for	ADP
ejpam-4945	61	91	ι	ι	PROPN
ejpam-4945	61	92	≥	≥	NOUN
ejpam-4945	61	93	ι1	ι1	ADJ
ejpam-4945	61	94	,	,	PUNCT
ejpam-4945	61	95	w	w	NOUN
ejpam-4945	61	96	(	(	PUNCT
ejpam-4945	61	97	ι)w(i	ι)w(i	PROPN
ejpam-4945	61	98	)	)	PUNCT
ejpam-4945	61	99	(	(	PUNCT
ejpam-4945	61	100	ι	ι	X
ejpam-4945	61	101	)	)	PUNCT
ejpam-4945	61	102	>	>	X
ejpam-4945	61	103	0	0	NUM
ejpam-4945	61	104	,	,	PUNCT
ejpam-4945	61	105	for	for	ADP
ejpam-4945	61	106	all	all	DET
ejpam-4945	61	107	i	i	PRON
ejpam-4945	61	108	=	=	NOUN
ejpam-4945	61	109	0	0	NUM
ejpam-4945	61	110	,	,	PUNCT
ejpam-4945	61	111	1	1	NUM
ejpam-4945	61	112	,	,	PUNCT
ejpam-4945	61	113	...	...	PUNCT
ejpam-4945	61	114	,	,	PUNCT
ejpam-4945	61	115	l	l	NOUN
ejpam-4945	61	116	and	and	CCONJ
ejpam-4945	61	117	(	(	PUNCT
ejpam-4945	61	118	−1)β+i+1w	−1)β+i+1w	PROPN
ejpam-4945	61	119	(	(	PUNCT
ejpam-4945	61	120	ι)w(i	ι)w(i	PROPN
ejpam-4945	61	121	)	)	PUNCT
ejpam-4945	61	122	(	(	PUNCT
ejpam-4945	61	123	ι	ι	X
ejpam-4945	61	124	)	)	PUNCT
ejpam-4945	61	125	>	>	X
ejpam-4945	61	126	0	0	NUM
ejpam-4945	61	127	,	,	PUNCT
ejpam-4945	61	128	for	for	ADP
ejpam-4945	61	129	all	all	DET
ejpam-4945	61	130	i	i	PRON
ejpam-4945	61	131	=	=	PUNCT
ejpam-4945	61	132	l	l	NOUN
ejpam-4945	62	1	+	+	NUM
ejpam-4945	62	2	1	1	NUM
ejpam-4945	62	3	,	,	PUNCT
ejpam-4945	62	4	...	...	PUNCT
ejpam-4945	62	5	,	,	PUNCT
ejpam-4945	62	6	β	β	X
ejpam-4945	62	7	.	.	PUNCT
ejpam-4945	62	8	a.	a.	PROPN
ejpam-4945	62	9	almutairi	almutairi	PROPN
ejpam-4945	62	10	/	/	SYM
ejpam-4945	62	11	eur	eur	PROPN
ejpam-4945	62	12	.	.	PUNCT
ejpam-4945	63	1	j.	j.	PROPN
ejpam-4945	63	2	pure	pure	PROPN
ejpam-4945	63	3	appl	appl	PROPN
ejpam-4945	63	4	.	.	PROPN
ejpam-4945	63	5	math	math	PROPN
ejpam-4945	63	6	,	,	PUNCT
ejpam-4945	63	7	16	16	NUM
ejpam-4945	63	8	(	(	PUNCT
ejpam-4945	63	9	4	4	NUM
ejpam-4945	63	10	)	)	PUNCT
ejpam-4945	63	11	(	(	PUNCT
ejpam-4945	63	12	2023	2023	NUM
ejpam-4945	63	13	)	)	PUNCT
ejpam-4945	63	14	,	,	PUNCT
ejpam-4945	63	15	2499	2499	NUM
ejpam-4945	63	16	-	-	SYM
ejpam-4945	63	17	2508	2508	NUM
ejpam-4945	63	18	2502	2502	NUM
ejpam-4945	63	19	lemma	lemma	PROPN
ejpam-4945	63	20	4	4	X
ejpam-4945	63	21	.	.	PUNCT
ejpam-4945	64	1	let	let	VERB
ejpam-4945	64	2	ξ	ξ	X
ejpam-4945	64	3	(	(	PUNCT
ejpam-4945	64	4	ι	ι	NOUN
ejpam-4945	64	5	)	)	PUNCT
ejpam-4945	64	6	is	be	AUX
ejpam-4945	64	7	an	an	DET
ejpam-4945	64	8	eventually	eventually	ADV
ejpam-4945	64	9	positive	positive	ADJ
ejpam-4945	64	10	solution	solution	NOUN
ejpam-4945	64	11	of	of	ADP
ejpam-4945	64	12	equation	equation	NOUN
ejpam-4945	64	13	(	(	PUNCT
ejpam-4945	64	14	1	1	NUM
ejpam-4945	64	15	)	)	PUNCT
ejpam-4945	64	16	.	.	PUNCT
ejpam-4945	65	1	then	then	ADV
ejpam-4945	65	2	w	w	PROPN
ejpam-4945	65	3	(	(	PUNCT
ejpam-4945	65	4	ι	ι	PROPN
ejpam-4945	65	5	)	)	PUNCT
ejpam-4945	65	6	>	>	X
ejpam-4945	65	7	0	0	NUM
ejpam-4945	65	8	,	,	PUNCT
ejpam-4945	65	9	w′	w′	PROPN
ejpam-4945	65	10	(	(	PUNCT
ejpam-4945	65	11	ι	ι	PROPN
ejpam-4945	65	12	)	)	PUNCT
ejpam-4945	65	13	>	>	X
ejpam-4945	65	14	0	0	NUM
ejpam-4945	65	15	,	,	PUNCT
ejpam-4945	65	16	w(β−1	w(β−1	X
ejpam-4945	65	17	)	)	PUNCT
ejpam-4945	65	18	(	(	PUNCT
ejpam-4945	65	19	ι	ι	X
ejpam-4945	65	20	)	)	PUNCT
ejpam-4945	65	21	≥	≥	NOUN
ejpam-4945	65	22	0	0	NUM
ejpam-4945	65	23	and	and	CCONJ
ejpam-4945	65	24	w(β	w(β	NOUN
ejpam-4945	65	25	)	)	PUNCT
ejpam-4945	65	26	(	(	PUNCT
ejpam-4945	65	27	ι	ι	X
ejpam-4945	65	28	)	)	PUNCT
ejpam-4945	65	29	≤	≤	NOUN
ejpam-4945	65	30	0	0	NUM
ejpam-4945	65	31	,	,	PUNCT
ejpam-4945	65	32	(	(	PUNCT
ejpam-4945	65	33	5	5	NUM
ejpam-4945	65	34	)	)	PUNCT
ejpam-4945	65	35	for	for	ADP
ejpam-4945	65	36	ι	ι	PROPN
ejpam-4945	65	37	≥	≥	NOUN
ejpam-4945	65	38	ι2	ι2	VERB
ejpam-4945	65	39	.	.	PUNCT
ejpam-4945	66	1	proof	proof	NOUN
ejpam-4945	66	2	.	.	PUNCT
ejpam-4945	67	1	suppose	suppose	VERB
ejpam-4945	67	2	ξ	ξ	X
ejpam-4945	67	3	(	(	PUNCT
ejpam-4945	67	4	ι	ι	NOUN
ejpam-4945	67	5	)	)	PUNCT
ejpam-4945	67	6	is	be	AUX
ejpam-4945	67	7	an	an	DET
ejpam-4945	67	8	eventually	eventually	ADV
ejpam-4945	67	9	positive	positive	ADJ
ejpam-4945	67	10	solution	solution	NOUN
ejpam-4945	67	11	of	of	ADP
ejpam-4945	67	12	(	(	PUNCT
ejpam-4945	67	13	1	1	NUM
ejpam-4945	67	14	)	)	PUNCT
ejpam-4945	67	15	.	.	PUNCT
ejpam-4945	68	1	then	then	ADV
ejpam-4945	68	2	w	w	PROPN
ejpam-4945	68	3	(	(	PUNCT
ejpam-4945	68	4	ι	ι	PROPN
ejpam-4945	68	5	)	)	PUNCT
ejpam-4945	68	6	>	>	X
ejpam-4945	68	7	0	0	PUNCT
ejpam-4945	69	1	and	and	CCONJ
ejpam-4945	69	2	(	(	PUNCT
ejpam-4945	69	3	aw(β−1	aw(β−1	PROPN
ejpam-4945	69	4	)	)	PUNCT
ejpam-4945	69	5	)	)	PUNCT
ejpam-4945	70	1	′	′	NUM
ejpam-4945	71	1	(	(	PUNCT
ejpam-4945	71	2	ι	ι	X
ejpam-4945	71	3	)	)	PUNCT
ejpam-4945	71	4	=	=	SYM
ejpam-4945	72	1	−	−	NOUN
ejpam-4945	72	2	r∑	r∑	NOUN
ejpam-4945	72	3	i=1	i=1	PROPN
ejpam-4945	72	4	bi	bi	NOUN
ejpam-4945	72	5	(	(	PUNCT
ejpam-4945	72	6	ι)φ	ι)φ	X
ejpam-4945	72	7	(	(	PUNCT
ejpam-4945	72	8	ξ	ξ	X
ejpam-4945	72	9	(	(	PUNCT
ejpam-4945	72	10	zi	zi	X
ejpam-4945	72	11	(	(	PUNCT
ejpam-4945	72	12	ι	ι	NOUN
ejpam-4945	72	13	)	)	PUNCT
ejpam-4945	72	14	)	)	PUNCT
ejpam-4945	72	15	)	)	PUNCT
ejpam-4945	72	16	≤	≤	ADV
ejpam-4945	72	17	0	0	NUM
ejpam-4945	72	18	.	.	PUNCT
ejpam-4945	73	1	(	(	PUNCT
ejpam-4945	73	2	6	6	NUM
ejpam-4945	73	3	)	)	PUNCT
ejpam-4945	73	4	which	which	PRON
ejpam-4945	73	5	means	mean	VERB
ejpam-4945	73	6	that	that	SCONJ
ejpam-4945	73	7	a	a	DET
ejpam-4945	73	8	(	(	PUNCT
ejpam-4945	73	9	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	73	10	)	)	PUNCT
ejpam-4945	73	11	(	(	PUNCT
ejpam-4945	73	12	ι	ι	X
ejpam-4945	73	13	)	)	PUNCT
ejpam-4945	73	14	is	be	AUX
ejpam-4945	73	15	decreasing	decrease	VERB
ejpam-4945	73	16	and	and	CCONJ
ejpam-4945	73	17	w(β−1	w(β−1	NUM
ejpam-4945	73	18	)	)	PUNCT
ejpam-4945	73	19	(	(	PUNCT
ejpam-4945	73	20	ι	ι	X
ejpam-4945	73	21	)	)	PUNCT
ejpam-4945	73	22	is	be	AUX
ejpam-4945	73	23	eventually	eventually	ADV
ejpam-4945	73	24	of	of	ADP
ejpam-4945	73	25	one	one	NUM
ejpam-4945	73	26	sign	sign	NOUN
ejpam-4945	73	27	.	.	PUNCT
ejpam-4945	74	1	we	we	PRON
ejpam-4945	74	2	claim	claim	VERB
ejpam-4945	74	3	that	that	PRON
ejpam-4945	74	4	w(β−1	w(β−1	PUNCT
ejpam-4945	74	5	)	)	PUNCT
ejpam-4945	74	6	(	(	PUNCT
ejpam-4945	74	7	ι	ι	X
ejpam-4945	74	8	)	)	PUNCT
ejpam-4945	74	9	≥	≥	NOUN
ejpam-4945	74	10	0	0	NUM
ejpam-4945	74	11	.	.	PUNCT
ejpam-4945	75	1	otherwise	otherwise	ADV
ejpam-4945	75	2	,	,	PUNCT
ejpam-4945	75	3	if	if	SCONJ
ejpam-4945	75	4	there	there	PRON
ejpam-4945	75	5	exists	exist	VERB
ejpam-4945	75	6	a	a	DET
ejpam-4945	75	7	ι2	ι2	PROPN
ejpam-4945	75	8	≥	≥	NOUN
ejpam-4945	75	9	ι1	ι1	NOUN
ejpam-4945	75	10	such	such	ADJ
ejpam-4945	75	11	that	that	PRON
ejpam-4945	75	12	w(β−1	w(β−1	PUNCT
ejpam-4945	75	13	)	)	PUNCT
ejpam-4945	75	14	(	(	PUNCT
ejpam-4945	75	15	ι	ι	X
ejpam-4945	75	16	)	)	PUNCT
ejpam-4945	75	17	<	<	X
ejpam-4945	75	18	0	0	PUNCT
ejpam-4945	75	19	for	for	ADP
ejpam-4945	75	20	ι	ι	PROPN
ejpam-4945	75	21	≥	≥	NOUN
ejpam-4945	75	22	ι2	ι2	NOUN
ejpam-4945	75	23	,	,	PUNCT
ejpam-4945	75	24	and	and	CCONJ
ejpam-4945	75	25	(	(	PUNCT
ejpam-4945	75	26	aw(β−1	aw(β−1	NOUN
ejpam-4945	75	27	)	)	PUNCT
ejpam-4945	75	28	)	)	PUNCT
ejpam-4945	76	1	(	(	PUNCT
ejpam-4945	76	2	ι	ι	X
ejpam-4945	76	3	)	)	PUNCT
ejpam-4945	76	4	≤	≤	NOUN
ejpam-4945	76	5	(	(	PUNCT
ejpam-4945	76	6	aw(β−1	aw(β−1	NOUN
ejpam-4945	76	7	)	)	PUNCT
ejpam-4945	76	8	)	)	PUNCT
ejpam-4945	77	1	(	(	PUNCT
ejpam-4945	77	2	ι2	ι2	ADJ
ejpam-4945	77	3	)	)	PUNCT
ejpam-4945	77	4	=	=	SYM
ejpam-4945	77	5	−l	−l	NOUN
ejpam-4945	77	6	,	,	PUNCT
ejpam-4945	77	7	where	where	SCONJ
ejpam-4945	77	8	l	l	NOUN
ejpam-4945	77	9	>	>	X
ejpam-4945	77	10	0	0	X
ejpam-4945	77	11	.	.	PUNCT
ejpam-4945	77	12	integrating	integrate	VERB
ejpam-4945	77	13	the	the	DET
ejpam-4945	77	14	above	above	ADJ
ejpam-4945	77	15	inequality	inequality	NOUN
ejpam-4945	77	16	from	from	ADP
ejpam-4945	77	17	ι2	ι2	PROPN
ejpam-4945	77	18	to	to	ADP
ejpam-4945	77	19	ι	ι	PRON
ejpam-4945	77	20	we	we	PRON
ejpam-4945	77	21	find	find	VERB
ejpam-4945	77	22	w(β−2	w(β−2	PROPN
ejpam-4945	77	23	)	)	PUNCT
ejpam-4945	77	24	(	(	PUNCT
ejpam-4945	77	25	ι	ι	X
ejpam-4945	77	26	)	)	PUNCT
ejpam-4945	77	27	≤	≤	NOUN
ejpam-4945	77	28	w(β−2	w(β−2	X
ejpam-4945	77	29	)	)	PUNCT
ejpam-4945	77	30	(	(	PUNCT
ejpam-4945	77	31	ι2)−	ι2)−	X
ejpam-4945	77	32	l	l	NOUN
ejpam-4945	77	33	∫	∫	PROPN
ejpam-4945	77	34	ι	ι	PROPN
ejpam-4945	78	1	ι2	ι2	PROPN
ejpam-4945	78	2	1	1	NUM
ejpam-4945	78	3	a	a	DET
ejpam-4945	78	4	(	(	PUNCT
ejpam-4945	78	5	s	s	NOUN
ejpam-4945	78	6	)	)	PUNCT
ejpam-4945	78	7	ds	ds	X
ejpam-4945	78	8	.	.	NOUN
ejpam-4945	79	1	letting	let	VERB
ejpam-4945	79	2	ι→	ι→	PUNCT
ejpam-4945	79	3	∞	∞	PROPN
ejpam-4945	79	4	,	,	PUNCT
ejpam-4945	79	5	we	we	PRON
ejpam-4945	79	6	have	have	AUX
ejpam-4945	79	7	limι→∞w(β−2	limι→∞w(β−2	VERB
ejpam-4945	79	8	)	)	PUNCT
ejpam-4945	80	1	(	(	PUNCT
ejpam-4945	80	2	ι	ι	X
ejpam-4945	80	3	)	)	PUNCT
ejpam-4945	80	4	=	=	SYM
ejpam-4945	80	5	−∞	−∞	NOUN
ejpam-4945	80	6	,	,	PUNCT
ejpam-4945	80	7	which	which	PRON
ejpam-4945	80	8	contradicts	contradict	VERB
ejpam-4945	80	9	the	the	DET
ejpam-4945	80	10	fact	fact	NOUN
ejpam-4945	80	11	that	that	SCONJ
ejpam-4945	80	12	w	w	X
ejpam-4945	80	13	(	(	PUNCT
ejpam-4945	80	14	ι	ι	PROPN
ejpam-4945	80	15	)	)	PUNCT
ejpam-4945	80	16	>	>	X
ejpam-4945	80	17	0	0	X
ejpam-4945	80	18	.	.	PUNCT
ejpam-4945	81	1	hence	hence	ADV
ejpam-4945	81	2	,	,	PUNCT
ejpam-4945	81	3	we	we	PRON
ejpam-4945	81	4	obtain	obtain	VERB
ejpam-4945	81	5	w(β−1	w(β−1	PUNCT
ejpam-4945	81	6	)	)	PUNCT
ejpam-4945	81	7	(	(	PUNCT
ejpam-4945	81	8	ι	ι	X
ejpam-4945	81	9	)	)	PUNCT
ejpam-4945	81	10	≥	≥	NOUN
ejpam-4945	81	11	0	0	NUM
ejpam-4945	81	12	for	for	ADP
ejpam-4945	81	13	ι	ι	PROPN
ejpam-4945	81	14	≥	≥	NOUN
ejpam-4945	81	15	ι1	ι1	ADJ
ejpam-4945	81	16	.	.	PUNCT
ejpam-4945	82	1	from	from	ADP
ejpam-4945	82	2	eq	eq	ADP
ejpam-4945	82	3	.	.	PUNCT
ejpam-4945	83	1	(	(	PUNCT
ejpam-4945	83	2	1	1	NUM
ejpam-4945	83	3	)	)	PUNCT
ejpam-4945	83	4	,	,	PUNCT
ejpam-4945	83	5	we	we	PRON
ejpam-4945	83	6	get	get	VERB
ejpam-4945	83	7	(	(	PUNCT
ejpam-4945	83	8	aw(β	aw(β	NOUN
ejpam-4945	83	9	)	)	PUNCT
ejpam-4945	83	10	)	)	PUNCT
ejpam-4945	84	1	(	(	PUNCT
ejpam-4945	84	2	ι	ι	X
ejpam-4945	84	3	)	)	PUNCT
ejpam-4945	84	4	=	=	SYM
ejpam-4945	85	1	−	−	PROPN
ejpam-4945	85	2	(	(	PUNCT
ejpam-4945	85	3	a′w(β−1	a′w(β−1	ADV
ejpam-4945	85	4	)	)	PUNCT
ejpam-4945	85	5	)	)	PUNCT
ejpam-4945	86	1	(	(	PUNCT
ejpam-4945	86	2	ι)−	ι)−	NOUN
ejpam-4945	86	3	r∑	r∑	NOUN
ejpam-4945	86	4	i=1	i=1	PROPN
ejpam-4945	86	5	bi	bi	NOUN
ejpam-4945	86	6	(	(	PUNCT
ejpam-4945	86	7	ι)φ	ι)φ	X
ejpam-4945	86	8	(	(	PUNCT
ejpam-4945	86	9	ξ	ξ	X
ejpam-4945	86	10	(	(	PUNCT
ejpam-4945	86	11	zi	zi	X
ejpam-4945	86	12	(	(	PUNCT
ejpam-4945	86	13	ι	ι	NOUN
ejpam-4945	86	14	)	)	PUNCT
ejpam-4945	86	15	)	)	PUNCT
ejpam-4945	86	16	)	)	PUNCT
ejpam-4945	86	17	≤	≤	ADV
ejpam-4945	86	18	0	0	NUM
ejpam-4945	86	19	,	,	PUNCT
ejpam-4945	86	20	this	this	PRON
ejpam-4945	86	21	implies	imply	VERB
ejpam-4945	86	22	that	that	SCONJ
ejpam-4945	86	23	w(β	w(β	NOUN
ejpam-4945	86	24	)	)	PUNCT
ejpam-4945	86	25	(	(	PUNCT
ejpam-4945	86	26	ι	ι	X
ejpam-4945	86	27	)	)	PUNCT
ejpam-4945	86	28	≤	≤	NOUN
ejpam-4945	86	29	0	0	NUM
ejpam-4945	86	30	,	,	PUNCT
ejpam-4945	86	31	ι	ι	PRON
ejpam-4945	86	32	≥	≥	NOUN
ejpam-4945	86	33	ι1	ι1	ADJ
ejpam-4945	86	34	.	.	PUNCT
ejpam-4945	87	1	from	from	ADP
ejpam-4945	87	2	lemma	lemma	PROPN
ejpam-4945	87	3	3	3	NUM
ejpam-4945	87	4	,	,	PUNCT
ejpam-4945	87	5	we	we	PRON
ejpam-4945	87	6	find	find	VERB
ejpam-4945	87	7	(	(	PUNCT
ejpam-4945	87	8	5	5	NUM
ejpam-4945	87	9	)	)	PUNCT
ejpam-4945	87	10	hold	hold	NOUN
ejpam-4945	87	11	.	.	PUNCT
ejpam-4945	88	1	the	the	DET
ejpam-4945	88	2	proof	proof	NOUN
ejpam-4945	88	3	is	be	AUX
ejpam-4945	88	4	complete	complete	ADJ
ejpam-4945	88	5	.	.	PUNCT
ejpam-4945	89	1	theorem	theorem	NOUN
ejpam-4945	89	2	1	1	X
ejpam-4945	89	3	.	.	PUNCT
ejpam-4945	90	1	let	let	VERB
ejpam-4945	90	2	ξ′	ξ′	NOUN
ejpam-4945	90	3	(	(	PUNCT
ejpam-4945	90	4	ι	ι	PROPN
ejpam-4945	90	5	)	)	PUNCT
ejpam-4945	90	6	+	+	NUM
ejpam-4945	90	7	k̂	k̂	X
ejpam-4945	90	8	(	(	PUNCT
ejpam-4945	90	9	ι	ι	X
ejpam-4945	90	10	)	)	PUNCT
ejpam-4945	90	11	ξ	ξ	PROPN
ejpam-4945	90	12	(	(	PUNCT
ejpam-4945	90	13	z	z	NOUN
ejpam-4945	90	14	(	(	PUNCT
ejpam-4945	90	15	ι	ι	NOUN
ejpam-4945	90	16	)	)	PUNCT
ejpam-4945	90	17	)	)	PUNCT
ejpam-4945	91	1	=	=	SYM
ejpam-4945	91	2	0	0	NUM
ejpam-4945	91	3	,	,	PUNCT
ejpam-4945	91	4	(	(	PUNCT
ejpam-4945	91	5	7	7	X
ejpam-4945	91	6	)	)	PUNCT
ejpam-4945	91	7	is	be	AUX
ejpam-4945	91	8	oscillatory	oscillatory	ADJ
ejpam-4945	91	9	,	,	PUNCT
ejpam-4945	91	10	where	where	SCONJ
ejpam-4945	91	11	k̂	k̂	PROPN
ejpam-4945	91	12	(	(	PUNCT
ejpam-4945	91	13	ι	ι	PROPN
ejpam-4945	91	14	)	)	PUNCT
ejpam-4945	91	15	:	:	PUNCT
ejpam-4945	92	1	=	=	SYM
ejpam-4945	92	2	µzβ−1	µzβ−1	X
ejpam-4945	92	3	(	(	PUNCT
ejpam-4945	92	4	ι	ι	PROPN
ejpam-4945	92	5	)	)	PUNCT
ejpam-4945	92	6	(	(	PUNCT
ejpam-4945	92	7	β	β	NOUN
ejpam-4945	92	8	−	−	NUM
ejpam-4945	92	9	1)!a	1)!a	NUM
ejpam-4945	92	10	(	(	PUNCT
ejpam-4945	92	11	z	z	NOUN
ejpam-4945	92	12	(	(	PUNCT
ejpam-4945	92	13	ι	ι	NOUN
ejpam-4945	92	14	)	)	PUNCT
ejpam-4945	92	15	)	)	PUNCT
ejpam-4945	93	1	k	k	PROPN
ejpam-4945	93	2	(	(	PUNCT
ejpam-4945	93	3	ι	ι	PROPN
ejpam-4945	93	4	)	)	PUNCT
ejpam-4945	93	5	,	,	PUNCT
ejpam-4945	94	1	k	k	PROPN
ejpam-4945	94	2	(	(	PUNCT
ejpam-4945	94	3	ι	ι	PROPN
ejpam-4945	94	4	)	)	PUNCT
ejpam-4945	94	5	:	:	PUNCT
ejpam-4945	95	1	=	=	PUNCT
ejpam-4945	95	2	r∑	r∑	X
ejpam-4945	95	3	i=1	i=1	PROPN
ejpam-4945	95	4	bi	bi	NOUN
ejpam-4945	95	5	(	(	PUNCT
ejpam-4945	95	6	ι	ι	PROPN
ejpam-4945	95	7	)	)	PUNCT
ejpam-4945	95	8	(	(	PUNCT
ejpam-4945	95	9	1−	1−	NUM
ejpam-4945	95	10	ς	ς	PROPN
ejpam-4945	95	11	(	(	PUNCT
ejpam-4945	95	12	z	z	NOUN
ejpam-4945	95	13	(	(	PUNCT
ejpam-4945	95	14	ι	ι	NOUN
ejpam-4945	95	15	)	)	PUNCT
ejpam-4945	95	16	)	)	PUNCT
ejpam-4945	95	17	)	)	PUNCT
ejpam-4945	95	18	,	,	PUNCT
ejpam-4945	95	19	then	then	ADV
ejpam-4945	95	20	eq	eq	ADP
ejpam-4945	95	21	.	.	PUNCT
ejpam-4945	96	1	(	(	PUNCT
ejpam-4945	96	2	1	1	X
ejpam-4945	96	3	)	)	PUNCT
ejpam-4945	96	4	is	be	AUX
ejpam-4945	96	5	oscillatory	oscillatory	ADJ
ejpam-4945	96	6	.	.	PUNCT
ejpam-4945	97	1	a.	a.	NOUN
ejpam-4945	97	2	almutairi	almutairi	PROPN
ejpam-4945	97	3	/	/	SYM
ejpam-4945	97	4	eur	eur	PROPN
ejpam-4945	97	5	.	.	PUNCT
ejpam-4945	98	1	j.	j.	PROPN
ejpam-4945	98	2	pure	pure	PROPN
ejpam-4945	98	3	appl	appl	PROPN
ejpam-4945	98	4	.	.	PROPN
ejpam-4945	98	5	math	math	PROPN
ejpam-4945	98	6	,	,	PUNCT
ejpam-4945	98	7	16	16	NUM
ejpam-4945	98	8	(	(	PUNCT
ejpam-4945	98	9	4	4	NUM
ejpam-4945	98	10	)	)	PUNCT
ejpam-4945	98	11	(	(	PUNCT
ejpam-4945	98	12	2023	2023	NUM
ejpam-4945	98	13	)	)	PUNCT
ejpam-4945	98	14	,	,	PUNCT
ejpam-4945	98	15	2499	2499	NUM
ejpam-4945	98	16	-	-	SYM
ejpam-4945	98	17	2508	2508	NUM
ejpam-4945	98	18	2503	2503	NUM
ejpam-4945	98	19	proof	proof	NOUN
ejpam-4945	98	20	.	.	PUNCT
ejpam-4945	99	1	let	let	VERB
ejpam-4945	99	2	(	(	PUNCT
ejpam-4945	99	3	1	1	X
ejpam-4945	99	4	)	)	PUNCT
ejpam-4945	99	5	has	have	VERB
ejpam-4945	99	6	a	a	DET
ejpam-4945	99	7	nonoscillatory	nonoscillatory	ADJ
ejpam-4945	99	8	solution	solution	NOUN
ejpam-4945	99	9	.	.	PUNCT
ejpam-4945	100	1	from	from	ADP
ejpam-4945	100	2	lemma	lemma	PROPN
ejpam-4945	100	3	4	4	NUM
ejpam-4945	100	4	,	,	PUNCT
ejpam-4945	100	5	we	we	PRON
ejpam-4945	100	6	find	find	VERB
ejpam-4945	100	7	(	(	PUNCT
ejpam-4945	100	8	5	5	NUM
ejpam-4945	100	9	)	)	PUNCT
ejpam-4945	100	10	holds	hold	VERB
ejpam-4945	100	11	.	.	PUNCT
ejpam-4945	101	1	from	from	ADP
ejpam-4945	101	2	w	w	PROPN
ejpam-4945	101	3	(	(	PUNCT
ejpam-4945	101	4	ι	ι	NOUN
ejpam-4945	101	5	)	)	PUNCT
ejpam-4945	101	6	=	=	PUNCT
ejpam-4945	101	7	|ξ	|ξ	NOUN
ejpam-4945	101	8	(	(	PUNCT
ejpam-4945	101	9	ι)|p−2	ι)|p−2	PUNCT
ejpam-4945	101	10	ξ	ξ	X
ejpam-4945	101	11	(	(	PUNCT
ejpam-4945	101	12	ι	ι	NOUN
ejpam-4945	101	13	)	)	PUNCT
ejpam-4945	101	14	+	+	CCONJ
ejpam-4945	101	15	ς	ς	PROPN
ejpam-4945	101	16	(	(	PUNCT
ejpam-4945	101	17	ι	ι	NOUN
ejpam-4945	101	18	)	)	PUNCT
ejpam-4945	101	19	ξ	ξ	PROPN
ejpam-4945	101	20	(	(	PUNCT
ejpam-4945	101	21	γ	γ	X
ejpam-4945	101	22	(	(	PUNCT
ejpam-4945	101	23	ι	ι	PROPN
ejpam-4945	101	24	)	)	PUNCT
ejpam-4945	101	25	)	)	PUNCT
ejpam-4945	101	26	,	,	PUNCT
ejpam-4945	101	27	we	we	PRON
ejpam-4945	101	28	see	see	VERB
ejpam-4945	101	29	that	that	DET
ejpam-4945	101	30	ξp−1	ξp−1	PROPN
ejpam-4945	101	31	(	(	PUNCT
ejpam-4945	101	32	ι	ι	NOUN
ejpam-4945	101	33	)	)	PUNCT
ejpam-4945	102	1	=	=	SYM
ejpam-4945	102	2	w	w	PROPN
ejpam-4945	102	3	(	(	PUNCT
ejpam-4945	102	4	ι)−	ι)−	PROPN
ejpam-4945	102	5	ς	ς	PROPN
ejpam-4945	102	6	(	(	PUNCT
ejpam-4945	102	7	ι	ι	PROPN
ejpam-4945	102	8	)	)	PUNCT
ejpam-4945	102	9	ξ	ξ	PROPN
ejpam-4945	102	10	(	(	PUNCT
ejpam-4945	102	11	γ	γ	X
ejpam-4945	102	12	(	(	PUNCT
ejpam-4945	102	13	ι	ι	PROPN
ejpam-4945	102	14	)	)	PUNCT
ejpam-4945	102	15	)	)	PUNCT
ejpam-4945	102	16	≥	≥	PROPN
ejpam-4945	103	1	w	w	NOUN
ejpam-4945	103	2	(	(	PUNCT
ejpam-4945	103	3	ι)−	ι)−	PROPN
ejpam-4945	103	4	ς	ς	PROPN
ejpam-4945	103	5	(	(	PUNCT
ejpam-4945	103	6	ι)w	ι)w	PRON
ejpam-4945	103	7	(	(	PUNCT
ejpam-4945	103	8	γ	γ	X
ejpam-4945	103	9	(	(	PUNCT
ejpam-4945	103	10	ι	ι	PROPN
ejpam-4945	103	11	)	)	PUNCT
ejpam-4945	103	12	)	)	PUNCT
ejpam-4945	103	13	≥	≥	PROPN
ejpam-4945	103	14	w	w	NOUN
ejpam-4945	103	15	(	(	PUNCT
ejpam-4945	103	16	ι)−	ι)−	PROPN
ejpam-4945	103	17	ς	ς	PROPN
ejpam-4945	103	18	(	(	PUNCT
ejpam-4945	103	19	ι)w	ι)w	NOUN
ejpam-4945	103	20	(	(	PUNCT
ejpam-4945	103	21	ι	ι	X
ejpam-4945	103	22	)	)	PUNCT
ejpam-4945	103	23	≥	≥	NOUN
ejpam-4945	103	24	(	(	PUNCT
ejpam-4945	103	25	1−	1−	NUM
ejpam-4945	103	26	ς	ς	PROPN
ejpam-4945	103	27	(	(	PUNCT
ejpam-4945	103	28	ι))w	ι))w	NOUN
ejpam-4945	103	29	(	(	PUNCT
ejpam-4945	103	30	ι	ι	NOUN
ejpam-4945	103	31	)	)	PUNCT
ejpam-4945	103	32	and	and	CCONJ
ejpam-4945	103	33	so	so	ADV
ejpam-4945	103	34	ξp−1	ξp−1	PROPN
ejpam-4945	103	35	(	(	PUNCT
ejpam-4945	103	36	zi	zi	X
ejpam-4945	103	37	(	(	PUNCT
ejpam-4945	103	38	ι	ι	NOUN
ejpam-4945	103	39	)	)	PUNCT
ejpam-4945	103	40	)	)	PUNCT
ejpam-4945	103	41	≥	≥	PROPN
ejpam-4945	103	42	w	w	PROPN
ejpam-4945	103	43	(	(	PUNCT
ejpam-4945	103	44	zi	zi	X
ejpam-4945	103	45	(	(	PUNCT
ejpam-4945	103	46	ι	ι	PROPN
ejpam-4945	103	47	)	)	PUNCT
ejpam-4945	103	48	)	)	PUNCT
ejpam-4945	104	1	(	(	PUNCT
ejpam-4945	104	2	1−	1−	NUM
ejpam-4945	104	3	ς	ς	PROPN
ejpam-4945	104	4	(	(	PUNCT
ejpam-4945	104	5	zi	zi	X
ejpam-4945	104	6	(	(	PUNCT
ejpam-4945	104	7	ι	ι	NOUN
ejpam-4945	104	8	)	)	PUNCT
ejpam-4945	104	9	)	)	PUNCT
ejpam-4945	104	10	)	)	PUNCT
ejpam-4945	104	11	.	.	PUNCT
ejpam-4945	105	1	(	(	PUNCT
ejpam-4945	105	2	8)	8)	NUM
ejpam-4945	105	3	from	from	ADP
ejpam-4945	105	4	(	(	PUNCT
ejpam-4945	105	5	8)	8)	NUM
ejpam-4945	105	6	,	,	PUNCT
ejpam-4945	105	7	we	we	PRON
ejpam-4945	105	8	get	get	VERB
ejpam-4945	105	9	φ	φ	X
ejpam-4945	105	10	(	(	PUNCT
ejpam-4945	105	11	ξ	ξ	PROPN
ejpam-4945	105	12	(	(	PUNCT
ejpam-4945	105	13	zi	zi	X
ejpam-4945	105	14	(	(	PUNCT
ejpam-4945	105	15	ι	ι	NOUN
ejpam-4945	105	16	)	)	PUNCT
ejpam-4945	105	17	)	)	PUNCT
ejpam-4945	105	18	)	)	PUNCT
ejpam-4945	105	19	≥	≥	PROPN
ejpam-4945	106	1	w	w	PROPN
ejpam-4945	106	2	(	(	PUNCT
ejpam-4945	106	3	zi	zi	X
ejpam-4945	106	4	(	(	PUNCT
ejpam-4945	106	5	ι	ι	PROPN
ejpam-4945	106	6	)	)	PUNCT
ejpam-4945	106	7	)	)	PUNCT
ejpam-4945	107	1	(	(	PUNCT
ejpam-4945	107	2	1−	1−	NUM
ejpam-4945	107	3	ς	ς	PROPN
ejpam-4945	107	4	(	(	PUNCT
ejpam-4945	107	5	zi	zi	X
ejpam-4945	107	6	(	(	PUNCT
ejpam-4945	107	7	ι	ι	NOUN
ejpam-4945	107	8	)	)	PUNCT
ejpam-4945	107	9	)	)	PUNCT
ejpam-4945	107	10	)	)	PUNCT
ejpam-4945	107	11	.	.	PUNCT
ejpam-4945	108	1	(	(	PUNCT
ejpam-4945	108	2	9	9	X
ejpam-4945	108	3	)	)	PUNCT
ejpam-4945	108	4	from	from	ADP
ejpam-4945	108	5	(	(	PUNCT
ejpam-4945	108	6	1	1	NUM
ejpam-4945	108	7	)	)	PUNCT
ejpam-4945	108	8	and	and	CCONJ
ejpam-4945	108	9	(	(	PUNCT
ejpam-4945	108	10	9	9	NUM
ejpam-4945	108	11	)	)	PUNCT
ejpam-4945	108	12	,	,	PUNCT
ejpam-4945	108	13	we	we	PRON
ejpam-4945	108	14	see	see	VERB
ejpam-4945	108	15	(	(	PUNCT
ejpam-4945	108	16	aw(β−1	aw(β−1	NOUN
ejpam-4945	108	17	)	)	PUNCT
ejpam-4945	108	18	)	)	PUNCT
ejpam-4945	109	1	′	′	NUM
ejpam-4945	109	2	(	(	PUNCT
ejpam-4945	109	3	ι	ι	NOUN
ejpam-4945	109	4	)	)	PUNCT
ejpam-4945	109	5	≤	≤	NOUN
ejpam-4945	110	1	−	−	NOUN
ejpam-4945	110	2	r∑	r∑	NOUN
ejpam-4945	110	3	i=1	i=1	PROPN
ejpam-4945	110	4	bi	bi	NOUN
ejpam-4945	110	5	(	(	PUNCT
ejpam-4945	110	6	ι)w	ι)w	X
ejpam-4945	110	7	(	(	PUNCT
ejpam-4945	110	8	zi	zi	X
ejpam-4945	110	9	(	(	PUNCT
ejpam-4945	110	10	ι	ι	PROPN
ejpam-4945	110	11	)	)	PUNCT
ejpam-4945	110	12	)	)	PUNCT
ejpam-4945	110	13	(	(	PUNCT
ejpam-4945	110	14	1−	1−	NUM
ejpam-4945	110	15	ς	ς	PROPN
ejpam-4945	110	16	(	(	PUNCT
ejpam-4945	110	17	zi	zi	X
ejpam-4945	110	18	(	(	PUNCT
ejpam-4945	110	19	ι	ι	NOUN
ejpam-4945	110	20	)	)	PUNCT
ejpam-4945	110	21	)	)	PUNCT
ejpam-4945	110	22	)	)	PUNCT
ejpam-4945	110	23	≤	≤	PUNCT
ejpam-4945	111	1	−w	−w	ADV
ejpam-4945	111	2	(	(	PUNCT
ejpam-4945	111	3	z	z	NOUN
ejpam-4945	111	4	(	(	PUNCT
ejpam-4945	111	5	ι	ι	NOUN
ejpam-4945	111	6	)	)	PUNCT
ejpam-4945	111	7	)	)	PUNCT
ejpam-4945	112	1	r∑	r∑	ADP
ejpam-4945	112	2	i=1	i=1	PROPN
ejpam-4945	112	3	bi	bi	NOUN
ejpam-4945	112	4	(	(	PUNCT
ejpam-4945	112	5	ι	ι	PROPN
ejpam-4945	112	6	)	)	PUNCT
ejpam-4945	112	7	(	(	PUNCT
ejpam-4945	112	8	1−	1−	NUM
ejpam-4945	112	9	ς	ς	PROPN
ejpam-4945	112	10	(	(	PUNCT
ejpam-4945	112	11	zi	zi	X
ejpam-4945	112	12	(	(	PUNCT
ejpam-4945	112	13	ι	ι	NOUN
ejpam-4945	112	14	)	)	PUNCT
ejpam-4945	112	15	)	)	PUNCT
ejpam-4945	112	16	)	)	PUNCT
ejpam-4945	113	1	=	=	PRON
ejpam-4945	113	2	−k	−k	PROPN
ejpam-4945	113	3	(	(	PUNCT
ejpam-4945	113	4	ι)w	ι)w	X
ejpam-4945	113	5	(	(	PUNCT
ejpam-4945	113	6	z	z	NOUN
ejpam-4945	113	7	(	(	PUNCT
ejpam-4945	113	8	ι	ι	NOUN
ejpam-4945	113	9	)	)	PUNCT
ejpam-4945	113	10	)	)	PUNCT
ejpam-4945	113	11	(	(	PUNCT
ejpam-4945	113	12	10	10	NUM
ejpam-4945	113	13	)	)	PUNCT
ejpam-4945	113	14	in	in	ADP
ejpam-4945	113	15	view	view	NOUN
ejpam-4945	113	16	of	of	ADP
ejpam-4945	113	17	lemma	lemma	PROPN
ejpam-4945	113	18	2	2	NUM
ejpam-4945	113	19	,	,	PUNCT
ejpam-4945	113	20	we	we	PRON
ejpam-4945	113	21	obtain	obtain	VERB
ejpam-4945	113	22	w	w	ADP
ejpam-4945	113	23	(	(	PUNCT
ejpam-4945	113	24	ι	ι	PROPN
ejpam-4945	113	25	)	)	PUNCT
ejpam-4945	113	26	≥	≥	NOUN
ejpam-4945	113	27	µ	µ	X
ejpam-4945	113	28	(	(	PUNCT
ejpam-4945	113	29	β	β	NOUN
ejpam-4945	113	30	−	−	NOUN
ejpam-4945	113	31	1	1	NUM
ejpam-4945	113	32	)	)	PUNCT
ejpam-4945	113	33	!	!	PUNCT
ejpam-4945	113	34	ιβ−1w(β−1	ιβ−1w(β−1	PUNCT
ejpam-4945	113	35	)	)	PUNCT
ejpam-4945	113	36	(	(	PUNCT
ejpam-4945	113	37	ι	ι	PROPN
ejpam-4945	113	38	)	)	PUNCT
ejpam-4945	113	39	,	,	PUNCT
ejpam-4945	113	40	for	for	ADP
ejpam-4945	113	41	all	all	PRON
ejpam-4945	113	42	ι	ι	DET
ejpam-4945	113	43	≥	≥	NOUN
ejpam-4945	113	44	ι2	ι2	PROPN
ejpam-4945	113	45	≥	≥	NUM
ejpam-4945	113	46	max	max	PROPN
ejpam-4945	113	47	{	{	PUNCT
ejpam-4945	113	48	ι1	ι1	PROPN
ejpam-4945	113	49	,	,	PUNCT
ejpam-4945	113	50	ιµ	ιµ	ADJ
ejpam-4945	113	51	}	}	PUNCT
ejpam-4945	113	52	.	.	PUNCT
ejpam-4945	114	1	thus	thus	ADV
ejpam-4945	114	2	,	,	PUNCT
ejpam-4945	114	3	by	by	ADP
ejpam-4945	114	4	using	use	VERB
ejpam-4945	114	5	(	(	PUNCT
ejpam-4945	114	6	10	10	NUM
ejpam-4945	114	7	)	)	PUNCT
ejpam-4945	114	8	,	,	PUNCT
ejpam-4945	114	9	we	we	PRON
ejpam-4945	114	10	find	find	VERB
ejpam-4945	114	11	(	(	PUNCT
ejpam-4945	114	12	a	a	DET
ejpam-4945	114	13	(	(	PUNCT
ejpam-4945	114	14	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	114	15	)	)	PUNCT
ejpam-4945	114	16	(	(	PUNCT
ejpam-4945	114	17	ι	ι	NOUN
ejpam-4945	114	18	)	)	PUNCT
ejpam-4945	114	19	)	)	PUNCT
ejpam-4945	114	20	′	′	PUNCT
ejpam-4945	115	1	+	+	CCONJ
ejpam-4945	115	2	µzβ−1	µzβ−1	X
ejpam-4945	115	3	(	(	PUNCT
ejpam-4945	115	4	ι)k	ι)k	X
ejpam-4945	115	5	(	(	PUNCT
ejpam-4945	115	6	ι	ι	X
ejpam-4945	115	7	)	)	PUNCT
ejpam-4945	115	8	(	(	PUNCT
ejpam-4945	115	9	β	β	NOUN
ejpam-4945	115	10	−	−	NUM
ejpam-4945	115	11	1)!a	1)!a	NUM
ejpam-4945	115	12	(	(	PUNCT
ejpam-4945	115	13	z	z	NOUN
ejpam-4945	115	14	(	(	PUNCT
ejpam-4945	115	15	ι	ι	NOUN
ejpam-4945	115	16	)	)	PUNCT
ejpam-4945	115	17	)	)	PUNCT
ejpam-4945	115	18	(	(	PUNCT
ejpam-4945	115	19	a	a	DET
ejpam-4945	115	20	(	(	PUNCT
ejpam-4945	115	21	z	z	NOUN
ejpam-4945	115	22	(	(	PUNCT
ejpam-4945	115	23	ι))w(β−1	ι))w(β−1	PROPN
ejpam-4945	115	24	)	)	PUNCT
ejpam-4945	115	25	(	(	PUNCT
ejpam-4945	115	26	z	z	NOUN
ejpam-4945	115	27	(	(	PUNCT
ejpam-4945	115	28	ι	ι	NOUN
ejpam-4945	115	29	)	)	PUNCT
ejpam-4945	115	30	)	)	PUNCT
ejpam-4945	115	31	)	)	PUNCT
ejpam-4945	115	32	≤	≤	ADV
ejpam-4945	115	33	0	0	X
ejpam-4945	115	34	.	.	PUNCT
ejpam-4945	116	1	therefore	therefore	ADV
ejpam-4945	116	2	,	,	PUNCT
ejpam-4945	116	3	we	we	PRON
ejpam-4945	116	4	get	get	VERB
ejpam-4945	116	5	ξ	ξ	PROPN
ejpam-4945	116	6	(	(	PUNCT
ejpam-4945	116	7	ι	ι	PROPN
ejpam-4945	116	8	)	)	PUNCT
ejpam-4945	116	9	=	=	SYM
ejpam-4945	116	10	a	a	DET
ejpam-4945	116	11	(	(	PUNCT
ejpam-4945	116	12	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	116	13	)	)	PUNCT
ejpam-4945	116	14	(	(	PUNCT
ejpam-4945	116	15	ι	ι	X
ejpam-4945	116	16	)	)	PUNCT
ejpam-4945	116	17	is	be	AUX
ejpam-4945	116	18	a	a	DET
ejpam-4945	116	19	positive	positive	ADJ
ejpam-4945	116	20	solution	solution	NOUN
ejpam-4945	116	21	of	of	ADP
ejpam-4945	116	22	the	the	DET
ejpam-4945	116	23	differential	differential	ADJ
ejpam-4945	116	24	inequality	inequality	NOUN
ejpam-4945	116	25	ξ′	ξ′	PROPN
ejpam-4945	116	26	(	(	PUNCT
ejpam-4945	116	27	ι	ι	PROPN
ejpam-4945	116	28	)	)	PUNCT
ejpam-4945	117	1	+	+	NUM
ejpam-4945	117	2	k̂	k̂	X
ejpam-4945	117	3	(	(	PUNCT
ejpam-4945	117	4	ι	ι	X
ejpam-4945	117	5	)	)	PUNCT
ejpam-4945	117	6	ξ	ξ	PROPN
ejpam-4945	117	7	(	(	PUNCT
ejpam-4945	117	8	z	z	NOUN
ejpam-4945	117	9	(	(	PUNCT
ejpam-4945	117	10	ι	ι	NOUN
ejpam-4945	117	11	)	)	PUNCT
ejpam-4945	117	12	)	)	PUNCT
ejpam-4945	117	13	≤	≤	ADV
ejpam-4945	117	14	0	0	X
ejpam-4945	117	15	.	.	PUNCT
ejpam-4945	117	16	from	from	ADP
ejpam-4945	117	17	[	[	X
ejpam-4945	117	18	14	14	NUM
ejpam-4945	117	19	,	,	PUNCT
ejpam-4945	117	20	corollary	corollary	ADJ
ejpam-4945	117	21	1	1	NUM
ejpam-4945	117	22	]	]	PUNCT
ejpam-4945	117	23	,	,	PUNCT
ejpam-4945	117	24	we	we	PRON
ejpam-4945	117	25	see	see	VERB
ejpam-4945	117	26	that	that	SCONJ
ejpam-4945	117	27	(	(	PUNCT
ejpam-4945	117	28	7	7	X
ejpam-4945	117	29	)	)	PUNCT
ejpam-4945	117	30	also	also	ADV
ejpam-4945	117	31	has	have	VERB
ejpam-4945	117	32	a	a	DET
ejpam-4945	117	33	positive	positive	ADJ
ejpam-4945	117	34	solution	solution	NOUN
ejpam-4945	117	35	,	,	PUNCT
ejpam-4945	117	36	a	a	DET
ejpam-4945	117	37	contradiction	contradiction	NOUN
ejpam-4945	117	38	.	.	PUNCT
ejpam-4945	118	1	this	this	PRON
ejpam-4945	118	2	completes	complete	VERB
ejpam-4945	118	3	the	the	DET
ejpam-4945	118	4	proof	proof	NOUN
ejpam-4945	118	5	.	.	PUNCT
ejpam-4945	119	1	using	use	VERB
ejpam-4945	119	2	theorem	theorem	ADJ
ejpam-4945	119	3	2.1.1	2.1.1	NUM
ejpam-4945	119	4	in	in	ADP
ejpam-4945	119	5	[	[	X
ejpam-4945	119	6	18	18	NUM
ejpam-4945	119	7	]	]	PUNCT
ejpam-4945	119	8	,	,	PUNCT
ejpam-4945	119	9	we	we	PRON
ejpam-4945	119	10	get	get	VERB
ejpam-4945	119	11	the	the	DET
ejpam-4945	119	12	following	follow	VERB
ejpam-4945	119	13	corollary	corollary	NOUN
ejpam-4945	119	14	.	.	PUNCT
ejpam-4945	120	1	corollary	corollary	ADJ
ejpam-4945	120	2	1	1	NUM
ejpam-4945	120	3	.	.	PUNCT
ejpam-4945	121	1	if	if	SCONJ
ejpam-4945	121	2	lim	lim	PROPN
ejpam-4945	121	3	inf	inf	PROPN
ejpam-4945	121	4	ι→∞	ι→∞	X
ejpam-4945	121	5	∫	∫	PROPN
ejpam-4945	121	6	ι	ι	X
ejpam-4945	121	7	z(ι	z(ι	NOUN
ejpam-4945	121	8	)	)	PUNCT
ejpam-4945	121	9	zβ−1	zβ−1	PROPN
ejpam-4945	121	10	(	(	PUNCT
ejpam-4945	121	11	s	s	X
ejpam-4945	121	12	)	)	PUNCT
ejpam-4945	121	13	a	a	DET
ejpam-4945	121	14	(	(	PUNCT
ejpam-4945	121	15	z	z	NOUN
ejpam-4945	121	16	(	(	PUNCT
ejpam-4945	121	17	s	s	NOUN
ejpam-4945	121	18	)	)	PUNCT
ejpam-4945	121	19	)	)	PUNCT
ejpam-4945	122	1	k	k	X
ejpam-4945	122	2	(	(	PUNCT
ejpam-4945	122	3	s	s	X
ejpam-4945	122	4	)	)	PUNCT
ejpam-4945	122	5	ds	ds	NOUN
ejpam-4945	122	6	>	>	X
ejpam-4945	122	7	(	(	PUNCT
ejpam-4945	122	8	β	β	NOUN
ejpam-4945	122	9	−	−	NOUN
ejpam-4945	122	10	1	1	NUM
ejpam-4945	122	11	)	)	PUNCT
ejpam-4945	122	12	!	!	PUNCT
ejpam-4945	123	1	µe	µe	INTJ
ejpam-4945	123	2	,	,	PUNCT
ejpam-4945	123	3	for	for	ADP
ejpam-4945	123	4	µ	µ	PRON
ejpam-4945	123	5	∈	∈	NOUN
ejpam-4945	123	6	(	(	PUNCT
ejpam-4945	123	7	0	0	NUM
ejpam-4945	123	8	,	,	PUNCT
ejpam-4945	123	9	1	1	NUM
ejpam-4945	123	10	)	)	PUNCT
ejpam-4945	123	11	,	,	PUNCT
ejpam-4945	123	12	then	then	ADV
ejpam-4945	123	13	(	(	PUNCT
ejpam-4945	123	14	1	1	X
ejpam-4945	123	15	)	)	PUNCT
ejpam-4945	123	16	is	be	AUX
ejpam-4945	123	17	oscillatory	oscillatory	ADJ
ejpam-4945	123	18	.	.	PUNCT
ejpam-4945	124	1	a.	a.	NOUN
ejpam-4945	124	2	almutairi	almutairi	PROPN
ejpam-4945	124	3	/	/	SYM
ejpam-4945	124	4	eur	eur	PROPN
ejpam-4945	124	5	.	.	PUNCT
ejpam-4945	125	1	j.	j.	PROPN
ejpam-4945	125	2	pure	pure	PROPN
ejpam-4945	125	3	appl	appl	PROPN
ejpam-4945	125	4	.	.	PROPN
ejpam-4945	125	5	math	math	PROPN
ejpam-4945	125	6	,	,	PUNCT
ejpam-4945	125	7	16	16	NUM
ejpam-4945	125	8	(	(	PUNCT
ejpam-4945	125	9	4	4	NUM
ejpam-4945	125	10	)	)	PUNCT
ejpam-4945	125	11	(	(	PUNCT
ejpam-4945	125	12	2023	2023	NUM
ejpam-4945	125	13	)	)	PUNCT
ejpam-4945	125	14	,	,	PUNCT
ejpam-4945	125	15	2499	2499	NUM
ejpam-4945	125	16	-	-	SYM
ejpam-4945	125	17	2508	2508	NUM
ejpam-4945	125	18	2504	2504	NUM
ejpam-4945	125	19	theorem	theorem	VERB
ejpam-4945	125	20	2	2	NUM
ejpam-4945	125	21	.	.	PUNCT
ejpam-4945	125	22	if∫	if∫	PROPN
ejpam-4945	125	23	∞	∞	PROPN
ejpam-4945	125	24	ι0	ι0	PROPN
ejpam-4945	125	25	(	(	PUNCT
ejpam-4945	125	26	ℏ	ℏ	PROPN
ejpam-4945	125	27	(	(	PUNCT
ejpam-4945	125	28	u)k	u)k	X
ejpam-4945	125	29	(	(	PUNCT
ejpam-4945	125	30	u)−	u)−	PROPN
ejpam-4945	125	31	1	1	NUM
ejpam-4945	125	32	4ν	4ν	NOUN
ejpam-4945	125	33	(	(	PUNCT
ejpam-4945	125	34	ℏ′	ℏ′	X
ejpam-4945	125	35	(	(	PUNCT
ejpam-4945	125	36	u	u	NOUN
ejpam-4945	125	37	)	)	PUNCT
ejpam-4945	125	38	ℏ	ℏ	PROPN
ejpam-4945	125	39	(	(	PUNCT
ejpam-4945	125	40	u	u	NOUN
ejpam-4945	125	41	)	)	PUNCT
ejpam-4945	125	42	)	)	PUNCT
ejpam-4945	125	43	2	2	NUM
ejpam-4945	125	44	b	b	X
ejpam-4945	125	45	(	(	PUNCT
ejpam-4945	125	46	u	u	NOUN
ejpam-4945	125	47	)	)	PUNCT
ejpam-4945	125	48	)	)	PUNCT
ejpam-4945	125	49	du	du	PROPN
ejpam-4945	125	50	=	=	SYM
ejpam-4945	125	51	∞	∞	PROPN
ejpam-4945	125	52	,	,	PUNCT
ejpam-4945	125	53	for	for	ADP
ejpam-4945	125	54	ν	ν	DET
ejpam-4945	125	55	∈	∈	PROPN
ejpam-4945	125	56	(	(	PUNCT
ejpam-4945	125	57	0	0	NUM
ejpam-4945	125	58	,	,	PUNCT
ejpam-4945	125	59	1	1	NUM
ejpam-4945	125	60	)	)	PUNCT
ejpam-4945	125	61	,	,	PUNCT
ejpam-4945	125	62	j	j	PROPN
ejpam-4945	125	63	>	>	X
ejpam-4945	125	64	0	0	PROPN
ejpam-4945	125	65	,	,	PUNCT
ejpam-4945	125	66	(	(	PUNCT
ejpam-4945	125	67	11	11	NUM
ejpam-4945	125	68	)	)	PUNCT
ejpam-4945	125	69	then	then	ADV
ejpam-4945	125	70	(	(	PUNCT
ejpam-4945	125	71	1	1	X
ejpam-4945	125	72	)	)	PUNCT
ejpam-4945	125	73	is	be	AUX
ejpam-4945	125	74	oscillatory	oscillatory	ADJ
ejpam-4945	125	75	,	,	PUNCT
ejpam-4945	125	76	where	where	SCONJ
ejpam-4945	125	77	ℏ	ℏ	PROPN
ejpam-4945	125	78	∈	∈	PROPN
ejpam-4945	125	79	c1	c1	NOUN
ejpam-4945	125	80	(	(	PUNCT
ejpam-4945	125	81	[	[	X
ejpam-4945	125	82	ι0,∞	ι0,∞	NOUN
ejpam-4945	125	83	)	)	PUNCT
ejpam-4945	125	84	,	,	PUNCT
ejpam-4945	125	85	r+	r+	X
ejpam-4945	125	86	)	)	PUNCT
ejpam-4945	125	87	and	and	CCONJ
ejpam-4945	125	88	b	b	X
ejpam-4945	125	89	(	(	PUNCT
ejpam-4945	125	90	ι	ι	NOUN
ejpam-4945	125	91	)	)	PUNCT
ejpam-4945	125	92	:	:	PUNCT
ejpam-4945	125	93	=	=	PUNCT
ejpam-4945	125	94	a	a	PRON
ejpam-4945	125	95	(	(	PUNCT
ejpam-4945	125	96	ι	ι	NOUN
ejpam-4945	125	97	)	)	PUNCT
ejpam-4945	125	98	ℏ	ℏ	PROPN
ejpam-4945	125	99	(	(	PUNCT
ejpam-4945	125	100	ι	ι	NOUN
ejpam-4945	125	101	)	)	PUNCT
ejpam-4945	125	102	jzβ−2	jzβ−2	PROPN
ejpam-4945	125	103	(	(	PUNCT
ejpam-4945	125	104	ι	ι	PROPN
ejpam-4945	125	105	)	)	PUNCT
ejpam-4945	125	106	z′	z′	NUM
ejpam-4945	125	107	(	(	PUNCT
ejpam-4945	125	108	ι	ι	PROPN
ejpam-4945	125	109	)	)	PUNCT
ejpam-4945	125	110	.	.	PUNCT
ejpam-4945	126	1	proof	proof	NOUN
ejpam-4945	126	2	.	.	PUNCT
ejpam-4945	127	1	let	let	VERB
ejpam-4945	127	2	(	(	PUNCT
ejpam-4945	127	3	1	1	X
ejpam-4945	127	4	)	)	PUNCT
ejpam-4945	127	5	has	have	VERB
ejpam-4945	127	6	a	a	DET
ejpam-4945	127	7	nonoscillatory	nonoscillatory	ADJ
ejpam-4945	127	8	solution	solution	NOUN
ejpam-4945	127	9	.	.	PUNCT
ejpam-4945	128	1	as	as	ADP
ejpam-4945	128	2	in	in	ADP
ejpam-4945	128	3	the	the	DET
ejpam-4945	128	4	proof	proof	NOUN
ejpam-4945	128	5	of	of	ADP
ejpam-4945	128	6	theorem	theorem	NOUN
ejpam-4945	128	7	1	1	NUM
ejpam-4945	128	8	,	,	PUNCT
ejpam-4945	128	9	we	we	PRON
ejpam-4945	128	10	arrive	arrive	VERB
ejpam-4945	128	11	at	at	ADP
ejpam-4945	128	12	(	(	PUNCT
ejpam-4945	128	13	10	10	NUM
ejpam-4945	128	14	)	)	PUNCT
ejpam-4945	128	15	.	.	PUNCT
ejpam-4945	129	1	from	from	ADP
ejpam-4945	129	2	lemma	lemma	PROPN
ejpam-4945	129	3	1	1	NUM
ejpam-4945	129	4	with	with	ADP
ejpam-4945	129	5	ξ	ξ	PROPN
ejpam-4945	129	6	=	=	PUNCT
ejpam-4945	129	7	w′	w′	NOUN
ejpam-4945	129	8	,	,	PUNCT
ejpam-4945	129	9	there	there	PRON
ejpam-4945	129	10	exists	exist	VERB
ejpam-4945	129	11	a	a	DET
ejpam-4945	129	12	j	j	PROPN
ejpam-4945	129	13	>	>	X
ejpam-4945	129	14	0	0	PUNCT
ejpam-4945	130	1	and	and	CCONJ
ejpam-4945	130	2	z	z	NOUN
ejpam-4945	130	3	(	(	PUNCT
ejpam-4945	130	4	ι	ι	NOUN
ejpam-4945	130	5	)	)	PUNCT
ejpam-4945	130	6	≤	≤	NOUN
ejpam-4945	131	1	ι	ι	ADP
ejpam-4945	131	2	such	such	ADJ
ejpam-4945	131	3	that	that	PRON
ejpam-4945	131	4	w′	w′	PROPN
ejpam-4945	131	5	(	(	PUNCT
ejpam-4945	131	6	νz	νz	PROPN
ejpam-4945	131	7	(	(	PUNCT
ejpam-4945	131	8	ι	ι	NOUN
ejpam-4945	131	9	)	)	PUNCT
ejpam-4945	131	10	)	)	PUNCT
ejpam-4945	131	11	≥	≥	NOUN
ejpam-4945	131	12	jzβ−2	jzβ−2	X
ejpam-4945	131	13	(	(	PUNCT
ejpam-4945	131	14	ι)w(β−1	ι)w(β−1	PROPN
ejpam-4945	131	15	)	)	PUNCT
ejpam-4945	131	16	(	(	PUNCT
ejpam-4945	131	17	z	z	NOUN
ejpam-4945	131	18	(	(	PUNCT
ejpam-4945	131	19	ι	ι	NOUN
ejpam-4945	131	20	)	)	PUNCT
ejpam-4945	131	21	)	)	PUNCT
ejpam-4945	131	22	≥	≥	NOUN
ejpam-4945	131	23	jzβ−2	jzβ−2	X
ejpam-4945	131	24	(	(	PUNCT
ejpam-4945	131	25	ι)w(β−1	ι)w(β−1	PROPN
ejpam-4945	131	26	)	)	PUNCT
ejpam-4945	131	27	(	(	PUNCT
ejpam-4945	131	28	ι	ι	NOUN
ejpam-4945	131	29	)	)	PUNCT
ejpam-4945	131	30	.	.	PUNCT
ejpam-4945	132	1	(	(	PUNCT
ejpam-4945	132	2	12	12	NUM
ejpam-4945	132	3	)	)	PUNCT
ejpam-4945	132	4	define	define	NOUN
ejpam-4945	132	5	ψ	ψ	X
ejpam-4945	132	6	(	(	PUNCT
ejpam-4945	132	7	ι	ι	NOUN
ejpam-4945	132	8	)	)	PUNCT
ejpam-4945	132	9	:	:	PUNCT
ejpam-4945	133	1	=	=	SYM
ejpam-4945	133	2	ℏ	ℏ	PROPN
ejpam-4945	133	3	(	(	PUNCT
ejpam-4945	133	4	ι	ι	PROPN
ejpam-4945	133	5	)	)	PUNCT
ejpam-4945	133	6	a	a	PRON
ejpam-4945	133	7	(	(	PUNCT
ejpam-4945	133	8	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	133	9	)	)	PUNCT
ejpam-4945	133	10	(	(	PUNCT
ejpam-4945	133	11	ι	ι	X
ejpam-4945	133	12	)	)	PUNCT
ejpam-4945	133	13	w	w	NOUN
ejpam-4945	133	14	(	(	PUNCT
ejpam-4945	133	15	νz	νz	PROPN
ejpam-4945	133	16	(	(	PUNCT
ejpam-4945	133	17	ι	ι	NOUN
ejpam-4945	133	18	)	)	PUNCT
ejpam-4945	133	19	)	)	PUNCT
ejpam-4945	133	20	>	>	X
ejpam-4945	133	21	0	0	NUM
ejpam-4945	133	22	,	,	PUNCT
ejpam-4945	133	23	we	we	PRON
ejpam-4945	133	24	have	have	VERB
ejpam-4945	133	25	ψ′	ψ′	NUM
ejpam-4945	133	26	(	(	PUNCT
ejpam-4945	133	27	ι	ι	X
ejpam-4945	133	28	)	)	PUNCT
ejpam-4945	133	29	=	=	SYM
ejpam-4945	133	30	ℏ′	ℏ′	X
ejpam-4945	133	31	(	(	PUNCT
ejpam-4945	133	32	ι	ι	NOUN
ejpam-4945	133	33	)	)	PUNCT
ejpam-4945	133	34	ℏ	ℏ	PROPN
ejpam-4945	133	35	(	(	PUNCT
ejpam-4945	133	36	ι	ι	NOUN
ejpam-4945	133	37	)	)	PUNCT
ejpam-4945	133	38	ψ	ψ	NOUN
ejpam-4945	133	39	(	(	PUNCT
ejpam-4945	133	40	ι	ι	PROPN
ejpam-4945	133	41	)	)	PUNCT
ejpam-4945	133	42	+	+	CCONJ
ejpam-4945	133	43	ℏ	ℏ	PROPN
ejpam-4945	133	44	(	(	PUNCT
ejpam-4945	133	45	ι	ι	PROPN
ejpam-4945	133	46	)	)	PUNCT
ejpam-4945	133	47	(	(	PUNCT
ejpam-4945	133	48	a	a	DET
ejpam-4945	133	49	(	(	PUNCT
ejpam-4945	133	50	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	133	51	)	)	PUNCT
ejpam-4945	133	52	(	(	PUNCT
ejpam-4945	133	53	ι	ι	NOUN
ejpam-4945	133	54	)	)	PUNCT
ejpam-4945	133	55	)	)	PUNCT
ejpam-4945	134	1	′	′	NUM
ejpam-4945	135	1	w	w	NOUN
ejpam-4945	135	2	(	(	PUNCT
ejpam-4945	135	3	νz	νz	PROPN
ejpam-4945	135	4	(	(	PUNCT
ejpam-4945	135	5	ι	ι	NOUN
ejpam-4945	135	6	)	)	PUNCT
ejpam-4945	135	7	)	)	PUNCT
ejpam-4945	136	1	−	−	PROPN
ejpam-4945	136	2	νℏ	νℏ	PROPN
ejpam-4945	136	3	(	(	PUNCT
ejpam-4945	136	4	ι	ι	PROPN
ejpam-4945	136	5	)	)	PUNCT
ejpam-4945	136	6	a	a	DET
ejpam-4945	136	7	(	(	PUNCT
ejpam-4945	136	8	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	136	9	)	)	PUNCT
ejpam-4945	136	10	(	(	PUNCT
ejpam-4945	136	11	ι)w′	ι)w′	PROPN
ejpam-4945	136	12	(	(	PUNCT
ejpam-4945	136	13	νz	νz	PROPN
ejpam-4945	136	14	(	(	PUNCT
ejpam-4945	136	15	ι	ι	NOUN
ejpam-4945	136	16	)	)	PUNCT
ejpam-4945	136	17	)	)	PUNCT
ejpam-4945	137	1	z′	z′	NUM
ejpam-4945	137	2	(	(	PUNCT
ejpam-4945	137	3	ι	ι	NOUN
ejpam-4945	137	4	)	)	PUNCT
ejpam-4945	137	5	(	(	PUNCT
ejpam-4945	137	6	w	w	NOUN
ejpam-4945	137	7	(	(	PUNCT
ejpam-4945	137	8	νz	νz	PROPN
ejpam-4945	137	9	(	(	PUNCT
ejpam-4945	137	10	ι)))2	ι)))2	NOUN
ejpam-4945	137	11	.	.	PUNCT
ejpam-4945	138	1	from	from	ADP
ejpam-4945	138	2	(	(	PUNCT
ejpam-4945	138	3	10	10	NUM
ejpam-4945	138	4	)	)	PUNCT
ejpam-4945	138	5	,	,	PUNCT
ejpam-4945	138	6	we	we	PRON
ejpam-4945	138	7	obtain	obtain	VERB
ejpam-4945	138	8	ψ′	ψ′	NUM
ejpam-4945	138	9	(	(	PUNCT
ejpam-4945	138	10	ι	ι	NOUN
ejpam-4945	138	11	)	)	PUNCT
ejpam-4945	138	12	≤	≤	NOUN
ejpam-4945	138	13	ℏ′	ℏ′	X
ejpam-4945	138	14	(	(	PUNCT
ejpam-4945	138	15	ι	ι	NOUN
ejpam-4945	138	16	)	)	PUNCT
ejpam-4945	138	17	ℏ	ℏ	PROPN
ejpam-4945	138	18	(	(	PUNCT
ejpam-4945	138	19	ι	ι	NOUN
ejpam-4945	138	20	)	)	PUNCT
ejpam-4945	138	21	ψ	ψ	NOUN
ejpam-4945	138	22	(	(	PUNCT
ejpam-4945	138	23	ι)−	ι)−	PROPN
ejpam-4945	138	24	ℏ	ℏ	PROPN
ejpam-4945	138	25	(	(	PUNCT
ejpam-4945	138	26	ι)k	ι)k	X
ejpam-4945	138	27	(	(	PUNCT
ejpam-4945	138	28	ι)−	ι)−	PROPN
ejpam-4945	138	29	ν	ν	PROPN
ejpam-4945	138	30	w′	w′	PROPN
ejpam-4945	138	31	(	(	PUNCT
ejpam-4945	138	32	z	z	NOUN
ejpam-4945	138	33	(	(	PUNCT
ejpam-4945	138	34	ι	ι	NOUN
ejpam-4945	138	35	)	)	PUNCT
ejpam-4945	138	36	)	)	PUNCT
ejpam-4945	139	1	z′	z′	NUM
ejpam-4945	139	2	(	(	PUNCT
ejpam-4945	139	3	ι	ι	PROPN
ejpam-4945	139	4	)	)	PUNCT
ejpam-4945	139	5	w	w	NOUN
ejpam-4945	139	6	(	(	PUNCT
ejpam-4945	139	7	νz	νz	PROPN
ejpam-4945	139	8	(	(	PUNCT
ejpam-4945	139	9	ι	ι	NOUN
ejpam-4945	139	10	)	)	PUNCT
ejpam-4945	139	11	)	)	PUNCT
ejpam-4945	140	1	ψ	ψ	X
ejpam-4945	140	2	(	(	PUNCT
ejpam-4945	140	3	ι	ι	NOUN
ejpam-4945	140	4	)	)	PUNCT
ejpam-4945	140	5	.	.	PUNCT
ejpam-4945	141	1	by	by	ADP
ejpam-4945	141	2	using	use	VERB
ejpam-4945	141	3	(	(	PUNCT
ejpam-4945	141	4	12	12	NUM
ejpam-4945	141	5	)	)	PUNCT
ejpam-4945	141	6	,	,	PUNCT
ejpam-4945	141	7	we	we	PRON
ejpam-4945	141	8	have	have	VERB
ejpam-4945	141	9	ψ′	ψ′	NUM
ejpam-4945	141	10	(	(	PUNCT
ejpam-4945	141	11	ι	ι	NOUN
ejpam-4945	141	12	)	)	PUNCT
ejpam-4945	141	13	≤	≤	NOUN
ejpam-4945	141	14	ℏ′	ℏ′	X
ejpam-4945	141	15	(	(	PUNCT
ejpam-4945	141	16	ι	ι	NOUN
ejpam-4945	141	17	)	)	PUNCT
ejpam-4945	141	18	ℏ	ℏ	PROPN
ejpam-4945	141	19	(	(	PUNCT
ejpam-4945	141	20	ι	ι	NOUN
ejpam-4945	141	21	)	)	PUNCT
ejpam-4945	141	22	ψ	ψ	NOUN
ejpam-4945	141	23	(	(	PUNCT
ejpam-4945	141	24	ι)−	ι)−	PROPN
ejpam-4945	141	25	ℏ	ℏ	PROPN
ejpam-4945	141	26	(	(	PUNCT
ejpam-4945	141	27	ι)k	ι)k	X
ejpam-4945	141	28	(	(	PUNCT
ejpam-4945	141	29	ι)−	ι)−	PROPN
ejpam-4945	141	30	ν	ν	X
ejpam-4945	141	31	jzβ−2	jzβ−2	PROPN
ejpam-4945	141	32	(	(	PUNCT
ejpam-4945	141	33	ι)w(β−1	ι)w(β−1	PROPN
ejpam-4945	141	34	)	)	PUNCT
ejpam-4945	141	35	(	(	PUNCT
ejpam-4945	141	36	ι	ι	X
ejpam-4945	141	37	)	)	PUNCT
ejpam-4945	141	38	z′	z′	NUM
ejpam-4945	141	39	(	(	PUNCT
ejpam-4945	141	40	ι	ι	PROPN
ejpam-4945	141	41	)	)	PUNCT
ejpam-4945	141	42	w	w	NOUN
ejpam-4945	141	43	(	(	PUNCT
ejpam-4945	141	44	νz	νz	PROPN
ejpam-4945	141	45	(	(	PUNCT
ejpam-4945	141	46	ι	ι	NOUN
ejpam-4945	141	47	)	)	PUNCT
ejpam-4945	141	48	)	)	PUNCT
ejpam-4945	142	1	ψ	ψ	X
ejpam-4945	142	2	(	(	PUNCT
ejpam-4945	142	3	ι	ι	NOUN
ejpam-4945	142	4	)	)	PUNCT
ejpam-4945	142	5	≤	≤	NOUN
ejpam-4945	142	6	ℏ′	ℏ′	X
ejpam-4945	142	7	(	(	PUNCT
ejpam-4945	142	8	ι	ι	NOUN
ejpam-4945	142	9	)	)	PUNCT
ejpam-4945	142	10	ℏ	ℏ	PROPN
ejpam-4945	142	11	(	(	PUNCT
ejpam-4945	142	12	ι	ι	NOUN
ejpam-4945	142	13	)	)	PUNCT
ejpam-4945	142	14	ψ	ψ	NOUN
ejpam-4945	142	15	(	(	PUNCT
ejpam-4945	142	16	ι)−	ι)−	PROPN
ejpam-4945	142	17	ℏ	ℏ	PROPN
ejpam-4945	142	18	(	(	PUNCT
ejpam-4945	142	19	ι)k	ι)k	X
ejpam-4945	142	20	(	(	PUNCT
ejpam-4945	142	21	ι)−	ι)−	PROPN
ejpam-4945	142	22	ν	ν	X
ejpam-4945	142	23	jzβ−2	jzβ−2	PROPN
ejpam-4945	142	24	(	(	PUNCT
ejpam-4945	142	25	ι	ι	PROPN
ejpam-4945	142	26	)	)	PUNCT
ejpam-4945	142	27	z′	z′	NUM
ejpam-4945	142	28	(	(	PUNCT
ejpam-4945	142	29	ι	ι	PROPN
ejpam-4945	142	30	)	)	PUNCT
ejpam-4945	142	31	a	a	PRON
ejpam-4945	142	32	(	(	PUNCT
ejpam-4945	142	33	ι	ι	NOUN
ejpam-4945	142	34	)	)	PUNCT
ejpam-4945	142	35	ℏ	ℏ	PROPN
ejpam-4945	142	36	(	(	PUNCT
ejpam-4945	142	37	ι	ι	NOUN
ejpam-4945	142	38	)	)	PUNCT
ejpam-4945	142	39	ℏ	ℏ	PROPN
ejpam-4945	142	40	(	(	PUNCT
ejpam-4945	142	41	ι	ι	PROPN
ejpam-4945	142	42	)	)	PUNCT
ejpam-4945	142	43	a	a	DET
ejpam-4945	142	44	(	(	PUNCT
ejpam-4945	142	45	ι)w(β−1	ι)w(β−1	NOUN
ejpam-4945	142	46	)	)	PUNCT
ejpam-4945	142	47	(	(	PUNCT
ejpam-4945	142	48	ι	ι	X
ejpam-4945	142	49	)	)	PUNCT
ejpam-4945	142	50	w	w	NOUN
ejpam-4945	142	51	(	(	PUNCT
ejpam-4945	142	52	νz	νz	PROPN
ejpam-4945	142	53	(	(	PUNCT
ejpam-4945	142	54	ι	ι	NOUN
ejpam-4945	142	55	)	)	PUNCT
ejpam-4945	142	56	)	)	PUNCT
ejpam-4945	143	1	ψ	ψ	X
ejpam-4945	143	2	(	(	PUNCT
ejpam-4945	143	3	ι	ι	NOUN
ejpam-4945	143	4	)	)	PUNCT
ejpam-4945	143	5	≤	≤	NOUN
ejpam-4945	143	6	ℏ′	ℏ′	X
ejpam-4945	143	7	(	(	PUNCT
ejpam-4945	143	8	ι	ι	NOUN
ejpam-4945	143	9	)	)	PUNCT
ejpam-4945	143	10	ℏ	ℏ	PROPN
ejpam-4945	143	11	(	(	PUNCT
ejpam-4945	143	12	ι	ι	NOUN
ejpam-4945	143	13	)	)	PUNCT
ejpam-4945	143	14	ψ	ψ	NOUN
ejpam-4945	143	15	(	(	PUNCT
ejpam-4945	143	16	ι)−	ι)−	PROPN
ejpam-4945	143	17	ℏ	ℏ	PROPN
ejpam-4945	143	18	(	(	PUNCT
ejpam-4945	143	19	ι)k	ι)k	X
ejpam-4945	143	20	(	(	PUNCT
ejpam-4945	143	21	ι)−	ι)−	PROPN
ejpam-4945	143	22	ν	ν	X
ejpam-4945	143	23	b	b	PROPN
ejpam-4945	143	24	(	(	PUNCT
ejpam-4945	143	25	ι	ι	NOUN
ejpam-4945	143	26	)	)	PUNCT
ejpam-4945	143	27	ψ2	ψ2	NOUN
ejpam-4945	143	28	(	(	PUNCT
ejpam-4945	143	29	ι	ι	NOUN
ejpam-4945	143	30	)	)	PUNCT
ejpam-4945	143	31	.	.	PUNCT
ejpam-4945	144	1	(	(	PUNCT
ejpam-4945	144	2	13	13	NUM
ejpam-4945	144	3	)	)	PUNCT
ejpam-4945	144	4	using	use	VERB
ejpam-4945	144	5	the	the	DET
ejpam-4945	144	6	inequality	inequality	NOUN
ejpam-4945	144	7	ξw	ξw	ADP
ejpam-4945	144	8	−	−	PROPN
ejpam-4945	144	9	uw	uw	PROPN
ejpam-4945	144	10	a+1	a+1	PROPN
ejpam-4945	144	11	a	a	DET
ejpam-4945	144	12	≤	≤	NUM
ejpam-4945	144	13	aa	aa	NOUN
ejpam-4945	144	14	(	(	PUNCT
ejpam-4945	144	15	a+	a+	SYM
ejpam-4945	144	16	1)a+1	1)a+1	NUM
ejpam-4945	144	17	ξa+1	ξa+1	PROPN
ejpam-4945	144	18	ua	ua	PROPN
ejpam-4945	144	19	,	,	PUNCT
ejpam-4945	144	20	with	with	ADP
ejpam-4945	144	21	ξ	ξ	PROPN
ejpam-4945	144	22	=	=	PUNCT
ejpam-4945	144	23	ℏ′/ℏ	ℏ′/ℏ	X
ejpam-4945	144	24	,	,	PUNCT
ejpam-4945	144	25	u	u	NOUN
ejpam-4945	144	26	=	=	VERB
ejpam-4945	144	27	νjzβ−2	νjzβ−2	PROPN
ejpam-4945	144	28	(	(	PUNCT
ejpam-4945	144	29	ι	ι	NOUN
ejpam-4945	144	30	)	)	PUNCT
ejpam-4945	144	31	z′	z′	NUM
ejpam-4945	144	32	(	(	PUNCT
ejpam-4945	144	33	ι	ι	PROPN
ejpam-4945	144	34	)	)	PUNCT
ejpam-4945	144	35	/	/	PUNCT
ejpam-4945	144	36	(	(	PUNCT
ejpam-4945	144	37	a	a	PRON
ejpam-4945	144	38	(	(	PUNCT
ejpam-4945	144	39	ι	ι	NOUN
ejpam-4945	144	40	)	)	PUNCT
ejpam-4945	144	41	ℏ	ℏ	PROPN
ejpam-4945	144	42	(	(	PUNCT
ejpam-4945	144	43	ι	ι	NOUN
ejpam-4945	144	44	)	)	PUNCT
ejpam-4945	144	45	)	)	PUNCT
ejpam-4945	144	46	and	and	CCONJ
ejpam-4945	144	47	w	w	NOUN
ejpam-4945	144	48	=	=	SYM
ejpam-4945	144	49	ψ	ψ	X
ejpam-4945	144	50	(	(	PUNCT
ejpam-4945	144	51	ι	ι	PROPN
ejpam-4945	144	52	)	)	PUNCT
ejpam-4945	144	53	,	,	PUNCT
ejpam-4945	144	54	we	we	PRON
ejpam-4945	144	55	find	find	VERB
ejpam-4945	144	56	ψ′	ψ′	NUM
ejpam-4945	144	57	(	(	PUNCT
ejpam-4945	144	58	ι	ι	NOUN
ejpam-4945	144	59	)	)	PUNCT
ejpam-4945	144	60	≤	≤	NOUN
ejpam-4945	145	1	−ℏ	−ℏ	ADV
ejpam-4945	145	2	(	(	PUNCT
ejpam-4945	145	3	ι)k	ι)k	X
ejpam-4945	145	4	(	(	PUNCT
ejpam-4945	145	5	ι	ι	X
ejpam-4945	145	6	)	)	PUNCT
ejpam-4945	145	7	+	+	CCONJ
ejpam-4945	145	8	1	1	NUM
ejpam-4945	145	9	4ν	4ν	NUM
ejpam-4945	145	10	(	(	PUNCT
ejpam-4945	145	11	ℏ′	ℏ′	X
ejpam-4945	145	12	(	(	PUNCT
ejpam-4945	145	13	ι	ι	NOUN
ejpam-4945	145	14	)	)	PUNCT
ejpam-4945	145	15	ℏ	ℏ	PROPN
ejpam-4945	145	16	(	(	PUNCT
ejpam-4945	145	17	ι	ι	NOUN
ejpam-4945	145	18	)	)	PUNCT
ejpam-4945	145	19	)	)	PUNCT
ejpam-4945	145	20	2	2	NUM
ejpam-4945	145	21	a	a	DET
ejpam-4945	145	22	(	(	PUNCT
ejpam-4945	145	23	ι	ι	NOUN
ejpam-4945	145	24	)	)	PUNCT
ejpam-4945	145	25	ℏ	ℏ	PROPN
ejpam-4945	145	26	(	(	PUNCT
ejpam-4945	145	27	ι	ι	NOUN
ejpam-4945	145	28	)	)	PUNCT
ejpam-4945	145	29	jzβ−2	jzβ−2	PROPN
ejpam-4945	145	30	(	(	PUNCT
ejpam-4945	145	31	ι	ι	PROPN
ejpam-4945	145	32	)	)	PUNCT
ejpam-4945	145	33	z′	z′	NUM
ejpam-4945	145	34	(	(	PUNCT
ejpam-4945	145	35	ι	ι	PROPN
ejpam-4945	145	36	)	)	PUNCT
ejpam-4945	145	37	.	.	PUNCT
ejpam-4945	146	1	(	(	PUNCT
ejpam-4945	146	2	14	14	NUM
ejpam-4945	146	3	)	)	PUNCT
ejpam-4945	146	4	a.	a.	NOUN
ejpam-4945	146	5	almutairi	almutairi	PROPN
ejpam-4945	146	6	/	/	SYM
ejpam-4945	146	7	eur	eur	PROPN
ejpam-4945	146	8	.	.	PUNCT
ejpam-4945	147	1	j.	j.	PROPN
ejpam-4945	147	2	pure	pure	PROPN
ejpam-4945	147	3	appl	appl	PROPN
ejpam-4945	147	4	.	.	PROPN
ejpam-4945	147	5	math	math	PROPN
ejpam-4945	147	6	,	,	PUNCT
ejpam-4945	147	7	16	16	NUM
ejpam-4945	147	8	(	(	PUNCT
ejpam-4945	147	9	4	4	NUM
ejpam-4945	147	10	)	)	PUNCT
ejpam-4945	147	11	(	(	PUNCT
ejpam-4945	147	12	2023	2023	NUM
ejpam-4945	147	13	)	)	PUNCT
ejpam-4945	147	14	,	,	PUNCT
ejpam-4945	147	15	2499	2499	NUM
ejpam-4945	147	16	-	-	SYM
ejpam-4945	147	17	2508	2508	NUM
ejpam-4945	147	18	2505	2505	NUM
ejpam-4945	147	19	integrating	integrating	NOUN
ejpam-4945	147	20	(	(	PUNCT
ejpam-4945	147	21	14	14	NUM
ejpam-4945	147	22	)	)	PUNCT
ejpam-4945	147	23	from	from	ADP
ejpam-4945	147	24	ι1	ι1	PROPN
ejpam-4945	147	25	to	to	ADP
ejpam-4945	147	26	ι	ι	PROPN
ejpam-4945	148	1	we	we	PRON
ejpam-4945	148	2	find∫	find∫	VERB
ejpam-4945	148	3	ι	ι	PRON
ejpam-4945	149	1	ι1	ι1	NOUN
ejpam-4945	149	2	(	(	PUNCT
ejpam-4945	149	3	ℏ	ℏ	PROPN
ejpam-4945	149	4	(	(	PUNCT
ejpam-4945	149	5	u)k	u)k	X
ejpam-4945	149	6	(	(	PUNCT
ejpam-4945	149	7	u)−	u)−	PROPN
ejpam-4945	149	8	1	1	NUM
ejpam-4945	149	9	4ν	4ν	NOUN
ejpam-4945	149	10	(	(	PUNCT
ejpam-4945	149	11	ℏ′	ℏ′	X
ejpam-4945	149	12	(	(	PUNCT
ejpam-4945	149	13	u	u	NOUN
ejpam-4945	149	14	)	)	PUNCT
ejpam-4945	149	15	ℏ	ℏ	PROPN
ejpam-4945	149	16	(	(	PUNCT
ejpam-4945	149	17	u	u	NOUN
ejpam-4945	149	18	)	)	PUNCT
ejpam-4945	149	19	)	)	PUNCT
ejpam-4945	149	20	2	2	NUM
ejpam-4945	149	21	b	b	X
ejpam-4945	149	22	(	(	PUNCT
ejpam-4945	149	23	u	u	NOUN
ejpam-4945	149	24	)	)	PUNCT
ejpam-4945	149	25	)	)	PUNCT
ejpam-4945	149	26	du	du	PROPN
ejpam-4945	149	27	≤	≤	PROPN
ejpam-4945	149	28	ψ	ψ	X
ejpam-4945	149	29	(	(	PUNCT
ejpam-4945	149	30	ι1)−	ι1)−	NOUN
ejpam-4945	149	31	ψ	ψ	X
ejpam-4945	149	32	(	(	PUNCT
ejpam-4945	149	33	ι	ι	NOUN
ejpam-4945	149	34	)	)	PUNCT
ejpam-4945	149	35	≤	≤	NOUN
ejpam-4945	150	1	ψ	ψ	X
ejpam-4945	150	2	(	(	PUNCT
ejpam-4945	150	3	ι1	ι1	NOUN
ejpam-4945	150	4	)	)	PUNCT
ejpam-4945	150	5	,	,	PUNCT
ejpam-4945	150	6	which	which	PRON
ejpam-4945	150	7	contradicts	contradict	VERB
ejpam-4945	150	8	(	(	PUNCT
ejpam-4945	150	9	11	11	NUM
ejpam-4945	150	10	)	)	PUNCT
ejpam-4945	150	11	.	.	PUNCT
ejpam-4945	151	1	this	this	PRON
ejpam-4945	151	2	completes	complete	VERB
ejpam-4945	151	3	the	the	DET
ejpam-4945	151	4	proof	proof	NOUN
ejpam-4945	151	5	.	.	PUNCT
ejpam-4945	152	1	theorem	theorem	NOUN
ejpam-4945	152	2	3	3	X
ejpam-4945	152	3	.	.	PUNCT
ejpam-4945	153	1	if	if	SCONJ
ejpam-4945	153	2	ℏ	ℏ	PROPN
ejpam-4945	153	3	∈	∈	PROPN
ejpam-4945	153	4	c1	c1	NOUN
ejpam-4945	153	5	(	(	PUNCT
ejpam-4945	153	6	[	[	X
ejpam-4945	153	7	ι0,∞	ι0,∞	NOUN
ejpam-4945	153	8	)	)	PUNCT
ejpam-4945	153	9	,	,	PUNCT
ejpam-4945	153	10	r+	r+	X
ejpam-4945	153	11	)	)	PUNCT
ejpam-4945	153	12	such	such	ADJ
ejpam-4945	153	13	that	that	SCONJ
ejpam-4945	153	14	lim	lim	PROPN
ejpam-4945	153	15	sup	sup	PROPN
ejpam-4945	153	16	ι→∞	ι→∞	NUM
ejpam-4945	153	17	1	1	NUM
ejpam-4945	153	18	w	w	NOUN
ejpam-4945	153	19	(	(	PUNCT
ejpam-4945	153	20	ι	ι	PROPN
ejpam-4945	153	21	,	,	PUNCT
ejpam-4945	153	22	ι0	ι0	NOUN
ejpam-4945	153	23	)	)	PUNCT
ejpam-4945	153	24	∫	∫	PROPN
ejpam-4945	153	25	ι	ι	PROPN
ejpam-4945	153	26	ι0	ι0	NOUN
ejpam-4945	153	27	w	w	PROPN
ejpam-4945	153	28	(	(	PUNCT
ejpam-4945	153	29	ι	ι	PROPN
ejpam-4945	153	30	,	,	PUNCT
ejpam-4945	153	31	u	u	NOUN
ejpam-4945	153	32	)	)	PUNCT
ejpam-4945	153	33	(	(	PUNCT
ejpam-4945	153	34	ℏ	ℏ	PROPN
ejpam-4945	153	35	(	(	PUNCT
ejpam-4945	153	36	u)k	u)k	X
ejpam-4945	153	37	(	(	PUNCT
ejpam-4945	153	38	u)−	u)−	PROPN
ejpam-4945	153	39	1	1	NUM
ejpam-4945	153	40	4ν	4ν	NUM
ejpam-4945	153	41	b	b	X
ejpam-4945	153	42	(	(	PUNCT
ejpam-4945	153	43	u	u	NOUN
ejpam-4945	153	44	)	)	PUNCT
ejpam-4945	153	45	ς2	ς2	PROPN
ejpam-4945	153	46	(	(	PUNCT
ejpam-4945	153	47	ι	ι	PROPN
ejpam-4945	153	48	,	,	PUNCT
ejpam-4945	153	49	u	u	NOUN
ejpam-4945	153	50	)	)	PUNCT
ejpam-4945	153	51	)	)	PUNCT
ejpam-4945	153	52	du	du	PROPN
ejpam-4945	153	53	=	=	SYM
ejpam-4945	153	54	∞	∞	PROPN
ejpam-4945	153	55	,	,	PUNCT
ejpam-4945	153	56	(	(	PUNCT
ejpam-4945	153	57	15	15	NUM
ejpam-4945	153	58	)	)	PUNCT
ejpam-4945	153	59	where	where	SCONJ
ejpam-4945	153	60	ς	ς	PROPN
ejpam-4945	153	61	(	(	PUNCT
ejpam-4945	153	62	ι	ι	PROPN
ejpam-4945	153	63	,	,	PUNCT
ejpam-4945	153	64	s	s	NOUN
ejpam-4945	153	65	)	)	PUNCT
ejpam-4945	153	66	=	=	SYM
ejpam-4945	153	67	ℏ′	ℏ′	X
ejpam-4945	153	68	(	(	PUNCT
ejpam-4945	153	69	s	s	NOUN
ejpam-4945	153	70	)	)	PUNCT
ejpam-4945	153	71	ℏ	ℏ	PROPN
ejpam-4945	153	72	(	(	PUNCT
ejpam-4945	153	73	s	s	NOUN
ejpam-4945	153	74	)	)	PUNCT
ejpam-4945	153	75	−	−	PROPN
ejpam-4945	153	76	g	g	PROPN
ejpam-4945	153	77	(	(	PUNCT
ejpam-4945	153	78	ι	ι	PROPN
ejpam-4945	153	79	,	,	PUNCT
ejpam-4945	153	80	s)√	s)√	PROPN
ejpam-4945	153	81	w	w	PROPN
ejpam-4945	153	82	(	(	PUNCT
ejpam-4945	153	83	ι	ι	PROPN
ejpam-4945	153	84	,	,	PUNCT
ejpam-4945	153	85	s	s	NOUN
ejpam-4945	153	86	)	)	PUNCT
ejpam-4945	153	87	,	,	PUNCT
ejpam-4945	153	88	then	then	ADV
ejpam-4945	153	89	eq.(1	eq.(1	NUM
ejpam-4945	153	90	)	)	PUNCT
ejpam-4945	153	91	is	be	AUX
ejpam-4945	153	92	oscillatory	oscillatory	ADJ
ejpam-4945	153	93	.	.	PUNCT
ejpam-4945	154	1	proof	proof	NOUN
ejpam-4945	154	2	.	.	PUNCT
ejpam-4945	155	1	multiplying	multiply	VERB
ejpam-4945	155	2	(	(	PUNCT
ejpam-4945	155	3	13	13	NUM
ejpam-4945	155	4	)	)	PUNCT
ejpam-4945	155	5	by	by	ADP
ejpam-4945	155	6	w	w	PROPN
ejpam-4945	155	7	(	(	PUNCT
ejpam-4945	155	8	ι	ι	PROPN
ejpam-4945	155	9	,	,	PUNCT
ejpam-4945	155	10	s	s	PART
ejpam-4945	155	11	)	)	PUNCT
ejpam-4945	155	12	and	and	CCONJ
ejpam-4945	155	13	integrating	integrate	VERB
ejpam-4945	155	14	both	both	DET
ejpam-4945	155	15	sides	side	NOUN
ejpam-4945	155	16	from	from	ADP
ejpam-4945	155	17	ι2	ι2	PROPN
ejpam-4945	155	18	to	to	ADP
ejpam-4945	155	19	ι	ι	PRON
ejpam-4945	155	20	,	,	PUNCT
ejpam-4945	155	21	we	we	PRON
ejpam-4945	155	22	obtain∫	obtain∫	VERB
ejpam-4945	155	23	ι	ι	ADP
ejpam-4945	155	24	ι2	ι2	PROPN
ejpam-4945	155	25	w	w	PROPN
ejpam-4945	155	26	(	(	PUNCT
ejpam-4945	155	27	ι	ι	PROPN
ejpam-4945	155	28	,	,	PUNCT
ejpam-4945	155	29	u	u	NOUN
ejpam-4945	155	30	)	)	PUNCT
ejpam-4945	155	31	ℏ	ℏ	PROPN
ejpam-4945	155	32	(	(	PUNCT
ejpam-4945	155	33	u)k	u)k	X
ejpam-4945	155	34	(	(	PUNCT
ejpam-4945	155	35	u	u	NOUN
ejpam-4945	155	36	)	)	PUNCT
ejpam-4945	155	37	du	du	PROPN
ejpam-4945	155	38	≤	≤	PROPN
ejpam-4945	156	1	−	−	PROPN
ejpam-4945	157	1	∫	∫	PROPN
ejpam-4945	158	1	ι	ι	PROPN
ejpam-4945	159	1	ι2	ι2	PROPN
ejpam-4945	159	2	w	w	PROPN
ejpam-4945	159	3	(	(	PUNCT
ejpam-4945	159	4	ι	ι	PROPN
ejpam-4945	159	5	,	,	PUNCT
ejpam-4945	159	6	u)ψ′	u)ψ′	NOUN
ejpam-4945	159	7	(	(	PUNCT
ejpam-4945	159	8	u	u	NOUN
ejpam-4945	159	9	)	)	PUNCT
ejpam-4945	159	10	du−	du−	NUM
ejpam-4945	159	11	∫	∫	PROPN
ejpam-4945	159	12	ι	ι	PROPN
ejpam-4945	160	1	ι2	ι2	PROPN
ejpam-4945	160	2	w	w	PROPN
ejpam-4945	160	3	(	(	PUNCT
ejpam-4945	160	4	ι	ι	PROPN
ejpam-4945	160	5	,	,	PUNCT
ejpam-4945	160	6	u	u	NOUN
ejpam-4945	160	7	)	)	PUNCT
ejpam-4945	160	8	ν	ν	X
ejpam-4945	160	9	b	b	PROPN
ejpam-4945	160	10	(	(	PUNCT
ejpam-4945	160	11	u	u	NOUN
ejpam-4945	160	12	)	)	PUNCT
ejpam-4945	160	13	ψ2	ψ2	NOUN
ejpam-4945	160	14	(	(	PUNCT
ejpam-4945	160	15	u	u	NOUN
ejpam-4945	160	16	)	)	PUNCT
ejpam-4945	160	17	du	du	PROPN
ejpam-4945	161	1	+	+	CCONJ
ejpam-4945	161	2	∫	∫	PROPN
ejpam-4945	162	1	ι	ι	X
ejpam-4945	162	2	ι2	ι2	PROPN
ejpam-4945	162	3	w	w	PROPN
ejpam-4945	162	4	(	(	PUNCT
ejpam-4945	162	5	ι	ι	PROPN
ejpam-4945	162	6	,	,	PUNCT
ejpam-4945	162	7	u	u	NOUN
ejpam-4945	162	8	)	)	PUNCT
ejpam-4945	162	9	ℏ′	ℏ′	X
ejpam-4945	162	10	(	(	PUNCT
ejpam-4945	162	11	u	u	NOUN
ejpam-4945	162	12	)	)	PUNCT
ejpam-4945	162	13	ℏ	ℏ	PROPN
ejpam-4945	162	14	(	(	PUNCT
ejpam-4945	162	15	u	u	NOUN
ejpam-4945	162	16	)	)	PUNCT
ejpam-4945	162	17	ψ	ψ	X
ejpam-4945	162	18	(	(	PUNCT
ejpam-4945	162	19	u	u	NOUN
ejpam-4945	162	20	)	)	PUNCT
ejpam-4945	162	21	du	du	PROPN
ejpam-4945	162	22	≤	≤	PROPN
ejpam-4945	162	23	w	w	PROPN
ejpam-4945	162	24	(	(	PUNCT
ejpam-4945	162	25	ι	ι	PROPN
ejpam-4945	162	26	,	,	PUNCT
ejpam-4945	162	27	ι2)ψ	ι2)ψ	PROPN
ejpam-4945	162	28	(	(	PUNCT
ejpam-4945	162	29	ι2)−	ι2)−	ADJ
ejpam-4945	162	30	∫	∫	X
ejpam-4945	162	31	ι	ι	X
ejpam-4945	162	32	ι2	ι2	PROPN
ejpam-4945	162	33	w	w	PROPN
ejpam-4945	162	34	(	(	PUNCT
ejpam-4945	162	35	ι	ι	PROPN
ejpam-4945	162	36	,	,	PUNCT
ejpam-4945	162	37	u	u	NOUN
ejpam-4945	162	38	)	)	PUNCT
ejpam-4945	162	39	ν	ν	X
ejpam-4945	162	40	b	b	PROPN
ejpam-4945	162	41	(	(	PUNCT
ejpam-4945	162	42	u	u	NOUN
ejpam-4945	162	43	)	)	PUNCT
ejpam-4945	162	44	ψ2	ψ2	NOUN
ejpam-4945	162	45	(	(	PUNCT
ejpam-4945	162	46	u	u	NOUN
ejpam-4945	162	47	)	)	PUNCT
ejpam-4945	162	48	du	du	PROPN
ejpam-4945	163	1	+	+	CCONJ
ejpam-4945	163	2	∫	∫	PROPN
ejpam-4945	164	1	ι	ι	X
ejpam-4945	165	1	ι2	ι2	PROPN
ejpam-4945	165	2	w	w	PROPN
ejpam-4945	165	3	(	(	PUNCT
ejpam-4945	165	4	ι	ι	PROPN
ejpam-4945	165	5	,	,	PUNCT
ejpam-4945	165	6	u)ψ	u)ψ	ADJ
ejpam-4945	165	7	(	(	PUNCT
ejpam-4945	165	8	u	u	NOUN
ejpam-4945	165	9	)	)	PUNCT
ejpam-4945	165	10	ς	ς	PROPN
ejpam-4945	165	11	(	(	PUNCT
ejpam-4945	165	12	ι	ι	PROPN
ejpam-4945	165	13	,	,	PUNCT
ejpam-4945	165	14	u	u	NOUN
ejpam-4945	165	15	)	)	PUNCT
ejpam-4945	165	16	du	du	PROPN
ejpam-4945	165	17	which	which	PRON
ejpam-4945	165	18	implies	imply	VERB
ejpam-4945	165	19	that∫	that∫	NOUN
ejpam-4945	165	20	ι	ι	PROPN
ejpam-4945	166	1	ι2	ι2	PROPN
ejpam-4945	166	2	w	w	PROPN
ejpam-4945	166	3	(	(	PUNCT
ejpam-4945	166	4	ι	ι	PROPN
ejpam-4945	166	5	,	,	PUNCT
ejpam-4945	166	6	u	u	NOUN
ejpam-4945	166	7	)	)	PUNCT
ejpam-4945	166	8	ℏ	ℏ	PROPN
ejpam-4945	166	9	(	(	PUNCT
ejpam-4945	166	10	u)k	u)k	X
ejpam-4945	166	11	(	(	PUNCT
ejpam-4945	166	12	u	u	NOUN
ejpam-4945	166	13	)	)	PUNCT
ejpam-4945	166	14	du	du	PROPN
ejpam-4945	166	15	≤	≤	PROPN
ejpam-4945	166	16	w	w	PROPN
ejpam-4945	166	17	(	(	PUNCT
ejpam-4945	166	18	ι	ι	PROPN
ejpam-4945	166	19	,	,	PUNCT
ejpam-4945	166	20	ι2)ψ	ι2)ψ	PROPN
ejpam-4945	166	21	(	(	PUNCT
ejpam-4945	166	22	ι2	ι2	PROPN
ejpam-4945	166	23	)	)	PUNCT
ejpam-4945	166	24	−	−	NUM
ejpam-4945	167	1	∫	∫	PROPN
ejpam-4945	167	2	ι	ι	PROPN
ejpam-4945	168	1	ι2	ι2	PROPN
ejpam-4945	168	2	w	w	PROPN
ejpam-4945	168	3	(	(	PUNCT
ejpam-4945	168	4	ι	ι	PROPN
ejpam-4945	168	5	,	,	PUNCT
ejpam-4945	168	6	u	u	NOUN
ejpam-4945	168	7	)	)	PUNCT
ejpam-4945	168	8	ν	ν	X
ejpam-4945	168	9	b	b	PROPN
ejpam-4945	168	10	(	(	PUNCT
ejpam-4945	168	11	u	u	NOUN
ejpam-4945	168	12	)	)	PUNCT
ejpam-4945	168	13	(	(	PUNCT
ejpam-4945	168	14	ψ2	ψ2	NOUN
ejpam-4945	168	15	(	(	PUNCT
ejpam-4945	168	16	u)−	u)−	PROPN
ejpam-4945	168	17	b	b	PROPN
ejpam-4945	168	18	(	(	PUNCT
ejpam-4945	168	19	u	u	NOUN
ejpam-4945	168	20	)	)	PUNCT
ejpam-4945	168	21	ν	ν	X
ejpam-4945	168	22	ς	ς	PROPN
ejpam-4945	168	23	(	(	PUNCT
ejpam-4945	168	24	ι	ι	PROPN
ejpam-4945	168	25	,	,	PUNCT
ejpam-4945	168	26	u)ψ	u)ψ	ADJ
ejpam-4945	168	27	(	(	PUNCT
ejpam-4945	168	28	u	u	NOUN
ejpam-4945	168	29	)	)	PUNCT
ejpam-4945	168	30	)	)	PUNCT
ejpam-4945	168	31	du	du	PROPN
ejpam-4945	168	32	it	it	PRON
ejpam-4945	168	33	follows	follow	VERB
ejpam-4945	168	34	that	that	SCONJ
ejpam-4945	168	35	1	1	NUM
ejpam-4945	168	36	w	w	PROPN
ejpam-4945	168	37	(	(	PUNCT
ejpam-4945	168	38	ι	ι	PROPN
ejpam-4945	168	39	,	,	PUNCT
ejpam-4945	168	40	ι2	ι2	ADJ
ejpam-4945	168	41	)	)	PUNCT
ejpam-4945	168	42	∫	∫	NOUN
ejpam-4945	168	43	ι	ι	PROPN
ejpam-4945	169	1	ι2	ι2	PROPN
ejpam-4945	169	2	w	w	PROPN
ejpam-4945	169	3	(	(	PUNCT
ejpam-4945	169	4	ι	ι	PROPN
ejpam-4945	169	5	,	,	PUNCT
ejpam-4945	169	6	u	u	NOUN
ejpam-4945	169	7	)	)	PUNCT
ejpam-4945	169	8	(	(	PUNCT
ejpam-4945	169	9	ℏ	ℏ	PROPN
ejpam-4945	169	10	(	(	PUNCT
ejpam-4945	169	11	u)k	u)k	X
ejpam-4945	169	12	(	(	PUNCT
ejpam-4945	169	13	u)−	u)−	PROPN
ejpam-4945	169	14	1	1	NUM
ejpam-4945	169	15	4ν	4ν	NUM
ejpam-4945	169	16	b	b	X
ejpam-4945	169	17	(	(	PUNCT
ejpam-4945	169	18	u	u	NOUN
ejpam-4945	169	19	)	)	PUNCT
ejpam-4945	169	20	ς2	ς2	PROPN
ejpam-4945	169	21	(	(	PUNCT
ejpam-4945	169	22	ι	ι	PROPN
ejpam-4945	169	23	,	,	PUNCT
ejpam-4945	169	24	u	u	NOUN
ejpam-4945	169	25	)	)	PUNCT
ejpam-4945	169	26	)	)	PUNCT
ejpam-4945	170	1	du	du	PROPN
ejpam-4945	170	2	≤	≤	PROPN
ejpam-4945	170	3	ψ	ψ	X
ejpam-4945	170	4	(	(	PUNCT
ejpam-4945	170	5	ι2)−	ι2)−	PROPN
ejpam-4945	170	6	1	1	NUM
ejpam-4945	170	7	w	w	NOUN
ejpam-4945	170	8	(	(	PUNCT
ejpam-4945	170	9	ι	ι	PROPN
ejpam-4945	170	10	,	,	PUNCT
ejpam-4945	170	11	ι2	ι2	ADJ
ejpam-4945	170	12	)	)	PUNCT
ejpam-4945	170	13	∫	∫	NOUN
ejpam-4945	170	14	ι	ι	PROPN
ejpam-4945	171	1	ι2	ι2	PROPN
ejpam-4945	171	2	w	w	PROPN
ejpam-4945	171	3	(	(	PUNCT
ejpam-4945	171	4	ι	ι	PROPN
ejpam-4945	171	5	,	,	PUNCT
ejpam-4945	171	6	u	u	NOUN
ejpam-4945	171	7	)	)	PUNCT
ejpam-4945	171	8	ν	ν	X
ejpam-4945	171	9	b	b	PROPN
ejpam-4945	171	10	(	(	PUNCT
ejpam-4945	171	11	u	u	NOUN
ejpam-4945	171	12	)	)	PUNCT
ejpam-4945	171	13	(	(	PUNCT
ejpam-4945	171	14	ψ	ψ	X
ejpam-4945	171	15	(	(	PUNCT
ejpam-4945	171	16	u)−	u)−	PROPN
ejpam-4945	171	17	1	1	NUM
ejpam-4945	171	18	2ν	2ν	NOUN
ejpam-4945	171	19	b	b	X
ejpam-4945	171	20	(	(	PUNCT
ejpam-4945	171	21	u	u	NOUN
ejpam-4945	171	22	)	)	PUNCT
ejpam-4945	171	23	ς	ς	PROPN
ejpam-4945	171	24	(	(	PUNCT
ejpam-4945	171	25	ι	ι	PROPN
ejpam-4945	171	26	,	,	PUNCT
ejpam-4945	171	27	u	u	NOUN
ejpam-4945	171	28	)	)	PUNCT
ejpam-4945	171	29	)	)	PUNCT
ejpam-4945	171	30	2	2	NUM
ejpam-4945	171	31	du	du	NOUN
ejpam-4945	171	32	,	,	PUNCT
ejpam-4945	171	33	a.	a.	NOUN
ejpam-4945	171	34	almutairi	almutairi	PROPN
ejpam-4945	171	35	/	/	SYM
ejpam-4945	171	36	eur	eur	PROPN
ejpam-4945	171	37	.	.	PUNCT
ejpam-4945	172	1	j.	j.	PROPN
ejpam-4945	172	2	pure	pure	PROPN
ejpam-4945	172	3	appl	appl	PROPN
ejpam-4945	172	4	.	.	PROPN
ejpam-4945	172	5	math	math	PROPN
ejpam-4945	172	6	,	,	PUNCT
ejpam-4945	172	7	16	16	NUM
ejpam-4945	172	8	(	(	PUNCT
ejpam-4945	172	9	4	4	NUM
ejpam-4945	172	10	)	)	PUNCT
ejpam-4945	172	11	(	(	PUNCT
ejpam-4945	172	12	2023	2023	NUM
ejpam-4945	172	13	)	)	PUNCT
ejpam-4945	172	14	,	,	PUNCT
ejpam-4945	172	15	2499	2499	NUM
ejpam-4945	172	16	-	-	SYM
ejpam-4945	172	17	2508	2508	NUM
ejpam-4945	172	18	2506	2506	NUM
ejpam-4945	172	19	which	which	PRON
ejpam-4945	172	20	implies	imply	VERB
ejpam-4945	172	21	lim	lim	PROPN
ejpam-4945	172	22	sup	sup	PROPN
ejpam-4945	172	23	ι→∞	ι→∞	NUM
ejpam-4945	172	24	1	1	NUM
ejpam-4945	172	25	w	w	NOUN
ejpam-4945	172	26	(	(	PUNCT
ejpam-4945	172	27	ι	ι	PROPN
ejpam-4945	172	28	,	,	PUNCT
ejpam-4945	172	29	ι2	ι2	ADJ
ejpam-4945	172	30	)	)	PUNCT
ejpam-4945	172	31	∫	∫	NOUN
ejpam-4945	172	32	ι	ι	PROPN
ejpam-4945	173	1	ι2	ι2	PROPN
ejpam-4945	173	2	w	w	PROPN
ejpam-4945	173	3	(	(	PUNCT
ejpam-4945	173	4	ι	ι	PROPN
ejpam-4945	173	5	,	,	PUNCT
ejpam-4945	173	6	u	u	NOUN
ejpam-4945	173	7	)	)	PUNCT
ejpam-4945	173	8	(	(	PUNCT
ejpam-4945	173	9	ℏ	ℏ	PROPN
ejpam-4945	173	10	(	(	PUNCT
ejpam-4945	173	11	u)k	u)k	X
ejpam-4945	173	12	(	(	PUNCT
ejpam-4945	173	13	u)−	u)−	PROPN
ejpam-4945	173	14	1	1	NUM
ejpam-4945	173	15	4ν	4ν	NUM
ejpam-4945	173	16	b	b	X
ejpam-4945	173	17	(	(	PUNCT
ejpam-4945	173	18	u	u	NOUN
ejpam-4945	173	19	)	)	PUNCT
ejpam-4945	173	20	ς2	ς2	PROPN
ejpam-4945	173	21	(	(	PUNCT
ejpam-4945	173	22	ι	ι	PROPN
ejpam-4945	173	23	,	,	PUNCT
ejpam-4945	173	24	u	u	NOUN
ejpam-4945	173	25	)	)	PUNCT
ejpam-4945	173	26	)	)	PUNCT
ejpam-4945	174	1	du	du	PROPN
ejpam-4945	174	2	≤	≤	PROPN
ejpam-4945	174	3	ψ	ψ	X
ejpam-4945	174	4	(	(	PUNCT
ejpam-4945	174	5	ι2	ι2	PROPN
ejpam-4945	174	6	)	)	PUNCT
ejpam-4945	174	7	.	.	PUNCT
ejpam-4945	175	1	from	from	ADP
ejpam-4945	175	2	(	(	PUNCT
ejpam-4945	175	3	15	15	NUM
ejpam-4945	175	4	)	)	PUNCT
ejpam-4945	175	5	,	,	PUNCT
ejpam-4945	175	6	we	we	PRON
ejpam-4945	175	7	have	have	VERB
ejpam-4945	175	8	a	a	DET
ejpam-4945	175	9	contradiction	contradiction	NOUN
ejpam-4945	175	10	.	.	PUNCT
ejpam-4945	176	1	this	this	PRON
ejpam-4945	176	2	completes	complete	VERB
ejpam-4945	176	3	the	the	DET
ejpam-4945	176	4	proof	proof	NOUN
ejpam-4945	176	5	.	.	PUNCT
ejpam-4945	177	1	corollary	corollary	ADJ
ejpam-4945	177	2	2	2	NUM
ejpam-4945	177	3	.	.	PUNCT
ejpam-4945	178	1	let	let	VERB
ejpam-4945	178	2	0	0	NUM
ejpam-4945	178	3	<	<	X
ejpam-4945	178	4	inf	inf	PROPN
ejpam-4945	178	5	s≥ι	s≥ι	PROPN
ejpam-4945	178	6	(	(	PUNCT
ejpam-4945	178	7	lim	lim	PROPN
ejpam-4945	178	8	inf	inf	PROPN
ejpam-4945	178	9	ι→∞	ι→∞	PROPN
ejpam-4945	178	10	w	w	PROPN
ejpam-4945	178	11	(	(	PUNCT
ejpam-4945	178	12	ι	ι	PROPN
ejpam-4945	178	13	,	,	PUNCT
ejpam-4945	178	14	s	s	NOUN
ejpam-4945	178	15	)	)	PUNCT
ejpam-4945	178	16	w	w	PROPN
ejpam-4945	178	17	(	(	PUNCT
ejpam-4945	178	18	ι	ι	PROPN
ejpam-4945	178	19	,	,	PUNCT
ejpam-4945	178	20	ι0	ι0	NOUN
ejpam-4945	178	21	)	)	PUNCT
ejpam-4945	178	22	)	)	PUNCT
ejpam-4945	179	1	≤	≤	NUM
ejpam-4945	179	2	∞	∞	PROPN
ejpam-4945	179	3	and	and	CCONJ
ejpam-4945	179	4	lim	lim	PROPN
ejpam-4945	179	5	sup	sup	PROPN
ejpam-4945	179	6	ι→∞	ι→∞	NUM
ejpam-4945	179	7	1	1	NUM
ejpam-4945	179	8	w	w	NOUN
ejpam-4945	179	9	(	(	PUNCT
ejpam-4945	179	10	ι	ι	PROPN
ejpam-4945	179	11	,	,	PUNCT
ejpam-4945	179	12	ι0	ι0	NOUN
ejpam-4945	179	13	)	)	PUNCT
ejpam-4945	179	14	∫	∫	PROPN
ejpam-4945	180	1	ι	ι	PROPN
ejpam-4945	180	2	ι0	ι0	NOUN
ejpam-4945	180	3	w	w	PROPN
ejpam-4945	180	4	(	(	PUNCT
ejpam-4945	180	5	ι	ι	PROPN
ejpam-4945	180	6	,	,	PUNCT
ejpam-4945	180	7	u	u	NOUN
ejpam-4945	180	8	)	)	PUNCT
ejpam-4945	180	9	b	b	PROPN
ejpam-4945	180	10	(	(	PUNCT
ejpam-4945	180	11	u	u	NOUN
ejpam-4945	180	12	)	)	PUNCT
ejpam-4945	180	13	ς2	ς2	PROPN
ejpam-4945	180	14	(	(	PUNCT
ejpam-4945	180	15	ι	ι	PROPN
ejpam-4945	180	16	,	,	PUNCT
ejpam-4945	180	17	u	u	NOUN
ejpam-4945	180	18	)	)	PUNCT
ejpam-4945	180	19	du	du	PROPN
ejpam-4945	181	1	<	<	X
ejpam-4945	181	2	∞.	∞.	PROPN
ejpam-4945	181	3	if	if	SCONJ
ejpam-4945	181	4	lim	lim	PROPN
ejpam-4945	181	5	sup	sup	PROPN
ejpam-4945	181	6	ι→∞	ι→∞	NUM
ejpam-4945	181	7	∫	∫	PROPN
ejpam-4945	181	8	ι	ι	X
ejpam-4945	181	9	ι0	ι0	NOUN
ejpam-4945	181	10	ς2	ς2	PROPN
ejpam-4945	181	11	(	(	PUNCT
ejpam-4945	181	12	s	s	NOUN
ejpam-4945	181	13	)	)	PUNCT
ejpam-4945	181	14	b	b	PROPN
ejpam-4945	181	15	(	(	PUNCT
ejpam-4945	181	16	s	s	NOUN
ejpam-4945	181	17	)	)	PUNCT
ejpam-4945	181	18	ds	ds	NOUN
ejpam-4945	181	19	=	=	SYM
ejpam-4945	181	20	∞	∞	PROPN
ejpam-4945	181	21	for	for	ADP
ejpam-4945	181	22	ς	ς	PROPN
ejpam-4945	181	23	∈	∈	PROPN
ejpam-4945	181	24	c	c	X
ejpam-4945	181	25	(	(	PUNCT
ejpam-4945	181	26	[	[	X
ejpam-4945	181	27	ι0,∞	ι0,∞	NOUN
ejpam-4945	181	28	)	)	PUNCT
ejpam-4945	181	29	,	,	PUNCT
ejpam-4945	181	30	r	r	NOUN
ejpam-4945	181	31	)	)	PUNCT
ejpam-4945	181	32	and	and	CCONJ
ejpam-4945	181	33	ς	ς	PROPN
ejpam-4945	181	34	(	(	PUNCT
ejpam-4945	181	35	ι	ι	PROPN
ejpam-4945	181	36	)	)	PUNCT
ejpam-4945	182	1	=	=	SYM
ejpam-4945	182	2	max	max	PROPN
ejpam-4945	182	3	{	{	PUNCT
ejpam-4945	182	4	ς	ς	PROPN
ejpam-4945	182	5	(	(	PUNCT
ejpam-4945	182	6	ι	ι	PROPN
ejpam-4945	182	7	)	)	PUNCT
ejpam-4945	182	8	,	,	PUNCT
ejpam-4945	182	9	0	0	NUM
ejpam-4945	182	10	}	}	PUNCT
ejpam-4945	182	11	,	,	PUNCT
ejpam-4945	182	12	also	also	ADV
ejpam-4945	182	13	,	,	PUNCT
ejpam-4945	182	14	lim	lim	PROPN
ejpam-4945	182	15	sup	sup	PROPN
ejpam-4945	182	16	ι→∞	ι→∞	NUM
ejpam-4945	182	17	1	1	NUM
ejpam-4945	182	18	w	w	NOUN
ejpam-4945	182	19	(	(	PUNCT
ejpam-4945	182	20	ι	ι	PROPN
ejpam-4945	182	21	,	,	PUNCT
ejpam-4945	182	22	ι0	ι0	NOUN
ejpam-4945	182	23	)	)	PUNCT
ejpam-4945	182	24	∫	∫	PROPN
ejpam-4945	182	25	ι	ι	PROPN
ejpam-4945	182	26	ι0	ι0	NOUN
ejpam-4945	182	27	w	w	PROPN
ejpam-4945	182	28	(	(	PUNCT
ejpam-4945	182	29	ι	ι	PROPN
ejpam-4945	182	30	,	,	PUNCT
ejpam-4945	182	31	u	u	NOUN
ejpam-4945	182	32	)	)	PUNCT
ejpam-4945	182	33	(	(	PUNCT
ejpam-4945	182	34	ℏ	ℏ	PROPN
ejpam-4945	182	35	(	(	PUNCT
ejpam-4945	182	36	u)k	u)k	X
ejpam-4945	182	37	(	(	PUNCT
ejpam-4945	182	38	u)−	u)−	PROPN
ejpam-4945	182	39	1	1	NUM
ejpam-4945	182	40	4ν	4ν	NUM
ejpam-4945	182	41	b	b	X
ejpam-4945	182	42	(	(	PUNCT
ejpam-4945	182	43	u	u	NOUN
ejpam-4945	182	44	)	)	PUNCT
ejpam-4945	182	45	ς2	ς2	PROPN
ejpam-4945	182	46	(	(	PUNCT
ejpam-4945	182	47	ι	ι	PROPN
ejpam-4945	182	48	,	,	PUNCT
ejpam-4945	182	49	u	u	NOUN
ejpam-4945	182	50	)	)	PUNCT
ejpam-4945	182	51	)	)	PUNCT
ejpam-4945	182	52	du	du	PROPN
ejpam-4945	182	53	≥	≥	PROPN
ejpam-4945	182	54	sup	sup	NOUN
ejpam-4945	182	55	ι≥ι0	ι≥ι0	PUNCT
ejpam-4945	182	56	ς	ς	PROPN
ejpam-4945	182	57	(	(	PUNCT
ejpam-4945	182	58	ι	ι	PROPN
ejpam-4945	182	59	)	)	PUNCT
ejpam-4945	182	60	,	,	PUNCT
ejpam-4945	182	61	then	then	ADV
ejpam-4945	182	62	(	(	PUNCT
ejpam-4945	182	63	1	1	X
ejpam-4945	182	64	)	)	PUNCT
ejpam-4945	182	65	is	be	AUX
ejpam-4945	182	66	oscillatory	oscillatory	ADJ
ejpam-4945	182	67	.	.	PUNCT
ejpam-4945	182	68	example	example	NOUN
ejpam-4945	183	1	1	1	NUM
ejpam-4945	183	2	.	.	X
ejpam-4945	183	3	consider	consider	VERB
ejpam-4945	183	4	the	the	DET
ejpam-4945	183	5	second	second	ADJ
ejpam-4945	183	6	-	-	PUNCT
ejpam-4945	183	7	order	order	NOUN
ejpam-4945	183	8	equation	equation	NOUN
ejpam-4945	183	9	:	:	PUNCT
ejpam-4945	183	10	[	[	PUNCT
ejpam-4945	183	11	ι	ι	X
ejpam-4945	183	12	(	(	PUNCT
ejpam-4945	183	13	ξ	ξ	X
ejpam-4945	183	14	(	(	PUNCT
ejpam-4945	183	15	ι	ι	NOUN
ejpam-4945	183	16	)	)	PUNCT
ejpam-4945	183	17	+	+	CCONJ
ejpam-4945	183	18	1	1	NUM
ejpam-4945	183	19	2	2	NUM
ejpam-4945	183	20	ξ	ξ	X
ejpam-4945	183	21	(	(	PUNCT
ejpam-4945	183	22	ι	ι	PROPN
ejpam-4945	183	23	3	3	NUM
ejpam-4945	183	24	)	)	PUNCT
ejpam-4945	183	25	)	)	PUNCT
ejpam-4945	183	26	′]′	′]′	VERB
ejpam-4945	183	27	+	+	CCONJ
ejpam-4945	183	28	b0	b0	ADP
ejpam-4945	183	29	ι	ι	PROPN
ejpam-4945	183	30	(	(	PUNCT
ejpam-4945	183	31	ξ2	ξ2	NOUN
ejpam-4945	183	32	+	+	CCONJ
ejpam-4945	183	33	ξ	ξ	PROPN
ejpam-4945	183	34	)	)	PUNCT
ejpam-4945	183	35	(	(	PUNCT
ejpam-4945	183	36	ι	ι	PROPN
ejpam-4945	183	37	2	2	X
ejpam-4945	183	38	)	)	PUNCT
ejpam-4945	183	39	=	=	SYM
ejpam-4945	183	40	0	0	NUM
ejpam-4945	183	41	,	,	PUNCT
ejpam-4945	183	42	ι	ι	PRON
ejpam-4945	183	43	≥	≥	NOUN
ejpam-4945	183	44	1	1	NUM
ejpam-4945	183	45	,	,	PUNCT
ejpam-4945	183	46	(	(	PUNCT
ejpam-4945	183	47	16	16	NUM
ejpam-4945	183	48	)	)	PUNCT
ejpam-4945	183	49	where	where	SCONJ
ejpam-4945	183	50	b0	b0	NOUN
ejpam-4945	183	51	>	>	X
ejpam-4945	183	52	0	0	NUM
ejpam-4945	183	53	is	be	AUX
ejpam-4945	183	54	a	a	DET
ejpam-4945	183	55	constant	constant	ADJ
ejpam-4945	183	56	.	.	PUNCT
ejpam-4945	184	1	let	let	VERB
ejpam-4945	184	2	β	β	X
ejpam-4945	184	3	=	=	PUNCT
ejpam-4945	185	1	p	p	X
ejpam-4945	185	2	=	=	SYM
ejpam-4945	185	3	2	2	NUM
ejpam-4945	185	4	,	,	PUNCT
ejpam-4945	185	5	a	a	DET
ejpam-4945	185	6	(	(	PUNCT
ejpam-4945	185	7	ι	ι	NOUN
ejpam-4945	185	8	)	)	PUNCT
ejpam-4945	185	9	=	=	SYM
ejpam-4945	185	10	ι	ι	PROPN
ejpam-4945	185	11	,	,	PUNCT
ejpam-4945	185	12	ς	ς	PROPN
ejpam-4945	185	13	(	(	PUNCT
ejpam-4945	185	14	ι	ι	NOUN
ejpam-4945	185	15	)	)	PUNCT
ejpam-4945	185	16	=	=	SYM
ejpam-4945	185	17	1/2	1/2	NUM
ejpam-4945	185	18	,	,	PUNCT
ejpam-4945	185	19	γ	γ	X
ejpam-4945	185	20	(	(	PUNCT
ejpam-4945	185	21	ι	ι	PROPN
ejpam-4945	185	22	)	)	PUNCT
ejpam-4945	185	23	=	=	SYM
ejpam-4945	185	24	ι/3	ι/3	PROPN
ejpam-4945	185	25	,	,	PUNCT
ejpam-4945	185	26	b	b	PROPN
ejpam-4945	185	27	(	(	PUNCT
ejpam-4945	185	28	ι	ι	NOUN
ejpam-4945	185	29	)	)	PUNCT
ejpam-4945	185	30	=	=	SYM
ejpam-4945	185	31	b0	b0	NOUN
ejpam-4945	185	32	/	/	SYM
ejpam-4945	185	33	ι	ι	PROPN
ejpam-4945	185	34	,	,	PUNCT
ejpam-4945	185	35	z	z	NOUN
ejpam-4945	185	36	(	(	PUNCT
ejpam-4945	185	37	ι	ι	NOUN
ejpam-4945	185	38	)	)	PUNCT
ejpam-4945	185	39	=	=	SYM
ejpam-4945	186	1	ι/2	ι/2	PROPN
ejpam-4945	186	2	,	,	PUNCT
ejpam-4945	186	3	φ	φ	X
ejpam-4945	186	4	(	(	PUNCT
ejpam-4945	186	5	ξ	ξ	NOUN
ejpam-4945	186	6	)	)	PUNCT
ejpam-4945	186	7	=	=	SYM
ejpam-4945	187	1	ξ2	ξ2	NOUN
ejpam-4945	187	2	+	+	CCONJ
ejpam-4945	187	3	ξ	ξ	X
ejpam-4945	187	4	.	.	PUNCT
ejpam-4945	188	1	now	now	ADV
ejpam-4945	188	2	,	,	PUNCT
ejpam-4945	188	3	we	we	PRON
ejpam-4945	188	4	see	see	VERB
ejpam-4945	188	5	that	that	SCONJ
ejpam-4945	189	1	k	k	PROPN
ejpam-4945	189	2	(	(	PUNCT
ejpam-4945	189	3	ι	ι	PROPN
ejpam-4945	189	4	)	)	PUNCT
ejpam-4945	189	5	=	=	SYM
ejpam-4945	189	6	b	b	X
ejpam-4945	189	7	(	(	PUNCT
ejpam-4945	189	8	ι	ι	PROPN
ejpam-4945	189	9	)	)	PUNCT
ejpam-4945	189	10	(	(	PUNCT
ejpam-4945	189	11	1−	1−	NUM
ejpam-4945	189	12	ς	ς	PROPN
ejpam-4945	189	13	(	(	PUNCT
ejpam-4945	189	14	z	z	NOUN
ejpam-4945	189	15	(	(	PUNCT
ejpam-4945	189	16	ι	ι	NOUN
ejpam-4945	189	17	)	)	PUNCT
ejpam-4945	189	18	)	)	PUNCT
ejpam-4945	189	19	)	)	PUNCT
ejpam-4945	190	1	=	=	PUNCT
ejpam-4945	190	2	b0	b0	NOUN
ejpam-4945	190	3	2ι	2ι	NUM
ejpam-4945	190	4	and	and	CCONJ
ejpam-4945	190	5	b	b	NOUN
ejpam-4945	190	6	(	(	PUNCT
ejpam-4945	190	7	ι	ι	PROPN
ejpam-4945	190	8	)	)	PUNCT
ejpam-4945	190	9	=	=	SYM
ejpam-4945	190	10	a	a	PRON
ejpam-4945	190	11	(	(	PUNCT
ejpam-4945	190	12	ι	ι	NOUN
ejpam-4945	190	13	)	)	PUNCT
ejpam-4945	190	14	ℏ	ℏ	PROPN
ejpam-4945	190	15	(	(	PUNCT
ejpam-4945	190	16	ι	ι	NOUN
ejpam-4945	190	17	)	)	PUNCT
ejpam-4945	190	18	jzβ−2	jzβ−2	PROPN
ejpam-4945	190	19	(	(	PUNCT
ejpam-4945	190	20	ι	ι	PROPN
ejpam-4945	190	21	)	)	PUNCT
ejpam-4945	190	22	z′	z′	NUM
ejpam-4945	190	23	(	(	PUNCT
ejpam-4945	190	24	ι	ι	X
ejpam-4945	190	25	)	)	PUNCT
ejpam-4945	190	26	=	=	SYM
ejpam-4945	190	27	2ι2	2ι2	NUM
ejpam-4945	190	28	j	j	NOUN
ejpam-4945	190	29	.	.	PUNCT
ejpam-4945	191	1	if	if	SCONJ
ejpam-4945	191	2	we	we	PRON
ejpam-4945	191	3	set	set	VERB
ejpam-4945	191	4	ℏ	ℏ	PROPN
ejpam-4945	191	5	=	=	PUNCT
ejpam-4945	191	6	ι	ι	X
ejpam-4945	191	7	then	then	ADV
ejpam-4945	191	8	any	any	PRON
ejpam-4945	191	9	for	for	ADP
ejpam-4945	191	10	constants	constant	NOUN
ejpam-4945	191	11	j	j	PROPN
ejpam-4945	191	12	>	>	X
ejpam-4945	191	13	0	0	PROPN
ejpam-4945	191	14	,	,	PUNCT
ejpam-4945	191	15	0	0	NUM
ejpam-4945	191	16	<	<	X
ejpam-4945	191	17	ν	ν	X
ejpam-4945	191	18	<	<	X
ejpam-4945	191	19	1∫	1∫	NUM
ejpam-4945	191	20	∞	∞	NUM
ejpam-4945	191	21	ι0	ι0	NOUN
ejpam-4945	191	22	(	(	PUNCT
ejpam-4945	191	23	ℏ	ℏ	PROPN
ejpam-4945	191	24	(	(	PUNCT
ejpam-4945	191	25	u)k	u)k	X
ejpam-4945	191	26	(	(	PUNCT
ejpam-4945	191	27	u)−	u)−	PROPN
ejpam-4945	191	28	1	1	NUM
ejpam-4945	191	29	4ν	4ν	NOUN
ejpam-4945	191	30	(	(	PUNCT
ejpam-4945	191	31	ℏ′	ℏ′	X
ejpam-4945	191	32	(	(	PUNCT
ejpam-4945	191	33	u	u	NOUN
ejpam-4945	191	34	)	)	PUNCT
ejpam-4945	191	35	ℏ	ℏ	PROPN
ejpam-4945	191	36	(	(	PUNCT
ejpam-4945	191	37	u	u	NOUN
ejpam-4945	191	38	)	)	PUNCT
ejpam-4945	191	39	)	)	PUNCT
ejpam-4945	191	40	2	2	NUM
ejpam-4945	191	41	b	b	X
ejpam-4945	191	42	(	(	PUNCT
ejpam-4945	191	43	u	u	NOUN
ejpam-4945	191	44	)	)	PUNCT
ejpam-4945	191	45	)	)	PUNCT
ejpam-4945	191	46	du	du	PROPN
ejpam-4945	191	47	,	,	PUNCT
ejpam-4945	191	48	=	=	SYM
ejpam-4945	191	49	∫	∫	PROPN
ejpam-4945	191	50	∞	∞	PROPN
ejpam-4945	191	51	ι0	ι0	PROPN
ejpam-4945	191	52	(	(	PUNCT
ejpam-4945	191	53	b0	b0	NOUN
ejpam-4945	191	54	2	2	NUM
ejpam-4945	191	55	−	−	NOUN
ejpam-4945	191	56	1	1	NUM
ejpam-4945	191	57	2νj	2νj	NOUN
ejpam-4945	191	58	)	)	PUNCT
ejpam-4945	191	59	du	du	PROPN
ejpam-4945	191	60	=	=	SYM
ejpam-4945	191	61	∞	∞	PROPN
ejpam-4945	191	62	if	if	SCONJ
ejpam-4945	191	63	b0	b0	VERB
ejpam-4945	191	64	>	>	X
ejpam-4945	191	65	1	1	NUM
ejpam-4945	191	66	.	.	PUNCT
ejpam-4945	191	67	from	from	ADP
ejpam-4945	191	68	theorem	theorem	ADJ
ejpam-4945	191	69	2	2	NUM
ejpam-4945	191	70	,	,	PUNCT
ejpam-4945	191	71	every	every	DET
ejpam-4945	191	72	solution	solution	NOUN
ejpam-4945	191	73	of	of	ADP
ejpam-4945	191	74	equation	equation	NOUN
ejpam-4945	191	75	(	(	PUNCT
ejpam-4945	191	76	16	16	NUM
ejpam-4945	191	77	)	)	PUNCT
ejpam-4945	191	78	is	be	AUX
ejpam-4945	191	79	oscillatory	oscillatory	ADJ
ejpam-4945	191	80	if	if	SCONJ
ejpam-4945	191	81	b0	b0	VERB
ejpam-4945	191	82	>	>	X
ejpam-4945	191	83	1	1	NUM
ejpam-4945	191	84	.	.	PUNCT
ejpam-4945	191	85	references	reference	NOUN
ejpam-4945	191	86	2507	2507	NUM
ejpam-4945	191	87	example	example	NOUN
ejpam-4945	191	88	2	2	NUM
ejpam-4945	191	89	.	.	X
ejpam-4945	191	90	consider	consider	VERB
ejpam-4945	191	91	the	the	DET
ejpam-4945	191	92	fourth	fourth	ADJ
ejpam-4945	191	93	-	-	PUNCT
ejpam-4945	191	94	order	order	NOUN
ejpam-4945	191	95	equation	equation	NOUN
ejpam-4945	191	96	:	:	PUNCT
ejpam-4945	191	97	[	[	PUNCT
ejpam-4945	191	98	ιw′′′	ιw′′′	X
ejpam-4945	191	99	(	(	PUNCT
ejpam-4945	191	100	ι	ι	NOUN
ejpam-4945	191	101	)	)	PUNCT
ejpam-4945	191	102	]	]	PUNCT
ejpam-4945	191	103	′	′	NUM
ejpam-4945	192	1	+	+	CCONJ
ejpam-4945	192	2	b	b	X
ejpam-4945	192	3	ι	ι	X
ejpam-4945	192	4	ξ	ξ	X
ejpam-4945	192	5	(	(	PUNCT
ejpam-4945	192	6	ι	ι	PROPN
ejpam-4945	192	7	3	3	NUM
ejpam-4945	192	8	)	)	PUNCT
ejpam-4945	192	9	=	=	SYM
ejpam-4945	193	1	0	0	NUM
ejpam-4945	193	2	,	,	PUNCT
ejpam-4945	193	3	ι	ι	PRON
ejpam-4945	193	4	≥	≥	NOUN
ejpam-4945	193	5	1	1	NUM
ejpam-4945	193	6	,	,	PUNCT
ejpam-4945	193	7	(	(	PUNCT
ejpam-4945	193	8	17	17	NUM
ejpam-4945	193	9	)	)	PUNCT
ejpam-4945	193	10	where	where	SCONJ
ejpam-4945	193	11	w	w	PROPN
ejpam-4945	193	12	(	(	PUNCT
ejpam-4945	193	13	ι	ι	NOUN
ejpam-4945	193	14	)	)	PUNCT
ejpam-4945	193	15	=	=	SYM
ejpam-4945	193	16	ξ	ξ	X
ejpam-4945	193	17	(	(	PUNCT
ejpam-4945	193	18	ι	ι	NOUN
ejpam-4945	193	19	)	)	PUNCT
ejpam-4945	193	20	+	+	CCONJ
ejpam-4945	193	21	1	1	NUM
ejpam-4945	193	22	3ξ	3ξ	NOUN
ejpam-4945	193	23	(	(	PUNCT
ejpam-4945	193	24	ι	ι	PROPN
ejpam-4945	193	25	2	2	NUM
ejpam-4945	193	26	)	)	PUNCT
ejpam-4945	193	27	and	and	CCONJ
ejpam-4945	193	28	b	b	X
ejpam-4945	193	29	>	>	X
ejpam-4945	193	30	0	0	NUM
ejpam-4945	193	31	is	be	AUX
ejpam-4945	193	32	a	a	DET
ejpam-4945	193	33	constant	constant	ADJ
ejpam-4945	193	34	.	.	PUNCT
ejpam-4945	194	1	let	let	VERB
ejpam-4945	194	2	β	β	X
ejpam-4945	194	3	=	=	SYM
ejpam-4945	194	4	4	4	NUM
ejpam-4945	194	5	,	,	PUNCT
ejpam-4945	194	6	p	p	NOUN
ejpam-4945	194	7	=	=	SYM
ejpam-4945	194	8	2	2	NUM
ejpam-4945	194	9	,	,	PUNCT
ejpam-4945	194	10	a	a	DET
ejpam-4945	194	11	(	(	PUNCT
ejpam-4945	194	12	ι	ι	NOUN
ejpam-4945	194	13	)	)	PUNCT
ejpam-4945	195	1	=	=	SYM
ejpam-4945	195	2	ι	ι	PROPN
ejpam-4945	195	3	,	,	PUNCT
ejpam-4945	195	4	ς	ς	PROPN
ejpam-4945	195	5	(	(	PUNCT
ejpam-4945	195	6	ι	ι	NOUN
ejpam-4945	195	7	)	)	PUNCT
ejpam-4945	195	8	=	=	SYM
ejpam-4945	195	9	1/3	1/3	NUM
ejpam-4945	195	10	,	,	PUNCT
ejpam-4945	195	11	γ	γ	X
ejpam-4945	195	12	(	(	PUNCT
ejpam-4945	195	13	ι	ι	PROPN
ejpam-4945	195	14	)	)	PUNCT
ejpam-4945	195	15	=	=	SYM
ejpam-4945	195	16	ι/2	ι/2	PROPN
ejpam-4945	195	17	,	,	PUNCT
ejpam-4945	195	18	b	b	PROPN
ejpam-4945	195	19	(	(	PUNCT
ejpam-4945	195	20	ι	ι	NOUN
ejpam-4945	195	21	)	)	PUNCT
ejpam-4945	195	22	=	=	SYM
ejpam-4945	195	23	b0	b0	NOUN
ejpam-4945	195	24	/	/	SYM
ejpam-4945	195	25	ι	ι	PROPN
ejpam-4945	195	26	,	,	PUNCT
ejpam-4945	195	27	z	z	NOUN
ejpam-4945	195	28	(	(	PUNCT
ejpam-4945	195	29	ι	ι	NOUN
ejpam-4945	195	30	)	)	PUNCT
ejpam-4945	195	31	=	=	SYM
ejpam-4945	195	32	ι/3	ι/3	PROPN
ejpam-4945	195	33	,	,	PUNCT
ejpam-4945	195	34	φ	φ	PROPN
ejpam-4945	195	35	(	(	PUNCT
ejpam-4945	195	36	ξ	ξ	NOUN
ejpam-4945	195	37	)	)	PUNCT
ejpam-4945	195	38	=	=	SYM
ejpam-4945	195	39	ξ	ξ	X
ejpam-4945	195	40	.	.	PUNCT
ejpam-4945	196	1	thus	thus	ADV
ejpam-4945	196	2	,	,	PUNCT
ejpam-4945	196	3	we	we	PRON
ejpam-4945	196	4	see	see	VERB
ejpam-4945	196	5	that	that	SCONJ
ejpam-4945	196	6	∫	∫	PROPN
ejpam-4945	196	7	∞	∞	PROPN
ejpam-4945	196	8	a−1	a−1	PROPN
ejpam-4945	196	9	(	(	PUNCT
ejpam-4945	196	10	ι	ι	NOUN
ejpam-4945	196	11	)	)	PUNCT
ejpam-4945	196	12	dι	dι	NOUN
ejpam-4945	197	1	=	=	SYM
ejpam-4945	197	2	∞.	∞.	PROPN
ejpam-4945	197	3	by	by	ADP
ejpam-4945	197	4	theorem	theorem	NOUN
ejpam-4945	197	5	3	3	NUM
ejpam-4945	197	6	,	,	PUNCT
ejpam-4945	197	7	every	every	DET
ejpam-4945	197	8	solution	solution	NOUN
ejpam-4945	197	9	of	of	ADP
ejpam-4945	197	10	equation	equation	NOUN
ejpam-4945	197	11	(	(	PUNCT
ejpam-4945	197	12	17	17	NUM
ejpam-4945	197	13	)	)	PUNCT
ejpam-4945	197	14	is	be	AUX
ejpam-4945	197	15	oscillatory	oscillatory	ADJ
ejpam-4945	197	16	.	.	PUNCT
ejpam-4945	198	1	3	3	X
ejpam-4945	198	2	.	.	X
ejpam-4945	198	3	conclusion	conclusion	NOUN
ejpam-4945	198	4	in	in	ADP
ejpam-4945	198	5	conclusion	conclusion	NOUN
ejpam-4945	198	6	,	,	PUNCT
ejpam-4945	198	7	this	this	DET
ejpam-4945	198	8	study	study	NOUN
ejpam-4945	198	9	aimed	aim	VERB
ejpam-4945	198	10	at	at	ADP
ejpam-4945	198	11	investigating	investigate	VERB
ejpam-4945	198	12	the	the	DET
ejpam-4945	198	13	oscillatory	oscillatory	ADJ
ejpam-4945	198	14	properties	property	NOUN
ejpam-4945	198	15	of	of	ADP
ejpam-4945	198	16	solutions	solution	NOUN
ejpam-4945	198	17	to	to	ADP
ejpam-4945	198	18	even	even	ADJ
ejpam-4945	198	19	-	-	PUNCT
ejpam-4945	198	20	order	order	NOUN
ejpam-4945	198	21	differential	differential	ADJ
ejpam-4945	198	22	equations	equation	NOUN
ejpam-4945	198	23	with	with	ADP
ejpam-4945	198	24	a	a	DET
ejpam-4945	198	25	p	p	NOUN
ejpam-4945	198	26	-	-	PUNCT
ejpam-4945	198	27	laplacian	laplacian	NOUN
ejpam-4945	198	28	.	.	PUNCT
ejpam-4945	199	1	the	the	DET
ejpam-4945	199	2	findings	finding	NOUN
ejpam-4945	199	3	of	of	ADP
ejpam-4945	199	4	this	this	DET
ejpam-4945	199	5	paper	paper	NOUN
ejpam-4945	199	6	contribute	contribute	VERB
ejpam-4945	199	7	to	to	ADP
ejpam-4945	199	8	the	the	DET
ejpam-4945	199	9	understanding	understanding	NOUN
ejpam-4945	199	10	of	of	ADP
ejpam-4945	199	11	the	the	DET
ejpam-4945	199	12	asymptotic	asymptotic	ADJ
ejpam-4945	199	13	and	and	CCONJ
ejpam-4945	199	14	oscillatory	oscillatory	ADJ
ejpam-4945	199	15	behavior	behavior	NOUN
ejpam-4945	199	16	of	of	ADP
ejpam-4945	199	17	such	such	ADJ
ejpam-4945	199	18	equations	equation	NOUN
ejpam-4945	199	19	and	and	CCONJ
ejpam-4945	199	20	provide	provide	VERB
ejpam-4945	199	21	new	new	ADJ
ejpam-4945	199	22	oscillation	oscillation	NOUN
ejpam-4945	199	23	criteria	criterion	NOUN
ejpam-4945	199	24	through	through	ADP
ejpam-4945	199	25	the	the	DET
ejpam-4945	199	26	use	use	NOUN
ejpam-4945	199	27	of	of	ADP
ejpam-4945	199	28	comparison	comparison	NOUN
ejpam-4945	199	29	methods	method	NOUN
ejpam-4945	199	30	with	with	ADP
ejpam-4945	199	31	firstorder	firstorder	NOUN
ejpam-4945	199	32	differential	differential	ADJ
ejpam-4945	199	33	equations	equation	NOUN
ejpam-4945	199	34	,	,	PUNCT
ejpam-4945	199	35	riccati	riccati	NOUN
ejpam-4945	199	36	technique	technique	NOUN
ejpam-4945	199	37	and	and	CCONJ
ejpam-4945	199	38	integral	integral	ADJ
ejpam-4945	199	39	averages	average	NOUN
ejpam-4945	199	40	technique	technique	NOUN
ejpam-4945	199	41	.	.	PUNCT
ejpam-4945	200	1	this	this	DET
ejpam-4945	200	2	work	work	NOUN
ejpam-4945	200	3	highlights	highlight	VERB
ejpam-4945	200	4	the	the	DET
ejpam-4945	200	5	relevance	relevance	NOUN
ejpam-4945	200	6	of	of	ADP
ejpam-4945	200	7	the	the	DET
ejpam-4945	200	8	theory	theory	NOUN
ejpam-4945	200	9	of	of	ADP
ejpam-4945	200	10	fourth	fourth	ADJ
ejpam-4945	200	11	-	-	PUNCT
ejpam-4945	200	12	order	order	NOUN
ejpam-4945	200	13	differential	differential	ADJ
ejpam-4945	200	14	equations	equation	NOUN
ejpam-4945	200	15	to	to	ADP
ejpam-4945	200	16	various	various	ADJ
ejpam-4945	200	17	fields	field	NOUN
ejpam-4945	200	18	of	of	ADP
ejpam-4945	200	19	mathematics	mathematic	NOUN
ejpam-4945	200	20	and	and	CCONJ
ejpam-4945	200	21	practical	practical	ADJ
ejpam-4945	200	22	sciences	science	NOUN
ejpam-4945	200	23	,	,	PUNCT
ejpam-4945	200	24	emphasizing	emphasize	VERB
ejpam-4945	200	25	the	the	DET
ejpam-4945	200	26	importance	importance	NOUN
ejpam-4945	200	27	of	of	ADP
ejpam-4945	200	28	continued	continue	VERB
ejpam-4945	200	29	research	research	NOUN
ejpam-4945	200	30	in	in	ADP
ejpam-4945	200	31	this	this	DET
ejpam-4945	200	32	area	area	NOUN
ejpam-4945	200	33	.	.	PUNCT
ejpam-4945	201	1	references	reference	NOUN
ejpam-4945	201	2	[	[	X
ejpam-4945	201	3	1	1	NUM
ejpam-4945	201	4	]	]	PUNCT
ejpam-4945	201	5	ravi	ravi	NOUN
ejpam-4945	201	6	p	p	PROPN
ejpam-4945	201	7	agarwal	agarwal	PROPN
ejpam-4945	201	8	,	,	PUNCT
ejpam-4945	201	9	martin	martin	PROPN
ejpam-4945	201	10	bohner	bohner	NOUN
ejpam-4945	201	11	,	,	PUNCT
ejpam-4945	201	12	tongxing	tongxe	VERB
ejpam-4945	201	13	li	li	NOUN
ejpam-4945	201	14	,	,	PUNCT
ejpam-4945	201	15	and	and	CCONJ
ejpam-4945	201	16	chenghui	chenghui	PROPN
ejpam-4945	201	17	zhang	zhang	PROPN
ejpam-4945	201	18	.	.	PUNCT
ejpam-4945	202	1	a	a	DET
ejpam-4945	202	2	new	new	ADJ
ejpam-4945	202	3	approach	approach	NOUN
ejpam-4945	202	4	in	in	ADP
ejpam-4945	202	5	the	the	DET
ejpam-4945	202	6	study	study	NOUN
ejpam-4945	202	7	of	of	ADP
ejpam-4945	202	8	oscillatory	oscillatory	ADJ
ejpam-4945	202	9	behavior	behavior	NOUN
ejpam-4945	202	10	of	of	ADP
ejpam-4945	202	11	even	even	ADJ
ejpam-4945	202	12	-	-	PUNCT
ejpam-4945	202	13	order	order	NOUN
ejpam-4945	202	14	neutral	neutral	ADJ
ejpam-4945	202	15	delay	delay	NOUN
ejpam-4945	202	16	differential	differential	ADJ
ejpam-4945	202	17	equations	equation	NOUN
ejpam-4945	202	18	.	.	PUNCT
ejpam-4945	203	1	applied	apply	VERB
ejpam-4945	203	2	mathematics	mathematic	NOUN
ejpam-4945	203	3	and	and	CCONJ
ejpam-4945	203	4	computation	computation	NOUN
ejpam-4945	203	5	,	,	PUNCT
ejpam-4945	203	6	225:787–794	225:787–794	NUM
ejpam-4945	203	7	,	,	PUNCT
ejpam-4945	203	8	2013	2013	NUM
ejpam-4945	203	9	.	.	PUNCT
ejpam-4945	204	1	[	[	X
ejpam-4945	204	2	2	2	X
ejpam-4945	204	3	]	]	PUNCT
ejpam-4945	204	4	ravi	ravi	NOUN
ejpam-4945	204	5	p	p	PROPN
ejpam-4945	204	6	agarwal	agarwal	PROPN
ejpam-4945	204	7	,	,	PUNCT
ejpam-4945	204	8	said	say	VERB
ejpam-4945	204	9	r	r	NOUN
ejpam-4945	204	10	grace	grace	NOUN
ejpam-4945	204	11	,	,	PUNCT
ejpam-4945	204	12	and	and	CCONJ
ejpam-4945	204	13	donal	donal	PROPN
ejpam-4945	204	14	o’regan	o’regan	PROPN
ejpam-4945	204	15	.	.	PUNCT
ejpam-4945	205	1	oscillation	oscillation	NOUN
ejpam-4945	205	2	criteria	criterion	NOUN
ejpam-4945	205	3	for	for	ADP
ejpam-4945	205	4	certain	certain	ADJ
ejpam-4945	205	5	nth	nth	NOUN
ejpam-4945	205	6	order	order	NOUN
ejpam-4945	205	7	differential	differential	ADJ
ejpam-4945	205	8	equations	equation	NOUN
ejpam-4945	205	9	with	with	ADP
ejpam-4945	205	10	deviating	deviate	VERB
ejpam-4945	205	11	arguments	argument	NOUN
ejpam-4945	205	12	.	.	PUNCT
ejpam-4945	206	1	journal	journal	NOUN
ejpam-4945	206	2	of	of	ADP
ejpam-4945	206	3	mathematical	mathematical	ADJ
ejpam-4945	206	4	analysis	analysis	NOUN
ejpam-4945	206	5	and	and	CCONJ
ejpam-4945	206	6	applications	application	NOUN
ejpam-4945	206	7	,	,	PUNCT
ejpam-4945	206	8	262(2):601–622	262(2):601–622	NUM
ejpam-4945	206	9	,	,	PUNCT
ejpam-4945	206	10	2001	2001	NUM
ejpam-4945	206	11	.	.	PUNCT
ejpam-4945	207	1	[	[	X
ejpam-4945	207	2	3	3	X
ejpam-4945	207	3	]	]	PUNCT
ejpam-4945	207	4	ravi	ravi	NOUN
ejpam-4945	207	5	p	p	PROPN
ejpam-4945	207	6	agarwal	agarwal	PROPN
ejpam-4945	207	7	,	,	PUNCT
ejpam-4945	207	8	said	say	VERB
ejpam-4945	207	9	r	r	NOUN
ejpam-4945	207	10	grace	grace	NOUN
ejpam-4945	207	11	,	,	PUNCT
ejpam-4945	207	12	and	and	CCONJ
ejpam-4945	207	13	donal	donal	PROPN
ejpam-4945	207	14	o’regan	o’regan	PROPN
ejpam-4945	207	15	.	.	PUNCT
ejpam-4945	208	1	oscillation	oscillation	NOUN
ejpam-4945	208	2	theory	theory	NOUN
ejpam-4945	208	3	for	for	ADP
ejpam-4945	208	4	difference	difference	NOUN
ejpam-4945	208	5	and	and	CCONJ
ejpam-4945	208	6	functional	functional	ADJ
ejpam-4945	208	7	differential	differential	ADJ
ejpam-4945	208	8	equations	equation	NOUN
ejpam-4945	208	9	.	.	PUNCT
ejpam-4945	209	1	springer	springer	NOUN
ejpam-4945	209	2	science	science	PROPN
ejpam-4945	209	3	&	&	CCONJ
ejpam-4945	209	4	business	business	NOUN
ejpam-4945	209	5	media	medium	NOUN
ejpam-4945	209	6	,	,	PUNCT
ejpam-4945	209	7	2013	2013	NUM
ejpam-4945	209	8	.	.	PUNCT
ejpam-4945	210	1	[	[	X
ejpam-4945	210	2	4	4	X
ejpam-4945	210	3	]	]	PUNCT
ejpam-4945	210	4	ravi	ravi	NOUN
ejpam-4945	210	5	p	p	PROPN
ejpam-4945	210	6	agarwal	agarwal	PROPN
ejpam-4945	210	7	,	,	PUNCT
ejpam-4945	210	8	chenghui	chenghui	PROPN
ejpam-4945	210	9	zhang	zhang	PROPN
ejpam-4945	210	10	,	,	PUNCT
ejpam-4945	210	11	and	and	CCONJ
ejpam-4945	210	12	tongxing	tongxe	VERB
ejpam-4945	210	13	li	li	NOUN
ejpam-4945	210	14	.	.	PUNCT
ejpam-4945	211	1	some	some	DET
ejpam-4945	211	2	remarks	remark	NOUN
ejpam-4945	211	3	on	on	ADP
ejpam-4945	211	4	oscillation	oscillation	NOUN
ejpam-4945	211	5	of	of	ADP
ejpam-4945	211	6	second	second	ADJ
ejpam-4945	211	7	order	order	NOUN
ejpam-4945	211	8	neutral	neutral	ADJ
ejpam-4945	211	9	differential	differential	NOUN
ejpam-4945	211	10	equations	equation	NOUN
ejpam-4945	211	11	.	.	PUNCT
ejpam-4945	212	1	applied	apply	VERB
ejpam-4945	212	2	mathematics	mathematic	NOUN
ejpam-4945	212	3	and	and	CCONJ
ejpam-4945	212	4	computation	computation	NOUN
ejpam-4945	212	5	,	,	PUNCT
ejpam-4945	212	6	274:178–181	274:178–181	NUM
ejpam-4945	212	7	,	,	PUNCT
ejpam-4945	212	8	2016	2016	NUM
ejpam-4945	212	9	.	.	PUNCT
ejpam-4945	213	1	[	[	X
ejpam-4945	213	2	5	5	X
ejpam-4945	213	3	]	]	PUNCT
ejpam-4945	213	4	barakah	barakah	PROPN
ejpam-4945	213	5	almarri	almarri	PROPN
ejpam-4945	213	6	,	,	PUNCT
ejpam-4945	213	7	ali	ali	PROPN
ejpam-4945	213	8	hasan	hasan	PROPN
ejpam-4945	213	9	ali	ali	PROPN
ejpam-4945	213	10	,	,	PUNCT
ejpam-4945	213	11	antónio	antónio	PROPN
ejpam-4945	213	12	m	m	PROPN
ejpam-4945	213	13	lopes	lopes	PROPN
ejpam-4945	213	14	,	,	PUNCT
ejpam-4945	213	15	and	and	CCONJ
ejpam-4945	213	16	omar	omar	PROPN
ejpam-4945	213	17	bazighifan	bazighifan	PROPN
ejpam-4945	213	18	.	.	PUNCT
ejpam-4945	214	1	nonlinear	nonlinear	ADJ
ejpam-4945	214	2	differential	differential	ADJ
ejpam-4945	214	3	equations	equation	NOUN
ejpam-4945	214	4	with	with	ADP
ejpam-4945	214	5	distributed	distributed	ADJ
ejpam-4945	214	6	delay	delay	NOUN
ejpam-4945	214	7	:	:	PUNCT
ejpam-4945	214	8	some	some	DET
ejpam-4945	214	9	new	new	ADJ
ejpam-4945	214	10	oscillatory	oscillatory	ADJ
ejpam-4945	214	11	solutions	solution	NOUN
ejpam-4945	214	12	.	.	PUNCT
ejpam-4945	215	1	mathematics	mathematic	NOUN
ejpam-4945	215	2	,	,	PUNCT
ejpam-4945	215	3	10(6):995	10(6):995	NUM
ejpam-4945	215	4	,	,	PUNCT
ejpam-4945	215	5	2022	2022	NUM
ejpam-4945	215	6	.	.	PUNCT
ejpam-4945	216	1	references	reference	NOUN
ejpam-4945	216	2	2508	2508	NUM
ejpam-4945	217	1	[	[	X
ejpam-4945	217	2	6	6	NUM
ejpam-4945	217	3	]	]	SYM
ejpam-4945	217	4	b	b	X
ejpam-4945	217	5	baculikova	baculikova	PROPN
ejpam-4945	217	6	,	,	PUNCT
ejpam-4945	217	7	j	j	PROPN
ejpam-4945	217	8	dzurina	dzurina	PROPN
ejpam-4945	217	9	,	,	PUNCT
ejpam-4945	217	10	and	and	CCONJ
ejpam-4945	217	11	jr	jr	PROPN
ejpam-4945	217	12	graef	graef	NOUN
ejpam-4945	217	13	.	.	PUNCT
ejpam-4945	218	1	on	on	ADP
ejpam-4945	218	2	the	the	DET
ejpam-4945	218	3	oscillation	oscillation	NOUN
ejpam-4945	218	4	of	of	ADP
ejpam-4945	218	5	higher	high	ADJ
ejpam-4945	218	6	order	order	NOUN
ejpam-4945	218	7	delay	delay	NOUN
ejpam-4945	218	8	differential	differential	ADJ
ejpam-4945	218	9	equations	equation	NOUN
ejpam-4945	218	10	.	.	PUNCT
ejpam-4945	218	11	?	?	PUNCT
ejpam-4945	218	12	?	?	PUNCT
ejpam-4945	218	13	?	?	PUNCT
ejpam-4945	218	14	?	?	PUNCT
ejpam-4945	218	15	?	?	PUNCT
ejpam-4945	218	16	?	?	PUNCT
ejpam-4945	218	17	?	?	PUNCT
ejpam-4945	218	18	?	?	PUNCT
ejpam-4945	218	19	?	?	PUNCT
ejpam-4945	218	20	?	?	PUNCT
ejpam-4945	218	21	?	?	PUNCT
ejpam-4945	218	22	?	?	PUNCT
ejpam-4945	218	23	?	?	PUNCT
ejpam-4945	218	24	?	?	PUNCT
ejpam-4945	218	25	?	?	PUNCT
ejpam-4945	218	26	?	?	PUNCT
ejpam-4945	218	27	?	?	PUNCT
ejpam-4945	218	28	?	?	PUNCT
ejpam-4945	218	29	,	,	PUNCT
ejpam-4945	218	30	2012	2012	NUM
ejpam-4945	218	31	.	.	PUNCT
ejpam-4945	219	1	[	[	X
ejpam-4945	219	2	7	7	X
ejpam-4945	219	3	]	]	X
ejpam-4945	219	4	omar	omar	PROPN
ejpam-4945	219	5	bazighifan	bazighifan	PROPN
ejpam-4945	219	6	,	,	PUNCT
ejpam-4945	219	7	ali	ali	PROPN
ejpam-4945	219	8	hasan	hasan	PROPN
ejpam-4945	219	9	ali	ali	PROPN
ejpam-4945	219	10	,	,	PUNCT
ejpam-4945	219	11	fatemah	fatemah	NOUN
ejpam-4945	219	12	mofarreh	mofarreh	NOUN
ejpam-4945	219	13	,	,	PUNCT
ejpam-4945	219	14	and	and	CCONJ
ejpam-4945	219	15	youssef	youssef	PROPN
ejpam-4945	219	16	n	n	PRON
ejpam-4945	219	17	raffoul	raffoul	PROPN
ejpam-4945	219	18	.	.	PROPN
ejpam-4945	219	19	extended	extend	VERB
ejpam-4945	219	20	approach	approach	NOUN
ejpam-4945	219	21	to	to	ADP
ejpam-4945	219	22	the	the	DET
ejpam-4945	219	23	asymptotic	asymptotic	ADJ
ejpam-4945	219	24	behavior	behavior	NOUN
ejpam-4945	219	25	and	and	CCONJ
ejpam-4945	219	26	symmetric	symmetric	ADJ
ejpam-4945	219	27	solutions	solution	NOUN
ejpam-4945	219	28	of	of	ADP
ejpam-4945	219	29	advanced	advanced	ADJ
ejpam-4945	219	30	differential	differential	ADJ
ejpam-4945	219	31	equations	equation	NOUN
ejpam-4945	219	32	.	.	PUNCT
ejpam-4945	220	1	symmetry	symmetry	NOUN
ejpam-4945	220	2	,	,	PUNCT
ejpam-4945	220	3	14(4):686	14(4):686	NUM
ejpam-4945	220	4	,	,	PUNCT
ejpam-4945	220	5	2022	2022	NUM
ejpam-4945	220	6	.	.	PUNCT
ejpam-4945	221	1	[	[	X
ejpam-4945	221	2	8	8	NUM
ejpam-4945	221	3	]	]	X
ejpam-4945	221	4	elmetwally	elmetwally	ADV
ejpam-4945	221	5	m	m	VERB
ejpam-4945	221	6	elabbasy	elabbasy	PROPN
ejpam-4945	221	7	,	,	PUNCT
ejpam-4945	221	8	clemente	clemente	PROPN
ejpam-4945	221	9	cesarano	cesarano	PROPN
ejpam-4945	221	10	,	,	PUNCT
ejpam-4945	221	11	omar	omar	PROPN
ejpam-4945	221	12	bazighifan	bazighifan	PROPN
ejpam-4945	221	13	,	,	PUNCT
ejpam-4945	221	14	and	and	CCONJ
ejpam-4945	221	15	osama	osama	PROPN
ejpam-4945	221	16	moaaz	moaaz	PROPN
ejpam-4945	221	17	.	.	PUNCT
ejpam-4945	222	1	asymptotic	asymptotic	ADJ
ejpam-4945	222	2	and	and	CCONJ
ejpam-4945	222	3	oscillatory	oscillatory	ADJ
ejpam-4945	222	4	behavior	behavior	NOUN
ejpam-4945	222	5	of	of	ADP
ejpam-4945	222	6	solutions	solution	NOUN
ejpam-4945	222	7	of	of	ADP
ejpam-4945	222	8	a	a	DET
ejpam-4945	222	9	class	class	NOUN
ejpam-4945	222	10	of	of	ADP
ejpam-4945	222	11	higher	high	ADJ
ejpam-4945	222	12	order	order	NOUN
ejpam-4945	222	13	differential	differential	ADJ
ejpam-4945	222	14	equation	equation	NOUN
ejpam-4945	222	15	.	.	PUNCT
ejpam-4945	223	1	symmetry	symmetry	NOUN
ejpam-4945	223	2	,	,	PUNCT
ejpam-4945	223	3	11(12):1434	11(12):1434	NUM
ejpam-4945	223	4	,	,	PUNCT
ejpam-4945	223	5	2019	2019	NUM
ejpam-4945	223	6	.	.	PUNCT
ejpam-4945	224	1	[	[	X
ejpam-4945	224	2	9	9	NUM
ejpam-4945	224	3	]	]	SYM
ejpam-4945	224	4	l	l	NOUN
ejpam-4945	224	5	erbe	erbe	PROPN
ejpam-4945	224	6	,	,	PUNCT
ejpam-4945	224	7	ts	ts	ADP
ejpam-4945	224	8	hassan	hassan	PROPN
ejpam-4945	224	9	,	,	PUNCT
ejpam-4945	224	10	and	and	CCONJ
ejpam-4945	224	11	a	a	DET
ejpam-4945	224	12	peterson	peterson	NOUN
ejpam-4945	224	13	.	.	PUNCT
ejpam-4945	225	1	oscillation	oscillation	NOUN
ejpam-4945	225	2	of	of	ADP
ejpam-4945	225	3	second	second	ADJ
ejpam-4945	225	4	order	order	NOUN
ejpam-4945	225	5	neutral	neutral	ADJ
ejpam-4945	225	6	delay	delay	NOUN
ejpam-4945	225	7	differential	differential	ADJ
ejpam-4945	225	8	equations	equation	NOUN
ejpam-4945	225	9	.	.	PUNCT
ejpam-4945	226	1	advances	advance	NOUN
ejpam-4945	226	2	in	in	ADP
ejpam-4945	226	3	dynamical	dynamical	ADJ
ejpam-4945	226	4	systems	system	NOUN
ejpam-4945	226	5	and	and	CCONJ
ejpam-4945	226	6	applications	application	NOUN
ejpam-4945	226	7	,	,	PUNCT
ejpam-4945	226	8	3(1):53–71	3(1):53–71	NUM
ejpam-4945	226	9	,	,	PUNCT
ejpam-4945	226	10	2008	2008	NUM
ejpam-4945	226	11	.	.	PUNCT
ejpam-4945	227	1	[	[	X
ejpam-4945	227	2	10	10	NUM
ejpam-4945	227	3	]	]	PUNCT
ejpam-4945	227	4	tongxing	tongxe	VERB
ejpam-4945	227	5	li	li	PROPN
ejpam-4945	227	6	,	,	PUNCT
ejpam-4945	227	7	blanka	blanka	PROPN
ejpam-4945	227	8	bacuĺıková	bacuĺıková	PROPN
ejpam-4945	227	9	,	,	PUNCT
ejpam-4945	227	10	jozef	jozef	PROPN
ejpam-4945	227	11	džurina	džurina	PROPN
ejpam-4945	227	12	,	,	PUNCT
ejpam-4945	227	13	and	and	CCONJ
ejpam-4945	227	14	chenghui	chenghui	PROPN
ejpam-4945	227	15	zhang	zhang	PROPN
ejpam-4945	227	16	.	.	PUNCT
ejpam-4945	228	1	oscillation	oscillation	NOUN
ejpam-4945	228	2	of	of	ADP
ejpam-4945	228	3	fourth	fourth	ADJ
ejpam-4945	228	4	-	-	PUNCT
ejpam-4945	228	5	order	order	NOUN
ejpam-4945	228	6	neutral	neutral	ADJ
ejpam-4945	228	7	differential	differential	ADJ
ejpam-4945	228	8	equations	equation	NOUN
ejpam-4945	228	9	with	with	ADP
ejpam-4945	228	10	p	p	NOUN
ejpam-4945	228	11	-	-	PUNCT
ejpam-4945	228	12	laplacian	laplacian	ADJ
ejpam-4945	228	13	like	like	ADP
ejpam-4945	228	14	operators	operator	NOUN
ejpam-4945	228	15	.	.	PUNCT
ejpam-4945	229	1	boundary	boundary	ADJ
ejpam-4945	229	2	value	value	NOUN
ejpam-4945	229	3	problems	problem	NOUN
ejpam-4945	229	4	,	,	PUNCT
ejpam-4945	229	5	2014:1–9	2014:1–9	PROPN
ejpam-4945	229	6	,	,	PUNCT
ejpam-4945	229	7	2014	2014	NUM
ejpam-4945	229	8	.	.	PUNCT
ejpam-4945	230	1	[	[	X
ejpam-4945	230	2	11	11	NUM
ejpam-4945	230	3	]	]	X
ejpam-4945	230	4	tongxing	tongxe	VERB
ejpam-4945	230	5	li	li	PROPN
ejpam-4945	230	6	and	and	CCONJ
ejpam-4945	230	7	yuriy	yuriy	PROPN
ejpam-4945	230	8	v	v	PROPN
ejpam-4945	230	9	rogovchenko	rogovchenko	PROPN
ejpam-4945	230	10	.	.	PUNCT
ejpam-4945	231	1	oscillation	oscillation	NOUN
ejpam-4945	231	2	criteria	criterion	NOUN
ejpam-4945	231	3	for	for	ADP
ejpam-4945	231	4	even	even	ADV
ejpam-4945	231	5	-	-	PUNCT
ejpam-4945	231	6	order	order	NOUN
ejpam-4945	231	7	neutral	neutral	ADJ
ejpam-4945	231	8	differential	differential	NOUN
ejpam-4945	231	9	equations	equation	NOUN
ejpam-4945	231	10	.	.	PUNCT
ejpam-4945	232	1	applied	apply	VERB
ejpam-4945	232	2	mathematics	mathematics	NOUN
ejpam-4945	232	3	letters	letter	NOUN
ejpam-4945	232	4	,	,	PUNCT
ejpam-4945	232	5	61:35–41	61:35–41	NUM
ejpam-4945	232	6	,	,	PUNCT
ejpam-4945	232	7	2016	2016	NUM
ejpam-4945	232	8	.	.	PUNCT
ejpam-4945	233	1	[	[	X
ejpam-4945	233	2	12	12	NUM
ejpam-4945	233	3	]	]	PUNCT
ejpam-4945	233	4	tongxing	tongxe	VERB
ejpam-4945	233	5	li	li	PROPN
ejpam-4945	233	6	and	and	CCONJ
ejpam-4945	233	7	yuriy	yuriy	PROPN
ejpam-4945	233	8	v	v	PROPN
ejpam-4945	233	9	rogovchenko	rogovchenko	PROPN
ejpam-4945	233	10	.	.	PUNCT
ejpam-4945	234	1	on	on	ADP
ejpam-4945	234	2	asymptotic	asymptotic	ADJ
ejpam-4945	234	3	behavior	behavior	NOUN
ejpam-4945	234	4	of	of	ADP
ejpam-4945	234	5	solutions	solution	NOUN
ejpam-4945	234	6	to	to	ADP
ejpam-4945	234	7	higher	high	ADJ
ejpam-4945	234	8	-	-	PUNCT
ejpam-4945	234	9	order	order	NOUN
ejpam-4945	234	10	sublinear	sublinear	NOUN
ejpam-4945	234	11	emden	emden	ADJ
ejpam-4945	234	12	–	–	PUNCT
ejpam-4945	234	13	fowler	fowler	PROPN
ejpam-4945	234	14	delay	delay	NOUN
ejpam-4945	234	15	differential	differential	ADJ
ejpam-4945	234	16	equations	equation	NOUN
ejpam-4945	234	17	.	.	PUNCT
ejpam-4945	235	1	applied	apply	VERB
ejpam-4945	235	2	mathematics	mathematics	NOUN
ejpam-4945	235	3	letters	letter	NOUN
ejpam-4945	235	4	,	,	PUNCT
ejpam-4945	235	5	67:53–59	67:53–59	NUM
ejpam-4945	235	6	,	,	PUNCT
ejpam-4945	235	7	2017	2017	NUM
ejpam-4945	235	8	.	.	PUNCT
ejpam-4945	236	1	[	[	X
ejpam-4945	236	2	13	13	NUM
ejpam-4945	236	3	]	]	PUNCT
ejpam-4945	236	4	shouhua	shouhua	PROPN
ejpam-4945	236	5	liu	liu	PROPN
ejpam-4945	236	6	,	,	PUNCT
ejpam-4945	236	7	quanxin	quanxin	PROPN
ejpam-4945	236	8	zhang	zhang	PROPN
ejpam-4945	236	9	,	,	PUNCT
ejpam-4945	236	10	and	and	CCONJ
ejpam-4945	236	11	yuanhong	yuanhong	PROPN
ejpam-4945	236	12	yu	yu	PROPN
ejpam-4945	236	13	.	.	PUNCT
ejpam-4945	236	14	oscillation	oscillation	NOUN
ejpam-4945	236	15	of	of	ADP
ejpam-4945	236	16	even	even	ADJ
ejpam-4945	236	17	-	-	PUNCT
ejpam-4945	236	18	order	order	NOUN
ejpam-4945	236	19	halflinear	halflinear	ADJ
ejpam-4945	236	20	functional	functional	ADJ
ejpam-4945	236	21	differential	differential	ADJ
ejpam-4945	236	22	equations	equation	NOUN
ejpam-4945	236	23	with	with	ADP
ejpam-4945	236	24	damping	damp	VERB
ejpam-4945	236	25	.	.	PUNCT
ejpam-4945	237	1	computers	computer	NOUN
ejpam-4945	237	2	&	&	CCONJ
ejpam-4945	237	3	mathematics	mathematics	PROPN
ejpam-4945	237	4	with	with	ADP
ejpam-4945	237	5	applications	application	NOUN
ejpam-4945	237	6	,	,	PUNCT
ejpam-4945	237	7	61(8):2191–2196	61(8):2191–2196	NUM
ejpam-4945	237	8	,	,	PUNCT
ejpam-4945	237	9	2011	2011	NUM
ejpam-4945	237	10	.	.	PUNCT
ejpam-4945	238	1	[	[	X
ejpam-4945	238	2	14	14	NUM
ejpam-4945	238	3	]	]	X
ejpam-4945	238	4	ch	ch	NOUN
ejpam-4945	238	5	g	g	PROPN
ejpam-4945	238	6	philos	philos	PROPN
ejpam-4945	238	7	.	.	PUNCT
ejpam-4945	239	1	on	on	ADP
ejpam-4945	239	2	the	the	DET
ejpam-4945	239	3	existence	existence	NOUN
ejpam-4945	239	4	of	of	ADP
ejpam-4945	239	5	nonoscillatory	nonoscillatory	ADJ
ejpam-4945	239	6	solutions	solution	NOUN
ejpam-4945	239	7	tending	tend	VERB
ejpam-4945	239	8	to	to	ADP
ejpam-4945	239	9	zero	zero	NUM
ejpam-4945	239	10	at8	at8	PROPN
ejpam-4945	239	11	for	for	ADP
ejpam-4945	239	12	differential	differential	ADJ
ejpam-4945	239	13	equations	equation	NOUN
ejpam-4945	239	14	with	with	ADP
ejpam-4945	239	15	positive	positive	ADJ
ejpam-4945	239	16	delays	delay	NOUN
ejpam-4945	239	17	.	.	PUNCT
ejpam-4945	240	1	archiv	archiv	PROPN
ejpam-4945	240	2	der	der	PROPN
ejpam-4945	240	3	mathematik	mathematik	PROPN
ejpam-4945	240	4	,	,	PUNCT
ejpam-4945	240	5	36:168–178	36:168–178	NUM
ejpam-4945	240	6	,	,	PUNCT
ejpam-4945	240	7	1981	1981	NUM
ejpam-4945	240	8	.	.	PUNCT
ejpam-4945	241	1	[	[	X
ejpam-4945	241	2	15	15	NUM
ejpam-4945	241	3	]	]	X
ejpam-4945	241	4	yanxiang	yanxiang	PROPN
ejpam-4945	241	5	shi	shi	PROPN
ejpam-4945	241	6	.	.	PUNCT
ejpam-4945	242	1	oscillation	oscillation	NOUN
ejpam-4945	242	2	criteria	criterion	NOUN
ejpam-4945	242	3	for	for	ADP
ejpam-4945	242	4	nth	nth	NOUN
ejpam-4945	242	5	order	order	NOUN
ejpam-4945	242	6	nonlinear	nonlinear	ADJ
ejpam-4945	242	7	neutral	neutral	ADJ
ejpam-4945	242	8	differential	differential	NOUN
ejpam-4945	242	9	equations	equation	NOUN
ejpam-4945	242	10	.	.	PUNCT
ejpam-4945	243	1	applied	apply	VERB
ejpam-4945	243	2	mathematics	mathematic	NOUN
ejpam-4945	243	3	and	and	CCONJ
ejpam-4945	243	4	computation	computation	NOUN
ejpam-4945	243	5	,	,	PUNCT
ejpam-4945	243	6	235:423–429	235:423–429	NUM
ejpam-4945	243	7	,	,	PUNCT
ejpam-4945	243	8	2014	2014	NUM
ejpam-4945	243	9	.	.	PUNCT
ejpam-4945	244	1	[	[	X
ejpam-4945	244	2	16	16	NUM
ejpam-4945	244	3	]	]	PUNCT
ejpam-4945	244	4	arun	arun	PROPN
ejpam-4945	244	5	kumar	kumar	PROPN
ejpam-4945	244	6	tripathy	tripathy	PROPN
ejpam-4945	244	7	and	and	CCONJ
ejpam-4945	244	8	rashmi	rashmi	PROPN
ejpam-4945	244	9	rekha	rekha	PROPN
ejpam-4945	244	10	mohanta	mohanta	NOUN
ejpam-4945	244	11	.	.	PUNCT
ejpam-4945	245	1	on	on	ADP
ejpam-4945	245	2	oscillatory	oscillatory	ADJ
ejpam-4945	245	3	fourth	fourth	ADJ
ejpam-4945	245	4	order	order	NOUN
ejpam-4945	245	5	nonlinear	nonlinear	ADJ
ejpam-4945	245	6	neutral	neutral	ADJ
ejpam-4945	245	7	differential	differential	NOUN
ejpam-4945	245	8	equations	equation	NOUN
ejpam-4945	245	9	–	–	PUNCT
ejpam-4945	245	10	iii	iii	PROPN
ejpam-4945	245	11	.	.	PUNCT
ejpam-4945	245	12	mathematica	mathematica	PROPN
ejpam-4945	245	13	slovaca	slovaca	PROPN
ejpam-4945	245	14	,	,	PUNCT
ejpam-4945	245	15	68(6):1385–1396	68(6):1385–1396	NUM
ejpam-4945	245	16	,	,	PUNCT
ejpam-4945	245	17	2018	2018	NUM
ejpam-4945	245	18	.	.	PUNCT
ejpam-4945	246	1	[	[	X
ejpam-4945	246	2	17	17	NUM
ejpam-4945	246	3	]	]	PUNCT
ejpam-4945	246	4	zhiting	zhiting	PROPN
ejpam-4945	246	5	xu	xu	PROPN
ejpam-4945	246	6	and	and	CCONJ
ejpam-4945	246	7	yong	yong	PROPN
ejpam-4945	246	8	xia	xia	PROPN
ejpam-4945	246	9	.	.	PUNCT
ejpam-4945	247	1	integral	integral	ADJ
ejpam-4945	247	2	averaging	averaging	NOUN
ejpam-4945	247	3	technique	technique	NOUN
ejpam-4945	247	4	and	and	CCONJ
ejpam-4945	247	5	oscillation	oscillation	NOUN
ejpam-4945	247	6	of	of	ADP
ejpam-4945	247	7	certain	certain	ADJ
ejpam-4945	247	8	even	even	ADJ
ejpam-4945	247	9	order	order	NOUN
ejpam-4945	247	10	delay	delay	NOUN
ejpam-4945	247	11	differential	differential	ADJ
ejpam-4945	247	12	equations	equation	NOUN
ejpam-4945	247	13	.	.	PUNCT
ejpam-4945	248	1	journal	journal	PROPN
ejpam-4945	248	2	of	of	ADP
ejpam-4945	248	3	mathematical	mathematical	ADJ
ejpam-4945	248	4	analysis	analysis	NOUN
ejpam-4945	248	5	and	and	CCONJ
ejpam-4945	248	6	applications	application	NOUN
ejpam-4945	248	7	,	,	PUNCT
ejpam-4945	248	8	292(1):238–246	292(1):238–246	NUM
ejpam-4945	248	9	,	,	PUNCT
ejpam-4945	248	10	2004	2004	NUM
ejpam-4945	248	11	.	.	PUNCT
ejpam-4945	249	1	[	[	X
ejpam-4945	249	2	18	18	NUM
ejpam-4945	249	3	]	]	PUNCT
ejpam-4945	249	4	chenghui	chenghui	PROPN
ejpam-4945	249	5	zhang	zhang	PROPN
ejpam-4945	249	6	,	,	PUNCT
ejpam-4945	249	7	tongxing	tongxe	VERB
ejpam-4945	249	8	li	li	NOUN
ejpam-4945	249	9	,	,	PUNCT
ejpam-4945	249	10	bo	bo	PROPN
ejpam-4945	249	11	sun	sun	PROPN
ejpam-4945	249	12	,	,	PUNCT
ejpam-4945	249	13	and	and	CCONJ
ejpam-4945	249	14	ethiraju	ethiraju	NOUN
ejpam-4945	249	15	thandapani	thandapani	NOUN
ejpam-4945	249	16	.	.	PUNCT
ejpam-4945	250	1	on	on	ADP
ejpam-4945	250	2	the	the	DET
ejpam-4945	250	3	oscillation	oscillation	NOUN
ejpam-4945	250	4	of	of	ADP
ejpam-4945	250	5	higher	high	ADJ
ejpam-4945	250	6	-	-	PUNCT
ejpam-4945	250	7	order	order	NOUN
ejpam-4945	250	8	half	half	ADJ
ejpam-4945	250	9	-	-	PUNCT
ejpam-4945	250	10	linear	linear	NOUN
ejpam-4945	250	11	delay	delay	NOUN
ejpam-4945	250	12	differential	differential	ADJ
ejpam-4945	250	13	equations	equation	NOUN
ejpam-4945	250	14	.	.	PUNCT
ejpam-4945	251	1	applied	apply	VERB
ejpam-4945	251	2	mathematics	mathematics	NOUN
ejpam-4945	251	3	letters	letter	NOUN
ejpam-4945	251	4	,	,	PUNCT
ejpam-4945	251	5	24(9):1618–1621	24(9):1618–1621	NUM
ejpam-4945	251	6	,	,	PUNCT
ejpam-4945	251	7	2011	2011	NUM
ejpam-4945	251	8	.	.	PUNCT