id	sid	tid	token	lemma	pos
ejpam-5591	1	1	european	european	PROPN
ejpam-5591	1	2	journal	journal	PROPN
ejpam-5591	1	3	of	of	ADP
ejpam-5591	1	4	pure	pure	ADJ
ejpam-5591	1	5	and	and	CCONJ
ejpam-5591	1	6	applied	applied	ADJ
ejpam-5591	1	7	mathematics	mathematic	NOUN
ejpam-5591	1	8	2025	2025	NUM
ejpam-5591	1	9	,	,	PUNCT
ejpam-5591	1	10	vol	vol	NOUN
ejpam-5591	1	11	.	.	PROPN
ejpam-5591	1	12	18	18	NUM
ejpam-5591	1	13	,	,	PUNCT
ejpam-5591	1	14	issue	issue	NOUN
ejpam-5591	1	15	1	1	NUM
ejpam-5591	1	16	,	,	PUNCT
ejpam-5591	1	17	article	article	NOUN
ejpam-5591	1	18	number	number	NOUN
ejpam-5591	1	19	5591	5591	NUM
ejpam-5591	1	20	issn	issn	VERB
ejpam-5591	1	21	1307	1307	NUM
ejpam-5591	1	22	-	-	SYM
ejpam-5591	1	23	5543	5543	NUM
ejpam-5591	1	24	–	–	PUNCT
ejpam-5591	1	25	ejpam.com	ejpam.com	X
ejpam-5591	1	26	published	publish	VERB
ejpam-5591	1	27	by	by	ADP
ejpam-5591	1	28	new	new	PROPN
ejpam-5591	1	29	york	york	PROPN
ejpam-5591	1	30	business	business	PROPN
ejpam-5591	1	31	global	global	ADJ
ejpam-5591	1	32	fourth	fourth	ADJ
ejpam-5591	1	33	-	-	PUNCT
ejpam-5591	1	34	order	order	NOUN
ejpam-5591	1	35	differential	differential	ADJ
ejpam-5591	1	36	equations	equation	NOUN
ejpam-5591	1	37	:	:	PUNCT
ejpam-5591	1	38	asymptotic	asymptotic	ADJ
ejpam-5591	1	39	and	and	CCONJ
ejpam-5591	1	40	oscillatory	oscillatory	ADJ
ejpam-5591	1	41	behaviors	behavior	NOUN
ejpam-5591	1	42	of	of	ADP
ejpam-5591	1	43	solutions	solution	NOUN
ejpam-5591	1	44	alanoud	alanoud	PROPN
ejpam-5591	1	45	almutairi	almutairi	PROPN
ejpam-5591	1	46	department	department	PROPN
ejpam-5591	1	47	of	of	ADP
ejpam-5591	1	48	mathematics	mathematic	NOUN
ejpam-5591	1	49	,	,	PUNCT
ejpam-5591	1	50	faculty	faculty	NOUN
ejpam-5591	1	51	of	of	ADP
ejpam-5591	1	52	science	science	NOUN
ejpam-5591	1	53	,	,	PUNCT
ejpam-5591	1	54	university	university	NOUN
ejpam-5591	1	55	of	of	ADP
ejpam-5591	1	56	hafr	hafr	PROPN
ejpam-5591	1	57	al	al	PROPN
ejpam-5591	1	58	batin	batin	PROPN
ejpam-5591	1	59	,	,	PUNCT
ejpam-5591	1	60	p.o	p.o	PROPN
ejpam-5591	1	61	.	.	PROPN
ejpam-5591	1	62	box	box	PROPN
ejpam-5591	1	63	1803	1803	NUM
ejpam-5591	1	64	,	,	PUNCT
ejpam-5591	1	65	hafar	hafar	ADV
ejpam-5591	1	66	al	al	PROPN
ejpam-5591	1	67	batin	batin	PROPN
ejpam-5591	1	68	31991	31991	NUM
ejpam-5591	1	69	,	,	PUNCT
ejpam-5591	1	70	saudi	saudi	PROPN
ejpam-5591	1	71	arabia	arabia	PROPN
ejpam-5591	1	72	abstract	abstract	NOUN
ejpam-5591	1	73	.	.	PUNCT
ejpam-5591	2	1	our	our	PRON
ejpam-5591	2	2	aim	aim	NOUN
ejpam-5591	2	3	in	in	ADP
ejpam-5591	2	4	this	this	DET
ejpam-5591	2	5	work	work	NOUN
ejpam-5591	2	6	is	be	AUX
ejpam-5591	2	7	to	to	PART
ejpam-5591	2	8	derive	derive	VERB
ejpam-5591	2	9	conditions	condition	NOUN
ejpam-5591	2	10	and	and	CCONJ
ejpam-5591	2	11	criteria	criterion	NOUN
ejpam-5591	2	12	for	for	ADP
ejpam-5591	2	13	the	the	DET
ejpam-5591	2	14	oscillation	oscillation	NOUN
ejpam-5591	2	15	of	of	ADP
ejpam-5591	2	16	some	some	DET
ejpam-5591	2	17	differential	differential	ADJ
ejpam-5591	2	18	equations	equation	NOUN
ejpam-5591	2	19	of	of	ADP
ejpam-5591	2	20	p	p	NOUN
ejpam-5591	2	21	-	-	PUNCT
ejpam-5591	2	22	laplace	laplace	NOUN
ejpam-5591	2	23	type	type	NOUN
ejpam-5591	2	24	with	with	ADP
ejpam-5591	2	25	a	a	DET
ejpam-5591	2	26	delayed	delay	VERB
ejpam-5591	2	27	term	term	NOUN
ejpam-5591	2	28	.	.	PUNCT
ejpam-5591	3	1	therefore	therefore	ADV
ejpam-5591	3	2	,	,	PUNCT
ejpam-5591	3	3	we	we	PRON
ejpam-5591	3	4	develop	develop	VERB
ejpam-5591	3	5	these	these	DET
ejpam-5591	3	6	criteria	criterion	NOUN
ejpam-5591	3	7	that	that	PRON
ejpam-5591	3	8	confirm	confirm	VERB
ejpam-5591	3	9	to	to	ADP
ejpam-5591	3	10	us	we	PRON
ejpam-5591	3	11	that	that	SCONJ
ejpam-5591	3	12	the	the	DET
ejpam-5591	3	13	equations	equation	NOUN
ejpam-5591	3	14	studied	study	VERB
ejpam-5591	3	15	are	be	AUX
ejpam-5591	3	16	oscillatory	oscillatory	ADJ
ejpam-5591	3	17	by	by	ADP
ejpam-5591	3	18	applying	apply	VERB
ejpam-5591	3	19	comparison	comparison	NOUN
ejpam-5591	3	20	with	with	ADP
ejpam-5591	3	21	lower	low	ADJ
ejpam-5591	3	22	-	-	PUNCT
ejpam-5591	3	23	order	order	NOUN
ejpam-5591	3	24	equations	equation	NOUN
ejpam-5591	3	25	and	and	CCONJ
ejpam-5591	3	26	riccati	riccati	PROPN
ejpam-5591	3	27	techniques	technique	NOUN
ejpam-5591	3	28	.	.	PUNCT
ejpam-5591	4	1	finally	finally	ADV
ejpam-5591	4	2	,	,	PUNCT
ejpam-5591	4	3	we	we	PRON
ejpam-5591	4	4	can	can	AUX
ejpam-5591	4	5	elucidate	elucidate	VERB
ejpam-5591	4	6	the	the	DET
ejpam-5591	4	7	meaning	meaning	NOUN
ejpam-5591	4	8	of	of	ADP
ejpam-5591	4	9	the	the	DET
ejpam-5591	4	10	new	new	ADJ
ejpam-5591	4	11	inequalities	inequality	NOUN
ejpam-5591	4	12	by	by	ADP
ejpam-5591	4	13	applying	apply	VERB
ejpam-5591	4	14	our	our	PRON
ejpam-5591	4	15	findings	finding	NOUN
ejpam-5591	4	16	to	to	ADP
ejpam-5591	4	17	a	a	DET
ejpam-5591	4	18	few	few	ADJ
ejpam-5591	4	19	particular	particular	ADJ
ejpam-5591	4	20	cases	case	NOUN
ejpam-5591	4	21	of	of	ADP
ejpam-5591	4	22	the	the	DET
ejpam-5591	4	23	studied	study	VERB
ejpam-5591	4	24	equation	equation	NOUN
ejpam-5591	4	25	.	.	PUNCT
ejpam-5591	5	1	our	our	PRON
ejpam-5591	5	2	findings	finding	NOUN
ejpam-5591	5	3	build	build	VERB
ejpam-5591	5	4	on	on	ADP
ejpam-5591	5	5	earlier	early	ADJ
ejpam-5591	5	6	findings	finding	NOUN
ejpam-5591	5	7	that	that	PRON
ejpam-5591	5	8	looked	look	VERB
ejpam-5591	5	9	at	at	ADP
ejpam-5591	5	10	equations	equation	NOUN
ejpam-5591	5	11	with	with	ADP
ejpam-5591	5	12	a	a	DET
ejpam-5591	5	13	delay	delay	NOUN
ejpam-5591	5	14	term	term	NOUN
ejpam-5591	5	15	and	and	CCONJ
ejpam-5591	5	16	operators	operator	NOUN
ejpam-5591	5	17	of	of	ADP
ejpam-5591	5	18	the	the	DET
ejpam-5591	5	19	p	p	ADJ
ejpam-5591	5	20	-	-	PUNCT
ejpam-5591	5	21	laplace	laplace	NOUN
ejpam-5591	5	22	type	type	NOUN
ejpam-5591	5	23	.	.	PUNCT
ejpam-5591	6	1	to	to	PART
ejpam-5591	6	2	demonstrate	demonstrate	VERB
ejpam-5591	6	3	the	the	DET
ejpam-5591	6	4	importance	importance	NOUN
ejpam-5591	6	5	of	of	ADP
ejpam-5591	6	6	the	the	DET
ejpam-5591	6	7	acquired	acquire	VERB
ejpam-5591	6	8	results	result	NOUN
ejpam-5591	6	9	,	,	PUNCT
ejpam-5591	6	10	we	we	PRON
ejpam-5591	6	11	provide	provide	VERB
ejpam-5591	6	12	an	an	DET
ejpam-5591	6	13	example	example	NOUN
ejpam-5591	6	14	.	.	PUNCT
ejpam-5591	7	1	2020	2020	NUM
ejpam-5591	7	2	mathematics	mathematic	NOUN
ejpam-5591	7	3	subject	subject	NOUN
ejpam-5591	7	4	classifications	classification	NOUN
ejpam-5591	7	5	:	:	PUNCT
ejpam-5591	7	6	34c10	34c10	NUM
ejpam-5591	7	7	,	,	PUNCT
ejpam-5591	7	8	34k11	34k11	NUM
ejpam-5591	7	9	key	key	ADJ
ejpam-5591	7	10	words	word	NOUN
ejpam-5591	7	11	and	and	CCONJ
ejpam-5591	7	12	phrases	phrase	NOUN
ejpam-5591	7	13	:	:	PUNCT
ejpam-5591	7	14	asymptotic	asymptotic	ADJ
ejpam-5591	7	15	behavior	behavior	NOUN
ejpam-5591	7	16	,	,	PUNCT
ejpam-5591	7	17	p	p	NOUN
ejpam-5591	7	18	-	-	PUNCT
ejpam-5591	7	19	laplacian	laplacian	ADJ
ejpam-5591	7	20	,	,	PUNCT
ejpam-5591	7	21	fourth	fourth	ADJ
ejpam-5591	7	22	-	-	PUNCT
ejpam-5591	7	23	order	order	NOUN
ejpam-5591	7	24	,	,	PUNCT
ejpam-5591	7	25	delay	delay	NOUN
ejpam-5591	7	26	differential	differential	ADJ
ejpam-5591	7	27	equations	equation	NOUN
ejpam-5591	7	28	1	1	NUM
ejpam-5591	7	29	.	.	PUNCT
ejpam-5591	7	30	introduction	introduction	NOUN
ejpam-5591	7	31	the	the	DET
ejpam-5591	7	32	study	study	NOUN
ejpam-5591	7	33	of	of	ADP
ejpam-5591	7	34	systems	system	NOUN
ejpam-5591	7	35	influenced	influence	VERB
ejpam-5591	7	36	by	by	ADP
ejpam-5591	7	37	their	their	PRON
ejpam-5591	7	38	historical	historical	ADJ
ejpam-5591	7	39	behavior	behavior	NOUN
ejpam-5591	7	40	requires	require	VERB
ejpam-5591	7	41	the	the	DET
ejpam-5591	7	42	use	use	NOUN
ejpam-5591	7	43	of	of	ADP
ejpam-5591	7	44	functional	functional	ADJ
ejpam-5591	7	45	equations	equation	NOUN
ejpam-5591	7	46	(	(	PUNCT
ejpam-5591	7	47	fdes	fde	NOUN
ejpam-5591	7	48	)	)	PUNCT
ejpam-5591	7	49	,	,	PUNCT
ejpam-5591	7	50	which	which	PRON
ejpam-5591	7	51	are	be	AUX
ejpam-5591	7	52	equations	equation	NOUN
ejpam-5591	7	53	where	where	SCONJ
ejpam-5591	7	54	the	the	DET
ejpam-5591	7	55	variables	variable	NOUN
ejpam-5591	7	56	’	'	PUNCT
ejpam-5591	7	57	current	current	ADJ
ejpam-5591	7	58	values	value	NOUN
ejpam-5591	7	59	are	be	AUX
ejpam-5591	7	60	dependent	dependent	ADJ
ejpam-5591	7	61	on	on	ADP
ejpam-5591	7	62	their	their	PRON
ejpam-5591	7	63	past	past	NOUN
ejpam-5591	7	64	or	or	CCONJ
ejpam-5591	7	65	future	future	ADJ
ejpam-5591	7	66	states	state	NOUN
ejpam-5591	7	67	.	.	PUNCT
ejpam-5591	8	1	delay	delay	NOUN
ejpam-5591	8	2	differential	differential	ADJ
ejpam-5591	8	3	equations	equation	NOUN
ejpam-5591	8	4	are	be	AUX
ejpam-5591	8	5	important	important	ADJ
ejpam-5591	8	6	categories	category	NOUN
ejpam-5591	8	7	of	of	ADP
ejpam-5591	8	8	these	these	DET
ejpam-5591	8	9	equations	equation	NOUN
ejpam-5591	8	10	.	.	PUNCT
ejpam-5591	9	1	these	these	DET
ejpam-5591	9	2	formulas	formula	NOUN
ejpam-5591	9	3	are	be	AUX
ejpam-5591	9	4	essential	essential	ADJ
ejpam-5591	9	5	for	for	ADP
ejpam-5591	9	6	simulating	simulate	VERB
ejpam-5591	9	7	intricate	intricate	ADJ
ejpam-5591	9	8	systems	system	NOUN
ejpam-5591	9	9	in	in	ADP
ejpam-5591	9	10	disciplines	discipline	NOUN
ejpam-5591	9	11	like	like	ADP
ejpam-5591	9	12	biology	biology	NOUN
ejpam-5591	9	13	,	,	PUNCT
ejpam-5591	9	14	engineering	engineering	NOUN
ejpam-5591	9	15	,	,	PUNCT
ejpam-5591	9	16	and	and	CCONJ
ejpam-5591	9	17	physics	physics	NOUN
ejpam-5591	9	18	.	.	PUNCT
ejpam-5591	10	1	for	for	ADP
ejpam-5591	10	2	instance	instance	NOUN
ejpam-5591	10	3	,	,	PUNCT
ejpam-5591	10	4	in	in	ADP
ejpam-5591	10	5	control	control	NOUN
ejpam-5591	10	6	theory	theory	NOUN
ejpam-5591	10	7	,	,	PUNCT
ejpam-5591	10	8	fdes	fde	NOUN
ejpam-5591	10	9	regulate	regulate	VERB
ejpam-5591	10	10	feedback	feedback	NOUN
ejpam-5591	10	11	systems	system	NOUN
ejpam-5591	10	12	to	to	PART
ejpam-5591	10	13	maintain	maintain	VERB
ejpam-5591	10	14	stability	stability	NOUN
ejpam-5591	10	15	,	,	PUNCT
ejpam-5591	10	16	and	and	CCONJ
ejpam-5591	10	17	in	in	ADP
ejpam-5591	10	18	ecology	ecology	NOUN
ejpam-5591	10	19	,	,	PUNCT
ejpam-5591	10	20	they	they	PRON
ejpam-5591	10	21	aid	aid	VERB
ejpam-5591	10	22	in	in	ADP
ejpam-5591	10	23	the	the	DET
ejpam-5591	10	24	analysis	analysis	NOUN
ejpam-5591	10	25	of	of	ADP
ejpam-5591	10	26	population	population	NOUN
ejpam-5591	10	27	dynamics	dynamic	NOUN
ejpam-5591	10	28	based	base	VERB
ejpam-5591	10	29	on	on	ADP
ejpam-5591	10	30	historical	historical	ADJ
ejpam-5591	10	31	states	state	NOUN
ejpam-5591	10	32	.	.	PUNCT
ejpam-5591	11	1	continuous	continuous	ADJ
ejpam-5591	11	2	research	research	NOUN
ejpam-5591	11	3	in	in	ADP
ejpam-5591	11	4	ddes	dde	NOUN
ejpam-5591	11	5	is	be	AUX
ejpam-5591	11	6	essential	essential	ADJ
ejpam-5591	11	7	for	for	ADP
ejpam-5591	11	8	creating	create	VERB
ejpam-5591	11	9	theoretical	theoretical	ADJ
ejpam-5591	11	10	underpinnings	underpinning	NOUN
ejpam-5591	11	11	and	and	CCONJ
ejpam-5591	11	12	some	some	DET
ejpam-5591	11	13	techniques	technique	NOUN
ejpam-5591	11	14	to	to	PART
ejpam-5591	11	15	address	address	VERB
ejpam-5591	11	16	real	real	ADJ
ejpam-5591	11	17	-	-	PUNCT
ejpam-5591	11	18	world	world	NOUN
ejpam-5591	11	19	issues	issue	NOUN
ejpam-5591	11	20	as	as	SCONJ
ejpam-5591	11	21	contemporary	contemporary	ADJ
ejpam-5591	11	22	systems	system	NOUN
ejpam-5591	11	23	become	become	VERB
ejpam-5591	11	24	more	more	ADV
ejpam-5591	11	25	complicated	complicated	ADJ
ejpam-5591	11	26	[	[	X
ejpam-5591	11	27	12]-[19	12]-[19	NUM
ejpam-5591	11	28	]	]	PUNCT
ejpam-5591	11	29	.	.	PUNCT
ejpam-5591	12	1	in	in	ADP
ejpam-5591	12	2	our	our	PRON
ejpam-5591	12	3	work	work	NOUN
ejpam-5591	12	4	,	,	PUNCT
ejpam-5591	12	5	we	we	PRON
ejpam-5591	12	6	focus	focus	VERB
ejpam-5591	12	7	on	on	ADP
ejpam-5591	12	8	the	the	DET
ejpam-5591	12	9	oscillation	oscillation	NOUN
ejpam-5591	12	10	of	of	ADP
ejpam-5591	12	11	(	(	PUNCT
ejpam-5591	12	12	κ	κ	PROPN
ejpam-5591	12	13	(	(	PUNCT
ejpam-5591	12	14	η	η	NOUN
ejpam-5591	12	15	)	)	PUNCT
ejpam-5591	12	16	∣∣z′′′	∣∣z′′′	PROPN
ejpam-5591	12	17	(	(	PUNCT
ejpam-5591	12	18	η)∣∣p−2	η)∣∣p−2	PROPN
ejpam-5591	12	19	z′′′	z′′′	PROPN
ejpam-5591	12	20	(	(	PUNCT
ejpam-5591	12	21	η	η	PROPN
ejpam-5591	12	22	)	)	PUNCT
ejpam-5591	12	23	)	)	PUNCT
ejpam-5591	12	24	′	′	NUM
ejpam-5591	13	1	+	+	CCONJ
ejpam-5591	13	2	j∑	j∑	VERB
ejpam-5591	13	3	i=1	i=1	PROPN
ejpam-5591	13	4	ai	ai	PROPN
ejpam-5591	13	5	(	(	PUNCT
ejpam-5591	13	6	η	η	PROPN
ejpam-5591	13	7	)	)	PUNCT
ejpam-5591	13	8	f	f	PROPN
ejpam-5591	13	9	(	(	PUNCT
ejpam-5591	13	10	z	z	NOUN
ejpam-5591	13	11	(	(	PUNCT
ejpam-5591	13	12	bi	bi	X
ejpam-5591	13	13	(	(	PUNCT
ejpam-5591	13	14	η	η	PROPN
ejpam-5591	13	15	)	)	PUNCT
ejpam-5591	13	16	)	)	PUNCT
ejpam-5591	13	17	)	)	PUNCT
ejpam-5591	14	1	=	=	SYM
ejpam-5591	14	2	0	0	NUM
ejpam-5591	14	3	,	,	PUNCT
ejpam-5591	14	4	η	η	PROPN
ejpam-5591	14	5	≥	≥	NOUN
ejpam-5591	14	6	η0	η0	NOUN
ejpam-5591	14	7	,	,	PUNCT
ejpam-5591	14	8	(	(	PUNCT
ejpam-5591	14	9	1	1	X
ejpam-5591	14	10	)	)	PUNCT
ejpam-5591	14	11	doi	doi	NOUN
ejpam-5591	14	12	:	:	PUNCT
ejpam-5591	14	13	https://doi.org/10.29020/nybg.ejpam.v18i1.5591	https://doi.org/10.29020/nybg.ejpam.v18i1.5591	VERB
ejpam-5591	14	14	email	email	NOUN
ejpam-5591	14	15	address	address	NOUN
ejpam-5591	14	16	:	:	PUNCT
ejpam-5591	14	17	amalmutairi@uhb.edu.sa	amalmutairi@uhb.edu.sa	PROPN
ejpam-5591	14	18	(	(	PUNCT
ejpam-5591	14	19	a.	a.	NOUN
ejpam-5591	14	20	almutairi	almutairi	PROPN
ejpam-5591	14	21	)	)	PUNCT
ejpam-5591	14	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5591	15	1	1	1	NUM
ejpam-5591	15	2	copyright	copyright	NOUN
ejpam-5591	15	3	:	:	PUNCT
ejpam-5591	15	4	©	©	PROPN
ejpam-5591	15	5	2025	2025	NUM
ejpam-5591	15	6	the	the	DET
ejpam-5591	15	7	author(s	author(s	NOUN
ejpam-5591	15	8	)	)	PUNCT
ejpam-5591	15	9	.	.	PUNCT
ejpam-5591	16	1	(	(	PUNCT
ejpam-5591	16	2	cc	cc	NOUN
ejpam-5591	16	3	by	by	ADP
ejpam-5591	16	4	-	-	PUNCT
ejpam-5591	16	5	nc	nc	PROPN
ejpam-5591	16	6	4.0	4.0	NUM
ejpam-5591	16	7	)	)	PUNCT
ejpam-5591	16	8	a.	a.	NOUN
ejpam-5591	16	9	almutairi	almutairi	PROPN
ejpam-5591	16	10	/	/	SYM
ejpam-5591	16	11	eur	eur	PROPN
ejpam-5591	16	12	.	.	PUNCT
ejpam-5591	17	1	j.	j.	PROPN
ejpam-5591	17	2	pure	pure	PROPN
ejpam-5591	17	3	appl	appl	PROPN
ejpam-5591	17	4	.	.	PROPN
ejpam-5591	17	5	math	math	PROPN
ejpam-5591	17	6	,	,	PUNCT
ejpam-5591	17	7	18	18	NUM
ejpam-5591	17	8	(	(	PUNCT
ejpam-5591	17	9	1	1	NUM
ejpam-5591	17	10	)	)	PUNCT
ejpam-5591	17	11	(	(	PUNCT
ejpam-5591	17	12	2025	2025	NUM
ejpam-5591	17	13	)	)	PUNCT
ejpam-5591	17	14	,	,	PUNCT
ejpam-5591	17	15	5591	5591	NUM
ejpam-5591	17	16	2	2	NUM
ejpam-5591	17	17	of	of	ADP
ejpam-5591	17	18	11	11	NUM
ejpam-5591	18	1	where	where	SCONJ
ejpam-5591	18	2	κ	κ	PROPN
ejpam-5591	18	3	∈	∈	PROPN
ejpam-5591	18	4	c1	c1	PROPN
ejpam-5591	18	5	(	(	PUNCT
ejpam-5591	18	6	[	[	X
ejpam-5591	18	7	η0,∞),r	η0,∞),r	ADJ
ejpam-5591	18	8	)	)	PUNCT
ejpam-5591	18	9	,	,	PUNCT
ejpam-5591	18	10	κ	κ	X
ejpam-5591	18	11	(	(	PUNCT
ejpam-5591	18	12	η	η	PROPN
ejpam-5591	18	13	)	)	PUNCT
ejpam-5591	18	14	>	>	X
ejpam-5591	18	15	0	0	NUM
ejpam-5591	18	16	,	,	PUNCT
ejpam-5591	18	17	κ′	κ′	NOUN
ejpam-5591	18	18	(	(	PUNCT
ejpam-5591	18	19	η	η	PROPN
ejpam-5591	18	20	)	)	PUNCT
ejpam-5591	18	21	≥	≥	NOUN
ejpam-5591	18	22	0	0	NUM
ejpam-5591	18	23	,	,	PUNCT
ejpam-5591	18	24	ai	ai	VERB
ejpam-5591	18	25	∈	∈	PROPN
ejpam-5591	18	26	c[η0,∞	c[η0,∞	NOUN
ejpam-5591	18	27	)	)	PUNCT
ejpam-5591	18	28	,	,	PUNCT
ejpam-5591	18	29	a	a	DET
ejpam-5591	18	30	(	(	PUNCT
ejpam-5591	18	31	η	η	NOUN
ejpam-5591	18	32	)	)	PUNCT
ejpam-5591	18	33	>	>	X
ejpam-5591	18	34	0	0	NUM
ejpam-5591	18	35	,	,	PUNCT
ejpam-5591	18	36	bi	bi	PROPN
ejpam-5591	18	37	∈	∈	PROPN
ejpam-5591	18	38	c[η0,∞	c[η0,∞	NOUN
ejpam-5591	18	39	)	)	PUNCT
ejpam-5591	18	40	,	,	PUNCT
ejpam-5591	18	41	bi	bi	NOUN
ejpam-5591	18	42	(	(	PUNCT
ejpam-5591	18	43	η	η	PROPN
ejpam-5591	18	44	)	)	PUNCT
ejpam-5591	18	45	≤	≤	PROPN
ejpam-5591	18	46	η	η	PROPN
ejpam-5591	18	47	,	,	PUNCT
ejpam-5591	18	48	limη→∞	limη→∞	PROPN
ejpam-5591	18	49	bi	bi	NOUN
ejpam-5591	18	50	(	(	PUNCT
ejpam-5591	18	51	η	η	PROPN
ejpam-5591	18	52	)	)	PUNCT
ejpam-5591	18	53	=	=	SYM
ejpam-5591	18	54	∞	∞	PROPN
ejpam-5591	18	55	;	;	PUNCT
ejpam-5591	19	1	i	i	PRON
ejpam-5591	19	2	=	=	NOUN
ejpam-5591	19	3	1	1	NUM
ejpam-5591	19	4	,	,	PUNCT
ejpam-5591	19	5	2	2	NUM
ejpam-5591	19	6	,	,	PUNCT
ejpam-5591	19	7	..	..	PUNCT
ejpam-5591	19	8	,	,	PUNCT
ejpam-5591	19	9	j	j	PROPN
ejpam-5591	19	10	,	,	PUNCT
ejpam-5591	19	11	f	f	PROPN
ejpam-5591	19	12	∈	∈	PROPN
ejpam-5591	19	13	c	c	PROPN
ejpam-5591	19	14	(	(	PUNCT
ejpam-5591	19	15	r	r	NOUN
ejpam-5591	19	16	,	,	PUNCT
ejpam-5591	19	17	r	r	NOUN
ejpam-5591	19	18	)	)	PUNCT
ejpam-5591	19	19	such	such	ADJ
ejpam-5591	19	20	that	that	SCONJ
ejpam-5591	19	21	f	f	PROPN
ejpam-5591	19	22	(	(	PUNCT
ejpam-5591	19	23	η	η	PROPN
ejpam-5591	19	24	)	)	PUNCT
ejpam-5591	19	25	/ηp−1	/ηp−1	PROPN
ejpam-5591	19	26	≥	≥	X
ejpam-5591	19	27	ℓ	ℓ	INTJ
ejpam-5591	19	28	>	>	X
ejpam-5591	19	29	0	0	NUM
ejpam-5591	19	30	,	,	PUNCT
ejpam-5591	19	31	for	for	ADP
ejpam-5591	19	32	η	η	PROPN
ejpam-5591	19	33	̸=	̸=	PROPN
ejpam-5591	19	34	0	0	NUM
ejpam-5591	19	35	,	,	PUNCT
ejpam-5591	19	36	p	p	X
ejpam-5591	19	37	>	>	X
ejpam-5591	19	38	1is	1is	ADJ
ejpam-5591	19	39	a	a	DET
ejpam-5591	19	40	constant	constant	ADJ
ejpam-5591	19	41	,	,	PUNCT
ejpam-5591	19	42	(	(	PUNCT
ejpam-5591	19	43	2	2	NUM
ejpam-5591	19	44	)	)	PUNCT
ejpam-5591	19	45	and	and	CCONJ
ejpam-5591	19	46	under	under	ADP
ejpam-5591	19	47	the	the	DET
ejpam-5591	19	48	condition	condition	NOUN
ejpam-5591	19	49	∫	∫	PROPN
ejpam-5591	19	50	∞	∞	PROPN
ejpam-5591	19	51	η0	η0	NOUN
ejpam-5591	19	52	1	1	NUM
ejpam-5591	19	53	κ1/(p−1	κ1/(p−1	NOUN
ejpam-5591	19	54	)	)	PUNCT
ejpam-5591	19	55	(	(	PUNCT
ejpam-5591	19	56	η	η	NOUN
ejpam-5591	19	57	)	)	PUNCT
ejpam-5591	19	58	dη	dη	NOUN
ejpam-5591	19	59	=	=	SYM
ejpam-5591	19	60	∞.	∞.	PROPN
ejpam-5591	19	61	(	(	PUNCT
ejpam-5591	19	62	3	3	NUM
ejpam-5591	19	63	)	)	PUNCT
ejpam-5591	19	64	definition	definition	NOUN
ejpam-5591	19	65	1	1	NUM
ejpam-5591	19	66	.	.	PUNCT
ejpam-5591	20	1	[	[	X
ejpam-5591	20	2	6	6	NUM
ejpam-5591	20	3	]	]	PUNCT
ejpam-5591	20	4	if	if	SCONJ
ejpam-5591	20	5	κ	κ	X
ejpam-5591	20	6	(	(	PUNCT
ejpam-5591	20	7	η	η	PROPN
ejpam-5591	20	8	)	)	PUNCT
ejpam-5591	20	9	(	(	PUNCT
ejpam-5591	20	10	z′′′	z′′′	PROPN
ejpam-5591	20	11	(	(	PUNCT
ejpam-5591	20	12	η))p−1	η))p−1	PROPN
ejpam-5591	20	13	∈	∈	PROPN
ejpam-5591	20	14	c1[ηz,∞	c1[ηz,∞	PROPN
ejpam-5591	20	15	)	)	PUNCT
ejpam-5591	20	16	,	,	PUNCT
ejpam-5591	20	17	and	and	CCONJ
ejpam-5591	20	18	z	z	PROPN
ejpam-5591	20	19	(	(	PUNCT
ejpam-5591	20	20	η	η	NOUN
ejpam-5591	20	21	)	)	PUNCT
ejpam-5591	20	22	satisfies	satisfie	NOUN
ejpam-5591	20	23	(	(	PUNCT
ejpam-5591	20	24	1	1	NUM
ejpam-5591	20	25	)	)	PUNCT
ejpam-5591	20	26	on	on	ADP
ejpam-5591	20	27	[	[	X
ejpam-5591	20	28	ηz,∞	ηz,∞	PROPN
ejpam-5591	20	29	)	)	PUNCT
ejpam-5591	20	30	,	,	PUNCT
ejpam-5591	20	31	then	then	ADV
ejpam-5591	20	32	a	a	DET
ejpam-5591	20	33	function	function	NOUN
ejpam-5591	20	34	z	z	NOUN
ejpam-5591	20	35	∈	∈	PROPN
ejpam-5591	20	36	c3[ηz,∞	c3[ηz,∞	PROPN
ejpam-5591	20	37	)	)	PUNCT
ejpam-5591	20	38	,	,	PUNCT
ejpam-5591	20	39	ηz	ηz	PROPN
ejpam-5591	20	40	≥	≥	NOUN
ejpam-5591	20	41	η0	η0	NOUN
ejpam-5591	20	42	,	,	PUNCT
ejpam-5591	20	43	is	be	AUX
ejpam-5591	20	44	a	a	DET
ejpam-5591	20	45	solution	solution	NOUN
ejpam-5591	20	46	of	of	ADP
ejpam-5591	20	47	(	(	PUNCT
ejpam-5591	20	48	1	1	NUM
ejpam-5591	20	49	)	)	PUNCT
ejpam-5591	20	50	.	.	PUNCT
ejpam-5591	21	1	if	if	SCONJ
ejpam-5591	21	2	a	a	DET
ejpam-5591	21	3	solution	solution	NOUN
ejpam-5591	21	4	of	of	ADP
ejpam-5591	21	5	(	(	PUNCT
ejpam-5591	21	6	1	1	NUM
ejpam-5591	21	7	)	)	PUNCT
ejpam-5591	21	8	contains	contain	VERB
ejpam-5591	21	9	arbitrarily	arbitrarily	ADV
ejpam-5591	21	10	large	large	ADJ
ejpam-5591	21	11	zeros	zero	NOUN
ejpam-5591	21	12	on	on	ADP
ejpam-5591	21	13	[	[	X
ejpam-5591	21	14	ηz,∞	ηz,∞	PROPN
ejpam-5591	21	15	)	)	PUNCT
ejpam-5591	21	16	,	,	PUNCT
ejpam-5591	21	17	it	it	PRON
ejpam-5591	21	18	is	be	AUX
ejpam-5591	21	19	said	say	VERB
ejpam-5591	21	20	to	to	PART
ejpam-5591	21	21	be	be	AUX
ejpam-5591	21	22	oscillatory	oscillatory	ADJ
ejpam-5591	21	23	;	;	PUNCT
ejpam-5591	21	24	if	if	SCONJ
ejpam-5591	21	25	not	not	PART
ejpam-5591	21	26	,	,	PUNCT
ejpam-5591	21	27	it	it	PRON
ejpam-5591	21	28	is	be	AUX
ejpam-5591	21	29	said	say	VERB
ejpam-5591	21	30	to	to	PART
ejpam-5591	21	31	be	be	AUX
ejpam-5591	21	32	nonoscillatory	nonoscillatory	ADJ
ejpam-5591	21	33	.	.	PUNCT
ejpam-5591	22	1	if	if	SCONJ
ejpam-5591	22	2	all	all	PRON
ejpam-5591	22	3	of	of	ADP
ejpam-5591	22	4	its	its	PRON
ejpam-5591	22	5	solutions	solution	NOUN
ejpam-5591	22	6	are	be	AUX
ejpam-5591	22	7	oscillatory	oscillatory	ADJ
ejpam-5591	22	8	,	,	PUNCT
ejpam-5591	22	9	the	the	DET
ejpam-5591	22	10	equations	equation	NOUN
ejpam-5591	22	11	(	(	PUNCT
ejpam-5591	22	12	1	1	X
ejpam-5591	22	13	)	)	PUNCT
ejpam-5591	22	14	are	be	AUX
ejpam-5591	22	15	considered	consider	VERB
ejpam-5591	22	16	oscillatory	oscillatory	ADJ
ejpam-5591	22	17	.	.	PUNCT
ejpam-5591	23	1	the	the	DET
ejpam-5591	23	2	oscillation	oscillation	NOUN
ejpam-5591	23	3	criteria	criterion	NOUN
ejpam-5591	23	4	for	for	ADP
ejpam-5591	23	5	equtions	eqution	NOUN
ejpam-5591	23	6	with	with	ADP
ejpam-5591	23	7	p	p	ADJ
ejpam-5591	23	8	-	-	PUNCT
ejpam-5591	23	9	laplace	laplace	NOUN
ejpam-5591	23	10	type	type	NOUN
ejpam-5591	23	11	have	have	AUX
ejpam-5591	23	12	drawn	draw	VERB
ejpam-5591	23	13	a	a	DET
ejpam-5591	23	14	lot	lot	NOUN
ejpam-5591	23	15	of	of	ADP
ejpam-5591	23	16	interest	interest	NOUN
ejpam-5591	23	17	from	from	ADP
ejpam-5591	23	18	scientists	scientist	NOUN
ejpam-5591	23	19	,	,	PUNCT
ejpam-5591	23	20	engineers	engineer	NOUN
ejpam-5591	23	21	,	,	PUNCT
ejpam-5591	23	22	and	and	CCONJ
ejpam-5591	23	23	researchers	researcher	NOUN
ejpam-5591	23	24	in	in	ADP
ejpam-5591	23	25	the	the	DET
ejpam-5591	23	26	study	study	NOUN
ejpam-5591	23	27	of	of	ADP
ejpam-5591	23	28	the	the	DET
ejpam-5591	23	29	oscillation	oscillation	NOUN
ejpam-5591	23	30	to	to	ADP
ejpam-5591	23	31	ddes	dde	NOUN
ejpam-5591	23	32	,	,	PUNCT
ejpam-5591	23	33	which	which	PRON
ejpam-5591	23	34	has	have	AUX
ejpam-5591	23	35	grown	grow	VERB
ejpam-5591	23	36	in	in	ADP
ejpam-5591	23	37	importance	importance	NOUN
ejpam-5591	23	38	and	and	CCONJ
ejpam-5591	23	39	prominence	prominence	NOUN
ejpam-5591	23	40	in	in	ADP
ejpam-5591	23	41	recent	recent	ADJ
ejpam-5591	23	42	years	year	NOUN
ejpam-5591	23	43	.	.	PUNCT
ejpam-5591	24	1	some	some	DET
ejpam-5591	24	2	advanced	advanced	ADJ
ejpam-5591	24	3	models	model	NOUN
ejpam-5591	24	4	based	base	VERB
ejpam-5591	24	5	on	on	ADP
ejpam-5591	24	6	delays	delay	NOUN
ejpam-5591	24	7	differential	differential	NOUN
ejpam-5591	24	8	equations	equation	NOUN
ejpam-5591	24	9	with	with	ADP
ejpam-5591	24	10	fractional	fractional	ADJ
ejpam-5591	24	11	characteristics	characteristic	NOUN
ejpam-5591	24	12	have	have	AUX
ejpam-5591	24	13	been	be	AUX
ejpam-5591	24	14	developed	develop	VERB
ejpam-5591	24	15	as	as	ADP
ejpam-5591	24	16	a	a	DET
ejpam-5591	24	17	result	result	NOUN
ejpam-5591	24	18	of	of	ADP
ejpam-5591	24	19	this	this	DET
ejpam-5591	24	20	interest	interest	NOUN
ejpam-5591	24	21	and	and	CCONJ
ejpam-5591	24	22	have	have	AUX
ejpam-5591	24	23	shown	show	VERB
ejpam-5591	24	24	value	value	NOUN
ejpam-5591	24	25	in	in	ADP
ejpam-5591	24	26	a	a	DET
ejpam-5591	24	27	variety	variety	NOUN
ejpam-5591	24	28	of	of	ADP
ejpam-5591	24	29	sectors	sector	NOUN
ejpam-5591	24	30	[	[	X
ejpam-5591	24	31	7]-[2	7]-[2	X
ejpam-5591	24	32	]	]	PUNCT
ejpam-5591	24	33	.	.	PUNCT
ejpam-5591	25	1	this	this	DET
ejpam-5591	25	2	technique	technique	NOUN
ejpam-5591	25	3	is	be	AUX
ejpam-5591	25	4	effective	effective	ADJ
ejpam-5591	25	5	for	for	ADP
ejpam-5591	25	6	researching	research	VERB
ejpam-5591	25	7	the	the	DET
ejpam-5591	25	8	transmission	transmission	NOUN
ejpam-5591	25	9	of	of	ADP
ejpam-5591	25	10	ultrasound	ultrasound	NOUN
ejpam-5591	25	11	,	,	PUNCT
ejpam-5591	25	12	mimicking	mimic	VERB
ejpam-5591	25	13	the	the	DET
ejpam-5591	25	14	behavior	behavior	NOUN
ejpam-5591	25	15	of	of	ADP
ejpam-5591	25	16	proteins	protein	NOUN
ejpam-5591	25	17	and	and	CCONJ
ejpam-5591	25	18	polymers	polymer	NOUN
ejpam-5591	25	19	,	,	PUNCT
ejpam-5591	25	20	and	and	CCONJ
ejpam-5591	25	21	examining	examine	VERB
ejpam-5591	25	22	the	the	DET
ejpam-5591	25	23	mechanical	mechanical	ADJ
ejpam-5591	25	24	behavior	behavior	NOUN
ejpam-5591	25	25	of	of	ADP
ejpam-5591	25	26	human	human	ADJ
ejpam-5591	25	27	tissues	tissue	NOUN
ejpam-5591	25	28	under	under	ADP
ejpam-5591	25	29	stress	stress	NOUN
ejpam-5591	25	30	.	.	PUNCT
ejpam-5591	26	1	we	we	PRON
ejpam-5591	26	2	can	can	AUX
ejpam-5591	26	3	better	well	ADV
ejpam-5591	26	4	comprehend	comprehend	VERB
ejpam-5591	26	5	numerous	numerous	ADJ
ejpam-5591	26	6	biological	biological	ADJ
ejpam-5591	26	7	and	and	CCONJ
ejpam-5591	26	8	physical	physical	ADJ
ejpam-5591	26	9	processes	process	NOUN
ejpam-5591	26	10	thanks	thank	NOUN
ejpam-5591	26	11	to	to	ADP
ejpam-5591	26	12	these	these	DET
ejpam-5591	26	13	models	model	NOUN
ejpam-5591	26	14	,	,	PUNCT
ejpam-5591	26	15	which	which	PRON
ejpam-5591	26	16	also	also	ADV
ejpam-5591	26	17	enable	enable	VERB
ejpam-5591	26	18	scientists	scientist	NOUN
ejpam-5591	26	19	come	come	VERB
ejpam-5591	26	20	up	up	ADP
ejpam-5591	26	21	with	with	ADP
ejpam-5591	26	22	creative	creative	ADJ
ejpam-5591	26	23	solutions	solution	NOUN
ejpam-5591	26	24	for	for	ADP
ejpam-5591	26	25	challenging	challenge	VERB
ejpam-5591	26	26	practical	practical	ADJ
ejpam-5591	26	27	problems	problem	NOUN
ejpam-5591	26	28	(	(	PUNCT
ejpam-5591	26	29	see	see	VERB
ejpam-5591	26	30	[	[	X
ejpam-5591	26	31	1]-[11	1]-[11	NUM
ejpam-5591	26	32	]	]	PUNCT
ejpam-5591	26	33	)	)	PUNCT
ejpam-5591	26	34	.	.	PUNCT
ejpam-5591	27	1	in	in	ADP
ejpam-5591	27	2	order	order	NOUN
ejpam-5591	27	3	to	to	PART
ejpam-5591	27	4	apply	apply	VERB
ejpam-5591	27	5	mathematical	mathematical	ADJ
ejpam-5591	27	6	methods	method	NOUN
ejpam-5591	27	7	to	to	ADP
ejpam-5591	27	8	practical	practical	ADJ
ejpam-5591	27	9	or	or	CCONJ
ejpam-5591	27	10	real	real	ADJ
ejpam-5591	27	11	-	-	PUNCT
ejpam-5591	27	12	world	world	NOUN
ejpam-5591	27	13	issues	issue	NOUN
ejpam-5591	27	14	,	,	PUNCT
ejpam-5591	27	15	the	the	DET
ejpam-5591	27	16	issue	issue	NOUN
ejpam-5591	27	17	must	must	AUX
ejpam-5591	27	18	be	be	AUX
ejpam-5591	27	19	stated	state	VERB
ejpam-5591	27	20	in	in	ADP
ejpam-5591	27	21	mathematical	mathematical	ADJ
ejpam-5591	27	22	terms	term	NOUN
ejpam-5591	27	23	.	.	PUNCT
ejpam-5591	28	1	this	this	PRON
ejpam-5591	28	2	entails	entail	VERB
ejpam-5591	28	3	developing	develop	VERB
ejpam-5591	28	4	a	a	DET
ejpam-5591	28	5	model	model	NOUN
ejpam-5591	28	6	a	a	DET
ejpam-5591	28	7	mathematical	mathematical	ADJ
ejpam-5591	28	8	description	description	NOUN
ejpam-5591	28	9	of	of	ADP
ejpam-5591	28	10	the	the	DET
ejpam-5591	28	11	issue	issue	NOUN
ejpam-5591	28	12	.	.	PUNCT
ejpam-5591	29	1	it	it	PRON
ejpam-5591	29	2	is	be	AUX
ejpam-5591	29	3	known	know	VERB
ejpam-5591	29	4	mathematically	mathematically	ADV
ejpam-5591	29	5	that	that	SCONJ
ejpam-5591	29	6	derivatives	derivative	NOUN
ejpam-5591	29	7	describe	describe	VERB
ejpam-5591	29	8	rates	rate	NOUN
ejpam-5591	29	9	of	of	ADP
ejpam-5591	29	10	change	change	NOUN
ejpam-5591	29	11	,	,	PUNCT
ejpam-5591	29	12	so	so	SCONJ
ejpam-5591	29	13	equations	equation	NOUN
ejpam-5591	29	14	that	that	PRON
ejpam-5591	29	15	link	link	VERB
ejpam-5591	29	16	functions	function	NOUN
ejpam-5591	29	17	and	and	CCONJ
ejpam-5591	29	18	their	their	PRON
ejpam-5591	29	19	derivatives	derivative	NOUN
ejpam-5591	29	20	are	be	AUX
ejpam-5591	29	21	often	often	ADV
ejpam-5591	29	22	included	include	VERB
ejpam-5591	29	23	in	in	ADP
ejpam-5591	29	24	mathematical	mathematical	ADJ
ejpam-5591	29	25	models	model	NOUN
ejpam-5591	29	26	.	.	PUNCT
ejpam-5591	30	1	these	these	DET
ejpam-5591	30	2	equations	equation	NOUN
ejpam-5591	30	3	,	,	PUNCT
ejpam-5591	30	4	also	also	ADV
ejpam-5591	30	5	referred	refer	VERB
ejpam-5591	30	6	to	to	ADP
ejpam-5591	30	7	as	as	ADP
ejpam-5591	30	8	differential	differential	ADJ
ejpam-5591	30	9	equations	equation	NOUN
ejpam-5591	30	10	,	,	PUNCT
ejpam-5591	30	11	are	be	AUX
ejpam-5591	30	12	used	use	VERB
ejpam-5591	30	13	in	in	ADP
ejpam-5591	30	14	many	many	ADJ
ejpam-5591	30	15	scientific	scientific	ADJ
ejpam-5591	30	16	domains	domain	NOUN
ejpam-5591	30	17	,	,	PUNCT
ejpam-5591	30	18	including	include	VERB
ejpam-5591	30	19	economics	economic	NOUN
ejpam-5591	30	20	,	,	PUNCT
ejpam-5591	30	21	chemistry	chemistry	NOUN
ejpam-5591	30	22	,	,	PUNCT
ejpam-5591	30	23	physics	physics	NOUN
ejpam-5591	30	24	,	,	PUNCT
ejpam-5591	30	25	and	and	CCONJ
ejpam-5591	30	26	biology	biology	NOUN
ejpam-5591	31	1	[	[	X
ejpam-5591	31	2	20]-[21	20]-[21	X
ejpam-5591	31	3	]	]	X
ejpam-5591	31	4	.	.	PUNCT
ejpam-5591	32	1	the	the	DET
ejpam-5591	32	2	qualitative	qualitative	ADJ
ejpam-5591	32	3	theory	theory	NOUN
ejpam-5591	32	4	of	of	ADP
ejpam-5591	32	5	differential	differential	ADJ
ejpam-5591	32	6	equations	equation	NOUN
ejpam-5591	32	7	has	have	VERB
ejpam-5591	32	8	an	an	DET
ejpam-5591	32	9	important	important	ADJ
ejpam-5591	32	10	place	place	NOUN
ejpam-5591	32	11	in	in	ADP
ejpam-5591	32	12	the	the	DET
ejpam-5591	32	13	study	study	NOUN
ejpam-5591	32	14	of	of	ADP
ejpam-5591	32	15	applied	apply	VERB
ejpam-5591	32	16	as	as	ADV
ejpam-5591	32	17	well	well	ADV
ejpam-5591	32	18	as	as	ADP
ejpam-5591	32	19	theoretical	theoretical	ADJ
ejpam-5591	32	20	mathematics	mathematic	NOUN
ejpam-5591	32	21	.	.	PUNCT
ejpam-5591	33	1	it	it	PRON
ejpam-5591	33	2	introduces	introduce	VERB
ejpam-5591	33	3	dynamical	dynamical	ADJ
ejpam-5591	33	4	systems	system	NOUN
ejpam-5591	33	5	,	,	PUNCT
ejpam-5591	33	6	a	a	DET
ejpam-5591	33	7	popular	popular	ADJ
ejpam-5591	33	8	area	area	NOUN
ejpam-5591	33	9	of	of	ADP
ejpam-5591	33	10	mathematics	mathematic	NOUN
ejpam-5591	33	11	in	in	ADP
ejpam-5591	33	12	recent	recent	ADJ
ejpam-5591	33	13	years	year	NOUN
ejpam-5591	33	14	,	,	PUNCT
ejpam-5591	33	15	and	and	CCONJ
ejpam-5591	33	16	it	it	PRON
ejpam-5591	33	17	is	be	AUX
ejpam-5591	33	18	works	work	NOUN
ejpam-5591	33	19	as	as	ADP
ejpam-5591	33	20	an	an	DET
ejpam-5591	33	21	expansion	expansion	NOUN
ejpam-5591	33	22	and	and	CCONJ
ejpam-5591	33	23	generalization	generalization	NOUN
ejpam-5591	33	24	of	of	ADP
ejpam-5591	33	25	some	some	DET
ejpam-5591	33	26	types	type	NOUN
ejpam-5591	33	27	of	of	ADP
ejpam-5591	33	28	ordinary	ordinary	ADJ
ejpam-5591	33	29	equations	equation	NOUN
ejpam-5591	33	30	.	.	PUNCT
ejpam-5591	34	1	it	it	PRON
ejpam-5591	34	2	also	also	ADV
ejpam-5591	34	3	comes	come	VERB
ejpam-5591	34	4	in	in	ADP
ejpam-5591	34	5	quite	quite	ADV
ejpam-5591	34	6	handy	handy	ADJ
ejpam-5591	34	7	when	when	SCONJ
ejpam-5591	34	8	dealing	deal	VERB
ejpam-5591	34	9	with	with	ADP
ejpam-5591	34	10	complicated	complicated	ADJ
ejpam-5591	34	11	differential	differential	ADJ
ejpam-5591	34	12	equations	equation	NOUN
ejpam-5591	34	13	that	that	PRON
ejpam-5591	34	14	are	be	AUX
ejpam-5591	34	15	impossible	impossible	ADJ
ejpam-5591	34	16	to	to	PART
ejpam-5591	34	17	solve	solve	VERB
ejpam-5591	34	18	with	with	ADP
ejpam-5591	34	19	traditional	traditional	ADJ
ejpam-5591	34	20	techniques	technique	NOUN
ejpam-5591	34	21	.	.	PUNCT
ejpam-5591	35	1	making	make	VERB
ejpam-5591	35	2	assumptions	assumption	NOUN
ejpam-5591	35	3	on	on	ADP
ejpam-5591	35	4	the	the	DET
ejpam-5591	35	5	solutions	solution	NOUN
ejpam-5591	35	6	behavior	behavior	NOUN
ejpam-5591	35	7	without	without	ADP
ejpam-5591	35	8	actually	actually	ADV
ejpam-5591	35	9	solving	solve	VERB
ejpam-5591	35	10	them	they	PRON
ejpam-5591	35	11	is	be	AUX
ejpam-5591	35	12	the	the	DET
ejpam-5591	35	13	basic	basic	ADJ
ejpam-5591	35	14	idea	idea	NOUN
ejpam-5591	35	15	underlying	underlie	VERB
ejpam-5591	35	16	qualitative	qualitative	ADJ
ejpam-5591	35	17	analysis	analysis	NOUN
ejpam-5591	35	18	of	of	ADP
ejpam-5591	35	19	differential	differential	ADJ
ejpam-5591	35	20	equations	equation	NOUN
ejpam-5591	35	21	[	[	X
ejpam-5591	35	22	16	16	NUM
ejpam-5591	35	23	,	,	PUNCT
ejpam-5591	35	24	23	23	NUM
ejpam-5591	35	25	]	]	PUNCT
ejpam-5591	35	26	.	.	PUNCT
ejpam-5591	36	1	in	in	ADP
ejpam-5591	36	2	mathematics	mathematics	PROPN
ejpam-5591	36	3	,	,	PUNCT
ejpam-5591	36	4	a	a	DET
ejpam-5591	36	5	delay	delay	NOUN
ejpam-5591	36	6	differential	differential	NOUN
ejpam-5591	36	7	equation	equation	NOUN
ejpam-5591	36	8	is	be	AUX
ejpam-5591	36	9	a	a	DET
ejpam-5591	36	10	kind	kind	NOUN
ejpam-5591	36	11	of	of	ADP
ejpam-5591	36	12	fdes	fde	NOUN
ejpam-5591	36	13	that	that	PRON
ejpam-5591	36	14	expresses	express	VERB
ejpam-5591	36	15	the	the	DET
ejpam-5591	36	16	derivative	derivative	NOUN
ejpam-5591	36	17	of	of	ADP
ejpam-5591	36	18	some	some	DET
ejpam-5591	36	19	function	function	NOUN
ejpam-5591	36	20	at	at	ADP
ejpam-5591	36	21	a	a	DET
ejpam-5591	36	22	given	give	VERB
ejpam-5591	36	23	time	time	NOUN
ejpam-5591	36	24	in	in	ADP
ejpam-5591	36	25	types	type	NOUN
ejpam-5591	36	26	of	of	ADP
ejpam-5591	36	27	the	the	DET
ejpam-5591	36	28	function	function	NOUN
ejpam-5591	36	29	’s	’s	PART
ejpam-5591	36	30	values	value	NOUN
ejpam-5591	36	31	at	at	ADP
ejpam-5591	36	32	previous	previous	ADJ
ejpam-5591	36	33	times	time	NOUN
ejpam-5591	36	34	.	.	PUNCT
ejpam-5591	37	1	these	these	DET
ejpam-5591	37	2	equations	equation	NOUN
ejpam-5591	37	3	are	be	AUX
ejpam-5591	37	4	called	call	VERB
ejpam-5591	37	5	hereditary	hereditary	ADJ
ejpam-5591	37	6	systems	system	NOUN
ejpam-5591	37	7	,	,	PUNCT
ejpam-5591	37	8	dead	dead	ADJ
ejpam-5591	37	9	time	time	NOUN
ejpam-5591	37	10	systems	system	NOUN
ejpam-5591	37	11	,	,	PUNCT
ejpam-5591	37	12	aftereffects	aftereffect	NOUN
ejpam-5591	37	13	systems	system	NOUN
ejpam-5591	37	14	,	,	PUNCT
ejpam-5591	37	15	time	time	NOUN
ejpam-5591	37	16	delay	delay	NOUN
ejpam-5591	37	17	systems	system	NOUN
ejpam-5591	37	18	.	.	PUNCT
ejpam-5591	38	1	additionally	additionally	ADV
ejpam-5591	38	2	,	,	PUNCT
ejpam-5591	38	3	there	there	PRON
ejpam-5591	38	4	are	be	VERB
ejpam-5591	38	5	sophisticated	sophisticated	ADJ
ejpam-5591	38	6	differential	differential	ADJ
ejpam-5591	38	7	equations	equation	NOUN
ejpam-5591	38	8	that	that	PRON
ejpam-5591	38	9	can	can	AUX
ejpam-5591	38	10	be	be	AUX
ejpam-5591	38	11	used	use	VERB
ejpam-5591	38	12	in	in	ADP
ejpam-5591	38	13	a	a	DET
ejpam-5591	38	14	variety	variety	NOUN
ejpam-5591	38	15	of	of	ADP
ejpam-5591	38	16	real	real	ADJ
ejpam-5591	38	17	-	-	PUNCT
ejpam-5591	38	18	world	world	NOUN
ejpam-5591	38	19	scenarios	scenario	NOUN
ejpam-5591	38	20	where	where	SCONJ
ejpam-5591	38	21	the	the	DET
ejpam-5591	38	22	rate	rate	NOUN
ejpam-5591	38	23	at	at	ADP
ejpam-5591	38	24	which	which	PRON
ejpam-5591	38	25	a	a	DET
ejpam-5591	38	26	system	system	NOUN
ejpam-5591	38	27	’s	’s	PART
ejpam-5591	38	28	state	state	NOUN
ejpam-5591	38	29	where	where	SCONJ
ejpam-5591	38	30	these	these	DET
ejpam-5591	38	31	changes	change	NOUN
ejpam-5591	38	32	are	be	AUX
ejpam-5591	38	33	based	base	VERB
ejpam-5591	38	34	on	on	ADP
ejpam-5591	38	35	the	the	DET
ejpam-5591	38	36	current	current	ADJ
ejpam-5591	38	37	and	and	CCONJ
ejpam-5591	38	38	future	future	ADJ
ejpam-5591	38	39	situation	situation	NOUN
ejpam-5591	38	40	.	.	PUNCT
ejpam-5591	39	1	the	the	DET
ejpam-5591	39	2	equation	equation	NOUN
ejpam-5591	39	3	can	can	AUX
ejpam-5591	39	4	be	be	AUX
ejpam-5591	39	5	changed	change	VERB
ejpam-5591	39	6	a.	a.	NOUN
ejpam-5591	39	7	almutairi	almutairi	PROPN
ejpam-5591	39	8	/	/	SYM
ejpam-5591	39	9	eur	eur	PROPN
ejpam-5591	39	10	.	.	PUNCT
ejpam-5591	40	1	j.	j.	PROPN
ejpam-5591	40	2	pure	pure	PROPN
ejpam-5591	40	3	appl	appl	PROPN
ejpam-5591	40	4	.	.	PROPN
ejpam-5591	40	5	math	math	PROPN
ejpam-5591	40	6	,	,	PUNCT
ejpam-5591	40	7	18	18	NUM
ejpam-5591	40	8	(	(	PUNCT
ejpam-5591	40	9	1	1	NUM
ejpam-5591	40	10	)	)	PUNCT
ejpam-5591	40	11	(	(	PUNCT
ejpam-5591	40	12	2025	2025	NUM
ejpam-5591	40	13	)	)	PUNCT
ejpam-5591	40	14	,	,	PUNCT
ejpam-5591	40	15	5591	5591	NUM
ejpam-5591	40	16	3	3	NUM
ejpam-5591	40	17	of	of	ADP
ejpam-5591	40	18	11	11	NUM
ejpam-5591	40	19	to	to	PART
ejpam-5591	40	20	highlight	highlight	VERB
ejpam-5591	40	21	the	the	DET
ejpam-5591	40	22	effects	effect	NOUN
ejpam-5591	40	23	of	of	ADP
ejpam-5591	40	24	possible	possible	ADJ
ejpam-5591	40	25	future	future	ADJ
ejpam-5591	40	26	actions	action	NOUN
ejpam-5591	40	27	.	.	PUNCT
ejpam-5591	41	1	population	population	NOUN
ejpam-5591	41	2	dynamics	dynamic	NOUN
ejpam-5591	41	3	,	,	PUNCT
ejpam-5591	41	4	mechanical	mechanical	ADJ
ejpam-5591	41	5	control	control	NOUN
ejpam-5591	41	6	engineering	engineering	NOUN
ejpam-5591	41	7	and	and	CCONJ
ejpam-5591	41	8	economic	economic	ADJ
ejpam-5591	41	9	issues	issue	NOUN
ejpam-5591	41	10	are	be	AUX
ejpam-5591	41	11	a	a	DET
ejpam-5591	41	12	few	few	ADJ
ejpam-5591	41	13	domains	domain	NOUN
ejpam-5591	41	14	where	where	SCONJ
ejpam-5591	41	15	these	these	DET
ejpam-5591	41	16	equations	equation	NOUN
ejpam-5591	41	17	are	be	AUX
ejpam-5591	41	18	frequently	frequently	ADV
ejpam-5591	41	19	applied	apply	VERB
ejpam-5591	41	20	.	.	PUNCT
ejpam-5591	42	1	ndes	nde	NOUN
ejpam-5591	42	2	are	be	AUX
ejpam-5591	42	3	used	use	VERB
ejpam-5591	42	4	in	in	ADP
ejpam-5591	42	5	many	many	ADJ
ejpam-5591	42	6	areas	area	NOUN
ejpam-5591	42	7	of	of	ADP
ejpam-5591	42	8	natural	natural	ADJ
ejpam-5591	42	9	and	and	CCONJ
ejpam-5591	42	10	technological	technological	ADJ
ejpam-5591	42	11	inquiry[3	inquiry[3	NOUN
ejpam-5591	42	12	,	,	PUNCT
ejpam-5591	42	13	14	14	NUM
ejpam-5591	42	14	]	]	PUNCT
ejpam-5591	42	15	.	.	PUNCT
ejpam-5591	43	1	one	one	NUM
ejpam-5591	43	2	subfield	subfield	NOUN
ejpam-5591	43	3	of	of	ADP
ejpam-5591	43	4	qualitative	qualitative	ADJ
ejpam-5591	43	5	theory	theory	NOUN
ejpam-5591	43	6	,	,	PUNCT
ejpam-5591	43	7	oscillation	oscillation	NOUN
ejpam-5591	43	8	theory	theory	NOUN
ejpam-5591	43	9	,	,	PUNCT
ejpam-5591	43	10	examines	examine	VERB
ejpam-5591	43	11	the	the	DET
ejpam-5591	43	12	qualitative	qualitative	ADJ
ejpam-5591	43	13	characteristics	characteristic	NOUN
ejpam-5591	43	14	of	of	ADP
ejpam-5591	43	15	differential	differential	ADJ
ejpam-5591	43	16	equation	equation	NOUN
ejpam-5591	43	17	solutions	solution	NOUN
ejpam-5591	43	18	,	,	PUNCT
ejpam-5591	43	19	including	include	VERB
ejpam-5591	43	20	stability	stability	NOUN
ejpam-5591	43	21	,	,	PUNCT
ejpam-5591	43	22	oscillation	oscillation	NOUN
ejpam-5591	43	23	,	,	PUNCT
ejpam-5591	43	24	and	and	CCONJ
ejpam-5591	43	25	others	other	NOUN
ejpam-5591	43	26	,	,	PUNCT
ejpam-5591	43	27	without	without	ADP
ejpam-5591	43	28	actually	actually	ADV
ejpam-5591	43	29	solving	solve	VERB
ejpam-5591	43	30	the	the	DET
ejpam-5591	43	31	problems	problem	NOUN
ejpam-5591	43	32	[	[	X
ejpam-5591	43	33	8]-[9	8]-[9	X
ejpam-5591	43	34	]	]	PUNCT
ejpam-5591	43	35	.	.	PUNCT
ejpam-5591	44	1	according	accord	VERB
ejpam-5591	44	2	to	to	ADP
ejpam-5591	44	3	[	[	X
ejpam-5591	44	4	?	?	PUNCT
ejpam-5591	44	5	]	]	X
ejpam-5591	44	6	-[15	-[15	X
ejpam-5591	44	7	]	]	X
ejpam-5591	44	8	,	,	PUNCT
ejpam-5591	44	9	the	the	DET
ejpam-5591	44	10	solutions	solution	NOUN
ejpam-5591	44	11	of	of	ADP
ejpam-5591	44	12	the	the	DET
ejpam-5591	44	13	examined	examine	VERB
ejpam-5591	44	14	equation	equation	NOUN
ejpam-5591	44	15	are	be	AUX
ejpam-5591	44	16	divided	divide	VERB
ejpam-5591	44	17	into	into	ADP
ejpam-5591	44	18	three	three	NUM
ejpam-5591	44	19	distinct	distinct	ADJ
ejpam-5591	44	20	classes	class	NOUN
ejpam-5591	44	21	:	:	PUNCT
ejpam-5591	44	22	oscillatory	oscillatory	ADJ
ejpam-5591	44	23	solutions	solution	NOUN
ejpam-5591	44	24	,	,	PUNCT
ejpam-5591	44	25	positive	positive	ADJ
ejpam-5591	44	26	and	and	CCONJ
ejpam-5591	44	27	negative	negative	ADJ
ejpam-5591	44	28	eventually	eventually	ADV
ejpam-5591	44	29	solutions	solution	NOUN
ejpam-5591	44	30	.	.	PUNCT
ejpam-5591	45	1	researchers	researcher	NOUN
ejpam-5591	45	2	started	start	VERB
ejpam-5591	45	3	studying	study	VERB
ejpam-5591	45	4	the	the	DET
ejpam-5591	45	5	equations	equation	NOUN
ejpam-5591	45	6	of	of	ADP
ejpam-5591	45	7	fourth	fourth	ADJ
ejpam-5591	45	8	-	-	PUNCT
ejpam-5591	45	9	order	order	NOUN
ejpam-5591	45	10	after	after	SCONJ
ejpam-5591	45	11	the	the	DET
ejpam-5591	45	12	oscillation	oscillation	NOUN
ejpam-5591	45	13	for	for	ADP
ejpam-5591	45	14	the	the	DET
ejpam-5591	45	15	second	second	ADJ
ejpam-5591	45	16	-	-	PUNCT
ejpam-5591	45	17	order	order	NOUN
ejpam-5591	45	18	equations	equation	NOUN
ejpam-5591	45	19	developed	develop	VERB
ejpam-5591	45	20	,	,	PUNCT
ejpam-5591	45	21	see	see	VERB
ejpam-5591	45	22	[	[	X
ejpam-5591	45	23	17	17	NUM
ejpam-5591	45	24	,	,	PUNCT
ejpam-5591	45	25	22	22	NUM
ejpam-5591	45	26	]	]	PUNCT
ejpam-5591	45	27	.	.	PUNCT
ejpam-5591	46	1	bazighifan	bazighifan	NOUN
ejpam-5591	46	2	and	and	CCONJ
ejpam-5591	46	3	colleagues	colleague	NOUN
ejpam-5591	47	1	[	[	X
ejpam-5591	47	2	6	6	NUM
ejpam-5591	47	3	]	]	PUNCT
ejpam-5591	47	4	,	,	PUNCT
ejpam-5591	47	5	we	we	PRON
ejpam-5591	47	6	employed	employ	VERB
ejpam-5591	47	7	some	some	DET
ejpam-5591	47	8	techniques	technique	NOUN
ejpam-5591	47	9	to	to	PART
ejpam-5591	47	10	ontain	ontain	VERB
ejpam-5591	47	11	the	the	DET
ejpam-5591	47	12	adequate	adequate	ADJ
ejpam-5591	47	13	and	and	CCONJ
ejpam-5591	47	14	required	required	ADJ
ejpam-5591	47	15	criteria	criterion	NOUN
ejpam-5591	47	16	for	for	ADP
ejpam-5591	47	17	the	the	DET
ejpam-5591	47	18	oscillation	oscillation	NOUN
ejpam-5591	47	19	of	of	ADP
ejpam-5591	47	20	(	(	PUNCT
ejpam-5591	47	21	κ	κ	PROPN
ejpam-5591	47	22	(	(	PUNCT
ejpam-5591	47	23	η	η	NOUN
ejpam-5591	47	24	)	)	PUNCT
ejpam-5591	47	25	∣∣z′′′	∣∣z′′′	PROPN
ejpam-5591	47	26	(	(	PUNCT
ejpam-5591	47	27	η)∣∣p−2	η)∣∣p−2	PROPN
ejpam-5591	47	28	z′′′	z′′′	PROPN
ejpam-5591	47	29	(	(	PUNCT
ejpam-5591	47	30	η	η	PROPN
ejpam-5591	47	31	)	)	PUNCT
ejpam-5591	47	32	)	)	PUNCT
ejpam-5591	47	33	′	′	NUM
ejpam-5591	48	1	+	+	CCONJ
ejpam-5591	48	2	a	a	DET
ejpam-5591	48	3	(	(	PUNCT
ejpam-5591	48	4	η	η	NOUN
ejpam-5591	48	5	)	)	PUNCT
ejpam-5591	48	6	f	f	PROPN
ejpam-5591	48	7	(	(	PUNCT
ejpam-5591	48	8	z	z	NOUN
ejpam-5591	48	9	(	(	PUNCT
ejpam-5591	48	10	b	b	PROPN
ejpam-5591	48	11	(	(	PUNCT
ejpam-5591	48	12	η	η	NOUN
ejpam-5591	48	13	)	)	PUNCT
ejpam-5591	48	14	)	)	PUNCT
ejpam-5591	48	15	)	)	PUNCT
ejpam-5591	49	1	=	=	PUNCT
ejpam-5591	49	2	0	0	NUM
ejpam-5591	49	3	,	,	PUNCT
ejpam-5591	49	4	(	(	PUNCT
ejpam-5591	49	5	4	4	NUM
ejpam-5591	49	6	)	)	PUNCT
ejpam-5591	49	7	under	under	ADP
ejpam-5591	49	8	the	the	DET
ejpam-5591	49	9	condition	condition	NOUN
ejpam-5591	49	10	∫	∫	PROPN
ejpam-5591	49	11	∞	∞	NUM
ejpam-5591	49	12	η0	η0	NOUN
ejpam-5591	49	13	1	1	NUM
ejpam-5591	49	14	κ1	κ1	NOUN
ejpam-5591	49	15	/	/	SYM
ejpam-5591	49	16	p−1	p−1	PROPN
ejpam-5591	49	17	(	(	PUNCT
ejpam-5591	49	18	η	η	PROPN
ejpam-5591	49	19	)	)	PUNCT
ejpam-5591	49	20	dη	dη	NOUN
ejpam-5591	49	21	=	=	SYM
ejpam-5591	49	22	∞.	∞.	PROPN
ejpam-5591	49	23	(	(	PUNCT
ejpam-5591	49	24	5	5	NUM
ejpam-5591	49	25	)	)	PUNCT
ejpam-5591	49	26	new	new	ADJ
ejpam-5591	49	27	standards	standard	NOUN
ejpam-5591	49	28	were	be	AUX
ejpam-5591	49	29	presented	present	VERB
ejpam-5591	49	30	by	by	ADP
ejpam-5591	49	31	bazighifan	bazighifan	NOUN
ejpam-5591	49	32	and	and	CCONJ
ejpam-5591	49	33	thabet	thabet	ADJ
ejpam-5591	49	34	[	[	X
ejpam-5591	49	35	5	5	NUM
ejpam-5591	49	36	]	]	PUNCT
ejpam-5591	49	37	to	to	PART
ejpam-5591	49	38	evaluate	evaluate	VERB
ejpam-5591	49	39	the	the	DET
ejpam-5591	49	40	oscillatory	oscillatory	NOUN
ejpam-5591	49	41	of	of	ADP
ejpam-5591	49	42	fourth	fourth	ADJ
ejpam-5591	49	43	-	-	PUNCT
ejpam-5591	49	44	order	order	NOUN
ejpam-5591	49	45	des	des	PROPN
ejpam-5591	49	46	.	.	PROPN
ejpam-5591	49	47	li	li	PROPN
ejpam-5591	49	48	et	et	PROPN
ejpam-5591	49	49	al	al	PROPN
ejpam-5591	49	50	.	.	PUNCT
ejpam-5591	50	1	[	[	X
ejpam-5591	50	2	13	13	NUM
ejpam-5591	50	3	]	]	PUNCT
ejpam-5591	50	4	concentrated	concentrate	VERB
ejpam-5591	50	5	on	on	ADP
ejpam-5591	50	6	the	the	DET
ejpam-5591	50	7	oscillation	oscillation	NOUN
ejpam-5591	50	8	of	of	ADP
ejpam-5591	50	9	(	(	PUNCT
ejpam-5591	50	10	(	(	PUNCT
ejpam-5591	50	11	z(u−1	z(u−1	PROPN
ejpam-5591	50	12	)	)	PUNCT
ejpam-5591	50	13	(	(	PUNCT
ejpam-5591	50	14	η	η	NOUN
ejpam-5591	50	15	)	)	PUNCT
ejpam-5591	50	16	)	)	PUNCT
ejpam-5591	50	17	p−1	p−1	PROPN
ejpam-5591	50	18	)	)	PUNCT
ejpam-5591	50	19	′	′	NUM
ejpam-5591	51	1	+	+	CCONJ
ejpam-5591	51	2	a	a	DET
ejpam-5591	51	3	(	(	PUNCT
ejpam-5591	51	4	η	η	NOUN
ejpam-5591	51	5	)	)	PUNCT
ejpam-5591	51	6	f	f	PROPN
ejpam-5591	51	7	(	(	PUNCT
ejpam-5591	51	8	z	z	NOUN
ejpam-5591	51	9	(	(	PUNCT
ejpam-5591	51	10	b	b	PROPN
ejpam-5591	51	11	(	(	PUNCT
ejpam-5591	51	12	η	η	NOUN
ejpam-5591	51	13	)	)	PUNCT
ejpam-5591	51	14	)	)	PUNCT
ejpam-5591	51	15	)	)	PUNCT
ejpam-5591	52	1	=	=	PUNCT
ejpam-5591	52	2	0	0	NUM
ejpam-5591	52	3	,	,	PUNCT
ejpam-5591	52	4	(	(	PUNCT
ejpam-5591	52	5	6	6	NUM
ejpam-5591	52	6	)	)	PUNCT
ejpam-5591	52	7	by	by	ADP
ejpam-5591	52	8	utilizing	utilize	VERB
ejpam-5591	52	9	the	the	DET
ejpam-5591	52	10	integral	integral	ADJ
ejpam-5591	52	11	averaging	averaging	NOUN
ejpam-5591	52	12	method	method	NOUN
ejpam-5591	52	13	with	with	ADP
ejpam-5591	52	14	riccati	riccati	PROPN
ejpam-5591	52	15	technique	technique	NOUN
ejpam-5591	52	16	and	and	CCONJ
ejpam-5591	52	17	found	find	VERB
ejpam-5591	52	18	new	new	ADJ
ejpam-5591	52	19	criteria	criterion	NOUN
ejpam-5591	52	20	for	for	ADP
ejpam-5591	52	21	oscillation	oscillation	NOUN
ejpam-5591	52	22	.	.	PUNCT
ejpam-5591	53	1	theorem	theorem	NOUN
ejpam-5591	53	2	1	1	NUM
ejpam-5591	53	3	.	.	PUNCT
ejpam-5591	54	1	(	(	PUNCT
ejpam-5591	54	2	[	[	X
ejpam-5591	54	3	1	1	NUM
ejpam-5591	54	4	]	]	PUNCT
ejpam-5591	54	5	)	)	PUNCT
ejpam-5591	54	6	if	if	SCONJ
ejpam-5591	54	7	lim	lim	PROPN
ejpam-5591	54	8	sup	sup	PROPN
ejpam-5591	54	9	η→∞	η→∞	NUM
ejpam-5591	54	10	∫	∫	PROPN
ejpam-5591	54	11	η	η	PROPN
ejpam-5591	54	12	η0	η0	PROPN
ejpam-5591	54	13	(	(	PUNCT
ejpam-5591	54	14	µ	µ	X
ejpam-5591	54	15	(	(	PUNCT
ejpam-5591	54	16	s	s	NOUN
ejpam-5591	54	17	)	)	PUNCT
ejpam-5591	54	18	a	a	PRON
ejpam-5591	54	19	(	(	PUNCT
ejpam-5591	54	20	s)−	s)−	NOUN
ejpam-5591	54	21	λφ	λφ	PART
ejpam-5591	54	22	(	(	PUNCT
ejpam-5591	54	23	µ′	µ′	PROPN
ejpam-5591	54	24	(	(	PUNCT
ejpam-5591	54	25	s))(p−1)+1	s))(p−1)+1	NOUN
ejpam-5591	54	26	(	(	PUNCT
ejpam-5591	54	27	µ	µ	X
ejpam-5591	54	28	(	(	PUNCT
ejpam-5591	54	29	s	s	NOUN
ejpam-5591	54	30	)	)	PUNCT
ejpam-5591	54	31	bu−2	bu−2	NOUN
ejpam-5591	54	32	(	(	PUNCT
ejpam-5591	54	33	s	s	NOUN
ejpam-5591	54	34	)	)	PUNCT
ejpam-5591	54	35	b′	b′	NUM
ejpam-5591	54	36	(	(	PUNCT
ejpam-5591	54	37	s))p−1	s))p−1	NOUN
ejpam-5591	54	38	)	)	PUNCT
ejpam-5591	54	39	ds	ds	PROPN
ejpam-5591	54	40	=	=	SYM
ejpam-5591	54	41	∞	∞	PROPN
ejpam-5591	54	42	,	,	PUNCT
ejpam-5591	54	43	(	(	PUNCT
ejpam-5591	54	44	7	7	X
ejpam-5591	54	45	)	)	PUNCT
ejpam-5591	54	46	where	where	SCONJ
ejpam-5591	54	47	λ	λ	X
ejpam-5591	54	48	:	:	PUNCT
ejpam-5591	54	49	=	=	SYM
ejpam-5591	54	50	(	(	PUNCT
ejpam-5591	54	51	1/	1/	NUM
ejpam-5591	54	52	(	(	PUNCT
ejpam-5591	54	53	(	(	PUNCT
ejpam-5591	54	54	p−	p−	NOUN
ejpam-5591	54	55	1	1	NUM
ejpam-5591	54	56	)	)	PUNCT
ejpam-5591	54	57	+	+	NUM
ejpam-5591	54	58	1))(p−1)+1	1))(p−1)+1	NUM
ejpam-5591	54	59	(	(	PUNCT
ejpam-5591	54	60	2	2	NUM
ejpam-5591	54	61	(	(	PUNCT
ejpam-5591	54	62	u−	u−	PROPN
ejpam-5591	54	63	1)!)p−1	1)!)p−1	NUM
ejpam-5591	54	64	,	,	PUNCT
ejpam-5591	54	65	µ	µ	PRON
ejpam-5591	54	66	∈	∈	PROPN
ejpam-5591	54	67	c1	c1	NOUN
ejpam-5591	54	68	(	(	PUNCT
ejpam-5591	54	69	[	[	X
ejpam-5591	54	70	η0,∞	η0,∞	X
ejpam-5591	54	71	)	)	PUNCT
ejpam-5591	54	72	,	,	PUNCT
ejpam-5591	54	73	(	(	PUNCT
ejpam-5591	54	74	0,∞	0,∞	NOUN
ejpam-5591	54	75	)	)	PUNCT
ejpam-5591	54	76	)	)	PUNCT
ejpam-5591	54	77	and	and	CCONJ
ejpam-5591	54	78	φ	φ	X
ejpam-5591	54	79	>	>	X
ejpam-5591	54	80	1	1	NUM
ejpam-5591	54	81	,	,	PUNCT
ejpam-5591	54	82	then	then	ADV
ejpam-5591	54	83	every	every	DET
ejpam-5591	54	84	solution	solution	NOUN
ejpam-5591	54	85	of	of	ADP
ejpam-5591	54	86	(	(	PUNCT
ejpam-5591	54	87	6	6	NUM
ejpam-5591	54	88	)	)	PUNCT
ejpam-5591	54	89	is	be	AUX
ejpam-5591	54	90	oscillatory	oscillatory	ADJ
ejpam-5591	54	91	.	.	PUNCT
ejpam-5591	55	1	theorem	theorem	NOUN
ejpam-5591	55	2	2	2	NUM
ejpam-5591	55	3	.	.	PUNCT
ejpam-5591	56	1	(	(	PUNCT
ejpam-5591	56	2	[	[	X
ejpam-5591	56	3	4	4	NUM
ejpam-5591	56	4	]	]	PUNCT
ejpam-5591	56	5	)	)	PUNCT
ejpam-5591	56	6	let	let	VERB
ejpam-5591	56	7	f	f	PROPN
ejpam-5591	56	8	(	(	PUNCT
ejpam-5591	56	9	η1	η1	PROPN
ejpam-5591	56	10	/	/	SYM
ejpam-5591	56	11	p−1	p−1	PROPN
ejpam-5591	56	12	)	)	PUNCT
ejpam-5591	56	13	/η	/η	PUNCT
ejpam-5591	57	1	≥	≥	NOUN
ejpam-5591	57	2	1	1	NUM
ejpam-5591	57	3	for	for	ADP
ejpam-5591	57	4	0	0	NUM
ejpam-5591	57	5	<	<	X
ejpam-5591	57	6	η	η	PROPN
ejpam-5591	57	7	≤	≤	PROPN
ejpam-5591	57	8	1	1	NUM
ejpam-5591	57	9	,	,	PUNCT
ejpam-5591	57	10	h	h	NOUN
ejpam-5591	57	11	∈	∈	PROPN
ejpam-5591	57	12	(	(	PUNCT
ejpam-5591	57	13	0	0	NUM
ejpam-5591	57	14	,	,	PUNCT
ejpam-5591	57	15	1	1	NUM
ejpam-5591	57	16	)	)	PUNCT
ejpam-5591	57	17	such	such	ADJ
ejpam-5591	57	18	that	that	SCONJ
ejpam-5591	57	19	lim	lim	PROPN
ejpam-5591	57	20	inf	inf	PROPN
ejpam-5591	57	21	η→∞	η→∞	NUM
ejpam-5591	57	22	∫	∫	PROPN
ejpam-5591	57	23	η	η	PROPN
ejpam-5591	57	24	bi(η	bi(η	PROPN
ejpam-5591	57	25	)	)	PUNCT
ejpam-5591	57	26	a	a	DET
ejpam-5591	57	27	(	(	PUNCT
ejpam-5591	57	28	s	s	NOUN
ejpam-5591	57	29	)	)	PUNCT
ejpam-5591	57	30	f	f	PROPN
ejpam-5591	58	1	(	(	PUNCT
ejpam-5591	58	2	h	h	NOUN
ejpam-5591	58	3	(	(	PUNCT
ejpam-5591	58	4	u−	u−	PROPN
ejpam-5591	58	5	1	1	NUM
ejpam-5591	58	6	)	)	PUNCT
ejpam-5591	58	7	!	!	PUNCT
ejpam-5591	59	1	bu−1	bu−1	ADV
ejpam-5591	59	2	(	(	PUNCT
ejpam-5591	59	3	s	s	NOUN
ejpam-5591	59	4	)	)	PUNCT
ejpam-5591	59	5	κ1	κ1	NOUN
ejpam-5591	59	6	/	/	SYM
ejpam-5591	59	7	p−1	p−1	PROPN
ejpam-5591	59	8	(	(	PUNCT
ejpam-5591	59	9	b	b	PROPN
ejpam-5591	59	10	(	(	PUNCT
ejpam-5591	59	11	s	s	NOUN
ejpam-5591	59	12	)	)	PUNCT
ejpam-5591	59	13	)	)	PUNCT
ejpam-5591	59	14	)	)	PUNCT
ejpam-5591	60	1	ds	ds	ADP
ejpam-5591	60	2	>	>	SYM
ejpam-5591	60	3	1	1	NUM
ejpam-5591	60	4	e	e	NOUN
ejpam-5591	60	5	,	,	PUNCT
ejpam-5591	60	6	(	(	PUNCT
ejpam-5591	60	7	8)	8)	NUM
ejpam-5591	60	8	then	then	ADV
ejpam-5591	60	9	(	(	PUNCT
ejpam-5591	60	10	6	6	NUM
ejpam-5591	60	11	)	)	PUNCT
ejpam-5591	60	12	is	be	AUX
ejpam-5591	60	13	oscillatory	oscillatory	ADJ
ejpam-5591	60	14	.	.	PUNCT
ejpam-5591	61	1	the	the	DET
ejpam-5591	61	2	goal	goal	NOUN
ejpam-5591	61	3	of	of	ADP
ejpam-5591	61	4	researching	research	VERB
ejpam-5591	61	5	this	this	DET
ejpam-5591	61	6	work	work	NOUN
ejpam-5591	61	7	is	be	AUX
ejpam-5591	61	8	to	to	PART
ejpam-5591	61	9	enhance	enhance	VERB
ejpam-5591	61	10	and	and	CCONJ
ejpam-5591	61	11	supplement	supplement	VERB
ejpam-5591	61	12	the	the	DET
ejpam-5591	61	13	findings	finding	NOUN
ejpam-5591	61	14	of	of	ADP
ejpam-5591	61	15	[	[	X
ejpam-5591	61	16	18	18	NUM
ejpam-5591	61	17	]	]	PUNCT
ejpam-5591	61	18	.	.	PUNCT
ejpam-5591	62	1	the	the	DET
ejpam-5591	62	2	structure	structure	NOUN
ejpam-5591	62	3	of	of	ADP
ejpam-5591	62	4	the	the	DET
ejpam-5591	62	5	paper	paper	NOUN
ejpam-5591	62	6	is	be	AUX
ejpam-5591	62	7	as	as	SCONJ
ejpam-5591	62	8	follows	follow	VERB
ejpam-5591	62	9	.	.	PUNCT
ejpam-5591	63	1	we	we	PRON
ejpam-5591	63	2	provide	provide	VERB
ejpam-5591	63	3	a	a	DET
ejpam-5591	63	4	few	few	ADJ
ejpam-5591	63	5	lemmas	lemma	NOUN
ejpam-5591	63	6	in	in	ADP
ejpam-5591	63	7	section	section	NOUN
ejpam-5591	63	8	2	2	NUM
ejpam-5591	63	9	that	that	PRON
ejpam-5591	63	10	will	will	AUX
ejpam-5591	63	11	be	be	AUX
ejpam-5591	63	12	helpful	helpful	ADJ
ejpam-5591	63	13	in	in	ADP
ejpam-5591	63	14	demonstrating	demonstrate	VERB
ejpam-5591	63	15	our	our	PRON
ejpam-5591	63	16	findings	finding	NOUN
ejpam-5591	63	17	.	.	PUNCT
ejpam-5591	64	1	we	we	PRON
ejpam-5591	64	2	provide	provide	VERB
ejpam-5591	64	3	a	a	DET
ejpam-5591	64	4	new	new	ADJ
ejpam-5591	64	5	standards	standard	NOUN
ejpam-5591	64	6	of	of	ADP
ejpam-5591	64	7	oscillation	oscillation	NOUN
ejpam-5591	64	8	for	for	ADP
ejpam-5591	64	9	(	(	PUNCT
ejpam-5591	64	10	1	1	NUM
ejpam-5591	64	11	)	)	PUNCT
ejpam-5591	64	12	by	by	ADP
ejpam-5591	64	13	the	the	DET
ejpam-5591	64	14	use	use	NOUN
ejpam-5591	64	15	of	of	ADP
ejpam-5591	64	16	generalized	generalized	ADJ
ejpam-5591	64	17	riccati	riccati	NOUN
ejpam-5591	64	18	transformations	transformation	NOUN
ejpam-5591	64	19	in	in	ADP
ejpam-5591	64	20	section	section	NOUN
ejpam-5591	64	21	3	3	NUM
ejpam-5591	64	22	.	.	PUNCT
ejpam-5591	65	1	lastly	lastly	ADV
ejpam-5591	65	2	,	,	PUNCT
ejpam-5591	65	3	a	a	DET
ejpam-5591	65	4	few	few	ADJ
ejpam-5591	65	5	examples	example	NOUN
ejpam-5591	65	6	are	be	AUX
ejpam-5591	65	7	taken	take	VERB
ejpam-5591	65	8	into	into	ADP
ejpam-5591	65	9	consideration	consideration	NOUN
ejpam-5591	65	10	to	to	PART
ejpam-5591	65	11	highlight	highlight	VERB
ejpam-5591	65	12	the	the	DET
ejpam-5591	65	13	main	main	ADJ
ejpam-5591	65	14	findings	finding	NOUN
ejpam-5591	65	15	.	.	PUNCT
ejpam-5591	66	1	a.	a.	NOUN
ejpam-5591	66	2	almutairi	almutairi	PROPN
ejpam-5591	66	3	/	/	SYM
ejpam-5591	66	4	eur	eur	PROPN
ejpam-5591	66	5	.	.	PUNCT
ejpam-5591	67	1	j.	j.	PROPN
ejpam-5591	67	2	pure	pure	PROPN
ejpam-5591	67	3	appl	appl	PROPN
ejpam-5591	67	4	.	.	PROPN
ejpam-5591	67	5	math	math	PROPN
ejpam-5591	67	6	,	,	PUNCT
ejpam-5591	67	7	18	18	NUM
ejpam-5591	67	8	(	(	PUNCT
ejpam-5591	67	9	1	1	NUM
ejpam-5591	67	10	)	)	PUNCT
ejpam-5591	67	11	(	(	PUNCT
ejpam-5591	67	12	2025	2025	NUM
ejpam-5591	67	13	)	)	PUNCT
ejpam-5591	67	14	,	,	PUNCT
ejpam-5591	67	15	5591	5591	NUM
ejpam-5591	67	16	4	4	NUM
ejpam-5591	67	17	of	of	ADP
ejpam-5591	67	18	11	11	NUM
ejpam-5591	67	19	2	2	NUM
ejpam-5591	67	20	.	.	PUNCT
ejpam-5591	67	21	preliminary	preliminary	ADJ
ejpam-5591	67	22	results	result	NOUN
ejpam-5591	67	23	the	the	DET
ejpam-5591	67	24	lemmas	lemmas	ADJ
ejpam-5591	67	25	,	,	PUNCT
ejpam-5591	67	26	and	and	CCONJ
ejpam-5591	67	27	presumptions	presumption	NOUN
ejpam-5591	67	28	presented	present	VERB
ejpam-5591	67	29	in	in	ADP
ejpam-5591	67	30	this	this	DET
ejpam-5591	67	31	part	part	NOUN
ejpam-5591	67	32	are	be	AUX
ejpam-5591	67	33	crucial	crucial	ADJ
ejpam-5591	67	34	for	for	ADP
ejpam-5591	67	35	streamlining	streamline	VERB
ejpam-5591	67	36	the	the	DET
ejpam-5591	67	37	mathematical	mathematical	ADJ
ejpam-5591	67	38	computations	computation	NOUN
ejpam-5591	67	39	utilized	utilize	VERB
ejpam-5591	67	40	in	in	ADP
ejpam-5591	67	41	this	this	DET
ejpam-5591	67	42	work	work	NOUN
ejpam-5591	67	43	.	.	PUNCT
ejpam-5591	68	1	there	there	PRON
ejpam-5591	68	2	are	be	VERB
ejpam-5591	68	3	just	just	ADV
ejpam-5591	68	4	two	two	NUM
ejpam-5591	68	5	instances	instance	NOUN
ejpam-5591	68	6	when	when	SCONJ
ejpam-5591	68	7	examining	examine	VERB
ejpam-5591	68	8	the	the	DET
ejpam-5591	68	9	asymptotic	asymptotic	ADJ
ejpam-5591	68	10	behavior	behavior	NOUN
ejpam-5591	68	11	of	of	ADP
ejpam-5591	68	12	the	the	DET
ejpam-5591	68	13	positive	positive	ADJ
ejpam-5591	68	14	solutions	solution	NOUN
ejpam-5591	68	15	of	of	ADP
ejpam-5591	68	16	(	(	PUNCT
ejpam-5591	68	17	1	1	NUM
ejpam-5591	68	18	)	)	PUNCT
ejpam-5591	68	19	.	.	PUNCT
ejpam-5591	69	1	case	case	NOUN
ejpam-5591	69	2	(	(	PUNCT
ejpam-5591	69	3	1	1	NUM
ejpam-5591	69	4	)	)	PUNCT
ejpam-5591	69	5	:	:	PUNCT
ejpam-5591	69	6	z(m	z(m	PROPN
ejpam-5591	69	7	)	)	PUNCT
ejpam-5591	69	8	(	(	PUNCT
ejpam-5591	69	9	η	η	PROPN
ejpam-5591	69	10	)	)	PUNCT
ejpam-5591	69	11	>	>	X
ejpam-5591	69	12	0	0	PUNCT
ejpam-5591	69	13	for	for	ADP
ejpam-5591	69	14	m	m	PROPN
ejpam-5591	69	15	=	=	SYM
ejpam-5591	69	16	0	0	NUM
ejpam-5591	69	17	,	,	PUNCT
ejpam-5591	69	18	1	1	NUM
ejpam-5591	69	19	,	,	PUNCT
ejpam-5591	69	20	2	2	NUM
ejpam-5591	69	21	,	,	PUNCT
ejpam-5591	69	22	3	3	NUM
ejpam-5591	69	23	;	;	PUNCT
ejpam-5591	69	24	case	case	NOUN
ejpam-5591	69	25	(	(	PUNCT
ejpam-5591	69	26	2	2	NUM
ejpam-5591	69	27	)	)	PUNCT
ejpam-5591	69	28	:	:	PUNCT
ejpam-5591	69	29	z(m	z(m	PROPN
ejpam-5591	69	30	)	)	PUNCT
ejpam-5591	69	31	(	(	PUNCT
ejpam-5591	69	32	η	η	PROPN
ejpam-5591	69	33	)	)	PUNCT
ejpam-5591	69	34	>	>	X
ejpam-5591	69	35	0	0	PUNCT
ejpam-5591	69	36	for	for	ADP
ejpam-5591	69	37	m	m	PROPN
ejpam-5591	69	38	=	=	SYM
ejpam-5591	69	39	0	0	NUM
ejpam-5591	69	40	,	,	PUNCT
ejpam-5591	69	41	1	1	NUM
ejpam-5591	69	42	,	,	PUNCT
ejpam-5591	69	43	3	3	NUM
ejpam-5591	69	44	and	and	CCONJ
ejpam-5591	69	45	z′′	z′′	PROPN
ejpam-5591	69	46	(	(	PUNCT
ejpam-5591	69	47	η	η	PROPN
ejpam-5591	69	48	)	)	PUNCT
ejpam-5591	69	49	<	<	X
ejpam-5591	69	50	0	0	X
ejpam-5591	69	51	.	.	PUNCT
ejpam-5591	70	1	for	for	ADP
ejpam-5591	70	2	convenience	convenience	NOUN
ejpam-5591	70	3	,	,	PUNCT
ejpam-5591	70	4	we	we	PRON
ejpam-5591	70	5	denote	denote	VERB
ejpam-5591	70	6	r	r	NOUN
ejpam-5591	70	7	(	(	PUNCT
ejpam-5591	70	8	η	η	NOUN
ejpam-5591	70	9	)	)	PUNCT
ejpam-5591	70	10	:	:	PUNCT
ejpam-5591	71	1	=	=	SYM
ejpam-5591	71	2	∫	∫	PROPN
ejpam-5591	71	3	∞	∞	PROPN
ejpam-5591	71	4	η	η	PROPN
ejpam-5591	71	5	1	1	NUM
ejpam-5591	71	6	κ1	κ1	PROPN
ejpam-5591	71	7	/	/	SYM
ejpam-5591	71	8	p−1	p−1	PROPN
ejpam-5591	71	9	(	(	PUNCT
ejpam-5591	71	10	s	s	NOUN
ejpam-5591	71	11	)	)	PUNCT
ejpam-5591	71	12	ds	ds	ADJ
ejpam-5591	71	13	,	,	PUNCT
ejpam-5591	71	14	f+	f+	X
ejpam-5591	71	15	(	(	PUNCT
ejpam-5591	71	16	η	η	NOUN
ejpam-5591	71	17	)	)	PUNCT
ejpam-5591	71	18	:	:	PUNCT
ejpam-5591	71	19	=	=	SYM
ejpam-5591	71	20	max	max	X
ejpam-5591	71	21	{	{	PUNCT
ejpam-5591	71	22	0	0	PROPN
ejpam-5591	71	23	,	,	PUNCT
ejpam-5591	71	24	f	f	PROPN
ejpam-5591	71	25	(	(	PUNCT
ejpam-5591	71	26	η	η	PROPN
ejpam-5591	71	27	)	)	PUNCT
ejpam-5591	71	28	}	}	PUNCT
ejpam-5591	71	29	,	,	PUNCT
ejpam-5591	71	30	ϱ	ϱ	PROPN
ejpam-5591	71	31	(	(	PUNCT
ejpam-5591	71	32	η	η	NOUN
ejpam-5591	71	33	)	)	PUNCT
ejpam-5591	71	34	:	:	PUNCT
ejpam-5591	71	35	=	=	SYM
ejpam-5591	71	36	µ	µ	X
ejpam-5591	71	37	(	(	PUNCT
ejpam-5591	71	38	η	η	NOUN
ejpam-5591	71	39	)	)	PUNCT
ejpam-5591	71	40	(	(	PUNCT
ejpam-5591	71	41	ℓ	ℓ	NOUN
ejpam-5591	71	42	j∑	j∑	PROPN
ejpam-5591	71	43	i=1	i=1	PROPN
ejpam-5591	71	44	ai	ai	PROPN
ejpam-5591	71	45	(	(	PUNCT
ejpam-5591	71	46	η	η	NOUN
ejpam-5591	71	47	)	)	PUNCT
ejpam-5591	71	48	(	(	PUNCT
ejpam-5591	71	49	b3i	b3i	NUM
ejpam-5591	71	50	(	(	PUNCT
ejpam-5591	71	51	η	η	NOUN
ejpam-5591	71	52	)	)	PUNCT
ejpam-5591	71	53	η3	η3	NOUN
ejpam-5591	71	54	)	)	PUNCT
ejpam-5591	71	55	p−1	p−1	PROPN
ejpam-5591	71	56	+	+	CCONJ
ejpam-5591	71	57	εν	εν	PROPN
ejpam-5591	71	58	(	(	PUNCT
ejpam-5591	71	59	1+(p−1))/p−1	1+(p−1))/p−1	NUM
ejpam-5591	71	60	1	1	NUM
ejpam-5591	71	61	η2	η2	NOUN
ejpam-5591	71	62	−	−	PROPN
ejpam-5591	71	63	2ν1p−	2ν1p−	NUM
ejpam-5591	71	64	1	1	NUM
ejpam-5591	71	65	2κ	2κ	NOUN
ejpam-5591	71	66	1	1	NUM
ejpam-5591	71	67	p−1	p−1	PROPN
ejpam-5591	71	68	(	(	PUNCT
ejpam-5591	71	69	η)r(p−1)+1(η	η)r(p−1)+1(η	PROPN
ejpam-5591	71	70	)	)	PUNCT
ejpam-5591	71	71	)	)	PUNCT
ejpam-5591	71	72	,	,	PUNCT
ejpam-5591	71	73	σ	σ	PROPN
ejpam-5591	71	74	(	(	PUNCT
ejpam-5591	71	75	η	η	PROPN
ejpam-5591	71	76	)	)	PUNCT
ejpam-5591	71	77	:	:	PUNCT
ejpam-5591	71	78	=	=	PUNCT
ejpam-5591	72	1	µ′	µ′	VERB
ejpam-5591	72	2	+	+	NUM
ejpam-5591	72	3	(	(	PUNCT
ejpam-5591	72	4	η	η	NOUN
ejpam-5591	72	5	)	)	PUNCT
ejpam-5591	72	6	µ	µ	X
ejpam-5591	72	7	(	(	PUNCT
ejpam-5591	72	8	η	η	NOUN
ejpam-5591	72	9	)	)	PUNCT
ejpam-5591	72	10	+	+	CCONJ
ejpam-5591	72	11	(	(	PUNCT
ejpam-5591	72	12	(	(	PUNCT
ejpam-5591	72	13	p−	p−	NOUN
ejpam-5591	72	14	1	1	NUM
ejpam-5591	72	15	)	)	PUNCT
ejpam-5591	72	16	+	+	CCONJ
ejpam-5591	72	17	1	1	X
ejpam-5591	72	18	)	)	PUNCT
ejpam-5591	72	19	ν	ν	NOUN
ejpam-5591	72	20	1	1	NUM
ejpam-5591	72	21	/	/	SYM
ejpam-5591	72	22	p−1	p−1	PROPN
ejpam-5591	72	23	1	1	NUM
ejpam-5591	72	24	εη2	εη2	NOUN
ejpam-5591	72	25	2κ	2κ	NOUN
ejpam-5591	72	26	1	1	NUM
ejpam-5591	72	27	(	(	PUNCT
ejpam-5591	72	28	p−1	p−1	PROPN
ejpam-5591	72	29	)	)	PUNCT
ejpam-5591	72	30	(	(	PUNCT
ejpam-5591	72	31	η)r(η	η)r(η	PROPN
ejpam-5591	72	32	)	)	PUNCT
ejpam-5591	72	33	,	,	PUNCT
ejpam-5591	72	34	σ∗	σ∗	X
ejpam-5591	72	35	(	(	PUNCT
ejpam-5591	72	36	η	η	NOUN
ejpam-5591	72	37	)	)	PUNCT
ejpam-5591	72	38	:	:	PUNCT
ejpam-5591	72	39	=	=	SYM
ejpam-5591	72	40	ς	ς	PROPN
ejpam-5591	72	41	′+	′+	PUNCT
ejpam-5591	72	42	(	(	PUNCT
ejpam-5591	72	43	η	η	NOUN
ejpam-5591	72	44	)	)	PUNCT
ejpam-5591	72	45	ς	ς	PROPN
ejpam-5591	72	46	(	(	PUNCT
ejpam-5591	72	47	η	η	NOUN
ejpam-5591	72	48	)	)	PUNCT
ejpam-5591	72	49	+	+	NUM
ejpam-5591	72	50	2ν2	2ν2	NUM
ejpam-5591	72	51	r(η	r(η	NUM
ejpam-5591	72	52	)	)	PUNCT
ejpam-5591	72	53	,	,	PUNCT
ejpam-5591	72	54	and	and	CCONJ
ejpam-5591	72	55	ϱ∗	ϱ∗	PROPN
ejpam-5591	72	56	(	(	PUNCT
ejpam-5591	72	57	η	η	NOUN
ejpam-5591	72	58	)	)	PUNCT
ejpam-5591	72	59	:	:	PUNCT
ejpam-5591	73	1	=	=	SYM
ejpam-5591	73	2	ς	ς	PROPN
ejpam-5591	73	3	(	(	PUNCT
ejpam-5591	73	4	η	η	NOUN
ejpam-5591	73	5	)	)	PUNCT
ejpam-5591	73	6	∫	∫	NUM
ejpam-5591	73	7	∞	∞	NUM
ejpam-5591	73	8	η	η	PROPN
ejpam-5591	73	9	(	(	PUNCT
ejpam-5591	73	10	ℓ	ℓ	PROPN
ejpam-5591	73	11	κ	κ	PROPN
ejpam-5591	73	12	(	(	PUNCT
ejpam-5591	73	13	v	v	NOUN
ejpam-5591	73	14	)	)	PUNCT
ejpam-5591	73	15	∫	∫	PROPN
ejpam-5591	73	16	∞	∞	PROPN
ejpam-5591	73	17	v	v	ADP
ejpam-5591	73	18	j∑	j∑	PROPN
ejpam-5591	73	19	i=1	i=1	PROPN
ejpam-5591	74	1	ai	ai	VERB
ejpam-5591	74	2	(	(	PUNCT
ejpam-5591	74	3	s	s	X
ejpam-5591	74	4	)	)	PUNCT
ejpam-5591	74	5	bp−1	bp−1	VERB
ejpam-5591	74	6	i	i	PRON
ejpam-5591	74	7	(	(	PUNCT
ejpam-5591	74	8	s	s	NOUN
ejpam-5591	74	9	)	)	PUNCT
ejpam-5591	74	10	sp−1	sp−1	PRON
ejpam-5591	74	11	ds	ds	ADJ
ejpam-5591	74	12	)	)	PUNCT
ejpam-5591	74	13	1	1	NUM
ejpam-5591	74	14	/	/	SYM
ejpam-5591	74	15	p−1	p−1	PROPN
ejpam-5591	74	16	dv	dv	PROPN
ejpam-5591	74	17	+	+	PROPN
ejpam-5591	74	18	ν22	ν22	NOUN
ejpam-5591	74	19	−	−	PROPN
ejpam-5591	74	20	ν2κ	ν2κ	PROPN
ejpam-5591	74	21	−1	−1	NOUN
ejpam-5591	74	22	p−1	p−1	PROPN
ejpam-5591	74	23	(	(	PUNCT
ejpam-5591	74	24	η	η	PROPN
ejpam-5591	74	25	)	)	PUNCT
ejpam-5591	74	26	r2(η	r2(η	NOUN
ejpam-5591	74	27	)	)	PUNCT
ejpam-5591	74	28			PROPN
ejpam-5591	74	29	,	,	PUNCT
ejpam-5591	74	30	where	where	SCONJ
ejpam-5591	74	31	µ	µ	X
ejpam-5591	74	32	,	,	PUNCT
ejpam-5591	74	33	ς	ς	PROPN
ejpam-5591	74	34	∈	∈	PROPN
ejpam-5591	74	35	c1	c1	NOUN
ejpam-5591	74	36	(	(	PUNCT
ejpam-5591	74	37	[	[	X
ejpam-5591	74	38	η0,∞	η0,∞	X
ejpam-5591	74	39	)	)	PUNCT
ejpam-5591	74	40	,	,	PUNCT
ejpam-5591	74	41	(	(	PUNCT
ejpam-5591	74	42	0,∞	0,∞	NOUN
ejpam-5591	74	43	)	)	PUNCT
ejpam-5591	74	44	)	)	PUNCT
ejpam-5591	74	45	and	and	CCONJ
ejpam-5591	74	46	ν1	ν1	NOUN
ejpam-5591	74	47	,	,	PUNCT
ejpam-5591	74	48	ν2	ν2	NOUN
ejpam-5591	74	49	are	be	AUX
ejpam-5591	74	50	constants	constant	NOUN
ejpam-5591	74	51	.	.	PUNCT
ejpam-5591	75	1	remark	remark	NOUN
ejpam-5591	75	2	1	1	NUM
ejpam-5591	75	3	.	.	PUNCT
ejpam-5591	76	1	the	the	DET
ejpam-5591	76	2	generalized	generalized	ADJ
ejpam-5591	76	3	riccati	riccati	NOUN
ejpam-5591	76	4	substitutions	substitution	NOUN
ejpam-5591	76	5	are	be	AUX
ejpam-5591	76	6	defined	define	VERB
ejpam-5591	76	7	by	by	ADP
ejpam-5591	76	8	us	we	PRON
ejpam-5591	76	9	.	.	PUNCT
ejpam-5591	77	1	ζ	ζ	PROPN
ejpam-5591	77	2	(	(	PUNCT
ejpam-5591	77	3	η	η	NOUN
ejpam-5591	77	4	)	)	PUNCT
ejpam-5591	77	5	:	:	PUNCT
ejpam-5591	77	6	=	=	SYM
ejpam-5591	77	7	µ	µ	X
ejpam-5591	77	8	(	(	PUNCT
ejpam-5591	77	9	η	η	PROPN
ejpam-5591	77	10	)	)	PUNCT
ejpam-5591	77	11	(	(	PUNCT
ejpam-5591	77	12	κ	κ	X
ejpam-5591	77	13	(	(	PUNCT
ejpam-5591	77	14	η	η	PROPN
ejpam-5591	77	15	)	)	PUNCT
ejpam-5591	77	16	(	(	PUNCT
ejpam-5591	77	17	z′′′)p−1	z′′′)p−1	X
ejpam-5591	77	18	(	(	PUNCT
ejpam-5591	77	19	η	η	NOUN
ejpam-5591	77	20	)	)	PUNCT
ejpam-5591	77	21	zp−1	zp−1	PROPN
ejpam-5591	77	22	(	(	PUNCT
ejpam-5591	77	23	η	η	NOUN
ejpam-5591	77	24	)	)	PUNCT
ejpam-5591	77	25	+	+	NUM
ejpam-5591	77	26	ν1	ν1	NOUN
ejpam-5591	77	27	rp−1(η	rp−1(η	PROPN
ejpam-5591	77	28	)	)	PUNCT
ejpam-5591	77	29	)	)	PUNCT
ejpam-5591	77	30	,	,	PUNCT
ejpam-5591	77	31	(	(	PUNCT
ejpam-5591	77	32	9	9	NUM
ejpam-5591	77	33	)	)	PUNCT
ejpam-5591	77	34	and	and	CCONJ
ejpam-5591	77	35	w	w	PROPN
ejpam-5591	77	36	(	(	PUNCT
ejpam-5591	77	37	η	η	PROPN
ejpam-5591	77	38	)	)	PUNCT
ejpam-5591	77	39	:	:	PUNCT
ejpam-5591	77	40	=	=	SYM
ejpam-5591	77	41	ς	ς	PROPN
ejpam-5591	77	42	(	(	PUNCT
ejpam-5591	77	43	η	η	PROPN
ejpam-5591	77	44	)	)	PUNCT
ejpam-5591	77	45	(	(	PUNCT
ejpam-5591	77	46	z′	z′	NUM
ejpam-5591	77	47	(	(	PUNCT
ejpam-5591	77	48	η	η	NOUN
ejpam-5591	77	49	)	)	PUNCT
ejpam-5591	77	50	z	z	PROPN
ejpam-5591	77	51	(	(	PUNCT
ejpam-5591	77	52	η	η	NOUN
ejpam-5591	77	53	)	)	PUNCT
ejpam-5591	77	54	+	+	CCONJ
ejpam-5591	77	55	ν2	ν2	PROPN
ejpam-5591	77	56	r(η	r(η	NUM
ejpam-5591	77	57	)	)	PUNCT
ejpam-5591	77	58	)	)	PUNCT
ejpam-5591	77	59	.	.	PUNCT
ejpam-5591	78	1	(	(	PUNCT
ejpam-5591	78	2	10	10	NUM
ejpam-5591	78	3	)	)	PUNCT
ejpam-5591	78	4	lemma	lemma	PROPN
ejpam-5591	78	5	1	1	NUM
ejpam-5591	78	6	.	.	PUNCT
ejpam-5591	79	1	[	[	X
ejpam-5591	79	2	2	2	X
ejpam-5591	79	3	]	]	PUNCT
ejpam-5591	79	4	assume	assume	VERB
ejpam-5591	79	5	that	that	SCONJ
ejpam-5591	79	6	v	v	X
ejpam-5591	79	7	>	>	X
ejpam-5591	79	8	0	0	NUM
ejpam-5591	79	9	,	,	PUNCT
ejpam-5591	79	10	u	u	PRON
ejpam-5591	79	11	be	be	VERB
ejpam-5591	79	12	constant	constant	ADJ
ejpam-5591	79	13	,	,	PUNCT
ejpam-5591	79	14	and	and	CCONJ
ejpam-5591	79	15	v	v	NOUN
ejpam-5591	79	16	is	be	AUX
ejpam-5591	79	17	the	the	DET
ejpam-5591	79	18	ratio	ratio	NOUN
ejpam-5591	79	19	of	of	ADP
ejpam-5591	79	20	two	two	NUM
ejpam-5591	79	21	odd	odd	ADJ
ejpam-5591	79	22	values	value	NOUN
ejpam-5591	79	23	.	.	PUNCT
ejpam-5591	80	1	then	then	ADV
ejpam-5591	80	2	p	p	X
ejpam-5591	80	3	(	(	PUNCT
ejpam-5591	80	4	ν+1)/ν	ν+1)/ν	PROPN
ejpam-5591	80	5	−	−	PROPN
ejpam-5591	81	1	(	(	PUNCT
ejpam-5591	81	2	p	p	NOUN
ejpam-5591	81	3	−	−	PROPN
ejpam-5591	81	4	a)(ν+1)/ν	a)(ν+1)/ν	PROPN
ejpam-5591	81	5	≤	≤	NUM
ejpam-5591	81	6	1	1	NUM
ejpam-5591	81	7	ν	ν	NOUN
ejpam-5591	81	8	a1	a1	PROPN
ejpam-5591	81	9	/	/	SYM
ejpam-5591	81	10	ν	ν	X
ejpam-5591	81	11	[	[	X
ejpam-5591	81	12	(	(	PUNCT
ejpam-5591	81	13	1	1	NUM
ejpam-5591	81	14	+	+	NOUN
ejpam-5591	81	15	ν)p	ν)p	ADJ
ejpam-5591	81	16	−	−	PROPN
ejpam-5591	81	17	a	a	X
ejpam-5591	81	18	]	]	X
ejpam-5591	81	19	,	,	PUNCT
ejpam-5591	81	20	pa	pa	PROPN
ejpam-5591	81	21	≥	≥	PROPN
ejpam-5591	81	22	0	0	NUM
ejpam-5591	81	23	,	,	PUNCT
ejpam-5591	81	24	ν	ν	X
ejpam-5591	81	25	≥	≥	NOUN
ejpam-5591	81	26	1	1	NUM
ejpam-5591	81	27	and	and	CCONJ
ejpam-5591	81	28	uz	uz	PROPN
ejpam-5591	81	29	−	−	PROPN
ejpam-5591	81	30	v	v	X
ejpam-5591	81	31	z(ν+1)/ν	z(ν+1)/ν	PROPN
ejpam-5591	81	32	≤	≤	NOUN
ejpam-5591	81	33	νν	νν	X
ejpam-5591	81	34	(	(	PUNCT
ejpam-5591	81	35	ν	ν	X
ejpam-5591	81	36	+	+	NOUN
ejpam-5591	81	37	1)ν+1	1)ν+1	NUM
ejpam-5591	81	38	uν+1	uν+1	NOUN
ejpam-5591	81	39	v	v	NUM
ejpam-5591	81	40	ν	ν	NOUN
ejpam-5591	81	41	.	.	PUNCT
ejpam-5591	81	42	a.	a.	NOUN
ejpam-5591	81	43	almutairi	almutairi	PROPN
ejpam-5591	81	44	/	/	SYM
ejpam-5591	81	45	eur	eur	PROPN
ejpam-5591	81	46	.	.	PUNCT
ejpam-5591	82	1	j.	j.	PROPN
ejpam-5591	82	2	pure	pure	PROPN
ejpam-5591	82	3	appl	appl	PROPN
ejpam-5591	82	4	.	.	PROPN
ejpam-5591	82	5	math	math	PROPN
ejpam-5591	82	6	,	,	PUNCT
ejpam-5591	82	7	18	18	NUM
ejpam-5591	82	8	(	(	PUNCT
ejpam-5591	82	9	1	1	NUM
ejpam-5591	82	10	)	)	PUNCT
ejpam-5591	82	11	(	(	PUNCT
ejpam-5591	82	12	2025	2025	NUM
ejpam-5591	82	13	)	)	PUNCT
ejpam-5591	82	14	,	,	PUNCT
ejpam-5591	82	15	5591	5591	NUM
ejpam-5591	82	16	5	5	NUM
ejpam-5591	82	17	of	of	ADP
ejpam-5591	82	18	11	11	NUM
ejpam-5591	82	19	lemma	lemma	PROPN
ejpam-5591	82	20	2	2	NUM
ejpam-5591	82	21	.	.	PUNCT
ejpam-5591	83	1	[	[	X
ejpam-5591	83	2	23	23	NUM
ejpam-5591	83	3	]	]	PUNCT
ejpam-5591	83	4	suppose	suppose	VERB
ejpam-5591	83	5	that	that	SCONJ
ejpam-5591	83	6	g	g	PROPN
ejpam-5591	83	7	∈	∈	PROPN
ejpam-5591	83	8	cu	cu	PROPN
ejpam-5591	83	9	(	(	PUNCT
ejpam-5591	83	10	[	[	X
ejpam-5591	83	11	η0,∞	η0,∞	X
ejpam-5591	83	12	)	)	PUNCT
ejpam-5591	83	13	,	,	PUNCT
ejpam-5591	83	14	(	(	PUNCT
ejpam-5591	83	15	0,∞	0,∞	NOUN
ejpam-5591	83	16	)	)	PUNCT
ejpam-5591	83	17	)	)	PUNCT
ejpam-5591	83	18	,	,	PUNCT
ejpam-5591	83	19	g(u	g(u	PROPN
ejpam-5591	83	20	)	)	PUNCT
ejpam-5591	83	21	is	be	AUX
ejpam-5591	83	22	of	of	ADP
ejpam-5591	83	23	a	a	DET
ejpam-5591	83	24	fixed	fix	VERB
ejpam-5591	83	25	sign	sign	NOUN
ejpam-5591	83	26	on	on	ADP
ejpam-5591	83	27	[	[	X
ejpam-5591	83	28	η0,∞	η0,∞	X
ejpam-5591	83	29	)	)	PUNCT
ejpam-5591	83	30	,	,	PUNCT
ejpam-5591	83	31	g(u	g(u	PROPN
ejpam-5591	83	32	)	)	PUNCT
ejpam-5591	83	33	not	not	PART
ejpam-5591	83	34	identically	identically	ADV
ejpam-5591	83	35	zero	zero	NUM
ejpam-5591	83	36	and	and	CCONJ
ejpam-5591	83	37	there	there	PRON
ejpam-5591	83	38	exists	exist	VERB
ejpam-5591	83	39	a	a	DET
ejpam-5591	83	40	η1	η1	NOUN
ejpam-5591	83	41	≥	≥	NOUN
ejpam-5591	83	42	η0	η0	NOUN
ejpam-5591	83	43	such	such	ADJ
ejpam-5591	83	44	that	that	DET
ejpam-5591	83	45	g(u−1	g(u−1	NOUN
ejpam-5591	83	46	)	)	PUNCT
ejpam-5591	83	47	(	(	PUNCT
ejpam-5591	83	48	η	η	NOUN
ejpam-5591	83	49	)	)	PUNCT
ejpam-5591	83	50	g(u	g(u	PROPN
ejpam-5591	83	51	)	)	PUNCT
ejpam-5591	83	52	(	(	PUNCT
ejpam-5591	83	53	η	η	NOUN
ejpam-5591	83	54	)	)	PUNCT
ejpam-5591	83	55	≤	≤	NOUN
ejpam-5591	83	56	0	0	NUM
ejpam-5591	83	57	,	,	PUNCT
ejpam-5591	83	58	for	for	ADP
ejpam-5591	83	59	all	all	DET
ejpam-5591	83	60	η	η	PROPN
ejpam-5591	83	61	≥	≥	NOUN
ejpam-5591	83	62	η1	η1	NOUN
ejpam-5591	83	63	.	.	PUNCT
ejpam-5591	84	1	if	if	SCONJ
ejpam-5591	84	2	we	we	PRON
ejpam-5591	84	3	have	have	VERB
ejpam-5591	84	4	limη→∞	limη→∞	PROPN
ejpam-5591	84	5	g	g	PROPN
ejpam-5591	84	6	(	(	PUNCT
ejpam-5591	84	7	η	η	PROPN
ejpam-5591	84	8	)	)	PUNCT
ejpam-5591	84	9	̸=	̸=	PROPN
ejpam-5591	84	10	0	0	NUM
ejpam-5591	84	11	,	,	PUNCT
ejpam-5591	84	12	then	then	ADV
ejpam-5591	84	13	there	there	PRON
ejpam-5591	84	14	exists	exist	VERB
ejpam-5591	84	15	ην	ην	NOUN
ejpam-5591	84	16	≥	≥	NOUN
ejpam-5591	84	17	η1	η1	NOUN
ejpam-5591	84	18	such	such	ADJ
ejpam-5591	84	19	that	that	SCONJ
ejpam-5591	84	20	g	g	PROPN
ejpam-5591	84	21	(	(	PUNCT
ejpam-5591	84	22	η	η	PROPN
ejpam-5591	84	23	)	)	PUNCT
ejpam-5591	84	24	≥	≥	NOUN
ejpam-5591	84	25	ν	ν	NOUN
ejpam-5591	84	26	(	(	PUNCT
ejpam-5591	84	27	u−	u−	PROPN
ejpam-5591	84	28	1	1	NUM
ejpam-5591	84	29	)	)	PUNCT
ejpam-5591	84	30	!	!	PUNCT
ejpam-5591	85	1	ηu−1	ηu−1	PROPN
ejpam-5591	85	2	∣∣∣g(u−1	∣∣∣g(u−1	PROPN
ejpam-5591	85	3	)	)	PUNCT
ejpam-5591	85	4	(	(	PUNCT
ejpam-5591	85	5	η	η	NOUN
ejpam-5591	85	6	)	)	PUNCT
ejpam-5591	85	7	∣∣∣	∣∣∣	NOUN
ejpam-5591	85	8	,	,	PUNCT
ejpam-5591	85	9	for	for	ADP
ejpam-5591	85	10	all	all	PRON
ejpam-5591	85	11	ν	ν	X
ejpam-5591	85	12	∈	∈	PROPN
ejpam-5591	85	13	(	(	PUNCT
ejpam-5591	85	14	0	0	NUM
ejpam-5591	85	15	,	,	PUNCT
ejpam-5591	85	16	1	1	NUM
ejpam-5591	85	17	)	)	PUNCT
ejpam-5591	85	18	and	and	CCONJ
ejpam-5591	85	19	η	η	PROPN
ejpam-5591	85	20	≥	≥	X
ejpam-5591	85	21	ην	ην	NOUN
ejpam-5591	85	22	.	.	PUNCT
ejpam-5591	86	1	lemma	lemma	PROPN
ejpam-5591	86	2	3	3	X
ejpam-5591	86	3	.	.	PUNCT
ejpam-5591	87	1	[	[	X
ejpam-5591	87	2	10	10	NUM
ejpam-5591	87	3	]	]	X
ejpam-5591	87	4	if	if	SCONJ
ejpam-5591	87	5	κ(j	κ(j	NOUN
ejpam-5591	87	6	)	)	PUNCT
ejpam-5591	87	7	>	>	X
ejpam-5591	87	8	0	0	PUNCT
ejpam-5591	87	9	and	and	CCONJ
ejpam-5591	87	10	κ(u+1	κ(u+1	NOUN
ejpam-5591	87	11	)	)	PUNCT
ejpam-5591	87	12	<	<	X
ejpam-5591	87	13	0	0	NUM
ejpam-5591	87	14	,	,	PUNCT
ejpam-5591	87	15	then	then	ADV
ejpam-5591	87	16	u	u	NOUN
ejpam-5591	87	17	!	!	NOUN
ejpam-5591	87	18	ηu	ηu	ADP
ejpam-5591	87	19	κ	κ	X
ejpam-5591	87	20	(	(	PUNCT
ejpam-5591	87	21	η)−	η)−	PROPN
ejpam-5591	87	22	(	(	PUNCT
ejpam-5591	87	23	u−	u−	PROPN
ejpam-5591	87	24	1	1	NUM
ejpam-5591	87	25	)	)	PUNCT
ejpam-5591	87	26	!	!	PUNCT
ejpam-5591	88	1	ηu−1	ηu−1	PROPN
ejpam-5591	88	2	d	d	PROPN
ejpam-5591	88	3	dη	dη	PRON
ejpam-5591	88	4	κ	κ	X
ejpam-5591	88	5	(	(	PUNCT
ejpam-5591	88	6	η	η	PROPN
ejpam-5591	88	7	)	)	PUNCT
ejpam-5591	88	8	≥	≥	NOUN
ejpam-5591	88	9	0	0	NUM
ejpam-5591	88	10	,	,	PUNCT
ejpam-5591	88	11	for	for	ADP
ejpam-5591	88	12	all	all	DET
ejpam-5591	88	13	j	j	NOUN
ejpam-5591	88	14	=	=	SYM
ejpam-5591	88	15	0	0	NUM
ejpam-5591	88	16	,	,	PUNCT
ejpam-5591	88	17	1	1	NUM
ejpam-5591	88	18	,	,	PUNCT
ejpam-5591	88	19	...	...	PUNCT
ejpam-5591	88	20	,	,	PUNCT
ejpam-5591	88	21	u.	u.	PROPN
ejpam-5591	88	22	3	3	NUM
ejpam-5591	88	23	.	.	PUNCT
ejpam-5591	89	1	oscillation	oscillation	NOUN
ejpam-5591	89	2	criteria	criterion	NOUN
ejpam-5591	89	3	we	we	PRON
ejpam-5591	89	4	will	will	AUX
ejpam-5591	89	5	define	define	VERB
ejpam-5591	89	6	various	various	ADJ
ejpam-5591	89	7	oscillation	oscillation	NOUN
ejpam-5591	89	8	criterion	criterion	NOUN
ejpam-5591	89	9	for	for	ADP
ejpam-5591	89	10	equation	equation	NOUN
ejpam-5591	89	11	(	(	PUNCT
ejpam-5591	89	12	1	1	NUM
ejpam-5591	89	13	)	)	PUNCT
ejpam-5591	89	14	in	in	ADP
ejpam-5591	89	15	this	this	DET
ejpam-5591	89	16	part	part	NOUN
ejpam-5591	89	17	.	.	PUNCT
ejpam-5591	90	1	lemma	lemma	PROPN
ejpam-5591	90	2	4	4	X
ejpam-5591	90	3	.	.	PUNCT
ejpam-5591	91	1	let	let	VERB
ejpam-5591	91	2	z	z	PRON
ejpam-5591	91	3	be	be	AUX
ejpam-5591	91	4	a	a	DET
ejpam-5591	91	5	positive	positive	ADJ
ejpam-5591	91	6	solution	solution	NOUN
ejpam-5591	91	7	of	of	ADP
ejpam-5591	91	8	(	(	PUNCT
ejpam-5591	91	9	1	1	NUM
ejpam-5591	91	10	)	)	PUNCT
ejpam-5591	91	11	in	in	ADP
ejpam-5591	91	12	the	the	DET
ejpam-5591	91	13	end	end	NOUN
ejpam-5591	91	14	,	,	PUNCT
ejpam-5591	91	15	and	and	CCONJ
ejpam-5591	91	16	for	for	ADP
ejpam-5591	91	17	all	all	DET
ejpam-5591	91	18	r	r	NOUN
ejpam-5591	91	19	=	=	SYM
ejpam-5591	91	20	1	1	NUM
ejpam-5591	91	21	,	,	PUNCT
ejpam-5591	91	22	2	2	NUM
ejpam-5591	91	23	,	,	PUNCT
ejpam-5591	91	24	3	3	NUM
ejpam-5591	91	25	,	,	PUNCT
ejpam-5591	91	26	z(r	z(r	NOUN
ejpam-5591	91	27	)	)	PUNCT
ejpam-5591	91	28	(	(	PUNCT
ejpam-5591	91	29	η	η	NOUN
ejpam-5591	91	30	)	)	PUNCT
ejpam-5591	91	31	>	>	X
ejpam-5591	91	32	0	0	X
ejpam-5591	91	33	.	.	PUNCT
ejpam-5591	92	1	in	in	ADP
ejpam-5591	92	2	the	the	DET
ejpam-5591	92	3	case	case	NOUN
ejpam-5591	93	1	where	where	SCONJ
ejpam-5591	93	2	µ	µ	X
ejpam-5591	93	3	∈	∈	PROPN
ejpam-5591	93	4	c1	c1	NOUN
ejpam-5591	93	5	(	(	PUNCT
ejpam-5591	93	6	[	[	X
ejpam-5591	93	7	η0,∞	η0,∞	X
ejpam-5591	93	8	)	)	PUNCT
ejpam-5591	93	9	,	,	PUNCT
ejpam-5591	93	10	(	(	PUNCT
ejpam-5591	93	11	0,∞	0,∞	NOUN
ejpam-5591	93	12	)	)	PUNCT
ejpam-5591	93	13	)	)	PUNCT
ejpam-5591	93	14	,	,	PUNCT
ejpam-5591	93	15	and	and	CCONJ
ejpam-5591	93	16	ζ	ζ	PROPN
ejpam-5591	93	17	∈	∈	PROPN
ejpam-5591	93	18	c1[η,∞	c1[η,∞	NOUN
ejpam-5591	93	19	)	)	PUNCT
ejpam-5591	93	20	defined	define	VERB
ejpam-5591	93	21	as	as	ADP
ejpam-5591	93	22	(	(	PUNCT
ejpam-5591	93	23	9	9	NUM
ejpam-5591	93	24	)	)	PUNCT
ejpam-5591	93	25	,	,	PUNCT
ejpam-5591	93	26	then	then	ADV
ejpam-5591	93	27	ζ	ζ	NOUN
ejpam-5591	93	28	′	′	NUM
ejpam-5591	93	29	(	(	PUNCT
ejpam-5591	93	30	η	η	NOUN
ejpam-5591	93	31	)	)	PUNCT
ejpam-5591	93	32	≤	≤	ADJ
ejpam-5591	93	33	−ϱ	−ϱ	NOUN
ejpam-5591	93	34	(	(	PUNCT
ejpam-5591	93	35	η	η	NOUN
ejpam-5591	93	36	)	)	PUNCT
ejpam-5591	93	37	+	+	PROPN
ejpam-5591	93	38	σ	σ	PROPN
ejpam-5591	93	39	(	(	PUNCT
ejpam-5591	93	40	η	η	NOUN
ejpam-5591	93	41	)	)	PUNCT
ejpam-5591	93	42	ζ	ζ	NOUN
ejpam-5591	93	43	(	(	PUNCT
ejpam-5591	93	44	η)−	η)−	PROPN
ejpam-5591	93	45	εη2(p−	εη2(p−	VERB
ejpam-5591	93	46	1	1	NUM
ejpam-5591	93	47	)	)	SYM
ejpam-5591	93	48	2	2	NUM
ejpam-5591	93	49	(	(	PUNCT
ejpam-5591	93	50	κ	κ	NOUN
ejpam-5591	93	51	(	(	PUNCT
ejpam-5591	93	52	η)µ	η)µ	X
ejpam-5591	93	53	(	(	PUNCT
ejpam-5591	93	54	η))1	η))1	NOUN
ejpam-5591	93	55	/	/	SYM
ejpam-5591	93	56	p−1	p−1	PROPN
ejpam-5591	93	57	(	(	PUNCT
ejpam-5591	93	58	ζ	ζ	PROPN
ejpam-5591	93	59	(	(	PUNCT
ejpam-5591	93	60	η	η	NOUN
ejpam-5591	93	61	)	)	PUNCT
ejpam-5591	93	62	)	)	PUNCT
ejpam-5591	94	1	p	p	PROPN
ejpam-5591	94	2	p−1	p−1	PROPN
ejpam-5591	94	3	,	,	PUNCT
ejpam-5591	94	4	(	(	PUNCT
ejpam-5591	94	5	11	11	NUM
ejpam-5591	94	6	)	)	PUNCT
ejpam-5591	94	7	for	for	ADP
ejpam-5591	94	8	all	all	DET
ejpam-5591	94	9	η	η	PROPN
ejpam-5591	94	10	>	>	X
ejpam-5591	94	11	η1	η1	NOUN
ejpam-5591	94	12	.	.	PUNCT
ejpam-5591	95	1	proof	proof	NOUN
ejpam-5591	95	2	.	.	PUNCT
ejpam-5591	96	1	let	let	VERB
ejpam-5591	96	2	z	z	NOUN
ejpam-5591	96	3	>	>	X
ejpam-5591	96	4	0	0	X
ejpam-5591	96	5	.	.	PUNCT
ejpam-5591	97	1	from	from	ADP
ejpam-5591	97	2	lemma	lemma	PROPN
ejpam-5591	97	3	2	2	NUM
ejpam-5591	97	4	,	,	PUNCT
ejpam-5591	97	5	wefind	wefind	ADJ
ejpam-5591	97	6	z′	z′	NUM
ejpam-5591	97	7	(	(	PUNCT
ejpam-5591	97	8	η	η	PROPN
ejpam-5591	97	9	)	)	PUNCT
ejpam-5591	97	10	≥	≥	NOUN
ejpam-5591	97	11	ε	ε	PROPN
ejpam-5591	97	12	2	2	NUM
ejpam-5591	97	13	η2z′′′	η2z′′′	PROPN
ejpam-5591	97	14	(	(	PUNCT
ejpam-5591	97	15	η	η	NOUN
ejpam-5591	97	16	)	)	PUNCT
ejpam-5591	97	17	,	,	PUNCT
ejpam-5591	97	18	ε	ε	PROPN
ejpam-5591	97	19	∈	∈	PROPN
ejpam-5591	97	20	(	(	PUNCT
ejpam-5591	97	21	0	0	NUM
ejpam-5591	97	22	,	,	PUNCT
ejpam-5591	97	23	1	1	NUM
ejpam-5591	97	24	)	)	PUNCT
ejpam-5591	97	25	.	.	PUNCT
ejpam-5591	98	1	(	(	PUNCT
ejpam-5591	98	2	12	12	NUM
ejpam-5591	98	3	)	)	PUNCT
ejpam-5591	98	4	by	by	ADP
ejpam-5591	98	5	(	(	PUNCT
ejpam-5591	98	6	9	9	NUM
ejpam-5591	98	7	)	)	PUNCT
ejpam-5591	98	8	,	,	PUNCT
ejpam-5591	98	9	we	we	PRON
ejpam-5591	98	10	find	find	VERB
ejpam-5591	98	11	ζ	ζ	X
ejpam-5591	98	12	(	(	PUNCT
ejpam-5591	98	13	η	η	NOUN
ejpam-5591	98	14	)	)	PUNCT
ejpam-5591	98	15	>	>	X
ejpam-5591	98	16	0	0	NUM
ejpam-5591	98	17	for	for	ADP
ejpam-5591	98	18	η	η	PROPN
ejpam-5591	98	19	≥	≥	NOUN
ejpam-5591	98	20	η1	η1	NOUN
ejpam-5591	98	21	,	,	PUNCT
ejpam-5591	98	22	and	and	CCONJ
ejpam-5591	98	23	ζ	ζ	NOUN
ejpam-5591	98	24	′	′	NUM
ejpam-5591	98	25	(	(	PUNCT
ejpam-5591	98	26	η	η	NOUN
ejpam-5591	98	27	)	)	PUNCT
ejpam-5591	98	28	=	=	SYM
ejpam-5591	98	29	µ′	µ′	PUNCT
ejpam-5591	98	30	(	(	PUNCT
ejpam-5591	98	31	η	η	X
ejpam-5591	98	32	)	)	PUNCT
ejpam-5591	98	33	(	(	PUNCT
ejpam-5591	98	34	κ	κ	X
ejpam-5591	98	35	(	(	PUNCT
ejpam-5591	98	36	η	η	PROPN
ejpam-5591	98	37	)	)	PUNCT
ejpam-5591	98	38	(	(	PUNCT
ejpam-5591	98	39	z′′′)p−1	z′′′)p−1	X
ejpam-5591	98	40	(	(	PUNCT
ejpam-5591	98	41	η	η	NOUN
ejpam-5591	98	42	)	)	PUNCT
ejpam-5591	98	43	zp−1	zp−1	PROPN
ejpam-5591	98	44	(	(	PUNCT
ejpam-5591	98	45	η	η	NOUN
ejpam-5591	98	46	)	)	PUNCT
ejpam-5591	98	47	+	+	NUM
ejpam-5591	98	48	ν1	ν1	NOUN
ejpam-5591	98	49	rp−1(η	rp−1(η	PROPN
ejpam-5591	98	50	)	)	PUNCT
ejpam-5591	98	51	)	)	PUNCT
ejpam-5591	99	1	+	+	CCONJ
ejpam-5591	99	2	µ	µ	X
ejpam-5591	99	3	(	(	PUNCT
ejpam-5591	99	4	η	η	NOUN
ejpam-5591	99	5	)	)	PUNCT
ejpam-5591	99	6	(	(	PUNCT
ejpam-5591	99	7	κ	κ	X
ejpam-5591	99	8	(	(	PUNCT
ejpam-5591	99	9	z′′′)p−1	z′′′)p−1	NOUN
ejpam-5591	99	10	)	)	PUNCT
ejpam-5591	99	11	′	′	PROPN
ejpam-5591	99	12	(	(	PUNCT
ejpam-5591	99	13	η	η	NOUN
ejpam-5591	99	14	)	)	PUNCT
ejpam-5591	99	15	zp−1	zp−1	PROPN
ejpam-5591	99	16	(	(	PUNCT
ejpam-5591	99	17	η	η	NOUN
ejpam-5591	99	18	)	)	PUNCT
ejpam-5591	99	19	−(p−	−(p−	VERB
ejpam-5591	99	20	1)µ	1)µ	PRON
ejpam-5591	99	21	(	(	PUNCT
ejpam-5591	99	22	η	η	NOUN
ejpam-5591	99	23	)	)	PUNCT
ejpam-5591	99	24	z(p−1)−1	z(p−1)−1	PROPN
ejpam-5591	99	25	(	(	PUNCT
ejpam-5591	99	26	η	η	PROPN
ejpam-5591	99	27	)	)	PUNCT
ejpam-5591	99	28	z′	z′	PROPN
ejpam-5591	99	29	(	(	PUNCT
ejpam-5591	99	30	η)κ	η)κ	X
ejpam-5591	99	31	(	(	PUNCT
ejpam-5591	99	32	η	η	NOUN
ejpam-5591	99	33	)	)	PUNCT
ejpam-5591	99	34	(	(	PUNCT
ejpam-5591	99	35	z′′′)p−1	z′′′)p−1	X
ejpam-5591	99	36	(	(	PUNCT
ejpam-5591	99	37	η	η	NOUN
ejpam-5591	99	38	)	)	PUNCT
ejpam-5591	99	39	z2p−1	z2p−1	PROPN
ejpam-5591	99	40	(	(	PUNCT
ejpam-5591	99	41	η	η	PROPN
ejpam-5591	99	42	)	)	PUNCT
ejpam-5591	99	43	+	+	CCONJ
ejpam-5591	99	44	(	(	PUNCT
ejpam-5591	99	45	p−	p−	NOUN
ejpam-5591	99	46	1)ν1µ	1)ν1µ	NUM
ejpam-5591	99	47	(	(	PUNCT
ejpam-5591	99	48	η	η	NOUN
ejpam-5591	99	49	)	)	PUNCT
ejpam-5591	99	50	κ	κ	PROPN
ejpam-5591	99	51	1	1	NUM
ejpam-5591	99	52	p−1	p−1	PROPN
ejpam-5591	99	53	(	(	PUNCT
ejpam-5591	99	54	η)rp(η	η)rp(η	PROPN
ejpam-5591	99	55	)	)	PUNCT
ejpam-5591	99	56	.	.	PUNCT
ejpam-5591	100	1	using	use	VERB
ejpam-5591	100	2	(	(	PUNCT
ejpam-5591	100	3	12	12	NUM
ejpam-5591	100	4	)	)	PUNCT
ejpam-5591	100	5	and	and	CCONJ
ejpam-5591	100	6	(	(	PUNCT
ejpam-5591	100	7	9	9	NUM
ejpam-5591	100	8	)	)	PUNCT
ejpam-5591	100	9	,	,	PUNCT
ejpam-5591	100	10	we	we	PRON
ejpam-5591	100	11	obtain	obtain	VERB
ejpam-5591	100	12	ζ	ζ	NOUN
ejpam-5591	100	13	′	′	NUM
ejpam-5591	100	14	(	(	PUNCT
ejpam-5591	100	15	η	η	NOUN
ejpam-5591	100	16	)	)	PUNCT
ejpam-5591	100	17	≤	≤	NOUN
ejpam-5591	100	18	µ′	µ′	PUNCT
ejpam-5591	101	1	+	+	CCONJ
ejpam-5591	101	2	(	(	PUNCT
ejpam-5591	101	3	η	η	NOUN
ejpam-5591	101	4	)	)	PUNCT
ejpam-5591	101	5	µ	µ	X
ejpam-5591	101	6	(	(	PUNCT
ejpam-5591	101	7	η	η	NOUN
ejpam-5591	101	8	)	)	PUNCT
ejpam-5591	101	9	ζ	ζ	PROPN
ejpam-5591	101	10	(	(	PUNCT
ejpam-5591	101	11	η	η	NOUN
ejpam-5591	101	12	)	)	PUNCT
ejpam-5591	101	13	+	+	NUM
ejpam-5591	101	14	µ	µ	X
ejpam-5591	101	15	(	(	PUNCT
ejpam-5591	101	16	η	η	NOUN
ejpam-5591	101	17	)	)	PUNCT
ejpam-5591	101	18	(	(	PUNCT
ejpam-5591	101	19	κ	κ	X
ejpam-5591	101	20	(	(	PUNCT
ejpam-5591	101	21	η	η	PROPN
ejpam-5591	101	22	)	)	PUNCT
ejpam-5591	101	23	(	(	PUNCT
ejpam-5591	101	24	z′′′	z′′′	PROPN
ejpam-5591	101	25	(	(	PUNCT
ejpam-5591	101	26	η))p−1	η))p−1	PROPN
ejpam-5591	101	27	)	)	PUNCT
ejpam-5591	101	28	′	′	NUM
ejpam-5591	102	1	zp−1	zp−1	PROPN
ejpam-5591	102	2	(	(	PUNCT
ejpam-5591	102	3	η	η	NOUN
ejpam-5591	102	4	)	)	PUNCT
ejpam-5591	102	5	a.	a.	NOUN
ejpam-5591	102	6	almutairi	almutairi	PROPN
ejpam-5591	102	7	/	/	SYM
ejpam-5591	102	8	eur	eur	PROPN
ejpam-5591	102	9	.	.	PUNCT
ejpam-5591	103	1	j.	j.	PROPN
ejpam-5591	103	2	pure	pure	PROPN
ejpam-5591	103	3	appl	appl	PROPN
ejpam-5591	103	4	.	.	PROPN
ejpam-5591	103	5	math	math	PROPN
ejpam-5591	103	6	,	,	PUNCT
ejpam-5591	103	7	18	18	NUM
ejpam-5591	103	8	(	(	PUNCT
ejpam-5591	103	9	1	1	NUM
ejpam-5591	103	10	)	)	PUNCT
ejpam-5591	103	11	(	(	PUNCT
ejpam-5591	103	12	2025	2025	NUM
ejpam-5591	103	13	)	)	PUNCT
ejpam-5591	103	14	,	,	PUNCT
ejpam-5591	103	15	5591	5591	NUM
ejpam-5591	103	16	6	6	NUM
ejpam-5591	103	17	of	of	ADP
ejpam-5591	103	18	11	11	NUM
ejpam-5591	103	19	−(p−	−(p−	VERB
ejpam-5591	103	20	1)µ	1)µ	PRON
ejpam-5591	103	21	(	(	PUNCT
ejpam-5591	103	22	η	η	NOUN
ejpam-5591	103	23	)	)	PUNCT
ejpam-5591	103	24	ε	ε	PROPN
ejpam-5591	103	25	2	2	NUM
ejpam-5591	103	26	η2	η2	PROPN
ejpam-5591	103	27	κ	κ	X
ejpam-5591	103	28	(	(	PUNCT
ejpam-5591	103	29	η	η	PROPN
ejpam-5591	103	30	)	)	PUNCT
ejpam-5591	103	31	(	(	PUNCT
ejpam-5591	103	32	z′′′	z′′′	PROPN
ejpam-5591	103	33	(	(	PUNCT
ejpam-5591	103	34	η))p	η))p	PROPN
ejpam-5591	103	35	zp	zp	PROPN
ejpam-5591	103	36	(	(	PUNCT
ejpam-5591	103	37	η	η	PROPN
ejpam-5591	103	38	)	)	PUNCT
ejpam-5591	103	39	+	+	CCONJ
ejpam-5591	104	1	(	(	PUNCT
ejpam-5591	104	2	p−	p−	NOUN
ejpam-5591	104	3	1)ν1µ	1)ν1µ	NUM
ejpam-5591	104	4	(	(	PUNCT
ejpam-5591	104	5	η	η	NOUN
ejpam-5591	104	6	)	)	PUNCT
ejpam-5591	104	7	κ	κ	PROPN
ejpam-5591	104	8	1	1	NUM
ejpam-5591	104	9	p−1	p−1	PROPN
ejpam-5591	104	10	(	(	PUNCT
ejpam-5591	104	11	η)rp(η	η)rp(η	PROPN
ejpam-5591	104	12	)	)	PUNCT
ejpam-5591	104	13	≤	≤	NOUN
ejpam-5591	104	14	µ′	µ′	PUNCT
ejpam-5591	104	15	(	(	PUNCT
ejpam-5591	104	16	η	η	NOUN
ejpam-5591	104	17	)	)	PUNCT
ejpam-5591	104	18	µ	µ	X
ejpam-5591	104	19	(	(	PUNCT
ejpam-5591	104	20	η	η	NOUN
ejpam-5591	104	21	)	)	PUNCT
ejpam-5591	104	22	ζ	ζ	PROPN
ejpam-5591	104	23	(	(	PUNCT
ejpam-5591	104	24	η	η	NOUN
ejpam-5591	104	25	)	)	PUNCT
ejpam-5591	104	26	+	+	NUM
ejpam-5591	104	27	µ	µ	X
ejpam-5591	104	28	(	(	PUNCT
ejpam-5591	104	29	η	η	NOUN
ejpam-5591	104	30	)	)	PUNCT
ejpam-5591	104	31	(	(	PUNCT
ejpam-5591	104	32	κ	κ	X
ejpam-5591	104	33	(	(	PUNCT
ejpam-5591	104	34	η	η	PROPN
ejpam-5591	104	35	)	)	PUNCT
ejpam-5591	104	36	(	(	PUNCT
ejpam-5591	104	37	z′′′	z′′′	PROPN
ejpam-5591	104	38	(	(	PUNCT
ejpam-5591	104	39	η))p−1	η))p−1	PROPN
ejpam-5591	104	40	)	)	PUNCT
ejpam-5591	104	41	′	′	NUM
ejpam-5591	104	42	zp−1	zp−1	PROPN
ejpam-5591	104	43	(	(	PUNCT
ejpam-5591	104	44	η	η	NOUN
ejpam-5591	104	45	)	)	PUNCT
ejpam-5591	104	46	−(p−	−(p−	VERB
ejpam-5591	104	47	1)µ	1)µ	PRON
ejpam-5591	104	48	(	(	PUNCT
ejpam-5591	104	49	η	η	NOUN
ejpam-5591	104	50	)	)	PUNCT
ejpam-5591	104	51	ε	ε	PROPN
ejpam-5591	104	52	2	2	NUM
ejpam-5591	104	53	η2κ	η2κ	PUNCT
ejpam-5591	104	54	(	(	PUNCT
ejpam-5591	104	55	η	η	NOUN
ejpam-5591	104	56	)	)	PUNCT
ejpam-5591	104	57	(	(	PUNCT
ejpam-5591	104	58	ζ	ζ	X
ejpam-5591	104	59	(	(	PUNCT
ejpam-5591	104	60	η	η	NOUN
ejpam-5591	104	61	)	)	PUNCT
ejpam-5591	104	62	µ	µ	X
ejpam-5591	104	63	(	(	PUNCT
ejpam-5591	104	64	η)κ	η)κ	X
ejpam-5591	104	65	(	(	PUNCT
ejpam-5591	104	66	η	η	NOUN
ejpam-5591	104	67	)	)	PUNCT
ejpam-5591	104	68	−	−	PROPN
ejpam-5591	104	69	ν1	ν1	NOUN
ejpam-5591	104	70	κ	κ	X
ejpam-5591	104	71	(	(	PUNCT
ejpam-5591	104	72	η)rp−1(η	η)rp−1(η	PROPN
ejpam-5591	104	73	)	)	PUNCT
ejpam-5591	104	74	)	)	PUNCT
ejpam-5591	105	1	p	p	PROPN
ejpam-5591	105	2	p−1	p−1	PROPN
ejpam-5591	105	3	+	+	CCONJ
ejpam-5591	105	4	(	(	PUNCT
ejpam-5591	105	5	p−	p−	NOUN
ejpam-5591	105	6	1	1	NUM
ejpam-5591	105	7	)	)	PUNCT
ejpam-5591	105	8	ν1µ	ν1µ	PROPN
ejpam-5591	105	9	(	(	PUNCT
ejpam-5591	105	10	η	η	NOUN
ejpam-5591	105	11	)	)	PUNCT
ejpam-5591	105	12	κ	κ	PROPN
ejpam-5591	105	13	1	1	NUM
ejpam-5591	105	14	p−1	p−1	PROPN
ejpam-5591	105	15	(	(	PUNCT
ejpam-5591	105	16	η)rp(η	η)rp(η	PROPN
ejpam-5591	105	17	)	)	PUNCT
ejpam-5591	105	18	.(13	.(13	PUNCT
ejpam-5591	105	19	)	)	PUNCT
ejpam-5591	105	20	using	use	VERB
ejpam-5591	105	21	lemma	lemma	PROPN
ejpam-5591	105	22	1	1	NUM
ejpam-5591	105	23	with	with	ADP
ejpam-5591	105	24	p	p	NOUN
ejpam-5591	105	25	=	=	NOUN
ejpam-5591	105	26	ζ	ζ	X
ejpam-5591	105	27	(	(	PUNCT
ejpam-5591	105	28	η	η	NOUN
ejpam-5591	105	29	)	)	PUNCT
ejpam-5591	105	30	/	/	SYM
ejpam-5591	105	31	(	(	PUNCT
ejpam-5591	105	32	µ	µ	X
ejpam-5591	105	33	(	(	PUNCT
ejpam-5591	105	34	η)κ	η)κ	X
ejpam-5591	105	35	(	(	PUNCT
ejpam-5591	105	36	η	η	NOUN
ejpam-5591	105	37	)	)	PUNCT
ejpam-5591	105	38	)	)	PUNCT
ejpam-5591	105	39	,	,	PUNCT
ejpam-5591	105	40	a	a	DET
ejpam-5591	105	41	=	=	X
ejpam-5591	105	42	ν1/	ν1/	X
ejpam-5591	105	43	(	(	PUNCT
ejpam-5591	105	44	κ	κ	X
ejpam-5591	105	45	(	(	PUNCT
ejpam-5591	105	46	η)r(p−1)(η	η)r(p−1)(η	PROPN
ejpam-5591	105	47	)	)	PUNCT
ejpam-5591	105	48	)	)	PUNCT
ejpam-5591	105	49	and	and	CCONJ
ejpam-5591	105	50	ν	ν	X
ejpam-5591	105	51	=	=	SYM
ejpam-5591	105	52	(	(	PUNCT
ejpam-5591	105	53	p−	p−	NOUN
ejpam-5591	105	54	1	1	NUM
ejpam-5591	105	55	)	)	PUNCT
ejpam-5591	105	56	,	,	PUNCT
ejpam-5591	105	57	we	we	PRON
ejpam-5591	105	58	get	get	VERB
ejpam-5591	105	59	(	(	PUNCT
ejpam-5591	105	60	ζ	ζ	X
ejpam-5591	105	61	(	(	PUNCT
ejpam-5591	105	62	η	η	NOUN
ejpam-5591	105	63	)	)	PUNCT
ejpam-5591	105	64	κ	κ	PROPN
ejpam-5591	105	65	(	(	PUNCT
ejpam-5591	105	66	η)µ	η)µ	X
ejpam-5591	105	67	(	(	PUNCT
ejpam-5591	105	68	η	η	NOUN
ejpam-5591	105	69	)	)	PUNCT
ejpam-5591	105	70	−	−	PROPN
ejpam-5591	105	71	ν1	ν1	NOUN
ejpam-5591	105	72	κ	κ	X
ejpam-5591	105	73	(	(	PUNCT
ejpam-5591	105	74	η)r(p−1)(η	η)r(p−1)(η	PROPN
ejpam-5591	105	75	)	)	PUNCT
ejpam-5591	105	76	)	)	PUNCT
ejpam-5591	106	1	p	p	PROPN
ejpam-5591	106	2	p−1	p−1	PROPN
ejpam-5591	106	3	≥	≥	NUM
ejpam-5591	106	4	(	(	PUNCT
ejpam-5591	106	5	ζ	ζ	X
ejpam-5591	106	6	(	(	PUNCT
ejpam-5591	106	7	η	η	NOUN
ejpam-5591	106	8	)	)	PUNCT
ejpam-5591	106	9	µ	µ	X
ejpam-5591	106	10	(	(	PUNCT
ejpam-5591	106	11	η)κ	η)κ	X
ejpam-5591	106	12	(	(	PUNCT
ejpam-5591	106	13	η	η	NOUN
ejpam-5591	106	14	)	)	PUNCT
ejpam-5591	106	15	)	)	PUNCT
ejpam-5591	107	1	p	p	PROPN
ejpam-5591	107	2	p−1	p−1	PROPN
ejpam-5591	107	3	−	−	PROPN
ejpam-5591	107	4	ν	ν	NOUN
ejpam-5591	107	5	1/(p−1	1/(p−1	NUM
ejpam-5591	107	6	)	)	PUNCT
ejpam-5591	107	7	1	1	NUM
ejpam-5591	107	8	(	(	PUNCT
ejpam-5591	107	9	p−	p−	NOUN
ejpam-5591	107	10	1)κ	1)κ	NOUN
ejpam-5591	107	11	1	1	NUM
ejpam-5591	107	12	(	(	PUNCT
ejpam-5591	107	13	p−1	p−1	PROPN
ejpam-5591	107	14	)	)	PUNCT
ejpam-5591	107	15	(	(	PUNCT
ejpam-5591	107	16	η)r(η	η)r(η	ADV
ejpam-5591	107	17	)	)	PUNCT
ejpam-5591	107	18	(	(	PUNCT
ejpam-5591	107	19	(	(	PUNCT
ejpam-5591	107	20	(	(	PUNCT
ejpam-5591	107	21	p−	p−	NOUN
ejpam-5591	107	22	1	1	NUM
ejpam-5591	107	23	)	)	PUNCT
ejpam-5591	107	24	+	+	CCONJ
ejpam-5591	107	25	1	1	X
ejpam-5591	107	26	)	)	PUNCT
ejpam-5591	107	27	ζ	ζ	NOUN
ejpam-5591	107	28	(	(	PUNCT
ejpam-5591	107	29	η	η	NOUN
ejpam-5591	107	30	)	)	PUNCT
ejpam-5591	107	31	µ	µ	X
ejpam-5591	107	32	(	(	PUNCT
ejpam-5591	107	33	η)κ	η)κ	X
ejpam-5591	107	34	(	(	PUNCT
ejpam-5591	107	35	η	η	NOUN
ejpam-5591	107	36	)	)	PUNCT
ejpam-5591	107	37	−	−	PROPN
ejpam-5591	107	38	ν1	ν1	NOUN
ejpam-5591	107	39	κ	κ	X
ejpam-5591	107	40	(	(	PUNCT
ejpam-5591	107	41	η)r(p−1)(η	η)r(p−1)(η	PROPN
ejpam-5591	107	42	)	)	PUNCT
ejpam-5591	107	43	)	)	PUNCT
ejpam-5591	107	44	.(14	.(14	PUNCT
ejpam-5591	107	45	)	)	PUNCT
ejpam-5591	108	1	from	from	ADP
ejpam-5591	108	2	lemma	lemma	PROPN
ejpam-5591	108	3	3	3	NUM
ejpam-5591	108	4	,	,	PUNCT
ejpam-5591	108	5	we	we	PRON
ejpam-5591	108	6	have	have	VERB
ejpam-5591	108	7	that	that	PRON
ejpam-5591	108	8	z	z	PROPN
ejpam-5591	108	9	(	(	PUNCT
ejpam-5591	108	10	η	η	PROPN
ejpam-5591	108	11	)	)	PUNCT
ejpam-5591	108	12	≥	≥	PROPN
ejpam-5591	108	13	η	η	PROPN
ejpam-5591	108	14	3z	3z	NUM
ejpam-5591	108	15	′	′	NUM
ejpam-5591	108	16	(	(	PUNCT
ejpam-5591	108	17	η	η	NOUN
ejpam-5591	108	18	)	)	PUNCT
ejpam-5591	108	19	and	and	CCONJ
ejpam-5591	108	20	hence	hence	ADV
ejpam-5591	108	21	,	,	PUNCT
ejpam-5591	108	22	z	z	PROPN
ejpam-5591	108	23	(	(	PUNCT
ejpam-5591	108	24	bi	bi	X
ejpam-5591	108	25	(	(	PUNCT
ejpam-5591	108	26	η	η	NOUN
ejpam-5591	108	27	)	)	PUNCT
ejpam-5591	108	28	)	)	PUNCT
ejpam-5591	109	1	z	z	NOUN
ejpam-5591	109	2	(	(	PUNCT
ejpam-5591	109	3	η	η	PROPN
ejpam-5591	109	4	)	)	PUNCT
ejpam-5591	109	5	≥	≥	NOUN
ejpam-5591	109	6	b3i	b3i	NOUN
ejpam-5591	109	7	(	(	PUNCT
ejpam-5591	109	8	η	η	NOUN
ejpam-5591	109	9	)	)	PUNCT
ejpam-5591	109	10	η3	η3	NOUN
ejpam-5591	109	11	.	.	PUNCT
ejpam-5591	110	1	(	(	PUNCT
ejpam-5591	110	2	15	15	NUM
ejpam-5591	110	3	)	)	PUNCT
ejpam-5591	110	4	from	from	ADP
ejpam-5591	110	5	(	(	PUNCT
ejpam-5591	110	6	1	1	NUM
ejpam-5591	110	7	)	)	PUNCT
ejpam-5591	110	8	,	,	PUNCT
ejpam-5591	110	9	(	(	PUNCT
ejpam-5591	110	10	13	13	NUM
ejpam-5591	110	11	)	)	PUNCT
ejpam-5591	110	12	and	and	CCONJ
ejpam-5591	110	13	(	(	PUNCT
ejpam-5591	110	14	14	14	NUM
ejpam-5591	110	15	)	)	PUNCT
ejpam-5591	110	16	,	,	PUNCT
ejpam-5591	110	17	we	we	PRON
ejpam-5591	110	18	obtain	obtain	VERB
ejpam-5591	110	19	ζ	ζ	NOUN
ejpam-5591	110	20	′	′	NUM
ejpam-5591	110	21	(	(	PUNCT
ejpam-5591	110	22	η	η	NOUN
ejpam-5591	110	23	)	)	PUNCT
ejpam-5591	110	24	≤	≤	NOUN
ejpam-5591	110	25	µ′	µ′	PUNCT
ejpam-5591	111	1	+	+	CCONJ
ejpam-5591	111	2	(	(	PUNCT
ejpam-5591	111	3	η	η	NOUN
ejpam-5591	111	4	)	)	PUNCT
ejpam-5591	111	5	µ	µ	X
ejpam-5591	111	6	(	(	PUNCT
ejpam-5591	111	7	η	η	NOUN
ejpam-5591	111	8	)	)	PUNCT
ejpam-5591	111	9	ζ	ζ	NOUN
ejpam-5591	111	10	(	(	PUNCT
ejpam-5591	111	11	η)−	η)−	NOUN
ejpam-5591	111	12	ℓµ	ℓµ	PROPN
ejpam-5591	111	13	(	(	PUNCT
ejpam-5591	111	14	η	η	NOUN
ejpam-5591	111	15	)	)	PUNCT
ejpam-5591	111	16	j∑	j∑	PROPN
ejpam-5591	111	17	i=1	i=1	PROPN
ejpam-5591	112	1	ai	ai	PROPN
ejpam-5591	112	2	(	(	PUNCT
ejpam-5591	112	3	η	η	NOUN
ejpam-5591	112	4	)	)	PUNCT
ejpam-5591	112	5	[	[	PUNCT
ejpam-5591	112	6	b3i	b3i	NUM
ejpam-5591	112	7	(	(	PUNCT
ejpam-5591	112	8	η	η	NOUN
ejpam-5591	112	9	)	)	PUNCT
ejpam-5591	112	10	η3	η3	NOUN
ejpam-5591	112	11	]	]	PUNCT
ejpam-5591	112	12	p−1	p−1	PROPN
ejpam-5591	112	13	−	−	PROPN
ejpam-5591	112	14	(	(	PUNCT
ejpam-5591	112	15	p−	p−	ADP
ejpam-5591	112	16	1)µ	1)µ	NUM
ejpam-5591	112	17	(	(	PUNCT
ejpam-5591	112	18	η	η	NOUN
ejpam-5591	112	19	)	)	PUNCT
ejpam-5591	112	20	ε	ε	PROPN
ejpam-5591	112	21	2	2	NUM
ejpam-5591	112	22	η2κ	η2κ	PUNCT
ejpam-5591	112	23	(	(	PUNCT
ejpam-5591	112	24	η	η	NOUN
ejpam-5591	112	25	)	)	PUNCT
ejpam-5591	112	26	(	(	PUNCT
ejpam-5591	112	27	ζ	ζ	X
ejpam-5591	112	28	(	(	PUNCT
ejpam-5591	112	29	η	η	NOUN
ejpam-5591	112	30	)	)	PUNCT
ejpam-5591	112	31	µ	µ	X
ejpam-5591	112	32	(	(	PUNCT
ejpam-5591	112	33	η)κ	η)κ	X
ejpam-5591	112	34	(	(	PUNCT
ejpam-5591	112	35	η	η	NOUN
ejpam-5591	112	36	)	)	PUNCT
ejpam-5591	112	37	)	)	PUNCT
ejpam-5591	113	1	p	p	NOUN
ejpam-5591	113	2	(	(	PUNCT
ejpam-5591	113	3	p−1	p−1	PROPN
ejpam-5591	113	4	)	)	PUNCT
ejpam-5591	113	5	−	−	PROPN
ejpam-5591	114	1	(	(	PUNCT
ejpam-5591	114	2	p−	p−	INTJ
ejpam-5591	114	3	1)µ	1)µ	NUM
ejpam-5591	114	4	(	(	PUNCT
ejpam-5591	114	5	η	η	NOUN
ejpam-5591	114	6	)	)	PUNCT
ejpam-5591	114	7	ε	ε	PROPN
ejpam-5591	114	8	2	2	NUM
ejpam-5591	114	9	η2κ	η2κ	PUNCT
ejpam-5591	114	10	(	(	PUNCT
ejpam-5591	114	11	η	η	NOUN
ejpam-5591	114	12	)	)	PUNCT
ejpam-5591	114	13	(	(	PUNCT
ejpam-5591	114	14	−ν	−ν	NOUN
ejpam-5591	114	15	1/(p−1	1/(p−1	NUM
ejpam-5591	114	16	)	)	PUNCT
ejpam-5591	114	17	1	1	NUM
ejpam-5591	114	18	(	(	PUNCT
ejpam-5591	114	19	p−	p−	NOUN
ejpam-5591	114	20	1)κ	1)κ	NOUN
ejpam-5591	114	21	1	1	NUM
ejpam-5591	114	22	(	(	PUNCT
ejpam-5591	114	23	p−1	p−1	PROPN
ejpam-5591	114	24	)	)	PUNCT
ejpam-5591	114	25	(	(	PUNCT
ejpam-5591	114	26	η)r(η	η)r(η	ADV
ejpam-5591	114	27	)	)	PUNCT
ejpam-5591	114	28	(	(	PUNCT
ejpam-5591	114	29	pζ	pζ	X
ejpam-5591	114	30	(	(	PUNCT
ejpam-5591	114	31	η	η	PROPN
ejpam-5591	114	32	)	)	PUNCT
ejpam-5591	114	33	µ	µ	X
ejpam-5591	114	34	(	(	PUNCT
ejpam-5591	114	35	η)κ	η)κ	X
ejpam-5591	114	36	(	(	PUNCT
ejpam-5591	114	37	η	η	NOUN
ejpam-5591	114	38	)	)	PUNCT
ejpam-5591	114	39	−	−	PROPN
ejpam-5591	114	40	ν1	ν1	NOUN
ejpam-5591	114	41	κ	κ	X
ejpam-5591	114	42	(	(	PUNCT
ejpam-5591	114	43	η)r(p−1)(η	η)r(p−1)(η	PROPN
ejpam-5591	114	44	)	)	PUNCT
ejpam-5591	114	45	)	)	PUNCT
ejpam-5591	114	46	)	)	PUNCT
ejpam-5591	115	1	+	+	CCONJ
ejpam-5591	115	2	(	(	PUNCT
ejpam-5591	115	3	p−	p−	NOUN
ejpam-5591	115	4	1	1	NUM
ejpam-5591	115	5	)	)	PUNCT
ejpam-5591	115	6	ν1µ	ν1µ	PROPN
ejpam-5591	115	7	(	(	PUNCT
ejpam-5591	115	8	η	η	NOUN
ejpam-5591	115	9	)	)	PUNCT
ejpam-5591	115	10	κ	κ	ADP
ejpam-5591	115	11	1	1	NUM
ejpam-5591	115	12	(	(	PUNCT
ejpam-5591	115	13	p−1	p−1	PROPN
ejpam-5591	115	14	)	)	PUNCT
ejpam-5591	115	15	(	(	PUNCT
ejpam-5591	115	16	η)rp(η	η)rp(η	PROPN
ejpam-5591	115	17	)	)	PUNCT
ejpam-5591	115	18	.	.	PUNCT
ejpam-5591	116	1	this	this	PRON
ejpam-5591	116	2	implies	imply	VERB
ejpam-5591	116	3	that	that	SCONJ
ejpam-5591	116	4	ζ	ζ	NOUN
ejpam-5591	116	5	′	′	NUM
ejpam-5591	116	6	(	(	PUNCT
ejpam-5591	116	7	η	η	NOUN
ejpam-5591	116	8	)	)	PUNCT
ejpam-5591	116	9	≤	≤	NOUN
ejpam-5591	116	10	(	(	PUNCT
ejpam-5591	116	11	µ′	µ′	VERB
ejpam-5591	116	12	+	+	CCONJ
ejpam-5591	116	13	(	(	PUNCT
ejpam-5591	116	14	η	η	NOUN
ejpam-5591	116	15	)	)	PUNCT
ejpam-5591	116	16	µ	µ	X
ejpam-5591	116	17	(	(	PUNCT
ejpam-5591	116	18	η	η	NOUN
ejpam-5591	116	19	)	)	PUNCT
ejpam-5591	116	20	+	+	CCONJ
ejpam-5591	116	21	pν	pν	PROPN
ejpam-5591	116	22	1/(p−1	1/(p−1	NUM
ejpam-5591	116	23	)	)	PUNCT
ejpam-5591	116	24	1	1	NUM
ejpam-5591	116	25	εη2	εη2	NOUN
ejpam-5591	116	26	2κ	2κ	NOUN
ejpam-5591	116	27	1	1	NUM
ejpam-5591	116	28	(	(	PUNCT
ejpam-5591	116	29	p−1	p−1	PROPN
ejpam-5591	116	30	)	)	PUNCT
ejpam-5591	116	31	(	(	PUNCT
ejpam-5591	116	32	η)r(η	η)r(η	NOUN
ejpam-5591	116	33	)	)	PUNCT
ejpam-5591	116	34	)	)	PUNCT
ejpam-5591	116	35	ζ	ζ	NOUN
ejpam-5591	116	36	(	(	PUNCT
ejpam-5591	116	37	η)−	η)−	NOUN
ejpam-5591	116	38	εη2	εη2	NOUN
ejpam-5591	116	39	(	(	PUNCT
ejpam-5591	116	40	p−	p−	NOUN
ejpam-5591	116	41	1	1	NUM
ejpam-5591	116	42	)	)	PUNCT
ejpam-5591	116	43	2κ1/(p−1	2κ1/(p−1	NUM
ejpam-5591	116	44	)	)	PUNCT
ejpam-5591	116	45	(	(	PUNCT
ejpam-5591	116	46	η)µ1/(p−1	η)µ1/(p−1	NOUN
ejpam-5591	116	47	)	)	PUNCT
ejpam-5591	116	48	(	(	PUNCT
ejpam-5591	116	49	η	η	NOUN
ejpam-5591	116	50	)	)	PUNCT
ejpam-5591	116	51	ζ	ζ	PROPN
ejpam-5591	116	52	p	p	PROPN
ejpam-5591	116	53	p−1	p−1	PROPN
ejpam-5591	116	54	(	(	PUNCT
ejpam-5591	116	55	η	η	NOUN
ejpam-5591	116	56	)	)	PUNCT
ejpam-5591	116	57	−µ	−µ	NOUN
ejpam-5591	116	58	(	(	PUNCT
ejpam-5591	116	59	η	η	PROPN
ejpam-5591	116	60	)	)	PUNCT
ejpam-5591	116	61	(	(	PUNCT
ejpam-5591	116	62	ℓ	ℓ	NOUN
ejpam-5591	116	63	j∑	j∑	PROPN
ejpam-5591	116	64	i=1	i=1	PROPN
ejpam-5591	117	1	ai	ai	PROPN
ejpam-5591	117	2	(	(	PUNCT
ejpam-5591	117	3	η	η	NOUN
ejpam-5591	117	4	)	)	PUNCT
ejpam-5591	117	5	(	(	PUNCT
ejpam-5591	117	6	b3i	b3i	NUM
ejpam-5591	117	7	(	(	PUNCT
ejpam-5591	117	8	η	η	NOUN
ejpam-5591	117	9	)	)	PUNCT
ejpam-5591	117	10	η3	η3	NOUN
ejpam-5591	117	11	)	)	PUNCT
ejpam-5591	117	12	(	(	PUNCT
ejpam-5591	117	13	p−1	p−1	PROPN
ejpam-5591	117	14	)	)	PUNCT
ejpam-5591	117	15	+	+	CCONJ
ejpam-5591	117	16	εν	εν	X
ejpam-5591	117	17	p/(p−1	p/(p−1	NUM
ejpam-5591	117	18	)	)	PUNCT
ejpam-5591	117	19	1	1	NUM
ejpam-5591	117	20	η2	η2	VERB
ejpam-5591	117	21	−	−	PROPN
ejpam-5591	117	22	2ν1	2ν1	NUM
ejpam-5591	117	23	(	(	PUNCT
ejpam-5591	117	24	p−	p−	NOUN
ejpam-5591	117	25	1	1	NUM
ejpam-5591	117	26	)	)	PUNCT
ejpam-5591	117	27	2κ	2κ	NOUN
ejpam-5591	117	28	1	1	NUM
ejpam-5591	117	29	(	(	PUNCT
ejpam-5591	117	30	p−1	p−1	PROPN
ejpam-5591	117	31	)	)	PUNCT
ejpam-5591	117	32	(	(	PUNCT
ejpam-5591	117	33	η)rp(η	η)rp(η	PROPN
ejpam-5591	117	34	)	)	PUNCT
ejpam-5591	117	35	)	)	PUNCT
ejpam-5591	117	36	.	.	PUNCT
ejpam-5591	118	1	thus	thus	ADV
ejpam-5591	118	2	,	,	PUNCT
ejpam-5591	118	3	ζ	ζ	PROPN
ejpam-5591	118	4	′	′	NUM
ejpam-5591	118	5	(	(	PUNCT
ejpam-5591	118	6	η	η	NOUN
ejpam-5591	118	7	)	)	PUNCT
ejpam-5591	118	8	≤	≤	ADJ
ejpam-5591	118	9	−ϱ	−ϱ	NOUN
ejpam-5591	118	10	(	(	PUNCT
ejpam-5591	118	11	η	η	NOUN
ejpam-5591	118	12	)	)	PUNCT
ejpam-5591	118	13	+	+	PROPN
ejpam-5591	118	14	σ	σ	PROPN
ejpam-5591	118	15	(	(	PUNCT
ejpam-5591	118	16	η	η	NOUN
ejpam-5591	118	17	)	)	PUNCT
ejpam-5591	118	18	ζ	ζ	NOUN
ejpam-5591	118	19	(	(	PUNCT
ejpam-5591	118	20	η)−	η)−	NOUN
ejpam-5591	118	21	(	(	PUNCT
ejpam-5591	118	22	p−	p−	NOUN
ejpam-5591	118	23	1	1	NUM
ejpam-5591	118	24	)	)	PUNCT
ejpam-5591	118	25	εη2	εη2	NOUN
ejpam-5591	118	26	2	2	NUM
ejpam-5591	118	27	(	(	PUNCT
ejpam-5591	118	28	κ	κ	NOUN
ejpam-5591	118	29	(	(	PUNCT
ejpam-5591	118	30	η)µ	η)µ	X
ejpam-5591	118	31	(	(	PUNCT
ejpam-5591	118	32	η))1/(p−1	η))1/(p−1	NOUN
ejpam-5591	118	33	)	)	PUNCT
ejpam-5591	118	34	ζ	ζ	NOUN
ejpam-5591	118	35	p	p	NOUN
ejpam-5591	118	36	(	(	PUNCT
ejpam-5591	118	37	p−1	p−1	PROPN
ejpam-5591	118	38	)	)	PUNCT
ejpam-5591	118	39	(	(	PUNCT
ejpam-5591	118	40	η	η	NOUN
ejpam-5591	118	41	)	)	PUNCT
ejpam-5591	118	42	.	.	PUNCT
ejpam-5591	119	1	the	the	DET
ejpam-5591	119	2	proof	proof	NOUN
ejpam-5591	119	3	is	be	AUX
ejpam-5591	119	4	complete	complete	ADJ
ejpam-5591	119	5	.	.	PUNCT
ejpam-5591	120	1	a.	a.	NOUN
ejpam-5591	120	2	almutairi	almutairi	PROPN
ejpam-5591	120	3	/	/	SYM
ejpam-5591	120	4	eur	eur	PROPN
ejpam-5591	120	5	.	.	PUNCT
ejpam-5591	121	1	j.	j.	PROPN
ejpam-5591	121	2	pure	pure	PROPN
ejpam-5591	121	3	appl	appl	PROPN
ejpam-5591	121	4	.	.	PROPN
ejpam-5591	121	5	math	math	PROPN
ejpam-5591	121	6	,	,	PUNCT
ejpam-5591	121	7	18	18	NUM
ejpam-5591	121	8	(	(	PUNCT
ejpam-5591	121	9	1	1	NUM
ejpam-5591	121	10	)	)	PUNCT
ejpam-5591	121	11	(	(	PUNCT
ejpam-5591	121	12	2025	2025	NUM
ejpam-5591	121	13	)	)	PUNCT
ejpam-5591	121	14	,	,	PUNCT
ejpam-5591	121	15	5591	5591	NUM
ejpam-5591	121	16	7	7	NUM
ejpam-5591	121	17	of	of	ADP
ejpam-5591	121	18	11	11	NUM
ejpam-5591	121	19	lemma	lemma	PROPN
ejpam-5591	121	20	5	5	NUM
ejpam-5591	121	21	.	.	PUNCT
ejpam-5591	122	1	let	let	VERB
ejpam-5591	122	2	z	z	PRON
ejpam-5591	122	3	be	be	AUX
ejpam-5591	122	4	a	a	DET
ejpam-5591	122	5	positive	positive	ADJ
ejpam-5591	122	6	solution	solution	NOUN
ejpam-5591	122	7	of	of	ADP
ejpam-5591	122	8	(	(	PUNCT
ejpam-5591	122	9	1	1	NUM
ejpam-5591	122	10	)	)	PUNCT
ejpam-5591	122	11	in	in	ADP
ejpam-5591	122	12	the	the	DET
ejpam-5591	122	13	end	end	NOUN
ejpam-5591	122	14	and	and	CCONJ
ejpam-5591	122	15	case	case	NOUN
ejpam-5591	122	16	(	(	PUNCT
ejpam-5591	122	17	2	2	X
ejpam-5591	122	18	)	)	PUNCT
ejpam-5591	122	19	hold	hold	NOUN
ejpam-5591	122	20	,	,	PUNCT
ejpam-5591	122	21	then	then	ADV
ejpam-5591	122	22	w′	w′	PROPN
ejpam-5591	122	23	(	(	PUNCT
ejpam-5591	122	24	η	η	NOUN
ejpam-5591	122	25	)	)	PUNCT
ejpam-5591	122	26	≤	≤	NUM
ejpam-5591	122	27	−ϱ∗	−ϱ∗	NUM
ejpam-5591	122	28	(	(	PUNCT
ejpam-5591	122	29	η	η	NOUN
ejpam-5591	122	30	)	)	PUNCT
ejpam-5591	122	31	+	+	NUM
ejpam-5591	122	32	σ∗	σ∗	X
ejpam-5591	122	33	(	(	PUNCT
ejpam-5591	122	34	η)w	η)w	X
ejpam-5591	122	35	(	(	PUNCT
ejpam-5591	122	36	η)−	η)−	PROPN
ejpam-5591	122	37	1	1	NUM
ejpam-5591	122	38	ς	ς	PROPN
ejpam-5591	122	39	(	(	PUNCT
ejpam-5591	122	40	η	η	NOUN
ejpam-5591	122	41	)	)	PUNCT
ejpam-5591	122	42	w2	w2	NOUN
ejpam-5591	122	43	(	(	PUNCT
ejpam-5591	122	44	η	η	PROPN
ejpam-5591	122	45	)	)	PUNCT
ejpam-5591	122	46	,	,	PUNCT
ejpam-5591	122	47	(	(	PUNCT
ejpam-5591	122	48	16	16	NUM
ejpam-5591	122	49	)	)	PUNCT
ejpam-5591	122	50	where	where	SCONJ
ejpam-5591	122	51	ς	ς	PROPN
ejpam-5591	122	52	∈	∈	PROPN
ejpam-5591	122	53	c1	c1	NOUN
ejpam-5591	122	54	(	(	PUNCT
ejpam-5591	122	55	[	[	X
ejpam-5591	122	56	η0,∞	η0,∞	X
ejpam-5591	122	57	)	)	PUNCT
ejpam-5591	122	58	,	,	PUNCT
ejpam-5591	122	59	(	(	PUNCT
ejpam-5591	122	60	0,∞	0,∞	NOUN
ejpam-5591	122	61	)	)	PUNCT
ejpam-5591	122	62	)	)	PUNCT
ejpam-5591	122	63	.	.	PUNCT
ejpam-5591	123	1	proof	proof	NOUN
ejpam-5591	123	2	.	.	PUNCT
ejpam-5591	124	1	let	let	VERB
ejpam-5591	124	2	z	z	NOUN
ejpam-5591	124	3	ultimately	ultimately	ADV
ejpam-5591	124	4	be	be	AUX
ejpam-5591	124	5	a	a	DET
ejpam-5591	124	6	positive	positive	ADJ
ejpam-5591	124	7	solution	solution	NOUN
ejpam-5591	124	8	of	of	ADP
ejpam-5591	124	9	(	(	PUNCT
ejpam-5591	124	10	1	1	NUM
ejpam-5591	124	11	)	)	PUNCT
ejpam-5591	124	12	and	and	CCONJ
ejpam-5591	124	13	case	case	NOUN
ejpam-5591	124	14	(	(	PUNCT
ejpam-5591	124	15	2	2	X
ejpam-5591	124	16	)	)	PUNCT
ejpam-5591	124	17	hold	hold	NOUN
ejpam-5591	124	18	.	.	PUNCT
ejpam-5591	125	1	lemma	lemma	PROPN
ejpam-5591	125	2	3	3	PROPN
ejpam-5591	125	3	gives	give	VERB
ejpam-5591	125	4	us	we	PRON
ejpam-5591	125	5	the	the	DET
ejpam-5591	125	6	result	result	NOUN
ejpam-5591	125	7	that	that	SCONJ
ejpam-5591	125	8	z	z	NOUN
ejpam-5591	125	9	(	(	PUNCT
ejpam-5591	125	10	η	η	PROPN
ejpam-5591	125	11	)	)	PUNCT
ejpam-5591	125	12	≥	≥	NOUN
ejpam-5591	125	13	ηz′	ηz′	NOUN
ejpam-5591	125	14	(	(	PUNCT
ejpam-5591	125	15	η	η	NOUN
ejpam-5591	125	16	)	)	PUNCT
ejpam-5591	125	17	.	.	PUNCT
ejpam-5591	126	1	this	this	DET
ejpam-5591	126	2	inequality	inequality	NOUN
ejpam-5591	126	3	can	can	AUX
ejpam-5591	126	4	be	be	AUX
ejpam-5591	126	5	integrated	integrate	VERB
ejpam-5591	126	6	from	from	ADP
ejpam-5591	126	7	bi	bi	PROPN
ejpam-5591	126	8	(	(	PUNCT
ejpam-5591	126	9	η	η	PROPN
ejpam-5591	126	10	)	)	PUNCT
ejpam-5591	126	11	to	to	ADP
ejpam-5591	126	12	η	η	PROPN
ejpam-5591	126	13	to	to	PART
ejpam-5591	126	14	obtain	obtain	VERB
ejpam-5591	126	15	z	z	NOUN
ejpam-5591	126	16	(	(	PUNCT
ejpam-5591	126	17	bi	bi	X
ejpam-5591	126	18	(	(	PUNCT
ejpam-5591	126	19	η	η	NOUN
ejpam-5591	126	20	)	)	PUNCT
ejpam-5591	126	21	)	)	PUNCT
ejpam-5591	126	22	≥	≥	PROPN
ejpam-5591	126	23	bi	bi	PROPN
ejpam-5591	126	24	(	(	PUNCT
ejpam-5591	126	25	η	η	PROPN
ejpam-5591	126	26	)	)	PUNCT
ejpam-5591	126	27	η	η	PROPN
ejpam-5591	126	28	z	z	PROPN
ejpam-5591	126	29	(	(	PUNCT
ejpam-5591	126	30	η	η	PROPN
ejpam-5591	126	31	)	)	PUNCT
ejpam-5591	126	32	.	.	PUNCT
ejpam-5591	127	1	from	from	ADP
ejpam-5591	127	2	(	(	PUNCT
ejpam-5591	127	3	2	2	NUM
ejpam-5591	127	4	)	)	PUNCT
ejpam-5591	127	5	,	,	PUNCT
ejpam-5591	127	6	we	we	PRON
ejpam-5591	127	7	so	so	ADV
ejpam-5591	127	8	have	have	VERB
ejpam-5591	127	9	f	f	PROPN
ejpam-5591	127	10	(	(	PUNCT
ejpam-5591	127	11	z	z	PROPN
ejpam-5591	127	12	(	(	PUNCT
ejpam-5591	127	13	bi	bi	X
ejpam-5591	127	14	(	(	PUNCT
ejpam-5591	127	15	η	η	PROPN
ejpam-5591	127	16	)	)	PUNCT
ejpam-5591	127	17	)	)	PUNCT
ejpam-5591	127	18	)	)	PUNCT
ejpam-5591	127	19	≥	≥	PROPN
ejpam-5591	127	20	ℓ	ℓ	PROPN
ejpam-5591	127	21	b	b	PROPN
ejpam-5591	127	22	(	(	PUNCT
ejpam-5591	127	23	p−1	p−1	PROPN
ejpam-5591	127	24	)	)	PUNCT
ejpam-5591	127	25	i	i	PROPN
ejpam-5591	127	26	(	(	PUNCT
ejpam-5591	127	27	η	η	NOUN
ejpam-5591	127	28	)	)	PUNCT
ejpam-5591	127	29	η(p−1	η(p−1	PROPN
ejpam-5591	127	30	)	)	PUNCT
ejpam-5591	127	31	z(p−1	z(p−1	PUNCT
ejpam-5591	127	32	)	)	PUNCT
ejpam-5591	127	33	(	(	PUNCT
ejpam-5591	127	34	η	η	NOUN
ejpam-5591	127	35	)	)	PUNCT
ejpam-5591	127	36	.	.	PUNCT
ejpam-5591	128	1	(	(	PUNCT
ejpam-5591	128	2	17	17	NUM
ejpam-5591	128	3	)	)	PUNCT
ejpam-5591	128	4	integrating	integrating	NOUN
ejpam-5591	128	5	(	(	PUNCT
ejpam-5591	128	6	1	1	NUM
ejpam-5591	128	7	)	)	PUNCT
ejpam-5591	128	8	from	from	ADP
ejpam-5591	128	9	η	η	PROPN
ejpam-5591	128	10	to	to	ADP
ejpam-5591	128	11	κ	κ	NOUN
ejpam-5591	128	12	and	and	CCONJ
ejpam-5591	128	13	using	use	VERB
ejpam-5591	128	14	z′	z′	NUM
ejpam-5591	128	15	(	(	PUNCT
ejpam-5591	128	16	η	η	PROPN
ejpam-5591	128	17	)	)	PUNCT
ejpam-5591	128	18	>	>	X
ejpam-5591	128	19	0	0	NUM
ejpam-5591	128	20	,	,	PUNCT
ejpam-5591	128	21	we	we	PRON
ejpam-5591	128	22	obtain	obtain	VERB
ejpam-5591	128	23	κ	κ	PRON
ejpam-5591	128	24	(	(	PUNCT
ejpam-5591	128	25	κ	κ	NOUN
ejpam-5591	128	26	)	)	PUNCT
ejpam-5591	128	27	(	(	PUNCT
ejpam-5591	128	28	z′′′	z′′′	X
ejpam-5591	128	29	(	(	PUNCT
ejpam-5591	128	30	κ	κ	NOUN
ejpam-5591	128	31	)	)	PUNCT
ejpam-5591	128	32	)	)	PUNCT
ejpam-5591	129	1	(	(	PUNCT
ejpam-5591	129	2	p−1	p−1	PROPN
ejpam-5591	129	3	)	)	PUNCT
ejpam-5591	129	4	−	−	PROPN
ejpam-5591	129	5	κ	κ	PROPN
ejpam-5591	129	6	(	(	PUNCT
ejpam-5591	129	7	η	η	PROPN
ejpam-5591	129	8	)	)	PUNCT
ejpam-5591	129	9	(	(	PUNCT
ejpam-5591	129	10	z′′′	z′′′	PROPN
ejpam-5591	129	11	(	(	PUNCT
ejpam-5591	129	12	η	η	NOUN
ejpam-5591	129	13	)	)	PUNCT
ejpam-5591	129	14	)	)	PUNCT
ejpam-5591	129	15	(	(	PUNCT
ejpam-5591	129	16	p−1	p−1	PROPN
ejpam-5591	129	17	)	)	PUNCT
ejpam-5591	129	18	=	=	PUNCT
ejpam-5591	130	1	−	−	PROPN
ejpam-5591	130	2	∫	∫	PROPN
ejpam-5591	130	3	κ	κ	PROPN
ejpam-5591	130	4	η	η	PROPN
ejpam-5591	130	5	j∑	j∑	PROPN
ejpam-5591	130	6	i=1	i=1	PROPN
ejpam-5591	130	7	ai	ai	VERB
ejpam-5591	130	8	(	(	PUNCT
ejpam-5591	130	9	s	s	NOUN
ejpam-5591	130	10	)	)	PUNCT
ejpam-5591	130	11	f	f	NOUN
ejpam-5591	130	12	(	(	PUNCT
ejpam-5591	130	13	z	z	NOUN
ejpam-5591	130	14	(	(	PUNCT
ejpam-5591	130	15	bi	bi	NOUN
ejpam-5591	130	16	(	(	PUNCT
ejpam-5591	130	17	s	s	NOUN
ejpam-5591	130	18	)	)	PUNCT
ejpam-5591	130	19	)	)	PUNCT
ejpam-5591	130	20	)	)	PUNCT
ejpam-5591	130	21	ds	ds	ADJ
ejpam-5591	130	22	≤	≤	NUM
ejpam-5591	130	23	−ℓz(p−1	−ℓz(p−1	NOUN
ejpam-5591	130	24	)	)	PUNCT
ejpam-5591	130	25	(	(	PUNCT
ejpam-5591	130	26	η	η	NOUN
ejpam-5591	130	27	)	)	PUNCT
ejpam-5591	130	28	∫	∫	PROPN
ejpam-5591	130	29	κ	κ	PROPN
ejpam-5591	130	30	η	η	PROPN
ejpam-5591	130	31	j∑	j∑	PROPN
ejpam-5591	130	32	i=1	i=1	PROPN
ejpam-5591	131	1	ai	ai	VERB
ejpam-5591	131	2	(	(	PUNCT
ejpam-5591	131	3	s	s	NOUN
ejpam-5591	131	4	)	)	PUNCT
ejpam-5591	131	5	b	b	PROPN
ejpam-5591	131	6	(	(	PUNCT
ejpam-5591	131	7	p−1	p−1	PROPN
ejpam-5591	131	8	)	)	PUNCT
ejpam-5591	132	1	i	i	PRON
ejpam-5591	132	2	(	(	PUNCT
ejpam-5591	132	3	s	s	NOUN
ejpam-5591	132	4	)	)	PUNCT
ejpam-5591	132	5	s(p−1	s(p−1	ADJ
ejpam-5591	132	6	)	)	PUNCT
ejpam-5591	132	7	ds	ds	PROPN
ejpam-5591	132	8	.	.	PUNCT
ejpam-5591	132	9	letting	let	VERB
ejpam-5591	132	10	κ	κ	X
ejpam-5591	132	11	→	→	SYM
ejpam-5591	132	12	∞	∞	PROPN
ejpam-5591	132	13	,	,	PUNCT
ejpam-5591	132	14	we	we	PRON
ejpam-5591	132	15	find	find	VERB
ejpam-5591	132	16	κ	κ	X
ejpam-5591	132	17	(	(	PUNCT
ejpam-5591	132	18	η	η	NOUN
ejpam-5591	132	19	)	)	PUNCT
ejpam-5591	132	20	(	(	PUNCT
ejpam-5591	132	21	z′′′	z′′′	PROPN
ejpam-5591	132	22	(	(	PUNCT
ejpam-5591	132	23	η	η	NOUN
ejpam-5591	132	24	)	)	PUNCT
ejpam-5591	132	25	)	)	PUNCT
ejpam-5591	132	26	(	(	PUNCT
ejpam-5591	132	27	p−1	p−1	PROPN
ejpam-5591	132	28	)	)	PUNCT
ejpam-5591	132	29	≥	≥	NOUN
ejpam-5591	132	30	ℓz(p−1	ℓz(p−1	PROPN
ejpam-5591	132	31	)	)	PUNCT
ejpam-5591	132	32	(	(	PUNCT
ejpam-5591	132	33	η	η	NOUN
ejpam-5591	132	34	)	)	PUNCT
ejpam-5591	132	35	∫	∫	PROPN
ejpam-5591	133	1	∞	∞	PROPN
ejpam-5591	133	2	η	η	PROPN
ejpam-5591	133	3	j∑	j∑	PROPN
ejpam-5591	133	4	i=1	i=1	PROPN
ejpam-5591	133	5	ai	ai	VERB
ejpam-5591	133	6	(	(	PUNCT
ejpam-5591	133	7	s	s	NOUN
ejpam-5591	133	8	)	)	PUNCT
ejpam-5591	133	9	b	b	PROPN
ejpam-5591	133	10	(	(	PUNCT
ejpam-5591	133	11	p−1	p−1	PROPN
ejpam-5591	133	12	)	)	PUNCT
ejpam-5591	133	13	i	i	PRON
ejpam-5591	133	14	(	(	PUNCT
ejpam-5591	133	15	s	s	NOUN
ejpam-5591	133	16	)	)	PUNCT
ejpam-5591	133	17	s(p−1	s(p−1	ADJ
ejpam-5591	133	18	)	)	PUNCT
ejpam-5591	133	19	ds	ds	NOUN
ejpam-5591	133	20	and	and	CCONJ
ejpam-5591	133	21	so	so	ADV
ejpam-5591	133	22	z′′′	z′′′	PROPN
ejpam-5591	133	23	(	(	PUNCT
ejpam-5591	133	24	η	η	PROPN
ejpam-5591	133	25	)	)	PUNCT
ejpam-5591	133	26	≥	≥	PROPN
ejpam-5591	133	27	z	z	PROPN
ejpam-5591	133	28	(	(	PUNCT
ejpam-5591	133	29	η	η	PROPN
ejpam-5591	133	30	)	)	PUNCT
ejpam-5591	133	31	(	(	PUNCT
ejpam-5591	133	32	ℓ	ℓ	PROPN
ejpam-5591	133	33	κ	κ	PROPN
ejpam-5591	133	34	(	(	PUNCT
ejpam-5591	133	35	η	η	PROPN
ejpam-5591	133	36	)	)	PUNCT
ejpam-5591	133	37	∫	∫	PROPN
ejpam-5591	134	1	∞	∞	PROPN
ejpam-5591	134	2	η	η	PROPN
ejpam-5591	134	3	j∑	j∑	PROPN
ejpam-5591	134	4	i=1	i=1	PROPN
ejpam-5591	134	5	ai	ai	VERB
ejpam-5591	134	6	(	(	PUNCT
ejpam-5591	134	7	s	s	NOUN
ejpam-5591	134	8	)	)	PUNCT
ejpam-5591	134	9	b	b	PROPN
ejpam-5591	134	10	(	(	PUNCT
ejpam-5591	134	11	p−1	p−1	PROPN
ejpam-5591	134	12	)	)	PUNCT
ejpam-5591	134	13	i	i	PRON
ejpam-5591	134	14	(	(	PUNCT
ejpam-5591	134	15	s	s	NOUN
ejpam-5591	134	16	)	)	PUNCT
ejpam-5591	134	17	s(p−1	s(p−1	ADJ
ejpam-5591	134	18	)	)	PUNCT
ejpam-5591	134	19	ds	ds	ADJ
ejpam-5591	134	20	)	)	PUNCT
ejpam-5591	134	21	1/(p−1	1/(p−1	NUM
ejpam-5591	134	22	)	)	PUNCT
ejpam-5591	134	23	.	.	PUNCT
ejpam-5591	135	1	once	once	ADV
ejpam-5591	135	2	more	more	ADJ
ejpam-5591	135	3	integrating	integrating	NOUN
ejpam-5591	135	4	from	from	ADP
ejpam-5591	135	5	η	η	PROPN
ejpam-5591	135	6	to	to	ADP
ejpam-5591	135	7	∞	∞	PROPN
ejpam-5591	135	8	,	,	PUNCT
ejpam-5591	135	9	we	we	PRON
ejpam-5591	135	10	obtain	obtain	VERB
ejpam-5591	135	11	z′′	z′′	NOUN
ejpam-5591	135	12	(	(	PUNCT
ejpam-5591	135	13	η	η	NOUN
ejpam-5591	135	14	)	)	PUNCT
ejpam-5591	135	15	≤	≤	ADJ
ejpam-5591	135	16	−z	−z	NOUN
ejpam-5591	135	17	(	(	PUNCT
ejpam-5591	135	18	η	η	PROPN
ejpam-5591	135	19	)	)	PUNCT
ejpam-5591	135	20	∫	∫	PROPN
ejpam-5591	135	21	∞	∞	PROPN
ejpam-5591	135	22	η	η	PROPN
ejpam-5591	135	23	(	(	PUNCT
ejpam-5591	135	24	ℓ	ℓ	PROPN
ejpam-5591	135	25	κ	κ	PROPN
ejpam-5591	135	26	(	(	PUNCT
ejpam-5591	135	27	v	v	NOUN
ejpam-5591	135	28	)	)	PUNCT
ejpam-5591	135	29	∫	∫	PROPN
ejpam-5591	136	1	∞	∞	PROPN
ejpam-5591	136	2	v	v	ADP
ejpam-5591	136	3	j∑	j∑	PROPN
ejpam-5591	136	4	i=1	i=1	PROPN
ejpam-5591	137	1	ai	ai	VERB
ejpam-5591	137	2	(	(	PUNCT
ejpam-5591	137	3	s	s	NOUN
ejpam-5591	137	4	)	)	PUNCT
ejpam-5591	137	5	b	b	PROPN
ejpam-5591	137	6	(	(	PUNCT
ejpam-5591	137	7	p−1	p−1	PROPN
ejpam-5591	137	8	)	)	PUNCT
ejpam-5591	138	1	i	i	PRON
ejpam-5591	138	2	(	(	PUNCT
ejpam-5591	138	3	s	s	NOUN
ejpam-5591	138	4	)	)	PUNCT
ejpam-5591	138	5	s(p−1	s(p−1	ADJ
ejpam-5591	138	6	)	)	PUNCT
ejpam-5591	138	7	ds	ds	ADJ
ejpam-5591	138	8	)	)	PUNCT
ejpam-5591	138	9	1/(p−1	1/(p−1	NUM
ejpam-5591	138	10	)	)	PUNCT
ejpam-5591	138	11	dv	dv	PROPN
ejpam-5591	138	12	.	.	PUNCT
ejpam-5591	139	1	(	(	PUNCT
ejpam-5591	139	2	18	18	NUM
ejpam-5591	139	3	)	)	PUNCT
ejpam-5591	139	4	by	by	ADP
ejpam-5591	139	5	differentiating	differentiate	VERB
ejpam-5591	139	6	w	w	PROPN
ejpam-5591	139	7	(	(	PUNCT
ejpam-5591	139	8	η	η	PROPN
ejpam-5591	139	9	)	)	PUNCT
ejpam-5591	139	10	,	,	PUNCT
ejpam-5591	139	11	we	we	PRON
ejpam-5591	139	12	find	find	VERB
ejpam-5591	139	13	w′	w′	PROPN
ejpam-5591	139	14	(	(	PUNCT
ejpam-5591	139	15	η	η	NOUN
ejpam-5591	139	16	)	)	PUNCT
ejpam-5591	139	17	=	=	SYM
ejpam-5591	139	18	ς	ς	PROPN
ejpam-5591	139	19	′	′	NUM
ejpam-5591	139	20	(	(	PUNCT
ejpam-5591	139	21	η	η	PROPN
ejpam-5591	139	22	)	)	PUNCT
ejpam-5591	139	23	ς	ς	PROPN
ejpam-5591	139	24	(	(	PUNCT
ejpam-5591	139	25	η	η	PROPN
ejpam-5591	139	26	)	)	PUNCT
ejpam-5591	139	27	w	w	PROPN
ejpam-5591	139	28	(	(	PUNCT
ejpam-5591	139	29	η	η	PROPN
ejpam-5591	139	30	)	)	PUNCT
ejpam-5591	139	31	+	+	CCONJ
ejpam-5591	139	32	ς	ς	PROPN
ejpam-5591	139	33	(	(	PUNCT
ejpam-5591	139	34	η	η	NOUN
ejpam-5591	139	35	)	)	PUNCT
ejpam-5591	139	36	z′′	z′′	PROPN
ejpam-5591	139	37	(	(	PUNCT
ejpam-5591	139	38	η	η	PROPN
ejpam-5591	139	39	)	)	PUNCT
ejpam-5591	139	40	z	z	PROPN
ejpam-5591	139	41	(	(	PUNCT
ejpam-5591	139	42	η	η	PROPN
ejpam-5591	139	43	)	)	PUNCT
ejpam-5591	140	1	−	−	PROPN
ejpam-5591	140	2	ς	ς	PROPN
ejpam-5591	140	3	(	(	PUNCT
ejpam-5591	140	4	η	η	PROPN
ejpam-5591	140	5	)	)	PUNCT
ejpam-5591	140	6	(	(	PUNCT
ejpam-5591	140	7	w	w	PROPN
ejpam-5591	140	8	(	(	PUNCT
ejpam-5591	140	9	η	η	PROPN
ejpam-5591	140	10	)	)	PUNCT
ejpam-5591	140	11	ς	ς	PROPN
ejpam-5591	140	12	(	(	PUNCT
ejpam-5591	140	13	η	η	NOUN
ejpam-5591	140	14	)	)	PUNCT
ejpam-5591	140	15	−	−	PROPN
ejpam-5591	140	16	ν2	ν2	PROPN
ejpam-5591	140	17	r(η	r(η	NUM
ejpam-5591	140	18	)	)	PUNCT
ejpam-5591	140	19	)	)	PUNCT
ejpam-5591	140	20	2	2	X
ejpam-5591	141	1	+	+	CCONJ
ejpam-5591	141	2	ς	ς	PROPN
ejpam-5591	141	3	(	(	PUNCT
ejpam-5591	141	4	η	η	NOUN
ejpam-5591	141	5	)	)	PUNCT
ejpam-5591	141	6	ν2	ν2	NOUN
ejpam-5591	141	7	κ1/(p−1	κ1/(p−1	PROPN
ejpam-5591	141	8	)	)	PUNCT
ejpam-5591	141	9	(	(	PUNCT
ejpam-5591	141	10	η)r2(η	η)r2(η	NOUN
ejpam-5591	141	11	)	)	PUNCT
ejpam-5591	141	12	.	.	PUNCT
ejpam-5591	142	1	(	(	PUNCT
ejpam-5591	142	2	19	19	NUM
ejpam-5591	142	3	)	)	PUNCT
ejpam-5591	142	4	using	use	VERB
ejpam-5591	142	5	lemma	lemma	PROPN
ejpam-5591	142	6	1	1	NUM
ejpam-5591	142	7	with	with	ADP
ejpam-5591	142	8	p	p	PROPN
ejpam-5591	142	9	=	=	PROPN
ejpam-5591	142	10	w	w	PROPN
ejpam-5591	142	11	(	(	PUNCT
ejpam-5591	142	12	η	η	PROPN
ejpam-5591	142	13	)	)	PUNCT
ejpam-5591	142	14	/ς	/ς	PUNCT
ejpam-5591	142	15	(	(	PUNCT
ejpam-5591	142	16	η	η	PROPN
ejpam-5591	142	17	)	)	PUNCT
ejpam-5591	142	18	,	,	PUNCT
ejpam-5591	142	19	a	a	DET
ejpam-5591	142	20	=	=	NOUN
ejpam-5591	142	21	ν2	ν2	NOUN
ejpam-5591	142	22	/	/	SYM
ejpam-5591	142	23	r(η	r(η	NUM
ejpam-5591	142	24	)	)	PUNCT
ejpam-5591	142	25	and	and	CCONJ
ejpam-5591	142	26	ν	ν	X
ejpam-5591	142	27	=	=	SYM
ejpam-5591	142	28	1	1	NUM
ejpam-5591	142	29	,	,	PUNCT
ejpam-5591	142	30	we	we	PRON
ejpam-5591	142	31	get	get	VERB
ejpam-5591	142	32	(	(	PUNCT
ejpam-5591	142	33	w	w	PROPN
ejpam-5591	142	34	(	(	PUNCT
ejpam-5591	142	35	η	η	PROPN
ejpam-5591	142	36	)	)	PUNCT
ejpam-5591	142	37	ς	ς	PROPN
ejpam-5591	142	38	(	(	PUNCT
ejpam-5591	142	39	η	η	NOUN
ejpam-5591	142	40	)	)	PUNCT
ejpam-5591	142	41	−	−	PROPN
ejpam-5591	142	42	ν2	ν2	PROPN
ejpam-5591	142	43	r(η	r(η	NUM
ejpam-5591	142	44	)	)	PUNCT
ejpam-5591	142	45	)	)	PUNCT
ejpam-5591	142	46	2	2	NUM
ejpam-5591	142	47	≥	≥	NOUN
ejpam-5591	142	48	(	(	PUNCT
ejpam-5591	142	49	w	w	PROPN
ejpam-5591	142	50	(	(	PUNCT
ejpam-5591	142	51	η	η	PROPN
ejpam-5591	142	52	)	)	PUNCT
ejpam-5591	142	53	ς	ς	PROPN
ejpam-5591	142	54	(	(	PUNCT
ejpam-5591	142	55	η	η	NOUN
ejpam-5591	142	56	)	)	PUNCT
ejpam-5591	142	57	)	)	PUNCT
ejpam-5591	142	58	2	2	NUM
ejpam-5591	142	59	−	−	PROPN
ejpam-5591	142	60	ν2	ν2	PROPN
ejpam-5591	142	61	r(η	r(η	NUM
ejpam-5591	142	62	)	)	PUNCT
ejpam-5591	142	63	(	(	PUNCT
ejpam-5591	142	64	2w	2w	NUM
ejpam-5591	142	65	(	(	PUNCT
ejpam-5591	142	66	η	η	NOUN
ejpam-5591	142	67	)	)	PUNCT
ejpam-5591	142	68	ς	ς	PROPN
ejpam-5591	142	69	(	(	PUNCT
ejpam-5591	142	70	η	η	NOUN
ejpam-5591	142	71	)	)	PUNCT
ejpam-5591	142	72	−	−	PROPN
ejpam-5591	142	73	ν2	ν2	PROPN
ejpam-5591	142	74	r(η	r(η	NUM
ejpam-5591	142	75	)	)	PUNCT
ejpam-5591	142	76	)	)	PUNCT
ejpam-5591	142	77	.	.	PUNCT
ejpam-5591	143	1	(	(	PUNCT
ejpam-5591	143	2	20	20	NUM
ejpam-5591	143	3	)	)	PUNCT
ejpam-5591	143	4	a.	a.	NOUN
ejpam-5591	143	5	almutairi	almutairi	PROPN
ejpam-5591	143	6	/	/	SYM
ejpam-5591	143	7	eur	eur	PROPN
ejpam-5591	143	8	.	.	PUNCT
ejpam-5591	144	1	j.	j.	PROPN
ejpam-5591	144	2	pure	pure	PROPN
ejpam-5591	144	3	appl	appl	PROPN
ejpam-5591	144	4	.	.	PROPN
ejpam-5591	144	5	math	math	PROPN
ejpam-5591	144	6	,	,	PUNCT
ejpam-5591	144	7	18	18	NUM
ejpam-5591	144	8	(	(	PUNCT
ejpam-5591	144	9	1	1	NUM
ejpam-5591	144	10	)	)	PUNCT
ejpam-5591	144	11	(	(	PUNCT
ejpam-5591	144	12	2025	2025	NUM
ejpam-5591	144	13	)	)	PUNCT
ejpam-5591	144	14	,	,	PUNCT
ejpam-5591	144	15	5591	5591	NUM
ejpam-5591	144	16	8	8	NUM
ejpam-5591	144	17	of	of	ADP
ejpam-5591	144	18	11	11	NUM
ejpam-5591	144	19	by	by	ADP
ejpam-5591	144	20	(	(	PUNCT
ejpam-5591	144	21	1	1	NUM
ejpam-5591	144	22	)	)	PUNCT
ejpam-5591	144	23	,	,	PUNCT
ejpam-5591	144	24	(	(	PUNCT
ejpam-5591	144	25	19	19	NUM
ejpam-5591	144	26	)	)	PUNCT
ejpam-5591	144	27	and	and	CCONJ
ejpam-5591	144	28	(	(	PUNCT
ejpam-5591	144	29	20	20	NUM
ejpam-5591	144	30	)	)	PUNCT
ejpam-5591	144	31	,	,	PUNCT
ejpam-5591	144	32	we	we	PRON
ejpam-5591	144	33	get	get	VERB
ejpam-5591	144	34	w′	w′	PROPN
ejpam-5591	144	35	(	(	PUNCT
ejpam-5591	144	36	η	η	NOUN
ejpam-5591	144	37	)	)	PUNCT
ejpam-5591	144	38	≤	≤	NUM
ejpam-5591	144	39	ς	ς	PROPN
ejpam-5591	144	40	′	′	NUM
ejpam-5591	144	41	(	(	PUNCT
ejpam-5591	144	42	η	η	PROPN
ejpam-5591	144	43	)	)	PUNCT
ejpam-5591	144	44	ς	ς	PROPN
ejpam-5591	144	45	(	(	PUNCT
ejpam-5591	144	46	η	η	PROPN
ejpam-5591	144	47	)	)	PUNCT
ejpam-5591	144	48	w	w	PROPN
ejpam-5591	145	1	(	(	PUNCT
ejpam-5591	145	2	η)−	η)−	PROPN
ejpam-5591	145	3	ς	ς	PROPN
ejpam-5591	145	4	(	(	PUNCT
ejpam-5591	145	5	η	η	NOUN
ejpam-5591	145	6	)	)	PUNCT
ejpam-5591	145	7	∫	∫	PROPN
ejpam-5591	146	1	∞	∞	PROPN
ejpam-5591	146	2	η	η	PROPN
ejpam-5591	146	3	(	(	PUNCT
ejpam-5591	146	4	ℓ	ℓ	PROPN
ejpam-5591	146	5	κ	κ	PROPN
ejpam-5591	146	6	(	(	PUNCT
ejpam-5591	146	7	v	v	NOUN
ejpam-5591	146	8	)	)	PUNCT
ejpam-5591	146	9	∫	∫	PROPN
ejpam-5591	147	1	∞	∞	PROPN
ejpam-5591	147	2	v	v	ADP
ejpam-5591	147	3	j∑	j∑	PROPN
ejpam-5591	147	4	i=1	i=1	PROPN
ejpam-5591	147	5	ai	ai	VERB
ejpam-5591	147	6	(	(	PUNCT
ejpam-5591	147	7	s	s	NOUN
ejpam-5591	147	8	)	)	PUNCT
ejpam-5591	147	9	b	b	PROPN
ejpam-5591	147	10	(	(	PUNCT
ejpam-5591	147	11	p−1	p−1	PROPN
ejpam-5591	147	12	)	)	PUNCT
ejpam-5591	148	1	i	i	PRON
ejpam-5591	148	2	(	(	PUNCT
ejpam-5591	148	3	s	s	NOUN
ejpam-5591	148	4	)	)	PUNCT
ejpam-5591	148	5	s(p−1	s(p−1	ADJ
ejpam-5591	148	6	)	)	PUNCT
ejpam-5591	148	7	ds	ds	ADJ
ejpam-5591	148	8	)	)	PUNCT
ejpam-5591	148	9	1/(p−1	1/(p−1	NUM
ejpam-5591	148	10	)	)	PUNCT
ejpam-5591	148	11	dv	dv	PROPN
ejpam-5591	148	12	−ς	−ς	PROPN
ejpam-5591	148	13	(	(	PUNCT
ejpam-5591	148	14	η	η	PROPN
ejpam-5591	148	15	)	)	PUNCT
ejpam-5591	148	16	(	(	PUNCT
ejpam-5591	148	17	(	(	PUNCT
ejpam-5591	148	18	w	w	PROPN
ejpam-5591	148	19	(	(	PUNCT
ejpam-5591	148	20	η	η	PROPN
ejpam-5591	148	21	)	)	PUNCT
ejpam-5591	148	22	ς	ς	PROPN
ejpam-5591	148	23	(	(	PUNCT
ejpam-5591	148	24	η	η	NOUN
ejpam-5591	148	25	)	)	PUNCT
ejpam-5591	148	26	)	)	PUNCT
ejpam-5591	148	27	2	2	NUM
ejpam-5591	148	28	−	−	PROPN
ejpam-5591	148	29	ν2	ν2	PROPN
ejpam-5591	148	30	r(η	r(η	NUM
ejpam-5591	148	31	)	)	PUNCT
ejpam-5591	148	32	(	(	PUNCT
ejpam-5591	148	33	2w	2w	NUM
ejpam-5591	148	34	(	(	PUNCT
ejpam-5591	148	35	η	η	NOUN
ejpam-5591	148	36	)	)	PUNCT
ejpam-5591	148	37	ς	ς	PROPN
ejpam-5591	148	38	(	(	PUNCT
ejpam-5591	148	39	η	η	NOUN
ejpam-5591	148	40	)	)	PUNCT
ejpam-5591	148	41	−	−	PROPN
ejpam-5591	148	42	ν2	ν2	PROPN
ejpam-5591	148	43	r(η	r(η	NUM
ejpam-5591	148	44	)	)	PUNCT
ejpam-5591	148	45	)	)	PUNCT
ejpam-5591	148	46	)	)	PUNCT
ejpam-5591	149	1	+	+	CCONJ
ejpam-5591	149	2	ν2ς	ν2ς	PROPN
ejpam-5591	149	3	(	(	PUNCT
ejpam-5591	149	4	η	η	PROPN
ejpam-5591	149	5	)	)	PUNCT
ejpam-5591	149	6	κ	κ	ADP
ejpam-5591	149	7	1	1	NUM
ejpam-5591	149	8	(	(	PUNCT
ejpam-5591	149	9	p−1	p−1	PROPN
ejpam-5591	149	10	)	)	PUNCT
ejpam-5591	149	11	(	(	PUNCT
ejpam-5591	149	12	η)r2(η	η)r2(η	NOUN
ejpam-5591	149	13	)	)	PUNCT
ejpam-5591	149	14	.	.	PUNCT
ejpam-5591	150	1	this	this	PRON
ejpam-5591	150	2	implies	imply	VERB
ejpam-5591	150	3	that	that	SCONJ
ejpam-5591	150	4	w′	w′	PROPN
ejpam-5591	150	5	(	(	PUNCT
ejpam-5591	150	6	η	η	NOUN
ejpam-5591	150	7	)	)	PUNCT
ejpam-5591	150	8	≤	≤	NOUN
ejpam-5591	150	9	(	(	PUNCT
ejpam-5591	150	10	ς	ς	PROPN
ejpam-5591	150	11	′+	′+	PUNCT
ejpam-5591	150	12	(	(	PUNCT
ejpam-5591	150	13	η	η	NOUN
ejpam-5591	150	14	)	)	PUNCT
ejpam-5591	150	15	ς	ς	PROPN
ejpam-5591	150	16	(	(	PUNCT
ejpam-5591	150	17	η	η	NOUN
ejpam-5591	150	18	)	)	PUNCT
ejpam-5591	150	19	+	+	NUM
ejpam-5591	150	20	2ν2	2ν2	NUM
ejpam-5591	150	21	r(η	r(η	NUM
ejpam-5591	150	22	)	)	PUNCT
ejpam-5591	150	23	)	)	PUNCT
ejpam-5591	151	1	w	w	X
ejpam-5591	151	2	(	(	PUNCT
ejpam-5591	151	3	η)−	η)−	PROPN
ejpam-5591	151	4	1	1	NUM
ejpam-5591	151	5	ς	ς	PROPN
ejpam-5591	151	6	(	(	PUNCT
ejpam-5591	151	7	η	η	NOUN
ejpam-5591	151	8	)	)	PUNCT
ejpam-5591	151	9	w2	w2	NOUN
ejpam-5591	151	10	(	(	PUNCT
ejpam-5591	151	11	η	η	PROPN
ejpam-5591	151	12	)	)	PUNCT
ejpam-5591	151	13	−ς	−ς	PROPN
ejpam-5591	151	14	(	(	PUNCT
ejpam-5591	151	15	η	η	NOUN
ejpam-5591	151	16	)	)	PUNCT
ejpam-5591	151	17	∫	∫	NUM
ejpam-5591	152	1	∞	∞	NUM
ejpam-5591	152	2	η	η	PROPN
ejpam-5591	152	3	(	(	PUNCT
ejpam-5591	152	4	ℓ	ℓ	PROPN
ejpam-5591	152	5	κ	κ	PROPN
ejpam-5591	152	6	(	(	PUNCT
ejpam-5591	152	7	v	v	NOUN
ejpam-5591	152	8	)	)	PUNCT
ejpam-5591	152	9	∫	∫	PROPN
ejpam-5591	152	10	∞	∞	PROPN
ejpam-5591	152	11	v	v	ADP
ejpam-5591	152	12	j∑	j∑	PROPN
ejpam-5591	152	13	i=1	i=1	PROPN
ejpam-5591	152	14	ai	ai	VERB
ejpam-5591	152	15	(	(	PUNCT
ejpam-5591	152	16	s	s	NOUN
ejpam-5591	152	17	)	)	PUNCT
ejpam-5591	152	18	b	b	PROPN
ejpam-5591	152	19	(	(	PUNCT
ejpam-5591	152	20	p−1	p−1	PROPN
ejpam-5591	152	21	)	)	PUNCT
ejpam-5591	152	22	i	i	PRON
ejpam-5591	152	23	(	(	PUNCT
ejpam-5591	152	24	s	s	NOUN
ejpam-5591	152	25	)	)	PUNCT
ejpam-5591	152	26	s(p−1	s(p−1	ADJ
ejpam-5591	152	27	)	)	PUNCT
ejpam-5591	152	28	ds	ds	ADJ
ejpam-5591	152	29	)	)	PUNCT
ejpam-5591	152	30	1/(p−1	1/(p−1	NUM
ejpam-5591	152	31	)	)	PUNCT
ejpam-5591	152	32	dv	dv	PROPN
ejpam-5591	152	33	+	+	PROPN
ejpam-5591	152	34	ν22	ν22	NOUN
ejpam-5591	152	35	−	−	PROPN
ejpam-5591	152	36	ν2κ	ν2κ	PROPN
ejpam-5591	152	37	−1	−1	NOUN
ejpam-5591	152	38	(	(	PUNCT
ejpam-5591	152	39	p−1	p−1	PROPN
ejpam-5591	152	40	)	)	PUNCT
ejpam-5591	152	41	(	(	PUNCT
ejpam-5591	152	42	η	η	NOUN
ejpam-5591	152	43	)	)	PUNCT
ejpam-5591	152	44	r2(η	r2(η	NOUN
ejpam-5591	152	45	)	)	PUNCT
ejpam-5591	152	46			PROPN
ejpam-5591	152	47	.	.	PUNCT
ejpam-5591	153	1	thus	thus	ADV
ejpam-5591	153	2	,	,	PUNCT
ejpam-5591	153	3	w′	w′	PROPN
ejpam-5591	153	4	(	(	PUNCT
ejpam-5591	153	5	η	η	NOUN
ejpam-5591	153	6	)	)	PUNCT
ejpam-5591	153	7	≤	≤	NUM
ejpam-5591	153	8	−ϱ∗	−ϱ∗	NUM
ejpam-5591	153	9	(	(	PUNCT
ejpam-5591	153	10	η	η	NOUN
ejpam-5591	153	11	)	)	PUNCT
ejpam-5591	153	12	+	+	NUM
ejpam-5591	153	13	σ∗	σ∗	X
ejpam-5591	153	14	(	(	PUNCT
ejpam-5591	153	15	η)w	η)w	X
ejpam-5591	153	16	(	(	PUNCT
ejpam-5591	153	17	η)−	η)−	PROPN
ejpam-5591	153	18	1	1	NUM
ejpam-5591	153	19	ς	ς	PROPN
ejpam-5591	153	20	(	(	PUNCT
ejpam-5591	153	21	η	η	NOUN
ejpam-5591	153	22	)	)	PUNCT
ejpam-5591	153	23	w2	w2	NOUN
ejpam-5591	153	24	(	(	PUNCT
ejpam-5591	153	25	η	η	PROPN
ejpam-5591	153	26	)	)	PUNCT
ejpam-5591	153	27	.	.	PUNCT
ejpam-5591	154	1	the	the	DET
ejpam-5591	154	2	proof	proof	NOUN
ejpam-5591	154	3	is	be	AUX
ejpam-5591	154	4	finished	finish	VERB
ejpam-5591	154	5	.	.	PUNCT
ejpam-5591	155	1	lemma	lemma	PROPN
ejpam-5591	155	2	6	6	NUM
ejpam-5591	155	3	.	.	PUNCT
ejpam-5591	156	1	let	let	VERB
ejpam-5591	156	2	z	z	PRON
ejpam-5591	156	3	be	be	AUX
ejpam-5591	156	4	a	a	DET
ejpam-5591	156	5	positive	positive	ADJ
ejpam-5591	156	6	solution	solution	NOUN
ejpam-5591	156	7	of	of	ADP
ejpam-5591	156	8	(	(	PUNCT
ejpam-5591	156	9	1	1	NUM
ejpam-5591	156	10	)	)	PUNCT
ejpam-5591	156	11	in	in	ADP
ejpam-5591	156	12	the	the	DET
ejpam-5591	156	13	end	end	NOUN
ejpam-5591	156	14	.	.	PUNCT
ejpam-5591	157	1	if∫	if∫	ADJ
ejpam-5591	157	2	∞	∞	NUM
ejpam-5591	157	3	η0	η0	NOUN
ejpam-5591	157	4	(	(	PUNCT
ejpam-5591	157	5	ϱ	ϱ	PROPN
ejpam-5591	157	6	(	(	PUNCT
ejpam-5591	157	7	s)−	s)−	PROPN
ejpam-5591	157	8	(	(	PUNCT
ejpam-5591	157	9	2	2	NUM
ejpam-5591	157	10	εs2	εs2	NOUN
ejpam-5591	157	11	)	)	PUNCT
ejpam-5591	157	12	(	(	PUNCT
ejpam-5591	157	13	p−1	p−1	PROPN
ejpam-5591	157	14	)	)	PUNCT
ejpam-5591	157	15	κ	κ	PROPN
ejpam-5591	157	16	(	(	PUNCT
ejpam-5591	157	17	s)µ	s)µ	X
ejpam-5591	157	18	(	(	PUNCT
ejpam-5591	157	19	s	s	X
ejpam-5591	157	20	)	)	PUNCT
ejpam-5591	157	21	(	(	PUNCT
ejpam-5591	157	22	σ	σ	PROPN
ejpam-5591	157	23	(	(	PUNCT
ejpam-5591	157	24	s))p	s))p	NOUN
ejpam-5591	157	25	pp	pp	ADV
ejpam-5591	157	26	)	)	PUNCT
ejpam-5591	157	27	ds	ds	PROPN
ejpam-5591	157	28	=	=	SYM
ejpam-5591	157	29	∞	∞	PROPN
ejpam-5591	157	30	,	,	PUNCT
ejpam-5591	157	31	(	(	PUNCT
ejpam-5591	157	32	21	21	NUM
ejpam-5591	157	33	)	)	PUNCT
ejpam-5591	157	34	where	where	SCONJ
ejpam-5591	157	35	µ	µ	X
ejpam-5591	157	36	∈	∈	X
ejpam-5591	157	37	c	c	X
ejpam-5591	157	38	(	(	PUNCT
ejpam-5591	157	39	[	[	X
ejpam-5591	157	40	η0,∞	η0,∞	PROPN
ejpam-5591	157	41	)	)	PUNCT
ejpam-5591	157	42	)	)	PUNCT
ejpam-5591	157	43	and	and	CCONJ
ejpam-5591	157	44	ε	ε	PROPN
ejpam-5591	157	45	∈	∈	PROPN
ejpam-5591	157	46	(	(	PUNCT
ejpam-5591	157	47	0	0	NUM
ejpam-5591	157	48	,	,	PUNCT
ejpam-5591	157	49	1	1	NUM
ejpam-5591	157	50	)	)	PUNCT
ejpam-5591	157	51	,	,	PUNCT
ejpam-5591	157	52	then	then	ADV
ejpam-5591	157	53	z	z	PROPN
ejpam-5591	157	54	does	do	AUX
ejpam-5591	157	55	n’t	not	PART
ejpam-5591	157	56	fulfill	fulfill	VERB
ejpam-5591	157	57	case	case	NOUN
ejpam-5591	157	58	(	(	PUNCT
ejpam-5591	157	59	1	1	NUM
ejpam-5591	157	60	)	)	PUNCT
ejpam-5591	157	61	.	.	PUNCT
ejpam-5591	158	1	proof	proof	NOUN
ejpam-5591	158	2	.	.	PUNCT
ejpam-5591	159	1	let	let	VERB
ejpam-5591	159	2	z	z	PRON
ejpam-5591	159	3	be	be	AUX
ejpam-5591	159	4	a	a	DET
ejpam-5591	159	5	positive	positive	ADJ
ejpam-5591	159	6	solution	solution	NOUN
ejpam-5591	159	7	of	of	ADP
ejpam-5591	159	8	(	(	PUNCT
ejpam-5591	159	9	1	1	NUM
ejpam-5591	159	10	)	)	PUNCT
ejpam-5591	159	11	in	in	ADP
ejpam-5591	159	12	the	the	DET
ejpam-5591	159	13	end	end	NOUN
ejpam-5591	159	14	.	.	PUNCT
ejpam-5591	160	1	by	by	ADP
ejpam-5591	160	2	lemma	lemma	PROPN
ejpam-5591	160	3	4	4	NUM
ejpam-5591	160	4	,	,	PUNCT
ejpam-5591	160	5	we	we	PRON
ejpam-5591	160	6	see	see	VERB
ejpam-5591	160	7	(	(	PUNCT
ejpam-5591	160	8	11	11	NUM
ejpam-5591	160	9	)	)	PUNCT
ejpam-5591	160	10	holds	hold	VERB
ejpam-5591	160	11	and	and	CCONJ
ejpam-5591	160	12	from	from	ADP
ejpam-5591	160	13	lemma	lemma	PROPN
ejpam-5591	160	14	1	1	NUM
ejpam-5591	160	15	with	with	ADP
ejpam-5591	160	16	u	u	PROPN
ejpam-5591	160	17	=	=	PROPN
ejpam-5591	160	18	σ	σ	PROPN
ejpam-5591	160	19	(	(	PUNCT
ejpam-5591	160	20	η	η	PROPN
ejpam-5591	160	21	)	)	PUNCT
ejpam-5591	160	22	,	,	PUNCT
ejpam-5591	160	23	v	v	NOUN
ejpam-5591	160	24	=	=	SYM
ejpam-5591	160	25	(	(	PUNCT
ejpam-5591	160	26	p−	p−	NOUN
ejpam-5591	160	27	1	1	NUM
ejpam-5591	160	28	)	)	PUNCT
ejpam-5591	160	29	εη2/	εη2/	PROPN
ejpam-5591	160	30	(	(	PUNCT
ejpam-5591	160	31	2	2	NUM
ejpam-5591	160	32	(	(	PUNCT
ejpam-5591	160	33	κ	κ	NOUN
ejpam-5591	160	34	(	(	PUNCT
ejpam-5591	160	35	η)µ	η)µ	X
ejpam-5591	160	36	(	(	PUNCT
ejpam-5591	160	37	η))1/(p−1	η))1/(p−1	NOUN
ejpam-5591	160	38	)	)	PUNCT
ejpam-5591	160	39	)	)	PUNCT
ejpam-5591	160	40	and	and	CCONJ
ejpam-5591	160	41	η	η	PROPN
ejpam-5591	160	42	=	=	SYM
ejpam-5591	160	43	ζ	ζ	PROPN
ejpam-5591	160	44	,	,	PUNCT
ejpam-5591	160	45	we	we	PRON
ejpam-5591	160	46	get	get	VERB
ejpam-5591	160	47	ζ	ζ	NOUN
ejpam-5591	160	48	′	′	NUM
ejpam-5591	160	49	(	(	PUNCT
ejpam-5591	160	50	η	η	NOUN
ejpam-5591	160	51	)	)	PUNCT
ejpam-5591	160	52	≤	≤	ADJ
ejpam-5591	160	53	−ϱ	−ϱ	NOUN
ejpam-5591	160	54	(	(	PUNCT
ejpam-5591	160	55	η	η	NOUN
ejpam-5591	160	56	)	)	PUNCT
ejpam-5591	160	57	+	+	CCONJ
ejpam-5591	160	58	(	(	PUNCT
ejpam-5591	160	59	2	2	NUM
ejpam-5591	160	60	εη2	εη2	NOUN
ejpam-5591	160	61	)	)	PUNCT
ejpam-5591	160	62	(	(	PUNCT
ejpam-5591	160	63	p−1	p−1	PROPN
ejpam-5591	160	64	)	)	PUNCT
ejpam-5591	160	65	κ	κ	PROPN
ejpam-5591	160	66	(	(	PUNCT
ejpam-5591	160	67	η)µ	η)µ	X
ejpam-5591	160	68	(	(	PUNCT
ejpam-5591	160	69	η	η	NOUN
ejpam-5591	160	70	)	)	PUNCT
ejpam-5591	160	71	(	(	PUNCT
ejpam-5591	160	72	σ	σ	PROPN
ejpam-5591	160	73	(	(	PUNCT
ejpam-5591	160	74	η))(p−1)+1	η))(p−1)+1	NOUN
ejpam-5591	160	75	pp	pp	ADV
ejpam-5591	160	76	.	.	PUNCT
ejpam-5591	161	1	(	(	PUNCT
ejpam-5591	161	2	22	22	NUM
ejpam-5591	161	3	)	)	PUNCT
ejpam-5591	161	4	once	once	ADV
ejpam-5591	161	5	more	more	ADJ
ejpam-5591	161	6	integrating	integrating	NOUN
ejpam-5591	161	7	from	from	ADP
ejpam-5591	161	8	η1	η1	NOUN
ejpam-5591	161	9	to	to	ADP
ejpam-5591	161	10	η	η	PROPN
ejpam-5591	161	11	,	,	PUNCT
ejpam-5591	161	12	we	we	PRON
ejpam-5591	161	13	find∫	find∫	VERB
ejpam-5591	161	14	η	η	PROPN
ejpam-5591	161	15	η1	η1	NOUN
ejpam-5591	161	16	(	(	PUNCT
ejpam-5591	161	17	ϱ	ϱ	PROPN
ejpam-5591	161	18	(	(	PUNCT
ejpam-5591	161	19	s)−	s)−	PROPN
ejpam-5591	161	20	(	(	PUNCT
ejpam-5591	161	21	2	2	NUM
ejpam-5591	161	22	εs2	εs2	NOUN
ejpam-5591	161	23	)	)	PUNCT
ejpam-5591	161	24	(	(	PUNCT
ejpam-5591	161	25	p−1	p−1	PROPN
ejpam-5591	161	26	)	)	PUNCT
ejpam-5591	161	27	κ	κ	PROPN
ejpam-5591	161	28	(	(	PUNCT
ejpam-5591	161	29	s)µ	s)µ	X
ejpam-5591	161	30	(	(	PUNCT
ejpam-5591	161	31	s	s	X
ejpam-5591	161	32	)	)	PUNCT
ejpam-5591	161	33	(	(	PUNCT
ejpam-5591	161	34	σ	σ	PROPN
ejpam-5591	161	35	(	(	PUNCT
ejpam-5591	161	36	s))p	s))p	NOUN
ejpam-5591	161	37	pp	pp	ADV
ejpam-5591	161	38	)	)	PUNCT
ejpam-5591	161	39	ds	ds	ADJ
ejpam-5591	161	40	≤	≤	NUM
ejpam-5591	161	41	ζ	ζ	NOUN
ejpam-5591	161	42	(	(	PUNCT
ejpam-5591	161	43	η1	η1	NOUN
ejpam-5591	161	44	)	)	PUNCT
ejpam-5591	161	45	,	,	PUNCT
ejpam-5591	161	46	which	which	PRON
ejpam-5591	161	47	contradicts	contradict	VERB
ejpam-5591	161	48	(	(	PUNCT
ejpam-5591	161	49	21	21	NUM
ejpam-5591	161	50	)	)	PUNCT
ejpam-5591	161	51	.	.	PUNCT
ejpam-5591	162	1	so	so	ADV
ejpam-5591	162	2	,	,	PUNCT
ejpam-5591	162	3	the	the	DET
ejpam-5591	162	4	proof	proof	NOUN
ejpam-5591	162	5	is	be	AUX
ejpam-5591	162	6	finished	finish	VERB
ejpam-5591	162	7	.	.	PUNCT
ejpam-5591	163	1	a.	a.	NOUN
ejpam-5591	163	2	almutairi	almutairi	PROPN
ejpam-5591	163	3	/	/	SYM
ejpam-5591	163	4	eur	eur	PROPN
ejpam-5591	163	5	.	.	PUNCT
ejpam-5591	164	1	j.	j.	PROPN
ejpam-5591	164	2	pure	pure	PROPN
ejpam-5591	164	3	appl	appl	PROPN
ejpam-5591	164	4	.	.	PROPN
ejpam-5591	164	5	math	math	PROPN
ejpam-5591	164	6	,	,	PUNCT
ejpam-5591	164	7	18	18	NUM
ejpam-5591	164	8	(	(	PUNCT
ejpam-5591	164	9	1	1	NUM
ejpam-5591	164	10	)	)	PUNCT
ejpam-5591	164	11	(	(	PUNCT
ejpam-5591	164	12	2025	2025	NUM
ejpam-5591	164	13	)	)	PUNCT
ejpam-5591	164	14	,	,	PUNCT
ejpam-5591	164	15	5591	5591	NUM
ejpam-5591	164	16	9	9	NUM
ejpam-5591	164	17	of	of	ADP
ejpam-5591	164	18	11	11	NUM
ejpam-5591	164	19	lemma	lemma	PROPN
ejpam-5591	164	20	7	7	NUM
ejpam-5591	164	21	.	.	PUNCT
ejpam-5591	165	1	let	let	VERB
ejpam-5591	165	2	z	z	PRON
ejpam-5591	165	3	be	be	AUX
ejpam-5591	165	4	an	an	DET
ejpam-5591	165	5	eventually	eventually	ADV
ejpam-5591	165	6	positive	positive	ADJ
ejpam-5591	165	7	solution	solution	NOUN
ejpam-5591	165	8	of	of	ADP
ejpam-5591	165	9	(	(	PUNCT
ejpam-5591	165	10	1	1	NUM
ejpam-5591	165	11	)	)	PUNCT
ejpam-5591	165	12	and	and	CCONJ
ejpam-5591	165	13	case	case	NOUN
ejpam-5591	165	14	(	(	PUNCT
ejpam-5591	165	15	2	2	X
ejpam-5591	165	16	)	)	PUNCT
ejpam-5591	165	17	hold	hold	NOUN
ejpam-5591	165	18	.	.	PUNCT
ejpam-5591	166	1	if∫	if∫	ADJ
ejpam-5591	166	2	∞	∞	NUM
ejpam-5591	166	3	η0	η0	NOUN
ejpam-5591	166	4	(	(	PUNCT
ejpam-5591	166	5	ϱ∗	ϱ∗	PROPN
ejpam-5591	166	6	(	(	PUNCT
ejpam-5591	166	7	s)−	s)−	NOUN
ejpam-5591	166	8	1	1	NUM
ejpam-5591	166	9	4	4	NUM
ejpam-5591	166	10	ς	ς	PROPN
ejpam-5591	166	11	(	(	PUNCT
ejpam-5591	166	12	s	s	NOUN
ejpam-5591	166	13	)	)	PUNCT
ejpam-5591	166	14	(	(	PUNCT
ejpam-5591	166	15	σ∗	σ∗	X
ejpam-5591	166	16	(	(	PUNCT
ejpam-5591	166	17	s))2	s))2	NOUN
ejpam-5591	166	18	)	)	PUNCT
ejpam-5591	166	19	ds	ds	PROPN
ejpam-5591	166	20	=	=	SYM
ejpam-5591	166	21	∞	∞	PROPN
ejpam-5591	166	22	,	,	PUNCT
ejpam-5591	166	23	where	where	SCONJ
ejpam-5591	166	24	ς	ς	PROPN
ejpam-5591	166	25	∈	∈	PROPN
ejpam-5591	166	26	c	c	X
ejpam-5591	166	27	(	(	PUNCT
ejpam-5591	166	28	[	[	X
ejpam-5591	166	29	η0,∞	η0,∞	PROPN
ejpam-5591	166	30	)	)	PUNCT
ejpam-5591	166	31	)	)	PUNCT
ejpam-5591	166	32	(	(	PUNCT
ejpam-5591	166	33	23	23	NUM
ejpam-5591	166	34	)	)	PUNCT
ejpam-5591	166	35	then	then	ADV
ejpam-5591	166	36	z	z	PROPN
ejpam-5591	166	37	does	do	AUX
ejpam-5591	166	38	n’t	not	PART
ejpam-5591	166	39	fulfill	fulfill	VERB
ejpam-5591	166	40	case	case	NOUN
ejpam-5591	166	41	(	(	PUNCT
ejpam-5591	166	42	2	2	NUM
ejpam-5591	166	43	)	)	PUNCT
ejpam-5591	166	44	.	.	PUNCT
ejpam-5591	167	1	proof	proof	NOUN
ejpam-5591	167	2	.	.	PUNCT
ejpam-5591	168	1	let	let	VERB
ejpam-5591	168	2	z	z	PRON
ejpam-5591	168	3	be	be	AUX
ejpam-5591	168	4	a	a	DET
ejpam-5591	168	5	positive	positive	ADJ
ejpam-5591	168	6	solution	solution	NOUN
ejpam-5591	168	7	of	of	ADP
ejpam-5591	168	8	(	(	PUNCT
ejpam-5591	168	9	1	1	NUM
ejpam-5591	168	10	)	)	PUNCT
ejpam-5591	168	11	in	in	ADP
ejpam-5591	168	12	the	the	DET
ejpam-5591	168	13	end	end	NOUN
ejpam-5591	168	14	.	.	PUNCT
ejpam-5591	169	1	(	(	PUNCT
ejpam-5591	169	2	16	16	NUM
ejpam-5591	169	3	)	)	PUNCT
ejpam-5591	169	4	holds	hold	VERB
ejpam-5591	169	5	according	accord	VERB
ejpam-5591	169	6	to	to	ADP
ejpam-5591	169	7	lemma	lemma	PROPN
ejpam-5591	169	8	5	5	NUM
ejpam-5591	169	9	.	.	PUNCT
ejpam-5591	170	1	lemma	lemma	PROPN
ejpam-5591	170	2	1	1	NUM
ejpam-5591	170	3	is	be	AUX
ejpam-5591	170	4	used	use	VERB
ejpam-5591	170	5	with	with	ADP
ejpam-5591	170	6	u	u	NOUN
ejpam-5591	170	7	=	=	NOUN
ejpam-5591	170	8	σ∗	σ∗	X
ejpam-5591	170	9	(	(	PUNCT
ejpam-5591	170	10	η	η	NOUN
ejpam-5591	170	11	)	)	PUNCT
ejpam-5591	170	12	,	,	PUNCT
ejpam-5591	170	13	v	v	NOUN
ejpam-5591	170	14	=	=	SYM
ejpam-5591	170	15	1	1	NUM
ejpam-5591	170	16	/	/	SYM
ejpam-5591	170	17	ς	ς	PROPN
ejpam-5591	170	18	(	(	PUNCT
ejpam-5591	170	19	η	η	PROPN
ejpam-5591	170	20	)	)	PUNCT
ejpam-5591	170	21	,	,	PUNCT
ejpam-5591	170	22	p	p	NOUN
ejpam-5591	170	23	=	=	SYM
ejpam-5591	170	24	2	2	NUM
ejpam-5591	170	25	and	and	CCONJ
ejpam-5591	170	26	η	η	PROPN
ejpam-5591	170	27	=	=	SYM
ejpam-5591	170	28	w	w	PROPN
ejpam-5591	170	29	,	,	PUNCT
ejpam-5591	170	30	we	we	PRON
ejpam-5591	170	31	obtainthe	obtainthe	VERB
ejpam-5591	170	32	formula	formula	NOUN
ejpam-5591	170	33	is	be	AUX
ejpam-5591	170	34	ζ	ζ	NOUN
ejpam-5591	170	35	′	′	NUM
ejpam-5591	170	36	(	(	PUNCT
ejpam-5591	170	37	η	η	NOUN
ejpam-5591	170	38	)	)	PUNCT
ejpam-5591	170	39	≤	≤	NUM
ejpam-5591	170	40	−ϱ∗	−ϱ∗	NUM
ejpam-5591	170	41	(	(	PUNCT
ejpam-5591	170	42	η	η	NOUN
ejpam-5591	170	43	)	)	PUNCT
ejpam-5591	170	44	+	+	CCONJ
ejpam-5591	170	45	1	1	NUM
ejpam-5591	170	46	4	4	NUM
ejpam-5591	170	47	ς	ς	PROPN
ejpam-5591	170	48	(	(	PUNCT
ejpam-5591	170	49	η	η	NOUN
ejpam-5591	170	50	)	)	PUNCT
ejpam-5591	170	51	(	(	PUNCT
ejpam-5591	170	52	σ∗	σ∗	X
ejpam-5591	170	53	(	(	PUNCT
ejpam-5591	170	54	η))2	η))2	NOUN
ejpam-5591	170	55	.	.	PUNCT
ejpam-5591	171	1	(	(	PUNCT
ejpam-5591	171	2	24	24	NUM
ejpam-5591	171	3	)	)	PUNCT
ejpam-5591	171	4	once	once	ADV
ejpam-5591	171	5	more	more	ADJ
ejpam-5591	171	6	integrating	integrating	NOUN
ejpam-5591	171	7	from	from	ADP
ejpam-5591	171	8	η1	η1	NOUN
ejpam-5591	171	9	to	to	ADP
ejpam-5591	171	10	η	η	PROPN
ejpam-5591	171	11	,	,	PUNCT
ejpam-5591	171	12	we	we	PRON
ejpam-5591	171	13	find∫	find∫	VERB
ejpam-5591	171	14	η	η	PROPN
ejpam-5591	171	15	η1	η1	NOUN
ejpam-5591	171	16	(	(	PUNCT
ejpam-5591	171	17	ϱ∗	ϱ∗	PROPN
ejpam-5591	171	18	(	(	PUNCT
ejpam-5591	171	19	s)−	s)−	NOUN
ejpam-5591	171	20	1	1	NUM
ejpam-5591	171	21	4	4	NUM
ejpam-5591	171	22	ς	ς	PROPN
ejpam-5591	171	23	(	(	PUNCT
ejpam-5591	171	24	s	s	NOUN
ejpam-5591	171	25	)	)	PUNCT
ejpam-5591	171	26	(	(	PUNCT
ejpam-5591	171	27	σ∗	σ∗	X
ejpam-5591	171	28	(	(	PUNCT
ejpam-5591	171	29	s))2	s))2	NOUN
ejpam-5591	171	30	)	)	PUNCT
ejpam-5591	171	31	ds	ds	ADJ
ejpam-5591	171	32	≤	≤	NUM
ejpam-5591	171	33	ζ	ζ	NOUN
ejpam-5591	171	34	(	(	PUNCT
ejpam-5591	171	35	η1	η1	NOUN
ejpam-5591	171	36	)	)	PUNCT
ejpam-5591	171	37	.	.	PUNCT
ejpam-5591	172	1	this	this	PRON
ejpam-5591	172	2	runs	run	VERB
ejpam-5591	172	3	counter	counter	ADV
ejpam-5591	172	4	to	to	ADP
ejpam-5591	172	5	(	(	PUNCT
ejpam-5591	172	6	23	23	NUM
ejpam-5591	172	7	)	)	PUNCT
ejpam-5591	172	8	.	.	PUNCT
ejpam-5591	173	1	the	the	DET
ejpam-5591	173	2	proof	proof	NOUN
ejpam-5591	173	3	is	be	AUX
ejpam-5591	173	4	finished	finish	VERB
ejpam-5591	173	5	.	.	PUNCT
ejpam-5591	174	1	theorem	theorem	NOUN
ejpam-5591	174	2	3	3	X
ejpam-5591	175	1	.	.	PUNCT
ejpam-5591	175	2	assume	assume	VERB
ejpam-5591	175	3	that	that	SCONJ
ejpam-5591	175	4	(	(	PUNCT
ejpam-5591	175	5	21	21	NUM
ejpam-5591	175	6	)	)	PUNCT
ejpam-5591	175	7	and	and	CCONJ
ejpam-5591	175	8	(	(	PUNCT
ejpam-5591	175	9	23	23	X
ejpam-5591	175	10	)	)	PUNCT
ejpam-5591	175	11	hold	hold	NOUN
ejpam-5591	175	12	.	.	PUNCT
ejpam-5591	176	1	then	then	ADV
ejpam-5591	176	2	(	(	PUNCT
ejpam-5591	176	3	1	1	X
ejpam-5591	176	4	)	)	PUNCT
ejpam-5591	176	5	is	be	AUX
ejpam-5591	176	6	oscillatory	oscillatory	ADJ
ejpam-5591	176	7	.	.	PUNCT
ejpam-5591	177	1	the	the	DET
ejpam-5591	177	2	oscillation	oscillation	NOUN
ejpam-5591	177	3	requirements	requirement	NOUN
ejpam-5591	177	4	that	that	PRON
ejpam-5591	177	5	result	result	VERB
ejpam-5591	177	6	from	from	ADP
ejpam-5591	177	7	applying	apply	VERB
ejpam-5591	177	8	µ	µ	PROPN
ejpam-5591	177	9	(	(	PUNCT
ejpam-5591	177	10	η	η	NOUN
ejpam-5591	177	11	)	)	PUNCT
ejpam-5591	177	12	=	=	SYM
ejpam-5591	177	13	η3	η3	NOUN
ejpam-5591	177	14	and	and	CCONJ
ejpam-5591	177	15	ς	ς	PROPN
ejpam-5591	177	16	(	(	PUNCT
ejpam-5591	177	17	η	η	NOUN
ejpam-5591	177	18	)	)	PUNCT
ejpam-5591	177	19	=	=	SYM
ejpam-5591	177	20	η	η	PROPN
ejpam-5591	177	21	to	to	PART
ejpam-5591	177	22	theorem	theorem	VERB
ejpam-5591	177	23	3	3	NUM
ejpam-5591	177	24	are	be	AUX
ejpam-5591	177	25	as	as	SCONJ
ejpam-5591	177	26	follows	follow	VERB
ejpam-5591	177	27	:	:	PUNCT
ejpam-5591	178	1	corollary	corollary	ADJ
ejpam-5591	178	2	1	1	X
ejpam-5591	178	3	.	.	PUNCT
ejpam-5591	179	1	let	let	VERB
ejpam-5591	179	2	(	(	PUNCT
ejpam-5591	179	3	3	3	X
ejpam-5591	179	4	)	)	PUNCT
ejpam-5591	179	5	hold	hold	NOUN
ejpam-5591	179	6	.	.	PUNCT
ejpam-5591	180	1	assume	assume	VERB
ejpam-5591	180	2	that	that	SCONJ
ejpam-5591	180	3	lim	lim	PROPN
ejpam-5591	180	4	sup	sup	PROPN
ejpam-5591	180	5	η→∞	η→∞	NUM
ejpam-5591	180	6	∫	∫	PROPN
ejpam-5591	180	7	η	η	PROPN
ejpam-5591	180	8	η1	η1	PROPN
ejpam-5591	180	9	(	(	PUNCT
ejpam-5591	180	10	β	β	X
ejpam-5591	180	11	(	(	PUNCT
ejpam-5591	180	12	s)−	s)−	PROPN
ejpam-5591	180	13	(	(	PUNCT
ejpam-5591	180	14	2	2	NUM
ejpam-5591	180	15	εs2	εs2	NOUN
ejpam-5591	180	16	)	)	PUNCT
ejpam-5591	180	17	(	(	PUNCT
ejpam-5591	180	18	p−1	p−1	PROPN
ejpam-5591	180	19	)	)	PUNCT
ejpam-5591	180	20	κ	κ	PROPN
ejpam-5591	180	21	(	(	PUNCT
ejpam-5591	180	22	s)µ	s)µ	X
ejpam-5591	180	23	(	(	PUNCT
ejpam-5591	180	24	s	s	X
ejpam-5591	180	25	)	)	PUNCT
ejpam-5591	180	26	(	(	PUNCT
ejpam-5591	180	27	β	β	X
ejpam-5591	180	28	(	(	PUNCT
ejpam-5591	180	29	s))p	s))p	NOUN
ejpam-5591	180	30	pp	pp	ADV
ejpam-5591	180	31	)	)	PUNCT
ejpam-5591	180	32	ds	ds	PROPN
ejpam-5591	180	33	=	=	SYM
ejpam-5591	180	34	∞	∞	PROPN
ejpam-5591	180	35	,	,	PUNCT
ejpam-5591	180	36	(	(	PUNCT
ejpam-5591	180	37	25	25	NUM
ejpam-5591	180	38	)	)	PUNCT
ejpam-5591	180	39	for	for	ADP
ejpam-5591	180	40	some	some	DET
ejpam-5591	180	41	ε	ε	PROPN
ejpam-5591	180	42	∈	∈	PROPN
ejpam-5591	180	43	(	(	PUNCT
ejpam-5591	180	44	0	0	NUM
ejpam-5591	180	45	,	,	PUNCT
ejpam-5591	180	46	1	1	NUM
ejpam-5591	180	47	)	)	PUNCT
ejpam-5591	180	48	.	.	PUNCT
ejpam-5591	181	1	if	if	SCONJ
ejpam-5591	181	2	lim	lim	PROPN
ejpam-5591	181	3	sup	sup	PROPN
ejpam-5591	181	4	η→∞	η→∞	NUM
ejpam-5591	181	5	∫	∫	PROPN
ejpam-5591	181	6	η	η	PROPN
ejpam-5591	181	7	η1	η1	PROPN
ejpam-5591	181	8	(	(	PUNCT
ejpam-5591	181	9	β1	β1	PROPN
ejpam-5591	181	10	(	(	PUNCT
ejpam-5591	181	11	s)−	s)−	PROPN
ejpam-5591	181	12	1	1	NUM
ejpam-5591	181	13	4	4	NUM
ejpam-5591	181	14	ς	ς	PROPN
ejpam-5591	181	15	(	(	PUNCT
ejpam-5591	181	16	s	s	NOUN
ejpam-5591	181	17	)	)	PUNCT
ejpam-5591	181	18	(	(	PUNCT
ejpam-5591	181	19	β1	β1	PROPN
ejpam-5591	181	20	(	(	PUNCT
ejpam-5591	181	21	s	s	NOUN
ejpam-5591	181	22	)	)	PUNCT
ejpam-5591	181	23	)	)	PUNCT
ejpam-5591	181	24	2	2	X
ejpam-5591	181	25	)	)	PUNCT
ejpam-5591	181	26	ds	ds	PROPN
ejpam-5591	181	27	=	=	SYM
ejpam-5591	181	28	∞	∞	PROPN
ejpam-5591	181	29	,	,	PUNCT
ejpam-5591	181	30	(	(	PUNCT
ejpam-5591	181	31	26	26	NUM
ejpam-5591	181	32	)	)	PUNCT
ejpam-5591	182	1	where	where	SCONJ
ejpam-5591	182	2	β	β	X
ejpam-5591	182	3	(	(	PUNCT
ejpam-5591	182	4	η	η	PROPN
ejpam-5591	182	5	)	)	PUNCT
ejpam-5591	182	6	:	:	PUNCT
ejpam-5591	182	7	=	=	PUNCT
ejpam-5591	182	8	η3	η3	NOUN
ejpam-5591	182	9	(	(	PUNCT
ejpam-5591	182	10	ℓ	ℓ	PROPN
ejpam-5591	182	11	j∑	j∑	PROPN
ejpam-5591	182	12	i=1	i=1	PROPN
ejpam-5591	182	13	ai	ai	PROPN
ejpam-5591	182	14	(	(	PUNCT
ejpam-5591	182	15	η	η	NOUN
ejpam-5591	182	16	)	)	PUNCT
ejpam-5591	182	17	(	(	PUNCT
ejpam-5591	182	18	b3i	b3i	NUM
ejpam-5591	182	19	(	(	PUNCT
ejpam-5591	182	20	η	η	NOUN
ejpam-5591	182	21	)	)	PUNCT
ejpam-5591	182	22	η3	η3	NOUN
ejpam-5591	182	23	)	)	PUNCT
ejpam-5591	182	24	(	(	PUNCT
ejpam-5591	182	25	p−1	p−1	PROPN
ejpam-5591	182	26	)	)	PUNCT
ejpam-5591	182	27	+	+	CCONJ
ejpam-5591	182	28	εν	εν	X
ejpam-5591	182	29	p/(p−1	p/(p−1	NUM
ejpam-5591	182	30	)	)	PUNCT
ejpam-5591	182	31	1	1	NUM
ejpam-5591	182	32	η2	η2	VERB
ejpam-5591	182	33	−	−	PROPN
ejpam-5591	182	34	2ν1	2ν1	NUM
ejpam-5591	182	35	(	(	PUNCT
ejpam-5591	182	36	p−	p−	NOUN
ejpam-5591	182	37	1	1	NUM
ejpam-5591	182	38	)	)	PUNCT
ejpam-5591	182	39	2κ	2κ	NOUN
ejpam-5591	182	40	1	1	NUM
ejpam-5591	182	41	(	(	PUNCT
ejpam-5591	182	42	p−1	p−1	PROPN
ejpam-5591	182	43	)	)	PUNCT
ejpam-5591	182	44	(	(	PUNCT
ejpam-5591	182	45	η)rp(η	η)rp(η	PROPN
ejpam-5591	182	46	)	)	PUNCT
ejpam-5591	182	47	)	)	PUNCT
ejpam-5591	183	1	β	β	X
ejpam-5591	183	2	(	(	PUNCT
ejpam-5591	183	3	η	η	PROPN
ejpam-5591	183	4	)	)	PUNCT
ejpam-5591	183	5	:	:	PUNCT
ejpam-5591	184	1	=	=	SYM
ejpam-5591	184	2	3	3	NUM
ejpam-5591	184	3	η	η	X
ejpam-5591	184	4	+	+	PUNCT
ejpam-5591	184	5	(	(	PUNCT
ejpam-5591	184	6	(	(	PUNCT
ejpam-5591	184	7	p−	p−	NOUN
ejpam-5591	184	8	1	1	NUM
ejpam-5591	184	9	)	)	PUNCT
ejpam-5591	184	10	+	+	CCONJ
ejpam-5591	184	11	1	1	X
ejpam-5591	184	12	)	)	PUNCT
ejpam-5591	184	13	ν	ν	NOUN
ejpam-5591	184	14	1/(p−1	1/(p−1	NUM
ejpam-5591	184	15	)	)	PUNCT
ejpam-5591	184	16	1	1	NUM
ejpam-5591	184	17	εη2	εη2	NOUN
ejpam-5591	184	18	2κ	2κ	NOUN
ejpam-5591	184	19	1	1	NUM
ejpam-5591	184	20	(	(	PUNCT
ejpam-5591	184	21	p−1	p−1	PROPN
ejpam-5591	184	22	)	)	PUNCT
ejpam-5591	184	23	(	(	PUNCT
ejpam-5591	184	24	η)r(η	η)r(η	PROPN
ejpam-5591	184	25	)	)	PUNCT
ejpam-5591	184	26	,	,	PUNCT
ejpam-5591	184	27	β1	β1	PROPN
ejpam-5591	184	28	(	(	PUNCT
ejpam-5591	184	29	η	η	PROPN
ejpam-5591	184	30	)	)	PUNCT
ejpam-5591	184	31	:	:	PUNCT
ejpam-5591	184	32	=	=	SYM
ejpam-5591	184	33	1	1	NUM
ejpam-5591	184	34	η	η	X
ejpam-5591	184	35	+	+	X
ejpam-5591	184	36	2ν2	2ν2	NUM
ejpam-5591	184	37	r(η	r(η	NUM
ejpam-5591	184	38	)	)	PUNCT
ejpam-5591	184	39	and	and	CCONJ
ejpam-5591	184	40	β1	β1	PROPN
ejpam-5591	184	41	(	(	PUNCT
ejpam-5591	184	42	η	η	PROPN
ejpam-5591	184	43	)	)	PUNCT
ejpam-5591	184	44	:	:	PUNCT
ejpam-5591	184	45	=	=	SYM
ejpam-5591	184	46	η	η	PROPN
ejpam-5591	184	47	∫	∫	NUM
ejpam-5591	184	48	∞	∞	PROPN
ejpam-5591	184	49	η	η	PROPN
ejpam-5591	184	50	(	(	PUNCT
ejpam-5591	184	51	ℓ	ℓ	PROPN
ejpam-5591	184	52	κ	κ	PROPN
ejpam-5591	184	53	(	(	PUNCT
ejpam-5591	184	54	v	v	NOUN
ejpam-5591	184	55	)	)	PUNCT
ejpam-5591	184	56	∫	∫	PROPN
ejpam-5591	184	57	∞	∞	PROPN
ejpam-5591	184	58	v	v	ADP
ejpam-5591	184	59	j∑	j∑	PROPN
ejpam-5591	184	60	i=1	i=1	PROPN
ejpam-5591	185	1	ai	ai	VERB
ejpam-5591	185	2	(	(	PUNCT
ejpam-5591	185	3	s	s	NOUN
ejpam-5591	185	4	)	)	PUNCT
ejpam-5591	185	5	b	b	PROPN
ejpam-5591	185	6	(	(	PUNCT
ejpam-5591	185	7	p−1	p−1	PROPN
ejpam-5591	185	8	)	)	PUNCT
ejpam-5591	186	1	i	i	PRON
ejpam-5591	186	2	(	(	PUNCT
ejpam-5591	186	3	s	s	NOUN
ejpam-5591	186	4	)	)	PUNCT
ejpam-5591	186	5	s(p−1	s(p−1	ADJ
ejpam-5591	186	6	)	)	PUNCT
ejpam-5591	186	7	ds	ds	ADJ
ejpam-5591	186	8	)	)	PUNCT
ejpam-5591	186	9	1/(p−1	1/(p−1	NUM
ejpam-5591	186	10	)	)	PUNCT
ejpam-5591	186	11	dv	dv	PROPN
ejpam-5591	186	12	+	+	PROPN
ejpam-5591	186	13	ν22	ν22	NOUN
ejpam-5591	186	14	−	−	PROPN
ejpam-5591	186	15	ν2κ	ν2κ	PROPN
ejpam-5591	186	16	−1	−1	NOUN
ejpam-5591	186	17	(	(	PUNCT
ejpam-5591	186	18	p−1	p−1	PROPN
ejpam-5591	186	19	)	)	PUNCT
ejpam-5591	186	20	(	(	PUNCT
ejpam-5591	186	21	η	η	NOUN
ejpam-5591	186	22	)	)	PUNCT
ejpam-5591	186	23	r2(η	r2(η	NOUN
ejpam-5591	186	24	)	)	PUNCT
ejpam-5591	186	25			PROPN
ejpam-5591	186	26	,	,	PUNCT
ejpam-5591	186	27	then	then	ADV
ejpam-5591	186	28	(	(	PUNCT
ejpam-5591	186	29	1	1	X
ejpam-5591	186	30	)	)	PUNCT
ejpam-5591	186	31	is	be	AUX
ejpam-5591	186	32	oscillatory	oscillatory	ADJ
ejpam-5591	186	33	.	.	PUNCT
ejpam-5591	187	1	a.	a.	NOUN
ejpam-5591	187	2	almutairi	almutairi	PROPN
ejpam-5591	187	3	/	/	SYM
ejpam-5591	187	4	eur	eur	PROPN
ejpam-5591	187	5	.	.	PUNCT
ejpam-5591	188	1	j.	j.	PROPN
ejpam-5591	188	2	pure	pure	PROPN
ejpam-5591	188	3	appl	appl	PROPN
ejpam-5591	188	4	.	.	PROPN
ejpam-5591	188	5	math	math	PROPN
ejpam-5591	188	6	,	,	PUNCT
ejpam-5591	188	7	18	18	NUM
ejpam-5591	188	8	(	(	PUNCT
ejpam-5591	188	9	1	1	NUM
ejpam-5591	188	10	)	)	PUNCT
ejpam-5591	188	11	(	(	PUNCT
ejpam-5591	188	12	2025	2025	NUM
ejpam-5591	188	13	)	)	PUNCT
ejpam-5591	188	14	,	,	PUNCT
ejpam-5591	188	15	5591	5591	NUM
ejpam-5591	188	16	10	10	NUM
ejpam-5591	188	17	of	of	ADP
ejpam-5591	188	18	11	11	NUM
ejpam-5591	188	19	example	example	NOUN
ejpam-5591	188	20	1	1	NUM
ejpam-5591	188	21	.	.	PUNCT
ejpam-5591	189	1	let	let	VERB
ejpam-5591	189	2	equation	equation	NOUN
ejpam-5591	189	3	z(4	z(4	PROPN
ejpam-5591	189	4	)	)	PUNCT
ejpam-5591	189	5	(	(	PUNCT
ejpam-5591	189	6	η	η	NOUN
ejpam-5591	189	7	)	)	PUNCT
ejpam-5591	189	8	+	+	CCONJ
ejpam-5591	189	9	c0	c0	PROPN
ejpam-5591	189	10	η4	η4	VERB
ejpam-5591	189	11	z	z	PROPN
ejpam-5591	189	12	(	(	PUNCT
ejpam-5591	189	13	1	1	NUM
ejpam-5591	189	14	2	2	NUM
ejpam-5591	189	15	η	η	NOUN
ejpam-5591	189	16	)	)	PUNCT
ejpam-5591	189	17	=	=	SYM
ejpam-5591	189	18	0	0	NUM
ejpam-5591	189	19	,	,	PUNCT
ejpam-5591	189	20	η	η	PROPN
ejpam-5591	189	21	≥	≥	PROPN
ejpam-5591	189	22	1	1	NUM
ejpam-5591	189	23	,	,	PUNCT
ejpam-5591	189	24	(	(	PUNCT
ejpam-5591	189	25	27	27	NUM
ejpam-5591	189	26	)	)	PUNCT
ejpam-5591	189	27	where	where	SCONJ
ejpam-5591	189	28	p	p	NOUN
ejpam-5591	189	29	=	=	SYM
ejpam-5591	189	30	2,κ	2,κ	PROPN
ejpam-5591	189	31	(	(	PUNCT
ejpam-5591	189	32	η	η	NOUN
ejpam-5591	189	33	)	)	PUNCT
ejpam-5591	189	34	=	=	SYM
ejpam-5591	189	35	1	1	NUM
ejpam-5591	189	36	,	,	PUNCT
ejpam-5591	189	37	c0	c0	NOUN
ejpam-5591	189	38	>	>	X
ejpam-5591	189	39	0	0	PROPN
ejpam-5591	189	40	,	,	PUNCT
ejpam-5591	189	41	a	a	DET
ejpam-5591	189	42	(	(	PUNCT
ejpam-5591	189	43	η	η	NOUN
ejpam-5591	189	44	)	)	PUNCT
ejpam-5591	189	45	=	=	SYM
ejpam-5591	189	46	c0	c0	PROPN
ejpam-5591	189	47	/	/	SYM
ejpam-5591	189	48	η	η	PROPN
ejpam-5591	189	49	4	4	NUM
ejpam-5591	189	50	and	and	CCONJ
ejpam-5591	189	51	b	b	PROPN
ejpam-5591	189	52	(	(	PUNCT
ejpam-5591	189	53	η	η	NOUN
ejpam-5591	189	54	)	)	PUNCT
ejpam-5591	189	55	=	=	SYM
ejpam-5591	189	56	η/2	η/2	NOUN
ejpam-5591	189	57	.	.	PUNCT
ejpam-5591	190	1	hence	hence	ADV
ejpam-5591	190	2	,	,	PUNCT
ejpam-5591	190	3	we	we	PRON
ejpam-5591	190	4	have	have	VERB
ejpam-5591	190	5	r	r	NOUN
ejpam-5591	190	6	(	(	PUNCT
ejpam-5591	190	7	η0	η0	NOUN
ejpam-5591	190	8	)	)	PUNCT
ejpam-5591	190	9	=	=	SYM
ejpam-5591	190	10	∞	∞	PROPN
ejpam-5591	190	11	,	,	PUNCT
ejpam-5591	190	12	β	β	X
ejpam-5591	190	13	(	(	PUNCT
ejpam-5591	190	14	s	s	NOUN
ejpam-5591	190	15	)	)	PUNCT
ejpam-5591	190	16	=	=	SYM
ejpam-5591	190	17	c0	c0	PROPN
ejpam-5591	190	18	8s	8s	PROPN
ejpam-5591	190	19	.	.	PUNCT
ejpam-5591	191	1	if	if	SCONJ
ejpam-5591	191	2	we	we	PRON
ejpam-5591	191	3	set	set	VERB
ejpam-5591	191	4	ℓ	ℓ	NOUN
ejpam-5591	191	5	=	=	SYM
ejpam-5591	191	6	ν1	ν1	NOUN
ejpam-5591	191	7	=	=	SYM
ejpam-5591	191	8	1	1	NUM
ejpam-5591	191	9	,	,	PUNCT
ejpam-5591	191	10	then	then	ADV
ejpam-5591	191	11	condition	condition	NOUN
ejpam-5591	191	12	(	(	PUNCT
ejpam-5591	191	13	25	25	NUM
ejpam-5591	191	14	)	)	PUNCT
ejpam-5591	191	15	becomes	become	VERB
ejpam-5591	191	16	lim	lim	PROPN
ejpam-5591	191	17	sup	sup	PROPN
ejpam-5591	191	18	η→∞	η→∞	NUM
ejpam-5591	191	19	∫	∫	PROPN
ejpam-5591	191	20	η	η	PROPN
ejpam-5591	191	21	η1	η1	PROPN
ejpam-5591	191	22	(	(	PUNCT
ejpam-5591	191	23	β	β	X
ejpam-5591	191	24	(	(	PUNCT
ejpam-5591	191	25	s)−	s)−	PROPN
ejpam-5591	191	26	(	(	PUNCT
ejpam-5591	191	27	2	2	NUM
ejpam-5591	191	28	εs2	εs2	NOUN
ejpam-5591	191	29	)	)	PUNCT
ejpam-5591	191	30	(	(	PUNCT
ejpam-5591	191	31	p−1	p−1	PROPN
ejpam-5591	191	32	)	)	PUNCT
ejpam-5591	191	33	κ	κ	PROPN
ejpam-5591	191	34	(	(	PUNCT
ejpam-5591	191	35	s)µ	s)µ	X
ejpam-5591	191	36	(	(	PUNCT
ejpam-5591	191	37	s	s	X
ejpam-5591	191	38	)	)	PUNCT
ejpam-5591	191	39	(	(	PUNCT
ejpam-5591	191	40	β	β	X
ejpam-5591	191	41	(	(	PUNCT
ejpam-5591	191	42	s))p	s))p	NOUN
ejpam-5591	191	43	pp	pp	ADV
ejpam-5591	191	44	)	)	PUNCT
ejpam-5591	191	45	ds	ds	PROPN
ejpam-5591	191	46	=	=	SYM
ejpam-5591	191	47	lim	lim	PROPN
ejpam-5591	191	48	sup	sup	PROPN
ejpam-5591	191	49	η→∞	η→∞	NUM
ejpam-5591	191	50	∫	∫	PROPN
ejpam-5591	191	51	η	η	PROPN
ejpam-5591	191	52	η1	η1	PROPN
ejpam-5591	191	53	(	(	PUNCT
ejpam-5591	191	54	c0	c0	PROPN
ejpam-5591	191	55	8s	8s	PROPN
ejpam-5591	192	1	−	−	PROPN
ejpam-5591	192	2	9	9	NUM
ejpam-5591	192	3	2s	2s	NUM
ejpam-5591	192	4	)	)	PUNCT
ejpam-5591	192	5	ds	ds	PROPN
ejpam-5591	192	6	=	=	SYM
ejpam-5591	192	7	∞	∞	PROPN
ejpam-5591	192	8	if	if	SCONJ
ejpam-5591	192	9	c0	c0	PROPN
ejpam-5591	192	10	>	>	X
ejpam-5591	192	11	36	36	NUM
ejpam-5591	192	12	.	.	PUNCT
ejpam-5591	193	1	therefore	therefore	ADV
ejpam-5591	193	2	,	,	PUNCT
ejpam-5591	193	3	from	from	ADP
ejpam-5591	193	4	corollary	corollary	ADJ
ejpam-5591	193	5	1	1	NUM
ejpam-5591	193	6	,	,	PUNCT
ejpam-5591	193	7	we	we	PRON
ejpam-5591	193	8	see	see	VERB
ejpam-5591	193	9	that	that	SCONJ
ejpam-5591	193	10	(	(	PUNCT
ejpam-5591	193	11	27	27	NUM
ejpam-5591	193	12	)	)	PUNCT
ejpam-5591	193	13	is	be	AUX
ejpam-5591	193	14	oscillatory	oscillatory	ADJ
ejpam-5591	193	15	if	if	SCONJ
ejpam-5591	193	16	c0	c0	PROPN
ejpam-5591	193	17	>	>	X
ejpam-5591	193	18	36	36	NUM
ejpam-5591	193	19	.	.	PUNCT
ejpam-5591	194	1	4	4	NUM
ejpam-5591	194	2	.	.	X
ejpam-5591	194	3	conclusion	conclusion	VERB
ejpam-5591	194	4	the	the	DET
ejpam-5591	194	5	asymptotic	asymptotic	ADJ
ejpam-5591	194	6	behavior	behavior	NOUN
ejpam-5591	194	7	oscillatory	oscillatory	ADJ
ejpam-5591	194	8	characteristics	characteristic	NOUN
ejpam-5591	194	9	of	of	ADP
ejpam-5591	194	10	a	a	DET
ejpam-5591	194	11	fourth	fourth	ADJ
ejpam-5591	194	12	-	-	PUNCT
ejpam-5591	194	13	order	order	NOUN
ejpam-5591	194	14	dde	dde	NOUN
ejpam-5591	194	15	with	with	ADP
ejpam-5591	194	16	a	a	DET
ejpam-5591	194	17	plaplacian	plaplacian	NOUN
ejpam-5591	194	18	were	be	AUX
ejpam-5591	194	19	examined	examine	VERB
ejpam-5591	194	20	in	in	ADP
ejpam-5591	194	21	our	our	PRON
ejpam-5591	194	22	work	work	NOUN
ejpam-5591	194	23	.	.	PUNCT
ejpam-5591	195	1	the	the	DET
ejpam-5591	195	2	goal	goal	NOUN
ejpam-5591	195	3	of	of	ADP
ejpam-5591	195	4	this	this	DET
ejpam-5591	195	5	work	work	NOUN
ejpam-5591	195	6	is	be	AUX
ejpam-5591	195	7	to	to	PART
ejpam-5591	195	8	apply	apply	VERB
ejpam-5591	195	9	the	the	DET
ejpam-5591	195	10	findings	finding	NOUN
ejpam-5591	195	11	of	of	ADP
ejpam-5591	195	12	[	[	X
ejpam-5591	195	13	18	18	NUM
ejpam-5591	195	14	]	]	PUNCT
ejpam-5591	195	15	to	to	ADP
ejpam-5591	195	16	equations	equation	NOUN
ejpam-5591	195	17	that	that	PRON
ejpam-5591	195	18	have	have	VERB
ejpam-5591	195	19	a	a	DET
ejpam-5591	195	20	sublinear	sublinear	NOUN
ejpam-5591	195	21	delay	delay	NOUN
ejpam-5591	195	22	term	term	NOUN
ejpam-5591	195	23	and	and	CCONJ
ejpam-5591	195	24	canonical	canonical	ADJ
ejpam-5591	195	25	operators	operator	NOUN
ejpam-5591	195	26	.	.	PUNCT
ejpam-5591	196	1	furthermore	furthermore	ADV
ejpam-5591	196	2	,	,	PUNCT
ejpam-5591	196	3	our	our	PRON
ejpam-5591	196	4	work	work	NOUN
ejpam-5591	196	5	streamlines	streamline	NOUN
ejpam-5591	196	6	and	and	CCONJ
ejpam-5591	196	7	builds	build	VERB
ejpam-5591	196	8	upon	upon	SCONJ
ejpam-5591	196	9	previous	previous	ADJ
ejpam-5591	196	10	discoveries	discovery	NOUN
ejpam-5591	196	11	in	in	ADP
ejpam-5591	196	12	the	the	DET
ejpam-5591	196	13	literature	literature	NOUN
ejpam-5591	196	14	while	while	SCONJ
ejpam-5591	196	15	also	also	ADV
ejpam-5591	196	16	advancing	advance	VERB
ejpam-5591	196	17	current	current	ADJ
ejpam-5591	196	18	knowledge	knowledge	NOUN
ejpam-5591	196	19	.	.	PUNCT
ejpam-5591	197	1	building	build	VERB
ejpam-5591	197	2	on	on	ADP
ejpam-5591	197	3	these	these	DET
ejpam-5591	197	4	discoveries	discovery	NOUN
ejpam-5591	197	5	,	,	PUNCT
ejpam-5591	197	6	we	we	PRON
ejpam-5591	197	7	created	create	VERB
ejpam-5591	197	8	new	new	ADJ
ejpam-5591	197	9	standards	standard	NOUN
ejpam-5591	197	10	that	that	PRON
ejpam-5591	197	11	ensure	ensure	VERB
ejpam-5591	197	12	all	all	DET
ejpam-5591	197	13	solutions	solution	NOUN
ejpam-5591	197	14	to	to	ADP
ejpam-5591	197	15	the	the	DET
ejpam-5591	197	16	examined	examine	VERB
ejpam-5591	197	17	equations	equation	NOUN
ejpam-5591	197	18	oscillate	oscillate	VERB
ejpam-5591	197	19	.	.	PUNCT
ejpam-5591	198	1	this	this	DET
ejpam-5591	198	2	contribution	contribution	NOUN
ejpam-5591	198	3	offers	offer	VERB
ejpam-5591	198	4	a	a	DET
ejpam-5591	198	5	strong	strong	ADJ
ejpam-5591	198	6	basis	basis	NOUN
ejpam-5591	198	7	for	for	ADP
ejpam-5591	198	8	upcoming	upcoming	ADJ
ejpam-5591	198	9	investigations	investigation	NOUN
ejpam-5591	198	10	and	and	CCONJ
ejpam-5591	198	11	is	be	AUX
ejpam-5591	198	12	essential	essential	ADJ
ejpam-5591	198	13	for	for	ADP
ejpam-5591	198	14	developing	develop	VERB
ejpam-5591	198	15	the	the	DET
ejpam-5591	198	16	theoretical	theoretical	ADJ
ejpam-5591	198	17	framework	framework	NOUN
ejpam-5591	198	18	of	of	ADP
ejpam-5591	198	19	delay	delay	NOUN
ejpam-5591	198	20	differential	differential	ADJ
ejpam-5591	198	21	equations	equation	NOUN
ejpam-5591	198	22	.	.	PUNCT
ejpam-5591	199	1	to	to	PART
ejpam-5591	199	2	illustrate	illustrate	VERB
ejpam-5591	199	3	the	the	DET
ejpam-5591	199	4	strength	strength	NOUN
ejpam-5591	199	5	of	of	ADP
ejpam-5591	199	6	our	our	PRON
ejpam-5591	199	7	findings	finding	NOUN
ejpam-5591	199	8	,	,	PUNCT
ejpam-5591	199	9	an	an	DET
ejpam-5591	199	10	example	example	NOUN
ejpam-5591	199	11	was	be	AUX
ejpam-5591	199	12	provided	provide	VERB
ejpam-5591	199	13	.	.	PUNCT
ejpam-5591	200	1	references	reference	NOUN
ejpam-5591	200	2	[	[	X
ejpam-5591	200	3	1	1	NUM
ejpam-5591	200	4	]	]	X
ejpam-5591	200	5	r.p	r.p	PROPN
ejpam-5591	200	6	.	.	PROPN
ejpam-5591	200	7	agarwal	agarwal	PROPN
ejpam-5591	200	8	,	,	PUNCT
ejpam-5591	200	9	s.r	s.r	PROPN
ejpam-5591	200	10	.	.	PROPN
ejpam-5591	200	11	grace	grace	NOUN
ejpam-5591	200	12	,	,	PUNCT
ejpam-5591	200	13	and	and	CCONJ
ejpam-5591	200	14	d.	d.	PROPN
ejpam-5591	200	15	o’regan	o’regan	PROPN
ejpam-5591	200	16	.	.	PUNCT
ejpam-5591	201	1	oscillation	oscillation	NOUN
ejpam-5591	201	2	criteria	criterion	NOUN
ejpam-5591	201	3	for	for	ADP
ejpam-5591	201	4	certain	certain	ADJ
ejpam-5591	201	5	nth	nth	ADJ
ejpam-5591	201	6	-	-	PUNCT
ejpam-5591	201	7	order	order	NOUN
ejpam-5591	201	8	differential	differential	ADJ
ejpam-5591	201	9	equations	equation	NOUN
ejpam-5591	201	10	with	with	ADP
ejpam-5591	201	11	deviating	deviate	VERB
ejpam-5591	201	12	arguments	argument	NOUN
ejpam-5591	201	13	.	.	PUNCT
ejpam-5591	202	1	j.	j.	PROPN
ejpam-5591	202	2	math	math	PROPN
ejpam-5591	202	3	.	.	PUNCT
ejpam-5591	203	1	appl	appl	PROPN
ejpam-5591	203	2	.	.	PUNCT
ejpam-5591	204	1	anal	anal	PROPN
ejpam-5591	204	2	.	.	PROPN
ejpam-5591	204	3	,	,	PUNCT
ejpam-5591	204	4	262:601–622	262:601–622	NUM
ejpam-5591	204	5	,	,	PUNCT
ejpam-5591	204	6	2001	2001	NUM
ejpam-5591	204	7	.	.	PUNCT
ejpam-5591	205	1	[	[	X
ejpam-5591	205	2	2	2	NUM
ejpam-5591	205	3	]	]	X
ejpam-5591	205	4	r.p	r.p	PROPN
ejpam-5591	205	5	.	.	PROPN
ejpam-5591	205	6	agarwal	agarwal	PROPN
ejpam-5591	205	7	,	,	PUNCT
ejpam-5591	205	8	ch	ch	PROPN
ejpam-5591	205	9	.	.	PROPN
ejpam-5591	205	10	zhang	zhang	PROPN
ejpam-5591	205	11	,	,	PUNCT
ejpam-5591	205	12	and	and	CCONJ
ejpam-5591	205	13	t.	t.	PROPN
ejpam-5591	205	14	li	li	PROPN
ejpam-5591	205	15	.	.	PUNCT
ejpam-5591	206	1	some	some	DET
ejpam-5591	206	2	remarks	remark	NOUN
ejpam-5591	206	3	on	on	ADP
ejpam-5591	206	4	oscillation	oscillation	NOUN
ejpam-5591	206	5	of	of	ADP
ejpam-5591	206	6	second	second	ADJ
ejpam-5591	206	7	order	order	NOUN
ejpam-5591	206	8	neutral	neutral	ADJ
ejpam-5591	206	9	differential	differential	NOUN
ejpam-5591	206	10	equations	equation	NOUN
ejpam-5591	206	11	.	.	PUNCT
ejpam-5591	207	1	appl	appl	PROPN
ejpam-5591	207	2	.	.	PROPN
ejpam-5591	207	3	math	math	PROPN
ejpam-5591	207	4	.	.	PUNCT
ejpam-5591	208	1	compt	compt	PROPN
ejpam-5591	208	2	.	.	PROPN
ejpam-5591	208	3	,	,	PUNCT
ejpam-5591	208	4	274:178–181	274:178–181	NUM
ejpam-5591	208	5	,	,	PUNCT
ejpam-5591	208	6	2016	2016	NUM
ejpam-5591	208	7	.	.	PUNCT
ejpam-5591	209	1	[	[	X
ejpam-5591	209	2	3	3	NUM
ejpam-5591	209	3	]	]	PUNCT
ejpam-5591	209	4	a.	a.	NOUN
ejpam-5591	209	5	almutairi	almutairi	NOUN
ejpam-5591	209	6	.	.	PUNCT
ejpam-5591	210	1	oscillatory	oscillatory	ADJ
ejpam-5591	210	2	properties	property	NOUN
ejpam-5591	210	3	test	test	VERB
ejpam-5591	210	4	for	for	ADP
ejpam-5591	210	5	even	even	ADV
ejpam-5591	210	6	-	-	PUNCT
ejpam-5591	210	7	order	order	NOUN
ejpam-5591	210	8	differential	differential	ADJ
ejpam-5591	210	9	equations	equation	NOUN
ejpam-5591	210	10	of	of	ADP
ejpam-5591	210	11	neutral	neutral	ADJ
ejpam-5591	210	12	type	type	NOUN
ejpam-5591	210	13	.	.	PUNCT
ejpam-5591	211	1	european	european	ADJ
ejpam-5591	211	2	journal	journal	PROPN
ejpam-5591	211	3	of	of	ADP
ejpam-5591	211	4	pure	pure	ADJ
ejpam-5591	211	5	and	and	CCONJ
ejpam-5591	211	6	applied	applied	ADJ
ejpam-5591	211	7	mathematics	mathematic	NOUN
ejpam-5591	211	8	,	,	PUNCT
ejpam-5591	211	9	16:2499–2508	16:2499–2508	NUM
ejpam-5591	211	10	,	,	PUNCT
ejpam-5591	211	11	2023	2023	NUM
ejpam-5591	211	12	.	.	PUNCT
ejpam-5591	212	1	[	[	X
ejpam-5591	212	2	4	4	X
ejpam-5591	212	3	]	]	PUNCT
ejpam-5591	212	4	b.	b.	PROPN
ejpam-5591	212	5	baculikova	baculikova	PROPN
ejpam-5591	212	6	,	,	PUNCT
ejpam-5591	212	7	j.	j.	PROPN
ejpam-5591	212	8	dzurina	dzurina	PROPN
ejpam-5591	212	9	,	,	PUNCT
ejpam-5591	212	10	and	and	CCONJ
ejpam-5591	212	11	j.r	j.r	PROPN
ejpam-5591	212	12	.	.	PROPN
ejpam-5591	212	13	graef	graef	PROPN
ejpam-5591	212	14	.	.	PUNCT
ejpam-5591	213	1	on	on	ADP
ejpam-5591	213	2	the	the	DET
ejpam-5591	213	3	oscillation	oscillation	NOUN
ejpam-5591	213	4	of	of	ADP
ejpam-5591	213	5	higher	high	ADJ
ejpam-5591	213	6	-	-	PUNCT
ejpam-5591	213	7	order	order	NOUN
ejpam-5591	213	8	delay	delay	NOUN
ejpam-5591	213	9	differential	differential	ADJ
ejpam-5591	213	10	equations	equation	NOUN
ejpam-5591	213	11	.	.	PUNCT
ejpam-5591	214	1	journal	journal	PROPN
ejpam-5591	214	2	of	of	ADP
ejpam-5591	214	3	mathematical	mathematical	ADJ
ejpam-5591	214	4	sciences	sciences	PROPN
ejpam-5591	214	5	,	,	PUNCT
ejpam-5591	214	6	187:387–400	187:387–400	NUM
ejpam-5591	214	7	,	,	PUNCT
ejpam-5591	214	8	2012	2012	NUM
ejpam-5591	214	9	.	.	PUNCT
ejpam-5591	215	1	[	[	X
ejpam-5591	215	2	5	5	NUM
ejpam-5591	215	3	]	]	X
ejpam-5591	215	4	o.	o.	NOUN
ejpam-5591	215	5	bazighifan	bazighifan	NOUN
ejpam-5591	215	6	and	and	CCONJ
ejpam-5591	215	7	t.	t.	NOUN
ejpam-5591	215	8	abdeljawad	abdeljawad	NOUN
ejpam-5591	215	9	.	.	PUNCT
ejpam-5591	216	1	improved	improve	VERB
ejpam-5591	216	2	approach	approach	NOUN
ejpam-5591	216	3	for	for	ADP
ejpam-5591	216	4	studying	study	VERB
ejpam-5591	216	5	oscillatory	oscillatory	ADJ
ejpam-5591	216	6	properties	property	NOUN
ejpam-5591	216	7	of	of	ADP
ejpam-5591	216	8	fourth	fourth	ADJ
ejpam-5591	216	9	-	-	PUNCT
ejpam-5591	216	10	order	order	NOUN
ejpam-5591	216	11	advanced	advanced	ADJ
ejpam-5591	216	12	differential	differential	ADJ
ejpam-5591	216	13	equations	equation	NOUN
ejpam-5591	216	14	with	with	ADP
ejpam-5591	216	15	p	p	NOUN
ejpam-5591	216	16	-	-	PUNCT
ejpam-5591	216	17	laplacian	laplacian	ADJ
ejpam-5591	216	18	like	like	ADP
ejpam-5591	216	19	operator	operator	NOUN
ejpam-5591	216	20	.	.	PUNCT
ejpam-5591	217	1	mathematics	mathematic	NOUN
ejpam-5591	217	2	,	,	PUNCT
ejpam-5591	217	3	8(656	8(656	NUM
ejpam-5591	217	4	)	)	PUNCT
ejpam-5591	217	5	,	,	PUNCT
ejpam-5591	217	6	2020	2020	NUM
ejpam-5591	217	7	.	.	PUNCT
ejpam-5591	218	1	a.	a.	NOUN
ejpam-5591	218	2	almutairi	almutairi	PROPN
ejpam-5591	218	3	/	/	SYM
ejpam-5591	218	4	eur	eur	PROPN
ejpam-5591	218	5	.	.	PUNCT
ejpam-5591	219	1	j.	j.	PROPN
ejpam-5591	219	2	pure	pure	PROPN
ejpam-5591	219	3	appl	appl	PROPN
ejpam-5591	219	4	.	.	PROPN
ejpam-5591	219	5	math	math	PROPN
ejpam-5591	219	6	,	,	PUNCT
ejpam-5591	219	7	18	18	NUM
ejpam-5591	219	8	(	(	PUNCT
ejpam-5591	219	9	1	1	NUM
ejpam-5591	219	10	)	)	PUNCT
ejpam-5591	219	11	(	(	PUNCT
ejpam-5591	219	12	2025	2025	NUM
ejpam-5591	219	13	)	)	PUNCT
ejpam-5591	219	14	,	,	PUNCT
ejpam-5591	219	15	5591	5591	NUM
ejpam-5591	219	16	11	11	NUM
ejpam-5591	219	17	of	of	ADP
ejpam-5591	219	18	11	11	NUM
ejpam-5591	219	19	[	[	SYM
ejpam-5591	219	20	6	6	NUM
ejpam-5591	219	21	]	]	PUNCT
ejpam-5591	219	22	o.	o.	NOUN
ejpam-5591	219	23	bazighifan	bazighifan	PROPN
ejpam-5591	219	24	,	,	PUNCT
ejpam-5591	219	25	n.	n.	PROPN
ejpam-5591	219	26	alshammari	alshammari	PROPN
ejpam-5591	219	27	,	,	PUNCT
ejpam-5591	219	28	k.s	k.s	PROPN
ejpam-5591	219	29	.	.	PROPN
ejpam-5591	219	30	al	al	PROPN
ejpam-5591	219	31	-	-	PUNCT
ejpam-5591	219	32	ghafri	ghafri	PROPN
ejpam-5591	219	33	,	,	PUNCT
ejpam-5591	219	34	and	and	CCONJ
ejpam-5591	219	35	l.f	l.f	PROPN
ejpam-5591	219	36	.	.	PROPN
ejpam-5591	219	37	iambor	iambor	PROPN
ejpam-5591	219	38	.	.	PUNCT
ejpam-5591	220	1	differential	differential	ADJ
ejpam-5591	220	2	equations	equation	NOUN
ejpam-5591	220	3	of	of	ADP
ejpam-5591	220	4	fourth	fourth	ADJ
ejpam-5591	220	5	-	-	PUNCT
ejpam-5591	220	6	order	order	NOUN
ejpam-5591	220	7	with	with	ADP
ejpam-5591	220	8	p	p	NOUN
ejpam-5591	220	9	-	-	PUNCT
ejpam-5591	220	10	laplacian	laplacian	ADJ
ejpam-5591	220	11	like	like	ADJ
ejpam-5591	220	12	operator	operator	NOUN
ejpam-5591	220	13	:	:	PUNCT
ejpam-5591	220	14	oscillation	oscillation	NOUN
ejpam-5591	220	15	theorems	theorem	NOUN
ejpam-5591	220	16	.	.	PUNCT
ejpam-5591	221	1	mathematics	mathematic	NOUN
ejpam-5591	221	2	,	,	PUNCT
ejpam-5591	221	3	12(3558	12(3558	NUM
ejpam-5591	221	4	)	)	PUNCT
ejpam-5591	221	5	,	,	PUNCT
ejpam-5591	221	6	2024	2024	NUM
ejpam-5591	221	7	.	.	PUNCT
ejpam-5591	222	1	[	[	X
ejpam-5591	222	2	7	7	X
ejpam-5591	222	3	]	]	X
ejpam-5591	222	4	o.	o.	NOUN
ejpam-5591	222	5	bazighifan	bazighifan	NOUN
ejpam-5591	222	6	and	and	CCONJ
ejpam-5591	222	7	c.	c.	PROPN
ejpam-5591	222	8	cesarano	cesarano	PROPN
ejpam-5591	222	9	.	.	PUNCT
ejpam-5591	223	1	some	some	DET
ejpam-5591	223	2	new	new	ADJ
ejpam-5591	223	3	oscillation	oscillation	NOUN
ejpam-5591	223	4	criteria	criterion	NOUN
ejpam-5591	223	5	for	for	ADP
ejpam-5591	223	6	second	second	ADJ
ejpam-5591	223	7	-	-	PUNCT
ejpam-5591	223	8	order	order	NOUN
ejpam-5591	223	9	neutral	neutral	ADJ
ejpam-5591	223	10	differential	differential	NOUN
ejpam-5591	223	11	equations	equation	NOUN
ejpam-5591	223	12	with	with	ADP
ejpam-5591	223	13	delayed	delay	VERB
ejpam-5591	223	14	arguments	argument	NOUN
ejpam-5591	223	15	.	.	PUNCT
ejpam-5591	224	1	mathematics	mathematic	NOUN
ejpam-5591	224	2	,	,	PUNCT
ejpam-5591	224	3	7:1–8	7:1–8	NUM
ejpam-5591	224	4	,	,	PUNCT
ejpam-5591	224	5	2019	2019	NUM
ejpam-5591	224	6	.	.	PUNCT
ejpam-5591	225	1	[	[	X
ejpam-5591	225	2	8	8	NUM
ejpam-5591	225	3	]	]	X
ejpam-5591	225	4	o.	o.	NOUN
ejpam-5591	225	5	bazighifan	bazighifan	NOUN
ejpam-5591	225	6	and	and	CCONJ
ejpam-5591	225	7	c.	c.	PROPN
ejpam-5591	225	8	cesarano	cesarano	PROPN
ejpam-5591	225	9	.	.	PUNCT
ejpam-5591	226	1	a	a	DET
ejpam-5591	226	2	philos	philos	NOUN
ejpam-5591	226	3	-	-	PUNCT
ejpam-5591	226	4	type	type	NOUN
ejpam-5591	226	5	oscillation	oscillation	NOUN
ejpam-5591	226	6	criteria	criterion	NOUN
ejpam-5591	226	7	for	for	ADP
ejpam-5591	226	8	fourth	fourth	ADJ
ejpam-5591	226	9	-	-	PUNCT
ejpam-5591	226	10	order	order	NOUN
ejpam-5591	226	11	neutral	neutral	ADJ
ejpam-5591	226	12	differential	differential	NOUN
ejpam-5591	226	13	equations	equation	NOUN
ejpam-5591	226	14	.	.	PUNCT
ejpam-5591	227	1	symmetry	symmetry	NOUN
ejpam-5591	227	2	,	,	PUNCT
ejpam-5591	227	3	12:1–9	12:1–9	NUM
ejpam-5591	227	4	,	,	PUNCT
ejpam-5591	227	5	2020	2020	NUM
ejpam-5591	227	6	.	.	PUNCT
ejpam-5591	228	1	[	[	X
ejpam-5591	228	2	9	9	NUM
ejpam-5591	228	3	]	]	X
ejpam-5591	228	4	c.	c.	NOUN
ejpam-5591	228	5	cesarano	cesarano	PROPN
ejpam-5591	228	6	,	,	PUNCT
ejpam-5591	228	7	s.	s.	PROPN
ejpam-5591	228	8	pinelas	pinelas	PROPN
ejpam-5591	228	9	,	,	PUNCT
ejpam-5591	228	10	f.	f.	PROPN
ejpam-5591	228	11	al	al	PROPN
ejpam-5591	228	12	-	-	PUNCT
ejpam-5591	228	13	showaikh	showaikh	NOUN
ejpam-5591	228	14	,	,	PUNCT
ejpam-5591	228	15	and	and	CCONJ
ejpam-5591	228	16	o.	o.	PROPN
ejpam-5591	228	17	bazighifan	bazighifan	PROPN
ejpam-5591	228	18	.	.	PUNCT
ejpam-5591	229	1	asymptotic	asymptotic	ADJ
ejpam-5591	229	2	properties	property	NOUN
ejpam-5591	229	3	of	of	ADP
ejpam-5591	229	4	solutions	solution	NOUN
ejpam-5591	229	5	of	of	ADP
ejpam-5591	229	6	fourth	fourth	ADJ
ejpam-5591	229	7	-	-	PUNCT
ejpam-5591	229	8	order	order	NOUN
ejpam-5591	229	9	delay	delay	NOUN
ejpam-5591	229	10	differential	differential	ADJ
ejpam-5591	229	11	equations	equation	NOUN
ejpam-5591	229	12	.	.	PUNCT
ejpam-5591	230	1	symmetry	symmetry	PROPN
ejpam-5591	230	2	,	,	PUNCT
ejpam-5591	230	3	11:1–10	11:1–10	NUM
ejpam-5591	230	4	,	,	PUNCT
ejpam-5591	230	5	2019	2019	NUM
ejpam-5591	230	6	.	.	PUNCT
ejpam-5591	231	1	[	[	X
ejpam-5591	231	2	10	10	NUM
ejpam-5591	231	3	]	]	X
ejpam-5591	231	4	g.e	g.e	PROPN
ejpam-5591	231	5	.	.	PUNCT
ejpam-5591	231	6	chatzarakis	chatzarakis	PROPN
ejpam-5591	231	7	,	,	PUNCT
ejpam-5591	231	8	e.m	e.m	PROPN
ejpam-5591	231	9	.	.	PROPN
ejpam-5591	231	10	elabbasy	elabbasy	PROPN
ejpam-5591	231	11	,	,	PUNCT
ejpam-5591	231	12	and	and	CCONJ
ejpam-5591	231	13	o.	o.	PROPN
ejpam-5591	231	14	bazighifan	bazighifan	PROPN
ejpam-5591	231	15	.	.	PUNCT
ejpam-5591	232	1	an	an	DET
ejpam-5591	232	2	oscillation	oscillation	NOUN
ejpam-5591	232	3	criterion	criterion	NOUN
ejpam-5591	232	4	in	in	ADP
ejpam-5591	232	5	4th	4th	ADJ
ejpam-5591	232	6	-	-	PUNCT
ejpam-5591	232	7	order	order	NOUN
ejpam-5591	232	8	neutral	neutral	ADJ
ejpam-5591	232	9	differential	differential	NOUN
ejpam-5591	232	10	equations	equation	NOUN
ejpam-5591	232	11	with	with	ADP
ejpam-5591	232	12	a	a	DET
ejpam-5591	232	13	continuously	continuously	ADV
ejpam-5591	232	14	distributed	distribute	VERB
ejpam-5591	232	15	delay	delay	NOUN
ejpam-5591	232	16	.	.	PUNCT
ejpam-5591	233	1	adv	adv	PROPN
ejpam-5591	233	2	.	.	PUNCT
ejpam-5591	233	3	difference	difference	PROPN
ejpam-5591	233	4	equ	equ	PROPN
ejpam-5591	233	5	.	.	PROPN
ejpam-5591	233	6	,	,	PUNCT
ejpam-5591	233	7	336:1–9	336:1–9	NUM
ejpam-5591	233	8	,	,	PUNCT
ejpam-5591	233	9	2019	2019	NUM
ejpam-5591	233	10	.	.	PUNCT
ejpam-5591	234	1	[	[	X
ejpam-5591	234	2	11	11	NUM
ejpam-5591	234	3	]	]	X
ejpam-5591	234	4	s.r	s.r	PROPN
ejpam-5591	234	5	.	.	PROPN
ejpam-5591	234	6	grace	grace	NOUN
ejpam-5591	234	7	.	.	PUNCT
ejpam-5591	235	1	oscillation	oscillation	NOUN
ejpam-5591	235	2	theorems	theorem	NOUN
ejpam-5591	235	3	for	for	ADP
ejpam-5591	235	4	nth	nth	NOUN
ejpam-5591	235	5	-	-	PUNCT
ejpam-5591	235	6	order	order	NOUN
ejpam-5591	235	7	differential	differential	ADJ
ejpam-5591	235	8	equations	equation	NOUN
ejpam-5591	235	9	with	with	ADP
ejpam-5591	235	10	deviating	deviate	VERB
ejpam-5591	235	11	arguments	argument	NOUN
ejpam-5591	235	12	.	.	PUNCT
ejpam-5591	236	1	j.	j.	PROPN
ejpam-5591	236	2	math	math	PROPN
ejpam-5591	236	3	.	.	PUNCT
ejpam-5591	237	1	appl	appl	PROPN
ejpam-5591	237	2	.	.	PUNCT
ejpam-5591	238	1	anal	anal	PROPN
ejpam-5591	238	2	.	.	PROPN
ejpam-5591	238	3	,	,	PUNCT
ejpam-5591	238	4	101:268–296	101:268–296	NUM
ejpam-5591	238	5	,	,	PUNCT
ejpam-5591	238	6	1984	1984	NUM
ejpam-5591	238	7	.	.	PUNCT
ejpam-5591	239	1	[	[	X
ejpam-5591	239	2	12	12	NUM
ejpam-5591	239	3	]	]	X
ejpam-5591	239	4	j.k	j.k	PROPN
ejpam-5591	239	5	.	.	PROPN
ejpam-5591	239	6	hale	hale	PROPN
ejpam-5591	239	7	.	.	PUNCT
ejpam-5591	240	1	theory	theory	NOUN
ejpam-5591	240	2	of	of	ADP
ejpam-5591	240	3	functional	functional	ADJ
ejpam-5591	240	4	differential	differential	ADJ
ejpam-5591	240	5	equations	equation	NOUN
ejpam-5591	240	6	.	.	PUNCT
ejpam-5591	241	1	springer	springer	NOUN
ejpam-5591	241	2	-	-	PUNCT
ejpam-5591	241	3	verlag	verlag	PROPN
ejpam-5591	241	4	,	,	PUNCT
ejpam-5591	241	5	new	new	PROPN
ejpam-5591	241	6	york	york	PROPN
ejpam-5591	241	7	,	,	PUNCT
ejpam-5591	241	8	1977	1977	NUM
ejpam-5591	241	9	.	.	PUNCT
ejpam-5591	242	1	[	[	X
ejpam-5591	242	2	13	13	NUM
ejpam-5591	242	3	]	]	PUNCT
ejpam-5591	242	4	t.	t.	PROPN
ejpam-5591	242	5	li	li	PROPN
ejpam-5591	242	6	,	,	PUNCT
ejpam-5591	242	7	b.	b.	PROPN
ejpam-5591	242	8	baculikova	baculikova	PROPN
ejpam-5591	242	9	,	,	PUNCT
ejpam-5591	242	10	j.	j.	PROPN
ejpam-5591	242	11	dzurina	dzurina	PROPN
ejpam-5591	242	12	,	,	PUNCT
ejpam-5591	242	13	and	and	CCONJ
ejpam-5591	242	14	c.	c.	PROPN
ejpam-5591	242	15	zhang	zhang	PROPN
ejpam-5591	242	16	.	.	PUNCT
ejpam-5591	243	1	oscillation	oscillation	NOUN
ejpam-5591	243	2	of	of	ADP
ejpam-5591	243	3	fourth	fourth	ADJ
ejpam-5591	243	4	-	-	PUNCT
ejpam-5591	243	5	order	order	NOUN
ejpam-5591	243	6	neutral	neutral	ADJ
ejpam-5591	243	7	differential	differential	ADJ
ejpam-5591	243	8	equations	equation	NOUN
ejpam-5591	243	9	with	with	ADP
ejpam-5591	243	10	p	p	NOUN
ejpam-5591	243	11	-	-	PUNCT
ejpam-5591	243	12	laplacian	laplacian	ADJ
ejpam-5591	243	13	like	like	ADP
ejpam-5591	243	14	operators	operator	NOUN
ejpam-5591	243	15	.	.	PUNCT
ejpam-5591	244	1	bound	bind	VERB
ejpam-5591	244	2	.	.	PUNCT
ejpam-5591	245	1	value	value	PROPN
ejpam-5591	245	2	probl	probl	NOUN
ejpam-5591	245	3	.	.	PUNCT
ejpam-5591	245	4	,	,	PUNCT
ejpam-5591	245	5	56:41–58	56:41–58	NUM
ejpam-5591	245	6	,	,	PUNCT
ejpam-5591	245	7	2014	2014	NUM
ejpam-5591	245	8	.	.	PUNCT
ejpam-5591	246	1	[	[	X
ejpam-5591	246	2	14	14	NUM
ejpam-5591	246	3	]	]	X
ejpam-5591	246	4	o.	o.	PROPN
ejpam-5591	246	5	moaaz	moaaz	PROPN
ejpam-5591	246	6	,	,	PUNCT
ejpam-5591	246	7	j.	j.	PROPN
ejpam-5591	246	8	awrejcewicz	awrejcewicz	PROPN
ejpam-5591	246	9	,	,	PUNCT
ejpam-5591	246	10	and	and	CCONJ
ejpam-5591	246	11	o.	o.	PROPN
ejpam-5591	246	12	bazighifan	bazighifan	PROPN
ejpam-5591	246	13	.	.	PUNCT
ejpam-5591	247	1	a	a	DET
ejpam-5591	247	2	new	new	ADJ
ejpam-5591	247	3	approach	approach	NOUN
ejpam-5591	247	4	in	in	ADP
ejpam-5591	247	5	the	the	DET
ejpam-5591	247	6	study	study	NOUN
ejpam-5591	247	7	of	of	ADP
ejpam-5591	247	8	oscillation	oscillation	NOUN
ejpam-5591	247	9	criteria	criterion	NOUN
ejpam-5591	247	10	of	of	ADP
ejpam-5591	247	11	even	even	ADJ
ejpam-5591	247	12	-	-	PUNCT
ejpam-5591	247	13	order	order	NOUN
ejpam-5591	247	14	neutral	neutral	ADJ
ejpam-5591	247	15	differential	differential	NOUN
ejpam-5591	247	16	equations	equation	NOUN
ejpam-5591	247	17	.	.	PUNCT
ejpam-5591	248	1	mathematics	mathematic	NOUN
ejpam-5591	248	2	,	,	PUNCT
ejpam-5591	248	3	12:1–10	12:1–10	NUM
ejpam-5591	248	4	,	,	PUNCT
ejpam-5591	248	5	2020	2020	NUM
ejpam-5591	248	6	.	.	PUNCT
ejpam-5591	249	1	[	[	X
ejpam-5591	249	2	15	15	NUM
ejpam-5591	249	3	]	]	X
ejpam-5591	249	4	o.	o.	NOUN
ejpam-5591	249	5	moaaz	moaaz	PROPN
ejpam-5591	249	6	,	,	PUNCT
ejpam-5591	249	7	r.	r.	PROPN
ejpam-5591	249	8	el	el	PROPN
ejpam-5591	249	9	-	-	PUNCT
ejpam-5591	249	10	nabulsi	nabulsi	PROPN
ejpam-5591	249	11	,	,	PUNCT
ejpam-5591	249	12	and	and	CCONJ
ejpam-5591	249	13	o.	o.	PROPN
ejpam-5591	249	14	bazighifan	bazighifan	PROPN
ejpam-5591	249	15	.	.	PUNCT
ejpam-5591	250	1	oscillatory	oscillatory	ADJ
ejpam-5591	250	2	behavior	behavior	NOUN
ejpam-5591	250	3	of	of	ADP
ejpam-5591	250	4	fourth	fourth	ADJ
ejpam-5591	250	5	-	-	PUNCT
ejpam-5591	250	6	order	order	NOUN
ejpam-5591	250	7	differential	differential	ADJ
ejpam-5591	250	8	equations	equation	NOUN
ejpam-5591	250	9	with	with	ADP
ejpam-5591	250	10	neutral	neutral	ADJ
ejpam-5591	250	11	delay	delay	NOUN
ejpam-5591	250	12	.	.	PUNCT
ejpam-5591	251	1	symmetry	symmetry	NOUN
ejpam-5591	251	2	,	,	PUNCT
ejpam-5591	251	3	12:1–9	12:1–9	NUM
ejpam-5591	251	4	,	,	PUNCT
ejpam-5591	251	5	2020	2020	NUM
ejpam-5591	251	6	.	.	PUNCT
ejpam-5591	252	1	[	[	X
ejpam-5591	252	2	16	16	NUM
ejpam-5591	252	3	]	]	X
ejpam-5591	252	4	o.	o.	PROPN
ejpam-5591	252	5	moaaz	moaaz	PROPN
ejpam-5591	252	6	,	,	PUNCT
ejpam-5591	252	7	c.	c.	PROPN
ejpam-5591	252	8	park	park	PROPN
ejpam-5591	252	9	,	,	PUNCT
ejpam-5591	252	10	a.	a.	NOUN
ejpam-5591	252	11	muhib	muhib	NOUN
ejpam-5591	252	12	,	,	PUNCT
ejpam-5591	252	13	and	and	CCONJ
ejpam-5591	252	14	o.	o.	PROPN
ejpam-5591	252	15	bazighifan	bazighifan	PROPN
ejpam-5591	252	16	.	.	PUNCT
ejpam-5591	253	1	oscillation	oscillation	NOUN
ejpam-5591	253	2	criteria	criterion	NOUN
ejpam-5591	253	3	for	for	ADP
ejpam-5591	253	4	a	a	DET
ejpam-5591	253	5	class	class	NOUN
ejpam-5591	253	6	of	of	ADP
ejpam-5591	253	7	even	even	ADJ
ejpam-5591	253	8	-	-	PUNCT
ejpam-5591	253	9	order	order	NOUN
ejpam-5591	253	10	neutral	neutral	ADJ
ejpam-5591	253	11	delay	delay	NOUN
ejpam-5591	253	12	differential	differential	ADJ
ejpam-5591	253	13	equations	equation	NOUN
ejpam-5591	253	14	.	.	PUNCT
ejpam-5591	254	1	j.	j.	PROPN
ejpam-5591	254	2	appl	appl	PROPN
ejpam-5591	254	3	.	.	PROPN
ejpam-5591	254	4	math	math	PROPN
ejpam-5591	254	5	.	.	PUNCT
ejpam-5591	255	1	comput	comput	NOUN
ejpam-5591	255	2	.	.	PUNCT
ejpam-5591	256	1	,	,	PUNCT
ejpam-5591	256	2	pages	page	NOUN
ejpam-5591	256	3	1–10	1–10	PROPN
ejpam-5591	256	4	,	,	PUNCT
ejpam-5591	256	5	2020	2020	NUM
ejpam-5591	256	6	.	.	PUNCT
ejpam-5591	257	1	[	[	X
ejpam-5591	257	2	17	17	NUM
ejpam-5591	257	3	]	]	X
ejpam-5591	257	4	n.	n.	NOUN
ejpam-5591	257	5	parhi	parhi	NOUN
ejpam-5591	257	6	and	and	CCONJ
ejpam-5591	257	7	a.	a.	NOUN
ejpam-5591	257	8	tripathy	tripathy	PROPN
ejpam-5591	257	9	.	.	PUNCT
ejpam-5591	258	1	on	on	ADP
ejpam-5591	258	2	oscillatory	oscillatory	ADJ
ejpam-5591	258	3	fourth	fourth	ADJ
ejpam-5591	258	4	order	order	NOUN
ejpam-5591	258	5	linear	linear	VERB
ejpam-5591	258	6	neutral	neutral	ADJ
ejpam-5591	258	7	differential	differential	NOUN
ejpam-5591	258	8	equations	equation	NOUN
ejpam-5591	258	9	-	-	PUNCT
ejpam-5591	258	10	i.	i.	PROPN
ejpam-5591	258	11	math	math	NOUN
ejpam-5591	258	12	.	.	PUNCT
ejpam-5591	259	1	slovaca	slovaca	PROPN
ejpam-5591	259	2	,	,	PUNCT
ejpam-5591	259	3	54:389–410	54:389–410	PROPN
ejpam-5591	259	4	,	,	PUNCT
ejpam-5591	259	5	2004	2004	NUM
ejpam-5591	259	6	.	.	PUNCT
ejpam-5591	260	1	[	[	X
ejpam-5591	260	2	18	18	NUM
ejpam-5591	260	3	]	]	PUNCT
ejpam-5591	260	4	c.	c.	PROPN
ejpam-5591	260	5	park	park	PROPN
ejpam-5591	260	6	,	,	PUNCT
ejpam-5591	260	7	o.	o.	PROPN
ejpam-5591	260	8	moaaz	moaaz	PROPN
ejpam-5591	260	9	,	,	PUNCT
ejpam-5591	260	10	and	and	CCONJ
ejpam-5591	260	11	o.	o.	PROPN
ejpam-5591	260	12	bazighifan	bazighifan	PROPN
ejpam-5591	260	13	.	.	PUNCT
ejpam-5591	261	1	oscillation	oscillation	NOUN
ejpam-5591	261	2	results	result	NOUN
ejpam-5591	261	3	for	for	ADP
ejpam-5591	261	4	higher	high	ADJ
ejpam-5591	261	5	order	order	NOUN
ejpam-5591	261	6	differential	differential	ADJ
ejpam-5591	261	7	equations	equation	NOUN
ejpam-5591	261	8	.	.	PUNCT
ejpam-5591	262	1	axioms	axiom	NOUN
ejpam-5591	262	2	,	,	PUNCT
ejpam-5591	262	3	9:1–10	9:1–10	PRON
ejpam-5591	262	4	,	,	PUNCT
ejpam-5591	262	5	2020	2020	NUM
ejpam-5591	262	6	.	.	PUNCT
ejpam-5591	263	1	[	[	X
ejpam-5591	263	2	19	19	NUM
ejpam-5591	263	3	]	]	X
ejpam-5591	263	4	ch	ch	NOUN
ejpam-5591	263	5	.	.	PUNCT
ejpam-5591	263	6	g.	g.	PROPN
ejpam-5591	263	7	philos	philos	PROPN
ejpam-5591	263	8	.	.	PUNCT
ejpam-5591	264	1	on	on	ADP
ejpam-5591	264	2	the	the	DET
ejpam-5591	264	3	existence	existence	NOUN
ejpam-5591	264	4	of	of	ADP
ejpam-5591	264	5	non	non	ADJ
ejpam-5591	264	6	-	-	ADJ
ejpam-5591	264	7	oscillatory	oscillatory	ADJ
ejpam-5591	264	8	solutions	solution	NOUN
ejpam-5591	264	9	tending	tend	VERB
ejpam-5591	264	10	to	to	ADP
ejpam-5591	264	11	zero	zero	NUM
ejpam-5591	264	12	at	at	ADP
ejpam-5591	264	13	∞	∞	PROPN
ejpam-5591	264	14	for	for	ADP
ejpam-5591	264	15	differential	differential	ADJ
ejpam-5591	264	16	equations	equation	NOUN
ejpam-5591	264	17	with	with	ADP
ejpam-5591	264	18	positive	positive	ADJ
ejpam-5591	264	19	delays	delay	NOUN
ejpam-5591	264	20	.	.	PUNCT
ejpam-5591	265	1	arch	arch	NOUN
ejpam-5591	265	2	.	.	PUNCT
ejpam-5591	266	1	math	math	NOUN
ejpam-5591	266	2	.	.	PUNCT
ejpam-5591	266	3	,	,	PUNCT
ejpam-5591	267	1	36:168–178	36:168–178	NUM
ejpam-5591	267	2	,	,	PUNCT
ejpam-5591	267	3	1981	1981	NUM
ejpam-5591	267	4	.	.	PUNCT
ejpam-5591	268	1	[	[	X
ejpam-5591	268	2	20	20	NUM
ejpam-5591	268	3	]	]	PUNCT
ejpam-5591	268	4	zhiting	zhiting	PROPN
ejpam-5591	268	5	xu	xu	PROPN
ejpam-5591	268	6	and	and	CCONJ
ejpam-5591	268	7	yong	yong	PROPN
ejpam-5591	268	8	xia	xia	PROPN
ejpam-5591	268	9	.	.	PUNCT
ejpam-5591	269	1	integral	integral	ADJ
ejpam-5591	269	2	averaging	averaging	NOUN
ejpam-5591	269	3	technique	technique	NOUN
ejpam-5591	269	4	and	and	CCONJ
ejpam-5591	269	5	oscillation	oscillation	NOUN
ejpam-5591	269	6	of	of	ADP
ejpam-5591	269	7	certain	certain	ADJ
ejpam-5591	269	8	even	even	ADJ
ejpam-5591	269	9	order	order	NOUN
ejpam-5591	269	10	delay	delay	NOUN
ejpam-5591	269	11	differential	differential	ADJ
ejpam-5591	269	12	equations	equation	NOUN
ejpam-5591	269	13	.	.	PUNCT
ejpam-5591	270	1	j.	j.	PROPN
ejpam-5591	270	2	math	math	PROPN
ejpam-5591	270	3	.	.	PUNCT
ejpam-5591	271	1	appl	appl	PROPN
ejpam-5591	271	2	.	.	PUNCT
ejpam-5591	272	1	anal	anal	PROPN
ejpam-5591	272	2	.	.	PROPN
ejpam-5591	272	3	,	,	PUNCT
ejpam-5591	272	4	292:238–246	292:238–246	NUM
ejpam-5591	272	5	,	,	PUNCT
ejpam-5591	272	6	2004	2004	NUM
ejpam-5591	272	7	.	.	PUNCT
ejpam-5591	273	1	[	[	X
ejpam-5591	273	2	21	21	NUM
ejpam-5591	273	3	]	]	X
ejpam-5591	273	4	c.	c.	PROPN
ejpam-5591	273	5	zhang	zhang	PROPN
ejpam-5591	273	6	,	,	PUNCT
ejpam-5591	273	7	r.p	r.p	PROPN
ejpam-5591	273	8	.	.	PROPN
ejpam-5591	273	9	agarwal	agarwal	PROPN
ejpam-5591	273	10	,	,	PUNCT
ejpam-5591	273	11	m.	m.	NOUN
ejpam-5591	273	12	bohner	bohner	NOUN
ejpam-5591	273	13	,	,	PUNCT
ejpam-5591	273	14	and	and	CCONJ
ejpam-5591	273	15	t.	t.	PROPN
ejpam-5591	273	16	li	li	PROPN
ejpam-5591	273	17	.	.	PUNCT
ejpam-5591	273	18	new	new	ADJ
ejpam-5591	273	19	results	result	NOUN
ejpam-5591	273	20	for	for	ADP
ejpam-5591	273	21	oscillatory	oscillatory	ADJ
ejpam-5591	273	22	behavior	behavior	NOUN
ejpam-5591	273	23	of	of	ADP
ejpam-5591	273	24	even	even	ADJ
ejpam-5591	273	25	-	-	PUNCT
ejpam-5591	273	26	order	order	NOUN
ejpam-5591	273	27	half	half	ADJ
ejpam-5591	273	28	-	-	PUNCT
ejpam-5591	273	29	linear	linear	NOUN
ejpam-5591	273	30	delay	delay	NOUN
ejpam-5591	273	31	differential	differential	ADJ
ejpam-5591	273	32	equations	equation	NOUN
ejpam-5591	273	33	.	.	PUNCT
ejpam-5591	274	1	appl	appl	PROPN
ejpam-5591	274	2	.	.	PROPN
ejpam-5591	274	3	math	math	PROPN
ejpam-5591	274	4	.	.	PUNCT
ejpam-5591	275	1	lett	lett	PROPN
ejpam-5591	275	2	.	.	PROPN
ejpam-5591	275	3	,	,	PUNCT
ejpam-5591	275	4	26:179–183	26:179–183	NUM
ejpam-5591	275	5	,	,	PUNCT
ejpam-5591	275	6	2013	2013	NUM
ejpam-5591	275	7	.	.	PUNCT
ejpam-5591	276	1	[	[	X
ejpam-5591	276	2	22	22	NUM
ejpam-5591	276	3	]	]	X
ejpam-5591	276	4	c.	c.	PROPN
ejpam-5591	276	5	zhang	zhang	PROPN
ejpam-5591	276	6	,	,	PUNCT
ejpam-5591	276	7	t.	t.	PROPN
ejpam-5591	276	8	li	li	PROPN
ejpam-5591	276	9	,	,	PUNCT
ejpam-5591	276	10	and	and	CCONJ
ejpam-5591	276	11	s.	s.	PROPN
ejpam-5591	276	12	saker	saker	PROPN
ejpam-5591	276	13	.	.	PUNCT
ejpam-5591	277	1	oscillation	oscillation	NOUN
ejpam-5591	277	2	of	of	ADP
ejpam-5591	277	3	fourth	fourth	ADJ
ejpam-5591	277	4	-	-	PUNCT
ejpam-5591	277	5	order	order	NOUN
ejpam-5591	277	6	delay	delay	NOUN
ejpam-5591	277	7	differential	differential	ADJ
ejpam-5591	277	8	equations	equation	NOUN
ejpam-5591	277	9	.	.	PUNCT
ejpam-5591	278	1	j.	j.	PROPN
ejpam-5591	278	2	math	math	PROPN
ejpam-5591	278	3	.	.	PUNCT
ejpam-5591	279	1	sci	sci	PROPN
ejpam-5591	279	2	.	.	PROPN
ejpam-5591	279	3	,	,	PUNCT
ejpam-5591	279	4	201:296–308	201:296–308	NUM
ejpam-5591	279	5	,	,	PUNCT
ejpam-5591	279	6	2014	2014	NUM
ejpam-5591	279	7	.	.	PUNCT
ejpam-5591	280	1	[	[	X
ejpam-5591	280	2	23	23	NUM
ejpam-5591	280	3	]	]	X
ejpam-5591	280	4	c.	c.	PROPN
ejpam-5591	280	5	zhang	zhang	PROPN
ejpam-5591	280	6	,	,	PUNCT
ejpam-5591	280	7	t.	t.	PROPN
ejpam-5591	280	8	li	li	PROPN
ejpam-5591	280	9	,	,	PUNCT
ejpam-5591	280	10	b.	b.	PROPN
ejpam-5591	280	11	sun	sun	PROPN
ejpam-5591	280	12	,	,	PUNCT
ejpam-5591	280	13	and	and	CCONJ
ejpam-5591	280	14	e.	e.	PROPN
ejpam-5591	280	15	thandapani	thandapani	PROPN
ejpam-5591	280	16	.	.	PUNCT
ejpam-5591	281	1	on	on	ADP
ejpam-5591	281	2	the	the	DET
ejpam-5591	281	3	oscillation	oscillation	NOUN
ejpam-5591	281	4	of	of	ADP
ejpam-5591	281	5	higher	high	ADJ
ejpam-5591	281	6	-	-	PUNCT
ejpam-5591	281	7	order	order	NOUN
ejpam-5591	281	8	half	half	ADJ
ejpam-5591	281	9	-	-	PUNCT
ejpam-5591	281	10	linear	linear	NOUN
ejpam-5591	281	11	delay	delay	NOUN
ejpam-5591	281	12	differential	differential	ADJ
ejpam-5591	281	13	equations	equation	NOUN
ejpam-5591	281	14	.	.	PUNCT
ejpam-5591	282	1	appl	appl	PROPN
ejpam-5591	282	2	.	.	PROPN
ejpam-5591	282	3	math	math	PROPN
ejpam-5591	282	4	.	.	PUNCT
ejpam-5591	283	1	lett	lett	PROPN
ejpam-5591	283	2	.	.	PROPN
ejpam-5591	283	3	,	,	PUNCT
ejpam-5591	283	4	24:1618–1621	24:1618–1621	NUM
ejpam-5591	283	5	,	,	PUNCT
ejpam-5591	283	6	2011	2011	NUM
ejpam-5591	283	7	.	.	PUNCT