id	sid	tid	token	lemma	pos
ejpam-4958	1	1	european	european	PROPN
ejpam-4958	1	2	journal	journal	PROPN
ejpam-4958	1	3	of	of	ADP
ejpam-4958	1	4	pure	pure	ADJ
ejpam-4958	1	5	and	and	CCONJ
ejpam-4958	1	6	applied	apply	VERB
ejpam-4958	1	7	mathematics	mathematic	NOUN
ejpam-4958	1	8	vol	vol	NOUN
ejpam-4958	1	9	.	.	PUNCT
ejpam-4958	2	1	16	16	NUM
ejpam-4958	2	2	,	,	PUNCT
ejpam-4958	2	3	no	no	INTJ
ejpam-4958	2	4	.	.	NOUN
ejpam-4958	2	5	4	4	NUM
ejpam-4958	2	6	,	,	PUNCT
ejpam-4958	2	7	2023	2023	NUM
ejpam-4958	2	8	,	,	PUNCT
ejpam-4958	2	9	2234	2234	NUM
ejpam-4958	2	10	-	-	SYM
ejpam-4958	2	11	2246	2246	NUM
ejpam-4958	2	12	issn	issn	VERB
ejpam-4958	2	13	1307	1307	NUM
ejpam-4958	2	14	-	-	SYM
ejpam-4958	2	15	5543	5543	NUM
ejpam-4958	2	16	–	–	PUNCT
ejpam-4958	2	17	ejpam.com	ejpam.com	X
ejpam-4958	2	18	published	publish	VERB
ejpam-4958	2	19	by	by	ADP
ejpam-4958	2	20	new	new	PROPN
ejpam-4958	2	21	york	york	PROPN
ejpam-4958	2	22	business	business	PROPN
ejpam-4958	2	23	global	global	ADJ
ejpam-4958	2	24	oscillatory	oscillatory	ADJ
ejpam-4958	2	25	behavior	behavior	NOUN
ejpam-4958	2	26	of	of	ADP
ejpam-4958	2	27	higher	high	ADJ
ejpam-4958	2	28	-	-	PUNCT
ejpam-4958	2	29	order	order	NOUN
ejpam-4958	2	30	des	de	NOUN
ejpam-4958	2	31	with	with	ADP
ejpam-4958	2	32	delay	delay	NOUN
ejpam-4958	2	33	terms	term	NOUN
ejpam-4958	2	34	shoura	shoura	PROPN
ejpam-4958	2	35	ahmed	ahmed	PROPN
ejpam-4958	2	36	balatta1,2,∗	balatta1,2,∗	PROPN
ejpam-4958	2	37	,	,	PUNCT
ejpam-4958	2	38	eddie	eddie	PROPN
ejpam-4958	2	39	shahril	shahril	PROPN
ejpam-4958	2	40	ismail1	ismail1	PROPN
ejpam-4958	2	41	,	,	PUNCT
ejpam-4958	2	42	ishak	ishak	VERB
ejpam-4958	2	43	hashim1,4	hashim1,4	PROPN
ejpam-4958	2	44	,	,	PUNCT
ejpam-4958	3	1	ahmad	ahmad	PROPN
ejpam-4958	3	2	sami	sami	PROPN
ejpam-4958	3	3	bataineh3	bataineh3	PROPN
ejpam-4958	3	4	,	,	PUNCT
ejpam-4958	3	5	shaher	shaher	ADJ
ejpam-4958	3	6	momani4	momani4	NOUN
ejpam-4958	3	7	1	1	NUM
ejpam-4958	3	8	department	department	NOUN
ejpam-4958	3	9	of	of	ADP
ejpam-4958	3	10	mathematical	mathematical	ADJ
ejpam-4958	3	11	sciences	science	NOUN
ejpam-4958	3	12	,	,	PUNCT
ejpam-4958	3	13	faculty	faculty	NOUN
ejpam-4958	3	14	of	of	ADP
ejpam-4958	3	15	science	science	PROPN
ejpam-4958	3	16	&	&	CCONJ
ejpam-4958	3	17	technology	technology	PROPN
ejpam-4958	3	18	,	,	PUNCT
ejpam-4958	3	19	universiti	universiti	PROPN
ejpam-4958	3	20	kebangsaan	kebangsaan	PROPN
ejpam-4958	3	21	malaysia	malaysia	PROPN
ejpam-4958	3	22	,	,	PUNCT
ejpam-4958	3	23	43600	43600	NUM
ejpam-4958	3	24	ukm	ukm	PROPN
ejpam-4958	3	25	bangi	bangi	PROPN
ejpam-4958	3	26	,	,	PUNCT
ejpam-4958	3	27	selangor	selangor	PROPN
ejpam-4958	3	28	,	,	PUNCT
ejpam-4958	3	29	malaysia	malaysia	PROPN
ejpam-4958	3	30	2	2	NUM
ejpam-4958	3	31	department	department	NOUN
ejpam-4958	3	32	of	of	ADP
ejpam-4958	3	33	mathematics	mathematic	NOUN
ejpam-4958	3	34	,	,	PUNCT
ejpam-4958	3	35	faculty	faculty	NOUN
ejpam-4958	3	36	of	of	ADP
ejpam-4958	3	37	education	education	NOUN
ejpam-4958	3	38	,	,	PUNCT
ejpam-4958	3	39	seiyun	seiyun	VERB
ejpam-4958	3	40	university	university	NOUN
ejpam-4958	3	41	,	,	PUNCT
ejpam-4958	3	42	hadhramout	hadhramout	PROPN
ejpam-4958	3	43	,	,	PUNCT
ejpam-4958	3	44	yemen	yemen	PROPN
ejpam-4958	3	45	3	3	NUM
ejpam-4958	3	46	department	department	NOUN
ejpam-4958	3	47	of	of	ADP
ejpam-4958	3	48	mathematics	mathematic	NOUN
ejpam-4958	3	49	,	,	PUNCT
ejpam-4958	3	50	faculty	faculty	NOUN
ejpam-4958	3	51	of	of	ADP
ejpam-4958	3	52	science	science	NOUN
ejpam-4958	3	53	,	,	PUNCT
ejpam-4958	3	54	al	al	PROPN
ejpam-4958	3	55	-	-	PUNCT
ejpam-4958	3	56	balqa	balqa	NOUN
ejpam-4958	3	57	applied	apply	VERB
ejpam-4958	3	58	university	university	NOUN
ejpam-4958	3	59	,	,	PUNCT
ejpam-4958	3	60	19117	19117	NUM
ejpam-4958	3	61	al	al	PROPN
ejpam-4958	3	62	salt	salt	NOUN
ejpam-4958	3	63	,	,	PUNCT
ejpam-4958	3	64	jordan	jordan	PROPN
ejpam-4958	3	65	4	4	NUM
ejpam-4958	3	66	nonlinear	nonlinear	ADJ
ejpam-4958	3	67	dynamics	dynamic	NOUN
ejpam-4958	3	68	research	research	NOUN
ejpam-4958	3	69	center	center	NOUN
ejpam-4958	3	70	(	(	PUNCT
ejpam-4958	3	71	ndrc	ndrc	PROPN
ejpam-4958	3	72	)	)	PUNCT
ejpam-4958	3	73	,	,	PUNCT
ejpam-4958	3	74	ajman	ajman	PROPN
ejpam-4958	3	75	university	university	PROPN
ejpam-4958	3	76	,	,	PUNCT
ejpam-4958	3	77	ajman	ajman	PROPN
ejpam-4958	3	78	p.o	p.o	PROPN
ejpam-4958	3	79	.	.	PROPN
ejpam-4958	3	80	box	box	PROPN
ejpam-4958	3	81	346	346	NUM
ejpam-4958	3	82	,	,	PUNCT
ejpam-4958	3	83	united	united	PROPN
ejpam-4958	3	84	arab	arab	PROPN
ejpam-4958	3	85	emirates	emirates	PROPN
ejpam-4958	3	86	abstract	abstract	PROPN
ejpam-4958	3	87	.	.	PUNCT
ejpam-4958	4	1	the	the	DET
ejpam-4958	4	2	aim	aim	NOUN
ejpam-4958	4	3	of	of	ADP
ejpam-4958	4	4	this	this	DET
ejpam-4958	4	5	research	research	NOUN
ejpam-4958	4	6	is	be	AUX
ejpam-4958	4	7	to	to	PART
ejpam-4958	4	8	study	study	VERB
ejpam-4958	4	9	the	the	DET
ejpam-4958	4	10	oscillatory	oscillatory	ADJ
ejpam-4958	4	11	properties	property	NOUN
ejpam-4958	4	12	of	of	ADP
ejpam-4958	4	13	higher	high	ADJ
ejpam-4958	4	14	-order	-order	PROPN
ejpam-4958	4	15	delay	delay	VERB
ejpam-4958	4	16	half	half	ADJ
ejpam-4958	4	17	linear	linear	ADJ
ejpam-4958	4	18	differential	differential	ADJ
ejpam-4958	4	19	equations	equation	NOUN
ejpam-4958	4	20	with	with	ADP
ejpam-4958	4	21	non	non	ADJ
ejpam-4958	4	22	-	-	ADJ
ejpam-4958	4	23	canonical	canonical	ADJ
ejpam-4958	4	24	operators	operator	NOUN
ejpam-4958	4	25	.	.	PUNCT
ejpam-4958	5	1	two	two	NUM
ejpam-4958	5	2	techniques	technique	NOUN
ejpam-4958	5	3	for	for	ADP
ejpam-4958	5	4	establishing	establish	VERB
ejpam-4958	5	5	new	new	ADJ
ejpam-4958	5	6	oscillation	oscillation	NOUN
ejpam-4958	5	7	conditions	condition	NOUN
ejpam-4958	5	8	for	for	ADP
ejpam-4958	5	9	all	all	DET
ejpam-4958	5	10	solutions	solution	NOUN
ejpam-4958	5	11	of	of	ADP
ejpam-4958	5	12	higher	high	ADJ
ejpam-4958	5	13	-	-	PUNCT
ejpam-4958	5	14	order	order	NOUN
ejpam-4958	5	15	differential	differential	ADJ
ejpam-4958	5	16	equations	equation	NOUN
ejpam-4958	5	17	will	will	AUX
ejpam-4958	5	18	be	be	AUX
ejpam-4958	5	19	presented	present	VERB
ejpam-4958	5	20	.	.	PUNCT
ejpam-4958	6	1	the	the	DET
ejpam-4958	6	2	first	first	ADJ
ejpam-4958	6	3	method	method	NOUN
ejpam-4958	6	4	to	to	PART
ejpam-4958	6	5	employ	employ	VERB
ejpam-4958	6	6	the	the	DET
ejpam-4958	6	7	riccati	riccati	PROPN
ejpam-4958	6	8	transformations	transformation	NOUN
ejpam-4958	6	9	,	,	PUNCT
ejpam-4958	6	10	which	which	PRON
ejpam-4958	6	11	differ	differ	VERB
ejpam-4958	6	12	from	from	ADP
ejpam-4958	6	13	those	those	PRON
ejpam-4958	6	14	described	describe	VERB
ejpam-4958	6	15	in	in	ADP
ejpam-4958	6	16	some	some	DET
ejpam-4958	6	17	published	publish	VERB
ejpam-4958	6	18	works	work	NOUN
ejpam-4958	6	19	.	.	PUNCT
ejpam-4958	7	1	the	the	DET
ejpam-4958	7	2	second	second	ADJ
ejpam-4958	7	3	method	method	NOUN
ejpam-4958	7	4	employs	employ	VERB
ejpam-4958	7	5	comparison	comparison	NOUN
ejpam-4958	7	6	principles	principle	NOUN
ejpam-4958	7	7	with	with	ADP
ejpam-4958	7	8	first	first	ADJ
ejpam-4958	7	9	-	-	PUNCT
ejpam-4958	7	10	order	order	NOUN
ejpam-4958	7	11	delay	delay	NOUN
ejpam-4958	7	12	differential	differential	ADJ
ejpam-4958	7	13	equations	equation	NOUN
ejpam-4958	7	14	,	,	PUNCT
ejpam-4958	7	15	from	from	ADP
ejpam-4958	7	16	which	which	PRON
ejpam-4958	7	17	it	it	PRON
ejpam-4958	7	18	is	be	AUX
ejpam-4958	7	19	straightforward	straightforward	ADJ
ejpam-4958	7	20	to	to	PART
ejpam-4958	7	21	deduce	deduce	VERB
ejpam-4958	7	22	oscillation	oscillation	NOUN
ejpam-4958	7	23	for	for	ADP
ejpam-4958	7	24	all	all	DET
ejpam-4958	7	25	studied	study	VERB
ejpam-4958	7	26	equation	equation	NOUN
ejpam-4958	7	27	solutions	solution	NOUN
ejpam-4958	7	28	.	.	PUNCT
ejpam-4958	8	1	in	in	ADP
ejpam-4958	8	2	addition	addition	NOUN
ejpam-4958	8	3	to	to	ADP
ejpam-4958	8	4	improving	improve	VERB
ejpam-4958	8	5	,	,	PUNCT
ejpam-4958	8	6	extending	extend	VERB
ejpam-4958	8	7	,	,	PUNCT
ejpam-4958	8	8	and	and	CCONJ
ejpam-4958	8	9	significantly	significantly	ADV
ejpam-4958	8	10	simplifying	simplify	VERB
ejpam-4958	8	11	the	the	DET
ejpam-4958	8	12	previously	previously	ADV
ejpam-4958	8	13	established	establish	VERB
ejpam-4958	8	14	criteria	criterion	NOUN
ejpam-4958	8	15	,	,	PUNCT
ejpam-4958	8	16	the	the	DET
ejpam-4958	8	17	newly	newly	ADV
ejpam-4958	8	18	proposed	propose	VERB
ejpam-4958	8	19	criteria	criterion	NOUN
ejpam-4958	8	20	have	have	VERB
ejpam-4958	8	21	the	the	DET
ejpam-4958	8	22	potential	potential	NOUN
ejpam-4958	8	23	to	to	PART
ejpam-4958	8	24	serve	serve	VERB
ejpam-4958	8	25	as	as	ADP
ejpam-4958	8	26	a	a	DET
ejpam-4958	8	27	benchmark	benchmark	NOUN
ejpam-4958	8	28	for	for	ADP
ejpam-4958	8	29	the	the	DET
ejpam-4958	8	30	theory	theory	NOUN
ejpam-4958	8	31	of	of	ADP
ejpam-4958	8	32	delay	delay	NOUN
ejpam-4958	8	33	differential	differential	ADJ
ejpam-4958	8	34	equations	equation	NOUN
ejpam-4958	8	35	of	of	ADP
ejpam-4958	8	36	higher	high	ADJ
ejpam-4958	8	37	order	order	NOUN
ejpam-4958	8	38	,	,	PUNCT
ejpam-4958	8	39	which	which	PRON
ejpam-4958	8	40	is	be	AUX
ejpam-4958	8	41	still	still	ADV
ejpam-4958	8	42	in	in	ADP
ejpam-4958	8	43	its	its	PRON
ejpam-4958	8	44	infancy	infancy	NOUN
ejpam-4958	8	45	of	of	ADP
ejpam-4958	8	46	development	development	NOUN
ejpam-4958	8	47	.	.	PUNCT
ejpam-4958	9	1	we	we	PRON
ejpam-4958	9	2	were	be	AUX
ejpam-4958	9	3	able	able	ADJ
ejpam-4958	9	4	to	to	PART
ejpam-4958	9	5	determine	determine	VERB
ejpam-4958	9	6	three	three	NUM
ejpam-4958	9	7	fundamental	fundamental	ADJ
ejpam-4958	9	8	theorems	theorem	NOUN
ejpam-4958	9	9	regarding	regard	VERB
ejpam-4958	9	10	the	the	DET
ejpam-4958	9	11	oscillation	oscillation	NOUN
ejpam-4958	9	12	of	of	ADP
ejpam-4958	9	13	this	this	DET
ejpam-4958	9	14	equation	equation	NOUN
ejpam-4958	9	15	.	.	PUNCT
ejpam-4958	10	1	some	some	DET
ejpam-4958	10	2	examples	example	NOUN
ejpam-4958	10	3	will	will	AUX
ejpam-4958	10	4	be	be	AUX
ejpam-4958	10	5	provided	provide	VERB
ejpam-4958	10	6	to	to	PART
ejpam-4958	10	7	illustrate	illustrate	VERB
ejpam-4958	10	8	the	the	DET
ejpam-4958	10	9	findings	finding	NOUN
ejpam-4958	10	10	.	.	PUNCT
ejpam-4958	11	1	2020	2020	NUM
ejpam-4958	11	2	mathematics	mathematic	NOUN
ejpam-4958	11	3	subject	subject	NOUN
ejpam-4958	11	4	classifications	classification	NOUN
ejpam-4958	11	5	:	:	PUNCT
ejpam-4958	11	6	34k10	34k10	NUM
ejpam-4958	11	7	,	,	PUNCT
ejpam-4958	11	8	34k11	34k11	NUM
ejpam-4958	11	9	key	key	ADJ
ejpam-4958	11	10	words	word	NOUN
ejpam-4958	11	11	and	and	CCONJ
ejpam-4958	11	12	phrases	phrase	NOUN
ejpam-4958	11	13	:	:	PUNCT
ejpam-4958	11	14	delay	delay	NOUN
ejpam-4958	11	15	,	,	PUNCT
ejpam-4958	11	16	differential	differential	ADJ
ejpam-4958	11	17	equations	equation	NOUN
ejpam-4958	11	18	,	,	PUNCT
ejpam-4958	11	19	oscillation	oscillation	NOUN
ejpam-4958	11	20	,	,	PUNCT
ejpam-4958	11	21	higher	high	ADJ
ejpam-4958	11	22	-	-	PUNCT
ejpam-4958	11	23	order	order	NOUN
ejpam-4958	11	24	comparison	comparison	NOUN
ejpam-4958	11	25	method	method	NOUN
ejpam-4958	11	26	,	,	PUNCT
ejpam-4958	11	27	riccati	riccati	PROPN
ejpam-4958	11	28	transformation	transformation	NOUN
ejpam-4958	11	29	1	1	X
ejpam-4958	11	30	.	.	PUNCT
ejpam-4958	11	31	introduction	introduction	NOUN
ejpam-4958	11	32	delay	delay	NOUN
ejpam-4958	11	33	differential	differential	ADJ
ejpam-4958	11	34	equations	equation	NOUN
ejpam-4958	11	35	(	(	PUNCT
ejpam-4958	11	36	ddes	ddes	PROPN
ejpam-4958	11	37	)	)	PUNCT
ejpam-4958	11	38	are	be	AUX
ejpam-4958	11	39	a	a	DET
ejpam-4958	11	40	mathematical	mathematical	ADJ
ejpam-4958	11	41	tool	tool	NOUN
ejpam-4958	11	42	employed	employ	VERB
ejpam-4958	11	43	to	to	PART
ejpam-4958	11	44	address	address	VERB
ejpam-4958	11	45	a	a	DET
ejpam-4958	11	46	wide	wide	ADJ
ejpam-4958	11	47	range	range	NOUN
ejpam-4958	11	48	of	of	ADP
ejpam-4958	11	49	challenges	challenge	NOUN
ejpam-4958	11	50	in	in	ADP
ejpam-4958	11	51	various	various	ADJ
ejpam-4958	11	52	fields	field	NOUN
ejpam-4958	11	53	such	such	ADJ
ejpam-4958	11	54	as	as	ADP
ejpam-4958	11	55	physics	physics	NOUN
ejpam-4958	11	56	,	,	PUNCT
ejpam-4958	11	57	medicine	medicine	NOUN
ejpam-4958	11	58	,	,	PUNCT
ejpam-4958	11	59	engineering	engineering	NOUN
ejpam-4958	11	60	,	,	PUNCT
ejpam-4958	11	61	aviation	aviation	NOUN
ejpam-4958	11	62	,	,	PUNCT
ejpam-4958	11	63	and	and	CCONJ
ejpam-4958	11	64	biology	biology	NOUN
ejpam-4958	11	65	.	.	PUNCT
ejpam-4958	12	1	in	in	ADP
ejpam-4958	12	2	addition	addition	NOUN
ejpam-4958	12	3	,	,	PUNCT
ejpam-4958	12	4	they	they	PRON
ejpam-4958	12	5	are	be	AUX
ejpam-4958	12	6	utilized	utilize	VERB
ejpam-4958	12	7	for	for	ADP
ejpam-4958	12	8	the	the	DET
ejpam-4958	12	9	purpose	purpose	NOUN
ejpam-4958	12	10	of	of	ADP
ejpam-4958	12	11	producing	produce	VERB
ejpam-4958	12	12	cardiac	cardiac	ADJ
ejpam-4958	12	13	rhythms	rhythm	NOUN
ejpam-4958	12	14	∗corresponding	∗corresponde	VERB
ejpam-4958	12	15	author	author	NOUN
ejpam-4958	12	16	.	.	PUNCT
ejpam-4958	13	1	doi	doi	NOUN
ejpam-4958	13	2	:	:	PUNCT
ejpam-4958	13	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4958	https://doi.org/10.29020/nybg.ejpam.v16i4.4958	SYM
ejpam-4958	13	4	email	email	NOUN
ejpam-4958	13	5	addresses	address	NOUN
ejpam-4958	13	6	:	:	PUNCT
ejpam-4958	13	7	p109940@siswa.ukm.edu.my	p109940@siswa.ukm.edu.my	NUM
ejpam-4958	13	8	,	,	PUNCT
ejpam-4958	13	9	sab74722@gmail.com	sab74722@gmail.com	X
ejpam-4958	13	10	(	(	PUNCT
ejpam-4958	13	11	s.	s.	PROPN
ejpam-4958	13	12	a.	a.	PROPN
ejpam-4958	13	13	balatta	balatta	PROPN
ejpam-4958	13	14	)	)	PUNCT
ejpam-4958	13	15	,	,	PUNCT
ejpam-4958	13	16	esbi@ukm.edu.my	esbi@ukm.edu.my	NOUN
ejpam-4958	13	17	(	(	PUNCT
ejpam-4958	13	18	e.	e.	PROPN
ejpam-4958	13	19	s.	s.	PROPN
ejpam-4958	13	20	ismail	ismail	PROPN
ejpam-4958	13	21	)	)	PUNCT
ejpam-4958	13	22	,	,	PUNCT
ejpam-4958	13	23	ishak	ishak	VERB
ejpam-4958	13	24	h@ukm.edu.my	h@ukm.edu.my	PROPN
ejpam-4958	13	25	(	(	PUNCT
ejpam-4958	13	26	i.	i.	PROPN
ejpam-4958	13	27	hashim	hashim	PROPN
ejpam-4958	13	28	)	)	PUNCT
ejpam-4958	13	29	,	,	PUNCT
ejpam-4958	13	30	a	a	DET
ejpam-4958	13	31	s	s	X
ejpam-4958	13	32	bataineh@yahoo.com	bataineh@yahoo.com	X
ejpam-4958	13	33	(	(	PUNCT
ejpam-4958	13	34	a.	a.	PROPN
ejpam-4958	13	35	s.	s.	PROPN
ejpam-4958	13	36	bataineh	bataineh	PROPN
ejpam-4958	13	37	)	)	PUNCT
ejpam-4958	13	38	,	,	PUNCT
ejpam-4958	13	39	s.momani@ajman.ac.ae	s.momani@ajman.ac.ae	PROPN
ejpam-4958	13	40	(	(	PUNCT
ejpam-4958	13	41	s.	s.	PROPN
ejpam-4958	13	42	momani	momani	PROPN
ejpam-4958	13	43	)	)	PUNCT
ejpam-4958	13	44	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4958	13	45	2234	2234	NUM
ejpam-4958	13	46	©	©	ADP
ejpam-4958	13	47	2023	2023	NUM
ejpam-4958	13	48	ejpam	ejpam	NOUN
ejpam-4958	13	49	all	all	DET
ejpam-4958	13	50	rights	right	NOUN
ejpam-4958	13	51	reserved	reserve	VERB
ejpam-4958	13	52	.	.	PUNCT
ejpam-4958	14	1	s.	s.	PROPN
ejpam-4958	14	2	a.	a.	PROPN
ejpam-4958	14	3	balatta	balatta	PROPN
ejpam-4958	14	4	et	et	PROPN
ejpam-4958	14	5	al	al	PROPN
ejpam-4958	14	6	.	.	PUNCT
ejpam-4958	14	7	/	/	SYM
ejpam-4958	14	8	eur	eur	PROPN
ejpam-4958	14	9	.	.	PUNCT
ejpam-4958	15	1	j.	j.	PROPN
ejpam-4958	15	2	pure	pure	PROPN
ejpam-4958	15	3	appl	appl	PROPN
ejpam-4958	15	4	.	.	PROPN
ejpam-4958	15	5	math	math	PROPN
ejpam-4958	15	6	,	,	PUNCT
ejpam-4958	15	7	16	16	NUM
ejpam-4958	15	8	(	(	PUNCT
ejpam-4958	15	9	4	4	NUM
ejpam-4958	15	10	)	)	PUNCT
ejpam-4958	15	11	(	(	PUNCT
ejpam-4958	15	12	2023	2023	NUM
ejpam-4958	15	13	)	)	PUNCT
ejpam-4958	15	14	,	,	PUNCT
ejpam-4958	15	15	2234	2234	NUM
ejpam-4958	15	16	-	-	SYM
ejpam-4958	15	17	2246	2246	NUM
ejpam-4958	15	18	2235	2235	NUM
ejpam-4958	15	19	and	and	CCONJ
ejpam-4958	15	20	facilitating	facilitate	VERB
ejpam-4958	15	21	the	the	DET
ejpam-4958	15	22	oscillations	oscillation	NOUN
ejpam-4958	15	23	of	of	ADP
ejpam-4958	15	24	bridges	bridge	NOUN
ejpam-4958	15	25	.	.	PUNCT
ejpam-4958	16	1	symmetric	symmetric	ADJ
ejpam-4958	16	2	properties	property	NOUN
ejpam-4958	16	3	can	can	AUX
ejpam-4958	16	4	have	have	VERB
ejpam-4958	16	5	an	an	DET
ejpam-4958	16	6	impact	impact	NOUN
ejpam-4958	16	7	on	on	ADP
ejpam-4958	16	8	the	the	DET
ejpam-4958	16	9	euler	euler	NOUN
ejpam-4958	16	10	equation	equation	NOUN
ejpam-4958	16	11	in	in	ADP
ejpam-4958	16	12	certain	certain	ADJ
ejpam-4958	16	13	variational	variational	ADJ
ejpam-4958	16	14	problems	problem	NOUN
ejpam-4958	16	15	.	.	PUNCT
ejpam-4958	17	1	the	the	DET
ejpam-4958	17	2	selection	selection	NOUN
ejpam-4958	17	3	of	of	ADP
ejpam-4958	17	4	an	an	DET
ejpam-4958	17	5	optimal	optimal	ADJ
ejpam-4958	17	6	solution	solution	NOUN
ejpam-4958	17	7	methodology	methodology	NOUN
ejpam-4958	17	8	for	for	ADP
ejpam-4958	17	9	the	the	DET
ejpam-4958	17	10	given	give	VERB
ejpam-4958	17	11	equation	equation	NOUN
ejpam-4958	17	12	is	be	AUX
ejpam-4958	17	13	facilitated	facilitate	VERB
ejpam-4958	17	14	,	,	PUNCT
ejpam-4958	17	15	as	as	SCONJ
ejpam-4958	17	16	evidenced	evidence	VERB
ejpam-4958	17	17	in	in	ADP
ejpam-4958	17	18	references	reference	NOUN
ejpam-4958	17	19	[	[	X
ejpam-4958	17	20	9	9	NUM
ejpam-4958	17	21	,	,	PUNCT
ejpam-4958	17	22	16	16	NUM
ejpam-4958	17	23	]	]	PUNCT
ejpam-4958	17	24	.	.	PUNCT
ejpam-4958	18	1	the	the	DET
ejpam-4958	18	2	findings	finding	NOUN
ejpam-4958	18	3	of	of	ADP
ejpam-4958	18	4	[	[	X
ejpam-4958	18	5	2	2	NUM
ejpam-4958	18	6	,	,	PUNCT
ejpam-4958	18	7	10	10	NUM
ejpam-4958	18	8	,	,	PUNCT
ejpam-4958	18	9	11	11	NUM
ejpam-4958	18	10	,	,	PUNCT
ejpam-4958	18	11	22	22	NUM
ejpam-4958	18	12	]	]	PUNCT
ejpam-4958	18	13	as	as	ADV
ejpam-4958	18	14	well	well	ADV
ejpam-4958	18	15	as	as	ADP
ejpam-4958	18	16	[	[	X
ejpam-4958	18	17	25	25	NUM
ejpam-4958	18	18	]	]	PUNCT
ejpam-4958	18	19	were	be	AUX
ejpam-4958	18	20	extended	extend	VERB
ejpam-4958	18	21	with	with	ADP
ejpam-4958	18	22	respect	respect	NOUN
ejpam-4958	18	23	to	to	ADP
ejpam-4958	18	24	a	a	DET
ejpam-4958	18	25	wide	wide	ADJ
ejpam-4958	18	26	range	range	NOUN
ejpam-4958	18	27	of	of	ADP
ejpam-4958	18	28	classes	class	NOUN
ejpam-4958	18	29	of	of	ADP
ejpam-4958	18	30	2nd	2nd	ADJ
ejpam-4958	18	31	order	order	NOUN
ejpam-4958	18	32	non	non	ADJ
ejpam-4958	18	33	-	-	ADJ
ejpam-4958	18	34	linear	linear	ADJ
ejpam-4958	18	35	equations	equation	NOUN
ejpam-4958	18	36	.	.	PUNCT
ejpam-4958	19	1	in	in	ADP
ejpam-4958	19	2	2016	2016	NUM
ejpam-4958	19	3	,	,	PUNCT
ejpam-4958	19	4	some	some	DET
ejpam-4958	19	5	new	new	ADJ
ejpam-4958	19	6	oscillatory	oscillatory	ADJ
ejpam-4958	19	7	behaviors	behavior	NOUN
ejpam-4958	19	8	of	of	ADP
ejpam-4958	19	9	a	a	DET
ejpam-4958	19	10	class	class	NOUN
ejpam-4958	19	11	of	of	ADP
ejpam-4958	19	12	non	non	ADJ
ejpam-4958	19	13	-	-	ADJ
ejpam-4958	19	14	linear	linear	ADJ
ejpam-4958	19	15	second	second	ADJ
ejpam-4958	19	16	-	-	PUNCT
ejpam-4958	19	17	order	order	NOUN
ejpam-4958	19	18	neutral	neutral	ADJ
ejpam-4958	19	19	des	de	NOUN
ejpam-4958	19	20	were	be	AUX
ejpam-4958	19	21	achieved	achieve	VERB
ejpam-4958	19	22	,	,	PUNCT
ejpam-4958	19	23	given	give	VERB
ejpam-4958	19	24	by	by	ADP
ejpam-4958	19	25	:(	:(	PROPN
ejpam-4958	19	26	µ(u	µ(u	NOUN
ejpam-4958	19	27	)	)	PUNCT
ejpam-4958	19	28	(	(	PUNCT
ejpam-4958	19	29	(	(	PUNCT
ejpam-4958	19	30	x(u	x(u	PROPN
ejpam-4958	19	31	)	)	PUNCT
ejpam-4958	20	1	+	+	CCONJ
ejpam-4958	20	2	p(u)x(τ(u)))′	p(u)x(τ(u)))′	PROPN
ejpam-4958	20	3	)	)	PUNCT
ejpam-4958	20	4	α)′	α)′	PROPN
ejpam-4958	20	5	+	+	NUM
ejpam-4958	20	6	q(u)xα(σ(u	q(u)xα(σ(u	NOUN
ejpam-4958	20	7	)	)	PUNCT
ejpam-4958	20	8	)	)	PUNCT
ejpam-4958	21	1	=	=	SYM
ejpam-4958	21	2	0	0	X
ejpam-4958	21	3	.	.	X
ejpam-4958	22	1	utilizing	utilize	VERB
ejpam-4958	22	2	the	the	DET
ejpam-4958	22	3	generalised	generalise	VERB
ejpam-4958	22	4	riccati	riccati	NOUN
ejpam-4958	22	5	transformations	transformation	NOUN
ejpam-4958	22	6	and	and	CCONJ
ejpam-4958	22	7	comparison	comparison	NOUN
ejpam-4958	22	8	method	method	NOUN
ejpam-4958	22	9	with	with	ADP
ejpam-4958	22	10	the	the	DET
ejpam-4958	22	11	first	first	ADJ
ejpam-4958	22	12	order	order	NOUN
ejpam-4958	22	13	dde	dde	PROPN
ejpam-4958	22	14	,	,	PUNCT
ejpam-4958	22	15	some	some	DET
ejpam-4958	22	16	additional	additional	ADJ
ejpam-4958	22	17	oscillatory	oscillatory	ADJ
ejpam-4958	22	18	criteria	criterion	NOUN
ejpam-4958	22	19	were	be	AUX
ejpam-4958	22	20	discovered	discover	VERB
ejpam-4958	22	21	.	.	PUNCT
ejpam-4958	23	1	a	a	DET
ejpam-4958	23	2	class	class	NOUN
ejpam-4958	23	3	of	of	ADP
ejpam-4958	23	4	second	second	ADJ
ejpam-4958	23	5	order	order	NOUN
ejpam-4958	23	6	dde	dde	PROPN
ejpam-4958	23	7	solutions	solution	NOUN
ejpam-4958	23	8	oscillations	oscillation	NOUN
ejpam-4958	23	9	is	be	AUX
ejpam-4958	23	10	addressed	address	VERB
ejpam-4958	23	11	in	in	ADP
ejpam-4958	23	12	the	the	DET
ejpam-4958	23	13	findings	finding	NOUN
ejpam-4958	23	14	,	,	PUNCT
ejpam-4958	23	15	which	which	PRON
ejpam-4958	23	16	extend	extend	VERB
ejpam-4958	23	17	and	and	CCONJ
ejpam-4958	23	18	enhance	enhance	VERB
ejpam-4958	23	19	numerous	numerous	ADJ
ejpam-4958	23	20	previous	previous	ADJ
ejpam-4958	23	21	findings	finding	NOUN
ejpam-4958	23	22	in	in	ADP
ejpam-4958	23	23	the	the	DET
ejpam-4958	23	24	field	field	NOUN
ejpam-4958	23	25	.	.	PUNCT
ejpam-4958	24	1	examples	example	NOUN
ejpam-4958	24	2	are	be	AUX
ejpam-4958	24	3	used	use	VERB
ejpam-4958	24	4	to	to	PART
ejpam-4958	24	5	demonstrate	demonstrate	VERB
ejpam-4958	24	6	how	how	SCONJ
ejpam-4958	24	7	well	well	ADV
ejpam-4958	24	8	the	the	DET
ejpam-4958	24	9	proposed	propose	VERB
ejpam-4958	24	10	criteria	criterion	NOUN
ejpam-4958	24	11	work	work	VERB
ejpam-4958	24	12	.	.	PUNCT
ejpam-4958	25	1	the	the	DET
ejpam-4958	25	2	manner	manner	NOUN
ejpam-4958	25	3	in	in	ADP
ejpam-4958	25	4	which	which	PRON
ejpam-4958	25	5	the	the	DET
ejpam-4958	25	6	study	study	NOUN
ejpam-4958	25	7	’s	’s	PART
ejpam-4958	25	8	findings	finding	NOUN
ejpam-4958	25	9	are	be	AUX
ejpam-4958	25	10	presented	present	VERB
ejpam-4958	25	11	is	be	AUX
ejpam-4958	25	12	both	both	PRON
ejpam-4958	25	13	fundamentally	fundamentally	ADV
ejpam-4958	25	14	novel	novel	ADJ
ejpam-4958	25	15	and	and	CCONJ
ejpam-4958	25	16	highly	highly	ADV
ejpam-4958	25	17	generic	generic	ADJ
ejpam-4958	25	18	(	(	PUNCT
ejpam-4958	25	19	(	(	PUNCT
ejpam-4958	25	20	author	author	NOUN
ejpam-4958	25	21	?	?	PUNCT
ejpam-4958	25	22	)	)	PUNCT
ejpam-4958	26	1	[	[	X
ejpam-4958	26	2	15	15	NUM
ejpam-4958	26	3	]	]	PUNCT
ejpam-4958	26	4	)	)	PUNCT
ejpam-4958	26	5	.	.	PUNCT
ejpam-4958	27	1	in	in	ADP
ejpam-4958	27	2	order	order	NOUN
ejpam-4958	27	3	to	to	PART
ejpam-4958	27	4	solve	solve	VERB
ejpam-4958	27	5	a	a	DET
ejpam-4958	27	6	class	class	NOUN
ejpam-4958	27	7	of	of	ADP
ejpam-4958	27	8	second	second	ADJ
ejpam-4958	27	9	-	-	PUNCT
ejpam-4958	27	10	order	order	NOUN
ejpam-4958	27	11	half	half	ADJ
ejpam-4958	27	12	-	-	PUNCT
ejpam-4958	27	13	linear	linear	ADJ
ejpam-4958	27	14	neutral	neutral	ADJ
ejpam-4958	27	15	des	de	NOUN
ejpam-4958	27	16	having	having	AUX
ejpam-4958	27	17	delayed	delay	VERB
ejpam-4958	27	18	arguments	argument	NOUN
ejpam-4958	27	19	of	of	ADP
ejpam-4958	27	20	the	the	DET
ejpam-4958	27	21	type	type	NOUN
ejpam-4958	27	22	,	,	PUNCT
ejpam-4958	27	23	(	(	PUNCT
ejpam-4958	27	24	author	author	NOUN
ejpam-4958	27	25	?	?	PUNCT
ejpam-4958	27	26	)	)	PUNCT
ejpam-4958	28	1	[	[	X
ejpam-4958	28	2	19	19	NUM
ejpam-4958	28	3	]	]	PUNCT
ejpam-4958	28	4	developed	develop	VERB
ejpam-4958	28	5	new	new	ADJ
ejpam-4958	28	6	oscillation	oscillation	NOUN
ejpam-4958	28	7	criteria	criterion	NOUN
ejpam-4958	28	8	:(	:(	PUNCT
ejpam-4958	28	9	µ(u	µ(u	NOUN
ejpam-4958	28	10	)	)	PUNCT
ejpam-4958	28	11	(	(	PUNCT
ejpam-4958	28	12	ϖ′(u	ϖ′(u	PROPN
ejpam-4958	28	13	)	)	PUNCT
ejpam-4958	28	14	)	)	PUNCT
ejpam-4958	28	15	α)′	α)′	PROPN
ejpam-4958	28	16	+	+	NUM
ejpam-4958	28	17	q(u)xα(σ(u	q(u)xα(σ(u	NOUN
ejpam-4958	28	18	)	)	PUNCT
ejpam-4958	28	19	)	)	PUNCT
ejpam-4958	29	1	=	=	SYM
ejpam-4958	29	2	0	0	NUM
ejpam-4958	29	3	,	,	PUNCT
ejpam-4958	29	4	u	u	PRON
ejpam-4958	29	5	≥	≥	NOUN
ejpam-4958	29	6	u0	u0	ADJ
ejpam-4958	29	7	.	.	PUNCT
ejpam-4958	30	1	here	here	ADV
ejpam-4958	30	2	,	,	PUNCT
ejpam-4958	30	3	including	include	VERB
ejpam-4958	30	4	those	those	PRON
ejpam-4958	30	5	for	for	ADP
ejpam-4958	30	6	non	non	ADJ
ejpam-4958	30	7	-	-	ADJ
ejpam-4958	30	8	neutral	neutral	ADJ
ejpam-4958	30	9	des	des	PROPN
ejpam-4958	30	10	,	,	PUNCT
ejpam-4958	30	11	it	it	PRON
ejpam-4958	30	12	substantially	substantially	ADV
ejpam-4958	30	13	enhanced	enhance	VERB
ejpam-4958	30	14	the	the	DET
ejpam-4958	30	15	renowned	renowned	ADJ
ejpam-4958	30	16	findings	finding	NOUN
ejpam-4958	30	17	given	give	VERB
ejpam-4958	30	18	in	in	ADP
ejpam-4958	30	19	the	the	DET
ejpam-4958	30	20	work	work	NOUN
ejpam-4958	30	21	.	.	PUNCT
ejpam-4958	31	1	by	by	ADP
ejpam-4958	31	2	accounting	account	VERB
ejpam-4958	31	3	for	for	ADP
ejpam-4958	31	4	the	the	DET
ejpam-4958	31	5	portion	portion	NOUN
ejpam-4958	31	6	of	of	ADP
ejpam-4958	31	7	the	the	DET
ejpam-4958	31	8	delay	delay	NOUN
ejpam-4958	31	9	’s	’s	PART
ejpam-4958	31	10	total	total	ADJ
ejpam-4958	31	11	impact	impact	NOUN
ejpam-4958	31	12	that	that	PRON
ejpam-4958	31	13	was	be	AUX
ejpam-4958	31	14	overlooked	overlook	VERB
ejpam-4958	31	15	in	in	ADP
ejpam-4958	31	16	the	the	DET
ejpam-4958	31	17	previous	previous	ADJ
ejpam-4958	31	18	findings	finding	NOUN
ejpam-4958	31	19	,	,	PUNCT
ejpam-4958	31	20	the	the	DET
ejpam-4958	31	21	method	method	NOUN
ejpam-4958	31	22	adopted	adopt	VERB
ejpam-4958	31	23	improves	improve	VERB
ejpam-4958	31	24	the	the	DET
ejpam-4958	31	25	traditional	traditional	ADJ
ejpam-4958	31	26	riccati	riccati	NOUN
ejpam-4958	31	27	transformation	transformation	NOUN
ejpam-4958	31	28	technique	technique	NOUN
ejpam-4958	31	29	.	.	PUNCT
ejpam-4958	32	1	the	the	DET
ejpam-4958	32	2	oscillation	oscillation	NOUN
ejpam-4958	32	3	of	of	ADP
ejpam-4958	32	4	second	second	ADJ
ejpam-4958	32	5	-	-	PUNCT
ejpam-4958	32	6	order	order	NOUN
ejpam-4958	32	7	ddes	dde	NOUN
ejpam-4958	32	8	was	be	AUX
ejpam-4958	32	9	researched	research	VERB
ejpam-4958	32	10	by	by	ADP
ejpam-4958	32	11	(	(	PUNCT
ejpam-4958	32	12	author	author	NOUN
ejpam-4958	32	13	?	?	PUNCT
ejpam-4958	32	14	)	)	PUNCT
ejpam-4958	33	1	[	[	X
ejpam-4958	33	2	5	5	NUM
ejpam-4958	33	3	]	]	PUNCT
ejpam-4958	33	4	,	,	PUNCT
ejpam-4958	33	5	given	give	VERB
ejpam-4958	33	6	as	as	SCONJ
ejpam-4958	33	7	follows	follow	VERB
ejpam-4958	33	8	[	[	PUNCT
ejpam-4958	33	9	a(y)w′(y	a(y)w′(y	PROPN
ejpam-4958	33	10	)	)	PUNCT
ejpam-4958	33	11	]	]	PUNCT
ejpam-4958	33	12	′	′	NUM
ejpam-4958	33	13	+	+	NUM
ejpam-4958	33	14	q(y)f(w(τ(y	q(y)f(w(τ(y	NOUN
ejpam-4958	33	15	)	)	PUNCT
ejpam-4958	33	16	)	)	PUNCT
ejpam-4958	33	17	)	)	PUNCT
ejpam-4958	34	1	=	=	SYM
ejpam-4958	34	2	0	0	NUM
ejpam-4958	34	3	,	,	PUNCT
ejpam-4958	34	4	y	y	PROPN
ejpam-4958	34	5	≥	≥	NOUN
ejpam-4958	34	6	y0	y0	NOUN
ejpam-4958	34	7	.	.	PUNCT
ejpam-4958	35	1	using	use	VERB
ejpam-4958	35	2	the	the	DET
ejpam-4958	35	3	generalized	generalized	ADJ
ejpam-4958	35	4	riccati	riccati	NOUN
ejpam-4958	35	5	substitution	substitution	NOUN
ejpam-4958	35	6	,	,	PUNCT
ejpam-4958	35	7	new	new	ADJ
ejpam-4958	35	8	oscillation	oscillation	NOUN
ejpam-4958	35	9	criterion	criterion	NOUN
ejpam-4958	35	10	was	be	AUX
ejpam-4958	35	11	developed	develop	VERB
ejpam-4958	35	12	.	.	PUNCT
ejpam-4958	36	1	however	however	ADV
ejpam-4958	36	2	,	,	PUNCT
ejpam-4958	36	3	it	it	PRON
ejpam-4958	36	4	is	be	AUX
ejpam-4958	36	5	not	not	PART
ejpam-4958	36	6	obvious	obvious	ADJ
ejpam-4958	36	7	how	how	SCONJ
ejpam-4958	36	8	symmetry	symmetry	NOUN
ejpam-4958	36	9	considerations	consideration	NOUN
ejpam-4958	36	10	aid	aid	VERB
ejpam-4958	36	11	in	in	ADP
ejpam-4958	36	12	choosing	choose	VERB
ejpam-4958	36	13	the	the	DET
ejpam-4958	36	14	most	most	ADV
ejpam-4958	36	15	appropriate	appropriate	ADJ
ejpam-4958	36	16	method	method	NOUN
ejpam-4958	36	17	of	of	ADP
ejpam-4958	36	18	inquiry	inquiry	NOUN
ejpam-4958	36	19	.	.	PUNCT
ejpam-4958	37	1	(	(	PUNCT
ejpam-4958	37	2	author	author	NOUN
ejpam-4958	37	3	?	?	PUNCT
ejpam-4958	37	4	)	)	PUNCT
ejpam-4958	38	1	[	[	X
ejpam-4958	38	2	12	12	NUM
ejpam-4958	38	3	]	]	PUNCT
ejpam-4958	38	4	presented	present	VERB
ejpam-4958	38	5	oscillation	oscillation	NOUN
ejpam-4958	38	6	criteria	criterion	NOUN
ejpam-4958	38	7	for	for	ADP
ejpam-4958	38	8	the	the	DET
ejpam-4958	38	9	third	third	ADJ
ejpam-4958	38	10	-	-	PUNCT
ejpam-4958	38	11	order	order	NOUN
ejpam-4958	38	12	nonlinear	nonlinear	PROPN
ejpam-4958	38	13	dde	dde	PROPN
ejpam-4958	38	14	[	[	PUNCT
ejpam-4958	38	15	c2(u	c2(u	NOUN
ejpam-4958	38	16	)	)	PUNCT
ejpam-4958	38	17	{	{	PUNCT
ejpam-4958	38	18	(	(	PUNCT
ejpam-4958	38	19	c1(u	c1(u	NOUN
ejpam-4958	38	20	)	)	PUNCT
ejpam-4958	38	21	(	(	PUNCT
ejpam-4958	38	22	x′(u	x′(u	PROPN
ejpam-4958	38	23	)	)	PUNCT
ejpam-4958	38	24	)	)	PUNCT
ejpam-4958	38	25	α1	α1	PROPN
ejpam-4958	38	26	)	)	PUNCT
ejpam-4958	38	27	′}α2	′}α2	NOUN
ejpam-4958	38	28	]	]	PUNCT
ejpam-4958	38	29	′	′	NOUN
ejpam-4958	39	1	+	+	CCONJ
ejpam-4958	39	2	q(u)g(x(f(u	q(u)g(x(f(u	NOUN
ejpam-4958	39	3	)	)	PUNCT
ejpam-4958	39	4	)	)	PUNCT
ejpam-4958	39	5	)	)	PUNCT
ejpam-4958	40	1	=	=	PUNCT
ejpam-4958	41	1	0	0	X
ejpam-4958	41	2	.	.	PUNCT
ejpam-4958	42	1	they	they	PRON
ejpam-4958	42	2	rely	rely	VERB
ejpam-4958	42	3	on	on	ADP
ejpam-4958	42	4	novel	novel	ADJ
ejpam-4958	42	5	comparison	comparison	NOUN
ejpam-4958	42	6	concepts	concept	NOUN
ejpam-4958	42	7	that	that	PRON
ejpam-4958	42	8	make	make	VERB
ejpam-4958	42	9	it	it	PRON
ejpam-4958	42	10	possible	possible	ADJ
ejpam-4958	42	11	to	to	PART
ejpam-4958	42	12	determine	determine	VERB
ejpam-4958	42	13	the	the	DET
ejpam-4958	42	14	characteristics	characteristic	NOUN
ejpam-4958	42	15	of	of	ADP
ejpam-4958	42	16	the	the	DET
ejpam-4958	42	17	first	first	ADJ
ejpam-4958	42	18	-	-	PUNCT
ejpam-4958	42	19	order	order	NOUN
ejpam-4958	42	20	non	non	ADJ
ejpam-4958	42	21	-	-	ADJ
ejpam-4958	42	22	linear	linear	ADJ
ejpam-4958	42	23	dde	dde	PROPN
ejpam-4958	42	24	’s	’s	PART
ejpam-4958	42	25	oscillation	oscillation	NOUN
ejpam-4958	42	26	in	in	ADP
ejpam-4958	42	27	the	the	DET
ejpam-4958	42	28	third	third	ADJ
ejpam-4958	42	29	-	-	PUNCT
ejpam-4958	42	30	order	order	NOUN
ejpam-4958	42	31	non	non	ADJ
ejpam-4958	42	32	-	-	ADJ
ejpam-4958	42	33	linear	linear	ADJ
ejpam-4958	42	34	de	de	X
ejpam-4958	42	35	.	.	PUNCT
ejpam-4958	43	1	the	the	DET
ejpam-4958	43	2	solutions	solution	NOUN
ejpam-4958	43	3	’	'	PUNCT
ejpam-4958	43	4	oscillation	oscillation	NOUN
ejpam-4958	43	5	to	to	ADP
ejpam-4958	43	6	a	a	DET
ejpam-4958	43	7	particular	particular	ADJ
ejpam-4958	43	8	class	class	NOUN
ejpam-4958	43	9	of	of	ADP
ejpam-4958	43	10	third	third	ADJ
ejpam-4958	43	11	-	-	PUNCT
ejpam-4958	43	12	order	order	NOUN
ejpam-4958	43	13	non	non	ADJ
ejpam-4958	43	14	-	-	ADJ
ejpam-4958	43	15	linear	linear	ADJ
ejpam-4958	43	16	dde	dde	NOUN
ejpam-4958	43	17	of	of	ADP
ejpam-4958	43	18	the	the	DET
ejpam-4958	43	19	type	type	NOUN
ejpam-4958	43	20	was	be	AUX
ejpam-4958	43	21	examined	examine	VERB
ejpam-4958	43	22	by	by	ADP
ejpam-4958	43	23	(	(	PUNCT
ejpam-4958	43	24	author	author	NOUN
ejpam-4958	43	25	?	?	PUNCT
ejpam-4958	43	26	)	)	PUNCT
ejpam-4958	44	1	[	[	X
ejpam-4958	44	2	21	21	NUM
ejpam-4958	44	3	]	]	PUNCT
ejpam-4958	44	4	,	,	PUNCT
ejpam-4958	44	5	given	give	VERB
ejpam-4958	44	6	by	by	ADP
ejpam-4958	44	7	ϖ′′′(u	ϖ′′′(u	PROPN
ejpam-4958	44	8	)	)	PUNCT
ejpam-4958	45	1	+	+	NUM
ejpam-4958	45	2	p(u)ϖ′(u	p(u)ϖ′(u	PROPN
ejpam-4958	45	3	)	)	PUNCT
ejpam-4958	46	1	+	+	NUM
ejpam-4958	46	2	q(u)f(ϖ(τ(u	q(u)f(ϖ(τ(u	ADJ
ejpam-4958	46	3	)	)	PUNCT
ejpam-4958	46	4	)	)	PUNCT
ejpam-4958	46	5	)	)	PUNCT
ejpam-4958	47	1	=	=	PUNCT
ejpam-4958	47	2	0	0	X
ejpam-4958	47	3	.	.	PUNCT
ejpam-4958	48	1	the	the	DET
ejpam-4958	48	2	newly	newly	ADV
ejpam-4958	48	3	presented	present	VERB
ejpam-4958	48	4	technique	technique	NOUN
ejpam-4958	48	5	could	could	AUX
ejpam-4958	48	6	perhaps	perhaps	ADV
ejpam-4958	48	7	act	act	VERB
ejpam-4958	48	8	as	as	ADP
ejpam-4958	48	9	a	a	DET
ejpam-4958	48	10	benchmark	benchmark	NOUN
ejpam-4958	48	11	in	in	ADP
ejpam-4958	48	12	the	the	DET
ejpam-4958	48	13	less	less	ADV
ejpam-4958	48	14	studied	studied	ADJ
ejpam-4958	48	15	theory	theory	NOUN
ejpam-4958	48	16	of	of	ADP
ejpam-4958	48	17	non	non	ADJ
ejpam-4958	48	18	-	-	ADJ
ejpam-4958	48	19	canonical	canonical	ADJ
ejpam-4958	48	20	equations	equation	NOUN
ejpam-4958	48	21	of	of	ADP
ejpam-4958	48	22	higher	high	ADJ
ejpam-4958	48	23	order	order	NOUN
ejpam-4958	48	24	.	.	PUNCT
ejpam-4958	49	1	the	the	DET
ejpam-4958	49	2	criteria	criterion	NOUN
ejpam-4958	49	3	not	not	PART
ejpam-4958	49	4	only	only	ADV
ejpam-4958	49	5	improved	improve	VERB
ejpam-4958	49	6	but	but	CCONJ
ejpam-4958	49	7	also	also	ADV
ejpam-4958	49	8	extended	extended	ADJ
ejpam-4958	49	9	and	and	CCONJ
ejpam-4958	49	10	greatly	greatly	ADV
ejpam-4958	49	11	simplified	simplify	VERB
ejpam-4958	49	12	the	the	DET
ejpam-4958	49	13	current	current	ADJ
ejpam-4958	49	14	ones	one	NOUN
ejpam-4958	49	15	.	.	PUNCT
ejpam-4958	50	1	the	the	DET
ejpam-4958	50	2	significance	significance	NOUN
ejpam-4958	50	3	of	of	ADP
ejpam-4958	50	4	the	the	DET
ejpam-4958	50	5	results	result	NOUN
ejpam-4958	50	6	is	be	AUX
ejpam-4958	50	7	demonstrated	demonstrate	VERB
ejpam-4958	50	8	by	by	ADP
ejpam-4958	50	9	the	the	DET
ejpam-4958	50	10	euler	euler	ADJ
ejpam-4958	50	11	-	-	PUNCT
ejpam-4958	50	12	type	type	NOUN
ejpam-4958	50	13	equations	equation	NOUN
ejpam-4958	50	14	,	,	PUNCT
ejpam-4958	50	15	which	which	PRON
ejpam-4958	50	16	are	be	AUX
ejpam-4958	50	17	crucial	crucial	ADJ
ejpam-4958	50	18	to	to	ADP
ejpam-4958	50	19	the	the	DET
ejpam-4958	50	20	oscillation	oscillation	NOUN
ejpam-4958	50	21	theory	theory	NOUN
ejpam-4958	50	22	s.	s.	PROPN
ejpam-4958	50	23	a.	a.	PROPN
ejpam-4958	50	24	balatta	balatta	PROPN
ejpam-4958	50	25	et	et	PROPN
ejpam-4958	50	26	al	al	PROPN
ejpam-4958	50	27	.	.	PUNCT
ejpam-4958	50	28	/	/	SYM
ejpam-4958	50	29	eur	eur	PROPN
ejpam-4958	50	30	.	.	PUNCT
ejpam-4958	51	1	j.	j.	PROPN
ejpam-4958	51	2	pure	pure	PROPN
ejpam-4958	51	3	appl	appl	PROPN
ejpam-4958	51	4	.	.	PROPN
ejpam-4958	51	5	math	math	PROPN
ejpam-4958	51	6	,	,	PUNCT
ejpam-4958	51	7	16	16	NUM
ejpam-4958	51	8	(	(	PUNCT
ejpam-4958	51	9	4	4	NUM
ejpam-4958	51	10	)	)	PUNCT
ejpam-4958	51	11	(	(	PUNCT
ejpam-4958	51	12	2023	2023	NUM
ejpam-4958	51	13	)	)	PUNCT
ejpam-4958	51	14	,	,	PUNCT
ejpam-4958	51	15	2234	2234	NUM
ejpam-4958	51	16	-	-	SYM
ejpam-4958	51	17	2246	2246	NUM
ejpam-4958	51	18	2236	2236	NUM
ejpam-4958	51	19	because	because	SCONJ
ejpam-4958	51	20	they	they	PRON
ejpam-4958	51	21	are	be	AUX
ejpam-4958	51	22	typically	typically	ADV
ejpam-4958	51	23	used	use	VERB
ejpam-4958	51	24	to	to	PART
ejpam-4958	51	25	compare	compare	VERB
ejpam-4958	51	26	the	the	DET
ejpam-4958	51	27	merit	merit	NOUN
ejpam-4958	51	28	of	of	ADP
ejpam-4958	51	29	various	various	ADJ
ejpam-4958	51	30	criteria	criterion	NOUN
ejpam-4958	51	31	.	.	PUNCT
ejpam-4958	52	1	the	the	DET
ejpam-4958	52	2	study	study	NOUN
ejpam-4958	52	3	of	of	ADP
ejpam-4958	52	4	non	non	ADJ
ejpam-4958	52	5	-	-	ADJ
ejpam-4958	52	6	canonical	canonical	ADJ
ejpam-4958	52	7	equations	equation	NOUN
ejpam-4958	52	8	was	be	AUX
ejpam-4958	52	9	significantly	significantly	ADV
ejpam-4958	52	10	streamlined	streamline	VERB
ejpam-4958	52	11	by	by	ADP
ejpam-4958	52	12	the	the	DET
ejpam-4958	52	13	recently	recently	ADV
ejpam-4958	52	14	developed	develop	VERB
ejpam-4958	52	15	method	method	NOUN
ejpam-4958	52	16	.	.	PUNCT
ejpam-4958	53	1	it	it	PRON
ejpam-4958	53	2	is	be	AUX
ejpam-4958	53	3	still	still	ADV
ejpam-4958	53	4	unclear	unclear	ADJ
ejpam-4958	53	5	how	how	SCONJ
ejpam-4958	53	6	to	to	PART
ejpam-4958	53	7	apply	apply	VERB
ejpam-4958	53	8	these	these	DET
ejpam-4958	53	9	findings	finding	NOUN
ejpam-4958	53	10	to	to	ADP
ejpam-4958	53	11	higher	high	ADJ
ejpam-4958	53	12	-	-	PUNCT
ejpam-4958	53	13	order	order	NOUN
ejpam-4958	53	14	non	non	ADJ
ejpam-4958	53	15	-	-	ADJ
ejpam-4958	53	16	canonical	canonical	ADJ
ejpam-4958	53	17	equations	equation	NOUN
ejpam-4958	53	18	.	.	PUNCT
ejpam-4958	54	1	less	less	ADJ
ejpam-4958	54	2	attention	attention	NOUN
ejpam-4958	54	3	has	have	AUX
ejpam-4958	54	4	been	be	AUX
ejpam-4958	54	5	paid	pay	VERB
ejpam-4958	54	6	in	in	ADP
ejpam-4958	54	7	the	the	DET
ejpam-4958	54	8	literature	literature	NOUN
ejpam-4958	54	9	to	to	ADP
ejpam-4958	54	10	the	the	DET
ejpam-4958	54	11	determination	determination	NOUN
ejpam-4958	54	12	of	of	ADP
ejpam-4958	54	13	the	the	DET
ejpam-4958	54	14	qualitative	qualitative	ADJ
ejpam-4958	54	15	behavior	behavior	NOUN
ejpam-4958	54	16	of	of	ADP
ejpam-4958	54	17	fourth	fourth	ADJ
ejpam-4958	54	18	-	-	PUNCT
ejpam-4958	54	19	order	order	NOUN
ejpam-4958	54	20	de	de	NOUN
ejpam-4958	54	21	,	,	PUNCT
ejpam-4958	54	22	particularly	particularly	ADV
ejpam-4958	54	23	the	the	DET
ejpam-4958	54	24	fourth	fourth	ADJ
ejpam-4958	54	25	-	-	PUNCT
ejpam-4958	54	26	order	order	NOUN
ejpam-4958	54	27	dde	dde	NOUN
ejpam-4958	54	28	.	.	PUNCT
ejpam-4958	55	1	nevertheless	nevertheless	ADV
ejpam-4958	55	2	,	,	PUNCT
ejpam-4958	55	3	some	some	DET
ejpam-4958	55	4	fourth	fourth	ADJ
ejpam-4958	55	5	-	-	PUNCT
ejpam-4958	55	6	order	order	NOUN
ejpam-4958	55	7	de	de	X
ejpam-4958	55	8	findings	finding	NOUN
ejpam-4958	55	9	are	be	AUX
ejpam-4958	55	10	well	well	ADV
ejpam-4958	55	11	known	know	VERB
ejpam-4958	55	12	and	and	CCONJ
ejpam-4958	55	13	have	have	VERB
ejpam-4958	55	14	some	some	DET
ejpam-4958	55	15	applications	application	NOUN
ejpam-4958	55	16	in	in	ADP
ejpam-4958	55	17	physics	physics	NOUN
ejpam-4958	55	18	and	and	CCONJ
ejpam-4958	55	19	biology	biology	NOUN
ejpam-4958	55	20	mathematical	mathematical	ADJ
ejpam-4958	55	21	modelling	modelling	NOUN
ejpam-4958	55	22	.	.	PUNCT
ejpam-4958	56	1	the	the	DET
ejpam-4958	56	2	fourth	fourth	ADJ
ejpam-4958	56	3	-	-	PUNCT
ejpam-4958	56	4	order	order	NOUN
ejpam-4958	56	5	de	de	NOUN
ejpam-4958	56	6	’s	’s	NOUN
ejpam-4958	56	7	oscillatory	oscillatory	ADJ
ejpam-4958	56	8	behavior	behavior	NOUN
ejpam-4958	56	9	has	have	AUX
ejpam-4958	56	10	been	be	AUX
ejpam-4958	56	11	examined	examine	VERB
ejpam-4958	56	12	by	by	ADP
ejpam-4958	56	13	(	(	PUNCT
ejpam-4958	56	14	author	author	NOUN
ejpam-4958	56	15	?	?	PUNCT
ejpam-4958	56	16	)	)	PUNCT
ejpam-4958	57	1	[	[	X
ejpam-4958	57	2	20	20	NUM
ejpam-4958	57	3	]	]	PUNCT
ejpam-4958	57	4	,	,	PUNCT
ejpam-4958	57	5	given	give	VERB
ejpam-4958	57	6	by	by	ADP
ejpam-4958	57	7	(	(	PUNCT
ejpam-4958	57	8	a(u	a(u	PROPN
ejpam-4958	57	9	)	)	PUNCT
ejpam-4958	57	10	(	(	PUNCT
ejpam-4958	57	11	x′(u	x′(u	PROPN
ejpam-4958	57	12	)	)	PUNCT
ejpam-4958	57	13	)	)	PUNCT
ejpam-4958	57	14	α)′′′	α)′′′	PUNCT
ejpam-4958	58	1	+	+	X
ejpam-4958	58	2	q(u)f(x(g(u	q(u)f(x(g(u	NOUN
ejpam-4958	58	3	)	)	PUNCT
ejpam-4958	58	4	)	)	PUNCT
ejpam-4958	58	5	)	)	PUNCT
ejpam-4958	59	1	=	=	PUNCT
ejpam-4958	59	2	0	0	X
ejpam-4958	59	3	.	.	PUNCT
ejpam-4958	60	1	furthermore	furthermore	ADV
ejpam-4958	60	2	,	,	PUNCT
ejpam-4958	60	3	(	(	PUNCT
ejpam-4958	60	4	author	author	NOUN
ejpam-4958	60	5	?	?	PUNCT
ejpam-4958	60	6	)	)	PUNCT
ejpam-4958	61	1	[	[	X
ejpam-4958	61	2	13	13	NUM
ejpam-4958	61	3	]	]	PUNCT
ejpam-4958	61	4	studied	study	VERB
ejpam-4958	61	5	the	the	DET
ejpam-4958	61	6	asymptotic	asymptotic	ADJ
ejpam-4958	61	7	behavior	behavior	NOUN
ejpam-4958	61	8	with	with	ADP
ejpam-4958	61	9	respect	respect	NOUN
ejpam-4958	61	10	to	to	ADP
ejpam-4958	61	11	the	the	DET
ejpam-4958	61	12	solutions	solution	NOUN
ejpam-4958	61	13	of	of	ADP
ejpam-4958	61	14	higher	high	ADJ
ejpam-4958	61	15	-	-	PUNCT
ejpam-4958	61	16	order	order	NOUN
ejpam-4958	61	17	de	de	NOUN
ejpam-4958	61	18	and	and	CCONJ
ejpam-4958	61	19	derived	derive	VERB
ejpam-4958	61	20	a	a	DET
ejpam-4958	61	21	new	new	ADJ
ejpam-4958	61	22	oscillation	oscillation	NOUN
ejpam-4958	61	23	criterion	criterion	NOUN
ejpam-4958	61	24	expressed	express	VERB
ejpam-4958	61	25	by	by	ADP
ejpam-4958	61	26	(	(	PUNCT
ejpam-4958	61	27	µ(v	µ(v	PROPN
ejpam-4958	61	28	)	)	PUNCT
ejpam-4958	61	29	(	(	PUNCT
ejpam-4958	61	30	w(m−1)(v	w(m−1)(v	NOUN
ejpam-4958	61	31	)	)	PUNCT
ejpam-4958	61	32	)	)	PUNCT
ejpam-4958	61	33	α)′	α)′	PROPN
ejpam-4958	61	34	+	+	NUM
ejpam-4958	61	35	p(v)f	p(v)f	PROPN
ejpam-4958	61	36	(	(	PUNCT
ejpam-4958	61	37	w(m−1)(v	w(m−1)(v	PROPN
ejpam-4958	61	38	)	)	PUNCT
ejpam-4958	61	39	)	)	PUNCT
ejpam-4958	62	1	+	+	CCONJ
ejpam-4958	62	2	q(v)g(w(σ(v	q(v)g(w(σ(v	NOUN
ejpam-4958	62	3	)	)	PUNCT
ejpam-4958	62	4	)	)	PUNCT
ejpam-4958	62	5	)	)	PUNCT
ejpam-4958	63	1	=	=	PUNCT
ejpam-4958	63	2	0	0	X
ejpam-4958	63	3	.	.	PUNCT
ejpam-4958	64	1	in	in	ADP
ejpam-4958	64	2	order	order	NOUN
ejpam-4958	64	3	to	to	PART
ejpam-4958	64	4	create	create	VERB
ejpam-4958	64	5	new	new	ADJ
ejpam-4958	64	6	oscillation	oscillation	NOUN
ejpam-4958	64	7	conditions	condition	NOUN
ejpam-4958	64	8	for	for	ADP
ejpam-4958	64	9	a	a	DET
ejpam-4958	64	10	specific	specific	ADJ
ejpam-4958	64	11	even	even	ADV
ejpam-4958	64	12	order	order	NOUN
ejpam-4958	64	13	dde	dde	PROPN
ejpam-4958	64	14	,	,	PUNCT
ejpam-4958	64	15	(	(	PUNCT
ejpam-4958	64	16	author	author	NOUN
ejpam-4958	64	17	?	?	PUNCT
ejpam-4958	64	18	)	)	PUNCT
ejpam-4958	65	1	[	[	X
ejpam-4958	65	2	26	26	NUM
ejpam-4958	65	3	]	]	PUNCT
ejpam-4958	65	4	used	use	VERB
ejpam-4958	65	5	the	the	DET
ejpam-4958	65	6	generalized	generalize	VERB
ejpam-4958	65	7	riccati	riccati	NOUN
ejpam-4958	65	8	approach	approach	NOUN
ejpam-4958	65	9	and	and	CCONJ
ejpam-4958	65	10	the	the	DET
ejpam-4958	65	11	integral	integral	ADJ
ejpam-4958	65	12	averaging	averaging	NOUN
ejpam-4958	65	13	technique	technique	NOUN
ejpam-4958	65	14	expressed	express	VERB
ejpam-4958	65	15	by	by	ADP
ejpam-4958	65	16	(	(	PUNCT
ejpam-4958	65	17	∣∣∣x(n−1)(h	∣∣∣x(n−1)(h	PROPN
ejpam-4958	65	18	)	)	PUNCT
ejpam-4958	65	19	∣∣∣e−1	∣∣∣e−1	NOUN
ejpam-4958	65	20	x(n−1)(h	x(n−1)(h	PROPN
ejpam-4958	65	21	)	)	PUNCT
ejpam-4958	65	22	)	)	PUNCT
ejpam-4958	65	23	′	′	NUM
ejpam-4958	66	1	+	+	CCONJ
ejpam-4958	67	1	f	f	X
ejpam-4958	67	2	(	(	PUNCT
ejpam-4958	67	3	h	h	NOUN
ejpam-4958	67	4	,	,	PUNCT
ejpam-4958	67	5	x[g(h	x[g(h	NOUN
ejpam-4958	67	6	)	)	PUNCT
ejpam-4958	67	7	]	]	PUNCT
ejpam-4958	67	8	)	)	PUNCT
ejpam-4958	67	9	=	=	SYM
ejpam-4958	67	10	0	0	NUM
ejpam-4958	67	11	,	,	PUNCT
ejpam-4958	67	12	(	(	PUNCT
ejpam-4958	67	13	n	n	CCONJ
ejpam-4958	67	14	even	even	ADV
ejpam-4958	67	15	)	)	PUNCT
ejpam-4958	67	16	.	.	PUNCT
ejpam-4958	68	1	(	(	PUNCT
ejpam-4958	68	2	author	author	NOUN
ejpam-4958	68	3	?	?	PUNCT
ejpam-4958	68	4	)	)	PUNCT
ejpam-4958	69	1	[	[	X
ejpam-4958	69	2	7	7	X
ejpam-4958	69	3	]	]	PUNCT
ejpam-4958	69	4	established	establish	VERB
ejpam-4958	69	5	new	new	ADJ
ejpam-4958	69	6	criteria	criterion	NOUN
ejpam-4958	69	7	with	with	ADP
ejpam-4958	69	8	regard	regard	NOUN
ejpam-4958	69	9	to	to	ADP
ejpam-4958	69	10	the	the	DET
ejpam-4958	69	11	oscillatory	oscillatory	ADJ
ejpam-4958	69	12	behaviour	behaviour	NOUN
ejpam-4958	69	13	of	of	ADP
ejpam-4958	69	14	even	even	ADV
ejpam-4958	69	15	order	order	NOUN
ejpam-4958	69	16	ddes	dde	NOUN
ejpam-4958	69	17	containing	contain	VERB
ejpam-4958	69	18	the	the	DET
ejpam-4958	69	19	neutral	neutral	ADJ
ejpam-4958	69	20	component	component	NOUN
ejpam-4958	69	21	by	by	ADP
ejpam-4958	69	22	using	use	VERB
ejpam-4958	69	23	the	the	DET
ejpam-4958	69	24	comparison	comparison	NOUN
ejpam-4958	69	25	approach	approach	NOUN
ejpam-4958	69	26	,	,	PUNCT
ejpam-4958	69	27	the	the	DET
ejpam-4958	69	28	riccati	riccati	PROPN
ejpam-4958	69	29	transformation	transformation	NOUN
ejpam-4958	69	30	,	,	PUNCT
ejpam-4958	69	31	and	and	CCONJ
ejpam-4958	69	32	the	the	DET
ejpam-4958	69	33	integral	integral	ADJ
ejpam-4958	69	34	averaging	averaging	NOUN
ejpam-4958	69	35	method	method	NOUN
ejpam-4958	69	36	.	.	PUNCT
ejpam-4958	70	1	all	all	DET
ejpam-4958	70	2	three	three	NUM
ejpam-4958	70	3	of	of	ADP
ejpam-4958	70	4	these	these	DET
ejpam-4958	70	5	methods	method	NOUN
ejpam-4958	70	6	are	be	AUX
ejpam-4958	70	7	statistical	statistical	ADJ
ejpam-4958	70	8	in	in	ADP
ejpam-4958	70	9	nature	nature	NOUN
ejpam-4958	70	10	.	.	PUNCT
ejpam-4958	71	1	(	(	PUNCT
ejpam-4958	71	2	γ(u)ϖ(r−1)(u	γ(u)ϖ(r−1)(u	PROPN
ejpam-4958	71	3	)	)	PUNCT
ejpam-4958	71	4	)	)	PUNCT
ejpam-4958	72	1	′	′	NUM
ejpam-4958	73	1	+	+	CCONJ
ejpam-4958	74	1	j∑	j∑	ADJ
ejpam-4958	74	2	i=1	i=1	X
ejpam-4958	75	1	ai(u)φ	ai(u)φ	INTJ
ejpam-4958	75	2	(	(	PUNCT
ejpam-4958	75	3	h	h	NOUN
ejpam-4958	75	4	(	(	PUNCT
ejpam-4958	75	5	wi(u	wi(u	NOUN
ejpam-4958	75	6	)	)	PUNCT
ejpam-4958	75	7	)	)	PUNCT
ejpam-4958	75	8	)	)	PUNCT
ejpam-4958	76	1	=	=	PUNCT
ejpam-4958	76	2	0	0	X
ejpam-4958	76	3	.	.	PUNCT
ejpam-4958	77	1	the	the	DET
ejpam-4958	77	2	researchers	researcher	NOUN
ejpam-4958	77	3	utilized	utilize	VERB
ejpam-4958	77	4	the	the	DET
ejpam-4958	77	5	riccati	riccati	PROPN
ejpam-4958	77	6	transformation	transformation	NOUN
ejpam-4958	77	7	and	and	CCONJ
ejpam-4958	77	8	integral	integral	ADJ
ejpam-4958	77	9	averaging	averaging	NOUN
ejpam-4958	77	10	technique	technique	NOUN
ejpam-4958	77	11	to	to	PART
ejpam-4958	77	12	extend	extend	VERB
ejpam-4958	77	13	the	the	DET
ejpam-4958	77	14	results	result	NOUN
ejpam-4958	77	15	presented	present	VERB
ejpam-4958	77	16	in	in	ADP
ejpam-4958	77	17	the	the	DET
ejpam-4958	77	18	study	study	NOUN
ejpam-4958	77	19	under∫	under∫	NOUN
ejpam-4958	77	20	∞	∞	NUM
ejpam-4958	77	21	t0	t0	PROPN
ejpam-4958	77	22	1	1	NUM
ejpam-4958	77	23	γ(a	γ(a	NOUN
ejpam-4958	77	24	)	)	PUNCT
ejpam-4958	77	25	da	da	PROPN
ejpam-4958	77	26	=	=	SYM
ejpam-4958	77	27	∞.	∞.	PROPN
ejpam-4958	77	28	(	(	PUNCT
ejpam-4958	77	29	author	author	NOUN
ejpam-4958	77	30	?	?	PUNCT
ejpam-4958	77	31	)	)	PUNCT
ejpam-4958	78	1	[	[	X
ejpam-4958	78	2	1	1	X
ejpam-4958	78	3	]	]	PUNCT
ejpam-4958	78	4	presented	present	VERB
ejpam-4958	78	5	several	several	ADJ
ejpam-4958	78	6	oscillatory	oscillatory	ADJ
ejpam-4958	78	7	properties	property	NOUN
ejpam-4958	78	8	of	of	ADP
ejpam-4958	78	9	higher	high	ADJ
ejpam-4958	78	10	-	-	PUNCT
ejpam-4958	78	11	order	order	NOUN
ejpam-4958	78	12	non	non	ADJ
ejpam-4958	78	13	-	-	ADJ
ejpam-4958	78	14	linear	linear	ADJ
ejpam-4958	78	15	de	de	X
ejpam-4958	78	16	with	with	ADP
ejpam-4958	78	17	a	a	DET
ejpam-4958	78	18	middle	middle	ADJ
ejpam-4958	78	19	term	term	NOUN
ejpam-4958	78	20	(	(	PUNCT
ejpam-4958	78	21	α1(ε	α1(ε	NUM
ejpam-4958	78	22	)	)	PUNCT
ejpam-4958	78	23	(	(	PUNCT
ejpam-4958	78	24	w(j−1)(ε	w(j−1)(ε	NOUN
ejpam-4958	78	25	)	)	PUNCT
ejpam-4958	78	26	)	)	PUNCT
ejpam-4958	79	1	γ)′	γ)′	PROPN
ejpam-4958	80	1	+	+	NUM
ejpam-4958	80	2	α2(ε	α2(ε	X
ejpam-4958	80	3	)	)	PUNCT
ejpam-4958	80	4	(	(	PUNCT
ejpam-4958	80	5	w(j−1)(ε	w(j−1)(ε	NOUN
ejpam-4958	80	6	)	)	PUNCT
ejpam-4958	80	7	)	)	PUNCT
ejpam-4958	81	1	γ	γ	PROPN
ejpam-4958	81	2	+	+	PROPN
ejpam-4958	81	3	n∑	n∑	PROPN
ejpam-4958	81	4	i=1	i=1	PROPN
ejpam-4958	82	1	σi(ε)w	σi(ε)w	PROPN
ejpam-4958	82	2	γ	γ	X
ejpam-4958	82	3	(	(	PUNCT
ejpam-4958	82	4	βi(ε	βi(ε	NUM
ejpam-4958	82	5	)	)	PUNCT
ejpam-4958	82	6	)	)	PUNCT
ejpam-4958	83	1	=	=	PUNCT
ejpam-4958	83	2	0	0	X
ejpam-4958	83	3	.	.	PUNCT
ejpam-4958	84	1	the	the	DET
ejpam-4958	84	2	subsequent	subsequent	ADJ
ejpam-4958	84	3	condition	condition	NOUN
ejpam-4958	84	4	is	be	AUX
ejpam-4958	84	5	met:∫	met:∫	NOUN
ejpam-4958	84	6	∞	∞	NUM
ejpam-4958	84	7	ε0	ε0	PROPN
ejpam-4958	84	8	(	(	PUNCT
ejpam-4958	84	9	1	1	NUM
ejpam-4958	84	10	α1(ϱ	α1(ϱ	NUM
ejpam-4958	84	11	)	)	PUNCT
ejpam-4958	84	12	exp	exp	NOUN
ejpam-4958	84	13	(	(	PUNCT
ejpam-4958	84	14	−	−	PROPN
ejpam-4958	84	15	∫	∫	PROPN
ejpam-4958	84	16	s	s	PROPN
ejpam-4958	84	17	z0	z0	PROPN
ejpam-4958	84	18	α2(x	α2(x	PROPN
ejpam-4958	84	19	)	)	PUNCT
ejpam-4958	84	20	α1(x	α1(x	NOUN
ejpam-4958	84	21	)	)	PUNCT
ejpam-4958	84	22	dx	dx	PROPN
ejpam-4958	84	23	)	)	PUNCT
ejpam-4958	84	24	)	)	PUNCT
ejpam-4958	85	1	1	1	X
ejpam-4958	85	2	/	/	SYM
ejpam-4958	85	3	y	y	NOUN
ejpam-4958	85	4	dϱ	dϱ	NOUN
ejpam-4958	85	5	=	=	PUNCT
ejpam-4958	85	6	∞.	∞.	PROPN
ejpam-4958	85	7	s.	s.	PROPN
ejpam-4958	85	8	a.	a.	PROPN
ejpam-4958	85	9	balatta	balatta	PROPN
ejpam-4958	85	10	et	et	PROPN
ejpam-4958	85	11	al	al	PROPN
ejpam-4958	85	12	.	.	PUNCT
ejpam-4958	85	13	/	/	SYM
ejpam-4958	85	14	eur	eur	PROPN
ejpam-4958	85	15	.	.	PUNCT
ejpam-4958	86	1	j.	j.	PROPN
ejpam-4958	86	2	pure	pure	PROPN
ejpam-4958	86	3	appl	appl	PROPN
ejpam-4958	86	4	.	.	PROPN
ejpam-4958	86	5	math	math	PROPN
ejpam-4958	86	6	,	,	PUNCT
ejpam-4958	86	7	16	16	NUM
ejpam-4958	86	8	(	(	PUNCT
ejpam-4958	86	9	4	4	NUM
ejpam-4958	86	10	)	)	PUNCT
ejpam-4958	86	11	(	(	PUNCT
ejpam-4958	86	12	2023	2023	NUM
ejpam-4958	86	13	)	)	PUNCT
ejpam-4958	86	14	,	,	PUNCT
ejpam-4958	86	15	2234	2234	NUM
ejpam-4958	86	16	-	-	SYM
ejpam-4958	86	17	2246	2246	NUM
ejpam-4958	86	18	2237	2237	NUM
ejpam-4958	86	19	they	they	PRON
ejpam-4958	86	20	produced	produce	VERB
ejpam-4958	86	21	several	several	ADJ
ejpam-4958	86	22	novel	novel	NOUN
ejpam-4958	86	23	oscillation	oscillation	NOUN
ejpam-4958	86	24	results	result	NOUN
ejpam-4958	86	25	that	that	PRON
ejpam-4958	86	26	expanded	expand	VERB
ejpam-4958	86	27	upon	upon	SCONJ
ejpam-4958	86	28	and	and	CCONJ
ejpam-4958	86	29	enhanced	enhance	VERB
ejpam-4958	86	30	existing	exist	VERB
ejpam-4958	86	31	findings	finding	NOUN
ejpam-4958	86	32	in	in	ADP
ejpam-4958	86	33	the	the	DET
ejpam-4958	86	34	literature	literature	NOUN
ejpam-4958	86	35	.	.	PUNCT
ejpam-4958	87	1	their	their	PRON
ejpam-4958	87	2	findings	finding	NOUN
ejpam-4958	87	3	do	do	AUX
ejpam-4958	87	4	not	not	PART
ejpam-4958	87	5	necessitate	necessitate	ADJ
ejpam-4958	87	6	that	that	SCONJ
ejpam-4958	87	7	τ	τ	PROPN
ejpam-4958	87	8	′(u	′(u	NOUN
ejpam-4958	87	9	)	)	PUNCT
ejpam-4958	87	10	≥	≥	NOUN
ejpam-4958	87	11	0	0	NUM
ejpam-4958	87	12	in	in	ADP
ejpam-4958	87	13	order	order	NOUN
ejpam-4958	87	14	to	to	PART
ejpam-4958	87	15	guarantee	guarantee	VERB
ejpam-4958	87	16	that	that	SCONJ
ejpam-4958	87	17	all	all	DET
ejpam-4958	87	18	solutions	solution	NOUN
ejpam-4958	87	19	to	to	ADP
ejpam-4958	87	20	the	the	DET
ejpam-4958	87	21	equation	equation	NOUN
ejpam-4958	87	22	is	be	AUX
ejpam-4958	87	23	oscillatory	oscillatory	ADJ
ejpam-4958	87	24	or	or	CCONJ
ejpam-4958	87	25	that	that	SCONJ
ejpam-4958	87	26	it	it	PRON
ejpam-4958	87	27	approaches	approach	VERB
ejpam-4958	87	28	zero	zero	NUM
ejpam-4958	87	29	as	as	SCONJ
ejpam-4958	87	30	u	u	NOUN
ejpam-4958	87	31	tends	tend	VERB
ejpam-4958	87	32	to	to	ADP
ejpam-4958	87	33	∞	∞	PROPN
ejpam-4958	87	34	,	,	PUNCT
ejpam-4958	87	35	where	where	SCONJ
ejpam-4958	87	36	some	some	DET
ejpam-4958	87	37	necessary	necessary	ADJ
ejpam-4958	87	38	conditions	condition	NOUN
ejpam-4958	87	39	were	be	AUX
ejpam-4958	87	40	created	create	VERB
ejpam-4958	87	41	.	.	PUNCT
ejpam-4958	88	1	in	in	ADP
ejpam-4958	88	2	2020	2020	NUM
ejpam-4958	88	3	(	(	PUNCT
ejpam-4958	88	4	author	author	NOUN
ejpam-4958	88	5	?	?	PUNCT
ejpam-4958	88	6	)	)	PUNCT
ejpam-4958	89	1	[	[	X
ejpam-4958	89	2	14	14	NUM
ejpam-4958	89	3	]	]	PUNCT
ejpam-4958	89	4	established	establish	VERB
ejpam-4958	89	5	new	new	ADJ
ejpam-4958	89	6	oscillation	oscillation	NOUN
ejpam-4958	89	7	results	result	NOUN
ejpam-4958	89	8	of	of	ADP
ejpam-4958	89	9	solutions	solution	NOUN
ejpam-4958	89	10	to	to	ADP
ejpam-4958	89	11	a	a	DET
ejpam-4958	89	12	class	class	NOUN
ejpam-4958	89	13	of	of	ADP
ejpam-4958	89	14	even	even	ADJ
ejpam-4958	89	15	-	-	PUNCT
ejpam-4958	89	16	order	order	NOUN
ejpam-4958	89	17	advanced	advanced	ADJ
ejpam-4958	89	18	differential	differential	ADJ
ejpam-4958	89	19	equations	equation	NOUN
ejpam-4958	89	20	with	with	ADP
ejpam-4958	89	21	a	a	DET
ejpam-4958	89	22	p	p	NOUN
ejpam-4958	89	23	-	-	PUNCT
ejpam-4958	89	24	laplacian	laplacian	ADJ
ejpam-4958	89	25	like	like	ADJ
ejpam-4958	89	26	operator	operator	NOUN
ejpam-4958	89	27	.	.	PUNCT
ejpam-4958	90	1	(	(	PUNCT
ejpam-4958	90	2	a(v	a(v	PROPN
ejpam-4958	90	3	)	)	PUNCT
ejpam-4958	90	4	∣∣∣y(κ−1)(v	∣∣∣y(κ−1)(v	PROPN
ejpam-4958	90	5	)	)	PUNCT
ejpam-4958	90	6	∣∣∣p−2	∣∣∣p−2	NUM
ejpam-4958	90	7	y(κ−1)(v	y(κ−1)(v	NOUN
ejpam-4958	90	8	)	)	PUNCT
ejpam-4958	90	9	)	)	PUNCT
ejpam-4958	91	1	′	′	NUM
ejpam-4958	92	1	+	+	CCONJ
ejpam-4958	93	1	j∑	j∑	VERB
ejpam-4958	93	2	i=1	i=1	X
ejpam-4958	93	3	qi(v)g	qi(v)g	PROPN
ejpam-4958	93	4	(	(	PUNCT
ejpam-4958	93	5	y	y	PROPN
ejpam-4958	93	6	(	(	PUNCT
ejpam-4958	93	7	ηi(v	ηi(v	PROPN
ejpam-4958	93	8	)	)	PUNCT
ejpam-4958	93	9	)	)	PUNCT
ejpam-4958	93	10	)	)	PUNCT
ejpam-4958	94	1	=	=	SYM
ejpam-4958	94	2	0	0	NUM
ejpam-4958	94	3	,	,	PUNCT
ejpam-4958	94	4	v	v	PRON
ejpam-4958	94	5	≥	≥	NUM
ejpam-4958	94	6	v0	v0	PROPN
ejpam-4958	94	7	.	.	PUNCT
ejpam-4958	95	1	riccati	riccati	PROPN
ejpam-4958	95	2	transformation	transformation	NOUN
ejpam-4958	95	3	and	and	CCONJ
ejpam-4958	95	4	the	the	DET
ejpam-4958	95	5	theory	theory	NOUN
ejpam-4958	95	6	of	of	ADP
ejpam-4958	95	7	comparison	comparison	NOUN
ejpam-4958	95	8	with	with	ADP
ejpam-4958	95	9	first	first	ADJ
ejpam-4958	95	10	and	and	CCONJ
ejpam-4958	95	11	second	second	ADJ
ejpam-4958	95	12	-	-	PUNCT
ejpam-4958	95	13	order	order	NOUN
ejpam-4958	95	14	delay	delay	NOUN
ejpam-4958	95	15	equation	equation	NOUN
ejpam-4958	95	16	had	have	AUX
ejpam-4958	95	17	been	be	AUX
ejpam-4958	95	18	used	use	VERB
ejpam-4958	95	19	.	.	PUNCT
ejpam-4958	96	1	in	in	ADP
ejpam-4958	96	2	addition	addition	NOUN
ejpam-4958	96	3	,	,	PUNCT
ejpam-4958	96	4	their	their	PRON
ejpam-4958	96	5	results	result	NOUN
ejpam-4958	96	6	were	be	AUX
ejpam-4958	96	7	continue	continue	VERB
ejpam-4958	96	8	by	by	ADP
ejpam-4958	96	9	(	(	PUNCT
ejpam-4958	96	10	author	author	NOUN
ejpam-4958	96	11	?	?	PUNCT
ejpam-4958	96	12	)	)	PUNCT
ejpam-4958	97	1	[	[	X
ejpam-4958	97	2	3	3	X
ejpam-4958	97	3	]	]	PUNCT
ejpam-4958	97	4	discussed	discuss	VERB
ejpam-4958	97	5	the	the	DET
ejpam-4958	97	6	properties	property	NOUN
ejpam-4958	97	7	of	of	ADP
ejpam-4958	97	8	non	non	ADJ
ejpam-4958	97	9	-	-	ADJ
ejpam-4958	97	10	oscillatory	oscillatory	ADJ
ejpam-4958	97	11	solutions	solution	NOUN
ejpam-4958	97	12	of	of	ADP
ejpam-4958	97	13	neutral	neutral	ADJ
ejpam-4958	97	14	differential	differential	ADJ
ejpam-4958	97	15	equations	equation	NOUN
ejpam-4958	97	16	related	relate	VERB
ejpam-4958	97	17	to	to	ADP
ejpam-4958	97	18	plaplacian	plaplacian	ADJ
ejpam-4958	97	19	operators	operator	NOUN
ejpam-4958	97	20	(	(	PUNCT
ejpam-4958	97	21	φ(1	φ(1	PROPN
ejpam-4958	97	22	)	)	PUNCT
ejpam-4958	97	23	(	(	PUNCT
ejpam-4958	97	24	y′′′(1	y′′′(1	INTJ
ejpam-4958	97	25	)	)	PUNCT
ejpam-4958	97	26	)	)	PUNCT
ejpam-4958	98	1	p−1	p−1	PROPN
ejpam-4958	98	2	)	)	PUNCT
ejpam-4958	98	3	′	′	NOUN
ejpam-4958	99	1	+	+	CCONJ
ejpam-4958	99	2	ω1(1)w	ω1(1)w	VERB
ejpam-4958	99	3	p−1	p−1	PROPN
ejpam-4958	99	4	(	(	PUNCT
ejpam-4958	99	5	ω2(1	ω2(1	PROPN
ejpam-4958	99	6	)	)	PUNCT
ejpam-4958	99	7	)	)	PUNCT
ejpam-4958	100	1	=	=	PUNCT
ejpam-4958	100	2	0	0	NUM
ejpam-4958	100	3	,	,	PUNCT
ejpam-4958	100	4	by	by	ADP
ejpam-4958	100	5	applying	apply	VERB
ejpam-4958	100	6	the	the	DET
ejpam-4958	100	7	comparison	comparison	NOUN
ejpam-4958	100	8	method	method	NOUN
ejpam-4958	100	9	.	.	PUNCT
ejpam-4958	101	1	recently	recently	ADV
ejpam-4958	101	2	,	,	PUNCT
ejpam-4958	101	3	the	the	DET
ejpam-4958	101	4	galpha	galpha	NOUN
ejpam-4958	101	5	-	-	PUNCT
ejpam-4958	101	6	transform	transform	NOUN
ejpam-4958	101	7	in	in	ADP
ejpam-4958	101	8	(	(	PUNCT
ejpam-4958	101	9	author	author	NOUN
ejpam-4958	101	10	?	?	PUNCT
ejpam-4958	101	11	)	)	PUNCT
ejpam-4958	102	1	[	[	X
ejpam-4958	102	2	24	24	NUM
ejpam-4958	102	3	]	]	PUNCT
ejpam-4958	102	4	was	be	AUX
ejpam-4958	102	5	used	use	VERB
ejpam-4958	102	6	to	to	PART
ejpam-4958	102	7	study	study	VERB
ejpam-4958	102	8	,	,	PUNCT
ejpam-4958	102	9	solutions	solution	NOUN
ejpam-4958	102	10	of	of	ADP
ejpam-4958	102	11	higher	high	ADJ
ejpam-4958	102	12	-	-	PUNCT
ejpam-4958	102	13	order	order	NOUN
ejpam-4958	102	14	differential	differential	ADJ
ejpam-4958	102	15	equations	equation	NOUN
ejpam-4958	102	16	with	with	ADP
ejpam-4958	102	17	polynomial	polynomial	ADJ
ejpam-4958	102	18	coefficients	coefficient	NOUN
ejpam-4958	102	19	(	(	PUNCT
ejpam-4958	102	20	hodepcs	hodepc	NOUN
ejpam-4958	102	21	)	)	PUNCT
ejpam-4958	102	22	and	and	CCONJ
ejpam-4958	102	23	based	base	VERB
ejpam-4958	102	24	on	on	ADP
ejpam-4958	102	25	some	some	DET
ejpam-4958	102	26	characterizations	characterization	NOUN
ejpam-4958	102	27	,	,	PUNCT
ejpam-4958	102	28	the	the	DET
ejpam-4958	102	29	solutions	solution	NOUN
ejpam-4958	102	30	of	of	ADP
ejpam-4958	102	31	hodepcs	hodepc	NOUN
ejpam-4958	102	32	were	be	AUX
ejpam-4958	102	33	investigated	investigate	VERB
ejpam-4958	102	34	.	.	PUNCT
ejpam-4958	103	1	(	(	PUNCT
ejpam-4958	103	2	author	author	NOUN
ejpam-4958	103	3	?	?	PUNCT
ejpam-4958	103	4	)	)	PUNCT
ejpam-4958	104	1	[	[	X
ejpam-4958	104	2	4	4	X
ejpam-4958	104	3	]	]	PUNCT
ejpam-4958	104	4	studied	study	VERB
ejpam-4958	104	5	n	n	CCONJ
ejpam-4958	104	6	-	-	PUNCT
ejpam-4958	104	7	th	th	VERB
ejpam-4958	104	8	order	order	NOUN
ejpam-4958	104	9	neutral	neutral	ADJ
ejpam-4958	104	10	nonlinear	nonlinear	ADJ
ejpam-4958	104	11	differential	differential	ADJ
ejpam-4958	104	12	equation	equation	NOUN
ejpam-4958	104	13	[	[	PUNCT
ejpam-4958	104	14	r(t)[x(t)−	r(t)[x(t)−	PROPN
ejpam-4958	104	15	p(t)x(t−	p(t)x(t−	NOUN
ejpam-4958	104	16	τ)](n−1	τ)](n−1	NOUN
ejpam-4958	104	17	)	)	PUNCT
ejpam-4958	104	18	]	]	PUNCT
ejpam-4958	104	19	′	′	NUM
ejpam-4958	105	1	+	+	CCONJ
ejpam-4958	105	2	(	(	PUNCT
ejpam-4958	105	3	−1)n	−1)n	X
ejpam-4958	105	4	[	[	X
ejpam-4958	105	5	f1	f1	NOUN
ejpam-4958	105	6	(	(	PUNCT
ejpam-4958	105	7	t	t	PROPN
ejpam-4958	105	8	,	,	PUNCT
ejpam-4958	105	9	x	x	X
ejpam-4958	105	10	(	(	PUNCT
ejpam-4958	105	11	σ1(t)))−	σ1(t)))−	NOUN
ejpam-4958	105	12	f2	f2	PROPN
ejpam-4958	105	13	(	(	PUNCT
ejpam-4958	105	14	t	t	PROPN
ejpam-4958	105	15	,	,	PUNCT
ejpam-4958	105	16	x	x	X
ejpam-4958	105	17	(	(	PUNCT
ejpam-4958	105	18	σ2(t)))−	σ2(t)))−	X
ejpam-4958	105	19	g(t	g(t	PROPN
ejpam-4958	105	20	)	)	PUNCT
ejpam-4958	105	21	]	]	PUNCT
ejpam-4958	106	1	=	=	PUNCT
ejpam-4958	106	2	0	0	NUM
ejpam-4958	106	3	,	,	PUNCT
ejpam-4958	106	4	they	they	PRON
ejpam-4958	106	5	used	use	VERB
ejpam-4958	106	6	the	the	DET
ejpam-4958	106	7	banach	banach	NOUN
ejpam-4958	106	8	contraction	contraction	NOUN
ejpam-4958	106	9	principle	principle	NOUN
ejpam-4958	106	10	and	and	CCONJ
ejpam-4958	106	11	some	some	DET
ejpam-4958	106	12	sufficient	sufficient	ADJ
ejpam-4958	106	13	conditions	condition	NOUN
ejpam-4958	106	14	are	be	AUX
ejpam-4958	106	15	established	establish	VERB
ejpam-4958	106	16	for	for	ADP
ejpam-4958	106	17	the	the	DET
ejpam-4958	106	18	existence	existence	NOUN
ejpam-4958	106	19	of	of	ADP
ejpam-4958	106	20	nonoscillatory	nonoscillatory	ADJ
ejpam-4958	106	21	solutions	solution	NOUN
ejpam-4958	106	22	.	.	PUNCT
ejpam-4958	107	1	the	the	DET
ejpam-4958	107	2	theory	theory	NOUN
ejpam-4958	107	3	of	of	ADP
ejpam-4958	107	4	higher	high	ADJ
ejpam-4958	107	5	-	-	PUNCT
ejpam-4958	107	6	order	order	NOUN
ejpam-4958	107	7	differential	differential	ADJ
ejpam-4958	107	8	equations	equation	NOUN
ejpam-4958	107	9	has	have	VERB
ejpam-4958	107	10	many	many	ADJ
ejpam-4958	107	11	connections	connection	NOUN
ejpam-4958	107	12	with	with	ADP
ejpam-4958	107	13	various	various	ADJ
ejpam-4958	107	14	branches	branch	NOUN
ejpam-4958	107	15	of	of	ADP
ejpam-4958	107	16	mathematics	mathematic	NOUN
ejpam-4958	107	17	and	and	CCONJ
ejpam-4958	107	18	applied	apply	VERB
ejpam-4958	107	19	sciences	science	NOUN
ejpam-4958	107	20	(	(	PUNCT
ejpam-4958	107	21	we	we	PRON
ejpam-4958	107	22	recall	recall	VERB
ejpam-4958	107	23	for	for	ADP
ejpam-4958	107	24	example	example	NOUN
ejpam-4958	107	25	the	the	DET
ejpam-4958	107	26	models	model	NOUN
ejpam-4958	107	27	of	of	ADP
ejpam-4958	107	28	suspension	suspension	NOUN
ejpam-4958	107	29	bridge	bridge	NOUN
ejpam-4958	107	30	and	and	CCONJ
ejpam-4958	107	31	noise	noise	NOUN
ejpam-4958	107	32	removal	removal	NOUN
ejpam-4958	107	33	)	)	PUNCT
ejpam-4958	107	34	.	.	PUNCT
ejpam-4958	108	1	the	the	DET
ejpam-4958	108	2	present	present	ADJ
ejpam-4958	108	3	investigation	investigation	NOUN
ejpam-4958	108	4	aims	aim	VERB
ejpam-4958	108	5	to	to	PART
ejpam-4958	108	6	establish	establish	VERB
ejpam-4958	108	7	specific	specific	ADJ
ejpam-4958	108	8	oscillation	oscillation	NOUN
ejpam-4958	108	9	and	and	CCONJ
ejpam-4958	108	10	asymptotic	asymptotic	ADJ
ejpam-4958	108	11	criteria	criterion	NOUN
ejpam-4958	108	12	for	for	ADP
ejpam-4958	108	13	delay	delay	NOUN
ejpam-4958	108	14	terms	term	NOUN
ejpam-4958	108	15	of	of	ADP
ejpam-4958	108	16	higher	high	ADJ
ejpam-4958	108	17	order	order	NOUN
ejpam-4958	108	18	in	in	ADP
ejpam-4958	108	19	the	the	DET
ejpam-4958	108	20	structure	structure	NOUN
ejpam-4958	108	21	of	of	ADP
ejpam-4958	108	22	halflinear	halflinear	ADJ
ejpam-4958	108	23	equations	equation	NOUN
ejpam-4958	108	24	.	.	PUNCT
ejpam-4958	109	1	the	the	DET
ejpam-4958	109	2	oscillatory	oscillatory	ADJ
ejpam-4958	109	3	behaviour	behaviour	NOUN
ejpam-4958	109	4	of	of	ADP
ejpam-4958	109	5	the	the	DET
ejpam-4958	109	6	following	following	NOUN
ejpam-4958	109	7	is	be	AUX
ejpam-4958	109	8	the	the	DET
ejpam-4958	109	9	subject	subject	NOUN
ejpam-4958	109	10	of	of	ADP
ejpam-4958	109	11	our	our	PRON
ejpam-4958	109	12	study	study	NOUN
ejpam-4958	109	13	,	,	PUNCT
ejpam-4958	109	14	(	(	PUNCT
ejpam-4958	109	15	r(u	r(u	PROPN
ejpam-4958	109	16	)	)	PUNCT
ejpam-4958	109	17	(	(	PUNCT
ejpam-4958	109	18	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	109	19	)	)	PUNCT
ejpam-4958	109	20	)	)	PUNCT
ejpam-4958	109	21	α)′	α)′	NOUN
ejpam-4958	110	1	+	+	CCONJ
ejpam-4958	110	2	m∑	m∑	NOUN
ejpam-4958	110	3	i=1	i=1	PROPN
ejpam-4958	110	4	qi(u)ϖ	qi(u)ϖ	NUM
ejpam-4958	110	5	β	β	X
ejpam-4958	110	6	(	(	PUNCT
ejpam-4958	110	7	τi(u	τi(u	NUM
ejpam-4958	110	8	)	)	PUNCT
ejpam-4958	110	9	)	)	PUNCT
ejpam-4958	110	10	=	=	SYM
ejpam-4958	110	11	0	0	NUM
ejpam-4958	110	12	,	,	PUNCT
ejpam-4958	110	13	u	u	PRON
ejpam-4958	110	14	≥	≥	NOUN
ejpam-4958	110	15	u0	u0	ADJ
ejpam-4958	110	16	,	,	PUNCT
ejpam-4958	110	17	(	(	PUNCT
ejpam-4958	110	18	1	1	X
ejpam-4958	110	19	)	)	PUNCT
ejpam-4958	110	20	under	under	ADP
ejpam-4958	110	21	the	the	DET
ejpam-4958	110	22	conditions	condition	NOUN
ejpam-4958	110	23	∫	∫	X
ejpam-4958	110	24	∞	∞	NUM
ejpam-4958	110	25	u0	u0	ADJ
ejpam-4958	110	26	1	1	NUM
ejpam-4958	110	27	r1	r1	PROPN
ejpam-4958	110	28	/	/	SYM
ejpam-4958	110	29	α(u	α(u	PROPN
ejpam-4958	110	30	)	)	PUNCT
ejpam-4958	110	31	du	du	X
ejpam-4958	110	32	<	<	X
ejpam-4958	110	33	∞	∞	PROPN
ejpam-4958	110	34	,	,	PUNCT
ejpam-4958	110	35	and	and	CCONJ
ejpam-4958	110	36	r′(u	r′(u	PROPN
ejpam-4958	110	37	)	)	PUNCT
ejpam-4958	110	38	≥	≥	NOUN
ejpam-4958	110	39	0	0	NUM
ejpam-4958	110	40	.	.	PUNCT
ejpam-4958	111	1	(	(	PUNCT
ejpam-4958	111	2	2	2	X
ejpam-4958	111	3	)	)	PUNCT
ejpam-4958	111	4	in	in	ADP
ejpam-4958	111	5	this	this	DET
ejpam-4958	111	6	work	work	NOUN
ejpam-4958	111	7	we	we	PRON
ejpam-4958	111	8	suppose	suppose	VERB
ejpam-4958	111	9	that	that	SCONJ
ejpam-4958	111	10	•	•	NUM
ejpam-4958	111	11	α	α	NOUN
ejpam-4958	111	12	,	,	PUNCT
ejpam-4958	111	13	β	β	NOUN
ejpam-4958	111	14	,	,	PUNCT
ejpam-4958	111	15	where	where	SCONJ
ejpam-4958	111	16	β	β	X
ejpam-4958	111	17	≤	≤	NOUN
ejpam-4958	111	18	α	α	X
ejpam-4958	111	19	,	,	PUNCT
ejpam-4958	111	20	are	be	AUX
ejpam-4958	111	21	the	the	DET
ejpam-4958	111	22	ratios	ratio	NOUN
ejpam-4958	111	23	of	of	ADP
ejpam-4958	111	24	odd	odd	ADJ
ejpam-4958	111	25	positive	positive	ADJ
ejpam-4958	111	26	integers	integer	NOUN
ejpam-4958	111	27	,	,	PUNCT
ejpam-4958	111	28	•	•	NUM
ejpam-4958	111	29	r(u	r(u	PROPN
ejpam-4958	111	30	)	)	PUNCT
ejpam-4958	111	31	∈	∈	PROPN
ejpam-4958	111	32	c1	c1	NOUN
ejpam-4958	111	33	[	[	X
ejpam-4958	111	34	u0,∞	u0,∞	PROPN
ejpam-4958	111	35	)	)	PUNCT
ejpam-4958	111	36	,	,	PUNCT
ejpam-4958	111	37	r(u	r(u	PROPN
ejpam-4958	111	38	)	)	PUNCT
ejpam-4958	111	39	>	>	X
ejpam-4958	111	40	0	0	NUM
ejpam-4958	111	41	,	,	PUNCT
ejpam-4958	111	42	•	•	NOUN
ejpam-4958	111	43	qi(u	qi(u	NUM
ejpam-4958	111	44	)	)	PUNCT
ejpam-4958	111	45	,	,	PUNCT
ejpam-4958	111	46	τi(u	τi(u	PUNCT
ejpam-4958	111	47	)	)	PUNCT
ejpam-4958	111	48	∈	∈	PROPN
ejpam-4958	111	49	c	c	X
ejpam-4958	112	1	[	[	X
ejpam-4958	112	2	u0,∞	u0,∞	PROPN
ejpam-4958	112	3	)	)	PUNCT
ejpam-4958	112	4	,	,	PUNCT
ejpam-4958	112	5	qi(u	qi(u	NUM
ejpam-4958	112	6	)	)	PUNCT
ejpam-4958	112	7	>	>	X
ejpam-4958	112	8	0	0	NUM
ejpam-4958	112	9	,	,	PUNCT
ejpam-4958	112	10	τi(u	τi(u	PUNCT
ejpam-4958	112	11	)	)	PUNCT
ejpam-4958	113	1	<	<	X
ejpam-4958	113	2	u	u	NOUN
ejpam-4958	113	3	and	and	CCONJ
ejpam-4958	113	4	limu→∞	limu→∞	NOUN
ejpam-4958	113	5	τi(u	τi(u	PUNCT
ejpam-4958	113	6	)	)	PUNCT
ejpam-4958	114	1	=	=	SYM
ejpam-4958	114	2	∞	∞	PROPN
ejpam-4958	114	3	,	,	PUNCT
ejpam-4958	114	4	i	i	PRON
ejpam-4958	114	5	=	=	NOUN
ejpam-4958	114	6	1	1	NUM
ejpam-4958	114	7	,	,	PUNCT
ejpam-4958	114	8	.	.	PUNCT
ejpam-4958	114	9	.	.	PUNCT
ejpam-4958	114	10	.	.	PUNCT
ejpam-4958	115	1	,	,	PUNCT
ejpam-4958	115	2	m.	m.	NOUN
ejpam-4958	115	3	s.	s.	PROPN
ejpam-4958	115	4	a.	a.	PROPN
ejpam-4958	115	5	balatta	balatta	PROPN
ejpam-4958	115	6	et	et	PROPN
ejpam-4958	115	7	al	al	PROPN
ejpam-4958	115	8	.	.	PUNCT
ejpam-4958	115	9	/	/	SYM
ejpam-4958	115	10	eur	eur	PROPN
ejpam-4958	115	11	.	.	PUNCT
ejpam-4958	116	1	j.	j.	PROPN
ejpam-4958	116	2	pure	pure	PROPN
ejpam-4958	116	3	appl	appl	PROPN
ejpam-4958	116	4	.	.	PROPN
ejpam-4958	116	5	math	math	PROPN
ejpam-4958	116	6	,	,	PUNCT
ejpam-4958	116	7	16	16	NUM
ejpam-4958	116	8	(	(	PUNCT
ejpam-4958	116	9	4	4	NUM
ejpam-4958	116	10	)	)	PUNCT
ejpam-4958	116	11	(	(	PUNCT
ejpam-4958	116	12	2023	2023	NUM
ejpam-4958	116	13	)	)	PUNCT
ejpam-4958	116	14	,	,	PUNCT
ejpam-4958	116	15	2234	2234	NUM
ejpam-4958	116	16	-	-	SYM
ejpam-4958	116	17	2246	2246	NUM
ejpam-4958	116	18	2238	2238	NUM
ejpam-4958	116	19	a	a	DET
ejpam-4958	116	20	solution	solution	NOUN
ejpam-4958	116	21	of	of	ADP
ejpam-4958	116	22	equation	equation	NOUN
ejpam-4958	116	23	(	(	PUNCT
ejpam-4958	116	24	1	1	X
ejpam-4958	116	25	)	)	PUNCT
ejpam-4958	116	26	is	be	AUX
ejpam-4958	116	27	defined	define	VERB
ejpam-4958	116	28	as	as	ADP
ejpam-4958	116	29	a	a	DET
ejpam-4958	116	30	function	function	NOUN
ejpam-4958	116	31	that	that	PRON
ejpam-4958	116	32	exhibits	exhibit	VERB
ejpam-4958	116	33	the	the	DET
ejpam-4958	116	34	property	property	NOUN
ejpam-4958	116	35	r(u	r(u	PROPN
ejpam-4958	116	36	)	)	PUNCT
ejpam-4958	116	37	(	(	PUNCT
ejpam-4958	116	38	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	116	39	)	)	PUNCT
ejpam-4958	116	40	)	)	PUNCT
ejpam-4958	117	1	α	α	PROPN
ejpam-4958	117	2	∈	∈	PROPN
ejpam-4958	117	3	c1	c1	NOUN
ejpam-4958	117	4	[	[	X
ejpam-4958	117	5	tz,∞	tz,∞	PROPN
ejpam-4958	117	6	)	)	PUNCT
ejpam-4958	117	7	and	and	CCONJ
ejpam-4958	117	8	satisfies	satisfy	VERB
ejpam-4958	117	9	the	the	DET
ejpam-4958	117	10	equation	equation	NOUN
ejpam-4958	117	11	on	on	ADP
ejpam-4958	117	12	the	the	DET
ejpam-4958	117	13	interval	interval	NOUN
ejpam-4958	117	14	[	[	X
ejpam-4958	117	15	tz,∞	tz,∞	PROPN
ejpam-4958	117	16	)	)	PUNCT
ejpam-4958	117	17	.	.	PUNCT
ejpam-4958	118	1	the	the	DET
ejpam-4958	118	2	solutions	solution	NOUN
ejpam-4958	118	3	of	of	ADP
ejpam-4958	118	4	(	(	PUNCT
ejpam-4958	118	5	1	1	X
ejpam-4958	118	6	)	)	PUNCT
ejpam-4958	118	7	that	that	PRON
ejpam-4958	118	8	satisfy	satisfy	VERB
ejpam-4958	118	9	sup{|ϖ(u)|	sup{|ϖ(u)|	NOUN
ejpam-4958	118	10	:	:	PUNCT
ejpam-4958	118	11	u	u	NOUN
ejpam-4958	118	12	≥	≥	NOUN
ejpam-4958	118	13	t	t	PROPN
ejpam-4958	118	14	}	}	PUNCT
ejpam-4958	118	15	>	>	X
ejpam-4958	118	16	0	0	PUNCT
ejpam-4958	118	17	for	for	ADP
ejpam-4958	118	18	all	all	DET
ejpam-4958	118	19	t	t	PROPN
ejpam-4958	118	20	≥	≥	NOUN
ejpam-4958	118	21	tz	tz	NOUN
ejpam-4958	118	22	are	be	AUX
ejpam-4958	118	23	the	the	DET
ejpam-4958	118	24	only	only	ADJ
ejpam-4958	118	25	ones	one	NOUN
ejpam-4958	118	26	that	that	PRON
ejpam-4958	118	27	we	we	PRON
ejpam-4958	118	28	consider	consider	VERB
ejpam-4958	118	29	.	.	PUNCT
ejpam-4958	119	1	it	it	PRON
ejpam-4958	119	2	is	be	AUX
ejpam-4958	119	3	postulated	postulate	VERB
ejpam-4958	119	4	that	that	SCONJ
ejpam-4958	119	5	a	a	DET
ejpam-4958	119	6	viable	viable	ADJ
ejpam-4958	119	7	solution	solution	NOUN
ejpam-4958	119	8	exists	exist	VERB
ejpam-4958	119	9	for	for	ADP
ejpam-4958	119	10	equation	equation	NOUN
ejpam-4958	119	11	(	(	PUNCT
ejpam-4958	119	12	1	1	NUM
ejpam-4958	119	13	)	)	PUNCT
ejpam-4958	119	14	.	.	PUNCT
ejpam-4958	120	1	definition	definition	NOUN
ejpam-4958	120	2	1	1	NUM
ejpam-4958	120	3	.	.	PUNCT
ejpam-4958	121	1	a	a	DET
ejpam-4958	121	2	solution	solution	NOUN
ejpam-4958	121	3	ϖ(u	ϖ(u	PROPN
ejpam-4958	121	4	)	)	PUNCT
ejpam-4958	121	5	of	of	ADP
ejpam-4958	121	6	(	(	PUNCT
ejpam-4958	121	7	1	1	X
ejpam-4958	121	8	)	)	PUNCT
ejpam-4958	121	9	is	be	AUX
ejpam-4958	121	10	called	call	VERB
ejpam-4958	121	11	oscillatory	oscillatory	ADJ
ejpam-4958	121	12	if	if	SCONJ
ejpam-4958	121	13	it	it	PRON
ejpam-4958	121	14	has	have	VERB
ejpam-4958	121	15	arbitrary	arbitrary	ADJ
ejpam-4958	121	16	large	large	ADJ
ejpam-4958	121	17	zeros	zero	NOUN
ejpam-4958	121	18	on	on	ADP
ejpam-4958	121	19	[	[	X
ejpam-4958	121	20	tz,∞	tz,∞	PROPN
ejpam-4958	121	21	)	)	PUNCT
ejpam-4958	121	22	,	,	PUNCT
ejpam-4958	121	23	and	and	CCONJ
ejpam-4958	121	24	otherwise	otherwise	ADV
ejpam-4958	121	25	,	,	PUNCT
ejpam-4958	121	26	it	it	PRON
ejpam-4958	121	27	is	be	AUX
ejpam-4958	121	28	said	say	VERB
ejpam-4958	121	29	to	to	PART
ejpam-4958	121	30	be	be	AUX
ejpam-4958	121	31	nonoscillatory	nonoscillatory	ADJ
ejpam-4958	121	32	.	.	PUNCT
ejpam-4958	122	1	we	we	PRON
ejpam-4958	122	2	point	point	VERB
ejpam-4958	122	3	out	out	ADP
ejpam-4958	122	4	that	that	SCONJ
ejpam-4958	122	5	there	there	PRON
ejpam-4958	122	6	are	be	VERB
ejpam-4958	122	7	only	only	ADV
ejpam-4958	122	8	two	two	NUM
ejpam-4958	122	9	cases	case	NOUN
ejpam-4958	122	10	in	in	ADP
ejpam-4958	122	11	the	the	DET
ejpam-4958	122	12	investigation	investigation	NOUN
ejpam-4958	122	13	of	of	ADP
ejpam-4958	122	14	the	the	DET
ejpam-4958	122	15	asymptotic	asymptotic	ADJ
ejpam-4958	122	16	behaviour	behaviour	NOUN
ejpam-4958	122	17	of	of	ADP
ejpam-4958	122	18	the	the	DET
ejpam-4958	122	19	positive	positive	ADJ
ejpam-4958	122	20	solutions	solution	NOUN
ejpam-4958	122	21	of	of	ADP
ejpam-4958	122	22	(	(	PUNCT
ejpam-4958	122	23	1	1	NUM
ejpam-4958	122	24	):	):	PUNCT
ejpam-4958	122	25	case	case	NOUN
ejpam-4958	122	26	1	1	NUM
ejpam-4958	122	27	:	:	PUNCT
ejpam-4958	122	28	ϖ(u	ϖ(u	PROPN
ejpam-4958	122	29	)	)	PUNCT
ejpam-4958	122	30	>	>	X
ejpam-4958	122	31	0	0	NUM
ejpam-4958	122	32	,	,	PUNCT
ejpam-4958	122	33	ϖ(n−1)(u	ϖ(n−1)(u	NOUN
ejpam-4958	122	34	)	)	PUNCT
ejpam-4958	122	35	>	>	X
ejpam-4958	122	36	0	0	NUM
ejpam-4958	122	37	,	,	PUNCT
ejpam-4958	122	38	ϖ(n)(u	ϖ(n)(u	X
ejpam-4958	122	39	)	)	PUNCT
ejpam-4958	122	40	<	<	X
ejpam-4958	122	41	0	0	NUM
ejpam-4958	122	42	,	,	PUNCT
ejpam-4958	122	43	(	(	PUNCT
ejpam-4958	122	44	r(u	r(u	PROPN
ejpam-4958	122	45	)	)	PUNCT
ejpam-4958	122	46	(	(	PUNCT
ejpam-4958	122	47	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	122	48	)	)	PUNCT
ejpam-4958	122	49	)	)	PUNCT
ejpam-4958	122	50	α)′	α)′	X
ejpam-4958	122	51	<	<	X
ejpam-4958	122	52	0	0	NUM
ejpam-4958	122	53	,	,	PUNCT
ejpam-4958	122	54	case	case	NOUN
ejpam-4958	122	55	2	2	NUM
ejpam-4958	122	56	:	:	PUNCT
ejpam-4958	122	57	ϖ(u	ϖ(u	NOUN
ejpam-4958	122	58	)	)	PUNCT
ejpam-4958	122	59	>	>	X
ejpam-4958	122	60	0	0	NUM
ejpam-4958	122	61	,	,	PUNCT
ejpam-4958	122	62	ϖ(n−2)(u	ϖ(n−2)(u	NOUN
ejpam-4958	122	63	)	)	PUNCT
ejpam-4958	122	64	>	>	X
ejpam-4958	122	65	0	0	NUM
ejpam-4958	122	66	,	,	PUNCT
ejpam-4958	122	67	ϖ(n−1)(u	ϖ(n−1)(u	NOUN
ejpam-4958	122	68	)	)	PUNCT
ejpam-4958	122	69	<	<	X
ejpam-4958	122	70	0	0	NUM
ejpam-4958	122	71	,	,	PUNCT
ejpam-4958	122	72	(	(	PUNCT
ejpam-4958	122	73	r(u	r(u	PROPN
ejpam-4958	122	74	)	)	PUNCT
ejpam-4958	122	75	(	(	PUNCT
ejpam-4958	122	76	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	122	77	)	)	PUNCT
ejpam-4958	122	78	)	)	PUNCT
ejpam-4958	122	79	α)′	α)′	X
ejpam-4958	122	80	<	<	NOUN
ejpam-4958	122	81	0	0	NUM
ejpam-4958	122	82	.	.	PUNCT
ejpam-4958	123	1	the	the	DET
ejpam-4958	123	2	following	follow	VERB
ejpam-4958	123	3	lemma	lemma	PROPN
ejpam-4958	123	4	will	will	AUX
ejpam-4958	123	5	serve	serve	VERB
ejpam-4958	123	6	as	as	ADP
ejpam-4958	123	7	our	our	PRON
ejpam-4958	123	8	starting	starting	NOUN
ejpam-4958	123	9	point	point	NOUN
ejpam-4958	123	10	.	.	PUNCT
ejpam-4958	124	1	lemma	lemma	PROPN
ejpam-4958	124	2	1	1	NUM
ejpam-4958	124	3	.	.	PUNCT
ejpam-4958	125	1	[	[	X
ejpam-4958	125	2	17	17	NUM
ejpam-4958	125	3	]	]	PUNCT
ejpam-4958	125	4	.	.	PUNCT
ejpam-4958	126	1	let	let	VERB
ejpam-4958	126	2	g	g	PROPN
ejpam-4958	126	3	∈	∈	PROPN
ejpam-4958	126	4	cm	cm	NOUN
ejpam-4958	126	5	(	(	PUNCT
ejpam-4958	126	6	[	[	X
ejpam-4958	126	7	h0,∞	h0,∞	NOUN
ejpam-4958	126	8	)	)	PUNCT
ejpam-4958	126	9	,	,	PUNCT
ejpam-4958	126	10	r+	r+	X
ejpam-4958	126	11	)	)	PUNCT
ejpam-4958	126	12	such	such	ADJ
ejpam-4958	126	13	that	that	DET
ejpam-4958	126	14	g(m−1)(h)g(m)(h	g(m−1)(h)g(m)(h	NOUN
ejpam-4958	126	15	)	)	PUNCT
ejpam-4958	126	16	≤	≤	NOUN
ejpam-4958	126	17	0	0	NUM
ejpam-4958	127	1	for	for	ADP
ejpam-4958	127	2	all	all	DET
ejpam-4958	127	3	h	h	PROPN
ejpam-4958	127	4	≥	≥	NOUN
ejpam-4958	127	5	h1	h1	PROPN
ejpam-4958	127	6	.	.	PUNCT
ejpam-4958	128	1	if	if	SCONJ
ejpam-4958	128	2	limh→∞	limh→∞	PROPN
ejpam-4958	128	3	g(h	g(h	NUM
ejpam-4958	128	4	)	)	PUNCT
ejpam-4958	128	5	̸=	̸=	PROPN
ejpam-4958	128	6	0	0	NUM
ejpam-4958	128	7	,	,	PUNCT
ejpam-4958	128	8	∀λ	∀λ	X
ejpam-4958	128	9	∈	∈	PROPN
ejpam-4958	128	10	(	(	PUNCT
ejpam-4958	128	11	0	0	NUM
ejpam-4958	128	12	,	,	PUNCT
ejpam-4958	128	13	1	1	NUM
ejpam-4958	128	14	)	)	PUNCT
ejpam-4958	128	15	,	,	PUNCT
ejpam-4958	128	16	there	there	PRON
ejpam-4958	128	17	exists	exist	VERB
ejpam-4958	128	18	hλ	hλ	ADP
ejpam-4958	128	19	∈	∈	PROPN
ejpam-4958	128	20	[	[	X
ejpam-4958	128	21	h1,∞	h1,∞	X
ejpam-4958	128	22	)	)	PUNCT
ejpam-4958	128	23	such	such	ADJ
ejpam-4958	128	24	that	that	SCONJ
ejpam-4958	128	25	g	g	PROPN
ejpam-4958	128	26	≥	≥	PROPN
ejpam-4958	128	27	λ	λ	X
ejpam-4958	128	28	(	(	PUNCT
ejpam-4958	128	29	m−	m−	PROPN
ejpam-4958	128	30	1	1	NUM
ejpam-4958	128	31	)	)	PUNCT
ejpam-4958	128	32	!	!	PUNCT
ejpam-4958	129	1	hm−1	hm−1	PROPN
ejpam-4958	129	2	∣∣∣g(m−1	∣∣∣g(m−1	PROPN
ejpam-4958	129	3	)	)	PUNCT
ejpam-4958	129	4	∣∣∣	∣∣∣	NOUN
ejpam-4958	129	5	.	.	PUNCT
ejpam-4958	130	1	(	(	PUNCT
ejpam-4958	130	2	3	3	X
ejpam-4958	130	3	)	)	PUNCT
ejpam-4958	130	4	for	for	ADP
ejpam-4958	130	5	convenience	convenience	NOUN
ejpam-4958	130	6	,	,	PUNCT
ejpam-4958	130	7	we	we	PRON
ejpam-4958	130	8	write	write	VERB
ejpam-4958	130	9	δ(η	δ(η	ADV
ejpam-4958	130	10	)	)	PUNCT
ejpam-4958	131	1	=	=	SYM
ejpam-4958	132	1	∫	∫	PROPN
ejpam-4958	133	1	∞	∞	PROPN
ejpam-4958	133	2	t	t	PROPN
ejpam-4958	133	3	∫	∫	NUM
ejpam-4958	133	4	∞	∞	NUM
ejpam-4958	133	5	v	v	PART
ejpam-4958	133	6	[	[	PUNCT
ejpam-4958	133	7	1	1	NUM
ejpam-4958	133	8	r(x	r(x	PROPN
ejpam-4958	133	9	)	)	PUNCT
ejpam-4958	133	10	∫	∫	PROPN
ejpam-4958	134	1	∞	∞	NUM
ejpam-4958	134	2	x	x	INTJ
ejpam-4958	134	3	m∑	m∑	INTJ
ejpam-4958	134	4	i=1	i=1	PROPN
ejpam-4958	134	5	qi(s	qi(s	NUM
ejpam-4958	134	6	)	)	PUNCT
ejpam-4958	134	7	(	(	PUNCT
ejpam-4958	134	8	τi(s	τi(s	NUM
ejpam-4958	134	9	)	)	PUNCT
ejpam-4958	134	10	s	s	PART
ejpam-4958	134	11	)	)	PUNCT
ejpam-4958	134	12	β	β	X
ejpam-4958	134	13	ds	ds	X
ejpam-4958	134	14	]	]	SYM
ejpam-4958	134	15	1	1	NUM
ejpam-4958	134	16	/	/	SYM
ejpam-4958	134	17	α	α	NUM
ejpam-4958	134	18	dx	dx	PROPN
ejpam-4958	134	19			PROPN
ejpam-4958	134	20	dv	dv	PROPN
ejpam-4958	134	21	,	,	PUNCT
ejpam-4958	134	22	ϕ(σ	ϕ(σ	PROPN
ejpam-4958	134	23	)	)	PUNCT
ejpam-4958	134	24	=	=	PUNCT
ejpam-4958	134	25	∫∞	∫∞	PROPN
ejpam-4958	134	26	t	t	PROPN
ejpam-4958	134	27	(	(	PUNCT
ejpam-4958	134	28	η	η	PROPN
ejpam-4958	134	29	−	−	NOUN
ejpam-4958	134	30	u)n−4δ(η	u)n−4δ(η	NOUN
ejpam-4958	134	31	)	)	PUNCT
ejpam-4958	134	32	dη	dη	NOUN
ejpam-4958	134	33	(	(	PUNCT
ejpam-4958	134	34	n−	n−	NOUN
ejpam-4958	134	35	4	4	NUM
ejpam-4958	134	36	)	)	PUNCT
ejpam-4958	134	37	!	!	PUNCT
ejpam-4958	134	38	.	.	PUNCT
ejpam-4958	135	1	2	2	X
ejpam-4958	135	2	.	.	X
ejpam-4958	135	3	oscillation	oscillation	NOUN
ejpam-4958	135	4	criteria	criterion	NOUN
ejpam-4958	135	5	in	in	ADP
ejpam-4958	135	6	this	this	DET
ejpam-4958	135	7	section	section	NOUN
ejpam-4958	135	8	,	,	PUNCT
ejpam-4958	135	9	we	we	PRON
ejpam-4958	135	10	will	will	AUX
ejpam-4958	135	11	determine	determine	VERB
ejpam-4958	135	12	some	some	DET
ejpam-4958	135	13	oscillation	oscillation	NOUN
ejpam-4958	135	14	criteria	criterion	NOUN
ejpam-4958	135	15	for	for	ADP
ejpam-4958	135	16	(	(	PUNCT
ejpam-4958	135	17	1	1	NUM
ejpam-4958	135	18	)	)	PUNCT
ejpam-4958	135	19	.	.	PUNCT
ejpam-4958	136	1	theorem	theorem	NOUN
ejpam-4958	136	2	1	1	NUM
ejpam-4958	136	3	.	.	PUNCT
ejpam-4958	136	4	assume	assume	VERB
ejpam-4958	136	5	that	that	SCONJ
ejpam-4958	136	6	n	n	PROPN
ejpam-4958	136	7	≥	≥	NUM
ejpam-4958	136	8	2	2	NUM
ejpam-4958	136	9	and	and	CCONJ
ejpam-4958	136	10	(	(	PUNCT
ejpam-4958	136	11	2	2	NUM
ejpam-4958	136	12	)	)	PUNCT
ejpam-4958	136	13	holds.if	holds.if	NUM
ejpam-4958	136	14	w′(u	w′(u	PUNCT
ejpam-4958	136	15	)	)	PUNCT
ejpam-4958	137	1	+	+	CCONJ
ejpam-4958	137	2	m∑	m∑	CCONJ
ejpam-4958	137	3	i=1	i=1	ADP
ejpam-4958	137	4	qi(u	qi(u	NUM
ejpam-4958	137	5	)	)	PUNCT
ejpam-4958	138	1	(	(	PUNCT
ejpam-4958	138	2	λ0τ	λ0τ	PROPN
ejpam-4958	138	3	n−1	n−1	PROPN
ejpam-4958	138	4	i	i	PRON
ejpam-4958	138	5	(	(	PUNCT
ejpam-4958	138	6	u	u	NOUN
ejpam-4958	138	7	)	)	PUNCT
ejpam-4958	138	8	(	(	PUNCT
ejpam-4958	138	9	n−	n−	NOUN
ejpam-4958	138	10	1)!r	1)!r	NUM
ejpam-4958	138	11	1	1	NUM
ejpam-4958	138	12	α	α	NOUN
ejpam-4958	138	13	(	(	PUNCT
ejpam-4958	138	14	τi(u	τi(u	NUM
ejpam-4958	138	15	)	)	PUNCT
ejpam-4958	138	16	)	)	PUNCT
ejpam-4958	138	17	)	)	PUNCT
ejpam-4958	139	1	β	β	X
ejpam-4958	139	2	w	w	ADP
ejpam-4958	139	3	β	β	X
ejpam-4958	139	4	α	α	PROPN
ejpam-4958	139	5	(	(	PUNCT
ejpam-4958	139	6	τi(u	τi(u	NUM
ejpam-4958	139	7	)	)	PUNCT
ejpam-4958	139	8	)	)	PUNCT
ejpam-4958	140	1	=	=	PUNCT
ejpam-4958	140	2	0	0	NUM
ejpam-4958	140	3	,	,	PUNCT
ejpam-4958	140	4	(	(	PUNCT
ejpam-4958	140	5	4	4	X
ejpam-4958	140	6	)	)	PUNCT
ejpam-4958	140	7	is	be	AUX
ejpam-4958	140	8	oscillatory	oscillatory	ADJ
ejpam-4958	140	9	for	for	ADP
ejpam-4958	140	10	λ0	λ0	NOUN
ejpam-4958	140	11	∈	∈	NOUN
ejpam-4958	140	12	(	(	PUNCT
ejpam-4958	140	13	0	0	NUM
ejpam-4958	140	14	,	,	PUNCT
ejpam-4958	140	15	1	1	NUM
ejpam-4958	140	16	)	)	PUNCT
ejpam-4958	140	17	,	,	PUNCT
ejpam-4958	140	18	then	then	ADV
ejpam-4958	140	19	(	(	PUNCT
ejpam-4958	140	20	1	1	X
ejpam-4958	140	21	)	)	PUNCT
ejpam-4958	140	22	is	be	AUX
ejpam-4958	140	23	oscillatory	oscillatory	ADJ
ejpam-4958	140	24	.	.	PUNCT
ejpam-4958	141	1	proof	proof	NOUN
ejpam-4958	141	2	.	.	PUNCT
ejpam-4958	142	1	assume	assume	VERB
ejpam-4958	142	2	that	that	SCONJ
ejpam-4958	142	3	the	the	DET
ejpam-4958	142	4	non	non	ADJ
ejpam-4958	142	5	-	-	ADJ
ejpam-4958	142	6	oscillatory	oscillatory	ADJ
ejpam-4958	142	7	solution	solution	NOUN
ejpam-4958	142	8	ϖ	ϖ	X
ejpam-4958	142	9	to	to	ADP
ejpam-4958	142	10	equation	equation	NOUN
ejpam-4958	142	11	(	(	PUNCT
ejpam-4958	142	12	1	1	X
ejpam-4958	142	13	)	)	PUNCT
ejpam-4958	142	14	exists	exist	VERB
ejpam-4958	142	15	.	.	PUNCT
ejpam-4958	143	1	we	we	PRON
ejpam-4958	143	2	can	can	AUX
ejpam-4958	143	3	make	make	VERB
ejpam-4958	143	4	the	the	DET
ejpam-4958	143	5	assumption	assumption	NOUN
ejpam-4958	143	6	that	that	SCONJ
ejpam-4958	143	7	ϖ	ϖ	NOUN
ejpam-4958	143	8	will	will	AUX
ejpam-4958	143	9	eventually	eventually	ADV
ejpam-4958	143	10	be	be	AUX
ejpam-4958	143	11	positive	positive	ADJ
ejpam-4958	143	12	without	without	ADP
ejpam-4958	143	13	losing	lose	VERB
ejpam-4958	143	14	generality	generality	NOUN
ejpam-4958	143	15	.	.	PUNCT
ejpam-4958	144	1	let	let	VERB
ejpam-4958	144	2	w(u	w(u	NOUN
ejpam-4958	144	3	)	)	PUNCT
ejpam-4958	145	1	:	:	PUNCT
ejpam-4958	145	2	=	=	SYM
ejpam-4958	145	3	r(u	r(u	X
ejpam-4958	145	4	)	)	PUNCT
ejpam-4958	145	5	(	(	PUNCT
ejpam-4958	145	6	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	145	7	)	)	PUNCT
ejpam-4958	145	8	)	)	PUNCT
ejpam-4958	146	1	α	α	PROPN
ejpam-4958	146	2	,	,	PUNCT
ejpam-4958	146	3	s.	s.	PROPN
ejpam-4958	146	4	a.	a.	PROPN
ejpam-4958	146	5	balatta	balatta	PROPN
ejpam-4958	146	6	et	et	PROPN
ejpam-4958	146	7	al	al	PROPN
ejpam-4958	146	8	.	.	PUNCT
ejpam-4958	146	9	/	/	SYM
ejpam-4958	146	10	eur	eur	PROPN
ejpam-4958	146	11	.	.	PUNCT
ejpam-4958	147	1	j.	j.	PROPN
ejpam-4958	147	2	pure	pure	PROPN
ejpam-4958	147	3	appl	appl	PROPN
ejpam-4958	147	4	.	.	PROPN
ejpam-4958	147	5	math	math	PROPN
ejpam-4958	147	6	,	,	PUNCT
ejpam-4958	147	7	16	16	NUM
ejpam-4958	147	8	(	(	PUNCT
ejpam-4958	147	9	4	4	NUM
ejpam-4958	147	10	)	)	PUNCT
ejpam-4958	147	11	(	(	PUNCT
ejpam-4958	147	12	2023	2023	NUM
ejpam-4958	147	13	)	)	PUNCT
ejpam-4958	147	14	,	,	PUNCT
ejpam-4958	147	15	2234	2234	NUM
ejpam-4958	147	16	-	-	SYM
ejpam-4958	147	17	2246	2246	NUM
ejpam-4958	147	18	2239	2239	NUM
ejpam-4958	147	19	which	which	PRON
ejpam-4958	147	20	when	when	SCONJ
ejpam-4958	147	21	combined	combine	VERB
ejpam-4958	147	22	with	with	ADP
ejpam-4958	147	23	(	(	PUNCT
ejpam-4958	147	24	1	1	X
ejpam-4958	147	25	)	)	PUNCT
ejpam-4958	147	26	yields	yield	NOUN
ejpam-4958	147	27	w′(u	w′(u	NUM
ejpam-4958	147	28	)	)	PUNCT
ejpam-4958	148	1	+	+	CCONJ
ejpam-4958	148	2	m∑	m∑	VERB
ejpam-4958	148	3	i=1	i=1	PROPN
ejpam-4958	148	4	qi(u)ϖ	qi(u)ϖ	NUM
ejpam-4958	148	5	β	β	X
ejpam-4958	148	6	(	(	PUNCT
ejpam-4958	148	7	τi(u	τi(u	NUM
ejpam-4958	148	8	)	)	PUNCT
ejpam-4958	148	9	)	)	PUNCT
ejpam-4958	149	1	=	=	PUNCT
ejpam-4958	149	2	0	0	X
ejpam-4958	149	3	.	.	PUNCT
ejpam-4958	150	1	(	(	PUNCT
ejpam-4958	150	2	5	5	NUM
ejpam-4958	150	3	)	)	PUNCT
ejpam-4958	150	4	since	since	SCONJ
ejpam-4958	150	5	limu→∞ϖ(u	limu→∞ϖ(u	PROPN
ejpam-4958	150	6	)	)	PUNCT
ejpam-4958	150	7	̸=	̸=	PROPN
ejpam-4958	150	8	0	0	NUM
ejpam-4958	150	9	and	and	CCONJ
ejpam-4958	150	10	by	by	ADP
ejpam-4958	150	11	lemma	lemma	PROPN
ejpam-4958	150	12	(	(	PUNCT
ejpam-4958	150	13	1	1	NUM
ejpam-4958	150	14	)	)	PUNCT
ejpam-4958	150	15	,	,	PUNCT
ejpam-4958	150	16	we	we	PRON
ejpam-4958	150	17	get	get	VERB
ejpam-4958	150	18	(	(	PUNCT
ejpam-4958	150	19	ϖ	ϖ	NOUN
ejpam-4958	150	20	(	(	PUNCT
ejpam-4958	150	21	τi(u	τi(u	NUM
ejpam-4958	150	22	)	)	PUNCT
ejpam-4958	150	23	)	)	PUNCT
ejpam-4958	150	24	)	)	PUNCT
ejpam-4958	151	1	β	β	NOUN
ejpam-4958	151	2	≥	≥	NOUN
ejpam-4958	152	1	λβτβn−β	λβτβn−β	NUM
ejpam-4958	153	1	i	i	INTJ
ejpam-4958	153	2	(	(	PUNCT
ejpam-4958	153	3	(	(	PUNCT
ejpam-4958	153	4	n−	n−	NOUN
ejpam-4958	153	5	1)!)βr	1)!)βr	NUM
ejpam-4958	153	6	β	β	X
ejpam-4958	153	7	α	α	PROPN
ejpam-4958	153	8	(	(	PUNCT
ejpam-4958	153	9	τi(u	τi(u	NUM
ejpam-4958	153	10	)	)	PUNCT
ejpam-4958	153	11	)	)	PUNCT
ejpam-4958	154	1	(	(	PUNCT
ejpam-4958	154	2	r	r	NOUN
ejpam-4958	154	3	1	1	NUM
ejpam-4958	154	4	α	α	NOUN
ejpam-4958	154	5	(	(	PUNCT
ejpam-4958	154	6	τi(u))ϖ	τi(u))ϖ	PUNCT
ejpam-4958	154	7	(	(	PUNCT
ejpam-4958	154	8	n−1	n−1	PROPN
ejpam-4958	154	9	)	)	PUNCT
ejpam-4958	154	10	(	(	PUNCT
ejpam-4958	154	11	τi(u	τi(u	NUM
ejpam-4958	154	12	)	)	PUNCT
ejpam-4958	154	13	)	)	PUNCT
ejpam-4958	154	14	)	)	PUNCT
ejpam-4958	155	1	β	β	NOUN
ejpam-4958	155	2	,	,	PUNCT
ejpam-4958	155	3	∀λ	∀λ	X
ejpam-4958	155	4	∈	∈	PROPN
ejpam-4958	155	5	(	(	PUNCT
ejpam-4958	155	6	0	0	NUM
ejpam-4958	155	7	,	,	PUNCT
ejpam-4958	155	8	1	1	NUM
ejpam-4958	155	9	)	)	PUNCT
ejpam-4958	155	10	(	(	PUNCT
ejpam-4958	155	11	6	6	NUM
ejpam-4958	155	12	)	)	PUNCT
ejpam-4958	155	13	from	from	ADP
ejpam-4958	155	14	(	(	PUNCT
ejpam-4958	155	15	5	5	NUM
ejpam-4958	155	16	)	)	PUNCT
ejpam-4958	155	17	and	and	CCONJ
ejpam-4958	155	18	(	(	PUNCT
ejpam-4958	155	19	6	6	NUM
ejpam-4958	155	20	)	)	PUNCT
ejpam-4958	155	21	,	,	PUNCT
ejpam-4958	155	22	it	it	PRON
ejpam-4958	155	23	can	can	AUX
ejpam-4958	155	24	be	be	AUX
ejpam-4958	155	25	observed	observe	VERB
ejpam-4958	155	26	that	that	SCONJ
ejpam-4958	155	27	w′(u	w′(u	PUNCT
ejpam-4958	155	28	)	)	PUNCT
ejpam-4958	156	1	+	+	CCONJ
ejpam-4958	156	2	m∑	m∑	CCONJ
ejpam-4958	156	3	i=1	i=1	ADP
ejpam-4958	156	4	qi(u	qi(u	NUM
ejpam-4958	156	5	)	)	PUNCT
ejpam-4958	157	1	λβτβn−β	λβτβn−β	PROPN
ejpam-4958	157	2	i	i	PRON
ejpam-4958	157	3	(	(	PUNCT
ejpam-4958	157	4	(	(	PUNCT
ejpam-4958	157	5	n−	n−	NOUN
ejpam-4958	157	6	1)!)βr	1)!)βr	NUM
ejpam-4958	157	7	β	β	X
ejpam-4958	157	8	α	α	PROPN
ejpam-4958	157	9	(	(	PUNCT
ejpam-4958	157	10	τi(u	τi(u	NUM
ejpam-4958	157	11	)	)	PUNCT
ejpam-4958	157	12	)	)	PUNCT
ejpam-4958	158	1	(	(	PUNCT
ejpam-4958	158	2	r	r	NOUN
ejpam-4958	158	3	1	1	NUM
ejpam-4958	158	4	α	α	NOUN
ejpam-4958	158	5	(	(	PUNCT
ejpam-4958	158	6	τi(u))ϖ	τi(u))ϖ	PUNCT
ejpam-4958	158	7	(	(	PUNCT
ejpam-4958	158	8	n−1	n−1	PROPN
ejpam-4958	158	9	)	)	PUNCT
ejpam-4958	158	10	(	(	PUNCT
ejpam-4958	158	11	τi(u	τi(u	NUM
ejpam-4958	158	12	)	)	PUNCT
ejpam-4958	158	13	)	)	PUNCT
ejpam-4958	158	14	)	)	PUNCT
ejpam-4958	159	1	β	β	PROPN
ejpam-4958	159	2	≤	≤	NUM
ejpam-4958	159	3	0	0	NUM
ejpam-4958	159	4	.	.	PUNCT
ejpam-4958	160	1	so	so	ADV
ejpam-4958	160	2	,	,	PUNCT
ejpam-4958	160	3	we	we	PRON
ejpam-4958	160	4	obtain	obtain	VERB
ejpam-4958	160	5	w(u	w(u	NOUN
ejpam-4958	160	6	)	)	PUNCT
ejpam-4958	160	7	>	>	X
ejpam-4958	160	8	0	0	PUNCT
ejpam-4958	160	9	and	and	CCONJ
ejpam-4958	160	10	w′(u	w′(u	NUM
ejpam-4958	160	11	)	)	PUNCT
ejpam-4958	160	12	+	+	CCONJ
ejpam-4958	160	13	m∑	m∑	CCONJ
ejpam-4958	160	14	i=1	i=1	ADP
ejpam-4958	160	15	qi(u	qi(u	NUM
ejpam-4958	160	16	)	)	PUNCT
ejpam-4958	160	17	(	(	PUNCT
ejpam-4958	160	18	λτn−1	λτn−1	PROPN
ejpam-4958	160	19	i	i	PRON
ejpam-4958	160	20	(	(	PUNCT
ejpam-4958	160	21	u	u	NOUN
ejpam-4958	160	22	)	)	PUNCT
ejpam-4958	160	23	(	(	PUNCT
ejpam-4958	160	24	n−	n−	NOUN
ejpam-4958	160	25	1)!r1	1)!r1	NUM
ejpam-4958	160	26	/	/	SYM
ejpam-4958	160	27	α	α	PROPN
ejpam-4958	160	28	(	(	PUNCT
ejpam-4958	160	29	τi(u	τi(u	NUM
ejpam-4958	160	30	)	)	PUNCT
ejpam-4958	160	31	)	)	PUNCT
ejpam-4958	160	32	)	)	PUNCT
ejpam-4958	160	33	β	β	X
ejpam-4958	160	34	wβ	wβ	ADP
ejpam-4958	160	35	/	/	SYM
ejpam-4958	160	36	α	α	PROPN
ejpam-4958	160	37	(	(	PUNCT
ejpam-4958	160	38	τi(u	τi(u	NUM
ejpam-4958	160	39	)	)	PUNCT
ejpam-4958	160	40	)	)	PUNCT
ejpam-4958	160	41	≤	≤	ADV
ejpam-4958	160	42	0	0	NUM
ejpam-4958	160	43	.	.	PUNCT
ejpam-4958	161	1	by	by	ADP
ejpam-4958	161	2	applying	apply	VERB
ejpam-4958	161	3	corollary	corollary	NOUN
ejpam-4958	161	4	1	1	NUM
ejpam-4958	161	5	from	from	ADP
ejpam-4958	161	6	reference	reference	NOUN
ejpam-4958	161	7	[	[	X
ejpam-4958	161	8	8	8	NUM
ejpam-4958	161	9	]	]	PUNCT
ejpam-4958	161	10	,	,	PUNCT
ejpam-4958	161	11	it	it	PRON
ejpam-4958	161	12	can	can	AUX
ejpam-4958	161	13	be	be	AUX
ejpam-4958	161	14	observed	observe	VERB
ejpam-4958	161	15	that	that	SCONJ
ejpam-4958	161	16	(	(	PUNCT
ejpam-4958	161	17	4	4	X
ejpam-4958	161	18	)	)	PUNCT
ejpam-4958	161	19	possesses	possess	VERB
ejpam-4958	161	20	a	a	DET
ejpam-4958	161	21	solution	solution	NOUN
ejpam-4958	161	22	that	that	PRON
ejpam-4958	161	23	is	be	AUX
ejpam-4958	161	24	positively	positively	ADV
ejpam-4958	161	25	valued	value	VERB
ejpam-4958	161	26	.	.	PUNCT
ejpam-4958	162	1	this	this	PRON
ejpam-4958	162	2	leads	lead	VERB
ejpam-4958	162	3	to	to	ADP
ejpam-4958	162	4	a	a	DET
ejpam-4958	162	5	clear	clear	ADJ
ejpam-4958	162	6	contradiction	contradiction	NOUN
ejpam-4958	162	7	,	,	PUNCT
ejpam-4958	162	8	thereby	thereby	ADV
ejpam-4958	162	9	establishing	establish	VERB
ejpam-4958	162	10	the	the	DET
ejpam-4958	162	11	completion	completion	NOUN
ejpam-4958	162	12	of	of	ADP
ejpam-4958	162	13	the	the	DET
ejpam-4958	162	14	proof	proof	NOUN
ejpam-4958	162	15	.	.	PUNCT
ejpam-4958	163	1	theorem	theorem	NOUN
ejpam-4958	163	2	2	2	NUM
ejpam-4958	163	3	.	.	PUNCT
ejpam-4958	164	1	let	let	VERB
ejpam-4958	164	2	n	n	PRON
ejpam-4958	164	3	≥	≥	NOUN
ejpam-4958	164	4	2	2	NUM
ejpam-4958	164	5	,	,	PUNCT
ejpam-4958	164	6	and	and	CCONJ
ejpam-4958	164	7	assume	assume	VERB
ejpam-4958	164	8	(	(	PUNCT
ejpam-4958	164	9	2	2	NUM
ejpam-4958	164	10	)	)	PUNCT
ejpam-4958	164	11	holds	hold	NOUN
ejpam-4958	164	12	and	and	CCONJ
ejpam-4958	164	13	there	there	PRON
ejpam-4958	164	14	exists	exist	VERB
ejpam-4958	164	15	a	a	DET
ejpam-4958	164	16	constant	constant	ADJ
ejpam-4958	164	17	λ0	λ0	NOUN
ejpam-4958	164	18	∈	∈	NOUN
ejpam-4958	164	19	(	(	PUNCT
ejpam-4958	164	20	0	0	NUM
ejpam-4958	164	21	,	,	PUNCT
ejpam-4958	164	22	1	1	NUM
ejpam-4958	164	23	)	)	PUNCT
ejpam-4958	164	24	.	.	PUNCT
ejpam-4958	165	1	if	if	SCONJ
ejpam-4958	165	2	lim	lim	PROPN
ejpam-4958	165	3	sup	sup	VERB
ejpam-4958	165	4	u→∞	u→∞	NUM
ejpam-4958	165	5	∫	∫	PROPN
ejpam-4958	165	6	u	u	NOUN
ejpam-4958	165	7	u0	u0	PROPN
ejpam-4958	165	8	[	[	PUNCT
ejpam-4958	165	9	hβ−α	hβ−α	NOUN
ejpam-4958	165	10	m∑	m∑	CCONJ
ejpam-4958	165	11	i=1	i=1	PROPN
ejpam-4958	165	12	qi(s	qi(s	VERB
ejpam-4958	165	13	)	)	PUNCT
ejpam-4958	165	14	(	(	PUNCT
ejpam-4958	165	15	λ1	λ1	PROPN
ejpam-4958	165	16	(	(	PUNCT
ejpam-4958	165	17	n−	n−	NOUN
ejpam-4958	165	18	2	2	NUM
ejpam-4958	165	19	)	)	PUNCT
ejpam-4958	165	20	!	!	PUNCT
ejpam-4958	166	1	τn−2	τn−2	INTJ
ejpam-4958	166	2	i	i	PRON
ejpam-4958	166	3	(	(	PUNCT
ejpam-4958	166	4	s	s	NOUN
ejpam-4958	166	5	)	)	PUNCT
ejpam-4958	166	6	)	)	PUNCT
ejpam-4958	167	1	β	β	PROPN
ejpam-4958	167	2	θα(s)−	θα(s)−	VERB
ejpam-4958	167	3	αα+1	αα+1	NUM
ejpam-4958	167	4	(	(	PUNCT
ejpam-4958	167	5	α+	α+	NUM
ejpam-4958	167	6	1)α+1	1)α+1	NUM
ejpam-4958	167	7	1	1	NUM
ejpam-4958	167	8	θ(s)r1	θ(s)r1	PROPN
ejpam-4958	167	9	/	/	SYM
ejpam-4958	167	10	α(s	α(s	PROPN
ejpam-4958	167	11	)	)	PUNCT
ejpam-4958	167	12	]	]	PUNCT
ejpam-4958	168	1	ds	ds	NOUN
ejpam-4958	168	2	=	=	SYM
ejpam-4958	168	3	∞	∞	PROPN
ejpam-4958	168	4	(	(	PUNCT
ejpam-4958	168	5	7	7	NUM
ejpam-4958	168	6	)	)	PUNCT
ejpam-4958	168	7	for	for	ADP
ejpam-4958	168	8	some	some	DET
ejpam-4958	168	9	λ1	λ1	PROPN
ejpam-4958	168	10	∈	∈	PROPN
ejpam-4958	168	11	(	(	PUNCT
ejpam-4958	168	12	0	0	NUM
ejpam-4958	168	13	,	,	PUNCT
ejpam-4958	168	14	1	1	NUM
ejpam-4958	168	15	)	)	PUNCT
ejpam-4958	168	16	and	and	CCONJ
ejpam-4958	168	17	∀h	∀h	X
ejpam-4958	168	18	>	>	X
ejpam-4958	168	19	0	0	NUM
ejpam-4958	168	20	,	,	PUNCT
ejpam-4958	168	21	then	then	ADV
ejpam-4958	168	22	each	each	DET
ejpam-4958	168	23	solution	solution	NOUN
ejpam-4958	168	24	to	to	ADP
ejpam-4958	168	25	(	(	PUNCT
ejpam-4958	168	26	1	1	X
ejpam-4958	168	27	)	)	PUNCT
ejpam-4958	168	28	is	be	AUX
ejpam-4958	168	29	oscillatory	oscillatory	ADJ
ejpam-4958	168	30	or	or	CCONJ
ejpam-4958	168	31	converges	converge	NOUN
ejpam-4958	168	32	to	to	ADP
ejpam-4958	168	33	zero	zero	NUM
ejpam-4958	168	34	,	,	PUNCT
ejpam-4958	168	35	i.e.	i.e.	X
ejpam-4958	168	36	θ(u	θ(u	NOUN
ejpam-4958	168	37	)	)	PUNCT
ejpam-4958	168	38	:	:	PUNCT
ejpam-4958	169	1	=	=	SYM
ejpam-4958	169	2	∫	∫	PROPN
ejpam-4958	169	3	∞	∞	NUM
ejpam-4958	169	4	u	u	NOUN
ejpam-4958	169	5	1	1	NUM
ejpam-4958	169	6	r1	r1	PROPN
ejpam-4958	169	7	/	/	SYM
ejpam-4958	169	8	α(s	α(s	PROPN
ejpam-4958	169	9	)	)	PUNCT
ejpam-4958	169	10	ds	ds	ADJ
ejpam-4958	169	11	.	.	NOUN
ejpam-4958	169	12	proof	proof	NOUN
ejpam-4958	169	13	.	.	PUNCT
ejpam-4958	170	1	let	let	VERB
ejpam-4958	170	2	ω(u	ω(u	NUM
ejpam-4958	170	3	)	)	PUNCT
ejpam-4958	171	1	=	=	PRON
ejpam-4958	171	2	(	(	PUNCT
ejpam-4958	171	3	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	171	4	)	)	PUNCT
ejpam-4958	171	5	)	)	PUNCT
ejpam-4958	172	1	α	α	PROPN
ejpam-4958	172	2	(	(	PUNCT
ejpam-4958	172	3	r(−1	r(−1	PROPN
ejpam-4958	172	4	/	/	SYM
ejpam-4958	172	5	α)(u)ϖ(n−2)(u	α)(u)ϖ(n−2)(u	VERB
ejpam-4958	172	6	)	)	PUNCT
ejpam-4958	172	7	)	)	PUNCT
ejpam-4958	173	1	α	α	PROPN
ejpam-4958	173	2	.	.	PUNCT
ejpam-4958	174	1	(	(	PUNCT
ejpam-4958	174	2	8)	8)	NUM
ejpam-4958	174	3	ω(u	ω(u	NUM
ejpam-4958	174	4	)	)	PUNCT
ejpam-4958	175	1	<	<	X
ejpam-4958	175	2	0	0	NUM
ejpam-4958	175	3	for	for	ADP
ejpam-4958	175	4	u	u	PROPN
ejpam-4958	175	5	≥	≥	NOUN
ejpam-4958	175	6	u1	u1	PROPN
ejpam-4958	175	7	.	.	PUNCT
ejpam-4958	176	1	divided	divide	VERB
ejpam-4958	176	2	(	(	PUNCT
ejpam-4958	176	3	8)by	8)by	PROPN
ejpam-4958	176	4	r1	r1	PROPN
ejpam-4958	176	5	/	/	SYM
ejpam-4958	176	6	α(s	α(s	PROPN
ejpam-4958	176	7	)	)	PUNCT
ejpam-4958	176	8	and	and	CCONJ
ejpam-4958	176	9	integrated	integrate	VERB
ejpam-4958	176	10	from	from	ADP
ejpam-4958	176	11	u	u	NOUN
ejpam-4958	176	12	to	to	ADP
ejpam-4958	176	13	ζ	ζ	NOUN
ejpam-4958	176	14	yields	yield	NOUN
ejpam-4958	176	15	ϖ(n−2)(ζ	ϖ(n−2)(ζ	NOUN
ejpam-4958	176	16	)	)	PUNCT
ejpam-4958	176	17	≤	≤	NOUN
ejpam-4958	176	18	ϖ(n−2)(u	ϖ(n−2)(u	NOUN
ejpam-4958	176	19	)	)	PUNCT
ejpam-4958	176	20	+	+	CCONJ
ejpam-4958	176	21	r1	r1	PROPN
ejpam-4958	176	22	/	/	SYM
ejpam-4958	176	23	α(u)ϖ(n−1)(u	α(u)ϖ(n−1)(u	PROPN
ejpam-4958	176	24	)	)	PUNCT
ejpam-4958	176	25	∫	∫	PROPN
ejpam-4958	176	26	ζ	ζ	PROPN
ejpam-4958	176	27	t	t	PROPN
ejpam-4958	176	28	1	1	NUM
ejpam-4958	176	29	r1	r1	PROPN
ejpam-4958	176	30	/	/	SYM
ejpam-4958	176	31	α(s	α(s	PROPN
ejpam-4958	176	32	)	)	PUNCT
ejpam-4958	176	33	ds	ds	PROPN
ejpam-4958	176	34	.	.	PROPN
ejpam-4958	176	35	s.	s.	PROPN
ejpam-4958	176	36	a.	a.	PROPN
ejpam-4958	176	37	balatta	balatta	PROPN
ejpam-4958	176	38	et	et	PROPN
ejpam-4958	176	39	al	al	PROPN
ejpam-4958	176	40	.	.	PUNCT
ejpam-4958	176	41	/	/	SYM
ejpam-4958	176	42	eur	eur	PROPN
ejpam-4958	176	43	.	.	PUNCT
ejpam-4958	177	1	j.	j.	PROPN
ejpam-4958	177	2	pure	pure	PROPN
ejpam-4958	177	3	appl	appl	PROPN
ejpam-4958	177	4	.	.	PROPN
ejpam-4958	177	5	math	math	PROPN
ejpam-4958	177	6	,	,	PUNCT
ejpam-4958	177	7	16	16	NUM
ejpam-4958	177	8	(	(	PUNCT
ejpam-4958	177	9	4	4	NUM
ejpam-4958	177	10	)	)	PUNCT
ejpam-4958	177	11	(	(	PUNCT
ejpam-4958	177	12	2023	2023	NUM
ejpam-4958	177	13	)	)	PUNCT
ejpam-4958	177	14	,	,	PUNCT
ejpam-4958	177	15	2234	2234	NUM
ejpam-4958	177	16	-	-	SYM
ejpam-4958	177	17	2246	2246	NUM
ejpam-4958	177	18	2240	2240	NUM
ejpam-4958	177	19	given	give	VERB
ejpam-4958	177	20	that	that	SCONJ
ejpam-4958	177	21	the	the	DET
ejpam-4958	177	22	function	function	NOUN
ejpam-4958	177	23	r(u	r(u	PROPN
ejpam-4958	177	24	)	)	PUNCT
ejpam-4958	177	25	(	(	PUNCT
ejpam-4958	177	26	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	177	27	)	)	PUNCT
ejpam-4958	177	28	)	)	PUNCT
ejpam-4958	178	1	α	α	PROPN
ejpam-4958	178	2	has	have	VERB
ejpam-4958	178	3	a	a	DET
ejpam-4958	178	4	decreasing	decrease	VERB
ejpam-4958	178	5	trend	trend	NOUN
ejpam-4958	178	6	,	,	PUNCT
ejpam-4958	178	7	it	it	PRON
ejpam-4958	178	8	can	can	AUX
ejpam-4958	178	9	be	be	AUX
ejpam-4958	178	10	concluded	conclude	VERB
ejpam-4958	178	11	that	that	SCONJ
ejpam-4958	178	12	r1	r1	PROPN
ejpam-4958	178	13	/	/	SYM
ejpam-4958	178	14	α(s)ϖ(n−1)(s	α(s)ϖ(n−1)(s	PROPN
ejpam-4958	178	15	)	)	PUNCT
ejpam-4958	178	16	≤	≤	PUNCT
ejpam-4958	178	17	r1	r1	PROPN
ejpam-4958	178	18	/	/	SYM
ejpam-4958	178	19	α(u)ϖ(n−1)(u	α(u)ϖ(n−1)(u	PROPN
ejpam-4958	178	20	)	)	PUNCT
ejpam-4958	178	21	,	,	PUNCT
ejpam-4958	178	22	s	s	VERB
ejpam-4958	178	23	≥	≥	PROPN
ejpam-4958	178	24	u	u	NOUN
ejpam-4958	178	25	≥	≥	NOUN
ejpam-4958	178	26	u1	u1	NOUN
ejpam-4958	178	27	.	.	PUNCT
ejpam-4958	179	1	hence	hence	ADV
ejpam-4958	179	2	we	we	PRON
ejpam-4958	179	3	obtain	obtain	VERB
ejpam-4958	179	4	0	0	NUM
ejpam-4958	179	5	≤	≤	NUM
ejpam-4958	179	6	r1	r1	PROPN
ejpam-4958	179	7	/	/	SYM
ejpam-4958	179	8	α(u)ϖ(n−1)(u)θ(u	α(u)ϖ(n−1)(u)θ(u	NUM
ejpam-4958	179	9	)	)	PUNCT
ejpam-4958	179	10	+	+	NOUN
ejpam-4958	179	11	ϖ(n−2)(u	ϖ(n−2)(u	NOUN
ejpam-4958	179	12	)	)	PUNCT
ejpam-4958	179	13	,	,	PUNCT
ejpam-4958	179	14	when	when	SCONJ
ejpam-4958	179	15	ζ	ζ	X
ejpam-4958	179	16	→	→	SYM
ejpam-4958	179	17	∞.	∞.	PROPN
ejpam-4958	179	18	this	this	PRON
ejpam-4958	179	19	leads	lead	VERB
ejpam-4958	179	20	to	to	ADP
ejpam-4958	179	21	−r1	−r1	PROPN
ejpam-4958	179	22	/	/	SYM
ejpam-4958	179	23	α(u)ϖ(n−1)(u	α(u)ϖ(n−1)(u	NOUN
ejpam-4958	179	24	)	)	PUNCT
ejpam-4958	180	1	ϖ(n−2)(u	ϖ(n−2)(u	ADJ
ejpam-4958	180	2	)	)	PUNCT
ejpam-4958	180	3	θ(u	θ(u	NUM
ejpam-4958	180	4	)	)	PUNCT
ejpam-4958	180	5	≤	≤	NOUN
ejpam-4958	180	6	1	1	NUM
ejpam-4958	180	7	.	.	PUNCT
ejpam-4958	181	1	therefore	therefore	ADV
ejpam-4958	181	2	,	,	PUNCT
ejpam-4958	181	3	based	base	VERB
ejpam-4958	181	4	on	on	ADP
ejpam-4958	181	5	(	(	PUNCT
ejpam-4958	181	6	8)	8)	NUM
ejpam-4958	181	7	,	,	PUNCT
ejpam-4958	181	8	it	it	PRON
ejpam-4958	181	9	can	can	AUX
ejpam-4958	181	10	be	be	AUX
ejpam-4958	181	11	observed	observe	VERB
ejpam-4958	181	12	that	that	SCONJ
ejpam-4958	181	13	−ω(u)θα(u	−ω(u)θα(u	NOUN
ejpam-4958	181	14	)	)	PUNCT
ejpam-4958	181	15	≤	≤	NUM
ejpam-4958	181	16	1	1	NUM
ejpam-4958	181	17	.	.	PUNCT
ejpam-4958	182	1	(	(	PUNCT
ejpam-4958	182	2	9	9	NUM
ejpam-4958	182	3	)	)	PUNCT
ejpam-4958	182	4	according	accord	VERB
ejpam-4958	182	5	to	to	ADP
ejpam-4958	182	6	(	(	PUNCT
ejpam-4958	182	7	8)	8)	NUM
ejpam-4958	182	8	ω′(u	ω′(u	NUM
ejpam-4958	182	9	)	)	PUNCT
ejpam-4958	182	10	=	=	PRON
ejpam-4958	182	11	(	(	PUNCT
ejpam-4958	182	12	r(u	r(u	PROPN
ejpam-4958	182	13	)	)	PUNCT
ejpam-4958	182	14	(	(	PUNCT
ejpam-4958	182	15	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	182	16	)	)	PUNCT
ejpam-4958	182	17	)	)	PUNCT
ejpam-4958	183	1	α)′	α)′	NOUN
ejpam-4958	183	2	(	(	PUNCT
ejpam-4958	183	3	ϖ(n−2)(u	ϖ(n−2)(u	NOUN
ejpam-4958	183	4	)	)	PUNCT
ejpam-4958	183	5	)	)	PUNCT
ejpam-4958	184	1	α	α	PRON
ejpam-4958	184	2	−	−	NOUN
ejpam-4958	184	3	α	α	PRON
ejpam-4958	184	4	r(u	r(u	PROPN
ejpam-4958	184	5	)	)	PUNCT
ejpam-4958	184	6	(	(	PUNCT
ejpam-4958	184	7	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	184	8	)	)	PUNCT
ejpam-4958	184	9	)	)	PUNCT
ejpam-4958	185	1	α+1	α+1	NOUN
ejpam-4958	185	2	(	(	PUNCT
ejpam-4958	185	3	ϖ(n−2)(u	ϖ(n−2)(u	ADJ
ejpam-4958	185	4	)	)	PUNCT
ejpam-4958	185	5	)	)	PUNCT
ejpam-4958	186	1	α+1	α+1	NUM
ejpam-4958	186	2	.	.	PUNCT
ejpam-4958	187	1	(	(	PUNCT
ejpam-4958	187	2	10	10	NUM
ejpam-4958	187	3	)	)	PUNCT
ejpam-4958	187	4	employing	employ	VERB
ejpam-4958	187	5	lemma	lemma	PROPN
ejpam-4958	187	6	1	1	NUM
ejpam-4958	187	7	yields	yield	NOUN
ejpam-4958	187	8	ϖ(u	ϖ(u	NOUN
ejpam-4958	187	9	)	)	PUNCT
ejpam-4958	187	10	ϖ(n−2)(u	ϖ(n−2)(u	NOUN
ejpam-4958	187	11	)	)	PUNCT
ejpam-4958	187	12	≥	≥	NOUN
ejpam-4958	187	13	λ	λ	NOUN
ejpam-4958	187	14	(	(	PUNCT
ejpam-4958	187	15	n−	n−	NOUN
ejpam-4958	187	16	2	2	NUM
ejpam-4958	187	17	)	)	PUNCT
ejpam-4958	187	18	!	!	PUNCT
ejpam-4958	188	1	un−2	un−2	VERB
ejpam-4958	188	2	,	,	PUNCT
ejpam-4958	188	3	∀λ	∀λ	X
ejpam-4958	188	4	∈	∈	PROPN
ejpam-4958	188	5	(	(	PUNCT
ejpam-4958	188	6	0	0	NUM
ejpam-4958	188	7	,	,	PUNCT
ejpam-4958	188	8	1	1	NUM
ejpam-4958	188	9	)	)	PUNCT
ejpam-4958	188	10	.	.	PUNCT
ejpam-4958	189	1	then	then	ADV
ejpam-4958	189	2	a	a	DET
ejpam-4958	189	3	constant	constant	ADJ
ejpam-4958	189	4	h	h	NOUN
ejpam-4958	189	5	>	>	X
ejpam-4958	189	6	0	0	NUM
ejpam-4958	189	7	exists	exist	VERB
ejpam-4958	189	8	so	so	SCONJ
ejpam-4958	189	9	that	that	SCONJ
ejpam-4958	189	10	ω′(u	ω′(u	NUM
ejpam-4958	189	11	)	)	PUNCT
ejpam-4958	189	12	=	=	SYM
ejpam-4958	190	1	−	−	NOUN
ejpam-4958	190	2	m∑	m∑	CCONJ
ejpam-4958	190	3	i=1	i=1	PRON
ejpam-4958	190	4	qi(u	qi(u	NUM
ejpam-4958	190	5	)	)	PUNCT
ejpam-4958	190	6	(	(	PUNCT
ejpam-4958	190	7	ϖ(n−2	ϖ(n−2	NOUN
ejpam-4958	190	8	)	)	PUNCT
ejpam-4958	190	9	(	(	PUNCT
ejpam-4958	190	10	τi(u	τi(u	NUM
ejpam-4958	190	11	)	)	PUNCT
ejpam-4958	190	12	)	)	PUNCT
ejpam-4958	191	1	)	)	PUNCT
ejpam-4958	191	2	β−α	β−α	NOUN
ejpam-4958	191	3	ϖβ	ϖβ	ADP
ejpam-4958	191	4	(	(	PUNCT
ejpam-4958	191	5	τi(u	τi(u	NUM
ejpam-4958	191	6	)	)	PUNCT
ejpam-4958	191	7	)	)	PUNCT
ejpam-4958	191	8	(	(	PUNCT
ejpam-4958	191	9	ϖ(n−2	ϖ(n−2	NOUN
ejpam-4958	191	10	)	)	PUNCT
ejpam-4958	191	11	(	(	PUNCT
ejpam-4958	191	12	τi(u	τi(u	NUM
ejpam-4958	191	13	)	)	PUNCT
ejpam-4958	191	14	)	)	PUNCT
ejpam-4958	191	15	)	)	PUNCT
ejpam-4958	192	1	β	β	X
ejpam-4958	192	2	(	(	PUNCT
ejpam-4958	192	3	ϖ(n−2	ϖ(n−2	PROPN
ejpam-4958	192	4	)	)	PUNCT
ejpam-4958	192	5	(	(	PUNCT
ejpam-4958	192	6	τi(u	τi(u	NUM
ejpam-4958	192	7	)	)	PUNCT
ejpam-4958	192	8	)	)	PUNCT
ejpam-4958	192	9	)	)	PUNCT
ejpam-4958	193	1	α	α	X
ejpam-4958	193	2	(	(	PUNCT
ejpam-4958	193	3	ϖ(n−2)(u	ϖ(n−2)(u	ADJ
ejpam-4958	193	4	)	)	PUNCT
ejpam-4958	193	5	)	)	PUNCT
ejpam-4958	193	6	α	α	PROPN
ejpam-4958	193	7	−α	−α	PROPN
ejpam-4958	193	8	ω(α+1)/α(u	ω(α+1)/α(u	NOUN
ejpam-4958	193	9	)	)	PUNCT
ejpam-4958	193	10	r1	r1	PROPN
ejpam-4958	193	11	/	/	SYM
ejpam-4958	193	12	α(u	α(u	PROPN
ejpam-4958	193	13	)	)	PUNCT
ejpam-4958	193	14	,	,	PUNCT
ejpam-4958	193	15	≤	≤	NUM
ejpam-4958	193	16	−hβ−α	−hβ−α	NOUN
ejpam-4958	193	17	m∑	m∑	CCONJ
ejpam-4958	193	18	i=1	i=1	PRON
ejpam-4958	193	19	qi(u	qi(u	NUM
ejpam-4958	193	20	)	)	PUNCT
ejpam-4958	193	21	(	(	PUNCT
ejpam-4958	193	22	λ	λ	X
ejpam-4958	193	23	(	(	PUNCT
ejpam-4958	193	24	n−	n−	NOUN
ejpam-4958	193	25	2	2	NUM
ejpam-4958	193	26	)	)	PUNCT
ejpam-4958	193	27	!	!	PUNCT
ejpam-4958	194	1	τn−2	τn−2	INTJ
ejpam-4958	194	2	i	i	PRON
ejpam-4958	194	3	(	(	PUNCT
ejpam-4958	194	4	u	u	NOUN
ejpam-4958	194	5	)	)	PUNCT
ejpam-4958	194	6	)	)	PUNCT
ejpam-4958	195	1	β	β	PROPN
ejpam-4958	195	2	−	−	PROPN
ejpam-4958	195	3	α	α	PROPN
ejpam-4958	195	4	ω(α+1)/α(u	ω(α+1)/α(u	NOUN
ejpam-4958	195	5	)	)	PUNCT
ejpam-4958	195	6	r1	r1	PROPN
ejpam-4958	195	7	/	/	SYM
ejpam-4958	195	8	α(u	α(u	PROPN
ejpam-4958	195	9	)	)	PUNCT
ejpam-4958	195	10	.	.	PUNCT
ejpam-4958	196	1	(	(	PUNCT
ejpam-4958	196	2	11	11	X
ejpam-4958	196	3	)	)	PUNCT
ejpam-4958	196	4	multiplying	multiply	VERB
ejpam-4958	196	5	this	this	DET
ejpam-4958	196	6	inequality	inequality	NOUN
ejpam-4958	196	7	by	by	ADP
ejpam-4958	196	8	θα(u	θα(u	NOUN
ejpam-4958	196	9	)	)	PUNCT
ejpam-4958	196	10	and	and	CCONJ
ejpam-4958	196	11	integrating	integrate	VERB
ejpam-4958	196	12	it	it	PRON
ejpam-4958	196	13	,	,	PUNCT
ejpam-4958	196	14	we	we	PRON
ejpam-4958	196	15	obtain	obtain	VERB
ejpam-4958	196	16	θα(u)ω(u)−	θα(u)ω(u)−	PROPN
ejpam-4958	196	17	θα	θα	NOUN
ejpam-4958	196	18	(	(	PUNCT
ejpam-4958	196	19	u1)ω	u1)ω	PROPN
ejpam-4958	196	20	(	(	PUNCT
ejpam-4958	196	21	u1	u1	NOUN
ejpam-4958	196	22	)	)	PUNCT
ejpam-4958	196	23	+	+	CCONJ
ejpam-4958	197	1	α	α	PRON
ejpam-4958	197	2	∫	∫	PROPN
ejpam-4958	197	3	u	u	PROPN
ejpam-4958	197	4	t1	t1	PROPN
ejpam-4958	197	5	r−	r−	PROPN
ejpam-4958	197	6	1	1	NUM
ejpam-4958	197	7	α	α	NOUN
ejpam-4958	197	8	(	(	PUNCT
ejpam-4958	197	9	s)θα−1(s)ω(s	s)θα−1(s)ω(s	ADJ
ejpam-4958	197	10	)	)	PUNCT
ejpam-4958	197	11	ds	ds	PROPN
ejpam-4958	198	1	+	+	CCONJ
ejpam-4958	198	2	∫	∫	NOUN
ejpam-4958	198	3	u	u	PROPN
ejpam-4958	198	4	u1	u1	NOUN
ejpam-4958	198	5	hβ−α	hβ−α	NOUN
ejpam-4958	198	6	m∑	m∑	CCONJ
ejpam-4958	198	7	i=1	i=1	PROPN
ejpam-4958	198	8	qi(s	qi(s	NUM
ejpam-4958	198	9	)	)	PUNCT
ejpam-4958	198	10	(	(	PUNCT
ejpam-4958	198	11	λ	λ	X
ejpam-4958	198	12	(	(	PUNCT
ejpam-4958	198	13	n−	n−	NOUN
ejpam-4958	198	14	2	2	NUM
ejpam-4958	198	15	)	)	PUNCT
ejpam-4958	198	16	!	!	PUNCT
ejpam-4958	199	1	τn−2	τn−2	INTJ
ejpam-4958	199	2	i	i	PRON
ejpam-4958	199	3	(	(	PUNCT
ejpam-4958	199	4	s	s	NOUN
ejpam-4958	199	5	)	)	PUNCT
ejpam-4958	199	6	)	)	PUNCT
ejpam-4958	200	1	β	β	NOUN
ejpam-4958	200	2	θα(s	θα(s	PRON
ejpam-4958	200	3	)	)	PUNCT
ejpam-4958	200	4	ds+	ds+	ADJ
ejpam-4958	200	5	∫	∫	PROPN
ejpam-4958	200	6	u	u	PROPN
ejpam-4958	200	7	u1	u1	VERB
ejpam-4958	200	8	α	α	NOUN
ejpam-4958	200	9	ω(α+1)/α(s	ω(α+1)/α(s	NOUN
ejpam-4958	200	10	)	)	PUNCT
ejpam-4958	200	11	r1	r1	PROPN
ejpam-4958	200	12	/	/	SYM
ejpam-4958	200	13	α(s	α(s	PROPN
ejpam-4958	200	14	)	)	PUNCT
ejpam-4958	200	15	θα(s	θα(s	PUNCT
ejpam-4958	200	16	)	)	PUNCT
ejpam-4958	200	17	ds	ds	ADJ
ejpam-4958	200	18	≤	≤	NOUN
ejpam-4958	200	19	0	0	X
ejpam-4958	200	20	.	.	PUNCT
ejpam-4958	201	1	now	now	ADV
ejpam-4958	201	2	let	let	VERB
ejpam-4958	201	3	b	b	NOUN
ejpam-4958	201	4	:	:	PUNCT
ejpam-4958	201	5	=	=	SYM
ejpam-4958	201	6	r−1	r−1	PROPN
ejpam-4958	201	7	/	/	SYM
ejpam-4958	201	8	α(s)θα−1(s	α(s)θα−1(	NOUN
ejpam-4958	201	9	)	)	PUNCT
ejpam-4958	201	10	,	,	PUNCT
ejpam-4958	201	11	a	a	DET
ejpam-4958	201	12	:	:	PUNCT
ejpam-4958	201	13	=	=	SYM
ejpam-4958	201	14	θα(s)/r1	θα(s)/r1	PROPN
ejpam-4958	201	15	/	/	SYM
ejpam-4958	201	16	α(s	α(s	PROPN
ejpam-4958	201	17	)	)	PUNCT
ejpam-4958	201	18	and	and	CCONJ
ejpam-4958	201	19	ε	ε	PROPN
ejpam-4958	201	20	:	:	PUNCT
ejpam-4958	201	21	=	=	PUNCT
ejpam-4958	201	22	−ω(s	−ω(s	NOUN
ejpam-4958	201	23	)	)	PUNCT
ejpam-4958	201	24	.	.	PUNCT
ejpam-4958	202	1	when	when	SCONJ
ejpam-4958	202	2	we	we	PRON
ejpam-4958	202	3	use	use	VERB
ejpam-4958	202	4	the	the	DET
ejpam-4958	202	5	inequality	inequality	NOUN
ejpam-4958	202	6	aε(α+1)/α	aε(α+1)/α	NOUN
ejpam-4958	202	7	≥	≥	NUM
ejpam-4958	202	8	−	−	NOUN
ejpam-4958	202	9	αα	αα	INTJ
ejpam-4958	202	10	(	(	PUNCT
ejpam-4958	202	11	α+	α+	NUM
ejpam-4958	202	12	1)α+1	1)α+1	NUM
ejpam-4958	202	13	bα+1	bα+1	NOUN
ejpam-4958	202	14	+	+	NOUN
ejpam-4958	202	15	aαb	aαb	NOUN
ejpam-4958	202	16	aα	aα	NOUN
ejpam-4958	202	17	ε	ε	PROPN
ejpam-4958	202	18	,	,	PUNCT
ejpam-4958	202	19	s.	s.	PROPN
ejpam-4958	202	20	a.	a.	PROPN
ejpam-4958	202	21	balatta	balatta	PROPN
ejpam-4958	202	22	et	et	PROPN
ejpam-4958	202	23	al	al	PROPN
ejpam-4958	202	24	.	.	PUNCT
ejpam-4958	202	25	/	/	SYM
ejpam-4958	202	26	eur	eur	PROPN
ejpam-4958	202	27	.	.	PUNCT
ejpam-4958	203	1	j.	j.	PROPN
ejpam-4958	203	2	pure	pure	PROPN
ejpam-4958	203	3	appl	appl	PROPN
ejpam-4958	203	4	.	.	PROPN
ejpam-4958	203	5	math	math	PROPN
ejpam-4958	203	6	,	,	PUNCT
ejpam-4958	203	7	16	16	NUM
ejpam-4958	203	8	(	(	PUNCT
ejpam-4958	203	9	4	4	NUM
ejpam-4958	203	10	)	)	PUNCT
ejpam-4958	203	11	(	(	PUNCT
ejpam-4958	203	12	2023	2023	NUM
ejpam-4958	203	13	)	)	PUNCT
ejpam-4958	203	14	,	,	PUNCT
ejpam-4958	203	15	2234	2234	NUM
ejpam-4958	203	16	-	-	SYM
ejpam-4958	203	17	2246	2246	NUM
ejpam-4958	203	18	2241	2241	NUM
ejpam-4958	203	19	we	we	PRON
ejpam-4958	203	20	have∫	have∫	VERB
ejpam-4958	203	21	u	u	PROPN
ejpam-4958	203	22	u1	u1	PROPN
ejpam-4958	203	23	[	[	PUNCT
ejpam-4958	203	24	hβ−α	hβ−α	NOUN
ejpam-4958	203	25	m∑	m∑	VERB
ejpam-4958	203	26	i=1	i=1	PROPN
ejpam-4958	203	27	qi(s	qi(s	NUM
ejpam-4958	203	28	)	)	PUNCT
ejpam-4958	203	29	(	(	PUNCT
ejpam-4958	203	30	λ	λ	X
ejpam-4958	203	31	(	(	PUNCT
ejpam-4958	203	32	n−	n−	NOUN
ejpam-4958	203	33	2	2	NUM
ejpam-4958	203	34	)	)	PUNCT
ejpam-4958	203	35	!	!	PUNCT
ejpam-4958	204	1	τi	τi	PROPN
ejpam-4958	204	2	n−2(s	n−2(s	PROPN
ejpam-4958	204	3	)	)	PUNCT
ejpam-4958	204	4	)	)	PUNCT
ejpam-4958	205	1	β	β	PROPN
ejpam-4958	205	2	θα(s)−	θα(s)−	VERB
ejpam-4958	205	3	αα+1	αα+1	NUM
ejpam-4958	205	4	(	(	PUNCT
ejpam-4958	205	5	α+	α+	NUM
ejpam-4958	205	6	1)α+1	1)α+1	NUM
ejpam-4958	205	7	1	1	NUM
ejpam-4958	205	8	θ(s)r1	θ(s)r1	PROPN
ejpam-4958	205	9	/	/	SYM
ejpam-4958	205	10	α(s	α(s	PROPN
ejpam-4958	205	11	)	)	PUNCT
ejpam-4958	205	12	]	]	PUNCT
ejpam-4958	205	13	ds	ds	ADJ
ejpam-4958	205	14	≤	≤	NUM
ejpam-4958	205	15	θα	θα	NOUN
ejpam-4958	205	16	(	(	PUNCT
ejpam-4958	205	17	u1)ω	u1)ω	PROPN
ejpam-4958	205	18	(	(	PUNCT
ejpam-4958	205	19	u1	u1	NOUN
ejpam-4958	205	20	)	)	PUNCT
ejpam-4958	205	21	+	+	NUM
ejpam-4958	206	1	1	1	NUM
ejpam-4958	206	2	,	,	PUNCT
ejpam-4958	206	3	due	due	ADP
ejpam-4958	206	4	to	to	ADP
ejpam-4958	206	5	(	(	PUNCT
ejpam-4958	206	6	9	9	NUM
ejpam-4958	206	7	)	)	PUNCT
ejpam-4958	206	8	,	,	PUNCT
ejpam-4958	206	9	which	which	PRON
ejpam-4958	206	10	contradicts	contradict	VERB
ejpam-4958	206	11	(	(	PUNCT
ejpam-4958	206	12	7	7	NUM
ejpam-4958	206	13	)	)	PUNCT
ejpam-4958	206	14	.	.	PUNCT
ejpam-4958	207	1	this	this	PRON
ejpam-4958	207	2	completes	complete	VERB
ejpam-4958	207	3	the	the	DET
ejpam-4958	207	4	proof	proof	NOUN
ejpam-4958	207	5	.	.	PUNCT
ejpam-4958	208	1	the	the	DET
ejpam-4958	208	2	next	next	ADJ
ejpam-4958	208	3	corollary	corollary	NOUN
ejpam-4958	208	4	presented	present	VERB
ejpam-4958	208	5	is	be	AUX
ejpam-4958	208	6	derived	derive	VERB
ejpam-4958	208	7	from	from	ADP
ejpam-4958	208	8	the	the	DET
ejpam-4958	208	9	oscillation	oscillation	NOUN
ejpam-4958	208	10	of	of	ADP
ejpam-4958	208	11	(	(	PUNCT
ejpam-4958	208	12	4	4	NUM
ejpam-4958	208	13	)	)	PUNCT
ejpam-4958	208	14	and	and	CCONJ
ejpam-4958	208	15	theorem	theorem	VERB
ejpam-4958	208	16	2.1.1	2.1.1	NUM
ejpam-4958	208	17	of	of	ADP
ejpam-4958	208	18	[	[	X
ejpam-4958	208	19	23	23	NUM
ejpam-4958	208	20	]	]	PUNCT
ejpam-4958	208	21	.	.	PUNCT
ejpam-4958	209	1	corollary	corollary	ADJ
ejpam-4958	209	2	1	1	NUM
ejpam-4958	209	3	.	.	PUNCT
ejpam-4958	210	1	let	let	VERB
ejpam-4958	210	2	n	n	PRON
ejpam-4958	210	3	≥	≥	NOUN
ejpam-4958	210	4	2	2	NUM
ejpam-4958	210	5	.	.	PUNCT
ejpam-4958	210	6	suppose	suppose	VERB
ejpam-4958	210	7	that	that	SCONJ
ejpam-4958	210	8	(	(	PUNCT
ejpam-4958	210	9	2	2	X
ejpam-4958	210	10	)	)	PUNCT
ejpam-4958	210	11	holds	hold	NOUN
ejpam-4958	210	12	and	and	CCONJ
ejpam-4958	210	13	α	α	NOUN
ejpam-4958	210	14	=	=	SYM
ejpam-4958	210	15	β	β	X
ejpam-4958	210	16	.	.	PUNCT
ejpam-4958	211	1	if	if	SCONJ
ejpam-4958	211	2	lim	lim	PROPN
ejpam-4958	211	3	inf	inf	PROPN
ejpam-4958	211	4	u→∞	u→∞	NUM
ejpam-4958	211	5	∫	∫	PROPN
ejpam-4958	211	6	u	u	PROPN
ejpam-4958	211	7	τ(u	τ(u	PROPN
ejpam-4958	211	8	)	)	PUNCT
ejpam-4958	212	1	m∑	m∑	CCONJ
ejpam-4958	212	2	i=1	i=1	PROPN
ejpam-4958	212	3	qi(s	qi(s	NUM
ejpam-4958	212	4	)	)	PUNCT
ejpam-4958	212	5	(	(	PUNCT
ejpam-4958	212	6	τn−1	τn−1	PROPN
ejpam-4958	212	7	i	i	PRON
ejpam-4958	212	8	(	(	PUNCT
ejpam-4958	212	9	s	s	NOUN
ejpam-4958	212	10	)	)	PUNCT
ejpam-4958	212	11	)	)	PUNCT
ejpam-4958	213	1	α	α	PRON
ejpam-4958	213	2	r	r	NOUN
ejpam-4958	213	3	(	(	PUNCT
ejpam-4958	213	4	τi(s	τi(s	NUM
ejpam-4958	213	5	)	)	PUNCT
ejpam-4958	213	6	)	)	PUNCT
ejpam-4958	214	1	ds	ds	ADP
ejpam-4958	214	2	>	>	X
ejpam-4958	214	3	(	(	PUNCT
ejpam-4958	214	4	(	(	PUNCT
ejpam-4958	214	5	n−	n−	NOUN
ejpam-4958	214	6	1)!)α	1)!)α	NUM
ejpam-4958	214	7	e	e	NOUN
ejpam-4958	214	8	,	,	PUNCT
ejpam-4958	214	9	(	(	PUNCT
ejpam-4958	214	10	12	12	NUM
ejpam-4958	214	11	)	)	PUNCT
ejpam-4958	214	12	and	and	CCONJ
ejpam-4958	214	13	lim	lim	PROPN
ejpam-4958	214	14	sup	sup	PROPN
ejpam-4958	214	15	∫	∫	PROPN
ejpam-4958	214	16	u	u	NOUN
ejpam-4958	214	17	u0	u0	PROPN
ejpam-4958	214	18	[	[	PUNCT
ejpam-4958	214	19	m∑	m∑	INTJ
ejpam-4958	214	20	i=1	i=1	PROPN
ejpam-4958	214	21	qi(s	qi(s	NUM
ejpam-4958	214	22	)	)	PUNCT
ejpam-4958	214	23	(	(	PUNCT
ejpam-4958	214	24	λ1	λ1	PROPN
ejpam-4958	214	25	(	(	PUNCT
ejpam-4958	214	26	n−	n−	NOUN
ejpam-4958	214	27	2	2	NUM
ejpam-4958	214	28	)	)	PUNCT
ejpam-4958	214	29	!	!	PUNCT
ejpam-4958	215	1	τn−2	τn−2	INTJ
ejpam-4958	215	2	i	i	PRON
ejpam-4958	215	3	(	(	PUNCT
ejpam-4958	215	4	s	s	NOUN
ejpam-4958	215	5	)	)	PUNCT
ejpam-4958	215	6	)	)	PUNCT
ejpam-4958	216	1	α	α	PRON
ejpam-4958	216	2	θα(s)−	θα(s)−	VERB
ejpam-4958	216	3	αα+1	αα+1	NUM
ejpam-4958	216	4	(	(	PUNCT
ejpam-4958	216	5	α+	α+	NUM
ejpam-4958	216	6	1)α+1	1)α+1	NUM
ejpam-4958	216	7	1	1	NUM
ejpam-4958	216	8	θ(s)r1	θ(s)r1	PROPN
ejpam-4958	216	9	/	/	SYM
ejpam-4958	216	10	α(s	α(s	PROPN
ejpam-4958	216	11	)	)	PUNCT
ejpam-4958	216	12	]	]	PUNCT
ejpam-4958	217	1	ds	ds	PROPN
ejpam-4958	217	2	=	=	SYM
ejpam-4958	217	3	∞	∞	PROPN
ejpam-4958	217	4	,	,	PUNCT
ejpam-4958	217	5	(	(	PUNCT
ejpam-4958	217	6	13	13	NUM
ejpam-4958	217	7	)	)	PUNCT
ejpam-4958	217	8	for	for	ADP
ejpam-4958	217	9	λ	λ	PROPN
ejpam-4958	217	10	∈	∈	PROPN
ejpam-4958	217	11	(	(	PUNCT
ejpam-4958	217	12	0	0	NUM
ejpam-4958	217	13	,	,	PUNCT
ejpam-4958	217	14	1	1	NUM
ejpam-4958	217	15	)	)	PUNCT
ejpam-4958	217	16	,	,	PUNCT
ejpam-4958	217	17	then	then	ADV
ejpam-4958	217	18	all	all	DET
ejpam-4958	217	19	solutions	solution	NOUN
ejpam-4958	217	20	of	of	ADP
ejpam-4958	217	21	(	(	PUNCT
ejpam-4958	217	22	1	1	NUM
ejpam-4958	217	23	)	)	PUNCT
ejpam-4958	217	24	are	be	AUX
ejpam-4958	217	25	oscillatory	oscillatory	ADJ
ejpam-4958	217	26	or	or	CCONJ
ejpam-4958	217	27	tend	tend	VERB
ejpam-4958	217	28	to	to	PART
ejpam-4958	217	29	zero	zero	NUM
ejpam-4958	217	30	.	.	PUNCT
ejpam-4958	218	1	the	the	DET
ejpam-4958	218	2	following	follow	VERB
ejpam-4958	218	3	corollary	corollary	NOUN
ejpam-4958	218	4	is	be	AUX
ejpam-4958	218	5	derived	derive	VERB
ejpam-4958	218	6	from	from	ADP
ejpam-4958	218	7	(	(	PUNCT
ejpam-4958	218	8	4	4	NUM
ejpam-4958	218	9	)	)	PUNCT
ejpam-4958	218	10	and	and	CCONJ
ejpam-4958	218	11	theorem	theorem	VERB
ejpam-4958	218	12	1	1	NUM
ejpam-4958	218	13	of	of	ADP
ejpam-4958	218	14	[	[	X
ejpam-4958	218	15	6	6	NUM
ejpam-4958	218	16	]	]	PUNCT
ejpam-4958	218	17	.	.	PUNCT
ejpam-4958	219	1	corollary	corollary	ADJ
ejpam-4958	219	2	2	2	NUM
ejpam-4958	219	3	.	.	PUNCT
ejpam-4958	220	1	let	let	VERB
ejpam-4958	220	2	n	n	PRON
ejpam-4958	220	3	≥	≥	NOUN
ejpam-4958	220	4	2	2	NUM
ejpam-4958	220	5	.	.	PUNCT
ejpam-4958	220	6	suppose	suppose	VERB
ejpam-4958	220	7	that	that	SCONJ
ejpam-4958	220	8	(	(	PUNCT
ejpam-4958	220	9	2	2	X
ejpam-4958	220	10	)	)	PUNCT
ejpam-4958	220	11	holds	hold	NOUN
ejpam-4958	220	12	and	and	CCONJ
ejpam-4958	220	13	lim	lim	PROPN
ejpam-4958	220	14	sup	sup	PROPN
ejpam-4958	220	15	u→∞	u→∞	NUM
ejpam-4958	220	16	∫	∫	PROPN
ejpam-4958	220	17	u	u	PROPN
ejpam-4958	220	18	τ(u	τ(u	PROPN
ejpam-4958	220	19	)	)	PUNCT
ejpam-4958	220	20	m∑	m∑	CCONJ
ejpam-4958	220	21	i=1	i=1	PROPN
ejpam-4958	220	22	qi(s	qi(s	NUM
ejpam-4958	220	23	)	)	PUNCT
ejpam-4958	220	24	(	(	PUNCT
ejpam-4958	220	25	τn−1	τn−1	PROPN
ejpam-4958	220	26	i	i	PRON
ejpam-4958	220	27	(	(	PUNCT
ejpam-4958	220	28	s	s	NOUN
ejpam-4958	220	29	)	)	PUNCT
ejpam-4958	220	30	)	)	PUNCT
ejpam-4958	220	31	β	β	NOUN
ejpam-4958	220	32	rβ	rβ	PROPN
ejpam-4958	220	33	/	/	SYM
ejpam-4958	220	34	α	α	PROPN
ejpam-4958	220	35	(	(	PUNCT
ejpam-4958	220	36	τi(s	τi(s	NUM
ejpam-4958	220	37	)	)	PUNCT
ejpam-4958	220	38	)	)	PUNCT
ejpam-4958	221	1	ds	ds	ADP
ejpam-4958	221	2	>	>	X
ejpam-4958	221	3	0	0	X
ejpam-4958	221	4	.	.	PUNCT
ejpam-4958	222	1	(	(	PUNCT
ejpam-4958	222	2	14	14	NUM
ejpam-4958	222	3	)	)	PUNCT
ejpam-4958	222	4	for	for	ADP
ejpam-4958	222	5	α	α	X
ejpam-4958	222	6	>	>	X
ejpam-4958	222	7	β	β	X
ejpam-4958	222	8	and	and	CCONJ
ejpam-4958	222	9	τ	τ	PROPN
ejpam-4958	222	10	is	be	AUX
ejpam-4958	222	11	an	an	DET
ejpam-4958	222	12	increasing	increase	VERB
ejpam-4958	222	13	function	function	NOUN
ejpam-4958	222	14	.	.	PUNCT
ejpam-4958	223	1	if	if	SCONJ
ejpam-4958	223	2	(	(	PUNCT
ejpam-4958	223	3	7	7	X
ejpam-4958	223	4	)	)	PUNCT
ejpam-4958	223	5	holds	hold	VERB
ejpam-4958	223	6	for	for	ADP
ejpam-4958	223	7	some	some	DET
ejpam-4958	223	8	λ	λ	NOUN
ejpam-4958	223	9	∈	∈	PROPN
ejpam-4958	223	10	(	(	PUNCT
ejpam-4958	223	11	0	0	NUM
ejpam-4958	223	12	,	,	PUNCT
ejpam-4958	223	13	1	1	NUM
ejpam-4958	223	14	)	)	PUNCT
ejpam-4958	223	15	and	and	CCONJ
ejpam-4958	223	16	∀h	∀h	X
ejpam-4958	223	17	>	>	X
ejpam-4958	223	18	0	0	NUM
ejpam-4958	223	19	,	,	PUNCT
ejpam-4958	223	20	then	then	ADV
ejpam-4958	223	21	all	all	DET
ejpam-4958	223	22	solutions	solution	NOUN
ejpam-4958	223	23	of	of	ADP
ejpam-4958	223	24	(	(	PUNCT
ejpam-4958	223	25	1	1	NUM
ejpam-4958	223	26	)	)	PUNCT
ejpam-4958	223	27	are	be	AUX
ejpam-4958	223	28	oscillatory	oscillatory	ADJ
ejpam-4958	223	29	or	or	CCONJ
ejpam-4958	223	30	tend	tend	VERB
ejpam-4958	223	31	to	to	PART
ejpam-4958	223	32	zero	zero	NUM
ejpam-4958	223	33	.	.	PUNCT
ejpam-4958	224	1	theorem	theorem	NOUN
ejpam-4958	224	2	3	3	NUM
ejpam-4958	224	3	.	.	PUNCT
ejpam-4958	225	1	if	if	SCONJ
ejpam-4958	225	2	all	all	DET
ejpam-4958	225	3	solutions	solution	NOUN
ejpam-4958	225	4	of	of	ADP
ejpam-4958	225	5	φ′(u	φ′(u	PROPN
ejpam-4958	225	6	)	)	PUNCT
ejpam-4958	225	7	+	+	NOUN
ejpam-4958	225	8	hβ−α	hβ−α	NOUN
ejpam-4958	225	9	m∑	m∑	CCONJ
ejpam-4958	225	10	i=1	i=1	PROPN
ejpam-4958	225	11	qi(u	qi(u	NUM
ejpam-4958	225	12	)	)	PUNCT
ejpam-4958	225	13	+	+	CCONJ
ejpam-4958	225	14	α	α	PRON
ejpam-4958	225	15	∫∞	∫∞	NOUN
ejpam-4958	225	16	t	t	PROPN
ejpam-4958	225	17	(	(	PUNCT
ejpam-4958	225	18	η	η	PROPN
ejpam-4958	225	19	−	−	NOUN
ejpam-4958	225	20	u)n−4δ(η	u)n−4δ(η	NOUN
ejpam-4958	225	21	)	)	PUNCT
ejpam-4958	225	22	dη	dη	NOUN
ejpam-4958	225	23	(	(	PUNCT
ejpam-4958	225	24	n−	n−	NOUN
ejpam-4958	225	25	4	4	NUM
ejpam-4958	225	26	)	)	PUNCT
ejpam-4958	225	27	!	!	PUNCT
ejpam-4958	226	1	φ	φ	NOUN
ejpam-4958	227	1	α+1	α+1	NUM
ejpam-4958	227	2	α	α	PROPN
ejpam-4958	227	3	(	(	PUNCT
ejpam-4958	227	4	u	u	NOUN
ejpam-4958	227	5	)	)	PUNCT
ejpam-4958	227	6	=	=	SYM
ejpam-4958	227	7	0	0	NUM
ejpam-4958	228	1	(	(	PUNCT
ejpam-4958	228	2	15	15	NUM
ejpam-4958	228	3	)	)	PUNCT
ejpam-4958	228	4	are	be	AUX
ejpam-4958	228	5	oscillatory	oscillatory	ADJ
ejpam-4958	228	6	,	,	PUNCT
ejpam-4958	228	7	then	then	ADV
ejpam-4958	228	8	(	(	PUNCT
ejpam-4958	228	9	1	1	X
ejpam-4958	228	10	)	)	PUNCT
ejpam-4958	228	11	is	be	AUX
ejpam-4958	228	12	oscillatory	oscillatory	ADJ
ejpam-4958	228	13	.	.	PUNCT
ejpam-4958	229	1	proof	proof	NOUN
ejpam-4958	229	2	.	.	PUNCT
ejpam-4958	230	1	by	by	ADP
ejpam-4958	230	2	lemma	lemma	PROPN
ejpam-4958	230	3	1	1	NUM
ejpam-4958	230	4	and	and	CCONJ
ejpam-4958	230	5	case	case	NOUN
ejpam-4958	230	6	2	2	NUM
ejpam-4958	230	7	,	,	PUNCT
ejpam-4958	230	8	and	and	CCONJ
ejpam-4958	230	9	integrating	integrate	VERB
ejpam-4958	230	10	(	(	PUNCT
ejpam-4958	230	11	1	1	NUM
ejpam-4958	230	12	)	)	PUNCT
ejpam-4958	230	13	from	from	ADP
ejpam-4958	230	14	u	u	PROPN
ejpam-4958	230	15	→	→	SYM
ejpam-4958	230	16	a	a	X
ejpam-4958	230	17	,	,	PUNCT
ejpam-4958	230	18	we	we	PRON
ejpam-4958	230	19	have	have	AUX
ejpam-4958	230	20	r(a	r(a	VERB
ejpam-4958	230	21	)	)	PUNCT
ejpam-4958	230	22	(	(	PUNCT
ejpam-4958	230	23	ϖ(n−1)(a	ϖ(n−1)(a	NOUN
ejpam-4958	230	24	)	)	PUNCT
ejpam-4958	230	25	)	)	PUNCT
ejpam-4958	231	1	α	α	NOUN
ejpam-4958	231	2	=	=	SYM
ejpam-4958	231	3	r(u	r(u	PROPN
ejpam-4958	231	4	)	)	PUNCT
ejpam-4958	231	5	(	(	PUNCT
ejpam-4958	231	6	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	231	7	)	)	PUNCT
ejpam-4958	231	8	)	)	PUNCT
ejpam-4958	232	1	κ	κ	PROPN
ejpam-4958	232	2	−	−	PROPN
ejpam-4958	232	3	∫	∫	PROPN
ejpam-4958	232	4	a	a	DET
ejpam-4958	232	5	u	u	NOUN
ejpam-4958	232	6	m∑	m∑	VERB
ejpam-4958	232	7	i=1	i=1	PROPN
ejpam-4958	232	8	qi(s)ϖ	qi(s)ϖ	PROPN
ejpam-4958	232	9	β	β	X
ejpam-4958	232	10	(	(	PUNCT
ejpam-4958	232	11	τi(s	τi(s	NUM
ejpam-4958	232	12	)	)	PUNCT
ejpam-4958	232	13	)	)	PUNCT
ejpam-4958	233	1	ds	ds	PROPN
ejpam-4958	233	2	.	.	PUNCT
ejpam-4958	233	3	(	(	PUNCT
ejpam-4958	233	4	16	16	NUM
ejpam-4958	233	5	)	)	PUNCT
ejpam-4958	233	6	by	by	ADP
ejpam-4958	233	7	lemma	lemma	PROPN
ejpam-4958	233	8	1	1	NUM
ejpam-4958	233	9	we	we	PRON
ejpam-4958	233	10	get	get	VERB
ejpam-4958	233	11	ϖ	ϖ	INTJ
ejpam-4958	233	12	(	(	PUNCT
ejpam-4958	233	13	τi(u	τi(u	NUM
ejpam-4958	233	14	)	)	PUNCT
ejpam-4958	233	15	)	)	PUNCT
ejpam-4958	234	1	ϖ(u	ϖ(u	PROPN
ejpam-4958	234	2	)	)	PUNCT
ejpam-4958	234	3	≥	≥	NOUN
ejpam-4958	234	4	λ	λ	PROPN
ejpam-4958	234	5	τi(u	τi(u	PUNCT
ejpam-4958	234	6	)	)	PUNCT
ejpam-4958	234	7	u	u	NOUN
ejpam-4958	234	8	,	,	PUNCT
ejpam-4958	234	9	s.	s.	PROPN
ejpam-4958	234	10	a.	a.	PROPN
ejpam-4958	234	11	balatta	balatta	PROPN
ejpam-4958	234	12	et	et	PROPN
ejpam-4958	234	13	al	al	PROPN
ejpam-4958	234	14	.	.	PUNCT
ejpam-4958	234	15	/	/	SYM
ejpam-4958	234	16	eur	eur	PROPN
ejpam-4958	234	17	.	.	PUNCT
ejpam-4958	235	1	j.	j.	PROPN
ejpam-4958	235	2	pure	pure	PROPN
ejpam-4958	235	3	appl	appl	PROPN
ejpam-4958	235	4	.	.	PROPN
ejpam-4958	235	5	math	math	PROPN
ejpam-4958	235	6	,	,	PUNCT
ejpam-4958	235	7	16	16	NUM
ejpam-4958	235	8	(	(	PUNCT
ejpam-4958	235	9	4	4	NUM
ejpam-4958	235	10	)	)	PUNCT
ejpam-4958	235	11	(	(	PUNCT
ejpam-4958	235	12	2023	2023	NUM
ejpam-4958	235	13	)	)	PUNCT
ejpam-4958	235	14	,	,	PUNCT
ejpam-4958	235	15	2234	2234	NUM
ejpam-4958	235	16	-	-	SYM
ejpam-4958	235	17	2246	2246	NUM
ejpam-4958	235	18	2242	2242	NUM
ejpam-4958	235	19	which	which	PRON
ejpam-4958	235	20	with	with	ADP
ejpam-4958	235	21	(	(	PUNCT
ejpam-4958	235	22	16	16	NUM
ejpam-4958	235	23	)	)	PUNCT
ejpam-4958	235	24	gives	give	VERB
ejpam-4958	235	25	r(a	r(a	PROPN
ejpam-4958	235	26	)	)	PUNCT
ejpam-4958	235	27	(	(	PUNCT
ejpam-4958	235	28	ϖ(n−1)(a	ϖ(n−1)(a	NOUN
ejpam-4958	235	29	)	)	PUNCT
ejpam-4958	235	30	)	)	PUNCT
ejpam-4958	236	1	α	α	PRON
ejpam-4958	236	2	−	−	NOUN
ejpam-4958	236	3	r(u	r(u	PROPN
ejpam-4958	236	4	)	)	PUNCT
ejpam-4958	236	5	(	(	PUNCT
ejpam-4958	236	6	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	236	7	)	)	PUNCT
ejpam-4958	236	8	)	)	PUNCT
ejpam-4958	237	1	α	α	PROPN
ejpam-4958	238	1	+	+	X
ejpam-4958	238	2	λβ	λβ	ADP
ejpam-4958	238	3	∫	∫	PROPN
ejpam-4958	238	4	a	a	DET
ejpam-4958	238	5	u	u	NOUN
ejpam-4958	238	6	m∑	m∑	VERB
ejpam-4958	238	7	i=1	i=1	PROPN
ejpam-4958	238	8	qi(s	qi(s	NUM
ejpam-4958	238	9	)	)	PUNCT
ejpam-4958	238	10	(	(	PUNCT
ejpam-4958	238	11	τi(s	τi(s	NUM
ejpam-4958	238	12	)	)	PUNCT
ejpam-4958	238	13	s	s	PART
ejpam-4958	238	14	)	)	PUNCT
ejpam-4958	238	15	β	β	X
ejpam-4958	238	16	ϖβ(s	ϖβ(	NOUN
ejpam-4958	238	17	)	)	PUNCT
ejpam-4958	238	18	ds	ds	ADJ
ejpam-4958	238	19	≤	≤	NOUN
ejpam-4958	238	20	0	0	NUM
ejpam-4958	238	21	.	.	PUNCT
ejpam-4958	239	1	(	(	PUNCT
ejpam-4958	239	2	17	17	NUM
ejpam-4958	239	3	)	)	PUNCT
ejpam-4958	239	4	since	since	SCONJ
ejpam-4958	239	5	ϖ′	ϖ′	X
ejpam-4958	239	6	>	>	X
ejpam-4958	239	7	0	0	NUM
ejpam-4958	239	8	,	,	PUNCT
ejpam-4958	239	9	we	we	PRON
ejpam-4958	239	10	find	find	VERB
ejpam-4958	239	11	r(a	r(a	PRON
ejpam-4958	239	12	)	)	PUNCT
ejpam-4958	239	13	(	(	PUNCT
ejpam-4958	239	14	ϖ(n−1)(a	ϖ(n−1)(a	NOUN
ejpam-4958	239	15	)	)	PUNCT
ejpam-4958	239	16	)	)	PUNCT
ejpam-4958	240	1	α	α	PRON
ejpam-4958	240	2	−	−	NOUN
ejpam-4958	240	3	r(u	r(u	PROPN
ejpam-4958	240	4	)	)	PUNCT
ejpam-4958	240	5	(	(	PUNCT
ejpam-4958	240	6	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	240	7	)	)	PUNCT
ejpam-4958	240	8	)	)	PUNCT
ejpam-4958	241	1	α	α	PROPN
ejpam-4958	241	2	+	+	NUM
ejpam-4958	241	3	λβϖβ(s	λβϖβ(s	PROPN
ejpam-4958	241	4	)	)	PUNCT
ejpam-4958	241	5	∫	∫	PROPN
ejpam-4958	241	6	a	a	DET
ejpam-4958	241	7	u	u	NOUN
ejpam-4958	241	8	m∑	m∑	VERB
ejpam-4958	241	9	i=1	i=1	PROPN
ejpam-4958	241	10	qi(s	qi(s	NUM
ejpam-4958	241	11	)	)	PUNCT
ejpam-4958	241	12	(	(	PUNCT
ejpam-4958	241	13	τi(s	τi(s	NUM
ejpam-4958	241	14	)	)	PUNCT
ejpam-4958	241	15	s	s	PART
ejpam-4958	241	16	)	)	PUNCT
ejpam-4958	241	17	β	β	X
ejpam-4958	241	18	ds	ds	ADJ
ejpam-4958	241	19	≤	≤	NUM
ejpam-4958	241	20	0	0	NUM
ejpam-4958	241	21	.	.	PUNCT
ejpam-4958	242	1	(	(	PUNCT
ejpam-4958	242	2	18	18	NUM
ejpam-4958	242	3	)	)	PUNCT
ejpam-4958	242	4	taking	take	VERB
ejpam-4958	242	5	a	a	DET
ejpam-4958	242	6	→	→	SYM
ejpam-4958	242	7	∞	∞	PROPN
ejpam-4958	242	8	,	,	PUNCT
ejpam-4958	242	9	we	we	PRON
ejpam-4958	242	10	obtain	obtain	VERB
ejpam-4958	242	11	−r(u	−r(u	NOUN
ejpam-4958	242	12	)	)	PUNCT
ejpam-4958	242	13	(	(	PUNCT
ejpam-4958	242	14	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	242	15	)	)	PUNCT
ejpam-4958	242	16	)	)	PUNCT
ejpam-4958	243	1	α	α	PROPN
ejpam-4958	243	2	+	+	NUM
ejpam-4958	243	3	λβϖβ(s	λβϖβ(s	PROPN
ejpam-4958	243	4	)	)	PUNCT
ejpam-4958	243	5	∫	∫	PROPN
ejpam-4958	244	1	∞	∞	PROPN
ejpam-4958	244	2	t	t	PROPN
ejpam-4958	244	3	m∑	m∑	CCONJ
ejpam-4958	244	4	i=1	i=1	PROPN
ejpam-4958	244	5	qi(s	qi(s	NUM
ejpam-4958	244	6	)	)	PUNCT
ejpam-4958	244	7	(	(	PUNCT
ejpam-4958	244	8	τi(s	τi(s	NUM
ejpam-4958	244	9	)	)	PUNCT
ejpam-4958	244	10	s	s	PART
ejpam-4958	244	11	)	)	PUNCT
ejpam-4958	244	12	β	β	X
ejpam-4958	244	13	ds	ds	ADJ
ejpam-4958	244	14	≤	≤	NUM
ejpam-4958	244	15	0	0	NUM
ejpam-4958	244	16	,	,	PUNCT
ejpam-4958	244	17	that	that	PRON
ejpam-4958	244	18	is	be	AUX
ejpam-4958	244	19	ϖ(n−1)(u	ϖ(n−1)(u	NOUN
ejpam-4958	244	20	)	)	PUNCT
ejpam-4958	244	21	≥	≥	NOUN
ejpam-4958	244	22	λβ	λβ	ADP
ejpam-4958	244	23	/	/	SYM
ejpam-4958	244	24	α	α	PRON
ejpam-4958	244	25	r1	r1	PROPN
ejpam-4958	244	26	/	/	SYM
ejpam-4958	244	27	α(u	α(u	PROPN
ejpam-4958	244	28	)	)	PUNCT
ejpam-4958	244	29	ϖβ	ϖβ	PROPN
ejpam-4958	244	30	/	/	SYM
ejpam-4958	244	31	α(u	α(u	NOUN
ejpam-4958	244	32	)	)	PUNCT
ejpam-4958	244	33	(	(	PUNCT
ejpam-4958	244	34	∫	∫	PROPN
ejpam-4958	244	35	∞	∞	PROPN
ejpam-4958	244	36	u	u	PROPN
ejpam-4958	244	37	m∑	m∑	VERB
ejpam-4958	244	38	i=1	i=1	PROPN
ejpam-4958	244	39	qi(s	qi(s	NUM
ejpam-4958	244	40	)	)	PUNCT
ejpam-4958	244	41	(	(	PUNCT
ejpam-4958	244	42	τi(s	τi(s	NUM
ejpam-4958	244	43	)	)	PUNCT
ejpam-4958	244	44	s	s	PART
ejpam-4958	244	45	)	)	PUNCT
ejpam-4958	244	46	β	β	X
ejpam-4958	244	47	ds	ds	X
ejpam-4958	244	48	)	)	PUNCT
ejpam-4958	244	49	1	1	PROPN
ejpam-4958	244	50	/	/	SYM
ejpam-4958	244	51	α	α	NOUN
ejpam-4958	244	52	.	.	PUNCT
ejpam-4958	245	1	integrating	integrate	VERB
ejpam-4958	245	2	from	from	ADP
ejpam-4958	245	3	u	u	PRON
ejpam-4958	245	4	to	to	ADP
ejpam-4958	245	5	∞	∞	PROPN
ejpam-4958	245	6	,	,	PUNCT
ejpam-4958	245	7	−ϖ(n−2)(u	−ϖ(n−2)(u	NUM
ejpam-4958	245	8	)	)	PUNCT
ejpam-4958	245	9	≥	≥	NOUN
ejpam-4958	245	10	λβ	λβ	NOUN
ejpam-4958	245	11	/	/	SYM
ejpam-4958	245	12	αϖβ	αϖβ	NOUN
ejpam-4958	245	13	/	/	SYM
ejpam-4958	245	14	α(u	α(u	PROPN
ejpam-4958	245	15	)	)	PUNCT
ejpam-4958	246	1	∫	∫	PROPN
ejpam-4958	246	2	∞	∞	PROPN
ejpam-4958	246	3	u	u	PROPN
ejpam-4958	246	4	(	(	PUNCT
ejpam-4958	246	5	1	1	NUM
ejpam-4958	246	6	r(x	r(x	PROPN
ejpam-4958	246	7	)	)	PUNCT
ejpam-4958	246	8	∫	∫	PROPN
ejpam-4958	247	1	∞	∞	NUM
ejpam-4958	247	2	x	x	INTJ
ejpam-4958	247	3	m∑	m∑	INTJ
ejpam-4958	247	4	i=1	i=1	PROPN
ejpam-4958	247	5	qi(s	qi(s	NUM
ejpam-4958	247	6	)	)	PUNCT
ejpam-4958	247	7	(	(	PUNCT
ejpam-4958	247	8	τi(s	τi(s	NUM
ejpam-4958	247	9	)	)	PUNCT
ejpam-4958	247	10	s	s	PART
ejpam-4958	247	11	)	)	PUNCT
ejpam-4958	247	12	β	β	X
ejpam-4958	247	13	ds	ds	X
ejpam-4958	247	14	)	)	PUNCT
ejpam-4958	247	15	1	1	NUM
ejpam-4958	247	16	α	α	NUM
ejpam-4958	247	17	dx	dx	PROPN
ejpam-4958	247	18	.	.	PUNCT
ejpam-4958	248	1	integrating	integrate	VERB
ejpam-4958	248	2	from	from	ADP
ejpam-4958	248	3	u	u	PRON
ejpam-4958	248	4	to	to	ADP
ejpam-4958	248	5	∞	∞	PROPN
ejpam-4958	248	6	,	,	PUNCT
ejpam-4958	248	7	we	we	PRON
ejpam-4958	248	8	find	find	VERB
ejpam-4958	248	9	−ϖ(n−3)(u	−ϖ(n−3)(u	ADJ
ejpam-4958	248	10	)	)	PUNCT
ejpam-4958	248	11	≥	≥	NOUN
ejpam-4958	248	12	λβ	λβ	NOUN
ejpam-4958	248	13	/	/	SYM
ejpam-4958	248	14	αϖβ	αϖβ	NOUN
ejpam-4958	248	15	/	/	SYM
ejpam-4958	248	16	α(u	α(u	PROPN
ejpam-4958	248	17	)	)	PUNCT
ejpam-4958	248	18	∫	∫	PROPN
ejpam-4958	249	1	∞	∞	NUM
ejpam-4958	249	2	u	u	PROPN
ejpam-4958	249	3	∫	∫	NUM
ejpam-4958	249	4	∞	∞	NUM
ejpam-4958	249	5	v	v	NOUN
ejpam-4958	249	6	(	(	PUNCT
ejpam-4958	249	7	1	1	NUM
ejpam-4958	249	8	r(x	r(x	PROPN
ejpam-4958	249	9	)	)	PUNCT
ejpam-4958	249	10	∫	∫	PROPN
ejpam-4958	250	1	∞	∞	NUM
ejpam-4958	250	2	x	x	INTJ
ejpam-4958	250	3	m∑	m∑	INTJ
ejpam-4958	250	4	i=1	i=1	PROPN
ejpam-4958	250	5	qi(s	qi(s	NUM
ejpam-4958	250	6	)	)	PUNCT
ejpam-4958	250	7	(	(	PUNCT
ejpam-4958	250	8	τi(s	τi(s	NUM
ejpam-4958	250	9	)	)	PUNCT
ejpam-4958	250	10	s	s	PART
ejpam-4958	250	11	)	)	PUNCT
ejpam-4958	250	12	β	β	X
ejpam-4958	250	13	ds	ds	X
ejpam-4958	250	14	)	)	PUNCT
ejpam-4958	250	15	1	1	NUM
ejpam-4958	250	16	α	α	NOUN
ejpam-4958	250	17	dx	dx	PROPN
ejpam-4958	251	1			PROPN
ejpam-4958	251	2	dv	dv	PROPN
ejpam-4958	251	3	.	.	PUNCT
ejpam-4958	251	4	integrating	integrate	VERB
ejpam-4958	251	5	the	the	DET
ejpam-4958	251	6	above	above	ADJ
ejpam-4958	251	7	inequality	inequality	NOUN
ejpam-4958	251	8	(	(	PUNCT
ejpam-4958	251	9	n−	n−	NOUN
ejpam-4958	251	10	4	4	NUM
ejpam-4958	251	11	)	)	PUNCT
ejpam-4958	251	12	times	time	NOUN
ejpam-4958	251	13	from	from	ADP
ejpam-4958	251	14	u	u	PRON
ejpam-4958	251	15	to	to	ADP
ejpam-4958	251	16	∞	∞	PROPN
ejpam-4958	251	17	,	,	PUNCT
ejpam-4958	251	18	we	we	PRON
ejpam-4958	251	19	get	get	VERB
ejpam-4958	251	20	−ϖ′(u	−ϖ′(u	PROPN
ejpam-4958	251	21	)	)	PUNCT
ejpam-4958	251	22	≥	≥	NOUN
ejpam-4958	252	1	−r1	−r1	NOUN
ejpam-4958	252	2	/	/	SYM
ejpam-4958	252	3	αλβ	αλβ	PROPN
ejpam-4958	252	4	/	/	SYM
ejpam-4958	252	5	α(u)ϖ(n−1)(u	α(u)ϖ(n−1)(u	PROPN
ejpam-4958	252	6	)	)	PUNCT
ejpam-4958	252	7	(	(	PUNCT
ejpam-4958	252	8	n−	n−	NOUN
ejpam-4958	252	9	4	4	NUM
ejpam-4958	252	10	)	)	PUNCT
ejpam-4958	252	11	!	!	PUNCT
ejpam-4958	253	1	∫	∫	PROPN
ejpam-4958	254	1	∞	∞	NUM
ejpam-4958	254	2	u	u	PROPN
ejpam-4958	254	3	(	(	PUNCT
ejpam-4958	254	4	η	η	NOUN
ejpam-4958	254	5	−	−	NOUN
ejpam-4958	254	6	u)n−4δ(η	u)n−4δ(η	NOUN
ejpam-4958	254	7	)	)	PUNCT
ejpam-4958	254	8	dη	dη	NOUN
ejpam-4958	254	9	.	.	PUNCT
ejpam-4958	254	10	(	(	PUNCT
ejpam-4958	254	11	19	19	NUM
ejpam-4958	254	12	)	)	PUNCT
ejpam-4958	254	13	in	in	ADP
ejpam-4958	254	14	the	the	DET
ejpam-4958	254	15	same	same	ADJ
ejpam-4958	254	16	way	way	NOUN
ejpam-4958	254	17	,	,	PUNCT
ejpam-4958	254	18	integrating	integrate	VERB
ejpam-4958	254	19	(	(	PUNCT
ejpam-4958	254	20	19	19	NUM
ejpam-4958	254	21	)	)	PUNCT
ejpam-4958	254	22	from	from	ADP
ejpam-4958	254	23	u	u	PRON
ejpam-4958	254	24	to	to	ADP
ejpam-4958	254	25	∞	∞	PROPN
ejpam-4958	254	26	implies	imply	VERB
ejpam-4958	254	27	that	that	SCONJ
ejpam-4958	254	28	ϖ(u	ϖ(u	PROPN
ejpam-4958	254	29	)	)	PUNCT
ejpam-4958	254	30	≥	≥	NOUN
ejpam-4958	254	31	−r	−r	VERB
ejpam-4958	254	32	1	1	NUM
ejpam-4958	254	33	α	α	NOUN
ejpam-4958	254	34	(	(	PUNCT
ejpam-4958	254	35	u)λβ	u)λβ	NOUN
ejpam-4958	254	36	/	/	SYM
ejpam-4958	254	37	α(u)ϖ(n−1)(u	α(u)ϖ(n−1)(u	NOUN
ejpam-4958	254	38	)	)	PUNCT
ejpam-4958	254	39	(	(	PUNCT
ejpam-4958	254	40	n−	n−	NOUN
ejpam-4958	254	41	3	3	NUM
ejpam-4958	254	42	)	)	PUNCT
ejpam-4958	254	43	!	!	PUNCT
ejpam-4958	255	1	∫	∫	PROPN
ejpam-4958	256	1	∞	∞	NUM
ejpam-4958	256	2	u	u	PROPN
ejpam-4958	256	3	(	(	PUNCT
ejpam-4958	256	4	η	η	PROPN
ejpam-4958	256	5	−	−	NOUN
ejpam-4958	256	6	u)n−3δ(η	u)n−3δ(η	ADJ
ejpam-4958	256	7	)	)	PUNCT
ejpam-4958	256	8	dη	dη	NOUN
ejpam-4958	256	9	.	.	PUNCT
ejpam-4958	256	10	define	define	VERB
ejpam-4958	256	11	φ	φ	NUM
ejpam-4958	256	12	by	by	ADP
ejpam-4958	256	13	φ(u	φ(u	NOUN
ejpam-4958	256	14	)	)	PUNCT
ejpam-4958	256	15	:	:	PUNCT
ejpam-4958	257	1	=	=	SYM
ejpam-4958	257	2	r(u	r(u	X
ejpam-4958	257	3	)	)	PUNCT
ejpam-4958	257	4	(	(	PUNCT
ejpam-4958	257	5	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	257	6	)	)	PUNCT
ejpam-4958	257	7	)	)	PUNCT
ejpam-4958	258	1	α	α	PROPN
ejpam-4958	258	2	(	(	PUNCT
ejpam-4958	258	3	ϖ(u))α	ϖ(u))α	PROPN
ejpam-4958	258	4	,	,	PUNCT
ejpam-4958	258	5	u	u	NOUN
ejpam-4958	258	6	≥	≥	NOUN
ejpam-4958	258	7	u1	u1	PROPN
ejpam-4958	258	8	.	.	PUNCT
ejpam-4958	259	1	(	(	PUNCT
ejpam-4958	259	2	20	20	NUM
ejpam-4958	259	3	)	)	PUNCT
ejpam-4958	259	4	then	then	ADV
ejpam-4958	259	5	φ(u	φ(u	NOUN
ejpam-4958	259	6	)	)	PUNCT
ejpam-4958	259	7	<	<	X
ejpam-4958	259	8	0	0	NUM
ejpam-4958	259	9	for	for	ADP
ejpam-4958	259	10	u	u	PROPN
ejpam-4958	259	11	≥	≥	NOUN
ejpam-4958	259	12	u1	u1	PROPN
ejpam-4958	259	13	.	.	PUNCT
ejpam-4958	260	1	differentiating	differentiate	VERB
ejpam-4958	260	2	(	(	PUNCT
ejpam-4958	260	3	20	20	NUM
ejpam-4958	260	4	)	)	PUNCT
ejpam-4958	260	5	,	,	PUNCT
ejpam-4958	260	6	we	we	PRON
ejpam-4958	260	7	have	have	VERB
ejpam-4958	260	8	φ′(u	φ′(u	VERB
ejpam-4958	260	9	)	)	PUNCT
ejpam-4958	261	1	=	=	SYM
ejpam-4958	261	2	(	(	PUNCT
ejpam-4958	261	3	r(u	r(u	PROPN
ejpam-4958	261	4	)	)	PUNCT
ejpam-4958	261	5	(	(	PUNCT
ejpam-4958	261	6	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	261	7	)	)	PUNCT
ejpam-4958	261	8	)	)	PUNCT
ejpam-4958	261	9	α)′	α)′	PROPN
ejpam-4958	261	10	(	(	PUNCT
ejpam-4958	261	11	ϖ(u))α	ϖ(u))α	PROPN
ejpam-4958	261	12	−	−	PROPN
ejpam-4958	261	13	α	α	PROPN
ejpam-4958	261	14	r(u	r(u	PROPN
ejpam-4958	261	15	)	)	PUNCT
ejpam-4958	261	16	(	(	PUNCT
ejpam-4958	261	17	ϖ(n−1)(u	ϖ(n−1)(u	PROPN
ejpam-4958	261	18	)	)	PUNCT
ejpam-4958	261	19	)	)	PUNCT
ejpam-4958	261	20	α	α	PROPN
ejpam-4958	261	21	ϖ′(u	ϖ′(u	PROPN
ejpam-4958	261	22	)	)	PUNCT
ejpam-4958	261	23	(	(	PUNCT
ejpam-4958	261	24	ϖ(u))α+1	ϖ(u))α+1	NOUN
ejpam-4958	261	25	.	.	PUNCT
ejpam-4958	262	1	s.	s.	PROPN
ejpam-4958	262	2	a.	a.	PROPN
ejpam-4958	262	3	balatta	balatta	PROPN
ejpam-4958	262	4	et	et	PROPN
ejpam-4958	262	5	al	al	PROPN
ejpam-4958	262	6	.	.	PUNCT
ejpam-4958	262	7	/	/	SYM
ejpam-4958	262	8	eur	eur	PROPN
ejpam-4958	262	9	.	.	PUNCT
ejpam-4958	263	1	j.	j.	PROPN
ejpam-4958	263	2	pure	pure	PROPN
ejpam-4958	263	3	appl	appl	PROPN
ejpam-4958	263	4	.	.	PROPN
ejpam-4958	263	5	math	math	PROPN
ejpam-4958	263	6	,	,	PUNCT
ejpam-4958	263	7	16	16	NUM
ejpam-4958	263	8	(	(	PUNCT
ejpam-4958	263	9	4	4	NUM
ejpam-4958	263	10	)	)	PUNCT
ejpam-4958	263	11	(	(	PUNCT
ejpam-4958	263	12	2023	2023	NUM
ejpam-4958	263	13	)	)	PUNCT
ejpam-4958	263	14	,	,	PUNCT
ejpam-4958	263	15	2234	2234	NUM
ejpam-4958	263	16	-	-	SYM
ejpam-4958	263	17	2246	2246	NUM
ejpam-4958	263	18	2243	2243	NUM
ejpam-4958	263	19	it	it	PRON
ejpam-4958	263	20	can	can	AUX
ejpam-4958	263	21	be	be	AUX
ejpam-4958	263	22	concluded	conclude	VERB
ejpam-4958	263	23	from	from	ADP
ejpam-4958	263	24	equations	equation	NOUN
ejpam-4958	263	25	(	(	PUNCT
ejpam-4958	263	26	1	1	NUM
ejpam-4958	263	27	)	)	PUNCT
ejpam-4958	263	28	and	and	CCONJ
ejpam-4958	263	29	(	(	PUNCT
ejpam-4958	263	30	19	19	NUM
ejpam-4958	263	31	)	)	PUNCT
ejpam-4958	263	32	that	that	PRON
ejpam-4958	263	33	φ′(u	φ′(u	VERB
ejpam-4958	263	34	)	)	PUNCT
ejpam-4958	263	35	≤	≤	NOUN
ejpam-4958	263	36	−	−	ADP
ejpam-4958	263	37	m∑	m∑	CCONJ
ejpam-4958	263	38	i=1	i=1	PRON
ejpam-4958	263	39	qi(u	qi(u	NUM
ejpam-4958	263	40	)	)	PUNCT
ejpam-4958	263	41	ϖβ	ϖβ	ADP
ejpam-4958	263	42	(	(	PUNCT
ejpam-4958	263	43	τi(u	τi(u	NUM
ejpam-4958	263	44	)	)	PUNCT
ejpam-4958	263	45	)	)	PUNCT
ejpam-4958	264	1	(	(	PUNCT
ejpam-4958	264	2	ϖ(u))α	ϖ(u))α	PROPN
ejpam-4958	264	3	−	−	PROPN
ejpam-4958	264	4	α	α	PROPN
ejpam-4958	264	5	∫∞	∫∞	NOUN
ejpam-4958	264	6	u	u	PROPN
ejpam-4958	264	7	(	(	PUNCT
ejpam-4958	264	8	η	η	PROPN
ejpam-4958	264	9	−	−	NOUN
ejpam-4958	264	10	u)n−4δ(η	u)n−4δ(η	NOUN
ejpam-4958	264	11	)	)	PUNCT
ejpam-4958	264	12	dη	dη	NOUN
ejpam-4958	264	13	(	(	PUNCT
ejpam-4958	264	14	n−	n−	NOUN
ejpam-4958	264	15	4	4	NUM
ejpam-4958	264	16	)	)	PUNCT
ejpam-4958	264	17	!	!	PUNCT
ejpam-4958	265	1	φ(α+1)/α(u	φ(α+1)/α(u	NOUN
ejpam-4958	265	2	)	)	PUNCT
ejpam-4958	265	3	.	.	PUNCT
ejpam-4958	266	1	recalling	recall	VERB
ejpam-4958	266	2	τ(u	τ(u	PROPN
ejpam-4958	266	3	)	)	PUNCT
ejpam-4958	266	4	<	<	X
ejpam-4958	266	5	u	u	NOUN
ejpam-4958	266	6	and	and	CCONJ
ejpam-4958	266	7	ϖ′	ϖ′	X
ejpam-4958	266	8	<	<	X
ejpam-4958	266	9	0	0	NUM
ejpam-4958	266	10	,	,	PUNCT
ejpam-4958	266	11	then	then	ADV
ejpam-4958	266	12	there	there	PRON
ejpam-4958	266	13	exists	exist	VERB
ejpam-4958	266	14	a	a	DET
ejpam-4958	266	15	constant	constant	ADJ
ejpam-4958	266	16	h	h	NOUN
ejpam-4958	266	17	>	>	X
ejpam-4958	266	18	0	0	NUM
ejpam-4958	267	1	such	such	ADJ
ejpam-4958	267	2	that	that	SCONJ
ejpam-4958	267	3	φ′(u	φ′(u	NOUN
ejpam-4958	267	4	)	)	PUNCT
ejpam-4958	267	5	≤	≤	NOUN
ejpam-4958	267	6	−	−	ADP
ejpam-4958	267	7	m∑	m∑	CCONJ
ejpam-4958	267	8	i=1	i=1	PRON
ejpam-4958	267	9	qi(u	qi(u	NUM
ejpam-4958	267	10	)	)	PUNCT
ejpam-4958	267	11	ϖα	ϖα	PROPN
ejpam-4958	267	12	(	(	PUNCT
ejpam-4958	267	13	τi(u	τi(u	NUM
ejpam-4958	267	14	)	)	PUNCT
ejpam-4958	267	15	)	)	PUNCT
ejpam-4958	268	1	(	(	PUNCT
ejpam-4958	268	2	ϖ(u))α	ϖ(u))α	PROPN
ejpam-4958	268	3	ϖβ−α	ϖβ−α	NOUN
ejpam-4958	268	4	(	(	PUNCT
ejpam-4958	268	5	τi(u))−	τi(u))−	VERB
ejpam-4958	268	6	α	α	PROPN
ejpam-4958	268	7	∫∞	∫∞	NOUN
ejpam-4958	268	8	u	u	PROPN
ejpam-4958	268	9	(	(	PUNCT
ejpam-4958	268	10	η	η	PROPN
ejpam-4958	268	11	−	−	NOUN
ejpam-4958	268	12	u)n−4δ(η	u)n−4δ(η	NOUN
ejpam-4958	268	13	)	)	PUNCT
ejpam-4958	268	14	dη	dη	NOUN
ejpam-4958	268	15	(	(	PUNCT
ejpam-4958	268	16	n−	n−	NOUN
ejpam-4958	268	17	4	4	NUM
ejpam-4958	268	18	)	)	PUNCT
ejpam-4958	268	19	!	!	PUNCT
ejpam-4958	269	1	φ(α+1)/α(u	φ(α+1)/α(u	NOUN
ejpam-4958	269	2	)	)	PUNCT
ejpam-4958	269	3	,	,	PUNCT
ejpam-4958	269	4	we	we	PRON
ejpam-4958	269	5	get	get	VERB
ejpam-4958	269	6	φ′(u	φ′(u	PUNCT
ejpam-4958	269	7	)	)	PUNCT
ejpam-4958	270	1	+	+	X
ejpam-4958	270	2	hβ−α	hβ−α	NOUN
ejpam-4958	270	3	m∑	m∑	CCONJ
ejpam-4958	270	4	i=1	i=1	PROPN
ejpam-4958	270	5	qi(u	qi(u	NUM
ejpam-4958	270	6	)	)	PUNCT
ejpam-4958	271	1	+	+	CCONJ
ejpam-4958	271	2	α	α	PRON
ejpam-4958	271	3	∫∞	∫∞	NOUN
ejpam-4958	271	4	u	u	PROPN
ejpam-4958	271	5	(	(	PUNCT
ejpam-4958	271	6	η	η	PROPN
ejpam-4958	271	7	−	−	PROPN
ejpam-4958	271	8	u)n−4δ(η)dη	u)n−4δ(η)dη	X
ejpam-4958	271	9	(	(	PUNCT
ejpam-4958	271	10	n−	n−	NOUN
ejpam-4958	271	11	4	4	NUM
ejpam-4958	271	12	)	)	PUNCT
ejpam-4958	271	13	!	!	PUNCT
ejpam-4958	272	1	φ	φ	NOUN
ejpam-4958	273	1	α+1	α+1	NUM
ejpam-4958	273	2	α	α	PROPN
ejpam-4958	273	3	(	(	PUNCT
ejpam-4958	273	4	u	u	NOUN
ejpam-4958	273	5	)	)	PUNCT
ejpam-4958	273	6	≤	≤	NOUN
ejpam-4958	273	7	0	0	NUM
ejpam-4958	273	8	.	.	PUNCT
ejpam-4958	274	1	from	from	ADP
ejpam-4958	274	2	[	[	X
ejpam-4958	274	3	18	18	NUM
ejpam-4958	274	4	]	]	PUNCT
ejpam-4958	274	5	theorem	theorem	VERB
ejpam-4958	274	6	2.6	2.6	NUM
ejpam-4958	274	7	,	,	PUNCT
ejpam-4958	274	8	we	we	PRON
ejpam-4958	274	9	obtain	obtain	VERB
ejpam-4958	274	10	(	(	PUNCT
ejpam-4958	274	11	15	15	NUM
ejpam-4958	274	12	)	)	PUNCT
ejpam-4958	274	13	is	be	AUX
ejpam-4958	274	14	non	non	ADJ
ejpam-4958	274	15	-	-	ADJ
ejpam-4958	274	16	oscillatory	oscillatory	ADJ
ejpam-4958	274	17	,	,	PUNCT
ejpam-4958	274	18	which	which	PRON
ejpam-4958	274	19	is	be	AUX
ejpam-4958	274	20	a	a	DET
ejpam-4958	274	21	contradiction	contradiction	NOUN
ejpam-4958	274	22	,	,	PUNCT
ejpam-4958	274	23	so	so	ADV
ejpam-4958	274	24	the	the	DET
ejpam-4958	274	25	proof	proof	NOUN
ejpam-4958	274	26	of	of	ADP
ejpam-4958	274	27	this	this	DET
ejpam-4958	274	28	theorem	theorem	NOUN
ejpam-4958	274	29	is	be	AUX
ejpam-4958	274	30	complete	complete	ADJ
ejpam-4958	274	31	.	.	PUNCT
ejpam-4958	275	1	3	3	X
ejpam-4958	275	2	.	.	X
ejpam-4958	275	3	examples	example	NOUN
ejpam-4958	275	4	this	this	DET
ejpam-4958	275	5	section	section	NOUN
ejpam-4958	275	6	presents	present	VERB
ejpam-4958	275	7	examples	example	NOUN
ejpam-4958	275	8	that	that	PRON
ejpam-4958	275	9	are	be	AUX
ejpam-4958	275	10	intended	intend	VERB
ejpam-4958	275	11	to	to	PART
ejpam-4958	275	12	demonstrate	demonstrate	VERB
ejpam-4958	275	13	the	the	DET
ejpam-4958	275	14	validity	validity	NOUN
ejpam-4958	275	15	of	of	ADP
ejpam-4958	275	16	the	the	DET
ejpam-4958	275	17	findings	finding	NOUN
ejpam-4958	275	18	stated	state	VERB
ejpam-4958	275	19	in	in	ADP
ejpam-4958	275	20	the	the	DET
ejpam-4958	275	21	previous	previous	ADJ
ejpam-4958	275	22	part	part	NOUN
ejpam-4958	275	23	.	.	PUNCT
ejpam-4958	276	1	example	example	NOUN
ejpam-4958	277	1	1	1	NUM
ejpam-4958	277	2	.	.	X
ejpam-4958	277	3	consider	consider	VERB
ejpam-4958	277	4	the	the	DET
ejpam-4958	277	5	following	follow	VERB
ejpam-4958	277	6	differential	differential	ADJ
ejpam-4958	277	7	equation	equation	NOUN
ejpam-4958	277	8	(	(	PUNCT
ejpam-4958	277	9	u2ϖ′′′(u	u2ϖ′′′(u	PROPN
ejpam-4958	277	10	)	)	PUNCT
ejpam-4958	277	11	)	)	PUNCT
ejpam-4958	278	1	′	′	NUM
ejpam-4958	279	1	+	+	CCONJ
ejpam-4958	279	2	(	(	PUNCT
ejpam-4958	279	3	√	√	NUM
ejpam-4958	279	4	10eu	10eu	PROPN
ejpam-4958	279	5	(	(	PUNCT
ejpam-4958	279	6	2earcsin	2earcsin	NUM
ejpam-4958	279	7	√	√	NUM
ejpam-4958	279	8	10	10	NUM
ejpam-4958	279	9	10	10	NUM
ejpam-4958	279	10	−	−	NUM
ejpam-4958	279	11	1	1	NUM
ejpam-4958	279	12	)	)	PUNCT
ejpam-4958	279	13	+	+	CCONJ
ejpam-4958	279	14	√	√	NUM
ejpam-4958	279	15	10eu	10eu	ADJ
ejpam-4958	279	16	)	)	PUNCT
ejpam-4958	279	17	ϖ	ϖ	PROPN
ejpam-4958	279	18	(	(	PUNCT
ejpam-4958	279	19	u−	u−	PROPN
ejpam-4958	279	20	arcsin	arcsin	PROPN
ejpam-4958	279	21	√	√	VERB
ejpam-4958	279	22	10	10	NUM
ejpam-4958	279	23	10	10	NUM
ejpam-4958	279	24	)	)	PUNCT
ejpam-4958	279	25	=	=	SYM
ejpam-4958	279	26	0	0	NUM
ejpam-4958	279	27	,	,	PUNCT
ejpam-4958	279	28	u	u	NOUN
ejpam-4958	279	29	≥	≥	NOUN
ejpam-4958	279	30	1	1	NUM
ejpam-4958	279	31	,	,	PUNCT
ejpam-4958	279	32	(	(	PUNCT
ejpam-4958	279	33	21	21	NUM
ejpam-4958	279	34	)	)	PUNCT
ejpam-4958	279	35	where	where	SCONJ
ejpam-4958	279	36	α	α	NOUN
ejpam-4958	279	37	=	=	SYM
ejpam-4958	279	38	1	1	NUM
ejpam-4958	279	39	,	,	PUNCT
ejpam-4958	279	40	β	β	X
ejpam-4958	279	41	=	=	SYM
ejpam-4958	279	42	1	1	NUM
ejpam-4958	279	43	,	,	PUNCT
ejpam-4958	279	44	q(u	q(u	ADJ
ejpam-4958	279	45	)	)	PUNCT
ejpam-4958	279	46	=	=	SYM
ejpam-4958	279	47	√	√	NUM
ejpam-4958	279	48	10eu	10eu	NOUN
ejpam-4958	279	49	(	(	PUNCT
ejpam-4958	279	50	2earcsin	2earcsin	NUM
ejpam-4958	279	51	√	√	NUM
ejpam-4958	279	52	10	10	NUM
ejpam-4958	279	53	10	10	NUM
ejpam-4958	279	54	−	−	NUM
ejpam-4958	279	55	1	1	NUM
ejpam-4958	279	56	)	)	PUNCT
ejpam-4958	279	57	+	+	CCONJ
ejpam-4958	279	58	√	√	NUM
ejpam-4958	279	59	10eu	10eu	NOUN
ejpam-4958	279	60	,	,	PUNCT
ejpam-4958	279	61	τ	τ	PROPN
ejpam-4958	279	62	=	=	SYM
ejpam-4958	279	63	u−	u−	PROPN
ejpam-4958	279	64	arcsin	arcsin	NOUN
ejpam-4958	279	65	√	√	VERB
ejpam-4958	279	66	10	10	NUM
ejpam-4958	279	67	10	10	NUM
ejpam-4958	279	68	.	.	PUNCT
ejpam-4958	280	1	using	use	VERB
ejpam-4958	280	2	corollary	corollary	ADJ
ejpam-4958	280	3	1	1	NUM
ejpam-4958	280	4	,	,	PUNCT
ejpam-4958	280	5	we	we	PRON
ejpam-4958	280	6	have	have	VERB
ejpam-4958	280	7	lim	lim	PROPN
ejpam-4958	280	8	u→∞	u→∞	NUM
ejpam-4958	280	9	inf	inf	PROPN
ejpam-4958	280	10	∫	∫	PROPN
ejpam-4958	280	11	u	u	PROPN
ejpam-4958	280	12	τ(u	τ(u	PROPN
ejpam-4958	280	13	)	)	PUNCT
ejpam-4958	280	14	(	(	PUNCT
ejpam-4958	280	15	√	√	NUM
ejpam-4958	280	16	10es	10es	NOUN
ejpam-4958	280	17	(	(	PUNCT
ejpam-4958	280	18	2earcsin	2earcsin	NUM
ejpam-4958	280	19	√	√	NUM
ejpam-4958	280	20	10	10	NUM
ejpam-4958	280	21	10	10	NUM
ejpam-4958	280	22	−	−	NUM
ejpam-4958	280	23	1	1	NUM
ejpam-4958	280	24	)	)	PUNCT
ejpam-4958	281	1	+	+	CCONJ
ejpam-4958	281	2	√	√	NUM
ejpam-4958	281	3	10es	10es	NOUN
ejpam-4958	281	4	)	)	PUNCT
ejpam-4958	281	5	(	(	PUNCT
ejpam-4958	281	6	s−	s−	PROPN
ejpam-4958	281	7	arcsin	arcsin	VERB
ejpam-4958	281	8	√	√	ADV
ejpam-4958	281	9	10	10	NUM
ejpam-4958	281	10	10	10	NUM
ejpam-4958	281	11	)	)	PUNCT
ejpam-4958	281	12	ds	ds	PROPN
ejpam-4958	281	13	=	=	SYM
ejpam-4958	281	14	lim	lim	PROPN
ejpam-4958	281	15	u→∞	u→∞	NUM
ejpam-4958	281	16	inf	inf	NOUN
ejpam-4958	281	17	2	2	NUM
ejpam-4958	281	18	√	√	NUM
ejpam-4958	281	19	10	10	NUM
ejpam-4958	281	20	∫	∫	PROPN
ejpam-4958	281	21	u	u	PROPN
ejpam-4958	281	22	τ(u	τ(u	PROPN
ejpam-4958	281	23	)	)	PUNCT
ejpam-4958	281	24	(	(	PUNCT
ejpam-4958	281	25	s	s	X
ejpam-4958	281	26	es+arcsin	es+arcsin	NOUN
ejpam-4958	281	27	√	√	ADV
ejpam-4958	281	28	10	10	NUM
ejpam-4958	281	29	10	10	NUM
ejpam-4958	281	30	−	−	PROPN
ejpam-4958	281	31	arcsin	arcsin	PROPN
ejpam-4958	281	32	√	√	VERB
ejpam-4958	281	33	10	10	NUM
ejpam-4958	281	34	10	10	NUM
ejpam-4958	281	35	es+arcsin	es+arcsin	NOUN
ejpam-4958	281	36	√	√	ADV
ejpam-4958	281	37	10	10	NUM
ejpam-4958	281	38	10	10	NUM
ejpam-4958	281	39	)	)	PUNCT
ejpam-4958	281	40	ds	ds	PROPN
ejpam-4958	281	41	=	=	SYM
ejpam-4958	281	42	∞	∞	PROPN
ejpam-4958	281	43	>	>	X
ejpam-4958	281	44	6	6	NUM
ejpam-4958	281	45	e	e	NOUN
ejpam-4958	281	46	and	and	CCONJ
ejpam-4958	281	47	condition	condition	NOUN
ejpam-4958	281	48	(	(	PUNCT
ejpam-4958	281	49	13	13	NUM
ejpam-4958	281	50	)	)	PUNCT
ejpam-4958	281	51	becomes	become	VERB
ejpam-4958	281	52	lim	lim	PROPN
ejpam-4958	281	53	sup	sup	NOUN
ejpam-4958	281	54	u→∞	u→∞	NUM
ejpam-4958	281	55	∫	∫	PROPN
ejpam-4958	281	56	u	u	PROPN
ejpam-4958	281	57	u0	u0	PROPN
ejpam-4958	281	58	2√10es+arcsin	2√10es+arcsin	PROPN
ejpam-4958	281	59	√	√	ADV
ejpam-4958	281	60	10	10	NUM
ejpam-4958	281	61	10	10	NUM
ejpam-4958	281	62			NOUN
ejpam-4958	281	63	λ1	λ1	ADJ
ejpam-4958	281	64	2	2	NUM
ejpam-4958	281	65	s	s	NOUN
ejpam-4958	281	66	(	(	PUNCT
ejpam-4958	281	67	s−	s−	PROPN
ejpam-4958	281	68	arcsin	arcsin	PROPN
ejpam-4958	281	69	√	√	ADV
ejpam-4958	281	70	10	10	NUM
ejpam-4958	281	71	10	10	NUM
ejpam-4958	281	72	)	)	PUNCT
ejpam-4958	281	73	2	2	NUM
ejpam-4958	281	74	−	−	X
ejpam-4958	282	1	1	1	NUM
ejpam-4958	282	2	4s	4s	NUM
ejpam-4958	282	3	ds	ds	NOUN
ejpam-4958	282	4	=	=	SYM
ejpam-4958	282	5	∞.	∞.	PROPN
ejpam-4958	283	1	it	it	PRON
ejpam-4958	283	2	is	be	AUX
ejpam-4958	283	3	clear	clear	ADJ
ejpam-4958	283	4	to	to	PART
ejpam-4958	283	5	notice	notice	VERB
ejpam-4958	283	6	that	that	SCONJ
ejpam-4958	283	7	all	all	DET
ejpam-4958	283	8	conditions	condition	NOUN
ejpam-4958	283	9	of	of	ADP
ejpam-4958	283	10	corollary	corollary	ADJ
ejpam-4958	283	11	(	(	PUNCT
ejpam-4958	283	12	1	1	NUM
ejpam-4958	283	13	)	)	PUNCT
ejpam-4958	283	14	hold	hold	NOUN
ejpam-4958	283	15	.	.	PUNCT
ejpam-4958	284	1	hence	hence	ADV
ejpam-4958	284	2	every	every	DET
ejpam-4958	284	3	solution	solution	NOUN
ejpam-4958	284	4	of	of	ADP
ejpam-4958	284	5	(	(	PUNCT
ejpam-4958	284	6	21	21	NUM
ejpam-4958	284	7	)	)	PUNCT
ejpam-4958	284	8	is	be	AUX
ejpam-4958	284	9	oscillatory	oscillatory	ADJ
ejpam-4958	284	10	or	or	CCONJ
ejpam-4958	284	11	tends	tend	VERB
ejpam-4958	284	12	to	to	ADP
ejpam-4958	284	13	zero	zero	NUM
ejpam-4958	284	14	.	.	PUNCT
ejpam-4958	285	1	references	reference	NOUN
ejpam-4958	285	2	2244	2244	NUM
ejpam-4958	285	3	example	example	NOUN
ejpam-4958	285	4	2	2	NUM
ejpam-4958	285	5	.	.	X
ejpam-4958	285	6	consider	consider	VERB
ejpam-4958	285	7	the	the	DET
ejpam-4958	285	8	following	follow	VERB
ejpam-4958	285	9	differential	differential	ADJ
ejpam-4958	285	10	equation	equation	NOUN
ejpam-4958	285	11	(	(	PUNCT
ejpam-4958	285	12	u6(ϖ(u))′′′	u6(ϖ(u))′′′	X
ejpam-4958	285	13	)	)	PUNCT
ejpam-4958	285	14	′	′	NUM
ejpam-4958	286	1	+	+	CCONJ
ejpam-4958	286	2	(	(	PUNCT
ejpam-4958	286	3	η	η	X
ejpam-4958	286	4	u	u	PROPN
ejpam-4958	286	5	(	(	PUNCT
ejpam-4958	286	6	u2	u2	PROPN
ejpam-4958	286	7	+	+	CCONJ
ejpam-4958	286	8	u+	u+	NUM
ejpam-4958	286	9	1	1	NUM
ejpam-4958	286	10	)	)	PUNCT
ejpam-4958	286	11	(	(	PUNCT
ejpam-4958	286	12	u−	u−	PROPN
ejpam-4958	286	13	1	1	NUM
ejpam-4958	286	14	)	)	PUNCT
ejpam-4958	286	15	+	+	NUM
ejpam-4958	286	16	η	η	PROPN
ejpam-4958	286	17	u	u	PROPN
ejpam-4958	286	18	)	)	PUNCT
ejpam-4958	286	19	ϖ	ϖ	PROPN
ejpam-4958	286	20	(	(	PUNCT
ejpam-4958	286	21	u	u	NOUN
ejpam-4958	286	22	2	2	NUM
ejpam-4958	286	23	)	)	PUNCT
ejpam-4958	286	24	=	=	SYM
ejpam-4958	286	25	0	0	NUM
ejpam-4958	286	26	,	,	PUNCT
ejpam-4958	286	27	(	(	PUNCT
ejpam-4958	286	28	22	22	NUM
ejpam-4958	286	29	)	)	PUNCT
ejpam-4958	286	30	where	where	SCONJ
ejpam-4958	286	31	u	u	PRON
ejpam-4958	286	32	≥	≥	NOUN
ejpam-4958	286	33	1	1	NUM
ejpam-4958	286	34	and	and	CCONJ
ejpam-4958	286	35	η	η	PROPN
ejpam-4958	286	36	>	>	X
ejpam-4958	286	37	0	0	NUM
ejpam-4958	286	38	.	.	PUNCT
ejpam-4958	287	1	we	we	PRON
ejpam-4958	287	2	observe	observe	VERB
ejpam-4958	287	3	that	that	SCONJ
ejpam-4958	287	4	α	α	NOUN
ejpam-4958	287	5	=	=	SYM
ejpam-4958	287	6	3	3	NUM
ejpam-4958	287	7	,	,	PUNCT
ejpam-4958	287	8	β	β	X
ejpam-4958	287	9	=	=	SYM
ejpam-4958	287	10	1	1	NUM
ejpam-4958	287	11	,	,	PUNCT
ejpam-4958	287	12	r(u	r(u	PROPN
ejpam-4958	287	13	)	)	PUNCT
ejpam-4958	287	14	=	=	SYM
ejpam-4958	287	15	u6	u6	PROPN
ejpam-4958	287	16	,	,	PUNCT
ejpam-4958	287	17	τ(u	τ(u	PROPN
ejpam-4958	287	18	)	)	PUNCT
ejpam-4958	287	19	=	=	PUNCT
ejpam-4958	287	20	u/2	u/2	NUM
ejpam-4958	287	21	and	and	CCONJ
ejpam-4958	287	22	q(u	q(u	ADJ
ejpam-4958	287	23	)	)	PUNCT
ejpam-4958	287	24	=	=	SYM
ejpam-4958	287	25	η	η	X
ejpam-4958	287	26	u(u	u(u	ADP
ejpam-4958	287	27	2+u+1	2+u+1	NUM
ejpam-4958	287	28	)	)	PUNCT
ejpam-4958	287	29	(	(	PUNCT
ejpam-4958	287	30	u−	u−	PROPN
ejpam-4958	287	31	1)+	1)+	NUM
ejpam-4958	287	32	η	η	PROPN
ejpam-4958	287	33	u	u	PROPN
ejpam-4958	287	34	.	.	PUNCT
ejpam-4958	288	1	thus	thus	ADV
ejpam-4958	288	2	,	,	PUNCT
ejpam-4958	288	3	it	it	PRON
ejpam-4958	288	4	is	be	AUX
ejpam-4958	288	5	easy	easy	ADJ
ejpam-4958	288	6	to	to	PART
ejpam-4958	288	7	verify	verify	VERB
ejpam-4958	288	8	condition	condition	NOUN
ejpam-4958	288	9	(	(	PUNCT
ejpam-4958	288	10	14	14	NUM
ejpam-4958	288	11	)	)	PUNCT
ejpam-4958	288	12	.	.	PUNCT
ejpam-4958	289	1	obviously	obviously	ADV
ejpam-4958	289	2	,	,	PUNCT
ejpam-4958	289	3	all	all	DET
ejpam-4958	289	4	conditions	condition	NOUN
ejpam-4958	289	5	for	for	ADP
ejpam-4958	289	6	corollary	corollary	ADJ
ejpam-4958	289	7	(	(	PUNCT
ejpam-4958	289	8	2	2	NUM
ejpam-4958	289	9	)	)	PUNCT
ejpam-4958	289	10	are	be	AUX
ejpam-4958	289	11	achieved	achieve	VERB
ejpam-4958	289	12	.	.	PUNCT
ejpam-4958	290	1	thus	thus	ADV
ejpam-4958	290	2	,	,	PUNCT
ejpam-4958	290	3	all	all	DET
ejpam-4958	290	4	solutions	solution	NOUN
ejpam-4958	290	5	of	of	ADP
ejpam-4958	290	6	(	(	PUNCT
ejpam-4958	290	7	22	22	NUM
ejpam-4958	290	8	)	)	PUNCT
ejpam-4958	290	9	are	be	AUX
ejpam-4958	290	10	oscillatory	oscillatory	ADJ
ejpam-4958	290	11	or	or	CCONJ
ejpam-4958	290	12	tend	tend	VERB
ejpam-4958	290	13	to	to	PART
ejpam-4958	290	14	zero	zero	NUM
ejpam-4958	290	15	.	.	PUNCT
ejpam-4958	291	1	4	4	X
ejpam-4958	291	2	.	.	X
ejpam-4958	291	3	conclusion	conclusion	NOUN
ejpam-4958	291	4	as	as	SCONJ
ejpam-4958	291	5	explained	explain	VERB
ejpam-4958	291	6	in	in	ADP
ejpam-4958	291	7	the	the	DET
ejpam-4958	291	8	introduction	introduction	NOUN
ejpam-4958	291	9	,	,	PUNCT
ejpam-4958	291	10	the	the	DET
ejpam-4958	291	11	theory	theory	NOUN
ejpam-4958	291	12	of	of	ADP
ejpam-4958	291	13	higher	high	ADJ
ejpam-4958	291	14	-	-	PUNCT
ejpam-4958	291	15	order	order	NOUN
ejpam-4958	291	16	differential	differential	ADJ
ejpam-4958	291	17	equations	equation	NOUN
ejpam-4958	291	18	has	have	VERB
ejpam-4958	291	19	connections	connection	NOUN
ejpam-4958	291	20	with	with	ADP
ejpam-4958	291	21	many	many	ADJ
ejpam-4958	291	22	different	different	ADJ
ejpam-4958	291	23	fields	field	NOUN
ejpam-4958	291	24	of	of	ADP
ejpam-4958	291	25	mathematics	mathematic	NOUN
ejpam-4958	291	26	and	and	CCONJ
ejpam-4958	291	27	the	the	DET
ejpam-4958	291	28	applied	apply	VERB
ejpam-4958	291	29	sciences	science	NOUN
ejpam-4958	291	30	.	.	PUNCT
ejpam-4958	292	1	the	the	DET
ejpam-4958	292	2	topic	topic	NOUN
ejpam-4958	292	3	of	of	ADP
ejpam-4958	292	4	oscillation	oscillation	NOUN
ejpam-4958	292	5	in	in	ADP
ejpam-4958	292	6	relation	relation	NOUN
ejpam-4958	292	7	to	to	ADP
ejpam-4958	292	8	(	(	PUNCT
ejpam-4958	292	9	1	1	X
ejpam-4958	292	10	)	)	PUNCT
ejpam-4958	292	11	is	be	AUX
ejpam-4958	292	12	heavily	heavily	ADV
ejpam-4958	292	13	emphasised	emphasised	ADJ
ejpam-4958	292	14	in	in	ADP
ejpam-4958	292	15	the	the	DET
ejpam-4958	292	16	present	present	ADJ
ejpam-4958	292	17	study	study	NOUN
ejpam-4958	292	18	.	.	PUNCT
ejpam-4958	293	1	utilising	utilise	VERB
ejpam-4958	293	2	riccati	riccati	PROPN
ejpam-4958	293	3	transformation	transformation	NOUN
ejpam-4958	293	4	and	and	CCONJ
ejpam-4958	293	5	comparison	comparison	NOUN
ejpam-4958	293	6	strategies	strategy	NOUN
ejpam-4958	293	7	involving	involve	VERB
ejpam-4958	293	8	first	first	ADJ
ejpam-4958	293	9	order	order	NOUN
ejpam-4958	293	10	differential	differential	ADJ
ejpam-4958	293	11	equations	equation	NOUN
ejpam-4958	293	12	has	have	AUX
ejpam-4958	293	13	resulted	result	VERB
ejpam-4958	293	14	in	in	ADP
ejpam-4958	293	15	the	the	DET
ejpam-4958	293	16	discovery	discovery	NOUN
ejpam-4958	293	17	of	of	ADP
ejpam-4958	293	18	new	new	ADJ
ejpam-4958	293	19	oscillatory	oscillatory	ADJ
ejpam-4958	293	20	properties	property	NOUN
ejpam-4958	293	21	.	.	PUNCT
ejpam-4958	294	1	the	the	DET
ejpam-4958	294	2	previously	previously	ADV
ejpam-4958	294	3	mentioned	mention	VERB
ejpam-4958	294	4	criteria	criterion	NOUN
ejpam-4958	294	5	serve	serve	VERB
ejpam-4958	294	6	as	as	ADP
ejpam-4958	294	7	a	a	DET
ejpam-4958	294	8	supplement	supplement	NOUN
ejpam-4958	294	9	to	to	ADP
ejpam-4958	294	10	the	the	DET
ejpam-4958	294	11	documented	document	VERB
ejpam-4958	294	12	outcomes	outcome	NOUN
ejpam-4958	294	13	in	in	ADP
ejpam-4958	294	14	the	the	DET
ejpam-4958	294	15	currently	currently	ADV
ejpam-4958	294	16	available	available	ADJ
ejpam-4958	294	17	collection	collection	NOUN
ejpam-4958	294	18	of	of	ADP
ejpam-4958	294	19	literature	literature	NOUN
ejpam-4958	294	20	.	.	PUNCT
ejpam-4958	295	1	acknowledgment	acknowledgment	NOUN
ejpam-4958	295	2	this	this	DET
ejpam-4958	295	3	work	work	NOUN
ejpam-4958	295	4	is	be	AUX
ejpam-4958	295	5	part	part	NOUN
ejpam-4958	295	6	of	of	ADP
ejpam-4958	295	7	ukm	ukm	PROPN
ejpam-4958	295	8	’s	’s	PART
ejpam-4958	295	9	research	research	NOUN
ejpam-4958	295	10	#	#	NOUN
ejpam-4958	295	11	dip-2021	dip-2021	NOUN
ejpam-4958	295	12	-	-	PUNCT
ejpam-4958	295	13	018	018	NUM
ejpam-4958	295	14	.	.	PUNCT
ejpam-4958	296	1	fundings	funding	NOUN
ejpam-4958	296	2	no	no	DET
ejpam-4958	296	3	funding	funding	NOUN
ejpam-4958	296	4	was	be	AUX
ejpam-4958	296	5	used	use	VERB
ejpam-4958	296	6	in	in	ADP
ejpam-4958	296	7	this	this	DET
ejpam-4958	296	8	study	study	NOUN
ejpam-4958	296	9	.	.	PUNCT
ejpam-4958	297	1	conflict	conflict	NOUN
ejpam-4958	297	2	of	of	ADP
ejpam-4958	297	3	interest	interest	NOUN
ejpam-4958	297	4	all	all	DET
ejpam-4958	297	5	authors	author	NOUN
ejpam-4958	297	6	have	have	AUX
ejpam-4958	297	7	declared	declare	VERB
ejpam-4958	297	8	they	they	PRON
ejpam-4958	297	9	do	do	AUX
ejpam-4958	297	10	not	not	PART
ejpam-4958	297	11	have	have	VERB
ejpam-4958	297	12	any	any	DET
ejpam-4958	297	13	competing	compete	VERB
ejpam-4958	297	14	interests	interest	NOUN
ejpam-4958	297	15	.	.	PUNCT
ejpam-4958	298	1	materials	material	NOUN
ejpam-4958	298	2	and	and	CCONJ
ejpam-4958	298	3	data	datum	NOUN
ejpam-4958	298	4	availability	availability	NOUN
ejpam-4958	298	5	no	no	DET
ejpam-4958	298	6	data	datum	NOUN
ejpam-4958	298	7	were	be	AUX
ejpam-4958	298	8	used	use	VERB
ejpam-4958	298	9	to	to	PART
ejpam-4958	298	10	support	support	VERB
ejpam-4958	298	11	this	this	DET
ejpam-4958	298	12	study	study	NOUN
ejpam-4958	298	13	.	.	PUNCT
ejpam-4958	299	1	references	reference	NOUN
ejpam-4958	299	2	[	[	X
ejpam-4958	299	3	1	1	NUM
ejpam-4958	299	4	]	]	PUNCT
ejpam-4958	299	5	almutairi	almutairi	NOUN
ejpam-4958	299	6	a.	a.	PROPN
ejpam-4958	299	7	,	,	PUNCT
ejpam-4958	299	8	bazighifan	bazighifan	NOUN
ejpam-4958	299	9	o.	o.	NOUN
ejpam-4958	299	10	,	,	PUNCT
ejpam-4958	299	11	and	and	CCONJ
ejpam-4958	299	12	raffoul	raffoul	PROPN
ejpam-4958	299	13	y.	y.	PROPN
ejpam-4958	299	14	n.	n.	PROPN
ejpam-4958	299	15	oscillation	oscillation	NOUN
ejpam-4958	299	16	results	result	NOUN
ejpam-4958	299	17	for	for	ADP
ejpam-4958	299	18	nonlinear	nonlinear	ADJ
ejpam-4958	299	19	higher	high	ADJ
ejpam-4958	299	20	-	-	PUNCT
ejpam-4958	299	21	order	order	NOUN
ejpam-4958	299	22	differential	differential	ADJ
ejpam-4958	299	23	equations	equation	NOUN
ejpam-4958	299	24	with	with	ADP
ejpam-4958	299	25	delay	delay	NOUN
ejpam-4958	299	26	term	term	NOUN
ejpam-4958	299	27	.	.	PUNCT
ejpam-4958	300	1	symmetry	symmetry	NOUN
ejpam-4958	300	2	,	,	PUNCT
ejpam-4958	300	3	13(3):446	13(3):446	NUM
ejpam-4958	300	4	,	,	PUNCT
ejpam-4958	300	5	2021	2021	NUM
ejpam-4958	300	6	.	.	PUNCT
ejpam-4958	301	1	[	[	X
ejpam-4958	301	2	2	2	NUM
ejpam-4958	301	3	]	]	X
ejpam-4958	301	4	wintner	wintn	ADJ
ejpam-4958	301	5	a.	a.	NOUN
ejpam-4958	301	6	a	a	DET
ejpam-4958	301	7	criterion	criterion	NOUN
ejpam-4958	301	8	of	of	ADP
ejpam-4958	301	9	oscillatory	oscillatory	ADJ
ejpam-4958	301	10	stability	stability	NOUN
ejpam-4958	301	11	.	.	PUNCT
ejpam-4958	302	1	quarterly	quarterly	ADV
ejpam-4958	302	2	of	of	ADP
ejpam-4958	302	3	applied	applied	ADJ
ejpam-4958	302	4	mathematics	mathematic	NOUN
ejpam-4958	302	5	,	,	PUNCT
ejpam-4958	302	6	7(1):115–117	7(1):115–117	NUM
ejpam-4958	302	7	,	,	PUNCT
ejpam-4958	302	8	1949	1949	NUM
ejpam-4958	302	9	.	.	PUNCT
ejpam-4958	303	1	references	reference	NOUN
ejpam-4958	303	2	2245	2245	NUM
ejpam-4958	303	3	[	[	X
ejpam-4958	303	4	3	3	NUM
ejpam-4958	303	5	]	]	X
ejpam-4958	303	6	almarri	almarri	PROPN
ejpam-4958	303	7	barakah	barakah	PROPN
ejpam-4958	303	8	,	,	PUNCT
ejpam-4958	303	9	ali	ali	PROPN
ejpam-4958	303	10	ali	ali	PROPN
ejpam-4958	303	11	hasan	hasan	PROPN
ejpam-4958	303	12	,	,	PUNCT
ejpam-4958	303	13	al	al	PROPN
ejpam-4958	303	14	-	-	PUNCT
ejpam-4958	303	15	ghafri	ghafri	PROPN
ejpam-4958	303	16	khalil	khalil	PROPN
ejpam-4958	303	17	s	s	PROPN
ejpam-4958	303	18	,	,	PUNCT
ejpam-4958	303	19	almutairi	almutairi	NOUN
ejpam-4958	303	20	alanoud	alanoud	PROPN
ejpam-4958	303	21	,	,	PUNCT
ejpam-4958	303	22	bazighifan	bazighifan	NOUN
ejpam-4958	303	23	omar	omar	PROPN
ejpam-4958	303	24	,	,	PUNCT
ejpam-4958	303	25	and	and	CCONJ
ejpam-4958	303	26	awrejcewicz	awrejcewicz	PROPN
ejpam-4958	303	27	jan	jan	PROPN
ejpam-4958	303	28	.	.	PROPN
ejpam-4958	303	29	symmetric	symmetric	PROPN
ejpam-4958	303	30	and	and	CCONJ
ejpam-4958	303	31	non	non	ADJ
ejpam-4958	303	32	-	-	ADJ
ejpam-4958	303	33	oscillatory	oscillatory	ADJ
ejpam-4958	303	34	characteristics	characteristic	NOUN
ejpam-4958	303	35	of	of	ADP
ejpam-4958	303	36	the	the	DET
ejpam-4958	303	37	neutral	neutral	ADJ
ejpam-4958	303	38	differential	differential	NOUN
ejpam-4958	303	39	equations	equation	NOUN
ejpam-4958	303	40	solutions	solution	NOUN
ejpam-4958	303	41	related	relate	VERB
ejpam-4958	303	42	to	to	ADP
ejpam-4958	303	43	p	p	NOUN
ejpam-4958	303	44	-	-	PUNCT
ejpam-4958	303	45	laplacian	laplacian	ADJ
ejpam-4958	303	46	operators	operator	NOUN
ejpam-4958	303	47	.	.	PUNCT
ejpam-4958	304	1	symmetry	symmetry	NOUN
ejpam-4958	304	2	,	,	PUNCT
ejpam-4958	304	3	14(3):566	14(3):566	NUM
ejpam-4958	304	4	,	,	PUNCT
ejpam-4958	304	5	2022	2022	NUM
ejpam-4958	304	6	.	.	PUNCT
ejpam-4958	305	1	[	[	X
ejpam-4958	305	2	4	4	NUM
ejpam-4958	305	3	]	]	X
ejpam-4958	305	4	cina	cina	PROPN
ejpam-4958	305	5	bengu	bengu	PROPN
ejpam-4958	305	6	,	,	PUNCT
ejpam-4958	305	7	candan	candan	PROPN
ejpam-4958	305	8	tuncay	tuncay	NOUN
ejpam-4958	305	9	,	,	PUNCT
ejpam-4958	305	10	and	and	CCONJ
ejpam-4958	305	11	senel	senel	PROPN
ejpam-4958	305	12	m	m	VERB
ejpam-4958	305	13	tamer	tame	ADJ
ejpam-4958	305	14	.	.	PUNCT
ejpam-4958	306	1	existence	existence	NOUN
ejpam-4958	306	2	of	of	ADP
ejpam-4958	306	3	nonoscillatory	nonoscillatory	ADJ
ejpam-4958	306	4	solutions	solution	NOUN
ejpam-4958	306	5	of	of	ADP
ejpam-4958	306	6	higher	high	ADJ
ejpam-4958	306	7	order	order	NOUN
ejpam-4958	306	8	nonlinear	nonlinear	ADJ
ejpam-4958	306	9	neutral	neutral	ADJ
ejpam-4958	306	10	differential	differential	NOUN
ejpam-4958	306	11	equations	equation	NOUN
ejpam-4958	306	12	.	.	PUNCT
ejpam-4958	307	1	european	european	PROPN
ejpam-4958	307	2	journal	journal	PROPN
ejpam-4958	307	3	of	of	ADP
ejpam-4958	307	4	pure	pure	ADJ
ejpam-4958	307	5	and	and	CCONJ
ejpam-4958	307	6	applied	applied	ADJ
ejpam-4958	307	7	mathematics	mathematic	NOUN
ejpam-4958	307	8	,	,	PUNCT
ejpam-4958	307	9	16(2):713–723	16(2):713–723	PROPN
ejpam-4958	307	10	,	,	PUNCT
ejpam-4958	307	11	2023	2023	NUM
ejpam-4958	307	12	.	.	PUNCT
ejpam-4958	308	1	[	[	X
ejpam-4958	308	2	5	5	NUM
ejpam-4958	308	3	]	]	PUNCT
ejpam-4958	308	4	cesarano	cesarano	PROPN
ejpam-4958	308	5	c.	c.	NOUN
ejpam-4958	308	6	and	and	CCONJ
ejpam-4958	308	7	bazighifan	bazighifan	PROPN
ejpam-4958	308	8	o.	o.	PROPN
ejpam-4958	308	9	qualitative	qualitative	ADJ
ejpam-4958	308	10	behavior	behavior	NOUN
ejpam-4958	308	11	of	of	ADP
ejpam-4958	308	12	solutions	solution	NOUN
ejpam-4958	308	13	of	of	ADP
ejpam-4958	308	14	second	second	ADJ
ejpam-4958	308	15	order	order	NOUN
ejpam-4958	308	16	differential	differential	NOUN
ejpam-4958	308	17	equations	equation	NOUN
ejpam-4958	308	18	.	.	PUNCT
ejpam-4958	309	1	symmetry	symmetry	NOUN
ejpam-4958	309	2	,	,	PUNCT
ejpam-4958	309	3	11(6):777	11(6):777	NUM
ejpam-4958	309	4	,	,	PUNCT
ejpam-4958	309	5	2019	2019	NUM
ejpam-4958	309	6	.	.	PUNCT
ejpam-4958	310	1	[	[	X
ejpam-4958	310	2	6	6	NUM
ejpam-4958	310	3	]	]	X
ejpam-4958	310	4	shreve	shreve	PROPN
ejpam-4958	310	5	w.	w.	PROPN
ejpam-4958	310	6	e.	e.	PROPN
ejpam-4958	310	7	oscillation	oscillation	PROPN
ejpam-4958	310	8	in	in	ADP
ejpam-4958	310	9	first	first	ADJ
ejpam-4958	310	10	order	order	NOUN
ejpam-4958	310	11	nonlinear	nonlinear	ADJ
ejpam-4958	310	12	retarded	retarded	ADJ
ejpam-4958	310	13	argument	argument	NOUN
ejpam-4958	310	14	differential	differential	NOUN
ejpam-4958	310	15	equations	equation	NOUN
ejpam-4958	310	16	.	.	PUNCT
ejpam-4958	311	1	proceedings	proceeding	NOUN
ejpam-4958	311	2	of	of	ADP
ejpam-4958	311	3	the	the	DET
ejpam-4958	311	4	american	american	PROPN
ejpam-4958	311	5	mathematical	mathematical	PROPN
ejpam-4958	311	6	society	society	NOUN
ejpam-4958	311	7	,	,	PUNCT
ejpam-4958	311	8	41(2):565–568	41(2):565–568	PROPN
ejpam-4958	311	9	,	,	PUNCT
ejpam-4958	311	10	1973	1973	NUM
ejpam-4958	311	11	.	.	PUNCT
ejpam-4958	312	1	[	[	X
ejpam-4958	312	2	7	7	X
ejpam-4958	312	3	]	]	SYM
ejpam-4958	312	4	mofarreh	mofarreh	NOUN
ejpam-4958	312	5	f.	f.	PROPN
ejpam-4958	312	6	,	,	PUNCT
ejpam-4958	312	7	almutairi	almutairi	PROPN
ejpam-4958	312	8	a.	a.	PROPN
ejpam-4958	312	9	,	,	PUNCT
ejpam-4958	312	10	bazighifan	bazighifan	PROPN
ejpam-4958	312	11	o.	o.	PROPN
ejpam-4958	312	12	,	,	PUNCT
ejpam-4958	312	13	aiyashi	aiyashi	PROPN
ejpam-4958	312	14	m.	m.	PROPN
ejpam-4958	312	15	a.	a.	PROPN
ejpam-4958	312	16	,	,	PUNCT
ejpam-4958	312	17	and	and	CCONJ
ejpam-4958	312	18	vı̂lcu	vı̂lcu	PROPN
ejpam-4958	312	19	a.	a.	PROPN
ejpam-4958	312	20	d.	d.	PROPN
ejpam-4958	312	21	on	on	ADP
ejpam-4958	312	22	the	the	DET
ejpam-4958	312	23	oscillation	oscillation	NOUN
ejpam-4958	312	24	of	of	ADP
ejpam-4958	312	25	solutions	solution	NOUN
ejpam-4958	312	26	of	of	ADP
ejpam-4958	312	27	differential	differential	ADJ
ejpam-4958	312	28	equations	equation	NOUN
ejpam-4958	312	29	with	with	ADP
ejpam-4958	312	30	neutral	neutral	ADJ
ejpam-4958	312	31	term	term	NOUN
ejpam-4958	312	32	.	.	PUNCT
ejpam-4958	313	1	mathematics	mathematic	NOUN
ejpam-4958	313	2	,	,	PUNCT
ejpam-4958	313	3	9(21):2709	9(21):2709	NOUN
ejpam-4958	313	4	,	,	PUNCT
ejpam-4958	313	5	2021	2021	NUM
ejpam-4958	313	6	.	.	PUNCT
ejpam-4958	314	1	[	[	X
ejpam-4958	314	2	8	8	NUM
ejpam-4958	314	3	]	]	X
ejpam-4958	314	4	philos	philos	PROPN
ejpam-4958	314	5	c.	c.	PROPN
ejpam-4958	314	6	g.	g.	PROPN
ejpam-4958	314	7	on	on	ADP
ejpam-4958	314	8	the	the	DET
ejpam-4958	314	9	existence	existence	NOUN
ejpam-4958	314	10	of	of	ADP
ejpam-4958	314	11	nonoscillatory	nonoscillatory	ADJ
ejpam-4958	314	12	solutions	solution	NOUN
ejpam-4958	314	13	tending	tend	VERB
ejpam-4958	314	14	to	to	ADP
ejpam-4958	314	15	zero	zero	NUM
ejpam-4958	314	16	at	at	ADP
ejpam-4958	314	17	∞	∞	PROPN
ejpam-4958	314	18	for	for	ADP
ejpam-4958	314	19	differential	differential	ADJ
ejpam-4958	314	20	equations	equation	NOUN
ejpam-4958	314	21	with	with	ADP
ejpam-4958	314	22	positive	positive	ADJ
ejpam-4958	314	23	delays	delay	NOUN
ejpam-4958	314	24	.	.	PUNCT
ejpam-4958	315	1	archiv	archiv	PROPN
ejpam-4958	315	2	der	der	PROPN
ejpam-4958	315	3	mathematik	mathematik	PROPN
ejpam-4958	315	4	,	,	PUNCT
ejpam-4958	315	5	36:168–178	36:168–178	NUM
ejpam-4958	315	6	,	,	PUNCT
ejpam-4958	315	7	1981	1981	NUM
ejpam-4958	315	8	.	.	PUNCT
ejpam-4958	316	1	[	[	X
ejpam-4958	316	2	9	9	NUM
ejpam-4958	316	3	]	]	PUNCT
ejpam-4958	316	4	hale	hale	PROPN
ejpam-4958	316	5	j.	j.	PROPN
ejpam-4958	316	6	k.	k.	PROPN
ejpam-4958	316	7	global	global	PROPN
ejpam-4958	316	8	theory	theory	PROPN
ejpam-4958	316	9	.	.	PUNCT
ejpam-4958	317	1	theory	theory	NOUN
ejpam-4958	317	2	of	of	ADP
ejpam-4958	317	3	functional	functional	ADJ
ejpam-4958	317	4	differential	differential	ADJ
ejpam-4958	317	5	equations	equation	NOUN
ejpam-4958	317	6	,	,	PUNCT
ejpam-4958	317	7	pages	page	NOUN
ejpam-4958	317	8	320–335	320–335	NUM
ejpam-4958	317	9	,	,	PUNCT
ejpam-4958	317	10	1977	1977	NUM
ejpam-4958	317	11	.	.	PUNCT
ejpam-4958	318	1	[	[	X
ejpam-4958	318	2	10	10	NUM
ejpam-4958	318	3	]	]	X
ejpam-4958	318	4	elabbasy	elabbasy	PROPN
ejpam-4958	318	5	e.	e.	PROPN
ejpam-4958	318	6	m.	m.	PROPN
ejpam-4958	318	7	on	on	ADP
ejpam-4958	318	8	the	the	DET
ejpam-4958	318	9	oscillation	oscillation	NOUN
ejpam-4958	318	10	of	of	ADP
ejpam-4958	318	11	nonlinear	nonlinear	ADJ
ejpam-4958	318	12	second	second	ADJ
ejpam-4958	318	13	order	order	NOUN
ejpam-4958	318	14	differential	differential	NOUN
ejpam-4958	318	15	equations	equation	NOUN
ejpam-4958	318	16	.	.	PUNCT
ejpam-4958	319	1	panamerican	panamerican	PROPN
ejpam-4958	319	2	mathematical	mathematical	ADJ
ejpam-4958	319	3	journal	journal	PROPN
ejpam-4958	319	4	,	,	PUNCT
ejpam-4958	319	5	6:69–84	6:69–84	NOUN
ejpam-4958	319	6	,	,	PUNCT
ejpam-4958	319	7	1996	1996	NUM
ejpam-4958	319	8	.	.	PUNCT
ejpam-4958	320	1	[	[	X
ejpam-4958	320	2	11	11	NUM
ejpam-4958	320	3	]	]	X
ejpam-4958	320	4	elabbasy	elabbasy	PROPN
ejpam-4958	320	5	e.	e.	PROPN
ejpam-4958	320	6	m.	m.	PROPN
ejpam-4958	320	7	and	and	CCONJ
ejpam-4958	320	8	elsharabasy	elsharabasy	ADJ
ejpam-4958	320	9	m.	m.	NOUN
ejpam-4958	320	10	a.	a.	NOUN
ejpam-4958	320	11	oscillation	oscillation	NOUN
ejpam-4958	320	12	properties	property	NOUN
ejpam-4958	320	13	for	for	ADP
ejpam-4958	320	14	second	second	ADJ
ejpam-4958	320	15	order	order	NOUN
ejpam-4958	320	16	nonlinear	nonlinear	ADJ
ejpam-4958	320	17	differential	differential	ADJ
ejpam-4958	320	18	equations	equation	NOUN
ejpam-4958	320	19	.	.	PUNCT
ejpam-4958	321	1	kyungpook	kyungpook	PROPN
ejpam-4958	321	2	mathematical	mathematical	PROPN
ejpam-4958	321	3	journal	journal	PROPN
ejpam-4958	321	4	,	,	PUNCT
ejpam-4958	321	5	37(2):211–211	37(2):211–211	PROPN
ejpam-4958	321	6	,	,	PUNCT
ejpam-4958	321	7	1997	1997	NUM
ejpam-4958	321	8	.	.	PUNCT
ejpam-4958	322	1	[	[	X
ejpam-4958	322	2	12	12	NUM
ejpam-4958	322	3	]	]	X
ejpam-4958	322	4	elabbasy	elabbasy	PROPN
ejpam-4958	322	5	e.	e.	PROPN
ejpam-4958	322	6	m.	m.	PROPN
ejpam-4958	322	7	,	,	PUNCT
ejpam-4958	322	8	hassan	hassan	PROPN
ejpam-4958	322	9	t.	t.	PROPN
ejpam-4958	322	10	,	,	PUNCT
ejpam-4958	322	11	and	and	CCONJ
ejpam-4958	322	12	elmatary	elmatary	PROPN
ejpam-4958	322	13	b.	b.	PROPN
ejpam-4958	322	14	m.	m.	PROPN
ejpam-4958	322	15	oscillation	oscillation	NOUN
ejpam-4958	322	16	criteria	criterion	NOUN
ejpam-4958	322	17	for	for	ADP
ejpam-4958	322	18	third	third	ADJ
ejpam-4958	322	19	order	order	NOUN
ejpam-4958	322	20	delay	delay	VERB
ejpam-4958	322	21	nonlinear	nonlinear	ADJ
ejpam-4958	322	22	differential	differential	ADJ
ejpam-4958	322	23	equations	equation	NOUN
ejpam-4958	322	24	.	.	PUNCT
ejpam-4958	323	1	electronic	electronic	ADJ
ejpam-4958	323	2	journal	journal	NOUN
ejpam-4958	323	3	of	of	ADP
ejpam-4958	323	4	qualitative	qualitative	ADJ
ejpam-4958	323	5	theory	theory	NOUN
ejpam-4958	323	6	of	of	ADP
ejpam-4958	323	7	differential	differential	ADJ
ejpam-4958	323	8	equations	equation	NOUN
ejpam-4958	323	9	,	,	PUNCT
ejpam-4958	323	10	2012(5):1–9	2012(5):1–9	NOUN
ejpam-4958	323	11	,	,	PUNCT
ejpam-4958	323	12	2012	2012	NUM
ejpam-4958	323	13	.	.	PUNCT
ejpam-4958	324	1	[	[	X
ejpam-4958	324	2	13	13	NUM
ejpam-4958	324	3	]	]	X
ejpam-4958	324	4	bazighifan	bazighifan	NOUN
ejpam-4958	324	5	o.	o.	PROPN
ejpam-4958	324	6	and	and	CCONJ
ejpam-4958	324	7	ramos	ramos	PROPN
ejpam-4958	324	8	h.	h.	PROPN
ejpam-4958	324	9	on	on	ADP
ejpam-4958	324	10	the	the	DET
ejpam-4958	324	11	asymptotic	asymptotic	ADJ
ejpam-4958	324	12	and	and	CCONJ
ejpam-4958	324	13	oscillatory	oscillatory	ADJ
ejpam-4958	324	14	behavior	behavior	NOUN
ejpam-4958	324	15	of	of	ADP
ejpam-4958	324	16	the	the	DET
ejpam-4958	324	17	solutions	solution	NOUN
ejpam-4958	324	18	of	of	ADP
ejpam-4958	324	19	a	a	DET
ejpam-4958	324	20	class	class	NOUN
ejpam-4958	324	21	of	of	ADP
ejpam-4958	324	22	higher	high	ADJ
ejpam-4958	324	23	-	-	PUNCT
ejpam-4958	324	24	order	order	NOUN
ejpam-4958	324	25	differential	differential	ADJ
ejpam-4958	324	26	equations	equation	NOUN
ejpam-4958	324	27	with	with	ADP
ejpam-4958	324	28	middle	middle	ADJ
ejpam-4958	324	29	term	term	NOUN
ejpam-4958	324	30	.	.	PUNCT
ejpam-4958	325	1	applied	apply	VERB
ejpam-4958	325	2	mathematics	mathematics	NOUN
ejpam-4958	325	3	letters	letter	NOUN
ejpam-4958	325	4	,	,	PUNCT
ejpam-4958	325	5	107:106431	107:106431	NUM
ejpam-4958	325	6	,	,	PUNCT
ejpam-4958	325	7	2020	2020	NUM
ejpam-4958	325	8	.	.	PUNCT
ejpam-4958	326	1	[	[	X
ejpam-4958	326	2	14	14	NUM
ejpam-4958	326	3	]	]	X
ejpam-4958	326	4	bazighifan	bazighifan	NOUN
ejpam-4958	326	5	omar	omar	PROPN
ejpam-4958	326	6	and	and	CCONJ
ejpam-4958	326	7	kumam	kumam	PROPN
ejpam-4958	326	8	poom	poom	NOUN
ejpam-4958	326	9	.	.	PUNCT
ejpam-4958	327	1	oscillation	oscillation	NOUN
ejpam-4958	327	2	theorems	theorem	NOUN
ejpam-4958	327	3	for	for	ADP
ejpam-4958	327	4	advanced	advanced	ADJ
ejpam-4958	327	5	differential	differential	ADJ
ejpam-4958	327	6	equations	equation	NOUN
ejpam-4958	327	7	with	with	ADP
ejpam-4958	327	8	p	p	NOUN
ejpam-4958	327	9	-	-	PUNCT
ejpam-4958	327	10	laplacian	laplacian	ADJ
ejpam-4958	327	11	like	like	ADP
ejpam-4958	327	12	operators	operator	NOUN
ejpam-4958	327	13	.	.	PUNCT
ejpam-4958	328	1	mathematics	mathematic	NOUN
ejpam-4958	328	2	,	,	PUNCT
ejpam-4958	328	3	8(5):821	8(5):821	NUM
ejpam-4958	328	4	,	,	PUNCT
ejpam-4958	328	5	2020	2020	NUM
ejpam-4958	328	6	.	.	PUNCT
ejpam-4958	329	1	[	[	X
ejpam-4958	329	2	15	15	NUM
ejpam-4958	329	3	]	]	X
ejpam-4958	329	4	agarwal	agarwal	PROPN
ejpam-4958	329	5	r.	r.	PROPN
ejpam-4958	329	6	p.	p.	PROPN
ejpam-4958	329	7	,	,	PUNCT
ejpam-4958	329	8	zhang	zhang	PROPN
ejpam-4958	329	9	c.	c.	PROPN
ejpam-4958	329	10	,	,	PUNCT
ejpam-4958	329	11	and	and	CCONJ
ejpam-4958	329	12	li	li	PROPN
ejpam-4958	329	13	t.	t.	PROPN
ejpam-4958	329	14	some	some	DET
ejpam-4958	329	15	remarks	remark	NOUN
ejpam-4958	329	16	on	on	ADP
ejpam-4958	329	17	oscillation	oscillation	NOUN
ejpam-4958	329	18	of	of	ADP
ejpam-4958	329	19	second	second	ADJ
ejpam-4958	329	20	order	order	NOUN
ejpam-4958	329	21	neutral	neutral	ADJ
ejpam-4958	329	22	differential	differential	NOUN
ejpam-4958	329	23	equations	equation	NOUN
ejpam-4958	329	24	.	.	PUNCT
ejpam-4958	330	1	applied	apply	VERB
ejpam-4958	330	2	mathematics	mathematic	NOUN
ejpam-4958	330	3	and	and	CCONJ
ejpam-4958	330	4	computation	computation	NOUN
ejpam-4958	330	5	,	,	PUNCT
ejpam-4958	330	6	274:178–181	274:178–181	NUM
ejpam-4958	330	7	,	,	PUNCT
ejpam-4958	330	8	2016	2016	NUM
ejpam-4958	330	9	.	.	PUNCT
ejpam-4958	331	1	[	[	X
ejpam-4958	331	2	16	16	NUM
ejpam-4958	331	3	]	]	X
ejpam-4958	331	4	agarwal	agarwal	PROPN
ejpam-4958	331	5	r.	r.	PROPN
ejpam-4958	331	6	p.	p.	PROPN
ejpam-4958	331	7	,	,	PUNCT
ejpam-4958	331	8	grace	grace	PROPN
ejpam-4958	331	9	s.	s.	PROPN
ejpam-4958	331	10	r.	r.	PROPN
ejpam-4958	331	11	,	,	PUNCT
ejpam-4958	331	12	and	and	CCONJ
ejpam-4958	331	13	o’regan	o’regan	PROPN
ejpam-4958	331	14	d.	d.	PROPN
ejpam-4958	331	15	oscillation	oscillation	PROPN
ejpam-4958	331	16	theory	theory	NOUN
ejpam-4958	331	17	for	for	ADP
ejpam-4958	331	18	difference	difference	NOUN
ejpam-4958	331	19	and	and	CCONJ
ejpam-4958	331	20	functional	functional	ADJ
ejpam-4958	331	21	differential	differential	ADJ
ejpam-4958	331	22	equations	equation	NOUN
ejpam-4958	331	23	.	.	PUNCT
ejpam-4958	332	1	springer	springer	NOUN
ejpam-4958	332	2	science	science	PROPN
ejpam-4958	332	3	&	&	CCONJ
ejpam-4958	332	4	business	business	NOUN
ejpam-4958	332	5	media	medium	NOUN
ejpam-4958	332	6	,	,	PUNCT
ejpam-4958	332	7	2000	2000	NUM
ejpam-4958	332	8	.	.	PUNCT
ejpam-4958	333	1	references	reference	NOUN
ejpam-4958	333	2	2246	2246	NUM
ejpam-4958	333	3	[	[	X
ejpam-4958	333	4	17	17	NUM
ejpam-4958	333	5	]	]	X
ejpam-4958	333	6	agarwal	agarwal	PROPN
ejpam-4958	333	7	r.	r.	PROPN
ejpam-4958	333	8	p.	p.	PROPN
ejpam-4958	333	9	,	,	PUNCT
ejpam-4958	333	10	grace	grace	PROPN
ejpam-4958	333	11	s.	s.	PROPN
ejpam-4958	333	12	r.	r.	PROPN
ejpam-4958	333	13	,	,	PUNCT
ejpam-4958	333	14	and	and	CCONJ
ejpam-4958	333	15	o’regan	o’regan	PROPN
ejpam-4958	333	16	d.	d.	PROPN
ejpam-4958	333	17	oscillation	oscillation	PROPN
ejpam-4958	333	18	criteria	criterion	NOUN
ejpam-4958	333	19	for	for	ADP
ejpam-4958	333	20	certain	certain	ADJ
ejpam-4958	333	21	nth	nth	NOUN
ejpam-4958	333	22	order	order	NOUN
ejpam-4958	333	23	differential	differential	ADJ
ejpam-4958	333	24	equations	equation	NOUN
ejpam-4958	333	25	with	with	ADP
ejpam-4958	333	26	deviating	deviate	VERB
ejpam-4958	333	27	arguments	argument	NOUN
ejpam-4958	333	28	.	.	PUNCT
ejpam-4958	334	1	journal	journal	NOUN
ejpam-4958	334	2	of	of	ADP
ejpam-4958	334	3	mathematical	mathematical	ADJ
ejpam-4958	334	4	analysis	analysis	NOUN
ejpam-4958	334	5	and	and	CCONJ
ejpam-4958	334	6	applications	application	NOUN
ejpam-4958	334	7	,	,	PUNCT
ejpam-4958	334	8	262(2):601–622	262(2):601–622	NUM
ejpam-4958	334	9	,	,	PUNCT
ejpam-4958	334	10	2001	2001	NUM
ejpam-4958	334	11	.	.	PUNCT
ejpam-4958	335	1	[	[	X
ejpam-4958	335	2	18	18	NUM
ejpam-4958	335	3	]	]	X
ejpam-4958	335	4	agarwal	agarwal	PROPN
ejpam-4958	335	5	r.	r.	PROPN
ejpam-4958	335	6	p.	p.	PROPN
ejpam-4958	335	7	,	,	PUNCT
ejpam-4958	335	8	shieh	shieh	ADJ
ejpam-4958	335	9	s.-l	s.-l	NOUN
ejpam-4958	335	10	.	.	PUNCT
ejpam-4958	336	1	,	,	PUNCT
ejpam-4958	336	2	and	and	CCONJ
ejpam-4958	336	3	yeh	yeh	PROPN
ejpam-4958	336	4	c.-c	c.-c	PROPN
ejpam-4958	336	5	.	.	PUNCT
ejpam-4958	337	1	oscillation	oscillation	NOUN
ejpam-4958	337	2	criteria	criterion	NOUN
ejpam-4958	337	3	for	for	ADP
ejpam-4958	337	4	second	second	ADJ
ejpam-4958	337	5	-	-	PUNCT
ejpam-4958	337	6	order	order	NOUN
ejpam-4958	337	7	retarded	retarded	ADJ
ejpam-4958	337	8	differential	differential	ADJ
ejpam-4958	337	9	equations	equation	NOUN
ejpam-4958	337	10	.	.	PUNCT
ejpam-4958	338	1	mathematical	mathematical	ADJ
ejpam-4958	338	2	and	and	CCONJ
ejpam-4958	338	3	computer	computer	NOUN
ejpam-4958	338	4	modelling	modelling	NOUN
ejpam-4958	338	5	,	,	PUNCT
ejpam-4958	338	6	26(4):1–11	26(4):1–11	NUM
ejpam-4958	338	7	,	,	PUNCT
ejpam-4958	338	8	1997	1997	NUM
ejpam-4958	338	9	.	.	PUNCT
ejpam-4958	339	1	[	[	X
ejpam-4958	339	2	19	19	NUM
ejpam-4958	339	3	]	]	PUNCT
ejpam-4958	339	4	grace	grace	NOUN
ejpam-4958	339	5	s.	s.	PROPN
ejpam-4958	339	6	r.	r.	PROPN
ejpam-4958	339	7	,	,	PUNCT
ejpam-4958	339	8	dzurina	dzurina	PROPN
ejpam-4958	339	9	j.	j.	PROPN
ejpam-4958	339	10	,	,	PUNCT
ejpam-4958	339	11	jadlovska	jadlovska	PROPN
ejpam-4958	339	12	i.	i.	NOUN
ejpam-4958	339	13	,	,	PUNCT
ejpam-4958	339	14	and	and	CCONJ
ejpam-4958	339	15	li	li	PROPN
ejpam-4958	339	16	t.	t.	PROPN
ejpam-4958	339	17	an	an	DET
ejpam-4958	339	18	improved	improved	ADJ
ejpam-4958	339	19	approach	approach	NOUN
ejpam-4958	339	20	for	for	ADP
ejpam-4958	339	21	studying	study	VERB
ejpam-4958	339	22	oscillation	oscillation	NOUN
ejpam-4958	339	23	of	of	ADP
ejpam-4958	339	24	second	second	ADJ
ejpam-4958	339	25	-	-	PUNCT
ejpam-4958	339	26	order	order	NOUN
ejpam-4958	339	27	neutral	neutral	ADJ
ejpam-4958	339	28	delay	delay	NOUN
ejpam-4958	339	29	differential	differential	ADJ
ejpam-4958	339	30	equations	equation	NOUN
ejpam-4958	339	31	.	.	PUNCT
ejpam-4958	340	1	journal	journal	PROPN
ejpam-4958	340	2	of	of	ADP
ejpam-4958	340	3	inequalities	inequality	NOUN
ejpam-4958	340	4	and	and	CCONJ
ejpam-4958	340	5	applications	application	NOUN
ejpam-4958	340	6	,	,	PUNCT
ejpam-4958	340	7	2018(1):1–13	2018(1):1–13	NOUN
ejpam-4958	340	8	,	,	PUNCT
ejpam-4958	340	9	2018	2018	NUM
ejpam-4958	340	10	.	.	PUNCT
ejpam-4958	341	1	[	[	X
ejpam-4958	341	2	20	20	NUM
ejpam-4958	341	3	]	]	PUNCT
ejpam-4958	341	4	grace	grace	NOUN
ejpam-4958	341	5	s.	s.	PROPN
ejpam-4958	341	6	r.	r.	PROPN
ejpam-4958	341	7	,	,	PUNCT
ejpam-4958	341	8	agarwal	agarwal	PROPN
ejpam-4958	341	9	r.	r.	PROPN
ejpam-4958	341	10	p.	p.	PROPN
ejpam-4958	341	11	,	,	PUNCT
ejpam-4958	341	12	and	and	CCONJ
ejpam-4958	341	13	graef	graef	PROPN
ejpam-4958	341	14	j.	j.	PROPN
ejpam-4958	341	15	r.	r.	PROPN
ejpam-4958	341	16	oscillation	oscillation	PROPN
ejpam-4958	341	17	theorems	theorem	NOUN
ejpam-4958	341	18	for	for	ADP
ejpam-4958	341	19	fourth	fourth	ADJ
ejpam-4958	341	20	order	order	NOUN
ejpam-4958	341	21	functional	functional	ADJ
ejpam-4958	341	22	differential	differential	ADJ
ejpam-4958	341	23	equations	equation	NOUN
ejpam-4958	341	24	.	.	PUNCT
ejpam-4958	342	1	journal	journal	NOUN
ejpam-4958	342	2	of	of	ADP
ejpam-4958	342	3	applied	apply	VERB
ejpam-4958	342	4	mathematics	mathematic	NOUN
ejpam-4958	342	5	and	and	CCONJ
ejpam-4958	342	6	computing	computing	NOUN
ejpam-4958	342	7	,	,	PUNCT
ejpam-4958	342	8	30(1	30(1	PROPN
ejpam-4958	342	9	-	-	SYM
ejpam-4958	342	10	2):75–88	2):75–88	NUM
ejpam-4958	342	11	,	,	PUNCT
ejpam-4958	342	12	2009	2009	NUM
ejpam-4958	342	13	.	.	PUNCT
ejpam-4958	343	1	[	[	X
ejpam-4958	343	2	21	21	NUM
ejpam-4958	343	3	]	]	X
ejpam-4958	343	4	graef	graef	PROPN
ejpam-4958	343	5	j.	j.	PROPN
ejpam-4958	343	6	r.	r.	PROPN
ejpam-4958	343	7	and	and	CCONJ
ejpam-4958	343	8	saker	saker	PROPN
ejpam-4958	343	9	s.	s.	PROPN
ejpam-4958	343	10	h.	h.	PROPN
ejpam-4958	343	11	oscillation	oscillation	PROPN
ejpam-4958	343	12	theory	theory	NOUN
ejpam-4958	343	13	of	of	ADP
ejpam-4958	343	14	third	third	ADJ
ejpam-4958	343	15	-	-	PUNCT
ejpam-4958	343	16	order	order	NOUN
ejpam-4958	343	17	nonlinear	nonlinear	ADJ
ejpam-4958	343	18	functional	functional	ADJ
ejpam-4958	343	19	differential	differential	ADJ
ejpam-4958	343	20	equations	equation	NOUN
ejpam-4958	343	21	.	.	PUNCT
ejpam-4958	344	1	hiroshima	hiroshima	PROPN
ejpam-4958	344	2	mathematical	mathematical	PROPN
ejpam-4958	344	3	journal	journal	PROPN
ejpam-4958	344	4	,	,	PUNCT
ejpam-4958	344	5	43(1):49–72	43(1):49–72	NUM
ejpam-4958	344	6	,	,	PUNCT
ejpam-4958	344	7	2013	2013	NUM
ejpam-4958	344	8	.	.	PUNCT
ejpam-4958	345	1	[	[	X
ejpam-4958	345	2	22	22	NUM
ejpam-4958	345	3	]	]	X
ejpam-4958	345	4	yan	yan	PROPN
ejpam-4958	345	5	j.	j.	PROPN
ejpam-4958	345	6	r.	r.	PROPN
ejpam-4958	345	7	oscillation	oscillation	PROPN
ejpam-4958	345	8	theorems	theorem	NOUN
ejpam-4958	345	9	for	for	ADP
ejpam-4958	345	10	second	second	ADJ
ejpam-4958	345	11	order	order	NOUN
ejpam-4958	345	12	linear	linear	NOUN
ejpam-4958	345	13	differential	differential	NOUN
ejpam-4958	345	14	equations	equation	NOUN
ejpam-4958	345	15	with	with	ADP
ejpam-4958	345	16	damping	damp	VERB
ejpam-4958	345	17	.	.	PUNCT
ejpam-4958	346	1	proceedings	proceeding	NOUN
ejpam-4958	346	2	of	of	ADP
ejpam-4958	346	3	the	the	DET
ejpam-4958	346	4	american	american	PROPN
ejpam-4958	346	5	mathematical	mathematical	PROPN
ejpam-4958	346	6	society	society	NOUN
ejpam-4958	346	7	,	,	PUNCT
ejpam-4958	346	8	98(2):276–282	98(2):276–282	PROPN
ejpam-4958	346	9	,	,	PUNCT
ejpam-4958	346	10	1986	1986	NUM
ejpam-4958	346	11	.	.	PUNCT
ejpam-4958	347	1	[	[	X
ejpam-4958	347	2	23	23	NUM
ejpam-4958	347	3	]	]	X
ejpam-4958	347	4	ladde	ladde	PROPN
ejpam-4958	347	5	g.	g.	PROPN
ejpam-4958	347	6	s.	s.	PROPN
ejpam-4958	347	7	,	,	PUNCT
ejpam-4958	347	8	lakshmikantham	lakshmikantham	VERB
ejpam-4958	347	9	v.	v.	ADV
ejpam-4958	347	10	,	,	PUNCT
ejpam-4958	347	11	and	and	CCONJ
ejpam-4958	347	12	zhang	zhang	PROPN
ejpam-4958	347	13	b.	b.	PROPN
ejpam-4958	347	14	g.	g.	PROPN
ejpam-4958	347	15	oscillation	oscillation	PROPN
ejpam-4958	347	16	theory	theory	NOUN
ejpam-4958	347	17	of	of	ADP
ejpam-4958	347	18	differential	differential	ADJ
ejpam-4958	347	19	equations	equation	NOUN
ejpam-4958	347	20	with	with	ADP
ejpam-4958	347	21	deviating	deviate	VERB
ejpam-4958	347	22	arguments	argument	NOUN
ejpam-4958	347	23	.	.	PUNCT
ejpam-4958	348	1	m.	m.	NOUN
ejpam-4958	348	2	dekker	dekker	PROPN
ejpam-4958	348	3	new	new	PROPN
ejpam-4958	348	4	york	york	PROPN
ejpam-4958	348	5	,	,	PUNCT
ejpam-4958	348	6	1987	1987	NUM
ejpam-4958	348	7	.	.	PUNCT
ejpam-4958	349	1	[	[	X
ejpam-4958	349	2	24	24	NUM
ejpam-4958	349	3	]	]	X
ejpam-4958	349	4	khan	khan	PROPN
ejpam-4958	349	5	sana	sana	PROPN
ejpam-4958	349	6	ullah	ullah	PROPN
ejpam-4958	349	7	,	,	PUNCT
ejpam-4958	349	8	khan	khan	PROPN
ejpam-4958	349	9	asif	asif	PROPN
ejpam-4958	349	10	,	,	PUNCT
ejpam-4958	349	11	ullah	ullah	PROPN
ejpam-4958	349	12	aman	aman	PROPN
ejpam-4958	349	13	,	,	PUNCT
ejpam-4958	349	14	ahmad	ahmad	PROPN
ejpam-4958	349	15	shabir	shabir	PROPN
ejpam-4958	349	16	,	,	PUNCT
ejpam-4958	349	17	awwad	awwad	PROPN
ejpam-4958	349	18	fuad	fuad	PROPN
ejpam-4958	349	19	a	a	PRON
ejpam-4958	349	20	,	,	PUNCT
ejpam-4958	349	21	ismail	ismail	PROPN
ejpam-4958	349	22	emad	emad	PROPN
ejpam-4958	349	23	aa	aa	PROPN
ejpam-4958	349	24	,	,	PUNCT
ejpam-4958	349	25	maitama	maitama	PROPN
ejpam-4958	349	26	shehu	shehu	PROPN
ejpam-4958	349	27	,	,	PUNCT
ejpam-4958	349	28	umar	umar	PROPN
ejpam-4958	349	29	huzaifa	huzaifa	PROPN
ejpam-4958	349	30	,	,	PUNCT
ejpam-4958	349	31	and	and	CCONJ
ejpam-4958	349	32	ahmad	ahmad	PROPN
ejpam-4958	349	33	hijaz	hijaz	PROPN
ejpam-4958	349	34	.	.	PUNCT
ejpam-4958	350	1	solving	solve	VERB
ejpam-4958	350	2	nthorder	nthorder	NOUN
ejpam-4958	350	3	integro	integro	PROPN
ejpam-4958	350	4	-	-	PUNCT
ejpam-4958	350	5	differential	differential	NOUN
ejpam-4958	350	6	equations	equation	NOUN
ejpam-4958	350	7	by	by	ADP
ejpam-4958	350	8	novel	novel	ADJ
ejpam-4958	350	9	generalized	generalize	VERB
ejpam-4958	350	10	hybrid	hybrid	NOUN
ejpam-4958	350	11	transform	transform	NOUN
ejpam-4958	350	12	.	.	PUNCT
ejpam-4958	351	1	european	european	PROPN
ejpam-4958	351	2	journal	journal	PROPN
ejpam-4958	351	3	of	of	ADP
ejpam-4958	351	4	pure	pure	ADJ
ejpam-4958	351	5	and	and	CCONJ
ejpam-4958	351	6	applied	applied	ADJ
ejpam-4958	351	7	mathematics	mathematic	NOUN
ejpam-4958	351	8	,	,	PUNCT
ejpam-4958	351	9	16(3):1940–1955	16(3):1940–1955	NUM
ejpam-4958	351	10	,	,	PUNCT
ejpam-4958	351	11	2023	2023	NUM
ejpam-4958	351	12	.	.	PUNCT
ejpam-4958	352	1	[	[	X
ejpam-4958	352	2	25	25	NUM
ejpam-4958	352	3	]	]	X
ejpam-4958	352	4	nagabuchi	nagabuchi	PROPN
ejpam-4958	352	5	y.	y.	PROPN
ejpam-4958	352	6	and	and	CCONJ
ejpam-4958	352	7	yamamoto	yamamoto	PROPN
ejpam-4958	352	8	m.	m.	NOUN
ejpam-4958	353	1	some	some	DET
ejpam-4958	353	2	oscillation	oscillation	NOUN
ejpam-4958	353	3	criteria	criterion	NOUN
ejpam-4958	353	4	for	for	ADP
ejpam-4958	353	5	second	second	ADJ
ejpam-4958	353	6	order	order	NOUN
ejpam-4958	353	7	nonlinear	nonlinear	ADJ
ejpam-4958	353	8	ordinary	ordinary	ADJ
ejpam-4958	353	9	differential	differential	ADJ
ejpam-4958	353	10	equations	equation	NOUN
ejpam-4958	353	11	with	with	ADP
ejpam-4958	353	12	damping	damp	VERB
ejpam-4958	353	13	.	.	PUNCT
ejpam-4958	354	1	proc	proc	PROPN
ejpam-4958	354	2	.	.	PUNCT
ejpam-4958	355	1	japan	japan	PROPN
ejpam-4958	355	2	acad	acad	PROPN
ejpam-4958	355	3	.	.	PUNCT
ejpam-4958	356	1	ser	ser	PROPN
ejpam-4958	356	2	.	.	PUNCT
ejpam-4958	357	1	a	a	DET
ejpam-4958	357	2	math	math	NOUN
ejpam-4958	357	3	.	.	PUNCT
ejpam-4958	358	1	sci	sci	PROPN
ejpam-4958	358	2	.	.	PROPN
ejpam-4958	358	3	,	,	PUNCT
ejpam-4958	358	4	64(8):282–285	64(8):282–285	PROPN
ejpam-4958	358	5	,	,	PUNCT
ejpam-4958	358	6	1988	1988	NUM
ejpam-4958	358	7	.	.	PUNCT
ejpam-4958	359	1	[	[	X
ejpam-4958	359	2	26	26	NUM
ejpam-4958	359	3	]	]	PUNCT
ejpam-4958	359	4	xu	xu	PROPN
ejpam-4958	359	5	z.	z.	PROPN
ejpam-4958	359	6	and	and	CCONJ
ejpam-4958	359	7	xia	xia	PROPN
ejpam-4958	359	8	y.	y.	PROPN
ejpam-4958	359	9	integral	integral	ADJ
ejpam-4958	359	10	averaging	averaging	NOUN
ejpam-4958	359	11	technique	technique	NOUN
ejpam-4958	359	12	and	and	CCONJ
ejpam-4958	359	13	oscillation	oscillation	NOUN
ejpam-4958	359	14	of	of	ADP
ejpam-4958	359	15	certain	certain	ADJ
ejpam-4958	359	16	even	even	ADJ
ejpam-4958	359	17	order	order	NOUN
ejpam-4958	359	18	delay	delay	NOUN
ejpam-4958	359	19	differential	differential	ADJ
ejpam-4958	359	20	equations	equation	NOUN
ejpam-4958	359	21	.	.	PUNCT
ejpam-4958	360	1	journal	journal	PROPN
ejpam-4958	360	2	of	of	ADP
ejpam-4958	360	3	mathematical	mathematical	ADJ
ejpam-4958	360	4	analysis	analysis	NOUN
ejpam-4958	360	5	and	and	CCONJ
ejpam-4958	360	6	applications	application	NOUN
ejpam-4958	360	7	,	,	PUNCT
ejpam-4958	360	8	292(1):292	292(1):292	NUM
ejpam-4958	360	9	,	,	PUNCT
ejpam-4958	360	10	2004	2004	NUM
ejpam-4958	360	11	.	.	PUNCT