id	sid	tid	token	lemma	pos
iajs-3515	1	1	407	407	NUM
iajs-3515	1	2	©	©	ADP
iajs-3515	1	3	2025	2025	NUM
iajs-3515	1	4	the	the	DET
iajs-3515	1	5	author(s	author(s	NOUN
iajs-3515	1	6	)	)	PUNCT
iajs-3515	1	7	.	.	PUNCT
iajs-3515	2	1	published	publish	VERB
iajs-3515	2	2	by	by	ADP
iajs-3515	2	3	college	college	NOUN
iajs-3515	2	4	of	of	ADP
iajs-3515	2	5	education	education	NOUN
iajs-3515	2	6	for	for	ADP
iajs-3515	2	7	pure	pure	ADJ
iajs-3515	2	8	science	science	NOUN
iajs-3515	2	9	(	(	PUNCT
iajs-3515	2	10	ibn	ibn	PROPN
iajs-3515	2	11	al	al	PROPN
iajs-3515	2	12	-	-	PUNCT
iajs-3515	2	13	haitham	haitham	PROPN
iajs-3515	2	14	)	)	PUNCT
iajs-3515	2	15	,	,	PUNCT
iajs-3515	2	16	university	university	NOUN
iajs-3515	2	17	of	of	ADP
iajs-3515	2	18	baghdad	baghdad	PROPN
iajs-3515	2	19	.	.	PUNCT
iajs-3515	3	1	this	this	PRON
iajs-3515	3	2	is	be	AUX
iajs-3515	3	3	an	an	DET
iajs-3515	3	4	open	open	ADJ
iajs-3515	3	5	-	-	PUNCT
iajs-3515	3	6	access	access	NOUN
iajs-3515	3	7	article	article	NOUN
iajs-3515	3	8	distributed	distribute	VERB
iajs-3515	3	9	under	under	ADP
iajs-3515	3	10	the	the	DET
iajs-3515	3	11	terms	term	NOUN
iajs-3515	3	12	of	of	ADP
iajs-3515	3	13	the	the	DET
iajs-3515	3	14	creative	creative	ADJ
iajs-3515	3	15	commons	common	NOUN
iajs-3515	3	16	attribution	attribution	NOUN
iajs-3515	3	17	4.0	4.0	NUM
iajs-3515	3	18	international	international	ADJ
iajs-3515	3	19	license	license	NOUN
iajs-3515	3	20	oscillation	oscillation	NOUN
iajs-3515	3	21	criteria	criterion	NOUN
iajs-3515	3	22	for	for	ADP
iajs-3515	3	23	solutions	solution	NOUN
iajs-3515	3	24	of	of	ADP
iajs-3515	3	25	neutral	neutral	ADJ
iajs-3515	3	26	differential	differential	ADJ
iajs-3515	3	27	equations	equation	NOUN
iajs-3515	3	28	of	of	ADP
iajs-3515	3	29	the	the	DET
iajs-3515	3	30	second	second	ADJ
iajs-3515	3	31	-	-	PUNCT
iajs-3515	3	32	order	order	NOUN
iajs-3515	3	33	emden	emden	ADJ
iajs-3515	3	34	-	-	PUNCT
iajs-3515	3	35	fowler	fowler	NOUN
iajs-3515	3	36	type	type	NOUN
iajs-3515	3	37	with	with	ADP
iajs-3515	3	38	forcing	force	VERB
iajs-3515	3	39	term	term	NOUN
iajs-3515	3	40	jihan	jihan	PROPN
iajs-3515	3	41	saad1	saad1	PROPN
iajs-3515	3	42	*	*	PUNCT
iajs-3515	3	43	and	and	CCONJ
iajs-3515	3	44	hussain	hussain	PROPN
iajs-3515	3	45	ali	ali	PROPN
iajs-3515	3	46	mohamad2	mohamad2	PROPN
iajs-3515	4	1	1,2department	1,2department	NUM
iajs-3515	4	2	of	of	ADP
iajs-3515	4	3	mathematics	mathematic	NOUN
iajs-3515	4	4	,	,	PUNCT
iajs-3515	4	5	college	college	NOUN
iajs-3515	4	6	of	of	ADP
iajs-3515	4	7	science	science	NOUN
iajs-3515	4	8	for	for	ADP
iajs-3515	4	9	women	woman	NOUN
iajs-3515	4	10	,	,	PUNCT
iajs-3515	4	11	university	university	NOUN
iajs-3515	4	12	of	of	ADP
iajs-3515	4	13	baghdad	baghdad	PROPN
iajs-3515	4	14	,	,	PUNCT
iajs-3515	4	15	baghdad	baghdad	PROPN
iajs-3515	4	16	,	,	PUNCT
iajs-3515	4	17	iraq	iraq	PROPN
iajs-3515	4	18	.	.	PUNCT
iajs-3515	5	1	*	*	PUNCT
iajs-3515	5	2	corresponding	correspond	VERB
iajs-3515	5	3	author	author	NOUN
iajs-3515	5	4	.	.	PUNCT
iajs-3515	6	1	received:22	received:22	PROPN
iajs-3515	7	1	may	may	AUX
iajs-3515	7	2	2023	2023	NUM
iajs-3515	7	3	accepted:14	accepted:14	PUNCT
iajs-3515	7	4	august	august	PROPN
iajs-3515	7	5	2023	2023	NUM
iajs-3515	7	6	published:20	published:20	NOUN
iajs-3515	7	7	january	january	PROPN
iajs-3515	7	8	2025	2025	NUM
iajs-3515	7	9	doi.org/10.30526/38.1.3515	doi.org/10.30526/38.1.3515	NOUN
iajs-3515	7	10	abstract	abstract	ADJ
iajs-3515	7	11	in	in	ADP
iajs-3515	7	12	this	this	DET
iajs-3515	7	13	paper	paper	NOUN
iajs-3515	7	14	,	,	PUNCT
iajs-3515	7	15	the	the	DET
iajs-3515	7	16	oscillation	oscillation	NOUN
iajs-3515	7	17	property	property	NOUN
iajs-3515	7	18	and	and	CCONJ
iajs-3515	7	19	the	the	DET
iajs-3515	7	20	asymptotic	asymptotic	ADJ
iajs-3515	7	21	behavior	behavior	NOUN
iajs-3515	7	22	of	of	ADP
iajs-3515	7	23	solutions	solution	NOUN
iajs-3515	7	24	of	of	ADP
iajs-3515	7	25	neutral	neutral	ADJ
iajs-3515	7	26	secondorder	secondorder	NOUN
iajs-3515	7	27	differential	differential	NOUN
iajs-3515	7	28	equations	equation	NOUN
iajs-3515	7	29	of	of	ADP
iajs-3515	7	30	the	the	DET
iajs-3515	7	31	emden	emden	ADJ
iajs-3515	7	32	-	-	PUNCT
iajs-3515	7	33	fowler	fowler	PROPN
iajs-3515	7	34	type	type	NOUN
iajs-3515	7	35	were	be	AUX
iajs-3515	7	36	studied	study	VERB
iajs-3515	7	37	under	under	ADP
iajs-3515	7	38	the	the	DET
iajs-3515	7	39	influence	influence	NOUN
iajs-3515	7	40	of	of	ADP
iajs-3515	7	41	the	the	DET
iajs-3515	7	42	coefficients	coefficient	NOUN
iajs-3515	7	43	of	of	ADP
iajs-3515	7	44	forces	force	NOUN
iajs-3515	7	45	.	.	PUNCT
iajs-3515	8	1	it	it	PRON
iajs-3515	8	2	has	have	AUX
iajs-3515	8	3	been	be	AUX
iajs-3515	8	4	shown	show	VERB
iajs-3515	8	5	through	through	ADP
iajs-3515	8	6	this	this	DET
iajs-3515	8	7	research	research	NOUN
iajs-3515	8	8	that	that	SCONJ
iajs-3515	8	9	the	the	DET
iajs-3515	8	10	coefficients	coefficient	NOUN
iajs-3515	8	11	of	of	ADP
iajs-3515	8	12	forces	force	NOUN
iajs-3515	8	13	in	in	ADP
iajs-3515	8	14	addition	addition	NOUN
iajs-3515	8	15	to	to	ADP
iajs-3515	8	16	the	the	DET
iajs-3515	8	17	emden	emden	ADJ
iajs-3515	8	18	-	-	PUNCT
iajs-3515	8	19	fowler	fowler	NOUN
iajs-3515	8	20	type	type	NOUN
iajs-3515	8	21	have	have	VERB
iajs-3515	8	22	a	a	DET
iajs-3515	8	23	major	major	ADJ
iajs-3515	8	24	role	role	NOUN
iajs-3515	8	25	on	on	ADP
iajs-3515	8	26	the	the	DET
iajs-3515	8	27	oscillation	oscillation	NOUN
iajs-3515	8	28	of	of	ADP
iajs-3515	8	29	solutions	solution	NOUN
iajs-3515	8	30	of	of	ADP
iajs-3515	8	31	neutral	neutral	ADJ
iajs-3515	8	32	equations	equation	NOUN
iajs-3515	8	33	.	.	PUNCT
iajs-3515	9	1	as	as	ADV
iajs-3515	9	2	well	well	ADV
iajs-3515	9	3	as	as	ADP
iajs-3515	9	4	its	its	PRON
iajs-3515	9	5	effect	effect	NOUN
iajs-3515	9	6	on	on	ADP
iajs-3515	9	7	the	the	DET
iajs-3515	9	8	convergence	convergence	NOUN
iajs-3515	9	9	and	and	CCONJ
iajs-3515	9	10	divergence	divergence	NOUN
iajs-3515	9	11	of	of	ADP
iajs-3515	9	12	nonoscillatory	nonoscillatory	ADJ
iajs-3515	9	13	solutions	solution	NOUN
iajs-3515	9	14	.	.	PUNCT
iajs-3515	10	1	for	for	ADP
iajs-3515	10	2	this	this	DET
iajs-3515	10	3	purpose	purpose	NOUN
iajs-3515	10	4	,	,	PUNCT
iajs-3515	10	5	some	some	DET
iajs-3515	10	6	conditions	condition	NOUN
iajs-3515	10	7	are	be	AUX
iajs-3515	10	8	obtained	obtain	VERB
iajs-3515	10	9	to	to	PART
iajs-3515	10	10	ensure	ensure	VERB
iajs-3515	10	11	that	that	SCONJ
iajs-3515	10	12	all	all	DET
iajs-3515	10	13	solutions	solution	NOUN
iajs-3515	10	14	of	of	ADP
iajs-3515	10	15	the	the	DET
iajs-3515	10	16	neutral	neutral	ADJ
iajs-3515	10	17	equations	equation	NOUN
iajs-3515	10	18	emden	emden	ADJ
iajs-3515	10	19	-	-	PUNCT
iajs-3515	10	20	fowler	fowler	NOUN
iajs-3515	10	21	type	type	NOUN
iajs-3515	10	22	oscillating	oscillating	NOUN
iajs-3515	10	23	or	or	CCONJ
iajs-3515	10	24	nonoscillating	nonoscillate	VERB
iajs-3515	10	25	go	go	VERB
iajs-3515	10	26	to	to	ADP
iajs-3515	10	27	∞	∞	PROPN
iajs-3515	10	28	,	,	PUNCT
iajs-3515	10	29	as	as	ADP
iajs-3515	10	30	t	t	PROPN
iajs-3515	10	31	→	→	SYM
iajs-3515	10	32	∞.	∞.	PROPN
iajs-3515	10	33	some	some	PRON
iajs-3515	10	34	of	of	ADP
iajs-3515	10	35	these	these	DET
iajs-3515	10	36	conditions	condition	NOUN
iajs-3515	10	37	are	be	AUX
iajs-3515	10	38	the	the	DET
iajs-3515	10	39	development	development	NOUN
iajs-3515	10	40	of	of	ADP
iajs-3515	10	41	conditions	condition	NOUN
iajs-3515	10	42	similar	similar	ADJ
iajs-3515	10	43	to	to	ADP
iajs-3515	10	44	them	they	PRON
iajs-3515	10	45	in	in	ADP
iajs-3515	10	46	some	some	PRON
iajs-3515	10	47	of	of	ADP
iajs-3515	10	48	the	the	DET
iajs-3515	10	49	well	well	ADV
iajs-3515	10	50	-	-	PUNCT
iajs-3515	10	51	known	know	VERB
iajs-3515	10	52	results	result	NOUN
iajs-3515	10	53	included	include	VERB
iajs-3515	10	54	in	in	ADP
iajs-3515	10	55	the	the	DET
iajs-3515	10	56	references	reference	NOUN
iajs-3515	10	57	,	,	PUNCT
iajs-3515	10	58	for	for	ADP
iajs-3515	10	59	example	example	NOUN
iajs-3515	10	60	,	,	PUNCT
iajs-3515	10	61	condition	condition	NOUN
iajs-3515	10	62	(	(	PUNCT
iajs-3515	10	63	8)	8)	NUM
iajs-3515	10	64	in	in	ADP
iajs-3515	10	65	this	this	DET
iajs-3515	10	66	research	research	NOUN
iajs-3515	10	67	with	with	ADP
iajs-3515	10	68	condition	condition	NOUN
iajs-3515	10	69	(	(	PUNCT
iajs-3515	10	70	4	4	NUM
iajs-3515	10	71	)	)	PUNCT
iajs-3515	10	72	in	in	ADP
iajs-3515	10	73	(	(	PUNCT
iajs-3515	10	74	9	9	NUM
iajs-3515	10	75	)	)	PUNCT
iajs-3515	10	76	.	.	PUNCT
iajs-3515	11	1	the	the	DET
iajs-3515	11	2	obtained	obtain	VERB
iajs-3515	11	3	results	result	NOUN
iajs-3515	11	4	included	include	VERB
iajs-3515	11	5	some	some	DET
iajs-3515	11	6	illustrative	illustrative	ADJ
iajs-3515	11	7	examples	example	NOUN
iajs-3515	11	8	showing	show	VERB
iajs-3515	11	9	that	that	SCONJ
iajs-3515	11	10	the	the	DET
iajs-3515	11	11	resulting	result	VERB
iajs-3515	11	12	conditions	condition	NOUN
iajs-3515	11	13	are	be	AUX
iajs-3515	11	14	easy	easy	ADJ
iajs-3515	11	15	to	to	PART
iajs-3515	11	16	apply	apply	VERB
iajs-3515	11	17	and	and	CCONJ
iajs-3515	11	18	guarantee	guarantee	VERB
iajs-3515	11	19	oscillation	oscillation	NOUN
iajs-3515	11	20	.	.	PUNCT
iajs-3515	12	1	keywords	keyword	NOUN
iajs-3515	12	2	:	:	PUNCT
iajs-3515	12	3	oscillation	oscillation	NOUN
iajs-3515	12	4	criteria	criterion	NOUN
iajs-3515	12	5	,	,	PUNCT
iajs-3515	12	6	asymptotic	asymptotic	ADJ
iajs-3515	12	7	behavior	behavior	NOUN
iajs-3515	12	8	,	,	PUNCT
iajs-3515	12	9	emden	emden	ADJ
iajs-3515	12	10	-	-	PUNCT
iajs-3515	12	11	fowler	fowler	PROPN
iajs-3515	12	12	type	type	NOUN
iajs-3515	12	13	,	,	PUNCT
iajs-3515	12	14	neutral	neutral	ADJ
iajs-3515	12	15	second	second	ADJ
iajs-3515	12	16	order	order	NOUN
iajs-3515	12	17	with	with	ADP
iajs-3515	12	18	forcing	force	VERB
iajs-3515	12	19	term	term	NOUN
iajs-3515	12	20	.	.	PUNCT
iajs-3515	13	1	1	1	X
iajs-3515	13	2	.	.	X
iajs-3515	13	3	introduction	introduction	NOUN
iajs-3515	13	4	this	this	DET
iajs-3515	13	5	paper	paper	NOUN
iajs-3515	13	6	aims	aim	VERB
iajs-3515	13	7	to	to	PART
iajs-3515	13	8	obtain	obtain	VERB
iajs-3515	13	9	sufficient	sufficient	ADJ
iajs-3515	13	10	conditions	condition	NOUN
iajs-3515	13	11	to	to	PART
iajs-3515	13	12	ensure	ensure	VERB
iajs-3515	13	13	that	that	SCONJ
iajs-3515	13	14	every	every	DET
iajs-3515	13	15	solution	solution	NOUN
iajs-3515	13	16	of	of	ADP
iajs-3515	13	17	the	the	DET
iajs-3515	13	18	neutral	neutral	ADJ
iajs-3515	13	19	force	force	NOUN
iajs-3515	13	20	equation	equation	NOUN
iajs-3515	13	21	of	of	ADP
iajs-3515	13	22	the	the	DET
iajs-3515	13	23	second	second	ADJ
iajs-3515	13	24	-	-	PUNCT
iajs-3515	13	25	order	order	NOUN
iajs-3515	13	26	type	type	NOUN
iajs-3515	13	27	emden	emden	VERB
iajs-3515	13	28	fowler	fowler	PROPN
iajs-3515	13	29	oscillates	oscillates	PROPN
iajs-3515	13	30	.	.	PUNCT
iajs-3515	14	1	consider	consider	VERB
iajs-3515	14	2	the	the	DET
iajs-3515	14	3	equation	equation	NOUN
iajs-3515	14	4	:	:	PUNCT
iajs-3515	14	5	(	(	PUNCT
iajs-3515	14	6	𝝃(𝒕)(𝝎′(𝒕	𝝃(𝒕)(𝝎′(𝒕	NUM
iajs-3515	14	7	)	)	PUNCT
iajs-3515	14	8	)	)	PUNCT
iajs-3515	15	1	𝜸	𝜸	X
iajs-3515	15	2	)	)	PUNCT
iajs-3515	15	3	′	′	NUM
iajs-3515	16	1	+	+	CCONJ
iajs-3515	16	2	∑	∑	PROPN
iajs-3515	16	3	𝒒𝒊(𝒕)𝒙𝜸(𝜹𝒊(𝒕	𝒒𝒊(𝒕)𝒙𝜸(𝜹𝒊(𝒕	NUM
iajs-3515	16	4	)	)	PUNCT
iajs-3515	16	5	)	)	PUNCT
iajs-3515	17	1	𝒏	𝒏	PROPN
iajs-3515	17	2	𝒊=𝟏	𝒊=𝟏	PROPN
iajs-3515	17	3	𝐬𝐠𝐧(𝒙	𝐬𝐠𝐧(𝒙	X
iajs-3515	17	4	)	)	PUNCT
iajs-3515	17	5	=	=	SYM
iajs-3515	17	6	∑	∑	PUNCT
iajs-3515	17	7	𝒓𝒋(𝒕	𝒓𝒋(𝒕	PROPN
iajs-3515	17	8	)	)	PUNCT
iajs-3515	17	9	𝒌	𝒌	PRON
iajs-3515	17	10	𝒋=𝟏	𝒋=𝟏	PUNCT
iajs-3515	17	11	.	.	PUNCT
iajs-3515	18	1	(	(	PUNCT
iajs-3515	18	2	𝟏	𝟏	X
iajs-3515	18	3	)	)	PUNCT
iajs-3515	18	4	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	18	5	)	)	PUNCT
iajs-3515	18	6	=	=	SYM
iajs-3515	18	7	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	18	8	)	)	PUNCT
iajs-3515	18	9	+	+	NUM
iajs-3515	18	10	𝑝(𝑡)𝑥(𝜏(𝑡	𝑝(𝑡)𝑥(𝜏(𝑡	NOUN
iajs-3515	18	11	)	)	PUNCT
iajs-3515	18	12	)	)	PUNCT
iajs-3515	18	13	.	.	PUNCT
iajs-3515	19	1	(	(	PUNCT
iajs-3515	19	2	2	2	X
iajs-3515	19	3	)	)	PUNCT
iajs-3515	19	4	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3515	19	5	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3515	19	6	https://doi.org/10.30526/38.1.3501	https://doi.org/10.30526/38.1.3501	PROPN
iajs-3515	19	7	https://orcid.org/0009-0000-2264-7057	https://orcid.org/0009-0000-2264-7057	PROPN
iajs-3515	19	8	mailto:jihan.saad2103m@csw.uobaghdad.edu.iq	mailto:jihan.saad2103m@csw.uobaghdad.edu.iq	PROPN
iajs-3515	19	9	https://orcid.org/0000-0002-4684-786x	https://orcid.org/0000-0002-4684-786x	PROPN
iajs-3515	19	10	mailto:hussainam_math@csw.uobaghdad.edu.iq	mailto:hussainam_math@csw.uobaghdad.edu.iq	NOUN
iajs-3515	19	11	ihjpas	ihjpa	NOUN
iajs-3515	19	12	.	.	PUNCT
iajs-3515	20	1	2024	2024	NUM
iajs-3515	20	2	,	,	PUNCT
iajs-3515	20	3	38	38	NUM
iajs-3515	20	4	(	(	PUNCT
iajs-3515	20	5	1	1	NUM
iajs-3515	20	6	)	)	PUNCT
iajs-3515	20	7	408	408	NUM
iajs-3515	20	8	the	the	DET
iajs-3515	20	9	number	number	NOUN
iajs-3515	20	10	𝛾	𝛾	NOUN
iajs-3515	20	11	is	be	AUX
iajs-3515	20	12	a	a	DET
iajs-3515	20	13	quotient	quotient	NOUN
iajs-3515	20	14	of	of	ADP
iajs-3515	20	15	odd	odd	ADJ
iajs-3515	20	16	positive	positive	ADJ
iajs-3515	20	17	integers	integer	NOUN
iajs-3515	20	18	.	.	PUNCT
iajs-3515	21	1	𝜏	𝜏	X
iajs-3515	21	2	,	,	PUNCT
iajs-3515	21	3	𝛿𝑖	𝛿𝑖	X
iajs-3515	21	4	∈	∈	PROPN
iajs-3515	21	5	∁	∁	PROPN
iajs-3515	21	6	(	(	PUNCT
iajs-3515	21	7	[	[	X
iajs-3515	21	8	𝑡0	𝑡0	NOUN
iajs-3515	21	9	,	,	PUNCT
iajs-3515	21	10	∞)𝕋	∞)𝕋	INTJ
iajs-3515	21	11	,	,	PUNCT
iajs-3515	21	12	𝑅	𝑅	PROPN
iajs-3515	21	13	)	)	PUNCT
iajs-3515	21	14	,	,	PUNCT
iajs-3515	21	15	𝑖	𝑖	NOUN
iajs-3515	21	16	=	=	SYM
iajs-3515	21	17	1,2	1,2	NUM
iajs-3515	21	18	,	,	PUNCT
iajs-3515	21	19	…	…	PUNCT
iajs-3515	21	20	,	,	PUNCT
iajs-3515	21	21	𝑛	𝑛	PROPN
iajs-3515	21	22	,	,	PUNCT
iajs-3515	21	23	lim	lim	PROPN
iajs-3515	21	24	t→∞	t→∞	X
iajs-3515	21	25	𝜏(𝑡	𝜏(𝑡	PROPN
iajs-3515	21	26	)	)	PUNCT
iajs-3515	22	1	=	=	SYM
iajs-3515	22	2	∞	∞	PROPN
iajs-3515	22	3	,	,	PUNCT
iajs-3515	22	4	lim	lim	PROPN
iajs-3515	22	5	t→∞	t→∞	PRON
iajs-3515	22	6	𝛿𝑖(𝑡	𝛿𝑖(𝑡	NUM
iajs-3515	22	7	)	)	PUNCT
iajs-3515	22	8	=	=	SYM
iajs-3515	22	9	∞	∞	PROPN
iajs-3515	22	10	,	,	PUNCT
iajs-3515	22	11	sgn(𝑥	sgn(𝑥	NOUN
iajs-3515	22	12	)	)	PUNCT
iajs-3515	22	13	=	=	VERB
iajs-3515	22	14	±1	±1	VERB
iajs-3515	22	15	if	if	SCONJ
iajs-3515	22	16	𝑥	𝑥	PROPN
iajs-3515	22	17	≷	≷	ADJ
iajs-3515	22	18	0	0	NUM
iajs-3515	22	19	,	,	PUNCT
iajs-3515	22	20	𝑠𝑔𝑛(0	𝑠𝑔𝑛(0	PUNCT
iajs-3515	22	21	)	)	PUNCT
iajs-3515	23	1	=	=	SYM
iajs-3515	23	2	0	0	NUM
iajs-3515	23	3	,	,	PUNCT
iajs-3515	23	4	𝑝	𝑝	PROPN
iajs-3515	23	5	∈	∈	PROPN
iajs-3515	23	6	∁([𝑡0	∁([𝑡0	PROPN
iajs-3515	23	7	,	,	PUNCT
iajs-3515	23	8	∞	∞	PROPN
iajs-3515	23	9	)	)	PUNCT
iajs-3515	23	10	,	,	PUNCT
iajs-3515	23	11	𝑅+	𝑅+	PROPN
iajs-3515	23	12	)	)	PUNCT
iajs-3515	23	13	and	and	CCONJ
iajs-3515	23	14	𝑞𝑖	𝑞𝑖	INTJ
iajs-3515	23	15	,	,	PUNCT
iajs-3515	23	16	𝑟𝑗	𝑟𝑗	ADP
iajs-3515	23	17	∈	∈	PROPN
iajs-3515	23	18	∁	∁	PROPN
iajs-3515	23	19	(	(	PUNCT
iajs-3515	23	20	[	[	X
iajs-3515	23	21	𝑡0	𝑡0	NOUN
iajs-3515	23	22	,	,	PUNCT
iajs-3515	23	23	∞	∞	PROPN
iajs-3515	23	24	)	)	PUNCT
iajs-3515	23	25	,	,	PUNCT
iajs-3515	23	26	𝑅	𝑅	PROPN
iajs-3515	23	27	)	)	PUNCT
iajs-3515	23	28	,	,	PUNCT
iajs-3515	23	29	𝑖	𝑖	NOUN
iajs-3515	23	30	=	=	SYM
iajs-3515	23	31	1,2	1,2	NUM
iajs-3515	23	32	,	,	PUNCT
iajs-3515	23	33	…	…	PUNCT
iajs-3515	23	34	,	,	PUNCT
iajs-3515	23	35	𝑛	𝑛	NOUN
iajs-3515	23	36	,	,	PUNCT
iajs-3515	23	37	𝑗	𝑗	NOUN
iajs-3515	23	38	=	=	SYM
iajs-3515	23	39	1,2	1,2	NUM
iajs-3515	23	40	,	,	PUNCT
iajs-3515	23	41	…	…	PUNCT
iajs-3515	23	42	,	,	PUNCT
iajs-3515	23	43	𝑘.	𝑘.	NOUN
iajs-3515	23	44	during	during	ADP
iajs-3515	23	45	this	this	DET
iajs-3515	23	46	research	research	NOUN
iajs-3515	23	47	,	,	PUNCT
iajs-3515	23	48	the	the	DET
iajs-3515	23	49	following	follow	VERB
iajs-3515	23	50	assumptions	assumption	NOUN
iajs-3515	23	51	will	will	AUX
iajs-3515	23	52	be	be	AUX
iajs-3515	23	53	used	use	VERB
iajs-3515	23	54	as	as	ADP
iajs-3515	23	55	needed	need	VERB
iajs-3515	23	56	:	:	PUNCT
iajs-3515	23	57	(	(	PUNCT
iajs-3515	23	58	m1	m1	NOUN
iajs-3515	23	59	)	)	PUNCT
iajs-3515	23	60	lim	lim	PROPN
iajs-3515	23	61	sup	sup	PROPN
iajs-3515	23	62	𝑡→∞	𝑡→∞	NUM
iajs-3515	23	63	∫	∫	PROPN
iajs-3515	23	64	(	(	PUNCT
iajs-3515	23	65	1	1	NUM
iajs-3515	23	66	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	23	67	)	)	PUNCT
iajs-3515	23	68	)	)	PUNCT
iajs-3515	23	69	1	1	NUM
iajs-3515	23	70	𝛾	𝛾	NOUN
iajs-3515	23	71	𝑑𝑠	𝑑𝑠	X
iajs-3515	23	72	=	=	SYM
iajs-3515	23	73	∞	∞	PROPN
iajs-3515	23	74	;	;	PUNCT
iajs-3515	23	75	𝑡	𝑡	PROPN
iajs-3515	23	76	𝑡0	𝑡0	PROPN
iajs-3515	23	77	(	(	PUNCT
iajs-3515	23	78	m2	m2	PROPN
iajs-3515	23	79	)	)	PUNCT
iajs-3515	23	80	0	0	PUNCT
iajs-3515	24	1	<	<	X
iajs-3515	24	2	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3515	24	3	)	)	PUNCT
iajs-3515	24	4	≤	≤	NOUN
iajs-3515	24	5	𝑎	𝑎	ADJ
iajs-3515	24	6	,	,	PUNCT
iajs-3515	24	7	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3515	24	8	)	)	PUNCT
iajs-3515	24	9	>	>	X
iajs-3515	24	10	0	0	NUM
iajs-3515	25	1	𝑄𝑖(𝑡	𝑄𝑖(𝑡	NOUN
iajs-3515	25	2	)	)	PUNCT
iajs-3515	25	3	=	=	SYM
iajs-3515	25	4	min	min	NOUN
iajs-3515	25	5	𝑡≥𝑡0	𝑡≥𝑡0	PROPN
iajs-3515	25	6	{	{	PUNCT
iajs-3515	25	7	𝑞𝑖(𝑡	𝑞𝑖(𝑡	NOUN
iajs-3515	25	8	)	)	PUNCT
iajs-3515	25	9	,	,	PUNCT
iajs-3515	25	10	𝑞𝑖(𝜏(𝑡	𝑞𝑖(𝜏(𝑡	NOUN
iajs-3515	25	11	)	)	PUNCT
iajs-3515	25	12	)	)	PUNCT
iajs-3515	25	13	,	,	PUNCT
iajs-3515	25	14	𝑄(𝑡	𝑄(𝑡	X
iajs-3515	25	15	)	)	PUNCT
iajs-3515	25	16	=	=	SYM
iajs-3515	25	17	min{𝑄𝑖(𝑡	min{𝑄𝑖(𝑡	NOUN
iajs-3515	25	18	)	)	PUNCT
iajs-3515	25	19	,	,	PUNCT
iajs-3515	25	20	𝑖	𝑖	NOUN
iajs-3515	25	21	=	=	SYM
iajs-3515	25	22	1,2	1,2	NUM
iajs-3515	25	23	,	,	PUNCT
iajs-3515	25	24	…	…	PUNCT
iajs-3515	25	25	,	,	PUNCT
iajs-3515	25	26	𝑛	𝑛	NOUN
iajs-3515	25	27	}	}	PUNCT
iajs-3515	25	28	,	,	PUNCT
iajs-3515	25	29	and	and	CCONJ
iajs-3515	25	30	𝐺𝑖(𝑡	𝐺𝑖(𝑡	NUM
iajs-3515	25	31	)	)	PUNCT
iajs-3515	25	32	=	=	SYM
iajs-3515	25	33	max	max	PROPN
iajs-3515	25	34	𝑡≥𝑡0	𝑡≥𝑡0	PROPN
iajs-3515	25	35	{	{	PUNCT
iajs-3515	25	36	𝑟𝑖(𝑡	𝑟𝑖(𝑡	NUM
iajs-3515	25	37	)	)	PUNCT
iajs-3515	25	38	,	,	PUNCT
iajs-3515	25	39	𝑟𝑖(𝜏(𝑡	𝑟𝑖(𝜏(𝑡	NOUN
iajs-3515	25	40	)	)	PUNCT
iajs-3515	25	41	)	)	PUNCT
iajs-3515	25	42	,	,	PUNCT
iajs-3515	25	43	𝑖	𝑖	NOUN
iajs-3515	25	44	=	=	SYM
iajs-3515	25	45	1,2	1,2	NUM
iajs-3515	25	46	,	,	PUNCT
iajs-3515	25	47	…	…	PUNCT
iajs-3515	25	48	,	,	PUNCT
iajs-3515	25	49	𝑘	𝑘	NOUN
iajs-3515	25	50	}	}	PUNCT
iajs-3515	25	51	,	,	PUNCT
iajs-3515	25	52	𝐺(𝑡	𝐺(𝑡	ADJ
iajs-3515	25	53	)	)	PUNCT
iajs-3515	25	54	=	=	SYM
iajs-3515	25	55	max{𝐺𝑖(𝑡	max{𝐺𝑖(𝑡	NOUN
iajs-3515	25	56	)	)	PUNCT
iajs-3515	25	57	,	,	PUNCT
iajs-3515	25	58	𝑖	𝑖	NOUN
iajs-3515	25	59	=	=	SYM
iajs-3515	25	60	1,2	1,2	NUM
iajs-3515	25	61	,	,	PUNCT
iajs-3515	25	62	…	…	PUNCT
iajs-3515	25	63	,	,	PUNCT
iajs-3515	25	64	𝑘	𝑘	NOUN
iajs-3515	25	65	}	}	PUNCT
iajs-3515	25	66	.	.	PUNCT
iajs-3515	26	1	(	(	PUNCT
iajs-3515	26	2	m3	m3	PROPN
iajs-3515	26	3	)	)	PUNCT
iajs-3515	26	4	∫	∫	PROPN
iajs-3515	26	5	|𝐺(𝑡)|𝑑𝑡	|𝐺(𝑡)|𝑑𝑡	VERB
iajs-3515	26	6	∞	∞	PROPN
iajs-3515	26	7	𝑇	𝑇	PROPN
iajs-3515	26	8	<	<	X
iajs-3515	26	9	∞	∞	PROPN
iajs-3515	26	10	,	,	PUNCT
iajs-3515	26	11	𝑇	𝑇	PROPN
iajs-3515	26	12	≥	≥	NOUN
iajs-3515	26	13	𝑡0	𝑡0	NOUN
iajs-3515	26	14	.	.	PUNCT
iajs-3515	27	1	(	(	PUNCT
iajs-3515	27	2	m4	m4	PROPN
iajs-3515	27	3	)	)	PUNCT
iajs-3515	27	4	∫	∫	PROPN
iajs-3515	27	5	|𝑄(𝑡)|𝑑𝑡	|𝑄(𝑡)|𝑑𝑡	X
iajs-3515	27	6	∞	∞	NUM
iajs-3515	27	7	𝑇	𝑇	PROPN
iajs-3515	27	8	=	=	SYM
iajs-3515	27	9	∞	∞	PROPN
iajs-3515	27	10	,	,	PUNCT
iajs-3515	27	11	𝑇	𝑇	PROPN
iajs-3515	27	12	≥	≥	NUM
iajs-3515	27	13	𝑡0	𝑡0	PROPN
iajs-3515	27	14	.	.	PUNCT
iajs-3515	28	1	the	the	DET
iajs-3515	28	2	emden	emden	ADJ
iajs-3515	28	3	-	-	PUNCT
iajs-3515	28	4	fowler	fowler	NOUN
iajs-3515	28	5	equation	equation	NOUN
iajs-3515	28	6	has	have	AUX
iajs-3515	28	7	emerged	emerge	VERB
iajs-3515	28	8	in	in	ADP
iajs-3515	28	9	recent	recent	ADJ
iajs-3515	28	10	decades	decade	NOUN
iajs-3515	28	11	as	as	ADP
iajs-3515	28	12	a	a	DET
iajs-3515	28	13	focus	focus	NOUN
iajs-3515	28	14	of	of	ADP
iajs-3515	28	15	interest	interest	NOUN
iajs-3515	28	16	for	for	ADP
iajs-3515	28	17	many	many	ADJ
iajs-3515	28	18	researchers	researcher	NOUN
iajs-3515	28	19	,	,	PUNCT
iajs-3515	28	20	specifically	specifically	ADV
iajs-3515	28	21	research	research	VERB
iajs-3515	28	22	in	in	ADP
iajs-3515	28	23	oscillation	oscillation	NOUN
iajs-3515	28	24	and	and	CCONJ
iajs-3515	28	25	the	the	DET
iajs-3515	28	26	asymptotic	asymptotic	ADJ
iajs-3515	28	27	behavior	behavior	NOUN
iajs-3515	28	28	of	of	ADP
iajs-3515	28	29	the	the	DET
iajs-3515	28	30	solutions	solution	NOUN
iajs-3515	28	31	of	of	ADP
iajs-3515	28	32	these	these	DET
iajs-3515	28	33	equations	equation	NOUN
iajs-3515	28	34	,	,	PUNCT
iajs-3515	28	35	emden	emden	ADJ
iajs-3515	28	36	-	-	PUNCT
iajs-3515	28	37	fowler	fowler	NOUN
iajs-3515	28	38	equation	equation	NOUN
iajs-3515	28	39	has	have	AUX
iajs-3515	28	40	been	be	AUX
iajs-3515	28	41	classified	classify	VERB
iajs-3515	28	42	as	as	ADP
iajs-3515	28	43	unconventional	unconventional	ADJ
iajs-3515	28	44	equations	equation	NOUN
iajs-3515	28	45	and	and	CCONJ
iajs-3515	28	46	its	its	PRON
iajs-3515	28	47	importance	importance	NOUN
iajs-3515	28	48	has	have	AUX
iajs-3515	28	49	emerged	emerge	VERB
iajs-3515	28	50	for	for	ADP
iajs-3515	28	51	its	its	PRON
iajs-3515	28	52	use	use	NOUN
iajs-3515	28	53	in	in	ADP
iajs-3515	28	54	many	many	ADJ
iajs-3515	28	55	applications	application	NOUN
iajs-3515	28	56	,	,	PUNCT
iajs-3515	28	57	and	and	CCONJ
iajs-3515	28	58	for	for	ADP
iajs-3515	28	59	this	this	DET
iajs-3515	28	60	reason	reason	NOUN
iajs-3515	28	61	many	many	ADJ
iajs-3515	28	62	researches	research	NOUN
iajs-3515	28	63	have	have	AUX
iajs-3515	28	64	appeared	appear	VERB
iajs-3515	28	65	that	that	PRON
iajs-3515	28	66	produce	produce	VERB
iajs-3515	28	67	a	a	DET
iajs-3515	28	68	lot	lot	NOUN
iajs-3515	28	69	of	of	ADP
iajs-3515	28	70	conditions	condition	NOUN
iajs-3515	28	71	to	to	PART
iajs-3515	28	72	ensure	ensure	VERB
iajs-3515	28	73	that	that	SCONJ
iajs-3515	28	74	each	each	DET
iajs-3515	28	75	solution	solution	NOUN
iajs-3515	28	76	of	of	ADP
iajs-3515	28	77	these	these	DET
iajs-3515	28	78	equations	equation	NOUN
iajs-3515	28	79	oscillates	oscillate	NOUN
iajs-3515	28	80	,	,	PUNCT
iajs-3515	28	81	or	or	CCONJ
iajs-3515	28	82	that	that	SCONJ
iajs-3515	28	83	their	their	PRON
iajs-3515	28	84	non	non	ADJ
iajs-3515	28	85	-	-	ADJ
iajs-3515	28	86	oscillating	oscillating	ADJ
iajs-3515	28	87	solutions	solution	NOUN
iajs-3515	28	88	are	be	AUX
iajs-3515	28	89	convergent	convergent	ADJ
iajs-3515	28	90	.	.	PUNCT
iajs-3515	29	1	ahmed	ahmed	PROPN
iajs-3515	29	2	et	et	PROPN
iajs-3515	29	3	al	al	PROPN
iajs-3515	29	4	.	.	PROPN
iajs-3515	30	1	(	(	PUNCT
iajs-3515	30	2	1	1	X
iajs-3515	30	3	)	)	PUNCT
iajs-3515	30	4	studied	study	VERB
iajs-3515	30	5	the	the	DET
iajs-3515	30	6	second	second	ADJ
iajs-3515	30	7	-	-	PUNCT
iajs-3515	30	8	order	order	NOUN
iajs-3515	30	9	neutral	neutral	ADJ
iajs-3515	30	10	dynamic	dynamic	ADJ
iajs-3515	30	11	linear	linear	NOUN
iajs-3515	30	12	equation	equation	NOUN
iajs-3515	30	13	and	and	CCONJ
iajs-3515	30	14	established	establish	VERB
iajs-3515	30	15	some	some	DET
iajs-3515	30	16	conditions	condition	NOUN
iajs-3515	30	17	for	for	ADP
iajs-3515	30	18	the	the	DET
iajs-3515	30	19	oscillation	oscillation	NOUN
iajs-3515	30	20	of	of	ADP
iajs-3515	30	21	every	every	DET
iajs-3515	30	22	solution	solution	NOUN
iajs-3515	30	23	of	of	ADP
iajs-3515	30	24	this	this	DET
iajs-3515	30	25	equation	equation	NOUN
iajs-3515	30	26	.	.	PUNCT
iajs-3515	31	1	yingzhu	yingzhu	VERB
iajs-3515	31	2	et	et	PROPN
iajs-3515	31	3	al	al	PROPN
iajs-3515	31	4	.	.	PROPN
iajs-3515	32	1	(	(	PUNCT
iajs-3515	32	2	2	2	X
iajs-3515	32	3	)	)	PUNCT
iajs-3515	32	4	obtained	obtain	VERB
iajs-3515	32	5	oscillation	oscillation	NOUN
iajs-3515	32	6	conditions	condition	NOUN
iajs-3515	32	7	of	of	ADP
iajs-3515	32	8	each	each	DET
iajs-3515	32	9	solution	solution	NOUN
iajs-3515	32	10	of	of	ADP
iajs-3515	32	11	second	second	ADJ
iajs-3515	32	12	-	-	PUNCT
iajs-3515	32	13	order	order	NOUN
iajs-3515	32	14	neutral	neutral	ADJ
iajs-3515	32	15	nonlinear	nonlinear	ADJ
iajs-3515	32	16	differential	differential	ADJ
iajs-3515	32	17	equations	equation	NOUN
iajs-3515	32	18	.	.	PUNCT
iajs-3515	33	1	the	the	DET
iajs-3515	33	2	obtained	obtain	VERB
iajs-3515	33	3	results	result	NOUN
iajs-3515	33	4	in	in	ADP
iajs-3515	33	5	(	(	PUNCT
iajs-3515	33	6	3	3	X
iajs-3515	33	7	)	)	PUNCT
iajs-3515	33	8	are	be	AUX
iajs-3515	33	9	based	base	VERB
iajs-3515	33	10	on	on	ADP
iajs-3515	33	11	comparison	comparison	NOUN
iajs-3515	33	12	theorems	theorem	NOUN
iajs-3515	33	13	which	which	PRON
iajs-3515	33	14	enable	enable	VERB
iajs-3515	33	15	to	to	PART
iajs-3515	33	16	address	address	VERB
iajs-3515	33	17	the	the	DET
iajs-3515	33	18	problem	problem	NOUN
iajs-3515	33	19	of	of	ADP
iajs-3515	33	20	second	second	ADJ
iajs-3515	33	21	order	order	NOUN
iajs-3515	33	22	equation	equation	NOUN
iajs-3515	33	23	oscillation	oscillation	NOUN
iajs-3515	33	24	to	to	PART
iajs-3515	33	25	first	first	ADJ
iajs-3515	33	26	order	order	NOUN
iajs-3515	33	27	equation	equation	NOUN
iajs-3515	33	28	oscillation	oscillation	NOUN
iajs-3515	33	29	.	.	PUNCT
iajs-3515	34	1	mehta	mehta	PROPN
iajs-3515	34	2	et	et	PROPN
iajs-3515	34	3	al	al	PROPN
iajs-3515	34	4	.	.	PROPN
iajs-3515	35	1	(	(	PUNCT
iajs-3515	35	2	4	4	X
iajs-3515	35	3	)	)	PUNCT
iajs-3515	35	4	investigated	investigate	VERB
iajs-3515	35	5	the	the	DET
iajs-3515	35	6	emden	emden	ADJ
iajs-3515	35	7	-	-	PUNCT
iajs-3515	35	8	fowler	fowler	ADJ
iajs-3515	35	9	equation	equation	NOUN
iajs-3515	35	10	of	of	ADP
iajs-3515	35	11	the	the	DET
iajs-3515	35	12	form	form	NOUN
iajs-3515	35	13	𝑑	𝑑	VERB
iajs-3515	35	14	𝑑𝑡	𝑑𝑡	ADP
iajs-3515	35	15	(	(	PUNCT
iajs-3515	35	16	𝑡𝛼	𝑡𝛼	PROPN
iajs-3515	35	17	𝑑𝑤	𝑑𝑤	PROPN
iajs-3515	35	18	𝑑𝑡	𝑑𝑡	ADP
iajs-3515	35	19	)	)	PUNCT
iajs-3515	36	1	=	=	SYM
iajs-3515	36	2	𝑡𝜎𝑤𝛼	𝑡𝜎𝑤𝛼	ADJ
iajs-3515	36	3	,	,	PUNCT
iajs-3515	36	4	where	where	SCONJ
iajs-3515	36	5	𝑤(𝑡	𝑤(𝑡	NOUN
iajs-3515	36	6	)	)	PUNCT
iajs-3515	36	7	=	=	SYM
iajs-3515	36	8	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	36	9	)	)	PUNCT
iajs-3515	36	10	±	±	NOUN
iajs-3515	36	11	𝑞(𝑡)𝑥(𝜏(𝑡	𝑞(𝑡)𝑥(𝜏(𝑡	NUM
iajs-3515	36	12	)	)	PUNCT
iajs-3515	36	13	)	)	PUNCT
iajs-3515	36	14	,	,	PUNCT
iajs-3515	36	15	and	and	CCONJ
iajs-3515	36	16	established	establish	VERB
iajs-3515	36	17	some	some	DET
iajs-3515	36	18	conditions	condition	NOUN
iajs-3515	36	19	for	for	SCONJ
iajs-3515	36	20	all	all	DET
iajs-3515	36	21	solutions	solution	NOUN
iajs-3515	36	22	to	to	PART
iajs-3515	36	23	oscillate	oscillate	VERB
iajs-3515	36	24	.	.	PUNCT
iajs-3515	37	1	mohamad	mohamad	PROPN
iajs-3515	37	2	et	et	PROPN
iajs-3515	37	3	al	al	PROPN
iajs-3515	37	4	.	.	PROPN
iajs-3515	38	1	(	(	PUNCT
iajs-3515	38	2	5	5	NUM
iajs-3515	38	3	,	,	PUNCT
iajs-3515	38	4	6	6	NUM
iajs-3515	38	5	)	)	PUNCT
iajs-3515	38	6	discussed	discuss	VERB
iajs-3515	38	7	the	the	DET
iajs-3515	38	8	oscillation	oscillation	NOUN
iajs-3515	38	9	property	property	NOUN
iajs-3515	38	10	of	of	ADP
iajs-3515	38	11	third	third	ADJ
iajs-3515	38	12	order	order	NOUN
iajs-3515	38	13	neutral	neutral	ADJ
iajs-3515	38	14	half	half	ADJ
iajs-3515	38	15	-	-	PUNCT
iajs-3515	38	16	linear	linear	NOUN
iajs-3515	38	17	equations	equation	NOUN
iajs-3515	38	18	and	and	CCONJ
iajs-3515	38	19	established	establish	VERB
iajs-3515	38	20	some	some	DET
iajs-3515	38	21	conditions	condition	NOUN
iajs-3515	38	22	to	to	PART
iajs-3515	38	23	insure	insure	VERB
iajs-3515	38	24	the	the	DET
iajs-3515	38	25	oscillation	oscillation	NOUN
iajs-3515	38	26	of	of	ADP
iajs-3515	38	27	every	every	DET
iajs-3515	38	28	solution	solution	NOUN
iajs-3515	38	29	of	of	ADP
iajs-3515	38	30	these	these	DET
iajs-3515	38	31	equations	equation	NOUN
iajs-3515	38	32	.	.	PUNCT
iajs-3515	39	1	moaaz	moaaz	PROPN
iajs-3515	39	2	et	et	PROPN
iajs-3515	39	3	al	al	PROPN
iajs-3515	39	4	.	.	PROPN
iajs-3515	40	1	(	(	PUNCT
iajs-3515	40	2	7	7	NUM
iajs-3515	40	3	)	)	PUNCT
iajs-3515	40	4	and	and	CCONJ
iajs-3515	40	5	xu	xu	INTJ
iajs-3515	40	6	et	et	PROPN
iajs-3515	40	7	al	al	PROPN
iajs-3515	40	8	.	.	PROPN
iajs-3515	41	1	(	(	PUNCT
iajs-3515	41	2	8)	8)	NUM
iajs-3515	41	3	obtained	obtain	VERB
iajs-3515	41	4	oscillation	oscillation	NOUN
iajs-3515	41	5	conditions	condition	NOUN
iajs-3515	41	6	of	of	ADP
iajs-3515	41	7	each	each	DET
iajs-3515	41	8	solution	solution	NOUN
iajs-3515	41	9	of	of	ADP
iajs-3515	41	10	second	second	ADJ
iajs-3515	41	11	order	order	NOUN
iajs-3515	41	12	neutral	neutral	ADJ
iajs-3515	41	13	emden	emden	ADJ
iajs-3515	41	14	-	-	PUNCT
iajs-3515	41	15	fowler	fowler	PROPN
iajs-3515	41	16	type	type	NOUN
iajs-3515	41	17	(	(	PUNCT
iajs-3515	41	18	𝑎(𝑡)[(𝑥(𝑡	𝑎(𝑡)[(𝑥(𝑡	PROPN
iajs-3515	41	19	)	)	PUNCT
iajs-3515	41	20	−	−	PROPN
iajs-3515	42	1	𝑝(𝑡)𝑥(𝜏(𝑡)))′]𝛾)′	𝑝(𝑡)𝑥(𝜏(𝑡)))′]𝛾)′	NOUN
iajs-3515	42	2	+	+	CCONJ
iajs-3515	42	3	𝑞(𝑡)𝑥𝛾(𝜎(𝑡	𝑞(𝑡)𝑥𝛾(𝜎(𝑡	ADJ
iajs-3515	42	4	)	)	PUNCT
iajs-3515	42	5	)	)	PUNCT
iajs-3515	43	1	=	=	SYM
iajs-3515	43	2	0	0	NUM
iajs-3515	43	3	,	,	PUNCT
iajs-3515	43	4	t	t	PROPN
iajs-3515	43	5	≥	≥	PROPN
iajs-3515	43	6	𝑡0	𝑡0	PROPN
iajs-3515	43	7	.	.	PUNCT
iajs-3515	44	1	thandapani	thandapani	PROPN
iajs-3515	44	2	et	et	PROPN
iajs-3515	44	3	al	al	PROPN
iajs-3515	44	4	.	.	PROPN
iajs-3515	45	1	(	(	PUNCT
iajs-3515	45	2	9	9	X
iajs-3515	45	3	)	)	PUNCT
iajs-3515	45	4	studied	study	VERB
iajs-3515	45	5	asymptotic	asymptotic	ADJ
iajs-3515	45	6	properties	property	NOUN
iajs-3515	45	7	of	of	ADP
iajs-3515	45	8	the	the	DET
iajs-3515	45	9	third	third	ADJ
iajs-3515	45	10	order	order	NOUN
iajs-3515	45	11	quasi	quasi	ADJ
iajs-3515	45	12	-	-	ADJ
iajs-3515	45	13	linear	linear	ADJ
iajs-3515	45	14	neutral	neutral	ADJ
iajs-3515	45	15	functional	functional	ADJ
iajs-3515	45	16	differential	differential	NOUN
iajs-3515	45	17	equation	equation	NOUN
iajs-3515	45	18	(	(	PUNCT
iajs-3515	45	19	𝑎(𝑡)[(𝑥(𝑡	𝑎(𝑡)[(𝑥(𝑡	PROPN
iajs-3515	45	20	)	)	PUNCT
iajs-3515	45	21	−	−	PROPN
iajs-3515	45	22	𝑝(𝑡)𝑥(𝜏(𝑡)))′′]𝛾)′	𝑝(𝑡)𝑥(𝜏(𝑡)))′′]𝛾)′	PROPN
iajs-3515	45	23	+	+	CCONJ
iajs-3515	45	24	𝑞(𝑡)𝑥𝛾(𝜎(𝑡	𝑞(𝑡)𝑥𝛾(𝜎(𝑡	NOUN
iajs-3515	45	25	)	)	PUNCT
iajs-3515	45	26	)	)	PUNCT
iajs-3515	46	1	=	=	PUNCT
iajs-3515	46	2	0	0	NUM
iajs-3515	46	3	,	,	PUNCT
iajs-3515	46	4	by	by	ADP
iajs-3515	46	5	using	use	VERB
iajs-3515	46	6	the	the	DET
iajs-3515	46	7	riccati	riccati	PROPN
iajs-3515	46	8	transformation	transformation	NOUN
iajs-3515	46	9	,	,	PUNCT
iajs-3515	46	10	and	and	CCONJ
iajs-3515	46	11	establishing	establish	VERB
iajs-3515	46	12	some	some	DET
iajs-3515	46	13	conditions	condition	NOUN
iajs-3515	46	14	which	which	PRON
iajs-3515	46	15	ensure	ensure	VERB
iajs-3515	46	16	that	that	SCONJ
iajs-3515	46	17	every	every	DET
iajs-3515	46	18	solution	solution	NOUN
iajs-3515	46	19	of	of	ADP
iajs-3515	46	20	that	that	DET
iajs-3515	46	21	equation	equation	NOUN
iajs-3515	46	22	is	be	AUX
iajs-3515	46	23	either	either	CCONJ
iajs-3515	46	24	oscillatory	oscillatory	ADJ
iajs-3515	46	25	or	or	CCONJ
iajs-3515	46	26	converges	converge	NOUN
iajs-3515	46	27	to	to	ADP
iajs-3515	46	28	zero	zero	NUM
iajs-3515	46	29	.	.	PUNCT
iajs-3515	47	1	hassan	hassan	PROPN
iajs-3515	47	2	et	et	PROPN
iajs-3515	47	3	al	al	PROPN
iajs-3515	47	4	.	.	PROPN
iajs-3515	48	1	(	(	PUNCT
iajs-3515	48	2	10	10	NUM
iajs-3515	48	3	)	)	PUNCT
iajs-3515	48	4	he	he	PRON
iajs-3515	48	5	dealt	deal	VERB
iajs-3515	48	6	with	with	ADP
iajs-3515	48	7	new	new	ADJ
iajs-3515	48	8	standards	standard	NOUN
iajs-3515	48	9	for	for	ADP
iajs-3515	48	10	the	the	DET
iajs-3515	48	11	oscillation	oscillation	NOUN
iajs-3515	48	12	of	of	ADP
iajs-3515	48	13	half	half	ADJ
iajs-3515	48	14	-	-	PUNCT
iajs-3515	48	15	linear	linear	NOUN
iajs-3515	48	16	differential	differential	ADJ
iajs-3515	48	17	equations	equation	NOUN
iajs-3515	48	18	developed	develop	VERB
iajs-3515	48	19	of	of	ADP
iajs-3515	48	20	the	the	DET
iajs-3515	48	21	second	second	ADJ
iajs-3515	48	22	order	order	NOUN
iajs-3515	48	23	,	,	PUNCT
iajs-3515	48	24	where	where	SCONJ
iajs-3515	48	25	he	he	PRON
iajs-3515	48	26	concluded	conclude	VERB
iajs-3515	48	27	that	that	SCONJ
iajs-3515	48	28	the	the	DET
iajs-3515	48	29	results	result	NOUN
iajs-3515	48	30	obtained	obtain	VERB
iajs-3515	48	31	work	work	NOUN
iajs-3515	48	32	to	to	PART
iajs-3515	48	33	expand	expand	VERB
iajs-3515	48	34	and	and	CCONJ
iajs-3515	48	35	develop	develop	VERB
iajs-3515	48	36	modern	modern	ADJ
iajs-3515	48	37	standards	standard	NOUN
iajs-3515	48	38	for	for	ADP
iajs-3515	48	39	the	the	DET
iajs-3515	48	40	same	same	ADJ
iajs-3515	48	41	equations	equation	NOUN
iajs-3515	48	42	that	that	PRON
iajs-3515	48	43	have	have	AUX
iajs-3515	48	44	been	be	AUX
iajs-3515	48	45	developed	develop	VERB
iajs-3515	48	46	by	by	ADP
iajs-3515	48	47	many	many	ADJ
iajs-3515	48	48	authors	author	NOUN
iajs-3515	48	49	.	.	PUNCT
iajs-3515	49	1	tripathy	tripathy	PROPN
iajs-3515	49	2	et	et	PROPN
iajs-3515	49	3	al	al	PROPN
iajs-3515	49	4	.	.	PROPN
iajs-3515	50	1	(	(	PUNCT
iajs-3515	50	2	11	11	NUM
iajs-3515	50	3	)	)	PUNCT
iajs-3515	50	4	find	find	VERB
iajs-3515	50	5	the	the	DET
iajs-3515	50	6	necessary	necessary	ADJ
iajs-3515	50	7	and	and	CCONJ
iajs-3515	50	8	sufficient	sufficient	ADJ
iajs-3515	50	9	conditions	condition	NOUN
iajs-3515	50	10	for	for	ADP
iajs-3515	50	11	volatility	volatility	NOUN
iajs-3515	50	12	one	one	NUM
iajs-3515	50	13	of	of	ADP
iajs-3515	50	14	the	the	DET
iajs-3515	50	15	impulsive	impulsive	ADJ
iajs-3515	50	16	neutral	neutral	ADJ
iajs-3515	50	17	differential	differential	NOUN
iajs-3515	50	18	system	system	NOUN
iajs-3515	50	19	solutions	solution	NOUN
iajs-3515	50	20	of	of	ADP
iajs-3515	50	21	the	the	DET
iajs-3515	50	22	second	second	ADJ
iajs-3515	50	23	order	order	NOUN
iajs-3515	50	24	under	under	ADP
iajs-3515	50	25	certain	certain	ADJ
iajs-3515	50	26	conditions	condition	NOUN
iajs-3515	50	27	that	that	PRON
iajs-3515	50	28	ensure	ensure	VERB
iajs-3515	50	29	the	the	DET
iajs-3515	50	30	occurrence	occurrence	NOUN
iajs-3515	50	31	of	of	ADP
iajs-3515	50	32	oscillation	oscillation	NOUN
iajs-3515	50	33	.	.	PUNCT
iajs-3515	51	1	see	see	VERB
iajs-3515	51	2	mehta	mehta	PROPN
iajs-3515	51	3	et	et	PROPN
iajs-3515	51	4	al	al	PROPN
iajs-3515	51	5	.	.	PUNCT
iajs-3515	52	1	(	(	PUNCT
iajs-3515	52	2	12	12	NUM
iajs-3515	52	3	)	)	PUNCT
iajs-3515	52	4	,	,	PUNCT
iajs-3515	52	5	and	and	CCONJ
iajs-3515	52	6	vidhyaa	vidhyaa	NOUN
iajs-3515	52	7	et	et	PROPN
iajs-3515	52	8	al	al	PROPN
iajs-3515	52	9	.	.	PROPN
iajs-3515	53	1	(	(	PUNCT
iajs-3515	53	2	13	13	NUM
iajs-3515	53	3	)	)	PUNCT
iajs-3515	53	4	they	they	PRON
iajs-3515	53	5	studied	study	VERB
iajs-3515	53	6	the	the	DET
iajs-3515	53	7	differential	differential	ADJ
iajs-3515	53	8	equations	equation	NOUN
iajs-3515	53	9	and	and	CCONJ
iajs-3515	53	10	obtained	obtain	VERB
iajs-3515	53	11	the	the	DET
iajs-3515	53	12	oscillation	oscillation	NOUN
iajs-3515	53	13	criteria	criterion	NOUN
iajs-3515	53	14	for	for	ADP
iajs-3515	53	15	all	all	DET
iajs-3515	53	16	the	the	DET
iajs-3515	53	17	ihjpas	ihjpa	NOUN
iajs-3515	53	18	.	.	PUNCT
iajs-3515	54	1	2024	2024	NUM
iajs-3515	54	2	,	,	PUNCT
iajs-3515	54	3	38	38	NUM
iajs-3515	54	4	(	(	PUNCT
iajs-3515	54	5	1	1	NUM
iajs-3515	54	6	)	)	PUNCT
iajs-3515	54	7	409	409	NUM
iajs-3515	54	8	solutions	solution	NOUN
iajs-3515	54	9	of	of	ADP
iajs-3515	54	10	the	the	DET
iajs-3515	54	11	neutral	neutral	ADJ
iajs-3515	54	12	differential	differential	ADJ
iajs-3515	54	13	equations	equation	NOUN
iajs-3515	54	14	of	of	ADP
iajs-3515	54	15	the	the	DET
iajs-3515	54	16	second	second	ADJ
iajs-3515	54	17	degree	degree	NOUN
iajs-3515	54	18	,	,	PUNCT
iajs-3515	54	19	half	half	ADJ
iajs-3515	54	20	-	-	PUNCT
iajs-3515	54	21	linear	linear	NOUN
iajs-3515	54	22	(	(	PUNCT
iajs-3515	54	23	𝑘(𝑡)((ℎ(𝑡)𝑧′	𝑘(𝑡)((ℎ(𝑡)𝑧′	INTJ
iajs-3515	54	24	(	(	PUNCT
iajs-3515	54	25	𝑡))′)𝜀)′	𝑡))′)𝜀)′	NOUN
iajs-3515	54	26	+	+	NOUN
iajs-3515	54	27	𝑘(𝑡)𝑥𝜀(𝑡	𝑘(𝑡)𝑥𝜀(𝑡	NOUN
iajs-3515	54	28	)	)	PUNCT
iajs-3515	54	29	=	=	SYM
iajs-3515	54	30	0	0	NUM
iajs-3515	54	31	,	,	PUNCT
iajs-3515	54	32	𝑡	𝑡	PROPN
iajs-3515	54	33	≥	≥	PROPN
iajs-3515	54	34	𝑡0	𝑡0	NOUN
iajs-3515	54	35	,	,	PUNCT
iajs-3515	54	36	where	where	SCONJ
iajs-3515	54	37	𝑧(𝑡	𝑧(𝑡	NOUN
iajs-3515	54	38	)	)	PUNCT
iajs-3515	54	39	=	=	SYM
iajs-3515	54	40	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	54	41	)	)	PUNCT
iajs-3515	54	42	+	+	NUM
iajs-3515	54	43	𝑝(𝑡)𝑥(𝜏(𝑡	𝑝(𝑡)𝑥(𝜏(𝑡	NOUN
iajs-3515	54	44	)	)	PUNCT
iajs-3515	54	45	)	)	PUNCT
iajs-3515	54	46	.	.	PUNCT
iajs-3515	55	1	dassios	dassio	NOUN
iajs-3515	55	2	et	et	PROPN
iajs-3515	55	3	al	al	PROPN
iajs-3515	55	4	.	.	PUNCT
iajs-3515	56	1	(	(	PUNCT
iajs-3515	56	2	14	14	NUM
iajs-3515	56	3	)	)	PUNCT
iajs-3515	56	4	he	he	PRON
iajs-3515	56	5	studied	study	VERB
iajs-3515	56	6	the	the	DET
iajs-3515	56	7	delayed	delay	VERB
iajs-3515	56	8	and	and	CCONJ
iajs-3515	56	9	neutral	neutral	ADJ
iajs-3515	56	10	differential	differential	ADJ
iajs-3515	56	11	equations	equation	NOUN
iajs-3515	56	12	,	,	PUNCT
iajs-3515	56	13	where	where	SCONJ
iajs-3515	56	14	he	he	PRON
iajs-3515	56	15	focused	focus	VERB
iajs-3515	56	16	on	on	ADP
iajs-3515	56	17	the	the	DET
iajs-3515	56	18	stability	stability	NOUN
iajs-3515	56	19	of	of	ADP
iajs-3515	56	20	the	the	DET
iajs-3515	56	21	important	important	ADJ
iajs-3515	56	22	joins	join	NOUN
iajs-3515	56	23	because	because	SCONJ
iajs-3515	56	24	these	these	PRON
iajs-3515	56	25	joins	join	VERB
iajs-3515	56	26	contain	contain	VERB
iajs-3515	56	27	delays	delay	NOUN
iajs-3515	56	28	in	in	ADP
iajs-3515	56	29	each	each	PRON
iajs-3515	56	30	of	of	ADP
iajs-3515	56	31	the	the	DET
iajs-3515	56	32	state	state	NOUN
iajs-3515	56	33	variables	variable	NOUN
iajs-3515	56	34	and	and	CCONJ
iajs-3515	56	35	their	their	PRON
iajs-3515	56	36	time	time	NOUN
iajs-3515	56	37	derivatives	derivative	NOUN
iajs-3515	56	38	,	,	PUNCT
iajs-3515	56	39	where	where	SCONJ
iajs-3515	56	40	the	the	DET
iajs-3515	56	41	proposed	propose	VERB
iajs-3515	56	42	approach	approach	NOUN
iajs-3515	56	43	consists	consist	VERB
iajs-3515	56	44	of	of	ADP
iajs-3515	56	45	model	model	NOUN
iajs-3515	56	46	transformation	transformation	NOUN
iajs-3515	56	47	that	that	PRON
iajs-3515	56	48	builds	build	VERB
iajs-3515	56	49	an	an	DET
iajs-3515	56	50	equivalent	equivalent	ADJ
iajs-3515	56	51	set	set	NOUN
iajs-3515	56	52	of	of	ADP
iajs-3515	56	53	algebraic	algebraic	PROPN
iajs-3515	56	54	differential	differential	NOUN
iajs-3515	56	55	equations	equation	NOUN
iajs-3515	56	56	.	.	PUNCT
iajs-3515	57	1	li	li	PROPN
iajs-3515	57	2	et	et	PROPN
iajs-3515	57	3	al	al	PROPN
iajs-3515	57	4	.	.	PROPN
iajs-3515	58	1	(	(	PUNCT
iajs-3515	58	2	15	15	NUM
iajs-3515	58	3	)	)	PUNCT
iajs-3515	58	4	and	and	CCONJ
iajs-3515	58	5	marappan	marappan	VERB
iajs-3515	58	6	et	et	PROPN
iajs-3515	58	7	al	al	PROPN
iajs-3515	58	8	.	.	PUNCT
iajs-3515	59	1	(	(	PUNCT
iajs-3515	59	2	16	16	NUM
iajs-3515	59	3	)	)	PUNCT
iajs-3515	59	4	the	the	DET
iajs-3515	59	5	oscillatory	oscillatory	ADJ
iajs-3515	59	6	behavior	behavior	NOUN
iajs-3515	59	7	of	of	ADP
iajs-3515	59	8	solutions	solution	NOUN
iajs-3515	59	9	of	of	ADP
iajs-3515	59	10	mixed	mixed	ADJ
iajs-3515	59	11	nonlinear	nonlinear	ADJ
iajs-3515	59	12	neutral	neutral	ADJ
iajs-3515	59	13	differential	differential	ADJ
iajs-3515	59	14	equations	equation	NOUN
iajs-3515	59	15	of	of	ADP
iajs-3515	59	16	the	the	DET
iajs-3515	59	17	emden	emden	ADJ
iajs-3515	59	18	-	-	PUNCT
iajs-3515	59	19	fowler	fowler	PROPN
iajs-3515	59	20	type	type	NOUN
iajs-3515	59	21	was	be	AUX
iajs-3515	59	22	studied	study	VERB
iajs-3515	59	23	by	by	ADP
iajs-3515	59	24	applying	apply	VERB
iajs-3515	59	25	the	the	DET
iajs-3515	59	26	integral	integral	ADJ
iajs-3515	59	27	conditions	condition	NOUN
iajs-3515	59	28	and	and	CCONJ
iajs-3515	59	29	the	the	DET
iajs-3515	59	30	integral	integral	ADJ
iajs-3515	59	31	average	average	ADJ
iajs-3515	59	32	method	method	NOUN
iajs-3515	59	33	.	.	PUNCT
iajs-3515	60	1	baty	baty	PROPN
iajs-3515	60	2	(	(	PUNCT
iajs-3515	60	3	17	17	NUM
iajs-3515	60	4	)	)	PUNCT
iajs-3515	60	5	he	he	PRON
iajs-3515	60	6	studied	study	VERB
iajs-3515	60	7	secondorder	secondorder	ADJ
iajs-3515	60	8	lane	lane	NOUN
iajs-3515	60	9	-	-	PUNCT
iajs-3515	60	10	emden	emden	VERB
iajs-3515	60	11	-	-	PUNCT
iajs-3515	60	12	fowler	fowler	PROPN
iajs-3515	60	13	differential	differential	PROPN
iajs-3515	60	14	equations	equation	NOUN
iajs-3515	60	15	,	,	PUNCT
iajs-3515	60	16	third	third	ADJ
iajs-3515	60	17	-	-	PUNCT
iajs-3515	60	18	order	order	NOUN
iajs-3515	60	19	emden	emden	ADJ
iajs-3515	60	20	-	-	PUNCT
iajs-3515	60	21	fowler	fowler	PROPN
iajs-3515	60	22	equations	equation	NOUN
iajs-3515	60	23	,	,	PUNCT
iajs-3515	60	24	and	and	CCONJ
iajs-3515	60	25	fourthorder	fourthorder	PROPN
iajs-3515	60	26	lane	lane	NOUN
iajs-3515	60	27	-	-	PUNCT
iajs-3515	60	28	emden	emden	VERB
iajs-3515	60	29	-	-	PUNCT
iajs-3515	60	30	fowler	fowler	PROPN
iajs-3515	60	31	equations	equation	NOUN
iajs-3515	60	32	.	.	PUNCT
iajs-3515	61	1	he	he	PRON
iajs-3515	61	2	presented	present	VERB
iajs-3515	61	3	numerical	numerical	ADJ
iajs-3515	61	4	methods	method	NOUN
iajs-3515	61	5	using	use	VERB
iajs-3515	61	6	neural	neural	ADJ
iajs-3515	61	7	networks	network	NOUN
iajs-3515	61	8	based	base	VERB
iajs-3515	61	9	on	on	ADP
iajs-3515	61	10	physics	physics	NOUN
iajs-3515	61	11	with	with	ADP
iajs-3515	61	12	the	the	DET
iajs-3515	61	13	aim	aim	NOUN
iajs-3515	61	14	of	of	ADP
iajs-3515	61	15	solving	solve	VERB
iajs-3515	61	16	higher	high	ADJ
iajs-3515	61	17	-	-	PUNCT
iajs-3515	61	18	order	order	NOUN
iajs-3515	61	19	differential	differential	ADJ
iajs-3515	61	20	equations	equation	NOUN
iajs-3515	61	21	.	.	PUNCT
iajs-3515	62	1	naeif	naeif	NOUN
iajs-3515	62	2	et	et	PROPN
iajs-3515	62	3	al	al	PROPN
iajs-3515	62	4	.	.	PROPN
iajs-3515	63	1	(	(	PUNCT
iajs-3515	63	2	18	18	NUM
iajs-3515	63	3	)	)	PUNCT
iajs-3515	63	4	he	he	PRON
iajs-3515	63	5	studied	study	VERB
iajs-3515	63	6	the	the	DET
iajs-3515	63	7	oscillation	oscillation	NOUN
iajs-3515	63	8	and	and	CCONJ
iajs-3515	63	9	asymptotic	asymptotic	ADJ
iajs-3515	63	10	behavior	behavior	NOUN
iajs-3515	63	11	of	of	ADP
iajs-3515	63	12	a	a	DET
iajs-3515	63	13	half	half	ADJ
iajs-3515	63	14	-	-	PUNCT
iajs-3515	63	15	linear	linear	ADJ
iajs-3515	63	16	three	three	NUM
iajs-3515	63	17	-	-	PUNCT
iajs-3515	63	18	dimensional	dimensional	ADJ
iajs-3515	63	19	neutral	neutral	ADJ
iajs-3515	63	20	system	system	NOUN
iajs-3515	63	21	of	of	ADP
iajs-3515	63	22	second	second	ADJ
iajs-3515	63	23	order	order	NOUN
iajs-3515	63	24	and	and	CCONJ
iajs-3515	63	25	gave	give	VERB
iajs-3515	63	26	sufficient	sufficient	ADJ
iajs-3515	63	27	conditions	condition	NOUN
iajs-3515	63	28	to	to	PART
iajs-3515	63	29	ensure	ensure	VERB
iajs-3515	63	30	oscillation	oscillation	NOUN
iajs-3515	63	31	or	or	CCONJ
iajs-3515	63	32	not	not	PART
iajs-3515	63	33	.	.	PUNCT
iajs-3515	64	1	see	see	VERB
iajs-3515	64	2	(	(	PUNCT
iajs-3515	64	3	19	19	NUM
iajs-3515	64	4	-	-	SYM
iajs-3515	64	5	22	22	NUM
iajs-3515	64	6	)	)	PUNCT
iajs-3515	64	7	they	they	PRON
iajs-3515	64	8	studied	study	VERB
iajs-3515	64	9	the	the	DET
iajs-3515	64	10	optimal	optimal	ADJ
iajs-3515	64	11	decomposition	decomposition	NOUN
iajs-3515	64	12	method	method	NOUN
iajs-3515	64	13	for	for	ADP
iajs-3515	64	14	solving	solve	VERB
iajs-3515	64	15	third	third	ADJ
iajs-3515	64	16	-	-	PUNCT
iajs-3515	64	17	order	order	NOUN
iajs-3515	64	18	nonlinear	nonlinear	ADJ
iajs-3515	64	19	emden	emden	ADJ
iajs-3515	64	20	-	-	PUNCT
iajs-3515	64	21	fowler	fowler	PROPN
iajs-3515	64	22	differential	differential	PROPN
iajs-3515	64	23	equations	equation	NOUN
iajs-3515	64	24	,	,	PUNCT
iajs-3515	64	25	to	to	PART
iajs-3515	64	26	avoid	avoid	VERB
iajs-3515	64	27	the	the	DET
iajs-3515	64	28	singularity	singularity	NOUN
iajs-3515	64	29	at	at	ADP
iajs-3515	64	30	x=0	x=0	PROPN
iajs-3515	64	31	,	,	PUNCT
iajs-3515	64	32	by	by	ADP
iajs-3515	64	33	transforming	transform	VERB
iajs-3515	64	34	the	the	DET
iajs-3515	64	35	emden	emden	ADJ
iajs-3515	64	36	-	-	PUNCT
iajs-3515	64	37	fowler	fowler	PROPN
iajs-3515	64	38	equation	equation	NOUN
iajs-3515	64	39	into	into	ADP
iajs-3515	64	40	an	an	DET
iajs-3515	64	41	integral	integral	ADJ
iajs-3515	64	42	volterra	volterra	NOUN
iajs-3515	64	43	equation	equation	NOUN
iajs-3515	64	44	.	.	PUNCT
iajs-3515	65	1	our	our	PRON
iajs-3515	65	2	paper	paper	NOUN
iajs-3515	65	3	was	be	AUX
iajs-3515	65	4	based	base	VERB
iajs-3515	65	5	on	on	ADP
iajs-3515	65	6	article	article	NOUN
iajs-3515	65	7	(	(	PUNCT
iajs-3515	65	8	9	9	NUM
iajs-3515	65	9	)	)	PUNCT
iajs-3515	65	10	,	,	PUNCT
iajs-3515	65	11	where	where	SCONJ
iajs-3515	65	12	a	a	DET
iajs-3515	65	13	more	more	ADV
iajs-3515	65	14	general	general	ADJ
iajs-3515	65	15	equation	equation	NOUN
iajs-3515	65	16	with	with	ADP
iajs-3515	65	17	a	a	DET
iajs-3515	65	18	forcing	force	VERB
iajs-3515	65	19	term	term	NOUN
iajs-3515	65	20	is	be	AUX
iajs-3515	65	21	used	use	VERB
iajs-3515	65	22	and	and	CCONJ
iajs-3515	65	23	condition	condition	NOUN
iajs-3515	65	24	(	(	PUNCT
iajs-3515	65	25	2	2	NUM
iajs-3515	65	26	)	)	PUNCT
iajs-3515	65	27	in	in	ADP
iajs-3515	65	28	(	(	PUNCT
iajs-3515	65	29	9	9	X
iajs-3515	65	30	)	)	PUNCT
iajs-3515	65	31	has	have	AUX
iajs-3515	65	32	been	be	AUX
iajs-3515	65	33	developed	develop	VERB
iajs-3515	65	34	into	into	ADP
iajs-3515	65	35	a	a	DET
iajs-3515	65	36	more	more	ADV
iajs-3515	65	37	general	general	ADJ
iajs-3515	65	38	case	case	NOUN
iajs-3515	65	39	.	.	PUNCT
iajs-3515	66	1	a	a	DET
iajs-3515	66	2	solution	solution	NOUN
iajs-3515	66	3	𝒙(𝒕	𝒙(𝒕	PROPN
iajs-3515	66	4	)	)	PUNCT
iajs-3515	66	5	is	be	AUX
iajs-3515	66	6	said	say	VERB
iajs-3515	66	7	to	to	PART
iajs-3515	66	8	be	be	AUX
iajs-3515	66	9	oscillatory	oscillatory	ADJ
iajs-3515	66	10	if	if	SCONJ
iajs-3515	66	11	it	it	PRON
iajs-3515	66	12	has	have	VERB
iajs-3515	66	13	arbitrarily	arbitrarily	ADV
iajs-3515	66	14	large	large	ADJ
iajs-3515	66	15	zeros	zero	NOUN
iajs-3515	66	16	on	on	ADP
iajs-3515	66	17	(	(	PUNCT
iajs-3515	66	18	𝒕𝟎	𝒕𝟎	PROPN
iajs-3515	66	19	,	,	PUNCT
iajs-3515	66	20	∞	∞	PROPN
iajs-3515	66	21	)	)	PUNCT
iajs-3515	66	22	,	,	PUNCT
iajs-3515	66	23	otherwise	otherwise	ADV
iajs-3515	66	24	it	it	PRON
iajs-3515	66	25	is	be	AUX
iajs-3515	66	26	said	say	VERB
iajs-3515	66	27	to	to	PART
iajs-3515	66	28	be	be	AUX
iajs-3515	66	29	nonoscillatory	nonoscillatory	ADJ
iajs-3515	66	30	that	that	PRON
iajs-3515	66	31	is	be	AUX
iajs-3515	66	32	either	either	CCONJ
iajs-3515	66	33	eventually	eventually	ADV
iajs-3515	66	34	positive	positive	ADJ
iajs-3515	66	35	or	or	CCONJ
iajs-3515	66	36	eventually	eventually	ADV
iajs-3515	66	37	negative	negative	ADJ
iajs-3515	66	38	(	(	PUNCT
iajs-3515	66	39	6	6	NUM
iajs-3515	66	40	)	)	PUNCT
iajs-3515	66	41	.	.	PUNCT
iajs-3515	67	1	2	2	X
iajs-3515	67	2	.	.	X
iajs-3515	67	3	main	main	ADJ
iajs-3515	67	4	results	result	NOUN
iajs-3515	67	5	in	in	ADP
iajs-3515	67	6	this	this	DET
iajs-3515	67	7	section	section	NOUN
iajs-3515	67	8	some	some	DET
iajs-3515	67	9	results	result	NOUN
iajs-3515	67	10	.established	.establishe	VERB
iajs-3515	67	11	for	for	ADP
iajs-3515	67	12	oscillation	oscillation	NOUN
iajs-3515	67	13	for	for	ADP
iajs-3515	67	14	every	every	DET
iajs-3515	67	15	solution	solution	NOUN
iajs-3515	67	16	of	of	ADP
iajs-3515	67	17	equation	equation	NOUN
iajs-3515	67	18	(	(	PUNCT
iajs-3515	67	19	1	1	NUM
iajs-3515	67	20	)	)	PUNCT
iajs-3515	67	21	.	.	PUNCT
iajs-3515	68	1	in	in	ADP
iajs-3515	68	2	the	the	DET
iajs-3515	68	3	beginning	beginning	NOUN
iajs-3515	68	4	,	,	PUNCT
iajs-3515	68	5	it	it	PRON
iajs-3515	68	6	is	be	AUX
iajs-3515	68	7	shown	show	VERB
iajs-3515	68	8	that	that	SCONJ
iajs-3515	68	9	every	every	DET
iajs-3515	68	10	non	non	ADJ
iajs-3515	68	11	-	-	ADJ
iajs-3515	68	12	oscillatory	oscillatory	ADJ
iajs-3515	68	13	solution	solution	NOUN
iajs-3515	68	14	is	be	AUX
iajs-3515	68	15	achieves	achieve	VERB
iajs-3515	68	16	the	the	DET
iajs-3515	68	17	following	follow	VERB
iajs-3515	68	18	cases	case	NOUN
iajs-3515	68	19	.	.	PUNCT
iajs-3515	69	1	lemma	lemma	PROPN
iajs-3515	69	2	2.1	2.1	NUM
iajs-3515	69	3	:	:	PUNCT
iajs-3515	69	4	assume	assume	VERB
iajs-3515	69	5	that	that	SCONJ
iajs-3515	69	6	𝑞𝑖(𝑡	𝑞𝑖(𝑡	NOUN
iajs-3515	69	7	)	)	PUNCT
iajs-3515	69	8	≥	≥	NOUN
iajs-3515	69	9	0	0	NUM
iajs-3515	69	10	,	,	PUNCT
iajs-3515	69	11	∑	∑	PUNCT
iajs-3515	69	12	𝑟𝑗(𝑡)𝑘	𝑟𝑗(𝑡)𝑘	NUM
iajs-3515	69	13	𝑗=1	𝑗=1	SYM
iajs-3515	69	14	≤	≤	NUM
iajs-3515	69	15	0	0	NUM
iajs-3515	69	16	,	,	PUNCT
iajs-3515	69	17	and	and	CCONJ
iajs-3515	69	18	(	(	PUNCT
iajs-3515	69	19	m1	m1	NOUN
iajs-3515	69	20	)	)	PUNCT
iajs-3515	69	21	holds	hold	VERB
iajs-3515	69	22	.	.	PUNCT
iajs-3515	70	1	let	let	VERB
iajs-3515	70	2	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	70	3	)	)	PUNCT
iajs-3515	70	4	be	be	AUX
iajs-3515	70	5	a	a	DET
iajs-3515	70	6	nonoscillatory	nonoscillatory	ADJ
iajs-3515	70	7	solution	solution	NOUN
iajs-3515	70	8	of	of	ADP
iajs-3515	70	9	equation	equation	NOUN
iajs-3515	70	10	(	(	PUNCT
iajs-3515	70	11	1	1	NUM
iajs-3515	70	12	)	)	PUNCT
iajs-3515	70	13	.	.	PUNCT
iajs-3515	71	1	then	then	ADV
iajs-3515	71	2	𝜔′(𝑡	𝜔′(𝑡	X
iajs-3515	71	3	)	)	PUNCT
iajs-3515	71	4	>	>	X
iajs-3515	71	5	0	0	NUM
iajs-3515	71	6	,	,	PUNCT
iajs-3515	71	7	and	and	CCONJ
iajs-3515	71	8	either	either	CCONJ
iajs-3515	71	9	lim	lim	PROPN
iajs-3515	71	10	𝑡→∞	𝑡→∞	NUM
iajs-3515	71	11	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	71	12	)	)	PUNCT
iajs-3515	71	13	=	=	SYM
iajs-3515	71	14	∞	∞	PROPN
iajs-3515	71	15	,	,	PUNCT
iajs-3515	71	16	or	or	CCONJ
iajs-3515	71	17	lim	lim	PROPN
iajs-3515	71	18	𝑡→∞	𝑡→∞	NUM
iajs-3515	71	19	𝜉(𝑡)(𝜔′(𝑡	𝜉(𝑡)(𝜔′(𝑡	NUM
iajs-3515	71	20	)	)	PUNCT
iajs-3515	71	21	)	)	PUNCT
iajs-3515	71	22	𝛾	𝛾	X
iajs-3515	71	23	=	=	SYM
iajs-3515	72	1	0	0	X
iajs-3515	72	2	.	.	PUNCT
iajs-3515	73	1	proof	proof	NOUN
iajs-3515	73	2	:	:	PUNCT
iajs-3515	73	3	assume	assume	VERB
iajs-3515	73	4	that	that	SCONJ
iajs-3515	73	5	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	73	6	)	)	PUNCT
iajs-3515	73	7	be	be	VERB
iajs-3515	73	8	eventually	eventually	ADV
iajs-3515	73	9	positive	positive	ADJ
iajs-3515	73	10	solution	solution	NOUN
iajs-3515	73	11	of	of	ADP
iajs-3515	73	12	equation	equation	NOUN
iajs-3515	73	13	(	(	PUNCT
iajs-3515	73	14	1	1	NUM
iajs-3515	73	15	)	)	PUNCT
iajs-3515	73	16	.	.	PUNCT
iajs-3515	74	1	from	from	ADP
iajs-3515	74	2	(	(	PUNCT
iajs-3515	74	3	1	1	X
iajs-3515	74	4	)	)	PUNCT
iajs-3515	74	5	it	it	PRON
iajs-3515	74	6	follows	follow	VERB
iajs-3515	74	7	that	that	SCONJ
iajs-3515	74	8	(	(	PUNCT
iajs-3515	74	9	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	74	10	≤	≤	NUM
iajs-3515	74	11	0	0	NUM
iajs-3515	74	12	,	,	PUNCT
iajs-3515	74	13	that	that	PRON
iajs-3515	74	14	is	be	AUX
iajs-3515	74	15	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	NOUN
iajs-3515	74	16	is	be	AUX
iajs-3515	74	17	non	non	ADJ
iajs-3515	74	18	-	-	ADJ
iajs-3515	74	19	increasing	increase	VERB
iajs-3515	74	20	for	for	ADP
iajs-3515	74	21	𝑡	𝑡	PROPN
iajs-3515	74	22	≥	≥	NUM
iajs-3515	74	23	𝑡0	𝑡0	NOUN
iajs-3515	74	24	.	.	PUNCT
iajs-3515	75	1	we	we	PRON
iajs-3515	75	2	claim	claim	VERB
iajs-3515	75	3	that	that	SCONJ
iajs-3515	75	4	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	75	5	is	be	AUX
iajs-3515	75	6	eventually	eventually	ADV
iajs-3515	75	7	positive	positive	ADJ
iajs-3515	75	8	,	,	PUNCT
iajs-3515	75	9	otherwise	otherwise	ADV
iajs-3515	75	10	if	if	SCONJ
iajs-3515	75	11	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	ADJ
iajs-3515	75	12	is	be	AUX
iajs-3515	75	13	eventually	eventually	ADV
iajs-3515	75	14	negative	negative	ADJ
iajs-3515	75	15	then	then	ADV
iajs-3515	75	16	there	there	PRON
iajs-3515	75	17	is	be	VERB
iajs-3515	75	18	𝜇	𝜇	ADP
iajs-3515	75	19	<	<	X
iajs-3515	75	20	0	0	NUM
iajs-3515	75	21	and	and	CCONJ
iajs-3515	75	22	𝑡1	𝑡1	PROPN
iajs-3515	75	23	≥	≥	NOUN
iajs-3515	75	24	𝑡0	𝑡0	PROPN
iajs-3515	75	25	such	such	ADJ
iajs-3515	75	26	that	that	PRON
iajs-3515	75	27	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	75	28	≤	≤	NOUN
iajs-3515	75	29	𝜇	𝜇	ADP
iajs-3515	75	30	<	<	X
iajs-3515	75	31	0	0	PROPN
iajs-3515	75	32	,	,	PUNCT
iajs-3515	75	33	𝑡	𝑡	PROPN
iajs-3515	75	34	≥	≥	NOUN
iajs-3515	75	35	𝑡1	𝑡1	NOUN
iajs-3515	75	36	,	,	PUNCT
iajs-3515	75	37	so	so	CCONJ
iajs-3515	75	38	it	it	PRON
iajs-3515	75	39	follows	follow	VERB
iajs-3515	75	40	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	75	41	)	)	PUNCT
iajs-3515	75	42	≤	≤	NOUN
iajs-3515	75	43	(	(	PUNCT
iajs-3515	75	44	𝜇	𝜇	ADP
iajs-3515	75	45	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3515	75	46	)	)	PUNCT
iajs-3515	75	47	)	)	PUNCT
iajs-3515	75	48	1	1	NUM
iajs-3515	75	49	𝛾	𝛾	NOUN
iajs-3515	75	50	,	,	PUNCT
iajs-3515	75	51	𝑡	𝑡	PROPN
iajs-3515	75	52	≥	≥	NOUN
iajs-3515	75	53	𝑡1	𝑡1	NOUN
iajs-3515	75	54	.	.	PUNCT
iajs-3515	76	1	(	(	PUNCT
iajs-3515	76	2	3	3	X
iajs-3515	76	3	)	)	PUNCT
iajs-3515	76	4	integrating	integrating	NOUN
iajs-3515	76	5	(	(	PUNCT
iajs-3515	76	6	3	3	NUM
iajs-3515	76	7	)	)	PUNCT
iajs-3515	76	8	from	from	ADP
iajs-3515	76	9	𝑡1	𝑡1	NOUN
iajs-3515	76	10	to	to	ADP
iajs-3515	76	11	𝑡	𝑡	NOUN
iajs-3515	76	12	we	we	PRON
iajs-3515	76	13	get	get	VERB
iajs-3515	76	14	𝜔(𝑡	𝜔(𝑡	NOUN
iajs-3515	76	15	)	)	PUNCT
iajs-3515	76	16	−	−	ADP
iajs-3515	76	17	𝜔(𝑡1	𝜔(𝑡1	NOUN
iajs-3515	76	18	)	)	PUNCT
iajs-3515	76	19	≤	≤	NOUN
iajs-3515	76	20	𝜇	𝜇	ADP
iajs-3515	76	21	1	1	NUM
iajs-3515	76	22	𝛾	𝛾	NOUN
iajs-3515	76	23	∫	∫	PROPN
iajs-3515	76	24	(	(	PUNCT
iajs-3515	76	25	1	1	NUM
iajs-3515	76	26	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	76	27	)	)	PUNCT
iajs-3515	76	28	)	)	PUNCT
iajs-3515	77	1	1	1	NUM
iajs-3515	77	2	𝛾𝑡	𝛾𝑡	ADP
iajs-3515	77	3	𝑡1	𝑡1	PROPN
iajs-3515	77	4	𝑑𝑠.	𝑑𝑠.	NOUN
iajs-3515	77	5	(	(	PUNCT
iajs-3515	77	6	4	4	X
iajs-3515	77	7	)	)	PUNCT
iajs-3515	77	8	letting	let	VERB
iajs-3515	77	9	𝑡	𝑡	PRON
iajs-3515	77	10	→	→	SYM
iajs-3515	77	11	∞	∞	PROPN
iajs-3515	77	12	,	,	PUNCT
iajs-3515	77	13	then	then	ADV
iajs-3515	77	14	from	from	ADP
iajs-3515	77	15	inequality	inequality	NOUN
iajs-3515	77	16	(	(	PUNCT
iajs-3515	77	17	4	4	NUM
iajs-3515	77	18	)	)	PUNCT
iajs-3515	77	19	yields	yield	NOUN
iajs-3515	77	20	lim	lim	PROPN
iajs-3515	77	21	𝑡→∞	𝑡→∞	NUM
iajs-3515	77	22	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	77	23	)	)	PUNCT
iajs-3515	77	24	=	=	PUNCT
iajs-3515	77	25	−∞	−∞	PROPN
iajs-3515	77	26	,	,	PUNCT
iajs-3515	77	27	a	a	DET
iajs-3515	77	28	contradiction	contradiction	NOUN
iajs-3515	77	29	.	.	PUNCT
iajs-3515	78	1	hence	hence	ADV
iajs-3515	78	2	our	our	PRON
iajs-3515	78	3	claim	claim	NOUN
iajs-3515	78	4	verified	verify	VERB
iajs-3515	78	5	and	and	CCONJ
iajs-3515	78	6	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	78	7	>	>	X
iajs-3515	78	8	0	0	NUM
iajs-3515	78	9	,	,	PUNCT
iajs-3515	78	10	that	that	PRON
iajs-3515	78	11	is	be	AUX
iajs-3515	78	12	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	78	13	)	)	PUNCT
iajs-3515	78	14	>	>	X
iajs-3515	78	15	0	0	NUM
iajs-3515	78	16	,	,	PUNCT
iajs-3515	78	17	𝑡	𝑡	PROPN
iajs-3515	78	18	≥	≥	PROPN
iajs-3515	78	19	𝑡1	𝑡1	PROPN
iajs-3515	78	20	≥	≥	NUM
iajs-3515	78	21	𝑡0	𝑡0	PROPN
iajs-3515	78	22	,	,	PUNCT
iajs-3515	78	23	then	then	ADV
iajs-3515	78	24	lim	lim	PROPN
iajs-3515	78	25	𝑡→∞	𝑡→∞	NUM
iajs-3515	78	26	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	78	27	=	=	SYM
iajs-3515	78	28	𝑙	𝑙	PRON
iajs-3515	78	29	≥	≥	NOUN
iajs-3515	78	30	0	0	NUM
iajs-3515	78	31	,	,	PUNCT
iajs-3515	78	32	thus	thus	ADV
iajs-3515	78	33	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	78	34	≥	≥	NUM
iajs-3515	78	35	𝑙	𝑙	NUM
iajs-3515	78	36	,	,	PUNCT
iajs-3515	78	37	𝑡	𝑡	PROPN
iajs-3515	78	38	≥	≥	NOUN
iajs-3515	78	39	𝑡1	𝑡1	NOUN
iajs-3515	78	40	or	or	CCONJ
iajs-3515	78	41	𝜔′(𝑡	𝜔′(𝑡	NUM
iajs-3515	78	42	)	)	PUNCT
iajs-3515	79	1	≥	≥	NOUN
iajs-3515	79	2	(	(	PUNCT
iajs-3515	79	3	𝑙	𝑙	PRON
iajs-3515	79	4	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3515	79	5	)	)	PUNCT
iajs-3515	79	6	)	)	PUNCT
iajs-3515	79	7	1	1	NUM
iajs-3515	79	8	𝛾	𝛾	NOUN
iajs-3515	79	9	,	,	PUNCT
iajs-3515	79	10	𝑡	𝑡	PROPN
iajs-3515	79	11	≥	≥	NOUN
iajs-3515	79	12	𝑡1	𝑡1	NOUN
iajs-3515	79	13	.	.	PUNCT
iajs-3515	80	1	(	(	PUNCT
iajs-3515	80	2	5	5	X
iajs-3515	80	3	)	)	PUNCT
iajs-3515	80	4	ihjpas	ihjpa	NOUN
iajs-3515	80	5	.	.	PUNCT
iajs-3515	81	1	2024	2024	NUM
iajs-3515	81	2	,	,	PUNCT
iajs-3515	81	3	38	38	NUM
iajs-3515	81	4	(	(	PUNCT
iajs-3515	81	5	1	1	NUM
iajs-3515	81	6	)	)	PUNCT
iajs-3515	81	7	410	410	NUM
iajs-3515	81	8	integrating	integrating	NOUN
iajs-3515	81	9	(	(	PUNCT
iajs-3515	81	10	5	5	NUM
iajs-3515	81	11	)	)	PUNCT
iajs-3515	81	12	from	from	ADP
iajs-3515	81	13	𝑡1	𝑡1	NOUN
iajs-3515	81	14	to	to	ADP
iajs-3515	81	15	𝑡	𝑡	PROPN
iajs-3515	81	16	,	,	PUNCT
iajs-3515	81	17	it	it	PRON
iajs-3515	81	18	follows	follow	VERB
iajs-3515	81	19	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	81	20	)	)	PUNCT
iajs-3515	81	21	−	−	PROPN
iajs-3515	81	22	𝜔(𝑡1	𝜔(𝑡1	NOUN
iajs-3515	81	23	)	)	PUNCT
iajs-3515	81	24	≥	≥	NOUN
iajs-3515	81	25	𝑙	𝑙	NOUN
iajs-3515	81	26	1	1	NUM
iajs-3515	81	27	𝛾	𝛾	NOUN
iajs-3515	81	28	∫	∫	PROPN
iajs-3515	81	29	(	(	PUNCT
iajs-3515	81	30	1	1	NUM
iajs-3515	81	31	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	81	32	)	)	PUNCT
iajs-3515	81	33	)	)	PUNCT
iajs-3515	81	34	1	1	NUM
iajs-3515	81	35	𝛾𝑡	𝛾𝑡	ADP
iajs-3515	81	36	𝑡1	𝑡1	NOUN
iajs-3515	81	37	𝑑𝑠.	𝑑𝑠.	NOUN
iajs-3515	81	38	if	if	SCONJ
iajs-3515	81	39	𝑙	𝑙	PROPN
iajs-3515	81	40	>	>	X
iajs-3515	81	41	0	0	NUM
iajs-3515	82	1	then	then	ADV
iajs-3515	82	2	lim	lim	PROPN
iajs-3515	82	3	𝑡→∞	𝑡→∞	NUM
iajs-3515	82	4	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	82	5	)	)	PUNCT
iajs-3515	82	6	=	=	SYM
iajs-3515	82	7	∞	∞	PROPN
iajs-3515	82	8	,	,	PUNCT
iajs-3515	82	9	implies	imply	VERB
iajs-3515	82	10	that	that	SCONJ
iajs-3515	82	11	lim	lim	PROPN
iajs-3515	82	12	𝑡→∞	𝑡→∞	NUM
iajs-3515	82	13	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	82	14	)	)	PUNCT
iajs-3515	82	15	=	=	SYM
iajs-3515	82	16	∞.	∞.	PROPN
iajs-3515	82	17	if	if	SCONJ
iajs-3515	82	18	𝑙	𝑙	PROPN
iajs-3515	82	19	=	=	NOUN
iajs-3515	82	20	0	0	PUNCT
iajs-3515	82	21	then	then	ADV
iajs-3515	82	22	lim	lim	PROPN
iajs-3515	82	23	𝑡→∞	𝑡→∞	NUM
iajs-3515	82	24	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	82	25	=	=	SYM
iajs-3515	83	1	0	0	X
iajs-3515	83	2	.	.	PUNCT
iajs-3515	84	1	lemma	lemma	PROPN
iajs-3515	84	2	2.2	2.2	NUM
iajs-3515	84	3	:	:	PUNCT
iajs-3515	84	4	assume	assume	VERB
iajs-3515	84	5	that	that	SCONJ
iajs-3515	84	6	𝑞𝑖(𝑡	𝑞𝑖(𝑡	NOUN
iajs-3515	84	7	)	)	PUNCT
iajs-3515	84	8	≤	≤	NUM
iajs-3515	84	9	0	0	NUM
iajs-3515	84	10	,	,	PUNCT
iajs-3515	84	11	∑	∑	PUNCT
iajs-3515	84	12	𝑟𝑗(𝑡)𝑘	𝑟𝑗(𝑡)𝑘	NUM
iajs-3515	84	13	𝑗=1	𝑗=1	PROPN
iajs-3515	84	14	≥	≥	NOUN
iajs-3515	84	15	0	0	NUM
iajs-3515	84	16	,	,	PUNCT
iajs-3515	84	17	and	and	CCONJ
iajs-3515	84	18	(	(	PUNCT
iajs-3515	84	19	m1	m1	NOUN
iajs-3515	84	20	)	)	PUNCT
iajs-3515	84	21	holds	hold	VERB
iajs-3515	84	22	.	.	PUNCT
iajs-3515	85	1	let	let	VERB
iajs-3515	85	2	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	85	3	)	)	PUNCT
iajs-3515	85	4	be	be	AUX
iajs-3515	85	5	a	a	DET
iajs-3515	85	6	nonoscillatory	nonoscillatory	ADJ
iajs-3515	85	7	solution	solution	NOUN
iajs-3515	85	8	of	of	ADP
iajs-3515	85	9	equation	equation	NOUN
iajs-3515	85	10	(	(	PUNCT
iajs-3515	85	11	1	1	NUM
iajs-3515	85	12	)	)	PUNCT
iajs-3515	85	13	.	.	PUNCT
iajs-3515	86	1	then	then	ADV
iajs-3515	86	2	the	the	DET
iajs-3515	86	3	following	following	ADJ
iajs-3515	86	4	statements	statement	NOUN
iajs-3515	86	5	hold	hold	VERB
iajs-3515	86	6	:	:	PUNCT
iajs-3515	86	7	(	(	PUNCT
iajs-3515	86	8	a	a	X
iajs-3515	86	9	)	)	PUNCT
iajs-3515	86	10	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	86	11	)	)	PUNCT
iajs-3515	86	12	>	>	X
iajs-3515	86	13	0	0	NUM
iajs-3515	86	14	,	,	PUNCT
iajs-3515	86	15	and	and	CCONJ
iajs-3515	86	16	lim	lim	PROPN
iajs-3515	86	17	𝑡→∞	𝑡→∞	NUM
iajs-3515	86	18	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	86	19	)	)	PUNCT
iajs-3515	86	20	=	=	SYM
iajs-3515	87	1	∞.	∞.	PROPN
iajs-3515	87	2	(	(	PUNCT
iajs-3515	87	3	b	b	NOUN
iajs-3515	87	4	)	)	PUNCT
iajs-3515	87	5	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	87	6	)	)	PUNCT
iajs-3515	87	7	<	<	X
iajs-3515	87	8	0	0	NUM
iajs-3515	87	9	,	,	PUNCT
iajs-3515	87	10	and	and	CCONJ
iajs-3515	87	11	lim	lim	PROPN
iajs-3515	87	12	𝑡→∞	𝑡→∞	NUM
iajs-3515	87	13	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	87	14	=	=	SYM
iajs-3515	87	15	0	0	X
iajs-3515	87	16	.	.	X
iajs-3515	87	17	proof	proof	NOUN
iajs-3515	87	18	:	:	PUNCT
iajs-3515	87	19	assume	assume	VERB
iajs-3515	87	20	that	that	SCONJ
iajs-3515	87	21	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	87	22	)	)	PUNCT
iajs-3515	87	23	be	be	VERB
iajs-3515	87	24	eventually	eventually	ADV
iajs-3515	87	25	positive	positive	ADJ
iajs-3515	87	26	solution	solution	NOUN
iajs-3515	87	27	of	of	ADP
iajs-3515	87	28	equation	equation	NOUN
iajs-3515	87	29	(	(	PUNCT
iajs-3515	87	30	1	1	NUM
iajs-3515	87	31	)	)	PUNCT
iajs-3515	87	32	.	.	PUNCT
iajs-3515	88	1	from	from	ADP
iajs-3515	88	2	equation	equation	NOUN
iajs-3515	88	3	(	(	PUNCT
iajs-3515	88	4	1	1	X
iajs-3515	88	5	)	)	PUNCT
iajs-3515	88	6	we	we	PRON
iajs-3515	88	7	get	get	VERB
iajs-3515	88	8	(	(	PUNCT
iajs-3515	88	9	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	88	10	≥	≥	NUM
iajs-3515	88	11	0	0	NUM
iajs-3515	89	1	that	that	PRON
iajs-3515	89	2	is	be	AUX
iajs-3515	89	3	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	NOUN
iajs-3515	89	4	is	be	AUX
iajs-3515	89	5	non	non	ADJ
iajs-3515	89	6	-	-	ADJ
iajs-3515	89	7	decreasing	decrease	VERB
iajs-3515	89	8	,	,	PUNCT
iajs-3515	89	9	we	we	PRON
iajs-3515	89	10	have	have	VERB
iajs-3515	89	11	two	two	NUM
iajs-3515	89	12	cases	case	NOUN
iajs-3515	89	13	to	to	PART
iajs-3515	89	14	consider	consider	VERB
iajs-3515	89	15	:	:	PUNCT
iajs-3515	89	16	1	1	X
iajs-3515	89	17	.	.	NOUN
iajs-3515	89	18	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	89	19	>	>	X
iajs-3515	89	20	0	0	NUM
iajs-3515	89	21	;	;	PUNCT
iajs-3515	89	22	2	2	NUM
iajs-3515	89	23	.	.	NOUN
iajs-3515	89	24	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	89	25	<	<	X
iajs-3515	89	26	0	0	PROPN
iajs-3515	89	27	,	,	PUNCT
iajs-3515	89	28	𝑡	𝑡	PROPN
iajs-3515	89	29	≥	≥	PROPN
iajs-3515	89	30	𝑡1	𝑡1	PROPN
iajs-3515	89	31	≥	≥	NUM
iajs-3515	89	32	𝑡0	𝑡0	PROPN
iajs-3515	89	33	.	.	PUNCT
iajs-3515	90	1	case	case	NOUN
iajs-3515	90	2	1	1	NUM
iajs-3515	90	3	:	:	PUNCT
iajs-3515	90	4	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	90	5	>	>	X
iajs-3515	90	6	0	0	PUNCT
iajs-3515	91	1	that	that	PRON
iajs-3515	91	2	is	be	AUX
iajs-3515	91	3	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	91	4	)	)	PUNCT
iajs-3515	91	5	>	>	X
iajs-3515	91	6	0	0	NUM
iajs-3515	91	7	,	,	PUNCT
iajs-3515	91	8	𝑡	𝑡	PROPN
iajs-3515	91	9	≥	≥	NOUN
iajs-3515	91	10	𝑡1	𝑡1	VERB
iajs-3515	91	11	then	then	ADV
iajs-3515	91	12	there	there	PRON
iajs-3515	91	13	exist	exist	VERB
iajs-3515	91	14	𝜇	𝜇	ADP
iajs-3515	91	15	>	>	X
iajs-3515	91	16	0	0	NUM
iajs-3515	91	17	such	such	ADJ
iajs-3515	91	18	that	that	SCONJ
iajs-3515	91	19	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	91	20	≥	≥	NOUN
iajs-3515	91	21	𝜇	𝜇	ADP
iajs-3515	91	22	,	,	PUNCT
iajs-3515	91	23	𝑡	𝑡	PROPN
iajs-3515	91	24	≥	≥	NOUN
iajs-3515	91	25	𝑡2	𝑡2	PROPN
iajs-3515	91	26	≥	≥	NOUN
iajs-3515	91	27	𝑡1	𝑡1	PROPN
iajs-3515	91	28	𝜔′(𝑡	𝜔′(𝑡	PROPN
iajs-3515	91	29	)	)	PUNCT
iajs-3515	91	30	≥	≥	NOUN
iajs-3515	91	31	(	(	PUNCT
iajs-3515	91	32	𝜇	𝜇	ADP
iajs-3515	91	33	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3515	91	34	)	)	PUNCT
iajs-3515	91	35	)	)	PUNCT
iajs-3515	91	36	1	1	NUM
iajs-3515	91	37	𝛾	𝛾	NOUN
iajs-3515	91	38	,	,	PUNCT
iajs-3515	91	39	𝑡	𝑡	PROPN
iajs-3515	91	40	≥	≥	NOUN
iajs-3515	91	41	𝑡2	𝑡2	PROPN
iajs-3515	91	42	.	.	PUNCT
iajs-3515	92	1	(	(	PUNCT
iajs-3515	92	2	6	6	NUM
iajs-3515	92	3	)	)	PUNCT
iajs-3515	92	4	by	by	ADP
iajs-3515	92	5	integrating	integrate	VERB
iajs-3515	92	6	(	(	PUNCT
iajs-3515	92	7	6	6	NUM
iajs-3515	92	8	)	)	PUNCT
iajs-3515	92	9	from	from	ADP
iajs-3515	92	10	𝑡2	𝑡2	NOUN
iajs-3515	92	11	to	to	ADP
iajs-3515	92	12	𝑡	𝑡	PROPN
iajs-3515	92	13	we	we	PRON
iajs-3515	92	14	get	get	VERB
iajs-3515	92	15	𝜔(𝑡	𝜔(𝑡	NOUN
iajs-3515	92	16	)	)	PUNCT
iajs-3515	92	17	−	−	PROPN
iajs-3515	92	18	𝜔(𝑡2	𝜔(𝑡2	NUM
iajs-3515	92	19	)	)	PUNCT
iajs-3515	92	20	≥	≥	NOUN
iajs-3515	92	21	𝜇	𝜇	ADP
iajs-3515	92	22	1	1	NUM
iajs-3515	92	23	𝛾	𝛾	NOUN
iajs-3515	92	24	∫	∫	PROPN
iajs-3515	92	25	(	(	PUNCT
iajs-3515	92	26	1	1	NUM
iajs-3515	92	27	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	92	28	)	)	PUNCT
iajs-3515	92	29	)	)	PUNCT
iajs-3515	93	1	1	1	NUM
iajs-3515	93	2	𝛾𝑡	𝛾𝑡	ADP
iajs-3515	93	3	𝑡2	𝑡2	PROPN
iajs-3515	93	4	𝑑𝑠.	𝑑𝑠.	NOUN
iajs-3515	93	5	as	as	SCONJ
iajs-3515	93	6	𝑡	𝑡	PROPN
iajs-3515	93	7	→	→	SYM
iajs-3515	93	8	∞	∞	NUM
iajs-3515	93	9	it	it	PRON
iajs-3515	93	10	follows	follow	VERB
iajs-3515	93	11	lim	lim	PROPN
iajs-3515	93	12	𝑡→∞	𝑡→∞	NUM
iajs-3515	93	13	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	93	14	)	)	PUNCT
iajs-3515	93	15	=	=	SYM
iajs-3515	93	16	∞	∞	PROPN
iajs-3515	93	17	,	,	PUNCT
iajs-3515	93	18	which	which	PRON
iajs-3515	93	19	implies	imply	VERB
iajs-3515	93	20	that	that	SCONJ
iajs-3515	93	21	lim	lim	PROPN
iajs-3515	93	22	𝑡→∞	𝑡→∞	NUM
iajs-3515	93	23	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	93	24	)	)	PUNCT
iajs-3515	93	25	=	=	SYM
iajs-3515	93	26	∞.	∞.	PROPN
iajs-3515	93	27	case	case	NOUN
iajs-3515	93	28	2	2	NUM
iajs-3515	93	29	:	:	PUNCT
iajs-3515	93	30	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	93	31	<	<	X
iajs-3515	93	32	0	0	PUNCT
iajs-3515	93	33	that	that	PRON
iajs-3515	93	34	is	be	AUX
iajs-3515	93	35	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	93	36	)	)	PUNCT
iajs-3515	93	37	<	<	X
iajs-3515	93	38	0	0	NUM
iajs-3515	93	39	,	,	PUNCT
iajs-3515	93	40	𝑡	𝑡	PROPN
iajs-3515	93	41	≥	≥	NOUN
iajs-3515	93	42	𝑡1	𝑡1	NOUN
iajs-3515	93	43	and	and	CCONJ
iajs-3515	93	44	lim	lim	PROPN
iajs-3515	93	45	𝑡→∞	𝑡→∞	NUM
iajs-3515	93	46	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	93	47	=	=	SYM
iajs-3515	94	1	𝑙	𝑙	SYM
iajs-3515	94	2	≤	≤	NUM
iajs-3515	94	3	0	0	NUM
iajs-3515	94	4	.	.	PUNCT
iajs-3515	95	1	we	we	PRON
iajs-3515	95	2	claim	claim	VERB
iajs-3515	95	3	that	that	SCONJ
iajs-3515	95	4	𝑙	𝑙	X
iajs-3515	95	5	=	=	SYM
iajs-3515	95	6	0	0	NUM
iajs-3515	95	7	otherwise	otherwise	ADV
iajs-3515	95	8	𝑙	𝑙	X
iajs-3515	95	9	<	<	X
iajs-3515	95	10	0	0	PUNCT
iajs-3515	95	11	thus	thus	ADV
iajs-3515	95	12	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	95	13	)	)	PUNCT
iajs-3515	95	14	≤	≤	NOUN
iajs-3515	95	15	(	(	PUNCT
iajs-3515	95	16	𝑙	𝑙	PRON
iajs-3515	95	17	𝜉(𝑡	𝜉(𝑡	NOUN
iajs-3515	95	18	)	)	PUNCT
iajs-3515	95	19	)	)	PUNCT
iajs-3515	95	20	1	1	NUM
iajs-3515	95	21	𝛾	𝛾	NOUN
iajs-3515	95	22	,	,	PUNCT
iajs-3515	95	23	𝑡	𝑡	PROPN
iajs-3515	95	24	≥	≥	NOUN
iajs-3515	95	25	𝑡2	𝑡2	PROPN
iajs-3515	95	26	≥	≥	NUM
iajs-3515	95	27	𝑡1	𝑡1	NOUN
iajs-3515	95	28	.	.	PUNCT
iajs-3515	96	1	(	(	PUNCT
iajs-3515	96	2	7	7	X
iajs-3515	96	3	)	)	PUNCT
iajs-3515	96	4	by	by	ADP
iajs-3515	96	5	integrating	integrate	VERB
iajs-3515	96	6	equation	equation	NOUN
iajs-3515	96	7	(	(	PUNCT
iajs-3515	96	8	7	7	NUM
iajs-3515	96	9	)	)	PUNCT
iajs-3515	96	10	from	from	ADP
iajs-3515	96	11	𝑡2	𝑡2	PROPN
iajs-3515	96	12	to	to	ADP
iajs-3515	96	13	t	t	PROPN
iajs-3515	96	14	we	we	PRON
iajs-3515	96	15	get	get	VERB
iajs-3515	96	16	𝜔(𝑡	𝜔(𝑡	NOUN
iajs-3515	96	17	)	)	PUNCT
iajs-3515	96	18	−	−	PROPN
iajs-3515	96	19	𝜔(𝑡2	𝜔(𝑡2	NUM
iajs-3515	96	20	)	)	PUNCT
iajs-3515	96	21	≤	≤	NOUN
iajs-3515	97	1	𝑙	𝑙	DET
iajs-3515	97	2	1	1	NUM
iajs-3515	97	3	𝛾	𝛾	NOUN
iajs-3515	97	4	∫	∫	PROPN
iajs-3515	97	5	(	(	PUNCT
iajs-3515	97	6	1	1	NUM
iajs-3515	97	7	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	97	8	)	)	PUNCT
iajs-3515	97	9	)	)	PUNCT
iajs-3515	97	10	1	1	NUM
iajs-3515	97	11	𝛾𝑡	𝛾𝑡	ADP
iajs-3515	97	12	𝑡2	𝑡2	PROPN
iajs-3515	97	13	𝑑𝑠.	𝑑𝑠.	NOUN
iajs-3515	97	14	as	as	ADP
iajs-3515	97	15	𝑡	𝑡	PROPN
iajs-3515	97	16	→	→	SYM
iajs-3515	97	17	∞	∞	NUM
iajs-3515	97	18	it	it	PRON
iajs-3515	97	19	follows	follow	VERB
iajs-3515	97	20	that	that	SCONJ
iajs-3515	97	21	lim	lim	PROPN
iajs-3515	97	22	𝑡→∞	𝑡→∞	NUM
iajs-3515	97	23	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	97	24	)	)	PUNCT
iajs-3515	97	25	=	=	PUNCT
iajs-3515	97	26	−∞	−∞	PROPN
iajs-3515	97	27	,	,	PUNCT
iajs-3515	97	28	a	a	DET
iajs-3515	97	29	contradiction	contradiction	NOUN
iajs-3515	97	30	.	.	PUNCT
iajs-3515	98	1	then	then	ADV
iajs-3515	98	2	𝑙	𝑙	X
iajs-3515	98	3	=	=	SYM
iajs-3515	98	4	0	0	PROPN
iajs-3515	98	5	.	.	PUNCT
iajs-3515	98	6	theorem	theorem	VERB
iajs-3515	98	7	2.1	2.1	NUM
iajs-3515	98	8	.	.	PUNCT
iajs-3515	99	1	assume	assume	VERB
iajs-3515	99	2	that	that	SCONJ
iajs-3515	99	3	𝑞𝑖(𝑡	𝑞𝑖(𝑡	NOUN
iajs-3515	99	4	)	)	PUNCT
iajs-3515	99	5	≥	≥	NOUN
iajs-3515	99	6	0	0	NUM
iajs-3515	99	7	,	,	PUNCT
iajs-3515	99	8	∑	∑	PUNCT
iajs-3515	99	9	𝑟𝑗(𝑡)𝑘	𝑟𝑗(𝑡)𝑘	NUM
iajs-3515	99	10	𝑗=1	𝑗=1	SYM
iajs-3515	99	11	≤	≤	NUM
iajs-3515	99	12	0	0	NUM
iajs-3515	99	13	,	,	PUNCT
iajs-3515	99	14	(	(	PUNCT
iajs-3515	99	15	𝑀1	𝑀1	NOUN
iajs-3515	99	16	)	)	PUNCT
iajs-3515	99	17	−	−	PROPN
iajs-3515	99	18	(	(	PUNCT
iajs-3515	99	19	𝑀4	𝑀4	PROPN
iajs-3515	99	20	)	)	PUNCT
iajs-3515	99	21	hold	hold	VERB
iajs-3515	99	22	,	,	PUNCT
iajs-3515	99	23	and	and	CCONJ
iajs-3515	99	24	for	for	ADP
iajs-3515	99	25	any	any	DET
iajs-3515	99	26	continuous	continuous	ADJ
iajs-3515	99	27	functions	function	NOUN
iajs-3515	99	28	𝑢(𝑡	𝑢(𝑡	NOUN
iajs-3515	99	29	)	)	PUNCT
iajs-3515	99	30	,	,	PUNCT
iajs-3515	99	31	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-3515	99	32	)	)	PUNCT
iajs-3515	99	33	,	,	PUNCT
iajs-3515	99	34	𝑢𝑣	𝑢𝑣	NOUN
iajs-3515	99	35	>	>	X
iajs-3515	99	36	0	0	NUM
iajs-3515	99	37	,	,	PUNCT
iajs-3515	99	38	there	there	PRON
iajs-3515	99	39	exists	exist	VERB
iajs-3515	99	40	𝜆	𝜆	ADP
iajs-3515	99	41	>	>	X
iajs-3515	99	42	0	0	NUM
iajs-3515	99	43	,	,	PUNCT
iajs-3515	99	44	such	such	ADJ
iajs-3515	99	45	that	that	SCONJ
iajs-3515	99	46	𝑢𝛾(𝑡	𝑢𝛾(𝑡	NUM
iajs-3515	99	47	)	)	PUNCT
iajs-3515	99	48	+	+	NUM
iajs-3515	99	49	𝑣𝛾(𝑡	𝑣𝛾(𝑡	X
iajs-3515	99	50	)	)	PUNCT
iajs-3515	99	51	≥	≥	NOUN
iajs-3515	99	52	𝜆(𝑢(𝑡	𝜆(𝑢(𝑡	PROPN
iajs-3515	99	53	)	)	PUNCT
iajs-3515	100	1	+	+	NUM
iajs-3515	100	2	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-3515	100	3	)	)	PUNCT
iajs-3515	100	4	)	)	PUNCT
iajs-3515	101	1	𝛾	𝛾	X
iajs-3515	101	2	.	.	PUNCT
iajs-3515	102	1	(	(	PUNCT
iajs-3515	102	2	8)	8)	NUM
iajs-3515	102	3	then	then	ADV
iajs-3515	102	4	every	every	DET
iajs-3515	102	5	solution	solution	NOUN
iajs-3515	102	6	of	of	ADP
iajs-3515	102	7	equation	equation	NOUN
iajs-3515	102	8	(	(	PUNCT
iajs-3515	102	9	1	1	X
iajs-3515	102	10	)	)	PUNCT
iajs-3515	102	11	oscillates	oscillate	NOUN
iajs-3515	102	12	.	.	PUNCT
iajs-3515	103	1	proof	proof	NOUN
iajs-3515	103	2	.	.	PUNCT
iajs-3515	104	1	assume	assume	VERB
iajs-3515	104	2	that	that	SCONJ
iajs-3515	104	3	equation	equation	NOUN
iajs-3515	104	4	(	(	PUNCT
iajs-3515	104	5	1	1	X
iajs-3515	104	6	)	)	PUNCT
iajs-3515	104	7	has	have	VERB
iajs-3515	104	8	a	a	DET
iajs-3515	104	9	non	non	ADJ
iajs-3515	104	10	-	-	ADJ
iajs-3515	104	11	oscillatory	oscillatory	ADJ
iajs-3515	104	12	solution	solution	NOUN
iajs-3515	104	13	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	104	14	)	)	PUNCT
iajs-3515	104	15	.	.	PUNCT
iajs-3515	105	1	for	for	ADP
iajs-3515	105	2	lack	lack	NOUN
iajs-3515	105	3	of	of	ADP
iajs-3515	105	4	prolongation	prolongation	NOUN
iajs-3515	105	5	and	and	CCONJ
iajs-3515	105	6	repetition	repetition	NOUN
iajs-3515	105	7	,	,	PUNCT
iajs-3515	105	8	it	it	PRON
iajs-3515	105	9	can	can	AUX
iajs-3515	105	10	be	be	AUX
iajs-3515	105	11	assumed	assume	VERB
iajs-3515	105	12	that	that	SCONJ
iajs-3515	105	13	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	105	14	)	)	PUNCT
iajs-3515	105	15	>	>	X
iajs-3515	105	16	0	0	NUM
iajs-3515	105	17	,	,	PUNCT
iajs-3515	105	18	𝑥(𝜏(𝑡	𝑥(𝜏(𝑡	NOUN
iajs-3515	105	19	)	)	PUNCT
iajs-3515	105	20	)	)	PUNCT
iajs-3515	105	21	>	>	X
iajs-3515	105	22	0	0	NUM
iajs-3515	105	23	,	,	PUNCT
iajs-3515	105	24	𝑥(𝛿𝑖(𝑡	𝑥(𝛿𝑖(𝑡	NUM
iajs-3515	105	25	)	)	PUNCT
iajs-3515	105	26	)	)	PUNCT
iajs-3515	105	27	>	>	X
iajs-3515	106	1	0	0	NUM
iajs-3515	106	2	,	,	PUNCT
iajs-3515	106	3	𝑖	𝑖	NOUN
iajs-3515	106	4	=	=	SYM
iajs-3515	106	5	1,2	1,2	NUM
iajs-3515	106	6	,	,	PUNCT
iajs-3515	106	7	…	…	PUNCT
iajs-3515	106	8	,	,	PUNCT
iajs-3515	106	9	𝑛	𝑛	PROPN
iajs-3515	106	10	,	,	PUNCT
iajs-3515	106	11	for	for	ADP
iajs-3515	106	12	𝑡	𝑡	PROPN
iajs-3515	106	13	≥	≥	NOUN
iajs-3515	106	14	𝑡0	𝑡0	NOUN
iajs-3515	106	15	.	.	PUNCT
iajs-3515	107	1	let	let	VERB
iajs-3515	107	2	𝑢(𝑡	𝑢(𝑡	NOUN
iajs-3515	107	3	)	)	PUNCT
iajs-3515	107	4	=	=	SYM
iajs-3515	107	5	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	107	6	)	)	PUNCT
iajs-3515	107	7	,	,	PUNCT
iajs-3515	107	8	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-3515	107	9	)	)	PUNCT
iajs-3515	107	10	=	=	SYM
iajs-3515	107	11	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3515	107	12	)	)	PUNCT
iajs-3515	107	13	𝑥(𝜏(𝑡	𝑥(𝜏(𝑡	NOUN
iajs-3515	107	14	)	)	PUNCT
iajs-3515	107	15	)	)	PUNCT
iajs-3515	107	16	,	,	PUNCT
iajs-3515	107	17	𝜂(𝑡	𝜂(𝑡	NOUN
iajs-3515	107	18	)	)	PUNCT
iajs-3515	107	19	=	=	SYM
iajs-3515	107	20	max	max	X
iajs-3515	107	21	{	{	PUNCT
iajs-3515	107	22	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	107	23	)	)	PUNCT
iajs-3515	107	24	,	,	PUNCT
iajs-3515	107	25	𝑥(𝜏(𝑡	𝑥(𝜏(𝑡	NOUN
iajs-3515	107	26	)	)	PUNCT
iajs-3515	107	27	)	)	PUNCT
iajs-3515	107	28	}	}	PUNCT
iajs-3515	107	29	,	,	PUNCT
iajs-3515	107	30	then	then	ADV
iajs-3515	107	31	(	(	PUNCT
iajs-3515	107	32	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	107	33	)	)	PUNCT
iajs-3515	107	34	+	+	CCONJ
iajs-3515	107	35	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	ADJ
iajs-3515	107	36	≤	≤	NUM
iajs-3515	107	37	(	(	PUNCT
iajs-3515	107	38	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	107	39	)	)	PUNCT
iajs-3515	107	40	+	+	CCONJ
iajs-3515	107	41	𝑎	𝑎	X
iajs-3515	107	42	𝑥(𝜏(𝑡)))𝛾	𝑥(𝜏(𝑡)))𝛾	ADJ
iajs-3515	107	43	≤	≤	NOUN
iajs-3515	107	44	(	(	PUNCT
iajs-3515	107	45	𝜂(𝑡	𝜂(𝑡	NOUN
iajs-3515	107	46	)	)	PUNCT
iajs-3515	108	1	+	+	CCONJ
iajs-3515	109	1	𝑎	𝑎	X
iajs-3515	109	2	𝜂(𝑡))𝛾	𝜂(𝑡))𝛾	X
iajs-3515	109	3	=	=	PUNCT
iajs-3515	109	4	𝜂𝛾(𝑡)(1	𝜂𝛾(𝑡)(1	NOUN
iajs-3515	109	5	+	+	CCONJ
iajs-3515	109	6	𝑎)𝛾.	𝑎)𝛾.	PROPN
iajs-3515	109	7	since	since	SCONJ
iajs-3515	109	8	𝜂(𝑡	𝜂(𝑡	NOUN
iajs-3515	109	9	)	)	PUNCT
iajs-3515	109	10	=	=	SYM
iajs-3515	109	11	max	max	X
iajs-3515	109	12	{	{	PUNCT
iajs-3515	109	13	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	109	14	)	)	PUNCT
iajs-3515	109	15	,	,	PUNCT
iajs-3515	109	16	𝑥(𝜏(𝑡	𝑥(𝜏(𝑡	NOUN
iajs-3515	109	17	)	)	PUNCT
iajs-3515	109	18	)	)	PUNCT
iajs-3515	109	19	}	}	PUNCT
iajs-3515	110	1	so	so	ADV
iajs-3515	110	2	there	there	PRON
iajs-3515	110	3	exists	exist	VERB
iajs-3515	110	4	휀	휀	PRON
iajs-3515	110	5	>	>	X
iajs-3515	110	6	0	0	NUM
iajs-3515	110	7	,	,	PUNCT
iajs-3515	110	8	such	such	ADJ
iajs-3515	110	9	that	that	SCONJ
iajs-3515	110	10	𝑥𝛾(𝑡	𝑥𝛾(𝑡	NUM
iajs-3515	110	11	)	)	PUNCT
iajs-3515	110	12	+	+	CCONJ
iajs-3515	110	13	𝑝𝛾(𝑡)𝑥𝛾(𝜏(𝑡	𝑝𝛾(𝑡)𝑥𝛾(𝜏(𝑡	NOUN
iajs-3515	110	14	)	)	PUNCT
iajs-3515	110	15	)	)	PUNCT
iajs-3515	110	16	≥	≥	NOUN
iajs-3515	110	17	휀𝜂𝛾(𝑡	휀𝜂𝛾(𝑡	NUM
iajs-3515	110	18	)	)	PUNCT
iajs-3515	111	1	=	=	VERB
iajs-3515	112	1	𝜀(1+𝑎)𝛾	𝜀(1+𝑎)𝛾	NOUN
iajs-3515	112	2	(	(	PUNCT
iajs-3515	112	3	1+𝑎)𝛾	1+𝑎)𝛾	NOUN
iajs-3515	112	4	𝜂𝛾(𝑡	𝜂𝛾(𝑡	NUM
iajs-3515	112	5	)	)	PUNCT
iajs-3515	112	6	=	=	SYM
iajs-3515	112	7	𝜀	𝜀	PROPN
iajs-3515	112	8	(	(	PUNCT
iajs-3515	112	9	1+𝑎)𝛾	1+𝑎)𝛾	NOUN
iajs-3515	112	10	(	(	PUNCT
iajs-3515	112	11	𝜂(𝑡	𝜂(𝑡	NOUN
iajs-3515	112	12	)	)	PUNCT
iajs-3515	112	13	+	+	CCONJ
iajs-3515	112	14	𝑎	𝑎	X
iajs-3515	112	15	𝜂(𝑡))𝛾	𝜂(𝑡))𝛾	PROPN
iajs-3515	112	16	≥	≥	NUM
iajs-3515	112	17	𝜀	𝜀	PROPN
iajs-3515	112	18	(	(	PUNCT
iajs-3515	112	19	1+𝑎)𝛾	1+𝑎)𝛾	NUM
iajs-3515	112	20	(	(	PUNCT
iajs-3515	112	21	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	112	22	)	)	PUNCT
iajs-3515	112	23	+	+	CCONJ
iajs-3515	112	24	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	ADJ
iajs-3515	112	25	,	,	PUNCT
iajs-3515	112	26	choose	choose	VERB
iajs-3515	112	27	𝜆	𝜆	PRON
iajs-3515	112	28	=	=	SYM
iajs-3515	112	29	𝜀	𝜀	X
iajs-3515	112	30	(	(	PUNCT
iajs-3515	112	31	1+𝒶)𝛾	1+𝒶)𝛾	NUM
iajs-3515	112	32	>	>	PUNCT
iajs-3515	112	33	0	0	X
iajs-3515	112	34	.	.	PUNCT
iajs-3515	113	1	hence	hence	ADV
iajs-3515	113	2	,	,	PUNCT
iajs-3515	113	3	ihjpas	ihjpas	PROPN
iajs-3515	113	4	.	.	PUNCT
iajs-3515	114	1	2024	2024	NUM
iajs-3515	114	2	,	,	PUNCT
iajs-3515	114	3	38	38	NUM
iajs-3515	114	4	(	(	PUNCT
iajs-3515	114	5	1	1	NUM
iajs-3515	114	6	)	)	PUNCT
iajs-3515	114	7	411	411	NUM
iajs-3515	114	8	𝑥𝛾(𝑡	𝑥𝛾(𝑡	NUM
iajs-3515	114	9	)	)	PUNCT
iajs-3515	115	1	+	+	CCONJ
iajs-3515	115	2	𝑝𝛾(𝑡)𝑥𝛾(𝜏(𝑡	𝑝𝛾(𝑡)𝑥𝛾(𝜏(𝑡	NOUN
iajs-3515	115	3	)	)	PUNCT
iajs-3515	115	4	)	)	PUNCT
iajs-3515	115	5	≥	≥	NOUN
iajs-3515	115	6	𝜆(𝑥(𝑡	𝜆(𝑥(𝑡	NOUN
iajs-3515	115	7	)	)	PUNCT
iajs-3515	116	1	+	+	NUM
iajs-3515	116	2	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	𝑝(𝑡)𝑥(𝜏(𝑡)))𝛾	X
iajs-3515	116	3	=	=	SYM
iajs-3515	116	4	𝜆𝜔𝛾(𝑡	𝜆𝜔𝛾(𝑡	PROPN
iajs-3515	116	5	)	)	PUNCT
iajs-3515	116	6	.	.	PUNCT
iajs-3515	117	1	(	(	PUNCT
iajs-3515	117	2	9	9	NUM
iajs-3515	117	3	)	)	PUNCT
iajs-3515	117	4	from	from	ADP
iajs-3515	117	5	equation	equation	NOUN
iajs-3515	117	6	(	(	PUNCT
iajs-3515	117	7	1	1	X
iajs-3515	117	8	)	)	PUNCT
iajs-3515	117	9	it	it	PRON
iajs-3515	117	10	follows	follow	VERB
iajs-3515	117	11	that	that	SCONJ
iajs-3515	117	12	:	:	PUNCT
iajs-3515	117	13	(	(	PUNCT
iajs-3515	117	14	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	117	15	+	+	CCONJ
iajs-3515	117	16	∑	∑	PUNCT
iajs-3515	117	17	𝑞𝑖(𝑡)(𝑥(𝛿𝑖(𝑡	𝑞𝑖(𝑡)(𝑥(𝛿𝑖(𝑡	NUM
iajs-3515	117	18	)	)	PUNCT
iajs-3515	117	19	)	)	PUNCT
iajs-3515	118	1	𝛾𝑛	𝛾𝑛	X
iajs-3515	118	2	𝑖=1	𝑖=1	PUNCT
iajs-3515	119	1	+	+	NUM
iajs-3515	119	2	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	NOUN
iajs-3515	119	3	+	+	CCONJ
iajs-3515	119	4	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	119	5	∑	∑	PUNCT
iajs-3515	119	6	𝑞𝑖(𝜏(𝑡))(𝑥	𝑞𝑖(𝜏(𝑡))(𝑥	ADJ
iajs-3515	119	7	(	(	PUNCT
iajs-3515	119	8	𝛿𝑖(𝜏(𝑡	𝛿𝑖(𝜏(𝑡	NOUN
iajs-3515	119	9	)	)	PUNCT
iajs-3515	119	10	)	)	PUNCT
iajs-3515	119	11	)	)	PUNCT
iajs-3515	119	12	𝛾𝑛	𝛾𝑛	X
iajs-3515	119	13	𝑖=1	𝑖=1	PUNCT
iajs-3515	119	14	=	=	PUNCT
iajs-3515	119	15	∑	∑	PUNCT
iajs-3515	119	16	(	(	PUNCT
iajs-3515	119	17	𝑟𝑗(𝑡	𝑟𝑗(𝑡	NOUN
iajs-3515	119	18	)	)	PUNCT
iajs-3515	119	19	𝑘	𝑘	ADP
iajs-3515	119	20	𝑗=1	𝑗=1	X
iajs-3515	119	21	+	+	CCONJ
iajs-3515	119	22	𝑎𝛾𝑟𝑗(𝜏(𝑡	𝑎𝛾𝑟𝑗(𝜏(𝑡	NUM
iajs-3515	119	23	)	)	PUNCT
iajs-3515	119	24	)	)	PUNCT
iajs-3515	119	25	(	(	PUNCT
iajs-3515	119	26	10	10	NUM
iajs-3515	119	27	)	)	PUNCT
iajs-3515	119	28	(	(	PUNCT
iajs-3515	119	29	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	119	30	+	+	NUM
iajs-3515	119	31	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	NOUN
iajs-3515	119	32	+	+	X
iajs-3515	119	33	𝑄(𝑡	𝑄(𝑡	PRON
iajs-3515	119	34	)	)	PUNCT
iajs-3515	119	35	∑	∑	PUNCT
iajs-3515	120	1	[	[	X
iajs-3515	120	2	𝑥𝛾(𝛿𝑖(𝑡	𝑥𝛾(𝛿𝑖(𝑡	X
iajs-3515	120	3	)	)	PUNCT
iajs-3515	121	1	𝑛	𝑛	PRON
iajs-3515	121	2	𝑖=1	𝑖=1	PROPN
iajs-3515	122	1	+	+	CCONJ
iajs-3515	122	2	𝑎𝛾𝑥𝛾(𝛿𝑖(𝜏(𝑡	𝑎𝛾𝑥𝛾(𝛿𝑖(𝜏(𝑡	NOUN
iajs-3515	122	3	)	)	PUNCT
iajs-3515	122	4	)	)	PUNCT
iajs-3515	122	5	]	]	PUNCT
iajs-3515	123	1	−	−	PUNCT
iajs-3515	123	2	∑	∑	INTJ
iajs-3515	123	3	(	(	PUNCT
iajs-3515	123	4	𝑟𝑗(𝑡	𝑟𝑗(𝑡	NOUN
iajs-3515	123	5	)	)	PUNCT
iajs-3515	123	6	𝑘	𝑘	ADP
iajs-3515	123	7	𝑗=1	𝑗=1	X
iajs-3515	123	8	+	+	CCONJ
iajs-3515	123	9	𝑎𝛾𝑟𝑗(𝜏(𝑡	𝑎𝛾𝑟𝑗(𝜏(𝑡	NUM
iajs-3515	123	10	)	)	PUNCT
iajs-3515	123	11	)	)	PUNCT
iajs-3515	123	12	≤	≤	NUM
iajs-3515	123	13	0	0	NUM
iajs-3515	124	1	(	(	PUNCT
iajs-3515	124	2	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	124	3	+	+	NUM
iajs-3515	124	4	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	PROPN
iajs-3515	124	5	+	+	NOUN
iajs-3515	124	6	𝑄(𝑡	𝑄(𝑡	X
iajs-3515	124	7	)	)	PUNCT
iajs-3515	124	8	∑	∑	PUNCT
iajs-3515	124	9	[	[	X
iajs-3515	124	10	𝑥𝛾(𝛿𝑖(𝑡	𝑥𝛾(𝛿𝑖(𝑡	X
iajs-3515	124	11	)	)	PUNCT
iajs-3515	124	12	)	)	PUNCT
iajs-3515	125	1	+	+	CCONJ
iajs-3515	125	2	𝑝𝛾(𝛿𝑖(𝑡))𝑥𝛾(𝛿𝑖(𝜏(𝑡	𝑝𝛾(𝛿𝑖(𝑡))𝑥𝛾(𝛿𝑖(𝜏(𝑡	NOUN
iajs-3515	125	3	)	)	PUNCT
iajs-3515	125	4	)	)	PUNCT
iajs-3515	125	5	]	]	PUNCT
iajs-3515	126	1	𝑛	𝑛	DET
iajs-3515	126	2	𝑖=1	𝑖=1	PROPN
iajs-3515	126	3	−	−	PROPN
iajs-3515	126	4	𝐺(𝑡	𝐺(𝑡	NOUN
iajs-3515	126	5	)	)	PUNCT
iajs-3515	126	6	∑	∑	PUNCT
iajs-3515	126	7	(	(	PUNCT
iajs-3515	126	8	1	1	NUM
iajs-3515	126	9	+	+	NUM
iajs-3515	126	10	𝑘	𝑘	PRON
iajs-3515	126	11	𝑗=1	𝑗=1	PROPN
iajs-3515	126	12	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	126	13	)	)	PUNCT
iajs-3515	126	14	≤	≤	NOUN
iajs-3515	126	15	0	0	NUM
iajs-3515	126	16	by	by	ADP
iajs-3515	126	17	using(9	using(9	PROPN
iajs-3515	126	18	)	)	PUNCT
iajs-3515	126	19	the	the	DET
iajs-3515	126	20	last	last	ADJ
iajs-3515	126	21	inequality	inequality	NOUN
iajs-3515	126	22	yields	yield	VERB
iajs-3515	126	23	:	:	PUNCT
iajs-3515	126	24	(	(	PUNCT
iajs-3515	126	25	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	126	26	+	+	NUM
iajs-3515	126	27	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	NOUN
iajs-3515	126	28	+	+	CCONJ
iajs-3515	126	29	𝜆𝑄(𝑡	𝜆𝑄(𝑡	PROPN
iajs-3515	126	30	)	)	PUNCT
iajs-3515	126	31	∑	∑	PUNCT
iajs-3515	126	32	𝜔𝛾(𝛿𝑖(𝑡	𝜔𝛾(𝛿𝑖(𝑡	NUM
iajs-3515	126	33	)	)	PUNCT
iajs-3515	126	34	)	)	PUNCT
iajs-3515	127	1	𝑛	𝑛	PRON
iajs-3515	127	2	𝑖=1	𝑖=1	PUNCT
iajs-3515	128	1	−	−	PROPN
iajs-3515	128	2	𝑘𝐺(𝑡)(1	𝑘𝐺(𝑡)(1	PROPN
iajs-3515	129	1	+	+	CCONJ
iajs-3515	130	1	𝑎𝛾	𝑎𝛾	NOUN
iajs-3515	130	2	)	)	PUNCT
iajs-3515	130	3	≤	≤	NOUN
iajs-3515	130	4	0	0	NUM
iajs-3515	131	1	let	let	VERB
iajs-3515	131	2	𝛿(𝑡	𝛿(𝑡	PROPN
iajs-3515	131	3	)	)	PUNCT
iajs-3515	131	4	=	=	SYM
iajs-3515	131	5	min	min	NOUN
iajs-3515	131	6	𝑡≥𝑡1	𝑡≥𝑡1	PUNCT
iajs-3515	131	7	{	{	PUNCT
iajs-3515	131	8	𝛿𝑖(𝑡	𝛿𝑖(𝑡	NUM
iajs-3515	131	9	)	)	PUNCT
iajs-3515	131	10	,	,	PUNCT
iajs-3515	131	11	𝑖	𝑖	PUNCT
iajs-3515	131	12	=	=	SYM
iajs-3515	131	13	1,2	1,2	NUM
iajs-3515	131	14	…	…	PUNCT
iajs-3515	131	15	,	,	PUNCT
iajs-3515	131	16	𝑛	𝑛	PROPN
iajs-3515	131	17	}	}	PUNCT
iajs-3515	131	18	,	,	PUNCT
iajs-3515	131	19	by	by	ADP
iajs-3515	131	20	lemma	lemma	PROPN
iajs-3515	131	21	2.1	2.1	NUM
iajs-3515	131	22	,	,	PUNCT
iajs-3515	131	23	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	131	24	)	)	PUNCT
iajs-3515	131	25	is	be	AUX
iajs-3515	131	26	positive	positive	ADJ
iajs-3515	131	27	and	and	CCONJ
iajs-3515	131	28	increasing	increase	VERB
iajs-3515	131	29	so	so	SCONJ
iajs-3515	131	30	there	there	PRON
iajs-3515	131	31	exist	exist	VERB
iajs-3515	131	32	a	a	DET
iajs-3515	131	33	constant	constant	ADJ
iajs-3515	131	34	𝑏	𝑏	NOUN
iajs-3515	131	35	>	>	X
iajs-3515	131	36	0	0	NUM
iajs-3515	131	37	,	,	PUNCT
iajs-3515	131	38	and	and	CCONJ
iajs-3515	131	39	𝑡2	𝑡2	ADJ
iajs-3515	131	40	≥	≥	NOUN
iajs-3515	131	41	𝑡1	𝑡1	VERB
iajs-3515	131	42	such	such	ADJ
iajs-3515	131	43	that	that	SCONJ
iajs-3515	131	44	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	131	45	)	)	PUNCT
iajs-3515	131	46	≥	≥	NOUN
iajs-3515	131	47	𝑏	𝑏	NOUN
iajs-3515	131	48	,	,	PUNCT
iajs-3515	131	49	𝑡	𝑡	PROPN
iajs-3515	131	50	≥	≥	NOUN
iajs-3515	131	51	𝑡2	𝑡2	PROPN
iajs-3515	131	52	.	.	PUNCT
iajs-3515	132	1	hence	hence	ADV
iajs-3515	132	2	the	the	DET
iajs-3515	132	3	last	last	ADJ
iajs-3515	132	4	inequality	inequality	NOUN
iajs-3515	132	5	leads	lead	VERB
iajs-3515	132	6	to	to	ADP
iajs-3515	132	7	:	:	PUNCT
iajs-3515	132	8	(	(	PUNCT
iajs-3515	132	9	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	132	10	+	+	NUM
iajs-3515	132	11	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾]′	NOUN
iajs-3515	132	12	+	+	CCONJ
iajs-3515	132	13	𝑛𝜆𝑄(𝑡)𝜔𝛾(𝛿(𝑡	𝑛𝜆𝑄(𝑡)𝜔𝛾(𝛿(𝑡	NOUN
iajs-3515	132	14	)	)	PUNCT
iajs-3515	132	15	)	)	PUNCT
iajs-3515	133	1	−	−	PROPN
iajs-3515	134	1	𝑘𝐺(𝑡)(1	𝑘𝐺(𝑡)(1	NOUN
iajs-3515	134	2	+	+	CCONJ
iajs-3515	134	3	𝑎𝛾	𝑎𝛾	NOUN
iajs-3515	134	4	)	)	PUNCT
iajs-3515	134	5	≤	≤	NOUN
iajs-3515	134	6	0	0	NUM
iajs-3515	134	7	,	,	PUNCT
iajs-3515	134	8	(	(	PUNCT
iajs-3515	134	9	11	11	NUM
iajs-3515	134	10	)	)	PUNCT
iajs-3515	134	11	𝑛𝜆𝑄(𝑡)𝑏𝛾	𝑛𝜆𝑄(𝑡)𝑏𝛾	NUM
iajs-3515	134	12	≤	≤	PUNCT
iajs-3515	134	13	−(𝜉(𝑡)(𝜔′(𝑡))𝛾)′	−(𝜉(𝑡)(𝜔′(𝑡))𝛾)′	VERB
iajs-3515	135	1	−	−	PROPN
iajs-3515	135	2	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾	𝑎𝛾[𝜉(𝜏(𝑡))(𝜔′(𝜏(𝑡)))𝛾	VERB
iajs-3515	135	3	]	]	PUNCT
iajs-3515	135	4	′	′	NUM
iajs-3515	136	1	+	+	CCONJ
iajs-3515	136	2	𝑘𝐺(𝑡)(1	𝑘𝐺(𝑡)(1	PROPN
iajs-3515	136	3	+	+	CCONJ
iajs-3515	136	4	𝑎𝛾	𝑎𝛾	NOUN
iajs-3515	136	5	)	)	PUNCT
iajs-3515	136	6	,	,	PUNCT
iajs-3515	136	7	(	(	PUNCT
iajs-3515	136	8	12	12	NUM
iajs-3515	136	9	)	)	PUNCT
iajs-3515	136	10	consequently	consequently	ADV
iajs-3515	136	11	,	,	PUNCT
iajs-3515	136	12	by	by	ADP
iajs-3515	136	13	integrating	integrate	VERB
iajs-3515	136	14	(	(	PUNCT
iajs-3515	136	15	12	12	NUM
iajs-3515	136	16	)	)	PUNCT
iajs-3515	136	17	from	from	ADP
iajs-3515	136	18	𝑡2	𝑡2	NOUN
iajs-3515	136	19	to	to	ADP
iajs-3515	136	20	𝑡	𝑡	PROPN
iajs-3515	136	21	yields	yield	NOUN
iajs-3515	136	22	𝑛𝜆𝑏𝛾	𝑛𝜆𝑏𝛾	PROPN
iajs-3515	136	23	∫	∫	PROPN
iajs-3515	136	24	𝑄(𝑠	𝑄(𝑠	NUM
iajs-3515	136	25	)	)	PUNCT
iajs-3515	136	26	𝑡	𝑡	PROPN
iajs-3515	136	27	𝑡2	𝑡2	NOUN
iajs-3515	136	28	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	136	29	≤	≤	NUM
iajs-3515	136	30	−	−	PROPN
iajs-3515	136	31	∫	∫	PROPN
iajs-3515	136	32	(	(	PUNCT
iajs-3515	136	33	𝜉(𝑠)(𝜔′(𝑠))𝛾)′	𝜉(𝑠)(𝜔′(𝑠))𝛾)′	NUM
iajs-3515	136	34	𝑡	𝑡	VERB
iajs-3515	136	35	𝑡2	𝑡2	NOUN
iajs-3515	136	36	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	136	37	−	−	PROPN
iajs-3515	136	38	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	136	39	∫	∫	PROPN
iajs-3515	137	1	[	[	X
iajs-3515	137	2	𝜉(𝜏(𝑠))(𝜔′(𝑠))𝛾]′	𝜉(𝜏(𝑠))(𝜔′(𝑠))𝛾]′	X
iajs-3515	137	3	𝑡	𝑡	ADP
iajs-3515	137	4	𝑡2	𝑡2	PROPN
iajs-3515	137	5	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	137	6	+	+	CCONJ
iajs-3515	137	7	𝑘(1	𝑘(1	PROPN
iajs-3515	137	8	+	+	CCONJ
iajs-3515	137	9	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	137	10	)	)	PUNCT
iajs-3515	137	11	∫	∫	PROPN
iajs-3515	137	12	𝐺(𝑠)𝑑𝑠	𝐺(𝑠)𝑑𝑠	PROPN
iajs-3515	137	13	𝑡	𝑡	PROPN
iajs-3515	137	14	𝑡2	𝑡2	PROPN
iajs-3515	137	15	𝑛𝜆𝑏𝛾	𝑛𝜆𝑏𝛾	PROPN
iajs-3515	137	16	∫	∫	PROPN
iajs-3515	137	17	𝑄(𝑠	𝑄(𝑠	NUM
iajs-3515	137	18	)	)	PUNCT
iajs-3515	137	19	𝑡	𝑡	PROPN
iajs-3515	137	20	𝑡2	𝑡2	NOUN
iajs-3515	137	21	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	137	22	≤	≤	ADJ
iajs-3515	137	23	𝜉(𝑡2)(𝜔′(𝑡2))𝛾	𝜉(𝑡2)(𝜔′(𝑡2))𝛾	PROPN
iajs-3515	137	24	+	+	CCONJ
iajs-3515	138	1	𝑎𝛾𝜉(𝜏(𝑡2))[𝜔′(𝜏(𝑡2))]𝛾	𝑎𝛾𝜉(𝜏(𝑡2))[𝜔′(𝜏(𝑡2))]𝛾	VERB
iajs-3515	139	1	+	+	CCONJ
iajs-3515	139	2	𝑘(1	𝑘(1	ADJ
iajs-3515	139	3	+	+	CCONJ
iajs-3515	139	4	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	139	5	)	)	PUNCT
iajs-3515	139	6	∫	∫	NOUN
iajs-3515	139	7	𝐺(𝑠	𝐺(𝑠	NUM
iajs-3515	139	8	)	)	PUNCT
iajs-3515	139	9	𝑡	𝑡	PROPN
iajs-3515	139	10	𝑡2	𝑡2	PROPN
iajs-3515	139	11	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	139	12	,	,	PUNCT
iajs-3515	139	13	(	(	PUNCT
iajs-3515	139	14	13	13	NUM
iajs-3515	139	15	)	)	PUNCT
iajs-3515	140	1	hence	hence	ADV
iajs-3515	140	2	by	by	ADP
iajs-3515	140	3	(	(	PUNCT
iajs-3515	140	4	m3	m3	PROPN
iajs-3515	140	5	)	)	PUNCT
iajs-3515	140	6	it	it	PRON
iajs-3515	140	7	follows	follow	VERB
iajs-3515	140	8	from	from	ADP
iajs-3515	140	9	(	(	PUNCT
iajs-3515	140	10	13	13	NUM
iajs-3515	140	11	)	)	PUNCT
iajs-3515	140	12	∫	∫	NOUN
iajs-3515	140	13	𝑄(𝑠	𝑄(𝑠	NUM
iajs-3515	140	14	)	)	PUNCT
iajs-3515	140	15	∞	∞	PROPN
iajs-3515	140	16	𝑡2	𝑡2	NOUN
iajs-3515	140	17	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	140	18	<	<	X
iajs-3515	140	19	∞	∞	PROPN
iajs-3515	140	20	,	,	PUNCT
iajs-3515	140	21	contradicts	contradict	VERB
iajs-3515	140	22	(	(	PUNCT
iajs-3515	140	23	𝑀4	𝑀4	PROPN
iajs-3515	140	24	)	)	PUNCT
iajs-3515	140	25	.	.	PUNCT
iajs-3515	141	1	theorem	theorem	VERB
iajs-3515	141	2	2.2	2.2	NUM
iajs-3515	141	3	.	.	PUNCT
iajs-3515	142	1	assume	assume	VERB
iajs-3515	142	2	that	that	SCONJ
iajs-3515	142	3	𝑞𝑖(𝑡	𝑞𝑖(𝑡	NOUN
iajs-3515	142	4	)	)	PUNCT
iajs-3515	142	5	≤	≤	NUM
iajs-3515	142	6	0	0	NUM
iajs-3515	142	7	,	,	PUNCT
iajs-3515	142	8	𝑖	𝑖	NOUN
iajs-3515	142	9	=	=	SYM
iajs-3515	142	10	1,2	1,2	NUM
iajs-3515	142	11	,	,	PUNCT
iajs-3515	142	12	…	…	PUNCT
iajs-3515	142	13	,	,	PUNCT
iajs-3515	142	14	𝑛	𝑛	PROPN
iajs-3515	142	15	,	,	PUNCT
iajs-3515	142	16	∑	∑	ADP
iajs-3515	142	17	𝑟𝑖(𝑡)𝑘	𝑟𝑖(𝑡)𝑘	PROPN
iajs-3515	142	18	𝑗=1	𝑗=1	PROPN
iajs-3515	142	19	≥	≥	NOUN
iajs-3515	142	20	0	0	NUM
iajs-3515	142	21	,	,	PUNCT
iajs-3515	142	22	𝜉′(𝑡	𝜉′(𝑡	PROPN
iajs-3515	142	23	)	)	PUNCT
iajs-3515	142	24	>	>	X
iajs-3515	142	25	0	0	PUNCT
iajs-3515	143	1	on	on	ADP
iajs-3515	143	2	[	[	X
iajs-3515	143	3	𝑡0	𝑡0	NOUN
iajs-3515	143	4	,	,	PUNCT
iajs-3515	143	5	∞	∞	PROPN
iajs-3515	143	6	)	)	PUNCT
iajs-3515	143	7	.	.	PUNCT
iajs-3515	144	1	let	let	VERB
iajs-3515	144	2	(	(	PUNCT
iajs-3515	144	3	m1	m1	NOUN
iajs-3515	144	4	)	)	PUNCT
iajs-3515	144	5	−	−	PROPN
iajs-3515	144	6	(	(	PUNCT
iajs-3515	144	7	m4	m4	PROPN
iajs-3515	144	8	)	)	PUNCT
iajs-3515	144	9	hold	hold	NOUN
iajs-3515	144	10	,	,	PUNCT
iajs-3515	144	11	and	and	CCONJ
iajs-3515	144	12	for	for	ADP
iajs-3515	144	13	any	any	DET
iajs-3515	144	14	continuous	continuous	ADJ
iajs-3515	144	15	functions𝑢(𝑡	functions𝑢(𝑡	NOUN
iajs-3515	144	16	)	)	PUNCT
iajs-3515	144	17	,	,	PUNCT
iajs-3515	144	18	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-3515	144	19	)	)	PUNCT
iajs-3515	144	20	,	,	PUNCT
iajs-3515	144	21	𝑢𝑣	𝑢𝑣	NOUN
iajs-3515	144	22	>	>	X
iajs-3515	144	23	0	0	NUM
iajs-3515	144	24	,	,	PUNCT
iajs-3515	144	25	there	there	PRON
iajs-3515	144	26	exists	exist	VERB
iajs-3515	144	27	𝜆	𝜆	ADP
iajs-3515	144	28	>	>	X
iajs-3515	144	29	0	0	NUM
iajs-3515	144	30	,	,	PUNCT
iajs-3515	144	31	such	such	ADJ
iajs-3515	144	32	that	that	SCONJ
iajs-3515	144	33	(	(	PUNCT
iajs-3515	144	34	8)	8)	NUM
iajs-3515	144	35	holds	hold	VERB
iajs-3515	144	36	,	,	PUNCT
iajs-3515	144	37	in	in	ADP
iajs-3515	144	38	addition	addition	NOUN
iajs-3515	144	39	to	to	ADP
iajs-3515	144	40	the	the	DET
iajs-3515	144	41	condition	condition	NOUN
iajs-3515	145	1	lim	lim	PROPN
iajs-3515	145	2	sup	sup	PROPN
iajs-3515	145	3	𝑡→∞	𝑡→∞	NUM
iajs-3515	145	4	∫	∫	PROPN
iajs-3515	145	5	[	[	PUNCT
iajs-3515	145	6	1	1	NUM
iajs-3515	145	7	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	145	8	)	)	PUNCT
iajs-3515	145	9	∫	∫	PROPN
iajs-3515	145	10	∑	∑	PROPN
iajs-3515	145	11	|𝑞𝑖(𝑣)|[1	|𝑞𝑖(𝑣)|[1	ADV
iajs-3515	145	12	−	−	PROPN
iajs-3515	145	13	𝑝(𝛿𝑖(𝑣))]𝛾	𝑝(𝛿𝑖(𝑣))]𝛾	NUM
iajs-3515	145	14	𝑛	𝑛	PRON
iajs-3515	145	15	𝑖=1	𝑖=1	PROPN
iajs-3515	145	16	𝛼(𝑠	𝛼(𝑠	PROPN
iajs-3515	145	17	)	)	PUNCT
iajs-3515	145	18	𝑠	𝑠	PROPN
iajs-3515	145	19	𝑑𝑣	𝑑𝑣	PROPN
iajs-3515	145	20	]	]	X
iajs-3515	145	21	1	1	NUM
iajs-3515	145	22	𝛾	𝛾	NOUN
iajs-3515	145	23	𝑑𝑠	𝑑𝑠	X
iajs-3515	145	24	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	145	25	)	)	PUNCT
iajs-3515	145	26	𝑡	𝑡	X
iajs-3515	145	27	>	>	X
iajs-3515	145	28	1	1	NUM
iajs-3515	145	29	.	.	PUNCT
iajs-3515	146	1	(	(	PUNCT
iajs-3515	146	2	14	14	NUM
iajs-3515	146	3	)	)	PUNCT
iajs-3515	146	4	then	then	ADV
iajs-3515	146	5	every	every	DET
iajs-3515	146	6	solution	solution	NOUN
iajs-3515	146	7	of	of	ADP
iajs-3515	146	8	equation	equation	NOUN
iajs-3515	146	9	(	(	PUNCT
iajs-3515	146	10	1	1	X
iajs-3515	146	11	)	)	PUNCT
iajs-3515	146	12	oscillates	oscillate	NOUN
iajs-3515	146	13	.	.	PUNCT
iajs-3515	147	1	ihjpas	ihjpas	PROPN
iajs-3515	147	2	.	.	PUNCT
iajs-3515	148	1	2024	2024	NUM
iajs-3515	148	2	,	,	PUNCT
iajs-3515	148	3	38	38	NUM
iajs-3515	148	4	(	(	PUNCT
iajs-3515	148	5	1	1	NUM
iajs-3515	148	6	)	)	PUNCT
iajs-3515	148	7	412	412	NUM
iajs-3515	148	8	proof	proof	NOUN
iajs-3515	148	9	.	.	PUNCT
iajs-3515	149	1	assume	assume	VERB
iajs-3515	149	2	that	that	SCONJ
iajs-3515	149	3	equation	equation	NOUN
iajs-3515	149	4	(	(	PUNCT
iajs-3515	149	5	1	1	X
iajs-3515	149	6	)	)	PUNCT
iajs-3515	149	7	has	have	VERB
iajs-3515	149	8	eventually	eventually	ADV
iajs-3515	149	9	positive	positive	ADJ
iajs-3515	149	10	solution	solution	NOUN
iajs-3515	149	11	𝑥(t	𝑥(t	NOUN
iajs-3515	149	12	)	)	PUNCT
iajs-3515	149	13	,	,	PUNCT
iajs-3515	149	14	that	that	PRON
iajs-3515	149	15	is	be	AUX
iajs-3515	149	16	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	149	17	)	)	PUNCT
iajs-3515	149	18	>	>	X
iajs-3515	149	19	0	0	NUM
iajs-3515	149	20	,	,	PUNCT
iajs-3515	149	21	𝑥(𝜏(𝑡	𝑥(𝜏(𝑡	NOUN
iajs-3515	149	22	)	)	PUNCT
iajs-3515	149	23	)	)	PUNCT
iajs-3515	149	24	>	>	X
iajs-3515	150	1	0	0	NUM
iajs-3515	150	2	,	,	PUNCT
iajs-3515	150	3	𝑥(𝛿𝑖(𝑡	𝑥(𝛿𝑖(𝑡	NUM
iajs-3515	150	4	)	)	PUNCT
iajs-3515	150	5	)	)	PUNCT
iajs-3515	151	1	>	>	X
iajs-3515	151	2	0	0	NUM
iajs-3515	151	3	,	,	PUNCT
iajs-3515	151	4	𝑖	𝑖	NOUN
iajs-3515	151	5	=	=	SYM
iajs-3515	151	6	1,2	1,2	NUM
iajs-3515	151	7	,	,	PUNCT
iajs-3515	151	8	…	…	PUNCT
iajs-3515	151	9	,	,	PUNCT
iajs-3515	151	10	𝑛.	𝑛.	NOUN
iajs-3515	151	11	from	from	ADP
iajs-3515	151	12	equation	equation	NOUN
iajs-3515	151	13	(	(	PUNCT
iajs-3515	151	14	1	1	X
iajs-3515	151	15	)	)	PUNCT
iajs-3515	151	16	we	we	PRON
iajs-3515	151	17	get	get	VERB
iajs-3515	151	18	(	(	PUNCT
iajs-3515	151	19	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	𝜉(𝑡)(𝜔′(𝑡))𝛾)′	PROPN
iajs-3515	151	20	≥	≥	NUM
iajs-3515	151	21	0	0	NUM
iajs-3515	151	22	,	,	PUNCT
iajs-3515	151	23	based	base	VERB
iajs-3515	151	24	on	on	ADP
iajs-3515	151	25	lemma	lemma	PROPN
iajs-3515	151	26	2.2	2.2	NUM
iajs-3515	151	27	,	,	PUNCT
iajs-3515	151	28	there	there	PRON
iajs-3515	151	29	are	be	VERB
iajs-3515	151	30	two	two	NUM
iajs-3515	151	31	cases	case	NOUN
iajs-3515	151	32	that	that	PRON
iajs-3515	151	33	need	need	VERB
iajs-3515	151	34	to	to	PART
iajs-3515	151	35	be	be	AUX
iajs-3515	151	36	investigated	investigate	VERB
iajs-3515	151	37	:	:	PUNCT
iajs-3515	151	38	(	(	PUNCT
iajs-3515	151	39	a	a	X
iajs-3515	151	40	)	)	PUNCT
iajs-3515	151	41	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	151	42	)	)	PUNCT
iajs-3515	151	43	>	>	X
iajs-3515	151	44	0	0	NUM
iajs-3515	151	45	,	,	PUNCT
iajs-3515	151	46	and	and	CCONJ
iajs-3515	151	47	lim	lim	PROPN
iajs-3515	151	48	𝑡→∞	𝑡→∞	NUM
iajs-3515	151	49	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	151	50	)	)	PUNCT
iajs-3515	152	1	=	=	SYM
iajs-3515	152	2	∞.	∞.	PROPN
iajs-3515	152	3	(	(	PUNCT
iajs-3515	152	4	b	b	NOUN
iajs-3515	152	5	)	)	PUNCT
iajs-3515	152	6	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	152	7	)	)	PUNCT
iajs-3515	152	8	<	<	X
iajs-3515	152	9	0	0	NUM
iajs-3515	152	10	,	,	PUNCT
iajs-3515	152	11	and	and	CCONJ
iajs-3515	152	12	lim	lim	PROPN
iajs-3515	152	13	𝑡→∞	𝑡→∞	NUM
iajs-3515	152	14	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	152	15	=	=	SYM
iajs-3515	152	16	0	0	X
iajs-3515	152	17	.	.	X
iajs-3515	152	18	case	case	NOUN
iajs-3515	152	19	(	(	PUNCT
iajs-3515	152	20	a	a	NOUN
iajs-3515	152	21	)	)	PUNCT
iajs-3515	152	22	proceeding	proceeding	NOUN
iajs-3515	152	23	as	as	ADP
iajs-3515	152	24	in	in	ADP
iajs-3515	152	25	the	the	DET
iajs-3515	152	26	proof	proof	NOUN
iajs-3515	152	27	of	of	ADP
iajs-3515	152	28	theorem	theorem	NOUN
iajs-3515	152	29	2.1	2.1	NUM
iajs-3515	152	30	,	,	PUNCT
iajs-3515	152	31	we	we	PRON
iajs-3515	152	32	conclude	conclude	VERB
iajs-3515	152	33	that	that	SCONJ
iajs-3515	152	34	(	(	PUNCT
iajs-3515	152	35	11	11	NUM
iajs-3515	152	36	)	)	PUNCT
iajs-3515	152	37	holds	hold	VERB
iajs-3515	152	38	.	.	PUNCT
iajs-3515	153	1	letting	let	VERB
iajs-3515	153	2	𝑧(𝑡	𝑧(𝑡	NOUN
iajs-3515	153	3	)	)	PUNCT
iajs-3515	153	4	=	=	SYM
iajs-3515	153	5	𝜉(𝑡)(𝜔′(𝑡))𝛾.	𝜉(𝑡)(𝜔′(𝑡))𝛾.	NOUN
iajs-3515	153	6	(	(	PUNCT
iajs-3515	153	7	15	15	NUM
iajs-3515	153	8	)	)	PUNCT
iajs-3515	153	9	then	then	ADV
iajs-3515	153	10	𝑧(𝑡	𝑧(𝑡	PROPN
iajs-3515	153	11	)	)	PUNCT
iajs-3515	153	12	is	be	AUX
iajs-3515	153	13	positive	positive	ADJ
iajs-3515	153	14	and	and	CCONJ
iajs-3515	153	15	non	non	ADJ
iajs-3515	153	16	-	-	ADJ
iajs-3515	153	17	decreasing	decrease	VERB
iajs-3515	153	18	,	,	PUNCT
iajs-3515	153	19	hence	hence	ADV
iajs-3515	153	20	(	(	PUNCT
iajs-3515	153	21	11	11	NUM
iajs-3515	153	22	)	)	PUNCT
iajs-3515	153	23	becomes	become	VERB
iajs-3515	153	24	:	:	PUNCT
iajs-3515	153	25	𝑧′(𝑡)+𝑎𝛾[𝑧(𝜏(𝑡	𝑧′(𝑡)+𝑎𝛾[𝑧(𝜏(𝑡	NOUN
iajs-3515	153	26	)	)	PUNCT
iajs-3515	153	27	)	)	PUNCT
iajs-3515	153	28	]	]	PUNCT
iajs-3515	154	1	′	′	NUM
iajs-3515	155	1	+	+	CCONJ
iajs-3515	155	2	𝑛𝜆𝑄(𝑡)𝜔𝛾(𝛿(𝑡	𝑛𝜆𝑄(𝑡)𝜔𝛾(𝛿(𝑡	NOUN
iajs-3515	155	3	)	)	PUNCT
iajs-3515	155	4	)	)	PUNCT
iajs-3515	156	1	<	<	X
iajs-3515	156	2	𝑘𝐺(𝑡)(1	𝑘𝐺(𝑡)(1	PROPN
iajs-3515	157	1	+	+	CCONJ
iajs-3515	157	2	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	157	3	)	)	PUNCT
iajs-3515	157	4	,	,	PUNCT
iajs-3515	157	5	for	for	ADP
iajs-3515	157	6	𝑡	𝑡	PROPN
iajs-3515	157	7	≥	≥	NOUN
iajs-3515	157	8	𝑡2	𝑡2	NOUN
iajs-3515	157	9	(	(	PUNCT
iajs-3515	157	10	16	16	NUM
iajs-3515	157	11	)	)	PUNCT
iajs-3515	157	12	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	157	13	)	)	PUNCT
iajs-3515	157	14	is	be	AUX
iajs-3515	157	15	positive	positive	ADJ
iajs-3515	157	16	and	and	CCONJ
iajs-3515	157	17	increasing	increase	VERB
iajs-3515	157	18	so	so	SCONJ
iajs-3515	157	19	there	there	PRON
iajs-3515	157	20	exist	exist	VERB
iajs-3515	157	21	a	a	DET
iajs-3515	157	22	constant	constant	ADJ
iajs-3515	157	23	𝑏	𝑏	NOUN
iajs-3515	157	24	>	>	X
iajs-3515	157	25	0	0	NUM
iajs-3515	157	26	,	,	PUNCT
iajs-3515	157	27	and	and	CCONJ
iajs-3515	157	28	𝑡3	𝑡3	PROPN
iajs-3515	157	29	≥	≥	PROPN
iajs-3515	157	30	𝑡2	𝑡2	PROPN
iajs-3515	157	31	such	such	ADJ
iajs-3515	157	32	that	that	SCONJ
iajs-3515	157	33	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	157	34	)	)	PUNCT
iajs-3515	157	35	≥	≥	NOUN
iajs-3515	157	36	𝑏	𝑏	NOUN
iajs-3515	157	37	,	,	PUNCT
iajs-3515	157	38	𝑡	𝑡	PROPN
iajs-3515	157	39	≥	≥	NOUN
iajs-3515	157	40	𝑡3	𝑡3	PROPN
iajs-3515	157	41	.	.	PROPN
iajs-3515	158	1	therefor	therefor	PROPN
iajs-3515	158	2	(	(	PUNCT
iajs-3515	158	3	16	16	NUM
iajs-3515	158	4	)	)	PUNCT
iajs-3515	158	5	reduce	reduce	VERB
iajs-3515	158	6	to	to	ADP
iajs-3515	158	7	𝑧′(𝑡)+𝑎𝛾[𝑧(𝜏(𝑡	𝑧′(𝑡)+𝑎𝛾[𝑧(𝜏(𝑡	NUM
iajs-3515	158	8	)	)	PUNCT
iajs-3515	158	9	)	)	PUNCT
iajs-3515	158	10	]	]	PUNCT
iajs-3515	159	1	′	′	NUM
iajs-3515	160	1	+	+	CCONJ
iajs-3515	160	2	𝑛𝜆𝑄(𝑡)𝑏𝛾	𝑛𝜆𝑄(𝑡)𝑏𝛾	NUM
iajs-3515	160	3	<	<	X
iajs-3515	160	4	𝑘𝐺(𝑡)(1	𝑘𝐺(𝑡)(1	PROPN
iajs-3515	160	5	+	+	CCONJ
iajs-3515	160	6	𝑎𝛾	𝑎𝛾	NOUN
iajs-3515	160	7	)	)	PUNCT
iajs-3515	160	8	,	,	PUNCT
iajs-3515	160	9	for	for	ADP
iajs-3515	160	10	𝑡	𝑡	PROPN
iajs-3515	160	11	≥	≥	PROPN
iajs-3515	160	12	𝑡3	𝑡3	PROPN
iajs-3515	160	13	(	(	PUNCT
iajs-3515	160	14	17	17	NUM
iajs-3515	160	15	)	)	PUNCT
iajs-3515	160	16	integration	integration	NOUN
iajs-3515	160	17	(	(	PUNCT
iajs-3515	160	18	17	17	NUM
iajs-3515	160	19	)	)	PUNCT
iajs-3515	160	20	from	from	ADP
iajs-3515	160	21	𝑡3	𝑡3	PROPN
iajs-3515	160	22	to	to	ADP
iajs-3515	160	23	𝑡	𝑡	PROPN
iajs-3515	160	24	,	,	PUNCT
iajs-3515	160	25	where	where	SCONJ
iajs-3515	160	26	𝑡	𝑡	PROPN
iajs-3515	160	27	is	be	AUX
iajs-3515	160	28	sufficiently	sufficiently	ADV
iajs-3515	160	29	large	large	ADJ
iajs-3515	160	30	𝑡3	𝑡3	NOUN
iajs-3515	160	31	,	,	PUNCT
iajs-3515	160	32	leads	lead	VERB
iajs-3515	160	33	to	to	ADP
iajs-3515	160	34	∫	∫	PROPN
iajs-3515	160	35	𝑧′(𝑠)𝑑𝑠	𝑧′(𝑠)𝑑𝑠	PROPN
iajs-3515	160	36	𝑡	𝑡	PROPN
iajs-3515	160	37	𝑡3	𝑡3	PROPN
iajs-3515	160	38	+	+	PROPN
iajs-3515	160	39	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	160	40	∫	∫	PROPN
iajs-3515	160	41	(	(	PUNCT
iajs-3515	160	42	𝑧(𝜏(𝑠)))′𝑑𝑠	𝑧(𝜏(𝑠)))′𝑑𝑠	NOUN
iajs-3515	160	43	𝑡	𝑡	PROPN
iajs-3515	160	44	𝑡3	𝑡3	PROPN
iajs-3515	160	45	+	+	CCONJ
iajs-3515	160	46	𝑛𝜆𝑏𝛾	𝑛𝜆𝑏𝛾	PROPN
iajs-3515	160	47	∫	∫	PROPN
iajs-3515	160	48	𝑄(𝑠)𝑑𝑠	𝑄(𝑠)𝑑𝑠	PROPN
iajs-3515	160	49	𝑡	𝑡	PROPN
iajs-3515	160	50	𝑡3	𝑡3	PROPN
iajs-3515	160	51	<	<	X
iajs-3515	160	52	𝑘(1	𝑘(1	PROPN
iajs-3515	161	1	+	+	CCONJ
iajs-3515	161	2	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	161	3	)	)	PUNCT
iajs-3515	161	4	∫	∫	PROPN
iajs-3515	161	5	𝐺(𝑠)𝑑𝑠	𝐺(𝑠)𝑑𝑠	PROPN
iajs-3515	161	6	𝑡	𝑡	PROPN
iajs-3515	161	7	𝑡3	𝑡3	PROPN
iajs-3515	161	8	since	since	SCONJ
iajs-3515	161	9	𝑧(𝑡	𝑧(𝑡	PROPN
iajs-3515	161	10	)	)	PUNCT
iajs-3515	161	11	is	be	AUX
iajs-3515	161	12	non	non	ADJ
iajs-3515	161	13	-	-	ADJ
iajs-3515	161	14	decreasing	decrease	VERB
iajs-3515	161	15	,	,	PUNCT
iajs-3515	161	16	then	then	ADV
iajs-3515	161	17	the	the	DET
iajs-3515	161	18	last	last	ADJ
iajs-3515	161	19	inequality	inequality	NOUN
iajs-3515	161	20	becomes	become	VERB
iajs-3515	161	21	:	:	PUNCT
iajs-3515	161	22	𝑧(𝑡	𝑧(𝑡	NOUN
iajs-3515	161	23	)	)	PUNCT
iajs-3515	161	24	−	−	PROPN
iajs-3515	161	25	𝑧(𝑡3	𝑧(𝑡3	NOUN
iajs-3515	161	26	)	)	PUNCT
iajs-3515	162	1	+	+	CCONJ
iajs-3515	162	2	𝑎𝛾𝑧(𝜏(𝑡	𝑎𝛾𝑧(𝜏(𝑡	NOUN
iajs-3515	162	3	)	)	PUNCT
iajs-3515	162	4	)	)	PUNCT
iajs-3515	163	1	−	−	PROPN
iajs-3515	163	2	𝑎𝛾𝑧(𝜏(𝑡3	𝑎𝛾𝑧(𝜏(𝑡3	PROPN
iajs-3515	163	3	)	)	PUNCT
iajs-3515	163	4	)	)	PUNCT
iajs-3515	164	1	+	+	CCONJ
iajs-3515	164	2	𝑛𝜆𝑏𝛾	𝑛𝜆𝑏𝛾	NOUN
iajs-3515	164	3	∫	∫	PROPN
iajs-3515	164	4	𝑄(𝑠	𝑄(𝑠	NUM
iajs-3515	164	5	)	)	PUNCT
iajs-3515	164	6	𝑡	𝑡	PROPN
iajs-3515	164	7	𝑡3	𝑡3	PROPN
iajs-3515	164	8	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	164	9	<	<	X
iajs-3515	164	10	𝑘	𝑘	X
iajs-3515	164	11	(	(	PUNCT
iajs-3515	164	12	1	1	NUM
iajs-3515	164	13	+	+	CCONJ
iajs-3515	164	14	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	164	15	)	)	PUNCT
iajs-3515	164	16	∫	∫	PROPN
iajs-3515	164	17	𝐺(𝑠)𝑑𝑠	𝐺(𝑠)𝑑𝑠	PROPN
iajs-3515	164	18	𝑡	𝑡	PROPN
iajs-3515	164	19	𝑡3	𝑡3	PROPN
iajs-3515	164	20	,	,	PUNCT
iajs-3515	164	21	there	there	ADV
iajs-3515	164	22	fore	fore	ADV
iajs-3515	164	23	−𝑧(𝑡3)𝛾	−𝑧(𝑡3)𝛾	PROPN
iajs-3515	164	24	−	−	PROPN
iajs-3515	164	25	𝑎𝛾𝑧(𝑡3	𝑎𝛾𝑧(𝑡3	PROPN
iajs-3515	164	26	)	)	PUNCT
iajs-3515	165	1	+	+	CCONJ
iajs-3515	165	2	𝑛𝜆𝑏𝛾	𝑛𝜆𝑏𝛾	PROPN
iajs-3515	165	3	∫	∫	PROPN
iajs-3515	165	4	𝑄(𝑠	𝑄(𝑠	NUM
iajs-3515	165	5	)	)	PUNCT
iajs-3515	165	6	𝑡	𝑡	PROPN
iajs-3515	165	7	𝑡3	𝑡3	PROPN
iajs-3515	165	8	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	165	9	<	<	X
iajs-3515	165	10	𝑘	𝑘	X
iajs-3515	165	11	(	(	PUNCT
iajs-3515	165	12	1	1	NUM
iajs-3515	165	13	+	+	CCONJ
iajs-3515	165	14	𝑎𝛾	𝑎𝛾	PROPN
iajs-3515	165	15	)	)	PUNCT
iajs-3515	165	16	∫	∫	PROPN
iajs-3515	165	17	𝐺(𝑠)𝑑𝑠	𝐺(𝑠)𝑑𝑠	PROPN
iajs-3515	165	18	,	,	PUNCT
iajs-3515	165	19	𝑡	𝑡	PROPN
iajs-3515	165	20	𝑡3	𝑡3	PROPN
iajs-3515	165	21	(	(	PUNCT
iajs-3515	165	22	18	18	NUM
iajs-3515	165	23	)	)	PUNCT
iajs-3515	165	24	as	as	ADP
iajs-3515	165	25	𝑡	𝑡	PROPN
iajs-3515	165	26	→	→	SYM
iajs-3515	165	27	∞	∞	PROPN
iajs-3515	165	28	a	a	DET
iajs-3515	165	29	contradiction	contradiction	NOUN
iajs-3515	165	30	will	will	AUX
iajs-3515	165	31	be	be	AUX
iajs-3515	165	32	got	get	VERB
iajs-3515	165	33	in	in	ADP
iajs-3515	165	34	(	(	PUNCT
iajs-3515	165	35	18	18	NUM
iajs-3515	165	36	)	)	PUNCT
iajs-3515	165	37	.	.	PUNCT
iajs-3515	166	1	case	case	NOUN
iajs-3515	166	2	(	(	PUNCT
iajs-3515	166	3	b	b	NOUN
iajs-3515	166	4	)	)	PUNCT
iajs-3515	166	5	in	in	ADP
iajs-3515	166	6	this	this	DET
iajs-3515	166	7	case	case	NOUN
iajs-3515	166	8	𝜔(𝑡	𝜔(𝑡	ADP
iajs-3515	166	9	)	)	PUNCT
iajs-3515	166	10	>	>	X
iajs-3515	166	11	0	0	NUM
iajs-3515	166	12	,	,	PUNCT
iajs-3515	166	13	𝜔′(𝑡	𝜔′(𝑡	PUNCT
iajs-3515	166	14	)	)	PUNCT
iajs-3515	166	15	<	<	X
iajs-3515	166	16	0	0	PROPN
iajs-3515	166	17	,	,	PUNCT
iajs-3515	166	18	lim	lim	PROPN
iajs-3515	166	19	𝑡→∞	𝑡→∞	NUM
iajs-3515	166	20	𝜉(𝑡)(𝜔′(𝑡))𝛾	𝜉(𝑡)(𝜔′(𝑡))𝛾	VERB
iajs-3515	166	21	=	=	SYM
iajs-3515	166	22	0	0	NUM
iajs-3515	166	23	,	,	PUNCT
iajs-3515	166	24	(	(	PUNCT
iajs-3515	166	25	𝜉(𝑡)(𝜔′(𝑡	𝜉(𝑡)(𝜔′(𝑡	NOUN
iajs-3515	166	26	)	)	PUNCT
iajs-3515	166	27	)	)	PUNCT
iajs-3515	167	1	𝛾	𝛾	AUX
iajs-3515	167	2	)	)	PUNCT
iajs-3515	167	3	′	′	NUM
iajs-3515	167	4	≥	≥	NOUN
iajs-3515	167	5	0	0	NUM
iajs-3515	167	6	since	since	SCONJ
iajs-3515	167	7	𝜉′(𝑡	𝜉′(𝑡	PROPN
iajs-3515	167	8	)	)	PUNCT
iajs-3515	167	9	>	>	X
iajs-3515	167	10	0	0	PUNCT
iajs-3515	167	11	and	and	CCONJ
iajs-3515	167	12	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	167	13	)	)	PUNCT
iajs-3515	167	14	is	be	AUX
iajs-3515	167	15	positive	positive	ADJ
iajs-3515	167	16	decreasing	decreasing	NOUN
iajs-3515	167	17	,	,	PUNCT
iajs-3515	167	18	so	so	SCONJ
iajs-3515	167	19	it	it	PRON
iajs-3515	167	20	can	can	AUX
iajs-3515	167	21	be	be	AUX
iajs-3515	167	22	conclude	conclude	VERB
iajs-3515	167	23	that	that	SCONJ
iajs-3515	167	24	𝜔′′(𝑡	𝜔′′(𝑡	VERB
iajs-3515	167	25	)	)	PUNCT
iajs-3515	167	26	≥	≥	NOUN
iajs-3515	167	27	0	0	NUM
iajs-3515	167	28	,	,	PUNCT
iajs-3515	167	29	for	for	ADP
iajs-3515	167	30	𝑡	𝑡	PROPN
iajs-3515	167	31	≥	≥	NOUN
iajs-3515	167	32	𝑡2	𝑡2	PROPN
iajs-3515	167	33	,	,	PUNCT
iajs-3515	167	34	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	167	35	)	)	PUNCT
iajs-3515	167	36	>	>	X
iajs-3515	167	37	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	167	38	)	)	PUNCT
iajs-3515	167	39	,	,	PUNCT
iajs-3515	167	40	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	167	41	)	)	PUNCT
iajs-3515	167	42	=	=	SYM
iajs-3515	167	43	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	167	44	)	)	PUNCT
iajs-3515	167	45	−	−	NOUN
iajs-3515	167	46	𝑝(𝑡)𝑥(𝜏(𝑡	𝑝(𝑡)𝑥(𝜏(𝑡	NOUN
iajs-3515	167	47	)	)	PUNCT
iajs-3515	167	48	)	)	PUNCT
iajs-3515	167	49	,	,	PUNCT
iajs-3515	167	50	𝑥(𝛿𝑖(𝑡	𝑥(𝛿𝑖(𝑡	NUM
iajs-3515	167	51	)	)	PUNCT
iajs-3515	167	52	)	)	PUNCT
iajs-3515	168	1	=	=	SYM
iajs-3515	168	2	𝜔(𝛿𝑖(𝑡	𝜔(𝛿𝑖(𝑡	X
iajs-3515	168	3	)	)	PUNCT
iajs-3515	168	4	)	)	PUNCT
iajs-3515	169	1	−	−	ADP
iajs-3515	169	2	𝑝(𝛿𝑖(𝑡))𝑥(𝜏(𝛿𝑖(𝑡	𝑝(𝛿𝑖(𝑡))𝑥(𝜏(𝛿𝑖(𝑡	NOUN
iajs-3515	169	3	)	)	PUNCT
iajs-3515	169	4	)	)	PUNCT
iajs-3515	169	5	)	)	PUNCT
iajs-3515	170	1	so	so	ADV
iajs-3515	170	2	equation	equation	NOUN
iajs-3515	170	3	(	(	PUNCT
iajs-3515	170	4	1	1	X
iajs-3515	170	5	)	)	PUNCT
iajs-3515	170	6	become	become	VERB
iajs-3515	170	7	(	(	PUNCT
iajs-3515	170	8	𝜉(𝑡)(𝜔′(𝑡	𝜉(𝑡)(𝜔′(𝑡	NOUN
iajs-3515	170	9	)	)	PUNCT
iajs-3515	170	10	)	)	PUNCT
iajs-3515	171	1	𝛾	𝛾	X
iajs-3515	171	2	)	)	PUNCT
iajs-3515	171	3	′	′	PUNCT
iajs-3515	172	1	+	+	CCONJ
iajs-3515	172	2	∑	∑	PROPN
iajs-3515	172	3	𝑞𝑖(𝑡)[𝜔(𝛿𝑖(𝑡	𝑞𝑖(𝑡)[𝜔(𝛿𝑖(𝑡	NOUN
iajs-3515	172	4	)	)	PUNCT
iajs-3515	172	5	)	)	PUNCT
iajs-3515	173	1	−	−	NOUN
iajs-3515	174	1	𝑝(𝛿𝑖(𝑡))𝑥(𝜏(𝛿𝑖(𝑡)))]𝛾	𝑝(𝛿𝑖(𝑡))𝑥(𝜏(𝛿𝑖(𝑡)))]𝛾	NOUN
iajs-3515	174	2	𝑛	𝑛	PRON
iajs-3515	174	3	𝑖=1	𝑖=1	PUNCT
iajs-3515	174	4	=	=	SYM
iajs-3515	174	5	∑	∑	PUNCT
iajs-3515	174	6	𝑟𝑗(𝑡	𝑟𝑗(𝑡	NOUN
iajs-3515	174	7	)	)	PUNCT
iajs-3515	174	8	𝑘	𝑘	ADP
iajs-3515	174	9	𝑗=1	𝑗=1	PROPN
iajs-3515	174	10	.	.	PUNCT
iajs-3515	175	1	(	(	PUNCT
iajs-3515	175	2	19	19	NUM
iajs-3515	175	3	)	)	PUNCT
iajs-3515	175	4	by	by	ADP
iajs-3515	175	5	integrating	integrate	VERB
iajs-3515	175	6	(	(	PUNCT
iajs-3515	175	7	19	19	NUM
iajs-3515	175	8	)	)	PUNCT
iajs-3515	175	9	from	from	ADP
iajs-3515	175	10	𝑡	𝑡	PRON
iajs-3515	175	11	to	to	ADP
iajs-3515	175	12	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	175	13	)	)	PUNCT
iajs-3515	175	14	,	,	PUNCT
iajs-3515	175	15	where	where	SCONJ
iajs-3515	175	16	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	175	17	)	)	PUNCT
iajs-3515	175	18	>	>	PUNCT
iajs-3515	176	1	𝑡	𝑡	PROPN
iajs-3515	176	2	and	and	CCONJ
iajs-3515	176	3	𝜏	𝜏	PROPN
iajs-3515	176	4	(	(	PUNCT
iajs-3515	176	5	𝛿𝑗	𝛿𝑗	PROPN
iajs-3515	176	6	(	(	PUNCT
iajs-3515	176	7	𝛼(𝛼(𝑡	𝛼(𝛼(𝑡	NOUN
iajs-3515	176	8	)	)	PUNCT
iajs-3515	176	9	)	)	PUNCT
iajs-3515	176	10	)	)	PUNCT
iajs-3515	176	11	)	)	PUNCT
iajs-3515	177	1	<	<	X
iajs-3515	177	2	𝑡	𝑡	X
iajs-3515	177	3	,	,	PUNCT
iajs-3515	177	4	𝛿𝑗(𝑡	𝛿𝑗(𝑡	NOUN
iajs-3515	177	5	)	)	PUNCT
iajs-3515	177	6	=	=	SYM
iajs-3515	177	7	min{𝛿𝑖(𝑡	min{𝛿𝑖(𝑡	NOUN
iajs-3515	177	8	)	)	PUNCT
iajs-3515	177	9	,	,	PUNCT
iajs-3515	177	10	𝑖	𝑖	NOUN
iajs-3515	177	11	=	=	SYM
iajs-3515	177	12	1,2	1,2	NUM
iajs-3515	177	13	,	,	PUNCT
iajs-3515	177	14	…	…	PUNCT
iajs-3515	177	15	,	,	PUNCT
iajs-3515	177	16	𝑛	𝑛	PROPN
iajs-3515	177	17	}	}	PUNCT
iajs-3515	177	18	,	,	PUNCT
iajs-3515	177	19	we	we	PRON
iajs-3515	177	20	get	get	VERB
iajs-3515	177	21	−𝜉(𝑡)(𝜔′(𝑡	−𝜉(𝑡)(𝜔′(𝑡	NOUN
iajs-3515	177	22	)	)	PUNCT
iajs-3515	177	23	)	)	PUNCT
iajs-3515	178	1	𝛾	𝛾	AUX
iajs-3515	178	2	≥	≥	NOUN
iajs-3515	178	3	−	−	NUM
iajs-3515	178	4	∫	∫	PROPN
iajs-3515	178	5	∑	∑	PROPN
iajs-3515	178	6	𝑞𝑖(𝑠)[𝜔(𝛿𝑖(𝑡	𝑞𝑖(𝑠)[𝜔(𝛿𝑖(𝑡	NOUN
iajs-3515	178	7	)	)	PUNCT
iajs-3515	178	8	)	)	PUNCT
iajs-3515	178	9	−𝑛	−𝑛	VERB
iajs-3515	178	10	𝑖=1	𝑖=1	PUNCT
iajs-3515	178	11	𝛼(𝑡	𝛼(𝑡	NUM
iajs-3515	178	12	)	)	PUNCT
iajs-3515	178	13	𝑡	𝑡	PROPN
iajs-3515	178	14	𝑝(𝛿𝑖(𝑡))𝜔(𝜏(𝛿𝑖(𝑡)))]𝛾	𝑝(𝛿𝑖(𝑡))𝜔(𝜏(𝛿𝑖(𝑡)))]𝛾	ADP
iajs-3515	178	15	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	178	16	,	,	PUNCT
iajs-3515	178	17	ihjpas	ihjpas	PROPN
iajs-3515	178	18	.	.	PUNCT
iajs-3515	179	1	2024	2024	NUM
iajs-3515	179	2	,	,	PUNCT
iajs-3515	179	3	38	38	NUM
iajs-3515	179	4	(	(	PUNCT
iajs-3515	179	5	1	1	NUM
iajs-3515	179	6	)	)	PUNCT
iajs-3515	179	7	413	413	NUM
iajs-3515	179	8	−𝜉(𝑡)(𝜔′(𝑡	−𝜉(𝑡)(𝜔′(𝑡	NOUN
iajs-3515	179	9	)	)	PUNCT
iajs-3515	179	10	)	)	PUNCT
iajs-3515	180	1	𝛾	𝛾	ADP
iajs-3515	180	2	≥	≥	NOUN
iajs-3515	180	3	−	−	NUM
iajs-3515	180	4	∫	∫	PROPN
iajs-3515	180	5	∑	∑	PROPN
iajs-3515	180	6	𝑞𝑖(𝑠)𝜔𝛾(𝜏(𝛿𝑖(𝑡)))[1	𝑞𝑖(𝑠)𝜔𝛾(𝜏(𝛿𝑖(𝑡)))[1	PRON
iajs-3515	180	7	−	−	PROPN
iajs-3515	180	8	𝑝(𝛿𝑖(𝑡))]𝛾	𝑝(𝛿𝑖(𝑡))]𝛾	NUM
iajs-3515	180	9	𝑛	𝑛	PRON
iajs-3515	180	10	𝑖=1	𝑖=1	PROPN
iajs-3515	180	11	𝛼(𝑡	𝛼(𝑡	NUM
iajs-3515	180	12	)	)	PUNCT
iajs-3515	180	13	𝑡	𝑡	PROPN
iajs-3515	180	14	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	180	15	,	,	PUNCT
iajs-3515	180	16	𝜔′(𝑡	𝜔′(𝑡	NOUN
iajs-3515	180	17	)	)	PUNCT
iajs-3515	180	18	≤	≤	NUM
iajs-3515	180	19	𝜔	𝜔	PART
iajs-3515	180	20	(	(	PUNCT
iajs-3515	180	21	𝜏	𝜏	X
iajs-3515	180	22	(	(	PUNCT
iajs-3515	180	23	𝛿𝑗(𝛼(𝑡	𝛿𝑗(𝛼(𝑡	NOUN
iajs-3515	180	24	)	)	PUNCT
iajs-3515	180	25	)	)	PUNCT
iajs-3515	180	26	)	)	PUNCT
iajs-3515	180	27	)	)	PUNCT
iajs-3515	181	1	[	[	PUNCT
iajs-3515	181	2	1	1	NUM
iajs-3515	181	3	𝜉(𝑡	𝜉(𝑡	NUM
iajs-3515	181	4	)	)	PUNCT
iajs-3515	181	5	∫	∫	PROPN
iajs-3515	181	6	∑	∑	PROPN
iajs-3515	181	7	𝑞𝑖(𝑠)[1	𝑞𝑖(𝑠)[1	PROPN
iajs-3515	181	8	−	−	ADP
iajs-3515	181	9	𝑝(𝛿𝑖(𝑡))]𝛾	𝑝(𝛿𝑖(𝑡))]𝛾	NUM
iajs-3515	181	10	𝑛	𝑛	PRON
iajs-3515	181	11	𝑖=1	𝑖=1	PROPN
iajs-3515	181	12	𝛼(𝑡	𝛼(𝑡	NUM
iajs-3515	181	13	)	)	PUNCT
iajs-3515	181	14	𝑡	𝑡	PROPN
iajs-3515	181	15	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	181	16	]	]	X
iajs-3515	181	17	1	1	NUM
iajs-3515	181	18	𝛾	𝛾	NOUN
iajs-3515	181	19	.	.	PUNCT
iajs-3515	182	1	(	(	PUNCT
iajs-3515	182	2	20	20	NUM
iajs-3515	182	3	)	)	PUNCT
iajs-3515	182	4	where	where	SCONJ
iajs-3515	182	5	𝜏(𝛿𝑗(𝑡	𝜏(𝛿𝑗(𝑡	NOUN
iajs-3515	182	6	)	)	PUNCT
iajs-3515	182	7	)	)	PUNCT
iajs-3515	183	1	=	=	SYM
iajs-3515	183	2	min{𝜏(𝛿𝑖(𝑡	min{𝜏(𝛿𝑖(𝑡	NOUN
iajs-3515	183	3	)	)	PUNCT
iajs-3515	183	4	)	)	PUNCT
iajs-3515	183	5	,	,	PUNCT
iajs-3515	184	1	𝑖	𝑖	NOUN
iajs-3515	184	2	=	=	SYM
iajs-3515	184	3	1,2	1,2	NUM
iajs-3515	184	4	,	,	PUNCT
iajs-3515	184	5	…	…	PUNCT
iajs-3515	184	6	,	,	PUNCT
iajs-3515	184	7	𝑛	𝑛	PROPN
iajs-3515	184	8	]	]	PUNCT
iajs-3515	184	9	,	,	PUNCT
iajs-3515	184	10	integrating	integrate	VERB
iajs-3515	184	11	(	(	PUNCT
iajs-3515	184	12	20	20	NUM
iajs-3515	184	13	)	)	PUNCT
iajs-3515	184	14	from	from	ADP
iajs-3515	184	15	𝑡	𝑡	PRON
iajs-3515	184	16	to	to	ADP
iajs-3515	184	17	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	184	18	)	)	PUNCT
iajs-3515	184	19	we	we	PRON
iajs-3515	184	20	get	get	VERB
iajs-3515	184	21	𝜔(𝛼(𝑡	𝜔(𝛼(𝑡	NOUN
iajs-3515	184	22	)	)	PUNCT
iajs-3515	184	23	)	)	PUNCT
iajs-3515	185	1	−	−	PROPN
iajs-3515	185	2	𝜔(𝑡	𝜔(𝑡	PROPN
iajs-3515	185	3	)	)	PUNCT
iajs-3515	185	4	≤	≤	NUM
iajs-3515	185	5	𝜔(𝜏(𝛿𝑗(𝛼(𝛼(𝑡	𝜔(𝜏(𝛿𝑗(𝛼(𝛼(𝑡	NOUN
iajs-3515	185	6	)	)	PUNCT
iajs-3515	185	7	)	)	PUNCT
iajs-3515	185	8	)	)	PUNCT
iajs-3515	185	9	)	)	PUNCT
iajs-3515	185	10	)	)	PUNCT
iajs-3515	186	1	∫	∫	PROPN
iajs-3515	186	2	[	[	PUNCT
iajs-3515	186	3	1	1	NUM
iajs-3515	186	4	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	186	5	)	)	PUNCT
iajs-3515	186	6	∫	∫	PROPN
iajs-3515	186	7	∑	∑	X
iajs-3515	186	8	𝑞𝑖(𝑣)[1	𝑞𝑖(𝑣)[1	PROPN
iajs-3515	186	9	−	−	NUM
iajs-3515	186	10	𝑝(𝛿𝑖(𝑣))]𝛾	𝑝(𝛿𝑖(𝑣))]𝛾	NUM
iajs-3515	186	11	𝑛	𝑛	PRON
iajs-3515	186	12	𝑖=1	𝑖=1	PROPN
iajs-3515	186	13	𝛼(𝑠	𝛼(𝑠	PROPN
iajs-3515	186	14	)	)	PUNCT
iajs-3515	186	15	𝑠	𝑠	PROPN
iajs-3515	186	16	𝑑𝑣	𝑑𝑣	PROPN
iajs-3515	186	17	]	]	X
iajs-3515	186	18	1	1	NUM
iajs-3515	186	19	𝛾	𝛾	NOUN
iajs-3515	186	20	𝑑𝑠	𝑑𝑠	X
iajs-3515	186	21	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	186	22	)	)	PUNCT
iajs-3515	186	23	𝑡	𝑡	NOUN
iajs-3515	186	24	,	,	PUNCT
iajs-3515	186	25	1	1	NUM
iajs-3515	186	26	≥	≥	NOUN
iajs-3515	186	27	𝜔(𝑡	𝜔(𝑡	NOUN
iajs-3515	186	28	)	)	PUNCT
iajs-3515	186	29	𝜔	𝜔	ADP
iajs-3515	186	30	(	(	PUNCT
iajs-3515	186	31	𝜏	𝜏	X
iajs-3515	186	32	(	(	PUNCT
iajs-3515	186	33	𝛿𝑗	𝛿𝑗	PROPN
iajs-3515	186	34	(	(	PUNCT
iajs-3515	186	35	𝛼(𝛼(𝑡	𝛼(𝛼(𝑡	NOUN
iajs-3515	186	36	)	)	PUNCT
iajs-3515	186	37	)	)	PUNCT
iajs-3515	186	38	)	)	PUNCT
iajs-3515	186	39	)	)	PUNCT
iajs-3515	186	40	)	)	PUNCT
iajs-3515	187	1	≥	≥	NOUN
iajs-3515	188	1	−	−	PROPN
iajs-3515	188	2	∫	∫	PROPN
iajs-3515	188	3	[	[	PUNCT
iajs-3515	188	4	1	1	NUM
iajs-3515	188	5	𝜉(𝑠	𝜉(𝑠	PROPN
iajs-3515	188	6	)	)	PUNCT
iajs-3515	188	7	∫	∫	PROPN
iajs-3515	188	8	∑	∑	X
iajs-3515	188	9	𝑞𝑖(𝑣)[1	𝑞𝑖(𝑣)[1	PROPN
iajs-3515	188	10	−	−	NUM
iajs-3515	188	11	𝑝(𝛿𝑖(𝑣))]𝛾	𝑝(𝛿𝑖(𝑣))]𝛾	NUM
iajs-3515	188	12	𝑛	𝑛	PRON
iajs-3515	188	13	𝑖=1	𝑖=1	PROPN
iajs-3515	188	14	𝛼(𝑠	𝛼(𝑠	PROPN
iajs-3515	188	15	)	)	PUNCT
iajs-3515	188	16	𝑠	𝑠	PROPN
iajs-3515	188	17	𝑑𝑣	𝑑𝑣	PROPN
iajs-3515	188	18	]	]	X
iajs-3515	188	19	1	1	NUM
iajs-3515	188	20	𝛾	𝛾	NOUN
iajs-3515	188	21	𝑑𝑠	𝑑𝑠	X
iajs-3515	188	22	𝛼(𝑡	𝛼(𝑡	NOUN
iajs-3515	188	23	)	)	PUNCT
iajs-3515	188	24	𝑡	𝑡	PROPN
iajs-3515	188	25	.	.	PUNCT
iajs-3515	189	1	the	the	DET
iajs-3515	189	2	last	last	ADJ
iajs-3515	189	3	inequality	inequality	NOUN
iajs-3515	189	4	contradicts	contradict	VERB
iajs-3515	189	5	the	the	DET
iajs-3515	189	6	condition	condition	NOUN
iajs-3515	189	7	(	(	PUNCT
iajs-3515	189	8	14	14	NUM
iajs-3515	189	9	)	)	PUNCT
iajs-3515	189	10	,	,	PUNCT
iajs-3515	189	11	thus	thus	ADV
iajs-3515	189	12	case	case	NOUN
iajs-3515	189	13	not	not	PART
iajs-3515	189	14	valid	valid	ADJ
iajs-3515	189	15	also	also	ADV
iajs-3515	189	16	,	,	PUNCT
iajs-3515	189	17	hence	hence	ADV
iajs-3515	189	18	every	every	DET
iajs-3515	189	19	solution	solution	NOUN
iajs-3515	189	20	of	of	ADP
iajs-3515	189	21	equation	equation	NOUN
iajs-3515	189	22	(	(	PUNCT
iajs-3515	189	23	1	1	X
iajs-3515	189	24	)	)	PUNCT
iajs-3515	189	25	oscillates	oscillate	NOUN
iajs-3515	189	26	.	.	PUNCT
iajs-3515	190	1	the	the	DET
iajs-3515	190	2	proof	proof	NOUN
iajs-3515	190	3	is	be	AUX
iajs-3515	190	4	complete	complete	ADJ
iajs-3515	190	5	.	.	PUNCT
iajs-3515	191	1	3	3	X
iajs-3515	191	2	.	.	X
iajs-3515	191	3	examples	example	NOUN
iajs-3515	191	4	in	in	ADP
iajs-3515	191	5	this	this	DET
iajs-3515	191	6	section	section	NOUN
iajs-3515	191	7	,	,	PUNCT
iajs-3515	191	8	two	two	NUM
iajs-3515	191	9	examples	example	NOUN
iajs-3515	191	10	are	be	AUX
iajs-3515	191	11	given	give	VERB
iajs-3515	191	12	to	to	PART
iajs-3515	191	13	illustrate	illustrate	VERB
iajs-3515	191	14	the	the	DET
iajs-3515	191	15	fulfillment	fulfillment	NOUN
iajs-3515	191	16	of	of	ADP
iajs-3515	191	17	all	all	PRON
iajs-3515	191	18	necessary	necessary	ADJ
iajs-3515	191	19	and	and	CCONJ
iajs-3515	191	20	sufficient	sufficient	ADJ
iajs-3515	191	21	conditions	condition	NOUN
iajs-3515	191	22	for	for	ADP
iajs-3515	191	23	the	the	DET
iajs-3515	191	24	results	result	NOUN
iajs-3515	191	25	presented	present	VERB
iajs-3515	191	26	in	in	ADP
iajs-3515	191	27	the	the	DET
iajs-3515	191	28	previous	previous	ADJ
iajs-3515	191	29	section	section	NOUN
iajs-3515	191	30	.	.	PUNCT
iajs-3515	192	1	example	example	NOUN
iajs-3515	192	2	3.1	3.1	NUM
iajs-3515	192	3	.	.	PUNCT
iajs-3515	193	1	consider	consider	VERB
iajs-3515	193	2	the	the	DET
iajs-3515	193	3	following	follow	VERB
iajs-3515	193	4	emden	emden	ADJ
iajs-3515	193	5	-	-	PUNCT
iajs-3515	193	6	fowler	fowler	NOUN
iajs-3515	193	7	equation	equation	NOUN
iajs-3515	193	8	:	:	PUNCT
iajs-3515	194	1	[	[	X
iajs-3515	194	2	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	194	3	)	)	PUNCT
iajs-3515	194	4	+	+	CCONJ
iajs-3515	194	5	1	1	NUM
iajs-3515	194	6	2	2	NUM
iajs-3515	194	7	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	194	8	−	−	PROPN
iajs-3515	194	9	𝜋	𝜋	NOUN
iajs-3515	194	10	)	)	PUNCT
iajs-3515	194	11	]	]	PUNCT
iajs-3515	195	1	′′	′′	PROPN
iajs-3515	195	2	=	=	PUNCT
iajs-3515	195	3	−	−	PROPN
iajs-3515	195	4	1	1	NUM
iajs-3515	195	5	2	2	NUM
iajs-3515	195	6	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	195	7	−	−	PROPN
iajs-3515	195	8	2𝜋	2𝜋	NUM
iajs-3515	195	9	)	)	PUNCT
iajs-3515	195	10	−	−	NOUN
iajs-3515	195	11	1	1	NUM
iajs-3515	195	12	4	4	NUM
iajs-3515	195	13	,	,	PUNCT
iajs-3515	195	14	𝑡	𝑡	X
iajs-3515	195	15	≥	≥	NOUN
iajs-3515	195	16	0	0	NUM
iajs-3515	195	17	.	.	PUNCT
iajs-3515	195	18	(	(	PUNCT
iajs-3515	195	19	21	21	NUM
iajs-3515	195	20	)	)	PUNCT
iajs-3515	195	21	where	where	SCONJ
iajs-3515	195	22	𝜉(𝑡	𝜉(𝑡	VERB
iajs-3515	195	23	)	)	PUNCT
iajs-3515	195	24	=	=	SYM
iajs-3515	195	25	1	1	NUM
iajs-3515	195	26	,	,	PUNCT
iajs-3515	195	27	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3515	195	28	)	)	PUNCT
iajs-3515	195	29	=	=	SYM
iajs-3515	195	30	1	1	NUM
iajs-3515	195	31	2	2	NUM
iajs-3515	195	32	,	,	PUNCT
iajs-3515	195	33	𝜏(𝑡	𝜏(𝑡	NOUN
iajs-3515	195	34	)	)	PUNCT
iajs-3515	195	35	=	=	PUNCT
iajs-3515	196	1	𝑡	𝑡	PROPN
iajs-3515	196	2	−	−	PROPN
iajs-3515	196	3	𝜋	𝜋	NOUN
iajs-3515	196	4	,	,	PUNCT
iajs-3515	196	5	𝑞1(𝑡	𝑞1(𝑡	SYM
iajs-3515	196	6	)	)	PUNCT
iajs-3515	196	7	=	=	PUNCT
iajs-3515	196	8	𝑄(𝑡	𝑄(𝑡	PRON
iajs-3515	196	9	)	)	PUNCT
iajs-3515	196	10	=	=	SYM
iajs-3515	196	11	1	1	NUM
iajs-3515	196	12	2	2	NUM
iajs-3515	196	13	,	,	PUNCT
iajs-3515	196	14	𝑟1(𝑡	𝑟1(𝑡	X
iajs-3515	196	15	)	)	PUNCT
iajs-3515	196	16	=	=	SYM
iajs-3515	197	1	−	−	PROPN
iajs-3515	197	2	1	1	NUM
iajs-3515	197	3	2	2	NUM
iajs-3515	197	4	,	,	PUNCT
iajs-3515	197	5	and	and	CCONJ
iajs-3515	197	6	𝛿(𝑡	𝛿(𝑡	PROPN
iajs-3515	197	7	)	)	PUNCT
iajs-3515	198	1	=	=	SYM
iajs-3515	198	2	𝑡	𝑡	PROPN
iajs-3515	198	3	−	−	NOUN
iajs-3515	198	4	2𝜋	2𝜋	NUM
iajs-3515	198	5	,	,	PUNCT
iajs-3515	198	6	𝑖	𝑖	NOUN
iajs-3515	198	7	=	=	SYM
iajs-3515	198	8	1,2	1,2	NUM
iajs-3515	198	9	,	,	PUNCT
iajs-3515	198	10	…	…	PUNCT
iajs-3515	198	11	,	,	PUNCT
iajs-3515	198	12	𝑛	𝑛	PROPN
iajs-3515	198	13	,	,	PUNCT
iajs-3515	198	14	𝛾	𝛾	NOUN
iajs-3515	198	15	=	=	SYM
iajs-3515	198	16	1	1	X
iajs-3515	198	17	.	.	PUNCT
iajs-3515	199	1	in	in	ADP
iajs-3515	199	2	reality	reality	NOUN
iajs-3515	199	3	m1	m1	NOUN
iajs-3515	199	4	−	−	PROPN
iajs-3515	199	5	m3	m3	PROPN
iajs-3515	199	6	are	be	AUX
iajs-3515	199	7	hold	hold	NOUN
iajs-3515	199	8	for	for	ADP
iajs-3515	199	9	every	every	DET
iajs-3515	199	10	𝑡	𝑡	PROPN
iajs-3515	199	11	≥	≥	NOUN
iajs-3515	199	12	𝑡0	𝑡0	NOUN
iajs-3515	199	13	=	=	SYM
iajs-3515	199	14	0	0	PROPN
iajs-3515	199	15	.	.	PUNCT
iajs-3515	200	1	and	and	CCONJ
iajs-3515	200	2	∫	∫	PROPN
iajs-3515	200	3	𝑄(𝑠)𝑑𝑠	𝑄(𝑠)𝑑𝑠	PROPN
iajs-3515	200	4	∞	∞	NUM
iajs-3515	200	5	𝑡0	𝑡0	PROPN
iajs-3515	200	6	=	=	SYM
iajs-3515	201	1	∫	∫	PROPN
iajs-3515	201	2	𝑑𝑠	𝑑𝑠	NOUN
iajs-3515	201	3	∞	∞	PROPN
iajs-3515	201	4	0	0	NUM
iajs-3515	202	1	=	=	SYM
iajs-3515	202	2	∞.	∞.	PROPN
iajs-3515	202	3	then	then	ADV
iajs-3515	202	4	(	(	PUNCT
iajs-3515	202	5	m4	m4	PROPN
iajs-3515	202	6	)	)	PUNCT
iajs-3515	202	7	is	be	AUX
iajs-3515	202	8	holds	hold	NOUN
iajs-3515	202	9	for	for	ADP
iajs-3515	202	10	every	every	DET
iajs-3515	202	11	𝑡	𝑡	NOUN
iajs-3515	202	12	≥	≥	NOUN
iajs-3515	202	13	1	1	NUM
iajs-3515	202	14	2	2	NUM
iajs-3515	202	15	.	.	PUNCT
iajs-3515	203	1	recall	recall	VERB
iajs-3515	203	2	that	that	PRON
iajs-3515	203	3	(	(	PUNCT
iajs-3515	203	4	8)	8)	NUM
iajs-3515	203	5	hold	hold	VERB
iajs-3515	203	6	for	for	ADP
iajs-3515	203	7	λ	λ	NOUN
iajs-3515	203	8	=	=	NOUN
iajs-3515	203	9	1	1	NUM
iajs-3515	203	10	.	.	PUNCT
iajs-3515	204	1	hence	hence	ADV
iajs-3515	204	2	all	all	DET
iajs-3515	204	3	the	the	DET
iajs-3515	204	4	conditions	condition	NOUN
iajs-3515	204	5	of	of	ADP
iajs-3515	204	6	theorem	theorem	ADJ
iajs-3515	204	7	2.1	2.1	NUM
iajs-3515	204	8	satisfy	satisfy	NOUN
iajs-3515	204	9	that	that	SCONJ
iajs-3515	204	10	according	accord	VERB
iajs-3515	204	11	to	to	ADP
iajs-3515	204	12	theorem	theorem	ADJ
iajs-3515	204	13	2.1	2.1	NUM
iajs-3515	204	14	,	,	PUNCT
iajs-3515	204	15	each	each	DET
iajs-3515	204	16	solution	solution	NOUN
iajs-3515	204	17	of	of	ADP
iajs-3515	204	18	equation	equation	NOUN
iajs-3515	204	19	(	(	PUNCT
iajs-3515	204	20	1	1	X
iajs-3515	204	21	)	)	PUNCT
iajs-3515	204	22	oscillates	oscillate	NOUN
iajs-3515	204	23	for	for	ADP
iajs-3515	204	24	example	example	NOUN
iajs-3515	204	25	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	204	26	)	)	PUNCT
iajs-3515	204	27	=	=	PUNCT
iajs-3515	204	28	sin	sin	NOUN
iajs-3515	204	29	𝑡	𝑡	NOUN
iajs-3515	204	30	−	−	NOUN
iajs-3515	204	31	1	1	NUM
iajs-3515	204	32	2	2	NUM
iajs-3515	204	33	such	such	ADJ
iajs-3515	204	34	as	as	ADP
iajs-3515	204	35	this	this	DET
iajs-3515	204	36	oscillation	oscillation	NOUN
iajs-3515	204	37	solution	solution	NOUN
iajs-3515	204	38	.	.	PUNCT
iajs-3515	205	1	see	see	VERB
iajs-3515	205	2	figure	figure	NOUN
iajs-3515	205	3	(	(	PUNCT
iajs-3515	205	4	1	1	NUM
iajs-3515	205	5	)	)	PUNCT
iajs-3515	205	6	figure	figure	NOUN
iajs-3515	205	7	1	1	NUM
iajs-3515	205	8	.	.	PUNCT
iajs-3515	205	9	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	205	10	)	)	PUNCT
iajs-3515	205	11	=	=	PUNCT
iajs-3515	205	12	sin	sin	NOUN
iajs-3515	206	1	𝑡	𝑡	NOUN
iajs-3515	206	2	−	−	NUM
iajs-3515	206	3	1	1	NUM
iajs-3515	206	4	2	2	NUM
iajs-3515	206	5	ihjpas	ihjpa	NOUN
iajs-3515	206	6	.	.	PUNCT
iajs-3515	207	1	2024	2024	NUM
iajs-3515	207	2	,	,	PUNCT
iajs-3515	207	3	38	38	NUM
iajs-3515	207	4	(	(	PUNCT
iajs-3515	207	5	1	1	NUM
iajs-3515	207	6	)	)	PUNCT
iajs-3515	207	7	414	414	NUM
iajs-3515	207	8	example	example	NOUN
iajs-3515	207	9	3	3	NUM
iajs-3515	207	10	.	.	NOUN
iajs-3515	207	11	2	2	NUM
iajs-3515	207	12	.	.	X
iajs-3515	207	13	consider	consider	VERB
iajs-3515	207	14	the	the	DET
iajs-3515	207	15	following	follow	VERB
iajs-3515	207	16	emden	emden	ADJ
iajs-3515	207	17	-	-	PUNCT
iajs-3515	207	18	fowler	fowler	NOUN
iajs-3515	207	19	equation	equation	NOUN
iajs-3515	207	20	:	:	PUNCT
iajs-3515	208	1	[	[	X
iajs-3515	208	2	𝑥(𝑡	𝑥(𝑡	NOUN
iajs-3515	208	3	)	)	PUNCT
iajs-3515	208	4	+	+	NUM
iajs-3515	208	5	2𝑒−𝜋𝑥(𝑡	2𝑒−𝜋𝑥(𝑡	NUM
iajs-3515	208	6	−	−	NOUN
iajs-3515	208	7	𝜋	𝜋	NOUN
iajs-3515	208	8	)	)	PUNCT
iajs-3515	208	9	]	]	PUNCT
iajs-3515	209	1	′′	′′	PROPN
iajs-3515	209	2	−	−	PROPN
iajs-3515	209	3	4𝑒−	4𝑒−	PROPN
iajs-3515	209	4	3𝜋	3𝜋	NUM
iajs-3515	209	5	2	2	NUM
iajs-3515	209	6	𝑥	𝑥	NOUN
iajs-3515	209	7	(	(	PUNCT
iajs-3515	209	8	𝑡	𝑡	X
iajs-3515	209	9	−	−	NOUN
iajs-3515	209	10	3𝜋	3𝜋	NUM
iajs-3515	209	11	2	2	NUM
iajs-3515	209	12	)	)	PUNCT
iajs-3515	209	13	=	=	SYM
iajs-3515	209	14	𝑒−𝑡	𝑒−𝑡	PROPN
iajs-3515	209	15	,	,	PUNCT
iajs-3515	209	16	𝑡	𝑡	X
iajs-3515	209	17	≥	≥	NOUN
iajs-3515	209	18	0	0	NUM
iajs-3515	209	19	.	.	PUNCT
iajs-3515	210	1	(	(	PUNCT
iajs-3515	210	2	22	22	NUM
iajs-3515	210	3	)	)	PUNCT
iajs-3515	210	4	where	where	SCONJ
iajs-3515	210	5	𝜉(𝑡	𝜉(𝑡	VERB
iajs-3515	210	6	)	)	PUNCT
iajs-3515	210	7	=	=	SYM
iajs-3515	210	8	1	1	NUM
iajs-3515	210	9	,	,	PUNCT
iajs-3515	210	10	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3515	210	11	)	)	PUNCT
iajs-3515	210	12	=	=	SYM
iajs-3515	210	13	2𝑒−𝜋	2𝑒−𝜋	NUM
iajs-3515	210	14	,	,	PUNCT
iajs-3515	210	15	𝜏(𝑡	𝜏(𝑡	PROPN
iajs-3515	210	16	)	)	PUNCT
iajs-3515	210	17	=	=	PUNCT
iajs-3515	211	1	𝑡	𝑡	PROPN
iajs-3515	211	2	−	−	NOUN
iajs-3515	211	3	𝜋	𝜋	NOUN
iajs-3515	211	4	,	,	PUNCT
iajs-3515	211	5	𝑟(𝑡	𝑟(𝑡	PROPN
iajs-3515	211	6	)	)	PUNCT
iajs-3515	211	7	=	=	SYM
iajs-3515	212	1	𝑒−𝑡	𝑒−𝑡	NOUN
iajs-3515	212	2	,	,	PUNCT
iajs-3515	212	3	𝑞1(𝑡	𝑞1(𝑡	NUM
iajs-3515	212	4	)	)	PUNCT
iajs-3515	212	5	=	=	PUNCT
iajs-3515	212	6	𝑄(𝑡	𝑄(𝑡	NOUN
iajs-3515	212	7	)	)	PUNCT
iajs-3515	212	8	=	=	SYM
iajs-3515	212	9	−4𝑒−	−4𝑒−	NOUN
iajs-3515	212	10	3𝜋	3𝜋	NUM
iajs-3515	212	11	2	2	NUM
iajs-3515	212	12	,	,	PUNCT
iajs-3515	212	13	and	and	CCONJ
iajs-3515	212	14	𝛿(𝑡	𝛿(𝑡	PROPN
iajs-3515	212	15	)	)	PUNCT
iajs-3515	212	16	=	=	SYM
iajs-3515	213	1	𝑡	𝑡	PROPN
iajs-3515	213	2	−	−	NOUN
iajs-3515	213	3	3𝜋	3𝜋	NUM
iajs-3515	213	4	2	2	NUM
iajs-3515	213	5	,	,	PUNCT
iajs-3515	213	6	𝛾	𝛾	NOUN
iajs-3515	213	7	=	=	SYM
iajs-3515	213	8	1	1	X
iajs-3515	213	9	.	.	PUNCT
iajs-3515	214	1	in	in	ADP
iajs-3515	214	2	reality	reality	NOUN
iajs-3515	214	3	m1	m1	NOUN
iajs-3515	214	4	−	−	PROPN
iajs-3515	214	5	m3	m3	PROPN
iajs-3515	214	6	are	be	AUX
iajs-3515	214	7	hold	hold	NOUN
iajs-3515	214	8	for	for	ADP
iajs-3515	214	9	every	every	DET
iajs-3515	214	10	𝑡	𝑡	PROPN
iajs-3515	214	11	≥	≥	NOUN
iajs-3515	214	12	𝑡0	𝑡0	NOUN
iajs-3515	214	13	=	=	SYM
iajs-3515	214	14	0	0	PROPN
iajs-3515	214	15	.	.	PUNCT
iajs-3515	215	1	and	and	CCONJ
iajs-3515	215	2	∫	∫	PROPN
iajs-3515	215	3	|𝑄(𝑠)|𝑑𝑠	|𝑄(𝑠)|𝑑𝑠	PROPN
iajs-3515	216	1	∞	∞	PROPN
iajs-3515	216	2	𝑡0	𝑡0	PROPN
iajs-3515	216	3	=	=	SYM
iajs-3515	217	1	∫	∫	PROPN
iajs-3515	218	1	4𝑒−	4𝑒−	PROPN
iajs-3515	218	2	3𝜋	3𝜋	NUM
iajs-3515	218	3	2	2	NUM
iajs-3515	218	4	𝑑𝑠	𝑑𝑠	ADP
iajs-3515	218	5	∞	∞	PROPN
iajs-3515	218	6	0	0	NUM
iajs-3515	219	1	=	=	SYM
iajs-3515	219	2	∞.	∞.	PROPN
iajs-3515	219	3	then	then	ADV
iajs-3515	219	4	(	(	PUNCT
iajs-3515	219	5	m4	m4	PROPN
iajs-3515	219	6	)	)	PUNCT
iajs-3515	219	7	is	be	AUX
iajs-3515	219	8	holds	hold	NOUN
iajs-3515	219	9	for	for	ADP
iajs-3515	219	10	every	every	DET
iajs-3515	219	11	𝑡	𝑡	PROPN
iajs-3515	219	12	≥	≥	NOUN
iajs-3515	219	13	0	0	NUM
iajs-3515	219	14	.	.	PUNCT
iajs-3515	220	1	recall	recall	VERB
iajs-3515	220	2	that	that	PRON
iajs-3515	220	3	(	(	PUNCT
iajs-3515	220	4	8)	8)	NUM
iajs-3515	220	5	hold	hold	VERB
iajs-3515	220	6	for	for	ADP
iajs-3515	220	7	λ	λ	NOUN
iajs-3515	220	8	=	=	NOUN
iajs-3515	220	9	1	1	NUM
iajs-3515	220	10	.	.	PUNCT
iajs-3515	221	1	hence	hence	ADV
iajs-3515	221	2	all	all	DET
iajs-3515	221	3	the	the	DET
iajs-3515	221	4	conditions	condition	NOUN
iajs-3515	221	5	of	of	ADP
iajs-3515	221	6	theorem	theorem	ADJ
iajs-3515	221	7	2.2	2.2	NUM
iajs-3515	221	8	satisfy	satisfy	NOUN
iajs-3515	221	9	that	that	SCONJ
iajs-3515	221	10	according	accord	VERB
iajs-3515	221	11	to	to	ADP
iajs-3515	221	12	theorem	theorem	ADJ
iajs-3515	221	13	2.2	2.2	NUM
iajs-3515	221	14	,	,	PUNCT
iajs-3515	221	15	each	each	DET
iajs-3515	221	16	solution	solution	NOUN
iajs-3515	221	17	of	of	ADP
iajs-3515	221	18	equation	equation	NOUN
iajs-3515	221	19	(	(	PUNCT
iajs-3515	221	20	1	1	X
iajs-3515	221	21	)	)	PUNCT
iajs-3515	221	22	oscillates	oscillate	NOUN
iajs-3515	221	23	,	,	PUNCT
iajs-3515	221	24	for	for	ADP
iajs-3515	221	25	example	example	NOUN
iajs-3515	221	26	𝑥(𝑡	𝑥(𝑡	PROPN
iajs-3515	221	27	)	)	PUNCT
iajs-3515	221	28	=	=	SYM
iajs-3515	221	29	𝑒−𝑡(sin	𝑒−𝑡(sin	PROPN
iajs-3515	221	30	𝑡	𝑡	PROPN
iajs-3515	221	31	−	−	PROPN
iajs-3515	221	32	1	1	NUM
iajs-3515	221	33	)	)	PUNCT
iajs-3515	221	34	is	be	AUX
iajs-3515	221	35	such	such	DET
iajs-3515	221	36	an	an	DET
iajs-3515	221	37	oscillatory	oscillatory	ADJ
iajs-3515	221	38	solution	solution	NOUN
iajs-3515	221	39	.	.	PUNCT
iajs-3515	222	1	see	see	VERB
iajs-3515	222	2	figure	figure	NOUN
iajs-3515	222	3	(	(	PUNCT
iajs-3515	222	4	2	2	NUM
iajs-3515	222	5	)	)	PUNCT
iajs-3515	222	6	figure	figure	NOUN
iajs-3515	222	7	𝟐.	𝟐.	PUNCT
iajs-3515	222	8	𝜑(𝑡	𝜑(𝑡	X
iajs-3515	222	9	)	)	PUNCT
iajs-3515	222	10	=	=	PUNCT
iajs-3515	222	11	𝑒−𝑡(sin	𝑒−𝑡(sin	PROPN
iajs-3515	223	1	𝑡	𝑡	PROPN
iajs-3515	223	2	−	−	PROPN
iajs-3515	223	3	1	1	NUM
iajs-3515	223	4	)	)	PUNCT
iajs-3515	223	5	4	4	NUM
iajs-3515	223	6	.	.	PUNCT
iajs-3515	223	7	conclusion	conclusion	NOUN
iajs-3515	223	8	in	in	ADP
iajs-3515	223	9	this	this	DET
iajs-3515	223	10	paper	paper	NOUN
iajs-3515	223	11	,	,	PUNCT
iajs-3515	223	12	we	we	PRON
iajs-3515	223	13	have	have	AUX
iajs-3515	223	14	studied	study	VERB
iajs-3515	223	15	the	the	DET
iajs-3515	223	16	oscillation	oscillation	NOUN
iajs-3515	223	17	property	property	NOUN
iajs-3515	223	18	of	of	ADP
iajs-3515	223	19	the	the	DET
iajs-3515	223	20	solutions	solution	NOUN
iajs-3515	223	21	of	of	ADP
iajs-3515	223	22	neutral	neutral	ADJ
iajs-3515	223	23	second	second	ADJ
iajs-3515	223	24	-	-	PUNCT
iajs-3515	223	25	order	order	NOUN
iajs-3515	223	26	differential	differential	ADJ
iajs-3515	223	27	equations	equation	NOUN
iajs-3515	223	28	of	of	ADP
iajs-3515	223	29	the	the	DET
iajs-3515	223	30	emden	emden	ADJ
iajs-3515	223	31	-	-	PUNCT
iajs-3515	223	32	fowler	fowler	PROPN
iajs-3515	223	33	type	type	NOUN
iajs-3515	223	34	.	.	PUNCT
iajs-3515	224	1	some	some	PRON
iajs-3515	224	2	of	of	ADP
iajs-3515	224	3	the	the	DET
iajs-3515	224	4	extracted	extract	VERB
iajs-3515	224	5	conditions	condition	NOUN
iajs-3515	224	6	are	be	AUX
iajs-3515	224	7	the	the	DET
iajs-3515	224	8	development	development	NOUN
iajs-3515	224	9	of	of	ADP
iajs-3515	224	10	conditions	condition	NOUN
iajs-3515	224	11	known	know	VERB
iajs-3515	224	12	in	in	ADP
iajs-3515	224	13	the	the	DET
iajs-3515	224	14	references	reference	NOUN
iajs-3515	224	15	,	,	PUNCT
iajs-3515	224	16	which	which	PRON
iajs-3515	224	17	ensure	ensure	VERB
iajs-3515	224	18	that	that	SCONJ
iajs-3515	224	19	either	either	CCONJ
iajs-3515	224	20	each	each	DET
iajs-3515	224	21	solution	solution	NOUN
iajs-3515	224	22	of	of	ADP
iajs-3515	224	23	this	this	DET
iajs-3515	224	24	equation	equation	NOUN
iajs-3515	224	25	oscillates	oscillate	NOUN
iajs-3515	224	26	,	,	PUNCT
iajs-3515	224	27	or	or	CCONJ
iajs-3515	224	28	each	each	DET
iajs-3515	224	29	nonoscillatory	nonoscillatory	ADJ
iajs-3515	224	30	solution	solution	NOUN
iajs-3515	224	31	convergence	convergence	NOUN
iajs-3515	224	32	to	to	ADP
iajs-3515	224	33	zero	zero	NUM
iajs-3515	224	34	or	or	CCONJ
iajs-3515	224	35	tends	tend	VERB
iajs-3515	224	36	to	to	PART
iajs-3515	224	37	infinity	infinity	VERB
iajs-3515	224	38	as	as	ADP
iajs-3515	224	39	𝑡	𝑡	PROPN
iajs-3515	224	40	→	→	SYM
iajs-3515	224	41	∞.	∞.	PROPN
iajs-3515	224	42	some	some	DET
iajs-3515	224	43	examples	example	NOUN
iajs-3515	224	44	are	be	AUX
iajs-3515	224	45	presented	present	VERB
iajs-3515	224	46	to	to	PART
iajs-3515	224	47	clarify	clarify	VERB
iajs-3515	224	48	the	the	DET
iajs-3515	224	49	results	result	NOUN
iajs-3515	224	50	obtained	obtain	VERB
iajs-3515	224	51	.	.	PUNCT
iajs-3515	225	1	acknowledgments	acknowledgment	NOUN
iajs-3515	225	2	i	i	PRON
iajs-3515	225	3	would	would	AUX
iajs-3515	225	4	like	like	VERB
iajs-3515	225	5	to	to	PART
iajs-3515	225	6	extend	extend	VERB
iajs-3515	225	7	my	my	PRON
iajs-3515	225	8	thinks	think	NOUN
iajs-3515	225	9	to	to	ADP
iajs-3515	225	10	my	my	PRON
iajs-3515	225	11	teacher	teacher	NOUN
iajs-3515	225	12	and	and	CCONJ
iajs-3515	225	13	supervisor	supervisor	NOUN
iajs-3515	225	14	,	,	PUNCT
iajs-3515	225	15	dr	dr	PROPN
iajs-3515	225	16	.	.	PROPN
iajs-3515	225	17	hussain	hussain	PROPN
iajs-3515	225	18	ali	ali	PROPN
iajs-3515	225	19	mohamad	mohamad	PROPN
iajs-3515	225	20	,	,	PUNCT
iajs-3515	225	21	for	for	ADP
iajs-3515	225	22	providing	provide	VERB
iajs-3515	225	23	guidance	guidance	NOUN
iajs-3515	225	24	and	and	CCONJ
iajs-3515	225	25	feedback	feedback	VERB
iajs-3515	225	26	throughout	throughout	ADP
iajs-3515	225	27	this	this	DET
iajs-3515	225	28	project	project	NOUN
iajs-3515	225	29	.	.	PUNCT
iajs-3515	226	1	conflict	conflict	NOUN
iajs-3515	226	2	of	of	ADP
iajs-3515	226	3	interest	interest	NOUN
iajs-3515	226	4	the	the	DET
iajs-3515	226	5	authors	author	NOUN
iajs-3515	226	6	declare	declare	VERB
iajs-3515	226	7	that	that	SCONJ
iajs-3515	226	8	there	there	PRON
iajs-3515	226	9	are	be	VERB
iajs-3515	226	10	no	no	DET
iajs-3515	226	11	competing	compete	VERB
iajs-3515	226	12	interests	interest	NOUN
iajs-3515	226	13	regarding	regard	VERB
iajs-3515	226	14	the	the	DET
iajs-3515	226	15	publication	publication	NOUN
iajs-3515	226	16	of	of	ADP
iajs-3515	226	17	this	this	DET
iajs-3515	226	18	paper	paper	NOUN
iajs-3515	226	19	.	.	PUNCT
iajs-3515	227	1	funding	fund	VERB
iajs-3515	227	2	this	this	DET
iajs-3515	227	3	work	work	NOUN
iajs-3515	227	4	is	be	AUX
iajs-3515	227	5	not	not	PART
iajs-3515	227	6	supported	support	VERB
iajs-3515	227	7	by	by	ADP
iajs-3515	227	8	any	any	DET
iajs-3515	227	9	the	the	DET
iajs-3515	227	10	foundation	foundation	NOUN
iajs-3515	227	11	.	.	PUNCT
iajs-3515	228	1	ethical	ethical	ADJ
iajs-3515	228	2	clearance	clearance	NOUN
iajs-3515	228	3	ethics	ethic	NOUN
iajs-3515	228	4	of	of	ADP
iajs-3515	228	5	scientific	scientific	ADJ
iajs-3515	228	6	research	research	NOUN
iajs-3515	228	7	were	be	AUX
iajs-3515	228	8	carried	carry	VERB
iajs-3515	228	9	out	out	ADP
iajs-3515	228	10	in	in	ADP
iajs-3515	228	11	accordance	accordance	NOUN
iajs-3515	228	12	with	with	ADP
iajs-3515	228	13	international	international	ADJ
iajs-3515	228	14	conditions	condition	NOUN
iajs-3515	228	15	.	.	PUNCT
iajs-3515	229	1	ihjpas	ihjpas	PROPN
iajs-3515	229	2	.	.	PUNCT
iajs-3515	230	1	2024	2024	NUM
iajs-3515	230	2	,	,	PUNCT
iajs-3515	230	3	38	38	NUM
iajs-3515	230	4	(	(	PUNCT
iajs-3515	230	5	1	1	NUM
iajs-3515	230	6	)	)	PUNCT
iajs-3515	230	7	415	415	NUM
iajs-3515	230	8	references	reference	NOUN
iajs-3515	230	9	1	1	NUM
iajs-3515	230	10	.	.	PUNCT
iajs-3515	231	1	ahmed	ahmed	PROPN
iajs-3515	231	2	f	f	PROPN
iajs-3515	231	3	a	a	PROPN
iajs-3515	231	4	,	,	PUNCT
iajs-3515	231	5	mohamad	mohamad	PROPN
iajs-3515	231	6	h	h	PROPN
iajs-3515	231	7	a.	a.	NOUN
iajs-3515	231	8	oscillation	oscillation	NOUN
iajs-3515	231	9	and	and	CCONJ
iajs-3515	231	10	asymptotic	asymptotic	ADJ
iajs-3515	231	11	behavior	behavior	NOUN
iajs-3515	231	12	of	of	ADP
iajs-3515	231	13	second	second	ADJ
iajs-3515	231	14	order	order	NOUN
iajs-3515	231	15	half	half	NOUN
iajs-3515	231	16	linear	linear	ADJ
iajs-3515	231	17	neutral	neutral	ADJ
iajs-3515	231	18	dynamic	dynamic	ADJ
iajs-3515	231	19	equations	equation	NOUN
iajs-3515	231	20	.	.	PUNCT
iajs-3515	232	1	iraqi	iraqi	ADJ
iajs-3515	232	2	journal	journal	PROPN
iajs-3515	232	3	of	of	ADP
iajs-3515	232	4	science	science	NOUN
iajs-3515	232	5	.	.	PUNCT
iajs-3515	233	1	2022	2022	NUM
iajs-3515	233	2	;	;	PUNCT
iajs-3515	233	3	63(12):5413	63(12):5413	X
iajs-3515	233	4	-	-	PUNCT
iajs-3515	233	5	542	542	NUM
iajs-3515	233	6	.	.	PUNCT
iajs-3515	234	1	https://doi.org/10.24996/ijs.2022.63.12.27	https://doi.org/10.24996/ijs.2022.63.12.27	X
iajs-3515	234	2	2	2	X
iajs-3515	234	3	.	.	PUNCT
iajs-3515	234	4	wu	wu	PROPN
iajs-3515	234	5	y	y	PROPN
iajs-3515	234	6	,	,	PUNCT
iajs-3515	234	7	yu	yu	PROPN
iajs-3515	234	8	y	y	PROPN
iajs-3515	234	9	,	,	PUNCT
iajs-3515	234	10	zhang	zhang	PROPN
iajs-3515	234	11	j	j	PROPN
iajs-3515	234	12	,	,	PUNCT
iajs-3515	234	13	xiao	xiao	PROPN
iajs-3515	234	14	j.	j.	PROPN
iajs-3515	234	15	oscillation	oscillation	PROPN
iajs-3515	234	16	criteria	criterion	NOUN
iajs-3515	234	17	for	for	ADP
iajs-3515	234	18	second	second	ADJ
iajs-3515	234	19	order	order	NOUN
iajs-3515	234	20	emden	emden	ADJ
iajs-3515	234	21	-	-	PUNCT
iajs-3515	234	22	fowler	fowler	ADJ
iajs-3515	234	23	functional	functional	ADJ
iajs-3515	234	24	differential	differential	ADJ
iajs-3515	234	25	equations	equation	NOUN
iajs-3515	234	26	of	of	ADP
iajs-3515	234	27	neutral	neutral	ADJ
iajs-3515	234	28	type	type	NOUN
iajs-3515	234	29	.	.	PUNCT
iajs-3515	235	1	journal	journal	NOUN
iajs-3515	235	2	of	of	ADP
iajs-3515	235	3	i	i	PROPN
iajs-3515	235	4	and	and	CCONJ
iajs-3515	235	5	applications	application	NOUN
iajs-3515	235	6	.	.	PUNCT
iajs-3515	236	1	2016	2016	NUM
iajs-3515	236	2	:	:	PUNCT
iajs-3515	236	3	1	1	NUM
iajs-3515	236	4	-	-	SYM
iajs-3515	236	5	11	11	NUM
iajs-3515	236	6	.	.	PUNCT
iajs-3515	236	7	https://doi.org/10.1186/s13660-0161268-9	https://doi.org/10.1186/s13660-0161268-9	NOUN
iajs-3515	236	8	3	3	NUM
iajs-3515	236	9	.	.	PUNCT
iajs-3515	236	10	baculikova	baculikova	PROPN
iajs-3515	236	11	b	b	X
iajs-3515	236	12	,	,	PUNCT
iajs-3515	236	13	džurina	džurina	PROPN
iajs-3515	236	14	j.	j.	PROPN
iajs-3515	236	15	oscillation	oscillation	PROPN
iajs-3515	236	16	theorems	theorem	VERB
iajs-3515	236	17	for	for	ADP
iajs-3515	236	18	second	second	ADJ
iajs-3515	236	19	order	order	NOUN
iajs-3515	236	20	neutral	neutral	ADJ
iajs-3515	236	21	differential	differential	NOUN
iajs-3515	236	22	equations	equation	NOUN
iajs-3515	236	23	.	.	PUNCT
iajs-3515	237	1	computers	computer	NOUN
iajs-3515	237	2	&	&	CCONJ
iajs-3515	237	3	mathematics	mathematic	NOUN
iajs-3515	237	4	with	with	ADP
iajs-3515	237	5	applications.2011;61(1	applications.2011;61(1	ADJ
iajs-3515	237	6	):	):	PUNCT
iajs-3515	237	7	94	94	NUM
iajs-3515	237	8	-	-	SYM
iajs-3515	237	9	99	99	NUM
iajs-3515	237	10	.	.	PUNCT
iajs-3515	237	11	https://doi.org/10.1016/j.camwa.2010.10.035	https://doi.org/10.1016/j.camwa.2010.10.035	PROPN
iajs-3515	237	12	4	4	NUM
iajs-3515	237	13	.	.	PUNCT
iajs-3515	238	1	mehta	mehta	PROPN
iajs-3515	238	2	b	b	PROPN
iajs-3515	238	3	n	n	CCONJ
iajs-3515	238	4	,	,	PUNCT
iajs-3515	238	5	aris	aris	PROPN
iajs-3515	238	6	r.	r.	PROPN
iajs-3515	238	7	a	a	DET
iajs-3515	238	8	note	note	NOUN
iajs-3515	238	9	on	on	ADP
iajs-3515	238	10	a	a	DET
iajs-3515	238	11	form	form	NOUN
iajs-3515	238	12	of	of	ADP
iajs-3515	238	13	the	the	DET
iajs-3515	238	14	emden	emden	ADJ
iajs-3515	238	15	-	-	PUNCT
iajs-3515	238	16	fowler	fowler	PROPN
iajs-3515	238	17	equation	equation	NOUN
iajs-3515	238	18	.	.	PUNCT
iajs-3515	239	1	journal	journal	PROPN
iajs-3515	239	2	of	of	ADP
iajs-3515	239	3	mathematical	mathematical	ADJ
iajs-3515	239	4	analysis	analysis	NOUN
iajs-3515	239	5	and	and	CCONJ
iajs-3515	239	6	applications	application	NOUN
iajs-3515	239	7	.	.	PUNCT
iajs-3515	240	1	1971	1971	NUM
iajs-3515	240	2	;	;	PUNCT
iajs-3515	240	3	6(3	6(3	NUM
iajs-3515	240	4	):	):	PUNCT
iajs-3515	240	5	611	611	NUM
iajs-3515	240	6	-	-	SYM
iajs-3515	240	7	621	621	NUM
iajs-3515	240	8	.	.	PUNCT
iajs-3515	241	1	https://doi.org/10.1016/0022-247x(71)90043-6	https://doi.org/10.1016/0022-247x(71)90043-6	PROPN
iajs-3515	241	2	5	5	X
iajs-3515	241	3	.	.	X
iajs-3515	241	4	mohamad	mohamad	PROPN
iajs-3515	241	5	h	h	PROPN
iajs-3515	241	6	a	a	PROPN
iajs-3515	241	7	,	,	PUNCT
iajs-3515	241	8	ketab	ketab	PROPN
iajs-3515	241	9	s	s	PROPN
iajs-3515	241	10	n.	n.	NOUN
iajs-3515	241	11	oscillation	oscillation	NOUN
iajs-3515	241	12	solution	solution	NOUN
iajs-3515	241	13	for	for	ADP
iajs-3515	241	14	nonlinear	nonlinear	ADJ
iajs-3515	241	15	third	third	ADJ
iajs-3515	241	16	order	order	NOUN
iajs-3515	241	17	neutral	neutral	ADJ
iajs-3515	241	18	differential	differential	NOUN
iajs-3515	241	19	equations	equation	NOUN
iajs-3515	241	20	.	.	PUNCT
iajs-3515	242	1	iraqi	iraqi	ADJ
iajs-3515	242	2	j.	j.	PROPN
iajs-3515	242	3	of	of	ADP
iajs-3515	242	4	science	science	PROPN
iajs-3515	242	5	.	.	PUNCT
iajs-3515	243	1	special	special	ADJ
iajs-3515	243	2	issue	issue	NOUN
iajs-3515	243	3	,	,	PUNCT
iajs-3515	243	4	part	part	NOUN
iajs-3515	243	5	b	b	PROPN
iajs-3515	243	6	,	,	PUNCT
iajs-3515	243	7	2016	2016	NUM
iajs-3515	243	8	:	:	PUNCT
iajs-3515	243	9	412	412	NUM
iajs-3515	243	10	-	-	SYM
iajs-3515	243	11	417	417	NUM
iajs-3515	243	12	.	.	PUNCT
iajs-3515	244	1	https://search.emarefa.net/detail/bim762600	https://search.emarefa.net/detail/bim762600	ADP
iajs-3515	244	2	6	6	NUM
iajs-3515	244	3	.	.	PUNCT
iajs-3515	245	1	mohamad	mohamad	PROPN
iajs-3515	245	2	h	h	PROPN
iajs-3515	245	3	a	a	X
iajs-3515	245	4	,	,	PUNCT
iajs-3515	245	5	shehab	shehab	PROPN
iajs-3515	245	6	l	l	NOUN
iajs-3515	245	7	m.	m.	NOUN
iajs-3515	245	8	oscillations	oscillation	NOUN
iajs-3515	245	9	of	of	ADP
iajs-3515	245	10	third	third	ADJ
iajs-3515	245	11	order	order	NOUN
iajs-3515	245	12	half	half	NOUN
iajs-3515	245	13	linear	linear	ADJ
iajs-3515	245	14	neutral	neutral	ADJ
iajs-3515	245	15	differential	differential	NOUN
iajs-3515	245	16	equations	equation	NOUN
iajs-3515	245	17	.	.	PUNCT
iajs-3515	246	1	baghdad	baghdad	PROPN
iajs-3515	246	2	science	science	PROPN
iajs-3515	246	3	journal	journal	PROPN
iajs-3515	246	4	.	.	PUNCT
iajs-3515	247	1	2015	2015	NUM
iajs-3515	247	2	;	;	PUNCT
iajs-3515	247	3	12(3	12(3	NUM
iajs-3515	247	4	):	):	PUNCT
iajs-3515	247	5	625	625	NUM
iajs-3515	247	6	-	-	SYM
iajs-3515	247	7	631	631	NUM
iajs-3515	247	8	.	.	PUNCT
iajs-3515	248	1	https://doi.org/10.21123/bsj.2015.12.3.625-631	https://doi.org/10.21123/bsj.2015.12.3.625-631	NOUN
iajs-3515	248	2	7	7	NUM
iajs-3515	248	3	.	.	PUNCT
iajs-3515	248	4	moaaz	moaaz	PROPN
iajs-3515	248	5	o	o	PROPN
iajs-3515	248	6	,	,	PUNCT
iajs-3515	248	7	ramos	ramos	PROPN
iajs-3515	248	8	h	h	PROPN
iajs-3515	248	9	,	,	PUNCT
iajs-3515	248	10	awrejcewicz	awrejcewicz	ADJ
iajs-3515	248	11	j.	j.	PROPN
iajs-3515	248	12	second	second	ADJ
iajs-3515	248	13	-	-	PUNCT
iajs-3515	248	14	order	order	NOUN
iajs-3515	248	15	emden	emden	ADJ
iajs-3515	248	16	-	-	PUNCT
iajs-3515	248	17	fowler	fowler	ADJ
iajs-3515	248	18	neutral	neutral	ADJ
iajs-3515	248	19	differential	differential	PROPN
iajs-3515	248	20	equations	equation	NOUN
iajs-3515	248	21	a	a	DET
iajs-3515	248	22	new	new	ADJ
iajs-3515	248	23	precise	precise	ADJ
iajs-3515	248	24	criterion	criterion	NOUN
iajs-3515	248	25	for	for	ADP
iajs-3515	248	26	oscillation	oscillation	NOUN
iajs-3515	248	27	.applied	.applie	VERB
iajs-3515	248	28	mathematics	mathematic	NOUN
iajs-3515	248	29	letters	letter	NOUN
iajs-3515	248	30	.	.	PUNCT
iajs-3515	249	1	2021	2021	NUM
iajs-3515	249	2	;	;	PUNCT
iajs-3515	249	3	118	118	NUM
iajs-3515	249	4	:	:	PUNCT
iajs-3515	249	5	107	107	NUM
iajs-3515	249	6	-	-	SYM
iajs-3515	249	7	172	172	NUM
iajs-3515	249	8	.	.	PUNCT
iajs-3515	250	1	https://doi.org/10.1016/j.aml.2021.107172	https://doi.org/10.1016/j.aml.2021.107172	NOUN
iajs-3515	250	2	8	8	NUM
iajs-3515	250	3	.	.	PUNCT
iajs-3515	250	4	xu	xu	PROPN
iajs-3515	251	1	r	r	NOUN
iajs-3515	251	2	,	,	PUNCT
iajs-3515	251	3	xia	xia	PROPN
iajs-3515	251	4	y.	y.	PROPN
iajs-3515	251	5	a	a	DET
iajs-3515	251	6	note	note	NOUN
iajs-3515	251	7	on	on	ADP
iajs-3515	251	8	the	the	DET
iajs-3515	251	9	oscillation	oscillation	NOUN
iajs-3515	251	10	of	of	ADP
iajs-3515	251	11	second	second	ADJ
iajs-3515	251	12	-	-	PUNCT
iajs-3515	251	13	order	order	NOUN
iajs-3515	251	14	nonlinear	nonlinear	ADJ
iajs-3515	251	15	neutral	neutral	ADJ
iajs-3515	251	16	functional	functional	ADJ
iajs-3515	251	17	differential	differential	NOUN
iajs-3515	251	18	equations	equation	NOUN
iajs-3515	251	19	.	.	PUNCT
iajs-3515	252	1	international	international	ADJ
iajs-3515	252	2	journal	journal	PROPN
iajs-3515	252	3	of	of	ADP
iajs-3515	252	4	contemporary	contemporary	PROPN
iajs-3515	252	5	mathematical	mathematical	PROPN
iajs-3515	252	6	sciences.2008	sciences.2008	PROPN
iajs-3515	252	7	;	;	PUNCT
iajs-3515	252	8	3(29	3(29	NUM
iajs-3515	252	9	-	-	SYM
iajs-3515	252	10	32	32	NUM
iajs-3515	252	11	):	):	PUNCT
iajs-3515	252	12	1441	1441	NUM
iajs-3515	252	13	-	-	SYM
iajs-3515	252	14	1450	1450	NUM
iajs-3515	252	15	.	.	PUNCT
iajs-3515	253	1	https://doi.org/10.1016/j.camwa.2008.09.004	https://doi.org/10.1016/j.camwa.2008.09.004	NUM
iajs-3515	253	2	9	9	NUM
iajs-3515	253	3	.	.	PUNCT
iajs-3515	253	4	thandapani	thandapani	PROPN
iajs-3515	253	5	e	e	PROPN
iajs-3515	253	6	,	,	PUNCT
iajs-3515	253	7	tongxing	tongxe	VERB
iajs-3515	253	8	li	li	NOUN
iajs-3515	253	9	.	.	PROPN
iajs-3515	254	1	on	on	ADP
iajs-3515	254	2	the	the	DET
iajs-3515	254	3	oscillation	oscillation	NOUN
iajs-3515	254	4	of	of	ADP
iajs-3515	254	5	third	third	ADJ
iajs-3515	254	6	-	-	PUNCT
iajs-3515	254	7	order	order	NOUN
iajs-3515	254	8	quasi	quasi	ADJ
iajs-3515	254	9	-	-	ADJ
iajs-3515	254	10	linear	linear	ADJ
iajs-3515	254	11	neutral	neutral	ADJ
iajs-3515	254	12	functional	functional	ADJ
iajs-3515	254	13	differential	differential	NOUN
iajs-3515	254	14	equations	equation	NOUN
iajs-3515	254	15	.	.	PUNCT
iajs-3515	255	1	archivum	archivum	PROPN
iajs-3515	255	2	mathematicum	mathematicum	PROPN
iajs-3515	255	3	(	(	PUNCT
iajs-3515	255	4	brno	brno	PROPN
iajs-3515	255	5	)	)	PUNCT
iajs-3515	255	6	tomus	tomus	PROPN
iajs-3515	255	7	.2011	.2011	PROPN
iajs-3515	255	8	;	;	PUNCT
iajs-3515	255	9	47	47	NUM
iajs-3515	255	10	:	:	SYM
iajs-3515	255	11	181–199	181–199	NUM
iajs-3515	255	12	.	.	PUNCT
iajs-3515	256	1	http://eudml.org/doc/246122	http://eudml.org/doc/246122	PROPN
iajs-3515	256	2	10	10	NUM
iajs-3515	256	3	.	.	PUNCT
iajs-3515	257	1	hassan	hassan	PROPN
iajs-3515	257	2	t	t	PROPN
iajs-3515	257	3	s	s	PROPN
iajs-3515	257	4	,	,	PUNCT
iajs-3515	257	5	kong	kong	PROPN
iajs-3515	257	6	q	q	PROPN
iajs-3515	257	7	,	,	PUNCT
iajs-3515	257	8	el	el	PROPN
iajs-3515	257	9	-	-	PROPN
iajs-3515	257	10	matary	matary	PROPN
iajs-3515	258	1	b	b	PROPN
iajs-3515	258	2	m.	m.	NOUN
iajs-3515	258	3	oscillation	oscillation	NOUN
iajs-3515	258	4	criteria	criterion	NOUN
iajs-3515	258	5	for	for	ADP
iajs-3515	258	6	advanced	advanced	ADJ
iajs-3515	258	7	half	half	ADJ
iajs-3515	258	8	-	-	PUNCT
iajs-3515	258	9	linear	linear	NOUN
iajs-3515	258	10	differential.equations	differential.equation	NOUN
iajs-3515	258	11	..	..	PUNCT
iajs-3515	258	12	of.second	of.second	NOUN
iajs-3515	258	13	order	order	NOUN
iajs-3515	258	14	.mathematics	.mathematic	NOUN
iajs-3515	258	15	.	.	PUNCT
iajs-3515	259	1	2023	2023	NUM
iajs-3515	259	2	;	;	PUNCT
iajs-3515	259	3	11(6):1385	11(6):1385	NUM
iajs-3515	259	4	.	.	PUNCT
iajs-3515	260	1	11	11	NUM
iajs-3515	260	2	.	.	X
iajs-3515	261	1	https://doi.org/10.3390/math11061385	https://doi.org/10.3390/math11061385	PROPN
iajs-3515	261	2	12	12	NUM
iajs-3515	261	3	.	.	PUNCT
iajs-3515	262	1	tripathy	tripathy	PROPN
iajs-3515	262	2	a	a	DET
iajs-3515	262	3	k	k	PROPN
iajs-3515	262	4	,	,	PUNCT
iajs-3515	262	5	santra	santra	PROPN
iajs-3515	262	6	s	s	PART
iajs-3515	262	7	s.	s.	PROPN
iajs-3515	262	8	necessary	necessary	ADJ
iajs-3515	262	9	and	and	CCONJ
iajs-3515	262	10	sufficient	sufficient	ADJ
iajs-3515	262	11	conditions	condition	NOUN
iajs-3515	262	12	for	for	ADP
iajs-3515	262	13	oscillations	oscillation	NOUN
iajs-3515	262	14	to	to	ADP
iajs-3515	262	15	a	a	DET
iajs-3515	262	16	second	second	ADJ
iajs-3515	262	17	-	-	PUNCT
iajs-3515	262	18	order	order	NOUN
iajs-3515	262	19	neutral	neutral	ADJ
iajs-3515	262	20	differential	differential	NOUN
iajs-3515	262	21	equations	equation	NOUN
iajs-3515	262	22	with	with	ADP
iajs-3515	262	23	impulses	impulse	NOUN
iajs-3515	262	24	.	.	PUNCT
iajs-3515	263	1	kragujev	kragujev	PROPN
iajs-3515	263	2	.	.	PUNCT
iajs-3515	264	1	j.	j.	PROPN
iajs-3515	264	2	math	math	PROPN
iajs-3515	264	3	.	.	PUNCT
iajs-3515	265	1	2023	2023	NUM
iajs-3515	265	2	;	;	PUNCT
iajs-3515	265	3	47(12	47(12	NUM
iajs-3515	265	4	):	):	PUNCT
iajs-3515	265	5	81–93	81–93	NUM
iajs-3515	265	6	.	.	PUNCT
iajs-3515	266	1	https://doi.org/10.46793/kgjmat2301.0	https://doi.org/10.46793/kgjmat2301.0	PROPN
iajs-3515	266	2	13	13	NUM
iajs-3515	266	3	.	.	PUNCT
iajs-3515	267	1	mehta	mehta	PROPN
iajs-3515	267	2	b	b	PROPN
iajs-3515	267	3	n	n	CCONJ
iajs-3515	267	4	,	,	PUNCT
iajs-3515	267	5	aris	aris	PROPN
iajs-3515	267	6	r.	r.	PROPN
iajs-3515	267	7	a	a	DET
iajs-3515	267	8	note	note	NOUN
iajs-3515	267	9	on	on	ADP
iajs-3515	267	10	a	a	DET
iajs-3515	267	11	form	form	NOUN
iajs-3515	267	12	of	of	ADP
iajs-3515	267	13	the	the	DET
iajs-3515	267	14	emden	emden	ADJ
iajs-3515	267	15	-	-	PUNCT
iajs-3515	267	16	fowler	fowler	NOUN
iajs-3515	267	17	equation	equation	NOUN
iajs-3515	267	18	.	.	PUNCT
iajs-3515	268	1	journal	journal	PROPN
iajs-3515	268	2	of	of	ADP
iajs-3515	268	3	mathematical	mathematical	ADJ
iajs-3515	268	4	analysis	analysis	NOUN
iajs-3515	268	5	and	and	CCONJ
iajs-3515	268	6	applications	application	NOUN
iajs-3515	268	7	.	.	PUNCT
iajs-3515	269	1	1971	1971	NUM
iajs-3515	269	2	;	;	PUNCT
iajs-3515	269	3	63	63	NUM
iajs-3515	269	4	:	:	SYM
iajs-3515	269	5	611	611	NUM
iajs-3515	269	6	-	-	SYM
iajs-3515	269	7	621	621	NUM
iajs-3515	269	8	.	.	PUNCT
iajs-3515	270	1	https://doi.org/10.1016/0022-247x(71)90043-6	https://doi.org/10.1016/0022-247x(71)90043-6	PROPN
iajs-3515	270	2	14	14	NUM
iajs-3515	270	3	.	.	PUNCT
iajs-3515	271	1	vidhyaa	vidhyaa	PROPN
iajs-3515	271	2	k	k	PROPN
iajs-3515	271	3	s	s	PROPN
iajs-3515	271	4	,	,	PUNCT
iajs-3515	271	5	graef	graef	NOUN
iajs-3515	271	6	j	j	PROPN
iajs-3515	271	7	r	r	PROPN
iajs-3515	271	8	,	,	PUNCT
iajs-3515	271	9	thandapani	thandapani	PROPN
iajs-3515	271	10	e.	e.	PROPN
iajs-3515	272	1	new	new	PROPN
iajs-3515	272	2	oscillation	oscillation	NOUN
iajs-3515	272	3	results	result	VERB
iajs-3515	272	4	for	for	ADP
iajs-3515	272	5	third	third	ADJ
iajs-3515	272	6	-	-	PUNCT
iajs-3515	272	7	order	order	NOUN
iajs-3515	272	8	half	half	ADJ
iajs-3515	272	9	-	-	PUNCT
iajs-3515	272	10	linear	linear	ADJ
iajs-3515	272	11	neutral	neutral	ADJ
iajs-3515	272	12	differential	differential	NOUN
iajs-3515	272	13	equations	equation	NOUN
iajs-3515	272	14	.	.	PUNCT
iajs-3515	273	1	mathematics	mathematic	NOUN
iajs-3515	273	2	.	.	PUNCT
iajs-3515	274	1	2020	2020	NUM
iajs-3515	274	2	;	;	PUNCT
iajs-3515	274	3	8(3	8(3	NUM
iajs-3515	274	4	):	):	PUNCT
iajs-3515	274	5	325	325	NUM
iajs-3515	274	6	.	.	PUNCT
iajs-3515	275	1	https://doi.org/10.3390/math8030325	https://doi.org/10.3390/math8030325	PROPN
iajs-3515	275	2	15	15	NUM
iajs-3515	275	3	.	.	PUNCT
iajs-3515	276	1	dassios	dassio	NOUN
iajs-3515	277	1	i	i	PRON
iajs-3515	277	2	,	,	PUNCT
iajs-3515	277	3	liu	liu	PROPN
iajs-3515	277	4	m	m	PROPN
iajs-3515	277	5	,	,	PUNCT
iajs-3515	277	6	milano	milano	PROPN
iajs-3515	277	7	f.	f.	PROPN
iajs-3515	277	8	on	on	ADP
iajs-3515	277	9	the	the	DET
iajs-3515	277	10	stability	stability	NOUN
iajs-3515	277	11	analysis	analysis	NOUN
iajs-3515	277	12	of	of	ADP
iajs-3515	277	13	systems	system	NOUN
iajs-3515	277	14	of	of	ADP
iajs-3515	277	15	neutral	neutral	ADJ
iajs-3515	277	16	delay	delay	NOUN
iajs-3515	277	17	differential	differential	PROPN
iajs-3515	277	18	equations.circuits	equations.circuits	PROPN
iajs-3515	277	19	,	,	PUNCT
iajs-3515	277	20	systems	system	NOUN
iajs-3515	277	21	,	,	PUNCT
iajs-3515	277	22	and	and	CCONJ
iajs-3515	277	23	signal	signal	ADJ
iajs-3515	277	24	processing	processing	NOUN
iajs-3515	277	25	.	.	PUNCT
iajs-3515	278	1	2019	2019	NUM
iajs-3515	278	2	;	;	PUNCT
iajs-3515	278	3	38	38	NUM
iajs-3515	278	4	:	:	PUNCT
iajs-3515	278	5	1639	1639	NUM
iajs-3515	278	6	-	-	SYM
iajs-3515	278	7	1653	1653	NUM
iajs-3515	278	8	.	.	PUNCT
iajs-3515	279	1	https://doi.org/10.1007/s00034018-0943-0	https://doi.org/10.1007/s00034018-0943-0	PROPN
iajs-3515	279	2	16	16	NUM
iajs-3515	279	3	.	.	PUNCT
iajs-3515	280	1	li	li	PROPN
iajs-3515	280	2	t	t	PROPN
iajs-3515	280	3	,	,	PUNCT
iajs-3515	280	4	rogovchenko	rogovchenko	PROPN
iajs-3515	280	5	yv	yv	PROPN
iajs-3515	280	6	.	.	PUNCT
iajs-3515	281	1	oscillation	oscillation	NOUN
iajs-3515	281	2	criteria	criterion	NOUN
iajs-3515	281	3	for	for	ADP
iajs-3515	281	4	second	second	ADJ
iajs-3515	281	5	-	-	PUNCT
iajs-3515	281	6	order	order	NOUN
iajs-3515	281	7	superlinear	superlinear	NOUN
iajs-3515	281	8	emden	emden	NOUN
iajs-3515	281	9	–	–	PUNCT
iajs-3515	281	10	fowler	fowler	PROPN
iajs-3515	281	11	neutral	neutral	ADJ
iajs-3515	281	12	differential	differential	PROPN
iajs-3515	281	13	equations	equation	NOUN
iajs-3515	281	14	.	.	PUNCT
iajs-3515	282	1	monatshefte	monatshefte	PROPN
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iajs-3515	282	3	math.2017	math.2017	PROPN
iajs-3515	282	4	;	;	PUNCT
iajs-3515	282	5	184	184	NUM
iajs-3515	282	6	:	:	PUNCT
iajs-3515	282	7	489–500.https://doi.org/10.1007	489–500.https://doi.org/10.1007	NUM
iajs-3515	282	8	/	/	SYM
iajs-3515	282	9	s00605	s00605	NOUN
iajs-3515	282	10	-	-	PUNCT
iajs-3515	282	11	0171039	0171039	NUM
iajs-3515	282	12	-	-	SYM
iajs-3515	282	13	9	9	NUM
iajs-3515	282	14	17	17	NUM
iajs-3515	282	15	.	.	PUNCT
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iajs-3515	283	3	k	k	PROPN
iajs-3515	283	4	,	,	PUNCT
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iajs-3515	283	6	a	a	X
iajs-3515	283	7	,	,	PUNCT
iajs-3515	283	8	iambor	iambor	NOUN
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iajs-3515	283	13	oscillation	oscillation	NOUN
iajs-3515	283	14	of	of	ADP
iajs-3515	283	15	emden	emden	ADJ
iajs-3515	283	16	–	–	PUNCT
iajs-3515	283	17	fowler	fowler	ADJ
iajs-3515	283	18	-	-	PUNCT
iajs-3515	283	19	type	type	NOUN
iajs-3515	283	20	differential	differential	ADJ
iajs-3515	283	21	equations	equation	NOUN
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iajs-3515	283	24	-	-	ADJ
iajs-3515	283	25	canonical	canonical	ADJ
iajs-3515	283	26	operators	operator	NOUN
iajs-3515	283	27	and	and	CCONJ
iajs-3515	283	28	mixed	mixed	ADJ
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iajs-3515	283	30	terms	term	NOUN
iajs-3515	283	31	.	.	PUNCT
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iajs-3515	284	2	.	.	PUNCT
iajs-3515	285	1	2023	2023	NUM
iajs-3515	285	2	;	;	PUNCT
iajs-3515	285	3	15(2	15(2	NUM
iajs-3515	285	4	):	):	PUNCT
iajs-3515	285	5	553	553	NUM
iajs-3515	285	6	.	.	PUNCT
iajs-3515	286	1	https://doi.org/10.3390/sym15020553	https://doi.org/10.3390/sym15020553	PRON
iajs-3515	286	2	https://doi.org/10.1016/j.camwa.2010.10.035	https://doi.org/10.1016/j.camwa.2010.10.035	PROPN
iajs-3515	287	1	https://doi.org/10.1016/0022-247x(71)90043-6	https://doi.org/10.1016/0022-247x(71)90043-6	PROPN
iajs-3515	287	2	https://doi.org/10.21123/bsj.2015.12.3.625-631	https://doi.org/10.21123/bsj.2015.12.3.625-631	NOUN
iajs-3515	287	3	https://doi.org/10.1016/j.aml.2021.107172	https://doi.org/10.1016/j.aml.2021.107172	NOUN
iajs-3515	287	4	https://doi.org/10.1016/j.camwa.2008.09.004	https://doi.org/10.1016/j.camwa.2008.09.004	PROPN
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iajs-3515	287	7	/	/	SYM
iajs-3515	287	8	kgjmat2301.0	kgjmat2301.0	PROPN
iajs-3515	287	9	https://doi.org/10.1016/0022-247x(71)90043-6	https://doi.org/10.1016/0022-247x(71)90043-6	PROPN
iajs-3515	287	10	https://doi.org/10.3390/math8030325	https://doi.org/10.3390/math8030325	PROPN
iajs-3515	287	11	https://doi.org/10.1007/s00034-018-0943-0	https://doi.org/10.1007/s00034-018-0943-0	PROPN
iajs-3515	287	12	https://doi.org/10.1007/s00034-018-0943-0	https://doi.org/10.1007/s00034-018-0943-0	PROPN
iajs-3515	287	13	https://doi.org/10.3390/sym15020553	https://doi.org/10.3390/sym15020553	NUM
iajs-3515	287	14	ihjpas	ihjpas	PROPN
iajs-3515	287	15	.	.	PUNCT
iajs-3515	288	1	2024	2024	NUM
iajs-3515	288	2	,	,	PUNCT
iajs-3515	288	3	38	38	NUM
iajs-3515	288	4	(	(	PUNCT
iajs-3515	288	5	1	1	NUM
iajs-3515	288	6	)	)	PUNCT
iajs-3515	288	7	416	416	NUM
iajs-3515	288	8	18	18	NUM
iajs-3515	288	9	.	.	PUNCT
iajs-3515	289	1	baty	baty	PROPN
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iajs-3515	289	4	higher	high	ADJ
iajs-3515	289	5	-	-	PUNCT
iajs-3515	289	6	order	order	NOUN
iajs-3515	289	7	laneemden	laneemden	NOUN
iajs-3515	289	8	fowler	fowler	PROPN
iajs-3515	289	9	type	type	NOUN
iajs-3515	289	10	equations	equation	NOUN
iajs-3515	289	11	using	use	VERB
iajs-3515	289	12	physics	physics	NOUN
iajs-3515	289	13	-	-	PUNCT
iajs-3515	289	14	informed	inform	VERB
iajs-3515	289	15	neural	neural	ADJ
iajs-3515	289	16	networks	network	NOUN
iajs-3515	289	17	:	:	PUNCT
iajs-3515	289	18	benchmark	benchmark	NOUN
iajs-3515	289	19	tests	test	NOUN
iajs-3515	289	20	comparing	compare	VERB
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iajs-3515	289	22	and	and	CCONJ
iajs-3515	289	23	hard	hard	ADJ
iajs-3515	289	24	constraints	constraint	NOUN
iajs-3515	289	25	.	.	PUNCT
iajs-3515	290	1	2023	2023	NUM
iajs-3515	290	2	;	;	PUNCT
iajs-3515	290	3	arxiv	arxiv	PROPN
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iajs-3515	290	5	arxiv:2307	arxiv:2307	NOUN
iajs-3515	290	6	.	.	PROPN
iajs-3515	290	7	07302	07302	NUM
iajs-3515	290	8	.	.	PUNCT
iajs-3515	291	1	https://doi.org/10.48550/arxiv.2307.07302	https://doi.org/10.48550/arxiv.2307.07302	PROPN
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iajs-3515	291	3	.	.	PUNCT
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iajs-3515	291	5	a	a	DET
iajs-3515	291	6	a	a	NOUN
iajs-3515	291	7	,	,	PUNCT
iajs-3515	291	8	mohamad	mohamad	PROPN
iajs-3515	291	9	h	h	NOUN
iajs-3515	291	10	a.	a.	NOUN
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iajs-3515	291	12	oscillatory	oscillatory	ADJ
iajs-3515	291	13	solutions	solution	NOUN
iajs-3515	291	14	of	of	ADP
iajs-3515	291	15	a	a	DET
iajs-3515	291	16	three	three	NUM
iajs-3515	291	17	-	-	PUNCT
iajs-3515	291	18	dimensional	dimensional	ADJ
iajs-3515	291	19	half	half	ADJ
iajs-3515	291	20	-	-	PUNCT
iajs-3515	291	21	linear	linear	ADJ
iajs-3515	291	22	neutral	neutral	ADJ
iajs-3515	291	23	differential	differential	NOUN
iajs-3515	291	24	system	system	NOUN
iajs-3515	291	25	of	of	ADP
iajs-3515	291	26	the	the	DET
iajs-3515	291	27	second	second	ADJ
iajs-3515	291	28	order	order	NOUN
iajs-3515	291	29	.	.	PUNCT
iajs-3515	292	1	journal	journal	NOUN
iajs-3515	292	2	of	of	ADP
iajs-3515	292	3	university	university	PROPN
iajs-3515	292	4	of	of	ADP
iajs-3515	292	5	babylon	babylon	PROPN
iajs-3515	292	6	for	for	ADP
iajs-3515	292	7	pure	pure	ADJ
iajs-3515	292	8	and	and	CCONJ
iajs-3515	292	9	applied	applied	ADJ
iajs-3515	292	10	sciences	science	NOUN
iajs-3515	292	11	.	.	PUNCT
iajs-3515	293	1	2023	2023	NUM
iajs-3515	293	2	;	;	PUNCT
iajs-3515	293	3	31)1	31)1	NUM
iajs-3515	293	4	)	)	PUNCT
iajs-3515	293	5	;	;	PUNCT
iajs-3515	294	1	48–71	48–71	NUM
iajs-3515	294	2	.	.	PUNCT
iajs-3515	294	3	https://doi.org/10.29196/jubpas.v31i1.4528	https://doi.org/10.29196/jubpas.v31i1.4528	NUM
iajs-3515	295	1	20	20	NUM
iajs-3515	295	2	.	.	PUNCT
iajs-3515	296	1	suha	suha	PROPN
iajs-3515	296	2	n	n	CCONJ
iajs-3515	296	3	,	,	PUNCT
iajs-3515	296	4	singh	singh	PROPN
iajs-3515	296	5	r.	r.	PROPN
iajs-3515	296	6	an	an	DET
iajs-3515	296	7	efficient	efficient	ADJ
iajs-3515	296	8	new	new	ADJ
iajs-3515	296	9	numerical	numerical	ADJ
iajs-3515	296	10	algorithm	algorithm	NOUN
iajs-3515	296	11	for	for	ADP
iajs-3515	296	12	solving	solve	VERB
iajs-3515	296	13	emden	emden	ADJ
iajs-3515	296	14	–	–	PUNCT
iajs-3515	296	15	fowlesr	fowlesr	NOUN
iajs-3515	296	16	pantograph	pantograph	NOUN
iajs-3515	296	17	differential	differential	NOUN
iajs-3515	296	18	equation	equation	NOUN
iajs-3515	296	19	using	use	VERB
iajs-3515	296	20	laguerre	laguerre	NOUN
iajs-3515	296	21	polynomials	polynomial	NOUN
iajs-3515	296	22	.	.	PUNCT
iajs-3515	297	1	journal	journal	NOUN
iajs-3515	297	2	of	of	ADP
iajs-3515	297	3	computational	computational	ADJ
iajs-3515	297	4	science	science	NOUN
iajs-3515	297	5	.	.	PUNCT
iajs-3515	298	1	2023	2023	NUM
iajs-3515	298	2	;	;	PUNCT
iajs-3515	298	3	72:102108	72:102108	NUM
iajs-3515	298	4	.https://doi.org/10.1016/j.jocs.2023.102108	.https://doi.org/10.1016/j.jocs.2023.102108	SYM
iajs-3515	298	5	21	21	NUM
iajs-3515	298	6	.	.	PUNCT
iajs-3515	299	1	rufai	rufai	NOUN
iajs-3515	299	2	m	m	VERB
iajs-3515	299	3	a	a	PRON
iajs-3515	299	4	,	,	PUNCT
iajs-3515	299	5	ramos	ramos	PROPN
iajs-3515	299	6	h.	h.	PROPN
iajs-3515	299	7	numerical	numerical	PROPN
iajs-3515	299	8	integration	integration	NOUN
iajs-3515	299	9	of	of	ADP
iajs-3515	299	10	third	third	ADJ
iajs-3515	299	11	-	-	PUNCT
iajs-3515	299	12	order	order	NOUN
iajs-3515	299	13	singular	singular	ADJ
iajs-3515	299	14	boundary	boundary	ADJ
iajs-3515	299	15	-	-	PUNCT
iajs-3515	299	16	value	value	NOUN
iajs-3515	299	17	problems	problem	NOUN
iajs-3515	299	18	of	of	ADP
iajs-3515	299	19	emden	emden	ADJ
iajs-3515	299	20	–	–	PUNCT
iajs-3515	299	21	fowler	fowler	NOUN
iajs-3515	299	22	type	type	NOUN
iajs-3515	299	23	using	use	VERB
iajs-3515	299	24	hybrid	hybrid	ADJ
iajs-3515	299	25	block	block	NOUN
iajs-3515	299	26	techniques	technique	NOUN
iajs-3515	299	27	.	.	PUNCT
iajs-3515	300	1	communications	communication	NOUN
iajs-3515	300	2	in	in	ADP
iajs-3515	300	3	nonlinear	nonlinear	ADJ
iajs-3515	300	4	science	science	NOUN
iajs-3515	300	5	and	and	CCONJ
iajs-3515	300	6	numerical	numerical	PROPN
iajs-3515	300	7	simulation	simulation	PROPN
iajs-3515	300	8	.	.	PUNCT
iajs-3515	300	9	2022	2022	NUM
iajs-3515	300	10	;	;	PUNCT
iajs-3515	300	11	105:106069	105:106069	NUM
iajs-3515	300	12	.https://doi.org/10.1016/j.cnsns.2021.106069	.https://doi.org/10.1016/j.cnsns.2021.106069	SYM
iajs-3515	300	13	22	22	NUM
iajs-3515	300	14	.	.	PUNCT
iajs-3515	300	15	mahdy	mahdy	PROPN
iajs-3515	300	16	a	a	DET
iajs-3515	300	17	m	m	PROPN
iajs-3515	300	18	s.	s.	PROPN
iajs-3515	300	19	a	a	DET
iajs-3515	300	20	numerical	numerical	ADJ
iajs-3515	300	21	method	method	NOUN
iajs-3515	300	22	for	for	ADP
iajs-3515	300	23	solving	solve	VERB
iajs-3515	300	24	the	the	DET
iajs-3515	300	25	nonlinear	nonlinear	ADJ
iajs-3515	300	26	equations	equation	NOUN
iajs-3515	300	27	of	of	ADP
iajs-3515	300	28	emden	emden	ADJ
iajs-3515	300	29	-	-	PUNCT
iajs-3515	300	30	fowler	fowler	NOUN
iajs-3515	300	31	models	model	NOUN
iajs-3515	300	32	.	.	PUNCT
iajs-3515	301	1	journal	journal	NOUN
iajs-3515	301	2	of	of	ADP
iajs-3515	301	3	ocean	ocean	PROPN
iajs-3515	301	4	engineering	engineering	NOUN
iajs-3515	301	5	and	and	CCONJ
iajs-3515	301	6	science	science	NOUN
iajs-3515	301	7	.	.	PUNCT
iajs-3515	302	1	2022	2022	NUM
iajs-3515	302	2	.	.	PUNCT
iajs-3515	303	1	https://doi.org/10.1016/j.joes.2022.04.019	https://doi.org/10.1016/j.joes.2022.04.019	PROPN
iajs-3515	303	2	23	23	NUM
iajs-3515	303	3	.	.	PUNCT
iajs-3515	304	1	singh	singh	PROPN
iajs-3515	304	2	r	r	PROPN
iajs-3515	304	3	,	,	PUNCT
iajs-3515	304	4	singh	singh	PROPN
iajs-3515	304	5	m.	m.	NOUN
iajs-3515	304	6	an	an	DET
iajs-3515	304	7	optimal	optimal	ADJ
iajs-3515	304	8	decomposition	decomposition	NOUN
iajs-3515	304	9	method	method	NOUN
iajs-3515	304	10	for	for	ADP
iajs-3515	304	11	analytical	analytical	ADJ
iajs-3515	304	12	and	and	CCONJ
iajs-3515	304	13	numerical	numerical	ADJ
iajs-3515	304	14	solution	solution	NOUN
iajs-3515	304	15	of	of	ADP
iajs-3515	304	16	third	third	ADJ
iajs-3515	304	17	-	-	PUNCT
iajs-3515	304	18	order	order	NOUN
iajs-3515	304	19	emden	emden	ADJ
iajs-3515	304	20	–	–	PUNCT
iajs-3515	304	21	fowler	fowler	PROPN
iajs-3515	304	22	type	type	NOUN
iajs-3515	304	23	equations	equation	NOUN
iajs-3515	304	24	.journal	.journal	ADJ
iajs-3515	304	25	of	of	ADP
iajs-3515	304	26	computational	computational	ADJ
iajs-3515	304	27	science	science	NOUN
iajs-3515	304	28	.	.	PUNCT
iajs-3515	304	29	2022	2022	NUM
iajs-3515	304	30	;	;	PUNCT
iajs-3515	304	31	63	63	NUM
iajs-3515	304	32	:	:	SYM
iajs-3515	304	33	101790	101790	NUM
iajs-3515	304	34	.	.	PUNCT
iajs-3515	305	1	https://doi.org/10.1016/j.jocs.2022.101790	https://doi.org/10.1016/j.jocs.2022.101790	ADJ
iajs-3515	305	2	https://doi./	https://doi./	ADP
iajs-3515	305	3	https://doi.org/10.29196/jubpas.v31i1.4528	https://doi.org/10.29196/jubpas.v31i1.4528	NUM
iajs-3515	305	4	https://doi.org/10.1016/j.jocs.2023.102108	https://doi.org/10.1016/j.jocs.2023.102108	PROPN
iajs-3515	305	5	https://doi.org/10.1016/j.cnsns.2021.106069	https://doi.org/10.1016/j.cnsns.2021.106069	PROPN
iajs-3515	305	6	https://doi.org/10.1016/j.joes.2022.04.019	https://doi.org/10.1016/j.joes.2022.04.019	PROPN
iajs-3515	305	7	https://doi.org/10.1016/j.jocs.2022.101790	https://doi.org/10.1016/j.jocs.2022.101790	NOUN