id	sid	tid	token	lemma	pos
iajs-4063	1	1	367	367	NUM
iajs-4063	1	2	©	©	ADP
iajs-4063	1	3	2025	2025	NUM
iajs-4063	1	4	the	the	DET
iajs-4063	1	5	author(s	author(s	NOUN
iajs-4063	1	6	)	)	PUNCT
iajs-4063	1	7	.	.	PUNCT
iajs-4063	2	1	published	publish	VERB
iajs-4063	2	2	by	by	ADP
iajs-4063	2	3	college	college	NOUN
iajs-4063	2	4	of	of	ADP
iajs-4063	2	5	education	education	NOUN
iajs-4063	2	6	for	for	ADP
iajs-4063	2	7	pure	pure	ADJ
iajs-4063	2	8	science	science	NOUN
iajs-4063	2	9	(	(	PUNCT
iajs-4063	2	10	ibn	ibn	PROPN
iajs-4063	2	11	al	al	PROPN
iajs-4063	2	12	-	-	PUNCT
iajs-4063	2	13	haitham	haitham	PROPN
iajs-4063	2	14	)	)	PUNCT
iajs-4063	2	15	,	,	PUNCT
iajs-4063	2	16	university	university	NOUN
iajs-4063	2	17	of	of	ADP
iajs-4063	2	18	baghdad	baghdad	PROPN
iajs-4063	2	19	.	.	PUNCT
iajs-4063	3	1	this	this	PRON
iajs-4063	3	2	is	be	AUX
iajs-4063	3	3	an	an	DET
iajs-4063	3	4	open	open	ADJ
iajs-4063	3	5	-	-	PUNCT
iajs-4063	3	6	access	access	NOUN
iajs-4063	3	7	article	article	NOUN
iajs-4063	3	8	distributed	distribute	VERB
iajs-4063	3	9	under	under	ADP
iajs-4063	3	10	the	the	DET
iajs-4063	3	11	terms	term	NOUN
iajs-4063	3	12	of	of	ADP
iajs-4063	3	13	the	the	DET
iajs-4063	3	14	creative	creative	ADJ
iajs-4063	3	15	commons	common	NOUN
iajs-4063	3	16	attribution	attribution	NOUN
iajs-4063	3	17	4.0	4.0	NUM
iajs-4063	3	18	international	international	ADJ
iajs-4063	3	19	license	license	NOUN
iajs-4063	3	20	some	some	DET
iajs-4063	3	21	oscillatory	oscillatory	ADJ
iajs-4063	3	22	results	result	NOUN
iajs-4063	3	23	of	of	ADP
iajs-4063	3	24	nonlinear	nonlinear	ADJ
iajs-4063	3	25	neutral	neutral	ADJ
iajs-4063	3	26	differential	differential	NOUN
iajs-4063	3	27	equation	equation	NOUN
iajs-4063	3	28	zahrah	zahrah	PROPN
iajs-4063	3	29	abdul	abdul	PROPN
iajs-4063	3	30	abbas	abbas	PROPN
iajs-4063	3	31	hussein	hussein	PROPN
iajs-4063	3	32	1	1	NUM
iajs-4063	3	33	and	and	CCONJ
iajs-4063	3	34	aqeel	aqeel	PROPN
iajs-4063	3	35	falih	falih	PROPN
iajs-4063	3	36	jaddoa	jaddoa	PROPN
iajs-4063	3	37	2	2	NUM
iajs-4063	3	38	*	*	SYM
iajs-4063	3	39	1,2	1,2	NUM
iajs-4063	3	40	mathematics	mathematic	NOUN
iajs-4063	3	41	,	,	PUNCT
iajs-4063	3	42	college	college	NOUN
iajs-4063	3	43	of	of	ADP
iajs-4063	3	44	education	education	NOUN
iajs-4063	3	45	for	for	ADP
iajs-4063	3	46	pure	pure	ADJ
iajs-4063	3	47	sciences/	sciences/	NUM
iajs-4063	3	48	ibn	ibn	PROPN
iajs-4063	3	49	-	-	PUNCT
iajs-4063	3	50	al	al	PROPN
iajs-4063	3	51	-	-	PUNCT
iajs-4063	3	52	haitham	haitham	PROPN
iajs-4063	3	53	,	,	PUNCT
iajs-4063	3	54	university	university	PROPN
iajs-4063	3	55	of	of	ADP
iajs-4063	3	56	baghdad	baghdad	PROPN
iajs-4063	3	57	,	,	PUNCT
iajs-4063	3	58	baghdad	baghdad	PROPN
iajs-4063	3	59	,	,	PUNCT
iajs-4063	3	60	iraq	iraq	PROPN
iajs-4063	3	61	.	.	PUNCT
iajs-4063	4	1	*	*	PUNCT
iajs-4063	4	2	corresponding	correspond	VERB
iajs-4063	4	3	author	author	NOUN
iajs-4063	4	4	.	.	PUNCT
iajs-4063	5	1	received	receive	VERB
iajs-4063	5	2	:	:	PUNCT
iajs-4063	5	3	7	7	NUM
iajs-4063	5	4	january	january	PROPN
iajs-4063	5	5	2025	2025	NUM
iajs-4063	5	6	accepted	accept	VERB
iajs-4063	5	7	:	:	PUNCT
iajs-4063	5	8	9	9	NUM
iajs-4063	5	9	april	april	PROPN
iajs-4063	5	10	2025	2025	NUM
iajs-4063	5	11	published	publish	VERB
iajs-4063	5	12	:	:	PUNCT
iajs-4063	5	13	20	20	NUM
iajs-4063	5	14	july	july	NOUN
iajs-4063	5	15	2025	2025	NUM
iajs-4063	5	16	doi.org/10.30526/38.3.4063	doi.org/10.30526/38.3.4063	NOUN
iajs-4063	5	17	abstract	abstract	ADJ
iajs-4063	5	18	in	in	ADP
iajs-4063	5	19	the	the	DET
iajs-4063	5	20	last	last	ADJ
iajs-4063	5	21	decades	decade	NOUN
iajs-4063	5	22	,	,	PUNCT
iajs-4063	5	23	functional	functional	ADJ
iajs-4063	5	24	differential	differential	ADJ
iajs-4063	5	25	equations	equation	NOUN
iajs-4063	5	26	have	have	AUX
iajs-4063	5	27	attracted	attract	VERB
iajs-4063	5	28	the	the	DET
iajs-4063	5	29	attention	attention	NOUN
iajs-4063	5	30	of	of	ADP
iajs-4063	5	31	many	many	ADJ
iajs-4063	5	32	researchers	researcher	NOUN
iajs-4063	5	33	;	;	PUNCT
iajs-4063	5	34	they	they	PRON
iajs-4063	5	35	were	be	AUX
iajs-4063	5	36	interested	interested	ADJ
iajs-4063	5	37	in	in	ADP
iajs-4063	5	38	the	the	DET
iajs-4063	5	39	theory	theory	NOUN
iajs-4063	5	40	and	and	CCONJ
iajs-4063	5	41	its	its	PRON
iajs-4063	5	42	applications	application	NOUN
iajs-4063	5	43	.	.	PUNCT
iajs-4063	6	1	the	the	DET
iajs-4063	6	2	most	most	ADV
iajs-4063	6	3	common	common	ADJ
iajs-4063	6	4	differential	differential	ADJ
iajs-4063	6	5	equations	equation	NOUN
iajs-4063	6	6	of	of	ADP
iajs-4063	6	7	functional	functional	ADJ
iajs-4063	6	8	type	type	NOUN
iajs-4063	6	9	are	be	AUX
iajs-4063	6	10	advanced	advanced	ADJ
iajs-4063	6	11	,	,	PUNCT
iajs-4063	6	12	neutral	neutral	ADJ
iajs-4063	6	13	,	,	PUNCT
iajs-4063	6	14	and	and	CCONJ
iajs-4063	6	15	delay	delay	PROPN
iajs-4063	6	16	des	des	PROPN
iajs-4063	6	17	.	.	PUNCT
iajs-4063	7	1	the	the	DET
iajs-4063	7	2	theory	theory	NOUN
iajs-4063	7	3	of	of	ADP
iajs-4063	7	4	oscillatory	oscillatory	ADJ
iajs-4063	7	5	des	de	NOUN
iajs-4063	7	6	with	with	ADP
iajs-4063	7	7	retarded	retarded	ADJ
iajs-4063	7	8	arguments	argument	NOUN
iajs-4063	7	9	has	have	VERB
iajs-4063	7	10	a	a	DET
iajs-4063	7	11	paramount	paramount	ADJ
iajs-4063	7	12	effect	effect	NOUN
iajs-4063	7	13	on	on	ADP
iajs-4063	7	14	the	the	DET
iajs-4063	7	15	qualitative	qualitative	ADJ
iajs-4063	7	16	properties	property	NOUN
iajs-4063	7	17	of	of	ADP
iajs-4063	7	18	des	des	PROPN
iajs-4063	7	19	.	.	PUNCT
iajs-4063	8	1	it	it	PRON
iajs-4063	8	2	is	be	AUX
iajs-4063	8	3	essential	essential	ADJ
iajs-4063	8	4	to	to	PART
iajs-4063	8	5	deduce	deduce	VERB
iajs-4063	8	6	conditions	condition	NOUN
iajs-4063	8	7	for	for	ADP
iajs-4063	8	8	oscillatory	oscillatory	ADJ
iajs-4063	8	9	and	and	CCONJ
iajs-4063	8	10	non	non	ADJ
iajs-4063	8	11	-	-	ADJ
iajs-4063	8	12	oscillatory	oscillatory	ADJ
iajs-4063	8	13	solutions	solution	NOUN
iajs-4063	8	14	.	.	PUNCT
iajs-4063	9	1	the	the	DET
iajs-4063	9	2	objective	objective	NOUN
iajs-4063	9	3	of	of	ADP
iajs-4063	9	4	this	this	DET
iajs-4063	9	5	paper	paper	NOUN
iajs-4063	9	6	is	be	AUX
iajs-4063	9	7	to	to	PART
iajs-4063	9	8	obtain	obtain	VERB
iajs-4063	9	9	oscillatory	oscillatory	ADJ
iajs-4063	9	10	conditions	condition	NOUN
iajs-4063	9	11	for	for	ADP
iajs-4063	9	12	differential	differential	ADJ
iajs-4063	9	13	equations	equation	NOUN
iajs-4063	9	14	with	with	ADP
iajs-4063	9	15	retarded	retarded	ADJ
iajs-4063	9	16	arguments	argument	NOUN
iajs-4063	9	17	.	.	PUNCT
iajs-4063	10	1	so	so	ADV
iajs-4063	10	2	,	,	PUNCT
iajs-4063	10	3	the	the	DET
iajs-4063	10	4	oscillatory	oscillatory	ADJ
iajs-4063	10	5	behavior	behavior	NOUN
iajs-4063	10	6	has	have	AUX
iajs-4063	10	7	been	be	AUX
iajs-4063	10	8	considered	consider	VERB
iajs-4063	10	9	in	in	ADP
iajs-4063	10	10	the	the	DET
iajs-4063	10	11	nonlinear	nonlinear	ADJ
iajs-4063	10	12	differential	differential	ADJ
iajs-4063	10	13	equations	equation	NOUN
iajs-4063	10	14	(	(	PUNCT
iajs-4063	10	15	des	des	PROPN
iajs-4063	10	16	)	)	PUNCT
iajs-4063	10	17	of	of	ADP
iajs-4063	10	18	neutral	neutral	ADJ
iajs-4063	10	19	type	type	NOUN
iajs-4063	10	20	with	with	ADP
iajs-4063	10	21	three	three	NUM
iajs-4063	10	22	delays	delay	NOUN
iajs-4063	10	23	.	.	PUNCT
iajs-4063	11	1	some	some	DET
iajs-4063	11	2	important	important	ADJ
iajs-4063	11	3	conditions	condition	NOUN
iajs-4063	11	4	of	of	ADP
iajs-4063	11	5	all	all	DET
iajs-4063	11	6	functions	function	NOUN
iajs-4063	11	7	have	have	AUX
iajs-4063	11	8	been	be	AUX
iajs-4063	11	9	submitted	submit	VERB
iajs-4063	11	10	.	.	PUNCT
iajs-4063	12	1	the	the	DET
iajs-4063	12	2	sufficient	sufficient	ADJ
iajs-4063	12	3	conditions	condition	NOUN
iajs-4063	12	4	to	to	PART
iajs-4063	12	5	secure	secure	VERB
iajs-4063	12	6	the	the	DET
iajs-4063	12	7	oscillatory	oscillatory	ADJ
iajs-4063	12	8	property	property	NOUN
iajs-4063	12	9	have	have	AUX
iajs-4063	12	10	been	be	AUX
iajs-4063	12	11	deduced	deduce	VERB
iajs-4063	12	12	.	.	PUNCT
iajs-4063	13	1	we	we	PRON
iajs-4063	13	2	dealt	deal	VERB
iajs-4063	13	3	with	with	ADP
iajs-4063	13	4	special	special	ADJ
iajs-4063	13	5	cases	case	NOUN
iajs-4063	13	6	for	for	ADP
iajs-4063	13	7	delays	delay	NOUN
iajs-4063	13	8	to	to	PART
iajs-4063	13	9	obtain	obtain	VERB
iajs-4063	13	10	some	some	DET
iajs-4063	13	11	desired	desire	VERB
iajs-4063	13	12	conditions	condition	NOUN
iajs-4063	13	13	for	for	ADP
iajs-4063	13	14	oscillation	oscillation	NOUN
iajs-4063	13	15	property	property	NOUN
iajs-4063	13	16	.	.	PUNCT
iajs-4063	14	1	in	in	ADP
iajs-4063	14	2	fact	fact	NOUN
iajs-4063	14	3	,	,	PUNCT
iajs-4063	14	4	all	all	DET
iajs-4063	14	5	new	new	ADJ
iajs-4063	14	6	results	result	NOUN
iajs-4063	14	7	and	and	CCONJ
iajs-4063	14	8	conditions	condition	NOUN
iajs-4063	14	9	innovate	innovate	VERB
iajs-4063	14	10	,	,	PUNCT
iajs-4063	14	11	and	and	CCONJ
iajs-4063	14	12	improved	improve	VERB
iajs-4063	14	13	some	some	DET
iajs-4063	14	14	oscillation	oscillation	NOUN
iajs-4063	14	15	properties	property	NOUN
iajs-4063	14	16	that	that	PRON
iajs-4063	14	17	appeared	appear	VERB
iajs-4063	14	18	in	in	ADP
iajs-4063	14	19	the	the	DET
iajs-4063	14	20	literature	literature	NOUN
iajs-4063	14	21	.	.	PUNCT
iajs-4063	15	1	some	some	DET
iajs-4063	15	2	application	application	NOUN
iajs-4063	15	3	examples	example	NOUN
iajs-4063	15	4	with	with	ADP
iajs-4063	15	5	specific	specific	ADJ
iajs-4063	15	6	functions	function	NOUN
iajs-4063	15	7	for	for	ADP
iajs-4063	15	8	important	important	ADJ
iajs-4063	15	9	results	result	NOUN
iajs-4063	15	10	have	have	AUX
iajs-4063	15	11	been	be	AUX
iajs-4063	15	12	illustrated	illustrate	VERB
iajs-4063	15	13	and	and	CCONJ
iajs-4063	15	14	applied	apply	VERB
iajs-4063	15	15	to	to	ADP
iajs-4063	15	16	all	all	DET
iajs-4063	15	17	conditions	condition	NOUN
iajs-4063	15	18	.	.	PUNCT
iajs-4063	16	1	two	two	NUM
iajs-4063	16	2	results	result	NOUN
iajs-4063	16	3	with	with	ADP
iajs-4063	16	4	some	some	DET
iajs-4063	16	5	different	different	ADJ
iajs-4063	16	6	conditions	condition	NOUN
iajs-4063	16	7	have	have	AUX
iajs-4063	16	8	been	be	AUX
iajs-4063	16	9	obtained	obtain	VERB
iajs-4063	16	10	to	to	PART
iajs-4063	16	11	get	get	VERB
iajs-4063	16	12	oscillatory	oscillatory	ADJ
iajs-4063	16	13	behavior	behavior	NOUN
iajs-4063	16	14	for	for	ADP
iajs-4063	16	15	de	de	PROPN
iajs-4063	16	16	.	.	PROPN
iajs-4063	16	17	a	a	DET
iajs-4063	16	18	new	new	ADJ
iajs-4063	16	19	relationship	relationship	NOUN
iajs-4063	16	20	between	between	ADP
iajs-4063	16	21	delays	delay	NOUN
iajs-4063	16	22	and	and	CCONJ
iajs-4063	16	23	other	other	ADJ
iajs-4063	16	24	functions	function	NOUN
iajs-4063	16	25	to	to	PART
iajs-4063	16	26	get	get	VERB
iajs-4063	16	27	desired	desire	VERB
iajs-4063	16	28	property	property	NOUN
iajs-4063	16	29	has	have	AUX
iajs-4063	16	30	been	be	AUX
iajs-4063	16	31	formulated	formulate	VERB
iajs-4063	16	32	.	.	PUNCT
iajs-4063	17	1	some	some	DET
iajs-4063	17	2	application	application	NOUN
iajs-4063	17	3	examples	example	NOUN
iajs-4063	17	4	explained	explain	VERB
iajs-4063	17	5	to	to	PART
iajs-4063	17	6	ensure	ensure	VERB
iajs-4063	17	7	the	the	DET
iajs-4063	17	8	importance	importance	NOUN
iajs-4063	17	9	of	of	ADP
iajs-4063	17	10	our	our	PRON
iajs-4063	17	11	results	result	NOUN
iajs-4063	17	12	compared	compare	VERB
iajs-4063	17	13	with	with	ADP
iajs-4063	17	14	other	other	ADJ
iajs-4063	17	15	previous	previous	ADJ
iajs-4063	17	16	studies	study	NOUN
iajs-4063	17	17	.	.	PUNCT
iajs-4063	18	1	keywords	keyword	NOUN
iajs-4063	18	2	:	:	PUNCT
iajs-4063	18	3	property	property	NOUN
iajs-4063	18	4	of	of	ADP
iajs-4063	18	5	oscillation	oscillation	NOUN
iajs-4063	18	6	,	,	PUNCT
iajs-4063	18	7	multiple	multiple	ADJ
iajs-4063	18	8	delays	delay	NOUN
iajs-4063	18	9	,	,	PUNCT
iajs-4063	18	10	nde	nde	PROPN
iajs-4063	18	11	,	,	PUNCT
iajs-4063	18	12	nonlinear	nonlinear	ADJ
iajs-4063	18	13	case	case	NOUN
iajs-4063	18	14	.	.	PUNCT
iajs-4063	19	1	1	1	X
iajs-4063	19	2	.	.	X
iajs-4063	19	3	introduction	introduction	NOUN
iajs-4063	19	4	the	the	DET
iajs-4063	19	5	continuous	continuous	ADJ
iajs-4063	19	6	development	development	NOUN
iajs-4063	19	7	in	in	ADP
iajs-4063	19	8	the	the	DET
iajs-4063	19	9	fields	field	NOUN
iajs-4063	19	10	of	of	ADP
iajs-4063	19	11	science	science	NOUN
iajs-4063	19	12	has	have	AUX
iajs-4063	19	13	led	lead	VERB
iajs-4063	19	14	to	to	ADP
iajs-4063	19	15	the	the	DET
iajs-4063	19	16	formulation	formulation	NOUN
iajs-4063	19	17	of	of	ADP
iajs-4063	19	18	many	many	ADJ
iajs-4063	19	19	physical	physical	ADJ
iajs-4063	19	20	laws	law	NOUN
iajs-4063	19	21	,	,	PUNCT
iajs-4063	19	22	which	which	PRON
iajs-4063	19	23	often	often	ADV
iajs-4063	19	24	appear	appear	VERB
iajs-4063	19	25	in	in	ADP
iajs-4063	19	26	the	the	DET
iajs-4063	19	27	form	form	NOUN
iajs-4063	19	28	of	of	ADP
iajs-4063	19	29	des	des	PROPN
iajs-4063	19	30	when	when	SCONJ
iajs-4063	19	31	reformulated	reformulate	VERB
iajs-4063	19	32	in	in	ADP
iajs-4063	19	33	mathematical	mathematical	ADJ
iajs-4063	19	34	form	form	NOUN
iajs-4063	19	35	.	.	PUNCT
iajs-4063	20	1	we	we	PRON
iajs-4063	20	2	can	can	AUX
iajs-4063	20	3	also	also	ADV
iajs-4063	20	4	describe	describe	VERB
iajs-4063	20	5	applied	apply	VERB
iajs-4063	20	6	problems	problem	NOUN
iajs-4063	20	7	mathematically	mathematically	ADV
iajs-4063	20	8	using	use	VERB
iajs-4063	20	9	des	des	PROPN
iajs-4063	20	10	;	;	PUNCT
iajs-4063	20	11	thus	thus	ADV
iajs-4063	20	12	,	,	PUNCT
iajs-4063	20	13	des	des	X
iajs-4063	20	14	play	play	VERB
iajs-4063	20	15	a	a	DET
iajs-4063	20	16	critical	critical	ADJ
iajs-4063	20	17	role	role	NOUN
iajs-4063	20	18	in	in	ADP
iajs-4063	20	19	solving	solve	VERB
iajs-4063	20	20	practical	practical	ADJ
iajs-4063	20	21	problems	problem	NOUN
iajs-4063	20	22	(	(	PUNCT
iajs-4063	20	23	1	1	NUM
iajs-4063	20	24	,	,	PUNCT
iajs-4063	20	25	2	2	NUM
iajs-4063	20	26	)	)	PUNCT
iajs-4063	20	27	.	.	PUNCT
iajs-4063	21	1	the	the	DET
iajs-4063	21	2	theory	theory	NOUN
iajs-4063	21	3	of	of	ADP
iajs-4063	21	4	des	des	PROPN
iajs-4063	21	5	is	be	AUX
iajs-4063	21	6	a	a	DET
iajs-4063	21	7	great	great	ADJ
iajs-4063	21	8	tool	tool	NOUN
iajs-4063	21	9	in	in	ADP
iajs-4063	21	10	modeling	model	VERB
iajs-4063	21	11	many	many	ADJ
iajs-4063	21	12	scientific	scientific	ADJ
iajs-4063	21	13	problems	problem	NOUN
iajs-4063	21	14	in	in	ADP
iajs-4063	21	15	population	population	NOUN
iajs-4063	21	16	dynamics	dynamic	NOUN
iajs-4063	21	17	,	,	PUNCT
iajs-4063	21	18	optimal	optimal	ADJ
iajs-4063	21	19	control	control	NOUN
iajs-4063	21	20	,	,	PUNCT
iajs-4063	21	21	and	and	CCONJ
iajs-4063	21	22	nonlinear	nonlinear	ADJ
iajs-4063	21	23	problems	problem	NOUN
iajs-4063	21	24	(	(	PUNCT
iajs-4063	21	25	3	3	NUM
iajs-4063	21	26	)	)	PUNCT
iajs-4063	21	27	.	.	PUNCT
iajs-4063	22	1	there	there	PRON
iajs-4063	22	2	are	be	VERB
iajs-4063	22	3	several	several	ADJ
iajs-4063	22	4	methods	method	NOUN
iajs-4063	22	5	for	for	ADP
iajs-4063	22	6	solving	solve	VERB
iajs-4063	22	7	this	this	DET
iajs-4063	22	8	kind	kind	NOUN
iajs-4063	22	9	of	of	ADP
iajs-4063	22	10	equation	equation	NOUN
iajs-4063	22	11	,	,	PUNCT
iajs-4063	22	12	such	such	ADJ
iajs-4063	22	13	as	as	ADP
iajs-4063	22	14	the	the	DET
iajs-4063	22	15	variational	variational	ADJ
iajs-4063	22	16	iteration	iteration	NOUN
iajs-4063	22	17	method	method	NOUN
iajs-4063	22	18	and	and	CCONJ
iajs-4063	22	19	the	the	DET
iajs-4063	22	20	homotopy	homotopy	NOUN
iajs-4063	22	21	transforms	transform	VERB
iajs-4063	22	22	analysis	analysis	NOUN
iajs-4063	22	23	method	method	NOUN
iajs-4063	22	24	(	(	PUNCT
iajs-4063	22	25	2	2	NUM
iajs-4063	22	26	,	,	PUNCT
iajs-4063	22	27	4	4	NUM
iajs-4063	22	28	)	)	PUNCT
iajs-4063	22	29	.	.	PUNCT
iajs-4063	23	1	furthermore	furthermore	ADV
iajs-4063	23	2	,	,	PUNCT
iajs-4063	23	3	some	some	DET
iajs-4063	23	4	researchers	researcher	NOUN
iajs-4063	23	5	considered	consider	VERB
iajs-4063	23	6	some	some	DET
iajs-4063	23	7	properties	property	NOUN
iajs-4063	23	8	that	that	PRON
iajs-4063	23	9	describe	describe	VERB
iajs-4063	23	10	all	all	DET
iajs-4063	23	11	solutions	solution	NOUN
iajs-4063	23	12	,	,	PUNCT
iajs-4063	23	13	such	such	ADJ
iajs-4063	23	14	as	as	ADP
iajs-4063	23	15	asymptotic	asymptotic	ADJ
iajs-4063	23	16	behavior	behavior	NOUN
iajs-4063	23	17	,	,	PUNCT
iajs-4063	23	18	oscillatory	oscillatory	ADJ
iajs-4063	23	19	property	property	NOUN
iajs-4063	23	20	,	,	PUNCT
iajs-4063	23	21	and	and	CCONJ
iajs-4063	23	22	stability	stability	NOUN
iajs-4063	23	23	to	to	ADP
iajs-4063	23	24	different	different	ADJ
iajs-4063	23	25	kinds	kind	NOUN
iajs-4063	23	26	of	of	ADP
iajs-4063	23	27	des	des	X
iajs-4063	23	28	(	(	PUNCT
iajs-4063	23	29	5	5	NUM
iajs-4063	23	30	-	-	SYM
iajs-4063	23	31	8)	8)	NUM
iajs-4063	23	32	.	.	PUNCT
iajs-4063	24	1	in	in	ADP
iajs-4063	24	2	publications	publication	NOUN
iajs-4063	24	3	,	,	PUNCT
iajs-4063	24	4	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	5	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	6	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	7	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	VERB
iajs-4063	24	8	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	9	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	10	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	11	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	VERB
iajs-4063	24	12	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	13	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	14	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	15	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	VERB
iajs-4063	24	16	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	17	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	18	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	19	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	VERB
iajs-4063	24	20	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	21	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	22	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	23	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	VERB
iajs-4063	24	24	https://orcid.org/0009-0009-8387-9316	https://orcid.org/0009-0009-8387-9316	PROPN
iajs-4063	24	25	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	mailto:zahra.abd2203m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4063	24	26	https://orcid.org/0000-0002-5590-7991	https://orcid.org/0000-0002-5590-7991	PROPN
iajs-4063	24	27	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	mailto:aqeel.f.j@ihcoedu.uobaghdad.edu.iq	ADV
iajs-4063	24	28	ihjpas	ihjpas	PROPN
iajs-4063	24	29	.	.	PUNCT
iajs-4063	25	1	2025	2025	NUM
iajs-4063	25	2	,	,	PUNCT
iajs-4063	25	3	38(3	38(3	NUM
iajs-4063	25	4	)	)	PUNCT
iajs-4063	25	5	368	368	NUM
iajs-4063	25	6	different	different	ADJ
iajs-4063	25	7	authors	author	NOUN
iajs-4063	25	8	established	establish	VERB
iajs-4063	25	9	some	some	DET
iajs-4063	25	10	conditions	condition	NOUN
iajs-4063	25	11	for	for	ADP
iajs-4063	25	12	oscillation	oscillation	NOUN
iajs-4063	25	13	behavior	behavior	NOUN
iajs-4063	25	14	and	and	CCONJ
iajs-4063	25	15	asymptotic	asymptotic	ADJ
iajs-4063	25	16	property	property	NOUN
iajs-4063	25	17	for	for	ADP
iajs-4063	25	18	nonlinear	nonlinear	ADJ
iajs-4063	25	19	ndes	nde	NOUN
iajs-4063	25	20	(	(	PUNCT
iajs-4063	25	21	9	9	NUM
iajs-4063	25	22	-	-	SYM
iajs-4063	25	23	17	17	NUM
iajs-4063	25	24	)	)	PUNCT
iajs-4063	25	25	.	.	PUNCT
iajs-4063	26	1	2	2	X
iajs-4063	26	2	.	.	X
iajs-4063	26	3	materials	material	NOUN
iajs-4063	26	4	and	and	CCONJ
iajs-4063	26	5	methods	method	NOUN
iajs-4063	26	6	consider	consider	VERB
iajs-4063	26	7	nonlinear	nonlinear	ADJ
iajs-4063	26	8	nde	nde	NOUN
iajs-4063	26	9	with	with	ADP
iajs-4063	26	10	several	several	ADJ
iajs-4063	26	11	delays	delay	NOUN
iajs-4063	26	12	:	:	PUNCT
iajs-4063	26	13	[	[	PUNCT
iajs-4063	26	14	(	(	PUNCT
iajs-4063	26	15	(	(	PUNCT
iajs-4063	26	16	)	)	PUNCT
iajs-4063	26	17	)	)	PUNCT
iajs-4063	26	18	]	]	PUNCT
iajs-4063	27	1	(	(	PUNCT
iajs-4063	27	2	)	)	PUNCT
iajs-4063	27	3	(	(	PUNCT
iajs-4063	27	4	)	)	PUNCT
iajs-4063	27	5	supposing	suppose	VERB
iajs-4063	27	6	the	the	DET
iajs-4063	27	7	below	below	ADJ
iajs-4063	27	8	conditions	condition	NOUN
iajs-4063	27	9	hold	hold	VERB
iajs-4063	27	10	:	:	PUNCT
iajs-4063	27	11	1	1	NUM
iajs-4063	27	12	:	:	PUNCT
iajs-4063	27	13	,	,	PUNCT
iajs-4063	27	14	,	,	PUNCT
iajs-4063	27	15	[	[	PUNCT
iajs-4063	27	16	[	[	PUNCT
iajs-4063	27	17	with	with	ADP
iajs-4063	27	18	∫	∫	PROPN
iajs-4063	27	19	∫	∫	PROPN
iajs-4063	27	20	3	3	NUM
iajs-4063	27	21	:	:	PUNCT
iajs-4063	27	22	[	[	PUNCT
iajs-4063	27	23	with	with	SCONJ
iajs-4063	27	24	and	and	CCONJ
iajs-4063	27	25	the	the	DET
iajs-4063	27	26	delays	delay	NOUN
iajs-4063	27	27	are	be	AUX
iajs-4063	27	28	continuous	continuous	ADJ
iajs-4063	27	29	strictly	strictly	ADV
iajs-4063	27	30	increasing	increase	VERB
iajs-4063	27	31	and	and	CCONJ
iajs-4063	27	32	invertible	invertible	ADJ
iajs-4063	27	33	.	.	PUNCT
iajs-4063	28	1	4	4	NUM
iajs-4063	28	2	:	:	PUNCT
iajs-4063	28	3	,	,	PUNCT
iajs-4063	28	4	for	for	ADP
iajs-4063	28	5	and	and	CCONJ
iajs-4063	28	6	are	be	AUX
iajs-4063	28	7	positive	positive	ADJ
iajs-4063	28	8	constants	constant	NOUN
iajs-4063	28	9	.	.	PUNCT
iajs-4063	29	1	5	5	NUM
iajs-4063	29	2	:	:	PUNCT
iajs-4063	29	3	let	let	VERB
iajs-4063	29	4	(	(	PUNCT
iajs-4063	29	5	)	)	PUNCT
iajs-4063	29	6	twice	twice	ADV
iajs-4063	29	7	continuously	continuously	ADV
iajs-4063	29	8	differentiable	differentiable	ADJ
iajs-4063	29	9	in	in	ADP
iajs-4063	29	10	(	(	PUNCT
iajs-4063	29	11	1	1	X
iajs-4063	29	12	)	)	PUNCT
iajs-4063	29	13	definition	definition	NOUN
iajs-4063	29	14	1.1	1.1	NUM
iajs-4063	29	15	(	(	PUNCT
iajs-4063	29	16	18	18	NUM
iajs-4063	29	17	)	)	PUNCT
iajs-4063	29	18	a	a	DET
iajs-4063	29	19	nontrivial	nontrivial	ADJ
iajs-4063	29	20	solution	solution	NOUN
iajs-4063	29	21	to	to	ADP
iajs-4063	29	22	eq	eq	PROPN
iajs-4063	29	23	.	.	PUNCT
iajs-4063	30	1	(	(	PUNCT
iajs-4063	30	2	1	1	X
iajs-4063	30	3	)	)	PUNCT
iajs-4063	30	4	is	be	AUX
iajs-4063	30	5	called	call	VERB
iajs-4063	30	6	non	non	ADJ
iajs-4063	30	7	-	-	ADJ
iajs-4063	30	8	oscillatory	oscillatory	ADJ
iajs-4063	30	9	if	if	SCONJ
iajs-4063	30	10	it	it	PRON
iajs-4063	30	11	is	be	AUX
iajs-4063	30	12	either	either	CCONJ
iajs-4063	30	13	eventually	eventually	ADV
iajs-4063	30	14	a	a	DET
iajs-4063	30	15	positive	positive	ADJ
iajs-4063	30	16	solution	solution	NOUN
iajs-4063	30	17	or	or	CCONJ
iajs-4063	30	18	it	it	PRON
iajs-4063	30	19	is	be	AUX
iajs-4063	30	20	eventually	eventually	ADV
iajs-4063	30	21	a	a	DET
iajs-4063	30	22	negative	negative	ADJ
iajs-4063	30	23	,	,	PUNCT
iajs-4063	30	24	if	if	SCONJ
iajs-4063	30	25	it	it	PRON
iajs-4063	30	26	does	do	VERB
iajs-4063	30	27	n’t	not	PART
iajs-4063	30	28	,	,	PUNCT
iajs-4063	30	29	so	so	SCONJ
iajs-4063	30	30	satisfies	satisfy	VERB
iajs-4063	30	31	oscillatory	oscillatory	ADJ
iajs-4063	30	32	property	property	NOUN
iajs-4063	30	33	.	.	PUNCT
iajs-4063	31	1	3	3	X
iajs-4063	31	2	.	.	X
iajs-4063	31	3	results	result	NOUN
iajs-4063	31	4	theorem1	theorem1	PROPN
iajs-4063	31	5	:	:	PUNCT
iajs-4063	31	6	assume	assume	VERB
iajs-4063	31	7	that	that	SCONJ
iajs-4063	31	8	h1h5	h1h5	PRON
iajs-4063	31	9	are	be	AUX
iajs-4063	31	10	true	true	ADJ
iajs-4063	31	11	with	with	ADP
iajs-4063	31	12	condition	condition	NOUN
iajs-4063	31	13	:	:	PUNCT
iajs-4063	31	14	∫	∫	PROPN
iajs-4063	31	15	∫	∫	PROPN
iajs-4063	31	16	(	(	PUNCT
iajs-4063	31	17	2	2	NUM
iajs-4063	31	18	)	)	PUNCT
iajs-4063	31	19	min	min	NOUN
iajs-4063	31	20	,	,	PUNCT
iajs-4063	31	21	(	(	PUNCT
iajs-4063	31	22	(	(	PUNCT
iajs-4063	31	23	)	)	PUNCT
iajs-4063	31	24	)	)	PUNCT
iajs-4063	31	25	(	(	PUNCT
iajs-4063	31	26	(	(	PUNCT
iajs-4063	31	27	)	)	PUNCT
iajs-4063	31	28	)	)	PUNCT
iajs-4063	31	29	mi	mi	PROPN
iajs-4063	31	30	,	,	PUNCT
iajs-4063	31	31	(	(	PUNCT
iajs-4063	31	32	(	(	PUNCT
iajs-4063	31	33	)	)	PUNCT
iajs-4063	31	34	)	)	PUNCT
iajs-4063	31	35	(	(	PUNCT
iajs-4063	31	36	(	(	PUNCT
iajs-4063	31	37	)	)	PUNCT
iajs-4063	31	38	)	)	PUNCT
iajs-4063	31	39	then	then	ADV
iajs-4063	31	40	the	the	DET
iajs-4063	31	41	oscillation	oscillation	NOUN
iajs-4063	31	42	property	property	NOUN
iajs-4063	31	43	holds	hold	VERB
iajs-4063	31	44	.	.	PUNCT
iajs-4063	32	1	proof	proof	NOUN
iajs-4063	32	2	:	:	PUNCT
iajs-4063	32	3	let	let	VERB
iajs-4063	32	4	a	a	DET
iajs-4063	32	5	solution	solution	NOUN
iajs-4063	32	6	has	have	VERB
iajs-4063	32	7	non	non	ADJ
iajs-4063	32	8	-	-	ADJ
iajs-4063	32	9	oscillatory	oscillatory	ADJ
iajs-4063	32	10	behaviour	behaviour	NOUN
iajs-4063	32	11	to	to	ADP
iajs-4063	32	12	eq	eq	PROPN
iajs-4063	32	13	.	.	PUNCT
iajs-4063	33	1	(	(	PUNCT
iajs-4063	33	2	1	1	NUM
iajs-4063	33	3	)	)	PUNCT
iajs-4063	33	4	.	.	PUNCT
iajs-4063	34	1	so	so	ADV
iajs-4063	34	2	,	,	PUNCT
iajs-4063	34	3	without	without	ADP
iajs-4063	34	4	loss	loss	NOUN
iajs-4063	34	5	of	of	ADP
iajs-4063	34	6	generality	generality	NOUN
iajs-4063	34	7	,	,	PUNCT
iajs-4063	34	8	we	we	PRON
iajs-4063	34	9	suppose	suppose	VERB
iajs-4063	34	10	that	that	SCONJ
iajs-4063	34	11	the	the	DET
iajs-4063	34	12	solution	solution	NOUN
iajs-4063	34	13	is	be	AUX
iajs-4063	34	14	eventually	eventually	ADV
iajs-4063	34	15	positive	positive	ADJ
iajs-4063	34	16	it	it	PRON
iajs-4063	34	17	is	be	AUX
iajs-4063	34	18	obvious	obvious	ADJ
iajs-4063	34	19	that	that	PRON
iajs-4063	34	20	.	.	PUNCT
iajs-4063	35	1	from	from	ADP
iajs-4063	35	2	equation	equation	NOUN
iajs-4063	35	3	(	(	PUNCT
iajs-4063	35	4	1	1	NUM
iajs-4063	35	5	)	)	PUNCT
iajs-4063	35	6	,	,	PUNCT
iajs-4063	35	7	we	we	PRON
iajs-4063	35	8	get	get	VERB
iajs-4063	35	9	:	:	PUNCT
iajs-4063	35	10	[	[	PUNCT
iajs-4063	35	11	]	]	X
iajs-4063	35	12	,	,	PUNCT
iajs-4063	35	13	so	so	ADV
iajs-4063	35	14	is	be	AUX
iajs-4063	35	15	nonincreasing	nonincrease	VERB
iajs-4063	35	16	eventually	eventually	ADV
iajs-4063	35	17	.	.	PUNCT
iajs-4063	36	1	[	[	PUNCT
iajs-4063	36	2	(	(	PUNCT
iajs-4063	36	3	)	)	PUNCT
iajs-4063	36	4	]	]	PUNCT
iajs-4063	36	5	(	(	PUNCT
iajs-4063	36	6	(	(	PUNCT
iajs-4063	36	7	)	)	PUNCT
iajs-4063	36	8	)	)	PUNCT
iajs-4063	36	9	(	(	PUNCT
iajs-4063	36	10	)	)	PUNCT
iajs-4063	36	11	(	(	PUNCT
iajs-4063	36	12	)	)	PUNCT
iajs-4063	36	13	is	be	AUX
iajs-4063	36	14	nonincreasing	nonincrease	VERB
iajs-4063	36	15	,	,	PUNCT
iajs-4063	36	16	we	we	PRON
iajs-4063	36	17	assume	assume	VERB
iajs-4063	36	18	that	that	SCONJ
iajs-4063	36	19	(	(	PUNCT
iajs-4063	36	20	)	)	PUNCT
iajs-4063	36	21	otherwise	otherwise	ADV
iajs-4063	36	22	,	,	PUNCT
iajs-4063	36	23	there	there	PRON
iajs-4063	36	24	exists	exist	VERB
iajs-4063	36	25	(	(	PUNCT
iajs-4063	36	26	)	)	PUNCT
iajs-4063	36	27	for	for	ADP
iajs-4063	36	28	then	then	ADV
iajs-4063	36	29	*	*	PUNCT
iajs-4063	36	30	(	(	PUNCT
iajs-4063	36	31	)	)	PUNCT
iajs-4063	36	32	(	(	PUNCT
iajs-4063	36	33	)	)	PUNCT
iajs-4063	37	1	+	+	CCONJ
iajs-4063	37	2	.	.	PUNCT
iajs-4063	38	1	∫	∫	PROPN
iajs-4063	38	2	(	(	PUNCT
iajs-4063	38	3	3	3	NUM
iajs-4063	38	4	)	)	PUNCT
iajs-4063	38	5	when	when	SCONJ
iajs-4063	38	6	in	in	ADP
iajs-4063	38	7	(	(	PUNCT
iajs-4063	38	8	3	3	NUM
iajs-4063	38	9	)	)	PUNCT
iajs-4063	38	10	,	,	PUNCT
iajs-4063	38	11	then	then	ADV
iajs-4063	38	12	contradiction	contradiction	NOUN
iajs-4063	38	13	.	.	PUNCT
iajs-4063	39	1	so	so	ADV
iajs-4063	39	2	,	,	PUNCT
iajs-4063	39	3	we	we	PRON
iajs-4063	39	4	have	have	AUX
iajs-4063	39	5	(	(	PUNCT
iajs-4063	39	6	)	)	PUNCT
iajs-4063	39	7	ihjpas	ihjpas	PROPN
iajs-4063	39	8	.	.	PUNCT
iajs-4063	40	1	2025	2025	NUM
iajs-4063	40	2	,	,	PUNCT
iajs-4063	40	3	38(3	38(3	NUM
iajs-4063	40	4	)	)	PUNCT
iajs-4063	40	5	369	369	NUM
iajs-4063	40	6	we	we	PRON
iajs-4063	40	7	replace	replace	VERB
iajs-4063	40	8	(	(	PUNCT
iajs-4063	40	9	)	)	PUNCT
iajs-4063	40	10	instead	instead	ADV
iajs-4063	40	11	of	of	ADP
iajs-4063	40	12	in	in	ADP
iajs-4063	40	13	(	(	PUNCT
iajs-4063	40	14	1	1	X
iajs-4063	40	15	)	)	PUNCT
iajs-4063	40	16	once	once	ADV
iajs-4063	40	17	and	and	CCONJ
iajs-4063	40	18	(	(	PUNCT
iajs-4063	40	19	)	)	PUNCT
iajs-4063	40	20	instead	instead	ADV
iajs-4063	40	21	of	of	ADP
iajs-4063	40	22	in	in	ADP
iajs-4063	40	23	(	(	PUNCT
iajs-4063	40	24	1	1	X
iajs-4063	40	25	)	)	PUNCT
iajs-4063	40	26	a	a	DET
iajs-4063	40	27	second	second	ADJ
iajs-4063	40	28	time	time	NOUN
iajs-4063	40	29	.	.	PUNCT
iajs-4063	41	1	so	so	ADV
iajs-4063	41	2	,	,	PUNCT
iajs-4063	41	3	we	we	PRON
iajs-4063	41	4	get	get	VERB
iajs-4063	41	5	:	:	PUNCT
iajs-4063	41	6	*	*	PUNCT
iajs-4063	41	7	(	(	PUNCT
iajs-4063	41	8	)	)	PUNCT
iajs-4063	41	9	(	(	PUNCT
iajs-4063	41	10	(	(	PUNCT
iajs-4063	41	11	(	(	PUNCT
iajs-4063	41	12	)	)	PUNCT
iajs-4063	41	13	)	)	PUNCT
iajs-4063	42	1	(	(	PUNCT
iajs-4063	42	2	(	(	PUNCT
iajs-4063	42	3	)	)	PUNCT
iajs-4063	42	4	)	)	PUNCT
iajs-4063	43	1	(	(	PUNCT
iajs-4063	43	2	(	(	PUNCT
iajs-4063	43	3	(	(	PUNCT
iajs-4063	43	4	)	)	PUNCT
iajs-4063	43	5	)	)	PUNCT
iajs-4063	43	6	)	)	PUNCT
iajs-4063	43	7	)	)	PUNCT
iajs-4063	44	1	+	+	CCONJ
iajs-4063	44	2	(	(	PUNCT
iajs-4063	44	3	(	(	PUNCT
iajs-4063	44	4	)	)	PUNCT
iajs-4063	44	5	)	)	PUNCT
iajs-4063	45	1	(	(	PUNCT
iajs-4063	45	2	(	(	PUNCT
iajs-4063	45	3	(	(	PUNCT
iajs-4063	45	4	)	)	PUNCT
iajs-4063	45	5	)	)	PUNCT
iajs-4063	45	6	)	)	PUNCT
iajs-4063	46	1	(	(	PUNCT
iajs-4063	46	2	(	(	PUNCT
iajs-4063	46	3	)	)	PUNCT
iajs-4063	46	4	)	)	PUNCT
iajs-4063	47	1	(	(	PUNCT
iajs-4063	47	2	(	(	PUNCT
iajs-4063	47	3	(	(	PUNCT
iajs-4063	47	4	)	)	PUNCT
iajs-4063	47	5	)	)	PUNCT
iajs-4063	47	6	)	)	PUNCT
iajs-4063	47	7	(	(	PUNCT
iajs-4063	47	8	4	4	X
iajs-4063	47	9	)	)	PUNCT
iajs-4063	47	10	*	*	PUNCT
iajs-4063	47	11	(	(	PUNCT
iajs-4063	47	12	)	)	PUNCT
iajs-4063	47	13	(	(	PUNCT
iajs-4063	47	14	(	(	PUNCT
iajs-4063	47	15	(	(	PUNCT
iajs-4063	47	16	)	)	PUNCT
iajs-4063	47	17	)	)	PUNCT
iajs-4063	47	18	(	(	PUNCT
iajs-4063	47	19	(	(	PUNCT
iajs-4063	47	20	)	)	PUNCT
iajs-4063	47	21	)	)	PUNCT
iajs-4063	47	22	(	(	PUNCT
iajs-4063	47	23	(	(	PUNCT
iajs-4063	47	24	)	)	PUNCT
iajs-4063	47	25	)	)	PUNCT
iajs-4063	47	26	)	)	PUNCT
iajs-4063	48	1	+	+	CCONJ
iajs-4063	48	2	(	(	PUNCT
iajs-4063	48	3	(	(	PUNCT
iajs-4063	48	4	)	)	PUNCT
iajs-4063	48	5	)	)	PUNCT
iajs-4063	49	1	(	(	PUNCT
iajs-4063	49	2	(	(	PUNCT
iajs-4063	49	3	(	(	PUNCT
iajs-4063	49	4	)	)	PUNCT
iajs-4063	49	5	)	)	PUNCT
iajs-4063	49	6	)	)	PUNCT
iajs-4063	50	1	(	(	PUNCT
iajs-4063	50	2	(	(	PUNCT
iajs-4063	50	3	)	)	PUNCT
iajs-4063	50	4	)	)	PUNCT
iajs-4063	51	1	(	(	PUNCT
iajs-4063	51	2	(	(	PUNCT
iajs-4063	51	3	(	(	PUNCT
iajs-4063	51	4	)	)	PUNCT
iajs-4063	51	5	)	)	PUNCT
iajs-4063	51	6	)	)	PUNCT
iajs-4063	51	7	(	(	PUNCT
iajs-4063	51	8	5	5	X
iajs-4063	51	9	)	)	PUNCT
iajs-4063	51	10	by	by	ADP
iajs-4063	51	11	multiplying	multiply	VERB
iajs-4063	51	12	equations	equation	NOUN
iajs-4063	51	13	and	and	CCONJ
iajs-4063	51	14	by	by	ADP
iajs-4063	51	15	and	and	CCONJ
iajs-4063	51	16	summing	sum	VERB
iajs-4063	51	17	equations	equation	NOUN
iajs-4063	51	18	and	and	CCONJ
iajs-4063	51	19	we	we	PRON
iajs-4063	51	20	get	get	VERB
iajs-4063	51	21	:	:	PUNCT
iajs-4063	51	22	*	*	PUNCT
iajs-4063	51	23	(	(	PUNCT
iajs-4063	51	24	(	(	PUNCT
iajs-4063	51	25	)	)	PUNCT
iajs-4063	51	26	)	)	PUNCT
iajs-4063	52	1	+	+	CCONJ
iajs-4063	52	2	(	(	PUNCT
iajs-4063	52	3	)	)	PUNCT
iajs-4063	52	4	(	(	PUNCT
iajs-4063	52	5	)	)	PUNCT
iajs-4063	52	6	*	*	PUNCT
iajs-4063	52	7	(	(	PUNCT
iajs-4063	52	8	)	)	PUNCT
iajs-4063	52	9	(	(	PUNCT
iajs-4063	52	10	(	(	PUNCT
iajs-4063	52	11	(	(	PUNCT
iajs-4063	52	12	)	)	PUNCT
iajs-4063	52	13	)	)	PUNCT
iajs-4063	53	1	(	(	PUNCT
iajs-4063	53	2	(	(	PUNCT
iajs-4063	53	3	)	)	PUNCT
iajs-4063	53	4	)	)	PUNCT
iajs-4063	54	1	(	(	PUNCT
iajs-4063	54	2	(	(	PUNCT
iajs-4063	54	3	(	(	PUNCT
iajs-4063	54	4	)	)	PUNCT
iajs-4063	54	5	)	)	PUNCT
iajs-4063	54	6	)	)	PUNCT
iajs-4063	54	7	)	)	PUNCT
iajs-4063	55	1	+	+	CCONJ
iajs-4063	55	2	(	(	PUNCT
iajs-4063	55	3	(	(	PUNCT
iajs-4063	55	4	)	)	PUNCT
iajs-4063	55	5	)	)	PUNCT
iajs-4063	56	1	(	(	PUNCT
iajs-4063	56	2	(	(	PUNCT
iajs-4063	56	3	(	(	PUNCT
iajs-4063	56	4	)	)	PUNCT
iajs-4063	56	5	)	)	PUNCT
iajs-4063	56	6	)	)	PUNCT
iajs-4063	57	1	(	(	PUNCT
iajs-4063	57	2	(	(	PUNCT
iajs-4063	57	3	)	)	PUNCT
iajs-4063	57	4	)	)	PUNCT
iajs-4063	57	5	(	(	PUNCT
iajs-4063	57	6	(	(	PUNCT
iajs-4063	57	7	(	(	PUNCT
iajs-4063	57	8	)	)	PUNCT
iajs-4063	57	9	)	)	PUNCT
iajs-4063	57	10	)	)	PUNCT
iajs-4063	58	1	*	*	PUNCT
iajs-4063	58	2	(	(	PUNCT
iajs-4063	58	3	)	)	PUNCT
iajs-4063	58	4	(	(	PUNCT
iajs-4063	58	5	(	(	PUNCT
iajs-4063	58	6	(	(	PUNCT
iajs-4063	58	7	)	)	PUNCT
iajs-4063	58	8	)	)	PUNCT
iajs-4063	59	1	(	(	PUNCT
iajs-4063	59	2	(	(	PUNCT
iajs-4063	59	3	)	)	PUNCT
iajs-4063	59	4	)	)	PUNCT
iajs-4063	60	1	(	(	PUNCT
iajs-4063	60	2	(	(	PUNCT
iajs-4063	60	3	)	)	PUNCT
iajs-4063	60	4	)	)	PUNCT
iajs-4063	60	5	)	)	PUNCT
iajs-4063	61	1	+	+	CCONJ
iajs-4063	61	2	(	(	PUNCT
iajs-4063	61	3	(	(	PUNCT
iajs-4063	61	4	)	)	PUNCT
iajs-4063	61	5	)	)	PUNCT
iajs-4063	62	1	(	(	PUNCT
iajs-4063	62	2	(	(	PUNCT
iajs-4063	62	3	(	(	PUNCT
iajs-4063	62	4	)	)	PUNCT
iajs-4063	62	5	)	)	PUNCT
iajs-4063	62	6	)	)	PUNCT
iajs-4063	63	1	(	(	PUNCT
iajs-4063	63	2	(	(	PUNCT
iajs-4063	63	3	)	)	PUNCT
iajs-4063	63	4	)	)	PUNCT
iajs-4063	63	5	(	(	PUNCT
iajs-4063	63	6	(	(	PUNCT
iajs-4063	63	7	(	(	PUNCT
iajs-4063	63	8	)	)	PUNCT
iajs-4063	63	9	)	)	PUNCT
iajs-4063	63	10	)	)	PUNCT
iajs-4063	64	1	(	(	PUNCT
iajs-4063	64	2	6	6	X
iajs-4063	64	3	)	)	PUNCT
iajs-4063	64	4	substituting	substitute	VERB
iajs-4063	64	5	by	by	ADV
iajs-4063	64	6	and	and	CCONJ
iajs-4063	64	7	in	in	ADP
iajs-4063	64	8	(	(	PUNCT
iajs-4063	64	9	6	6	NUM
iajs-4063	64	10	)	)	PUNCT
iajs-4063	64	11	with	with	ADP
iajs-4063	64	12	deleting	delete	VERB
iajs-4063	64	13	some	some	DET
iajs-4063	64	14	terms	term	NOUN
iajs-4063	64	15	:	:	PUNCT
iajs-4063	64	16	*	*	PUNCT
iajs-4063	64	17	(	(	PUNCT
iajs-4063	64	18	)	)	PUNCT
iajs-4063	64	19	+	+	CCONJ
iajs-4063	64	20	(	(	PUNCT
iajs-4063	64	21	)	)	PUNCT
iajs-4063	64	22	(	(	PUNCT
iajs-4063	64	23	)	)	PUNCT
iajs-4063	64	24	*	*	PUNCT
iajs-4063	64	25	(	(	PUNCT
iajs-4063	64	26	)	)	PUNCT
iajs-4063	64	27	(	(	PUNCT
iajs-4063	64	28	(	(	PUNCT
iajs-4063	64	29	(	(	PUNCT
iajs-4063	64	30	)	)	PUNCT
iajs-4063	64	31	)	)	PUNCT
iajs-4063	64	32	)	)	PUNCT
iajs-4063	65	1	+	+	CCONJ
iajs-4063	65	2	(	(	PUNCT
iajs-4063	65	3	(	(	PUNCT
iajs-4063	65	4	(	(	PUNCT
iajs-4063	65	5	)	)	PUNCT
iajs-4063	65	6	)	)	PUNCT
iajs-4063	65	7	)	)	PUNCT
iajs-4063	66	1	*	*	PUNCT
iajs-4063	66	2	(	(	PUNCT
iajs-4063	66	3	)	)	PUNCT
iajs-4063	66	4	(	(	PUNCT
iajs-4063	66	5	(	(	PUNCT
iajs-4063	66	6	(	(	PUNCT
iajs-4063	66	7	)	)	PUNCT
iajs-4063	66	8	)	)	PUNCT
iajs-4063	66	9	)	)	PUNCT
iajs-4063	67	1	+	+	CCONJ
iajs-4063	67	2	(	(	PUNCT
iajs-4063	67	3	(	(	PUNCT
iajs-4063	67	4	(	(	PUNCT
iajs-4063	67	5	)	)	PUNCT
iajs-4063	67	6	)	)	PUNCT
iajs-4063	67	7	)	)	PUNCT
iajs-4063	68	1	(	(	PUNCT
iajs-4063	68	2	7	7	X
iajs-4063	68	3	)	)	PUNCT
iajs-4063	68	4	from	from	ADP
iajs-4063	68	5	condition	condition	NOUN
iajs-4063	68	6	h4	h4	NOUN
iajs-4063	68	7	,	,	PUNCT
iajs-4063	68	8	we	we	PRON
iajs-4063	68	9	have	have	VERB
iajs-4063	68	10	:	:	PUNCT
iajs-4063	68	11	[	[	PUNCT
iajs-4063	68	12	(	(	PUNCT
iajs-4063	68	13	)	)	PUNCT
iajs-4063	68	14	]	]	PUNCT
iajs-4063	69	1	[	[	PUNCT
iajs-4063	69	2	(	(	PUNCT
iajs-4063	69	3	)	)	PUNCT
iajs-4063	69	4	(	(	PUNCT
iajs-4063	69	5	(	(	PUNCT
iajs-4063	69	6	(	(	PUNCT
iajs-4063	69	7	)	)	PUNCT
iajs-4063	69	8	)	)	PUNCT
iajs-4063	69	9	)	)	PUNCT
iajs-4063	69	10	]	]	PUNCT
iajs-4063	69	11	(	(	PUNCT
iajs-4063	69	12	(	(	PUNCT
iajs-4063	69	13	)	)	PUNCT
iajs-4063	69	14	)	)	PUNCT
iajs-4063	69	15	[	[	PUNCT
iajs-4063	69	16	(	(	PUNCT
iajs-4063	69	17	)	)	PUNCT
iajs-4063	69	18	(	(	PUNCT
iajs-4063	69	19	(	(	PUNCT
iajs-4063	69	20	(	(	PUNCT
iajs-4063	69	21	)	)	PUNCT
iajs-4063	69	22	)	)	PUNCT
iajs-4063	69	23	)	)	PUNCT
iajs-4063	69	24	]	]	PUNCT
iajs-4063	69	25	(	(	PUNCT
iajs-4063	69	26	(	(	PUNCT
iajs-4063	69	27	)	)	PUNCT
iajs-4063	69	28	)	)	PUNCT
iajs-4063	70	1	or	or	CCONJ
iajs-4063	70	2	*	*	PUNCT
iajs-4063	70	3	(	(	PUNCT
iajs-4063	70	4	)	)	PUNCT
iajs-4063	70	5	+	+	NUM
iajs-4063	70	6	*	*	PUNCT
iajs-4063	70	7	(	(	PUNCT
iajs-4063	70	8	)	)	PUNCT
iajs-4063	70	9	(	(	PUNCT
iajs-4063	70	10	(	(	PUNCT
iajs-4063	70	11	(	(	PUNCT
iajs-4063	70	12	)	)	PUNCT
iajs-4063	70	13	)	)	PUNCT
iajs-4063	70	14	)	)	PUNCT
iajs-4063	71	1	+	+	PUNCT
iajs-4063	72	1	*	*	PUNCT
iajs-4063	72	2	(	(	PUNCT
iajs-4063	72	3	)	)	PUNCT
iajs-4063	72	4	(	(	PUNCT
iajs-4063	72	5	(	(	PUNCT
iajs-4063	72	6	(	(	PUNCT
iajs-4063	72	7	)	)	PUNCT
iajs-4063	72	8	)	)	PUNCT
iajs-4063	72	9	)	)	PUNCT
iajs-4063	73	1	+	+	CCONJ
iajs-4063	73	2	(	(	PUNCT
iajs-4063	73	3	8)	8)	NUM
iajs-4063	73	4	we	we	PRON
iajs-4063	73	5	integrate	integrate	VERB
iajs-4063	73	6	the	the	DET
iajs-4063	73	7	inequality	inequality	NOUN
iajs-4063	73	8	(	(	PUNCT
iajs-4063	73	9	8)	8)	NUM
iajs-4063	73	10	from	from	ADP
iajs-4063	73	11	to	to	ADP
iajs-4063	73	12	:	:	PUNCT
iajs-4063	73	13	ihjpas	ihjpas	PROPN
iajs-4063	73	14	.	.	PUNCT
iajs-4063	74	1	2025	2025	NUM
iajs-4063	74	2	,	,	PUNCT
iajs-4063	74	3	38(3	38(3	NUM
iajs-4063	74	4	)	)	PUNCT
iajs-4063	74	5	370	370	NUM
iajs-4063	74	6	∫	∫	PROPN
iajs-4063	74	7	∫	∫	PROPN
iajs-4063	74	8	(	(	PUNCT
iajs-4063	74	9	)	)	PUNCT
iajs-4063	74	10	(	(	PUNCT
iajs-4063	74	11	)	)	PUNCT
iajs-4063	74	12	(	(	PUNCT
iajs-4063	74	13	(	(	PUNCT
iajs-4063	74	14	)	)	PUNCT
iajs-4063	74	15	)	)	PUNCT
iajs-4063	74	16	(	(	PUNCT
iajs-4063	74	17	(	(	PUNCT
iajs-4063	74	18	(	(	PUNCT
iajs-4063	74	19	)	)	PUNCT
iajs-4063	74	20	)	)	PUNCT
iajs-4063	74	21	)	)	PUNCT
iajs-4063	75	1	(	(	PUNCT
iajs-4063	75	2	(	(	PUNCT
iajs-4063	75	3	)	)	PUNCT
iajs-4063	75	4	)	)	PUNCT
iajs-4063	75	5	(	(	PUNCT
iajs-4063	75	6	(	(	PUNCT
iajs-4063	75	7	(	(	PUNCT
iajs-4063	75	8	)	)	PUNCT
iajs-4063	75	9	)	)	PUNCT
iajs-4063	75	10	)	)	PUNCT
iajs-4063	76	1	(	(	PUNCT
iajs-4063	76	2	)	)	PUNCT
iajs-4063	76	3	(	(	PUNCT
iajs-4063	76	4	(	(	PUNCT
iajs-4063	76	5	)	)	PUNCT
iajs-4063	76	6	)	)	PUNCT
iajs-4063	77	1	(	(	PUNCT
iajs-4063	77	2	(	(	PUNCT
iajs-4063	77	3	)	)	PUNCT
iajs-4063	77	4	)	)	PUNCT
iajs-4063	77	5	(	(	PUNCT
iajs-4063	77	6	)	)	PUNCT
iajs-4063	77	7	is	be	AUX
iajs-4063	77	8	nonincreasing	nonincrease	VERB
iajs-4063	77	9	function	function	NOUN
iajs-4063	77	10	,	,	PUNCT
iajs-4063	77	11	so	so	SCONJ
iajs-4063	77	12	as	as	SCONJ
iajs-4063	77	13	goes	go	VERB
iajs-4063	77	14	to	to	ADP
iajs-4063	77	15	infinity	infinity	NOUN
iajs-4063	77	16	,	,	PUNCT
iajs-4063	77	17	we	we	PRON
iajs-4063	77	18	conclude	conclude	VERB
iajs-4063	77	19	that	that	PRON
iajs-4063	77	20	:	:	PUNCT
iajs-4063	77	21	∫	∫	PROPN
iajs-4063	77	22	∫	∫	PROPN
iajs-4063	77	23	a	a	DET
iajs-4063	77	24	contradiction	contradiction	NOUN
iajs-4063	77	25	!	!	PUNCT
iajs-4063	78	1	theorem2	theorem2	NOUN
iajs-4063	78	2	:	:	PUNCT
iajs-4063	78	3	assume	assume	VERB
iajs-4063	78	4	that	that	SCONJ
iajs-4063	78	5	h1h5	h1h5	NOUN
iajs-4063	78	6	hold	hold	VERB
iajs-4063	78	7	,	,	PUNCT
iajs-4063	78	8	with	with	ADP
iajs-4063	78	9	condition	condition	NOUN
iajs-4063	78	10	(	(	PUNCT
iajs-4063	78	11	2	2	NUM
iajs-4063	78	12	)	)	PUNCT
iajs-4063	78	13	in	in	ADP
iajs-4063	78	14	addition	addition	NOUN
iajs-4063	78	15	to	to	ADP
iajs-4063	78	16	:	:	PUNCT
iajs-4063	78	17	∫	∫	PROPN
iajs-4063	78	18	(	(	PUNCT
iajs-4063	78	19	)	)	PUNCT
iajs-4063	78	20	∫	∫	PROPN
iajs-4063	78	21	.	.	PUNCT
iajs-4063	79	1	(	(	PUNCT
iajs-4063	79	2	(	(	PUNCT
iajs-4063	79	3	(	(	PUNCT
iajs-4063	79	4	)	)	PUNCT
iajs-4063	79	5	)	)	PUNCT
iajs-4063	79	6	)	)	PUNCT
iajs-4063	79	7	/	/	SYM
iajs-4063	79	8	(	(	PUNCT
iajs-4063	79	9	(	(	PUNCT
iajs-4063	79	10	(	(	PUNCT
iajs-4063	79	11	)	)	PUNCT
iajs-4063	79	12	)	)	PUNCT
iajs-4063	79	13	)	)	PUNCT
iajs-4063	80	1	(	(	PUNCT
iajs-4063	80	2	9	9	X
iajs-4063	80	3	)	)	PUNCT
iajs-4063	80	4	then	then	ADV
iajs-4063	80	5	the	the	DET
iajs-4063	80	6	oscillation	oscillation	NOUN
iajs-4063	80	7	property	property	NOUN
iajs-4063	80	8	holds	hold	VERB
iajs-4063	80	9	.	.	PUNCT
iajs-4063	81	1	proof	proof	NOUN
iajs-4063	81	2	:	:	PUNCT
iajs-4063	81	3	let	let	VERB
iajs-4063	81	4	a	a	DET
iajs-4063	81	5	solution	solution	NOUN
iajs-4063	81	6	has	have	VERB
iajs-4063	81	7	non	non	ADJ
iajs-4063	81	8	-	-	ADJ
iajs-4063	81	9	oscillatory	oscillatory	ADJ
iajs-4063	81	10	behaviour	behaviour	NOUN
iajs-4063	81	11	to	to	ADP
iajs-4063	81	12	eq	eq	PROPN
iajs-4063	81	13	.	.	PUNCT
iajs-4063	82	1	(	(	PUNCT
iajs-4063	82	2	1	1	NUM
iajs-4063	82	3	)	)	PUNCT
iajs-4063	82	4	.	.	PUNCT
iajs-4063	83	1	so	so	ADV
iajs-4063	83	2	,	,	PUNCT
iajs-4063	83	3	without	without	ADP
iajs-4063	83	4	loss	loss	NOUN
iajs-4063	83	5	of	of	ADP
iajs-4063	83	6	generality	generality	NOUN
iajs-4063	83	7	,	,	PUNCT
iajs-4063	83	8	we	we	PRON
iajs-4063	83	9	suppose	suppose	VERB
iajs-4063	83	10	that	that	SCONJ
iajs-4063	83	11	the	the	DET
iajs-4063	83	12	solution	solution	NOUN
iajs-4063	83	13	is	be	AUX
iajs-4063	83	14	eventually	eventually	ADV
iajs-4063	83	15	positive	positive	ADJ
iajs-4063	83	16	it	it	PRON
iajs-4063	83	17	is	be	AUX
iajs-4063	83	18	obvious	obvious	ADJ
iajs-4063	83	19	that	that	PRON
iajs-4063	83	20	.	.	PUNCT
iajs-4063	84	1	in	in	ADP
iajs-4063	84	2	the	the	DET
iajs-4063	84	3	same	same	ADJ
iajs-4063	84	4	steps	step	NOUN
iajs-4063	84	5	as	as	ADP
iajs-4063	84	6	theorem	theorem	NOUN
iajs-4063	84	7	(	(	PUNCT
iajs-4063	84	8	1	1	NUM
iajs-4063	84	9	)	)	PUNCT
iajs-4063	84	10	,	,	PUNCT
iajs-4063	84	11	we	we	PRON
iajs-4063	84	12	get	get	VERB
iajs-4063	84	13	inequality	inequality	NOUN
iajs-4063	84	14	(	(	PUNCT
iajs-4063	84	15	8)	8)	NUM
iajs-4063	84	16	.	.	PUNCT
iajs-4063	85	1	let	let	VERB
iajs-4063	85	2	(	(	PUNCT
iajs-4063	85	3	)	)	PUNCT
iajs-4063	85	4	(	(	PUNCT
iajs-4063	85	5	(	(	PUNCT
iajs-4063	85	6	)	)	PUNCT
iajs-4063	85	7	)	)	PUNCT
iajs-4063	85	8	(	(	PUNCT
iajs-4063	85	9	(	(	PUNCT
iajs-4063	85	10	(	(	PUNCT
iajs-4063	85	11	)	)	PUNCT
iajs-4063	85	12	)	)	PUNCT
iajs-4063	85	13	)	)	PUNCT
iajs-4063	86	1	(	(	PUNCT
iajs-4063	86	2	(	(	PUNCT
iajs-4063	86	3	)	)	PUNCT
iajs-4063	86	4	)	)	PUNCT
iajs-4063	86	5	(	(	PUNCT
iajs-4063	86	6	(	(	PUNCT
iajs-4063	86	7	(	(	PUNCT
iajs-4063	86	8	)	)	PUNCT
iajs-4063	86	9	)	)	PUNCT
iajs-4063	86	10	)	)	PUNCT
iajs-4063	87	1	(	(	PUNCT
iajs-4063	87	2	10	10	X
iajs-4063	87	3	)	)	PUNCT
iajs-4063	87	4	substituting	substitute	VERB
iajs-4063	87	5	about	about	ADP
iajs-4063	87	6	in	in	ADP
iajs-4063	87	7	(	(	PUNCT
iajs-4063	87	8	8)	8)	NUM
iajs-4063	87	9	,	,	PUNCT
iajs-4063	87	10	we	we	PRON
iajs-4063	87	11	get	get	VERB
iajs-4063	87	12	:	:	PUNCT
iajs-4063	87	13	(	(	PUNCT
iajs-4063	87	14	)	)	PUNCT
iajs-4063	87	15	or	or	CCONJ
iajs-4063	87	16	(	(	PUNCT
iajs-4063	87	17	)	)	PUNCT
iajs-4063	87	18	(	(	PUNCT
iajs-4063	87	19	11	11	NUM
iajs-4063	87	20	)	)	PUNCT
iajs-4063	87	21	but	but	CCONJ
iajs-4063	87	22	(	(	PUNCT
iajs-4063	87	23	)	)	PUNCT
iajs-4063	87	24	is	be	AUX
iajs-4063	87	25	nonincreasing	nonincrease	VERB
iajs-4063	87	26	,	,	PUNCT
iajs-4063	87	27	so	so	ADV
iajs-4063	87	28	:	:	PUNCT
iajs-4063	87	29	(	(	PUNCT
iajs-4063	87	30	)	)	PUNCT
iajs-4063	87	31	(	(	PUNCT
iajs-4063	87	32	)	)	PUNCT
iajs-4063	87	33	now	now	ADV
iajs-4063	87	34	,	,	PUNCT
iajs-4063	87	35	we	we	PRON
iajs-4063	87	36	divide	divide	VERB
iajs-4063	87	37	last	last	ADJ
iajs-4063	87	38	inequality	inequality	NOUN
iajs-4063	87	39	by	by	ADP
iajs-4063	87	40	and	and	CCONJ
iajs-4063	87	41	integrates	integrate	VERB
iajs-4063	87	42	it	it	PRON
iajs-4063	87	43	from	from	ADP
iajs-4063	87	44	to	to	ADP
iajs-4063	87	45	,	,	PUNCT
iajs-4063	87	46	we	we	PRON
iajs-4063	87	47	have	have	VERB
iajs-4063	87	48	:	:	PUNCT
iajs-4063	87	49	(	(	PUNCT
iajs-4063	87	50	)	)	PUNCT
iajs-4063	87	51	∫	∫	PROPN
iajs-4063	87	52	ihjpas	ihjpas	PROPN
iajs-4063	87	53	.	.	PUNCT
iajs-4063	88	1	2025	2025	NUM
iajs-4063	88	2	,	,	PUNCT
iajs-4063	88	3	38(3	38(3	NUM
iajs-4063	88	4	)	)	PUNCT
iajs-4063	88	5	371	371	NUM
iajs-4063	88	6	(	(	PUNCT
iajs-4063	88	7	)	)	PUNCT
iajs-4063	88	8	or	or	CCONJ
iajs-4063	88	9	(	(	PUNCT
iajs-4063	88	10	)	)	PUNCT
iajs-4063	88	11	(	(	PUNCT
iajs-4063	88	12	12	12	NUM
iajs-4063	88	13	)	)	PUNCT
iajs-4063	88	14	but	but	CCONJ
iajs-4063	88	15	(	(	PUNCT
iajs-4063	88	16	)	)	PUNCT
iajs-4063	88	17	,	,	PUNCT
iajs-4063	88	18	so	so	ADV
iajs-4063	88	19	we	we	PRON
iajs-4063	88	20	have	have	VERB
iajs-4063	88	21	:	:	PUNCT
iajs-4063	88	22	(	(	PUNCT
iajs-4063	88	23	(	(	PUNCT
iajs-4063	88	24	)	)	PUNCT
iajs-4063	88	25	)	)	PUNCT
iajs-4063	89	1	(	(	PUNCT
iajs-4063	89	2	(	(	PUNCT
iajs-4063	89	3	(	(	PUNCT
iajs-4063	89	4	)	)	PUNCT
iajs-4063	89	5	)	)	PUNCT
iajs-4063	89	6	)	)	PUNCT
iajs-4063	90	1	(	(	PUNCT
iajs-4063	90	2	(	(	PUNCT
iajs-4063	90	3	)	)	PUNCT
iajs-4063	90	4	)	)	PUNCT
iajs-4063	90	5	(	(	PUNCT
iajs-4063	90	6	(	(	PUNCT
iajs-4063	90	7	(	(	PUNCT
iajs-4063	90	8	)	)	PUNCT
iajs-4063	90	9	)	)	PUNCT
iajs-4063	90	10	)	)	PUNCT
iajs-4063	91	1	(	(	PUNCT
iajs-4063	91	2	(	(	PUNCT
iajs-4063	91	3	)	)	PUNCT
iajs-4063	91	4	)	)	PUNCT
iajs-4063	91	5	(	(	PUNCT
iajs-4063	91	6	(	(	PUNCT
iajs-4063	91	7	(	(	PUNCT
iajs-4063	91	8	)	)	PUNCT
iajs-4063	91	9	)	)	PUNCT
iajs-4063	91	10	)	)	PUNCT
iajs-4063	92	1	and	and	CCONJ
iajs-4063	92	2	so	so	ADV
iajs-4063	92	3	,	,	PUNCT
iajs-4063	92	4	(	(	PUNCT
iajs-4063	92	5	(	(	PUNCT
iajs-4063	92	6	(	(	PUNCT
iajs-4063	92	7	)	)	PUNCT
iajs-4063	92	8	)	)	PUNCT
iajs-4063	92	9	)	)	PUNCT
iajs-4063	93	1	(	(	PUNCT
iajs-4063	93	2	(	(	PUNCT
iajs-4063	93	3	(	(	PUNCT
iajs-4063	93	4	)	)	PUNCT
iajs-4063	93	5	)	)	PUNCT
iajs-4063	93	6	)	)	PUNCT
iajs-4063	93	7	(	(	PUNCT
iajs-4063	93	8	13	13	NUM
iajs-4063	93	9	)	)	PUNCT
iajs-4063	93	10	from	from	ADP
iajs-4063	93	11	(	(	PUNCT
iajs-4063	93	12	11	11	NUM
iajs-4063	93	13	)	)	PUNCT
iajs-4063	93	14	and	and	CCONJ
iajs-4063	93	15	(	(	PUNCT
iajs-4063	93	16	12	12	NUM
iajs-4063	93	17	)	)	PUNCT
iajs-4063	93	18	,	,	PUNCT
iajs-4063	93	19	we	we	PRON
iajs-4063	93	20	get	get	VERB
iajs-4063	93	21	:	:	PUNCT
iajs-4063	93	22	(	(	PUNCT
iajs-4063	93	23	(	(	PUNCT
iajs-4063	93	24	)	)	PUNCT
iajs-4063	93	25	)	)	PUNCT
iajs-4063	94	1	(	(	PUNCT
iajs-4063	94	2	(	(	PUNCT
iajs-4063	94	3	)	)	PUNCT
iajs-4063	94	4	)	)	PUNCT
iajs-4063	95	1	or	or	CCONJ
iajs-4063	95	2	(	(	PUNCT
iajs-4063	95	3	(	(	PUNCT
iajs-4063	95	4	)	)	PUNCT
iajs-4063	95	5	)	)	PUNCT
iajs-4063	96	1	(	(	PUNCT
iajs-4063	96	2	(	(	PUNCT
iajs-4063	96	3	)	)	PUNCT
iajs-4063	96	4	)	)	PUNCT
iajs-4063	96	5	(	(	PUNCT
iajs-4063	96	6	14	14	NUM
iajs-4063	96	7	)	)	PUNCT
iajs-4063	96	8	(	(	PUNCT
iajs-4063	96	9	)	)	PUNCT
iajs-4063	96	10	(	(	PUNCT
iajs-4063	96	11	)	)	PUNCT
iajs-4063	96	12	(	(	PUNCT
iajs-4063	96	13	(	(	PUNCT
iajs-4063	96	14	(	(	PUNCT
iajs-4063	96	15	)	)	PUNCT
iajs-4063	96	16	)	)	PUNCT
iajs-4063	96	17	)	)	PUNCT
iajs-4063	96	18	from	from	ADP
iajs-4063	96	19	(	(	PUNCT
iajs-4063	96	20	10	10	NUM
iajs-4063	96	21	)	)	PUNCT
iajs-4063	96	22	,	,	PUNCT
iajs-4063	96	23	we	we	PRON
iajs-4063	96	24	get	get	VERB
iajs-4063	96	25	:	:	PUNCT
iajs-4063	96	26	(	(	PUNCT
iajs-4063	96	27	)	)	PUNCT
iajs-4063	96	28	(	(	PUNCT
iajs-4063	96	29	(	(	PUNCT
iajs-4063	96	30	(	(	PUNCT
iajs-4063	96	31	(	(	PUNCT
iajs-4063	96	32	)	)	PUNCT
iajs-4063	96	33	)	)	PUNCT
iajs-4063	96	34	)	)	PUNCT
iajs-4063	96	35	)	)	PUNCT
iajs-4063	97	1	(	(	PUNCT
iajs-4063	97	2	15	15	X
iajs-4063	97	3	)	)	PUNCT
iajs-4063	97	4	we	we	PRON
iajs-4063	97	5	combine	combine	VERB
iajs-4063	97	6	(	(	PUNCT
iajs-4063	97	7	13	13	NUM
iajs-4063	97	8	)	)	PUNCT
iajs-4063	97	9	and	and	CCONJ
iajs-4063	97	10	(	(	PUNCT
iajs-4063	97	11	14	14	NUM
iajs-4063	97	12	)	)	PUNCT
iajs-4063	97	13	,	,	PUNCT
iajs-4063	97	14	reducing	reduce	VERB
iajs-4063	97	15	:	:	PUNCT
iajs-4063	97	16	(	(	PUNCT
iajs-4063	97	17	)	)	PUNCT
iajs-4063	97	18	(	(	PUNCT
iajs-4063	97	19	(	(	PUNCT
iajs-4063	97	20	(	(	PUNCT
iajs-4063	97	21	(	(	PUNCT
iajs-4063	97	22	)	)	PUNCT
iajs-4063	97	23	)	)	PUNCT
iajs-4063	97	24	)	)	PUNCT
iajs-4063	97	25	)	)	PUNCT
iajs-4063	98	1	(	(	PUNCT
iajs-4063	98	2	16	16	NUM
iajs-4063	98	3	)	)	PUNCT
iajs-4063	98	4	from	from	ADP
iajs-4063	98	5	(	(	PUNCT
iajs-4063	98	6	13	13	NUM
iajs-4063	98	7	)	)	PUNCT
iajs-4063	98	8	and	and	CCONJ
iajs-4063	98	9	(	(	PUNCT
iajs-4063	98	10	15	15	NUM
iajs-4063	98	11	)	)	PUNCT
iajs-4063	98	12	,	,	PUNCT
iajs-4063	98	13	we	we	PRON
iajs-4063	98	14	get	get	VERB
iajs-4063	98	15	:	:	PUNCT
iajs-4063	98	16	(	(	PUNCT
iajs-4063	98	17	)	)	PUNCT
iajs-4063	98	18	.	.	PUNCT
iajs-4063	99	1	(	(	PUNCT
iajs-4063	99	2	(	(	PUNCT
iajs-4063	99	3	(	(	PUNCT
iajs-4063	99	4	)	)	PUNCT
iajs-4063	99	5	)	)	PUNCT
iajs-4063	99	6	)	)	PUNCT
iajs-4063	99	7	/	/	SYM
iajs-4063	99	8	(	(	PUNCT
iajs-4063	99	9	(	(	PUNCT
iajs-4063	99	10	(	(	PUNCT
iajs-4063	99	11	)	)	PUNCT
iajs-4063	99	12	)	)	PUNCT
iajs-4063	99	13	)	)	PUNCT
iajs-4063	100	1	(	(	PUNCT
iajs-4063	100	2	17	17	NUM
iajs-4063	100	3	)	)	PUNCT
iajs-4063	100	4	by	by	ADP
iajs-4063	100	5	theorem	theorem	ADJ
iajs-4063	100	6	2.2.9	2.2.9	NUM
iajs-4063	100	7	in	in	ADP
iajs-4063	100	8	(	(	PUNCT
iajs-4063	100	9	30	30	NUM
iajs-4063	100	10	)	)	PUNCT
iajs-4063	100	11	the	the	DET
iajs-4063	100	12	inequality	inequality	NOUN
iajs-4063	100	13	(	(	PUNCT
iajs-4063	100	14	17	17	NUM
iajs-4063	100	15	)	)	PUNCT
iajs-4063	100	16	does	do	AUX
iajs-4063	100	17	not	not	PART
iajs-4063	100	18	have	have	VERB
iajs-4063	100	19	eventually	eventually	ADV
iajs-4063	100	20	positive	positive	ADJ
iajs-4063	100	21	solution	solution	NOUN
iajs-4063	100	22	,	,	PUNCT
iajs-4063	100	23	a	a	DET
iajs-4063	100	24	contradiction	contradiction	NOUN
iajs-4063	100	25	!	!	PUNCT
iajs-4063	101	1	4.1	4.1	NUM
iajs-4063	101	2	.	.	PUNCT
iajs-4063	102	1	illustrative	illustrative	ADJ
iajs-4063	102	2	examples	example	NOUN
iajs-4063	102	3	in	in	ADP
iajs-4063	102	4	this	this	DET
iajs-4063	102	5	section	section	NOUN
iajs-4063	102	6	,	,	PUNCT
iajs-4063	102	7	we	we	PRON
iajs-4063	102	8	present	present	VERB
iajs-4063	102	9	some	some	DET
iajs-4063	102	10	examples	example	NOUN
iajs-4063	102	11	to	to	PART
iajs-4063	102	12	support	support	VERB
iajs-4063	102	13	the	the	DET
iajs-4063	102	14	obtained	obtain	VERB
iajs-4063	102	15	results	result	NOUN
iajs-4063	102	16	ihjpas	ihjpa	VERB
iajs-4063	102	17	.	.	PUNCT
iajs-4063	103	1	2025	2025	NUM
iajs-4063	103	2	,	,	PUNCT
iajs-4063	103	3	38(3	38(3	NUM
iajs-4063	103	4	)	)	PUNCT
iajs-4063	103	5	372	372	NUM
iajs-4063	103	6	4.1.1	4.1.1	NUM
iajs-4063	103	7	.	.	PUNCT
iajs-4063	103	8	example	example	NOUN
iajs-4063	104	1	1	1	NUM
iajs-4063	104	2	let	let	VERB
iajs-4063	104	3	us	we	PRON
iajs-4063	104	4	consider	consider	VERB
iajs-4063	104	5	nonlinear	nonlinear	ADJ
iajs-4063	104	6	neutral	neutral	ADJ
iajs-4063	104	7	differential	differential	ADJ
iajs-4063	104	8	equation	equation	NOUN
iajs-4063	104	9	as	as	SCONJ
iajs-4063	104	10	follows	follow	VERB
iajs-4063	104	11	:	:	PUNCT
iajs-4063	104	12	0	0	NUM
iajs-4063	104	13	.	.	PUNCT
iajs-4063	105	1	/1	/1	PROPN
iajs-4063	105	2	(	(	PUNCT
iajs-4063	105	3	18	18	NUM
iajs-4063	105	4	)	)	PUNCT
iajs-4063	105	5	to	to	PART
iajs-4063	105	6	satisfy	satisfy	VERB
iajs-4063	105	7	all	all	DET
iajs-4063	105	8	conditions	condition	NOUN
iajs-4063	105	9	of	of	ADP
iajs-4063	105	10	theorem	theorem	NOUN
iajs-4063	105	11	(	(	PUNCT
iajs-4063	105	12	1	1	NUM
iajs-4063	105	13	):	):	PUNCT
iajs-4063	105	14	∫	∫	PROPN
iajs-4063	105	15	∫	∫	PROPN
iajs-4063	105	16	min	min	PROPN
iajs-4063	105	17	,	,	PUNCT
iajs-4063	105	18	(	(	PUNCT
iajs-4063	105	19	(	(	PUNCT
iajs-4063	105	20	)	)	PUNCT
iajs-4063	105	21	)	)	PUNCT
iajs-4063	106	1	(	(	PUNCT
iajs-4063	106	2	(	(	PUNCT
iajs-4063	106	3	)	)	PUNCT
iajs-4063	106	4	)	)	PUNCT
iajs-4063	106	5	mi	mi	PROPN
iajs-4063	106	6	,	,	PUNCT
iajs-4063	106	7	(	(	PUNCT
iajs-4063	106	8	(	(	PUNCT
iajs-4063	106	9	)	)	PUNCT
iajs-4063	106	10	)	)	PUNCT
iajs-4063	106	11	(	(	PUNCT
iajs-4063	106	12	(	(	PUNCT
iajs-4063	106	13	)	)	PUNCT
iajs-4063	106	14	)	)	PUNCT
iajs-4063	106	15	{	{	PUNCT
iajs-4063	106	16	}	}	PUNCT
iajs-4063	106	17	∫	∫	PROPN
iajs-4063	106	18	∫	∫	PROPN
iajs-4063	106	19	]	]	PUNCT
iajs-4063	106	20	also	also	ADV
iajs-4063	106	21	,	,	PUNCT
iajs-4063	106	22	we	we	PRON
iajs-4063	106	23	get	get	VERB
iajs-4063	106	24	:	:	PUNCT
iajs-4063	107	1	∫	∫	PROPN
iajs-4063	107	2	∫	∫	PROPN
iajs-4063	107	3	we	we	PRON
iajs-4063	107	4	satisfied	satisfy	VERB
iajs-4063	107	5	all	all	DET
iajs-4063	107	6	conditions	condition	NOUN
iajs-4063	107	7	for	for	ADP
iajs-4063	107	8	theorem	theorem	NOUN
iajs-4063	107	9	(	(	PUNCT
iajs-4063	107	10	1	1	NUM
iajs-4063	107	11	)	)	PUNCT
iajs-4063	107	12	are	be	AUX
iajs-4063	107	13	satisfied	satisfied	ADJ
iajs-4063	107	14	,	,	PUNCT
iajs-4063	107	15	so	so	ADV
iajs-4063	107	16	all	all	DET
iajs-4063	107	17	solutions	solution	NOUN
iajs-4063	107	18	of	of	ADP
iajs-4063	107	19	eq	eq	PROPN
iajs-4063	107	20	.	.	PUNCT
iajs-4063	108	1	(	(	PUNCT
iajs-4063	108	2	1	1	X
iajs-4063	108	3	)	)	PUNCT
iajs-4063	108	4	oscillate	oscillate	NOUN
iajs-4063	108	5	.	.	PUNCT
iajs-4063	109	1	4.1.2	4.1.2	X
iajs-4063	109	2	.	.	PUNCT
iajs-4063	109	3	example	example	NOUN
iajs-4063	109	4	2	2	NUM
iajs-4063	109	5	let	let	VERB
iajs-4063	109	6	us	we	PRON
iajs-4063	109	7	consider	consider	VERB
iajs-4063	109	8	nonlinear	nonlinear	ADJ
iajs-4063	109	9	neutral	neutral	ADJ
iajs-4063	109	10	differential	differential	ADJ
iajs-4063	109	11	equation	equation	NOUN
iajs-4063	109	12	as	as	SCONJ
iajs-4063	109	13	follows	follow	VERB
iajs-4063	109	14	:	:	PUNCT
iajs-4063	109	15	0	0	NUM
iajs-4063	109	16	.	.	PUNCT
iajs-4063	110	1	/1	/1	PROPN
iajs-4063	111	1	(	(	PUNCT
iajs-4063	111	2	19	19	NUM
iajs-4063	111	3	)	)	PUNCT
iajs-4063	111	4	to	to	PART
iajs-4063	111	5	satisfy	satisfy	VERB
iajs-4063	111	6	all	all	DET
iajs-4063	111	7	conditions	condition	NOUN
iajs-4063	111	8	of	of	ADP
iajs-4063	111	9	theorem	theorem	NOUN
iajs-4063	111	10	(	(	PUNCT
iajs-4063	111	11	2	2	NUM
iajs-4063	111	12	):	):	PUNCT
iajs-4063	112	1	∫	∫	PROPN
iajs-4063	112	2	∫	∫	PROPN
iajs-4063	112	3	∫	∫	PROPN
iajs-4063	112	4	∫	∫	PROPN
iajs-4063	112	5	.	.	PUNCT
iajs-4063	113	1	(	(	PUNCT
iajs-4063	113	2	(	(	PUNCT
iajs-4063	113	3	(	(	PUNCT
iajs-4063	113	4	)	)	PUNCT
iajs-4063	113	5	)	)	PUNCT
iajs-4063	113	6	)	)	PUNCT
iajs-4063	113	7	/	/	SYM
iajs-4063	113	8	mi	mi	PROPN
iajs-4063	113	9	,	,	PUNCT
iajs-4063	113	10	(	(	PUNCT
iajs-4063	113	11	(	(	PUNCT
iajs-4063	113	12	)	)	PUNCT
iajs-4063	113	13	)	)	PUNCT
iajs-4063	114	1	(	(	PUNCT
iajs-4063	114	2	(	(	PUNCT
iajs-4063	114	3	)	)	PUNCT
iajs-4063	114	4	)	)	PUNCT
iajs-4063	114	5	{	{	PUNCT
iajs-4063	114	6	}	}	PUNCT
iajs-4063	114	7	to	to	PART
iajs-4063	114	8	satisfy	satisfy	VERB
iajs-4063	114	9	the	the	DET
iajs-4063	114	10	condition	condition	NOUN
iajs-4063	114	11	(	(	PUNCT
iajs-4063	114	12	9	9	NUM
iajs-4063	114	13	)	)	PUNCT
iajs-4063	114	14	with	with	ADP
iajs-4063	114	15	∫	∫	PROPN
iajs-4063	114	16	ihjpas	ihjpas	PROPN
iajs-4063	114	17	.	.	PUNCT
iajs-4063	115	1	2025	2025	NUM
iajs-4063	115	2	,	,	PUNCT
iajs-4063	115	3	38(3	38(3	NUM
iajs-4063	115	4	)	)	PUNCT
iajs-4063	115	5	373	373	NUM
iajs-4063	115	6	∫	∫	NOUN
iajs-4063	115	7	all	all	DET
iajs-4063	115	8	the	the	DET
iajs-4063	115	9	conditions	condition	NOUN
iajs-4063	115	10	of	of	ADP
iajs-4063	115	11	theorem	theorem	NOUN
iajs-4063	115	12	(	(	PUNCT
iajs-4063	115	13	2	2	NUM
iajs-4063	115	14	)	)	PUNCT
iajs-4063	115	15	are	be	AUX
iajs-4063	115	16	satisfied	satisfied	ADJ
iajs-4063	115	17	,	,	PUNCT
iajs-4063	115	18	so	so	ADV
iajs-4063	115	19	all	all	DET
iajs-4063	115	20	solutions	solution	NOUN
iajs-4063	115	21	of	of	ADP
iajs-4063	115	22	eq	eq	PROPN
iajs-4063	115	23	.	.	PUNCT
iajs-4063	116	1	(	(	PUNCT
iajs-4063	116	2	1	1	X
iajs-4063	116	3	)	)	PUNCT
iajs-4063	116	4	oscillate	oscillate	NOUN
iajs-4063	116	5	.	.	PUNCT
iajs-4063	117	1	5	5	X
iajs-4063	117	2	.	.	X
iajs-4063	117	3	discussion	discussion	NOUN
iajs-4063	117	4	through	through	ADP
iajs-4063	117	5	the	the	DET
iajs-4063	117	6	paper	paper	NOUN
iajs-4063	117	7	,	,	PUNCT
iajs-4063	117	8	qualitative	qualitative	ADJ
iajs-4063	117	9	properties	property	NOUN
iajs-4063	117	10	are	be	AUX
iajs-4063	117	11	studied	study	VERB
iajs-4063	117	12	as	as	ADP
iajs-4063	117	13	oscillatory	oscillatory	ADJ
iajs-4063	117	14	properties	property	NOUN
iajs-4063	117	15	.	.	PUNCT
iajs-4063	118	1	it	it	PRON
iajs-4063	118	2	can	can	AUX
iajs-4063	118	3	be	be	AUX
iajs-4063	118	4	noted	note	VERB
iajs-4063	118	5	that	that	SCONJ
iajs-4063	118	6	the	the	DET
iajs-4063	118	7	influence	influence	NOUN
iajs-4063	118	8	of	of	ADP
iajs-4063	118	9	changing	change	VERB
iajs-4063	118	10	delays	delay	NOUN
iajs-4063	118	11	in	in	ADP
iajs-4063	118	12	main	main	ADJ
iajs-4063	118	13	results	result	NOUN
iajs-4063	118	14	takes	take	VERB
iajs-4063	118	15	a	a	DET
iajs-4063	118	16	huge	huge	ADJ
iajs-4063	118	17	role	role	NOUN
iajs-4063	118	18	to	to	PART
iajs-4063	118	19	control	control	VERB
iajs-4063	118	20	in	in	ADP
iajs-4063	118	21	sufficient	sufficient	ADJ
iajs-4063	118	22	conditions	condition	NOUN
iajs-4063	118	23	to	to	PART
iajs-4063	118	24	obtain	obtain	VERB
iajs-4063	118	25	the	the	DET
iajs-4063	118	26	oscillation	oscillation	NOUN
iajs-4063	118	27	property	property	NOUN
iajs-4063	118	28	;	;	PUNCT
iajs-4063	118	29	it	it	PRON
iajs-4063	118	30	is	be	AUX
iajs-4063	118	31	explained	explain	VERB
iajs-4063	118	32	in	in	ADP
iajs-4063	118	33	application	application	NOUN
iajs-4063	118	34	examples	example	NOUN
iajs-4063	118	35	.	.	PUNCT
iajs-4063	119	1	6	6	X
iajs-4063	119	2	.	.	X
iajs-4063	119	3	conclusion	conclusion	NOUN
iajs-4063	119	4	in	in	ADP
iajs-4063	119	5	this	this	DET
iajs-4063	119	6	search	search	NOUN
iajs-4063	119	7	,	,	PUNCT
iajs-4063	119	8	oscillatory	oscillatory	ADJ
iajs-4063	119	9	behavior	behavior	NOUN
iajs-4063	119	10	of	of	ADP
iajs-4063	119	11	second	second	ADJ
iajs-4063	119	12	-	-	PUNCT
iajs-4063	119	13	order	order	NOUN
iajs-4063	119	14	nde	nde	NOUN
iajs-4063	119	15	is	be	AUX
iajs-4063	119	16	considered	consider	VERB
iajs-4063	119	17	in	in	ADP
iajs-4063	119	18	the	the	DET
iajs-4063	119	19	nonlinear	nonlinear	ADJ
iajs-4063	119	20	case	case	NOUN
iajs-4063	119	21	.	.	PUNCT
iajs-4063	120	1	specific	specific	ADJ
iajs-4063	120	2	conditions	condition	NOUN
iajs-4063	120	3	have	have	AUX
iajs-4063	120	4	been	be	AUX
iajs-4063	120	5	established	establish	VERB
iajs-4063	120	6	for	for	ADP
iajs-4063	120	7	known	know	VERB
iajs-4063	120	8	functions	function	NOUN
iajs-4063	120	9	in	in	ADP
iajs-4063	120	10	the	the	DET
iajs-4063	120	11	delay	delay	NOUN
iajs-4063	120	12	differential	differential	NOUN
iajs-4063	120	13	eq	eq	ADP
iajs-4063	120	14	.	.	PUNCT
iajs-4063	121	1	(	(	PUNCT
iajs-4063	121	2	1	1	NUM
iajs-4063	121	3	)	)	PUNCT
iajs-4063	121	4	.	.	PUNCT
iajs-4063	122	1	a	a	DET
iajs-4063	122	2	new	new	ADJ
iajs-4063	122	3	relationship	relationship	NOUN
iajs-4063	122	4	between	between	ADP
iajs-4063	122	5	the	the	DET
iajs-4063	122	6	deviating	deviate	VERB
iajs-4063	122	7	arguments	argument	NOUN
iajs-4063	122	8	and	and	CCONJ
iajs-4063	122	9	known	know	VERB
iajs-4063	122	10	functions	function	NOUN
iajs-4063	122	11	to	to	PART
iajs-4063	122	12	get	get	VERB
iajs-4063	122	13	oscillatory	oscillatory	ADJ
iajs-4063	122	14	property	property	NOUN
iajs-4063	122	15	has	have	AUX
iajs-4063	122	16	been	be	AUX
iajs-4063	122	17	built	build	VERB
iajs-4063	122	18	.	.	PUNCT
iajs-4063	123	1	application	application	NOUN
iajs-4063	123	2	examples	example	NOUN
iajs-4063	123	3	are	be	AUX
iajs-4063	123	4	presented	present	VERB
iajs-4063	123	5	to	to	PART
iajs-4063	123	6	show	show	VERB
iajs-4063	123	7	the	the	DET
iajs-4063	123	8	importance	importance	NOUN
iajs-4063	123	9	of	of	ADP
iajs-4063	123	10	our	our	PRON
iajs-4063	123	11	results	result	NOUN
iajs-4063	123	12	compared	compare	VERB
iajs-4063	123	13	with	with	ADP
iajs-4063	123	14	other	other	ADJ
iajs-4063	123	15	previous	previous	ADJ
iajs-4063	123	16	studies	study	NOUN
iajs-4063	123	17	.	.	PUNCT
iajs-4063	124	1	in	in	ADP
iajs-4063	124	2	theorem	theorem	NOUN
iajs-4063	124	3	2	2	NUM
iajs-4063	124	4	,	,	PUNCT
iajs-4063	124	5	a	a	DET
iajs-4063	124	6	new	new	ADJ
iajs-4063	124	7	condition	condition	NOUN
iajs-4063	124	8	is	be	AUX
iajs-4063	124	9	submitted	submit	VERB
iajs-4063	124	10	to	to	PART
iajs-4063	124	11	get	get	VERB
iajs-4063	124	12	oscillatory	oscillatory	ADJ
iajs-4063	124	13	behavior	behavior	NOUN
iajs-4063	124	14	of	of	ADP
iajs-4063	124	15	equation	equation	NOUN
iajs-4063	124	16	(	(	PUNCT
iajs-4063	124	17	1	1	NUM
iajs-4063	124	18	)	)	PUNCT
iajs-4063	124	19	with	with	ADP
iajs-4063	124	20	an	an	DET
iajs-4063	124	21	application	application	NOUN
iajs-4063	124	22	example	example	NOUN
iajs-4063	124	23	.	.	PUNCT
iajs-4063	125	1	we	we	PRON
iajs-4063	125	2	improved	improve	VERB
iajs-4063	125	3	some	some	DET
iajs-4063	125	4	previous	previous	ADJ
iajs-4063	125	5	theorems	theorem	NOUN
iajs-4063	125	6	in	in	ADP
iajs-4063	125	7	the	the	DET
iajs-4063	125	8	literature	literature	NOUN
iajs-4063	125	9	by	by	ADP
iajs-4063	125	10	taking	take	VERB
iajs-4063	125	11	the	the	DET
iajs-4063	125	12	delays	delay	NOUN
iajs-4063	125	13	as	as	ADP
iajs-4063	125	14	functions	function	NOUN
iajs-4063	125	15	.	.	PUNCT
iajs-4063	126	1	as	as	ADP
iajs-4063	126	2	future	future	ADJ
iajs-4063	126	3	works	work	NOUN
iajs-4063	126	4	,	,	PUNCT
iajs-4063	126	5	it	it	PRON
iajs-4063	126	6	would	would	AUX
iajs-4063	126	7	be	be	AUX
iajs-4063	126	8	interesting	interesting	ADJ
iajs-4063	126	9	to	to	PART
iajs-4063	126	10	extend	extend	VERB
iajs-4063	126	11	the	the	DET
iajs-4063	126	12	results	result	NOUN
iajs-4063	126	13	of	of	ADP
iajs-4063	126	14	this	this	DET
iajs-4063	126	15	article	article	NOUN
iajs-4063	126	16	to	to	ADP
iajs-4063	126	17	higher	high	ADJ
iajs-4063	126	18	-	-	PUNCT
iajs-4063	126	19	order	order	NOUN
iajs-4063	126	20	nonlinear	nonlinear	PROPN
iajs-4063	126	21	des	des	PROPN
iajs-4063	126	22	.	.	PROPN
iajs-4063	126	23	acknowledgment	acknowledgment	NOUN
iajs-4063	126	24	our	our	PRON
iajs-4063	126	25	acknowledgments	acknowledgment	NOUN
iajs-4063	126	26	are	be	AUX
iajs-4063	126	27	to	to	ADP
iajs-4063	126	28	all	all	DET
iajs-4063	126	29	authors	author	NOUN
iajs-4063	126	30	whose	whose	DET
iajs-4063	126	31	results	result	NOUN
iajs-4063	126	32	we	we	PRON
iajs-4063	126	33	have	have	AUX
iajs-4063	126	34	improved	improve	VERB
iajs-4063	126	35	and	and	CCONJ
iajs-4063	126	36	to	to	ADP
iajs-4063	126	37	reviewers	reviewer	NOUN
iajs-4063	126	38	for	for	ADP
iajs-4063	126	39	their	their	PRON
iajs-4063	126	40	remarks	remark	NOUN
iajs-4063	126	41	.	.	PUNCT
iajs-4063	127	1	conflict	conflict	NOUN
iajs-4063	127	2	of	of	ADP
iajs-4063	127	3	interest	interest	NOUN
iajs-4063	127	4	the	the	DET
iajs-4063	127	5	authors	author	NOUN
iajs-4063	127	6	declare	declare	VERB
iajs-4063	127	7	that	that	SCONJ
iajs-4063	127	8	they	they	PRON
iajs-4063	127	9	have	have	VERB
iajs-4063	127	10	no	no	DET
iajs-4063	127	11	conflicts	conflict	NOUN
iajs-4063	127	12	of	of	ADP
iajs-4063	127	13	interest	interest	NOUN
iajs-4063	127	14	.	.	PUNCT
iajs-4063	128	1	funding	fund	VERB
iajs-4063	128	2	no	no	DET
iajs-4063	128	3	funding	funding	NOUN
iajs-4063	128	4	.	.	PUNCT
iajs-4063	129	1	references	reference	NOUN
iajs-4063	129	2	1	1	NUM
iajs-4063	129	3	.	.	PUNCT
iajs-4063	129	4	esuabana	esuabana	PROPN
iajs-4063	129	5	i.m	i.m	PROPN
iajs-4063	129	6	.	.	PROPN
iajs-4063	129	7	,	,	PUNCT
iajs-4063	129	8	ugboh	ugboh	PROPN
iajs-4063	129	9	j.a	j.a	PROPN
iajs-4063	129	10	.	.	PROPN
iajs-4063	129	11	survey	survey	NOUN
iajs-4063	129	12	of	of	ADP
iajs-4063	129	13	impulsive	impulsive	ADJ
iajs-4063	129	14	differential	differential	ADJ
iajs-4063	129	15	equations	equation	NOUN
iajs-4063	129	16	with	with	ADP
iajs-4063	129	17	continuous	continuous	ADJ
iajs-4063	129	18	delay	delay	NOUN
iajs-4063	129	19	.	.	PUNCT
iajs-4063	130	1	int	int	PROPN
iajs-4063	130	2	j	j	PROPN
iajs-4063	130	3	math	math	PROPN
iajs-4063	130	4	trends	trend	NOUN
iajs-4063	130	5	technol	technol	PROPN
iajs-4063	130	6	2018;60(1):22–28	2018;60(1):22–28	PROPN
iajs-4063	130	7	.	.	PUNCT
iajs-4063	131	1	https://doi.org/10.14445/22315373/ijmtt-v60p504	https://doi.org/10.14445/22315373/ijmtt-v60p504	PROPN
iajs-4063	131	2	2	2	NUM
iajs-4063	131	3	.	.	PUNCT
iajs-4063	131	4	nemah	nemah	PROPN
iajs-4063	131	5	e.m	e.m	PROPN
iajs-4063	131	6	.	.	PROPN
iajs-4063	131	7	homotopy	homotopy	PROPN
iajs-4063	131	8	transforms	transform	VERB
iajs-4063	131	9	analysis	analysis	NOUN
iajs-4063	131	10	method	method	NOUN
iajs-4063	131	11	for	for	ADP
iajs-4063	131	12	solving	solve	VERB
iajs-4063	131	13	fractional	fractional	ADJ
iajs-4063	131	14	navier	navier	NOUN
iajs-4063	131	15	-	-	PUNCT
iajs-4063	131	16	stokes	stoke	NOUN
iajs-4063	131	17	equations	equation	NOUN
iajs-4063	131	18	with	with	ADP
iajs-4063	131	19	applications	application	NOUN
iajs-4063	131	20	.	.	PUNCT
iajs-4063	132	1	iraqi	iraqi	ADJ
iajs-4063	132	2	j	j	PROPN
iajs-4063	132	3	sci	sci	PROPN
iajs-4063	132	4	2020;61(8):2048–2054	2020;61(8):2048–2054	PROPN
iajs-4063	132	5	.	.	PUNCT
iajs-4063	133	1	https://doi.org/10.24996/ijs.2020.61.8.20	https://doi.org/10.24996/ijs.2020.61.8.20	PROPN
iajs-4063	133	2	3	3	NUM
iajs-4063	133	3	.	.	PROPN
iajs-4063	133	4	nemah	nemah	PROPN
iajs-4063	133	5	e.m	e.m	PROPN
iajs-4063	133	6	.	.	PROPN
iajs-4063	133	7	efficiency	efficiency	NOUN
iajs-4063	133	8	algorithm	algorithm	NOUN
iajs-4063	133	9	for	for	ADP
iajs-4063	133	10	solving	solve	VERB
iajs-4063	133	11	some	some	DET
iajs-4063	133	12	models	model	NOUN
iajs-4063	133	13	of	of	ADP
iajs-4063	133	14	nonlinear	nonlinear	ADJ
iajs-4063	133	15	problems	problem	NOUN
iajs-4063	133	16	.	.	PUNCT
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iajs-4063	138	6	differential	differential	ADJ
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iajs-4063	139	1	j	j	PROPN
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iajs-4063	139	6	.	.	PUNCT
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iajs-4063	140	3	.	.	PUNCT
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iajs-4063	142	5	.	.	PUNCT
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iajs-4063	143	10	.	.	PUNCT
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iajs-4063	144	2	,	,	PUNCT
iajs-4063	144	3	38(3	38(3	NUM
iajs-4063	144	4	)	)	PUNCT
iajs-4063	144	5	374	374	NUM
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iajs-4063	144	7	.	.	PUNCT
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iajs-4063	145	15	-	-	PUNCT
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iajs-4063	145	19	differential	differential	PROPN
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iajs-4063	145	21	.	.	PUNCT
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iajs-4063	146	5	.	.	PUNCT
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iajs-4063	147	3	.	.	PUNCT
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iajs-4063	148	14	.	.	PUNCT
iajs-4063	149	1	iraqi	iraqi	ADJ
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iajs-4063	149	5	.	.	PUNCT
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iajs-4063	150	3	.	.	PUNCT
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iajs-4063	152	8	.	.	PUNCT
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iajs-4063	154	9	delay	delay	NOUN
iajs-4063	154	10	differential	differential	ADJ
iajs-4063	154	11	equation	equation	NOUN
iajs-4063	154	12	.	.	PUNCT
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iajs-4063	155	5	.	.	PUNCT
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iajs-4063	156	3	.	.	PUNCT
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