id	sid	tid	token	lemma	pos
cana-3474	1	1	communications	communication	NOUN
cana-3474	1	2	on	on	ADP
cana-3474	1	3	applied	apply	VERB
cana-3474	1	4	nonlinear	nonlinear	ADJ
cana-3474	1	5	analysis	analysis	NOUN
cana-3474	1	6	issn	issn	NOUN
cana-3474	1	7	:	:	PUNCT
cana-3474	1	8	1074	1074	NUM
cana-3474	1	9	-	-	PUNCT
cana-3474	1	10	133x	133x	NUM
cana-3474	1	11	vol	vol	NOUN
cana-3474	1	12	32	32	NUM
cana-3474	1	13	no	no	NOUN
cana-3474	1	14	.	.	PUNCT
cana-3474	2	1	7s	7	NOUN
cana-3474	2	2	(	(	PUNCT
cana-3474	2	3	2025	2025	NUM
cana-3474	2	4	)	)	PUNCT
cana-3474	2	5	675	675	NUM
cana-3474	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	2	7	using	use	VERB
cana-3474	2	8	w	w	NOUN
cana-3474	2	9	transform	transform	NOUN
cana-3474	2	10	for	for	ADP
cana-3474	2	11	solving	solve	VERB
cana-3474	2	12	volterra	volterra	NOUN
cana-3474	2	13	integro	integro	PROPN
cana-3474	2	14	-	-	PUNCT
cana-3474	2	15	differential	differential	NOUN
cana-3474	2	16	equations	equation	NOUN
cana-3474	2	17	amal	amal	PROPN
cana-3474	2	18	m.	m.	PROPN
cana-3474	2	19	wadi	wadi	PROPN
cana-3474	2	20	*	*	PUNCT
cana-3474	2	21	,	,	PUNCT
cana-3474	2	22	nejmaddin	nejmaddin	VERB
cana-3474	2	23	a.	a.	NOUN
cana-3474	2	24	sulaiman	sulaiman	PROPN
cana-3474	2	25	*	*	PUNCT
cana-3474	3	1	*	*	PUNCT
cana-3474	3	2	*	*	PUNCT
cana-3474	3	3	,	,	PUNCT
cana-3474	3	4	*	*	PUNCT
cana-3474	3	5	*	*	NOUN
cana-3474	3	6	department	department	NOUN
cana-3474	3	7	of	of	ADP
cana-3474	3	8	mathematics	mathematic	NOUN
cana-3474	3	9	,	,	PUNCT
cana-3474	3	10	college	college	NOUN
cana-3474	3	11	of	of	ADP
cana-3474	3	12	education	education	NOUN
cana-3474	3	13	,	,	PUNCT
cana-3474	3	14	salahaddin	salahaddin	VERB
cana-3474	3	15	university	university	NOUN
cana-3474	3	16	-	-	PUNCT
cana-3474	3	17	erbil	erbil	PROPN
cana-3474	3	18	,	,	PUNCT
cana-3474	3	19	kurdistan	kurdistan	ADJ
cana-3474	3	20	region	region	NOUN
cana-3474	3	21	,	,	PUNCT
cana-3474	3	22	iraq	iraq	PROPN
cana-3474	3	23	)	)	PUNCT
cana-3474	3	24	amal.wadi@su.edu.krd	amal.wadi@su.edu.krd	PROPN
cana-3474	3	25	,	,	PUNCT
cana-3474	3	26	nejmaddin.sulaiman@su.edu.krd	nejmaddin.sulaiman@su.edu.krd	NUM
cana-3474	3	27	)	)	PUNCT
cana-3474	3	28	article	article	NOUN
cana-3474	3	29	history	history	NOUN
cana-3474	3	30	:	:	PUNCT
cana-3474	3	31	received	receive	VERB
cana-3474	3	32	:	:	PUNCT
cana-3474	3	33	27	27	NUM
cana-3474	3	34	-	-	SYM
cana-3474	3	35	10	10	NUM
cana-3474	3	36	-	-	PUNCT
cana-3474	3	37	2024	2024	NUM
cana-3474	3	38	revised	revise	VERB
cana-3474	3	39	:	:	PUNCT
cana-3474	3	40	11	11	NUM
cana-3474	3	41	-	-	SYM
cana-3474	3	42	11	11	NUM
cana-3474	3	43	-	-	PUNCT
cana-3474	3	44	2024	2024	NUM
cana-3474	3	45	accepted	accept	VERB
cana-3474	3	46	:	:	PUNCT
cana-3474	3	47	19	19	NUM
cana-3474	3	48	-	-	SYM
cana-3474	3	49	12	12	NUM
cana-3474	3	50	-	-	PUNCT
cana-3474	3	51	2024	2024	NUM
cana-3474	3	52	abstract	abstract	NOUN
cana-3474	3	53	:	:	PUNCT
cana-3474	3	54	there	there	PRON
cana-3474	3	55	are	be	VERB
cana-3474	3	56	numerous	numerous	ADJ
cana-3474	3	57	uses	use	NOUN
cana-3474	3	58	for	for	ADP
cana-3474	3	59	the	the	DET
cana-3474	3	60	volterra	volterra	PROPN
cana-3474	3	61	integro	integro	PROPN
cana-3474	3	62	-	-	PUNCT
cana-3474	3	63	differential	differential	NOUN
cana-3474	3	64	equation	equation	NOUN
cana-3474	3	65	in	in	ADP
cana-3474	3	66	the	the	DET
cana-3474	3	67	fields	field	NOUN
cana-3474	3	68	of	of	ADP
cana-3474	3	69	mechanics	mechanic	NOUN
cana-3474	3	70	,	,	PUNCT
cana-3474	3	71	geometric	geometric	ADJ
cana-3474	3	72	probability	probability	NOUN
cana-3474	3	73	,	,	PUNCT
cana-3474	3	74	population	population	NOUN
cana-3474	3	75	dynamics	dynamic	NOUN
cana-3474	3	76	,	,	PUNCT
cana-3474	3	77	theory	theory	NOUN
cana-3474	3	78	of	of	ADP
cana-3474	3	79	rejuvenation	rejuvenation	NOUN
cana-3474	3	80	,	,	PUNCT
cana-3474	3	81	facts	fact	NOUN
cana-3474	3	82	on	on	ADP
cana-3474	3	83	particle	particle	NOUN
cana-3474	3	84	size	size	NOUN
cana-3474	3	85	and	and	CCONJ
cana-3474	3	86	the	the	DET
cana-3474	3	87	damping	damping	NOUN
cana-3474	3	88	of	of	ADP
cana-3474	3	89	string	string	NOUN
cana-3474	3	90	vibration	vibration	NOUN
cana-3474	3	91	,	,	PUNCT
cana-3474	3	92	and	and	CCONJ
cana-3474	3	93	transmission	transmission	NOUN
cana-3474	3	94	of	of	ADP
cana-3474	3	95	heat	heat	NOUN
cana-3474	3	96	issues	issue	NOUN
cana-3474	3	97	.	.	PUNCT
cana-3474	4	1	finding	find	VERB
cana-3474	4	2	the	the	DET
cana-3474	4	3	approximate	approximate	ADJ
cana-3474	4	4	or	or	CCONJ
cana-3474	4	5	exact	exact	ADJ
cana-3474	4	6	solutions	solution	NOUN
cana-3474	4	7	to	to	ADP
cana-3474	4	8	these	these	DET
cana-3474	4	9	equations	equation	NOUN
cana-3474	4	10	is	be	AUX
cana-3474	4	11	of	of	ADP
cana-3474	4	12	interest	interest	NOUN
cana-3474	4	13	to	to	ADP
cana-3474	4	14	many	many	ADJ
cana-3474	4	15	mathematicians	mathematician	NOUN
cana-3474	4	16	and	and	CCONJ
cana-3474	4	17	scientists	scientist	NOUN
cana-3474	4	18	.	.	PUNCT
cana-3474	5	1	our	our	PRON
cana-3474	5	2	aim	aim	NOUN
cana-3474	5	3	of	of	ADP
cana-3474	5	4	this	this	DET
cana-3474	5	5	paper	paper	NOUN
cana-3474	5	6	is	be	AUX
cana-3474	5	7	to	to	PART
cana-3474	5	8	explore	explore	VERB
cana-3474	5	9	and	and	CCONJ
cana-3474	5	10	figure	figure	VERB
cana-3474	5	11	out	out	ADP
cana-3474	5	12	the	the	DET
cana-3474	5	13	solution	solution	NOUN
cana-3474	5	14	of	of	ADP
cana-3474	5	15	the	the	DET
cana-3474	5	16	volterra	volterra	NOUN
cana-3474	5	17	integro	integro	PROPN
cana-3474	5	18	-	-	PUNCT
cana-3474	5	19	differential	differential	NOUN
cana-3474	5	20	equation	equation	NOUN
cana-3474	5	21	with	with	ADP
cana-3474	5	22	a	a	DET
cana-3474	5	23	convolution	convolution	NOUN
cana-3474	5	24	kernel	kernel	NOUN
cana-3474	5	25	.	.	PUNCT
cana-3474	6	1	we	we	PRON
cana-3474	6	2	now	now	ADV
cana-3474	6	3	introduce	introduce	VERB
cana-3474	6	4	the	the	DET
cana-3474	6	5	w	w	NOUN
cana-3474	6	6	transform	transform	NOUN
cana-3474	6	7	for	for	ADP
cana-3474	6	8	determining	determine	VERB
cana-3474	6	9	the	the	DET
cana-3474	6	10	solution	solution	NOUN
cana-3474	6	11	of	of	ADP
cana-3474	6	12	linear	linear	PROPN
cana-3474	6	13	volterra	volterra	PROPN
cana-3474	6	14	integro	integro	PROPN
cana-3474	6	15	-	-	PUNCT
cana-3474	6	16	differential	differential	NOUN
cana-3474	6	17	equation	equation	NOUN
cana-3474	6	18	of	of	ADP
cana-3474	6	19	the	the	DET
cana-3474	6	20	second	second	ADJ
cana-3474	6	21	kind	kind	NOUN
cana-3474	6	22	and	and	CCONJ
cana-3474	6	23	their	their	PRON
cana-3474	6	24	system	system	NOUN
cana-3474	6	25	.	.	PUNCT
cana-3474	7	1	the	the	DET
cana-3474	7	2	ability	ability	NOUN
cana-3474	7	3	of	of	ADP
cana-3474	7	4	the	the	DET
cana-3474	7	5	w	w	PROPN
cana-3474	7	6	transform	transform	NOUN
cana-3474	7	7	to	to	PART
cana-3474	7	8	solve	solve	VERB
cana-3474	7	9	these	these	DET
cana-3474	7	10	equations	equation	NOUN
cana-3474	7	11	is	be	AUX
cana-3474	7	12	shown	show	VERB
cana-3474	7	13	by	by	ADP
cana-3474	7	14	realworld	realworld	PROPN
cana-3474	7	15	applications	application	NOUN
cana-3474	7	16	.	.	PUNCT
cana-3474	8	1	based	base	VERB
cana-3474	8	2	on	on	ADP
cana-3474	8	3	what	what	PRON
cana-3474	8	4	we	we	PRON
cana-3474	8	5	discovered	discover	VERB
cana-3474	8	6	,	,	PUNCT
cana-3474	8	7	the	the	DET
cana-3474	8	8	w	w	PROPN
cana-3474	8	9	transform	transform	NOUN
cana-3474	8	10	is	be	AUX
cana-3474	8	11	an	an	DET
cana-3474	8	12	effective	effective	ADJ
cana-3474	8	13	method	method	NOUN
cana-3474	8	14	for	for	ADP
cana-3474	8	15	locating	locate	VERB
cana-3474	8	16	precise	precise	ADJ
cana-3474	8	17	answers	answer	NOUN
cana-3474	8	18	to	to	ADP
cana-3474	8	19	the	the	DET
cana-3474	8	20	linear	linear	PROPN
cana-3474	8	21	volterra	volterra	PROPN
cana-3474	8	22	integro	integro	PROPN
cana-3474	8	23	-	-	PUNCT
cana-3474	8	24	differential	differential	NOUN
cana-3474	8	25	equation	equation	NOUN
cana-3474	8	26	of	of	ADP
cana-3474	8	27	the	the	DET
cana-3474	8	28	second	second	ADJ
cana-3474	8	29	kind	kind	NOUN
cana-3474	8	30	and	and	CCONJ
cana-3474	8	31	their	their	PRON
cana-3474	8	32	system	system	NOUN
cana-3474	8	33	.	.	PUNCT
cana-3474	9	1	keywords	keyword	NOUN
cana-3474	9	2	:	:	PUNCT
cana-3474	9	3	volterra	volterra	PROPN
cana-3474	9	4	integro	integro	PROPN
cana-3474	9	5	-	-	PUNCT
cana-3474	9	6	differential	differential	NOUN
cana-3474	9	7	equation	equation	NOUN
cana-3474	9	8	,	,	PUNCT
cana-3474	9	9	w	w	NOUN
cana-3474	9	10	transform	transform	NOUN
cana-3474	9	11	,	,	PUNCT
cana-3474	9	12	convolution	convolution	NOUN
cana-3474	9	13	,	,	PUNCT
cana-3474	9	14	inverse	inverse	NOUN
cana-3474	9	15	of	of	ADP
cana-3474	9	16	w	w	PROPN
cana-3474	9	17	transform	transform	NOUN
cana-3474	9	18	.	.	PUNCT
cana-3474	10	1	1	1	NUM
cana-3474	10	2	introduction	introduction	NOUN
cana-3474	10	3	:	:	PUNCT
cana-3474	10	4	the	the	DET
cana-3474	10	5	study	study	NOUN
cana-3474	10	6	of	of	ADP
cana-3474	10	7	integral	integral	ADJ
cana-3474	10	8	equations	equation	NOUN
cana-3474	10	9	possibly	possibly	ADV
cana-3474	10	10	considered	consider	VERB
cana-3474	10	11	fundamentally	fundamentally	ADV
cana-3474	10	12	more	more	ADV
cana-3474	10	13	significant	significant	ADJ
cana-3474	10	14	than	than	ADP
cana-3474	10	15	differential	differential	ADJ
cana-3474	10	16	equations	equation	NOUN
cana-3474	10	17	since	since	SCONJ
cana-3474	10	18	,	,	PUNCT
cana-3474	10	19	compared	compare	VERB
cana-3474	10	20	to	to	ADP
cana-3474	10	21	differential	differential	ADJ
cana-3474	10	22	equations	equation	NOUN
cana-3474	10	23	,	,	PUNCT
cana-3474	10	24	integral	integral	ADJ
cana-3474	10	25	equations	equation	NOUN
cana-3474	10	26	frequently	frequently	ADV
cana-3474	10	27	offer	offer	VERB
cana-3474	10	28	more	more	ADV
cana-3474	10	29	effective	effective	ADJ
cana-3474	10	30	models	model	NOUN
cana-3474	10	31	and	and	CCONJ
cana-3474	10	32	less	less	ADJ
cana-3474	10	33	restrictions	restriction	NOUN
cana-3474	10	34	.	.	PUNCT
cana-3474	11	1	additionally	additionally	ADV
cana-3474	11	2	,	,	PUNCT
cana-3474	11	3	differentiation	differentiation	NOUN
cana-3474	11	4	in	in	ADP
cana-3474	11	5	numerical	numerical	ADJ
cana-3474	11	6	analysis	analysis	NOUN
cana-3474	11	7	tends	tend	VERB
cana-3474	11	8	to	to	PART
cana-3474	11	9	increase	increase	VERB
cana-3474	11	10	error	error	NOUN
cana-3474	11	11	,	,	PUNCT
cana-3474	11	12	whereas	whereas	SCONJ
cana-3474	11	13	integration	integration	NOUN
cana-3474	11	14	tends	tend	VERB
cana-3474	11	15	to	to	PART
cana-3474	11	16	reduce	reduce	VERB
cana-3474	11	17	error	error	NOUN
cana-3474	11	18	.	.	PUNCT
cana-3474	12	1	the	the	DET
cana-3474	12	2	growing	grow	VERB
cana-3474	12	3	use	use	NOUN
cana-3474	12	4	of	of	ADP
cana-3474	12	5	integral	integral	ADJ
cana-3474	12	6	equations	equation	NOUN
cana-3474	12	7	in	in	ADP
cana-3474	12	8	the	the	DET
cana-3474	12	9	literature	literature	NOUN
cana-3474	12	10	and	and	CCONJ
cana-3474	12	11	in	in	ADP
cana-3474	12	12	many	many	ADJ
cana-3474	12	13	areas	area	NOUN
cana-3474	12	14	of	of	ADP
cana-3474	12	15	applied	apply	VERB
cana-3474	12	16	mathematics	mathematic	NOUN
cana-3474	12	17	is	be	AUX
cana-3474	12	18	evidence	evidence	NOUN
cana-3474	12	19	of	of	ADP
cana-3474	12	20	their	their	PRON
cana-3474	12	21	advantages	advantage	NOUN
cana-3474	12	22	,	,	PUNCT
cana-3474	12	23	as	as	SCONJ
cana-3474	12	24	stated	state	VERB
cana-3474	12	25	that	that	SCONJ
cana-3474	12	26	certain	certain	ADJ
cana-3474	12	27	issues	issue	NOUN
cana-3474	12	28	naturally	naturally	ADV
cana-3474	12	29	and	and	CCONJ
cana-3474	12	30	directly	directly	ADV
cana-3474	12	31	exhibit	exhibit	VERB
cana-3474	12	32	their	their	PRON
cana-3474	12	33	mathematical	mathematical	ADJ
cana-3474	12	34	representation	representation	NOUN
cana-3474	12	35	,	,	PUNCT
cana-3474	12	36	according	accord	VERB
cana-3474	12	37	to	to	ADP
cana-3474	12	38	integral	integral	ADJ
cana-3474	12	39	equations	equation	NOUN
cana-3474	12	40	.	.	PUNCT
cana-3474	13	1	additional	additional	ADJ
cana-3474	13	2	issues	issue	NOUN
cana-3474	13	3	,	,	PUNCT
cana-3474	13	4	whose	whose	DET
cana-3474	13	5	direct	direct	ADJ
cana-3474	13	6	form	form	NOUN
cana-3474	13	7	is	be	AUX
cana-3474	13	8	in	in	ADP
cana-3474	13	9	terms	term	NOUN
cana-3474	13	10	of	of	ADP
cana-3474	13	11	differential	differential	ADJ
cana-3474	13	12	equations	equation	NOUN
cana-3474	13	13	,	,	PUNCT
cana-3474	13	14	have	have	VERB
cana-3474	13	15	integral	integral	ADJ
cana-3474	13	16	equations	equation	NOUN
cana-3474	13	17	more	more	ADV
cana-3474	13	18	eloquently	eloquently	ADV
cana-3474	13	19	and	and	CCONJ
cana-3474	13	20	compactly	compactly	ADV
cana-3474	13	21	substituted	substitute	VERB
cana-3474	13	22	for	for	ADP
cana-3474	13	23	their	their	PRON
cana-3474	13	24	auxiliary	auxiliary	ADJ
cana-3474	13	25	conditions	condition	NOUN
cana-3474	13	26	.	.	PUNCT
cana-3474	14	1	integro	integro	ADJ
cana-3474	14	2	-	-	PUNCT
cana-3474	14	3	differential	differential	NOUN
cana-3474	14	4	equations	equation	NOUN
cana-3474	14	5	are	be	AUX
cana-3474	14	6	a	a	DET
cana-3474	14	7	common	common	ADJ
cana-3474	14	8	mathematical	mathematical	ADJ
cana-3474	14	9	formulation	formulation	NOUN
cana-3474	14	10	used	use	VERB
cana-3474	14	11	to	to	PART
cana-3474	14	12	describe	describe	VERB
cana-3474	14	13	physical	physical	ADJ
cana-3474	14	14	processes	process	NOUN
cana-3474	14	15	,	,	PUNCT
cana-3474	14	16	several	several	ADJ
cana-3474	14	17	domains	domain	NOUN
cana-3474	14	18	,	,	PUNCT
cana-3474	14	19	including	include	VERB
cana-3474	14	20	physics	physics	NOUN
cana-3474	14	21	,	,	PUNCT
cana-3474	14	22	astronomy	astronomy	NOUN
cana-3474	14	23	,	,	PUNCT
cana-3474	14	24	potential	potential	ADJ
cana-3474	14	25	theory	theory	NOUN
cana-3474	14	26	,	,	PUNCT
cana-3474	14	27	fluid	fluid	ADJ
cana-3474	14	28	dynamics	dynamic	NOUN
cana-3474	14	29	,	,	PUNCT
cana-3474	14	30	chemical	chemical	NOUN
cana-3474	14	31	kinetics	kinetic	NOUN
cana-3474	14	32	,	,	PUNCT
cana-3474	14	33	and	and	CCONJ
cana-3474	14	34	biological	biological	ADJ
cana-3474	14	35	models	model	NOUN
cana-3474	14	36	,	,	PUNCT
cana-3474	14	37	use	use	VERB
cana-3474	14	38	these	these	DET
cana-3474	14	39	equations	equation	NOUN
cana-3474	14	40	.	.	PUNCT
cana-3474	15	1	multiple	multiple	ADJ
cana-3474	15	2	techniques	technique	NOUN
cana-3474	15	3	have	have	AUX
cana-3474	15	4	been	be	AUX
cana-3474	15	5	applied	apply	VERB
cana-3474	15	6	in	in	ADP
cana-3474	15	7	recent	recent	ADJ
cana-3474	15	8	years	year	NOUN
cana-3474	15	9	through	through	ADP
cana-3474	15	10	certain	certain	ADJ
cana-3474	15	11	investigators	investigator	NOUN
cana-3474	15	12	to	to	PART
cana-3474	15	13	solve	solve	VERB
cana-3474	15	14	linear	linear	PROPN
cana-3474	15	15	volterra	volterra	PROPN
cana-3474	15	16	integro	integro	PROPN
cana-3474	15	17	-	-	PUNCT
cana-3474	15	18	differential	differential	NOUN
cana-3474	15	19	equation	equation	NOUN
cana-3474	15	20	of	of	ADP
cana-3474	15	21	the	the	DET
cana-3474	15	22	second	second	ADJ
cana-3474	15	23	kind	kind	NOUN
cana-3474	15	24	and	and	CCONJ
cana-3474	15	25	their	their	PRON
cana-3474	15	26	system	system	NOUN
cana-3474	15	27	(	(	PUNCT
cana-3474	15	28	lvi	lvi	NOUN
cana-3474	15	29	-	-	PUNCT
cana-3474	15	30	de	de	PROPN
cana-3474	15	31	of	of	ADP
cana-3474	15	32	2nd	2nd	ADJ
cana-3474	15	33	kind	kind	NOUN
cana-3474	15	34	&	&	CCONJ
cana-3474	15	35	lsvi	lsvi	PROPN
cana-3474	15	36	-	-	PUNCT
cana-3474	15	37	de	de	NOUN
cana-3474	15	38	of	of	ADP
cana-3474	15	39	2nd	2nd	ADJ
cana-3474	15	40	kind	kind	NOUN
cana-3474	15	41	)	)	PUNCT
cana-3474	15	42	.	.	PUNCT
cana-3474	16	1	we	we	PRON
cana-3474	16	2	introduce	introduce	VERB
cana-3474	16	3	some	some	DET
cana-3474	16	4	numerical	numerical	ADJ
cana-3474	16	5	and	and	CCONJ
cana-3474	16	6	analytical	analytical	ADJ
cana-3474	16	7	methods	method	NOUN
cana-3474	16	8	for	for	ADP
cana-3474	16	9	solving	solve	VERB
cana-3474	16	10	vi	vi	NOUN
cana-3474	16	11	-	-	PUNCT
cana-3474	16	12	de	de	NOUN
cana-3474	16	13	of	of	ADP
cana-3474	16	14	2nd	2nd	ADJ
cana-3474	16	15	kind	kind	NOUN
cana-3474	16	16	&	&	CCONJ
cana-3474	16	17	svi	svi	PROPN
cana-3474	16	18	-	-	PROPN
cana-3474	16	19	de	de	X
cana-3474	16	20	of	of	ADP
cana-3474	16	21	2nd	2nd	ADJ
cana-3474	16	22	kind	kind	NOUN
cana-3474	16	23	.	.	PUNCT
cana-3474	17	1	communications	communication	NOUN
cana-3474	17	2	on	on	ADP
cana-3474	17	3	applied	apply	VERB
cana-3474	17	4	nonlinear	nonlinear	ADJ
cana-3474	17	5	analysis	analysis	NOUN
cana-3474	17	6	issn	issn	NOUN
cana-3474	17	7	:	:	PUNCT
cana-3474	17	8	1074	1074	NUM
cana-3474	17	9	-	-	PUNCT
cana-3474	17	10	133x	133x	NUM
cana-3474	17	11	vol	vol	NOUN
cana-3474	17	12	32	32	NUM
cana-3474	17	13	no	no	NOUN
cana-3474	17	14	.	.	PUNCT
cana-3474	18	1	7s	7	NOUN
cana-3474	18	2	(	(	PUNCT
cana-3474	18	3	2025	2025	NUM
cana-3474	18	4	)	)	PUNCT
cana-3474	18	5	676	676	NUM
cana-3474	18	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	18	7	taiye	taiye	PRON
cana-3474	18	8	oyedepo	oyedepo	NOUN
cana-3474	18	9	et	et	PROPN
cana-3474	18	10	al	al	PROPN
cana-3474	18	11	.	.	PROPN
cana-3474	18	12	,	,	PUNCT
cana-3474	18	13	presented	present	VERB
cana-3474	18	14	a	a	DET
cana-3474	18	15	computing	compute	VERB
cana-3474	18	16	methodology	methodology	NOUN
cana-3474	18	17	to	to	PART
cana-3474	18	18	deal	deal	VERB
cana-3474	18	19	with	with	ADP
cana-3474	18	20	vides	vide	NOUN
cana-3474	18	21	using	use	VERB
cana-3474	18	22	shifted	shift	VERB
cana-3474	18	23	vietalucas	vietalucas	ADJ
cana-3474	18	24	polynomials	polynomial	NOUN
cana-3474	18	25	as	as	ADP
cana-3474	18	26	the	the	DET
cana-3474	18	27	foundational	foundational	ADJ
cana-3474	18	28	basis	basis	NOUN
cana-3474	19	1	functions[1].g.a	functions[1].g.a	PROPN
cana-3474	19	2	.	.	PROPN
cana-3474	19	3	aghayeva	aghayeva	PROPN
cana-3474	19	4	,	,	PUNCT
cana-3474	19	5	et	et	PROPN
cana-3474	19	6	al	al	PROPN
cana-3474	19	7	.	.	PROPN
cana-3474	19	8	,	,	PUNCT
cana-3474	19	9	provides	provide	VERB
cana-3474	19	10	a	a	DET
cana-3474	19	11	comparison	comparison	NOUN
cana-3474	19	12	among	among	ADP
cana-3474	19	13	the	the	DET
cana-3474	19	14	mathematical	mathematical	ADJ
cana-3474	19	15	methods	method	NOUN
cana-3474	19	16	used	use	VERB
cana-3474	19	17	to	to	PART
cana-3474	19	18	address	address	VERB
cana-3474	19	19	the	the	DET
cana-3474	19	20	integral	integral	ADJ
cana-3474	19	21	volterra	volterra	NOUN
cana-3474	19	22	,	,	PUNCT
cana-3474	19	23	and	and	CCONJ
cana-3474	19	24	odes	ode	VERB
cana-3474	19	25	[	[	X
cana-3474	19	26	2	2	NUM
cana-3474	19	27	]	]	PUNCT
cana-3474	19	28	.	.	PUNCT
cana-3474	20	1	asiya	asiya	PROPN
cana-3474	20	2	ansari	ansari	PROPN
cana-3474	20	3	et	et	PROPN
cana-3474	20	4	al	al	PROPN
cana-3474	20	5	.	.	PROPN
cana-3474	20	6	,	,	PUNCT
cana-3474	20	7	to	to	PART
cana-3474	20	8	solve	solve	VERB
cana-3474	20	9	the	the	DET
cana-3474	20	10	linear	linear	ADJ
cana-3474	20	11	or	or	CCONJ
cana-3474	20	12	non	non	ADJ
cana-3474	20	13	-	-	ADJ
cana-3474	20	14	linear	linear	ADJ
cana-3474	20	15	vide	vide	NOUN
cana-3474	20	16	,	,	PUNCT
cana-3474	20	17	the	the	DET
cana-3474	20	18	series	series	PROPN
cana-3474	20	19	solution	solution	NOUN
cana-3474	20	20	method	method	NOUN
cana-3474	20	21	(	(	PUNCT
cana-3474	20	22	ssm	ssm	NOUN
cana-3474	20	23	)	)	PUNCT
cana-3474	20	24	is	be	AUX
cana-3474	20	25	utilized[3	utilized[3	NOUN
cana-3474	20	26	]	]	PUNCT
cana-3474	20	27	.	.	PUNCT
cana-3474	21	1	ahmad	ahmad	PROPN
cana-3474	21	2	issa	issa	PROPN
cana-3474	21	3	apply	apply	VERB
cana-3474	21	4	the	the	DET
cana-3474	21	5	rebuilding	rebuilding	NOUN
cana-3474	21	6	of	of	ADP
cana-3474	21	7	method	method	NOUN
cana-3474	21	8	of	of	ADP
cana-3474	21	9	variational	variational	ADJ
cana-3474	21	10	iteration	iteration	NOUN
cana-3474	21	11	for	for	ADP
cana-3474	21	12	finding	find	VERB
cana-3474	21	13	numerical	numerical	ADJ
cana-3474	21	14	solution	solution	NOUN
cana-3474	21	15	of	of	ADP
cana-3474	21	16	lsvide	lsvide	NOUN
cana-3474	21	17	[	[	X
cana-3474	21	18	4	4	NUM
cana-3474	21	19	]	]	PUNCT
cana-3474	21	20	,	,	PUNCT
cana-3474	21	21	mohamed	mohamed	PROPN
cana-3474	21	22	e.a	e.a	PROPN
cana-3474	21	23	.	.	PROPN
cana-3474	21	24	alnair	alnair	PROPN
cana-3474	21	25	and	and	CCONJ
cana-3474	21	26	ahmed	ahmed	PROPN
cana-3474	21	27	a.	a.	PROPN
cana-3474	21	28	khidir	khidir	PROPN
cana-3474	21	29	are	be	AUX
cana-3474	21	30	displays	display	NOUN
cana-3474	21	31	a	a	DET
cana-3474	21	32	new	new	ADJ
cana-3474	21	33	novel	novel	NOUN
cana-3474	21	34	method	method	NOUN
cana-3474	21	35	for	for	ADP
cana-3474	21	36	resolving	resolve	VERB
cana-3474	21	37	lvi	lvi	NOUN
cana-3474	21	38	-	-	PUNCT
cana-3474	21	39	des	de	NOUN
cana-3474	21	40	under	under	ADP
cana-3474	21	41	border	border	NOUN
cana-3474	21	42	restrictions	restriction	NOUN
cana-3474	21	43	,	,	PUNCT
cana-3474	21	44	the	the	DET
cana-3474	21	45	technique	technique	NOUN
cana-3474	21	46	is	be	AUX
cana-3474	21	47	founded	found	VERB
cana-3474	21	48	on	on	ADP
cana-3474	21	49	combining	combine	VERB
cana-3474	21	50	the	the	DET
cana-3474	21	51	chebyshev	chebyshev	NOUN
cana-3474	21	52	spectral	spectral	ADJ
cana-3474	21	53	techniques	technique	NOUN
cana-3474	21	54	[	[	X
cana-3474	21	55	5	5	NUM
cana-3474	21	56	]	]	PUNCT
cana-3474	21	57	.	.	PUNCT
cana-3474	22	1	r.a	r.a	PROPN
cana-3474	22	2	.	.	PROPN
cana-3474	22	3	olowe	olowe	PROPN
cana-3474	22	4	et	et	PROPN
cana-3474	22	5	al	al	PROPN
cana-3474	22	6	.	.	PROPN
cana-3474	22	7	,	,	PUNCT
cana-3474	22	8	by	by	ADP
cana-3474	22	9	using	use	VERB
cana-3474	22	10	the	the	DET
cana-3474	22	11	multistep	multistep	ADJ
cana-3474	22	12	collocation	collocation	NOUN
cana-3474	22	13	method	method	NOUN
cana-3474	22	14	,	,	PUNCT
cana-3474	22	15	trigonometry	trigonometry	NOUN
cana-3474	22	16	third	third	ADJ
cana-3474	22	17	derivative	derivative	ADJ
cana-3474	22	18	matched	match	VERB
cana-3474	22	19	simpson	simpson	PROPN
cana-3474	22	20	's	's	PART
cana-3474	22	21	method	method	NOUN
cana-3474	22	22	is	be	AUX
cana-3474	22	23	created	create	VERB
cana-3474	22	24	and	and	CCONJ
cana-3474	22	25	used	use	VERB
cana-3474	22	26	in	in	ADP
cana-3474	22	27	order	order	NOUN
cana-3474	22	28	to	to	PART
cana-3474	22	29	get	get	VERB
cana-3474	22	30	close	close	ADJ
cana-3474	22	31	to	to	ADP
cana-3474	22	32	the	the	DET
cana-3474	22	33	answer	answer	NOUN
cana-3474	22	34	of	of	ADP
cana-3474	22	35	vides[6	vides[6	ADP
cana-3474	22	36	]	]	PUNCT
cana-3474	22	37	.	.	PUNCT
cana-3474	23	1	o.	o.	PROPN
cana-3474	23	2	a.	a.	PROPN
cana-3474	23	3	uwaheren	uwaheren	PROPN
cana-3474	23	4	et	et	PROPN
cana-3474	23	5	al	al	PROPN
cana-3474	23	6	.	.	PROPN
cana-3474	23	7	,	,	PUNCT
cana-3474	23	8	utilizing	utilize	VERB
cana-3474	23	9	legendre	legendre	NOUN
cana-3474	23	10	polynomials	polynomial	NOUN
cana-3474	23	11	as	as	SCONJ
cana-3474	23	12	basis	basis	NOUN
cana-3474	23	13	functions	function	NOUN
cana-3474	23	14	,	,	PUNCT
cana-3474	23	15	akbari	akbari	PROPN
cana-3474	23	16	-	-	PUNCT
cana-3474	23	17	ganji	ganji	NOUN
cana-3474	23	18	's	's	PART
cana-3474	23	19	method	method	NOUN
cana-3474	23	20	(	(	PUNCT
cana-3474	23	21	agm	agm	PROPN
cana-3474	23	22	)	)	PUNCT
cana-3474	23	23	was	be	AUX
cana-3474	23	24	utilized	utilize	VERB
cana-3474	23	25	to	to	PART
cana-3474	23	26	solve	solve	VERB
cana-3474	23	27	vide[7	vide[7	NOUN
cana-3474	23	28	]	]	PUNCT
cana-3474	23	29	.	.	PUNCT
cana-3474	24	1	a.	a.	PROPN
cana-3474	24	2	al	al	PROPN
cana-3474	24	3	-	-	PROPN
cana-3474	24	4	shimmary	shimmary	PROPN
cana-3474	24	5	et	et	PROPN
cana-3474	24	6	al	al	PROPN
cana-3474	24	7	.	.	PROPN
cana-3474	24	8	,	,	PUNCT
cana-3474	24	9	by	by	ADP
cana-3474	24	10	using	use	VERB
cana-3474	24	11	the	the	DET
cana-3474	24	12	sixth	sixth	ADJ
cana-3474	24	13	-	-	PUNCT
cana-3474	24	14	order	order	NOUN
cana-3474	24	15	rungekutta	rungekutta	NOUN
cana-3474	24	16	method	method	NOUN
cana-3474	24	17	,	,	PUNCT
cana-3474	24	18	they	they	PRON
cana-3474	24	19	can	can	AUX
cana-3474	24	20	solve	solve	VERB
cana-3474	24	21	vide	vide	ADV
cana-3474	24	22	numerically[8	numerically[8	NOUN
cana-3474	24	23	]	]	PUNCT
cana-3474	24	24	.	.	PUNCT
cana-3474	25	1	monali	monali	PROPN
cana-3474	25	2	derle	derle	PROPN
cana-3474	25	3	and	and	CCONJ
cana-3474	25	4	dinkar	dinkar	PROPN
cana-3474	25	5	patil	patil	PROPN
cana-3474	25	6	,	,	PUNCT
cana-3474	25	7	convolution	convolution	NOUN
cana-3474	25	8	theory	theory	NOUN
cana-3474	25	9	and	and	CCONJ
cana-3474	25	10	dual	dual	ADJ
cana-3474	25	11	generalization	generalization	NOUN
cana-3474	25	12	with	with	ADP
cana-3474	25	13	the	the	DET
cana-3474	25	14	purpose	purpose	NOUN
cana-3474	25	15	of	of	ADP
cana-3474	25	16	solving	solve	VERB
cana-3474	25	17	ide	ide	NOUN
cana-3474	25	18	,	,	PUNCT
cana-3474	25	19	the	the	DET
cana-3474	25	20	rangaig	rangaig	ADJ
cana-3474	25	21	integral	integral	ADJ
cana-3474	25	22	transformation	transformation	NOUN
cana-3474	25	23	had	have	AUX
cana-3474	25	24	been	be	AUX
cana-3474	25	25	employed[9	employed[9	NOUN
cana-3474	25	26	]	]	X
cana-3474	25	27	.	.	PUNCT
cana-3474	26	1	s.	s.	PROPN
cana-3474	26	2	aggarwal	aggarwal	PROPN
cana-3474	26	3	et	et	PROPN
cana-3474	26	4	al	al	PROPN
cana-3474	26	5	.	.	PROPN
cana-3474	26	6	,	,	PUNCT
cana-3474	26	7	when	when	SCONJ
cana-3474	26	8	dealing	deal	VERB
cana-3474	26	9	with	with	ADP
cana-3474	26	10	lvi	lvi	NOUN
cana-3474	26	11	-	-	PUNCT
cana-3474	26	12	de	de	PROPN
cana-3474	26	13	of	of	ADP
cana-3474	26	14	2nd	2nd	ADJ
cana-3474	26	15	kind	kind	NOUN
cana-3474	26	16	,	,	PUNCT
cana-3474	26	17	apply	apply	VERB
cana-3474	26	18	the	the	DET
cana-3474	26	19	sadik	sadik	ADJ
cana-3474	26	20	transform[10	transform[10	PROPN
cana-3474	26	21	]	]	PUNCT
cana-3474	26	22	.	.	PUNCT
cana-3474	27	1	s.	s.	PROPN
cana-3474	27	2	al	al	PROPN
cana-3474	27	3	-	-	PUNCT
cana-3474	27	4	ahmad	ahmad	PROPN
cana-3474	27	5	et	et	PROPN
cana-3474	27	6	al	al	PROPN
cana-3474	27	7	.	.	PROPN
cana-3474	27	8	,	,	PUNCT
cana-3474	27	9	utilize	utilize	VERB
cana-3474	27	10	the	the	DET
cana-3474	27	11	modified	modify	VERB
cana-3474	27	12	differential	differential	NOUN
cana-3474	27	13	transform	transform	NOUN
cana-3474	27	14	approach	approach	NOUN
cana-3474	27	15	to	to	PART
cana-3474	27	16	discover	discover	VERB
cana-3474	27	17	the	the	DET
cana-3474	27	18	analytical	analytical	ADJ
cana-3474	27	19	solution	solution	NOUN
cana-3474	27	20	for	for	ADP
cana-3474	27	21	the	the	DET
cana-3474	27	22	lsvi	lsvi	NOUN
cana-3474	27	23	-	-	PUNCT
cana-3474	27	24	de[11	de[11	NOUN
cana-3474	27	25	]	]	PUNCT
cana-3474	27	26	.	.	PUNCT
cana-3474	28	1	h.	h.	PROPN
cana-3474	28	2	bozburun	bozburun	PROPN
cana-3474	28	3	and	and	CCONJ
cana-3474	28	4	h.	h.	PROPN
cana-3474	28	5	a.	a.	NOUN
cana-3474	28	6	peker	peker	PROPN
cana-3474	28	7	,	,	PUNCT
cana-3474	28	8	apply	apply	VERB
cana-3474	28	9	the	the	DET
cana-3474	28	10	shehu	shehu	NOUN
cana-3474	28	11	transform	transform	VERB
cana-3474	28	12	to	to	PART
cana-3474	28	13	solve	solve	VERB
cana-3474	28	14	the	the	DET
cana-3474	28	15	lvi	lvi	NOUN
cana-3474	28	16	-	-	PUNCT
cana-3474	28	17	de	de	PROPN
cana-3474	28	18	of	of	ADP
cana-3474	28	19	2nd	2nd	PROPN
cana-3474	28	20	kind[12	kind[12	PROPN
cana-3474	28	21	]	]	PUNCT
cana-3474	28	22	.	.	PUNCT
cana-3474	29	1	n.	n.	PROPN
cana-3474	29	2	a.	a.	PROPN
cana-3474	29	3	elbhilil	elbhilil	PROPN
cana-3474	29	4	et	et	PROPN
cana-3474	29	5	al	al	PROPN
cana-3474	29	6	.	.	PROPN
cana-3474	29	7	,	,	PUNCT
cana-3474	29	8	solved	solve	VERB
cana-3474	29	9	the	the	DET
cana-3474	29	10	volterra	volterra	NOUN
cana-3474	29	11	integral	integral	ADJ
cana-3474	29	12	and	and	CCONJ
cana-3474	29	13	lvi	lvi	PROPN
cana-3474	29	14	-	-	PUNCT
cana-3474	29	15	de	de	ADV
cana-3474	29	16	using	use	VERB
cana-3474	29	17	the	the	DET
cana-3474	29	18	abaoub	abaoub	NOUN
cana-3474	29	19	-	-	PUNCT
cana-3474	29	20	shkheam	shkheam	NOUN
cana-3474	29	21	transform	transform	NOUN
cana-3474	29	22	techniques[13	techniques[13	NOUN
cana-3474	29	23	]	]	PUNCT
cana-3474	29	24	.	.	PUNCT
cana-3474	30	1	h.	h.	PROPN
cana-3474	30	2	k.	k.	PROPN
cana-3474	30	3	jassim	jassim	PROPN
cana-3474	30	4	use	use	VERB
cana-3474	30	5	the	the	DET
cana-3474	30	6	yang	yang	PROPN
cana-3474	30	7	-	-	PUNCT
cana-3474	30	8	laplace	laplace	PROPN
cana-3474	30	9	transform	transform	NOUN
cana-3474	30	10	to	to	PART
cana-3474	30	11	determine	determine	VERB
cana-3474	30	12	the	the	DET
cana-3474	30	13	analytical	analytical	ADJ
cana-3474	30	14	solutions	solution	NOUN
cana-3474	30	15	for	for	ADP
cana-3474	30	16	lvi	lvi	NOUN
cana-3474	30	17	-	-	PUNCT
cana-3474	30	18	de	de	NOUN
cana-3474	30	19	within	within	ADP
cana-3474	30	20	local	local	ADJ
cana-3474	30	21	fractional	fractional	ADJ
cana-3474	30	22	operators[14	operators[14	PROPN
cana-3474	30	23	]	]	PUNCT
cana-3474	30	24	.	.	PUNCT
cana-3474	31	1	z.	z.	PROPN
cana-3474	31	2	rustam	rustam	PROPN
cana-3474	31	3	and	and	CCONJ
cana-3474	31	4	n.	n.	PROPN
cana-3474	31	5	sulaiman	sulaiman	PROPN
cana-3474	31	6	are	be	AUX
cana-3474	31	7	used	use	VERB
cana-3474	31	8	(	(	PUNCT
cana-3474	31	9	kamal	kamal	PROPN
cana-3474	31	10	&	&	CCONJ
cana-3474	31	11	see	see	VERB
cana-3474	31	12	)	)	PUNCT
cana-3474	31	13	transformation	transformation	NOUN
cana-3474	31	14	methodology	methodology	NOUN
cana-3474	31	15	for	for	ADP
cana-3474	31	16	solving	solve	VERB
cana-3474	31	17	lsvi	lsvi	NOUN
cana-3474	31	18	-	-	PUNCT
cana-3474	31	19	de	de	NOUN
cana-3474	31	20	of	of	ADP
cana-3474	31	21	2nd	2nd	ADJ
cana-3474	31	22	kind[15	kind[15	PROPN
cana-3474	31	23	,	,	PUNCT
cana-3474	31	24	16	16	NUM
cana-3474	31	25	]	]	PUNCT
cana-3474	31	26	.	.	PUNCT
cana-3474	32	1	marjan	marjan	PROPN
cana-3474	32	2	uddin	uddin	PROPN
cana-3474	32	3	and	and	CCONJ
cana-3474	32	4	musafir	musafir	PROPN
cana-3474	32	5	uddin	uddin	PROPN
cana-3474	32	6	,	,	PUNCT
cana-3474	32	7	regarding	regard	VERB
cana-3474	32	8	the	the	DET
cana-3474	32	9	laplace	laplace	NOUN
cana-3474	32	10	transform	transform	NOUN
cana-3474	32	11	-	-	PUNCT
cana-3474	32	12	based	base	VERB
cana-3474	32	13	numerical	numerical	ADJ
cana-3474	32	14	approximation	approximation	NOUN
cana-3474	32	15	of	of	ADP
cana-3474	32	16	the	the	DET
cana-3474	32	17	lvi	lvi	NOUN
cana-3474	32	18	-	-	PUNCT
cana-3474	32	19	de[17	de[17	PROPN
cana-3474	32	20	]	]	PUNCT
cana-3474	32	21	.	.	PUNCT
cana-3474	33	1	an	an	DET
cana-3474	33	2	investigation	investigation	NOUN
cana-3474	33	3	and	and	CCONJ
cana-3474	33	4	use	use	NOUN
cana-3474	33	5	of	of	ADP
cana-3474	33	6	a	a	DET
cana-3474	33	7	recently	recently	ADV
cana-3474	33	8	developed	develop	VERB
cana-3474	33	9	integral	integral	ADJ
cana-3474	33	10	transform	transform	NOUN
cana-3474	33	11	,	,	PUNCT
cana-3474	33	12	or	or	CCONJ
cana-3474	33	13	w	w	NOUN
cana-3474	33	14	transform	transform	NOUN
cana-3474	33	15	,	,	PUNCT
cana-3474	33	16	were	be	AUX
cana-3474	33	17	conducted	conduct	VERB
cana-3474	33	18	by	by	ADP
cana-3474	33	19	ping	ping	PROPN
cana-3474	33	20	wang	wang	PROPN
cana-3474	33	21	et	et	PROPN
cana-3474	33	22	al	al	PROPN
cana-3474	33	23	.	.	PUNCT
cana-3474	34	1	at	at	ADP
cana-3474	34	2	this	this	DET
cana-3474	34	3	point	point	NOUN
cana-3474	34	4	,	,	PUNCT
cana-3474	34	5	it	it	PRON
cana-3474	34	6	has	have	AUX
cana-3474	34	7	also	also	ADV
cana-3474	34	8	been	be	AUX
cana-3474	34	9	established	establish	VERB
cana-3474	34	10	how	how	SCONJ
cana-3474	34	11	the	the	DET
cana-3474	34	12	w	w	NOUN
cana-3474	34	13	transform	transform	NOUN
cana-3474	34	14	relates	relate	VERB
cana-3474	34	15	to	to	ADP
cana-3474	34	16	other	other	ADJ
cana-3474	34	17	transforms	transform	NOUN
cana-3474	34	18	like	like	INTJ
cana-3474	34	19	(	(	PUNCT
cana-3474	34	20	laplace	laplace	NOUN
cana-3474	34	21	,	,	PUNCT
cana-3474	34	22	sumudu	sumudu	NOUN
cana-3474	34	23	,	,	PUNCT
cana-3474	34	24	natural	natural	ADJ
cana-3474	34	25	transform	transform	NOUN
cana-3474	34	26	,	,	PUNCT
cana-3474	34	27	elzaki	elzaki	NOUN
cana-3474	34	28	,	,	PUNCT
cana-3474	34	29	mohand	mohand	NOUN
cana-3474	34	30	,	,	PUNCT
cana-3474	34	31	aboodh	aboodh	PROPN
cana-3474	34	32	,	,	PUNCT
cana-3474	34	33	sawi	sawi	PROPN
cana-3474	34	34	,	,	PUNCT
cana-3474	34	35	yang	yang	PROPN
cana-3474	34	36	,	,	PUNCT
cana-3474	34	37	emadfalih	emadfalih	VERB
cana-3474	34	38	,	,	PUNCT
cana-3474	34	39	fareeha	fareeha	ADJ
cana-3474	34	40	and	and	CCONJ
cana-3474	34	41	pourreza	pourreza	ADV
cana-3474	34	42	transform	transform	NOUN
cana-3474	34	43	)	)	PUNCT
cana-3474	34	44	.	.	PUNCT
cana-3474	35	1	to	to	PART
cana-3474	35	2	show	show	VERB
cana-3474	35	3	how	how	SCONJ
cana-3474	35	4	successful	successful	ADJ
cana-3474	35	5	this	this	DET
cana-3474	35	6	transformation	transformation	NOUN
cana-3474	35	7	is	be	AUX
cana-3474	35	8	,	,	PUNCT
cana-3474	35	9	they	they	PRON
cana-3474	35	10	have	have	AUX
cana-3474	35	11	solved	solve	VERB
cana-3474	35	12	the	the	DET
cana-3474	35	13	differential	differential	ADJ
cana-3474	35	14	and	and	CCONJ
cana-3474	35	15	integral	integral	ADJ
cana-3474	35	16	equations[18	equations[18	NOUN
cana-3474	35	17	]	]	PUNCT
cana-3474	35	18	.	.	PUNCT
cana-3474	36	1	kind	kind	ADJ
cana-3474	36	2	ndde	ndde	PROPN
cana-3474	36	3	of	of	ADP
cana-3474	36	4	2	2	NUM
cana-3474	36	5	-	-	NUM
cana-3474	36	6	the	the	DET
cana-3474	36	7	goal	goal	NOUN
cana-3474	36	8	of	of	ADP
cana-3474	36	9	this	this	DET
cana-3474	36	10	work	work	NOUN
cana-3474	36	11	is	be	AUX
cana-3474	36	12	to	to	PART
cana-3474	36	13	use	use	VERB
cana-3474	36	14	the	the	DET
cana-3474	36	15	w	w	NOUN
cana-3474	36	16	transform	transform	NOUN
cana-3474	36	17	to	to	PART
cana-3474	36	18	quickly	quickly	ADV
cana-3474	36	19	and	and	CCONJ
cana-3474	36	20	simply	simply	ADV
cana-3474	36	21	solve	solve	VERB
cana-3474	36	22	the	the	DET
cana-3474	36	23	lvi	lvi	NOUN
cana-3474	36	24	kind	kind	NOUN
cana-3474	36	25	.	.	PUNCT
cana-3474	37	1	ndde	ndde	PROPN
cana-3474	37	2	of	of	ADP
cana-3474	37	3	2-	2-	PROPN
cana-3474	37	4	&	&	CCONJ
cana-3474	37	5	lsvi	lsvi	PROPN
cana-3474	37	6	2	2	NUM
cana-3474	37	7	basic	basic	ADJ
cana-3474	37	8	definitions	definition	NOUN
cana-3474	37	9	definition	definition	NOUN
cana-3474	37	10	1	1	NUM
cana-3474	37	11	:	:	PUNCT
cana-3474	37	12	the	the	DET
cana-3474	37	13	lvi	lvi	PROPN
cana-3474	37	14	-	-	PUNCT
cana-3474	37	15	de	de	PROPN
cana-3474	37	16	of	of	ADP
cana-3474	37	17	2nd	2nd	ADJ
cana-3474	37	18	kind	kind	NOUN
cana-3474	37	19	is	be	AUX
cana-3474	37	20	provided	provide	VERB
cana-3474	37	21	by	by	ADP
cana-3474	37	22	[	[	X
cana-3474	37	23	19	19	NUM
cana-3474	37	24	]	]	PUNCT
cana-3474	37	25	:	:	PUNCT
cana-3474	37	26	𝜑(𝑛)(ω	𝜑(𝑛)(ω	NUM
cana-3474	37	27	)	)	PUNCT
cana-3474	37	28	=	=	SYM
cana-3474	37	29	h(ω	h(ω	PROPN
cana-3474	37	30	)	)	PUNCT
cana-3474	38	1	+	+	CCONJ
cana-3474	38	2	∫k(ω	∫k(ω	PROPN
cana-3474	38	3	,	,	PUNCT
cana-3474	38	4	τ	τ	X
cana-3474	38	5	)	)	PUNCT
cana-3474	38	6	φ(τ)dτ	φ(τ)dτ	PROPN
cana-3474	39	1	ω	ω	NOUN
cana-3474	39	2	0	0	NUM
cana-3474	39	3	(	(	PUNCT
cana-3474	39	4	1	1	NUM
cana-3474	39	5	)	)	PUNCT
cana-3474	39	6	with	with	ADP
cana-3474	39	7	𝜑(𝑚)(0	𝜑(𝑚)(0	PROPN
cana-3474	39	8	)	)	PUNCT
cana-3474	39	9	=	=	SYM
cana-3474	39	10	𝑏𝑚	𝑏𝑚	ADP
cana-3474	39	11	,	,	PUNCT
cana-3474	39	12	0	0	PUNCT
cana-3474	39	13	<	<	X
cana-3474	39	14	𝑚	𝑚	X
cana-3474	39	15	<	<	X
cana-3474	39	16	𝑛	𝑛	PRON
cana-3474	39	17	−	−	PROPN
cana-3474	39	18	1	1	NUM
cana-3474	39	19	in	in	ADP
cana-3474	39	20	which	which	PRON
cana-3474	39	21	the	the	DET
cana-3474	39	22	unidentified	unidentified	ADJ
cana-3474	39	23	function	function	NOUN
cana-3474	39	24	𝜑(τ	𝜑(τ	PROPN
cana-3474	39	25	)	)	PUNCT
cana-3474	39	26	will	will	AUX
cana-3474	39	27	be	be	AUX
cana-3474	39	28	decided	decide	VERB
cana-3474	39	29	,	,	PUNCT
cana-3474	39	30	only	only	ADV
cana-3474	39	31	show	show	VERB
cana-3474	39	32	up	up	ADP
cana-3474	39	33	within	within	ADP
cana-3474	39	34	the	the	DET
cana-3474	39	35	integral	integral	ADJ
cana-3474	39	36	sign	sign	NOUN
cana-3474	39	37	,	,	PUNCT
cana-3474	39	38	whereas	whereas	SCONJ
cana-3474	39	39	the	the	DET
cana-3474	39	40	derivative	derivative	NOUN
cana-3474	39	41	of	of	ADP
cana-3474	39	42	𝜑(ω	𝜑(ω	PROPN
cana-3474	39	43	)	)	PUNCT
cana-3474	39	44	usually	usually	ADV
cana-3474	39	45	take	take	VERB
cana-3474	39	46	place	place	NOUN
cana-3474	39	47	outside	outside	ADP
cana-3474	39	48	of	of	ADP
cana-3474	39	49	the	the	DET
cana-3474	39	50	sign	sign	NOUN
cana-3474	39	51	of	of	ADP
cana-3474	39	52	integral	integral	ADJ
cana-3474	39	53	.	.	PUNCT
cana-3474	40	1	communications	communication	NOUN
cana-3474	40	2	on	on	ADP
cana-3474	40	3	applied	apply	VERB
cana-3474	40	4	nonlinear	nonlinear	ADJ
cana-3474	40	5	analysis	analysis	NOUN
cana-3474	40	6	issn	issn	NOUN
cana-3474	40	7	:	:	PUNCT
cana-3474	40	8	1074	1074	NUM
cana-3474	40	9	-	-	PUNCT
cana-3474	40	10	133x	133x	NUM
cana-3474	40	11	vol	vol	NOUN
cana-3474	40	12	32	32	NUM
cana-3474	40	13	no	no	NOUN
cana-3474	40	14	.	.	PUNCT
cana-3474	41	1	7s	7	NOUN
cana-3474	41	2	(	(	PUNCT
cana-3474	41	3	2025	2025	NUM
cana-3474	41	4	)	)	PUNCT
cana-3474	41	5	677	677	NUM
cana-3474	41	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	41	7	the	the	DET
cana-3474	41	8	kernels	kernel	NOUN
cana-3474	41	9	𝐾(ω	𝐾(ω	PROPN
cana-3474	41	10	,	,	PUNCT
cana-3474	41	11	τ	τ	PROPN
cana-3474	41	12	)	)	PUNCT
cana-3474	41	13	,	,	PUNCT
cana-3474	41	14	and	and	CCONJ
cana-3474	41	15	the	the	DET
cana-3474	41	16	function	function	NOUN
cana-3474	41	17	h(ω	h(ω	PROPN
cana-3474	41	18	)	)	PUNCT
cana-3474	41	19	provided	provide	VERB
cana-3474	41	20	functions	function	NOUN
cana-3474	41	21	with	with	ADP
cana-3474	41	22	real	real	ADJ
cana-3474	41	23	values	value	NOUN
cana-3474	41	24	,	,	PUNCT
cana-3474	41	25	𝑏𝑚	𝑏𝑚	SCONJ
cana-3474	41	26	are	be	AUX
cana-3474	41	27	constants	constant	NOUN
cana-3474	41	28	that	that	PRON
cana-3474	41	29	define	define	VERB
cana-3474	41	30	the	the	DET
cana-3474	41	31	initial	initial	ADJ
cana-3474	41	32	conditions	condition	NOUN
cana-3474	41	33	.	.	PUNCT
cana-3474	42	1	definition	definition	NOUN
cana-3474	42	2	2	2	NUM
cana-3474	42	3	:	:	PUNCT
cana-3474	42	4	the	the	DET
cana-3474	42	5	general	general	ADJ
cana-3474	42	6	lsvi	lsvi	NOUN
cana-3474	42	7	-	-	PUNCT
cana-3474	42	8	de	de	NOUN
cana-3474	42	9	of	of	ADP
cana-3474	42	10	2nd	2nd	ADJ
cana-3474	42	11	kind	kind	NOUN
cana-3474	42	12	is	be	AUX
cana-3474	42	13	supplied	supply	VERB
cana-3474	42	14	by	by	ADP
cana-3474	42	15	[	[	X
cana-3474	42	16	20	20	NUM
cana-3474	42	17	]	]	PUNCT
cana-3474	42	18	,	,	PUNCT
cana-3474	42	19	𝜑1	𝜑1	NOUN
cana-3474	42	20	(	(	PUNCT
cana-3474	42	21	m)(ω	m)(ω	NOUN
cana-3474	42	22	)	)	PUNCT
cana-3474	42	23	=	=	SYM
cana-3474	43	1	h1(ω	h1(ω	PROPN
cana-3474	43	2	)	)	PUNCT
cana-3474	43	3	+	+	CCONJ
cana-3474	43	4	{	{	PUNCT
cana-3474	43	5	∫	∫	PROPN
cana-3474	43	6	k11(ω−	k11(ω−	PROPN
cana-3474	43	7	τ	τ	PROPN
cana-3474	43	8	)	)	PUNCT
cana-3474	43	9	𝜑1(τ)dτ+	𝜑1(τ)dτ+	X
cana-3474	43	10	ω	ω	X
cana-3474	43	11	0	0	NUM
cana-3474	43	12	∫	∫	PROPN
cana-3474	44	1	k12(ω−	k12(ω−	PROPN
cana-3474	44	2	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	45	1	ω	ω	NOUN
cana-3474	45	2	0	0	PUNCT
cana-3474	46	1	+	+	ADJ
cana-3474	46	2	⋯	⋯	ADP
cana-3474	46	3	.+∫	.+∫	X
cana-3474	46	4	k1p(ω−	k1p(ω−	NOUN
cana-3474	46	5	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PUNCT
cana-3474	47	1	ω	ω	NOUN
cana-3474	47	2	0	0	NUM
cana-3474	47	3	}	}	PUNCT
cana-3474	47	4	𝜑2	𝜑2	PROPN
cana-3474	47	5	(	(	PUNCT
cana-3474	47	6	m)(ω	m)(ω	NOUN
cana-3474	47	7	)	)	PUNCT
cana-3474	47	8	=	=	SYM
cana-3474	47	9	h2(ω	h2(ω	NOUN
cana-3474	47	10	)	)	PUNCT
cana-3474	47	11	+	+	CCONJ
cana-3474	47	12	{	{	PUNCT
cana-3474	47	13	∫	∫	PROPN
cana-3474	47	14	k21(ω−	k21(ω−	PROPN
cana-3474	47	15	τ)𝜑1(τ)dτ+	τ)𝜑1(τ)dτ+	PROPN
cana-3474	47	16	ω	ω	SYM
cana-3474	47	17	0	0	NUM
cana-3474	47	18	∫	∫	PROPN
cana-3474	47	19	k22(ω−	k22(ω−	PROPN
cana-3474	47	20	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	47	21	ω	ω	NOUN
cana-3474	47	22	0	0	PUNCT
cana-3474	48	1	+	+	ADJ
cana-3474	48	2	⋯	⋯	ADP
cana-3474	48	3	.+∫	.+∫	NUM
cana-3474	48	4	k2p(ω−	k2p(ω−	NOUN
cana-3474	48	5	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PROPN
cana-3474	49	1	ω	ω	NUM
cana-3474	49	2	0	0	NUM
cana-3474	49	3	}	}	PUNCT
cana-3474	49	4	…	…	PUNCT
cana-3474	49	5	…	…	PUNCT
cana-3474	49	6	…	…	PUNCT
cana-3474	49	7	…	…	PUNCT
cana-3474	49	8	…	…	PUNCT
cana-3474	49	9	…	…	PUNCT
cana-3474	49	10	…	…	PUNCT
cana-3474	49	11	…	…	PUNCT
cana-3474	49	12	…	…	PUNCT
cana-3474	49	13	…	…	PUNCT
cana-3474	49	14	…	…	PUNCT
cana-3474	49	15	…	…	PUNCT
cana-3474	49	16	……	……	NOUN
cana-3474	49	17	……	……	NOUN
cana-3474	49	18	……	……	NOUN
cana-3474	49	19	……	……	NOUN
cana-3474	49	20	……	……	NOUN
cana-3474	49	21	……	……	NOUN
cana-3474	49	22	……	……	NOUN
cana-3474	49	23	……	……	NOUN
cana-3474	49	24	……	……	NOUN
cana-3474	49	25	.	.	PUNCT
cana-3474	50	1	𝜑p	𝜑p	PROPN
cana-3474	50	2	(	(	PUNCT
cana-3474	50	3	m)(ω	m)(ω	NOUN
cana-3474	50	4	)	)	PUNCT
cana-3474	50	5	=	=	SYM
cana-3474	50	6	hp(ω	hp(ω	X
cana-3474	50	7	)	)	PUNCT
cana-3474	51	1	+	+	CCONJ
cana-3474	51	2	{	{	PUNCT
cana-3474	51	3	∫	∫	PROPN
cana-3474	51	4	kn1(ω−	kn1(ω−	PROPN
cana-3474	51	5	τ)𝜑1(τ)dτ+	τ)𝜑1(τ)dτ+	PROPN
cana-3474	51	6	ω	ω	SYM
cana-3474	51	7	0	0	NUM
cana-3474	51	8	∫	∫	PROPN
cana-3474	51	9	kn2(ω−	kn2(ω−	PROPN
cana-3474	51	10	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	51	11	ω	ω	NOUN
cana-3474	51	12	0	0	PUNCT
cana-3474	52	1	+	+	ADJ
cana-3474	52	2	⋯	⋯	VERB
cana-3474	52	3	.+∫	.+∫	X
cana-3474	52	4	kpp(ω−	kpp(ω−	NOUN
cana-3474	53	1	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PROPN
cana-3474	54	1	ω	ω	NOUN
cana-3474	54	2	0	0	NUM
cana-3474	54	3	}	}	PUNCT
cana-3474	54	4	]	]	PUNCT
cana-3474	54	5	(	(	PUNCT
cana-3474	54	6	2	2	X
cana-3474	54	7	)	)	PUNCT
cana-3474	54	8	where	where	SCONJ
cana-3474	54	9	the	the	DET
cana-3474	54	10	unidentified	unidentified	ADJ
cana-3474	54	11	operations	operation	NOUN
cana-3474	54	12	𝜑1(τ	𝜑1(τ	NOUN
cana-3474	54	13	)	)	PUNCT
cana-3474	54	14	,	,	PUNCT
cana-3474	54	15	𝜑2(τ	𝜑2(τ	PROPN
cana-3474	54	16	)	)	PUNCT
cana-3474	54	17	,	,	PUNCT
cana-3474	54	18	…	…	PUNCT
cana-3474	54	19	,	,	PUNCT
cana-3474	54	20	𝜑p(τ	𝜑p(τ	NUM
cana-3474	54	21	)	)	PUNCT
cana-3474	54	22	that	that	PRON
cana-3474	54	23	is	be	AUX
cana-3474	54	24	only	only	ADV
cana-3474	54	25	show	show	VERB
cana-3474	54	26	up	up	ADP
cana-3474	54	27	within	within	ADP
cana-3474	54	28	the	the	DET
cana-3474	54	29	integral	integral	ADJ
cana-3474	54	30	symbol	symbol	NOUN
cana-3474	54	31	,	,	PUNCT
cana-3474	54	32	in	in	ADP
cana-3474	54	33	contrast	contrast	NOUN
cana-3474	54	34	,	,	PUNCT
cana-3474	54	35	the	the	DET
cana-3474	54	36	derivatives	derivative	NOUN
cana-3474	54	37	of	of	ADP
cana-3474	54	38	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	54	39	)	)	PUNCT
cana-3474	54	40	,	,	PUNCT
cana-3474	54	41	𝜑2(ω	𝜑2(ω	ADV
cana-3474	54	42	)	)	PUNCT
cana-3474	54	43	,	,	PUNCT
cana-3474	54	44	…	…	PUNCT
cana-3474	54	45	,	,	PUNCT
cana-3474	54	46	𝜑p(ω	𝜑p(ω	NUM
cana-3474	54	47	)	)	PUNCT
cana-3474	54	48	,	,	PUNCT
cana-3474	54	49	usually	usually	ADV
cana-3474	54	50	take	take	VERB
cana-3474	54	51	place	place	NOUN
cana-3474	54	52	outside	outside	ADP
cana-3474	54	53	of	of	ADP
cana-3474	54	54	the	the	DET
cana-3474	54	55	integral	integral	ADJ
cana-3474	54	56	sign	sign	NOUN
cana-3474	54	57	.	.	PUNCT
cana-3474	55	1	the	the	DET
cana-3474	55	2	kernels	kernel	NOUN
cana-3474	55	3	kij(ω	kij(ω	PROPN
cana-3474	55	4	,	,	PUNCT
cana-3474	55	5	τ	τ	X
cana-3474	55	6	)	)	PUNCT
cana-3474	55	7	and	and	CCONJ
cana-3474	55	8	hn(ω	hn(ω	NOUN
cana-3474	55	9	)	)	PUNCT
cana-3474	55	10	for	for	ADP
cana-3474	55	11	𝑖	𝑖	SYM
cana-3474	55	12	,	,	PUNCT
cana-3474	55	13	𝑗	𝑗	NOUN
cana-3474	55	14	=	=	SYM
cana-3474	55	15	1,2	1,2	NUM
cana-3474	55	16	,	,	PUNCT
cana-3474	55	17	…	…	PUNCT
cana-3474	55	18	,	,	PUNCT
cana-3474	55	19	𝑝	𝑝	NOUN
cana-3474	55	20	functions	function	NOUN
cana-3474	55	21	with	with	ADP
cana-3474	55	22	real	real	ADJ
cana-3474	55	23	values	value	NOUN
cana-3474	55	24	.	.	PUNCT
cana-3474	56	1	definition	definition	NOUN
cana-3474	56	2	3	3	NUM
cana-3474	56	3	:	:	PUNCT
cana-3474	56	4	the	the	DET
cana-3474	56	5	w	w	NOUN
cana-3474	56	6	transform	transform	NOUN
cana-3474	56	7	defined	define	VERB
cana-3474	56	8	for	for	ADP
cana-3474	56	9	an	an	DET
cana-3474	56	10	exponentially	exponentially	ADV
cana-3474	56	11	ordered	order	VERB
cana-3474	56	12	function	function	NOUN
cana-3474	56	13	we	we	PRON
cana-3474	56	14	examine	examine	VERB
cana-3474	56	15	functions	function	NOUN
cana-3474	56	16	within	within	ADP
cana-3474	56	17	the	the	DET
cana-3474	56	18	set	set	NOUN
cana-3474	56	19	a	a	PRON
cana-3474	56	20	,	,	PUNCT
cana-3474	56	21	described	describe	VERB
cana-3474	56	22	by	by	ADP
cana-3474	56	23	a	a	DET
cana-3474	56	24	=	=	X
cana-3474	56	25	{	{	PUNCT
cana-3474	56	26	𝜑(ω	𝜑(ω	PROPN
cana-3474	56	27	):	):	PUNCT
cana-3474	56	28	∃	∃	PROPN
cana-3474	56	29	m	m	PROPN
cana-3474	56	30	>	>	X
cana-3474	56	31	0	0	PROPN
cana-3474	56	32	,	,	PUNCT
cana-3474	56	33	k	k	PROPN
cana-3474	56	34	>	>	X
cana-3474	56	35	0	0	PROPN
cana-3474	56	36	,	,	PUNCT
cana-3474	56	37	|𝜑(ω)|	|𝜑(ω)|	X
cana-3474	56	38	<	<	X
cana-3474	56	39	mekω	mekω	PROPN
cana-3474	56	40	,	,	PUNCT
cana-3474	56	41	ω	ω	PROPN
cana-3474	56	42	∈	∈	PROPN
cana-3474	56	43	{	{	PUNCT
cana-3474	56	44	0,∞	0,∞	NOUN
cana-3474	56	45	}	}	PUNCT
cana-3474	56	46	}	}	PUNCT
cana-3474	56	47	,	,	PUNCT
cana-3474	56	48	the	the	DET
cana-3474	56	49	new	new	ADJ
cana-3474	56	50	general	general	ADJ
cana-3474	56	51	integral	integral	ADJ
cana-3474	56	52	transform	transform	NOUN
cana-3474	56	53	[	[	X
cana-3474	56	54	18	18	NUM
cana-3474	56	55	]	]	PUNCT
cana-3474	56	56	,	,	PUNCT
cana-3474	56	57	w{𝜑(ω	w{𝜑(ω	NOUN
cana-3474	56	58	)	)	PUNCT
cana-3474	56	59	}	}	PUNCT
cana-3474	57	1	=	=	PUNCT
cana-3474	57	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	57	3	∫	∫	NOUN
cana-3474	57	4	𝜑(ω)e−𝑠	𝜑(ω)e−𝑠	PROPN
cana-3474	57	5	𝑛ωdω	𝑛ωdω	NOUN
cana-3474	57	6	=	=	SYM
cana-3474	57	7	ℱ(s	ℱ(s	PROPN
cana-3474	57	8	)	)	PUNCT
cana-3474	57	9	∞	∞	NOUN
cana-3474	57	10	0	0	NUM
cana-3474	57	11	(	(	PUNCT
cana-3474	57	12	3	3	NUM
cana-3474	57	13	)	)	PUNCT
cana-3474	57	14	where	where	SCONJ
cana-3474	57	15	𝑠	𝑠	PROPN
cana-3474	57	16	=	=	SYM
cana-3474	57	17	𝛼	𝛼	PROPN
cana-3474	57	18	+	+	SYM
cana-3474	57	19	𝑖𝛽.	𝑖𝛽.	X
cana-3474	57	20	definition	definition	NOUN
cana-3474	57	21	4	4	NUM
cana-3474	57	22	:	:	PUNCT
cana-3474	57	23	w	w	NOUN
cana-3474	57	24	transform	transform	NOUN
cana-3474	57	25	's	's	PART
cana-3474	57	26	inverse	inverse	NOUN
cana-3474	57	27	for	for	ADP
cana-3474	57	28	the	the	DET
cana-3474	57	29	given	give	VERB
cana-3474	57	30	function	function	NOUN
cana-3474	57	31	𝜑(ω	𝜑(ω	PROPN
cana-3474	57	32	)	)	PUNCT
cana-3474	57	33	is	be	AUX
cana-3474	57	34	provided	provide	VERB
cana-3474	57	35	by[18	by[18	PROPN
cana-3474	57	36	]	]	X
cana-3474	57	37	:	:	PUNCT
cana-3474	57	38	𝑊−1{ℱ(s	𝑊−1{ℱ(s	NOUN
cana-3474	57	39	)	)	PUNCT
cana-3474	57	40	)	)	PUNCT
cana-3474	57	41	}	}	PUNCT
cana-3474	57	42	=	=	SYM
cana-3474	57	43	1	1	NUM
cana-3474	57	44	2πi	2πi	NOUN
cana-3474	57	45	∫	∫	NOUN
cana-3474	57	46	1	1	NUM
cana-3474	57	47	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	57	48	e𝑠	e𝑠	ADP
cana-3474	57	49	𝑛ωℱ(s)ds	𝑛ωℱ(s)ds	NUM
cana-3474	57	50	=	=	SYM
cana-3474	57	51	𝜑(ω	𝜑(ω	PROPN
cana-3474	57	52	)	)	PUNCT
cana-3474	57	53	(	(	PUNCT
cana-3474	57	54	4	4	X
cana-3474	57	55	)	)	PUNCT
cana-3474	57	56	α+i∞	α+i∞	ADV
cana-3474	57	57	α−i∞	α−i∞	PROPN
cana-3474	57	58	table	table	VERB
cana-3474	57	59	1	1	NUM
cana-3474	57	60	:	:	PUNCT
cana-3474	57	61	features	feature	NOUN
cana-3474	57	62	of	of	ADP
cana-3474	57	63	the	the	DET
cana-3474	57	64	w	w	NOUN
cana-3474	57	65	transform	transform	VERB
cana-3474	57	66	s.n	s.n	PRON
cana-3474	57	67	name	name	NOUN
cana-3474	57	68	of	of	ADP
cana-3474	57	69	property	property	NOUN
cana-3474	57	70	form	form	NOUN
cana-3474	57	71	in	in	ADP
cana-3474	57	72	mathematics	mathematic	NOUN
cana-3474	57	73	1	1	NUM
cana-3474	57	74	.	.	PUNCT
cana-3474	58	1	the	the	DET
cana-3474	58	2	ability	ability	NOUN
cana-3474	58	3	to	to	PART
cana-3474	58	4	linearize	linearize	VERB
cana-3474	58	5	𝑊{𝑐𝜑1(ω	𝑊{𝑐𝜑1(ω	PROPN
cana-3474	58	6	)	)	PUNCT
cana-3474	58	7	+	+	X
cana-3474	58	8	𝑑𝜑2(ω	𝑑𝜑2(ω	NOUN
cana-3474	58	9	)	)	PUNCT
cana-3474	58	10	}	}	PUNCT
cana-3474	58	11	=	=	SYM
cana-3474	58	12	𝑐𝑊{𝜑1(ω	𝑐𝑊{𝜑1(ω	NOUN
cana-3474	58	13	)	)	PUNCT
cana-3474	58	14	}	}	PUNCT
cana-3474	59	1	+	+	CCONJ
cana-3474	59	2	𝑑𝑊{𝜑2(ω	𝑑𝑊{𝜑2(ω	X
cana-3474	59	3	)	)	PUNCT
cana-3474	59	4	}	}	PUNCT
cana-3474	59	5	2	2	NUM
cana-3474	59	6	.	.	X
cana-3474	59	7	first	first	ADJ
cana-3474	59	8	derivative	derivative	ADJ
cana-3474	59	9	𝑊{𝜑′(ω	𝑊{𝜑′(ω	NOUN
cana-3474	59	10	)	)	PUNCT
cana-3474	59	11	}	}	PUNCT
cana-3474	59	12	=	=	SYM
cana-3474	59	13	𝑠𝑛𝑊(𝜑(ω	𝑠𝑛𝑊(𝜑(ω	NUM
cana-3474	59	14	)	)	PUNCT
cana-3474	59	15	)	)	PUNCT
cana-3474	60	1	−	−	NOUN
cana-3474	60	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	60	3	𝜑(0	𝜑(0	NOUN
cana-3474	60	4	)	)	PUNCT
cana-3474	60	5	3	3	NUM
cana-3474	60	6	.	.	X
cana-3474	60	7	second	second	ADJ
cana-3474	60	8	derivative	derivative	ADJ
cana-3474	60	9	𝑊{𝜑′′(ω	𝑊{𝜑′′(ω	NOUN
cana-3474	60	10	)	)	PUNCT
cana-3474	60	11	}	}	PUNCT
cana-3474	60	12	=	=	SYM
cana-3474	60	13	𝑠2𝑛𝑊(𝜑(ω	𝑠2𝑛𝑊(𝜑(ω	PROPN
cana-3474	60	14	)	)	PUNCT
cana-3474	60	15	)	)	PUNCT
cana-3474	61	1	−	−	PROPN
cana-3474	61	2	𝑠𝑚+𝑛	𝑠𝑚+𝑛	PROPN
cana-3474	61	3	𝜑(0	𝜑(0	NOUN
cana-3474	61	4	)	)	PUNCT
cana-3474	61	5	−	−	PROPN
cana-3474	61	6	𝑠𝑚	𝑠𝑚	ADP
cana-3474	61	7	𝜑′(0	𝜑′(0	NOUN
cana-3474	61	8	)	)	PUNCT
cana-3474	61	9	communications	communication	NOUN
cana-3474	61	10	on	on	ADP
cana-3474	61	11	applied	apply	VERB
cana-3474	61	12	nonlinear	nonlinear	ADJ
cana-3474	61	13	analysis	analysis	NOUN
cana-3474	61	14	issn	issn	NOUN
cana-3474	61	15	:	:	PUNCT
cana-3474	61	16	1074	1074	NUM
cana-3474	61	17	-	-	PUNCT
cana-3474	61	18	133x	133x	NUM
cana-3474	61	19	vol	vol	NOUN
cana-3474	61	20	32	32	NUM
cana-3474	61	21	no	no	NOUN
cana-3474	61	22	.	.	PUNCT
cana-3474	62	1	7s	7	NOUN
cana-3474	62	2	(	(	PUNCT
cana-3474	62	3	2025	2025	NUM
cana-3474	62	4	)	)	PUNCT
cana-3474	62	5	678	678	NUM
cana-3474	63	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	63	2	4	4	X
cana-3474	63	3	.	.	X
cana-3474	64	1	nth	nth	PROPN
cana-3474	64	2	derivative	derivative	ADJ
cana-3474	64	3	𝑊{𝜑(k)(ω	𝑊{𝜑(k)(ω	NOUN
cana-3474	64	4	)	)	PUNCT
cana-3474	64	5	}	}	PUNCT
cana-3474	64	6	=	=	SYM
cana-3474	64	7	𝑠𝑘𝑛𝑊(𝜑(ω	𝑠𝑘𝑛𝑊(𝜑(ω	NUM
cana-3474	64	8	)	)	PUNCT
cana-3474	64	9	)	)	PUNCT
cana-3474	65	1	−	−	PROPN
cana-3474	66	1	𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	NOUN
cana-3474	66	2	)	)	PUNCT
cana-3474	67	1	𝑘−1	𝑘−1	PROPN
cana-3474	67	2	𝑗=0	𝑗=0	PUNCT
cana-3474	68	1	𝜑(𝑗)(0	𝜑(𝑗)(0	PROPN
cana-3474	68	2	)	)	PUNCT
cana-3474	68	3	,	,	PUNCT
cana-3474	68	4	𝑘	𝑘	PRON
cana-3474	68	5	≥	≥	NOUN
cana-3474	68	6	1	1	NUM
cana-3474	68	7	5	5	NUM
cana-3474	68	8	.	.	PUNCT
cana-3474	68	9	convolution	convolution	PROPN
cana-3474	68	10	𝑊{𝜑1(ω	𝑊{𝜑1(ω	PROPN
cana-3474	68	11	)	)	PUNCT
cana-3474	68	12	∗	∗	NOUN
cana-3474	68	13	𝜑2(ω	𝜑2(ω	NUM
cana-3474	68	14	)	)	PUNCT
cana-3474	68	15	}	}	PUNCT
cana-3474	68	16	=	=	SYM
cana-3474	69	1	1	1	NUM
cana-3474	69	2	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	69	3	𝑊{𝜑1(ω	𝑊{𝜑1(ω	NOUN
cana-3474	69	4	)	)	PUNCT
cana-3474	69	5	}	}	PUNCT
cana-3474	69	6	∗	∗	NOUN
cana-3474	69	7	𝑊{𝜑2(ω	𝑊{𝜑2(ω	ADV
cana-3474	69	8	)	)	PUNCT
cana-3474	69	9	}	}	PUNCT
cana-3474	69	10	table	table	NOUN
cana-3474	69	11	2	2	NUM
cana-3474	69	12	:	:	PUNCT
cana-3474	69	13	w	w	NOUN
cana-3474	69	14	transform	transform	NOUN
cana-3474	69	15	of	of	ADP
cana-3474	69	16	useful	useful	ADJ
cana-3474	69	17	functions	function	NOUN
cana-3474	69	18	s.n	s.n	PROPN
cana-3474	69	19	φ(ω	φ(ω	NOUN
cana-3474	69	20	)	)	PUNCT
cana-3474	69	21	𝑊{φ(ω	𝑊{φ(ω	NUM
cana-3474	69	22	)	)	PUNCT
cana-3474	69	23	}	}	PUNCT
cana-3474	69	24	=	=	SYM
cana-3474	70	1	ℱ(s	ℱ(s	X
cana-3474	70	2	)	)	PUNCT
cana-3474	70	3	1	1	NUM
cana-3474	70	4	c	c	NOUN
cana-3474	70	5	𝑐	𝑐	NOUN
cana-3474	70	6	𝑠𝑚	𝑠𝑚	PUNCT
cana-3474	70	7	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	70	8	2	2	NUM
cana-3474	70	9	.	.	PUNCT
cana-3474	70	10	ω	ω	NOUN
cana-3474	70	11	𝑠𝑚	𝑠𝑚	ADP
cana-3474	70	12	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	70	13	3	3	NUM
cana-3474	70	14	.	.	PUNCT
cana-3474	70	15	aω𝑘	aω𝑘	PROPN
cana-3474	70	16	𝑎	𝑎	NOUN
cana-3474	70	17	𝑘	𝑘	NOUN
cana-3474	70	18	!	!	NOUN
cana-3474	70	19	𝑠𝑚	𝑠𝑚	VERB
cana-3474	70	20	𝑠𝑛(𝑘+1	𝑠𝑛(𝑘+1	NOUN
cana-3474	70	21	)	)	PUNCT
cana-3474	70	22	,	,	PUNCT
cana-3474	70	23	a	a	DET
cana-3474	70	24	constant	constant	ADJ
cana-3474	70	25	.4	.4	NUM
cana-3474	70	26	𝑒𝑎ω	𝑒𝑎ω	NOUN
cana-3474	70	27	𝑠𝑚	𝑠𝑚	ADP
cana-3474	70	28	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	70	29	−	−	PROPN
cana-3474	70	30	𝑎	𝑎	PRON
cana-3474	70	31	5	5	NUM
cana-3474	70	32	.	.	PUNCT
cana-3474	70	33	sin	sin	NOUN
cana-3474	70	34	(	(	PUNCT
cana-3474	70	35	𝑎ω	𝑎ω	PROPN
cana-3474	70	36	)	)	PUNCT
cana-3474	70	37	𝑎	𝑎	NOUN
cana-3474	70	38	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	70	39	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	70	40	+	+	CCONJ
cana-3474	70	41	𝑎2	𝑎2	PROPN
cana-3474	70	42	6	6	NUM
cana-3474	70	43	.	.	PUNCT
cana-3474	70	44	cos	cos	PROPN
cana-3474	70	45	(	(	PUNCT
cana-3474	70	46	𝑎ω	𝑎ω	PROPN
cana-3474	70	47	)	)	PUNCT
cana-3474	70	48	𝑠𝑚+𝑛	𝑠𝑚+𝑛	PROPN
cana-3474	70	49	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	70	50	+	+	PUNCT
cana-3474	70	51	𝑎2	𝑎2	PROPN
cana-3474	70	52	7	7	NUM
cana-3474	70	53	.	.	PUNCT
cana-3474	71	1	sinh	sinh	PROPN
cana-3474	71	2	(	(	PUNCT
cana-3474	71	3	𝑎ω	𝑎ω	PROPN
cana-3474	71	4	)	)	PUNCT
cana-3474	71	5	𝑎	𝑎	NOUN
cana-3474	71	6	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	71	7	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	71	8	−	−	PROPN
cana-3474	71	9	𝑎2	𝑎2	NOUN
cana-3474	71	10	8	8	NUM
cana-3474	71	11	.	.	PUNCT
cana-3474	72	1	cosh	cosh	PROPN
cana-3474	72	2	(	(	PUNCT
cana-3474	72	3	𝑎ω	𝑎ω	NOUN
cana-3474	72	4	)	)	PUNCT
cana-3474	72	5	𝑠𝑚+𝑛	𝑠𝑚+𝑛	PROPN
cana-3474	72	6	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	72	7	−	−	PROPN
cana-3474	72	8	𝑎2	𝑎2	NOUN
cana-3474	72	9	3	3	NUM
cana-3474	72	10	methodology	methodology	NOUN
cana-3474	72	11	within	within	ADP
cana-3474	72	12	this	this	DET
cana-3474	72	13	part	part	NOUN
cana-3474	72	14	,	,	PUNCT
cana-3474	72	15	we	we	PRON
cana-3474	72	16	introduce	introduce	VERB
cana-3474	72	17	the	the	DET
cana-3474	72	18	w	w	NOUN
cana-3474	72	19	transform	transform	NOUN
cana-3474	72	20	as	as	ADP
cana-3474	72	21	a	a	DET
cana-3474	72	22	means	means	NOUN
cana-3474	72	23	of	of	ADP
cana-3474	72	24	solving	solve	VERB
cana-3474	72	25	lvi	lvi	NOUN
cana-3474	72	26	-	-	PUNCT
cana-3474	72	27	de	de	PROPN
cana-3474	72	28	of	of	ADP
cana-3474	72	29	2nd	2nd	ADJ
cana-3474	72	30	kind	kind	NOUN
cana-3474	72	31	and	and	CCONJ
cana-3474	72	32	lsvi	lsvi	NOUN
cana-3474	72	33	-	-	PUNCT
cana-3474	72	34	de	de	NOUN
cana-3474	72	35	of	of	ADP
cana-3474	72	36	2nd	2nd	ADJ
cana-3474	72	37	kind	kind	NOUN
cana-3474	72	38	.	.	PUNCT
cana-3474	73	1	in	in	ADP
cana-3474	73	2	this	this	DET
cana-3474	73	3	piece	piece	NOUN
cana-3474	73	4	of	of	ADP
cana-3474	73	5	writing	writing	NOUN
cana-3474	73	6	,	,	PUNCT
cana-3474	73	7	assumed	assume	VERB
cana-3474	73	8	to	to	PART
cana-3474	73	9	be	be	AUX
cana-3474	73	10	the	the	DET
cana-3474	73	11	kernel	kernel	PROPN
cana-3474	73	12	k(ω	k(ω	PROPN
cana-3474	73	13	,	,	PUNCT
cana-3474	73	14	τ	τ	X
cana-3474	73	15	)	)	PUNCT
cana-3474	73	16	can	can	AUX
cana-3474	73	17	be	be	AUX
cana-3474	73	18	expressed	express	VERB
cana-3474	73	19	by	by	ADP
cana-3474	73	20	difference	difference	NOUN
cana-3474	73	21	,	,	PUNCT
cana-3474	73	22	which	which	PRON
cana-3474	73	23	is	be	AUX
cana-3474	73	24	(	(	PUNCT
cana-3474	73	25	ω−	ω−	PROPN
cana-3474	73	26	τ	τ	PROPN
cana-3474	73	27	)	)	PUNCT
cana-3474	73	28	.	.	PUNCT
cana-3474	74	1	i.use	i.use	VERB
cana-3474	74	2	w	w	NOUN
cana-3474	74	3	transform	transform	NOUN
cana-3474	74	4	to	to	PART
cana-3474	74	5	resolve	resolve	VERB
cana-3474	74	6	lvi	lvi	NOUN
cana-3474	74	7	-	-	PUNCT
cana-3474	74	8	de	de	PROPN
cana-3474	74	9	of	of	ADP
cana-3474	74	10	2nd	2nd	ADJ
cana-3474	74	11	kind	kind	NOUN
cana-3474	74	12	:	:	PUNCT
cana-3474	74	13	𝜑(𝑛)(ω	𝜑(𝑛)(ω	NUM
cana-3474	74	14	)	)	PUNCT
cana-3474	74	15	=	=	SYM
cana-3474	74	16	h(ω	h(ω	PROPN
cana-3474	74	17	)	)	PUNCT
cana-3474	75	1	+	+	CCONJ
cana-3474	76	1	∫	∫	PROPN
cana-3474	76	2	k(ω−	k(ω−	PROPN
cana-3474	76	3	τ	τ	PROPN
cana-3474	76	4	)	)	PUNCT
cana-3474	76	5	φ(τ)dτ	φ(τ)dτ	PROPN
cana-3474	76	6	ω	ω	NOUN
cana-3474	76	7	0	0	NUM
cana-3474	76	8	(	(	PUNCT
cana-3474	76	9	5	5	NUM
cana-3474	76	10	)	)	PUNCT
cana-3474	76	11	with	with	ADP
cana-3474	76	12	communications	communication	NOUN
cana-3474	76	13	on	on	ADP
cana-3474	76	14	applied	apply	VERB
cana-3474	76	15	nonlinear	nonlinear	ADJ
cana-3474	76	16	analysis	analysis	NOUN
cana-3474	76	17	issn	issn	NOUN
cana-3474	76	18	:	:	PUNCT
cana-3474	76	19	1074	1074	NUM
cana-3474	76	20	-	-	PUNCT
cana-3474	76	21	133x	133x	NUM
cana-3474	76	22	vol	vol	NOUN
cana-3474	76	23	32	32	NUM
cana-3474	76	24	no	no	NOUN
cana-3474	76	25	.	.	PUNCT
cana-3474	77	1	7s	7	NOUN
cana-3474	77	2	(	(	PUNCT
cana-3474	77	3	2025	2025	NUM
cana-3474	77	4	)	)	PUNCT
cana-3474	77	5	679	679	NUM
cana-3474	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	77	7	𝜑(𝑚)(0	𝜑(𝑚)(0	PROPN
cana-3474	77	8	)	)	PUNCT
cana-3474	78	1	=	=	SYM
cana-3474	78	2	𝑏𝑚	𝑏𝑚	ADP
cana-3474	78	3	,	,	PUNCT
cana-3474	78	4	0	0	PUNCT
cana-3474	78	5	<	<	X
cana-3474	78	6	𝑚	𝑚	X
cana-3474	78	7	<	<	X
cana-3474	78	8	𝑛	𝑛	PRON
cana-3474	78	9	−	−	NUM
cana-3474	78	10	1	1	NUM
cana-3474	78	11	(	(	PUNCT
cana-3474	78	12	6	6	NUM
cana-3474	78	13	)	)	PUNCT
cana-3474	78	14	taking	take	VERB
cana-3474	78	15	w	w	NOUN
cana-3474	78	16	transform	transform	NOUN
cana-3474	78	17	's	's	PART
cana-3474	78	18	on	on	ADP
cana-3474	78	19	(	(	PUNCT
cana-3474	78	20	5	5	NUM
cana-3474	78	21	)	)	PUNCT
cana-3474	78	22	and	and	CCONJ
cana-3474	78	23	making	make	VERB
cana-3474	78	24	use	use	NOUN
cana-3474	78	25	of	of	ADP
cana-3474	78	26	convolution	convolution	NOUN
cana-3474	78	27	theorem	theorem	VERB
cana-3474	78	28	,	,	PUNCT
cana-3474	78	29	we	we	PRON
cana-3474	78	30	get	get	VERB
cana-3474	78	31	𝑊{𝜑(𝑛)(ω	𝑊{𝜑(𝑛)(ω	NOUN
cana-3474	78	32	)	)	PUNCT
cana-3474	78	33	}	}	PUNCT
cana-3474	78	34	=	=	SYM
cana-3474	78	35	𝑊{h(ω	𝑊{h(ω	NOUN
cana-3474	78	36	)	)	PUNCT
cana-3474	78	37	}	}	PUNCT
cana-3474	79	1	+	+	CCONJ
cana-3474	79	2	1	1	NUM
cana-3474	79	3	𝑠𝑚	𝑠𝑚	NUM
cana-3474	79	4	𝑊{k(ω)}𝑊{φ(ω	𝑊{k(ω)}𝑊{φ(ω	NOUN
cana-3474	79	5	)	)	PUNCT
cana-3474	79	6	}	}	PUNCT
cana-3474	79	7	(	(	PUNCT
cana-3474	79	8	7	7	X
cana-3474	79	9	)	)	PUNCT
cana-3474	79	10	making	make	VERB
cana-3474	79	11	use	use	NOUN
cana-3474	79	12	of	of	ADP
cana-3474	79	13	the	the	DET
cana-3474	79	14	property	property	NOUN
cana-3474	79	15	“	"	PUNCT
cana-3474	79	16	w	w	NOUN
cana-3474	79	17	transforms	transform	NOUN
cana-3474	79	18	of	of	ADP
cana-3474	79	19	derivatives	derivative	NOUN
cana-3474	79	20	”	"	PUNCT
cana-3474	79	21	on	on	ADP
cana-3474	79	22	(	(	PUNCT
cana-3474	79	23	7	7	NUM
cana-3474	79	24	)	)	PUNCT
cana-3474	79	25	,	,	PUNCT
cana-3474	79	26	we	we	PRON
cana-3474	79	27	obtain	obtain	VERB
cana-3474	79	28	𝑠𝑘𝑛𝑊{𝜑(ω	𝑠𝑘𝑛𝑊{𝜑(ω	CCONJ
cana-3474	79	29	)	)	PUNCT
cana-3474	79	30	}	}	PUNCT
cana-3474	80	1	−	−	PROPN
cana-3474	80	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	80	3	∑	∑	PROPN
cana-3474	80	4	𝑠𝑛(𝑘−𝑗−1)𝑘−1	𝑠𝑛(𝑘−𝑗−1)𝑘−1	NOUN
cana-3474	80	5	𝑗=0	𝑗=0	PUNCT
cana-3474	80	6	𝜑(𝑗)(0	𝜑(𝑗)(0	PROPN
cana-3474	80	7	)	)	PUNCT
cana-3474	80	8	=	=	SYM
cana-3474	80	9	𝑊{h(ω	𝑊{h(ω	NOUN
cana-3474	80	10	)	)	PUNCT
cana-3474	80	11	}	}	PUNCT
cana-3474	81	1	+	+	CCONJ
cana-3474	81	2	1	1	NUM
cana-3474	81	3	𝑠𝑚	𝑠𝑚	NUM
cana-3474	81	4	𝑊{k(ω)}𝑊{φ(ω	𝑊{k(ω)}𝑊{φ(ω	NOUN
cana-3474	81	5	)	)	PUNCT
cana-3474	81	6	}	}	PUNCT
cana-3474	81	7	(	(	PUNCT
cana-3474	81	8	8)	8)	NUM
cana-3474	81	9	substituting	substitute	VERB
cana-3474	81	10	equation	equation	NOUN
cana-3474	81	11	(	(	PUNCT
cana-3474	81	12	6	6	NUM
cana-3474	81	13	)	)	PUNCT
cana-3474	81	14	in	in	ADP
cana-3474	81	15	equation	equation	NOUN
cana-3474	81	16	(	(	PUNCT
cana-3474	81	17	8)	8)	NUM
cana-3474	81	18	,	,	PUNCT
cana-3474	81	19	after	after	ADP
cana-3474	81	20	simplification	simplification	NOUN
cana-3474	81	21	of	of	ADP
cana-3474	81	22	equation	equation	NOUN
cana-3474	81	23	(	(	PUNCT
cana-3474	81	24	8)	8)	NUM
cana-3474	81	25	,	,	PUNCT
cana-3474	81	26	and	and	CCONJ
cana-3474	81	27	we	we	PRON
cana-3474	81	28	have	have	VERB
cana-3474	81	29	the	the	DET
cana-3474	81	30	values	value	NOUN
cana-3474	81	31	of	of	ADP
cana-3474	81	32	𝑊{h(ω)},𝑊{k(ω	𝑊{h(ω)},𝑊{k(ω	NOUN
cana-3474	81	33	)	)	PUNCT
cana-3474	81	34	}	}	PUNCT
cana-3474	81	35	.	.	PUNCT
cana-3474	82	1	following	follow	VERB
cana-3474	82	2	the	the	DET
cana-3474	82	3	inverse	inverse	NOUN
cana-3474	82	4	w	w	PROPN
cana-3474	82	5	transform	transform	NOUN
cana-3474	82	6	according	accord	VERB
cana-3474	82	7	to	to	ADP
cana-3474	82	8	these	these	DET
cana-3474	82	9	principles	principle	NOUN
cana-3474	82	10	,	,	PUNCT
cana-3474	82	11	we	we	PRON
cana-3474	82	12	receive	receive	VERB
cana-3474	82	13	the	the	DET
cana-3474	82	14	necessary	necessary	ADJ
cana-3474	82	15	value	value	NOUN
cana-3474	82	16	of	of	ADP
cana-3474	82	17	𝜑(ω	𝜑(ω	PROPN
cana-3474	82	18	)	)	PUNCT
cana-3474	82	19	.	.	PUNCT
cana-3474	83	1	ii.use	ii.use	ADP
cana-3474	83	2	w	w	NOUN
cana-3474	83	3	transform	transform	NOUN
cana-3474	83	4	to	to	PART
cana-3474	83	5	resolve	resolve	VERB
cana-3474	83	6	lsvi	lsvi	NOUN
cana-3474	83	7	-	-	PUNCT
cana-3474	83	8	de	de	NOUN
cana-3474	83	9	of	of	ADP
cana-3474	83	10	2	2	NUM
cana-3474	83	11	nd	nd	ADV
cana-3474	83	12	kind	kind	NOUN
cana-3474	83	13	:	:	PUNCT
cana-3474	83	14	𝜑1	𝜑1	VERB
cana-3474	83	15	(	(	PUNCT
cana-3474	83	16	k)(ω	k)(ω	X
cana-3474	83	17	)	)	PUNCT
cana-3474	83	18	=	=	SYM
cana-3474	83	19	h1(ω	h1(ω	PROPN
cana-3474	83	20	)	)	PUNCT
cana-3474	83	21	+	+	CCONJ
cana-3474	83	22	{	{	PUNCT
cana-3474	83	23	∫	∫	PROPN
cana-3474	83	24	k11(ω−	k11(ω−	PROPN
cana-3474	83	25	τ	τ	PROPN
cana-3474	83	26	)	)	PUNCT
cana-3474	83	27	𝜑1(τ)dτ+	𝜑1(τ)dτ+	X
cana-3474	83	28	ω	ω	X
cana-3474	83	29	0	0	NUM
cana-3474	83	30	∫	∫	PROPN
cana-3474	83	31	k12(ω−	k12(ω−	PROPN
cana-3474	83	32	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	84	1	ω	ω	NOUN
cana-3474	84	2	0	0	PUNCT
cana-3474	85	1	+	+	ADJ
cana-3474	85	2	⋯	⋯	ADP
cana-3474	85	3	.+∫	.+∫	X
cana-3474	85	4	k1p(ω−	k1p(ω−	NOUN
cana-3474	85	5	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PUNCT
cana-3474	86	1	ω	ω	NOUN
cana-3474	86	2	0	0	NUM
cana-3474	86	3	}	}	PUNCT
cana-3474	86	4	𝜑2	𝜑2	NOUN
cana-3474	86	5	(	(	PUNCT
cana-3474	86	6	k)(ω	k)(ω	NOUN
cana-3474	86	7	)	)	PUNCT
cana-3474	86	8	=	=	SYM
cana-3474	86	9	h2(ω	h2(ω	NOUN
cana-3474	86	10	)	)	PUNCT
cana-3474	86	11	+	+	CCONJ
cana-3474	86	12	{	{	PUNCT
cana-3474	86	13	∫	∫	PROPN
cana-3474	86	14	k21(ω−	k21(ω−	PROPN
cana-3474	86	15	τ)𝜑1(τ)dτ+	τ)𝜑1(τ)dτ+	PROPN
cana-3474	86	16	ω	ω	SYM
cana-3474	86	17	0	0	NUM
cana-3474	86	18	∫	∫	PROPN
cana-3474	86	19	k22(ω−	k22(ω−	PROPN
cana-3474	86	20	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	86	21	ω	ω	NOUN
cana-3474	86	22	0	0	PUNCT
cana-3474	87	1	+	+	ADJ
cana-3474	87	2	⋯	⋯	ADP
cana-3474	87	3	.+∫	.+∫	NUM
cana-3474	87	4	k2p(ω−	k2p(ω−	NOUN
cana-3474	87	5	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PROPN
cana-3474	88	1	ω	ω	NUM
cana-3474	88	2	0	0	NUM
cana-3474	88	3	}	}	PUNCT
cana-3474	88	4	…	…	PUNCT
cana-3474	88	5	…	…	PUNCT
cana-3474	88	6	…	…	PUNCT
cana-3474	88	7	…	…	PUNCT
cana-3474	88	8	…	…	PUNCT
cana-3474	88	9	…	…	PUNCT
cana-3474	88	10	…	…	PUNCT
cana-3474	88	11	…	…	PUNCT
cana-3474	88	12	…	…	PUNCT
cana-3474	88	13	…	…	PUNCT
cana-3474	88	14	…	…	PUNCT
cana-3474	88	15	…	…	PUNCT
cana-3474	88	16	……	……	NOUN
cana-3474	88	17	……	……	NOUN
cana-3474	88	18	……	……	NOUN
cana-3474	88	19	……	……	NOUN
cana-3474	88	20	……	……	NOUN
cana-3474	88	21	……	……	NOUN
cana-3474	88	22	……	……	NOUN
cana-3474	88	23	……	……	NOUN
cana-3474	88	24	……	……	NOUN
cana-3474	88	25	.	.	PUNCT
cana-3474	89	1	𝜑p	𝜑p	PROPN
cana-3474	89	2	(	(	PUNCT
cana-3474	89	3	k)(ω	k)(ω	PROPN
cana-3474	89	4	)	)	PUNCT
cana-3474	89	5	=	=	SYM
cana-3474	89	6	hp(ω	hp(ω	X
cana-3474	89	7	)	)	PUNCT
cana-3474	90	1	+	+	CCONJ
cana-3474	90	2	{	{	PUNCT
cana-3474	90	3	∫	∫	PROPN
cana-3474	90	4	kp1(ω−	kp1(ω−	PROPN
cana-3474	90	5	τ)𝜑1(τ)dτ+	τ)𝜑1(τ)dτ+	X
cana-3474	90	6	ω	ω	SYM
cana-3474	90	7	0	0	NUM
cana-3474	90	8	∫	∫	PROPN
cana-3474	90	9	kp2(ω−	kp2(ω−	NOUN
cana-3474	90	10	τ)𝜑2(τ)dτ	τ)𝜑2(τ)dτ	NOUN
cana-3474	90	11	ω	ω	NOUN
cana-3474	90	12	0	0	PUNCT
cana-3474	91	1	+	+	ADJ
cana-3474	91	2	⋯	⋯	VERB
cana-3474	91	3	.+∫	.+∫	X
cana-3474	91	4	kpp(ω−	kpp(ω−	NOUN
cana-3474	92	1	τ)𝜑p(τ)dτ	τ)𝜑p(τ)dτ	PROPN
cana-3474	93	1	ω	ω	NOUN
cana-3474	93	2	0	0	NUM
cana-3474	93	3	}	}	PUNCT
cana-3474	93	4	]	]	PUNCT
cana-3474	93	5	(	(	PUNCT
cana-3474	93	6	9	9	X
cana-3474	93	7	)	)	PUNCT
cana-3474	93	8	with	with	ADP
cana-3474	93	9	{	{	PUNCT
cana-3474	93	10	𝜑	𝜑	PROPN
cana-3474	93	11	1	1	NUM
cana-3474	93	12	(	(	PUNCT
cana-3474	93	13	j)(0	j)(0	X
cana-3474	93	14	)	)	PUNCT
cana-3474	93	15	=	=	SYM
cana-3474	93	16	a1j	a1j	PROPN
cana-3474	93	17	,	,	PUNCT
cana-3474	93	18	j	j	PROPN
cana-3474	93	19	=	=	SYM
cana-3474	93	20	0,1,2	0,1,2	NUM
cana-3474	93	21	,	,	PUNCT
cana-3474	93	22	…	…	PUNCT
cana-3474	93	23	,	,	PUNCT
cana-3474	93	24	k−	k−	PROPN
cana-3474	93	25	1	1	NUM
cana-3474	93	26	;	;	PUNCT
cana-3474	93	27	𝜑	𝜑	PROPN
cana-3474	93	28	2	2	NUM
cana-3474	93	29	(	(	PUNCT
cana-3474	93	30	j)(0	j)(0	X
cana-3474	93	31	)	)	PUNCT
cana-3474	93	32	=	=	SYM
cana-3474	93	33	a2j	a2j	PROPN
cana-3474	93	34	,	,	PUNCT
cana-3474	93	35	j	j	PROPN
cana-3474	94	1	=	=	SYM
cana-3474	94	2	0,1,2	0,1,2	NUM
cana-3474	94	3	,	,	PUNCT
cana-3474	94	4	…	…	PUNCT
cana-3474	94	5	,	,	PUNCT
cana-3474	94	6	k−	k−	PROPN
cana-3474	94	7	1	1	NUM
cana-3474	94	8	;	;	PUNCT
cana-3474	94	9	…	…	PUNCT
cana-3474	94	10	…	…	PUNCT
cana-3474	94	11	…	…	PUNCT
cana-3474	94	12	…	…	PUNCT
cana-3474	94	13	…	…	PUNCT
cana-3474	94	14	…	…	PUNCT
cana-3474	94	15	…	…	PUNCT
cana-3474	94	16	……	……	NOUN
cana-3474	94	17	……	……	NOUN
cana-3474	94	18	……	……	NOUN
cana-3474	94	19	……	……	NOUN
cana-3474	94	20	……	……	NOUN
cana-3474	94	21	𝜑p	𝜑p	PROPN
cana-3474	94	22	(	(	PUNCT
cana-3474	94	23	j)(0	j)(0	X
cana-3474	94	24	)	)	PUNCT
cana-3474	94	25	=	=	SYM
cana-3474	94	26	apj	apj	PROPN
cana-3474	94	27	,	,	PUNCT
cana-3474	94	28	j	j	PROPN
cana-3474	94	29	=	=	SYM
cana-3474	94	30	0,1,2	0,1,2	NUM
cana-3474	94	31	,	,	PUNCT
cana-3474	94	32	…	…	PUNCT
cana-3474	94	33	,	,	PUNCT
cana-3474	94	34	k−	k−	PROPN
cana-3474	94	35	1	1	NUM
cana-3474	94	36	;	;	PUNCT
cana-3474	94	37	}	}	PUNCT
cana-3474	94	38	(	(	PUNCT
cana-3474	94	39	10	10	X
cana-3474	94	40	)	)	PUNCT
cana-3474	94	41	taking	take	VERB
cana-3474	94	42	w	w	PROPN
cana-3474	94	43	transformation	transformation	NOUN
cana-3474	94	44	proprietor	proprietor	NOUN
cana-3474	94	45	on	on	ADP
cana-3474	94	46	system	system	NOUN
cana-3474	94	47	(	(	PUNCT
cana-3474	94	48	9	9	NUM
cana-3474	94	49	)	)	PUNCT
cana-3474	94	50	,	,	PUNCT
cana-3474	94	51	then	then	ADV
cana-3474	94	52	applying	apply	VERB
cana-3474	94	53	the	the	DET
cana-3474	94	54	convolution	convolution	NOUN
cana-3474	94	55	theorem	theorem	VERB
cana-3474	94	56	,	,	PUNCT
cana-3474	94	57	we	we	PRON
cana-3474	94	58	obtain	obtain	VERB
cana-3474	94	59	communications	communication	NOUN
cana-3474	94	60	on	on	ADP
cana-3474	94	61	applied	apply	VERB
cana-3474	94	62	nonlinear	nonlinear	ADJ
cana-3474	94	63	analysis	analysis	NOUN
cana-3474	94	64	issn	issn	NOUN
cana-3474	94	65	:	:	PUNCT
cana-3474	94	66	1074	1074	NUM
cana-3474	94	67	-	-	PUNCT
cana-3474	94	68	133x	133x	NUM
cana-3474	94	69	vol	vol	NOUN
cana-3474	94	70	32	32	NUM
cana-3474	94	71	no	no	NOUN
cana-3474	94	72	.	.	PUNCT
cana-3474	95	1	7s	7	NOUN
cana-3474	95	2	(	(	PUNCT
cana-3474	95	3	2025	2025	NUM
cana-3474	95	4	)	)	PUNCT
cana-3474	96	1	680	680	NUM
cana-3474	96	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	96	3	𝑊{𝜑1	𝑊{𝜑1	PROPN
cana-3474	96	4	(	(	PUNCT
cana-3474	96	5	k)(ω	k)(ω	NOUN
cana-3474	96	6	)	)	PUNCT
cana-3474	96	7	}	}	PUNCT
cana-3474	96	8	=	=	SYM
cana-3474	96	9	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	96	10	)	)	PUNCT
cana-3474	96	11	}	}	PUNCT
cana-3474	97	1	+	+	CCONJ
cana-3474	97	2	[	[	PUNCT
cana-3474	97	3	1	1	NUM
cana-3474	97	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	97	5	𝑊{𝐾11(ω)}𝑊	𝑊{𝐾11(ω)}𝑊	PROPN
cana-3474	97	6	{	{	PUNCT
cana-3474	97	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	97	8	)	)	PUNCT
cana-3474	97	9	}	}	PUNCT
cana-3474	97	10	+	+	CCONJ
cana-3474	97	11	1	1	NUM
cana-3474	97	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	97	13	𝑊{𝐾12(ω)}𝑊	𝑊{𝐾12(ω)}𝑊	NOUN
cana-3474	97	14	{	{	PUNCT
cana-3474	97	15	𝜑2(ω	𝜑2(ω	ADV
cana-3474	97	16	)	)	PUNCT
cana-3474	97	17	}	}	PUNCT
cana-3474	97	18	+	+	ADJ
cana-3474	97	19	⋯+	⋯+	NOUN
cana-3474	97	20	1	1	NUM
cana-3474	97	21	𝑠𝑚	𝑠𝑚	ADP
cana-3474	97	22	𝑊{𝐾1𝑝(ω)}𝑊	𝑊{𝐾1𝑝(ω)}𝑊	PROPN
cana-3474	97	23	{	{	PUNCT
cana-3474	97	24	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	97	25	)	)	PUNCT
cana-3474	97	26	}	}	PUNCT
cana-3474	97	27	]	]	PUNCT
cana-3474	98	1	𝑊{𝜑2	𝑊{𝜑2	PROPN
cana-3474	98	2	(	(	PUNCT
cana-3474	98	3	k)(ω	k)(ω	VERB
cana-3474	98	4	)	)	PUNCT
cana-3474	98	5	}	}	PUNCT
cana-3474	98	6	=	=	SYM
cana-3474	98	7	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	98	8	)	)	PUNCT
cana-3474	98	9	}	}	PUNCT
cana-3474	99	1	+	+	CCONJ
cana-3474	99	2	[	[	PUNCT
cana-3474	99	3	1	1	NUM
cana-3474	99	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	99	5	𝑊{𝐾21(ω)}𝑊	𝑊{𝐾21(ω)}𝑊	NOUN
cana-3474	99	6	{	{	PUNCT
cana-3474	99	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	99	8	)	)	PUNCT
cana-3474	99	9	}	}	PUNCT
cana-3474	99	10	+	+	CCONJ
cana-3474	99	11	1	1	NUM
cana-3474	99	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	99	13	𝑊{𝐾22(ω)}𝑊	𝑊{𝐾22(ω)}𝑊	NOUN
cana-3474	99	14	{	{	PUNCT
cana-3474	99	15	𝜑2(ω	𝜑2(ω	ADV
cana-3474	99	16	)	)	PUNCT
cana-3474	99	17	}	}	PUNCT
cana-3474	100	1	+	+	ADJ
cana-3474	100	2	⋯+	⋯+	NOUN
cana-3474	100	3	1	1	NUM
cana-3474	100	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	100	5	𝑊{𝐾2𝑝(ω)}𝑊	𝑊{𝐾2𝑝(ω)}𝑊	NOUN
cana-3474	100	6	{	{	PUNCT
cana-3474	100	7	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	100	8	)	)	PUNCT
cana-3474	100	9	}	}	PUNCT
cana-3474	100	10	]	]	PUNCT
cana-3474	100	11	…	…	PUNCT
cana-3474	100	12	…	…	PUNCT
cana-3474	100	13	…	…	PUNCT
cana-3474	100	14	…	…	PUNCT
cana-3474	100	15	…	…	PUNCT
cana-3474	100	16	……	……	NOUN
cana-3474	100	17	……	……	NOUN
cana-3474	100	18	……	……	NOUN
cana-3474	100	19	……	……	NOUN
cana-3474	100	20	.	.	PUNCT
cana-3474	101	1	…	…	PUNCT
cana-3474	101	2	……	……	NOUN
cana-3474	101	3	……	……	NOUN
cana-3474	101	4	……	……	NOUN
cana-3474	101	5	……	……	NOUN
cana-3474	101	6	……	……	NOUN
cana-3474	101	7	……	……	NOUN
cana-3474	101	8	……	……	NOUN
cana-3474	101	9	……	……	NOUN
cana-3474	101	10	……	……	NOUN
cana-3474	101	11	𝑊{𝜑p	𝑊{𝜑p	NOUN
cana-3474	101	12	(	(	PUNCT
cana-3474	101	13	k)(ω	k)(ω	NOUN
cana-3474	101	14	)	)	PUNCT
cana-3474	101	15	}	}	PUNCT
cana-3474	101	16	=	=	SYM
cana-3474	101	17	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	101	18	)	)	PUNCT
cana-3474	101	19	}	}	PUNCT
cana-3474	101	20	+	+	CCONJ
cana-3474	101	21	[	[	PUNCT
cana-3474	101	22	1	1	NUM
cana-3474	101	23	𝑠𝑚	𝑠𝑚	ADP
cana-3474	101	24	𝑊{𝐾𝑝1(ω)}𝑊	𝑊{𝐾𝑝1(ω)}𝑊	PROPN
cana-3474	101	25	{	{	PUNCT
cana-3474	101	26	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	101	27	)	)	PUNCT
cana-3474	101	28	}	}	PUNCT
cana-3474	101	29	+	+	CCONJ
cana-3474	101	30	1	1	NUM
cana-3474	101	31	𝑠𝑚	𝑠𝑚	ADJ
cana-3474	101	32	𝑊{𝐾𝑝2(ω)}𝑊	𝑊{𝐾𝑝2(ω)}𝑊	NOUN
cana-3474	101	33	{	{	PUNCT
cana-3474	101	34	𝜑2(ω	𝜑2(ω	ADV
cana-3474	101	35	)	)	PUNCT
cana-3474	101	36	}	}	PUNCT
cana-3474	101	37	+	+	ADJ
cana-3474	101	38	⋯+	⋯+	NOUN
cana-3474	101	39	1	1	NUM
cana-3474	101	40	𝑠𝑚	𝑠𝑚	ADP
cana-3474	101	41	𝑊{𝐾𝑝𝑝(ω)}𝑊	𝑊{𝐾𝑝𝑝(ω)}𝑊	NOUN
cana-3474	101	42	{	{	PUNCT
cana-3474	101	43	𝜑p(ω	𝜑p(ω	NUM
cana-3474	101	44	)	)	PUNCT
cana-3474	101	45	}	}	PUNCT
cana-3474	101	46	]	]	PUNCT
cana-3474	101	47	]	]	PUNCT
cana-3474	101	48	(	(	PUNCT
cana-3474	101	49	11	11	X
cana-3474	101	50	)	)	PUNCT
cana-3474	101	51	making	make	VERB
cana-3474	101	52	use	use	NOUN
cana-3474	101	53	of	of	ADP
cana-3474	101	54	the	the	DET
cana-3474	101	55	property	property	NOUN
cana-3474	101	56	“	"	PUNCT
cana-3474	101	57	w	w	NOUN
cana-3474	101	58	transforms	transform	NOUN
cana-3474	101	59	of	of	ADP
cana-3474	101	60	derivatives	derivative	NOUN
cana-3474	101	61	”	"	PUNCT
cana-3474	101	62	on	on	ADP
cana-3474	101	63	system	system	NOUN
cana-3474	101	64	(	(	PUNCT
cana-3474	101	65	11	11	NUM
cana-3474	101	66	)	)	PUNCT
cana-3474	101	67	,	,	PUNCT
cana-3474	101	68	we	we	PRON
cana-3474	101	69	get	get	VERB
cana-3474	101	70	{	{	PUNCT
cana-3474	101	71	𝑠𝑘𝑛𝑊	𝑠𝑘𝑛𝑊	NOUN
cana-3474	101	72	(	(	PUNCT
cana-3474	101	73	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	101	74	)	)	PUNCT
cana-3474	101	75	)	)	PUNCT
cana-3474	102	1	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	NUM
cana-3474	102	2	)	)	PUNCT
cana-3474	103	1	𝑘−1	𝑘−1	PROPN
cana-3474	103	2	𝑗=0	𝑗=0	PUNCT
cana-3474	104	1	𝜑1	𝜑1	VERB
cana-3474	104	2	(	(	PUNCT
cana-3474	104	3	𝑗)(0	𝑗)(0	NUM
cana-3474	104	4	)	)	PUNCT
cana-3474	104	5	}	}	PUNCT
cana-3474	104	6	=	=	SYM
cana-3474	104	7	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	104	8	)	)	PUNCT
cana-3474	104	9	}	}	PUNCT
cana-3474	105	1	+	+	CCONJ
cana-3474	105	2	[	[	PUNCT
cana-3474	105	3	1	1	NUM
cana-3474	105	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	105	5	𝑊{𝐾11(ω)}𝑊	𝑊{𝐾11(ω)}𝑊	PROPN
cana-3474	105	6	{	{	PUNCT
cana-3474	105	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	105	8	)	)	PUNCT
cana-3474	105	9	}	}	PUNCT
cana-3474	105	10	+	+	CCONJ
cana-3474	105	11	1	1	NUM
cana-3474	105	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	105	13	𝑊{𝐾12(ω)}𝑊	𝑊{𝐾12(ω)}𝑊	NOUN
cana-3474	105	14	{	{	PUNCT
cana-3474	105	15	𝜑2(ω	𝜑2(ω	ADV
cana-3474	105	16	)	)	PUNCT
cana-3474	105	17	}	}	PUNCT
cana-3474	105	18	+	+	ADJ
cana-3474	105	19	⋯+	⋯+	NOUN
cana-3474	105	20	1	1	NUM
cana-3474	105	21	𝑠𝑚	𝑠𝑚	ADP
cana-3474	105	22	𝑊{𝐾1𝑝(ω)}𝑊	𝑊{𝐾1𝑝(ω)}𝑊	PROPN
cana-3474	105	23	{	{	PUNCT
cana-3474	105	24	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	105	25	)	)	PUNCT
cana-3474	105	26	}	}	PUNCT
cana-3474	105	27	]	]	PUNCT
cana-3474	105	28	{	{	PUNCT
cana-3474	105	29	𝑠𝑘𝑛𝑊	𝑠𝑘𝑛𝑊	NOUN
cana-3474	105	30	(	(	PUNCT
cana-3474	105	31	𝜑2(ω	𝜑2(ω	ADJ
cana-3474	105	32	)	)	PUNCT
cana-3474	105	33	)	)	PUNCT
cana-3474	105	34	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	NUM
cana-3474	105	35	)	)	PUNCT
cana-3474	106	1	𝑘−1	𝑘−1	PROPN
cana-3474	106	2	𝑗=0	𝑗=0	PROPN
cana-3474	107	1	𝜑2	𝜑2	PROPN
cana-3474	107	2	(	(	PUNCT
cana-3474	107	3	𝑗)(0	𝑗)(0	NUM
cana-3474	107	4	)	)	PUNCT
cana-3474	107	5	}	}	PUNCT
cana-3474	107	6	=	=	SYM
cana-3474	107	7	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	107	8	)	)	PUNCT
cana-3474	107	9	}	}	PUNCT
cana-3474	108	1	+	+	CCONJ
cana-3474	108	2	[	[	PUNCT
cana-3474	108	3	1	1	NUM
cana-3474	108	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	108	5	𝑊{𝐾21(ω)}𝑊	𝑊{𝐾21(ω)}𝑊	NOUN
cana-3474	108	6	{	{	PUNCT
cana-3474	108	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	108	8	)	)	PUNCT
cana-3474	108	9	}	}	PUNCT
cana-3474	108	10	+	+	CCONJ
cana-3474	108	11	1	1	NUM
cana-3474	108	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	108	13	𝑊{𝐾22(ω)}𝑊	𝑊{𝐾22(ω)}𝑊	NOUN
cana-3474	108	14	{	{	PUNCT
cana-3474	108	15	𝜑2(ω	𝜑2(ω	ADV
cana-3474	108	16	)	)	PUNCT
cana-3474	108	17	}	}	PUNCT
cana-3474	109	1	+	+	ADJ
cana-3474	109	2	⋯+	⋯+	NOUN
cana-3474	109	3	1	1	NUM
cana-3474	109	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	109	5	𝑊{𝐾2𝑝(ω)}𝑊	𝑊{𝐾2𝑝(ω)}𝑊	NOUN
cana-3474	109	6	{	{	PUNCT
cana-3474	109	7	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	109	8	)	)	PUNCT
cana-3474	109	9	}	}	PUNCT
cana-3474	109	10	]	]	PUNCT
cana-3474	109	11	…	…	PUNCT
cana-3474	109	12	……	……	X
cana-3474	109	13	.	.	PUNCT
cana-3474	109	14	.	.	PUNCT
cana-3474	110	1	…	…	PUNCT
cana-3474	110	2	…	…	PUNCT
cana-3474	110	3	…	…	PUNCT
cana-3474	110	4	…	…	PUNCT
cana-3474	110	5	…	…	PUNCT
cana-3474	110	6	…	…	PUNCT
cana-3474	110	7	…	…	PUNCT
cana-3474	110	8	…	…	PUNCT
cana-3474	110	9	…	…	PUNCT
cana-3474	110	10	…	…	PUNCT
cana-3474	110	11	…	…	PUNCT
cana-3474	110	12	……	……	NOUN
cana-3474	110	13	……	……	NOUN
cana-3474	110	14	……	……	NOUN
cana-3474	110	15	……	……	NOUN
cana-3474	110	16	……	……	NOUN
cana-3474	110	17	……	……	NOUN
cana-3474	110	18	……	……	NOUN
cana-3474	110	19	……	……	NOUN
cana-3474	110	20	……	……	NOUN
cana-3474	110	21	……	……	NOUN
cana-3474	110	22	……	……	NOUN
cana-3474	110	23	{	{	PUNCT
cana-3474	110	24	𝑠𝑘𝑛𝑊	𝑠𝑘𝑛𝑊	NOUN
cana-3474	110	25	(	(	PUNCT
cana-3474	110	26	𝜑p(ω	𝜑p(ω	NUM
cana-3474	110	27	)	)	PUNCT
cana-3474	110	28	)	)	PUNCT
cana-3474	110	29	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	−𝑠𝑚∑𝑠𝑛(𝑘−𝑗−1	NUM
cana-3474	110	30	)	)	PUNCT
cana-3474	111	1	𝑘−1	𝑘−1	PROPN
cana-3474	111	2	𝑗=0	𝑗=0	PROPN
cana-3474	112	1	𝜑p	𝜑p	PROPN
cana-3474	112	2	(	(	PUNCT
cana-3474	112	3	𝑗)(0	𝑗)(0	NUM
cana-3474	112	4	)	)	PUNCT
cana-3474	112	5	}	}	PUNCT
cana-3474	112	6	=	=	PUNCT
cana-3474	112	7	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	112	8	)	)	PUNCT
cana-3474	112	9	}	}	PUNCT
cana-3474	113	1	+	+	CCONJ
cana-3474	113	2	[	[	PUNCT
cana-3474	113	3	1	1	NUM
cana-3474	113	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	113	5	𝑊{𝐾𝑝1(ω)}𝑊	𝑊{𝐾𝑝1(ω)}𝑊	PROPN
cana-3474	113	6	{	{	PUNCT
cana-3474	113	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	113	8	)	)	PUNCT
cana-3474	113	9	}	}	PUNCT
cana-3474	114	1	+	+	CCONJ
cana-3474	114	2	1	1	NUM
cana-3474	114	3	𝑠𝑚	𝑠𝑚	ADJ
cana-3474	114	4	𝑊{𝐾𝑝2(ω)}𝑊	𝑊{𝐾𝑝2(ω)}𝑊	NOUN
cana-3474	114	5	{	{	PUNCT
cana-3474	114	6	𝜑2(ω	𝜑2(ω	ADV
cana-3474	114	7	)	)	PUNCT
cana-3474	114	8	}	}	PUNCT
cana-3474	114	9	+	+	ADJ
cana-3474	114	10	⋯+	⋯+	NOUN
cana-3474	114	11	1	1	NUM
cana-3474	114	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	114	13	𝑊{𝐾𝑝𝑝(ω)}𝑊	𝑊{𝐾𝑝𝑝(ω)}𝑊	NOUN
cana-3474	114	14	{	{	PUNCT
cana-3474	114	15	𝜑p(ω	𝜑p(ω	NUM
cana-3474	114	16	)	)	PUNCT
cana-3474	114	17	}	}	PUNCT
cana-3474	114	18	]	]	PUNCT
cana-3474	114	19	]	]	PUNCT
cana-3474	114	20	(	(	PUNCT
cana-3474	114	21	12	12	NUM
cana-3474	114	22	)	)	PUNCT
cana-3474	114	23	substituting	substitute	VERB
cana-3474	114	24	initial	initial	ADJ
cana-3474	114	25	condition	condition	NOUN
cana-3474	114	26	(	(	PUNCT
cana-3474	114	27	10	10	NUM
cana-3474	114	28	)	)	PUNCT
cana-3474	114	29	in	in	ADP
cana-3474	114	30	system	system	NOUN
cana-3474	114	31	(	(	PUNCT
cana-3474	114	32	12	12	NUM
cana-3474	114	33	)	)	PUNCT
cana-3474	114	34	,	,	PUNCT
cana-3474	114	35	we	we	PRON
cana-3474	114	36	obtain	obtain	VERB
cana-3474	114	37	communications	communication	NOUN
cana-3474	114	38	on	on	ADP
cana-3474	114	39	applied	apply	VERB
cana-3474	114	40	nonlinear	nonlinear	ADJ
cana-3474	114	41	analysis	analysis	NOUN
cana-3474	114	42	issn	issn	NOUN
cana-3474	114	43	:	:	PUNCT
cana-3474	114	44	1074	1074	NUM
cana-3474	114	45	-	-	PUNCT
cana-3474	114	46	133x	133x	NUM
cana-3474	114	47	vol	vol	NOUN
cana-3474	114	48	32	32	NUM
cana-3474	114	49	no	no	NOUN
cana-3474	114	50	.	.	PUNCT
cana-3474	115	1	7s	7	NOUN
cana-3474	115	2	(	(	PUNCT
cana-3474	115	3	2025	2025	NUM
cana-3474	115	4	)	)	PUNCT
cana-3474	116	1	681	681	NUM
cana-3474	116	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	116	3	{	{	PUNCT
cana-3474	116	4	𝑠	𝑠	PROPN
cana-3474	116	5	𝑘𝑛𝑊	𝑘𝑛𝑊	PROPN
cana-3474	116	6	(	(	PUNCT
cana-3474	116	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	116	8	)	)	PUNCT
cana-3474	116	9	)	)	PUNCT
cana-3474	116	10	−𝑠𝑚+𝑛(𝑘−1)𝑎10	−𝑠𝑚+𝑛(𝑘−1)𝑎10	NOUN
cana-3474	116	11	−𝑠𝑚+𝑛(𝑘−2)𝑎11	−𝑠𝑚+𝑛(𝑘−2)𝑎11	ADV
cana-3474	116	12	−⋯−	−⋯−	ADP
cana-3474	116	13	𝑠𝑚𝑎1𝑘−1	𝑠𝑚𝑎1𝑘−1	PROPN
cana-3474	116	14	}	}	PUNCT
cana-3474	116	15	=	=	SYM
cana-3474	116	16	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	116	17	)	)	PUNCT
cana-3474	116	18	}	}	PUNCT
cana-3474	117	1	+	+	CCONJ
cana-3474	117	2	[	[	PUNCT
cana-3474	117	3	1	1	NUM
cana-3474	117	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	117	5	𝑊{𝐾11(ω)}𝑊	𝑊{𝐾11(ω)}𝑊	PROPN
cana-3474	117	6	{	{	PUNCT
cana-3474	117	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	117	8	)	)	PUNCT
cana-3474	117	9	}	}	PUNCT
cana-3474	117	10	+	+	CCONJ
cana-3474	117	11	1	1	NUM
cana-3474	117	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	117	13	𝑊{𝐾12(ω)}𝑊	𝑊{𝐾12(ω)}𝑊	NOUN
cana-3474	117	14	{	{	PUNCT
cana-3474	117	15	𝜑2(ω	𝜑2(ω	ADV
cana-3474	117	16	)	)	PUNCT
cana-3474	117	17	}	}	PUNCT
cana-3474	117	18	+	+	ADJ
cana-3474	117	19	⋯+	⋯+	NOUN
cana-3474	117	20	1	1	NUM
cana-3474	117	21	𝑠𝑚	𝑠𝑚	ADP
cana-3474	117	22	𝑊{𝐾1𝑝(ω)}𝑊	𝑊{𝐾1𝑝(ω)}𝑊	PROPN
cana-3474	117	23	{	{	PUNCT
cana-3474	117	24	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	117	25	)	)	PUNCT
cana-3474	117	26	}	}	PUNCT
cana-3474	117	27	]	]	PUNCT
cana-3474	117	28	{	{	PUNCT
cana-3474	117	29	𝑠	𝑠	X
cana-3474	117	30	𝑘𝑛𝑊	𝑘𝑛𝑊	PROPN
cana-3474	117	31	(	(	PUNCT
cana-3474	117	32	𝜑2(ω	𝜑2(ω	NOUN
cana-3474	117	33	)	)	PUNCT
cana-3474	117	34	)	)	PUNCT
cana-3474	117	35	−𝑠𝑚+𝑛(𝑘−1)𝑎20	−𝑠𝑚+𝑛(𝑘−1)𝑎20	PROPN
cana-3474	117	36	−𝑠𝑚+𝑛(𝑘−2)𝑎21	−𝑠𝑚+𝑛(𝑘−2)𝑎21	PROPN
cana-3474	117	37	−⋯−	−⋯−	ADP
cana-3474	117	38	𝑠𝑚𝑎2𝑘−1	𝑠𝑚𝑎2𝑘−1	PROPN
cana-3474	117	39	}	}	PUNCT
cana-3474	117	40	=	=	SYM
cana-3474	117	41	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	117	42	)	)	PUNCT
cana-3474	117	43	}	}	PUNCT
cana-3474	117	44	+	+	CCONJ
cana-3474	117	45	[	[	PUNCT
cana-3474	117	46	1	1	NUM
cana-3474	117	47	𝑠𝑚	𝑠𝑚	ADP
cana-3474	117	48	𝑊{𝐾21(ω)}𝑊	𝑊{𝐾21(ω)}𝑊	NOUN
cana-3474	117	49	{	{	PUNCT
cana-3474	117	50	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	117	51	)	)	PUNCT
cana-3474	117	52	}	}	PUNCT
cana-3474	117	53	+	+	CCONJ
cana-3474	117	54	1	1	NUM
cana-3474	117	55	𝑠𝑚	𝑠𝑚	ADP
cana-3474	117	56	𝑊{𝐾22(ω)}𝑊	𝑊{𝐾22(ω)}𝑊	NOUN
cana-3474	117	57	{	{	PUNCT
cana-3474	117	58	𝜑2(ω	𝜑2(ω	ADV
cana-3474	117	59	)	)	PUNCT
cana-3474	117	60	}	}	PUNCT
cana-3474	118	1	+	+	ADJ
cana-3474	118	2	⋯+	⋯+	NOUN
cana-3474	118	3	1	1	NUM
cana-3474	118	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	118	5	𝑊{𝐾2𝑝(ω)}𝑊	𝑊{𝐾2𝑝(ω)}𝑊	NOUN
cana-3474	118	6	{	{	PUNCT
cana-3474	118	7	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	118	8	)	)	PUNCT
cana-3474	118	9	}	}	PUNCT
cana-3474	118	10	]	]	PUNCT
cana-3474	118	11	…	…	PUNCT
cana-3474	118	12	……	……	X
cana-3474	118	13	.	.	PUNCT
cana-3474	118	14	.	.	PUNCT
cana-3474	119	1	…	…	PUNCT
cana-3474	119	2	…	…	PUNCT
cana-3474	119	3	…	…	PUNCT
cana-3474	119	4	…	…	PUNCT
cana-3474	119	5	…	…	PUNCT
cana-3474	119	6	…	…	PUNCT
cana-3474	119	7	…	…	PUNCT
cana-3474	119	8	…	…	PUNCT
cana-3474	119	9	…	…	PUNCT
cana-3474	119	10	…	…	PUNCT
cana-3474	119	11	…	…	PUNCT
cana-3474	119	12	…	…	PUNCT
cana-3474	119	13	……	……	NOUN
cana-3474	119	14	……	……	NOUN
cana-3474	119	15	……	……	NOUN
cana-3474	119	16	……	……	NOUN
cana-3474	119	17	……	……	NOUN
cana-3474	119	18	……	……	NOUN
cana-3474	119	19	……	……	NOUN
cana-3474	119	20	……	……	NOUN
cana-3474	119	21	……	……	NOUN
cana-3474	119	22	……	……	NOUN
cana-3474	119	23	{	{	PUNCT
cana-3474	119	24	𝑠	𝑠	X
cana-3474	119	25	𝑘𝑛𝑊	𝑘𝑛𝑊	PROPN
cana-3474	119	26	(	(	PUNCT
cana-3474	119	27	𝜑𝑝(ω	𝜑𝑝(ω	NUM
cana-3474	119	28	)	)	PUNCT
cana-3474	119	29	)	)	PUNCT
cana-3474	119	30	−𝑠𝑚+𝑛(𝑘−1)𝑎𝑝0	−𝑠𝑚+𝑛(𝑘−1)𝑎𝑝0	NOUN
cana-3474	119	31	−𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	−𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	NOUN
cana-3474	119	32	−⋯−	−⋯−	ADP
cana-3474	119	33	𝑠𝑚𝑎𝑝𝑘−1	𝑠𝑚𝑎𝑝𝑘−1	PROPN
cana-3474	119	34	}	}	PUNCT
cana-3474	119	35	=	=	SYM
cana-3474	119	36	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	119	37	)	)	PUNCT
cana-3474	119	38	}	}	PUNCT
cana-3474	120	1	+	+	CCONJ
cana-3474	120	2	[	[	PUNCT
cana-3474	120	3	1	1	NUM
cana-3474	120	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	120	5	𝑊{𝐾𝑝1(ω)}𝑊	𝑊{𝐾𝑝1(ω)}𝑊	PROPN
cana-3474	120	6	{	{	PUNCT
cana-3474	120	7	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	120	8	)	)	PUNCT
cana-3474	120	9	}	}	PUNCT
cana-3474	121	1	+	+	CCONJ
cana-3474	121	2	1	1	NUM
cana-3474	121	3	𝑠𝑚	𝑠𝑚	ADJ
cana-3474	121	4	𝑊{𝐾𝑝2(ω)}𝑊	𝑊{𝐾𝑝2(ω)}𝑊	NOUN
cana-3474	121	5	{	{	PUNCT
cana-3474	121	6	𝜑2(ω	𝜑2(ω	ADV
cana-3474	121	7	)	)	PUNCT
cana-3474	121	8	}	}	PUNCT
cana-3474	121	9	+	+	ADJ
cana-3474	121	10	⋯+	⋯+	NOUN
cana-3474	121	11	1	1	NUM
cana-3474	121	12	𝑠𝑚	𝑠𝑚	ADP
cana-3474	121	13	𝑊{𝐾𝑝𝑝(ω)}𝑊	𝑊{𝐾𝑝𝑝(ω)}𝑊	NOUN
cana-3474	121	14	{	{	PUNCT
cana-3474	121	15	𝜑p(ω	𝜑p(ω	NUM
cana-3474	121	16	)	)	PUNCT
cana-3474	121	17	}	}	PUNCT
cana-3474	121	18	]	]	PUNCT
cana-3474	121	19	]	]	PUNCT
cana-3474	121	20	(	(	PUNCT
cana-3474	121	21	13	13	NUM
cana-3474	121	22	)	)	PUNCT
cana-3474	121	23	after	after	ADP
cana-3474	121	24	simplification	simplification	NOUN
cana-3474	121	25	system	system	NOUN
cana-3474	121	26	(	(	PUNCT
cana-3474	121	27	13	13	NUM
cana-3474	121	28	)	)	PUNCT
cana-3474	121	29	,	,	PUNCT
cana-3474	121	30	we	we	PRON
cana-3474	121	31	get	get	VERB
cana-3474	121	32	{	{	PUNCT
cana-3474	121	33	[	[	X
cana-3474	121	34	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	121	35	−	−	NOUN
cana-3474	121	36	1	1	NUM
cana-3474	121	37	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	121	38	𝑊{𝐾11(ω	𝑊{𝐾11(ω	NOUN
cana-3474	121	39	)	)	PUNCT
cana-3474	121	40	}	}	PUNCT
cana-3474	121	41	]	]	PUNCT
cana-3474	122	1	𝑊	𝑊	PROPN
cana-3474	122	2	{	{	PUNCT
cana-3474	122	3	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	122	4	)	)	PUNCT
cana-3474	122	5	}	}	PUNCT
cana-3474	122	6	−	−	PROPN
cana-3474	122	7	1	1	NUM
cana-3474	122	8	𝑠𝑚	𝑠𝑚	ADP
cana-3474	122	9	𝑊{𝐾12(ω)}𝑊	𝑊{𝐾12(ω)}𝑊	NOUN
cana-3474	122	10	{	{	PUNCT
cana-3474	122	11	𝜑2(ω	𝜑2(ω	NOUN
cana-3474	122	12	)	)	PUNCT
cana-3474	122	13	}	}	PUNCT
cana-3474	122	14	−⋯−	−⋯−	ADP
cana-3474	122	15	1	1	NUM
cana-3474	122	16	𝑠𝑚	𝑠𝑚	ADP
cana-3474	122	17	𝑊{𝐾1𝑝(ω)}𝑊	𝑊{𝐾1𝑝(ω)}𝑊	NOUN
cana-3474	122	18	{	{	PUNCT
cana-3474	122	19	𝜑𝑝(ω	𝜑𝑝(ω	NUM
cana-3474	122	20	)	)	PUNCT
cana-3474	122	21	}	}	PUNCT
cana-3474	122	22	}	}	PUNCT
cana-3474	122	23	=	=	SYM
cana-3474	122	24	[	[	PUNCT
cana-3474	122	25	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	122	26	)	)	PUNCT
cana-3474	122	27	}	}	PUNCT
cana-3474	123	1	+	+	CCONJ
cana-3474	123	2	𝑠	𝑠	X
cana-3474	123	3	𝑚+𝑛(𝑘−1)𝑎10	𝑚+𝑛(𝑘−1)𝑎10	ADP
cana-3474	123	4	+	+	NOUN
cana-3474	123	5	𝑠𝑚+𝑛(𝑘−2)𝑎11	𝑠𝑚+𝑛(𝑘−2)𝑎11	NOUN
cana-3474	123	6	+	+	X
cana-3474	123	7	⋯+𝑠𝑚𝑎1𝑘−1	⋯+𝑠𝑚𝑎1𝑘−1	X
cana-3474	123	8	]	]	PUNCT
cana-3474	123	9	{	{	PUNCT
cana-3474	123	10	+	+	CCONJ
cana-3474	123	11	−	−	NUM
cana-3474	123	12	1	1	NUM
cana-3474	123	13	𝑠𝑚	𝑠𝑚	ADP
cana-3474	123	14	𝑊{𝐾21(ω)}𝑊	𝑊{𝐾21(ω)}𝑊	NOUN
cana-3474	123	15	{	{	PUNCT
cana-3474	123	16	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	123	17	)	)	PUNCT
cana-3474	123	18	}	}	PUNCT
cana-3474	123	19	[	[	PUNCT
cana-3474	123	20	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	123	21	−	−	NOUN
cana-3474	123	22	1	1	NUM
cana-3474	123	23	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	123	24	𝑊{𝐾22(ω	𝑊{𝐾22(ω	NOUN
cana-3474	123	25	)	)	PUNCT
cana-3474	123	26	}	}	PUNCT
cana-3474	123	27	]	]	PUNCT
cana-3474	123	28	𝑊	𝑊	NOUN
cana-3474	123	29	{	{	PUNCT
cana-3474	123	30	𝜑2(ω	𝜑2(ω	NOUN
cana-3474	123	31	)	)	PUNCT
cana-3474	123	32	}	}	PUNCT
cana-3474	123	33	−⋯−	−⋯−	ADP
cana-3474	123	34	1	1	NUM
cana-3474	123	35	𝑠𝑚	𝑠𝑚	ADP
cana-3474	123	36	𝑊{𝐾2𝑝(ω)}𝑊	𝑊{𝐾2𝑝(ω)}𝑊	NOUN
cana-3474	123	37	{	{	PUNCT
cana-3474	123	38	𝜑p(ω	𝜑p(ω	PROPN
cana-3474	123	39	)	)	PUNCT
cana-3474	123	40	}	}	PUNCT
cana-3474	123	41	}	}	PUNCT
cana-3474	123	42	=	=	SYM
cana-3474	123	43	[	[	PUNCT
cana-3474	123	44	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	123	45	)	)	PUNCT
cana-3474	123	46	}	}	PUNCT
cana-3474	124	1	+	+	CCONJ
cana-3474	124	2	𝑠	𝑠	X
cana-3474	124	3	𝑚+𝑛(𝑘−1)𝑎20	𝑚+𝑛(𝑘−1)𝑎20	ADJ
cana-3474	124	4	+	+	NOUN
cana-3474	124	5	𝑠𝑚+𝑛(𝑘−2)𝑎21	𝑠𝑚+𝑛(𝑘−2)𝑎21	ADJ
cana-3474	124	6	+	+	ADJ
cana-3474	124	7	⋯+	⋯+	NOUN
cana-3474	124	8	𝑠𝑚𝑎2𝑘−1	𝑠𝑚𝑎2𝑘−1	PROPN
cana-3474	124	9	]	]	PUNCT
cana-3474	124	10	…	…	PUNCT
cana-3474	124	11	…	…	PUNCT
cana-3474	124	12	.	.	PUNCT
cana-3474	124	13	.	.	PUNCT
cana-3474	125	1	…	…	PUNCT
cana-3474	125	2	…	…	PUNCT
cana-3474	125	3	…	…	PUNCT
cana-3474	125	4	…	…	PUNCT
cana-3474	125	5	…	…	PUNCT
cana-3474	125	6	…	…	PUNCT
cana-3474	125	7	…	…	PUNCT
cana-3474	125	8	…	…	PUNCT
cana-3474	125	9	…	…	PUNCT
cana-3474	125	10	…	…	PUNCT
cana-3474	125	11	……	……	NOUN
cana-3474	125	12	……	……	NOUN
cana-3474	125	13	……	……	NOUN
cana-3474	125	14	……	……	NOUN
cana-3474	125	15	……	……	NOUN
cana-3474	125	16	……	……	NOUN
cana-3474	125	17	……	……	NOUN
cana-3474	125	18	……	……	NOUN
cana-3474	125	19	……	……	NOUN
cana-3474	125	20	……	……	NOUN
cana-3474	125	21	{	{	PUNCT
cana-3474	125	22	−1	−1	NOUN
cana-3474	125	23	𝑠𝑚	𝑠𝑚	ADP
cana-3474	125	24	𝑊{𝐾𝑝1(ω)}𝑊	𝑊{𝐾𝑝1(ω)}𝑊	PROPN
cana-3474	125	25	{	{	PUNCT
cana-3474	125	26	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	125	27	)	)	PUNCT
cana-3474	125	28	}	}	PUNCT
cana-3474	125	29	−	−	PROPN
cana-3474	125	30	1	1	NUM
cana-3474	125	31	𝑠𝑚	𝑠𝑚	ADP
cana-3474	125	32	𝑊{𝐾𝑝2(ω)}𝑊	𝑊{𝐾𝑝2(ω)}𝑊	NOUN
cana-3474	125	33	{	{	PUNCT
cana-3474	125	34	𝜑2(ω	𝜑2(ω	ADV
cana-3474	125	35	)	)	PUNCT
cana-3474	125	36	}	}	PUNCT
cana-3474	125	37	−⋯+	−⋯+	PROPN
cana-3474	126	1	[	[	X
cana-3474	126	2	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	126	3	−	−	NOUN
cana-3474	126	4	1	1	NUM
cana-3474	126	5	𝑠𝑚	𝑠𝑚	ADP
cana-3474	126	6	𝑊{𝐾𝑝𝑝(ω	𝑊{𝐾𝑝𝑝(ω	NOUN
cana-3474	126	7	)	)	PUNCT
cana-3474	126	8	}	}	PUNCT
cana-3474	126	9	]	]	PUNCT
cana-3474	126	10	𝑊	𝑊	PROPN
cana-3474	126	11	{	{	PUNCT
cana-3474	126	12	𝜑p(ω	𝜑p(ω	NUM
cana-3474	126	13	)	)	PUNCT
cana-3474	126	14	}	}	PUNCT
cana-3474	126	15	}	}	PUNCT
cana-3474	126	16	=	=	SYM
cana-3474	126	17	[	[	PUNCT
cana-3474	126	18	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	126	19	)	)	PUNCT
cana-3474	126	20	}	}	PUNCT
cana-3474	127	1	+	+	CCONJ
cana-3474	127	2	𝑠	𝑠	DET
cana-3474	127	3	𝑚+𝑛(𝑘−1)𝑎𝑝0	𝑚+𝑛(𝑘−1)𝑎𝑝0	NOUN
cana-3474	127	4	+	+	NOUN
cana-3474	127	5	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	PROPN
cana-3474	127	6	+	+	PROPN
cana-3474	127	7	⋯+𝑠𝑚𝑎𝑝𝑘−1	⋯+𝑠𝑚𝑎𝑝𝑘−1	X
cana-3474	127	8	]	]	PUNCT
cana-3474	127	9	]	]	PUNCT
cana-3474	127	10	(	(	PUNCT
cana-3474	127	11	14	14	NUM
cana-3474	127	12	)	)	PUNCT
cana-3474	127	13	the	the	DET
cana-3474	127	14	solution	solution	NOUN
cana-3474	127	15	of	of	ADP
cana-3474	127	16	system	system	NOUN
cana-3474	127	17	(	(	PUNCT
cana-3474	127	18	14	14	NUM
cana-3474	127	19	)	)	PUNCT
cana-3474	127	20	is	be	AUX
cana-3474	127	21	given	give	VERB
cana-3474	127	22	as	as	SCONJ
cana-3474	127	23	communications	communication	NOUN
cana-3474	127	24	on	on	ADP
cana-3474	127	25	applied	apply	VERB
cana-3474	127	26	nonlinear	nonlinear	ADJ
cana-3474	127	27	analysis	analysis	NOUN
cana-3474	127	28	issn	issn	NOUN
cana-3474	127	29	:	:	PUNCT
cana-3474	127	30	1074	1074	NUM
cana-3474	127	31	-	-	PUNCT
cana-3474	127	32	133x	133x	NUM
cana-3474	127	33	vol	vol	NOUN
cana-3474	127	34	32	32	NUM
cana-3474	127	35	no	no	NOUN
cana-3474	127	36	.	.	PUNCT
cana-3474	128	1	7s	7	NOUN
cana-3474	128	2	(	(	PUNCT
cana-3474	128	3	2025	2025	NUM
cana-3474	128	4	)	)	PUNCT
cana-3474	128	5	682	682	NUM
cana-3474	128	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	128	7	𝑊	𝑊	PROPN
cana-3474	128	8	{	{	PUNCT
cana-3474	128	9	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	128	10	)	)	PUNCT
cana-3474	128	11	}	}	PUNCT
cana-3474	129	1	=	=	PUNCT
cana-3474	129	2	|	|	ADV
cana-3474	130	1	|	|	ADV
cana-3474	131	1	|	|	ADV
cana-3474	132	1	|	|	ADV
cana-3474	132	2	{	{	PUNCT
cana-3474	132	3	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	132	4	)	)	PUNCT
cana-3474	132	5	}	}	PUNCT
cana-3474	133	1	+	+	CCONJ
cana-3474	133	2	𝑠	𝑠	X
cana-3474	133	3	𝑚+𝑛(𝑘−1)𝑎10	𝑚+𝑛(𝑘−1)𝑎10	ADP
cana-3474	133	4	+	+	NOUN
cana-3474	133	5	𝑠𝑚+𝑛(𝑘−2)𝑎11	𝑠𝑚+𝑛(𝑘−2)𝑎11	NOUN
cana-3474	133	6	+	+	NOUN
cana-3474	133	7	⋯+𝑠𝑚𝑎1𝑘−1	⋯+𝑠𝑚𝑎1𝑘−1	X
cana-3474	133	8	}	}	PUNCT
cana-3474	133	9	−	−	PROPN
cana-3474	133	10	1	1	NUM
cana-3474	133	11	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	12	{	{	PUNCT
cana-3474	133	13	𝐾12(ω	𝐾12(ω	ADV
cana-3474	133	14	)	)	PUNCT
cana-3474	133	15	}	}	PUNCT
cana-3474	133	16	…	…	PUNCT
cana-3474	133	17	……	……	NOUN
cana-3474	133	18	−	−	PROPN
cana-3474	133	19	1	1	NUM
cana-3474	133	20	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	21	{	{	PUNCT
cana-3474	133	22	𝐾1𝑝(ω	𝐾1𝑝(ω	NOUN
cana-3474	133	23	)	)	PUNCT
cana-3474	133	24	}	}	PUNCT
cana-3474	133	25	{	{	PUNCT
cana-3474	133	26	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	133	27	)	)	PUNCT
cana-3474	133	28	}	}	PUNCT
cana-3474	133	29	+	+	CCONJ
cana-3474	133	30	𝑠	𝑠	X
cana-3474	133	31	𝑚+𝑛(𝑘−1)𝑎20	𝑚+𝑛(𝑘−1)𝑎20	ADJ
cana-3474	133	32	+	+	NOUN
cana-3474	133	33	𝑠𝑚+𝑛(𝑘−2)𝑎21	𝑠𝑚+𝑛(𝑘−2)𝑎21	ADJ
cana-3474	133	34	+	+	ADJ
cana-3474	133	35	⋯+	⋯+	NOUN
cana-3474	133	36	𝑠𝑚𝑎2𝑘−1	𝑠𝑚𝑎2𝑘−1	NUM
cana-3474	133	37	}	}	PUNCT
cana-3474	133	38	(	(	PUNCT
cana-3474	133	39	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	133	40	−	−	PROPN
cana-3474	133	41	1	1	NUM
cana-3474	133	42	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	43	{	{	PUNCT
cana-3474	133	44	𝐾22(ω	𝐾22(ω	ADJ
cana-3474	133	45	)	)	PUNCT
cana-3474	133	46	}	}	PUNCT
cana-3474	133	47	)	)	PUNCT
cana-3474	133	48	…	…	PUNCT
cana-3474	133	49	……	……	X
cana-3474	133	50	−	−	PROPN
cana-3474	133	51	1	1	NUM
cana-3474	133	52	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	53	{	{	PUNCT
cana-3474	133	54	𝐾2𝑝(ω	𝐾2𝑝(ω	ADJ
cana-3474	133	55	)	)	PUNCT
cana-3474	133	56	}	}	PUNCT
cana-3474	133	57	…	…	PUNCT
cana-3474	133	58	…	…	PUNCT
cana-3474	133	59	…	…	PUNCT
cana-3474	133	60	…	…	PUNCT
cana-3474	133	61	…	…	PUNCT
cana-3474	133	62	…	…	PUNCT
cana-3474	133	63	…	…	PUNCT
cana-3474	133	64	…	…	PUNCT
cana-3474	133	65	…	…	PUNCT
cana-3474	133	66	……	……	NOUN
cana-3474	133	67	……	……	NOUN
cana-3474	133	68	……	……	NOUN
cana-3474	133	69	……	……	NOUN
cana-3474	133	70	……	……	NOUN
cana-3474	133	71	……	……	NOUN
cana-3474	133	72	……	……	NOUN
cana-3474	133	73	{	{	PUNCT
cana-3474	133	74	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	133	75	)	)	PUNCT
cana-3474	133	76	}	}	PUNCT
cana-3474	133	77	+	+	CCONJ
cana-3474	133	78	𝑠	𝑠	PRON
cana-3474	133	79	𝑚+𝑛(𝑘−1)𝑎𝑝0	𝑚+𝑛(𝑘−1)𝑎𝑝0	NOUN
cana-3474	133	80	+	+	NOUN
cana-3474	133	81	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	ADJ
cana-3474	133	82	+	+	ADJ
cana-3474	133	83	⋯+𝑠𝑚𝑎𝑝𝑘−1	⋯+𝑠𝑚𝑎𝑝𝑘−1	PROPN
cana-3474	133	84	}	}	PUNCT
cana-3474	133	85	−	−	PROPN
cana-3474	133	86	1	1	NUM
cana-3474	133	87	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	88	{	{	PUNCT
cana-3474	133	89	𝐾𝑝2(ω	𝐾𝑝2(ω	PROPN
cana-3474	133	90	)	)	PUNCT
cana-3474	133	91	}	}	PUNCT
cana-3474	133	92	…	…	PUNCT
cana-3474	133	93	……	……	NOUN
cana-3474	133	94	(	(	PUNCT
cana-3474	133	95	𝑠	𝑠	INTJ
cana-3474	133	96	𝑘𝑛	𝑘𝑛	INTJ
cana-3474	133	97	−	−	NUM
cana-3474	133	98	1	1	NUM
cana-3474	133	99	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	133	100	{	{	PUNCT
cana-3474	133	101	𝐾𝑝𝑝(ω)})|	𝐾𝑝𝑝(ω)})|	PROPN
cana-3474	134	1	|	|	ADV
cana-3474	134	2	|	|	ADV
cana-3474	134	3	|	|	INTJ
cana-3474	135	1	|	|	INTJ
cana-3474	135	2	|	|	ADV
cana-3474	136	1	|	|	ADV
cana-3474	137	1	[	[	X
cana-3474	137	2	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	137	3	−	−	NOUN
cana-3474	137	4	1	1	NUM
cana-3474	137	5	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	137	6	{	{	PUNCT
cana-3474	137	7	𝐾11(ω	𝐾11(ω	PROPN
cana-3474	137	8	)	)	PUNCT
cana-3474	137	9	}	}	PUNCT
cana-3474	137	10	]	]	PUNCT
cana-3474	138	1	−	−	PROPN
cana-3474	138	2	1	1	NUM
cana-3474	138	3	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	4	{	{	PUNCT
cana-3474	138	5	𝐾12(ω	𝐾12(ω	ADV
cana-3474	138	6	)	)	PUNCT
cana-3474	138	7	}	}	PUNCT
cana-3474	138	8	…	…	PUNCT
cana-3474	138	9	……	……	NOUN
cana-3474	138	10	−	−	PROPN
cana-3474	138	11	1	1	NUM
cana-3474	138	12	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	13	{	{	PUNCT
cana-3474	138	14	𝐾1𝑝(ω	𝐾1𝑝(ω	NOUN
cana-3474	138	15	)	)	PUNCT
cana-3474	138	16	}	}	PUNCT
cana-3474	138	17	−	−	PROPN
cana-3474	138	18	1	1	NUM
cana-3474	138	19	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	20	{	{	PUNCT
cana-3474	138	21	𝐾21(ω	𝐾21(ω	NOUN
cana-3474	138	22	)	)	PUNCT
cana-3474	138	23	}	}	PUNCT
cana-3474	138	24	[	[	PUNCT
cana-3474	138	25	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	138	26	−	−	PROPN
cana-3474	138	27	1	1	NUM
cana-3474	138	28	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	29	{	{	PUNCT
cana-3474	138	30	𝐾22(ω	𝐾22(ω	ADJ
cana-3474	138	31	)	)	PUNCT
cana-3474	138	32	}	}	PUNCT
cana-3474	138	33	]	]	PUNCT
cana-3474	138	34	…	…	PUNCT
cana-3474	138	35	……	……	X
cana-3474	138	36	−	−	PROPN
cana-3474	138	37	1	1	NUM
cana-3474	138	38	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	39	{	{	PUNCT
cana-3474	138	40	𝐾2𝑝(ω	𝐾2𝑝(ω	ADJ
cana-3474	138	41	)	)	PUNCT
cana-3474	138	42	}	}	PUNCT
cana-3474	138	43	…	…	PUNCT
cana-3474	138	44	…	…	PUNCT
cana-3474	138	45	…	…	PUNCT
cana-3474	138	46	…	…	PUNCT
cana-3474	138	47	…	…	PUNCT
cana-3474	138	48	…	…	PUNCT
cana-3474	138	49	……	……	NOUN
cana-3474	138	50	……	……	NOUN
cana-3474	138	51	……	……	NOUN
cana-3474	138	52	……	……	NOUN
cana-3474	138	53	……	……	NOUN
cana-3474	138	54	−1	−1	NOUN
cana-3474	138	55	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	56	{	{	PUNCT
cana-3474	138	57	𝐾𝑝1(ω	𝐾𝑝1(ω	NOUN
cana-3474	138	58	)	)	PUNCT
cana-3474	138	59	}	}	PUNCT
cana-3474	138	60	−	−	PROPN
cana-3474	138	61	1	1	NUM
cana-3474	138	62	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	63	{	{	PUNCT
cana-3474	138	64	𝐾𝑝2(ω	𝐾𝑝2(ω	PROPN
cana-3474	138	65	)	)	PUNCT
cana-3474	138	66	}	}	PUNCT
cana-3474	138	67	…	…	PUNCT
cana-3474	138	68	……	……	NOUN
cana-3474	138	69	[	[	X
cana-3474	138	70	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	138	71	−	−	NOUN
cana-3474	138	72	1	1	NUM
cana-3474	138	73	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	138	74	{	{	PUNCT
cana-3474	138	75	𝐾𝑝𝑝(ω	𝐾𝑝𝑝(ω	NOUN
cana-3474	138	76	)	)	PUNCT
cana-3474	138	77	}	}	PUNCT
cana-3474	138	78	]	]	PUNCT
cana-3474	139	1	|	|	ADV
cana-3474	139	2	|	|	ADV
cana-3474	139	3	|	|	ADV
cana-3474	139	4	𝑊	𝑊	PROPN
cana-3474	139	5	{	{	PUNCT
cana-3474	139	6	𝜑2(ω	𝜑2(ω	NOUN
cana-3474	139	7	)	)	PUNCT
cana-3474	139	8	}	}	PUNCT
cana-3474	140	1	=	=	PUNCT
cana-3474	141	1	|	|	ADV
cana-3474	142	1	|	|	ADV
cana-3474	142	2	|	|	ADV
cana-3474	143	1	|	|	ADV
cana-3474	144	1	[	[	X
cana-3474	144	2	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	144	3	−	−	NOUN
cana-3474	144	4	1	1	NUM
cana-3474	144	5	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	144	6	{	{	PUNCT
cana-3474	144	7	𝐾11(ω	𝐾11(ω	PROPN
cana-3474	144	8	)	)	PUNCT
cana-3474	144	9	}	}	PUNCT
cana-3474	144	10	]	]	PUNCT
cana-3474	144	11	{	{	PUNCT
cana-3474	144	12	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	144	13	)	)	PUNCT
cana-3474	144	14	}	}	PUNCT
cana-3474	144	15	+	+	CCONJ
cana-3474	144	16	𝑠	𝑠	X
cana-3474	145	1	𝑚+𝑛(𝑘−1)𝑎10	𝑚+𝑛(𝑘−1)𝑎10	ADP
cana-3474	145	2	+	+	NOUN
cana-3474	145	3	𝑠𝑚+𝑛(𝑘−2)𝑎11	𝑠𝑚+𝑛(𝑘−2)𝑎11	NOUN
cana-3474	145	4	+	+	NOUN
cana-3474	145	5	⋯+𝑠𝑚𝑎1𝑘−1	⋯+𝑠𝑚𝑎1𝑘−1	X
cana-3474	145	6	}	}	PUNCT
cana-3474	145	7	…	…	PUNCT
cana-3474	145	8	……	……	X
cana-3474	145	9	−	−	PROPN
cana-3474	145	10	1	1	NUM
cana-3474	145	11	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	145	12	{	{	PUNCT
cana-3474	145	13	𝐾1𝑝(ω	𝐾1𝑝(ω	NOUN
cana-3474	145	14	)	)	PUNCT
cana-3474	145	15	}	}	PUNCT
cana-3474	145	16	−	−	PROPN
cana-3474	145	17	1	1	NUM
cana-3474	145	18	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	145	19	{	{	PUNCT
cana-3474	145	20	𝐾21(ω	𝐾21(ω	NOUN
cana-3474	145	21	)	)	PUNCT
cana-3474	145	22	}	}	PUNCT
cana-3474	145	23	{	{	PUNCT
cana-3474	145	24	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	145	25	)	)	PUNCT
cana-3474	145	26	}	}	PUNCT
cana-3474	146	1	+	+	CCONJ
cana-3474	146	2	𝑠	𝑠	X
cana-3474	146	3	𝑚+𝑛(𝑘−1)𝑎20	𝑚+𝑛(𝑘−1)𝑎20	ADJ
cana-3474	146	4	+	+	NOUN
cana-3474	146	5	𝑠𝑚+𝑛(𝑘−2)𝑎21	𝑠𝑚+𝑛(𝑘−2)𝑎21	ADJ
cana-3474	146	6	+	+	ADJ
cana-3474	146	7	⋯+	⋯+	NOUN
cana-3474	146	8	𝑠𝑚𝑎2𝑘−1	𝑠𝑚𝑎2𝑘−1	NUM
cana-3474	146	9	}	}	PUNCT
cana-3474	146	10	…	…	PUNCT
cana-3474	146	11	…	…	PUNCT
cana-3474	146	12	…	…	PUNCT
cana-3474	146	13	−	−	NUM
cana-3474	146	14	1	1	NUM
cana-3474	146	15	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	146	16	{	{	PUNCT
cana-3474	146	17	𝐾2𝑝(ω	𝐾2𝑝(ω	ADJ
cana-3474	146	18	)	)	PUNCT
cana-3474	146	19	}	}	PUNCT
cana-3474	146	20	…	…	PUNCT
cana-3474	146	21	…	…	PUNCT
cana-3474	146	22	…	…	PUNCT
cana-3474	146	23	…	…	PUNCT
cana-3474	146	24	…	…	PUNCT
cana-3474	146	25	…	…	PUNCT
cana-3474	146	26	…	…	PUNCT
cana-3474	146	27	…	…	PUNCT
cana-3474	146	28	…	…	PUNCT
cana-3474	146	29	……	……	NOUN
cana-3474	146	30	……	……	NOUN
cana-3474	146	31	……	……	NOUN
cana-3474	146	32	……	……	NOUN
cana-3474	146	33	……	……	NOUN
cana-3474	146	34	……	……	NOUN
cana-3474	146	35	……	……	NOUN
cana-3474	146	36	−1	−1	NOUN
cana-3474	146	37	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	146	38	{	{	PUNCT
cana-3474	146	39	𝐾𝑝1(ω	𝐾𝑝1(ω	NOUN
cana-3474	146	40	)	)	PUNCT
cana-3474	146	41	}	}	PUNCT
cana-3474	146	42	{	{	PUNCT
cana-3474	146	43	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	146	44	)	)	PUNCT
cana-3474	146	45	}	}	PUNCT
cana-3474	146	46	+	+	CCONJ
cana-3474	146	47	𝑠	𝑠	DET
cana-3474	146	48	𝑚+𝑛(𝑘−1)𝑎𝑝0	𝑚+𝑛(𝑘−1)𝑎𝑝0	NOUN
cana-3474	146	49	+	+	NOUN
cana-3474	146	50	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	ADJ
cana-3474	146	51	+	+	ADJ
cana-3474	146	52	⋯+𝑠𝑚𝑎𝑝𝑘−1	⋯+𝑠𝑚𝑎𝑝𝑘−1	PROPN
cana-3474	146	53	}	}	PUNCT
cana-3474	146	54	…	…	PUNCT
cana-3474	146	55	……	……	NOUN
cana-3474	146	56	(	(	PUNCT
cana-3474	146	57	𝑠𝑘𝑛	𝑠𝑘𝑛	NOUN
cana-3474	146	58	−	−	PROPN
cana-3474	146	59	1	1	NUM
cana-3474	146	60	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	146	61	{	{	PUNCT
cana-3474	146	62	𝐾𝑝𝑝(ω)})|	𝐾𝑝𝑝(ω)})|	PROPN
cana-3474	147	1	|	|	ADV
cana-3474	147	2	|	|	ADV
cana-3474	147	3	|	|	INTJ
cana-3474	148	1	|	|	INTJ
cana-3474	148	2	|	|	ADV
cana-3474	149	1	|	|	ADV
cana-3474	150	1	[	[	X
cana-3474	150	2	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	150	3	−	−	NOUN
cana-3474	150	4	1	1	NUM
cana-3474	150	5	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	150	6	{	{	PUNCT
cana-3474	150	7	𝐾11(ω	𝐾11(ω	PROPN
cana-3474	150	8	)	)	PUNCT
cana-3474	150	9	}	}	PUNCT
cana-3474	150	10	]	]	PUNCT
cana-3474	151	1	−	−	PROPN
cana-3474	151	2	1	1	NUM
cana-3474	151	3	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	4	{	{	PUNCT
cana-3474	151	5	𝐾12(ω	𝐾12(ω	ADV
cana-3474	151	6	)	)	PUNCT
cana-3474	151	7	}	}	PUNCT
cana-3474	151	8	…	…	PUNCT
cana-3474	151	9	……	……	NOUN
cana-3474	151	10	−	−	PROPN
cana-3474	151	11	1	1	NUM
cana-3474	151	12	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	13	{	{	PUNCT
cana-3474	151	14	𝐾1𝑝(ω	𝐾1𝑝(ω	NOUN
cana-3474	151	15	)	)	PUNCT
cana-3474	151	16	}	}	PUNCT
cana-3474	151	17	−	−	PROPN
cana-3474	151	18	1	1	NUM
cana-3474	151	19	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	20	{	{	PUNCT
cana-3474	151	21	𝐾21(ω	𝐾21(ω	NOUN
cana-3474	151	22	)	)	PUNCT
cana-3474	151	23	}	}	PUNCT
cana-3474	151	24	[	[	PUNCT
cana-3474	151	25	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	151	26	−	−	PROPN
cana-3474	151	27	1	1	NUM
cana-3474	151	28	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	29	{	{	PUNCT
cana-3474	151	30	𝐾22(ω	𝐾22(ω	ADJ
cana-3474	151	31	)	)	PUNCT
cana-3474	151	32	}	}	PUNCT
cana-3474	151	33	]	]	PUNCT
cana-3474	151	34	…	…	PUNCT
cana-3474	151	35	……	……	X
cana-3474	151	36	−	−	PROPN
cana-3474	151	37	1	1	NUM
cana-3474	151	38	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	39	{	{	PUNCT
cana-3474	151	40	𝐾2𝑝(ω	𝐾2𝑝(ω	ADJ
cana-3474	151	41	)	)	PUNCT
cana-3474	151	42	}	}	PUNCT
cana-3474	151	43	…	…	PUNCT
cana-3474	151	44	…	…	PUNCT
cana-3474	151	45	…	…	PUNCT
cana-3474	151	46	…	…	PUNCT
cana-3474	151	47	…	…	PUNCT
cana-3474	151	48	……	……	NOUN
cana-3474	151	49	……	……	NOUN
cana-3474	151	50	……	……	NOUN
cana-3474	151	51	……	……	NOUN
cana-3474	151	52	……	……	NOUN
cana-3474	151	53	−1	−1	NOUN
cana-3474	151	54	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	55	{	{	PUNCT
cana-3474	151	56	𝐾𝑝1(ω	𝐾𝑝1(ω	NOUN
cana-3474	151	57	)	)	PUNCT
cana-3474	151	58	}	}	PUNCT
cana-3474	151	59	−	−	PROPN
cana-3474	151	60	1	1	NUM
cana-3474	151	61	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	62	{	{	PUNCT
cana-3474	151	63	𝐾𝑝2(ω	𝐾𝑝2(ω	PROPN
cana-3474	151	64	)	)	PUNCT
cana-3474	151	65	}	}	PUNCT
cana-3474	151	66	…	…	PUNCT
cana-3474	151	67	……	……	NOUN
cana-3474	151	68	[	[	X
cana-3474	151	69	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	151	70	−	−	NOUN
cana-3474	151	71	1	1	NUM
cana-3474	151	72	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	151	73	{	{	PUNCT
cana-3474	151	74	𝐾𝑝𝑝(ω	𝐾𝑝𝑝(ω	NOUN
cana-3474	151	75	)	)	PUNCT
cana-3474	151	76	}	}	PUNCT
cana-3474	151	77	]	]	PUNCT
cana-3474	152	1	|	|	ADV
cana-3474	152	2	|	|	ADV
cana-3474	152	3	|	|	ADV
cana-3474	152	4	communications	communication	VERB
cana-3474	152	5	on	on	ADP
cana-3474	152	6	applied	apply	VERB
cana-3474	152	7	nonlinear	nonlinear	ADJ
cana-3474	152	8	analysis	analysis	NOUN
cana-3474	152	9	issn	issn	NOUN
cana-3474	152	10	:	:	PUNCT
cana-3474	152	11	1074	1074	NUM
cana-3474	152	12	-	-	PUNCT
cana-3474	152	13	133x	133x	NUM
cana-3474	152	14	vol	vol	NOUN
cana-3474	152	15	32	32	NUM
cana-3474	152	16	no	no	NOUN
cana-3474	152	17	.	.	PUNCT
cana-3474	153	1	7s	7	NOUN
cana-3474	153	2	(	(	PUNCT
cana-3474	153	3	2025	2025	NUM
cana-3474	153	4	)	)	PUNCT
cana-3474	153	5	683	683	NUM
cana-3474	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	153	7	…	…	PUNCT
cana-3474	153	8	…	…	PUNCT
cana-3474	153	9	…	…	PUNCT
cana-3474	153	10	…	…	PUNCT
cana-3474	153	11	…	…	PUNCT
cana-3474	153	12	…	…	PUNCT
cana-3474	153	13	…	…	PUNCT
cana-3474	153	14	…	…	PUNCT
cana-3474	153	15	…	…	PUNCT
cana-3474	153	16	…	…	PUNCT
cana-3474	153	17	…	…	PUNCT
cana-3474	153	18	…	…	PUNCT
cana-3474	153	19	……	……	NOUN
cana-3474	153	20	……	……	NOUN
cana-3474	153	21	……	……	NOUN
cana-3474	153	22	……	……	NOUN
cana-3474	153	23	……	……	NOUN
cana-3474	153	24	……	……	NOUN
cana-3474	153	25	……	……	NOUN
cana-3474	153	26	……	……	NOUN
cana-3474	153	27	……	……	NOUN
cana-3474	153	28	……	……	NOUN
cana-3474	153	29	……	……	NOUN
cana-3474	153	30	𝑊	𝑊	NOUN
cana-3474	153	31	{	{	PUNCT
cana-3474	153	32	𝜑p(ω	𝜑p(ω	NUM
cana-3474	153	33	)	)	PUNCT
cana-3474	153	34	}	}	PUNCT
cana-3474	154	1	=	=	PUNCT
cana-3474	154	2	|	|	ADV
cana-3474	155	1	|	|	ADV
cana-3474	156	1	|	|	ADV
cana-3474	157	1	|	|	ADV
cana-3474	158	1	[	[	X
cana-3474	158	2	𝑠	𝑠	X
cana-3474	158	3	𝑘𝑛	𝑘𝑛	INTJ
cana-3474	158	4	−	−	NUM
cana-3474	158	5	1	1	NUM
cana-3474	158	6	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	158	7	{	{	PUNCT
cana-3474	158	8	𝐾11(ω	𝐾11(ω	PROPN
cana-3474	158	9	)	)	PUNCT
cana-3474	158	10	}	}	PUNCT
cana-3474	158	11	]	]	PUNCT
cana-3474	159	1	−	−	PROPN
cana-3474	159	2	1	1	NUM
cana-3474	159	3	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	159	4	{	{	PUNCT
cana-3474	159	5	𝐾12(ω	𝐾12(ω	ADV
cana-3474	159	6	)	)	PUNCT
cana-3474	159	7	}	}	PUNCT
cana-3474	160	1	…	…	PUNCT
cana-3474	160	2	……	……	X
cana-3474	160	3	{	{	PUNCT
cana-3474	160	4	𝑊{h1(ω	𝑊{h1(ω	NOUN
cana-3474	160	5	)	)	PUNCT
cana-3474	160	6	}	}	PUNCT
cana-3474	161	1	+	+	CCONJ
cana-3474	161	2	𝑠	𝑠	X
cana-3474	161	3	𝑚+𝑛(𝑘−1)𝑎10	𝑚+𝑛(𝑘−1)𝑎10	ADP
cana-3474	161	4	+	+	NOUN
cana-3474	161	5	𝑠𝑚+𝑛(𝑘−2)𝑎11	𝑠𝑚+𝑛(𝑘−2)𝑎11	NOUN
cana-3474	161	6	+	+	NOUN
cana-3474	161	7	⋯+𝑠𝑚𝑎1𝑘−1	⋯+𝑠𝑚𝑎1𝑘−1	X
cana-3474	161	8	}	}	PUNCT
cana-3474	161	9	−	−	PROPN
cana-3474	161	10	1	1	NUM
cana-3474	161	11	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	161	12	{	{	PUNCT
cana-3474	161	13	𝐾21(ω	𝐾21(ω	NOUN
cana-3474	161	14	)	)	PUNCT
cana-3474	161	15	}	}	PUNCT
cana-3474	162	1	[	[	PUNCT
cana-3474	162	2	𝑠	𝑠	X
cana-3474	162	3	𝑘𝑛	𝑘𝑛	INTJ
cana-3474	162	4	−	−	NUM
cana-3474	162	5	1	1	NUM
cana-3474	162	6	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	162	7	{	{	PUNCT
cana-3474	162	8	𝐾22(ω	𝐾22(ω	ADJ
cana-3474	162	9	)	)	PUNCT
cana-3474	162	10	}	}	PUNCT
cana-3474	162	11	]	]	PUNCT
cana-3474	162	12	…	…	PUNCT
cana-3474	162	13	……	……	X
cana-3474	162	14	{	{	PUNCT
cana-3474	162	15	𝑊{h2(ω	𝑊{h2(ω	NOUN
cana-3474	162	16	)	)	PUNCT
cana-3474	162	17	}	}	PUNCT
cana-3474	162	18	+	+	CCONJ
cana-3474	162	19	𝑠	𝑠	X
cana-3474	162	20	𝑚+𝑛(𝑘−1)𝑎20	𝑚+𝑛(𝑘−1)𝑎20	ADJ
cana-3474	162	21	+	+	NOUN
cana-3474	162	22	𝑠𝑚+𝑛(𝑘−2)𝑎21	𝑠𝑚+𝑛(𝑘−2)𝑎21	ADJ
cana-3474	162	23	+	+	ADJ
cana-3474	162	24	⋯+	⋯+	NOUN
cana-3474	162	25	𝑠𝑚𝑎2𝑘−1	𝑠𝑚𝑎2𝑘−1	NUM
cana-3474	162	26	}	}	PUNCT
cana-3474	162	27	…	…	PUNCT
cana-3474	162	28	…	…	PUNCT
cana-3474	162	29	…	…	PUNCT
cana-3474	162	30	…	…	PUNCT
cana-3474	162	31	…	…	PUNCT
cana-3474	162	32	…	…	PUNCT
cana-3474	162	33	…	…	PUNCT
cana-3474	162	34	…	…	PUNCT
cana-3474	162	35	…	…	PUNCT
cana-3474	162	36	……	……	NOUN
cana-3474	162	37	……	……	NOUN
cana-3474	162	38	……	……	NOUN
cana-3474	162	39	……	……	NOUN
cana-3474	162	40	……	……	NOUN
cana-3474	162	41	……	……	NOUN
cana-3474	162	42	……	……	NOUN
cana-3474	162	43	−1	−1	NOUN
cana-3474	162	44	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	162	45	{	{	PUNCT
cana-3474	162	46	𝐾𝑝1(ω	𝐾𝑝1(ω	NOUN
cana-3474	162	47	)	)	PUNCT
cana-3474	162	48	}	}	PUNCT
cana-3474	162	49	−	−	PROPN
cana-3474	162	50	1	1	NUM
cana-3474	162	51	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	162	52	{	{	PUNCT
cana-3474	162	53	𝐾𝑝2(ω	𝐾𝑝2(ω	PROPN
cana-3474	162	54	)	)	PUNCT
cana-3474	162	55	}	}	PUNCT
cana-3474	162	56	…	…	PUNCT
cana-3474	162	57	……	……	X
cana-3474	162	58	{	{	PUNCT
cana-3474	162	59	𝑊{hp(ω	𝑊{hp(ω	NOUN
cana-3474	162	60	)	)	PUNCT
cana-3474	162	61	}	}	PUNCT
cana-3474	162	62	+	+	CCONJ
cana-3474	162	63	𝑠	𝑠	DET
cana-3474	162	64	𝑚+𝑛(𝑘−1)𝑎𝑝0	𝑚+𝑛(𝑘−1)𝑎𝑝0	NOUN
cana-3474	162	65	+	+	NOUN
cana-3474	162	66	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	𝑠𝑚+𝑛(𝑘−2)𝑎𝑝1	ADJ
cana-3474	162	67	+	+	ADJ
cana-3474	162	68	⋯+𝑠𝑚𝑎𝑝𝑘−1	⋯+𝑠𝑚𝑎𝑝𝑘−1	PROPN
cana-3474	162	69	}	}	PUNCT
cana-3474	162	70	|	|	ADV
cana-3474	163	1	|	|	ADV
cana-3474	163	2	|	|	INTJ
cana-3474	164	1	|	|	INTJ
cana-3474	164	2	|	|	INTJ
cana-3474	165	1	|	|	ADV
cana-3474	165	2	|	|	ADV
cana-3474	166	1	[	[	X
cana-3474	166	2	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	166	3	−	−	NOUN
cana-3474	166	4	1	1	NUM
cana-3474	166	5	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	166	6	{	{	PUNCT
cana-3474	166	7	𝐾11(ω	𝐾11(ω	PROPN
cana-3474	166	8	)	)	PUNCT
cana-3474	166	9	}	}	PUNCT
cana-3474	166	10	]	]	PUNCT
cana-3474	167	1	−	−	PROPN
cana-3474	167	2	1	1	NUM
cana-3474	167	3	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	4	{	{	PUNCT
cana-3474	167	5	𝐾12(ω	𝐾12(ω	ADV
cana-3474	167	6	)	)	PUNCT
cana-3474	167	7	}	}	PUNCT
cana-3474	167	8	…	…	PUNCT
cana-3474	167	9	……	……	NOUN
cana-3474	167	10	−	−	PROPN
cana-3474	167	11	1	1	NUM
cana-3474	167	12	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	13	{	{	PUNCT
cana-3474	167	14	𝐾1𝑝(ω	𝐾1𝑝(ω	NOUN
cana-3474	167	15	)	)	PUNCT
cana-3474	167	16	}	}	PUNCT
cana-3474	167	17	−	−	PROPN
cana-3474	167	18	1	1	NUM
cana-3474	167	19	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	20	{	{	PUNCT
cana-3474	167	21	𝐾21(ω	𝐾21(ω	NOUN
cana-3474	167	22	)	)	PUNCT
cana-3474	167	23	}	}	PUNCT
cana-3474	167	24	[	[	PUNCT
cana-3474	167	25	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	167	26	−	−	PROPN
cana-3474	167	27	1	1	NUM
cana-3474	167	28	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	29	{	{	PUNCT
cana-3474	167	30	𝐾22(ω	𝐾22(ω	ADJ
cana-3474	167	31	)	)	PUNCT
cana-3474	167	32	}	}	PUNCT
cana-3474	167	33	]	]	PUNCT
cana-3474	167	34	…	…	PUNCT
cana-3474	167	35	……	……	X
cana-3474	167	36	−	−	PROPN
cana-3474	167	37	1	1	NUM
cana-3474	167	38	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	39	{	{	PUNCT
cana-3474	167	40	𝐾2𝑝(ω	𝐾2𝑝(ω	ADJ
cana-3474	167	41	)	)	PUNCT
cana-3474	167	42	}	}	PUNCT
cana-3474	167	43	…	…	PUNCT
cana-3474	167	44	…	…	PUNCT
cana-3474	167	45	…	…	PUNCT
cana-3474	167	46	…	…	PUNCT
cana-3474	167	47	…	…	PUNCT
cana-3474	167	48	…	…	PUNCT
cana-3474	167	49	……	……	NOUN
cana-3474	167	50	……	……	NOUN
cana-3474	167	51	……	……	NOUN
cana-3474	167	52	……	……	NOUN
cana-3474	167	53	……	……	NOUN
cana-3474	167	54	−1	−1	NOUN
cana-3474	167	55	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	56	{	{	PUNCT
cana-3474	167	57	𝐾𝑝1(ω	𝐾𝑝1(ω	NOUN
cana-3474	167	58	)	)	PUNCT
cana-3474	167	59	}	}	PUNCT
cana-3474	167	60	−	−	PROPN
cana-3474	167	61	1	1	NUM
cana-3474	167	62	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	63	{	{	PUNCT
cana-3474	167	64	𝐾𝑝2(ω	𝐾𝑝2(ω	PROPN
cana-3474	167	65	)	)	PUNCT
cana-3474	167	66	}	}	PUNCT
cana-3474	167	67	…	…	PUNCT
cana-3474	167	68	……	……	NOUN
cana-3474	167	69	[	[	X
cana-3474	167	70	𝑠𝑘𝑛	𝑠𝑘𝑛	NUM
cana-3474	167	71	−	−	NOUN
cana-3474	167	72	1	1	NUM
cana-3474	167	73	𝑠𝑚𝑊	𝑠𝑚𝑊	NOUN
cana-3474	167	74	{	{	PUNCT
cana-3474	167	75	𝐾𝑝𝑝(ω	𝐾𝑝𝑝(ω	NOUN
cana-3474	167	76	)	)	PUNCT
cana-3474	167	77	}	}	PUNCT
cana-3474	167	78	]	]	PUNCT
cana-3474	168	1	|	|	ADV
cana-3474	168	2	|	|	ADV
cana-3474	168	3	|	|	ADV
cana-3474	168	4	when	when	SCONJ
cana-3474	168	5	the	the	DET
cana-3474	168	6	aforementioned	aforementioned	ADJ
cana-3474	168	7	equations	equation	NOUN
cana-3474	168	8	are	be	AUX
cana-3474	168	9	simplified	simplify	VERB
cana-3474	168	10	,	,	PUNCT
cana-3474	168	11	we	we	PRON
cana-3474	168	12	obtain	obtain	VERB
cana-3474	168	13	the	the	DET
cana-3474	168	14	values	value	NOUN
cana-3474	168	15	of	of	ADP
cana-3474	168	16	𝑊	𝑊	PROPN
cana-3474	168	17	{	{	PUNCT
cana-3474	168	18	𝜑1(ω)},𝑊	𝜑1(ω)},𝑊	NUM
cana-3474	168	19	{	{	PUNCT
cana-3474	168	20	𝜑2(ω	𝜑2(ω	ADV
cana-3474	168	21	)	)	PUNCT
cana-3474	168	22	}	}	PUNCT
cana-3474	168	23	,	,	PUNCT
cana-3474	168	24	…	…	PUNCT
cana-3474	168	25	,	,	PUNCT
cana-3474	168	26	𝑊	𝑊	PROPN
cana-3474	168	27	{	{	PUNCT
cana-3474	168	28	𝜑p(ω	𝜑p(ω	NUM
cana-3474	168	29	)	)	PUNCT
cana-3474	168	30	}	}	PUNCT
cana-3474	168	31	.	.	PUNCT
cana-3474	169	1	following	follow	VERB
cana-3474	169	2	the	the	DET
cana-3474	169	3	inverse	inverse	NOUN
cana-3474	169	4	w	w	PROPN
cana-3474	169	5	transform	transform	NOUN
cana-3474	169	6	according	accord	VERB
cana-3474	169	7	to	to	ADP
cana-3474	169	8	these	these	DET
cana-3474	169	9	principles	principle	NOUN
cana-3474	169	10	,	,	PUNCT
cana-3474	169	11	we	we	PRON
cana-3474	169	12	get	get	VERB
cana-3474	169	13	the	the	DET
cana-3474	169	14	necessary	necessary	ADJ
cana-3474	169	15	values	value	NOUN
cana-3474	169	16	of	of	ADP
cana-3474	169	17	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	169	18	)	)	PUNCT
cana-3474	169	19	,	,	PUNCT
cana-3474	169	20	𝜑2(ω	𝜑2(ω	ADV
cana-3474	169	21	)	)	PUNCT
cana-3474	169	22	,	,	PUNCT
cana-3474	169	23	…	…	PUNCT
cana-3474	169	24	,	,	PUNCT
cana-3474	169	25	𝜑p(ω	𝜑p(ω	NUM
cana-3474	169	26	)	)	PUNCT
cana-3474	169	27	.	.	PUNCT
cana-3474	170	1	4	4	NUM
cana-3474	170	2	numerical	numerical	ADJ
cana-3474	170	3	problems	problem	NOUN
cana-3474	170	4	:	:	PUNCT
cana-3474	170	5	this	this	DET
cana-3474	170	6	section	section	NOUN
cana-3474	170	7	presents	present	VERB
cana-3474	170	8	several	several	ADJ
cana-3474	170	9	applications	application	NOUN
cana-3474	170	10	that	that	PRON
cana-3474	170	11	illustrate	illustrate	VERB
cana-3474	170	12	the	the	DET
cana-3474	170	13	efficiency	efficiency	NOUN
cana-3474	170	14	of	of	ADP
cana-3474	170	15	the	the	DET
cana-3474	170	16	w	w	PROPN
cana-3474	170	17	transform	transform	NOUN
cana-3474	170	18	in	in	ADP
cana-3474	170	19	resolving	resolve	VERB
cana-3474	170	20	lvi	lvi	PROPN
cana-3474	170	21	-	-	PUNCT
cana-3474	170	22	de	de	PROPN
cana-3474	170	23	of	of	ADP
cana-3474	170	24	2nd	2nd	ADJ
cana-3474	170	25	kind	kind	NOUN
cana-3474	170	26	and	and	CCONJ
cana-3474	170	27	lsvi	lsvi	NOUN
cana-3474	170	28	-	-	PUNCT
cana-3474	170	29	de	de	NOUN
cana-3474	170	30	of	of	ADP
cana-3474	170	31	2nd	2nd	ADJ
cana-3474	170	32	kind	kind	NOUN
cana-3474	170	33	.	.	PUNCT
cana-3474	171	1	problem	problem	NOUN
cana-3474	171	2	1	1	NUM
cana-3474	171	3	:	:	PUNCT
cana-3474	171	4	consider	consider	VERB
cana-3474	171	5	the	the	DET
cana-3474	171	6	lvi	lvi	NOUN
cana-3474	171	7	-	-	PUNCT
cana-3474	171	8	de	de	PROPN
cana-3474	171	9	of	of	ADP
cana-3474	171	10	2nd	2nd	ADJ
cana-3474	171	11	kind	kind	NOUN
cana-3474	171	12	.	.	PUNCT
cana-3474	172	1	𝜑′(ω	𝜑′(ω	X
cana-3474	172	2	)	)	PUNCT
cana-3474	172	3	=	=	SYM
cana-3474	173	1	1−∫	1−∫	NUM
cana-3474	173	2	φ(τ)dτ	φ(τ)dτ	NUM
cana-3474	173	3	ω	ω	NOUN
cana-3474	173	4	0	0	NUM
cana-3474	173	5	(	(	PUNCT
cana-3474	173	6	15	15	NUM
cana-3474	173	7	)	)	PUNCT
cana-3474	173	8	with	with	ADP
cana-3474	173	9	φ(0	φ(0	ADJ
cana-3474	173	10	)	)	PUNCT
cana-3474	173	11	=	=	SYM
cana-3474	173	12	0	0	NUM
cana-3474	173	13	(	(	PUNCT
cana-3474	173	14	16	16	NUM
cana-3474	173	15	)	)	PUNCT
cana-3474	173	16	operating	operate	VERB
cana-3474	173	17	w	w	NOUN
cana-3474	173	18	transform	transform	NOUN
cana-3474	173	19	on	on	ADP
cana-3474	173	20	equation	equation	NOUN
cana-3474	173	21	(	(	PUNCT
cana-3474	173	22	15	15	NUM
cana-3474	173	23	)	)	PUNCT
cana-3474	173	24	𝑊{𝜑′(ω	𝑊{𝜑′(ω	NOUN
cana-3474	173	25	)	)	PUNCT
cana-3474	173	26	}	}	PUNCT
cana-3474	173	27	=	=	SYM
cana-3474	173	28	𝑊{1	𝑊{1	PROPN
cana-3474	173	29	}	}	PUNCT
cana-3474	173	30	−	−	PROPN
cana-3474	173	31	𝑊{∫	𝑊{∫	NOUN
cana-3474	173	32	φ(τ)dτ	φ(τ)dτ	PROPN
cana-3474	173	33	}	}	PUNCT
cana-3474	173	34	ω	ω	NOUN
cana-3474	173	35	0	0	NUM
cana-3474	173	36	(	(	PUNCT
cana-3474	173	37	17	17	NUM
cana-3474	173	38	)	)	PUNCT
cana-3474	173	39	as	as	ADV
cana-3474	173	40	well	well	ADV
cana-3474	173	41	as	as	ADP
cana-3474	173	42	employing	employ	VERB
cana-3474	173	43	the	the	DET
cana-3474	173	44	convolution	convolution	NOUN
cana-3474	173	45	theorem	theorem	VERB
cana-3474	173	46	,	,	PUNCT
cana-3474	173	47	we	we	PRON
cana-3474	173	48	've	have	AUX
cana-3474	173	49	got	get	VERB
cana-3474	173	50	𝑊{𝜑′(ω	𝑊{𝜑′(ω	NOUN
cana-3474	173	51	)	)	PUNCT
cana-3474	173	52	}	}	PUNCT
cana-3474	173	53	=	=	SYM
cana-3474	173	54	𝑊{1	𝑊{1	PROPN
cana-3474	173	55	}	}	PUNCT
cana-3474	173	56	−	−	PROPN
cana-3474	173	57	1	1	NUM
cana-3474	173	58	𝑠𝑚	𝑠𝑚	ADP
cana-3474	173	59	𝑊{1}𝑊{φ(ω	𝑊{1}𝑊{φ(ω	PROPN
cana-3474	173	60	)	)	PUNCT
cana-3474	173	61	}	}	PUNCT
cana-3474	173	62	(	(	PUNCT
cana-3474	173	63	18	18	NUM
cana-3474	173	64	)	)	PUNCT
cana-3474	173	65	communications	communication	NOUN
cana-3474	173	66	on	on	ADP
cana-3474	173	67	applied	apply	VERB
cana-3474	173	68	nonlinear	nonlinear	ADJ
cana-3474	173	69	analysis	analysis	NOUN
cana-3474	173	70	issn	issn	NOUN
cana-3474	173	71	:	:	PUNCT
cana-3474	173	72	1074	1074	NUM
cana-3474	173	73	-	-	PUNCT
cana-3474	173	74	133x	133x	NUM
cana-3474	173	75	vol	vol	NOUN
cana-3474	173	76	32	32	NUM
cana-3474	174	1	no	no	NOUN
cana-3474	174	2	.	.	PUNCT
cana-3474	175	1	7s	7	NOUN
cana-3474	175	2	(	(	PUNCT
cana-3474	175	3	2025	2025	NUM
cana-3474	175	4	)	)	PUNCT
cana-3474	175	5	684	684	NUM
cana-3474	175	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	175	7	utilizing	utilize	VERB
cana-3474	175	8	the	the	DET
cana-3474	175	9	asset	asset	NOUN
cana-3474	175	10	“	"	PUNCT
cana-3474	175	11	w	w	NOUN
cana-3474	175	12	transforms	transform	NOUN
cana-3474	175	13	of	of	ADP
cana-3474	175	14	derivatives	derivative	NOUN
cana-3474	175	15	”	"	PUNCT
cana-3474	175	16	in	in	ADP
cana-3474	175	17	equation	equation	NOUN
cana-3474	175	18	(	(	PUNCT
cana-3474	175	19	18	18	NUM
cana-3474	175	20	)	)	PUNCT
cana-3474	175	21	,	,	PUNCT
cana-3474	175	22	we	we	PRON
cana-3474	175	23	own	own	VERB
cana-3474	175	24	𝑠𝑛𝑊{φ(ω	𝑠𝑛𝑊{φ(ω	NUM
cana-3474	175	25	)	)	PUNCT
cana-3474	175	26	}	}	PUNCT
cana-3474	175	27	−	−	NOUN
cana-3474	175	28	𝑠𝑚φ(0	𝑠𝑚φ(0	NOUN
cana-3474	175	29	)	)	PUNCT
cana-3474	176	1	=	=	NOUN
cana-3474	176	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	176	3	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	176	4	−	−	NUM
cana-3474	176	5	1	1	NUM
cana-3474	176	6	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	176	7	(	(	PUNCT
cana-3474	176	8	𝑠𝑚	𝑠𝑚	ADP
cana-3474	176	9	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	176	10	)	)	PUNCT
cana-3474	176	11	𝑊{φ(ω	𝑊{φ(ω	NUM
cana-3474	176	12	)	)	PUNCT
cana-3474	176	13	}	}	PUNCT
cana-3474	176	14	(	(	PUNCT
cana-3474	176	15	19	19	NUM
cana-3474	176	16	)	)	PUNCT
cana-3474	176	17	substituting	substitute	VERB
cana-3474	176	18	initial	initial	ADJ
cana-3474	176	19	condition	condition	NOUN
cana-3474	176	20	(	(	PUNCT
cana-3474	176	21	16	16	NUM
cana-3474	176	22	)	)	PUNCT
cana-3474	176	23	in	in	ADP
cana-3474	176	24	(	(	PUNCT
cana-3474	176	25	19	19	NUM
cana-3474	176	26	)	)	PUNCT
cana-3474	176	27	,	,	PUNCT
cana-3474	176	28	after	after	ADP
cana-3474	176	29	simplification	simplification	NOUN
cana-3474	176	30	of	of	ADP
cana-3474	176	31	equation	equation	NOUN
cana-3474	176	32	(	(	PUNCT
cana-3474	176	33	19	19	NUM
cana-3474	176	34	)	)	PUNCT
cana-3474	176	35	and	and	CCONJ
cana-3474	176	36	operating	operate	VERB
cana-3474	176	37	inverse	inverse	NOUN
cana-3474	176	38	w	w	NOUN
cana-3474	176	39	transforms	transform	VERB
cana-3474	176	40	,	,	PUNCT
cana-3474	176	41	we	we	PRON
cana-3474	176	42	get	get	VERB
cana-3474	176	43	the	the	DET
cana-3474	176	44	required	require	VERB
cana-3474	176	45	solution	solution	NOUN
cana-3474	176	46	of	of	ADP
cana-3474	176	47	equation	equation	NOUN
cana-3474	176	48	φ(ω	φ(ω	ADV
cana-3474	176	49	)	)	PUNCT
cana-3474	177	1	=	=	SYM
cana-3474	177	2	sin(ω	sin(ω	PROPN
cana-3474	177	3	)	)	PUNCT
cana-3474	177	4	(	(	PUNCT
cana-3474	177	5	20	20	NUM
cana-3474	177	6	)	)	PUNCT
cana-3474	177	7	problem	problem	NOUN
cana-3474	177	8	2	2	NUM
cana-3474	177	9	:	:	PUNCT
cana-3474	177	10	consider	consider	VERB
cana-3474	177	11	the	the	DET
cana-3474	177	12	lvi	lvi	NOUN
cana-3474	177	13	-	-	PUNCT
cana-3474	177	14	de	de	PROPN
cana-3474	177	15	of	of	ADP
cana-3474	177	16	2nd	2nd	ADJ
cana-3474	177	17	kind	kind	NOUN
cana-3474	177	18	.	.	PUNCT
cana-3474	178	1	φ′′(ω	φ′′(ω	NOUN
cana-3474	178	2	)	)	PUNCT
cana-3474	178	3	=	=	SYM
cana-3474	178	4	1	1	NUM
cana-3474	178	5	+	+	NUM
cana-3474	178	6	∫	∫	PROPN
cana-3474	178	7	(	(	PUNCT
cana-3474	178	8	ω−	ω−	PROPN
cana-3474	178	9	τ	τ	PROPN
cana-3474	178	10	)	)	PUNCT
cana-3474	178	11	φ(τ)dτ	φ(τ)dτ	PROPN
cana-3474	179	1	ω	ω	NOUN
cana-3474	179	2	0	0	NUM
cana-3474	179	3	(	(	PUNCT
cana-3474	179	4	21	21	NUM
cana-3474	179	5	)	)	PUNCT
cana-3474	179	6	with	with	ADP
cana-3474	179	7	φ(0	φ(0	ADJ
cana-3474	179	8	)	)	PUNCT
cana-3474	179	9	=	=	SYM
cana-3474	179	10	1	1	NUM
cana-3474	179	11	,	,	PUNCT
cana-3474	179	12	φ′(0	φ′(0	X
cana-3474	179	13	)	)	PUNCT
cana-3474	179	14	=	=	SYM
cana-3474	179	15	0	0	NUM
cana-3474	179	16	(	(	PUNCT
cana-3474	179	17	22	22	NUM
cana-3474	179	18	)	)	PUNCT
cana-3474	179	19	utilizing	utilize	VERB
cana-3474	179	20	the	the	DET
cana-3474	179	21	w	w	NOUN
cana-3474	179	22	transform	transform	NOUN
cana-3474	179	23	to	to	ADP
cana-3474	179	24	each	each	DET
cana-3474	179	25	side	side	NOUN
cana-3474	179	26	of	of	ADP
cana-3474	179	27	(	(	PUNCT
cana-3474	179	28	21	21	NUM
cana-3474	179	29	)	)	PUNCT
cana-3474	179	30	,	,	PUNCT
cana-3474	179	31	we	we	PRON
cana-3474	179	32	've	have	AUX
cana-3474	179	33	got	get	VERB
cana-3474	179	34	𝑊{φ′′(ω	𝑊{φ′′(ω	PROPN
cana-3474	179	35	)	)	PUNCT
cana-3474	179	36	}	}	PUNCT
cana-3474	179	37	=	=	SYM
cana-3474	179	38	𝑊{1	𝑊{1	PROPN
cana-3474	179	39	}	}	PUNCT
cana-3474	179	40	+	+	PROPN
cana-3474	179	41	𝑊{∫	𝑊{∫	NOUN
cana-3474	179	42	(	(	PUNCT
cana-3474	179	43	ω−	ω−	PROPN
cana-3474	179	44	τ	τ	PROPN
cana-3474	179	45	)	)	PUNCT
cana-3474	179	46	φ(τ)dτ	φ(τ)dτ	PROPN
cana-3474	180	1	ω	ω	NOUN
cana-3474	180	2	0	0	NUM
cana-3474	180	3	}	}	PUNCT
cana-3474	180	4	(	(	PUNCT
cana-3474	180	5	23	23	NUM
cana-3474	180	6	)	)	PUNCT
cana-3474	180	7	as	as	ADV
cana-3474	180	8	well	well	ADV
cana-3474	180	9	as	as	ADP
cana-3474	180	10	employing	employ	VERB
cana-3474	180	11	the	the	DET
cana-3474	180	12	convolution	convolution	NOUN
cana-3474	180	13	theorem	theorem	VERB
cana-3474	180	14	on	on	ADP
cana-3474	180	15	equation	equation	NOUN
cana-3474	180	16	(	(	PUNCT
cana-3474	180	17	23	23	NUM
cana-3474	180	18	)	)	PUNCT
cana-3474	180	19	,	,	PUNCT
cana-3474	180	20	we	we	PRON
cana-3474	180	21	obtain	obtain	VERB
cana-3474	180	22	𝑊{φ′′(ω	𝑊{φ′′(ω	PROPN
cana-3474	180	23	)	)	PUNCT
cana-3474	180	24	}	}	PUNCT
cana-3474	181	1	=	=	SYM
cana-3474	181	2	𝑊{1	𝑊{1	PROPN
cana-3474	181	3	}	}	PUNCT
cana-3474	181	4	+	+	NOUN
cana-3474	181	5	1	1	NUM
cana-3474	181	6	𝑠𝑚	𝑠𝑚	ADP
cana-3474	181	7	𝑊{ω	𝑊{ω	NOUN
cana-3474	181	8	}	}	PUNCT
cana-3474	181	9	𝑊{φ(ω	𝑊{φ(ω	NUM
cana-3474	181	10	)	)	PUNCT
cana-3474	181	11	}	}	PUNCT
cana-3474	181	12	(	(	PUNCT
cana-3474	181	13	24	24	NUM
cana-3474	181	14	)	)	PUNCT
cana-3474	181	15	making	make	VERB
cana-3474	181	16	use	use	NOUN
cana-3474	181	17	of	of	ADP
cana-3474	181	18	the	the	DET
cana-3474	181	19	asset	asset	NOUN
cana-3474	181	20	“	"	PUNCT
cana-3474	181	21	w	w	NOUN
cana-3474	181	22	transforms	transform	NOUN
cana-3474	181	23	of	of	ADP
cana-3474	181	24	derivatives	derivative	NOUN
cana-3474	181	25	”	"	PUNCT
cana-3474	181	26	on	on	ADP
cana-3474	181	27	equation	equation	NOUN
cana-3474	181	28	(	(	PUNCT
cana-3474	181	29	24	24	NUM
cana-3474	181	30	)	)	PUNCT
cana-3474	181	31	,	,	PUNCT
cana-3474	181	32	we	we	PRON
cana-3474	181	33	own	own	VERB
cana-3474	181	34	𝑠2𝑛𝑊{φ(ω	𝑠2𝑛𝑊{φ(ω	NOUN
cana-3474	181	35	)	)	PUNCT
cana-3474	181	36	}	}	PUNCT
cana-3474	181	37	−	−	PROPN
cana-3474	181	38	𝑠𝑚+𝑛φ(0	𝑠𝑚+𝑛φ(0	PROPN
cana-3474	181	39	)	)	PUNCT
cana-3474	181	40	−	−	PROPN
cana-3474	182	1	𝑠𝑚φ′(0	𝑠𝑚φ′(0	NOUN
cana-3474	182	2	)	)	PUNCT
cana-3474	182	3	=	=	NOUN
cana-3474	182	4	𝑠𝑚	𝑠𝑚	ADP
cana-3474	182	5	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	182	6	+	+	CCONJ
cana-3474	182	7	1	1	NUM
cana-3474	182	8	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	182	9	(	(	PUNCT
cana-3474	182	10	𝑠𝑚	𝑠𝑚	ADP
cana-3474	182	11	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	182	12	)	)	PUNCT
cana-3474	182	13	𝑊{φ(ω	𝑊{φ(ω	NUM
cana-3474	182	14	)	)	PUNCT
cana-3474	182	15	}	}	PUNCT
cana-3474	182	16	(	(	PUNCT
cana-3474	182	17	25	25	NUM
cana-3474	182	18	)	)	PUNCT
cana-3474	182	19	substituting	substitute	VERB
cana-3474	182	20	initial	initial	ADJ
cana-3474	182	21	condition	condition	NOUN
cana-3474	182	22	(	(	PUNCT
cana-3474	182	23	22	22	NUM
cana-3474	182	24	)	)	PUNCT
cana-3474	182	25	in	in	ADP
cana-3474	182	26	(	(	PUNCT
cana-3474	182	27	25	25	NUM
cana-3474	182	28	)	)	PUNCT
cana-3474	182	29	,	,	PUNCT
cana-3474	182	30	after	after	ADP
cana-3474	182	31	simplification	simplification	NOUN
cana-3474	182	32	of	of	ADP
cana-3474	182	33	equation	equation	NOUN
cana-3474	182	34	(	(	PUNCT
cana-3474	182	35	25	25	NUM
cana-3474	182	36	)	)	PUNCT
cana-3474	182	37	and	and	CCONJ
cana-3474	182	38	operating	operate	VERB
cana-3474	182	39	inverse	inverse	NOUN
cana-3474	182	40	w	w	NOUN
cana-3474	182	41	transforms	transform	VERB
cana-3474	182	42	,	,	PUNCT
cana-3474	182	43	we	we	PRON
cana-3474	182	44	get	get	VERB
cana-3474	182	45	the	the	DET
cana-3474	182	46	required	require	VERB
cana-3474	182	47	solution	solution	NOUN
cana-3474	182	48	of	of	ADP
cana-3474	182	49	equation	equation	NOUN
cana-3474	182	50	φ(ω	φ(ω	ADV
cana-3474	182	51	)	)	PUNCT
cana-3474	183	1	=	=	SYM
cana-3474	183	2	cosh(ω	cosh(ω	PROPN
cana-3474	183	3	)	)	PUNCT
cana-3474	183	4	(	(	PUNCT
cana-3474	183	5	26	26	NUM
cana-3474	183	6	)	)	PUNCT
cana-3474	183	7	problem	problem	NOUN
cana-3474	183	8	3	3	NUM
cana-3474	183	9	:	:	PUNCT
cana-3474	183	10	consider	consider	VERB
cana-3474	183	11	the	the	DET
cana-3474	183	12	lsvi	lsvi	NOUN
cana-3474	183	13	-	-	PUNCT
cana-3474	183	14	de	de	NOUN
cana-3474	183	15	of	of	ADP
cana-3474	183	16	2nd	2nd	ADJ
cana-3474	183	17	kind	kind	NOUN
cana-3474	183	18	.	.	PUNCT
cana-3474	184	1	{	{	PUNCT
cana-3474	184	2	𝜑1	𝜑1	VERB
cana-3474	184	3	′(ω	′(ω	NOUN
cana-3474	184	4	)	)	PUNCT
cana-3474	184	5	=	=	SYM
cana-3474	185	1	2ω2	2ω2	NUM
cana-3474	186	1	+	+	NOUN
cana-3474	186	2	∫	∫	X
cana-3474	186	3	[	[	X
cana-3474	186	4	(	(	PUNCT
cana-3474	186	5	ω−	ω−	ADJ
cana-3474	186	6	τ)𝜑1(τ	τ)𝜑1(τ	NOUN
cana-3474	186	7	)	)	PUNCT
cana-3474	186	8	+	+	CCONJ
cana-3474	186	9	(	(	PUNCT
cana-3474	186	10	ω−	ω−	INTJ
cana-3474	186	11	τ)𝜑2(τ)]dτ	τ)𝜑2(τ)]dτ	PROPN
cana-3474	186	12	ω	ω	NUM
cana-3474	186	13	0	0	NUM
cana-3474	186	14	𝜑2	𝜑2	PROPN
cana-3474	186	15	′(ω	′(ω	NOUN
cana-3474	186	16	)	)	PUNCT
cana-3474	186	17	=	=	SYM
cana-3474	187	1	−3ω2	−3ω2	NUM
cana-3474	187	2	−	−	NOUN
cana-3474	187	3	1	1	NUM
cana-3474	187	4	10	10	NUM
cana-3474	187	5	ω5	ω5	NOUN
cana-3474	187	6	+	+	PROPN
cana-3474	187	7	∫	∫	PROPN
cana-3474	187	8	[	[	X
cana-3474	187	9	(	(	PUNCT
cana-3474	187	10	ω−	ω−	ADJ
cana-3474	187	11	τ)𝜑1(τ	τ)𝜑1(τ	NOUN
cana-3474	187	12	)	)	PUNCT
cana-3474	187	13	−	−	PROPN
cana-3474	187	14	(	(	PUNCT
cana-3474	187	15	ω−	ω−	ADP
cana-3474	187	16	τ)𝜑2(τ)]dτ	τ)𝜑2(τ)]dτ	PROPN
cana-3474	187	17	ω	ω	NOUN
cana-3474	187	18	0	0	NUM
cana-3474	187	19	}	}	PUNCT
cana-3474	187	20	(	(	PUNCT
cana-3474	187	21	27	27	NUM
cana-3474	187	22	)	)	PUNCT
cana-3474	187	23	with	with	ADP
cana-3474	187	24	𝜑1(0	𝜑1(0	PROPN
cana-3474	187	25	)	)	PUNCT
cana-3474	187	26	=	=	SYM
cana-3474	187	27	1	1	NUM
cana-3474	187	28	,	,	PUNCT
cana-3474	187	29	𝜑2(0	𝜑2(0	PROPN
cana-3474	187	30	)	)	PUNCT
cana-3474	187	31	=	=	SYM
cana-3474	187	32	1	1	NUM
cana-3474	187	33	(	(	PUNCT
cana-3474	187	34	28	28	NUM
cana-3474	187	35	)	)	PUNCT
cana-3474	187	36	implementing	implement	VERB
cana-3474	187	37	the	the	DET
cana-3474	187	38	w	w	PROPN
cana-3474	187	39	transform	transform	NOUN
cana-3474	187	40	to	to	ADP
cana-3474	187	41	both	both	DET
cana-3474	187	42	parties	party	NOUN
cana-3474	187	43	of	of	ADP
cana-3474	187	44	(	(	PUNCT
cana-3474	187	45	27	27	NUM
cana-3474	187	46	)	)	PUNCT
cana-3474	187	47	,	,	PUNCT
cana-3474	187	48	we	we	PRON
cana-3474	187	49	've	have	AUX
cana-3474	187	50	got	get	VERB
cana-3474	187	51	{	{	PUNCT
cana-3474	187	52	𝑊{𝜑1	𝑊{𝜑1	PROPN
cana-3474	187	53	′(ω	′(ω	NOUN
cana-3474	187	54	)	)	PUNCT
cana-3474	187	55	}	}	PUNCT
cana-3474	187	56	=	=	SYM
cana-3474	187	57	w{2ω2	w{2ω2	NOUN
cana-3474	187	58	}	}	PUNCT
cana-3474	188	1	+	+	NOUN
cana-3474	188	2	w{∫	w{∫	ADJ
cana-3474	188	3	[	[	X
cana-3474	188	4	(	(	PUNCT
cana-3474	188	5	ω−	ω−	ADJ
cana-3474	188	6	τ)𝜑1(τ	τ)𝜑1(τ	NOUN
cana-3474	188	7	)	)	PUNCT
cana-3474	188	8	+	+	CCONJ
cana-3474	188	9	(	(	PUNCT
cana-3474	188	10	ω−	ω−	INTJ
cana-3474	188	11	τ)𝜑2(τ)]dτ	τ)𝜑2(τ)]dτ	PROPN
cana-3474	188	12	}	}	PUNCT
cana-3474	188	13	ω	ω	X
cana-3474	188	14	0	0	X
cana-3474	188	15	𝑊{𝜑2	𝑊{𝜑2	ADJ
cana-3474	188	16	′(ω	′(ω	NOUN
cana-3474	188	17	)	)	PUNCT
cana-3474	188	18	}	}	PUNCT
cana-3474	188	19	=	=	SYM
cana-3474	188	20	w{−3ω2	w{−3ω2	ADP
cana-3474	188	21	}	}	PUNCT
cana-3474	188	22	−	−	PROPN
cana-3474	188	23	w	w	NOUN
cana-3474	188	24	{	{	PUNCT
cana-3474	188	25	1	1	NUM
cana-3474	188	26	10	10	NUM
cana-3474	188	27	ω5	ω5	VERB
cana-3474	188	28	}	}	PUNCT
cana-3474	188	29	+	+	NUM
cana-3474	188	30	𝑊{∫	𝑊{∫	NOUN
cana-3474	189	1	[	[	X
cana-3474	189	2	(	(	PUNCT
cana-3474	189	3	ω−	ω−	ADJ
cana-3474	189	4	τ)𝜑1(τ	τ)𝜑1(τ	NOUN
cana-3474	189	5	)	)	PUNCT
cana-3474	189	6	−	−	PROPN
cana-3474	189	7	(	(	PUNCT
cana-3474	189	8	ω−	ω−	PROPN
cana-3474	189	9	τ)𝜑2(τ)]dτ	τ)𝜑2(τ)]dτ	PROPN
cana-3474	189	10	}	}	PUNCT
cana-3474	189	11	ω	ω	NOUN
cana-3474	189	12	0	0	NUM
cana-3474	189	13	}	}	PUNCT
cana-3474	189	14	(	(	PUNCT
cana-3474	189	15	29	29	NUM
cana-3474	189	16	)	)	PUNCT
cana-3474	189	17	communications	communication	NOUN
cana-3474	189	18	on	on	ADP
cana-3474	189	19	applied	apply	VERB
cana-3474	189	20	nonlinear	nonlinear	ADJ
cana-3474	189	21	analysis	analysis	NOUN
cana-3474	189	22	issn	issn	NOUN
cana-3474	189	23	:	:	PUNCT
cana-3474	189	24	1074	1074	NUM
cana-3474	189	25	-	-	PUNCT
cana-3474	189	26	133x	133x	NUM
cana-3474	189	27	vol	vol	NOUN
cana-3474	189	28	32	32	NUM
cana-3474	189	29	no	no	NOUN
cana-3474	189	30	.	.	PUNCT
cana-3474	190	1	7s	7	NOUN
cana-3474	190	2	(	(	PUNCT
cana-3474	190	3	2025	2025	NUM
cana-3474	190	4	)	)	PUNCT
cana-3474	190	5	685	685	NUM
cana-3474	190	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	190	7	and	and	CCONJ
cana-3474	190	8	using	use	VERB
cana-3474	190	9	the	the	DET
cana-3474	190	10	convolution	convolution	NOUN
cana-3474	190	11	theorem	theorem	NOUN
cana-3474	190	12	of	of	ADP
cana-3474	190	13	the	the	DET
cana-3474	190	14	w	w	PROPN
cana-3474	190	15	transform	transform	NOUN
cana-3474	190	16	on	on	ADP
cana-3474	190	17	equation	equation	NOUN
cana-3474	190	18	(	(	PUNCT
cana-3474	190	19	29	29	NUM
cana-3474	190	20	)	)	PUNCT
cana-3474	190	21	,	,	PUNCT
cana-3474	190	22	we	we	PRON
cana-3474	190	23	get	get	VERB
cana-3474	190	24	{	{	PUNCT
cana-3474	190	25	𝑊{𝜑1	𝑊{𝜑1	PROPN
cana-3474	190	26	′(ω	′(ω	NOUN
cana-3474	190	27	)	)	PUNCT
cana-3474	190	28	}	}	PUNCT
cana-3474	190	29	=	=	SYM
cana-3474	191	1	w{2ω2	w{2ω2	NOUN
cana-3474	191	2	}	}	PUNCT
cana-3474	191	3	+	+	CCONJ
cana-3474	191	4	1	1	NUM
cana-3474	191	5	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	191	6	[	[	PUNCT
cana-3474	191	7	w{ω}w{𝜑1(ω	w{ω}w{𝜑1(ω	NOUN
cana-3474	191	8	)	)	PUNCT
cana-3474	191	9	}	}	PUNCT
cana-3474	192	1	+	+	ADJ
cana-3474	192	2	w{ω}w{𝜑2(ω	w{ω}w{𝜑2(ω	NUM
cana-3474	192	3	)	)	PUNCT
cana-3474	192	4	}	}	PUNCT
cana-3474	192	5	]	]	PUNCT
cana-3474	193	1	𝑊{𝜑2	𝑊{𝜑2	PROPN
cana-3474	193	2	′(ω	′(ω	NOUN
cana-3474	193	3	)	)	PUNCT
cana-3474	193	4	}	}	PUNCT
cana-3474	193	5	=	=	SYM
cana-3474	193	6	w{−3ω2	w{−3ω2	ADP
cana-3474	193	7	}	}	PUNCT
cana-3474	193	8	−w	−w	ADV
cana-3474	193	9	{	{	PUNCT
cana-3474	193	10	1	1	NUM
cana-3474	193	11	10	10	NUM
cana-3474	193	12	ω5	ω5	VERB
cana-3474	193	13	}	}	PUNCT
cana-3474	193	14	+	+	CCONJ
cana-3474	193	15	1	1	NUM
cana-3474	193	16	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	193	17	[	[	PUNCT
cana-3474	193	18	w{ω}w{𝜑1(ω	w{ω}w{𝜑1(ω	NOUN
cana-3474	193	19	)	)	PUNCT
cana-3474	193	20	}	}	PUNCT
cana-3474	193	21	−	−	PROPN
cana-3474	193	22	w{ω}w{𝜑2(ω	w{ω}w{𝜑2(ω	NUM
cana-3474	193	23	)	)	PUNCT
cana-3474	193	24	}	}	PUNCT
cana-3474	193	25	]	]	PUNCT
cana-3474	193	26	}	}	PUNCT
cana-3474	193	27	(	(	PUNCT
cana-3474	193	28	30	30	X
cana-3474	193	29	)	)	PUNCT
cana-3474	193	30	making	make	VERB
cana-3474	193	31	use	use	NOUN
cana-3474	193	32	of	of	ADP
cana-3474	193	33	the	the	DET
cana-3474	193	34	asset	asset	NOUN
cana-3474	193	35	“	"	PUNCT
cana-3474	193	36	w	w	NOUN
cana-3474	193	37	transforms	transform	NOUN
cana-3474	193	38	of	of	ADP
cana-3474	193	39	derivatives	derivative	NOUN
cana-3474	193	40	”	"	PUNCT
cana-3474	193	41	on	on	ADP
cana-3474	193	42	equation	equation	NOUN
cana-3474	193	43	(	(	PUNCT
cana-3474	193	44	30	30	NUM
cana-3474	193	45	)	)	PUNCT
cana-3474	193	46	,	,	PUNCT
cana-3474	193	47	we	we	PRON
cana-3474	193	48	've	have	AUX
cana-3474	193	49	got	get	VERB
cana-3474	193	50	{	{	PUNCT
cana-3474	193	51	𝑠𝑛𝑊{𝜑1(ω	𝑠𝑛𝑊{𝜑1(ω	NOUN
cana-3474	193	52	)	)	PUNCT
cana-3474	193	53	}	}	PUNCT
cana-3474	194	1	−	−	PROPN
cana-3474	194	2	𝑠	𝑠	INTJ
cana-3474	194	3	𝑚φ	𝑚φ	NUM
cana-3474	194	4	1	1	NUM
cana-3474	194	5	(	(	PUNCT
cana-3474	194	6	0	0	NUM
cana-3474	194	7	)	)	PUNCT
cana-3474	194	8	=	=	SYM
cana-3474	194	9	2	2	NUM
cana-3474	194	10	(	(	PUNCT
cana-3474	194	11	2	2	NUM
cana-3474	194	12	!	!	NOUN
cana-3474	194	13	𝑠𝑚	𝑠𝑚	ADP
cana-3474	194	14	𝑠3𝑛	𝑠3𝑛	PROPN
cana-3474	194	15	)	)	PUNCT
cana-3474	195	1	+	+	CCONJ
cana-3474	195	2	1	1	NUM
cana-3474	195	3	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	195	4	[	[	PUNCT
cana-3474	195	5	𝑠𝑚	𝑠𝑚	ADP
cana-3474	195	6	𝑠2𝑛	𝑠2𝑛	ADJ
cana-3474	195	7	w{𝜑1(ω	w{𝜑1(ω	NOUN
cana-3474	195	8	)	)	PUNCT
cana-3474	195	9	}	}	PUNCT
cana-3474	196	1	+	+	CCONJ
cana-3474	196	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	196	3	𝑠2𝑛	𝑠2𝑛	ADJ
cana-3474	196	4	w{𝜑2(ω	w{𝜑2(ω	ADV
cana-3474	196	5	)	)	PUNCT
cana-3474	196	6	}	}	PUNCT
cana-3474	196	7	]	]	PUNCT
cana-3474	196	8	𝑠𝑛𝑊{𝜑2(ω	𝑠𝑛𝑊{𝜑2(ω	NOUN
cana-3474	196	9	)	)	PUNCT
cana-3474	196	10	}	}	PUNCT
cana-3474	196	11	−	−	PROPN
cana-3474	197	1	𝑠	𝑠	INTJ
cana-3474	197	2	𝑚φ	𝑚φ	INTJ
cana-3474	197	3	2	2	NUM
cana-3474	197	4	(	(	PUNCT
cana-3474	197	5	0	0	NUM
cana-3474	197	6	)	)	PUNCT
cana-3474	197	7	=	=	VERB
cana-3474	198	1	−3	−3	ADJ
cana-3474	198	2	(	(	PUNCT
cana-3474	198	3	2	2	X
cana-3474	198	4	!	!	NOUN
cana-3474	198	5	𝑠𝑚	𝑠𝑚	ADP
cana-3474	198	6	𝑠3𝑛	𝑠3𝑛	PROPN
cana-3474	198	7	)	)	PUNCT
cana-3474	198	8	−	−	PROPN
cana-3474	198	9	1	1	NUM
cana-3474	198	10	10	10	NUM
cana-3474	198	11	(	(	PUNCT
cana-3474	198	12	5	5	NUM
cana-3474	198	13	!	!	PUNCT
cana-3474	198	14	𝑠𝑚	𝑠𝑚	ADP
cana-3474	198	15	𝑠6𝑛	𝑠6𝑛	NOUN
cana-3474	198	16	)	)	PUNCT
cana-3474	199	1	+	+	CCONJ
cana-3474	199	2	1	1	NUM
cana-3474	199	3	𝑠𝑚	𝑠𝑚	NOUN
cana-3474	199	4	[	[	PUNCT
cana-3474	199	5	𝑠𝑚	𝑠𝑚	ADP
cana-3474	199	6	𝑠2𝑛	𝑠2𝑛	ADJ
cana-3474	199	7	w{𝜑1(ω	w{𝜑1(ω	NOUN
cana-3474	199	8	)	)	PUNCT
cana-3474	199	9	}	}	PUNCT
cana-3474	199	10	−	−	PROPN
cana-3474	199	11	𝑠𝑚	𝑠𝑚	ADP
cana-3474	199	12	𝑠2𝑛	𝑠2𝑛	ADJ
cana-3474	199	13	w{𝜑2(ω	w{𝜑2(ω	ADV
cana-3474	199	14	)	)	PUNCT
cana-3474	199	15	}	}	PUNCT
cana-3474	199	16	]	]	PUNCT
cana-3474	199	17	}	}	PUNCT
cana-3474	199	18	(	(	PUNCT
cana-3474	199	19	31	31	NUM
cana-3474	199	20	)	)	PUNCT
cana-3474	199	21	substituting	substitute	VERB
cana-3474	199	22	initial	initial	ADJ
cana-3474	199	23	condition	condition	NOUN
cana-3474	199	24	(	(	PUNCT
cana-3474	199	25	28	28	NUM
cana-3474	199	26	)	)	PUNCT
cana-3474	199	27	in	in	ADP
cana-3474	199	28	system	system	NOUN
cana-3474	199	29	(	(	PUNCT
cana-3474	199	30	31)and	31)and	NUM
cana-3474	199	31	after	after	ADP
cana-3474	199	32	simplification	simplification	NOUN
cana-3474	199	33	we	we	PRON
cana-3474	199	34	get	get	VERB
cana-3474	199	35	{	{	PUNCT
cana-3474	199	36	(	(	PUNCT
cana-3474	199	37	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	199	38	−	−	NOUN
cana-3474	199	39	1	1	NUM
cana-3474	199	40	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	199	41	)	)	PUNCT
cana-3474	199	42	𝑊{𝜑1(ω	𝑊{𝜑1(ω	NOUN
cana-3474	199	43	)	)	PUNCT
cana-3474	199	44	}	}	PUNCT
cana-3474	199	45	−	−	PROPN
cana-3474	200	1	(	(	PUNCT
cana-3474	200	2	1	1	NUM
cana-3474	200	3	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	200	4	)	)	PUNCT
cana-3474	200	5	𝑊{𝜑2(ω	𝑊{𝜑2(ω	ADV
cana-3474	200	6	)	)	PUNCT
cana-3474	200	7	}	}	PUNCT
cana-3474	200	8	=	=	SYM
cana-3474	201	1	4𝑠𝑚	4𝑠𝑚	NOUN
cana-3474	201	2	+	+	CCONJ
cana-3474	201	3	𝑠𝑚+3𝑛	𝑠𝑚+3𝑛	NOUN
cana-3474	201	4	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	201	5	(	(	PUNCT
cana-3474	201	6	−1	−1	NOUN
cana-3474	201	7	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	201	8	)	)	PUNCT
cana-3474	201	9	𝑊{𝜑1(ω	𝑊{𝜑1(ω	NOUN
cana-3474	201	10	)	)	PUNCT
cana-3474	201	11	}	}	PUNCT
cana-3474	202	1	+	+	CCONJ
cana-3474	202	2	(	(	PUNCT
cana-3474	202	3	𝑠3𝑛	𝑠3𝑛	VERB
cana-3474	202	4	+	+	CCONJ
cana-3474	202	5	1	1	NUM
cana-3474	202	6	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	202	7	)	)	PUNCT
cana-3474	202	8	𝑊{𝜑2(ω	𝑊{𝜑2(ω	ADV
cana-3474	202	9	)	)	PUNCT
cana-3474	202	10	}	}	PUNCT
cana-3474	202	11	=	=	SYM
cana-3474	202	12	−6𝑠𝑚+3𝑛	−6𝑠𝑚+3𝑛	NOUN
cana-3474	202	13	−	−	PROPN
cana-3474	202	14	12𝑠𝑚	12𝑠𝑚	NOUN
cana-3474	202	15	+	+	CCONJ
cana-3474	202	16	𝑠𝑚+6𝑛	𝑠𝑚+6𝑛	NOUN
cana-3474	202	17	𝑠6𝑛	𝑠6𝑛	X
cana-3474	202	18	}	}	PUNCT
cana-3474	202	19	(	(	PUNCT
cana-3474	202	20	32	32	NUM
cana-3474	202	21	)	)	PUNCT
cana-3474	202	22	the	the	DET
cana-3474	202	23	solution	solution	NOUN
cana-3474	202	24	of	of	ADP
cana-3474	202	25	system	system	NOUN
cana-3474	202	26	(	(	PUNCT
cana-3474	202	27	32	32	NUM
cana-3474	202	28	)	)	PUNCT
cana-3474	202	29	is	be	AUX
cana-3474	202	30	given	give	VERB
cana-3474	202	31	as	as	ADP
cana-3474	202	32	𝑊{𝜑1(ω	𝑊{𝜑1(ω	NOUN
cana-3474	202	33	)	)	PUNCT
cana-3474	202	34	}	}	PUNCT
cana-3474	202	35	=	=	PUNCT
cana-3474	203	1	|	|	NOUN
cana-3474	203	2	4𝑠𝑚	4𝑠𝑚	NOUN
cana-3474	203	3	+	+	CCONJ
cana-3474	203	4	𝑠𝑚+3𝑛	𝑠𝑚+3𝑛	NOUN
cana-3474	203	5	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	203	6	−	−	NOUN
cana-3474	203	7	1	1	NUM
cana-3474	203	8	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	203	9	−6𝑠𝑚+3𝑛	−6𝑠𝑚+3𝑛	NOUN
cana-3474	203	10	−	−	PROPN
cana-3474	203	11	12𝑠𝑚	12𝑠𝑚	NOUN
cana-3474	203	12	+	+	CCONJ
cana-3474	203	13	𝑠𝑚+6𝑛	𝑠𝑚+6𝑛	NOUN
cana-3474	203	14	𝑠6𝑛	𝑠6𝑛	NOUN
cana-3474	203	15	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	203	16	+	+	CCONJ
cana-3474	203	17	1	1	NUM
cana-3474	203	18	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	203	19	|	|	ADV
cana-3474	203	20	|	|	ADV
cana-3474	203	21	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	203	22	−	−	ADP
cana-3474	203	23	1	1	NUM
cana-3474	203	24	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	203	25	−	−	NOUN
cana-3474	203	26	1	1	NUM
cana-3474	203	27	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	203	28	−1	−1	NOUN
cana-3474	203	29	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	203	30	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	203	31	+	+	CCONJ
cana-3474	203	32	1	1	NUM
cana-3474	203	33	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	203	34	|	|	ADV
cana-3474	203	35	𝑊{𝜑2(ω	𝑊{𝜑2(ω	ADV
cana-3474	203	36	)	)	PUNCT
cana-3474	203	37	}	}	PUNCT
cana-3474	203	38	=	=	PUNCT
cana-3474	204	1	|	|	ADV
cana-3474	204	2	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	204	3	−	−	NOUN
cana-3474	204	4	1	1	NUM
cana-3474	204	5	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	204	6	4𝑠𝑚	4𝑠𝑚	NOUN
cana-3474	205	1	+	+	CCONJ
cana-3474	205	2	𝑠𝑚+3𝑛	𝑠𝑚+3𝑛	ADJ
cana-3474	205	3	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	205	4	−1	−1	NOUN
cana-3474	205	5	𝑠2𝑛	𝑠2𝑛	ADJ
cana-3474	205	6	−6𝑠𝑚+3𝑛	−6𝑠𝑚+3𝑛	NOUN
cana-3474	205	7	−	−	PROPN
cana-3474	205	8	12𝑠𝑚	12𝑠𝑚	NOUN
cana-3474	205	9	+	+	CCONJ
cana-3474	205	10	𝑠𝑚+6𝑛	𝑠𝑚+6𝑛	NOUN
cana-3474	205	11	𝑠6𝑛	𝑠6𝑛	NOUN
cana-3474	205	12	|	|	ADV
cana-3474	205	13	|	|	ADV
cana-3474	205	14	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	205	15	−	−	ADP
cana-3474	205	16	1	1	NUM
cana-3474	205	17	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	205	18	−	−	NOUN
cana-3474	205	19	1	1	NUM
cana-3474	205	20	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	205	21	−1	−1	NOUN
cana-3474	205	22	𝑠2𝑛	𝑠2𝑛	VERB
cana-3474	205	23	𝑠3𝑛	𝑠3𝑛	ADJ
cana-3474	205	24	+	+	CCONJ
cana-3474	205	25	1	1	NUM
cana-3474	205	26	𝑠2𝑛	𝑠2𝑛	NOUN
cana-3474	205	27	|	|	ADV
cana-3474	205	28	when	when	SCONJ
cana-3474	205	29	the	the	DET
cana-3474	205	30	aforementioned	aforementioned	ADJ
cana-3474	205	31	equations	equation	NOUN
cana-3474	205	32	are	be	AUX
cana-3474	205	33	simplified	simplify	VERB
cana-3474	205	34	,	,	PUNCT
cana-3474	205	35	we	we	PRON
cana-3474	205	36	obtain	obtain	VERB
cana-3474	205	37	the	the	DET
cana-3474	205	38	values	value	NOUN
cana-3474	205	39	of	of	ADP
cana-3474	205	40	𝑊	𝑊	PROPN
cana-3474	205	41	{	{	PUNCT
cana-3474	205	42	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	205	43	)	)	PUNCT
cana-3474	205	44	}	}	PUNCT
cana-3474	206	1	=	=	NOUN
cana-3474	206	2	𝑠𝑚	𝑠𝑚	ADP
cana-3474	206	3	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	206	4	+	+	CCONJ
cana-3474	206	5	6	6	NUM
cana-3474	206	6	𝑠𝑚	𝑠𝑚	ADP
cana-3474	206	7	𝑠4𝑛	𝑠4𝑛	NOUN
cana-3474	206	8	𝑊	𝑊	PROPN
cana-3474	206	9	{	{	PUNCT
cana-3474	206	10	𝜑2(ω	𝜑2(ω	NOUN
cana-3474	206	11	)	)	PUNCT
cana-3474	206	12	}	}	PUNCT
cana-3474	206	13	=	=	SYM
cana-3474	206	14	𝑠𝑚	𝑠𝑚	ADP
cana-3474	206	15	𝑠𝑛	𝑠𝑛	NOUN
cana-3474	206	16	−	−	PROPN
cana-3474	206	17	6	6	NUM
cana-3474	206	18	𝑠𝑚	𝑠𝑚	ADP
cana-3474	206	19	𝑠4𝑛	𝑠4𝑛	NOUN
cana-3474	206	20	communications	communication	NOUN
cana-3474	206	21	on	on	ADP
cana-3474	206	22	applied	apply	VERB
cana-3474	206	23	nonlinear	nonlinear	ADJ
cana-3474	206	24	analysis	analysis	NOUN
cana-3474	206	25	issn	issn	NOUN
cana-3474	206	26	:	:	PUNCT
cana-3474	206	27	1074	1074	NUM
cana-3474	206	28	-	-	PUNCT
cana-3474	206	29	133x	133x	NUM
cana-3474	206	30	vol	vol	NOUN
cana-3474	206	31	32	32	NUM
cana-3474	206	32	no	no	NOUN
cana-3474	206	33	.	.	PUNCT
cana-3474	207	1	7s	7	NOUN
cana-3474	207	2	(	(	PUNCT
cana-3474	207	3	2025	2025	NUM
cana-3474	207	4	)	)	PUNCT
cana-3474	207	5	686	686	NUM
cana-3474	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3474	207	7	operating	operate	VERB
cana-3474	207	8	inverse	inverse	NOUN
cana-3474	207	9	w	w	NOUN
cana-3474	207	10	transforms	transform	VERB
cana-3474	207	11	,	,	PUNCT
cana-3474	207	12	we	we	PRON
cana-3474	207	13	get	get	VERB
cana-3474	207	14	the	the	DET
cana-3474	207	15	required	require	VERB
cana-3474	207	16	solution	solution	NOUN
cana-3474	207	17	of	of	ADP
cana-3474	207	18	equations	equation	NOUN
cana-3474	207	19	𝜑1(ω	𝜑1(ω	NOUN
cana-3474	207	20	)	)	PUNCT
cana-3474	207	21	=	=	SYM
cana-3474	208	1	1	1	NUM
cana-3474	208	2	+	+	NUM
cana-3474	208	3	ω3	ω3	NOUN
cana-3474	208	4	𝜑2(ω	𝜑2(ω	ADV
cana-3474	208	5	)	)	PUNCT
cana-3474	208	6	=	=	SYM
cana-3474	209	1	1−	1−	NUM
cana-3474	209	2	ω3	ω3	NOUN
cana-3474	209	3	5	5	NUM
cana-3474	209	4	conclusion	conclusion	NOUN
cana-3474	209	5	:	:	PUNCT
cana-3474	209	6	in	in	ADP
cana-3474	209	7	this	this	DET
cana-3474	209	8	research	research	NOUN
cana-3474	209	9	,	,	PUNCT
cana-3474	209	10	we	we	PRON
cana-3474	209	11	have	have	AUX
cana-3474	209	12	effectively	effectively	ADV
cana-3474	209	13	addressed	address	VERB
cana-3474	209	14	the	the	DET
cana-3474	209	15	w	w	NOUN
cana-3474	209	16	transform	transform	NOUN
cana-3474	209	17	for	for	ADP
cana-3474	209	18	resolving	resolve	VERB
cana-3474	209	19	lvi	lvi	NOUN
cana-3474	209	20	-	-	PUNCT
cana-3474	209	21	de	de	PROPN
cana-3474	209	22	of	of	ADP
cana-3474	209	23	2nd	2nd	ADJ
cana-3474	209	24	kind	kind	NOUN
cana-3474	209	25	and	and	CCONJ
cana-3474	209	26	lsvi	lsvi	NOUN
cana-3474	209	27	-	-	PUNCT
cana-3474	209	28	de	de	NOUN
cana-3474	209	29	of	of	ADP
cana-3474	209	30	2nd	2nd	ADJ
cana-3474	209	31	kind	kind	NOUN
cana-3474	209	32	,	,	PUNCT
cana-3474	209	33	and	and	CCONJ
cana-3474	209	34	we	we	PRON
cana-3474	209	35	have	have	AUX
cana-3474	209	36	extensively	extensively	ADV
cana-3474	209	37	detailed	detail	VERB
cana-3474	209	38	the	the	DET
cana-3474	209	39	process	process	NOUN
cana-3474	209	40	by	by	ADP
cana-3474	209	41	considering	consider	VERB
cana-3474	209	42	three	three	NUM
cana-3474	209	43	numerical	numerical	ADJ
cana-3474	209	44	problems	problem	NOUN
cana-3474	209	45	.	.	PUNCT
cana-3474	210	1	the	the	DET
cana-3474	210	2	answers	answer	NOUN
cana-3474	210	3	to	to	ADP
cana-3474	210	4	these	these	DET
cana-3474	210	5	issues	issue	NOUN
cana-3474	210	6	show	show	VERB
cana-3474	210	7	how	how	SCONJ
cana-3474	210	8	beneficial	beneficial	ADJ
cana-3474	210	9	and	and	CCONJ
cana-3474	210	10	efficient	efficient	ADJ
cana-3474	210	11	the	the	DET
cana-3474	210	12	w	w	NOUN
cana-3474	210	13	transform	transform	NOUN
cana-3474	210	14	in	in	ADP
cana-3474	210	15	whitening	whiten	VERB
cana-3474	210	16	the	the	DET
cana-3474	210	17	resolving	resolve	VERB
cana-3474	210	18	lvi	lvi	NOUN
cana-3474	210	19	-	-	PUNCT
cana-3474	210	20	de	de	PROPN
cana-3474	210	21	of	of	ADP
cana-3474	210	22	2nd	2nd	ADJ
cana-3474	210	23	kind	kind	NOUN
cana-3474	210	24	and	and	CCONJ
cana-3474	210	25	lsvi	lsvi	NOUN
cana-3474	210	26	-	-	PUNCT
cana-3474	210	27	de	de	NOUN
cana-3474	210	28	of	of	ADP
cana-3474	210	29	2nd	2nd	ADJ
cana-3474	210	30	kind	kind	NOUN
cana-3474	210	31	.	.	PUNCT
cana-3474	211	1	the	the	DET
cana-3474	211	2	provided	provide	VERB
cana-3474	211	3	applications	application	NOUN
cana-3474	211	4	demonstrate	demonstrate	VERB
cana-3474	211	5	that	that	SCONJ
cana-3474	211	6	a	a	DET
cana-3474	211	7	precise	precise	ADJ
cana-3474	211	8	solution	solution	NOUN
cana-3474	211	9	was	be	AUX
cana-3474	211	10	found	find	VERB
cana-3474	211	11	in	in	ADP
cana-3474	211	12	a	a	DET
cana-3474	211	13	very	very	ADV
cana-3474	211	14	short	short	ADJ
cana-3474	211	15	amount	amount	NOUN
cana-3474	211	16	of	of	ADP
cana-3474	211	17	time	time	NOUN
cana-3474	211	18	and	and	CCONJ
cana-3474	211	19	with	with	ADP
cana-3474	211	20	very	very	ADV
cana-3474	211	21	little	little	ADJ
cana-3474	211	22	processing	processing	NOUN
cana-3474	211	23	power	power	NOUN
cana-3474	211	24	.	.	PUNCT
cana-3474	212	1	references	reference	NOUN
cana-3474	212	2	[	[	X
cana-3474	212	3	1	1	NUM
cana-3474	212	4	]	]	PUNCT
cana-3474	212	5	oyedepo	oyedepo	NOUN
cana-3474	212	6	,	,	PUNCT
cana-3474	212	7	t.	t.	PROPN
cana-3474	212	8	,	,	PUNCT
cana-3474	212	9	a.m.	a.m.	PROPN
cana-3474	212	10	ayinde	ayinde	PROPN
cana-3474	212	11	,	,	PUNCT
cana-3474	212	12	and	and	CCONJ
cana-3474	212	13	e.n	e.n	PROPN
cana-3474	212	14	.	.	PROPN
cana-3474	212	15	didigwu	didigwu	PROPN
cana-3474	212	16	,	,	PUNCT
cana-3474	212	17	vieta	vieta	ADJ
cana-3474	212	18	-	-	PUNCT
cana-3474	212	19	lucas	lucas	PROPN
cana-3474	212	20	polynomial	polynomial	ADJ
cana-3474	212	21	computational	computational	ADJ
cana-3474	212	22	tecnique	tecnique	NOUN
cana-3474	212	23	for	for	ADP
cana-3474	212	24	volterra	volterra	PROPN
cana-3474	212	25	integro	integro	PROPN
cana-3474	212	26	-	-	PUNCT
cana-3474	212	27	differential	differential	NOUN
cana-3474	212	28	equations	equation	NOUN
cana-3474	212	29	.	.	PUNCT
cana-3474	213	1	electronic	electronic	ADJ
cana-3474	213	2	journal	journal	NOUN
cana-3474	213	3	of	of	ADP
cana-3474	213	4	mathematical	mathematical	ADJ
cana-3474	213	5	analysis	analysis	NOUN
cana-3474	213	6	and	and	CCONJ
cana-3474	213	7	applications	application	NOUN
cana-3474	213	8	,	,	PUNCT
cana-3474	213	9	2024	2024	NUM
cana-3474	213	10	.	.	PUNCT
cana-3474	214	1	12(1	12(1	NUM
cana-3474	214	2	):	):	PUNCT
cana-3474	214	3	p.	p.	NOUN
cana-3474	214	4	1	1	NUM
cana-3474	214	5	-	-	SYM
cana-3474	214	6	8	8	NUM
cana-3474	214	7	.	.	PUNCT
cana-3474	215	1	[	[	X
cana-3474	215	2	2	2	NUM
cana-3474	215	3	]	]	PUNCT
cana-3474	215	4	aghayeva	aghayeva	ADV
cana-3474	215	5	,	,	PUNCT
cana-3474	215	6	g.	g.	PROPN
cana-3474	215	7	,	,	PUNCT
cana-3474	215	8	v.	v.	ADP
cana-3474	215	9	ibrahimov	ibrahimov	ADJ
cana-3474	215	10	,	,	PUNCT
cana-3474	215	11	and	and	CCONJ
cana-3474	215	12	d.	d.	PROPN
cana-3474	215	13	juraev	juraev	PROPN
cana-3474	215	14	,	,	PUNCT
cana-3474	215	15	on	on	ADP
cana-3474	215	16	some	some	DET
cana-3474	215	17	comparision	comparision	NOUN
cana-3474	215	18	of	of	ADP
cana-3474	215	19	the	the	DET
cana-3474	215	20	numerical	numerical	ADJ
cana-3474	215	21	methods	method	NOUN
cana-3474	215	22	applied	apply	VERB
cana-3474	215	23	to	to	PART
cana-3474	215	24	solve	solve	VERB
cana-3474	215	25	odes	ode	NOUN
cana-3474	215	26	,	,	PUNCT
cana-3474	215	27	volterra	volterra	NOUN
cana-3474	215	28	integral	integral	ADJ
cana-3474	215	29	and	and	CCONJ
cana-3474	215	30	integro	integro	PROPN
cana-3474	215	31	differential	differential	ADJ
cana-3474	215	32	equations	equation	NOUN
cana-3474	215	33	.	.	PUNCT
cana-3474	216	1	karshi	karshi	PROPN
cana-3474	216	2	multidisciplinary	multidisciplinary	ADJ
cana-3474	216	3	international	international	ADJ
cana-3474	216	4	scientific	scientific	ADJ
cana-3474	216	5	journal	journal	NOUN
cana-3474	216	6	,	,	PUNCT
cana-3474	216	7	2024	2024	NUM
cana-3474	216	8	.	.	PUNCT
cana-3474	216	9	1(1	1(1	NUM
cana-3474	216	10	)	)	PUNCT
cana-3474	216	11	.	.	PUNCT
cana-3474	217	1	[	[	X
cana-3474	217	2	3	3	NUM
cana-3474	217	3	]	]	X
cana-3474	217	4	ansari	ansari	X
cana-3474	217	5	,	,	PUNCT
cana-3474	217	6	a.	a.	NOUN
cana-3474	217	7	,	,	PUNCT
cana-3474	217	8	n.	n.	PROPN
cana-3474	217	9	ahmad	ahmad	PROPN
cana-3474	217	10	,	,	PUNCT
cana-3474	217	11	and	and	CCONJ
cana-3474	217	12	a.h	a.h	PROPN
cana-3474	217	13	.	.	PROPN
cana-3474	217	14	ali	ali	PROPN
cana-3474	217	15	,	,	PUNCT
cana-3474	217	16	numerical	numerical	ADJ
cana-3474	217	17	study	study	NOUN
cana-3474	217	18	of	of	ADP
cana-3474	217	19	the	the	DET
cana-3474	217	20	series	series	NOUN
cana-3474	217	21	solution	solution	NOUN
cana-3474	217	22	method	method	NOUN
cana-3474	217	23	to	to	ADP
cana-3474	217	24	analysis	analysis	NOUN
cana-3474	217	25	of	of	ADP
cana-3474	217	26	volterra	volterra	PROPN
cana-3474	217	27	integro	integro	PROPN
cana-3474	217	28	-	-	PUNCT
cana-3474	217	29	differential	differential	NOUN
cana-3474	217	30	equations	equation	NOUN
cana-3474	217	31	.	.	PUNCT
cana-3474	218	1	journal	journal	PROPN
cana-3474	218	2	of	of	ADP
cana-3474	218	3	applied	apply	VERB
cana-3474	218	4	mathematics	mathematics	PROPN
cana-3474	218	5	&	&	CCONJ
cana-3474	218	6	informatics	informatic	NOUN
cana-3474	218	7	,	,	PUNCT
cana-3474	218	8	2024	2024	NUM
cana-3474	218	9	.	.	PUNCT
cana-3474	219	1	42(4	42(4	PROPN
cana-3474	219	2	):	):	PUNCT
cana-3474	220	1	p.	p.	NOUN
cana-3474	220	2	899	899	NUM
cana-3474	220	3	-	-	SYM
cana-3474	220	4	913	913	NUM
cana-3474	220	5	.	.	PUNCT
cana-3474	221	1	[	[	X
cana-3474	221	2	4	4	NUM
cana-3474	221	3	]	]	X
cana-3474	221	4	issa	issa	ADJ
cana-3474	221	5	,	,	PUNCT
cana-3474	221	6	a.	a.	NOUN
cana-3474	221	7	,	,	PUNCT
cana-3474	221	8	numerical	numerical	ADJ
cana-3474	221	9	solution	solution	NOUN
cana-3474	221	10	of	of	ADP
cana-3474	221	11	system	system	NOUN
cana-3474	221	12	of	of	ADP
cana-3474	221	13	linear	linear	PROPN
cana-3474	221	14	volterra	volterra	PROPN
cana-3474	221	15	integro	integro	PROPN
cana-3474	221	16	-	-	PUNCT
cana-3474	221	17	differential	differential	NOUN
cana-3474	221	18	equations	equation	NOUN
cana-3474	221	19	by	by	ADP
cana-3474	221	20	reconstruction	reconstruction	NOUN
cana-3474	221	21	of	of	ADP
cana-3474	221	22	variational	variational	ADJ
cana-3474	221	23	iteration	iteration	NOUN
cana-3474	221	24	method	method	NOUN
cana-3474	221	25	.	.	PUNCT
cana-3474	222	1	palestine	palestine	PROPN
cana-3474	222	2	journal	journal	PROPN
cana-3474	222	3	of	of	ADP
cana-3474	222	4	mathematics	mathematic	NOUN
cana-3474	222	5	,	,	PUNCT
cana-3474	222	6	2023	2023	NUM
cana-3474	222	7	.	.	PUNCT
cana-3474	223	1	12(4	12(4	NUM
cana-3474	223	2	)	)	PUNCT
cana-3474	223	3	.	.	PUNCT
cana-3474	224	1	[	[	X
cana-3474	224	2	5	5	NUM
cana-3474	224	3	]	]	PUNCT
cana-3474	224	4	alnair	alnair	NOUN
cana-3474	224	5	,	,	PUNCT
cana-3474	224	6	m.e	m.e	PROPN
cana-3474	224	7	.	.	PROPN
cana-3474	224	8	and	and	CCONJ
cana-3474	224	9	a.a	a.a	PROPN
cana-3474	224	10	.	.	PROPN
cana-3474	224	11	khidir	khidir	PROPN
cana-3474	224	12	.	.	PUNCT
cana-3474	225	1	approximation	approximation	NOUN
cana-3474	225	2	technique	technique	NOUN
cana-3474	225	3	for	for	ADP
cana-3474	225	4	solving	solve	VERB
cana-3474	225	5	linear	linear	PROPN
cana-3474	225	6	volterra	volterra	PROPN
cana-3474	225	7	integro‐differential	integro‐differential	PROPN
cana-3474	225	8	equations	equation	NOUN
cana-3474	225	9	with	with	ADP
cana-3474	225	10	boundary	boundary	ADJ
cana-3474	225	11	conditions	condition	NOUN
cana-3474	225	12	.	.	PUNCT
cana-3474	226	1	in	in	ADP
cana-3474	226	2	abstract	abstract	ADJ
cana-3474	226	3	and	and	CCONJ
cana-3474	226	4	applied	apply	VERB
cana-3474	226	5	analysis	analysis	NOUN
cana-3474	226	6	.	.	PUNCT
cana-3474	227	1	2022	2022	NUM
cana-3474	227	2	.	.	PUNCT
cana-3474	228	1	wiley	wiley	PROPN
cana-3474	228	2	online	online	PROPN
cana-3474	228	3	library	library	PROPN
cana-3474	228	4	.	.	PUNCT
cana-3474	229	1	[	[	X
cana-3474	229	2	6	6	NUM
cana-3474	229	3	]	]	PUNCT
cana-3474	229	4	olowe	olowe	NOUN
cana-3474	229	5	,	,	PUNCT
cana-3474	229	6	r.	r.	PROPN
cana-3474	229	7	,	,	PUNCT
cana-3474	229	8	et	et	PROPN
cana-3474	229	9	al	al	PROPN
cana-3474	229	10	.	.	PROPN
cana-3474	229	11	,	,	PUNCT
cana-3474	229	12	trigonometrically	trigonometrically	ADV
cana-3474	229	13	-	-	PUNCT
cana-3474	229	14	fitted	fit	VERB
cana-3474	229	15	simpson	simpson	PROPN
cana-3474	229	16	’s	’s	PART
cana-3474	229	17	method	method	NOUN
cana-3474	229	18	for	for	ADP
cana-3474	229	19	solving	solve	VERB
cana-3474	229	20	volterra	volterra	NOUN
cana-3474	229	21	integro	integro	ADJ
cana-3474	229	22	-	-	PUNCT
cana-3474	229	23	differential	differential	NOUN
cana-3474	229	24	equations	equation	NOUN
cana-3474	229	25	.	.	PUNCT
cana-3474	230	1	international	international	ADJ
cana-3474	230	2	journal	journal	PROPN
cana-3474	230	3	of	of	ADP
cana-3474	230	4	mathematical	mathematical	ADJ
cana-3474	230	5	sciences	science	NOUN
cana-3474	230	6	and	and	CCONJ
cana-3474	230	7	optimization	optimization	NOUN
cana-3474	230	8	:	:	PUNCT
cana-3474	230	9	theory	theory	NOUN
cana-3474	230	10	and	and	CCONJ
cana-3474	230	11	applications	application	NOUN
cana-3474	230	12	,	,	PUNCT
cana-3474	230	13	2022	2022	NUM
cana-3474	230	14	.	.	PUNCT
cana-3474	231	1	8(2	8(2	NUM
cana-3474	231	2	):	):	PUNCT
cana-3474	231	3	p.	p.	NOUN
cana-3474	231	4	68	68	NUM
cana-3474	231	5	-	-	SYM
cana-3474	231	6	78	78	NUM
cana-3474	231	7	.	.	PUNCT
cana-3474	232	1	[	[	X
cana-3474	232	2	7	7	NUM
cana-3474	232	3	]	]	X
cana-3474	232	4	uwaheren	uwaheren	NOUN
cana-3474	232	5	,	,	PUNCT
cana-3474	232	6	o.	o.	PROPN
cana-3474	232	7	,	,	PUNCT
cana-3474	232	8	et	et	PROPN
cana-3474	232	9	al	al	PROPN
cana-3474	232	10	.	.	PROPN
cana-3474	232	11	,	,	PUNCT
cana-3474	232	12	numerical	numerical	ADJ
cana-3474	232	13	solution	solution	NOUN
cana-3474	232	14	of	of	ADP
cana-3474	232	15	volterra	volterra	PROPN
cana-3474	232	16	integro	integro	PROPN
cana-3474	232	17	-	-	PUNCT
cana-3474	232	18	differential	differential	NOUN
cana-3474	232	19	equations	equation	NOUN
cana-3474	232	20	by	by	ADP
cana-3474	232	21	akbari	akbari	PROPN
cana-3474	232	22	-	-	PUNCT
cana-3474	232	23	ganji	ganji	NOUN
cana-3474	232	24	’s	’s	PART
cana-3474	232	25	method	method	NOUN
cana-3474	232	26	.	.	PUNCT
cana-3474	233	1	barekeng	barekeng	NOUN
cana-3474	233	2	:	:	PUNCT
cana-3474	233	3	jurnal	jurnal	ADJ
cana-3474	233	4	ilmu	ilmu	PROPN
cana-3474	233	5	matematika	matematika	PROPN
cana-3474	233	6	dan	dan	PROPN
cana-3474	233	7	terapan	terapan	PROPN
cana-3474	233	8	,	,	PUNCT
cana-3474	233	9	2022	2022	NUM
cana-3474	233	10	.	.	PUNCT
cana-3474	234	1	16(3	16(3	NUM
cana-3474	234	2	):	):	PUNCT
cana-3474	234	3	p.	p.	NOUN
cana-3474	234	4	1123	1123	NUM
cana-3474	234	5	-	-	SYM
cana-3474	234	6	1130	1130	NUM
cana-3474	234	7	.	.	PUNCT
cana-3474	235	1	[	[	X
cana-3474	235	2	8	8	NUM
cana-3474	235	3	]	]	X
cana-3474	235	4	al	al	PROPN
cana-3474	235	5	-	-	PUNCT
cana-3474	235	6	shimmary	shimmary	PROPN
cana-3474	235	7	,	,	PUNCT
cana-3474	235	8	a.	a.	NOUN
cana-3474	235	9	,	,	PUNCT
cana-3474	235	10	a.	a.	NOUN
cana-3474	235	11	hussain	hussain	PROPN
cana-3474	235	12	,	,	PUNCT
cana-3474	235	13	and	and	CCONJ
cana-3474	235	14	s.	s.	PROPN
cana-3474	235	15	radhi	radhi	PROPN
cana-3474	235	16	.	.	PUNCT
cana-3474	236	1	numerical	numerical	ADJ
cana-3474	236	2	solution	solution	NOUN
cana-3474	236	3	of	of	ADP
cana-3474	236	4	volterra	volterra	PROPN
cana-3474	236	5	integro	integro	PROPN
cana-3474	236	6	–	–	PUNCT
cana-3474	236	7	differential	differential	NOUN
cana-3474	236	8	equation	equation	NOUN
cana-3474	236	9	using	use	VERB
cana-3474	236	10	6th	6th	ADJ
cana-3474	236	11	order	order	NOUN
cana-3474	236	12	runge	runge	NOUN
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cana-3474	237	8	.	.	PUNCT
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cana-3474	238	2	.	.	PUNCT
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cana-3474	242	5	-	-	SYM
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cana-3474	251	5	.	.	PUNCT
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cana-3474	252	3	]	]	PUNCT
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cana-3474	270	9	.	.	PUNCT
cana-3474	271	1	peng	peng	PROPN
cana-3474	271	2	,	,	PUNCT
cana-3474	271	3	and	and	CCONJ
cana-3474	271	4	f.	f.	PROPN
cana-3474	271	5	wang	wang	PROPN
cana-3474	271	6	,	,	PUNCT
cana-3474	271	7	the	the	DET
cana-3474	271	8	analysis	analysis	NOUN
cana-3474	271	9	and	and	CCONJ
cana-3474	271	10	application	application	NOUN
cana-3474	271	11	of	of	ADP
cana-3474	271	12	a	a	DET
cana-3474	271	13	new	new	ADJ
cana-3474	271	14	integral	integral	ADJ
cana-3474	271	15	transform	transform	NOUN
cana-3474	271	16	w	w	NOUN
cana-3474	271	17	transform	transform	NOUN
cana-3474	271	18	.	.	PUNCT
cana-3474	272	1	thermal	thermal	ADJ
cana-3474	272	2	science	science	NOUN
cana-3474	272	3	,	,	PUNCT
cana-3474	272	4	2023	2023	NUM
cana-3474	272	5	.	.	PUNCT
cana-3474	273	1	27(5	27(5	PROPN
cana-3474	273	2	part	part	NOUN
cana-3474	273	3	a	a	PRON
cana-3474	273	4	):	):	PUNCT
cana-3474	273	5	p.	p.	NOUN
cana-3474	273	6	3823	3823	NUM
cana-3474	273	7	-	-	SYM
cana-3474	273	8	3827	3827	NUM
cana-3474	273	9	.	.	PUNCT
cana-3474	274	1	[	[	X
cana-3474	274	2	19	19	NUM
cana-3474	274	3	]	]	SYM
cana-3474	274	4	wazwaz	wazwaz	NOUN
cana-3474	274	5	,	,	PUNCT
cana-3474	274	6	a.-m	a.-m	ADV
cana-3474	274	7	.	.	PUNCT
cana-3474	274	8	,	,	PUNCT
cana-3474	274	9	linear	linear	ADJ
cana-3474	274	10	and	and	CCONJ
cana-3474	274	11	nonlinear	nonlinear	ADJ
cana-3474	274	12	integral	integral	ADJ
cana-3474	274	13	equations	equation	NOUN
cana-3474	274	14	.	.	PUNCT
cana-3474	275	1	vol	vol	NOUN
cana-3474	275	2	.	.	PUNCT
cana-3474	276	1	639	639	NUM
cana-3474	276	2	.	.	PUNCT
cana-3474	277	1	2011	2011	NUM
cana-3474	277	2	:	:	PUNCT
cana-3474	278	1	springer	springer	NOUN
cana-3474	278	2	.	.	PUNCT
cana-3474	279	1	20	20	NUM
cana-3474	279	2	.	.	X
cana-3474	279	3	aggarwal	aggarwal	PROPN
cana-3474	279	4	,	,	PUNCT
cana-3474	279	5	s.	s.	PROPN
cana-3474	279	6	and	and	CCONJ
cana-3474	279	7	s.	s.	PROPN
cana-3474	279	8	kumar	kumar	PROPN
cana-3474	279	9	,	,	PUNCT
cana-3474	279	10	solution	solution	NOUN
cana-3474	279	11	of	of	ADP
cana-3474	279	12	system	system	NOUN
cana-3474	279	13	of	of	ADP
cana-3474	279	14	linear	linear	PROPN
cana-3474	279	15	volterra	volterra	PROPN
cana-3474	279	16	integro	integro	PROPN
cana-3474	279	17	-	-	PUNCT
cana-3474	279	18	differential	differential	NOUN
cana-3474	279	19	equations	equation	NOUN
cana-3474	279	20	of	of	ADP
cana-3474	279	21	second	second	ADJ
cana-3474	279	22	kind	kind	NOUN
cana-3474	279	23	via	via	ADP
cana-3474	279	24	laplace	laplace	NOUN
cana-3474	279	25	-	-	PUNCT
cana-3474	279	26	carson	carson	PROPN
cana-3474	279	27	transform	transform	NOUN
cana-3474	279	28	.	.	PUNCT
cana-3474	280	1	j.	j.	PROPN
cana-3474	280	2	emerg	emerg	PROPN
cana-3474	280	3	.	.	PUNCT
cana-3474	281	1	technol	technol	PROPN
cana-3474	281	2	.	.	PUNCT
cana-3474	281	3	innov	innov	PROPN
cana-3474	281	4	.	.	PUNCT
cana-3474	282	1	res	re	NOUN
cana-3474	282	2	,	,	PUNCT
cana-3474	282	3	2021	2021	NUM
cana-3474	282	4	.	.	PUNCT
cana-3474	283	1	8	8	NUM
cana-3474	283	2	.	.	PUNCT