id	sid	tid	token	lemma	pos
cana-2203	1	1	communications	communication	NOUN
cana-2203	1	2	on	on	ADP
cana-2203	1	3	applied	apply	VERB
cana-2203	1	4	nonlinear	nonlinear	ADJ
cana-2203	1	5	analysis	analysis	NOUN
cana-2203	1	6	issn	issn	NOUN
cana-2203	1	7	:	:	PUNCT
cana-2203	1	8	1074	1074	NUM
cana-2203	1	9	-	-	PUNCT
cana-2203	1	10	133x	133x	NUM
cana-2203	1	11	vol	vol	NOUN
cana-2203	1	12	32	32	NUM
cana-2203	1	13	no	no	NOUN
cana-2203	1	14	.	.	PUNCT
cana-2203	2	1	1s	1s	NUM
cana-2203	2	2	(	(	PUNCT
cana-2203	2	3	2025	2025	NUM
cana-2203	2	4	)	)	PUNCT
cana-2203	2	5	388	388	NUM
cana-2203	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	2	7	stability	stability	NOUN
cana-2203	2	8	analysis	analysis	NOUN
cana-2203	2	9	of	of	ADP
cana-2203	2	10	two	two	NUM
cana-2203	2	11	point	point	NOUN
cana-2203	2	12	boundary	boundary	ADJ
cana-2203	2	13	value	value	NOUN
cana-2203	2	14	problem	problem	NOUN
cana-2203	2	15	on	on	ADP
cana-2203	2	16	time	time	NOUN
cana-2203	2	17	scales	scale	VERB
cana-2203	2	18	g.	g.	PROPN
cana-2203	2	19	v.	v.	PROPN
cana-2203	2	20	ramana1	ramana1	PROPN
cana-2203	2	21	,	,	PUNCT
cana-2203	2	22	m.	m.	NOUN
cana-2203	2	23	bala	bala	PROPN
cana-2203	2	24	prabhakar2	prabhakar2	PROPN
cana-2203	2	25	and	and	CCONJ
cana-2203	2	26	n.	n.	PROPN
cana-2203	2	27	veerraju3	veerraju3	PROPN
cana-2203	2	28	*	*	PROPN
cana-2203	2	29	1associate	1associate	NUM
cana-2203	2	30	professor	professor	NOUN
cana-2203	2	31	,	,	PUNCT
cana-2203	2	32	department	department	NOUN
cana-2203	2	33	of	of	ADP
cana-2203	2	34	mathematics	mathematics	PROPN
cana-2203	2	35	,	,	PUNCT
cana-2203	2	36	aditya	aditya	PROPN
cana-2203	2	37	university	university	PROPN
cana-2203	2	38	,	,	PUNCT
cana-2203	2	39	surampalem-533	surampalem-533	NOUN
cana-2203	2	40	437	437	NUM
cana-2203	2	41	,	,	PUNCT
cana-2203	2	42	a.	a.	NOUN
cana-2203	2	43	p.	p.	PROPN
cana-2203	2	44	,	,	PUNCT
cana-2203	2	45	india	india	PROPN
cana-2203	2	46	.	.	PUNCT
cana-2203	3	1	mail	mail	NOUN
cana-2203	3	2	:	:	PUNCT
cana-2203	3	3	ramanaginjala9@gmail.com	ramanaginjala9@gmail.com	X
cana-2203	3	4	2associate	2associate	NUM
cana-2203	3	5	professor	professor	NOUN
cana-2203	3	6	,	,	PUNCT
cana-2203	3	7	department	department	NOUN
cana-2203	3	8	of	of	ADP
cana-2203	3	9	mathematics	mathematics	PROPN
cana-2203	3	10	,	,	PUNCT
cana-2203	3	11	aditya	aditya	PROPN
cana-2203	3	12	university	university	PROPN
cana-2203	3	13	,	,	PUNCT
cana-2203	3	14	surampalem-533	surampalem-533	NOUN
cana-2203	3	15	437	437	NUM
cana-2203	3	16	,	,	PUNCT
cana-2203	3	17	a.	a.	NOUN
cana-2203	3	18	p.	p.	PROPN
cana-2203	3	19	,	,	PUNCT
cana-2203	3	20	india	india	PROPN
cana-2203	3	21	.	.	PUNCT
cana-2203	4	1	mail	mail	NOUN
cana-2203	4	2	:	:	PUNCT
cana-2203	4	3	prabhakar_mb@yahoo.co.in	prabhakar_mb@yahoo.co.in	NOUN
cana-2203	4	4	3assistant	3assistant	NUM
cana-2203	4	5	professor	professor	NOUN
cana-2203	4	6	,	,	PUNCT
cana-2203	4	7	department	department	NOUN
cana-2203	4	8	of	of	ADP
cana-2203	4	9	mathematics	mathematic	NOUN
cana-2203	4	10	,	,	PUNCT
cana-2203	4	11	srkr	srkr	NOUN
cana-2203	4	12	engineering	engineering	NOUN
cana-2203	4	13	college	college	NOUN
cana-2203	4	14	,	,	PUNCT
cana-2203	4	15	bhimavaram-534	bhimavaram-534	ADJ
cana-2203	4	16	204	204	NUM
cana-2203	4	17	,	,	PUNCT
cana-2203	4	18	a.p	a.p	PROPN
cana-2203	4	19	.	.	PROPN
cana-2203	4	20	,	,	PUNCT
cana-2203	4	21	india	india	PROPN
cana-2203	4	22	.	.	PUNCT
cana-2203	5	1	mail:veerrajunalla@gmail.com	mail:veerrajunalla@gmail.com	X
cana-2203	5	2	*	*	PUNCT
cana-2203	5	3	corresponding	correspond	VERB
cana-2203	5	4	author	author	NOUN
cana-2203	5	5	.	.	PUNCT
cana-2203	6	1	article	article	NOUN
cana-2203	6	2	history	history	NOUN
cana-2203	6	3	:	:	PUNCT
cana-2203	6	4	received	receive	VERB
cana-2203	6	5	:	:	PUNCT
cana-2203	6	6	20	20	NUM
cana-2203	6	7	-	-	SYM
cana-2203	6	8	08	08	NUM
cana-2203	6	9	-	-	PUNCT
cana-2203	6	10	2024	2024	NUM
cana-2203	6	11	revised	revise	VERB
cana-2203	6	12	:	:	PUNCT
cana-2203	6	13	01	01	NUM
cana-2203	6	14	-	-	SYM
cana-2203	6	15	10	10	NUM
cana-2203	6	16	-	-	PUNCT
cana-2203	6	17	2024	2024	NUM
cana-2203	6	18	accepted	accept	VERB
cana-2203	6	19	:	:	PUNCT
cana-2203	6	20	19	19	NUM
cana-2203	6	21	-	-	SYM
cana-2203	6	22	10	10	NUM
cana-2203	6	23	-	-	PUNCT
cana-2203	6	24	2024	2024	NUM
cana-2203	6	25	abstract	abstract	NOUN
cana-2203	6	26	:	:	PUNCT
cana-2203	7	1	v.	v.	ADP
cana-2203	7	2	lakshmi	lakshmi	PROPN
cana-2203	7	3	kantham	kantham	PROPN
cana-2203	7	4	and	and	CCONJ
cana-2203	7	5	m.	m.	PROPN
cana-2203	7	6	rama	rama	PROPN
cana-2203	7	7	mohana	mohana	PROPN
cana-2203	7	8	rao	rao	PROPN
cana-2203	7	9	contributed	contribute	VERB
cana-2203	7	10	a	a	DET
cana-2203	7	11	lot	lot	NOUN
cana-2203	7	12	for	for	ADP
cana-2203	7	13	the	the	DET
cana-2203	7	14	theory	theory	NOUN
cana-2203	7	15	of	of	ADP
cana-2203	7	16	integrodifferential	integrodifferential	ADJ
cana-2203	7	17	equations	equation	NOUN
cana-2203	7	18	of	of	ADP
cana-2203	7	19	volterra	volterra	PROPN
cana-2203	7	20	type	type	NOUN
cana-2203	7	21	and	and	CCONJ
cana-2203	7	22	its	its	PRON
cana-2203	7	23	various	various	ADJ
cana-2203	7	24	properties	property	NOUN
cana-2203	7	25	.	.	PUNCT
cana-2203	8	1	in	in	ADP
cana-2203	8	2	this	this	DET
cana-2203	8	3	paper	paper	NOUN
cana-2203	8	4	,	,	PUNCT
cana-2203	8	5	an	an	DET
cana-2203	8	6	attempt	attempt	NOUN
cana-2203	8	7	is	be	AUX
cana-2203	8	8	made	make	VERB
cana-2203	8	9	to	to	PART
cana-2203	8	10	explore	explore	VERB
cana-2203	8	11	the	the	DET
cana-2203	8	12	existence	existence	NOUN
cana-2203	8	13	of	of	ADP
cana-2203	8	14	a	a	DET
cana-2203	8	15	solution	solution	NOUN
cana-2203	8	16	for	for	ADP
cana-2203	8	17	a	a	DET
cana-2203	8	18	matrix	matrix	NOUN
cana-2203	8	19	integrodynamical	integrodynamical	ADJ
cana-2203	8	20	equation	equation	NOUN
cana-2203	8	21	of	of	ADP
cana-2203	8	22	volterra	volterra	PROPN
cana-2203	8	23	type	type	NOUN
cana-2203	8	24	(	(	PUNCT
cana-2203	8	25	midt	midt	ADJ
cana-2203	8	26	)	)	PUNCT
cana-2203	8	27	with	with	ADP
cana-2203	8	28	two	two	NUM
cana-2203	8	29	-	-	PUNCT
cana-2203	8	30	point	point	NOUN
cana-2203	8	31	boundary	boundary	ADJ
cana-2203	8	32	value	value	NOUN
cana-2203	8	33	problem	problem	NOUN
cana-2203	8	34	(	(	PUNCT
cana-2203	8	35	tbvp	tbvp	NOUN
cana-2203	8	36	)	)	PUNCT
cana-2203	8	37	in	in	ADP
cana-2203	8	38	terms	term	NOUN
cana-2203	8	39	of	of	ADP
cana-2203	8	40	green	green	PROPN
cana-2203	8	41	’s	’s	PART
cana-2203	8	42	matrix	matrix	NOUN
cana-2203	8	43	(	(	PUNCT
cana-2203	8	44	gm	gm	PROPN
cana-2203	8	45	)	)	PUNCT
cana-2203	8	46	on	on	ADP
cana-2203	8	47	time	time	NOUN
cana-2203	8	48	scales	scale	NOUN
cana-2203	8	49	(	(	PUNCT
cana-2203	8	50	ts	ts	NOUN
cana-2203	8	51	)	)	PUNCT
cana-2203	8	52	.	.	PUNCT
cana-2203	9	1	and	and	CCONJ
cana-2203	9	2	properties	property	NOUN
cana-2203	9	3	of	of	ADP
cana-2203	9	4	gm	gm	PROPN
cana-2203	9	5	and	and	CCONJ
cana-2203	9	6	stability	stability	NOUN
cana-2203	9	7	of	of	ADP
cana-2203	9	8	the	the	DET
cana-2203	9	9	system	system	NOUN
cana-2203	9	10	on	on	ADP
cana-2203	9	11	ts	t	NOUN
cana-2203	9	12	are	be	AUX
cana-2203	9	13	discussed	discuss	VERB
cana-2203	9	14	.	.	PUNCT
cana-2203	10	1	keywords	keyword	NOUN
cana-2203	10	2	:	:	PUNCT
cana-2203	10	3	green	green	PROPN
cana-2203	10	4	’s	’s	PART
cana-2203	10	5	matrix	matrix	NOUN
cana-2203	10	6	,	,	PUNCT
cana-2203	10	7	stability	stability	NOUN
cana-2203	10	8	,	,	PUNCT
cana-2203	10	9	time	time	NOUN
cana-2203	10	10	scales	scale	NOUN
cana-2203	10	11	.	.	PUNCT
cana-2203	11	1	ams	am	NOUN
cana-2203	11	2	subject	subject	ADJ
cana-2203	11	3	classification	classification	NOUN
cana-2203	11	4	:	:	PUNCT
cana-2203	11	5	34n05	34n05	NUM
cana-2203	11	6	.	.	X
cana-2203	12	1	1	1	X
cana-2203	12	2	.	.	X
cana-2203	12	3	introduction	introduction	NOUN
cana-2203	12	4	mathematical	mathematical	ADJ
cana-2203	12	5	models	model	NOUN
cana-2203	12	6	,	,	PUNCT
cana-2203	12	7	that	that	PRON
cana-2203	12	8	describe	describe	VERB
cana-2203	12	9	physical	physical	ADJ
cana-2203	12	10	phenomenon	phenomenon	NOUN
cana-2203	12	11	are	be	AUX
cana-2203	12	12	expressed	express	VERB
cana-2203	12	13	or	or	CCONJ
cana-2203	12	14	described	describe	VERB
cana-2203	12	15	in	in	ADP
cana-2203	12	16	most	most	ADJ
cana-2203	12	17	cases	case	NOUN
cana-2203	12	18	either	either	CCONJ
cana-2203	12	19	differential	differential	ADJ
cana-2203	12	20	or	or	CCONJ
cana-2203	12	21	difference	difference	NOUN
cana-2203	12	22	equations	equation	NOUN
cana-2203	12	23	with	with	ADP
cana-2203	12	24	respect	respect	NOUN
cana-2203	12	25	to	to	ADP
cana-2203	12	26	continuous	continuous	ADJ
cana-2203	12	27	cases	case	NOUN
cana-2203	12	28	or	or	CCONJ
cana-2203	12	29	discrete	discrete	ADJ
cana-2203	12	30	cases	case	NOUN
cana-2203	12	31	respectively	respectively	ADV
cana-2203	12	32	.	.	PUNCT
cana-2203	13	1	in	in	ADP
cana-2203	13	2	previous	previous	ADJ
cana-2203	13	3	years	year	NOUN
cana-2203	13	4	,	,	PUNCT
cana-2203	13	5	so	so	ADV
cana-2203	13	6	many	many	ADJ
cana-2203	13	7	authors	author	NOUN
cana-2203	13	8	have	have	AUX
cana-2203	13	9	worked	work	VERB
cana-2203	13	10	on	on	ADP
cana-2203	13	11	dynamical	dynamical	ADJ
cana-2203	13	12	systems	system	NOUN
cana-2203	13	13	either	either	CCONJ
cana-2203	13	14	in	in	ADP
cana-2203	13	15	continuous	continuous	ADJ
cana-2203	13	16	cases	case	NOUN
cana-2203	13	17	or	or	CCONJ
cana-2203	13	18	discrete	discrete	ADJ
cana-2203	13	19	cases	case	NOUN
cana-2203	13	20	.	.	PUNCT
cana-2203	14	1	stefan	stefan	PROPN
cana-2203	14	2	hilger	hilger	PROPN
cana-2203	14	3	observed	observe	VERB
cana-2203	14	4	some	some	DET
cana-2203	14	5	interesting	interesting	ADJ
cana-2203	14	6	patterns	pattern	NOUN
cana-2203	14	7	in	in	ADP
cana-2203	14	8	nature	nature	NOUN
cana-2203	14	9	.	.	PUNCT
cana-2203	15	1	according	accord	VERB
cana-2203	15	2	to	to	ADP
cana-2203	15	3	stefan	stefan	PROPN
cana-2203	15	4	hilger	hilger	PROPN
cana-2203	15	5	observation	observation	PROPN
cana-2203	15	6	,	,	PUNCT
cana-2203	15	7	some	some	DET
cana-2203	15	8	plants	plant	NOUN
cana-2203	15	9	in	in	ADP
cana-2203	15	10	poles	pole	NOUN
cana-2203	15	11	show	show	VERB
cana-2203	15	12	growing	grow	VERB
cana-2203	15	13	nature	nature	NOUN
cana-2203	15	14	for	for	ADP
cana-2203	15	15	6	6	NUM
cana-2203	15	16	months	month	NOUN
cana-2203	15	17	and	and	CCONJ
cana-2203	15	18	non	non	ADJ
cana-2203	15	19	-	-	ADJ
cana-2203	15	20	growing	growing	ADJ
cana-2203	15	21	nature	nature	NOUN
cana-2203	15	22	for	for	ADP
cana-2203	15	23	remaining	remain	VERB
cana-2203	15	24	6	6	NUM
cana-2203	15	25	months	month	NOUN
cana-2203	15	26	.	.	PUNCT
cana-2203	16	1	further	far	ADV
cana-2203	16	2	,	,	PUNCT
cana-2203	16	3	in	in	ADP
cana-2203	16	4	some	some	DET
cana-2203	16	5	species	specie	NOUN
cana-2203	16	6	existing	exist	VERB
cana-2203	16	7	in	in	ADP
cana-2203	16	8	japan	japan	PROPN
cana-2203	16	9	,	,	PUNCT
cana-2203	16	10	mother	mother	NOUN
cana-2203	16	11	dies	die	VERB
cana-2203	16	12	soon	soon	ADV
cana-2203	16	13	after	after	SCONJ
cana-2203	16	14	it	it	PRON
cana-2203	16	15	gives	give	VERB
cana-2203	16	16	birth	birth	NOUN
cana-2203	16	17	to	to	ADP
cana-2203	16	18	its	its	PRON
cana-2203	16	19	baby	baby	NOUN
cana-2203	16	20	.	.	PUNCT
cana-2203	17	1	after	after	ADP
cana-2203	17	2	having	having	AUX
cana-2203	17	3	noticed	notice	VERB
cana-2203	17	4	this	this	DET
cana-2203	17	5	physical	physical	ADJ
cana-2203	17	6	phenomenon	phenomenon	NOUN
cana-2203	17	7	,	,	PUNCT
cana-2203	17	8	stefan	stefan	PROPN
cana-2203	17	9	hilger	hilger	PROPN
cana-2203	17	10	drew	draw	VERB
cana-2203	17	11	a	a	DET
cana-2203	17	12	conclusion	conclusion	NOUN
cana-2203	17	13	that	that	SCONJ
cana-2203	17	14	there	there	PRON
cana-2203	17	15	exists	exist	VERB
cana-2203	17	16	some	some	DET
cana-2203	17	17	systems	system	NOUN
cana-2203	17	18	in	in	ADP
cana-2203	17	19	real	real	ADJ
cana-2203	17	20	world	world	NOUN
cana-2203	17	21	which	which	PRON
cana-2203	17	22	contains	contain	VERB
cana-2203	17	23	both	both	CCONJ
cana-2203	17	24	discrete	discrete	ADJ
cana-2203	17	25	and	and	CCONJ
cana-2203	17	26	continuous	continuous	ADJ
cana-2203	17	27	nature	nature	NOUN
cana-2203	17	28	.	.	PUNCT
cana-2203	18	1	based	base	VERB
cana-2203	18	2	on	on	ADP
cana-2203	18	3	this	this	PRON
cana-2203	18	4	,	,	PUNCT
cana-2203	18	5	stefan	stefan	PROPN
cana-2203	18	6	hilger	hilger	PROPN
cana-2203	18	7	invented	invent	VERB
cana-2203	18	8	a	a	DET
cana-2203	18	9	new	new	ADJ
cana-2203	18	10	technique	technique	NOUN
cana-2203	18	11	ts	ts	ADP
cana-2203	18	12	in	in	ADP
cana-2203	18	13	1998	1998	NUM
cana-2203	18	14	as	as	ADP
cana-2203	18	15	an	an	DET
cana-2203	18	16	integral	integral	ADJ
cana-2203	18	17	part	part	NOUN
cana-2203	18	18	of	of	ADP
cana-2203	18	19	his	his	PRON
cana-2203	18	20	ph.d	ph.d	ADJ
cana-2203	18	21	thesis	thesis	NOUN
cana-2203	18	22	which	which	PRON
cana-2203	18	23	can	can	AUX
cana-2203	18	24	work	work	VERB
cana-2203	18	25	with	with	ADP
cana-2203	18	26	systems	system	NOUN
cana-2203	18	27	involving	involve	VERB
cana-2203	18	28	both	both	DET
cana-2203	18	29	cases[5	cases[5	NOUN
cana-2203	18	30	]	]	PUNCT
cana-2203	18	31	.	.	PUNCT
cana-2203	19	1	in	in	ADP
cana-2203	19	2	recent	recent	ADJ
cana-2203	19	3	years	year	NOUN
cana-2203	19	4	,	,	PUNCT
cana-2203	19	5	owing	owe	VERB
cana-2203	19	6	to	to	ADP
cana-2203	19	7	the	the	DET
cana-2203	19	8	unified	unified	ADJ
cana-2203	19	9	treatment	treatment	NOUN
cana-2203	19	10	of	of	ADP
cana-2203	19	11	analysing	analyse	VERB
cana-2203	19	12	both	both	CCONJ
cana-2203	19	13	continuous	continuous	ADJ
cana-2203	19	14	and	and	CCONJ
cana-2203	19	15	discrete	discrete	ADJ
cana-2203	19	16	systems	system	NOUN
cana-2203	19	17	at	at	ADP
cana-2203	19	18	a	a	DET
cana-2203	19	19	time	time	NOUN
cana-2203	19	20	[	[	X
cana-2203	19	21	1	1	NUM
cana-2203	19	22	,	,	PUNCT
cana-2203	19	23	3	3	NUM
cana-2203	19	24	,	,	PUNCT
cana-2203	19	25	6	6	NUM
cana-2203	19	26	]	]	PUNCT
cana-2203	19	27	,	,	PUNCT
cana-2203	19	28	research	research	NOUN
cana-2203	19	29	related	relate	VERB
cana-2203	19	30	to	to	ADP
cana-2203	19	31	dynamic	dynamic	ADJ
cana-2203	19	32	systems	system	NOUN
cana-2203	19	33	on	on	ADP
cana-2203	19	34	ts	ts	ADP
cana-2203	19	35	experienced	experienced	ADJ
cana-2203	19	36	significant	significant	ADJ
cana-2203	19	37	significance	significance	NOUN
cana-2203	19	38	in	in	ADP
cana-2203	19	39	diversified	diversified	ADJ
cana-2203	19	40	fields	field	NOUN
cana-2203	19	41	.	.	PUNCT
cana-2203	20	1	the	the	DET
cana-2203	20	2	ts	ts	PROPN
cana-2203	20	3	applications	application	NOUN
cana-2203	20	4	has	have	VERB
cana-2203	20	5	a	a	DET
cana-2203	20	6	tremendous	tremendous	ADJ
cana-2203	20	7	potential	potential	NOUN
cana-2203	20	8	in	in	ADP
cana-2203	20	9	biology	biology	NOUN
cana-2203	20	10	,	,	PUNCT
cana-2203	20	11	engineering	engineering	NOUN
cana-2203	20	12	,	,	PUNCT
cana-2203	20	13	economics	economic	NOUN
cana-2203	20	14	,	,	PUNCT
cana-2203	20	15	physics	physics	NOUN
cana-2203	20	16	,	,	PUNCT
cana-2203	20	17	neural	neural	ADJ
cana-2203	20	18	networks	network	NOUN
cana-2203	20	19	,	,	PUNCT
cana-2203	20	20	etc	etc	X
cana-2203	20	21	.	.	X
cana-2203	20	22	burton	burton	PROPN
cana-2203	20	23	studied	study	VERB
cana-2203	20	24	the	the	DET
cana-2203	20	25	an	an	DET
cana-2203	20	26	integro	integro	ADJ
cana-2203	20	27	-	-	PUNCT
cana-2203	20	28	differential	differential	NOUN
cana-2203	20	29	equations	equation	NOUN
cana-2203	20	30	and	and	CCONJ
cana-2203	20	31	stability	stability	NOUN
cana-2203	20	32	theory	theory	NOUN
cana-2203	20	33	for	for	ADP
cana-2203	20	34	volterra	volterra	NOUN
cana-2203	20	35	equations	equation	NOUN
cana-2203	21	1	[	[	X
cana-2203	21	2	2	2	NUM
cana-2203	21	3	]	]	PUNCT
cana-2203	21	4	.	.	PUNCT
cana-2203	22	1	making	make	VERB
cana-2203	22	2	use	use	NOUN
cana-2203	22	3	of	of	ADP
cana-2203	22	4	asymptotic	asymptotic	ADJ
cana-2203	22	5	stability	stability	NOUN
cana-2203	22	6	,	,	PUNCT
cana-2203	22	7	g.	g.	PROPN
cana-2203	22	8	v.	v.	PROPN
cana-2203	22	9	s.	s.	PROPN
cana-2203	22	10	r.	r.	PROPN
cana-2203	22	11	deekshitulu	deekshitulu	PROPN
cana-2203	22	12	and	and	CCONJ
cana-2203	22	13	g.	g.	PROPN
cana-2203	23	1	v.	v.	PROPN
cana-2203	23	2	ramana	ramana	PROPN
cana-2203	23	3	studied	study	VERB
cana-2203	23	4	lyapunov	lyapunov	ADJ
cana-2203	23	5	type	type	NOUN
cana-2203	23	6	linear	linear	PROPN
cana-2203	23	7	matrix	matrix	NOUN
cana-2203	23	8	volterra	volterra	NOUN
cana-2203	23	9	integro	integro	PROPN
cana-2203	23	10	dynamical	dynamical	ADJ
cana-2203	23	11	system	system	NOUN
cana-2203	23	12	on	on	ADP
cana-2203	23	13	ts	ts	ADP
cana-2203	24	1	[	[	X
cana-2203	24	2	4	4	NUM
cana-2203	24	3	]	]	PUNCT
cana-2203	24	4	.	.	PUNCT
cana-2203	25	1	shah	shah	PROPN
cana-2203	25	2	,	,	PUNCT
cana-2203	25	3	zada	zada	PROPN
cana-2203	25	4	and	and	CCONJ
cana-2203	25	5	sabrina	sabrina	PROPN
cana-2203	25	6	streipert	streipert	PROPN
cana-2203	25	7	are	be	AUX
cana-2203	25	8	discussed	discuss	VERB
cana-2203	25	9	the	the	DET
cana-2203	25	10	stability	stability	NOUN
cana-2203	25	11	of	of	ADP
cana-2203	25	12	non	non	ADJ
cana-2203	25	13	-	-	ADJ
cana-2203	25	14	linear	linear	ADJ
cana-2203	25	15	volterra	volterra	NOUN
cana-2203	25	16	integro	integro	PROPN
cana-2203	25	17	dynamic	dynamic	ADJ
cana-2203	25	18	equations	equation	NOUN
cana-2203	25	19	on	on	ADP
cana-2203	25	20	ts	ts	ADP
cana-2203	26	1	[	[	X
cana-2203	26	2	7	7	NUM
cana-2203	26	3	,	,	PUNCT
cana-2203	26	4	8	8	NUM
cana-2203	26	5	]	]	PUNCT
cana-2203	26	6	.	.	PUNCT
cana-2203	27	1	having	having	AUX
cana-2203	27	2	seen	see	VERB
cana-2203	27	3	the	the	DET
cana-2203	27	4	potential	potential	ADJ
cana-2203	27	5	exploring	explore	VERB
cana-2203	27	6	possibilities	possibility	NOUN
cana-2203	27	7	in	in	ADP
cana-2203	27	8	this	this	PRON
cana-2203	27	9	,	,	PUNCT
cana-2203	27	10	an	an	DET
cana-2203	27	11	endeavour	endeavour	NOUN
cana-2203	27	12	is	be	AUX
cana-2203	27	13	made	make	VERB
cana-2203	27	14	to	to	PART
cana-2203	27	15	obtain	obtain	VERB
cana-2203	27	16	a	a	DET
cana-2203	27	17	solution	solution	NOUN
cana-2203	27	18	of	of	ADP
cana-2203	27	19	bvp	bvp	NOUN
cana-2203	27	20	concerned	concern	VERB
cana-2203	27	21	with	with	ADP
cana-2203	27	22	midt	midt	NOUN
cana-2203	27	23	.	.	PUNCT
cana-2203	28	1	communications	communication	NOUN
cana-2203	28	2	on	on	ADP
cana-2203	28	3	applied	apply	VERB
cana-2203	28	4	nonlinear	nonlinear	ADJ
cana-2203	28	5	analysis	analysis	NOUN
cana-2203	28	6	issn	issn	NOUN
cana-2203	28	7	:	:	PUNCT
cana-2203	28	8	1074	1074	NUM
cana-2203	28	9	-	-	PUNCT
cana-2203	28	10	133x	133x	NUM
cana-2203	28	11	vol	vol	NOUN
cana-2203	28	12	32	32	NUM
cana-2203	28	13	no	no	NOUN
cana-2203	28	14	.	.	PUNCT
cana-2203	29	1	1s	1s	NUM
cana-2203	29	2	(	(	PUNCT
cana-2203	29	3	2025	2025	NUM
cana-2203	29	4	)	)	PUNCT
cana-2203	29	5	389	389	NUM
cana-2203	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	29	7	and	and	CCONJ
cana-2203	29	8	the	the	DET
cana-2203	29	9	obtained	obtain	VERB
cana-2203	29	10	solution	solution	NOUN
cana-2203	29	11	is	be	AUX
cana-2203	29	12	tabled	table	VERB
cana-2203	29	13	in	in	ADP
cana-2203	29	14	the	the	DET
cana-2203	29	15	form	form	NOUN
cana-2203	29	16	of	of	ADP
cana-2203	29	17	gm	gm	PROPN
cana-2203	29	18	.	.	PUNCT
cana-2203	30	1	further	far	ADV
cana-2203	30	2	,	,	PUNCT
cana-2203	30	3	properties	property	NOUN
cana-2203	30	4	of	of	ADP
cana-2203	30	5	gm	gm	PROPN
cana-2203	30	6	and	and	CCONJ
cana-2203	30	7	stability	stability	NOUN
cana-2203	30	8	are	be	AUX
cana-2203	30	9	also	also	ADV
cana-2203	30	10	discussed	discuss	VERB
cana-2203	30	11	for	for	ADP
cana-2203	30	12	the	the	DET
cana-2203	30	13	system	system	NOUN
cana-2203	30	14	on	on	ADP
cana-2203	30	15	ts	ts	PROPN
cana-2203	30	16	.	.	PUNCT
cana-2203	31	1	in	in	ADP
cana-2203	31	2	this	this	DET
cana-2203	31	3	paper	paper	NOUN
cana-2203	31	4	,	,	PUNCT
cana-2203	31	5	the	the	DET
cana-2203	31	6	following	follow	VERB
cana-2203	31	7	matrix	matrix	NOUN
cana-2203	31	8	integro	integro	ADJ
cana-2203	31	9	-	-	PUNCT
cana-2203	31	10	dynamical	dynamical	ADJ
cana-2203	31	11	equation	equation	NOUN
cana-2203	31	12	on	on	ADP
cana-2203	31	13	ts	ts	X
cana-2203	31	14	has	have	AUX
cana-2203	31	15	been	be	AUX
cana-2203	31	16	considered	consider	VERB
cana-2203	31	17	.	.	PUNCT
cana-2203	32	1	𝑥∆(𝑡	𝑥∆(𝑡	PRON
cana-2203	32	2	)	)	PUNCT
cana-2203	32	3	=	=	SYM
cana-2203	32	4	𝐴(𝑡)𝑥(𝑡	𝐴(𝑡)𝑥(𝑡	NOUN
cana-2203	32	5	)	)	PUNCT
cana-2203	33	1	+	+	CCONJ
cana-2203	33	2	∫	∫	PROPN
cana-2203	33	3	𝐾(𝑡	𝐾(𝑡	NUM
cana-2203	33	4	,	,	PUNCT
cana-2203	33	5	𝑠	𝑠	NOUN
cana-2203	33	6	)	)	PUNCT
cana-2203	33	7	𝑥(𝑠)∆𝑠	𝑥(𝑠)∆𝑠	PROPN
cana-2203	33	8	𝜎(𝜌(𝑡	𝜎(𝜌(𝑡	PROPN
cana-2203	33	9	)	)	PUNCT
cana-2203	33	10	)	)	PUNCT
cana-2203	34	1	𝑡0	𝑡0	PROPN
cana-2203	34	2	+	+	CCONJ
cana-2203	34	3	℥	℥	NOUN
cana-2203	34	4	(	(	PUNCT
cana-2203	34	5	𝑡	𝑡	NOUN
cana-2203	34	6	,	,	PUNCT
cana-2203	34	7	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	34	8	)	)	PUNCT
cana-2203	34	9	)	)	PUNCT
cana-2203	34	10	,	,	PUNCT
cana-2203	34	11	(	(	PUNCT
cana-2203	34	12	1.1	1.1	NUM
cana-2203	34	13	)	)	PUNCT
cana-2203	34	14	𝑤𝑎	𝑤𝑎	NOUN
cana-2203	34	15	𝑥(𝑎	𝑥(𝑎	NOUN
cana-2203	34	16	)	)	PUNCT
cana-2203	35	1	+	+	CCONJ
cana-2203	35	2	𝑤𝑏	𝑤𝑏	PROPN
cana-2203	35	3	𝑥(𝑏	𝑥(𝑏	PROPN
cana-2203	35	4	)	)	PUNCT
cana-2203	35	5	=	=	SYM
cana-2203	35	6	0	0	NUM
cana-2203	35	7	(	(	PUNCT
cana-2203	35	8	1.2	1.2	NUM
cana-2203	35	9	)	)	PUNCT
cana-2203	35	10	here	here	ADV
cana-2203	35	11	𝐴𝑛×𝑛	𝐴𝑛×𝑛	PROPN
cana-2203	35	12	is	be	AUX
cana-2203	35	13	rd	rd	NOUN
cana-2203	35	14	-	-	NOUN
cana-2203	35	15	continuous	continuous	ADJ
cana-2203	35	16	in	in	ADP
cana-2203	35	17	𝕋	𝕋	PROPN
cana-2203	35	18	and	and	CCONJ
cana-2203	35	19	𝐾(𝑡	𝐾(𝑡	NUM
cana-2203	35	20	,	,	PUNCT
cana-2203	35	21	𝑠	𝑠	NOUN
cana-2203	35	22	)	)	PUNCT
cana-2203	35	23	∈	∈	PROPN
cana-2203	35	24	𝐶𝑟𝑑[𝕋	𝐶𝑟𝑑[𝕋	ADJ
cana-2203	35	25	×	×	NOUN
cana-2203	35	26	𝕋	𝕋	PROPN
cana-2203	35	27	,	,	PUNCT
cana-2203	35	28	ℝ𝑛×𝑛	ℝ𝑛×𝑛	PROPN
cana-2203	35	29	]	]	X
cana-2203	35	30	,	,	PUNCT
cana-2203	35	31	𝑤𝑎	𝑤𝑎	NOUN
cana-2203	35	32	and	and	CCONJ
cana-2203	35	33	𝑤𝑏are(𝑛	𝑤𝑏are(𝑛	NUM
cana-2203	35	34	×	×	PROPN
cana-2203	35	35	𝑛	𝑛	NOUN
cana-2203	35	36	)	)	PUNCT
cana-2203	35	37	constant	constant	ADJ
cana-2203	35	38	matrices	matrix	NOUN
cana-2203	35	39	,	,	PUNCT
cana-2203	35	40	℥	℥	X
cana-2203	35	41	(	(	PUNCT
cana-2203	35	42	𝑡	𝑡	NOUN
cana-2203	35	43	,	,	PUNCT
cana-2203	35	44	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	35	45	)	)	PUNCT
cana-2203	35	46	)	)	PUNCT
cana-2203	36	1	∈	∈	PROPN
cana-2203	36	2	𝐶𝑟𝑑[𝕋	𝐶𝑟𝑑[𝕋	ADJ
cana-2203	36	3	×	×	NOUN
cana-2203	36	4	𝕋	𝕋	PROPN
cana-2203	36	5	,	,	PUNCT
cana-2203	36	6	ℝ𝑛]and	ℝ𝑛]and	NOUN
cana-2203	36	7	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	36	8	)	)	PUNCT
cana-2203	36	9	is	be	AUX
cana-2203	36	10	a	a	DET
cana-2203	36	11	column	column	NOUN
cana-2203	36	12	vector	vector	NOUN
cana-2203	36	13	.	.	PUNCT
cana-2203	37	1	2	2	NUM
cana-2203	37	2	.	.	X
cana-2203	37	3	preliminary	preliminary	ADJ
cana-2203	37	4	results	result	NOUN
cana-2203	37	5	definition	definition	NOUN
cana-2203	37	6	2.1.[bohner	2.1.[bohner	NOUN
cana-2203	37	7	et	et	PROPN
cana-2203	37	8	al	al	PROPN
cana-2203	37	9	.	.	PROPN
cana-2203	37	10	2003	2003	NUM
cana-2203	37	11	]	]	PUNCT
cana-2203	37	12	the	the	DET
cana-2203	37	13	mappings	mapping	NOUN
cana-2203	37	14	σ	σ	NOUN
cana-2203	37	15	and	and	CCONJ
cana-2203	37	16	ρ	ρ	NOUN
cana-2203	37	17	:	:	PUNCT
cana-2203	37	18	t	t	PROPN
cana-2203	37	19	→	→	SYM
cana-2203	37	20	r	r	NOUN
cana-2203	37	21	are	be	AUX
cana-2203	37	22	defined	define	VERB
cana-2203	37	23	as	as	ADP
cana-2203	37	24	(	(	PUNCT
cana-2203	37	25	i	i	NOUN
cana-2203	37	26	)	)	PUNCT
cana-2203	37	27	σ(t	σ(t	PROPN
cana-2203	37	28	)	)	PUNCT
cana-2203	38	1	=	=	SYM
cana-2203	38	2	inf	inf	NOUN
cana-2203	38	3	{	{	PUNCT
cana-2203	38	4	m	m	PROPN
cana-2203	38	5	∈	∈	PROPN
cana-2203	38	6	t	t	PROPN
cana-2203	38	7	:	:	PUNCT
cana-2203	38	8	m	m	VERB
cana-2203	38	9	>	>	X
cana-2203	38	10	t	t	PROPN
cana-2203	38	11	}	}	PUNCT
cana-2203	38	12	,	,	PUNCT
cana-2203	38	13	(	(	PUNCT
cana-2203	38	14	ii	ii	NOUN
cana-2203	38	15	)	)	PUNCT
cana-2203	38	16	(	(	PUNCT
cana-2203	38	17	ii	ii	NOUN
cana-2203	38	18	)	)	PUNCT
cana-2203	38	19	ρ(t	ρ(t	NUM
cana-2203	38	20	)	)	PUNCT
cana-2203	39	1	=	=	SYM
cana-2203	39	2	sup	sup	NOUN
cana-2203	39	3	{	{	PUNCT
cana-2203	39	4	m	m	PROPN
cana-2203	39	5	∈	∈	PROPN
cana-2203	39	6	t	t	PROPN
cana-2203	39	7	:	:	PUNCT
cana-2203	39	8	m	m	VERB
cana-2203	39	9	<	<	X
cana-2203	39	10	t	t	X
cana-2203	39	11	}	}	PUNCT
cana-2203	39	12	.	.	PUNCT
cana-2203	40	1	definition	definition	NOUN
cana-2203	40	2	2.2.[bohner	2.2.[bohner	NOUN
cana-2203	40	3	et	et	PROPN
cana-2203	40	4	al	al	PROPN
cana-2203	40	5	.	.	PROPN
cana-2203	40	6	2003	2003	NUM
cana-2203	40	7	]	]	PUNCT
cana-2203	41	1	the	the	DET
cana-2203	41	2	graininess	graininess	NOUN
cana-2203	41	3	function	function	VERB
cana-2203	41	4	µ	µ	NOUN
cana-2203	41	5	:	:	PUNCT
cana-2203	41	6	t	t	PROPN
cana-2203	41	7	→	→	SYM
cana-2203	41	8	[	[	X
cana-2203	41	9	0	0	NUM
cana-2203	41	10	,	,	PUNCT
cana-2203	41	11	∞	∞	PROPN
cana-2203	41	12	]	]	PUNCT
cana-2203	41	13	is	be	AUX
cana-2203	41	14	defined	define	VERB
cana-2203	41	15	as	as	ADP
cana-2203	41	16	µ(t	µ(t	ADJ
cana-2203	41	17	)	)	PUNCT
cana-2203	41	18	=	=	SYM
cana-2203	42	1	σ(t	σ(t	PROPN
cana-2203	42	2	)	)	PUNCT
cana-2203	42	3	–	–	PUNCT
cana-2203	42	4	t	t	PROPN
cana-2203	42	5	and	and	CCONJ
cana-2203	42	6	(	(	PUNCT
cana-2203	42	7	i	i	NOUN
cana-2203	42	8	)	)	PUNCT
cana-2203	42	9	if	if	SCONJ
cana-2203	42	10	t	t	NOUN
cana-2203	42	11	=	=	SYM
cana-2203	42	12	r	r	NOUN
cana-2203	42	13	,	,	PUNCT
cana-2203	42	14	then	then	ADV
cana-2203	42	15	µ(t	µ(t	ADJ
cana-2203	42	16	)	)	PUNCT
cana-2203	42	17	=	=	SYM
cana-2203	42	18	0	0	NUM
cana-2203	42	19	and	and	CCONJ
cana-2203	42	20	(	(	PUNCT
cana-2203	42	21	ii	ii	NOUN
cana-2203	42	22	)	)	PUNCT
cana-2203	42	23	if	if	SCONJ
cana-2203	42	24	t	t	NOUN
cana-2203	42	25	=	=	SYM
cana-2203	42	26	z	z	PROPN
cana-2203	42	27	,	,	PUNCT
cana-2203	42	28	then	then	ADV
cana-2203	42	29	µ(t	µ(t	ADJ
cana-2203	42	30	)	)	PUNCT
cana-2203	42	31	=	=	SYM
cana-2203	42	32	1	1	X
cana-2203	42	33	.	.	PUNCT
cana-2203	42	34	theorem	theorem	VERB
cana-2203	42	35	2.3.[bohner	2.3.[bohner	PROPN
cana-2203	42	36	et	et	PROPN
cana-2203	42	37	al	al	PROPN
cana-2203	42	38	.	.	PROPN
cana-2203	42	39	2003	2003	NUM
cana-2203	42	40	]	]	PUNCT
cana-2203	42	41	assume	assume	VERB
cana-2203	42	42	v	v	ADP
cana-2203	42	43	:	:	PUNCT
cana-2203	42	44	t	t	NOUN
cana-2203	42	45	→	→	SYM
cana-2203	42	46	r	r	NOUN
cana-2203	42	47	and	and	CCONJ
cana-2203	42	48	let	let	VERB
cana-2203	42	49	t	t	PROPN
cana-2203	42	50	∈	∈	PROPN
cana-2203	42	51	tk	tk	PROPN
cana-2203	42	52	and	and	CCONJ
cana-2203	42	53	v	v	ADP
cana-2203	42	54	△	△	X
cana-2203	42	55	(t	(t	NOUN
cana-2203	42	56	)	)	PUNCT
cana-2203	42	57	exist	exist	VERB
cana-2203	42	58	then	then	ADV
cana-2203	42	59	v(σ(t	v(σ(t	NOUN
cana-2203	42	60	)	)	PUNCT
cana-2203	42	61	)	)	PUNCT
cana-2203	43	1	=	=	SYM
cana-2203	43	2	v(t	v(t	NUM
cana-2203	43	3	)	)	PUNCT
cana-2203	43	4	+	+	CCONJ
cana-2203	43	5	µ(t)v	µ(t)v	NOUN
cana-2203	43	6	△	△	NOUN
cana-2203	43	7	(t	(t	NOUN
cana-2203	43	8	)	)	PUNCT
cana-2203	43	9	.	.	PUNCT
cana-2203	44	1	lemma	lemma	PROPN
cana-2203	44	2	2.4.[bohner	2.4.[bohner	PROPN
cana-2203	44	3	et	et	PROPN
cana-2203	44	4	al	al	PROPN
cana-2203	44	5	.	.	PROPN
cana-2203	44	6	2003	2003	NUM
cana-2203	44	7	]	]	PUNCT
cana-2203	44	8	let	let	VERB
cana-2203	44	9	u	u	NOUN
cana-2203	44	10	,	,	PUNCT
cana-2203	44	11	v	v	NOUN
cana-2203	44	12	and	and	CCONJ
cana-2203	44	13	w	w	PROPN
cana-2203	44	14	be	be	AUX
cana-2203	44	15	matrix	matrix	NOUN
cana-2203	44	16	-	-	PUNCT
cana-2203	44	17	valued	value	VERB
cana-2203	44	18	of	of	ADP
cana-2203	44	19	order	order	NOUN
cana-2203	44	20	(	(	PUNCT
cana-2203	44	21	n	n	CCONJ
cana-2203	44	22	×	×	NOUN
cana-2203	44	23	n	n	CCONJ
cana-2203	44	24	)	)	PUNCT
cana-2203	44	25	and	and	CCONJ
cana-2203	44	26	differentiable	differentiable	ADJ
cana-2203	44	27	.	.	PUNCT
cana-2203	45	1	then	then	ADV
cana-2203	45	2	(	(	PUNCT
cana-2203	45	3	i	i	NOUN
cana-2203	45	4	)	)	PUNCT
cana-2203	45	5	(	(	PUNCT
cana-2203	45	6	u	u	NOUN
cana-2203	45	7	+	+	NOUN
cana-2203	45	8	v	v	NOUN
cana-2203	45	9	)	)	PUNCT
cana-2203	45	10	△	△	X
cana-2203	45	11	=	=	SYM
cana-2203	45	12	u	u	NOUN
cana-2203	45	13	△	△	X
cana-2203	45	14	+	+	X
cana-2203	45	15	v	v	NOUN
cana-2203	45	16	△	△	X
cana-2203	45	17	(	(	PUNCT
cana-2203	45	18	ii	ii	NOUN
cana-2203	45	19	)	)	PUNCT
cana-2203	45	20	(	(	PUNCT
cana-2203	45	21	αu	αu	NOUN
cana-2203	45	22	)	)	PUNCT
cana-2203	45	23	△	△	X
cana-2203	45	24	=	=	SYM
cana-2203	45	25	αu	αu	PROPN
cana-2203	45	26	△	△	PROPN
cana-2203	45	27	if	if	SCONJ
cana-2203	45	28	α	α	PRON
cana-2203	45	29	is	be	AUX
cana-2203	45	30	constant	constant	ADJ
cana-2203	45	31	(	(	PUNCT
cana-2203	45	32	iii	iii	NOUN
cana-2203	45	33	)	)	PUNCT
cana-2203	45	34	(	(	PUNCT
cana-2203	45	35	uv	uv	NOUN
cana-2203	45	36	)	)	PUNCT
cana-2203	45	37	△	△	X
cana-2203	45	38	=	=	SYM
cana-2203	45	39	u	u	NOUN
cana-2203	45	40	△	△	X
cana-2203	45	41	vσ	vσ	NOUN
cana-2203	45	42	+	+	X
cana-2203	45	43	uv	uv	NOUN
cana-2203	45	44	△	△	NOUN
cana-2203	45	45	=	=	SYM
cana-2203	45	46	uσv	uσv	X
cana-2203	45	47	△	△	X
cana-2203	45	48	+	+	CCONJ
cana-2203	45	49	u	u	NOUN
cana-2203	45	50	△	△	PROPN
cana-2203	45	51	v	v	X
cana-2203	45	52	(	(	PUNCT
cana-2203	45	53	iv	iv	NUM
cana-2203	45	54	)	)	PUNCT
cana-2203	45	55	(	(	PUNCT
cana-2203	45	56	uvw	uvw	NOUN
cana-2203	45	57	)	)	PUNCT
cana-2203	45	58	△	△	X
cana-2203	45	59	=	=	SYM
cana-2203	45	60	u	u	PROPN
cana-2203	45	61	△	△	X
cana-2203	45	62	vw	vw	X
cana-2203	45	63	+	+	CCONJ
cana-2203	45	64	uσv	uσv	X
cana-2203	45	65	△	△	NOUN
cana-2203	45	66	wσ	wσ	ADJ
cana-2203	45	67	+	+	X
cana-2203	45	68	uσvw	uσvw	ADJ
cana-2203	45	69	△	△	NOUN
cana-2203	45	70	=	=	SYM
cana-2203	45	71	u	u	PROPN
cana-2203	45	72	△	△	X
cana-2203	45	73	vw	vw	X
cana-2203	45	74	+	+	CCONJ
cana-2203	45	75	uσv	uσv	PROPN
cana-2203	45	76	△	△	PROPN
cana-2203	45	77	w	w	PROPN
cana-2203	45	78	+	+	PUNCT
cana-2203	45	79	uσvσw	uσvσw	ADJ
cana-2203	45	80	△	△	NOUN
cana-2203	45	81	definition	definition	NOUN
cana-2203	45	82	2.5	2.5	NUM
cana-2203	45	83	.	.	PUNCT
cana-2203	46	1	[	[	X
cana-2203	46	2	bohner	bohner	X
cana-2203	46	3	et	et	PROPN
cana-2203	46	4	al	al	PROPN
cana-2203	46	5	.	.	PROPN
cana-2203	46	6	2003	2003	NUM
cana-2203	46	7	]	]	X
cana-2203	46	8	u	u	NOUN
cana-2203	46	9	is	be	AUX
cana-2203	46	10	a	a	DET
cana-2203	46	11	matrix	matrix	NOUN
cana-2203	46	12	of	of	ADP
cana-2203	46	13	order	order	NOUN
cana-2203	46	14	(	(	PUNCT
cana-2203	46	15	n	n	CCONJ
cana-2203	46	16	×	×	NOUN
cana-2203	46	17	n	n	CCONJ
cana-2203	46	18	)	)	PUNCT
cana-2203	46	19	on	on	ADP
cana-2203	46	20	a	a	DET
cana-2203	46	21	time	time	NOUN
cana-2203	46	22	scale	scale	NOUN
cana-2203	46	23	t	t	PROPN
cana-2203	46	24	is	be	AUX
cana-2203	46	25	said	say	VERB
cana-2203	46	26	to	to	PART
cana-2203	46	27	be	be	AUX
cana-2203	46	28	regressive	regressive	ADJ
cana-2203	46	29	if	if	SCONJ
cana-2203	46	30	i	i	PRON
cana-2203	46	31	+	+	CCONJ
cana-2203	46	32	µ(t)u(t	µ(t)u(t	NOUN
cana-2203	46	33	)	)	PUNCT
cana-2203	46	34	≠	≠	PROPN
cana-2203	46	35	0	0	NUM
cana-2203	46	36	for	for	ADP
cana-2203	46	37	all	all	DET
cana-2203	46	38	t	t	PROPN
cana-2203	46	39	∈	∈	PROPN
cana-2203	46	40	tk	tk	PROPN
cana-2203	46	41	.	.	PROPN
cana-2203	46	42	lemma	lemma	PROPN
cana-2203	46	43	2.6	2.6	NUM
cana-2203	46	44	.	.	PUNCT
cana-2203	47	1	[	[	X
cana-2203	47	2	bohner	bohner	NOUN
cana-2203	47	3	et	et	PROPN
cana-2203	47	4	al	al	PROPN
cana-2203	47	5	.	.	PROPN
cana-2203	47	6	2001	2001	NUM
cana-2203	47	7	]	]	PUNCT
cana-2203	47	8	let	let	VERB
cana-2203	47	9	u	u	PRON
cana-2203	47	10	∈	∈	PROPN
cana-2203	47	11	crd(t	crd(t	PROPN
cana-2203	47	12	,	,	PUNCT
cana-2203	47	13	r	r	NOUN
cana-2203	47	14	)	)	PUNCT
cana-2203	47	15	,	,	PUNCT
cana-2203	47	16	ξ	ξ	PROPN
cana-2203	47	17	∈	∈	PROPN
cana-2203	47	18	r+	r+	X
cana-2203	47	19	,	,	PUNCT
cana-2203	47	20	ξ	ξ	X
cana-2203	47	21	≥	≥	NOUN
cana-2203	47	22	0	0	NUM
cana-2203	47	23	,	,	PUNCT
cana-2203	47	24	β∈	β∈	PROPN
cana-2203	47	25	r.	r.	VERB
cana-2203	47	26	the	the	DET
cana-2203	47	27	u(t	u(t	NOUN
cana-2203	47	28	)	)	PUNCT
cana-2203	47	29	≤	≤	NOUN
cana-2203	47	30	β	β	X
cana-2203	48	1	+	+	NUM
cana-2203	48	2	∫	∫	PROPN
cana-2203	48	3	u(s)ξ(s	u(s)ξ(	NOUN
cana-2203	48	4	)	)	PUNCT
cana-2203	48	5	△	△	PROPN
cana-2203	48	6	s	s	PART
cana-2203	48	7	𝑡	𝑡	PROPN
cana-2203	48	8	0	0	NUM
cana-2203	48	9	implies	imply	VERB
cana-2203	48	10	u(t	u(t	NOUN
cana-2203	48	11	)	)	PUNCT
cana-2203	48	12	≤	≤	NUM
cana-2203	48	13	β𝑒ξ(𝑡	β𝑒ξ(𝑡	NOUN
cana-2203	48	14	,	,	PUNCT
cana-2203	48	15	𝑡0	𝑡0	NOUN
cana-2203	48	16	)	)	PUNCT
cana-2203	48	17	,	,	PUNCT
cana-2203	48	18	for	for	ADP
cana-2203	48	19	all	all	DET
cana-2203	48	20	t	t	NOUN
cana-2203	48	21	∈	∈	PROPN
cana-2203	48	22	t.	t.	PROPN
cana-2203	48	23	lemma	lemma	PROPN
cana-2203	48	24	2.7	2.7	NUM
cana-2203	48	25	.	.	PUNCT
cana-2203	49	1	[	[	X
cana-2203	49	2	bohner	bohner	X
cana-2203	49	3	et	et	PROPN
cana-2203	49	4	al	al	PROPN
cana-2203	49	5	.	.	PROPN
cana-2203	49	6	2003	2003	NUM
cana-2203	49	7	]	]	PUNCT
cana-2203	49	8	let	let	VERB
cana-2203	49	9	ξ	ξ	PROPN
cana-2203	49	10	∈	∈	PROPN
cana-2203	49	11	r+	r+	X
cana-2203	49	12	.	.	PUNCT
cana-2203	50	1	then	then	ADV
cana-2203	50	2	eξ(ϱ	eξ(ϱ	NOUN
cana-2203	50	3	,	,	PUNCT
cana-2203	50	4	ς	ς	PROPN
cana-2203	50	5	)	)	PUNCT
cana-2203	50	6	≥	≥	NOUN
cana-2203	50	7	1	1	NUM
cana-2203	50	8	+	+	NUM
cana-2203	50	9	ξ(ϱ	ξ(ϱ	PROPN
cana-2203	50	10	−	−	PROPN
cana-2203	50	11	ς	ς	NOUN
cana-2203	50	12	)	)	PUNCT
cana-2203	50	13	,	,	PUNCT
cana-2203	50	14	for	for	SCONJ
cana-2203	50	15	all	all	PRON
cana-2203	50	16	ϱ	ϱ	ADP
cana-2203	50	17	≥	≥	PROPN
cana-2203	50	18	ς	ς	NOUN
cana-2203	50	19	.	.	PUNCT
cana-2203	50	20	communications	communication	NOUN
cana-2203	50	21	on	on	ADP
cana-2203	50	22	applied	apply	VERB
cana-2203	50	23	nonlinear	nonlinear	ADJ
cana-2203	50	24	analysis	analysis	NOUN
cana-2203	50	25	issn	issn	NOUN
cana-2203	50	26	:	:	PUNCT
cana-2203	50	27	1074	1074	NUM
cana-2203	50	28	-	-	PUNCT
cana-2203	50	29	133x	133x	NUM
cana-2203	50	30	vol	vol	NOUN
cana-2203	50	31	32	32	NUM
cana-2203	50	32	no	no	NOUN
cana-2203	50	33	.	.	PUNCT
cana-2203	51	1	1s	1s	NUM
cana-2203	51	2	(	(	PUNCT
cana-2203	51	3	2025	2025	NUM
cana-2203	51	4	)	)	PUNCT
cana-2203	51	5	390	390	NUM
cana-2203	51	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	51	7	3	3	X
cana-2203	51	8	.	.	X
cana-2203	51	9	main	main	ADJ
cana-2203	51	10	results	result	NOUN
cana-2203	51	11	theorem	theorem	VERB
cana-2203	51	12	3.1	3.1	NUM
cana-2203	51	13	.	.	PUNCT
cana-2203	52	1	let	let	VERB
cana-2203	52	2	𝐴(𝑡	𝐴(𝑡	X
cana-2203	52	3	)	)	PUNCT
cana-2203	52	4	,	,	PUNCT
cana-2203	52	5	𝐾(𝑡	𝐾(𝑡	PROPN
cana-2203	52	6	,	,	PUNCT
cana-2203	52	7	s	s	PART
cana-2203	52	8	)	)	PUNCT
cana-2203	52	9	,	,	PUNCT
cana-2203	52	10	𝑤𝑎	𝑤𝑎	INTJ
cana-2203	52	11	,	,	PUNCT
cana-2203	52	12	𝑤𝑏	𝑤𝑏	PROPN
cana-2203	52	13	and	and	CCONJ
cana-2203	52	14	℥	℥	PROPN
cana-2203	52	15	(	(	PUNCT
cana-2203	52	16	𝑡	𝑡	NOUN
cana-2203	52	17	,	,	PUNCT
cana-2203	52	18	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	52	19	)	)	PUNCT
cana-2203	52	20	)	)	PUNCT
cana-2203	52	21	be	be	AUX
cana-2203	52	22	previously	previously	ADV
cana-2203	52	23	defined	define	VERB
cana-2203	52	24	.	.	PUNCT
cana-2203	53	1	then	then	ADV
cana-2203	53	2	the	the	DET
cana-2203	53	3	solution	solution	NOUN
cana-2203	53	4	of	of	ADP
cana-2203	53	5	(	(	PUNCT
cana-2203	53	6	1.1	1.1	NUM
cana-2203	53	7	)	)	PUNCT
cana-2203	53	8	and	and	CCONJ
cana-2203	53	9	(	(	PUNCT
cana-2203	53	10	1.2	1.2	NUM
cana-2203	53	11	)	)	PUNCT
cana-2203	53	12	is	be	AUX
cana-2203	53	13	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	53	14	)	)	PUNCT
cana-2203	53	15	=	=	SYM
cana-2203	53	16	∫	∫	PROPN
cana-2203	53	17	𝐺(𝑡	𝐺(𝑡	X
cana-2203	53	18	,	,	PUNCT
cana-2203	53	19	𝜎(s	𝜎(	NOUN
cana-2203	53	20	)	)	PUNCT
cana-2203	53	21	)	)	PUNCT
cana-2203	54	1	𝐻(s	𝐻(s	ADP
cana-2203	54	2	,	,	PUNCT
cana-2203	54	3	𝜏)∆𝑠	𝜏)∆𝑠	PRON
cana-2203	54	4	𝑏	𝑏	SYM
cana-2203	54	5	𝑎	𝑎	PRON
cana-2203	54	6	(	(	PUNCT
cana-2203	54	7	3.1	3.1	NUM
cana-2203	54	8	)	)	PUNCT
cana-2203	54	9	where	where	SCONJ
cana-2203	54	10	𝐻(𝑠	𝐻(𝑠	PROPN
cana-2203	54	11	,	,	PUNCT
cana-2203	54	12	𝜏	𝜏	NOUN
cana-2203	54	13	)	)	PUNCT
cana-2203	54	14	=	=	SYM
cana-2203	54	15	∫	∫	PROPN
cana-2203	54	16	𝐾(s	𝐾(s	PROPN
cana-2203	54	17	,	,	PUNCT
cana-2203	54	18	𝜏	𝜏	NOUN
cana-2203	54	19	)	)	PUNCT
cana-2203	54	20	𝑦(𝜏)∆𝜏	𝑦(𝜏)∆𝜏	NOUN
cana-2203	54	21	+	+	NOUN
cana-2203	54	22	℥	℥	NOUN
cana-2203	54	23	(	(	PUNCT
cana-2203	54	24	𝜏.	𝜏.	PROPN
cana-2203	54	25	𝑥(𝜏	𝑥(𝜏	PROPN
cana-2203	54	26	)	)	PUNCT
cana-2203	54	27	)	)	PUNCT
cana-2203	55	1	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	55	2	)	)	PUNCT
cana-2203	55	3	)	)	PUNCT
cana-2203	55	4	𝑡0	𝑡0	NOUN
cana-2203	55	5	and	and	CCONJ
cana-2203	55	6	𝐺(𝑡	𝐺(𝑡	PROPN
cana-2203	55	7	,	,	PUNCT
cana-2203	55	8	𝜎(s	𝜎(	NOUN
cana-2203	55	9	)	)	PUNCT
cana-2203	55	10	)	)	PUNCT
cana-2203	55	11	is	be	AUX
cana-2203	55	12	the	the	DET
cana-2203	55	13	gm	gm	PROPN
cana-2203	55	14	.	.	PUNCT
cana-2203	56	1	proof	proof	NOUN
cana-2203	56	2	:	:	PUNCT
cana-2203	56	3	consider	consider	VERB
cana-2203	56	4	the	the	DET
cana-2203	56	5	non	non	ADJ
cana-2203	56	6	-	-	ADJ
cana-2203	56	7	homogeneous	homogeneous	ADJ
cana-2203	56	8	bvp	bvp	NOUN
cana-2203	56	9	(	(	PUNCT
cana-2203	56	10	1.1	1.1	NUM
cana-2203	56	11	)	)	PUNCT
cana-2203	56	12	and	and	CCONJ
cana-2203	56	13	(	(	PUNCT
cana-2203	56	14	1.2	1.2	NUM
cana-2203	56	15	)	)	PUNCT
cana-2203	56	16	where	where	SCONJ
cana-2203	56	17	𝐴𝑛×𝑛is	𝐴𝑛×𝑛is	NOUN
cana-2203	56	18	rd	rd	NOUN
cana-2203	56	19	-	-	NOUN
cana-2203	56	20	continuous	continuous	ADJ
cana-2203	56	21	in	in	ADP
cana-2203	56	22	𝕋	𝕋	PROPN
cana-2203	56	23	and	and	CCONJ
cana-2203	56	24	𝐾(𝑡	𝐾(𝑡	NUM
cana-2203	56	25	,	,	PUNCT
cana-2203	56	26	s	s	X
cana-2203	56	27	)	)	PUNCT
cana-2203	56	28	∈	∈	NOUN
cana-2203	56	29	𝐶𝑟𝑑[𝕋	𝐶𝑟𝑑[𝕋	ADJ
cana-2203	56	30	×	×	NOUN
cana-2203	56	31	𝕋	𝕋	PROPN
cana-2203	56	32	,	,	PUNCT
cana-2203	56	33	ℝ𝑛×𝑛	ℝ𝑛×𝑛	PROPN
cana-2203	56	34	]	]	X
cana-2203	56	35	,	,	PUNCT
cana-2203	56	36	𝑤𝑎	𝑤𝑎	PROPN
cana-2203	56	37	and	and	CCONJ
cana-2203	56	38	𝑤𝑏	𝑤𝑏	PROPN
cana-2203	56	39	are	be	AUX
cana-2203	56	40	(	(	PUNCT
cana-2203	56	41	𝑛	𝑛	PRON
cana-2203	56	42	×	×	PROPN
cana-2203	56	43	𝑛	𝑛	ADJ
cana-2203	56	44	)	)	PUNCT
cana-2203	56	45	constant	constant	ADJ
cana-2203	56	46	matrices	matrix	NOUN
cana-2203	56	47	,	,	PUNCT
cana-2203	56	48	℥	℥	X
cana-2203	56	49	(	(	PUNCT
cana-2203	56	50	𝑡	𝑡	NOUN
cana-2203	56	51	,	,	PUNCT
cana-2203	56	52	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	56	53	)	)	PUNCT
cana-2203	56	54	)	)	PUNCT
cana-2203	57	1	∈	∈	PROPN
cana-2203	57	2	𝐶𝑟𝑑[𝕋	𝐶𝑟𝑑[𝕋	ADJ
cana-2203	57	3	×	×	NOUN
cana-2203	57	4	𝕋	𝕋	PROPN
cana-2203	57	5	,	,	PUNCT
cana-2203	57	6	ℝ𝑛	ℝ𝑛	NOUN
cana-2203	57	7	]	]	PUNCT
cana-2203	57	8	.	.	PUNCT
cana-2203	58	1	assume	assume	VERB
cana-2203	58	2	that	that	SCONJ
cana-2203	58	3	the	the	DET
cana-2203	58	4	homogeneous	homogeneous	ADJ
cana-2203	58	5	bvp	bvp	NOUN
cana-2203	58	6	corresponding	correspond	VERB
cana-2203	58	7	to	to	ADP
cana-2203	58	8	given	give	VERB
cana-2203	58	9	non	non	ADJ
cana-2203	58	10	-	-	ADJ
cana-2203	58	11	homogeneous	homogeneous	ADJ
cana-2203	58	12	bvp	bvp	NOUN
cana-2203	58	13	is	be	AUX
cana-2203	58	14	incompatible	incompatible	ADJ
cana-2203	58	15	.	.	PUNCT
cana-2203	59	1	let	let	VERB
cana-2203	59	2	∅(𝑡	∅(𝑡	NOUN
cana-2203	59	3	)	)	PUNCT
cana-2203	59	4	be	be	AUX
cana-2203	59	5	a	a	DET
cana-2203	59	6	fundamental	fundamental	ADJ
cana-2203	59	7	matrix	matrix	NOUN
cana-2203	59	8	of	of	ADP
cana-2203	59	9	homogeneous	homogeneous	ADJ
cana-2203	59	10	equation	equation	NOUN
cana-2203	59	11	(	(	PUNCT
cana-2203	59	12	he	he	PRON
cana-2203	59	13	)	)	PUNCT
cana-2203	59	14	in	in	ADP
cana-2203	59	15	the	the	DET
cana-2203	59	16	form	form	NOUN
cana-2203	59	17	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	59	18	)	)	PUNCT
cana-2203	59	19	=	=	SYM
cana-2203	60	1	∅(𝑡)𝐶	∅(𝑡)𝐶	PROPN
cana-2203	60	2	,	,	PUNCT
cana-2203	60	3	where	where	SCONJ
cana-2203	60	4	𝐶	𝐶	PROPN
cana-2203	60	5	is	be	AUX
cana-2203	60	6	a	a	DET
cana-2203	60	7	constant	constant	ADJ
cana-2203	60	8	matrix	matrix	NOUN
cana-2203	60	9	.	.	PUNCT
cana-2203	61	1	let	let	VERB
cana-2203	61	2	𝑥(𝑡)̅̅	𝑥(𝑡)̅̅	PROPN
cana-2203	61	3	̅̅	̅̅	PROPN
cana-2203	61	4	̅̅	̅̅	PROPN
cana-2203	61	5	be	be	AUX
cana-2203	61	6	a	a	DET
cana-2203	61	7	particular	particular	ADJ
cana-2203	61	8	solution	solution	NOUN
cana-2203	61	9	of	of	ADP
cana-2203	61	10	non	non	ADJ
cana-2203	61	11	-	-	ADJ
cana-2203	61	12	homogeneous	homogeneous	ADJ
cana-2203	61	13	equation	equation	NOUN
cana-2203	61	14	(	(	PUNCT
cana-2203	61	15	nhe	nhe	PROPN
cana-2203	61	16	)	)	PUNCT
cana-2203	61	17	.	.	PUNCT
cana-2203	62	1	then	then	ADV
cana-2203	62	2	any	any	DET
cana-2203	62	3	solution	solution	NOUN
cana-2203	62	4	of	of	ADP
cana-2203	62	5	the	the	DET
cana-2203	62	6	given	give	VERB
cana-2203	62	7	nhe	nhe	NOUN
cana-2203	62	8	takes	take	VERB
cana-2203	62	9	form	form	NOUN
cana-2203	62	10	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	62	11	)	)	PUNCT
cana-2203	63	1	=	=	VERB
cana-2203	64	1	∅(𝑡)𝐶	∅(𝑡)𝐶	ADJ
cana-2203	64	2	+	+	CCONJ
cana-2203	64	3	𝑥(𝑡)̅̅	𝑥(𝑡)̅̅	PROPN
cana-2203	64	4	̅̅	̅̅	PROPN
cana-2203	64	5	̅̅	̅̅	PROPN
cana-2203	64	6	.	.	PUNCT
cana-2203	65	1	(	(	PUNCT
cana-2203	65	2	3.2	3.2	NUM
cana-2203	65	3	)	)	PUNCT
cana-2203	65	4	since	since	SCONJ
cana-2203	65	5	the	the	DET
cana-2203	65	6	particular	particular	ADJ
cana-2203	65	7	solution	solution	NOUN
cana-2203	65	8	of	of	ADP
cana-2203	65	9	(	(	PUNCT
cana-2203	65	10	1.1	1.1	NUM
cana-2203	65	11	)	)	PUNCT
cana-2203	65	12	is	be	AUX
cana-2203	65	13	𝑥(𝑡)̅̅	𝑥(𝑡)̅̅	PROPN
cana-2203	65	14	̅̅	̅̅	PROPN
cana-2203	65	15	̅̅	̅̅	PROPN
cana-2203	65	16	=	=	SYM
cana-2203	65	17	∅(𝑡	∅(𝑡	PROPN
cana-2203	65	18	)	)	PUNCT
cana-2203	65	19	∫	∫	PROPN
cana-2203	65	20	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	65	21	)	)	PUNCT
cana-2203	65	22	)	)	PUNCT
cana-2203	66	1	[	[	X
cana-2203	66	2	∫	∫	X
cana-2203	66	3	𝐾(s	𝐾(s	X
cana-2203	66	4	,	,	PUNCT
cana-2203	66	5	𝜏	𝜏	NOUN
cana-2203	66	6	)	)	PUNCT
cana-2203	66	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	66	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	66	9	)	)	PUNCT
cana-2203	66	10	)	)	PUNCT
cana-2203	66	11	𝑡0	𝑡0	PROPN
cana-2203	66	12	+	+	CCONJ
cana-2203	66	13	℥	℥	NOUN
cana-2203	66	14	(	(	PUNCT
cana-2203	66	15	s	s	NOUN
cana-2203	66	16	,	,	PUNCT
cana-2203	66	17	𝑥(s	𝑥(	NOUN
cana-2203	66	18	)	)	PUNCT
cana-2203	66	19	)	)	PUNCT
cana-2203	66	20	]	]	PUNCT
cana-2203	67	1	∆s	∆s	NOUN
cana-2203	67	2	𝑡	𝑡	X
cana-2203	67	3	𝑎	𝑎	X
cana-2203	67	4	(	(	PUNCT
cana-2203	67	5	3.3	3.3	NUM
cana-2203	67	6	)	)	PUNCT
cana-2203	67	7	the	the	DET
cana-2203	67	8	general	general	ADJ
cana-2203	67	9	solution	solution	NOUN
cana-2203	67	10	of	of	ADP
cana-2203	67	11	(	(	PUNCT
cana-2203	67	12	1.1	1.1	NUM
cana-2203	67	13	)	)	PUNCT
cana-2203	67	14	is	be	AUX
cana-2203	67	15	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	67	16	)	)	PUNCT
cana-2203	68	1	=	=	PRON
cana-2203	68	2	∅(𝑡)𝐶	∅(𝑡)𝐶	PROPN
cana-2203	68	3	+	+	CCONJ
cana-2203	68	4	∅(𝑡	∅(𝑡	NOUN
cana-2203	68	5	)	)	PUNCT
cana-2203	68	6	∫	∫	PROPN
cana-2203	68	7	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	68	8	)	)	PUNCT
cana-2203	68	9	)	)	PUNCT
cana-2203	69	1	[	[	X
cana-2203	69	2	∫	∫	X
cana-2203	69	3	𝐾(s	𝐾(s	X
cana-2203	69	4	,	,	PUNCT
cana-2203	69	5	𝜏	𝜏	NOUN
cana-2203	69	6	)	)	PUNCT
cana-2203	69	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	69	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	69	9	)	)	PUNCT
cana-2203	69	10	)	)	PUNCT
cana-2203	69	11	𝑡0	𝑡0	PROPN
cana-2203	69	12	+	+	CCONJ
cana-2203	69	13	℥	℥	NOUN
cana-2203	69	14	(	(	PUNCT
cana-2203	69	15	s	s	NOUN
cana-2203	69	16	,	,	PUNCT
cana-2203	69	17	𝑥(s	𝑥(	NOUN
cana-2203	69	18	)	)	PUNCT
cana-2203	69	19	)	)	PUNCT
cana-2203	69	20	]	]	PUNCT
cana-2203	70	1	∆s	∆s	NOUN
cana-2203	70	2	𝑡	𝑡	PROPN
cana-2203	70	3	𝑎	𝑎	X
cana-2203	70	4	.	.	PUNCT
cana-2203	70	5	(	(	PUNCT
cana-2203	70	6	3.4	3.4	NUM
cana-2203	70	7	)	)	PUNCT
cana-2203	70	8	now	now	ADV
cana-2203	70	9	calculate	calculate	VERB
cana-2203	70	10	the	the	DET
cana-2203	70	11	general	general	ADJ
cana-2203	70	12	solution	solution	NOUN
cana-2203	70	13	in	in	ADP
cana-2203	70	14	the	the	DET
cana-2203	70	15	given	give	VERB
cana-2203	70	16	boundary	boundary	ADJ
cana-2203	70	17	condition	condition	NOUN
cana-2203	70	18	0	0	NUM
cana-2203	70	19	=	=	SYM
cana-2203	70	20	𝑤(𝑎)𝑥(𝑎	𝑤(𝑎)𝑥(𝑎	NOUN
cana-2203	70	21	)	)	PUNCT
cana-2203	70	22	+	+	X
cana-2203	70	23	𝑤(𝑏)𝑥(𝑏	𝑤(𝑏)𝑥(𝑏	NOUN
cana-2203	70	24	)	)	PUNCT
cana-2203	70	25	=	=	SYM
cana-2203	70	26	𝑤(𝑎	𝑤(𝑎	NOUN
cana-2203	70	27	)	)	PUNCT
cana-2203	71	1	[	[	X
cana-2203	71	2	∅(𝑎)𝐶	∅(𝑎)𝐶	X
cana-2203	71	3	+	+	CCONJ
cana-2203	71	4	∅(𝑎	∅(𝑎	PROPN
cana-2203	71	5	)	)	PUNCT
cana-2203	71	6	∫	∫	NOUN
cana-2203	71	7	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	71	8	)	)	PUNCT
cana-2203	71	9	)	)	PUNCT
cana-2203	72	1	[	[	X
cana-2203	72	2	∫	∫	X
cana-2203	72	3	𝐾(s	𝐾(s	X
cana-2203	72	4	,	,	PUNCT
cana-2203	72	5	𝜏	𝜏	NOUN
cana-2203	72	6	)	)	PUNCT
cana-2203	72	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	72	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	72	9	)	)	PUNCT
cana-2203	72	10	)	)	PUNCT
cana-2203	72	11	𝑡0	𝑡0	PROPN
cana-2203	72	12	+	+	CCONJ
cana-2203	72	13	℥	℥	NOUN
cana-2203	72	14	(	(	PUNCT
cana-2203	72	15	s	s	NOUN
cana-2203	72	16	,	,	PUNCT
cana-2203	72	17	𝑥(s	𝑥(	NOUN
cana-2203	72	18	)	)	PUNCT
cana-2203	72	19	)	)	PUNCT
cana-2203	72	20	]	]	PUNCT
cana-2203	73	1	∆s	∆s	NOUN
cana-2203	73	2	𝑎	𝑎	SYM
cana-2203	73	3	𝑎	𝑎	X
cana-2203	73	4	]	]	X
cana-2203	73	5	+	+	X
cana-2203	73	6	𝑤(𝑏	𝑤(𝑏	X
cana-2203	73	7	)	)	PUNCT
cana-2203	74	1	[	[	X
cana-2203	74	2	∅(𝑏)𝐶	∅(𝑏)𝐶	NOUN
cana-2203	74	3	+	+	CCONJ
cana-2203	74	4	∅(𝑏	∅(𝑏	ADJ
cana-2203	74	5	)	)	PUNCT
cana-2203	74	6	∫	∫	NOUN
cana-2203	74	7	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	74	8	)	)	PUNCT
cana-2203	74	9	)	)	PUNCT
cana-2203	75	1	[	[	X
cana-2203	75	2	∫	∫	X
cana-2203	75	3	𝐾(s	𝐾(s	X
cana-2203	75	4	,	,	PUNCT
cana-2203	75	5	𝜏	𝜏	NOUN
cana-2203	75	6	)	)	PUNCT
cana-2203	75	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	75	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	75	9	)	)	PUNCT
cana-2203	75	10	)	)	PUNCT
cana-2203	75	11	𝑡0	𝑡0	PROPN
cana-2203	75	12	+	+	CCONJ
cana-2203	75	13	℥	℥	NOUN
cana-2203	75	14	(	(	PUNCT
cana-2203	75	15	s	s	NOUN
cana-2203	75	16	,	,	PUNCT
cana-2203	75	17	𝑥(s	𝑥(	NOUN
cana-2203	75	18	)	)	PUNCT
cana-2203	75	19	)	)	PUNCT
cana-2203	75	20	]	]	PUNCT
cana-2203	76	1	∆s	∆s	NOUN
cana-2203	76	2	𝑏	𝑏	NOUN
cana-2203	76	3	𝑎	𝑎	NOUN
cana-2203	76	4	]	]	X
cana-2203	76	5	=	=	PUNCT
cana-2203	76	6	𝑤(𝑎)∅(𝑎)𝐶	𝑤(𝑎)∅(𝑎)𝐶	NOUN
cana-2203	76	7	+	+	NOUN
cana-2203	76	8	𝑤(𝑏)∅(𝑏)𝐶	𝑤(𝑏)∅(𝑏)𝐶	SYM
cana-2203	76	9	+	+	NUM
cana-2203	76	10	𝑤𝑏∅(𝑏	𝑤𝑏∅(𝑏	NUM
cana-2203	76	11	)	)	PUNCT
cana-2203	76	12	∫	∫	PROPN
cana-2203	76	13	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	76	14	)	)	PUNCT
cana-2203	76	15	)	)	PUNCT
cana-2203	77	1	[	[	X
cana-2203	77	2	∫	∫	X
cana-2203	77	3	𝐾(s	𝐾(s	X
cana-2203	77	4	,	,	PUNCT
cana-2203	77	5	𝜏	𝜏	NOUN
cana-2203	77	6	)	)	PUNCT
cana-2203	77	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	77	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	77	9	)	)	PUNCT
cana-2203	77	10	)	)	PUNCT
cana-2203	77	11	𝑡0	𝑡0	PROPN
cana-2203	77	12	+	+	CCONJ
cana-2203	77	13	℥	℥	NOUN
cana-2203	77	14	(	(	PUNCT
cana-2203	77	15	s	s	NOUN
cana-2203	77	16	,	,	PUNCT
cana-2203	77	17	𝑥(s	𝑥(	NOUN
cana-2203	77	18	)	)	PUNCT
cana-2203	77	19	)	)	PUNCT
cana-2203	77	20	]	]	PUNCT
cana-2203	78	1	∆s	∆s	NOUN
cana-2203	78	2	𝑏	𝑏	NOUN
cana-2203	78	3	𝑎	𝑎	NOUN
cana-2203	78	4	=	=	X
cana-2203	79	1	[	[	X
cana-2203	79	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	79	3	)	)	PUNCT
cana-2203	79	4	+	+	CCONJ
cana-2203	79	5	𝑤(𝑏)∅(𝑏)]𝐶	𝑤(𝑏)∅(𝑏)]𝐶	VERB
cana-2203	79	6	+	+	NUM
cana-2203	79	7	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	ADJ
cana-2203	79	8	)	)	PUNCT
cana-2203	79	9	∫	∫	PROPN
cana-2203	79	10	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	79	11	)	)	PUNCT
cana-2203	79	12	)	)	PUNCT
cana-2203	80	1	[	[	X
cana-2203	80	2	∫	∫	X
cana-2203	80	3	𝐾(s	𝐾(s	X
cana-2203	80	4	,	,	PUNCT
cana-2203	80	5	𝜏	𝜏	NOUN
cana-2203	80	6	)	)	PUNCT
cana-2203	80	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	80	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	80	9	)	)	PUNCT
cana-2203	80	10	)	)	PUNCT
cana-2203	80	11	𝑡0	𝑡0	PROPN
cana-2203	80	12	+	+	CCONJ
cana-2203	80	13	℥	℥	NOUN
cana-2203	80	14	(	(	PUNCT
cana-2203	80	15	s	s	NOUN
cana-2203	80	16	,	,	PUNCT
cana-2203	80	17	𝑥(s	𝑥(	NOUN
cana-2203	80	18	)	)	PUNCT
cana-2203	80	19	)	)	PUNCT
cana-2203	80	20	]	]	PUNCT
cana-2203	81	1	∆s	∆s	NOUN
cana-2203	81	2	𝑏	𝑏	NOUN
cana-2203	81	3	𝑎	𝑎	VERB
cana-2203	81	4	the	the	DET
cana-2203	81	5	characteristic	characteristic	ADJ
cana-2203	81	6	matrix	matrix	NOUN
cana-2203	81	7	𝐷	𝐷	NOUN
cana-2203	81	8	=	=	PUNCT
cana-2203	82	1	[	[	X
cana-2203	82	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	82	3	)	)	PUNCT
cana-2203	82	4	+	+	NUM
cana-2203	82	5	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NOUN
cana-2203	82	6	)	)	PUNCT
cana-2203	82	7	]	]	PUNCT
cana-2203	82	8	.	.	PUNCT
cana-2203	83	1	hence	hence	ADV
cana-2203	83	2	the	the	DET
cana-2203	83	3	above	above	ADJ
cana-2203	83	4	identity	identity	NOUN
cana-2203	83	5	becomes	become	VERB
cana-2203	83	6	0	0	NUM
cana-2203	83	7	=	=	SYM
cana-2203	83	8	𝐷𝐶	𝐷𝐶	PROPN
cana-2203	83	9	+	+	CCONJ
cana-2203	83	10	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	ADJ
cana-2203	83	11	)	)	PUNCT
cana-2203	83	12	∫	∫	PROPN
cana-2203	83	13	∅−1(𝜎(𝑠	∅−1(𝜎(𝑠	PROPN
cana-2203	83	14	)	)	PUNCT
cana-2203	83	15	)	)	PUNCT
cana-2203	84	1	[	[	X
cana-2203	84	2	∫	∫	X
cana-2203	84	3	𝐾(s	𝐾(s	X
cana-2203	84	4	,	,	PUNCT
cana-2203	84	5	𝜏	𝜏	NOUN
cana-2203	84	6	)	)	PUNCT
cana-2203	84	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	84	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	84	9	)	)	PUNCT
cana-2203	84	10	)	)	PUNCT
cana-2203	84	11	𝑡0	𝑡0	PROPN
cana-2203	84	12	+	+	CCONJ
cana-2203	84	13	℥	℥	NOUN
cana-2203	84	14	(	(	PUNCT
cana-2203	84	15	s	s	NOUN
cana-2203	84	16	,	,	PUNCT
cana-2203	84	17	𝑥(s	𝑥(	NOUN
cana-2203	84	18	)	)	PUNCT
cana-2203	84	19	)	)	PUNCT
cana-2203	84	20	]	]	PUNCT
cana-2203	85	1	∆s	∆s	NOUN
cana-2203	85	2	𝑏	𝑏	NOUN
cana-2203	85	3	𝑎	𝑎	NOUN
cana-2203	85	4	communications	communication	NOUN
cana-2203	85	5	on	on	ADP
cana-2203	85	6	applied	apply	VERB
cana-2203	85	7	nonlinear	nonlinear	ADJ
cana-2203	85	8	analysis	analysis	NOUN
cana-2203	85	9	issn	issn	NOUN
cana-2203	85	10	:	:	PUNCT
cana-2203	85	11	1074	1074	NUM
cana-2203	85	12	-	-	PUNCT
cana-2203	85	13	133x	133x	NUM
cana-2203	85	14	vol	vol	NOUN
cana-2203	85	15	32	32	NUM
cana-2203	85	16	no	no	NOUN
cana-2203	85	17	.	.	PUNCT
cana-2203	86	1	1s	1s	NUM
cana-2203	86	2	(	(	PUNCT
cana-2203	86	3	2025	2025	NUM
cana-2203	86	4	)	)	PUNCT
cana-2203	86	5	391	391	NUM
cana-2203	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	86	7	since	since	SCONJ
cana-2203	86	8	the	the	DET
cana-2203	86	9	homogeneous	homogeneous	ADJ
cana-2203	86	10	bvp	bvp	NOUN
cana-2203	86	11	is	be	AUX
cana-2203	86	12	incompatible	incompatible	ADJ
cana-2203	86	13	,	,	PUNCT
cana-2203	86	14	the	the	DET
cana-2203	86	15	index	index	NOUN
cana-2203	86	16	of	of	ADP
cana-2203	86	17	compatibility	compatibility	NOUN
cana-2203	86	18	is	be	AUX
cana-2203	86	19	zero	zero	NUM
cana-2203	86	20	and	and	CCONJ
cana-2203	86	21	hence	hence	ADV
cana-2203	86	22	𝐷	𝐷	PROPN
cana-2203	86	23	is	be	AUX
cana-2203	86	24	nonsingular	nonsingular	ADJ
cana-2203	86	25	.	.	PUNCT
cana-2203	87	1	𝐷𝐶	𝐷𝐶	NOUN
cana-2203	87	2	=	=	SYM
cana-2203	87	3	−𝑤(𝑏)∅(𝑏	−𝑤(𝑏)∅(𝑏	NOUN
cana-2203	87	4	)	)	PUNCT
cana-2203	87	5	∫	∫	PROPN
cana-2203	87	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	87	7	)	)	PUNCT
cana-2203	87	8	)	)	PUNCT
cana-2203	88	1	[	[	X
cana-2203	88	2	∫	∫	X
cana-2203	88	3	𝐾(s	𝐾(s	X
cana-2203	88	4	,	,	PUNCT
cana-2203	88	5	𝜏	𝜏	NOUN
cana-2203	88	6	)	)	PUNCT
cana-2203	88	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	88	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	88	9	)	)	PUNCT
cana-2203	88	10	)	)	PUNCT
cana-2203	88	11	𝑡0	𝑡0	PROPN
cana-2203	88	12	+	+	CCONJ
cana-2203	88	13	℥	℥	NOUN
cana-2203	88	14	(	(	PUNCT
cana-2203	88	15	s	s	NOUN
cana-2203	88	16	,	,	PUNCT
cana-2203	88	17	𝑥(s	𝑥(	NOUN
cana-2203	88	18	)	)	PUNCT
cana-2203	88	19	)	)	PUNCT
cana-2203	88	20	]	]	PUNCT
cana-2203	89	1	∆s	∆s	NOUN
cana-2203	89	2	𝑏	𝑏	NUM
cana-2203	89	3	𝑎	𝑎	PROPN
cana-2203	89	4	𝐶	𝐶	PROPN
cana-2203	89	5	=	=	SYM
cana-2203	89	6	−𝐷−1𝑤(𝑏)∅(𝑏	−𝐷−1𝑤(𝑏)∅(𝑏	PROPN
cana-2203	89	7	)	)	PUNCT
cana-2203	89	8	∫	∫	PROPN
cana-2203	89	9	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	89	10	)	)	PUNCT
cana-2203	89	11	)	)	PUNCT
cana-2203	90	1	[	[	X
cana-2203	90	2	∫	∫	X
cana-2203	90	3	𝐾(s	𝐾(s	X
cana-2203	90	4	,	,	PUNCT
cana-2203	90	5	𝜏	𝜏	NOUN
cana-2203	90	6	)	)	PUNCT
cana-2203	90	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	90	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	90	9	)	)	PUNCT
cana-2203	90	10	)	)	PUNCT
cana-2203	90	11	𝑡0	𝑡0	PROPN
cana-2203	90	12	+	+	CCONJ
cana-2203	90	13	℥	℥	NOUN
cana-2203	90	14	(	(	PUNCT
cana-2203	90	15	s	s	NOUN
cana-2203	90	16	,	,	PUNCT
cana-2203	90	17	𝑥(s	𝑥(	NOUN
cana-2203	90	18	)	)	PUNCT
cana-2203	90	19	)	)	PUNCT
cana-2203	90	20	]	]	PUNCT
cana-2203	91	1	∆s	∆s	NOUN
cana-2203	91	2	𝑏	𝑏	NOUN
cana-2203	91	3	𝑎	𝑎	NOUN
cana-2203	91	4	from	from	ADP
cana-2203	91	5	equation	equation	NOUN
cana-2203	91	6	(	(	PUNCT
cana-2203	91	7	3.4	3.4	NUM
cana-2203	91	8	)	)	PUNCT
cana-2203	91	9	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2203	91	10	)	)	PUNCT
cana-2203	91	11	=	=	SYM
cana-2203	91	12	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	PROPN
cana-2203	91	13	)	)	PUNCT
cana-2203	91	14	∫	∫	PROPN
cana-2203	91	15	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	91	16	)	)	PUNCT
cana-2203	91	17	)	)	PUNCT
cana-2203	92	1	[	[	X
cana-2203	92	2	∫	∫	X
cana-2203	92	3	𝐾(s	𝐾(s	X
cana-2203	92	4	,	,	PUNCT
cana-2203	92	5	𝜏	𝜏	NOUN
cana-2203	92	6	)	)	PUNCT
cana-2203	92	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	92	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	92	9	)	)	PUNCT
cana-2203	92	10	)	)	PUNCT
cana-2203	92	11	𝑡0	𝑡0	PROPN
cana-2203	92	12	+	+	CCONJ
cana-2203	92	13	℥	℥	NOUN
cana-2203	92	14	(	(	PUNCT
cana-2203	92	15	s	s	NOUN
cana-2203	92	16	,	,	PUNCT
cana-2203	92	17	𝑥(s	𝑥(	NOUN
cana-2203	92	18	)	)	PUNCT
cana-2203	92	19	)	)	PUNCT
cana-2203	92	20	]	]	PUNCT
cana-2203	93	1	∆s	∆s	NOUN
cana-2203	93	2	𝑏	𝑏	NOUN
cana-2203	93	3	𝑎	𝑎	PROPN
cana-2203	93	4	+	+	X
cana-2203	93	5	∅(𝑡	∅(𝑡	NOUN
cana-2203	93	6	)	)	PUNCT
cana-2203	93	7	∫	∫	PROPN
cana-2203	93	8	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	93	9	)	)	PUNCT
cana-2203	93	10	)	)	PUNCT
cana-2203	94	1	[	[	X
cana-2203	94	2	∫	∫	X
cana-2203	94	3	𝐾(s	𝐾(s	X
cana-2203	94	4	,	,	PUNCT
cana-2203	94	5	𝜏	𝜏	NOUN
cana-2203	94	6	)	)	PUNCT
cana-2203	94	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	94	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	94	9	)	)	PUNCT
cana-2203	94	10	)	)	PUNCT
cana-2203	94	11	𝑡0	𝑡0	PROPN
cana-2203	94	12	+	+	CCONJ
cana-2203	94	13	℥	℥	NOUN
cana-2203	94	14	(	(	PUNCT
cana-2203	94	15	s	s	NOUN
cana-2203	94	16	,	,	PUNCT
cana-2203	94	17	𝑥(s	𝑥(	NOUN
cana-2203	94	18	)	)	PUNCT
cana-2203	94	19	)	)	PUNCT
cana-2203	94	20	]	]	PUNCT
cana-2203	95	1	∆s	∆s	NOUN
cana-2203	95	2	𝑡	𝑡	NOUN
cana-2203	95	3	𝑎	𝑎	PROPN
cana-2203	95	4	=	=	SYM
cana-2203	95	5	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏)[∫	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏)[∫	PROPN
cana-2203	95	6	+	+	NUM
cana-2203	95	7	∫	∫	PROPN
cana-2203	95	8	]	]	X
cana-2203	95	9	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	95	10	)	)	PUNCT
cana-2203	95	11	)	)	PUNCT
cana-2203	96	1	𝑏	𝑏	PROPN
cana-2203	96	2	𝑡	𝑡	NOUN
cana-2203	96	3	𝑡	𝑡	NOUN
cana-2203	96	4	𝑎	𝑎	PRON
cana-2203	96	5	[	[	X
cana-2203	96	6	∫	∫	PROPN
cana-2203	96	7	𝐾(s	𝐾(s	PROPN
cana-2203	96	8	,	,	PUNCT
cana-2203	96	9	𝜏	𝜏	NOUN
cana-2203	96	10	)	)	PUNCT
cana-2203	96	11	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	96	12	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	96	13	)	)	PUNCT
cana-2203	96	14	)	)	PUNCT
cana-2203	97	1	𝑡0	𝑡0	PROPN
cana-2203	98	1	+	+	CCONJ
cana-2203	98	2	℥	℥	NOUN
cana-2203	98	3	(	(	PUNCT
cana-2203	98	4	s	s	NOUN
cana-2203	98	5	,	,	PUNCT
cana-2203	98	6	𝑥(s	𝑥(	NOUN
cana-2203	98	7	)	)	PUNCT
cana-2203	98	8	)	)	PUNCT
cana-2203	98	9	]	]	PUNCT
cana-2203	99	1	∆s	∆s	NOUN
cana-2203	99	2	+	+	CCONJ
cana-2203	99	3	∅(𝑡	∅(𝑡	NOUN
cana-2203	99	4	)	)	PUNCT
cana-2203	99	5	∫	∫	PROPN
cana-2203	99	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	99	7	)	)	PUNCT
cana-2203	99	8	)	)	PUNCT
cana-2203	100	1	[	[	X
cana-2203	100	2	∫	∫	X
cana-2203	100	3	𝐾(s	𝐾(s	X
cana-2203	100	4	,	,	PUNCT
cana-2203	100	5	𝜏	𝜏	NOUN
cana-2203	100	6	)	)	PUNCT
cana-2203	100	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	100	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	100	9	)	)	PUNCT
cana-2203	100	10	)	)	PUNCT
cana-2203	100	11	𝑡0	𝑡0	PROPN
cana-2203	100	12	+	+	CCONJ
cana-2203	100	13	℥	℥	NOUN
cana-2203	100	14	(	(	PUNCT
cana-2203	100	15	s	s	NOUN
cana-2203	100	16	,	,	PUNCT
cana-2203	100	17	𝑥(s	𝑥(	NOUN
cana-2203	100	18	)	)	PUNCT
cana-2203	100	19	)	)	PUNCT
cana-2203	100	20	]	]	PUNCT
cana-2203	101	1	∆s	∆s	NOUN
cana-2203	101	2	𝑡	𝑡	NOUN
cana-2203	101	3	𝑎	𝑎	X
cana-2203	101	4	=	=	SYM
cana-2203	101	5	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	PROPN
cana-2203	101	6	)	)	PUNCT
cana-2203	101	7	∫	∫	PROPN
cana-2203	101	8	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	101	9	)	)	PUNCT
cana-2203	101	10	)	)	PUNCT
cana-2203	102	1	𝑡	𝑡	NOUN
cana-2203	103	1	𝑎	𝑎	X
cana-2203	103	2	[	[	X
cana-2203	103	3	∫	∫	PROPN
cana-2203	103	4	𝐾(s	𝐾(s	PROPN
cana-2203	103	5	,	,	PUNCT
cana-2203	103	6	𝜏	𝜏	NOUN
cana-2203	103	7	)	)	PUNCT
cana-2203	103	8	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	103	9	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	103	10	)	)	PUNCT
cana-2203	103	11	)	)	PUNCT
cana-2203	103	12	𝑡0	𝑡0	PROPN
cana-2203	103	13	+	+	CCONJ
cana-2203	103	14	℥	℥	NOUN
cana-2203	103	15	(	(	PUNCT
cana-2203	103	16	s	s	NOUN
cana-2203	103	17	,	,	PUNCT
cana-2203	103	18	𝑥(s	𝑥(	NOUN
cana-2203	103	19	)	)	PUNCT
cana-2203	103	20	)	)	PUNCT
cana-2203	103	21	]	]	PUNCT
cana-2203	104	1	∆s	∆s	NOUN
cana-2203	104	2	+	+	CCONJ
cana-2203	104	3	∅(𝑡	∅(𝑡	NOUN
cana-2203	104	4	)	)	PUNCT
cana-2203	104	5	∫	∫	PROPN
cana-2203	104	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	104	7	)	)	PUNCT
cana-2203	104	8	)	)	PUNCT
cana-2203	105	1	[	[	X
cana-2203	105	2	∫	∫	X
cana-2203	105	3	𝐾(s	𝐾(s	X
cana-2203	105	4	,	,	PUNCT
cana-2203	105	5	𝜏	𝜏	NOUN
cana-2203	105	6	)	)	PUNCT
cana-2203	105	7	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	105	8	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	105	9	)	)	PUNCT
cana-2203	105	10	)	)	PUNCT
cana-2203	105	11	𝑡0	𝑡0	PROPN
cana-2203	105	12	+	+	CCONJ
cana-2203	105	13	℥	℥	NOUN
cana-2203	105	14	(	(	PUNCT
cana-2203	105	15	s	s	NOUN
cana-2203	105	16	,	,	PUNCT
cana-2203	105	17	𝑥(s	𝑥(	NOUN
cana-2203	105	18	)	)	PUNCT
cana-2203	105	19	)	)	PUNCT
cana-2203	105	20	]	]	PUNCT
cana-2203	106	1	∆s	∆s	NOUN
cana-2203	106	2	𝑡	𝑡	X
cana-2203	106	3	𝑎	𝑎	PRON
cana-2203	106	4	−	−	NOUN
cana-2203	106	5	∅(𝑡)𝐷−1𝑤𝑏∅(𝑏	∅(𝑡)𝐷−1𝑤𝑏∅(𝑏	NOUN
cana-2203	106	6	)	)	PUNCT
cana-2203	106	7	∫	∫	NOUN
cana-2203	106	8	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	106	9	)	)	PUNCT
cana-2203	106	10	)	)	PUNCT
cana-2203	107	1	𝑏	𝑏	DET
cana-2203	107	2	𝑡	𝑡	PROPN
cana-2203	107	3	[	[	X
cana-2203	107	4	∫	∫	PROPN
cana-2203	107	5	𝐾(s	𝐾(s	PROPN
cana-2203	107	6	,	,	PUNCT
cana-2203	107	7	𝜏	𝜏	NOUN
cana-2203	107	8	)	)	PUNCT
cana-2203	107	9	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	107	10	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	107	11	)	)	PUNCT
cana-2203	107	12	)	)	PUNCT
cana-2203	108	1	𝑡0	𝑡0	PROPN
cana-2203	108	2	+	+	CCONJ
cana-2203	108	3	℥	℥	NOUN
cana-2203	108	4	(	(	PUNCT
cana-2203	108	5	s	s	NOUN
cana-2203	108	6	,	,	PUNCT
cana-2203	108	7	𝑥(s	𝑥(	NOUN
cana-2203	108	8	)	)	PUNCT
cana-2203	108	9	)	)	PUNCT
cana-2203	108	10	]	]	PUNCT
cana-2203	109	1	∆s	∆s	NOUN
cana-2203	109	2	=	=	SYM
cana-2203	109	3	∅(𝑡)[𝐼	∅(𝑡)[𝐼	NOUN
cana-2203	109	4	−	−	NOUN
cana-2203	109	5	𝐷−1𝑤(𝑏)∅(𝑏	𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	109	6	)	)	PUNCT
cana-2203	109	7	]	]	PUNCT
cana-2203	109	8	∫	∫	PROPN
cana-2203	109	9	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	109	10	)	)	PUNCT
cana-2203	109	11	)	)	PUNCT
cana-2203	110	1	𝑡	𝑡	NOUN
cana-2203	111	1	𝑎	𝑎	X
cana-2203	111	2	[	[	X
cana-2203	111	3	∫	∫	PROPN
cana-2203	111	4	𝐾(s	𝐾(s	PROPN
cana-2203	111	5	,	,	PUNCT
cana-2203	111	6	𝜏	𝜏	NOUN
cana-2203	111	7	)	)	PUNCT
cana-2203	111	8	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	111	9	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	111	10	)	)	PUNCT
cana-2203	111	11	)	)	PUNCT
cana-2203	111	12	𝑡0	𝑡0	PROPN
cana-2203	111	13	+	+	CCONJ
cana-2203	111	14	℥	℥	NOUN
cana-2203	111	15	(	(	PUNCT
cana-2203	111	16	s	s	NOUN
cana-2203	111	17	,	,	PUNCT
cana-2203	111	18	𝑥(s	𝑥(	NOUN
cana-2203	111	19	)	)	PUNCT
cana-2203	111	20	)	)	PUNCT
cana-2203	111	21	]	]	PUNCT
cana-2203	112	1	∆s	∆s	NOUN
cana-2203	112	2	−	−	NOUN
cana-2203	112	3	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	112	4	)	)	PUNCT
cana-2203	112	5	∫	∫	PROPN
cana-2203	112	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	112	7	)	)	PUNCT
cana-2203	112	8	)	)	PUNCT
cana-2203	113	1	𝑏	𝑏	DET
cana-2203	113	2	𝑡	𝑡	PROPN
cana-2203	113	3	[	[	X
cana-2203	113	4	∫	∫	PROPN
cana-2203	113	5	𝐾(s	𝐾(s	PROPN
cana-2203	113	6	,	,	PUNCT
cana-2203	113	7	𝜏	𝜏	NOUN
cana-2203	113	8	)	)	PUNCT
cana-2203	113	9	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	113	10	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	113	11	)	)	PUNCT
cana-2203	113	12	)	)	PUNCT
cana-2203	114	1	𝑡0	𝑡0	PROPN
cana-2203	114	2	+	+	CCONJ
cana-2203	114	3	℥	℥	NOUN
cana-2203	114	4	(	(	PUNCT
cana-2203	114	5	s	s	NOUN
cana-2203	114	6	,	,	PUNCT
cana-2203	114	7	𝑥(s	𝑥(	NOUN
cana-2203	114	8	)	)	PUNCT
cana-2203	114	9	)	)	PUNCT
cana-2203	114	10	]	]	PUNCT
cana-2203	115	1	∆s	∆s	NOUN
cana-2203	115	2	=	=	SYM
cana-2203	115	3	∅(𝑡)𝐷−1[𝐷	∅(𝑡)𝐷−1[𝐷	PROPN
cana-2203	115	4	−	−	PROPN
cana-2203	115	5	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NOUN
cana-2203	115	6	)	)	PUNCT
cana-2203	115	7	]	]	PUNCT
cana-2203	116	1	∫	∫	PROPN
cana-2203	116	2	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	116	3	)	)	PUNCT
cana-2203	116	4	)	)	PUNCT
cana-2203	117	1	𝑡	𝑡	NOUN
cana-2203	118	1	𝑎	𝑎	X
cana-2203	118	2	[	[	X
cana-2203	118	3	∫	∫	PROPN
cana-2203	118	4	𝐾(s	𝐾(s	PROPN
cana-2203	118	5	,	,	PUNCT
cana-2203	118	6	𝜏	𝜏	NOUN
cana-2203	118	7	)	)	PUNCT
cana-2203	118	8	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	118	9	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	118	10	)	)	PUNCT
cana-2203	118	11	)	)	PUNCT
cana-2203	118	12	𝑡0	𝑡0	PROPN
cana-2203	118	13	+	+	CCONJ
cana-2203	118	14	℥	℥	NOUN
cana-2203	118	15	(	(	PUNCT
cana-2203	118	16	s	s	NOUN
cana-2203	118	17	,	,	PUNCT
cana-2203	118	18	𝑥(s	𝑥(	NOUN
cana-2203	118	19	)	)	PUNCT
cana-2203	118	20	)	)	PUNCT
cana-2203	118	21	]	]	PUNCT
cana-2203	119	1	∆s	∆s	NOUN
cana-2203	119	2	−	−	NOUN
cana-2203	119	3	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	119	4	)	)	PUNCT
cana-2203	119	5	∫	∫	PROPN
cana-2203	119	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	119	7	)	)	PUNCT
cana-2203	119	8	)	)	PUNCT
cana-2203	120	1	𝑏	𝑏	DET
cana-2203	120	2	𝑡	𝑡	PROPN
cana-2203	120	3	[	[	X
cana-2203	120	4	∫	∫	PROPN
cana-2203	120	5	𝐾(s	𝐾(s	PROPN
cana-2203	120	6	,	,	PUNCT
cana-2203	120	7	𝜏	𝜏	NOUN
cana-2203	120	8	)	)	PUNCT
cana-2203	120	9	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	120	10	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	120	11	)	)	PUNCT
cana-2203	120	12	)	)	PUNCT
cana-2203	121	1	𝑡0	𝑡0	PROPN
cana-2203	121	2	+	+	CCONJ
cana-2203	121	3	℥	℥	NOUN
cana-2203	121	4	(	(	PUNCT
cana-2203	121	5	s	s	NOUN
cana-2203	121	6	,	,	PUNCT
cana-2203	121	7	𝑥(s	𝑥(	NOUN
cana-2203	121	8	)	)	PUNCT
cana-2203	121	9	)	)	PUNCT
cana-2203	121	10	]	]	PUNCT
cana-2203	122	1	∆s	∆s	NOUN
cana-2203	122	2	=	=	SYM
cana-2203	122	3	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	PROPN
cana-2203	122	4	)	)	PUNCT
cana-2203	122	5	]	]	PUNCT
cana-2203	123	1	∫	∫	PROPN
cana-2203	123	2	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	123	3	)	)	PUNCT
cana-2203	123	4	)	)	PUNCT
cana-2203	124	1	𝑡	𝑡	NOUN
cana-2203	125	1	𝑎	𝑎	X
cana-2203	125	2	[	[	X
cana-2203	125	3	∫	∫	PROPN
cana-2203	125	4	𝐾(s	𝐾(s	PROPN
cana-2203	125	5	,	,	PUNCT
cana-2203	125	6	𝜏	𝜏	NOUN
cana-2203	125	7	)	)	PUNCT
cana-2203	125	8	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	125	9	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	125	10	)	)	PUNCT
cana-2203	125	11	)	)	PUNCT
cana-2203	125	12	𝑡0	𝑡0	PROPN
cana-2203	125	13	+	+	CCONJ
cana-2203	125	14	℥	℥	NOUN
cana-2203	125	15	(	(	PUNCT
cana-2203	125	16	s	s	NOUN
cana-2203	125	17	,	,	PUNCT
cana-2203	125	18	𝑥(s	𝑥(	NOUN
cana-2203	125	19	)	)	PUNCT
cana-2203	125	20	)	)	PUNCT
cana-2203	125	21	]	]	PUNCT
cana-2203	126	1	∆s	∆s	NOUN
cana-2203	126	2	−	−	NOUN
cana-2203	126	3	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	126	4	)	)	PUNCT
cana-2203	126	5	∫	∫	PROPN
cana-2203	126	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	126	7	)	)	PUNCT
cana-2203	126	8	)	)	PUNCT
cana-2203	127	1	𝑏	𝑏	DET
cana-2203	127	2	𝑡	𝑡	PROPN
cana-2203	127	3	[	[	X
cana-2203	127	4	∫	∫	PROPN
cana-2203	127	5	𝐾(s	𝐾(s	PROPN
cana-2203	127	6	,	,	PUNCT
cana-2203	127	7	𝜏	𝜏	NOUN
cana-2203	127	8	)	)	PUNCT
cana-2203	127	9	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	127	10	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	127	11	)	)	PUNCT
cana-2203	127	12	)	)	PUNCT
cana-2203	128	1	𝑡0	𝑡0	PROPN
cana-2203	128	2	+	+	CCONJ
cana-2203	128	3	℥	℥	NOUN
cana-2203	128	4	(	(	PUNCT
cana-2203	128	5	s	s	NOUN
cana-2203	128	6	,	,	PUNCT
cana-2203	128	7	𝑥(s	𝑥(	NOUN
cana-2203	128	8	)	)	PUNCT
cana-2203	128	9	)	)	PUNCT
cana-2203	128	10	]	]	PUNCT
cana-2203	128	11	∆s	∆s	PROPN
cana-2203	128	12	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2203	128	13	)	)	PUNCT
cana-2203	128	14	=	=	SYM
cana-2203	128	15	∫	∫	PROPN
cana-2203	128	16	𝐺(𝑡	𝐺(𝑡	X
cana-2203	128	17	,	,	PUNCT
cana-2203	128	18	𝜎(s	𝜎(	NOUN
cana-2203	128	19	)	)	PUNCT
cana-2203	128	20	)	)	PUNCT
cana-2203	129	1	𝑏	𝑏	PROPN
cana-2203	129	2	𝑎	𝑎	X
cana-2203	129	3	[	[	X
cana-2203	129	4	∫	∫	PROPN
cana-2203	129	5	𝐾(s	𝐾(s	PROPN
cana-2203	129	6	,	,	PUNCT
cana-2203	129	7	𝜏	𝜏	NOUN
cana-2203	129	8	)	)	PUNCT
cana-2203	129	9	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	129	10	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	129	11	)	)	PUNCT
cana-2203	129	12	)	)	PUNCT
cana-2203	129	13	𝑡0	𝑡0	PROPN
cana-2203	129	14	+	+	CCONJ
cana-2203	129	15	℥	℥	NOUN
cana-2203	129	16	(	(	PUNCT
cana-2203	129	17	s	s	NOUN
cana-2203	129	18	,	,	PUNCT
cana-2203	129	19	𝑥(s	𝑥(	NOUN
cana-2203	129	20	)	)	PUNCT
cana-2203	129	21	)	)	PUNCT
cana-2203	129	22	]	]	PUNCT
cana-2203	130	1	∆s	∆s	NOUN
cana-2203	130	2	=	=	SYM
cana-2203	130	3	∫	∫	PROPN
cana-2203	130	4	𝐺(𝑡	𝐺(𝑡	X
cana-2203	130	5	,	,	PUNCT
cana-2203	130	6	𝜎(s	𝜎(	NOUN
cana-2203	130	7	)	)	PUNCT
cana-2203	130	8	)	)	PUNCT
cana-2203	131	1	𝑏	𝑏	PROPN
cana-2203	131	2	𝑎	𝑎	PRON
cana-2203	131	3	𝐻(s	𝐻(	NOUN
cana-2203	131	4	,	,	PUNCT
cana-2203	131	5	𝜏)∆s	𝜏)∆s	NOUN
cana-2203	131	6	.	.	PUNCT
cana-2203	131	7	communications	communication	NOUN
cana-2203	131	8	on	on	ADP
cana-2203	131	9	applied	apply	VERB
cana-2203	131	10	nonlinear	nonlinear	ADJ
cana-2203	131	11	analysis	analysis	NOUN
cana-2203	131	12	issn	issn	NOUN
cana-2203	131	13	:	:	PUNCT
cana-2203	131	14	1074	1074	NUM
cana-2203	131	15	-	-	PUNCT
cana-2203	131	16	133x	133x	NUM
cana-2203	131	17	vol	vol	NOUN
cana-2203	131	18	32	32	NUM
cana-2203	131	19	no	no	NOUN
cana-2203	131	20	.	.	PUNCT
cana-2203	132	1	1s	1s	NUM
cana-2203	132	2	(	(	PUNCT
cana-2203	132	3	2025	2025	NUM
cana-2203	132	4	)	)	PUNCT
cana-2203	132	5	392	392	NUM
cana-2203	132	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	132	7	where	where	SCONJ
cana-2203	132	8	𝐻(𝑠	𝐻(𝑠	PROPN
cana-2203	132	9	,	,	PUNCT
cana-2203	132	10	𝜏	𝜏	NOUN
cana-2203	132	11	)	)	PUNCT
cana-2203	132	12	=	=	SYM
cana-2203	133	1	∫	∫	PROPN
cana-2203	133	2	𝐾(s	𝐾(s	PROPN
cana-2203	133	3	,	,	PUNCT
cana-2203	133	4	𝜏	𝜏	NOUN
cana-2203	133	5	)	)	PUNCT
cana-2203	133	6	𝑥(𝜏)∆𝜏	𝑥(𝜏)∆𝜏	PROPN
cana-2203	133	7	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	133	8	)	)	PUNCT
cana-2203	133	9	)	)	PUNCT
cana-2203	134	1	𝑡0	𝑡0	PROPN
cana-2203	134	2	+	+	CCONJ
cana-2203	134	3	℥	℥	NOUN
cana-2203	134	4	(	(	PUNCT
cana-2203	134	5	s	s	NOUN
cana-2203	134	6	,	,	PUNCT
cana-2203	134	7	𝑥(s	𝑥(	NOUN
cana-2203	134	8	)	)	PUNCT
cana-2203	134	9	)	)	PUNCT
cana-2203	134	10	and	and	CCONJ
cana-2203	134	11	𝐺(𝑡	𝐺(𝑡	PROPN
cana-2203	134	12	,	,	PUNCT
cana-2203	134	13	𝜎(s	𝜎(	NOUN
cana-2203	134	14	)	)	PUNCT
cana-2203	134	15	)	)	PUNCT
cana-2203	134	16	is	be	AUX
cana-2203	134	17	the	the	DET
cana-2203	134	18	greens	green	NOUN
cana-2203	134	19	matrix	matrix	NOUN
cana-2203	134	20	and	and	CCONJ
cana-2203	134	21	is	be	AUX
cana-2203	134	22	given	give	VERB
cana-2203	134	23	by	by	ADP
cana-2203	134	24	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	134	25	,	,	PUNCT
cana-2203	134	26	𝜎(s	𝜎(	NOUN
cana-2203	134	27	)	)	PUNCT
cana-2203	134	28	)	)	PUNCT
cana-2203	135	1	=	=	PRON
cana-2203	135	2	{	{	PUNCT
cana-2203	135	3	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	NOUN
cana-2203	135	4	)	)	PUNCT
cana-2203	135	5	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	135	6	)	)	PUNCT
cana-2203	135	7	)	)	PUNCT
cana-2203	135	8	,	,	PUNCT
cana-2203	135	9	𝑎	𝑎	X
cana-2203	135	10	≤	≤	NUM
cana-2203	135	11	s	s	PART
cana-2203	135	12	≤	≤	NUM
cana-2203	135	13	𝑡	𝑡	PROPN
cana-2203	135	14	≤	≤	NOUN
cana-2203	135	15	𝑏	𝑏	DET
cana-2203	135	16	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	135	17	)	)	PUNCT
cana-2203	135	18	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	135	19	)	)	PUNCT
cana-2203	135	20	)	)	PUNCT
cana-2203	135	21	,	,	PUNCT
cana-2203	135	22	𝑎	𝑎	PROPN
cana-2203	135	23	≤	≤	NUM
cana-2203	135	24	𝑡	𝑡	PROPN
cana-2203	135	25	≤	≤	PROPN
cana-2203	135	26	s	s	PART
cana-2203	135	27	≤	≤	NOUN
cana-2203	135	28	𝑏.	𝑏.	ADV
cana-2203	135	29	next	next	ADV
cana-2203	135	30	,	,	PUNCT
cana-2203	135	31	we	we	PRON
cana-2203	135	32	discuss	discuss	VERB
cana-2203	135	33	the	the	DET
cana-2203	135	34	two	two	NUM
cana-2203	135	35	extreme	extreme	ADJ
cana-2203	135	36	cases	case	NOUN
cana-2203	135	37	of	of	ADP
cana-2203	135	38	𝕋	𝕋	NOUN
cana-2203	135	39	and	and	CCONJ
cana-2203	135	40	obtain	obtain	VERB
cana-2203	135	41	some	some	DET
cana-2203	135	42	interesting	interesting	ADJ
cana-2203	135	43	results	result	NOUN
cana-2203	135	44	.	.	PUNCT
cana-2203	136	1	corollary	corollary	ADJ
cana-2203	136	2	3.2	3.2	NUM
cana-2203	136	3	.	.	PUNCT
cana-2203	137	1	if	if	SCONJ
cana-2203	137	2	𝕋	𝕋	NOUN
cana-2203	137	3	=	=	SYM
cana-2203	137	4	ℝ+	ℝ+	PROPN
cana-2203	137	5	,	,	PUNCT
cana-2203	137	6	we	we	PRON
cana-2203	137	7	have	have	VERB
cana-2203	137	8	𝜎(𝑡	𝜎(𝑡	NUM
cana-2203	137	9	)	)	PUNCT
cana-2203	137	10	=	=	SYM
cana-2203	137	11	𝑡	𝑡	PROPN
cana-2203	137	12	and	and	CCONJ
cana-2203	137	13	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	137	14	)	)	PUNCT
cana-2203	137	15	)	)	PUNCT
cana-2203	138	1	=	=	SYM
cana-2203	138	2	∅−1(s	∅−1(s	NOUN
cana-2203	138	3	)	)	PUNCT
cana-2203	138	4	in	in	ADP
cana-2203	138	5	theorem	theorem	NOUN
cana-2203	138	6	3.1	3.1	NUM
cana-2203	138	7	the	the	DET
cana-2203	138	8	state	state	NOUN
cana-2203	138	9	equation	equation	NOUN
cana-2203	138	10	is	be	AUX
cana-2203	138	11	𝑥′(𝑡	𝑥′(𝑡	NOUN
cana-2203	138	12	)	)	PUNCT
cana-2203	138	13	=	=	SYM
cana-2203	138	14	𝐴(𝑡)𝑥(𝑡	𝐴(𝑡)𝑥(𝑡	NOUN
cana-2203	138	15	)	)	PUNCT
cana-2203	139	1	+	+	CCONJ
cana-2203	139	2	∫	∫	PROPN
cana-2203	139	3	𝐾(𝑡	𝐾(𝑡	NUM
cana-2203	139	4	,	,	PUNCT
cana-2203	139	5	s	s	X
cana-2203	139	6	)	)	PUNCT
cana-2203	139	7	𝑥(s)∆s	𝑥(s)∆s	NOUN
cana-2203	139	8	𝑡	𝑡	NOUN
cana-2203	139	9	𝑡0	𝑡0	NOUN
cana-2203	139	10	+	+	CCONJ
cana-2203	139	11	℥	℥	NOUN
cana-2203	139	12	(	(	PUNCT
cana-2203	139	13	𝑡	𝑡	NOUN
cana-2203	139	14	,	,	PUNCT
cana-2203	139	15	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	139	16	)	)	PUNCT
cana-2203	139	17	)	)	PUNCT
cana-2203	139	18	,	,	PUNCT
cana-2203	139	19	0	0	X
cana-2203	139	20	=	=	SYM
cana-2203	139	21	𝑤(𝑎)𝑥(𝑎	𝑤(𝑎)𝑥(𝑎	NOUN
cana-2203	139	22	)	)	PUNCT
cana-2203	139	23	+	+	CCONJ
cana-2203	139	24	𝑤(𝑏)𝑥(𝑏	𝑤(𝑏)𝑥(𝑏	NOUN
cana-2203	139	25	)	)	PUNCT
cana-2203	139	26	}	}	PUNCT
cana-2203	139	27	(	(	PUNCT
cana-2203	139	28	3.5	3.5	NUM
cana-2203	139	29	)	)	PUNCT
cana-2203	139	30	where	where	SCONJ
cana-2203	139	31	𝐴𝑛×𝑛	𝐴𝑛×𝑛	PROPN
cana-2203	139	32	is	be	AUX
cana-2203	139	33	a	a	DET
cana-2203	139	34	continuous	continuous	ADJ
cana-2203	139	35	matrix	matrix	NOUN
cana-2203	139	36	on	on	ADP
cana-2203	139	37	ℝ+	ℝ+	NOUN
cana-2203	139	38	,	,	PUNCT
cana-2203	139	39	𝐾(𝑡	𝐾(𝑡	ADV
cana-2203	139	40	,	,	PUNCT
cana-2203	139	41	s)𝑛×𝑛	s)𝑛×𝑛	PROPN
cana-2203	139	42	is	be	AUX
cana-2203	139	43	a	a	DET
cana-2203	139	44	continuous	continuous	ADJ
cana-2203	139	45	matrix	matrix	NOUN
cana-2203	139	46	for	for	ADP
cana-2203	139	47	0	0	NUM
cana-2203	139	48	≤	≤	NUM
cana-2203	139	49	s	s	PART
cana-2203	139	50	≤	≤	NUM
cana-2203	139	51	𝑡	𝑡	VERB
cana-2203	139	52	≤	≤	NOUN
cana-2203	139	53	∞	∞	PROPN
cana-2203	140	1	and	and	CCONJ
cana-2203	140	2	𝐹	𝐹	PROPN
cana-2203	140	3	∈	∈	PROPN
cana-2203	140	4	𝐶[ℝ+	𝐶[ℝ+	VERB
cana-2203	140	5	×	×	NOUN
cana-2203	140	6	ℝ+	ℝ+	NOUN
cana-2203	140	7	,	,	PUNCT
cana-2203	140	8	ℝ𝑛	ℝ𝑛	ADP
cana-2203	140	9	]	]	PUNCT
cana-2203	140	10	,	,	PUNCT
cana-2203	140	11	then	then	ADV
cana-2203	140	12	the	the	DET
cana-2203	140	13	solution	solution	NOUN
cana-2203	140	14	of	of	ADP
cana-2203	140	15	(	(	PUNCT
cana-2203	140	16	3.5	3.5	NUM
cana-2203	140	17	)	)	PUNCT
cana-2203	140	18	is	be	AUX
cana-2203	140	19	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	140	20	)	)	PUNCT
cana-2203	140	21	=	=	SYM
cana-2203	140	22	∫	∫	PROPN
cana-2203	141	1	𝐺(𝑡	𝐺(𝑡	X
cana-2203	141	2	,	,	PUNCT
cana-2203	141	3	s	s	NOUN
cana-2203	141	4	)	)	PUNCT
cana-2203	141	5	𝑏	𝑏	PROPN
cana-2203	141	6	𝑎	𝑎	PRON
cana-2203	141	7	𝐻(s	𝐻(	NOUN
cana-2203	141	8	,	,	PUNCT
cana-2203	141	9	𝜏)∆s	𝜏)∆s	ADP
cana-2203	141	10	where	where	SCONJ
cana-2203	141	11	𝐻(s	𝐻(s	X
cana-2203	141	12	,	,	PUNCT
cana-2203	141	13	𝜏	𝜏	NOUN
cana-2203	141	14	)	)	PUNCT
cana-2203	141	15	=	=	SYM
cana-2203	141	16	∫	∫	PROPN
cana-2203	141	17	𝐾(s	𝐾(s	PROPN
cana-2203	141	18	,	,	PUNCT
cana-2203	141	19	𝜏	𝜏	NOUN
cana-2203	141	20	)	)	PUNCT
cana-2203	141	21	𝑥(𝜏)𝑑𝜏	𝑥(𝜏)𝑑𝜏	PART
cana-2203	141	22	s	s	NOUN
cana-2203	141	23	𝑡0	𝑡0	NOUN
cana-2203	141	24	+	+	CCONJ
cana-2203	141	25	℥	℥	X
cana-2203	141	26	(	(	PUNCT
cana-2203	141	27	𝜏	𝜏	NOUN
cana-2203	141	28	,	,	PUNCT
cana-2203	141	29	𝑥(𝜏	𝑥(𝜏	PROPN
cana-2203	141	30	)	)	PUNCT
cana-2203	141	31	)	)	PUNCT
cana-2203	141	32	and	and	CCONJ
cana-2203	141	33	𝐺(𝑡	𝐺(𝑡	ADP
cana-2203	141	34	,	,	PUNCT
cana-2203	141	35	s	s	PART
cana-2203	141	36	)	)	PUNCT
cana-2203	141	37	is	be	AUX
cana-2203	141	38	the	the	DET
cana-2203	141	39	gm	gm	PROPN
cana-2203	141	40	and	and	CCONJ
cana-2203	141	41	is	be	AUX
cana-2203	141	42	given	give	VERB
cana-2203	141	43	by	by	ADP
cana-2203	141	44	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	141	45	,	,	PUNCT
cana-2203	141	46	s	s	PART
cana-2203	141	47	)	)	PUNCT
cana-2203	141	48	=	=	SYM
cana-2203	141	49	{	{	PUNCT
cana-2203	141	50	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	PROPN
cana-2203	141	51	)	)	PUNCT
cana-2203	141	52	∅−1(s	∅−1(s	PROPN
cana-2203	141	53	)	)	PUNCT
cana-2203	141	54	,	,	PUNCT
cana-2203	141	55	𝑎	𝑎	PROPN
cana-2203	141	56	≤	≤	NUM
cana-2203	141	57	s	s	PART
cana-2203	141	58	≤	≤	NUM
cana-2203	141	59	𝑡	𝑡	PROPN
cana-2203	141	60	≤	≤	NOUN
cana-2203	141	61	𝑏	𝑏	DET
cana-2203	141	62	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	PROPN
cana-2203	141	63	)	)	PUNCT
cana-2203	141	64	∅−1(s	∅−1(s	PROPN
cana-2203	141	65	)	)	PUNCT
cana-2203	141	66	,	,	PUNCT
cana-2203	141	67	𝑎	𝑎	PROPN
cana-2203	141	68	≤	≤	NUM
cana-2203	141	69	𝑡	𝑡	PROPN
cana-2203	141	70	≤	≤	PROPN
cana-2203	141	71	s	s	PART
cana-2203	141	72	≤	≤	NOUN
cana-2203	141	73	𝑏.	𝑏.	NOUN
cana-2203	141	74	where	where	SCONJ
cana-2203	141	75	∅(𝑡	∅(𝑡	NOUN
cana-2203	141	76	)	)	PUNCT
cana-2203	141	77	is	be	AUX
cana-2203	141	78	a	a	DET
cana-2203	141	79	fundamental	fundamental	ADJ
cana-2203	141	80	matrix	matrix	NOUN
cana-2203	141	81	and	and	CCONJ
cana-2203	141	82	𝐷	𝐷	NOUN
cana-2203	141	83	=	=	PUNCT
cana-2203	142	1	[	[	X
cana-2203	142	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	142	3	)	)	PUNCT
cana-2203	142	4	+	+	NUM
cana-2203	142	5	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NUM
cana-2203	142	6	)	)	PUNCT
cana-2203	142	7	]	]	PUNCT
cana-2203	142	8	.	.	PUNCT
cana-2203	143	1	corollary	corollary	ADJ
cana-2203	143	2	3.3	3.3	NUM
cana-2203	143	3	.	.	PUNCT
cana-2203	144	1	if	if	SCONJ
cana-2203	144	2	𝕋	𝕋	PROPN
cana-2203	144	3	=	=	SYM
cana-2203	144	4	ℕ	ℕ	PROPN
cana-2203	144	5	,	,	PUNCT
cana-2203	144	6	we	we	PRON
cana-2203	144	7	have	have	VERB
cana-2203	144	8	𝜎(𝜉	𝜎(𝜉	NOUN
cana-2203	144	9	)	)	PUNCT
cana-2203	145	1	=	=	SYM
cana-2203	145	2	𝜉	𝜉	ADP
cana-2203	145	3	+	+	NOUN
cana-2203	145	4	1	1	NUM
cana-2203	145	5	and	and	CCONJ
cana-2203	145	6	∅−1(𝜎(𝜉	∅−1(𝜎(𝜉	NUM
cana-2203	145	7	)	)	PUNCT
cana-2203	145	8	)	)	PUNCT
cana-2203	146	1	=	=	PUNCT
cana-2203	146	2	∅−1(𝜉	∅−1(𝜉	NUM
cana-2203	147	1	+	+	CCONJ
cana-2203	147	2	1	1	X
cana-2203	147	3	)	)	PUNCT
cana-2203	147	4	in	in	ADP
cana-2203	147	5	theorem	theorem	NOUN
cana-2203	147	6	3.1	3.1	NUM
cana-2203	147	7	the	the	DET
cana-2203	147	8	state	state	NOUN
cana-2203	147	9	equation	equation	NOUN
cana-2203	147	10	is	be	AUX
cana-2203	147	11	∆𝑥(𝜉	∆𝑥(𝜉	VERB
cana-2203	147	12	)	)	PUNCT
cana-2203	147	13	=	=	SYM
cana-2203	147	14	𝐴(𝜉)𝑥(𝜉	𝐴(𝜉)𝑥(𝜉	NOUN
cana-2203	147	15	)	)	PUNCT
cana-2203	148	1	+	+	CCONJ
cana-2203	148	2	∑	∑	PROPN
cana-2203	148	3	𝐾(𝜉	𝐾(𝜉	SYM
cana-2203	148	4	,	,	PUNCT
cana-2203	148	5	s	s	NOUN
cana-2203	148	6	)	)	PUNCT
cana-2203	148	7	𝑥(s)𝜉−1	𝑥(s)𝜉−1	NOUN
cana-2203	148	8	s=𝜉0	s=𝜉0	NOUN
cana-2203	148	9	+	+	SYM
cana-2203	148	10	℥	℥	NOUN
cana-2203	148	11	(	(	PUNCT
cana-2203	148	12	𝜉	𝜉	X
cana-2203	148	13	,	,	PUNCT
cana-2203	148	14	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	148	15	)	)	PUNCT
cana-2203	148	16	)	)	PUNCT
cana-2203	148	17	,	,	PUNCT
cana-2203	148	18	0	0	X
cana-2203	148	19	=	=	SYM
cana-2203	148	20	𝑤(𝑎)𝑥(𝑎	𝑤(𝑎)𝑥(𝑎	NOUN
cana-2203	148	21	)	)	PUNCT
cana-2203	148	22	+	+	CCONJ
cana-2203	148	23	𝑤(𝑏)𝑥(𝑏	𝑤(𝑏)𝑥(𝑏	NOUN
cana-2203	148	24	)	)	PUNCT
cana-2203	148	25	}	}	PUNCT
cana-2203	148	26	(	(	PUNCT
cana-2203	148	27	3.6	3.6	NUM
cana-2203	148	28	)	)	PUNCT
cana-2203	148	29	where	where	SCONJ
cana-2203	148	30	𝐴(𝜉	𝐴(𝜉	VERB
cana-2203	148	31	)	)	PUNCT
cana-2203	148	32	and	and	CCONJ
cana-2203	148	33	𝐾(𝜉	𝐾(𝜉	NUM
cana-2203	148	34	,	,	PUNCT
cana-2203	148	35	s	s	PART
cana-2203	148	36	)	)	PUNCT
cana-2203	148	37	are	be	AUX
cana-2203	148	38	𝜂	𝜂	NUM
cana-2203	148	39	×	×	NOUN
cana-2203	148	40	𝜂	𝜂	NOUN
cana-2203	148	41	matrices	matrix	NOUN
cana-2203	148	42	for	for	ADP
cana-2203	148	43	each𝜉	each𝜉	NOUN
cana-2203	148	44	,	,	PUNCT
cana-2203	148	45	s	s	VERB
cana-2203	148	46	∈	∈	PROPN
cana-2203	148	47	ℕ	ℕ	PROPN
cana-2203	148	48	and	and	CCONJ
cana-2203	148	49	𝐹	𝐹	PROPN
cana-2203	148	50	:	:	PUNCT
cana-2203	148	51	ℕ𝜉0	ℕ𝜉0	VERB
cana-2203	149	1	+	+	CCONJ
cana-2203	149	2	×	×	NOUN
cana-2203	149	3	ℕ𝜉0	ℕ𝜉0	NOUN
cana-2203	149	4	+	+	X
cana-2203	149	5	→	→	SYM
cana-2203	149	6	ℝ𝑑	ℝ𝑑	PROPN
cana-2203	149	7	,	,	PUNCT
cana-2203	149	8	ℕ𝜉0	ℕ𝜉0	ADV
cana-2203	149	9	+	+	X
cana-2203	149	10	=	=	SYM
cana-2203	149	11	{	{	PUNCT
cana-2203	149	12	𝜉0	𝜉0	NOUN
cana-2203	149	13	,	,	PUNCT
cana-2203	149	14	𝜉0	𝜉0	NOUN
cana-2203	149	15	+	+	CCONJ
cana-2203	149	16	1	1	NUM
cana-2203	149	17	…	…	PUNCT
cana-2203	149	18	𝜉0	𝜉0	NOUN
cana-2203	149	19	+	+	CCONJ
cana-2203	149	20	𝑘	𝑘	PROPN
cana-2203	149	21	,	,	PUNCT
cana-2203	149	22	…	…	PUNCT
cana-2203	149	23	}	}	PUNCT
cana-2203	149	24	,	,	PUNCT
cana-2203	149	25	𝜉0	𝜉0	NOUN
cana-2203	149	26	,	,	PUNCT
cana-2203	149	27	𝑘	𝑘	PRON
cana-2203	149	28	∈	∈	PROPN
cana-2203	149	29	ℕ	ℕ	PROPN
cana-2203	149	30	then	then	ADV
cana-2203	149	31	the	the	DET
cana-2203	149	32	solution	solution	NOUN
cana-2203	149	33	of	of	ADP
cana-2203	149	34	(	(	PUNCT
cana-2203	149	35	3.6	3.6	NUM
cana-2203	149	36	)	)	PUNCT
cana-2203	149	37	is	be	AUX
cana-2203	149	38	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	149	39	)	)	PUNCT
cana-2203	149	40	=	=	PUNCT
cana-2203	149	41	∑	∑	PUNCT
cana-2203	149	42	𝐺(𝜉	𝐺(𝜉	NOUN
cana-2203	149	43	,	,	PUNCT
cana-2203	149	44	s	s	PART
cana-2203	149	45	+	+	NUM
cana-2203	149	46	1)𝑏−1	1)𝑏−1	NUM
cana-2203	149	47	s=𝑎	s=𝑎	PROPN
cana-2203	149	48	𝐻(s	𝐻(	NOUN
cana-2203	149	49	,	,	PUNCT
cana-2203	149	50	𝜏	𝜏	NOUN
cana-2203	149	51	)	)	PUNCT
cana-2203	149	52	.	.	PUNCT
cana-2203	150	1	where	where	SCONJ
cana-2203	150	2	𝐻(s	𝐻(s	X
cana-2203	150	3	,	,	PUNCT
cana-2203	150	4	𝜏	𝜏	NOUN
cana-2203	150	5	)	)	PUNCT
cana-2203	150	6	=	=	SYM
cana-2203	150	7	∑	∑	PUNCT
cana-2203	150	8	𝐾(s	𝐾(s	X
cana-2203	150	9	,	,	PUNCT
cana-2203	150	10	𝜏	𝜏	NOUN
cana-2203	150	11	)	)	PUNCT
cana-2203	150	12	𝑥(𝜏	𝑥(𝜏	PROPN
cana-2203	150	13	)	)	PUNCT
cana-2203	151	1	+	+	X
cana-2203	151	2	s−1	s−1	PROPN
cana-2203	151	3	𝜏=𝜉0	𝜏=𝜉0	NOUN
cana-2203	151	4	℥	℥	SYM
cana-2203	151	5	(	(	PUNCT
cana-2203	151	6	𝜉	𝜉	X
cana-2203	151	7	,	,	PUNCT
cana-2203	151	8	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	151	9	)	)	PUNCT
cana-2203	151	10	)	)	PUNCT
cana-2203	151	11	and	and	CCONJ
cana-2203	151	12	𝐺(𝜉	𝐺(𝜉	NUM
cana-2203	151	13	,	,	PUNCT
cana-2203	151	14	s	s	PART
cana-2203	151	15	+	+	NOUN
cana-2203	151	16	1	1	NUM
cana-2203	151	17	)	)	PUNCT
cana-2203	151	18	is	be	AUX
cana-2203	151	19	the	the	DET
cana-2203	151	20	gm	gm	PROPN
cana-2203	151	21	and	and	CCONJ
cana-2203	151	22	is	be	AUX
cana-2203	151	23	given	give	VERB
cana-2203	151	24	by	by	ADP
cana-2203	151	25	𝐺(𝜉	𝐺(𝜉	NOUN
cana-2203	151	26	,	,	PUNCT
cana-2203	151	27	s	s	AUX
cana-2203	151	28	+	+	NOUN
cana-2203	151	29	1	1	NUM
cana-2203	151	30	)	)	PUNCT
cana-2203	151	31	=	=	PRON
cana-2203	151	32	{	{	PUNCT
cana-2203	151	33	∅(𝜉)𝐷−1𝑤(𝑎)∅(𝑎	∅(𝜉)𝐷−1𝑤(𝑎)∅(𝑎	PROPN
cana-2203	151	34	)	)	PUNCT
cana-2203	151	35	∅−1(s	∅−1(s	PART
cana-2203	152	1	+	+	ADJ
cana-2203	152	2	1	1	NUM
cana-2203	152	3	)	)	PUNCT
cana-2203	152	4	,	,	PUNCT
cana-2203	152	5	𝑎	𝑎	PROPN
cana-2203	152	6	≤	≤	NUM
cana-2203	152	7	s	s	PART
cana-2203	152	8	≤	≤	NUM
cana-2203	152	9	𝜉	𝜉	ADP
cana-2203	152	10	≤	≤	NOUN
cana-2203	152	11	𝑏	𝑏	DET
cana-2203	152	12	−	−	NUM
cana-2203	152	13	1	1	NUM
cana-2203	152	14	−∅(𝜉)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝜉)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	152	15	)	)	PUNCT
cana-2203	152	16	∅−1(s	∅−1(	NOUN
cana-2203	153	1	+	+	ADJ
cana-2203	153	2	1	1	NUM
cana-2203	153	3	)	)	PUNCT
cana-2203	153	4	,	,	PUNCT
cana-2203	153	5	𝑎	𝑎	PROPN
cana-2203	153	6	≤	≤	NUM
cana-2203	153	7	𝜉	𝜉	ADP
cana-2203	153	8	≤	≤	NUM
cana-2203	153	9	s	s	PART
cana-2203	153	10	≤	≤	NOUN
cana-2203	153	11	𝑏	𝑏	PRON
cana-2203	153	12	−	−	PROPN
cana-2203	153	13	1	1	NUM
cana-2203	153	14	.	.	PUNCT
cana-2203	153	15	where	where	SCONJ
cana-2203	153	16	∅(𝜉	∅(𝜉	NOUN
cana-2203	153	17	)	)	PUNCT
cana-2203	153	18	is	be	AUX
cana-2203	153	19	a	a	DET
cana-2203	153	20	fundamental	fundamental	ADJ
cana-2203	153	21	matrix	matrix	NOUN
cana-2203	153	22	and	and	CCONJ
cana-2203	153	23	𝐷	𝐷	NOUN
cana-2203	153	24	=	=	PUNCT
cana-2203	154	1	[	[	X
cana-2203	154	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	154	3	)	)	PUNCT
cana-2203	154	4	+	+	NUM
cana-2203	154	5	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NUM
cana-2203	154	6	)	)	PUNCT
cana-2203	154	7	]	]	PUNCT
cana-2203	154	8	.	.	PUNCT
cana-2203	155	1	theorem	theorem	VERB
cana-2203	155	2	3.4	3.4	NUM
cana-2203	155	3	.	.	PUNCT
cana-2203	156	1	gm	gm	PROPN
cana-2203	156	2	exhibits	exhibit	VERB
cana-2203	156	3	the	the	DET
cana-2203	156	4	below	below	ADP
cana-2203	156	5	mentioned	mention	VERB
cana-2203	156	6	characteristics	characteristic	NOUN
cana-2203	156	7	:	:	PUNCT
cana-2203	156	8	i.	i.	NOUN
cana-2203	156	9	the	the	DET
cana-2203	156	10	components	component	NOUN
cana-2203	156	11	of	of	ADP
cana-2203	156	12	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	156	13	,	,	PUNCT
cana-2203	156	14	𝜎(s	𝜎(	NOUN
cana-2203	156	15	)	)	PUNCT
cana-2203	156	16	)	)	PUNCT
cana-2203	156	17	are	be	AUX
cana-2203	156	18	functions	function	NOUN
cana-2203	156	19	of	of	ADP
cana-2203	156	20	𝑡	𝑡	NOUN
cana-2203	156	21	withfixeds	withfixed	NOUN
cana-2203	156	22	,	,	PUNCT
cana-2203	156	23	possess	possess	VERB
cana-2203	156	24	rd	rd	NOUN
cana-2203	156	25	-	-	ADJ
cana-2203	156	26	continuous	continuous	ADJ
cana-2203	156	27	delta	delta	NOUN
cana-2203	156	28	differentiable	differentiable	VERB
cana-2203	156	29	on	on	ADP
cana-2203	156	30	the	the	DET
cana-2203	156	31	intervals	interval	NOUN
cana-2203	156	32	[	[	X
cana-2203	156	33	𝑎	𝑎	X
cana-2203	156	34	,	,	PUNCT
cana-2203	156	35	s)and	s)and	PROPN
cana-2203	156	36	(	(	PUNCT
cana-2203	156	37	s	s	PROPN
cana-2203	156	38	,	,	PUNCT
cana-2203	156	39	𝑏	𝑏	NOUN
cana-2203	156	40	]	]	X
cana-2203	156	41	.	.	PUNCT
cana-2203	157	1	at	at	ADP
cana-2203	157	2	the	the	DET
cana-2203	157	3	point	point	NOUN
cana-2203	157	4	𝑡	𝑡	PROPN
cana-2203	157	5	=	=	SYM
cana-2203	157	6	s	s	PROPN
cana-2203	157	7	,	,	PUNCT
cana-2203	157	8	𝐺	𝐺	PROPN
cana-2203	157	9	exhibits	exhibit	VERB
cana-2203	157	10	an	an	DET
cana-2203	157	11	upward	upward	ADJ
cana-2203	157	12	jump	jump	NOUN
cana-2203	157	13	of	of	ADP
cana-2203	157	14	magnitude	magnitude	NOUN
cana-2203	157	15	∅(𝑎	∅(𝑎	NOUN
cana-2203	157	16	)	)	PUNCT
cana-2203	157	17	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	157	18	)	)	PUNCT
cana-2203	157	19	)	)	PUNCT
cana-2203	157	20	.	.	PUNCT
cana-2203	158	1	communications	communication	NOUN
cana-2203	158	2	on	on	ADP
cana-2203	158	3	applied	apply	VERB
cana-2203	158	4	nonlinear	nonlinear	ADJ
cana-2203	158	5	analysis	analysis	NOUN
cana-2203	158	6	issn	issn	NOUN
cana-2203	158	7	:	:	PUNCT
cana-2203	158	8	1074	1074	NUM
cana-2203	158	9	-	-	PUNCT
cana-2203	158	10	133x	133x	NUM
cana-2203	158	11	vol	vol	NOUN
cana-2203	158	12	32	32	NUM
cana-2203	158	13	no	no	NOUN
cana-2203	158	14	.	.	PUNCT
cana-2203	159	1	1s	1s	NUM
cana-2203	159	2	(	(	PUNCT
cana-2203	159	3	2025	2025	NUM
cana-2203	159	4	)	)	PUNCT
cana-2203	159	5	393	393	NUM
cana-2203	159	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	159	7	i.e.	i.e.	X
cana-2203	159	8	,𝐺(s+	,𝐺(s+	PUNCT
cana-2203	159	9	,	,	PUNCT
cana-2203	159	10	𝜎(s	𝜎(s	PROPN
cana-2203	159	11	)	)	PUNCT
cana-2203	159	12	)	)	PUNCT
cana-2203	160	1	−	−	PROPN
cana-2203	161	1	𝐺(s−	𝐺(s−	PROPN
cana-2203	161	2	,	,	PUNCT
cana-2203	161	3	𝜎(s	𝜎(	NOUN
cana-2203	161	4	)	)	PUNCT
cana-2203	161	5	)	)	PUNCT
cana-2203	162	1	=	=	SYM
cana-2203	162	2	∅(𝑎	∅(𝑎	ADJ
cana-2203	162	3	)	)	PUNCT
cana-2203	162	4	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	162	5	)	)	PUNCT
cana-2203	162	6	)	)	PUNCT
cana-2203	162	7	.	.	PUNCT
cana-2203	163	1	ii	ii	PROPN
cana-2203	163	2	.	.	PUNCT
cana-2203	164	1	𝐺(𝑡	𝐺(𝑡	X
cana-2203	164	2	,	,	PUNCT
cana-2203	164	3	𝜎(s))is	𝜎(s))is	NOUN
cana-2203	164	4	a	a	DET
cana-2203	164	5	formal	formal	ADJ
cana-2203	164	6	solution	solution	NOUN
cana-2203	164	7	of	of	ADP
cana-2203	164	8	the	the	DET
cana-2203	164	9	homogeneous	homogeneous	ADJ
cana-2203	164	10	bvp	bvp	NOUN
cana-2203	164	11	𝑥∆(𝑡	𝑥∆(𝑡	PRON
cana-2203	164	12	)	)	PUNCT
cana-2203	164	13	=	=	SYM
cana-2203	164	14	𝐴(𝑡)𝑥(𝑡	𝐴(𝑡)𝑥(𝑡	NOUN
cana-2203	164	15	)	)	PUNCT
cana-2203	164	16	0	0	NUM
cana-2203	165	1	=	=	SYM
cana-2203	165	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	165	3	)	)	PUNCT
cana-2203	166	1	+	+	CCONJ
cana-2203	166	2	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	X
cana-2203	166	3	)	)	PUNCT
cana-2203	166	4	}	}	PUNCT
cana-2203	166	5	(	(	PUNCT
cana-2203	166	6	3.7	3.7	NUM
cana-2203	166	7	)	)	PUNCT
cana-2203	166	8	𝐺	𝐺	PROPN
cana-2203	166	9	,	,	PUNCT
cana-2203	166	10	ceases	cease	VERB
cana-2203	166	11	to	to	PART
cana-2203	166	12	be	be	AUX
cana-2203	166	13	a	a	DET
cana-2203	166	14	true	true	ADJ
cana-2203	166	15	solution	solution	NOUN
cana-2203	166	16	solely	solely	ADV
cana-2203	166	17	due	due	ADJ
cana-2203	166	18	to	to	ADP
cana-2203	166	19	its	its	PRON
cana-2203	166	20	jump	jump	NOUN
cana-2203	166	21	condition	condition	NOUN
cana-2203	166	22	at	at	ADP
cana-2203	166	23	𝑡	𝑡	PROPN
cana-2203	166	24	=	=	PROPN
cana-2203	166	25	s.	s.	PROPN
cana-2203	166	26	iii	iii	PROPN
cana-2203	166	27	.	.	PUNCT
cana-2203	167	1	the	the	DET
cana-2203	167	2	green	green	PROPN
cana-2203	167	3	’s	’s	PART
cana-2203	167	4	matrix	matrix	NOUN
cana-2203	167	5	𝐺(𝑡	𝐺(𝑡	ADP
cana-2203	167	6	,	,	PUNCT
cana-2203	167	7	𝜎(s	𝜎(	NOUN
cana-2203	167	8	)	)	PUNCT
cana-2203	167	9	)	)	PUNCT
cana-2203	168	1	having	have	VERB
cana-2203	168	2	the	the	DET
cana-2203	168	3	properties	property	NOUN
cana-2203	168	4	(	(	PUNCT
cana-2203	168	5	i	i	NOUN
cana-2203	168	6	)	)	PUNCT
cana-2203	168	7	and	and	CCONJ
cana-2203	168	8	(	(	PUNCT
cana-2203	168	9	ii	ii	NOUN
cana-2203	168	10	)	)	PUNCT
cana-2203	168	11	is	be	AUX
cana-2203	168	12	unique	unique	ADJ
cana-2203	168	13	.	.	PUNCT
cana-2203	169	1	proof:(i	proof:(i	NOUN
cana-2203	169	2	)	)	PUNCT
cana-2203	169	3	.	.	PUNCT
cana-2203	170	1	the	the	DET
cana-2203	170	2	gm	gm	PROPN
cana-2203	170	3	for	for	ADP
cana-2203	170	4	the	the	DET
cana-2203	170	5	bvp	bvp	NOUN
cana-2203	170	6	𝑥∆(𝑡	𝑥∆(𝑡	PRON
cana-2203	170	7	)	)	PUNCT
cana-2203	170	8	=	=	SYM
cana-2203	170	9	𝐴(𝑡)𝑥(𝑡	𝐴(𝑡)𝑥(𝑡	NOUN
cana-2203	170	10	)	)	PUNCT
cana-2203	170	11	0	0	NUM
cana-2203	171	1	=	=	SYM
cana-2203	171	2	𝑤(𝑎)∅(𝑎	𝑤(𝑎)∅(𝑎	NUM
cana-2203	171	3	)	)	PUNCT
cana-2203	172	1	+	+	CCONJ
cana-2203	172	2	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	ADJ
cana-2203	172	3	)	)	PUNCT
cana-2203	172	4	.	.	PUNCT
cana-2203	173	1	is	be	AUX
cana-2203	173	2	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	173	3	,	,	PUNCT
cana-2203	173	4	𝜎(s	𝜎(	NOUN
cana-2203	173	5	)	)	PUNCT
cana-2203	173	6	)	)	PUNCT
cana-2203	174	1	=	=	PRON
cana-2203	174	2	{	{	PUNCT
cana-2203	174	3	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	∅(𝑡)𝐷−1𝑤(𝑎)∅(𝑎	NOUN
cana-2203	174	4	)	)	PUNCT
cana-2203	174	5	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	174	6	)	)	PUNCT
cana-2203	174	7	)	)	PUNCT
cana-2203	174	8	,	,	PUNCT
cana-2203	174	9	𝑎	𝑎	X
cana-2203	174	10	≤	≤	NUM
cana-2203	174	11	s	s	PART
cana-2203	174	12	≤	≤	NUM
cana-2203	174	13	𝑡	𝑡	PROPN
cana-2203	174	14	≤	≤	NOUN
cana-2203	174	15	𝑏	𝑏	DET
cana-2203	174	16	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	−∅(𝑡)𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	174	17	)	)	PUNCT
cana-2203	174	18	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	174	19	)	)	PUNCT
cana-2203	174	20	)	)	PUNCT
cana-2203	174	21	,	,	PUNCT
cana-2203	174	22	𝑎	𝑎	PROPN
cana-2203	174	23	≤	≤	NUM
cana-2203	174	24	𝑡	𝑡	PROPN
cana-2203	174	25	≤	≤	PROPN
cana-2203	174	26	s	s	PART
cana-2203	174	27	≤	≤	NOUN
cana-2203	174	28	𝑏	𝑏	NUM
cana-2203	174	29	where	where	SCONJ
cana-2203	174	30	𝐺	𝐺	PROPN
cana-2203	174	31	is	be	AUX
cana-2203	174	32	considered	consider	VERB
cana-2203	174	33	as	as	ADP
cana-2203	174	34	a	a	DET
cana-2203	174	35	function	function	NOUN
cana-2203	174	36	of	of	ADP
cana-2203	174	37	𝑡	𝑡	PROPN
cana-2203	174	38	with	with	ADP
cana-2203	174	39	fixed	fix	VERB
cana-2203	174	40	s	s	PROPN
cana-2203	174	41	,	,	PUNCT
cana-2203	174	42	the	the	DET
cana-2203	174	43	gm	gm	PROPN
cana-2203	174	44	can	can	AUX
cana-2203	174	45	be	be	AUX
cana-2203	174	46	written	write	VERB
cana-2203	174	47	as	as	ADP
cana-2203	174	48	𝐺(𝑡	𝐺(𝑡	X
cana-2203	174	49	,	,	PUNCT
cana-2203	174	50	𝜎(s	𝜎(	NOUN
cana-2203	174	51	)	)	PUNCT
cana-2203	174	52	)	)	PUNCT
cana-2203	175	1	=	=	PRON
cana-2203	175	2	{	{	PUNCT
cana-2203	175	3	∅(𝑡)𝐻+	∅(𝑡)𝐻+	PROPN
cana-2203	175	4	,	,	PUNCT
cana-2203	175	5	s	s	PART
cana-2203	175	6	≤	≤	NOUN
cana-2203	175	7	𝑡	𝑡	X
cana-2203	175	8	∅(𝑡)𝐻−	∅(𝑡)𝐻−	PROPN
cana-2203	175	9	,	,	PUNCT
cana-2203	175	10	𝑡	𝑡	PROPN
cana-2203	175	11	≤	≤	ADJ
cana-2203	175	12	s.	s.	PROPN
cana-2203	175	13	where	where	SCONJ
cana-2203	175	14	the	the	DET
cana-2203	175	15	matrices	matrix	NOUN
cana-2203	175	16	𝐻+	𝐻+	X
cana-2203	175	17	=	=	SYM
cana-2203	175	18	𝐷−1𝑤(𝑎)∅(𝑎	𝐷−1𝑤(𝑎)∅(𝑎	PROPN
cana-2203	175	19	)	)	PUNCT
cana-2203	175	20	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	175	21	)	)	PUNCT
cana-2203	175	22	)	)	PUNCT
cana-2203	175	23	𝐻−	𝐻−	NOUN
cana-2203	175	24	=	=	SYM
cana-2203	175	25	−𝐷−1𝑤(𝑏)∅(𝑏	−𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	175	26	)	)	PUNCT
cana-2203	175	27	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	175	28	)	)	PUNCT
cana-2203	175	29	)	)	PUNCT
cana-2203	175	30	they	they	PRON
cana-2203	175	31	are	be	AUX
cana-2203	175	32	independent	independent	ADJ
cana-2203	175	33	of	of	ADP
cana-2203	175	34	𝑡.consequently	𝑡.consequently	ADV
cana-2203	175	35	,	,	PUNCT
cana-2203	175	36	the	the	DET
cana-2203	175	37	components	component	NOUN
cana-2203	175	38	of	of	ADP
cana-2203	175	39	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	175	40	,	,	PUNCT
cana-2203	175	41	𝜎(s	𝜎(	NOUN
cana-2203	175	42	)	)	PUNCT
cana-2203	175	43	)	)	PUNCT
cana-2203	175	44	possess	possess	VERB
cana-2203	175	45	rd	rd	NOUN
cana-2203	175	46	-	-	ADJ
cana-2203	175	47	continuous	continuous	ADJ
cana-2203	175	48	first	first	ADJ
cana-2203	175	49	delta	delta	NOUN
cana-2203	175	50	derivatives	derivative	NOUN
cana-2203	175	51	with	with	ADP
cana-2203	175	52	respect	respect	NOUN
cana-2203	175	53	to𝑡on	to𝑡on	NOUN
cana-2203	176	1	[	[	X
cana-2203	176	2	𝑎	𝑎	X
cana-2203	176	3	,	,	PUNCT
cana-2203	176	4	s	s	PART
cana-2203	176	5	)	)	PUNCT
cana-2203	176	6	and	and	CCONJ
cana-2203	176	7	(	(	PUNCT
cana-2203	176	8	s	s	X
cana-2203	176	9	,	,	PUNCT
cana-2203	176	10	𝑏	𝑏	NOUN
cana-2203	176	11	]	]	PUNCT
cana-2203	176	12	.	.	PUNCT
cana-2203	177	1	further	far	ADV
cana-2203	177	2	𝐻+	𝐻+	CCONJ
cana-2203	177	3	−	−	PROPN
cana-2203	177	4	𝐻−	𝐻−	PROPN
cana-2203	177	5	=	=	SYM
cana-2203	177	6	𝐷−1𝑤(𝑎)∅(𝑎	𝐷−1𝑤(𝑎)∅(𝑎	PROPN
cana-2203	177	7	)	)	PUNCT
cana-2203	177	8	∅−1(𝜎(s))+𝐷−1𝑤(𝑏)∅(𝑏	∅−1(𝜎(s))+𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	177	9	)	)	PUNCT
cana-2203	177	10	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	177	11	)	)	PUNCT
cana-2203	177	12	)	)	PUNCT
cana-2203	178	1	=	=	PUNCT
cana-2203	178	2	𝐷−1[𝑤(𝑎)∅(𝑎	𝐷−1[𝑤(𝑎)∅(𝑎	PROPN
cana-2203	178	3	)	)	PUNCT
cana-2203	179	1	+	+	CCONJ
cana-2203	179	2	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NOUN
cana-2203	179	3	)	)	PUNCT
cana-2203	179	4	]	]	PUNCT
cana-2203	180	1	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	180	2	)	)	PUNCT
cana-2203	180	3	)	)	PUNCT
cana-2203	181	1	=	=	PUNCT
cana-2203	182	1	𝐷−1𝐷	𝐷−1𝐷	NOUN
cana-2203	182	2	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	182	3	)	)	PUNCT
cana-2203	182	4	)	)	PUNCT
cana-2203	183	1	=	=	PUNCT
cana-2203	183	2	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	183	3	)	)	PUNCT
cana-2203	183	4	)	)	PUNCT
cana-2203	183	5	.	.	PUNCT
cana-2203	184	1	therefore	therefore	ADV
cana-2203	184	2	𝐺(s+	𝐺(s+	NUM
cana-2203	184	3	,	,	PUNCT
cana-2203	184	4	𝜎(s	𝜎(s	PROPN
cana-2203	184	5	)	)	PUNCT
cana-2203	184	6	)	)	PUNCT
cana-2203	185	1	−	−	PROPN
cana-2203	186	1	𝐺(s−	𝐺(s−	PROPN
cana-2203	186	2	,	,	PUNCT
cana-2203	186	3	𝜎(s	𝜎(	NOUN
cana-2203	186	4	)	)	PUNCT
cana-2203	186	5	)	)	PUNCT
cana-2203	187	1	=	=	PUNCT
cana-2203	188	1	∅(s)𝐻+	∅(s)𝐻+	NOUN
cana-2203	188	2	−	−	NOUN
cana-2203	188	3	∅(s)𝐻−	∅(s)𝐻−	NOUN
cana-2203	189	1	=	=	PUNCT
cana-2203	190	1	∅(s)[𝐻+	∅(s)[𝐻+	NOUN
cana-2203	191	1	−	−	NOUN
cana-2203	191	2	𝐻−	𝐻−	NOUN
cana-2203	191	3	]	]	X
cana-2203	191	4	=	=	SYM
cana-2203	191	5	∅(s)∅−1(𝜎(s	∅(s)∅−1(𝜎(	NOUN
cana-2203	191	6	)	)	PUNCT
cana-2203	191	7	)	)	PUNCT
cana-2203	191	8	.	.	PUNCT
cana-2203	192	1	(	(	PUNCT
cana-2203	192	2	ii	ii	NOUN
cana-2203	192	3	)	)	PUNCT
cana-2203	192	4	.	.	PUNCT
cana-2203	193	1	we	we	PRON
cana-2203	193	2	want	want	VERB
cana-2203	193	3	to	to	PART
cana-2203	193	4	show	show	VERB
cana-2203	193	5	that	that	SCONJ
cana-2203	193	6	𝐺(𝑡	𝐺(𝑡	ADP
cana-2203	193	7	,	,	PUNCT
cana-2203	193	8	𝜎(s	𝜎(	NOUN
cana-2203	193	9	)	)	PUNCT
cana-2203	193	10	)	)	PUNCT
cana-2203	193	11	is	be	AUX
cana-2203	193	12	a	a	DET
cana-2203	193	13	matrix	matrix	NOUN
cana-2203	193	14	solution	solution	NOUN
cana-2203	193	15	of	of	ADP
cana-2203	193	16	homogeneous	homogeneous	ADJ
cana-2203	193	17	bvp	bvp	NOUN
cana-2203	193	18	.	.	PUNCT
cana-2203	194	1	the	the	DET
cana-2203	194	2	representation	representation	NOUN
cana-2203	194	3	of	of	ADP
cana-2203	194	4	𝐺(𝑡	𝐺(𝑡	NOUN
cana-2203	194	5	,	,	PUNCT
cana-2203	194	6	𝜎(s))is	𝜎(s))is	NOUN
cana-2203	194	7	the	the	DET
cana-2203	194	8	solution	solution	NOUN
cana-2203	194	9	of	of	ADP
cana-2203	194	10	(	(	PUNCT
cana-2203	194	11	3.7	3.7	NUM
cana-2203	194	12	)	)	PUNCT
cana-2203	194	13	on	on	ADP
cana-2203	194	14	[	[	X
cana-2203	194	15	𝑎	𝑎	X
cana-2203	194	16	,	,	PUNCT
cana-2203	194	17	s	s	PART
cana-2203	194	18	)	)	PUNCT
cana-2203	194	19	and	and	CCONJ
cana-2203	194	20	(	(	PUNCT
cana-2203	194	21	s	s	X
cana-2203	194	22	,	,	PUNCT
cana-2203	194	23	𝑏	𝑏	NOUN
cana-2203	194	24	]	]	X
cana-2203	194	25	.	.	PUNCT
cana-2203	195	1	now	now	ADV
cana-2203	195	2	to	to	PART
cana-2203	195	3	show	show	VERB
cana-2203	195	4	that	that	SCONJ
cana-2203	195	5	𝐺(𝑡	𝐺(𝑡	ADP
cana-2203	195	6	,	,	PUNCT
cana-2203	195	7	𝜎(s	𝜎(	NOUN
cana-2203	195	8	)	)	PUNCT
cana-2203	195	9	)	)	PUNCT
cana-2203	195	10	satisfies	satisfy	VERB
cana-2203	195	11	the	the	DET
cana-2203	195	12	given	give	VERB
cana-2203	195	13	boundary	boundary	ADJ
cana-2203	195	14	condition	condition	NOUN
cana-2203	195	15	,	,	PUNCT
cana-2203	195	16	we	we	PRON
cana-2203	195	17	obtain	obtain	VERB
cana-2203	195	18	𝑤(𝑎)𝐺(𝑎	𝑤(𝑎)𝐺(𝑎	PROPN
cana-2203	195	19	,	,	PUNCT
cana-2203	195	20	𝜎(s	𝜎(	NOUN
cana-2203	195	21	)	)	PUNCT
cana-2203	195	22	)	)	PUNCT
cana-2203	196	1	+	+	CCONJ
cana-2203	196	2	𝑤(𝑏)𝐺(𝑏	𝑤(𝑏)𝐺(𝑏	NOUN
cana-2203	196	3	,	,	PUNCT
cana-2203	196	4	𝜎(s	𝜎(	NOUN
cana-2203	196	5	)	)	PUNCT
cana-2203	196	6	)	)	PUNCT
cana-2203	197	1	=	=	PUNCT
cana-2203	198	1	𝑤(𝑎)∅(𝑎)𝐻−	𝑤(𝑎)∅(𝑎)𝐻−	NOUN
cana-2203	198	2	+	+	CCONJ
cana-2203	198	3	𝑤(𝑏)∅(𝑏)𝐻+	𝑤(𝑏)∅(𝑏)𝐻+	X
cana-2203	198	4	=	=	PUNCT
cana-2203	198	5	𝑤(𝑎)∅(𝑎)𝐻−	𝑤(𝑎)∅(𝑎)𝐻−	NOUN
cana-2203	198	6	+	+	CCONJ
cana-2203	198	7	𝑤(𝑏)∅(𝑏)𝐻+	𝑤(𝑏)∅(𝑏)𝐻+	X
cana-2203	198	8	+	+	X
cana-2203	198	9	𝑤(𝑏)∅(𝑏)𝐻−	𝑤(𝑏)∅(𝑏)𝐻−	ADJ
cana-2203	198	10	−	−	PROPN
cana-2203	198	11	𝑤(𝑏)∅(𝑏)𝐻−	𝑤(𝑏)∅(𝑏)𝐻−	ADJ
cana-2203	198	12	communications	communication	NOUN
cana-2203	198	13	on	on	ADP
cana-2203	198	14	applied	apply	VERB
cana-2203	198	15	nonlinear	nonlinear	ADJ
cana-2203	198	16	analysis	analysis	NOUN
cana-2203	198	17	issn	issn	NOUN
cana-2203	198	18	:	:	PUNCT
cana-2203	198	19	1074	1074	NUM
cana-2203	198	20	-	-	PUNCT
cana-2203	198	21	133x	133x	NUM
cana-2203	198	22	vol	vol	NOUN
cana-2203	198	23	32	32	NUM
cana-2203	198	24	no	no	NOUN
cana-2203	198	25	.	.	PUNCT
cana-2203	199	1	1s	1s	NUM
cana-2203	199	2	(	(	PUNCT
cana-2203	199	3	2025	2025	NUM
cana-2203	199	4	)	)	PUNCT
cana-2203	199	5	394	394	NUM
cana-2203	199	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	199	7	=	=	SYM
cana-2203	199	8	𝑤(𝑎)∅(𝑎)𝐻−	𝑤(𝑎)∅(𝑎)𝐻−	NOUN
cana-2203	199	9	+	+	CCONJ
cana-2203	199	10	𝑤(𝑏)∅(𝑏)𝐻−	𝑤(𝑏)∅(𝑏)𝐻−	ADJ
cana-2203	199	11	+	+	CCONJ
cana-2203	199	12	𝑤(𝑏)∅(𝑏)[𝐻+	𝑤(𝑏)∅(𝑏)[𝐻+	NOUN
cana-2203	199	13	−	−	NOUN
cana-2203	199	14	𝐻−	𝐻−	NOUN
cana-2203	199	15	]	]	X
cana-2203	199	16	=	=	SYM
cana-2203	199	17	𝑤(𝑎)[∅(𝑎	𝑤(𝑎)[∅(𝑎	NOUN
cana-2203	199	18	)	)	PUNCT
cana-2203	199	19	+	+	NUM
cana-2203	199	20	𝑤(𝑏)∅(𝑏)]𝐻−	𝑤(𝑏)∅(𝑏)]𝐻−	VERB
cana-2203	199	21	+	+	CCONJ
cana-2203	199	22	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	ADJ
cana-2203	199	23	)	)	PUNCT
cana-2203	199	24	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	199	25	)	)	PUNCT
cana-2203	199	26	)	)	PUNCT
cana-2203	200	1	=	=	PUNCT
cana-2203	200	2	𝐷𝐻−	𝐷𝐻−	ADP
cana-2203	200	3	+	+	NUM
cana-2203	200	4	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	NUM
cana-2203	200	5	)	)	PUNCT
cana-2203	200	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	200	7	)	)	PUNCT
cana-2203	200	8	)	)	PUNCT
cana-2203	201	1	=	=	SYM
cana-2203	201	2	𝐷	𝐷	PROPN
cana-2203	201	3	[	[	PUNCT
cana-2203	201	4	−𝐷−1𝑤(𝑏)∅(𝑏	−𝐷−1𝑤(𝑏)∅(𝑏	NOUN
cana-2203	201	5	)	)	PUNCT
cana-2203	201	6	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	201	7	)	)	PUNCT
cana-2203	201	8	)	)	PUNCT
cana-2203	201	9	]	]	PUNCT
cana-2203	202	1	+	+	CCONJ
cana-2203	202	2	𝑤(𝑏)∅(𝑏)∅	𝑤(𝑏)∅(𝑏)∅	NOUN
cana-2203	202	3	−1(𝜎(s	−1(𝜎(s	NOUN
cana-2203	202	4	)	)	PUNCT
cana-2203	202	5	)	)	PUNCT
cana-2203	203	1	=	=	SYM
cana-2203	203	2	−𝑤(𝑏)∅(𝑏	−𝑤(𝑏)∅(𝑏	X
cana-2203	203	3	)	)	PUNCT
cana-2203	203	4	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	203	5	)	)	PUNCT
cana-2203	203	6	)	)	PUNCT
cana-2203	204	1	+	+	CCONJ
cana-2203	204	2	𝑤(𝑏)∅(𝑏	𝑤(𝑏)∅(𝑏	X
cana-2203	204	3	)	)	PUNCT
cana-2203	204	4	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	204	5	)	)	PUNCT
cana-2203	204	6	)	)	PUNCT
cana-2203	205	1	=	=	SYM
cana-2203	205	2	0	0	PUNCT
cana-2203	206	1	thus	thus	ADV
cana-2203	206	2	𝐺	𝐺	PROPN
cana-2203	206	3	is	be	AUX
cana-2203	206	4	a	a	DET
cana-2203	206	5	solution	solution	NOUN
cana-2203	206	6	of	of	ADP
cana-2203	206	7	the	the	DET
cana-2203	206	8	homogeneous	homogeneous	ADJ
cana-2203	206	9	bvp	bvp	NOUN
cana-2203	206	10	.	.	PUNCT
cana-2203	207	1	(	(	PUNCT
cana-2203	207	2	iii	iii	NOUN
cana-2203	207	3	)	)	PUNCT
cana-2203	207	4	.	.	PUNCT
cana-2203	208	1	now	now	ADV
cana-2203	208	2	,	,	PUNCT
cana-2203	208	3	let	let	VERB
cana-2203	208	4	us	we	PRON
cana-2203	208	5	prove	prove	VERB
cana-2203	208	6	the	the	DET
cana-2203	208	7	uniqueness	uniqueness	NOUN
cana-2203	208	8	of	of	ADP
cana-2203	208	9	g	g	NOUN
cana-2203	208	10	,	,	PUNCT
cana-2203	208	11	let	let	VERB
cana-2203	208	12	𝐺1(𝑡	𝐺1(𝑡	NOUN
cana-2203	208	13	,	,	PUNCT
cana-2203	208	14	𝜎(s	𝜎(	NOUN
cana-2203	208	15	)	)	PUNCT
cana-2203	208	16	)	)	PUNCT
cana-2203	208	17	and	and	CCONJ
cana-2203	208	18	𝐺2(𝑡	𝐺2(𝑡	PROPN
cana-2203	208	19	,	,	PUNCT
cana-2203	208	20	𝜎(s	𝜎(s	PROPN
cana-2203	208	21	)	)	PUNCT
cana-2203	208	22	)	)	PUNCT
cana-2203	208	23	be	be	VERB
cana-2203	208	24	rd	rd	NOUN
cana-2203	208	25	-	-	ADJ
cana-2203	208	26	continuous	continuous	ADJ
cana-2203	208	27	matrices	matrix	NOUN
cana-2203	208	28	with	with	ADP
cana-2203	208	29	(	(	PUNCT
cana-2203	208	30	i	i	NOUN
cana-2203	208	31	)	)	PUNCT
cana-2203	208	32	and	and	CCONJ
cana-2203	208	33	(	(	PUNCT
cana-2203	208	34	ii	ii	NOUN
cana-2203	208	35	)	)	PUNCT
cana-2203	208	36	.	.	PUNCT
cana-2203	209	1	write	write	VERB
cana-2203	209	2	𝐿(𝑡	𝐿(𝑡	PRON
cana-2203	209	3	,	,	PUNCT
cana-2203	209	4	s	s	PART
cana-2203	209	5	)	)	PUNCT
cana-2203	209	6	=	=	SYM
cana-2203	209	7	𝐺1(𝑡	𝐺1(𝑡	NOUN
cana-2203	209	8	,	,	PUNCT
cana-2203	209	9	𝜎(s	𝜎(	NOUN
cana-2203	209	10	)	)	PUNCT
cana-2203	209	11	)	)	PUNCT
cana-2203	210	1	−	−	PROPN
cana-2203	210	2	𝐺2(𝑡	𝐺2(𝑡	PROPN
cana-2203	210	3	,	,	PUNCT
cana-2203	210	4	𝜎(s	𝜎(s	PROPN
cana-2203	210	5	)	)	PUNCT
cana-2203	210	6	)	)	PUNCT
cana-2203	210	7	.	.	PUNCT
cana-2203	211	1	clearly	clearly	ADV
cana-2203	211	2	𝐿	𝐿	PROPN
cana-2203	211	3	satisfies	satisfy	VERB
cana-2203	211	4	the	the	DET
cana-2203	211	5	following	follow	VERB
cana-2203	211	6	at𝑡	at𝑡	PROPN
cana-2203	211	7	=	=	SYM
cana-2203	211	8	s	s	PART
cana-2203	211	9	𝐿(s+	𝐿(s+	PROPN
cana-2203	211	10	,	,	PUNCT
cana-2203	211	11	s	s	NOUN
cana-2203	211	12	)	)	PUNCT
cana-2203	211	13	−	−	PROPN
cana-2203	211	14	𝐿(s−	𝐿(s−	PROPN
cana-2203	211	15	,	,	PUNCT
cana-2203	211	16	s	s	PART
cana-2203	211	17	)	)	PUNCT
cana-2203	211	18	=	=	NOUN
cana-2203	212	1	[	[	X
cana-2203	212	2	𝐺1(s+	𝐺1(s+	ADP
cana-2203	212	3	,	,	PUNCT
cana-2203	212	4	𝜎(s	𝜎(	NOUN
cana-2203	212	5	)	)	PUNCT
cana-2203	212	6	)	)	PUNCT
cana-2203	213	1	−	−	ADP
cana-2203	213	2	𝐺2(s+	𝐺2(s+	NOUN
cana-2203	213	3	,	,	PUNCT
cana-2203	213	4	𝜎(s	𝜎(	NOUN
cana-2203	213	5	)	)	PUNCT
cana-2203	213	6	)	)	PUNCT
cana-2203	213	7	]	]	PUNCT
cana-2203	214	1	−	−	PUNCT
cana-2203	215	1	[	[	X
cana-2203	215	2	𝐺1(s−	𝐺1(s−	X
cana-2203	215	3	,	,	PUNCT
cana-2203	215	4	𝜎(s	𝜎(	NOUN
cana-2203	215	5	)	)	PUNCT
cana-2203	215	6	)	)	PUNCT
cana-2203	215	7	−	−	ADP
cana-2203	215	8	𝐺2(s−	𝐺2(s−	NOUN
cana-2203	215	9	,	,	PUNCT
cana-2203	215	10	𝜎(s	𝜎(	NOUN
cana-2203	215	11	)	)	PUNCT
cana-2203	215	12	)	)	PUNCT
cana-2203	215	13	]	]	PUNCT
cana-2203	216	1	=	=	PUNCT
cana-2203	217	1	[	[	X
cana-2203	217	2	𝐺1(s+	𝐺1(s+	ADP
cana-2203	217	3	,	,	PUNCT
cana-2203	217	4	𝜎(s	𝜎(	NOUN
cana-2203	217	5	)	)	PUNCT
cana-2203	217	6	)	)	PUNCT
cana-2203	218	1	−	−	PUNCT
cana-2203	219	1	𝐺1(s−	𝐺1(s−	NOUN
cana-2203	219	2	,	,	PUNCT
cana-2203	219	3	𝜎(s	𝜎(	NOUN
cana-2203	219	4	)	)	PUNCT
cana-2203	219	5	)	)	PUNCT
cana-2203	219	6	]	]	PUNCT
cana-2203	220	1	−	−	PUNCT
cana-2203	221	1	[	[	X
cana-2203	221	2	𝐺2(s+	𝐺2(s+	NOUN
cana-2203	221	3	,	,	PUNCT
cana-2203	221	4	𝜎(s	𝜎(	NOUN
cana-2203	221	5	)	)	PUNCT
cana-2203	221	6	)	)	PUNCT
cana-2203	221	7	−	−	ADP
cana-2203	221	8	𝐺2(s−	𝐺2(s−	NOUN
cana-2203	221	9	,	,	PUNCT
cana-2203	221	10	𝜎(s	𝜎(	NOUN
cana-2203	221	11	)	)	PUNCT
cana-2203	221	12	)	)	PUNCT
cana-2203	221	13	]	]	PUNCT
cana-2203	221	14	=	=	PUNCT
cana-2203	221	15	∅(s	∅(s	NOUN
cana-2203	221	16	)	)	PUNCT
cana-2203	221	17	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	221	18	)	)	PUNCT
cana-2203	221	19	)	)	PUNCT
cana-2203	222	1	−	−	ADP
cana-2203	222	2	∅(s	∅(s	NOUN
cana-2203	222	3	)	)	PUNCT
cana-2203	222	4	∅−1(𝜎(s	∅−1(𝜎(	NOUN
cana-2203	222	5	)	)	PUNCT
cana-2203	222	6	)	)	PUNCT
cana-2203	223	1	=	=	PUNCT
cana-2203	223	2	0	0	X
cana-2203	223	3	.	.	PUNCT
cana-2203	224	1	thus	thus	ADV
cana-2203	224	2	,	,	PUNCT
cana-2203	224	3	𝐿	𝐿	PROPN
cana-2203	224	4	exhibits	exhibit	VERB
cana-2203	224	5	a	a	DET
cana-2203	224	6	removable	removable	ADJ
cana-2203	224	7	jump	jump	NOUN
cana-2203	224	8	condition	condition	NOUN
cana-2203	224	9	at	at	ADP
cana-2203	224	10	𝑡	𝑡	PROPN
cana-2203	224	11	=	=	SYM
cana-2203	224	12	s	s	PROPN
cana-2203	224	13	and	and	CCONJ
cana-2203	224	14	𝑤(𝑎)𝐿(𝑎	𝑤(𝑎)𝐿(𝑎	PROPN
cana-2203	224	15	,	,	PUNCT
cana-2203	224	16	s	s	PART
cana-2203	224	17	)	)	PUNCT
cana-2203	224	18	+	+	CCONJ
cana-2203	224	19	𝑤(𝑏)𝐿(𝑏	𝑤(𝑏)𝐿(𝑏	NOUN
cana-2203	224	20	,	,	PUNCT
cana-2203	224	21	s	s	NOUN
cana-2203	224	22	)	)	PUNCT
cana-2203	224	23	=	=	SYM
cana-2203	224	24	𝑤(𝑎)[𝐺1(𝑎	𝑤(𝑎)[𝐺1(𝑎	NOUN
cana-2203	224	25	,	,	PUNCT
cana-2203	224	26	𝜎(s	𝜎(	NOUN
cana-2203	224	27	)	)	PUNCT
cana-2203	224	28	)	)	PUNCT
cana-2203	225	1	−	−	PROPN
cana-2203	225	2	𝐺2(𝑎	𝐺2(𝑎	PROPN
cana-2203	225	3	,	,	PUNCT
cana-2203	225	4	𝜎(s	𝜎(	NOUN
cana-2203	225	5	)	)	PUNCT
cana-2203	225	6	)	)	PUNCT
cana-2203	225	7	]	]	PUNCT
cana-2203	226	1	+	+	CCONJ
cana-2203	226	2	𝑤(𝑏)[𝐺1(𝑏	𝑤(𝑏)[𝐺1(𝑏	NOUN
cana-2203	226	3	,	,	PUNCT
cana-2203	226	4	𝜎(s	𝜎(	NOUN
cana-2203	226	5	)	)	PUNCT
cana-2203	226	6	)	)	PUNCT
cana-2203	227	1	−	−	PUNCT
cana-2203	228	1	𝐺2(𝑏	𝐺2(𝑏	PROPN
cana-2203	228	2	,	,	PUNCT
cana-2203	228	3	𝜎(s	𝜎(	NOUN
cana-2203	228	4	)	)	PUNCT
cana-2203	228	5	)	)	PUNCT
cana-2203	228	6	]	]	PUNCT
cana-2203	229	1	=	=	PUNCT
cana-2203	230	1	[	[	X
cana-2203	230	2	𝑤(𝑎)𝐺1(𝑎	𝑤(𝑎)𝐺1(𝑎	NOUN
cana-2203	230	3	,	,	PUNCT
cana-2203	230	4	𝜎(s	𝜎(	NOUN
cana-2203	230	5	)	)	PUNCT
cana-2203	230	6	)	)	PUNCT
cana-2203	231	1	+	+	CCONJ
cana-2203	231	2	𝑤(𝑏)𝐺1(𝑏	𝑤(𝑏)𝐺1(𝑏	NOUN
cana-2203	231	3	,	,	PUNCT
cana-2203	231	4	𝜎(s	𝜎(	NOUN
cana-2203	231	5	)	)	PUNCT
cana-2203	231	6	)	)	PUNCT
cana-2203	231	7	]	]	PUNCT
cana-2203	232	1	−	−	PUNCT
cana-2203	233	1	[	[	X
cana-2203	233	2	𝑤(𝑎)𝐺2(𝑎	𝑤(𝑎)𝐺2(𝑎	PROPN
cana-2203	233	3	,	,	PUNCT
cana-2203	233	4	𝜎(s	𝜎(	NOUN
cana-2203	233	5	)	)	PUNCT
cana-2203	233	6	)	)	PUNCT
cana-2203	234	1	+	+	CCONJ
cana-2203	234	2	𝑤(𝑏)𝐺2(𝑏	𝑤(𝑏)𝐺2(𝑏	PROPN
cana-2203	234	3	,	,	PUNCT
cana-2203	234	4	𝜎(s	𝜎(	NOUN
cana-2203	234	5	)	)	PUNCT
cana-2203	234	6	)	)	PUNCT
cana-2203	234	7	]	]	PUNCT
cana-2203	235	1	=	=	PUNCT
cana-2203	235	2	0	0	X
cana-2203	235	3	.	.	PUNCT
cana-2203	236	1	since	since	SCONJ
cana-2203	236	2	𝐿	𝐿	PROPN
cana-2203	236	3	is	be	AUX
cana-2203	236	4	a	a	DET
cana-2203	236	5	solution	solution	NOUN
cana-2203	236	6	of	of	ADP
cana-2203	236	7	homogeneous	homogeneous	ADJ
cana-2203	236	8	bvp	bvp	NOUN
cana-2203	236	9	and	and	CCONJ
cana-2203	236	10	𝐿(𝑡	𝐿(𝑡	PRON
cana-2203	236	11	,	,	PUNCT
cana-2203	236	12	s	s	PART
cana-2203	236	13	)	)	PUNCT
cana-2203	236	14	=	=	SYM
cana-2203	236	15	0	0	X
cana-2203	236	16	.	.	PUNCT
cana-2203	237	1	i.e.	i.e.	X
cana-2203	237	2	,	,	PUNCT
cana-2203	237	3	𝐺1(𝑡	𝐺1(𝑡	NOUN
cana-2203	237	4	,	,	PUNCT
cana-2203	237	5	𝜎(s	𝜎(	NOUN
cana-2203	237	6	)	)	PUNCT
cana-2203	237	7	)	)	PUNCT
cana-2203	238	1	−	−	PROPN
cana-2203	238	2	𝐺2(𝑡	𝐺2(𝑡	PROPN
cana-2203	238	3	,	,	PUNCT
cana-2203	238	4	𝜎(s	𝜎(s	PROPN
cana-2203	238	5	)	)	PUNCT
cana-2203	238	6	)	)	PUNCT
cana-2203	239	1	=	=	SYM
cana-2203	239	2	0	0	NUM
cana-2203	239	3	implies	imply	VERB
cana-2203	239	4	𝐺1(𝑡	𝐺1(𝑡	NOUN
cana-2203	239	5	,	,	PUNCT
cana-2203	239	6	𝜎(s	𝜎(	NOUN
cana-2203	239	7	)	)	PUNCT
cana-2203	239	8	)	)	PUNCT
cana-2203	240	1	=	=	SYM
cana-2203	240	2	𝐺2(𝑡	𝐺2(𝑡	PROPN
cana-2203	240	3	,	,	PUNCT
cana-2203	240	4	𝜎(s	𝜎(s	PROPN
cana-2203	240	5	)	)	PUNCT
cana-2203	240	6	)	)	PUNCT
cana-2203	240	7	.	.	PUNCT
cana-2203	241	1	thus	thus	ADV
cana-2203	241	2	g	g	PROPN
cana-2203	241	3	is	be	AUX
cana-2203	241	4	unique	unique	ADJ
cana-2203	241	5	.	.	PUNCT
cana-2203	242	1	theorem	theorem	ADJ
cana-2203	242	2	3.5	3.5	NUM
cana-2203	242	3	.	.	PUNCT
cana-2203	243	1	assume	assume	VERB
cana-2203	243	2	that	that	SCONJ
cana-2203	243	3	(	(	PUNCT
cana-2203	243	4	a	a	X
cana-2203	243	5	)	)	PUNCT
cana-2203	243	6	|∅(𝑡)|	|∅(𝑡)|	NOUN
cana-2203	243	7	≤	≤	NUM
cana-2203	243	8	𝑅	𝑅	PROPN
cana-2203	243	9	,	,	PUNCT
cana-2203	243	10	(	(	PUNCT
cana-2203	243	11	b	b	NOUN
cana-2203	243	12	)	)	PUNCT
cana-2203	243	13	|∅(𝑡	|∅(𝑡	ADJ
cana-2203	243	14	)	)	PUNCT
cana-2203	243	15	∅−1(𝜎(𝑡))|	∅−1(𝜎(𝑡))|	NOUN
cana-2203	243	16	≤	≤	PUNCT
cana-2203	243	17	𝑆	𝑆	PROPN
cana-2203	243	18	,	,	PUNCT
cana-2203	243	19	(	(	PUNCT
cana-2203	243	20	c	c	X
cana-2203	243	21	)	)	PUNCT
cana-2203	243	22	sup∫	sup∫	NOUN
cana-2203	243	23	|𝐾(s	|𝐾(	NOUN
cana-2203	243	24	,	,	PUNCT
cana-2203	243	25	𝜏)||𝑥(𝜏)|∆𝜏	𝜏)||𝑥(𝜏)|∆𝜏	X
cana-2203	243	26	+	+	NUM
cana-2203	243	27	℥	℥	NOUN
cana-2203	243	28	(	(	PUNCT
cana-2203	243	29	s	s	NOUN
cana-2203	243	30	,	,	PUNCT
cana-2203	243	31	𝑥(s	𝑥(	NOUN
cana-2203	243	32	)	)	PUNCT
cana-2203	243	33	)	)	PUNCT
cana-2203	243	34	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	243	35	)	)	PUNCT
cana-2203	243	36	)	)	PUNCT
cana-2203	244	1	𝑡0	𝑡0	PROPN
cana-2203	244	2	≤	≤	PUNCT
cana-2203	244	3	𝑇|𝑥(𝑡)|	𝑇|𝑥(𝑡)|	PROPN
cana-2203	244	4	,	,	PUNCT
cana-2203	244	5	where	where	SCONJ
cana-2203	244	6	𝑅	𝑅	PROPN
cana-2203	244	7	,	,	PUNCT
cana-2203	244	8	𝑆	𝑆	PROPN
cana-2203	244	9	,	,	PUNCT
cana-2203	244	10	𝑇	𝑇	PROPN
cana-2203	244	11	>	>	X
cana-2203	244	12	0	0	PROPN
cana-2203	244	13	.	.	PUNCT
cana-2203	245	1	then	then	ADV
cana-2203	245	2	solution	solution	NOUN
cana-2203	245	3	of	of	ADP
cana-2203	245	4	(	(	PUNCT
cana-2203	245	5	1.1	1.1	NUM
cana-2203	245	6	)	)	PUNCT
cana-2203	245	7	is	be	AUX
cana-2203	245	8	uniformly	uniformly	ADV
cana-2203	245	9	stable	stable	ADJ
cana-2203	245	10	.	.	PUNCT
cana-2203	246	1	proof	proof	NOUN
cana-2203	246	2	:	:	PUNCT
cana-2203	246	3	for	for	ADP
cana-2203	246	4	any	any	PRON
cana-2203	246	5	휀	휀	NOUN
cana-2203	246	6	>	>	X
cana-2203	246	7	0	0	NUM
cana-2203	246	8	,	,	PUNCT
cana-2203	246	9	let	let	VERB
cana-2203	246	10	𝛿(휀	𝛿(휀	NOUN
cana-2203	246	11	)	)	PUNCT
cana-2203	246	12	<	<	X
cana-2203	246	13	𝜀	𝜀	X
cana-2203	246	14	𝑅𝑒𝑆𝑇(𝑡,𝑎	𝑅𝑒𝑆𝑇(𝑡,𝑎	NOUN
cana-2203	246	15	)	)	PUNCT
cana-2203	246	16	and	and	CCONJ
cana-2203	246	17	|𝐶|	|𝐶|	NOUN
cana-2203	246	18	≤	≤	PROPN
cana-2203	246	19	𝛿𝜀.	𝛿𝜀.	ADV
cana-2203	246	20	suppose	suppose	VERB
cana-2203	246	21	∃	∃	PROPN
cana-2203	246	22	,	,	PUNCT
cana-2203	246	23	𝑡1	𝑡1	NOUN
cana-2203	246	24	≥	≥	NUM
cana-2203	246	25	𝑎	𝑎	X
cana-2203	246	26	such	such	ADJ
cana-2203	246	27	that	that	SCONJ
cana-2203	246	28	|𝑥(𝑡1)|	|𝑥(𝑡1)|	PROPN
cana-2203	246	29	=	=	PUNCT
cana-2203	246	30	휀	휀	NOUN
cana-2203	246	31	and	and	CCONJ
cana-2203	246	32	|𝑥(𝑡)|	|𝑥(𝑡)|	X
cana-2203	246	33	<	<	X
cana-2203	246	34	휀	휀	X
cana-2203	246	35	on	on	ADP
cana-2203	246	36	[	[	X
cana-2203	246	37	𝑎	𝑎	X
cana-2203	246	38	,	,	PUNCT
cana-2203	246	39	𝑡1	𝑡1	NOUN
cana-2203	246	40	)	)	PUNCT
cana-2203	246	41	.	.	PUNCT
cana-2203	247	1	from	from	ADP
cana-2203	247	2	(	(	PUNCT
cana-2203	247	3	3.4	3.4	NUM
cana-2203	247	4	)	)	PUNCT
cana-2203	247	5	,	,	PUNCT
cana-2203	247	6	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	247	7	)	)	PUNCT
cana-2203	247	8	=	=	PRON
cana-2203	247	9	∅(𝑡)𝐶	∅(𝑡)𝐶	PROPN
cana-2203	247	10	+	+	CCONJ
cana-2203	247	11	∅(𝑡	∅(𝑡	NOUN
cana-2203	247	12	)	)	PUNCT
cana-2203	247	13	∫	∫	PROPN
cana-2203	247	14	∅−1(𝜎(s))[∫	∅−1(𝜎(s))[∫	PROPN
cana-2203	247	15	𝐾(s	𝐾(s	PROPN
cana-2203	247	16	,	,	PUNCT
cana-2203	247	17	𝜏)𝑥(𝜏)∆𝜏	𝜏)𝑥(𝜏)∆𝜏	PROPN
cana-2203	247	18	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	247	19	)	)	PUNCT
cana-2203	247	20	)	)	PUNCT
cana-2203	247	21	𝑡0	𝑡0	PROPN
cana-2203	247	22	𝑡	𝑡	PROPN
cana-2203	247	23	𝑎	𝑎	X
cana-2203	247	24	+	+	X
cana-2203	247	25	℥	℥	NOUN
cana-2203	247	26	(	(	PUNCT
cana-2203	247	27	s	s	NOUN
cana-2203	247	28	,	,	PUNCT
cana-2203	247	29	𝑥(s)]∆s	𝑥(s)]∆s	X
cana-2203	247	30	on	on	ADP
cana-2203	247	31	[	[	X
cana-2203	247	32	𝑎	𝑎	X
cana-2203	247	33	,	,	PUNCT
cana-2203	247	34	𝑡1	𝑡1	NOUN
cana-2203	247	35	]	]	PUNCT
cana-2203	247	36	communications	communication	NOUN
cana-2203	247	37	on	on	ADP
cana-2203	247	38	applied	apply	VERB
cana-2203	247	39	nonlinear	nonlinear	ADJ
cana-2203	247	40	analysis	analysis	NOUN
cana-2203	247	41	issn	issn	NOUN
cana-2203	247	42	:	:	PUNCT
cana-2203	247	43	1074	1074	NUM
cana-2203	247	44	-	-	PUNCT
cana-2203	247	45	133x	133x	NUM
cana-2203	247	46	vol	vol	NOUN
cana-2203	247	47	32	32	NUM
cana-2203	247	48	no	no	NOUN
cana-2203	247	49	.	.	PUNCT
cana-2203	248	1	1s	1s	NUM
cana-2203	248	2	(	(	PUNCT
cana-2203	248	3	2025	2025	NUM
cana-2203	248	4	)	)	PUNCT
cana-2203	248	5	395	395	NUM
cana-2203	248	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	248	7	|𝑥(𝑡)|	|𝑥(𝑡)|	PROPN
cana-2203	248	8	≤	≤	X
cana-2203	248	9	|∅(𝑡)||𝐶|	|∅(𝑡)||𝐶|	NOUN
cana-2203	249	1	+	+	CCONJ
cana-2203	249	2	|∅(𝑡)|	|∅(𝑡)|	NOUN
cana-2203	249	3	∫	∫	NOUN
cana-2203	249	4	|	|	CCONJ
cana-2203	249	5	∅−1(𝜎(s))|[∫	∅−1(𝜎(s))|[∫	NOUN
cana-2203	249	6	|𝐾(s	|𝐾(	NOUN
cana-2203	249	7	,	,	PUNCT
cana-2203	249	8	𝜏)||𝑥(𝜏)|∆𝜏	𝜏)||𝑥(𝜏)|∆𝜏	PROPN
cana-2203	249	9	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	249	10	)	)	PUNCT
cana-2203	249	11	)	)	PUNCT
cana-2203	250	1	𝑡0	𝑡0	PROPN
cana-2203	250	2	𝑡	𝑡	PROPN
cana-2203	251	1	𝑎	𝑎	PROPN
cana-2203	251	2	+	+	NOUN
cana-2203	251	3	|	|	ADV
cana-2203	251	4	℥	℥	SYM
cana-2203	251	5	(s	(s	NOUN
cana-2203	251	6	,	,	PUNCT
cana-2203	251	7	𝑥(s)|]∆s	𝑥(s)|]∆s	PROPN
cana-2203	251	8	≤	≤	PROPN
cana-2203	251	9	𝑅𝛿𝜀	𝑅𝛿𝜀	PROPN
cana-2203	251	10	+	+	CCONJ
cana-2203	251	11	𝑆𝑇	𝑆𝑇	PROPN
cana-2203	251	12	∫	∫	PROPN
cana-2203	251	13	|𝑥(𝑡)|∆𝑡	|𝑥(𝑡)|∆𝑡	PROPN
cana-2203	251	14	𝑡	𝑡	PROPN
cana-2203	251	15	𝑎	𝑎	VERB
cana-2203	251	16	by	by	ADP
cana-2203	251	17	lemma	lemma	PROPN
cana-2203	251	18	2.6	2.6	NUM
cana-2203	251	19	,	,	PUNCT
cana-2203	251	20	|𝑥(𝑡)|	|𝑥(𝑡)|	PROPN
cana-2203	251	21	≤	≤	NUM
cana-2203	251	22	𝑅𝛿𝜀𝑒𝑆𝑇(𝑡	𝑅𝛿𝜀𝑒𝑆𝑇(𝑡	NOUN
cana-2203	251	23	,	,	PUNCT
cana-2203	251	24	𝑎	𝑎	NOUN
cana-2203	251	25	)	)	PUNCT
cana-2203	251	26	≤	≤	NOUN
cana-2203	251	27	𝑅𝑒𝑆𝑇(𝑡	𝑅𝑒𝑆𝑇(𝑡	PUNCT
cana-2203	251	28	,	,	PUNCT
cana-2203	251	29	𝑎	𝑎	NOUN
cana-2203	251	30	)	)	PUNCT
cana-2203	251	31	𝜀	𝜀	NOUN
cana-2203	251	32	𝑅𝑒𝑆𝑇(𝑡,𝑎	𝑅𝑒𝑆𝑇(𝑡,𝑎	NOUN
cana-2203	251	33	)	)	PUNCT
cana-2203	251	34	=	=	PUNCT
cana-2203	252	1	휀	휀	PRON
cana-2203	252	2	therefore	therefore	ADV
cana-2203	252	3	|𝑥(𝑡1)|	|𝑥(𝑡1)|	PROPN
cana-2203	252	4	<	<	X
cana-2203	252	5	휀	휀	NOUN
cana-2203	252	6	,	,	PUNCT
cana-2203	252	7	which	which	PRON
cana-2203	252	8	contradicts	contradict	VERB
cana-2203	252	9	.	.	PUNCT
cana-2203	253	1	thus	thus	ADV
cana-2203	253	2	,	,	PUNCT
cana-2203	253	3	the	the	DET
cana-2203	253	4	solution	solution	NOUN
cana-2203	253	5	of	of	ADP
cana-2203	253	6	(	(	PUNCT
cana-2203	253	7	1.1	1.1	NUM
cana-2203	253	8	)	)	PUNCT
cana-2203	253	9	is	be	AUX
cana-2203	253	10	uniformly	uniformly	ADV
cana-2203	253	11	stable	stable	ADJ
cana-2203	253	12	.	.	PUNCT
cana-2203	254	1	theorem	theorem	VERB
cana-2203	254	2	3.6	3.6	NUM
cana-2203	254	3	.	.	PUNCT
cana-2203	255	1	assume	assume	VERB
cana-2203	255	2	(	(	PUNCT
cana-2203	255	3	a	a	X
cana-2203	255	4	)	)	PUNCT
cana-2203	255	5	|∅(𝑡)||𝐶|	|∅(𝑡)||𝐶|	NOUN
cana-2203	255	6	≤	≤	NUM
cana-2203	255	7	𝑅𝑒𝑃(𝑡0	𝑅𝑒𝑃(𝑡0	PROPN
cana-2203	255	8	,	,	PUNCT
cana-2203	255	9	𝑡	𝑡	X
cana-2203	255	10	)	)	PUNCT
cana-2203	255	11	(	(	PUNCT
cana-2203	255	12	b	b	X
cana-2203	255	13	)	)	PUNCT
cana-2203	255	14	|∅(𝑡	|∅(𝑡	ADJ
cana-2203	255	15	)	)	PUNCT
cana-2203	255	16	∅−1(𝜎(𝑡))|	∅−1(𝜎(𝑡))|	NOUN
cana-2203	255	17	≤	≤	PUNCT
cana-2203	255	18	𝑆𝑒𝑃(0	𝑆𝑒𝑃(0	PROPN
cana-2203	255	19	,	,	PUNCT
cana-2203	255	20	𝑡	𝑡	NOUN
cana-2203	255	21	)	)	PUNCT
cana-2203	255	22	,	,	PUNCT
cana-2203	255	23	(	(	PUNCT
cana-2203	255	24	c	c	X
cana-2203	255	25	)	)	PUNCT
cana-2203	255	26	sup∫	sup∫	NOUN
cana-2203	255	27	|𝐾(s	|𝐾(	NOUN
cana-2203	255	28	,	,	PUNCT
cana-2203	255	29	𝜏)||𝑥(𝜏)|∆𝜏	𝜏)||𝑥(𝜏)|∆𝜏	X
cana-2203	255	30	+	+	NUM
cana-2203	255	31	℥	℥	NOUN
cana-2203	255	32	(	(	PUNCT
cana-2203	255	33	s	s	NOUN
cana-2203	255	34	,	,	PUNCT
cana-2203	255	35	𝑥(s	𝑥(	NOUN
cana-2203	255	36	)	)	PUNCT
cana-2203	255	37	)	)	PUNCT
cana-2203	255	38	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	255	39	)	)	PUNCT
cana-2203	255	40	)	)	PUNCT
cana-2203	256	1	𝑡0	𝑡0	PROPN
cana-2203	256	2	≤	≤	NOUN
cana-2203	256	3	𝐿𝑒𝑃(s	𝐿𝑒𝑃(s	PROPN
cana-2203	256	4	,	,	PUNCT
cana-2203	256	5	0)𝑥(s	0)𝑥(s	NUM
cana-2203	256	6	)	)	PUNCT
cana-2203	256	7	,	,	PUNCT
cana-2203	256	8	where	where	SCONJ
cana-2203	256	9	s	s	X
cana-2203	256	10	,	,	PUNCT
cana-2203	256	11	t	t	PROPN
cana-2203	256	12	,	,	PUNCT
cana-2203	256	13	l	l	NOUN
cana-2203	256	14	>	>	X
cana-2203	256	15	0	0	PUNCT
cana-2203	256	16	and	and	CCONJ
cana-2203	256	17	(	(	PUNCT
cana-2203	256	18	p	p	NOUN
cana-2203	256	19	⊖	⊖	X
cana-2203	256	20	lt	lt	PROPN
cana-2203	256	21	)	)	PUNCT
cana-2203	256	22	>	>	X
cana-2203	256	23	0	0	X
cana-2203	256	24	.	.	PUNCT
cana-2203	257	1	then	then	ADV
cana-2203	257	2	each	each	DET
cana-2203	257	3	solution	solution	NOUN
cana-2203	257	4	u(t	u(t	NOUN
cana-2203	257	5	)	)	PUNCT
cana-2203	257	6	of	of	ADP
cana-2203	257	7	(	(	PUNCT
cana-2203	257	8	3.1	3.1	NUM
cana-2203	257	9	)	)	PUNCT
cana-2203	257	10	tends	tend	VERB
cana-2203	257	11	to	to	ADP
cana-2203	257	12	0	0	NUM
cana-2203	257	13	,	,	PUNCT
cana-2203	257	14	as	as	ADP
cana-2203	257	15	t	t	PROPN
cana-2203	257	16	→	→	SYM
cana-2203	257	17	∞.	∞.	PROPN
cana-2203	257	18	proof	proof	NOUN
cana-2203	257	19	:	:	PUNCT
cana-2203	257	20	from	from	ADP
cana-2203	257	21	(	(	PUNCT
cana-2203	257	22	3.4	3.4	NUM
cana-2203	257	23	)	)	PUNCT
cana-2203	257	24	,	,	PUNCT
cana-2203	257	25	we	we	PRON
cana-2203	257	26	have	have	VERB
cana-2203	257	27	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	257	28	)	)	PUNCT
cana-2203	258	1	=	=	PRON
cana-2203	258	2	∅(𝑡)𝐶	∅(𝑡)𝐶	PROPN
cana-2203	258	3	+	+	CCONJ
cana-2203	258	4	∅(𝑡	∅(𝑡	NOUN
cana-2203	258	5	)	)	PUNCT
cana-2203	258	6	∫	∫	PROPN
cana-2203	258	7	∅−1(𝜎(s))[∫	∅−1(𝜎(s))[∫	PROPN
cana-2203	258	8	𝐾(s	𝐾(s	PROPN
cana-2203	258	9	,	,	PUNCT
cana-2203	258	10	𝜏)𝑥(𝜏)∆𝜏	𝜏)𝑥(𝜏)∆𝜏	PROPN
cana-2203	258	11	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	258	12	)	)	PUNCT
cana-2203	258	13	)	)	PUNCT
cana-2203	259	1	𝑡0	𝑡0	PROPN
cana-2203	259	2	𝑡	𝑡	PROPN
cana-2203	259	3	𝑎	𝑎	X
cana-2203	259	4	+	+	X
cana-2203	259	5	℥	℥	NOUN
cana-2203	259	6	(	(	PUNCT
cana-2203	259	7	s	s	NOUN
cana-2203	259	8	,	,	PUNCT
cana-2203	259	9	𝑥(s)]∆s	𝑥(s)]∆s	X
cana-2203	259	10	on	on	ADP
cana-2203	259	11	[	[	X
cana-2203	259	12	𝑎	𝑎	X
cana-2203	259	13	,	,	PUNCT
cana-2203	259	14	𝑡1	𝑡1	NOUN
cana-2203	259	15	]	]	PUNCT
cana-2203	259	16	|𝑥(𝑡)|	|𝑥(𝑡)|	PROPN
cana-2203	259	17	≤	≤	X
cana-2203	259	18	|∅(𝑡)||𝐶|	|∅(𝑡)||𝐶|	PRON
cana-2203	259	19	+	+	CCONJ
cana-2203	259	20	|∅(𝑡)|	|∅(𝑡)|	NOUN
cana-2203	259	21	∫	∫	NOUN
cana-2203	259	22	|	|	CCONJ
cana-2203	259	23	∅−1(𝜎(s))|[∫	∅−1(𝜎(s))|[∫	NOUN
cana-2203	259	24	|𝐾(s	|𝐾(	NOUN
cana-2203	259	25	,	,	PUNCT
cana-2203	259	26	𝜏)||𝑥(𝜏)|∆𝜏	𝜏)||𝑥(𝜏)|∆𝜏	PROPN
cana-2203	259	27	𝜎(𝜌(s	𝜎(𝜌(s	PROPN
cana-2203	259	28	)	)	PUNCT
cana-2203	259	29	)	)	PUNCT
cana-2203	259	30	𝑡0	𝑡0	PROPN
cana-2203	260	1	𝑡	𝑡	PROPN
cana-2203	260	2	𝑎	𝑎	PROPN
cana-2203	260	3	+	+	NOUN
cana-2203	260	4	|	|	ADV
cana-2203	260	5	℥	℥	NOUN
cana-2203	260	6	(s	(s	NOUN
cana-2203	260	7	,	,	PUNCT
cana-2203	260	8	𝑥(s)|]∆s	𝑥(s)|]∆s	PROPN
cana-2203	260	9	=	=	SYM
cana-2203	260	10	rep(t0	rep(t0	PROPN
cana-2203	260	11	,	,	PUNCT
cana-2203	260	12	t	t	PROPN
cana-2203	260	13	)	)	PUNCT
cana-2203	260	14	+	+	NUM
cana-2203	261	1	slep(0	slep(0	PROPN
cana-2203	261	2	,	,	PUNCT
cana-2203	261	3	t	t	PROPN
cana-2203	261	4	)	)	PUNCT
cana-2203	261	5	∫	∫	PROPN
cana-2203	261	6	ep(s	ep(s	PROPN
cana-2203	261	7	,	,	PUNCT
cana-2203	261	8	0)|x(s)|	0)|x(s)|	AUX
cana-2203	261	9	△	△	PROPN
cana-2203	261	10	s	s	PART
cana-2203	261	11	t	t	X
cana-2203	261	12	t0	t0	NOUN
cana-2203	261	13	=	=	SYM
cana-2203	261	14	rep(t0	rep(t0	PROPN
cana-2203	261	15	,	,	PUNCT
cana-2203	261	16	0)ep(0	0)ep(0	NUM
cana-2203	261	17	,	,	PUNCT
cana-2203	261	18	t	t	PROPN
cana-2203	261	19	)	)	PUNCT
cana-2203	261	20	+	+	NUM
cana-2203	261	21	slep(0	slep(0	PROPN
cana-2203	261	22	,	,	PUNCT
cana-2203	261	23	t	t	PROPN
cana-2203	261	24	)	)	PUNCT
cana-2203	261	25	∫	∫	PROPN
cana-2203	261	26	ep(s	ep(s	PROPN
cana-2203	261	27	,	,	PUNCT
cana-2203	261	28	0)|x(s)|	0)|x(s)|	AUX
cana-2203	261	29	△	△	PROPN
cana-2203	261	30	s	s	PROPN
cana-2203	261	31	t	t	PROPN
cana-2203	261	32	t0	t0	PROPN
cana-2203	261	33	|u(t)|ep(t	|u(t)|ep(t	PROPN
cana-2203	261	34	,	,	PUNCT
cana-2203	261	35	0	0	NUM
cana-2203	261	36	)	)	PUNCT
cana-2203	261	37	≤	≤	NOUN
cana-2203	262	1	rep(t0	rep(t0	PROPN
cana-2203	262	2	,	,	PUNCT
cana-2203	262	3	0	0	NUM
cana-2203	262	4	)	)	PUNCT
cana-2203	263	1	+	+	CCONJ
cana-2203	263	2	sl	sl	NUM
cana-2203	263	3	∫	∫	PROPN
cana-2203	263	4	ep(s	ep(s	PROPN
cana-2203	263	5	,	,	PUNCT
cana-2203	263	6	0)|x(s)|	0)|x(s)|	X
cana-2203	263	7	△	△	PROPN
cana-2203	263	8	s	s	PART
cana-2203	263	9	t	t	X
cana-2203	263	10	t0	t0	NUM
cana-2203	263	11	by	by	ADP
cana-2203	263	12	lemma	lemma	PROPN
cana-2203	263	13	2.6	2.6	NUM
cana-2203	263	14	,	,	PUNCT
cana-2203	263	15	|x(t)|ep(t	|x(t)|ep(t	NOUN
cana-2203	263	16	,	,	PUNCT
cana-2203	263	17	0	0	NUM
cana-2203	263	18	)	)	PUNCT
cana-2203	263	19	≤	≤	NUM
cana-2203	263	20	𝑅ep(t0	𝑅ep(t0	NOUN
cana-2203	263	21	,	,	PUNCT
cana-2203	263	22	0)esl(t	0)esl(t	NUM
cana-2203	263	23	,	,	PUNCT
cana-2203	263	24	t0	t0	NOUN
cana-2203	263	25	)	)	PUNCT
cana-2203	264	1	|x(t)|	|x(t)|	PROPN
cana-2203	264	2	≤	≤	PROPN
cana-2203	264	3	rep(t0	rep(t0	PROPN
cana-2203	264	4	,	,	PUNCT
cana-2203	264	5	0)ep(0	0)ep(0	NUM
cana-2203	264	6	,	,	PUNCT
cana-2203	264	7	t)esl(t	t)esl(t	NUM
cana-2203	264	8	,	,	PUNCT
cana-2203	264	9	t0	t0	PROPN
cana-2203	264	10	)	)	PUNCT
cana-2203	264	11	=	=	SYM
cana-2203	264	12	𝑅ep(t0	𝑅ep(t0	NOUN
cana-2203	264	13	,	,	PUNCT
cana-2203	264	14	0)ep(0	0)ep(0	NUM
cana-2203	264	15	,	,	PUNCT
cana-2203	264	16	t)e⊖sl(t0	t)e⊖sl(t0	NOUN
cana-2203	264	17	,	,	PUNCT
cana-2203	264	18	t	t	PROPN
cana-2203	264	19	)	)	PUNCT
cana-2203	264	20	=	=	SYM
cana-2203	264	21	𝑅ep(t0	𝑅ep(t0	NOUN
cana-2203	264	22	,	,	PUNCT
cana-2203	264	23	0)ep(0	0)ep(0	NUM
cana-2203	264	24	,	,	PUNCT
cana-2203	264	25	t)e⊖sl(t0	t)e⊖sl(t0	NOUN
cana-2203	264	26	,	,	PUNCT
cana-2203	264	27	0)e⊖sl(0	0)e⊖sl(0	PROPN
cana-2203	264	28	,	,	PUNCT
cana-2203	264	29	t	t	PROPN
cana-2203	264	30	)	)	PUNCT
cana-2203	264	31	=	=	SYM
cana-2203	264	32	𝑅ep⊖sl(t0	𝑅ep⊖sl(t0	PROPN
cana-2203	264	33	,	,	PUNCT
cana-2203	264	34	0)ep⊖sl(0	0)ep⊖sl(0	NOUN
cana-2203	264	35	,	,	PUNCT
cana-2203	264	36	t	t	PROPN
cana-2203	264	37	)	)	PUNCT
cana-2203	264	38	communications	communication	NOUN
cana-2203	264	39	on	on	ADP
cana-2203	264	40	applied	apply	VERB
cana-2203	264	41	nonlinear	nonlinear	ADJ
cana-2203	264	42	analysis	analysis	NOUN
cana-2203	264	43	issn	issn	NOUN
cana-2203	264	44	:	:	PUNCT
cana-2203	264	45	1074	1074	NUM
cana-2203	264	46	-	-	PUNCT
cana-2203	264	47	133x	133x	NUM
cana-2203	264	48	vol	vol	NOUN
cana-2203	264	49	32	32	NUM
cana-2203	264	50	no	no	NOUN
cana-2203	264	51	.	.	PUNCT
cana-2203	265	1	1s	1s	NUM
cana-2203	265	2	(	(	PUNCT
cana-2203	265	3	2025	2025	NUM
cana-2203	265	4	)	)	PUNCT
cana-2203	265	5	396	396	NUM
cana-2203	265	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	265	7	by	by	ADP
cana-2203	265	8	lemma	lemma	PROPN
cana-2203	265	9	2.7	2.7	NUM
cana-2203	265	10	,	,	PUNCT
cana-2203	265	11	ep⊖sl(0	ep⊖sl(0	X
cana-2203	265	12	,	,	PUNCT
cana-2203	265	13	t	t	PROPN
cana-2203	265	14	)	)	PUNCT
cana-2203	265	15	≤	≤	NUM
cana-2203	265	16	1	1	NUM
cana-2203	265	17	1+(p⊖sl)t	1+(p⊖sl)t	NOUN
cana-2203	265	18	,	,	PUNCT
cana-2203	265	19	so	so	ADV
cana-2203	265	20	we	we	PRON
cana-2203	265	21	obtain	obtain	VERB
cana-2203	265	22	|x(t)|	|x(t)|	PROPN
cana-2203	265	23	≤	≤	PROPN
cana-2203	265	24	𝑅ep⊖sl(t0	𝑅ep⊖sl(t0	PROPN
cana-2203	265	25	,	,	PUNCT
cana-2203	265	26	0	0	NUM
cana-2203	265	27	)	)	PUNCT
cana-2203	265	28	1	1	NUM
cana-2203	265	29	1	1	NUM
cana-2203	265	30	+	+	CCONJ
cana-2203	265	31	(	(	PUNCT
cana-2203	265	32	p	p	NOUN
cana-2203	265	33	⊖	⊖	X
cana-2203	265	34	sl)t	sl)t	PROPN
cana-2203	265	35	since	since	SCONJ
cana-2203	265	36	(	(	PUNCT
cana-2203	265	37	p	p	NOUN
cana-2203	265	38	⊖	⊖	X
cana-2203	265	39	sl	sl	NUM
cana-2203	265	40	)	)	PUNCT
cana-2203	265	41	>	>	X
cana-2203	266	1	0	0	X
cana-2203	266	2	.	.	PUNCT
cana-2203	267	1	hence	hence	ADV
cana-2203	267	2	,	,	PUNCT
cana-2203	267	3	we	we	PRON
cana-2203	267	4	obtain	obtain	VERB
cana-2203	267	5	desired	desire	VERB
cana-2203	267	6	result	result	NOUN
cana-2203	267	7	.	.	PUNCT
cana-2203	268	1	4	4	X
cana-2203	268	2	.	.	NOUN
cana-2203	268	3	example	example	NOUN
cana-2203	268	4	example	example	NOUN
cana-2203	268	5	4.1	4.1	NUM
cana-2203	268	6	.	.	PUNCT
cana-2203	268	7	consider	consider	VERB
cana-2203	268	8	non	non	ADJ
cana-2203	268	9	-	-	ADJ
cana-2203	268	10	homogeneous	homogeneous	ADJ
cana-2203	268	11	boundary	boundary	ADJ
cana-2203	268	12	value	value	NOUN
cana-2203	268	13	problem	problem	NOUN
cana-2203	268	14	on	on	ADP
cana-2203	268	15	time	time	NOUN
cana-2203	268	16	scales	scale	NOUN
cana-2203	268	17	𝑥∆(𝑡	𝑥∆(𝑡	PRON
cana-2203	268	18	)	)	PUNCT
cana-2203	268	19	=	=	PUNCT
cana-2203	269	1	[	[	PUNCT
cana-2203	269	2	0	0	NUM
cana-2203	269	3	1	1	NUM
cana-2203	269	4	0	0	NUM
cana-2203	269	5	0	0	NUM
cana-2203	269	6	]	]	PUNCT
cana-2203	269	7	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	269	8	)	)	PUNCT
cana-2203	269	9	+	+	NUM
cana-2203	269	10	∫	∫	PROPN
cana-2203	269	11	[	[	PUNCT
cana-2203	269	12	1	1	NUM
cana-2203	269	13	0	0	NUM
cana-2203	269	14	0	0	NUM
cana-2203	269	15	1	1	NUM
cana-2203	269	16	]	]	PUNCT
cana-2203	269	17	𝑥(s	𝑥(s	PROPN
cana-2203	269	18	)	)	PUNCT
cana-2203	269	19	𝜎(𝜌(𝑡	𝜎(𝜌(𝑡	PROPN
cana-2203	269	20	)	)	PUNCT
cana-2203	269	21	)	)	PUNCT
cana-2203	269	22	0	0	NUM
cana-2203	270	1	∆s	∆s	NOUN
cana-2203	270	2	+	+	PUNCT
cana-2203	270	3	[	[	PUNCT
cana-2203	270	4	𝑡	𝑡	X
cana-2203	270	5	𝑡	𝑡	X
cana-2203	270	6	]	]	PUNCT
cana-2203	270	7	,	,	PUNCT
cana-2203	270	8	0	0	X
cana-2203	271	1	=	=	PUNCT
cana-2203	271	2	[	[	PUNCT
cana-2203	271	3	1	1	NUM
cana-2203	271	4	−1	−1	NOUN
cana-2203	271	5	0	0	NUM
cana-2203	271	6	0	0	NUM
cana-2203	271	7	]	]	PUNCT
cana-2203	271	8	𝑥(0	𝑥(0	PROPN
cana-2203	271	9	)	)	PUNCT
cana-2203	272	1	+	+	PUNCT
cana-2203	272	2	[	[	PUNCT
cana-2203	272	3	0	0	NUM
cana-2203	272	4	0	0	NUM
cana-2203	272	5	1	1	NUM
cana-2203	272	6	1	1	NUM
cana-2203	272	7	]	]	PUNCT
cana-2203	272	8	𝑥(10	𝑥(10	NOUN
cana-2203	272	9	)	)	PUNCT
cana-2203	272	10	,	,	PUNCT
cana-2203	272	11	}	}	PUNCT
cana-2203	272	12	(	(	PUNCT
cana-2203	272	13	4.1	4.1	NUM
cana-2203	272	14	)	)	PUNCT
cana-2203	272	15	for	for	ADP
cana-2203	272	16	0	0	NUM
cana-2203	272	17	≤	≤	NUM
cana-2203	272	18	s	s	PART
cana-2203	272	19	≤	≤	NUM
cana-2203	272	20	𝑡	𝑡	X
cana-2203	272	21	<	<	X
cana-2203	272	22	∞.	∞.	PROPN
cana-2203	272	23	case(a	case(a	NOUN
cana-2203	272	24	):	):	PUNCT
cana-2203	272	25	if	if	SCONJ
cana-2203	272	26	𝕋	𝕋	PROPN
cana-2203	272	27	=	=	PUNCT
cana-2203	272	28	ℝ+	ℝ+	PUNCT
cana-2203	272	29	then	then	ADV
cana-2203	272	30	(	(	PUNCT
cana-2203	272	31	4.1	4.1	NUM
cana-2203	272	32	)	)	PUNCT
cana-2203	272	33	is	be	AUX
cana-2203	272	34	𝑥′(𝑡	𝑥′(𝑡	NOUN
cana-2203	272	35	)	)	PUNCT
cana-2203	272	36	=	=	NOUN
cana-2203	273	1	[	[	PUNCT
cana-2203	273	2	0	0	NUM
cana-2203	273	3	1	1	NUM
cana-2203	273	4	0	0	NUM
cana-2203	273	5	0	0	NUM
cana-2203	273	6	]	]	PUNCT
cana-2203	273	7	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	273	8	)	)	PUNCT
cana-2203	273	9	+	+	NUM
cana-2203	273	10	∫	∫	PROPN
cana-2203	273	11	[	[	PUNCT
cana-2203	273	12	1	1	NUM
cana-2203	273	13	0	0	NUM
cana-2203	273	14	0	0	NUM
cana-2203	273	15	1	1	NUM
cana-2203	273	16	]	]	PUNCT
cana-2203	273	17	𝑥(s	𝑥(s	PROPN
cana-2203	273	18	)	)	PUNCT
cana-2203	273	19	𝑡	𝑡	NOUN
cana-2203	273	20	0	0	NUM
cana-2203	273	21	𝑑s	𝑑s	ADP
cana-2203	273	22	+	+	CCONJ
cana-2203	273	23	[	[	PUNCT
cana-2203	273	24	𝑡	𝑡	X
cana-2203	273	25	𝑡	𝑡	X
cana-2203	273	26	]	]	PUNCT
cana-2203	273	27	,	,	PUNCT
cana-2203	273	28	0	0	X
cana-2203	274	1	=	=	PUNCT
cana-2203	274	2	[	[	PUNCT
cana-2203	274	3	1	1	NUM
cana-2203	274	4	−1	−1	NOUN
cana-2203	274	5	0	0	NUM
cana-2203	274	6	0	0	NUM
cana-2203	274	7	]	]	PUNCT
cana-2203	274	8	𝑥(0	𝑥(0	PROPN
cana-2203	274	9	)	)	PUNCT
cana-2203	275	1	+	+	PUNCT
cana-2203	275	2	[	[	PUNCT
cana-2203	275	3	0	0	NUM
cana-2203	275	4	0	0	NUM
cana-2203	275	5	1	1	NUM
cana-2203	275	6	1	1	NUM
cana-2203	275	7	]	]	PUNCT
cana-2203	275	8	𝑥(10	𝑥(10	NOUN
cana-2203	275	9	)	)	PUNCT
cana-2203	275	10	.	.	PUNCT
cana-2203	275	11	}	}	PUNCT
cana-2203	276	1	(	(	PUNCT
cana-2203	276	2	4.2	4.2	NUM
cana-2203	276	3	)	)	PUNCT
cana-2203	276	4	the	the	DET
cana-2203	276	5	fundamental	fundamental	ADJ
cana-2203	276	6	matrix	matrix	NOUN
cana-2203	276	7	of	of	ADP
cana-2203	276	8	𝑥′(𝑡	𝑥′(𝑡	NOUN
cana-2203	276	9	)	)	PUNCT
cana-2203	276	10	=	=	NOUN
cana-2203	277	1	[	[	PUNCT
cana-2203	277	2	0	0	NUM
cana-2203	277	3	1	1	NUM
cana-2203	277	4	0	0	NUM
cana-2203	277	5	0	0	NUM
cana-2203	277	6	]	]	PUNCT
cana-2203	277	7	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	277	8	)	)	PUNCT
cana-2203	277	9	is	be	AUX
cana-2203	277	10	∅(𝑡	∅(𝑡	NOUN
cana-2203	277	11	)	)	PUNCT
cana-2203	278	1	=	=	PUNCT
cana-2203	278	2	[	[	PUNCT
cana-2203	278	3	1	1	NUM
cana-2203	278	4	𝑡	𝑡	NOUN
cana-2203	278	5	0	0	NUM
cana-2203	278	6	1	1	NUM
cana-2203	278	7	]	]	PUNCT
cana-2203	278	8	.	.	PUNCT
cana-2203	279	1	hence	hence	ADV
cana-2203	279	2	the	the	DET
cana-2203	279	3	solution	solution	NOUN
cana-2203	279	4	of	of	ADP
cana-2203	279	5	(	(	PUNCT
cana-2203	279	6	4.2	4.2	NUM
cana-2203	279	7	)	)	PUNCT
cana-2203	279	8	is	be	AUX
cana-2203	279	9	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2203	279	10	)	)	PUNCT
cana-2203	279	11	=	=	SYM
cana-2203	279	12	1	1	NUM
cana-2203	279	13	12	12	NUM
cana-2203	279	14	∫	∫	NOUN
cana-2203	279	15	[	[	PUNCT
cana-2203	279	16	11	11	NUM
cana-2203	279	17	−	−	PROPN
cana-2203	279	18	𝑡	𝑡	PROPN
cana-2203	279	19	−11	−11	X
cana-2203	279	20	−	−	PROPN
cana-2203	279	21	s(11	s(11	NOUN
cana-2203	279	22	−	−	PROPN
cana-2203	279	23	𝑡	𝑡	PROPN
cana-2203	279	24	)	)	PUNCT
cana-2203	280	1	+	+	NUM
cana-2203	280	2	𝑡	𝑡	NUM
cana-2203	280	3	−1	−1	NOUN
cana-2203	280	4	s	s	PART
cana-2203	280	5	+	+	NOUN
cana-2203	280	6	1	1	NUM
cana-2203	280	7	]	]	PUNCT
cana-2203	280	8	[	[	PUNCT
cana-2203	280	9	𝑒s	𝑒s	NOUN
cana-2203	280	10	−	−	PROPN
cana-2203	280	11	1	1	NUM
cana-2203	280	12	𝑒s	𝑒s	NOUN
cana-2203	280	13	−	−	NOUN
cana-2203	280	14	1	1	NUM
cana-2203	280	15	]	]	PUNCT
cana-2203	280	16	𝑡	𝑡	X
cana-2203	280	17	0	0	NUM
cana-2203	280	18	𝑑s	𝑑s	ADP
cana-2203	280	19	−	−	PROPN
cana-2203	280	20	1	1	NUM
cana-2203	280	21	12	12	NUM
cana-2203	280	22	∫	∫	NOUN
cana-2203	280	23	[	[	PUNCT
cana-2203	280	24	1	1	NUM
cana-2203	280	25	+	+	NUM
cana-2203	280	26	𝑡	𝑡	PROPN
cana-2203	280	27	1	1	NUM
cana-2203	280	28	+	+	NUM
cana-2203	280	29	𝑡	𝑡	NOUN
cana-2203	280	30	+	+	X
cana-2203	280	31	10(1	10(1	ADJ
cana-2203	280	32	+	+	NUM
cana-2203	280	33	𝑡	𝑡	NOUN
cana-2203	280	34	)	)	PUNCT
cana-2203	280	35	−	−	PROPN
cana-2203	280	36	s(1	s(1	PROPN
cana-2203	280	37	+	+	CCONJ
cana-2203	280	38	𝑡	𝑡	PROPN
cana-2203	280	39	)	)	PUNCT
cana-2203	280	40	1	1	NUM
cana-2203	280	41	11	11	NUM
cana-2203	280	42	−	−	NOUN
cana-2203	280	43	s	s	X
cana-2203	280	44	]	]	X
cana-2203	280	45	[	[	PUNCT
cana-2203	280	46	𝑒s	𝑒s	NOUN
cana-2203	280	47	−	−	PROPN
cana-2203	280	48	1	1	NUM
cana-2203	280	49	𝑒s	𝑒s	NOUN
cana-2203	280	50	−	−	NOUN
cana-2203	280	51	1	1	NUM
cana-2203	280	52	]	]	SYM
cana-2203	280	53	10	10	NUM
cana-2203	280	54	𝑡	𝑡	NOUN
cana-2203	280	55	𝑑s	𝑑s	ADP
cana-2203	280	56	=	=	NOUN
cana-2203	280	57	1	1	NUM
cana-2203	280	58	12	12	NUM
cana-2203	280	59	[	[	PUNCT
cana-2203	280	60	59	59	NUM
cana-2203	280	61	+	+	CCONJ
cana-2203	280	62	24𝑒𝑡	24𝑒𝑡	ADJ
cana-2203	280	63	+	+	CCONJ
cana-2203	280	64	59𝑡	59𝑡	NOUN
cana-2203	280	65	−	−	ADP
cana-2203	280	66	6𝑡2	6𝑡2	NUM
cana-2203	280	67	−	−	PROPN
cana-2203	280	68	3𝑒10(1	3𝑒10(1	NUM
cana-2203	280	69	+	+	CCONJ
cana-2203	280	70	𝑡	𝑡	NOUN
cana-2203	280	71	)	)	PUNCT
cana-2203	280	72	71	71	NUM
cana-2203	280	73	−	−	NUM
cana-2203	281	1	3𝑒10	3𝑒10	NUM
cana-2203	281	2	+	+	NUM
cana-2203	281	3	12𝑒𝑡	12𝑒𝑡	ADJ
cana-2203	281	4	−	−	PROPN
cana-2203	281	5	12𝑡	12𝑡	NOUN
cana-2203	281	6	]	]	PUNCT
cana-2203	281	7	.	.	PUNCT
cana-2203	282	1	figure	figure	NOUN
cana-2203	282	2	1	1	NUM
cana-2203	282	3	.	.	PUNCT
cana-2203	282	4	continuous	continuous	ADJ
cana-2203	282	5	solution	solution	NOUN
cana-2203	282	6	graph	graph	NOUN
cana-2203	282	7	case(b	case(b	ADP
cana-2203	282	8	):	):	PUNCT
cana-2203	282	9	if	if	SCONJ
cana-2203	282	10	𝕋	𝕋	PROPN
cana-2203	282	11	=	=	SYM
cana-2203	282	12	ℕ	ℕ	PROPN
cana-2203	282	13	then	then	ADV
cana-2203	282	14	(	(	PUNCT
cana-2203	282	15	4.1	4.1	NUM
cana-2203	282	16	)	)	PUNCT
cana-2203	282	17	is	be	AUX
cana-2203	282	18	communications	communication	NOUN
cana-2203	282	19	on	on	ADP
cana-2203	282	20	applied	apply	VERB
cana-2203	282	21	nonlinear	nonlinear	ADJ
cana-2203	282	22	analysis	analysis	NOUN
cana-2203	282	23	issn	issn	NOUN
cana-2203	282	24	:	:	PUNCT
cana-2203	282	25	1074	1074	NUM
cana-2203	282	26	-	-	PUNCT
cana-2203	282	27	133x	133x	NUM
cana-2203	282	28	vol	vol	NOUN
cana-2203	282	29	32	32	NUM
cana-2203	282	30	no	no	NOUN
cana-2203	282	31	.	.	PUNCT
cana-2203	283	1	1s	1s	NUM
cana-2203	283	2	(	(	PUNCT
cana-2203	283	3	2025	2025	NUM
cana-2203	283	4	)	)	PUNCT
cana-2203	283	5	397	397	NUM
cana-2203	283	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	283	7	∆𝑥(𝜉	∆𝑥(𝜉	PROPN
cana-2203	283	8	)	)	PUNCT
cana-2203	283	9	=	=	PUNCT
cana-2203	284	1	[	[	PUNCT
cana-2203	284	2	0	0	NUM
cana-2203	284	3	1	1	NUM
cana-2203	284	4	0	0	NUM
cana-2203	284	5	0	0	NUM
cana-2203	284	6	]	]	PUNCT
cana-2203	284	7	𝑥(𝜉	𝑥(𝜉	PROPN
cana-2203	284	8	)	)	PUNCT
cana-2203	284	9	+	+	CCONJ
cana-2203	284	10	∑	∑	PUNCT
cana-2203	284	11	[	[	PUNCT
cana-2203	284	12	1	1	NUM
cana-2203	284	13	0	0	NUM
cana-2203	284	14	0	0	NUM
cana-2203	284	15	1	1	NUM
cana-2203	284	16	]	]	PUNCT
cana-2203	284	17	𝑥(s	𝑥(s	X
cana-2203	284	18	)	)	PUNCT
cana-2203	284	19	+	+	PUNCT
cana-2203	285	1	𝜉−1	𝜉−1	NOUN
cana-2203	285	2	s=0	s=0	NOUN
cana-2203	285	3	[	[	PUNCT
cana-2203	285	4	𝜉	𝜉	X
cana-2203	285	5	𝜉	𝜉	X
cana-2203	285	6	]	]	PUNCT
cana-2203	285	7	,	,	PUNCT
cana-2203	285	8	0	0	X
cana-2203	285	9	=	=	PUNCT
cana-2203	285	10	[	[	PUNCT
cana-2203	285	11	1	1	NUM
cana-2203	285	12	−1	−1	NOUN
cana-2203	285	13	0	0	NUM
cana-2203	285	14	0	0	NUM
cana-2203	285	15	]	]	PUNCT
cana-2203	285	16	𝑥(0	𝑥(0	PROPN
cana-2203	285	17	)	)	PUNCT
cana-2203	286	1	+	+	PUNCT
cana-2203	286	2	[	[	PUNCT
cana-2203	286	3	0	0	NUM
cana-2203	286	4	0	0	NUM
cana-2203	286	5	1	1	NUM
cana-2203	286	6	1	1	NUM
cana-2203	286	7	]	]	PUNCT
cana-2203	286	8	𝑥(10	𝑥(10	NOUN
cana-2203	286	9	)	)	PUNCT
cana-2203	286	10	,	,	PUNCT
cana-2203	286	11	}	}	PUNCT
cana-2203	286	12	(	(	PUNCT
cana-2203	286	13	4.3	4.3	NUM
cana-2203	286	14	)	)	PUNCT
cana-2203	286	15	the	the	DET
cana-2203	286	16	fundamental	fundamental	ADJ
cana-2203	286	17	matrix	matrix	NOUN
cana-2203	286	18	of	of	ADP
cana-2203	286	19	∆𝑥(𝜉	∆𝑥(𝜉	PROPN
cana-2203	286	20	)	)	PUNCT
cana-2203	286	21	=	=	PUNCT
cana-2203	287	1	[	[	PUNCT
cana-2203	287	2	0	0	NUM
cana-2203	287	3	1	1	NUM
cana-2203	287	4	0	0	NUM
cana-2203	287	5	0	0	NUM
cana-2203	287	6	]	]	PUNCT
cana-2203	287	7	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	287	8	)	)	PUNCT
cana-2203	287	9	is∅(𝜉	is∅(𝜉	NOUN
cana-2203	287	10	)	)	PUNCT
cana-2203	287	11	=	=	PUNCT
cana-2203	288	1	[	[	PUNCT
cana-2203	288	2	1	1	NUM
cana-2203	288	3	𝜉	𝜉	NOUN
cana-2203	288	4	0	0	NUM
cana-2203	288	5	1	1	NUM
cana-2203	288	6	]	]	PUNCT
cana-2203	288	7	.	.	PUNCT
cana-2203	289	1	using	use	VERB
cana-2203	289	2	laplace	laplace	NOUN
cana-2203	289	3	transformation	transformation	NOUN
cana-2203	289	4	on	on	ADP
cana-2203	289	5	discrete	discrete	ADJ
cana-2203	289	6	case	case	NOUN
cana-2203	289	7	then	then	ADV
cana-2203	289	8	the	the	DET
cana-2203	289	9	solution	solution	NOUN
cana-2203	289	10	of	of	ADP
cana-2203	289	11	(	(	PUNCT
cana-2203	289	12	4.3	4.3	NUM
cana-2203	289	13	)	)	PUNCT
cana-2203	289	14	is	be	AUX
cana-2203	289	15	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	289	16	)	)	PUNCT
cana-2203	289	17	=	=	SYM
cana-2203	290	1	1	1	NUM
cana-2203	290	2	12	12	NUM
cana-2203	290	3	∑	∑	PUNCT
cana-2203	290	4	[	[	PUNCT
cana-2203	290	5	11	11	NUM
cana-2203	290	6	−	−	NOUN
cana-2203	290	7	𝜉	𝜉	NOUN
cana-2203	290	8	−11	−11	NOUN
cana-2203	290	9	+	+	NOUN
cana-2203	290	10	𝜉	𝜉	X
cana-2203	290	11	+	+	CCONJ
cana-2203	290	12	(	(	PUNCT
cana-2203	290	13	11	11	NUM
cana-2203	290	14	−	−	PROPN
cana-2203	290	15	𝜉)(−1	𝜉)(−1	PROPN
cana-2203	290	16	−	−	PROPN
cana-2203	290	17	s	s	NOUN
cana-2203	290	18	)	)	PUNCT
cana-2203	290	19	−1	−1	NOUN
cana-2203	290	20	s	s	NOUN
cana-2203	290	21	+	+	NOUN
cana-2203	290	22	2	2	NUM
cana-2203	290	23	]	]	PUNCT
cana-2203	291	1	[	[	PUNCT
cana-2203	291	2	2s	2s	NUM
cana-2203	291	3	−	−	NUM
cana-2203	291	4	1	1	NUM
cana-2203	291	5	2s	2s	NUM
cana-2203	291	6	−	−	NOUN
cana-2203	291	7	1	1	NUM
cana-2203	291	8	]	]	PUNCT
cana-2203	291	9	𝜉−1	𝜉−1	NUM
cana-2203	291	10	s=0	s=0	NOUN
cana-2203	291	11	−	−	NOUN
cana-2203	291	12	1	1	NUM
cana-2203	291	13	12	12	NUM
cana-2203	291	14	∑	∑	PUNCT
cana-2203	291	15	[	[	PUNCT
cana-2203	291	16	1	1	NUM
cana-2203	291	17	+	+	CCONJ
cana-2203	291	18	𝜉	𝜉	X
cana-2203	291	19	1	1	NUM
cana-2203	291	20	+	+	NUM
cana-2203	291	21	𝜉	𝜉	X
cana-2203	291	22	+	+	X
cana-2203	291	23	10(1	10(1	ADJ
cana-2203	291	24	+	+	NUM
cana-2203	291	25	𝜉	𝜉	X
cana-2203	291	26	)	)	PUNCT
cana-2203	291	27	+	+	CCONJ
cana-2203	291	28	(	(	PUNCT
cana-2203	291	29	1	1	X
cana-2203	291	30	+	+	NUM
cana-2203	291	31	𝜉)(−1	𝜉)(−1	PROPN
cana-2203	291	32	−	−	PROPN
cana-2203	291	33	s	s	PART
cana-2203	291	34	)	)	PUNCT
cana-2203	291	35	1	1	NUM
cana-2203	291	36	10	10	NUM
cana-2203	291	37	−	−	NOUN
cana-2203	291	38	s	s	X
cana-2203	291	39	]	]	X
cana-2203	291	40	[	[	PUNCT
cana-2203	291	41	2s	2s	NUM
cana-2203	291	42	−	−	NUM
cana-2203	291	43	1	1	NUM
cana-2203	291	44	2s	2s	NUM
cana-2203	291	45	−	−	NOUN
cana-2203	291	46	1	1	NUM
cana-2203	291	47	]	]	SYM
cana-2203	291	48	9	9	NUM
cana-2203	291	49	s=𝜉	s=𝜉	NOUN
cana-2203	291	50	=	=	SYM
cana-2203	291	51	1	1	NUM
cana-2203	291	52	12	12	NUM
cana-2203	291	53	[	[	PUNCT
cana-2203	291	54	6(−503	6(−503	NOUN
cana-2203	291	55	+	+	SYM
cana-2203	291	56	22+𝜉	22+𝜉	NUM
cana-2203	291	57	−	−	NOUN
cana-2203	291	58	502𝜉	502𝜉	PROPN
cana-2203	291	59	−	−	PROPN
cana-2203	291	60	𝜉2	𝜉2	PROPN
cana-2203	291	61	)	)	PUNCT
cana-2203	291	62	6(−501	6(−501	NUM
cana-2203	291	63	+	+	CCONJ
cana-2203	291	64	21+𝜉	21+𝜉	NUM
cana-2203	291	65	−	−	NOUN
cana-2203	291	66	2𝜉	2𝜉	NUM
cana-2203	291	67	)	)	PUNCT
cana-2203	291	68	]	]	PUNCT
cana-2203	291	69	figure	figure	NOUN
cana-2203	291	70	2	2	NUM
cana-2203	291	71	.	.	NOUN
cana-2203	291	72	discrete	discrete	ADJ
cana-2203	291	73	solution	solution	NOUN
cana-2203	291	74	graph	graph	NOUN
cana-2203	291	75	(	(	PUNCT
cana-2203	291	76	take	take	VERB
cana-2203	291	77	n	n	NOUN
cana-2203	291	78	=	=	SYM
cana-2203	291	79	𝜉	𝜉	X
cana-2203	291	80	)	)	PUNCT
cana-2203	291	81	using	use	VERB
cana-2203	291	82	ztransformation	ztransformation	NOUN
cana-2203	291	83	on	on	ADP
cana-2203	291	84	discrete	discrete	ADJ
cana-2203	291	85	case	case	NOUN
cana-2203	291	86	then	then	ADV
cana-2203	291	87	the	the	DET
cana-2203	291	88	solution	solution	NOUN
cana-2203	291	89	of	of	ADP
cana-2203	291	90	(	(	PUNCT
cana-2203	291	91	4.3	4.3	NUM
cana-2203	291	92	)	)	PUNCT
cana-2203	291	93	is	be	AUX
cana-2203	291	94	𝑥(𝜉	𝑥(𝜉	NOUN
cana-2203	291	95	)	)	PUNCT
cana-2203	291	96	=	=	SYM
cana-2203	292	1	1	1	NUM
cana-2203	292	2	12	12	NUM
cana-2203	292	3	∑	∑	PUNCT
cana-2203	292	4	[	[	PUNCT
cana-2203	292	5	11	11	NUM
cana-2203	292	6	−	−	NOUN
cana-2203	292	7	𝜉	𝜉	NOUN
cana-2203	292	8	−11	−11	NOUN
cana-2203	292	9	+	+	NOUN
cana-2203	292	10	𝜉	𝜉	X
cana-2203	292	11	+	+	CCONJ
cana-2203	292	12	(	(	PUNCT
cana-2203	292	13	11	11	NUM
cana-2203	292	14	−	−	PROPN
cana-2203	292	15	𝜉)(−1	𝜉)(−1	PROPN
cana-2203	292	16	−	−	PROPN
cana-2203	292	17	s	s	NOUN
cana-2203	292	18	)	)	PUNCT
cana-2203	292	19	−1	−1	NOUN
cana-2203	292	20	s	s	NOUN
cana-2203	292	21	+	+	NOUN
cana-2203	292	22	2	2	NUM
cana-2203	292	23	]	]	PUNCT
cana-2203	292	24	[	[	PUNCT
cana-2203	292	25	−1	−1	NOUN
cana-2203	292	26	−1	−1	NOUN
cana-2203	292	27	]	]	PUNCT
cana-2203	293	1	𝜉−1	𝜉−1	NOUN
cana-2203	293	2	s=0	s=0	PUNCT
cana-2203	293	3	−	−	NOUN
cana-2203	293	4	1	1	NUM
cana-2203	293	5	12	12	NUM
cana-2203	293	6	∑	∑	PUNCT
cana-2203	293	7	[	[	PUNCT
cana-2203	293	8	1	1	NUM
cana-2203	293	9	+	+	CCONJ
cana-2203	293	10	𝜉	𝜉	X
cana-2203	293	11	1	1	NUM
cana-2203	293	12	+	+	NUM
cana-2203	293	13	𝜉	𝜉	X
cana-2203	293	14	+	+	X
cana-2203	293	15	10(1	10(1	ADJ
cana-2203	293	16	+	+	NUM
cana-2203	293	17	𝜉	𝜉	X
cana-2203	293	18	)	)	PUNCT
cana-2203	293	19	+	+	CCONJ
cana-2203	293	20	(	(	PUNCT
cana-2203	293	21	1	1	X
cana-2203	293	22	+	+	NUM
cana-2203	293	23	𝜉)(−1	𝜉)(−1	PROPN
cana-2203	293	24	−	−	PROPN
cana-2203	293	25	s	s	PART
cana-2203	293	26	)	)	PUNCT
cana-2203	293	27	1	1	NUM
cana-2203	293	28	10	10	NUM
cana-2203	293	29	−	−	NOUN
cana-2203	293	30	s	s	X
cana-2203	293	31	]	]	X
cana-2203	293	32	[	[	PUNCT
cana-2203	293	33	−1	−1	NOUN
cana-2203	293	34	−1	−1	NOUN
cana-2203	293	35	]	]	PUNCT
cana-2203	293	36	9	9	NUM
cana-2203	293	37	s=𝜉	s=𝜉	NOUN
cana-2203	293	38	=	=	SYM
cana-2203	293	39	1	1	NUM
cana-2203	293	40	12	12	NUM
cana-2203	293	41	[	[	PUNCT
cana-2203	293	42	65	65	NUM
cana-2203	293	43	+	+	NUM
cana-2203	293	44	59𝜉	59𝜉	NOUN
cana-2203	293	45	−	−	ADP
cana-2203	293	46	6𝜉2	6𝜉2	NUM
cana-2203	293	47	65	65	NUM
cana-2203	293	48	−	−	PROPN
cana-2203	293	49	12𝜉	12𝜉	NOUN
cana-2203	293	50	]	]	PUNCT
cana-2203	293	51	communications	communication	NOUN
cana-2203	293	52	on	on	ADP
cana-2203	293	53	applied	apply	VERB
cana-2203	293	54	nonlinear	nonlinear	ADJ
cana-2203	293	55	analysis	analysis	NOUN
cana-2203	293	56	issn	issn	NOUN
cana-2203	293	57	:	:	PUNCT
cana-2203	293	58	1074	1074	NUM
cana-2203	293	59	-	-	PUNCT
cana-2203	293	60	133x	133x	NUM
cana-2203	293	61	vol	vol	NOUN
cana-2203	293	62	32	32	NUM
cana-2203	293	63	no	no	NOUN
cana-2203	293	64	.	.	PUNCT
cana-2203	294	1	1s	1s	NUM
cana-2203	294	2	(	(	PUNCT
cana-2203	294	3	2025	2025	NUM
cana-2203	294	4	)	)	PUNCT
cana-2203	294	5	398	398	NUM
cana-2203	294	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2203	294	7	figure	figure	NOUN
cana-2203	294	8	3	3	NUM
cana-2203	294	9	.	.	NOUN
cana-2203	294	10	discrete	discrete	ADJ
cana-2203	294	11	solution	solution	NOUN
cana-2203	294	12	graph	graph	NOUN
cana-2203	294	13	(	(	PUNCT
cana-2203	294	14	take	take	VERB
cana-2203	294	15	n	n	NOUN
cana-2203	294	16	=	=	SYM
cana-2203	294	17	𝜉	𝜉	X
cana-2203	294	18	)	)	PUNCT
cana-2203	294	19	5	5	NUM
cana-2203	294	20	.	.	PUNCT
cana-2203	294	21	conclusion	conclusion	NOUN
cana-2203	294	22	in	in	ADP
cana-2203	294	23	this	this	DET
cana-2203	294	24	work	work	NOUN
cana-2203	294	25	,	,	PUNCT
cana-2203	294	26	a	a	DET
cana-2203	294	27	solution	solution	NOUN
cana-2203	294	28	is	be	AUX
cana-2203	294	29	obtained	obtain	VERB
cana-2203	294	30	for	for	ADP
cana-2203	294	31	integro	integro	ADJ
cana-2203	294	32	-	-	PUNCT
cana-2203	294	33	dynamical	dynamical	ADJ
cana-2203	294	34	system	system	NOUN
cana-2203	294	35	of	of	ADP
cana-2203	294	36	volterra	volterra	NOUN
cana-2203	294	37	type	type	NOUN
cana-2203	294	38	in	in	ADP
cana-2203	294	39	the	the	DET
cana-2203	294	40	form	form	NOUN
cana-2203	294	41	of	of	ADP
cana-2203	294	42	greens	green	NOUN
cana-2203	294	43	matrix	matrix	NOUN
cana-2203	294	44	.	.	PUNCT
cana-2203	295	1	further	far	ADV
cana-2203	295	2	,	,	PUNCT
cana-2203	295	3	properties	property	NOUN
cana-2203	295	4	of	of	ADP
cana-2203	295	5	obtained	obtain	VERB
cana-2203	295	6	green	green	ADJ
cana-2203	295	7	matrix	matrix	NOUN
cana-2203	295	8	and	and	CCONJ
cana-2203	295	9	stability	stability	NOUN
cana-2203	295	10	analysis	analysis	NOUN
cana-2203	295	11	for	for	ADP
cana-2203	295	12	the	the	DET
cana-2203	295	13	said	say	VERB
cana-2203	295	14	system	system	NOUN
cana-2203	295	15	are	be	AUX
cana-2203	295	16	discussed	discuss	VERB
cana-2203	295	17	.	.	PUNCT
cana-2203	296	1	most	most	ADV
cana-2203	296	2	importantly	importantly	ADV
cana-2203	296	3	,	,	PUNCT
cana-2203	296	4	even	even	ADV
cana-2203	296	5	the	the	DET
cana-2203	296	6	system	system	NOUN
cana-2203	296	7	is	be	AUX
cana-2203	296	8	not	not	PART
cana-2203	296	9	continuous	continuous	ADJ
cana-2203	296	10	on	on	ADP
cana-2203	296	11	some	some	DET
cana-2203	296	12	finite	finite	ADJ
cana-2203	296	13	piecewise	piecewise	NOUN
cana-2203	296	14	continuous	continuous	ADJ
cana-2203	296	15	intervals	interval	NOUN
cana-2203	296	16	,	,	PUNCT
cana-2203	296	17	still	still	ADV
cana-2203	296	18	the	the	DET
cana-2203	296	19	solution	solution	NOUN
cana-2203	296	20	is	be	AUX
cana-2203	296	21	obtained	obtain	VERB
cana-2203	296	22	with	with	ADP
cana-2203	296	23	the	the	DET
cana-2203	296	24	help	help	NOUN
cana-2203	296	25	of	of	ADP
cana-2203	296	26	green	green	ADJ
cana-2203	296	27	matrix	matrix	NOUN
cana-2203	296	28	.	.	PUNCT
cana-2203	297	1	this	this	DET
cana-2203	297	2	work	work	NOUN
cana-2203	297	3	is	be	AUX
cana-2203	297	4	authenticated	authenticate	VERB
cana-2203	297	5	with	with	ADP
cana-2203	297	6	numerical	numerical	ADJ
cana-2203	297	7	examples	example	NOUN
cana-2203	297	8	.	.	PUNCT
cana-2203	298	1	graphs	graph	NOUN
cana-2203	298	2	are	be	AUX
cana-2203	298	3	also	also	ADV
cana-2203	298	4	provided	provide	VERB
cana-2203	298	5	to	to	PART
cana-2203	298	6	explore	explore	VERB
cana-2203	298	7	the	the	DET
cana-2203	298	8	existence	existence	NOUN
cana-2203	298	9	of	of	ADP
cana-2203	298	10	solution	solution	NOUN
cana-2203	298	11	and	and	CCONJ
cana-2203	298	12	analyse	analyse	NOUN
cana-2203	298	13	stability	stability	NOUN
cana-2203	298	14	of	of	ADP
cana-2203	298	15	system	system	NOUN
cana-2203	298	16	.	.	PUNCT
cana-2203	299	1	future	future	ADJ
cana-2203	299	2	work	work	NOUN
cana-2203	299	3	:	:	PUNCT
cana-2203	299	4	this	this	DET
cana-2203	299	5	work	work	NOUN
cana-2203	299	6	can	can	AUX
cana-2203	299	7	be	be	AUX
cana-2203	299	8	extended	extend	VERB
cana-2203	299	9	onto	onto	ADP
cana-2203	299	10	the	the	DET
cana-2203	299	11	systems	system	NOUN
cana-2203	299	12	of	of	ADP
cana-2203	299	13	lyapunov	lyapunov	ADJ
cana-2203	299	14	type	type	NOUN
cana-2203	299	15	,	,	PUNCT
cana-2203	299	16	impulsive	impulsive	ADJ
cana-2203	299	17	and	and	CCONJ
cana-2203	299	18	fractional	fractional	ADJ
cana-2203	299	19	order	order	NOUN
cana-2203	299	20	.	.	PUNCT
cana-2203	300	1	this	this	DET
cana-2203	300	2	work	work	NOUN
cana-2203	300	3	may	may	AUX
cana-2203	300	4	make	make	VERB
cana-2203	300	5	better	well	ADJ
cana-2203	300	6	some	some	DET
cana-2203	300	7	processes	process	NOUN
cana-2203	300	8	concerned	concern	VERB
cana-2203	300	9	with	with	ADP
cana-2203	300	10	robotics	robotic	NOUN
cana-2203	300	11	,	,	PUNCT
cana-2203	300	12	image	image	NOUN
cana-2203	300	13	processing	processing	NOUN
cana-2203	300	14	,	,	PUNCT
cana-2203	300	15	system	system	NOUN
cana-2203	300	16	trajectories	trajectory	NOUN
cana-2203	300	17	and	and	CCONJ
cana-2203	300	18	various	various	ADJ
cana-2203	300	19	other	other	ADJ
cana-2203	300	20	fields	field	NOUN
cana-2203	300	21	.	.	PUNCT
cana-2203	301	1	acknowledgement	acknowledgement	NOUN
cana-2203	301	2	:	:	PUNCT
cana-2203	301	3	the	the	DET
cana-2203	301	4	authors	author	NOUN
cana-2203	301	5	thank	thank	VERB
cana-2203	301	6	their	their	PRON
cana-2203	301	7	respective	respective	ADJ
cana-2203	301	8	college	college	NOUN
cana-2203	301	9	managements	management	NOUN
cana-2203	301	10	for	for	ADP
cana-2203	301	11	their	their	PRON
cana-2203	301	12	continuous	continuous	ADJ
cana-2203	301	13	support	support	NOUN
cana-2203	301	14	and	and	CCONJ
cana-2203	301	15	constant	constant	ADJ
cana-2203	301	16	encouragement	encouragement	NOUN
cana-2203	301	17	.	.	PUNCT
cana-2203	302	1	references	reference	NOUN
cana-2203	302	2	[	[	X
cana-2203	302	3	1	1	NUM
cana-2203	302	4	]	]	X
cana-2203	302	5	bohner	bohner	NOUN
cana-2203	302	6	,	,	PUNCT
cana-2203	302	7	m.	m.	NOUN
cana-2203	302	8	,	,	PUNCT
cana-2203	302	9	peterson	peterson	PROPN
cana-2203	302	10	,	,	PUNCT
cana-2203	302	11	a.	a.	PROPN
cana-2203	302	12	,	,	PUNCT
cana-2203	302	13	advances	advance	VERB
cana-2203	302	14	in	in	ADP
cana-2203	302	15	dynamic	dynamic	ADJ
cana-2203	302	16	equations	equation	NOUN
cana-2203	302	17	on	on	ADP
cana-2203	302	18	time	time	NOUN
cana-2203	302	19	scales	scale	NOUN
cana-2203	302	20	,	,	PUNCT
cana-2203	302	21	birkhauser	birkhauser	PROPN
cana-2203	302	22	,	,	PUNCT
cana-2203	302	23	boston	boston	PROPN
cana-2203	302	24	,	,	PUNCT
cana-2203	302	25	2003	2003	NUM
cana-2203	302	26	.	.	PUNCT
cana-2203	303	1	[	[	X
cana-2203	303	2	2	2	NUM
cana-2203	303	3	]	]	SYM
cana-2203	303	4	burton	burton	PROPN
cana-2203	303	5	,	,	PUNCT
cana-2203	303	6	t.a	t.a	PROPN
cana-2203	303	7	.	.	PROPN
cana-2203	303	8	,	,	PUNCT
cana-2203	303	9	stability	stability	NOUN
cana-2203	303	10	theory	theory	NOUN
cana-2203	303	11	for	for	ADP
cana-2203	303	12	volterra	volterra	PROPN
cana-2203	303	13	equations	equation	NOUN
cana-2203	303	14	,	,	PUNCT
cana-2203	303	15	j.	j.	PROPN
cana-2203	303	16	diff	diff	PROPN
cana-2203	303	17	equs	equs	PROPN
cana-2203	303	18	.	.	PROPN
cana-2203	303	19	,	,	PUNCT
cana-2203	303	20	32	32	NUM
cana-2203	303	21	(	(	PUNCT
cana-2203	303	22	1979	1979	NUM
cana-2203	303	23	)	)	PUNCT
cana-2203	303	24	,	,	PUNCT
cana-2203	303	25	101	101	NUM
cana-2203	303	26	-	-	SYM
cana-2203	303	27	118	118	NUM
cana-2203	303	28	.	.	PUNCT
cana-2203	304	1	[	[	X
cana-2203	304	2	3	3	NUM
cana-2203	304	3	]	]	X
cana-2203	304	4	burton	burton	PROPN
cana-2203	304	5	,	,	PUNCT
cana-2203	304	6	t.a	t.a	PROPN
cana-2203	304	7	.	.	PROPN
cana-2203	304	8	,	,	PUNCT
cana-2203	304	9	an	an	DET
cana-2203	304	10	integro	integro	PROPN
cana-2203	304	11	differential	differential	ADJ
cana-2203	304	12	equations	equation	NOUN
cana-2203	304	13	,	,	PUNCT
cana-2203	304	14	proc	proc	NOUN
cana-2203	304	15	.	.	PUNCT
cana-2203	304	16	amer	amer	PROPN
cana-2203	304	17	.	.	PUNCT
cana-2203	304	18	math	math	PROPN
cana-2203	304	19	.	.	PUNCT
cana-2203	305	1	soc	soc	PROPN
cana-2203	305	2	.	.	PUNCT
cana-2203	305	3	,	,	PUNCT
cana-2203	305	4	79	79	NUM
cana-2203	305	5	(	(	PUNCT
cana-2203	305	6	1980	1980	NUM
cana-2203	305	7	)	)	PUNCT
cana-2203	305	8	,	,	PUNCT
cana-2203	305	9	393	393	NUM
cana-2203	305	10	-	-	SYM
cana-2203	305	11	399	399	NUM
cana-2203	305	12	.	.	PUNCT
cana-2203	306	1	[	[	X
cana-2203	306	2	4	4	NUM
cana-2203	306	3	]	]	X
cana-2203	306	4	g.v.s.r	g.v.s.r	PROPN
cana-2203	306	5	.	.	PROPN
cana-2203	306	6	deekshitulu	deekshitulu	PROPN
cana-2203	306	7	g.v	g.v	PROPN
cana-2203	306	8	.	.	PROPN
cana-2203	306	9	ramana	ramana	PROPN
cana-2203	306	10	,	,	PUNCT
cana-2203	306	11	asymptotic	asymptotic	ADJ
cana-2203	306	12	stability	stability	NOUN
cana-2203	306	13	of	of	ADP
cana-2203	306	14	lyapunov	lyapunov	ADJ
cana-2203	306	15	type	type	NOUN
cana-2203	306	16	matrix	matrix	NOUN
cana-2203	306	17	volterra	volterra	NOUN
cana-2203	306	18	integro	integro	PROPN
cana-2203	306	19	dynamic	dynamic	ADJ
cana-2203	306	20	system	system	NOUN
cana-2203	306	21	on	on	ADP
cana-2203	306	22	time	time	NOUN
cana-2203	306	23	scales	scale	NOUN
cana-2203	306	24	.	.	PUNCT
cana-2203	307	1	ijet	ijet	PROPN
cana-2203	307	2	,	,	PUNCT
cana-2203	307	3	(	(	PUNCT
cana-2203	307	4	2017	2017	NUM
cana-2203	307	5	)	)	PUNCT
cana-2203	307	6	,	,	PUNCT
cana-2203	307	7	179	179	NUM
cana-2203	307	8	-	-	SYM
cana-2203	307	9	185	185	NUM
cana-2203	307	10	.	.	PUNCT
cana-2203	308	1	[	[	X
cana-2203	308	2	5	5	NUM
cana-2203	308	3	]	]	PUNCT
cana-2203	308	4	hilger	hilger	NOUN
cana-2203	308	5	,	,	PUNCT
cana-2203	308	6	s.	s.	PROPN
cana-2203	308	7	,	,	PUNCT
cana-2203	308	8	ein	ein	PROPN
cana-2203	308	9	mabkettenkalkulmit	mabkettenkalkulmit	PROPN
cana-2203	308	10	anwendung	anwendung	PROPN
cana-2203	308	11	auf	auf	PROPN
cana-2203	308	12	zentrumsmannigfaltigkeiten	zentrumsmannigfaltigkeiten	PROPN
cana-2203	308	13	,	,	PUNCT
cana-2203	308	14	phd	phd	NOUN
cana-2203	308	15	thesis	thesis	NOUN
cana-2203	308	16	,	,	PUNCT
cana-2203	308	17	universitat	universitat	PROPN
cana-2203	308	18	wurzburg	wurzburg	PROPN
cana-2203	308	19	,	,	PUNCT
cana-2203	308	20	1988	1988	NUM
cana-2203	308	21	.	.	PUNCT
cana-2203	309	1	[	[	X
cana-2203	309	2	6	6	NUM
cana-2203	309	3	]	]	SYM
cana-2203	309	4	lakshmikantham	lakshmikantham	ADJ
cana-2203	309	5	,	,	PUNCT
cana-2203	309	6	v.	v.	ADV
cana-2203	309	7	,	,	PUNCT
cana-2203	309	8	sivasundaram	sivasundaram	PROPN
cana-2203	309	9	,	,	PUNCT
cana-2203	309	10	s.	s.	PROPN
cana-2203	309	11	,	,	PUNCT
cana-2203	309	12	kaymakcalan	kaymakcalan	PROPN
cana-2203	309	13	,	,	PUNCT
cana-2203	309	14	b.	b.	PROPN
cana-2203	309	15	,	,	PUNCT
cana-2203	309	16	dynamic	dynamic	ADJ
cana-2203	309	17	systems	system	NOUN
cana-2203	309	18	on	on	ADP
cana-2203	309	19	measure	measure	NOUN
cana-2203	309	20	chains	chain	NOUN
cana-2203	309	21	,	,	PUNCT
cana-2203	309	22	kluwer	kluwer	NOUN
cana-2203	309	23	,	,	PUNCT
cana-2203	309	24	1996	1996	NUM
cana-2203	309	25	.	.	PUNCT
cana-2203	310	1	[	[	X
cana-2203	310	2	7	7	NUM
cana-2203	310	3	]	]	X
cana-2203	310	4	sabrina	sabrina	PROPN
cana-2203	310	5	streipert	streipert	PROPN
cana-2203	310	6	.	.	PUNCT
cana-2203	311	1	(	(	PUNCT
cana-2203	311	2	2023	2023	NUM
cana-2203	311	3	)	)	PUNCT
cana-2203	311	4	.	.	PUNCT
cana-2203	312	1	dynamic	dynamic	ADJ
cana-2203	312	2	equations	equation	NOUN
cana-2203	312	3	on	on	ADP
cana-2203	312	4	time	time	NOUN
cana-2203	312	5	scales	scale	NOUN
cana-2203	312	6	.	.	PUNCT
cana-2203	313	1	nonlinear	nonlinear	ADJ
cana-2203	313	2	systems	system	NOUN
cana-2203	313	3	.	.	PUNCT
cana-2203	314	1	[	[	X
cana-2203	314	2	8	8	X
cana-2203	314	3	]	]	PUNCT
cana-2203	314	4	s.	s.	PROPN
cana-2203	314	5	o.	o.	PROPN
cana-2203	314	6	shah	shah	PROPN
cana-2203	314	7	and	and	CCONJ
cana-2203	314	8	a.	a.	PROPN
cana-2203	314	9	zada	zada	PROPN
cana-2203	314	10	,	,	PUNCT
cana-2203	314	11	stability	stability	NOUN
cana-2203	314	12	of	of	ADP
cana-2203	314	13	non	non	ADJ
cana-2203	314	14	-	-	ADJ
cana-2203	314	15	linear	linear	ADJ
cana-2203	314	16	volterra	volterra	NOUN
cana-2203	314	17	integro	integro	PROPN
cana-2203	314	18	dynamic	dynamic	ADJ
cana-2203	314	19	equations	equation	NOUN
cana-2203	314	20	on	on	ADP
cana-2203	314	21	time	time	NOUN
cana-2203	314	22	scales	scale	NOUN
cana-2203	314	23	,	,	PUNCT
cana-2203	314	24	di	di	X
cana-2203	314	25	matematica	matematica	PROPN
cana-2203	314	26	,	,	PUNCT
cana-2203	314	27	(	(	PUNCT
cana-2203	314	28	2019	2019	NUM
cana-2203	314	29	)	)	PUNCT
cana-2203	314	30	,	,	PUNCT
cana-2203	314	31	no.2	no.2	PROPN
cana-2203	314	32	.	.	PROPN
cana-2203	314	33	57	57	NUM
cana-2203	314	34	-	-	SYM
cana-2203	314	35	69	69	NUM
cana-2203	314	36	.	.	PUNCT