id	sid	tid	token	lemma	pos
cana-3476	1	1	communications	communication	NOUN
cana-3476	1	2	on	on	ADP
cana-3476	1	3	applied	apply	VERB
cana-3476	1	4	nonlinear	nonlinear	ADJ
cana-3476	1	5	analysis	analysis	NOUN
cana-3476	1	6	issn	issn	NOUN
cana-3476	1	7	:	:	PUNCT
cana-3476	1	8	1074	1074	NUM
cana-3476	1	9	-	-	PUNCT
cana-3476	1	10	133x	133x	NUM
cana-3476	1	11	vol	vol	NOUN
cana-3476	1	12	32	32	NUM
cana-3476	1	13	no	no	NOUN
cana-3476	1	14	.	.	PUNCT
cana-3476	2	1	7s	7	NOUN
cana-3476	2	2	(	(	PUNCT
cana-3476	2	3	2025	2025	NUM
cana-3476	2	4	)	)	PUNCT
cana-3476	2	5	694	694	NUM
cana-3476	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	3	2	new	new	ADJ
cana-3476	3	3	general	general	ADJ
cana-3476	3	4	complex	complex	ADJ
cana-3476	3	5	integral	integral	ADJ
cana-3476	3	6	transform	transform	NOUN
cana-3476	3	7	on	on	ADP
cana-3476	3	8	time	time	NOUN
cana-3476	3	9	scales	scale	NOUN
cana-3476	3	10	dipali	dipali	VERB
cana-3476	3	11	kaklij1	kaklij1	PROPN
cana-3476	3	12	,	,	PUNCT
cana-3476	3	13	dinkar	dinkar	PROPN
cana-3476	3	14	patil2	patil2	PROPN
cana-3476	3	15	1k	1k	X
cana-3476	3	16	.	.	PUNCT
cana-3476	4	1	r.	r.	PROPN
cana-3476	4	2	t.	t.	PROPN
cana-3476	4	3	art	art	PROPN
cana-3476	4	4	’s	’s	PART
cana-3476	4	5	,	,	PUNCT
cana-3476	4	6	b.	b.	PROPN
cana-3476	4	7	h.	h.	PROPN
cana-3476	4	8	commerce	commerce	PROPN
cana-3476	4	9	and	and	CCONJ
cana-3476	4	10	a.	a.	NOUN
cana-3476	4	11	m.	m.	PROPN
cana-3476	4	12	science	science	PROPN
cana-3476	4	13	college	college	PROPN
cana-3476	4	14	,	,	PUNCT
cana-3476	4	15	nashik	nashik	PROPN
cana-3476	4	16	,	,	PUNCT
cana-3476	4	17	maharashtra	maharashtra	PROPN
cana-3476	4	18	,	,	PUNCT
cana-3476	4	19	india	india	PROPN
cana-3476	4	20	.	.	PUNCT
cana-3476	5	1	2art	2art	PROPN
cana-3476	5	2	’s	’s	PART
cana-3476	5	3	and	and	CCONJ
cana-3476	5	4	commerce	commerce	PROPN
cana-3476	5	5	college	college	PROPN
cana-3476	5	6	,	,	PUNCT
cana-3476	5	7	wadala	wadala	PROPN
cana-3476	5	8	,	,	PUNCT
cana-3476	5	9	nashik	nashik	PROPN
cana-3476	5	10	,	,	PUNCT
cana-3476	5	11	maharashtra	maharashtra	PROPN
cana-3476	5	12	,	,	PUNCT
cana-3476	5	13	india	india	PROPN
cana-3476	5	14	.	.	PUNCT
cana-3476	6	1	article	article	PROPN
cana-3476	6	2	history	history	NOUN
cana-3476	6	3	:	:	PUNCT
cana-3476	6	4	received	receive	VERB
cana-3476	6	5	:	:	PUNCT
cana-3476	6	6	27	27	NUM
cana-3476	6	7	-	-	SYM
cana-3476	6	8	10	10	NUM
cana-3476	6	9	-	-	PUNCT
cana-3476	6	10	2024	2024	NUM
cana-3476	6	11	revised:11	revised:11	VERB
cana-3476	6	12	-	-	SYM
cana-3476	6	13	11	11	NUM
cana-3476	6	14	-	-	PUNCT
cana-3476	6	15	2024	2024	NUM
cana-3476	6	16	accepted:19	accepted:19	VERB
cana-3476	6	17	-	-	PUNCT
cana-3476	6	18	12	12	NUM
cana-3476	6	19	-	-	PUNCT
cana-3476	6	20	2024	2024	NUM
cana-3476	6	21	abstract	abstract	NOUN
cana-3476	6	22	:	:	PUNCT
cana-3476	6	23	introduction	introduction	NOUN
cana-3476	6	24	:	:	PUNCT
cana-3476	6	25	we	we	PRON
cana-3476	6	26	begin	begin	VERB
cana-3476	6	27	by	by	ADP
cana-3476	6	28	defining	define	VERB
cana-3476	6	29	the	the	DET
cana-3476	6	30	new	new	ADJ
cana-3476	6	31	general	general	ADJ
cana-3476	6	32	complex	complex	ADJ
cana-3476	6	33	integral	integral	ADJ
cana-3476	6	34	transform	transform	NOUN
cana-3476	6	35	[	[	X
cana-3476	6	36	13	13	NUM
cana-3476	6	37	]	]	PUNCT
cana-3476	6	38	,	,	PUNCT
cana-3476	6	39	and	and	CCONJ
cana-3476	6	40	then	then	ADV
cana-3476	6	41	we	we	PRON
cana-3476	6	42	present	present	VERB
cana-3476	6	43	a	a	DET
cana-3476	6	44	new	new	ADJ
cana-3476	6	45	general	general	ADJ
cana-3476	6	46	complex	complex	ADJ
cana-3476	6	47	integral	integral	ADJ
cana-3476	6	48	transform	transform	NOUN
cana-3476	6	49	on	on	ADP
cana-3476	6	50	time	time	NOUN
cana-3476	6	51	scales	scale	VERB
cana-3476	6	52	𝕋.	𝕋.	NOUN
cana-3476	6	53	to	to	PART
cana-3476	6	54	solve	solve	VERB
cana-3476	6	55	a	a	DET
cana-3476	6	56	variety	variety	NOUN
cana-3476	6	57	of	of	ADP
cana-3476	6	58	dynamic	dynamic	ADJ
cana-3476	6	59	equations	equation	NOUN
cana-3476	6	60	with	with	ADP
cana-3476	6	61	beginning	begin	VERB
cana-3476	6	62	values	value	NOUN
cana-3476	6	63	or	or	CCONJ
cana-3476	6	64	boundary	boundary	ADJ
cana-3476	6	65	conditions	condition	NOUN
cana-3476	6	66	that	that	PRON
cana-3476	6	67	are	be	AUX
cana-3476	6	68	represented	represent	VERB
cana-3476	6	69	by	by	ADP
cana-3476	6	70	integral	integral	ADJ
cana-3476	6	71	equations	equation	NOUN
cana-3476	6	72	,	,	PUNCT
cana-3476	6	73	integral	integral	ADJ
cana-3476	6	74	transform	transform	NOUN
cana-3476	6	75	methods	method	NOUN
cana-3476	6	76	are	be	AUX
cana-3476	6	77	frequently	frequently	ADV
cana-3476	6	78	employed	employ	VERB
cana-3476	6	79	.	.	PUNCT
cana-3476	7	1	in	in	ADP
cana-3476	7	2	order	order	NOUN
cana-3476	7	3	to	to	PART
cana-3476	7	4	solve	solve	VERB
cana-3476	7	5	dynamic	dynamic	ADJ
cana-3476	7	6	equations	equation	NOUN
cana-3476	7	7	,	,	PUNCT
cana-3476	7	8	the	the	DET
cana-3476	7	9	new	new	ADJ
cana-3476	7	10	general	general	ADJ
cana-3476	7	11	complex	complex	ADJ
cana-3476	7	12	integral	integral	ADJ
cana-3476	7	13	transform	transform	NOUN
cana-3476	7	14	on	on	ADP
cana-3476	7	15	time	time	NOUN
cana-3476	7	16	scale	scale	NOUN
cana-3476	7	17	is	be	AUX
cana-3476	7	18	presented	present	VERB
cana-3476	7	19	in	in	ADP
cana-3476	7	20	this	this	DET
cana-3476	7	21	article	article	NOUN
cana-3476	7	22	.	.	PUNCT
cana-3476	8	1	objectives	objective	NOUN
cana-3476	8	2	:	:	PUNCT
cana-3476	8	3	within	within	ADP
cana-3476	8	4	the	the	DET
cana-3476	8	5	laplace	laplace	NOUN
cana-3476	8	6	transform	transform	NOUN
cana-3476	8	7	class	class	NOUN
cana-3476	8	8	,	,	PUNCT
cana-3476	8	9	we	we	PRON
cana-3476	8	10	provide	provide	VERB
cana-3476	8	11	the	the	DET
cana-3476	8	12	new	new	ADJ
cana-3476	8	13	general	general	ADJ
cana-3476	8	14	complex	complex	ADJ
cana-3476	8	15	integral	integral	ADJ
cana-3476	8	16	transform	transform	NOUN
cana-3476	8	17	on	on	ADP
cana-3476	8	18	time	time	NOUN
cana-3476	8	19	scales	scale	NOUN
cana-3476	8	20	in	in	ADP
cana-3476	8	21	this	this	DET
cana-3476	8	22	study	study	NOUN
cana-3476	8	23	.	.	PUNCT
cana-3476	9	1	we	we	PRON
cana-3476	9	2	examine	examine	VERB
cana-3476	9	3	this	this	DET
cana-3476	9	4	transform	transform	NOUN
cana-3476	9	5	's	's	PART
cana-3476	9	6	characteristics	characteristic	NOUN
cana-3476	9	7	.	.	PUNCT
cana-3476	10	1	an	an	DET
cana-3476	10	2	initial	initial	ADJ
cana-3476	10	3	value	value	NOUN
cana-3476	10	4	problem	problem	NOUN
cana-3476	10	5	with	with	ADP
cana-3476	10	6	a	a	DET
cana-3476	10	7	dynamic	dynamic	ADJ
cana-3476	10	8	form	form	NOUN
cana-3476	10	9	of	of	ADP
cana-3476	10	10	the	the	DET
cana-3476	10	11	equation	equation	NOUN
cana-3476	10	12	is	be	AUX
cana-3476	10	13	the	the	DET
cana-3476	10	14	primary	primary	ADJ
cana-3476	10	15	focus	focus	NOUN
cana-3476	10	16	of	of	ADP
cana-3476	10	17	this	this	DET
cana-3476	10	18	research	research	NOUN
cana-3476	10	19	.	.	PUNCT
cana-3476	11	1	methods	method	NOUN
cana-3476	11	2	:	:	PUNCT
cana-3476	11	3	differential	differential	ADJ
cana-3476	11	4	equations	equation	NOUN
cana-3476	11	5	of	of	ADP
cana-3476	11	6	any	any	DET
cana-3476	11	7	order	order	NOUN
cana-3476	11	8	and	and	CCONJ
cana-3476	11	9	the	the	DET
cana-3476	11	10	integral	integral	NOUN
cana-3476	11	11	of	of	ADP
cana-3476	11	12	a	a	DET
cana-3476	11	13	function	function	NOUN
cana-3476	11	14	can	can	AUX
cana-3476	11	15	both	both	PRON
cana-3476	11	16	be	be	AUX
cana-3476	11	17	solved	solve	VERB
cana-3476	11	18	using	use	VERB
cana-3476	11	19	the	the	DET
cana-3476	11	20	new	new	ADJ
cana-3476	11	21	general	general	ADJ
cana-3476	11	22	complex	complex	ADJ
cana-3476	11	23	integral	integral	ADJ
cana-3476	11	24	transform	transform	NOUN
cana-3476	11	25	on	on	ADP
cana-3476	11	26	time	time	NOUN
cana-3476	11	27	scales	scale	NOUN
cana-3476	11	28	.	.	PUNCT
cana-3476	12	1	by	by	ADP
cana-3476	12	2	establishing	establish	VERB
cana-3476	12	3	the	the	DET
cana-3476	12	4	convolution	convolution	NOUN
cana-3476	12	5	theorem	theorem	VERB
cana-3476	12	6	,	,	PUNCT
cana-3476	12	7	the	the	DET
cana-3476	12	8	idea	idea	NOUN
cana-3476	12	9	of	of	ADP
cana-3476	12	10	convolution	convolution	NOUN
cana-3476	12	11	is	be	AUX
cana-3476	12	12	examined	examine	VERB
cana-3476	12	13	in	in	ADP
cana-3476	12	14	further	further	ADJ
cana-3476	12	15	detail	detail	NOUN
cana-3476	12	16	.	.	PUNCT
cana-3476	13	1	results	result	NOUN
cana-3476	13	2	:	:	PUNCT
cana-3476	13	3	this	this	DET
cana-3476	13	4	integral	integral	ADJ
cana-3476	13	5	transform	transform	NOUN
cana-3476	13	6	is	be	AUX
cana-3476	13	7	used	use	VERB
cana-3476	13	8	for	for	ADP
cana-3476	13	9	solving	solve	VERB
cana-3476	13	10	higher	high	ADJ
cana-3476	13	11	order	order	NOUN
cana-3476	13	12	initial	initial	ADJ
cana-3476	13	13	value	value	NOUN
cana-3476	13	14	problems	problem	NOUN
cana-3476	13	15	and	and	CCONJ
cana-3476	13	16	integral	integral	ADJ
cana-3476	13	17	equations	equation	NOUN
cana-3476	13	18	.	.	PUNCT
cana-3476	14	1	keywords	keyword	NOUN
cana-3476	14	2	:	:	PUNCT
cana-3476	14	3	time	time	NOUN
cana-3476	14	4	scales	scale	NOUN
cana-3476	14	5	,	,	PUNCT
cana-3476	14	6	new	new	ADJ
cana-3476	14	7	general	general	ADJ
cana-3476	14	8	integral	integral	ADJ
cana-3476	14	9	transform	transform	NOUN
cana-3476	14	10	,	,	PUNCT
cana-3476	14	11	dynamic	dynamic	ADJ
cana-3476	14	12	equation	equation	NOUN
cana-3476	14	13	.	.	PUNCT
cana-3476	15	1	1	1	X
cana-3476	15	2	.	.	X
cana-3476	15	3	introduction	introduction	NOUN
cana-3476	15	4	an	an	DET
cana-3476	15	5	arbitrary	arbitrary	ADJ
cana-3476	15	6	nonempty	nonempty	X
cana-3476	15	7	closed	close	VERB
cana-3476	15	8	subset	subset	NOUN
cana-3476	15	9	of	of	ADP
cana-3476	15	10	real	real	ADJ
cana-3476	15	11	numbers	number	NOUN
cana-3476	15	12	is	be	AUX
cana-3476	15	13	called	call	VERB
cana-3476	15	14	a	a	DET
cana-3476	15	15	time	time	NOUN
cana-3476	15	16	scale	scale	NOUN
cana-3476	15	17	𝕋.	𝕋.	NOUN
cana-3476	15	18	due	due	ADJ
cana-3476	15	19	in	in	ADP
cana-3476	15	20	part	part	NOUN
cana-3476	15	21	to	to	PART
cana-3476	15	22	transform	transform	VERB
cana-3476	15	23	methods	method	NOUN
cana-3476	15	24	for	for	ADP
cana-3476	15	25	solving	solve	VERB
cana-3476	15	26	differential	differential	ADJ
cana-3476	15	27	equations	equation	NOUN
cana-3476	15	28	,	,	PUNCT
cana-3476	15	29	transforms	transform	VERB
cana-3476	15	30	are	be	AUX
cana-3476	15	31	essential	essential	ADJ
cana-3476	15	32	in	in	ADP
cana-3476	15	33	analysis	analysis	NOUN
cana-3476	15	34	.	.	PUNCT
cana-3476	16	1	many	many	ADJ
cana-3476	16	2	significant	significant	ADJ
cana-3476	16	3	changes	change	NOUN
cana-3476	16	4	have	have	AUX
cana-3476	16	5	been	be	AUX
cana-3476	16	6	introduced	introduce	VERB
cana-3476	16	7	over	over	ADP
cana-3476	16	8	the	the	DET
cana-3476	16	9	past	past	ADJ
cana-3476	16	10	20	20	NUM
cana-3476	16	11	years	year	NOUN
cana-3476	16	12	,	,	PUNCT
cana-3476	16	13	including	include	VERB
cana-3476	16	14	kamal	kamal	PROPN
cana-3476	16	15	[	[	X
cana-3476	16	16	2	2	NUM
cana-3476	16	17	]	]	PUNCT
cana-3476	16	18	,	,	PUNCT
cana-3476	16	19	shehu	shehu	X
cana-3476	17	1	[	[	X
cana-3476	17	2	6	6	NUM
cana-3476	17	3	]	]	PUNCT
cana-3476	17	4	,	,	PUNCT
cana-3476	17	5	soham	soham	PROPN
cana-3476	18	1	[	[	X
cana-3476	18	2	7	7	NUM
cana-3476	18	3	]	]	PUNCT
cana-3476	18	4	,	,	PUNCT
cana-3476	18	5	sumudu	sumudu	NOUN
cana-3476	18	6	[	[	X
cana-3476	18	7	10	10	NUM
cana-3476	18	8	]	]	PUNCT
cana-3476	18	9	,	,	PUNCT
cana-3476	18	10	sawi	sawi	ADJ
cana-3476	19	1	[	[	X
cana-3476	19	2	12	12	NUM
cana-3476	19	3	]	]	PUNCT
cana-3476	19	4	,	,	PUNCT
cana-3476	19	5	kushare	kushare	PROPN
cana-3476	20	1	[	[	X
cana-3476	20	2	14	14	NUM
cana-3476	20	3	]	]	PUNCT
cana-3476	20	4	,	,	PUNCT
cana-3476	20	5	elzaki	elzaki	VERB
cana-3476	20	6	[	[	X
cana-3476	20	7	17	17	NUM
cana-3476	20	8	]	]	PUNCT
cana-3476	20	9	and	and	CCONJ
cana-3476	20	10	others	other	NOUN
cana-3476	20	11	.	.	PUNCT
cana-3476	21	1	additionally	additionally	ADV
cana-3476	21	2	,	,	PUNCT
cana-3476	21	3	a	a	DET
cana-3476	21	4	few	few	ADJ
cana-3476	21	5	time	time	NOUN
cana-3476	21	6	-	-	PUNCT
cana-3476	21	7	scale	scale	NOUN
cana-3476	21	8	integral	integral	ADJ
cana-3476	21	9	transforms	transform	NOUN
cana-3476	21	10	are	be	AUX
cana-3476	21	11	previously	previously	ADV
cana-3476	21	12	introduced	introduce	VERB
cana-3476	21	13	.	.	PUNCT
cana-3476	22	1	in	in	ADP
cana-3476	22	2	2007	2007	NUM
cana-3476	22	3	,	,	PUNCT
cana-3476	22	4	john	john	PROPN
cana-3476	22	5	m.	m.	PROPN
cana-3476	22	6	devis	devis	PROPN
cana-3476	22	7	et	et	PROPN
cana-3476	22	8	al	al	PROPN
cana-3476	22	9	.	.	PROPN
cana-3476	22	10	examined	examine	VERB
cana-3476	22	11	the	the	DET
cana-3476	22	12	laplace	laplace	NOUN
cana-3476	22	13	transform	transform	NOUN
cana-3476	22	14	on	on	ADP
cana-3476	22	15	time	time	NOUN
cana-3476	22	16	scales	scale	NOUN
cana-3476	22	17	[	[	X
cana-3476	22	18	8	8	NUM
cana-3476	22	19	]	]	PUNCT
cana-3476	22	20	.	.	PUNCT
cana-3476	23	1	in	in	ADP
cana-3476	23	2	2012	2012	NUM
cana-3476	23	3	,	,	PUNCT
cana-3476	23	4	hassan	hassan	PROPN
cana-3476	23	5	ahmed	ahme	VERB
cana-3476	23	6	agwa	agwa	PROPN
cana-3476	23	7	introduced	introduce	VERB
cana-3476	23	8	the	the	DET
cana-3476	23	9	sumudu	sumudu	NOUN
cana-3476	23	10	transform	transform	NOUN
cana-3476	23	11	on	on	ADP
cana-3476	23	12	time	time	NOUN
cana-3476	23	13	scales	scale	NOUN
cana-3476	23	14	[	[	X
cana-3476	23	15	1	1	NUM
cana-3476	23	16	]	]	PUNCT
cana-3476	23	17	.	.	PUNCT
cana-3476	24	1	the	the	DET
cana-3476	24	2	α	α	NOUN
cana-3476	24	3	-	-	ADJ
cana-3476	24	4	laplace	laplace	NOUN
cana-3476	24	5	transform	transform	NOUN
cana-3476	24	6	on	on	ADP
cana-3476	24	7	time	time	NOUN
cana-3476	24	8	scales	scale	NOUN
cana-3476	24	9	[	[	X
cana-3476	24	10	16	16	NUM
cana-3476	24	11	]	]	PUNCT
cana-3476	24	12	was	be	AUX
cana-3476	24	13	introduced	introduce	VERB
cana-3476	24	14	by	by	ADP
cana-3476	24	15	t.g	t.g	PROPN
cana-3476	24	16	.	.	PROPN
cana-3476	24	17	thange	thange	PROPN
cana-3476	24	18	et	et	PROPN
cana-3476	24	19	al	al	PROPN
cana-3476	24	20	.	.	PROPN
cana-3476	25	1	in	in	ADP
cana-3476	25	2	2023	2023	NUM
cana-3476	25	3	.	.	PUNCT
cana-3476	26	1	he	he	PRON
cana-3476	26	2	also	also	ADV
cana-3476	26	3	presented	present	VERB
cana-3476	26	4	a	a	DET
cana-3476	26	5	new	new	ADJ
cana-3476	26	6	general	general	ADJ
cana-3476	26	7	integral	integral	ADJ
cana-3476	26	8	transform	transform	NOUN
cana-3476	26	9	on	on	ADP
cana-3476	26	10	time	time	NOUN
cana-3476	26	11	scales	scale	NOUN
cana-3476	26	12	[	[	X
cana-3476	26	13	15	15	NUM
cana-3476	26	14	]	]	PUNCT
cana-3476	26	15	in	in	ADP
cana-3476	26	16	2024	2024	NUM
cana-3476	26	17	.	.	PUNCT
cana-3476	27	1	noting	note	VERB
cana-3476	27	2	that	that	SCONJ
cana-3476	27	3	it	it	PRON
cana-3476	27	4	is	be	AUX
cana-3476	27	5	an	an	DET
cana-3476	27	6	extension	extension	NOUN
cana-3476	27	7	of	of	ADP
cana-3476	27	8	the	the	DET
cana-3476	27	9	new	new	ADJ
cana-3476	27	10	general	general	ADJ
cana-3476	27	11	complex	complex	ADJ
cana-3476	27	12	integral	integral	ADJ
cana-3476	27	13	transform	transform	NOUN
cana-3476	27	14	,	,	PUNCT
cana-3476	27	15	we	we	PRON
cana-3476	27	16	define	define	VERB
cana-3476	27	17	the	the	DET
cana-3476	27	18	new	new	ADJ
cana-3476	27	19	general	general	ADJ
cana-3476	27	20	complex	complex	ADJ
cana-3476	27	21	integral	integral	ADJ
cana-3476	27	22	transform	transform	NOUN
cana-3476	27	23	on	on	ADP
cana-3476	27	24	time	time	NOUN
cana-3476	27	25	scales	scale	NOUN
cana-3476	27	26	.	.	PUNCT
cana-3476	28	1	in	in	ADP
cana-3476	28	2	addition	addition	NOUN
cana-3476	28	3	to	to	ADP
cana-3476	28	4	discussing	discuss	VERB
cana-3476	28	5	situations	situation	NOUN
cana-3476	28	6	when	when	SCONJ
cana-3476	28	7	results	result	NOUN
cana-3476	28	8	might	might	AUX
cana-3476	28	9	not	not	PART
cana-3476	28	10	be	be	AUX
cana-3476	28	11	generalized	generalize	VERB
cana-3476	28	12	from	from	ADP
cana-3476	28	13	the	the	DET
cana-3476	28	14	real	real	ADJ
cana-3476	28	15	example	example	NOUN
cana-3476	28	16	to	to	ADP
cana-3476	28	17	time	time	NOUN
cana-3476	28	18	scales	scale	NOUN
cana-3476	28	19	,	,	PUNCT
cana-3476	28	20	we	we	PRON
cana-3476	28	21	provide	provide	VERB
cana-3476	28	22	features	feature	NOUN
cana-3476	28	23	of	of	ADP
cana-3476	28	24	this	this	DET
cana-3476	28	25	transform	transform	NOUN
cana-3476	28	26	.	.	PUNCT
cana-3476	29	1	this	this	DET
cana-3476	29	2	transform	transform	NOUN
cana-3476	29	3	is	be	AUX
cana-3476	29	4	used	use	VERB
cana-3476	29	5	in	in	ADP
cana-3476	29	6	examples	example	NOUN
cana-3476	29	7	to	to	PART
cana-3476	29	8	solve	solve	VERB
cana-3476	29	9	dynamic	dynamic	ADJ
cana-3476	29	10	equations	equation	NOUN
cana-3476	29	11	.	.	PUNCT
cana-3476	30	1	the	the	DET
cana-3476	30	2	integral	integral	ADJ
cana-3476	30	3	equations	equation	NOUN
cana-3476	30	4	are	be	AUX
cana-3476	30	5	also	also	ADV
cana-3476	30	6	solved	solve	VERB
cana-3476	30	7	using	use	VERB
cana-3476	30	8	the	the	DET
cana-3476	30	9	transform	transform	NOUN
cana-3476	30	10	.	.	PUNCT
cana-3476	31	1	the	the	DET
cana-3476	31	2	prospects	prospect	NOUN
cana-3476	31	3	for	for	ADP
cana-3476	31	4	a	a	DET
cana-3476	31	5	general	general	ADJ
cana-3476	31	6	complex	complex	ADJ
cana-3476	31	7	integral	integral	ADJ
cana-3476	31	8	transform	transform	NOUN
cana-3476	31	9	theory	theory	NOUN
cana-3476	31	10	based	base	VERB
cana-3476	31	11	on	on	ADP
cana-3476	31	12	time	time	NOUN
cana-3476	31	13	scales	scale	NOUN
cana-3476	31	14	are	be	AUX
cana-3476	31	15	finally	finally	ADV
cana-3476	31	16	discussed	discuss	VERB
cana-3476	31	17	.	.	PUNCT
cana-3476	32	1	2	2	X
cana-3476	32	2	.	.	X
cana-3476	32	3	basic	basic	ADJ
cana-3476	32	4	results	result	NOUN
cana-3476	32	5	communications	communication	NOUN
cana-3476	32	6	on	on	ADP
cana-3476	32	7	applied	apply	VERB
cana-3476	32	8	nonlinear	nonlinear	ADJ
cana-3476	32	9	analysis	analysis	NOUN
cana-3476	32	10	issn	issn	NOUN
cana-3476	32	11	:	:	PUNCT
cana-3476	32	12	1074	1074	NUM
cana-3476	32	13	-	-	PUNCT
cana-3476	32	14	133x	133x	NUM
cana-3476	32	15	vol	vol	NOUN
cana-3476	32	16	32	32	NUM
cana-3476	32	17	no	no	NOUN
cana-3476	32	18	.	.	PUNCT
cana-3476	33	1	7s	7	NOUN
cana-3476	33	2	(	(	PUNCT
cana-3476	33	3	2025	2025	NUM
cana-3476	33	4	)	)	PUNCT
cana-3476	33	5	695	695	NUM
cana-3476	33	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	33	7	2.1	2.1	NUM
cana-3476	33	8	forward	forward	ADV
cana-3476	33	9	jump	jump	NOUN
cana-3476	33	10	operator	operator	NOUN
cana-3476	33	11	[	[	X
cana-3476	33	12	4	4	NUM
cana-3476	33	13	]	]	PUNCT
cana-3476	33	14	:	:	PUNCT
cana-3476	33	15	𝜎	𝜎	X
cana-3476	33	16	:	:	PUNCT
cana-3476	33	17	𝕋	𝕋	NOUN
cana-3476	33	18	→	→	SYM
cana-3476	33	19	𝕋	𝕋	NOUN
cana-3476	33	20	is	be	AUX
cana-3476	33	21	defined	define	VERB
cana-3476	33	22	by	by	ADP
cana-3476	33	23	𝜎(𝑡	𝜎(𝑡	NUM
cana-3476	33	24	)	)	PUNCT
cana-3476	33	25	=	=	PUNCT
cana-3476	34	1	inf{𝑠	inf{𝑠	NOUN
cana-3476	34	2	∈	∈	PROPN
cana-3476	34	3	𝕋	𝕋	NOUN
cana-3476	34	4	|	|	NOUN
cana-3476	34	5	𝑠	𝑠	INTJ
cana-3476	34	6	>	>	X
cana-3476	34	7	𝑡	𝑡	X
cana-3476	34	8	}	}	PUNCT
cana-3476	34	9	.	.	PUNCT
cana-3476	35	1	2.2	2.2	NUM
cana-3476	35	2	backward	backward	ADJ
cana-3476	35	3	jump	jump	NOUN
cana-3476	35	4	operator	operator	NOUN
cana-3476	35	5	[	[	X
cana-3476	35	6	4	4	NUM
cana-3476	35	7	]	]	SYM
cana-3476	35	8	:	:	PUNCT
cana-3476	35	9	𝜌	𝜌	ADP
cana-3476	35	10	:	:	PUNCT
cana-3476	35	11	𝕋	𝕋	NOUN
cana-3476	35	12	→	→	SYM
cana-3476	35	13	𝕋	𝕋	NOUN
cana-3476	35	14	is	be	AUX
cana-3476	35	15	defined	define	VERB
cana-3476	35	16	by	by	ADP
cana-3476	35	17	𝜌(𝑡	𝜌(𝑡	NOUN
cana-3476	35	18	)	)	PUNCT
cana-3476	36	1	=	=	PUNCT
cana-3476	36	2	sup{𝑠	sup{𝑠	NOUN
cana-3476	36	3	∈	∈	PROPN
cana-3476	36	4	𝕋	𝕋	NOUN
cana-3476	36	5	|	|	NOUN
cana-3476	36	6	𝑠	𝑠	X
cana-3476	36	7	<	<	X
cana-3476	36	8	𝑡	𝑡	X
cana-3476	36	9	}	}	PUNCT
cana-3476	36	10	.	.	PUNCT
cana-3476	37	1	2.3	2.3	NUM
cana-3476	37	2	forward	forward	ADV
cana-3476	37	3	graininess	graininess	NOUN
cana-3476	37	4	function	function	NOUN
cana-3476	37	5	[	[	X
cana-3476	37	6	4	4	NUM
cana-3476	37	7	]	]	PUNCT
cana-3476	37	8	:	:	PUNCT
cana-3476	37	9	𝜇	𝜇	ADP
cana-3476	37	10	:	:	PUNCT
cana-3476	37	11	𝕋	𝕋	X
cana-3476	37	12	→	→	SYM
cana-3476	37	13	[	[	X
cana-3476	37	14	0	0	NUM
cana-3476	37	15	,	,	PUNCT
cana-3476	37	16	∞	∞	NUM
cana-3476	37	17	)	)	PUNCT
cana-3476	37	18	is	be	AUX
cana-3476	37	19	defined	define	VERB
cana-3476	37	20	by	by	ADP
cana-3476	37	21	𝜇(𝑡	𝜇(𝑡	NOUN
cana-3476	37	22	)	)	PUNCT
cana-3476	37	23	=	=	SYM
cana-3476	37	24	𝜎(𝑡	𝜎(𝑡	NUM
cana-3476	37	25	)	)	PUNCT
cana-3476	37	26	−	−	NOUN
cana-3476	37	27	𝑡.	𝑡.	VERB
cana-3476	37	28	2.4	2.4	NUM
cana-3476	37	29	definition	definition	NOUN
cana-3476	37	30	1	1	NUM
cana-3476	37	31	[	[	X
cana-3476	37	32	5	5	NUM
cana-3476	37	33	]	]	PUNCT
cana-3476	37	34	a	a	DET
cana-3476	37	35	function	function	NOUN
cana-3476	37	36	𝑓	𝑓	NOUN
cana-3476	37	37	is	be	AUX
cana-3476	37	38	called	call	VERB
cana-3476	37	39	regulated	regulate	VERB
cana-3476	37	40	provided	provide	VERB
cana-3476	37	41	its	its	PRON
cana-3476	37	42	right	right	ADV
cana-3476	37	43	-	-	PUNCT
cana-3476	37	44	sided	side	VERB
cana-3476	37	45	limits	limit	NOUN
cana-3476	37	46	exist	exist	VERB
cana-3476	37	47	at	at	ADV
cana-3476	37	48	all	all	ADV
cana-3476	37	49	right	right	ADJ
cana-3476	37	50	dense	dense	ADJ
cana-3476	37	51	points	point	NOUN
cana-3476	37	52	in	in	ADP
cana-3476	37	53	𝕋	𝕋	NOUN
cana-3476	37	54	and	and	CCONJ
cana-3476	37	55	left	leave	VERB
cana-3476	37	56	sided	sided	ADJ
cana-3476	37	57	limits	limit	NOUN
cana-3476	37	58	exists	exist	VERB
cana-3476	37	59	at	at	ADP
cana-3476	37	60	all	all	ADV
cana-3476	37	61	left	leave	VERB
cana-3476	37	62	dense	dense	ADJ
cana-3476	37	63	points	point	NOUN
cana-3476	37	64	in	in	ADP
cana-3476	37	65	𝕋.	𝕋.	NOUN
cana-3476	37	66	2.5	2.5	NUM
cana-3476	37	67	definition	definition	NOUN
cana-3476	37	68	2	2	NUM
cana-3476	37	69	[	[	X
cana-3476	37	70	5	5	NUM
cana-3476	37	71	]	]	PUNCT
cana-3476	37	72	a	a	DET
cana-3476	37	73	function	function	NOUN
cana-3476	37	74	𝑓	𝑓	NOUN
cana-3476	37	75	is	be	AUX
cana-3476	37	76	called	call	VERB
cana-3476	37	77	rd	rd	NOUN
cana-3476	37	78	-	-	ADJ
cana-3476	37	79	continuous	continuous	ADJ
cana-3476	37	80	provided	provide	VERB
cana-3476	37	81	it	it	PRON
cana-3476	37	82	is	be	AUX
cana-3476	37	83	continuous	continuous	ADJ
cana-3476	37	84	at	at	ADP
cana-3476	37	85	right	right	ADJ
cana-3476	37	86	dense	dense	ADJ
cana-3476	37	87	points	point	NOUN
cana-3476	37	88	in	in	ADP
cana-3476	37	89	𝕋	𝕋	NOUN
cana-3476	37	90	and	and	CCONJ
cana-3476	37	91	its	its	PRON
cana-3476	37	92	left	left	ADJ
cana-3476	37	93	-	-	PUNCT
cana-3476	37	94	sided	side	VERB
cana-3476	37	95	limits	limit	NOUN
cana-3476	37	96	exists	exist	VERB
cana-3476	37	97	at	at	ADP
cana-3476	37	98	left	left	ADJ
cana-3476	37	99	dense	dense	ADJ
cana-3476	37	100	points	point	NOUN
cana-3476	37	101	in	in	ADP
cana-3476	37	102	𝕋.	𝕋.	NOUN
cana-3476	37	103	we	we	PRON
cana-3476	37	104	denote	denote	VERB
cana-3476	37	105	the	the	DET
cana-3476	37	106	set	set	NOUN
cana-3476	37	107	of	of	ADP
cana-3476	37	108	rd	rd	NOUN
cana-3476	37	109	-	-	ADJ
cana-3476	37	110	continuous	continuous	ADJ
cana-3476	37	111	functions	function	NOUN
cana-3476	37	112	by	by	ADP
cana-3476	37	113	𝐶𝑟𝑑.	𝐶𝑟𝑑.	ADV
cana-3476	37	114	2.6	2.6	NUM
cana-3476	37	115	definition	definition	NOUN
cana-3476	37	116	3	3	NUM
cana-3476	37	117	[	[	X
cana-3476	37	118	5	5	NUM
cana-3476	37	119	]	]	PUNCT
cana-3476	37	120	a	a	DET
cana-3476	37	121	function	function	NOUN
cana-3476	37	122	𝑓:𝕋→	𝑓:𝕋→	ADJ
cana-3476	37	123	ℂ	ℂ	PROPN
cana-3476	37	124	is	be	AUX
cana-3476	37	125	called	call	VERB
cana-3476	37	126	regressive	regressive	ADJ
cana-3476	37	127	if	if	SCONJ
cana-3476	37	128	1	1	NUM
cana-3476	37	129	+	+	NUM
cana-3476	37	130	𝜇(𝑡)𝑓(𝑡	𝜇(𝑡)𝑓(𝑡	X
cana-3476	37	131	)	)	PUNCT
cana-3476	37	132	≠	≠	PROPN
cana-3476	37	133	0	0	NUM
cana-3476	37	134	∀𝑡	∀𝑡	NUM
cana-3476	37	135	∈	∈	NOUN
cana-3476	37	136	𝕋.	𝕋.	NOUN
cana-3476	37	137	here	here	ADV
cana-3476	37	138	ℛ	ℛ	PROPN
cana-3476	37	139	denotes	denote	VERB
cana-3476	37	140	the	the	DET
cana-3476	37	141	set	set	NOUN
cana-3476	37	142	of	of	ADP
cana-3476	37	143	regressive	regressive	ADJ
cana-3476	37	144	functions	function	NOUN
cana-3476	37	145	.	.	PUNCT
cana-3476	38	1	2.7	2.7	NUM
cana-3476	38	2	definition	definition	NOUN
cana-3476	38	3	4	4	NUM
cana-3476	38	4	[	[	X
cana-3476	38	5	5	5	NUM
cana-3476	38	6	]	]	PUNCT
cana-3476	38	7	the	the	DET
cana-3476	38	8	function	function	NOUN
cana-3476	38	9	𝑓	𝑓	NOUN
cana-3476	38	10	:	:	PUNCT
cana-3476	38	11	𝕋	𝕋	PROPN
cana-3476	38	12	→	→	SYM
cana-3476	38	13	ℝ	ℝ	PROPN
cana-3476	38	14	is	be	AUX
cana-3476	38	15	said	say	VERB
cana-3476	38	16	to	to	PART
cana-3476	38	17	be	be	AUX
cana-3476	38	18	of	of	ADP
cana-3476	38	19	exponential	exponential	ADJ
cana-3476	38	20	type	type	NOUN
cana-3476	38	21	-	-	PUNCT
cana-3476	38	22	i	i	PRON
cana-3476	38	23	if	if	SCONJ
cana-3476	38	24	there	there	PRON
cana-3476	38	25	exists	exist	VERB
cana-3476	38	26	constants	constant	NOUN
cana-3476	38	27	𝑀	𝑀	PROPN
cana-3476	38	28	,	,	PUNCT
cana-3476	38	29	𝑐	𝑐	PROPN
cana-3476	38	30	>	>	X
cana-3476	38	31	0	0	NUM
cana-3476	38	32	such	such	ADJ
cana-3476	38	33	that	that	SCONJ
cana-3476	38	34	|𝑓(𝑡)|	|𝑓(𝑡)|	PROPN
cana-3476	38	35	≤	≤	PROPN
cana-3476	38	36	𝑀𝑒𝑐𝑡.	𝑀𝑒𝑐𝑡.	PROPN
cana-3476	38	37	furthermore	furthermore	ADV
cana-3476	38	38	,	,	PUNCT
cana-3476	38	39	𝑓	𝑓	PRON
cana-3476	38	40	is	be	AUX
cana-3476	38	41	said	say	VERB
cana-3476	38	42	to	to	PART
cana-3476	38	43	be	be	AUX
cana-3476	38	44	of	of	ADP
cana-3476	38	45	exponential	exponential	ADJ
cana-3476	38	46	type	type	NOUN
cana-3476	38	47	-	-	PUNCT
cana-3476	38	48	ii	ii	NOUN
cana-3476	38	49	if	if	SCONJ
cana-3476	38	50	there	there	PRON
cana-3476	38	51	exists	exist	VERB
cana-3476	38	52	constants	constant	NOUN
cana-3476	38	53	𝑀	𝑀	PROPN
cana-3476	38	54	,	,	PUNCT
cana-3476	38	55	𝑐	𝑐	PROPN
cana-3476	38	56	>	>	X
cana-3476	38	57	0	0	NUM
cana-3476	38	58	such	such	ADJ
cana-3476	38	59	that	that	SCONJ
cana-3476	38	60	|𝑓(𝑡)|	|𝑓(𝑡)|	PROPN
cana-3476	38	61	≤	≤	PROPN
cana-3476	38	62	𝑀𝑒𝑐(𝑡	𝑀𝑒𝑐(𝑡	PROPN
cana-3476	38	63	,	,	PUNCT
cana-3476	38	64	0	0	NUM
cana-3476	38	65	)	)	PUNCT
cana-3476	38	66	.	.	PUNCT
cana-3476	39	1	2.8	2.8	NUM
cana-3476	39	2	definition	definition	NOUN
cana-3476	39	3	5	5	NUM
cana-3476	39	4	[	[	X
cana-3476	39	5	5	5	NUM
cana-3476	39	6	]	]	PUNCT
cana-3476	39	7	for	for	ADP
cana-3476	39	8	𝑓	𝑓	DET
cana-3476	39	9	∈	∈	PROPN
cana-3476	39	10	ℛ	ℛ	NOUN
cana-3476	39	11	the	the	DET
cana-3476	39	12	time	time	NOUN
cana-3476	39	13	scale	scale	NOUN
cana-3476	39	14	exponential	exponential	ADJ
cana-3476	39	15	function	function	NOUN
cana-3476	39	16	is	be	AUX
cana-3476	39	17	defined	define	VERB
cana-3476	39	18	as	as	ADP
cana-3476	39	19	𝑒𝑓(𝑡	𝑒𝑓(𝑡	ADJ
cana-3476	39	20	,	,	PUNCT
cana-3476	39	21	𝑠	𝑠	X
cana-3476	39	22	)	)	PUNCT
cana-3476	39	23	=	=	SYM
cana-3476	39	24	𝑒𝑥𝑝	𝑒𝑥𝑝	INTJ
cana-3476	39	25	(	(	PUNCT
cana-3476	39	26	∫	∫	PROPN
cana-3476	39	27	𝜉𝜇(𝜏)𝑓(𝜏)∆𝜏	𝜉𝜇(𝜏)𝑓(𝜏)∆𝜏	PROPN
cana-3476	40	1	𝑡	𝑡	PROPN
cana-3476	40	2	𝑠	𝑠	PROPN
cana-3476	40	3	)	)	PUNCT
cana-3476	40	4	for	for	ADP
cana-3476	40	5	𝑠	𝑠	PROPN
cana-3476	40	6	,	,	PUNCT
cana-3476	40	7	𝑡	𝑡	PROPN
cana-3476	40	8	∈	∈	PROPN
cana-3476	40	9	𝕋	𝕋	NOUN
cana-3476	40	10	and	and	CCONJ
cana-3476	40	11	𝜉𝜇(𝑡	𝜉𝜇(𝑡	NUM
cana-3476	40	12	)	)	PUNCT
cana-3476	40	13	is	be	AUX
cana-3476	40	14	a	a	DET
cana-3476	40	15	cylinder	cylinder	NOUN
cana-3476	40	16	transformation	transformation	NOUN
cana-3476	40	17	.	.	PUNCT
cana-3476	41	1	2.9	2.9	NUM
cana-3476	41	2	definition	definition	NOUN
cana-3476	41	3	6	6	NUM
cana-3476	41	4	[	[	NOUN
cana-3476	41	5	4	4	X
cana-3476	41	6	]	]	PUNCT
cana-3476	41	7	we	we	PRON
cana-3476	41	8	say	say	VERB
cana-3476	41	9	that	that	SCONJ
cana-3476	41	10	a	a	DET
cana-3476	41	11	function	function	NOUN
cana-3476	41	12	𝑓	𝑓	NOUN
cana-3476	41	13	:	:	PUNCT
cana-3476	41	14	𝕋	𝕋	PROPN
cana-3476	41	15	→	→	SYM
cana-3476	41	16	ℝ	ℝ	PROPN
cana-3476	41	17	is	be	AUX
cana-3476	41	18	delta	delta	NOUN
cana-3476	41	19	differentiable	differentiable	ADJ
cana-3476	41	20	at	at	ADP
cana-3476	41	21	𝑡	𝑡	PROPN
cana-3476	41	22	∈	∈	PROPN
cana-3476	42	1	𝕋𝜅	𝕋𝜅	NOUN
cana-3476	42	2	if	if	SCONJ
cana-3476	42	3	there	there	PRON
cana-3476	42	4	exists	exist	VERB
cana-3476	42	5	a	a	DET
cana-3476	42	6	number	number	NOUN
cana-3476	42	7	𝑓∆(𝑡	𝑓∆(𝑡	NUM
cana-3476	42	8	)	)	PUNCT
cana-3476	42	9	such	such	ADJ
cana-3476	42	10	that	that	PRON
cana-3476	42	11	for	for	ADP
cana-3476	42	12	all	all	PRON
cana-3476	42	13	𝜖	𝜖	X
cana-3476	42	14	>	>	X
cana-3476	42	15	0	0	PUNCT
cana-3476	42	16	there	there	PRON
cana-3476	42	17	exists	exist	VERB
cana-3476	42	18	a	a	DET
cana-3476	42	19	neighbourhood	neighbourhood	NOUN
cana-3476	42	20	𝑈	𝑈	NOUN
cana-3476	42	21	of	of	ADP
cana-3476	42	22	𝑡	𝑡	PROPN
cana-3476	42	23	such	such	ADJ
cana-3476	42	24	that	that	SCONJ
cana-3476	42	25	|𝑓(𝜎(𝑡	|𝑓(𝜎(𝑡	PROPN
cana-3476	42	26	)	)	PUNCT
cana-3476	42	27	)	)	PUNCT
cana-3476	42	28	−	−	PROPN
cana-3476	42	29	𝑓(𝑠	𝑓(𝑠	NOUN
cana-3476	42	30	)	)	PUNCT
cana-3476	42	31	−	−	PROPN
cana-3476	42	32	𝑓∆(𝑡)(𝜎(𝑡	𝑓∆(𝑡)(𝜎(𝑡	PROPN
cana-3476	42	33	)	)	PUNCT
cana-3476	42	34	−	−	NOUN
cana-3476	42	35	𝑠)|	𝑠)|	VERB
cana-3476	42	36	≤	≤	NUM
cana-3476	42	37	𝜖|𝜎(𝑡	𝜖|𝜎(𝑡	NOUN
cana-3476	42	38	)	)	PUNCT
cana-3476	42	39	−	−	PROPN
cana-3476	43	1	𝑠|	𝑠|	NOUN
cana-3476	43	2	for	for	ADP
cana-3476	43	3	all	all	PRON
cana-3476	43	4	𝑠	𝑠	PROPN
cana-3476	43	5	∈	∈	PROPN
cana-3476	43	6	𝑈.	𝑈.	NOUN
cana-3476	43	7	(	(	PUNCT
cana-3476	43	8	𝕋𝜅	𝕋𝜅	PROPN
cana-3476	43	9	≔	≔	VERB
cana-3476	43	10	𝕋\{sup	𝕋\{sup	NOUN
cana-3476	43	11	𝕋	𝕋	NOUN
cana-3476	43	12	}	}	PUNCT
cana-3476	43	13	)	)	PUNCT
cana-3476	43	14	2.10	2.10	NUM
cana-3476	43	15	if	if	SCONJ
cana-3476	43	16	𝕋	𝕋	NOUN
cana-3476	43	17	=	=	SYM
cana-3476	43	18	ℝ	ℝ	PROPN
cana-3476	43	19	,	,	PUNCT
cana-3476	43	20	then	then	ADV
cana-3476	43	21	𝑓	𝑓	X
cana-3476	43	22	:	:	PUNCT
cana-3476	43	23	ℝ	ℝ	PROPN
cana-3476	43	24	→	→	SYM
cana-3476	43	25	ℝ	ℝ	PROPN
cana-3476	43	26	is	be	AUX
cana-3476	43	27	delta	delta	NOUN
cana-3476	43	28	differentiable	differentiable	ADJ
cana-3476	43	29	at	at	ADP
cana-3476	43	30	𝑡	𝑡	PROPN
cana-3476	43	31	∈	∈	PROPN
cana-3476	43	32	ℝ	ℝ	PROPN
cana-3476	43	33	if	if	SCONJ
cana-3476	43	34	and	and	CCONJ
cana-3476	43	35	only	only	ADV
cana-3476	43	36	if	if	SCONJ
cana-3476	43	37	𝑓	𝑓	PRON
cana-3476	43	38	is	be	AUX
cana-3476	43	39	differentiable	differentiable	ADJ
cana-3476	43	40	in	in	ADP
cana-3476	43	41	the	the	DET
cana-3476	43	42	ordinary	ordinary	ADJ
cana-3476	43	43	sense	sense	NOUN
cana-3476	43	44	at	at	ADP
cana-3476	43	45	𝑡.	𝑡.	NOUN
cana-3476	43	46	that	that	PRON
cana-3476	43	47	is	be	AUX
cana-3476	43	48	𝑓∆(𝑡	𝑓∆(𝑡	NOUN
cana-3476	43	49	)	)	PUNCT
cana-3476	43	50	=	=	SYM
cana-3476	43	51	𝑑𝑓	𝑑𝑓	PROPN
cana-3476	43	52	𝑑𝑡	𝑑𝑡	ADP
cana-3476	43	53	.	.	PUNCT
cana-3476	44	1	[	[	X
cana-3476	44	2	9	9	NUM
cana-3476	44	3	]	]	SYM
cana-3476	44	4	2.11	2.11	NUM
cana-3476	44	5	laplace	laplace	NOUN
cana-3476	44	6	transform	transform	NOUN
cana-3476	44	7	on	on	ADP
cana-3476	44	8	time	time	NOUN
cana-3476	44	9	scales	scale	NOUN
cana-3476	44	10	[	[	X
cana-3476	44	11	5	5	NUM
cana-3476	44	12	]	]	PUNCT
cana-3476	44	13	:	:	PUNCT
cana-3476	44	14	assume	assume	VERB
cana-3476	44	15	that	that	SCONJ
cana-3476	44	16	𝑥	𝑥	X
cana-3476	44	17	:	:	PUNCT
cana-3476	44	18	𝕋	𝕋	NOUN
cana-3476	44	19	→	→	SYM
cana-3476	44	20	ℝ	ℝ	PROPN
cana-3476	44	21	is	be	AUX
cana-3476	44	22	regulated	regulate	VERB
cana-3476	44	23	.	.	PUNCT
cana-3476	45	1	then	then	ADV
cana-3476	45	2	the	the	DET
cana-3476	45	3	laplace	laplace	NOUN
cana-3476	45	4	transform	transform	NOUN
cana-3476	45	5	of	of	ADP
cana-3476	45	6	𝑥	𝑥	PROPN
cana-3476	45	7	is	be	AUX
cana-3476	45	8	defined	define	VERB
cana-3476	45	9	by	by	ADP
cana-3476	45	10	𝓛	𝓛	PROPN
cana-3476	45	11	{	{	PUNCT
cana-3476	45	12	𝑥}(𝑧	𝑥}(𝑧	PROPN
cana-3476	45	13	)	)	PUNCT
cana-3476	45	14	=	=	SYM
cana-3476	46	1	∫	∫	PROPN
cana-3476	46	2	𝑒⊖𝑧	𝑒⊖𝑧	PROPN
cana-3476	46	3	𝜎	𝜎	PROPN
cana-3476	46	4	(	(	PUNCT
cana-3476	46	5	𝑡	𝑡	PROPN
cana-3476	46	6	,	,	PUNCT
cana-3476	46	7	0)𝑥(𝑡)∆𝑡	0)𝑥(𝑡)∆𝑡	X
cana-3476	46	8	∞	∞	NUM
cana-3476	46	9	0	0	NUM
cana-3476	46	10	for	for	ADP
cana-3476	46	11	𝑧	𝑧	PRON
cana-3476	46	12	∈	∈	PROPN
cana-3476	46	13	𝒟	𝒟	NOUN
cana-3476	46	14	{	{	PUNCT
cana-3476	46	15	𝑥	𝑥	NOUN
cana-3476	46	16	}	}	PUNCT
cana-3476	46	17	where	where	SCONJ
cana-3476	46	18	𝒟	𝒟	NOUN
cana-3476	46	19	{	{	PUNCT
cana-3476	46	20	𝑥	𝑥	NOUN
cana-3476	46	21	}	}	PUNCT
cana-3476	46	22	consists	consist	VERB
cana-3476	46	23	of	of	ADP
cana-3476	46	24	all	all	DET
cana-3476	46	25	complex	complex	ADJ
cana-3476	46	26	numbers	number	NOUN
cana-3476	46	27	𝑧	𝑧	DET
cana-3476	46	28	∈	∈	PROPN
cana-3476	46	29	ℛ	ℛ	NOUN
cana-3476	46	30	for	for	ADP
cana-3476	46	31	which	which	PRON
cana-3476	46	32	improper	improper	ADJ
cana-3476	46	33	integral	integral	ADJ
cana-3476	46	34	exists	exist	NOUN
cana-3476	46	35	.	.	PUNCT
cana-3476	47	1	2.12	2.12	NUM
cana-3476	47	2	sumudu	sumudu	NOUN
cana-3476	47	3	transform	transform	NOUN
cana-3476	47	4	on	on	ADP
cana-3476	47	5	time	time	NOUN
cana-3476	47	6	scales	scale	NOUN
cana-3476	47	7	[	[	X
cana-3476	47	8	1	1	NUM
cana-3476	47	9	]	]	PUNCT
cana-3476	47	10	:	:	PUNCT
cana-3476	47	11	assume	assume	VERB
cana-3476	47	12	that	that	SCONJ
cana-3476	47	13	𝑓	𝑓	X
cana-3476	47	14	:	:	PUNCT
cana-3476	47	15	𝕋	𝕋	PROPN
cana-3476	47	16	→	→	SYM
cana-3476	47	17	ℝ	ℝ	PROPN
cana-3476	47	18	is	be	AUX
cana-3476	47	19	rd	rd	NOUN
cana-3476	47	20	-	-	ADJ
cana-3476	47	21	continuous	continuous	ADJ
cana-3476	47	22	function	function	NOUN
cana-3476	47	23	,	,	PUNCT
cana-3476	47	24	then	then	ADV
cana-3476	47	25	the	the	DET
cana-3476	47	26	sumudu	sumudu	NOUN
cana-3476	47	27	transform	transform	NOUN
cana-3476	47	28	of	of	ADP
cana-3476	47	29	𝑓	𝑓	PRON
cana-3476	47	30	is	be	AUX
cana-3476	47	31	𝑆{𝑓}(𝑢	𝑆{𝑓}(𝑢	NOUN
cana-3476	47	32	)	)	PUNCT
cana-3476	47	33	=	=	SYM
cana-3476	47	34	1	1	NUM
cana-3476	47	35	𝑢	𝑢	DET
cana-3476	47	36	∫	∫	PROPN
cana-3476	47	37	𝑒	𝑒	X
cana-3476	47	38	⊖	⊖	PUNCT
cana-3476	47	39	1	1	NUM
cana-3476	47	40	𝑢	𝑢	PROPN
cana-3476	47	41	𝜎	𝜎	PROPN
cana-3476	47	42	(	(	PUNCT
cana-3476	47	43	𝑡	𝑡	PROPN
cana-3476	47	44	,	,	PUNCT
cana-3476	47	45	𝑡0)𝑓(𝑡)∆𝑡	𝑡0)𝑓(𝑡)∆𝑡	ADJ
cana-3476	47	46	∞	∞	NUM
cana-3476	47	47	𝑡0	𝑡0	NOUN
cana-3476	47	48	for	for	ADP
cana-3476	47	49	𝑢	𝑢	PROPN
cana-3476	47	50	∈	∈	PROPN
cana-3476	47	51	𝒟	𝒟	PROPN
cana-3476	47	52	{	{	PUNCT
cana-3476	47	53	𝑓	𝑓	PROPN
cana-3476	47	54	}	}	PUNCT
cana-3476	47	55	where	where	SCONJ
cana-3476	47	56	𝒟	𝒟	PROPN
cana-3476	47	57	{	{	PUNCT
cana-3476	47	58	𝑓	𝑓	PROPN
cana-3476	47	59	}	}	PUNCT
cana-3476	47	60	consists	consist	VERB
cana-3476	47	61	of	of	ADP
cana-3476	47	62	all	all	DET
cana-3476	47	63	complex	complex	ADJ
cana-3476	47	64	numbers	number	NOUN
cana-3476	47	65	𝑢	𝑢	X
cana-3476	47	66	∈	∈	PROPN
cana-3476	47	67	ℛ	ℛ	PROPN
cana-3476	47	68	for	for	ADP
cana-3476	47	69	which	which	PRON
cana-3476	47	70	improper	improper	ADJ
cana-3476	47	71	integral	integral	ADJ
cana-3476	47	72	exists	exist	NOUN
cana-3476	47	73	.	.	PUNCT
cana-3476	48	1	2.13	2.13	NUM
cana-3476	48	2	new	new	ADJ
cana-3476	48	3	general	general	ADJ
cana-3476	48	4	integral	integral	ADJ
cana-3476	48	5	transform	transform	NOUN
cana-3476	48	6	[	[	X
cana-3476	48	7	11	11	NUM
cana-3476	48	8	]	]	PUNCT
cana-3476	48	9	:	:	PUNCT
cana-3476	48	10	let	let	VERB
cana-3476	48	11	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	48	12	)	)	PUNCT
cana-3476	48	13	be	be	AUX
cana-3476	48	14	an	an	DET
cana-3476	48	15	integrable	integrable	ADJ
cana-3476	48	16	function	function	NOUN
cana-3476	48	17	defined	define	VERB
cana-3476	48	18	for	for	ADP
cana-3476	48	19	𝑡	𝑡	PROPN
cana-3476	48	20	≥	≥	NOUN
cana-3476	48	21	0	0	NUM
cana-3476	48	22	,	,	PUNCT
cana-3476	48	23	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	48	24	)	)	PUNCT
cana-3476	48	25	≠	≠	PROPN
cana-3476	48	26	0	0	NUM
cana-3476	48	27	and	and	CCONJ
cana-3476	48	28	𝑞(𝑠	𝑞(𝑠	NUM
cana-3476	48	29	)	)	PUNCT
cana-3476	48	30	are	be	AUX
cana-3476	48	31	positive	positive	ADJ
cana-3476	48	32	real	real	ADJ
cana-3476	48	33	functions	function	NOUN
cana-3476	48	34	then	then	ADV
cana-3476	48	35	define	define	VERB
cana-3476	48	36	new	new	ADJ
cana-3476	48	37	general	general	ADJ
cana-3476	48	38	integral	integral	ADJ
cana-3476	48	39	transform	transform	NOUN
cana-3476	48	40	𝒯(𝑠	𝒯(𝑠	NOUN
cana-3476	48	41	)	)	PUNCT
cana-3476	48	42	of	of	ADP
cana-3476	48	43	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	48	44	)	)	PUNCT
cana-3476	48	45	by	by	ADP
cana-3476	48	46	the	the	DET
cana-3476	48	47	formula	formula	NOUN
cana-3476	48	48	𝑇{𝑓(𝑡	𝑇{𝑓(𝑡	NUM
cana-3476	48	49	)	)	PUNCT
cana-3476	48	50	,	,	PUNCT
cana-3476	48	51	𝑠	𝑠	PROPN
cana-3476	48	52	}	}	PUNCT
cana-3476	48	53	=	=	SYM
cana-3476	48	54	𝒯	𝒯	PROPN
cana-3476	48	55	(	(	PUNCT
cana-3476	48	56	𝑠	𝑠	NOUN
cana-3476	48	57	)	)	PUNCT
cana-3476	48	58	=	=	SYM
cana-3476	48	59	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	48	60	)	)	PUNCT
cana-3476	48	61	∫	∫	PROPN
cana-3476	48	62	𝑓(𝑡)𝑒−𝑞(𝑠)𝑡𝑑𝑡	𝑓(𝑡)𝑒−𝑞(𝑠)𝑡𝑑𝑡	NOUN
cana-3476	48	63	∞	∞	PROPN
cana-3476	48	64	0	0	NUM
cana-3476	48	65	.	.	PUNCT
cana-3476	49	1	provided	provide	VERB
cana-3476	49	2	that	that	SCONJ
cana-3476	49	3	the	the	DET
cana-3476	49	4	integral	integral	ADJ
cana-3476	49	5	exists	exist	VERB
cana-3476	49	6	for	for	ADP
cana-3476	49	7	some	some	DET
cana-3476	49	8	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	49	9	)	)	PUNCT
cana-3476	49	10	.	.	PUNCT
cana-3476	50	1	2.14	2.14	NUM
cana-3476	50	2	new	new	ADJ
cana-3476	50	3	general	general	ADJ
cana-3476	50	4	integral	integral	ADJ
cana-3476	50	5	transform	transform	NOUN
cana-3476	50	6	on	on	ADP
cana-3476	50	7	time	time	NOUN
cana-3476	50	8	scales	scale	NOUN
cana-3476	50	9	[	[	X
cana-3476	50	10	15	15	NUM
cana-3476	50	11	]	]	PUNCT
cana-3476	50	12	:	:	PUNCT
cana-3476	50	13	let	let	VERB
cana-3476	50	14	𝑔	𝑔	NUM
cana-3476	50	15	:	:	PUNCT
cana-3476	50	16	𝕋	𝕋	PROPN
cana-3476	50	17	→	→	SYM
cana-3476	50	18	ℂ	ℂ	PROPN
cana-3476	50	19	is	be	AUX
cana-3476	50	20	an	an	DET
cana-3476	50	21	rd	rd	NOUN
cana-3476	50	22	-	-	ADJ
cana-3476	50	23	continuous	continuous	ADJ
cana-3476	50	24	function	function	NOUN
cana-3476	50	25	with	with	ADP
cana-3476	50	26	𝑝1(𝑧	𝑝1(𝑧	NOUN
cana-3476	50	27	)	)	PUNCT
cana-3476	50	28	,	,	PUNCT
cana-3476	50	29	𝑝2(𝑧	𝑝2(𝑧	PROPN
cana-3476	50	30	):	):	PUNCT
cana-3476	50	31	ℝ	ℝ	PROPN
cana-3476	50	32	→	→	SYM
cana-3476	50	33	ℂ	ℂ	PROPN
cana-3476	50	34	are	be	AUX
cana-3476	50	35	positively	positively	ADV
cana-3476	50	36	regressive	regressive	ADJ
cana-3476	50	37	functions	function	NOUN
cana-3476	50	38	.	.	PUNCT
cana-3476	51	1	define	define	VERB
cana-3476	51	2	the	the	DET
cana-3476	51	3	new	new	ADJ
cana-3476	51	4	general	general	ADJ
cana-3476	51	5	integral	integral	ADJ
cana-3476	51	6	transform	transform	NOUN
cana-3476	51	7	on	on	ADP
cana-3476	51	8	time	time	NOUN
cana-3476	51	9	scale	scale	NOUN
cana-3476	51	10	𝒢(𝑧	𝒢(𝑧	X
cana-3476	51	11	)	)	PUNCT
cana-3476	51	12	for	for	ADP
cana-3476	51	13	the	the	DET
cana-3476	51	14	function	function	NOUN
cana-3476	51	15	𝑔(𝑡	𝑔(𝑡	PROPN
cana-3476	51	16	)	)	PUNCT
cana-3476	51	17	by	by	ADP
cana-3476	51	18	the	the	DET
cana-3476	51	19	formula	formula	NOUN
cana-3476	51	20	ɲ(𝑔(𝑡))(𝑧	ɲ(𝑔(𝑡))(𝑧	NUM
cana-3476	51	21	)	)	PUNCT
cana-3476	51	22	=	=	SYM
cana-3476	52	1	𝒢(𝑧	𝒢(𝑧	X
cana-3476	52	2	)	)	PUNCT
cana-3476	52	3	=	=	SYM
cana-3476	52	4	𝑝1(𝑧	𝑝1(𝑧	PROPN
cana-3476	52	5	)	)	PUNCT
cana-3476	52	6	∫	∫	PROPN
cana-3476	52	7	𝑒⊖𝑝2(𝑧	𝑒⊖𝑝2(𝑧	NOUN
cana-3476	52	8	)	)	PUNCT
cana-3476	52	9	𝜎∞	𝜎∞	PROPN
cana-3476	52	10	𝑡0	𝑡0	PROPN
cana-3476	52	11	(	(	PUNCT
cana-3476	52	12	𝑡	𝑡	PROPN
cana-3476	52	13	,	,	PUNCT
cana-3476	52	14	𝑡0)𝑔(𝑡)∆𝑡	𝑡0)𝑔(𝑡)∆𝑡	NOUN
cana-3476	52	15	provided	provide	VERB
cana-3476	52	16	that	that	SCONJ
cana-3476	52	17	the	the	DET
cana-3476	52	18	integral	integral	ADJ
cana-3476	52	19	exists	exist	VERB
cana-3476	52	20	for	for	ADP
cana-3476	52	21	some	some	DET
cana-3476	52	22	𝑝2(𝑧	𝑝2(𝑧	NOUN
cana-3476	52	23	)	)	PUNCT
cana-3476	52	24	and	and	CCONJ
cana-3476	52	25	𝑝1(𝑧	𝑝1(𝑧	NOUN
cana-3476	52	26	)	)	PUNCT
cana-3476	52	27	≠	≠	PROPN
cana-3476	52	28	0	0	NUM
cana-3476	52	29	.	.	PUNCT
cana-3476	52	30	communications	communication	NOUN
cana-3476	52	31	on	on	ADP
cana-3476	52	32	applied	apply	VERB
cana-3476	52	33	nonlinear	nonlinear	ADJ
cana-3476	52	34	analysis	analysis	NOUN
cana-3476	52	35	issn	issn	NOUN
cana-3476	52	36	:	:	PUNCT
cana-3476	52	37	1074	1074	NUM
cana-3476	52	38	-	-	PUNCT
cana-3476	52	39	133x	133x	NUM
cana-3476	52	40	vol	vol	NOUN
cana-3476	52	41	32	32	NUM
cana-3476	52	42	no	no	NOUN
cana-3476	52	43	.	.	PUNCT
cana-3476	53	1	7s	7	NOUN
cana-3476	53	2	(	(	PUNCT
cana-3476	53	3	2025	2025	NUM
cana-3476	53	4	)	)	PUNCT
cana-3476	53	5	696	696	NUM
cana-3476	53	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	53	7	3	3	X
cana-3476	53	8	.	.	NOUN
cana-3476	53	9	results	result	VERB
cana-3476	53	10	3.1	3.1	NUM
cana-3476	53	11	theorem	theorem	NOUN
cana-3476	53	12	1	1	NUM
cana-3476	53	13	the	the	DET
cana-3476	53	14	set	set	NOUN
cana-3476	53	15	of	of	ADP
cana-3476	53	16	all	all	DET
cana-3476	53	17	regressive	regressive	ADJ
cana-3476	53	18	functions	function	NOUN
cana-3476	54	1	ℛ	ℛ	NOUN
cana-3476	54	2	form	form	VERB
cana-3476	54	3	an	an	DET
cana-3476	54	4	abelian	abelian	ADJ
cana-3476	54	5	group	group	NOUN
cana-3476	54	6	under	under	ADP
cana-3476	54	7	the	the	DET
cana-3476	54	8	operation	operation	NOUN
cana-3476	54	9	⊕	⊕	PROPN
cana-3476	54	10	defined	define	VERB
cana-3476	54	11	by	by	ADP
cana-3476	54	12	𝑓	𝑓	DET
cana-3476	54	13	⊕	⊕	PROPN
cana-3476	54	14	𝑔	𝑔	PROPN
cana-3476	54	15	=	=	PUNCT
cana-3476	54	16	𝑓	𝑓	PROPN
cana-3476	54	17	+	+	NUM
cana-3476	54	18	𝑔	𝑔	PROPN
cana-3476	54	19	+	+	CCONJ
cana-3476	54	20	𝜇(𝑡)𝑓𝑔.	𝜇(𝑡)𝑓𝑔.	VERB
cana-3476	54	21	the	the	DET
cana-3476	54	22	additive	additive	ADJ
cana-3476	54	23	inverse	inverse	NOUN
cana-3476	54	24	of	of	ADP
cana-3476	54	25	f	f	PROPN
cana-3476	54	26	in	in	ADP
cana-3476	54	27	this	this	DET
cana-3476	54	28	group	group	NOUN
cana-3476	54	29	given	give	VERB
cana-3476	54	30	by	by	ADP
cana-3476	54	31	⊖	⊖	X
cana-3476	54	32	𝑓	𝑓	X
cana-3476	54	33	=	=	SYM
cana-3476	54	34	−	−	PROPN
cana-3476	54	35	𝑓	𝑓	DET
cana-3476	54	36	1+𝜇𝑓	1+𝜇𝑓	NUM
cana-3476	54	37	3.2	3.2	NUM
cana-3476	54	38	lemma	lemma	PROPN
cana-3476	54	39	1	1	NUM
cana-3476	54	40	if	if	SCONJ
cana-3476	54	41	𝑞	𝑞	X
cana-3476	54	42	:	:	PUNCT
cana-3476	54	43	𝕋	𝕋	NOUN
cana-3476	54	44	→	→	SYM
cana-3476	54	45	ℝ	ℝ	PROPN
cana-3476	54	46	is	be	AUX
cana-3476	54	47	regressive	regressive	ADJ
cana-3476	54	48	then	then	ADV
cana-3476	54	49	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	ADJ
cana-3476	54	50	)	)	PUNCT
cana-3476	55	1	𝜎	𝜎	PROPN
cana-3476	55	2	(	(	PUNCT
cana-3476	55	3	𝑡	𝑡	PROPN
cana-3476	55	4	,	,	PUNCT
cana-3476	55	5	0	0	NUM
cana-3476	55	6	)	)	PUNCT
cana-3476	55	7	=	=	SYM
cana-3476	55	8	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	NOUN
cana-3476	55	9	)	)	PUNCT
cana-3476	55	10	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	55	11	)	)	PUNCT
cana-3476	55	12	=	=	SYM
cana-3476	56	1	−	−	NUM
cana-3476	56	2	⊖𝑖𝑞(𝑠	⊖𝑖𝑞(𝑠	PROPN
cana-3476	56	3	)	)	PUNCT
cana-3476	56	4	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	56	5	)	)	PUNCT
cana-3476	56	6	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	7	,	,	PUNCT
cana-3476	56	8	0	0	NUM
cana-3476	56	9	)	)	PUNCT
cana-3476	56	10	=	=	SYM
cana-3476	56	11	𝑖⊖𝑖𝑞(𝑠	𝑖⊖𝑖𝑞(𝑠	NOUN
cana-3476	56	12	)	)	PUNCT
cana-3476	56	13	𝑞(𝑠	𝑞(𝑠	VERB
cana-3476	56	14	)	)	PUNCT
cana-3476	56	15	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	16	,	,	PUNCT
cana-3476	56	17	0	0	NUM
cana-3476	56	18	)	)	PUNCT
cana-3476	56	19	proof	proof	NOUN
cana-3476	56	20	:	:	PUNCT
cana-3476	56	21	we	we	PRON
cana-3476	56	22	have	have	VERB
cana-3476	56	23	the	the	DET
cana-3476	56	24	result	result	NOUN
cana-3476	56	25	𝑒𝑝	𝑒𝑝	PROPN
cana-3476	56	26	𝜎(𝑡	𝜎(𝑡	PROPN
cana-3476	56	27	,	,	PUNCT
cana-3476	56	28	𝑠	𝑠	NOUN
cana-3476	56	29	)	)	PUNCT
cana-3476	56	30	=	=	SYM
cana-3476	56	31	𝑒𝑝(𝑡	𝑒𝑝(𝑡	X
cana-3476	56	32	,	,	PUNCT
cana-3476	56	33	𝑠	𝑠	PROPN
cana-3476	56	34	)	)	PUNCT
cana-3476	56	35	+	+	CCONJ
cana-3476	56	36	𝜇(𝑡)𝑒𝑝	𝜇(𝑡)𝑒𝑝	PROPN
cana-3476	56	37	∆(𝑡	∆(𝑡	PROPN
cana-3476	56	38	,	,	PUNCT
cana-3476	56	39	𝑠	𝑠	PROPN
cana-3476	56	40	)	)	PUNCT
cana-3476	56	41	and	and	CCONJ
cana-3476	56	42	𝑒𝑝	𝑒𝑝	PRON
cana-3476	56	43	∆(𝑡	∆(𝑡	PROPN
cana-3476	56	44	,	,	PUNCT
cana-3476	56	45	0	0	NUM
cana-3476	56	46	)	)	PUNCT
cana-3476	56	47	=	=	SYM
cana-3476	56	48	𝑝(𝑡)𝑒𝑝(𝑡	𝑝(𝑡)𝑒𝑝(𝑡	X
cana-3476	56	49	,	,	PUNCT
cana-3476	56	50	0	0	NUM
cana-3476	56	51	)	)	PUNCT
cana-3476	56	52	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	56	53	)	)	PUNCT
cana-3476	56	54	𝜎	𝜎	PROPN
cana-3476	56	55	(	(	PUNCT
cana-3476	56	56	𝑡	𝑡	PROPN
cana-3476	56	57	,	,	PUNCT
cana-3476	56	58	0	0	NUM
cana-3476	56	59	)	)	PUNCT
cana-3476	56	60	=	=	SYM
cana-3476	56	61	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	62	,	,	PUNCT
cana-3476	56	63	0	0	NUM
cana-3476	56	64	)	)	PUNCT
cana-3476	56	65	+	+	CCONJ
cana-3476	56	66	𝜇(𝑡)𝑒⊖𝑖𝑞(𝑠	𝜇(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	56	67	)	)	PUNCT
cana-3476	56	68	∆	∆	PROPN
cana-3476	56	69	(	(	PUNCT
cana-3476	56	70	𝑡	𝑡	X
cana-3476	56	71	,	,	PUNCT
cana-3476	56	72	0	0	NUM
cana-3476	56	73	)	)	PUNCT
cana-3476	56	74	=	=	SYM
cana-3476	56	75	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	76	,	,	PUNCT
cana-3476	56	77	0	0	NUM
cana-3476	56	78	)	)	PUNCT
cana-3476	56	79	+	+	CCONJ
cana-3476	56	80	𝜇(𝑡)(⊖	𝜇(𝑡)(⊖	NOUN
cana-3476	56	81	𝑖𝑞(𝑠))𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑖𝑞(𝑠))𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	82	,	,	PUNCT
cana-3476	56	83	0	0	NUM
cana-3476	56	84	)	)	PUNCT
cana-3476	56	85	∴	∴	NOUN
cana-3476	56	86	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	56	87	)	)	PUNCT
cana-3476	56	88	𝜎	𝜎	PROPN
cana-3476	56	89	(	(	PUNCT
cana-3476	56	90	𝑡	𝑡	PROPN
cana-3476	56	91	,	,	PUNCT
cana-3476	56	92	0	0	NUM
cana-3476	56	93	)	)	PUNCT
cana-3476	56	94	=	=	SYM
cana-3476	56	95	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	56	96	,	,	PUNCT
cana-3476	56	97	0	0	NUM
cana-3476	56	98	)	)	PUNCT
cana-3476	56	99	(	(	PUNCT
cana-3476	56	100	1	1	NUM
cana-3476	56	101	+	+	CCONJ
cana-3476	56	102	𝜇(𝑡	𝜇(𝑡	NOUN
cana-3476	56	103	)	)	PUNCT
cana-3476	56	104	(	(	PUNCT
cana-3476	56	105	−𝑖𝑞(𝑠	−𝑖𝑞(𝑠	NOUN
cana-3476	56	106	)	)	PUNCT
cana-3476	56	107	1	1	NUM
cana-3476	56	108	+	+	CCONJ
cana-3476	56	109	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	56	110	)	)	PUNCT
cana-3476	56	111	)	)	PUNCT
cana-3476	56	112	)	)	PUNCT
cana-3476	57	1	∴	∴	PROPN
cana-3476	57	2	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	57	3	)	)	PUNCT
cana-3476	57	4	𝜎	𝜎	PROPN
cana-3476	57	5	(	(	PUNCT
cana-3476	57	6	𝑡	𝑡	PROPN
cana-3476	57	7	,	,	PUNCT
cana-3476	57	8	0	0	NUM
cana-3476	57	9	)	)	PUNCT
cana-3476	57	10	=	=	SYM
cana-3476	57	11	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	57	12	,	,	PUNCT
cana-3476	57	13	0	0	NUM
cana-3476	57	14	)	)	PUNCT
cana-3476	57	15	(	(	PUNCT
cana-3476	57	16	1+𝑖𝜇(𝑡)𝑞(𝑠)−𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠)−𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	57	17	)	)	PUNCT
cana-3476	57	18	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	57	19	)	)	PUNCT
cana-3476	57	20	)	)	PUNCT
cana-3476	58	1	=	=	PUNCT
cana-3476	58	2	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	NOUN
cana-3476	58	3	)	)	PUNCT
cana-3476	58	4	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	58	5	)	)	PUNCT
cana-3476	58	6	(	(	PUNCT
cana-3476	58	7	1	1	X
cana-3476	58	8	)	)	PUNCT
cana-3476	58	9	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	58	10	)	)	PUNCT
cana-3476	58	11	𝜎	𝜎	PROPN
cana-3476	58	12	(	(	PUNCT
cana-3476	58	13	𝑡	𝑡	PROPN
cana-3476	58	14	,	,	PUNCT
cana-3476	58	15	0	0	NUM
cana-3476	58	16	)	)	PUNCT
cana-3476	58	17	=	=	SYM
cana-3476	58	18	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	58	19	,	,	PUNCT
cana-3476	58	20	0	0	NUM
cana-3476	58	21	)	)	PUNCT
cana-3476	58	22	−𝑖𝑞(𝑠	−𝑖𝑞(𝑠	NOUN
cana-3476	58	23	)	)	PUNCT
cana-3476	58	24	(	(	PUNCT
cana-3476	58	25	−𝑖𝑞(𝑠	−𝑖𝑞(𝑠	PROPN
cana-3476	58	26	)	)	PUNCT
cana-3476	58	27	1	1	NUM
cana-3476	58	28	+	+	CCONJ
cana-3476	58	29	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	58	30	)	)	PUNCT
cana-3476	58	31	)	)	PUNCT
cana-3476	59	1	=	=	PUNCT
cana-3476	60	1	−	−	PROPN
cana-3476	60	2	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	60	3	,	,	PUNCT
cana-3476	60	4	0	0	NUM
cana-3476	60	5	)	)	PUNCT
cana-3476	60	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	60	7	)	)	PUNCT
cana-3476	60	8	(	(	PUNCT
cana-3476	60	9	⊖	⊖	NOUN
cana-3476	60	10	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	60	11	)	)	PUNCT
cana-3476	60	12	)	)	PUNCT
cana-3476	60	13	∴	∴	NOUN
cana-3476	60	14	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	60	15	)	)	PUNCT
cana-3476	60	16	𝜎	𝜎	NOUN
cana-3476	60	17	=	=	SYM
cana-3476	60	18	−	−	NUM
cana-3476	60	19	⊖𝑖𝑞(𝑠	⊖𝑖𝑞(𝑠	PROPN
cana-3476	60	20	)	)	PUNCT
cana-3476	60	21	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	60	22	)	)	PUNCT
cana-3476	60	23	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	60	24	,	,	PUNCT
cana-3476	60	25	0	0	NUM
cana-3476	60	26	)	)	PUNCT
cana-3476	60	27	(	(	PUNCT
cana-3476	60	28	2	2	X
cana-3476	60	29	)	)	PUNCT
cana-3476	60	30	also	also	ADV
cana-3476	60	31	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	VERB
cana-3476	60	32	)	)	PUNCT
cana-3476	60	33	𝜎	𝜎	NOUN
cana-3476	60	34	=	=	SYM
cana-3476	60	35	𝑖⊖𝑖𝑞(𝑠	𝑖⊖𝑖𝑞(𝑠	PROPN
cana-3476	60	36	)	)	PUNCT
cana-3476	60	37	𝑞(𝑠	𝑞(𝑠	VERB
cana-3476	60	38	)	)	PUNCT
cana-3476	60	39	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	60	40	,	,	PUNCT
cana-3476	60	41	0	0	NUM
cana-3476	60	42	)	)	PUNCT
cana-3476	60	43	(	(	PUNCT
cana-3476	60	44	3	3	X
cana-3476	60	45	)	)	PUNCT
cana-3476	60	46	from	from	ADP
cana-3476	60	47	equations	equation	NOUN
cana-3476	60	48	(	(	PUNCT
cana-3476	60	49	1	1	NUM
cana-3476	60	50	)	)	PUNCT
cana-3476	60	51	,	,	PUNCT
cana-3476	60	52	(	(	PUNCT
cana-3476	60	53	2	2	X
cana-3476	60	54	)	)	PUNCT
cana-3476	60	55	and	and	CCONJ
cana-3476	60	56	(	(	PUNCT
cana-3476	60	57	3	3	X
cana-3476	60	58	)	)	PUNCT
cana-3476	60	59	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	60	60	)	)	PUNCT
cana-3476	60	61	𝜎	𝜎	PROPN
cana-3476	60	62	(	(	PUNCT
cana-3476	60	63	𝑡	𝑡	PROPN
cana-3476	60	64	,	,	PUNCT
cana-3476	60	65	0	0	NUM
cana-3476	60	66	)	)	PUNCT
cana-3476	60	67	=	=	SYM
cana-3476	60	68	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	NOUN
cana-3476	60	69	)	)	PUNCT
cana-3476	60	70	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	60	71	)	)	PUNCT
cana-3476	60	72	=	=	SYM
cana-3476	61	1	−	−	NUM
cana-3476	61	2	⊖𝑖𝑞(𝑠	⊖𝑖𝑞(𝑠	PROPN
cana-3476	61	3	)	)	PUNCT
cana-3476	61	4	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	61	5	)	)	PUNCT
cana-3476	61	6	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	61	7	,	,	PUNCT
cana-3476	61	8	0	0	NUM
cana-3476	61	9	)	)	PUNCT
cana-3476	61	10	=	=	SYM
cana-3476	61	11	𝑖⊖𝑖𝑞(𝑠	𝑖⊖𝑖𝑞(𝑠	NOUN
cana-3476	61	12	)	)	PUNCT
cana-3476	61	13	𝑞(𝑠	𝑞(𝑠	VERB
cana-3476	61	14	)	)	PUNCT
cana-3476	61	15	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	61	16	,	,	PUNCT
cana-3476	61	17	0	0	NUM
cana-3476	61	18	)	)	PUNCT
cana-3476	61	19	3.3	3.3	NUM
cana-3476	61	20	new	new	ADJ
cana-3476	61	21	general	general	ADJ
cana-3476	61	22	complex	complex	ADJ
cana-3476	61	23	integral	integral	ADJ
cana-3476	61	24	transform	transform	NOUN
cana-3476	61	25	on	on	ADP
cana-3476	61	26	time	time	NOUN
cana-3476	61	27	scales	scale	VERB
cana-3476	61	28	𝕋	𝕋	NOUN
cana-3476	61	29	in	in	ADP
cana-3476	61	30	2022	2022	NUM
cana-3476	61	31	,	,	PUNCT
cana-3476	61	32	jinan	jinan	PROPN
cana-3476	61	33	a.	a.	PROPN
cana-3476	61	34	jasim	jasim	PROPN
cana-3476	61	35	,	,	PUNCT
cana-3476	61	36	sadiq	sadiq	PROPN
cana-3476	61	37	a.	a.	PROPN
cana-3476	61	38	mehdi	mehdi	PROPN
cana-3476	61	39	and	and	CCONJ
cana-3476	61	40	emad	emad	PROPN
cana-3476	61	41	a.	a.	PROPN
cana-3476	61	42	kuffi	kuffi	PROPN
cana-3476	61	43	presented	present	VERB
cana-3476	61	44	a	a	DET
cana-3476	61	45	novel	novel	ADJ
cana-3476	61	46	general	general	ADJ
cana-3476	61	47	complex	complex	ADJ
cana-3476	61	48	integral	integral	ADJ
cana-3476	61	49	transform	transform	NOUN
cana-3476	61	50	[	[	X
cana-3476	61	51	13	13	NUM
cana-3476	61	52	]	]	PUNCT
cana-3476	61	53	.	.	PUNCT
cana-3476	62	1	for	for	ADP
cana-3476	62	2	an	an	DET
cana-3476	62	3	integrable	integrable	ADJ
cana-3476	62	4	function	function	NOUN
cana-3476	62	5	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	62	6	)	)	PUNCT
cana-3476	62	7	defined	define	VERB
cana-3476	62	8	for	for	ADP
cana-3476	62	9	𝑡	𝑡	PROPN
cana-3476	62	10	≥	≥	NOUN
cana-3476	62	11	0	0	NUM
cana-3476	62	12	,	,	PUNCT
cana-3476	62	13	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	62	14	)	)	PUNCT
cana-3476	62	15	≠	≠	PROPN
cana-3476	62	16	0	0	NUM
cana-3476	62	17	and	and	CCONJ
cana-3476	62	18	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	62	19	)	)	PUNCT
cana-3476	62	20	are	be	AUX
cana-3476	62	21	real	real	ADJ
cana-3476	62	22	functions	function	NOUN
cana-3476	62	23	that	that	PRON
cana-3476	62	24	are	be	AUX
cana-3476	62	25	positive	positive	ADJ
cana-3476	62	26	,	,	PUNCT
cana-3476	62	27	𝑖	𝑖	VERB
cana-3476	62	28	is	be	AUX
cana-3476	62	29	the	the	DET
cana-3476	62	30	complex	complex	ADJ
cana-3476	62	31	number	number	NOUN
cana-3476	62	32	then	then	ADV
cana-3476	62	33	the	the	DET
cana-3476	62	34	transform	transform	NOUN
cana-3476	62	35	𝑇𝑔	𝑇𝑔	PROPN
cana-3476	62	36	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	62	37	)	)	PUNCT
cana-3476	62	38	of	of	ADP
cana-3476	62	39	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	62	40	)	)	PUNCT
cana-3476	62	41	is	be	AUX
cana-3476	62	42	given	give	VERB
cana-3476	62	43	by	by	ADP
cana-3476	62	44	𝑇𝑔	𝑇𝑔	PROPN
cana-3476	62	45	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	62	46	)	)	PUNCT
cana-3476	62	47	,	,	PUNCT
cana-3476	62	48	𝑠	𝑠	PROPN
cana-3476	62	49	}	}	PUNCT
cana-3476	62	50	=	=	SYM
cana-3476	62	51	𝐹𝑔	𝐹𝑔	NOUN
cana-3476	62	52	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	62	53	)	)	PUNCT
cana-3476	62	54	=	=	SYM
cana-3476	63	1	𝑝(𝑠	𝑝(𝑠	X
cana-3476	63	2	)	)	PUNCT
cana-3476	63	3	∫	∫	PROPN
cana-3476	63	4	𝑒−𝑖𝑞(𝑠)𝑡𝑓(𝑡)𝑑𝑡	𝑒−𝑖𝑞(𝑠)𝑡𝑓(𝑡)𝑑𝑡	PROPN
cana-3476	63	5	∞	∞	PROPN
cana-3476	63	6	0	0	NUM
cana-3476	64	1	if	if	SCONJ
cana-3476	64	2	the	the	DET
cana-3476	64	3	integral	integral	ADJ
cana-3476	64	4	exists	exist	VERB
cana-3476	64	5	for	for	ADP
cana-3476	64	6	some	some	DET
cana-3476	64	7	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	64	8	)	)	PUNCT
cana-3476	64	9	.	.	PUNCT
cana-3476	65	1	in	in	ADP
cana-3476	65	2	this	this	DET
cana-3476	65	3	section	section	NOUN
cana-3476	65	4	we	we	PRON
cana-3476	65	5	present	present	VERB
cana-3476	65	6	a	a	DET
cana-3476	65	7	new	new	ADJ
cana-3476	65	8	general	general	ADJ
cana-3476	65	9	complex	complex	ADJ
cana-3476	65	10	integral	integral	ADJ
cana-3476	65	11	transform	transform	NOUN
cana-3476	65	12	on	on	ADP
cana-3476	65	13	time	time	NOUN
cana-3476	65	14	scales	scale	VERB
cana-3476	65	15	𝕋.	𝕋.	NOUN
cana-3476	65	16	definition	definition	NOUN
cana-3476	65	17	7	7	NUM
cana-3476	65	18	let	let	VERB
cana-3476	65	19	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	65	20	)	)	PUNCT
cana-3476	65	21	be	be	AUX
cana-3476	65	22	an	an	DET
cana-3476	65	23	integrable	integrable	ADJ
cana-3476	65	24	function	function	NOUN
cana-3476	65	25	,	,	PUNCT
cana-3476	65	26	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	65	27	)	)	PUNCT
cana-3476	65	28	≠	≠	PROPN
cana-3476	65	29	0	0	NUM
cana-3476	65	30	,	,	PUNCT
cana-3476	65	31	∀𝑠	∀𝑠	NOUN
cana-3476	65	32	∈	∈	PROPN
cana-3476	65	33	ℂ	ℂ	PROPN
cana-3476	65	34	and	and	CCONJ
cana-3476	65	35	(	(	PUNCT
cana-3476	65	36	𝑠	𝑠	X
cana-3476	65	37	)	)	PUNCT
cana-3476	65	38	∈	∈	NOUN
cana-3476	65	39	𝒟{𝑓	𝒟{𝑓	NUM
cana-3476	65	40	}	}	PUNCT
cana-3476	65	41	.	.	PUNCT
cana-3476	66	1	where	where	SCONJ
cana-3476	66	2	𝒟{𝑓	𝒟{𝑓	NOUN
cana-3476	66	3	}	}	PUNCT
cana-3476	66	4	consists	consist	VERB
cana-3476	66	5	of	of	ADP
cana-3476	66	6	all	all	DET
cana-3476	66	7	complex	complex	ADJ
cana-3476	66	8	numbers	number	NOUN
cana-3476	66	9	for	for	ADP
cana-3476	66	10	which	which	PRON
cana-3476	66	11	the	the	DET
cana-3476	66	12	improper	improper	ADJ
cana-3476	66	13	integral	integral	ADJ
cana-3476	66	14	exists	exist	NOUN
cana-3476	66	15	.	.	PUNCT
cana-3476	67	1	then	then	ADV
cana-3476	67	2	we	we	PRON
cana-3476	67	3	define	define	VERB
cana-3476	67	4	the	the	DET
cana-3476	67	5	new	new	ADJ
cana-3476	67	6	general	general	ADJ
cana-3476	67	7	complex	complex	ADJ
cana-3476	67	8	integral	integral	ADJ
cana-3476	67	9	transform	transform	NOUN
cana-3476	67	10	on	on	ADP
cana-3476	67	11	time	time	NOUN
cana-3476	67	12	scales	scale	NOUN
cana-3476	67	13	𝕋	𝕋	NOUN
cana-3476	67	14	by	by	ADP
cana-3476	67	15	the	the	DET
cana-3476	67	16	formula	formula	NOUN
cana-3476	67	17	communications	communication	NOUN
cana-3476	67	18	on	on	ADP
cana-3476	67	19	applied	apply	VERB
cana-3476	67	20	nonlinear	nonlinear	ADJ
cana-3476	67	21	analysis	analysis	NOUN
cana-3476	67	22	issn	issn	NOUN
cana-3476	67	23	:	:	PUNCT
cana-3476	67	24	1074	1074	NUM
cana-3476	67	25	-	-	PUNCT
cana-3476	67	26	133x	133x	NUM
cana-3476	67	27	vol	vol	NOUN
cana-3476	67	28	32	32	NUM
cana-3476	67	29	no	no	NOUN
cana-3476	67	30	.	.	PUNCT
cana-3476	68	1	7s	7	NOUN
cana-3476	68	2	(	(	PUNCT
cana-3476	68	3	2025	2025	NUM
cana-3476	68	4	)	)	PUNCT
cana-3476	68	5	697	697	NUM
cana-3476	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	68	7	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	68	8	𝑐(𝑓(𝑡	𝑐(𝑓(𝑡	PROPN
cana-3476	68	9	)	)	PUNCT
cana-3476	68	10	,	,	PUNCT
cana-3476	68	11	𝑠	𝑠	X
cana-3476	68	12	)	)	PUNCT
cana-3476	68	13	=	=	SYM
cana-3476	69	1	ℱ𝑔	ℱ𝑔	NOUN
cana-3476	69	2	𝑐𝑝(𝑠	𝑐𝑝(𝑠	X
cana-3476	69	3	)	)	PUNCT
cana-3476	69	4	=	=	SYM
cana-3476	69	5	∫	∫	PROPN
cana-3476	69	6	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	69	7	)	)	PUNCT
cana-3476	69	8	𝜎	𝜎	PROPN
cana-3476	69	9	(	(	PUNCT
cana-3476	69	10	𝑡	𝑡	PROPN
cana-3476	69	11	,	,	PUNCT
cana-3476	69	12	0	0	NUM
cana-3476	69	13	)	)	PUNCT
cana-3476	69	14	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	69	15	)	)	PUNCT
cana-3476	69	16	∆𝑡	∆𝑡	PROPN
cana-3476	69	17	∞	∞	NUM
cana-3476	69	18	0	0	NUM
cana-3476	69	19	.	.	PUNCT
cana-3476	70	1	3.3.1	3.3.1	NUM
cana-3476	70	2	linearity	linearity	NOUN
cana-3476	70	3	property	property	NOUN
cana-3476	70	4	:	:	PUNCT
cana-3476	70	5	assume	assume	VERB
cana-3476	70	6	that	that	SCONJ
cana-3476	70	7	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	70	8	𝑐{𝑓	𝑐{𝑓	ADJ
cana-3476	70	9	}	}	PUNCT
cana-3476	70	10	and	and	CCONJ
cana-3476	70	11	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	70	12	𝑐{𝑔	𝑐{𝑔	NOUN
cana-3476	70	13	}	}	PUNCT
cana-3476	70	14	exists	exist	VERB
cana-3476	70	15	for	for	ADP
cana-3476	70	16	𝑞(𝑠	𝑞(𝑠	ADJ
cana-3476	70	17	)	)	PUNCT
cana-3476	70	18	∈	∈	NOUN
cana-3476	70	19	𝒟{𝑓	𝒟{𝑓	NOUN
cana-3476	70	20	}	}	PUNCT
cana-3476	70	21	and	and	CCONJ
cana-3476	70	22	𝒟{𝑔	𝒟{𝑔	ADP
cana-3476	70	23	}	}	PUNCT
cana-3476	70	24	,	,	PUNCT
cana-3476	70	25	where	where	SCONJ
cana-3476	70	26	𝑓	𝑓	PRON
cana-3476	70	27	and	and	CCONJ
cana-3476	70	28	𝑔	𝑔	PROPN
cana-3476	70	29	are	be	AUX
cana-3476	70	30	rd	rd	NOUN
cana-3476	70	31	-	-	ADJ
cana-3476	70	32	continuous	continuous	ADJ
cana-3476	70	33	functions	function	NOUN
cana-3476	70	34	on	on	ADP
cana-3476	70	35	𝕋	𝕋	PROPN
cana-3476	70	36	and	and	CCONJ
cana-3476	70	37	𝛼	𝛼	NOUN
cana-3476	70	38	,	,	PUNCT
cana-3476	70	39	𝛽	𝛽	NOUN
cana-3476	70	40	∈	∈	NOUN
cana-3476	70	41	ℝ	ℝ	PROPN
cana-3476	70	42	are	be	AUX
cana-3476	70	43	constants	constant	NOUN
cana-3476	70	44	.	.	PUNCT
cana-3476	71	1	then	then	ADV
cana-3476	71	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	71	3	𝑐{𝛼𝑓	𝑐{𝛼𝑓	PROPN
cana-3476	71	4	+	+	CCONJ
cana-3476	71	5	𝛽𝑔}(𝑠	𝛽𝑔}(𝑠	NOUN
cana-3476	71	6	)	)	PUNCT
cana-3476	71	7	=	=	PUNCT
cana-3476	72	1	𝛼𝒯𝑔	𝛼𝒯𝑔	NUM
cana-3476	72	2	𝑐{𝑓}(𝑠	𝑐{𝑓}(𝑠	NOUN
cana-3476	72	3	)	)	PUNCT
cana-3476	73	1	+	+	CCONJ
cana-3476	73	2	𝛽𝒯𝑔	𝛽𝒯𝑔	ADJ
cana-3476	73	3	𝑐{𝑔}(𝑠	𝑐{𝑔}(𝑠	NOUN
cana-3476	73	4	)	)	PUNCT
cana-3476	73	5	.	.	PUNCT
cana-3476	74	1	∵	∵	ADJ
cana-3476	74	2	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	74	3	)	)	PUNCT
cana-3476	74	4	∈	∈	NOUN
cana-3476	74	5	𝒟{𝑓	𝒟{𝑓	NOUN
cana-3476	74	6	}	}	PUNCT
cana-3476	74	7	∩	∩	NOUN
cana-3476	74	8	𝒟{𝑔	𝒟{𝑔	ADJ
cana-3476	74	9	}	}	PUNCT
cana-3476	74	10	proof	proof	NOUN
cana-3476	74	11	:	:	PUNCT
cana-3476	74	12	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	74	13	𝑐{(𝛼𝑓	𝑐{(𝛼𝑓	PROPN
cana-3476	74	14	+	+	CCONJ
cana-3476	74	15	𝛽𝑔)(𝑡	𝛽𝑔)(𝑡	ADJ
cana-3476	74	16	)	)	PUNCT
cana-3476	74	17	}	}	PUNCT
cana-3476	74	18	=	=	SYM
cana-3476	74	19	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	74	20	)	)	PUNCT
cana-3476	74	21	∫	∫	PROPN
cana-3476	74	22	(	(	PUNCT
cana-3476	74	23	𝛼𝑓	𝛼𝑓	X
cana-3476	74	24	+	+	X
cana-3476	74	25	𝛽𝑔)(𝑡	𝛽𝑔)(𝑡	ADJ
cana-3476	74	26	)	)	PUNCT
cana-3476	74	27	∞	∞	PROPN
cana-3476	74	28	0	0	NUM
cana-3476	74	29	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	74	30	)	)	PUNCT
cana-3476	74	31	𝜎	𝜎	PROPN
cana-3476	74	32	(	(	PUNCT
cana-3476	74	33	𝑡	𝑡	PROPN
cana-3476	74	34	,	,	PUNCT
cana-3476	74	35	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	74	36	=	=	SYM
cana-3476	74	37	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	74	38	)	)	PUNCT
cana-3476	74	39	∫	∫	PROPN
cana-3476	74	40	(	(	PUNCT
cana-3476	74	41	𝛼𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝛼𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	74	42	)	)	PUNCT
cana-3476	74	43	𝜎	𝜎	PROPN
cana-3476	74	44	(	(	PUNCT
cana-3476	74	45	𝑡	𝑡	X
cana-3476	74	46	,	,	PUNCT
cana-3476	74	47	0	0	NUM
cana-3476	74	48	)	)	PUNCT
cana-3476	75	1	+	+	CCONJ
cana-3476	75	2	𝛽𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	𝛽𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	75	3	)	)	PUNCT
cana-3476	75	4	𝜎	𝜎	NOUN
cana-3476	75	5	)	)	PUNCT
cana-3476	76	1	∆𝑡	∆𝑡	PROPN
cana-3476	76	2	∞	∞	NUM
cana-3476	76	3	0	0	NUM
cana-3476	77	1	=	=	SYM
cana-3476	77	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	77	3	)	)	PUNCT
cana-3476	77	4	∫	∫	PROPN
cana-3476	77	5	𝛼𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝛼𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	77	6	)	)	PUNCT
cana-3476	77	7	𝜎	𝜎	PROPN
cana-3476	77	8	∆𝑡	∆𝑡	PROPN
cana-3476	78	1	+	+	NUM
cana-3476	78	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	78	3	)	)	PUNCT
cana-3476	78	4	∫	∫	PROPN
cana-3476	78	5	𝛽𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	𝛽𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	78	6	)	)	PUNCT
cana-3476	79	1	𝜎	𝜎	PROPN
cana-3476	80	1	∆𝑡	∆𝑡	NOUN
cana-3476	80	2	∞	∞	NUM
cana-3476	80	3	0	0	NUM
cana-3476	81	1	∞	∞	NUM
cana-3476	81	2	0	0	NUM
cana-3476	81	3	=	=	SYM
cana-3476	81	4	𝛼	𝛼	X
cana-3476	81	5	(	(	PUNCT
cana-3476	81	6	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	81	7	)	)	PUNCT
cana-3476	81	8	∫	∫	PROPN
cana-3476	81	9	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	81	10	)	)	PUNCT
cana-3476	81	11	𝜎	𝜎	NOUN
cana-3476	82	1	∆𝑡	∆𝑡	NOUN
cana-3476	82	2	∞	∞	NUM
cana-3476	82	3	0	0	NUM
cana-3476	82	4	)	)	PUNCT
cana-3476	83	1	+	+	CCONJ
cana-3476	83	2	𝛽	𝛽	NOUN
cana-3476	83	3	(	(	PUNCT
cana-3476	83	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	83	5	)	)	PUNCT
cana-3476	83	6	∫	∫	PROPN
cana-3476	83	7	𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑔(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	83	8	)	)	PUNCT
cana-3476	83	9	𝜎	𝜎	PROPN
cana-3476	84	1	∆𝑡	∆𝑡	NOUN
cana-3476	84	2	∞	∞	NUM
cana-3476	84	3	0	0	NUM
cana-3476	84	4	)	)	PUNCT
cana-3476	85	1	∴	∴	PROPN
cana-3476	85	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	85	3	𝑐{(𝛼𝑓	𝑐{(𝛼𝑓	PROPN
cana-3476	85	4	+	+	X
cana-3476	85	5	𝛽𝑔)(𝑡	𝛽𝑔)(𝑡	ADJ
cana-3476	85	6	)	)	PUNCT
cana-3476	85	7	}	}	PUNCT
cana-3476	85	8	=	=	PUNCT
cana-3476	85	9	𝛼𝒯𝑔	𝛼𝒯𝑔	NUM
cana-3476	85	10	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	85	11	)	)	PUNCT
cana-3476	85	12	+	+	CCONJ
cana-3476	85	13	𝛽𝒯𝑔	𝛽𝒯𝑔	ADJ
cana-3476	85	14	𝑐{𝑔(𝑡)}(𝑠	𝑐{𝑔(𝑡)}(𝑠	NOUN
cana-3476	85	15	)	)	PUNCT
cana-3476	85	16	.	.	PUNCT
cana-3476	86	1	3.3.2	3.3.2	NUM
cana-3476	86	2	theorem	theorem	VERB
cana-3476	86	3	2	2	NUM
cana-3476	86	4	(	(	PUNCT
cana-3476	86	5	convergence	convergence	NOUN
cana-3476	86	6	theorem	theorem	VERB
cana-3476	86	7	)	)	PUNCT
cana-3476	86	8	the	the	DET
cana-3476	86	9	integral	integral	ADJ
cana-3476	86	10	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	86	11	)	)	PUNCT
cana-3476	86	12	∫	∫	PROPN
cana-3476	86	13	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	86	14	)	)	PUNCT
cana-3476	86	15	𝜎	𝜎	PROPN
cana-3476	86	16	(	(	PUNCT
cana-3476	86	17	𝑡	𝑡	PROPN
cana-3476	86	18	,	,	PUNCT
cana-3476	86	19	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	87	1	∞	∞	NUM
cana-3476	87	2	0	0	NUM
cana-3476	87	3	converges	converge	VERB
cana-3476	87	4	absolutely	absolutely	ADV
cana-3476	87	5	for	for	ADP
cana-3476	87	6	𝑞(𝑠	𝑞(𝑠	ADJ
cana-3476	87	7	)	)	PUNCT
cana-3476	87	8	∈	∈	PROPN
cana-3476	87	9	𝒟	𝒟	NOUN
cana-3476	87	10	if	if	SCONJ
cana-3476	87	11	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	87	12	)	)	PUNCT
cana-3476	87	13	is	be	AUX
cana-3476	87	14	of	of	ADP
cana-3476	87	15	exponential	exponential	ADJ
cana-3476	87	16	type	type	NOUN
cana-3476	87	17	ii	ii	NOUN
cana-3476	87	18	with	with	ADP
cana-3476	87	19	exponential	exponential	ADJ
cana-3476	87	20	constant	constant	ADJ
cana-3476	87	21	𝑘.	𝑘.	NOUN
cana-3476	87	22	proof	proof	NOUN
cana-3476	87	23	:	:	PUNCT
cana-3476	87	24	consider	consider	VERB
cana-3476	87	25	|𝑝(𝑠	|𝑝(𝑠	PRON
cana-3476	87	26	)	)	PUNCT
cana-3476	87	27	∫	∫	PROPN
cana-3476	87	28	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	87	29	)	)	PUNCT
cana-3476	87	30	𝜎	𝜎	PROPN
cana-3476	87	31	(	(	PUNCT
cana-3476	87	32	𝑡	𝑡	PROPN
cana-3476	87	33	,	,	PUNCT
cana-3476	87	34	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	88	1	∞	∞	NUM
cana-3476	88	2	0	0	NUM
cana-3476	89	1	|	|	ADV
cana-3476	89	2	≤	≤	NOUN
cana-3476	89	3	|𝑝(𝑠)|	|𝑝(𝑠)|	PROPN
cana-3476	89	4	∫	∫	PROPN
cana-3476	89	5	|𝑒⊖𝑖𝑞(𝑠	|𝑒⊖𝑖𝑞(𝑠	NUM
cana-3476	89	6	)	)	PUNCT
cana-3476	89	7	𝜎	𝜎	PROPN
cana-3476	89	8	(	(	PUNCT
cana-3476	89	9	𝑡	𝑡	PROPN
cana-3476	89	10	,	,	PUNCT
cana-3476	89	11	0)𝑓(𝑡)∆𝑡|	0)𝑓(𝑡)∆𝑡|	NOUN
cana-3476	89	12	∞	∞	NOUN
cana-3476	89	13	0	0	NUM
cana-3476	89	14	but	but	CCONJ
cana-3476	89	15	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	89	16	)	)	PUNCT
cana-3476	89	17	is	be	AUX
cana-3476	89	18	of	of	ADP
cana-3476	89	19	exponential	exponential	ADJ
cana-3476	89	20	type	type	NOUN
cana-3476	89	21	ii	ii	NOUN
cana-3476	89	22	with	with	ADP
cana-3476	89	23	exponential	exponential	ADJ
cana-3476	89	24	constant	constant	ADJ
cana-3476	89	25	𝑘.	𝑘.	NOUN
cana-3476	89	26	∴	∴	PROPN
cana-3476	89	27	|𝑓(𝑡)|	|𝑓(𝑡)|	PROPN
cana-3476	89	28	≤	≤	PROPN
cana-3476	89	29	𝑀𝑒𝑘(𝑡	𝑀𝑒𝑘(𝑡	NOUN
cana-3476	89	30	,	,	PUNCT
cana-3476	89	31	0	0	NUM
cana-3476	89	32	)	)	PUNCT
cana-3476	89	33	,	,	PUNCT
cana-3476	89	34	𝑀	𝑀	PROPN
cana-3476	89	35	,	,	PUNCT
cana-3476	89	36	𝑘	𝑘	PROPN
cana-3476	89	37	>	>	X
cana-3476	89	38	0	0	PUNCT
cana-3476	89	39	hence	hence	ADV
cana-3476	89	40	above	above	ADP
cana-3476	89	41	equation	equation	NOUN
cana-3476	89	42	gives	give	VERB
cana-3476	89	43	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	89	44	)	)	PUNCT
cana-3476	89	45	∫	∫	PROPN
cana-3476	89	46	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	89	47	)	)	PUNCT
cana-3476	89	48	𝜎	𝜎	PROPN
cana-3476	89	49	(	(	PUNCT
cana-3476	89	50	𝑡	𝑡	PROPN
cana-3476	89	51	,	,	PUNCT
cana-3476	89	52	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	90	1	∞	∞	NUM
cana-3476	90	2	0	0	NUM
cana-3476	91	1	|	|	ADV
cana-3476	91	2	≤	≤	X
cana-3476	91	3	|𝑝(𝑠)|	|𝑝(𝑠)|	PROPN
cana-3476	91	4	∫	∫	PROPN
cana-3476	91	5	|𝑀𝑒𝑘(𝑡	|𝑀𝑒𝑘(𝑡	NOUN
cana-3476	91	6	,	,	PUNCT
cana-3476	91	7	0)𝑒⊖𝑖𝑞(𝑠	0)𝑒⊖𝑖𝑞(𝑠	ADJ
cana-3476	91	8	)	)	PUNCT
cana-3476	91	9	𝜎	𝜎	PROPN
cana-3476	91	10	(	(	PUNCT
cana-3476	91	11	𝑡	𝑡	PROPN
cana-3476	91	12	,	,	PUNCT
cana-3476	91	13	0)∆𝑡|	0)∆𝑡|	NUM
cana-3476	91	14	∞	∞	PROPN
cana-3476	91	15	0	0	NUM
cana-3476	91	16	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	91	17	)	)	PUNCT
cana-3476	91	18	∫	∫	PROPN
cana-3476	91	19	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	91	20	)	)	PUNCT
cana-3476	91	21	𝜎	𝜎	PROPN
cana-3476	91	22	(	(	PUNCT
cana-3476	91	23	𝑡	𝑡	PROPN
cana-3476	91	24	,	,	PUNCT
cana-3476	91	25	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	92	1	∞	∞	NUM
cana-3476	92	2	0	0	NUM
cana-3476	93	1	|	|	ADV
cana-3476	93	2	≤	≤	NOUN
cana-3476	93	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	93	4	∫	∫	PROPN
cana-3476	93	5	|𝑒𝑘(𝑡	|𝑒𝑘(𝑡	PROPN
cana-3476	93	6	,	,	PUNCT
cana-3476	93	7	0)𝑒⊖𝑖𝑞(𝑠	0)𝑒⊖𝑖𝑞(𝑠	ADJ
cana-3476	93	8	)	)	PUNCT
cana-3476	93	9	𝜎	𝜎	PROPN
cana-3476	93	10	(	(	PUNCT
cana-3476	93	11	𝑡	𝑡	PROPN
cana-3476	93	12	,	,	PUNCT
cana-3476	93	13	0)∆𝑡|	0)∆𝑡|	NUM
cana-3476	94	1	∞	∞	PROPN
cana-3476	94	2	0	0	NUM
cana-3476	94	3	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	94	4	)	)	PUNCT
cana-3476	94	5	∫	∫	PROPN
cana-3476	94	6	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	94	7	)	)	PUNCT
cana-3476	94	8	𝜎	𝜎	PROPN
cana-3476	94	9	(	(	PUNCT
cana-3476	94	10	𝑡	𝑡	PROPN
cana-3476	94	11	,	,	PUNCT
cana-3476	94	12	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	95	1	∞	∞	NUM
cana-3476	95	2	0	0	NUM
cana-3476	96	1	|	|	ADV
cana-3476	96	2	≤	≤	NOUN
cana-3476	96	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	96	4	∫	∫	PROPN
cana-3476	96	5	|𝑒𝑘(𝑡	|𝑒𝑘(𝑡	PROPN
cana-3476	96	6	,	,	PUNCT
cana-3476	96	7	0	0	NUM
cana-3476	96	8	)	)	PUNCT
cana-3476	96	9	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	NOUN
cana-3476	96	10	)	)	PUNCT
cana-3476	96	11	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	96	12	)	)	PUNCT
cana-3476	97	1	∆𝑡|	∆𝑡|	PROPN
cana-3476	97	2	∞	∞	NOUN
cana-3476	97	3	0	0	NUM
cana-3476	97	4	⸪	⸪	NUM
cana-3476	97	5	by	by	ADP
cana-3476	97	6	using	use	VERB
cana-3476	97	7	lemma	lemma	PROPN
cana-3476	97	8	(	(	PUNCT
cana-3476	97	9	1	1	NUM
cana-3476	97	10	)	)	PUNCT
cana-3476	97	11	.	.	PUNCT
cana-3476	98	1	∴	∴	PROPN
cana-3476	98	2	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	98	3	)	)	PUNCT
cana-3476	98	4	∫	∫	PROPN
cana-3476	98	5	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	98	6	)	)	PUNCT
cana-3476	98	7	𝜎	𝜎	PROPN
cana-3476	98	8	(	(	PUNCT
cana-3476	98	9	𝑡	𝑡	PROPN
cana-3476	98	10	,	,	PUNCT
cana-3476	98	11	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	99	1	∞	∞	NUM
cana-3476	99	2	0	0	NUM
cana-3476	100	1	|	|	ADV
cana-3476	100	2	≤	≤	NOUN
cana-3476	100	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	100	4	∫	∫	PROPN
cana-3476	100	5	|	|	CCONJ
cana-3476	100	6	1	1	NUM
cana-3476	100	7	1	1	NUM
cana-3476	100	8	+	+	CCONJ
cana-3476	100	9	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	100	10	)	)	PUNCT
cana-3476	100	11	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	100	12	,	,	PUNCT
cana-3476	100	13	0)∆𝑡|	0)∆𝑡|	NUM
cana-3476	100	14	∞	∞	NUM
cana-3476	100	15	0	0	PUNCT
cana-3476	101	1	(	(	PUNCT
cana-3476	101	2	⸪	⸪	NUM
cana-3476	101	3	by	by	ADP
cana-3476	101	4	property	property	NOUN
cana-3476	101	5	𝑒𝑝(𝑡	𝑒𝑝(𝑡	NOUN
cana-3476	101	6	,	,	PUNCT
cana-3476	101	7	𝑠)𝑒𝑞(𝑡	𝑠)𝑒𝑞(𝑡	NUM
cana-3476	101	8	,	,	PUNCT
cana-3476	101	9	𝑠	𝑠	NOUN
cana-3476	101	10	)	)	PUNCT
cana-3476	101	11	=	=	PUNCT
cana-3476	101	12	𝑒𝑝⊕𝑞(𝑡	𝑒𝑝⊕𝑞(𝑡	PROPN
cana-3476	101	13	,	,	PUNCT
cana-3476	101	14	𝑠	𝑠	NOUN
cana-3476	101	15	)	)	PUNCT
cana-3476	101	16	)	)	PUNCT
cana-3476	102	1	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	102	2	)	)	PUNCT
cana-3476	102	3	∫	∫	PROPN
cana-3476	102	4	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	102	5	)	)	PUNCT
cana-3476	102	6	𝜎	𝜎	PROPN
cana-3476	102	7	(	(	PUNCT
cana-3476	102	8	𝑡	𝑡	PROPN
cana-3476	102	9	,	,	PUNCT
cana-3476	102	10	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	103	1	∞	∞	NUM
cana-3476	103	2	0	0	NUM
cana-3476	104	1	|	|	ADV
cana-3476	104	2	≤	≤	NOUN
cana-3476	104	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	104	4	𝑘−𝑖𝑞(𝑠	𝑘−𝑖𝑞(𝑠	ADV
cana-3476	104	5	)	)	PUNCT
cana-3476	104	6	∫	∫	PROPN
cana-3476	105	1	|	|	CCONJ
cana-3476	105	2	𝑘−𝑖𝑞(𝑠	𝑘−𝑖𝑞(𝑠	NUM
cana-3476	105	3	)	)	PUNCT
cana-3476	105	4	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	105	5	)	)	PUNCT
cana-3476	105	6	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	105	7	,	,	PUNCT
cana-3476	105	8	0)∆𝑡|	0)∆𝑡|	NUM
cana-3476	106	1	∞	∞	PROPN
cana-3476	106	2	0	0	NUM
cana-3476	107	1	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	107	2	)	)	PUNCT
cana-3476	107	3	∫	∫	PROPN
cana-3476	107	4	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	107	5	)	)	PUNCT
cana-3476	107	6	𝜎	𝜎	PROPN
cana-3476	107	7	(	(	PUNCT
cana-3476	107	8	𝑡	𝑡	PROPN
cana-3476	107	9	,	,	PUNCT
cana-3476	107	10	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	108	1	∞	∞	NUM
cana-3476	108	2	0	0	NUM
cana-3476	109	1	|	|	ADV
cana-3476	109	2	≤	≤	NOUN
cana-3476	109	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	109	4	𝑘−𝑖𝑞(𝑠	𝑘−𝑖𝑞(𝑠	ADV
cana-3476	109	5	)	)	PUNCT
cana-3476	109	6	∫	∫	PROPN
cana-3476	109	7	|𝑘	|𝑘	NOUN
cana-3476	109	8	⊖	⊖	ADJ
cana-3476	109	9	𝑖𝑞(𝑠)𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	𝑖𝑞(𝑠)𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	109	10	,	,	PUNCT
cana-3476	109	11	0)∆𝑡|	0)∆𝑡|	NUM
cana-3476	109	12	∞	∞	PROPN
cana-3476	109	13	0	0	NUM
cana-3476	109	14	communications	communication	NOUN
cana-3476	109	15	on	on	ADP
cana-3476	109	16	applied	apply	VERB
cana-3476	109	17	nonlinear	nonlinear	ADJ
cana-3476	109	18	analysis	analysis	NOUN
cana-3476	109	19	issn	issn	NOUN
cana-3476	109	20	:	:	PUNCT
cana-3476	109	21	1074	1074	NUM
cana-3476	109	22	-	-	PUNCT
cana-3476	109	23	133x	133x	NUM
cana-3476	109	24	vol	vol	NOUN
cana-3476	109	25	32	32	NUM
cana-3476	109	26	no	no	NOUN
cana-3476	109	27	.	.	PUNCT
cana-3476	110	1	7s	7	NOUN
cana-3476	110	2	(	(	PUNCT
cana-3476	110	3	2025	2025	NUM
cana-3476	110	4	)	)	PUNCT
cana-3476	111	1	698	698	NUM
cana-3476	111	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	111	3	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	111	4	)	)	PUNCT
cana-3476	111	5	∫	∫	PROPN
cana-3476	111	6	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	111	7	)	)	PUNCT
cana-3476	111	8	𝜎	𝜎	PROPN
cana-3476	111	9	(	(	PUNCT
cana-3476	111	10	𝑡	𝑡	PROPN
cana-3476	111	11	,	,	PUNCT
cana-3476	111	12	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	112	1	∞	∞	NUM
cana-3476	112	2	0	0	NUM
cana-3476	113	1	|	|	ADV
cana-3476	113	2	≤	≤	NOUN
cana-3476	113	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	113	4	𝑘	𝑘	ADP
cana-3476	113	5	−	−	PROPN
cana-3476	113	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	113	7	)	)	PUNCT
cana-3476	113	8	∫	∫	PROPN
cana-3476	113	9	𝑒𝑘⊖𝑖𝑞(𝑠	𝑒𝑘⊖𝑖𝑞(𝑠	X
cana-3476	113	10	)	)	PUNCT
cana-3476	113	11	∆	∆	PROPN
cana-3476	113	12	(	(	PUNCT
cana-3476	113	13	𝑡	𝑡	X
cana-3476	113	14	,	,	PUNCT
cana-3476	113	15	0	0	NUM
cana-3476	113	16	)	)	PUNCT
cana-3476	113	17	∞	∞	NOUN
cana-3476	113	18	0	0	X
cana-3476	113	19	|𝑝(𝑠	|𝑝(𝑠	PROPN
cana-3476	113	20	)	)	PUNCT
cana-3476	113	21	∫	∫	PROPN
cana-3476	113	22	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	113	23	)	)	PUNCT
cana-3476	113	24	𝜎	𝜎	PROPN
cana-3476	113	25	(	(	PUNCT
cana-3476	113	26	𝑡	𝑡	PROPN
cana-3476	113	27	,	,	PUNCT
cana-3476	113	28	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	114	1	∞	∞	NUM
cana-3476	114	2	0	0	NUM
cana-3476	115	1	|	|	ADV
cana-3476	115	2	≤	≤	NOUN
cana-3476	115	3	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	115	4	𝑘−𝑖𝑞(𝑠	𝑘−𝑖𝑞(𝑠	ADV
cana-3476	115	5	)	)	PUNCT
cana-3476	116	1	[	[	X
cana-3476	116	2	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	𝑒𝑘⊖𝑖𝑞(𝑠)(𝑡	NOUN
cana-3476	116	3	,	,	PUNCT
cana-3476	116	4	0	0	NUM
cana-3476	116	5	)	)	PUNCT
cana-3476	116	6	]	]	PUNCT
cana-3476	116	7	0	0	NUM
cana-3476	116	8	∞	∞	NUM
cana-3476	116	9	=	=	PUNCT
cana-3476	116	10	𝑀|𝑝(𝑠)|	𝑀|𝑝(𝑠)|	VERB
cana-3476	116	11	𝑘−𝑖𝑞(𝑠	𝑘−𝑖𝑞(𝑠	ADV
cana-3476	116	12	)	)	PUNCT
cana-3476	116	13	since	since	SCONJ
cana-3476	116	14	𝑞(𝑠	𝑞(𝑠	NUM
cana-3476	116	15	)	)	PUNCT
cana-3476	116	16	∈	∈	PROPN
cana-3476	116	17	ℂ𝜇∗	ℂ𝜇∗	X
cana-3476	116	18	(	(	PUNCT
cana-3476	116	19	𝑘	𝑘	NOUN
cana-3476	116	20	)	)	PUNCT
cana-3476	116	21	and	and	CCONJ
cana-3476	116	22	|𝑝(𝑠)|	|𝑝(𝑠)|	NOUN
cana-3476	116	23	is	be	AUX
cana-3476	116	24	a	a	DET
cana-3476	116	25	real	real	ADJ
cana-3476	116	26	number	number	NOUN
cana-3476	116	27	.	.	PUNCT
cana-3476	117	1	hence	hence	ADV
cana-3476	117	2	the	the	DET
cana-3476	117	3	integral	integral	ADJ
cana-3476	117	4	converges	converge	NOUN
cana-3476	117	5	if	if	SCONJ
cana-3476	117	6	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	117	7	)	)	PUNCT
cana-3476	117	8	is	be	AUX
cana-3476	117	9	of	of	ADP
cana-3476	117	10	exponential	exponential	ADJ
cana-3476	117	11	type	type	NOUN
cana-3476	117	12	ii	ii	PROPN
cana-3476	117	13	.	.	PROPN
cana-3476	117	14	3.4	3.4	NUM
cana-3476	117	15	new	new	ADJ
cana-3476	117	16	general	general	ADJ
cana-3476	117	17	complex	complex	ADJ
cana-3476	117	18	integral	integral	ADJ
cana-3476	117	19	transform	transform	NOUN
cana-3476	117	20	on	on	ADP
cana-3476	117	21	time	time	NOUN
cana-3476	117	22	scales	scale	NOUN
cana-3476	117	23	of	of	ADP
cana-3476	117	24	some	some	DET
cana-3476	117	25	functions	function	NOUN
cana-3476	117	26	.	.	PUNCT
cana-3476	118	1	3.4.1	3.4.1	NUM
cana-3476	118	2	if	if	SCONJ
cana-3476	118	3	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	118	4	)	)	PUNCT
cana-3476	118	5	=	=	SYM
cana-3476	119	1	1	1	NUM
cana-3476	119	2	then	then	ADV
cana-3476	119	3	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	119	4	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	119	5	)	)	PUNCT
cana-3476	119	6	=	=	SYM
cana-3476	119	7	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	119	8	)	)	PUNCT
cana-3476	119	9	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	119	10	)	)	PUNCT
cana-3476	119	11	.	.	PUNCT
cana-3476	120	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	120	2	𝑐{1}(𝑠	𝑐{1}(𝑠	VERB
cana-3476	120	3	)	)	PUNCT
cana-3476	121	1	=	=	SYM
cana-3476	121	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	121	3	)	)	PUNCT
cana-3476	121	4	∫	∫	PROPN
cana-3476	121	5	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	121	6	)	)	PUNCT
cana-3476	122	1	𝜎	𝜎	PROPN
cana-3476	122	2	(	(	PUNCT
cana-3476	122	3	𝑡	𝑡	PROPN
cana-3476	122	4	,	,	PUNCT
cana-3476	122	5	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	123	1	∞	∞	NUM
cana-3476	123	2	0	0	NUM
cana-3476	123	3	=	=	SYM
cana-3476	123	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	123	5	)	)	PUNCT
cana-3476	123	6	∫	∫	PROPN
cana-3476	123	7	−	−	PROPN
cana-3476	123	8	⊖	⊖	X
cana-3476	123	9	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	123	10	)	)	PUNCT
cana-3476	123	11	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	123	12	)	)	PUNCT
cana-3476	123	13	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	123	14	,	,	PUNCT
cana-3476	123	15	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	124	1	∞	∞	NUM
cana-3476	124	2	0	0	NUM
cana-3476	124	3	=	=	SYM
cana-3476	124	4	−	−	PROPN
cana-3476	124	5	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	124	6	)	)	PUNCT
cana-3476	124	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	124	8	)	)	PUNCT
cana-3476	124	9	∫	∫	PROPN
cana-3476	124	10	⊖	⊖	PROPN
cana-3476	124	11	𝑖𝑞(𝑠)𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑖𝑞(𝑠)𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	124	12	,	,	PUNCT
cana-3476	124	13	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	125	1	∞	∞	NUM
cana-3476	125	2	0	0	NUM
cana-3476	125	3	=	=	SYM
cana-3476	125	4	−	−	PROPN
cana-3476	125	5	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	125	6	)	)	PUNCT
cana-3476	125	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	125	8	)	)	PUNCT
cana-3476	125	9	∫	∫	PROPN
cana-3476	125	10	(	(	PUNCT
cana-3476	125	11	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	125	12	,	,	PUNCT
cana-3476	125	13	0	0	NUM
cana-3476	125	14	)	)	PUNCT
cana-3476	125	15	)	)	PUNCT
cana-3476	125	16	∆	∆	PROPN
cana-3476	126	1	∆𝑡	∆𝑡	NOUN
cana-3476	126	2	∞	∞	NUM
cana-3476	126	3	0	0	X
cana-3476	127	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	127	2	𝑐{1}(𝑠	𝑐{1}(𝑠	VERB
cana-3476	127	3	)	)	PUNCT
cana-3476	127	4	=	=	SYM
cana-3476	128	1	−	−	PROPN
cana-3476	128	2	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	128	3	)	)	PUNCT
cana-3476	128	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	128	5	)	)	PUNCT
cana-3476	128	6	(	(	PUNCT
cana-3476	128	7	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	128	8	,	,	PUNCT
cana-3476	128	9	0	0	NUM
cana-3476	128	10	)	)	PUNCT
cana-3476	128	11	)	)	PUNCT
cana-3476	128	12	𝑡=0	𝑡=0	X
cana-3476	128	13	∞	∞	X
cana-3476	128	14	=	=	SYM
cana-3476	128	15	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	128	16	)	)	PUNCT
cana-3476	128	17	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	128	18	)	)	PUNCT
cana-3476	128	19	3.4.2	3.4.2	NUM
cana-3476	128	20	if	if	SCONJ
cana-3476	128	21	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	128	22	)	)	PUNCT
cana-3476	128	23	=	=	SYM
cana-3476	128	24	𝑒𝛼(𝑡	𝑒𝛼(𝑡	X
cana-3476	128	25	,	,	PUNCT
cana-3476	128	26	0	0	NUM
cana-3476	128	27	)	)	PUNCT
cana-3476	128	28	then	then	ADV
cana-3476	128	29	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	128	30	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	128	31	)	)	PUNCT
cana-3476	128	32	=	=	SYM
cana-3476	128	33	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	128	34	)	)	PUNCT
cana-3476	128	35	𝑖𝑞(𝑠)−𝛼	𝑖𝑞(𝑠)−𝛼	NOUN
cana-3476	128	36	=	=	SYM
cana-3476	128	37	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	128	38	)	)	PUNCT
cana-3476	128	39	(	(	PUNCT
cana-3476	128	40	𝛼	𝛼	NOUN
cana-3476	128	41	𝛼2+(𝑞(𝑠))2	𝛼2+(𝑞(𝑠))2	NOUN
cana-3476	128	42	+	+	CCONJ
cana-3476	128	43	𝑖	𝑖	DET
cana-3476	128	44	𝑞(𝑠	𝑞(𝑠	ADJ
cana-3476	128	45	)	)	PUNCT
cana-3476	128	46	𝛼2+(𝑞(𝑠))2	𝛼2+(𝑞(𝑠))2	NOUN
cana-3476	128	47	)	)	PUNCT
cana-3476	128	48	.	.	PUNCT
cana-3476	129	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	129	2	𝑐{𝑒𝛼(𝑡	𝑐{𝑒𝛼(𝑡	NOUN
cana-3476	129	3	,	,	PUNCT
cana-3476	129	4	0)}(𝑠	0)}(𝑠	NUM
cana-3476	129	5	)	)	PUNCT
cana-3476	129	6	=	=	SYM
cana-3476	129	7	𝑝(𝑠	𝑝(𝑠	X
cana-3476	129	8	)	)	PUNCT
cana-3476	129	9	∫	∫	PROPN
cana-3476	129	10	𝑒𝛼(𝑡	𝑒𝛼(𝑡	PROPN
cana-3476	129	11	,	,	PUNCT
cana-3476	129	12	0)𝑒⊖𝑖𝑞(𝑠	0)𝑒⊖𝑖𝑞(𝑠	ADJ
cana-3476	129	13	)	)	PUNCT
cana-3476	129	14	𝜎	𝜎	PROPN
cana-3476	129	15	(	(	PUNCT
cana-3476	129	16	𝑡	𝑡	PROPN
cana-3476	129	17	,	,	PUNCT
cana-3476	129	18	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	130	1	∞	∞	NUM
cana-3476	130	2	0	0	NUM
cana-3476	130	3	=	=	SYM
cana-3476	130	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	130	5	)	)	PUNCT
cana-3476	130	6	∫	∫	PROPN
cana-3476	130	7	𝑒𝛼(𝑡	𝑒𝛼(𝑡	PROPN
cana-3476	130	8	,	,	PUNCT
cana-3476	130	9	0	0	NUM
cana-3476	130	10	)	)	PUNCT
cana-3476	130	11	(	(	PUNCT
cana-3476	130	12	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	130	13	,	,	PUNCT
cana-3476	130	14	0	0	NUM
cana-3476	130	15	)	)	PUNCT
cana-3476	130	16	1	1	NUM
cana-3476	130	17	+	+	CCONJ
cana-3476	130	18	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	130	19	)	)	PUNCT
cana-3476	130	20	)	)	PUNCT
cana-3476	131	1	∆𝑡	∆𝑡	PROPN
cana-3476	132	1	∞	∞	NUM
cana-3476	132	2	0	0	NUM
cana-3476	133	1	=	=	SYM
cana-3476	133	2	𝑝(𝑠	𝑝(𝑠	X
cana-3476	133	3	)	)	PUNCT
cana-3476	133	4	𝛼	𝛼	PROPN
cana-3476	133	5	−	−	NOUN
cana-3476	133	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	133	7	)	)	PUNCT
cana-3476	133	8	∫	∫	PROPN
cana-3476	133	9	𝑒𝛼(𝑡	𝑒𝛼(𝑡	PROPN
cana-3476	133	10	,	,	PUNCT
cana-3476	133	11	0)𝑒⊖𝑖𝑞(𝑠)(𝑡	0)𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	133	12	,	,	PUNCT
cana-3476	133	13	0	0	NUM
cana-3476	133	14	)	)	PUNCT
cana-3476	133	15	(	(	PUNCT
cana-3476	133	16	𝛼	𝛼	NOUN
cana-3476	133	17	−	−	NOUN
cana-3476	133	18	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	133	19	)	)	PUNCT
cana-3476	133	20	1	1	NUM
cana-3476	133	21	+	+	PUNCT
cana-3476	133	22	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	133	23	)	)	PUNCT
cana-3476	133	24	)	)	PUNCT
cana-3476	134	1	∆𝑡	∆𝑡	PROPN
cana-3476	135	1	∞	∞	NUM
cana-3476	135	2	0	0	NUM
cana-3476	136	1	=	=	SYM
cana-3476	136	2	𝑝(𝑠	𝑝(𝑠	X
cana-3476	136	3	)	)	PUNCT
cana-3476	136	4	𝛼	𝛼	PROPN
cana-3476	136	5	−	−	NOUN
cana-3476	136	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	136	7	)	)	PUNCT
cana-3476	136	8	∫	∫	PROPN
cana-3476	136	9	𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	136	10	,	,	PUNCT
cana-3476	136	11	0	0	NUM
cana-3476	136	12	)	)	PUNCT
cana-3476	136	13	(	(	PUNCT
cana-3476	136	14	𝛼	𝛼	NOUN
cana-3476	136	15	−	−	NOUN
cana-3476	136	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	136	17	)	)	PUNCT
cana-3476	136	18	1	1	NUM
cana-3476	136	19	+	+	PUNCT
cana-3476	136	20	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	136	21	)	)	PUNCT
cana-3476	136	22	)	)	PUNCT
cana-3476	137	1	∆𝑡	∆𝑡	PROPN
cana-3476	138	1	∞	∞	NUM
cana-3476	138	2	0	0	NUM
cana-3476	139	1	but	but	CCONJ
cana-3476	139	2	𝛼	𝛼	PRON
cana-3476	139	3	⊖	⊖	PUNCT
cana-3476	139	4	𝑞(𝑠	𝑞(𝑠	ADJ
cana-3476	139	5	)	)	PUNCT
cana-3476	139	6	=	=	SYM
cana-3476	139	7	𝛼−𝑞(𝑠	𝛼−𝑞(𝑠	NOUN
cana-3476	139	8	)	)	PUNCT
cana-3476	139	9	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	139	10	)	)	PUNCT
cana-3476	139	11	∴	∴	PROPN
cana-3476	139	12	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	139	13	𝑐{𝑒𝛼(𝑡	𝑐{𝑒𝛼(𝑡	NOUN
cana-3476	139	14	,	,	PUNCT
cana-3476	139	15	0)}(𝑠	0)}(𝑠	NUM
cana-3476	139	16	)	)	PUNCT
cana-3476	140	1	=	=	SYM
cana-3476	140	2	𝑝(𝑠	𝑝(𝑠	X
cana-3476	140	3	)	)	PUNCT
cana-3476	140	4	𝛼	𝛼	PROPN
cana-3476	140	5	−	−	NOUN
cana-3476	140	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	140	7	)	)	PUNCT
cana-3476	140	8	∫	∫	PROPN
cana-3476	141	1	(	(	PUNCT
cana-3476	141	2	𝛼	𝛼	X
cana-3476	141	3	⊖	⊖	NOUN
cana-3476	141	4	𝑖𝑞(𝑠))𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	𝑖𝑞(𝑠))𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	NUM
cana-3476	141	5	,	,	PUNCT
cana-3476	141	6	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	142	1	∞	∞	NUM
cana-3476	142	2	0	0	NUM
cana-3476	142	3	=	=	SYM
cana-3476	142	4	𝑝(𝑠	𝑝(𝑠	X
cana-3476	142	5	)	)	PUNCT
cana-3476	142	6	𝛼	𝛼	PROPN
cana-3476	142	7	−	−	NOUN
cana-3476	142	8	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	142	9	)	)	PUNCT
cana-3476	142	10	∫	∫	PROPN
cana-3476	142	11	(	(	PUNCT
cana-3476	142	12	𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	𝑒𝛼⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	142	13	,	,	PUNCT
cana-3476	142	14	0	0	NUM
cana-3476	142	15	)	)	PUNCT
cana-3476	142	16	)	)	PUNCT
cana-3476	142	17	∆	∆	PROPN
cana-3476	143	1	∆𝑡	∆𝑡	PROPN
cana-3476	143	2	∞	∞	NUM
cana-3476	143	3	0	0	PUNCT
cana-3476	144	1	=	=	SYM
cana-3476	144	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	144	3	)	)	PUNCT
cana-3476	144	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	144	5	)	)	PUNCT
cana-3476	144	6	−	−	PRON
cana-3476	144	7	𝛼	𝛼	NOUN
cana-3476	144	8	=	=	PUNCT
cana-3476	144	9	𝑝(𝑠	𝑝(𝑠	X
cana-3476	144	10	)	)	PUNCT
cana-3476	144	11	𝛼2	𝛼2	PROPN
cana-3476	144	12	+	+	CCONJ
cana-3476	144	13	(	(	PUNCT
cana-3476	144	14	𝑞(𝑠))2	𝑞(𝑠))2	NOUN
cana-3476	144	15	(	(	PUNCT
cana-3476	144	16	−𝛼	−𝛼	PROPN
cana-3476	144	17	−	−	PROPN
cana-3476	144	18	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	144	19	)	)	PUNCT
cana-3476	144	20	)	)	PUNCT
cana-3476	145	1	∴	∴	PROPN
cana-3476	145	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	145	3	𝑐𝑇{𝑒𝛼(𝑡	𝑐𝑇{𝑒𝛼(𝑡	PROPN
cana-3476	145	4	,	,	PUNCT
cana-3476	145	5	0)}(𝑠	0)}(𝑠	NUM
cana-3476	145	6	)	)	PUNCT
cana-3476	145	7	=	=	SYM
cana-3476	145	8	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	145	9	)	)	PUNCT
cana-3476	145	10	𝑖𝑞(𝑠)−𝛼	𝑖𝑞(𝑠)−𝛼	NOUN
cana-3476	145	11	=	=	SYM
cana-3476	145	12	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	145	13	)	)	PUNCT
cana-3476	145	14	(	(	PUNCT
cana-3476	145	15	𝛼	𝛼	NOUN
cana-3476	145	16	𝛼2+(𝑞(𝑠))2	𝛼2+(𝑞(𝑠))2	NOUN
cana-3476	145	17	+	+	CCONJ
cana-3476	145	18	𝑖	𝑖	DET
cana-3476	145	19	𝑞(𝑠	𝑞(𝑠	ADJ
cana-3476	145	20	)	)	PUNCT
cana-3476	145	21	𝛼2+(𝑞(𝑠))2	𝛼2+(𝑞(𝑠))2	NOUN
cana-3476	145	22	)	)	PUNCT
cana-3476	145	23	.	.	PUNCT
cana-3476	146	1	3.4.3	3.4.3	PUNCT
cana-3476	146	2	if	if	SCONJ
cana-3476	146	3	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	146	4	)	)	PUNCT
cana-3476	146	5	=	=	SYM
cana-3476	146	6	𝑐𝑜𝑠𝛼(𝑡	𝑐𝑜𝑠𝛼(𝑡	NOUN
cana-3476	146	7	,	,	PUNCT
cana-3476	146	8	0	0	NUM
cana-3476	146	9	)	)	PUNCT
cana-3476	146	10	then	then	ADV
cana-3476	146	11	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	146	12	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	146	13	)	)	PUNCT
cana-3476	146	14	=	=	SYM
cana-3476	147	1	−𝑖𝑝(𝑠)𝑞(𝑠	−𝑖𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	147	2	)	)	PUNCT
cana-3476	147	3	(	(	PUNCT
cana-3476	147	4	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	X
cana-3476	147	5	where	where	SCONJ
cana-3476	147	6	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	147	7	>	>	X
cana-3476	147	8	|𝛼|	|𝛼|	PRON
cana-3476	147	9	let	let	VERB
cana-3476	147	10	𝑐𝑜𝑠𝛼(𝑡	𝑐𝑜𝑠𝛼(𝑡	VERB
cana-3476	147	11	,	,	PUNCT
cana-3476	147	12	0	0	NUM
cana-3476	147	13	)	)	PUNCT
cana-3476	147	14	=	=	SYM
cana-3476	147	15	𝑒𝑖𝛼(𝑡,0)+𝑒−𝑖𝛼(𝑡,0	𝑒𝑖𝛼(𝑡,0)+𝑒−𝑖𝛼(𝑡,0	ADJ
cana-3476	147	16	)	)	PUNCT
cana-3476	147	17	2	2	NUM
cana-3476	147	18	∴	∴	NOUN
cana-3476	147	19	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	147	20	𝑐{𝑐𝑜𝑠𝛼(𝑡	𝑐{𝑐𝑜𝑠𝛼(𝑡	ADJ
cana-3476	147	21	,	,	PUNCT
cana-3476	147	22	0)}(𝑠	0)}(𝑠	NUM
cana-3476	147	23	)	)	PUNCT
cana-3476	147	24	=	=	PUNCT
cana-3476	148	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	148	2	𝑐	𝑐	PROPN
cana-3476	148	3	{	{	PUNCT
cana-3476	148	4	𝑒𝑖𝛼(𝑡,0)+𝑒−𝑖𝛼(𝑡,0	𝑒𝑖𝛼(𝑡,0)+𝑒−𝑖𝛼(𝑡,0	PROPN
cana-3476	148	5	)	)	PUNCT
cana-3476	148	6	2	2	NUM
cana-3476	148	7	}	}	PUNCT
cana-3476	148	8	=	=	SYM
cana-3476	148	9	1	1	NUM
cana-3476	148	10	2	2	NUM
cana-3476	148	11	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	148	12	𝑐{𝑒𝑖𝛼(𝑡	𝑐{𝑒𝑖𝛼(𝑡	NOUN
cana-3476	148	13	,	,	PUNCT
cana-3476	148	14	0	0	NUM
cana-3476	148	15	)	)	PUNCT
cana-3476	148	16	}	}	PUNCT
cana-3476	149	1	+	+	CCONJ
cana-3476	149	2	1	1	NUM
cana-3476	149	3	2	2	NUM
cana-3476	149	4	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	149	5	𝑐{𝑒−𝑖𝛼(𝑡	𝑐{𝑒−𝑖𝛼(𝑡	NOUN
cana-3476	149	6	,	,	PUNCT
cana-3476	149	7	0	0	NUM
cana-3476	149	8	)	)	PUNCT
cana-3476	149	9	}	}	PUNCT
cana-3476	149	10	communications	communication	NOUN
cana-3476	149	11	on	on	ADP
cana-3476	149	12	applied	apply	VERB
cana-3476	149	13	nonlinear	nonlinear	ADJ
cana-3476	149	14	analysis	analysis	NOUN
cana-3476	149	15	issn	issn	NOUN
cana-3476	149	16	:	:	PUNCT
cana-3476	149	17	1074	1074	NUM
cana-3476	149	18	-	-	PUNCT
cana-3476	149	19	133x	133x	NUM
cana-3476	149	20	vol	vol	NOUN
cana-3476	149	21	32	32	NUM
cana-3476	149	22	no	no	NOUN
cana-3476	149	23	.	.	PUNCT
cana-3476	150	1	7s	7	NOUN
cana-3476	150	2	(	(	PUNCT
cana-3476	150	3	2025	2025	NUM
cana-3476	150	4	)	)	PUNCT
cana-3476	150	5	699	699	NUM
cana-3476	150	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	150	7	=	=	SYM
cana-3476	150	8	1	1	NUM
cana-3476	150	9	2	2	NUM
cana-3476	150	10	(	(	PUNCT
cana-3476	150	11	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	150	12	)	)	PUNCT
cana-3476	150	13	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	150	14	)	)	PUNCT
cana-3476	150	15	−	−	PROPN
cana-3476	151	1	𝑖𝛼	𝑖𝛼	NOUN
cana-3476	151	2	)	)	PUNCT
cana-3476	152	1	+	+	CCONJ
cana-3476	152	2	1	1	NUM
cana-3476	152	3	2	2	NUM
cana-3476	152	4	(	(	PUNCT
cana-3476	152	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	152	6	)	)	PUNCT
cana-3476	152	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	152	8	)	)	PUNCT
cana-3476	153	1	+	+	CCONJ
cana-3476	153	2	𝑖𝛼	𝑖𝛼	NOUN
cana-3476	153	3	)	)	PUNCT
cana-3476	153	4	=	=	SYM
cana-3476	153	5	𝑝(𝑠	𝑝(𝑠	X
cana-3476	153	6	)	)	PUNCT
cana-3476	153	7	2𝑖	2𝑖	NOUN
cana-3476	153	8	(	(	PUNCT
cana-3476	153	9	1	1	NUM
cana-3476	153	10	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	153	11	)	)	PUNCT
cana-3476	153	12	−	−	ADP
cana-3476	153	13	𝛼	𝛼	PRON
cana-3476	153	14	+	+	ADJ
cana-3476	153	15	1	1	NUM
cana-3476	153	16	𝑞(𝑠	𝑞(𝑠	NUM
cana-3476	153	17	)	)	PUNCT
cana-3476	153	18	+	+	NUM
cana-3476	153	19	𝛼	𝛼	X
cana-3476	153	20	)	)	PUNCT
cana-3476	153	21	=	=	SYM
cana-3476	153	22	𝑝(𝑠)𝑞(𝑠	𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	153	23	)	)	PUNCT
cana-3476	153	24	𝑖((𝑞(𝑠))2	𝑖((𝑞(𝑠))2	PUNCT
cana-3476	154	1	−	−	PROPN
cana-3476	154	2	𝛼2	𝛼2	ADJ
cana-3476	154	3	)	)	PUNCT
cana-3476	154	4	∴	∴	PROPN
cana-3476	154	5	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	154	6	𝑐{𝑐𝑜𝑠𝛼(𝑡	𝑐{𝑐𝑜𝑠𝛼(𝑡	ADJ
cana-3476	154	7	,	,	PUNCT
cana-3476	154	8	0)}(𝑠	0)}(𝑠	NUM
cana-3476	154	9	)	)	PUNCT
cana-3476	155	1	=	=	SYM
cana-3476	155	2	𝑖𝑝(𝑠)𝑞(𝑠	𝑖𝑝(𝑠)𝑞(𝑠	ADJ
cana-3476	155	3	)	)	PUNCT
cana-3476	155	4	(	(	PUNCT
cana-3476	155	5	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	X
cana-3476	155	6	.	.	NOUN
cana-3476	155	7	3.4.4	3.4.4	NUM
cana-3476	155	8	if	if	SCONJ
cana-3476	155	9	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	155	10	)	)	PUNCT
cana-3476	155	11	=	=	SYM
cana-3476	155	12	𝑐𝑜𝑠ℎ𝛼(𝑡	𝑐𝑜𝑠ℎ𝛼(𝑡	PROPN
cana-3476	155	13	,	,	PUNCT
cana-3476	155	14	0	0	NUM
cana-3476	155	15	)	)	PUNCT
cana-3476	156	1	then	then	ADV
cana-3476	156	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	156	3	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	156	4	)	)	PUNCT
cana-3476	156	5	=	=	SYM
cana-3476	157	1	𝑖𝑝(𝑠)𝑞(𝑠	𝑖𝑝(𝑠)𝑞(𝑠	ADJ
cana-3476	157	2	)	)	PUNCT
cana-3476	157	3	(	(	PUNCT
cana-3476	157	4	𝑞(𝑠))2+𝛼2	𝑞(𝑠))2+𝛼2	NOUN
cana-3476	157	5	where	where	SCONJ
cana-3476	157	6	𝑞(𝑠	𝑞(𝑠	VERB
cana-3476	157	7	)	)	PUNCT
cana-3476	157	8	>	>	X
cana-3476	157	9	0	0	PUNCT
cana-3476	157	10	let	let	VERB
cana-3476	157	11	𝑐𝑜𝑠ℎ𝛼(𝑡	𝑐𝑜𝑠ℎ𝛼(𝑡	ADJ
cana-3476	157	12	,	,	PUNCT
cana-3476	157	13	0	0	NUM
cana-3476	157	14	)	)	PUNCT
cana-3476	157	15	=	=	SYM
cana-3476	157	16	𝑒𝛼(𝑡,0)+𝑒−𝛼(𝑡,0	𝑒𝛼(𝑡,0)+𝑒−𝛼(𝑡,0	X
cana-3476	157	17	)	)	PUNCT
cana-3476	157	18	2	2	NUM
cana-3476	157	19	∴	∴	NOUN
cana-3476	157	20	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	157	21	𝑐{𝑐𝑜𝑠ℎ𝛼(𝑡	𝑐{𝑐𝑜𝑠ℎ𝛼(𝑡	NOUN
cana-3476	157	22	,	,	PUNCT
cana-3476	157	23	0)}(𝑠	0)}(𝑠	NUM
cana-3476	157	24	)	)	PUNCT
cana-3476	157	25	=	=	PUNCT
cana-3476	158	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	158	2	𝑐	𝑐	PROPN
cana-3476	158	3	{	{	PUNCT
cana-3476	158	4	𝑒𝛼(𝑡,0)+𝑒−𝛼(𝑡,0	𝑒𝛼(𝑡,0)+𝑒−𝛼(𝑡,0	PROPN
cana-3476	158	5	)	)	PUNCT
cana-3476	158	6	2	2	NUM
cana-3476	158	7	}	}	PUNCT
cana-3476	158	8	=	=	SYM
cana-3476	158	9	1	1	NUM
cana-3476	158	10	2	2	NUM
cana-3476	158	11	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	158	12	𝑐{𝑒𝛼(𝑡	𝑐{𝑒𝛼(𝑡	NOUN
cana-3476	158	13	,	,	PUNCT
cana-3476	158	14	0	0	NUM
cana-3476	158	15	)	)	PUNCT
cana-3476	158	16	}	}	PUNCT
cana-3476	159	1	+	+	CCONJ
cana-3476	159	2	1	1	NUM
cana-3476	159	3	2	2	NUM
cana-3476	159	4	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	159	5	𝑐{𝑒−𝛼(𝑡	𝑐{𝑒−𝛼(𝑡	NOUN
cana-3476	159	6	,	,	PUNCT
cana-3476	159	7	0	0	NUM
cana-3476	159	8	)	)	PUNCT
cana-3476	159	9	}	}	PUNCT
cana-3476	159	10	=	=	SYM
cana-3476	159	11	1	1	NUM
cana-3476	159	12	2	2	NUM
cana-3476	159	13	(	(	PUNCT
cana-3476	159	14	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	159	15	)	)	PUNCT
cana-3476	159	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	159	17	)	)	PUNCT
cana-3476	159	18	−	−	PROPN
cana-3476	159	19	𝛼	𝛼	X
cana-3476	159	20	)	)	PUNCT
cana-3476	160	1	+	+	CCONJ
cana-3476	160	2	1	1	NUM
cana-3476	160	3	2	2	NUM
cana-3476	160	4	(	(	PUNCT
cana-3476	160	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	160	6	)	)	PUNCT
cana-3476	160	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	160	8	)	)	PUNCT
cana-3476	161	1	+	+	SYM
cana-3476	161	2	𝛼	𝛼	X
cana-3476	161	3	)	)	PUNCT
cana-3476	161	4	=	=	SYM
cana-3476	161	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	161	6	)	)	PUNCT
cana-3476	161	7	2	2	NUM
cana-3476	161	8	(	(	PUNCT
cana-3476	161	9	1	1	NUM
cana-3476	161	10	𝑖𝑞(𝑠	𝑖𝑞(𝑠	NUM
cana-3476	161	11	)	)	PUNCT
cana-3476	161	12	−	−	ADP
cana-3476	161	13	𝛼	𝛼	PRON
cana-3476	161	14	+	+	NOUN
cana-3476	161	15	1	1	NUM
cana-3476	161	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	161	17	)	)	PUNCT
cana-3476	161	18	+	+	NUM
cana-3476	161	19	𝛼	𝛼	X
cana-3476	161	20	)	)	PUNCT
cana-3476	161	21	∴	∴	PROPN
cana-3476	161	22	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	161	23	𝑐{𝑐𝑜𝑠ℎ𝛼(𝑡	𝑐{𝑐𝑜𝑠ℎ𝛼(𝑡	NOUN
cana-3476	161	24	,	,	PUNCT
cana-3476	161	25	0)}(𝑠	0)}(𝑠	NUM
cana-3476	161	26	)	)	PUNCT
cana-3476	161	27	=	=	SYM
cana-3476	162	1	−𝑖𝑝(𝑠)𝑞(𝑠	−𝑖𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	162	2	)	)	PUNCT
cana-3476	162	3	(	(	PUNCT
cana-3476	162	4	𝑞(𝑠))2+𝛼2	𝑞(𝑠))2+𝛼2	NOUN
cana-3476	162	5	.	.	PUNCT
cana-3476	163	1	3.4.5	3.4.5	NUM
cana-3476	163	2	if	if	SCONJ
cana-3476	163	3	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	163	4	)	)	PUNCT
cana-3476	164	1	=	=	SYM
cana-3476	164	2	𝑠𝑖𝑛𝛼(𝑡	𝑠𝑖𝑛𝛼(𝑡	NOUN
cana-3476	164	3	,	,	PUNCT
cana-3476	164	4	0	0	NUM
cana-3476	164	5	)	)	PUNCT
cana-3476	164	6	then	then	ADV
cana-3476	164	7	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	164	8	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	164	9	)	)	PUNCT
cana-3476	164	10	=	=	SYM
cana-3476	165	1	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	X
cana-3476	165	2	)	)	PUNCT
cana-3476	165	3	(	(	PUNCT
cana-3476	165	4	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	X
cana-3476	165	5	.	.	PUNCT
cana-3476	165	6	let	let	AUX
cana-3476	165	7	𝑠𝑖𝑛𝛼(𝑡	𝑠𝑖𝑛𝛼(𝑡	VERB
cana-3476	165	8	,	,	PUNCT
cana-3476	165	9	0	0	NUM
cana-3476	165	10	)	)	PUNCT
cana-3476	165	11	=	=	SYM
cana-3476	165	12	𝑒𝑖𝛼(𝑡,0)−𝑒−𝑖𝛼(𝑡,0	𝑒𝑖𝛼(𝑡,0)−𝑒−𝑖𝛼(𝑡,0	NOUN
cana-3476	165	13	)	)	PUNCT
cana-3476	165	14	2𝑖	2𝑖	NOUN
cana-3476	165	15	∴	∴	PROPN
cana-3476	165	16	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	165	17	𝑐{𝑠𝑖𝑛𝛼(𝑡	𝑐{𝑠𝑖𝑛𝛼(𝑡	PROPN
cana-3476	165	18	,	,	PUNCT
cana-3476	165	19	0)}(𝑠	0)}(𝑠	NUM
cana-3476	165	20	)	)	PUNCT
cana-3476	165	21	=	=	PUNCT
cana-3476	166	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	166	2	𝑐	𝑐	PROPN
cana-3476	166	3	{	{	PUNCT
cana-3476	166	4	𝑒𝑖𝛼(𝑡,0)−𝑒−𝑖𝛼(𝑡,0	𝑒𝑖𝛼(𝑡,0)−𝑒−𝑖𝛼(𝑡,0	NOUN
cana-3476	166	5	)	)	PUNCT
cana-3476	166	6	2𝑖	2𝑖	NOUN
cana-3476	166	7	}	}	PUNCT
cana-3476	166	8	=	=	PUNCT
cana-3476	166	9	1	1	NUM
cana-3476	166	10	2𝑖	2𝑖	NOUN
cana-3476	166	11	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	166	12	𝑐{𝑒𝑖𝛼(𝑡	𝑐{𝑒𝑖𝛼(𝑡	PROPN
cana-3476	166	13	,	,	PUNCT
cana-3476	166	14	0	0	NUM
cana-3476	166	15	)	)	PUNCT
cana-3476	166	16	}	}	PUNCT
cana-3476	166	17	−	−	PROPN
cana-3476	166	18	1	1	NUM
cana-3476	166	19	2𝑖	2𝑖	NOUN
cana-3476	166	20	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	166	21	𝑐{𝑒−𝑖𝛼(𝑡	𝑐{𝑒−𝑖𝛼(𝑡	ADJ
cana-3476	166	22	,	,	PUNCT
cana-3476	166	23	0	0	NUM
cana-3476	166	24	)	)	PUNCT
cana-3476	166	25	}	}	PUNCT
cana-3476	166	26	=	=	SYM
cana-3476	166	27	1	1	NUM
cana-3476	166	28	2𝑖	2𝑖	NOUN
cana-3476	166	29	(	(	PUNCT
cana-3476	166	30	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	166	31	)	)	PUNCT
cana-3476	166	32	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	166	33	)	)	PUNCT
cana-3476	166	34	−	−	PROPN
cana-3476	167	1	𝑖𝛼	𝑖𝛼	NOUN
cana-3476	167	2	)	)	PUNCT
cana-3476	168	1	−	−	PROPN
cana-3476	168	2	1	1	NUM
cana-3476	168	3	2𝑖	2𝑖	NOUN
cana-3476	168	4	(	(	PUNCT
cana-3476	168	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	168	6	)	)	PUNCT
cana-3476	168	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	168	8	)	)	PUNCT
cana-3476	169	1	+	+	CCONJ
cana-3476	169	2	𝑖𝛼	𝑖𝛼	NOUN
cana-3476	169	3	)	)	PUNCT
cana-3476	169	4	=	=	SYM
cana-3476	169	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	169	6	)	)	PUNCT
cana-3476	169	7	−2	−2	NOUN
cana-3476	169	8	(	(	PUNCT
cana-3476	169	9	1	1	NUM
cana-3476	169	10	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	169	11	)	)	PUNCT
cana-3476	169	12	−	−	ADP
cana-3476	169	13	𝛼	𝛼	NOUN
cana-3476	169	14	−	−	PROPN
cana-3476	169	15	1	1	NUM
cana-3476	169	16	𝑞(𝑠	𝑞(𝑠	PROPN
cana-3476	169	17	)	)	PUNCT
cana-3476	170	1	+	+	NUM
cana-3476	170	2	𝛼	𝛼	X
cana-3476	170	3	)	)	PUNCT
cana-3476	170	4	∴	∴	PROPN
cana-3476	170	5	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	170	6	𝑐{𝑠𝑖𝑛𝛼(𝑡	𝑐{𝑠𝑖𝑛𝛼(𝑡	PROPN
cana-3476	170	7	,	,	PUNCT
cana-3476	170	8	0)}(𝑠	0)}(𝑠	NUM
cana-3476	170	9	)	)	PUNCT
cana-3476	170	10	=	=	SYM
cana-3476	171	1	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	X
cana-3476	171	2	)	)	PUNCT
cana-3476	171	3	(	(	PUNCT
cana-3476	171	4	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	X
cana-3476	171	5	.	.	X
cana-3476	171	6	3.4.6	3.4.6	NUM
cana-3476	171	7	if	if	SCONJ
cana-3476	171	8	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	171	9	)	)	PUNCT
cana-3476	171	10	=	=	SYM
cana-3476	171	11	𝑠𝑖𝑛ℎ𝛼(𝑡	𝑠𝑖𝑛ℎ𝛼(𝑡	NOUN
cana-3476	171	12	,	,	PUNCT
cana-3476	171	13	0	0	NUM
cana-3476	171	14	)	)	PUNCT
cana-3476	171	15	then	then	ADV
cana-3476	171	16	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	171	17	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	171	18	)	)	PUNCT
cana-3476	171	19	=	=	SYM
cana-3476	172	1	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	X
cana-3476	172	2	)	)	PUNCT
cana-3476	172	3	(	(	PUNCT
cana-3476	172	4	𝑞(𝑠))2+𝛼2	𝑞(𝑠))2+𝛼2	NOUN
cana-3476	172	5	where	where	SCONJ
cana-3476	172	6	𝑞(𝑠	𝑞(𝑠	VERB
cana-3476	172	7	)	)	PUNCT
cana-3476	172	8	>	>	X
cana-3476	172	9	0	0	PUNCT
cana-3476	172	10	let	let	VERB
cana-3476	172	11	𝑠𝑖𝑛ℎ𝛼(𝑡	𝑠𝑖𝑛ℎ𝛼(𝑡	NOUN
cana-3476	172	12	,	,	PUNCT
cana-3476	172	13	0	0	NUM
cana-3476	172	14	)	)	PUNCT
cana-3476	172	15	=	=	SYM
cana-3476	172	16	𝑒𝛼(𝑡,0)−𝑒−𝛼(𝑡,0	𝑒𝛼(𝑡,0)−𝑒−𝛼(𝑡,0	NOUN
cana-3476	172	17	)	)	PUNCT
cana-3476	172	18	2	2	NUM
cana-3476	172	19	∴	∴	NOUN
cana-3476	172	20	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	172	21	𝑐{𝑠𝑖𝑛ℎ𝛼(𝑡	𝑐{𝑠𝑖𝑛ℎ𝛼(𝑡	NOUN
cana-3476	172	22	,	,	PUNCT
cana-3476	172	23	0)}(𝑠	0)}(𝑠	NUM
cana-3476	172	24	)	)	PUNCT
cana-3476	172	25	=	=	PUNCT
cana-3476	173	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	173	2	𝑐	𝑐	PROPN
cana-3476	173	3	{	{	PUNCT
cana-3476	173	4	𝑒𝛼(𝑡,0)−𝑒−𝛼(𝑡,0	𝑒𝛼(𝑡,0)−𝑒−𝛼(𝑡,0	PROPN
cana-3476	173	5	)	)	PUNCT
cana-3476	173	6	2	2	NUM
cana-3476	173	7	}	}	PUNCT
cana-3476	173	8	=	=	SYM
cana-3476	173	9	1	1	NUM
cana-3476	173	10	2	2	NUM
cana-3476	173	11	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	173	12	𝑐{𝑒𝛼(𝑡	𝑐{𝑒𝛼(𝑡	NOUN
cana-3476	173	13	,	,	PUNCT
cana-3476	173	14	0	0	NUM
cana-3476	173	15	)	)	PUNCT
cana-3476	173	16	}	}	PUNCT
cana-3476	173	17	−	−	NUM
cana-3476	173	18	1	1	NUM
cana-3476	173	19	2	2	NUM
cana-3476	173	20	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	173	21	𝑐{𝑒−𝛼(𝑡	𝑐{𝑒−𝛼(𝑡	NOUN
cana-3476	173	22	,	,	PUNCT
cana-3476	173	23	0	0	NUM
cana-3476	173	24	)	)	PUNCT
cana-3476	173	25	}	}	PUNCT
cana-3476	173	26	=	=	SYM
cana-3476	173	27	1	1	NUM
cana-3476	173	28	2	2	NUM
cana-3476	173	29	(	(	PUNCT
cana-3476	173	30	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	173	31	)	)	PUNCT
cana-3476	173	32	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	173	33	)	)	PUNCT
cana-3476	173	34	−	−	PROPN
cana-3476	173	35	𝛼	𝛼	X
cana-3476	173	36	)	)	PUNCT
cana-3476	173	37	−	−	PROPN
cana-3476	173	38	1	1	NUM
cana-3476	173	39	2	2	NUM
cana-3476	173	40	(	(	PUNCT
cana-3476	173	41	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	173	42	)	)	PUNCT
cana-3476	173	43	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	173	44	)	)	PUNCT
cana-3476	174	1	+	+	SYM
cana-3476	174	2	𝛼	𝛼	X
cana-3476	174	3	)	)	PUNCT
cana-3476	174	4	=	=	SYM
cana-3476	174	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	174	6	)	)	PUNCT
cana-3476	174	7	2	2	NUM
cana-3476	174	8	(	(	PUNCT
cana-3476	174	9	1	1	NUM
cana-3476	174	10	𝑖𝑞(𝑠	𝑖𝑞(𝑠	NUM
cana-3476	174	11	)	)	PUNCT
cana-3476	174	12	−	−	ADP
cana-3476	174	13	𝛼	𝛼	INTJ
cana-3476	174	14	−	−	PROPN
cana-3476	174	15	1	1	NUM
cana-3476	174	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	174	17	)	)	PUNCT
cana-3476	174	18	+	+	NUM
cana-3476	174	19	𝛼	𝛼	X
cana-3476	174	20	)	)	PUNCT
cana-3476	174	21	∴	∴	PROPN
cana-3476	174	22	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	174	23	𝑐{𝑠𝑖𝑛ℎ𝛼(𝑡	𝑐{𝑠𝑖𝑛ℎ𝛼(𝑡	NOUN
cana-3476	174	24	,	,	PUNCT
cana-3476	174	25	0)}(𝑠	0)}(𝑠	NUM
cana-3476	174	26	)	)	PUNCT
cana-3476	174	27	=	=	SYM
cana-3476	175	1	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	X
cana-3476	175	2	)	)	PUNCT
cana-3476	175	3	(	(	PUNCT
cana-3476	175	4	𝑞(𝑠))2+𝛼2	𝑞(𝑠))2+𝛼2	NOUN
cana-3476	175	5	.	.	PUNCT
cana-3476	176	1	now	now	ADV
cana-3476	176	2	we	we	PRON
cana-3476	176	3	introduce	introduce	VERB
cana-3476	176	4	the	the	DET
cana-3476	176	5	new	new	ADJ
cana-3476	176	6	general	general	ADJ
cana-3476	176	7	integral	integral	ADJ
cana-3476	176	8	transform	transform	NOUN
cana-3476	176	9	and	and	CCONJ
cana-3476	176	10	new	new	ADJ
cana-3476	176	11	general	general	ADJ
cana-3476	176	12	complex	complex	ADJ
cana-3476	176	13	integral	integral	ADJ
cana-3476	176	14	transform	transform	NOUN
cana-3476	176	15	on	on	ADP
cana-3476	176	16	time	time	NOUN
cana-3476	176	17	scales	scale	NOUN
cana-3476	176	18	for	for	ADP
cana-3476	176	19	some	some	DET
cana-3476	176	20	basic	basic	ADJ
cana-3476	176	21	functions	function	NOUN
cana-3476	176	22	in	in	ADP
cana-3476	176	23	the	the	DET
cana-3476	176	24	following	follow	VERB
cana-3476	176	25	table	table	NOUN
cana-3476	176	26	.	.	PUNCT
cana-3476	177	1	functions	function	NOUN
cana-3476	177	2	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	177	3	)	)	PUNCT
cana-3476	177	4	ɲ(𝑓(𝑡))(𝑧	ɲ(𝑓(𝑡))(𝑧	NUM
cana-3476	177	5	)	)	PUNCT
cana-3476	177	6	=	=	SYM
cana-3476	178	1	ℱ(𝑧	ℱ(𝑧	X
cana-3476	178	2	)	)	PUNCT
cana-3476	178	3	new	new	ADJ
cana-3476	178	4	general	general	ADJ
cana-3476	178	5	integral	integral	ADJ
cana-3476	178	6	transform	transform	NOUN
cana-3476	178	7	on	on	ADP
cana-3476	178	8	time	time	NOUN
cana-3476	178	9	scales	scale	VERB
cana-3476	178	10	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	178	11	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	PROPN
cana-3476	178	12	)	)	PUNCT
cana-3476	178	13	}	}	PUNCT
cana-3476	179	1	=	=	SYM
cana-3476	179	2	ℱ𝑔	ℱ𝑔	NOUN
cana-3476	179	3	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	179	4	)	)	PUNCT
cana-3476	179	5	new	new	ADJ
cana-3476	179	6	general	general	ADJ
cana-3476	179	7	complex	complex	ADJ
cana-3476	179	8	integral	integral	ADJ
cana-3476	179	9	transform	transform	NOUN
cana-3476	179	10	on	on	ADP
cana-3476	179	11	time	time	NOUN
cana-3476	179	12	scales	scale	VERB
cana-3476	179	13	1	1	NUM
cana-3476	179	14	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	179	15	)	)	PUNCT
cana-3476	179	16	𝑞(𝑠	𝑞(𝑠	PROPN
cana-3476	179	17	)	)	PUNCT
cana-3476	179	18	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	179	19	)	)	PUNCT
cana-3476	179	20	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	179	21	)	)	PUNCT
cana-3476	179	22	𝑒𝛼(𝑡	𝑒𝛼(𝑡	X
cana-3476	179	23	,	,	PUNCT
cana-3476	179	24	0	0	X
cana-3476	179	25	)	)	PUNCT
cana-3476	179	26	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	179	27	)	)	PUNCT
cana-3476	179	28	𝑞(𝑠)−𝛼	𝑞(𝑠)−𝛼	NOUN
cana-3476	179	29	,	,	PUNCT
cana-3476	179	30	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	179	31	>	>	X
cana-3476	179	32	|𝛼|	|𝛼|	PROPN
cana-3476	179	33	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	179	34	)	)	PUNCT
cana-3476	179	35	𝑖𝑞(𝑠)−𝛼	𝑖𝑞(𝑠)−𝛼	NOUN
cana-3476	179	36	,	,	PUNCT
cana-3476	179	37	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	179	38	>	>	PRON
cana-3476	179	39	|𝛼|	|𝛼|	PROPN
cana-3476	179	40	communications	communication	NOUN
cana-3476	179	41	on	on	ADP
cana-3476	179	42	applied	apply	VERB
cana-3476	179	43	nonlinear	nonlinear	ADJ
cana-3476	179	44	analysis	analysis	NOUN
cana-3476	179	45	issn	issn	NOUN
cana-3476	179	46	:	:	PUNCT
cana-3476	179	47	1074	1074	NUM
cana-3476	179	48	-	-	PUNCT
cana-3476	179	49	133x	133x	NUM
cana-3476	179	50	vol	vol	NOUN
cana-3476	179	51	32	32	NUM
cana-3476	179	52	no	no	NOUN
cana-3476	179	53	.	.	PUNCT
cana-3476	180	1	7s	7	NOUN
cana-3476	180	2	(	(	PUNCT
cana-3476	180	3	2025	2025	NUM
cana-3476	180	4	)	)	PUNCT
cana-3476	180	5	700	700	NUM
cana-3476	181	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	181	2	𝑐𝑜𝑠𝛼(𝑡	𝑐𝑜𝑠𝛼(𝑡	NOUN
cana-3476	181	3	,	,	PUNCT
cana-3476	181	4	0	0	NUM
cana-3476	181	5	)	)	PUNCT
cana-3476	181	6	𝑝(𝑠)𝑞(𝑠	𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	181	7	)	)	PUNCT
cana-3476	181	8	(	(	PUNCT
cana-3476	181	9	𝑞(𝑠))2	𝑞(𝑠))2	NOUN
cana-3476	181	10	+	+	CCONJ
cana-3476	181	11	𝛼2	𝛼2	PROPN
cana-3476	181	12	𝑖𝑝(𝑠)𝑞(𝑠	𝑖𝑝(𝑠)𝑞(𝑠	PROPN
cana-3476	181	13	)	)	PUNCT
cana-3476	181	14	(	(	PUNCT
cana-3476	181	15	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	ADJ
cana-3476	181	16	,	,	PUNCT
cana-3476	181	17	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	181	18	>	>	PUNCT
cana-3476	181	19	|𝛼|	|𝛼|	PROPN
cana-3476	181	20	𝑠𝑖𝑛𝛼(𝑡	𝑠𝑖𝑛𝛼(𝑡	NOUN
cana-3476	181	21	,	,	PUNCT
cana-3476	181	22	0	0	NUM
cana-3476	181	23	)	)	PUNCT
cana-3476	181	24	𝛼𝑝(𝑠	𝛼𝑝(𝑠	NOUN
cana-3476	181	25	)	)	PUNCT
cana-3476	181	26	(	(	PUNCT
cana-3476	181	27	𝑞(𝑠))2	𝑞(𝑠))2	NOUN
cana-3476	181	28	+	+	CCONJ
cana-3476	181	29	𝛼2	𝛼2	PROPN
cana-3476	181	30	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	NUM
cana-3476	181	31	)	)	PUNCT
cana-3476	181	32	(	(	PUNCT
cana-3476	181	33	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	ADJ
cana-3476	181	34	,	,	PUNCT
cana-3476	181	35	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	181	36	>	>	PUNCT
cana-3476	181	37	|𝛼|	|𝛼|	PROPN
cana-3476	181	38	𝑐𝑜𝑠ℎ𝛼(𝑡	𝑐𝑜𝑠ℎ𝛼(𝑡	PROPN
cana-3476	181	39	,	,	PUNCT
cana-3476	181	40	0	0	NUM
cana-3476	181	41	)	)	PUNCT
cana-3476	181	42	𝑝(𝑠)𝑞(𝑠	𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	181	43	)	)	PUNCT
cana-3476	181	44	(	(	PUNCT
cana-3476	181	45	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	ADJ
cana-3476	181	46	,	,	PUNCT
cana-3476	181	47	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	181	48	>	>	PUNCT
cana-3476	181	49	|𝛼|	|𝛼|	PROPN
cana-3476	181	50	−𝑖𝑝(𝑠)𝑞(𝑠	−𝑖𝑝(𝑠)𝑞(𝑠	NOUN
cana-3476	181	51	)	)	PUNCT
cana-3476	181	52	(	(	PUNCT
cana-3476	181	53	𝑞(𝑠))2+𝛼2	𝑞(𝑠))2+𝛼2	NOUN
cana-3476	181	54	,	,	PUNCT
cana-3476	181	55	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	181	56	>	>	PUNCT
cana-3476	181	57	|𝛼|	|𝛼|	PROPN
cana-3476	181	58	𝑠𝑖𝑛ℎ𝛼(𝑡	𝑠𝑖𝑛ℎ𝛼(𝑡	NOUN
cana-3476	181	59	,	,	PUNCT
cana-3476	181	60	0	0	NUM
cana-3476	181	61	)	)	PUNCT
cana-3476	181	62	𝛼𝑝(𝑠	𝛼𝑝(𝑠	NOUN
cana-3476	181	63	)	)	PUNCT
cana-3476	181	64	(	(	PUNCT
cana-3476	181	65	𝑞(𝑠))2−𝛼2	𝑞(𝑠))2−𝛼2	ADJ
cana-3476	181	66	,	,	PUNCT
cana-3476	181	67	|𝑞(𝑠)|	|𝑞(𝑠)|	NOUN
cana-3476	181	68	>	>	PUNCT
cana-3476	181	69	|𝛼|	|𝛼|	PROPN
cana-3476	181	70	−𝛼𝑝(𝑠	−𝛼𝑝(𝑠	NOUN
cana-3476	181	71	)	)	PUNCT
cana-3476	181	72	(	(	PUNCT
cana-3476	181	73	𝑞(𝑠))2	𝑞(𝑠))2	NOUN
cana-3476	181	74	+	+	CCONJ
cana-3476	181	75	𝛼2	𝛼2	PROPN
cana-3476	181	76	table	table	NOUN
cana-3476	181	77	1	1	NUM
cana-3476	181	78	3.5	3.5	NUM
cana-3476	181	79	theorem	theorem	NOUN
cana-3476	181	80	3	3	NUM
cana-3476	181	81	let	let	VERB
cana-3476	181	82	𝜔	𝜔	PRON
cana-3476	181	83	∈	∈	NOUN
cana-3476	181	84	𝕋	𝕋	NOUN
cana-3476	181	85	,	,	PUNCT
cana-3476	181	86	𝜔	𝜔	X
cana-3476	181	87	>	>	X
cana-3476	181	88	0	0	NUM
cana-3476	181	89	and	and	CCONJ
cana-3476	181	90	𝑢𝑣(𝑡	𝑢𝑣(𝑡	PUNCT
cana-3476	181	91	)	)	PUNCT
cana-3476	181	92	is	be	AUX
cana-3476	181	93	the	the	DET
cana-3476	181	94	unit	unit	NOUN
cana-3476	181	95	step	step	NOUN
cana-3476	181	96	function	function	VERB
cana-3476	181	97	the	the	DET
cana-3476	181	98	the	the	DET
cana-3476	181	99	new	new	ADJ
cana-3476	181	100	general	general	ADJ
cana-3476	181	101	complex	complex	ADJ
cana-3476	181	102	integral	integral	ADJ
cana-3476	181	103	transform	transform	NOUN
cana-3476	181	104	on	on	ADP
cana-3476	181	105	time	time	NOUN
cana-3476	181	106	scales	scale	VERB
cana-3476	181	107	𝕋	𝕋	PROPN
cana-3476	181	108	of	of	ADP
cana-3476	181	109	the	the	DET
cana-3476	181	110	function	function	NOUN
cana-3476	181	111	𝑢𝑣(𝑡)𝑓(𝑡	𝑢𝑣(𝑡)𝑓(𝑡	ADJ
cana-3476	181	112	)	)	PUNCT
cana-3476	181	113	is	be	AUX
cana-3476	181	114	𝑒⊖𝑖𝑞(𝑠)(𝑣	𝑒⊖𝑖𝑞(𝑠)(𝑣	NOUN
cana-3476	181	115	,	,	PUNCT
cana-3476	181	116	0)𝒯𝑔	0)𝒯𝑔	PROPN
cana-3476	181	117	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	181	118	)	)	PUNCT
cana-3476	181	119	}	}	PUNCT
cana-3476	182	1	where	where	SCONJ
cana-3476	182	2	𝑢𝑣(𝑡	𝑢𝑣(𝑡	VERB
cana-3476	182	3	)	)	PUNCT
cana-3476	182	4	=	=	SYM
cana-3476	182	5	{	{	PUNCT
cana-3476	182	6	0	0	NUM
cana-3476	182	7	,	,	PUNCT
cana-3476	182	8	𝑖𝑓	𝑖𝑓	NUM
cana-3476	182	9	𝑡	𝑡	PROPN
cana-3476	182	10	∈	∈	PROPN
cana-3476	182	11	𝕋	𝕋	NOUN
cana-3476	182	12	∩	∩	NOUN
cana-3476	182	13	(	(	PUNCT
cana-3476	182	14	−∞	−∞	NOUN
cana-3476	182	15	,	,	PUNCT
cana-3476	182	16	𝑣	𝑣	NOUN
cana-3476	182	17	)	)	PUNCT
cana-3476	182	18	1	1	NUM
cana-3476	182	19	,	,	PUNCT
cana-3476	182	20	𝑖𝑓	𝑖𝑓	NUM
cana-3476	183	1	𝑡	𝑡	PROPN
cana-3476	183	2	∈	∈	PROPN
cana-3476	183	3	𝕋	𝕋	NOUN
cana-3476	183	4	∩	∩	NOUN
cana-3476	183	5	[	[	X
cana-3476	183	6	𝑣	𝑣	X
cana-3476	183	7	,	,	PUNCT
cana-3476	183	8	∞	∞	NOUN
cana-3476	183	9	)	)	PUNCT
cana-3476	183	10	proof	proof	NOUN
cana-3476	183	11	:	:	PUNCT
cana-3476	183	12	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	183	13	𝑐{𝑢𝑣(𝑡)𝑓(𝑡)}(𝑠	𝑐{𝑢𝑣(𝑡)𝑓(𝑡)}(𝑠	X
cana-3476	183	14	)	)	PUNCT
cana-3476	183	15	=	=	SYM
cana-3476	183	16	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	183	17	)	)	PUNCT
cana-3476	183	18	∫	∫	PROPN
cana-3476	183	19	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	183	20	)	)	PUNCT
cana-3476	183	21	𝜎	𝜎	PROPN
cana-3476	183	22	(	(	PUNCT
cana-3476	183	23	𝑡	𝑡	PROPN
cana-3476	183	24	,	,	PUNCT
cana-3476	183	25	0	0	NUM
cana-3476	183	26	)	)	PUNCT
cana-3476	183	27	𝑢𝑣(𝑡)𝑓(𝑡	𝑢𝑣(𝑡)𝑓(𝑡	ADJ
cana-3476	183	28	)	)	PUNCT
cana-3476	183	29	∆𝑡	∆𝑡	PROPN
cana-3476	183	30	∞	∞	NUM
cana-3476	183	31	0	0	NUM
cana-3476	184	1	=	=	SYM
cana-3476	184	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	184	3	)	)	PUNCT
cana-3476	184	4	∫	∫	PROPN
cana-3476	184	5	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	184	6	)	)	PUNCT
cana-3476	184	7	𝜎	𝜎	PROPN
cana-3476	184	8	(	(	PUNCT
cana-3476	184	9	𝑡	𝑡	PROPN
cana-3476	184	10	,	,	PUNCT
cana-3476	184	11	0	0	NUM
cana-3476	184	12	)	)	PUNCT
cana-3476	184	13	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	184	14	)	)	PUNCT
cana-3476	184	15	∆𝑡	∆𝑡	PROPN
cana-3476	184	16	=	=	SYM
cana-3476	184	17	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	184	18	)	)	PUNCT
cana-3476	184	19	∫	∫	PROPN
cana-3476	184	20	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	184	21	,	,	PUNCT
cana-3476	184	22	0	0	NUM
cana-3476	184	23	)	)	PUNCT
cana-3476	184	24	1	1	NUM
cana-3476	184	25	+	+	CCONJ
cana-3476	184	26	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	184	27	)	)	PUNCT
cana-3476	184	28	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	184	29	)	)	PUNCT
cana-3476	184	30	∆𝑡	∆𝑡	PROPN
cana-3476	184	31	∞	∞	NUM
cana-3476	184	32	𝑣	𝑣	ADP
cana-3476	184	33	∞	∞	NUM
cana-3476	184	34	𝑣	𝑣	PROPN
cana-3476	184	35	=	=	PUNCT
cana-3476	184	36	𝑝(𝑠	𝑝(𝑠	X
cana-3476	184	37	)	)	PUNCT
cana-3476	184	38	∫	∫	PROPN
cana-3476	184	39	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	184	40	,	,	PUNCT
cana-3476	184	41	𝑣)𝑒⊖𝑖𝑞(𝑠)(𝑣	𝑣)𝑒⊖𝑖𝑞(𝑠)(𝑣	PROPN
cana-3476	184	42	,	,	PUNCT
cana-3476	184	43	0	0	NUM
cana-3476	184	44	)	)	PUNCT
cana-3476	184	45	1	1	NUM
cana-3476	184	46	+	+	CCONJ
cana-3476	184	47	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	184	48	)	)	PUNCT
cana-3476	184	49	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	184	50	)	)	PUNCT
cana-3476	184	51	∆𝑡	∆𝑡	PROPN
cana-3476	184	52	∞	∞	NUM
cana-3476	184	53	𝑣	𝑣	X
cana-3476	184	54	=	=	SYM
cana-3476	184	55	𝑝(𝑠)𝑒⊖𝑖𝑞(𝑠)(𝑣	𝑝(𝑠)𝑒⊖𝑖𝑞(𝑠)(𝑣	PROPN
cana-3476	184	56	,	,	PUNCT
cana-3476	184	57	0	0	NUM
cana-3476	184	58	)	)	PUNCT
cana-3476	184	59	∫	∫	PROPN
cana-3476	184	60	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	184	61	,	,	PUNCT
cana-3476	184	62	𝑣	𝑣	NOUN
cana-3476	184	63	)	)	PUNCT
cana-3476	184	64	1	1	NUM
cana-3476	184	65	+	+	CCONJ
cana-3476	184	66	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	184	67	)	)	PUNCT
cana-3476	184	68	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	184	69	)	)	PUNCT
cana-3476	184	70	∆𝑡	∆𝑡	PROPN
cana-3476	184	71	∞	∞	NUM
cana-3476	184	72	𝑣	𝑣	X
cana-3476	184	73	=	=	PUNCT
cana-3476	184	74	𝑒⊖𝑖𝑞(𝑠)(𝑣	𝑒⊖𝑖𝑞(𝑠)(𝑣	NOUN
cana-3476	184	75	,	,	PUNCT
cana-3476	184	76	0	0	NUM
cana-3476	184	77	)	)	PUNCT
cana-3476	184	78	(	(	PUNCT
cana-3476	184	79	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	184	80	)	)	PUNCT
cana-3476	184	81	∫	∫	PROPN
cana-3476	184	82	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	184	83	)	)	PUNCT
cana-3476	184	84	𝜎	𝜎	PROPN
cana-3476	184	85	(	(	PUNCT
cana-3476	184	86	𝑡	𝑡	NOUN
cana-3476	184	87	,	,	PUNCT
cana-3476	184	88	𝑣)𝑓(𝑡)∆𝑡	𝑣)𝑓(𝑡)∆𝑡	X
cana-3476	184	89	∞	∞	NUM
cana-3476	184	90	𝑣	𝑣	NOUN
cana-3476	184	91	)	)	PUNCT
cana-3476	184	92	=	=	SYM
cana-3476	184	93	𝑒⊖𝑖𝑞(𝑠)(𝑣	𝑒⊖𝑖𝑞(𝑠)(𝑣	PROPN
cana-3476	184	94	,	,	PUNCT
cana-3476	184	95	0)𝒯𝑔	0)𝒯𝑔	PROPN
cana-3476	184	96	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	184	97	)	)	PUNCT
cana-3476	184	98	}	}	PUNCT
cana-3476	184	99	3.6	3.6	NUM
cana-3476	184	100	definition	definition	NOUN
cana-3476	184	101	8	8	NUM
cana-3476	184	102	[	[	X
cana-3476	184	103	3	3	NUM
cana-3476	184	104	]	]	X
cana-3476	184	105	convolution	convolution	NOUN
cana-3476	184	106	of	of	ADP
cana-3476	184	107	two	two	NUM
cana-3476	184	108	functions	function	NOUN
cana-3476	184	109	.	.	PUNCT
cana-3476	185	1	if	if	SCONJ
cana-3476	185	2	𝑓	𝑓	ADJ
cana-3476	185	3	:	:	PUNCT
cana-3476	185	4	𝕋	𝕋	PROPN
cana-3476	185	5	→	→	SYM
cana-3476	185	6	ℂ	ℂ	PROPN
cana-3476	185	7	and	and	CCONJ
cana-3476	185	8	𝑔	𝑔	PROPN
cana-3476	185	9	∈	∈	PROPN
cana-3476	185	10	𝐶𝑝𝑟𝑑−𝑒2	𝐶𝑝𝑟𝑑−𝑒2	PROPN
cana-3476	185	11	(	(	PUNCT
cana-3476	185	12	𝕋	𝕋	PROPN
cana-3476	185	13	,	,	PUNCT
cana-3476	185	14	ℂ	ℂ	PROPN
cana-3476	185	15	)	)	PUNCT
cana-3476	185	16	then	then	ADV
cana-3476	185	17	the	the	DET
cana-3476	185	18	convolution	convolution	NOUN
cana-3476	185	19	of	of	ADP
cana-3476	185	20	two	two	NUM
cana-3476	185	21	functions	function	NOUN
cana-3476	185	22	𝑓	𝑓	PRON
cana-3476	185	23	and	and	CCONJ
cana-3476	185	24	𝑔	𝑔	PROPN
cana-3476	185	25	is	be	AUX
cana-3476	185	26	denoted	denote	VERB
cana-3476	185	27	by	by	ADP
cana-3476	185	28	𝑓	𝑓	DET
cana-3476	185	29	∗	∗	NOUN
cana-3476	185	30	𝑔	𝑔	PROPN
cana-3476	185	31	and	and	CCONJ
cana-3476	185	32	is	be	AUX
cana-3476	185	33	given	give	VERB
cana-3476	185	34	by	by	ADP
cana-3476	185	35	(	(	PUNCT
cana-3476	185	36	𝑓	𝑓	DET
cana-3476	185	37	∗	∗	NOUN
cana-3476	185	38	𝑔)(𝑡	𝑔)(𝑡	PUNCT
cana-3476	185	39	)	)	PUNCT
cana-3476	185	40	=	=	SYM
cana-3476	185	41	∫	∫	PROPN
cana-3476	185	42	𝑓(𝜏)𝑔(𝑡	𝑓(𝜏)𝑔(𝑡	NOUN
cana-3476	185	43	,	,	PUNCT
cana-3476	185	44	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	185	45	𝑡	𝑡	X
cana-3476	185	46	0	0	NUM
cana-3476	185	47	where	where	SCONJ
cana-3476	185	48	𝐶𝑝𝑟𝑑−𝑒2	𝐶𝑝𝑟𝑑−𝑒2	PROPN
cana-3476	185	49	(	(	PUNCT
cana-3476	185	50	𝕋	𝕋	PROPN
cana-3476	185	51	,	,	PUNCT
cana-3476	185	52	ℂ	ℂ	PROPN
cana-3476	185	53	)	)	PUNCT
cana-3476	185	54	denotes	denote	VERB
cana-3476	185	55	the	the	DET
cana-3476	185	56	space	space	NOUN
cana-3476	185	57	of	of	ADP
cana-3476	185	58	piecewise	piecewise	NOUN
cana-3476	185	59	right	right	ADJ
cana-3476	185	60	dese	dese	ADJ
cana-3476	185	61	continuous	continuous	ADJ
cana-3476	185	62	functions	function	NOUN
cana-3476	185	63	of	of	ADP
cana-3476	185	64	exponential	exponential	ADJ
cana-3476	185	65	type	type	NOUN
cana-3476	185	66	-	-	PUNCT
cana-3476	185	67	ii	ii	NOUN
cana-3476	185	68	.	.	PUNCT
cana-3476	186	1	3.6.1	3.6.1	NUM
cana-3476	186	2	theorem	theorem	VERB
cana-3476	186	3	4	4	NUM
cana-3476	186	4	convolution	convolution	NOUN
cana-3476	186	5	theorem	theorem	NOUN
cana-3476	186	6	let	let	VERB
cana-3476	186	7	𝑓	𝑓	X
cana-3476	186	8	:	:	PUNCT
cana-3476	186	9	𝕋	𝕋	PROPN
cana-3476	186	10	→	→	SYM
cana-3476	186	11	ℂ	ℂ	PROPN
cana-3476	186	12	and	and	CCONJ
cana-3476	186	13	𝑔	𝑔	NOUN
cana-3476	186	14	:	:	PUNCT
cana-3476	186	15	ℂ	ℂ	PROPN
cana-3476	186	16	→	→	SYM
cana-3476	186	17	ℂ	ℂ	PROPN
cana-3476	186	18	have	have	VERB
cana-3476	186	19	new	new	ADJ
cana-3476	186	20	general	general	ADJ
cana-3476	186	21	complex	complex	ADJ
cana-3476	186	22	integral	integral	ADJ
cana-3476	186	23	transforms	transform	NOUN
cana-3476	186	24	on	on	ADP
cana-3476	186	25	time	time	NOUN
cana-3476	186	26	scales	scale	NOUN
cana-3476	186	27	𝕋	𝕋	NOUN
cana-3476	186	28	are	be	AUX
cana-3476	186	29	ℱ𝑔	ℱ𝑔	NOUN
cana-3476	186	30	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	186	31	)	)	PUNCT
cana-3476	186	32	and	and	CCONJ
cana-3476	186	33	𝒢𝑔	𝒢𝑔	VERB
cana-3476	186	34	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	186	35	)	)	PUNCT
cana-3476	186	36	respectively	respectively	ADV
cana-3476	186	37	.	.	PUNCT
cana-3476	187	1	then	then	ADV
cana-3476	187	2	the	the	DET
cana-3476	187	3	new	new	ADJ
cana-3476	187	4	general	general	ADJ
cana-3476	187	5	complex	complex	ADJ
cana-3476	187	6	integral	integral	ADJ
cana-3476	187	7	transform	transform	NOUN
cana-3476	187	8	on	on	ADP
cana-3476	187	9	time	time	NOUN
cana-3476	187	10	scales	scale	NOUN
cana-3476	187	11	for	for	ADP
cana-3476	187	12	the	the	DET
cana-3476	187	13	convolution	convolution	NOUN
cana-3476	187	14	of	of	ADP
cana-3476	187	15	these	these	DET
cana-3476	187	16	functions	function	NOUN
cana-3476	187	17	is	be	AUX
cana-3476	187	18	1	1	NUM
cana-3476	187	19	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	187	20	)	)	PUNCT
cana-3476	188	1	ℱ𝑔	ℱ𝑔	NOUN
cana-3476	188	2	𝑐(𝑠)𝒢𝑔	𝑐(𝑠)𝒢𝑔	ADJ
cana-3476	188	3	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	188	4	)	)	PUNCT
cana-3476	188	5	.	.	PUNCT
cana-3476	189	1	proof	proof	NOUN
cana-3476	189	2	:	:	PUNCT
cana-3476	189	3	let	let	VERB
cana-3476	189	4	(	(	PUNCT
cana-3476	189	5	𝑓	𝑓	DET
cana-3476	189	6	∗	∗	NOUN
cana-3476	189	7	𝑔)(𝑡	𝑔)(𝑡	PUNCT
cana-3476	189	8	)	)	PUNCT
cana-3476	189	9	=	=	SYM
cana-3476	190	1	∫	∫	PROPN
cana-3476	190	2	𝑓(𝜏)𝑔(𝑡	𝑓(𝜏)𝑔(𝑡	NOUN
cana-3476	190	3	,	,	PUNCT
cana-3476	190	4	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	190	5	𝑡	𝑡	X
cana-3476	190	6	0	0	NUM
cana-3476	190	7	.	.	PUNCT
cana-3476	191	1	applying	apply	VERB
cana-3476	191	2	the	the	DET
cana-3476	191	3	new	new	ADJ
cana-3476	191	4	general	general	ADJ
cana-3476	191	5	complex	complex	ADJ
cana-3476	191	6	integral	integral	ADJ
cana-3476	191	7	transform	transform	NOUN
cana-3476	191	8	to	to	ADP
cana-3476	191	9	both	both	DET
cana-3476	191	10	sides	side	NOUN
cana-3476	191	11	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	191	12	𝑐	𝑐	VERB
cana-3476	191	13	{	{	PUNCT
cana-3476	191	14	(	(	PUNCT
cana-3476	191	15	𝑓	𝑓	DET
cana-3476	191	16	∗	∗	NOUN
cana-3476	191	17	𝑔)(𝑡	𝑔)(𝑡	PUNCT
cana-3476	191	18	)	)	PUNCT
cana-3476	191	19	}	}	PUNCT
cana-3476	192	1	=	=	PUNCT
cana-3476	192	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	192	3	𝑐	𝑐	PROPN
cana-3476	192	4	{	{	PUNCT
cana-3476	192	5	∫	∫	PROPN
cana-3476	192	6	𝑓(𝜏)𝑔(𝑡	𝑓(𝜏)𝑔(𝑡	PROPN
cana-3476	192	7	,	,	PUNCT
cana-3476	192	8	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	192	9	𝑡	𝑡	X
cana-3476	192	10	0	0	PUNCT
cana-3476	192	11	}	}	PUNCT
cana-3476	192	12	=	=	SYM
cana-3476	192	13	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	192	14	)	)	PUNCT
cana-3476	192	15	∫	∫	PROPN
cana-3476	192	16	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	192	17	)	)	PUNCT
cana-3476	192	18	𝜎	𝜎	PROPN
cana-3476	192	19	(	(	PUNCT
cana-3476	192	20	𝑡	𝑡	PROPN
cana-3476	192	21	,	,	PUNCT
cana-3476	192	22	0	0	NUM
cana-3476	192	23	)	)	PUNCT
cana-3476	192	24	(	(	PUNCT
cana-3476	192	25	∫	∫	PROPN
cana-3476	192	26	𝑓(𝜏)𝑔(𝑡	𝑓(𝜏)𝑔(𝑡	PROPN
cana-3476	192	27	,	,	PUNCT
cana-3476	192	28	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	192	29	𝑡	𝑡	X
cana-3476	192	30	0	0	NUM
cana-3476	192	31	)	)	PUNCT
cana-3476	192	32	∆𝑡	∆𝑡	PROPN
cana-3476	192	33	∞	∞	NUM
cana-3476	192	34	0	0	NUM
cana-3476	192	35	communications	communication	NOUN
cana-3476	192	36	on	on	ADP
cana-3476	192	37	applied	apply	VERB
cana-3476	192	38	nonlinear	nonlinear	ADJ
cana-3476	192	39	analysis	analysis	NOUN
cana-3476	192	40	issn	issn	NOUN
cana-3476	192	41	:	:	PUNCT
cana-3476	192	42	1074	1074	NUM
cana-3476	192	43	-	-	PUNCT
cana-3476	192	44	133x	133x	NUM
cana-3476	192	45	vol	vol	NOUN
cana-3476	192	46	32	32	NUM
cana-3476	192	47	no	no	NOUN
cana-3476	192	48	.	.	PUNCT
cana-3476	193	1	7s	7	NOUN
cana-3476	193	2	(	(	PUNCT
cana-3476	193	3	2025	2025	NUM
cana-3476	193	4	)	)	PUNCT
cana-3476	193	5	701	701	NUM
cana-3476	193	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	193	7	=	=	SYM
cana-3476	193	8	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	193	9	)	)	PUNCT
cana-3476	193	10	∫	∫	PROPN
cana-3476	193	11	𝑓(𝜏	𝑓(𝜏	PROPN
cana-3476	193	12	)	)	PUNCT
cana-3476	193	13	(	(	PUNCT
cana-3476	193	14	∫	∫	PROPN
cana-3476	193	15	𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	PROPN
cana-3476	193	16	,	,	PUNCT
cana-3476	193	17	𝜎(𝜏))𝑒⊖𝑖𝑞(𝑠	𝜎(𝜏))𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	193	18	)	)	PUNCT
cana-3476	193	19	𝜎	𝜎	PROPN
cana-3476	193	20	(	(	PUNCT
cana-3476	193	21	𝑡	𝑡	PROPN
cana-3476	193	22	,	,	PUNCT
cana-3476	193	23	0)∆𝑡	0)∆𝑡	NUM
cana-3476	193	24	∞	∞	NUM
cana-3476	193	25	𝜎(𝜏	𝜎(𝜏	PROPN
cana-3476	193	26	)	)	PUNCT
cana-3476	193	27	)	)	PUNCT
cana-3476	194	1	∆𝜏	∆𝜏	X
cana-3476	194	2	∞	∞	NOUN
cana-3476	194	3	0	0	NUM
cana-3476	195	1	=	=	SYM
cana-3476	195	2	∫	∫	PROPN
cana-3476	195	3	𝑓(𝜏	𝑓(𝜏	PROPN
cana-3476	195	4	)	)	PUNCT
cana-3476	196	1	∞	∞	NOUN
cana-3476	196	2	0	0	X
cana-3476	197	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	197	2	𝑐{𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	𝑐{𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	PROPN
cana-3476	197	3	,	,	PUNCT
cana-3476	197	4	𝜎(𝜏))}∆𝜏	𝜎(𝜏))}∆𝜏	NUM
cana-3476	197	5	but	but	CCONJ
cana-3476	197	6	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	197	7	𝑐{𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	𝑐{𝑢𝜎(𝜏)(𝑡)𝑔(𝑡	PROPN
cana-3476	197	8	,	,	PUNCT
cana-3476	197	9	𝜎(𝜏	𝜎(𝜏	PROPN
cana-3476	197	10	)	)	PUNCT
cana-3476	197	11	)	)	PUNCT
cana-3476	197	12	}	}	PUNCT
cana-3476	198	1	=	=	SYM
cana-3476	198	2	𝒢𝑔	𝒢𝑔	PROPN
cana-3476	198	3	𝑐(𝑠)𝑒⊖𝑖𝑞(𝑠	𝑐(𝑠)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	198	4	)	)	PUNCT
cana-3476	198	5	𝜎	𝜎	PROPN
cana-3476	198	6	(	(	PUNCT
cana-3476	198	7	𝜏	𝜏	NOUN
cana-3476	198	8	,	,	PUNCT
cana-3476	198	9	0	0	NUM
cana-3476	198	10	)	)	PUNCT
cana-3476	198	11	hence	hence	ADV
cana-3476	198	12	the	the	DET
cana-3476	198	13	above	above	ADJ
cana-3476	198	14	equation	equation	NOUN
cana-3476	198	15	gives	give	VERB
cana-3476	198	16	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	198	17	𝑐	𝑐	PROPN
cana-3476	198	18	{	{	PUNCT
cana-3476	198	19	(	(	PUNCT
cana-3476	198	20	𝑓	𝑓	DET
cana-3476	198	21	∗	∗	NOUN
cana-3476	198	22	𝑔)(𝑡	𝑔)(𝑡	PUNCT
cana-3476	198	23	)	)	PUNCT
cana-3476	198	24	}	}	PUNCT
cana-3476	199	1	=	=	SYM
cana-3476	199	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	199	3	)	)	PUNCT
cana-3476	199	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	199	5	)	)	PUNCT
cana-3476	199	6	∫	∫	PROPN
cana-3476	199	7	𝑓(𝜏	𝑓(𝜏	PROPN
cana-3476	199	8	)	)	PUNCT
cana-3476	199	9	∞	∞	PROPN
cana-3476	199	10	0	0	X
cana-3476	200	1	𝒢𝑔	𝒢𝑔	PROPN
cana-3476	200	2	𝑐(𝑠)𝑒⊖𝑖𝑞(𝑠	𝑐(𝑠)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	200	3	)	)	PUNCT
cana-3476	200	4	𝜎	𝜎	PROPN
cana-3476	200	5	(	(	PUNCT
cana-3476	200	6	𝜏	𝜏	NOUN
cana-3476	200	7	,	,	PUNCT
cana-3476	200	8	0)∆𝜏	0)∆𝜏	PUNCT
cana-3476	201	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	201	2	𝑐	𝑐	X
cana-3476	201	3	{	{	PUNCT
cana-3476	201	4	(	(	PUNCT
cana-3476	201	5	𝑓	𝑓	PRON
cana-3476	201	6	∗	∗	NOUN
cana-3476	201	7	𝑔)(𝑡	𝑔)(𝑡	PUNCT
cana-3476	201	8	)	)	PUNCT
cana-3476	201	9	}	}	PUNCT
cana-3476	201	10	=	=	SYM
cana-3476	201	11	𝒢𝑔	𝒢𝑔	PROPN
cana-3476	201	12	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	201	13	)	)	PUNCT
cana-3476	201	14	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	201	15	)	)	PUNCT
cana-3476	201	16	(	(	PUNCT
cana-3476	201	17	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	201	18	)	)	PUNCT
cana-3476	201	19	∫	∫	PROPN
cana-3476	201	20	𝑓(𝜏	𝑓(𝜏	PROPN
cana-3476	201	21	)	)	PUNCT
cana-3476	201	22	∞	∞	PROPN
cana-3476	201	23	0	0	NUM
cana-3476	201	24	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	201	25	)	)	PUNCT
cana-3476	201	26	𝜎	𝜎	PROPN
cana-3476	201	27	(	(	PUNCT
cana-3476	201	28	𝜏	𝜏	NOUN
cana-3476	201	29	,	,	PUNCT
cana-3476	201	30	0)∆𝜏	0)∆𝜏	NUM
cana-3476	201	31	)	)	PUNCT
cana-3476	201	32	=	=	SYM
cana-3476	201	33	1	1	NUM
cana-3476	201	34	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	201	35	)	)	PUNCT
cana-3476	202	1	ℱ𝑔	ℱ𝑔	NOUN
cana-3476	202	2	𝑐(𝑠)𝒢𝑔	𝑐(𝑠)𝒢𝑔	ADJ
cana-3476	202	3	𝑐(𝑠	𝑐(𝑠	NOUN
cana-3476	202	4	)	)	PUNCT
cana-3476	202	5	as	as	ADP
cana-3476	202	6	𝑓	𝑓	PRON
cana-3476	202	7	and	and	CCONJ
cana-3476	202	8	𝑔	𝑔	PROPN
cana-3476	202	9	are	be	AUX
cana-3476	202	10	of	of	ADP
cana-3476	202	11	exponential	exponential	ADJ
cana-3476	202	12	type	type	NOUN
cana-3476	202	13	ii	ii	PROPN
cana-3476	202	14	with	with	ADP
cana-3476	202	15	constants	constant	NOUN
cana-3476	202	16	𝑘𝑓	𝑘𝑓	X
cana-3476	202	17	and	and	CCONJ
cana-3476	202	18	𝑘𝑔	𝑘𝑔	VERB
cana-3476	202	19	respectively	respectively	ADV
cana-3476	202	20	,	,	PUNCT
cana-3476	202	21	we	we	PRON
cana-3476	202	22	have	have	VERB
cana-3476	202	23	|(𝑓	|(𝑓	PROPN
cana-3476	202	24	∗	∗	NOUN
cana-3476	202	25	𝑔)(𝑡)|	𝑔)(𝑡)|	X
cana-3476	202	26	=	=	SYM
cana-3476	202	27	|∫	|∫	ADJ
cana-3476	202	28	𝑓(𝜏)𝑔(𝑡	𝑓(𝜏)𝑔(𝑡	NOUN
cana-3476	202	29	,	,	PUNCT
cana-3476	202	30	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	202	31	𝑡	𝑡	X
cana-3476	202	32	0	0	NUM
cana-3476	203	1	|	|	ADV
cana-3476	203	2	≤	≤	NUM
cana-3476	203	3	∫	∫	PROPN
cana-3476	203	4	|𝑓(𝜏)||𝑔(𝑡	|𝑓(𝜏)||𝑔(𝑡	PROPN
cana-3476	203	5	,	,	PUNCT
cana-3476	203	6	𝜎(𝜏))|∆𝜏	𝜎(𝜏))|∆𝜏	PROPN
cana-3476	203	7	𝑡	𝑡	PROPN
cana-3476	203	8	0	0	NUM
cana-3476	203	9	∴	∴	PROPN
cana-3476	203	10	|(𝑓	|(𝑓	PROPN
cana-3476	203	11	∗	∗	VERB
cana-3476	203	12	𝑔)(𝑡)|	𝑔)(𝑡)|	PROPN
cana-3476	203	13	≤	≤	NUM
cana-3476	203	14	∫	∫	PROPN
cana-3476	204	1	𝑀1𝑒𝑘𝑓	𝑀1𝑒𝑘𝑓	PROPN
cana-3476	204	2	(	(	PUNCT
cana-3476	204	3	𝜏	𝜏	NOUN
cana-3476	204	4	,	,	PUNCT
cana-3476	204	5	0)𝑀2𝑒𝑘𝑔	0)𝑀2𝑒𝑘𝑔	NUM
cana-3476	204	6	(	(	PUNCT
cana-3476	204	7	𝑡	𝑡	X
cana-3476	204	8	,	,	PUNCT
cana-3476	204	9	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	NOUN
cana-3476	204	10	=	=	SYM
cana-3476	205	1	∫	∫	PROPN
cana-3476	205	2	𝑀𝑒𝑘𝑓	𝑀𝑒𝑘𝑓	PROPN
cana-3476	205	3	(	(	PUNCT
cana-3476	205	4	𝜏	𝜏	NOUN
cana-3476	205	5	,	,	PUNCT
cana-3476	205	6	0)𝑒𝑘𝑔	0)𝑒𝑘𝑔	NUM
cana-3476	205	7	(	(	PUNCT
cana-3476	205	8	𝑡	𝑡	PROPN
cana-3476	205	9	,	,	PUNCT
cana-3476	205	10	0)𝑒𝑘𝑔	0)𝑒𝑘𝑔	NUM
cana-3476	205	11	(	(	PUNCT
cana-3476	205	12	0	0	NUM
cana-3476	205	13	,	,	PUNCT
cana-3476	205	14	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	205	15	∞	∞	NOUN
cana-3476	205	16	0	0	PUNCT
cana-3476	205	17	𝑡	𝑡	NOUN
cana-3476	205	18	0	0	NUM
cana-3476	205	19	where	where	SCONJ
cana-3476	205	20	|𝑓(𝜏)|	|𝑓(𝜏)|	PROPN
cana-3476	205	21	≤	≤	PROPN
cana-3476	205	22	𝑀1𝑒𝑘𝑓	𝑀1𝑒𝑘𝑓	X
cana-3476	205	23	(	(	PUNCT
cana-3476	205	24	𝜏	𝜏	NOUN
cana-3476	205	25	,	,	PUNCT
cana-3476	205	26	0	0	NUM
cana-3476	205	27	)	)	PUNCT
cana-3476	205	28	,	,	PUNCT
cana-3476	205	29	|𝑔(𝑡	|𝑔(𝑡	PROPN
cana-3476	205	30	,	,	PUNCT
cana-3476	205	31	𝜎(𝜏))|	𝜎(𝜏))|	NOUN
cana-3476	205	32	≤	≤	X
cana-3476	205	33	𝑀2𝑒𝑘𝑔	𝑀2𝑒𝑘𝑔	PROPN
cana-3476	205	34	(	(	PUNCT
cana-3476	205	35	𝑡	𝑡	X
cana-3476	205	36	,	,	PUNCT
cana-3476	205	37	𝜎(𝜏	𝜎(𝜏	NOUN
cana-3476	205	38	)	)	PUNCT
cana-3476	205	39	)	)	PUNCT
cana-3476	205	40	and	and	CCONJ
cana-3476	205	41	𝑀	𝑀	PROPN
cana-3476	205	42	=	=	PUNCT
cana-3476	205	43	𝑀1𝑀2	𝑀1𝑀2	PROPN
cana-3476	205	44	∴	∴	PROPN
cana-3476	205	45	|(𝑓	|(𝑓	PROPN
cana-3476	205	46	∗	∗	VERB
cana-3476	205	47	𝑔)(𝑡)|	𝑔)(𝑡)|	X
cana-3476	205	48	≤	≤	NOUN
cana-3476	205	49	𝑀𝑒𝑘𝑔	𝑀𝑒𝑘𝑔	PROPN
cana-3476	205	50	(	(	PUNCT
cana-3476	205	51	𝑡	𝑡	PROPN
cana-3476	205	52	,	,	PUNCT
cana-3476	205	53	0	0	NUM
cana-3476	205	54	)	)	PUNCT
cana-3476	205	55	∫	∫	PROPN
cana-3476	206	1	𝑒𝑘𝑓	𝑒𝑘𝑓	PROPN
cana-3476	206	2	(	(	PUNCT
cana-3476	206	3	𝜏	𝜏	PROPN
cana-3476	206	4	,	,	PUNCT
cana-3476	206	5	0)𝑒𝑘𝑔	0)𝑒𝑘𝑔	NUM
cana-3476	206	6	(	(	PUNCT
cana-3476	206	7	0	0	NUM
cana-3476	206	8	,	,	PUNCT
cana-3476	206	9	𝜎(𝜏))∆𝜏	𝜎(𝜏))∆𝜏	X
cana-3476	206	10	∞	∞	NUM
cana-3476	206	11	0	0	SYM
cana-3476	206	12	|(𝑓	|(𝑓	PROPN
cana-3476	206	13	∗	∗	VERB
cana-3476	206	14	𝑔)(𝑡)|	𝑔)(𝑡)|	X
cana-3476	206	15	≤	≤	NOUN
cana-3476	206	16	𝑀𝑒𝑘𝑔	𝑀𝑒𝑘𝑔	PROPN
cana-3476	206	17	(	(	PUNCT
cana-3476	206	18	𝑡	𝑡	PROPN
cana-3476	206	19	,	,	PUNCT
cana-3476	206	20	0	0	NUM
cana-3476	206	21	)	)	PUNCT
cana-3476	206	22	∫	∫	PROPN
cana-3476	207	1	𝑒𝑘𝑓	𝑒𝑘𝑓	PROPN
cana-3476	207	2	(	(	PUNCT
cana-3476	207	3	𝜏	𝜏	PROPN
cana-3476	207	4	,	,	PUNCT
cana-3476	207	5	0)𝑒⊖𝑘𝑔	0)𝑒⊖𝑘𝑔	NOUN
cana-3476	207	6	(	(	PUNCT
cana-3476	207	7	𝜏	𝜏	NOUN
cana-3476	207	8	,	,	PUNCT
cana-3476	207	9	0)∆𝜏	0)∆𝜏	NUM
cana-3476	207	10	∞	∞	NUM
cana-3476	207	11	0	0	NUM
cana-3476	207	12	|(𝑓	|(𝑓	PROPN
cana-3476	207	13	∗	∗	VERB
cana-3476	207	14	𝑔)(𝑡)|	𝑔)(𝑡)|	X
cana-3476	207	15	≤	≤	NOUN
cana-3476	207	16	𝑀𝑒𝑘𝑔	𝑀𝑒𝑘𝑔	PROPN
cana-3476	207	17	(	(	PUNCT
cana-3476	207	18	𝑡	𝑡	PROPN
cana-3476	207	19	,	,	PUNCT
cana-3476	207	20	0	0	NUM
cana-3476	207	21	)	)	PUNCT
cana-3476	207	22	∫	∫	PROPN
cana-3476	207	23	𝑒𝑘𝑓⊖𝑘𝑔	𝑒𝑘𝑓⊖𝑘𝑔	SYM
cana-3476	207	24	(	(	PUNCT
cana-3476	207	25	𝜏	𝜏	NOUN
cana-3476	207	26	,	,	PUNCT
cana-3476	207	27	0)∆𝜏	0)∆𝜏	NUM
cana-3476	207	28	∞	∞	NUM
cana-3476	207	29	0	0	PUNCT
cana-3476	207	30	hence	hence	ADV
cana-3476	207	31	|(𝑓	|(𝑓	PROPN
cana-3476	207	32	∗	∗	VERB
cana-3476	207	33	𝑔)(𝑡)|	𝑔)(𝑡)|	PROPN
cana-3476	207	34	≤	≤	NOUN
cana-3476	207	35	𝑀	𝑀	PROPN
cana-3476	207	36	|𝑘𝑓−𝑘𝑔|	|𝑘𝑓−𝑘𝑔|	PROPN
cana-3476	207	37	𝑒𝑘𝑔	𝑒𝑘𝑔	PROPN
cana-3476	207	38	(	(	PUNCT
cana-3476	207	39	𝑡	𝑡	PROPN
cana-3476	207	40	,	,	PUNCT
cana-3476	207	41	0	0	NUM
cana-3476	207	42	)	)	PUNCT
cana-3476	207	43	(	(	PUNCT
cana-3476	207	44	𝑒𝑘𝑓⊖𝑘𝑔	𝑒𝑘𝑓⊖𝑘𝑔	X
cana-3476	207	45	(	(	PUNCT
cana-3476	207	46	𝑡	𝑡	NOUN
cana-3476	207	47	,	,	PUNCT
cana-3476	207	48	0	0	NUM
cana-3476	207	49	)	)	PUNCT
cana-3476	207	50	−	−	ADP
cana-3476	207	51	1	1	X
cana-3476	207	52	)	)	PUNCT
cana-3476	207	53	≤	≤	NUM
cana-3476	207	54	𝑀	𝑀	PROPN
cana-3476	207	55	|𝑘𝑓−𝑘𝑔|	|𝑘𝑓−𝑘𝑔|	PROPN
cana-3476	207	56	(	(	PUNCT
cana-3476	207	57	𝑒𝑘𝑓	𝑒𝑘𝑓	X
cana-3476	207	58	(	(	PUNCT
cana-3476	207	59	𝑡	𝑡	PROPN
cana-3476	207	60	,	,	PUNCT
cana-3476	207	61	0	0	NUM
cana-3476	207	62	)	)	PUNCT
cana-3476	208	1	+	+	CCONJ
cana-3476	208	2	𝑒𝑘𝑔	𝑒𝑘𝑔	X
cana-3476	208	3	(	(	PUNCT
cana-3476	208	4	𝑡	𝑡	PROPN
cana-3476	208	5	,	,	PUNCT
cana-3476	208	6	0	0	NUM
cana-3476	208	7	)	)	PUNCT
cana-3476	208	8	)	)	PUNCT
cana-3476	209	1	|(𝑓	|(𝑓	PROPN
cana-3476	209	2	∗	∗	VERB
cana-3476	209	3	𝑔)(𝑡)|	𝑔)(𝑡)|	PROPN
cana-3476	209	4	≤	≤	NOUN
cana-3476	209	5	2𝑀	2𝑀	NOUN
cana-3476	209	6	|𝑘𝑓	|𝑘𝑓	NUM
cana-3476	210	1	−	−	PROPN
cana-3476	210	2	𝑘𝑔|	𝑘𝑔|	PROPN
cana-3476	210	3	𝑒	𝑒	PROPN
cana-3476	210	4	�	�	PROPN
cana-3476	210	5	̂	̂	NOUN
cana-3476	210	6	�	�	NOUN
cana-3476	210	7	(𝑡	(𝑡	PROPN
cana-3476	210	8	,	,	PUNCT
cana-3476	210	9	0	0	NUM
cana-3476	210	10	)	)	PUNCT
cana-3476	210	11	hence	hence	ADV
cana-3476	210	12	𝑓	𝑓	DET
cana-3476	210	13	∗	∗	NOUN
cana-3476	210	14	𝑔	𝑔	PROPN
cana-3476	210	15	is	be	AUX
cana-3476	210	16	of	of	ADP
cana-3476	210	17	exponential	exponential	ADJ
cana-3476	210	18	type	type	NOUN
cana-3476	210	19	ii	ii	NOUN
cana-3476	210	20	with	with	ADP
cana-3476	210	21	exponential	exponential	ADJ
cana-3476	210	22	constant	constant	ADJ
cana-3476	210	23	�	�	PROPN
cana-3476	210	24	̂	̂	NOUN
cana-3476	210	25	�	�	NOUN
cana-3476	210	26	.	.	PUNCT
cana-3476	211	1	4	4	NUM
cana-3476	211	2	.	.	X
cana-3476	211	3	discussion	discussion	NOUN
cana-3476	211	4	4.1	4.1	NUM
cana-3476	211	5	theorem	theorem	VERB
cana-3476	211	6	5	5	NUM
cana-3476	211	7	assume	assume	VERB
cana-3476	211	8	that	that	SCONJ
cana-3476	211	9	𝑓	𝑓	X
cana-3476	211	10	:	:	PUNCT
cana-3476	211	11	𝕋	𝕋	PROPN
cana-3476	211	12	→	→	SYM
cana-3476	211	13	ℂ	ℂ	PROPN
cana-3476	211	14	is	be	AUX
cana-3476	211	15	such	such	ADJ
cana-3476	211	16	that	that	SCONJ
cana-3476	211	17	𝑓∆	𝑓∆	ADJ
cana-3476	211	18	and	and	CCONJ
cana-3476	211	19	𝑓∆∆	𝑓∆∆	PROPN
cana-3476	211	20	are	be	AUX
cana-3476	211	21	regulated	regulate	VERB
cana-3476	211	22	.	.	PUNCT
cana-3476	212	1	then	then	ADV
cana-3476	212	2	i	i	PRON
cana-3476	212	3	)	)	PUNCT
cana-3476	213	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	213	2	𝑐{𝑓∆(𝑡)}(𝑠	𝑐{𝑓∆(𝑡)}(𝑠	NOUN
cana-3476	213	3	)	)	PUNCT
cana-3476	213	4	=	=	PUNCT
cana-3476	213	5	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	213	6	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	213	7	)	)	PUNCT
cana-3476	213	8	}	}	PUNCT
cana-3476	213	9	−	−	PROPN
cana-3476	213	10	𝑝(𝑠)𝑓(0	𝑝(𝑠)𝑓(0	NOUN
cana-3476	213	11	)	)	PUNCT
cana-3476	213	12	.	.	PUNCT
cana-3476	214	1	ii	ii	X
cana-3476	214	2	)	)	PUNCT
cana-3476	215	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	215	2	𝑐{𝑓∆∆(𝑡)}(𝑠	𝑐{𝑓∆∆(𝑡)}(𝑠	NOUN
cana-3476	215	3	)	)	PUNCT
cana-3476	215	4	=	=	SYM
cana-3476	215	5	(	(	PUNCT
cana-3476	215	6	𝑖𝑞(𝑠))2𝒯𝑔	𝑖𝑞(𝑠))2𝒯𝑔	PUNCT
cana-3476	215	7	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	215	8	)	)	PUNCT
cana-3476	215	9	}	}	PUNCT
cana-3476	215	10	−	−	ADP
cana-3476	215	11	𝑖𝑞(𝑠)𝑝(𝑠	𝑖𝑞(𝑠)𝑝(𝑠	ADJ
cana-3476	215	12	)	)	PUNCT
cana-3476	215	13	−	−	ADP
cana-3476	215	14	𝑝(𝑠)𝑓∆(0	𝑝(𝑠)𝑓∆(0	NOUN
cana-3476	215	15	)	)	PUNCT
cana-3476	215	16	for	for	ADP
cana-3476	215	17	those	those	DET
cana-3476	215	18	regressive	regressive	ADJ
cana-3476	215	19	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	215	20	)	)	PUNCT
cana-3476	215	21	∈	∈	PROPN
cana-3476	215	22	ℂ	ℂ	PROPN
cana-3476	215	23	satisfying	satisfy	VERB
cana-3476	215	24	lim	lim	PROPN
cana-3476	215	25	𝑡→∞	𝑡→∞	NUM
cana-3476	215	26	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	215	27	,	,	PUNCT
cana-3476	215	28	0	0	NUM
cana-3476	215	29	)	)	PUNCT
cana-3476	215	30	=	=	SYM
cana-3476	215	31	0	0	PUNCT
cana-3476	215	32	and	and	CCONJ
cana-3476	215	33	lim	lim	PROPN
cana-3476	215	34	𝑡→∞	𝑡→∞	NUM
cana-3476	215	35	𝑓∆(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑓∆(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	215	36	,	,	PUNCT
cana-3476	215	37	0	0	NUM
cana-3476	215	38	)	)	PUNCT
cana-3476	215	39	=	=	SYM
cana-3476	215	40	0	0	NUM
cana-3476	216	1	proof	proof	NOUN
cana-3476	216	2	:	:	PUNCT
cana-3476	216	3	i	i	NOUN
cana-3476	216	4	)	)	PUNCT
cana-3476	217	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	217	2	𝑐{𝑓∆(𝑡)}(𝑠	𝑐{𝑓∆(𝑡)}(𝑠	NOUN
cana-3476	217	3	)	)	PUNCT
cana-3476	217	4	=	=	SYM
cana-3476	217	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	217	6	)	)	PUNCT
cana-3476	217	7	∫	∫	PROPN
cana-3476	217	8	𝑓∆(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓∆(𝑡)𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	217	9	)	)	PUNCT
cana-3476	218	1	𝜎	𝜎	PROPN
cana-3476	218	2	(	(	PUNCT
cana-3476	218	3	𝑡	𝑡	PROPN
cana-3476	218	4	,	,	PUNCT
cana-3476	218	5	0)∆𝑡	0)∆𝑡	PUNCT
cana-3476	218	6	∞	∞	NUM
cana-3476	218	7	0	0	NUM
cana-3476	218	8	communications	communication	NOUN
cana-3476	218	9	on	on	ADP
cana-3476	218	10	applied	apply	VERB
cana-3476	218	11	nonlinear	nonlinear	ADJ
cana-3476	218	12	analysis	analysis	NOUN
cana-3476	218	13	issn	issn	NOUN
cana-3476	218	14	:	:	PUNCT
cana-3476	218	15	1074	1074	NUM
cana-3476	218	16	-	-	PUNCT
cana-3476	218	17	133x	133x	NUM
cana-3476	218	18	vol	vol	NOUN
cana-3476	218	19	32	32	NUM
cana-3476	218	20	no	no	NOUN
cana-3476	218	21	.	.	PUNCT
cana-3476	219	1	7s	7	NOUN
cana-3476	219	2	(	(	PUNCT
cana-3476	219	3	2025	2025	NUM
cana-3476	219	4	)	)	PUNCT
cana-3476	219	5	702	702	NUM
cana-3476	219	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	219	7	=	=	PUNCT
cana-3476	219	8	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	219	9	)	)	PUNCT
cana-3476	219	10	(	(	PUNCT
cana-3476	219	11	(	(	PUNCT
cana-3476	219	12	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	219	13	,	,	PUNCT
cana-3476	219	14	0	0	NUM
cana-3476	219	15	)	)	PUNCT
cana-3476	219	16	)	)	PUNCT
cana-3476	219	17	𝑡=0	𝑡=0	X
cana-3476	219	18	𝑡=∞	𝑡=∞	NOUN
cana-3476	219	19	−	−	PROPN
cana-3476	219	20	∫	∫	PROPN
cana-3476	219	21	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	219	22	)	)	PUNCT
cana-3476	219	23	∆	∆	PROPN
cana-3476	219	24	(	(	PUNCT
cana-3476	219	25	𝑡	𝑡	X
cana-3476	219	26	,	,	PUNCT
cana-3476	219	27	0	0	NUM
cana-3476	219	28	)	)	PUNCT
cana-3476	219	29	∞	∞	NOUN
cana-3476	219	30	0	0	NUM
cana-3476	219	31	∆𝑡	∆𝑡	NOUN
cana-3476	219	32	)	)	PUNCT
cana-3476	219	33	⸪	⸪	NOUN
cana-3476	219	34	by	by	ADP
cana-3476	219	35	rule	rule	NOUN
cana-3476	219	36	for	for	ADP
cana-3476	219	37	integration	integration	NOUN
cana-3476	219	38	by	by	ADP
cana-3476	219	39	parts	part	NOUN
cana-3476	219	40	.	.	PUNCT
cana-3476	220	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	220	2	𝑐{𝑓∆(𝑡)}(𝑠	𝑐{𝑓∆(𝑡)}(𝑠	NOUN
cana-3476	220	3	)	)	PUNCT
cana-3476	220	4	=	=	PUNCT
cana-3476	221	1	𝑝(𝑠)((0	𝑝(𝑠)((0	ADP
cana-3476	221	2	−	−	PROPN
cana-3476	221	3	𝑓(0	𝑓(0	PROPN
cana-3476	221	4	)	)	PUNCT
cana-3476	221	5	)	)	PUNCT
cana-3476	222	1	−	−	NUM
cana-3476	222	2	∫	∫	PROPN
cana-3476	222	3	𝑓(𝑡)(⊖	𝑓(𝑡)(⊖	PROPN
cana-3476	222	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	222	5	)	)	PUNCT
cana-3476	222	6	)	)	PUNCT
cana-3476	223	1	∞	∞	NUM
cana-3476	223	2	0	0	NUM
cana-3476	223	3	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	223	4	,	,	PUNCT
cana-3476	223	5	0)∆𝑡	0)∆𝑡	NUM
cana-3476	223	6	)	)	PUNCT
cana-3476	223	7	=	=	SYM
cana-3476	223	8	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	223	9	)	)	PUNCT
cana-3476	223	10	(	(	PUNCT
cana-3476	223	11	−𝑓(0	−𝑓(0	NOUN
cana-3476	223	12	)	)	PUNCT
cana-3476	223	13	−	−	NOUN
cana-3476	223	14	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	223	15	)	)	PUNCT
cana-3476	223	16	∫	∫	PROPN
cana-3476	223	17	𝑓(𝑡	𝑓(𝑡	PROPN
cana-3476	223	18	)	)	PUNCT
cana-3476	223	19	(	(	PUNCT
cana-3476	223	20	⊖	⊖	NOUN
cana-3476	223	21	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	223	22	)	)	PUNCT
cana-3476	223	23	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	223	24	)	)	PUNCT
cana-3476	223	25	)	)	PUNCT
cana-3476	224	1	∞	∞	NOUN
cana-3476	224	2	0	0	NUM
cana-3476	224	3	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	224	4	,	,	PUNCT
cana-3476	224	5	0)∆𝑡	0)∆𝑡	NUM
cana-3476	224	6	)	)	PUNCT
cana-3476	224	7	=	=	SYM
cana-3476	224	8	−𝑝(𝑠)𝑓(0	−𝑝(𝑠)𝑓(0	NUM
cana-3476	224	9	)	)	PUNCT
cana-3476	225	1	+	+	CCONJ
cana-3476	225	2	𝑖𝑝(𝑠)𝑞(𝑠	𝑖𝑝(𝑠)𝑞(𝑠	ADJ
cana-3476	225	3	)	)	PUNCT
cana-3476	225	4	∫	∫	PROPN
cana-3476	225	5	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	225	6	)	)	PUNCT
cana-3476	225	7	𝜎	𝜎	PROPN
cana-3476	225	8	(	(	PUNCT
cana-3476	225	9	𝑡	𝑡	PROPN
cana-3476	225	10	,	,	PUNCT
cana-3476	225	11	0)∆𝑡	0)∆𝑡	NUM
cana-3476	226	1	∞	∞	NUM
cana-3476	226	2	0	0	NUM
cana-3476	226	3	∵	∵	NOUN
cana-3476	226	4	by	by	ADP
cana-3476	226	5	using	use	VERB
cana-3476	226	6	lemma	lemma	PROPN
cana-3476	226	7	(	(	PUNCT
cana-3476	226	8	1	1	NUM
cana-3476	226	9	)	)	PUNCT
cana-3476	226	10	=	=	SYM
cana-3476	226	11	−𝑝(𝑠)𝑓(0	−𝑝(𝑠)𝑓(0	NUM
cana-3476	226	12	)	)	PUNCT
cana-3476	227	1	+	+	CCONJ
cana-3476	227	2	𝑖𝑞(𝑠	𝑖𝑞(𝑠	X
cana-3476	227	3	)	)	PUNCT
cana-3476	227	4	(	(	PUNCT
cana-3476	227	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	227	6	)	)	PUNCT
cana-3476	227	7	∫	∫	PROPN
cana-3476	227	8	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	𝑓(𝑡)𝑒⊖𝑖𝑞(𝑠	NOUN
cana-3476	227	9	)	)	PUNCT
cana-3476	227	10	𝜎	𝜎	PROPN
cana-3476	227	11	(	(	PUNCT
cana-3476	227	12	𝑡	𝑡	PROPN
cana-3476	227	13	,	,	PUNCT
cana-3476	227	14	0)∆𝑡	0)∆𝑡	NUM
cana-3476	227	15	∞	∞	NUM
cana-3476	227	16	0	0	NUM
cana-3476	227	17	)	)	PUNCT
cana-3476	227	18	∴	∴	PROPN
cana-3476	227	19	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	227	20	𝑐{𝑓∆(𝑡)}(𝑠	𝑐{𝑓∆(𝑡)}(𝑠	PROPN
cana-3476	227	21	)	)	PUNCT
cana-3476	227	22	=	=	PUNCT
cana-3476	227	23	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	227	24	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	227	25	)	)	PUNCT
cana-3476	227	26	}	}	PUNCT
cana-3476	228	1	−	−	PROPN
cana-3476	228	2	𝑝(𝑠)𝑓(0	𝑝(𝑠)𝑓(0	NOUN
cana-3476	228	3	)	)	PUNCT
cana-3476	228	4	ii	ii	NOUN
cana-3476	228	5	)	)	PUNCT
cana-3476	229	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	229	2	𝑐{𝑓∆∆(𝑡)}(𝑠	𝑐{𝑓∆∆(𝑡)}(𝑠	NOUN
cana-3476	229	3	)	)	PUNCT
cana-3476	229	4	=	=	PUNCT
cana-3476	230	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	230	2	𝑐	𝑐	PROPN
cana-3476	230	3	{	{	PUNCT
cana-3476	230	4	(	(	PUNCT
cana-3476	230	5	𝑓∆(𝑡	𝑓∆(𝑡	NUM
cana-3476	230	6	)	)	PUNCT
cana-3476	230	7	)	)	PUNCT
cana-3476	230	8	∆	∆	PROPN
cana-3476	230	9	}	}	PUNCT
cana-3476	230	10	=	=	SYM
cana-3476	230	11	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	230	12	𝑐{𝑓∆(𝑡	𝑐{𝑓∆(𝑡	NUM
cana-3476	230	13	)	)	PUNCT
cana-3476	230	14	}	}	PUNCT
cana-3476	230	15	−	−	ADP
cana-3476	230	16	𝑝(𝑠)𝑓∆(0	𝑝(𝑠)𝑓∆(0	NOUN
cana-3476	230	17	)	)	PUNCT
cana-3476	230	18	=	=	SYM
cana-3476	230	19	𝑖𝑞(𝑠	𝑖𝑞(𝑠	X
cana-3476	230	20	)	)	PUNCT
cana-3476	230	21	(	(	PUNCT
cana-3476	230	22	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	230	23	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	230	24	)	)	PUNCT
cana-3476	230	25	}	}	PUNCT
cana-3476	230	26	−	−	PROPN
cana-3476	230	27	𝑝(𝑠)𝑓(0	𝑝(𝑠)𝑓(0	NOUN
cana-3476	230	28	)	)	PUNCT
cana-3476	230	29	)	)	PUNCT
cana-3476	231	1	−	−	ADP
cana-3476	231	2	𝑝(𝑠)𝑓∆(0	𝑝(𝑠)𝑓∆(0	NOUN
cana-3476	231	3	)	)	PUNCT
cana-3476	231	4	∴	∴	PROPN
cana-3476	231	5	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	231	6	𝑐{𝑓∆∆(𝑡)}(𝑠	𝑐{𝑓∆∆(𝑡)}(𝑠	PROPN
cana-3476	231	7	)	)	PUNCT
cana-3476	231	8	=	=	SYM
cana-3476	231	9	(	(	PUNCT
cana-3476	231	10	𝑖𝑞(𝑠))2𝒯𝑔	𝑖𝑞(𝑠))2𝒯𝑔	PUNCT
cana-3476	231	11	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	231	12	)	)	PUNCT
cana-3476	231	13	}	}	PUNCT
cana-3476	232	1	−	−	PROPN
cana-3476	232	2	𝑖𝑞(𝑠)𝑝(𝑠)𝑓(0	𝑖𝑞(𝑠)𝑝(𝑠)𝑓(0	PROPN
cana-3476	232	3	)	)	PUNCT
cana-3476	232	4	−	−	ADP
cana-3476	232	5	𝑝(𝑠)𝑓∆(0	𝑝(𝑠)𝑓∆(0	NOUN
cana-3476	232	6	)	)	PUNCT
cana-3476	232	7	more	more	ADV
cana-3476	232	8	generally	generally	ADV
cana-3476	232	9	we	we	PRON
cana-3476	232	10	obtain	obtain	VERB
cana-3476	232	11	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	232	12	𝑐{(𝑓∆)𝑛(𝑡)}(𝑠	𝑐{(𝑓∆)𝑛(𝑡)}(𝑠	PROPN
cana-3476	232	13	)	)	PUNCT
cana-3476	232	14	=	=	SYM
cana-3476	232	15	(	(	PUNCT
cana-3476	232	16	𝑖𝑞(𝑠))𝑛𝒯𝑔	𝑖𝑞(𝑠))𝑛𝒯𝑔	ADJ
cana-3476	232	17	𝑐{𝑓(𝑡	𝑐{𝑓(𝑡	NUM
cana-3476	232	18	)	)	PUNCT
cana-3476	232	19	}	}	PUNCT
cana-3476	232	20	−	−	PROPN
cana-3476	233	1	∑	∑	PUNCT
cana-3476	233	2	𝑝(𝑠)(𝑖𝑞(𝑠))𝑘−1(𝑓∆)𝑛−𝑘(0)𝑛	𝑝(𝑠)(𝑖𝑞(𝑠))𝑘−1(𝑓∆)𝑛−𝑘(0)𝑛	PROPN
cana-3476	233	3	𝑘=1	𝑘=1	PROPN
cana-3476	233	4	for	for	ADP
cana-3476	233	5	any	any	DET
cana-3476	233	6	integer	integer	NOUN
cana-3476	233	7	𝑛	𝑛	PRON
cana-3476	233	8	≥	≥	NOUN
cana-3476	233	9	2	2	NUM
cana-3476	233	10	.	.	X
cana-3476	233	11	4.2	4.2	NUM
cana-3476	233	12	theorem	theorem	VERB
cana-3476	233	13	6	6	NUM
cana-3476	233	14	assume	assume	VERB
cana-3476	233	15	that	that	SCONJ
cana-3476	233	16	𝑓(𝑡	𝑓(𝑡	NOUN
cana-3476	233	17	)	)	PUNCT
cana-3476	233	18	is	be	AUX
cana-3476	233	19	a	a	DET
cana-3476	233	20	regulated	regulated	ADJ
cana-3476	233	21	function	function	NOUN
cana-3476	233	22	with	with	ADP
cana-3476	233	23	𝐹(𝑡	𝐹(𝑡	NOUN
cana-3476	233	24	)	)	PUNCT
cana-3476	233	25	=	=	SYM
cana-3476	234	1	∫	∫	PROPN
cana-3476	234	2	𝑓(𝑠)∆𝑠	𝑓(𝑠)∆𝑠	PROPN
cana-3476	234	3	𝑡	𝑡	PROPN
cana-3476	234	4	0	0	PUNCT
cana-3476	234	5	then	then	ADV
cana-3476	234	6	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	234	7	𝑐{𝐹(𝑡)}(𝑠	𝑐{𝐹(𝑡)}(𝑠	NOUN
cana-3476	234	8	)	)	PUNCT
cana-3476	234	9	=	=	SYM
cana-3476	234	10	1	1	NUM
cana-3476	234	11	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	234	12	)	)	PUNCT
cana-3476	234	13	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	234	14	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	234	15	)	)	PUNCT
cana-3476	234	16	for	for	ADP
cana-3476	234	17	all	all	DET
cana-3476	234	18	regressive	regressive	ADJ
cana-3476	234	19	functions	function	NOUN
cana-3476	234	20	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	234	21	)	)	PUNCT
cana-3476	234	22	≠	≠	PROPN
cana-3476	234	23	0	0	NUM
cana-3476	234	24	satisfying	satisfy	VERB
cana-3476	234	25	lim	lim	PROPN
cana-3476	234	26	𝑡→∞	𝑡→∞	NUM
cana-3476	234	27	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	234	28	,	,	PUNCT
cana-3476	234	29	0	0	NUM
cana-3476	234	30	)	)	PUNCT
cana-3476	234	31	∫	∫	PROPN
cana-3476	235	1	𝑓(𝑠)∆𝑠	𝑓(𝑠)∆𝑠	PROPN
cana-3476	235	2	𝑡	𝑡	PROPN
cana-3476	235	3	0	0	PUNCT
cana-3476	235	4	=	=	SYM
cana-3476	235	5	0	0	NUM
cana-3476	235	6	proof	proof	NOUN
cana-3476	235	7	:	:	PUNCT
cana-3476	235	8	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	235	9	𝑐(𝐹(𝑡	𝑐(𝐹(𝑡	NOUN
cana-3476	235	10	)	)	PUNCT
cana-3476	235	11	,	,	PUNCT
cana-3476	235	12	𝑠	𝑠	X
cana-3476	235	13	)	)	PUNCT
cana-3476	235	14	=	=	SYM
cana-3476	235	15	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	235	16	)	)	PUNCT
cana-3476	235	17	∫	∫	PROPN
cana-3476	235	18	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	235	19	)	)	PUNCT
cana-3476	235	20	𝜎	𝜎	PROPN
cana-3476	235	21	(	(	PUNCT
cana-3476	235	22	𝑡	𝑡	PROPN
cana-3476	235	23	,	,	PUNCT
cana-3476	235	24	0	0	NUM
cana-3476	235	25	)	)	PUNCT
cana-3476	235	26	𝐹(𝑡	𝐹(𝑡	NUM
cana-3476	235	27	)	)	PUNCT
cana-3476	235	28	∆𝑡	∆𝑡	PROPN
cana-3476	235	29	=	=	SYM
cana-3476	235	30	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	235	31	)	)	PUNCT
cana-3476	235	32	∫	∫	PROPN
cana-3476	235	33	(	(	PUNCT
cana-3476	235	34	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	𝑒⊖𝑖𝑞(𝑠)(𝑡,0	NOUN
cana-3476	235	35	)	)	PUNCT
cana-3476	235	36	1+𝑖𝜇(𝑡)𝑞(𝑠	1+𝑖𝜇(𝑡)𝑞(𝑠	NUM
cana-3476	235	37	)	)	PUNCT
cana-3476	235	38	)	)	PUNCT
cana-3476	236	1	𝐹(𝑡)∆𝑡	𝐹(𝑡)∆𝑡	PUNCT
cana-3476	237	1	∞	∞	NUM
cana-3476	237	2	0	0	NUM
cana-3476	238	1	∞	∞	NUM
cana-3476	238	2	0	0	NUM
cana-3476	238	3	=	=	SYM
cana-3476	238	4	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	238	5	)	)	PUNCT
cana-3476	238	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	238	7	)	)	PUNCT
cana-3476	238	8	∫	∫	PROPN
cana-3476	238	9	(	(	PUNCT
cana-3476	238	10	−𝑖𝑞(𝑠	−𝑖𝑞(𝑠	PROPN
cana-3476	238	11	)	)	PUNCT
cana-3476	238	12	1	1	NUM
cana-3476	238	13	+	+	CCONJ
cana-3476	238	14	𝑖𝜇(𝑡)𝑞(𝑠	𝑖𝜇(𝑡)𝑞(𝑠	ADJ
cana-3476	238	15	)	)	PUNCT
cana-3476	238	16	)	)	PUNCT
cana-3476	239	1	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	239	2	,	,	PUNCT
cana-3476	239	3	0)𝐹(𝑡)∆𝑡	0)𝐹(𝑡)∆𝑡	NUM
cana-3476	239	4	=	=	SYM
cana-3476	239	5	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	239	6	)	)	PUNCT
cana-3476	239	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	239	8	)	)	PUNCT
cana-3476	239	9	∫	∫	PROPN
cana-3476	239	10	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	239	11	)	)	PUNCT
cana-3476	239	12	∆	∆	PROPN
cana-3476	239	13	(	(	PUNCT
cana-3476	239	14	𝑡	𝑡	X
cana-3476	239	15	,	,	PUNCT
cana-3476	239	16	0)𝐹(𝑡)∆𝑡	0)𝐹(𝑡)∆𝑡	NUM
cana-3476	239	17	∞	∞	NUM
cana-3476	239	18	0	0	NUM
cana-3476	240	1	∞	∞	NUM
cana-3476	240	2	0	0	NUM
cana-3476	240	3	=	=	SYM
cana-3476	240	4	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	240	5	)	)	PUNCT
cana-3476	240	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	240	7	)	)	PUNCT
cana-3476	240	8	∫	∫	PROPN
cana-3476	241	1	[	[	X
cana-3476	241	2	(	(	PUNCT
cana-3476	241	3	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	241	4	,	,	PUNCT
cana-3476	241	5	0)𝐹(𝑡	0)𝐹(𝑡	NUM
cana-3476	241	6	)	)	PUNCT
cana-3476	241	7	)	)	PUNCT
cana-3476	241	8	∆	∆	PROPN
cana-3476	241	9	−	−	PROPN
cana-3476	241	10	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	241	11	)	)	PUNCT
cana-3476	241	12	𝜎	𝜎	PROPN
cana-3476	241	13	(	(	PUNCT
cana-3476	241	14	𝑡	𝑡	PROPN
cana-3476	241	15	,	,	PUNCT
cana-3476	241	16	0)𝐹∆(𝑡	0)𝐹∆(𝑡	NOUN
cana-3476	241	17	)	)	PUNCT
cana-3476	241	18	]	]	PUNCT
cana-3476	242	1	∆𝑡	∆𝑡	PROPN
cana-3476	242	2	∞	∞	NUM
cana-3476	242	3	0	0	NUM
cana-3476	243	1	=	=	SYM
cana-3476	243	2	−	−	PROPN
cana-3476	243	3	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	243	4	)	)	PUNCT
cana-3476	243	5	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	243	6	)	)	PUNCT
cana-3476	244	1	[	[	X
cana-3476	244	2	(	(	PUNCT
cana-3476	244	3	𝑒⊖𝑖𝑞(𝑠)(𝑡	𝑒⊖𝑖𝑞(𝑠)(𝑡	PROPN
cana-3476	244	4	,	,	PUNCT
cana-3476	244	5	0)𝐹(𝑡	0)𝐹(𝑡	NUM
cana-3476	244	6	)	)	PUNCT
cana-3476	244	7	)	)	PUNCT
cana-3476	244	8	0	0	NUM
cana-3476	245	1	∞	∞	NUM
cana-3476	246	1	−	−	PROPN
cana-3476	246	2	∫	∫	PROPN
cana-3476	246	3	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	246	4	)	)	PUNCT
cana-3476	246	5	𝜎	𝜎	PROPN
cana-3476	246	6	(	(	PUNCT
cana-3476	246	7	𝑡	𝑡	NOUN
cana-3476	246	8	,	,	PUNCT
cana-3476	246	9	0)𝐹∆(𝑡)∆𝑡	0)𝐹∆(𝑡)∆𝑡	NOUN
cana-3476	246	10	∞	∞	NOUN
cana-3476	246	11	0	0	NUM
cana-3476	246	12	]	]	PUNCT
cana-3476	246	13	=	=	SYM
cana-3476	246	14	𝑝(𝑠)𝐹(0	𝑝(𝑠)𝐹(0	PROPN
cana-3476	246	15	)	)	PUNCT
cana-3476	246	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	246	17	)	)	PUNCT
cana-3476	247	1	+	+	CCONJ
cana-3476	247	2	1	1	NUM
cana-3476	247	3	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	247	4	)	)	PUNCT
cana-3476	247	5	(	(	PUNCT
cana-3476	247	6	𝑝(𝑠	𝑝(𝑠	NOUN
cana-3476	247	7	)	)	PUNCT
cana-3476	247	8	∫	∫	PROPN
cana-3476	247	9	𝑒⊖𝑖𝑞(𝑠	𝑒⊖𝑖𝑞(𝑠	PROPN
cana-3476	247	10	)	)	PUNCT
cana-3476	247	11	𝜎	𝜎	PROPN
cana-3476	247	12	(	(	PUNCT
cana-3476	247	13	𝑡	𝑡	X
cana-3476	247	14	,	,	PUNCT
cana-3476	247	15	0)𝑓(𝑡)∆𝑡	0)𝑓(𝑡)∆𝑡	X
cana-3476	247	16	∞	∞	NOUN
cana-3476	247	17	0	0	NUM
cana-3476	247	18	)	)	PUNCT
cana-3476	248	1	=	=	NOUN
cana-3476	248	2	1	1	NUM
cana-3476	248	3	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	248	4	)	)	PUNCT
cana-3476	248	5	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	248	6	𝑐{𝑓(𝑡)}(𝑠	𝑐{𝑓(𝑡)}(𝑠	NOUN
cana-3476	248	7	)	)	PUNCT
cana-3476	248	8	communications	communication	NOUN
cana-3476	248	9	on	on	ADP
cana-3476	248	10	applied	apply	VERB
cana-3476	248	11	nonlinear	nonlinear	ADJ
cana-3476	248	12	analysis	analysis	NOUN
cana-3476	248	13	issn	issn	NOUN
cana-3476	248	14	:	:	PUNCT
cana-3476	248	15	1074	1074	NUM
cana-3476	248	16	-	-	PUNCT
cana-3476	248	17	133x	133x	NUM
cana-3476	248	18	vol	vol	NOUN
cana-3476	248	19	32	32	NUM
cana-3476	248	20	no	no	NOUN
cana-3476	248	21	.	.	PUNCT
cana-3476	249	1	7s	7	NOUN
cana-3476	249	2	(	(	PUNCT
cana-3476	249	3	2025	2025	NUM
cana-3476	249	4	)	)	PUNCT
cana-3476	249	5	703	703	NUM
cana-3476	249	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	249	7	4.3	4.3	NUM
cana-3476	249	8	applications	application	NOUN
cana-3476	249	9	example	example	NOUN
cana-3476	249	10	1	1	NUM
cana-3476	249	11	consider	consider	VERB
cana-3476	249	12	the	the	DET
cana-3476	249	13	following	follow	VERB
cana-3476	249	14	initial	initial	ADJ
cana-3476	249	15	value	value	NOUN
cana-3476	249	16	problem	problem	NOUN
cana-3476	249	17	.	.	PUNCT
cana-3476	250	1	𝑦∆∆(𝑡	𝑦∆∆(𝑡	X
cana-3476	250	2	)	)	PUNCT
cana-3476	251	1	−	−	PROPN
cana-3476	251	2	6𝑦∆(𝑡	6𝑦∆(𝑡	NUM
cana-3476	251	3	)	)	PUNCT
cana-3476	252	1	+	+	CCONJ
cana-3476	252	2	8𝑦(𝑡	8𝑦(𝑡	NUM
cana-3476	252	3	)	)	PUNCT
cana-3476	252	4	=	=	SYM
cana-3476	252	5	𝑒3(𝑡	𝑒3(𝑡	PROPN
cana-3476	252	6	,	,	PUNCT
cana-3476	252	7	0	0	NUM
cana-3476	252	8	)	)	PUNCT
cana-3476	252	9	,	,	PUNCT
cana-3476	252	10	𝑦(0	𝑦(0	PROPN
cana-3476	252	11	)	)	PUNCT
cana-3476	252	12	=	=	SYM
cana-3476	252	13	1	1	NUM
cana-3476	252	14	,	,	PUNCT
cana-3476	252	15	𝑦∆(0	𝑦∆(0	NOUN
cana-3476	252	16	)	)	PUNCT
cana-3476	252	17	=	=	SYM
cana-3476	252	18	0	0	PUNCT
cana-3476	252	19	applying	apply	VERB
cana-3476	252	20	new	new	ADJ
cana-3476	252	21	general	general	ADJ
cana-3476	252	22	complex	complex	ADJ
cana-3476	252	23	integral	integral	ADJ
cana-3476	252	24	transform	transform	NOUN
cana-3476	252	25	to	to	ADP
cana-3476	252	26	both	both	DET
cana-3476	252	27	sides	side	NOUN
cana-3476	252	28	of	of	ADP
cana-3476	252	29	the	the	DET
cana-3476	252	30	dynamic	dynamic	ADJ
cana-3476	252	31	equation	equation	NOUN
cana-3476	252	32	.	.	PUNCT
cana-3476	253	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	253	2	𝑐{𝑦∆∆(𝑡	𝑐{𝑦∆∆(𝑡	NUM
cana-3476	253	3	)	)	PUNCT
cana-3476	254	1	−	−	PROPN
cana-3476	254	2	6𝑦∆(𝑡	6𝑦∆(𝑡	NUM
cana-3476	254	3	)	)	PUNCT
cana-3476	255	1	+	+	NUM
cana-3476	255	2	8𝑦(𝑡)}(𝑠	8𝑦(𝑡)}(𝑠	NUM
cana-3476	255	3	)	)	PUNCT
cana-3476	256	1	=	=	SYM
cana-3476	257	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	257	2	𝑐{𝑒3(𝑡	𝑐{𝑒3(𝑡	PROPN
cana-3476	257	3	,	,	PUNCT
cana-3476	257	4	0)}(𝑠	0)}(𝑠	NUM
cana-3476	257	5	)	)	PUNCT
cana-3476	258	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	258	2	𝑐{𝑦∆∆(𝑡	𝑐{𝑦∆∆(𝑡	NUM
cana-3476	258	3	)	)	PUNCT
cana-3476	258	4	}	}	PUNCT
cana-3476	258	5	−	−	PROPN
cana-3476	259	1	6𝒯𝑔	6𝒯𝑔	NUM
cana-3476	259	2	𝑐{𝑦∆(𝑡	𝑐{𝑦∆(𝑡	PROPN
cana-3476	259	3	)	)	PUNCT
cana-3476	259	4	}	}	PUNCT
cana-3476	260	1	+	+	CCONJ
cana-3476	260	2	8𝒯𝑔	8𝒯𝑔	NUM
cana-3476	260	3	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	260	4	)	)	PUNCT
cana-3476	260	5	}	}	PUNCT
cana-3476	261	1	=	=	PUNCT
cana-3476	262	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	262	2	𝑐{𝑒3(𝑡	𝑐{𝑒3(𝑡	PROPN
cana-3476	262	3	,	,	PUNCT
cana-3476	262	4	0	0	NUM
cana-3476	262	5	)	)	PUNCT
cana-3476	262	6	}	}	PUNCT
cana-3476	262	7	(	(	PUNCT
cana-3476	262	8	𝑖𝑞(𝑠))2𝒯𝑔	𝑖𝑞(𝑠))2𝒯𝑔	PROPN
cana-3476	262	9	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	262	10	)	)	PUNCT
cana-3476	262	11	}	}	PUNCT
cana-3476	262	12	−	−	PROPN
cana-3476	262	13	𝑖𝑞(𝑠)𝑝(𝑠)𝑦(0	𝑖𝑞(𝑠)𝑝(𝑠)𝑦(0	PROPN
cana-3476	262	14	)	)	PUNCT
cana-3476	262	15	−	−	PROPN
cana-3476	262	16	𝑝(𝑠)𝑦∆(0	𝑝(𝑠)𝑦∆(0	NOUN
cana-3476	262	17	)	)	PUNCT
cana-3476	262	18	−	−	PROPN
cana-3476	262	19	6	6	NUM
cana-3476	262	20	(	(	PUNCT
cana-3476	262	21	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	262	22	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	262	23	)	)	PUNCT
cana-3476	262	24	}	}	PUNCT
cana-3476	262	25	−	−	PROPN
cana-3476	262	26	𝑝(𝑠)𝑦(0	𝑝(𝑠)𝑦(0	NOUN
cana-3476	262	27	)	)	PUNCT
cana-3476	262	28	)	)	PUNCT
cana-3476	263	1	+	+	CCONJ
cana-3476	263	2	8𝒯𝑔	8𝒯𝑔	NUM
cana-3476	263	3	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	263	4	)	)	PUNCT
cana-3476	263	5	}	}	PUNCT
cana-3476	264	1	=	=	PUNCT
cana-3476	265	1	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	265	2	𝑐{𝑒3(𝑡	𝑐{𝑒3(𝑡	PROPN
cana-3476	265	3	,	,	PUNCT
cana-3476	265	4	0	0	NUM
cana-3476	265	5	)	)	PUNCT
cana-3476	265	6	}	}	PUNCT
cana-3476	265	7	⇒	⇒	VERB
cana-3476	265	8	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	265	9	𝑐{𝑦(𝑡)}((𝑖𝑞(𝑠))2	𝑐{𝑦(𝑡)}((𝑖𝑞(𝑠))2	NOUN
cana-3476	265	10	−	−	NOUN
cana-3476	265	11	6𝑖𝑞(𝑠	6𝑖𝑞(𝑠	NUM
cana-3476	265	12	)	)	PUNCT
cana-3476	266	1	+	+	CCONJ
cana-3476	266	2	8)	8)	NUM
cana-3476	266	3	=	=	SYM
cana-3476	266	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	266	5	)	)	PUNCT
cana-3476	266	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	266	7	)	)	PUNCT
cana-3476	266	8	−	−	ADP
cana-3476	266	9	3	3	NUM
cana-3476	266	10	+	+	NUM
cana-3476	266	11	𝑝(𝑠)(𝑖𝑞(𝑠	𝑝(𝑠)(𝑖𝑞(𝑠	NOUN
cana-3476	266	12	)	)	PUNCT
cana-3476	266	13	)	)	PUNCT
cana-3476	267	1	−	−	PROPN
cana-3476	267	2	6𝑝(𝑠	6𝑝(𝑠	NUM
cana-3476	267	3	)	)	PUNCT
cana-3476	267	4	⇒	⇒	VERB
cana-3476	267	5	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	267	6	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	267	7	)	)	PUNCT
cana-3476	267	8	}	}	PUNCT
cana-3476	268	1	=	=	SYM
cana-3476	268	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	268	3	)	)	PUNCT
cana-3476	268	4	(	(	PUNCT
cana-3476	268	5	(	(	PUNCT
cana-3476	268	6	𝑖𝑞(𝑠))2	𝑖𝑞(𝑠))2	X
cana-3476	268	7	−	−	PROPN
cana-3476	268	8	9(𝑖𝑞(𝑠	9(𝑖𝑞(𝑠	NUM
cana-3476	268	9	)	)	PUNCT
cana-3476	269	1	+	+	CCONJ
cana-3476	269	2	19	19	NUM
cana-3476	269	3	(	(	PUNCT
cana-3476	269	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	ADJ
cana-3476	269	5	)	)	PUNCT
cana-3476	269	6	−	−	PROPN
cana-3476	269	7	3)(𝑖𝑞(𝑠	3)(𝑖𝑞(𝑠	NOUN
cana-3476	269	8	)	)	PUNCT
cana-3476	269	9	−	−	PROPN
cana-3476	269	10	4)(𝑖𝑞(𝑠	4)(𝑖𝑞(𝑠	NUM
cana-3476	269	11	)	)	PUNCT
cana-3476	269	12	−	−	PROPN
cana-3476	269	13	2	2	NUM
cana-3476	269	14	)	)	PUNCT
cana-3476	269	15	)	)	PUNCT
cana-3476	269	16	⇒	⇒	VERB
cana-3476	269	17	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	269	18	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	269	19	)	)	PUNCT
cana-3476	269	20	}	}	PUNCT
cana-3476	270	1	=	=	SYM
cana-3476	270	2	−	−	PROPN
cana-3476	270	3	(	(	PUNCT
cana-3476	270	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	270	5	)	)	PUNCT
cana-3476	270	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	270	7	)	)	PUNCT
cana-3476	270	8	−	−	PROPN
cana-3476	270	9	3	3	X
cana-3476	270	10	)	)	PUNCT
cana-3476	270	11	−	−	NOUN
cana-3476	270	12	1	1	NUM
cana-3476	270	13	2	2	NUM
cana-3476	270	14	(	(	PUNCT
cana-3476	270	15	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	270	16	)	)	PUNCT
cana-3476	270	17	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	270	18	)	)	PUNCT
cana-3476	270	19	−	−	ADP
cana-3476	270	20	4	4	NUM
cana-3476	270	21	)	)	PUNCT
cana-3476	270	22	+	+	CCONJ
cana-3476	270	23	5	5	NUM
cana-3476	270	24	2	2	NUM
cana-3476	270	25	(	(	PUNCT
cana-3476	270	26	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	270	27	)	)	PUNCT
cana-3476	270	28	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	270	29	)	)	PUNCT
cana-3476	270	30	−	−	PROPN
cana-3476	270	31	2	2	NUM
cana-3476	270	32	)	)	PUNCT
cana-3476	270	33	hence	hence	ADV
cana-3476	270	34	from	from	ADP
cana-3476	270	35	the	the	DET
cana-3476	270	36	table	table	NOUN
cana-3476	270	37	(	(	PUNCT
cana-3476	270	38	1	1	NUM
cana-3476	270	39	)	)	PUNCT
cana-3476	270	40	𝑦(𝑡	𝑦(𝑡	PROPN
cana-3476	270	41	)	)	PUNCT
cana-3476	270	42	=	=	SYM
cana-3476	270	43	−𝑒3(𝑡	−𝑒3(𝑡	PROPN
cana-3476	270	44	,	,	PUNCT
cana-3476	270	45	0	0	NUM
cana-3476	270	46	)	)	PUNCT
cana-3476	270	47	−	−	NOUN
cana-3476	270	48	1	1	NUM
cana-3476	270	49	2	2	NUM
cana-3476	270	50	𝑒4(𝑡	𝑒4(𝑡	NOUN
cana-3476	270	51	,	,	PUNCT
cana-3476	270	52	0	0	NUM
cana-3476	270	53	)	)	PUNCT
cana-3476	270	54	+	+	CCONJ
cana-3476	270	55	5	5	NUM
cana-3476	270	56	2	2	NUM
cana-3476	270	57	𝑒2(𝑡	𝑒2(𝑡	PROPN
cana-3476	270	58	,	,	PUNCT
cana-3476	270	59	0	0	NUM
cana-3476	270	60	)	)	PUNCT
cana-3476	270	61	.	.	PUNCT
cana-3476	271	1	example	example	NOUN
cana-3476	272	1	2	2	NUM
cana-3476	272	2	consider	consider	VERB
cana-3476	272	3	the	the	DET
cana-3476	272	4	following	follow	VERB
cana-3476	272	5	third	third	ADJ
cana-3476	272	6	order	order	NOUN
cana-3476	272	7	dynamic	dynamic	ADJ
cana-3476	272	8	equation	equation	NOUN
cana-3476	272	9	𝑦∆∆∆	𝑦∆∆∆	PROPN
cana-3476	272	10	+	+	CCONJ
cana-3476	272	11	𝑦∆	𝑦∆	PROPN
cana-3476	272	12	=	=	SYM
cana-3476	272	13	𝑒1(𝑡	𝑒1(𝑡	PROPN
cana-3476	272	14	,	,	PUNCT
cana-3476	272	15	0	0	NUM
cana-3476	272	16	)	)	PUNCT
cana-3476	272	17	,	,	PUNCT
cana-3476	272	18	𝑦(0	𝑦(0	PROPN
cana-3476	272	19	)	)	PUNCT
cana-3476	272	20	=	=	SYM
cana-3476	272	21	𝑦∆	𝑦∆	PROPN
cana-3476	272	22	=	=	SYM
cana-3476	273	1	𝑦∆∆	𝑦∆∆	PROPN
cana-3476	273	2	=	=	SYM
cana-3476	273	3	0	0	NUM
cana-3476	273	4	applying	apply	VERB
cana-3476	273	5	new	new	ADJ
cana-3476	273	6	general	general	ADJ
cana-3476	273	7	complex	complex	ADJ
cana-3476	273	8	integral	integral	ADJ
cana-3476	273	9	transform	transform	NOUN
cana-3476	273	10	on	on	ADP
cana-3476	273	11	time	time	NOUN
cana-3476	273	12	scale	scale	NOUN
cana-3476	273	13	to	to	ADP
cana-3476	273	14	both	both	DET
cana-3476	273	15	sides	side	NOUN
cana-3476	273	16	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	273	17	𝑐{𝑦∆∆∆(𝑡	𝑐{𝑦∆∆∆(𝑡	PROPN
cana-3476	273	18	)	)	PUNCT
cana-3476	273	19	+	+	NUM
cana-3476	273	20	𝑦∆(𝑡	𝑦∆(𝑡	NOUN
cana-3476	273	21	)	)	PUNCT
cana-3476	273	22	}	}	PUNCT
cana-3476	274	1	=	=	PUNCT
cana-3476	274	2	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	274	3	𝑐{𝑒1(𝑡	𝑐{𝑒1(𝑡	PROPN
cana-3476	274	4	,	,	PUNCT
cana-3476	274	5	0)}(𝑠	0)}(𝑠	NUM
cana-3476	274	6	)	)	PUNCT
cana-3476	274	7	(	(	PUNCT
cana-3476	274	8	(	(	PUNCT
cana-3476	274	9	𝑖𝑞(𝑠	𝑖𝑞(𝑠	X
cana-3476	274	10	)	)	PUNCT
cana-3476	274	11	)	)	PUNCT
cana-3476	274	12	3	3	NUM
cana-3476	275	1	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	275	2	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	275	3	)	)	PUNCT
cana-3476	275	4	}	}	PUNCT
cana-3476	275	5	−	−	PROPN
cana-3476	275	6	(	(	PUNCT
cana-3476	275	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	ADJ
cana-3476	275	8	)	)	PUNCT
cana-3476	275	9	)	)	PUNCT
cana-3476	275	10	2	2	NUM
cana-3476	275	11	𝑝(𝑠)𝑦(0	𝑝(𝑠)𝑦(0	NOUN
cana-3476	275	12	)	)	PUNCT
cana-3476	275	13	−	−	ADP
cana-3476	275	14	𝑖𝑞(𝑠)𝑝(𝑠)𝑦∆(0	𝑖𝑞(𝑠)𝑝(𝑠)𝑦∆(0	SYM
cana-3476	275	15	)	)	PUNCT
cana-3476	275	16	−	−	PROPN
cana-3476	275	17	𝑝(𝑠)𝑦∆∆(0	𝑝(𝑠)𝑦∆∆(0	NUM
cana-3476	275	18	)	)	PUNCT
cana-3476	275	19	)	)	PUNCT
cana-3476	276	1	+	+	CCONJ
cana-3476	276	2	(	(	PUNCT
cana-3476	276	3	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	276	4	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	276	5	)	)	PUNCT
cana-3476	276	6	}	}	PUNCT
cana-3476	276	7	−	−	PROPN
cana-3476	276	8	𝑝(𝑠)𝑦(0	𝑝(𝑠)𝑦(0	NOUN
cana-3476	276	9	)	)	PUNCT
cana-3476	276	10	)	)	PUNCT
cana-3476	277	1	=	=	SYM
cana-3476	277	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	277	3	)	)	PUNCT
cana-3476	277	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	277	5	)	)	PUNCT
cana-3476	277	6	−	−	PROPN
cana-3476	277	7	1	1	NUM
cana-3476	277	8	using	use	VERB
cana-3476	277	9	given	give	VERB
cana-3476	277	10	initial	initial	ADJ
cana-3476	277	11	conditions	condition	NOUN
cana-3476	277	12	we	we	PRON
cana-3476	277	13	obtain	obtain	VERB
cana-3476	277	14	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	277	15	𝑐{𝑦(𝑡)}((𝑖𝑞(𝑠))3	𝑐{𝑦(𝑡)}((𝑖𝑞(𝑠))3	PROPN
cana-3476	277	16	+	+	CCONJ
cana-3476	277	17	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	277	18	)	)	PUNCT
cana-3476	277	19	)	)	PUNCT
cana-3476	278	1	=	=	SYM
cana-3476	278	2	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	278	3	)	)	PUNCT
cana-3476	278	4	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	278	5	)	)	PUNCT
cana-3476	278	6	−	−	ADP
cana-3476	278	7	1	1	NUM
cana-3476	278	8	⇒	⇒	NOUN
cana-3476	278	9	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	278	10	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	278	11	)	)	PUNCT
cana-3476	278	12	}	}	PUNCT
cana-3476	278	13	=	=	SYM
cana-3476	278	14	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	278	15	)	)	PUNCT
cana-3476	278	16	𝑖𝑞(𝑠)(𝑖𝑞(𝑠	𝑖𝑞(𝑠)(𝑖𝑞(𝑠	NUM
cana-3476	278	17	)	)	PUNCT
cana-3476	278	18	−	−	PROPN
cana-3476	279	1	1)((𝑖𝑞(𝑠))2	1)((𝑖𝑞(𝑠))2	NUM
cana-3476	280	1	+	+	CCONJ
cana-3476	280	2	1	1	X
cana-3476	280	3	)	)	PUNCT
cana-3476	280	4	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	280	5	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	280	6	)	)	PUNCT
cana-3476	280	7	}	}	PUNCT
cana-3476	280	8	=	=	SYM
cana-3476	280	9	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	280	10	)	)	PUNCT
cana-3476	280	11	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	280	12	)	)	PUNCT
cana-3476	281	1	+	+	CCONJ
cana-3476	281	2	1	1	NUM
cana-3476	281	3	2	2	NUM
cana-3476	281	4	(	(	PUNCT
cana-3476	281	5	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	281	6	)	)	PUNCT
cana-3476	281	7	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	281	8	)	)	PUNCT
cana-3476	281	9	−	−	PROPN
cana-3476	281	10	1	1	NUM
cana-3476	281	11	)	)	PUNCT
cana-3476	281	12	+	+	CCONJ
cana-3476	281	13	1	1	NUM
cana-3476	281	14	2	2	NUM
cana-3476	281	15	(	(	PUNCT
cana-3476	281	16	−𝑖𝑞(𝑠)𝑝(𝑠	−𝑖𝑞(𝑠)𝑝(𝑠	NOUN
cana-3476	281	17	)	)	PUNCT
cana-3476	281	18	(	(	PUNCT
cana-3476	281	19	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	281	20	)	)	PUNCT
cana-3476	281	21	)	)	PUNCT
cana-3476	281	22	2	2	NUM
cana-3476	281	23	−	−	NOUN
cana-3476	281	24	1	1	NUM
cana-3476	281	25	)	)	PUNCT
cana-3476	281	26	−	−	NOUN
cana-3476	281	27	1	1	NUM
cana-3476	281	28	2	2	NUM
cana-3476	281	29	(	(	PUNCT
cana-3476	281	30	−𝑝(𝑠	−𝑝(𝑠	PROPN
cana-3476	281	31	)	)	PUNCT
cana-3476	281	32	(	(	PUNCT
cana-3476	281	33	𝑞(𝑠	𝑞(𝑠	NOUN
cana-3476	281	34	)	)	PUNCT
cana-3476	281	35	)	)	PUNCT
cana-3476	281	36	2	2	NUM
cana-3476	281	37	−	−	NOUN
cana-3476	281	38	1	1	NUM
cana-3476	281	39	)	)	PUNCT
cana-3476	281	40	using	use	VERB
cana-3476	281	41	the	the	DET
cana-3476	281	42	table	table	NOUN
cana-3476	281	43	1	1	NUM
cana-3476	281	44	we	we	PRON
cana-3476	281	45	get	get	VERB
cana-3476	281	46	𝑦(𝑡	𝑦(𝑡	NUM
cana-3476	281	47	)	)	PUNCT
cana-3476	281	48	=	=	PUNCT
cana-3476	282	1	−1	−1	NOUN
cana-3476	282	2	+	+	CCONJ
cana-3476	282	3	1	1	NUM
cana-3476	282	4	2	2	NUM
cana-3476	282	5	𝑒1(𝑡	𝑒1(𝑡	NOUN
cana-3476	282	6	,	,	PUNCT
cana-3476	282	7	0	0	NUM
cana-3476	282	8	)	)	PUNCT
cana-3476	283	1	+	+	CCONJ
cana-3476	283	2	1	1	NUM
cana-3476	283	3	2	2	NUM
cana-3476	283	4	𝑐𝑜𝑠1(𝑡	𝑐𝑜𝑠1(𝑡	NOUN
cana-3476	283	5	,	,	PUNCT
cana-3476	283	6	0	0	NUM
cana-3476	283	7	)	)	PUNCT
cana-3476	283	8	−	−	NOUN
cana-3476	283	9	1	1	NUM
cana-3476	283	10	2	2	NUM
cana-3476	283	11	𝑠𝑖𝑛1(𝑡	𝑠𝑖𝑛1(𝑡	NOUN
cana-3476	283	12	,	,	PUNCT
cana-3476	283	13	0	0	NUM
cana-3476	283	14	)	)	PUNCT
cana-3476	283	15	example	example	NOUN
cana-3476	284	1	3	3	NUM
cana-3476	284	2	consider	consider	VERB
cana-3476	284	3	the	the	DET
cana-3476	284	4	volterra	volterra	NOUN
cana-3476	284	5	integral	integral	ADJ
cana-3476	284	6	equation	equation	NOUN
cana-3476	284	7	𝑦(𝑡	𝑦(𝑡	NUM
cana-3476	284	8	)	)	PUNCT
cana-3476	284	9	=	=	SYM
cana-3476	285	1	𝑒2(𝑡	𝑒2(𝑡	PROPN
cana-3476	285	2	,	,	PUNCT
cana-3476	285	3	0	0	NUM
cana-3476	285	4	)	)	PUNCT
cana-3476	285	5	+	+	CCONJ
cana-3476	285	6	4	4	NUM
cana-3476	285	7	∫	∫	NOUN
cana-3476	285	8	𝑦(𝜏)∆𝜏	𝑦(𝜏)∆𝜏	PROPN
cana-3476	285	9	𝑡	𝑡	PROPN
cana-3476	285	10	0	0	NUM
cana-3476	285	11	communications	communication	NOUN
cana-3476	285	12	on	on	ADP
cana-3476	285	13	applied	apply	VERB
cana-3476	285	14	nonlinear	nonlinear	ADJ
cana-3476	285	15	analysis	analysis	NOUN
cana-3476	285	16	issn	issn	NOUN
cana-3476	285	17	:	:	PUNCT
cana-3476	285	18	1074	1074	NUM
cana-3476	285	19	-	-	PUNCT
cana-3476	285	20	133x	133x	NUM
cana-3476	285	21	vol	vol	NOUN
cana-3476	285	22	32	32	NUM
cana-3476	285	23	no	no	NOUN
cana-3476	285	24	.	.	PUNCT
cana-3476	286	1	7s	7	NOUN
cana-3476	286	2	(	(	PUNCT
cana-3476	286	3	2025	2025	NUM
cana-3476	286	4	)	)	PUNCT
cana-3476	286	5	704	704	NUM
cana-3476	286	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3476	286	7	applying	apply	VERB
cana-3476	286	8	the	the	DET
cana-3476	286	9	new	new	ADJ
cana-3476	286	10	general	general	ADJ
cana-3476	286	11	complex	complex	ADJ
cana-3476	286	12	integral	integral	ADJ
cana-3476	286	13	transform	transform	NOUN
cana-3476	286	14	on	on	ADP
cana-3476	286	15	time	time	NOUN
cana-3476	286	16	scales	scale	NOUN
cana-3476	286	17	to	to	ADP
cana-3476	286	18	the	the	DET
cana-3476	286	19	equation	equation	NOUN
cana-3476	286	20	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	286	21	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	286	22	)	)	PUNCT
cana-3476	286	23	}	}	PUNCT
cana-3476	287	1	=	=	PUNCT
cana-3476	287	2	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	287	3	𝑐{𝑒2(𝑡	𝑐{𝑒2(𝑡	PROPN
cana-3476	287	4	,	,	PUNCT
cana-3476	287	5	0	0	NUM
cana-3476	287	6	)	)	PUNCT
cana-3476	287	7	}	}	PUNCT
cana-3476	288	1	+	+	CCONJ
cana-3476	289	1	4𝒯𝑔	4𝒯𝑔	X
cana-3476	289	2	𝑐	𝑐	X
cana-3476	289	3	{	{	PUNCT
cana-3476	289	4	∫	∫	PROPN
cana-3476	289	5	𝑦(𝜏)∆𝜏	𝑦(𝜏)∆𝜏	PROPN
cana-3476	289	6	𝑡	𝑡	PROPN
cana-3476	289	7	0	0	NUM
cana-3476	289	8	}	}	PUNCT
cana-3476	289	9	𝒯𝑔	𝒯𝑔	NOUN
cana-3476	289	10	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	289	11	)	)	PUNCT
cana-3476	289	12	}	}	PUNCT
cana-3476	289	13	=	=	SYM
cana-3476	289	14	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	289	15	)	)	PUNCT
cana-3476	289	16	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	289	17	)	)	PUNCT
cana-3476	289	18	−	−	ADP
cana-3476	289	19	2	2	NUM
cana-3476	289	20	+	+	CCONJ
cana-3476	289	21	4	4	NUM
cana-3476	289	22	(	(	PUNCT
cana-3476	289	23	1	1	NUM
cana-3476	289	24	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	289	25	)	)	PUNCT
cana-3476	289	26	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	289	27	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	289	28	)	)	PUNCT
cana-3476	289	29	}	}	PUNCT
cana-3476	289	30	)	)	PUNCT
cana-3476	289	31	⇒	⇒	VERB
cana-3476	289	32	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	289	33	𝑐{𝑦(𝑡	𝑐{𝑦(𝑡	NOUN
cana-3476	289	34	)	)	PUNCT
cana-3476	289	35	}	}	PUNCT
cana-3476	289	36	=	=	SYM
cana-3476	289	37	(	(	PUNCT
cana-3476	289	38	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	289	39	)	)	PUNCT
cana-3476	289	40	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	289	41	)	)	PUNCT
cana-3476	289	42	−	−	PROPN
cana-3476	289	43	2	2	NUM
cana-3476	289	44	)	)	PUNCT
cana-3476	289	45	(	(	PUNCT
cana-3476	289	46	𝑖𝑞(𝑠	𝑖𝑞(𝑠	X
cana-3476	289	47	)	)	PUNCT
cana-3476	289	48	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	289	49	)	)	PUNCT
cana-3476	290	1	−	−	ADP
cana-3476	290	2	4	4	X
cana-3476	290	3	)	)	PUNCT
cana-3476	290	4	=	=	SYM
cana-3476	291	1	−	−	PROPN
cana-3476	291	2	(	(	PUNCT
cana-3476	291	3	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	291	4	)	)	PUNCT
cana-3476	291	5	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	291	6	)	)	PUNCT
cana-3476	291	7	−	−	PROPN
cana-3476	291	8	2	2	NUM
cana-3476	291	9	)	)	PUNCT
cana-3476	291	10	+	+	CCONJ
cana-3476	291	11	2	2	NUM
cana-3476	291	12	(	(	PUNCT
cana-3476	291	13	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	291	14	)	)	PUNCT
cana-3476	291	15	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	291	16	)	)	PUNCT
cana-3476	291	17	−	−	ADP
cana-3476	291	18	4	4	X
cana-3476	291	19	)	)	PUNCT
cana-3476	291	20	∴	∴	PROPN
cana-3476	291	21	𝑦(𝑡	𝑦(𝑡	PROPN
cana-3476	291	22	)	)	PUNCT
cana-3476	291	23	=	=	SYM
cana-3476	291	24	−𝑒2(𝑡	−𝑒2(𝑡	NOUN
cana-3476	291	25	,	,	PUNCT
cana-3476	291	26	0	0	NUM
cana-3476	291	27	)	)	PUNCT
cana-3476	291	28	+	+	CCONJ
cana-3476	291	29	2𝑒4(𝑡	2𝑒4(𝑡	NUM
cana-3476	291	30	,	,	PUNCT
cana-3476	291	31	0	0	NUM
cana-3476	291	32	)	)	PUNCT
cana-3476	291	33	example	example	NOUN
cana-3476	291	34	4	4	NUM
cana-3476	291	35	we	we	PRON
cana-3476	291	36	consider	consider	VERB
cana-3476	291	37	the	the	DET
cana-3476	291	38	problem	problem	NOUN
cana-3476	291	39	from	from	ADP
cana-3476	291	40	the	the	DET
cana-3476	291	41	field	field	NOUN
cana-3476	291	42	of	of	ADP
cana-3476	291	43	pharmacokinetics	pharmacokinetic	NOUN
cana-3476	291	44	to	to	PART
cana-3476	291	45	find	find	VERB
cana-3476	291	46	the	the	DET
cana-3476	291	47	concentration	concentration	NOUN
cana-3476	291	48	of	of	ADP
cana-3476	291	49	drug	drug	NOUN
cana-3476	291	50	in	in	ADP
cana-3476	291	51	the	the	DET
cana-3476	291	52	blood	blood	NOUN
cana-3476	291	53	at	at	ADP
cana-3476	291	54	any	any	DET
cana-3476	291	55	given	give	VERB
cana-3476	291	56	time	time	NOUN
cana-3476	291	57	t	t	NOUN
cana-3476	291	58	during	during	ADP
cana-3476	291	59	continuous	continuous	ADJ
cana-3476	291	60	intravenous	intravenous	ADJ
cana-3476	291	61	injection	injection	NOUN
cana-3476	291	62	of	of	ADP
cana-3476	291	63	drug	drug	NOUN
cana-3476	291	64	and	and	CCONJ
cana-3476	291	65	find	find	VERB
cana-3476	291	66	its	its	PRON
cana-3476	291	67	solution	solution	NOUN
cana-3476	291	68	in	in	ADP
cana-3476	291	69	this	this	DET
cana-3476	291	70	problem	problem	NOUN
cana-3476	291	71	for	for	ADP
cana-3476	291	72	physical	physical	ADJ
cana-3476	291	73	explanation	explanation	NOUN
cana-3476	291	74	of	of	ADP
cana-3476	291	75	the	the	DET
cana-3476	291	76	present	present	ADJ
cana-3476	291	77	method	method	NOUN
cana-3476	291	78	.	.	PUNCT
cana-3476	292	1	the	the	DET
cana-3476	292	2	following	follow	VERB
cana-3476	292	3	is	be	AUX
cana-3476	292	4	the	the	DET
cana-3476	292	5	first	first	ADJ
cana-3476	292	6	order	order	NOUN
cana-3476	292	7	ordinary	ordinary	ADJ
cana-3476	292	8	differential	differential	ADJ
cana-3476	292	9	equation	equation	NOUN
cana-3476	292	10	with	with	ADP
cana-3476	292	11	constant	constant	ADJ
cana-3476	292	12	coefficients	coefficient	NOUN
cana-3476	292	13	that	that	PRON
cana-3476	292	14	can	can	AUX
cana-3476	292	15	be	be	AUX
cana-3476	292	16	used	use	VERB
cana-3476	292	17	to	to	PART
cana-3476	292	18	solve	solve	VERB
cana-3476	292	19	this	this	DET
cana-3476	292	20	problem	problem	NOUN
cana-3476	292	21	.	.	PUNCT
cana-3476	293	1	𝑑𝑔(𝑡	𝑑𝑔(𝑡	PROPN
cana-3476	293	2	)	)	PUNCT
cana-3476	294	1	𝑑𝑡	𝑑𝑡	ADP
cana-3476	294	2	+	+	ADJ
cana-3476	294	3	𝜉𝑔(𝑡	𝜉𝑔(𝑡	NOUN
cana-3476	294	4	)	)	PUNCT
cana-3476	294	5	=	=	PUNCT
cana-3476	295	1	𝜌	𝜌	X
cana-3476	295	2	𝑣𝑜𝑙	𝑣𝑜𝑙	NOUN
cana-3476	295	3	,	,	PUNCT
cana-3476	295	4	where	where	SCONJ
cana-3476	295	5	𝑡	𝑡	X
cana-3476	295	6	>	>	X
cana-3476	295	7	0	0	PUNCT
cana-3476	295	8	(	(	PUNCT
cana-3476	295	9	1	1	NUM
cana-3476	295	10	)	)	PUNCT
cana-3476	295	11	with	with	ADP
cana-3476	295	12	𝑔(0	𝑔(0	NOUN
cana-3476	295	13	)	)	PUNCT
cana-3476	295	14	=	=	SYM
cana-3476	295	15	0	0	X
cana-3476	295	16	.	.	PUNCT
cana-3476	295	17	here	here	ADV
cana-3476	295	18	𝑔(𝑡	𝑔(𝑡	PROPN
cana-3476	295	19	)	)	PUNCT
cana-3476	295	20	is	be	AUX
cana-3476	295	21	the	the	DET
cana-3476	295	22	amount	amount	NOUN
cana-3476	295	23	of	of	ADP
cana-3476	295	24	a	a	DET
cana-3476	295	25	drug	drug	NOUN
cana-3476	295	26	in	in	ADP
cana-3476	295	27	the	the	DET
cana-3476	295	28	blood	blood	NOUN
cana-3476	295	29	at	at	ADP
cana-3476	295	30	any	any	DET
cana-3476	295	31	given	give	VERB
cana-3476	295	32	time	time	NOUN
cana-3476	295	33	𝑡	𝑡	NOUN
cana-3476	295	34	,	,	PUNCT
cana-3476	295	35	ξ	ξ	NOUN
cana-3476	295	36	:	:	PUNCT
cana-3476	295	37	elimination	elimination	NOUN
cana-3476	295	38	at	at	ADP
cana-3476	295	39	a	a	DET
cana-3476	295	40	fixed	fix	VERB
cana-3476	295	41	speed	speed	NOUN
cana-3476	295	42	,	,	PUNCT
cana-3476	295	43	𝜌	𝜌	ADP
cana-3476	295	44	:	:	PUNCT
cana-3476	295	45	the	the	DET
cana-3476	295	46	rate	rate	NOUN
cana-3476	295	47	of	of	ADP
cana-3476	295	48	infusion(in	infusion(in	ADJ
cana-3476	295	49	mg	mg	PROPN
cana-3476	295	50	/	/	SYM
cana-3476	295	51	min	min	NOUN
cana-3476	295	52	.	.	PROPN
cana-3476	295	53	)	)	PUNCT
cana-3476	295	54	,	,	PUNCT
cana-3476	295	55	vol	vol	NOUN
cana-3476	295	56	:	:	PUNCT
cana-3476	295	57	the	the	DET
cana-3476	295	58	total	total	ADJ
cana-3476	295	59	amount	amount	NOUN
cana-3476	295	60	of	of	ADP
cana-3476	295	61	medication	medication	NOUN
cana-3476	295	62	distributed	distribute	VERB
cana-3476	295	63	.	.	PUNCT
cana-3476	296	1	by	by	ADP
cana-3476	296	2	using	use	VERB
cana-3476	296	3	the	the	DET
cana-3476	296	4	result	result	NOUN
cana-3476	296	5	(	(	PUNCT
cana-3476	296	6	2.10	2.10	NUM
cana-3476	296	7	)	)	PUNCT
cana-3476	296	8	for	for	ADP
cana-3476	296	9	the	the	DET
cana-3476	296	10	equation	equation	NOUN
cana-3476	296	11	(	(	PUNCT
cana-3476	296	12	1	1	X
cana-3476	296	13	)	)	PUNCT
cana-3476	296	14	we	we	PRON
cana-3476	296	15	get	get	VERB
cana-3476	296	16	𝑔∆(𝑡	𝑔∆(𝑡	NOUN
cana-3476	296	17	)	)	PUNCT
cana-3476	296	18	+	+	NUM
cana-3476	296	19	𝜉𝑔(𝑡	𝜉𝑔(𝑡	NOUN
cana-3476	296	20	)	)	PUNCT
cana-3476	296	21	=	=	PUNCT
cana-3476	297	1	𝜌	𝜌	X
cana-3476	297	2	𝑣𝑜𝑙	𝑣𝑜𝑙	NOUN
cana-3476	297	3	applying	apply	VERB
cana-3476	297	4	the	the	DET
cana-3476	297	5	new	new	ADJ
cana-3476	297	6	general	general	ADJ
cana-3476	297	7	complex	complex	ADJ
cana-3476	297	8	integral	integral	ADJ
cana-3476	297	9	transform	transform	NOUN
cana-3476	297	10	on	on	ADP
cana-3476	297	11	time	time	NOUN
cana-3476	297	12	scales	scale	NOUN
cana-3476	297	13	to	to	ADP
cana-3476	297	14	this	this	DET
cana-3476	297	15	equations	equation	NOUN
cana-3476	297	16	we	we	PRON
cana-3476	297	17	get	get	VERB
cana-3476	297	18	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	297	19	𝑐{𝑔∆(𝑡	𝑐{𝑔∆(𝑡	PROPN
cana-3476	297	20	)	)	PUNCT
cana-3476	297	21	}	}	PUNCT
cana-3476	298	1	+	+	CCONJ
cana-3476	298	2	𝜉𝒯𝑔	𝜉𝒯𝑔	NUM
cana-3476	298	3	𝑐{𝑔(𝑡	𝑐{𝑔(𝑡	NOUN
cana-3476	298	4	)	)	PUNCT
cana-3476	298	5	}	}	PUNCT
cana-3476	298	6	=	=	PUNCT
cana-3476	298	7	𝜌	𝜌	PRON
cana-3476	298	8	𝑣𝑜𝑙	𝑣𝑜𝑙	NOUN
cana-3476	298	9	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	298	10	𝑐{1	𝑐{1	PROPN
cana-3476	298	11	}	}	PUNCT
cana-3476	298	12	𝑖𝑞(𝑠)𝒯𝑔	𝑖𝑞(𝑠)𝒯𝑔	NOUN
cana-3476	298	13	𝑐{𝑔(𝑡	𝑐{𝑔(𝑡	NOUN
cana-3476	298	14	)	)	PUNCT
cana-3476	298	15	}	}	PUNCT
cana-3476	298	16	−	−	PROPN
cana-3476	298	17	𝑝(𝑠)𝑔(0	𝑝(𝑠)𝑔(0	ADJ
cana-3476	298	18	)	)	PUNCT
cana-3476	299	1	+	+	CCONJ
cana-3476	299	2	𝜉𝒯𝑔	𝜉𝒯𝑔	NUM
cana-3476	299	3	𝑐{𝑔(𝑡	𝑐{𝑔(𝑡	NOUN
cana-3476	299	4	)	)	PUNCT
cana-3476	299	5	}	}	PUNCT
cana-3476	299	6	=	=	PUNCT
cana-3476	299	7	𝜌	𝜌	X
cana-3476	299	8	𝑣𝑜𝑙	𝑣𝑜𝑙	ADJ
cana-3476	299	9	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	299	10	)	)	PUNCT
cana-3476	299	11	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	299	12	)	)	PUNCT
cana-3476	299	13	⇒	⇒	VERB
cana-3476	299	14	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	299	15	𝑐{𝑔(𝑡)}(𝑖𝑞(𝑠	𝑐{𝑔(𝑡)}(𝑖𝑞(𝑠	NOUN
cana-3476	299	16	)	)	PUNCT
cana-3476	299	17	+	+	NUM
cana-3476	299	18	𝜉	𝜉	X
cana-3476	299	19	)	)	PUNCT
cana-3476	299	20	=	=	PUNCT
cana-3476	299	21	𝜌	𝜌	X
cana-3476	299	22	𝑣𝑜𝑙	𝑣𝑜𝑙	ADJ
cana-3476	299	23	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	299	24	)	)	PUNCT
cana-3476	299	25	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	299	26	)	)	PUNCT
cana-3476	299	27	⇒	⇒	VERB
cana-3476	299	28	𝒯𝑔	𝒯𝑔	PROPN
cana-3476	299	29	𝑐{𝑔(𝑡	𝑐{𝑔(𝑡	PROPN
cana-3476	299	30	)	)	PUNCT
cana-3476	299	31	}	}	PUNCT
cana-3476	299	32	=	=	PUNCT
cana-3476	299	33	𝜌	𝜌	X
cana-3476	299	34	𝑣𝑜𝑙	𝑣𝑜𝑙	NOUN
cana-3476	299	35	(	(	PUNCT
cana-3476	299	36	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	299	37	)	)	PUNCT
cana-3476	299	38	𝑖𝑞(𝑠)(𝑖𝑞(𝑠	𝑖𝑞(𝑠)(𝑖𝑞(𝑠	NUM
cana-3476	299	39	)	)	PUNCT
cana-3476	299	40	+	+	NUM
cana-3476	299	41	𝜉	𝜉	X
cana-3476	299	42	)	)	PUNCT
cana-3476	299	43	)	)	PUNCT
cana-3476	299	44	=	=	PUNCT
cana-3476	300	1	𝜌	𝜌	PRON
cana-3476	300	2	𝜉𝑣𝑜𝑙	𝜉𝑣𝑜𝑙	NOUN
cana-3476	300	3	(	(	PUNCT
cana-3476	300	4	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	300	5	)	)	PUNCT
cana-3476	300	6	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	300	7	)	)	PUNCT
cana-3476	300	8	−	−	PROPN
cana-3476	300	9	𝑝(𝑠	𝑝(𝑠	PROPN
cana-3476	300	10	)	)	PUNCT
cana-3476	300	11	𝑖𝑞(𝑠	𝑖𝑞(𝑠	PUNCT
cana-3476	300	12	)	)	PUNCT
cana-3476	301	1	+	+	CCONJ
cana-3476	301	2	𝜉	𝜉	X
cana-3476	301	3	)	)	PUNCT
cana-3476	301	4	hence	hence	ADV
cana-3476	301	5	𝑔(𝑡	𝑔(𝑡	PROPN
cana-3476	301	6	)	)	PUNCT
cana-3476	301	7	=	=	PUNCT
cana-3476	301	8	𝜌	𝜌	PRON
cana-3476	301	9	𝜉𝑣𝑜𝑙	𝜉𝑣𝑜𝑙	NOUN
cana-3476	301	10	(	(	PUNCT
cana-3476	301	11	1	1	NUM
cana-3476	301	12	−	−	NOUN
cana-3476	301	13	𝑒−𝜉(𝑡	𝑒−𝜉(𝑡	NOUN
cana-3476	301	14	,	,	PUNCT
cana-3476	301	15	0	0	NUM
cana-3476	301	16	)	)	PUNCT
cana-3476	301	17	)	)	PUNCT
cana-3476	301	18	.	.	PUNCT
cana-3476	302	1	therefore	therefore	ADV
cana-3476	302	2	continuous	continuous	ADJ
cana-3476	302	3	intravenous	intravenous	ADJ
cana-3476	302	4	drug	drug	NOUN
cana-3476	302	5	administration	administration	NOUN
cana-3476	302	6	requires	require	VERB
cana-3476	302	7	a	a	DET
cana-3476	302	8	certain	certain	ADJ
cana-3476	302	9	concentration	concentration	NOUN
cana-3476	302	10	of	of	ADP
cana-3476	302	11	drug	drug	NOUN
cana-3476	302	12	in	in	ADP
cana-3476	302	13	the	the	DET
cana-3476	302	14	blood	blood	NOUN
cana-3476	302	15	at	at	ADP
cana-3476	302	16	all	all	DET
cana-3476	302	17	the	the	DET
cana-3476	302	18	times	time	NOUN
cana-3476	302	19	.	.	PUNCT
cana-3476	303	1	conclusion	conclusion	VERB
cana-3476	303	2	the	the	DET
cana-3476	303	3	novel	novel	ADJ
cana-3476	303	4	general	general	ADJ
cana-3476	303	5	complex	complex	ADJ
cana-3476	303	6	integral	integral	ADJ
cana-3476	303	7	transform	transform	NOUN
cana-3476	303	8	on	on	ADP
cana-3476	303	9	time	time	NOUN
cana-3476	303	10	scales	scale	VERB
cana-3476	303	11	𝕋	𝕋	PRON
cana-3476	303	12	for	for	ADP
cana-3476	303	13	solving	solve	VERB
cana-3476	303	14	dynamic	dynamic	ADJ
cana-3476	303	15	equations	equation	NOUN
cana-3476	303	16	of	of	ADP
cana-3476	303	17	any	any	DET
cana-3476	303	18	given	give	VERB
cana-3476	303	19	order	order	NOUN
cana-3476	303	20	and	and	CCONJ
cana-3476	303	21	integral	integral	ADJ
cana-3476	303	22	equations	equation	NOUN
cana-3476	303	23	has	have	AUX
cana-3476	303	24	been	be	AUX
cana-3476	303	25	proven	prove	VERB
cana-3476	303	26	in	in	ADP
cana-3476	303	27	terms	term	NOUN
cana-3476	303	28	of	of	ADP
cana-3476	303	29	definition	definition	NOUN
cana-3476	303	30	and	and	CCONJ
cana-3476	303	31	applications	application	NOUN
cana-3476	303	32	.	.	PUNCT
cana-3476	304	1	few	few	ADJ
cana-3476	304	2	examples	example	NOUN
cana-3476	304	3	in	in	ADP
cana-3476	304	4	real	real	ADJ
cana-3476	304	5	life	life	NOUN
cana-3476	304	6	problems	problem	NOUN
cana-3476	304	7	such	such	ADJ
cana-3476	304	8	as	as	ADP
cana-3476	304	9	pharmacokinetics	pharmacokinetic	NOUN
cana-3476	304	10	.	.	PUNCT
cana-3476	305	1	communications	communication	NOUN
cana-3476	305	2	on	on	ADP
cana-3476	305	3	applied	apply	VERB
cana-3476	305	4	nonlinear	nonlinear	ADJ
cana-3476	305	5	analysis	analysis	NOUN
cana-3476	305	6	issn	issn	NOUN
cana-3476	305	7	:	:	PUNCT
cana-3476	305	8	1074	1074	NUM
cana-3476	305	9	-	-	PUNCT
cana-3476	305	10	133x	133x	NUM
cana-3476	305	11	vol	vol	NOUN
cana-3476	305	12	32	32	NUM
cana-3476	305	13	no	no	NOUN
cana-3476	305	14	.	.	PUNCT
cana-3476	306	1	7s	7	NOUN
cana-3476	306	2	(	(	PUNCT
cana-3476	306	3	2025	2025	NUM
cana-3476	306	4	)	)	PUNCT
cana-3476	306	5	705	705	NUM
cana-3476	306	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3476	306	7	references	reference	NOUN
cana-3476	306	8	[	[	X
cana-3476	306	9	1	1	NUM
cana-3476	306	10	]	]	PUNCT
cana-3476	306	11	agwa	agwa	NOUN
cana-3476	306	12	h.	h.	PROPN
cana-3476	306	13	a.	a.	PROPN
cana-3476	306	14	,	,	PUNCT
cana-3476	306	15	ali	ali	PROPN
cana-3476	306	16	f.	f.	PROPN
cana-3476	306	17	m.	m.	PROPN
cana-3476	306	18	&	&	CCONJ
cana-3476	306	19	kılıçman	kılıçman	PROPN
cana-3476	306	20	a.	a.	PROPN
cana-3476	306	21	,	,	PUNCT
cana-3476	306	22	a	a	DET
cana-3476	306	23	new	new	ADJ
cana-3476	306	24	integral	integral	ADJ
cana-3476	306	25	transform	transform	NOUN
cana-3476	306	26	on	on	ADP
cana-3476	306	27	time	time	NOUN
cana-3476	306	28	scales	scale	NOUN
cana-3476	306	29	and	and	CCONJ
cana-3476	306	30	its	its	PRON
cana-3476	306	31	applications	application	NOUN
cana-3476	306	32	,	,	PUNCT
cana-3476	306	33	advances	advance	NOUN
cana-3476	306	34	in	in	ADP
cana-3476	306	35	difference	difference	NOUN
cana-3476	306	36	equations2012	equations2012	PROPN
cana-3476	306	37	,	,	PUNCT
cana-3476	306	38	2012:60	2012:60	NUM
cana-3476	306	39	(	(	PUNCT
cana-3476	306	40	2012	2012	NUM
cana-3476	306	41	)	)	PUNCT
cana-3476	306	42	.	.	PUNCT
cana-3476	307	1	doi.org/10.1186/1687-1847-2012-60	doi.org/10.1186/1687-1847-2012-60	PRON
cana-3476	307	2	[	[	X
cana-3476	307	3	2	2	NUM
cana-3476	307	4	]	]	PUNCT
cana-3476	307	5	abdelilah	abdelilah	PROPN
cana-3476	307	6	kamal	kamal	PROPN
cana-3476	307	7	,	,	PUNCT
cana-3476	307	8	h.	h.	PROPN
cana-3476	307	9	sedeeg	sedeeg	PROPN
cana-3476	307	10	,	,	PUNCT
cana-3476	307	11	the	the	DET
cana-3476	307	12	new	new	ADJ
cana-3476	307	13	integral	integral	ADJ
cana-3476	307	14	transform	transform	NOUN
cana-3476	307	15	“	"	PUNCT
cana-3476	307	16	kamal	kamal	ADJ
cana-3476	307	17	transform	transform	NOUN
cana-3476	307	18	”	"	PUNCT
cana-3476	307	19	,	,	PUNCT
cana-3476	307	20	advances	advance	NOUN
cana-3476	307	21	in	in	ADP
cana-3476	307	22	theoretical	theoretical	ADJ
cana-3476	307	23	and	and	CCONJ
cana-3476	307	24	applied	applied	ADJ
cana-3476	307	25	mathematics	mathematic	NOUN
cana-3476	307	26	,	,	PUNCT
cana-3476	307	27	vo.11	vo.11	NOUN
cana-3476	307	28	,	,	PUNCT
cana-3476	307	29	no	no	INTJ
cana-3476	307	30	.	.	NOUN
cana-3476	307	31	4	4	NUM
cana-3476	307	32	(	(	PUNCT
cana-3476	307	33	2016	2016	NUM
cana-3476	307	34	)	)	PUNCT
cana-3476	307	35	,	,	PUNCT
cana-3476	307	36	451	451	NUM
cana-3476	307	37	-	-	SYM
cana-3476	307	38	458	458	NUM
cana-3476	307	39	.	.	PUNCT
cana-3476	308	1	[	[	X
cana-3476	308	2	3	3	X
cana-3476	308	3	]	]	X
cana-3476	308	4	bohner	bohner	ADJ
cana-3476	308	5	m.	m.	NOUN
cana-3476	308	6	,	,	PUNCT
cana-3476	308	7	gusein	gusein	PROPN
cana-3476	308	8	sh	sh	PROPN
cana-3476	308	9	.	.	PUNCT
cana-3476	308	10	guseinov	guseinov	PROPN
cana-3476	308	11	,	,	PUNCT
cana-3476	308	12	the	the	DET
cana-3476	308	13	convolution	convolution	NOUN
cana-3476	308	14	on	on	ADP
cana-3476	308	15	time	time	NOUN
cana-3476	308	16	scales	scale	NOUN
cana-3476	308	17	.	.	PUNCT
cana-3476	309	1	abstract	abstract	ADJ
cana-3476	309	2	and	and	CCONJ
cana-3476	309	3	applied	apply	VERB
cana-3476	309	4	analysis	analysis	NOUN
cana-3476	309	5	,	,	PUNCT
cana-3476	309	6	vol	vol	NOUN
cana-3476	309	7	.	.	PROPN
cana-3476	309	8	2007	2007	NUM
cana-3476	309	9	,	,	PUNCT
cana-3476	309	10	24	24	NUM
cana-3476	309	11	,	,	PUNCT
cana-3476	309	12	article	article	NOUN
cana-3476	309	13	i	i	PROPN
cana-3476	309	14	d	d	PROPN
cana-3476	309	15	58373	58373	NUM
cana-3476	309	16	.	.	PUNCT
cana-3476	310	1	doi:10.1155/2007/58373	doi:10.1155/2007/58373	NOUN
cana-3476	310	2	[	[	X
cana-3476	310	3	4	4	NUM
cana-3476	310	4	]	]	PUNCT
cana-3476	310	5	bohner	bohner	ADJ
cana-3476	310	6	m.	m.	NOUN
cana-3476	310	7	,	,	PUNCT
cana-3476	310	8	peterson	peterson	PROPN
cana-3476	310	9	a.	a.	PROPN
cana-3476	310	10	,	,	PUNCT
cana-3476	310	11	dynamic	dynamic	ADJ
cana-3476	310	12	equations	equation	NOUN
cana-3476	310	13	on	on	ADP
cana-3476	310	14	time	time	NOUN
cana-3476	310	15	scales	scale	NOUN
cana-3476	310	16	:	:	PUNCT
cana-3476	310	17	an	an	DET
cana-3476	310	18	introduction	introduction	NOUN
cana-3476	310	19	with	with	ADP
cana-3476	310	20	application	application	NOUN
cana-3476	310	21	.	.	PUNCT
cana-3476	311	1	birkhäuser	birkhäuser	PROPN
cana-3476	311	2	publication	publication	PROPN
cana-3476	311	3	,	,	PUNCT
cana-3476	311	4	ma	ma	PROPN
cana-3476	311	5	2001	2001	NUM
cana-3476	311	6	.	.	PUNCT
cana-3476	312	1	[	[	X
cana-3476	312	2	5	5	NUM
cana-3476	312	3	]	]	X
cana-3476	312	4	bohner	bohner	NOUN
cana-3476	312	5	,	,	PUNCT
cana-3476	312	6	m	m	PROPN
cana-3476	312	7	,	,	PUNCT
cana-3476	312	8	peterson	peterson	PROPN
cana-3476	312	9	,	,	PUNCT
cana-3476	312	10	a	a	PRON
cana-3476	312	11	:	:	PUNCT
cana-3476	312	12	advances	advance	NOUN
cana-3476	312	13	in	in	ADP
cana-3476	312	14	dynamic	dynamic	ADJ
cana-3476	312	15	equations	equation	NOUN
cana-3476	312	16	on	on	ADP
cana-3476	312	17	time	time	NOUN
cana-3476	312	18	scales	scale	NOUN
cana-3476	312	19	,	,	PUNCT
cana-3476	312	20	birkhäuser	birkhäuser	NOUN
cana-3476	312	21	,	,	PUNCT
cana-3476	312	22	boston	boston	PROPN
cana-3476	312	23	,	,	PUNCT
cana-3476	312	24	ma	ma	PROPN
cana-3476	312	25	(	(	PUNCT
cana-3476	312	26	2003	2003	NUM
cana-3476	312	27	)	)	PUNCT
cana-3476	312	28	.	.	PUNCT
cana-3476	313	1	[	[	X
cana-3476	313	2	6	6	NUM
cana-3476	313	3	]	]	PUNCT
cana-3476	313	4	d.	d.	PROPN
cana-3476	313	5	p.	p.	PROPN
cana-3476	313	6	patil	patil	PROPN
cana-3476	313	7	,	,	PUNCT
cana-3476	313	8	application	application	NOUN
cana-3476	313	9	of	of	ADP
cana-3476	313	10	integral	integral	ADJ
cana-3476	313	11	transform	transform	NOUN
cana-3476	313	12	(	(	PUNCT
cana-3476	313	13	laplace	laplace	NOUN
cana-3476	313	14	and	and	CCONJ
cana-3476	313	15	shehu	shehu	NOUN
cana-3476	313	16	)	)	PUNCT
cana-3476	313	17	in	in	ADP
cana-3476	313	18	chemical	chemical	ADJ
cana-3476	313	19	sciences	science	NOUN
cana-3476	313	20	.	.	PUNCT
cana-3476	314	1	aayushi	aayushi	PROPN
cana-3476	314	2	international	international	ADJ
cana-3476	314	3	interdisciplinary	interdisciplinary	ADJ
cana-3476	314	4	research	research	NOUN
cana-3476	314	5	journal	journal	NOUN
cana-3476	314	6	,	,	PUNCT
cana-3476	314	7	special	special	ADJ
cana-3476	314	8	issue	issue	NOUN
cana-3476	314	9	no	no	NOUN
cana-3476	314	10	.	.	PROPN
cana-3476	314	11	88	88	NUM
cana-3476	314	12	(	(	PUNCT
cana-3476	314	13	2022	2022	NUM
cana-3476	314	14	)	)	PUNCT
cana-3476	314	15	.	.	PUNCT
cana-3476	315	1	doi.org/10.2139/ssrn.4006213	doi.org/10.2139/ssrn.4006213	NOUN
cana-3476	315	2	[	[	PUNCT
cana-3476	315	3	7	7	X
cana-3476	315	4	]	]	PUNCT
cana-3476	315	5	d.	d.	PROPN
cana-3476	315	6	p.	p.	PROPN
cana-3476	315	7	patil	patil	PROPN
cana-3476	315	8	,	,	PUNCT
cana-3476	315	9	s.	s.	PROPN
cana-3476	315	10	s.	s.	PROPN
cana-3476	315	11	khakale	khakale	PROPN
cana-3476	315	12	,	,	PUNCT
cana-3476	315	13	new	new	ADJ
cana-3476	315	14	integral	integral	ADJ
cana-3476	315	15	transform	transform	NOUN
cana-3476	315	16	”	"	PUNCT
cana-3476	315	17	soham	soham	PROPN
cana-3476	315	18	transform	transform	NOUN
cana-3476	315	19	”	"	PUNCT
cana-3476	315	20	,	,	PUNCT
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cana-3476	315	22	journal	journal	NOUN
cana-3476	315	23	of	of	ADP
cana-3476	315	24	advances	advance	NOUN
cana-3476	315	25	in	in	ADP
cana-3476	315	26	engineering	engineering	NOUN
cana-3476	315	27	and	and	CCONJ
cana-3476	315	28	management	management	NOUN
cana-3476	315	29	,	,	PUNCT
cana-3476	315	30	vol	vol	NOUN
cana-3476	315	31	.	.	PROPN
cana-3476	315	32	3	3	NUM
cana-3476	315	33	,	,	PUNCT
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cana-3476	315	36	10	10	NUM
cana-3476	315	37	(	(	PUNCT
cana-3476	315	38	2021	2021	NUM
cana-3476	315	39	)	)	PUNCT
cana-3476	315	40	,	,	PUNCT
cana-3476	315	41	126	126	NUM
cana-3476	315	42	-	-	SYM
cana-3476	315	43	132	132	NUM
cana-3476	315	44	.	.	PUNCT
cana-3476	316	1	doi	doi	NOUN
cana-3476	316	2	:	:	PUNCT
cana-3476	316	3	10.35629/5252	10.35629/5252	NUM
cana-3476	316	4	-	-	SYM
cana-3476	316	5	0310126132	0310126132	NUM
cana-3476	317	1	[	[	X
cana-3476	317	2	8	8	NUM
cana-3476	317	3	]	]	X
cana-3476	317	4	davis	davis	PROPN
cana-3476	317	5	jm	jm	PROPN
cana-3476	317	6	,	,	PUNCT
cana-3476	317	7	gravagne	gravagne	PROPN
cana-3476	317	8	ia	ia	PROPN
cana-3476	317	9	,	,	PUNCT
cana-3476	317	10	jackson	jackson	PROPN
cana-3476	317	11	bj	bj	PROPN
cana-3476	317	12	,	,	PUNCT
cana-3476	317	13	marks	marks	PROPN
cana-3476	317	14	rj	rj	PROPN
cana-3476	317	15	,	,	PUNCT
cana-3476	317	16	ramos	ramos	PROPN
cana-3476	317	17	aa	aa	PROPN
cana-3476	317	18	,	,	PUNCT
cana-3476	317	19	the	the	DET
cana-3476	317	20	laplace	laplace	NOUN
cana-3476	317	21	transform	transform	NOUN
cana-3476	317	22	on	on	ADP
cana-3476	317	23	time	time	NOUN
cana-3476	317	24	scales	scale	NOUN
cana-3476	317	25	revisited	revisit	VERB
cana-3476	317	26	,	,	PUNCT
cana-3476	317	27	journal	journal	NOUN
cana-3476	317	28	of	of	ADP
cana-3476	317	29	mathematical	mathematical	ADJ
cana-3476	317	30	analysis	analysis	NOUN
cana-3476	317	31	and	and	CCONJ
cana-3476	317	32	applications	application	NOUN
cana-3476	317	33	,	,	PUNCT
cana-3476	317	34	332(2007	332(2007	NUM
cana-3476	317	35	)	)	PUNCT
cana-3476	317	36	,	,	PUNCT
cana-3476	317	37	1291–1307	1291–1307	NUM
cana-3476	317	38	(	(	PUNCT
cana-3476	317	39	2007	2007	NUM
cana-3476	317	40	)	)	PUNCT
cana-3476	317	41	.	.	PUNCT
cana-3476	318	1	doi:10.1016	doi:10.1016	PROPN
cana-3476	318	2	/	/	SYM
cana-3476	318	3	j.jmaa.2006.10.089	j.jmaa.2006.10.089	PROPN
cana-3476	319	1	[	[	X
cana-3476	319	2	9	9	NUM
cana-3476	319	3	]	]	SYM
cana-3476	319	4	delfim	delfim	PROPN
cana-3476	319	5	f.	f.	PROPN
cana-3476	319	6	m.	m.	PROPN
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cana-3476	319	8	,	,	PUNCT
cana-3476	319	9	a	a	DET
cana-3476	319	10	table	table	NOUN
cana-3476	319	11	of	of	ADP
cana-3476	319	12	derivatives	derivative	NOUN
cana-3476	319	13	on	on	ADP
cana-3476	319	14	arbitrary	arbitrary	ADJ
cana-3476	319	15	time	time	NOUN
cana-3476	319	16	scales	scale	NOUN
cana-3476	319	17	,	,	PUNCT
cana-3476	319	18	global	global	ADJ
cana-3476	319	19	and	and	CCONJ
cana-3476	319	20	stochastic	stochastic	ADJ
cana-3476	319	21	analysis	analysis	NOUN
cana-3476	319	22	,	,	PUNCT
cana-3476	319	23	vol	vol	NOUN
cana-3476	319	24	4	4	NUM
cana-3476	319	25	(	(	PUNCT
cana-3476	319	26	2017	2017	NUM
cana-3476	319	27	)	)	PUNCT
cana-3476	319	28	,	,	PUNCT
cana-3476	319	29	no	no	INTJ
cana-3476	319	30	.	.	NOUN
cana-3476	319	31	2	2	NUM
cana-3476	319	32	,	,	PUNCT
cana-3476	319	33	199	199	NUM
cana-3476	319	34	-	-	SYM
cana-3476	319	35	205	205	NUM
cana-3476	319	36	.	.	PUNCT
cana-3476	320	1	doi.org/10.48550/arxiv.1611.08717	doi.org/10.48550/arxiv.1611.08717	X
cana-3476	321	1	[	[	X
cana-3476	321	2	10	10	NUM
cana-3476	321	3	]	]	X
cana-3476	321	4	fethi	fethi	PROPN
cana-3476	321	5	bin	bin	PROPN
cana-3476	321	6	muhammed	muhamme	VERB
cana-3476	321	7	belgacem	belgacem	PROPN
cana-3476	321	8	,	,	PUNCT
cana-3476	321	9	ahmed	ahmed	PROPN
cana-3476	321	10	abdullatif	abdullatif	PROPN
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cana-3476	321	12	,	,	PUNCT
cana-3476	321	13	sumudu	sumudu	NOUN
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cana-3476	321	17	investigations	investigation	NOUN
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cana-3476	321	19	applications	application	NOUN
cana-3476	321	20	,	,	PUNCT
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cana-3476	321	25	and	and	CCONJ
cana-3476	321	26	stochastic	stochastic	ADJ
cana-3476	321	27	analysis	analysis	NOUN
cana-3476	321	28	,	,	PUNCT
cana-3476	321	29	vol	vol	NOUN
cana-3476	321	30	.	.	PUNCT
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cana-3476	321	32	,	,	PUNCT
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cana-3476	321	34	i	i	PROPN
cana-3476	321	35	d	d	PROPN
cana-3476	321	36	91083	91083	NUM
cana-3476	321	37	,	,	PUNCT
cana-3476	321	38	(	(	PUNCT
cana-3476	321	39	2006	2006	NUM
cana-3476	321	40	)	)	PUNCT
cana-3476	321	41	1	1	NUM
cana-3476	321	42	-	-	SYM
cana-3476	321	43	23	23	NUM
cana-3476	321	44	.	.	PUNCT
cana-3476	322	1	doi	doi	PROPN
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cana-3476	322	3	/	/	SYM
cana-3476	322	4	jamsa/2006/91083	jamsa/2006/91083	NOUN
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cana-3476	323	10	integral	integral	ADJ
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cana-3476	323	12	for	for	ADP
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cana-3476	323	16	,	,	PUNCT
cana-3476	323	17	journal	journal	NOUN
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cana-3476	323	25	(	(	PUNCT
cana-3476	323	26	2021	2021	NUM
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cana-3476	323	28	133–138	133–138	NUM
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cana-3476	324	1	doi.org/10.1016/j.jare.2020.08.016	doi.org/10.1016/j.jare.2020.08.016	X
cana-3476	325	1	[	[	X
cana-3476	325	2	12	12	NUM
cana-3476	325	3	]	]	X
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cana-3476	325	5	m.	m.	NOUN
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cana-3476	325	8	,	,	PUNCT
cana-3476	325	9	the	the	DET
cana-3476	325	10	new	new	ADJ
cana-3476	325	11	integral	integral	ADJ
cana-3476	325	12	transform	transform	NOUN
cana-3476	325	13	”	"	PUNCT
cana-3476	325	14	sawi	sawi	ADJ
cana-3476	325	15	transform	transform	NOUN
cana-3476	325	16	”	"	PUNCT
cana-3476	325	17	,	,	PUNCT
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cana-3476	325	19	in	in	ADP
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cana-3476	325	21	and	and	CCONJ
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cana-3476	325	24	,	,	PUNCT
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cana-3476	326	6	(	(	PUNCT
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cana-3476	326	8	)	)	PUNCT
cana-3476	326	9	,	,	PUNCT
cana-3476	326	10	81	81	NUM
cana-3476	326	11	-	-	SYM
cana-3476	326	12	87	87	NUM
cana-3476	326	13	.	.	PUNCT
cana-3476	327	1	[	[	X
cana-3476	327	2	13	13	NUM
cana-3476	327	3	]	]	PUNCT
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cana-3476	327	5	a.	a.	PROPN
cana-3476	327	6	mehdi	mehdi	PROPN
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cana-3476	327	9	a.kuffi	a.kuffi	PROPN
cana-3476	327	10	,	,	PUNCT
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cana-3476	327	13	,	,	PUNCT
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cana-3476	327	22	complex	complex	ADJ
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cana-3476	327	25	,	,	PUNCT
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cana-3476	327	40	)	)	PUNCT
cana-3476	327	41	,	,	PUNCT
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cana-3476	327	43	-	-	SYM
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cana-3476	327	45	.	.	PUNCT
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cana-3476	329	1	[	[	X
cana-3476	329	2	14	14	NUM
cana-3476	329	3	]	]	X
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cana-3476	330	6	(	(	PUNCT
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cana-3476	330	8	)	)	PUNCT
cana-3476	330	9	,	,	PUNCT
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cana-3476	330	11	-	-	SYM
cana-3476	330	12	1592	1592	NUM
cana-3476	330	13	.	.	PUNCT
cana-3476	331	1	doi	doi	NOUN
cana-3476	331	2	:	:	PUNCT
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cana-3476	331	4	-	-	SYM
cana-3476	331	5	030915891592	030915891592	NUM
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cana-3476	331	7	15	15	NUM
cana-3476	331	8	]	]	X
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cana-3476	331	33	,	,	PUNCT
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cana-3476	331	38	(	(	PUNCT
cana-3476	331	39	2024	2024	NUM
cana-3476	331	40	)	)	PUNCT
cana-3476	331	41	,	,	PUNCT
cana-3476	331	42	655	655	NUM
cana-3476	331	43	-	-	SYM
cana-3476	331	44	669	669	NUM
cana-3476	331	45	.	.	PUNCT
cana-3476	332	1	doi	doi	NOUN
cana-3476	332	2	:	:	PUNCT
cana-3476	332	3	10.22124	10.22124	NUM
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cana-3476	333	1	[	[	X
cana-3476	333	2	16	16	NUM
cana-3476	333	3	]	]	PUNCT
cana-3476	333	4	t.	t.	PROPN
cana-3476	333	5	g.	g.	PROPN
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cana-3476	333	29	53(2	53(2	NUM
cana-3476	333	30	)	)	PUNCT
cana-3476	333	31	,	,	PUNCT
cana-3476	333	32	(	(	PUNCT
cana-3476	333	33	2023	2023	NUM
cana-3476	333	34	)	)	PUNCT
cana-3476	333	35	,	,	PUNCT
cana-3476	333	36	151	151	NUM
cana-3476	333	37	-	-	SYM
cana-3476	333	38	160	160	NUM
cana-3476	333	39	.	.	PUNCT
cana-3476	334	1	doi.org/10.58250/jnanabha.2023.53218	doi.org/10.58250/jnanabha.2023.53218	NOUN
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cana-3476	334	3	17	17	NUM
cana-3476	334	4	]	]	PUNCT
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cana-3476	335	1	m.	m.	NOUN
cana-3476	335	2	elzaki	elzaki	PROPN
cana-3476	335	3	,	,	PUNCT
cana-3476	335	4	the	the	DET
cana-3476	335	5	new	new	ADJ
cana-3476	335	6	integral	integral	ADJ
cana-3476	335	7	transform	transform	NOUN
cana-3476	335	8	“	"	PUNCT
cana-3476	335	9	elzaki	elzaki	NOUN
cana-3476	335	10	transform	transform	NOUN
cana-3476	335	11	”	"	PUNCT
cana-3476	335	12	,	,	PUNCT
cana-3476	335	13	global	global	ADJ
cana-3476	335	14	journal	journal	NOUN
cana-3476	335	15	of	of	ADP
cana-3476	335	16	pure	pure	ADJ
cana-3476	335	17	and	and	CCONJ
cana-3476	335	18	applied	applied	ADJ
cana-3476	335	19	mathematics	mathematic	NOUN
cana-3476	335	20	,	,	PUNCT
cana-3476	335	21	vol	vol	NOUN
cana-3476	335	22	.	.	PROPN
cana-3476	335	23	7	7	NUM
cana-3476	335	24	,	,	PUNCT
cana-3476	335	25	no	no	INTJ
cana-3476	335	26	.	.	NOUN
cana-3476	335	27	1	1	NUM
cana-3476	335	28	(	(	PUNCT
cana-3476	335	29	2011	2011	NUM
cana-3476	335	30	)	)	PUNCT
cana-3476	335	31	,	,	PUNCT
cana-3476	335	32	57–64	57–64	NUM
cana-3476	335	33	https://doi.org/10.1186/1687-1847-2012-60	https://doi.org/10.1186/1687-1847-2012-60	NOUN