id	sid	tid	token	lemma	pos
cana-6219	1	1	communications	communication	NOUN
cana-6219	1	2	on	on	ADP
cana-6219	1	3	applied	apply	VERB
cana-6219	1	4	nonlinear	nonlinear	ADJ
cana-6219	1	5	analysis	analysis	NOUN
cana-6219	1	6	issn	issn	NOUN
cana-6219	1	7	:	:	PUNCT
cana-6219	1	8	1074	1074	NUM
cana-6219	1	9	-	-	PUNCT
cana-6219	1	10	133x	133x	NUM
cana-6219	1	11	vol	vol	VERB
cana-6219	1	12	32	32	NUM
cana-6219	1	13	no	no	NOUN
cana-6219	1	14	.	.	PUNCT
cana-6219	2	1	10s	10	NOUN
cana-6219	2	2	(	(	PUNCT
cana-6219	2	3	2025	2025	NUM
cana-6219	2	4	)	)	PUNCT
cana-6219	2	5	3528	3528	NUM
cana-6219	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	2	7	fractional	fractional	ADJ
cana-6219	2	8	order	order	NOUN
cana-6219	2	9	three	three	NUM
cana-6219	2	10	-	-	PUNCT
cana-6219	2	11	dimensional	dimensional	ADJ
cana-6219	2	12	generalized	generalized	ADJ
cana-6219	2	13	boundary	boundary	ADJ
cana-6219	2	14	value	value	NOUN
cana-6219	2	15	problem	problem	NOUN
cana-6219	2	16	for	for	ADP
cana-6219	2	17	rectangular	rectangular	ADJ
cana-6219	2	18	plate	plate	NOUN
cana-6219	2	19	moving	move	VERB
cana-6219	2	20	with	with	ADP
cana-6219	2	21	heat	heat	NOUN
cana-6219	2	22	source	source	NOUN
cana-6219	2	23	changdev	changdev	PROPN
cana-6219	2	24	b.	b.	PROPN
cana-6219	2	25	kothule1	kothule1	PROPN
cana-6219	2	26	,	,	PUNCT
cana-6219	2	27	tarachand	tarachand	PROPN
cana-6219	2	28	l.	l.	PROPN
cana-6219	2	29	holambe2	holambe2	PROPN
cana-6219	2	30	,	,	PUNCT
cana-6219	2	31	satish	satish	PROPN
cana-6219	2	32	g.	g.	PROPN
cana-6219	2	33	khavale1	khavale1	PROPN
cana-6219	2	34	*	*	PROPN
cana-6219	2	35	,	,	PUNCT
cana-6219	2	36	bhausaheb	bhausaheb	PROPN
cana-6219	2	37	r.	r.	PROPN
cana-6219	2	38	sontakke3	sontakke3	PROPN
cana-6219	3	1	1,3	1,3	NUM
cana-6219	3	2	department	department	NOUN
cana-6219	3	3	of	of	ADP
cana-6219	3	4	mathematics	mathematic	NOUN
cana-6219	3	5	,	,	PUNCT
cana-6219	3	6	pratishthan	pratishthan	PROPN
cana-6219	3	7	mahavidyalaya	mahavidyalaya	PROPN
cana-6219	3	8	paithan	paithan	NOUN
cana-6219	3	9	,	,	PUNCT
cana-6219	3	10	chhatrapati	chhatrapati	NOUN
cana-6219	3	11	sambhajinagar	sambhajinagar	NOUN
cana-6219	3	12	(	(	PUNCT
cana-6219	3	13	m.s	m.s	PROPN
cana-6219	3	14	.	.	PROPN
cana-6219	3	15	)	)	PUNCT
cana-6219	4	1	india	india	PROPN
cana-6219	4	2	2	2	NUM
cana-6219	4	3	department	department	NOUN
cana-6219	4	4	of	of	ADP
cana-6219	4	5	mathematics	mathematics	PROPN
cana-6219	4	6	,	,	PUNCT
cana-6219	4	7	kai	kai	PROPN
cana-6219	4	8	.	.	PROPN
cana-6219	5	1	shankarrao	shankarrao	PROPN
cana-6219	5	2	gutte	gutte	PROPN
cana-6219	5	3	acs	acs	PROPN
cana-6219	5	4	college	college	PROPN
cana-6219	5	5	,	,	PUNCT
cana-6219	5	6	dharmapuri	dharmapuri	PROPN
cana-6219	5	7	,	,	PUNCT
cana-6219	5	8	beed	be	VERB
cana-6219	5	9	,	,	PUNCT
cana-6219	5	10	(	(	PUNCT
cana-6219	5	11	m.s	m.s	PROPN
cana-6219	5	12	.	.	PROPN
cana-6219	5	13	)	)	PUNCT
cana-6219	6	1	india	india	PROPN
cana-6219	6	2	1department	1department	NUM
cana-6219	6	3	of	of	ADP
cana-6219	6	4	mathematics	mathematic	NOUN
cana-6219	6	5	,	,	PUNCT
cana-6219	6	6	statistics	statistic	NOUN
cana-6219	6	7	&	&	CCONJ
cana-6219	6	8	computer	computer	PROPN
cana-6219	6	9	science	science	NOUN
cana-6219	6	10	,	,	PUNCT
cana-6219	6	11	chetna	chetna	PROPN
cana-6219	6	12	’s	’s	PART
cana-6219	6	13	hazarimal	hazarimal	NOUN
cana-6219	6	14	somani	somani	PROPN
cana-6219	6	15	college	college	PROPN
cana-6219	6	16	of	of	ADP
cana-6219	6	17	commerce	commerce	PROPN
cana-6219	6	18	&	&	CCONJ
cana-6219	6	19	economics	economics	PROPN
cana-6219	6	20	,	,	PUNCT
cana-6219	6	21	smt	smt	PROPN
cana-6219	6	22	.	.	PUNCT
cana-6219	7	1	kusumtai	kusumtai	PROPN
cana-6219	7	2	chaudhari	chaudhari	PROPN
cana-6219	7	3	college	college	PROPN
cana-6219	7	4	of	of	ADP
cana-6219	7	5	arts	art	NOUN
cana-6219	7	6	,	,	PUNCT
cana-6219	7	7	bandra(e	bandra(e	NOUN
cana-6219	7	8	)	)	PUNCT
cana-6219	7	9	,	,	PUNCT
cana-6219	7	10	mumbai	mumbai	PROPN
cana-6219	7	11	,	,	PUNCT
cana-6219	7	12	(	(	PUNCT
cana-6219	7	13	m.s	m.s	PROPN
cana-6219	7	14	.	.	PROPN
cana-6219	7	15	)	)	PUNCT
cana-6219	8	1	india	india	PROPN
cana-6219	8	2	kothulepatil1995@gmail.com	kothulepatil1995@gmail.com	PROPN
cana-6219	8	3	,	,	PUNCT
cana-6219	8	4	tarachandholambe@gmail.com	tarachandholambe@gmail.com	PROPN
cana-6219	8	5	,	,	PUNCT
cana-6219	8	6	khavalesatish8@gmail.com	khavalesatish8@gmail.com	X
cana-6219	8	7	,	,	PUNCT
cana-6219	8	8	satish.khavale@chetanacollege.in	satish.khavale@chetanacollege.in	PROPN
cana-6219	8	9	article	article	NOUN
cana-6219	8	10	history	history	NOUN
cana-6219	8	11	:	:	PUNCT
cana-6219	8	12	received	receive	VERB
cana-6219	8	13	:	:	PUNCT
cana-6219	8	14	19	19	NUM
cana-6219	8	15	-	-	PUNCT
cana-6219	8	16	09	09	NUM
cana-6219	8	17	-	-	PUNCT
cana-6219	8	18	2024	2024	NUM
cana-6219	8	19	revised	revise	VERB
cana-6219	8	20	:	:	PUNCT
cana-6219	8	21	24	24	NUM
cana-6219	8	22	-	-	SYM
cana-6219	8	23	10	10	NUM
cana-6219	8	24	-	-	PUNCT
cana-6219	8	25	2024	2024	NUM
cana-6219	8	26	accepted	accept	VERB
cana-6219	8	27	:	:	PUNCT
cana-6219	8	28	11	11	NUM
cana-6219	8	29	-	-	SYM
cana-6219	8	30	11	11	NUM
cana-6219	8	31	-	-	PUNCT
cana-6219	8	32	2025	2025	NUM
cana-6219	8	33	abstract	abstract	NOUN
cana-6219	8	34	:	:	PUNCT
cana-6219	8	35	this	this	DET
cana-6219	8	36	paper	paper	NOUN
cana-6219	8	37	investigates	investigate	VERB
cana-6219	8	38	a	a	DET
cana-6219	8	39	three	three	NUM
cana-6219	8	40	-	-	PUNCT
cana-6219	8	41	dimensional	dimensional	ADJ
cana-6219	8	42	generalized	generalized	ADJ
cana-6219	8	43	boundary	boundary	ADJ
cana-6219	8	44	value	value	NOUN
cana-6219	8	45	problem	problem	NOUN
cana-6219	8	46	(	(	PUNCT
cana-6219	8	47	bvp	bvp	PROPN
cana-6219	8	48	)	)	PUNCT
cana-6219	8	49	for	for	ADP
cana-6219	8	50	a	a	DET
cana-6219	8	51	rectangular	rectangular	ADJ
cana-6219	8	52	plate	plate	NOUN
cana-6219	8	53	subjected	subject	VERB
cana-6219	8	54	to	to	ADP
cana-6219	8	55	a	a	DET
cana-6219	8	56	moving	move	VERB
cana-6219	8	57	heat	heat	NOUN
cana-6219	8	58	source	source	NOUN
cana-6219	8	59	within	within	ADP
cana-6219	8	60	the	the	DET
cana-6219	8	61	framework	framework	NOUN
cana-6219	8	62	of	of	ADP
cana-6219	8	63	fractional	fractional	ADJ
cana-6219	8	64	-	-	PUNCT
cana-6219	8	65	order	order	NOUN
cana-6219	8	66	thermoelasticity	thermoelasticity	NOUN
cana-6219	8	67	.	.	PUNCT
cana-6219	9	1	the	the	DET
cana-6219	9	2	study	study	NOUN
cana-6219	9	3	employs	employ	VERB
cana-6219	9	4	a	a	DET
cana-6219	9	5	combination	combination	NOUN
cana-6219	9	6	of	of	ADP
cana-6219	9	7	laplace	laplace	NOUN
cana-6219	9	8	and	and	CCONJ
cana-6219	9	9	double	double	ADJ
cana-6219	9	10	fourier	fourier	NOUN
cana-6219	9	11	transform	transform	VERB
cana-6219	9	12	techniques	technique	NOUN
cana-6219	9	13	to	to	PART
cana-6219	9	14	obtain	obtain	VERB
cana-6219	9	15	analytical	analytical	ADJ
cana-6219	9	16	solutions	solution	NOUN
cana-6219	9	17	in	in	ADP
cana-6219	9	18	the	the	DET
cana-6219	9	19	transform	transform	NOUN
cana-6219	9	20	domain	domain	NOUN
cana-6219	9	21	.	.	PUNCT
cana-6219	10	1	these	these	PRON
cana-6219	10	2	are	be	AUX
cana-6219	10	3	subsequently	subsequently	ADV
cana-6219	10	4	inverted	invert	VERB
cana-6219	10	5	using	use	VERB
cana-6219	10	6	numerical	numerical	ADJ
cana-6219	10	7	methods	method	NOUN
cana-6219	10	8	,	,	PUNCT
cana-6219	10	9	including	include	VERB
cana-6219	10	10	fourier	fourier	NOUN
cana-6219	10	11	expansion	expansion	NOUN
cana-6219	10	12	and	and	CCONJ
cana-6219	10	13	riemann	riemann	PROPN
cana-6219	10	14	-	-	PUNCT
cana-6219	10	15	sum	sum	NOUN
cana-6219	10	16	approximation	approximation	NOUN
cana-6219	10	17	,	,	PUNCT
cana-6219	10	18	to	to	PART
cana-6219	10	19	derive	derive	VERB
cana-6219	10	20	physical	physical	ADJ
cana-6219	10	21	field	field	NOUN
cana-6219	10	22	quantities	quantity	NOUN
cana-6219	10	23	such	such	ADJ
cana-6219	10	24	as	as	ADP
cana-6219	10	25	temperature	temperature	NOUN
cana-6219	10	26	increment	increment	NOUN
cana-6219	10	27	,	,	PUNCT
cana-6219	10	28	stress	stress	NOUN
cana-6219	10	29	,	,	PUNCT
cana-6219	10	30	strain	strain	NOUN
cana-6219	10	31	,	,	PUNCT
cana-6219	10	32	and	and	CCONJ
cana-6219	10	33	displacement	displacement	NOUN
cana-6219	10	34	.	.	PUNCT
cana-6219	11	1	the	the	DET
cana-6219	11	2	model	model	NOUN
cana-6219	11	3	accounts	account	VERB
cana-6219	11	4	for	for	ADP
cana-6219	11	5	the	the	DET
cana-6219	11	6	memory	memory	NOUN
cana-6219	11	7	and	and	CCONJ
cana-6219	11	8	non	non	ADJ
cana-6219	11	9	-	-	ADJ
cana-6219	11	10	local	local	ADJ
cana-6219	11	11	effects	effect	NOUN
cana-6219	11	12	characteristic	characteristic	ADJ
cana-6219	11	13	of	of	ADP
cana-6219	11	14	fractional	fractional	ADJ
cana-6219	11	15	calculus	calculus	NOUN
cana-6219	11	16	,	,	PUNCT
cana-6219	11	17	providing	provide	VERB
cana-6219	11	18	a	a	DET
cana-6219	11	19	more	more	ADV
cana-6219	11	20	accurate	accurate	ADJ
cana-6219	11	21	description	description	NOUN
cana-6219	11	22	of	of	ADP
cana-6219	11	23	thermal	thermal	ADJ
cana-6219	11	24	and	and	CCONJ
cana-6219	11	25	mechanical	mechanical	ADJ
cana-6219	11	26	responses	response	NOUN
cana-6219	11	27	.	.	PUNCT
cana-6219	12	1	numerical	numerical	ADJ
cana-6219	12	2	results	result	NOUN
cana-6219	12	3	are	be	AUX
cana-6219	12	4	presented	present	VERB
cana-6219	12	5	for	for	ADP
cana-6219	12	6	various	various	ADJ
cana-6219	12	7	fractional	fractional	ADJ
cana-6219	12	8	orders	order	NOUN
cana-6219	12	9	and	and	CCONJ
cana-6219	12	10	heat	heat	NOUN
cana-6219	12	11	source	source	NOUN
cana-6219	12	12	velocities	velocity	NOUN
cana-6219	12	13	,	,	PUNCT
cana-6219	12	14	demonstrating	demonstrate	VERB
cana-6219	12	15	the	the	DET
cana-6219	12	16	significant	significant	ADJ
cana-6219	12	17	influence	influence	NOUN
cana-6219	12	18	of	of	ADP
cana-6219	12	19	these	these	DET
cana-6219	12	20	parameters	parameter	NOUN
cana-6219	12	21	on	on	ADP
cana-6219	12	22	the	the	DET
cana-6219	12	23	physical	physical	ADJ
cana-6219	12	24	behaviour	behaviour	NOUN
cana-6219	12	25	of	of	ADP
cana-6219	12	26	the	the	DET
cana-6219	12	27	plate	plate	NOUN
cana-6219	12	28	.	.	PUNCT
cana-6219	13	1	the	the	DET
cana-6219	13	2	findings	finding	NOUN
cana-6219	13	3	have	have	VERB
cana-6219	13	4	direct	direct	ADJ
cana-6219	13	5	implications	implication	NOUN
cana-6219	13	6	for	for	ADP
cana-6219	13	7	materials	material	NOUN
cana-6219	13	8	and	and	CCONJ
cana-6219	13	9	processes	process	NOUN
cana-6219	13	10	involving	involve	VERB
cana-6219	13	11	transient	transient	ADJ
cana-6219	13	12	thermal	thermal	ADJ
cana-6219	13	13	loading	loading	NOUN
cana-6219	13	14	,	,	PUNCT
cana-6219	13	15	such	such	ADJ
cana-6219	13	16	as	as	ADP
cana-6219	13	17	in	in	ADP
cana-6219	13	18	aerospace	aerospace	NOUN
cana-6219	13	19	,	,	PUNCT
cana-6219	13	20	electronics	electronic	NOUN
cana-6219	13	21	cooling	cooling	NOUN
cana-6219	13	22	,	,	PUNCT
cana-6219	13	23	and	and	CCONJ
cana-6219	13	24	advanced	advanced	ADJ
cana-6219	13	25	manufacturing	manufacturing	NOUN
cana-6219	13	26	systems	system	NOUN
cana-6219	13	27	.	.	PUNCT
cana-6219	14	1	introduction	introduction	NOUN
cana-6219	14	2	:	:	PUNCT
cana-6219	14	3	in	in	ADP
cana-6219	14	4	recent	recent	ADJ
cana-6219	14	5	years	year	NOUN
cana-6219	14	6	,	,	PUNCT
cana-6219	14	7	fractional	fractional	ADJ
cana-6219	14	8	-	-	PUNCT
cana-6219	14	9	order	order	NOUN
cana-6219	14	10	thermoelasticity	thermoelasticity	NOUN
cana-6219	14	11	has	have	AUX
cana-6219	14	12	emerged	emerge	VERB
cana-6219	14	13	as	as	ADP
cana-6219	14	14	a	a	DET
cana-6219	14	15	powerful	powerful	ADJ
cana-6219	14	16	framework	framework	NOUN
cana-6219	14	17	for	for	ADP
cana-6219	14	18	modelling	model	VERB
cana-6219	14	19	materials	material	NOUN
cana-6219	14	20	exhibiting	exhibit	VERB
cana-6219	14	21	memory	memory	NOUN
cana-6219	14	22	and	and	CCONJ
cana-6219	14	23	non	non	ADJ
cana-6219	14	24	-	-	ADJ
cana-6219	14	25	local	local	ADJ
cana-6219	14	26	effects	effect	NOUN
cana-6219	14	27	,	,	PUNCT
cana-6219	14	28	where	where	SCONJ
cana-6219	14	29	traditional	traditional	ADJ
cana-6219	14	30	integer	integer	NOUN
cana-6219	14	31	-	-	PUNCT
cana-6219	14	32	order	order	NOUN
cana-6219	14	33	theories	theory	NOUN
cana-6219	14	34	fail	fail	VERB
cana-6219	14	35	to	to	PART
cana-6219	14	36	capture	capture	VERB
cana-6219	14	37	the	the	DET
cana-6219	14	38	true	true	ADJ
cana-6219	14	39	dynamic	dynamic	ADJ
cana-6219	14	40	response	response	NOUN
cana-6219	14	41	.	.	PUNCT
cana-6219	15	1	the	the	DET
cana-6219	15	2	present	present	ADJ
cana-6219	15	3	study	study	NOUN
cana-6219	15	4	extends	extend	VERB
cana-6219	15	5	the	the	DET
cana-6219	15	6	generalized	generalized	ADJ
cana-6219	15	7	thermoelastic	thermoelastic	ADJ
cana-6219	15	8	theory	theory	NOUN
cana-6219	15	9	to	to	ADP
cana-6219	15	10	a	a	DET
cana-6219	15	11	three	three	NUM
cana-6219	15	12	-	-	PUNCT
cana-6219	15	13	dimensional	dimensional	ADJ
cana-6219	15	14	rectangular	rectangular	ADJ
cana-6219	15	15	plate	plate	NOUN
cana-6219	15	16	subjected	subject	VERB
cana-6219	15	17	to	to	ADP
cana-6219	15	18	a	a	DET
cana-6219	15	19	moving	move	VERB
cana-6219	15	20	heat	heat	NOUN
cana-6219	15	21	source	source	NOUN
cana-6219	15	22	,	,	PUNCT
cana-6219	15	23	using	use	VERB
cana-6219	15	24	fractional	fractional	ADJ
cana-6219	15	25	calculus	calculus	NOUN
cana-6219	15	26	.	.	PUNCT
cana-6219	16	1	earlier	early	ADJ
cana-6219	16	2	works	work	VERB
cana-6219	16	3	by	by	ADP
cana-6219	16	4	ezzat	ezzat	PROPN
cana-6219	16	5	,	,	PUNCT
cana-6219	16	6	youssef	youssef	PROPN
cana-6219	16	7	,	,	PUNCT
cana-6219	16	8	and	and	CCONJ
cana-6219	16	9	gaikwad	gaikwad	NOUN
cana-6219	16	10	established	establish	VERB
cana-6219	16	11	the	the	DET
cana-6219	16	12	groundwork	groundwork	NOUN
cana-6219	16	13	for	for	ADP
cana-6219	16	14	fractional	fractional	ADJ
cana-6219	16	15	thermoelastic	thermoelastic	ADJ
cana-6219	16	16	behaviour	behaviour	NOUN
cana-6219	16	17	in	in	ADP
cana-6219	16	18	simpler	simple	ADJ
cana-6219	16	19	geometries	geometry	NOUN
cana-6219	16	20	.	.	PUNCT
cana-6219	17	1	this	this	DET
cana-6219	17	2	research	research	NOUN
cana-6219	17	3	aims	aim	VERB
cana-6219	17	4	to	to	PART
cana-6219	17	5	advance	advance	VERB
cana-6219	17	6	that	that	SCONJ
cana-6219	17	7	understanding	understanding	NOUN
cana-6219	17	8	by	by	ADP
cana-6219	17	9	solving	solve	VERB
cana-6219	17	10	a	a	DET
cana-6219	17	11	fractional	fractional	ADJ
cana-6219	17	12	-	-	PUNCT
cana-6219	17	13	order	order	NOUN
cana-6219	17	14	boundary	boundary	ADJ
cana-6219	17	15	value	value	NOUN
cana-6219	17	16	problem	problem	NOUN
cana-6219	17	17	(	(	PUNCT
cana-6219	17	18	bvp	bvp	PROPN
cana-6219	17	19	)	)	PUNCT
cana-6219	17	20	that	that	PRON
cana-6219	17	21	accounts	account	VERB
cana-6219	17	22	for	for	ADP
cana-6219	17	23	transient	transient	ADJ
cana-6219	17	24	thermal	thermal	ADJ
cana-6219	17	25	and	and	CCONJ
cana-6219	17	26	mechanical	mechanical	ADJ
cana-6219	17	27	interactions	interaction	NOUN
cana-6219	17	28	in	in	ADP
cana-6219	17	29	a	a	DET
cana-6219	17	30	continuously	continuously	ADV
cana-6219	17	31	moving	move	VERB
cana-6219	17	32	thermal	thermal	ADJ
cana-6219	17	33	environment	environment	NOUN
cana-6219	17	34	.	.	PUNCT
cana-6219	18	1	the	the	DET
cana-6219	18	2	results	result	NOUN
cana-6219	18	3	provide	provide	VERB
cana-6219	18	4	valuable	valuable	ADJ
cana-6219	18	5	insights	insight	NOUN
cana-6219	18	6	for	for	ADP
cana-6219	18	7	engineering	engineering	NOUN
cana-6219	18	8	systems	system	NOUN
cana-6219	18	9	involving	involve	VERB
cana-6219	18	10	rapid	rapid	ADJ
cana-6219	18	11	thermal	thermal	ADJ
cana-6219	18	12	loading	loading	NOUN
cana-6219	18	13	,	,	PUNCT
cana-6219	18	14	such	such	ADJ
cana-6219	18	15	as	as	ADP
cana-6219	18	16	in	in	ADP
cana-6219	18	17	aerospace	aerospace	NOUN
cana-6219	18	18	components	component	NOUN
cana-6219	18	19	,	,	PUNCT
cana-6219	18	20	electronic	electronic	ADJ
cana-6219	18	21	cooling	cooling	NOUN
cana-6219	18	22	,	,	PUNCT
cana-6219	18	23	and	and	CCONJ
cana-6219	18	24	high	high	ADJ
cana-6219	18	25	-	-	PUNCT
cana-6219	18	26	precision	precision	NOUN
cana-6219	18	27	manufacturing	manufacturing	NOUN
cana-6219	18	28	.	.	PUNCT
cana-6219	19	1	objectives	objective	NOUN
cana-6219	19	2	:	:	PUNCT
cana-6219	19	3	•	•	NOUN
cana-6219	19	4	to	to	PART
cana-6219	19	5	formulate	formulate	VERB
cana-6219	19	6	and	and	CCONJ
cana-6219	19	7	analyse	analyse	VERB
cana-6219	19	8	a	a	DET
cana-6219	19	9	three	three	NUM
cana-6219	19	10	-	-	PUNCT
cana-6219	19	11	dimensional	dimensional	ADJ
cana-6219	19	12	generalized	generalized	ADJ
cana-6219	19	13	fractional	fractional	ADJ
cana-6219	19	14	-	-	PUNCT
cana-6219	19	15	order	order	NOUN
cana-6219	19	16	boundary	boundary	ADJ
cana-6219	19	17	value	value	NOUN
cana-6219	19	18	problem	problem	NOUN
cana-6219	19	19	for	for	ADP
cana-6219	19	20	a	a	DET
cana-6219	19	21	rectangular	rectangular	ADJ
cana-6219	19	22	plate	plate	NOUN
cana-6219	19	23	under	under	ADP
cana-6219	19	24	a	a	DET
cana-6219	19	25	moving	move	VERB
cana-6219	19	26	heat	heat	NOUN
cana-6219	19	27	source	source	NOUN
cana-6219	19	28	.	.	PUNCT
cana-6219	20	1	•	•	NUM
cana-6219	20	2	to	to	PART
cana-6219	20	3	apply	apply	VERB
cana-6219	20	4	laplace	laplace	NOUN
cana-6219	20	5	and	and	CCONJ
cana-6219	20	6	double	double	ADJ
cana-6219	20	7	fourier	fourier	NOUN
cana-6219	20	8	transform	transform	VERB
cana-6219	20	9	techniques	technique	NOUN
cana-6219	20	10	to	to	PART
cana-6219	20	11	derive	derive	VERB
cana-6219	20	12	analytical	analytical	ADJ
cana-6219	20	13	expressions	expression	NOUN
cana-6219	20	14	for	for	ADP
cana-6219	20	15	temperature	temperature	NOUN
cana-6219	20	16	,	,	PUNCT
cana-6219	20	17	stress	stress	NOUN
cana-6219	20	18	,	,	PUNCT
cana-6219	20	19	strain	strain	NOUN
cana-6219	20	20	,	,	PUNCT
cana-6219	20	21	and	and	CCONJ
cana-6219	20	22	displacement	displacement	ADJ
cana-6219	20	23	fields	field	NOUN
cana-6219	20	24	.	.	PUNCT
cana-6219	21	1	•	•	X
cana-6219	21	2	to	to	PART
cana-6219	21	3	evaluate	evaluate	VERB
cana-6219	21	4	the	the	DET
cana-6219	21	5	influence	influence	NOUN
cana-6219	21	6	of	of	ADP
cana-6219	21	7	fractional	fractional	ADJ
cana-6219	21	8	order	order	NOUN
cana-6219	21	9	(	(	PUNCT
cana-6219	21	10	α	α	NOUN
cana-6219	21	11	)	)	PUNCT
cana-6219	21	12	,	,	PUNCT
cana-6219	21	13	heat	heat	NOUN
cana-6219	21	14	source	source	NOUN
cana-6219	21	15	velocity	velocity	NOUN
cana-6219	21	16	(	(	PUNCT
cana-6219	21	17	ν	ν	NOUN
cana-6219	21	18	)	)	PUNCT
cana-6219	21	19	,	,	PUNCT
cana-6219	21	20	and	and	CCONJ
cana-6219	21	21	time	time	NOUN
cana-6219	21	22	(	(	PUNCT
cana-6219	21	23	t	t	NOUN
cana-6219	21	24	)	)	PUNCT
cana-6219	21	25	on	on	ADP
cana-6219	21	26	thermoelastic	thermoelastic	ADJ
cana-6219	21	27	field	field	NOUN
cana-6219	21	28	quantities	quantity	NOUN
cana-6219	21	29	.	.	PUNCT
cana-6219	22	1	•	•	NUM
cana-6219	22	2	to	to	PART
cana-6219	22	3	validate	validate	VERB
cana-6219	22	4	the	the	DET
cana-6219	22	5	significance	significance	NOUN
cana-6219	22	6	of	of	ADP
cana-6219	22	7	fractional	fractional	ADJ
cana-6219	22	8	-	-	PUNCT
cana-6219	22	9	order	order	NOUN
cana-6219	22	10	parameters	parameter	NOUN
cana-6219	22	11	in	in	ADP
cana-6219	22	12	accurately	accurately	ADV
cana-6219	22	13	describing	describe	VERB
cana-6219	22	14	memory	memory	NOUN
cana-6219	22	15	-	-	PUNCT
cana-6219	22	16	dependent	dependent	ADJ
cana-6219	22	17	and	and	CCONJ
cana-6219	22	18	non	non	ADJ
cana-6219	22	19	-	-	ADJ
cana-6219	22	20	local	local	ADJ
cana-6219	22	21	thermoelastic	thermoelastic	ADJ
cana-6219	22	22	effects	effect	NOUN
cana-6219	22	23	.	.	PUNCT
cana-6219	23	1	methods	method	NOUN
cana-6219	23	2	:	:	PUNCT
cana-6219	23	3	the	the	DET
cana-6219	23	4	model	model	NOUN
cana-6219	23	5	is	be	AUX
cana-6219	23	6	developed	develop	VERB
cana-6219	23	7	under	under	ADP
cana-6219	23	8	the	the	DET
cana-6219	23	9	assumptions	assumption	NOUN
cana-6219	23	10	of	of	ADP
cana-6219	23	11	homogeneous	homogeneous	ADJ
cana-6219	23	12	and	and	CCONJ
cana-6219	23	13	isotropic	isotropic	ADJ
cana-6219	23	14	material	material	NOUN
cana-6219	23	15	behaviour	behaviour	NOUN
cana-6219	23	16	using	use	VERB
cana-6219	23	17	the	the	DET
cana-6219	23	18	generalized	generalized	ADJ
cana-6219	23	19	thermoelasticity	thermoelasticity	NOUN
cana-6219	23	20	theory	theory	NOUN
cana-6219	23	21	with	with	ADP
cana-6219	23	22	one	one	NUM
cana-6219	23	23	relaxation	relaxation	NOUN
cana-6219	23	24	time	time	NOUN
cana-6219	23	25	.	.	PUNCT
cana-6219	24	1	the	the	DET
cana-6219	24	2	governing	govern	VERB
cana-6219	24	3	equations	equation	NOUN
cana-6219	24	4	of	of	ADP
cana-6219	24	5	motion	motion	NOUN
cana-6219	24	6	,	,	PUNCT
cana-6219	24	7	heat	heat	NOUN
cana-6219	24	8	conduction	conduction	NOUN
cana-6219	24	9	,	,	PUNCT
cana-6219	24	10	and	and	CCONJ
cana-6219	24	11	constitutive	constitutive	ADJ
cana-6219	24	12	relations	relation	NOUN
cana-6219	24	13	are	be	AUX
cana-6219	24	14	mailto:kothulepatil1995@gmail.com	mailto:kothulepatil1995@gmail.com	PROPN
cana-6219	24	15	mailto:tarachandholambe@gmail.com	mailto:tarachandholambe@gmail.com	PROPN
cana-6219	24	16	mailto:khavalesatish8@gmail.com	mailto:khavalesatish8@gmail.com	X
cana-6219	24	17	mailto:satish.khavale@chetanacollege.in	mailto:satish.khavale@chetanacollege.in	PROPN
cana-6219	24	18	communications	communication	NOUN
cana-6219	24	19	on	on	ADP
cana-6219	24	20	applied	apply	VERB
cana-6219	24	21	nonlinear	nonlinear	ADJ
cana-6219	24	22	analysis	analysis	NOUN
cana-6219	24	23	issn	issn	NOUN
cana-6219	24	24	:	:	PUNCT
cana-6219	24	25	1074	1074	NUM
cana-6219	24	26	-	-	PUNCT
cana-6219	24	27	133x	133x	NUM
cana-6219	24	28	vol	vol	VERB
cana-6219	24	29	32	32	NUM
cana-6219	24	30	no	no	NOUN
cana-6219	24	31	.	.	PUNCT
cana-6219	25	1	10s	10	NOUN
cana-6219	25	2	(	(	PUNCT
cana-6219	25	3	2025	2025	NUM
cana-6219	25	4	)	)	PUNCT
cana-6219	25	5	3529	3529	NUM
cana-6219	25	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-6219	25	7	expressed	express	VERB
cana-6219	25	8	in	in	ADP
cana-6219	25	9	fractional	fractional	ADJ
cana-6219	25	10	differential	differential	NOUN
cana-6219	25	11	form	form	NOUN
cana-6219	25	12	.	.	PUNCT
cana-6219	26	1	the	the	DET
cana-6219	26	2	analytical	analytical	ADJ
cana-6219	26	3	solution	solution	NOUN
cana-6219	26	4	is	be	AUX
cana-6219	26	5	obtained	obtain	VERB
cana-6219	26	6	through	through	ADP
cana-6219	26	7	the	the	DET
cana-6219	26	8	laplace	laplace	NOUN
cana-6219	26	9	and	and	CCONJ
cana-6219	26	10	double	double	ADJ
cana-6219	26	11	fourier	fourier	NOUN
cana-6219	26	12	transforms	transform	VERB
cana-6219	26	13	for	for	ADP
cana-6219	26	14	dimensional	dimensional	ADJ
cana-6219	26	15	reduction	reduction	NOUN
cana-6219	26	16	and	and	CCONJ
cana-6219	26	17	solution	solution	NOUN
cana-6219	26	18	in	in	ADP
cana-6219	26	19	the	the	DET
cana-6219	26	20	transform	transform	NOUN
cana-6219	26	21	domain	domain	NOUN
cana-6219	26	22	.	.	PUNCT
cana-6219	27	1	also	also	ADV
cana-6219	27	2	the	the	DET
cana-6219	27	3	numerical	numerical	ADJ
cana-6219	27	4	inversion	inversion	NOUN
cana-6219	27	5	of	of	ADP
cana-6219	27	6	the	the	DET
cana-6219	27	7	transforms	transform	NOUN
cana-6219	27	8	using	use	VERB
cana-6219	27	9	fourier	fourier	ADJ
cana-6219	27	10	expansion	expansion	NOUN
cana-6219	27	11	and	and	CCONJ
cana-6219	27	12	riemann	riemann	PROPN
cana-6219	27	13	-	-	PUNCT
cana-6219	27	14	sum	sum	NOUN
cana-6219	27	15	approximation	approximation	NOUN
cana-6219	27	16	techniques	technique	NOUN
cana-6219	27	17	to	to	PART
cana-6219	27	18	obtain	obtain	VERB
cana-6219	27	19	results	result	NOUN
cana-6219	27	20	in	in	ADP
cana-6219	27	21	the	the	DET
cana-6219	27	22	physical	physical	ADJ
cana-6219	27	23	domain	domain	NOUN
cana-6219	27	24	.	.	PUNCT
cana-6219	28	1	copper	copper	NOUN
cana-6219	28	2	is	be	AUX
cana-6219	28	3	used	use	VERB
cana-6219	28	4	as	as	ADP
cana-6219	28	5	the	the	DET
cana-6219	28	6	reference	reference	NOUN
cana-6219	28	7	material	material	NOUN
cana-6219	28	8	,	,	PUNCT
cana-6219	28	9	and	and	CCONJ
cana-6219	28	10	its	its	PRON
cana-6219	28	11	standard	standard	ADJ
cana-6219	28	12	thermophysical	thermophysical	ADJ
cana-6219	28	13	constants	constant	NOUN
cana-6219	28	14	are	be	AUX
cana-6219	28	15	employed	employ	VERB
cana-6219	28	16	for	for	ADP
cana-6219	28	17	numerical	numerical	ADJ
cana-6219	28	18	simulation	simulation	PROPN
cana-6219	28	19	.	.	PUNCT
cana-6219	29	1	field	field	NOUN
cana-6219	29	2	variables	variable	NOUN
cana-6219	29	3	such	such	ADJ
cana-6219	29	4	as	as	ADP
cana-6219	29	5	temperature	temperature	NOUN
cana-6219	29	6	increment	increment	NOUN
cana-6219	29	7	,	,	PUNCT
cana-6219	29	8	stress	stress	NOUN
cana-6219	29	9	,	,	PUNCT
cana-6219	29	10	strain	strain	NOUN
cana-6219	29	11	,	,	PUNCT
cana-6219	29	12	and	and	CCONJ
cana-6219	29	13	displacement	displacement	NOUN
cana-6219	29	14	are	be	AUX
cana-6219	29	15	evaluated	evaluate	VERB
cana-6219	29	16	for	for	ADP
cana-6219	29	17	varying	vary	VERB
cana-6219	29	18	heat	heat	NOUN
cana-6219	29	19	source	source	NOUN
cana-6219	29	20	speeds	speed	NOUN
cana-6219	29	21	and	and	CCONJ
cana-6219	29	22	fractional	fractional	ADJ
cana-6219	29	23	orders	order	NOUN
cana-6219	29	24	.	.	PUNCT
cana-6219	30	1	results	result	NOUN
cana-6219	30	2	:	:	PUNCT
cana-6219	30	3	the	the	DET
cana-6219	30	4	numerical	numerical	ADJ
cana-6219	30	5	analysis	analysis	NOUN
cana-6219	30	6	demonstrates	demonstrate	VERB
cana-6219	30	7	that	that	SCONJ
cana-6219	30	8	the	the	DET
cana-6219	30	9	fractional	fractional	ADJ
cana-6219	30	10	-	-	PUNCT
cana-6219	30	11	order	order	NOUN
cana-6219	30	12	parameter	parameter	NOUN
cana-6219	30	13	,	,	PUNCT
cana-6219	30	14	heat	heat	NOUN
cana-6219	30	15	source	source	NOUN
cana-6219	30	16	velocity	velocity	NOUN
cana-6219	30	17	,	,	PUNCT
cana-6219	30	18	and	and	CCONJ
cana-6219	30	19	time	time	NOUN
cana-6219	30	20	significantly	significantly	ADV
cana-6219	30	21	influence	influence	VERB
cana-6219	30	22	the	the	DET
cana-6219	30	23	thermoelastic	thermoelastic	ADJ
cana-6219	30	24	behaviour	behaviour	NOUN
cana-6219	30	25	of	of	ADP
cana-6219	30	26	the	the	DET
cana-6219	30	27	rectangular	rectangular	ADJ
cana-6219	30	28	plate	plate	NOUN
cana-6219	30	29	.	.	PUNCT
cana-6219	31	1	the	the	DET
cana-6219	31	2	temperature	temperature	NOUN
cana-6219	31	3	increment	increment	NOUN
cana-6219	31	4	is	be	AUX
cana-6219	31	5	found	find	VERB
cana-6219	31	6	to	to	PART
cana-6219	31	7	depend	depend	VERB
cana-6219	31	8	strongly	strongly	ADV
cana-6219	31	9	on	on	ADP
cana-6219	31	10	the	the	DET
cana-6219	31	11	speed	speed	NOUN
cana-6219	31	12	of	of	ADP
cana-6219	31	13	the	the	DET
cana-6219	31	14	moving	move	VERB
cana-6219	31	15	heat	heat	NOUN
cana-6219	31	16	source	source	NOUN
cana-6219	31	17	.	.	PUNCT
cana-6219	32	1	as	as	ADP
cana-6219	32	2	the	the	DET
cana-6219	32	3	heat	heat	NOUN
cana-6219	32	4	source	source	NOUN
cana-6219	32	5	velocity	velocity	NOUN
cana-6219	32	6	increases	increase	NOUN
cana-6219	32	7	,	,	PUNCT
cana-6219	32	8	the	the	DET
cana-6219	32	9	temperature	temperature	NOUN
cana-6219	32	10	initially	initially	ADV
cana-6219	32	11	rises	rise	VERB
cana-6219	32	12	rapidly	rapidly	ADV
cana-6219	32	13	and	and	CCONJ
cana-6219	32	14	then	then	ADV
cana-6219	32	15	decreases	decrease	VERB
cana-6219	32	16	once	once	SCONJ
cana-6219	32	17	the	the	DET
cana-6219	32	18	source	source	NOUN
cana-6219	32	19	moves	move	VERB
cana-6219	32	20	beyond	beyond	ADP
cana-6219	32	21	a	a	DET
cana-6219	32	22	particular	particular	ADJ
cana-6219	32	23	region	region	NOUN
cana-6219	32	24	,	,	PUNCT
cana-6219	32	25	indicating	indicate	VERB
cana-6219	32	26	the	the	DET
cana-6219	32	27	transient	transient	ADJ
cana-6219	32	28	nature	nature	NOUN
cana-6219	32	29	of	of	ADP
cana-6219	32	30	the	the	DET
cana-6219	32	31	thermal	thermal	ADJ
cana-6219	32	32	field	field	NOUN
cana-6219	32	33	.	.	PUNCT
cana-6219	33	1	for	for	ADP
cana-6219	33	2	lower	low	ADJ
cana-6219	33	3	fractional	fractional	ADJ
cana-6219	33	4	orders	order	NOUN
cana-6219	33	5	,	,	PUNCT
cana-6219	33	6	the	the	DET
cana-6219	33	7	temperature	temperature	NOUN
cana-6219	33	8	distribution	distribution	NOUN
cana-6219	33	9	exhibits	exhibit	VERB
cana-6219	33	10	sharper	sharp	ADJ
cana-6219	33	11	gradients	gradient	NOUN
cana-6219	33	12	and	and	CCONJ
cana-6219	33	13	slower	slow	ADJ
cana-6219	33	14	diffusion	diffusion	NOUN
cana-6219	33	15	,	,	PUNCT
cana-6219	33	16	which	which	PRON
cana-6219	33	17	highlights	highlight	VERB
cana-6219	33	18	the	the	DET
cana-6219	33	19	nonlocal	nonlocal	ADJ
cana-6219	33	20	and	and	CCONJ
cana-6219	33	21	memory	memory	NOUN
cana-6219	33	22	-	-	PUNCT
cana-6219	33	23	dependent	dependent	ADJ
cana-6219	33	24	characteristics	characteristic	NOUN
cana-6219	33	25	of	of	ADP
cana-6219	33	26	fractional	fractional	ADJ
cana-6219	33	27	thermoelasticity	thermoelasticity	NOUN
cana-6219	33	28	.	.	PUNCT
cana-6219	34	1	the	the	DET
cana-6219	34	2	stress	stress	NOUN
cana-6219	34	3	distribution	distribution	NOUN
cana-6219	34	4	shows	show	VERB
cana-6219	34	5	a	a	DET
cana-6219	34	6	dual	dual	ADJ
cana-6219	34	7	-	-	PUNCT
cana-6219	34	8	phase	phase	NOUN
cana-6219	34	9	response	response	NOUN
cana-6219	34	10	:	:	PUNCT
cana-6219	34	11	it	it	PRON
cana-6219	34	12	decreases	decrease	VERB
cana-6219	34	13	initially	initially	ADV
cana-6219	34	14	with	with	ADP
cana-6219	34	15	an	an	DET
cana-6219	34	16	increase	increase	NOUN
cana-6219	34	17	in	in	ADP
cana-6219	34	18	heat	heat	NOUN
cana-6219	34	19	source	source	NOUN
cana-6219	34	20	velocity	velocity	NOUN
cana-6219	34	21	due	due	ADP
cana-6219	34	22	to	to	ADP
cana-6219	34	23	reduced	reduce	VERB
cana-6219	34	24	thermal	thermal	ADJ
cana-6219	34	25	gradients	gradient	NOUN
cana-6219	34	26	,	,	PUNCT
cana-6219	34	27	but	but	CCONJ
cana-6219	34	28	later	later	ADV
cana-6219	34	29	rises	rise	VERB
cana-6219	34	30	because	because	ADV
cana-6219	34	31	of	of	ADP
cana-6219	34	32	rapid	rapid	ADJ
cana-6219	34	33	cooling	cool	VERB
cana-6219	34	34	and	and	CCONJ
cana-6219	34	35	thermal	thermal	ADJ
cana-6219	34	36	mismatch	mismatch	NOUN
cana-6219	34	37	effects	effect	NOUN
cana-6219	34	38	.	.	PUNCT
cana-6219	35	1	similarly	similarly	ADV
cana-6219	35	2	,	,	PUNCT
cana-6219	35	3	the	the	DET
cana-6219	35	4	displacement	displacement	ADJ
cana-6219	35	5	component	component	NOUN
cana-6219	35	6	along	along	ADP
cana-6219	35	7	the	the	DET
cana-6219	35	8	x	x	ADJ
cana-6219	35	9	-	-	ADJ
cana-6219	35	10	axis	axis	ADJ
cana-6219	35	11	decreases	decrease	NOUN
cana-6219	35	12	with	with	ADP
cana-6219	35	13	increasing	increase	VERB
cana-6219	35	14	source	source	NOUN
cana-6219	35	15	velocity	velocity	NOUN
cana-6219	35	16	,	,	PUNCT
cana-6219	35	17	showing	show	VERB
cana-6219	35	18	that	that	SCONJ
cana-6219	35	19	higher	high	ADJ
cana-6219	35	20	velocities	velocity	NOUN
cana-6219	35	21	allow	allow	VERB
cana-6219	35	22	less	less	ADJ
cana-6219	35	23	time	time	NOUN
cana-6219	35	24	for	for	ADP
cana-6219	35	25	thermal	thermal	ADJ
cana-6219	35	26	expansion	expansion	NOUN
cana-6219	35	27	,	,	PUNCT
cana-6219	35	28	resulting	result	VERB
cana-6219	35	29	in	in	ADP
cana-6219	35	30	smaller	small	ADJ
cana-6219	35	31	mechanical	mechanical	ADJ
cana-6219	35	32	deformation	deformation	NOUN
cana-6219	35	33	.	.	PUNCT
cana-6219	36	1	spatially	spatially	ADV
cana-6219	36	2	,	,	PUNCT
cana-6219	36	3	the	the	DET
cana-6219	36	4	effects	effect	NOUN
cana-6219	36	5	are	be	AUX
cana-6219	36	6	more	more	ADV
cana-6219	36	7	prominent	prominent	ADJ
cana-6219	36	8	near	near	ADP
cana-6219	36	9	the	the	DET
cana-6219	36	10	centre	centre	NOUN
cana-6219	36	11	(	(	PUNCT
cana-6219	36	12	y	y	NOUN
cana-6219	36	13	=	=	SYM
cana-6219	36	14	z	z	NOUN
cana-6219	36	15	=	=	NOUN
cana-6219	36	16	0	0	NUM
cana-6219	36	17	)	)	PUNCT
cana-6219	36	18	due	due	ADP
cana-6219	36	19	to	to	ADP
cana-6219	36	20	direct	direct	ADJ
cana-6219	36	21	exposure	exposure	NOUN
cana-6219	36	22	to	to	ADP
cana-6219	36	23	the	the	DET
cana-6219	36	24	heat	heat	NOUN
cana-6219	36	25	source	source	NOUN
cana-6219	36	26	,	,	PUNCT
cana-6219	36	27	while	while	SCONJ
cana-6219	36	28	off	off	ADP
cana-6219	36	29	-	-	PUNCT
cana-6219	36	30	centre	centre	NOUN
cana-6219	36	31	regions	region	NOUN
cana-6219	36	32	(	(	PUNCT
cana-6219	36	33	y	y	NOUN
cana-6219	36	34	=	=	SYM
cana-6219	36	35	z	z	NOUN
cana-6219	36	36	=	=	SYM
cana-6219	36	37	0.5	0.5	NUM
cana-6219	36	38	)	)	PUNCT
cana-6219	36	39	experience	experience	NOUN
cana-6219	36	40	attenuated	attenuate	VERB
cana-6219	36	41	responses	response	NOUN
cana-6219	36	42	.	.	PUNCT
cana-6219	37	1	these	these	DET
cana-6219	37	2	results	result	NOUN
cana-6219	37	3	collectively	collectively	ADV
cana-6219	37	4	confirm	confirm	VERB
cana-6219	37	5	that	that	SCONJ
cana-6219	37	6	fractional	fractional	ADJ
cana-6219	37	7	-	-	PUNCT
cana-6219	37	8	order	order	NOUN
cana-6219	37	9	modelling	modelling	NOUN
cana-6219	37	10	provides	provide	VERB
cana-6219	37	11	deeper	deep	ADJ
cana-6219	37	12	insight	insight	NOUN
cana-6219	37	13	into	into	ADP
cana-6219	37	14	the	the	DET
cana-6219	37	15	coupled	couple	VERB
cana-6219	37	16	thermal	thermal	ADJ
cana-6219	37	17	and	and	CCONJ
cana-6219	37	18	mechanical	mechanical	ADJ
cana-6219	37	19	behaviour	behaviour	NOUN
cana-6219	37	20	of	of	ADP
cana-6219	37	21	materials	material	NOUN
cana-6219	37	22	under	under	ADP
cana-6219	37	23	moving	move	VERB
cana-6219	37	24	heat	heat	NOUN
cana-6219	37	25	loads	load	NOUN
cana-6219	37	26	.	.	PUNCT
cana-6219	38	1	conclusions	conclusion	NOUN
cana-6219	38	2	:	:	PUNCT
cana-6219	38	3	the	the	DET
cana-6219	38	4	present	present	ADJ
cana-6219	38	5	investigation	investigation	NOUN
cana-6219	38	6	establishes	establish	VERB
cana-6219	38	7	that	that	SCONJ
cana-6219	38	8	the	the	DET
cana-6219	38	9	fractional	fractional	ADJ
cana-6219	38	10	-	-	PUNCT
cana-6219	38	11	order	order	NOUN
cana-6219	38	12	generalized	generalize	VERB
cana-6219	38	13	thermoelastic	thermoelastic	ADJ
cana-6219	38	14	model	model	NOUN
cana-6219	38	15	effectively	effectively	ADV
cana-6219	38	16	captures	capture	VERB
cana-6219	38	17	the	the	DET
cana-6219	38	18	nonlocal	nonlocal	ADJ
cana-6219	38	19	and	and	CCONJ
cana-6219	38	20	memory	memory	NOUN
cana-6219	38	21	-	-	PUNCT
cana-6219	38	22	dependent	dependent	ADJ
cana-6219	38	23	behavior	behavior	NOUN
cana-6219	38	24	of	of	ADP
cana-6219	38	25	materials	material	NOUN
cana-6219	38	26	subjected	subject	VERB
cana-6219	38	27	to	to	ADP
cana-6219	38	28	a	a	DET
cana-6219	38	29	moving	move	VERB
cana-6219	38	30	heat	heat	NOUN
cana-6219	38	31	source	source	NOUN
cana-6219	38	32	.	.	PUNCT
cana-6219	39	1	the	the	DET
cana-6219	39	2	study	study	NOUN
cana-6219	39	3	concludes	conclude	VERB
cana-6219	39	4	that	that	SCONJ
cana-6219	39	5	the	the	DET
cana-6219	39	6	fractionalorder	fractionalorder	PROPN
cana-6219	39	7	parameter	parameter	NOUN
cana-6219	39	8	(	(	PUNCT
cana-6219	39	9	α	α	NOUN
cana-6219	39	10	)	)	PUNCT
cana-6219	39	11	,	,	PUNCT
cana-6219	39	12	heat	heat	NOUN
cana-6219	39	13	source	source	NOUN
cana-6219	39	14	velocity	velocity	NOUN
cana-6219	39	15	,	,	PUNCT
cana-6219	39	16	and	and	CCONJ
cana-6219	39	17	time	time	NOUN
cana-6219	39	18	play	play	VERB
cana-6219	39	19	vital	vital	ADJ
cana-6219	39	20	roles	role	NOUN
cana-6219	39	21	in	in	ADP
cana-6219	39	22	determining	determine	VERB
cana-6219	39	23	temperature	temperature	NOUN
cana-6219	39	24	,	,	PUNCT
cana-6219	39	25	displacement	displacement	NOUN
cana-6219	39	26	,	,	PUNCT
cana-6219	39	27	and	and	CCONJ
cana-6219	39	28	stress	stress	NOUN
cana-6219	39	29	distributions	distribution	NOUN
cana-6219	39	30	in	in	ADP
cana-6219	39	31	the	the	DET
cana-6219	39	32	rectangular	rectangular	ADJ
cana-6219	39	33	plate	plate	NOUN
cana-6219	39	34	.	.	PUNCT
cana-6219	40	1	as	as	ADP
cana-6219	40	2	the	the	DET
cana-6219	40	3	fractional	fractional	ADJ
cana-6219	40	4	order	order	NOUN
cana-6219	40	5	increases	increase	NOUN
cana-6219	40	6	toward	toward	ADP
cana-6219	40	7	unity	unity	NOUN
cana-6219	40	8	,	,	PUNCT
cana-6219	40	9	the	the	DET
cana-6219	40	10	system	system	NOUN
cana-6219	40	11	behavior	behavior	NOUN
cana-6219	40	12	gradually	gradually	ADV
cana-6219	40	13	approaches	approach	VERB
cana-6219	40	14	that	that	PRON
cana-6219	40	15	predicted	predict	VERB
cana-6219	40	16	by	by	ADP
cana-6219	40	17	classical	classical	ADJ
cana-6219	40	18	thermoelastic	thermoelastic	ADJ
cana-6219	40	19	theory	theory	NOUN
cana-6219	40	20	,	,	PUNCT
cana-6219	40	21	while	while	SCONJ
cana-6219	40	22	smaller	small	ADJ
cana-6219	40	23	values	value	NOUN
cana-6219	40	24	of	of	ADP
cana-6219	40	25	α	α	PRON
cana-6219	40	26	produce	produce	VERB
cana-6219	40	27	stronger	strong	ADJ
cana-6219	40	28	thermal	thermal	ADJ
cana-6219	40	29	gradients	gradient	NOUN
cana-6219	40	30	and	and	CCONJ
cana-6219	40	31	higher	high	ADJ
cana-6219	40	32	stress	stress	NOUN
cana-6219	40	33	magnitudes	magnitude	NOUN
cana-6219	40	34	due	due	ADJ
cana-6219	40	35	to	to	ADP
cana-6219	40	36	enhanced	enhance	VERB
cana-6219	40	37	memory	memory	NOUN
cana-6219	40	38	effects	effect	NOUN
cana-6219	40	39	.	.	PUNCT
cana-6219	41	1	the	the	DET
cana-6219	41	2	heat	heat	NOUN
cana-6219	41	3	source	source	NOUN
cana-6219	41	4	velocity	velocity	NOUN
cana-6219	41	5	influences	influence	VERB
cana-6219	41	6	both	both	CCONJ
cana-6219	41	7	the	the	DET
cana-6219	41	8	magnitude	magnitude	NOUN
cana-6219	41	9	and	and	CCONJ
cana-6219	41	10	distribution	distribution	NOUN
cana-6219	41	11	of	of	ADP
cana-6219	41	12	thermal	thermal	ADJ
cana-6219	41	13	and	and	CCONJ
cana-6219	41	14	mechanical	mechanical	ADJ
cana-6219	41	15	responses	response	NOUN
cana-6219	41	16	-	-	PUNCT
cana-6219	41	17	higher	high	ADJ
cana-6219	41	18	speeds	speed	NOUN
cana-6219	41	19	result	result	VERB
cana-6219	41	20	in	in	ADP
cana-6219	41	21	lower	low	ADJ
cana-6219	41	22	displacements	displacement	NOUN
cana-6219	41	23	and	and	CCONJ
cana-6219	41	24	reduced	reduce	VERB
cana-6219	41	25	peak	peak	NOUN
cana-6219	41	26	temperatures	temperature	NOUN
cana-6219	41	27	.	.	PUNCT
cana-6219	42	1	these	these	DET
cana-6219	42	2	findings	finding	NOUN
cana-6219	42	3	demonstrate	demonstrate	VERB
cana-6219	42	4	that	that	SCONJ
cana-6219	42	5	the	the	DET
cana-6219	42	6	fractional	fractional	ADJ
cana-6219	42	7	-	-	PUNCT
cana-6219	42	8	order	order	NOUN
cana-6219	42	9	approach	approach	NOUN
cana-6219	42	10	provides	provide	VERB
cana-6219	42	11	a	a	DET
cana-6219	42	12	more	more	ADV
cana-6219	42	13	accurate	accurate	ADJ
cana-6219	42	14	and	and	CCONJ
cana-6219	42	15	generalized	generalized	ADJ
cana-6219	42	16	framework	framework	NOUN
cana-6219	42	17	than	than	ADP
cana-6219	42	18	traditional	traditional	ADJ
cana-6219	42	19	models	model	NOUN
cana-6219	42	20	,	,	PUNCT
cana-6219	42	21	particularly	particularly	ADV
cana-6219	42	22	for	for	ADP
cana-6219	42	23	materials	material	NOUN
cana-6219	42	24	and	and	CCONJ
cana-6219	42	25	processes	process	NOUN
cana-6219	42	26	that	that	PRON
cana-6219	42	27	involve	involve	VERB
cana-6219	42	28	transient	transient	ADJ
cana-6219	42	29	heat	heat	NOUN
cana-6219	42	30	transfer	transfer	NOUN
cana-6219	42	31	and	and	CCONJ
cana-6219	42	32	time	time	NOUN
cana-6219	42	33	-	-	PUNCT
cana-6219	42	34	dependent	dependent	ADJ
cana-6219	42	35	deformation	deformation	NOUN
cana-6219	42	36	.	.	PUNCT
cana-6219	43	1	the	the	DET
cana-6219	43	2	proposed	propose	VERB
cana-6219	43	3	model	model	NOUN
cana-6219	43	4	can	can	AUX
cana-6219	43	5	therefore	therefore	ADV
cana-6219	43	6	be	be	AUX
cana-6219	43	7	effectively	effectively	ADV
cana-6219	43	8	applied	apply	VERB
cana-6219	43	9	to	to	ADP
cana-6219	43	10	engineering	engineering	NOUN
cana-6219	43	11	systems	system	NOUN
cana-6219	43	12	in	in	ADP
cana-6219	43	13	aerospace	aerospace	NOUN
cana-6219	43	14	,	,	PUNCT
cana-6219	43	15	electronics	electronic	NOUN
cana-6219	43	16	cooling	cooling	NOUN
cana-6219	43	17	,	,	PUNCT
cana-6219	43	18	and	and	CCONJ
cana-6219	43	19	precision	precision	NOUN
cana-6219	43	20	manufacturing	manufacturing	NOUN
cana-6219	43	21	,	,	PUNCT
cana-6219	43	22	where	where	SCONJ
cana-6219	43	23	rapid	rapid	ADJ
cana-6219	43	24	and	and	CCONJ
cana-6219	43	25	localized	localized	ADJ
cana-6219	43	26	thermal	thermal	ADJ
cana-6219	43	27	loading	loading	NOUN
cana-6219	43	28	plays	play	VERB
cana-6219	43	29	a	a	DET
cana-6219	43	30	significant	significant	ADJ
cana-6219	43	31	role	role	NOUN
cana-6219	43	32	in	in	ADP
cana-6219	43	33	material	material	NOUN
cana-6219	43	34	performance	performance	NOUN
cana-6219	43	35	.	.	PUNCT
cana-6219	44	1	keywords	keyword	NOUN
cana-6219	44	2	:	:	PUNCT
cana-6219	44	3	fractional	fractional	ADJ
cana-6219	44	4	-	-	PUNCT
cana-6219	44	5	order	order	NOUN
cana-6219	44	6	,	,	PUNCT
cana-6219	44	7	thermoelasticity	thermoelasticity	NOUN
cana-6219	44	8	,	,	PUNCT
cana-6219	44	9	boundary	boundary	ADJ
cana-6219	44	10	value	value	NOUN
cana-6219	44	11	problem	problem	NOUN
cana-6219	44	12	,	,	PUNCT
cana-6219	44	13	rectangular	rectangular	ADJ
cana-6219	44	14	plate	plate	NOUN
cana-6219	44	15	,	,	PUNCT
cana-6219	44	16	moving	move	VERB
cana-6219	44	17	heat	heat	NOUN
cana-6219	44	18	source	source	NOUN
cana-6219	44	19	,	,	PUNCT
cana-6219	44	20	integral	integral	ADJ
cana-6219	44	21	transforms	transform	NOUN
cana-6219	44	22	.	.	PUNCT
cana-6219	45	1	communications	communication	NOUN
cana-6219	45	2	on	on	ADP
cana-6219	45	3	applied	apply	VERB
cana-6219	45	4	nonlinear	nonlinear	ADJ
cana-6219	45	5	analysis	analysis	NOUN
cana-6219	45	6	issn	issn	NOUN
cana-6219	45	7	:	:	PUNCT
cana-6219	45	8	1074	1074	NUM
cana-6219	45	9	-	-	PUNCT
cana-6219	45	10	133x	133x	NUM
cana-6219	45	11	vol	vol	VERB
cana-6219	45	12	32	32	NUM
cana-6219	45	13	no	no	NOUN
cana-6219	45	14	.	.	PUNCT
cana-6219	46	1	10s	10	NOUN
cana-6219	46	2	(	(	PUNCT
cana-6219	46	3	2025	2025	NUM
cana-6219	46	4	)	)	PUNCT
cana-6219	46	5	3530	3530	NUM
cana-6219	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	46	7	nomenclature	nomenclature	NOUN
cana-6219	46	8	λ	λ	PROPN
cana-6219	46	9	,	,	PUNCT
cana-6219	46	10	𝜇	𝜇	ADP
cana-6219	46	11	lame	lame	NOUN
cana-6219	46	12	’s	’s	PART
cana-6219	46	13	parameters	parameter	NOUN
cana-6219	46	14	𝜌	𝜌	ADP
cana-6219	46	15	density	density	NOUN
cana-6219	46	16	𝐶𝐸	𝐶𝐸	PROPN
cana-6219	46	17	specific	specific	ADJ
cana-6219	46	18	heat	heat	NOUN
cana-6219	46	19	of	of	ADP
cana-6219	46	20	the	the	DET
cana-6219	46	21	material	material	NOUN
cana-6219	46	22	with	with	ADP
cana-6219	46	23	constant	constant	ADJ
cana-6219	46	24	strain	strain	NOUN
cana-6219	46	25	t	t	PROPN
cana-6219	46	26	time	time	NOUN
cana-6219	46	27	t	t	PROPN
cana-6219	46	28	absolute	absolute	ADJ
cana-6219	46	29	temperature	temperature	NOUN
cana-6219	46	30	𝑇0	𝑇0	NOUN
cana-6219	46	31	reference	reference	NOUN
cana-6219	46	32	temperature	temperature	NOUN
cana-6219	46	33	𝜃	𝜃	NOUN
cana-6219	46	34	=	=	PUNCT
cana-6219	46	35	(	(	PUNCT
cana-6219	46	36	t	t	PROPN
cana-6219	46	37	−𝑇0	−𝑇0	NOUN
cana-6219	46	38	)	)	PUNCT
cana-6219	46	39	temperature	temperature	NOUN
cana-6219	46	40	increment	increment	NOUN
cana-6219	46	41	|𝑇	|𝑇	X
cana-6219	46	42	−	−	PROPN
cana-6219	46	43	𝑇0|	𝑇0|	PROPN
cana-6219	46	44	/	/	SYM
cana-6219	46	45	𝑇0	𝑇0	NOUN
cana-6219	46	46	≪	≪	ADJ
cana-6219	46	47	1	1	X
cana-6219	46	48	.	.	PUNCT
cana-6219	47	1	𝜔𝑇	𝜔𝑇	ADJ
cana-6219	47	2	linear	linear	ADJ
cana-6219	47	3	thermal	thermal	ADJ
cana-6219	47	4	expansion	expansion	NOUN
cana-6219	47	5	coefficient	coefficient	NOUN
cana-6219	47	6	𝛾	𝛾	PROPN
cana-6219	47	7	=	=	SYM
cana-6219	47	8	𝜔𝑇(3𝜆	𝜔𝑇(3𝜆	PROPN
cana-6219	47	9	+	+	NUM
cana-6219	47	10	2𝜇	2𝜇	NOUN
cana-6219	47	11	)	)	PUNCT
cana-6219	47	12	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-6219	47	13	stress	stress	NOUN
cana-6219	47	14	tensor	tensor	NOUN
cana-6219	47	15	𝑒𝑖𝑗	𝑒𝑖𝑗	PROPN
cana-6219	47	16	strain	strain	NOUN
cana-6219	47	17	tensor	tensor	NOUN
cana-6219	47	18	𝑢𝑖	𝑢𝑖	PRON
cana-6219	47	19	displacement	displacement	ADJ
cana-6219	47	20	components	component	NOUN
cana-6219	47	21	k	k	PROPN
cana-6219	47	22	thermal	thermal	ADJ
cana-6219	47	23	conductivity	conductivity	NOUN
cana-6219	47	24	𝜏0	𝜏0	PROPN
cana-6219	47	25	relaxation	relaxation	NOUN
cana-6219	47	26	time	time	NOUN
cana-6219	47	27	𝑐0	𝑐0	NOUN
cana-6219	47	28	=	=	SYM
cana-6219	47	29	√	√	NUM
cana-6219	47	30	𝜆+2𝜇	𝜆+2𝜇	NOUN
cana-6219	47	31	𝜌	𝜌	ADP
cana-6219	47	32	𝜂	𝜂	NOUN
cana-6219	47	33	=	=	PUNCT
cana-6219	47	34	𝜌𝐶𝐸	𝜌𝐶𝐸	NOUN
cana-6219	47	35	𝐾	𝐾	NOUN
cana-6219	47	36	휀	휀	NOUN
cana-6219	47	37	=	=	X
cana-6219	47	38	𝛾2𝑇0	𝛾2𝑇0	PROPN
cana-6219	47	39	𝜌𝐶𝐸(𝜆+2𝜇	𝜌𝐶𝐸(𝜆+2𝜇	PROPN
cana-6219	47	40	)	)	PUNCT
cana-6219	48	1	𝛽	𝛽	NOUN
cana-6219	48	2	=	=	PUNCT
cana-6219	48	3	(	(	PUNCT
cana-6219	48	4	𝜆+2𝜇	𝜆+2𝜇	PROPN
cana-6219	48	5	𝜇	𝜇	PROPN
cana-6219	48	6	)	)	PUNCT
cana-6219	48	7	1/2	1/2	NUM
cana-6219	48	8	1	1	NUM
cana-6219	48	9	.	.	PUNCT
cana-6219	49	1	introduction	introduction	NOUN
cana-6219	49	2	de	de	X
cana-6219	49	3	chant	chant	NOUN
cana-6219	49	4	[	[	X
cana-6219	49	5	1	1	NUM
cana-6219	49	6	]	]	PUNCT
cana-6219	49	7	introduced	introduce	VERB
cana-6219	49	8	a	a	DET
cana-6219	49	9	numerical	numerical	ADJ
cana-6219	49	10	approach	approach	NOUN
cana-6219	49	11	to	to	AUX
cana-6219	49	12	model	model	VERB
cana-6219	49	13	impulsive	impulsive	ADJ
cana-6219	49	14	displacement	displacement	NOUN
cana-6219	49	15	in	in	ADP
cana-6219	49	16	quasi	quasi	ADJ
cana-6219	49	17	-	-	ADJ
cana-6219	49	18	linear	linear	ADJ
cana-6219	49	19	viscoelastic	viscoelastic	ADJ
cana-6219	49	20	materials	material	NOUN
cana-6219	49	21	,	,	PUNCT
cana-6219	49	22	a	a	DET
cana-6219	49	23	topic	topic	NOUN
cana-6219	49	24	with	with	ADP
cana-6219	49	25	broad	broad	ADJ
cana-6219	49	26	implications	implication	NOUN
cana-6219	49	27	in	in	ADP
cana-6219	49	28	dynamic	dynamic	ADJ
cana-6219	49	29	systems	system	NOUN
cana-6219	49	30	where	where	SCONJ
cana-6219	49	31	viscoelastic	viscoelastic	ADJ
cana-6219	49	32	effects	effect	NOUN
cana-6219	49	33	are	be	AUX
cana-6219	49	34	significant	significant	ADJ
cana-6219	49	35	.	.	PUNCT
cana-6219	50	1	duan	duan	PROPN
cana-6219	50	2	et	et	PROPN
cana-6219	50	3	al	al	PROPN
cana-6219	50	4	.	.	PUNCT
cana-6219	51	1	[	[	X
cana-6219	51	2	3	3	NUM
cana-6219	51	3	]	]	PUNCT
cana-6219	51	4	expanded	expand	VERB
cana-6219	51	5	on	on	ADP
cana-6219	51	6	the	the	DET
cana-6219	51	7	fundamental	fundamental	ADJ
cana-6219	51	8	principles	principle	NOUN
cana-6219	51	9	of	of	ADP
cana-6219	51	10	fluid	fluid	ADJ
cana-6219	51	11	-	-	PUNCT
cana-6219	51	12	structure	structure	NOUN
cana-6219	51	13	interaction	interaction	NOUN
cana-6219	51	14	under	under	ADP
cana-6219	51	15	dynamic	dynamic	ADJ
cana-6219	51	16	loading	loading	NOUN
cana-6219	51	17	by	by	ADP
cana-6219	51	18	examining	examine	VERB
cana-6219	51	19	the	the	DET
cana-6219	51	20	nonlinear	nonlinear	ADJ
cana-6219	51	21	stability	stability	NOUN
cana-6219	51	22	of	of	ADP
cana-6219	51	23	rarefaction	rarefaction	NOUN
cana-6219	51	24	waves	wave	NOUN
cana-6219	51	25	in	in	ADP
cana-6219	51	26	compressible	compressible	ADJ
cana-6219	51	27	fluids	fluid	NOUN
cana-6219	51	28	.	.	PUNCT
cana-6219	52	1	these	these	DET
cana-6219	52	2	approaches	approach	NOUN
cana-6219	52	3	are	be	AUX
cana-6219	52	4	essential	essential	ADJ
cana-6219	52	5	for	for	ADP
cana-6219	52	6	understanding	understand	VERB
cana-6219	52	7	how	how	SCONJ
cana-6219	52	8	complex	complex	ADJ
cana-6219	52	9	material	material	NOUN
cana-6219	52	10	responses	response	NOUN
cana-6219	52	11	influence	influence	VERB
cana-6219	52	12	the	the	DET
cana-6219	52	13	design	design	NOUN
cana-6219	52	14	and	and	CCONJ
cana-6219	52	15	performance	performance	NOUN
cana-6219	52	16	of	of	ADP
cana-6219	52	17	structures	structure	NOUN
cana-6219	52	18	subjected	subject	VERB
cana-6219	52	19	to	to	ADP
cana-6219	52	20	thermal	thermal	ADJ
cana-6219	52	21	and	and	CCONJ
cana-6219	52	22	mechanical	mechanical	ADJ
cana-6219	52	23	loads	load	NOUN
cana-6219	52	24	.	.	PUNCT
cana-6219	53	1	ezzat	ezzat	ADJ
cana-6219	53	2	and	and	CCONJ
cana-6219	53	3	youssef	youssef	PROPN
cana-6219	53	4	focused	focus	VERB
cana-6219	53	5	on	on	ADP
cana-6219	53	6	generalized	generalized	ADJ
cana-6219	53	7	thermoelastic	thermoelastic	ADJ
cana-6219	53	8	models	model	NOUN
cana-6219	53	9	,	,	PUNCT
cana-6219	53	10	extending	extend	VERB
cana-6219	53	11	classical	classical	ADJ
cana-6219	53	12	theories	theory	NOUN
cana-6219	53	13	to	to	PART
cana-6219	53	14	include	include	VERB
cana-6219	53	15	more	more	ADJ
cana-6219	53	16	complex	complex	ADJ
cana-6219	53	17	material	material	NOUN
cana-6219	53	18	behaviours	behaviour	NOUN
cana-6219	53	19	.	.	PUNCT
cana-6219	54	1	youssef	youssef	PROPN
cana-6219	55	1	[	[	X
cana-6219	55	2	4	4	X
cana-6219	55	3	]	]	PUNCT
cana-6219	55	4	presented	present	VERB
cana-6219	55	5	a	a	DET
cana-6219	55	6	two	two	NUM
cana-6219	55	7	-	-	PUNCT
cana-6219	55	8	temperature	temperature	NOUN
cana-6219	55	9	generalized	generalize	VERB
cana-6219	55	10	thermoelastic	thermoelastic	ADJ
cana-6219	55	11	medium	medium	NOUN
cana-6219	55	12	subjected	subject	VERB
cana-6219	55	13	to	to	ADP
cana-6219	55	14	a	a	DET
cana-6219	55	15	moving	move	VERB
cana-6219	55	16	heat	heat	NOUN
cana-6219	55	17	source	source	NOUN
cana-6219	55	18	,	,	PUNCT
cana-6219	55	19	emphasizing	emphasize	VERB
cana-6219	55	20	the	the	DET
cana-6219	55	21	roles	role	NOUN
cana-6219	55	22	of	of	ADP
cana-6219	55	23	heat	heat	NOUN
cana-6219	55	24	conduction	conduction	NOUN
cana-6219	55	25	and	and	CCONJ
cana-6219	55	26	mechanical	mechanical	ADJ
cana-6219	55	27	stress	stress	NOUN
cana-6219	55	28	in	in	ADP
cana-6219	55	29	the	the	DET
cana-6219	55	30	material	material	NOUN
cana-6219	55	31	.	.	PUNCT
cana-6219	56	1	ezzat	ezzat	ADJ
cana-6219	56	2	and	and	CCONJ
cana-6219	56	3	youssef	youssef	PROPN
cana-6219	56	4	’s	’s	PART
cana-6219	56	5	work	work	NOUN
cana-6219	56	6	[	[	X
cana-6219	56	7	5	5	X
cana-6219	56	8	]	]	PUNCT
cana-6219	56	9	on	on	ADP
cana-6219	56	10	three	three	NUM
cana-6219	56	11	-	-	PUNCT
cana-6219	56	12	dimensional	dimensional	ADJ
cana-6219	56	13	thermal	thermal	ADJ
cana-6219	56	14	shock	shock	NOUN
cana-6219	56	15	problems	problem	NOUN
cana-6219	56	16	in	in	ADP
cana-6219	56	17	generalized	generalized	ADJ
cana-6219	56	18	thermoelastic	thermoelastic	ADJ
cana-6219	56	19	half	half	ADJ
cana-6219	56	20	-	-	PUNCT
cana-6219	56	21	spaces	space	NOUN
cana-6219	56	22	provided	provide	VERB
cana-6219	56	23	deeper	deep	ADJ
cana-6219	56	24	insights	insight	NOUN
cana-6219	56	25	into	into	ADP
cana-6219	56	26	the	the	DET
cana-6219	56	27	impact	impact	NOUN
cana-6219	56	28	of	of	ADP
cana-6219	56	29	rapid	rapid	ADJ
cana-6219	56	30	thermal	thermal	ADJ
cana-6219	56	31	loading	loading	NOUN
cana-6219	56	32	on	on	ADP
cana-6219	56	33	material	material	NOUN
cana-6219	56	34	responses	response	NOUN
cana-6219	56	35	.	.	PUNCT
cana-6219	57	1	these	these	DET
cana-6219	57	2	studies	study	NOUN
cana-6219	57	3	are	be	AUX
cana-6219	57	4	critical	critical	ADJ
cana-6219	57	5	for	for	ADP
cana-6219	57	6	applications	application	NOUN
cana-6219	57	7	in	in	ADP
cana-6219	57	8	heat	heat	NOUN
cana-6219	57	9	treatment	treatment	NOUN
cana-6219	57	10	processes	process	NOUN
cana-6219	57	11	,	,	PUNCT
cana-6219	57	12	aerospace	aerospace	NOUN
cana-6219	57	13	engineering	engineering	NOUN
cana-6219	57	14	,	,	PUNCT
cana-6219	57	15	and	and	CCONJ
cana-6219	57	16	industries	industry	NOUN
cana-6219	57	17	involving	involve	VERB
cana-6219	57	18	rapid	rapid	ADJ
cana-6219	57	19	temperature	temperature	NOUN
cana-6219	57	20	variations	variation	NOUN
cana-6219	57	21	.	.	PUNCT
cana-6219	58	1	gaikwad	gaikwad	NOUN
cana-6219	58	2	and	and	CCONJ
cana-6219	58	3	ghadle	ghadle	VERB
cana-6219	58	4	[	[	X
cana-6219	58	5	28	28	NUM
cana-6219	58	6	,	,	PUNCT
cana-6219	58	7	29	29	NUM
cana-6219	58	8	]	]	PUNCT
cana-6219	58	9	investigated	investigate	VERB
cana-6219	58	10	the	the	DET
cana-6219	58	11	thermoelastic	thermoelastic	ADJ
cana-6219	58	12	deformation	deformation	NOUN
cana-6219	58	13	of	of	ADP
cana-6219	58	14	thin	thin	ADJ
cana-6219	58	15	circular	circular	ADJ
cana-6219	58	16	disks	disk	NOUN
cana-6219	58	17	and	and	CCONJ
cana-6219	58	18	plates	plate	NOUN
cana-6219	58	19	with	with	ADP
cana-6219	58	20	internal	internal	ADJ
cana-6219	58	21	heat	heat	NOUN
cana-6219	58	22	generation	generation	NOUN
cana-6219	58	23	and	and	CCONJ
cana-6219	58	24	non	non	ADJ
cana-6219	58	25	-	-	ADJ
cana-6219	58	26	uniform	uniform	ADJ
cana-6219	58	27	heat	heat	NOUN
cana-6219	58	28	supply	supply	NOUN
cana-6219	58	29	.	.	PUNCT
cana-6219	59	1	their	their	PRON
cana-6219	59	2	studies	study	NOUN
cana-6219	59	3	are	be	AUX
cana-6219	59	4	particularly	particularly	ADV
cana-6219	59	5	relevant	relevant	ADJ
cana-6219	59	6	for	for	ADP
cana-6219	59	7	structural	structural	ADJ
cana-6219	59	8	health	health	NOUN
cana-6219	59	9	monitoring	monitoring	NOUN
cana-6219	59	10	and	and	CCONJ
cana-6219	59	11	the	the	DET
cana-6219	59	12	design	design	NOUN
cana-6219	59	13	of	of	ADP
cana-6219	59	14	thermally	thermally	ADV
cana-6219	59	15	stressed	stressed	ADJ
cana-6219	59	16	components	component	NOUN
cana-6219	59	17	in	in	ADP
cana-6219	59	18	engineering	engineering	NOUN
cana-6219	59	19	applications	application	NOUN
cana-6219	59	20	.	.	PUNCT
cana-6219	60	1	the	the	DET
cana-6219	60	2	practical	practical	ADJ
cana-6219	60	3	applications	application	NOUN
cana-6219	60	4	of	of	ADP
cana-6219	60	5	these	these	DET
cana-6219	60	6	theoretical	theoretical	ADJ
cana-6219	60	7	studies	study	NOUN
cana-6219	60	8	are	be	AUX
cana-6219	60	9	vast	vast	ADJ
cana-6219	60	10	.	.	PUNCT
cana-6219	61	1	for	for	ADP
cana-6219	61	2	instance	instance	NOUN
cana-6219	61	3	,	,	PUNCT
cana-6219	61	4	parnell	parnell	PROPN
cana-6219	61	5	et	et	PROPN
cana-6219	61	6	al	al	PROPN
cana-6219	61	7	.	.	PUNCT
cana-6219	61	8	communications	communication	NOUN
cana-6219	61	9	on	on	ADP
cana-6219	61	10	applied	apply	VERB
cana-6219	61	11	nonlinear	nonlinear	ADJ
cana-6219	61	12	analysis	analysis	NOUN
cana-6219	61	13	issn	issn	NOUN
cana-6219	61	14	:	:	PUNCT
cana-6219	61	15	1074	1074	NUM
cana-6219	61	16	-	-	PUNCT
cana-6219	61	17	133x	133x	NUM
cana-6219	61	18	vol	vol	VERB
cana-6219	61	19	32	32	NUM
cana-6219	61	20	no	no	NOUN
cana-6219	61	21	.	.	PUNCT
cana-6219	62	1	10s	10	NOUN
cana-6219	62	2	(	(	PUNCT
cana-6219	62	3	2025	2025	NUM
cana-6219	62	4	)	)	PUNCT
cana-6219	62	5	3531	3531	NUM
cana-6219	62	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	63	1	[	[	X
cana-6219	63	2	8	8	NUM
cana-6219	63	3	]	]	PUNCT
cana-6219	63	4	addressed	address	VERB
cana-6219	63	5	transient	transient	ADJ
cana-6219	63	6	thermal	thermal	ADJ
cana-6219	63	7	mixed	mixed	ADJ
cana-6219	63	8	boundary	boundary	ADJ
cana-6219	63	9	value	value	NOUN
cana-6219	63	10	problems	problem	NOUN
cana-6219	63	11	in	in	ADP
cana-6219	63	12	half	half	ADJ
cana-6219	63	13	-	-	PUNCT
cana-6219	63	14	spaces	space	NOUN
cana-6219	63	15	,	,	PUNCT
cana-6219	63	16	applying	apply	VERB
cana-6219	63	17	advanced	advanced	ADJ
cana-6219	63	18	computational	computational	ADJ
cana-6219	63	19	methods	method	NOUN
cana-6219	63	20	to	to	PART
cana-6219	63	21	solve	solve	VERB
cana-6219	63	22	these	these	DET
cana-6219	63	23	systems	system	NOUN
cana-6219	63	24	.	.	PUNCT
cana-6219	64	1	numerical	numerical	ADJ
cana-6219	64	2	solutions	solution	NOUN
cana-6219	64	3	are	be	AUX
cana-6219	64	4	essential	essential	ADJ
cana-6219	64	5	for	for	ADP
cana-6219	64	6	real	real	ADJ
cana-6219	64	7	-	-	PUNCT
cana-6219	64	8	world	world	NOUN
cana-6219	64	9	problems	problem	NOUN
cana-6219	64	10	where	where	SCONJ
cana-6219	64	11	exact	exact	ADJ
cana-6219	64	12	analytical	analytical	ADJ
cana-6219	64	13	solutions	solution	NOUN
cana-6219	64	14	are	be	AUX
cana-6219	64	15	unavailable	unavailable	ADJ
cana-6219	64	16	.	.	PUNCT
cana-6219	65	1	tahouneh	tahouneh	PROPN
cana-6219	65	2	and	and	CCONJ
cana-6219	65	3	naei	naei	NOUN
cana-6219	66	1	[	[	X
cana-6219	66	2	9	9	NUM
cana-6219	66	3	]	]	PUNCT
cana-6219	66	4	examined	examine	VERB
cana-6219	66	5	the	the	DET
cana-6219	66	6	effect	effect	NOUN
cana-6219	66	7	of	of	ADP
cana-6219	66	8	multi	multi	ADJ
cana-6219	66	9	-	-	ADJ
cana-6219	66	10	directional	directional	ADJ
cana-6219	66	11	nanocomposite	nanocomposite	NOUN
cana-6219	66	12	materials	material	NOUN
cana-6219	66	13	on	on	ADP
cana-6219	66	14	the	the	DET
cana-6219	66	15	vibrational	vibrational	ADJ
cana-6219	66	16	response	response	NOUN
cana-6219	66	17	of	of	ADP
cana-6219	66	18	thick	thick	ADJ
cana-6219	66	19	shell	shell	NOUN
cana-6219	66	20	panels	panel	NOUN
cana-6219	66	21	,	,	PUNCT
cana-6219	66	22	highlighting	highlight	VERB
cana-6219	66	23	the	the	DET
cana-6219	66	24	interaction	interaction	NOUN
cana-6219	66	25	between	between	ADP
cana-6219	66	26	thermal	thermal	ADJ
cana-6219	66	27	and	and	CCONJ
cana-6219	66	28	mechanical	mechanical	ADJ
cana-6219	66	29	loading	loading	NOUN
cana-6219	66	30	in	in	ADP
cana-6219	66	31	structures	structure	NOUN
cana-6219	66	32	with	with	ADP
cana-6219	66	33	complex	complex	ADJ
cana-6219	66	34	material	material	NOUN
cana-6219	66	35	properties	property	NOUN
cana-6219	66	36	.	.	PUNCT
cana-6219	67	1	the	the	DET
cana-6219	67	2	work	work	NOUN
cana-6219	67	3	by	by	ADP
cana-6219	67	4	parnell	parnell	PROPN
cana-6219	67	5	et	et	PROPN
cana-6219	67	6	al	al	PROPN
cana-6219	67	7	.	.	PUNCT
cana-6219	68	1	[	[	X
cana-6219	68	2	8	8	NUM
cana-6219	68	3	]	]	PUNCT
cana-6219	68	4	on	on	ADP
cana-6219	68	5	transient	transient	ADJ
cana-6219	68	6	thermal	thermal	ADJ
cana-6219	68	7	problems	problem	NOUN
cana-6219	68	8	in	in	ADP
cana-6219	68	9	half	half	ADJ
cana-6219	68	10	-	-	PUNCT
cana-6219	68	11	spaces	space	NOUN
cana-6219	68	12	and	and	CCONJ
cana-6219	68	13	youssef	youssef	PROPN
cana-6219	68	14	and	and	CCONJ
cana-6219	68	15	al	al	PROPN
cana-6219	68	16	-	-	PUNCT
cana-6219	68	17	lehaibi	lehaibi	NOUN
cana-6219	68	18	[	[	X
cana-6219	68	19	12	12	NUM
cana-6219	68	20	]	]	PUNCT
cana-6219	68	21	on	on	ADP
cana-6219	68	22	thermoelastic	thermoelastic	ADJ
cana-6219	68	23	half	half	ADJ
cana-6219	68	24	-	-	PUNCT
cana-6219	68	25	spaces	space	NOUN
cana-6219	68	26	subjected	subject	VERB
cana-6219	68	27	to	to	ADP
cana-6219	68	28	moving	move	VERB
cana-6219	68	29	heat	heat	NOUN
cana-6219	68	30	sources	source	NOUN
cana-6219	68	31	are	be	AUX
cana-6219	68	32	directly	directly	ADV
cana-6219	68	33	applicable	applicable	ADJ
cana-6219	68	34	to	to	ADP
cana-6219	68	35	scenarios	scenario	NOUN
cana-6219	68	36	in	in	ADP
cana-6219	68	37	aerospace	aerospace	NOUN
cana-6219	68	38	engineering	engineering	NOUN
cana-6219	68	39	,	,	PUNCT
cana-6219	68	40	electronics	electronic	NOUN
cana-6219	68	41	cooling	cooling	NOUN
cana-6219	68	42	,	,	PUNCT
cana-6219	68	43	and	and	CCONJ
cana-6219	68	44	geophysics	geophysic	NOUN
cana-6219	68	45	.	.	PUNCT
cana-6219	69	1	gaikwad	gaikwad	PROPN
cana-6219	69	2	et.al	et.al	PROPN
cana-6219	69	3	.	.	PUNCT
cana-6219	70	1	[	[	X
cana-6219	70	2	13	13	NUM
cana-6219	70	3	-	-	SYM
cana-6219	70	4	26	26	NUM
cana-6219	70	5	]	]	PUNCT
cana-6219	70	6	focused	focus	VERB
cana-6219	70	7	on	on	ADP
cana-6219	70	8	time	time	NOUN
cana-6219	70	9	-	-	PUNCT
cana-6219	70	10	fractional	fractional	ADJ
cana-6219	70	11	heat	heat	NOUN
cana-6219	70	12	conduction	conduction	NOUN
cana-6219	70	13	and	and	CCONJ
cana-6219	70	14	thermoelastic	thermoelastic	ADJ
cana-6219	70	15	stress	stress	NOUN
cana-6219	70	16	analysis	analysis	NOUN
cana-6219	70	17	in	in	ADP
cana-6219	70	18	various	various	ADJ
cana-6219	70	19	geometries	geometry	NOUN
cana-6219	70	20	,	,	PUNCT
cana-6219	70	21	such	such	ADJ
cana-6219	70	22	as	as	ADP
cana-6219	70	23	thin	thin	ADJ
cana-6219	70	24	hollow	hollow	ADJ
cana-6219	70	25	circular	circular	ADJ
cana-6219	70	26	disks	disk	NOUN
cana-6219	70	27	and	and	CCONJ
cana-6219	70	28	rectangular	rectangular	ADJ
cana-6219	70	29	plates	plate	NOUN
cana-6219	70	30	.	.	PUNCT
cana-6219	71	1	their	their	PRON
cana-6219	71	2	studies	study	NOUN
cana-6219	71	3	demonstrate	demonstrate	VERB
cana-6219	71	4	the	the	DET
cana-6219	71	5	application	application	NOUN
cana-6219	71	6	of	of	ADP
cana-6219	71	7	fractional	fractional	ADJ
cana-6219	71	8	calculus	calculus	NOUN
cana-6219	71	9	to	to	PART
cana-6219	71	10	address	address	VERB
cana-6219	71	11	complex	complex	ADJ
cana-6219	71	12	boundary	boundary	ADJ
cana-6219	71	13	conditions	condition	NOUN
cana-6219	71	14	and	and	CCONJ
cana-6219	71	15	material	material	NOUN
cana-6219	71	16	responses	response	NOUN
cana-6219	71	17	.	.	PUNCT
cana-6219	72	1	fractional	fractional	ADJ
cana-6219	72	2	-	-	PUNCT
cana-6219	72	3	order	order	NOUN
cana-6219	72	4	models	model	NOUN
cana-6219	72	5	provide	provide	VERB
cana-6219	72	6	a	a	DET
cana-6219	72	7	more	more	ADV
cana-6219	72	8	accurate	accurate	ADJ
cana-6219	72	9	description	description	NOUN
cana-6219	72	10	of	of	ADP
cana-6219	72	11	memory	memory	NOUN
cana-6219	72	12	effects	effect	NOUN
cana-6219	72	13	and	and	CCONJ
cana-6219	72	14	non	non	ADJ
cana-6219	72	15	-	-	ADJ
cana-6219	72	16	local	local	ADJ
cana-6219	72	17	behaviour	behaviour	NOUN
cana-6219	72	18	,	,	PUNCT
cana-6219	72	19	which	which	PRON
cana-6219	72	20	are	be	AUX
cana-6219	72	21	not	not	PART
cana-6219	72	22	captured	capture	VERB
cana-6219	72	23	by	by	ADP
cana-6219	72	24	traditional	traditional	ADJ
cana-6219	72	25	integer	integer	NOUN
cana-6219	72	26	-	-	PUNCT
cana-6219	72	27	order	order	NOUN
cana-6219	72	28	models	model	NOUN
cana-6219	72	29	.	.	PUNCT
cana-6219	73	1	khavale	khavale	NOUN
cana-6219	73	2	and	and	CCONJ
cana-6219	73	3	gaikwad	gaikwad	NOUN
cana-6219	73	4	[	[	X
cana-6219	73	5	14	14	NUM
cana-6219	73	6	,	,	PUNCT
cana-6219	73	7	18	18	NUM
cana-6219	73	8	]	]	PUNCT
cana-6219	73	9	explored	explore	VERB
cana-6219	73	10	transient	transient	ADJ
cana-6219	73	11	thermoelastic	thermoelastic	ADJ
cana-6219	73	12	problems	problem	NOUN
cana-6219	73	13	,	,	PUNCT
cana-6219	73	14	using	use	VERB
cana-6219	73	15	fractional	fractional	ADJ
cana-6219	73	16	derivatives	derivative	NOUN
cana-6219	73	17	to	to	PART
cana-6219	73	18	analyse	analyse	VERB
cana-6219	73	19	temperature	temperature	NOUN
cana-6219	73	20	distributions	distribution	NOUN
cana-6219	73	21	and	and	CCONJ
cana-6219	73	22	thermal	thermal	ADJ
cana-6219	73	23	deflections	deflection	NOUN
cana-6219	73	24	in	in	ADP
cana-6219	73	25	thin	thin	ADJ
cana-6219	73	26	circular	circular	ADJ
cana-6219	73	27	disks	disk	NOUN
cana-6219	73	28	.	.	PUNCT
cana-6219	74	1	these	these	DET
cana-6219	74	2	models	model	NOUN
cana-6219	74	3	are	be	AUX
cana-6219	74	4	particularly	particularly	ADV
cana-6219	74	5	useful	useful	ADJ
cana-6219	74	6	in	in	ADP
cana-6219	74	7	cases	case	NOUN
cana-6219	74	8	where	where	SCONJ
cana-6219	74	9	materials	material	NOUN
cana-6219	74	10	exhibit	exhibit	VERB
cana-6219	74	11	anomalous	anomalous	ADJ
cana-6219	74	12	diffusion	diffusion	NOUN
cana-6219	74	13	or	or	CCONJ
cana-6219	74	14	time	time	NOUN
cana-6219	74	15	-	-	PUNCT
cana-6219	74	16	dependent	dependent	ADJ
cana-6219	74	17	behaviour	behaviour	NOUN
cana-6219	74	18	.	.	PUNCT
cana-6219	75	1	youssef	youssef	PROPN
cana-6219	75	2	and	and	CCONJ
cana-6219	75	3	al	al	PROPN
cana-6219	75	4	-	-	PUNCT
cana-6219	75	5	lehaibi	lehaibi	NOUN
cana-6219	76	1	[	[	X
cana-6219	76	2	12	12	NUM
cana-6219	76	3	]	]	PUNCT
cana-6219	76	4	studied	study	VERB
cana-6219	76	5	generalized	generalized	ADJ
cana-6219	76	6	thermoelastic	thermoelastic	ADJ
cana-6219	76	7	diffusion	diffusion	NOUN
cana-6219	76	8	,	,	PUNCT
cana-6219	76	9	where	where	SCONJ
cana-6219	76	10	thermal	thermal	ADJ
cana-6219	76	11	and	and	CCONJ
cana-6219	76	12	mass	mass	NOUN
cana-6219	76	13	diffusion	diffusion	NOUN
cana-6219	76	14	processes	process	NOUN
cana-6219	76	15	are	be	AUX
cana-6219	76	16	coupled	couple	VERB
cana-6219	76	17	,	,	PUNCT
cana-6219	76	18	applying	apply	VERB
cana-6219	76	19	this	this	DET
cana-6219	76	20	model	model	NOUN
cana-6219	76	21	to	to	ADP
cana-6219	76	22	a	a	DET
cana-6219	76	23	thermoelastic	thermoelastic	ADJ
cana-6219	76	24	half	half	ADJ
cana-6219	76	25	-	-	PUNCT
cana-6219	76	26	space	space	NOUN
cana-6219	76	27	subjected	subject	VERB
cana-6219	76	28	to	to	ADP
cana-6219	76	29	thermal	thermal	ADJ
cana-6219	76	30	pulses	pulse	NOUN
cana-6219	76	31	.	.	PUNCT
cana-6219	77	1	this	this	DET
cana-6219	77	2	work	work	NOUN
cana-6219	77	3	is	be	AUX
cana-6219	77	4	important	important	ADJ
cana-6219	77	5	for	for	ADP
cana-6219	77	6	analysing	analyse	VERB
cana-6219	77	7	materials	material	NOUN
cana-6219	77	8	undergoing	undergo	VERB
cana-6219	77	9	both	both	CCONJ
cana-6219	77	10	heat	heat	NOUN
cana-6219	77	11	transfer	transfer	NOUN
cana-6219	77	12	and	and	CCONJ
cana-6219	77	13	mass	mass	NOUN
cana-6219	77	14	transport	transport	NOUN
cana-6219	77	15	,	,	PUNCT
cana-6219	77	16	such	such	ADJ
cana-6219	77	17	as	as	ADP
cana-6219	77	18	semiconductors	semiconductor	NOUN
cana-6219	77	19	and	and	CCONJ
cana-6219	77	20	porous	porous	ADJ
cana-6219	77	21	materials	material	NOUN
cana-6219	77	22	.	.	PUNCT
cana-6219	78	1	similarly	similarly	ADV
cana-6219	78	2	,	,	PUNCT
cana-6219	78	3	khavale	khavale	NOUN
cana-6219	78	4	and	and	CCONJ
cana-6219	78	5	gaikwad	gaikwad	NOUN
cana-6219	79	1	[	[	X
cana-6219	79	2	21	21	NUM
cana-6219	79	3	,	,	PUNCT
cana-6219	79	4	24	24	NUM
cana-6219	79	5	]	]	PUNCT
cana-6219	79	6	investigated	investigate	VERB
cana-6219	79	7	magneto	magneto	NOUN
cana-6219	79	8	-	-	PUNCT
cana-6219	79	9	thermoviscoelasticity	thermoviscoelasticity	NOUN
cana-6219	79	10	,	,	PUNCT
cana-6219	79	11	considering	consider	VERB
cana-6219	79	12	the	the	DET
cana-6219	79	13	interaction	interaction	NOUN
cana-6219	79	14	between	between	ADP
cana-6219	79	15	thermal	thermal	ADJ
cana-6219	79	16	,	,	PUNCT
cana-6219	79	17	mechanical	mechanical	ADJ
cana-6219	79	18	,	,	PUNCT
cana-6219	79	19	and	and	CCONJ
cana-6219	79	20	magnetic	magnetic	ADJ
cana-6219	79	21	fields	field	NOUN
cana-6219	79	22	in	in	ADP
cana-6219	79	23	materials	material	NOUN
cana-6219	79	24	exhibiting	exhibit	VERB
cana-6219	79	25	fractional	fractional	ADJ
cana-6219	79	26	-	-	PUNCT
cana-6219	79	27	order	order	NOUN
cana-6219	79	28	behaviour	behaviour	NOUN
cana-6219	79	29	.	.	PUNCT
cana-6219	80	1	these	these	DET
cana-6219	80	2	studies	study	NOUN
cana-6219	80	3	are	be	AUX
cana-6219	80	4	vital	vital	ADJ
cana-6219	80	5	for	for	ADP
cana-6219	80	6	understanding	understand	VERB
cana-6219	80	7	the	the	DET
cana-6219	80	8	behaviour	behaviour	NOUN
cana-6219	80	9	of	of	ADP
cana-6219	80	10	materials	material	NOUN
cana-6219	80	11	in	in	ADP
cana-6219	80	12	applications	application	NOUN
cana-6219	80	13	like	like	ADP
cana-6219	80	14	electromagnetic	electromagnetic	ADJ
cana-6219	80	15	heating	heating	NOUN
cana-6219	80	16	and	and	CCONJ
cana-6219	80	17	advanced	advanced	ADJ
cana-6219	80	18	materials	material	NOUN
cana-6219	80	19	science	science	NOUN
cana-6219	80	20	.	.	PUNCT
cana-6219	81	1	the	the	DET
cana-6219	81	2	use	use	NOUN
cana-6219	81	3	of	of	ADP
cana-6219	81	4	fractional	fractional	ADJ
cana-6219	81	5	-	-	PUNCT
cana-6219	81	6	order	order	NOUN
cana-6219	81	7	models	model	NOUN
cana-6219	81	8	,	,	PUNCT
cana-6219	81	9	as	as	SCONJ
cana-6219	81	10	demonstrated	demonstrate	VERB
cana-6219	81	11	in	in	ADP
cana-6219	81	12	the	the	DET
cana-6219	81	13	studies	study	NOUN
cana-6219	81	14	by	by	ADP
cana-6219	81	15	khavale	khavale	NOUN
cana-6219	81	16	and	and	CCONJ
cana-6219	81	17	gaikwad	gaikwad	NOUN
cana-6219	81	18	[	[	X
cana-6219	81	19	14	14	NUM
cana-6219	81	20	,	,	PUNCT
cana-6219	81	21	25	25	NUM
cana-6219	81	22	]	]	PUNCT
cana-6219	81	23	,	,	PUNCT
cana-6219	81	24	can	can	AUX
cana-6219	81	25	enhance	enhance	VERB
cana-6219	81	26	predictions	prediction	NOUN
cana-6219	81	27	of	of	ADP
cana-6219	81	28	material	material	NOUN
cana-6219	81	29	performance	performance	NOUN
cana-6219	81	30	in	in	ADP
cana-6219	81	31	systems	system	NOUN
cana-6219	81	32	where	where	SCONJ
cana-6219	81	33	heat	heat	NOUN
cana-6219	81	34	conduction	conduction	NOUN
cana-6219	81	35	does	do	AUX
cana-6219	81	36	not	not	PART
cana-6219	81	37	follow	follow	VERB
cana-6219	81	38	classical	classical	ADJ
cana-6219	81	39	diffusion	diffusion	NOUN
cana-6219	81	40	laws	law	NOUN
cana-6219	81	41	.	.	PUNCT
cana-6219	82	1	2	2	X
cana-6219	82	2	.	.	X
cana-6219	82	3	the	the	DET
cana-6219	82	4	basic	basic	ADJ
cana-6219	82	5	equations	equation	NOUN
cana-6219	82	6	the	the	DET
cana-6219	82	7	system	system	NOUN
cana-6219	82	8	a	a	DET
cana-6219	82	9	homogeneous	homogeneous	ADJ
cana-6219	82	10	and	and	CCONJ
cana-6219	82	11	isotropic	isotropic	ADJ
cana-6219	82	12	boundary	boundary	ADJ
cana-6219	82	13	value	value	NOUN
cana-6219	82	14	problem	problem	NOUN
cana-6219	82	15	on	on	ADP
cana-6219	82	16	the	the	DET
cana-6219	82	17	generalized	generalized	ADJ
cana-6219	82	18	thermoelasticity	thermoelasticity	NOUN
cana-6219	82	19	with	with	ADP
cana-6219	82	20	one	one	NUM
cana-6219	82	21	relaxation	relaxation	NOUN
cana-6219	82	22	time	time	NOUN
cana-6219	82	23	and	and	CCONJ
cana-6219	82	24	without	without	ADP
cana-6219	82	25	any	any	DET
cana-6219	82	26	external	external	ADJ
cana-6219	82	27	body	body	NOUN
cana-6219	82	28	forces	force	NOUN
cana-6219	82	29	in	in	ADP
cana-6219	82	30	undefined	undefined	ADJ
cana-6219	82	31	coordinates	coordinate	NOUN
cana-6219	82	32	{	{	PUNCT
cana-6219	82	33	𝑖	𝑖	SYM
cana-6219	82	34	,	,	PUNCT
cana-6219	82	35	𝑗	𝑗	INTJ
cana-6219	82	36	,	,	PUNCT
cana-6219	82	37	𝑘	𝑘	X
cana-6219	82	38	=	=	SYM
cana-6219	82	39	1	1	NUM
cana-6219	82	40	,	,	PUNCT
cana-6219	82	41	2	2	NUM
cana-6219	82	42	,	,	PUNCT
cana-6219	82	43	3	3	NUM
cana-6219	82	44	}	}	PUNCT
cana-6219	82	45	takes	take	VERB
cana-6219	82	46	the	the	DET
cana-6219	82	47	(	(	PUNCT
cana-6219	82	48	ezzat	ezzat	ADJ
cana-6219	82	49	,	,	PUNCT
cana-6219	82	50	youssef	youssef	PROPN
cana-6219	83	1	[	[	X
cana-6219	83	2	5	5	NUM
cana-6219	83	3	]	]	PUNCT
cana-6219	83	4	;	;	PUNCT
cana-6219	83	5	youssef	youssef	PROPN
cana-6219	83	6	,	,	PUNCT
cana-6219	83	7	al	al	PROPN
cana-6219	83	8	-	-	PUNCT
cana-6219	83	9	lehaibi	lehaibi	NOUN
cana-6219	84	1	[	[	X
cana-6219	84	2	12	12	NUM
cana-6219	84	3	]	]	PUNCT
cana-6219	84	4	):	):	PUNCT
cana-6219	84	5	the	the	DET
cana-6219	84	6	equations	equation	NOUN
cana-6219	84	7	of	of	ADP
cana-6219	84	8	motion	motion	NOUN
cana-6219	84	9	are	be	AUX
cana-6219	84	10	𝜇𝑢𝑖,𝑗𝑗	𝜇𝑢𝑖,𝑗𝑗	VERB
cana-6219	84	11	+	+	CCONJ
cana-6219	85	1	(	(	PUNCT
cana-6219	85	2	𝜇	𝜇	X
cana-6219	85	3	+	+	X
cana-6219	85	4	𝜆)𝑢𝑖,𝑗𝑗	𝜆)𝑢𝑖,𝑗𝑗	ADJ
cana-6219	85	5	−	−	PROPN
cana-6219	85	6	(	(	PUNCT
cana-6219	85	7	3𝜆	3𝜆	ADJ
cana-6219	85	8	−	−	PROPN
cana-6219	85	9	2𝜇)𝛼𝜃𝑖	2𝜇)𝛼𝜃𝑖	PROPN
cana-6219	86	1	=	=	SYM
cana-6219	86	2	𝜌𝑢𝑖̈	𝜌𝑢𝑖̈	PROPN
cana-6219	86	3	(	(	PUNCT
cana-6219	86	4	1	1	X
cana-6219	86	5	)	)	PUNCT
cana-6219	86	6	the	the	DET
cana-6219	86	7	heat	heat	NOUN
cana-6219	86	8	equation	equation	NOUN
cana-6219	86	9	is	be	AUX
cana-6219	86	10	,	,	PUNCT
cana-6219	86	11	𝐾𝜃𝑖𝑖	𝐾𝜃𝑖𝑖	PROPN
cana-6219	86	12	=	=	PUNCT
cana-6219	86	13	(	(	PUNCT
cana-6219	86	14	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	86	15	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	87	1	+	+	CCONJ
cana-6219	87	2	𝜏0	𝜏0	PROPN
cana-6219	87	3	𝜕𝛼+1	𝜕𝛼+1	VERB
cana-6219	87	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	87	5	)	)	PUNCT
cana-6219	88	1	[	[	X
cana-6219	88	2	𝜌𝐶𝑒𝜃	𝜌𝐶𝑒𝜃	PROPN
cana-6219	88	3	+	+	X
cana-6219	88	4	𝛾𝑇0𝑒	𝛾𝑇0𝑒	ADJ
cana-6219	88	5	]	]	X
cana-6219	88	6	−	−	PROPN
cana-6219	88	7	(	(	PUNCT
cana-6219	88	8	1	1	NUM
cana-6219	88	9	+	+	NUM
cana-6219	88	10	𝜏0	𝜏0	PROPN
cana-6219	88	11	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	88	12	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	88	13	)	)	PUNCT
cana-6219	88	14	𝑄	𝑄	PROPN
cana-6219	88	15	(	(	PUNCT
cana-6219	88	16	2	2	X
cana-6219	88	17	)	)	PUNCT
cana-6219	88	18	the	the	DET
cana-6219	88	19	constitutive	constitutive	ADJ
cana-6219	88	20	relations	relation	NOUN
cana-6219	88	21	are	be	AUX
cana-6219	88	22	𝜎𝑖𝑗	𝜎𝑖𝑗	ADJ
cana-6219	88	23	=	=	PUNCT
cana-6219	88	24	2𝜇𝑒𝑖𝑗	2𝜇𝑒𝑖𝑗	NUM
cana-6219	88	25	+	+	NUM
cana-6219	88	26	𝜆𝑒𝑘𝑘𝛿𝑖𝑗	𝜆𝑒𝑘𝑘𝛿𝑖𝑗	NOUN
cana-6219	88	27	−	−	PROPN
cana-6219	88	28	𝛾𝜃𝛿𝑖𝑗	𝛾𝜃𝛿𝑖𝑗	NOUN
cana-6219	88	29	(	(	PUNCT
cana-6219	88	30	3	3	NUM
cana-6219	88	31	)	)	PUNCT
cana-6219	88	32	communications	communication	NOUN
cana-6219	88	33	on	on	ADP
cana-6219	88	34	applied	apply	VERB
cana-6219	88	35	nonlinear	nonlinear	ADJ
cana-6219	88	36	analysis	analysis	NOUN
cana-6219	88	37	issn	issn	NOUN
cana-6219	88	38	:	:	PUNCT
cana-6219	88	39	1074	1074	NUM
cana-6219	88	40	-	-	PUNCT
cana-6219	88	41	133x	133x	NUM
cana-6219	88	42	vol	vol	VERB
cana-6219	88	43	32	32	NUM
cana-6219	88	44	no	no	NOUN
cana-6219	88	45	.	.	PUNCT
cana-6219	89	1	10s	10	NOUN
cana-6219	89	2	(	(	PUNCT
cana-6219	89	3	2025	2025	NUM
cana-6219	89	4	)	)	PUNCT
cana-6219	89	5	3532	3532	NUM
cana-6219	89	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	90	1	the	the	DET
cana-6219	90	2	displacement	displacement	ADJ
cana-6219	90	3	relation	relation	NOUN
cana-6219	90	4	with	with	ADP
cana-6219	90	5	the	the	DET
cana-6219	90	6	strain	strain	NOUN
cana-6219	90	7	takes	take	VERB
cana-6219	90	8	the	the	DET
cana-6219	90	9	form	form	NOUN
cana-6219	90	10	𝑒𝑖𝑗	𝑒𝑖𝑗	NOUN
cana-6219	90	11	=	=	SYM
cana-6219	90	12	1	1	NUM
cana-6219	90	13	2	2	NUM
cana-6219	90	14	(	(	PUNCT
cana-6219	90	15	𝑢𝑖,𝑗	𝑢𝑖,𝑗	PART
cana-6219	90	16	−	−	NOUN
cana-6219	90	17	𝑢𝑗,𝑖	𝑢𝑗,𝑖	NOUN
cana-6219	90	18	)	)	PUNCT
cana-6219	90	19	.	.	PUNCT
cana-6219	91	1	(	(	PUNCT
cana-6219	91	2	4	4	X
cana-6219	91	3	)	)	PUNCT
cana-6219	91	4	3	3	NUM
cana-6219	91	5	.	.	X
cana-6219	91	6	problem	problem	NOUN
cana-6219	91	7	formulation	formulation	NOUN
cana-6219	91	8	assume	assume	VERB
cana-6219	91	9	an	an	DET
cana-6219	91	10	isotropic	isotropic	NOUN
cana-6219	91	11	,	,	PUNCT
cana-6219	91	12	homogeneous	homogeneous	ADJ
cana-6219	91	13	boundary	boundary	ADJ
cana-6219	91	14	value	value	NOUN
cana-6219	91	15	problem	problem	NOUN
cana-6219	91	16	in	in	ADP
cana-6219	91	17	three	three	NUM
cana-6219	91	18	dimensions	dimension	NOUN
cana-6219	91	19	occupies	occupy	VERB
cana-6219	91	20	the	the	DET
cana-6219	91	21	space	space	NOUN
cana-6219	91	22	𝜓	𝜓	NOUN
cana-6219	91	23	=	=	PUNCT
cana-6219	91	24	{	{	PUNCT
cana-6219	91	25	𝑥	𝑥	PROPN
cana-6219	91	26	,	,	PUNCT
cana-6219	91	27	𝑦	𝑦	NOUN
cana-6219	91	28	,	,	PUNCT
cana-6219	91	29	𝑧	𝑧	DET
cana-6219	91	30	∶	∶	NOUN
cana-6219	91	31	0	0	NUM
cana-6219	91	32	≤	≤	NUM
cana-6219	92	1	𝑥	𝑥	ADP
cana-6219	92	2	<	<	X
cana-6219	92	3	∞	∞	PROPN
cana-6219	92	4	,	,	PUNCT
cana-6219	92	5	−∞	−∞	ADP
cana-6219	92	6	<	<	X
cana-6219	92	7	𝑦	𝑦	X
cana-6219	92	8	<	<	X
cana-6219	92	9	∞	∞	PROPN
cana-6219	92	10	,	,	PUNCT
cana-6219	92	11	−∞	−∞	ADP
cana-6219	92	12	<	<	X
cana-6219	92	13	𝑧	𝑧	X
cana-6219	92	14	<	<	X
cana-6219	92	15	∞	∞	PROPN
cana-6219	92	16	}	}	PUNCT
cana-6219	92	17	where	where	SCONJ
cana-6219	92	18	the	the	DET
cana-6219	92	19	body	body	NOUN
cana-6219	92	20	is	be	AUX
cana-6219	92	21	quiescent	quiescent	ADJ
cana-6219	92	22	initially	initially	ADV
cana-6219	92	23	and	and	CCONJ
cana-6219	92	24	is	be	AUX
cana-6219	92	25	loaded	load	VERB
cana-6219	92	26	thermally	thermally	ADV
cana-6219	92	27	by	by	ADP
cana-6219	92	28	a	a	DET
cana-6219	92	29	moving	move	VERB
cana-6219	92	30	heat	heat	NOUN
cana-6219	92	31	source	source	NOUN
cana-6219	92	32	with	with	ADP
cana-6219	92	33	constant	constant	ADJ
cana-6219	92	34	speed	speed	NOUN
cana-6219	92	35	𝜐	𝜐	NOUN
cana-6219	92	36	,	,	PUNCT
cana-6219	92	37	which	which	PRON
cana-6219	92	38	starts	start	VERB
cana-6219	92	39	from	from	ADP
cana-6219	92	40	the	the	DET
cana-6219	92	41	bounding	bounding	NOUN
cana-6219	92	42	plane	plane	NOUN
cana-6219	92	43	of	of	ADP
cana-6219	92	44	the	the	DET
cana-6219	92	45	surface	surface	NOUN
cana-6219	92	46	𝑥	𝑥	NOUN
cana-6219	92	47	=	=	SYM
cana-6219	92	48	0	0	NUM
cana-6219	92	49	and	and	CCONJ
cana-6219	92	50	moves	move	NOUN
cana-6219	92	51	along	along	ADP
cana-6219	92	52	the	the	DET
cana-6219	92	53	x	x	NOUN
cana-6219	92	54	-	-	NOUN
cana-6219	92	55	axis	axis	ADJ
cana-6219	92	56	when	when	SCONJ
cana-6219	92	57	these	these	DET
cana-6219	92	58	surfaces	surface	NOUN
cana-6219	92	59	are	be	AUX
cana-6219	92	60	traction	traction	NOUN
cana-6219	92	61	-	-	PUNCT
cana-6219	92	62	free	free	ADJ
cana-6219	92	63	as	as	ADP
cana-6219	92	64	in	in	ADP
cana-6219	92	65	fig	fig	NOUN
cana-6219	92	66	.	.	PUNCT
cana-6219	93	1	1	1	NUM
cana-6219	93	2	fig.1	fig.1	PROPN
cana-6219	93	3	.	.	PUNCT
cana-6219	93	4	graphical	graphical	ADJ
cana-6219	93	5	representation	representation	NOUN
cana-6219	93	6	of	of	ADP
cana-6219	93	7	problem	problem	NOUN
cana-6219	93	8	the	the	DET
cana-6219	93	9	equations	equation	NOUN
cana-6219	93	10	of	of	ADP
cana-6219	93	11	motion	motion	NOUN
cana-6219	93	12	are	be	AUX
cana-6219	93	13	(	(	PUNCT
cana-6219	93	14	𝜆	𝜆	NOUN
cana-6219	93	15	+	+	NOUN
cana-6219	93	16	2𝜇	2𝜇	NOUN
cana-6219	93	17	)	)	PUNCT
cana-6219	93	18	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6219	93	19	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	93	20	+	+	CCONJ
cana-6219	93	21	𝜇	𝜇	ADP
cana-6219	93	22	(	(	PUNCT
cana-6219	93	23	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6219	93	24	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	93	25	+	+	CCONJ
cana-6219	93	26	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6219	93	27	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	93	28	)	)	PUNCT
cana-6219	94	1	+	+	CCONJ
cana-6219	94	2	(	(	PUNCT
cana-6219	94	3	𝜆	𝜆	NOUN
cana-6219	94	4	+	+	X
cana-6219	94	5	𝜇	𝜇	X
cana-6219	94	6	)	)	PUNCT
cana-6219	94	7	(	(	PUNCT
cana-6219	94	8	𝜕2𝑣	𝜕2𝑣	NOUN
cana-6219	94	9	𝜕𝑥𝜕𝑦	𝜕𝑥𝜕𝑦	NOUN
cana-6219	94	10	+	+	CCONJ
cana-6219	94	11	𝜕2𝑤	𝜕2𝑤	CCONJ
cana-6219	94	12	𝜕𝑥𝜕𝑧	𝜕𝑥𝜕𝑧	NOUN
cana-6219	94	13	)	)	PUNCT
cana-6219	95	1	−	−	ADP
cana-6219	95	2	𝛾	𝛾	NOUN
cana-6219	95	3	𝜕𝜃	𝜕𝜃	NOUN
cana-6219	95	4	𝜕𝑥	𝜕𝑥	X
cana-6219	95	5	=	=	PUNCT
cana-6219	95	6	𝜌𝑢	𝜌𝑢	NOUN
cana-6219	95	7	̈	̈	PUNCT
cana-6219	95	8	(	(	PUNCT
cana-6219	95	9	5	5	NUM
cana-6219	95	10	)	)	PUNCT
cana-6219	95	11	(	(	PUNCT
cana-6219	95	12	𝜆	𝜆	NOUN
cana-6219	95	13	+	+	NOUN
cana-6219	95	14	2𝜇	2𝜇	NUM
cana-6219	95	15	)	)	PUNCT
cana-6219	95	16	𝜕2𝑣	𝜕2𝑣	PROPN
cana-6219	95	17	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	95	18	+	+	CCONJ
cana-6219	95	19	𝜇	𝜇	X
cana-6219	95	20	(	(	PUNCT
cana-6219	95	21	𝜕2𝑣	𝜕2𝑣	PROPN
cana-6219	95	22	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	95	23	+	+	CCONJ
cana-6219	95	24	𝜕2𝑣	𝜕2𝑣	NOUN
cana-6219	95	25	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	95	26	)	)	PUNCT
cana-6219	96	1	+	+	CCONJ
cana-6219	96	2	(	(	PUNCT
cana-6219	96	3	𝜆	𝜆	NOUN
cana-6219	96	4	+	+	X
cana-6219	96	5	𝜇	𝜇	X
cana-6219	96	6	)	)	PUNCT
cana-6219	96	7	(	(	PUNCT
cana-6219	96	8	𝜕2𝑢	𝜕2𝑢	PROPN
cana-6219	96	9	𝜕𝑥𝜕𝑦	𝜕𝑥𝜕𝑦	NOUN
cana-6219	96	10	+	+	CCONJ
cana-6219	96	11	𝜕2𝑤	𝜕2𝑤	CCONJ
cana-6219	96	12	𝜕𝑧𝜕𝑦	𝜕𝑧𝜕𝑦	ADJ
cana-6219	96	13	)	)	PUNCT
cana-6219	97	1	−	−	ADP
cana-6219	97	2	𝛾	𝛾	NOUN
cana-6219	97	3	𝜕𝜃	𝜕𝜃	NOUN
cana-6219	97	4	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	97	5	=	=	SYM
cana-6219	97	6	𝜌𝑣	𝜌𝑣	X
cana-6219	97	7	̈	̈	PUNCT
cana-6219	97	8	(	(	PUNCT
cana-6219	97	9	6	6	NUM
cana-6219	97	10	)	)	PUNCT
cana-6219	97	11	(	(	PUNCT
cana-6219	97	12	𝜆	𝜆	NOUN
cana-6219	97	13	+	+	NUM
cana-6219	97	14	2𝜇	2𝜇	NUM
cana-6219	97	15	)	)	PUNCT
cana-6219	98	1	𝜕2𝑤	𝜕2𝑤	ADP
cana-6219	98	2	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	98	3	+	+	CCONJ
cana-6219	98	4	𝜇	𝜇	X
cana-6219	98	5	(	(	PUNCT
cana-6219	98	6	𝜕2𝑤	𝜕2𝑤	ADP
cana-6219	98	7	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	98	8	+	+	CCONJ
cana-6219	98	9	𝜕2𝑤	𝜕2𝑤	CCONJ
cana-6219	98	10	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	98	11	)	)	PUNCT
cana-6219	99	1	+	+	CCONJ
cana-6219	99	2	(	(	PUNCT
cana-6219	99	3	𝜆	𝜆	NOUN
cana-6219	99	4	+	+	X
cana-6219	99	5	𝜇	𝜇	X
cana-6219	99	6	)	)	PUNCT
cana-6219	99	7	(	(	PUNCT
cana-6219	99	8	𝜕2𝑢	𝜕2𝑢	NUM
cana-6219	99	9	𝜕𝑧𝜕𝑥	𝜕𝑧𝜕𝑥	NOUN
cana-6219	99	10	+	+	CCONJ
cana-6219	99	11	𝜕2𝑣	𝜕2𝑣	NOUN
cana-6219	99	12	𝜕𝑧𝜕𝑦	𝜕𝑧𝜕𝑦	ADJ
cana-6219	99	13	)	)	PUNCT
cana-6219	99	14	−	−	ADP
cana-6219	99	15	𝛾	𝛾	NOUN
cana-6219	99	16	𝜕𝜃	𝜕𝜃	NOUN
cana-6219	99	17	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	99	18	=	=	SYM
cana-6219	99	19	𝜌𝑤	𝜌𝑤	ADP
cana-6219	99	20	̈	̈	PUNCT
cana-6219	99	21	(	(	PUNCT
cana-6219	99	22	7	7	NUM
cana-6219	99	23	)	)	PUNCT
cana-6219	99	24	the	the	DET
cana-6219	99	25	heat	heat	NOUN
cana-6219	99	26	equation	equation	NOUN
cana-6219	99	27	is	be	AUX
cana-6219	99	28	𝐾	𝐾	PROPN
cana-6219	99	29	(	(	PUNCT
cana-6219	99	30	𝜕2𝜃	𝜕2𝜃	NUM
cana-6219	99	31	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	99	32	+	+	CCONJ
cana-6219	99	33	𝜕2𝜃	𝜕2𝜃	NUM
cana-6219	99	34	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	99	35	+	+	CCONJ
cana-6219	99	36	𝜕2𝜃	𝜕2𝜃	NOUN
cana-6219	99	37	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	99	38	)	)	PUNCT
cana-6219	100	1	=	=	SYM
cana-6219	100	2	𝜌𝐶𝐸	𝜌𝐶𝐸	NOUN
cana-6219	100	3	(	(	PUNCT
cana-6219	100	4	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	100	5	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	101	1	+	+	CCONJ
cana-6219	101	2	𝜏0	𝜏0	PROPN
cana-6219	101	3	𝜕𝛼+1	𝜕𝛼+1	VERB
cana-6219	101	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	101	5	)	)	PUNCT
cana-6219	101	6	𝜃	𝜃	X
cana-6219	102	1	+	+	NOUN
cana-6219	102	2	𝛾𝑇0	𝛾𝑇0	PROPN
cana-6219	102	3	(	(	PUNCT
cana-6219	102	4	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	102	5	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	102	6	+	+	CCONJ
cana-6219	102	7	𝜏0	𝜏0	PROPN
cana-6219	102	8	𝜕𝛼+1	𝜕𝛼+1	VERB
cana-6219	102	9	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	102	10	)	)	PUNCT
cana-6219	103	1	(	(	PUNCT
cana-6219	103	2	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	103	3	𝜕𝑥	𝜕𝑥	NOUN
cana-6219	103	4	+	+	CCONJ
cana-6219	103	5	𝜕𝑣	𝜕𝑣	NOUN
cana-6219	103	6	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	104	1	+	+	NUM
cana-6219	104	2	𝜕𝑤	𝜕𝑤	VERB
cana-6219	104	3	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	104	4	)	)	PUNCT
cana-6219	104	5	−	−	PROPN
cana-6219	105	1	(	(	PUNCT
cana-6219	105	2	1	1	NUM
cana-6219	105	3	+	+	NUM
cana-6219	105	4	𝜏0	𝜏0	PROPN
cana-6219	105	5	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	105	6	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	105	7	)	)	PUNCT
cana-6219	106	1	𝑄	𝑄	PROPN
cana-6219	106	2	(	(	PUNCT
cana-6219	106	3	8)	8)	NUM
cana-6219	106	4	the	the	DET
cana-6219	106	5	stress	stress	NOUN
cana-6219	106	6	-	-	PUNCT
cana-6219	106	7	strain	strain	NOUN
cana-6219	106	8	relations	relation	NOUN
cana-6219	106	9	as	as	ADP
cana-6219	106	10	:	:	PUNCT
cana-6219	106	11	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6219	106	12	=	=	SYM
cana-6219	106	13	2𝜇𝑒𝑥𝑥	2𝜇𝑒𝑥𝑥	NUM
cana-6219	106	14	+	+	NOUN
cana-6219	106	15	𝜆𝑒	𝜆𝑒	NOUN
cana-6219	106	16	−	−	ADV
cana-6219	106	17	𝛾𝜃	𝛾𝜃	INTJ
cana-6219	106	18	,	,	PUNCT
cana-6219	106	19	(	(	PUNCT
cana-6219	106	20	9	9	X
cana-6219	106	21	)	)	PUNCT
cana-6219	106	22	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6219	106	23	=	=	SYM
cana-6219	106	24	2𝜇𝑒𝑦𝑦	2𝜇𝑒𝑦𝑦	PROPN
cana-6219	107	1	+	+	CCONJ
cana-6219	107	2	𝜆𝑒	𝜆𝑒	NOUN
cana-6219	107	3	−	−	ADV
cana-6219	107	4	𝛾𝜃	𝛾𝜃	INTJ
cana-6219	107	5	,	,	PUNCT
cana-6219	107	6	(	(	PUNCT
cana-6219	107	7	10	10	NUM
cana-6219	107	8	)	)	PUNCT
cana-6219	107	9	communications	communication	NOUN
cana-6219	107	10	on	on	ADP
cana-6219	107	11	applied	apply	VERB
cana-6219	107	12	nonlinear	nonlinear	ADJ
cana-6219	107	13	analysis	analysis	NOUN
cana-6219	107	14	issn	issn	NOUN
cana-6219	107	15	:	:	PUNCT
cana-6219	107	16	1074	1074	NUM
cana-6219	107	17	-	-	PUNCT
cana-6219	107	18	133x	133x	NUM
cana-6219	107	19	vol	vol	VERB
cana-6219	107	20	32	32	NUM
cana-6219	107	21	no	no	NOUN
cana-6219	107	22	.	.	PUNCT
cana-6219	108	1	10s	10	NOUN
cana-6219	108	2	(	(	PUNCT
cana-6219	108	3	2025	2025	NUM
cana-6219	108	4	)	)	PUNCT
cana-6219	108	5	3533	3533	NUM
cana-6219	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	108	7	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6219	108	8	=	=	PUNCT
cana-6219	109	1	2𝜇𝑒𝑧𝑧	2𝜇𝑒𝑧𝑧	NUM
cana-6219	109	2	+	+	CCONJ
cana-6219	109	3	𝜆𝑒	𝜆𝑒	NOUN
cana-6219	109	4	−	−	NOUN
cana-6219	109	5	𝛾𝜃	𝛾𝜃	INTJ
cana-6219	109	6	,	,	PUNCT
cana-6219	109	7	(	(	PUNCT
cana-6219	109	8	11	11	NUM
cana-6219	109	9	)	)	PUNCT
cana-6219	109	10	𝜎𝑥𝑦	𝜎𝑥𝑦	NOUN
cana-6219	109	11	=	=	SYM
cana-6219	109	12	2𝜇𝑒𝑥𝑦	2𝜇𝑒𝑥𝑦	NUM
cana-6219	109	13	(	(	PUNCT
cana-6219	109	14	12	12	NUM
cana-6219	109	15	)	)	PUNCT
cana-6219	109	16	𝜎𝑥𝑧	𝜎𝑥𝑧	NOUN
cana-6219	109	17	=	=	SYM
cana-6219	109	18	2𝜇𝑒𝑥𝑧	2𝜇𝑒𝑥𝑧	NUM
cana-6219	109	19	(	(	PUNCT
cana-6219	109	20	13	13	NUM
cana-6219	109	21	)	)	PUNCT
cana-6219	109	22	𝜎𝑦𝑧	𝜎𝑦𝑧	NOUN
cana-6219	109	23	=	=	SYM
cana-6219	109	24	2𝜇𝑒𝑦𝑧	2𝜇𝑒𝑦𝑧	NUM
cana-6219	109	25	(	(	PUNCT
cana-6219	109	26	14	14	NUM
cana-6219	109	27	)	)	PUNCT
cana-6219	109	28	the	the	DET
cana-6219	109	29	strain	strain	NOUN
cana-6219	109	30	components	component	NOUN
cana-6219	109	31	are	be	AUX
cana-6219	109	32	:	:	PUNCT
cana-6219	109	33	𝜎𝑥𝑥	𝜎𝑥𝑥	ADJ
cana-6219	109	34	=	=	SYM
cana-6219	109	35	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	109	36	𝜕𝑥	𝜕𝑥	NOUN
cana-6219	109	37	,	,	PUNCT
cana-6219	109	38	𝜎𝑦𝑦	𝜎𝑦𝑦	ADJ
cana-6219	109	39	=	=	SYM
cana-6219	109	40	𝜕𝑣	𝜕𝑣	PROPN
cana-6219	109	41	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	109	42	,	,	PUNCT
cana-6219	109	43	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6219	109	44	=	=	PUNCT
cana-6219	109	45	𝜕𝑤	𝜕𝑤	VERB
cana-6219	109	46	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	109	47	(	(	PUNCT
cana-6219	109	48	15	15	NUM
cana-6219	109	49	)	)	PUNCT
cana-6219	109	50	𝜎𝑥𝑦	𝜎𝑥𝑦	NOUN
cana-6219	109	51	=	=	SYM
cana-6219	109	52	1	1	NUM
cana-6219	109	53	2	2	NUM
cana-6219	109	54	(	(	PUNCT
cana-6219	109	55	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	109	56	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	109	57	+	+	CCONJ
cana-6219	109	58	𝜕𝑣	𝜕𝑣	PROPN
cana-6219	109	59	𝜕𝑥	𝜕𝑥	X
cana-6219	109	60	)	)	PUNCT
cana-6219	109	61	,	,	PUNCT
cana-6219	109	62	𝜎𝑥𝑧	𝜎𝑥𝑧	NOUN
cana-6219	109	63	=	=	NOUN
cana-6219	109	64	1	1	NUM
cana-6219	109	65	2	2	NUM
cana-6219	109	66	(	(	PUNCT
cana-6219	109	67	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	109	68	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	109	69	+	+	NUM
cana-6219	109	70	𝜕𝑤	𝜕𝑤	NOUN
cana-6219	109	71	𝜕𝑥	𝜕𝑥	X
cana-6219	109	72	)	)	PUNCT
cana-6219	109	73	,	,	PUNCT
cana-6219	109	74	𝜎𝑦𝑧	𝜎𝑦𝑧	NOUN
cana-6219	109	75	=	=	SYM
cana-6219	109	76	1	1	NUM
cana-6219	109	77	2	2	NUM
cana-6219	109	78	(	(	PUNCT
cana-6219	109	79	𝜕𝑤	𝜕𝑤	VERB
cana-6219	109	80	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	109	81	+	+	PUNCT
cana-6219	109	82	𝜕𝑣	𝜕𝑣	PROPN
cana-6219	109	83	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	109	84	)	)	PUNCT
cana-6219	109	85	(	(	PUNCT
cana-6219	109	86	16	16	NUM
cana-6219	109	87	)	)	PUNCT
cana-6219	109	88	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	109	89	𝜕𝑥	𝜕𝑥	NOUN
cana-6219	109	90	+	+	CCONJ
cana-6219	109	91	𝜕𝑣	𝜕𝑣	NOUN
cana-6219	109	92	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	109	93	+	+	CCONJ
cana-6219	109	94	𝜕𝑤	𝜕𝑤	VERB
cana-6219	109	95	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	109	96	=	=	SYM
cana-6219	109	97	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6219	109	98	+	+	CCONJ
cana-6219	109	99	𝜎𝑦𝑦	𝜎𝑦𝑦	ADJ
cana-6219	109	100	+	+	CCONJ
cana-6219	109	101	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6219	109	102	=	=	PUNCT
cana-6219	109	103	𝑒.	𝑒.	NOUN
cana-6219	109	104	(	(	PUNCT
cana-6219	109	105	17	17	NUM
cana-6219	109	106	)	)	PUNCT
cana-6219	109	107	equations	equation	NOUN
cana-6219	109	108	(	(	PUNCT
cana-6219	109	109	5)-(7	5)-(7	NUM
cana-6219	109	110	)	)	PUNCT
cana-6219	109	111	can	can	AUX
cana-6219	109	112	be	be	AUX
cana-6219	109	113	rewritten	rewrite	VERB
cana-6219	109	114	by	by	ADP
cana-6219	109	115	using	use	VERB
cana-6219	109	116	eq	eq	ADP
cana-6219	109	117	.	.	PUNCT
cana-6219	110	1	(	(	PUNCT
cana-6219	110	2	17	17	NUM
cana-6219	110	3	)	)	PUNCT
cana-6219	110	4	as	as	ADP
cana-6219	110	5	:	:	PUNCT
cana-6219	110	6	𝜇∇2	𝜇∇2	PROPN
cana-6219	110	7	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	110	8	𝜕𝑥	𝜕𝑥	NOUN
cana-6219	110	9	+	+	CCONJ
cana-6219	110	10	(	(	PUNCT
cana-6219	110	11	𝜆	𝜆	NOUN
cana-6219	110	12	+	+	X
cana-6219	110	13	𝜇	𝜇	X
cana-6219	110	14	)	)	PUNCT
cana-6219	110	15	𝜕2𝑒	𝜕2𝑒	NUM
cana-6219	110	16	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	110	17	−	−	NOUN
cana-6219	110	18	𝛾	𝛾	ADP
cana-6219	110	19	𝜕2𝜃	𝜕2𝜃	PRON
cana-6219	110	20	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	110	21	=	=	PUNCT
cana-6219	110	22	𝜌	𝜌	X
cana-6219	110	23	𝜕𝑢	𝜕𝑢	NUM
cana-6219	110	24	̈	̈	PUNCT
cana-6219	110	25	𝜕𝑥	𝜕𝑥	X
cana-6219	110	26	(	(	PUNCT
cana-6219	110	27	18	18	NUM
cana-6219	110	28	)	)	PUNCT
cana-6219	110	29	𝜇∇2	𝜇∇2	NOUN
cana-6219	110	30	𝜕𝑣	𝜕𝑣	PROPN
cana-6219	110	31	𝜕𝑦	𝜕𝑦	PROPN
cana-6219	111	1	+	+	CCONJ
cana-6219	111	2	(	(	PUNCT
cana-6219	111	3	𝜆	𝜆	NOUN
cana-6219	111	4	+	+	X
cana-6219	111	5	𝜇	𝜇	X
cana-6219	111	6	)	)	PUNCT
cana-6219	111	7	𝜕2𝑒	𝜕2𝑒	PROPN
cana-6219	111	8	𝜕𝑦2	𝜕𝑦2	PROPN
cana-6219	111	9	−	−	PROPN
cana-6219	111	10	𝛾	𝛾	ADP
cana-6219	111	11	𝜕2𝜃	𝜕2𝜃	DET
cana-6219	111	12	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	111	13	=	=	PUNCT
cana-6219	111	14	𝜌	𝜌	ADP
cana-6219	111	15	𝜕𝑣	𝜕𝑣	NOUN
cana-6219	111	16	̈	̈	X
cana-6219	111	17	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	111	18	(	(	PUNCT
cana-6219	111	19	19	19	NUM
cana-6219	111	20	)	)	PUNCT
cana-6219	111	21	𝜇∇2	𝜇∇2	NOUN
cana-6219	111	22	𝜕𝑤	𝜕𝑤	VERB
cana-6219	111	23	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	111	24	+	+	CCONJ
cana-6219	111	25	(	(	PUNCT
cana-6219	111	26	𝜆	𝜆	AUX
cana-6219	111	27	+	+	X
cana-6219	111	28	𝜇	𝜇	X
cana-6219	111	29	)	)	PUNCT
cana-6219	111	30	𝜕2𝑒	𝜕2𝑒	VERB
cana-6219	111	31	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	111	32	−	−	NOUN
cana-6219	111	33	𝛾	𝛾	AUX
cana-6219	111	34	𝜕2𝜃	𝜕2𝜃	NUM
cana-6219	111	35	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	111	36	=	=	PUNCT
cana-6219	111	37	𝜌	𝜌	X
cana-6219	111	38	𝜕𝑤	𝜕𝑤	VERB
cana-6219	111	39	̈	̈	X
cana-6219	111	40	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	111	41	(	(	PUNCT
cana-6219	111	42	20	20	NUM
cana-6219	111	43	)	)	PUNCT
cana-6219	112	1	where	where	SCONJ
cana-6219	112	2	,	,	PUNCT
cana-6219	112	3	∇2=	∇2=	PROPN
cana-6219	112	4	𝜕2	𝜕2	NOUN
cana-6219	112	5	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	112	6	+	+	CCONJ
cana-6219	112	7	𝜕2	𝜕2	NOUN
cana-6219	112	8	𝜕𝑦2	𝜕𝑦2	ADJ
cana-6219	112	9	+	+	CCONJ
cana-6219	112	10	𝜕2	𝜕2	NOUN
cana-6219	112	11	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	112	12	.	.	PUNCT
cana-6219	113	1	the	the	DET
cana-6219	113	2	heat	heat	NOUN
cana-6219	113	3	conduction	conduction	NOUN
cana-6219	113	4	equation	equation	NOUN
cana-6219	113	5	takes	take	VERB
cana-6219	113	6	the	the	DET
cana-6219	113	7	form	form	NOUN
cana-6219	113	8	𝐾∇2𝜃	𝐾∇2𝜃	X
cana-6219	113	9	=	=	PUNCT
cana-6219	113	10	𝜌𝐶𝐸	𝜌𝐶𝐸	PROPN
cana-6219	113	11	(	(	PUNCT
cana-6219	113	12	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	113	13	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	114	1	+	+	CCONJ
cana-6219	114	2	𝜏0	𝜏0	PROPN
cana-6219	114	3	𝜕𝛼+1	𝜕𝛼+1	VERB
cana-6219	114	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	114	5	)	)	PUNCT
cana-6219	115	1	𝜃	𝜃	PROPN
cana-6219	116	1	+	+	NUM
cana-6219	116	2	𝛾𝑇0	𝛾𝑇0	PROPN
cana-6219	116	3	(	(	PUNCT
cana-6219	116	4	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	116	5	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	117	1	+	+	CCONJ
cana-6219	117	2	𝜏0	𝜏0	PROPN
cana-6219	117	3	𝜕𝛼+1	𝜕𝛼+1	ADV
cana-6219	117	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	117	5	)	)	PUNCT
cana-6219	117	6	𝑒	𝑒	ADP
cana-6219	117	7	−	−	PROPN
cana-6219	117	8	(	(	PUNCT
cana-6219	117	9	1	1	NUM
cana-6219	117	10	+	+	NUM
cana-6219	117	11	𝜏0	𝜏0	PROPN
cana-6219	117	12	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	117	13	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	117	14	)	)	PUNCT
cana-6219	118	1	𝑄	𝑄	PROPN
cana-6219	118	2	(	(	PUNCT
cana-6219	118	3	21	21	NUM
cana-6219	118	4	)	)	PUNCT
cana-6219	118	5	now	now	ADV
cana-6219	118	6	,	,	PUNCT
cana-6219	118	7	the	the	DET
cana-6219	118	8	following	follow	VERB
cana-6219	118	9	dimensionless	dimensionless	NOUN
cana-6219	118	10	variables	variable	NOUN
cana-6219	118	11	will	will	AUX
cana-6219	118	12	be	be	AUX
cana-6219	118	13	applied	apply	VERB
cana-6219	118	14	(	(	PUNCT
cana-6219	118	15	ezzat	ezzat	ADJ
cana-6219	118	16	,	,	PUNCT
cana-6219	118	17	youssef	youssef	PROPN
cana-6219	119	1	[	[	X
cana-6219	119	2	5	5	NUM
cana-6219	119	3	-	-	SYM
cana-6219	119	4	6	6	NUM
cana-6219	119	5	-	-	SYM
cana-6219	119	6	10	10	NUM
cana-6219	119	7	]	]	PUNCT
cana-6219	119	8	:	:	PUNCT
cana-6219	119	9	(	(	PUNCT
cana-6219	119	10	𝑥∗	𝑥∗	PROPN
cana-6219	119	11	,	,	PUNCT
cana-6219	119	12	𝑦∗	𝑦∗	PROPN
cana-6219	119	13	,	,	PUNCT
cana-6219	119	14	𝑧∗	𝑧∗	PROPN
cana-6219	119	15	)	)	PUNCT
cana-6219	119	16	=	=	SYM
cana-6219	120	1	𝑐𝜂(𝑥	𝑐𝜂(𝑥	PROPN
cana-6219	120	2	,	,	PUNCT
cana-6219	120	3	𝑦	𝑦	NOUN
cana-6219	120	4	,	,	PUNCT
cana-6219	120	5	𝑧	𝑧	NOUN
cana-6219	120	6	)	)	PUNCT
cana-6219	120	7	,	,	PUNCT
cana-6219	120	8	(	(	PUNCT
cana-6219	120	9	𝑡∗	𝑡∗	NOUN
cana-6219	120	10	,	,	PUNCT
cana-6219	120	11	𝜏0	𝜏0	NOUN
cana-6219	120	12	∗	∗	NOUN
cana-6219	120	13	)	)	PUNCT
cana-6219	120	14	=	=	SYM
cana-6219	121	1	𝑐2𝜂(𝑡	𝑐2𝜂(𝑡	PROPN
cana-6219	121	2	,	,	PUNCT
cana-6219	121	3	𝜏0	𝜏0	PROPN
cana-6219	121	4	)	)	PUNCT
cana-6219	121	5	,	,	PUNCT
cana-6219	121	6	𝜃∗	𝜃∗	PROPN
cana-6219	121	7	=	=	PUNCT
cana-6219	121	8	𝛾𝜃	𝛾𝜃	PROPN
cana-6219	121	9	(	(	PUNCT
cana-6219	121	10	𝛾	𝛾	NOUN
cana-6219	121	11	+	+	X
cana-6219	121	12	2𝜇	2𝜇	NUM
cana-6219	121	13	)	)	PUNCT
cana-6219	121	14	𝑄∗	𝑄∗	PUNCT
cana-6219	122	1	=	=	PUNCT
cana-6219	122	2	𝑄	𝑄	PROPN
cana-6219	122	3	𝐾𝑐2𝜂2𝑇0	𝐾𝑐2𝜂2𝑇0	X
cana-6219	122	4	,	,	PUNCT
cana-6219	122	5	𝜎𝑖𝑗	𝜎𝑖𝑗	NOUN
cana-6219	122	6	∗	∗	NOUN
cana-6219	122	7	=	=	PUNCT
cana-6219	123	1	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-6219	123	2	𝛾	𝛾	NOUN
cana-6219	123	3	+	+	CCONJ
cana-6219	123	4	2𝜇	2𝜇	NUM
cana-6219	123	5	,	,	PUNCT
cana-6219	123	6	𝑐	𝑐	NOUN
cana-6219	123	7	=	=	PUNCT
cana-6219	123	8	√	√	PROPN
cana-6219	123	9	𝛾	𝛾	ADP
cana-6219	123	10	+	+	NUM
cana-6219	123	11	2𝜇	2𝜇	NUM
cana-6219	123	12	𝜌	𝜌	NOUN
cana-6219	123	13	,	,	PUNCT
cana-6219	123	14	𝜂	𝜂	X
cana-6219	123	15	=	=	PUNCT
cana-6219	123	16	𝜌𝐶𝐸	𝜌𝐶𝐸	NOUN
cana-6219	123	17	𝐾	𝐾	NOUN
cana-6219	123	18	.	.	PUNCT
cana-6219	124	1	thus	thus	ADV
cana-6219	124	2	,	,	PUNCT
cana-6219	124	3	we	we	PRON
cana-6219	124	4	obtain	obtain	VERB
cana-6219	124	5	communications	communication	NOUN
cana-6219	124	6	on	on	ADP
cana-6219	124	7	applied	apply	VERB
cana-6219	124	8	nonlinear	nonlinear	ADJ
cana-6219	124	9	analysis	analysis	NOUN
cana-6219	124	10	issn	issn	NOUN
cana-6219	124	11	:	:	PUNCT
cana-6219	124	12	1074	1074	NUM
cana-6219	124	13	-	-	PUNCT
cana-6219	124	14	133x	133x	NUM
cana-6219	124	15	vol	vol	VERB
cana-6219	124	16	32	32	NUM
cana-6219	124	17	no	no	NOUN
cana-6219	124	18	.	.	PUNCT
cana-6219	125	1	10s	10	NOUN
cana-6219	125	2	(	(	PUNCT
cana-6219	125	3	2025	2025	NUM
cana-6219	125	4	)	)	PUNCT
cana-6219	125	5	3534	3534	NUM
cana-6219	125	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	125	7	𝛽∇2	𝛽∇2	ADJ
cana-6219	125	8	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	125	9	𝜕𝑥	𝜕𝑥	NOUN
cana-6219	125	10	+	+	CCONJ
cana-6219	125	11	(	(	PUNCT
cana-6219	125	12	1	1	NUM
cana-6219	125	13	−	−	PROPN
cana-6219	125	14	𝛽	𝛽	NOUN
cana-6219	125	15	)	)	PUNCT
cana-6219	125	16	𝜕2𝑒	𝜕2𝑒	NUM
cana-6219	125	17	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	125	18	−	−	NOUN
cana-6219	125	19	𝜕2𝜃	𝜕2𝜃	NUM
cana-6219	125	20	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	125	21	=	=	SYM
cana-6219	125	22	𝜕𝑢	𝜕𝑢	NOUN
cana-6219	125	23	̈	̈	X
cana-6219	125	24	𝜕𝑥	𝜕𝑥	X
cana-6219	125	25	(	(	PUNCT
cana-6219	125	26	22	22	NUM
cana-6219	125	27	)	)	PUNCT
cana-6219	125	28	𝛽∇2	𝛽∇2	VERB
cana-6219	125	29	𝜕𝑣	𝜕𝑣	NOUN
cana-6219	125	30	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	125	31	+	+	CCONJ
cana-6219	125	32	(	(	PUNCT
cana-6219	125	33	1	1	NUM
cana-6219	125	34	−	−	PROPN
cana-6219	125	35	𝛽	𝛽	NOUN
cana-6219	125	36	)	)	PUNCT
cana-6219	125	37	𝜕2𝑒	𝜕2𝑒	PROPN
cana-6219	125	38	𝜕𝑦2	𝜕𝑦2	VERB
cana-6219	125	39	−	−	PROPN
cana-6219	125	40	𝜕2𝜃	𝜕2𝜃	NUM
cana-6219	125	41	𝜕𝑦2	𝜕𝑦2	NOUN
cana-6219	125	42	=	=	SYM
cana-6219	125	43	𝜕𝑣	𝜕𝑣	NOUN
cana-6219	125	44	̈	̈	X
cana-6219	125	45	𝜕𝑦	𝜕𝑦	NOUN
cana-6219	125	46	(	(	PUNCT
cana-6219	125	47	23	23	NUM
cana-6219	125	48	)	)	PUNCT
cana-6219	125	49	𝛽∇2	𝛽∇2	ADJ
cana-6219	125	50	𝜕𝑤	𝜕𝑤	VERB
cana-6219	125	51	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	125	52	+	+	CCONJ
cana-6219	125	53	(	(	PUNCT
cana-6219	125	54	1	1	NUM
cana-6219	125	55	−	−	PROPN
cana-6219	125	56	𝛽	𝛽	NOUN
cana-6219	125	57	)	)	PUNCT
cana-6219	125	58	𝜕2𝑒	𝜕2𝑒	VERB
cana-6219	125	59	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	125	60	−	−	ADP
cana-6219	125	61	𝜕2𝜃	𝜕2𝜃	NOUN
cana-6219	125	62	𝜕𝑧2	𝜕𝑧2	NOUN
cana-6219	125	63	=	=	PUNCT
cana-6219	125	64	𝜕𝑤	𝜕𝑤	VERB
cana-6219	125	65	̈	̈	PUNCT
cana-6219	125	66	𝜕𝑧	𝜕𝑧	NOUN
cana-6219	125	67	(	(	PUNCT
cana-6219	125	68	24	24	NUM
cana-6219	125	69	)	)	PUNCT
cana-6219	125	70	∇2𝜃	∇2𝜃	NOUN
cana-6219	126	1	=	=	PUNCT
cana-6219	126	2	(	(	PUNCT
cana-6219	126	3	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	126	4	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	127	1	+	+	CCONJ
cana-6219	127	2	𝜏0	𝜏0	PROPN
cana-6219	127	3	𝜕𝛼+1	𝜕𝛼+1	VERB
cana-6219	127	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	127	5	)	)	PUNCT
cana-6219	128	1	𝜃	𝜃	PROPN
cana-6219	129	1	+	+	PUNCT
cana-6219	129	2	휀1	휀1	NOUN
cana-6219	129	3	(	(	PUNCT
cana-6219	129	4	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	129	5	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	130	1	+	+	CCONJ
cana-6219	130	2	𝜏0	𝜏0	PROPN
cana-6219	130	3	𝜕𝛼+1	𝜕𝛼+1	ADV
cana-6219	130	4	𝜕𝑡𝛼+1	𝜕𝑡𝛼+1	ADV
cana-6219	130	5	)	)	PUNCT
cana-6219	130	6	𝑒	𝑒	ADP
cana-6219	130	7	−	−	PROPN
cana-6219	130	8	휀2	휀2	NOUN
cana-6219	130	9	(	(	PUNCT
cana-6219	130	10	1	1	NUM
cana-6219	130	11	+	+	NUM
cana-6219	130	12	𝜏0	𝜏0	PROPN
cana-6219	130	13	𝜕𝛼	𝜕𝛼	NOUN
cana-6219	130	14	𝜕𝑡𝛼	𝜕𝑡𝛼	PUNCT
cana-6219	130	15	)	)	PUNCT
cana-6219	131	1	𝑄	𝑄	PROPN
cana-6219	131	2	(	(	PUNCT
cana-6219	131	3	25	25	NUM
cana-6219	131	4	)	)	PUNCT
cana-6219	131	5	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6219	132	1	=	=	SYM
cana-6219	132	2	2𝛽𝑒𝑥𝑥	2𝛽𝑒𝑥𝑥	NUM
cana-6219	132	3	+	+	CCONJ
cana-6219	132	4	(	(	PUNCT
cana-6219	132	5	1	1	NUM
cana-6219	132	6	−	−	NUM
cana-6219	132	7	2𝛽)𝑒	2𝛽)𝑒	NUM
cana-6219	133	1	−	−	PROPN
cana-6219	133	2	𝜃	𝜃	NOUN
cana-6219	133	3	,	,	PUNCT
cana-6219	133	4	(	(	PUNCT
cana-6219	133	5	26	26	NUM
cana-6219	133	6	)	)	PUNCT
cana-6219	133	7	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
cana-6219	133	8	=	=	SYM
cana-6219	133	9	2𝛽𝑒𝑦𝑦	2𝛽𝑒𝑦𝑦	PROPN
cana-6219	133	10	+	+	CCONJ
cana-6219	133	11	(	(	PUNCT
cana-6219	133	12	1	1	NUM
cana-6219	133	13	−	−	NUM
cana-6219	133	14	2𝛽)𝑒	2𝛽)𝑒	NUM
cana-6219	133	15	−	−	PROPN
cana-6219	134	1	𝜃	𝜃	NOUN
cana-6219	134	2	,	,	PUNCT
cana-6219	134	3	(	(	PUNCT
cana-6219	134	4	27	27	NUM
cana-6219	134	5	)	)	PUNCT
cana-6219	134	6	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6219	134	7	=	=	PUNCT
cana-6219	134	8	2𝛽𝑒𝑧𝑧	2𝛽𝑒𝑧𝑧	NUM
cana-6219	134	9	+	+	CCONJ
cana-6219	134	10	(	(	PUNCT
cana-6219	134	11	1	1	NUM
cana-6219	134	12	−	−	NUM
cana-6219	134	13	2𝛽)𝑒	2𝛽)𝑒	NUM
cana-6219	134	14	−	−	PROPN
cana-6219	135	1	𝜃	𝜃	NOUN
cana-6219	135	2	,	,	PUNCT
cana-6219	135	3	(	(	PUNCT
cana-6219	135	4	28	28	NUM
cana-6219	135	5	)	)	PUNCT
cana-6219	135	6	𝜎𝑥𝑦	𝜎𝑥𝑦	NOUN
cana-6219	135	7	=	=	SYM
cana-6219	135	8	2𝛽𝑒𝑥𝑦	2𝛽𝑒𝑥𝑦	NUM
cana-6219	135	9	(	(	PUNCT
cana-6219	135	10	29	29	NUM
cana-6219	135	11	)	)	PUNCT
cana-6219	135	12	𝜎𝑥𝑧	𝜎𝑥𝑧	NOUN
cana-6219	135	13	=	=	SYM
cana-6219	135	14	2𝛽𝑒𝑥𝑧	2𝛽𝑒𝑥𝑧	NUM
cana-6219	135	15	(	(	PUNCT
cana-6219	135	16	30	30	NUM
cana-6219	135	17	)	)	PUNCT
cana-6219	135	18	𝜎𝑦𝑧	𝜎𝑦𝑧	NOUN
cana-6219	135	19	=	=	PUNCT
cana-6219	136	1	2𝛽𝑒𝑦𝑧	2𝛽𝑒𝑦𝑧	NUM
cana-6219	136	2	(	(	PUNCT
cana-6219	136	3	31	31	NUM
cana-6219	136	4	)	)	PUNCT
cana-6219	136	5	where	where	SCONJ
cana-6219	136	6	,	,	PUNCT
cana-6219	136	7	𝛽	𝛽	NOUN
cana-6219	136	8	=	=	X
cana-6219	136	9	𝜇	𝜇	X
cana-6219	136	10	𝜆	𝜆	DET
cana-6219	136	11	+	+	NUM
cana-6219	136	12	2𝜇	2𝜇	NOUN
cana-6219	136	13	,	,	PUNCT
cana-6219	136	14	휀1	휀1	NOUN
cana-6219	136	15	=	=	SYM
cana-6219	136	16	𝛾2𝑇0	𝛾2𝑇0	PROPN
cana-6219	136	17	𝜌𝐶𝐸(𝜆	𝜌𝐶𝐸(𝜆	PUNCT
cana-6219	136	18	+	+	NUM
cana-6219	136	19	2𝜇	2𝜇	NUM
cana-6219	136	20	)	)	PUNCT
cana-6219	136	21	휀2	휀2	NOUN
cana-6219	136	22	=	=	SYM
cana-6219	136	23	𝛾𝑇0	𝛾𝑇0	PROPN
cana-6219	136	24	(	(	PUNCT
cana-6219	136	25	𝜆	𝜆	NOUN
cana-6219	136	26	+	+	NUM
cana-6219	136	27	2𝜇	2𝜇	NUM
cana-6219	136	28	)	)	PUNCT
cana-6219	136	29	.	.	PUNCT
cana-6219	137	1	by	by	ADP
cana-6219	137	2	taking	take	VERB
cana-6219	137	3	the	the	DET
cana-6219	137	4	sum	sum	NOUN
cana-6219	137	5	of	of	ADP
cana-6219	137	6	the	the	DET
cana-6219	137	7	eq	eq	NOUN
cana-6219	137	8	.	.	PUNCT
cana-6219	138	1	(	(	PUNCT
cana-6219	138	2	22)-(24	22)-(24	NUM
cana-6219	138	3	)	)	PUNCT
cana-6219	138	4	and	and	CCONJ
cana-6219	138	5	substituting	substitute	VERB
cana-6219	138	6	eq	eq	ADP
cana-6219	138	7	.	.	PUNCT
cana-6219	139	1	(	(	PUNCT
cana-6219	139	2	17	17	NUM
cana-6219	139	3	)	)	PUNCT
cana-6219	139	4	,	,	PUNCT
cana-6219	139	5	we	we	PRON
cana-6219	139	6	get	get	AUX
cana-6219	139	7	∇2𝑒	∇2𝑒	VERB
cana-6219	139	8	−	−	NOUN
cana-6219	140	1	∇2𝜃	∇2𝜃	X
cana-6219	140	2	=	=	SYM
cana-6219	140	3	�	�	PROPN
cana-6219	140	4	̈	̈	X
cana-6219	140	5	�	�	PROPN
cana-6219	140	6	(	(	PUNCT
cana-6219	140	7	32	32	NUM
cana-6219	140	8	)	)	PUNCT
cana-6219	140	9	assume	assume	VERB
cana-6219	140	10	that	that	SCONJ
cana-6219	140	11	the	the	DET
cana-6219	140	12	function	function	NOUN
cana-6219	140	13	𝜎	𝜎	PROPN
cana-6219	140	14	is	be	AUX
cana-6219	140	15	the	the	DET
cana-6219	140	16	invariant	invariant	ADJ
cana-6219	140	17	stress	stress	NOUN
cana-6219	140	18	,	,	PUNCT
cana-6219	140	19	as	as	SCONJ
cana-6219	140	20	follows	follow	VERB
cana-6219	140	21	:	:	PUNCT
cana-6219	140	22	𝜎	𝜎	PROPN
cana-6219	140	23	=	=	PUNCT
cana-6219	141	1	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-6219	141	2	+	+	CCONJ
cana-6219	141	3	𝜎𝑦𝑦	𝜎𝑦𝑦	VERB
cana-6219	141	4	+	+	CCONJ
cana-6219	141	5	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-6219	141	6	3	3	NUM
cana-6219	141	7	.	.	PUNCT
cana-6219	142	1	(	(	PUNCT
cana-6219	142	2	33	33	NUM
cana-6219	142	3	)	)	PUNCT
cana-6219	142	4	by	by	ADP
cana-6219	142	5	using	use	VERB
cana-6219	142	6	eq	eq	PROPN
cana-6219	142	7	.	.	PUNCT
cana-6219	143	1	(	(	PUNCT
cana-6219	143	2	26)-(28	26)-(28	NOUN
cana-6219	143	3	)	)	PUNCT
cana-6219	143	4	,	,	PUNCT
cana-6219	143	5	we	we	PRON
cana-6219	143	6	obtain	obtain	VERB
cana-6219	143	7	𝜎	𝜎	NOUN
cana-6219	143	8	=	=	SYM
cana-6219	143	9	𝜔𝑒	𝜔𝑒	X
cana-6219	143	10	−	−	PROPN
cana-6219	143	11	𝜃	𝜃	PROPN
cana-6219	143	12	(	(	PUNCT
cana-6219	143	13	34	34	NUM
cana-6219	143	14	)	)	PUNCT
cana-6219	143	15	where	where	SCONJ
cana-6219	143	16	,	,	PUNCT
cana-6219	143	17	𝜔	𝜔	PROPN
cana-6219	143	18	=	=	SYM
cana-6219	143	19	3−4𝛽	3−4𝛽	NUM
cana-6219	143	20	3	3	NUM
cana-6219	143	21	.	.	PUNCT
cana-6219	144	1	4	4	X
cana-6219	144	2	.	.	X
cana-6219	144	3	solution	solution	NOUN
cana-6219	144	4	of	of	ADP
cana-6219	144	5	the	the	DET
cana-6219	144	6	problem	problem	NOUN
cana-6219	144	7	using	use	VERB
cana-6219	144	8	laplace	laplace	NOUN
cana-6219	144	9	transform	transform	NOUN
cana-6219	144	10	,	,	PUNCT
cana-6219	144	11	which	which	PRON
cana-6219	144	12	is	be	AUX
cana-6219	144	13	defined	define	VERB
cana-6219	144	14	for	for	ADP
cana-6219	144	15	any	any	DET
cana-6219	144	16	function	function	NOUN
cana-6219	144	17	g(t	g(t	PROPN
cana-6219	144	18	)	)	PUNCT
cana-6219	144	19	as	as	SCONJ
cana-6219	144	20	follows	follow	VERB
cana-6219	144	21	:	:	PUNCT
cana-6219	144	22	�	�	NOUN
cana-6219	144	23	̅	̅	NOUN
cana-6219	144	24	�	�	NOUN
cana-6219	144	25	(𝑠	(𝑠	NOUN
cana-6219	144	26	)	)	PUNCT
cana-6219	145	1	=	=	SYM
cana-6219	145	2	∫	∫	PROPN
cana-6219	145	3	𝐺(𝑡	𝐺(𝑡	X
cana-6219	145	4	)	)	PUNCT
cana-6219	145	5	∞	∞	NUM
cana-6219	145	6	0	0	NUM
cana-6219	145	7	𝑒−𝑠𝑡𝑑𝑡.	𝑒−𝑠𝑡𝑑𝑡.	NOUN
cana-6219	145	8	(	(	PUNCT
cana-6219	145	9	35	35	NUM
cana-6219	145	10	)	)	PUNCT
cana-6219	145	11	applying	apply	VERB
cana-6219	145	12	the	the	DET
cana-6219	145	13	transform	transform	NOUN
cana-6219	145	14	to	to	ADP
cana-6219	145	15	(	(	PUNCT
cana-6219	145	16	35	35	NUM
cana-6219	145	17	)	)	PUNCT
cana-6219	145	18	,	,	PUNCT
cana-6219	145	19	we	we	PRON
cana-6219	145	20	obtain	obtain	VERB
cana-6219	145	21	:	:	PUNCT
cana-6219	145	22	communications	communication	NOUN
cana-6219	145	23	on	on	ADP
cana-6219	145	24	applied	apply	VERB
cana-6219	145	25	nonlinear	nonlinear	ADJ
cana-6219	145	26	analysis	analysis	NOUN
cana-6219	145	27	issn	issn	NOUN
cana-6219	145	28	:	:	PUNCT
cana-6219	145	29	1074	1074	NUM
cana-6219	145	30	-	-	PUNCT
cana-6219	145	31	133x	133x	NUM
cana-6219	145	32	vol	vol	VERB
cana-6219	145	33	32	32	NUM
cana-6219	145	34	no	no	NOUN
cana-6219	145	35	.	.	PUNCT
cana-6219	146	1	10s	10	NOUN
cana-6219	146	2	(	(	PUNCT
cana-6219	146	3	2025	2025	NUM
cana-6219	146	4	)	)	PUNCT
cana-6219	146	5	3535	3535	NUM
cana-6219	146	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	146	7	𝛽∇2	𝛽∇2	VERB
cana-6219	146	8	𝜕	𝜕	NOUN
cana-6219	146	9	�	�	NOUN
cana-6219	146	10	̅	̅	NOUN
cana-6219	146	11	�	�	NOUN
cana-6219	146	12	𝜕𝑥	𝜕𝑥	X
cana-6219	146	13	+	+	CCONJ
cana-6219	146	14	(	(	PUNCT
cana-6219	146	15	1	1	NUM
cana-6219	146	16	−	−	PROPN
cana-6219	146	17	𝛽	𝛽	NOUN
cana-6219	146	18	)	)	PUNCT
cana-6219	146	19	𝜕2𝑒̅	𝜕2𝑒̅	ADJ
cana-6219	146	20	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	146	21	−	−	PROPN
cana-6219	146	22	𝜕2	𝜕2	NOUN
cana-6219	146	23	�	�	NOUN
cana-6219	146	24	̅	̅	NOUN
cana-6219	146	25	�	�	NOUN
cana-6219	146	26	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	146	27	=	=	SYM
cana-6219	146	28	𝑠2	𝑠2	PROPN
cana-6219	146	29	𝜕	𝜕	PROPN
cana-6219	146	30	�	�	PROPN
cana-6219	146	31	̅	̅	NOUN
cana-6219	146	32	�	�	PROPN
cana-6219	146	33	𝜕𝑥	𝜕𝑥	X
cana-6219	146	34	(	(	PUNCT
cana-6219	146	35	36	36	NUM
cana-6219	146	36	)	)	PUNCT
cana-6219	146	37	𝛽∇2	𝛽∇2	ADJ
cana-6219	146	38	𝜕	𝜕	NOUN
cana-6219	146	39	�	�	NOUN
cana-6219	146	40	̅	̅	NOUN
cana-6219	146	41	�	�	PROPN
cana-6219	146	42	𝜕𝑦	𝜕𝑦	PROPN
cana-6219	146	43	+	+	CCONJ
cana-6219	146	44	(	(	PUNCT
cana-6219	146	45	1	1	NUM
cana-6219	146	46	−	−	PROPN
cana-6219	146	47	𝛽	𝛽	NOUN
cana-6219	146	48	)	)	PUNCT
cana-6219	146	49	𝜕2𝑒̅	𝜕2𝑒̅	VERB
cana-6219	146	50	𝜕𝑦2	𝜕𝑦2	ADJ
cana-6219	147	1	−	−	NUM
cana-6219	147	2	𝜕2	𝜕2	NOUN
cana-6219	147	3	�	�	NOUN
cana-6219	147	4	̅	̅	NOUN
cana-6219	147	5	�	�	PROPN
cana-6219	147	6	𝜕𝑦2	𝜕𝑦2	ADJ
cana-6219	147	7	=	=	SYM
cana-6219	147	8	𝑠2	𝑠2	PROPN
cana-6219	147	9	𝜕	𝜕	PROPN
cana-6219	147	10	�	�	PROPN
cana-6219	147	11	̅	̅	NOUN
cana-6219	147	12	�	�	PROPN
cana-6219	147	13	𝜕𝑦	𝜕𝑦	PROPN
cana-6219	147	14	(	(	PUNCT
cana-6219	147	15	37	37	NUM
cana-6219	147	16	)	)	PUNCT
cana-6219	147	17	𝛽∇2	𝛽∇2	ADJ
cana-6219	147	18	𝜕	𝜕	NOUN
cana-6219	147	19	�	�	NOUN
cana-6219	147	20	̅	̅	NOUN
cana-6219	147	21	�	�	PROPN
cana-6219	147	22	𝜕𝑧	𝜕𝑧	PROPN
cana-6219	147	23	+	+	CCONJ
cana-6219	147	24	(	(	PUNCT
cana-6219	147	25	1	1	NUM
cana-6219	147	26	−	−	PROPN
cana-6219	147	27	𝛽	𝛽	NOUN
cana-6219	147	28	)	)	PUNCT
cana-6219	148	1	𝜕2𝑒̅	𝜕2𝑒̅	VERB
cana-6219	148	2	𝜕𝑧2	𝜕𝑧2	ADJ
cana-6219	148	3	−	−	ADP
cana-6219	148	4	𝜕2	𝜕2	SYM
cana-6219	148	5	�	�	NOUN
cana-6219	148	6	̅	̅	NOUN
cana-6219	148	7	�	�	NOUN
cana-6219	148	8	𝜕𝑧2	𝜕𝑧2	ADJ
cana-6219	148	9	=	=	SYM
cana-6219	148	10	𝑠2	𝑠2	PROPN
cana-6219	148	11	𝜕	𝜕	PROPN
cana-6219	148	12	�	�	PROPN
cana-6219	148	13	̅	̅	NOUN
cana-6219	148	14	�	�	PROPN
cana-6219	148	15	𝜕𝑧	𝜕𝑧	PROPN
cana-6219	148	16	(	(	PUNCT
cana-6219	148	17	38	38	NUM
cana-6219	148	18	)	)	PUNCT
cana-6219	148	19	∇2𝑒̅	∇2𝑒̅	NUM
cana-6219	149	1	−	−	ADP
cana-6219	149	2	∇2	∇2	PROPN
cana-6219	149	3	�	�	SYM
cana-6219	149	4	̅	̅	NOUN
cana-6219	149	5	�	�	NOUN
cana-6219	149	6	=	=	SYM
cana-6219	149	7	𝑠2𝑒̅	𝑠2𝑒̅	ADJ
cana-6219	149	8	(	(	PUNCT
cana-6219	149	9	39	39	NUM
cana-6219	149	10	)	)	PUNCT
cana-6219	149	11	∇2	∇2	PROPN
cana-6219	149	12	�	�	NOUN
cana-6219	149	13	̅	̅	NOUN
cana-6219	149	14	�	�	NOUN
cana-6219	149	15	=	=	SYM
cana-6219	149	16	(	(	PUNCT
cana-6219	149	17	𝑠𝛼	𝑠𝛼	PROPN
cana-6219	149	18	+	+	CCONJ
cana-6219	149	19	𝜏0𝑠𝛼+1)	𝜏0𝑠𝛼+1)	PROPN
cana-6219	149	20	�	�	NOUN
cana-6219	149	21	̅	̅	NOUN
cana-6219	149	22	�	�	NOUN
cana-6219	149	23	+	+	CCONJ
cana-6219	149	24	휀1(𝑠𝛼	휀1(𝑠𝛼	PROPN
cana-6219	149	25	+	+	NUM
cana-6219	149	26	𝜏0𝑠𝛼+1)𝑒̅	𝜏0𝑠𝛼+1)𝑒̅	PROPN
cana-6219	149	27	−	−	PROPN
cana-6219	149	28	휀2(1	휀2(1	PROPN
cana-6219	149	29	+	+	NOUN
cana-6219	149	30	𝜏0𝑠𝛼)	𝜏0𝑠𝛼)	NOUN
cana-6219	149	31	�	�	SYM
cana-6219	149	32	̅	̅	NOUN
cana-6219	149	33	�	�	PROPN
cana-6219	149	34	(	(	PUNCT
cana-6219	149	35	40	40	NUM
cana-6219	149	36	)	)	PUNCT
cana-6219	149	37	�	�	PROPN
cana-6219	149	38	̅	̅	NOUN
cana-6219	149	39	�	�	NOUN
cana-6219	149	40	𝑥𝑥	𝑥𝑥	ADP
cana-6219	149	41	=	=	SYM
cana-6219	149	42	2𝛽𝑒	2𝛽𝑒	ADJ
cana-6219	149	43	�	�	PROPN
cana-6219	149	44	̅	̅	NOUN
cana-6219	149	45	�	�	NOUN
cana-6219	149	46	𝑥	𝑥	NOUN
cana-6219	149	47	+	+	CCONJ
cana-6219	149	48	(	(	PUNCT
cana-6219	149	49	1	1	NUM
cana-6219	149	50	−	−	NUM
cana-6219	149	51	2𝛽)𝑒̅	2𝛽)𝑒̅	NUM
cana-6219	149	52	−	−	PRON
cana-6219	149	53	�	�	PROPN
cana-6219	149	54	̅	̅	NOUN
cana-6219	149	55	�	�	NOUN
cana-6219	149	56	,	,	PUNCT
cana-6219	149	57	(	(	PUNCT
cana-6219	149	58	41	41	NUM
cana-6219	149	59	)	)	PUNCT
cana-6219	149	60	�	�	PROPN
cana-6219	149	61	̅	̅	NOUN
cana-6219	149	62	�	�	NOUN
cana-6219	149	63	𝑦𝑦	𝑦𝑦	NOUN
cana-6219	149	64	=	=	PROPN
cana-6219	149	65	2𝛽𝑒	2𝛽𝑒	PROPN
cana-6219	149	66	�	�	PROPN
cana-6219	149	67	̅	̅	NOUN
cana-6219	149	68	�	�	NOUN
cana-6219	149	69	𝑦	𝑦	NOUN
cana-6219	149	70	+	+	X
cana-6219	149	71	(	(	PUNCT
cana-6219	149	72	1	1	NUM
cana-6219	149	73	−	−	NUM
cana-6219	149	74	2𝛽)𝑒̅	2𝛽)𝑒̅	NUM
cana-6219	149	75	−	−	PRON
cana-6219	149	76	�	�	PROPN
cana-6219	149	77	̅	̅	NOUN
cana-6219	149	78	�	�	NOUN
cana-6219	149	79	,	,	PUNCT
cana-6219	149	80	(	(	PUNCT
cana-6219	149	81	42	42	NUM
cana-6219	149	82	)	)	PUNCT
cana-6219	149	83	�	�	PROPN
cana-6219	149	84	̅	̅	NOUN
cana-6219	149	85	�	�	NOUN
cana-6219	149	86	𝑧𝑧	𝑧𝑧	PRON
cana-6219	149	87	=	=	PROPN
cana-6219	149	88	2𝛽𝑒	2𝛽𝑒	ADJ
cana-6219	149	89	�	�	PROPN
cana-6219	149	90	̅	̅	NOUN
cana-6219	149	91	�	�	NOUN
cana-6219	149	92	𝑧	𝑧	NOUN
cana-6219	149	93	+	+	X
cana-6219	149	94	(	(	PUNCT
cana-6219	149	95	1	1	NUM
cana-6219	149	96	−	−	NUM
cana-6219	149	97	2𝛽)𝑒̅	2𝛽)𝑒̅	NUM
cana-6219	149	98	−	−	PRON
cana-6219	149	99	�	�	PROPN
cana-6219	149	100	̅	̅	NOUN
cana-6219	149	101	�	�	NOUN
cana-6219	149	102	,	,	PUNCT
cana-6219	149	103	(	(	PUNCT
cana-6219	149	104	43	43	NUM
cana-6219	149	105	)	)	PUNCT
cana-6219	149	106	�	�	PROPN
cana-6219	149	107	̅	̅	NOUN
cana-6219	149	108	�	�	NOUN
cana-6219	149	109	𝑥𝑦	𝑥𝑦	ADJ
cana-6219	149	110	=	=	ADJ
cana-6219	149	111	2𝛽𝑒	2𝛽𝑒	ADJ
cana-6219	149	112	�	�	PROPN
cana-6219	149	113	̅	̅	NOUN
cana-6219	149	114	�	�	NOUN
cana-6219	149	115	𝑦	𝑦	NOUN
cana-6219	149	116	(	(	PUNCT
cana-6219	149	117	44	44	NUM
cana-6219	149	118	)	)	PUNCT
cana-6219	149	119	�	�	PROPN
cana-6219	149	120	̅	̅	NOUN
cana-6219	149	121	�	�	NOUN
cana-6219	149	122	𝑥𝑧	𝑥𝑧	NOUN
cana-6219	149	123	=	=	PUNCT
cana-6219	149	124	2𝛽𝑒	2𝛽𝑒	ADJ
cana-6219	149	125	�	�	PROPN
cana-6219	149	126	̅	̅	NOUN
cana-6219	149	127	�	�	NOUN
cana-6219	149	128	𝑧	𝑧	X
cana-6219	149	129	(	(	PUNCT
cana-6219	149	130	45	45	NUM
cana-6219	149	131	)	)	PUNCT
cana-6219	149	132	and	and	CCONJ
cana-6219	149	133	�	�	PROPN
cana-6219	149	134	̅	̅	NOUN
cana-6219	149	135	�	�	NOUN
cana-6219	149	136	𝑦𝑧	𝑦𝑧	NOUN
cana-6219	149	137	=	=	SYM
cana-6219	149	138	2𝛽𝑒	2𝛽𝑒	ADJ
cana-6219	149	139	�	�	PROPN
cana-6219	149	140	̅	̅	NOUN
cana-6219	149	141	�	�	NOUN
cana-6219	149	142	𝑧	𝑧	X
cana-6219	149	143	(	(	PUNCT
cana-6219	149	144	46	46	NUM
cana-6219	149	145	)	)	PUNCT
cana-6219	149	146	�	�	NOUN
cana-6219	149	147	̅	̅	NOUN
cana-6219	149	148	�	�	NOUN
cana-6219	149	149	=	=	SYM
cana-6219	149	150	𝜔	𝜔	NOUN
cana-6219	149	151	�	�	NOUN
cana-6219	149	152	̅	̅	NOUN
cana-6219	149	153	�	�	PROPN
cana-6219	149	154	−	−	PROPN
cana-6219	149	155	�	�	PROPN
cana-6219	149	156	̅	̅	NOUN
cana-6219	149	157	�	�	PROPN
cana-6219	149	158	(	(	PUNCT
cana-6219	149	159	47	47	NUM
cana-6219	149	160	)	)	PUNCT
cana-6219	149	161	using	use	VERB
cana-6219	149	162	the	the	DET
cana-6219	149	163	laplace	laplace	NOUN
cana-6219	149	164	transform	transform	NOUN
cana-6219	149	165	,	,	PUNCT
cana-6219	149	166	we	we	PRON
cana-6219	149	167	applied	apply	VERB
cana-6219	149	168	the	the	DET
cana-6219	149	169	following	following	ADJ
cana-6219	149	170	initial	initial	ADJ
cana-6219	149	171	conditions	condition	NOUN
cana-6219	149	172	:	:	PUNCT
cana-6219	149	173	𝑢(𝑟	𝑢(𝑟	NOUN
cana-6219	149	174	,	,	PUNCT
cana-6219	149	175	𝑡)|𝑡=0	𝑡)|𝑡=0	PROPN
cana-6219	149	176	=	=	SYM
cana-6219	149	177	𝑣(𝑟	𝑣(𝑟	PROPN
cana-6219	149	178	,	,	PUNCT
cana-6219	149	179	𝑡)|𝑡=0	𝑡)|𝑡=0	PROPN
cana-6219	149	180	=	=	SYM
cana-6219	149	181	𝑤(𝑟	𝑤(𝑟	NOUN
cana-6219	149	182	,	,	PUNCT
cana-6219	149	183	𝑡)|𝑡=0	𝑡)|𝑡=0	PROPN
cana-6219	149	184	=	=	PUNCT
cana-6219	149	185	𝜃(𝑟	𝜃(𝑟	NOUN
cana-6219	149	186	,	,	PUNCT
cana-6219	149	187	𝑡)|𝑡=0	𝑡)|𝑡=0	PROPN
cana-6219	149	188	=	=	SYM
cana-6219	149	189	0	0	NUM
cana-6219	149	190	𝜕𝑢(𝑟	𝜕𝑢(𝑟	PROPN
cana-6219	149	191	,	,	PUNCT
cana-6219	149	192	𝑡	𝑡	NOUN
cana-6219	149	193	)	)	PUNCT
cana-6219	149	194	𝜕𝑡	𝜕𝑡	NOUN
cana-6219	149	195	|	|	ADV
cana-6219	149	196	𝑡=0	𝑡=0	ADP
cana-6219	149	197	=	=	SYM
cana-6219	149	198	𝜕𝑣(𝑟	𝜕𝑣(𝑟	PROPN
cana-6219	149	199	,	,	PUNCT
cana-6219	149	200	𝑡	𝑡	NOUN
cana-6219	149	201	)	)	PUNCT
cana-6219	149	202	𝜕𝑡	𝜕𝑡	NOUN
cana-6219	149	203	|	|	CCONJ
cana-6219	149	204	𝑡=0	𝑡=0	ADP
cana-6219	149	205	=	=	SYM
cana-6219	149	206	𝜕𝑤(𝑟	𝜕𝑤(𝑟	PROPN
cana-6219	149	207	,	,	PUNCT
cana-6219	149	208	𝑡	𝑡	PROPN
cana-6219	149	209	)	)	PUNCT
cana-6219	149	210	𝜕𝑡	𝜕𝑡	NOUN
cana-6219	149	211	|	|	ADV
cana-6219	149	212	𝑡=0	𝑡=0	ADP
cana-6219	149	213	=	=	SYM
cana-6219	149	214	𝜕𝜃(𝑟	𝜕𝜃(𝑟	NOUN
cana-6219	149	215	,	,	PUNCT
cana-6219	149	216	𝑡	𝑡	PROPN
cana-6219	149	217	)	)	PUNCT
cana-6219	149	218	𝜕𝑡	𝜕𝑡	NOUN
cana-6219	149	219	|	|	ADV
cana-6219	149	220	𝑡=0	𝑡=0	ADP
cana-6219	149	221	=	=	SYM
cana-6219	149	222	0	0	NUM
cana-6219	149	223	𝑟	𝑟	X
cana-6219	149	224	=	=	SYM
cana-6219	149	225	𝑥	𝑥	PROPN
cana-6219	149	226	,	,	PUNCT
cana-6219	149	227	𝑦	𝑦	NOUN
cana-6219	149	228	,	,	PUNCT
cana-6219	149	229	𝑧	𝑧	X
cana-6219	149	230	.	.	PUNCT
cana-6219	150	1	(	(	PUNCT
cana-6219	150	2	48	48	NUM
cana-6219	150	3	)	)	PUNCT
cana-6219	150	4	we	we	PRON
cana-6219	150	5	assumed	assume	VERB
cana-6219	150	6	the	the	DET
cana-6219	150	7	medium	medium	NOUN
cana-6219	150	8	is	be	AUX
cana-6219	150	9	subjected	subject	VERB
cana-6219	150	10	to	to	ADP
cana-6219	150	11	a	a	DET
cana-6219	150	12	rectangular	rectangular	ADJ
cana-6219	150	13	heat	heat	NOUN
cana-6219	150	14	source	source	NOUN
cana-6219	150	15	moving	move	VERB
cana-6219	150	16	with	with	ADP
cana-6219	150	17	constant	constant	ADJ
cana-6219	150	18	speed	speed	NOUN
cana-6219	150	19	and	and	CCONJ
cana-6219	150	20	constant	constant	ADJ
cana-6219	150	21	strength	strength	NOUN
cana-6219	150	22	,	,	PUNCT
cana-6219	150	23	releasing	release	VERB
cana-6219	150	24	its	its	PRON
cana-6219	150	25	energy	energy	NOUN
cana-6219	150	26	continuously	continuously	ADV
cana-6219	150	27	on	on	ADP
cana-6219	150	28	a	a	DET
cana-6219	150	29	band	band	NOUN
cana-6219	150	30	of	of	ADP
cana-6219	150	31	constant	constant	ADJ
cana-6219	150	32	dimensions	dimension	NOUN
cana-6219	150	33	2𝑎	2𝑎	NUM
cana-6219	150	34	×	×	NOUN
cana-6219	150	35	2𝑏	2𝑏	NUM
cana-6219	150	36	centered	center	VERB
cana-6219	150	37	on	on	ADP
cana-6219	150	38	the	the	DET
cana-6219	150	39	y	y	NOUN
cana-6219	150	40	-	-	PUNCT
cana-6219	150	41	axis	axis	NOUN
cana-6219	150	42	and	and	CCONJ
cana-6219	150	43	z	z	NOUN
cana-6219	150	44	-	-	PUNCT
cana-6219	150	45	axis	axis	ADJ
cana-6219	150	46	,	,	PUNCT
cana-6219	150	47	respectively	respectively	ADV
cana-6219	150	48	,	,	PUNCT
cana-6219	150	49	while	while	SCONJ
cana-6219	150	50	moving	move	VERB
cana-6219	150	51	with	with	ADP
cana-6219	150	52	constant	constant	ADJ
cana-6219	150	53	speed	speed	NOUN
cana-6219	150	54	υ	υ	NOUN
cana-6219	150	55	along	along	ADP
cana-6219	150	56	the	the	DET
cana-6219	150	57	x	x	NOUN
cana-6219	150	58	-	-	NOUN
cana-6219	150	59	axis	axis	NOUN
cana-6219	150	60	and	and	CCONJ
cana-6219	150	61	being	be	AUX
cana-6219	150	62	zero	zero	NUM
cana-6219	150	63	elsewhere	elsewhere	ADV
cana-6219	150	64	as	as	ADP
cana-6219	150	65	in	in	ADP
cana-6219	150	66	fig.1	fig.1	PROPN
cana-6219	150	67	.	.	PUNCT
cana-6219	151	1	thus	thus	ADV
cana-6219	151	2	,	,	PUNCT
cana-6219	151	3	the	the	DET
cana-6219	151	4	rectangular	rectangular	ADJ
cana-6219	151	5	moving	move	VERB
cana-6219	151	6	heat	heat	NOUN
cana-6219	151	7	source	source	NOUN
cana-6219	151	8	is	be	AUX
cana-6219	151	9	assumed	assume	VERB
cana-6219	151	10	to	to	PART
cana-6219	151	11	be	be	AUX
cana-6219	151	12	of	of	ADP
cana-6219	151	13	the	the	DET
cana-6219	151	14	following	follow	VERB
cana-6219	151	15	dimensionless	dimensionless	NOUN
cana-6219	151	16	form	form	NOUN
cana-6219	151	17	[	[	X
cana-6219	151	18	4	4	NUM
cana-6219	151	19	]	]	PUNCT
cana-6219	151	20	:	:	PUNCT
cana-6219	151	21	𝑄	𝑄	PROPN
cana-6219	151	22	=	=	PUNCT
cana-6219	151	23	𝑄0𝛿(𝑥	𝑄0𝛿(𝑥	ADP
cana-6219	151	24	−	−	NOUN
cana-6219	151	25	𝜐𝑡)𝐻(𝑎	𝜐𝑡)𝐻(𝑎	NOUN
cana-6219	151	26	−	−	PROPN
cana-6219	151	27	|𝑦|)𝐻(𝑏	|𝑦|)𝐻(𝑏	PROPN
cana-6219	151	28	−	−	PROPN
cana-6219	151	29	|𝑧|	|𝑧|	PROPN
cana-6219	151	30	)	)	PUNCT
cana-6219	151	31	,	,	PUNCT
cana-6219	151	32	(	(	PUNCT
cana-6219	151	33	49	49	NUM
cana-6219	151	34	)	)	PUNCT
cana-6219	151	35	where	where	SCONJ
cana-6219	151	36	a	a	PRON
cana-6219	151	37	and	and	CCONJ
cana-6219	151	38	b	b	NOUN
cana-6219	151	39	are	be	AUX
cana-6219	151	40	constants	constant	NOUN
cana-6219	151	41	,	,	PUNCT
cana-6219	151	42	𝑄0	𝑄0	PROPN
cana-6219	151	43	is	be	AUX
cana-6219	151	44	the	the	DET
cana-6219	151	45	heat	heat	NOUN
cana-6219	151	46	source	source	NOUN
cana-6219	151	47	strength	strength	NOUN
cana-6219	151	48	(	(	PUNCT
cana-6219	151	49	constant	constant	ADJ
cana-6219	151	50	)	)	PUNCT
cana-6219	151	51	,	,	PUNCT
cana-6219	151	52	𝛿	𝛿	PROPN
cana-6219	151	53	is	be	AUX
cana-6219	151	54	the	the	DET
cana-6219	151	55	dirac	dirac	PROPN
cana-6219	151	56	delta	delta	NOUN
cana-6219	151	57	function	function	NOUN
cana-6219	151	58	,	,	PUNCT
cana-6219	151	59	and	and	CCONJ
cana-6219	151	60	h(t	h(t	NUM
cana-6219	151	61	)	)	PUNCT
cana-6219	151	62	is	be	AUX
cana-6219	151	63	the	the	DET
cana-6219	151	64	heaviside	heaviside	ADJ
cana-6219	151	65	function	function	NOUN
cana-6219	151	66	.	.	PUNCT
cana-6219	152	1	applying	apply	VERB
cana-6219	152	2	the	the	DET
cana-6219	152	3	laplace	laplace	NOUN
cana-6219	152	4	transform	transform	NOUN
cana-6219	152	5	,	,	PUNCT
cana-6219	152	6	we	we	PRON
cana-6219	152	7	get	get	VERB
cana-6219	152	8	𝑄	𝑄	PRON
cana-6219	152	9	=	=	PRON
cana-6219	152	10	𝑄0	𝑄0	PROPN
cana-6219	153	1	υ	υ	PROPN
cana-6219	153	2	𝐻(𝑎	𝐻(𝑎	PROPN
cana-6219	153	3	−	−	PROPN
cana-6219	153	4	|𝑦|)𝐻(𝑏	|𝑦|)𝐻(𝑏	PROPN
cana-6219	153	5	−	−	PROPN
cana-6219	153	6	|𝑧|)𝑒−	|𝑧|)𝑒−	ADV
cana-6219	153	7	(	(	PUNCT
cana-6219	153	8	𝑠	𝑠	PROPN
cana-6219	153	9	𝜐	𝜐	PROPN
cana-6219	153	10	)	)	PUNCT
cana-6219	153	11	𝑥	𝑥	NOUN
cana-6219	153	12	.	.	PUNCT
cana-6219	154	1	(	(	PUNCT
cana-6219	154	2	50	50	NUM
cana-6219	154	3	)	)	PUNCT
cana-6219	154	4	communications	communication	NOUN
cana-6219	154	5	on	on	ADP
cana-6219	154	6	applied	apply	VERB
cana-6219	154	7	nonlinear	nonlinear	ADJ
cana-6219	154	8	analysis	analysis	NOUN
cana-6219	154	9	issn	issn	NOUN
cana-6219	154	10	:	:	PUNCT
cana-6219	154	11	1074	1074	NUM
cana-6219	154	12	-	-	PUNCT
cana-6219	154	13	133x	133x	NUM
cana-6219	154	14	vol	vol	VERB
cana-6219	154	15	32	32	NUM
cana-6219	154	16	no	no	NOUN
cana-6219	154	17	.	.	PUNCT
cana-6219	155	1	10s	10	NOUN
cana-6219	155	2	(	(	PUNCT
cana-6219	155	3	2025	2025	NUM
cana-6219	155	4	)	)	PUNCT
cana-6219	155	5	3536	3536	NUM
cana-6219	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	155	7	eliminating	eliminate	VERB
cana-6219	155	8	𝑒̅	𝑒̅	NOUN
cana-6219	155	9	in	in	ADP
cana-6219	155	10	eq	eq	ADP
cana-6219	155	11	.	.	PUNCT
cana-6219	155	12	(	(	PUNCT
cana-6219	155	13	39	39	NUM
cana-6219	155	14	)	)	PUNCT
cana-6219	155	15	,	,	PUNCT
cana-6219	155	16	(	(	PUNCT
cana-6219	155	17	40	40	NUM
cana-6219	155	18	)	)	PUNCT
cana-6219	155	19	and	and	CCONJ
cana-6219	155	20	(	(	PUNCT
cana-6219	155	21	47	47	NUM
cana-6219	155	22	)	)	PUNCT
cana-6219	155	23	,	,	PUNCT
cana-6219	155	24	we	we	PRON
cana-6219	155	25	get	get	VERB
cana-6219	155	26	∇2	∇2	PROPN
cana-6219	155	27	�	�	NOUN
cana-6219	155	28	̅	̅	NOUN
cana-6219	155	29	�	�	NOUN
cana-6219	155	30	=	=	SYM
cana-6219	155	31	𝛼1	𝛼1	NOUN
cana-6219	155	32	�	�	NOUN
cana-6219	155	33	̅	̅	NOUN
cana-6219	155	34	�	�	PROPN
cana-6219	155	35	+	+	CCONJ
cana-6219	155	36	𝛼2	𝛼2	PROPN
cana-6219	155	37	�	�	NOUN
cana-6219	155	38	̅	̅	NOUN
cana-6219	155	39	�	�	NOUN
cana-6219	155	40	−	−	NOUN
cana-6219	155	41	𝛾1𝐻(𝑎	𝛾1𝐻(𝑎	PART
cana-6219	155	42	−	−	PROPN
cana-6219	155	43	|𝑦|)𝐻(𝑏	|𝑦|)𝐻(𝑏	NOUN
cana-6219	155	44	−	−	PROPN
cana-6219	155	45	|𝑧|)𝑒	|𝑧|)𝑒	PROPN
cana-6219	155	46	−	−	PROPN
cana-6219	155	47	(	(	PUNCT
cana-6219	155	48	𝑠	𝑠	NOUN
cana-6219	155	49	𝜐	𝜐	PROPN
cana-6219	155	50	)	)	PUNCT
cana-6219	156	1	𝑥	𝑥	NOUN
cana-6219	156	2	.	.	PUNCT
cana-6219	157	1	(	(	PUNCT
cana-6219	157	2	51	51	NUM
cana-6219	157	3	)	)	PUNCT
cana-6219	157	4	and	and	CCONJ
cana-6219	157	5	∇2	∇2	PROPN
cana-6219	157	6	�	�	SYM
cana-6219	157	7	̅	̅	NOUN
cana-6219	157	8	�	�	NOUN
cana-6219	157	9	=	=	PUNCT
cana-6219	157	10	𝛼3	𝛼3	VERB
cana-6219	157	11	�	�	NOUN
cana-6219	157	12	̅	̅	NOUN
cana-6219	157	13	�	�	NOUN
cana-6219	157	14	+	+	CCONJ
cana-6219	157	15	𝛼4	𝛼4	NOUN
cana-6219	157	16	�	�	NOUN
cana-6219	157	17	̅	̅	NOUN
cana-6219	157	18	�	�	NOUN
cana-6219	157	19	−	−	NOUN
cana-6219	157	20	𝛾2𝐻(𝑎	𝛾2𝐻(𝑎	PROPN
cana-6219	157	21	−	−	PROPN
cana-6219	157	22	|𝑦|)𝐻(𝑏	|𝑦|)𝐻(𝑏	PROPN
cana-6219	157	23	−	−	PROPN
cana-6219	157	24	|𝑧|)𝑒−	|𝑧|)𝑒−	ADV
cana-6219	157	25	(	(	PUNCT
cana-6219	157	26	𝑠	𝑠	PROPN
cana-6219	157	27	𝜐	𝜐	PROPN
cana-6219	157	28	)	)	PUNCT
cana-6219	157	29	𝑥	𝑥	NOUN
cana-6219	157	30	.	.	PUNCT
cana-6219	158	1	(	(	PUNCT
cana-6219	158	2	52	52	NUM
cana-6219	158	3	)	)	PUNCT
cana-6219	158	4	where	where	SCONJ
cana-6219	158	5	,	,	PUNCT
cana-6219	158	6	𝛼1	𝛼1	NOUN
cana-6219	158	7	=	=	SYM
cana-6219	158	8	𝑠2𝜔	𝑠2𝜔	PROPN
cana-6219	158	9	−	−	PROPN
cana-6219	158	10	(	(	PUNCT
cana-6219	158	11	𝑠𝛼	𝑠𝛼	PROPN
cana-6219	158	12	+	+	PROPN
cana-6219	158	13	𝜏0𝑠𝛼+1)(1	𝜏0𝑠𝛼+1)(1	ADP
cana-6219	158	14	−	−	PROPN
cana-6219	158	15	𝜔)(𝜔	𝜔)(𝜔	PROPN
cana-6219	158	16	+	+	CCONJ
cana-6219	158	17	휀1	휀1	NOUN
cana-6219	158	18	)	)	PUNCT
cana-6219	158	19	𝜔	𝜔	PROPN
cana-6219	158	20	,	,	PUNCT
cana-6219	158	21	𝛼2	𝛼2	PROPN
cana-6219	158	22	=	=	SYM
cana-6219	158	23	𝑠2𝜔	𝑠2𝜔	PROPN
cana-6219	158	24	−	−	PROPN
cana-6219	158	25	휀1(1	휀1(1	ADJ
cana-6219	158	26	−	−	NOUN
cana-6219	158	27	𝜔	𝜔	NOUN
cana-6219	158	28	)	)	PUNCT
cana-6219	158	29	𝜔	𝜔	NOUN
cana-6219	158	30	,	,	PUNCT
cana-6219	158	31	𝛼3	𝛼3	NOUN
cana-6219	158	32	=	=	PUNCT
cana-6219	159	1	(	(	PUNCT
cana-6219	159	2	𝑠𝛼	𝑠𝛼	PROPN
cana-6219	159	3	+	+	CCONJ
cana-6219	159	4	𝜏0𝑠𝛼+1)(𝛼	𝜏0𝑠𝛼+1)(𝛼	PROPN
cana-6219	159	5	+	+	CCONJ
cana-6219	159	6	휀1	휀1	NOUN
cana-6219	159	7	)	)	PUNCT
cana-6219	159	8	𝜔	𝜔	NOUN
cana-6219	159	9	,	,	PUNCT
cana-6219	159	10	𝛼4	𝛼4	NOUN
cana-6219	159	11	=	=	SYM
cana-6219	159	12	휀1(𝑠𝛼	휀1(𝑠𝛼	PROPN
cana-6219	159	13	+	+	NUM
cana-6219	159	14	𝜏0𝑠𝛼+1	𝜏0𝑠𝛼+1	NOUN
cana-6219	159	15	)	)	PUNCT
cana-6219	159	16	𝜔	𝜔	PROPN
cana-6219	159	17	,	,	PUNCT
cana-6219	159	18	𝛾1	𝛾1	PROPN
cana-6219	159	19	=	=	SYM
cana-6219	159	20	휀2(1	휀2(1	PROPN
cana-6219	159	21	+	+	NUM
cana-6219	159	22	𝜏0𝑠𝛼)(𝜔	𝜏0𝑠𝛼)(𝜔	PROPN
cana-6219	159	23	−	−	NOUN
cana-6219	159	24	1	1	NUM
cana-6219	159	25	)	)	PUNCT
cana-6219	159	26	𝑄0	𝑄0	PROPN
cana-6219	160	1	𝜐	𝜐	NOUN
cana-6219	160	2	,	,	PUNCT
cana-6219	160	3	𝛾2	𝛾2	VERB
cana-6219	160	4	=	=	SYM
cana-6219	160	5	휀2(1	휀2(1	NOUN
cana-6219	160	6	+	+	CCONJ
cana-6219	160	7	𝜏0𝑠𝛼	𝜏0𝑠𝛼	NOUN
cana-6219	160	8	)	)	PUNCT
cana-6219	160	9	𝑄0	𝑄0	PROPN
cana-6219	161	1	𝜐	𝜐	INTJ
cana-6219	161	2	.	.	PUNCT
cana-6219	162	1	the	the	DET
cana-6219	162	2	double	double	ADJ
cana-6219	162	3	fourier	fourier	NOUN
cana-6219	162	4	transform	transform	NOUN
cana-6219	162	5	for	for	ADP
cana-6219	162	6	any	any	DET
cana-6219	162	7	function	function	NOUN
cana-6219	162	8	𝑓(𝑥	𝑓(𝑥	NOUN
cana-6219	162	9	,	,	PUNCT
cana-6219	162	10	𝑦	𝑦	NOUN
cana-6219	162	11	,	,	PUNCT
cana-6219	162	12	𝑧	𝑧	PRON
cana-6219	162	13	)	)	PUNCT
cana-6219	162	14	is	be	AUX
cana-6219	162	15	defined	define	VERB
cana-6219	162	16	as	as	SCONJ
cana-6219	162	17	follows	follow	VERB
cana-6219	162	18	:	:	PUNCT
cana-6219	162	19	𝐹[𝑓	𝐹[𝑓	NOUN
cana-6219	162	20	̅(𝑥	̅(𝑥	ADP
cana-6219	162	21	,	,	PUNCT
cana-6219	162	22	𝑦	𝑦	NOUN
cana-6219	162	23	,	,	PUNCT
cana-6219	162	24	𝑧	𝑧	PROPN
cana-6219	162	25	,	,	PUNCT
cana-6219	162	26	𝑠	𝑠	NOUN
cana-6219	162	27	)	)	PUNCT
cana-6219	162	28	]	]	PUNCT
cana-6219	163	1	=	=	SYM
cana-6219	163	2	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	163	3	,	,	PUNCT
cana-6219	163	4	𝑝	𝑝	NOUN
cana-6219	163	5	,	,	PUNCT
cana-6219	163	6	𝑞	𝑞	NOUN
cana-6219	163	7	,	,	PUNCT
cana-6219	163	8	𝑠	𝑠	PROPN
cana-6219	163	9	)	)	PUNCT
cana-6219	163	10	=	=	SYM
cana-6219	163	11	1	1	NUM
cana-6219	163	12	2𝜋	2𝜋	NUM
cana-6219	163	13	∫	∫	PROPN
cana-6219	163	14	∫	∫	PROPN
cana-6219	163	15	𝑓	𝑓	DET
cana-6219	163	16	̅	̅	NOUN
cana-6219	163	17	∞	∞	PROPN
cana-6219	163	18	−∞	−∞	ADP
cana-6219	163	19	∞	∞	PROPN
cana-6219	163	20	−∞	−∞	X
cana-6219	163	21	(	(	PUNCT
cana-6219	163	22	𝑥	𝑥	PROPN
cana-6219	163	23	,	,	PUNCT
cana-6219	163	24	𝑦	𝑦	NOUN
cana-6219	163	25	,	,	PUNCT
cana-6219	163	26	𝑧	𝑧	VERB
cana-6219	163	27	,	,	PUNCT
cana-6219	163	28	𝑠)𝑒−𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑦	𝑠)𝑒−𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑦	NOUN
cana-6219	163	29	𝑑𝑧	𝑑𝑧	NOUN
cana-6219	163	30	,	,	PUNCT
cana-6219	163	31	(	(	PUNCT
cana-6219	163	32	53	53	NUM
cana-6219	163	33	)	)	PUNCT
cana-6219	163	34	where	where	SCONJ
cana-6219	163	35	the	the	DET
cana-6219	163	36	inverse	inverse	NOUN
cana-6219	163	37	of	of	ADP
cana-6219	163	38	the	the	DET
cana-6219	163	39	double	double	ADJ
cana-6219	163	40	fourier	fourier	NOUN
cana-6219	163	41	transform	transform	NOUN
cana-6219	163	42	takes	take	VERB
cana-6219	163	43	the	the	DET
cana-6219	163	44	form	form	NOUN
cana-6219	163	45	𝐹−1	𝐹−1	X
cana-6219	163	46	[	[	X
cana-6219	163	47	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	163	48	,	,	PUNCT
cana-6219	163	49	𝑝	𝑝	NOUN
cana-6219	163	50	,	,	PUNCT
cana-6219	163	51	𝑞	𝑞	PROPN
cana-6219	163	52	,	,	PUNCT
cana-6219	163	53	𝑠	𝑠	PROPN
cana-6219	163	54	)	)	PUNCT
cana-6219	163	55	]	]	PUNCT
cana-6219	164	1	=	=	PUNCT
cana-6219	164	2	𝑓	𝑓	DET
cana-6219	164	3	̅	̅	NOUN
cana-6219	164	4	(	(	PUNCT
cana-6219	164	5	𝑥	𝑥	NOUN
cana-6219	164	6	,	,	PUNCT
cana-6219	164	7	𝑦	𝑦	NOUN
cana-6219	164	8	,	,	PUNCT
cana-6219	164	9	𝑧	𝑧	PROPN
cana-6219	164	10	,	,	PUNCT
cana-6219	164	11	𝑠	𝑠	NOUN
cana-6219	164	12	)	)	PUNCT
cana-6219	164	13	=	=	SYM
cana-6219	164	14	1	1	NUM
cana-6219	164	15	2𝜋	2𝜋	NUM
cana-6219	164	16	∫	∫	PROPN
cana-6219	164	17	∫	∫	PROPN
cana-6219	164	18	𝑓̅̃	𝑓̅̃	VERB
cana-6219	164	19	∞	∞	PROPN
cana-6219	164	20	−∞	−∞	ADP
cana-6219	164	21	∞	∞	PROPN
cana-6219	164	22	−∞	−∞	X
cana-6219	164	23	(	(	PUNCT
cana-6219	164	24	𝑥	𝑥	PROPN
cana-6219	164	25	,	,	PUNCT
cana-6219	164	26	𝑝	𝑝	PROPN
cana-6219	164	27	,	,	PUNCT
cana-6219	164	28	𝑞	𝑞	PROPN
cana-6219	164	29	,	,	PUNCT
cana-6219	164	30	𝑠)𝑒−𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑝	𝑠)𝑒−𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑝	NOUN
cana-6219	164	31	𝑑𝑞	𝑑𝑞	PROPN
cana-6219	164	32	,	,	PUNCT
cana-6219	164	33	(	(	PUNCT
cana-6219	164	34	54	54	NUM
cana-6219	164	35	)	)	PUNCT
cana-6219	164	36	thus	thus	ADV
cana-6219	164	37	,	,	PUNCT
cana-6219	164	38	we	we	PRON
cana-6219	164	39	have	have	VERB
cana-6219	164	40	𝐹[∇2𝑓(̅𝑥	𝐹[∇2𝑓(̅𝑥	PROPN
cana-6219	164	41	,	,	PUNCT
cana-6219	164	42	𝑦	𝑦	NOUN
cana-6219	164	43	,	,	PUNCT
cana-6219	164	44	𝑧	𝑧	PROPN
cana-6219	164	45	,	,	PUNCT
cana-6219	164	46	𝑠	𝑠	NOUN
cana-6219	164	47	)	)	PUNCT
cana-6219	164	48	]	]	PUNCT
cana-6219	165	1	=	=	PUNCT
cana-6219	165	2	(	(	PUNCT
cana-6219	165	3	𝜕2	𝜕2	NUM
cana-6219	165	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	165	5	−	−	PROPN
cana-6219	165	6	𝑞2	𝑞2	PROPN
cana-6219	165	7	−	−	PROPN
cana-6219	165	8	𝑝2	𝑝2	NOUN
cana-6219	165	9	)	)	PUNCT
cana-6219	165	10	𝑓̅̃	𝑓̅̃	NOUN
cana-6219	165	11	(	(	PUNCT
cana-6219	165	12	𝑥	𝑥	NOUN
cana-6219	165	13	,	,	PUNCT
cana-6219	165	14	𝑝	𝑝	PROPN
cana-6219	165	15	,	,	PUNCT
cana-6219	165	16	𝑞	𝑞	PROPN
cana-6219	165	17	,	,	PUNCT
cana-6219	165	18	𝑠	𝑠	PROPN
cana-6219	165	19	)	)	PUNCT
cana-6219	165	20	(	(	PUNCT
cana-6219	165	21	55	55	NUM
cana-6219	165	22	)	)	PUNCT
cana-6219	165	23	applying	apply	VERB
cana-6219	165	24	the	the	DET
cana-6219	165	25	transforms	transform	NOUN
cana-6219	165	26	to	to	ADP
cana-6219	165	27	(	(	PUNCT
cana-6219	165	28	53	53	NUM
cana-6219	165	29	)	)	PUNCT
cana-6219	165	30	and	and	CCONJ
cana-6219	165	31	(	(	PUNCT
cana-6219	165	32	55	55	NUM
cana-6219	165	33	)	)	PUNCT
cana-6219	165	34	,	,	PUNCT
cana-6219	165	35	we	we	PRON
cana-6219	165	36	get	get	VERB
cana-6219	165	37	the	the	DET
cana-6219	165	38	following	follow	VERB
cana-6219	165	39	ordinary	ordinary	ADJ
cana-6219	165	40	differential	differential	ADJ
cana-6219	165	41	equations	equation	NOUN
cana-6219	165	42	:	:	PUNCT
cana-6219	165	43	𝜕2	𝜕2	NOUN
cana-6219	165	44	�	�	PROPN
cana-6219	165	45	̃̅	̃̅	NUM
cana-6219	165	46	�	�	PROPN
cana-6219	165	47	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	165	48	=	=	SYM
cana-6219	165	49	𝛼1𝜃	𝛼1𝜃	NOUN
cana-6219	165	50	̃̅	̃̅	PROPN
cana-6219	165	51	+	+	CCONJ
cana-6219	165	52	𝛽1	𝛽1	PROPN
cana-6219	165	53	�	�	PROPN
cana-6219	165	54	̃̅	̃̅	NUM
cana-6219	165	55	�	�	PROPN
cana-6219	165	56	−	−	ADP
cana-6219	165	57	𝛾3𝑒−	𝛾3𝑒−	PROPN
cana-6219	165	58	(	(	PUNCT
cana-6219	165	59	𝑠	𝑠	PROPN
cana-6219	165	60	𝜐	𝜐	PROPN
cana-6219	165	61	)	)	PUNCT
cana-6219	165	62	𝑥	𝑥	PROPN
cana-6219	165	63	(	(	PUNCT
cana-6219	165	64	56	56	NUM
cana-6219	165	65	)	)	PUNCT
cana-6219	165	66	and	and	CCONJ
cana-6219	165	67	𝜕2	𝜕2	NOUN
cana-6219	165	68	�	�	PROPN
cana-6219	165	69	̃̅	̃̅	NUM
cana-6219	165	70	�	�	PROPN
cana-6219	165	71	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	165	72	=	=	PUNCT
cana-6219	166	1	𝛽2𝜃	𝛽2𝜃	NUM
cana-6219	166	2	̃̅	̃̅	NUM
cana-6219	167	1	+	+	NUM
cana-6219	167	2	𝛼4	𝛼4	PROPN
cana-6219	167	3	�	�	PROPN
cana-6219	167	4	̃̅	̃̅	NUM
cana-6219	167	5	�	�	PROPN
cana-6219	167	6	−	−	PROPN
cana-6219	167	7	𝛾4𝑒−	𝛾4𝑒−	NOUN
cana-6219	167	8	(	(	PUNCT
cana-6219	167	9	𝑠	𝑠	PROPN
cana-6219	167	10	𝜐	𝜐	PROPN
cana-6219	167	11	)	)	PUNCT
cana-6219	167	12	𝑥	𝑥	PROPN
cana-6219	167	13	(	(	PUNCT
cana-6219	167	14	57	57	NUM
cana-6219	167	15	)	)	PUNCT
cana-6219	167	16	where	where	SCONJ
cana-6219	167	17	𝛽1	𝛽1	NOUN
cana-6219	167	18	=	=	SYM
cana-6219	167	19	𝑝2	𝑝2	NOUN
cana-6219	167	20	+	+	CCONJ
cana-6219	167	21	𝑞2	𝑞2	NOUN
cana-6219	167	22	+	+	CCONJ
cana-6219	167	23	𝛼2	𝛼2	ADJ
cana-6219	167	24	,	,	PUNCT
cana-6219	167	25	𝛽2	𝛽2	PROPN
cana-6219	167	26	=	=	SYM
cana-6219	167	27	𝑝2	𝑝2	PROPN
cana-6219	167	28	+	+	CCONJ
cana-6219	167	29	𝑞2	𝑞2	NOUN
cana-6219	167	30	+	+	CCONJ
cana-6219	167	31	𝛼3	𝛼3	NOUN
cana-6219	167	32	𝛾3	𝛾3	NOUN
cana-6219	167	33	=	=	SYM
cana-6219	167	34	2	2	NUM
cana-6219	167	35	𝜋	𝜋	NOUN
cana-6219	167	36	𝛾1	𝛾1	PROPN
cana-6219	167	37	sin(𝑞𝑎	sin(𝑞𝑎	PROPN
cana-6219	167	38	)	)	PUNCT
cana-6219	167	39	sin	sin	NOUN
cana-6219	167	40	(	(	PUNCT
cana-6219	167	41	𝑝𝑎	𝑝𝑎	X
cana-6219	167	42	)	)	PUNCT
cana-6219	167	43	𝑞𝑝	𝑞𝑝	ADP
cana-6219	167	44	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-6219	167	45	𝛾4	𝛾4	NOUN
cana-6219	167	46	=	=	SYM
cana-6219	167	47	2	2	NUM
cana-6219	167	48	𝜋	𝜋	NOUN
cana-6219	167	49	𝛾2	𝛾2	PROPN
cana-6219	167	50	sin(𝑞𝑏	sin(𝑞𝑏	NOUN
cana-6219	167	51	)	)	PUNCT
cana-6219	167	52	sin	sin	NOUN
cana-6219	167	53	(	(	PUNCT
cana-6219	167	54	𝑝𝑏	𝑝𝑏	NUM
cana-6219	167	55	)	)	PUNCT
cana-6219	167	56	𝑞𝑝	𝑞𝑝	ADP
cana-6219	167	57	eliminating	eliminate	VERB
cana-6219	167	58	�	�	PROPN
cana-6219	167	59	̃̅	̃̅	PROPN
cana-6219	167	60	�	�	PROPN
cana-6219	167	61	from	from	ADP
cana-6219	167	62	eq	eq	PROPN
cana-6219	167	63	.	.	PUNCT
cana-6219	167	64	(	(	PUNCT
cana-6219	167	65	56	56	NUM
cana-6219	167	66	)	)	PUNCT
cana-6219	167	67	and	and	CCONJ
cana-6219	167	68	(	(	PUNCT
cana-6219	167	69	57	57	NUM
cana-6219	167	70	)	)	PUNCT
cana-6219	168	1	,	,	PUNCT
cana-6219	168	2	we	we	PRON
cana-6219	168	3	get	get	VERB
cana-6219	168	4	communications	communication	NOUN
cana-6219	168	5	on	on	ADP
cana-6219	168	6	applied	apply	VERB
cana-6219	168	7	nonlinear	nonlinear	ADJ
cana-6219	168	8	analysis	analysis	NOUN
cana-6219	168	9	issn	issn	NOUN
cana-6219	168	10	:	:	PUNCT
cana-6219	168	11	1074	1074	NUM
cana-6219	168	12	-	-	PUNCT
cana-6219	168	13	133x	133x	NUM
cana-6219	168	14	vol	vol	VERB
cana-6219	168	15	32	32	NUM
cana-6219	168	16	no	no	NOUN
cana-6219	168	17	.	.	PUNCT
cana-6219	169	1	10s	10	NOUN
cana-6219	169	2	(	(	PUNCT
cana-6219	169	3	2025	2025	NUM
cana-6219	169	4	)	)	PUNCT
cana-6219	169	5	3537	3537	NUM
cana-6219	169	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	169	7	[	[	PUNCT
cana-6219	169	8	𝜕4	𝜕4	NOUN
cana-6219	169	9	𝜕𝑥4	𝜕𝑥4	ADV
cana-6219	169	10	−	−	PROPN
cana-6219	169	11	(	(	PUNCT
cana-6219	169	12	𝛽1	𝛽1	NOUN
cana-6219	169	13	+	+	CCONJ
cana-6219	169	14	𝛽2	𝛽2	NOUN
cana-6219	169	15	)	)	PUNCT
cana-6219	169	16	𝜕2	𝜕2	PUNCT
cana-6219	169	17	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	169	18	+	+	CCONJ
cana-6219	169	19	(	(	PUNCT
cana-6219	169	20	𝛽1𝛽2	𝛽1𝛽2	ADV
cana-6219	169	21	−	−	NOUN
cana-6219	169	22	𝛼1𝛼4	𝛼1𝛼4	NOUN
cana-6219	169	23	)	)	PUNCT
cana-6219	169	24	]	]	PUNCT
cana-6219	170	1	𝜃	𝜃	X
cana-6219	170	2	̃̅	̃̅	NUM
cana-6219	170	3	=	=	SYM
cana-6219	170	4	−𝛽5𝑒−	−𝛽5𝑒−	PROPN
cana-6219	170	5	(	(	PUNCT
cana-6219	170	6	𝑠	𝑠	NOUN
cana-6219	170	7	𝜐	𝜐	PROPN
cana-6219	170	8	)	)	PUNCT
cana-6219	171	1	𝑥	𝑥	PROPN
cana-6219	171	2	(	(	PUNCT
cana-6219	171	3	58	58	NUM
cana-6219	171	4	)	)	PUNCT
cana-6219	171	5	similarly	similarly	ADV
cana-6219	171	6	,	,	PUNCT
cana-6219	171	7	eliminating	eliminate	VERB
cana-6219	171	8	𝜃	𝜃	PRON
cana-6219	171	9	̃̅	̃̅	NUM
cana-6219	171	10	from	from	ADP
cana-6219	171	11	(	(	PUNCT
cana-6219	171	12	56	56	NUM
cana-6219	171	13	)	)	PUNCT
cana-6219	171	14	and	and	CCONJ
cana-6219	171	15	(	(	PUNCT
cana-6219	171	16	57	57	NUM
cana-6219	171	17	)	)	PUNCT
cana-6219	171	18	we	we	PRON
cana-6219	171	19	obtain	obtain	VERB
cana-6219	171	20	[	[	PUNCT
cana-6219	171	21	𝜕4	𝜕4	NOUN
cana-6219	171	22	𝜕𝑥4	𝜕𝑥4	ADV
cana-6219	171	23	−	−	PROPN
cana-6219	171	24	(	(	PUNCT
cana-6219	171	25	𝛽1	𝛽1	NOUN
cana-6219	171	26	+	+	CCONJ
cana-6219	171	27	𝛽2	𝛽2	NOUN
cana-6219	171	28	)	)	PUNCT
cana-6219	171	29	𝜕2	𝜕2	PUNCT
cana-6219	172	1	𝜕𝑥2	𝜕𝑥2	NOUN
cana-6219	173	1	+	+	CCONJ
cana-6219	173	2	(	(	PUNCT
cana-6219	173	3	𝛽1𝛽2	𝛽1𝛽2	ADV
cana-6219	173	4	−	−	NOUN
cana-6219	173	5	𝛼1𝛼4	𝛼1𝛼4	NOUN
cana-6219	173	6	)	)	PUNCT
cana-6219	173	7	]	]	PUNCT
cana-6219	173	8	�	�	PROPN
cana-6219	173	9	̃̅	̃̅	NUM
cana-6219	173	10	�	�	PROPN
cana-6219	173	11	=	=	SYM
cana-6219	173	12	−𝛽6𝑒−	−𝛽6𝑒−	PROPN
cana-6219	173	13	(	(	PUNCT
cana-6219	173	14	𝑠	𝑠	PROPN
cana-6219	173	15	𝜐	𝜐	PROPN
cana-6219	173	16	)	)	PUNCT
cana-6219	174	1	𝑥	𝑥	PROPN
cana-6219	174	2	(	(	PUNCT
cana-6219	174	3	59	59	NUM
cana-6219	174	4	)	)	PUNCT
cana-6219	174	5	where	where	SCONJ
cana-6219	174	6	𝛽5	𝛽5	ADJ
cana-6219	174	7	=	=	SYM
cana-6219	174	8	𝛾4	𝛾4	NOUN
cana-6219	174	9	(	(	PUNCT
cana-6219	174	10	𝑠2	𝑠2	NOUN
cana-6219	174	11	𝑣2	𝑣2	PROPN
cana-6219	174	12	−	−	PROPN
cana-6219	174	13	𝛽1	𝛽1	NOUN
cana-6219	174	14	)	)	PUNCT
cana-6219	174	15	+	+	CCONJ
cana-6219	174	16	𝛼4𝛾3	𝛼4𝛾3	NOUN
cana-6219	174	17	,	,	PUNCT
cana-6219	174	18	𝛽6	𝛽6	NOUN
cana-6219	174	19	=	=	SYM
cana-6219	174	20	𝛾3	𝛾3	NOUN
cana-6219	174	21	(	(	PUNCT
cana-6219	174	22	𝑠2	𝑠2	PROPN
cana-6219	174	23	𝑣2	𝑣2	PROPN
cana-6219	174	24	−	−	PROPN
cana-6219	174	25	𝛽2	𝛽2	PROPN
cana-6219	174	26	)	)	PUNCT
cana-6219	175	1	+	+	CCONJ
cana-6219	175	2	𝛾4𝛼1	𝛾4𝛼1	X
cana-6219	175	3	the	the	DET
cana-6219	175	4	solution	solution	NOUN
cana-6219	175	5	of	of	ADP
cana-6219	175	6	eq	eq	PROPN
cana-6219	175	7	.	.	PUNCT
cana-6219	176	1	(	(	PUNCT
cana-6219	176	2	58	58	NUM
cana-6219	176	3	)	)	PUNCT
cana-6219	176	4	takes	take	VERB
cana-6219	176	5	the	the	DET
cana-6219	176	6	form	form	NOUN
cana-6219	176	7	𝜃	𝜃	NOUN
cana-6219	176	8	̃̅	̃̅	PUNCT
cana-6219	176	9	=	=	PUNCT
cana-6219	177	1	𝐴1𝑒−𝑘1𝑥	𝐴1𝑒−𝑘1𝑥	NOUN
cana-6219	178	1	+	+	CCONJ
cana-6219	178	2	𝐴2𝑒−𝑘2𝑥	𝐴2𝑒−𝑘2𝑥	ADP
cana-6219	178	3	−	−	NOUN
cana-6219	178	4	𝐴3𝑒−	𝐴3𝑒−	VERB
cana-6219	178	5	(	(	PUNCT
cana-6219	178	6	𝑠	𝑠	NOUN
cana-6219	178	7	𝜐	𝜐	PROPN
cana-6219	178	8	)	)	PUNCT
cana-6219	178	9	𝑥	𝑥	PROPN
cana-6219	178	10	(	(	PUNCT
cana-6219	178	11	60	60	NUM
cana-6219	178	12	)	)	PUNCT
cana-6219	178	13	where	where	SCONJ
cana-6219	178	14	𝐴3	𝐴3	PROPN
cana-6219	178	15	=	=	SYM
cana-6219	178	16	𝛽5	𝛽5	PROPN
cana-6219	178	17	(	(	PUNCT
cana-6219	178	18	𝑠2	𝑠2	NOUN
cana-6219	178	19	𝑣2−𝑘1	𝑣2−𝑘1	NUM
cana-6219	178	20	2	2	NUM
cana-6219	178	21	)	)	PUNCT
cana-6219	178	22	(	(	PUNCT
cana-6219	178	23	𝑠2	𝑠2	NOUN
cana-6219	178	24	𝑣2−𝑘2	𝑣2−𝑘2	NUM
cana-6219	178	25	2	2	NUM
cana-6219	178	26	)	)	PUNCT
cana-6219	178	27	.	.	PUNCT
cana-6219	179	1	the	the	DET
cana-6219	179	2	solution	solution	NOUN
cana-6219	179	3	of	of	ADP
cana-6219	179	4	eq	eq	PROPN
cana-6219	179	5	.	.	PUNCT
cana-6219	180	1	(	(	PUNCT
cana-6219	180	2	59	59	NUM
cana-6219	180	3	)	)	PUNCT
cana-6219	180	4	takes	take	VERB
cana-6219	180	5	the	the	DET
cana-6219	180	6	form	form	NOUN
cana-6219	180	7	�	�	SYM
cana-6219	180	8	̃̅	̃̅	NUM
cana-6219	180	9	�	�	NOUN
cana-6219	180	10	=	=	SYM
cana-6219	180	11	𝐵1𝑒−𝑘1𝑥	𝐵1𝑒−𝑘1𝑥	PROPN
cana-6219	180	12	+	+	NOUN
cana-6219	180	13	𝐵2𝑒−𝑘2𝑥	𝐵2𝑒−𝑘2𝑥	ADJ
cana-6219	180	14	−	−	NOUN
cana-6219	180	15	𝐵3𝑒−	𝐵3𝑒−	NOUN
cana-6219	180	16	(	(	PUNCT
cana-6219	180	17	𝑠	𝑠	PROPN
cana-6219	180	18	𝜐	𝜐	PROPN
cana-6219	180	19	)	)	PUNCT
cana-6219	181	1	𝑥	𝑥	PROPN
cana-6219	181	2	(	(	PUNCT
cana-6219	181	3	61	61	NUM
cana-6219	181	4	)	)	PUNCT
cana-6219	181	5	where	where	SCONJ
cana-6219	181	6	𝐵3	𝐵3	NOUN
cana-6219	181	7	=	=	SYM
cana-6219	181	8	𝛽6	𝛽6	PROPN
cana-6219	181	9	(	(	PUNCT
cana-6219	181	10	𝑠2	𝑠2	NOUN
cana-6219	181	11	𝑣2−𝑘1	𝑣2−𝑘1	NUM
cana-6219	181	12	2	2	NUM
cana-6219	181	13	)	)	PUNCT
cana-6219	181	14	(	(	PUNCT
cana-6219	181	15	𝑠2	𝑠2	NOUN
cana-6219	181	16	𝑣2−𝑘2	𝑣2−𝑘2	NUM
cana-6219	181	17	2	2	NUM
cana-6219	181	18	)	)	PUNCT
cana-6219	181	19	with	with	ADP
cana-6219	181	20	𝐴1	𝐴1	PROPN
cana-6219	181	21	,	,	PUNCT
cana-6219	181	22	𝐴2	𝐴2	PROPN
cana-6219	181	23	,	,	PUNCT
cana-6219	181	24	𝐵1	𝐵1	NOUN
cana-6219	181	25	and	and	CCONJ
cana-6219	181	26	𝐵2	𝐵2	NOUN
cana-6219	181	27	being	be	AUX
cana-6219	181	28	some	some	DET
cana-6219	181	29	parameters	parameter	NOUN
cana-6219	181	30	,	,	PUNCT
cana-6219	181	31	and	and	CCONJ
cana-6219	181	32	±𝑘1	±𝑘1	X
cana-6219	181	33	2	2	NUM
cana-6219	181	34	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-6219	181	35	±	±	NUM
cana-6219	181	36	𝑘2	𝑘2	PROPN
cana-6219	181	37	2	2	NUM
cana-6219	181	38	the	the	DET
cana-6219	181	39	roots	root	NOUN
cana-6219	181	40	of	of	ADP
cana-6219	181	41	the	the	DET
cana-6219	181	42	characteristic	characteristic	ADJ
cana-6219	181	43	equation	equation	NOUN
cana-6219	181	44	:	:	PUNCT
cana-6219	181	45	𝑘4	𝑘4	PROPN
cana-6219	181	46	−	−	PROPN
cana-6219	181	47	𝐿𝑘2	𝐿𝑘2	NOUN
cana-6219	181	48	+	+	NUM
cana-6219	181	49	𝑀	𝑀	PROPN
cana-6219	181	50	=	=	SYM
cana-6219	181	51	0	0	NUM
cana-6219	181	52	(	(	PUNCT
cana-6219	181	53	62	62	NUM
cana-6219	181	54	)	)	PUNCT
cana-6219	181	55	where	where	SCONJ
cana-6219	181	56	𝐿	𝐿	PROPN
cana-6219	181	57	=	=	PROPN
cana-6219	181	58	𝛽1	𝛽1	PROPN
cana-6219	181	59	+	+	CCONJ
cana-6219	181	60	𝛽2	𝛽2	PROPN
cana-6219	181	61	and	and	CCONJ
cana-6219	181	62	𝑀	𝑀	PROPN
cana-6219	181	63	=	=	PUNCT
cana-6219	182	1	𝛽1𝛽2	𝛽1𝛽2	ADP
cana-6219	182	2	−	−	PROPN
cana-6219	182	3	𝛼1𝛼4	𝛼1𝛼4	NOUN
cana-6219	182	4	,	,	PUNCT
cana-6219	182	5	which	which	PRON
cana-6219	182	6	satisfy	satisfy	VERB
cana-6219	182	7	the	the	DET
cana-6219	182	8	relations	relation	NOUN
cana-6219	182	9	:	:	PUNCT
cana-6219	182	10	𝑘1	𝑘1	NOUN
cana-6219	182	11	2	2	NUM
cana-6219	183	1	+	+	CCONJ
cana-6219	183	2	𝑘2	𝑘2	PROPN
cana-6219	183	3	2	2	NUM
cana-6219	183	4	=	=	SYM
cana-6219	183	5	𝛽1	𝛽1	NOUN
cana-6219	183	6	+	+	CCONJ
cana-6219	183	7	𝛽2	𝛽2	NOUN
cana-6219	183	8	,	,	PUNCT
cana-6219	183	9	𝑘1	𝑘1	ADJ
cana-6219	183	10	2𝑘2	2𝑘2	NUM
cana-6219	183	11	2	2	NUM
cana-6219	183	12	=	=	SYM
cana-6219	183	13	𝛽1𝛽2	𝛽1𝛽2	ADP
cana-6219	183	14	−	−	PROPN
cana-6219	183	15	𝛼1𝛼4	𝛼1𝛼4	NOUN
cana-6219	183	16	.	.	PUNCT
cana-6219	184	1	(	(	PUNCT
cana-6219	184	2	63	63	NUM
cana-6219	184	3	)	)	PUNCT
cana-6219	184	4	from	from	ADP
cana-6219	184	5	eq	eq	ADP
cana-6219	184	6	.	.	PUNCT
cana-6219	185	1	(	(	PUNCT
cana-6219	185	2	60	60	NUM
cana-6219	185	3	)	)	PUNCT
cana-6219	185	4	,	,	PUNCT
cana-6219	185	5	(	(	PUNCT
cana-6219	185	6	61	61	NUM
cana-6219	185	7	)	)	PUNCT
cana-6219	185	8	and	and	CCONJ
cana-6219	185	9	(	(	PUNCT
cana-6219	185	10	56	56	NUM
cana-6219	185	11	)	)	PUNCT
cana-6219	185	12	,	,	PUNCT
cana-6219	185	13	we	we	PRON
cana-6219	185	14	get	get	VERB
cana-6219	185	15	𝐵1	𝐵1	NOUN
cana-6219	185	16	=	=	PUNCT
cana-6219	185	17	(	(	PUNCT
cana-6219	185	18	𝑘1	𝑘1	NOUN
cana-6219	185	19	2	2	NUM
cana-6219	185	20	−	−	PROPN
cana-6219	185	21	𝛼1	𝛼1	NOUN
cana-6219	185	22	)	)	PUNCT
cana-6219	185	23	𝛽1	𝛽1	NOUN
cana-6219	185	24	𝐴1	𝐴1	PROPN
cana-6219	185	25	𝐵2	𝐵2	NOUN
cana-6219	185	26	=	=	PUNCT
cana-6219	186	1	(	(	PUNCT
cana-6219	186	2	𝑘2	𝑘2	PROPN
cana-6219	186	3	2	2	NUM
cana-6219	186	4	−	−	PROPN
cana-6219	186	5	𝛼1	𝛼1	NOUN
cana-6219	186	6	)	)	PUNCT
cana-6219	186	7	𝛽1	𝛽1	NOUN
cana-6219	186	8	𝐴2	𝐴2	NOUN
cana-6219	186	9	(	(	PUNCT
cana-6219	186	10	64	64	NUM
cana-6219	186	11	)	)	PUNCT
cana-6219	186	12	hence	hence	ADV
cana-6219	186	13	,	,	PUNCT
cana-6219	186	14	we	we	PRON
cana-6219	186	15	have	have	VERB
cana-6219	186	16	�	�	PROPN
cana-6219	186	17	̃̅	̃̅	NUM
cana-6219	186	18	�	�	PROPN
cana-6219	186	19	=	=	PUNCT
cana-6219	186	20	(	(	PUNCT
cana-6219	186	21	𝑘1	𝑘1	NOUN
cana-6219	186	22	2	2	NUM
cana-6219	186	23	−	−	PROPN
cana-6219	186	24	𝛼1)𝐴1	𝛼1)𝐴1	NOUN
cana-6219	186	25	𝛽1	𝛽1	NOUN
cana-6219	186	26	𝑒−𝑘1𝑥	𝑒−𝑘1𝑥	NUM
cana-6219	187	1	+	+	CCONJ
cana-6219	187	2	(	(	PUNCT
cana-6219	187	3	𝑘2	𝑘2	PROPN
cana-6219	187	4	2	2	NUM
cana-6219	187	5	−	−	PROPN
cana-6219	187	6	𝛼1)𝐴2	𝛼1)𝐴2	ADJ
cana-6219	187	7	𝛽1	𝛽1	NOUN
cana-6219	187	8	𝑒−𝑘2𝑥	𝑒−𝑘2𝑥	X
cana-6219	188	1	+	+	X
cana-6219	188	2	𝐵3𝑒−	𝐵3𝑒−	NOUN
cana-6219	188	3	(	(	PUNCT
cana-6219	188	4	𝑠	𝑠	NOUN
cana-6219	188	5	𝜐	𝜐	PROPN
cana-6219	188	6	)	)	PUNCT
cana-6219	188	7	𝑥	𝑥	NOUN
cana-6219	188	8	.	.	PUNCT
cana-6219	189	1	(	(	PUNCT
cana-6219	189	2	65	65	NUM
cana-6219	189	3	)	)	PUNCT
cana-6219	189	4	to	to	PART
cana-6219	189	5	finalize	finalize	VERB
cana-6219	189	6	the	the	DET
cana-6219	189	7	solution	solution	NOUN
cana-6219	189	8	,	,	PUNCT
cana-6219	189	9	we	we	PRON
cana-6219	189	10	have	have	VERB
cana-6219	189	11	to	to	PART
cana-6219	189	12	obtain	obtain	VERB
cana-6219	189	13	the	the	DET
cana-6219	189	14	parameters	parameter	NOUN
cana-6219	189	15	𝐴1	𝐴1	PROPN
cana-6219	189	16	,	,	PUNCT
cana-6219	189	17	𝐴2	𝐴2	NOUN
cana-6219	189	18	by	by	ADP
cana-6219	189	19	applying	apply	VERB
cana-6219	189	20	certain	certain	ADJ
cana-6219	189	21	boundary	boundary	ADJ
cana-6219	189	22	conditions	condition	NOUN
cana-6219	189	23	.	.	PUNCT
cana-6219	190	1	we	we	PRON
cana-6219	190	2	consider	consider	VERB
cana-6219	190	3	that	that	SCONJ
cana-6219	190	4	the	the	DET
cana-6219	190	5	bounding	bounding	NOUN
cana-6219	190	6	plane	plane	NOUN
cana-6219	190	7	of	of	ADP
cana-6219	190	8	the	the	DET
cana-6219	190	9	surface	surface	NOUN
cana-6219	190	10	is	be	AUX
cana-6219	190	11	traction	traction	NOUN
cana-6219	190	12	-	-	PUNCT
cana-6219	190	13	free	free	ADJ
cana-6219	190	14	and	and	CCONJ
cana-6219	190	15	it	it	PRON
cana-6219	190	16	has	have	VERB
cana-6219	190	17	no	no	DET
cana-6219	190	18	external	external	ADJ
cana-6219	190	19	thermal	thermal	ADJ
cana-6219	190	20	loading	loading	NOUN
cana-6219	190	21	which	which	PRON
cana-6219	190	22	gives	give	VERB
cana-6219	190	23	,	,	PUNCT
cana-6219	190	24	by	by	ADP
cana-6219	190	25	using	use	VERB
cana-6219	190	26	all	all	DET
cana-6219	190	27	the	the	DET
cana-6219	190	28	above	above	ADJ
cana-6219	190	29	transformations	transformation	NOUN
cana-6219	190	30	,	,	PUNCT
cana-6219	190	31	the	the	DET
cana-6219	190	32	following	follow	VERB
cana-6219	190	33	conditions	condition	NOUN
cana-6219	190	34	:	:	PUNCT
cana-6219	190	35	communications	communication	NOUN
cana-6219	190	36	on	on	ADP
cana-6219	190	37	applied	apply	VERB
cana-6219	190	38	nonlinear	nonlinear	ADJ
cana-6219	190	39	analysis	analysis	NOUN
cana-6219	190	40	issn	issn	NOUN
cana-6219	190	41	:	:	PUNCT
cana-6219	190	42	1074	1074	NUM
cana-6219	190	43	-	-	PUNCT
cana-6219	190	44	133x	133x	NUM
cana-6219	190	45	vol	vol	VERB
cana-6219	190	46	32	32	NUM
cana-6219	190	47	no	no	NOUN
cana-6219	190	48	.	.	PUNCT
cana-6219	191	1	10s	10	NOUN
cana-6219	191	2	(	(	PUNCT
cana-6219	191	3	2025	2025	NUM
cana-6219	191	4	)	)	PUNCT
cana-6219	191	5	3538	3538	NUM
cana-6219	191	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	191	7	�	�	PROPN
cana-6219	191	8	̃̅	̃̅	PROPN
cana-6219	191	9	�	�	PROPN
cana-6219	191	10	(0	(0	PROPN
cana-6219	191	11	,	,	PUNCT
cana-6219	191	12	𝑞	𝑞	PROPN
cana-6219	191	13	,	,	PUNCT
cana-6219	191	14	𝑝	𝑝	PROPN
cana-6219	191	15	,	,	PUNCT
cana-6219	191	16	𝑠	𝑠	NOUN
cana-6219	191	17	)	)	PUNCT
cana-6219	191	18	=	=	SYM
cana-6219	191	19	�	�	PROPN
cana-6219	191	20	̃̅	̃̅	NUM
cana-6219	191	21	�	�	PROPN
cana-6219	191	22	(0	(0	PROPN
cana-6219	191	23	,	,	PUNCT
cana-6219	191	24	𝑦	𝑦	NOUN
cana-6219	191	25	,	,	PUNCT
cana-6219	191	26	𝑧	𝑧	NOUN
cana-6219	191	27	,	,	PUNCT
cana-6219	191	28	𝑡	𝑡	NOUN
cana-6219	191	29	)	)	PUNCT
cana-6219	191	30	=	=	SYM
cana-6219	191	31	0	0	NUM
cana-6219	191	32	(	(	PUNCT
cana-6219	191	33	66	66	NUM
cana-6219	191	34	)	)	PUNCT
cana-6219	191	35	substituting	substitute	VERB
cana-6219	191	36	(	(	PUNCT
cana-6219	191	37	66	66	NUM
cana-6219	191	38	)	)	PUNCT
cana-6219	191	39	into	into	ADP
cana-6219	191	40	eq	eq	NOUN
cana-6219	191	41	.	.	PUNCT
cana-6219	192	1	(	(	PUNCT
cana-6219	192	2	60	60	NUM
cana-6219	192	3	)	)	PUNCT
cana-6219	192	4	and	and	CCONJ
cana-6219	192	5	(	(	PUNCT
cana-6219	192	6	61	61	NUM
cana-6219	192	7	)	)	PUNCT
cana-6219	192	8	,	,	PUNCT
cana-6219	192	9	we	we	PRON
cana-6219	192	10	get	get	VERB
cana-6219	192	11	the	the	DET
cana-6219	192	12	following	follow	VERB
cana-6219	192	13	system	system	NOUN
cana-6219	192	14	:	:	PUNCT
cana-6219	192	15	𝐴1	𝐴1	PROPN
cana-6219	192	16	+	+	CCONJ
cana-6219	192	17	𝐴2	𝐴2	PROPN
cana-6219	192	18	=	=	SYM
cana-6219	192	19	𝐴3	𝐴3	PROPN
cana-6219	192	20	(	(	PUNCT
cana-6219	192	21	67	67	NUM
cana-6219	192	22	)	)	PUNCT
cana-6219	192	23	(	(	PUNCT
cana-6219	192	24	𝑘1	𝑘1	PROPN
cana-6219	192	25	2	2	NUM
cana-6219	192	26	−	−	PROPN
cana-6219	192	27	𝛼1)𝐴1	𝛼1)𝐴1	NOUN
cana-6219	192	28	+	+	CCONJ
cana-6219	193	1	(	(	PUNCT
cana-6219	193	2	𝑘2	𝑘2	PROPN
cana-6219	193	3	2	2	NUM
cana-6219	193	4	−	−	PROPN
cana-6219	193	5	𝛼1)𝐴2	𝛼1)𝐴2	NOUN
cana-6219	193	6	=	=	PUNCT
cana-6219	193	7	𝛽1𝐵3	𝛽1𝐵3	PROPN
cana-6219	193	8	(	(	PUNCT
cana-6219	193	9	68	68	NUM
cana-6219	193	10	)	)	PUNCT
cana-6219	193	11	the	the	DET
cana-6219	193	12	solution	solution	NOUN
cana-6219	193	13	of	of	ADP
cana-6219	193	14	the	the	DET
cana-6219	193	15	above	above	ADJ
cana-6219	193	16	system	system	NOUN
cana-6219	193	17	gives	give	VERB
cana-6219	193	18	𝐴1	𝐴1	PROPN
cana-6219	193	19	=	=	PUNCT
cana-6219	193	20	𝐴3(𝑘2	𝐴3(𝑘2	VERB
cana-6219	193	21	2	2	NUM
cana-6219	193	22	−	−	PROPN
cana-6219	193	23	𝛼1	𝛼1	NOUN
cana-6219	193	24	)	)	PUNCT
cana-6219	193	25	−	−	PROPN
cana-6219	194	1	𝛽1𝐵3	𝛽1𝐵3	PROPN
cana-6219	194	2	𝑘2	𝑘2	PROPN
cana-6219	194	3	2	2	NUM
cana-6219	194	4	−	−	NOUN
cana-6219	194	5	𝑘1	𝑘1	PROPN
cana-6219	194	6	2	2	NUM
cana-6219	194	7	,	,	PUNCT
cana-6219	194	8	𝐴2	𝐴2	PROPN
cana-6219	194	9	=	=	SYM
cana-6219	194	10	−	−	PROPN
cana-6219	194	11	𝐴3(𝑘1	𝐴3(𝑘1	NOUN
cana-6219	194	12	2	2	NUM
cana-6219	194	13	−	−	NOUN
cana-6219	194	14	𝛼1	𝛼1	NOUN
cana-6219	194	15	)	)	PUNCT
cana-6219	194	16	−	−	PROPN
cana-6219	195	1	𝛽1𝐵3	𝛽1𝐵3	PROPN
cana-6219	195	2	𝑘2	𝑘2	PROPN
cana-6219	195	3	2	2	NUM
cana-6219	195	4	−	−	NOUN
cana-6219	195	5	𝑘1	𝑘1	NOUN
cana-6219	195	6	2	2	NUM
cana-6219	195	7	(	(	PUNCT
cana-6219	195	8	69	69	NUM
cana-6219	195	9	)	)	PUNCT
cana-6219	195	10	hence	hence	ADV
cana-6219	195	11	,	,	PUNCT
cana-6219	195	12	we	we	PRON
cana-6219	195	13	have	have	VERB
cana-6219	195	14	the	the	DET
cana-6219	195	15	solutions	solution	NOUN
cana-6219	195	16	in	in	ADP
cana-6219	195	17	fourier	fourier	NOUN
cana-6219	195	18	and	and	CCONJ
cana-6219	195	19	laplace	laplace	NOUN
cana-6219	195	20	transform	transform	NOUN
cana-6219	195	21	domain	domain	NOUN
cana-6219	195	22	as	as	SCONJ
cana-6219	195	23	follows	follow	VERB
cana-6219	195	24	:	:	PUNCT
cana-6219	195	25	�	�	PROPN
cana-6219	195	26	̃̅	̃̅	NUM
cana-6219	195	27	�	�	PROPN
cana-6219	195	28	(𝑥	(𝑥	PROPN
cana-6219	195	29	,	,	PUNCT
cana-6219	195	30	𝑝	𝑝	PROPN
cana-6219	195	31	,	,	PUNCT
cana-6219	195	32	𝑞	𝑞	PROPN
cana-6219	195	33	,	,	PUNCT
cana-6219	195	34	𝑠	𝑠	PROPN
cana-6219	195	35	)	)	PUNCT
cana-6219	195	36	=	=	VERB
cana-6219	195	37	𝐴3(𝑘2	𝐴3(𝑘2	VERB
cana-6219	195	38	2	2	NUM
cana-6219	195	39	−	−	PROPN
cana-6219	195	40	𝛼1	𝛼1	NOUN
cana-6219	195	41	)	)	PUNCT
cana-6219	195	42	−	−	PROPN
cana-6219	196	1	𝛽1𝐵3	𝛽1𝐵3	PUNCT
cana-6219	197	1	(	(	PUNCT
cana-6219	197	2	𝑘2	𝑘2	PROPN
cana-6219	197	3	2	2	NUM
cana-6219	197	4	−	−	NOUN
cana-6219	197	5	𝑘1	𝑘1	PROPN
cana-6219	197	6	2	2	NUM
cana-6219	197	7	)	)	PUNCT
cana-6219	197	8	𝑒−𝑘1𝑥	𝑒−𝑘1𝑥	NOUN
cana-6219	198	1	−	−	NOUN
cana-6219	198	2	𝐴3(𝑘1	𝐴3(𝑘1	NOUN
cana-6219	198	3	2	2	NUM
cana-6219	198	4	−	−	NOUN
cana-6219	198	5	𝛼1	𝛼1	NOUN
cana-6219	198	6	)	)	PUNCT
cana-6219	198	7	−	−	PROPN
cana-6219	199	1	𝛽1𝐵3	𝛽1𝐵3	PUNCT
cana-6219	200	1	(	(	PUNCT
cana-6219	200	2	𝑘2	𝑘2	PROPN
cana-6219	200	3	2	2	NUM
cana-6219	200	4	−	−	NOUN
cana-6219	200	5	𝑘1	𝑘1	PROPN
cana-6219	200	6	2	2	NUM
cana-6219	200	7	)	)	PUNCT
cana-6219	200	8	𝑒−𝑘2𝑥	𝑒−𝑘2𝑥	X
cana-6219	200	9	−	−	NOUN
cana-6219	200	10	𝐴3𝑒−	𝐴3𝑒−	VERB
cana-6219	200	11	(	(	PUNCT
cana-6219	200	12	𝑠	𝑠	NOUN
cana-6219	200	13	𝜐	𝜐	PROPN
cana-6219	200	14	)	)	PUNCT
cana-6219	200	15	𝑥	𝑥	PROPN
cana-6219	200	16	(	(	PUNCT
cana-6219	200	17	70	70	NUM
cana-6219	200	18	)	)	PUNCT
cana-6219	200	19	�	�	PROPN
cana-6219	200	20	̃̅	̃̅	NUM
cana-6219	200	21	�	�	PROPN
cana-6219	200	22	(𝑥	(𝑥	PROPN
cana-6219	200	23	,	,	PUNCT
cana-6219	200	24	𝑝	𝑝	PROPN
cana-6219	200	25	,	,	PUNCT
cana-6219	200	26	𝑞	𝑞	PROPN
cana-6219	200	27	,	,	PUNCT
cana-6219	200	28	𝑠	𝑠	PROPN
cana-6219	200	29	)	)	PUNCT
cana-6219	200	30	=	=	SYM
cana-6219	201	1	(	(	PUNCT
cana-6219	201	2	𝑘1	𝑘1	NOUN
cana-6219	201	3	2	2	NUM
cana-6219	201	4	−	−	NOUN
cana-6219	201	5	𝛼1)[𝐴3(𝑘2	𝛼1)[𝐴3(𝑘2	VERB
cana-6219	201	6	2	2	NUM
cana-6219	201	7	−	−	NOUN
cana-6219	201	8	𝛼1	𝛼1	NOUN
cana-6219	201	9	)	)	PUNCT
cana-6219	201	10	−	−	PROPN
cana-6219	202	1	𝛽1𝐵3	𝛽1𝐵3	SYM
cana-6219	202	2	]	]	X
cana-6219	202	3	𝛽1(𝑘2	𝛽1(𝑘2	VERB
cana-6219	202	4	2	2	NUM
cana-6219	202	5	−	−	NOUN
cana-6219	202	6	𝑘1	𝑘1	PROPN
cana-6219	202	7	2	2	NUM
cana-6219	202	8	)	)	PUNCT
cana-6219	202	9	𝑒−𝑘1𝑥	𝑒−𝑘1𝑥	NOUN
cana-6219	203	1	−	−	PROPN
cana-6219	203	2	(	(	PUNCT
cana-6219	203	3	𝑘2	𝑘2	PROPN
cana-6219	203	4	2	2	NUM
cana-6219	203	5	−	−	NOUN
cana-6219	203	6	𝛼1)[𝐴3(𝑘1	𝛼1)[𝐴3(𝑘1	ADJ
cana-6219	203	7	2	2	NUM
cana-6219	203	8	−	−	NOUN
cana-6219	203	9	𝛼1	𝛼1	NOUN
cana-6219	203	10	)	)	PUNCT
cana-6219	203	11	−	−	PROPN
cana-6219	204	1	𝛽1𝐵3	𝛽1𝐵3	SYM
cana-6219	204	2	]	]	X
cana-6219	204	3	𝛽1(𝑘2	𝛽1(𝑘2	VERB
cana-6219	204	4	2	2	NUM
cana-6219	204	5	−	−	NOUN
cana-6219	204	6	𝑘1	𝑘1	PROPN
cana-6219	204	7	2	2	NUM
cana-6219	204	8	)	)	PUNCT
cana-6219	204	9	𝑒−𝑘2𝑥	𝑒−𝑘2𝑥	VERB
cana-6219	205	1	−	−	PROPN
cana-6219	206	1	𝐵3𝑒	𝐵3𝑒	PROPN
cana-6219	206	2	−	−	PROPN
cana-6219	206	3	(	(	PUNCT
cana-6219	206	4	𝑠	𝑠	PROPN
cana-6219	206	5	𝜐	𝜐	PROPN
cana-6219	206	6	)	)	PUNCT
cana-6219	206	7	𝑥	𝑥	PROPN
cana-6219	206	8	(	(	PUNCT
cana-6219	206	9	71	71	NUM
cana-6219	206	10	)	)	PUNCT
cana-6219	206	11	and	and	CCONJ
cana-6219	206	12	𝑒̅̃(𝑥	𝑒̅̃(𝑥	ADJ
cana-6219	206	13	,	,	PUNCT
cana-6219	206	14	𝑝	𝑝	NOUN
cana-6219	206	15	,	,	PUNCT
cana-6219	206	16	𝑞	𝑞	NOUN
cana-6219	206	17	,	,	PUNCT
cana-6219	206	18	𝑠	𝑠	PROPN
cana-6219	206	19	)	)	PUNCT
cana-6219	206	20	=	=	SYM
cana-6219	206	21	1	1	NUM
cana-6219	206	22	𝛼	𝛼	X
cana-6219	206	23	[	[	X
cana-6219	206	24	�	�	PROPN
cana-6219	206	25	̃̅	̃̅	PROPN
cana-6219	206	26	�	�	PROPN
cana-6219	206	27	(𝑥	(𝑥	PROPN
cana-6219	206	28	,	,	PUNCT
cana-6219	206	29	𝑝	𝑝	PROPN
cana-6219	206	30	,	,	PUNCT
cana-6219	206	31	𝑞	𝑞	PROPN
cana-6219	206	32	,	,	PUNCT
cana-6219	206	33	𝑠	𝑠	PROPN
cana-6219	206	34	)	)	PUNCT
cana-6219	206	35	+	+	CCONJ
cana-6219	206	36	�	�	PROPN
cana-6219	206	37	̃̅	̃̅	NUM
cana-6219	206	38	�	�	PROPN
cana-6219	206	39	(𝑥	(𝑥	PROPN
cana-6219	206	40	,	,	PUNCT
cana-6219	206	41	𝑝	𝑝	PROPN
cana-6219	206	42	,	,	PUNCT
cana-6219	206	43	𝑞	𝑞	PROPN
cana-6219	206	44	,	,	PUNCT
cana-6219	206	45	𝑠	𝑠	PROPN
cana-6219	206	46	)	)	PUNCT
cana-6219	206	47	]	]	PUNCT
cana-6219	206	48	(	(	PUNCT
cana-6219	206	49	72	72	NUM
cana-6219	206	50	)	)	PUNCT
cana-6219	206	51	5	5	NUM
cana-6219	206	52	.	.	PUNCT
cana-6219	206	53	inversion	inversion	NOUN
cana-6219	206	54	of	of	ADP
cana-6219	206	55	fourier	fourier	NOUN
cana-6219	206	56	and	and	CCONJ
cana-6219	206	57	laplace	laplace	NOUN
cana-6219	206	58	transforms	transform	VERB
cana-6219	206	59	to	to	PART
cana-6219	206	60	get	get	VERB
cana-6219	206	61	the	the	DET
cana-6219	206	62	final	final	ADJ
cana-6219	206	63	solution	solution	NOUN
cana-6219	206	64	in	in	ADP
cana-6219	206	65	its	its	PRON
cana-6219	206	66	original	original	ADJ
cana-6219	206	67	variables	variable	NOUN
cana-6219	206	68	,	,	PUNCT
cana-6219	206	69	we	we	PRON
cana-6219	206	70	should	should	AUX
cana-6219	206	71	calculate	calculate	VERB
cana-6219	206	72	the	the	DET
cana-6219	206	73	inverse	inverse	NOUN
cana-6219	206	74	of	of	ADP
cana-6219	206	75	the	the	DET
cana-6219	206	76	double	double	ADJ
cana-6219	206	77	fourier	fourier	NOUN
cana-6219	206	78	and	and	CCONJ
cana-6219	206	79	laplace	laplace	NOUN
cana-6219	206	80	transforms	transform	VERB
cana-6219	206	81	in	in	ADP
cana-6219	206	82	eq	eq	ADP
cana-6219	206	83	.	.	PUNCT
cana-6219	207	1	(	(	PUNCT
cana-6219	207	2	70)-(72	70)-(72	NOUN
cana-6219	207	3	)	)	PUNCT
cana-6219	207	4	.	.	PUNCT
cana-6219	208	1	these	these	DET
cana-6219	208	2	expressions	expression	NOUN
cana-6219	208	3	may	may	AUX
cana-6219	208	4	be	be	AUX
cana-6219	208	5	formally	formally	ADV
cana-6219	208	6	written	write	VERB
cana-6219	208	7	as	as	ADP
cana-6219	208	8	functions	function	NOUN
cana-6219	208	9	of	of	ADP
cana-6219	208	10	𝑥	𝑥	NOUN
cana-6219	208	11	,	,	PUNCT
cana-6219	208	12	and	and	CCONJ
cana-6219	208	13	all	all	DET
cana-6219	208	14	the	the	DET
cana-6219	208	15	parameters	parameter	NOUN
cana-6219	208	16	of	of	ADP
cana-6219	208	17	the	the	DET
cana-6219	208	18	fourier	fourier	NOUN
cana-6219	208	19	and	and	CCONJ
cana-6219	208	20	laplace	laplace	NOUN
cana-6219	208	21	transforms	transform	VERB
cana-6219	208	22	,	,	PUNCT
cana-6219	208	23	namely	namely	ADV
cana-6219	208	24	𝑝	𝑝	NOUN
cana-6219	208	25	,	,	PUNCT
cana-6219	208	26	𝑞	𝑞	PROPN
cana-6219	208	27	and	and	CCONJ
cana-6219	208	28	𝑠	𝑠	PROPN
cana-6219	208	29	in	in	ADP
cana-6219	208	30	the	the	DET
cana-6219	208	31	form	form	NOUN
cana-6219	208	32	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	208	33	,	,	PUNCT
cana-6219	208	34	𝑞	𝑞	NOUN
cana-6219	208	35	,	,	PUNCT
cana-6219	208	36	𝑝	𝑝	PROPN
cana-6219	208	37	,	,	PUNCT
cana-6219	208	38	𝑠	𝑠	PROPN
cana-6219	208	39	)	)	PUNCT
cana-6219	208	40	(	(	PUNCT
cana-6219	208	41	ezzat	ezzat	ADJ
cana-6219	208	42	,	,	PUNCT
cana-6219	208	43	youssef	youssef	PROPN
cana-6219	209	1	[	[	X
cana-6219	209	2	5	5	NUM
cana-6219	209	3	,	,	PUNCT
cana-6219	209	4	6	6	NUM
cana-6219	209	5	,	,	PUNCT
cana-6219	209	6	10	10	NUM
cana-6219	209	7	]	]	NUM
cana-6219	209	8	)	)	PUNCT
cana-6219	209	9	.	.	PUNCT
cana-6219	210	1	in	in	ADP
cana-6219	210	2	the	the	DET
cana-6219	210	3	beginning	beginning	NOUN
cana-6219	210	4	we	we	PRON
cana-6219	210	5	invert	invert	VERB
cana-6219	210	6	the	the	DET
cana-6219	210	7	double	double	ADJ
cana-6219	210	8	fourier	fourier	NOUN
cana-6219	210	9	transforms	transform	VERB
cana-6219	210	10	using	use	VERB
cana-6219	210	11	the	the	DET
cana-6219	210	12	formula	formula	NOUN
cana-6219	210	13	in	in	ADP
cana-6219	210	14	(	(	PUNCT
cana-6219	210	15	54	54	NUM
cana-6219	210	16	)	)	PUNCT
cana-6219	210	17	which	which	PRON
cana-6219	210	18	gives	give	VERB
cana-6219	210	19	the	the	DET
cana-6219	210	20	expression	expression	NOUN
cana-6219	210	21	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	210	22	,	,	PUNCT
cana-6219	210	23	𝑦	𝑦	NOUN
cana-6219	210	24	,	,	PUNCT
cana-6219	210	25	𝑧	𝑧	PROPN
cana-6219	210	26	,	,	PUNCT
cana-6219	210	27	𝑠	𝑠	NOUN
cana-6219	210	28	)	)	PUNCT
cana-6219	210	29	in	in	ADP
cana-6219	210	30	the	the	DET
cana-6219	210	31	laplace	laplace	NOUN
cana-6219	210	32	transform	transform	NOUN
cana-6219	210	33	domain	domain	NOUN
cana-6219	210	34	as	as	SCONJ
cana-6219	210	35	follows	follow	VERB
cana-6219	210	36	(	(	PUNCT
cana-6219	210	37	ezzat	ezzat	ADJ
cana-6219	210	38	,	,	PUNCT
cana-6219	210	39	youssef	youssef	PROPN
cana-6219	211	1	[	[	X
cana-6219	211	2	5	5	NUM
cana-6219	211	3	]	]	SYM
cana-6219	211	4	):	):	PUNCT
cana-6219	211	5	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	211	6	,	,	PUNCT
cana-6219	211	7	𝑦	𝑦	NOUN
cana-6219	211	8	,	,	PUNCT
cana-6219	211	9	𝑧	𝑧	PROPN
cana-6219	211	10	,	,	PUNCT
cana-6219	211	11	𝑠	𝑠	NOUN
cana-6219	211	12	)	)	PUNCT
cana-6219	211	13	=	=	PUNCT
cana-6219	211	14	𝐹−1[𝑓̅̃	𝐹−1[𝑓̅̃	X
cana-6219	211	15	(	(	PUNCT
cana-6219	211	16	𝑥	𝑥	NOUN
cana-6219	211	17	,	,	PUNCT
cana-6219	211	18	𝑝	𝑝	PROPN
cana-6219	211	19	,	,	PUNCT
cana-6219	211	20	𝑞	𝑞	PROPN
cana-6219	211	21	,	,	PUNCT
cana-6219	211	22	𝑠	𝑠	PROPN
cana-6219	211	23	)	)	PUNCT
cana-6219	211	24	=	=	SYM
cana-6219	211	25	1	1	NUM
cana-6219	211	26	2𝜋	2𝜋	NUM
cana-6219	211	27	∫	∫	PROPN
cana-6219	211	28	∫	∫	PROPN
cana-6219	211	29	𝑓̅̃(𝑥	𝑓̅̃(𝑥	PROPN
cana-6219	211	30	,	,	PUNCT
cana-6219	211	31	𝑞	𝑞	NOUN
cana-6219	211	32	,	,	PUNCT
cana-6219	211	33	𝑝	𝑝	PROPN
cana-6219	211	34	,	,	PUNCT
cana-6219	211	35	𝑠	𝑠	NOUN
cana-6219	211	36	)	)	PUNCT
cana-6219	211	37	∞	∞	PROPN
cana-6219	211	38	−∞	−∞	ADP
cana-6219	211	39	∞	∞	PROPN
cana-6219	211	40	−∞	−∞	ADP
cana-6219	211	41	𝑒𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑝	𝑒𝑖(𝑝𝑦+𝑞𝑧)𝑑𝑝	NUM
cana-6219	211	42	𝑑𝑞	𝑑𝑞	PROPN
cana-6219	211	43	=	=	SYM
cana-6219	211	44	1	1	NUM
cana-6219	211	45	2𝜋	2𝜋	NUM
cana-6219	211	46	∫	∫	PROPN
cana-6219	211	47	∫	∫	PROPN
cana-6219	212	1	[	[	X
cana-6219	212	2	cos	cos	X
cana-6219	212	3	(	(	PUNCT
cana-6219	212	4	𝑝𝑦	𝑝𝑦	PROPN
cana-6219	212	5	+	+	CCONJ
cana-6219	212	6	𝑞𝑧)𝑓̅̃	𝑞𝑧)𝑓̅̃	PROPN
cana-6219	212	7	𝑒	𝑒	PROPN
cana-6219	212	8	∞	∞	PROPN
cana-6219	212	9	−∞	−∞	ADP
cana-6219	212	10	∞	∞	PROPN
cana-6219	212	11	−∞	−∞	X
cana-6219	212	12	+	+	PUNCT
cana-6219	212	13	𝑖𝑠𝑖𝑛(𝑝𝑦	𝑖𝑠𝑖𝑛(𝑝𝑦	PROPN
cana-6219	212	14	+	+	CCONJ
cana-6219	212	15	𝑞𝑧)𝑓̅̃	𝑞𝑧)𝑓̅̃	ADJ
cana-6219	212	16	0	0	NUM
cana-6219	212	17	]	]	X
cana-6219	212	18	𝑑𝑝	𝑑𝑝	ADP
cana-6219	212	19	𝑑𝑞	𝑑𝑞	PROPN
cana-6219	212	20	(	(	PUNCT
cana-6219	212	21	73	73	NUM
cana-6219	212	22	)	)	PUNCT
cana-6219	212	23	where	where	SCONJ
cana-6219	212	24	𝑓̅̃	𝑓̅̃	NOUN
cana-6219	212	25	0	0	NUM
cana-6219	212	26	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-6219	212	27	𝑓̅̃	𝑓̅̃	VERB
cana-6219	212	28	𝑒	𝑒	NOUN
cana-6219	212	29	denote	denote	VERB
cana-6219	212	30	the	the	DET
cana-6219	212	31	odd	odd	ADJ
cana-6219	212	32	and	and	CCONJ
cana-6219	212	33	even	even	ADV
cana-6219	212	34	parts	part	NOUN
cana-6219	212	35	of	of	ADP
cana-6219	212	36	the	the	DET
cana-6219	212	37	function	function	NOUN
cana-6219	212	38	𝑓̅̃(𝑥	𝑓̅̃(𝑥	NUM
cana-6219	212	39	,	,	PUNCT
cana-6219	212	40	𝑞	𝑞	NOUN
cana-6219	212	41	,	,	PUNCT
cana-6219	212	42	𝑝	𝑝	PROPN
cana-6219	212	43	,	,	PUNCT
cana-6219	212	44	𝑠	𝑠	PROPN
cana-6219	212	45	)	)	PUNCT
cana-6219	212	46	,	,	PUNCT
cana-6219	212	47	respectively	respectively	ADV
cana-6219	212	48	.	.	PUNCT
cana-6219	213	1	to	to	PART
cana-6219	213	2	invert	invert	VERB
cana-6219	213	3	the	the	DET
cana-6219	213	4	laplace	laplace	NOUN
cana-6219	213	5	,	,	PUNCT
cana-6219	213	6	transform	transform	NOUN
cana-6219	213	7	,	,	PUNCT
cana-6219	213	8	the	the	DET
cana-6219	213	9	technique	technique	NOUN
cana-6219	213	10	of	of	ADP
cana-6219	213	11	the	the	DET
cana-6219	213	12	riemann	riemann	PROPN
cana-6219	213	13	-	-	PUNCT
cana-6219	213	14	sum	sum	NOUN
cana-6219	213	15	approximation	approximation	NOUN
cana-6219	213	16	will	will	AUX
cana-6219	213	17	be	be	AUX
cana-6219	213	18	applied	apply	VERB
cana-6219	213	19	as	as	ADP
cana-6219	213	20	(	(	PUNCT
cana-6219	213	21	tzou	tzou	NOUN
cana-6219	213	22	[	[	X
cana-6219	213	23	31	31	NUM
cana-6219	213	24	]	]	PUNCT
cana-6219	213	25	):	):	PUNCT
cana-6219	213	26	communications	communication	NOUN
cana-6219	213	27	on	on	ADP
cana-6219	213	28	applied	apply	VERB
cana-6219	213	29	nonlinear	nonlinear	ADJ
cana-6219	213	30	analysis	analysis	NOUN
cana-6219	213	31	issn	issn	NOUN
cana-6219	213	32	:	:	PUNCT
cana-6219	213	33	1074	1074	NUM
cana-6219	213	34	-	-	PUNCT
cana-6219	213	35	133x	133x	NUM
cana-6219	213	36	vol	vol	VERB
cana-6219	213	37	32	32	NUM
cana-6219	213	38	no	no	NOUN
cana-6219	213	39	.	.	PUNCT
cana-6219	214	1	10s	10	NOUN
cana-6219	214	2	(	(	PUNCT
cana-6219	214	3	2025	2025	NUM
cana-6219	214	4	)	)	PUNCT
cana-6219	214	5	3539	3539	NUM
cana-6219	214	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	214	7	𝑔(𝑡	𝑔(𝑡	PROPN
cana-6219	214	8	)	)	PUNCT
cana-6219	215	1	=	=	PRON
cana-6219	215	2	𝑒𝑘𝑡	𝑒𝑘𝑡	NUM
cana-6219	215	3	𝑡	𝑡	PROPN
cana-6219	215	4	[	[	PUNCT
cana-6219	215	5	1	1	NUM
cana-6219	215	6	2	2	NUM
cana-6219	215	7	�	�	NOUN
cana-6219	215	8	̅	̅	NOUN
cana-6219	215	9	�	�	NOUN
cana-6219	215	10	(𝑘	(𝑘	NOUN
cana-6219	215	11	)	)	PUNCT
cana-6219	216	1	+	+	CCONJ
cana-6219	216	2	𝑅𝑒	𝑅𝑒	VERB
cana-6219	216	3	∑(−1)𝑛	∑(−1)𝑛	NOUN
cana-6219	216	4	�	�	NOUN
cana-6219	216	5	̅	̅	NOUN
cana-6219	216	6	�	�	NOUN
cana-6219	216	7	(	(	PUNCT
cana-6219	216	8	𝐾	𝐾	PROPN
cana-6219	216	9	+	+	NUM
cana-6219	216	10	𝑖𝑛𝜋	𝑖𝑛𝜋	PROPN
cana-6219	216	11	𝑡	𝑡	PROPN
cana-6219	216	12	)	)	PUNCT
cana-6219	216	13	𝑁	𝑁	PROPN
cana-6219	216	14	𝑛=1	𝑛=1	NOUN
cana-6219	216	15	]	]	PUNCT
cana-6219	216	16	(	(	PUNCT
cana-6219	216	17	74	74	NUM
cana-6219	216	18	)	)	PUNCT
cana-6219	216	19	here	here	ADV
cana-6219	216	20	re	re	VERB
cana-6219	216	21	means	mean	VERB
cana-6219	216	22	the	the	DET
cana-6219	216	23	real	real	ADJ
cana-6219	216	24	part	part	NOUN
cana-6219	216	25	and	and	CCONJ
cana-6219	216	26	𝑖	𝑖	NOUN
cana-6219	216	27	=	=	NOUN
cana-6219	216	28	√−1	√−1	PROPN
cana-6219	216	29	.	.	PUNCT
cana-6219	217	1	almost	almost	ADV
cana-6219	217	2	all	all	DET
cana-6219	217	3	the	the	DET
cana-6219	217	4	computational	computational	ADJ
cana-6219	217	5	experiments	experiment	NOUN
cana-6219	217	6	have	have	AUX
cana-6219	217	7	shown	show	VERB
cana-6219	217	8	that	that	SCONJ
cana-6219	217	9	the	the	DET
cana-6219	217	10	value	value	NOUN
cana-6219	217	11	of	of	ADP
cana-6219	217	12	k	k	PROPN
cana-6219	217	13	comes	come	VERB
cana-6219	217	14	from	from	ADP
cana-6219	217	15	the	the	DET
cana-6219	217	16	relation	relation	NOUN
cana-6219	218	1	𝐾𝑡	𝐾𝑡	PROPN
cana-6219	218	2	≈	≈	PROPN
cana-6219	218	3	4.7	4.7	NUM
cana-6219	218	4	,	,	PUNCT
cana-6219	218	5	which	which	PRON
cana-6219	218	6	gives	give	VERB
cana-6219	218	7	faster	fast	ADJ
cana-6219	218	8	convergence	convergence	NOUN
cana-6219	218	9	[	[	X
cana-6219	218	10	31	31	NUM
cana-6219	218	11	]	]	SYM
cana-6219	218	12	.	.	PUNCT
cana-6219	219	1	6	6	NUM
cana-6219	219	2	.	.	X
cana-6219	219	3	numerical	numerical	ADJ
cana-6219	219	4	result	result	NOUN
cana-6219	219	5	and	and	CCONJ
cana-6219	219	6	discussion	discussion	NOUN
cana-6219	219	7	copper	copper	NOUN
cana-6219	219	8	plate	plate	NOUN
cana-6219	219	9	was	be	AUX
cana-6219	219	10	taken	take	VERB
cana-6219	219	11	for	for	ADP
cana-6219	219	12	the	the	DET
cana-6219	219	13	numerical	numerical	ADJ
cana-6219	219	14	calculations	calculation	NOUN
cana-6219	219	15	and	and	CCONJ
cana-6219	219	16	the	the	DET
cana-6219	219	17	constants	constant	NOUN
cana-6219	219	18	of	of	ADP
cana-6219	219	19	the	the	DET
cana-6219	219	20	material	material	NOUN
cana-6219	219	21	have	have	AUX
cana-6219	219	22	been	be	AUX
cana-6219	219	23	taken	take	VERB
cana-6219	219	24	as	as	SCONJ
cana-6219	219	25	follows	follow	VERB
cana-6219	219	26	[	[	X
cana-6219	219	27	7	7	NUM
cana-6219	219	28	]	]	X
cana-6219	219	29	:	:	PUNCT
cana-6219	219	30	physical	physical	ADJ
cana-6219	219	31	constant	constant	ADJ
cana-6219	219	32	value	value	NOUN
cana-6219	219	33	thermal	thermal	ADJ
cana-6219	219	34	conductivity	conductivity	NOUN
cana-6219	219	35	(	(	PUNCT
cana-6219	219	36	k	k	NOUN
cana-6219	219	37	)	)	PUNCT
cana-6219	219	38	386	386	NUM
cana-6219	219	39	n	n	CCONJ
cana-6219	219	40	/	/	SYM
cana-6219	219	41	k	k	PROPN
cana-6219	219	42	sec	sec	PROPN
cana-6219	219	43	linear	linear	ADJ
cana-6219	219	44	thermal	thermal	ADJ
cana-6219	219	45	expansion	expansion	NOUN
cana-6219	219	46	coefficient	coefficient	NOUN
cana-6219	219	47	(	(	PUNCT
cana-6219	219	48	𝜔𝑇	𝜔𝑇	NOUN
cana-6219	219	49	)	)	PUNCT
cana-6219	219	50	1.78	1.78	NUM
cana-6219	219	51	×	×	NOUN
cana-6219	219	52	10−5𝐾−1	10−5𝐾−1	ADJ
cana-6219	219	53	specific	specific	ADJ
cana-6219	219	54	heat	heat	NOUN
cana-6219	219	55	of	of	ADP
cana-6219	219	56	the	the	DET
cana-6219	219	57	material	material	NOUN
cana-6219	219	58	with	with	ADP
cana-6219	219	59	constant	constant	ADJ
cana-6219	219	60	strain	strain	NOUN
cana-6219	219	61	(	(	PUNCT
cana-6219	219	62	𝐶𝐸	𝐶𝐸	PROPN
cana-6219	219	63	)	)	PUNCT
cana-6219	219	64	383.1	383.1	NUM
cana-6219	219	65	𝑚2	𝑚2	NOUN
cana-6219	219	66	/	/	SYM
cana-6219	219	67	k	k	PROPN
cana-6219	219	68	reference	reference	NOUN
cana-6219	219	69	temperature	temperature	NOUN
cana-6219	219	70	(	(	PUNCT
cana-6219	219	71	𝑇0	𝑇0	NOUN
cana-6219	219	72	)	)	PUNCT
cana-6219	220	1	293	293	NUM
cana-6219	220	2	k	k	PRON
cana-6219	220	3	lame	lame	PROPN
cana-6219	220	4	’s	’s	PART
cana-6219	220	5	parameters	parameter	NOUN
cana-6219	220	6	(	(	PUNCT
cana-6219	220	7	𝜇	𝜇	NOUN
cana-6219	220	8	)	)	PUNCT
cana-6219	220	9	3.86×1010	3.86×1010	PROPN
cana-6219	220	10	n	n	CCONJ
cana-6219	220	11	/	/	SYM
cana-6219	220	12	m2	m2	PROPN
cana-6219	220	13	lame	lame	NOUN
cana-6219	220	14	’s	’s	PART
cana-6219	220	15	parameters	parameter	NOUN
cana-6219	220	16	(	(	PUNCT
cana-6219	220	17	λ	λ	X
cana-6219	220	18	)	)	PUNCT
cana-6219	220	19	7.79	7.79	NUM
cana-6219	220	20	×1010	×1010	NOUN
cana-6219	220	21	n	n	CCONJ
cana-6219	220	22	/	/	SYM
cana-6219	220	23	m2	m2	PROPN
cana-6219	220	24	density	density	NOUN
cana-6219	220	25	(	(	PUNCT
cana-6219	220	26	𝜌	𝜌	NOUN
cana-6219	220	27	)	)	PUNCT
cana-6219	220	28	8954	8954	NUM
cana-6219	220	29	kg	kg	NOUN
cana-6219	220	30	/	/	SYM
cana-6219	220	31	m2	m2	PROPN
cana-6219	220	32	relaxation	relaxation	NOUN
cana-6219	220	33	time	time	NOUN
cana-6219	220	34	(	(	PUNCT
cana-6219	220	35	𝜏0	𝜏0	PROPN
cana-6219	220	36	)	)	PUNCT
cana-6219	220	37	0.33	0.33	NUM
cana-6219	220	38	×	×	NOUN
cana-6219	220	39	10	10	NUM
cana-6219	220	40	-	-	SYM
cana-6219	220	41	15	15	NUM
cana-6219	220	42	sec	sec	PROPN
cana-6219	220	43	𝜏0	𝜏0	PROPN
cana-6219	220	44	=	=	PROPN
cana-6219	220	45	0.002	0.002	NUM
cana-6219	220	46	𝛽	𝛽	NOUN
cana-6219	220	47	=	=	NUM
cana-6219	220	48	0.25	0.25	NUM
cana-6219	220	49	𝛼	𝛼	NOUN
cana-6219	220	50	=	=	X
cana-6219	220	51	0.67	0.67	NUM
cana-6219	220	52	휀1	휀1	NOUN
cana-6219	220	53	=	=	PUNCT
cana-6219	220	54	0.0168	0.0168	NUM
cana-6219	220	55	휀2	휀2	NOUN
cana-6219	220	56	=	=	SYM
cana-6219	220	57	0.010444	0.010444	NUM
cana-6219	220	58	𝜂	𝜂	X
cana-6219	220	59	=	=	SYM
cana-6219	220	60	8886.73	8886.73	NUM
cana-6219	220	61	m	m	PROPN
cana-6219	220	62	/	/	SYM
cana-6219	220	63	sec2	sec2	NOUN
cana-6219	220	64	the	the	DET
cana-6219	220	65	study	study	NOUN
cana-6219	220	66	investigates	investigate	VERB
cana-6219	220	67	the	the	DET
cana-6219	220	68	distribution	distribution	NOUN
cana-6219	220	69	of	of	ADP
cana-6219	220	70	temperature	temperature	NOUN
cana-6219	220	71	increment	increment	NOUN
cana-6219	220	72	,	,	PUNCT
cana-6219	220	73	stress	stress	NOUN
cana-6219	220	74	,	,	PUNCT
cana-6219	220	75	strain	strain	NOUN
cana-6219	220	76	and	and	CCONJ
cana-6219	220	77	displacement	displacement	NOUN
cana-6219	220	78	(	(	PUNCT
cana-6219	220	79	𝑢𝑥	𝑢𝑥	NOUN
cana-6219	220	80	)	)	PUNCT
cana-6219	220	81	components	component	NOUN
cana-6219	220	82	over	over	ADP
cana-6219	220	83	a	a	DET
cana-6219	220	84	wide	wide	ADJ
cana-6219	220	85	range	range	NOUN
cana-6219	220	86	of	of	ADP
cana-6219	220	87	distance	distance	NOUN
cana-6219	220	88	x	x	INTJ
cana-6219	220	89	(	(	PUNCT
cana-6219	220	90	from	from	ADP
cana-6219	220	91	0	0	NUM
cana-6219	220	92	to	to	ADP
cana-6219	220	93	1	1	NUM
cana-6219	220	94	)	)	PUNCT
cana-6219	220	95	for	for	ADP
cana-6219	220	96	varying	vary	VERB
cana-6219	220	97	heat	heat	NOUN
cana-6219	220	98	source	source	NOUN
cana-6219	220	99	speeds	speed	VERB
cana-6219	220	100	𝜈	𝜈	X
cana-6219	220	101	(	(	PUNCT
cana-6219	220	102	values	value	NOUN
cana-6219	220	103	0.1	0.1	NUM
cana-6219	220	104	,	,	PUNCT
cana-6219	220	105	0.3	0.3	NUM
cana-6219	220	106	,	,	PUNCT
cana-6219	220	107	0.5	0.5	NUM
cana-6219	220	108	,	,	PUNCT
cana-6219	220	109	0.7	0.7	NUM
cana-6219	220	110	)	)	PUNCT
cana-6219	220	111	.	.	PUNCT
cana-6219	221	1	specifically	specifically	ADV
cana-6219	221	2	,	,	PUNCT
cana-6219	221	3	the	the	DET
cana-6219	221	4	analysis	analysis	NOUN
cana-6219	221	5	forces	force	NOUN
cana-6219	221	6	on	on	ADP
cana-6219	221	7	two	two	NUM
cana-6219	221	8	distinct	distinct	ADJ
cana-6219	221	9	cases	case	NOUN
cana-6219	221	10	for	for	ADP
cana-6219	221	11	the	the	DET
cana-6219	221	12	positions	position	NOUN
cana-6219	221	13	y	y	PROPN
cana-6219	221	14	and	and	CCONJ
cana-6219	221	15	z	z	PROPN
cana-6219	221	16	where	where	SCONJ
cana-6219	221	17	y	y	NOUN
cana-6219	221	18	=	=	PUNCT
cana-6219	221	19	z	z	PROPN
cana-6219	221	20	=	=	SYM
cana-6219	221	21	0.0	0.0	NUM
cana-6219	221	22	and	and	CCONJ
cana-6219	221	23	y	y	NOUN
cana-6219	221	24	=	=	SYM
cana-6219	221	25	z	z	NOUN
cana-6219	221	26	=	=	SYM
cana-6219	221	27	0.5	0.5	NUM
cana-6219	221	28	.	.	PUNCT
cana-6219	222	1	temperature	temperature	NOUN
cana-6219	222	2	increment	increment	NOUN
cana-6219	222	3	:	:	PUNCT
cana-6219	222	4	-the	-the	DET
cana-6219	222	5	temperature	temperature	NOUN
cana-6219	222	6	increment	increment	NOUN
cana-6219	222	7	shows	show	VERB
cana-6219	222	8	a	a	DET
cana-6219	222	9	significant	significant	ADJ
cana-6219	222	10	dependence	dependence	NOUN
cana-6219	222	11	on	on	ADP
cana-6219	222	12	the	the	DET
cana-6219	222	13	heat	heat	NOUN
cana-6219	222	14	speed	speed	NOUN
cana-6219	222	15	𝜈.	𝜈.	NOUN
cana-6219	222	16	as	as	ADP
cana-6219	222	17	the	the	DET
cana-6219	222	18	speed	speed	NOUN
cana-6219	222	19	increases	increase	NOUN
cana-6219	222	20	,	,	PUNCT
cana-6219	222	21	the	the	DET
cana-6219	222	22	temperature	temperature	NOUN
cana-6219	222	23	increment	increment	NOUN
cana-6219	222	24	values	value	NOUN
cana-6219	222	25	are	be	AUX
cana-6219	222	26	initially	initially	ADV
cana-6219	222	27	large	large	ADJ
cana-6219	222	28	but	but	CCONJ
cana-6219	222	29	decrease	decrease	NOUN
cana-6219	222	30	after	after	ADP
cana-6219	222	31	reaching	reach	VERB
cana-6219	222	32	a	a	DET
cana-6219	222	33	critical	critical	ADJ
cana-6219	222	34	position	position	NOUN
cana-6219	222	35	𝑥	𝑥	NOUN
cana-6219	222	36	=	=	SYM
cana-6219	222	37	𝜈	𝜈	X
cana-6219	222	38	𝑡	𝑡	X
cana-6219	222	39	where	where	SCONJ
cana-6219	222	40	t	t	PROPN
cana-6219	222	41	is	be	AUX
cana-6219	222	42	time	time	NOUN
cana-6219	222	43	.	.	PUNCT
cana-6219	223	1	for	for	ADP
cana-6219	223	2	position	position	NOUN
cana-6219	223	3	𝑥	𝑥	X
cana-6219	223	4	<	<	X
cana-6219	223	5	𝜈	𝜈	X
cana-6219	223	6	𝑡	𝑡	PROPN
cana-6219	223	7	,	,	PUNCT
cana-6219	223	8	the	the	DET
cana-6219	223	9	heat	heat	NOUN
cana-6219	223	10	source	source	NOUN
cana-6219	223	11	is	be	AUX
cana-6219	223	12	still	still	ADV
cana-6219	223	13	influencing	influence	VERB
cana-6219	223	14	the	the	DET
cana-6219	223	15	region	region	NOUN
cana-6219	223	16	,	,	PUNCT
cana-6219	223	17	leading	lead	VERB
cana-6219	223	18	to	to	ADP
cana-6219	223	19	rapid	rapid	ADJ
cana-6219	223	20	increases	increase	NOUN
cana-6219	223	21	in	in	ADP
cana-6219	223	22	temperature	temperature	NOUN
cana-6219	223	23	increment	increment	NOUN
cana-6219	223	24	.	.	PUNCT
cana-6219	224	1	for	for	ADP
cana-6219	224	2	position	position	NOUN
cana-6219	224	3	𝑥	𝑥	PROPN
cana-6219	224	4	≥	≥	NOUN
cana-6219	224	5	𝜈	𝜈	X
cana-6219	224	6	𝑡	𝑡	X
cana-6219	224	7	the	the	DET
cana-6219	224	8	heat	heat	NOUN
cana-6219	224	9	source	source	NOUN
cana-6219	224	10	is	be	AUX
cana-6219	224	11	no	no	ADV
cana-6219	224	12	longer	long	ADV
cana-6219	224	13	present	present	ADJ
cana-6219	224	14	which	which	PRON
cana-6219	224	15	leads	lead	VERB
cana-6219	224	16	to	to	ADP
cana-6219	224	17	rapid	rapid	ADJ
cana-6219	224	18	decrease	decrease	NOUN
cana-6219	224	19	in	in	ADP
cana-6219	224	20	temperature	temperature	NOUN
cana-6219	224	21	increment	increment	NOUN
cana-6219	224	22	.	.	PUNCT
cana-6219	225	1	stress	stress	ADJ
cana-6219	225	2	distribution	distribution	NOUN
cana-6219	225	3	:	:	PUNCT
cana-6219	225	4	-thermal	-thermal	ADJ
cana-6219	225	5	stress	stress	NOUN
cana-6219	225	6	initially	initially	ADV
cana-6219	225	7	decreases	decrease	VERB
cana-6219	225	8	with	with	ADP
cana-6219	225	9	increasing	increase	VERB
cana-6219	225	10	heat	heat	NOUN
cana-6219	225	11	source	source	NOUN
cana-6219	225	12	speed	speed	NOUN
cana-6219	225	13	,	,	PUNCT
cana-6219	225	14	due	due	ADP
cana-6219	225	15	to	to	ADP
cana-6219	225	16	a	a	DET
cana-6219	225	17	lower	low	ADJ
cana-6219	225	18	thermal	thermal	ADJ
cana-6219	225	19	gradient	gradient	NOUN
cana-6219	225	20	.	.	PUNCT
cana-6219	226	1	after	after	ADP
cana-6219	226	2	the	the	DET
cana-6219	226	3	peak	peak	NOUN
cana-6219	226	4	stress	stress	NOUN
cana-6219	226	5	point	point	NOUN
cana-6219	226	6	,	,	PUNCT
cana-6219	226	7	further	further	ADJ
cana-6219	226	8	increases	increase	NOUN
cana-6219	226	9	in	in	ADP
cana-6219	226	10	speed	speed	NOUN
cana-6219	226	11	lead	lead	NOUN
cana-6219	226	12	to	to	ADP
cana-6219	226	13	higher	high	ADJ
cana-6219	226	14	stress	stress	NOUN
cana-6219	226	15	,	,	PUNCT
cana-6219	226	16	possibly	possibly	ADV
cana-6219	226	17	because	because	SCONJ
cana-6219	226	18	of	of	ADP
cana-6219	226	19	rapid	rapid	ADJ
cana-6219	226	20	cooling	cooling	NOUN
cana-6219	226	21	and	and	CCONJ
cana-6219	226	22	thermal	thermal	ADJ
cana-6219	226	23	mismatch	mismatch	NOUN
cana-6219	226	24	.	.	PUNCT
cana-6219	227	1	this	this	DET
cana-6219	227	2	behaviour	behaviour	NOUN
cana-6219	227	3	illustrates	illustrate	VERB
cana-6219	227	4	a	a	DET
cana-6219	227	5	dual	dual	ADJ
cana-6219	227	6	-	-	PUNCT
cana-6219	227	7	phase	phase	NOUN
cana-6219	227	8	response	response	NOUN
cana-6219	227	9	:	:	PUNCT
cana-6219	227	10	lower	low	ADJ
cana-6219	227	11	stress	stress	NOUN
cana-6219	227	12	due	due	ADP
cana-6219	227	13	to	to	ADP
cana-6219	227	14	milder	mild	ADJ
cana-6219	227	15	gradients	gradient	NOUN
cana-6219	227	16	early	early	ADV
cana-6219	227	17	on	on	ADV
cana-6219	227	18	,	,	PUNCT
cana-6219	227	19	but	but	CCONJ
cana-6219	227	20	higher	high	ADJ
cana-6219	227	21	stress	stress	NOUN
cana-6219	227	22	post	post	ADJ
cana-6219	227	23	-	-	ADJ
cana-6219	227	24	heating	heating	ADJ
cana-6219	227	25	due	due	ADJ
cana-6219	227	26	to	to	ADP
cana-6219	227	27	quicker	quick	ADJ
cana-6219	227	28	relaxation	relaxation	NOUN
cana-6219	227	29	/	/	SYM
cana-6219	227	30	cooling	cooling	NOUN
cana-6219	227	31	.	.	PUNCT
cana-6219	228	1	displacement	displacement	NOUN
cana-6219	228	2	(	(	PUNCT
cana-6219	228	3	𝑢ₓ	𝑢ₓ	NOUN
cana-6219	228	4	):	):	PUNCT
cana-6219	228	5	displacement	displacement	NOUN
cana-6219	228	6	decreases	decrease	VERB
cana-6219	228	7	with	with	ADP
cana-6219	228	8	increasing	increase	VERB
cana-6219	228	9	speed	speed	NOUN
cana-6219	228	10	of	of	ADP
cana-6219	228	11	the	the	DET
cana-6219	228	12	heat	heat	NOUN
cana-6219	228	13	source	source	NOUN
cana-6219	228	14	.	.	PUNCT
cana-6219	229	1	higher	high	ADJ
cana-6219	229	2	speeds	speed	NOUN
cana-6219	229	3	give	give	VERB
cana-6219	229	4	the	the	DET
cana-6219	229	5	material	material	NOUN
cana-6219	229	6	less	less	ADJ
cana-6219	229	7	time	time	NOUN
cana-6219	229	8	to	to	PART
cana-6219	229	9	undergo	undergo	VERB
cana-6219	229	10	thermal	thermal	ADJ
cana-6219	229	11	expansion	expansion	NOUN
cana-6219	229	12	,	,	PUNCT
cana-6219	229	13	resulting	result	VERB
cana-6219	229	14	in	in	ADP
cana-6219	229	15	smaller	small	ADJ
cana-6219	229	16	net	net	ADJ
cana-6219	229	17	displacement	displacement	NOUN
cana-6219	229	18	.	.	PUNCT
cana-6219	230	1	this	this	DET
cana-6219	230	2	communications	communication	NOUN
cana-6219	230	3	on	on	ADP
cana-6219	230	4	applied	apply	VERB
cana-6219	230	5	nonlinear	nonlinear	ADJ
cana-6219	230	6	analysis	analysis	NOUN
cana-6219	230	7	issn	issn	NOUN
cana-6219	230	8	:	:	PUNCT
cana-6219	230	9	1074	1074	NUM
cana-6219	230	10	-	-	PUNCT
cana-6219	230	11	133x	133x	NUM
cana-6219	230	12	vol	vol	VERB
cana-6219	230	13	32	32	NUM
cana-6219	230	14	no	no	NOUN
cana-6219	230	15	.	.	PUNCT
cana-6219	231	1	10s	10	NOUN
cana-6219	231	2	(	(	PUNCT
cana-6219	231	3	2025	2025	NUM
cana-6219	231	4	)	)	PUNCT
cana-6219	231	5	3540	3540	NUM
cana-6219	231	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	231	7	shows	show	VERB
cana-6219	231	8	that	that	SCONJ
cana-6219	231	9	rapid	rapid	ADJ
cana-6219	231	10	heating	heating	NOUN
cana-6219	231	11	minimizes	minimize	VERB
cana-6219	231	12	mechanical	mechanical	ADJ
cana-6219	231	13	deformation	deformation	NOUN
cana-6219	231	14	,	,	PUNCT
cana-6219	231	15	which	which	PRON
cana-6219	231	16	could	could	AUX
cana-6219	231	17	be	be	AUX
cana-6219	231	18	important	important	ADJ
cana-6219	231	19	in	in	ADP
cana-6219	231	20	precision	precision	NOUN
cana-6219	231	21	thermal	thermal	ADJ
cana-6219	231	22	processing	processing	NOUN
cana-6219	231	23	applications	application	NOUN
cana-6219	231	24	.	.	PUNCT
cana-6219	232	1	influence	influence	NOUN
cana-6219	232	2	of	of	ADP
cana-6219	232	3	position	position	NOUN
cana-6219	232	4	(	(	PUNCT
cana-6219	232	5	y	y	NOUN
cana-6219	232	6	=	=	PUNCT
cana-6219	232	7	z	z	NOUN
cana-6219	232	8	=	=	PUNCT
cana-6219	232	9	0	0	PROPN
cana-6219	233	1	vs	vs	ADP
cana-6219	233	2	y	y	NOUN
cana-6219	233	3	=	=	PUNCT
cana-6219	233	4	z	z	NOUN
cana-6219	233	5	=	=	SYM
cana-6219	233	6	0.5	0.5	NUM
cana-6219	233	7	):	):	PUNCT
cana-6219	233	8	at	at	ADP
cana-6219	233	9	the	the	DET
cana-6219	233	10	canter	canter	NOUN
cana-6219	233	11	(	(	PUNCT
cana-6219	233	12	y	y	NOUN
cana-6219	233	13	=	=	SYM
cana-6219	233	14	z	z	NOUN
cana-6219	233	15	=	=	NOUN
cana-6219	233	16	0	0	NUM
cana-6219	233	17	)	)	PUNCT
cana-6219	233	18	,	,	PUNCT
cana-6219	233	19	effects	effect	NOUN
cana-6219	233	20	are	be	AUX
cana-6219	233	21	more	more	ADV
cana-6219	233	22	pronounced	pronounced	ADJ
cana-6219	233	23	in	in	ADP
cana-6219	233	24	all	all	DET
cana-6219	233	25	aspect	aspect	NOUN
cana-6219	233	26	’s	’s	PART
cana-6219	233	27	temperature	temperature	NOUN
cana-6219	233	28	,	,	PUNCT
cana-6219	233	29	stress	stress	NOUN
cana-6219	233	30	,	,	PUNCT
cana-6219	233	31	and	and	CCONJ
cana-6219	233	32	displacement	displacement	NOUN
cana-6219	233	33	due	due	ADP
cana-6219	233	34	to	to	ADP
cana-6219	233	35	direct	direct	ADJ
cana-6219	233	36	exposure	exposure	NOUN
cana-6219	233	37	to	to	ADP
cana-6219	233	38	the	the	DET
cana-6219	233	39	heat	heat	NOUN
cana-6219	233	40	source	source	NOUN
cana-6219	233	41	.	.	PUNCT
cana-6219	234	1	at	at	ADP
cana-6219	234	2	offcentre	offcentre	NOUN
cana-6219	234	3	positions	position	NOUN
cana-6219	234	4	(	(	PUNCT
cana-6219	234	5	y	y	NOUN
cana-6219	234	6	=	=	PUNCT
cana-6219	234	7	z	z	NOUN
cana-6219	234	8	=	=	NUM
cana-6219	234	9	0.5	0.5	NUM
cana-6219	234	10	)	)	PUNCT
cana-6219	234	11	,	,	PUNCT
cana-6219	234	12	responses	response	NOUN
cana-6219	234	13	are	be	AUX
cana-6219	234	14	attenuated	attenuate	VERB
cana-6219	234	15	,	,	PUNCT
cana-6219	234	16	confirming	confirm	VERB
cana-6219	234	17	the	the	DET
cana-6219	234	18	localized	localized	ADJ
cana-6219	234	19	nature	nature	NOUN
cana-6219	234	20	of	of	ADP
cana-6219	234	21	thermal	thermal	ADJ
cana-6219	234	22	effects	effect	NOUN
cana-6219	234	23	in	in	ADP
cana-6219	234	24	the	the	DET
cana-6219	234	25	analysed	analyse	VERB
cana-6219	234	26	geometry	geometry	NOUN
cana-6219	234	27	.	.	PUNCT
cana-6219	235	1	temperature	temperature	NOUN
cana-6219	235	2	for	for	ADP
cana-6219	235	3	different	different	ADJ
cana-6219	235	4	values	value	NOUN
cana-6219	235	5	of	of	ADP
cana-6219	235	6	time	time	NOUN
cana-6219	235	7	temp	temp	NOUN
cana-6219	235	8	for	for	ADP
cana-6219	235	9	different	different	ADJ
cana-6219	235	10	values	value	NOUN
cana-6219	235	11	of	of	ADP
cana-6219	235	12	alpha	alpha	NOUN
cana-6219	235	13	displacement	displacement	NOUN
cana-6219	235	14	for	for	ADP
cana-6219	235	15	different	different	ADJ
cana-6219	235	16	values	value	NOUN
cana-6219	235	17	of	of	ADP
cana-6219	235	18	time	time	NOUN
cana-6219	235	19	displacement	displacement	NOUN
cana-6219	235	20	of	of	ADP
cana-6219	235	21	different	different	ADJ
cana-6219	235	22	values	value	NOUN
cana-6219	235	23	of	of	ADP
cana-6219	235	24	alpha	alpha	NOUN
cana-6219	235	25	communications	communication	NOUN
cana-6219	235	26	on	on	ADP
cana-6219	235	27	applied	apply	VERB
cana-6219	235	28	nonlinear	nonlinear	ADJ
cana-6219	235	29	analysis	analysis	NOUN
cana-6219	235	30	issn	issn	NOUN
cana-6219	235	31	:	:	PUNCT
cana-6219	235	32	1074	1074	NUM
cana-6219	235	33	-	-	PUNCT
cana-6219	235	34	133x	133x	NUM
cana-6219	235	35	vol	vol	VERB
cana-6219	235	36	32	32	NUM
cana-6219	235	37	no	no	NOUN
cana-6219	235	38	.	.	PUNCT
cana-6219	236	1	10s	10	NOUN
cana-6219	236	2	(	(	PUNCT
cana-6219	236	3	2025	2025	NUM
cana-6219	236	4	)	)	PUNCT
cana-6219	236	5	3541	3541	NUM
cana-6219	236	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	236	7	stresses	stress	VERB
cana-6219	236	8	for	for	ADP
cana-6219	236	9	different	different	ADJ
cana-6219	236	10	values	value	NOUN
cana-6219	236	11	of	of	ADP
cana-6219	236	12	time	time	NOUN
cana-6219	236	13	stresses	stress	NOUN
cana-6219	236	14	for	for	ADP
cana-6219	236	15	different	different	ADJ
cana-6219	236	16	values	value	NOUN
cana-6219	236	17	of	of	ADP
cana-6219	236	18	alpha	alpha	NOUN
cana-6219	236	19	7	7	NUM
cana-6219	236	20	.	.	PUNCT
cana-6219	236	21	concluding	conclude	VERB
cana-6219	236	22	remarks	remark	NOUN
cana-6219	236	23	effect	effect	NOUN
cana-6219	236	24	of	of	ADP
cana-6219	236	25	time	time	NOUN
cana-6219	236	26	(	(	PUNCT
cana-6219	236	27	t	t	NOUN
cana-6219	236	28	):	):	PUNCT
cana-6219	236	29	1	1	NUM
cana-6219	236	30	.	.	X
cana-6219	237	1	temperature	temperature	NOUN
cana-6219	237	2	(	(	PUNCT
cana-6219	237	3	θ	θ	NOUN
cana-6219	237	4	):	):	PUNCT
cana-6219	237	5	•	•	X
cana-6219	237	6	temperature	temperature	NOUN
cana-6219	237	7	rises	rise	VERB
cana-6219	237	8	sharply	sharply	ADV
cana-6219	237	9	at	at	ADP
cana-6219	237	10	early	early	ADJ
cana-6219	237	11	times	time	NOUN
cana-6219	237	12	due	due	ADP
cana-6219	237	13	to	to	ADP
cana-6219	237	14	active	active	ADJ
cana-6219	237	15	heating	heating	NOUN
cana-6219	237	16	by	by	ADP
cana-6219	237	17	the	the	DET
cana-6219	237	18	moving	move	VERB
cana-6219	237	19	source	source	NOUN
cana-6219	237	20	.	.	PUNCT
cana-6219	238	1	•	•	NUM
cana-6219	238	2	over	over	ADP
cana-6219	238	3	time	time	NOUN
cana-6219	238	4	,	,	PUNCT
cana-6219	238	5	the	the	DET
cana-6219	238	6	temperature	temperature	NOUN
cana-6219	238	7	profile	profile	NOUN
cana-6219	238	8	shifts	shift	NOUN
cana-6219	238	9	along	along	ADP
cana-6219	238	10	the	the	DET
cana-6219	238	11	x	x	NOUN
cana-6219	238	12	-	-	NOUN
cana-6219	238	13	axis	axis	NOUN
cana-6219	238	14	in	in	ADP
cana-6219	238	15	the	the	DET
cana-6219	238	16	direction	direction	NOUN
cana-6219	238	17	of	of	ADP
cana-6219	238	18	heat	heat	NOUN
cana-6219	238	19	source	source	NOUN
cana-6219	238	20	motion	motion	NOUN
cana-6219	238	21	,	,	PUNCT
cana-6219	238	22	indicating	indicate	VERB
cana-6219	238	23	the	the	DET
cana-6219	238	24	transient	transient	ADJ
cana-6219	238	25	nature	nature	NOUN
cana-6219	238	26	of	of	ADP
cana-6219	238	27	thermal	thermal	ADJ
cana-6219	238	28	propagation	propagation	NOUN
cana-6219	238	29	.	.	PUNCT
cana-6219	239	1	•	•	NOUN
cana-6219	239	2	after	after	SCONJ
cana-6219	239	3	the	the	DET
cana-6219	239	4	source	source	NOUN
cana-6219	239	5	passes	pass	VERB
cana-6219	239	6	,	,	PUNCT
cana-6219	239	7	cooling	cool	VERB
cana-6219	239	8	is	be	AUX
cana-6219	239	9	evident	evident	ADJ
cana-6219	239	10	as	as	SCONJ
cana-6219	239	11	temperature	temperature	NOUN
cana-6219	239	12	falls	fall	VERB
cana-6219	239	13	significantly	significantly	ADV
cana-6219	239	14	.	.	PUNCT
cana-6219	240	1	2	2	X
cana-6219	240	2	.	.	X
cana-6219	240	3	displacement	displacement	NOUN
cana-6219	240	4	(	(	PUNCT
cana-6219	240	5	uₓ	uₓ	ADV
cana-6219	240	6	):	):	PUNCT
cana-6219	240	7	•	•	X
cana-6219	240	8	displacement	displacement	NOUN
cana-6219	240	9	increases	increase	NOUN
cana-6219	240	10	initially	initially	ADV
cana-6219	240	11	with	with	ADP
cana-6219	240	12	time	time	NOUN
cana-6219	240	13	due	due	ADP
cana-6219	240	14	to	to	ADP
cana-6219	240	15	thermal	thermal	ADJ
cana-6219	240	16	expansion	expansion	NOUN
cana-6219	240	17	.	.	PUNCT
cana-6219	241	1	•	•	NUM
cana-6219	241	2	later	later	ADV
cana-6219	241	3	,	,	PUNCT
cana-6219	241	4	it	it	PRON
cana-6219	241	5	stabilizes	stabilize	VERB
cana-6219	241	6	or	or	CCONJ
cana-6219	241	7	decreases	decrease	NOUN
cana-6219	241	8	as	as	SCONJ
cana-6219	241	9	the	the	DET
cana-6219	241	10	material	material	NOUN
cana-6219	241	11	begins	begin	VERB
cana-6219	241	12	to	to	PART
cana-6219	241	13	cool	cool	VERB
cana-6219	241	14	.	.	PUNCT
cana-6219	242	1	•	•	NUM
cana-6219	242	2	peak	peak	NOUN
cana-6219	242	3	displacement	displacement	ADJ
cana-6219	242	4	shifts	shift	NOUN
cana-6219	242	5	with	with	ADP
cana-6219	242	6	time	time	NOUN
cana-6219	242	7	,	,	PUNCT
cana-6219	242	8	indicating	indicate	VERB
cana-6219	242	9	delayed	delay	VERB
cana-6219	242	10	mechanical	mechanical	ADJ
cana-6219	242	11	response	response	NOUN
cana-6219	242	12	to	to	ADP
cana-6219	242	13	thermal	thermal	ADJ
cana-6219	242	14	input	input	NOUN
cana-6219	242	15	.	.	PUNCT
cana-6219	243	1	3	3	X
cana-6219	243	2	.	.	X
cana-6219	243	3	stress	stress	NOUN
cana-6219	243	4	(	(	PUNCT
cana-6219	243	5	σ	σ	NOUN
cana-6219	243	6	):	):	PUNCT
cana-6219	243	7	•	•	NUM
cana-6219	243	8	stress	stress	NOUN
cana-6219	243	9	shows	show	VERB
cana-6219	243	10	an	an	DET
cana-6219	243	11	initial	initial	ADJ
cana-6219	243	12	increase	increase	NOUN
cana-6219	243	13	,	,	PUNCT
cana-6219	243	14	followed	follow	VERB
cana-6219	243	15	by	by	ADP
cana-6219	243	16	a	a	DET
cana-6219	243	17	decrease	decrease	NOUN
cana-6219	243	18	over	over	ADP
cana-6219	243	19	time	time	NOUN
cana-6219	243	20	,	,	PUNCT
cana-6219	243	21	aligned	align	VERB
cana-6219	243	22	with	with	ADP
cana-6219	243	23	temperature	temperature	NOUN
cana-6219	243	24	and	and	CCONJ
cana-6219	243	25	strain	strain	NOUN
cana-6219	243	26	variations	variation	NOUN
cana-6219	243	27	.	.	PUNCT
cana-6219	244	1	•	•	NUM
cana-6219	244	2	peak	peak	NOUN
cana-6219	244	3	stress	stress	NOUN
cana-6219	244	4	shifts	shift	NOUN
cana-6219	244	5	downstream	downstream	ADJ
cana-6219	244	6	over	over	ADP
cana-6219	244	7	time	time	NOUN
cana-6219	244	8	,	,	PUNCT
cana-6219	244	9	mimicking	mimic	VERB
cana-6219	244	10	the	the	DET
cana-6219	244	11	thermal	thermal	ADJ
cana-6219	244	12	gradient	gradient	NOUN
cana-6219	244	13	progression	progression	NOUN
cana-6219	244	14	.	.	PUNCT
cana-6219	245	1	•	•	ADJ
cana-6219	245	2	temporal	temporal	ADJ
cana-6219	245	3	evolution	evolution	NOUN
cana-6219	245	4	reflects	reflect	VERB
cana-6219	245	5	thermoelastic	thermoelastic	ADJ
cana-6219	245	6	coupling	coupling	NOUN
cana-6219	245	7	and	and	CCONJ
cana-6219	245	8	relaxation	relaxation	NOUN
cana-6219	245	9	behaviour	behaviour	NOUN
cana-6219	245	10	.	.	PUNCT
cana-6219	246	1	effect	effect	NOUN
cana-6219	246	2	of	of	ADP
cana-6219	246	3	fractional	fractional	ADJ
cana-6219	246	4	order	order	NOUN
cana-6219	246	5	parameter	parameter	NOUN
cana-6219	246	6	(	(	PUNCT
cana-6219	246	7	α	α	NOUN
cana-6219	246	8	):	):	PUNCT
cana-6219	246	9	1	1	NUM
cana-6219	246	10	.	.	X
cana-6219	246	11	temperature	temperature	NOUN
cana-6219	246	12	(	(	PUNCT
cana-6219	246	13	θ	θ	NOUN
cana-6219	246	14	):	):	PUNCT
cana-6219	246	15	•	•	ADV
cana-6219	246	16	as	as	ADP
cana-6219	246	17	α	α	NOUN
cana-6219	246	18	increases	increase	NOUN
cana-6219	246	19	(	(	PUNCT
cana-6219	246	20	approaching	approach	VERB
cana-6219	246	21	classical	classical	ADJ
cana-6219	246	22	behaviour	behaviour	NOUN
cana-6219	246	23	)	)	PUNCT
cana-6219	246	24	,	,	PUNCT
cana-6219	246	25	the	the	DET
cana-6219	246	26	temperature	temperature	NOUN
cana-6219	246	27	distribution	distribution	NOUN
cana-6219	246	28	becomes	become	VERB
cana-6219	246	29	smoother	smooth	ADJ
cana-6219	246	30	and	and	CCONJ
cana-6219	246	31	more	more	ADV
cana-6219	246	32	diffused	diffused	ADJ
cana-6219	246	33	.	.	PUNCT
cana-6219	247	1	•	•	NUM
cana-6219	247	2	lower	low	ADJ
cana-6219	247	3	α	α	NOUN
cana-6219	247	4	values	value	NOUN
cana-6219	247	5	(	(	PUNCT
cana-6219	247	6	more	more	ADV
cana-6219	247	7	fractional	fractional	ADJ
cana-6219	247	8	behaviour	behaviour	NOUN
cana-6219	247	9	)	)	PUNCT
cana-6219	247	10	produce	produce	VERB
cana-6219	247	11	sharper	sharp	ADJ
cana-6219	247	12	temperature	temperature	NOUN
cana-6219	247	13	gradients	gradient	NOUN
cana-6219	247	14	and	and	CCONJ
cana-6219	247	15	delayed	delayed	ADJ
cana-6219	247	16	diffusion	diffusion	NOUN
cana-6219	247	17	,	,	PUNCT
cana-6219	247	18	highlighting	highlight	VERB
cana-6219	247	19	memory	memory	NOUN
cana-6219	247	20	effects	effect	NOUN
cana-6219	247	21	.	.	PUNCT
cana-6219	248	1	2	2	X
cana-6219	248	2	.	.	X
cana-6219	248	3	displacement	displacement	NOUN
cana-6219	248	4	(	(	PUNCT
cana-6219	248	5	uₓ	uₓ	ADV
cana-6219	248	6	):	):	PUNCT
cana-6219	248	7	•	•	NOUN
cana-6219	248	8	displacement	displacement	NOUN
cana-6219	248	9	decreases	decrease	VERB
cana-6219	248	10	with	with	ADP
cana-6219	248	11	increasing	increase	VERB
cana-6219	248	12	α	α	NOUN
cana-6219	248	13	.	.	PUNCT
cana-6219	249	1	communications	communication	NOUN
cana-6219	249	2	on	on	ADP
cana-6219	249	3	applied	apply	VERB
cana-6219	249	4	nonlinear	nonlinear	ADJ
cana-6219	249	5	analysis	analysis	NOUN
cana-6219	249	6	issn	issn	NOUN
cana-6219	249	7	:	:	PUNCT
cana-6219	249	8	1074	1074	NUM
cana-6219	249	9	-	-	PUNCT
cana-6219	249	10	133x	133x	NUM
cana-6219	249	11	vol	vol	VERB
cana-6219	249	12	32	32	NUM
cana-6219	249	13	no	no	NOUN
cana-6219	249	14	.	.	PUNCT
cana-6219	250	1	10s	10	NOUN
cana-6219	250	2	(	(	PUNCT
cana-6219	250	3	2025	2025	NUM
cana-6219	250	4	)	)	PUNCT
cana-6219	250	5	3542	3542	NUM
cana-6219	250	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-6219	250	7	•	•	ADV
cana-6219	250	8	fractional	fractional	ADJ
cana-6219	250	9	models	model	NOUN
cana-6219	250	10	(	(	PUNCT
cana-6219	250	11	lower	lower	X
cana-6219	250	12	α	α	NOUN
cana-6219	250	13	)	)	PUNCT
cana-6219	250	14	capture	capture	VERB
cana-6219	250	15	stronger	strong	ADJ
cana-6219	250	16	nonlocal	nonlocal	ADJ
cana-6219	250	17	and	and	CCONJ
cana-6219	250	18	history	history	NOUN
cana-6219	250	19	-	-	PUNCT
cana-6219	250	20	dependent	dependent	ADJ
cana-6219	250	21	mechanical	mechanical	ADJ
cana-6219	250	22	responses	response	NOUN
cana-6219	250	23	,	,	PUNCT
cana-6219	250	24	leading	lead	VERB
cana-6219	250	25	to	to	ADP
cana-6219	250	26	higher	high	ADJ
cana-6219	250	27	displacements	displacement	NOUN
cana-6219	250	28	.	.	PUNCT
cana-6219	251	1	3	3	X
cana-6219	251	2	.	.	X
cana-6219	251	3	stress	stress	NOUN
cana-6219	251	4	(	(	PUNCT
cana-6219	251	5	σ	σ	NOUN
cana-6219	251	6	):	):	PUNCT
cana-6219	251	7	•	•	NUM
cana-6219	251	8	stress	stress	NOUN
cana-6219	251	9	magnitude	magnitude	NOUN
cana-6219	251	10	reduces	reduce	VERB
cana-6219	251	11	with	with	ADP
cana-6219	251	12	increasing	increase	VERB
cana-6219	251	13	α	α	NOUN
cana-6219	251	14	.	.	PROPN
cana-6219	252	1	•	•	NOUN
cana-6219	252	2	this	this	PRON
cana-6219	252	3	suggests	suggest	VERB
cana-6219	252	4	that	that	SCONJ
cana-6219	252	5	fractional	fractional	ADJ
cana-6219	252	6	models	model	NOUN
cana-6219	252	7	(	(	PUNCT
cana-6219	252	8	lower	lower	X
cana-6219	252	9	α	α	NOUN
cana-6219	252	10	)	)	PUNCT
cana-6219	252	11	result	result	NOUN
cana-6219	252	12	in	in	ADP
cana-6219	252	13	stronger	strong	ADJ
cana-6219	252	14	stress	stress	NOUN
cana-6219	252	15	responses	response	NOUN
cana-6219	252	16	due	due	ADJ
cana-6219	252	17	to	to	ADP
cana-6219	252	18	enhanced	enhanced	ADJ
cana-6219	252	19	memory	memory	NOUN
cana-6219	252	20	and	and	CCONJ
cana-6219	252	21	time	time	NOUN
cana-6219	252	22	-	-	PUNCT
cana-6219	252	23	delayed	delay	VERB
cana-6219	252	24	effects	effect	NOUN
cana-6219	252	25	.	.	PUNCT
cana-6219	253	1	3	3	X
cana-6219	253	2	.	.	X
cana-6219	253	3	general	general	ADJ
cana-6219	253	4	observations	observation	NOUN
cana-6219	253	5	:	:	PUNCT
cana-6219	253	6	•	•	NUM
cana-6219	253	7	heat	heat	NOUN
cana-6219	253	8	source	source	NOUN
cana-6219	253	9	speed	speed	NOUN
cana-6219	253	10	,	,	PUNCT
cana-6219	253	11	time	time	NOUN
cana-6219	253	12	,	,	PUNCT
cana-6219	253	13	and	and	CCONJ
cana-6219	253	14	fractional	fractional	ADJ
cana-6219	253	15	order	order	NOUN
cana-6219	253	16	α	α	PRON
cana-6219	253	17	all	all	PRON
cana-6219	253	18	significantly	significantly	ADV
cana-6219	253	19	influence	influence	VERB
cana-6219	253	20	the	the	DET
cana-6219	253	21	physical	physical	ADJ
cana-6219	253	22	behaviour	behaviour	NOUN
cana-6219	253	23	.	.	PUNCT
cana-6219	254	1	•	•	NUM
cana-6219	254	2	fractional	fractional	ADJ
cana-6219	254	3	order	order	NOUN
cana-6219	254	4	models	model	NOUN
cana-6219	254	5	provide	provide	VERB
cana-6219	254	6	more	more	ADV
cana-6219	254	7	realistic	realistic	ADJ
cana-6219	254	8	and	and	CCONJ
cana-6219	254	9	flexible	flexible	ADJ
cana-6219	254	10	descriptions	description	NOUN
cana-6219	254	11	of	of	ADP
cana-6219	254	12	thermoelastic	thermoelastic	ADJ
cana-6219	254	13	responses	response	NOUN
cana-6219	254	14	,	,	PUNCT
cana-6219	254	15	especially	especially	ADV
cana-6219	254	16	in	in	ADP
cana-6219	254	17	materials	material	NOUN
cana-6219	254	18	exhibiting	exhibit	VERB
cana-6219	254	19	non	non	ADJ
cana-6219	254	20	-	-	ADJ
cana-6219	254	21	fourier	fourier	ADJ
cana-6219	254	22	heat	heat	NOUN
cana-6219	254	23	conduction	conduction	NOUN
cana-6219	254	24	or	or	CCONJ
cana-6219	254	25	memory	memory	NOUN
cana-6219	254	26	effects	effect	NOUN
cana-6219	254	27	.	.	PUNCT
cana-6219	255	1	•	•	NOUN
cana-6219	255	2	these	these	DET
cana-6219	255	3	insights	insight	NOUN
cana-6219	255	4	are	be	AUX
cana-6219	255	5	critical	critical	ADJ
cana-6219	255	6	for	for	ADP
cana-6219	255	7	advanced	advanced	ADJ
cana-6219	255	8	materials	material	NOUN
cana-6219	255	9	and	and	CCONJ
cana-6219	255	10	structures	structure	NOUN
cana-6219	255	11	used	use	VERB
cana-6219	255	12	in	in	ADP
cana-6219	255	13	aerospace	aerospace	NOUN
cana-6219	255	14	,	,	PUNCT
cana-6219	255	15	electronics	electronic	NOUN
cana-6219	255	16	,	,	PUNCT
cana-6219	255	17	and	and	CCONJ
cana-6219	255	18	thermal	thermal	ADJ
cana-6219	255	19	management	management	NOUN
cana-6219	255	20	systems	system	NOUN
cana-6219	255	21	.	.	PUNCT
cana-6219	256	1	acknowledgment	acknowledgment	NOUN
cana-6219	256	2	the	the	DET
cana-6219	256	3	authors	author	NOUN
cana-6219	256	4	are	be	AUX
cana-6219	256	5	grateful	grateful	ADJ
cana-6219	256	6	thanks	thank	NOUN
cana-6219	256	7	to	to	ADP
cana-6219	256	8	chhatrapati	chhatrapati	NOUN
cana-6219	256	9	shahu	shahu	NOUN
cana-6219	256	10	maharaj	maharaj	PROPN
cana-6219	256	11	research	research	PROPN
cana-6219	256	12	,	,	PUNCT
cana-6219	256	13	training	training	NOUN
cana-6219	256	14	and	and	CCONJ
cana-6219	256	15	human	human	PROPN
cana-6219	256	16	development	development	PROPN
cana-6219	256	17	institute	institute	PROPN
cana-6219	256	18	(	(	PUNCT
cana-6219	256	19	sarthi	sarthi	PROPN
cana-6219	256	20	)	)	PUNCT
cana-6219	256	21	for	for	ADP
cana-6219	256	22	awarding	award	VERB
cana-6219	256	23	the	the	DET
cana-6219	256	24	chhatrapati	chhatrapati	NOUN
cana-6219	256	25	shahu	shahu	NOUN
cana-6219	256	26	maharaj	maharaj	PROPN
cana-6219	256	27	national	national	PROPN
cana-6219	256	28	research	research	PROPN
cana-6219	256	29	fellowship	fellowship	NOUN
cana-6219	256	30	2022	2022	NUM
cana-6219	256	31	(	(	PUNCT
cana-6219	256	32	csmnrf	csmnrf	NOUN
cana-6219	256	33	2022	2022	NUM
cana-6219	256	34	)	)	PUNCT
cana-6219	256	35	.	.	PUNCT
cana-6219	257	1	refrences	refrence	VERB
cana-6219	258	1	[	[	X
cana-6219	258	2	1	1	NUM
cana-6219	258	3	]	]	X
cana-6219	258	4	de	de	X
cana-6219	258	5	chant	chant	X
cana-6219	258	6	,	,	PUNCT
cana-6219	258	7	l.	l.	PROPN
cana-6219	258	8	:	:	PUNCT
cana-6219	258	9	impulsive	impulsive	ADJ
cana-6219	258	10	displacement	displacement	NOUN
cana-6219	258	11	of	of	ADP
cana-6219	258	12	a	a	DET
cana-6219	258	13	quasi	quasi	ADJ
cana-6219	258	14	-	-	ADJ
cana-6219	258	15	linear	linear	ADJ
cana-6219	258	16	viscoelastic	viscoelastic	NOUN
cana-6219	258	17	material	material	NOUN
cana-6219	258	18	through	through	ADP
cana-6219	258	19	accurate	accurate	ADJ
cana-6219	258	20	numerical	numerical	ADJ
cana-6219	258	21	inversion	inversion	NOUN
cana-6219	258	22	of	of	ADP
cana-6219	258	23	the	the	DET
cana-6219	258	24	laplace	laplace	NOUN
cana-6219	258	25	transform	transform	NOUN
cana-6219	258	26	.	.	PUNCT
cana-6219	259	1	comput	comput	NOUN
cana-6219	259	2	.	.	PUNCT
cana-6219	260	1	math	math	PROPN
cana-6219	260	2	appl	appl	PROPN
cana-6219	260	3	.	.	PUNCT
cana-6219	261	1	43(8	43(8	NUM
cana-6219	261	2	-	-	SYM
cana-6219	261	3	9	9	NUM
cana-6219	261	4	)	)	PUNCT
cana-6219	261	5	,	,	PUNCT
cana-6219	261	6	pp	pp	ADP
cana-6219	261	7	.	.	PUNCT
cana-6219	262	1	1161	1161	NUM
cana-6219	262	2	-	-	SYM
cana-6219	262	3	1170	1170	NUM
cana-6219	262	4	,	,	PUNCT
cana-6219	262	5	(	(	PUNCT
cana-6219	262	6	2002	2002	NUM
cana-6219	262	7	)	)	PUNCT
cana-6219	262	8	.	.	PUNCT
cana-6219	263	1	[	[	X
cana-6219	263	2	2	2	NUM
cana-6219	263	3	]	]	PUNCT
cana-6219	263	4	musll	musll	PROPN
cana-6219	263	5	,	,	PUNCT
cana-6219	263	6	r.	r.	PROPN
cana-6219	263	7	:	:	PUNCT
cana-6219	263	8	equations	equation	NOUN
cana-6219	263	9	in	in	ADP
cana-6219	263	10	stresses	stress	NOUN
cana-6219	263	11	for	for	ADP
cana-6219	263	12	two	two	NUM
cana-6219	263	13	-	-	PUNCT
cana-6219	263	14	dimensional	dimensional	ADJ
cana-6219	263	15	dynamic	dynamic	ADJ
cana-6219	263	16	problems	problem	NOUN
cana-6219	263	17	of	of	ADP
cana-6219	263	18	thermoelasticity	thermoelasticity	NOUN
cana-6219	263	19	in	in	ADP
cana-6219	263	20	spherical	spherical	ADJ
cana-6219	263	21	coordinates	coordinate	NOUN
cana-6219	263	22	.	.	PUNCT
cana-6219	264	1	mater	mater	NOUN
cana-6219	264	2	.	.	PUNCT
cana-6219	265	1	sci	sci	PROPN
cana-6219	265	2	.	.	PROPN
cana-6219	266	1	39(1	39(1	NUM
cana-6219	266	2	)	)	PUNCT
cana-6219	266	3	,	,	PUNCT
cana-6219	267	1	pp	pp	ADP
cana-6219	267	2	.	.	PUNCT
cana-6219	268	1	48	48	NUM
cana-6219	268	2	-	-	SYM
cana-6219	268	3	53	53	NUM
cana-6219	268	4	,	,	PUNCT
cana-6219	268	5	(	(	PUNCT
cana-6219	268	6	2003	2003	NUM
cana-6219	268	7	)	)	PUNCT
cana-6219	268	8	.	.	PUNCT
cana-6219	269	1	[	[	X
cana-6219	269	2	3	3	NUM
cana-6219	269	3	]	]	X
cana-6219	269	4	duan	duan	PROPN
cana-6219	269	5	,	,	PUNCT
cana-6219	269	6	r.	r.	PROPN
cana-6219	269	7	,	,	PUNCT
cana-6219	269	8	liu	liu	PROPN
cana-6219	269	9	,	,	PUNCT
cana-6219	269	10	h.	h.	PROPN
cana-6219	269	11	,	,	PUNCT
cana-6219	269	12	zhao	zhao	PROPN
cana-6219	269	13	h.	h.	PROPN
cana-6219	269	14	:	:	PUNCT
cana-6219	269	15	nonlinear	nonlinear	ADJ
cana-6219	269	16	stability	stability	NOUN
cana-6219	269	17	of	of	ADP
cana-6219	269	18	rarefaction	rarefaction	NOUN
cana-6219	269	19	waves	wave	NOUN
cana-6219	269	20	for	for	ADP
cana-6219	269	21	the	the	DET
cana-6219	269	22	compressible	compressible	ADJ
cana-6219	269	23	navierstokes	navierstoke	NOUN
cana-6219	269	24	equations	equation	NOUN
cana-6219	269	25	with	with	ADP
cana-6219	269	26	large	large	ADJ
cana-6219	269	27	initial	initial	ADJ
cana-6219	269	28	perturbation	perturbation	NOUN
cana-6219	269	29	.	.	PUNCT
cana-6219	270	1	trans	trans	AUX
cana-6219	270	2	.	.	PROPN
cana-6219	270	3	am	be	AUX
cana-6219	270	4	.	.	PUNCT
cana-6219	271	1	math	math	NOUN
cana-6219	271	2	.	.	PUNCT
cana-6219	272	1	soc	soc	PROPN
cana-6219	272	2	.	.	PUNCT
cana-6219	273	1	361(1	361(1	NUM
cana-6219	273	2	)	)	PUNCT
cana-6219	273	3	,	,	PUNCT
cana-6219	273	4	pp	pp	ADP
cana-6219	273	5	.	.	PUNCT
cana-6219	274	1	453	453	NUM
cana-6219	274	2	-	-	SYM
cana-6219	274	3	493	493	NUM
cana-6219	274	4	,	,	PUNCT
cana-6219	274	5	(	(	PUNCT
cana-6219	274	6	2009	2009	NUM
cana-6219	274	7	)	)	PUNCT
cana-6219	274	8	.	.	PUNCT
cana-6219	275	1	[	[	X
cana-6219	275	2	4	4	NUM
cana-6219	275	3	]	]	X
cana-6219	275	4	youssef	youssef	PROPN
cana-6219	275	5	,	,	PUNCT
cana-6219	275	6	h.	h.	PROPN
cana-6219	275	7	:	:	PUNCT
cana-6219	275	8	a	a	DET
cana-6219	275	9	two	two	NUM
cana-6219	275	10	-	-	PUNCT
cana-6219	275	11	temperature	temperature	NOUN
cana-6219	275	12	generalized	generalize	VERB
cana-6219	275	13	thermoelastic	thermoelastic	ADJ
cana-6219	275	14	medium	medium	NOUN
cana-6219	275	15	subjected	subject	VERB
cana-6219	275	16	to	to	ADP
cana-6219	275	17	a	a	DET
cana-6219	275	18	moving	move	VERB
cana-6219	275	19	heat	heat	NOUN
cana-6219	275	20	source	source	NOUN
cana-6219	275	21	and	and	CCONJ
cana-6219	275	22	ramp	ramp	NOUN
cana-6219	275	23	-	-	PUNCT
cana-6219	275	24	type	type	NOUN
cana-6219	275	25	heating	heating	NOUN
cana-6219	275	26	.	.	PUNCT
cana-6219	276	1	a	a	DET
cana-6219	276	2	state	state	NOUN
cana-6219	276	3	-	-	PUNCT
cana-6219	276	4	space	space	NOUN
cana-6219	276	5	approach	approach	NOUN
cana-6219	276	6	.	.	PUNCT
cana-6219	277	1	j.	j.	PROPN
cana-6219	277	2	mech	mech	PROPN
cana-6219	277	3	mater	mater	PROPN
cana-6219	277	4	.	.	PUNCT
cana-6219	277	5	struct	struct	NOUN
cana-6219	277	6	.	.	PUNCT
cana-6219	278	1	4(9	4(9	NUM
cana-6219	278	2	)	)	PUNCT
cana-6219	279	1	pp	pp	ADP
cana-6219	279	2	.	.	PUNCT
cana-6219	280	1	1637	1637	NUM
cana-6219	280	2	-	-	SYM
cana-6219	280	3	1649	1649	NUM
cana-6219	280	4	,	,	PUNCT
cana-6219	280	5	(	(	PUNCT
cana-6219	280	6	2010	2010	NUM
cana-6219	280	7	)	)	PUNCT
cana-6219	280	8	.	.	PUNCT
cana-6219	281	1	[	[	X
cana-6219	281	2	5	5	NUM
cana-6219	281	3	]	]	X
cana-6219	281	4	ezzat	ezzat	ADJ
cana-6219	281	5	,	,	PUNCT
cana-6219	281	6	m.a	m.a	PROPN
cana-6219	281	7	.	.	PROPN
cana-6219	281	8	,	,	PUNCT
cana-6219	281	9	youssef	youssef	PROPN
cana-6219	281	10	,	,	PUNCT
cana-6219	281	11	h.m	h.m	PROPN
cana-6219	281	12	.	.	PROPN
cana-6219	281	13	:	:	PUNCT
cana-6219	281	14	three	three	NUM
cana-6219	281	15	-	-	PUNCT
cana-6219	281	16	dimensional	dimensional	ADJ
cana-6219	281	17	thermal	thermal	ADJ
cana-6219	281	18	shock	shock	NOUN
cana-6219	281	19	problem	problem	NOUN
cana-6219	281	20	of	of	ADP
cana-6219	281	21	generalized	generalized	ADJ
cana-6219	281	22	thermoelastic	thermoelastic	ADJ
cana-6219	281	23	half	half	ADJ
cana-6219	281	24	-	-	PUNCT
cana-6219	281	25	space	space	NOUN
cana-6219	281	26	.	.	PUNCT
cana-6219	282	1	appl	appl	PROPN
cana-6219	282	2	.	.	PROPN
cana-6219	282	3	math	math	PROPN
cana-6219	282	4	.	.	PUNCT
cana-6219	283	1	model	model	PROPN
cana-6219	283	2	34(11	34(11	NUM
cana-6219	283	3	)	)	PUNCT
cana-6219	283	4	,	,	PUNCT
cana-6219	283	5	pp	pp	ADJ
cana-6219	283	6	.	.	PUNCT
cana-6219	284	1	3608	3608	NUM
cana-6219	284	2	-	-	SYM
cana-6219	284	3	3622	3622	NUM
cana-6219	284	4	,	,	PUNCT
cana-6219	284	5	(	(	PUNCT
cana-6219	284	6	2010	2010	NUM
cana-6219	284	7	)	)	PUNCT
cana-6219	284	8	.	.	PUNCT
cana-6219	285	1	[	[	X
cana-6219	285	2	6	6	NUM
cana-6219	285	3	]	]	X
cana-6219	285	4	ezzat	ezzat	ADJ
cana-6219	285	5	m.	m.	NOUN
cana-6219	285	6	a.	a.	PROPN
cana-6219	285	7	,	,	PUNCT
cana-6219	285	8	youssef	youssef	PROPN
cana-6219	285	9	,	,	PUNCT
cana-6219	285	10	h.	h.	PROPN
cana-6219	285	11	a.	a.	PROPN
cana-6219	285	12	:	:	PUNCT
cana-6219	285	13	two	two	NUM
cana-6219	285	14	-	-	PUNCT
cana-6219	285	15	temperature	temperature	NOUN
cana-6219	285	16	theory	theory	NOUN
cana-6219	285	17	in	in	ADP
cana-6219	285	18	three	three	NUM
cana-6219	285	19	-	-	PUNCT
cana-6219	285	20	dimensional	dimensional	ADJ
cana-6219	285	21	problem	problem	NOUN
cana-6219	285	22	for	for	ADP
cana-6219	285	23	thermoelastic	thermoelastic	ADJ
cana-6219	285	24	half	half	ADJ
cana-6219	285	25	space	space	NOUN
cana-6219	285	26	subjected	subject	VERB
cana-6219	285	27	to	to	ADP
cana-6219	285	28	ramp	ramp	NOUN
cana-6219	285	29	type	type	NOUN
cana-6219	285	30	heating	heating	NOUN
cana-6219	285	31	.	.	PUNCT
cana-6219	286	1	mech	mech	PROPN
cana-6219	286	2	.	.	PUNCT
cana-6219	287	1	mat	mat	NOUN
cana-6219	287	2	struct	struct	NOUN
cana-6219	287	3	.	.	PUNCT
cana-6219	288	1	21(4	21(4	NUM
cana-6219	288	2	)	)	PUNCT
cana-6219	288	3	,	,	PUNCT
cana-6219	288	4	pp	pp	ADP
cana-6219	288	5	.	.	PUNCT
cana-6219	289	1	293	293	NUM
cana-6219	289	2	-	-	SYM
cana-6219	289	3	304	304	NUM
cana-6219	289	4	,	,	PUNCT
cana-6219	289	5	(	(	PUNCT
cana-6219	289	6	2014	2014	NUM
cana-6219	289	7	)	)	PUNCT
cana-6219	289	8	.	.	PUNCT
cana-6219	290	1	[	[	X
cana-6219	290	2	7	7	NUM
cana-6219	290	3	]	]	SYM
cana-6219	290	4	abbas	abbas	PROPN
cana-6219	290	5	,	,	PUNCT
cana-6219	290	6	i.	i.	PROPN
cana-6219	290	7	a.	a.	PROPN
cana-6219	290	8	,	,	PUNCT
cana-6219	290	9	youssef	youssef	PROPN
cana-6219	290	10	,	,	PUNCT
cana-6219	290	11	h.	h.	PROPN
cana-6219	290	12	m.	m.	PROPN
cana-6219	290	13	:	:	PUNCT
cana-6219	290	14	two	two	NUM
cana-6219	290	15	-	-	PUNCT
cana-6219	290	16	dimensional	dimensional	ADJ
cana-6219	290	17	fractional	fractional	ADJ
cana-6219	290	18	order	order	NOUN
cana-6219	290	19	generalized	generalize	VERB
cana-6219	290	20	thermoelastic	thermoelastic	ADJ
cana-6219	290	21	porous	porous	ADJ
cana-6219	290	22	material	material	NOUN
cana-6219	290	23	.	.	PUNCT
cana-6219	291	1	lat	lat	PROPN
cana-6219	291	2	am	be	AUX
cana-6219	291	3	.	.	PUNCT
cana-6219	292	1	j.	j.	PROPN
cana-6219	292	2	solids	solids	PROPN
cana-6219	292	3	struct	struct	NOUN
cana-6219	292	4	.	.	PUNCT
cana-6219	293	1	12(7	12(7	NUM
cana-6219	293	2	)	)	PUNCT
cana-6219	293	3	,	,	PUNCT
cana-6219	294	1	pp	pp	ADP
cana-6219	294	2	.	.	PUNCT
cana-6219	295	1	14	14	NUM
cana-6219	295	2	-	-	SYM
cana-6219	295	3	31	31	NUM
cana-6219	295	4	,	,	PUNCT
cana-6219	295	5	(	(	PUNCT
cana-6219	295	6	2015	2015	NUM
cana-6219	295	7	)	)	PUNCT
cana-6219	295	8	.	.	PUNCT
cana-6219	296	1	[	[	X
cana-6219	296	2	8	8	NUM
cana-6219	296	3	]	]	X
cana-6219	296	4	parnell	parnell	PROPN
cana-6219	296	5	,	,	PUNCT
cana-6219	296	6	w.	w.	PROPN
cana-6219	296	7	j.	j.	PROPN
cana-6219	296	8	,	,	PUNCT
cana-6219	296	9	nguyen	nguyen	PROPN
cana-6219	296	10	,	,	PUNCT
cana-6219	296	11	v.	v.	PROPN
cana-6219	296	12	h.	h.	PROPN
cana-6219	296	13	,	,	PUNCT
cana-6219	296	14	assier	assier	PROPN
cana-6219	296	15	,	,	PUNCT
cana-6219	296	16	r.	r.	PROPN
cana-6219	296	17	naili	naili	PROPN
cana-6219	296	18	,	,	PUNCT
cana-6219	296	19	s.	s.	PROPN
cana-6219	296	20	,	,	PUNCT
cana-6219	296	21	abrahams	abrahams	PROPN
cana-6219	296	22	,	,	PUNCT
cana-6219	296	23	i.	i.	PROPN
cana-6219	296	24	d.	d.	PROPN
cana-6219	296	25	:	:	PUNCT
cana-6219	296	26	transient	transient	VERB
cana-6219	296	27	thermal	thermal	ADJ
cana-6219	296	28	mixed	mixed	ADJ
cana-6219	296	29	boundary	boundary	ADJ
cana-6219	296	30	value	value	NOUN
cana-6219	296	31	problems	problem	NOUN
cana-6219	296	32	in	in	ADP
cana-6219	296	33	the	the	DET
cana-6219	296	34	half	half	ADJ
cana-6219	296	35	-	-	PUNCT
cana-6219	296	36	space	space	NOUN
cana-6219	296	37	.	.	PUNCT
cana-6219	297	1	siam	siam	PROPN
cana-6219	297	2	j.	j.	PROPN
cana-6219	297	3	appl	appl	PROPN
cana-6219	297	4	.	.	PROPN
cana-6219	297	5	math	math	PROPN
cana-6219	297	6	,	,	PUNCT
cana-6219	297	7	76(3	76(3	PROPN
cana-6219	297	8	)	)	PUNCT
cana-6219	297	9	,	,	PUNCT
cana-6219	297	10	pp	pp	PROPN
cana-6219	297	11	.	.	PUNCT
cana-6219	298	1	845	845	NUM
cana-6219	298	2	-	-	NUM
cana-6219	298	3	866	866	NUM
cana-6219	298	4	,	,	PUNCT
cana-6219	298	5	(	(	PUNCT
cana-6219	298	6	2016	2016	NUM
cana-6219	298	7	)	)	PUNCT
cana-6219	298	8	.	.	PUNCT
cana-6219	299	1	[	[	X
cana-6219	299	2	9	9	NUM
cana-6219	299	3	]	]	SYM
cana-6219	299	4	tahouneh	tahouneh	NOUN
cana-6219	299	5	,	,	PUNCT
cana-6219	299	6	v.	v.	ADV
cana-6219	299	7	,	,	PUNCT
cana-6219	299	8	naei	naei	PROPN
cana-6219	299	9	,	,	PUNCT
cana-6219	299	10	m.	m.	NOUN
cana-6219	299	11	h.	h.	PROPN
cana-6219	299	12	:	:	PUNCT
cana-6219	299	13	the	the	DET
cana-6219	299	14	effect	effect	NOUN
cana-6219	299	15	of	of	ADP
cana-6219	299	16	multi	multi	ADJ
cana-6219	299	17	-	-	ADJ
cana-6219	299	18	directional	directional	ADJ
cana-6219	299	19	nanocomposite	nanocomposite	NOUN
cana-6219	299	20	materials	material	NOUN
cana-6219	299	21	on	on	ADP
cana-6219	299	22	the	the	DET
cana-6219	299	23	vibrational	vibrational	ADJ
cana-6219	299	24	response	response	NOUN
cana-6219	299	25	of	of	ADP
cana-6219	299	26	thick	thick	ADJ
cana-6219	299	27	shell	shell	NOUN
cana-6219	299	28	panels	panel	NOUN
cana-6219	299	29	with	with	ADP
cana-6219	299	30	finite	finite	ADJ
cana-6219	299	31	length	length	NOUN
cana-6219	299	32	and	and	CCONJ
cana-6219	299	33	rested	rest	VERB
cana-6219	299	34	on	on	ADP
cana-6219	299	35	two	two	NUM
cana-6219	299	36	-	-	PUNCT
cana-6219	299	37	parameter	parameter	NOUN
cana-6219	299	38	elastic	elastic	ADJ
cana-6219	299	39	foundations	foundation	NOUN
cana-6219	299	40	.	.	PUNCT
cana-6219	300	1	int	int	NOUN
cana-6219	300	2	.	.	PUNCT
cana-6219	301	1	j.	j.	PROPN
cana-6219	301	2	adv	adv	PROPN
cana-6219	301	3	.	.	PROPN
cana-6219	301	4	struct	struct	NOUN
cana-6219	301	5	.	.	PUNCT
cana-6219	302	1	eng	eng	PROPN
cana-6219	302	2	.	.	PUNCT
cana-6219	303	1	8(1	8(1	NOUN
cana-6219	303	2	)	)	PUNCT
cana-6219	303	3	,	,	PUNCT
cana-6219	303	4	pp	pp	ADJ
cana-6219	303	5	.	.	PUNCT
cana-6219	304	1	11	11	NUM
cana-6219	304	2	-	-	SYM
cana-6219	304	3	28	28	NUM
cana-6219	304	4	,	,	PUNCT
cana-6219	304	5	(	(	PUNCT
cana-6219	304	6	2016	2016	NUM
cana-6219	304	7	)	)	PUNCT
cana-6219	304	8	.	.	PUNCT
cana-6219	305	1	[	[	X
cana-6219	305	2	10	10	NUM
cana-6219	305	3	]	]	X
cana-6219	305	4	ezzat	ezzat	ADJ
cana-6219	305	5	m.	m.	NOUN
cana-6219	305	6	a.	a.	PROPN
cana-6219	305	7	,	,	PUNCT
cana-6219	305	8	youssef	youssef	PROPN
cana-6219	305	9	,	,	PUNCT
cana-6219	305	10	h.	h.	PROPN
cana-6219	305	11	a.	a.	PROPN
cana-6219	305	12	:	:	PUNCT
cana-6219	305	13	three	three	NUM
cana-6219	305	14	-	-	PUNCT
cana-6219	305	15	dimensional	dimensional	ADJ
cana-6219	305	16	thermos	thermos	ADJ
cana-6219	305	17	-	-	PUNCT
cana-6219	305	18	viscoelastic	viscoelastic	ADJ
cana-6219	305	19	material	material	NOUN
cana-6219	305	20	.	.	PUNCT
cana-6219	306	1	mech	mech	PROPN
cana-6219	306	2	.	.	PUNCT
cana-6219	307	1	adv	adv	PROPN
cana-6219	307	2	.	.	PUNCT
cana-6219	307	3	mat	mat	PROPN
cana-6219	307	4	.	.	NOUN
cana-6219	307	5	struct	struct	NOUN
cana-6219	307	6	.	.	PUNCT
cana-6219	308	1	23(1	23(1	X
cana-6219	308	2	)	)	PUNCT
cana-6219	309	1	,	,	PUNCT
cana-6219	309	2	pp	pp	PROPN
cana-6219	309	3	.	.	PUNCT
cana-6219	310	1	108	108	NUM
cana-6219	310	2	-	-	SYM
cana-6219	310	3	116	116	NUM
cana-6219	310	4	,	,	PUNCT
cana-6219	310	5	(	(	PUNCT
cana-6219	310	6	2016	2016	NUM
cana-6219	310	7	)	)	PUNCT
cana-6219	310	8	.	.	PUNCT
cana-6219	311	1	[	[	X
cana-6219	311	2	11	11	NUM
cana-6219	311	3	]	]	X
cana-6219	311	4	marin	marin	NOUN
cana-6219	311	5	,	,	PUNCT
cana-6219	311	6	m.	m.	NOUN
cana-6219	311	7	:	:	PUNCT
cana-6219	311	8	an	an	DET
cana-6219	311	9	approach	approach	NOUN
cana-6219	311	10	of	of	ADP
cana-6219	311	11	a	a	DET
cana-6219	311	12	heat	heat	NOUN
cana-6219	311	13	flux	flux	NOUN
cana-6219	311	14	dependent	dependent	ADJ
cana-6219	311	15	theory	theory	NOUN
cana-6219	311	16	for	for	ADP
cana-6219	311	17	micropolar	micropolar	ADJ
cana-6219	311	18	porous	porous	ADJ
cana-6219	311	19	media	medium	NOUN
cana-6219	311	20	.	.	PUNCT
cana-6219	312	1	meccanica	meccanica	PROPN
cana-6219	312	2	51(5	51(5	NUM
cana-6219	312	3	)	)	PUNCT
cana-6219	312	4	,	,	PUNCT
cana-6219	312	5	pp	pp	ADP
cana-6219	312	6	.	.	PUNCT
cana-6219	312	7	1127	1127	NUM
cana-6219	312	8	-	-	SYM
cana-6219	312	9	1133	1133	NUM
cana-6219	312	10	,	,	PUNCT
cana-6219	312	11	(	(	PUNCT
cana-6219	312	12	2016	2016	NUM
cana-6219	312	13	)	)	PUNCT
cana-6219	312	14	.	.	PUNCT
cana-6219	313	1	communications	communication	NOUN
cana-6219	313	2	on	on	ADP
cana-6219	313	3	applied	apply	VERB
cana-6219	313	4	nonlinear	nonlinear	ADJ
cana-6219	313	5	analysis	analysis	NOUN
cana-6219	313	6	issn	issn	NOUN
cana-6219	313	7	:	:	PUNCT
cana-6219	313	8	1074	1074	NUM
cana-6219	313	9	-	-	PUNCT
cana-6219	313	10	133x	133x	NUM
cana-6219	313	11	vol	vol	VERB
cana-6219	313	12	32	32	NUM
cana-6219	313	13	no	no	NOUN
cana-6219	313	14	.	.	PUNCT
cana-6219	314	1	10s	10	NOUN
cana-6219	314	2	(	(	PUNCT
cana-6219	314	3	2025	2025	NUM
cana-6219	314	4	)	)	PUNCT
cana-6219	314	5	3543	3543	NUM
cana-6219	314	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	315	1	[	[	X
cana-6219	315	2	12	12	NUM
cana-6219	315	3	]	]	X
cana-6219	315	4	youssef	youssef	PROPN
cana-6219	315	5	,	,	PUNCT
cana-6219	315	6	h.	h.	PROPN
cana-6219	315	7	m.	m.	PROPN
cana-6219	315	8	,	,	PUNCT
cana-6219	315	9	ai	ai	NOUN
cana-6219	315	10	-	-	PUNCT
cana-6219	315	11	lehaibi	lehaibi	NOUN
cana-6219	315	12	,	,	PUNCT
cana-6219	315	13	e.	e.	PROPN
cana-6219	315	14	a.	a.	PROPN
cana-6219	315	15	:	:	PUNCT
cana-6219	315	16	three	three	NUM
cana-6219	315	17	-	-	PUNCT
cana-6219	315	18	dimensional	dimensional	ADJ
cana-6219	315	19	generalized	generalize	VERB
cana-6219	315	20	thermoelastic	thermoelastic	ADJ
cana-6219	315	21	diffusion	diffusion	NOUN
cana-6219	315	22	and	and	CCONJ
cana-6219	315	23	application	application	NOUN
cana-6219	315	24	for	for	ADP
cana-6219	315	25	a	a	DET
cana-6219	315	26	thermoelastic	thermoelastic	ADJ
cana-6219	315	27	half	half	ADJ
cana-6219	315	28	-	-	PUNCT
cana-6219	315	29	space	space	NOUN
cana-6219	315	30	subjected	subject	VERB
cana-6219	315	31	to	to	ADP
cana-6219	315	32	rectangular	rectangular	ADJ
cana-6219	315	33	thermal	thermal	ADJ
cana-6219	315	34	pulse	pulse	NOUN
cana-6219	315	35	.	.	PUNCT
cana-6219	316	1	j.	j.	PROPN
cana-6219	316	2	therm	therm	PROPN
cana-6219	316	3	.	.	PUNCT
cana-6219	316	4	stresses	stress	VERB
cana-6219	316	5	41(8	41(8	PROPN
cana-6219	316	6	)	)	PUNCT
cana-6219	316	7	,	,	PUNCT
cana-6219	316	8	pp	pp	PROPN
cana-6219	316	9	.	.	PUNCT
cana-6219	317	1	1008	1008	NUM
cana-6219	317	2	-	-	SYM
cana-6219	317	3	1021	1021	NUM
cana-6219	317	4	,	,	PUNCT
cana-6219	317	5	(	(	PUNCT
cana-6219	317	6	2018	2018	NUM
cana-6219	317	7	)	)	PUNCT
cana-6219	317	8	.	.	PUNCT
cana-6219	318	1	[	[	X
cana-6219	318	2	13	13	NUM
cana-6219	318	3	]	]	PUNCT
cana-6219	318	4	gaikwad	gaikwad	PROPN
cana-6219	318	5	k.	k.	PROPN
cana-6219	318	6	r.	r.	PROPN
cana-6219	318	7	&	&	CCONJ
cana-6219	318	8	s.	s.	PROPN
cana-6219	318	9	g.	g.	PROPN
cana-6219	318	10	khavale	khavale	PROPN
cana-6219	318	11	.	.	PUNCT
cana-6219	319	1	:	:	PUNCT
cana-6219	319	2	time	time	NOUN
cana-6219	319	3	fractional	fractional	ADJ
cana-6219	319	4	heat	heat	NOUN
cana-6219	319	5	conduction	conduction	NOUN
cana-6219	319	6	problem	problem	NOUN
cana-6219	319	7	in	in	ADP
cana-6219	319	8	a	a	DET
cana-6219	319	9	thin	thin	ADJ
cana-6219	319	10	hollow	hollow	ADJ
cana-6219	319	11	circular	circular	ADJ
cana-6219	319	12	disk	disk	NOUN
cana-6219	319	13	and	and	CCONJ
cana-6219	319	14	its	its	PRON
cana-6219	319	15	thermal	thermal	ADJ
cana-6219	319	16	deflection	deflection	NOUN
cana-6219	319	17	,	,	PUNCT
cana-6219	319	18	easy	easy	ADJ
cana-6219	319	19	chair	chair	NOUN
cana-6219	319	20	preprint	preprint	VERB
cana-6219	319	21	no	no	INTJ
cana-6219	319	22	.	.	PROPN
cana-6219	319	23	1672	1672	NUM
cana-6219	319	24	,	,	PUNCT
cana-6219	319	25	pp.1	pp.1	NOUN
cana-6219	319	26	-	-	PUNCT
cana-6219	319	27	11	11	NUM
cana-6219	319	28	,	,	PUNCT
cana-6219	319	29	(	(	PUNCT
cana-6219	319	30	2019	2019	NUM
cana-6219	319	31	)	)	PUNCT
cana-6219	319	32	.	.	PUNCT
cana-6219	320	1	[	[	X
cana-6219	320	2	14	14	NUM
cana-6219	320	3	]	]	PUNCT
cana-6219	320	4	khavale	khavale	PROPN
cana-6219	320	5	s.	s.	PROPN
cana-6219	320	6	g.	g.	PROPN
cana-6219	320	7	&	&	CCONJ
cana-6219	320	8	k.	k.	PROPN
cana-6219	320	9	r.	r.	PROPN
cana-6219	320	10	gaikwad	gaikwad	PROPN
cana-6219	320	11	.	.	PUNCT
cana-6219	320	12	:	:	PUNCT
cana-6219	321	1	generalized	generalize	VERB
cana-6219	321	2	theory	theory	NOUN
cana-6219	321	3	of	of	ADP
cana-6219	321	4	magneto	magneto	ADJ
cana-6219	321	5	-	-	PUNCT
cana-6219	321	6	thermoviscoelastic	thermoviscoelastic	ADJ
cana-6219	321	7	spherical	spherical	ADJ
cana-6219	321	8	cavity	cavity	NOUN
cana-6219	321	9	problem	problem	NOUN
cana-6219	321	10	under	under	ADP
cana-6219	321	11	fractional	fractional	ADJ
cana-6219	321	12	order	order	NOUN
cana-6219	321	13	derivative	derivative	NOUN
cana-6219	321	14	:	:	PUNCT
cana-6219	321	15	state	state	NOUN
cana-6219	321	16	space	space	NOUN
cana-6219	321	17	,	,	PUNCT
cana-6219	321	18	approach	approach	NOUN
cana-6219	321	19	,	,	PUNCT
cana-6219	321	20	advances	advance	NOUN
cana-6219	321	21	in	in	ADP
cana-6219	321	22	mathematics	mathematic	NOUN
cana-6219	321	23	:	:	PUNCT
cana-6219	321	24	scientific	scientific	ADJ
cana-6219	321	25	journal	journal	NOUN
cana-6219	321	26	,	,	PUNCT
cana-6219	321	27	vol	vol	NOUN
cana-6219	321	28	.	.	PROPN
cana-6219	321	29	9	9	NUM
cana-6219	321	30	(	(	PUNCT
cana-6219	321	31	11	11	NUM
cana-6219	321	32	)	)	PUNCT
cana-6219	321	33	,	,	PUNCT
cana-6219	321	34	pp	pp	ADP
cana-6219	321	35	.	.	PUNCT
cana-6219	321	36	9769	9769	NUM
cana-6219	321	37	-9780	-9780	NOUN
cana-6219	321	38	,	,	PUNCT
cana-6219	321	39	(	(	PUNCT
cana-6219	321	40	2020	2020	NUM
cana-6219	321	41	)	)	PUNCT
cana-6219	321	42	.	.	PUNCT
cana-6219	322	1	[	[	X
cana-6219	322	2	15	15	NUM
cana-6219	322	3	]	]	X
cana-6219	322	4	hamdy	hamdy	PROPN
cana-6219	322	5	m.	m.	PROPN
cana-6219	322	6	youssef	youssef	PROPN
cana-6219	322	7	&	&	CCONJ
cana-6219	322	8	eman	eman	PROPN
cana-6219	322	9	a.n	a.n	PROPN
cana-6219	322	10	.	.	PROPN
cana-6219	322	11	al	al	PROPN
cana-6219	322	12	-	-	PUNCT
cana-6219	322	13	lehaibi	lehaibi	NOUN
cana-6219	322	14	.	.	PUNCT
cana-6219	323	1	:	:	PUNCT
cana-6219	323	2	the	the	DET
cana-6219	323	3	boundary	boundary	ADJ
cana-6219	323	4	value	value	NOUN
cana-6219	323	5	problem	problem	NOUN
cana-6219	323	6	of	of	ADP
cana-6219	323	7	a	a	DET
cana-6219	323	8	three	three	NUM
cana-6219	323	9	-	-	PUNCT
cana-6219	323	10	dimensional	dimensional	ADJ
cana-6219	323	11	generalized	generalized	ADJ
cana-6219	323	12	thermoelastic	thermoelastic	ADJ
cana-6219	323	13	half	half	ADJ
cana-6219	323	14	-	-	PUNCT
cana-6219	323	15	space	space	NOUN
cana-6219	323	16	subjected	subject	VERB
cana-6219	323	17	to	to	ADP
cana-6219	323	18	moving	move	VERB
cana-6219	323	19	rectangular	rectangular	ADJ
cana-6219	323	20	heat	heat	NOUN
cana-6219	323	21	source	source	NOUN
cana-6219	323	22	,	,	PUNCT
cana-6219	323	23	boundary	boundary	ADJ
cana-6219	323	24	value	value	NOUN
cana-6219	323	25	problems	problem	NOUN
cana-6219	323	26	,	,	PUNCT
cana-6219	323	27	pp	pp	ADV
cana-6219	323	28	.	.	PUNCT
cana-6219	324	1	1	1	NUM
cana-6219	324	2	-	-	SYM
cana-6219	324	3	15	15	NUM
cana-6219	324	4	,	,	PUNCT
cana-6219	324	5	(	(	PUNCT
cana-6219	324	6	2019	2019	NUM
cana-6219	324	7	)	)	PUNCT
cana-6219	324	8	.	.	PUNCT
cana-6219	325	1	[	[	X
cana-6219	325	2	16	16	NUM
cana-6219	325	3	]	]	PUNCT
cana-6219	325	4	gaikwad	gaikwad	PROPN
cana-6219	325	5	k.	k.	PROPN
cana-6219	325	6	r.	r.	PROPN
cana-6219	325	7	&	&	CCONJ
cana-6219	325	8	s.	s.	PROPN
cana-6219	325	9	g.	g.	PROPN
cana-6219	325	10	khavale	khavale	PROPN
cana-6219	325	11	.	.	PUNCT
cana-6219	325	12	:	:	PUNCT
cana-6219	326	1	time	time	NOUN
cana-6219	326	2	fractional	fractional	PROPN
cana-6219	326	3	2d	2d	PROPN
cana-6219	326	4	thermoelastic	thermoelastic	ADJ
cana-6219	326	5	problem	problem	NOUN
cana-6219	326	6	of	of	ADP
cana-6219	326	7	thin	thin	ADJ
cana-6219	326	8	hollow	hollow	ADJ
cana-6219	326	9	circular	circular	ADJ
cana-6219	326	10	disk	disk	NOUN
cana-6219	326	11	associated	associate	VERB
cana-6219	326	12	thermal	thermal	ADJ
cana-6219	326	13	stresses	stress	NOUN
cana-6219	326	14	,	,	PUNCT
cana-6219	326	15	bulletin	bulletin	NOUN
cana-6219	326	16	of	of	ADP
cana-6219	326	17	marathwada	marathwada	PROPN
cana-6219	326	18	mathematical	mathematical	PROPN
cana-6219	326	19	society	society	NOUN
cana-6219	326	20	,	,	PUNCT
cana-6219	326	21	vol	vol	NOUN
cana-6219	326	22	.	.	PUNCT
cana-6219	326	23	21(1&2	21(1&2	NUM
cana-6219	326	24	)	)	PUNCT
cana-6219	326	25	,	,	PUNCT
cana-6219	326	26	june	june	PROPN
cana-6219	326	27	&	&	CCONJ
cana-6219	326	28	dec	dec	PROPN
cana-6219	326	29	,	,	PUNCT
cana-6219	326	30	pp	pp	PROPN
cana-6219	326	31	.	.	PUNCT
cana-6219	327	1	37	37	NUM
cana-6219	327	2	-	-	SYM
cana-6219	327	3	47	47	NUM
cana-6219	327	4	,	,	PUNCT
cana-6219	327	5	(	(	PUNCT
cana-6219	327	6	2020	2020	NUM
cana-6219	327	7	)	)	PUNCT
cana-6219	327	8	.	.	PUNCT
cana-6219	328	1	[	[	X
cana-6219	328	2	17	17	NUM
cana-6219	328	3	]	]	PUNCT
cana-6219	328	4	gaikwad	gaikwad	PROPN
cana-6219	328	5	k.	k.	PROPN
cana-6219	328	6	r.	r.	PROPN
cana-6219	328	7	,	,	PUNCT
cana-6219	328	8	y.	y.	PROPN
cana-6219	328	9	u.	u.	PROPN
cana-6219	328	10	naner	naner	NOUN
cana-6219	328	11	,	,	PUNCT
cana-6219	328	12	s.	s.	PROPN
cana-6219	328	13	g.	g.	PROPN
cana-6219	328	14	khavale	khavale	PROPN
cana-6219	328	15	.	.	PUNCT
cana-6219	328	16	:	:	PUNCT
cana-6219	328	17	time	time	NOUN
cana-6219	328	18	fractional	fractional	ADJ
cana-6219	328	19	thermoelastic	thermoelastic	ADJ
cana-6219	328	20	stress	stress	NOUN
cana-6219	328	21	analysis	analysis	NOUN
cana-6219	328	22	of	of	ADP
cana-6219	328	23	a	a	DET
cana-6219	328	24	thin	thin	ADJ
cana-6219	328	25	rectangular	rectangular	ADJ
cana-6219	328	26	plate	plate	NOUN
cana-6219	328	27	,	,	PUNCT
cana-6219	328	28	novyi	novyi	PROPN
cana-6219	328	29	mir	mir	PROPN
cana-6219	328	30	research	research	PROPN
cana-6219	328	31	journal	journal	PROPN
cana-6219	328	32	,	,	PUNCT
cana-6219	328	33	vol	vol	NOUN
cana-6219	328	34	.	.	PUNCT
cana-6219	328	35	6(1	6(1	NUM
cana-6219	328	36	)	)	PUNCT
cana-6219	328	37	,	,	PUNCT
cana-6219	329	1	pp	pp	ADP
cana-6219	329	2	.	.	PUNCT
cana-6219	330	1	42	42	NUM
cana-6219	330	2	-	-	SYM
cana-6219	330	3	56	56	NUM
cana-6219	330	4	,	,	PUNCT
cana-6219	330	5	(	(	PUNCT
cana-6219	330	6	2021	2021	NUM
cana-6219	330	7	)	)	PUNCT
cana-6219	330	8	.	.	PUNCT
cana-6219	331	1	[	[	X
cana-6219	331	2	18	18	NUM
cana-6219	331	3	]	]	PUNCT
cana-6219	331	4	khavale	khavale	NOUN
cana-6219	331	5	s.	s.	PROPN
cana-6219	331	6	g.	g.	PROPN
cana-6219	331	7	&	&	CCONJ
cana-6219	331	8	k.	k.	PROPN
cana-6219	331	9	r.	r.	PROPN
cana-6219	331	10	gaikwad	gaikwad	PROPN
cana-6219	331	11	.	.	PUNCT
cana-6219	331	12	:	:	PUNCT
cana-6219	331	13	fractional	fractional	ADJ
cana-6219	331	14	order	order	NOUN
cana-6219	331	15	thermoelastic	thermoelastic	ADJ
cana-6219	331	16	problem	problem	NOUN
cana-6219	331	17	of	of	ADP
cana-6219	331	18	thin	thin	ADJ
cana-6219	331	19	hollow	hollow	ADJ
cana-6219	331	20	circular	circular	ADJ
cana-6219	331	21	disk	disk	NOUN
cana-6219	331	22	and	and	CCONJ
cana-6219	331	23	its	its	PRON
cana-6219	331	24	thermal	thermal	ADJ
cana-6219	331	25	stresses	stress	NOUN
cana-6219	331	26	under	under	ADP
cana-6219	331	27	axi	axi	NOUN
cana-6219	331	28	-	-	PUNCT
cana-6219	331	29	symmetric	symmetric	ADJ
cana-6219	331	30	heat	heat	NOUN
cana-6219	331	31	supply	supply	NOUN
cana-6219	331	32	,	,	PUNCT
cana-6219	331	33	design	design	NOUN
cana-6219	331	34	engineering	engineering	NOUN
cana-6219	331	35	(	(	PUNCT
cana-6219	331	36	toronto	toronto	PROPN
cana-6219	331	37	)	)	PUNCT
cana-6219	331	38	,	,	PUNCT
cana-6219	331	39	vol	vol	NOUN
cana-6219	331	40	.	.	PUNCT
cana-6219	332	1	2021(9	2021(9	NOUN
cana-6219	332	2	)	)	PUNCT
cana-6219	332	3	,	,	PUNCT
cana-6219	332	4	pp	pp	ADP
cana-6219	332	5	.	.	PUNCT
cana-6219	333	1	13851	13851	NUM
cana-6219	333	2	-	-	SYM
cana-6219	333	3	13862	13862	NUM
cana-6219	333	4	,	,	PUNCT
cana-6219	333	5	(	(	PUNCT
cana-6219	333	6	2021	2021	NUM
cana-6219	333	7	)	)	PUNCT
cana-6219	333	8	.	.	PUNCT
cana-6219	334	1	[	[	X
cana-6219	334	2	19	19	NUM
cana-6219	334	3	]	]	PUNCT
cana-6219	334	4	khavale	khavale	NOUN
cana-6219	334	5	s.	s.	PROPN
cana-6219	334	6	g.	g.	PROPN
cana-6219	334	7	&	&	CCONJ
cana-6219	334	8	k.	k.	PROPN
cana-6219	334	9	r.	r.	PROPN
cana-6219	334	10	gaikwad	gaikwad	PROPN
cana-6219	334	11	.	.	PUNCT
cana-6219	334	12	:	:	PUNCT
cana-6219	335	1	2d	2d	NUM
cana-6219	335	2	problem	problem	NOUN
cana-6219	335	3	for	for	ADP
cana-6219	335	4	a	a	DET
cana-6219	335	5	sphere	sphere	NOUN
cana-6219	335	6	in	in	ADP
cana-6219	335	7	the	the	DET
cana-6219	335	8	fractional	fractional	ADJ
cana-6219	335	9	order	order	NOUN
cana-6219	335	10	theory	theory	NOUN
cana-6219	335	11	thermoelasticity	thermoelasticity	NOUN
cana-6219	335	12	to	to	PART
cana-6219	335	13	axisymmetric	axisymmetric	VERB
cana-6219	335	14	temperature	temperature	NOUN
cana-6219	335	15	distribution	distribution	NOUN
cana-6219	335	16	,	,	PUNCT
cana-6219	335	17	advances	advance	NOUN
cana-6219	335	18	in	in	ADP
cana-6219	335	19	mathematics	mathematic	NOUN
cana-6219	335	20	:	:	PUNCT
cana-6219	335	21	scientific	scientific	ADJ
cana-6219	335	22	journal	journal	NOUN
cana-6219	335	23	,	,	PUNCT
cana-6219	335	24	vol	vol	NOUN
cana-6219	335	25	.	.	PUNCT
cana-6219	335	26	11(1	11(1	NUM
cana-6219	335	27	)	)	PUNCT
cana-6219	335	28	,	,	PUNCT
cana-6219	335	29	pp	pp	PROPN
cana-6219	335	30	.	.	PUNCT
cana-6219	336	1	1–15	1–15	NUM
cana-6219	336	2	,	,	PUNCT
cana-6219	336	3	(	(	PUNCT
cana-6219	336	4	2022	2022	NUM
cana-6219	336	5	)	)	PUNCT
cana-6219	336	6	.	.	PUNCT
cana-6219	337	1	[	[	X
cana-6219	337	2	20	20	NUM
cana-6219	337	3	]	]	PUNCT
cana-6219	337	4	gaikwad	gaikwad	PROPN
cana-6219	337	5	k.	k.	PROPN
cana-6219	337	6	r.	r.	PROPN
cana-6219	337	7	&	&	CCONJ
cana-6219	337	8	s.	s.	PROPN
cana-6219	337	9	g.	g.	PROPN
cana-6219	337	10	khavale	khavale	PROPN
cana-6219	337	11	.	.	PUNCT
cana-6219	338	1	:	:	PUNCT
cana-6219	339	1	fractional	fractional	ADJ
cana-6219	339	2	order	order	NOUN
cana-6219	339	3	transient	transient	VERB
cana-6219	339	4	thermoelastic	thermoelastic	ADJ
cana-6219	339	5	stress	stress	NOUN
cana-6219	339	6	analysis	analysis	NOUN
cana-6219	339	7	of	of	ADP
cana-6219	339	8	a	a	DET
cana-6219	339	9	thin	thin	ADJ
cana-6219	339	10	circular	circular	ADJ
cana-6219	339	11	sector	sector	NOUN
cana-6219	339	12	disk	disk	NOUN
cana-6219	339	13	,	,	PUNCT
cana-6219	339	14	international	international	ADJ
cana-6219	339	15	journal	journal	NOUN
cana-6219	339	16	of	of	ADP
cana-6219	339	17	thermodynamics	thermodynamic	NOUN
cana-6219	339	18	,	,	PUNCT
cana-6219	339	19	vol	vol	NOUN
cana-6219	339	20	.	.	PUNCT
cana-6219	340	1	25(1	25(1	NUM
cana-6219	340	2	)	)	PUNCT
cana-6219	340	3	,	,	PUNCT
cana-6219	341	1	pp	pp	PROPN
cana-6219	341	2	.	.	PUNCT
cana-6219	342	1	1–8	1–8	NUM
cana-6219	342	2	,	,	PUNCT
cana-6219	342	3	(	(	PUNCT
cana-6219	342	4	2022	2022	NUM
cana-6219	342	5	)	)	PUNCT
cana-6219	342	6	.	.	PUNCT
cana-6219	343	1	[	[	X
cana-6219	343	2	21	21	NUM
cana-6219	343	3	]	]	PUNCT
cana-6219	343	4	khavale	khavale	PROPN
cana-6219	343	5	s.	s.	PROPN
cana-6219	343	6	g.	g.	PROPN
cana-6219	343	7	&	&	CCONJ
cana-6219	343	8	k.	k.	PROPN
cana-6219	343	9	r.	r.	PROPN
cana-6219	343	10	gaikwad	gaikwad	PROPN
cana-6219	343	11	.	.	PUNCT
cana-6219	344	1	:	:	PUNCT
cana-6219	344	2	two	two	NUM
cana-6219	344	3	-	-	PUNCT
cana-6219	344	4	dimensional	dimensional	ADJ
cana-6219	344	5	generalized	generalized	ADJ
cana-6219	344	6	magneto	magneto	NOUN
cana-6219	344	7	-	-	PUNCT
cana-6219	344	8	thermoviscoelasticity	thermoviscoelasticity	NOUN
cana-6219	344	9	problem	problem	NOUN
cana-6219	344	10	for	for	ADP
cana-6219	344	11	a	a	DET
cana-6219	344	12	spherical	spherical	ADJ
cana-6219	344	13	cavity	cavity	NOUN
cana-6219	344	14	with	with	ADP
cana-6219	344	15	one	one	NUM
cana-6219	344	16	relaxation	relaxation	NOUN
cana-6219	344	17	time	time	NOUN
cana-6219	344	18	using	use	VERB
cana-6219	344	19	fractional	fractional	ADJ
cana-6219	344	20	derivative	derivative	ADJ
cana-6219	344	21	,	,	PUNCT
cana-6219	344	22	international	international	ADJ
cana-6219	344	23	journal	journal	NOUN
cana-6219	344	24	of	of	ADP
cana-6219	344	25	thermodynamics	thermodynamic	NOUN
cana-6219	344	26	,	,	PUNCT
cana-6219	344	27	vol	vol	NOUN
cana-6219	344	28	.	.	PUNCT
cana-6219	345	1	25(2	25(2	NUM
cana-6219	345	2	)	)	PUNCT
cana-6219	345	3	,	,	PUNCT
cana-6219	346	1	pp	pp	PROPN
cana-6219	346	2	.	.	PUNCT
cana-6219	347	1	89–97	89–97	NUM
cana-6219	347	2	,	,	PUNCT
cana-6219	347	3	(	(	PUNCT
cana-6219	347	4	2022	2022	NUM
cana-6219	347	5	)	)	PUNCT
cana-6219	347	6	.	.	PUNCT
cana-6219	348	1	[	[	X
cana-6219	348	2	22	22	NUM
cana-6219	348	3	]	]	PUNCT
cana-6219	348	4	khavale	khavale	NOUN
cana-6219	348	5	s.	s.	PROPN
cana-6219	348	6	g.	g.	PROPN
cana-6219	348	7	&	&	CCONJ
cana-6219	348	8	k.	k.	PROPN
cana-6219	348	9	r.	r.	PROPN
cana-6219	348	10	gaikwad	gaikwad	PROPN
cana-6219	348	11	.	.	PUNCT
cana-6219	348	12	:	:	PUNCT
cana-6219	349	1	analysis	analysis	NOUN
cana-6219	349	2	of	of	ADP
cana-6219	349	3	non	non	ADJ
cana-6219	349	4	-	-	ADJ
cana-6219	349	5	integer	integer	ADJ
cana-6219	349	6	order	order	NOUN
cana-6219	349	7	thermoelastic	thermoelastic	ADJ
cana-6219	349	8	temperature	temperature	NOUN
cana-6219	349	9	distribution	distribution	NOUN
cana-6219	349	10	and	and	CCONJ
cana-6219	349	11	thermal	thermal	ADJ
cana-6219	349	12	deflection	deflection	NOUN
cana-6219	349	13	of	of	ADP
cana-6219	349	14	thin	thin	ADJ
cana-6219	349	15	hollow	hollow	ADJ
cana-6219	349	16	circular	circular	ADJ
cana-6219	349	17	disk	disk	NOUN
cana-6219	349	18	under	under	ADP
cana-6219	349	19	the	the	DET
cana-6219	349	20	axisymmetric	axisymmetric	ADJ
cana-6219	349	21	heat	heat	NOUN
cana-6219	349	22	supply	supply	NOUN
cana-6219	349	23	,	,	PUNCT
cana-6219	349	24	j.	j.	PROPN
cana-6219	349	25	korean	korean	PROPN
cana-6219	349	26	soc	soc	PROPN
cana-6219	349	27	.	.	PUNCT
cana-6219	350	1	ind	ind	PROPN
cana-6219	350	2	.	.	PUNCT
cana-6219	351	1	appl	appl	PROPN
cana-6219	351	2	.	.	PROPN
cana-6219	351	3	math	math	PROPN
cana-6219	351	4	.	.	PUNCT
cana-6219	352	1	,	,	PUNCT
cana-6219	352	2	vol	vol	NOUN
cana-6219	352	3	.	.	PUNCT
cana-6219	353	1	26(1	26(1	NUM
cana-6219	353	2	)	)	PUNCT
cana-6219	353	3	,	,	PUNCT
cana-6219	353	4	pp	pp	ADJ
cana-6219	353	5	.	.	PUNCT
cana-6219	354	1	67–75	67–75	NUM
cana-6219	354	2	,	,	PUNCT
cana-6219	354	3	(	(	PUNCT
cana-6219	354	4	2022	2022	NUM
cana-6219	354	5	)	)	PUNCT
cana-6219	354	6	.	.	PUNCT
cana-6219	355	1	[	[	X
cana-6219	355	2	23	23	NUM
cana-6219	355	3	]	]	PUNCT
cana-6219	355	4	gaikwad	gaikwad	PROPN
cana-6219	355	5	k.	k.	PROPN
cana-6219	355	6	r.	r.	PROPN
cana-6219	355	7	,	,	PUNCT
cana-6219	355	8	y.	y.	PROPN
cana-6219	355	9	u.	u.	PROPN
cana-6219	355	10	naner	naner	NOUN
cana-6219	355	11	,	,	PUNCT
cana-6219	355	12	s.	s.	PROPN
cana-6219	355	13	g.	g.	PROPN
cana-6219	355	14	khavale	khavale	PROPN
cana-6219	355	15	.	.	PUNCT
cana-6219	355	16	:	:	PUNCT
cana-6219	356	1	transient	transient	VERB
cana-6219	356	2	thermoelastic	thermoelastic	ADJ
cana-6219	356	3	bending	bending	NOUN
cana-6219	356	4	analysis	analysis	NOUN
cana-6219	356	5	of	of	ADP
cana-6219	356	6	a	a	DET
cana-6219	356	7	rectangular	rectangular	ADJ
cana-6219	356	8	plate	plate	NOUN
cana-6219	356	9	with	with	ADP
cana-6219	356	10	a	a	DET
cana-6219	356	11	simply	simply	ADV
cana-6219	356	12	supported	support	VERB
cana-6219	356	13	edge	edge	NOUN
cana-6219	356	14	under	under	ADP
cana-6219	356	15	heat	heat	NOUN
cana-6219	356	16	source	source	NOUN
cana-6219	356	17	:	:	PUNCT
cana-6219	356	18	green	green	PROPN
cana-6219	356	19	’s	’s	PART
cana-6219	356	20	function	function	NOUN
cana-6219	356	21	approach	approach	NOUN
cana-6219	356	22	,	,	PUNCT
cana-6219	356	23	int	int	NOUN
cana-6219	356	24	.	.	PUNCT
cana-6219	357	1	j.	j.	PROPN
cana-6219	357	2	nonlinear	nonlinear	PROPN
cana-6219	357	3	anal	anal	PROPN
cana-6219	357	4	.	.	PUNCT
cana-6219	358	1	appl	appl	PROPN
cana-6219	358	2	,	,	PUNCT
cana-6219	358	3	vol	vol	NOUN
cana-6219	358	4	.	.	PUNCT
cana-6219	358	5	14(1	14(1	NUM
cana-6219	358	6	)	)	PUNCT
cana-6219	358	7	,	,	PUNCT
cana-6219	358	8	pp	pp	ADP
cana-6219	358	9	.	.	PUNCT
cana-6219	359	1	805–818	805–818	NUM
cana-6219	359	2	,	,	PUNCT
cana-6219	359	3	(	(	PUNCT
cana-6219	359	4	2023	2023	NUM
cana-6219	359	5	)	)	PUNCT
cana-6219	359	6	.	.	PUNCT
cana-6219	360	1	[	[	X
cana-6219	360	2	24	24	NUM
cana-6219	360	3	]	]	PUNCT
cana-6219	360	4	khavale	khavale	NOUN
cana-6219	360	5	s.	s.	PROPN
cana-6219	360	6	g.	g.	PROPN
cana-6219	360	7	&	&	CCONJ
cana-6219	360	8	k.	k.	PROPN
cana-6219	360	9	r.	r.	PROPN
cana-6219	360	10	gaikwad	gaikwad	PROPN
cana-6219	360	11	.	.	PUNCT
cana-6219	360	12	:	:	PUNCT
cana-6219	360	13	fractional	fractional	ADJ
cana-6219	360	14	thermoelasticity	thermoelasticity	NOUN
cana-6219	360	15	:	:	PUNCT
cana-6219	360	16	a	a	DET
cana-6219	360	17	review	review	NOUN
cana-6219	360	18	,	,	PUNCT
cana-6219	360	19	easy	easy	ADJ
cana-6219	360	20	chair	chair	NOUN
cana-6219	360	21	preprint	preprint	VERB
cana-6219	360	22	no	no	INTJ
cana-6219	360	23	.	.	PUNCT
cana-6219	361	1	9531	9531	NUM
cana-6219	361	2	,	,	PUNCT
cana-6219	361	3	pp	pp	ADJ
cana-6219	361	4	.	.	NOUN
cana-6219	361	5	1	1	NUM
cana-6219	361	6	–	–	PUNCT
cana-6219	361	7	9	9	NUM
cana-6219	361	8	,	,	PUNCT
cana-6219	361	9	(	(	PUNCT
cana-6219	361	10	2023	2023	NUM
cana-6219	361	11	)	)	PUNCT
cana-6219	361	12	.	.	PUNCT
cana-6219	362	1	[	[	X
cana-6219	362	2	25	25	NUM
cana-6219	362	3	]	]	PUNCT
cana-6219	362	4	khavale	khavale	NOUN
cana-6219	362	5	s.	s.	PROPN
cana-6219	362	6	g.	g.	PROPN
cana-6219	362	7	&	&	CCONJ
cana-6219	362	8	k.	k.	PROPN
cana-6219	362	9	r.	r.	PROPN
cana-6219	362	10	gaikwad	gaikwad	PROPN
cana-6219	362	11	.	.	PUNCT
cana-6219	362	12	:	:	PUNCT
cana-6219	363	1	fractional	fractional	PROPN
cana-6219	363	2	ordered	order	VERB
cana-6219	363	3	thermoelastic	thermoelastic	ADJ
cana-6219	363	4	stress	stress	NOUN
cana-6219	363	5	analysis	analysis	NOUN
cana-6219	363	6	of	of	ADP
cana-6219	363	7	a	a	DET
cana-6219	363	8	thin	thin	ADJ
cana-6219	363	9	circular	circular	ADJ
cana-6219	363	10	plate	plate	NOUN
cana-6219	363	11	under	under	ADP
cana-6219	363	12	axi	axi	NOUN
cana-6219	363	13	-	-	PUNCT
cana-6219	363	14	symmetric	symmetric	ADJ
cana-6219	363	15	heat	heat	NOUN
cana-6219	363	16	supply	supply	NOUN
cana-6219	363	17	,	,	PUNCT
cana-6219	363	18	international	international	ADJ
cana-6219	363	19	journal	journal	NOUN
cana-6219	363	20	of	of	ADP
cana-6219	363	21	nonlinear	nonlinear	ADJ
cana-6219	363	22	analysis	analysis	NOUN
cana-6219	363	23	and	and	CCONJ
cana-6219	363	24	applications	application	NOUN
cana-6219	363	25	,	,	PUNCT
cana-6219	363	26	vol	vol	NOUN
cana-6219	363	27	.	.	PUNCT
cana-6219	363	28	14(4	14(4	NUM
cana-6219	363	29	)	)	PUNCT
cana-6219	363	30	,	,	PUNCT
cana-6219	363	31	pp	pp	ADJ
cana-6219	363	32	.	.	PUNCT
cana-6219	364	1	207–219	207–219	NUM
cana-6219	364	2	,	,	PUNCT
cana-6219	364	3	(	(	PUNCT
cana-6219	364	4	2023	2023	NUM
cana-6219	364	5	)	)	PUNCT
cana-6219	364	6	.	.	PUNCT
cana-6219	365	1	[	[	X
cana-6219	365	2	26	26	NUM
cana-6219	365	3	]	]	X
cana-6219	365	4	c.	c.	PROPN
cana-6219	365	5	b.	b.	PROPN
cana-6219	365	6	kothule	kothule	PROPN
cana-6219	365	7	,	,	PUNCT
cana-6219	365	8	t.	t.	PROPN
cana-6219	365	9	l.	l.	PROPN
cana-6219	365	10	holambe	holambe	PROPN
cana-6219	365	11	,	,	PUNCT
cana-6219	365	12	khavale	khavale	PROPN
cana-6219	365	13	s.	s.	PROPN
cana-6219	365	14	g.	g.	PROPN
cana-6219	365	15	,	,	PUNCT
cana-6219	365	16	b.	b.	PROPN
cana-6219	365	17	r	r	PROPN
cana-6219	365	18	sontakke	sontakke	PROPN
cana-6219	365	19	.	.	PUNCT
cana-6219	365	20	:	:	PUNCT
cana-6219	366	1	analysis	analysis	NOUN
cana-6219	366	2	of	of	ADP
cana-6219	366	3	fractional	fractional	ADJ
cana-6219	366	4	order	order	NOUN
cana-6219	366	5	heat	heat	NOUN
cana-6219	366	6	conduction	conduction	NOUN
cana-6219	366	7	problems	problem	NOUN
cana-6219	366	8	in	in	ADP
cana-6219	366	9	noncylindrical	noncylindrical	ADJ
cana-6219	366	10	domains	domain	NOUN
cana-6219	366	11	with	with	ADP
cana-6219	366	12	different	different	ADJ
cana-6219	366	13	boundary	boundary	ADJ
cana-6219	366	14	conditions	condition	NOUN
cana-6219	366	15	,	,	PUNCT
cana-6219	366	16	econophysics	econophysic	NOUN
cana-6219	366	17	,	,	PUNCT
cana-6219	366	18	sociophysics	sociophysic	NOUN
cana-6219	366	19	&	&	CCONJ
cana-6219	366	20	other	other	ADJ
cana-6219	366	21	multidisciplinary	multidisciplinary	ADJ
cana-6219	366	22	sciences	science	NOUN
cana-6219	366	23	journal	journal	PROPN
cana-6219	366	24	(	(	PUNCT
cana-6219	366	25	esmsj	esmsj	PROPN
cana-6219	366	26	)	)	PUNCT
cana-6219	366	27	,	,	PUNCT
cana-6219	366	28	vol	vol	NOUN
cana-6219	366	29	.	.	PUNCT
cana-6219	366	30	12(2	12(2	NUM
cana-6219	366	31	)	)	PUNCT
cana-6219	366	32	,	,	PUNCT
cana-6219	366	33	pp	pp	PROPN
cana-6219	366	34	.	.	PUNCT
cana-6219	367	1	23	23	NUM
cana-6219	367	2	-	-	SYM
cana-6219	367	3	26	26	NUM
cana-6219	367	4	,	,	PUNCT
cana-6219	367	5	(	(	PUNCT
cana-6219	367	6	2023	2023	NUM
cana-6219	367	7	)	)	PUNCT
cana-6219	367	8	.	.	PUNCT
cana-6219	368	1	[	[	X
cana-6219	368	2	27	27	NUM
cana-6219	368	3	]	]	X
cana-6219	368	4	n.	n.	PROPN
cana-6219	368	5	b.	b.	PROPN
cana-6219	368	6	jadhav	jadhav	PROPN
cana-6219	368	7	,	,	PUNCT
cana-6219	368	8	k.	k.	PROPN
cana-6219	368	9	r.	r.	PROPN
cana-6219	368	10	gaikwad	gaikwad	PROPN
cana-6219	368	11	&	&	CCONJ
cana-6219	368	12	s.	s.	PROPN
cana-6219	368	13	g.	g.	PROPN
cana-6219	368	14	khavale	khavale	PROPN
cana-6219	368	15	,	,	PUNCT
cana-6219	368	16	fractional	fractional	ADJ
cana-6219	368	17	order	order	NOUN
cana-6219	368	18	thermoelastic	thermoelastic	ADJ
cana-6219	368	19	problem	problem	NOUN
cana-6219	368	20	for	for	ADP
cana-6219	368	21	a	a	DET
cana-6219	368	22	thin	thin	ADJ
cana-6219	368	23	circular	circular	ADJ
cana-6219	368	24	plate	plate	NOUN
cana-6219	368	25	with	with	ADP
cana-6219	368	26	uniform	uniform	ADJ
cana-6219	368	27	internal	internal	ADJ
cana-6219	368	28	heat	heat	NOUN
cana-6219	368	29	generation	generation	NOUN
cana-6219	368	30	,	,	PUNCT
cana-6219	368	31	jp	jp	NOUN
cana-6219	368	32	journal	journal	PROPN
cana-6219	368	33	of	of	ADP
cana-6219	368	34	heat	heat	NOUN
cana-6219	368	35	and	and	CCONJ
cana-6219	368	36	mass	mass	NOUN
cana-6219	368	37	transfer	transfer	NOUN
cana-6219	368	38	,	,	PUNCT
cana-6219	368	39	vol	vol	NOUN
cana-6219	368	40	.	.	PROPN
cana-6219	368	41	35	35	NUM
cana-6219	368	42	,	,	PUNCT
cana-6219	368	43	pp	pp	ADJ
cana-6219	368	44	.	.	PUNCT
cana-6219	369	1	107	107	NUM
cana-6219	369	2	-	-	SYM
cana-6219	369	3	124	124	NUM
cana-6219	369	4	,	,	PUNCT
cana-6219	369	5	(	(	PUNCT
cana-6219	369	6	2023	2023	NUM
cana-6219	369	7	)	)	PUNCT
cana-6219	369	8	.	.	PUNCT
cana-6219	370	1	communications	communication	NOUN
cana-6219	370	2	on	on	ADP
cana-6219	370	3	applied	apply	VERB
cana-6219	370	4	nonlinear	nonlinear	ADJ
cana-6219	370	5	analysis	analysis	NOUN
cana-6219	370	6	issn	issn	NOUN
cana-6219	370	7	:	:	PUNCT
cana-6219	370	8	1074	1074	NUM
cana-6219	370	9	-	-	PUNCT
cana-6219	370	10	133x	133x	NUM
cana-6219	370	11	vol	vol	VERB
cana-6219	370	12	32	32	NUM
cana-6219	370	13	no	no	NOUN
cana-6219	370	14	.	.	PUNCT
cana-6219	371	1	10s	10	NOUN
cana-6219	371	2	(	(	PUNCT
cana-6219	371	3	2025	2025	NUM
cana-6219	371	4	)	)	PUNCT
cana-6219	371	5	3544	3544	NUM
cana-6219	371	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6219	372	1	[	[	X
cana-6219	372	2	28	28	NUM
cana-6219	372	3	]	]	X
cana-6219	372	4	kishor	kishor	PROPN
cana-6219	372	5	r.	r.	PROPN
cana-6219	372	6	gaikwad	gaikwad	PROPN
cana-6219	372	7	,	,	PUNCT
cana-6219	372	8	kirtiwant	kirtiwant	ADJ
cana-6219	372	9	p.	p.	PROPN
cana-6219	372	10	ghadle	ghadle	PROPN
cana-6219	372	11	.	.	PUNCT
cana-6219	372	12	:	:	PUNCT
cana-6219	373	1	nonhomogeneous	nonhomogeneous	ADJ
cana-6219	373	2	heat	heat	NOUN
cana-6219	373	3	conduction	conduction	NOUN
cana-6219	373	4	problem	problem	NOUN
cana-6219	373	5	and	and	CCONJ
cana-6219	373	6	its	its	PRON
cana-6219	373	7	thermal	thermal	ADJ
cana-6219	373	8	deflection	deflection	NOUN
cana-6219	373	9	due	due	ADP
cana-6219	373	10	to	to	ADP
cana-6219	373	11	internal	internal	ADJ
cana-6219	373	12	heat	heat	NOUN
cana-6219	373	13	generation	generation	NOUN
cana-6219	373	14	in	in	ADP
cana-6219	373	15	a	a	DET
cana-6219	373	16	thin	thin	ADJ
cana-6219	373	17	hollow	hollow	ADJ
cana-6219	373	18	circular	circular	ADJ
cana-6219	373	19	disk	disk	NOUN
cana-6219	373	20	,	,	PUNCT
cana-6219	373	21	journal	journal	NOUN
cana-6219	373	22	of	of	ADP
cana-6219	373	23	thermal	thermal	ADJ
cana-6219	373	24	stresses	stress	NOUN
cana-6219	373	25	35(6	35(6	NUM
cana-6219	373	26	)	)	PUNCT
cana-6219	373	27	,	,	PUNCT
cana-6219	373	28	pp	pp	ADP
cana-6219	373	29	.	.	PUNCT
cana-6219	374	1	485	485	NUM
cana-6219	374	2	-	-	SYM
cana-6219	374	3	498	498	NUM
cana-6219	374	4	,	,	PUNCT
cana-6219	374	5	(	(	PUNCT
cana-6219	374	6	2012	2012	NUM
cana-6219	374	7	)	)	PUNCT
cana-6219	374	8	.	.	PUNCT
cana-6219	375	1	[	[	X
cana-6219	375	2	29	29	NUM
cana-6219	375	3	]	]	PUNCT
cana-6219	375	4	k.	k.	PROPN
cana-6219	375	5	r.	r.	PROPN
cana-6219	375	6	gaikwad	gaikwad	PROPN
cana-6219	375	7	.	.	PUNCT
cana-6219	375	8	:	:	PUNCT
cana-6219	376	1	analysis	analysis	NOUN
cana-6219	376	2	of	of	ADP
cana-6219	376	3	thermoelastic	thermoelastic	ADJ
cana-6219	376	4	deformation	deformation	NOUN
cana-6219	376	5	of	of	ADP
cana-6219	376	6	a	a	DET
cana-6219	376	7	thin	thin	ADJ
cana-6219	376	8	hollow	hollow	ADJ
cana-6219	376	9	circular	circular	ADJ
cana-6219	376	10	disk	disk	NOUN
cana-6219	376	11	due	due	ADP
cana-6219	376	12	to	to	PART
cana-6219	376	13	partially	partially	ADV
cana-6219	376	14	distributed	distribute	VERB
cana-6219	376	15	heat	heat	NOUN
cana-6219	376	16	supply	supply	NOUN
cana-6219	376	17	.	.	PUNCT
cana-6219	377	1	journal	journal	NOUN
cana-6219	377	2	of	of	ADP
cana-6219	377	3	thermal	thermal	ADJ
cana-6219	377	4	stresses	stress	NOUN
cana-6219	377	5	36(2	36(2	NUM
cana-6219	377	6	)	)	PUNCT
cana-6219	377	7	,	,	PUNCT
cana-6219	377	8	pp.207	pp.207	NOUN
cana-6219	377	9	-	-	SYM
cana-6219	377	10	224	224	NUM
cana-6219	377	11	,	,	PUNCT
cana-6219	377	12	(	(	PUNCT
cana-6219	377	13	2013	2013	NUM
cana-6219	377	14	)	)	PUNCT
cana-6219	377	15	.	.	PUNCT
cana-6219	378	1	[	[	X
cana-6219	378	2	30	30	NUM
cana-6219	378	3	]	]	PUNCT
cana-6219	378	4	k.	k.	PROPN
cana-6219	378	5	r.	r.	PROPN
cana-6219	378	6	gaikwad	gaikwad	PROPN
cana-6219	378	7	,	,	PUNCT
cana-6219	378	8	y.	y.	PROPN
cana-6219	378	9	u.	u.	PROPN
cana-6219	378	10	naner	naner	NOUN
cana-6219	378	11	.	.	PUNCT
cana-6219	378	12	:	:	PUNCT
cana-6219	379	1	analysis	analysis	NOUN
cana-6219	379	2	of	of	ADP
cana-6219	379	3	transient	transient	ADJ
cana-6219	379	4	thermoelastic	thermoelastic	ADJ
cana-6219	379	5	temperature	temperature	NOUN
cana-6219	379	6	distribution	distribution	NOUN
cana-6219	379	7	of	of	ADP
cana-6219	379	8	a	a	DET
cana-6219	379	9	thin	thin	ADJ
cana-6219	379	10	circular	circular	ADJ
cana-6219	379	11	plate	plate	NOUN
cana-6219	379	12	and	and	CCONJ
cana-6219	379	13	its	its	PRON
cana-6219	379	14	thermal	thermal	ADJ
cana-6219	379	15	deflection	deflection	NOUN
cana-6219	379	16	under	under	ADP
cana-6219	379	17	uniform	uniform	ADJ
cana-6219	379	18	heat	heat	NOUN
cana-6219	379	19	generation	generation	NOUN
cana-6219	379	20	.	.	PUNCT
cana-6219	380	1	journal	journal	NOUN
cana-6219	380	2	of	of	ADP
cana-6219	380	3	thermal	thermal	ADJ
cana-6219	380	4	stresses	stress	VERB
cana-6219	380	5	44(1	44(1	PROPN
cana-6219	380	6	)	)	PUNCT
cana-6219	380	7	,	,	PUNCT
cana-6219	380	8	pp	pp	ADP
cana-6219	380	9	.	.	PUNCT
cana-6219	381	1	75	75	NUM
cana-6219	381	2	-	-	SYM
cana-6219	381	3	85	85	NUM
cana-6219	381	4	,	,	PUNCT
cana-6219	381	5	(	(	PUNCT
cana-6219	381	6	2020	2020	NUM
cana-6219	381	7	)	)	PUNCT
cana-6219	381	8	.	.	PUNCT
cana-6219	382	1	[	[	X
cana-6219	382	2	31	31	NUM
cana-6219	382	3	]	]	PUNCT
cana-6219	382	4	tzou	tzou	PROPN
cana-6219	382	5	,	,	PUNCT
cana-6219	382	6	d.	d.	PROPN
cana-6219	382	7	,	,	PUNCT
cana-6219	382	8	macro	macro	ADJ
cana-6219	382	9	to	to	PART
cana-6219	382	10	micro	micro	ADJ
cana-6219	382	11	heat	heat	NOUN
cana-6219	382	12	transfer	transfer	NOUN
cana-6219	382	13	.	.	PUNCT
cana-6219	383	1	taylor	taylor	PROPN
cana-6219	383	2	&	&	CCONJ
cana-6219	383	3	francis	francis	PROPN
cana-6219	383	4	,	,	PUNCT
cana-6219	383	5	washington	washington	PROPN
cana-6219	383	6	(	(	PUNCT
cana-6219	383	7	1996	1996	NUM
cana-6219	383	8	)	)	PUNCT
cana-6219	383	9	.	.	PUNCT