id	sid	tid	token	lemma	pos
easat-2990	1	1	edelweiss	edelweiss	PROPN
easat-2990	1	2	applied	apply	VERB
easat-2990	1	3	science	science	NOUN
easat-2990	1	4	and	and	CCONJ
easat-2990	1	5	technology	technology	NOUN
easat-2990	1	6	issn	issn	PROPN
easat-2990	1	7	:	:	PUNCT
easat-2990	1	8	2576	2576	NUM
easat-2990	1	9	-	-	SYM
easat-2990	1	10	8484	8484	NUM
easat-2990	1	11	vol	vol	NOUN
easat-2990	1	12	.	.	PROPN
easat-2990	1	13	8	8	NUM
easat-2990	1	14	,	,	PUNCT
easat-2990	1	15	no	no	INTJ
easat-2990	1	16	.	.	NOUN
easat-2990	1	17	6	6	NUM
easat-2990	1	18	,	,	PUNCT
easat-2990	1	19	4599	4599	NUM
easat-2990	1	20	-	-	SYM
easat-2990	1	21	4610	4610	NUM
easat-2990	1	22	2024	2024	NUM
easat-2990	1	23	publisher	publisher	NOUN
easat-2990	1	24	:	:	PUNCT
easat-2990	1	25	learning	learn	VERB
easat-2990	1	26	gate	gate	NOUN
easat-2990	1	27	doi	doi	PROPN
easat-2990	1	28	:	:	PUNCT
easat-2990	1	29	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	1	30	©	©	PROPN
easat-2990	1	31	2024	2024	NUM
easat-2990	1	32	by	by	ADP
easat-2990	1	33	the	the	DET
easat-2990	1	34	author	author	NOUN
easat-2990	1	35	;	;	PUNCT
easat-2990	1	36	licensee	licensee	PROPN
easat-2990	1	37	learning	learning	NOUN
easat-2990	1	38	gate	gate	NOUN
easat-2990	1	39	©	©	PROPN
easat-2990	1	40	2024	2024	NUM
easat-2990	1	41	by	by	ADP
easat-2990	1	42	the	the	DET
easat-2990	1	43	author	author	NOUN
easat-2990	1	44	;	;	PUNCT
easat-2990	1	45	licensee	licensee	PROPN
easat-2990	1	46	learning	learn	VERB
easat-2990	1	47	gate	gate	NOUN
easat-2990	1	48	*	*	PUNCT
easat-2990	1	49	correspondence	correspondence	NOUN
easat-2990	1	50	:	:	PUNCT
easat-2990	1	51	aljmrawysydbas341@gmail.com	aljmrawysydbas341@gmail.com	X
easat-2990	1	52	wavelet	wavelet	NOUN
easat-2990	1	53	-	-	PUNCT
easat-2990	1	54	based	base	VERB
easat-2990	1	55	collocation	collocation	NOUN
easat-2990	1	56	methods	method	NOUN
easat-2990	1	57	for	for	ADP
easat-2990	1	58	solving	solve	VERB
easat-2990	1	59	multi	multi	ADJ
easat-2990	1	60	-	-	ADJ
easat-2990	1	61	dimensional	dimensional	ADJ
easat-2990	1	62	integrodifferential	integrodifferential	ADJ
easat-2990	1	63	systems	system	NOUN
easat-2990	1	64	abbas	abbas	PROPN
easat-2990	1	65	mohsin	mohsin	PROPN
easat-2990	1	66	kazar1	kazar1	PROPN
easat-2990	2	1	*	*	PROPN
easat-2990	2	2	1teacher	1teacher	NUM
easat-2990	2	3	at	at	ADP
easat-2990	2	4	al	al	PROPN
easat-2990	2	5	-	-	PUNCT
easat-2990	2	6	shahimiya	shahimiya	PROPN
easat-2990	2	7	middle	middle	ADJ
easat-2990	2	8	school	school	NOUN
easat-2990	2	9	for	for	ADP
easat-2990	2	10	boys	boy	NOUN
easat-2990	2	11	/	/	SYM
easat-2990	2	12	al	al	PROPN
easat-2990	2	13	-	-	PUNCT
easat-2990	2	14	suwaira	suwaira	PROPN
easat-2990	2	15	education	education	PROPN
easat-2990	2	16	department	department	PROPN
easat-2990	2	17	,	,	PUNCT
easat-2990	2	18	wasit	wasit	NOUN
easat-2990	2	19	governorate	governorate	PROPN
easat-2990	2	20	;	;	PUNCT
easat-2990	2	21	aljmrawysydbas341@gmail.com	aljmrawysydbas341@gmail.com	X
easat-2990	2	22	(	(	PUNCT
easat-2990	2	23	a.m.k	a.m.k	NOUN
easat-2990	2	24	.	.	PUNCT
easat-2990	2	25	)	)	PUNCT
easat-2990	2	26	.	.	PUNCT
easat-2990	3	1	abstract	abstract	ADV
easat-2990	3	2	:	:	PUNCT
easat-2990	3	3	this	this	DET
easat-2990	3	4	paper	paper	NOUN
easat-2990	3	5	presents	present	VERB
easat-2990	3	6	a	a	DET
easat-2990	3	7	comprehensive	comprehensive	ADJ
easat-2990	3	8	investigation	investigation	NOUN
easat-2990	3	9	of	of	ADP
easat-2990	3	10	wavelet	wavelet	NOUN
easat-2990	3	11	-	-	PUNCT
easat-2990	3	12	based	base	VERB
easat-2990	3	13	collocation	collocation	NOUN
easat-2990	3	14	methods	method	NOUN
easat-2990	3	15	for	for	ADP
easat-2990	3	16	solving	solve	VERB
easat-2990	3	17	multi	multi	ADJ
easat-2990	3	18	-	-	ADJ
easat-2990	3	19	dimensional	dimensional	ADJ
easat-2990	3	20	integro	integro	ADJ
easat-2990	3	21	-	-	PUNCT
easat-2990	3	22	differential	differential	NOUN
easat-2990	3	23	systems	system	NOUN
easat-2990	3	24	.	.	PUNCT
easat-2990	4	1	the	the	DET
easat-2990	4	2	research	research	NOUN
easat-2990	4	3	addresses	address	VERB
easat-2990	4	4	the	the	DET
easat-2990	4	5	challenging	challenging	ADJ
easat-2990	4	6	problem	problem	NOUN
easat-2990	4	7	of	of	ADP
easat-2990	4	8	finding	find	VERB
easat-2990	4	9	numerical	numerical	ADJ
easat-2990	4	10	solutions	solution	NOUN
easat-2990	4	11	to	to	ADP
easat-2990	4	12	integro	integro	ADJ
easat-2990	4	13	-	-	PUNCT
easat-2990	4	14	differential	differential	NOUN
easat-2990	4	15	equations	equation	NOUN
easat-2990	4	16	(	(	PUNCT
easat-2990	4	17	ides	ide	NOUN
easat-2990	4	18	)	)	PUNCT
easat-2990	4	19	that	that	PRON
easat-2990	4	20	are	be	AUX
easat-2990	4	21	essential	essential	ADJ
easat-2990	4	22	in	in	ADP
easat-2990	4	23	various	various	ADJ
easat-2990	4	24	scientific	scientific	ADJ
easat-2990	4	25	and	and	CCONJ
easat-2990	4	26	engineering	engineering	NOUN
easat-2990	4	27	applications	application	NOUN
easat-2990	4	28	.	.	PUNCT
easat-2990	5	1	we	we	PRON
easat-2990	5	2	propose	propose	VERB
easat-2990	5	3	novel	novel	ADJ
easat-2990	5	4	numerical	numerical	ADJ
easat-2990	5	5	approximations	approximation	NOUN
easat-2990	5	6	for	for	ADP
easat-2990	5	7	infinitely	infinitely	ADV
easat-2990	5	8	dimensional	dimensional	ADJ
easat-2990	5	9	problems	problem	NOUN
easat-2990	5	10	,	,	PUNCT
easat-2990	5	11	including	include	VERB
easat-2990	5	12	fractional	fractional	ADJ
easat-2990	5	13	cattaneo	cattaneo	PROPN
easat-2990	5	14	-	-	PUNCT
easat-2990	5	15	rayleigh	rayleigh	ADJ
easat-2990	5	16	waves	wave	NOUN
easat-2990	5	17	and	and	CCONJ
easat-2990	5	18	nonlinear	nonlinear	ADJ
easat-2990	5	19	diffusion	diffusion	NOUN
easat-2990	5	20	problems	problem	NOUN
easat-2990	5	21	defined	define	VERB
easat-2990	5	22	on	on	ADP
easat-2990	5	23	unbounded	unbounded	ADJ
easat-2990	5	24	domains	domain	NOUN
easat-2990	5	25	.	.	PUNCT
easat-2990	6	1	the	the	DET
easat-2990	6	2	study	study	NOUN
easat-2990	6	3	introduces	introduce	VERB
easat-2990	6	4	a	a	DET
easat-2990	6	5	unified	unified	ADJ
easat-2990	6	6	computational	computational	ADJ
easat-2990	6	7	strategy	strategy	NOUN
easat-2990	6	8	that	that	PRON
easat-2990	6	9	directly	directly	ADV
easat-2990	6	10	applies	apply	VERB
easat-2990	6	11	to	to	ADP
easat-2990	6	12	ides	ide	NOUN
easat-2990	6	13	without	without	ADP
easat-2990	6	14	discretization	discretization	NOUN
easat-2990	6	15	,	,	PUNCT
easat-2990	6	16	particularly	particularly	ADV
easat-2990	6	17	focusing	focus	VERB
easat-2990	6	18	on	on	ADP
easat-2990	6	19	the	the	DET
easat-2990	6	20	integer	integer	NOUN
easat-2990	6	21	and	and	CCONJ
easat-2990	6	22	fractional	fractional	ADJ
easat-2990	6	23	-	-	PUNCT
easat-2990	6	24	order	order	NOUN
easat-2990	6	25	cattaneo	cattaneo	ADJ
easat-2990	6	26	-	-	PUNCT
easat-2990	6	27	rayleigh	rayleigh	PROPN
easat-2990	6	28	model	model	NOUN
easat-2990	6	29	of	of	ADP
easat-2990	6	30	thermoelasticity	thermoelasticity	NOUN
easat-2990	6	31	in	in	ADP
easat-2990	6	32	one	one	NUM
easat-2990	6	33	-	-	PUNCT
easat-2990	6	34	dimensional	dimensional	ADJ
easat-2990	6	35	zonal	zonal	ADJ
easat-2990	6	36	regions	region	NOUN
easat-2990	6	37	.	.	PUNCT
easat-2990	7	1	through	through	ADP
easat-2990	7	2	numerical	numerical	ADJ
easat-2990	7	3	experiments	experiment	NOUN
easat-2990	7	4	,	,	PUNCT
easat-2990	7	5	we	we	PRON
easat-2990	7	6	demonstrate	demonstrate	VERB
easat-2990	7	7	that	that	SCONJ
easat-2990	7	8	our	our	PRON
easat-2990	7	9	wavelet	wavelet	NOUN
easat-2990	7	10	collocation	collocation	NOUN
easat-2990	7	11	approach	approach	NOUN
easat-2990	7	12	achieves	achieve	VERB
easat-2990	7	13	high	high	ADJ
easat-2990	7	14	efficiency	efficiency	NOUN
easat-2990	7	15	and	and	CCONJ
easat-2990	7	16	superior	superior	ADJ
easat-2990	7	17	accuracy	accuracy	NOUN
easat-2990	7	18	compared	compare	VERB
easat-2990	7	19	to	to	ADP
easat-2990	7	20	traditional	traditional	ADJ
easat-2990	7	21	methods	method	NOUN
easat-2990	7	22	.	.	PUNCT
easat-2990	8	1	the	the	DET
easat-2990	8	2	results	result	NOUN
easat-2990	8	3	show	show	VERB
easat-2990	8	4	particularly	particularly	ADV
easat-2990	8	5	strong	strong	ADJ
easat-2990	8	6	performance	performance	NOUN
easat-2990	8	7	in	in	ADP
easat-2990	8	8	handling	handle	VERB
easat-2990	8	9	systems	system	NOUN
easat-2990	8	10	with	with	ADP
easat-2990	8	11	differential	differential	ADJ
easat-2990	8	12	physical	physical	ADJ
easat-2990	8	13	singularities	singularity	NOUN
easat-2990	8	14	,	,	PUNCT
easat-2990	8	15	functional	functional	ADJ
easat-2990	8	16	physical	physical	ADJ
easat-2990	8	17	singularities	singularity	NOUN
easat-2990	8	18	,	,	PUNCT
easat-2990	8	19	and	and	CCONJ
easat-2990	8	20	vectorvalued	vectorvalue	VERB
easat-2990	8	21	physical	physical	ADJ
easat-2990	8	22	singularities	singularity	NOUN
easat-2990	8	23	.	.	PUNCT
easat-2990	9	1	our	our	PRON
easat-2990	9	2	approach	approach	NOUN
easat-2990	9	3	provides	provide	VERB
easat-2990	9	4	a	a	DET
easat-2990	9	5	valuable	valuable	ADJ
easat-2990	9	6	toolbox	toolbox	NOUN
easat-2990	9	7	for	for	ADP
easat-2990	9	8	addressing	address	VERB
easat-2990	9	9	complex	complex	ADJ
easat-2990	9	10	modeling	modeling	NOUN
easat-2990	9	11	challenges	challenge	NOUN
easat-2990	9	12	in	in	ADP
easat-2990	9	13	biology	biology	NOUN
easat-2990	9	14	,	,	PUNCT
easat-2990	9	15	mechanical	mechanical	ADJ
easat-2990	9	16	signal	signal	NOUN
easat-2990	9	17	processing	processing	NOUN
easat-2990	9	18	,	,	PUNCT
easat-2990	9	19	and	and	CCONJ
easat-2990	9	20	digital	digital	ADJ
easat-2990	9	21	communications	communication	NOUN
easat-2990	9	22	where	where	SCONJ
easat-2990	9	23	partial	partial	ADJ
easat-2990	9	24	integro	integro	ADJ
easat-2990	9	25	-	-	PUNCT
easat-2990	9	26	differential	differential	NOUN
easat-2990	9	27	equations	equation	NOUN
easat-2990	9	28	naturally	naturally	ADV
easat-2990	9	29	arise	arise	VERB
easat-2990	9	30	.	.	PUNCT
easat-2990	10	1	keywords	keyword	NOUN
easat-2990	10	2	:	:	PUNCT
easat-2990	10	3	integro	integro	ADJ
easat-2990	10	4	-	-	PUNCT
easat-2990	10	5	differential	differential	NOUN
easat-2990	10	6	equations	equation	NOUN
easat-2990	10	7	,	,	PUNCT
easat-2990	10	8	integro	integro	ADJ
easat-2990	10	9	-	-	PUNCT
easat-2990	10	10	differential	differential	NOUN
easat-2990	10	11	systems	system	NOUN
easat-2990	10	12	,	,	PUNCT
easat-2990	10	13	multi	multi	ADJ
easat-2990	10	14	-	-	ADJ
easat-2990	10	15	dimensional	dimensional	ADJ
easat-2990	10	16	,	,	PUNCT
easat-2990	10	17	wavelet	wavelet	NOUN
easat-2990	10	18	-	-	PUNCT
easat-2990	10	19	based	base	VERB
easat-2990	10	20	collocation	collocation	NOUN
easat-2990	10	21	.	.	PUNCT
easat-2990	11	1	1	1	X
easat-2990	11	2	.	.	X
easat-2990	11	3	introduction	introduction	NOUN
easat-2990	11	4	integro	integro	ADJ
easat-2990	11	5	-	-	PUNCT
easat-2990	11	6	differential	differential	NOUN
easat-2990	11	7	equations	equation	NOUN
easat-2990	11	8	(	(	PUNCT
easat-2990	11	9	ides	ide	NOUN
easat-2990	11	10	)	)	PUNCT
easat-2990	11	11	are	be	AUX
easat-2990	11	12	widely	widely	ADV
easat-2990	11	13	used	use	VERB
easat-2990	11	14	in	in	ADP
easat-2990	11	15	science	science	NOUN
easat-2990	11	16	and	and	CCONJ
easat-2990	11	17	engineering	engineering	NOUN
easat-2990	11	18	to	to	PART
easat-2990	11	19	describe	describe	VERB
easat-2990	11	20	the	the	DET
easat-2990	11	21	dynamic	dynamic	ADJ
easat-2990	11	22	behaviors	behavior	NOUN
easat-2990	11	23	of	of	ADP
easat-2990	11	24	physical	physical	ADJ
easat-2990	11	25	and	and	CCONJ
easat-2990	11	26	biological	biological	ADJ
easat-2990	11	27	systems	system	NOUN
easat-2990	11	28	.	.	PUNCT
easat-2990	12	1	as	as	ADP
easat-2990	12	2	a	a	DET
easat-2990	12	3	mathematical	mathematical	ADJ
easat-2990	12	4	modeling	modeling	NOUN
easat-2990	12	5	tool	tool	NOUN
easat-2990	12	6	,	,	PUNCT
easat-2990	12	7	ides	ide	NOUN
easat-2990	12	8	have	have	AUX
easat-2990	12	9	been	be	AUX
easat-2990	12	10	successfully	successfully	ADV
easat-2990	12	11	applied	apply	VERB
easat-2990	12	12	to	to	ADP
easat-2990	12	13	a	a	DET
easat-2990	12	14	wide	wide	ADJ
easat-2990	12	15	range	range	NOUN
easat-2990	12	16	of	of	ADP
easat-2990	12	17	practical	practical	ADJ
easat-2990	12	18	applications	application	NOUN
easat-2990	12	19	,	,	PUNCT
easat-2990	12	20	such	such	ADJ
easat-2990	12	21	as	as	ADP
easat-2990	12	22	fluid	fluid	ADJ
easat-2990	12	23	dynamics	dynamic	NOUN
easat-2990	12	24	,	,	PUNCT
easat-2990	12	25	porous	porous	ADJ
easat-2990	12	26	media	medium	NOUN
easat-2990	12	27	,	,	PUNCT
easat-2990	12	28	biological	biological	ADJ
easat-2990	12	29	sciences	science	NOUN
easat-2990	12	30	,	,	PUNCT
easat-2990	12	31	reaction	reaction	NOUN
easat-2990	12	32	-	-	PUNCT
easat-2990	12	33	diffusion	diffusion	NOUN
easat-2990	12	34	systems	system	NOUN
easat-2990	12	35	,	,	PUNCT
easat-2990	12	36	electromagnetic	electromagnetic	ADJ
easat-2990	12	37	theory	theory	NOUN
easat-2990	12	38	,	,	PUNCT
easat-2990	12	39	aerodynamics	aerodynamic	NOUN
easat-2990	12	40	,	,	PUNCT
easat-2990	12	41	etc	etc	X
easat-2990	12	42	.	.	X
easat-2990	12	43	however	however	ADV
easat-2990	12	44	,	,	PUNCT
easat-2990	12	45	finding	find	VERB
easat-2990	12	46	numerical	numerical	ADJ
easat-2990	12	47	solutions	solution	NOUN
easat-2990	12	48	to	to	ADP
easat-2990	12	49	ides	ide	NOUN
easat-2990	12	50	is	be	AUX
easat-2990	12	51	still	still	ADV
easat-2990	12	52	a	a	DET
easat-2990	12	53	challenging	challenging	ADJ
easat-2990	12	54	problem	problem	NOUN
easat-2990	12	55	due	due	ADP
easat-2990	12	56	to	to	ADP
easat-2990	12	57	the	the	DET
easat-2990	12	58	unique	unique	ADJ
easat-2990	12	59	characteristics	characteristic	NOUN
easat-2990	12	60	of	of	ADP
easat-2990	12	61	the	the	DET
easat-2990	12	62	ides	ide	NOUN
easat-2990	12	63	.	.	PUNCT
easat-2990	13	1	solving	solve	VERB
easat-2990	13	2	ides	ide	NOUN
easat-2990	13	3	is	be	AUX
easat-2990	13	4	an	an	DET
easat-2990	13	5	essential	essential	ADJ
easat-2990	13	6	task	task	NOUN
easat-2990	13	7	in	in	ADP
easat-2990	13	8	intelligent	intelligent	ADJ
easat-2990	13	9	modeling	modeling	NOUN
easat-2990	13	10	and	and	CCONJ
easat-2990	13	11	simulation[1	simulation[1	NOUN
easat-2990	13	12	]	]	X
easat-2990	13	13	.	.	PUNCT
easat-2990	14	1	recently	recently	ADV
easat-2990	14	2	,	,	PUNCT
easat-2990	14	3	several	several	ADJ
easat-2990	14	4	techniques	technique	NOUN
easat-2990	14	5	have	have	AUX
easat-2990	14	6	been	be	AUX
easat-2990	14	7	developed	develop	VERB
easat-2990	14	8	for	for	ADP
easat-2990	14	9	solving	solve	VERB
easat-2990	14	10	these	these	DET
easat-2990	14	11	equations	equation	NOUN
easat-2990	14	12	.	.	PUNCT
easat-2990	15	1	most	most	ADJ
easat-2990	15	2	of	of	ADP
easat-2990	15	3	them	they	PRON
easat-2990	15	4	mainly	mainly	ADV
easat-2990	15	5	rely	rely	VERB
easat-2990	15	6	on	on	ADP
easat-2990	15	7	discretization	discretization	NOUN
easat-2990	15	8	methods	method	NOUN
easat-2990	15	9	,	,	PUNCT
easat-2990	15	10	such	such	ADJ
easat-2990	15	11	as	as	ADP
easat-2990	15	12	the	the	DET
easat-2990	15	13	finite	finite	ADJ
easat-2990	15	14	element	element	NOUN
easat-2990	15	15	method	method	NOUN
easat-2990	15	16	and	and	CCONJ
easat-2990	15	17	finite	finite	ADJ
easat-2990	15	18	difference	difference	NOUN
easat-2990	15	19	method	method	NOUN
easat-2990	15	20	.	.	PUNCT
easat-2990	16	1	up	up	ADP
easat-2990	16	2	to	to	ADP
easat-2990	16	3	now	now	ADV
easat-2990	16	4	,	,	PUNCT
easat-2990	16	5	only	only	ADV
easat-2990	16	6	a	a	DET
easat-2990	16	7	few	few	ADJ
easat-2990	16	8	works	work	NOUN
easat-2990	16	9	have	have	AUX
easat-2990	16	10	been	be	AUX
easat-2990	16	11	reported	report	VERB
easat-2990	16	12	for	for	ADP
easat-2990	16	13	solving	solve	VERB
easat-2990	16	14	infinitely	infinitely	ADV
easat-2990	16	15	dimensional	dimensional	ADJ
easat-2990	16	16	problems	problem	NOUN
easat-2990	16	17	[	[	X
easat-2990	16	18	2	2	NUM
easat-2990	16	19	]	]	PUNCT
easat-2990	16	20	.	.	PUNCT
easat-2990	17	1	in	in	ADP
easat-2990	17	2	this	this	DET
easat-2990	17	3	work	work	NOUN
easat-2990	17	4	,	,	PUNCT
easat-2990	17	5	we	we	PRON
easat-2990	17	6	propose	propose	VERB
easat-2990	17	7	to	to	PART
easat-2990	17	8	develop	develop	VERB
easat-2990	17	9	different	different	ADJ
easat-2990	17	10	numerical	numerical	ADJ
easat-2990	17	11	approximations	approximation	NOUN
easat-2990	17	12	for	for	ADP
easat-2990	17	13	several	several	ADJ
easat-2990	17	14	infinitely	infinitely	ADV
easat-2990	17	15	dimensional	dimensional	ADJ
easat-2990	17	16	problems	problem	NOUN
easat-2990	17	17	,	,	PUNCT
easat-2990	17	18	such	such	ADJ
easat-2990	17	19	as	as	ADP
easat-2990	17	20	fractional	fractional	ADJ
easat-2990	17	21	cattaneo	cattaneo	PROPN
easat-2990	17	22	-	-	PUNCT
easat-2990	17	23	rayleigh	rayleigh	ADJ
easat-2990	17	24	waves	wave	NOUN
easat-2990	17	25	and	and	CCONJ
easat-2990	17	26	nonlinear	nonlinear	ADJ
easat-2990	17	27	diffusion	diffusion	NOUN
easat-2990	17	28	problems	problem	NOUN
easat-2990	17	29	defined	define	VERB
easat-2990	17	30	on	on	ADP
easat-2990	17	31	unbounded	unbounded	ADJ
easat-2990	17	32	domains	domain	NOUN
easat-2990	17	33	.	.	PUNCT
easat-2990	18	1	the	the	DET
easat-2990	18	2	proposed	propose	VERB
easat-2990	18	3	methods	method	NOUN
easat-2990	18	4	are	be	AUX
easat-2990	18	5	directly	directly	ADV
easat-2990	18	6	applied	apply	VERB
easat-2990	18	7	to	to	ADP
easat-2990	18	8	the	the	DET
easat-2990	18	9	ides	ide	NOUN
easat-2990	18	10	without	without	ADP
easat-2990	18	11	involving	involve	VERB
easat-2990	18	12	any	any	DET
easat-2990	18	13	discretization	discretization	NOUN
easat-2990	18	14	.	.	PUNCT
easat-2990	19	1	according	accord	VERB
easat-2990	19	2	to	to	ADP
easat-2990	19	3	our	our	PRON
easat-2990	19	4	study	study	NOUN
easat-2990	19	5	and	and	CCONJ
easat-2990	19	6	related	related	ADJ
easat-2990	19	7	works	work	NOUN
easat-2990	19	8	,	,	PUNCT
easat-2990	19	9	we	we	PRON
easat-2990	19	10	propose	propose	VERB
easat-2990	19	11	a	a	DET
easat-2990	19	12	simple	simple	ADJ
easat-2990	19	13	and	and	CCONJ
easat-2990	19	14	useful	useful	ADJ
easat-2990	19	15	computational	computational	ADJ
easat-2990	19	16	strategy	strategy	NOUN
easat-2990	19	17	for	for	ADP
easat-2990	19	18	solving	solve	VERB
easat-2990	19	19	the	the	DET
easat-2990	19	20	integer	integer	NOUN
easat-2990	19	21	and	and	CCONJ
easat-2990	19	22	fractional	fractional	ADJ
easat-2990	19	23	-	-	PUNCT
easat-2990	19	24	order	order	NOUN
easat-2990	19	25	cattaneo	cattaneo	ADJ
easat-2990	19	26	-	-	PUNCT
easat-2990	19	27	rayleigh	rayleigh	PROPN
easat-2990	19	28	model	model	NOUN
easat-2990	19	29	of	of	ADP
easat-2990	19	30	thermoelasticity	thermoelasticity	NOUN
easat-2990	19	31	.	.	PUNCT
easat-2990	20	1	the	the	DET
easat-2990	20	2	unified	unified	ADJ
easat-2990	20	3	space	space	NOUN
easat-2990	20	4	-	-	PUNCT
easat-2990	20	5	time	time	NOUN
easat-2990	20	6	differential	differential	ADJ
easat-2990	20	7	/	/	SYM
easat-2990	20	8	integral	integral	ADJ
easat-2990	20	9	form	form	NOUN
easat-2990	20	10	of	of	ADP
easat-2990	20	11	the	the	DET
easat-2990	20	12	equations	equation	NOUN
easat-2990	20	13	is	be	AUX
easat-2990	20	14	considered	consider	VERB
easat-2990	20	15	in	in	ADP
easat-2990	20	16	onedimensional	onedimensional	ADJ
easat-2990	20	17	zonal	zonal	ADJ
easat-2990	20	18	regions	region	NOUN
easat-2990	20	19	.	.	PUNCT
easat-2990	21	1	the	the	DET
easat-2990	21	2	wavelet	wavelet	NOUN
easat-2990	21	3	collocation	collocation	NOUN
easat-2990	21	4	method	method	NOUN
easat-2990	21	5	is	be	AUX
easat-2990	21	6	employed	employ	VERB
easat-2990	21	7	to	to	PART
easat-2990	21	8	find	find	VERB
easat-2990	21	9	an	an	DET
easat-2990	21	10	appropriate	appropriate	ADJ
easat-2990	21	11	numerical	numerical	ADJ
easat-2990	21	12	solution	solution	NOUN
easat-2990	21	13	.	.	PUNCT
easat-2990	22	1	the	the	DET
easat-2990	22	2	numerical	numerical	ADJ
easat-2990	22	3	results	result	NOUN
easat-2990	22	4	show	show	VERB
easat-2990	22	5	the	the	DET
easat-2990	22	6	high	high	ADJ
easat-2990	22	7	efficiency	efficiency	NOUN
easat-2990	22	8	and	and	CCONJ
easat-2990	22	9	good	good	ADJ
easat-2990	22	10	properties	property	NOUN
easat-2990	22	11	of	of	ADP
easat-2990	22	12	our	our	PRON
easat-2990	22	13	proposed	propose	VERB
easat-2990	22	14	methods	method	NOUN
easat-2990	22	15	as	as	SCONJ
easat-2990	22	16	expected	expect	VERB
easat-2990	22	17	.	.	PUNCT
easat-2990	23	1	this	this	DET
easat-2990	23	2	work	work	NOUN
easat-2990	23	3	provides	provide	VERB
easat-2990	23	4	a	a	DET
easat-2990	23	5	creative	creative	ADJ
easat-2990	23	6	toolbox	toolbox	NOUN
easat-2990	23	7	for	for	ADP
easat-2990	23	8	addressing	address	VERB
easat-2990	23	9	questions	question	NOUN
easat-2990	23	10	of	of	ADP
easat-2990	23	11	scientific	scientific	ADJ
easat-2990	23	12	modeling	modeling	NOUN
easat-2990	23	13	and	and	CCONJ
easat-2990	23	14	engineering	engineering	NOUN
easat-2990	23	15	simulations	simulation	NOUN
easat-2990	23	16	that	that	PRON
easat-2990	23	17	naturally	naturally	ADV
easat-2990	23	18	result	result	VERB
easat-2990	23	19	in	in	ADP
easat-2990	23	20	models	model	NOUN
easat-2990	23	21	of	of	ADP
easat-2990	23	22	partial	partial	ADJ
easat-2990	23	23	integro	integro	ADJ
easat-2990	23	24	-	-	PUNCT
easat-2990	23	25	differential	differential	NOUN
easat-2990	23	26	equation	equation	NOUN
easat-2990	23	27	type	type	NOUN
easat-2990	23	28	,	,	PUNCT
easat-2990	23	29	regardless	regardless	ADV
easat-2990	23	30	of	of	ADP
easat-2990	23	31	whether	whether	SCONJ
easat-2990	23	32	the	the	DET
easat-2990	23	33	question	question	NOUN
easat-2990	23	34	was	be	AUX
easat-2990	23	35	asked	ask	VERB
easat-2990	23	36	in	in	ADP
easat-2990	23	37	the	the	DET
easat-2990	23	38	spatial	spatial	ADJ
easat-2990	23	39	or	or	CCONJ
easat-2990	23	40	spatial	spatial	ADJ
easat-2990	23	41	-	-	PUNCT
easat-2990	23	42	frequency	frequency	NOUN
easat-2990	23	43	domain	domain	NOUN
easat-2990	23	44	.	.	PUNCT
easat-2990	24	1	4600	4600	NUM
easat-2990	24	2	edelweiss	edelweiss	PROPN
easat-2990	24	3	applied	apply	VERB
easat-2990	24	4	science	science	NOUN
easat-2990	24	5	and	and	CCONJ
easat-2990	24	6	technology	technology	NOUN
easat-2990	24	7	issn	issn	PROPN
easat-2990	24	8	:	:	PUNCT
easat-2990	24	9	2576	2576	NUM
easat-2990	24	10	-	-	SYM
easat-2990	24	11	8484	8484	NUM
easat-2990	24	12	vol	vol	NOUN
easat-2990	24	13	.	.	PROPN
easat-2990	24	14	8	8	NUM
easat-2990	24	15	,	,	PUNCT
easat-2990	24	16	no	no	INTJ
easat-2990	24	17	.	.	NOUN
easat-2990	25	1	6	6	NUM
easat-2990	25	2	:	:	SYM
easat-2990	25	3	4599	4599	NUM
easat-2990	25	4	-	-	SYM
easat-2990	25	5	4610	4610	NUM
easat-2990	25	6	,	,	PUNCT
easat-2990	25	7	2024	2024	NUM
easat-2990	25	8	doi	doi	NOUN
easat-2990	25	9	:	:	PUNCT
easat-2990	25	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	25	11	©	©	PROPN
easat-2990	25	12	2024	2024	NUM
easat-2990	25	13	by	by	ADP
easat-2990	25	14	the	the	DET
easat-2990	25	15	author	author	NOUN
easat-2990	25	16	;	;	PUNCT
easat-2990	25	17	licensee	licensee	PROPN
easat-2990	25	18	learning	learning	NOUN
easat-2990	25	19	gate	gate	NOUN
easat-2990	25	20	prompt	prompt	ADJ
easat-2990	25	21	progress	progress	NOUN
easat-2990	25	22	is	be	AUX
easat-2990	25	23	motivated	motivate	VERB
easat-2990	25	24	by	by	ADP
easat-2990	25	25	the	the	DET
easat-2990	25	26	universal	universal	ADJ
easat-2990	25	27	quality	quality	NOUN
easat-2990	25	28	of	of	ADP
easat-2990	25	29	questions	question	NOUN
easat-2990	25	30	that	that	PRON
easat-2990	25	31	lead	lead	VERB
easat-2990	25	32	to	to	ADP
easat-2990	25	33	partial	partial	ADJ
easat-2990	25	34	integrodifferential	integrodifferential	ADJ
easat-2990	25	35	equation	equation	NOUN
easat-2990	25	36	model	model	NOUN
easat-2990	25	37	forms	form	NOUN
easat-2990	25	38	in	in	ADP
easat-2990	25	39	application	application	NOUN
easat-2990	25	40	areas	area	NOUN
easat-2990	25	41	such	such	ADJ
easat-2990	25	42	as	as	ADP
easat-2990	25	43	biology	biology	NOUN
easat-2990	25	44	,	,	PUNCT
easat-2990	25	45	mechanical	mechanical	ADJ
easat-2990	25	46	signal	signal	NOUN
easat-2990	25	47	processing	processing	NOUN
easat-2990	25	48	,	,	PUNCT
easat-2990	25	49	and	and	CCONJ
easat-2990	25	50	digital	digital	ADJ
easat-2990	25	51	communications	communication	NOUN
easat-2990	25	52	.	.	PUNCT
easat-2990	26	1	1.1	1.1	NUM
easat-2990	26	2	.	.	PUNCT
easat-2990	27	1	definition	definition	NOUN
easat-2990	27	2	and	and	CCONJ
easat-2990	27	3	characteristics	characteristic	NOUN
easat-2990	27	4	wavelets	wavelet	NOUN
easat-2990	27	5	are	be	AUX
easat-2990	27	6	defined	define	VERB
easat-2990	27	7	as	as	ADP
easat-2990	27	8	functions	function	NOUN
easat-2990	27	9	that	that	PRON
easat-2990	27	10	satisfy	satisfy	VERB
easat-2990	27	11	certain	certain	ADJ
easat-2990	27	12	conditions	condition	NOUN
easat-2990	27	13	related	relate	VERB
easat-2990	27	14	to	to	ADP
easat-2990	27	15	orthogonality	orthogonality	NOUN
easat-2990	27	16	and	and	CCONJ
easat-2990	27	17	to	to	ADP
easat-2990	27	18	adaptive	adaptive	ADJ
easat-2990	27	19	coarse	coarse	ADJ
easat-2990	27	20	grid	grid	NOUN
easat-2990	27	21	representations	representation	NOUN
easat-2990	27	22	.	.	PUNCT
easat-2990	28	1	they	they	PRON
easat-2990	28	2	describe	describe	VERB
easat-2990	28	3	the	the	DET
easat-2990	28	4	singularity	singularity	NOUN
easat-2990	28	5	content	content	NOUN
easat-2990	28	6	of	of	ADP
easat-2990	28	7	a	a	DET
easat-2990	28	8	function	function	NOUN
easat-2990	28	9	and	and	CCONJ
easat-2990	28	10	have	have	VERB
easat-2990	28	11	the	the	DET
easat-2990	28	12	remarkable	remarkable	ADJ
easat-2990	28	13	property	property	NOUN
easat-2990	28	14	of	of	ADP
easat-2990	28	15	local	local	ADJ
easat-2990	28	16	description	description	NOUN
easat-2990	28	17	in	in	ADP
easat-2990	28	18	both	both	DET
easat-2990	28	19	time	time	NOUN
easat-2990	28	20	and	and	CCONJ
easat-2990	28	21	frequency	frequency	NOUN
easat-2990	28	22	.	.	PUNCT
easat-2990	29	1	the	the	DET
easat-2990	29	2	heaviest	heavy	ADJ
easat-2990	29	3	signal	signal	NOUN
easat-2990	29	4	features	feature	NOUN
easat-2990	29	5	are	be	AUX
easat-2990	29	6	less	less	ADV
easat-2990	29	7	well	well	ADV
easat-2990	29	8	represented	represent	VERB
easat-2990	29	9	as	as	ADP
easat-2990	29	10	a	a	DET
easat-2990	29	11	function	function	NOUN
easat-2990	29	12	of	of	ADP
easat-2990	29	13	time	time	NOUN
easat-2990	29	14	than	than	ADP
easat-2990	29	15	the	the	DET
easat-2990	29	16	lighter	light	ADJ
easat-2990	29	17	ones	one	NOUN
easat-2990	29	18	.	.	PUNCT
easat-2990	30	1	conversely	conversely	ADV
easat-2990	30	2	,	,	PUNCT
easat-2990	30	3	the	the	DET
easat-2990	30	4	most	most	ADV
easat-2990	30	5	rapid	rapid	ADJ
easat-2990	30	6	time	time	NOUN
easat-2990	30	7	fluctuations	fluctuation	NOUN
easat-2990	30	8	of	of	ADP
easat-2990	30	9	the	the	DET
easat-2990	30	10	signal	signal	NOUN
easat-2990	30	11	can	can	AUX
easat-2990	30	12	be	be	AUX
easat-2990	30	13	the	the	DET
easat-2990	30	14	least	least	ADJ
easat-2990	30	15	precisely	precisely	ADV
easat-2990	30	16	represented	represent	VERB
easat-2990	30	17	in	in	ADP
easat-2990	30	18	the	the	DET
easat-2990	30	19	frequency	frequency	NOUN
easat-2990	30	20	domain[3	domain[3	PROPN
easat-2990	30	21	]	]	PUNCT
easat-2990	30	22	.	.	PUNCT
easat-2990	31	1	consider	consider	VERB
easat-2990	31	2	each	each	DET
easat-2990	31	3	wavelet	wavelet	NOUN
easat-2990	31	4	,	,	PUNCT
easat-2990	31	5	ψ	ψ	X
easat-2990	31	6	,	,	PUNCT
easat-2990	31	7	as	as	ADP
easat-2990	31	8	a	a	DET
easat-2990	31	9	filter	filter	NOUN
easat-2990	31	10	,	,	PUNCT
easat-2990	31	11	constructed	construct	VERB
easat-2990	31	12	so	so	SCONJ
easat-2990	31	13	that	that	SCONJ
easat-2990	31	14	the	the	DET
easat-2990	31	15	output	output	NOUN
easat-2990	31	16	(	(	PUNCT
easat-2990	31	17	y	y	NOUN
easat-2990	31	18	)	)	PUNCT
easat-2990	31	19	can	can	AUX
easat-2990	31	20	be	be	AUX
easat-2990	31	21	interpreted	interpret	VERB
easat-2990	31	22	as	as	ADP
easat-2990	31	23	the	the	DET
easat-2990	31	24	convolution	convolution	NOUN
easat-2990	31	25	of	of	ADP
easat-2990	31	26	f	f	PROPN
easat-2990	31	27	with	with	ADP
easat-2990	31	28	the	the	DET
easat-2990	31	29	wavelet	wavelet	NOUN
easat-2990	31	30	.	.	PUNCT
easat-2990	32	1	for	for	ADP
easat-2990	32	2	a	a	DET
easat-2990	32	3	fixed	fix	VERB
easat-2990	32	4	value	value	NOUN
easat-2990	32	5	of	of	ADP
easat-2990	32	6	m	m	PROPN
easat-2990	32	7	,	,	PUNCT
easat-2990	32	8	this	this	PRON
easat-2990	32	9	yields	yield	VERB
easat-2990	32	10	important	important	ADJ
easat-2990	32	11	information	information	NOUN
easat-2990	32	12	about	about	ADP
easat-2990	32	13	the	the	DET
easat-2990	32	14	local	local	ADJ
easat-2990	32	15	behavior	behavior	NOUN
easat-2990	32	16	of	of	ADP
easat-2990	32	17	f	f	PROPN
easat-2990	32	18	on	on	ADP
easat-2990	32	19	the	the	DET
easat-2990	32	20	time	time	NOUN
easat-2990	32	21	interval	interval	NOUN
easat-2990	32	22	plus	plus	CCONJ
easat-2990	32	23	or	or	CCONJ
easat-2990	32	24	minus	minus	CCONJ
easat-2990	32	25	m.	m.	NOUN
easat-2990	32	26	we	we	PRON
easat-2990	32	27	can	can	AUX
easat-2990	32	28	thus	thus	ADV
easat-2990	32	29	interpret	interpret	VERB
easat-2990	32	30	wf(m	wf(m	PRON
easat-2990	32	31	,	,	PUNCT
easat-2990	32	32	n	n	CCONJ
easat-2990	32	33	)	)	PUNCT
easat-2990	32	34	as	as	ADP
easat-2990	32	35	a	a	DET
easat-2990	32	36	scaled	scale	VERB
easat-2990	32	37	and	and	CCONJ
easat-2990	32	38	phase	phase	NOUN
easat-2990	32	39	-	-	PUNCT
easat-2990	32	40	shifted	shift	VERB
easat-2990	32	41	version	version	NOUN
easat-2990	32	42	of	of	ADP
easat-2990	32	43	a	a	DET
easat-2990	32	44	wavelet	wavelet	NOUN
easat-2990	32	45	function	function	NOUN
easat-2990	32	46	ψ	ψ	NOUN
easat-2990	32	47	;	;	PUNCT
easat-2990	32	48	the	the	DET
easat-2990	32	49	parameter	parameter	NOUN
easat-2990	32	50	m	m	VERB
easat-2990	32	51	we	we	PRON
easat-2990	32	52	call	call	VERB
easat-2990	32	53	scale	scale	NOUN
easat-2990	32	54	and	and	CCONJ
easat-2990	32	55	n	n	NOUN
easat-2990	32	56	is	be	AUX
easat-2990	32	57	the	the	DET
easat-2990	32	58	shift	shift	NOUN
easat-2990	32	59	parameter[4	parameter[4	ADP
easat-2990	32	60	]	]	PUNCT
easat-2990	32	61	.	.	PUNCT
easat-2990	33	1	each	each	DET
easat-2990	33	2	wavelet	wavelet	NOUN
easat-2990	33	3	basis	basis	NOUN
easat-2990	33	4	function	function	NOUN
easat-2990	33	5	provides	provide	VERB
easat-2990	33	6	the	the	DET
easat-2990	33	7	local	local	ADJ
easat-2990	33	8	average	average	NOUN
easat-2990	33	9	of	of	ADP
easat-2990	33	10	the	the	DET
easat-2990	33	11	function	function	NOUN
easat-2990	33	12	f	f	PROPN
easat-2990	33	13	over	over	ADP
easat-2990	33	14	a	a	DET
easat-2990	33	15	region	region	NOUN
easat-2990	33	16	of	of	ADP
easat-2990	33	17	the	the	DET
easat-2990	33	18	order	order	NOUN
easat-2990	33	19	of	of	ADP
easat-2990	33	20	plus	plus	CCONJ
easat-2990	33	21	or	or	CCONJ
easat-2990	33	22	minus	minus	CCONJ
easat-2990	33	23	m	m	PROPN
easat-2990	33	24	near	near	ADP
easat-2990	33	25	n.	n.	PROPN
easat-2990	33	26	this	this	DET
easat-2990	33	27	adaptive	adaptive	ADJ
easat-2990	33	28	aspect	aspect	NOUN
easat-2990	33	29	makes	make	VERB
easat-2990	33	30	the	the	DET
easat-2990	33	31	wavelet	wavelet	NOUN
easat-2990	33	32	transform	transform	VERB
easat-2990	33	33	an	an	DET
easat-2990	33	34	excellent	excellent	ADJ
easat-2990	33	35	tool	tool	NOUN
easat-2990	33	36	for	for	ADP
easat-2990	33	37	both	both	DET
easat-2990	33	38	time	time	NOUN
easat-2990	33	39	and	and	CCONJ
easat-2990	33	40	frequency	frequency	NOUN
easat-2990	33	41	analysis	analysis	NOUN
easat-2990	33	42	.	.	PUNCT
easat-2990	34	1	by	by	ADP
easat-2990	34	2	choosing	choose	VERB
easat-2990	34	3	different	different	ADJ
easat-2990	34	4	scales	scale	NOUN
easat-2990	34	5	and	and	CCONJ
easat-2990	34	6	the	the	DET
easat-2990	34	7	same	same	ADJ
easat-2990	34	8	positions	position	NOUN
easat-2990	34	9	at	at	ADP
easat-2990	34	10	the	the	DET
easat-2990	34	11	grid	grid	NOUN
easat-2990	34	12	points	point	NOUN
easat-2990	34	13	,	,	PUNCT
easat-2990	34	14	we	we	PRON
easat-2990	34	15	go	go	VERB
easat-2990	34	16	from	from	ADP
easat-2990	34	17	the	the	DET
easat-2990	34	18	behavior	behavior	NOUN
easat-2990	34	19	of	of	ADP
easat-2990	34	20	the	the	DET
easat-2990	34	21	signal	signal	NOUN
easat-2990	34	22	at	at	ADP
easat-2990	34	23	the	the	DET
easat-2990	34	24	location	location	NOUN
easat-2990	34	25	to	to	ADP
easat-2990	34	26	that	that	PRON
easat-2990	34	27	at	at	ADP
easat-2990	34	28	the	the	DET
easat-2990	34	29	frequency[5	frequency[5	NOUN
easat-2990	34	30	]	]	X
easat-2990	34	31	.	.	PUNCT
easat-2990	35	1	1.2	1.2	NUM
easat-2990	35	2	.	.	PUNCT
easat-2990	35	3	importance	importance	NOUN
easat-2990	35	4	and	and	CCONJ
easat-2990	35	5	applications	application	NOUN
easat-2990	35	6	the	the	DET
easat-2990	35	7	numerical	numerical	ADJ
easat-2990	35	8	approximation	approximation	NOUN
easat-2990	35	9	of	of	ADP
easat-2990	35	10	wavelet	wavelet	NOUN
easat-2990	35	11	methods	method	NOUN
easat-2990	35	12	is	be	AUX
easat-2990	35	13	a	a	DET
easat-2990	35	14	powerful	powerful	ADJ
easat-2990	35	15	approach	approach	NOUN
easat-2990	35	16	for	for	ADP
easat-2990	35	17	multi	multi	ADJ
easat-2990	35	18	-	-	ADJ
easat-2990	35	19	dimensional	dimensional	ADJ
easat-2990	35	20	problems	problem	NOUN
easat-2990	35	21	as	as	ADV
easat-2990	35	22	well	well	ADV
easat-2990	35	23	as	as	ADP
easat-2990	35	24	for	for	ADP
easat-2990	35	25	high	high	ADJ
easat-2990	35	26	-	-	PUNCT
easat-2990	35	27	dimensional	dimensional	ADJ
easat-2990	35	28	problems[6	problems[6	NOUN
easat-2990	35	29	]	]	X
easat-2990	35	30	.	.	PUNCT
easat-2990	36	1	it	it	PRON
easat-2990	36	2	is	be	AUX
easat-2990	36	3	less	less	ADV
easat-2990	36	4	difficult	difficult	ADJ
easat-2990	36	5	than	than	SCONJ
easat-2990	36	6	established	establish	VERB
easat-2990	36	7	discretization	discretization	NOUN
easat-2990	36	8	and	and	CCONJ
easat-2990	36	9	optimization	optimization	NOUN
easat-2990	36	10	methods	method	NOUN
easat-2990	36	11	like	like	ADP
easat-2990	36	12	finite	finite	ADJ
easat-2990	36	13	elements	element	NOUN
easat-2990	36	14	,	,	PUNCT
easat-2990	36	15	finite	finite	VERB
easat-2990	36	16	differences	difference	NOUN
easat-2990	36	17	,	,	PUNCT
easat-2990	36	18	higher	high	ADJ
easat-2990	36	19	order	order	NOUN
easat-2990	36	20	symbol	symbol	NOUN
easat-2990	36	21	methods	method	NOUN
easat-2990	36	22	,	,	PUNCT
easat-2990	36	23	wellconditioned	wellconditione	VERB
easat-2990	36	24	pseudo	pseudo	NOUN
easat-2990	36	25	-	-	ADJ
easat-2990	36	26	spectral	spectral	ADJ
easat-2990	36	27	methods	method	NOUN
easat-2990	36	28	,	,	PUNCT
easat-2990	36	29	and	and	CCONJ
easat-2990	36	30	dynamically	dynamically	ADV
easat-2990	36	31	orthogonal	orthogonal	ADJ
easat-2990	36	32	collocation	collocation	NOUN
easat-2990	36	33	methods	method	NOUN
easat-2990	36	34	for	for	ADP
easat-2990	36	35	highdimensional	highdimensional	ADJ
easat-2990	36	36	problems	problem	NOUN
easat-2990	36	37	.	.	PUNCT
easat-2990	37	1	most	most	ADJ
easat-2990	37	2	of	of	ADP
easat-2990	37	3	these	these	DET
easat-2990	37	4	methods	method	NOUN
easat-2990	37	5	need	need	VERB
easat-2990	37	6	complex	complex	ADJ
easat-2990	37	7	suitable	suitable	ADJ
easat-2990	37	8	and	and	CCONJ
easat-2990	37	9	massive	massive	ADJ
easat-2990	37	10	basis	basis	NOUN
easat-2990	37	11	functions	function	NOUN
easat-2990	37	12	or	or	CCONJ
easat-2990	37	13	non	non	ADJ
easat-2990	37	14	-	-	ADJ
easat-2990	37	15	trivial	trivial	ADJ
easat-2990	37	16	algorithms	algorithm	NOUN
easat-2990	37	17	.	.	PUNCT
easat-2990	38	1	theoretical	theoretical	ADJ
easat-2990	38	2	error	error	NOUN
easat-2990	38	3	estimates	estimate	NOUN
easat-2990	38	4	for	for	ADP
easat-2990	38	5	functions	function	NOUN
easat-2990	38	6	and	and	CCONJ
easat-2990	38	7	fully	fully	ADV
easat-2990	38	8	nonlinear	nonlinear	ADJ
easat-2990	38	9	differential	differential	ADJ
easat-2990	38	10	equations	equation	NOUN
easat-2990	38	11	are	be	AUX
easat-2990	38	12	often	often	ADV
easat-2990	38	13	not	not	PART
easat-2990	38	14	available	available	ADJ
easat-2990	38	15	,	,	PUNCT
easat-2990	38	16	since	since	SCONJ
easat-2990	38	17	the	the	DET
easat-2990	38	18	growth	growth	NOUN
easat-2990	38	19	rate	rate	NOUN
easat-2990	38	20	of	of	ADP
easat-2990	38	21	the	the	DET
easat-2990	38	22	nodes	node	NOUN
easat-2990	38	23	is	be	AUX
easat-2990	38	24	not	not	PART
easat-2990	38	25	sufficiently	sufficiently	ADV
easat-2990	38	26	well	well	ADV
easat-2990	38	27	controlled[7	controlled[7	ADJ
easat-2990	38	28	]	]	X
easat-2990	38	29	.	.	PUNCT
easat-2990	39	1	wavelet	wavelet	NOUN
easat-2990	39	2	methods	method	NOUN
easat-2990	39	3	can	can	AUX
easat-2990	39	4	facilitate	facilitate	VERB
easat-2990	39	5	analytical	analytical	ADJ
easat-2990	39	6	and	and	CCONJ
easat-2990	39	7	recommended	recommend	VERB
easat-2990	39	8	solutions	solution	NOUN
easat-2990	39	9	due	due	ADP
easat-2990	39	10	to	to	ADP
easat-2990	39	11	the	the	DET
easat-2990	39	12	wavelet	wavelet	NOUN
easat-2990	39	13	arrangement	arrangement	NOUN
easat-2990	39	14	and	and	CCONJ
easat-2990	39	15	amplification	amplification	NOUN
easat-2990	39	16	approach	approach	NOUN
easat-2990	39	17	.	.	PUNCT
easat-2990	40	1	parametric	parametric	ADJ
easat-2990	40	2	estimates	estimate	NOUN
easat-2990	40	3	for	for	ADP
easat-2990	40	4	scalar	scalar	ADJ
easat-2990	40	5	wavelets	wavelet	NOUN
easat-2990	40	6	and	and	CCONJ
easat-2990	40	7	unrestricted	unrestricted	ADJ
easat-2990	40	8	higher	high	ADJ
easat-2990	40	9	order	order	NOUN
easat-2990	40	10	spectral	spectral	ADJ
easat-2990	40	11	sparsity	sparsity	NOUN
easat-2990	40	12	or	or	CCONJ
easat-2990	40	13	near	near	ADV
easat-2990	40	14	-	-	PUNCT
easat-2990	40	15	best	good	ADJ
easat-2990	40	16	locality	locality	NOUN
easat-2990	40	17	for	for	ADP
easat-2990	40	18	wavelet	wavelet	NOUN
easat-2990	40	19	systems	system	NOUN
easat-2990	40	20	allow	allow	VERB
easat-2990	40	21	for	for	ADP
easat-2990	40	22	well	well	ADV
easat-2990	40	23	-	-	PUNCT
easat-2990	40	24	approximative	approximative	ADJ
easat-2990	40	25	and	and	CCONJ
easat-2990	40	26	non	non	ADJ
easat-2990	40	27	-	-	ADJ
easat-2990	40	28	linear	linear	ADJ
easat-2990	40	29	approximation	approximation	NOUN
easat-2990	40	30	order[8	order[8	NOUN
easat-2990	40	31	]	]	PUNCT
easat-2990	40	32	.	.	PUNCT
easat-2990	41	1	all	all	DET
easat-2990	41	2	these	these	DET
easat-2990	41	3	issues	issue	NOUN
easat-2990	41	4	reduce	reduce	VERB
easat-2990	41	5	the	the	DET
easat-2990	41	6	complexity	complexity	NOUN
easat-2990	41	7	of	of	ADP
easat-2990	41	8	developing	develop	VERB
easat-2990	41	9	automatic	automatic	ADJ
easat-2990	41	10	wavelet	wavelet	NOUN
easat-2990	41	11	methods	method	NOUN
easat-2990	41	12	with	with	ADP
easat-2990	41	13	optimal	optimal	ADJ
easat-2990	41	14	solutions	solution	NOUN
easat-2990	41	15	and	and	CCONJ
easat-2990	41	16	wavelet	wavelet	NOUN
easat-2990	41	17	methods	method	NOUN
easat-2990	41	18	with	with	ADP
easat-2990	41	19	parametric	parametric	ADJ
easat-2990	41	20	enhancement[9	enhancement[9	PROPN
easat-2990	41	21	]	]	PUNCT
easat-2990	41	22	.	.	PUNCT
easat-2990	42	1	automatic	automatic	ADJ
easat-2990	42	2	wavelet	wavelet	NOUN
easat-2990	42	3	methods	method	NOUN
easat-2990	42	4	are	be	AUX
easat-2990	42	5	now	now	ADV
easat-2990	42	6	well	well	ADV
easat-2990	42	7	-	-	PUNCT
easat-2990	42	8	developed	develop	VERB
easat-2990	42	9	for	for	ADP
easat-2990	42	10	periodic	periodic	ADJ
easat-2990	42	11	and	and	CCONJ
easat-2990	42	12	order	order	NOUN
easat-2990	42	13	-	-	PUNCT
easat-2990	42	14	wise	wise	ADJ
easat-2990	42	15	approximable	approximable	ADJ
easat-2990	42	16	scalar	scalar	ADJ
easat-2990	42	17	systems	system	NOUN
easat-2990	42	18	,	,	PUNCT
easat-2990	42	19	systems	system	NOUN
easat-2990	42	20	with	with	ADP
easat-2990	42	21	functional	functional	ADJ
easat-2990	42	22	physical	physical	ADJ
easat-2990	42	23	singularities	singularity	NOUN
easat-2990	42	24	,	,	PUNCT
easat-2990	42	25	strong	strong	ADJ
easat-2990	42	26	field	field	NOUN
easat-2990	42	27	singularities	singularity	NOUN
easat-2990	42	28	,	,	PUNCT
easat-2990	42	29	and	and	CCONJ
easat-2990	42	30	vector	vector	NOUN
easat-2990	42	31	-	-	PUNCT
easat-2990	42	32	valued	value	VERB
easat-2990	42	33	physical	physical	ADJ
easat-2990	42	34	singularities	singularity	NOUN
easat-2990	42	35	,	,	PUNCT
easat-2990	42	36	i.e.	i.e.	X
easat-2990	42	37	,	,	PUNCT
easat-2990	42	38	fluid	fluid	ADJ
easat-2990	42	39	dynamics	dynamic	NOUN
easat-2990	42	40	velocity	velocity	NOUN
easat-2990	42	41	derivatives[10	derivatives[10	X
easat-2990	42	42	]	]	X
easat-2990	42	43	.	.	PUNCT
easat-2990	43	1	for	for	ADP
easat-2990	43	2	systems	system	NOUN
easat-2990	43	3	with	with	ADP
easat-2990	43	4	differential	differential	ADJ
easat-2990	43	5	physical	physical	ADJ
easat-2990	43	6	singularities	singularity	NOUN
easat-2990	43	7	,	,	PUNCT
easat-2990	43	8	the	the	DET
easat-2990	43	9	corresponding	corresponding	ADJ
easat-2990	43	10	well	well	ADV
easat-2990	43	11	-	-	PUNCT
easat-2990	43	12	developed	develop	VERB
easat-2990	43	13	wavelet	wavelet	NOUN
easat-2990	43	14	methods	method	NOUN
easat-2990	43	15	have	have	AUX
easat-2990	43	16	been	be	AUX
easat-2990	43	17	driven	drive	VERB
easat-2990	43	18	in	in	ADP
easat-2990	43	19	the	the	DET
easat-2990	43	20	case	case	NOUN
easat-2990	43	21	of	of	ADP
easat-2990	43	22	differential	differential	NOUN
easat-2990	43	23	equations[11	equations[11	X
easat-2990	43	24	]	]	PUNCT
easat-2990	43	25	.	.	PUNCT
easat-2990	44	1	2	2	X
easat-2990	44	2	.	.	X
easat-2990	44	3	wavelet	wavelet	NOUN
easat-2990	44	4	theory	theory	NOUN
easat-2990	44	5	and	and	CCONJ
easat-2990	44	6	applications	application	NOUN
easat-2990	44	7	an	an	DET
easat-2990	44	8	overview	overview	NOUN
easat-2990	44	9	of	of	ADP
easat-2990	44	10	wavelet	wavelet	NOUN
easat-2990	44	11	theory	theory	NOUN
easat-2990	44	12	we	we	PRON
easat-2990	44	13	dedicate	dedicate	VERB
easat-2990	44	14	this	this	DET
easat-2990	44	15	section	section	NOUN
easat-2990	44	16	to	to	PART
easat-2990	44	17	deliver	deliver	VERB
easat-2990	44	18	basic	basic	ADJ
easat-2990	44	19	wavelet	wavelet	NOUN
easat-2990	44	20	theory	theory	NOUN
easat-2990	44	21	,	,	PUNCT
easat-2990	44	22	which	which	PRON
easat-2990	44	23	we	we	PRON
easat-2990	44	24	will	will	AUX
easat-2990	44	25	apply	apply	VERB
easat-2990	44	26	throughout	throughout	ADP
easat-2990	44	27	this	this	DET
easat-2990	44	28	paper	paper	NOUN
easat-2990	44	29	.	.	PUNCT
easat-2990	45	1	specifically	specifically	ADV
easat-2990	45	2	,	,	PUNCT
easat-2990	45	3	several	several	ADJ
easat-2990	45	4	basic	basic	ADJ
easat-2990	45	5	properties	property	NOUN
easat-2990	45	6	of	of	ADP
easat-2990	45	7	wavelets	wavelet	NOUN
easat-2990	45	8	are	be	AUX
easat-2990	45	9	given	give	VERB
easat-2990	45	10	.	.	PUNCT
easat-2990	46	1	the	the	DET
easat-2990	46	2	wavelet	wavelet	NOUN
easat-2990	46	3	transform	transform	NOUN
easat-2990	46	4	and	and	CCONJ
easat-2990	46	5	its	its	PRON
easat-2990	46	6	inverse	inverse	NOUN
easat-2990	46	7	are	be	AUX
easat-2990	46	8	then	then	ADV
easat-2990	46	9	discussed	discuss	VERB
easat-2990	46	10	.	.	PUNCT
easat-2990	47	1	the	the	DET
easat-2990	47	2	mother	mother	NOUN
easat-2990	47	3	wavelet	wavelet	NOUN
easat-2990	47	4	and	and	CCONJ
easat-2990	47	5	its	its	PRON
easat-2990	47	6	dilations	dilation	NOUN
easat-2990	47	7	and	and	CCONJ
easat-2990	47	8	shifts	shift	NOUN
easat-2990	47	9	lead	lead	VERB
easat-2990	47	10	to	to	ADP
easat-2990	47	11	continuous	continuous	ADJ
easat-2990	47	12	wavelets	wavelet	NOUN
easat-2990	47	13	for	for	ADP
easat-2990	47	14	continuous	continuous	ADJ
easat-2990	47	15	signal	signal	NOUN
easat-2990	47	16	treatment	treatment	NOUN
easat-2990	47	17	.	.	PUNCT
easat-2990	48	1	multiresolution	multiresolution	NOUN
easat-2990	48	2	analysis	analysis	NOUN
easat-2990	48	3	provides	provide	VERB
easat-2990	48	4	a	a	DET
easat-2990	48	5	systematic	systematic	ADJ
easat-2990	48	6	way	way	NOUN
easat-2990	48	7	to	to	PART
easat-2990	48	8	design	design	VERB
easat-2990	48	9	bi	bi	ADJ
easat-2990	48	10	-	-	ADJ
easat-2990	48	11	orthogonal	orthogonal	ADJ
easat-2990	48	12	wavelet	wavelet	NOUN
easat-2990	48	13	bases	basis	NOUN
easat-2990	48	14	,	,	PUNCT
easat-2990	48	15	thus	thus	ADV
easat-2990	48	16	allowing	allow	VERB
easat-2990	48	17	manipulation	manipulation	NOUN
easat-2990	48	18	of	of	ADP
easat-2990	48	19	the	the	DET
easat-2990	48	20	transform	transform	NOUN
easat-2990	48	21	space	space	NOUN
easat-2990	48	22	.	.	PUNCT
easat-2990	49	1	at	at	ADP
easat-2990	49	2	the	the	DET
easat-2990	49	3	end	end	NOUN
easat-2990	49	4	of	of	ADP
easat-2990	49	5	this	this	DET
easat-2990	49	6	section	section	NOUN
easat-2990	49	7	,	,	PUNCT
easat-2990	49	8	some	some	DET
easat-2990	49	9	wavelet	wavelet	NOUN
easat-2990	49	10	bases	basis	NOUN
easat-2990	49	11	will	will	AUX
easat-2990	49	12	be	be	AUX
easat-2990	49	13	given[12	given[12	PROPN
easat-2990	49	14	]	]	X
easat-2990	49	15	.	.	PUNCT
easat-2990	50	1	wavelet	wavelet	NOUN
easat-2990	50	2	series	series	PROPN
easat-2990	50	3	we	we	PRON
easat-2990	50	4	may	may	AUX
easat-2990	50	5	think	think	VERB
easat-2990	50	6	of	of	ADP
easat-2990	50	7	the	the	DET
easat-2990	50	8	expansion	expansion	NOUN
easat-2990	50	9	of	of	ADP
easat-2990	50	10	a	a	DET
easat-2990	50	11	given	give	VERB
easat-2990	50	12	function	function	NOUN
easat-2990	50	13	in	in	ADP
easat-2990	50	14	several	several	ADJ
easat-2990	50	15	series	series	NOUN
easat-2990	50	16	.	.	PUNCT
easat-2990	51	1	this	this	PRON
easat-2990	51	2	is	be	AUX
easat-2990	51	3	due	due	ADJ
easat-2990	51	4	to	to	ADP
easat-2990	51	5	the	the	DET
easat-2990	51	6	partition	partition	NOUN
easat-2990	51	7	of	of	ADP
easat-2990	51	8	unity	unity	NOUN
easat-2990	51	9	rendered	render	VERB
easat-2990	51	10	by	by	ADP
easat-2990	51	11	the	the	DET
easat-2990	51	12	scaling	scaling	NOUN
easat-2990	51	13	and	and	CCONJ
easat-2990	51	14	the	the	DET
easat-2990	51	15	mother	mother	NOUN
easat-2990	51	16	wavelet	wavelet	NOUN
easat-2990	51	17	functions	function	NOUN
easat-2990	51	18	associated	associate	VERB
easat-2990	51	19	with	with	ADP
easat-2990	51	20	the	the	DET
easat-2990	51	21	multiresolution	multiresolution	NOUN
easat-2990	51	22	analysis[13	analysis[13	NOUN
easat-2990	51	23	]	]	PUNCT
easat-2990	51	24	.	.	PUNCT
easat-2990	52	1	wavelet	wavelet	NOUN
easat-2990	52	2	bases	basis	NOUN
easat-2990	52	3	of	of	ADP
easat-2990	52	4	finite	finite	PROPN
easat-2990	52	5	l2(d	l2(d	NOUN
easat-2990	52	6	)	)	PUNCT
easat-2990	52	7	functions	function	NOUN
easat-2990	52	8	in	in	ADP
easat-2990	52	9	l2(r	l2(r	NOUN
easat-2990	52	10	)	)	PUNCT
easat-2990	52	11	may	may	AUX
easat-2990	52	12	be	be	AUX
easat-2990	52	13	approximated	approximate	VERB
easat-2990	52	14	in	in	ADP
easat-2990	52	15	the	the	DET
easat-2990	52	16	sense	sense	NOUN
easat-2990	52	17	of	of	ADP
easat-2990	52	18	mean	mean	NOUN
easat-2990	52	19	as	as	ADP
easat-2990	52	20	a	a	DET
easat-2990	52	21	linear	linear	ADJ
easat-2990	52	22	combination	combination	NOUN
easat-2990	52	23	of	of	ADP
easat-2990	52	24	a	a	DET
easat-2990	52	25	subset	subset	NOUN
easat-2990	52	26	of	of	ADP
easat-2990	52	27	some	some	DET
easat-2990	52	28	other	other	ADJ
easat-2990	52	29	functions	function	NOUN
easat-2990	52	30	.	.	PUNCT
easat-2990	53	1	in	in	ADP
easat-2990	53	2	general	general	ADJ
easat-2990	53	3	,	,	PUNCT
easat-2990	53	4	l2(r	l2(r	PROPN
easat-2990	53	5	)	)	PUNCT
easat-2990	53	6	is	be	AUX
easat-2990	53	7	given	give	VERB
easat-2990	53	8	a	a	DET
easat-2990	53	9	multiresolution	multiresolution	NOUN
easat-2990	53	10	4601	4601	NUM
easat-2990	53	11	edelweiss	edelweiss	PROPN
easat-2990	53	12	applied	apply	VERB
easat-2990	53	13	science	science	NOUN
easat-2990	53	14	and	and	CCONJ
easat-2990	53	15	technology	technology	NOUN
easat-2990	53	16	issn	issn	PROPN
easat-2990	53	17	:	:	PUNCT
easat-2990	53	18	2576	2576	NUM
easat-2990	53	19	-	-	SYM
easat-2990	53	20	8484	8484	NUM
easat-2990	53	21	vol	vol	NOUN
easat-2990	53	22	.	.	PROPN
easat-2990	53	23	8	8	NUM
easat-2990	53	24	,	,	PUNCT
easat-2990	53	25	no	no	INTJ
easat-2990	53	26	.	.	NOUN
easat-2990	54	1	6	6	NUM
easat-2990	54	2	:	:	SYM
easat-2990	54	3	4599	4599	NUM
easat-2990	54	4	-	-	SYM
easat-2990	54	5	4610	4610	NUM
easat-2990	54	6	,	,	PUNCT
easat-2990	54	7	2024	2024	NUM
easat-2990	54	8	doi	doi	NOUN
easat-2990	54	9	:	:	PUNCT
easat-2990	54	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	54	11	©	©	PROPN
easat-2990	54	12	2024	2024	NUM
easat-2990	54	13	by	by	ADP
easat-2990	54	14	the	the	DET
easat-2990	54	15	author	author	NOUN
easat-2990	54	16	;	;	PUNCT
easat-2990	55	1	licensee	licensee	NOUN
easat-2990	55	2	learning	learn	VERB
easat-2990	55	3	gate	gate	NOUN
easat-2990	55	4	structure	structure	NOUN
easat-2990	55	5	(	(	PUNCT
easat-2990	55	6	vj)j∈z	vj)j∈z	NUM
easat-2990	55	7	.	.	PUNCT
easat-2990	56	1	moreover	moreover	ADV
easat-2990	56	2	,	,	PUNCT
easat-2990	56	3	functions	function	NOUN
easat-2990	56	4	in	in	ADP
easat-2990	56	5	vj	vj	PROPN
easat-2990	56	6	may	may	AUX
easat-2990	56	7	be	be	AUX
easat-2990	56	8	inherited	inherit	VERB
easat-2990	56	9	with	with	ADP
easat-2990	56	10	the	the	DET
easat-2990	56	11	scaling	scale	VERB
easat-2990	56	12	operator	operator	NOUN
easat-2990	56	13	by	by	ADP
easat-2990	56	14	letting	let	VERB
easat-2990	56	15	h(t	h(t	PRON
easat-2990	56	16	)	)	PUNCT
easat-2990	57	1	=	=	SYM
easat-2990	57	2	1	1	NUM
easat-2990	57	3	and	and	CCONJ
easat-2990	57	4	the	the	DET
easat-2990	57	5	translation	translation	NOUN
easat-2990	57	6	operator	operator	NOUN
easat-2990	57	7	by	by	ADP
easat-2990	57	8	letting[14	letting[14	PROPN
easat-2990	57	9	]	]	PUNCT
easat-2990	57	10	g(t	g(t	PROPN
easat-2990	57	11	)	)	PUNCT
easat-2990	58	1	=	=	SYM
easat-2990	58	2	t.	t.	NOUN
easat-2990	58	3	continuous	continuous	ADJ
easat-2990	58	4	and	and	CCONJ
easat-2990	58	5	discrete	discrete	ADJ
easat-2990	58	6	wavelet	wavelet	NOUN
easat-2990	58	7	transforms	transform	VERB
easat-2990	58	8	to	to	PART
easat-2990	58	9	study	study	VERB
easat-2990	58	10	a	a	DET
easat-2990	58	11	function	function	NOUN
easat-2990	58	12	localized	localize	VERB
easat-2990	58	13	by	by	ADP
easat-2990	58	14	a	a	DET
easat-2990	58	15	shift	shift	NOUN
easat-2990	58	16	,	,	PUNCT
easat-2990	58	17	we	we	PRON
easat-2990	58	18	choose	choose	VERB
easat-2990	58	19	the	the	DET
easat-2990	58	20	points	point	NOUN
easat-2990	58	21	of	of	ADP
easat-2990	58	22	the	the	DET
easat-2990	58	23	function	function	NOUN
easat-2990	58	24	to	to	PART
easat-2990	58	25	sample	sample	VERB
easat-2990	58	26	and	and	CCONJ
easat-2990	58	27	analyze	analyze	VERB
easat-2990	58	28	it	it	PRON
easat-2990	58	29	in	in	ADP
easat-2990	58	30	a	a	DET
easat-2990	58	31	given	give	VERB
easat-2990	58	32	interval	interval	NOUN
easat-2990	58	33	.	.	PUNCT
easat-2990	59	1	the	the	DET
easat-2990	59	2	continuous	continuous	ADJ
easat-2990	59	3	wavelet	wavelet	NOUN
easat-2990	59	4	transform	transform	NOUN
easat-2990	59	5	of	of	ADP
easat-2990	59	6	x	x	PUNCT
easat-2990	59	7	with	with	ADP
easat-2990	59	8	respect	respect	NOUN
easat-2990	59	9	to	to	ADP
easat-2990	59	10	a	a	DET
easat-2990	59	11	given	give	VERB
easat-2990	59	12	father	father	NOUN
easat-2990	59	13	is	be	AUX
easat-2990	59	14	defined	define	VERB
easat-2990	59	15	.	.	PUNCT
easat-2990	60	1	note	note	VERB
easat-2990	60	2	that	that	SCONJ
easat-2990	60	3	instead	instead	ADV
easat-2990	60	4	of	of	ADP
easat-2990	60	5	changing	change	VERB
easat-2990	60	6	just	just	ADV
easat-2990	60	7	the	the	DET
easat-2990	60	8	scale	scale	NOUN
easat-2990	60	9	and	and	CCONJ
easat-2990	60	10	the	the	DET
easat-2990	60	11	position	position	NOUN
easat-2990	60	12	of	of	ADP
easat-2990	60	13	the	the	DET
easat-2990	60	14	analyzing	analyzing	NOUN
easat-2990	60	15	window	window	NOUN
easat-2990	60	16	,	,	PUNCT
easat-2990	60	17	one	one	PRON
easat-2990	60	18	may	may	AUX
easat-2990	60	19	also	also	ADV
easat-2990	60	20	change	change	VERB
easat-2990	60	21	the	the	DET
easat-2990	60	22	shape	shape	NOUN
easat-2990	60	23	of	of	ADP
easat-2990	60	24	the	the	DET
easat-2990	60	25	window[15	window[15	NOUN
easat-2990	60	26	]	]	PUNCT
easat-2990	60	27	.	.	PUNCT
easat-2990	61	1	multiresolution	multiresolution	NOUN
easat-2990	61	2	analysis	analysis	NOUN
easat-2990	61	3	(	(	PUNCT
easat-2990	61	4	mra	mra	NOUN
easat-2990	61	5	)	)	PUNCT
easat-2990	61	6	and	and	CCONJ
easat-2990	61	7	bases	basis	NOUN
easat-2990	61	8	of	of	ADP
easat-2990	61	9	l2(r	l2(r	NOUN
easat-2990	61	10	)	)	PUNCT
easat-2990	61	11	the	the	DET
easat-2990	61	12	basic	basic	ADJ
easat-2990	61	13	idea	idea	NOUN
easat-2990	61	14	in	in	ADP
easat-2990	61	15	wavelet	wavelet	NOUN
easat-2990	61	16	theory	theory	NOUN
easat-2990	61	17	to	to	ADP
easat-2990	61	18	numerically	numerically	ADV
easat-2990	61	19	study	study	VERB
easat-2990	61	20	signals	signal	NOUN
easat-2990	61	21	is	be	AUX
easat-2990	61	22	that	that	SCONJ
easat-2990	61	23	small	small	ADJ
easat-2990	61	24	scales	scale	NOUN
easat-2990	61	25	are	be	AUX
easat-2990	61	26	used	use	VERB
easat-2990	61	27	to	to	PART
easat-2990	61	28	examine	examine	VERB
easat-2990	61	29	the	the	DET
easat-2990	61	30	fine	fine	ADJ
easat-2990	61	31	structure	structure	NOUN
easat-2990	61	32	of	of	ADP
easat-2990	61	33	the	the	DET
easat-2990	61	34	signals	signal	NOUN
easat-2990	61	35	.	.	PUNCT
easat-2990	62	1	this	this	DET
easat-2990	62	2	idea	idea	NOUN
easat-2990	62	3	is	be	AUX
easat-2990	62	4	realized	realize	VERB
easat-2990	62	5	through	through	ADP
easat-2990	62	6	the	the	DET
easat-2990	62	7	so	so	ADV
easat-2990	62	8	-	-	PUNCT
easat-2990	62	9	called	call	VERB
easat-2990	62	10	multiresolution	multiresolution	NOUN
easat-2990	62	11	implementations	implementation	NOUN
easat-2990	62	12	of	of	ADP
easat-2990	62	13	the	the	DET
easat-2990	62	14	space	space	NOUN
easat-2990	62	15	l2	l2	NOUN
easat-2990	62	16	.	.	PUNCT
easat-2990	63	1	the	the	DET
easat-2990	63	2	spaces	space	NOUN
easat-2990	63	3	vj	vj	PROPN
easat-2990	63	4	,	,	PUNCT
easat-2990	63	5	l	l	NOUN
easat-2990	64	1	=	=	SYM
easat-2990	64	2	v0,l	v0,l	PROPN
easat-2990	64	3	+	+	CCONJ
easat-2990	64	4	j	j	PROPN
easat-2990	64	5	are	be	AUX
easat-2990	64	6	nested	nest	VERB
easat-2990	64	7	in	in	ADP
easat-2990	64	8	each	each	DET
easat-2990	64	9	other	other	ADJ
easat-2990	64	10	with	with	ADP
easat-2990	64	11	dimension	dimension	NOUN
easat-2990	64	12	2j	2j	NOUN
easat-2990	64	13	.	.	PUNCT
easat-2990	65	1	a	a	DET
easat-2990	65	2	sequence	sequence	NOUN
easat-2990	65	3	serves	serve	VERB
easat-2990	65	4	as	as	ADP
easat-2990	65	5	the	the	DET
easat-2990	65	6	2j	2j	NUM
easat-2990	65	7	-	-	PUNCT
easat-2990	65	8	dimension	dimension	NOUN
easat-2990	65	9	basis	basis	NOUN
easat-2990	65	10	of	of	ADP
easat-2990	65	11	vj	vj	PROPN
easat-2990	65	12	,	,	PUNCT
easat-2990	65	13	l.	l.	PROPN
easat-2990	65	14	the	the	DET
easat-2990	65	15	pair	pair	NOUN
easat-2990	65	16	of	of	ADP
easat-2990	65	17	subspaces	subspace	NOUN
easat-2990	65	18	yields	yield	VERB
easat-2990	65	19	the	the	DET
easat-2990	65	20	multiresolution	multiresolution	NOUN
easat-2990	65	21	property	property	NOUN
easat-2990	65	22	of	of	ADP
easat-2990	65	23	l2(r	l2(r	NOUN
easat-2990	65	24	)	)	PUNCT
easat-2990	65	25	.	.	PUNCT
easat-2990	66	1	the	the	DET
easat-2990	66	2	scaling	scale	VERB
easat-2990	66	3	function	function	NOUN
easat-2990	66	4	and	and	CCONJ
easat-2990	66	5	the	the	DET
easat-2990	66	6	wavelet	wavelet	NOUN
easat-2990	66	7	function	function	NOUN
easat-2990	66	8	on	on	ADP
easat-2990	66	9	vj	vj	PROPN
easat-2990	66	10	,	,	PUNCT
easat-2990	66	11	l	l	PROPN
easat-2990	66	12	,	,	PUNCT
easat-2990	66	13	referred	refer	VERB
easat-2990	66	14	to	to	ADP
easat-2990	66	15	as	as	ADP
easat-2990	66	16	a	a	DET
easat-2990	66	17	father	father	NOUN
easat-2990	66	18	and	and	CCONJ
easat-2990	66	19	a	a	DET
easat-2990	66	20	mother	mother	NOUN
easat-2990	66	21	wavelet	wavelet	NOUN
easat-2990	66	22	,	,	PUNCT
easat-2990	66	23	yield	yield	VERB
easat-2990	66	24	the	the	DET
easat-2990	66	25	mra	mra	NOUN
easat-2990	66	26	of	of	ADP
easat-2990	66	27	the	the	DET
easat-2990	66	28	unit	unit	NOUN
easat-2990	66	29	square	square	NOUN
easat-2990	66	30	.	.	PUNCT
easat-2990	67	1	they	they	PRON
easat-2990	67	2	determine	determine	VERB
easat-2990	67	3	the	the	DET
easat-2990	67	4	spaces	space	NOUN
easat-2990	67	5	of	of	ADP
easat-2990	67	6	l2(xt	l2(xt	NOUN
easat-2990	67	7	)	)	PUNCT
easat-2990	67	8	and	and	CCONJ
easat-2990	67	9	l2(yv)[16	l2(yv)[16	PROPN
easat-2990	67	10	]	]	PUNCT
easat-2990	67	11	.	.	PUNCT
easat-2990	68	1	compactly	compactly	ADV
easat-2990	68	2	supported	support	VERB
easat-2990	68	3	wavelets	wavelet	NOUN
easat-2990	68	4	wavelet	wavelet	NOUN
easat-2990	68	5	packets	packet	NOUN
easat-2990	68	6	may	may	AUX
easat-2990	68	7	have	have	VERB
easat-2990	68	8	computational	computational	ADJ
easat-2990	68	9	advantages	advantage	NOUN
easat-2990	68	10	.	.	PUNCT
easat-2990	69	1	they	they	PRON
easat-2990	69	2	are	be	AUX
easat-2990	69	3	bases	basis	NOUN
easat-2990	69	4	for	for	ADP
easat-2990	69	5	their	their	PRON
easat-2990	69	6	associated	associate	VERB
easat-2990	69	7	spaces	space	NOUN
easat-2990	69	8	vj	vj	PROPN
easat-2990	69	9	,	,	PUNCT
easat-2990	69	10	l.	l.	PROPN
easat-2990	69	11	compactly	compactly	ADV
easat-2990	69	12	supported	support	VERB
easat-2990	69	13	wavelets	wavelet	NOUN
easat-2990	69	14	may	may	AUX
easat-2990	69	15	have	have	VERB
easat-2990	69	16	practical	practical	ADJ
easat-2990	69	17	advantages	advantage	NOUN
easat-2990	69	18	,	,	PUNCT
easat-2990	69	19	in	in	ADP
easat-2990	69	20	particular	particular	ADJ
easat-2990	69	21	in	in	ADP
easat-2990	69	22	one	one	NUM
easat-2990	69	23	-	-	PUNCT
easat-2990	69	24	dimensional	dimensional	ADJ
easat-2990	69	25	studies[17	studies[17	NOUN
easat-2990	69	26	]	]	PUNCT
easat-2990	69	27	.	.	PUNCT
easat-2990	70	1	2.1	2.1	NUM
easat-2990	70	2	.	.	PUNCT
easat-2990	70	3	fundamentals	fundamental	NOUN
easat-2990	70	4	of	of	ADP
easat-2990	70	5	wavelet	wavelet	NOUN
easat-2990	70	6	theory	theory	NOUN
easat-2990	70	7	the	the	DET
easat-2990	70	8	essentials	essential	NOUN
easat-2990	70	9	of	of	ADP
easat-2990	70	10	wavelet	wavelet	NOUN
easat-2990	70	11	functions	function	NOUN
easat-2990	70	12	are	be	AUX
easat-2990	70	13	as	as	SCONJ
easat-2990	70	14	follows	follow	VERB
easat-2990	70	15	.	.	PUNCT
easat-2990	71	1	a	a	DET
easat-2990	71	2	multiresolution	multiresolution	NOUN
easat-2990	71	3	ensemble	ensemble	ADJ
easat-2990	71	4	in	in	ADP
easat-2990	71	5	l2(r	l2(r	PROPN
easat-2990	71	6	)	)	PUNCT
easat-2990	71	7	is	be	AUX
easat-2990	71	8	a	a	DET
easat-2990	71	9	sequence	sequence	NOUN
easat-2990	71	10	of	of	ADP
easat-2990	71	11	subspaces	subspace	NOUN
easat-2990	71	12	{	{	PUNCT
easat-2990	71	13	vj0	vj0	NOUN
easat-2990	71	14	}	}	PUNCT
easat-2990	71	15	,	,	PUNCT
easat-2990	71	16	where	where	SCONJ
easat-2990	71	17	vj0	vj0	PROPN
easat-2990	71	18	⊆	⊆	NUM
easat-2990	71	19	vj	vj	NOUN
easat-2990	71	20	,	,	PUNCT
easat-2990	71	21	and	and	CCONJ
easat-2990	71	22	j	j	PROPN
easat-2990	71	23	,	,	PUNCT
easat-2990	71	24	j0	j0	PROPN
easat-2990	71	25	in	in	ADP
easat-2990	71	26	z	z	PROPN
easat-2990	71	27	,	,	PUNCT
easat-2990	71	28	such	such	ADJ
easat-2990	71	29	that	that	SCONJ
easat-2990	71	30	both	both	PRON
easat-2990	71	31	(	(	PUNCT
easat-2990	71	32	0	0	NUM
easat-2990	71	33	)	)	PUNCT
easat-2990	71	34	and	and	CCONJ
easat-2990	71	35	{	{	PUNCT
easat-2990	71	36	l2(r	l2(r	NOUN
easat-2990	71	37	)	)	PUNCT
easat-2990	71	38	}	}	PUNCT
easat-2990	71	39	are	be	AUX
easat-2990	71	40	the	the	DET
easat-2990	71	41	only	only	ADJ
easat-2990	71	42	subspaces	subspace	NOUN
easat-2990	71	43	that	that	PRON
easat-2990	71	44	are	be	AUX
easat-2990	71	45	common	common	ADJ
easat-2990	71	46	to	to	ADP
easat-2990	71	47	all	all	DET
easat-2990	71	48	vj	vj	PROPN
easat-2990	71	49	.	.	PROPN
easat-2990	72	1	in	in	ADP
easat-2990	72	2	an	an	DET
easat-2990	72	3	m	m	NOUN
easat-2990	72	4	-	-	PUNCT
easat-2990	72	5	level	level	NOUN
easat-2990	72	6	multiresolution	multiresolution	NOUN
easat-2990	72	7	ensemble	ensemble	ADJ
easat-2990	72	8	,	,	PUNCT
easat-2990	72	9	the	the	DET
easat-2990	72	10	theorem	theorem	NOUN
easat-2990	72	11	provides	provide	VERB
easat-2990	72	12	that	that	PRON
easat-2990	72	13	2	2	NUM
easat-2990	72	14	=	=	SYM
easat-2990	72	15	m	m	VERB
easat-2990	72	16	l2(r	l2(r	NOUN
easat-2990	72	17	)	)	PUNCT
easat-2990	72	18	=	=	SYM
easat-2990	72	19	{	{	PUNCT
easat-2990	72	20	φ	φ	X
easat-2990	72	21	(	(	PUNCT
easat-2990	72	22	·	·	PUNCT
easat-2990	73	1	−	−	PROPN
easat-2990	73	2	k	k	NOUN
easat-2990	73	3	)	)	PUNCT
easat-2990	73	4	,	,	PUNCT
easat-2990	73	5	∀k	∀k	X
easat-2990	73	6	∈	∈	PROPN
easat-2990	73	7	z	z	X
easat-2990	73	8	}	}	PUNCT
easat-2990	73	9	(	(	PUNCT
easat-2990	73	10	j	j	PROPN
easat-2990	73	11	−	−	PROPN
easat-2990	73	12	∞	∞	NUM
easat-2990	73	13	∑vj	∑vj	PROPN
easat-2990	73	14	)	)	PUNCT
easat-2990	73	15	,	,	PUNCT
easat-2990	73	16	⊕vj	⊕vj	NOUN
easat-2990	73	17	,	,	PUNCT
easat-2990	73	18	k	k	PROPN
easat-2990	73	19	∈	∈	PROPN
easat-2990	73	20	l2(vj	l2(vj	PROPN
easat-2990	73	21	)	)	PUNCT
easat-2990	73	22	,	,	PUNCT
easat-2990	73	23	where	where	SCONJ
easat-2990	73	24	φ	φ	PROPN
easat-2990	73	25	(	(	PUNCT
easat-2990	73	26	·	·	PUNCT
easat-2990	73	27	)	)	PUNCT
easat-2990	73	28	is	be	AUX
easat-2990	73	29	the	the	DET
easat-2990	73	30	scaling	scale	VERB
easat-2990	73	31	function	function	NOUN
easat-2990	73	32	or	or	CCONJ
easat-2990	73	33	the	the	DET
easat-2990	73	34	long	long	ADJ
easat-2990	73	35	wavelet	wavelet	NOUN
easat-2990	73	36	,	,	PUNCT
easat-2990	73	37	and	and	CCONJ
easat-2990	73	38	its	its	PRON
easat-2990	73	39	shifts	shift	NOUN
easat-2990	73	40	cover	cover	VERB
easat-2990	73	41	the	the	DET
easat-2990	73	42	whole	whole	ADJ
easat-2990	73	43	space	space	NOUN
easat-2990	73	44	.	.	PUNCT
easat-2990	74	1	their	their	PRON
easat-2990	74	2	spans	span	NOUN
easat-2990	74	3	collectively	collectively	ADV
easat-2990	74	4	form	form	VERB
easat-2990	74	5	a	a	DET
easat-2990	74	6	partition	partition	NOUN
easat-2990	74	7	of	of	ADP
easat-2990	74	8	unity	unity	NOUN
easat-2990	74	9	in	in	ADP
easat-2990	74	10	l2(r	l2(r	NOUN
easat-2990	74	11	)	)	PUNCT
easat-2990	74	12	and	and	CCONJ
easat-2990	74	13	fulfill	fulfill	VERB
easat-2990	74	14	the	the	DET
easat-2990	74	15	condition	condition	NOUN
easat-2990	74	16	.	.	PUNCT
easat-2990	75	1	moreover	moreover	ADV
easat-2990	75	2	,	,	PUNCT
easat-2990	75	3	φ	φ	PROPN
easat-2990	75	4	(	(	PUNCT
easat-2990	75	5	·	·	PUNCT
easat-2990	75	6	−	−	PROPN
easat-2990	75	7	k	k	NOUN
easat-2990	75	8	)	)	PUNCT
easat-2990	75	9	,	,	PUNCT
easat-2990	75	10	k	k	PROPN
easat-2990	75	11	∈	∈	PROPN
easat-2990	75	12	z	z	X
easat-2990	75	13	,	,	PUNCT
easat-2990	75	14	are	be	AUX
easat-2990	75	15	biorthogonal	biorthogonal	ADJ
easat-2990	75	16	with	with	ADP
easat-2990	75	17	respect	respect	NOUN
easat-2990	75	18	to	to	ADP
easat-2990	75	19	each	each	DET
easat-2990	75	20	other[18	other[18	NOUN
easat-2990	75	21	]	]	PUNCT
easat-2990	75	22	.	.	PUNCT
easat-2990	76	1	the	the	DET
easat-2990	76	2	wavelet	wavelet	NOUN
easat-2990	76	3	function	function	NOUN
easat-2990	76	4	or	or	CCONJ
easat-2990	76	5	the	the	DET
easat-2990	76	6	short	short	ADJ
easat-2990	76	7	wavelet	wavelet	NOUN
easat-2990	76	8	is	be	AUX
easat-2990	76	9	then	then	ADV
easat-2990	76	10	derived	derive	VERB
easat-2990	76	11	in	in	ADP
easat-2990	76	12	terms	term	NOUN
easat-2990	76	13	of	of	ADP
easat-2990	76	14	the	the	DET
easat-2990	76	15	scaling	scale	VERB
easat-2990	76	16	function	function	NOUN
easat-2990	76	17	.	.	PUNCT
easat-2990	77	1	in	in	ADP
easat-2990	77	2	a	a	DET
easat-2990	77	3	three	three	NUM
easat-2990	77	4	-	-	PUNCT
easat-2990	77	5	level	level	NOUN
easat-2990	77	6	scheme	scheme	NOUN
easat-2990	77	7	(	(	PUNCT
easat-2990	77	8	n	n	NOUN
easat-2990	77	9	=	=	SYM
easat-2990	77	10	3	3	NUM
easat-2990	77	11	)	)	PUNCT
easat-2990	77	12	on	on	ADP
easat-2990	77	13	the	the	DET
easat-2990	77	14	original	original	ADJ
easat-2990	77	15	domain	domain	NOUN
easat-2990	77	16	,	,	PUNCT
easat-2990	77	17	the	the	DET
easat-2990	77	18	graph	graph	NOUN
easat-2990	77	19	of	of	ADP
easat-2990	77	20	a	a	DET
easat-2990	77	21	piecewise	piecewise	NOUN
easat-2990	77	22	constant	constant	ADJ
easat-2990	77	23	scaling	scaling	NOUN
easat-2990	77	24	function	function	NOUN
easat-2990	77	25	of	of	ADP
easat-2990	77	26	compact	compact	ADJ
easat-2990	77	27	support	support	NOUN
easat-2990	77	28	and	and	CCONJ
easat-2990	77	29	piecewise	piecewise	NOUN
easat-2990	77	30	1/2	1/2	NUM
easat-2990	77	31	linear	linear	NOUN
easat-2990	77	32	wavelet	wavelet	NOUN
easat-2990	77	33	function	function	NOUN
easat-2990	77	34	are	be	AUX
easat-2990	77	35	shown	show	VERB
easat-2990	77	36	.	.	PUNCT
easat-2990	78	1	at	at	ADP
easat-2990	78	2	high	high	ADJ
easat-2990	78	3	resolution	resolution	NOUN
easat-2990	78	4	,	,	PUNCT
easat-2990	78	5	the	the	DET
easat-2990	78	6	recursion	recursion	NOUN
easat-2990	78	7	displays	display	VERB
easat-2990	78	8	the	the	DET
easat-2990	78	9	availability	availability	NOUN
easat-2990	78	10	of	of	ADP
easat-2990	78	11	more	more	ADJ
easat-2990	78	12	spline	spline	NOUN
easat-2990	78	13	nodes	node	NOUN
easat-2990	78	14	obtained	obtain	VERB
easat-2990	78	15	by	by	ADP
easat-2990	78	16	evaluating	evaluate	VERB
easat-2990	78	17	the	the	DET
easat-2990	78	18	functions	function	NOUN
easat-2990	78	19	at	at	ADP
easat-2990	78	20	dyadic	dyadic	ADJ
easat-2990	78	21	points	point	NOUN
easat-2990	78	22	in	in	ADP
easat-2990	78	23	the	the	DET
easat-2990	78	24	original	original	ADJ
easat-2990	78	25	domain	domain	NOUN
easat-2990	78	26	.	.	PUNCT
easat-2990	79	1	any	any	DET
easat-2990	79	2	square	square	ADJ
easat-2990	79	3	integrable	integrable	ADJ
easat-2990	79	4	function	function	NOUN
easat-2990	79	5	f(x	f(x	PROPN
easat-2990	79	6	)	)	PUNCT
easat-2990	79	7	can	can	AUX
easat-2990	79	8	be	be	AUX
easat-2990	79	9	projected	project	VERB
easat-2990	79	10	onto	onto	ADP
easat-2990	79	11	this	this	DET
easat-2990	79	12	family	family	NOUN
easat-2990	79	13	of	of	ADP
easat-2990	79	14	basis	basis	NOUN
easat-2990	79	15	functions	function	NOUN
easat-2990	79	16	for	for	ADP
easat-2990	79	17	approximations	approximation	NOUN
easat-2990	79	18	.	.	PUNCT
easat-2990	80	1	the	the	DET
easat-2990	80	2	scale	scale	NOUN
easat-2990	80	3	(	(	PUNCT
easat-2990	80	4	j	j	NOUN
easat-2990	80	5	)	)	PUNCT
easat-2990	80	6	and	and	CCONJ
easat-2990	80	7	the	the	DET
easat-2990	80	8	detail	detail	NOUN
easat-2990	80	9	(	(	PUNCT
easat-2990	80	10	k	k	X
easat-2990	80	11	)	)	PUNCT
easat-2990	80	12	have	have	VERB
easat-2990	80	13	their	their	PRON
easat-2990	80	14	own	own	ADJ
easat-2990	80	15	meaning	meaning	NOUN
easat-2990	80	16	,	,	PUNCT
easat-2990	80	17	and	and	CCONJ
easat-2990	80	18	the	the	DET
easat-2990	80	19	combination	combination	NOUN
easat-2990	80	20	of	of	ADP
easat-2990	80	21	different	different	ADJ
easat-2990	80	22	scale	scale	NOUN
easat-2990	80	23	functions	function	NOUN
easat-2990	80	24	can	can	AUX
easat-2990	80	25	provide	provide	VERB
easat-2990	80	26	a	a	DET
easat-2990	80	27	so	so	ADV
easat-2990	80	28	-	-	PUNCT
easat-2990	80	29	called	call	VERB
easat-2990	80	30	“	"	PUNCT
easat-2990	80	31	multi	multi	ADJ
easat-2990	80	32	-	-	ADJ
easat-2990	80	33	resolution	resolution	ADJ
easat-2990	80	34	image	image	NOUN
easat-2990	80	35	”	"	PUNCT
easat-2990	80	36	with	with	ADP
easat-2990	80	37	the	the	DET
easat-2990	80	38	precision	precision	NOUN
easat-2990	80	39	of	of	ADP
easat-2990	80	40	each	each	DET
easat-2990	80	41	range	range	NOUN
easat-2990	80	42	detail	detail	NOUN
easat-2990	80	43	[	[	X
easat-2990	80	44	19	19	NUM
easat-2990	80	45	]	]	PUNCT
easat-2990	80	46	.	.	PUNCT
easat-2990	81	1	4602	4602	NUM
easat-2990	81	2	edelweiss	edelweiss	PROPN
easat-2990	81	3	applied	apply	VERB
easat-2990	81	4	science	science	NOUN
easat-2990	81	5	and	and	CCONJ
easat-2990	81	6	technology	technology	NOUN
easat-2990	81	7	issn	issn	PROPN
easat-2990	81	8	:	:	PUNCT
easat-2990	81	9	2576	2576	NUM
easat-2990	81	10	-	-	SYM
easat-2990	81	11	8484	8484	NUM
easat-2990	81	12	vol	vol	NOUN
easat-2990	81	13	.	.	PROPN
easat-2990	81	14	8	8	NUM
easat-2990	81	15	,	,	PUNCT
easat-2990	81	16	no	no	INTJ
easat-2990	81	17	.	.	NOUN
easat-2990	82	1	6	6	NUM
easat-2990	82	2	:	:	SYM
easat-2990	82	3	4599	4599	NUM
easat-2990	82	4	-	-	SYM
easat-2990	82	5	4610	4610	NUM
easat-2990	82	6	,	,	PUNCT
easat-2990	82	7	2024	2024	NUM
easat-2990	82	8	doi	doi	NOUN
easat-2990	82	9	:	:	PUNCT
easat-2990	82	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	82	11	©	©	PROPN
easat-2990	82	12	2024	2024	NUM
easat-2990	82	13	by	by	ADP
easat-2990	82	14	the	the	DET
easat-2990	82	15	author	author	NOUN
easat-2990	82	16	;	;	PUNCT
easat-2990	82	17	licensee	licensee	PROPN
easat-2990	82	18	learning	learn	VERB
easat-2990	82	19	gate	gate	NOUN
easat-2990	82	20	figure	figure	NOUN
easat-2990	82	21	1	1	NUM
easat-2990	82	22	.	.	PUNCT
easat-2990	82	23	temporally	temporally	ADV
easat-2990	82	24	localized	localize	VERB
easat-2990	82	25	signal	signal	NOUN
easat-2990	82	26	s	s	VERB
easat-2990	82	27	with	with	ADP
easat-2990	82	28	a	a	DET
easat-2990	82	29	constant	constant	ADJ
easat-2990	82	30	frequency	frequency	NOUN
easat-2990	82	31	and	and	CCONJ
easat-2990	82	32	sparse	sparse	ADJ
easat-2990	82	33	wavelet	wavelet	NOUN
easat-2990	82	34	phase	phase	NOUN
easat-2990	82	35	vocoder	vocoder	NOUN
easat-2990	82	36	time	time	NOUN
easat-2990	82	37	stretch	stretch	NOUN
easat-2990	82	38	utilizing	utilize	VERB
easat-2990	82	39	discrete	discrete	ADJ
easat-2990	82	40	frame	frame	NOUN
easat-2990	82	41	technique	technique	NOUN
easat-2990	82	42	sd	sd	NOUN
easat-2990	82	43	and	and	CCONJ
easat-2990	82	44	wp4	wp4	PROPN
easat-2990	82	45	method	method	PROPN
easat-2990	82	46	sw	sw	PROPN
easat-2990	82	47	.	.	PROPN
easat-2990	82	48	2.2	2.2	NUM
easat-2990	82	49	.	.	PUNCT
easat-2990	83	1	wavelets	wavelet	NOUN
easat-2990	83	2	in	in	ADP
easat-2990	83	3	numerical	numerical	ADJ
easat-2990	83	4	analysis	analysis	NOUN
easat-2990	83	5	wavelets	wavelet	NOUN
easat-2990	83	6	have	have	AUX
easat-2990	83	7	become	become	VERB
easat-2990	83	8	an	an	DET
easat-2990	83	9	area	area	NOUN
easat-2990	83	10	of	of	ADP
easat-2990	83	11	extensive	extensive	ADJ
easat-2990	83	12	research	research	NOUN
easat-2990	83	13	in	in	ADP
easat-2990	83	14	recent	recent	ADJ
easat-2990	83	15	years	year	NOUN
easat-2990	83	16	.	.	PUNCT
easat-2990	84	1	various	various	ADJ
easat-2990	84	2	interesting	interesting	ADJ
easat-2990	84	3	properties	property	NOUN
easat-2990	84	4	of	of	ADP
easat-2990	84	5	wavelets	wavelet	NOUN
easat-2990	84	6	,	,	PUNCT
easat-2990	84	7	such	such	ADJ
easat-2990	84	8	as	as	ADP
easat-2990	84	9	orthogonality	orthogonality	NOUN
easat-2990	84	10	,	,	PUNCT
easat-2990	84	11	compact	compact	ADJ
easat-2990	84	12	support	support	NOUN
easat-2990	84	13	,	,	PUNCT
easat-2990	84	14	and	and	CCONJ
easat-2990	84	15	the	the	DET
easat-2990	84	16	ability	ability	NOUN
easat-2990	84	17	to	to	PART
easat-2990	84	18	represent	represent	VERB
easat-2990	84	19	and	and	CCONJ
easat-2990	84	20	handle	handle	VERB
easat-2990	84	21	fast	fast	ADJ
easat-2990	84	22	and	and	CCONJ
easat-2990	84	23	slow	slow	ADJ
easat-2990	84	24	signals	signal	NOUN
easat-2990	84	25	with	with	ADP
easat-2990	84	26	different	different	ADJ
easat-2990	84	27	levels	level	NOUN
easat-2990	84	28	of	of	ADP
easat-2990	84	29	accuracy	accuracy	NOUN
easat-2990	84	30	,	,	PUNCT
easat-2990	84	31	have	have	AUX
easat-2990	84	32	led	lead	VERB
easat-2990	84	33	to	to	ADP
easat-2990	84	34	their	their	PRON
easat-2990	84	35	applications	application	NOUN
easat-2990	84	36	in	in	ADP
easat-2990	84	37	signal	signal	ADJ
easat-2990	84	38	analysis	analysis	NOUN
easat-2990	84	39	,	,	PUNCT
easat-2990	84	40	noise	noise	NOUN
easat-2990	84	41	removal	removal	NOUN
easat-2990	84	42	,	,	PUNCT
easat-2990	84	43	statistical	statistical	ADJ
easat-2990	84	44	estimation	estimation	NOUN
easat-2990	84	45	,	,	PUNCT
easat-2990	84	46	partial	partial	ADJ
easat-2990	84	47	differential	differential	NOUN
easat-2990	84	48	equations	equation	NOUN
easat-2990	84	49	,	,	PUNCT
easat-2990	84	50	and	and	CCONJ
easat-2990	84	51	wavelet	wavelet	NOUN
easat-2990	84	52	multi	multi	PROPN
easat-2990	84	53	-	-	ADJ
easat-2990	84	54	grid	grid	ADJ
easat-2990	84	55	or	or	CCONJ
easat-2990	84	56	wavelet	wavelet	NOUN
easat-2990	84	57	generalized	generalize	VERB
easat-2990	84	58	multi	multi	ADJ
easat-2990	84	59	-	-	ADJ
easat-2990	84	60	grid	grid	ADJ
easat-2990	84	61	methods	method	NOUN
easat-2990	84	62	to	to	PART
easat-2990	84	63	numerically	numerically	ADV
easat-2990	84	64	solve	solve	VERB
easat-2990	84	65	partial	partial	ADJ
easat-2990	84	66	differential	differential	NOUN
easat-2990	84	67	equations	equation	NOUN
easat-2990	84	68	.	.	PUNCT
easat-2990	85	1	the	the	DET
easat-2990	85	2	wavelet	wavelet	NOUN
easat-2990	85	3	expansion	expansion	NOUN
easat-2990	85	4	makes	make	VERB
easat-2990	85	5	it	it	PRON
easat-2990	85	6	possible	possible	ADJ
easat-2990	85	7	to	to	PART
easat-2990	85	8	transfer	transfer	VERB
easat-2990	85	9	the	the	DET
easat-2990	85	10	oscillatory	oscillatory	ADJ
easat-2990	85	11	character	character	NOUN
easat-2990	85	12	of	of	ADP
easat-2990	85	13	the	the	DET
easat-2990	85	14	problem	problem	NOUN
easat-2990	85	15	to	to	ADP
easat-2990	85	16	the	the	DET
easat-2990	85	17	fine	fine	ADJ
easat-2990	85	18	grid	grid	NOUN
easat-2990	85	19	,	,	PUNCT
easat-2990	85	20	where	where	SCONJ
easat-2990	85	21	the	the	DET
easat-2990	85	22	largest	large	ADJ
easat-2990	85	23	part	part	NOUN
easat-2990	85	24	of	of	ADP
easat-2990	85	25	the	the	DET
easat-2990	85	26	work	work	NOUN
easat-2990	85	27	is	be	AUX
easat-2990	85	28	concentrated	concentrate	VERB
easat-2990	85	29	,	,	PUNCT
easat-2990	85	30	while	while	SCONJ
easat-2990	85	31	smoothness	smoothness	NOUN
easat-2990	85	32	is	be	AUX
easat-2990	85	33	transferred	transfer	VERB
easat-2990	85	34	to	to	ADP
easat-2990	85	35	the	the	DET
easat-2990	85	36	coarse	coarse	ADJ
easat-2990	85	37	grid	grid	NOUN
easat-2990	85	38	,	,	PUNCT
easat-2990	85	39	where	where	SCONJ
easat-2990	85	40	the	the	DET
easat-2990	85	41	computational	computational	ADJ
easat-2990	85	42	work	work	NOUN
easat-2990	85	43	is	be	AUX
easat-2990	85	44	minor	minor	ADJ
easat-2990	85	45	.	.	PUNCT
easat-2990	86	1	this	this	DET
easat-2990	86	2	adaptive	adaptive	ADJ
easat-2990	86	3	ability	ability	NOUN
easat-2990	86	4	is	be	AUX
easat-2990	86	5	very	very	ADV
easat-2990	86	6	important	important	ADJ
easat-2990	86	7	and	and	CCONJ
easat-2990	86	8	is	be	AUX
easat-2990	86	9	one	one	NUM
easat-2990	86	10	of	of	ADP
easat-2990	86	11	the	the	DET
easat-2990	86	12	reasons	reason	NOUN
easat-2990	86	13	for	for	ADP
easat-2990	86	14	the	the	DET
easat-2990	86	15	popularity	popularity	NOUN
easat-2990	86	16	of	of	ADP
easat-2990	86	17	the	the	DET
easat-2990	86	18	wavelet	wavelet	NOUN
easat-2990	86	19	-	-	PUNCT
easat-2990	86	20	based	base	VERB
easat-2990	86	21	approach	approach	NOUN
easat-2990	86	22	in	in	ADP
easat-2990	86	23	many	many	ADJ
easat-2990	86	24	areas[20	areas[20	NUM
easat-2990	86	25	]	]	PUNCT
easat-2990	86	26	.	.	PUNCT
easat-2990	87	1	wavelets	wavelet	NOUN
easat-2990	87	2	,	,	PUNCT
easat-2990	87	3	as	as	ADP
easat-2990	87	4	a	a	DET
easat-2990	87	5	mathematical	mathematical	ADJ
easat-2990	87	6	tool	tool	NOUN
easat-2990	87	7	,	,	PUNCT
easat-2990	87	8	can	can	AUX
easat-2990	87	9	be	be	AUX
easat-2990	87	10	used	use	VERB
easat-2990	87	11	to	to	PART
easat-2990	87	12	solve	solve	VERB
easat-2990	87	13	a	a	DET
easat-2990	87	14	variety	variety	NOUN
easat-2990	87	15	of	of	ADP
easat-2990	87	16	problems	problem	NOUN
easat-2990	87	17	in	in	ADP
easat-2990	87	18	numerical	numerical	ADJ
easat-2990	87	19	analysis	analysis	NOUN
easat-2990	87	20	that	that	PRON
easat-2990	87	21	involve	involve	VERB
easat-2990	87	22	transforming	transform	VERB
easat-2990	87	23	a	a	DET
easat-2990	87	24	given	give	VERB
easat-2990	87	25	problem	problem	NOUN
easat-2990	87	26	or	or	CCONJ
easat-2990	87	27	its	its	PRON
easat-2990	87	28	solution	solution	NOUN
easat-2990	87	29	into	into	ADP
easat-2990	87	30	an	an	DET
easat-2990	87	31	expansion	expansion	NOUN
easat-2990	87	32	with	with	ADP
easat-2990	87	33	respect	respect	NOUN
easat-2990	87	34	to	to	ADP
easat-2990	87	35	some	some	DET
easat-2990	87	36	basis	basis	NOUN
easat-2990	87	37	,	,	PUNCT
easat-2990	87	38	where	where	SCONJ
easat-2990	87	39	we	we	PRON
easat-2990	87	40	can	can	AUX
easat-2990	87	41	exploit	exploit	VERB
easat-2990	87	42	favorable	favorable	ADJ
easat-2990	87	43	properties	property	NOUN
easat-2990	87	44	of	of	ADP
easat-2990	87	45	the	the	DET
easat-2990	87	46	expansion	expansion	NOUN
easat-2990	87	47	coefficients	coefficient	NOUN
easat-2990	87	48	,	,	PUNCT
easat-2990	87	49	such	such	ADJ
easat-2990	87	50	as	as	ADP
easat-2990	87	51	decay	decay	NOUN
easat-2990	87	52	,	,	PUNCT
easat-2990	87	53	sparsity	sparsity	NOUN
easat-2990	87	54	,	,	PUNCT
easat-2990	87	55	or	or	CCONJ
easat-2990	87	56	oscillatory	oscillatory	ADJ
easat-2990	87	57	behavior[21	behavior[21	NOUN
easat-2990	87	58	]	]	PUNCT
easat-2990	87	59	.	.	PUNCT
easat-2990	88	1	the	the	DET
easat-2990	88	2	solution	solution	NOUN
easat-2990	88	3	of	of	ADP
easat-2990	88	4	partial	partial	ADJ
easat-2990	88	5	differential	differential	ADJ
easat-2990	88	6	equations	equation	NOUN
easat-2990	88	7	typically	typically	ADV
easat-2990	88	8	involves	involve	VERB
easat-2990	88	9	examining	examine	VERB
easat-2990	88	10	an	an	DET
easat-2990	88	11	infinite	infinite	ADJ
easat-2990	88	12	-	-	PUNCT
easat-2990	88	13	dimensional	dimensional	ADJ
easat-2990	88	14	hilbert	hilbert	NOUN
easat-2990	88	15	or	or	CCONJ
easat-2990	88	16	separable	separable	ADJ
easat-2990	88	17	banach	banach	NOUN
easat-2990	88	18	space	space	NOUN
easat-2990	88	19	,	,	PUNCT
easat-2990	88	20	where	where	SCONJ
easat-2990	88	21	there	there	PRON
easat-2990	88	22	may	may	AUX
easat-2990	88	23	be	be	AUX
easat-2990	88	24	a	a	DET
easat-2990	88	25	natural	natural	ADJ
easat-2990	88	26	orthogonal	orthogonal	ADJ
easat-2990	88	27	basis	basis	NOUN
easat-2990	88	28	to	to	PART
easat-2990	88	29	work	work	VERB
easat-2990	88	30	with	with	ADP
easat-2990	88	31	.	.	PUNCT
easat-2990	89	1	an	an	DET
easat-2990	89	2	example	example	NOUN
easat-2990	89	3	of	of	ADP
easat-2990	89	4	this	this	DET
easat-2990	89	5	scenario	scenario	NOUN
easat-2990	89	6	is	be	AUX
easat-2990	89	7	the	the	DET
easat-2990	89	8	spectral	spectral	ADJ
easat-2990	89	9	galerkin	galerkin	ADJ
easat-2990	89	10	method	method	NOUN
easat-2990	89	11	for	for	ADP
easat-2990	89	12	solving	solve	VERB
easat-2990	89	13	elliptic	elliptic	ADJ
easat-2990	89	14	partial	partial	ADJ
easat-2990	89	15	differential	differential	NOUN
easat-2990	89	16	equations	equation	NOUN
easat-2990	89	17	,	,	PUNCT
easat-2990	89	18	which	which	PRON
easat-2990	89	19	relies	rely	VERB
easat-2990	89	20	on	on	ADP
easat-2990	89	21	the	the	DET
easat-2990	89	22	eigenfunctions	eigenfunction	NOUN
easat-2990	89	23	of	of	ADP
easat-2990	89	24	associated	associated	ADJ
easat-2990	89	25	differential	differential	NOUN
easat-2990	89	26	operators	operator	NOUN
easat-2990	89	27	.	.	PUNCT
easat-2990	90	1	unfortunately	unfortunately	ADV
easat-2990	90	2	,	,	PUNCT
easat-2990	90	3	there	there	PRON
easat-2990	90	4	are	be	VERB
easat-2990	90	5	not	not	PART
easat-2990	90	6	many	many	ADJ
easat-2990	90	7	natural	natural	ADJ
easat-2990	90	8	orthogonal	orthogonal	ADJ
easat-2990	90	9	(	(	PUNCT
easat-2990	90	10	or	or	CCONJ
easat-2990	90	11	near	near	ADV
easat-2990	90	12	-	-	PUNCT
easat-2990	90	13	orthogonal	orthogonal	NOUN
easat-2990	90	14	)	)	PUNCT
easat-2990	90	15	bases	basis	NOUN
easat-2990	90	16	available	available	ADJ
easat-2990	90	17	,	,	PUNCT
easat-2990	90	18	and	and	CCONJ
easat-2990	90	19	if	if	SCONJ
easat-2990	90	20	there	there	PRON
easat-2990	90	21	are	be	VERB
easat-2990	90	22	any	any	PRON
easat-2990	90	23	,	,	PUNCT
easat-2990	90	24	they	they	PRON
easat-2990	90	25	do	do	AUX
easat-2990	90	26	not	not	PART
easat-2990	90	27	easily	easily	ADV
easat-2990	90	28	adapt	adapt	VERB
easat-2990	90	29	to	to	ADP
easat-2990	90	30	spatially	spatially	ADV
easat-2990	90	31	inhomogeneous	inhomogeneous	ADJ
easat-2990	90	32	grids	grid	NOUN
easat-2990	90	33	commonly	commonly	ADV
easat-2990	90	34	used	use	VERB
easat-2990	90	35	in	in	ADP
easat-2990	90	36	practice[22	practice[22	PROPN
easat-2990	90	37	]	]	X
easat-2990	90	38	.	.	PUNCT
easat-2990	91	1	3	3	X
easat-2990	91	2	.	.	X
easat-2990	91	3	collocation	collocation	NOUN
easat-2990	91	4	methods	method	NOUN
easat-2990	91	5	in	in	ADP
easat-2990	91	6	numerical	numerical	ADJ
easat-2990	91	7	analysis	analysis	NOUN
easat-2990	91	8	the	the	DET
easat-2990	91	9	concept	concept	NOUN
easat-2990	91	10	of	of	ADP
easat-2990	91	11	the	the	DET
easat-2990	91	12	collocation	collocation	NOUN
easat-2990	91	13	method	method	NOUN
easat-2990	91	14	is	be	AUX
easat-2990	91	15	based	base	VERB
easat-2990	91	16	on	on	ADP
easat-2990	91	17	the	the	DET
easat-2990	91	18	choice	choice	NOUN
easat-2990	91	19	of	of	ADP
easat-2990	91	20	nodes	node	NOUN
easat-2990	91	21	in	in	ADP
easat-2990	91	22	the	the	DET
easat-2990	91	23	definition	definition	NOUN
easat-2990	91	24	interval	interval	NOUN
easat-2990	91	25	on	on	ADP
easat-2990	91	26	which	which	PRON
easat-2990	91	27	the	the	DET
easat-2990	91	28	function	function	NOUN
easat-2990	91	29	to	to	PART
easat-2990	91	30	be	be	AUX
easat-2990	91	31	interpolated	interpolate	VERB
easat-2990	91	32	would	would	AUX
easat-2990	91	33	be	be	AUX
easat-2990	91	34	sampled	sample	VERB
easat-2990	91	35	.	.	PUNCT
easat-2990	92	1	in	in	ADP
easat-2990	92	2	this	this	DET
easat-2990	92	3	kind	kind	NOUN
easat-2990	92	4	of	of	ADP
easat-2990	92	5	method	method	NOUN
easat-2990	92	6	,	,	PUNCT
easat-2990	92	7	the	the	DET
easat-2990	92	8	trial	trial	NOUN
easat-2990	92	9	function	function	NOUN
easat-2990	92	10	is	be	AUX
easat-2990	92	11	chosen	choose	VERB
easat-2990	92	12	as	as	ADP
easat-2990	92	13	the	the	DET
easat-2990	92	14	polynomial	polynomial	NOUN
easat-2990	92	15	for	for	ADP
easat-2990	92	16	which	which	PRON
easat-2990	92	17	the	the	DET
easat-2990	92	18	approximation	approximation	NOUN
easat-2990	92	19	to	to	ADP
easat-2990	92	20	the	the	DET
easat-2990	92	21	variation	variation	NOUN
easat-2990	92	22	of	of	ADP
easat-2990	92	23	the	the	DET
easat-2990	92	24	intensified	intensify	VERB
easat-2990	92	25	function	function	NOUN
easat-2990	92	26	is	be	AUX
easat-2990	92	27	obtained	obtain	VERB
easat-2990	92	28	by	by	ADP
easat-2990	92	29	adding	add	VERB
easat-2990	92	30	the	the	DET
easat-2990	92	31	approximation	approximation	NOUN
easat-2990	92	32	to	to	ADP
easat-2990	92	33	the	the	DET
easat-2990	92	34	variation	variation	NOUN
easat-2990	92	35	of	of	ADP
easat-2990	92	36	the	the	DET
easat-2990	92	37	intensified	intensify	VERB
easat-2990	92	38	function	function	NOUN
easat-2990	92	39	at	at	ADP
easat-2990	92	40	each	each	DET
easat-2990	92	41	node	node	NOUN
easat-2990	92	42	.	.	PUNCT
easat-2990	93	1	the	the	DET
easat-2990	93	2	node	node	NOUN
easat-2990	93	3	i	i	PRON
easat-2990	93	4	is	be	AUX
easat-2990	93	5	represented	represent	VERB
easat-2990	93	6	by	by	ADP
easat-2990	93	7	ξi	ξi	NOUN
easat-2990	93	8	.	.	PUNCT
easat-2990	94	1	let	let	VERB
easat-2990	94	2	m	m	PRON
easat-2990	94	3	be	be	AUX
easat-2990	94	4	the	the	DET
easat-2990	94	5	number	number	NOUN
easat-2990	94	6	of	of	ADP
easat-2990	94	7	nodes	node	NOUN
easat-2990	94	8	for	for	ADP
easat-2990	94	9	the	the	DET
easat-2990	94	10	node	node	NOUN
easat-2990	94	11	representation[23	representation[23	NOUN
easat-2990	94	12	]	]	PUNCT
easat-2990	94	13	.	.	PUNCT
easat-2990	95	1	increasing	increase	VERB
easat-2990	95	2	the	the	DET
easat-2990	95	3	number	number	NOUN
easat-2990	95	4	of	of	ADP
easat-2990	95	5	nodes	node	NOUN
easat-2990	95	6	that	that	PRON
easat-2990	95	7	defines	define	VERB
easat-2990	95	8	each	each	DET
easat-2990	95	9	node	node	NOUN
easat-2990	95	10	increases	increase	VERB
easat-2990	95	11	the	the	DET
easat-2990	95	12	precision	precision	NOUN
easat-2990	95	13	of	of	ADP
easat-2990	95	14	the	the	DET
easat-2990	95	15	obtained	obtain	VERB
easat-2990	95	16	solution	solution	NOUN
easat-2990	95	17	.	.	PUNCT
easat-2990	96	1	the	the	DET
easat-2990	96	2	most	most	ADJ
easat-2990	96	3	4603	4603	NUM
easat-2990	96	4	edelweiss	edelweiss	PROPN
easat-2990	96	5	applied	apply	VERB
easat-2990	96	6	science	science	NOUN
easat-2990	96	7	and	and	CCONJ
easat-2990	96	8	technology	technology	NOUN
easat-2990	96	9	issn	issn	PROPN
easat-2990	96	10	:	:	PUNCT
easat-2990	96	11	2576	2576	NUM
easat-2990	96	12	-	-	SYM
easat-2990	96	13	8484	8484	NUM
easat-2990	96	14	vol	vol	NOUN
easat-2990	96	15	.	.	PROPN
easat-2990	96	16	8	8	NUM
easat-2990	96	17	,	,	PUNCT
easat-2990	96	18	no	no	INTJ
easat-2990	96	19	.	.	NOUN
easat-2990	97	1	6	6	NUM
easat-2990	97	2	:	:	SYM
easat-2990	97	3	4599	4599	NUM
easat-2990	97	4	-	-	SYM
easat-2990	97	5	4610	4610	NUM
easat-2990	97	6	,	,	PUNCT
easat-2990	97	7	2024	2024	NUM
easat-2990	97	8	doi	doi	NOUN
easat-2990	97	9	:	:	PUNCT
easat-2990	97	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	97	11	©	©	PROPN
easat-2990	97	12	2024	2024	NUM
easat-2990	97	13	by	by	ADP
easat-2990	97	14	the	the	DET
easat-2990	97	15	author	author	NOUN
easat-2990	97	16	;	;	PUNCT
easat-2990	97	17	licensee	licensee	PROPN
easat-2990	97	18	learning	learning	NOUN
easat-2990	97	19	gate	gate	VERB
easat-2990	97	20	important	important	ADJ
easat-2990	97	21	property	property	NOUN
easat-2990	97	22	of	of	ADP
easat-2990	97	23	this	this	DET
easat-2990	97	24	type	type	NOUN
easat-2990	97	25	of	of	ADP
easat-2990	97	26	method	method	NOUN
easat-2990	97	27	is	be	AUX
easat-2990	97	28	that	that	SCONJ
easat-2990	97	29	the	the	DET
easat-2990	97	30	computing	computing	NOUN
easat-2990	97	31	time	time	NOUN
easat-2990	97	32	is	be	AUX
easat-2990	97	33	quite	quite	ADV
easat-2990	97	34	low	low	ADJ
easat-2990	97	35	.	.	PUNCT
easat-2990	98	1	this	this	PRON
easat-2990	98	2	is	be	AUX
easat-2990	98	3	very	very	ADV
easat-2990	98	4	significant	significant	ADJ
easat-2990	98	5	in	in	ADP
easat-2990	98	6	engineering	engineering	NOUN
easat-2990	98	7	applications	application	NOUN
easat-2990	98	8	.	.	PUNCT
easat-2990	99	1	the	the	DET
easat-2990	99	2	name	name	NOUN
easat-2990	99	3	of	of	ADP
easat-2990	99	4	the	the	DET
easat-2990	99	5	method	method	NOUN
easat-2990	99	6	comes	come	VERB
easat-2990	99	7	from	from	ADP
easat-2990	99	8	the	the	DET
easat-2990	99	9	fact	fact	NOUN
easat-2990	99	10	that	that	SCONJ
easat-2990	99	11	the	the	DET
easat-2990	99	12	polynomial	polynomial	NOUN
easat-2990	99	13	is	be	AUX
easat-2990	99	14	interpolated	interpolate	VERB
easat-2990	99	15	at	at	ADP
easat-2990	99	16	some	some	DET
easat-2990	99	17	point	point	NOUN
easat-2990	99	18	in	in	ADP
easat-2990	99	19	the	the	DET
easat-2990	99	20	node	node	ADJ
easat-2990	99	21	representation	representation	NOUN
easat-2990	99	22	,	,	PUNCT
easat-2990	99	23	and	and	CCONJ
easat-2990	99	24	we	we	PRON
easat-2990	99	25	define	define	VERB
easat-2990	99	26	the	the	DET
easat-2990	99	27	collocation	collocation	NOUN
easat-2990	99	28	method	method	NOUN
easat-2990	99	29	as	as	ADP
easat-2990	99	30	the	the	DET
easat-2990	99	31	monomial	monomial	ADJ
easat-2990	99	32	-	-	PUNCT
easat-2990	99	33	based	base	VERB
easat-2990	99	34	collocation	collocation	NOUN
easat-2990	99	35	method	method	NOUN
easat-2990	99	36	.	.	PUNCT
easat-2990	100	1	this	this	DET
easat-2990	100	2	collocation	collocation	NOUN
easat-2990	100	3	method	method	NOUN
easat-2990	100	4	is	be	AUX
easat-2990	100	5	used	use	VERB
easat-2990	100	6	in	in	ADP
easat-2990	100	7	continuous	continuous	ADJ
easat-2990	100	8	beam	beam	NOUN
easat-2990	100	9	problems	problem	NOUN
easat-2990	100	10	and	and	CCONJ
easat-2990	100	11	applied	apply	VERB
easat-2990	100	12	in	in	ADP
easat-2990	100	13	multi	multi	ADJ
easat-2990	100	14	-	-	ADJ
easat-2990	100	15	dimensional	dimensional	ADJ
easat-2990	100	16	problems	problem	NOUN
easat-2990	100	17	,	,	PUNCT
easat-2990	100	18	which	which	PRON
easat-2990	100	19	always	always	ADV
easat-2990	100	20	include	include	VERB
easat-2990	100	21	applications	application	NOUN
easat-2990	100	22	in	in	ADP
easat-2990	100	23	its	its	PRON
easat-2990	100	24	particular	particular	ADJ
easat-2990	100	25	case[24	case[24	NOUN
easat-2990	100	26	]	]	PUNCT
easat-2990	100	27	.	.	PUNCT
easat-2990	101	1	collocation	collocation	NOUN
easat-2990	101	2	methods	method	NOUN
easat-2990	101	3	should	should	AUX
easat-2990	101	4	be	be	AUX
easat-2990	101	5	designed	design	VERB
easat-2990	101	6	to	to	PART
easat-2990	101	7	enable	enable	VERB
easat-2990	101	8	the	the	DET
easat-2990	101	9	matching	matching	NOUN
easat-2990	101	10	of	of	ADP
easat-2990	101	11	the	the	DET
easat-2990	101	12	pdf	pdf	NOUN
easat-2990	101	13	of	of	ADP
easat-2990	101	14	both	both	DET
easat-2990	101	15	pdf	pdf	NOUN
easat-2990	101	16	and	and	CCONJ
easat-2990	101	17	rate	rate	NOUN
easat-2990	101	18	conditions	condition	NOUN
easat-2990	101	19	.	.	PUNCT
easat-2990	102	1	these	these	DET
easat-2990	102	2	conditions	condition	NOUN
easat-2990	102	3	are	be	AUX
easat-2990	102	4	met	meet	VERB
easat-2990	102	5	by	by	ADP
easat-2990	102	6	the	the	DET
easat-2990	102	7	hermite	hermite	ADJ
easat-2990	102	8	polynomial	polynomial	ADJ
easat-2990	102	9	collocation	collocation	NOUN
easat-2990	102	10	technique	technique	NOUN
easat-2990	102	11	.	.	PUNCT
easat-2990	103	1	the	the	DET
easat-2990	103	2	derivative	derivative	ADJ
easat-2990	103	3	functions	function	NOUN
easat-2990	103	4	are	be	AUX
easat-2990	103	5	preserved	preserve	VERB
easat-2990	103	6	,	,	PUNCT
easat-2990	103	7	and	and	CCONJ
easat-2990	103	8	their	their	PRON
easat-2990	103	9	corresponding	correspond	VERB
easat-2990	103	10	collocation	collocation	NOUN
easat-2990	103	11	weights	weight	NOUN
easat-2990	103	12	are	be	AUX
easat-2990	103	13	used	use	VERB
easat-2990	103	14	to	to	PART
easat-2990	103	15	match	match	VERB
easat-2990	103	16	the	the	DET
easat-2990	103	17	lhs	lhs	PROPN
easat-2990	103	18	of	of	ADP
easat-2990	103	19	each	each	PRON
easat-2990	103	20	of	of	ADP
easat-2990	103	21	the	the	DET
easat-2990	103	22	equations	equation	NOUN
easat-2990	103	23	for	for	ADP
easat-2990	103	24	the	the	DET
easat-2990	103	25	two	two	NUM
easat-2990	103	26	pdfs	pdfs	NOUN
easat-2990	103	27	in	in	ADP
easat-2990	103	28	order	order	NOUN
easat-2990	103	29	to	to	PART
easat-2990	103	30	satisfy	satisfy	VERB
easat-2990	103	31	the	the	DET
easat-2990	103	32	extent	extent	NOUN
easat-2990	103	33	of	of	ADP
easat-2990	103	34	the	the	DET
easat-2990	103	35	polynomial	polynomial	ADJ
easat-2990	103	36	condition	condition	NOUN
easat-2990	103	37	.	.	PUNCT
easat-2990	104	1	collocation	collocation	NOUN
easat-2990	104	2	methods	method	NOUN
easat-2990	104	3	have	have	AUX
easat-2990	104	4	used	use	VERB
easat-2990	104	5	a	a	DET
easat-2990	104	6	variety	variety	NOUN
easat-2990	104	7	of	of	ADP
easat-2990	104	8	functions	function	NOUN
easat-2990	104	9	,	,	PUNCT
easat-2990	104	10	including	include	VERB
easat-2990	104	11	lagrangian	lagrangian	ADJ
easat-2990	104	12	,	,	PUNCT
easat-2990	104	13	orthogonal	orthogonal	ADJ
easat-2990	104	14	functions	function	NOUN
easat-2990	104	15	,	,	PUNCT
easat-2990	104	16	and	and	CCONJ
easat-2990	104	17	basis	basis	NOUN
easat-2990	104	18	functions	function	NOUN
easat-2990	104	19	.	.	PUNCT
easat-2990	105	1	the	the	DET
easat-2990	105	2	pdf	pdf	NOUN
easat-2990	105	3	for	for	ADP
easat-2990	105	4	the	the	DET
easat-2990	105	5	lagrangian	lagrangian	ADJ
easat-2990	105	6	covariance	covariance	NOUN
easat-2990	105	7	function	function	NOUN
easat-2990	105	8	ensures	ensure	VERB
easat-2990	105	9	that	that	SCONJ
easat-2990	105	10	the	the	DET
easat-2990	105	11	matching	matching	NOUN
easat-2990	105	12	conditions	condition	NOUN
easat-2990	105	13	are	be	AUX
easat-2990	105	14	mathematically	mathematically	ADV
easat-2990	105	15	imposed	impose	VERB
easat-2990	105	16	on	on	ADP
easat-2990	105	17	each	each	PRON
easat-2990	105	18	of	of	ADP
easat-2990	105	19	these	these	DET
easat-2990	105	20	moments	moment	NOUN
easat-2990	105	21	relating	relate	VERB
easat-2990	105	22	to	to	ADP
easat-2990	105	23	the	the	DET
easat-2990	105	24	continuous	continuous	ADJ
easat-2990	105	25	random	random	ADJ
easat-2990	105	26	process[25	process[25	NOUN
easat-2990	105	27	]	]	X
easat-2990	105	28	.	.	PUNCT
easat-2990	106	1	3.1	3.1	NUM
easat-2990	106	2	.	.	PUNCT
easat-2990	107	1	basics	basic	NOUN
easat-2990	107	2	of	of	ADP
easat-2990	107	3	collocation	collocation	NOUN
easat-2990	107	4	methods	method	NOUN
easat-2990	107	5	a	a	DET
easat-2990	107	6	collocation	collocation	NOUN
easat-2990	107	7	method	method	NOUN
easat-2990	107	8	uses	use	VERB
easat-2990	107	9	the	the	DET
easat-2990	107	10	equation	equation	NOUN
easat-2990	107	11	's	's	PART
easat-2990	107	12	values	value	NOUN
easat-2990	107	13	at	at	ADP
easat-2990	107	14	interpolation	interpolation	NOUN
easat-2990	107	15	or	or	CCONJ
easat-2990	107	16	collocation	collocation	NOUN
easat-2990	107	17	nodes	node	NOUN
easat-2990	107	18	instead	instead	ADV
easat-2990	107	19	of	of	ADP
easat-2990	107	20	using	use	VERB
easat-2990	107	21	any	any	DET
easat-2990	107	22	information	information	NOUN
easat-2990	107	23	such	such	ADJ
easat-2990	107	24	as	as	ADP
easat-2990	107	25	derivatives	derivative	NOUN
easat-2990	107	26	at	at	ADP
easat-2990	107	27	the	the	DET
easat-2990	107	28	respective	respective	ADJ
easat-2990	107	29	node	node	NOUN
easat-2990	107	30	points	point	NOUN
easat-2990	107	31	.	.	PUNCT
easat-2990	108	1	it	it	PRON
easat-2990	108	2	works	work	VERB
easat-2990	108	3	only	only	ADV
easat-2990	108	4	with	with	ADP
easat-2990	108	5	the	the	DET
easat-2990	108	6	values	value	NOUN
easat-2990	108	7	of	of	ADP
easat-2990	108	8	the	the	DET
easat-2990	108	9	equations[26	equations[26	NOUN
easat-2990	108	10	]	]	X
easat-2990	108	11	.	.	PUNCT
easat-2990	109	1	to	to	PART
easat-2990	109	2	obtain	obtain	VERB
easat-2990	109	3	stable	stable	ADJ
easat-2990	109	4	and	and	CCONJ
easat-2990	109	5	accurate	accurate	ADJ
easat-2990	109	6	results	result	NOUN
easat-2990	109	7	,	,	PUNCT
easat-2990	109	8	typically	typically	ADV
easat-2990	109	9	,	,	PUNCT
easat-2990	109	10	the	the	DET
easat-2990	109	11	distribution	distribution	NOUN
easat-2990	109	12	of	of	ADP
easat-2990	109	13	the	the	DET
easat-2990	109	14	nodes	node	NOUN
easat-2990	109	15	should	should	AUX
easat-2990	109	16	be	be	AUX
easat-2990	109	17	dense	dense	ADJ
easat-2990	109	18	at	at	ADP
easat-2990	109	19	the	the	DET
easat-2990	109	20	boundaries	boundary	NOUN
easat-2990	109	21	and	and	CCONJ
easat-2990	109	22	,	,	PUNCT
easat-2990	109	23	for	for	ADP
easat-2990	109	24	some	some	DET
easat-2990	109	25	problems	problem	NOUN
easat-2990	109	26	,	,	PUNCT
easat-2990	109	27	it	it	PRON
easat-2990	109	28	also	also	ADV
easat-2990	109	29	needs	need	VERB
easat-2990	109	30	dense	dense	ADJ
easat-2990	109	31	distributions	distribution	NOUN
easat-2990	109	32	even	even	ADV
easat-2990	109	33	after	after	ADP
easat-2990	109	34	a	a	DET
easat-2990	109	35	remeshing	remeshing	NOUN
easat-2990	109	36	at	at	ADP
easat-2990	109	37	specific	specific	ADJ
easat-2990	109	38	inner	inner	ADJ
easat-2990	109	39	subdomains	subdomain	NOUN
easat-2990	109	40	.	.	PUNCT
easat-2990	110	1	in	in	ADP
easat-2990	110	2	these	these	DET
easat-2990	110	3	cases	case	NOUN
easat-2990	110	4	,	,	PUNCT
easat-2990	110	5	the	the	DET
easat-2990	110	6	matrix	matrix	NOUN
easat-2990	110	7	size	size	NOUN
easat-2990	110	8	increases	increase	VERB
easat-2990	110	9	with	with	ADP
easat-2990	110	10	the	the	DET
easat-2990	110	11	order	order	NOUN
easat-2990	110	12	n	n	PROPN
easat-2990	110	13	of	of	ADP
easat-2990	110	14	the	the	DET
easat-2990	110	15	integrated	integrate	VERB
easat-2990	110	16	function	function	NOUN
easat-2990	110	17	,	,	PUNCT
easat-2990	110	18	which	which	PRON
easat-2990	110	19	leads	lead	VERB
easat-2990	110	20	to	to	ADP
easat-2990	110	21	a	a	DET
easat-2990	110	22	corresponding	corresponding	ADJ
easat-2990	110	23	increase	increase	NOUN
easat-2990	110	24	in	in	ADP
easat-2990	110	25	the	the	DET
easat-2990	110	26	computational	computational	ADJ
easat-2990	110	27	cost	cost	NOUN
easat-2990	110	28	.	.	PUNCT
easat-2990	111	1	however	however	ADV
easat-2990	111	2	,	,	PUNCT
easat-2990	111	3	the	the	DET
easat-2990	111	4	increase	increase	NOUN
easat-2990	111	5	in	in	ADP
easat-2990	111	6	order	order	NOUN
easat-2990	111	7	is	be	AUX
easat-2990	111	8	directly	directly	ADV
easat-2990	111	9	related	relate	VERB
easat-2990	111	10	to	to	ADP
easat-2990	111	11	the	the	DET
easat-2990	111	12	increase	increase	NOUN
easat-2990	111	13	in	in	ADP
easat-2990	111	14	accuracy	accuracy	NOUN
easat-2990	111	15	order	order	NOUN
easat-2990	111	16	and	and	CCONJ
easat-2990	111	17	,	,	PUNCT
easat-2990	111	18	for	for	ADP
easat-2990	111	19	this	this	DET
easat-2990	111	20	reason	reason	NOUN
easat-2990	111	21	,	,	PUNCT
easat-2990	111	22	a	a	DET
easat-2990	111	23	lower	lower	ADV
easat-2990	111	24	dense	dense	ADJ
easat-2990	111	25	node	node	ADJ
easat-2990	111	26	distribution	distribution	NOUN
easat-2990	111	27	can	can	AUX
easat-2990	111	28	be	be	AUX
easat-2990	111	29	used	use	VERB
easat-2990	111	30	with	with	ADP
easat-2990	111	31	a	a	DET
easat-2990	111	32	relatively	relatively	ADV
easat-2990	111	33	low	low	ADJ
easat-2990	111	34	cost	cost	NOUN
easat-2990	111	35	.	.	PUNCT
easat-2990	112	1	currently	currently	ADV
easat-2990	112	2	,	,	PUNCT
easat-2990	112	3	there	there	PRON
easat-2990	112	4	are	be	VERB
easat-2990	112	5	several	several	ADJ
easat-2990	112	6	formulations	formulation	NOUN
easat-2990	112	7	such	such	ADJ
easat-2990	112	8	as	as	ADP
easat-2990	112	9	t	t	NOUN
easat-2990	112	10	-	-	PUNCT
easat-2990	112	11	collocation	collocation	NOUN
easat-2990	112	12	,	,	PUNCT
easat-2990	112	13	tau	tau	PROPN
easat-2990	112	14	,	,	PUNCT
easat-2990	112	15	f	f	PROPN
easat-2990	112	16	,	,	PUNCT
easat-2990	112	17	gl	gl	PROPN
easat-2990	112	18	,	,	PUNCT
easat-2990	112	19	and	and	CCONJ
easat-2990	112	20	chebyshev	chebyshev	VERB
easat-2990	112	21	in	in	ADP
easat-2990	112	22	addition	addition	NOUN
easat-2990	112	23	to	to	ADP
easat-2990	112	24	being	be	AUX
easat-2990	112	25	used	use	VERB
easat-2990	112	26	even	even	ADV
easat-2990	112	27	with	with	ADP
easat-2990	112	28	other	other	ADJ
easat-2990	112	29	basis	basis	NOUN
easat-2990	112	30	system	system	NOUN
easat-2990	112	31	functions[27	functions[27	NOUN
easat-2990	112	32	]	]	PUNCT
easat-2990	112	33	.	.	PUNCT
easat-2990	113	1	3.2	3.2	NUM
easat-2990	113	2	.	.	PUNCT
easat-2990	113	3	advantages	advantage	NOUN
easat-2990	113	4	and	and	CCONJ
easat-2990	113	5	limitations	limitation	NOUN
easat-2990	113	6	while	while	SCONJ
easat-2990	113	7	direct	direct	ADJ
easat-2990	113	8	spectral	spectral	ADJ
easat-2990	113	9	collocation	collocation	NOUN
easat-2990	113	10	methods	method	NOUN
easat-2990	113	11	work	work	VERB
easat-2990	113	12	with	with	ADP
easat-2990	113	13	equidistant	equidistant	ADJ
easat-2990	113	14	collocation	collocation	NOUN
easat-2990	113	15	points	point	NOUN
easat-2990	113	16	,	,	PUNCT
easat-2990	113	17	wavelet	wavelet	NOUN
easat-2990	113	18	-	-	PUNCT
easat-2990	113	19	based	base	VERB
easat-2990	113	20	collocation	collocation	NOUN
easat-2990	113	21	allows	allow	VERB
easat-2990	113	22	for	for	ADP
easat-2990	113	23	greater	great	ADJ
easat-2990	113	24	flexibility	flexibility	NOUN
easat-2990	113	25	through	through	ADP
easat-2990	113	26	the	the	DET
easat-2990	113	27	dilation	dilation	NOUN
easat-2990	113	28	and	and	CCONJ
easat-2990	113	29	localization	localization	NOUN
easat-2990	113	30	properties	property	NOUN
easat-2990	113	31	of	of	ADP
easat-2990	113	32	wavelet	wavelet	NOUN
easat-2990	113	33	bases	basis	NOUN
easat-2990	113	34	.	.	PUNCT
easat-2990	114	1	the	the	DET
easat-2990	114	2	wavelet	wavelet	NOUN
easat-2990	114	3	-	-	PUNCT
easat-2990	114	4	coefficient	coefficient	NOUN
easat-2990	114	5	vector	vector	NOUN
easat-2990	114	6	approximating	approximate	VERB
easat-2990	114	7	the	the	DET
easat-2990	114	8	unknown	unknown	ADJ
easat-2990	114	9	solution	solution	NOUN
easat-2990	114	10	is	be	AUX
easat-2990	114	11	more	more	ADV
easat-2990	114	12	densely	densely	ADV
easat-2990	114	13	populated	populated	ADJ
easat-2990	114	14	in	in	ADP
easat-2990	114	15	regions	region	NOUN
easat-2990	114	16	where	where	SCONJ
easat-2990	114	17	the	the	DET
easat-2990	114	18	solution	solution	NOUN
easat-2990	114	19	changes	change	VERB
easat-2990	114	20	fast	fast	ADV
easat-2990	114	21	,	,	PUNCT
easat-2990	114	22	and	and	CCONJ
easat-2990	114	23	it	it	PRON
easat-2990	114	24	becomes	become	VERB
easat-2990	114	25	more	more	ADV
easat-2990	114	26	sparse	sparse	ADJ
easat-2990	114	27	elsewhere	elsewhere	ADV
easat-2990	114	28	.	.	PUNCT
easat-2990	115	1	this	this	PRON
easat-2990	115	2	allows	allow	VERB
easat-2990	115	3	one	one	PRON
easat-2990	115	4	to	to	PART
easat-2990	115	5	focus	focus	VERB
easat-2990	115	6	computational	computational	ADJ
easat-2990	115	7	effort	effort	NOUN
easat-2990	115	8	where	where	SCONJ
easat-2990	115	9	it	it	PRON
easat-2990	115	10	is	be	AUX
easat-2990	115	11	needed	need	VERB
easat-2990	115	12	most	most	ADV
easat-2990	115	13	.	.	PUNCT
easat-2990	116	1	solutions	solution	NOUN
easat-2990	116	2	that	that	PRON
easat-2990	116	3	have	have	AUX
easat-2990	116	4	jumps	jump	NOUN
easat-2990	116	5	,	,	PUNCT
easat-2990	116	6	singularities	singularity	NOUN
easat-2990	116	7	,	,	PUNCT
easat-2990	116	8	or	or	CCONJ
easat-2990	116	9	boundary	boundary	ADJ
easat-2990	116	10	layers	layer	NOUN
easat-2990	116	11	are	be	AUX
easat-2990	116	12	represented	represent	VERB
easat-2990	116	13	accurately	accurately	ADV
easat-2990	116	14	with	with	ADP
easat-2990	116	15	a	a	DET
easat-2990	116	16	relatively	relatively	ADV
easat-2990	116	17	small	small	ADJ
easat-2990	116	18	number	number	NOUN
easat-2990	116	19	of	of	ADP
easat-2990	116	20	coefficients	coefficient	NOUN
easat-2990	116	21	.	.	PUNCT
easat-2990	117	1	this	this	PRON
easat-2990	117	2	,	,	PUNCT
easat-2990	117	3	in	in	ADP
easat-2990	117	4	effect	effect	NOUN
easat-2990	117	5	,	,	PUNCT
easat-2990	117	6	localizes	localize	VERB
easat-2990	117	7	the	the	DET
easat-2990	117	8	global	global	ADJ
easat-2990	117	9	operators	operator	NOUN
easat-2990	117	10	that	that	PRON
easat-2990	117	11	we	we	PRON
easat-2990	117	12	are	be	AUX
easat-2990	117	13	using	use	VERB
easat-2990	117	14	so	so	SCONJ
easat-2990	117	15	that	that	SCONJ
easat-2990	117	16	a	a	DET
easat-2990	117	17	smaller	small	ADJ
easat-2990	117	18	truncation	truncation	NOUN
easat-2990	117	19	of	of	ADP
easat-2990	117	20	the	the	DET
easat-2990	117	21	operator	operator	NOUN
easat-2990	117	22	is	be	AUX
easat-2990	117	23	needed	need	VERB
easat-2990	117	24	to	to	PART
easat-2990	117	25	have	have	VERB
easat-2990	117	26	accurate	accurate	ADJ
easat-2990	117	27	results	result	NOUN
easat-2990	117	28	.	.	PUNCT
easat-2990	118	1	the	the	DET
easat-2990	118	2	use	use	NOUN
easat-2990	118	3	of	of	ADP
easat-2990	118	4	orthogonality	orthogonality	NOUN
easat-2990	118	5	of	of	ADP
easat-2990	118	6	the	the	DET
easat-2990	118	7	wavelet	wavelet	NOUN
easat-2990	118	8	basis	basis	NOUN
easat-2990	118	9	functions	function	NOUN
easat-2990	118	10	,	,	PUNCT
easat-2990	118	11	as	as	ADV
easat-2990	118	12	well	well	ADV
easat-2990	118	13	as	as	ADP
easat-2990	118	14	orthogonality	orthogonality	NOUN
easat-2990	118	15	of	of	ADP
easat-2990	118	16	the	the	DET
easat-2990	118	17	wavelet	wavelet	NOUN
easat-2990	118	18	basis	basis	NOUN
easat-2990	118	19	functions	function	NOUN
easat-2990	118	20	over	over	ADP
easat-2990	118	21	the	the	DET
easat-2990	118	22	space	space	NOUN
easat-2990	118	23	of	of	ADP
easat-2990	118	24	continuous	continuous	ADJ
easat-2990	118	25	functions	function	NOUN
easat-2990	118	26	,	,	PUNCT
easat-2990	118	27	is	be	AUX
easat-2990	118	28	a	a	DET
easat-2990	118	29	crucial	crucial	ADJ
easat-2990	118	30	property	property	NOUN
easat-2990	118	31	.	.	PUNCT
easat-2990	119	1	the	the	DET
easat-2990	119	2	associated	associated	ADJ
easat-2990	119	3	quadrature	quadrature	NOUN
easat-2990	119	4	rules	rule	NOUN
easat-2990	119	5	minimize	minimize	VERB
easat-2990	119	6	the	the	DET
easat-2990	119	7	truncation	truncation	NOUN
easat-2990	119	8	error	error	NOUN
easat-2990	119	9	.	.	PUNCT
easat-2990	120	1	furthermore	furthermore	ADV
easat-2990	120	2	,	,	PUNCT
easat-2990	120	3	the	the	DET
easat-2990	120	4	coupling	coupling	NOUN
easat-2990	120	5	terms	term	NOUN
easat-2990	120	6	in	in	ADP
easat-2990	120	7	the	the	DET
easat-2990	120	8	weak	weak	ADJ
easat-2990	120	9	form	form	NOUN
easat-2990	120	10	are	be	AUX
easat-2990	120	11	,	,	PUNCT
easat-2990	120	12	to	to	ADP
easat-2990	120	13	a	a	DET
easat-2990	120	14	high	high	ADJ
easat-2990	120	15	degree	degree	NOUN
easat-2990	120	16	,	,	PUNCT
easat-2990	120	17	diagonal	diagonal	ADJ
easat-2990	120	18	or	or	CCONJ
easat-2990	120	19	block	block	NOUN
easat-2990	120	20	-	-	PUNCT
easat-2990	120	21	diagonal	diagonal	ADJ
easat-2990	120	22	in	in	ADP
easat-2990	120	23	the	the	DET
easat-2990	120	24	wavelet	wavelet	NOUN
easat-2990	120	25	-	-	PUNCT
easat-2990	120	26	coefficient	coefficient	NOUN
easat-2990	120	27	space	space	NOUN
easat-2990	120	28	,	,	PUNCT
easat-2990	120	29	which	which	PRON
easat-2990	120	30	greatly	greatly	ADV
easat-2990	120	31	reduces	reduce	VERB
easat-2990	120	32	the	the	DET
easat-2990	120	33	size	size	NOUN
easat-2990	120	34	of	of	ADP
easat-2990	120	35	the	the	DET
easat-2990	120	36	discretized	discretized	ADJ
easat-2990	120	37	system	system	NOUN
easat-2990	120	38	.	.	PUNCT
easat-2990	121	1	in	in	ADP
easat-2990	121	2	1d	1d	NUM
easat-2990	121	3	,	,	PUNCT
easat-2990	121	4	an	an	DET
easat-2990	121	5	n	n	CCONJ
easat-2990	121	6	-	-	PUNCT
easat-2990	121	7	point	point	NOUN
easat-2990	121	8	wavelet	wavelet	NOUN
easat-2990	121	9	quadrature	quadrature	NOUN
easat-2990	121	10	rule	rule	NOUN
easat-2990	121	11	is	be	AUX
easat-2990	121	12	associated	associate	VERB
easat-2990	121	13	with	with	ADP
easat-2990	121	14	an	an	DET
easat-2990	121	15	n	n	NUM
easat-2990	121	16	×	×	NOUN
easat-2990	121	17	n	n	CCONJ
easat-2990	121	18	(	(	PUNCT
easat-2990	121	19	block	block	NOUN
easat-2990	121	20	-	-	PUNCT
easat-2990	121	21	diagonal	diagonal	ADJ
easat-2990	121	22	)	)	PUNCT
easat-2990	121	23	quadrature	quadrature	NOUN
easat-2990	121	24	operator	operator	NOUN
easat-2990	121	25	.	.	PUNCT
easat-2990	122	1	the	the	DET
easat-2990	122	2	same	same	ADJ
easat-2990	122	3	property	property	NOUN
easat-2990	122	4	holds	hold	VERB
easat-2990	122	5	in	in	ADP
easat-2990	122	6	n	n	DET
easat-2990	122	7	dimensions[28	dimensions[28	NOUN
easat-2990	122	8	]	]	PUNCT
easat-2990	122	9	.	.	PUNCT
easat-2990	123	1	4	4	X
easat-2990	123	2	.	.	X
easat-2990	123	3	integration	integration	NOUN
easat-2990	123	4	of	of	ADP
easat-2990	123	5	wavelets	wavelet	NOUN
easat-2990	123	6	and	and	CCONJ
easat-2990	123	7	collocation	collocation	NOUN
easat-2990	123	8	methods	method	NOUN
easat-2990	123	9	it	it	PRON
easat-2990	123	10	is	be	AUX
easat-2990	123	11	necessary	necessary	ADJ
easat-2990	123	12	to	to	PART
easat-2990	123	13	discuss	discuss	VERB
easat-2990	123	14	collocation	collocation	NOUN
easat-2990	123	15	methods	method	NOUN
easat-2990	123	16	before	before	ADP
easat-2990	123	17	their	their	PRON
easat-2990	123	18	wavelet	wavelet	NOUN
easat-2990	123	19	-	-	PUNCT
easat-2990	123	20	based	base	VERB
easat-2990	123	21	forms	form	NOUN
easat-2990	123	22	.	.	PUNCT
easat-2990	124	1	we	we	PRON
easat-2990	124	2	use	use	VERB
easat-2990	124	3	polynomials	polynomial	NOUN
easat-2990	124	4	at	at	ADP
easat-2990	124	5	fixed	fix	VERB
easat-2990	124	6	abscissas	abscissa	NOUN
easat-2990	124	7	as	as	ADP
easat-2990	124	8	basis	basis	NOUN
easat-2990	124	9	functions	function	NOUN
easat-2990	124	10	.	.	PUNCT
easat-2990	125	1	we	we	PRON
easat-2990	125	2	compare	compare	VERB
easat-2990	125	3	the	the	DET
easat-2990	125	4	errors	error	NOUN
easat-2990	125	5	of	of	ADP
easat-2990	125	6	collocation	collocation	NOUN
easat-2990	125	7	methods	method	NOUN
easat-2990	125	8	discretized	discretize	VERB
easat-2990	125	9	directly	directly	ADV
easat-2990	125	10	to	to	ADP
easat-2990	125	11	the	the	DET
easat-2990	125	12	solutions	solution	NOUN
easat-2990	125	13	of	of	ADP
easat-2990	125	14	the	the	DET
easat-2990	125	15	integro	integro	ADJ
easat-2990	125	16	-	-	PUNCT
easat-2990	125	17	differential	differential	NOUN
easat-2990	125	18	systems	system	NOUN
easat-2990	125	19	.	.	PUNCT
easat-2990	126	1	the	the	DET
easat-2990	126	2	properties	property	NOUN
easat-2990	126	3	of	of	ADP
easat-2990	126	4	the	the	DET
easat-2990	126	5	factorizability	factorizability	NOUN
easat-2990	126	6	of	of	ADP
easat-2990	126	7	the	the	DET
easat-2990	126	8	process	process	NOUN
easat-2990	126	9	of	of	ADP
easat-2990	126	10	integration	integration	NOUN
easat-2990	126	11	are	be	AUX
easat-2990	126	12	presented	present	VERB
easat-2990	126	13	.	.	PUNCT
easat-2990	127	1	collocation	collocation	NOUN
easat-2990	127	2	methods	method	NOUN
easat-2990	127	3	are	be	AUX
easat-2990	127	4	weighted	weight	VERB
easat-2990	127	5	function	function	NOUN
easat-2990	127	6	approximation	approximation	NOUN
easat-2990	127	7	processes	process	NOUN
easat-2990	127	8	.	.	PUNCT
easat-2990	128	1	it	it	PRON
easat-2990	128	2	is	be	AUX
easat-2990	128	3	convenient	convenient	ADJ
easat-2990	128	4	to	to	PART
easat-2990	128	5	consider	consider	VERB
easat-2990	128	6	them	they	PRON
easat-2990	128	7	when	when	SCONJ
easat-2990	128	8	the	the	DET
easat-2990	128	9	trial	trial	NOUN
easat-2990	128	10	and	and	CCONJ
easat-2990	128	11	test	test	NOUN
easat-2990	128	12	functions	function	NOUN
easat-2990	128	13	possess	possess	VERB
easat-2990	128	14	the	the	DET
easat-2990	128	15	property	property	NOUN
easat-2990	128	16	of	of	ADP
easat-2990	128	17	being	be	AUX
easat-2990	128	18	delta	delta	NOUN
easat-2990	128	19	functions	function	NOUN
easat-2990	128	20	centered	center	VERB
easat-2990	128	21	at	at	ADP
easat-2990	128	22	different	different	ADJ
easat-2990	128	23	locations	location	NOUN
easat-2990	128	24	,	,	PUNCT
easat-2990	128	25	although	although	SCONJ
easat-2990	128	26	they	they	PRON
easat-2990	128	27	are	be	AUX
easat-2990	128	28	defined	define	VERB
easat-2990	128	29	on	on	ADP
easat-2990	128	30	the	the	DET
easat-2990	128	31	same	same	ADJ
easat-2990	128	32	domain	domain	NOUN
easat-2990	128	33	.	.	PUNCT
easat-2990	129	1	in	in	ADP
easat-2990	129	2	particular	particular	ADJ
easat-2990	129	3	,	,	PUNCT
easat-2990	129	4	such	such	DET
easat-2990	129	5	a	a	DET
easat-2990	129	6	property	property	NOUN
easat-2990	129	7	allows	allow	VERB
easat-2990	129	8	an	an	DET
easat-2990	129	9	application	application	NOUN
easat-2990	129	10	of	of	ADP
easat-2990	129	11	the	the	DET
easat-2990	129	12	algorithm	algorithm	NOUN
easat-2990	129	13	to	to	ADP
easat-2990	129	14	problems	problem	NOUN
easat-2990	129	15	with	with	ADP
easat-2990	129	16	periodic	periodic	ADJ
easat-2990	129	17	solutions	solution	NOUN
easat-2990	129	18	.	.	PUNCT
easat-2990	130	1	no	no	DET
easat-2990	130	2	doubt	doubt	NOUN
easat-2990	130	3	that	that	SCONJ
easat-2990	130	4	the	the	DET
easat-2990	130	5	use	use	NOUN
easat-2990	130	6	of	of	ADP
easat-2990	130	7	the	the	DET
easat-2990	130	8	functions	function	NOUN
easat-2990	130	9	gives	give	VERB
easat-2990	130	10	the	the	DET
easat-2990	130	11	best	good	ADJ
easat-2990	130	12	results[29	results[29	NOUN
easat-2990	130	13	]	]	PUNCT
easat-2990	130	14	.	.	PUNCT
easat-2990	131	1	however	however	ADV
easat-2990	131	2	,	,	PUNCT
easat-2990	131	3	for	for	ADP
easat-2990	131	4	a	a	DET
easat-2990	131	5	long	long	ADJ
easat-2990	131	6	time	time	NOUN
easat-2990	131	7	,	,	PUNCT
easat-2990	131	8	the	the	DET
easat-2990	131	9	oversampling	oversampling	NOUN
easat-2990	131	10	in	in	ADP
easat-2990	131	11	approximations	approximation	NOUN
easat-2990	131	12	prevented	prevent	VERB
easat-2990	131	13	any	any	DET
easat-2990	131	14	serious	serious	ADJ
easat-2990	131	15	competition	competition	NOUN
easat-2990	131	16	of	of	ADP
easat-2990	131	17	collocation	collocation	NOUN
easat-2990	131	18	methods	method	NOUN
easat-2990	131	19	within	within	ADP
easat-2990	131	20	the	the	DET
easat-2990	131	21	class	class	NOUN
easat-2990	131	22	of	of	ADP
easat-2990	131	23	galerkin	galerkin	ADJ
easat-2990	131	24	methods	method	NOUN
easat-2990	131	25	.	.	PUNCT
easat-2990	132	1	the	the	DET
easat-2990	132	2	given	give	VERB
easat-2990	132	3	estimates	estimate	NOUN
easat-2990	132	4	have	have	AUX
easat-2990	132	5	been	be	AUX
easat-2990	132	6	derived	derive	VERB
easat-2990	132	7	with	with	ADP
easat-2990	132	8	the	the	DET
easat-2990	132	9	help	help	NOUN
easat-2990	132	10	of	of	ADP
easat-2990	132	11	the	the	DET
easat-2990	132	12	analytic	analytic	ADJ
easat-2990	132	13	properties	property	NOUN
easat-2990	132	14	of	of	ADP
easat-2990	132	15	the	the	DET
easat-2990	132	16	delta	delta	NOUN
easat-2990	132	17	.	.	PUNCT
easat-2990	133	1	due	due	ADP
easat-2990	133	2	to	to	ADP
easat-2990	133	3	this	this	DET
easat-2990	133	4	property	property	NOUN
easat-2990	133	5	,	,	PUNCT
easat-2990	133	6	at	at	ADP
easat-2990	133	7	least	least	ADV
easat-2990	133	8	two	two	NUM
easat-2990	133	9	vectors	vector	NOUN
easat-2990	133	10	can	can	AUX
easat-2990	133	11	be	be	AUX
easat-2990	133	12	4604	4604	NUM
easat-2990	133	13	edelweiss	edelweiss	PROPN
easat-2990	133	14	applied	apply	VERB
easat-2990	133	15	science	science	NOUN
easat-2990	133	16	and	and	CCONJ
easat-2990	133	17	technology	technology	NOUN
easat-2990	133	18	issn	issn	PROPN
easat-2990	133	19	:	:	PUNCT
easat-2990	133	20	2576	2576	NUM
easat-2990	133	21	-	-	SYM
easat-2990	133	22	8484	8484	NUM
easat-2990	133	23	vol	vol	NOUN
easat-2990	133	24	.	.	PROPN
easat-2990	134	1	8	8	NUM
easat-2990	134	2	,	,	PUNCT
easat-2990	134	3	no	no	INTJ
easat-2990	134	4	.	.	NOUN
easat-2990	135	1	6	6	NUM
easat-2990	135	2	:	:	SYM
easat-2990	135	3	4599	4599	NUM
easat-2990	135	4	-	-	SYM
easat-2990	135	5	4610	4610	NUM
easat-2990	135	6	,	,	PUNCT
easat-2990	135	7	2024	2024	NUM
easat-2990	135	8	doi	doi	NOUN
easat-2990	135	9	:	:	PUNCT
easat-2990	135	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	135	11	©	©	PROPN
easat-2990	135	12	2024	2024	NUM
easat-2990	135	13	by	by	ADP
easat-2990	135	14	the	the	DET
easat-2990	135	15	author	author	NOUN
easat-2990	135	16	;	;	PUNCT
easat-2990	135	17	licensee	licensee	PROPN
easat-2990	135	18	learning	learning	PROPN
easat-2990	135	19	gate	gate	NOUN
easat-2990	135	20	generated	generate	VERB
easat-2990	135	21	with	with	ADP
easat-2990	135	22	the	the	DET
easat-2990	135	23	number	number	NOUN
easat-2990	135	24	of	of	ADP
easat-2990	135	25	expensive	expensive	ADJ
easat-2990	135	26	flops	flop	NOUN
easat-2990	135	27	three	three	NUM
easat-2990	135	28	times	time	NOUN
easat-2990	135	29	higher	high	ADJ
easat-2990	135	30	than	than	ADP
easat-2990	135	31	the	the	DET
easat-2990	135	32	number	number	NOUN
easat-2990	135	33	of	of	ADP
easat-2990	135	34	unknowns	unknown	NOUN
easat-2990	135	35	at	at	ADP
easat-2990	135	36	the	the	DET
easat-2990	135	37	same	same	ADJ
easat-2990	135	38	approximate	approximate	ADJ
easat-2990	135	39	level	level	NOUN
easat-2990	135	40	of	of	ADP
easat-2990	135	41	collocation	collocation	NOUN
easat-2990	135	42	methods	method	NOUN
easat-2990	135	43	.	.	PUNCT
easat-2990	136	1	we	we	PRON
easat-2990	136	2	try	try	VERB
easat-2990	136	3	to	to	PART
easat-2990	136	4	keep	keep	VERB
easat-2990	136	5	their	their	PRON
easat-2990	136	6	discussion	discussion	NOUN
easat-2990	136	7	as	as	ADV
easat-2990	136	8	sufficient	sufficient	ADJ
easat-2990	136	9	as	as	ADP
easat-2990	136	10	possible[30	possible[30	NOUN
easat-2990	136	11	]	]	PUNCT
easat-2990	136	12	.	.	PUNCT
easat-2990	137	1	the	the	DET
easat-2990	137	2	traditional	traditional	ADJ
easat-2990	137	3	approach	approach	NOUN
easat-2990	137	4	to	to	ADP
easat-2990	137	5	the	the	DET
easat-2990	137	6	collocation	collocation	NOUN
easat-2990	137	7	methods	method	NOUN
easat-2990	137	8	assumes	assume	VERB
easat-2990	137	9	that	that	SCONJ
easat-2990	137	10	they	they	PRON
easat-2990	137	11	use	use	VERB
easat-2990	137	12	the	the	DET
easat-2990	137	13	polynomial	polynomial	ADJ
easat-2990	137	14	basis	basis	NOUN
easat-2990	137	15	.	.	PUNCT
easat-2990	138	1	for	for	ADP
easat-2990	138	2	a	a	DET
easat-2990	138	3	given	give	VERB
easat-2990	138	4	polynomial	polynomial	ADJ
easat-2990	138	5	degree	degree	NOUN
easat-2990	138	6	,	,	PUNCT
easat-2990	138	7	the	the	DET
easat-2990	138	8	polynomial	polynomial	ADJ
easat-2990	138	9	basis	basis	NOUN
easat-2990	138	10	uses	use	VERB
easat-2990	138	11	the	the	DET
easat-2990	138	12	unknown	unknown	ADJ
easat-2990	138	13	expansion	expansion	NOUN
easat-2990	138	14	coefficients	coefficient	NOUN
easat-2990	138	15	to	to	PART
easat-2990	138	16	approximate	approximate	VERB
easat-2990	138	17	the	the	DET
easat-2990	138	18	trial	trial	NOUN
easat-2990	138	19	and	and	CCONJ
easat-2990	138	20	test	test	NOUN
easat-2990	138	21	functions	function	NOUN
easat-2990	138	22	.	.	PUNCT
easat-2990	139	1	unfortunately	unfortunately	ADV
easat-2990	139	2	,	,	PUNCT
easat-2990	139	3	the	the	DET
easat-2990	139	4	errors	error	NOUN
easat-2990	139	5	for	for	ADP
easat-2990	139	6	smooth	smooth	ADJ
easat-2990	139	7	or	or	CCONJ
easat-2990	139	8	almost	almost	ADV
easat-2990	139	9	smooth	smooth	ADJ
easat-2990	139	10	approximations	approximation	NOUN
easat-2990	139	11	are	be	AUX
easat-2990	139	12	very	very	ADV
easat-2990	139	13	sensitive	sensitive	ADJ
easat-2990	139	14	to	to	ADP
easat-2990	139	15	the	the	DET
easat-2990	139	16	derivatives	derivative	NOUN
easat-2990	139	17	of	of	ADP
easat-2990	139	18	the	the	DET
easat-2990	139	19	approximated	approximate	VERB
easat-2990	139	20	functions	function	NOUN
easat-2990	139	21	at	at	ADP
easat-2990	139	22	the	the	DET
easat-2990	139	23	collocation	collocation	NOUN
easat-2990	139	24	points	point	NOUN
easat-2990	139	25	.	.	PUNCT
easat-2990	140	1	in	in	ADP
easat-2990	140	2	particular	particular	ADJ
easat-2990	140	3	,	,	PUNCT
easat-2990	140	4	in	in	ADP
easat-2990	140	5	space	space	NOUN
easat-2990	140	6	,	,	PUNCT
easat-2990	140	7	this	this	DET
easat-2990	140	8	sensitivity	sensitivity	NOUN
easat-2990	140	9	exponentially	exponentially	ADV
easat-2990	140	10	depends	depend	VERB
easat-2990	140	11	on	on	ADP
easat-2990	140	12	the	the	DET
easat-2990	140	13	number	number	NOUN
easat-2990	140	14	of	of	ADP
easat-2990	140	15	dependent	dependent	ADJ
easat-2990	140	16	variables	variable	NOUN
easat-2990	140	17	as	as	ADV
easat-2990	140	18	well	well	ADV
easat-2990	140	19	as	as	ADP
easat-2990	140	20	on	on	ADP
easat-2990	140	21	the	the	DET
easat-2990	140	22	dimension	dimension	NOUN
easat-2990	140	23	of	of	ADP
easat-2990	140	24	the	the	DET
easat-2990	140	25	integro	integro	ADJ
easat-2990	140	26	-	-	PUNCT
easat-2990	140	27	differential	differential	NOUN
easat-2990	140	28	system[30	system[30	NOUN
easat-2990	140	29	]	]	PUNCT
easat-2990	140	30	.	.	PUNCT
easat-2990	141	1	5	5	X
easat-2990	141	2	.	.	NOUN
easat-2990	141	3	numerical	numerical	ADJ
easat-2990	141	4	experiments	experiment	NOUN
easat-2990	141	5	and	and	CCONJ
easat-2990	141	6	results	result	NOUN
easat-2990	141	7	we	we	PRON
easat-2990	141	8	develop	develop	VERB
easat-2990	141	9	wavelet	wavelet	NOUN
easat-2990	141	10	collocation	collocation	NOUN
easat-2990	141	11	methods	method	NOUN
easat-2990	141	12	for	for	ADP
easat-2990	141	13	solving	solve	VERB
easat-2990	141	14	multi	multi	ADJ
easat-2990	141	15	-	-	ADJ
easat-2990	141	16	dimensional	dimensional	ADJ
easat-2990	141	17	weakly	weakly	ADJ
easat-2990	141	18	singular	singular	PROPN
easat-2990	141	19	volterra	volterra	NOUN
easat-2990	141	20	type	type	PROPN
easat-2990	141	21	fredholm	fredholm	PROPN
easat-2990	141	22	function	function	NOUN
easat-2990	141	23	volterra	volterra	NOUN
easat-2990	141	24	type	type	PROPN
easat-2990	141	25	integro	integro	PROPN
easat-2990	141	26	-	-	PUNCT
easat-2990	141	27	differential	differential	NOUN
easat-2990	141	28	systems	system	NOUN
easat-2990	141	29	with	with	ADP
easat-2990	141	30	multiple	multiple	ADJ
easat-2990	141	31	time	time	NOUN
easat-2990	141	32	delays	delay	NOUN
easat-2990	141	33	,	,	PUNCT
easat-2990	141	34	and	and	CCONJ
easat-2990	141	35	thus	thus	ADV
easat-2990	141	36	extend	extend	VERB
easat-2990	141	37	some	some	DET
easat-2990	141	38	existing	exist	VERB
easat-2990	141	39	results	result	NOUN
easat-2990	141	40	of	of	ADP
easat-2990	141	41	delay	delay	NOUN
easat-2990	141	42	integro	integro	ADJ
easat-2990	141	43	-	-	PUNCT
easat-2990	141	44	differential	differential	NOUN
easat-2990	141	45	equations	equation	NOUN
easat-2990	141	46	to	to	ADP
easat-2990	141	47	systems	system	NOUN
easat-2990	141	48	.	.	PUNCT
easat-2990	142	1	the	the	DET
easat-2990	142	2	wavelet	wavelet	NOUN
easat-2990	142	3	collocation	collocation	NOUN
easat-2990	142	4	method	method	NOUN
easat-2990	142	5	also	also	ADV
easat-2990	142	6	comes	come	VERB
easat-2990	142	7	with	with	ADP
easat-2990	142	8	some	some	DET
easat-2990	142	9	numerical	numerical	ADJ
easat-2990	142	10	results	result	NOUN
easat-2990	142	11	,	,	PUNCT
easat-2990	142	12	and	and	CCONJ
easat-2990	142	13	the	the	DET
easat-2990	142	14	wavelet	wavelet	NOUN
easat-2990	142	15	collocation	collocation	NOUN
easat-2990	142	16	method	method	NOUN
easat-2990	142	17	is	be	AUX
easat-2990	142	18	stable	stable	ADJ
easat-2990	142	19	and	and	CCONJ
easat-2990	142	20	reliable	reliable	ADJ
easat-2990	142	21	.	.	PUNCT
easat-2990	143	1	so	so	ADV
easat-2990	143	2	the	the	DET
easat-2990	143	3	new	new	ADJ
easat-2990	143	4	method	method	NOUN
easat-2990	143	5	has	have	VERB
easat-2990	143	6	low	low	ADJ
easat-2990	143	7	complexity	complexity	NOUN
easat-2990	143	8	and	and	CCONJ
easat-2990	143	9	is	be	AUX
easat-2990	143	10	suitable	suitable	ADJ
easat-2990	143	11	for	for	ADP
easat-2990	143	12	use	use	NOUN
easat-2990	143	13	in	in	ADP
easat-2990	143	14	large	large	ADJ
easat-2990	143	15	-	-	PUNCT
easat-2990	143	16	scale	scale	NOUN
easat-2990	143	17	applications	application	NOUN
easat-2990	143	18	.	.	PUNCT
easat-2990	144	1	in	in	ADP
easat-2990	144	2	this	this	DET
easat-2990	144	3	paper	paper	NOUN
easat-2990	144	4	,	,	PUNCT
easat-2990	144	5	the	the	DET
easat-2990	144	6	multi	multi	ADJ
easat-2990	144	7	-	-	ADJ
easat-2990	144	8	dimensional	dimensional	ADJ
easat-2990	144	9	weakly	weakly	ADJ
easat-2990	144	10	singular	singular	PROPN
easat-2990	144	11	volterra	volterra	NOUN
easat-2990	144	12	type	type	PROPN
easat-2990	144	13	fredholm	fredholm	PROPN
easat-2990	144	14	function	function	NOUN
easat-2990	144	15	volterra	volterra	NOUN
easat-2990	144	16	type	type	NOUN
easat-2990	144	17	integrodifferential	integrodifferential	ADJ
easat-2990	144	18	systems	system	NOUN
easat-2990	144	19	with	with	ADP
easat-2990	144	20	multiple	multiple	ADJ
easat-2990	144	21	time	time	NOUN
easat-2990	144	22	delays	delay	NOUN
easat-2990	144	23	are	be	AUX
easat-2990	144	24	considered	consider	VERB
easat-2990	144	25	.	.	PUNCT
easat-2990	145	1	we	we	PRON
easat-2990	145	2	develop	develop	VERB
easat-2990	145	3	wavelet	wavelet	NOUN
easat-2990	145	4	collocation	collocation	NOUN
easat-2990	145	5	methods	method	NOUN
easat-2990	145	6	for	for	ADP
easat-2990	145	7	solving	solve	VERB
easat-2990	145	8	these	these	DET
easat-2990	145	9	weakly	weakly	ADJ
easat-2990	145	10	singular	singular	ADJ
easat-2990	145	11	type	type	NOUN
easat-2990	145	12	integro	integro	ADJ
easat-2990	145	13	-	-	PUNCT
easat-2990	145	14	differential	differential	NOUN
easat-2990	145	15	systems	system	NOUN
easat-2990	145	16	.	.	PUNCT
easat-2990	146	1	the	the	DET
easat-2990	146	2	wavelet	wavelet	NOUN
easat-2990	146	3	method	method	NOUN
easat-2990	146	4	is	be	AUX
easat-2990	146	5	common	common	ADJ
easat-2990	146	6	for	for	ADP
easat-2990	146	7	solving	solve	VERB
easat-2990	146	8	a	a	DET
easat-2990	146	9	function	function	NOUN
easat-2990	146	10	defined	define	VERB
easat-2990	146	11	on	on	ADP
easat-2990	146	12	a	a	DET
easat-2990	146	13	one	one	NUM
easat-2990	146	14	-	-	PUNCT
easat-2990	146	15	norm	norm	NOUN
easat-2990	146	16	high	high	ADJ
easat-2990	146	17	-	-	PUNCT
easat-2990	146	18	dimensional	dimensional	ADJ
easat-2990	146	19	space	space	NOUN
easat-2990	146	20	with	with	ADP
easat-2990	146	21	a	a	DET
easat-2990	146	22	number	number	NOUN
easat-2990	146	23	of	of	ADP
easat-2990	146	24	finite	finite	ADJ
easat-2990	146	25	moments	moment	NOUN
easat-2990	146	26	,	,	PUNCT
easat-2990	146	27	which	which	PRON
easat-2990	146	28	can	can	AUX
easat-2990	146	29	have	have	VERB
easat-2990	146	30	a	a	DET
easat-2990	146	31	small	small	ADJ
easat-2990	146	32	number	number	NOUN
easat-2990	146	33	of	of	ADP
easat-2990	146	34	non	non	ADJ
easat-2990	146	35	-	-	ADJ
easat-2990	146	36	zero	zero	NUM
easat-2990	146	37	wavelet	wavelet	NOUN
easat-2990	146	38	coefficients	coefficient	NOUN
easat-2990	146	39	.	.	PUNCT
easat-2990	147	1	numerical	numerical	ADJ
easat-2990	147	2	methods	method	NOUN
easat-2990	147	3	are	be	AUX
easat-2990	147	4	also	also	ADV
easat-2990	147	5	presented	present	VERB
easat-2990	147	6	.	.	PUNCT
easat-2990	148	1	these	these	DET
easat-2990	148	2	numerical	numerical	ADJ
easat-2990	148	3	methods	method	NOUN
easat-2990	148	4	are	be	AUX
easat-2990	148	5	simple	simple	ADJ
easat-2990	148	6	and	and	CCONJ
easat-2990	148	7	effective	effective	ADJ
easat-2990	148	8	.	.	PUNCT
easat-2990	149	1	finally	finally	ADV
easat-2990	149	2	,	,	PUNCT
easat-2990	149	3	some	some	DET
easat-2990	149	4	numerical	numerical	ADJ
easat-2990	149	5	results	result	NOUN
easat-2990	149	6	show	show	VERB
easat-2990	149	7	that	that	SCONJ
easat-2990	149	8	the	the	DET
easat-2990	149	9	new	new	ADJ
easat-2990	149	10	methods	method	NOUN
easat-2990	149	11	are	be	AUX
easat-2990	149	12	stable	stable	ADJ
easat-2990	149	13	and	and	CCONJ
easat-2990	149	14	reliable	reliable	ADJ
easat-2990	149	15	.	.	PUNCT
easat-2990	150	1	%	%	NOUN
easat-2990	150	2	signal	signal	NOUN
easat-2990	150	3	parameters	parameter	NOUN
easat-2990	150	4	t	t	PROPN
easat-2990	150	5	=	=	SYM
easat-2990	150	6	1300:1:1700	1300:1:1700	NUM
easat-2990	150	7	;	;	PUNCT
easat-2990	151	1	f0	f0	PROPN
easat-2990	151	2	=	=	NOUN
easat-2990	151	3	0.1	0.1	NUM
easat-2990	151	4	;	;	PUNCT
easat-2990	151	5	%	%	NOUN
easat-2990	151	6	base	base	NOUN
easat-2990	151	7	frequency	frequency	NOUN
easat-2990	151	8	signal	signal	NOUN
easat-2990	151	9	=	=	SYM
easat-2990	151	10	sin(2*pi*f0*(t-1300)/400).*exp(-(t-1500).^2/20000	sin(2*pi*f0*(t-1300)/400).*exp(-(t-1500).^2/20000	NUM
easat-2990	151	11	)	)	PUNCT
easat-2990	151	12	;	;	PUNCT
easat-2990	151	13	%	%	NOUN
easat-2990	151	14	time	time	NOUN
easat-2990	151	15	vector	vector	NOUN
easat-2990	151	16	for	for	ADP
easat-2990	151	17	atoms	atom	NOUN
easat-2990	151	18	t_atoms	t_atom	NOUN
easat-2990	151	19	=	=	SYM
easat-2990	151	20	0:500	0:500	NOUN
easat-2990	151	21	;	;	PUNCT
easat-2990	151	22	%	%	NOUN
easat-2990	151	23	create	create	VERB
easat-2990	151	24	figure	figure	NOUN
easat-2990	151	25	figure('position	figure('position	NOUN
easat-2990	151	26	'	'	PUNCT
easat-2990	151	27	,	,	PUNCT
easat-2990	152	1	[	[	X
easat-2990	152	2	100	100	NUM
easat-2990	152	3	100	100	NUM
easat-2990	152	4	1000	1000	NUM
easat-2990	152	5	800	800	NUM
easat-2990	152	6	]	]	PUNCT
easat-2990	152	7	)	)	PUNCT
easat-2990	152	8	;	;	PUNCT
easat-2990	152	9	%	%	NOUN
easat-2990	152	10	continuous	continuous	ADJ
easat-2990	152	11	method	method	NOUN
easat-2990	152	12	sparse	sparse	ADJ
easat-2990	152	13	approximation	approximation	NOUN
easat-2990	152	14	atoms	atom	NOUN
easat-2990	152	15	subplot(4,2,1	subplot(4,2,1	NOUN
easat-2990	152	16	)	)	PUNCT
easat-2990	152	17	num_atoms	num_atom	VERB
easat-2990	152	18	=	=	SYM
easat-2990	152	19	5	5	NUM
easat-2990	152	20	;	;	PUNCT
easat-2990	152	21	colors	color	NOUN
easat-2990	152	22	=	=	SYM
easat-2990	152	23	lines(num_atoms	lines(num_atoms	PROPN
easat-2990	152	24	)	)	PUNCT
easat-2990	152	25	;	;	PUNCT
easat-2990	152	26	hold	hold	VERB
easat-2990	152	27	on	on	ADP
easat-2990	152	28	for	for	ADP
easat-2990	152	29	i	i	PRON
easat-2990	152	30	=	=	NOUN
easat-2990	152	31	1	1	NUM
easat-2990	152	32	:	:	PUNCT
easat-2990	152	33	num_atoms	num_atom	NOUN
easat-2990	152	34	center	center	NOUN
easat-2990	152	35	=	=	NOUN
easat-2990	152	36	100	100	NUM
easat-2990	152	37	+	+	NUM
easat-2990	152	38	80*i	80*i	NUM
easat-2990	152	39	;	;	PUNCT
easat-2990	152	40	atom	atom	NOUN
easat-2990	152	41	=	=	SYM
easat-2990	152	42	cos(2*pi*0.05*i*(t_atoms	cos(2*pi*0.05*i*(t_atom	NOUN
easat-2990	152	43	-	-	PUNCT
easat-2990	152	44	center)).*exp(-(t_atoms	center)).*exp(-(t_atom	NOUN
easat-2990	152	45	-	-	PUNCT
easat-2990	152	46	center).^2/1000	center).^2/1000	NOUN
easat-2990	152	47	)	)	PUNCT
easat-2990	152	48	;	;	PUNCT
easat-2990	152	49	plot(t_atoms	plot(t_atom	NOUN
easat-2990	152	50	,	,	PUNCT
easat-2990	152	51	atom	atom	NOUN
easat-2990	152	52	+	+	CCONJ
easat-2990	152	53	0.2	0.2	NUM
easat-2990	152	54	,	,	PUNCT
easat-2990	152	55	'	'	PUNCT
easat-2990	152	56	color	color	NOUN
easat-2990	152	57	'	'	NUM
easat-2990	152	58	,	,	PUNCT
easat-2990	152	59	colors(i	colors(i	NOUN
easat-2990	152	60	,	,	PUNCT
easat-2990	152	61	:))	:))	PROPN
easat-2990	152	62	;	;	PUNCT
easat-2990	152	63	end	end	NOUN
easat-2990	152	64	plot(t_atoms	plot(t_atom	NOUN
easat-2990	152	65	,	,	PUNCT
easat-2990	152	66	zeros(size(t_atoms	zeros(size(t_atoms	NUM
easat-2990	152	67	)	)	PUNCT
easat-2990	152	68	)	)	PUNCT
easat-2990	152	69	,	,	PUNCT
easat-2990	152	70	'	'	PUNCT
easat-2990	152	71	k--	k--	ADJ
easat-2990	152	72	'	'	NUM
easat-2990	152	73	)	)	PUNCT
easat-2990	152	74	title('continuous	title('continuous	ADJ
easat-2990	152	75	method	method	NOUN
easat-2990	152	76	sparse	sparse	ADJ
easat-2990	152	77	approximation	approximation	NOUN
easat-2990	152	78	atoms	atom	NOUN
easat-2990	152	79	'	'	PART
easat-2990	152	80	)	)	PUNCT
easat-2990	152	81	ylim([-0.5	ylim([-0.5	X
easat-2990	152	82	0.5	0.5	NUM
easat-2990	152	83	]	]	PUNCT
easat-2990	152	84	)	)	PUNCT
easat-2990	152	85	hold	hold	VERB
easat-2990	152	86	off	off	ADP
easat-2990	152	87	%	%	NOUN
easat-2990	152	88	continuous	continuous	ADJ
easat-2990	152	89	method	method	NOUN
easat-2990	152	90	time	time	NOUN
easat-2990	152	91	stretched	stretch	VERB
easat-2990	152	92	atoms	atom	NOUN
easat-2990	152	93	subplot(4,2,2	subplot(4,2,2	NOUN
easat-2990	152	94	)	)	PUNCT
easat-2990	152	95	plot(t	plot(t	NOUN
easat-2990	152	96	,	,	PUNCT
easat-2990	152	97	signal	signal	NOUN
easat-2990	152	98	,	,	PUNCT
easat-2990	152	99	'	'	PUNCT
easat-2990	152	100	b-	b-	NOUN
easat-2990	152	101	'	'	PUNCT
easat-2990	152	102	)	)	PUNCT
easat-2990	152	103	title('signal	title('signal	NOUN
easat-2990	152	104	in	in	ADP
easat-2990	152	105	time	time	NOUN
easat-2990	152	106	'	'	PUNCT
easat-2990	152	107	)	)	PUNCT
easat-2990	152	108	ylim([-1	ylim([-1	NOUN
easat-2990	152	109	1	1	NUM
easat-2990	152	110	]	]	PUNCT
easat-2990	152	111	)	)	PUNCT
easat-2990	152	112	grid	grid	NOUN
easat-2990	152	113	on	on	ADP
easat-2990	152	114	4605	4605	NUM
easat-2990	152	115	edelweiss	edelweiss	PROPN
easat-2990	152	116	applied	apply	VERB
easat-2990	152	117	science	science	NOUN
easat-2990	152	118	and	and	CCONJ
easat-2990	152	119	technology	technology	NOUN
easat-2990	152	120	issn	issn	PROPN
easat-2990	152	121	:	:	PUNCT
easat-2990	152	122	2576	2576	NUM
easat-2990	152	123	-	-	SYM
easat-2990	152	124	8484	8484	NUM
easat-2990	152	125	vol	vol	NOUN
easat-2990	152	126	.	.	PROPN
easat-2990	153	1	8	8	NUM
easat-2990	153	2	,	,	PUNCT
easat-2990	153	3	no	no	INTJ
easat-2990	153	4	.	.	NOUN
easat-2990	154	1	6	6	NUM
easat-2990	154	2	:	:	SYM
easat-2990	154	3	4599	4599	NUM
easat-2990	154	4	-	-	SYM
easat-2990	154	5	4610	4610	NUM
easat-2990	154	6	,	,	PUNCT
easat-2990	154	7	2024	2024	NUM
easat-2990	154	8	doi	doi	NOUN
easat-2990	154	9	:	:	PUNCT
easat-2990	154	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	154	11	©	©	PROPN
easat-2990	154	12	2024	2024	NUM
easat-2990	154	13	by	by	ADP
easat-2990	154	14	the	the	DET
easat-2990	154	15	author	author	NOUN
easat-2990	154	16	;	;	PUNCT
easat-2990	154	17	licensee	licensee	NOUN
easat-2990	154	18	learning	learn	VERB
easat-2990	154	19	gate	gate	NOUN
easat-2990	154	20	%	%	PROPN
easat-2990	154	21	discrete	discrete	ADJ
easat-2990	154	22	method	method	NOUN
easat-2990	154	23	sparse	sparse	ADJ
easat-2990	154	24	approximation	approximation	NOUN
easat-2990	154	25	atoms	atom	NOUN
easat-2990	154	26	subplot(4,2,3	subplot(4,2,3	NOUN
easat-2990	154	27	)	)	PUNCT
easat-2990	154	28	hold	hold	VERB
easat-2990	154	29	on	on	ADP
easat-2990	154	30	for	for	ADP
easat-2990	154	31	i	i	PRON
easat-2990	154	32	=	=	NOUN
easat-2990	154	33	1	1	NUM
easat-2990	154	34	:	:	PUNCT
easat-2990	154	35	num_atoms	num_atom	NOUN
easat-2990	154	36	center	center	NOUN
easat-2990	154	37	=	=	NOUN
easat-2990	154	38	100	100	NUM
easat-2990	155	1	+	+	NUM
easat-2990	155	2	80*i	80*i	NUM
easat-2990	155	3	;	;	PUNCT
easat-2990	155	4	scale	scale	NOUN
easat-2990	155	5	=	=	SYM
easat-2990	155	6	1	1	NUM
easat-2990	155	7	+	+	NUM
easat-2990	155	8	0.5*i	0.5*i	NUM
easat-2990	155	9	;	;	PUNCT
easat-2990	155	10	atom	atom	NOUN
easat-2990	155	11	=	=	SYM
easat-2990	155	12	cos(2*pi*0.05*i*(t_atoms	cos(2*pi*0.05*i*(t_atom	NOUN
easat-2990	155	13	-	-	PUNCT
easat-2990	155	14	center)/scale).*exp(-(t_atoms	center)/scale).*exp(-(t_atom	NOUN
easat-2990	155	15	-	-	PUNCT
easat-2990	155	16	center).^2/(1000*scale	center).^2/(1000*scale	NOUN
easat-2990	155	17	)	)	PUNCT
easat-2990	155	18	)	)	PUNCT
easat-2990	155	19	;	;	PUNCT
easat-2990	155	20	plot(t_atoms	plot(t_atom	NOUN
easat-2990	155	21	,	,	PUNCT
easat-2990	155	22	atom	atom	NOUN
easat-2990	155	23	+	+	CCONJ
easat-2990	155	24	0.2	0.2	NUM
easat-2990	155	25	,	,	PUNCT
easat-2990	155	26	'	'	PUNCT
easat-2990	155	27	color	color	NOUN
easat-2990	155	28	'	'	NUM
easat-2990	155	29	,	,	PUNCT
easat-2990	155	30	colors(i	colors(i	NOUN
easat-2990	155	31	,	,	PUNCT
easat-2990	155	32	:))	:))	PROPN
easat-2990	155	33	;	;	PUNCT
easat-2990	155	34	end	end	NOUN
easat-2990	155	35	plot(t_atoms	plot(t_atom	NOUN
easat-2990	155	36	,	,	PUNCT
easat-2990	155	37	zeros(size(t_atoms	zeros(size(t_atoms	NUM
easat-2990	155	38	)	)	PUNCT
easat-2990	155	39	)	)	PUNCT
easat-2990	155	40	,	,	PUNCT
easat-2990	155	41	'	'	PUNCT
easat-2990	155	42	k--	k--	NOUN
easat-2990	155	43	'	'	PUNCT
easat-2990	155	44	)	)	PUNCT
easat-2990	155	45	title('discrete	title('discrete	PRON
easat-2990	155	46	method	method	NOUN
easat-2990	155	47	sparse	sparse	ADJ
easat-2990	155	48	approximation	approximation	NOUN
easat-2990	155	49	atoms	atom	NOUN
easat-2990	155	50	'	'	PART
easat-2990	155	51	)	)	PUNCT
easat-2990	155	52	ylim([-0.5	ylim([-0.5	X
easat-2990	155	53	0.5	0.5	NUM
easat-2990	155	54	]	]	PUNCT
easat-2990	155	55	)	)	PUNCT
easat-2990	155	56	hold	hold	VERB
easat-2990	155	57	off	off	ADP
easat-2990	155	58	%	%	NOUN
easat-2990	155	59	time	time	NOUN
easat-2990	155	60	-	-	PUNCT
easat-2990	155	61	frequency	frequency	NOUN
easat-2990	155	62	analysis	analysis	NOUN
easat-2990	155	63	f	f	NOUN
easat-2990	155	64	=	=	SYM
easat-2990	155	65	500:750	500:750	NOUN
easat-2990	155	66	;	;	PUNCT
easat-2990	155	67	freq_response	freq_response	NOUN
easat-2990	155	68	=	=	SYM
easat-2990	155	69	zeros(size(f	zeros(size(f	NUM
easat-2990	155	70	)	)	PUNCT
easat-2990	155	71	)	)	PUNCT
easat-2990	155	72	;	;	PUNCT
easat-2990	155	73	freq_response_stretched	freq_response_stretche	VERB
easat-2990	155	74	=	=	PROPN
easat-2990	155	75	zeros(size(f	zeros(size(f	NUM
easat-2990	155	76	)	)	PUNCT
easat-2990	155	77	)	)	PUNCT
easat-2990	155	78	;	;	PUNCT
easat-2990	155	79	%	%	NOUN
easat-2990	155	80	calculate	calculate	NOUN
easat-2990	155	81	frequency	frequency	NOUN
easat-2990	155	82	responses	response	NOUN
easat-2990	155	83	for	for	ADP
easat-2990	155	84	i	i	PRON
easat-2990	155	85	=	=	NOUN
easat-2990	155	86	1	1	NUM
easat-2990	155	87	:	:	PUNCT
easat-2990	155	88	length(f	length(f	NOUN
easat-2990	155	89	)	)	PUNCT
easat-2990	155	90	freq_response(i	freq_response(i	NOUN
easat-2990	155	91	)	)	PUNCT
easat-2990	155	92	=	=	SYM
easat-2990	155	93	sum(exp(-2*pi*1i*f(i)*t/1000).*signal	sum(exp(-2*pi*1i*f(i)*t/1000).*signal	ADJ
easat-2990	155	94	)	)	PUNCT
easat-2990	155	95	;	;	PUNCT
easat-2990	155	96	freq_response_stretched(i	freq_response_stretched(i	X
easat-2990	155	97	)	)	PUNCT
easat-2990	155	98	=	=	SYM
easat-2990	155	99	sum(exp(-2*pi*1i*f(i)*t/2000).*signal	sum(exp(-2*pi*1i*f(i)*t/2000).*signal	PROPN
easat-2990	155	100	)	)	PUNCT
easat-2990	155	101	;	;	PUNCT
easat-2990	155	102	end	end	NOUN
easat-2990	155	103	%	%	NOUN
easat-2990	155	104	normalize	normalize	VERB
easat-2990	155	105	frequency	frequency	NOUN
easat-2990	155	106	responses	response	NOUN
easat-2990	155	107	freq_response	freq_response	NOUN
easat-2990	155	108	=	=	SYM
easat-2990	155	109	abs(freq_response)/max(abs(freq_response	abs(freq_response)/max(abs(freq_response	NOUN
easat-2990	155	110	)	)	PUNCT
easat-2990	155	111	)	)	PUNCT
easat-2990	155	112	;	;	PUNCT
easat-2990	155	113	freq_response_stretched	freq_response_stretched	PROPN
easat-2990	155	114	=	=	PUNCT
easat-2990	155	115	abs(freq_response_stretched)/max(abs(freq_response_stretched	abs(freq_response_stretched)/max(abs(freq_response_stretche	VERB
easat-2990	155	116	)	)	PUNCT
easat-2990	155	117	)	)	PUNCT
easat-2990	155	118	;	;	PUNCT
easat-2990	155	119	%	%	NOUN
easat-2990	155	120	plot	plot	NOUN
easat-2990	155	121	frequency	frequency	NOUN
easat-2990	155	122	analysis	analysis	NOUN
easat-2990	155	123	subplot(4,2,4	subplot(4,2,4	NOUN
easat-2990	155	124	)	)	PUNCT
easat-2990	155	125	plot(f	plot(f	PROPN
easat-2990	155	126	,	,	PUNCT
easat-2990	155	127	freq_response	freq_response	NOUN
easat-2990	155	128	,	,	PUNCT
easat-2990	155	129	'	'	PUNCT
easat-2990	155	130	b-	b-	NOUN
easat-2990	155	131	'	'	PUNCT
easat-2990	155	132	,	,	PUNCT
easat-2990	155	133	'	'	PUNCT
easat-2990	155	134	linewidth	linewidth	NOUN
easat-2990	155	135	'	'	PUNCT
easat-2990	155	136	,	,	PUNCT
easat-2990	155	137	2	2	X
easat-2990	155	138	)	)	PUNCT
easat-2990	155	139	hold	hold	VERB
easat-2990	155	140	on	on	ADP
easat-2990	155	141	plot(f	plot(f	PROPN
easat-2990	155	142	,	,	PUNCT
easat-2990	155	143	freq_response_stretched	freq_response_stretche	VERB
easat-2990	155	144	,	,	PUNCT
easat-2990	155	145	'	'	PUNCT
easat-2990	155	146	g-	g-	X
easat-2990	155	147	'	'	PUNCT
easat-2990	155	148	,	,	PUNCT
easat-2990	155	149	'	'	PUNCT
easat-2990	155	150	linewidth	linewidth	NOUN
easat-2990	155	151	'	'	PUNCT
easat-2990	155	152	,	,	PUNCT
easat-2990	155	153	2	2	X
easat-2990	155	154	)	)	PUNCT
easat-2990	155	155	plot(f	plot(f	PROPN
easat-2990	155	156	,	,	PUNCT
easat-2990	155	157	0.3*ones(size(f	0.3*ones(size(f	NOUN
easat-2990	155	158	)	)	PUNCT
easat-2990	155	159	)	)	PUNCT
easat-2990	155	160	,	,	PUNCT
easat-2990	155	161	'	'	PUNCT
easat-2990	155	162	r--	r--	NOUN
easat-2990	155	163	'	'	PART
easat-2990	155	164	)	)	PUNCT
easat-2990	155	165	title('signal	title('signal	ADJ
easat-2990	155	166	and	and	CCONJ
easat-2990	155	167	stretched	stretch	VERB
easat-2990	155	168	signal	signal	NOUN
easat-2990	155	169	in	in	ADP
easat-2990	155	170	frequency	frequency	NOUN
easat-2990	155	171	'	'	PUNCT
easat-2990	155	172	)	)	PUNCT
easat-2990	155	173	xlabel('frequency	xlabel('frequency	NOUN
easat-2990	155	174	'	'	PUNCT
easat-2990	155	175	)	)	PUNCT
easat-2990	155	176	ylabel('magnitude	ylabel('magnitude	NOUN
easat-2990	155	177	'	'	PUNCT
easat-2990	155	178	)	)	PUNCT
easat-2990	155	179	ylim([0	ylim([0	VERB
easat-2990	155	180	1	1	NUM
easat-2990	155	181	]	]	PUNCT
easat-2990	155	182	)	)	PUNCT
easat-2990	155	183	grid	grid	NOUN
easat-2990	155	184	on	on	ADP
easat-2990	155	185	hold	hold	NOUN
easat-2990	155	186	off	off	ADP
easat-2990	155	187	%	%	NOUN
easat-2990	155	188	adjust	adjust	VERB
easat-2990	155	189	layout	layout	PROPN
easat-2990	155	190	sgtitle('wavelet	sgtitle('wavelet	PROPN
easat-2990	155	191	analysis	analysis	NOUN
easat-2990	155	192	'	'	PUNCT
easat-2990	155	193	)	)	PUNCT
easat-2990	155	194	4606	4606	NUM
easat-2990	155	195	edelweiss	edelweiss	PROPN
easat-2990	155	196	applied	apply	VERB
easat-2990	155	197	science	science	NOUN
easat-2990	155	198	and	and	CCONJ
easat-2990	155	199	technology	technology	NOUN
easat-2990	155	200	issn	issn	PROPN
easat-2990	155	201	:	:	PUNCT
easat-2990	155	202	2576	2576	NUM
easat-2990	155	203	-	-	SYM
easat-2990	155	204	8484	8484	NUM
easat-2990	155	205	vol	vol	NOUN
easat-2990	155	206	.	.	PROPN
easat-2990	156	1	8	8	NUM
easat-2990	156	2	,	,	PUNCT
easat-2990	156	3	no	no	INTJ
easat-2990	156	4	.	.	NOUN
easat-2990	157	1	6	6	NUM
easat-2990	157	2	:	:	SYM
easat-2990	157	3	4599	4599	NUM
easat-2990	157	4	-	-	SYM
easat-2990	157	5	4610	4610	NUM
easat-2990	157	6	,	,	PUNCT
easat-2990	157	7	2024	2024	NUM
easat-2990	157	8	doi	doi	NOUN
easat-2990	157	9	:	:	PUNCT
easat-2990	157	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	157	11	©	©	PROPN
easat-2990	157	12	2024	2024	NUM
easat-2990	157	13	by	by	ADP
easat-2990	157	14	the	the	DET
easat-2990	157	15	author	author	NOUN
easat-2990	157	16	;	;	PUNCT
easat-2990	157	17	licensee	licensee	PROPN
easat-2990	157	18	learning	learn	VERB
easat-2990	157	19	gate	gate	NOUN
easat-2990	157	20	figure	figure	NOUN
easat-2990	157	21	1	1	NUM
easat-2990	157	22	.	.	PUNCT
easat-2990	157	23	fredholm	fredholm	PROPN
easat-2990	157	24	function	function	PROPN
easat-2990	157	25	volterra	volterra	PROPN
easat-2990	157	26	type	type	PROPN
easat-2990	157	27	integro	integro	PROPN
easat-2990	157	28	-	-	PUNCT
easat-2990	157	29	differential	differential	NOUN
easat-2990	157	30	systems	system	NOUN
easat-2990	157	31	.	.	PUNCT
easat-2990	158	1	5.1	5.1	NUM
easat-2990	158	2	.	.	PUNCT
easat-2990	159	1	benchmark	benchmark	NOUN
easat-2990	159	2	problems	problem	NOUN
easat-2990	159	3	benchmarking	benchmarke	VERB
easat-2990	159	4	is	be	AUX
easat-2990	159	5	an	an	DET
easat-2990	159	6	essential	essential	ADJ
easat-2990	159	7	activity	activity	NOUN
easat-2990	159	8	in	in	ADP
easat-2990	159	9	organizations	organization	NOUN
easat-2990	159	10	that	that	PRON
easat-2990	159	11	wish	wish	VERB
easat-2990	159	12	to	to	PART
easat-2990	159	13	improve	improve	VERB
easat-2990	159	14	the	the	DET
easat-2990	159	15	performance	performance	NOUN
easat-2990	159	16	of	of	ADP
easat-2990	159	17	their	their	PRON
easat-2990	159	18	organizations	organization	NOUN
easat-2990	159	19	and	and	CCONJ
easat-2990	159	20	compete	compete	VERB
easat-2990	159	21	effectively	effectively	ADV
easat-2990	159	22	in	in	ADP
easat-2990	159	23	their	their	PRON
easat-2990	159	24	markets	market	NOUN
easat-2990	159	25	.	.	PUNCT
easat-2990	160	1	however	however	ADV
easat-2990	160	2	,	,	PUNCT
easat-2990	160	3	there	there	PRON
easat-2990	160	4	are	be	VERB
easat-2990	160	5	several	several	ADJ
easat-2990	160	6	factors	factor	NOUN
easat-2990	160	7	that	that	PRON
easat-2990	160	8	can	can	AUX
easat-2990	160	9	hamper	hamper	VERB
easat-2990	160	10	benchmarking	benchmarke	VERB
easat-2990	160	11	activities	activity	NOUN
easat-2990	160	12	as	as	SCONJ
easat-2990	160	13	follows	follow	VERB
easat-2990	160	14	;	;	PUNCT
easat-2990	160	15	one	one	NUM
easat-2990	160	16	important	important	ADJ
easat-2990	160	17	question	question	NOUN
easat-2990	160	18	is	be	AUX
easat-2990	160	19	what	what	PRON
easat-2990	160	20	benchmarks	benchmark	NOUN
easat-2990	160	21	to	to	PART
easat-2990	160	22	use	use	VERB
easat-2990	160	23	and	and	CCONJ
easat-2990	160	24	where	where	SCONJ
easat-2990	160	25	to	to	PART
easat-2990	160	26	obtain	obtain	VERB
easat-2990	160	27	the	the	DET
easat-2990	160	28	information	information	NOUN
easat-2990	160	29	from	from	ADP
easat-2990	160	30	in	in	ADP
easat-2990	160	31	order	order	NOUN
easat-2990	160	32	to	to	PART
easat-2990	160	33	avoid	avoid	VERB
easat-2990	160	34	misguiding	misguide	VERB
easat-2990	160	35	conclusions	conclusion	NOUN
easat-2990	160	36	.	.	PUNCT
easat-2990	161	1	also	also	ADV
easat-2990	161	2	,	,	PUNCT
easat-2990	161	3	it	it	PRON
easat-2990	161	4	is	be	AUX
easat-2990	161	5	challenging	challenge	VERB
easat-2990	161	6	to	to	PART
easat-2990	161	7	identify	identify	VERB
easat-2990	161	8	the	the	DET
easat-2990	161	9	best	good	ADJ
easat-2990	161	10	practice	practice	NOUN
easat-2990	161	11	companies	company	NOUN
easat-2990	161	12	that	that	PRON
easat-2990	161	13	are	be	AUX
easat-2990	161	14	similar	similar	ADJ
easat-2990	161	15	to	to	ADP
easat-2990	161	16	the	the	DET
easat-2990	161	17	organization	organization	NOUN
easat-2990	161	18	’s	’s	PART
easat-2990	161	19	goals	goal	NOUN
easat-2990	161	20	and	and	CCONJ
easat-2990	161	21	objectives	objective	NOUN
easat-2990	161	22	to	to	PART
easat-2990	161	23	make	make	VERB
easat-2990	161	24	valid	valid	ADJ
easat-2990	161	25	conclusions	conclusion	NOUN
easat-2990	161	26	.	.	PUNCT
easat-2990	162	1	having	have	VERB
easat-2990	162	2	a	a	DET
easat-2990	162	3	clear	clear	ADJ
easat-2990	162	4	market	market	NOUN
easat-2990	162	5	value	value	NOUN
easat-2990	162	6	proposition	proposition	NOUN
easat-2990	162	7	is	be	AUX
easat-2990	162	8	always	always	ADV
easat-2990	162	9	important	important	ADJ
easat-2990	162	10	,	,	PUNCT
easat-2990	162	11	especially	especially	ADV
easat-2990	162	12	in	in	ADP
easat-2990	162	13	defining	define	VERB
easat-2990	162	14	to	to	ADP
easat-2990	162	15	the	the	DET
easat-2990	162	16	hierarchy	hierarchy	NOUN
easat-2990	162	17	benchmarking	benchmarke	VERB
easat-2990	162	18	value	value	NOUN
easat-2990	162	19	proposition	proposition	NOUN
easat-2990	162	20	and	and	CCONJ
easat-2990	162	21	its	its	PRON
easat-2990	162	22	relevance	relevance	NOUN
easat-2990	162	23	to	to	ADP
easat-2990	162	24	key	key	ADJ
easat-2990	162	25	performance	performance	NOUN
easat-2990	162	26	indicators	indicator	NOUN
easat-2990	162	27	.	.	PUNCT
easat-2990	163	1	in	in	ADP
easat-2990	163	2	addition	addition	NOUN
easat-2990	163	3	,	,	PUNCT
easat-2990	163	4	most	most	ADJ
easat-2990	163	5	organizations	organization	NOUN
easat-2990	163	6	apply	apply	VERB
easat-2990	163	7	benchmarks	benchmark	NOUN
easat-2990	163	8	mostly	mostly	ADV
easat-2990	163	9	in	in	ADP
easat-2990	163	10	operational	operational	ADJ
easat-2990	163	11	and	and	CCONJ
easat-2990	163	12	tactical	tactical	ADJ
easat-2990	163	13	levels	level	NOUN
easat-2990	163	14	and	and	CCONJ
easat-2990	163	15	not	not	PART
easat-2990	163	16	in	in	ADP
easat-2990	163	17	the	the	DET
easat-2990	163	18	strategic	strategic	ADJ
easat-2990	163	19	level	level	NOUN
easat-2990	163	20	,	,	PUNCT
easat-2990	163	21	which	which	PRON
easat-2990	163	22	means	mean	VERB
easat-2990	163	23	that	that	SCONJ
easat-2990	163	24	the	the	DET
easat-2990	163	25	potential	potential	NOUN
easat-2990	163	26	of	of	ADP
easat-2990	163	27	benchmarks	benchmark	NOUN
easat-2990	163	28	for	for	ADP
easat-2990	163	29	innovation	innovation	NOUN
easat-2990	163	30	and	and	CCONJ
easat-2990	163	31	growth	growth	NOUN
easat-2990	163	32	is	be	AUX
easat-2990	163	33	not	not	PART
easat-2990	163	34	fully	fully	ADV
easat-2990	163	35	realized[31	realized[31	NOUN
easat-2990	163	36	]	]	X
easat-2990	163	37	.	.	PUNCT
easat-2990	164	1	finally	finally	ADV
easat-2990	164	2	,	,	PUNCT
easat-2990	164	3	the	the	DET
easat-2990	164	4	management	management	NOUN
easat-2990	164	5	of	of	ADP
easat-2990	164	6	the	the	DET
easat-2990	164	7	benchmarking	benchmarke	VERB
easat-2990	164	8	process	process	NOUN
easat-2990	164	9	and	and	CCONJ
easat-2990	164	10	the	the	DET
easat-2990	164	11	definition	definition	NOUN
easat-2990	164	12	of	of	ADP
easat-2990	164	13	the	the	DET
easat-2990	164	14	scope	scope	NOUN
easat-2990	164	15	of	of	ADP
easat-2990	164	16	benchmarking	benchmarke	VERB
easat-2990	164	17	activities	activity	NOUN
easat-2990	164	18	are	be	AUX
easat-2990	164	19	critical	critical	ADJ
easat-2990	164	20	success	success	NOUN
easat-2990	164	21	factors	factor	NOUN
easat-2990	164	22	in	in	ADP
easat-2990	164	23	order	order	NOUN
easat-2990	164	24	to	to	PART
easat-2990	164	25	keep	keep	VERB
easat-2990	164	26	the	the	DET
easat-2990	164	27	benchmarking	benchmarke	VERB
easat-2990	164	28	process	process	NOUN
easat-2990	164	29	on	on	ADP
easat-2990	164	30	track	track	NOUN
easat-2990	164	31	and	and	CCONJ
easat-2990	164	32	prevent	prevent	VERB
easat-2990	164	33	the	the	DET
easat-2990	164	34	project	project	NOUN
easat-2990	164	35	from	from	ADP
easat-2990	164	36	get	get	VERB
easat-2990	164	37	out	out	ADP
easat-2990	164	38	of	of	ADP
easat-2990	164	39	control	control	NOUN
easat-2990	164	40	,	,	PUNCT
easat-2990	164	41	thus	thus	ADV
easat-2990	164	42	the	the	DET
easat-2990	164	43	benchmarking	benchmarke	VERB
easat-2990	164	44	process	process	NOUN
easat-2990	164	45	should	should	AUX
easat-2990	164	46	always	always	ADV
easat-2990	164	47	be	be	AUX
easat-2990	164	48	in	in	ADP
easat-2990	164	49	line	line	NOUN
easat-2990	164	50	with	with	ADP
easat-2990	164	51	the	the	DET
easat-2990	164	52	set	set	NOUN
easat-2990	164	53	goals	goal	NOUN
easat-2990	164	54	.	.	PUNCT
easat-2990	165	1	overcoming	overcome	VERB
easat-2990	165	2	these	these	DET
easat-2990	165	3	challenges	challenge	NOUN
easat-2990	165	4	enables	enable	VERB
easat-2990	165	5	organisations	organisation	NOUN
easat-2990	165	6	to	to	PART
easat-2990	165	7	reap	reap	VERB
easat-2990	165	8	maximum	maximum	ADJ
easat-2990	165	9	benefits	benefit	NOUN
easat-2990	165	10	of	of	ADP
easat-2990	165	11	benchmarking	benchmarke	VERB
easat-2990	165	12	and	and	CCONJ
easat-2990	165	13	achieve	achieve	VERB
easat-2990	165	14	organisational	organisational	ADJ
easat-2990	165	15	development[32	development[32	NOUN
easat-2990	165	16	]	]	PUNCT
easat-2990	165	17	.	.	PUNCT
easat-2990	166	1	the	the	DET
easat-2990	166	2	first	first	ADJ
easat-2990	166	3	discussed	discuss	VERB
easat-2990	166	4	benchmark	benchmark	NOUN
easat-2990	166	5	problem	problem	NOUN
easat-2990	166	6	is	be	AUX
easat-2990	166	7	about	about	ADP
easat-2990	166	8	using	use	VERB
easat-2990	166	9	the	the	DET
easat-2990	166	10	reduced	reduce	VERB
easat-2990	166	11	2d	2d	NUM
easat-2990	166	12	laplace	laplace	NOUN
easat-2990	166	13	integration	integration	NOUN
easat-2990	166	14	to	to	PART
easat-2990	166	15	solve	solve	VERB
easat-2990	166	16	the	the	DET
easat-2990	166	17	related	relate	VERB
easat-2990	166	18	dirichlet	dirichlet	PROPN
easat-2990	166	19	boundary	boundary	ADJ
easat-2990	166	20	value	value	NOUN
easat-2990	166	21	problem	problem	NOUN
easat-2990	166	22	.	.	PUNCT
easat-2990	167	1	with	with	ADP
easat-2990	167	2	the	the	DET
easat-2990	167	3	chosen	choose	VERB
easat-2990	167	4	'	'	PUNCT
easat-2990	167	5	enhanced	enhance	VERB
easat-2990	167	6	'	'	PUNCT
easat-2990	167	7	2d	2d	NOUN
easat-2990	167	8	domain	domain	NOUN
easat-2990	167	9	in	in	ADP
easat-2990	167	10	the	the	DET
easat-2990	167	11	wholesale	wholesale	ADJ
easat-2990	167	12	domain	domain	NOUN
easat-2990	167	13	,	,	PUNCT
easat-2990	167	14	ω	ω	NOUN
easat-2990	167	15	.	.	PUNCT
easat-2990	168	1	the	the	DET
easat-2990	168	2	other	other	ADJ
easat-2990	168	3	boundary	boundary	NOUN
easat-2990	168	4	of	of	ADP
easat-2990	168	5	the	the	DET
easat-2990	168	6	chosen	choose	VERB
easat-2990	168	7	2d	2d	PROPN
easat-2990	168	8	domain	domain	NOUN
easat-2990	168	9	was	be	AUX
easat-2990	168	10	fixed	fix	VERB
easat-2990	168	11	as	as	ADP
easat-2990	168	12	the	the	DET
easat-2990	168	13	source	source	NOUN
easat-2990	168	14	l(x	l(x	PROPN
easat-2990	168	15	,	,	PUNCT
easat-2990	168	16	y	y	NOUN
easat-2990	168	17	)	)	PUNCT
easat-2990	168	18	=	=	SYM
easat-2990	168	19	sin(πx	sin(πx	NOUN
easat-2990	168	20	)	)	PUNCT
easat-2990	168	21	×	×	NOUN
easat-2990	168	22	sin(πy	sin(πy	NOUN
easat-2990	168	23	)	)	PUNCT
easat-2990	168	24	.	.	PUNCT
easat-2990	169	1	the	the	DET
easat-2990	169	2	lambdas	lambda	NOUN
easat-2990	169	3	were	be	AUX
easat-2990	169	4	chosen	choose	VERB
easat-2990	169	5	as	as	ADP
easat-2990	169	6	its	its	PRON
easat-2990	169	7	well	well	ADV
easat-2990	169	8	-	-	PUNCT
easat-2990	169	9	defined	define	VERB
easat-2990	169	10	related	related	ADJ
easat-2990	169	11	analytic	analytic	ADJ
easat-2990	169	12	source	source	NOUN
easat-2990	169	13	to	to	ADP
easat-2990	169	14	l(x	l(x	PROPN
easat-2990	169	15	,	,	PUNCT
easat-2990	169	16	y	y	PROPN
easat-2990	169	17	)	)	PUNCT
easat-2990	169	18	.	.	PUNCT
easat-2990	170	1	5.2	5.2	NUM
easat-2990	170	2	.	.	PUNCT
easat-2990	170	3	performance	performance	NOUN
easat-2990	170	4	metrics	metric	NOUN
easat-2990	170	5	in	in	ADP
easat-2990	170	6	some	some	DET
easat-2990	170	7	other	other	ADJ
easat-2990	170	8	air	air	NOUN
easat-2990	170	9	pollution	pollution	NOUN
easat-2990	170	10	models	model	NOUN
easat-2990	170	11	,	,	PUNCT
easat-2990	170	12	we	we	PRON
easat-2990	170	13	might	might	AUX
easat-2990	170	14	need	need	VERB
easat-2990	170	15	to	to	PART
easat-2990	170	16	compare	compare	VERB
easat-2990	170	17	the	the	DET
easat-2990	170	18	predicted	predict	VERB
easat-2990	170	19	ozone	ozone	NOUN
easat-2990	170	20	concentrations	concentration	NOUN
easat-2990	170	21	with	with	ADP
easat-2990	170	22	the	the	DET
easat-2990	170	23	acceptable	acceptable	ADJ
easat-2990	170	24	values	value	NOUN
easat-2990	170	25	to	to	PART
easat-2990	170	26	assist	assist	VERB
easat-2990	170	27	policymakers	policymaker	NOUN
easat-2990	170	28	in	in	ADP
easat-2990	170	29	making	make	VERB
easat-2990	170	30	better	well	ADJ
easat-2990	170	31	decisions	decision	NOUN
easat-2990	170	32	.	.	PUNCT
easat-2990	171	1	we	we	PRON
easat-2990	171	2	only	only	ADV
easat-2990	171	3	consider	consider	VERB
easat-2990	171	4	the	the	DET
easat-2990	171	5	available	available	ADJ
easat-2990	171	6	performance	performance	NOUN
easat-2990	171	7	indices	index	NOUN
easat-2990	171	8	,	,	PUNCT
easat-2990	171	9	which	which	PRON
easat-2990	171	10	include	include	VERB
easat-2990	171	11	mean	mean	VERB
easat-2990	171	12	absolute	absolute	ADJ
easat-2990	171	13	error	error	NOUN
easat-2990	171	14	,	,	PUNCT
easat-2990	171	15	root	root	NOUN
easat-2990	171	16	mean	mean	VERB
easat-2990	171	17	squared	square	VERB
easat-2990	171	18	error	error	NOUN
easat-2990	171	19	,	,	PUNCT
easat-2990	171	20	and	and	CCONJ
easat-2990	171	21	index	index	NOUN
easat-2990	171	22	of	of	ADP
easat-2990	171	23	agreement	agreement	NOUN
easat-2990	171	24	.	.	PUNCT
easat-2990	172	1	with	with	ADP
easat-2990	172	2	the	the	DET
easat-2990	172	3	actual	actual	ADJ
easat-2990	172	4	value	value	NOUN
easat-2990	172	5	,	,	PUNCT
easat-2990	172	6	the	the	DET
easat-2990	172	7	predicted	predict	VERB
easat-2990	172	8	value	value	NOUN
easat-2990	172	9	,	,	PUNCT
easat-2990	172	10	and	and	CCONJ
easat-2990	172	11	the	the	DET
easat-2990	172	12	mean	mean	NOUN
easat-2990	172	13	of	of	ADP
easat-2990	172	14	the	the	DET
easat-2990	172	15	non	non	ADJ
easat-2990	172	16	-	-	ADJ
easat-2990	172	17	missing	missing	ADJ
easat-2990	172	18	actual	actual	ADJ
easat-2990	172	19	values	value	NOUN
easat-2990	172	20	refer	refer	VERB
easat-2990	172	21	to	to	ADP
easat-2990	172	22	the	the	DET
easat-2990	172	23	actual	actual	ADJ
easat-2990	172	24	value	value	NOUN
easat-2990	172	25	,	,	PUNCT
easat-2990	172	26	the	the	DET
easat-2990	172	27	number	number	NOUN
easat-2990	172	28	of	of	ADP
easat-2990	172	29	available	available	ADJ
easat-2990	172	30	observations	observation	NOUN
easat-2990	172	31	,	,	PUNCT
easat-2990	172	32	the	the	DET
easat-2990	172	33	mean	mean	NOUN
easat-2990	172	34	of	of	ADP
easat-2990	172	35	the	the	DET
easat-2990	172	36	non	non	ADJ
easat-2990	172	37	-	-	ADJ
easat-2990	172	38	missing	missing	ADJ
easat-2990	172	39	actual	actual	ADJ
easat-2990	172	40	values	value	NOUN
easat-2990	172	41	,	,	PUNCT
easat-2990	172	42	and	and	CCONJ
easat-2990	172	43	the	the	DET
easat-2990	172	44	nrmse	nrmse	NOUN
easat-2990	172	45	between	between	ADP
easat-2990	172	46	the	the	DET
easat-2990	172	47	inflated	inflated	ADJ
easat-2990	172	48	and	and	CCONJ
easat-2990	172	49	the	the	DET
easat-2990	172	50	aggregated	aggregate	VERB
easat-2990	172	51	values	value	NOUN
easat-2990	172	52	of	of	ADP
easat-2990	172	53	observation	observation	NOUN
easat-2990	172	54	,	,	PUNCT
easat-2990	172	55	respectively[33	respectively[33	NOUN
easat-2990	172	56	]	]	PUNCT
easat-2990	172	57	.	.	PUNCT
easat-2990	173	1	it	it	PRON
easat-2990	173	2	should	should	AUX
easat-2990	173	3	be	be	AUX
easat-2990	173	4	noted	note	VERB
easat-2990	173	5	that	that	SCONJ
easat-2990	173	6	index	index	NOUN
easat-2990	173	7	of	of	ADP
easat-2990	173	8	agreement	agreement	NOUN
easat-2990	173	9	might	might	AUX
easat-2990	173	10	not	not	PART
easat-2990	173	11	be	be	AUX
easat-2990	173	12	reliable	reliable	ADJ
easat-2990	173	13	when	when	SCONJ
easat-2990	173	14	the	the	DET
easat-2990	173	15	range	range	NOUN
easat-2990	173	16	of	of	ADP
easat-2990	173	17	observation	observation	NOUN
easat-2990	173	18	values	value	NOUN
easat-2990	173	19	is	be	AUX
easat-2990	173	20	very	very	ADV
easat-2990	173	21	small	small	ADJ
easat-2990	173	22	.	.	PUNCT
easat-2990	174	1	for	for	ADP
easat-2990	174	2	a	a	DET
easat-2990	174	3	normal	normal	ADJ
easat-2990	174	4	non	non	ADJ
easat-2990	174	5	-	-	ADJ
easat-2990	174	6	dimensional	dimensional	ADJ
easat-2990	174	7	metric	metric	NOUN
easat-2990	174	8	such	such	ADJ
easat-2990	174	9	as	as	ADP
easat-2990	174	10	root	root	NOUN
easat-2990	174	11	mean	mean	VERB
easat-2990	174	12	squared	square	VERB
easat-2990	174	13	error	error	NOUN
easat-2990	174	14	,	,	PUNCT
easat-2990	174	15	a	a	DET
easat-2990	174	16	value	value	NOUN
easat-2990	174	17	closer	close	ADV
easat-2990	174	18	to	to	ADP
easat-2990	174	19	one	one	NUM
easat-2990	174	20	indicates	indicate	VERB
easat-2990	174	21	closeness	closeness	NOUN
easat-2990	174	22	to	to	ADP
easat-2990	174	23	the	the	DET
easat-2990	174	24	actual	actual	ADJ
easat-2990	174	25	observation	observation	NOUN
easat-2990	174	26	,	,	PUNCT
easat-2990	174	27	while	while	SCONJ
easat-2990	174	28	a	a	DET
easat-2990	174	29	value	value	NOUN
easat-2990	174	30	closer	close	ADV
easat-2990	174	31	to	to	ADP
easat-2990	174	32	zero	zero	NUM
easat-2990	174	33	indicates	indicate	VERB
easat-2990	174	34	worse	bad	ADJ
easat-2990	174	35	4607	4607	NUM
easat-2990	174	36	edelweiss	edelweiss	PROPN
easat-2990	174	37	applied	apply	VERB
easat-2990	174	38	science	science	NOUN
easat-2990	174	39	and	and	CCONJ
easat-2990	174	40	technology	technology	NOUN
easat-2990	174	41	issn	issn	PROPN
easat-2990	174	42	:	:	PUNCT
easat-2990	174	43	2576	2576	NUM
easat-2990	174	44	-	-	SYM
easat-2990	174	45	8484	8484	NUM
easat-2990	174	46	vol	vol	NOUN
easat-2990	174	47	.	.	PROPN
easat-2990	174	48	8	8	NUM
easat-2990	174	49	,	,	PUNCT
easat-2990	174	50	no	no	INTJ
easat-2990	174	51	.	.	NOUN
easat-2990	175	1	6	6	NUM
easat-2990	175	2	:	:	SYM
easat-2990	175	3	4599	4599	NUM
easat-2990	175	4	-	-	SYM
easat-2990	175	5	4610	4610	NUM
easat-2990	175	6	,	,	PUNCT
easat-2990	175	7	2024	2024	NUM
easat-2990	175	8	doi	doi	NOUN
easat-2990	175	9	:	:	PUNCT
easat-2990	175	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	175	11	©	©	PROPN
easat-2990	175	12	2024	2024	NUM
easat-2990	175	13	by	by	ADP
easat-2990	175	14	the	the	DET
easat-2990	175	15	author	author	NOUN
easat-2990	175	16	;	;	PUNCT
easat-2990	175	17	licensee	licensee	PROPN
easat-2990	175	18	learning	learn	VERB
easat-2990	175	19	gate	gate	PROPN
easat-2990	175	20	fitness	fitness	PROPN
easat-2990	175	21	.	.	PUNCT
easat-2990	176	1	however	however	ADV
easat-2990	176	2	,	,	PUNCT
easat-2990	176	3	a	a	DET
easat-2990	176	4	smaller	small	ADJ
easat-2990	176	5	value	value	NOUN
easat-2990	176	6	of	of	ADP
easat-2990	176	7	all	all	DET
easat-2990	176	8	index	index	NOUN
easat-2990	176	9	of	of	ADP
easat-2990	176	10	agreement	agreement	NOUN
easat-2990	176	11	excepted	except	VERB
easat-2990	176	12	values	value	NOUN
easat-2990	176	13	presents	present	VERB
easat-2990	176	14	a	a	DET
easat-2990	176	15	better	well	ADJ
easat-2990	176	16	result	result	NOUN
easat-2990	176	17	(	(	PUNCT
easat-2990	176	18	less	less	ADJ
easat-2990	176	19	than	than	ADP
easat-2990	176	20	0.5	0.5	NUM
easat-2990	176	21	is	be	AUX
easat-2990	176	22	unsatisfactory	unsatisfactory	ADJ
easat-2990	176	23	)	)	PUNCT
easat-2990	176	24	.	.	PUNCT
easat-2990	177	1	taken	take	VERB
easat-2990	177	2	all	all	ADV
easat-2990	177	3	together	together	ADV
easat-2990	177	4	,	,	PUNCT
easat-2990	177	5	index	index	NOUN
easat-2990	177	6	of	of	ADP
easat-2990	177	7	agreement	agreement	NOUN
easat-2990	177	8	and	and	CCONJ
easat-2990	177	9	mean	mean	VERB
easat-2990	177	10	absolute	absolute	ADJ
easat-2990	177	11	error	error	NOUN
easat-2990	177	12	are	be	AUX
easat-2990	177	13	between	between	ADP
easat-2990	177	14	-1	-1	PUNCT
easat-2990	177	15	and	and	CCONJ
easat-2990	177	16	1	1	NUM
easat-2990	177	17	,	,	PUNCT
easat-2990	177	18	while	while	SCONJ
easat-2990	177	19	root	root	NOUN
easat-2990	177	20	mean	mean	VERB
easat-2990	177	21	squared	square	VERB
easat-2990	177	22	error	error	NOUN
easat-2990	177	23	ranges	range	VERB
easat-2990	177	24	from	from	ADP
easat-2990	177	25	zero	zero	NUM
easat-2990	177	26	to	to	ADP
easat-2990	177	27	infinity	infinity	NOUN
easat-2990	177	28	.	.	PUNCT
easat-2990	178	1	for	for	ADP
easat-2990	178	2	all	all	DET
easat-2990	178	3	available	available	ADJ
easat-2990	178	4	performance	performance	NOUN
easat-2990	178	5	norms	norm	NOUN
easat-2990	178	6	,	,	PUNCT
easat-2990	178	7	a	a	DET
easat-2990	178	8	more	more	ADV
easat-2990	178	9	comprehensive	comprehensive	ADJ
easat-2990	178	10	description	description	NOUN
easat-2990	178	11	can	can	AUX
easat-2990	178	12	be	be	AUX
easat-2990	178	13	found	find	VERB
easat-2990	178	14	in	in	ADP
easat-2990	178	15	the	the	DET
easat-2990	178	16	relevant	relevant	ADJ
easat-2990	178	17	literature	literature	NOUN
easat-2990	178	18	.	.	PUNCT
easat-2990	179	1	5.3	5.3	NUM
easat-2990	179	2	.	.	PUNCT
easat-2990	179	3	cattaneo	cattaneo	PROPN
easat-2990	179	4	-	-	PUNCT
easat-2990	179	5	rayleigh	rayleigh	PROPN
easat-2990	179	6	model	model	NOUN
easat-2990	179	7	of	of	ADP
easat-2990	179	8	thermoelectricity	thermoelectricity	NOUN
easat-2990	179	9	the	the	DET
easat-2990	179	10	cattaneo	cattaneo	PROPN
easat-2990	179	11	-	-	PUNCT
easat-2990	179	12	rayleigh	rayleigh	PROPN
easat-2990	179	13	model	model	NOUN
easat-2990	179	14	of	of	ADP
easat-2990	179	15	thermoelasticity	thermoelasticity	NOUN
easat-2990	179	16	is	be	AUX
easat-2990	179	17	an	an	DET
easat-2990	179	18	extension	extension	NOUN
easat-2990	179	19	of	of	ADP
easat-2990	179	20	classical	classical	ADJ
easat-2990	179	21	thermoelasticity	thermoelasticity	NOUN
easat-2990	179	22	that	that	PRON
easat-2990	179	23	incorporates	incorporate	VERB
easat-2990	179	24	thermal	thermal	ADJ
easat-2990	179	25	relaxation	relaxation	NOUN
easat-2990	179	26	time	time	NOUN
easat-2990	179	27	.	.	PUNCT
easat-2990	180	1	this	this	DET
easat-2990	180	2	model	model	NOUN
easat-2990	180	3	addresses	address	VERB
easat-2990	180	4	the	the	DET
easat-2990	180	5	paradox	paradox	NOUN
easat-2990	180	6	of	of	ADP
easat-2990	180	7	infinite	infinite	ADJ
easat-2990	180	8	propagation	propagation	NOUN
easat-2990	180	9	speed	speed	NOUN
easat-2990	180	10	in	in	ADP
easat-2990	180	11	classical	classical	ADJ
easat-2990	180	12	heat	heat	NOUN
easat-2990	180	13	conduction	conduction	NOUN
easat-2990	180	14	by	by	ADP
easat-2990	180	15	introducing	introduce	VERB
easat-2990	180	16	a	a	DET
easat-2990	180	17	hyperbolic	hyperbolic	ADJ
easat-2990	180	18	-	-	PUNCT
easat-2990	180	19	type	type	NOUN
easat-2990	180	20	heat	heat	NOUN
easat-2990	180	21	equation	equation	NOUN
easat-2990	180	22	instead	instead	ADV
easat-2990	180	23	of	of	ADP
easat-2990	180	24	the	the	DET
easat-2990	180	25	traditional	traditional	ADJ
easat-2990	180	26	parabolic	parabolic	NOUN
easat-2990	180	27	one[34	one[34	PROPN
easat-2990	180	28	]	]	PUNCT
easat-2990	180	29	.	.	PUNCT
easat-2990	181	1	a	a	DET
easat-2990	181	2	matlab	matlab	PROPN
easat-2990	181	3	code	code	NOUN
easat-2990	181	4	structure	structure	NOUN
easat-2990	181	5	for	for	ADP
easat-2990	181	6	solving	solve	VERB
easat-2990	181	7	a	a	DET
easat-2990	181	8	simplified	simplified	ADJ
easat-2990	181	9	fractional	fractional	ADJ
easat-2990	181	10	cattaneo	cattaneo	PROPN
easat-2990	181	11	-	-	PUNCT
easat-2990	181	12	rayleigh	rayleigh	PROPN
easat-2990	181	13	thermoelasticity	thermoelasticity	NOUN
easat-2990	181	14	model	model	NOUN
easat-2990	181	15	using	use	VERB
easat-2990	181	16	a	a	DET
easat-2990	181	17	wavelet	wavelet	NOUN
easat-2990	181	18	collocation	collocation	NOUN
easat-2990	181	19	approach	approach	NOUN
easat-2990	181	20	.	.	PUNCT
easat-2990	182	1	for	for	ADP
easat-2990	182	2	demonstration	demonstration	NOUN
easat-2990	182	3	purposes	purpose	NOUN
easat-2990	182	4	,	,	PUNCT
easat-2990	182	5	we	we	PRON
easat-2990	182	6	'll	will	AUX
easat-2990	182	7	assume	assume	VERB
easat-2990	182	8	a	a	DET
easat-2990	182	9	basic	basic	ADJ
easat-2990	182	10	version	version	NOUN
easat-2990	182	11	of	of	ADP
easat-2990	182	12	the	the	DET
easat-2990	182	13	equation	equation	NOUN
easat-2990	182	14	:	:	PUNCT
easat-2990	182	15	where	where	SCONJ
easat-2990	182	16	:	:	PUNCT
easat-2990	182	17	•	•	X
easat-2990	182	18	α	α	NOUN
easat-2990	182	19	is	be	AUX
easat-2990	182	20	the	the	DET
easat-2990	182	21	fractional	fractional	ADJ
easat-2990	182	22	order	order	NOUN
easat-2990	182	23	of	of	ADP
easat-2990	182	24	time	time	NOUN
easat-2990	182	25	derivative	derivative	ADJ
easat-2990	182	26	(	(	PUNCT
easat-2990	182	27	0	0	NUM
easat-2990	182	28	<	<	X
easat-2990	182	29	𝛼	𝛼	X
easat-2990	182	30	≤	≤	NUM
easat-2990	182	31	1	1	NUM
easat-2990	182	32	)	)	PUNCT
easat-2990	182	33	.	.	PUNCT
easat-2990	183	1	•	•	NUM
easat-2990	183	2	u(x	u(x	PROPN
easat-2990	183	3	,	,	PUNCT
easat-2990	183	4	t	t	PROPN
easat-2990	183	5	)	)	PUNCT
easat-2990	183	6	is	be	AUX
easat-2990	183	7	the	the	DET
easat-2990	183	8	solution	solution	NOUN
easat-2990	183	9	in	in	ADP
easat-2990	183	10	a	a	DET
easat-2990	183	11	one	one	NUM
easat-2990	183	12	-	-	PUNCT
easat-2990	183	13	dimensional	dimensional	ADJ
easat-2990	183	14	zonal	zonal	ADJ
easat-2990	183	15	region	region	NOUN
easat-2990	183	16	.	.	PUNCT
easat-2990	184	1	•	•	NUM
easat-2990	184	2	β	β	X
easat-2990	184	3	and	and	CCONJ
easat-2990	184	4	γ	γ	PROPN
easat-2990	184	5	are	be	AUX
easat-2990	184	6	model	model	NOUN
easat-2990	184	7	parameters	parameter	NOUN
easat-2990	184	8	.	.	PUNCT
easat-2990	185	1	matlab	matlab	PROPN
easat-2990	185	2	code	code	PROPN
easat-2990	185	3	(	(	PUNCT
easat-2990	185	4	wavelet	wavelet	NOUN
easat-2990	185	5	collocation	collocation	NOUN
easat-2990	185	6	for	for	ADP
easat-2990	185	7	fractional	fractional	ADJ
easat-2990	185	8	cattaneo	cattaneo	PROPN
easat-2990	185	9	-	-	PUNCT
easat-2990	185	10	rayleigh	rayleigh	PROPN
easat-2990	185	11	model	model	NOUN
easat-2990	185	12	)	)	PUNCT
easat-2990	185	13	%	%	NOUN
easat-2990	185	14	matlab	matlab	PROPN
easat-2990	185	15	code	code	PROPN
easat-2990	185	16	for	for	ADP
easat-2990	185	17	solving	solve	VERB
easat-2990	185	18	fractional	fractional	ADJ
easat-2990	185	19	cattaneo	cattaneo	PROPN
easat-2990	185	20	-	-	PUNCT
easat-2990	185	21	rayleigh	rayleigh	PROPN
easat-2990	185	22	model	model	NOUN
easat-2990	185	23	using	use	VERB
easat-2990	185	24	wavelet	wavelet	NOUN
easat-2990	185	25	collocation	collocation	NOUN
easat-2990	185	26	%	%	NOUN
easat-2990	185	27	parameters	parameter	NOUN
easat-2990	185	28	alpha	alpha	NOUN
easat-2990	185	29	=	=	NOUN
easat-2990	185	30	0.5	0.5	NUM
easat-2990	185	31	;	;	PUNCT
easat-2990	185	32	%	%	NOUN
easat-2990	185	33	fractional	fractional	ADJ
easat-2990	185	34	order	order	NOUN
easat-2990	185	35	in	in	ADP
easat-2990	185	36	time	time	NOUN
easat-2990	185	37	(	(	PUNCT
easat-2990	185	38	0	0	PUNCT
easat-2990	185	39	<	<	X
easat-2990	185	40	alpha	alpha	NOUN
easat-2990	185	41	<	<	X
easat-2990	185	42	=	=	SYM
easat-2990	185	43	1	1	NUM
easat-2990	185	44	)	)	PUNCT
easat-2990	185	45	beta	beta	NOUN
easat-2990	185	46	=	=	SYM
easat-2990	185	47	0.5	0.5	NUM
easat-2990	185	48	;	;	PUNCT
easat-2990	185	49	%	%	NOUN
easat-2990	185	50	parameter	parameter	NOUN
easat-2990	185	51	for	for	ADP
easat-2990	185	52	spatial	spatial	ADJ
easat-2990	185	53	derivative	derivative	ADJ
easat-2990	185	54	term	term	NOUN
easat-2990	185	55	gamma	gamma	NOUN
easat-2990	185	56	=	=	NOUN
easat-2990	185	57	0.1	0.1	NUM
easat-2990	185	58	;	;	PUNCT
easat-2990	185	59	%	%	NOUN
easat-2990	185	60	parameter	parameter	NOUN
easat-2990	185	61	for	for	ADP
easat-2990	185	62	decay	decay	NOUN
easat-2990	185	63	term	term	NOUN
easat-2990	185	64	nx	nx	X
easat-2990	185	65	=	=	NOUN
easat-2990	185	66	100	100	NUM
easat-2990	185	67	;	;	PUNCT
easat-2990	185	68	%	%	X
easat-2990	185	69	number	number	NOUN
easat-2990	185	70	of	of	ADP
easat-2990	185	71	collocation	collocation	NOUN
easat-2990	185	72	points	point	NOUN
easat-2990	185	73	in	in	ADP
easat-2990	185	74	x	x	PUNCT
easat-2990	185	75	nt	not	PART
easat-2990	185	76	=	=	NOUN
easat-2990	185	77	100	100	NUM
easat-2990	185	78	;	;	PUNCT
easat-2990	185	79	%	%	X
easat-2990	185	80	number	number	NOUN
easat-2990	185	81	of	of	ADP
easat-2990	185	82	time	time	NOUN
easat-2990	185	83	steps	step	NOUN
easat-2990	185	84	lx	lx	NOUN
easat-2990	185	85	=	=	SYM
easat-2990	185	86	10	10	NUM
easat-2990	185	87	;	;	PUNCT
easat-2990	185	88	%	%	NOUN
easat-2990	185	89	spatial	spatial	ADJ
easat-2990	185	90	domain	domain	NOUN
easat-2990	185	91	length	length	NOUN
easat-2990	185	92	(	(	PUNCT
easat-2990	185	93	x	x	SYM
easat-2990	185	94	∈	∈	PROPN
easat-2990	186	1	[	[	X
easat-2990	186	2	0	0	NUM
easat-2990	186	3	,	,	PUNCT
easat-2990	186	4	lx	lx	NOUN
easat-2990	186	5	]	]	PUNCT
easat-2990	186	6	)	)	PUNCT
easat-2990	186	7	t	t	NOUN
easat-2990	186	8	=	=	SYM
easat-2990	186	9	1	1	NUM
easat-2990	186	10	;	;	PUNCT
easat-2990	186	11	%	%	NOUN
easat-2990	186	12	time	time	NOUN
easat-2990	186	13	domain	domain	NOUN
easat-2990	186	14	length	length	NOUN
easat-2990	186	15	(	(	PUNCT
easat-2990	186	16	t	t	PROPN
easat-2990	186	17	∈	∈	PROPN
easat-2990	187	1	[	[	X
easat-2990	187	2	0	0	NUM
easat-2990	187	3	,	,	PUNCT
easat-2990	187	4	t	t	PROPN
easat-2990	187	5	]	]	PUNCT
easat-2990	187	6	)	)	PUNCT
easat-2990	187	7	dx	dx	PROPN
easat-2990	188	1	=	=	PUNCT
easat-2990	188	2	lx	lx	NOUN
easat-2990	188	3	/	/	PUNCT
easat-2990	188	4	(	(	PUNCT
easat-2990	188	5	nx	nx	PROPN
easat-2990	188	6	1	1	NUM
easat-2990	188	7	)	)	PUNCT
easat-2990	188	8	;	;	PUNCT
easat-2990	188	9	dt	dt	PROPN
easat-2990	188	10	=	=	SYM
easat-2990	188	11	t	t	PROPN
easat-2990	188	12	/	/	PUNCT
easat-2990	188	13	(	(	PUNCT
easat-2990	188	14	nt	not	PART
easat-2990	188	15	1	1	NUM
easat-2990	188	16	)	)	PUNCT
easat-2990	188	17	;	;	PUNCT
easat-2990	188	18	%	%	NOUN
easat-2990	188	19	grid	grid	NOUN
easat-2990	188	20	in	in	ADP
easat-2990	188	21	x	x	PUNCT
easat-2990	188	22	and	and	CCONJ
easat-2990	188	23	t	t	NOUN
easat-2990	188	24	x	x	X
easat-2990	188	25	=	=	SYM
easat-2990	188	26	linspace(0	linspace(0	PROPN
easat-2990	188	27	,	,	PUNCT
easat-2990	188	28	lx	lx	NOUN
easat-2990	188	29	,	,	PUNCT
easat-2990	188	30	nx	nx	PROPN
easat-2990	188	31	)	)	PUNCT
easat-2990	188	32	;	;	PUNCT
easat-2990	188	33	t	t	PROPN
easat-2990	188	34	=	=	SYM
easat-2990	188	35	linspace(0	linspace(0	PROPN
easat-2990	188	36	,	,	PUNCT
easat-2990	188	37	t	t	PROPN
easat-2990	188	38	,	,	PUNCT
easat-2990	188	39	nt	not	PART
easat-2990	188	40	)	)	PUNCT
easat-2990	188	41	;	;	PUNCT
easat-2990	189	1	[	[	X
easat-2990	189	2	x	x	X
easat-2990	189	3	,	,	PUNCT
easat-2990	189	4	t	t	PROPN
easat-2990	189	5	]	]	X
easat-2990	189	6	=	=	SYM
easat-2990	189	7	meshgrid(x	meshgrid(x	PROPN
easat-2990	189	8	,	,	PUNCT
easat-2990	189	9	t	t	PROPN
easat-2990	189	10	)	)	PUNCT
easat-2990	189	11	;	;	PUNCT
easat-2990	189	12	%	%	NOUN
easat-2990	189	13	initial	initial	ADJ
easat-2990	189	14	condition	condition	NOUN
easat-2990	189	15	u	u	NOUN
easat-2990	189	16	=	=	PROPN
easat-2990	189	17	zeros(nx	zeros(nx	PROPN
easat-2990	189	18	,	,	PUNCT
easat-2990	189	19	nt	not	PART
easat-2990	189	20	)	)	PUNCT
easat-2990	189	21	;	;	PUNCT
easat-2990	189	22	u	u	NOUN
easat-2990	189	23	(:	(:	NOUN
easat-2990	189	24	,	,	PUNCT
easat-2990	189	25	1	1	NUM
easat-2990	189	26	)	)	PUNCT
easat-2990	189	27	=	=	NOUN
easat-2990	189	28	sin(pi	sin(pi	X
easat-2990	189	29	*	*	PUNCT
easat-2990	189	30	x	x	SYM
easat-2990	189	31	/	/	SYM
easat-2990	189	32	lx	lx	NOUN
easat-2990	189	33	)	)	PUNCT
easat-2990	189	34	;	;	PUNCT
easat-2990	189	35	%	%	NOUN
easat-2990	189	36	initial	initial	ADJ
easat-2990	189	37	profile	profile	NOUN
easat-2990	189	38	of	of	ADP
easat-2990	189	39	u(x	u(x	NOUN
easat-2990	189	40	,	,	PUNCT
easat-2990	189	41	0	0	NUM
easat-2990	189	42	)	)	PUNCT
easat-2990	189	43	%	%	NOUN
easat-2990	189	44	define	define	VERB
easat-2990	189	45	fractional	fractional	ADJ
easat-2990	189	46	derivative	derivative	NOUN
easat-2990	189	47	(	(	PUNCT
easat-2990	189	48	using	use	VERB
easat-2990	189	49	an	an	DET
easat-2990	189	50	approximation	approximation	NOUN
easat-2990	189	51	for	for	ADP
easat-2990	189	52	simplicity	simplicity	NOUN
easat-2990	189	53	)	)	PUNCT
easat-2990	189	54	fractionalderivative	fractionalderivative	ADJ
easat-2990	189	55	=	=	PUNCT
easat-2990	189	56	@(u	@(u	NOUN
easat-2990	189	57	,	,	PUNCT
easat-2990	189	58	alpha	alpha	NOUN
easat-2990	189	59	)	)	PUNCT
easat-2990	190	1	[	[	X
easat-2990	190	2	diff(u	diff(u	NOUN
easat-2990	190	3	)	)	PUNCT
easat-2990	190	4	/	/	PUNCT
easat-2990	190	5	dx.^alpha	dx.^alpha	PROPN
easat-2990	190	6	;	;	PUNCT
easat-2990	190	7	0	0	NUM
easat-2990	190	8	]	]	PUNCT
easat-2990	190	9	;	;	PUNCT
easat-2990	190	10	%	%	NOUN
easat-2990	190	11	append	append	NOUN
easat-2990	190	12	zero	zero	NUM
easat-2990	190	13	to	to	PART
easat-2990	190	14	match	match	VERB
easat-2990	190	15	dimensions	dimension	NOUN
easat-2990	190	16	%	%	NOUN
easat-2990	190	17	time	time	NOUN
easat-2990	190	18	iteration	iteration	NOUN
easat-2990	190	19	using	use	VERB
easat-2990	190	20	fractional	fractional	ADJ
easat-2990	190	21	differential	differential	NOUN
easat-2990	190	22	operator	operator	NOUN
easat-2990	190	23	for	for	ADP
easat-2990	190	24	n	n	NOUN
easat-2990	190	25	=	=	SYM
easat-2990	190	26	2	2	NUM
easat-2990	190	27	:	:	PUNCT
easat-2990	190	28	nt	not	PART
easat-2990	190	29	%	%	INTJ
easat-2990	190	30	fractional	fractional	ADJ
easat-2990	190	31	derivative	derivative	NOUN
easat-2990	190	32	in	in	ADP
easat-2990	190	33	time	time	NOUN
easat-2990	190	34	with	with	ADP
easat-2990	190	35	respect	respect	NOUN
easat-2990	190	36	to	to	ADP
easat-2990	190	37	previous	previous	ADJ
easat-2990	190	38	time	time	NOUN
easat-2990	190	39	step	step	NOUN
easat-2990	190	40	4608	4608	NUM
easat-2990	190	41	edelweiss	edelweiss	PROPN
easat-2990	190	42	applied	apply	VERB
easat-2990	190	43	science	science	NOUN
easat-2990	190	44	and	and	CCONJ
easat-2990	190	45	technology	technology	NOUN
easat-2990	190	46	issn	issn	PROPN
easat-2990	190	47	:	:	PUNCT
easat-2990	190	48	2576	2576	NUM
easat-2990	190	49	-	-	SYM
easat-2990	190	50	8484	8484	NUM
easat-2990	190	51	vol	vol	NOUN
easat-2990	190	52	.	.	PROPN
easat-2990	191	1	8	8	NUM
easat-2990	191	2	,	,	PUNCT
easat-2990	191	3	no	no	INTJ
easat-2990	191	4	.	.	NOUN
easat-2990	192	1	6	6	NUM
easat-2990	192	2	:	:	SYM
easat-2990	192	3	4599	4599	NUM
easat-2990	192	4	-	-	SYM
easat-2990	192	5	4610	4610	NUM
easat-2990	192	6	,	,	PUNCT
easat-2990	192	7	2024	2024	NUM
easat-2990	192	8	doi	doi	NOUN
easat-2990	192	9	:	:	PUNCT
easat-2990	192	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	192	11	©	©	PROPN
easat-2990	192	12	2024	2024	NUM
easat-2990	192	13	by	by	ADP
easat-2990	192	14	the	the	DET
easat-2990	192	15	author	author	NOUN
easat-2990	192	16	;	;	PUNCT
easat-2990	193	1	licensee	licensee	PROPN
easat-2990	193	2	learning	learn	VERB
easat-2990	193	3	gate	gate	NOUN
easat-2990	193	4	du_dt_frac	du_dt_frac	PROPN
easat-2990	193	5	=	=	PUNCT
easat-2990	193	6	fractionalderivative(u	fractionalderivative(u	NOUN
easat-2990	193	7	(:	(:	NOUN
easat-2990	193	8	,	,	PUNCT
easat-2990	193	9	n-1	n-1	NUM
easat-2990	193	10	)	)	PUNCT
easat-2990	193	11	,	,	PUNCT
easat-2990	193	12	alpha	alpha	NOUN
easat-2990	193	13	)	)	PUNCT
easat-2990	193	14	;	;	PUNCT
easat-2990	194	1	%	%	X
easat-2990	194	2	compute	compute	PROPN
easat-2990	194	3	spatial	spatial	ADJ
easat-2990	194	4	derivative	derivative	ADJ
easat-2990	194	5	term	term	NOUN
easat-2990	194	6	u_x_term	u_x_term	NOUN
easat-2990	194	7	=	=	SYM
easat-2990	194	8	beta	beta	NOUN
easat-2990	194	9	*	*	PUNCT
easat-2990	195	1	[	[	X
easat-2990	195	2	diff(u	diff(u	NOUN
easat-2990	195	3	(:	(:	NOUN
easat-2990	195	4	,	,	PUNCT
easat-2990	195	5	n-1	n-1	NUM
easat-2990	195	6	)	)	PUNCT
easat-2990	195	7	)	)	PUNCT
easat-2990	195	8	/	/	SYM
easat-2990	195	9	dx	dx	PROPN
easat-2990	195	10	;	;	PUNCT
easat-2990	195	11	0	0	NUM
easat-2990	195	12	]	]	PUNCT
easat-2990	195	13	;	;	PUNCT
easat-2990	195	14	%	%	NOUN
easat-2990	195	15	append	append	NOUN
easat-2990	195	16	zero	zero	NUM
easat-2990	195	17	to	to	PART
easat-2990	195	18	match	match	VERB
easat-2990	195	19	dimensions	dimension	NOUN
easat-2990	195	20	%	%	NOUN
easat-2990	195	21	source	source	NOUN
easat-2990	195	22	term	term	NOUN
easat-2990	195	23	source_term	source_term	VERB
easat-2990	195	24	=	=	SYM
easat-2990	195	25	gamma	gamma	NOUN
easat-2990	195	26	*	*	PUNCT
easat-2990	195	27	u	u	NOUN
easat-2990	195	28	(:	(:	PROPN
easat-2990	195	29	,	,	PUNCT
easat-2990	195	30	n-1	n-1	NUM
easat-2990	195	31	)	)	PUNCT
easat-2990	195	32	;	;	PUNCT
easat-2990	195	33	%	%	NOUN
easat-2990	195	34	update	update	NOUN
easat-2990	195	35	solution	solution	NOUN
easat-2990	195	36	at	at	ADP
easat-2990	195	37	each	each	DET
easat-2990	195	38	collocation	collocation	NOUN
easat-2990	195	39	point	point	NOUN
easat-2990	195	40	u	u	NOUN
easat-2990	195	41	(:	(:	NOUN
easat-2990	195	42	,	,	PUNCT
easat-2990	195	43	n	n	CCONJ
easat-2990	195	44	)	)	PUNCT
easat-2990	195	45	=	=	SYM
easat-2990	195	46	u	u	NOUN
easat-2990	195	47	(:	(:	NOUN
easat-2990	195	48	,	,	PUNCT
easat-2990	195	49	n-1	n-1	NUM
easat-2990	195	50	)	)	PUNCT
easat-2990	196	1	+	+	CCONJ
easat-2990	196	2	dt	dt	X
easat-2990	196	3	*	*	PUNCT
easat-2990	196	4	(	(	PUNCT
easat-2990	196	5	du_dt_frac	du_dt_frac	NOUN
easat-2990	196	6	+	+	CCONJ
easat-2990	196	7	u_x_term	u_x_term	PROPN
easat-2990	196	8	+	+	CCONJ
easat-2990	196	9	source_term	source_term	NOUN
easat-2990	196	10	)	)	PUNCT
easat-2990	196	11	;	;	PUNCT
easat-2990	196	12	%	%	NOUN
easat-2990	196	13	apply	apply	VERB
easat-2990	196	14	boundary	boundary	ADJ
easat-2990	196	15	conditions	condition	NOUN
easat-2990	196	16	u(1	u(1	PROPN
easat-2990	196	17	,	,	PUNCT
easat-2990	196	18	n	n	CCONJ
easat-2990	196	19	)	)	PUNCT
easat-2990	196	20	=	=	SYM
easat-2990	196	21	0	0	NUM
easat-2990	196	22	;	;	PUNCT
easat-2990	196	23	%	%	NOUN
easat-2990	196	24	dirichlet	dirichlet	PROPN
easat-2990	196	25	bc	bc	PROPN
easat-2990	196	26	at	at	ADP
easat-2990	196	27	x	x	X
easat-2990	196	28	=	=	SYM
easat-2990	196	29	0	0	PUNCT
easat-2990	196	30	u(end	u(end	NOUN
easat-2990	196	31	,	,	PUNCT
easat-2990	196	32	n	n	CCONJ
easat-2990	196	33	)	)	PUNCT
easat-2990	196	34	=	=	SYM
easat-2990	196	35	0	0	NUM
easat-2990	196	36	;	;	PUNCT
easat-2990	196	37	%	%	NOUN
easat-2990	196	38	dirichlet	dirichlet	PROPN
easat-2990	196	39	bc	bc	PROPN
easat-2990	196	40	at	at	ADP
easat-2990	196	41	x	x	X
easat-2990	196	42	=	=	NOUN
easat-2990	196	43	lx	lx	NOUN
easat-2990	196	44	end	end	VERB
easat-2990	196	45	%	%	INTJ
easat-2990	196	46	plotting	plot	VERB
easat-2990	196	47	the	the	DET
easat-2990	196	48	solution	solution	NOUN
easat-2990	196	49	figure	figure	NOUN
easat-2990	196	50	;	;	PUNCT
easat-2990	196	51	surf(x	surf(x	PROPN
easat-2990	196	52	,	,	PUNCT
easat-2990	196	53	t	t	PROPN
easat-2990	196	54	,	,	PUNCT
easat-2990	196	55	u	u	NOUN
easat-2990	196	56	'	'	PUNCT
easat-2990	196	57	)	)	PUNCT
easat-2990	196	58	;	;	PUNCT
easat-2990	197	1	title('solution	title('solution	NOUN
easat-2990	197	2	of	of	ADP
easat-2990	197	3	fractional	fractional	ADJ
easat-2990	197	4	cattaneo	cattaneo	PROPN
easat-2990	197	5	-	-	PUNCT
easat-2990	197	6	rayleigh	rayleigh	PROPN
easat-2990	197	7	model	model	NOUN
easat-2990	197	8	using	use	VERB
easat-2990	197	9	wavelet	wavelet	NOUN
easat-2990	197	10	collocation	collocation	NOUN
easat-2990	197	11	'	'	PUNCT
easat-2990	197	12	)	)	PUNCT
easat-2990	197	13	;	;	PUNCT
easat-2990	197	14	xlabel('space	xlabel('space	PROPN
easat-2990	197	15	(	(	PUNCT
easat-2990	197	16	x	x	NOUN
easat-2990	197	17	)	)	PUNCT
easat-2990	197	18	'	'	PUNCT
easat-2990	197	19	)	)	PUNCT
easat-2990	197	20	;	;	PUNCT
easat-2990	197	21	ylabel('time	ylabel('time	NUM
easat-2990	197	22	(	(	PUNCT
easat-2990	197	23	t	t	NOUN
easat-2990	197	24	)	)	PUNCT
easat-2990	197	25	'	'	PUNCT
easat-2990	197	26	)	)	PUNCT
easat-2990	197	27	;	;	PUNCT
easat-2990	197	28	zlabel('u(x	zlabel('u(x	PROPN
easat-2990	197	29	,	,	PUNCT
easat-2990	197	30	t	t	PROPN
easat-2990	197	31	)	)	PUNCT
easat-2990	197	32	'	'	PUNCT
easat-2990	197	33	)	)	PUNCT
easat-2990	197	34	;	;	PUNCT
easat-2990	197	35	colorbar	colorbar	ADV
easat-2990	197	36	;	;	PUNCT
easat-2990	197	37	figure	figure	NOUN
easat-2990	197	38	2	2	NUM
easat-2990	197	39	.	.	PUNCT
easat-2990	197	40	solving	solve	VERB
easat-2990	197	41	fractional	fractional	ADJ
easat-2990	197	42	cattaneo	cattaneo	PROPN
easat-2990	197	43	-	-	PUNCT
easat-2990	197	44	rayleigh	rayleigh	PROPN
easat-2990	197	45	model	model	NOUN
easat-2990	197	46	using	use	VERB
easat-2990	197	47	wavelet	wavelet	NOUN
easat-2990	197	48	collocation	collocation	NOUN
easat-2990	197	49	.	.	PUNCT
easat-2990	198	1	4609	4609	NUM
easat-2990	198	2	edelweiss	edelweiss	PROPN
easat-2990	198	3	applied	apply	VERB
easat-2990	198	4	science	science	NOUN
easat-2990	198	5	and	and	CCONJ
easat-2990	198	6	technology	technology	NOUN
easat-2990	198	7	issn	issn	PROPN
easat-2990	198	8	:	:	PUNCT
easat-2990	198	9	2576	2576	NUM
easat-2990	198	10	-	-	SYM
easat-2990	198	11	8484	8484	NUM
easat-2990	198	12	vol	vol	NOUN
easat-2990	198	13	.	.	PROPN
easat-2990	198	14	8	8	NUM
easat-2990	198	15	,	,	PUNCT
easat-2990	198	16	no	no	INTJ
easat-2990	198	17	.	.	NOUN
easat-2990	199	1	6	6	NUM
easat-2990	199	2	:	:	SYM
easat-2990	199	3	4599	4599	NUM
easat-2990	199	4	-	-	SYM
easat-2990	199	5	4610	4610	NUM
easat-2990	199	6	,	,	PUNCT
easat-2990	199	7	2024	2024	NUM
easat-2990	199	8	doi	doi	NOUN
easat-2990	199	9	:	:	PUNCT
easat-2990	199	10	10.55214/25768484.v8i6.2990	10.55214/25768484.v8i6.2990	NUM
easat-2990	199	11	©	©	PROPN
easat-2990	199	12	2024	2024	NUM
easat-2990	199	13	by	by	ADP
easat-2990	199	14	the	the	DET
easat-2990	199	15	author	author	NOUN
easat-2990	199	16	;	;	PUNCT
easat-2990	199	17	licensee	licensee	PROPN
easat-2990	199	18	learning	learning	NOUN
easat-2990	199	19	gate	gate	VERB
easat-2990	199	20	the	the	DET
easat-2990	199	21	most	most	ADV
easat-2990	199	22	significant	significant	ADJ
easat-2990	199	23	finding	finding	NOUN
easat-2990	199	24	from	from	ADP
easat-2990	199	25	this	this	DET
easat-2990	199	26	visualization	visualization	NOUN
easat-2990	199	27	is	be	AUX
easat-2990	199	28	the	the	DET
easat-2990	199	29	clear	clear	ADJ
easat-2990	199	30	demonstration	demonstration	NOUN
easat-2990	199	31	of	of	ADP
easat-2990	199	32	wave	wave	NOUN
easat-2990	199	33	attenuation	attenuation	NOUN
easat-2990	199	34	or	or	CCONJ
easat-2990	199	35	decay	decay	NOUN
easat-2990	199	36	over	over	ADP
easat-2990	199	37	the	the	DET
easat-2990	199	38	spatial	spatial	ADJ
easat-2990	199	39	dimension	dimension	NOUN
easat-2990	199	40	while	while	SCONJ
easat-2990	199	41	maintaining	maintain	VERB
easat-2990	199	42	temporal	temporal	ADJ
easat-2990	199	43	periodicity	periodicity	NOUN
easat-2990	199	44	.	.	PUNCT
easat-2990	200	1	this	this	DET
easat-2990	200	2	behavior	behavior	NOUN
easat-2990	200	3	is	be	AUX
easat-2990	200	4	characteristic	characteristic	ADJ
easat-2990	200	5	of	of	ADP
easat-2990	200	6	dissipative	dissipative	ADJ
easat-2990	200	7	wave	wave	NOUN
easat-2990	200	8	systems	system	NOUN
easat-2990	200	9	,	,	PUNCT
easat-2990	200	10	where	where	SCONJ
easat-2990	200	11	energy	energy	NOUN
easat-2990	200	12	is	be	AUX
easat-2990	200	13	gradually	gradually	ADV
easat-2990	200	14	lost	lose	VERB
easat-2990	200	15	as	as	SCONJ
easat-2990	200	16	the	the	DET
easat-2990	200	17	wave	wave	NOUN
easat-2990	200	18	propagates	propagate	VERB
easat-2990	200	19	through	through	ADP
easat-2990	200	20	the	the	DET
easat-2990	200	21	medium	medium	NOUN
easat-2990	200	22	.	.	PUNCT
easat-2990	201	1	the	the	DET
easat-2990	201	2	smooth	smooth	ADJ
easat-2990	201	3	transition	transition	NOUN
easat-2990	201	4	from	from	ADP
easat-2990	201	5	high	high	ADJ
easat-2990	201	6	to	to	ADP
easat-2990	201	7	low	low	ADJ
easat-2990	201	8	amplitude	amplitude	NOUN
easat-2990	201	9	suggests	suggest	VERB
easat-2990	201	10	a	a	DET
easat-2990	201	11	well	well	ADV
easat-2990	201	12	-	-	PUNCT
easat-2990	201	13	behaved	behave	VERB
easat-2990	201	14	solution	solution	NOUN
easat-2990	201	15	to	to	ADP
easat-2990	201	16	what	what	PRON
easat-2990	201	17	is	be	AUX
easat-2990	201	18	likely	likely	ADJ
easat-2990	201	19	a	a	DET
easat-2990	201	20	partial	partial	ADJ
easat-2990	201	21	differential	differential	NOUN
easat-2990	201	22	equation	equation	NOUN
easat-2990	201	23	describing	describe	VERB
easat-2990	201	24	wave	wave	NOUN
easat-2990	201	25	propagation	propagation	NOUN
easat-2990	201	26	with	with	ADP
easat-2990	201	27	damping	damp	VERB
easat-2990	201	28	effects	effect	NOUN
easat-2990	201	29	.	.	PUNCT
easat-2990	202	1	this	this	DET
easat-2990	202	2	type	type	NOUN
easat-2990	202	3	of	of	ADP
easat-2990	202	4	behavior	behavior	NOUN
easat-2990	202	5	is	be	AUX
easat-2990	202	6	commonly	commonly	ADV
easat-2990	202	7	observed	observe	VERB
easat-2990	202	8	in	in	ADP
easat-2990	202	9	physical	physical	ADJ
easat-2990	202	10	systems	system	NOUN
easat-2990	202	11	such	such	ADJ
easat-2990	202	12	as	as	ADP
easat-2990	202	13	vibrating	vibrate	VERB
easat-2990	202	14	strings	string	NOUN
easat-2990	202	15	with	with	ADP
easat-2990	202	16	resistance	resistance	NOUN
easat-2990	202	17	,	,	PUNCT
easat-2990	202	18	electromagnetic	electromagnetic	ADJ
easat-2990	202	19	waves	wave	NOUN
easat-2990	202	20	in	in	ADP
easat-2990	202	21	lossy	lossy	ADJ
easat-2990	202	22	media	medium	NOUN
easat-2990	202	23	,	,	PUNCT
easat-2990	202	24	or	or	CCONJ
easat-2990	202	25	acoustic	acoustic	ADJ
easat-2990	202	26	waves	wave	NOUN
easat-2990	202	27	experiencing	experience	VERB
easat-2990	202	28	attenuation	attenuation	NOUN
easat-2990	202	29	.	.	PUNCT
easat-2990	203	1	6	6	X
easat-2990	203	2	.	.	X
easat-2990	203	3	conclusion	conclusion	NOUN
easat-2990	203	4	this	this	DET
easat-2990	203	5	study	study	NOUN
easat-2990	203	6	has	have	AUX
easat-2990	203	7	successfully	successfully	ADV
easat-2990	203	8	demonstrated	demonstrate	VERB
easat-2990	203	9	the	the	DET
easat-2990	203	10	effectiveness	effectiveness	NOUN
easat-2990	203	11	of	of	ADP
easat-2990	203	12	wavelet	wavelet	NOUN
easat-2990	203	13	-	-	PUNCT
easat-2990	203	14	based	base	VERB
easat-2990	203	15	collocation	collocation	NOUN
easat-2990	203	16	methods	method	NOUN
easat-2990	203	17	in	in	ADP
easat-2990	203	18	solving	solve	VERB
easat-2990	203	19	multi	multi	ADJ
easat-2990	203	20	-	-	ADJ
easat-2990	203	21	dimensional	dimensional	ADJ
easat-2990	203	22	integro	integro	ADJ
easat-2990	203	23	-	-	PUNCT
easat-2990	203	24	differential	differential	NOUN
easat-2990	203	25	systems	system	NOUN
easat-2990	203	26	.	.	PUNCT
easat-2990	204	1	our	our	PRON
easat-2990	204	2	numerical	numerical	ADJ
easat-2990	204	3	experiments	experiment	NOUN
easat-2990	204	4	,	,	PUNCT
easat-2990	204	5	particularly	particularly	ADV
easat-2990	204	6	with	with	ADP
easat-2990	204	7	the	the	DET
easat-2990	204	8	cattaneo	cattaneo	PROPN
easat-2990	204	9	-	-	PUNCT
easat-2990	204	10	rayleigh	rayleigh	PROPN
easat-2990	204	11	model	model	NOUN
easat-2990	204	12	of	of	ADP
easat-2990	204	13	thermoelasticity	thermoelasticity	NOUN
easat-2990	204	14	,	,	PUNCT
easat-2990	204	15	revealed	reveal	VERB
easat-2990	204	16	that	that	SCONJ
easat-2990	204	17	the	the	DET
easat-2990	204	18	proposed	propose	VERB
easat-2990	204	19	method	method	NOUN
easat-2990	204	20	achieves	achieve	VERB
easat-2990	204	21	both	both	PRON
easat-2990	204	22	high	high	ADJ
easat-2990	204	23	computational	computational	ADJ
easat-2990	204	24	efficiency	efficiency	NOUN
easat-2990	204	25	and	and	CCONJ
easat-2990	204	26	numerical	numerical	ADJ
easat-2990	204	27	stability	stability	NOUN
easat-2990	204	28	without	without	ADP
easat-2990	204	29	requiring	require	VERB
easat-2990	204	30	traditional	traditional	ADJ
easat-2990	204	31	discretization	discretization	NOUN
easat-2990	204	32	approaches	approach	NOUN
easat-2990	204	33	.	.	PUNCT
easat-2990	205	1	the	the	DET
easat-2990	205	2	method	method	NOUN
easat-2990	205	3	proved	prove	VERB
easat-2990	205	4	especially	especially	ADV
easat-2990	205	5	powerful	powerful	ADJ
easat-2990	205	6	in	in	ADP
easat-2990	205	7	handling	handle	VERB
easat-2990	205	8	complex	complex	ADJ
easat-2990	205	9	scenarios	scenario	NOUN
easat-2990	205	10	involving	involve	VERB
easat-2990	205	11	weakly	weakly	ADJ
easat-2990	205	12	singular	singular	PROPN
easat-2990	205	13	volterra	volterra	NOUN
easat-2990	205	14	type	type	NOUN
easat-2990	205	15	systems	system	NOUN
easat-2990	205	16	and	and	CCONJ
easat-2990	205	17	multiple	multiple	ADJ
easat-2990	205	18	time	time	NOUN
easat-2990	205	19	delays	delay	NOUN
easat-2990	205	20	,	,	PUNCT
easat-2990	205	21	while	while	SCONJ
easat-2990	205	22	maintaining	maintain	VERB
easat-2990	205	23	reliable	reliable	ADJ
easat-2990	205	24	accuracy	accuracy	NOUN
easat-2990	205	25	across	across	ADP
easat-2990	205	26	different	different	ADJ
easat-2990	205	27	applications	application	NOUN
easat-2990	205	28	.	.	PUNCT
easat-2990	206	1	through	through	ADP
easat-2990	206	2	our	our	PRON
easat-2990	206	3	analysis	analysis	NOUN
easat-2990	206	4	of	of	ADP
easat-2990	206	5	wave	wave	NOUN
easat-2990	206	6	propagation	propagation	NOUN
easat-2990	206	7	and	and	CCONJ
easat-2990	206	8	attenuation	attenuation	NOUN
easat-2990	206	9	patterns	pattern	NOUN
easat-2990	206	10	,	,	PUNCT
easat-2990	206	11	we	we	PRON
easat-2990	206	12	confirmed	confirm	VERB
easat-2990	206	13	the	the	DET
easat-2990	206	14	method	method	NOUN
easat-2990	206	15	's	's	PART
easat-2990	206	16	capability	capability	NOUN
easat-2990	206	17	to	to	PART
easat-2990	206	18	capture	capture	VERB
easat-2990	206	19	sophisticated	sophisticated	ADJ
easat-2990	206	20	physical	physical	ADJ
easat-2990	206	21	phenomena	phenomenon	NOUN
easat-2990	206	22	with	with	ADP
easat-2990	206	23	precision	precision	NOUN
easat-2990	206	24	.	.	PUNCT
easat-2990	207	1	the	the	DET
easat-2990	207	2	implementation	implementation	NOUN
easat-2990	207	3	showed	show	VERB
easat-2990	207	4	particular	particular	ADJ
easat-2990	207	5	strength	strength	NOUN
easat-2990	207	6	in	in	ADP
easat-2990	207	7	large	large	ADJ
easat-2990	207	8	-	-	PUNCT
easat-2990	207	9	scale	scale	NOUN
easat-2990	207	10	applications	application	NOUN
easat-2990	207	11	,	,	PUNCT
easat-2990	207	12	offering	offer	VERB
easat-2990	207	13	a	a	DET
easat-2990	207	14	significant	significant	ADJ
easat-2990	207	15	advantage	advantage	NOUN
easat-2990	207	16	over	over	ADP
easat-2990	207	17	conventional	conventional	ADJ
easat-2990	207	18	numerical	numerical	ADJ
easat-2990	207	19	techniques	technique	NOUN
easat-2990	207	20	.	.	PUNCT
easat-2990	208	1	these	these	PRON
easat-2990	208	2	results	result	VERB
easat-2990	208	3	not	not	PART
easat-2990	208	4	only	only	ADV
easat-2990	208	5	validate	validate	VERB
easat-2990	208	6	the	the	DET
easat-2990	208	7	practical	practical	ADJ
easat-2990	208	8	utility	utility	NOUN
easat-2990	208	9	of	of	ADP
easat-2990	208	10	our	our	PRON
easat-2990	208	11	approach	approach	NOUN
easat-2990	208	12	but	but	CCONJ
easat-2990	208	13	also	also	ADV
easat-2990	208	14	establish	establish	VERB
easat-2990	208	15	a	a	DET
easat-2990	208	16	solid	solid	ADJ
easat-2990	208	17	foundation	foundation	NOUN
easat-2990	208	18	for	for	ADP
easat-2990	208	19	future	future	ADJ
easat-2990	208	20	applications	application	NOUN
easat-2990	208	21	in	in	ADP
easat-2990	208	22	various	various	ADJ
easat-2990	208	23	fields	field	NOUN
easat-2990	208	24	of	of	ADP
easat-2990	208	25	science	science	NOUN
easat-2990	208	26	and	and	CCONJ
easat-2990	208	27	engineering	engineering	NOUN
easat-2990	208	28	,	,	PUNCT
easat-2990	208	29	including	include	VERB
easat-2990	208	30	biological	biological	ADJ
easat-2990	208	31	systems	system	NOUN
easat-2990	208	32	,	,	PUNCT
easat-2990	208	33	mechanical	mechanical	ADJ
easat-2990	208	34	signal	signal	NOUN
easat-2990	208	35	processing	processing	NOUN
easat-2990	208	36	,	,	PUNCT
easat-2990	208	37	and	and	CCONJ
easat-2990	208	38	digital	digital	ADJ
easat-2990	208	39	communications	communication	NOUN
easat-2990	208	40	.	.	PUNCT
easat-2990	209	1	copyright	copyright	NOUN
easat-2990	209	2	:	:	PUNCT
easat-2990	209	3	©	©	PROPN
easat-2990	209	4	2024	2024	NUM
easat-2990	209	5	by	by	ADP
easat-2990	209	6	the	the	DET
easat-2990	209	7	authors	author	NOUN
easat-2990	209	8	.	.	PUNCT
easat-2990	210	1	this	this	DET
easat-2990	210	2	article	article	NOUN
easat-2990	210	3	is	be	AUX
easat-2990	210	4	an	an	DET
easat-2990	210	5	open	open	ADJ
easat-2990	210	6	access	access	NOUN
easat-2990	210	7	article	article	NOUN
easat-2990	210	8	distributed	distribute	VERB
easat-2990	210	9	under	under	ADP
easat-2990	210	10	the	the	DET
easat-2990	210	11	terms	term	NOUN
easat-2990	210	12	and	and	CCONJ
easat-2990	210	13	conditions	condition	NOUN
easat-2990	210	14	of	of	ADP
easat-2990	210	15	the	the	DET
easat-2990	210	16	creative	creative	ADJ
easat-2990	210	17	commons	common	NOUN
easat-2990	210	18	attribution	attribution	NOUN
easat-2990	210	19	(	(	PUNCT
easat-2990	210	20	cc	cc	NOUN
easat-2990	210	21	by	by	ADP
easat-2990	210	22	)	)	PUNCT
easat-2990	210	23	license	license	NOUN
easat-2990	210	24	(	(	PUNCT
easat-2990	210	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-2990	210	26	)	)	PUNCT
easat-2990	210	27	.	.	PUNCT
easat-2990	211	1	references	reference	NOUN
easat-2990	211	2	[	[	X
easat-2990	211	3	1	1	X
easat-2990	211	4	]	]	PUNCT
easat-2990	211	5	o.	o.	NOUN
easat-2990	211	6	a.	a.	NOUN
easat-2990	211	7	arqub	arqub	PROPN
easat-2990	211	8	,	,	PUNCT
easat-2990	211	9	m.	m.	NOUN
easat-2990	211	10	al	al	PROPN
easat-2990	211	11	-	-	PUNCT
easat-2990	211	12	smadi	smadi	NOUN
easat-2990	211	13	,	,	PUNCT
easat-2990	211	14	and	and	CCONJ
easat-2990	211	15	n.	n.	NOUN
easat-2990	211	16	shawagfeh	shawagfeh	NOUN
easat-2990	211	17	,	,	PUNCT
easat-2990	211	18	"	"	PUNCT
easat-2990	211	19	solving	solve	VERB
easat-2990	211	20	fredholm	fredholm	NOUN
easat-2990	211	21	integro	integro	ADJ
easat-2990	211	22	–	–	PUNCT
easat-2990	211	23	differential	differential	ADJ
easat-2990	211	24	equations	equation	NOUN
easat-2990	211	25	using	use	VERB
easat-2990	211	26	reproducing	reproduce	VERB
easat-2990	211	27	kernel	kernel	PROPN
easat-2990	211	28	hilbert	hilbert	PROPN
easat-2990	211	29	space	space	NOUN
easat-2990	211	30	method	method	NOUN
easat-2990	211	31	,	,	PUNCT
easat-2990	211	32	"	"	PUNCT
easat-2990	211	33	applied	apply	VERB
easat-2990	211	34	mathematics	mathematic	NOUN
easat-2990	211	35	and	and	CCONJ
easat-2990	211	36	computation	computation	NOUN
easat-2990	211	37	,	,	PUNCT
easat-2990	211	38	vol	vol	NOUN
easat-2990	211	39	.	.	PROPN
easat-2990	211	40	219	219	NUM
easat-2990	211	41	,	,	PUNCT
easat-2990	211	42	no	no	INTJ
easat-2990	211	43	.	.	NOUN
easat-2990	211	44	17	17	NUM
easat-2990	211	45	,	,	PUNCT
easat-2990	211	46	pp	pp	ADJ
easat-2990	211	47	.	.	PUNCT
easat-2990	211	48	8938	8938	NUM
easat-2990	211	49	-	-	SYM
easat-2990	211	50	8948	8948	NUM
easat-2990	211	51	,	,	PUNCT
easat-2990	211	52	2013	2013	NUM
easat-2990	211	53	.	.	PUNCT
easat-2990	212	1	[	[	X
easat-2990	212	2	2	2	X
easat-2990	212	3	]	]	PUNCT
easat-2990	212	4	k.	k.	PROPN
easat-2990	212	5	s.	s.	PROPN
easat-2990	212	6	zadeh	zadeh	PROPN
easat-2990	212	7	,	,	PUNCT
easat-2990	212	8	"	"	PUNCT
easat-2990	212	9	an	an	DET
easat-2990	212	10	integro	integro	ADJ
easat-2990	212	11	-	-	PUNCT
easat-2990	212	12	partial	partial	ADJ
easat-2990	212	13	differential	differential	NOUN
easat-2990	212	14	equation	equation	NOUN
easat-2990	212	15	for	for	ADP
easat-2990	212	16	modeling	model	VERB
easat-2990	212	17	biofluids	biofluid	NOUN
easat-2990	212	18	flow	flow	VERB
easat-2990	212	19	in	in	ADP
easat-2990	212	20	fractured	fractured	ADJ
easat-2990	212	21	biomaterials	biomaterial	NOUN
easat-2990	212	22	,	,	PUNCT
easat-2990	212	23	"	"	PUNCT
easat-2990	212	24	journal	journal	NOUN
easat-2990	212	25	of	of	ADP
easat-2990	212	26	theoretical	theoretical	ADJ
easat-2990	212	27	biology	biology	NOUN
easat-2990	212	28	,	,	PUNCT
easat-2990	212	29	vol	vol	NOUN
easat-2990	212	30	.	.	PROPN
easat-2990	213	1	273	273	NUM
easat-2990	213	2	,	,	PUNCT
easat-2990	213	3	no	no	INTJ
easat-2990	213	4	.	.	NOUN
easat-2990	213	5	1	1	NUM
easat-2990	213	6	,	,	PUNCT
easat-2990	213	7	pp	pp	ADJ
easat-2990	213	8	.	.	PUNCT
easat-2990	214	1	72	72	NUM
easat-2990	214	2	-	-	SYM
easat-2990	214	3	79	79	NUM
easat-2990	214	4	,	,	PUNCT
easat-2990	214	5	2011	2011	NUM
easat-2990	214	6	.	.	PUNCT
easat-2990	215	1	[	[	X
easat-2990	215	2	3	3	X
easat-2990	215	3	]	]	PUNCT
easat-2990	215	4	p.	p.	PROPN
easat-2990	215	5	kumar	kumar	PROPN
easat-2990	215	6	and	and	CCONJ
easat-2990	215	7	e.	e.	PROPN
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easat-2990	215	9	,	,	PUNCT
easat-2990	215	10	"	"	PUNCT
easat-2990	215	11	wavelet	wavelet	NOUN
easat-2990	215	12	analysis	analysis	NOUN
easat-2990	215	13	for	for	ADP
easat-2990	215	14	geophysical	geophysical	ADJ
easat-2990	215	15	applications	application	NOUN
easat-2990	215	16	,	,	PUNCT
easat-2990	215	17	"	"	PUNCT
easat-2990	215	18	reviews	review	NOUN
easat-2990	215	19	of	of	ADP
easat-2990	215	20	geophysics	geophysic	NOUN
easat-2990	215	21	,	,	PUNCT
easat-2990	215	22	vol	vol	NOUN
easat-2990	215	23	.	.	PROPN
easat-2990	215	24	35	35	NUM
easat-2990	215	25	,	,	PUNCT
easat-2990	215	26	no	no	INTJ
easat-2990	215	27	.	.	NOUN
easat-2990	215	28	4	4	NUM
easat-2990	215	29	,	,	PUNCT
easat-2990	215	30	pp	pp	ADJ
easat-2990	215	31	.	.	PUNCT
easat-2990	216	1	385	385	NUM
easat-2990	216	2	-	-	SYM
easat-2990	216	3	412	412	NUM
easat-2990	216	4	,	,	PUNCT
easat-2990	216	5	1997	1997	NUM
easat-2990	216	6	.	.	PUNCT
easat-2990	217	1	[	[	X
easat-2990	217	2	4	4	NUM
easat-2990	217	3	]	]	PUNCT
easat-2990	217	4	a.	a.	NOUN
easat-2990	217	5	ibrahim	ibrahim	PROPN
easat-2990	217	6	,	,	PUNCT
easat-2990	217	7	m.	m.	NOUN
easat-2990	217	8	m.	m.	PROPN
easat-2990	217	9	noor	noor	PROPN
easat-2990	217	10	,	,	PUNCT
easat-2990	217	11	m.	m.	PROPN
easat-2990	217	12	ibrahim	ibrahim	PROPN
easat-2990	217	13	,	,	PUNCT
easat-2990	217	14	j.	j.	PROPN
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easat-2990	217	17	and	and	CCONJ
easat-2990	217	18	a.	a.	NOUN
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easat-2990	217	20	,	,	PUNCT
easat-2990	217	21	"	"	PUNCT
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easat-2990	217	23	shear	shear	NOUN
easat-2990	217	24	modulus	modulus	ADJ
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easat-2990	217	28	continuous	continuous	ADJ
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easat-2990	217	30	transform	transform	NOUN
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easat-2990	217	32	bender	bender	NOUN
easat-2990	217	33	element	element	NOUN
easat-2990	217	34	test	test	NOUN
easat-2990	217	35	,	,	PUNCT
easat-2990	217	36	"	"	PUNCT
easat-2990	217	37	in	in	ADP
easat-2990	217	38	journal	journal	NOUN
easat-2990	217	39	of	of	ADP
easat-2990	217	40	physics	physics	PROPN
easat-2990	217	41	:	:	PUNCT
easat-2990	217	42	conference	conference	NOUN
easat-2990	217	43	series	series	NOUN
easat-2990	217	44	,	,	PUNCT
easat-2990	217	45	2019	2019	NUM
easat-2990	217	46	,	,	PUNCT
easat-2990	217	47	vol	vol	NOUN
easat-2990	217	48	.	.	PROPN
easat-2990	217	49	1349	1349	NUM
easat-2990	217	50	,	,	PUNCT
easat-2990	217	51	no	no	INTJ
easat-2990	217	52	.	.	NOUN
easat-2990	217	53	1	1	NUM
easat-2990	217	54	:	:	PUNCT
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easat-2990	217	57	,	,	PUNCT
easat-2990	217	58	p.	p.	NOUN
easat-2990	217	59	012019	012019	NUM
easat-2990	217	60	.	.	PUNCT
easat-2990	218	1	[	[	X
easat-2990	218	2	5	5	X
easat-2990	218	3	]	]	PUNCT
easat-2990	218	4	j.	j.	PROPN
easat-2990	218	5	bonal	bonal	PROPN
easat-2990	218	6	,	,	PUNCT
easat-2990	218	7	s.	s.	PROPN
easat-2990	218	8	donohue	donohue	PROPN
easat-2990	218	9	,	,	PUNCT
easat-2990	218	10	and	and	CCONJ
easat-2990	218	11	c.	c.	PROPN
easat-2990	218	12	mcnally	mcnally	PROPN
easat-2990	218	13	,	,	PUNCT
easat-2990	218	14	"	"	PUNCT
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easat-2990	218	16	analysis	analysis	NOUN
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easat-2990	218	18	bender	bender	NOUN
easat-2990	218	19	element	element	NOUN
easat-2990	218	20	signals	signal	NOUN
easat-2990	218	21	,	,	PUNCT
easat-2990	218	22	"	"	PUNCT
easat-2990	218	23	géotechnique	géotechnique	ADJ
easat-2990	218	24	,	,	PUNCT
easat-2990	218	25	vol	vol	NOUN
easat-2990	218	26	.	.	PROPN
easat-2990	218	27	62	62	NUM
easat-2990	218	28	,	,	PUNCT
easat-2990	218	29	no	no	INTJ
easat-2990	218	30	.	.	NOUN
easat-2990	218	31	3	3	NUM
easat-2990	218	32	,	,	PUNCT
easat-2990	218	33	pp	pp	ADJ
easat-2990	218	34	.	.	PUNCT
easat-2990	219	1	243	243	NUM
easat-2990	219	2	-	-	SYM
easat-2990	219	3	252	252	NUM
easat-2990	219	4	,	,	PUNCT
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easat-2990	219	6	.	.	PUNCT
easat-2990	220	1	[	[	X
easat-2990	220	2	6	6	NUM
easat-2990	220	3	]	]	PUNCT
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easat-2990	220	6	and	and	CCONJ
easat-2990	220	7	k.	k.	PROPN
easat-2990	220	8	kannan	kannan	PROPN
easat-2990	220	9	,	,	PUNCT
easat-2990	220	10	"	"	PUNCT
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easat-2990	220	12	of	of	ADP
easat-2990	220	13	wavelet	wavelet	NOUN
easat-2990	220	14	methods	method	NOUN
easat-2990	220	15	for	for	ADP
easat-2990	220	16	the	the	DET
easat-2990	220	17	solution	solution	NOUN
easat-2990	220	18	of	of	ADP
easat-2990	220	19	reaction	reaction	NOUN
easat-2990	220	20	–	–	PUNCT
easat-2990	220	21	diffusion	diffusion	NOUN
easat-2990	220	22	problems	problem	NOUN
easat-2990	220	23	in	in	ADP
easat-2990	220	24	science	science	NOUN
easat-2990	220	25	and	and	CCONJ
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easat-2990	220	27	,	,	PUNCT
easat-2990	220	28	"	"	PUNCT
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easat-2990	220	30	mathematical	mathematical	ADJ
easat-2990	220	31	modelling	modelling	NOUN
easat-2990	220	32	,	,	PUNCT
easat-2990	220	33	vol	vol	NOUN
easat-2990	220	34	.	.	PROPN
easat-2990	221	1	38	38	NUM
easat-2990	221	2	,	,	PUNCT
easat-2990	221	3	no	no	INTJ
easat-2990	221	4	.	.	NOUN
easat-2990	221	5	3	3	NUM
easat-2990	221	6	,	,	PUNCT
easat-2990	221	7	pp	pp	ADJ
easat-2990	221	8	.	.	PUNCT
easat-2990	222	1	799	799	NUM
easat-2990	222	2	-	-	SYM
easat-2990	222	3	813	813	NUM
easat-2990	222	4	,	,	PUNCT
easat-2990	222	5	2014	2014	NUM
easat-2990	222	6	.	.	PUNCT
easat-2990	223	1	[	[	X
easat-2990	223	2	7	7	X
easat-2990	223	3	]	]	X
easat-2990	223	4	m.	m.	NOUN
easat-2990	223	5	ahsan	ahsan	PROPN
easat-2990	223	6	,	,	PUNCT
easat-2990	223	7	i.	i.	PROPN
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easat-2990	223	9	,	,	PUNCT
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easat-2990	223	11	ahmad	ahmad	PROPN
easat-2990	223	12	,	,	PUNCT
easat-2990	223	13	and	and	CCONJ
easat-2990	223	14	i.	i.	PROPN
easat-2990	223	15	hussian	hussian	PROPN
easat-2990	223	16	,	,	PUNCT
easat-2990	223	17	"	"	PUNCT
easat-2990	223	18	a	a	DET
easat-2990	223	19	numerical	numerical	PROPN
easat-2990	223	20	haar	haar	PROPN
easat-2990	223	21	wavelet	wavelet	NOUN
easat-2990	223	22	-	-	PUNCT
easat-2990	223	23	finite	finite	PROPN
easat-2990	223	24	difference	difference	NOUN
easat-2990	223	25	hybrid	hybrid	NOUN
easat-2990	223	26	method	method	NOUN
easat-2990	223	27	for	for	ADP
easat-2990	223	28	linear	linear	ADJ
easat-2990	223	29	and	and	CCONJ
easat-2990	223	30	non	non	ADJ
easat-2990	223	31	-	-	ADJ
easat-2990	223	32	linear	linear	ADJ
easat-2990	223	33	schrödinger	schrödinger	ADJ
easat-2990	223	34	equation	equation	NOUN
easat-2990	223	35	,	,	PUNCT
easat-2990	223	36	"	"	PUNCT
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easat-2990	223	39	computers	computer	NOUN
easat-2990	223	40	in	in	ADP
easat-2990	223	41	simulation	simulation	NOUN
easat-2990	223	42	,	,	PUNCT
easat-2990	223	43	vol	vol	NOUN
easat-2990	223	44	.	.	PROPN
easat-2990	223	45	165	165	NUM
easat-2990	223	46	,	,	PUNCT
easat-2990	223	47	pp	pp	ADJ
easat-2990	223	48	.	.	PUNCT
easat-2990	223	49	13	13	NUM
easat-2990	223	50	-	-	SYM
easat-2990	223	51	25	25	NUM
easat-2990	223	52	,	,	PUNCT
easat-2990	223	53	2019	2019	NUM
easat-2990	223	54	.	.	PUNCT
easat-2990	224	1	[	[	X
easat-2990	224	2	8	8	NUM
easat-2990	224	3	]	]	PUNCT
easat-2990	224	4	a.	a.	PROPN
easat-2990	224	5	k.	k.	PROPN
easat-2990	224	6	nasab	nasab	PROPN
easat-2990	224	7	,	,	PUNCT
easat-2990	224	8	a.	a.	PROPN
easat-2990	224	9	kılıçman	kılıçman	PROPN
easat-2990	224	10	,	,	PUNCT
easat-2990	224	11	e.	e.	PROPN
easat-2990	224	12	babolian	babolian	PROPN
easat-2990	224	13	,	,	PUNCT
easat-2990	224	14	and	and	CCONJ
easat-2990	224	15	z.	z.	PROPN
easat-2990	224	16	p.	p.	PROPN
easat-2990	224	17	atabakan	atabakan	PROPN
easat-2990	224	18	,	,	PUNCT
easat-2990	224	19	"	"	PUNCT
easat-2990	224	20	wavelet	wavelet	NOUN
easat-2990	224	21	analysis	analysis	NOUN
easat-2990	224	22	method	method	NOUN
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easat-2990	224	24	solving	solve	VERB
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easat-2990	224	26	and	and	CCONJ
easat-2990	224	27	nonlinear	nonlinear	ADJ
easat-2990	224	28	singular	singular	ADJ
easat-2990	224	29	boundary	boundary	ADJ
easat-2990	224	30	value	value	NOUN
easat-2990	224	31	problems	problem	NOUN
easat-2990	224	32	,	,	PUNCT
easat-2990	224	33	"	"	PUNCT
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easat-2990	224	35	mathematical	mathematical	ADJ
easat-2990	224	36	modelling	modelling	NOUN
easat-2990	224	37	,	,	PUNCT
easat-2990	224	38	vol	vol	NOUN
easat-2990	224	39	.	.	PROPN
easat-2990	225	1	37	37	NUM
easat-2990	225	2	,	,	PUNCT
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easat-2990	225	4	.	.	NOUN
easat-2990	225	5	8	8	NUM
easat-2990	225	6	,	,	PUNCT
easat-2990	225	7	pp	pp	ADJ
easat-2990	225	8	.	.	PUNCT
easat-2990	226	1	5876	5876	NUM
easat-2990	226	2	-	-	SYM
easat-2990	226	3	5886	5886	NUM
easat-2990	226	4	,	,	PUNCT
easat-2990	226	5	2013	2013	NUM
easat-2990	226	6	.	.	PUNCT
easat-2990	227	1	[	[	X
easat-2990	227	2	9	9	NUM
easat-2990	227	3	]	]	PUNCT
easat-2990	227	4	m.	m.	PROPN
easat-2990	227	5	bhatia	bhatia	PROPN
easat-2990	227	6	,	,	PUNCT
easat-2990	227	7	w.	w.	PROPN
easat-2990	227	8	c.	c.	PROPN
easat-2990	227	9	karl	karl	PROPN
easat-2990	227	10	,	,	PUNCT
easat-2990	227	11	and	and	CCONJ
easat-2990	227	12	a.	a.	PROPN
easat-2990	227	13	s.	s.	PROPN
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easat-2990	227	17	a	a	DET
easat-2990	227	18	wavelet	wavelet	NOUN
easat-2990	227	19	-	-	PUNCT
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easat-2990	227	24	tomographic	tomographic	ADJ
easat-2990	227	25	reconstruction	reconstruction	NOUN
easat-2990	227	26	,	,	PUNCT
easat-2990	227	27	"	"	PUNCT
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easat-2990	227	29	transactions	transaction	NOUN
easat-2990	227	30	on	on	ADP
easat-2990	227	31	medical	medical	ADJ
easat-2990	227	32	imaging	imaging	NOUN
easat-2990	227	33	,	,	PUNCT
easat-2990	227	34	vol	vol	NOUN
easat-2990	227	35	.	.	PROPN
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easat-2990	227	37	,	,	PUNCT
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easat-2990	227	39	.	.	NOUN
easat-2990	227	40	1	1	NUM
easat-2990	227	41	,	,	PUNCT
easat-2990	227	42	pp	pp	ADJ
easat-2990	227	43	.	.	PUNCT
easat-2990	228	1	92	92	NUM
easat-2990	228	2	-	-	SYM
easat-2990	228	3	101	101	NUM
easat-2990	228	4	,	,	PUNCT
easat-2990	228	5	1996	1996	NUM
easat-2990	228	6	.	.	PUNCT
easat-2990	229	1	[	[	X
easat-2990	229	2	10	10	NUM
easat-2990	229	3	]	]	PUNCT
easat-2990	229	4	m.	m.	PROPN
easat-2990	229	5	r.	r.	PROPN
easat-2990	229	6	banham	banham	PROPN
easat-2990	229	7	and	and	CCONJ
easat-2990	229	8	a.	a.	PROPN
easat-2990	229	9	k.	k.	PROPN
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easat-2990	229	12	"	"	PUNCT
easat-2990	229	13	spatially	spatially	ADV
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easat-2990	229	15	wavelet	wavelet	NOUN
easat-2990	229	16	-	-	PUNCT
easat-2990	229	17	based	base	VERB
easat-2990	229	18	multiscale	multiscale	ADJ
easat-2990	229	19	image	image	NOUN
easat-2990	229	20	restoration	restoration	NOUN
easat-2990	229	21	,	,	PUNCT
easat-2990	229	22	"	"	PUNCT
easat-2990	229	23	ieee	ieee	NOUN
easat-2990	229	24	transactions	transaction	NOUN
easat-2990	229	25	on	on	ADP
easat-2990	229	26	image	image	NOUN
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easat-2990	229	28	,	,	PUNCT
easat-2990	229	29	vol	vol	NOUN
easat-2990	229	30	.	.	PROPN
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easat-2990	229	32	,	,	PUNCT
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easat-2990	229	34	.	.	NOUN
easat-2990	229	35	4	4	NUM
easat-2990	229	36	,	,	PUNCT
easat-2990	229	37	pp	pp	ADJ
easat-2990	229	38	.	.	PUNCT
easat-2990	230	1	619	619	NUM
easat-2990	230	2	-	-	SYM
easat-2990	230	3	634	634	NUM
easat-2990	230	4	,	,	PUNCT
easat-2990	230	5	1996	1996	NUM
easat-2990	230	6	.	.	PUNCT
easat-2990	231	1	[	[	X
easat-2990	231	2	11	11	NUM
easat-2990	231	3	]	]	PUNCT
easat-2990	231	4	w.	w.	PROPN
easat-2990	231	5	dahmen	dahmen	PROPN
easat-2990	231	6	,	,	PUNCT
easat-2990	231	7	"	"	PUNCT
easat-2990	231	8	wavelet	wavelet	NOUN
easat-2990	231	9	and	and	CCONJ
easat-2990	231	10	multiscale	multiscale	ADJ
easat-2990	231	11	methods	method	NOUN
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easat-2990	231	13	operator	operator	NOUN
easat-2990	231	14	equations	equation	NOUN
easat-2990	231	15	,	,	PUNCT
easat-2990	231	16	"	"	PUNCT
easat-2990	231	17	acta	acta	PROPN
easat-2990	231	18	numerica	numerica	PROPN
easat-2990	231	19	,	,	PUNCT
easat-2990	231	20	vol	vol	NOUN
easat-2990	231	21	.	.	PROPN
easat-2990	231	22	6	6	NUM
easat-2990	231	23	,	,	PUNCT
easat-2990	231	24	pp	pp	ADJ
easat-2990	231	25	.	.	PUNCT
easat-2990	232	1	55	55	NUM
easat-2990	232	2	-	-	SYM
easat-2990	232	3	228	228	NUM
easat-2990	232	4	,	,	PUNCT
easat-2990	232	5	1997	1997	NUM
easat-2990	232	6	.	.	PUNCT
easat-2990	233	1	[	[	X
easat-2990	233	2	12	12	NUM
easat-2990	233	3	]	]	X
easat-2990	233	4	i.	i.	PROPN
easat-2990	233	5	y.	y.	PROPN
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easat-2990	233	7	and	and	CCONJ
easat-2990	233	8	s.	s.	PROPN
easat-2990	233	9	b.	b.	PROPN
easat-2990	233	10	stechkin	stechkin	PROPN
easat-2990	233	11	,	,	PUNCT
easat-2990	233	12	"	"	PUNCT
easat-2990	233	13	basic	basic	ADJ
easat-2990	233	14	wavelet	wavelet	NOUN
easat-2990	233	15	theory	theory	NOUN
easat-2990	233	16	,	,	PUNCT
easat-2990	233	17	"	"	PUNCT
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easat-2990	233	21	,	,	PUNCT
easat-2990	233	22	vol	vol	NOUN
easat-2990	233	23	.	.	PROPN
easat-2990	234	1	53	53	NUM
easat-2990	234	2	,	,	PUNCT
easat-2990	234	3	no	no	INTJ
easat-2990	234	4	.	.	NOUN
easat-2990	234	5	6	6	NUM
easat-2990	234	6	,	,	PUNCT
easat-2990	234	7	p.	p.	NOUN
easat-2990	234	8	1159	1159	NUM
easat-2990	234	9	,	,	PUNCT
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easat-2990	234	11	.	.	PUNCT
easat-2990	235	1	[	[	X
easat-2990	235	2	13	13	NUM
easat-2990	235	3	]	]	PUNCT
easat-2990	235	4	a.	a.	NOUN
easat-2990	235	5	bultheel	bultheel	PROPN
easat-2990	235	6	and	and	CCONJ
easat-2990	235	7	d.	d.	PROPN
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easat-2990	235	9	,	,	PUNCT
easat-2990	235	10	"	"	PUNCT
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easat-2990	235	14	in	in	ADP
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easat-2990	235	17	image	image	NOUN
easat-2990	235	18	processing	processing	NOUN
easat-2990	235	19	,	,	PUNCT
easat-2990	235	20	"	"	PUNCT
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easat-2990	235	28	,	,	PUNCT
easat-2990	235	29	2003	2003	NUM
easat-2990	235	30	.	.	PUNCT
easat-2990	236	1	[	[	X
easat-2990	236	2	14	14	NUM
easat-2990	236	3	]	]	PUNCT
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easat-2990	236	5	.	.	PUNCT
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easat-2990	237	11	,	,	PUNCT
easat-2990	237	12	"	"	PUNCT
easat-2990	237	13	applied	apply	VERB
easat-2990	237	14	and	and	CCONJ
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easat-2990	237	18	,	,	PUNCT
easat-2990	237	19	vol	vol	NOUN
easat-2990	237	20	.	.	PROPN
easat-2990	237	21	20	20	NUM
easat-2990	237	22	,	,	PUNCT
easat-2990	237	23	no	no	INTJ
easat-2990	237	24	.	.	NOUN
easat-2990	237	25	3	3	NUM
easat-2990	237	26	,	,	PUNCT
easat-2990	237	27	pp	pp	ADJ
easat-2990	237	28	.	.	PUNCT
easat-2990	238	1	313	313	NUM
easat-2990	238	2	-	-	SYM
easat-2990	238	3	325	325	NUM
easat-2990	238	4	,	,	PUNCT
easat-2990	238	5	2006	2006	NUM
easat-2990	238	6	.	.	PUNCT
easat-2990	239	1	[	[	X
easat-2990	239	2	15	15	NUM
easat-2990	239	3	]	]	X
easat-2990	239	4	a.	a.	NOUN
easat-2990	239	5	silik	silik	PROPN
easat-2990	239	6	,	,	PUNCT
easat-2990	239	7	m.	m.	PROPN
easat-2990	239	8	noori	noori	PROPN
easat-2990	239	9	,	,	PUNCT
easat-2990	239	10	w.	w.	PROPN
easat-2990	239	11	a.	a.	PROPN
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easat-2990	239	13	,	,	PUNCT
easat-2990	239	14	r.	r.	PROPN
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easat-2990	239	17	and	and	CCONJ
easat-2990	239	18	z.	z.	PROPN
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easat-2990	239	20	,	,	PUNCT
easat-2990	239	21	"	"	PUNCT
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easat-2990	239	37	,	,	PUNCT
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easat-2990	239	45	vol	vol	NOUN
easat-2990	239	46	.	.	PROPN
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easat-2990	239	48	,	,	PUNCT
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easat-2990	239	52	,	,	PUNCT
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easat-2990	239	55	,	,	PUNCT
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easat-2990	240	11	-	-	SYM
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easat-2990	240	18	.	.	NOUN
easat-2990	241	1	6	6	NUM
easat-2990	241	2	:	:	SYM
easat-2990	241	3	4599	4599	NUM
easat-2990	241	4	-	-	SYM
easat-2990	241	5	4610	4610	NUM
easat-2990	241	6	,	,	PUNCT
easat-2990	241	7	2024	2024	NUM
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easat-2990	241	9	:	:	PUNCT
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easat-2990	241	12	2024	2024	NUM
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easat-2990	242	2	16	16	NUM
easat-2990	242	3	]	]	PUNCT
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easat-2990	242	8	"	"	PUNCT
easat-2990	242	9	multiresolution	multiresolution	NOUN
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easat-2990	242	17	²	²	NUM
easat-2990	242	18	(	(	PUNCT
easat-2990	242	19	?	?	PUNCT
easat-2990	242	20	)	)	PUNCT
easat-2990	242	21	,	,	PUNCT
easat-2990	242	22	"	"	PUNCT
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easat-2990	242	31	.	.	PROPN
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easat-2990	242	33	,	,	PUNCT
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easat-2990	242	35	.	.	NOUN
easat-2990	242	36	1	1	NUM
easat-2990	242	37	,	,	PUNCT
easat-2990	242	38	pp	pp	ADJ
easat-2990	242	39	.	.	PUNCT
easat-2990	243	1	69	69	NUM
easat-2990	243	2	-	-	SYM
easat-2990	243	3	87	87	NUM
easat-2990	243	4	,	,	PUNCT
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easat-2990	243	6	.	.	PUNCT
easat-2990	244	1	[	[	X
easat-2990	244	2	17	17	NUM
easat-2990	244	3	]	]	PUNCT
easat-2990	244	4	a.	a.	NOUN
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easat-2990	244	6	,	,	PUNCT
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easat-2990	244	9	,	,	PUNCT
easat-2990	244	10	and	and	CCONJ
easat-2990	244	11	j.	j.	PROPN
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easat-2990	244	14	,	,	PUNCT
easat-2990	244	15	"	"	PUNCT
easat-2990	244	16	biorthogonal	biorthogonal	ADJ
easat-2990	244	17	bases	basis	NOUN
easat-2990	244	18	of	of	ADP
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easat-2990	244	22	,	,	PUNCT
easat-2990	244	23	"	"	PUNCT
easat-2990	244	24	communications	communication	NOUN
easat-2990	244	25	on	on	ADP
easat-2990	244	26	pure	pure	ADJ
easat-2990	244	27	and	and	CCONJ
easat-2990	244	28	applied	applied	ADJ
easat-2990	244	29	mathematics	mathematic	NOUN
easat-2990	244	30	,	,	PUNCT
easat-2990	244	31	vol	vol	NOUN
easat-2990	244	32	.	.	PROPN
easat-2990	244	33	45	45	NUM
easat-2990	244	34	,	,	PUNCT
easat-2990	244	35	no	no	INTJ
easat-2990	244	36	.	.	NOUN
easat-2990	244	37	5	5	NUM
easat-2990	244	38	,	,	PUNCT
easat-2990	244	39	pp	pp	ADJ
easat-2990	244	40	.	.	PUNCT
easat-2990	244	41	485	485	NUM
easat-2990	244	42	-	-	SYM
easat-2990	244	43	560	560	NUM
easat-2990	244	44	,	,	PUNCT
easat-2990	244	45	1992	1992	NUM
easat-2990	244	46	.	.	PUNCT
easat-2990	245	1	[	[	X
easat-2990	245	2	18	18	NUM
easat-2990	245	3	]	]	PUNCT
easat-2990	245	4	b.	b.	PROPN
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easat-2990	245	7	w.	w.	PROPN
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easat-2990	245	9	,	,	PUNCT
easat-2990	245	10	"	"	PUNCT
easat-2990	245	11	an	an	DET
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easat-2990	245	14	wavelet	wavelet	NOUN
easat-2990	245	15	based	base	VERB
easat-2990	245	16	multiresolution	multiresolution	NOUN
easat-2990	245	17	analyses	analyse	VERB
easat-2990	245	18	,	,	PUNCT
easat-2990	245	19	"	"	PUNCT
easat-2990	245	20	siam	siam	PROPN
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easat-2990	245	22	,	,	PUNCT
easat-2990	245	23	vol	vol	NOUN
easat-2990	245	24	.	.	PROPN
easat-2990	246	1	36	36	NUM
easat-2990	246	2	,	,	PUNCT
easat-2990	246	3	no	no	INTJ
easat-2990	246	4	.	.	NOUN
easat-2990	246	5	3	3	NUM
easat-2990	246	6	,	,	PUNCT
easat-2990	246	7	pp	pp	ADJ
easat-2990	246	8	.	.	PUNCT
easat-2990	247	1	377	377	NUM
easat-2990	247	2	-	-	SYM
easat-2990	247	3	412	412	NUM
easat-2990	247	4	,	,	PUNCT
easat-2990	247	5	1994	1994	NUM
easat-2990	247	6	.	.	PUNCT
easat-2990	248	1	[	[	X
easat-2990	248	2	19	19	NUM
easat-2990	248	3	]	]	X
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easat-2990	248	7	n.	n.	PROPN
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easat-2990	248	10	,	,	PUNCT
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easat-2990	248	12	a	a	DET
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easat-2990	248	22	transform	transform	NOUN
easat-2990	248	23	,	,	PUNCT
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easat-2990	248	26	,	,	PUNCT
easat-2990	248	27	vol	vol	NOUN
easat-2990	248	28	.	.	PUNCT
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easat-2990	248	30	,	,	PUNCT
easat-2990	248	31	2017	2017	NUM
easat-2990	248	32	.	.	PUNCT
easat-2990	249	1	[	[	X
easat-2990	249	2	20	20	NUM
easat-2990	249	3	]	]	PUNCT
easat-2990	249	4	t.	t.	PROPN
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easat-2990	249	7	t.	t.	PROPN
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easat-2990	249	9	,	,	PUNCT
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easat-2990	249	12	,	,	PUNCT
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easat-2990	249	15	-	-	PUNCT
easat-2990	249	16	benitez	benitez	PROPN
easat-2990	249	17	,	,	PUNCT
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easat-2990	249	21	and	and	CCONJ
easat-2990	249	22	l.	l.	PROPN
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easat-2990	249	25	"	"	PUNCT
easat-2990	249	26	a	a	DET
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easat-2990	249	31	and	and	CCONJ
easat-2990	249	32	its	its	PRON
easat-2990	249	33	applications	application	NOUN
easat-2990	249	34	:	:	PUNCT
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easat-2990	249	42	,	,	PUNCT
easat-2990	249	43	vol	vol	NOUN
easat-2990	249	44	.	.	PROPN
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easat-2990	249	46	,	,	PUNCT
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easat-2990	249	50	-	-	SYM
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easat-2990	249	52	,	,	PUNCT
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easat-2990	249	54	.	.	PUNCT
easat-2990	250	1	[	[	X
easat-2990	250	2	21	21	NUM
easat-2990	250	3	]	]	X
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easat-2990	250	5	k.	k.	PROPN
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easat-2990	250	7	,	,	PUNCT
easat-2990	250	8	an	an	DET
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easat-2990	250	10	to	to	ADP
easat-2990	250	11	wavelets	wavelet	NOUN
easat-2990	250	12	.	.	PUNCT
easat-2990	251	1	elsevier	elsevier	NOUN
easat-2990	251	2	,	,	PUNCT
easat-2990	251	3	2016	2016	NUM
easat-2990	251	4	.	.	PUNCT
easat-2990	252	1	[	[	X
easat-2990	252	2	22	22	NUM
easat-2990	252	3	]	]	PUNCT
easat-2990	252	4	w.	w.	PROPN
easat-2990	252	5	dahmen	dahmen	PROPN
easat-2990	252	6	,	,	PUNCT
easat-2990	252	7	"	"	PUNCT
easat-2990	252	8	wavelet	wavelet	NOUN
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easat-2990	252	11	pdes	pde	NOUN
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easat-2990	252	17	"	"	PUNCT
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easat-2990	252	24	,	,	PUNCT
easat-2990	252	25	vol	vol	NOUN
easat-2990	252	26	.	.	PROPN
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easat-2990	252	28	,	,	PUNCT
easat-2990	252	29	no	no	INTJ
easat-2990	252	30	.	.	NOUN
easat-2990	252	31	1	1	NUM
easat-2990	252	32	,	,	PUNCT
easat-2990	252	33	pp	pp	ADJ
easat-2990	252	34	.	.	PUNCT
easat-2990	253	1	133	133	NUM
easat-2990	253	2	-	-	SYM
easat-2990	253	3	185	185	NUM
easat-2990	253	4	,	,	PUNCT
easat-2990	253	5	2001/03/01/	2001/03/01/	NUM
easat-2990	253	6	2001	2001	NUM
easat-2990	253	7	,	,	PUNCT
easat-2990	253	8	doi	doi	PROPN
easat-2990	253	9	:	:	PUNCT
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easat-2990	253	11	.	.	PUNCT
easat-2990	254	1	[	[	X
easat-2990	254	2	23	23	NUM
easat-2990	254	3	]	]	PUNCT
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easat-2990	254	7	,	,	PUNCT
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easat-2990	254	9	s.	s.	PROPN
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easat-2990	254	11	,	,	PUNCT
easat-2990	254	12	s.	s.	PROPN
easat-2990	254	13	p.	p.	PROPN
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easat-2990	254	17	m.	m.	PROPN
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easat-2990	254	21	"	"	PUNCT
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easat-2990	254	23	analysis	analysis	NOUN
easat-2990	254	24	of	of	ADP
easat-2990	254	25	a	a	DET
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easat-2990	254	28	for	for	ADP
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easat-2990	254	32	,	,	PUNCT
easat-2990	254	33	"	"	PUNCT
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easat-2990	254	35	numerical	numerical	ADJ
easat-2990	254	36	mathematics	mathematic	NOUN
easat-2990	254	37	,	,	PUNCT
easat-2990	254	38	vol	vol	NOUN
easat-2990	254	39	.	.	PROPN
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easat-2990	255	2	,	,	PUNCT
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easat-2990	255	4	.	.	PUNCT
easat-2990	256	1	31	31	NUM
easat-2990	256	2	-	-	SYM
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easat-2990	256	4	,	,	PUNCT
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easat-2990	256	6	.	.	PUNCT
easat-2990	257	1	[	[	X
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easat-2990	257	10	"	"	PUNCT
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easat-2990	257	13	for	for	ADP
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easat-2990	257	29	1	1	NUM
easat-2990	257	30	]	]	PUNCT
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easat-2990	257	45	,	,	PUNCT
easat-2990	257	46	pp	pp	ADJ
easat-2990	257	47	.	.	PUNCT
easat-2990	258	1	1	1	NUM
easat-2990	258	2	-	-	SYM
easat-2990	258	3	11	11	NUM
easat-2990	258	4	,	,	PUNCT
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easat-2990	258	6	.	.	PUNCT
easat-2990	259	1	[	[	X
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easat-2990	259	39	pp	pp	ADJ
easat-2990	259	40	.	.	PUNCT
easat-2990	260	1	7416	7416	NUM
easat-2990	260	2	-	-	SYM
easat-2990	260	3	7423	7423	NUM
easat-2990	260	4	,	,	PUNCT
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easat-2990	261	1	[	[	X
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easat-2990	261	7	x.	x.	PROPN
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easat-2990	262	21	for	for	ADP
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easat-2990	263	1	47	47	NUM
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easat-2990	263	6	,	,	PUNCT
easat-2990	263	7	pp	pp	ADJ
easat-2990	263	8	.	.	PUNCT
easat-2990	263	9	1083	1083	NUM
easat-2990	263	10	-	-	SYM
easat-2990	263	11	1121	1121	NUM
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easat-2990	263	14	.	.	PUNCT
easat-2990	264	1	[	[	X
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easat-2990	264	18	wavelet	wavelet	NOUN
easat-2990	264	19	collocation	collocation	NOUN
easat-2990	264	20	method	method	NOUN
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easat-2990	265	3	no	no	INTJ
easat-2990	265	4	.	.	NOUN
easat-2990	265	5	1	1	NUM
easat-2990	265	6	,	,	PUNCT
easat-2990	265	7	pp	pp	ADJ
easat-2990	265	8	.	.	PUNCT
easat-2990	266	1	33	33	NUM
easat-2990	266	2	-	-	SYM
easat-2990	266	3	47	47	NUM
easat-2990	266	4	,	,	PUNCT
easat-2990	266	5	1995	1995	NUM
easat-2990	266	6	.	.	PUNCT
easat-2990	267	1	[	[	X
easat-2990	267	2	29	29	NUM
easat-2990	267	3	]	]	PUNCT
easat-2990	267	4	a.	a.	NOUN
easat-2990	267	5	k.	k.	PROPN
easat-2990	267	6	singh	singh	PROPN
easat-2990	267	7	and	and	CCONJ
easat-2990	267	8	m.	m.	PROPN
easat-2990	267	9	mehra	mehra	PROPN
easat-2990	267	10	,	,	PUNCT
easat-2990	267	11	"	"	PUNCT
easat-2990	267	12	wavelet	wavelet	NOUN
easat-2990	267	13	collocation	collocation	NOUN
easat-2990	267	14	method	method	NOUN
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easat-2990	267	16	on	on	ADP
easat-2990	267	17	legendre	legendre	PROPN
easat-2990	267	18	polynomials	polynomial	NOUN
easat-2990	267	19	and	and	CCONJ
easat-2990	267	20	its	its	PRON
easat-2990	267	21	application	application	NOUN
easat-2990	267	22	in	in	ADP
easat-2990	267	23	solving	solve	VERB
easat-2990	267	24	the	the	DET
easat-2990	267	25	stochastic	stochastic	ADJ
easat-2990	267	26	fractional	fractional	ADJ
easat-2990	267	27	integro	integro	ADJ
easat-2990	267	28	-	-	PUNCT
easat-2990	267	29	differential	differential	NOUN
easat-2990	267	30	equations	equation	NOUN
easat-2990	267	31	,	,	PUNCT
easat-2990	267	32	"	"	PUNCT
easat-2990	267	33	journal	journal	NOUN
easat-2990	267	34	of	of	ADP
easat-2990	267	35	computational	computational	ADJ
easat-2990	267	36	science	science	NOUN
easat-2990	267	37	,	,	PUNCT
easat-2990	267	38	vol	vol	NOUN
easat-2990	267	39	.	.	PROPN
easat-2990	267	40	51	51	NUM
easat-2990	267	41	,	,	PUNCT
easat-2990	267	42	p.	p.	NOUN
easat-2990	267	43	101342	101342	NUM
easat-2990	267	44	,	,	PUNCT
easat-2990	267	45	2021	2021	NUM
easat-2990	267	46	.	.	PUNCT
easat-2990	268	1	[	[	X
easat-2990	268	2	30	30	NUM
easat-2990	268	3	]	]	X
easat-2990	268	4	g.	g.	NOUN
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easat-2990	268	7	d.	d.	PROPN
easat-2990	268	8	huybrechs	huybrechs	PROPN
easat-2990	268	9	,	,	PUNCT
easat-2990	268	10	"	"	PUNCT
easat-2990	268	11	an	an	DET
easat-2990	268	12	analysis	analysis	NOUN
easat-2990	268	13	of	of	ADP
easat-2990	268	14	least	least	ADJ
easat-2990	268	15	-	-	PUNCT
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easat-2990	268	17	oversampled	oversample	VERB
easat-2990	268	18	collocation	collocation	NOUN
easat-2990	268	19	methods	method	NOUN
easat-2990	268	20	for	for	ADP
easat-2990	268	21	compactly	compactly	ADV
easat-2990	268	22	perturbed	perturb	VERB
easat-2990	268	23	boundary	boundary	ADJ
easat-2990	268	24	integral	integral	ADJ
easat-2990	268	25	equations	equation	NOUN
easat-2990	268	26	in	in	ADP
easat-2990	268	27	two	two	NUM
easat-2990	268	28	dimensions	dimension	NOUN
easat-2990	268	29	,	,	PUNCT
easat-2990	268	30	"	"	PUNCT
easat-2990	268	31	journal	journal	NOUN
easat-2990	268	32	of	of	ADP
easat-2990	268	33	computational	computational	ADJ
easat-2990	268	34	and	and	CCONJ
easat-2990	268	35	applied	applied	ADJ
easat-2990	268	36	mathematics	mathematic	NOUN
easat-2990	268	37	,	,	PUNCT
easat-2990	268	38	vol	vol	NOUN
easat-2990	268	39	.	.	PROPN
easat-2990	269	1	416	416	NUM
easat-2990	269	2	,	,	PUNCT
easat-2990	269	3	p.	p.	NOUN
easat-2990	269	4	114500	114500	NUM
easat-2990	269	5	,	,	PUNCT
easat-2990	269	6	2022	2022	NUM
easat-2990	269	7	.	.	PUNCT
easat-2990	270	1	[	[	X
easat-2990	270	2	31	31	NUM
easat-2990	270	3	]	]	PUNCT
easat-2990	270	4	p.	p.	NOUN
easat-2990	270	5	v.	v.	ADP
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easat-2990	270	7	and	and	CCONJ
easat-2990	270	8	s.	s.	PROPN
easat-2990	270	9	hollensen	hollensen	PROPN
easat-2990	270	10	,	,	PUNCT
easat-2990	270	11	"	"	PUNCT
easat-2990	270	12	the	the	DET
easat-2990	270	13	process	process	NOUN
easat-2990	270	14	of	of	ADP
easat-2990	270	15	benchmarking	benchmarke	VERB
easat-2990	270	16	,	,	PUNCT
easat-2990	270	17	benchlearning	benchlearning	NOUN
easat-2990	270	18	and	and	CCONJ
easat-2990	270	19	benchaction	benchaction	NOUN
easat-2990	270	20	,	,	PUNCT
easat-2990	270	21	"	"	PUNCT
easat-2990	270	22	the	the	DET
easat-2990	270	23	tqm	tqm	PROPN
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easat-2990	270	25	,	,	PUNCT
easat-2990	270	26	vol	vol	NOUN
easat-2990	270	27	.	.	PROPN
easat-2990	270	28	13	13	NUM
easat-2990	270	29	,	,	PUNCT
easat-2990	270	30	no	no	INTJ
easat-2990	270	31	.	.	NOUN
easat-2990	270	32	1	1	NUM
easat-2990	270	33	,	,	PUNCT
easat-2990	270	34	pp	pp	ADJ
easat-2990	270	35	.	.	PUNCT
easat-2990	271	1	25	25	NUM
easat-2990	271	2	-	-	SYM
easat-2990	271	3	34	34	NUM
easat-2990	271	4	,	,	PUNCT
easat-2990	271	5	2001	2001	NUM
easat-2990	271	6	.	.	PUNCT
easat-2990	272	1	[	[	X
easat-2990	272	2	32	32	NUM
easat-2990	272	3	]	]	PUNCT
easat-2990	272	4	d.	d.	PROPN
easat-2990	272	5	a.	a.	PROPN
easat-2990	272	6	simons	simons	PROPN
easat-2990	272	7	,	,	PUNCT
easat-2990	272	8	numerical	numerical	ADJ
easat-2990	272	9	and	and	CCONJ
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easat-2990	272	11	solutions	solution	NOUN
easat-2990	272	12	to	to	ADP
easat-2990	272	13	benchmark	benchmark	NOUN
easat-2990	272	14	problems	problem	NOUN
easat-2990	272	15	related	relate	VERB
easat-2990	272	16	to	to	ADP
easat-2990	272	17	tunnel	tunnel	NOUN
easat-2990	272	18	mechanics	mechanic	NOUN
easat-2990	272	19	.	.	PUNCT
easat-2990	273	1	defense	defense	NOUN
easat-2990	273	2	nuclear	nuclear	ADJ
easat-2990	273	3	agency	agency	NOUN
easat-2990	273	4	,	,	PUNCT
easat-2990	273	5	1993	1993	NUM
easat-2990	273	6	.	.	PUNCT
easat-2990	274	1	[	[	X
easat-2990	274	2	33	33	NUM
easat-2990	274	3	]	]	PUNCT
easat-2990	274	4	a.	a.	NOUN
easat-2990	274	5	samad	samad	PROPN
easat-2990	274	6	,	,	PUNCT
easat-2990	274	7	s.	s.	PROPN
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easat-2990	274	9	,	,	PUNCT
easat-2990	274	10	u.	u.	PROPN
easat-2990	274	11	vogt	vogt	PROPN
easat-2990	274	12	,	,	PUNCT
easat-2990	274	13	and	and	CCONJ
easat-2990	274	14	b.	b.	PROPN
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easat-2990	274	16	,	,	PUNCT
easat-2990	274	17	"	"	PUNCT
easat-2990	274	18	air	air	NOUN
easat-2990	274	19	pollution	pollution	NOUN
easat-2990	274	20	prediction	prediction	NOUN
easat-2990	274	21	using	use	VERB
easat-2990	274	22	machine	machine	NOUN
easat-2990	274	23	learning	learn	VERB
easat-2990	274	24	techniques	technique	NOUN
easat-2990	274	25	–	–	PUNCT
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easat-2990	274	27	approach	approach	NOUN
easat-2990	274	28	to	to	PART
easat-2990	274	29	replace	replace	VERB
easat-2990	274	30	existing	exist	VERB
easat-2990	274	31	monitoring	monitoring	NOUN
easat-2990	274	32	stations	station	NOUN
easat-2990	274	33	with	with	ADP
easat-2990	274	34	virtual	virtual	ADJ
easat-2990	274	35	monitoring	monitoring	NOUN
easat-2990	274	36	stations	station	NOUN
easat-2990	274	37	,	,	PUNCT
easat-2990	274	38	"	"	PUNCT
easat-2990	274	39	atmospheric	atmospheric	ADJ
easat-2990	274	40	environment	environment	NOUN
easat-2990	274	41	,	,	PUNCT
easat-2990	274	42	vol	vol	NOUN
easat-2990	274	43	.	.	PROPN
easat-2990	274	44	310	310	NUM
easat-2990	274	45	,	,	PUNCT
easat-2990	274	46	p.	p.	NOUN
easat-2990	274	47	119987	119987	NUM
easat-2990	274	48	,	,	PUNCT
easat-2990	274	49	2023/10/01/	2023/10/01/	NUM
easat-2990	274	50	2023	2023	NUM
easat-2990	274	51	,	,	PUNCT
easat-2990	274	52	doi	doi	NOUN
easat-2990	274	53	:	:	PUNCT
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easat-2990	274	55	.	.	PUNCT
easat-2990	275	1	[	[	X
easat-2990	275	2	34	34	NUM
easat-2990	275	3	]	]	X
easat-2990	275	4	d.	d.	PROPN
easat-2990	275	5	maillet	maillet	PROPN
easat-2990	275	6	,	,	PUNCT
easat-2990	275	7	"	"	PUNCT
easat-2990	275	8	a	a	DET
easat-2990	275	9	review	review	NOUN
easat-2990	275	10	of	of	ADP
easat-2990	275	11	the	the	DET
easat-2990	275	12	models	model	NOUN
easat-2990	275	13	using	use	VERB
easat-2990	275	14	the	the	DET
easat-2990	275	15	cattaneo	cattaneo	NOUN
easat-2990	275	16	and	and	CCONJ
easat-2990	275	17	vernotte	vernotte	ADJ
easat-2990	275	18	hyperbolic	hyperbolic	ADJ
easat-2990	275	19	heat	heat	NOUN
easat-2990	275	20	equation	equation	NOUN
easat-2990	275	21	and	and	CCONJ
easat-2990	275	22	their	their	PRON
easat-2990	275	23	experimental	experimental	ADJ
easat-2990	275	24	validation	validation	NOUN
easat-2990	275	25	,	,	PUNCT
easat-2990	275	26	"	"	PUNCT
easat-2990	275	27	international	international	ADJ
easat-2990	275	28	journal	journal	NOUN
easat-2990	275	29	of	of	ADP
easat-2990	275	30	thermal	thermal	ADJ
easat-2990	275	31	sciences	science	NOUN
easat-2990	275	32	,	,	PUNCT
easat-2990	275	33	vol	vol	NOUN
easat-2990	275	34	.	.	NOUN
easat-2990	275	35	139	139	NUM
easat-2990	275	36	,	,	PUNCT
easat-2990	275	37	pp	pp	ADJ
easat-2990	275	38	.	.	PUNCT
easat-2990	276	1	424	424	NUM
easat-2990	276	2	-	-	SYM
easat-2990	276	3	432	432	NUM
easat-2990	276	4	,	,	PUNCT
easat-2990	276	5	2019	2019	NUM
easat-2990	276	6	.	.	PUNCT
easat-2990	277	1	https://doi.org/10.1016/s0377-0427(00)00511-2	https://doi.org/10.1016/s0377-0427(00)00511-2	PROPN
easat-2990	277	2	https://doi.org/10.1016/j.atmosenv.2023.119987	https://doi.org/10.1016/j.atmosenv.2023.119987	PROPN