id	sid	tid	token	lemma	pos
ejpam-4470	1	1	european	european	PROPN
ejpam-4470	1	2	journal	journal	PROPN
ejpam-4470	1	3	of	of	ADP
ejpam-4470	1	4	pure	pure	ADJ
ejpam-4470	1	5	and	and	CCONJ
ejpam-4470	1	6	applied	apply	VERB
ejpam-4470	1	7	mathematics	mathematic	NOUN
ejpam-4470	1	8	vol	vol	NOUN
ejpam-4470	1	9	.	.	PROPN
ejpam-4470	2	1	15	15	NUM
ejpam-4470	2	2	,	,	PUNCT
ejpam-4470	2	3	no	no	INTJ
ejpam-4470	2	4	.	.	NOUN
ejpam-4470	2	5	3	3	NUM
ejpam-4470	2	6	,	,	PUNCT
ejpam-4470	2	7	2022	2022	NUM
ejpam-4470	2	8	,	,	PUNCT
ejpam-4470	2	9	1363	1363	NUM
ejpam-4470	2	10	-	-	SYM
ejpam-4470	2	11	1375	1375	NUM
ejpam-4470	2	12	issn	issn	PROPN
ejpam-4470	2	13	1307	1307	NUM
ejpam-4470	2	14	-	-	SYM
ejpam-4470	2	15	5543	5543	NUM
ejpam-4470	2	16	–	–	PUNCT
ejpam-4470	2	17	ejpam.com	ejpam.com	X
ejpam-4470	2	18	published	publish	VERB
ejpam-4470	2	19	by	by	ADP
ejpam-4470	2	20	new	new	PROPN
ejpam-4470	2	21	york	york	PROPN
ejpam-4470	2	22	business	business	PROPN
ejpam-4470	2	23	global	global	ADJ
ejpam-4470	2	24	applications	application	NOUN
ejpam-4470	2	25	of	of	ADP
ejpam-4470	2	26	double	double	ADJ
ejpam-4470	2	27	fuzzy	fuzzy	ADJ
ejpam-4470	2	28	sumudu	sumudu	NOUN
ejpam-4470	2	29	adomian	adomian	NOUN
ejpam-4470	2	30	decomposition	decomposition	NOUN
ejpam-4470	2	31	method	method	NOUN
ejpam-4470	2	32	for	for	ADP
ejpam-4470	2	33	two	two	NUM
ejpam-4470	2	34	-	-	PUNCT
ejpam-4470	2	35	dimensional	dimensional	ADJ
ejpam-4470	2	36	fuzzy	fuzzy	ADJ
ejpam-4470	2	37	volterra	volterra	NOUN
ejpam-4470	2	38	integral	integral	ADJ
ejpam-4470	2	39	equations	equation	NOUN
ejpam-4470	2	40	artan	artan	VERB
ejpam-4470	2	41	f.alidema	f.alidema	ADJ
ejpam-4470	2	42	1	1	NUM
ejpam-4470	2	43	department	department	NOUN
ejpam-4470	2	44	of	of	ADP
ejpam-4470	2	45	mathematics	mathematic	NOUN
ejpam-4470	2	46	,	,	PUNCT
ejpam-4470	2	47	faculty	faculty	NOUN
ejpam-4470	2	48	of	of	ADP
ejpam-4470	2	49	mathematical	mathematical	ADJ
ejpam-4470	2	50	and	and	CCONJ
ejpam-4470	2	51	natural	natural	ADJ
ejpam-4470	2	52	science	science	NOUN
ejpam-4470	2	53	,	,	PUNCT
ejpam-4470	2	54	university	university	PROPN
ejpam-4470	2	55	of	of	ADP
ejpam-4470	2	56	prishtina	prishtina	PROPN
ejpam-4470	2	57	”	"	PUNCT
ejpam-4470	2	58	hasan	hasan	PROPN
ejpam-4470	2	59	prishtina	prishtina	PROPN
ejpam-4470	2	60	”	"	PUNCT
ejpam-4470	2	61	,	,	PUNCT
ejpam-4470	2	62	prishtinë	prishtinë	PROPN
ejpam-4470	2	63	,	,	PUNCT
ejpam-4470	2	64	10000	10000	NUM
ejpam-4470	2	65	,	,	PUNCT
ejpam-4470	2	66	kosovë	kosovë	NOUN
ejpam-4470	2	67	abstract	abstract	NOUN
ejpam-4470	2	68	.	.	PUNCT
ejpam-4470	3	1	in	in	ADP
ejpam-4470	3	2	this	this	DET
ejpam-4470	3	3	paper	paper	NOUN
ejpam-4470	3	4	,	,	PUNCT
ejpam-4470	3	5	we	we	PRON
ejpam-4470	3	6	combine	combine	VERB
ejpam-4470	3	7	double	double	ADJ
ejpam-4470	3	8	sumudu	sumudu	NOUN
ejpam-4470	3	9	transform	transform	NOUN
ejpam-4470	3	10	with	with	ADP
ejpam-4470	3	11	adomian	adomian	NOUN
ejpam-4470	3	12	decomposition	decomposition	NOUN
ejpam-4470	3	13	method	method	NOUN
ejpam-4470	3	14	to	to	PART
ejpam-4470	3	15	solve	solve	VERB
ejpam-4470	3	16	two	two	NUM
ejpam-4470	3	17	dimensional	dimensional	ADJ
ejpam-4470	3	18	fuzzy	fuzzy	ADJ
ejpam-4470	3	19	convolution	convolution	NOUN
ejpam-4470	3	20	volterra	volterra	NOUN
ejpam-4470	3	21	integral	integral	ADJ
ejpam-4470	3	22	equations	equation	NOUN
ejpam-4470	3	23	.	.	PUNCT
ejpam-4470	4	1	we	we	PRON
ejpam-4470	4	2	give	give	VERB
ejpam-4470	4	3	some	some	DET
ejpam-4470	4	4	definition	definition	NOUN
ejpam-4470	4	5	for	for	ADP
ejpam-4470	4	6	fuzzy	fuzzy	ADJ
ejpam-4470	4	7	number	number	NOUN
ejpam-4470	4	8	,	,	PUNCT
ejpam-4470	4	9	fuzzy	fuzzy	ADJ
ejpam-4470	4	10	valued	value	VERB
ejpam-4470	4	11	function	function	NOUN
ejpam-4470	4	12	which	which	PRON
ejpam-4470	4	13	are	be	AUX
ejpam-4470	4	14	prerequest	prerequ	ADJ
ejpam-4470	4	15	for	for	ADP
ejpam-4470	4	16	combine	combine	VERB
ejpam-4470	4	17	the	the	DET
ejpam-4470	4	18	double	double	ADJ
ejpam-4470	4	19	fuzzy	fuzzy	ADJ
ejpam-4470	4	20	sumudu	sumudu	NOUN
ejpam-4470	4	21	transform	transform	NOUN
ejpam-4470	4	22	with	with	ADP
ejpam-4470	4	23	adomian	adomian	NOUN
ejpam-4470	4	24	decomposition	decomposition	NOUN
ejpam-4470	4	25	transform	transform	NOUN
ejpam-4470	4	26	method	method	NOUN
ejpam-4470	4	27	.	.	PUNCT
ejpam-4470	5	1	we	we	PRON
ejpam-4470	5	2	describe	describe	VERB
ejpam-4470	5	3	the	the	DET
ejpam-4470	5	4	method	method	NOUN
ejpam-4470	5	5	and	and	CCONJ
ejpam-4470	5	6	finally	finally	ADV
ejpam-4470	5	7	,	,	PUNCT
ejpam-4470	5	8	numerical	numerical	ADJ
ejpam-4470	5	9	examples	example	NOUN
ejpam-4470	5	10	are	be	AUX
ejpam-4470	5	11	given	give	VERB
ejpam-4470	5	12	to	to	PART
ejpam-4470	5	13	illustrate	illustrate	VERB
ejpam-4470	5	14	the	the	DET
ejpam-4470	5	15	efficiency	efficiency	NOUN
ejpam-4470	5	16	and	and	CCONJ
ejpam-4470	5	17	applicability	applicability	NOUN
ejpam-4470	5	18	of	of	ADP
ejpam-4470	5	19	our	our	PRON
ejpam-4470	5	20	method	method	NOUN
ejpam-4470	5	21	.	.	PUNCT
ejpam-4470	6	1	2020	2020	NUM
ejpam-4470	6	2	mathematics	mathematic	NOUN
ejpam-4470	6	3	subject	subject	NOUN
ejpam-4470	6	4	classifications	classification	NOUN
ejpam-4470	6	5	:	:	PUNCT
ejpam-4470	6	6	41a25,45g10,65r20	41a25,45g10,65r20	NUM
ejpam-4470	6	7	key	key	ADJ
ejpam-4470	6	8	words	word	NOUN
ejpam-4470	6	9	and	and	CCONJ
ejpam-4470	6	10	phrases	phrase	NOUN
ejpam-4470	6	11	:	:	PUNCT
ejpam-4470	6	12	sumudu	sumudu	NOUN
ejpam-4470	6	13	transform	transform	NOUN
ejpam-4470	6	14	,	,	PUNCT
ejpam-4470	6	15	convolution	convolution	NOUN
ejpam-4470	6	16	,	,	PUNCT
ejpam-4470	6	17	adomian	adomian	NOUN
ejpam-4470	6	18	decompositon	decompositon	PROPN
ejpam-4470	6	19	method(adm	method(adm	PROPN
ejpam-4470	6	20	)	)	PUNCT
ejpam-4470	6	21	,	,	PUNCT
ejpam-4470	6	22	two	two	NUM
ejpam-4470	6	23	dimensional	dimensional	ADJ
ejpam-4470	6	24	fuzzy	fuzzy	ADJ
ejpam-4470	6	25	volterra	volterra	NOUN
ejpam-4470	6	26	integral	integral	ADJ
ejpam-4470	6	27	equations(2d	equations(2d	NOUN
ejpam-4470	6	28	-	-	PUNCT
ejpam-4470	6	29	fvies	fvie	NOUN
ejpam-4470	6	30	)	)	PUNCT
ejpam-4470	6	31	1	1	NUM
ejpam-4470	6	32	.	.	X
ejpam-4470	6	33	introduction	introduction	NOUN
ejpam-4470	6	34	an	an	DET
ejpam-4470	6	35	important	important	ADJ
ejpam-4470	6	36	branch	branch	NOUN
ejpam-4470	6	37	in	in	ADP
ejpam-4470	6	38	fuzzy	fuzzy	ADJ
ejpam-4470	6	39	mathematics	mathematic	NOUN
ejpam-4470	6	40	is	be	AUX
ejpam-4470	6	41	the	the	DET
ejpam-4470	6	42	topics	topic	NOUN
ejpam-4470	6	43	of	of	ADP
ejpam-4470	6	44	fuzzy	fuzzy	ADJ
ejpam-4470	6	45	integral	integral	ADJ
ejpam-4470	6	46	equations	equation	NOUN
ejpam-4470	6	47	.	.	PUNCT
ejpam-4470	7	1	the	the	DET
ejpam-4470	7	2	concept	concept	NOUN
ejpam-4470	7	3	of	of	ADP
ejpam-4470	7	4	fuzzy	fuzzy	ADJ
ejpam-4470	7	5	numbers	number	NOUN
ejpam-4470	7	6	and	and	CCONJ
ejpam-4470	7	7	arithmetic	arithmetic	ADJ
ejpam-4470	7	8	operations	operation	NOUN
ejpam-4470	7	9	firstly	firstly	ADV
ejpam-4470	7	10	introduced	introduce	VERB
ejpam-4470	7	11	by	by	ADP
ejpam-4470	7	12	zadeh	zadeh	PROPN
ejpam-4470	8	1	[	[	X
ejpam-4470	8	2	11	11	NUM
ejpam-4470	8	3	]	]	PUNCT
ejpam-4470	8	4	.	.	PUNCT
ejpam-4470	9	1	the	the	DET
ejpam-4470	9	2	topic	topic	NOUN
ejpam-4470	9	3	of	of	ADP
ejpam-4470	9	4	integration	integration	NOUN
ejpam-4470	9	5	of	of	ADP
ejpam-4470	9	6	fuzzy	fuzzy	ADJ
ejpam-4470	9	7	functions	function	NOUN
ejpam-4470	9	8	was	be	AUX
ejpam-4470	9	9	initially	initially	ADV
ejpam-4470	9	10	coined	coin	VERB
ejpam-4470	9	11	out	out	ADP
ejpam-4470	9	12	by	by	ADP
ejpam-4470	9	13	dubois	dubois	PROPN
ejpam-4470	9	14	and	and	CCONJ
ejpam-4470	9	15	prade	prade	NOUN
ejpam-4470	9	16	[	[	X
ejpam-4470	9	17	12	12	NUM
ejpam-4470	9	18	]	]	PUNCT
ejpam-4470	9	19	.	.	PUNCT
ejpam-4470	10	1	the	the	DET
ejpam-4470	10	2	study	study	NOUN
ejpam-4470	10	3	of	of	ADP
ejpam-4470	10	4	fuzzy	fuzzy	ADJ
ejpam-4470	10	5	volterra	volterra	PROPN
ejpam-4470	10	6	integral	integral	ADJ
ejpam-4470	10	7	equations	equation	NOUN
ejpam-4470	10	8	begins	begin	VERB
ejpam-4470	10	9	in	in	ADP
ejpam-4470	10	10	kaleva	kaleva	PROPN
ejpam-4470	10	11	[	[	X
ejpam-4470	10	12	20	20	NUM
ejpam-4470	10	13	]	]	PUNCT
ejpam-4470	10	14	,	,	PUNCT
ejpam-4470	10	15	seikkala	seikkala	ADP
ejpam-4470	11	1	[	[	X
ejpam-4470	11	2	26	26	NUM
ejpam-4470	11	3	]	]	PUNCT
ejpam-4470	11	4	and	and	CCONJ
ejpam-4470	11	5	mordeson	mordeson	NOUN
ejpam-4470	11	6	and	and	CCONJ
ejpam-4470	11	7	newman	newman	PROPN
ejpam-4470	12	1	[	[	X
ejpam-4470	12	2	24	24	NUM
ejpam-4470	12	3	]	]	X
ejpam-4470	12	4	,	,	PUNCT
ejpam-4470	12	5	such	such	ADJ
ejpam-4470	12	6	integral	integral	ADJ
ejpam-4470	12	7	equations	equation	NOUN
ejpam-4470	12	8	are	be	AUX
ejpam-4470	12	9	applied	apply	VERB
ejpam-4470	12	10	in	in	ADP
ejpam-4470	12	11	control	control	NOUN
ejpam-4470	12	12	mathematical	mathematical	ADJ
ejpam-4470	12	13	models	model	NOUN
ejpam-4470	12	14	.	.	PUNCT
ejpam-4470	13	1	the	the	DET
ejpam-4470	13	2	problems	problem	NOUN
ejpam-4470	13	3	posed	pose	VERB
ejpam-4470	13	4	in	in	ADP
ejpam-4470	13	5	the	the	DET
ejpam-4470	13	6	study	study	NOUN
ejpam-4470	13	7	of	of	ADP
ejpam-4470	13	8	fuzzy	fuzzy	ADJ
ejpam-4470	13	9	integral	integral	ADJ
ejpam-4470	13	10	equations	equation	NOUN
ejpam-4470	13	11	are	be	AUX
ejpam-4470	13	12	:	:	PUNCT
ejpam-4470	13	13	existence	existence	NOUN
ejpam-4470	13	14	and	and	CCONJ
ejpam-4470	13	15	uniqueness	uniqueness	NOUN
ejpam-4470	13	16	,	,	PUNCT
ejpam-4470	13	17	boundedness	boundedness	NOUN
ejpam-4470	13	18	of	of	ADP
ejpam-4470	13	19	the	the	DET
ejpam-4470	13	20	solutions	solution	NOUN
ejpam-4470	13	21	[	[	X
ejpam-4470	13	22	13	13	NUM
ejpam-4470	13	23	,	,	PUNCT
ejpam-4470	13	24	16	16	NUM
ejpam-4470	13	25	]	]	PUNCT
ejpam-4470	13	26	and	and	CCONJ
ejpam-4470	13	27	the	the	DET
ejpam-4470	13	28	construction	construction	NOUN
ejpam-4470	13	29	of	of	ADP
ejpam-4470	13	30	numerical	numerical	ADJ
ejpam-4470	13	31	methods	method	NOUN
ejpam-4470	13	32	for	for	ADP
ejpam-4470	13	33	the	the	DET
ejpam-4470	13	34	approximate	approximate	ADJ
ejpam-4470	13	35	solution	solution	NOUN
ejpam-4470	13	36	.	.	PUNCT
ejpam-4470	14	1	integral	integral	ADJ
ejpam-4470	14	2	transforms	transform	NOUN
ejpam-4470	14	3	constitute	constitute	VERB
ejpam-4470	14	4	fundamental	fundamental	ADJ
ejpam-4470	14	5	tools	tool	NOUN
ejpam-4470	14	6	in	in	ADP
ejpam-4470	14	7	operational	operational	ADJ
ejpam-4470	14	8	calculus	calculus	NOUN
ejpam-4470	14	9	.	.	PUNCT
ejpam-4470	15	1	they	they	PRON
ejpam-4470	15	2	are	be	AUX
ejpam-4470	15	3	mathematical	mathematical	ADJ
ejpam-4470	15	4	operators	operator	NOUN
ejpam-4470	15	5	that	that	PRON
ejpam-4470	15	6	have	have	AUX
ejpam-4470	15	7	been	be	AUX
ejpam-4470	15	8	used	use	VERB
ejpam-4470	15	9	widely	widely	ADV
ejpam-4470	15	10	in	in	ADP
ejpam-4470	15	11	solving	solve	VERB
ejpam-4470	15	12	many	many	ADJ
ejpam-4470	15	13	practical	practical	ADJ
ejpam-4470	15	14	problems	problem	NOUN
ejpam-4470	15	15	in	in	ADP
ejpam-4470	15	16	applied	applied	ADJ
ejpam-4470	15	17	mathematics	mathematic	NOUN
ejpam-4470	15	18	,	,	PUNCT
ejpam-4470	15	19	physics	physics	NOUN
ejpam-4470	15	20	and	and	CCONJ
ejpam-4470	15	21	engineering	engineering	NOUN
ejpam-4470	15	22	[	[	X
ejpam-4470	15	23	25	25	NUM
ejpam-4470	15	24	,	,	PUNCT
ejpam-4470	15	25	27	27	NUM
ejpam-4470	15	26	]	]	PUNCT
ejpam-4470	15	27	.	.	PUNCT
ejpam-4470	16	1	there	there	PRON
ejpam-4470	16	2	are	be	VERB
ejpam-4470	16	3	a	a	DET
ejpam-4470	16	4	number	number	NOUN
ejpam-4470	16	5	of	of	ADP
ejpam-4470	16	6	papers	paper	NOUN
ejpam-4470	16	7	on	on	ADP
ejpam-4470	16	8	the	the	DET
ejpam-4470	16	9	theories	theory	NOUN
ejpam-4470	16	10	and	and	CCONJ
ejpam-4470	16	11	applications	application	NOUN
ejpam-4470	16	12	of	of	ADP
ejpam-4470	16	13	integral	integral	ADJ
ejpam-4470	16	14	transforms	transform	NOUN
ejpam-4470	16	15	,	,	PUNCT
ejpam-4470	16	16	some	some	PRON
ejpam-4470	16	17	of	of	ADP
ejpam-4470	16	18	which	which	PRON
ejpam-4470	16	19	are	be	AUX
ejpam-4470	16	20	laplace	laplace	NOUN
ejpam-4470	16	21	,	,	PUNCT
ejpam-4470	16	22	mellin	mellin	PROPN
ejpam-4470	16	23	doi	doi	NOUN
ejpam-4470	16	24	:	:	PUNCT
ejpam-4470	16	25	https://doi.org/10.29020/nybg.ejpam.v15i3.4470	https://doi.org/10.29020/nybg.ejpam.v15i3.4470	PRON
ejpam-4470	16	26	email	email	NOUN
ejpam-4470	16	27	address	address	NOUN
ejpam-4470	16	28	:	:	PUNCT
ejpam-4470	16	29	artan.alidema@uni-pr.edu	artan.alidema@uni-pr.edu	PROPN
ejpam-4470	16	30	(	(	PUNCT
ejpam-4470	16	31	a	a	DET
ejpam-4470	16	32	f.alidema	f.alidema	ADV
ejpam-4470	16	33	)	)	PUNCT
ejpam-4470	16	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4470	16	35	1363	1363	NUM
ejpam-4470	17	1	©	©	ADP
ejpam-4470	17	2	2022	2022	NUM
ejpam-4470	17	3	ejpam	ejpam	VERB
ejpam-4470	17	4	all	all	DET
ejpam-4470	17	5	rights	right	NOUN
ejpam-4470	17	6	reserved	reserve	VERB
ejpam-4470	17	7	.	.	PUNCT
ejpam-4470	18	1	a.	a.	NOUN
ejpam-4470	18	2	f.alidema	f.alidema	PROPN
ejpam-4470	18	3	/	/	SYM
ejpam-4470	18	4	eur	eur	PROPN
ejpam-4470	18	5	.	.	PUNCT
ejpam-4470	19	1	j.	j.	PROPN
ejpam-4470	19	2	pure	pure	PROPN
ejpam-4470	19	3	appl	appl	PROPN
ejpam-4470	19	4	.	.	PROPN
ejpam-4470	19	5	math	math	PROPN
ejpam-4470	19	6	,	,	PUNCT
ejpam-4470	19	7	15	15	NUM
ejpam-4470	19	8	(	(	PUNCT
ejpam-4470	19	9	3	3	NUM
ejpam-4470	19	10	)	)	PUNCT
ejpam-4470	19	11	(	(	PUNCT
ejpam-4470	19	12	2022	2022	NUM
ejpam-4470	19	13	)	)	PUNCT
ejpam-4470	19	14	,	,	PUNCT
ejpam-4470	19	15	1363	1363	NUM
ejpam-4470	19	16	-	-	SYM
ejpam-4470	19	17	1375	1375	NUM
ejpam-4470	19	18	1364	1364	NUM
ejpam-4470	19	19	and	and	CCONJ
ejpam-4470	19	20	hankel	hankel	NOUN
ejpam-4470	19	21	transforms	transform	VERB
ejpam-4470	19	22	[	[	PRON
ejpam-4470	19	23	23	23	NUM
ejpam-4470	19	24	,	,	PUNCT
ejpam-4470	19	25	28	28	NUM
ejpam-4470	19	26	,	,	PUNCT
ejpam-4470	19	27	29	29	NUM
ejpam-4470	19	28	]	]	PUNCT
ejpam-4470	19	29	.	.	PUNCT
ejpam-4470	20	1	subsequently	subsequently	ADV
ejpam-4470	20	2	,	,	PUNCT
ejpam-4470	20	3	the	the	DET
ejpam-4470	20	4	concept	concept	NOUN
ejpam-4470	20	5	of	of	ADP
ejpam-4470	20	6	integral	integral	ADJ
ejpam-4470	20	7	transforms	transform	NOUN
ejpam-4470	20	8	was	be	AUX
ejpam-4470	20	9	expanded	expand	VERB
ejpam-4470	20	10	to	to	PART
ejpam-4470	20	11	remove	remove	VERB
ejpam-4470	20	12	the	the	DET
ejpam-4470	20	13	necessity	necessity	NOUN
ejpam-4470	20	14	of	of	ADP
ejpam-4470	20	15	finite	finite	ADJ
ejpam-4470	20	16	intervals	interval	NOUN
ejpam-4470	20	17	.	.	PUNCT
ejpam-4470	21	1	watugala	watugala	VERB
ejpam-4470	22	1	[	[	X
ejpam-4470	22	2	18	18	NUM
ejpam-4470	22	3	,	,	PUNCT
ejpam-4470	22	4	19	19	NUM
ejpam-4470	22	5	]	]	PUNCT
ejpam-4470	22	6	has	have	AUX
ejpam-4470	22	7	proposed	propose	VERB
ejpam-4470	22	8	a	a	DET
ejpam-4470	22	9	new	new	ADJ
ejpam-4470	22	10	integral	integral	ADJ
ejpam-4470	22	11	transform	transform	NOUN
ejpam-4470	22	12	called	call	VERB
ejpam-4470	22	13	the	the	DET
ejpam-4470	22	14	sumudu	sumudu	NOUN
ejpam-4470	22	15	transform	transform	NOUN
ejpam-4470	22	16	.	.	PUNCT
ejpam-4470	23	1	one	one	NUM
ejpam-4470	23	2	of	of	ADP
ejpam-4470	23	3	the	the	DET
ejpam-4470	23	4	most	most	ADV
ejpam-4470	23	5	recent	recent	ADJ
ejpam-4470	23	6	methods	method	NOUN
ejpam-4470	23	7	in	in	ADP
ejpam-4470	23	8	handling	handle	VERB
ejpam-4470	23	9	problems	problem	NOUN
ejpam-4470	23	10	modelled	model	VERB
ejpam-4470	23	11	under	under	ADP
ejpam-4470	23	12	fuzzy	fuzzy	ADJ
ejpam-4470	23	13	environment	environment	NOUN
ejpam-4470	23	14	is	be	AUX
ejpam-4470	23	15	fuzzy	fuzzy	ADJ
ejpam-4470	23	16	sumudu	sumudu	NOUN
ejpam-4470	23	17	transform	transform	NOUN
ejpam-4470	23	18	(	(	PUNCT
ejpam-4470	23	19	fst	fst	NOUN
ejpam-4470	23	20	)	)	PUNCT
ejpam-4470	23	21	.	.	PUNCT
ejpam-4470	24	1	fst	fst	PROPN
ejpam-4470	24	2	has	have	AUX
ejpam-4470	24	3	been	be	AUX
ejpam-4470	24	4	used	use	VERB
ejpam-4470	24	5	for	for	ADP
ejpam-4470	24	6	solving	solve	VERB
ejpam-4470	24	7	various	various	ADJ
ejpam-4470	24	8	kinds	kind	NOUN
ejpam-4470	24	9	of	of	ADP
ejpam-4470	24	10	fuzzy	fuzzy	ADJ
ejpam-4470	24	11	differential	differential	NOUN
ejpam-4470	24	12	and	and	CCONJ
ejpam-4470	24	13	integral	integral	ADJ
ejpam-4470	24	14	equations	equation	NOUN
ejpam-4470	24	15	[	[	X
ejpam-4470	24	16	21	21	NUM
ejpam-4470	24	17	,	,	PUNCT
ejpam-4470	24	18	30	30	NUM
ejpam-4470	24	19	]	]	PUNCT
ejpam-4470	24	20	.	.	PUNCT
ejpam-4470	25	1	by	by	ADP
ejpam-4470	25	2	using	use	VERB
ejpam-4470	25	3	fst	fst	NOUN
ejpam-4470	25	4	,	,	PUNCT
ejpam-4470	25	5	the	the	DET
ejpam-4470	25	6	problem	problem	NOUN
ejpam-4470	25	7	is	be	AUX
ejpam-4470	25	8	reduced	reduce	VERB
ejpam-4470	25	9	to	to	ADP
ejpam-4470	25	10	algebraic	algebraic	ADJ
ejpam-4470	25	11	problem	problem	NOUN
ejpam-4470	25	12	which	which	PRON
ejpam-4470	25	13	is	be	AUX
ejpam-4470	25	14	much	much	ADV
ejpam-4470	25	15	simpler	simple	ADJ
ejpam-4470	25	16	to	to	PART
ejpam-4470	25	17	be	be	AUX
ejpam-4470	25	18	solved	solve	VERB
ejpam-4470	25	19	.	.	PUNCT
ejpam-4470	26	1	this	this	DET
ejpam-4470	26	2	fall	fall	NOUN
ejpam-4470	26	3	under	under	ADP
ejpam-4470	26	4	the	the	DET
ejpam-4470	26	5	topic	topic	NOUN
ejpam-4470	26	6	of	of	ADP
ejpam-4470	26	7	operational	operational	ADJ
ejpam-4470	26	8	calculus	calculus	NOUN
ejpam-4470	26	9	and	and	CCONJ
ejpam-4470	26	10	under	under	ADP
ejpam-4470	26	11	this	this	DET
ejpam-4470	26	12	topic	topic	NOUN
ejpam-4470	26	13	,	,	PUNCT
ejpam-4470	26	14	fst	fst	NOUN
ejpam-4470	26	15	is	be	AUX
ejpam-4470	26	16	considered	consider	VERB
ejpam-4470	26	17	as	as	ADP
ejpam-4470	26	18	one	one	NUM
ejpam-4470	26	19	of	of	ADP
ejpam-4470	26	20	a	a	DET
ejpam-4470	26	21	powerful	powerful	ADJ
ejpam-4470	26	22	method	method	NOUN
ejpam-4470	26	23	alongside	alongside	ADV
ejpam-4470	26	24	with	with	ADP
ejpam-4470	26	25	fuzzy	fuzzy	ADJ
ejpam-4470	26	26	laplace	laplace	NOUN
ejpam-4470	26	27	transform	transform	NOUN
ejpam-4470	26	28	.	.	PUNCT
ejpam-4470	26	29	.	.	PUNCT
ejpam-4470	27	1	the	the	DET
ejpam-4470	27	2	adomian	adomian	NOUN
ejpam-4470	27	3	decompositon	decompositon	PROPN
ejpam-4470	27	4	method	method	NOUN
ejpam-4470	27	5	(	(	PUNCT
ejpam-4470	27	6	adm	adm	PROPN
ejpam-4470	27	7	)	)	PUNCT
ejpam-4470	27	8	has	have	AUX
ejpam-4470	27	9	been	be	AUX
ejpam-4470	27	10	recently	recently	ADV
ejpam-4470	27	11	intensively	intensively	ADV
ejpam-4470	27	12	studied	study	VERB
ejpam-4470	27	13	by	by	ADP
ejpam-4470	27	14	scientists	scientist	NOUN
ejpam-4470	27	15	and	and	CCONJ
ejpam-4470	27	16	engineers	engineer	NOUN
ejpam-4470	27	17	and	and	CCONJ
ejpam-4470	27	18	used	use	VERB
ejpam-4470	27	19	for	for	ADP
ejpam-4470	27	20	solving	solve	VERB
ejpam-4470	27	21	nonlinear	nonlinear	ADJ
ejpam-4470	27	22	diferencial	diferencial	ADJ
ejpam-4470	27	23	and	and	CCONJ
ejpam-4470	27	24	integral	integral	ADJ
ejpam-4470	27	25	problems	problem	NOUN
ejpam-4470	27	26	.	.	PUNCT
ejpam-4470	28	1	the	the	DET
ejpam-4470	28	2	adomian	adomian	NOUN
ejpam-4470	28	3	decompositon	decompositon	PROPN
ejpam-4470	28	4	method	method	NOUN
ejpam-4470	28	5	(	(	PUNCT
ejpam-4470	28	6	adm	adm	PROPN
ejpam-4470	28	7	)	)	PUNCT
ejpam-4470	28	8	intruduced	intruduce	VERB
ejpam-4470	28	9	by	by	ADP
ejpam-4470	28	10	adomian	adomian	NOUN
ejpam-4470	28	11	[	[	X
ejpam-4470	28	12	1	1	NUM
ejpam-4470	28	13	,	,	PUNCT
ejpam-4470	28	14	2	2	NUM
ejpam-4470	28	15	]	]	PUNCT
ejpam-4470	28	16	for	for	ADP
ejpam-4470	28	17	solving	solve	VERB
ejpam-4470	28	18	different	different	ADJ
ejpam-4470	28	19	kind	kind	NOUN
ejpam-4470	28	20	of	of	ADP
ejpam-4470	28	21	functional	functional	ADJ
ejpam-4470	28	22	equations	equation	NOUN
ejpam-4470	28	23	and	and	CCONJ
ejpam-4470	28	24	has	have	AUX
ejpam-4470	28	25	been	be	AUX
ejpam-4470	28	26	subject	subject	ADJ
ejpam-4470	28	27	of	of	ADP
ejpam-4470	28	28	extensive	extensive	ADJ
ejpam-4470	28	29	numerical	numerical	ADJ
ejpam-4470	28	30	and	and	CCONJ
ejpam-4470	28	31	analytical	analytical	ADJ
ejpam-4470	28	32	studies	study	NOUN
ejpam-4470	28	33	.	.	PUNCT
ejpam-4470	29	1	babolian	babolian	PROPN
ejpam-4470	29	2	at	at	ADP
ejpam-4470	29	3	al.[7	al.[7	PROPN
ejpam-4470	29	4	]	]	PUNCT
ejpam-4470	29	5	,	,	PUNCT
ejpam-4470	29	6	adm	adm	PROPN
ejpam-4470	29	7	to	to	PART
ejpam-4470	29	8	solve	solve	VERB
ejpam-4470	29	9	fuzzy	fuzzy	ADJ
ejpam-4470	29	10	fredholm	fredholm	ADJ
ejpam-4470	29	11	integral	integral	ADJ
ejpam-4470	29	12	equations	equation	NOUN
ejpam-4470	29	13	,	,	PUNCT
ejpam-4470	29	14	respectively	respectively	ADV
ejpam-4470	29	15	allahviranloo	allahviranloo	NOUN
ejpam-4470	29	16	at	at	ADP
ejpam-4470	29	17	al.[8	al.[8	PROPN
ejpam-4470	29	18	]	]	PUNCT
ejpam-4470	29	19	,	,	PUNCT
ejpam-4470	29	20	solved	solve	VERB
ejpam-4470	29	21	fuzzy	fuzzy	ADJ
ejpam-4470	29	22	system	system	NOUN
ejpam-4470	29	23	of	of	ADP
ejpam-4470	29	24	fredholm	fredholm	ADJ
ejpam-4470	29	25	integral	integral	ADJ
ejpam-4470	29	26	equations	equation	NOUN
ejpam-4470	29	27	.	.	PUNCT
ejpam-4470	30	1	also	also	ADV
ejpam-4470	30	2	,	,	PUNCT
ejpam-4470	30	3	behzadi	behzadi	NOUN
ejpam-4470	30	4	[	[	X
ejpam-4470	30	5	5	5	NUM
ejpam-4470	30	6	]	]	PUNCT
ejpam-4470	30	7	,	,	PUNCT
ejpam-4470	30	8	solving	solve	VERB
ejpam-4470	30	9	nonlinear	nonlinear	NOUN
ejpam-4470	30	10	i	i	PRON
ejpam-4470	30	11	fuzzy	fuzzy	ADJ
ejpam-4470	30	12	volterra	volterra	NOUN
ejpam-4470	30	13	fredholm	fredholm	VERB
ejpam-4470	30	14	integral	integral	ADJ
ejpam-4470	30	15	equations	equation	NOUN
ejpam-4470	30	16	with	with	ADP
ejpam-4470	30	17	adomain	adomain	NOUN
ejpam-4470	30	18	decompositon	decompositon	NOUN
ejpam-4470	30	19	method	method	NOUN
ejpam-4470	30	20	.	.	PUNCT
ejpam-4470	31	1	in	in	ADP
ejpam-4470	31	2	many	many	ADJ
ejpam-4470	31	3	papers	paper	NOUN
ejpam-4470	31	4	have	have	AUX
ejpam-4470	31	5	combine	combine	VERB
ejpam-4470	31	6	with	with	ADP
ejpam-4470	31	7	laplace	laplace	NOUN
ejpam-4470	31	8	-adomian	-adomian	PROPN
ejpam-4470	31	9	transform	transform	NOUN
ejpam-4470	31	10	method	method	NOUN
ejpam-4470	31	11	and	and	CCONJ
ejpam-4470	31	12	sumudu	sumudu	VERB
ejpam-4470	31	13	-adomain	-adomain	PROPN
ejpam-4470	31	14	transform	transform	NOUN
ejpam-4470	31	15	to	to	PART
ejpam-4470	31	16	solve	solve	VERB
ejpam-4470	31	17	diferential	diferential	ADJ
ejpam-4470	31	18	and	and	CCONJ
ejpam-4470	31	19	integral	integral	ADJ
ejpam-4470	31	20	equations	equation	NOUN
ejpam-4470	31	21	.	.	PUNCT
ejpam-4470	32	1	alidema	alidema	PROPN
ejpam-4470	33	1	[	[	X
ejpam-4470	33	2	3	3	X
ejpam-4470	33	3	]	]	PUNCT
ejpam-4470	33	4	using	use	VERB
ejpam-4470	33	5	adomian	adomian	NOUN
ejpam-4470	33	6	decomposition	decomposition	NOUN
ejpam-4470	33	7	method	method	NOUN
ejpam-4470	33	8	for	for	ADP
ejpam-4470	33	9	solving	solve	VERB
ejpam-4470	33	10	two	two	NUM
ejpam-4470	33	11	-	-	PUNCT
ejpam-4470	33	12	dimensional	dimensional	ADJ
ejpam-4470	33	13	nonlinear	nonlinear	ADJ
ejpam-4470	33	14	volterra	volterra	NOUN
ejpam-4470	33	15	fuzzy	fuzzy	ADJ
ejpam-4470	33	16	integral	integral	ADJ
ejpam-4470	33	17	equations	equation	NOUN
ejpam-4470	33	18	.	.	PUNCT
ejpam-4470	34	1	morever	morever	PROPN
ejpam-4470	34	2	in	in	ADP
ejpam-4470	34	3	the	the	DET
ejpam-4470	34	4	recent	recent	ADJ
ejpam-4470	34	5	years	year	NOUN
ejpam-4470	34	6	contributed	contribute	VERB
ejpam-4470	34	7	in	in	ADP
ejpam-4470	34	8	this	this	DET
ejpam-4470	34	9	field	field	NOUN
ejpam-4470	35	1	[	[	X
ejpam-4470	35	2	36–38	36–38	NUM
ejpam-4470	35	3	]	]	PUNCT
ejpam-4470	35	4	and	and	CCONJ
ejpam-4470	35	5	[	[	X
ejpam-4470	35	6	39–41	39–41	NUM
ejpam-4470	35	7	]	]	PUNCT
ejpam-4470	35	8	.	.	PUNCT
ejpam-4470	36	1	bushnaq	bushnaq	PROPN
ejpam-4470	36	2	at	at	ADP
ejpam-4470	36	3	al	al	PROPN
ejpam-4470	36	4	.	.	PUNCT
ejpam-4470	37	1	[	[	X
ejpam-4470	37	2	9	9	NUM
ejpam-4470	37	3	]	]	PUNCT
ejpam-4470	37	4	find	find	VERB
ejpam-4470	37	5	solution	solution	NOUN
ejpam-4470	37	6	a	a	DET
ejpam-4470	37	7	fuzzy	fuzzy	ADJ
ejpam-4470	37	8	volterra	volterra	NOUN
ejpam-4470	37	9	abel	abel	PROPN
ejpam-4470	37	10	’s	’s	PART
ejpam-4470	37	11	integral	integral	ADJ
ejpam-4470	37	12	equation	equation	NOUN
ejpam-4470	37	13	of	of	ADP
ejpam-4470	37	14	the	the	DET
ejpam-4470	37	15	second	second	ADJ
ejpam-4470	37	16	kind	kind	NOUN
ejpam-4470	37	17	with	with	ADP
ejpam-4470	37	18	laplace	laplace	PROPN
ejpam-4470	37	19	adm	adm	PROPN
ejpam-4470	37	20	.	.	PUNCT
ejpam-4470	38	1	georgieva	georgieva	PROPN
ejpam-4470	39	1	[	[	X
ejpam-4470	39	2	4	4	NUM
ejpam-4470	39	3	,	,	PUNCT
ejpam-4470	39	4	5	5	NUM
ejpam-4470	39	5	,	,	PUNCT
ejpam-4470	39	6	14	14	NUM
ejpam-4470	39	7	]	]	PUNCT
ejpam-4470	39	8	,	,	PUNCT
ejpam-4470	39	9	gave	give	VERB
ejpam-4470	39	10	solution	solution	NOUN
ejpam-4470	39	11	two	two	NUM
ejpam-4470	39	12	dimensional	dimensional	ADJ
ejpam-4470	39	13	fuzzy	fuzzy	ADJ
ejpam-4470	39	14	volterra	volterra	NOUN
ejpam-4470	39	15	-	-	PUNCT
ejpam-4470	39	16	fredholm	fredholm	NOUN
ejpam-4470	39	17	with	with	ADP
ejpam-4470	39	18	adomain	adomain	NOUN
ejpam-4470	39	19	and	and	CCONJ
ejpam-4470	39	20	use	use	VERB
ejpam-4470	39	21	double	double	ADJ
ejpam-4470	39	22	fuzzy	fuzzy	ADJ
ejpam-4470	39	23	sumudu	sumudu	NOUN
ejpam-4470	39	24	transform	transform	NOUN
ejpam-4470	39	25	to	to	PART
ejpam-4470	39	26	solve	solve	VERB
ejpam-4470	39	27	partial	partial	ADJ
ejpam-4470	39	28	volterra	volterra	NOUN
ejpam-4470	39	29	fuzzy	fuzzy	ADJ
ejpam-4470	39	30	integrodifferential	integrodifferential	ADJ
ejpam-4470	39	31	equations	equation	NOUN
ejpam-4470	39	32	and	and	CCONJ
ejpam-4470	39	33	fuzzy	fuzzy	ADJ
ejpam-4470	39	34	sawi	sawi	ADJ
ejpam-4470	39	35	decompositon	decompositon	NOUN
ejpam-4470	39	36	for	for	ADP
ejpam-4470	39	37	nonlinear	nonlinear	ADJ
ejpam-4470	39	38	differential	differential	ADJ
ejpam-4470	39	39	equations	equation	NOUN
ejpam-4470	39	40	.	.	PUNCT
ejpam-4470	40	1	l.	l.	PROPN
ejpam-4470	40	2	al	al	PROPN
ejpam-4470	40	3	-	-	PROPN
ejpam-4470	40	4	taee	taee	PROPN
ejpam-4470	40	5	at	at	ADP
ejpam-4470	40	6	al.[34	al.[34	PROPN
ejpam-4470	40	7	,	,	PUNCT
ejpam-4470	40	8	35	35	NUM
ejpam-4470	40	9	]	]	PUNCT
ejpam-4470	40	10	,	,	PUNCT
ejpam-4470	40	11	solving	solve	VERB
ejpam-4470	40	12	system	system	NOUN
ejpam-4470	40	13	of	of	ADP
ejpam-4470	40	14	nonlinear	nonlinear	PROPN
ejpam-4470	40	15	volterra	volterra	PROPN
ejpam-4470	40	16	integral	integral	ADJ
ejpam-4470	40	17	equations	equation	NOUN
ejpam-4470	40	18	with	with	ADP
ejpam-4470	40	19	sumudu	sumudu	NOUN
ejpam-4470	40	20	-	-	PUNCT
ejpam-4470	40	21	adm	adm	NOUN
ejpam-4470	40	22	and	and	CCONJ
ejpam-4470	40	23	fuzzy	fuzzy	ADJ
ejpam-4470	40	24	system	system	NOUN
ejpam-4470	40	25	of	of	ADP
ejpam-4470	40	26	volterra	volterra	PROPN
ejpam-4470	40	27	integro	integro	PROPN
ejpam-4470	40	28	-	-	PUNCT
ejpam-4470	40	29	differential	differential	NOUN
ejpam-4470	40	30	equations	equation	NOUN
ejpam-4470	40	31	by	by	ADP
ejpam-4470	40	32	using	use	VERB
ejpam-4470	40	33	adm	adm	PROPN
ejpam-4470	40	34	.	.	PUNCT
ejpam-4470	41	1	the	the	DET
ejpam-4470	41	2	subject	subject	NOUN
ejpam-4470	41	3	of	of	ADP
ejpam-4470	41	4	this	this	DET
ejpam-4470	41	5	paper	paper	NOUN
ejpam-4470	41	6	is	be	AUX
ejpam-4470	41	7	to	to	PART
ejpam-4470	41	8	apply	apply	VERB
ejpam-4470	41	9	the	the	DET
ejpam-4470	41	10	double	double	ADJ
ejpam-4470	41	11	fuzzy	fuzzy	ADJ
ejpam-4470	41	12	sumudu	sumudu	NOUN
ejpam-4470	41	13	transform	transform	NOUN
ejpam-4470	41	14	with	with	ADP
ejpam-4470	41	15	adomian	adomian	NOUN
ejpam-4470	41	16	decomposition	decomposition	NOUN
ejpam-4470	41	17	method	method	NOUN
ejpam-4470	41	18	for	for	ADP
ejpam-4470	41	19	solving	solve	VERB
ejpam-4470	41	20	fuzzy	fuzzy	ADJ
ejpam-4470	41	21	convolution	convolution	NOUN
ejpam-4470	41	22	volterra	volterra	NOUN
ejpam-4470	41	23	integral	integral	ADJ
ejpam-4470	41	24	equation	equation	NOUN
ejpam-4470	41	25	in	in	ADP
ejpam-4470	41	26	two	two	NUM
ejpam-4470	41	27	variables	variable	NOUN
ejpam-4470	41	28	.	.	PUNCT
ejpam-4470	42	1	we	we	PRON
ejpam-4470	42	2	give	give	VERB
ejpam-4470	42	3	some	some	DET
ejpam-4470	42	4	preliminaries	preliminary	NOUN
ejpam-4470	42	5	on	on	ADP
ejpam-4470	42	6	fuzzy	fuzzy	ADJ
ejpam-4470	42	7	numbers	number	NOUN
ejpam-4470	42	8	,	,	PUNCT
ejpam-4470	42	9	fuzzy	fuzzy	ADJ
ejpam-4470	42	10	functions	function	NOUN
ejpam-4470	42	11	and	and	CCONJ
ejpam-4470	42	12	fuzzy	fuzzy	ADJ
ejpam-4470	42	13	integrals	integral	NOUN
ejpam-4470	42	14	.	.	PUNCT
ejpam-4470	43	1	then	then	ADV
ejpam-4470	43	2	we	we	PRON
ejpam-4470	43	3	provide	provide	VERB
ejpam-4470	43	4	the	the	DET
ejpam-4470	43	5	proposed	propose	VERB
ejpam-4470	43	6	dfst	dfst	NOUN
ejpam-4470	43	7	with	with	ADP
ejpam-4470	43	8	adm	adm	PROPN
ejpam-4470	43	9	,	,	PUNCT
ejpam-4470	43	10	properties	property	NOUN
ejpam-4470	43	11	with	with	ADP
ejpam-4470	43	12	dfst	dfst	NOUN
ejpam-4470	43	13	.	.	PUNCT
ejpam-4470	44	1	we	we	PRON
ejpam-4470	44	2	introduced	introduce	VERB
ejpam-4470	44	3	the	the	DET
ejpam-4470	44	4	concept	concept	NOUN
ejpam-4470	44	5	of	of	ADP
ejpam-4470	44	6	double	double	ADJ
ejpam-4470	44	7	fuzzy	fuzzy	ADJ
ejpam-4470	44	8	convolution	convolution	NOUN
ejpam-4470	44	9	.	.	PUNCT
ejpam-4470	45	1	later	later	ADV
ejpam-4470	45	2	we	we	PRON
ejpam-4470	45	3	construct	construct	VERB
ejpam-4470	45	4	in	in	ADP
ejpam-4470	45	5	detail	detail	NOUN
ejpam-4470	45	6	procedure	procedure	NOUN
ejpam-4470	45	7	for	for	ADP
ejpam-4470	45	8	solving	solve	VERB
ejpam-4470	45	9	two	two	NUM
ejpam-4470	45	10	-	-	PUNCT
ejpam-4470	45	11	dimensional	dimensional	ADJ
ejpam-4470	45	12	fuzzy	fuzzy	ADJ
ejpam-4470	45	13	convolution	convolution	NOUN
ejpam-4470	45	14	volterra	volterra	NOUN
ejpam-4470	45	15	integral	integral	ADJ
ejpam-4470	45	16	equation	equation	NOUN
ejpam-4470	45	17	using	use	VERB
ejpam-4470	45	18	dfst	dfst	NOUN
ejpam-4470	45	19	with	with	ADP
ejpam-4470	45	20	adm	adm	PROPN
ejpam-4470	45	21	.	.	PUNCT
ejpam-4470	46	1	numerical	numerical	PROPN
ejpam-4470	46	2	example	example	NOUN
ejpam-4470	46	3	is	be	AUX
ejpam-4470	46	4	provided	provide	VERB
ejpam-4470	46	5	to	to	PART
ejpam-4470	46	6	demonstrate	demonstrate	VERB
ejpam-4470	46	7	the	the	DET
ejpam-4470	46	8	proposed	propose	VERB
ejpam-4470	46	9	method	method	NOUN
ejpam-4470	46	10	.	.	PUNCT
ejpam-4470	47	1	2	2	X
ejpam-4470	47	2	.	.	NUM
ejpam-4470	47	3	basic	basic	ADJ
ejpam-4470	47	4	preliminaries	preliminary	NOUN
ejpam-4470	47	5	definition	definition	NOUN
ejpam-4470	47	6	1	1	NUM
ejpam-4470	47	7	.	.	PUNCT
ejpam-4470	48	1	[	[	X
ejpam-4470	48	2	31]a	31]a	NUM
ejpam-4470	48	3	fuzzy	fuzzy	ADJ
ejpam-4470	48	4	number	number	NOUN
ejpam-4470	48	5	is	be	AUX
ejpam-4470	48	6	a	a	DET
ejpam-4470	48	7	function	function	NOUN
ejpam-4470	48	8	u	u	NOUN
ejpam-4470	48	9	:	:	PUNCT
ejpam-4470	48	10	r	r	NOUN
ejpam-4470	48	11	→	→	SYM
ejpam-4470	48	12	[	[	X
ejpam-4470	48	13	0	0	NUM
ejpam-4470	48	14	,	,	PUNCT
ejpam-4470	48	15	1	1	NUM
ejpam-4470	48	16	]	]	PUNCT
ejpam-4470	48	17	satisfying	satisfy	VERB
ejpam-4470	48	18	the	the	DET
ejpam-4470	48	19	following	follow	VERB
ejpam-4470	48	20	properties	property	NOUN
ejpam-4470	48	21	:	:	PUNCT
ejpam-4470	48	22	(	(	PUNCT
ejpam-4470	48	23	i	i	NOUN
ejpam-4470	48	24	)	)	PUNCT
ejpam-4470	48	25	u	u	NOUN
ejpam-4470	48	26	is	be	AUX
ejpam-4470	48	27	upper	upper	ADJ
ejpam-4470	48	28	semi	semi	ADJ
ejpam-4470	48	29	-	-	ADJ
ejpam-4470	48	30	continuous	continuous	ADJ
ejpam-4470	48	31	on	on	ADP
ejpam-4470	48	32	r	r	NOUN
ejpam-4470	48	33	,	,	PUNCT
ejpam-4470	48	34	a.	a.	NOUN
ejpam-4470	48	35	f.alidema	f.alidema	PROPN
ejpam-4470	48	36	/	/	SYM
ejpam-4470	48	37	eur	eur	PROPN
ejpam-4470	48	38	.	.	PUNCT
ejpam-4470	49	1	j.	j.	PROPN
ejpam-4470	49	2	pure	pure	PROPN
ejpam-4470	49	3	appl	appl	PROPN
ejpam-4470	49	4	.	.	PROPN
ejpam-4470	49	5	math	math	PROPN
ejpam-4470	49	6	,	,	PUNCT
ejpam-4470	49	7	15	15	NUM
ejpam-4470	49	8	(	(	PUNCT
ejpam-4470	49	9	3	3	NUM
ejpam-4470	49	10	)	)	PUNCT
ejpam-4470	49	11	(	(	PUNCT
ejpam-4470	49	12	2022	2022	NUM
ejpam-4470	49	13	)	)	PUNCT
ejpam-4470	49	14	,	,	PUNCT
ejpam-4470	49	15	1363	1363	NUM
ejpam-4470	49	16	-	-	SYM
ejpam-4470	49	17	1375	1375	NUM
ejpam-4470	49	18	1365	1365	NUM
ejpam-4470	49	19	(	(	PUNCT
ejpam-4470	49	20	ii	ii	NOUN
ejpam-4470	49	21	)	)	PUNCT
ejpam-4470	49	22	u(x	u(x	PROPN
ejpam-4470	49	23	)	)	PUNCT
ejpam-4470	49	24	=	=	SYM
ejpam-4470	49	25	0	0	NUM
ejpam-4470	50	1	outside	outside	ADP
ejpam-4470	50	2	of	of	ADP
ejpam-4470	50	3	some	some	DET
ejpam-4470	50	4	interval	interval	NOUN
ejpam-4470	50	5	[	[	X
ejpam-4470	50	6	c	c	X
ejpam-4470	50	7	,	,	PUNCT
ejpam-4470	50	8	d	d	X
ejpam-4470	50	9	]	]	X
ejpam-4470	50	10	,	,	PUNCT
ejpam-4470	50	11	(	(	PUNCT
ejpam-4470	50	12	iii	iii	X
ejpam-4470	50	13	)	)	PUNCT
ejpam-4470	50	14	there	there	PRON
ejpam-4470	50	15	are	be	VERB
ejpam-4470	50	16	the	the	DET
ejpam-4470	50	17	real	real	ADJ
ejpam-4470	50	18	numbers	number	NOUN
ejpam-4470	50	19	a	a	PRON
ejpam-4470	50	20	and	and	CCONJ
ejpam-4470	50	21	b	b	NOUN
ejpam-4470	50	22	with	with	ADP
ejpam-4470	50	23	c	c	NOUN
ejpam-4470	50	24	≤	≤	NOUN
ejpam-4470	50	25	a	a	DET
ejpam-4470	50	26	≤	≤	NUM
ejpam-4470	50	27	b	b	NOUN
ejpam-4470	50	28	≤	≤	NUM
ejpam-4470	50	29	d	d	NOUN
ejpam-4470	50	30	,	,	PUNCT
ejpam-4470	50	31	such	such	ADJ
ejpam-4470	50	32	that	that	SCONJ
ejpam-4470	50	33	u	u	PROPN
ejpam-4470	50	34	is	be	AUX
ejpam-4470	50	35	increasing	increase	VERB
ejpam-4470	50	36	on	on	ADP
ejpam-4470	50	37	[	[	X
ejpam-4470	50	38	c	c	X
ejpam-4470	50	39	,	,	PUNCT
ejpam-4470	50	40	a	a	PRON
ejpam-4470	50	41	]	]	X
ejpam-4470	50	42	,	,	PUNCT
ejpam-4470	50	43	decreasing	decrease	VERB
ejpam-4470	50	44	on	on	ADP
ejpam-4470	50	45	[	[	X
ejpam-4470	50	46	b	b	X
ejpam-4470	50	47	,	,	PUNCT
ejpam-4470	50	48	d	d	X
ejpam-4470	50	49	]	]	X
ejpam-4470	50	50	and	and	CCONJ
ejpam-4470	50	51	u(x	u(x	PROPN
ejpam-4470	50	52	)	)	PUNCT
ejpam-4470	50	53	=	=	SYM
ejpam-4470	50	54	1	1	NUM
ejpam-4470	50	55	for	for	ADP
ejpam-4470	50	56	each	each	DET
ejpam-4470	50	57	x	x	SYM
ejpam-4470	50	58	∈	∈	PROPN
ejpam-4470	51	1	[	[	X
ejpam-4470	51	2	a	a	X
ejpam-4470	51	3	,	,	PUNCT
ejpam-4470	51	4	b	b	NOUN
ejpam-4470	51	5	]	]	X
ejpam-4470	51	6	,	,	PUNCT
ejpam-4470	51	7	(	(	PUNCT
ejpam-4470	51	8	iv	iv	X
ejpam-4470	51	9	)	)	PUNCT
ejpam-4470	51	10	u	u	NOUN
ejpam-4470	51	11	is	be	AUX
ejpam-4470	51	12	fuzzy	fuzzy	ADJ
ejpam-4470	51	13	convex	convex	NOUN
ejpam-4470	51	14	set	set	VERB
ejpam-4470	51	15	i.	i.	PROPN
ejpam-4470	51	16	e.	e.	PROPN
ejpam-4470	52	1	that	that	PRON
ejpam-4470	52	2	is	be	AUX
ejpam-4470	52	3	u(λx+	u(λx+	ADJ
ejpam-4470	52	4	(	(	PUNCT
ejpam-4470	52	5	1−	1−	NUM
ejpam-4470	52	6	λ)y	λ)y	NOUN
ejpam-4470	52	7	)	)	PUNCT
ejpam-4470	52	8	≥	≥	NOUN
ejpam-4470	52	9	min{u(x	min{u(x	NOUN
ejpam-4470	52	10	)	)	PUNCT
ejpam-4470	52	11	,	,	PUNCT
ejpam-4470	52	12	u(y	u(y	NOUN
ejpam-4470	52	13	)	)	PUNCT
ejpam-4470	52	14	}	}	PUNCT
ejpam-4470	52	15	for	for	ADP
ejpam-4470	52	16	all	all	DET
ejpam-4470	52	17	x	x	NOUN
ejpam-4470	52	18	,	,	PUNCT
ejpam-4470	52	19	y	y	PROPN
ejpam-4470	52	20	∈	∈	PROPN
ejpam-4470	52	21	r	r	NOUN
ejpam-4470	52	22	and	and	CCONJ
ejpam-4470	52	23	λ	λ	X
ejpam-4470	52	24	∈	∈	PROPN
ejpam-4470	53	1	[	[	X
ejpam-4470	53	2	0	0	NUM
ejpam-4470	53	3	,	,	PUNCT
ejpam-4470	53	4	1	1	NUM
ejpam-4470	53	5	]	]	PUNCT
ejpam-4470	53	6	.	.	PUNCT
ejpam-4470	54	1	the	the	DET
ejpam-4470	54	2	set	set	NOUN
ejpam-4470	54	3	of	of	ADP
ejpam-4470	54	4	all	all	DET
ejpam-4470	54	5	fuzzy	fuzzy	ADJ
ejpam-4470	54	6	numbers	number	NOUN
ejpam-4470	54	7	is	be	AUX
ejpam-4470	54	8	denoted	denote	VERB
ejpam-4470	54	9	by	by	ADP
ejpam-4470	54	10	e1	e1	NOUN
ejpam-4470	54	11	.	.	PUNCT
ejpam-4470	55	1	any	any	DET
ejpam-4470	55	2	real	real	ADJ
ejpam-4470	55	3	number	number	NOUN
ejpam-4470	55	4	a	a	DET
ejpam-4470	55	5	∈	∈	NOUN
ejpam-4470	55	6	r	r	NOUN
ejpam-4470	55	7	can	can	AUX
ejpam-4470	55	8	be	be	AUX
ejpam-4470	55	9	interpreted	interpret	VERB
ejpam-4470	55	10	as	as	ADP
ejpam-4470	55	11	a	a	DET
ejpam-4470	55	12	fuzzy	fuzzy	ADJ
ejpam-4470	55	13	number	number	NOUN
ejpam-4470	55	14	ã	ã	PROPN
ejpam-4470	55	15	=	=	SYM
ejpam-4470	55	16	χ[a	χ[a	X
ejpam-4470	55	17	]	]	PUNCT
ejpam-4470	55	18	and	and	CCONJ
ejpam-4470	55	19	therefore	therefore	ADV
ejpam-4470	55	20	r	r	PROPN
ejpam-4470	55	21	⊂	⊂	PROPN
ejpam-4470	55	22	e1	e1	PROPN
ejpam-4470	55	23	.	.	PUNCT
ejpam-4470	56	1	according	accord	VERB
ejpam-4470	56	2	to	to	ADP
ejpam-4470	56	3	[	[	X
ejpam-4470	56	4	32	32	NUM
ejpam-4470	56	5	]	]	PUNCT
ejpam-4470	56	6	for	for	ADP
ejpam-4470	56	7	any	any	DET
ejpam-4470	56	8	0	0	PUNCT
ejpam-4470	56	9	<	<	X
ejpam-4470	56	10	r	r	NOUN
ejpam-4470	56	11	≤	≤	NUM
ejpam-4470	56	12	1	1	NUM
ejpam-4470	56	13	we	we	PRON
ejpam-4470	56	14	denote	denote	VERB
ejpam-4470	56	15	the	the	DET
ejpam-4470	56	16	r−level	r−level	NOUN
ejpam-4470	56	17	set	set	VERB
ejpam-4470	56	18	[	[	X
ejpam-4470	56	19	u]r	u]r	X
ejpam-4470	56	20	=	=	SYM
ejpam-4470	56	21	{	{	PUNCT
ejpam-4470	56	22	x	x	PUNCT
ejpam-4470	56	23	∈	∈	PROPN
ejpam-4470	56	24	r	r	NOUN
ejpam-4470	56	25	:	:	PUNCT
ejpam-4470	56	26	u(x	u(x	PROPN
ejpam-4470	56	27	)	)	PUNCT
ejpam-4470	56	28	≥	≥	NOUN
ejpam-4470	56	29	r	r	NOUN
ejpam-4470	56	30	}	}	PUNCT
ejpam-4470	56	31	that	that	PRON
ejpam-4470	56	32	is	be	AUX
ejpam-4470	56	33	a	a	DET
ejpam-4470	56	34	closed	closed	ADJ
ejpam-4470	56	35	interval	interval	NOUN
ejpam-4470	56	36	and	and	CCONJ
ejpam-4470	56	37	[	[	X
ejpam-4470	56	38	u]r	u]r	X
ejpam-4470	56	39	=	=	X
ejpam-4470	57	1	[	[	X
ejpam-4470	57	2	ur−	ur−	PROPN
ejpam-4470	57	3	,	,	PUNCT
ejpam-4470	57	4	u	u	NOUN
ejpam-4470	57	5	r	r	NOUN
ejpam-4470	57	6	+	+	NOUN
ejpam-4470	57	7	]	]	X
ejpam-4470	57	8	for	for	ADP
ejpam-4470	57	9	all	all	DET
ejpam-4470	57	10	r	r	NOUN
ejpam-4470	57	11	∈	∈	PROPN
ejpam-4470	58	1	[	[	X
ejpam-4470	58	2	0	0	NUM
ejpam-4470	58	3	,	,	PUNCT
ejpam-4470	58	4	1	1	NUM
ejpam-4470	58	5	]	]	PUNCT
ejpam-4470	58	6	.	.	PUNCT
ejpam-4470	59	1	these	these	PRON
ejpam-4470	59	2	lead	lead	VERB
ejpam-4470	59	3	to	to	ADP
ejpam-4470	59	4	the	the	DET
ejpam-4470	59	5	usual	usual	ADJ
ejpam-4470	59	6	parametric	parametric	ADJ
ejpam-4470	59	7	representation	representation	NOUN
ejpam-4470	59	8	of	of	ADP
ejpam-4470	59	9	a	a	DET
ejpam-4470	59	10	fuzzy	fuzzy	ADJ
ejpam-4470	59	11	number	number	NOUN
ejpam-4470	59	12	,	,	PUNCT
ejpam-4470	59	13	by	by	ADP
ejpam-4470	59	14	an	an	DET
ejpam-4470	59	15	ordered	order	VERB
ejpam-4470	59	16	pair	pair	NOUN
ejpam-4470	59	17	of	of	ADP
ejpam-4470	59	18	functions	function	NOUN
ejpam-4470	59	19	(	(	PUNCT
ejpam-4470	59	20	ur−	ur−	NUM
ejpam-4470	59	21	,	,	PUNCT
ejpam-4470	59	22	u	u	NOUN
ejpam-4470	59	23	r	r	NOUN
ejpam-4470	59	24	+	+	NOUN
ejpam-4470	59	25	)	)	PUNCT
ejpam-4470	59	26	,	,	PUNCT
ejpam-4470	59	27	which	which	PRON
ejpam-4470	59	28	satisfies	satisfy	VERB
ejpam-4470	59	29	the	the	DET
ejpam-4470	59	30	following	follow	VERB
ejpam-4470	59	31	properties	property	NOUN
ejpam-4470	59	32	:	:	PUNCT
ejpam-4470	59	33	ur−	ur−	NUM
ejpam-4470	59	34	is	be	AUX
ejpam-4470	59	35	bounded	bound	VERB
ejpam-4470	59	36	left	leave	VERB
ejpam-4470	59	37	continuous	continuous	ADJ
ejpam-4470	59	38	non	non	ADJ
ejpam-4470	59	39	-	-	ADJ
ejpam-4470	59	40	decreasing	decrease	VERB
ejpam-4470	59	41	function	function	NOUN
ejpam-4470	59	42	over	over	ADP
ejpam-4470	59	43	[	[	X
ejpam-4470	59	44	0	0	NUM
ejpam-4470	59	45	,	,	PUNCT
ejpam-4470	59	46	1	1	NUM
ejpam-4470	59	47	]	]	PUNCT
ejpam-4470	59	48	,	,	PUNCT
ejpam-4470	59	49	ur+	ur+	PROPN
ejpam-4470	59	50	is	be	AUX
ejpam-4470	59	51	bounded	bound	VERB
ejpam-4470	59	52	left	leave	VERB
ejpam-4470	59	53	continuous	continuous	ADJ
ejpam-4470	59	54	non	non	ADJ
ejpam-4470	59	55	-	-	ADJ
ejpam-4470	59	56	increasing	increase	VERB
ejpam-4470	59	57	function	function	NOUN
ejpam-4470	59	58	over	over	ADP
ejpam-4470	59	59	[	[	X
ejpam-4470	59	60	0	0	NUM
ejpam-4470	59	61	,	,	PUNCT
ejpam-4470	59	62	1	1	NUM
ejpam-4470	59	63	]	]	PUNCT
ejpam-4470	59	64	and	and	CCONJ
ejpam-4470	59	65	ur−	ur−	PUNCT
ejpam-4470	59	66	<	<	X
ejpam-4470	59	67	ur+	ur+	NOUN
ejpam-4470	59	68	.	.	PUNCT
ejpam-4470	60	1	for	for	ADP
ejpam-4470	60	2	u	u	NOUN
ejpam-4470	60	3	,	,	PUNCT
ejpam-4470	60	4	v	v	PROPN
ejpam-4470	60	5	∈	∈	PROPN
ejpam-4470	60	6	e1	e1	NOUN
ejpam-4470	60	7	,	,	PUNCT
ejpam-4470	60	8	k	k	PROPN
ejpam-4470	60	9	∈	∈	PROPN
ejpam-4470	60	10	r	r	NOUN
ejpam-4470	60	11	,	,	PUNCT
ejpam-4470	60	12	the	the	DET
ejpam-4470	60	13	addition	addition	NOUN
ejpam-4470	60	14	and	and	CCONJ
ejpam-4470	60	15	the	the	DET
ejpam-4470	60	16	scalar	scalar	ADJ
ejpam-4470	60	17	multiplication	multiplication	NOUN
ejpam-4470	60	18	are	be	AUX
ejpam-4470	60	19	defined	define	VERB
ejpam-4470	60	20	by	by	ADP
ejpam-4470	60	21	[	[	X
ejpam-4470	60	22	u⊕	u⊕	X
ejpam-4470	60	23	v]r	v]r	NOUN
ejpam-4470	60	24	=	=	PUNCT
ejpam-4470	61	1	[	[	X
ejpam-4470	61	2	u]r+[v]r	u]r+[v]r	X
ejpam-4470	61	3	=	=	PUNCT
ejpam-4470	62	1	[	[	X
ejpam-4470	62	2	ur−+vr−	ur−+vr−	PROPN
ejpam-4470	62	3	,	,	PUNCT
ejpam-4470	62	4	u	u	NOUN
ejpam-4470	62	5	r	r	NOUN
ejpam-4470	62	6	+	+	PROPN
ejpam-4470	62	7	+	+	PROPN
ejpam-4470	62	8	vr+	vr+	NOUN
ejpam-4470	62	9	]	]	PUNCT
ejpam-4470	62	10	and	and	CCONJ
ejpam-4470	62	11	[	[	X
ejpam-4470	62	12	k	k	X
ejpam-4470	62	13	⊙	⊙	PROPN
ejpam-4470	62	14	u]r	u]r	PROPN
ejpam-4470	63	1	=	=	PUNCT
ejpam-4470	63	2	k.[u]r	k.[u]r	PROPN
ejpam-4470	63	3	=	=	PUNCT
ejpam-4470	63	4	{	{	PUNCT
ejpam-4470	64	1	[	[	X
ejpam-4470	64	2	kur−	kur−	PROPN
ejpam-4470	64	3	,	,	PUNCT
ejpam-4470	64	4	ku	ku	NOUN
ejpam-4470	64	5	r	r	NOUN
ejpam-4470	64	6	+	+	PROPN
ejpam-4470	64	7	]	]	X
ejpam-4470	64	8	,	,	PUNCT
ejpam-4470	64	9	if	if	SCONJ
ejpam-4470	64	10	k	k	PROPN
ejpam-4470	64	11	≥	≥	VERB
ejpam-4470	64	12	0	0	PUNCT
ejpam-4470	65	1	[	[	X
ejpam-4470	65	2	kur+	kur+	PROPN
ejpam-4470	65	3	,	,	PUNCT
ejpam-4470	65	4	ku	ku	PROPN
ejpam-4470	65	5	r	r	NOUN
ejpam-4470	65	6	−	−	PROPN
ejpam-4470	65	7	]	]	PUNCT
ejpam-4470	65	8	,	,	PUNCT
ejpam-4470	65	9	if	if	SCONJ
ejpam-4470	65	10	k	k	PROPN
ejpam-4470	65	11	<	<	X
ejpam-4470	65	12	0	0	PUNCT
ejpam-4470	65	13	for	for	ADP
ejpam-4470	65	14	all	all	DET
ejpam-4470	65	15	r	r	NOUN
ejpam-4470	65	16	∈	∈	PROPN
ejpam-4470	66	1	[	[	X
ejpam-4470	66	2	0	0	NUM
ejpam-4470	66	3	,	,	PUNCT
ejpam-4470	66	4	1	1	NUM
ejpam-4470	66	5	]	]	PUNCT
ejpam-4470	66	6	.	.	PUNCT
ejpam-4470	67	1	the	the	DET
ejpam-4470	67	2	neutral	neutral	ADJ
ejpam-4470	67	3	element	element	NOUN
ejpam-4470	67	4	respect	respect	NOUN
ejpam-4470	67	5	to	to	ADP
ejpam-4470	67	6	⊕	⊕	PROPN
ejpam-4470	67	7	in	in	ADP
ejpam-4470	67	8	e1	e1	PROPN
ejpam-4470	67	9	,	,	PUNCT
ejpam-4470	67	10	denoted	denote	VERB
ejpam-4470	67	11	by	by	ADP
ejpam-4470	67	12	0̃	0̃	NOUN
ejpam-4470	67	13	=	=	SYM
ejpam-4470	67	14	χ[0	χ[0	NOUN
ejpam-4470	67	15	]	]	PUNCT
ejpam-4470	67	16	.	.	PUNCT
ejpam-4470	68	1	the	the	DET
ejpam-4470	68	2	algebraic	algebraic	ADJ
ejpam-4470	68	3	properties	property	NOUN
ejpam-4470	68	4	of	of	ADP
ejpam-4470	68	5	addition	addition	NOUN
ejpam-4470	68	6	and	and	CCONJ
ejpam-4470	68	7	scalar	scalar	ADJ
ejpam-4470	68	8	multiplication	multiplication	NOUN
ejpam-4470	68	9	of	of	ADP
ejpam-4470	68	10	fuzzy	fuzzy	ADJ
ejpam-4470	68	11	numbers	number	NOUN
ejpam-4470	68	12	are	be	AUX
ejpam-4470	68	13	given	give	VERB
ejpam-4470	68	14	in	in	ADP
ejpam-4470	68	15	[	[	X
ejpam-4470	68	16	32	32	NUM
ejpam-4470	68	17	]	]	PUNCT
ejpam-4470	68	18	.	.	PUNCT
ejpam-4470	69	1	as	as	ADP
ejpam-4470	69	2	a	a	DET
ejpam-4470	69	3	distance	distance	NOUN
ejpam-4470	69	4	between	between	ADP
ejpam-4470	69	5	fuzzy	fuzzy	ADJ
ejpam-4470	69	6	numbers	number	NOUN
ejpam-4470	69	7	we	we	PRON
ejpam-4470	69	8	use	use	VERB
ejpam-4470	69	9	the	the	DET
ejpam-4470	69	10	hausdorff	hausdorff	NOUN
ejpam-4470	69	11	metric	metric	NOUN
ejpam-4470	69	12	[	[	X
ejpam-4470	69	13	32	32	NUM
ejpam-4470	69	14	]	]	PUNCT
ejpam-4470	69	15	defined	define	VERB
ejpam-4470	69	16	by	by	ADP
ejpam-4470	69	17	d(u	d(u	PROPN
ejpam-4470	69	18	,	,	PUNCT
ejpam-4470	69	19	v	v	NOUN
ejpam-4470	69	20	)	)	PUNCT
ejpam-4470	69	21	=	=	SYM
ejpam-4470	69	22	sup	sup	NOUN
ejpam-4470	69	23	r∈[0,1	r∈[0,1	NUM
ejpam-4470	69	24	]	]	PUNCT
ejpam-4470	69	25	max{|ur−	max{|ur−	NOUN
ejpam-4470	69	26	−	−	NOUN
ejpam-4470	69	27	vr−|	vr−|	PROPN
ejpam-4470	69	28	,	,	PUNCT
ejpam-4470	69	29	|ur+	|ur+	NOUN
ejpam-4470	69	30	−	−	NOUN
ejpam-4470	69	31	vr+|	vr+|	VERB
ejpam-4470	69	32	}	}	PUNCT
ejpam-4470	69	33	for	for	ADP
ejpam-4470	69	34	any	any	DET
ejpam-4470	69	35	u	u	NOUN
ejpam-4470	69	36	,	,	PUNCT
ejpam-4470	69	37	v	v	PROPN
ejpam-4470	69	38	∈	∈	PROPN
ejpam-4470	69	39	e1	e1	NOUN
ejpam-4470	69	40	.	.	PUNCT
ejpam-4470	70	1	the	the	DET
ejpam-4470	70	2	metric	metric	ADJ
ejpam-4470	70	3	space	space	NOUN
ejpam-4470	70	4	(	(	PUNCT
ejpam-4470	70	5	e1	e1	NOUN
ejpam-4470	70	6	,	,	PUNCT
ejpam-4470	70	7	d	d	NOUN
ejpam-4470	70	8	)	)	PUNCT
ejpam-4470	70	9	is	be	AUX
ejpam-4470	70	10	complete	complete	ADJ
ejpam-4470	70	11	,	,	PUNCT
ejpam-4470	70	12	separable	separable	ADJ
ejpam-4470	70	13	and	and	CCONJ
ejpam-4470	70	14	local	local	ADJ
ejpam-4470	70	15	compact	compact	NOUN
ejpam-4470	70	16	.	.	PUNCT
ejpam-4470	71	1	lemma	lemma	PROPN
ejpam-4470	71	2	1	1	NUM
ejpam-4470	71	3	.	.	PUNCT
ejpam-4470	72	1	[	[	X
ejpam-4470	72	2	32	32	NUM
ejpam-4470	72	3	]	]	PUNCT
ejpam-4470	72	4	the	the	DET
ejpam-4470	72	5	hausdorff	hausdorff	PROPN
ejpam-4470	72	6	metric	metric	NOUN
ejpam-4470	72	7	has	have	VERB
ejpam-4470	72	8	the	the	DET
ejpam-4470	72	9	following	follow	VERB
ejpam-4470	72	10	properties	property	NOUN
ejpam-4470	72	11	:	:	PUNCT
ejpam-4470	72	12	(	(	PUNCT
ejpam-4470	72	13	i	i	NOUN
ejpam-4470	72	14	)	)	PUNCT
ejpam-4470	72	15	d(u⊕	d(u⊕	PROPN
ejpam-4470	72	16	w	w	PROPN
ejpam-4470	72	17	,	,	PUNCT
ejpam-4470	72	18	v	v	PROPN
ejpam-4470	72	19	⊕	⊕	PROPN
ejpam-4470	72	20	w	w	PROPN
ejpam-4470	72	21	)	)	PUNCT
ejpam-4470	72	22	=	=	SYM
ejpam-4470	73	1	d(u	d(u	PROPN
ejpam-4470	73	2	,	,	PUNCT
ejpam-4470	73	3	v	v	NOUN
ejpam-4470	73	4	)	)	PUNCT
ejpam-4470	73	5	for	for	ADP
ejpam-4470	73	6	all	all	DET
ejpam-4470	73	7	u	u	NOUN
ejpam-4470	73	8	,	,	PUNCT
ejpam-4470	73	9	v	v	NOUN
ejpam-4470	73	10	,	,	PUNCT
ejpam-4470	73	11	w	w	PROPN
ejpam-4470	73	12	∈	∈	PROPN
ejpam-4470	73	13	e1	e1	NOUN
ejpam-4470	73	14	,	,	PUNCT
ejpam-4470	73	15	(	(	PUNCT
ejpam-4470	73	16	ii	ii	NOUN
ejpam-4470	73	17	)	)	PUNCT
ejpam-4470	73	18	d(u⊕	d(u⊕	PROPN
ejpam-4470	73	19	v	v	PROPN
ejpam-4470	73	20	,	,	PUNCT
ejpam-4470	73	21	w	w	PROPN
ejpam-4470	73	22	⊕	⊕	PROPN
ejpam-4470	73	23	e	e	NOUN
ejpam-4470	73	24	)	)	PUNCT
ejpam-4470	73	25	≤	≤	PUNCT
ejpam-4470	74	1	d(u	d(u	PROPN
ejpam-4470	74	2	,	,	PUNCT
ejpam-4470	74	3	w	w	NOUN
ejpam-4470	74	4	)	)	PUNCT
ejpam-4470	74	5	+	+	NOUN
ejpam-4470	74	6	d(v	d(v	ADJ
ejpam-4470	74	7	,	,	PUNCT
ejpam-4470	74	8	e	e	NOUN
ejpam-4470	74	9	)	)	PUNCT
ejpam-4470	74	10	for	for	ADP
ejpam-4470	74	11	all	all	DET
ejpam-4470	74	12	u	u	NOUN
ejpam-4470	74	13	,	,	PUNCT
ejpam-4470	74	14	v	v	NOUN
ejpam-4470	74	15	,	,	PUNCT
ejpam-4470	74	16	w	w	PROPN
ejpam-4470	74	17	,	,	PUNCT
ejpam-4470	74	18	e	e	PROPN
ejpam-4470	74	19	∈	∈	PROPN
ejpam-4470	74	20	e1	e1	PROPN
ejpam-4470	74	21	,	,	PUNCT
ejpam-4470	74	22	(	(	PUNCT
ejpam-4470	74	23	iii	iii	NOUN
ejpam-4470	74	24	)	)	PUNCT
ejpam-4470	74	25	d(u⊕	d(u⊕	PROPN
ejpam-4470	74	26	v	v	NOUN
ejpam-4470	74	27	,	,	PUNCT
ejpam-4470	74	28	0̃	0̃	NOUN
ejpam-4470	74	29	)	)	PUNCT
ejpam-4470	74	30	≤	≤	PUNCT
ejpam-4470	75	1	d(u	d(u	PROPN
ejpam-4470	75	2	,	,	PUNCT
ejpam-4470	75	3	0̃	0̃	PROPN
ejpam-4470	75	4	)	)	PUNCT
ejpam-4470	76	1	+	+	NOUN
ejpam-4470	76	2	d(v	d(v	ADJ
ejpam-4470	76	3	,	,	PUNCT
ejpam-4470	76	4	0̃	0̃	NOUN
ejpam-4470	76	5	)	)	PUNCT
ejpam-4470	76	6	for	for	ADP
ejpam-4470	76	7	all	all	DET
ejpam-4470	76	8	u	u	NOUN
ejpam-4470	76	9	,	,	PUNCT
ejpam-4470	76	10	v	v	PROPN
ejpam-4470	76	11	∈	∈	PROPN
ejpam-4470	76	12	e1	e1	NOUN
ejpam-4470	76	13	,	,	PUNCT
ejpam-4470	76	14	(	(	PUNCT
ejpam-4470	76	15	iv	iv	X
ejpam-4470	76	16	)	)	PUNCT
ejpam-4470	76	17	d(λ⊙	d(λ⊙	PROPN
ejpam-4470	76	18	u	u	PROPN
ejpam-4470	76	19	,	,	PUNCT
ejpam-4470	76	20	λ⊙	λ⊙	NOUN
ejpam-4470	76	21	v	v	NOUN
ejpam-4470	76	22	)	)	PUNCT
ejpam-4470	77	1	=	=	SYM
ejpam-4470	77	2	|k|d(u	|k|d(u	PROPN
ejpam-4470	77	3	,	,	PUNCT
ejpam-4470	77	4	v	v	NOUN
ejpam-4470	77	5	)	)	PUNCT
ejpam-4470	77	6	for	for	ADP
ejpam-4470	77	7	all	all	DET
ejpam-4470	77	8	u	u	NOUN
ejpam-4470	77	9	,	,	PUNCT
ejpam-4470	77	10	v	v	PROPN
ejpam-4470	77	11	∈	∈	PROPN
ejpam-4470	77	12	e1	e1	NOUN
ejpam-4470	77	13	,	,	PUNCT
ejpam-4470	77	14	for	for	ADP
ejpam-4470	77	15	allλ	allλ	PROPN
ejpam-4470	77	16	∈	∈	PROPN
ejpam-4470	77	17	r	r	NOUN
ejpam-4470	77	18	,	,	PUNCT
ejpam-4470	77	19	(	(	PUNCT
ejpam-4470	77	20	vi	vi	NOUN
ejpam-4470	77	21	)	)	PUNCT
ejpam-4470	77	22	d(λ1	d(λ1	NOUN
ejpam-4470	77	23	⊙	⊙	PROPN
ejpam-4470	77	24	u	u	PROPN
ejpam-4470	77	25	,	,	PUNCT
ejpam-4470	77	26	λ2	λ2	PROPN
ejpam-4470	77	27	⊙	⊙	NOUN
ejpam-4470	77	28	u	u	NOUN
ejpam-4470	77	29	)	)	PUNCT
ejpam-4470	77	30	=	=	SYM
ejpam-4470	77	31	|λ1	|λ1	NOUN
ejpam-4470	78	1	−	−	PROPN
ejpam-4470	78	2	λ2|d(u	λ2|d(u	PROPN
ejpam-4470	78	3	,	,	PUNCT
ejpam-4470	78	4	0̃	0̃	NOUN
ejpam-4470	78	5	)	)	PUNCT
ejpam-4470	78	6	for	for	ADP
ejpam-4470	78	7	all	all	DET
ejpam-4470	78	8	λ1	λ1	ADJ
ejpam-4470	78	9	,	,	PUNCT
ejpam-4470	78	10	λ2	λ2	PROPN
ejpam-4470	78	11	∈	∈	PROPN
ejpam-4470	78	12	e1	e1	NOUN
ejpam-4470	78	13	,	,	PUNCT
ejpam-4470	78	14	with	with	ADP
ejpam-4470	78	15	λ1	λ1	ADJ
ejpam-4470	78	16	,	,	PUNCT
ejpam-4470	78	17	λ2	λ2	PROPN
ejpam-4470	78	18	≥	≥	NOUN
ejpam-4470	78	19	0	0	NUM
ejpam-4470	78	20	and	and	CCONJ
ejpam-4470	78	21	for	for	ADP
ejpam-4470	78	22	all	all	DET
ejpam-4470	78	23	u	u	PROPN
ejpam-4470	78	24	∈	∈	PROPN
ejpam-4470	78	25	e1	e1	NOUN
ejpam-4470	78	26	.	.	PUNCT
ejpam-4470	79	1	for	for	ADP
ejpam-4470	79	2	any	any	DET
ejpam-4470	79	3	two	two	NUM
ejpam-4470	79	4	-	-	PUNCT
ejpam-4470	79	5	variable	variable	NOUN
ejpam-4470	79	6	fuzzy	fuzzy	ADV
ejpam-4470	79	7	-	-	PUNCT
ejpam-4470	79	8	valued	value	VERB
ejpam-4470	79	9	function	function	NOUN
ejpam-4470	79	10	f	f	NOUN
ejpam-4470	79	11	:	:	PUNCT
ejpam-4470	79	12	r2	r2	PROPN
ejpam-4470	79	13	+	+	CCONJ
ejpam-4470	79	14	→	→	PUNCT
ejpam-4470	79	15	e1	e1	NOUN
ejpam-4470	79	16	we	we	PRON
ejpam-4470	79	17	can	can	AUX
ejpam-4470	79	18	define	define	VERB
ejpam-4470	79	19	the	the	DET
ejpam-4470	79	20	functions	function	NOUN
ejpam-4470	79	21	f	f	X
ejpam-4470	79	22	(	(	PUNCT
ejpam-4470	79	23	.	.	PUNCT
ejpam-4470	79	24	,	,	PUNCT
ejpam-4470	79	25	.	.	PUNCT
ejpam-4470	79	26	,	,	PUNCT
ejpam-4470	80	1	r	r	NOUN
ejpam-4470	80	2	)	)	PUNCT
ejpam-4470	80	3	,	,	PUNCT
ejpam-4470	80	4	f	f	X
ejpam-4470	80	5	(	(	PUNCT
ejpam-4470	80	6	.	.	PUNCT
ejpam-4470	80	7	,	,	PUNCT
ejpam-4470	80	8	.	.	PUNCT
ejpam-4470	80	9	,	,	PUNCT
ejpam-4470	80	10	r	r	NOUN
ejpam-4470	80	11	)	)	PUNCT
ejpam-4470	80	12	:	:	PUNCT
ejpam-4470	80	13	r2	r2	PROPN
ejpam-4470	80	14	+	+	CCONJ
ejpam-4470	80	15	→	→	PUNCT
ejpam-4470	80	16	r.	r.	NOUN
ejpam-4470	80	17	these	these	DET
ejpam-4470	80	18	functions	function	NOUN
ejpam-4470	80	19	are	be	AUX
ejpam-4470	80	20	called	call	VERB
ejpam-4470	80	21	the	the	DET
ejpam-4470	80	22	left	left	ADJ
ejpam-4470	80	23	and	and	CCONJ
ejpam-4470	80	24	right	right	ADJ
ejpam-4470	80	25	r−level	r−level	VERB
ejpam-4470	80	26	functions	function	NOUN
ejpam-4470	80	27	of	of	ADP
ejpam-4470	80	28	f.	f.	PROPN
ejpam-4470	80	29	a.	a.	PROPN
ejpam-4470	80	30	f.alidema	f.alidema	PROPN
ejpam-4470	80	31	/	/	SYM
ejpam-4470	80	32	eur	eur	PROPN
ejpam-4470	80	33	.	.	PUNCT
ejpam-4470	81	1	j.	j.	PROPN
ejpam-4470	81	2	pure	pure	PROPN
ejpam-4470	81	3	appl	appl	PROPN
ejpam-4470	81	4	.	.	PROPN
ejpam-4470	81	5	math	math	PROPN
ejpam-4470	81	6	,	,	PUNCT
ejpam-4470	81	7	15	15	NUM
ejpam-4470	81	8	(	(	PUNCT
ejpam-4470	81	9	3	3	NUM
ejpam-4470	81	10	)	)	PUNCT
ejpam-4470	81	11	(	(	PUNCT
ejpam-4470	81	12	2022	2022	NUM
ejpam-4470	81	13	)	)	PUNCT
ejpam-4470	81	14	,	,	PUNCT
ejpam-4470	81	15	1363	1363	NUM
ejpam-4470	81	16	-	-	SYM
ejpam-4470	81	17	1375	1375	NUM
ejpam-4470	81	18	1366	1366	NUM
ejpam-4470	81	19	definition	definition	NOUN
ejpam-4470	81	20	2	2	NUM
ejpam-4470	81	21	.	.	PUNCT
ejpam-4470	82	1	[	[	X
ejpam-4470	82	2	33	33	NUM
ejpam-4470	82	3	]	]	PUNCT
ejpam-4470	82	4	a	a	DET
ejpam-4470	82	5	fuzzy	fuzzy	ADJ
ejpam-4470	82	6	-	-	PUNCT
ejpam-4470	82	7	number	number	NOUN
ejpam-4470	82	8	-	-	PUNCT
ejpam-4470	82	9	valued	value	VERB
ejpam-4470	82	10	function	function	NOUN
ejpam-4470	82	11	f	f	NOUN
ejpam-4470	82	12	:	:	PUNCT
ejpam-4470	82	13	r×	r×	NOUN
ejpam-4470	82	14	r	r	NOUN
ejpam-4470	82	15	→	→	PUNCT
ejpam-4470	82	16	e1	e1	NOUN
ejpam-4470	82	17	is	be	AUX
ejpam-4470	82	18	said	say	VERB
ejpam-4470	82	19	to	to	PART
ejpam-4470	82	20	be	be	AUX
ejpam-4470	82	21	continuous	continuous	ADJ
ejpam-4470	82	22	at	at	ADP
ejpam-4470	82	23	(	(	PUNCT
ejpam-4470	82	24	s0	s0	PROPN
ejpam-4470	82	25	,	,	PUNCT
ejpam-4470	82	26	t0	t0	PROPN
ejpam-4470	82	27	)	)	PUNCT
ejpam-4470	82	28	∈	∈	PROPN
ejpam-4470	82	29	r×	r×	NOUN
ejpam-4470	82	30	r	r	NOUN
ejpam-4470	82	31	if	if	SCONJ
ejpam-4470	82	32	for	for	ADP
ejpam-4470	82	33	each	each	DET
ejpam-4470	82	34	ε	ε	PROPN
ejpam-4470	82	35	>	>	X
ejpam-4470	82	36	0	0	PUNCT
ejpam-4470	83	1	there	there	PRON
ejpam-4470	83	2	is	be	VERB
ejpam-4470	83	3	δ	δ	PROPN
ejpam-4470	83	4	>	>	X
ejpam-4470	83	5	0	0	NUM
ejpam-4470	83	6	such	such	ADJ
ejpam-4470	83	7	that	that	PRON
ejpam-4470	83	8	d(f(s	d(f(s	PROPN
ejpam-4470	83	9	,	,	PUNCT
ejpam-4470	83	10	t	t	PROPN
ejpam-4470	83	11	)	)	PUNCT
ejpam-4470	83	12	,	,	PUNCT
ejpam-4470	83	13	f(s0	f(s0	NOUN
ejpam-4470	83	14	,	,	PUNCT
ejpam-4470	83	15	t0	t0	PROPN
ejpam-4470	83	16	)	)	PUNCT
ejpam-4470	83	17	)	)	PUNCT
ejpam-4470	84	1	<	<	X
ejpam-4470	84	2	ε	ε	PROPN
ejpam-4470	84	3	whenever	whenever	SCONJ
ejpam-4470	84	4	(	(	PUNCT
ejpam-4470	84	5	(	(	PUNCT
ejpam-4470	84	6	s−	s−	PROPN
ejpam-4470	84	7	s0	s0	PROPN
ejpam-4470	84	8	)	)	PUNCT
ejpam-4470	84	9	2	2	NUM
ejpam-4470	84	10	+	+	CCONJ
ejpam-4470	84	11	(	(	PUNCT
ejpam-4470	84	12	t−	t−	PROPN
ejpam-4470	84	13	t0	t0	PROPN
ejpam-4470	84	14	)	)	PUNCT
ejpam-4470	84	15	2	2	NUM
ejpam-4470	84	16	)	)	PUNCT
ejpam-4470	84	17	1	1	NUM
ejpam-4470	84	18	2	2	NUM
ejpam-4470	84	19	<	<	X
ejpam-4470	84	20	δ	δ	PROPN
ejpam-4470	84	21	.	.	PUNCT
ejpam-4470	85	1	if	if	SCONJ
ejpam-4470	85	2	f	f	PRON
ejpam-4470	85	3	be	be	VERB
ejpam-4470	85	4	continuous	continuous	ADJ
ejpam-4470	85	5	for	for	ADP
ejpam-4470	85	6	each	each	PRON
ejpam-4470	85	7	(	(	PUNCT
ejpam-4470	85	8	s	s	PROPN
ejpam-4470	85	9	,	,	PUNCT
ejpam-4470	85	10	t	t	PROPN
ejpam-4470	85	11	)	)	PUNCT
ejpam-4470	85	12	∈	∈	PROPN
ejpam-4470	85	13	r	r	NOUN
ejpam-4470	85	14	×	×	NOUN
ejpam-4470	85	15	r	r	NOUN
ejpam-4470	85	16	then	then	ADV
ejpam-4470	85	17	we	we	PRON
ejpam-4470	85	18	say	say	VERB
ejpam-4470	85	19	that	that	SCONJ
ejpam-4470	85	20	f	f	PROPN
ejpam-4470	85	21	is	be	AUX
ejpam-4470	85	22	continuous	continuous	ADJ
ejpam-4470	85	23	on	on	ADP
ejpam-4470	85	24	r	r	PROPN
ejpam-4470	85	25	×	×	PROPN
ejpam-4470	85	26	r.	r.	NOUN
ejpam-4470	85	27	a	a	DET
ejpam-4470	85	28	fuzzy	fuzzy	ADJ
ejpam-4470	85	29	number	number	NOUN
ejpam-4470	85	30	u	u	PROPN
ejpam-4470	85	31	∈	∈	PROPN
ejpam-4470	85	32	e1	e1	NOUN
ejpam-4470	85	33	is	be	AUX
ejpam-4470	85	34	upper	upper	ADJ
ejpam-4470	85	35	bound	bind	VERB
ejpam-4470	85	36	for	for	ADP
ejpam-4470	85	37	a	a	DET
ejpam-4470	85	38	fuzzy	fuzzy	ADJ
ejpam-4470	85	39	-	-	PUNCT
ejpam-4470	85	40	number	number	NOUN
ejpam-4470	85	41	-	-	PUNCT
ejpam-4470	85	42	valued	value	VERB
ejpam-4470	85	43	function	function	NOUN
ejpam-4470	85	44	f	f	NOUN
ejpam-4470	85	45	:	:	PUNCT
ejpam-4470	85	46	r	r	NOUN
ejpam-4470	85	47	×	×	NOUN
ejpam-4470	85	48	r	r	NOUN
ejpam-4470	85	49	→	→	SYM
ejpam-4470	85	50	e1	e1	NOUN
ejpam-4470	85	51	if	if	SCONJ
ejpam-4470	85	52	f(s	f(	NOUN
ejpam-4470	85	53	,	,	PUNCT
ejpam-4470	85	54	t	t	PROPN
ejpam-4470	85	55	,	,	PUNCT
ejpam-4470	85	56	r)r	r)r	PUNCT
ejpam-4470	85	57	≤	≤	X
ejpam-4470	85	58	ur−	ur−	NUM
ejpam-4470	85	59	and	and	CCONJ
ejpam-4470	85	60	f(s	f(s	PROPN
ejpam-4470	85	61	,	,	PUNCT
ejpam-4470	85	62	t	t	PROPN
ejpam-4470	85	63	,	,	PUNCT
ejpam-4470	85	64	r	r	NOUN
ejpam-4470	85	65	)	)	PUNCT
ejpam-4470	85	66	≤	≤	NOUN
ejpam-4470	85	67	ur+	ur+	NOUN
ejpam-4470	85	68	for	for	ADP
ejpam-4470	85	69	all	all	DET
ejpam-4470	85	70	(	(	PUNCT
ejpam-4470	85	71	s	s	PROPN
ejpam-4470	85	72	,	,	PUNCT
ejpam-4470	85	73	t	t	PROPN
ejpam-4470	85	74	)	)	PUNCT
ejpam-4470	85	75	∈	∈	PROPN
ejpam-4470	85	76	r	r	NOUN
ejpam-4470	85	77	×	×	NOUN
ejpam-4470	85	78	r	r	NOUN
ejpam-4470	85	79	,	,	PUNCT
ejpam-4470	85	80	r	r	NOUN
ejpam-4470	85	81	∈	∈	PROPN
ejpam-4470	86	1	[	[	X
ejpam-4470	86	2	0	0	NUM
ejpam-4470	86	3	,	,	PUNCT
ejpam-4470	86	4	1	1	NUM
ejpam-4470	86	5	]	]	PUNCT
ejpam-4470	86	6	.	.	PUNCT
ejpam-4470	87	1	a	a	DET
ejpam-4470	87	2	fuzzy	fuzzy	ADJ
ejpam-4470	87	3	number	number	NOUN
ejpam-4470	87	4	u	u	PROPN
ejpam-4470	87	5	∈	∈	PROPN
ejpam-4470	87	6	e1	e1	NOUN
ejpam-4470	87	7	is	be	AUX
ejpam-4470	87	8	lower	low	ADJ
ejpam-4470	87	9	bound	bind	VERB
ejpam-4470	87	10	for	for	ADP
ejpam-4470	87	11	a	a	DET
ejpam-4470	87	12	fuzzy	fuzzy	ADJ
ejpam-4470	87	13	number	number	NOUN
ejpam-4470	87	14	-	-	PUNCT
ejpam-4470	87	15	valued	value	VERB
ejpam-4470	87	16	function	function	NOUN
ejpam-4470	88	1	f	f	NOUN
ejpam-4470	88	2	:	:	PUNCT
ejpam-4470	88	3	r	r	NOUN
ejpam-4470	88	4	×	×	NOUN
ejpam-4470	88	5	r	r	NOUN
ejpam-4470	88	6	→	→	SYM
ejpam-4470	88	7	e1	e1	NOUN
ejpam-4470	88	8	if	if	SCONJ
ejpam-4470	88	9	ur+	ur+	ADJ
ejpam-4470	88	10	≤	≤	PROPN
ejpam-4470	88	11	f(s	f(	VERB
ejpam-4470	88	12	,	,	PUNCT
ejpam-4470	88	13	t	t	PROPN
ejpam-4470	88	14	,	,	PUNCT
ejpam-4470	88	15	r	r	NOUN
ejpam-4470	88	16	)	)	PUNCT
ejpam-4470	88	17	and	and	CCONJ
ejpam-4470	88	18	ur−	ur−	SYM
ejpam-4470	88	19	≤	≤	NOUN
ejpam-4470	88	20	f(s	f(	NOUN
ejpam-4470	88	21	,	,	PUNCT
ejpam-4470	88	22	t	t	PROPN
ejpam-4470	88	23	,	,	PUNCT
ejpam-4470	88	24	r	r	NOUN
ejpam-4470	88	25	)	)	PUNCT
ejpam-4470	88	26	for	for	ADP
ejpam-4470	88	27	all	all	DET
ejpam-4470	88	28	(	(	PUNCT
ejpam-4470	88	29	s	s	PROPN
ejpam-4470	88	30	,	,	PUNCT
ejpam-4470	88	31	t	t	PROPN
ejpam-4470	88	32	)	)	PUNCT
ejpam-4470	88	33	∈	∈	PROPN
ejpam-4470	88	34	r	r	NOUN
ejpam-4470	88	35	×	×	NOUN
ejpam-4470	88	36	r	r	NOUN
ejpam-4470	88	37	,	,	PUNCT
ejpam-4470	88	38	r	r	NOUN
ejpam-4470	88	39	∈	∈	PROPN
ejpam-4470	89	1	[	[	X
ejpam-4470	89	2	0	0	NUM
ejpam-4470	89	3	,	,	PUNCT
ejpam-4470	89	4	1	1	NUM
ejpam-4470	89	5	]	]	PUNCT
ejpam-4470	89	6	.	.	PUNCT
ejpam-4470	90	1	a	a	DET
ejpam-4470	90	2	fuzzy	fuzzy	ADJ
ejpam-4470	90	3	-	-	PUNCT
ejpam-4470	90	4	number	number	NOUN
ejpam-4470	90	5	-	-	PUNCT
ejpam-4470	90	6	valued	value	VERB
ejpam-4470	90	7	function	function	NOUN
ejpam-4470	90	8	f	f	NOUN
ejpam-4470	90	9	:	:	PUNCT
ejpam-4470	90	10	a	a	DET
ejpam-4470	90	11	→	→	PUNCT
ejpam-4470	90	12	e1	e1	NOUN
ejpam-4470	90	13	is	be	AUX
ejpam-4470	90	14	said	say	VERB
ejpam-4470	90	15	to	to	PART
ejpam-4470	90	16	be	be	AUX
ejpam-4470	90	17	bounded	bound	VERB
ejpam-4470	90	18	it	it	PRON
ejpam-4470	90	19	has	have	VERB
ejpam-4470	90	20	a	a	DET
ejpam-4470	90	21	lower	lower	ADV
ejpam-4470	90	22	bound	bind	VERB
ejpam-4470	90	23	and	and	CCONJ
ejpam-4470	90	24	an	an	DET
ejpam-4470	90	25	upper	upper	ADJ
ejpam-4470	90	26	bound	bind	VERB
ejpam-4470	90	27	.	.	PUNCT
ejpam-4470	91	1	for	for	ADP
ejpam-4470	91	2	any	any	DET
ejpam-4470	91	3	two	two	NUM
ejpam-4470	91	4	-	-	PUNCT
ejpam-4470	91	5	variable	variable	NOUN
ejpam-4470	91	6	fuzzy	fuzzy	ADV
ejpam-4470	91	7	-	-	PUNCT
ejpam-4470	91	8	valued	value	VERB
ejpam-4470	91	9	function	function	NOUN
ejpam-4470	91	10	f	f	NOUN
ejpam-4470	91	11	:	:	PUNCT
ejpam-4470	91	12	r2	r2	PROPN
ejpam-4470	91	13	+	+	CCONJ
ejpam-4470	91	14	→	→	PUNCT
ejpam-4470	91	15	e1	e1	NOUN
ejpam-4470	91	16	we	we	PRON
ejpam-4470	91	17	can	can	AUX
ejpam-4470	91	18	define	define	VERB
ejpam-4470	91	19	the	the	DET
ejpam-4470	91	20	functions	function	NOUN
ejpam-4470	91	21	f	f	X
ejpam-4470	91	22	(	(	PUNCT
ejpam-4470	91	23	.	.	PUNCT
ejpam-4470	91	24	,	,	PUNCT
ejpam-4470	91	25	.	.	PUNCT
ejpam-4470	91	26	,	,	PUNCT
ejpam-4470	92	1	r	r	NOUN
ejpam-4470	92	2	)	)	PUNCT
ejpam-4470	92	3	,	,	PUNCT
ejpam-4470	92	4	f	f	X
ejpam-4470	92	5	(	(	PUNCT
ejpam-4470	92	6	.	.	PUNCT
ejpam-4470	92	7	,	,	PUNCT
ejpam-4470	92	8	.	.	PUNCT
ejpam-4470	92	9	,	,	PUNCT
ejpam-4470	92	10	r	r	NOUN
ejpam-4470	92	11	)	)	PUNCT
ejpam-4470	92	12	:	:	PUNCT
ejpam-4470	92	13	r2	r2	PROPN
ejpam-4470	92	14	+	+	CCONJ
ejpam-4470	92	15	→	→	PUNCT
ejpam-4470	92	16	r.	r.	NOUN
ejpam-4470	92	17	these	these	DET
ejpam-4470	92	18	functions	function	NOUN
ejpam-4470	92	19	are	be	AUX
ejpam-4470	92	20	called	call	VERB
ejpam-4470	92	21	the	the	DET
ejpam-4470	92	22	left	left	ADJ
ejpam-4470	92	23	and	and	CCONJ
ejpam-4470	92	24	right	right	ADJ
ejpam-4470	92	25	r−level	r−level	VERB
ejpam-4470	92	26	functions	function	NOUN
ejpam-4470	92	27	of	of	ADP
ejpam-4470	92	28	f.	f.	PROPN
ejpam-4470	92	29	definition	definition	NOUN
ejpam-4470	92	30	3	3	NUM
ejpam-4470	92	31	.	.	PUNCT
ejpam-4470	93	1	[	[	X
ejpam-4470	93	2	31	31	NUM
ejpam-4470	93	3	]	]	PUNCT
ejpam-4470	93	4	a	a	DET
ejpam-4470	93	5	fuzzy	fuzzy	ADV
ejpam-4470	93	6	-	-	PUNCT
ejpam-4470	93	7	valued	value	VERB
ejpam-4470	93	8	function	function	NOUN
ejpam-4470	93	9	f	f	NOUN
ejpam-4470	93	10	:	:	PUNCT
ejpam-4470	93	11	r2	r2	PROPN
ejpam-4470	93	12	→	→	SYM
ejpam-4470	93	13	e1	e1	PROPN
ejpam-4470	93	14	is	be	AUX
ejpam-4470	93	15	said	say	VERB
ejpam-4470	93	16	to	to	PART
ejpam-4470	93	17	be	be	AUX
ejpam-4470	93	18	continuous	continuous	ADJ
ejpam-4470	93	19	at	at	ADP
ejpam-4470	93	20	(	(	PUNCT
ejpam-4470	93	21	s0	s0	PROPN
ejpam-4470	93	22	,	,	PUNCT
ejpam-4470	93	23	t0	t0	PROPN
ejpam-4470	93	24	)	)	PUNCT
ejpam-4470	93	25	∈	∈	PROPN
ejpam-4470	93	26	r2	r2	NOUN
ejpam-4470	93	27	if	if	SCONJ
ejpam-4470	93	28	for	for	ADP
ejpam-4470	93	29	each	each	DET
ejpam-4470	93	30	ε	ε	PROPN
ejpam-4470	93	31	>	>	X
ejpam-4470	93	32	0	0	PUNCT
ejpam-4470	94	1	there	there	PRON
ejpam-4470	94	2	is	be	VERB
ejpam-4470	94	3	δ	δ	PROPN
ejpam-4470	94	4	>	>	X
ejpam-4470	94	5	0	0	NUM
ejpam-4470	94	6	such	such	ADJ
ejpam-4470	94	7	that	that	PRON
ejpam-4470	94	8	d(f(s	d(f(s	PROPN
ejpam-4470	94	9	,	,	PUNCT
ejpam-4470	94	10	t	t	PROPN
ejpam-4470	94	11	)	)	PUNCT
ejpam-4470	94	12	,	,	PUNCT
ejpam-4470	94	13	f(s0	f(s0	NOUN
ejpam-4470	94	14	,	,	PUNCT
ejpam-4470	94	15	t0	t0	PROPN
ejpam-4470	94	16	)	)	PUNCT
ejpam-4470	94	17	)	)	PUNCT
ejpam-4470	94	18	<	<	X
ejpam-4470	94	19	ε	ε	PROPN
ejpam-4470	94	20	whenever	whenever	SCONJ
ejpam-4470	94	21	|s	|s	PROPN
ejpam-4470	94	22	−	−	PROPN
ejpam-4470	94	23	s0|	s0|	VERB
ejpam-4470	94	24	+	+	CCONJ
ejpam-4470	94	25	|t	|t	VERB
ejpam-4470	94	26	−	−	PROPN
ejpam-4470	94	27	t0|	t0|	X
ejpam-4470	94	28	<	<	X
ejpam-4470	94	29	δ	δ	PROPN
ejpam-4470	94	30	.	.	PUNCT
ejpam-4470	95	1	we	we	PRON
ejpam-4470	95	2	say	say	VERB
ejpam-4470	95	3	that	that	SCONJ
ejpam-4470	95	4	f	f	PROPN
ejpam-4470	95	5	is	be	AUX
ejpam-4470	95	6	continuous	continuous	ADJ
ejpam-4470	95	7	on	on	ADP
ejpam-4470	95	8	r2	r2	PROPN
ejpam-4470	95	9	if	if	SCONJ
ejpam-4470	95	10	f	f	PROPN
ejpam-4470	95	11	is	be	AUX
ejpam-4470	95	12	continuous	continuous	ADJ
ejpam-4470	95	13	at	at	ADP
ejpam-4470	95	14	each	each	DET
ejpam-4470	95	15	(	(	PUNCT
ejpam-4470	95	16	s	s	PROPN
ejpam-4470	95	17	,	,	PUNCT
ejpam-4470	95	18	t	t	NOUN
ejpam-4470	95	19	)	)	PUNCT
ejpam-4470	95	20	∈	∈	PROPN
ejpam-4470	95	21	r2	r2	PROPN
ejpam-4470	95	22	.	.	PUNCT
ejpam-4470	96	1	theorem	theorem	VERB
ejpam-4470	96	2	1	1	NUM
ejpam-4470	96	3	(	(	PUNCT
ejpam-4470	96	4	[	[	X
ejpam-4470	96	5	4	4	NUM
ejpam-4470	96	6	]	]	NUM
ejpam-4470	96	7	)	)	PUNCT
ejpam-4470	96	8	.	.	PUNCT
ejpam-4470	97	1	let	let	VERB
ejpam-4470	97	2	the	the	DET
ejpam-4470	97	3	fuzzy	fuzzy	ADV
ejpam-4470	97	4	-	-	PUNCT
ejpam-4470	97	5	valued	value	VERB
ejpam-4470	97	6	function	function	NOUN
ejpam-4470	97	7	of	of	ADP
ejpam-4470	97	8	two	two	NUM
ejpam-4470	97	9	-	-	PUNCT
ejpam-4470	97	10	variable	variable	NOUN
ejpam-4470	97	11	f	f	NOUN
ejpam-4470	97	12	:	:	PUNCT
ejpam-4470	97	13	r2	r2	PROPN
ejpam-4470	97	14	+	+	CCONJ
ejpam-4470	97	15	→	→	PUNCT
ejpam-4470	97	16	e1	e1	NOUN
ejpam-4470	97	17	represented	represent	VERB
ejpam-4470	97	18	by	by	ADP
ejpam-4470	97	19	(	(	PUNCT
ejpam-4470	97	20	f(x	f(x	PROPN
ejpam-4470	97	21	,	,	PUNCT
ejpam-4470	97	22	y	y	PROPN
ejpam-4470	97	23	,	,	PUNCT
ejpam-4470	97	24	r	r	NOUN
ejpam-4470	97	25	)	)	PUNCT
ejpam-4470	97	26	,	,	PUNCT
ejpam-4470	97	27	f(x	f(x	PROPN
ejpam-4470	97	28	,	,	PUNCT
ejpam-4470	97	29	y	y	PROPN
ejpam-4470	97	30	,	,	PUNCT
ejpam-4470	97	31	r	r	NOUN
ejpam-4470	97	32	)	)	PUNCT
ejpam-4470	97	33	)	)	PUNCT
ejpam-4470	97	34	.	.	PUNCT
ejpam-4470	98	1	for	for	ADP
ejpam-4470	98	2	any	any	DET
ejpam-4470	98	3	r	r	NOUN
ejpam-4470	98	4	∈	∈	NOUN
ejpam-4470	98	5	[	[	X
ejpam-4470	98	6	0	0	NUM
ejpam-4470	98	7	,	,	PUNCT
ejpam-4470	98	8	1	1	NUM
ejpam-4470	98	9	]	]	PUNCT
ejpam-4470	98	10	assume	assume	VERB
ejpam-4470	98	11	that	that	SCONJ
ejpam-4470	98	12	the	the	DET
ejpam-4470	98	13	functions	function	NOUN
ejpam-4470	98	14	f(x	f(x	PROPN
ejpam-4470	98	15	,	,	PUNCT
ejpam-4470	98	16	y	y	PROPN
ejpam-4470	98	17	,	,	PUNCT
ejpam-4470	98	18	r	r	NOUN
ejpam-4470	98	19	)	)	PUNCT
ejpam-4470	98	20	and	and	CCONJ
ejpam-4470	98	21	f(x	f(x	PROPN
ejpam-4470	98	22	,	,	PUNCT
ejpam-4470	98	23	y	y	PROPN
ejpam-4470	98	24	,	,	PUNCT
ejpam-4470	98	25	r	r	NOUN
ejpam-4470	98	26	)	)	PUNCT
ejpam-4470	98	27	are	be	AUX
ejpam-4470	98	28	riemann	riemann	PROPN
ejpam-4470	98	29	-	-	PUNCT
ejpam-4470	98	30	integrable	integrable	ADJ
ejpam-4470	98	31	on	on	ADP
ejpam-4470	98	32	[	[	X
ejpam-4470	98	33	0	0	NUM
ejpam-4470	98	34	,	,	PUNCT
ejpam-4470	98	35	x	x	X
ejpam-4470	98	36	]	]	X
ejpam-4470	98	37	×	×	NOUN
ejpam-4470	99	1	[	[	X
ejpam-4470	99	2	0	0	NUM
ejpam-4470	99	3	,	,	PUNCT
ejpam-4470	99	4	y	y	PROPN
ejpam-4470	99	5	]	]	PUNCT
ejpam-4470	99	6	and	and	CCONJ
ejpam-4470	99	7	there	there	PRON
ejpam-4470	99	8	are	be	VERB
ejpam-4470	99	9	positive	positive	ADJ
ejpam-4470	99	10	constants	constant	NOUN
ejpam-4470	99	11	n(r	n(r	NUM
ejpam-4470	99	12	)	)	PUNCT
ejpam-4470	99	13	and	and	CCONJ
ejpam-4470	99	14	n(r	n(r	NUM
ejpam-4470	99	15	)	)	PUNCT
ejpam-4470	99	16	,	,	PUNCT
ejpam-4470	99	17	such	such	ADJ
ejpam-4470	99	18	that	that	SCONJ
ejpam-4470	99	19	y∫	y∫	PROPN
ejpam-4470	99	20	0	0	PUNCT
ejpam-4470	100	1	x∫	x∫	ADJ
ejpam-4470	100	2	0	0	X
ejpam-4470	100	3	|f(x	|f(x	PROPN
ejpam-4470	100	4	,	,	PUNCT
ejpam-4470	100	5	y	y	PROPN
ejpam-4470	100	6	,	,	PUNCT
ejpam-4470	100	7	r)|dxdy	r)|dxdy	VERB
ejpam-4470	100	8	≤	≤	ADJ
ejpam-4470	100	9	n(r	n(r	NOUN
ejpam-4470	100	10	)	)	PUNCT
ejpam-4470	100	11	,	,	PUNCT
ejpam-4470	100	12	y∫	y∫	PROPN
ejpam-4470	100	13	0	0	PUNCT
ejpam-4470	101	1	x∫	x∫	ADJ
ejpam-4470	101	2	0	0	X
ejpam-4470	101	3	|f(x	|f(x	PROPN
ejpam-4470	101	4	,	,	PUNCT
ejpam-4470	101	5	y	y	PROPN
ejpam-4470	101	6	,	,	PUNCT
ejpam-4470	101	7	r)|dxdy	r)|dxdy	VERB
ejpam-4470	101	8	≤	≤	ADJ
ejpam-4470	101	9	n(r	n(r	NOUN
ejpam-4470	101	10	)	)	PUNCT
ejpam-4470	101	11	for	for	ADP
ejpam-4470	101	12	every	every	DET
ejpam-4470	101	13	x	x	PROPN
ejpam-4470	101	14	,	,	PUNCT
ejpam-4470	101	15	y	y	PROPN
ejpam-4470	101	16	>	>	X
ejpam-4470	101	17	0	0	PROPN
ejpam-4470	101	18	.	.	PUNCT
ejpam-4470	102	1	then	then	ADV
ejpam-4470	102	2	the	the	DET
ejpam-4470	102	3	function	function	NOUN
ejpam-4470	102	4	f(x	f(x	PROPN
ejpam-4470	102	5	,	,	PUNCT
ejpam-4470	102	6	y	y	NOUN
ejpam-4470	102	7	)	)	PUNCT
ejpam-4470	102	8	is	be	AUX
ejpam-4470	102	9	improper	improper	ADJ
ejpam-4470	102	10	fuzzy	fuzzy	ADJ
ejpam-4470	102	11	riemann	riemann	PROPN
ejpam-4470	102	12	-	-	PUNCT
ejpam-4470	102	13	integrable	integrable	ADJ
ejpam-4470	102	14	on	on	ADP
ejpam-4470	102	15	r2	r2	PROPN
ejpam-4470	102	16	+	+	CCONJ
ejpam-4470	102	17	and	and	CCONJ
ejpam-4470	102	18	(	(	PUNCT
ejpam-4470	102	19	fr	fr	ADJ
ejpam-4470	102	20	)	)	PUNCT
ejpam-4470	102	21	∞∫	∞∫	NOUN
ejpam-4470	102	22	0	0	PUNCT
ejpam-4470	103	1	(	(	PUNCT
ejpam-4470	103	2	fr	fr	NOUN
ejpam-4470	103	3	)	)	PUNCT
ejpam-4470	103	4	∞∫	∞∫	PROPN
ejpam-4470	103	5	0	0	NUM
ejpam-4470	104	1	f(x	f(x	PROPN
ejpam-4470	104	2	,	,	PUNCT
ejpam-4470	104	3	y)dxdy	y)dxdy	X
ejpam-4470	104	4	=	=	SYM
ejpam-4470	105	1			PROPN
ejpam-4470	105	2	∞∫	∞∫	PROPN
ejpam-4470	105	3	0	0	NUM
ejpam-4470	105	4	∞∫	∞∫	PROPN
ejpam-4470	105	5	0	0	NUM
ejpam-4470	105	6	f(x	f(x	PROPN
ejpam-4470	105	7	,	,	PUNCT
ejpam-4470	105	8	y	y	PROPN
ejpam-4470	105	9	,	,	PUNCT
ejpam-4470	105	10	r)dxdy	r)dxdy	PROPN
ejpam-4470	105	11	,	,	PUNCT
ejpam-4470	105	12	∞∫	∞∫	PROPN
ejpam-4470	105	13	0	0	NUM
ejpam-4470	105	14	∞∫	∞∫	PROPN
ejpam-4470	105	15	0	0	NUM
ejpam-4470	106	1	f(x	f(x	PROPN
ejpam-4470	106	2	,	,	PUNCT
ejpam-4470	106	3	y	y	PROPN
ejpam-4470	106	4	,	,	PUNCT
ejpam-4470	106	5	r)dxdy	r)dxdy	PROPN
ejpam-4470	107	1			PROPN
ejpam-4470	107	2	theorem	theorem	VERB
ejpam-4470	107	3	2	2	NUM
ejpam-4470	107	4	.	.	PUNCT
ejpam-4470	108	1	[	[	X
ejpam-4470	108	2	4	4	X
ejpam-4470	108	3	]	]	PUNCT
ejpam-4470	108	4	let	let	VERB
ejpam-4470	108	5	f	f	NOUN
ejpam-4470	108	6	:	:	PUNCT
ejpam-4470	108	7	r2	r2	PROPN
ejpam-4470	108	8	+	+	CCONJ
ejpam-4470	108	9	→	→	PUNCT
ejpam-4470	108	10	e1	e1	NOUN
ejpam-4470	108	11	be	be	VERB
ejpam-4470	108	12	fuzzy	fuzzy	ADV
ejpam-4470	108	13	-	-	PUNCT
ejpam-4470	108	14	valued	value	VERB
ejpam-4470	108	15	function	function	NOUN
ejpam-4470	108	16	of	of	ADP
ejpam-4470	108	17	two	two	NUM
ejpam-4470	108	18	-	-	PUNCT
ejpam-4470	108	19	variable	variable	NOUN
ejpam-4470	108	20	.	.	PUNCT
ejpam-4470	109	1	suppose	suppose	VERB
ejpam-4470	109	2	that	that	SCONJ
ejpam-4470	109	3	for	for	ADP
ejpam-4470	109	4	each	each	DET
ejpam-4470	109	5	x	x	SYM
ejpam-4470	109	6	∈	∈	PROPN
ejpam-4470	109	7	[	[	X
ejpam-4470	109	8	0,∞	0,∞	NOUN
ejpam-4470	109	9	)	)	PUNCT
ejpam-4470	109	10	,	,	PUNCT
ejpam-4470	109	11	the	the	DET
ejpam-4470	109	12	fuzzy	fuzzy	ADJ
ejpam-4470	109	13	integral	integral	ADJ
ejpam-4470	109	14	(	(	PUNCT
ejpam-4470	109	15	fr	fr	ADJ
ejpam-4470	109	16	)	)	PUNCT
ejpam-4470	109	17	∞∫	∞∫	PROPN
ejpam-4470	109	18	0	0	NUM
ejpam-4470	109	19	f(x	f(x	PROPN
ejpam-4470	109	20	,	,	PUNCT
ejpam-4470	109	21	y)dy	y)dy	PROPN
ejpam-4470	109	22	is	be	AUX
ejpam-4470	109	23	convergent	convergent	ADJ
ejpam-4470	109	24	and	and	CCONJ
ejpam-4470	109	25	moreover	moreover	ADV
ejpam-4470	109	26	the	the	DET
ejpam-4470	109	27	fuzzy	fuzzy	ADJ
ejpam-4470	109	28	integral	integral	ADJ
ejpam-4470	109	29	(	(	PUNCT
ejpam-4470	109	30	fr	fr	ADJ
ejpam-4470	109	31	)	)	PUNCT
ejpam-4470	109	32	∞∫	∞∫	PROPN
ejpam-4470	109	33	0	0	NUM
ejpam-4470	110	1	f(x	f(x	PROPN
ejpam-4470	110	2	,	,	PUNCT
ejpam-4470	110	3	y)dx	y)dx	PROPN
ejpam-4470	110	4	as	as	ADP
ejpam-4470	110	5	a	a	DET
ejpam-4470	110	6	function	function	NOUN
ejpam-4470	110	7	of	of	ADP
ejpam-4470	110	8	y	y	PROPN
ejpam-4470	110	9	is	be	AUX
ejpam-4470	110	10	convergent	convergent	ADJ
ejpam-4470	110	11	on	on	ADP
ejpam-4470	110	12	[	[	X
ejpam-4470	110	13	0,∞	0,∞	NOUN
ejpam-4470	110	14	)	)	PUNCT
ejpam-4470	110	15	.	.	PUNCT
ejpam-4470	111	1	then	then	ADV
ejpam-4470	111	2	(	(	PUNCT
ejpam-4470	111	3	fr	fr	X
ejpam-4470	111	4	)	)	PUNCT
ejpam-4470	111	5	∞∫	∞∫	NOUN
ejpam-4470	111	6	0	0	PUNCT
ejpam-4470	112	1	(	(	PUNCT
ejpam-4470	112	2	fr	fr	NOUN
ejpam-4470	112	3	)	)	PUNCT
ejpam-4470	112	4	∞∫	∞∫	PROPN
ejpam-4470	112	5	0	0	NUM
ejpam-4470	112	6	f(x	f(x	PROPN
ejpam-4470	112	7	,	,	PUNCT
ejpam-4470	112	8	y)dydx	y)dydx	PROPN
ejpam-4470	113	1	=	=	PUNCT
ejpam-4470	114	1	(	(	PUNCT
ejpam-4470	114	2	fr	fr	PROPN
ejpam-4470	114	3	)	)	PUNCT
ejpam-4470	114	4	∞∫	∞∫	NOUN
ejpam-4470	114	5	0	0	PUNCT
ejpam-4470	114	6	(	(	PUNCT
ejpam-4470	114	7	fr	fr	NOUN
ejpam-4470	114	8	)	)	PUNCT
ejpam-4470	114	9	∞∫	∞∫	PROPN
ejpam-4470	114	10	0	0	NUM
ejpam-4470	115	1	f(x	f(x	PROPN
ejpam-4470	115	2	,	,	PUNCT
ejpam-4470	115	3	y)dxdy	y)dxdy	PROPN
ejpam-4470	115	4	.	.	PUNCT
ejpam-4470	115	5	a.	a.	PROPN
ejpam-4470	115	6	f.alidema	f.alidema	PROPN
ejpam-4470	115	7	/	/	SYM
ejpam-4470	115	8	eur	eur	PROPN
ejpam-4470	115	9	.	.	PUNCT
ejpam-4470	116	1	j.	j.	PROPN
ejpam-4470	116	2	pure	pure	PROPN
ejpam-4470	116	3	appl	appl	PROPN
ejpam-4470	116	4	.	.	PROPN
ejpam-4470	116	5	math	math	PROPN
ejpam-4470	116	6	,	,	PUNCT
ejpam-4470	116	7	15	15	NUM
ejpam-4470	116	8	(	(	PUNCT
ejpam-4470	116	9	3	3	NUM
ejpam-4470	116	10	)	)	PUNCT
ejpam-4470	116	11	(	(	PUNCT
ejpam-4470	116	12	2022	2022	NUM
ejpam-4470	116	13	)	)	PUNCT
ejpam-4470	116	14	,	,	PUNCT
ejpam-4470	116	15	1363	1363	NUM
ejpam-4470	116	16	-	-	SYM
ejpam-4470	116	17	1375	1375	NUM
ejpam-4470	116	18	1367	1367	NUM
ejpam-4470	116	19	theorem	theorem	NOUN
ejpam-4470	116	20	3	3	NUM
ejpam-4470	116	21	.	.	PUNCT
ejpam-4470	117	1	[	[	X
ejpam-4470	117	2	6	6	NUM
ejpam-4470	117	3	]	]	PUNCT
ejpam-4470	117	4	let	let	VERB
ejpam-4470	117	5	f	f	PROPN
ejpam-4470	117	6	and	and	CCONJ
ejpam-4470	117	7	g	g	PROPN
ejpam-4470	117	8	be	be	AUX
ejpam-4470	117	9	fuzzy	fuzzy	ADV
ejpam-4470	117	10	-	-	PUNCT
ejpam-4470	117	11	valued	value	VERB
ejpam-4470	117	12	functions	function	NOUN
ejpam-4470	117	13	.	.	PUNCT
ejpam-4470	118	1	let	let	VERB
ejpam-4470	118	2	f	f	PROPN
ejpam-4470	118	3	(	(	PUNCT
ejpam-4470	118	4	u	u	NOUN
ejpam-4470	118	5	,	,	PUNCT
ejpam-4470	118	6	v	v	NOUN
ejpam-4470	118	7	)	)	PUNCT
ejpam-4470	118	8	and	and	CCONJ
ejpam-4470	118	9	g(u	g(u	PROPN
ejpam-4470	118	10	,	,	PUNCT
ejpam-4470	118	11	v	v	NOUN
ejpam-4470	118	12	)	)	PUNCT
ejpam-4470	118	13	be	be	VERB
ejpam-4470	118	14	double	double	ADV
ejpam-4470	118	15	fuzzy	fuzzy	ADJ
ejpam-4470	118	16	sumudu	sumudu	NOUN
ejpam-4470	118	17	transforms	transform	VERB
ejpam-4470	118	18	for	for	ADP
ejpam-4470	118	19	f	f	PROPN
ejpam-4470	118	20	and	and	CCONJ
ejpam-4470	118	21	g	g	NOUN
ejpam-4470	118	22	,	,	PUNCT
ejpam-4470	118	23	respectively	respectively	ADV
ejpam-4470	118	24	.	.	PUNCT
ejpam-4470	119	1	then	then	ADV
ejpam-4470	119	2	the	the	DET
ejpam-4470	119	3	dfst	dfst	NOUN
ejpam-4470	119	4	of	of	ADP
ejpam-4470	119	5	the	the	DET
ejpam-4470	119	6	double	double	ADJ
ejpam-4470	119	7	fuzzy	fuzzy	ADJ
ejpam-4470	119	8	convolution	convolution	NOUN
ejpam-4470	119	9	f	f	PROPN
ejpam-4470	119	10	and	and	CCONJ
ejpam-4470	119	11	g	g	PROPN
ejpam-4470	119	12	,	,	PUNCT
ejpam-4470	119	13	(	(	PUNCT
ejpam-4470	119	14	f	f	NOUN
ejpam-4470	119	15	∗	∗	NOUN
ejpam-4470	119	16	∗g)(x	∗g)(x	PROPN
ejpam-4470	119	17	,	,	PUNCT
ejpam-4470	119	18	y	y	NOUN
ejpam-4470	119	19	)	)	PUNCT
ejpam-4470	119	20	=	=	PUNCT
ejpam-4470	120	1	y∫	y∫	NOUN
ejpam-4470	120	2	0	0	PUNCT
ejpam-4470	121	1	x∫	x∫	ADJ
ejpam-4470	121	2	0	0	PUNCT
ejpam-4470	122	1	f(α	f(α	NOUN
ejpam-4470	122	2	,	,	PUNCT
ejpam-4470	122	3	β)g(x−	β)g(x−	PROPN
ejpam-4470	122	4	α	α	NUM
ejpam-4470	122	5	,	,	PUNCT
ejpam-4470	122	6	y	y	PROPN
ejpam-4470	122	7	−	−	PROPN
ejpam-4470	122	8	β)dαdβ	β)dαdβ	NOUN
ejpam-4470	122	9	is	be	AUX
ejpam-4470	122	10	given	give	VERB
ejpam-4470	122	11	by	by	ADP
ejpam-4470	122	12	s[(f	s[(f	PROPN
ejpam-4470	122	13	∗	∗	PROPN
ejpam-4470	122	14	g)(x	g)(x	PROPN
ejpam-4470	122	15	,	,	PUNCT
ejpam-4470	122	16	y	y	PROPN
ejpam-4470	122	17	)	)	PUNCT
ejpam-4470	122	18	]	]	PUNCT
ejpam-4470	123	1	=	=	PUNCT
ejpam-4470	123	2	uvf	uvf	INTJ
ejpam-4470	123	3	(	(	PUNCT
ejpam-4470	123	4	u	u	NOUN
ejpam-4470	123	5	,	,	PUNCT
ejpam-4470	123	6	v)g(u	v)g(u	NOUN
ejpam-4470	123	7	,	,	PUNCT
ejpam-4470	123	8	v	v	NOUN
ejpam-4470	123	9	)	)	PUNCT
ejpam-4470	123	10	.	.	PUNCT
ejpam-4470	124	1	definition	definition	NOUN
ejpam-4470	124	2	4	4	NUM
ejpam-4470	124	3	.	.	PUNCT
ejpam-4470	125	1	[	[	X
ejpam-4470	125	2	6	6	NUM
ejpam-4470	125	3	]	]	PUNCT
ejpam-4470	125	4	let	let	VERB
ejpam-4470	125	5	f	f	NOUN
ejpam-4470	125	6	:	:	PUNCT
ejpam-4470	125	7	a	a	DET
ejpam-4470	125	8	→	→	NOUN
ejpam-4470	125	9	e1	e1	NOUN
ejpam-4470	125	10	,	,	PUNCT
ejpam-4470	125	11	for	for	ADP
ejpam-4470	125	12	∆n	∆n	PROPN
ejpam-4470	125	13	x	x	NOUN
ejpam-4470	125	14	:	:	PUNCT
ejpam-4470	125	15	a	a	DET
ejpam-4470	125	16	=	=	X
ejpam-4470	125	17	x0	x0	PROPN
ejpam-4470	125	18	<	<	X
ejpam-4470	126	1	x1	x1	X
ejpam-4470	126	2	<	<	X
ejpam-4470	126	3	...	...	PUNCT
ejpam-4470	126	4	<	<	X
ejpam-4470	126	5	xn	xn	PUNCT
ejpam-4470	126	6	=	=	SYM
ejpam-4470	126	7	b	b	PROPN
ejpam-4470	126	8	and	and	CCONJ
ejpam-4470	126	9	∆n	∆n	PROPN
ejpam-4470	126	10	y	y	NOUN
ejpam-4470	126	11	:	:	PUNCT
ejpam-4470	127	1	c	c	X
ejpam-4470	127	2	=	=	SYM
ejpam-4470	127	3	y0	y0	PROPN
ejpam-4470	127	4	<	<	X
ejpam-4470	127	5	y1	y1	X
ejpam-4470	127	6	<	<	X
ejpam-4470	127	7	...	...	PUNCT
ejpam-4470	127	8	<	<	X
ejpam-4470	127	9	yn	yn	X
ejpam-4470	127	10	=	=	SYM
ejpam-4470	127	11	d	d	PROPN
ejpam-4470	127	12	,	,	PUNCT
ejpam-4470	127	13	be	be	AUX
ejpam-4470	127	14	two	two	NUM
ejpam-4470	127	15	partitions	partition	NOUN
ejpam-4470	127	16	of	of	ADP
ejpam-4470	127	17	the	the	DET
ejpam-4470	127	18	intervals	interval	NOUN
ejpam-4470	127	19	[	[	X
ejpam-4470	127	20	a	a	X
ejpam-4470	127	21	,	,	PUNCT
ejpam-4470	127	22	b	b	NOUN
ejpam-4470	127	23	]	]	PUNCT
ejpam-4470	127	24	and	and	CCONJ
ejpam-4470	127	25	[	[	X
ejpam-4470	127	26	c	c	X
ejpam-4470	127	27	,	,	PUNCT
ejpam-4470	127	28	d	d	X
ejpam-4470	127	29	]	]	X
ejpam-4470	127	30	,	,	PUNCT
ejpam-4470	127	31	respectively	respectively	ADV
ejpam-4470	127	32	.	.	PUNCT
ejpam-4470	128	1	let	let	VERB
ejpam-4470	128	2	one	one	PRON
ejpam-4470	128	3	consider	consider	VERB
ejpam-4470	128	4	the	the	DET
ejpam-4470	128	5	intermediates	intermediate	NOUN
ejpam-4470	128	6	points	point	VERB
ejpam-4470	128	7	ξi	ξi	NOUN
ejpam-4470	128	8	∈	∈	PROPN
ejpam-4470	129	1	[	[	X
ejpam-4470	129	2	xi−1	xi−1	PROPN
ejpam-4470	129	3	,	,	PUNCT
ejpam-4470	129	4	xi	xi	ADP
ejpam-4470	129	5	]	]	PUNCT
ejpam-4470	129	6	and	and	CCONJ
ejpam-4470	129	7	ηj	ηj	ADP
ejpam-4470	129	8	∈	∈	PROPN
ejpam-4470	130	1	[	[	X
ejpam-4470	130	2	yj−1	yj−1	PROPN
ejpam-4470	130	3	,	,	PUNCT
ejpam-4470	130	4	yj	yj	PROPN
ejpam-4470	130	5	]	]	PUNCT
ejpam-4470	130	6	,	,	PUNCT
ejpam-4470	130	7	i	i	PRON
ejpam-4470	130	8	=	=	NOUN
ejpam-4470	130	9	1	1	NUM
ejpam-4470	130	10	,	,	PUNCT
ejpam-4470	130	11	...	...	PUNCT
ejpam-4470	130	12	,	,	PUNCT
ejpam-4470	130	13	n	n	CCONJ
ejpam-4470	130	14	;	;	PUNCT
ejpam-4470	130	15	j	j	PROPN
ejpam-4470	130	16	=	=	SYM
ejpam-4470	130	17	1	1	NUM
ejpam-4470	130	18	,	,	PUNCT
ejpam-4470	130	19	...	...	PUNCT
ejpam-4470	130	20	,	,	PUNCT
ejpam-4470	130	21	n	n	CCONJ
ejpam-4470	130	22	,	,	PUNCT
ejpam-4470	130	23	and	and	CCONJ
ejpam-4470	130	24	δ	δ	NOUN
ejpam-4470	130	25	:	:	PUNCT
ejpam-4470	131	1	[	[	X
ejpam-4470	131	2	a	a	X
ejpam-4470	131	3	,	,	PUNCT
ejpam-4470	131	4	b	b	NOUN
ejpam-4470	131	5	]	]	X
ejpam-4470	131	6	→	→	NOUN
ejpam-4470	131	7	r+	r+	NOUN
ejpam-4470	131	8	and	and	CCONJ
ejpam-4470	131	9	σ	σ	NOUN
ejpam-4470	132	1	:	:	PUNCT
ejpam-4470	132	2	[	[	X
ejpam-4470	132	3	c	c	X
ejpam-4470	132	4	,	,	PUNCT
ejpam-4470	132	5	d	d	X
ejpam-4470	132	6	]	]	X
ejpam-4470	132	7	→	→	SYM
ejpam-4470	132	8	r+	r+	X
ejpam-4470	132	9	.	.	PUNCT
ejpam-4470	133	1	the	the	DET
ejpam-4470	133	2	divisions	division	NOUN
ejpam-4470	133	3	px	px	X
ejpam-4470	133	4	=	=	PUNCT
ejpam-4470	133	5	(	(	PUNCT
ejpam-4470	133	6	[	[	X
ejpam-4470	133	7	xi−1	xi−1	PROPN
ejpam-4470	133	8	,	,	PUNCT
ejpam-4470	133	9	xi	xi	ADP
ejpam-4470	133	10	]	]	X
ejpam-4470	133	11	;	;	PUNCT
ejpam-4470	133	12	ξi	ξi	NUM
ejpam-4470	133	13	)	)	PUNCT
ejpam-4470	133	14	,	,	PUNCT
ejpam-4470	133	15	i	i	PRON
ejpam-4470	133	16	=	=	NOUN
ejpam-4470	133	17	1	1	NUM
ejpam-4470	133	18	,	,	PUNCT
ejpam-4470	133	19	...	...	PUNCT
ejpam-4470	133	20	,	,	PUNCT
ejpam-4470	133	21	n	n	CCONJ
ejpam-4470	133	22	,	,	PUNCT
ejpam-4470	133	23	and	and	CCONJ
ejpam-4470	133	24	py	py	INTJ
ejpam-4470	133	25	=	=	PUNCT
ejpam-4470	133	26	(	(	PUNCT
ejpam-4470	133	27	[	[	X
ejpam-4470	133	28	yj−1	yj−1	PROPN
ejpam-4470	133	29	,	,	PUNCT
ejpam-4470	133	30	yi	yi	NOUN
ejpam-4470	133	31	]	]	PUNCT
ejpam-4470	133	32	;	;	PUNCT
ejpam-4470	133	33	ηj	ηj	NOUN
ejpam-4470	133	34	)	)	PUNCT
ejpam-4470	133	35	,	,	PUNCT
ejpam-4470	133	36	j	j	PROPN
ejpam-4470	134	1	=	=	SYM
ejpam-4470	134	2	1	1	NUM
ejpam-4470	134	3	,	,	PUNCT
ejpam-4470	134	4	...	...	PUNCT
ejpam-4470	134	5	,	,	PUNCT
ejpam-4470	134	6	n	n	PRON
ejpam-4470	134	7	are	be	AUX
ejpam-4470	134	8	said	say	VERB
ejpam-4470	134	9	to	to	PART
ejpam-4470	134	10	be	be	AUX
ejpam-4470	134	11	δ	δ	NOUN
ejpam-4470	134	12	-	-	ADJ
ejpam-4470	134	13	fine	fine	PROPN
ejpam-4470	134	14	and	and	CCONJ
ejpam-4470	134	15	σ	σ	NOUN
ejpam-4470	134	16	-	-	PUNCT
ejpam-4470	134	17	fine	fine	NOUN
ejpam-4470	134	18	,	,	PUNCT
ejpam-4470	134	19	respectively	respectively	ADV
ejpam-4470	134	20	,	,	PUNCT
ejpam-4470	134	21	if	if	SCONJ
ejpam-4470	134	22	[	[	X
ejpam-4470	134	23	xi−1	xi−1	PROPN
ejpam-4470	134	24	,	,	PUNCT
ejpam-4470	134	25	xi	xi	ADP
ejpam-4470	134	26	]	]	X
ejpam-4470	134	27	⊆	⊆	NUM
ejpam-4470	134	28	(	(	PUNCT
ejpam-4470	134	29	ξi	ξi	NOUN
ejpam-4470	134	30	−	−	NOUN
ejpam-4470	134	31	δ(ξi	δ(ξi	ADP
ejpam-4470	134	32	)	)	PUNCT
ejpam-4470	134	33	,	,	PUNCT
ejpam-4470	134	34	ξi	ξi	NOUN
ejpam-4470	134	35	+	+	CCONJ
ejpam-4470	134	36	δ(ξi	δ(ξi	NOUN
ejpam-4470	134	37	)	)	PUNCT
ejpam-4470	134	38	)	)	PUNCT
ejpam-4470	134	39	and	and	CCONJ
ejpam-4470	135	1	[	[	X
ejpam-4470	135	2	yj−1	yj−1	PROPN
ejpam-4470	135	3	,	,	PUNCT
ejpam-4470	135	4	yj	yj	PROPN
ejpam-4470	135	5	]	]	PUNCT
ejpam-4470	135	6	⊆	⊆	NUM
ejpam-4470	135	7	(	(	PUNCT
ejpam-4470	135	8	ηj	ηj	ADP
ejpam-4470	135	9	−	−	PROPN
ejpam-4470	135	10	σ(ηj	σ(ηj	NOUN
ejpam-4470	135	11	)	)	PUNCT
ejpam-4470	135	12	,	,	PUNCT
ejpam-4470	135	13	ηj	ηj	ADP
ejpam-4470	135	14	+	+	NOUN
ejpam-4470	135	15	σ(ηj	σ(ηj	NOUN
ejpam-4470	135	16	)	)	PUNCT
ejpam-4470	135	17	)	)	PUNCT
ejpam-4470	135	18	.	.	PUNCT
ejpam-4470	136	1	the	the	DET
ejpam-4470	136	2	function	function	NOUN
ejpam-4470	136	3	f	f	PROPN
ejpam-4470	136	4	is	be	AUX
ejpam-4470	136	5	said	say	VERB
ejpam-4470	136	6	to	to	PART
ejpam-4470	136	7	be	be	AUX
ejpam-4470	136	8	two	two	NUM
ejpam-4470	136	9	-	-	PUNCT
ejpam-4470	136	10	dimensional	dimensional	ADJ
ejpam-4470	136	11	henstock	henstock	NOUN
ejpam-4470	136	12	integrable	integrable	ADJ
ejpam-4470	136	13	to	to	ADP
ejpam-4470	136	14	i	i	PROPN
ejpam-4470	136	15	∈	∈	PROPN
ejpam-4470	136	16	e1	e1	NOUN
ejpam-4470	136	17	if	if	SCONJ
ejpam-4470	136	18	for	for	ADP
ejpam-4470	136	19	every	every	DET
ejpam-4470	136	20	ε	ε	PROPN
ejpam-4470	136	21	>	>	X
ejpam-4470	136	22	0	0	PUNCT
ejpam-4470	137	1	there	there	PRON
ejpam-4470	137	2	are	be	VERB
ejpam-4470	137	3	functions	function	NOUN
ejpam-4470	137	4	δ	δ	NOUN
ejpam-4470	137	5	:	:	PUNCT
ejpam-4470	138	1	[	[	X
ejpam-4470	138	2	a	a	X
ejpam-4470	138	3	,	,	PUNCT
ejpam-4470	138	4	b	b	NOUN
ejpam-4470	138	5	]	]	X
ejpam-4470	138	6	→	→	NOUN
ejpam-4470	138	7	r+	r+	NOUN
ejpam-4470	138	8	and	and	CCONJ
ejpam-4470	138	9	σ	σ	NOUN
ejpam-4470	139	1	:	:	PUNCT
ejpam-4470	139	2	[	[	X
ejpam-4470	139	3	c	c	X
ejpam-4470	139	4	,	,	PUNCT
ejpam-4470	139	5	d	d	X
ejpam-4470	139	6	]	]	X
ejpam-4470	139	7	→	→	PUNCT
ejpam-4470	139	8	r+	r+	NOUN
ejpam-4470	139	9	such	such	ADJ
ejpam-4470	139	10	that	that	PRON
ejpam-4470	139	11	for	for	ADP
ejpam-4470	139	12	any	any	DET
ejpam-4470	139	13	δ	δ	NOUN
ejpam-4470	139	14	-	-	PUNCT
ejpam-4470	139	15	fine	fine	PROPN
ejpam-4470	139	16	and	and	CCONJ
ejpam-4470	139	17	σ	σ	NOUN
ejpam-4470	139	18	-	-	PUNCT
ejpam-4470	139	19	fine	fine	ADJ
ejpam-4470	139	20	divisions	division	NOUN
ejpam-4470	139	21	we	we	PRON
ejpam-4470	139	22	have	have	VERB
ejpam-4470	139	23	d	d	NOUN
ejpam-4470	139	24	(	(	PUNCT
ejpam-4470	139	25	n∑	n∑	NOUN
ejpam-4470	139	26	j=1	j=1	PROPN
ejpam-4470	140	1	n∑	n∑	PROPN
ejpam-4470	141	1	i=1	i=1	PROPN
ejpam-4470	142	1	(	(	PUNCT
ejpam-4470	142	2	xi−xi−1)(yj−yj−1)⊙f(ξi	xi−xi−1)(yj−yj−1)⊙f(ξi	PROPN
ejpam-4470	142	3	,	,	PUNCT
ejpam-4470	142	4	ηj	ηj	NOUN
ejpam-4470	142	5	)	)	PUNCT
ejpam-4470	142	6	,	,	PUNCT
ejpam-4470	142	7	i	i	NOUN
ejpam-4470	142	8	)	)	PUNCT
ejpam-4470	142	9	<	<	X
ejpam-4470	142	10	ε	ε	PROPN
ejpam-4470	142	11	,	,	PUNCT
ejpam-4470	142	12	where	where	SCONJ
ejpam-4470	142	13	∑	∑	PUNCT
ejpam-4470	142	14	denotes	denote	VERB
ejpam-4470	142	15	the	the	DET
ejpam-4470	142	16	fuzzy	fuzzy	ADJ
ejpam-4470	142	17	summation	summation	NOUN
ejpam-4470	142	18	.	.	PUNCT
ejpam-4470	143	1	then	then	ADV
ejpam-4470	143	2	,	,	PUNCT
ejpam-4470	143	3	i	i	PRON
ejpam-4470	143	4	is	be	AUX
ejpam-4470	143	5	called	call	VERB
ejpam-4470	143	6	the	the	DET
ejpam-4470	143	7	two	two	NUM
ejpam-4470	143	8	-	-	PUNCT
ejpam-4470	143	9	dimensional	dimensional	ADJ
ejpam-4470	143	10	henstock	henstock	NOUN
ejpam-4470	143	11	integral	integral	ADJ
ejpam-4470	143	12	of	of	ADP
ejpam-4470	143	13	f	f	PROPN
ejpam-4470	143	14	and	and	CCONJ
ejpam-4470	143	15	is	be	AUX
ejpam-4470	143	16	denoted	denote	VERB
ejpam-4470	143	17	by	by	ADP
ejpam-4470	143	18	i(f	i(f	NOUN
ejpam-4470	143	19	)	)	PUNCT
ejpam-4470	143	20	=	=	PRON
ejpam-4470	143	21	(	(	PUNCT
ejpam-4470	143	22	fh	fh	PROPN
ejpam-4470	143	23	)	)	PUNCT
ejpam-4470	143	24	d∫	d∫	NOUN
ejpam-4470	143	25	c	c	PROPN
ejpam-4470	143	26	(	(	PUNCT
ejpam-4470	143	27	fh	fh	PROPN
ejpam-4470	143	28	)	)	PUNCT
ejpam-4470	143	29	b∫	b∫	NOUN
ejpam-4470	143	30	a	a	DET
ejpam-4470	143	31	f(s	f(	NOUN
ejpam-4470	143	32	,	,	PUNCT
ejpam-4470	143	33	t)dsdt	t)dsdt	PROPN
ejpam-4470	143	34	.	.	PUNCT
ejpam-4470	144	1	if	if	SCONJ
ejpam-4470	144	2	the	the	DET
ejpam-4470	144	3	above	above	ADJ
ejpam-4470	144	4	δ	δ	PROPN
ejpam-4470	144	5	and	and	CCONJ
ejpam-4470	144	6	σ	σ	PROPN
ejpam-4470	144	7	are	be	AUX
ejpam-4470	144	8	constant	constant	ADJ
ejpam-4470	144	9	functions	function	NOUN
ejpam-4470	144	10	,	,	PUNCT
ejpam-4470	144	11	then	then	ADV
ejpam-4470	144	12	one	one	NUM
ejpam-4470	144	13	recaptures	recapture	VERB
ejpam-4470	144	14	the	the	DET
ejpam-4470	144	15	concept	concept	NOUN
ejpam-4470	144	16	of	of	ADP
ejpam-4470	144	17	riemann	riemann	PROPN
ejpam-4470	144	18	integral	integral	PROPN
ejpam-4470	144	19	.	.	PUNCT
ejpam-4470	145	1	in	in	ADP
ejpam-4470	145	2	this	this	DET
ejpam-4470	145	3	case	case	NOUN
ejpam-4470	145	4	,	,	PUNCT
ejpam-4470	145	5	i	i	PRON
ejpam-4470	145	6	∈	∈	PROPN
ejpam-4470	145	7	e1	e1	NOUN
ejpam-4470	145	8	will	will	AUX
ejpam-4470	145	9	be	be	AUX
ejpam-4470	145	10	called	call	VERB
ejpam-4470	145	11	two	two	NUM
ejpam-4470	145	12	-	-	PUNCT
ejpam-4470	145	13	dimensional	dimensional	ADJ
ejpam-4470	145	14	integral	integral	ADJ
ejpam-4470	145	15	of	of	ADP
ejpam-4470	145	16	f	f	PROPN
ejpam-4470	145	17	on	on	ADP
ejpam-4470	145	18	a	a	PRON
ejpam-4470	145	19	and	and	CCONJ
ejpam-4470	145	20	will	will	AUX
ejpam-4470	145	21	be	be	AUX
ejpam-4470	145	22	denoted	denote	VERB
ejpam-4470	145	23	by	by	ADP
ejpam-4470	145	24	(	(	PUNCT
ejpam-4470	145	25	fr	fr	NOUN
ejpam-4470	145	26	)	)	PUNCT
ejpam-4470	145	27	d∫	d∫	NOUN
ejpam-4470	145	28	c	c	NOUN
ejpam-4470	145	29	(	(	PUNCT
ejpam-4470	145	30	fr	fr	PROPN
ejpam-4470	145	31	)	)	PUNCT
ejpam-4470	145	32	b∫	b∫	NOUN
ejpam-4470	145	33	a	a	DET
ejpam-4470	145	34	f(s	f(	NOUN
ejpam-4470	145	35	,	,	PUNCT
ejpam-4470	145	36	t)dsdt	t)dsdt	PROPN
ejpam-4470	145	37	.	.	PROPN
ejpam-4470	146	1	3	3	NUM
ejpam-4470	146	2	.	.	X
ejpam-4470	146	3	double	double	ADJ
ejpam-4470	146	4	fuzzy	fuzzy	ADJ
ejpam-4470	146	5	sumudu	sumudu	NOUN
ejpam-4470	146	6	transform	transform	VERB
ejpam-4470	146	7	definition	definition	NOUN
ejpam-4470	146	8	5	5	NUM
ejpam-4470	146	9	.	.	PUNCT
ejpam-4470	147	1	[	[	X
ejpam-4470	147	2	6	6	NUM
ejpam-4470	147	3	]	]	PUNCT
ejpam-4470	147	4	let	let	VERB
ejpam-4470	147	5	f	f	NOUN
ejpam-4470	147	6	:	:	PUNCT
ejpam-4470	147	7	r	r	NOUN
ejpam-4470	147	8	×	×	NOUN
ejpam-4470	147	9	r	r	NOUN
ejpam-4470	147	10	→	→	PUNCT
ejpam-4470	147	11	e1	e1	NOUN
ejpam-4470	147	12	be	be	VERB
ejpam-4470	147	13	a	a	DET
ejpam-4470	147	14	continuous	continuous	ADJ
ejpam-4470	147	15	fuzzy	fuzzy	ADV
ejpam-4470	147	16	-	-	PUNCT
ejpam-4470	147	17	valued	value	VERB
ejpam-4470	147	18	function	function	NOUN
ejpam-4470	147	19	.	.	PUNCT
ejpam-4470	148	1	suppose	suppose	VERB
ejpam-4470	148	2	that	that	SCONJ
ejpam-4470	148	3	e−x−y	e−x−y	PROPN
ejpam-4470	148	4	⊙	⊙	PROPN
ejpam-4470	148	5	f(ux	f(ux	PROPN
ejpam-4470	148	6	,	,	PUNCT
ejpam-4470	148	7	vy	vy	NOUN
ejpam-4470	148	8	)	)	PUNCT
ejpam-4470	148	9	is	be	AUX
ejpam-4470	148	10	improper	improper	ADJ
ejpam-4470	148	11	fuzzy	fuzzy	ADJ
ejpam-4470	148	12	riemann	riemann	PROPN
ejpam-4470	148	13	-	-	PUNCT
ejpam-4470	148	14	integrable	integrable	ADJ
ejpam-4470	148	15	on	on	ADP
ejpam-4470	148	16	r+	r+	X
ejpam-4470	148	17	×	×	NOUN
ejpam-4470	148	18	r+	r+	NOUN
ejpam-4470	148	19	,	,	PUNCT
ejpam-4470	148	20	then	then	ADV
ejpam-4470	148	21	(	(	PUNCT
ejpam-4470	148	22	fr	fr	ADJ
ejpam-4470	148	23	)	)	PUNCT
ejpam-4470	148	24	∞∫	∞∫	NOUN
ejpam-4470	148	25	0	0	PUNCT
ejpam-4470	148	26	(	(	PUNCT
ejpam-4470	148	27	fr	fr	NOUN
ejpam-4470	148	28	)	)	PUNCT
ejpam-4470	148	29	∞∫	∞∫	NOUN
ejpam-4470	148	30	0	0	NUM
ejpam-4470	148	31	e−x−y	e−x−y	NOUN
ejpam-4470	148	32	⊙	⊙	NOUN
ejpam-4470	148	33	f(ux	f(ux	PROPN
ejpam-4470	148	34	,	,	PUNCT
ejpam-4470	148	35	vy)dxdy	vy)dxdy	PROPN
ejpam-4470	148	36	is	be	AUX
ejpam-4470	148	37	called	call	VERB
ejpam-4470	148	38	the	the	DET
ejpam-4470	148	39	double	double	ADJ
ejpam-4470	148	40	fuzzy	fuzzy	ADJ
ejpam-4470	148	41	sumudu	sumudu	NOUN
ejpam-4470	148	42	transform	transform	NOUN
ejpam-4470	148	43	and	and	CCONJ
ejpam-4470	148	44	is	be	AUX
ejpam-4470	148	45	denoted	denote	VERB
ejpam-4470	148	46	by	by	ADP
ejpam-4470	148	47	f	f	PROPN
ejpam-4470	148	48	(	(	PUNCT
ejpam-4470	148	49	u	u	NOUN
ejpam-4470	148	50	,	,	PUNCT
ejpam-4470	148	51	v	v	NOUN
ejpam-4470	148	52	)	)	PUNCT
ejpam-4470	148	53	=	=	SYM
ejpam-4470	148	54	s[f(x	s[f(x	PROPN
ejpam-4470	148	55	,	,	PUNCT
ejpam-4470	148	56	y	y	NOUN
ejpam-4470	148	57	)	)	PUNCT
ejpam-4470	148	58	]	]	PUNCT
ejpam-4470	149	1	=	=	PUNCT
ejpam-4470	149	2	(	(	PUNCT
ejpam-4470	149	3	fr	fr	PROPN
ejpam-4470	149	4	)	)	PUNCT
ejpam-4470	149	5	∞∫	∞∫	NOUN
ejpam-4470	149	6	0	0	PUNCT
ejpam-4470	150	1	(	(	PUNCT
ejpam-4470	150	2	fr	fr	NOUN
ejpam-4470	150	3	)	)	PUNCT
ejpam-4470	150	4	∞∫	∞∫	NOUN
ejpam-4470	150	5	0	0	NUM
ejpam-4470	150	6	e−x−y⊙f(ux	e−x−y⊙f(ux	NOUN
ejpam-4470	150	7	,	,	PUNCT
ejpam-4470	150	8	vy)dxdy	vy)dxdy	NOUN
ejpam-4470	150	9	,	,	PUNCT
ejpam-4470	150	10	for	for	ADP
ejpam-4470	150	11	u	u	PROPN
ejpam-4470	150	12	∈	∈	PROPN
ejpam-4470	151	1	[	[	X
ejpam-4470	151	2	−τ1	−τ1	PROPN
ejpam-4470	151	3	,	,	PUNCT
ejpam-4470	151	4	τ2	τ2	NOUN
ejpam-4470	151	5	]	]	PUNCT
ejpam-4470	151	6	and	and	CCONJ
ejpam-4470	151	7	v	v	ADP
ejpam-4470	151	8	∈	∈	PROPN
ejpam-4470	152	1	[	[	X
ejpam-4470	152	2	−σ1	−σ1	PROPN
ejpam-4470	152	3	,	,	PUNCT
ejpam-4470	152	4	σ2	σ2	PROPN
ejpam-4470	152	5	]	]	PUNCT
ejpam-4470	152	6	,	,	PUNCT
ejpam-4470	152	7	(	(	PUNCT
ejpam-4470	152	8	1	1	X
ejpam-4470	152	9	)	)	PUNCT
ejpam-4470	152	10	where	where	SCONJ
ejpam-4470	152	11	the	the	DET
ejpam-4470	152	12	variables	variables	PROPN
ejpam-4470	152	13	u	u	NOUN
ejpam-4470	152	14	,	,	PUNCT
ejpam-4470	152	15	v	v	NUM
ejpam-4470	152	16	are	be	AUX
ejpam-4470	152	17	used	use	VERB
ejpam-4470	152	18	to	to	PART
ejpam-4470	152	19	factor	factor	VERB
ejpam-4470	152	20	the	the	DET
ejpam-4470	152	21	variables	variable	NOUN
ejpam-4470	152	22	x	x	NOUN
ejpam-4470	152	23	,	,	PUNCT
ejpam-4470	152	24	y	y	PROPN
ejpam-4470	152	25	in	in	ADP
ejpam-4470	152	26	the	the	DET
ejpam-4470	152	27	argument	argument	NOUN
ejpam-4470	152	28	of	of	ADP
ejpam-4470	152	29	the	the	DET
ejpam-4470	152	30	fuzzyvalued	fuzzyvalue	VERB
ejpam-4470	152	31	function	function	NOUN
ejpam-4470	152	32	and	and	CCONJ
ejpam-4470	152	33	τ1	τ1	NOUN
ejpam-4470	152	34	,	,	PUNCT
ejpam-4470	152	35	τ2	τ2	PROPN
ejpam-4470	152	36	,	,	PUNCT
ejpam-4470	152	37	σ1	σ1	PROPN
ejpam-4470	152	38	,	,	PUNCT
ejpam-4470	152	39	σ2	σ2	PROPN
ejpam-4470	152	40	>	>	X
ejpam-4470	152	41	0	0	PROPN
ejpam-4470	152	42	.	.	PUNCT
ejpam-4470	152	43	dfst	dfst	PROPN
ejpam-4470	152	44	also	also	ADV
ejpam-4470	152	45	can	can	AUX
ejpam-4470	152	46	be	be	AUX
ejpam-4470	152	47	presented	present	VERB
ejpam-4470	152	48	parametrically	parametrically	ADV
ejpam-4470	152	49	as	as	SCONJ
ejpam-4470	152	50	follows	follow	VERB
ejpam-4470	152	51	s[f(x	s[f(x	PROPN
ejpam-4470	152	52	,	,	PUNCT
ejpam-4470	152	53	y	y	NOUN
ejpam-4470	152	54	)	)	PUNCT
ejpam-4470	152	55	]	]	PUNCT
ejpam-4470	153	1	=	=	PUNCT
ejpam-4470	153	2	(	(	PUNCT
ejpam-4470	153	3	s[f(x	s[f(x	PROPN
ejpam-4470	153	4	,	,	PUNCT
ejpam-4470	153	5	y	y	PROPN
ejpam-4470	153	6	,	,	PUNCT
ejpam-4470	153	7	r	r	NOUN
ejpam-4470	153	8	)	)	PUNCT
ejpam-4470	153	9	]	]	PUNCT
ejpam-4470	153	10	,	,	PUNCT
ejpam-4470	153	11	s[f(x	s[f(x	PROPN
ejpam-4470	153	12	,	,	PUNCT
ejpam-4470	153	13	y	y	PROPN
ejpam-4470	153	14	,	,	PUNCT
ejpam-4470	153	15	r	r	NOUN
ejpam-4470	153	16	)	)	PUNCT
ejpam-4470	153	17	]	]	PUNCT
ejpam-4470	153	18	)	)	PUNCT
ejpam-4470	154	1	=	=	SYM
ejpam-4470	154	2	(	(	PUNCT
ejpam-4470	154	3	f	f	X
ejpam-4470	154	4	(	(	PUNCT
ejpam-4470	154	5	u	u	NOUN
ejpam-4470	154	6	,	,	PUNCT
ejpam-4470	154	7	v	v	NOUN
ejpam-4470	154	8	,	,	PUNCT
ejpam-4470	154	9	r	r	NOUN
ejpam-4470	154	10	)	)	PUNCT
ejpam-4470	154	11	,	,	PUNCT
ejpam-4470	154	12	f	f	PROPN
ejpam-4470	154	13	(	(	PUNCT
ejpam-4470	154	14	u	u	NOUN
ejpam-4470	154	15	,	,	PUNCT
ejpam-4470	154	16	v	v	NOUN
ejpam-4470	154	17	,	,	PUNCT
ejpam-4470	154	18	r	r	NOUN
ejpam-4470	154	19	)	)	PUNCT
ejpam-4470	154	20	)	)	PUNCT
ejpam-4470	155	1	=	=	SYM
ejpam-4470	155	2	f	f	PROPN
ejpam-4470	155	3	(	(	PUNCT
ejpam-4470	155	4	u	u	NOUN
ejpam-4470	155	5	,	,	PUNCT
ejpam-4470	155	6	v	v	NOUN
ejpam-4470	155	7	)	)	PUNCT
ejpam-4470	155	8	.	.	PUNCT
ejpam-4470	156	1	a.	a.	NOUN
ejpam-4470	156	2	f.alidema	f.alidema	PROPN
ejpam-4470	156	3	/	/	SYM
ejpam-4470	156	4	eur	eur	PROPN
ejpam-4470	156	5	.	.	PUNCT
ejpam-4470	157	1	j.	j.	PROPN
ejpam-4470	157	2	pure	pure	PROPN
ejpam-4470	157	3	appl	appl	PROPN
ejpam-4470	157	4	.	.	PROPN
ejpam-4470	157	5	math	math	PROPN
ejpam-4470	157	6	,	,	PUNCT
ejpam-4470	157	7	15	15	NUM
ejpam-4470	157	8	(	(	PUNCT
ejpam-4470	157	9	3	3	NUM
ejpam-4470	157	10	)	)	PUNCT
ejpam-4470	157	11	(	(	PUNCT
ejpam-4470	157	12	2022	2022	NUM
ejpam-4470	157	13	)	)	PUNCT
ejpam-4470	157	14	,	,	PUNCT
ejpam-4470	157	15	1363	1363	NUM
ejpam-4470	157	16	-	-	SYM
ejpam-4470	157	17	1375	1375	NUM
ejpam-4470	157	18	1368	1368	NUM
ejpam-4470	157	19	from	from	ADP
ejpam-4470	157	20	the	the	DET
ejpam-4470	157	21	classical	classical	ADJ
ejpam-4470	157	22	double	double	ADJ
ejpam-4470	157	23	sumudu	sumudu	NOUN
ejpam-4470	157	24	transform	transform	NOUN
ejpam-4470	157	25	,	,	PUNCT
ejpam-4470	157	26	we	we	PRON
ejpam-4470	157	27	have	have	VERB
ejpam-4470	157	28	s[f(x	s[f(x	PROPN
ejpam-4470	157	29	,	,	PUNCT
ejpam-4470	157	30	y	y	PROPN
ejpam-4470	157	31	,	,	PUNCT
ejpam-4470	157	32	r	r	NOUN
ejpam-4470	157	33	)	)	PUNCT
ejpam-4470	157	34	]	]	PUNCT
ejpam-4470	158	1	=	=	PUNCT
ejpam-4470	158	2	∞∫	∞∫	PROPN
ejpam-4470	158	3	0	0	NUM
ejpam-4470	158	4	∞∫	∞∫	PROPN
ejpam-4470	158	5	0	0	NUM
ejpam-4470	158	6	e−x−yf(ux	e−x−yf(ux	PROPN
ejpam-4470	158	7	,	,	PUNCT
ejpam-4470	158	8	vy	vy	NOUN
ejpam-4470	158	9	,	,	PUNCT
ejpam-4470	158	10	r)dxdy	r)dxdy	PROPN
ejpam-4470	158	11	and	and	CCONJ
ejpam-4470	158	12	s[f(x	s[f(x	PROPN
ejpam-4470	158	13	,	,	PUNCT
ejpam-4470	158	14	y	y	PROPN
ejpam-4470	158	15	,	,	PUNCT
ejpam-4470	158	16	r	r	NOUN
ejpam-4470	158	17	)	)	PUNCT
ejpam-4470	158	18	]	]	PUNCT
ejpam-4470	158	19	=	=	PUNCT
ejpam-4470	158	20	∞∫	∞∫	PROPN
ejpam-4470	158	21	0	0	NUM
ejpam-4470	159	1	∞∫	∞∫	PROPN
ejpam-4470	159	2	0	0	NUM
ejpam-4470	159	3	e−x−yf(ux	e−x−yf(ux	PROPN
ejpam-4470	159	4	,	,	PUNCT
ejpam-4470	159	5	vy	vy	NOUN
ejpam-4470	159	6	,	,	PUNCT
ejpam-4470	159	7	r)dxdy	r)dxdy	PROPN
ejpam-4470	159	8	definition	definition	NOUN
ejpam-4470	159	9	6	6	NUM
ejpam-4470	159	10	.	.	PUNCT
ejpam-4470	160	1	[	[	X
ejpam-4470	160	2	6	6	NUM
ejpam-4470	160	3	]	]	SYM
ejpam-4470	160	4	double	double	ADJ
ejpam-4470	160	5	fuzzy	fuzzy	ADJ
ejpam-4470	160	6	inverse	inverse	NOUN
ejpam-4470	160	7	sumudu	sumudu	NOUN
ejpam-4470	160	8	transform	transform	NOUN
ejpam-4470	160	9	can	can	AUX
ejpam-4470	160	10	be	be	AUX
ejpam-4470	160	11	written	write	VERB
ejpam-4470	160	12	as	as	ADP
ejpam-4470	160	13	the	the	DET
ejpam-4470	160	14	formula	formula	NOUN
ejpam-4470	160	15	s−1	s−1	PROPN
ejpam-4470	161	1	[	[	X
ejpam-4470	161	2	f	f	X
ejpam-4470	161	3	(	(	PUNCT
ejpam-4470	161	4	u	u	NOUN
ejpam-4470	161	5	,	,	PUNCT
ejpam-4470	161	6	v	v	NOUN
ejpam-4470	161	7	)	)	PUNCT
ejpam-4470	161	8	]	]	PUNCT
ejpam-4470	162	1	=	=	SYM
ejpam-4470	162	2	f(x	f(x	PROPN
ejpam-4470	162	3	,	,	PUNCT
ejpam-4470	162	4	y	y	NOUN
ejpam-4470	162	5	)	)	PUNCT
ejpam-4470	162	6	=	=	SYM
ejpam-4470	162	7	(	(	PUNCT
ejpam-4470	162	8	s−1[f	s−1[f	NOUN
ejpam-4470	162	9	(	(	PUNCT
ejpam-4470	162	10	u	u	NOUN
ejpam-4470	162	11	,	,	PUNCT
ejpam-4470	162	12	v	v	NOUN
ejpam-4470	162	13	,	,	PUNCT
ejpam-4470	162	14	r	r	NOUN
ejpam-4470	162	15	)	)	PUNCT
ejpam-4470	162	16	]	]	PUNCT
ejpam-4470	162	17	,	,	PUNCT
ejpam-4470	162	18	s−1[f	s−1[f	NOUN
ejpam-4470	162	19	(	(	PUNCT
ejpam-4470	162	20	u	u	NOUN
ejpam-4470	162	21	,	,	PUNCT
ejpam-4470	162	22	v	v	NOUN
ejpam-4470	162	23	,	,	PUNCT
ejpam-4470	162	24	r	r	NOUN
ejpam-4470	162	25	)	)	PUNCT
ejpam-4470	162	26	]	]	PUNCT
ejpam-4470	162	27	)	)	PUNCT
ejpam-4470	162	28	,	,	PUNCT
ejpam-4470	162	29	where	where	SCONJ
ejpam-4470	162	30	s−1[f	s−1[f	NOUN
ejpam-4470	162	31	(	(	PUNCT
ejpam-4470	162	32	u	u	NOUN
ejpam-4470	162	33	,	,	PUNCT
ejpam-4470	162	34	v	v	NOUN
ejpam-4470	162	35	,	,	PUNCT
ejpam-4470	162	36	r	r	NOUN
ejpam-4470	162	37	)	)	PUNCT
ejpam-4470	162	38	]	]	PUNCT
ejpam-4470	162	39	=	=	SYM
ejpam-4470	162	40	1	1	NUM
ejpam-4470	162	41	2πı	2πı	NOUN
ejpam-4470	162	42	γ+ı∞∫	γ+ı∞∫	NOUN
ejpam-4470	163	1	γ−ı∞	γ−ı∞	PRON
ejpam-4470	163	2	e	e	NOUN
ejpam-4470	163	3	x	x	SYM
ejpam-4470	163	4	udu	udu	ADJ
ejpam-4470	163	5	1	1	NUM
ejpam-4470	163	6	2πı	2πı	NOUN
ejpam-4470	163	7	δ+ı∞∫	δ+ı∞∫	NOUN
ejpam-4470	163	8	δ−ı∞	δ−ı∞	PROPN
ejpam-4470	163	9	e	e	NOUN
ejpam-4470	163	10	y	y	PROPN
ejpam-4470	163	11	vf	vf	X
ejpam-4470	163	12	(	(	PUNCT
ejpam-4470	163	13	u	u	NOUN
ejpam-4470	163	14	,	,	PUNCT
ejpam-4470	163	15	v	v	NOUN
ejpam-4470	163	16	,	,	PUNCT
ejpam-4470	163	17	r)dv	r)dv	PROPN
ejpam-4470	163	18	,	,	PUNCT
ejpam-4470	163	19	s−1[f	s−1[f	NOUN
ejpam-4470	163	20	(	(	PUNCT
ejpam-4470	163	21	u	u	NOUN
ejpam-4470	163	22	,	,	PUNCT
ejpam-4470	163	23	v	v	NOUN
ejpam-4470	163	24	,	,	PUNCT
ejpam-4470	163	25	r	r	NOUN
ejpam-4470	163	26	)	)	PUNCT
ejpam-4470	163	27	]	]	PUNCT
ejpam-4470	163	28	=	=	SYM
ejpam-4470	163	29	1	1	NUM
ejpam-4470	163	30	2πı	2πı	NOUN
ejpam-4470	163	31	γ+ı∞∫	γ+ı∞∫	NOUN
ejpam-4470	164	1	γ−ı∞	γ−ı∞	PRON
ejpam-4470	164	2	e	e	NOUN
ejpam-4470	164	3	x	x	SYM
ejpam-4470	164	4	udu	udu	ADJ
ejpam-4470	164	5	1	1	NUM
ejpam-4470	164	6	2πı	2πı	NOUN
ejpam-4470	164	7	δ+ı∞∫	δ+ı∞∫	NOUN
ejpam-4470	164	8	δ−ı∞	δ−ı∞	PROPN
ejpam-4470	164	9	e	e	NOUN
ejpam-4470	164	10	y	y	PROPN
ejpam-4470	164	11	vf	vf	X
ejpam-4470	164	12	(	(	PUNCT
ejpam-4470	164	13	u	u	NOUN
ejpam-4470	164	14	,	,	PUNCT
ejpam-4470	164	15	v	v	NOUN
ejpam-4470	164	16	,	,	PUNCT
ejpam-4470	164	17	r)dv	r)dv	PROPN
ejpam-4470	164	18	.	.	PROPN
ejpam-4470	165	1	for	for	ADP
ejpam-4470	165	2	all	all	DET
ejpam-4470	165	3	r	r	NOUN
ejpam-4470	165	4	∈	∈	PROPN
ejpam-4470	165	5	[	[	X
ejpam-4470	165	6	0	0	NUM
ejpam-4470	165	7	,	,	PUNCT
ejpam-4470	165	8	1	1	NUM
ejpam-4470	165	9	]	]	PUNCT
ejpam-4470	165	10	the	the	DET
ejpam-4470	165	11	functions	function	NOUN
ejpam-4470	165	12	f	f	X
ejpam-4470	165	13	(	(	PUNCT
ejpam-4470	165	14	u	u	NOUN
ejpam-4470	165	15	,	,	PUNCT
ejpam-4470	165	16	v	v	NOUN
ejpam-4470	165	17	,	,	PUNCT
ejpam-4470	165	18	r	r	NOUN
ejpam-4470	165	19	)	)	PUNCT
ejpam-4470	165	20	and	and	CCONJ
ejpam-4470	165	21	f	f	PROPN
ejpam-4470	165	22	(	(	PUNCT
ejpam-4470	165	23	u	u	NOUN
ejpam-4470	165	24	,	,	PUNCT
ejpam-4470	165	25	v	v	NOUN
ejpam-4470	165	26	,	,	PUNCT
ejpam-4470	165	27	r	r	NOUN
ejpam-4470	165	28	)	)	PUNCT
ejpam-4470	165	29	must	must	AUX
ejpam-4470	165	30	be	be	AUX
ejpam-4470	165	31	analytic	analytic	ADJ
ejpam-4470	165	32	functions	function	NOUN
ejpam-4470	165	33	for	for	ADP
ejpam-4470	165	34	all	all	DET
ejpam-4470	165	35	u	u	NOUN
ejpam-4470	165	36	and	and	CCONJ
ejpam-4470	165	37	v	v	NOUN
ejpam-4470	165	38	in	in	ADP
ejpam-4470	165	39	the	the	DET
ejpam-4470	165	40	region	region	NOUN
ejpam-4470	165	41	defined	define	VERB
ejpam-4470	165	42	by	by	ADP
ejpam-4470	165	43	the	the	DET
ejpam-4470	165	44	inequalities	inequality	NOUN
ejpam-4470	165	45	reu	reu	PROPN
ejpam-4470	165	46	≥	≥	PROPN
ejpam-4470	165	47	γ	γ	PROPN
ejpam-4470	165	48	and	and	CCONJ
ejpam-4470	165	49	rev	rev	PROPN
ejpam-4470	165	50	≥	≥	PROPN
ejpam-4470	165	51	δ	δ	PROPN
ejpam-4470	165	52	,	,	PUNCT
ejpam-4470	165	53	where	where	SCONJ
ejpam-4470	165	54	γ	γ	PROPN
ejpam-4470	165	55	and	and	CCONJ
ejpam-4470	165	56	δ	δ	PROPN
ejpam-4470	165	57	are	be	AUX
ejpam-4470	165	58	real	real	ADJ
ejpam-4470	165	59	constants	constant	NOUN
ejpam-4470	165	60	to	to	PART
ejpam-4470	165	61	be	be	AUX
ejpam-4470	165	62	chosen	choose	VERB
ejpam-4470	165	63	suitably	suitably	ADV
ejpam-4470	165	64	.	.	PUNCT
ejpam-4470	166	1	some	some	DET
ejpam-4470	166	2	properties	property	NOUN
ejpam-4470	166	3	of	of	ADP
ejpam-4470	166	4	sumudu	sumudu	NOUN
ejpam-4470	166	5	transform	transform	NOUN
ejpam-4470	166	6	and	and	CCONJ
ejpam-4470	166	7	double	double	ADJ
ejpam-4470	166	8	sumudu	sumudu	NOUN
ejpam-4470	166	9	transform	transform	NOUN
ejpam-4470	166	10	in	in	ADP
ejpam-4470	166	11	[	[	X
ejpam-4470	166	12	9	9	NUM
ejpam-4470	166	13	,	,	PUNCT
ejpam-4470	166	14	10	10	NUM
ejpam-4470	166	15	,	,	PUNCT
ejpam-4470	166	16	22	22	NUM
ejpam-4470	166	17	]	]	PUNCT
ejpam-4470	166	18	.	.	PUNCT
ejpam-4470	167	1	the	the	DET
ejpam-4470	167	2	convolution	convolution	NOUN
ejpam-4470	167	3	theorem	theorem	NOUN
ejpam-4470	167	4	is	be	AUX
ejpam-4470	167	5	provided	provide	VERB
ejpam-4470	167	6	below	below	ADV
ejpam-4470	167	7	.	.	PUNCT
ejpam-4470	168	1	definition	definition	NOUN
ejpam-4470	168	2	7	7	NUM
ejpam-4470	168	3	.	.	PUNCT
ejpam-4470	169	1	[	[	X
ejpam-4470	169	2	6	6	NUM
ejpam-4470	169	3	]	]	X
ejpam-4470	169	4	if	if	SCONJ
ejpam-4470	169	5	f(x	f(x	PROPN
ejpam-4470	169	6	,	,	PUNCT
ejpam-4470	169	7	y	y	PROPN
ejpam-4470	169	8	)	)	PUNCT
ejpam-4470	169	9	and	and	CCONJ
ejpam-4470	169	10	g(x	g(x	PROPN
ejpam-4470	169	11	,	,	PUNCT
ejpam-4470	169	12	y	y	NOUN
ejpam-4470	169	13	)	)	PUNCT
ejpam-4470	169	14	are	be	AUX
ejpam-4470	169	15	fuzzy	fuzzy	ADJ
ejpam-4470	169	16	riemann	riemann	PROPN
ejpam-4470	169	17	integrable	integrable	ADJ
ejpam-4470	169	18	functions	function	NOUN
ejpam-4470	169	19	,	,	PUNCT
ejpam-4470	169	20	then	then	ADV
ejpam-4470	169	21	double	double	ADJ
ejpam-4470	169	22	fuzzy	fuzzy	ADJ
ejpam-4470	169	23	convolution	convolution	NOUN
ejpam-4470	169	24	of	of	ADP
ejpam-4470	169	25	f(x	f(x	PROPN
ejpam-4470	169	26	,	,	PUNCT
ejpam-4470	169	27	y	y	NOUN
ejpam-4470	169	28	)	)	PUNCT
ejpam-4470	169	29	and	and	CCONJ
ejpam-4470	169	30	g(x	g(x	PROPN
ejpam-4470	169	31	,	,	PUNCT
ejpam-4470	169	32	y	y	NOUN
ejpam-4470	169	33	)	)	PUNCT
ejpam-4470	169	34	is	be	AUX
ejpam-4470	169	35	given	give	VERB
ejpam-4470	169	36	by	by	ADP
ejpam-4470	169	37	(	(	PUNCT
ejpam-4470	169	38	f	f	PROPN
ejpam-4470	169	39	∗	∗	NOUN
ejpam-4470	169	40	∗g)(x	∗g)(x	PROPN
ejpam-4470	169	41	,	,	PUNCT
ejpam-4470	169	42	y	y	NOUN
ejpam-4470	169	43	)	)	PUNCT
ejpam-4470	169	44	=	=	PUNCT
ejpam-4470	170	1	y∫	y∫	NOUN
ejpam-4470	170	2	0	0	PUNCT
ejpam-4470	171	1	x∫	x∫	ADJ
ejpam-4470	171	2	0	0	PUNCT
ejpam-4470	172	1	f(α	f(α	NOUN
ejpam-4470	172	2	,	,	PUNCT
ejpam-4470	172	3	β)g(x−	β)g(x−	PROPN
ejpam-4470	172	4	α	α	NUM
ejpam-4470	172	5	,	,	PUNCT
ejpam-4470	172	6	y	y	PROPN
ejpam-4470	172	7	−	−	NOUN
ejpam-4470	172	8	β)dαdβ	β)dαdβ	NOUN
ejpam-4470	172	9	and	and	CCONJ
ejpam-4470	172	10	the	the	DET
ejpam-4470	172	11	symbol	symbol	NOUN
ejpam-4470	172	12	∗∗	∗∗	PROPN
ejpam-4470	172	13	denotes	denote	VERB
ejpam-4470	172	14	the	the	DET
ejpam-4470	172	15	double	double	ADJ
ejpam-4470	172	16	convolution	convolution	NOUN
ejpam-4470	172	17	respect	respect	NOUN
ejpam-4470	172	18	to	to	ADP
ejpam-4470	172	19	x	x	PUNCT
ejpam-4470	172	20	and	and	CCONJ
ejpam-4470	172	21	y.	y.	NOUN
ejpam-4470	172	22	from	from	ADP
ejpam-4470	172	23	the	the	DET
ejpam-4470	172	24	definition	definition	NOUN
ejpam-4470	172	25	6	6	NUM
ejpam-4470	172	26	,	,	PUNCT
ejpam-4470	172	27	it	it	PRON
ejpam-4470	172	28	can	can	AUX
ejpam-4470	172	29	easily	easily	ADV
ejpam-4470	172	30	be	be	AUX
ejpam-4470	172	31	verified	verify	VERB
ejpam-4470	172	32	that	that	SCONJ
ejpam-4470	172	33	the	the	DET
ejpam-4470	172	34	following	follow	VERB
ejpam-4470	172	35	properties	property	NOUN
ejpam-4470	172	36	of	of	ADP
ejpam-4470	172	37	convolution	convolution	NOUN
ejpam-4470	172	38	hold	hold	VERB
ejpam-4470	172	39	:	:	PUNCT
ejpam-4470	172	40	(	(	PUNCT
ejpam-4470	172	41	i	i	NOUN
ejpam-4470	172	42	)	)	PUNCT
ejpam-4470	173	1	(	(	PUNCT
ejpam-4470	173	2	f	f	NOUN
ejpam-4470	173	3	∗	∗	NOUN
ejpam-4470	173	4	∗g)(x	∗g)(x	PROPN
ejpam-4470	173	5	,	,	PUNCT
ejpam-4470	173	6	y	y	NOUN
ejpam-4470	173	7	)	)	PUNCT
ejpam-4470	173	8	=	=	PUNCT
ejpam-4470	173	9	(	(	PUNCT
ejpam-4470	173	10	g	g	NOUN
ejpam-4470	173	11	∗	∗	NOUN
ejpam-4470	173	12	∗f)(x	∗f)(x	NOUN
ejpam-4470	173	13	,	,	PUNCT
ejpam-4470	173	14	y	y	PROPN
ejpam-4470	173	15	)	)	PUNCT
ejpam-4470	173	16	,	,	PUNCT
ejpam-4470	173	17	(	(	PUNCT
ejpam-4470	173	18	commutative	commutative	ADJ
ejpam-4470	173	19	)	)	PUNCT
ejpam-4470	173	20	;	;	PUNCT
ejpam-4470	173	21	(	(	PUNCT
ejpam-4470	173	22	ii	ii	NOUN
ejpam-4470	173	23	)	)	PUNCT
ejpam-4470	173	24	c(f	c(f	PROPN
ejpam-4470	173	25	∗	∗	NOUN
ejpam-4470	173	26	∗g)(x	∗g)(x	PROPN
ejpam-4470	173	27	,	,	PUNCT
ejpam-4470	173	28	y	y	NOUN
ejpam-4470	173	29	)	)	PUNCT
ejpam-4470	173	30	=	=	PUNCT
ejpam-4470	174	1	[	[	X
ejpam-4470	174	2	(	(	PUNCT
ejpam-4470	174	3	cf	cf	NOUN
ejpam-4470	174	4	)	)	PUNCT
ejpam-4470	174	5	∗	∗	NOUN
ejpam-4470	174	6	∗g](x	∗g](x	X
ejpam-4470	174	7	,	,	PUNCT
ejpam-4470	174	8	y	y	NOUN
ejpam-4470	174	9	)	)	PUNCT
ejpam-4470	174	10	,	,	PUNCT
ejpam-4470	174	11	c	c	PROPN
ejpam-4470	174	12	is	be	AUX
ejpam-4470	174	13	constant	constant	ADJ
ejpam-4470	174	14	;	;	PUNCT
ejpam-4470	174	15	(	(	PUNCT
ejpam-4470	174	16	iii	iii	X
ejpam-4470	174	17	)	)	PUNCT
ejpam-4470	175	1	[	[	X
ejpam-4470	175	2	f	f	X
ejpam-4470	175	3	∗	∗	X
ejpam-4470	175	4	∗(g	∗(g	PROPN
ejpam-4470	175	5	∗	∗	NOUN
ejpam-4470	175	6	∗h)](x	∗h)](x	PROPN
ejpam-4470	175	7	,	,	PUNCT
ejpam-4470	175	8	y	y	NOUN
ejpam-4470	175	9	)	)	PUNCT
ejpam-4470	175	10	=	=	PUNCT
ejpam-4470	176	1	[	[	X
ejpam-4470	176	2	(	(	PUNCT
ejpam-4470	176	3	f	f	PROPN
ejpam-4470	176	4	∗	∗	NOUN
ejpam-4470	176	5	∗g	∗g	PROPN
ejpam-4470	176	6	)	)	PUNCT
ejpam-4470	176	7	∗	∗	NOUN
ejpam-4470	176	8	∗h](x	∗h](x	NOUN
ejpam-4470	176	9	,	,	PUNCT
ejpam-4470	176	10	y	y	NOUN
ejpam-4470	176	11	)	)	PUNCT
ejpam-4470	176	12	,	,	PUNCT
ejpam-4470	176	13	(	(	PUNCT
ejpam-4470	176	14	associative	associative	ADJ
ejpam-4470	176	15	)	)	PUNCT
ejpam-4470	176	16	.	.	PUNCT
ejpam-4470	177	1	4	4	X
ejpam-4470	177	2	.	.	X
ejpam-4470	177	3	double	double	ADJ
ejpam-4470	177	4	fuzzy	fuzzy	ADJ
ejpam-4470	177	5	sumudu	sumudu	NOUN
ejpam-4470	177	6	adm	adm	NOUN
ejpam-4470	177	7	for	for	ADP
ejpam-4470	177	8	solving	solve	VERB
ejpam-4470	177	9	2d	2d	NOUN
ejpam-4470	177	10	-	-	PUNCT
ejpam-4470	177	11	vies	vie	NOUN
ejpam-4470	177	12	this	this	DET
ejpam-4470	177	13	section	section	NOUN
ejpam-4470	177	14	contains	contain	VERB
ejpam-4470	177	15	sumudu	sumudu	NOUN
ejpam-4470	177	16	decomposition	decomposition	NOUN
ejpam-4470	177	17	method	method	NOUN
ejpam-4470	177	18	for	for	ADP
ejpam-4470	177	19	solving	solve	VERB
ejpam-4470	177	20	two	two	NUM
ejpam-4470	177	21	dimensional	dimensional	ADJ
ejpam-4470	177	22	fuzzy	fuzzy	ADJ
ejpam-4470	177	23	convolution	convolution	NOUN
ejpam-4470	177	24	volterra	volterra	NOUN
ejpam-4470	177	25	integral	integral	ADJ
ejpam-4470	177	26	equations	equation	NOUN
ejpam-4470	177	27	.	.	PUNCT
ejpam-4470	178	1	a.	a.	NOUN
ejpam-4470	178	2	f.alidema	f.alidema	PROPN
ejpam-4470	178	3	/	/	SYM
ejpam-4470	178	4	eur	eur	PROPN
ejpam-4470	178	5	.	.	PUNCT
ejpam-4470	179	1	j.	j.	PROPN
ejpam-4470	179	2	pure	pure	PROPN
ejpam-4470	179	3	appl	appl	PROPN
ejpam-4470	179	4	.	.	PROPN
ejpam-4470	179	5	math	math	PROPN
ejpam-4470	179	6	,	,	PUNCT
ejpam-4470	179	7	15	15	NUM
ejpam-4470	179	8	(	(	PUNCT
ejpam-4470	179	9	3	3	NUM
ejpam-4470	179	10	)	)	PUNCT
ejpam-4470	179	11	(	(	PUNCT
ejpam-4470	179	12	2022	2022	NUM
ejpam-4470	179	13	)	)	PUNCT
ejpam-4470	179	14	,	,	PUNCT
ejpam-4470	179	15	1363	1363	NUM
ejpam-4470	179	16	-	-	SYM
ejpam-4470	179	17	1375	1375	NUM
ejpam-4470	179	18	1369	1369	NUM
ejpam-4470	179	19	the	the	DET
ejpam-4470	179	20	general	general	ADJ
ejpam-4470	179	21	form	form	NOUN
ejpam-4470	179	22	of	of	ADP
ejpam-4470	179	23	this	this	DET
ejpam-4470	179	24	integral	integral	ADJ
ejpam-4470	179	25	equation	equation	NOUN
ejpam-4470	179	26	is	be	AUX
ejpam-4470	179	27	given	give	VERB
ejpam-4470	179	28	by	by	ADP
ejpam-4470	179	29	f(x	f(x	PROPN
ejpam-4470	179	30	,	,	PUNCT
ejpam-4470	179	31	y	y	NOUN
ejpam-4470	179	32	)	)	PUNCT
ejpam-4470	179	33	=	=	SYM
ejpam-4470	180	1	g(x	g(x	NOUN
ejpam-4470	180	2	,	,	PUNCT
ejpam-4470	180	3	y)⊕	y)⊕	NOUN
ejpam-4470	180	4	(	(	PUNCT
ejpam-4470	180	5	fr	fr	NOUN
ejpam-4470	180	6	)	)	PUNCT
ejpam-4470	180	7	t∫	t∫	PROPN
ejpam-4470	180	8	0	0	NUM
ejpam-4470	180	9	s∫	s∫	NOUN
ejpam-4470	180	10	0	0	NUM
ejpam-4470	180	11	k(x−α	k(x−α	PROPN
ejpam-4470	180	12	,	,	PUNCT
ejpam-4470	180	13	y−	y−	PROPN
ejpam-4470	180	14	β)⊙g(f(α	β)⊙g(f(α	NOUN
ejpam-4470	180	15	,	,	PUNCT
ejpam-4470	180	16	β))dαdβ	β))dαdβ	PRON
ejpam-4470	180	17	,	,	PUNCT
ejpam-4470	180	18	(	(	PUNCT
ejpam-4470	180	19	x	x	X
ejpam-4470	180	20	,	,	PUNCT
ejpam-4470	180	21	y	y	NOUN
ejpam-4470	180	22	)	)	PUNCT
ejpam-4470	180	23	∈	∈	PROPN
ejpam-4470	181	1	[	[	X
ejpam-4470	181	2	0	0	NUM
ejpam-4470	181	3	,	,	PUNCT
ejpam-4470	181	4	b]x[0	b]x[0	PROPN
ejpam-4470	181	5	,	,	PUNCT
ejpam-4470	181	6	b	b	NOUN
ejpam-4470	181	7	]	]	X
ejpam-4470	181	8	,	,	PUNCT
ejpam-4470	181	9	(	(	PUNCT
ejpam-4470	181	10	2	2	X
ejpam-4470	181	11	)	)	PUNCT
ejpam-4470	181	12	where	where	SCONJ
ejpam-4470	181	13	k(x−α	k(x−α	PROPN
ejpam-4470	181	14	,	,	PUNCT
ejpam-4470	181	15	y−β	y−β	PROPN
ejpam-4470	181	16	)	)	PUNCT
ejpam-4470	181	17	are	be	AUX
ejpam-4470	181	18	arbitrary	arbitrary	ADJ
ejpam-4470	181	19	given	give	VERB
ejpam-4470	181	20	convolution	convolution	NOUN
ejpam-4470	181	21	kernel	kernel	NOUN
ejpam-4470	181	22	functions	function	NOUN
ejpam-4470	181	23	and	and	CCONJ
ejpam-4470	181	24	g	g	NOUN
ejpam-4470	181	25	is	be	AUX
ejpam-4470	181	26	a	a	DET
ejpam-4470	181	27	continuous	continuous	ADJ
ejpam-4470	181	28	fuzzy	fuzzy	ADV
ejpam-4470	181	29	-	-	PUNCT
ejpam-4470	181	30	valued	value	VERB
ejpam-4470	181	31	function	function	NOUN
ejpam-4470	181	32	.	.	PUNCT
ejpam-4470	182	1	5	5	X
ejpam-4470	182	2	.	.	X
ejpam-4470	182	3	main	main	ADJ
ejpam-4470	182	4	results	result	NOUN
ejpam-4470	182	5	we	we	PRON
ejpam-4470	182	6	combine	combine	VERB
ejpam-4470	182	7	dfst	dfst	NOUN
ejpam-4470	182	8	with	with	ADP
ejpam-4470	182	9	adm	adm	PROPN
ejpam-4470	182	10	to	to	PART
ejpam-4470	182	11	solve	solve	VERB
ejpam-4470	182	12	two	two	NUM
ejpam-4470	182	13	dimensional	dimensional	ADJ
ejpam-4470	182	14	fuzzy	fuzzy	ADJ
ejpam-4470	182	15	convolution	convolution	NOUN
ejpam-4470	182	16	vies	vie	NOUN
ejpam-4470	182	17	.	.	PUNCT
ejpam-4470	183	1	operating	operate	VERB
ejpam-4470	183	2	sumudu	sumudu	NOUN
ejpam-4470	183	3	transform	transform	NOUN
ejpam-4470	183	4	method	method	NOUN
ejpam-4470	183	5	in	in	ADP
ejpam-4470	183	6	both	both	DET
ejpam-4470	183	7	sides	side	NOUN
ejpam-4470	183	8	of	of	ADP
ejpam-4470	183	9	equation	equation	NOUN
ejpam-4470	183	10	(	(	PUNCT
ejpam-4470	183	11	2	2	NUM
ejpam-4470	183	12	)	)	PUNCT
ejpam-4470	183	13	.	.	PUNCT
ejpam-4470	184	1	after	after	ADP
ejpam-4470	184	2	that	that	PRON
ejpam-4470	184	3	using	use	VERB
ejpam-4470	184	4	the	the	DET
ejpam-4470	184	5	property	property	NOUN
ejpam-4470	184	6	and	and	CCONJ
ejpam-4470	184	7	convulotion	convulotion	NOUN
ejpam-4470	184	8	theorem	theorem	NOUN
ejpam-4470	184	9	of	of	ADP
ejpam-4470	184	10	sumudu	sumudu	NOUN
ejpam-4470	184	11	transform	transform	NOUN
ejpam-4470	184	12	.	.	PUNCT
ejpam-4470	185	1	by	by	ADP
ejpam-4470	185	2	using	use	VERB
ejpam-4470	185	3	convolution	convolution	NOUN
ejpam-4470	185	4	,	,	PUNCT
ejpam-4470	185	5	we	we	PRON
ejpam-4470	185	6	have	have	VERB
ejpam-4470	185	7	,	,	PUNCT
ejpam-4470	185	8	s[f(x	s[f(x	PROPN
ejpam-4470	185	9	,	,	PUNCT
ejpam-4470	185	10	y	y	NOUN
ejpam-4470	185	11	)	)	PUNCT
ejpam-4470	185	12	]	]	PUNCT
ejpam-4470	186	1	=	=	PUNCT
ejpam-4470	186	2	s[g(x	s[g(x	X
ejpam-4470	186	3	,	,	PUNCT
ejpam-4470	186	4	y)]⊕	y)]⊕	NOUN
ejpam-4470	186	5	uvs[k(x	uvs[k(x	VERB
ejpam-4470	186	6	,	,	PUNCT
ejpam-4470	186	7	y)]⊙	y)]⊙	PROPN
ejpam-4470	186	8	s[gf(x	s[gf(x	PROPN
ejpam-4470	186	9	,	,	PUNCT
ejpam-4470	186	10	y	y	PROPN
ejpam-4470	186	11	)	)	PUNCT
ejpam-4470	186	12	]	]	PUNCT
ejpam-4470	186	13	,	,	PUNCT
ejpam-4470	186	14	(	(	PUNCT
ejpam-4470	186	15	3	3	X
ejpam-4470	186	16	)	)	PUNCT
ejpam-4470	186	17	operating	operate	VERB
ejpam-4470	186	18	inverse	inverse	NOUN
ejpam-4470	186	19	fuzzy	fuzzy	ADJ
ejpam-4470	186	20	sumudu	sumudu	NOUN
ejpam-4470	186	21	transformation	transformation	NOUN
ejpam-4470	186	22	on	on	ADP
ejpam-4470	186	23	both	both	DET
ejpam-4470	186	24	sides	side	NOUN
ejpam-4470	186	25	.	.	PUNCT
ejpam-4470	187	1	f(x	f(x	PROPN
ejpam-4470	187	2	,	,	PUNCT
ejpam-4470	187	3	y	y	NOUN
ejpam-4470	187	4	)	)	PUNCT
ejpam-4470	187	5	=	=	SYM
ejpam-4470	188	1	g(x	g(x	NOUN
ejpam-4470	188	2	,	,	PUNCT
ejpam-4470	188	3	y)⊕	y)⊕	NOUN
ejpam-4470	188	4	uvs−1(k(x	uvs−1(k(x	PROPN
ejpam-4470	188	5	,	,	PUNCT
ejpam-4470	188	6	y))⊙	y))⊙	NOUN
ejpam-4470	188	7	s(gf(x	s(gf(x	PROPN
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ejpam-4470	188	10	)	)	PUNCT
ejpam-4470	188	11	)	)	PUNCT
ejpam-4470	188	12	,	,	PUNCT
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ejpam-4470	188	14	4	4	X
ejpam-4470	188	15	)	)	PUNCT
ejpam-4470	188	16	∞∑	∞∑	NUM
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ejpam-4470	188	19	,	,	PUNCT
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ejpam-4470	188	21	,	,	PUNCT
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ejpam-4470	188	24	=	=	SYM
ejpam-4470	189	1	g(x	g(x	NOUN
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ejpam-4470	189	5	r	r	NOUN
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ejpam-4470	189	8	s−1[uv[k(x	s−1[uv[k(x	NOUN
ejpam-4470	189	9	,	,	PUNCT
ejpam-4470	189	10	y)]s	y)]s	PRON
ejpam-4470	189	11	[	[	PUNCT
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ejpam-4470	189	15	,	,	PUNCT
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ejpam-4470	189	21	]	]	PUNCT
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ejpam-4470	189	25	k(x−	k(x−	PROPN
ejpam-4470	189	26	α	α	PROPN
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ejpam-4470	189	30	β	β	NOUN
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ejpam-4470	189	37	β	β	X
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ejpam-4470	189	49	1	1	NUM
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ejpam-4470	189	53	β	β	X
ejpam-4470	189	54	≤	≤	NUM
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ejpam-4470	190	13	(	(	PUNCT
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ejpam-4470	190	15	,	,	PUNCT
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ejpam-4470	190	18	r	r	NOUN
ejpam-4470	190	19	)	)	PUNCT
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ejpam-4470	190	22	,	,	PUNCT
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ejpam-4470	190	24	,	,	PUNCT
ejpam-4470	190	25	r	r	NOUN
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ejpam-4470	191	1	+	+	NOUN
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ejpam-4470	191	4	y)]s[f	y)]s[f	PROPN
ejpam-4470	191	5	i	i	PRON
ejpam-4470	191	6	(	(	PUNCT
ejpam-4470	191	7	x	x	X
ejpam-4470	191	8	,	,	PUNCT
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ejpam-4470	191	10	,	,	PUNCT
ejpam-4470	191	11	r	r	NOUN
ejpam-4470	191	12	)	)	PUNCT
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ejpam-4470	191	14	]	]	PUNCT
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ejpam-4470	191	18	0	0	NUM
ejpam-4470	191	19	.	.	PUNCT
ejpam-4470	192	1	f	f	PROPN
ejpam-4470	192	2	i+1(x	i+1(x	PROPN
ejpam-4470	192	3	,	,	PUNCT
ejpam-4470	192	4	y	y	PROPN
ejpam-4470	192	5	,	,	PUNCT
ejpam-4470	192	6	r	r	NOUN
ejpam-4470	192	7	)	)	PUNCT
ejpam-4470	192	8	=	=	SYM
ejpam-4470	193	1	g(x	g(x	NOUN
ejpam-4470	193	2	,	,	PUNCT
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ejpam-4470	193	4	,	,	PUNCT
ejpam-4470	193	5	r	r	NOUN
ejpam-4470	193	6	)	)	PUNCT
ejpam-4470	193	7	+	+	NOUN
ejpam-4470	193	8	s−1[uv[k(x	s−1[uv[k(x	PROPN
ejpam-4470	193	9	,	,	PUNCT
ejpam-4470	193	10	y)]s[f	y)]s[f	PROPN
ejpam-4470	193	11	i(x	i(x	PROPN
ejpam-4470	193	12	,	,	PUNCT
ejpam-4470	193	13	y	y	PROPN
ejpam-4470	193	14	,	,	PUNCT
ejpam-4470	193	15	r	r	NOUN
ejpam-4470	193	16	)	)	PUNCT
ejpam-4470	193	17	]	]	X
ejpam-4470	193	18	]	]	PUNCT
ejpam-4470	193	19	,	,	PUNCT
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ejpam-4470	193	22	0	0	NUM
ejpam-4470	193	23	.	.	PUNCT
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ejpam-4470	194	5	α	α	PROPN
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ejpam-4470	194	11	=	=	SYM
ejpam-4470	194	12	(	(	PUNCT
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ejpam-4470	194	14	α)(y	α)(y	NUM
ejpam-4470	194	15	−	−	NOUN
ejpam-4470	194	16	β	β	X
ejpam-4470	194	17	)	)	PUNCT
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ejpam-4470	195	1	α	α	NOUN
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ejpam-4470	195	5	1	1	NUM
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ejpam-4470	195	7	0	0	NUM
ejpam-4470	195	8	≤	≤	NUM
ejpam-4470	195	9	β	β	X
ejpam-4470	195	10	≤	≤	NUM
ejpam-4470	195	11	y	y	PROPN
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ejpam-4470	195	13	1	1	NUM
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ejpam-4470	196	13	(	(	PUNCT
ejpam-4470	196	14	x	x	NOUN
ejpam-4470	196	15	,	,	PUNCT
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ejpam-4470	196	17	,	,	PUNCT
ejpam-4470	196	18	r	r	NOUN
ejpam-4470	196	19	)	)	PUNCT
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ejpam-4470	196	22	,	,	PUNCT
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ejpam-4470	196	25	r	r	NOUN
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ejpam-4470	197	1	+	+	NOUN
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ejpam-4470	198	4	i(x	i(x	PROPN
ejpam-4470	198	5	,	,	PUNCT
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ejpam-4470	198	7	,	,	PUNCT
ejpam-4470	198	8	r	r	NOUN
ejpam-4470	198	9	)	)	PUNCT
ejpam-4470	198	10	]	]	X
ejpam-4470	198	11	]	]	PUNCT
ejpam-4470	198	12	,	,	PUNCT
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ejpam-4470	199	3	,	,	PUNCT
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ejpam-4470	199	5	,	,	PUNCT
ejpam-4470	199	6	r	r	NOUN
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ejpam-4470	199	8	=	=	SYM
ejpam-4470	200	1	g(x	g(x	NOUN
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ejpam-4470	200	4	,	,	PUNCT
ejpam-4470	200	5	r	r	NOUN
ejpam-4470	200	6	)	)	PUNCT
ejpam-4470	200	7	+	+	NOUN
ejpam-4470	200	8	s−1[uv[k(x	s−1[uv[k(x	PROPN
ejpam-4470	200	9	,	,	PUNCT
ejpam-4470	200	10	y)]s[f	y)]s[f	PROPN
ejpam-4470	200	11	i	i	PRON
ejpam-4470	200	12	(	(	PUNCT
ejpam-4470	200	13	x	x	X
ejpam-4470	200	14	,	,	PUNCT
ejpam-4470	200	15	y	y	PROPN
ejpam-4470	200	16	,	,	PUNCT
ejpam-4470	200	17	r	r	NOUN
ejpam-4470	200	18	)	)	PUNCT
ejpam-4470	200	19	]	]	X
ejpam-4470	200	20	]	]	PUNCT
ejpam-4470	200	21	,	,	PUNCT
ejpam-4470	200	22	i	i	PRON
ejpam-4470	200	23	≥	≥	VERB
ejpam-4470	200	24	0	0	NUM
ejpam-4470	200	25	.	.	PUNCT
ejpam-4470	201	1	the	the	DET
ejpam-4470	201	2	adm	adm	PROPN
ejpam-4470	201	3	assume	assume	VERB
ejpam-4470	201	4	an	an	DET
ejpam-4470	201	5	infinite	infinite	ADJ
ejpam-4470	201	6	series	series	NOUN
ejpam-4470	201	7	solution	solution	NOUN
ejpam-4470	201	8	for	for	ADP
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ejpam-4470	201	11	(	(	PUNCT
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ejpam-4470	201	13	,	,	PUNCT
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ejpam-4470	201	18	)	)	PUNCT
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ejpam-4470	201	22	,	,	PUNCT
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ejpam-4470	201	25	r	r	NOUN
ejpam-4470	201	26	)	)	PUNCT
ejpam-4470	201	27	)	)	PUNCT
ejpam-4470	202	1	f(x	f(x	PROPN
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ejpam-4470	202	5	r	r	NOUN
ejpam-4470	202	6	)	)	PUNCT
ejpam-4470	202	7	=	=	PUNCT
ejpam-4470	203	1	∞∑	∞∑	NUM
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ejpam-4470	203	4	,	,	PUNCT
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ejpam-4470	203	6	,	,	PUNCT
ejpam-4470	203	7	r	r	NOUN
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ejpam-4470	203	9	,	,	PUNCT
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ejpam-4470	203	11	,	,	PUNCT
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ejpam-4470	203	13	,	,	PUNCT
ejpam-4470	203	14	r	r	NOUN
ejpam-4470	203	15	)	)	PUNCT
ejpam-4470	203	16	=	=	PUNCT
ejpam-4470	203	17	∞∑	∞∑	NUM
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ejpam-4470	203	20	,	,	PUNCT
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ejpam-4470	203	22	,	,	PUNCT
ejpam-4470	203	23	r	r	NOUN
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ejpam-4470	203	25	(	(	PUNCT
ejpam-4470	203	26	5	5	X
ejpam-4470	203	27	)	)	PUNCT
ejpam-4470	203	28	the	the	DET
ejpam-4470	203	29	parametric	parametric	ADJ
ejpam-4470	203	30	form	form	NOUN
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ejpam-4470	203	35	[	[	X
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ejpam-4470	203	37	]	]	PUNCT
ejpam-4470	203	38	a.	a.	NOUN
ejpam-4470	203	39	f.alidema	f.alidema	PROPN
ejpam-4470	203	40	/	/	SYM
ejpam-4470	203	41	eur	eur	PROPN
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ejpam-4470	204	2	pure	pure	PROPN
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ejpam-4470	204	5	math	math	PROPN
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ejpam-4470	204	9	3	3	NUM
ejpam-4470	204	10	)	)	PUNCT
ejpam-4470	204	11	(	(	PUNCT
ejpam-4470	204	12	2022	2022	NUM
ejpam-4470	204	13	)	)	PUNCT
ejpam-4470	204	14	,	,	PUNCT
ejpam-4470	204	15	1363	1363	NUM
ejpam-4470	204	16	-	-	SYM
ejpam-4470	204	17	1375	1375	NUM
ejpam-4470	204	18	1370	1370	NUM
ejpam-4470	205	1	∞∑	∞∑	PRON
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ejpam-4470	205	4	i	i	PRON
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ejpam-4470	205	7	,	,	PUNCT
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ejpam-4470	206	6	r	r	NOUN
ejpam-4470	206	7	)	)	PUNCT
ejpam-4470	206	8	+	+	NOUN
ejpam-4470	206	9	s−1[uv[k(x	s−1[uv[k(x	NOUN
ejpam-4470	206	10	,	,	PUNCT
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ejpam-4470	206	13	∞∑	∞∑	PROPN
ejpam-4470	206	14	i=0	i=0	PROPN
ejpam-4470	206	15	f	f	X
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ejpam-4470	206	19	,	,	PUNCT
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ejpam-4470	206	24	]	]	PUNCT
ejpam-4470	206	25	]	]	X
ejpam-4470	206	26	(	(	PUNCT
ejpam-4470	206	27	6	6	X
ejpam-4470	206	28	)	)	PUNCT
ejpam-4470	206	29	∞∑	∞∑	NUM
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ejpam-4470	206	34	y	y	PROPN
ejpam-4470	206	35	,	,	PUNCT
ejpam-4470	206	36	r	r	NOUN
ejpam-4470	206	37	)	)	PUNCT
ejpam-4470	206	38	=	=	SYM
ejpam-4470	207	1	g(x	g(x	NOUN
ejpam-4470	207	2	,	,	PUNCT
ejpam-4470	207	3	y	y	PROPN
ejpam-4470	207	4	,	,	PUNCT
ejpam-4470	207	5	r	r	NOUN
ejpam-4470	207	6	)	)	PUNCT
ejpam-4470	207	7	+	+	NOUN
ejpam-4470	207	8	s−1[uv[k(x	s−1[uv[k(x	NOUN
ejpam-4470	207	9	,	,	PUNCT
ejpam-4470	207	10	y)]s	y)]s	PRON
ejpam-4470	207	11	[	[	PUNCT
ejpam-4470	207	12	∞∑	∞∑	NUM
ejpam-4470	207	13	i=0	i=0	PROPN
ejpam-4470	207	14	f	f	SYM
ejpam-4470	207	15	i(x	i(x	PROPN
ejpam-4470	207	16	,	,	PUNCT
ejpam-4470	207	17	y	y	PROPN
ejpam-4470	207	18	,	,	PUNCT
ejpam-4470	207	19	r	r	NOUN
ejpam-4470	207	20	)	)	PUNCT
ejpam-4470	207	21	]	]	PUNCT
ejpam-4470	207	22	]	]	X
ejpam-4470	207	23	(	(	PUNCT
ejpam-4470	207	24	7	7	X
ejpam-4470	207	25	)	)	PUNCT
ejpam-4470	207	26	the	the	DET
ejpam-4470	207	27	operator	operator	NOUN
ejpam-4470	207	28	g(f(x	g(f(x	PROPN
ejpam-4470	207	29	,	,	PUNCT
ejpam-4470	207	30	y	y	PROPN
ejpam-4470	207	31	,	,	PUNCT
ejpam-4470	207	32	r	r	NOUN
ejpam-4470	207	33	)	)	PUNCT
ejpam-4470	207	34	)	)	PUNCT
ejpam-4470	207	35	and	and	CCONJ
ejpam-4470	207	36	g(f(x	g(f(x	PROPN
ejpam-4470	207	37	,	,	PUNCT
ejpam-4470	207	38	y	y	PROPN
ejpam-4470	207	39	,	,	PUNCT
ejpam-4470	207	40	r	r	NOUN
ejpam-4470	207	41	)	)	PUNCT
ejpam-4470	207	42	)	)	PUNCT
ejpam-4470	207	43	into	into	ADP
ejpam-4470	207	44	an	an	DET
ejpam-4470	207	45	infinite	infinite	ADJ
ejpam-4470	207	46	series	series	NOUN
ejpam-4470	207	47	of	of	ADP
ejpam-4470	207	48	polynomials	polynomial	NOUN
ejpam-4470	207	49	given	give	VERB
ejpam-4470	207	50	by	by	ADP
ejpam-4470	207	51	g(f(x	g(f(x	PROPN
ejpam-4470	207	52	,	,	PUNCT
ejpam-4470	207	53	y	y	PROPN
ejpam-4470	207	54	,	,	PUNCT
ejpam-4470	207	55	r	r	NOUN
ejpam-4470	207	56	)	)	PUNCT
ejpam-4470	207	57	)	)	PUNCT
ejpam-4470	208	1	=	=	PUNCT
ejpam-4470	209	1	∞∑	∞∑	NUM
ejpam-4470	209	2	i=0	i=0	ADJ
ejpam-4470	209	3	ai(f0	ai(f0	NOUN
ejpam-4470	209	4	(	(	PUNCT
ejpam-4470	209	5	x	x	X
ejpam-4470	209	6	,	,	PUNCT
ejpam-4470	209	7	y	y	PROPN
ejpam-4470	209	8	,	,	PUNCT
ejpam-4470	209	9	r	r	NOUN
ejpam-4470	209	10	)	)	PUNCT
ejpam-4470	209	11	,	,	PUNCT
ejpam-4470	209	12	f	f	PROPN
ejpam-4470	209	13	1	1	NUM
ejpam-4470	209	14	(	(	PUNCT
ejpam-4470	209	15	x	x	NOUN
ejpam-4470	209	16	,	,	PUNCT
ejpam-4470	209	17	y	y	PROPN
ejpam-4470	209	18	,	,	PUNCT
ejpam-4470	209	19	r	r	NOUN
ejpam-4470	209	20	)	)	PUNCT
ejpam-4470	209	21	,	,	PUNCT
ejpam-4470	209	22	...	...	PUNCT
ejpam-4470	209	23	,	,	PUNCT
ejpam-4470	209	24	f	f	PROPN
ejpam-4470	209	25	i	i	PRON
ejpam-4470	209	26	(	(	PUNCT
ejpam-4470	209	27	x	x	X
ejpam-4470	209	28	,	,	PUNCT
ejpam-4470	209	29	y	y	PROPN
ejpam-4470	209	30	,	,	PUNCT
ejpam-4470	209	31	r	r	NOUN
ejpam-4470	209	32	)	)	PUNCT
ejpam-4470	209	33	)	)	PUNCT
ejpam-4470	209	34	,	,	PUNCT
ejpam-4470	209	35	g(f(x	g(f(x	PROPN
ejpam-4470	209	36	,	,	PUNCT
ejpam-4470	209	37	y	y	PROPN
ejpam-4470	209	38	,	,	PUNCT
ejpam-4470	209	39	r	r	NOUN
ejpam-4470	209	40	)	)	PUNCT
ejpam-4470	209	41	)	)	PUNCT
ejpam-4470	209	42	=	=	PUNCT
ejpam-4470	210	1	∞∑	∞∑	NUM
ejpam-4470	210	2	i=0	i=0	PROPN
ejpam-4470	210	3	ai(f0(x	ai(f0(x	PROPN
ejpam-4470	210	4	,	,	PUNCT
ejpam-4470	210	5	y	y	PROPN
ejpam-4470	210	6	,	,	PUNCT
ejpam-4470	210	7	r	r	NOUN
ejpam-4470	210	8	)	)	PUNCT
ejpam-4470	210	9	,	,	PUNCT
ejpam-4470	210	10	f1(x	f1(x	PROPN
ejpam-4470	210	11	,	,	PUNCT
ejpam-4470	210	12	y	y	PROPN
ejpam-4470	210	13	,	,	PUNCT
ejpam-4470	210	14	r	r	NOUN
ejpam-4470	210	15	)	)	PUNCT
ejpam-4470	210	16	,	,	PUNCT
ejpam-4470	210	17	...	...	PUNCT
ejpam-4470	210	18	,	,	PUNCT
ejpam-4470	210	19	f	f	PROPN
ejpam-4470	210	20	i(x	i(x	PROPN
ejpam-4470	210	21	,	,	PUNCT
ejpam-4470	210	22	y	y	PROPN
ejpam-4470	210	23	,	,	PUNCT
ejpam-4470	210	24	r	r	NOUN
ejpam-4470	210	25	)	)	PUNCT
ejpam-4470	210	26	)	)	PUNCT
ejpam-4470	210	27	,	,	PUNCT
ejpam-4470	210	28	where	where	SCONJ
ejpam-4470	210	29	the	the	DET
ejpam-4470	210	30	ai	ai	NOUN
ejpam-4470	210	31	=	=	PUNCT
ejpam-4470	210	32	(	(	PUNCT
ejpam-4470	210	33	ai	ai	PROPN
ejpam-4470	210	34	,	,	PUNCT
ejpam-4470	210	35	ai	ai	NOUN
ejpam-4470	210	36	)	)	PUNCT
ejpam-4470	210	37	,	,	PUNCT
ejpam-4470	210	38	i	i	PRON
ejpam-4470	210	39	≥	≥	VERB
ejpam-4470	210	40	0	0	NUM
ejpam-4470	210	41	are	be	AUX
ejpam-4470	210	42	the	the	DET
ejpam-4470	210	43	so	so	ADV
ejpam-4470	210	44	-	-	PUNCT
ejpam-4470	210	45	called	call	VERB
ejpam-4470	210	46	adomian	adomian	NOUN
ejpam-4470	210	47	polynomials	polynomial	NOUN
ejpam-4470	210	48	defined	define	VERB
ejpam-4470	210	49	by	by	ADP
ejpam-4470	210	50	the	the	DET
ejpam-4470	210	51	components	component	NOUN
ejpam-4470	210	52	f(x	f(x	PROPN
ejpam-4470	210	53	,	,	PUNCT
ejpam-4470	210	54	y	y	PROPN
ejpam-4470	210	55	,	,	PUNCT
ejpam-4470	210	56	r)and	r)and	PROPN
ejpam-4470	210	57	f(x	f(x	PROPN
ejpam-4470	210	58	,	,	PUNCT
ejpam-4470	210	59	y	y	PROPN
ejpam-4470	210	60	,	,	PUNCT
ejpam-4470	210	61	r	r	NOUN
ejpam-4470	210	62	)	)	PUNCT
ejpam-4470	210	63	,	,	PUNCT
ejpam-4470	210	64	i	i	PRON
ejpam-4470	210	65	≥	≥	VERB
ejpam-4470	210	66	0	0	NUM
ejpam-4470	210	67	.	.	PUNCT
ejpam-4470	210	68	,	,	PUNCT
ejpam-4470	210	69	computed	compute	VERB
ejpam-4470	210	70	using	use	VERB
ejpam-4470	210	71	the	the	DET
ejpam-4470	210	72	following	follow	VERB
ejpam-4470	210	73	recursive	recursive	ADJ
ejpam-4470	210	74	relations	relation	NOUN
ejpam-4470	210	75	f	f	PROPN
ejpam-4470	210	76	0	0	PUNCT
ejpam-4470	211	1	(	(	PUNCT
ejpam-4470	211	2	x	x	X
ejpam-4470	211	3	,	,	PUNCT
ejpam-4470	211	4	y	y	PROPN
ejpam-4470	211	5	,	,	PUNCT
ejpam-4470	211	6	r	r	NOUN
ejpam-4470	211	7	)	)	PUNCT
ejpam-4470	211	8	=	=	SYM
ejpam-4470	211	9	g(x	g(x	NOUN
ejpam-4470	211	10	,	,	PUNCT
ejpam-4470	211	11	y	y	PROPN
ejpam-4470	211	12	,	,	PUNCT
ejpam-4470	211	13	r	r	NOUN
ejpam-4470	211	14	)	)	PUNCT
ejpam-4470	211	15	,	,	PUNCT
ejpam-4470	211	16	(	(	PUNCT
ejpam-4470	211	17	8)	8)	NUM
ejpam-4470	211	18	f	f	NOUN
ejpam-4470	211	19	0	0	PUNCT
ejpam-4470	211	20	(	(	PUNCT
ejpam-4470	211	21	x	x	X
ejpam-4470	211	22	,	,	PUNCT
ejpam-4470	211	23	y	y	PROPN
ejpam-4470	211	24	,	,	PUNCT
ejpam-4470	211	25	r	r	NOUN
ejpam-4470	211	26	)	)	PUNCT
ejpam-4470	211	27	=	=	SYM
ejpam-4470	212	1	g(x	g(x	NOUN
ejpam-4470	212	2	,	,	PUNCT
ejpam-4470	212	3	y	y	PROPN
ejpam-4470	212	4	,	,	PUNCT
ejpam-4470	212	5	r	r	NOUN
ejpam-4470	212	6	)	)	PUNCT
ejpam-4470	212	7	,	,	PUNCT
ejpam-4470	212	8	f1(x	f1(x	PROPN
ejpam-4470	212	9	,	,	PUNCT
ejpam-4470	212	10	y	y	PROPN
ejpam-4470	212	11	,	,	PUNCT
ejpam-4470	212	12	r	r	NOUN
ejpam-4470	212	13	)	)	PUNCT
ejpam-4470	212	14	=	=	SYM
ejpam-4470	212	15	s−1(u2v2s(a0	s−1(u2v2s(a0	NOUN
ejpam-4470	212	16	)	)	PUNCT
ejpam-4470	212	17	)	)	PUNCT
ejpam-4470	212	18	,	,	PUNCT
ejpam-4470	212	19	f2(x	f2(x	PROPN
ejpam-4470	212	20	,	,	PUNCT
ejpam-4470	212	21	y	y	PROPN
ejpam-4470	212	22	,	,	PUNCT
ejpam-4470	212	23	r	r	NOUN
ejpam-4470	212	24	)	)	PUNCT
ejpam-4470	212	25	=	=	SYM
ejpam-4470	212	26	s−1(u2v2s(a1	s−1(u2v2s(a1	NOUN
ejpam-4470	212	27	)	)	PUNCT
ejpam-4470	212	28	)	)	PUNCT
ejpam-4470	212	29	,	,	PUNCT
ejpam-4470	212	30	...	...	PUNCT
ejpam-4470	212	31	,	,	PUNCT
ejpam-4470	212	32	f	f	PROPN
ejpam-4470	212	33	i+1	i+1	X
ejpam-4470	212	34	(	(	PUNCT
ejpam-4470	212	35	x	x	NOUN
ejpam-4470	212	36	,	,	PUNCT
ejpam-4470	212	37	y	y	PROPN
ejpam-4470	212	38	,	,	PUNCT
ejpam-4470	212	39	r	r	NOUN
ejpam-4470	212	40	)	)	PUNCT
ejpam-4470	212	41	=	=	SYM
ejpam-4470	212	42	s−1[uv[k(x	s−1[uv[k(x	PROPN
ejpam-4470	212	43	,	,	PUNCT
ejpam-4470	212	44	y)]s(ai	y)]s(ai	NUM
ejpam-4470	212	45	)	)	PUNCT
ejpam-4470	212	46	,	,	PUNCT
ejpam-4470	212	47	i	i	PRON
ejpam-4470	212	48	≥	≥	VERB
ejpam-4470	212	49	0	0	NUM
ejpam-4470	212	50	.	.	PUNCT
ejpam-4470	213	1	and	and	CCONJ
ejpam-4470	213	2	,	,	PUNCT
ejpam-4470	213	3	f0(x	f0(x	PROPN
ejpam-4470	213	4	,	,	PUNCT
ejpam-4470	213	5	y	y	PROPN
ejpam-4470	213	6	,	,	PUNCT
ejpam-4470	213	7	r	r	NOUN
ejpam-4470	213	8	)	)	PUNCT
ejpam-4470	213	9	=	=	SYM
ejpam-4470	214	1	g(x	g(x	NOUN
ejpam-4470	214	2	,	,	PUNCT
ejpam-4470	214	3	y	y	PROPN
ejpam-4470	214	4	,	,	PUNCT
ejpam-4470	214	5	r	r	NOUN
ejpam-4470	214	6	)	)	PUNCT
ejpam-4470	214	7	,	,	PUNCT
ejpam-4470	214	8	f1(x	f1(x	PROPN
ejpam-4470	214	9	,	,	PUNCT
ejpam-4470	214	10	y	y	PROPN
ejpam-4470	214	11	,	,	PUNCT
ejpam-4470	214	12	r	r	NOUN
ejpam-4470	214	13	)	)	PUNCT
ejpam-4470	214	14	=	=	SYM
ejpam-4470	214	15	s−1(u2v2s(a0	s−1(u2v2s(a0	NOUN
ejpam-4470	214	16	)	)	PUNCT
ejpam-4470	214	17	)	)	PUNCT
ejpam-4470	214	18	,	,	PUNCT
ejpam-4470	214	19	f2(x	f2(x	PROPN
ejpam-4470	214	20	,	,	PUNCT
ejpam-4470	214	21	y	y	PROPN
ejpam-4470	214	22	,	,	PUNCT
ejpam-4470	214	23	r	r	NOUN
ejpam-4470	214	24	)	)	PUNCT
ejpam-4470	214	25	=	=	SYM
ejpam-4470	214	26	s−1(u2v2s(a1)),f3(x	s−1(u2v2s(a1)),f3(x	PROPN
ejpam-4470	214	27	,	,	PUNCT
ejpam-4470	214	28	y	y	PROPN
ejpam-4470	214	29	,	,	PUNCT
ejpam-4470	214	30	r	r	NOUN
ejpam-4470	214	31	)	)	PUNCT
ejpam-4470	214	32	=	=	SYM
ejpam-4470	214	33	s−1(u2v2s(a2	s−1(u2v2s(a2	NOUN
ejpam-4470	214	34	)	)	PUNCT
ejpam-4470	214	35	)	)	PUNCT
ejpam-4470	214	36	,	,	PUNCT
ejpam-4470	214	37	...	...	PUNCT
ejpam-4470	214	38	,	,	PUNCT
ejpam-4470	214	39	(	(	PUNCT
ejpam-4470	214	40	9	9	X
ejpam-4470	214	41	)	)	PUNCT
ejpam-4470	214	42	f	f	PROPN
ejpam-4470	214	43	i+1(x	i+1(x	PROPN
ejpam-4470	214	44	,	,	PUNCT
ejpam-4470	214	45	y	y	PROPN
ejpam-4470	214	46	,	,	PUNCT
ejpam-4470	214	47	r	r	NOUN
ejpam-4470	214	48	)	)	PUNCT
ejpam-4470	214	49	=	=	SYM
ejpam-4470	214	50	s−1[uv[k(x	s−1[uv[k(x	PROPN
ejpam-4470	214	51	,	,	PUNCT
ejpam-4470	214	52	y)]s[ai(x	y)]s[ai(x	INTJ
ejpam-4470	214	53	,	,	PUNCT
ejpam-4470	214	54	y	y	PROPN
ejpam-4470	214	55	,	,	PUNCT
ejpam-4470	214	56	r	r	NOUN
ejpam-4470	214	57	)	)	PUNCT
ejpam-4470	214	58	]	]	X
ejpam-4470	214	59	]	]	PUNCT
ejpam-4470	214	60	,	,	PUNCT
ejpam-4470	214	61	i	i	PRON
ejpam-4470	214	62	≥	≥	VERB
ejpam-4470	214	63	0	0	NUM
ejpam-4470	214	64	.	.	PUNCT
ejpam-4470	215	1	using	use	VERB
ejpam-4470	215	2	relation	relation	NOUN
ejpam-4470	215	3	(	(	PUNCT
ejpam-4470	215	4	4.5	4.5	NUM
ejpam-4470	215	5	)	)	PUNCT
ejpam-4470	215	6	respectively	respectively	ADV
ejpam-4470	215	7	(	(	PUNCT
ejpam-4470	215	8	4.6	4.6	NUM
ejpam-4470	215	9	)	)	PUNCT
ejpam-4470	215	10	,	,	PUNCT
ejpam-4470	215	11	we	we	PRON
ejpam-4470	215	12	find	find	VERB
ejpam-4470	215	13	the	the	DET
ejpam-4470	215	14	values	value	NOUN
ejpam-4470	215	15	of	of	ADP
ejpam-4470	215	16	f	f	PROPN
ejpam-4470	215	17	0	0	PUNCT
ejpam-4470	216	1	(	(	PUNCT
ejpam-4470	216	2	x	x	X
ejpam-4470	216	3	,	,	PUNCT
ejpam-4470	216	4	y	y	PROPN
ejpam-4470	216	5	,	,	PUNCT
ejpam-4470	216	6	r	r	NOUN
ejpam-4470	216	7	)	)	PUNCT
ejpam-4470	216	8	,	,	PUNCT
ejpam-4470	216	9	f	f	PROPN
ejpam-4470	216	10	1	1	NUM
ejpam-4470	216	11	(	(	PUNCT
ejpam-4470	216	12	x	x	NOUN
ejpam-4470	216	13	,	,	PUNCT
ejpam-4470	216	14	y	y	PROPN
ejpam-4470	216	15	,	,	PUNCT
ejpam-4470	216	16	r	r	NOUN
ejpam-4470	216	17	)	)	PUNCT
ejpam-4470	216	18	,	,	PUNCT
ejpam-4470	216	19	f	f	PROPN
ejpam-4470	216	20	2	2	NUM
ejpam-4470	216	21	(	(	PUNCT
ejpam-4470	216	22	x	x	NOUN
ejpam-4470	216	23	,	,	PUNCT
ejpam-4470	216	24	y	y	PROPN
ejpam-4470	216	25	,	,	PUNCT
ejpam-4470	216	26	r	r	NOUN
ejpam-4470	216	27	)	)	PUNCT
ejpam-4470	216	28	,	,	PUNCT
ejpam-4470	216	29	f	f	PROPN
ejpam-4470	216	30	3	3	NUM
ejpam-4470	216	31	(	(	PUNCT
ejpam-4470	216	32	x	x	PROPN
ejpam-4470	216	33	,	,	PUNCT
ejpam-4470	216	34	y	y	PROPN
ejpam-4470	216	35	,	,	PUNCT
ejpam-4470	216	36	r	r	NOUN
ejpam-4470	216	37	)	)	PUNCT
ejpam-4470	216	38	,	,	PUNCT
ejpam-4470	216	39	f0(x	f0(x	PROPN
ejpam-4470	216	40	,	,	PUNCT
ejpam-4470	216	41	y	y	PROPN
ejpam-4470	216	42	,	,	PUNCT
ejpam-4470	216	43	r	r	NOUN
ejpam-4470	216	44	)	)	PUNCT
ejpam-4470	216	45	,	,	PUNCT
ejpam-4470	216	46	f1(x	f1(x	PROPN
ejpam-4470	216	47	,	,	PUNCT
ejpam-4470	216	48	y	y	PROPN
ejpam-4470	216	49	,	,	PUNCT
ejpam-4470	216	50	r	r	NOUN
ejpam-4470	216	51	)	)	PUNCT
ejpam-4470	216	52	,	,	PUNCT
ejpam-4470	216	53	f2(x	f2(x	PROPN
ejpam-4470	216	54	,	,	PUNCT
ejpam-4470	216	55	y	y	PROPN
ejpam-4470	216	56	,	,	PUNCT
ejpam-4470	216	57	r	r	NOUN
ejpam-4470	216	58	)	)	PUNCT
ejpam-4470	216	59	,	,	PUNCT
ejpam-4470	216	60	f3(x	f3(x	PROPN
ejpam-4470	216	61	,	,	PUNCT
ejpam-4470	216	62	y	y	PROPN
ejpam-4470	216	63	,	,	PUNCT
ejpam-4470	216	64	r)	r)	NOUN
ejpam-4470	216	65	...	...	PUNCT
ejpam-4470	216	66	easily	easily	ADV
ejpam-4470	216	67	.	.	PUNCT
ejpam-4470	217	1	after	after	ADP
ejpam-4470	217	2	finding	find	VERB
ejpam-4470	217	3	these	these	DET
ejpam-4470	217	4	values	value	NOUN
ejpam-4470	217	5	,	,	PUNCT
ejpam-4470	217	6	we	we	PRON
ejpam-4470	217	7	use	use	VERB
ejpam-4470	217	8	for	for	ADP
ejpam-4470	217	9	required	require	VERB
ejpam-4470	217	10	solution	solution	NOUN
ejpam-4470	217	11	.	.	PUNCT
ejpam-4470	218	1	then	then	ADV
ejpam-4470	218	2	,	,	PUNCT
ejpam-4470	218	3	we	we	PRON
ejpam-4470	218	4	find	find	VERB
ejpam-4470	218	5	approximate	approximate	ADJ
ejpam-4470	218	6	solution	solution	NOUN
ejpam-4470	218	7	for	for	ADP
ejpam-4470	218	8	f(s	f(	NOUN
ejpam-4470	218	9	,	,	PUNCT
ejpam-4470	218	10	t	t	PROPN
ejpam-4470	218	11	,	,	PUNCT
ejpam-4470	218	12	r	r	NOUN
ejpam-4470	218	13	)	)	PUNCT
ejpam-4470	218	14	6	6	NUM
ejpam-4470	218	15	.	.	PUNCT
ejpam-4470	219	1	numerical	numerical	ADJ
ejpam-4470	219	2	examples	example	NOUN
ejpam-4470	219	3	consider	consider	VERB
ejpam-4470	219	4	the	the	DET
ejpam-4470	219	5	following	follow	VERB
ejpam-4470	219	6	2d	2d	NUM
ejpam-4470	219	7	-	-	PUNCT
ejpam-4470	219	8	vfies	vfie	NOUN
ejpam-4470	219	9	f(x	f(x	PROPN
ejpam-4470	219	10	,	,	PUNCT
ejpam-4470	219	11	y	y	NOUN
ejpam-4470	219	12	)	)	PUNCT
ejpam-4470	219	13	=	=	SYM
ejpam-4470	220	1	g(x	g(x	NOUN
ejpam-4470	220	2	,	,	PUNCT
ejpam-4470	220	3	y)⊕	y)⊕	NOUN
ejpam-4470	220	4	y∫	y∫	VERB
ejpam-4470	220	5	0	0	PUNCT
ejpam-4470	221	1	x∫	x∫	PROPN
ejpam-4470	221	2	0	0	NUM
ejpam-4470	222	1	(	(	PUNCT
ejpam-4470	222	2	x−α)(y−β)⊙f2(α	x−α)(y−β)⊙f2(α	PROPN
ejpam-4470	222	3	,	,	PUNCT
ejpam-4470	222	4	β)dαdβ	β)dαdβ	NOUN
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ejpam-4470	222	6	(	(	PUNCT
ejpam-4470	222	7	x	x	X
ejpam-4470	222	8	,	,	PUNCT
ejpam-4470	222	9	y	y	NOUN
ejpam-4470	222	10	)	)	PUNCT
ejpam-4470	222	11	∈	∈	PROPN
ejpam-4470	223	1	[	[	X
ejpam-4470	223	2	0	0	NUM
ejpam-4470	223	3	,	,	PUNCT
ejpam-4470	223	4	1]×[0	1]×[0	NUM
ejpam-4470	223	5	,	,	PUNCT
ejpam-4470	223	6	1	1	NUM
ejpam-4470	223	7	]	]	PUNCT
ejpam-4470	223	8	r	r	NOUN
ejpam-4470	223	9	∈	∈	PROPN
ejpam-4470	224	1	[	[	X
ejpam-4470	224	2	0	0	NUM
ejpam-4470	224	3	,	,	PUNCT
ejpam-4470	224	4	1	1	NUM
ejpam-4470	224	5	]	]	PUNCT
ejpam-4470	224	6	(	(	PUNCT
ejpam-4470	224	7	10	10	NUM
ejpam-4470	224	8	)	)	PUNCT
ejpam-4470	224	9	a.	a.	NOUN
ejpam-4470	224	10	f.alidema	f.alidema	NUM
ejpam-4470	224	11	/	/	SYM
ejpam-4470	224	12	eur	eur	PROPN
ejpam-4470	224	13	.	.	PUNCT
ejpam-4470	225	1	j.	j.	PROPN
ejpam-4470	225	2	pure	pure	PROPN
ejpam-4470	225	3	appl	appl	PROPN
ejpam-4470	225	4	.	.	PROPN
ejpam-4470	225	5	math	math	PROPN
ejpam-4470	225	6	,	,	PUNCT
ejpam-4470	225	7	15	15	NUM
ejpam-4470	225	8	(	(	PUNCT
ejpam-4470	225	9	3	3	NUM
ejpam-4470	225	10	)	)	PUNCT
ejpam-4470	225	11	(	(	PUNCT
ejpam-4470	225	12	2022	2022	NUM
ejpam-4470	225	13	)	)	PUNCT
ejpam-4470	225	14	,	,	PUNCT
ejpam-4470	225	15	1363	1363	NUM
ejpam-4470	225	16	-	-	SYM
ejpam-4470	225	17	1375	1375	NUM
ejpam-4470	225	18	1371	1371	NUM
ejpam-4470	225	19	where	where	SCONJ
ejpam-4470	225	20	,	,	PUNCT
ejpam-4470	225	21	g(x	g(x	PROPN
ejpam-4470	225	22	,	,	PUNCT
ejpam-4470	225	23	y	y	PROPN
ejpam-4470	225	24	,	,	PUNCT
ejpam-4470	225	25	r	r	NOUN
ejpam-4470	225	26	)	)	PUNCT
ejpam-4470	225	27	=	=	SYM
ejpam-4470	225	28	(	(	PUNCT
ejpam-4470	225	29	(	(	PUNCT
ejpam-4470	225	30	xy	xy	NOUN
ejpam-4470	225	31	−	−	PROPN
ejpam-4470	225	32	1	1	NUM
ejpam-4470	225	33	144	144	NUM
ejpam-4470	225	34	x4y4)(1	x4y4)(1	PUNCT
ejpam-4470	226	1	+	+	CCONJ
ejpam-4470	226	2	r	r	X
ejpam-4470	226	3	)	)	PUNCT
ejpam-4470	226	4	,	,	PUNCT
ejpam-4470	226	5	(	(	PUNCT
ejpam-4470	226	6	xy	xy	NOUN
ejpam-4470	226	7	−	−	PROPN
ejpam-4470	226	8	1	1	NUM
ejpam-4470	226	9	144	144	NUM
ejpam-4470	226	10	x4y4)(3−	x4y4)(3−	ADP
ejpam-4470	226	11	r	r	NOUN
ejpam-4470	226	12	)	)	PUNCT
ejpam-4470	226	13	)	)	PUNCT
ejpam-4470	227	1	and	and	CCONJ
ejpam-4470	227	2	k(x	k(x	PROPN
ejpam-4470	227	3	−	−	PROPN
ejpam-4470	227	4	α	α	NOUN
ejpam-4470	227	5	,	,	PUNCT
ejpam-4470	227	6	y	y	PROPN
ejpam-4470	227	7	−	−	PROPN
ejpam-4470	227	8	β	β	NOUN
ejpam-4470	227	9	)	)	PUNCT
ejpam-4470	227	10	=	=	SYM
ejpam-4470	227	11	(	(	PUNCT
ejpam-4470	227	12	x	x	X
ejpam-4470	227	13	−	−	PROPN
ejpam-4470	227	14	α)(y	α)(y	NUM
ejpam-4470	227	15	−	−	NOUN
ejpam-4470	227	16	β	β	X
ejpam-4470	227	17	)	)	PUNCT
ejpam-4470	227	18	>	>	X
ejpam-4470	227	19	0	0	X
ejpam-4470	227	20	.	.	PUNCT
ejpam-4470	228	1	the	the	DET
ejpam-4470	228	2	exact	exact	ADJ
ejpam-4470	228	3	solution	solution	NOUN
ejpam-4470	228	4	is	be	AUX
ejpam-4470	228	5	fexact(x	fexact(x	PROPN
ejpam-4470	228	6	,	,	PUNCT
ejpam-4470	228	7	y	y	PROPN
ejpam-4470	228	8	,	,	PUNCT
ejpam-4470	228	9	r	r	NOUN
ejpam-4470	228	10	)	)	PUNCT
ejpam-4470	228	11	=	=	SYM
ejpam-4470	228	12	(	(	PUNCT
ejpam-4470	228	13	xy(1	xy(1	PROPN
ejpam-4470	228	14	+	+	NUM
ejpam-4470	228	15	r	r	NOUN
ejpam-4470	228	16	)	)	PUNCT
ejpam-4470	228	17	,	,	PUNCT
ejpam-4470	228	18	xy(3−	xy(3−	PROPN
ejpam-4470	228	19	r	r	NOUN
ejpam-4470	228	20	)	)	PUNCT
ejpam-4470	228	21	)	)	PUNCT
ejpam-4470	228	22	.	.	PUNCT
ejpam-4470	229	1	using	use	VERB
ejpam-4470	229	2	double	double	ADJ
ejpam-4470	229	3	fuzzy	fuzzy	ADJ
ejpam-4470	229	4	sumudu	sumudu	NOUN
ejpam-4470	229	5	-	-	PUNCT
ejpam-4470	229	6	adomain	adomain	NOUN
ejpam-4470	229	7	,	,	PUNCT
ejpam-4470	229	8	we	we	PRON
ejpam-4470	229	9	have	have	VERB
ejpam-4470	229	10	and	and	CCONJ
ejpam-4470	229	11	the	the	DET
ejpam-4470	229	12	general	general	ADJ
ejpam-4470	229	13	form	form	NOUN
ejpam-4470	229	14	of	of	ADP
ejpam-4470	229	15	the	the	DET
ejpam-4470	229	16	equations	equation	NOUN
ejpam-4470	229	17	is	be	AUX
ejpam-4470	229	18	sf(x	sf(x	NOUN
ejpam-4470	229	19	,	,	PUNCT
ejpam-4470	229	20	y	y	NOUN
ejpam-4470	229	21	)	)	PUNCT
ejpam-4470	230	1	=	=	PUNCT
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ejpam-4470	230	3	,	,	PUNCT
ejpam-4470	230	4	y	y	NOUN
ejpam-4470	230	5	)	)	PUNCT
ejpam-4470	231	1	+	+	CCONJ
ejpam-4470	231	2	y∫	y∫	NOUN
ejpam-4470	231	3	0	0	PUNCT
ejpam-4470	232	1	x∫	x∫	PROPN
ejpam-4470	232	2	0	0	NUM
ejpam-4470	232	3	(	(	PUNCT
ejpam-4470	232	4	x−	x−	PROPN
ejpam-4470	232	5	α)(y	α)(y	NUM
ejpam-4470	232	6	−	−	PROPN
ejpam-4470	232	7	β)f2(α	β)f2(α	SYM
ejpam-4470	232	8	,	,	PUNCT
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ejpam-4470	232	10	,	,	PUNCT
ejpam-4470	232	11	f(x	f(x	PROPN
ejpam-4470	232	12	,	,	PUNCT
ejpam-4470	232	13	y	y	NOUN
ejpam-4470	232	14	)	)	PUNCT
ejpam-4470	232	15	=	=	SYM
ejpam-4470	233	1	g(x	g(x	NOUN
ejpam-4470	233	2	,	,	PUNCT
ejpam-4470	233	3	y	y	NOUN
ejpam-4470	233	4	)	)	PUNCT
ejpam-4470	234	1	+	+	CCONJ
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ejpam-4470	234	3	,	,	PUNCT
ejpam-4470	234	4	β))dαdβ	β))dαdβ	NOUN
ejpam-4470	234	5	,	,	PUNCT
ejpam-4470	234	6	f(x	f(x	PROPN
ejpam-4470	234	7	,	,	PUNCT
ejpam-4470	234	8	y	y	NOUN
ejpam-4470	234	9	)	)	PUNCT
ejpam-4470	234	10	=	=	SYM
ejpam-4470	235	1	g(x	g(x	NOUN
ejpam-4470	235	2	,	,	PUNCT
ejpam-4470	235	3	y	y	NOUN
ejpam-4470	235	4	)	)	PUNCT
ejpam-4470	235	5	+	+	X
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ejpam-4470	235	7	,	,	PUNCT
ejpam-4470	235	8	β)dαdβ	β)dαdβ	NOUN
ejpam-4470	235	9	,	,	PUNCT
ejpam-4470	235	10	∞∑	∞∑	PROPN
ejpam-4470	235	11	i=0	i=0	PROPN
ejpam-4470	235	12	f	f	X
ejpam-4470	235	13	i	i	PRON
ejpam-4470	235	14	(	(	PUNCT
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ejpam-4470	235	16	,	,	PUNCT
ejpam-4470	235	17	y	y	NOUN
ejpam-4470	235	18	)	)	PUNCT
ejpam-4470	236	1	=	=	SYM
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ejpam-4470	236	3	,	,	PUNCT
ejpam-4470	236	4	y	y	NOUN
ejpam-4470	236	5	)	)	PUNCT
ejpam-4470	236	6	+	+	X
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ejpam-4470	236	8	(	(	PUNCT
ejpam-4470	236	9	∞∑	∞∑	PROPN
ejpam-4470	236	10	i=0	i=0	PROPN
ejpam-4470	236	11	ai	ai	NOUN
ejpam-4470	236	12	)	)	PUNCT
ejpam-4470	236	13	)	)	PUNCT
ejpam-4470	237	1	f	f	PROPN
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ejpam-4470	238	1	(	(	PUNCT
ejpam-4470	238	2	x	x	X
ejpam-4470	238	3	,	,	PUNCT
ejpam-4470	238	4	y	y	PROPN
ejpam-4470	238	5	,	,	PUNCT
ejpam-4470	238	6	r	r	NOUN
ejpam-4470	238	7	)	)	PUNCT
ejpam-4470	238	8	=	=	SYM
ejpam-4470	238	9	g(x	g(x	NOUN
ejpam-4470	238	10	,	,	PUNCT
ejpam-4470	238	11	y	y	PROPN
ejpam-4470	238	12	,	,	PUNCT
ejpam-4470	238	13	r	r	NOUN
ejpam-4470	238	14	)	)	PUNCT
ejpam-4470	238	15	f	f	NOUN
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ejpam-4470	239	1	(	(	PUNCT
ejpam-4470	239	2	x	x	X
ejpam-4470	239	3	,	,	PUNCT
ejpam-4470	239	4	y	y	PROPN
ejpam-4470	239	5	,	,	PUNCT
ejpam-4470	239	6	r	r	NOUN
ejpam-4470	239	7	)	)	PUNCT
ejpam-4470	239	8	=	=	SYM
ejpam-4470	239	9	(	(	PUNCT
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ejpam-4470	239	12	1	1	NUM
ejpam-4470	239	13	144	144	NUM
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ejpam-4470	240	1	+	+	CCONJ
ejpam-4470	240	2	r	r	X
ejpam-4470	240	3	)	)	PUNCT
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ejpam-4470	240	5	of	of	ADP
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ejpam-4470	240	7	transform	transform	NOUN
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ejpam-4470	240	9	,	,	PUNCT
ejpam-4470	240	10	s(xmyn	s(xmyn	PROPN
ejpam-4470	240	11	)	)	PUNCT
ejpam-4470	241	1	=	=	SYM
ejpam-4470	241	2	(	(	PUNCT
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ejpam-4470	241	5	=	=	PUNCT
ejpam-4470	241	6	(	(	PUNCT
ejpam-4470	241	7	m!)(n!)s−1(umvn	m!)(n!)s−1(umvn	X
ejpam-4470	241	8	)	)	PUNCT
ejpam-4470	241	9	s−1(umvn	s−1(umvn	ADJ
ejpam-4470	241	10	)	)	PUNCT
ejpam-4470	241	11	=	=	SYM
ejpam-4470	241	12	1	1	NUM
ejpam-4470	241	13	(	(	PUNCT
ejpam-4470	241	14	m!)(n	m!)(n	PROPN
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ejpam-4470	241	16	)	)	PUNCT
ejpam-4470	242	1	(	(	PUNCT
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ejpam-4470	242	3	)	)	PUNCT
ejpam-4470	242	4	f	f	PROPN
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ejpam-4470	242	13	=	=	SYM
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ejpam-4470	242	15	)	)	PUNCT
ejpam-4470	242	16	)	)	PUNCT
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ejpam-4470	243	3	)	)	PUNCT
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ejpam-4470	244	3	1	1	NUM
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ejpam-4470	245	1	+	+	PUNCT
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ejpam-4470	245	5	−	−	X
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ejpam-4470	246	3	+	+	CCONJ
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ejpam-4470	246	5	20736	20736	NUM
ejpam-4470	246	6	)	)	PUNCT
ejpam-4470	246	7	]	]	PUNCT
ejpam-4470	246	8	(	(	PUNCT
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ejpam-4470	246	26	=	=	SYM
ejpam-4470	247	1	(	(	PUNCT
ejpam-4470	247	2	x4y4	x4y4	NUM
ejpam-4470	247	3	24	24	NUM
ejpam-4470	247	4	−	−	NOUN
ejpam-4470	247	5	x7y7	x7y7	PROPN
ejpam-4470	247	6	(	(	PUNCT
ejpam-4470	247	7	42)272	42)272	NUM
ejpam-4470	247	8	+	+	CCONJ
ejpam-4470	247	9	x10y10	x10y10	PROPN
ejpam-4470	247	10	(	(	PUNCT
ejpam-4470	247	11	90)220736	90)220736	NOUN
ejpam-4470	247	12	)	)	PUNCT
ejpam-4470	247	13	(	(	PUNCT
ejpam-4470	247	14	1	1	NUM
ejpam-4470	247	15	+	+	CCONJ
ejpam-4470	247	16	r)2	r)2	ADJ
ejpam-4470	247	17	f	f	NOUN
ejpam-4470	247	18	2	2	NUM
ejpam-4470	247	19	(	(	PUNCT
ejpam-4470	247	20	x	x	NOUN
ejpam-4470	247	21	,	,	PUNCT
ejpam-4470	247	22	y	y	PROPN
ejpam-4470	247	23	,	,	PUNCT
ejpam-4470	247	24	r	r	NOUN
ejpam-4470	247	25	)	)	PUNCT
ejpam-4470	247	26	=	=	SYM
ejpam-4470	247	27	s−1(u2v2s(a1	s−1(u2v2s(a1	X
ejpam-4470	247	28	)	)	PUNCT
ejpam-4470	247	29	)	)	PUNCT
ejpam-4470	248	1	=	=	PUNCT
ejpam-4470	248	2	s−1(u2v2s(2f0f1	s−1(u2v2s(2f0f1	X
ejpam-4470	248	3	)	)	PUNCT
ejpam-4470	248	4	)	)	PUNCT
ejpam-4470	249	1	=	=	PUNCT
ejpam-4470	249	2	s−1(u2v2s[2((xy)−	s−1(u2v2s[2((xy)−	VERB
ejpam-4470	249	3	1	1	NUM
ejpam-4470	249	4	144	144	NUM
ejpam-4470	249	5	x4y4	x4y4	NOUN
ejpam-4470	249	6	)	)	PUNCT
ejpam-4470	249	7	)	)	PUNCT
ejpam-4470	250	1	(	(	PUNCT
ejpam-4470	250	2	x4y4	x4y4	NUM
ejpam-4470	250	3	24	24	NUM
ejpam-4470	250	4	−	−	NOUN
ejpam-4470	250	5	x7y7	x7y7	PROPN
ejpam-4470	250	6	(	(	PUNCT
ejpam-4470	250	7	(	(	PUNCT
ejpam-4470	250	8	42)2	42)2	NUM
ejpam-4470	250	9	∗	∗	NOUN
ejpam-4470	250	10	72	72	NUM
ejpam-4470	250	11	)	)	PUNCT
ejpam-4470	251	1	+	+	CCONJ
ejpam-4470	251	2	x10y10	x10y10	PROPN
ejpam-4470	251	3	(	(	PUNCT
ejpam-4470	251	4	(	(	PUNCT
ejpam-4470	251	5	90)2	90)2	NUM
ejpam-4470	251	6	∗	∗	NOUN
ejpam-4470	251	7	20736	20736	NUM
ejpam-4470	251	8	)	)	PUNCT
ejpam-4470	251	9	)	)	PUNCT
ejpam-4470	252	1	(	(	PUNCT
ejpam-4470	252	2	1	1	NUM
ejpam-4470	252	3	+	+	CCONJ
ejpam-4470	252	4	r)3	r)3	PROPN
ejpam-4470	252	5	f	f	PROPN
ejpam-4470	252	6	2	2	NUM
ejpam-4470	252	7	(	(	PUNCT
ejpam-4470	252	8	x	x	NOUN
ejpam-4470	252	9	,	,	PUNCT
ejpam-4470	252	10	y	y	PROPN
ejpam-4470	252	11	,	,	PUNCT
ejpam-4470	252	12	r	r	NOUN
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ejpam-4470	252	14	=	=	SYM
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ejpam-4470	252	16	(	(	PUNCT
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ejpam-4470	252	19	−	−	NUM
ejpam-4470	252	20	151x8y8	151x8y8	NUM
ejpam-4470	252	21	254016	254016	NUM
ejpam-4470	252	22	+	+	CCONJ
ejpam-4470	252	23	499x11y11	499x11y11	NUM
ejpam-4470	252	24	4115059200	4115059200	NUM
ejpam-4470	252	25	−	−	NOUN
ejpam-4470	252	26	x14y14	x14y14	X
ejpam-4470	252	27	12093235200	12093235200	NUM
ejpam-4470	252	28	)	)	PUNCT
ejpam-4470	252	29	(	(	PUNCT
ejpam-4470	252	30	1	1	NUM
ejpam-4470	252	31	+	+	CCONJ
ejpam-4470	252	32	r)3	r)3	NOUN
ejpam-4470	252	33	references	reference	NOUN
ejpam-4470	252	34	1372	1372	NUM
ejpam-4470	252	35	using	use	VERB
ejpam-4470	252	36	sumudu	sumudu	NOUN
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ejpam-4470	252	38	,	,	PUNCT
ejpam-4470	252	39	f	f	PROPN
ejpam-4470	252	40	2	2	NUM
ejpam-4470	252	41	(	(	PUNCT
ejpam-4470	252	42	x	x	NOUN
ejpam-4470	252	43	,	,	PUNCT
ejpam-4470	252	44	y	y	PROPN
ejpam-4470	252	45	,	,	PUNCT
ejpam-4470	252	46	r	r	NOUN
ejpam-4470	252	47	)	)	PUNCT
ejpam-4470	252	48	=	=	SYM
ejpam-4470	252	49	(	(	PUNCT
ejpam-4470	252	50	x7y7	x7y7	PROPN
ejpam-4470	252	51	18144	18144	NUM
ejpam-4470	252	52	−	−	PROPN
ejpam-4470	252	53	151x10y10	151x10y10	NUM
ejpam-4470	252	54	2057529600	2057529600	NUM
ejpam-4470	252	55	+	+	CCONJ
ejpam-4470	252	56	499x13y13	499x13y13	NUM
ejpam-4470	252	57	10014408069120	10014408069120	NUM
ejpam-4470	252	58	−	−	ADP
ejpam-4470	252	59	x16y16	x16y16	PROPN
ejpam-4470	252	60	792542262067200	792542262067200	NUM
ejpam-4470	252	61	)	)	PUNCT
ejpam-4470	252	62	(	(	PUNCT
ejpam-4470	252	63	1	1	NUM
ejpam-4470	252	64	+	+	CCONJ
ejpam-4470	252	65	r)3	r)3	PROPN
ejpam-4470	252	66	f	f	X
ejpam-4470	252	67	3	3	NUM
ejpam-4470	252	68	(	(	PUNCT
ejpam-4470	252	69	x	x	PROPN
ejpam-4470	252	70	,	,	PUNCT
ejpam-4470	252	71	y	y	PROPN
ejpam-4470	252	72	,	,	PUNCT
ejpam-4470	252	73	r	r	NOUN
ejpam-4470	252	74	)	)	PUNCT
ejpam-4470	252	75	=	=	SYM
ejpam-4470	252	76	s−1(u2v2s(a2	s−1(u2v2s(a2	NOUN
ejpam-4470	252	77	)	)	PUNCT
ejpam-4470	252	78	)	)	PUNCT
ejpam-4470	253	1	=	=	PUNCT
ejpam-4470	253	2	s−1(u2v2s2(f2	s−1(u2v2s2(f2	VERB
ejpam-4470	253	3	1	1	NUM
ejpam-4470	253	4	+	+	CCONJ
ejpam-4470	253	5	2u0u2	2u0u2	NUM
ejpam-4470	253	6	)	)	PUNCT
ejpam-4470	253	7	)	)	PUNCT
ejpam-4470	254	1	f	f	PROPN
ejpam-4470	254	2	4	4	NUM
ejpam-4470	254	3	(	(	PUNCT
ejpam-4470	254	4	x	x	NOUN
ejpam-4470	254	5	,	,	PUNCT
ejpam-4470	254	6	y	y	PROPN
ejpam-4470	254	7	,	,	PUNCT
ejpam-4470	254	8	r	r	NOUN
ejpam-4470	254	9	)	)	PUNCT
ejpam-4470	254	10	=	=	SYM
ejpam-4470	254	11	s−1(u2v2s(a3	s−1(u2v2s(a3	NOUN
ejpam-4470	254	12	)	)	PUNCT
ejpam-4470	254	13	)	)	PUNCT
ejpam-4470	255	1	=	=	PUNCT
ejpam-4470	256	1	s−1(u2v2s2(f1f2	s−1(u2v2s2(f1f2	PROPN
ejpam-4470	256	2	+	+	CCONJ
ejpam-4470	256	3	2u0u3	2u0u3	NUM
ejpam-4470	256	4	)	)	PUNCT
ejpam-4470	256	5	)	)	PUNCT
ejpam-4470	256	6	...	...	PUNCT
ejpam-4470	257	1	using	use	VERB
ejpam-4470	257	2	relation	relation	NOUN
ejpam-4470	257	3	(	(	PUNCT
ejpam-4470	257	4	4.7	4.7	NUM
ejpam-4470	257	5	)	)	PUNCT
ejpam-4470	257	6	,	,	PUNCT
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ejpam-4470	257	8	find	find	VERB
ejpam-4470	257	9	the	the	DET
ejpam-4470	257	10	values	value	NOUN
ejpam-4470	257	11	of	of	ADP
ejpam-4470	257	12	f	f	PROPN
ejpam-4470	257	13	3	3	NUM
ejpam-4470	257	14	(	(	PUNCT
ejpam-4470	257	15	x	x	PROPN
ejpam-4470	257	16	,	,	PUNCT
ejpam-4470	257	17	y	y	PROPN
ejpam-4470	257	18	,	,	PUNCT
ejpam-4470	257	19	r	r	NOUN
ejpam-4470	257	20	)	)	PUNCT
ejpam-4470	257	21	,	,	PUNCT
ejpam-4470	257	22	f	f	PROPN
ejpam-4470	257	23	4	4	NUM
ejpam-4470	257	24	=	=	SYM
ejpam-4470	257	25	(	(	PUNCT
ejpam-4470	257	26	x	x	X
ejpam-4470	257	27	,	,	PUNCT
ejpam-4470	257	28	y	y	PROPN
ejpam-4470	257	29	,	,	PUNCT
ejpam-4470	257	30	r	r	NOUN
ejpam-4470	257	31	)	)	PUNCT
ejpam-4470	257	32	,	,	PUNCT
ejpam-4470	257	33	f	f	PROPN
ejpam-4470	257	34	5	5	NUM
ejpam-4470	257	35	(	(	PUNCT
ejpam-4470	257	36	x	x	NOUN
ejpam-4470	257	37	,	,	PUNCT
ejpam-4470	257	38	y	y	PROPN
ejpam-4470	257	39	,	,	PUNCT
ejpam-4470	257	40	r	r	NOUN
ejpam-4470	257	41	)	)	PUNCT
ejpam-4470	257	42	,	,	PUNCT
ejpam-4470	257	43	f	f	PROPN
ejpam-4470	257	44	6	6	NUM
ejpam-4470	257	45	(	(	PUNCT
ejpam-4470	257	46	x	x	NOUN
ejpam-4470	257	47	,	,	PUNCT
ejpam-4470	257	48	y	y	PROPN
ejpam-4470	257	49	,	,	PUNCT
ejpam-4470	257	50	r),	r),	PRON
ejpam-4470	257	51	...	...	PUNCT
ejpam-4470	257	52	easily	easily	ADV
ejpam-4470	257	53	.	.	PUNCT
ejpam-4470	258	1	after	after	ADP
ejpam-4470	258	2	finding	find	VERB
ejpam-4470	258	3	these	these	DET
ejpam-4470	258	4	values	value	NOUN
ejpam-4470	258	5	,	,	PUNCT
ejpam-4470	258	6	we	we	PRON
ejpam-4470	258	7	use	use	VERB
ejpam-4470	258	8	(	(	PUNCT
ejpam-4470	258	9	14	14	NUM
ejpam-4470	258	10	)	)	PUNCT
ejpam-4470	258	11	for	for	ADP
ejpam-4470	258	12	required	require	VERB
ejpam-4470	258	13	solution	solution	NOUN
ejpam-4470	258	14	.	.	PUNCT
ejpam-4470	259	1	analogously	analogously	ADV
ejpam-4470	259	2	,	,	PUNCT
ejpam-4470	259	3	we	we	PRON
ejpam-4470	259	4	can	can	AUX
ejpam-4470	259	5	obtain	obtain	VERB
ejpam-4470	259	6	the	the	DET
ejpam-4470	259	7	solution	solution	NOUN
ejpam-4470	259	8	of	of	ADP
ejpam-4470	259	9	equation	equation	NOUN
ejpam-4470	259	10	f0(x	f0(x	NOUN
ejpam-4470	259	11	,	,	PUNCT
ejpam-4470	259	12	y	y	PROPN
ejpam-4470	259	13	,	,	PUNCT
ejpam-4470	259	14	r	r	NOUN
ejpam-4470	259	15	)	)	PUNCT
ejpam-4470	259	16	=	=	SYM
ejpam-4470	260	1	(	(	PUNCT
ejpam-4470	260	2	xy	xy	NOUN
ejpam-4470	260	3	−	−	PROPN
ejpam-4470	260	4	1	1	NUM
ejpam-4470	260	5	144	144	NUM
ejpam-4470	260	6	x4y4)(3−	x4y4)(3−	ADP
ejpam-4470	260	7	r	r	PROPN
ejpam-4470	260	8	)	)	PUNCT
ejpam-4470	260	9	f1(x	f1(x	PROPN
ejpam-4470	260	10	,	,	PUNCT
ejpam-4470	260	11	y	y	PROPN
ejpam-4470	260	12	,	,	PUNCT
ejpam-4470	260	13	r	r	NOUN
ejpam-4470	260	14	)	)	PUNCT
ejpam-4470	260	15	=	=	SYM
ejpam-4470	261	1	(	(	PUNCT
ejpam-4470	261	2	x4y4	x4y4	NUM
ejpam-4470	261	3	24	24	NUM
ejpam-4470	261	4	−	−	NOUN
ejpam-4470	261	5	x7y7	x7y7	PROPN
ejpam-4470	261	6	(	(	PUNCT
ejpam-4470	261	7	42)272	42)272	NUM
ejpam-4470	261	8	+	+	CCONJ
ejpam-4470	261	9	x10y10	x10y10	PROPN
ejpam-4470	261	10	(	(	PUNCT
ejpam-4470	261	11	90)220736	90)220736	NOUN
ejpam-4470	261	12	)	)	PUNCT
ejpam-4470	261	13	(	(	PUNCT
ejpam-4470	261	14	3−	3−	NUM
ejpam-4470	261	15	r)2	r)2	NOUN
ejpam-4470	261	16	f2(x	f2(x	PROPN
ejpam-4470	261	17	,	,	PUNCT
ejpam-4470	261	18	y	y	PROPN
ejpam-4470	261	19	,	,	PUNCT
ejpam-4470	261	20	r	r	NOUN
ejpam-4470	261	21	)	)	PUNCT
ejpam-4470	261	22	=	=	SYM
ejpam-4470	261	23	(	(	PUNCT
ejpam-4470	261	24	x7y7	x7y7	PROPN
ejpam-4470	261	25	18144	18144	NUM
ejpam-4470	261	26	−	−	PROPN
ejpam-4470	261	27	151x10y10	151x10y10	NUM
ejpam-4470	261	28	2057529600	2057529600	NUM
ejpam-4470	261	29	+	+	CCONJ
ejpam-4470	261	30	499x13y13	499x13y13	NUM
ejpam-4470	261	31	10014408069120	10014408069120	NUM
ejpam-4470	261	32	−	−	ADP
ejpam-4470	261	33	x16y16	x16y16	PROPN
ejpam-4470	261	34	792542262067200	792542262067200	NUM
ejpam-4470	261	35	)	)	PUNCT
ejpam-4470	261	36	(	(	PUNCT
ejpam-4470	261	37	3−	3−	X
ejpam-4470	261	38	r)3	r)3	VERB
ejpam-4470	261	39	using	use	VERB
ejpam-4470	261	40	relation	relation	NOUN
ejpam-4470	261	41	(	(	PUNCT
ejpam-4470	261	42	4.8	4.8	NUM
ejpam-4470	261	43	)	)	PUNCT
ejpam-4470	261	44	,	,	PUNCT
ejpam-4470	261	45	we	we	PRON
ejpam-4470	261	46	find	find	VERB
ejpam-4470	261	47	the	the	DET
ejpam-4470	261	48	values	value	NOUN
ejpam-4470	261	49	of	of	ADP
ejpam-4470	261	50	f3(x	f3(x	PROPN
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ejpam-4470	261	62	y	y	PROPN
ejpam-4470	261	63	,	,	PUNCT
ejpam-4470	261	64	r	r	NOUN
ejpam-4470	261	65	)	)	PUNCT
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ejpam-4470	261	67	f5(x	f5(x	PROPN
ejpam-4470	261	68	,	,	PUNCT
ejpam-4470	261	69	y	y	PROPN
ejpam-4470	261	70	,	,	PUNCT
ejpam-4470	261	71	r	r	NOUN
ejpam-4470	261	72	)	)	PUNCT
ejpam-4470	261	73	,	,	PUNCT
ejpam-4470	261	74	f6(x	f6(x	PROPN
ejpam-4470	261	75	,	,	PUNCT
ejpam-4470	261	76	y	y	PROPN
ejpam-4470	261	77	,	,	PUNCT
ejpam-4470	261	78	r),	r),	PRON
ejpam-4470	261	79	...	...	PUNCT
ejpam-4470	261	80	easily	easily	ADV
ejpam-4470	261	81	after	after	ADP
ejpam-4470	261	82	finding	find	VERB
ejpam-4470	261	83	these	these	DET
ejpam-4470	261	84	values	value	NOUN
ejpam-4470	261	85	,	,	PUNCT
ejpam-4470	261	86	we	we	PRON
ejpam-4470	261	87	use	use	VERB
ejpam-4470	261	88	for	for	ADP
ejpam-4470	261	89	required	require	VERB
ejpam-4470	261	90	solution	solution	NOUN
ejpam-4470	261	91	of	of	ADP
ejpam-4470	261	92	the	the	DET
ejpam-4470	261	93	approximate	approximate	ADJ
ejpam-4470	261	94	solution	solution	NOUN
ejpam-4470	261	95	is	be	AUX
ejpam-4470	261	96	f(x	f(x	PROPN
ejpam-4470	261	97	,	,	PUNCT
ejpam-4470	261	98	y	y	PROPN
ejpam-4470	261	99	,	,	PUNCT
ejpam-4470	261	100	r	r	NOUN
ejpam-4470	261	101	)	)	PUNCT
ejpam-4470	261	102	=	=	SYM
ejpam-4470	261	103	(	(	PUNCT
ejpam-4470	261	104	f(x	f(x	PROPN
ejpam-4470	261	105	,	,	PUNCT
ejpam-4470	261	106	y	y	PROPN
ejpam-4470	261	107	,	,	PUNCT
ejpam-4470	261	108	r	r	NOUN
ejpam-4470	261	109	)	)	PUNCT
ejpam-4470	261	110	,	,	PUNCT
ejpam-4470	261	111	f(x	f(x	PROPN
ejpam-4470	261	112	,	,	PUNCT
ejpam-4470	261	113	y	y	PROPN
ejpam-4470	261	114	,	,	PUNCT
ejpam-4470	261	115	r	r	NOUN
ejpam-4470	261	116	)	)	PUNCT
ejpam-4470	261	117	)	)	PUNCT
ejpam-4470	261	118	.	.	PUNCT
ejpam-4470	262	1	conlusion	conlusion	NOUN
ejpam-4470	262	2	in	in	ADP
ejpam-4470	262	3	this	this	DET
ejpam-4470	262	4	article	article	NOUN
ejpam-4470	262	5	,	,	PUNCT
ejpam-4470	262	6	we	we	PRON
ejpam-4470	262	7	successfully	successfully	ADV
ejpam-4470	262	8	combine	combine	VERB
ejpam-4470	262	9	the	the	DET
ejpam-4470	262	10	double	double	ADJ
ejpam-4470	262	11	fuzzy	fuzzy	ADJ
ejpam-4470	262	12	sumudu	sumudu	NOUN
ejpam-4470	262	13	transform	transform	NOUN
ejpam-4470	262	14	and	and	CCONJ
ejpam-4470	262	15	adomian	adomian	NOUN
ejpam-4470	262	16	decomposition	decomposition	NOUN
ejpam-4470	262	17	method	method	NOUN
ejpam-4470	262	18	to	to	PART
ejpam-4470	262	19	solve	solve	VERB
ejpam-4470	262	20	two	two	NUM
ejpam-4470	262	21	dimensional	dimensional	ADJ
ejpam-4470	262	22	fuzzy	fuzzy	ADJ
ejpam-4470	262	23	volterra	volterra	NOUN
ejpam-4470	262	24	integral	integral	ADJ
ejpam-4470	262	25	equations	equation	NOUN
ejpam-4470	262	26	.	.	PUNCT
ejpam-4470	263	1	the	the	DET
ejpam-4470	263	2	results	result	NOUN
ejpam-4470	263	3	demonstrate	demonstrate	VERB
ejpam-4470	263	4	the	the	DET
ejpam-4470	263	5	method	method	NOUN
ejpam-4470	263	6	are	be	AUX
ejpam-4470	263	7	efficient	efficient	ADJ
ejpam-4470	263	8	and	and	CCONJ
ejpam-4470	263	9	reliable	reliable	ADJ
ejpam-4470	263	10	.	.	PUNCT
ejpam-4470	264	1	moreover	moreover	ADV
ejpam-4470	264	2	,	,	PUNCT
ejpam-4470	264	3	the	the	DET
ejpam-4470	264	4	proposed	propose	VERB
ejpam-4470	264	5	method	method	NOUN
ejpam-4470	264	6	was	be	AUX
ejpam-4470	264	7	evaluated	evaluate	VERB
ejpam-4470	264	8	by	by	ADP
ejpam-4470	264	9	solving	solve	VERB
ejpam-4470	264	10	numerical	numerical	ADJ
ejpam-4470	264	11	examples	example	NOUN
ejpam-4470	264	12	.	.	PUNCT
ejpam-4470	265	1	references	reference	NOUN
ejpam-4470	265	2	[	[	X
ejpam-4470	265	3	1	1	NUM
ejpam-4470	265	4	]	]	X
ejpam-4470	265	5	g.	g.	PROPN
ejpam-4470	265	6	adomian	adomian	PROPN
ejpam-4470	265	7	.	.	PUNCT
ejpam-4470	266	1	a	a	DET
ejpam-4470	266	2	review	review	NOUN
ejpam-4470	266	3	of	of	ADP
ejpam-4470	266	4	the	the	DET
ejpam-4470	266	5	decomposition	decomposition	NOUN
ejpam-4470	266	6	method	method	NOUN
ejpam-4470	266	7	in	in	ADP
ejpam-4470	266	8	applied	applied	ADJ
ejpam-4470	266	9	mathematics	mathematic	NOUN
ejpam-4470	266	10	.	.	PUNCT
ejpam-4470	267	1	journal	journal	PROPN
ejpam-4470	267	2	mathematics	mathematics	PROPN
ejpam-4470	267	3	anal	anal	PROPN
ejpam-4470	267	4	app	app	PROPN
ejpam-4470	267	5	.	.	PROPN
ejpam-4470	267	6	,135:501–544	,135:501–544	PROPN
ejpam-4470	267	7	,	,	PUNCT
ejpam-4470	267	8	1988	1988	NUM
ejpam-4470	267	9	.	.	PUNCT
ejpam-4470	268	1	[	[	X
ejpam-4470	268	2	2	2	NUM
ejpam-4470	268	3	]	]	X
ejpam-4470	268	4	g.	g.	NOUN
ejpam-4470	268	5	adomian	adomian	PROPN
ejpam-4470	268	6	.	.	PUNCT
ejpam-4470	269	1	solving	solve	VERB
ejpam-4470	269	2	frontier	frontier	NOUN
ejpam-4470	269	3	problems	problem	NOUN
ejpam-4470	269	4	of	of	ADP
ejpam-4470	269	5	physics	physics	PROPN
ejpam-4470	269	6	.	.	PUNCT
ejpam-4470	270	1	the	the	DET
ejpam-4470	270	2	decompositon	decompositon	NOUN
ejpam-4470	270	3	method	method	NOUN
ejpam-4470	270	4	.	.	PUNCT
ejpam-4470	271	1	kluver	kluver	NOUN
ejpam-4470	271	2	academic	academic	ADJ
ejpam-4470	271	3	publishers	publisher	NOUN
ejpam-4470	271	4	,	,	PUNCT
ejpam-4470	271	5	boston	boston	PROPN
ejpam-4470	271	6	,	,	PUNCT
ejpam-4470	271	7	12	12	NUM
ejpam-4470	271	8	,	,	PUNCT
ejpam-4470	271	9	1994	1994	NUM
ejpam-4470	271	10	.	.	PUNCT
ejpam-4470	272	1	[	[	X
ejpam-4470	272	2	3	3	NUM
ejpam-4470	272	3	]	]	PUNCT
ejpam-4470	272	4	a.	a.	NOUN
ejpam-4470	272	5	alidema	alidema	PROPN
ejpam-4470	272	6	,	,	PUNCT
ejpam-4470	272	7	a.	a.	NOUN
ejpam-4470	272	8	georgieva	georgieva	PROPN
ejpam-4470	272	9	adomian	adomian	PROPN
ejpam-4470	272	10	decomposition	decomposition	NOUN
ejpam-4470	272	11	method	method	NOUN
ejpam-4470	272	12	for	for	ADP
ejpam-4470	272	13	solving	solve	VERB
ejpam-4470	272	14	two	two	NUM
ejpam-4470	272	15	-	-	PUNCT
ejpam-4470	272	16	dimensional	dimensional	ADJ
ejpam-4470	272	17	nonlinear	nonlinear	ADJ
ejpam-4470	272	18	volterra	volterra	NOUN
ejpam-4470	272	19	fuzzy	fuzzy	ADJ
ejpam-4470	272	20	integral	integral	ADJ
ejpam-4470	272	21	equations	equation	NOUN
ejpam-4470	272	22	.	.	PUNCT
ejpam-4470	273	1	aip	aip	PROPN
ejpam-4470	273	2	conference	conference	NOUN
ejpam-4470	273	3	proceedings	proceeding	NOUN
ejpam-4470	273	4	.	.	PUNCT
ejpam-4470	274	1	2048:050009	2048:050009	NUM
ejpam-4470	274	2	,	,	PUNCT
ejpam-4470	274	3	2018	2018	NUM
ejpam-4470	274	4	.	.	PUNCT
ejpam-4470	275	1	[	[	X
ejpam-4470	275	2	4	4	NUM
ejpam-4470	275	3	]	]	PUNCT
ejpam-4470	275	4	a.georgieva	a.georgieva	ADJ
ejpam-4470	275	5	.	.	PUNCT
ejpam-4470	275	6	double	double	ADJ
ejpam-4470	275	7	fuzzy	fuzzy	ADJ
ejpam-4470	275	8	sumudu	sumudu	NOUN
ejpam-4470	275	9	transfor	transfor	NOUN
ejpam-4470	275	10	to	to	PART
ejpam-4470	275	11	solve	solve	VERB
ejpam-4470	275	12	partial	partial	ADJ
ejpam-4470	275	13	volterra	volterra	NOUN
ejpam-4470	275	14	fuzzy	fuzzy	ADJ
ejpam-4470	275	15	integrodifferential	integrodifferential	ADJ
ejpam-4470	275	16	equations	equation	NOUN
ejpam-4470	275	17	.	.	PUNCT
ejpam-4470	276	1	mathematics	mathematic	NOUN
ejpam-4470	276	2	8(5	8(5	NUM
ejpam-4470	276	3	)	)	PUNCT
ejpam-4470	276	4	,	,	PUNCT
ejpam-4470	276	5	692	692	NUM
ejpam-4470	276	6	;	;	PUNCT
ejpam-4470	276	7	2020	2020	NUM
ejpam-4470	276	8	.	.	PUNCT
ejpam-4470	277	1	references	reference	NOUN
ejpam-4470	277	2	1373	1373	NUM
ejpam-4470	277	3	[	[	X
ejpam-4470	277	4	5	5	NUM
ejpam-4470	277	5	]	]	PUNCT
ejpam-4470	277	6	a.	a.	NOUN
ejpam-4470	277	7	georgieva	georgieva	NOUN
ejpam-4470	277	8	fuzzy	fuzzy	ADJ
ejpam-4470	277	9	sawi	sawi	ADJ
ejpam-4470	277	10	decomposition	decomposition	NOUN
ejpam-4470	277	11	method	method	NOUN
ejpam-4470	277	12	for	for	ADP
ejpam-4470	277	13	solving	solve	VERB
ejpam-4470	277	14	nonlinear	nonlinear	ADJ
ejpam-4470	277	15	partial	partial	ADJ
ejpam-4470	277	16	fuzzy	fuzzy	ADJ
ejpam-4470	277	17	differential	differential	NOUN
ejpam-4470	277	18	equations	equation	NOUN
ejpam-4470	277	19	symmetry	symmetry	NOUN
ejpam-4470	277	20	13(9	13(9	NUM
ejpam-4470	277	21	)	)	PUNCT
ejpam-4470	277	22	,	,	PUNCT
ejpam-4470	277	23	1580;2021	1580;2021	NUM
ejpam-4470	277	24	.	.	PUNCT
ejpam-4470	278	1	[	[	X
ejpam-4470	278	2	6	6	NUM
ejpam-4470	278	3	]	]	PUNCT
ejpam-4470	278	4	a.	a.	NOUN
ejpam-4470	278	5	alidema	alidema	PROPN
ejpam-4470	278	6	a.	a.	PROPN
ejpam-4470	278	7	georgieva	georgieva	PROPN
ejpam-4470	278	8	.	.	PUNCT
ejpam-4470	279	1	applications	application	NOUN
ejpam-4470	279	2	of	of	ADP
ejpam-4470	279	3	the	the	DET
ejpam-4470	279	4	double	double	ADJ
ejpam-4470	279	5	fuzzy	fuzzy	ADJ
ejpam-4470	279	6	sumudu	sumudu	NOUN
ejpam-4470	279	7	transform	transform	NOUN
ejpam-4470	279	8	for	for	ADP
ejpam-4470	279	9	solving	solve	VERB
ejpam-4470	279	10	volterra	volterra	NOUN
ejpam-4470	279	11	fuzzy	fuzzy	ADJ
ejpam-4470	279	12	integral	integral	ADJ
ejpam-4470	279	13	equations	equation	NOUN
ejpam-4470	279	14	aip	aip	PROPN
ejpam-4470	279	15	conference	conference	NOUN
ejpam-4470	279	16	proceedings	proceeding	NOUN
ejpam-4470	279	17	2172,060006	2172,060006	NUM
ejpam-4470	279	18	(	(	PUNCT
ejpam-4470	279	19	2019	2019	NUM
ejpam-4470	279	20	)	)	PUNCT
ejpam-4470	279	21	;	;	PUNCT
ejpam-4470	279	22	https://doi.org/10.1063/1.5133534	https://doi.org/10.1063/1.5133534	NOUN
ejpam-4470	279	23	[	[	X
ejpam-4470	279	24	7	7	X
ejpam-4470	279	25	]	]	X
ejpam-4470	279	26	e.	e.	PROPN
ejpam-4470	279	27	babolian	babolian	PROPN
ejpam-4470	279	28	,	,	PUNCT
ejpam-4470	279	29	h.	h.	PROPN
ejpam-4470	279	30	s.	s.	PROPN
ejpam-4470	279	31	goghary	goghary	PROPN
ejpam-4470	279	32	ans	ans	PROPN
ejpam-4470	279	33	s.	s.	PROPN
ejpam-4470	279	34	abbasbandy	abbasbandy	PROPN
ejpam-4470	279	35	.	.	PUNCT
ejpam-4470	280	1	numerical	numerical	ADJ
ejpam-4470	280	2	solution	solution	NOUN
ejpam-4470	280	3	of	of	ADP
ejpam-4470	280	4	linear	linear	ADJ
ejpam-4470	280	5	fredholm	fredholm	NOUN
ejpam-4470	280	6	fuzzy	fuzzy	ADJ
ejpam-4470	280	7	integral	integral	ADJ
ejpam-4470	280	8	equations	equation	NOUN
ejpam-4470	280	9	of	of	ADP
ejpam-4470	280	10	the	the	DET
ejpam-4470	280	11	second	second	ADJ
ejpam-4470	280	12	kind	kind	NOUN
ejpam-4470	280	13	by	by	ADP
ejpam-4470	280	14	adomain	adomain	NOUN
ejpam-4470	280	15	method	method	NOUN
ejpam-4470	280	16	.	.	PUNCT
ejpam-4470	281	1	applied	apply	VERB
ejpam-4470	281	2	math.comput	math.comput	PROPN
ejpam-4470	281	3	.	.	PUNCT
ejpam-4470	281	4	,	,	PUNCT
ejpam-4470	281	5	161:733	161:733	PROPN
ejpam-4470	281	6	-	-	PUNCT
ejpam-4470	281	7	744	744	NUM
ejpam-4470	281	8	,	,	PUNCT
ejpam-4470	281	9	2005	2005	NUM
ejpam-4470	281	10	.	.	PUNCT
ejpam-4470	282	1	[	[	X
ejpam-4470	282	2	8	8	X
ejpam-4470	282	3	]	]	X
ejpam-4470	282	4	t.	t.	NOUN
ejpam-4470	282	5	allahvirnaloo	allahvirnaloo	PROPN
ejpam-4470	282	6	,	,	PUNCT
ejpam-4470	282	7	s.	s.	PROPN
ejpam-4470	282	8	abbasbandy	abbasbandy	PROPN
ejpam-4470	282	9	.	.	PUNCT
ejpam-4470	283	1	the	the	DET
ejpam-4470	283	2	adomian	adomian	PROPN
ejpam-4470	283	3	decompositon	decompositon	PROPN
ejpam-4470	283	4	method	method	NOUN
ejpam-4470	283	5	applied	apply	VERB
ejpam-4470	283	6	to	to	ADP
ejpam-4470	283	7	fuzzy	fuzzy	ADJ
ejpam-4470	283	8	system	system	NOUN
ejpam-4470	283	9	of	of	ADP
ejpam-4470	283	10	fredholm	fredholm	ADJ
ejpam-4470	283	11	integral	integral	ADJ
ejpam-4470	283	12	equations	equation	NOUN
ejpam-4470	283	13	of	of	ADP
ejpam-4470	283	14	the	the	DET
ejpam-4470	283	15	second	second	ADJ
ejpam-4470	283	16	kind	kind	NOUN
ejpam-4470	283	17	.	.	PUNCT
ejpam-4470	284	1	int	int	NOUN
ejpam-4470	284	2	.	.	PUNCT
ejpam-4470	285	1	j.	j.	PROPN
ejpam-4470	285	2	uncertainty	uncertainty	PROPN
ejpam-4470	285	3	fuzziness	fuzziness	VERB
ejpam-4470	285	4	knowl	knowl	NOUN
ejpam-4470	285	5	-	-	PUNCT
ejpam-4470	285	6	based	base	VERB
ejpam-4470	285	7	systems	system	NOUN
ejpam-4470	285	8	,	,	PUNCT
ejpam-4470	285	9	10:101	10:101	NUM
ejpam-4470	285	10	-	-	SYM
ejpam-4470	285	11	110	110	NUM
ejpam-4470	285	12	,	,	PUNCT
ejpam-4470	285	13	2006	2006	NUM
ejpam-4470	285	14	[	[	X
ejpam-4470	285	15	9	9	NUM
ejpam-4470	285	16	]	]	PUNCT
ejpam-4470	285	17	s.	s.	PROPN
ejpam-4470	285	18	bushnaq	bushnaq	PROPN
ejpam-4470	285	19	,	,	PUNCT
ejpam-4470	285	20	z.	z.	PROPN
ejpam-4470	285	21	ullah	ullah	PROPN
ejpam-4470	285	22	,	,	PUNCT
ejpam-4470	285	23	a.	a.	PROPN
ejpam-4470	285	24	ullah	ullah	PROPN
ejpam-4470	285	25	and	and	CCONJ
ejpam-4470	285	26	k.	k.	PROPN
ejpam-4470	285	27	shah	shah	PROPN
ejpam-4470	285	28	.	.	PUNCT
ejpam-4470	286	1	solution	solution	NOUN
ejpam-4470	286	2	of	of	ADP
ejpam-4470	286	3	fuzzy	fuzzy	ADJ
ejpam-4470	286	4	singular	singular	ADJ
ejpam-4470	286	5	integral	integral	ADJ
ejpam-4470	286	6	equation	equation	NOUN
ejpam-4470	286	7	with	with	ADP
ejpam-4470	286	8	abel	abel	PROPN
ejpam-4470	286	9	’s	’s	PART
ejpam-4470	286	10	type	type	NOUN
ejpam-4470	286	11	kernel	kernel	NOUN
ejpam-4470	286	12	using	use	VERB
ejpam-4470	286	13	a	a	DET
ejpam-4470	286	14	novel	novel	ADJ
ejpam-4470	286	15	hybrid	hybrid	NOUN
ejpam-4470	286	16	method	method	NOUN
ejpam-4470	286	17	advances	advance	NOUN
ejpam-4470	286	18	in	in	ADP
ejpam-4470	286	19	difference	difference	NOUN
ejpam-4470	286	20	equations	equation	NOUN
ejpam-4470	286	21	volume	volume	NOUN
ejpam-4470	286	22	2020	2020	NUM
ejpam-4470	286	23	,	,	PUNCT
ejpam-4470	286	24	156	156	NUM
ejpam-4470	286	25	(	(	PUNCT
ejpam-4470	286	26	2020	2020	NUM
ejpam-4470	286	27	)	)	PUNCT
ejpam-4470	287	1	[	[	X
ejpam-4470	287	2	10	10	NUM
ejpam-4470	287	3	]	]	X
ejpam-4470	287	4	f.	f.	NOUN
ejpam-4470	287	5	belgacem	belgacem	PROPN
ejpam-4470	287	6	,	,	PUNCT
ejpam-4470	287	7	a.karaballi	a.karaballi	PROPN
ejpam-4470	287	8	.	.	PUNCT
ejpam-4470	288	1	sumudu	sumudu	NOUN
ejpam-4470	288	2	transform	transform	VERB
ejpam-4470	288	3	fundamental	fundamental	ADJ
ejpam-4470	288	4	properties	property	NOUN
ejpam-4470	288	5	investigations	investigation	NOUN
ejpam-4470	288	6	and	and	CCONJ
ejpam-4470	288	7	application	application	NOUN
ejpam-4470	288	8	.	.	PUNCT
ejpam-4470	289	1	journal	journal	PROPN
ejpam-4470	289	2	of	of	ADP
ejpam-4470	289	3	applied	apply	VERB
ejpam-4470	289	4	mathematics	mathematic	NOUN
ejpam-4470	289	5	and	and	CCONJ
ejpam-4470	289	6	stochastic	stochastic	ADJ
ejpam-4470	289	7	analysisl	analysisl	PROPN
ejpam-4470	289	8	volume	volume	NOUN
ejpam-4470	289	9	2006	2006	NUM
ejpam-4470	289	10	,	,	PUNCT
ejpam-4470	289	11	article	article	NOUN
ejpam-4470	289	12	i	i	PROPN
ejpam-4470	289	13	d	d	PROPN
ejpam-4470	289	14	91083,pages	91083,pages	NUM
ejpam-4470	289	15	1–23	1–23	NOUN
ejpam-4470	289	16	,	,	PUNCT
ejpam-4470	289	17	[	[	X
ejpam-4470	289	18	11	11	NUM
ejpam-4470	289	19	]	]	PUNCT
ejpam-4470	289	20	s.	s.	PROPN
ejpam-4470	289	21	chang	chang	PROPN
ejpam-4470	289	22	,	,	PUNCT
ejpam-4470	289	23	l.	l.	PROPN
ejpam-4470	289	24	zadeh	zadeh	PROPN
ejpam-4470	289	25	.	.	PUNCT
ejpam-4470	290	1	on	on	ADP
ejpam-4470	290	2	fuzzy	fuzzy	ADJ
ejpam-4470	290	3	mapping	mapping	NOUN
ejpam-4470	290	4	and	and	CCONJ
ejpam-4470	290	5	control	control	NOUN
ejpam-4470	290	6	.	.	PUNCT
ejpam-4470	291	1	ieee	ieee	NOUN
ejpam-4470	291	2	transactions	transaction	NOUN
ejpam-4470	291	3	on	on	ADP
ejpam-4470	291	4	systems	system	NOUN
ejpam-4470	291	5	,	,	PUNCT
ejpam-4470	291	6	man	man	NOUN
ejpam-4470	291	7	,	,	PUNCT
ejpam-4470	291	8	and	and	CCONJ
ejpam-4470	291	9	cybernetics,1:30–34	cybernetics,1:30–34	NOUN
ejpam-4470	291	10	,	,	PUNCT
ejpam-4470	291	11	1972	1972	NUM
ejpam-4470	291	12	.	.	PUNCT
ejpam-4470	292	1	[	[	X
ejpam-4470	292	2	12	12	NUM
ejpam-4470	292	3	]	]	X
ejpam-4470	292	4	d.	d.	PROPN
ejpam-4470	292	5	dubois	dubois	PROPN
ejpam-4470	292	6	,	,	PUNCT
ejpam-4470	292	7	and	and	CCONJ
ejpam-4470	292	8	h.	h.	PROPN
ejpam-4470	292	9	prade	prade	NOUN
ejpam-4470	292	10	.	.	PUNCT
ejpam-4470	293	1	towards	towards	ADP
ejpam-4470	293	2	fuzzy	fuzzy	ADJ
ejpam-4470	293	3	differential	differential	NOUN
ejpam-4470	293	4	calculus	calculus	NOUN
ejpam-4470	293	5	i	i	PROPN
ejpam-4470	293	6	,	,	PUNCT
ejpam-4470	293	7	ii	ii	PROPN
ejpam-4470	293	8	,	,	PUNCT
ejpam-4470	293	9	iii	iii	PROPN
ejpam-4470	293	10	.	.	NOUN
ejpam-4470	293	11	fuzzy	fuzzy	ADJ
ejpam-4470	293	12	sets	set	NOUN
ejpam-4470	293	13	and	and	CCONJ
ejpam-4470	293	14	systems,8:105	systems,8:105	PROPN
ejpam-4470	293	15	-	-	PUNCT
ejpam-4470	293	16	116	116	NUM
ejpam-4470	293	17	,	,	PUNCT
ejpam-4470	293	18	225–233	225–233	NUM
ejpam-4470	293	19	,	,	PUNCT
ejpam-4470	293	20	1982	1982	NUM
ejpam-4470	293	21	.	.	PUNCT
ejpam-4470	294	1	[	[	X
ejpam-4470	294	2	13	13	NUM
ejpam-4470	294	3	]	]	PUNCT
ejpam-4470	294	4	s.	s.	PROPN
ejpam-4470	294	5	enkov	enkov	PROPN
ejpam-4470	294	6	,	,	PUNCT
ejpam-4470	294	7	a.	a.	PROPN
ejpam-4470	294	8	georgieva	georgieva	PROPN
ejpam-4470	294	9	.	.	PUNCT
ejpam-4470	295	1	numerical	numerical	ADJ
ejpam-4470	295	2	solution	solution	NOUN
ejpam-4470	295	3	of	of	ADP
ejpam-4470	295	4	two	two	NUM
ejpam-4470	295	5	-	-	PUNCT
ejpam-4470	295	6	dimensional	dimensional	ADJ
ejpam-4470	295	7	nonlinear	nonlinear	ADJ
ejpam-4470	295	8	hammerstein	hammerstein	PROPN
ejpam-4470	295	9	fuzzy	fuzzy	ADJ
ejpam-4470	295	10	functional	functional	ADJ
ejpam-4470	295	11	integral	integral	ADJ
ejpam-4470	295	12	equations	equation	NOUN
ejpam-4470	295	13	based	base	VERB
ejpam-4470	295	14	on	on	ADP
ejpam-4470	295	15	fuzzy	fuzzy	ADJ
ejpam-4470	295	16	haar	haar	PROPN
ejpam-4470	295	17	wavelets	wavelet	NOUN
ejpam-4470	295	18	.	.	PUNCT
ejpam-4470	296	1	aip	aip	PROPN
ejpam-4470	296	2	conference	conference	NOUN
ejpam-4470	296	3	proceedings	proceeding	NOUN
ejpam-4470	296	4	,	,	PUNCT
ejpam-4470	296	5	1910:050004	1910:050004	NUM
ejpam-4470	296	6	-	-	SYM
ejpam-4470	296	7	1	1	NUM
ejpam-4470	296	8	-	-	PUNCT
ejpam-4470	296	9	050004	050004	NUM
ejpam-4470	296	10	-	-	SYM
ejpam-4470	296	11	8	8	NUM
ejpam-4470	296	12	,	,	PUNCT
ejpam-4470	296	13	2017	2017	NUM
ejpam-4470	296	14	.	.	PUNCT
ejpam-4470	297	1	[	[	X
ejpam-4470	297	2	14	14	NUM
ejpam-4470	297	3	]	]	PUNCT
ejpam-4470	297	4	a.	a.	NOUN
ejpam-4470	297	5	georgieva	georgieva	NOUN
ejpam-4470	297	6	solving	solve	VERB
ejpam-4470	297	7	two	two	NUM
ejpam-4470	297	8	-	-	PUNCT
ejpam-4470	297	9	dimensional	dimensional	ADJ
ejpam-4470	297	10	nonlinear	nonlinear	ADJ
ejpam-4470	297	11	volterra	volterra	NOUN
ejpam-4470	297	12	-	-	PUNCT
ejpam-4470	297	13	fredholm	fredholm	NOUN
ejpam-4470	297	14	fuzzy	fuzzy	ADJ
ejpam-4470	297	15	integral	integral	ADJ
ejpam-4470	297	16	equations	equation	NOUN
ejpam-4470	297	17	by	by	ADP
ejpam-4470	297	18	using	use	VERB
ejpam-4470	297	19	adomian	adomian	NOUN
ejpam-4470	297	20	decomposition	decomposition	NOUN
ejpam-4470	297	21	method	method	NOUN
ejpam-4470	297	22	.	.	PUNCT
ejpam-4470	298	1	dynamic	dynamic	ADJ
ejpam-4470	298	2	systems	system	NOUN
ejpam-4470	298	3	and	and	CCONJ
ejpam-4470	298	4	applications.27:819–837	applications.27:819–837	NOUN
ejpam-4470	298	5	,	,	PUNCT
ejpam-4470	298	6	2018	2018	NUM
ejpam-4470	298	7	.	.	PUNCT
ejpam-4470	299	1	[	[	X
ejpam-4470	299	2	15	15	NUM
ejpam-4470	299	3	]	]	PUNCT
ejpam-4470	299	4	z.	z.	PROPN
ejpam-4470	299	5	gouyandeh	gouyandeh	PROPN
ejpam-4470	299	6	t.	t.	PROPN
ejpam-4470	299	7	allahvirnaloo	allahvirnaloo	PROPN
ejpam-4470	299	8	,	,	PUNCT
ejpam-4470	299	9	s.	s.	PROPN
ejpam-4470	299	10	abbasbandy	abbasbandy	PROPN
ejpam-4470	299	11	and	and	CCONJ
ejpam-4470	299	12	armand	armand	PROPN
ejpam-4470	299	13	a	a	PRON
ejpam-4470	299	14	.	.	PUNCT
ejpam-4470	300	1	a	a	DET
ejpam-4470	300	2	fuzzy	fuzzy	ADJ
ejpam-4470	300	3	solution	solution	NOUN
ejpam-4470	300	4	of	of	ADP
ejpam-4470	300	5	heat	heat	NOUN
ejpam-4470	300	6	equations	equation	NOUN
ejpam-4470	300	7	under	under	ADP
ejpam-4470	300	8	generalized	generalized	ADJ
ejpam-4470	300	9	hukuhara	hukuhara	ADJ
ejpam-4470	300	10	differentiability	differentiability	NOUN
ejpam-4470	300	11	by	by	ADP
ejpam-4470	300	12	fuzzy	fuzzy	ADJ
ejpam-4470	300	13	fourier	fourier	NOUN
ejpam-4470	300	14	transform	transform	NOUN
ejpam-4470	300	15	,	,	PUNCT
ejpam-4470	300	16	fuzzy	fuzzy	ADJ
ejpam-4470	300	17	sets	set	NOUN
ejpam-4470	300	18	and	and	CCONJ
ejpam-4470	300	19	systems	system	NOUN
ejpam-4470	300	20	mathematics,81	mathematics,81	PROPN
ejpam-4470	300	21	-	-	PUNCT
ejpam-4470	300	22	97	97	NUM
ejpam-4470	300	23	309	309	NUM
ejpam-4470	300	24	,	,	PUNCT
ejpam-4470	300	25	2017	2017	NUM
ejpam-4470	300	26	.	.	PUNCT
ejpam-4470	301	1	[	[	X
ejpam-4470	301	2	16	16	NUM
ejpam-4470	301	3	]	]	PUNCT
ejpam-4470	301	4	a.	a.	NOUN
ejpam-4470	301	5	georgieva	georgieva	PROPN
ejpam-4470	301	6	,	,	PUNCT
ejpam-4470	301	7	i.	i.	PROPN
ejpam-4470	301	8	naydenova	naydenova	PROPN
ejpam-4470	301	9	.	.	PUNCT
ejpam-4470	302	1	numerical	numerical	ADJ
ejpam-4470	302	2	solution	solution	NOUN
ejpam-4470	302	3	of	of	ADP
ejpam-4470	302	4	nonlinear	nonlinear	ADJ
ejpam-4470	302	5	urisohn	urisohn	ADJ
ejpam-4470	302	6	-	-	PUNCT
ejpam-4470	302	7	volterra	volterra	NOUN
ejpam-4470	302	8	fuzzy	fuzzy	ADJ
ejpam-4470	302	9	functional	functional	ADJ
ejpam-4470	302	10	integral	integral	ADJ
ejpam-4470	302	11	equations	equation	NOUN
ejpam-4470	302	12	.	.	PUNCT
ejpam-4470	303	1	aip	aip	PROPN
ejpam-4470	303	2	conference	conference	PROPN
ejpam-4470	303	3	proceedings,1910:050010	proceedings,1910:050010	PROPN
ejpam-4470	303	4	-	-	SYM
ejpam-4470	303	5	1	1	NUM
ejpam-4470	303	6	-	-	PUNCT
ejpam-4470	303	7	050010	050010	NUM
ejpam-4470	303	8	-	-	PUNCT
ejpam-4470	303	9	8	8	NUM
ejpam-4470	303	10	,	,	PUNCT
ejpam-4470	303	11	2017	2017	NUM
ejpam-4470	303	12	.	.	PUNCT
ejpam-4470	304	1	references	reference	NOUN
ejpam-4470	304	2	1374	1374	NUM
ejpam-4470	304	3	[	[	X
ejpam-4470	304	4	17	17	NUM
ejpam-4470	304	5	]	]	PUNCT
ejpam-4470	304	6	a.	a.	NOUN
ejpam-4470	304	7	georgieva	georgieva	PROPN
ejpam-4470	304	8	,	,	PUNCT
ejpam-4470	304	9	a.	a.	PROPN
ejpam-4470	304	10	pavlova	pavlova	PROPN
ejpam-4470	304	11	,	,	PUNCT
ejpam-4470	304	12	i.	i.	PROPN
ejpam-4470	304	13	naydenova	naydenova	PROPN
ejpam-4470	304	14	.	.	PUNCT
ejpam-4470	305	1	error	error	NOUN
ejpam-4470	305	2	estimate	estimate	NOUN
ejpam-4470	305	3	in	in	ADP
ejpam-4470	305	4	the	the	DET
ejpam-4470	305	5	iterative	iterative	NOUN
ejpam-4470	305	6	numerical	numerical	ADJ
ejpam-4470	305	7	method	method	NOUN
ejpam-4470	305	8	for	for	ADP
ejpam-4470	305	9	two	two	NUM
ejpam-4470	305	10	-	-	PUNCT
ejpam-4470	305	11	dimensional	dimensional	ADJ
ejpam-4470	305	12	nonlinear	nonlinear	ADJ
ejpam-4470	305	13	hammerstein	hammerstein	NOUN
ejpam-4470	305	14	-	-	PUNCT
ejpam-4470	305	15	fredholm	fredholm	NOUN
ejpam-4470	305	16	fuzzy	fuzzy	ADJ
ejpam-4470	305	17	functional	functional	ADJ
ejpam-4470	305	18	integral	integral	ADJ
ejpam-4470	305	19	equations	equation	NOUN
ejpam-4470	305	20	.	.	PUNCT
ejpam-4470	306	1	advanced	advanced	ADJ
ejpam-4470	306	2	computing	computing	NOUN
ejpam-4470	306	3	in	in	ADP
ejpam-4470	306	4	industrial	industrial	ADJ
ejpam-4470	306	5	mathematics	mathematic	NOUN
ejpam-4470	306	6	,	,	PUNCT
ejpam-4470	306	7	studies	study	NOUN
ejpam-4470	306	8	in	in	ADP
ejpam-4470	306	9	computational	computational	ADJ
ejpam-4470	306	10	intelligence,728:41–45	intelligence,728:41–45	NOUN
ejpam-4470	306	11	,	,	PUNCT
ejpam-4470	306	12	2018	2018	NUM
ejpam-4470	306	13	.	.	PUNCT
ejpam-4470	307	1	[	[	X
ejpam-4470	307	2	18	18	NUM
ejpam-4470	307	3	]	]	X
ejpam-4470	307	4	g.	g.	PROPN
ejpam-4470	307	5	k.	k.	PROPN
ejpam-4470	307	6	watugala	watugala	PROPN
ejpam-4470	307	7	.	.	PUNCT
ejpam-4470	308	1	sumudu	sumudu	NOUN
ejpam-4470	308	2	transform	transform	VERB
ejpam-4470	308	3	a	a	DET
ejpam-4470	308	4	new	new	ADJ
ejpam-4470	308	5	integral	integral	ADJ
ejpam-4470	308	6	transform	transform	NOUN
ejpam-4470	308	7	to	to	PART
ejpam-4470	308	8	solve	solve	VERB
ejpam-4470	308	9	differential	differential	ADJ
ejpam-4470	308	10	equations	equation	NOUN
ejpam-4470	308	11	and	and	CCONJ
ejpam-4470	308	12	control	control	NOUN
ejpam-4470	308	13	engineering	engineering	NOUN
ejpam-4470	308	14	problems	problem	NOUN
ejpam-4470	308	15	.	.	PUNCT
ejpam-4470	309	1	internat	internat	PROPN
ejpam-4470	309	2	.	.	PUNCT
ejpam-4470	310	1	j.	j.	PROPN
ejpam-4470	310	2	math	math	PROPN
ejpam-4470	310	3	.	.	PUNCT
ejpam-4470	311	1	ed	ed	NOUN
ejpam-4470	311	2	.	.	PUNCT
ejpam-4470	312	1	sci	sci	PROPN
ejpam-4470	312	2	.	.	PUNCT
ejpam-4470	312	3	tech	tech	PROPN
ejpam-4470	312	4	.	.	PUNCT
ejpam-4470	313	1	,24:3543	,24:3543	PROPN
ejpam-4470	313	2	,	,	PUNCT
ejpam-4470	313	3	1993	1993	NUM
ejpam-4470	313	4	.	.	PUNCT
ejpam-4470	314	1	[	[	X
ejpam-4470	314	2	19	19	NUM
ejpam-4470	314	3	]	]	X
ejpam-4470	314	4	g.	g.	PROPN
ejpam-4470	314	5	k.	k.	PROPN
ejpam-4470	314	6	watugala	watugala	PROPN
ejpam-4470	314	7	.	.	PUNCT
ejpam-4470	315	1	the	the	DET
ejpam-4470	315	2	sumudu	sumudu	NOUN
ejpam-4470	315	3	transform	transform	VERB
ejpam-4470	315	4	for	for	ADP
ejpam-4470	315	5	functions	function	NOUN
ejpam-4470	315	6	of	of	ADP
ejpam-4470	315	7	two	two	NUM
ejpam-4470	315	8	variables	variable	NOUN
ejpam-4470	315	9	.	.	PUNCT
ejpam-4470	316	1	mathematical	mathematical	ADJ
ejpam-4470	316	2	engineering	engineering	NOUN
ejpam-4470	316	3	in	in	ADP
ejpam-4470	316	4	industry,8:293–302	industry,8:293–302	PROPN
ejpam-4470	316	5	,	,	PUNCT
ejpam-4470	316	6	2002	2002	NUM
ejpam-4470	316	7	.	.	PUNCT
ejpam-4470	317	1	[	[	X
ejpam-4470	317	2	20	20	NUM
ejpam-4470	317	3	]	]	X
ejpam-4470	317	4	o.	o.	PROPN
ejpam-4470	317	5	kaleva	kaleva	PROPN
ejpam-4470	317	6	,	,	PUNCT
ejpam-4470	317	7	fuzzy	fuzzy	ADJ
ejpam-4470	317	8	differential	differential	NOUN
ejpam-4470	317	9	equations	equation	NOUN
ejpam-4470	317	10	,	,	PUNCT
ejpam-4470	317	11	fuzzy	fuzzy	ADJ
ejpam-4470	317	12	sets	set	NOUN
ejpam-4470	317	13	and	and	CCONJ
ejpam-4470	317	14	systems,24:301–317	systems,24:301–317	NOUN
ejpam-4470	317	15	,	,	PUNCT
ejpam-4470	317	16	1987	1987	NUM
ejpam-4470	317	17	.	.	PUNCT
ejpam-4470	318	1	[	[	X
ejpam-4470	318	2	21	21	NUM
ejpam-4470	318	3	]	]	X
ejpam-4470	318	4	n.	n.	PROPN
ejpam-4470	318	5	a.	a.	PROPN
ejpam-4470	318	6	khan	khan	PROPN
ejpam-4470	318	7	,	,	PUNCT
ejpam-4470	318	8	o.	o.	PROPN
ejpam-4470	318	9	a.	a.	PROPN
ejpam-4470	318	10	razzaq	razzaq	PROPN
ejpam-4470	318	11	and	and	CCONJ
ejpam-4470	318	12	m.	m.	NOUN
ejpam-4470	318	13	ayyaz	ayyaz	NOUN
ejpam-4470	318	14	.	.	PUNCT
ejpam-4470	319	1	on	on	ADP
ejpam-4470	319	2	the	the	DET
ejpam-4470	319	3	solution	solution	NOUN
ejpam-4470	319	4	of	of	ADP
ejpam-4470	319	5	fuzzy	fuzzy	ADJ
ejpam-4470	319	6	differential	differential	ADJ
ejpam-4470	319	7	equations	equation	NOUN
ejpam-4470	319	8	by	by	ADP
ejpam-4470	319	9	fuzzy	fuzzy	ADJ
ejpam-4470	319	10	sumudu	sumudu	NOUN
ejpam-4470	319	11	transform	transform	NOUN
ejpam-4470	319	12	.	.	PUNCT
ejpam-4470	319	13	nonlinear	nonlinear	ADJ
ejpam-4470	319	14	engineering,4:49–60	engineering,4:49–60	NOUN
ejpam-4470	319	15	,	,	PUNCT
ejpam-4470	319	16	2015	2015	NUM
ejpam-4470	319	17	.	.	PUNCT
ejpam-4470	320	1	[	[	X
ejpam-4470	320	2	22	22	NUM
ejpam-4470	320	3	]	]	PUNCT
ejpam-4470	320	4	a.	a.	NOUN
ejpam-4470	320	5	kilicman	kilicman	PROPN
ejpam-4470	320	6	,	,	PUNCT
ejpam-4470	320	7	h.	h.	PROPN
ejpam-4470	320	8	eltaybed	eltaybed	PROPN
ejpam-4470	320	9	and	and	CCONJ
ejpam-4470	320	10	k.	k.	PROPN
ejpam-4470	320	11	a.	a.	PROPN
ejpam-4470	320	12	m.	m.	PROPN
ejpam-4470	320	13	atan	atan	PROPN
ejpam-4470	320	14	.	.	PUNCT
ejpam-4470	321	1	a	a	DET
ejpam-4470	321	2	note	note	NOUN
ejpam-4470	321	3	on	on	ADP
ejpam-4470	321	4	the	the	DET
ejpam-4470	321	5	comparison	comparison	NOUN
ejpam-4470	321	6	between	between	ADP
ejpam-4470	321	7	laplace	laplace	NOUN
ejpam-4470	321	8	and	and	CCONJ
ejpam-4470	321	9	sumudu	sumudu	NOUN
ejpam-4470	321	10	transforms	transform	VERB
ejpam-4470	321	11	.	.	PUNCT
ejpam-4470	322	1	bulletin	bulletin	NOUN
ejpam-4470	322	2	of	of	ADP
ejpam-4470	322	3	the	the	DET
ejpam-4470	322	4	iranian	iranian	ADJ
ejpam-4470	322	5	mathematical	mathematical	ADJ
ejpam-4470	322	6	society,37:131	society,37:131	PROPN
ejpam-4470	322	7	–	–	PUNCT
ejpam-4470	322	8	141	141	NUM
ejpam-4470	322	9	,	,	PUNCT
ejpam-4470	322	10	2011	2011	NUM
ejpam-4470	322	11	.	.	PUNCT
ejpam-4470	323	1	[	[	X
ejpam-4470	323	2	23	23	NUM
ejpam-4470	323	3	]	]	PUNCT
ejpam-4470	323	4	j.	j.	PROPN
ejpam-4470	323	5	w.	w.	PROPN
ejpam-4470	323	6	layman	layman	PROPN
ejpam-4470	323	7	.	.	PUNCT
ejpam-4470	324	1	the	the	DET
ejpam-4470	324	2	hankel	hankel	NOUN
ejpam-4470	324	3	transform	transform	NOUN
ejpam-4470	324	4	and	and	CCONJ
ejpam-4470	324	5	some	some	PRON
ejpam-4470	324	6	of	of	ADP
ejpam-4470	324	7	its	its	PRON
ejpam-4470	324	8	properties	property	NOUN
ejpam-4470	324	9	.	.	PUNCT
ejpam-4470	325	1	journal	journal	NOUN
ejpam-4470	325	2	of	of	ADP
ejpam-4470	325	3	integer	integer	PROPN
ejpam-4470	325	4	sequences,4:1–11	sequences,4:1–11	PROPN
ejpam-4470	325	5	,	,	PUNCT
ejpam-4470	325	6	2001	2001	NUM
ejpam-4470	325	7	.	.	PUNCT
ejpam-4470	326	1	[	[	X
ejpam-4470	326	2	24	24	NUM
ejpam-4470	326	3	]	]	X
ejpam-4470	326	4	j.	j.	PROPN
ejpam-4470	326	5	mordeson	mordeson	PROPN
ejpam-4470	326	6	,	,	PUNCT
ejpam-4470	326	7	w.	w.	PROPN
ejpam-4470	326	8	newman	newman	PROPN
ejpam-4470	326	9	.	.	PUNCT
ejpam-4470	327	1	fuzzy	fuzzy	ADJ
ejpam-4470	327	2	integral	integral	ADJ
ejpam-4470	327	3	equations	equation	NOUN
ejpam-4470	327	4	.	.	PUNCT
ejpam-4470	328	1	information	information	NOUN
ejpam-4470	328	2	sciences,87:215–229	sciences,87:215–229	PROPN
ejpam-4470	328	3	,	,	PUNCT
ejpam-4470	328	4	1995	1995	NUM
ejpam-4470	328	5	.	.	PUNCT
ejpam-4470	329	1	[	[	X
ejpam-4470	329	2	25	25	NUM
ejpam-4470	329	3	]	]	X
ejpam-4470	329	4	v.	v.	ADP
ejpam-4470	329	5	namias	namias	PROPN
ejpam-4470	329	6	.	.	PUNCT
ejpam-4470	330	1	the	the	DET
ejpam-4470	330	2	fractional	fractional	ADJ
ejpam-4470	330	3	order	order	NOUN
ejpam-4470	330	4	fourier	fourier	NOUN
ejpam-4470	330	5	transform	transform	NOUN
ejpam-4470	330	6	and	and	CCONJ
ejpam-4470	330	7	its	its	PRON
ejpam-4470	330	8	application	application	NOUN
ejpam-4470	330	9	to	to	ADP
ejpam-4470	330	10	quantum	quantum	ADJ
ejpam-4470	330	11	mechanics	mechanic	NOUN
ejpam-4470	330	12	.	.	PUNCT
ejpam-4470	331	1	i	i	PRON
ejpam-4470	331	2	m	m	VERB
ejpam-4470	331	3	a	a	DET
ejpam-4470	331	4	journal	journal	NOUN
ejpam-4470	331	5	appllied	appllie	VERB
ejpam-4470	331	6	mathemathics,25:241–265	mathemathics,25:241–265	NOUN
ejpam-4470	331	7	,	,	PUNCT
ejpam-4470	331	8	1980	1980	NUM
ejpam-4470	331	9	.	.	PUNCT
ejpam-4470	332	1	[	[	X
ejpam-4470	332	2	26	26	NUM
ejpam-4470	332	3	]	]	X
ejpam-4470	332	4	s.	s.	PROPN
ejpam-4470	332	5	seikkala	seikkala	PROPN
ejpam-4470	332	6	.	.	PUNCT
ejpam-4470	333	1	on	on	ADP
ejpam-4470	333	2	the	the	DET
ejpam-4470	333	3	fuzzy	fuzzy	ADJ
ejpam-4470	333	4	initial	initial	ADJ
ejpam-4470	333	5	value	value	NOUN
ejpam-4470	333	6	problem	problem	NOUN
ejpam-4470	333	7	.	.	PUNCT
ejpam-4470	334	1	fuzzy	fuzzy	ADJ
ejpam-4470	334	2	sets	set	NOUN
ejpam-4470	334	3	and	and	CCONJ
ejpam-4470	334	4	systems,24:319–330	systems,24:319–330	NOUN
ejpam-4470	334	5	,	,	PUNCT
ejpam-4470	334	6	1987	1987	NUM
ejpam-4470	334	7	.	.	PUNCT
ejpam-4470	335	1	[	[	X
ejpam-4470	335	2	27	27	NUM
ejpam-4470	335	3	]	]	X
ejpam-4470	335	4	s.	s.	PROPN
ejpam-4470	335	5	saitoh	saitoh	PROPN
ejpam-4470	335	6	.	.	PUNCT
ejpam-4470	336	1	the	the	DET
ejpam-4470	336	2	weierstrass	weierstrass	NOUN
ejpam-4470	336	3	transform	transform	NOUN
ejpam-4470	336	4	and	and	CCONJ
ejpam-4470	336	5	an	an	DET
ejpam-4470	336	6	isometry	isometry	NOUN
ejpam-4470	336	7	in	in	ADP
ejpam-4470	336	8	the	the	DET
ejpam-4470	336	9	heat	heat	NOUN
ejpam-4470	336	10	equation	equation	NOUN
ejpam-4470	336	11	.	.	PUNCT
ejpam-4470	337	1	applicable	applicable	ADJ
ejpam-4470	337	2	analysis	analysis	NOUN
ejpam-4470	337	3	,	,	PUNCT
ejpam-4470	337	4	16:1–6	16:1–6	NUM
ejpam-4470	337	5	,	,	PUNCT
ejpam-4470	337	6	1983	1983	NUM
ejpam-4470	337	7	.	.	PUNCT
ejpam-4470	338	1	[	[	X
ejpam-4470	338	2	28	28	NUM
ejpam-4470	338	3	]	]	X
ejpam-4470	338	4	r.	r.	PROPN
ejpam-4470	338	5	spinelli	spinelli	PROPN
ejpam-4470	338	6	.	.	PUNCT
ejpam-4470	339	1	numerical	numerical	ADJ
ejpam-4470	339	2	inversion	inversion	NOUN
ejpam-4470	339	3	of	of	ADP
ejpam-4470	339	4	a	a	DET
ejpam-4470	339	5	laplace	laplace	NOUN
ejpam-4470	339	6	transform	transform	NOUN
ejpam-4470	339	7	.	.	PUNCT
ejpam-4470	340	1	siam	siam	PROPN
ejpam-4470	340	2	journal	journal	PROPN
ejpam-4470	340	3	numerical	numerical	PROPN
ejpam-4470	340	4	analysis,3:636–649	analysis,3:636–649	PROPN
ejpam-4470	340	5	,	,	PUNCT
ejpam-4470	340	6	1966	1966	NUM
ejpam-4470	340	7	.	.	PUNCT
ejpam-4470	341	1	[	[	X
ejpam-4470	341	2	29	29	NUM
ejpam-4470	341	3	]	]	X
ejpam-4470	341	4	c.	c.	NOUN
ejpam-4470	341	5	tranter	tranter	NOUN
ejpam-4470	341	6	.	.	PUNCT
ejpam-4470	342	1	the	the	DET
ejpam-4470	342	2	use	use	NOUN
ejpam-4470	342	3	of	of	ADP
ejpam-4470	342	4	the	the	DET
ejpam-4470	342	5	mellin	mellin	PROPN
ejpam-4470	342	6	transform	transform	NOUN
ejpam-4470	342	7	in	in	ADP
ejpam-4470	342	8	finding	find	VERB
ejpam-4470	342	9	the	the	DET
ejpam-4470	342	10	stress	stress	NOUN
ejpam-4470	342	11	distribution	distribution	NOUN
ejpam-4470	342	12	in	in	ADP
ejpam-4470	342	13	an	an	DET
ejpam-4470	342	14	infinite	infinite	ADJ
ejpam-4470	342	15	wedge	wedge	NOUN
ejpam-4470	342	16	,	,	PUNCT
ejpam-4470	342	17	q.	q.	PROPN
ejpam-4470	342	18	j.	j.	PROPN
ejpam-4470	342	19	mech	mech	PROPN
ejpam-4470	342	20	.	.	PUNCT
ejpam-4470	343	1	appl	appl	PROPN
ejpam-4470	343	2	.	.	PROPN
ejpam-4470	343	3	math	math	PROPN
ejpam-4470	343	4	.	.	PUNCT
ejpam-4470	344	1	,1:125–130	,1:125–130	PROPN
ejpam-4470	344	2	,	,	PUNCT
ejpam-4470	344	3	1948	1948	NUM
ejpam-4470	344	4	.	.	PUNCT
ejpam-4470	345	1	[	[	X
ejpam-4470	345	2	30	30	NUM
ejpam-4470	345	3	]	]	X
ejpam-4470	345	4	j.	j.	PROPN
ejpam-4470	345	5	m.	m.	PROPN
ejpam-4470	345	6	tchuenche	tchuenche	PROPN
ejpam-4470	345	7	and	and	CCONJ
ejpam-4470	345	8	n.	n.	PROPN
ejpam-4470	345	9	s.	s.	PROPN
ejpam-4470	345	10	mbare	mbare	PROPN
ejpam-4470	345	11	.	.	PUNCT
ejpam-4470	346	1	an	an	DET
ejpam-4470	346	2	application	application	NOUN
ejpam-4470	346	3	of	of	ADP
ejpam-4470	346	4	the	the	DET
ejpam-4470	346	5	double	double	ADJ
ejpam-4470	346	6	sumudu	sumudu	NOUN
ejpam-4470	346	7	transform	transform	NOUN
ejpam-4470	346	8	.	.	PUNCT
ejpam-4470	347	1	applied	apply	VERB
ejpam-4470	347	2	mathematical	mathematical	ADJ
ejpam-4470	347	3	sciences,1	sciences,1	ADJ
ejpam-4470	347	4	:	:	PUNCT
ejpam-4470	347	5	31	31	NUM
ejpam-4470	347	6	39	39	NUM
ejpam-4470	347	7	,	,	PUNCT
ejpam-4470	347	8	2007	2007	NUM
ejpam-4470	347	9	.	.	PUNCT
ejpam-4470	348	1	[	[	X
ejpam-4470	348	2	31	31	NUM
ejpam-4470	348	3	]	]	PUNCT
ejpam-4470	348	4	r.	r.	PROPN
ejpam-4470	348	5	goetschel	goetschel	PROPN
ejpam-4470	348	6	,	,	PUNCT
ejpam-4470	348	7	w.	w.	PROPN
ejpam-4470	348	8	voxman	voxman	PROPN
ejpam-4470	348	9	.	.	PUNCT
ejpam-4470	349	1	elementary	elementary	ADJ
ejpam-4470	349	2	fuzzy	fuzzy	ADJ
ejpam-4470	349	3	calculus	calculus	NOUN
ejpam-4470	349	4	,	,	PUNCT
ejpam-4470	349	5	fuzzy	fuzzy	ADJ
ejpam-4470	349	6	sets	set	NOUN
ejpam-4470	349	7	and	and	CCONJ
ejpam-4470	349	8	systems	system	NOUN
ejpam-4470	349	9	,	,	PUNCT
ejpam-4470	349	10	18:31—43	18:31—43	NUM
ejpam-4470	349	11	,	,	PUNCT
ejpam-4470	349	12	1986	1986	NUM
ejpam-4470	349	13	.	.	PUNCT
ejpam-4470	350	1	references	reference	NOUN
ejpam-4470	350	2	1375	1375	NUM
ejpam-4470	351	1	[	[	X
ejpam-4470	351	2	32	32	NUM
ejpam-4470	351	3	]	]	PUNCT
ejpam-4470	351	4	c.	c.	PROPN
ejpam-4470	351	5	wu	wu	PROPN
ejpam-4470	351	6	,	,	PUNCT
ejpam-4470	351	7	z.	z.	PROPN
ejpam-4470	351	8	gong	gong	PROPN
ejpam-4470	351	9	.	.	PUNCT
ejpam-4470	352	1	on	on	ADP
ejpam-4470	352	2	henstock	henstock	PROPN
ejpam-4470	352	3	integral	integral	ADJ
ejpam-4470	352	4	of	of	ADP
ejpam-4470	352	5	fuzzy	fuzzy	ADJ
ejpam-4470	352	6	-	-	PUNCT
ejpam-4470	352	7	number	number	NOUN
ejpam-4470	352	8	-	-	PUNCT
ejpam-4470	352	9	valued	value	VERB
ejpam-4470	352	10	functions(i	functions(i	NOUN
ejpam-4470	352	11	)	)	PUNCT
ejpam-4470	352	12	.	.	PUNCT
ejpam-4470	353	1	fuzzy	fuzzy	ADJ
ejpam-4470	353	2	sets	set	NOUN
ejpam-4470	353	3	and	and	CCONJ
ejpam-4470	353	4	systems	system	NOUN
ejpam-4470	353	5	,	,	PUNCT
ejpam-4470	353	6	120:523–532	120:523–532	NUM
ejpam-4470	353	7	,	,	PUNCT
ejpam-4470	353	8	2001	2001	NUM
ejpam-4470	353	9	.	.	PUNCT
ejpam-4470	354	1	[	[	X
ejpam-4470	354	2	33	33	NUM
ejpam-4470	354	3	]	]	PUNCT
ejpam-4470	354	4	c.	c.	PROPN
ejpam-4470	354	5	wu	wu	PROPN
ejpam-4470	354	6	,	,	PUNCT
ejpam-4470	354	7	c.	c.	PROPN
ejpam-4470	354	8	wu	wu	PROPN
ejpam-4470	354	9	.	.	PUNCT
ejpam-4470	355	1	the	the	DET
ejpam-4470	355	2	supremum	supremum	ADJ
ejpam-4470	355	3	and	and	CCONJ
ejpam-4470	355	4	infimum	infimum	ADJ
ejpam-4470	355	5	of	of	ADP
ejpam-4470	355	6	these	these	PRON
ejpam-4470	355	7	to	to	ADP
ejpam-4470	355	8	fuzzy	fuzzy	ADJ
ejpam-4470	355	9	-	-	PUNCT
ejpam-4470	355	10	numbers	number	NOUN
ejpam-4470	355	11	and	and	CCONJ
ejpam-4470	355	12	its	its	PRON
ejpam-4470	355	13	applications	application	NOUN
ejpam-4470	355	14	,	,	PUNCT
ejpam-4470	355	15	j.	j.	PROPN
ejpam-4470	355	16	math	math	PROPN
ejpam-4470	355	17	.	.	PUNCT
ejpam-4470	355	18	anal	anal	PROPN
ejpam-4470	355	19	.	.	PUNCT
ejpam-4470	356	1	appl	appl	PROPN
ejpam-4470	356	2	.	.	PROPN
ejpam-4470	356	3	,	,	PUNCT
ejpam-4470	356	4	210:499–511	210:499–511	NUM
ejpam-4470	356	5	,	,	PUNCT
ejpam-4470	356	6	1997	1997	NUM
ejpam-4470	356	7	.	.	PUNCT
ejpam-4470	357	1	[	[	X
ejpam-4470	357	2	34	34	NUM
ejpam-4470	357	3	]	]	X
ejpam-4470	357	4	l.h	l.h	PROPN
ejpam-4470	357	5	.	.	PROPN
ejpam-4470	357	6	al	al	PROPN
ejpam-4470	357	7	-	-	PUNCT
ejpam-4470	357	8	taee	taee	PROPN
ejpam-4470	357	9	,	,	PUNCT
ejpam-4470	357	10	w	w	PROPN
ejpam-4470	357	11	al	al	PROPN
ejpam-4470	357	12	-	-	PUNCT
ejpam-4470	357	13	hayani	hayani	PROPN
ejpam-4470	357	14	.	.	PUNCT
ejpam-4470	358	1	solving	solve	VERB
ejpam-4470	358	2	systems	system	NOUN
ejpam-4470	358	3	of	of	ADP
ejpam-4470	358	4	non	non	ADJ
ejpam-4470	358	5	-	-	ADJ
ejpam-4470	358	6	linear	linear	ADJ
ejpam-4470	358	7	volterra	volterra	NOUN
ejpam-4470	358	8	integral	integral	ADJ
ejpam-4470	358	9	equations	equation	NOUN
ejpam-4470	358	10	by	by	ADP
ejpam-4470	358	11	combined	combine	VERB
ejpam-4470	358	12	sumudu	sumudu	NOUN
ejpam-4470	358	13	transform	transform	NOUN
ejpam-4470	358	14	-	-	PUNCT
ejpam-4470	358	15	adomian	adomian	NOUN
ejpam-4470	358	16	decomposition	decomposition	NOUN
ejpam-4470	358	17	method.iraqi	method.iraqi	PROPN
ejpam-4470	358	18	journal	journal	NOUN
ejpam-4470	358	19	of	of	ADP
ejpam-4470	358	20	science	science	NOUN
ejpam-4470	358	21	,	,	PUNCT
ejpam-4470	358	22	62(1	62(1	NOUN
ejpam-4470	358	23	)	)	PUNCT
ejpam-4470	358	24	,	,	PUNCT
ejpam-4470	358	25	252	252	NUM
ejpam-4470	358	26	-	-	SYM
ejpam-4470	358	27	268	268	NUM
ejpam-4470	358	28	,	,	PUNCT
ejpam-4470	358	29	2021	2021	NUM
ejpam-4470	358	30	.	.	PUNCT
ejpam-4470	359	1	doi:10.24996	doi:10.24996	NOUN
ejpam-4470	359	2	/	/	SYM
ejpam-4470	359	3	ijs.2021.62.1.24	ijs.2021.62.1.24	PROPN
ejpam-4470	360	1	[	[	X
ejpam-4470	360	2	35	35	NUM
ejpam-4470	360	3	]	]	X
ejpam-4470	360	4	m.t	m.t	PROPN
ejpam-4470	360	5	younis	younis	PROPN
ejpam-4470	360	6	,	,	PUNCT
ejpam-4470	360	7	w.al	w.al	ADJ
ejpam-4470	360	8	-	-	PUNCT
ejpam-4470	360	9	hayani	hayani	ADJ
ejpam-4470	360	10	solving	solve	VERB
ejpam-4470	360	11	fuzzy	fuzzy	ADJ
ejpam-4470	360	12	system	system	NOUN
ejpam-4470	360	13	of	of	ADP
ejpam-4470	360	14	volterra	volterra	PROPN
ejpam-4470	360	15	integro	integro	PROPN
ejpam-4470	360	16	-	-	PUNCT
ejpam-4470	360	17	differential	differential	NOUN
ejpam-4470	360	18	equations	equation	NOUN
ejpam-4470	360	19	by	by	ADP
ejpam-4470	360	20	using	use	VERB
ejpam-4470	360	21	adomian	adomian	NOUN
ejpam-4470	360	22	decomposition	decomposition	NOUN
ejpam-4470	360	23	method	method	NOUN
ejpam-4470	360	24	,	,	PUNCT
ejpam-4470	360	25	european	european	PROPN
ejpam-4470	360	26	journal	journal	NOUN
ejpam-4470	360	27	of	of	ADP
ejpam-4470	360	28	pure	pure	ADJ
ejpam-4470	360	29	and	and	CCONJ
ejpam-4470	360	30	applied	apply	VERB
ejpam-4470	360	31	mathematics	mathematic	NOUN
ejpam-4470	360	32	15(1	15(1	NUM
ejpam-4470	360	33	)	)	PUNCT
ejpam-4470	360	34	,	,	PUNCT
ejpam-4470	360	35	290	290	NUM
ejpam-4470	360	36	-	-	SYM
ejpam-4470	360	37	313	313	NUM
ejpam-4470	360	38	,	,	PUNCT
ejpam-4470	360	39	2022	2022	NUM
ejpam-4470	360	40	.	.	PUNCT
ejpam-4470	361	1	[	[	X
ejpam-4470	361	2	36	36	NUM
ejpam-4470	361	3	]	]	X
ejpam-4470	361	4	jin	jin	NOUN
ejpam-4470	361	5	-	-	PUNCT
ejpam-4470	361	6	fa	fa	PROPN
ejpam-4470	361	7	cheng	cheng	PROPN
ejpam-4470	361	8	and	and	CCONJ
ejpam-4470	361	9	yu	yu	PROPN
ejpam-4470	361	10	-	-	PROPN
ejpam-4470	361	11	ming	ming	PROPN
ejpam-4470	361	12	chu	chu	PROPN
ejpam-4470	361	13	study	study	NOUN
ejpam-4470	361	14	of	of	ADP
ejpam-4470	361	15	hybrid	hybrid	ADJ
ejpam-4470	361	16	orthonormal	orthonormal	ADJ
ejpam-4470	361	17	functions	function	NOUN
ejpam-4470	361	18	methodfor	methodfor	NOUN
ejpam-4470	361	19	solving	solve	VERB
ejpam-4470	361	20	second	second	ADJ
ejpam-4470	361	21	kind	kind	NOUN
ejpam-4470	361	22	fuzzy	fuzzy	ADJ
ejpam-4470	361	23	fredholm	fredholm	NOUN
ejpam-4470	361	24	integral	integral	ADJ
ejpam-4470	361	25	equations.mathematical	equations.mathematical	ADJ
ejpam-4470	361	26	problems	problem	NOUN
ejpam-4470	361	27	in	in	ADP
ejpam-4470	361	28	engineering	engineering	NOUN
ejpam-4470	361	29	article	article	NOUN
ejpam-4470	361	30	i	i	PROPN
ejpam-4470	361	31	d	d	PROPN
ejpam-4470	361	32	587068	587068	NUM
ejpam-4470	361	33	,	,	PUNCT
ejpam-4470	361	34	14	14	NUM
ejpam-4470	361	35	volume	volume	NOUN
ejpam-4470	361	36	2011	2011	NUM
ejpam-4470	361	37	.	.	PUNCT
ejpam-4470	362	1	[	[	X
ejpam-4470	362	2	37	37	NUM
ejpam-4470	362	3	]	]	X
ejpam-4470	362	4	yu	yu	PROPN
ejpam-4470	362	5	-	-	PROPN
ejpam-4470	362	6	ming	ming	PROPN
ejpam-4470	362	7	chu	chu	PROPN
ejpam-4470	362	8	,	,	PUNCT
ejpam-4470	362	9	ehab	ehab	PROPN
ejpam-4470	362	10	hussein	hussein	PROPN
ejpam-4470	362	11	bani	bani	PROPN
ejpam-4470	362	12	hani	hani	PROPN
ejpam-4470	362	13	,	,	PUNCT
ejpam-4470	362	14	essam	essam	PROPN
ejpam-4470	362	15	r.	r.	PROPN
ejpam-4470	362	16	el	el	PROPN
ejpam-4470	362	17	zahar	zahar	PROPN
ejpam-4470	362	18	,	,	PUNCT
ejpam-4470	362	19	abdelhalim	abdelhalim	PROPN
ejpam-4470	362	20	ebaid	ebaid	PROPN
ejpam-4470	362	21	,	,	PUNCT
ejpam-4470	362	22	nehad	nehad	VERB
ejpam-4470	362	23	ali	ali	PROPN
ejpam-4470	362	24	shah	shah	PROPN
ejpam-4470	362	25	combination	combination	NOUN
ejpam-4470	362	26	of	of	ADP
ejpam-4470	362	27	shehu	shehu	NOUN
ejpam-4470	362	28	decomposition	decomposition	NOUN
ejpam-4470	362	29	and	and	CCONJ
ejpam-4470	362	30	variational	variational	ADJ
ejpam-4470	362	31	iteration	iteration	NOUN
ejpam-4470	362	32	transform	transform	NOUN
ejpam-4470	362	33	methods	method	NOUN
ejpam-4470	362	34	for	for	ADP
ejpam-4470	362	35	solving	solve	VERB
ejpam-4470	362	36	fractional	fractional	ADJ
ejpam-4470	362	37	third	third	ADJ
ejpam-4470	362	38	order	order	NOUN
ejpam-4470	362	39	dispersive	dispersive	ADJ
ejpam-4470	362	40	partial	partial	ADJ
ejpam-4470	362	41	differential	differential	NOUN
ejpam-4470	362	42	equations	equation	NOUN
ejpam-4470	362	43	.	.	PUNCT
ejpam-4470	363	1	numerical	numerical	ADJ
ejpam-4470	363	2	methods	method	NOUN
ejpam-4470	363	3	for	for	ADP
ejpam-4470	363	4	differential	differential	ADJ
ejpam-4470	363	5	equations	equation	NOUN
ejpam-4470	363	6	https://doi.org/10.1002/num.22755	https://doi.org/10.1002/num.22755	PROPN
ejpam-4470	363	7	[	[	PUNCT
ejpam-4470	363	8	38	38	NUM
ejpam-4470	363	9	]	]	PUNCT
ejpam-4470	363	10	xiaoli	xiaoli	PROPN
ejpam-4470	363	11	qiang	qiang	PROPN
ejpam-4470	363	12	,	,	PUNCT
ejpam-4470	363	13	kamran	kamran	PROPN
ejpam-4470	363	14	,	,	PUNCT
ejpam-4470	363	15	abid	abid	PROPN
ejpam-4470	363	16	mahboob	mahboob	PROPN
ejpam-4470	363	17	,	,	PUNCT
ejpam-4470	363	18	yu	yu	PROPN
ejpam-4470	363	19	ming	ming	PROPN
ejpam-4470	363	20	chu	chu	PROPN
ejpam-4470	363	21	numerical	numerical	PROPN
ejpam-4470	363	22	approximation	approximation	NOUN
ejpam-4470	363	23	of	of	ADP
ejpam-4470	363	24	fractional	fractional	ADJ
ejpam-4470	363	25	-	-	PUNCT
ejpam-4470	363	26	order	order	NOUN
ejpam-4470	363	27	volterra	volterra	NOUN
ejpam-4470	363	28	integrodifferential	integrodifferential	ADJ
ejpam-4470	363	29	equation	equation	NOUN
ejpam-4470	363	30	,	,	PUNCT
ejpam-4470	363	31	journal	journal	NOUN
ejpam-4470	363	32	of	of	ADP
ejpam-4470	363	33	function	function	NOUN
ejpam-4470	363	34	spaces	space	NOUN
ejpam-4470	363	35	—	—	PUNCT
ejpam-4470	363	36	article	article	NOUN
ejpam-4470	363	37	i	i	PROPN
ejpam-4470	363	38	d	d	PROPN
ejpam-4470	363	39	8875792	8875792	NUM
ejpam-4470	363	40	volume	volume	NOUN
ejpam-4470	363	41	2020	2020	NUM
ejpam-4470	363	42	.	.	PUNCT
ejpam-4470	364	1	[	[	X
ejpam-4470	364	2	39	39	NUM
ejpam-4470	364	3	]	]	PUNCT
ejpam-4470	364	4	n.ahmad	n.ahmad	NOUN
ejpam-4470	364	5	,	,	PUNCT
ejpam-4470	364	6	a	a	DET
ejpam-4470	364	7	ullah	ullah	PROPN
ejpam-4470	364	8	,	,	PUNCT
ejpam-4470	364	9	a	a	DET
ejpam-4470	364	10	ullah	ullah	PROPN
ejpam-4470	364	11	,	,	PUNCT
ejpam-4470	364	12	sh	sh	PROPN
ejpam-4470	364	13	ahmad	ahmad	PROPN
ejpam-4470	364	14	,	,	PUNCT
ejpam-4470	364	15	k	k	PROPN
ejpam-4470	364	16	shah	shah	PROPN
ejpam-4470	364	17	,	,	PUNCT
ejpam-4470	364	18	i	i	PRON
ejpam-4470	364	19	ahmad	ahmad	VERB
ejpam-4470	364	20	on	on	ADP
ejpam-4470	364	21	analysis	analysis	NOUN
ejpam-4470	364	22	of	of	ADP
ejpam-4470	364	23	the	the	DET
ejpam-4470	364	24	fuzzy	fuzzy	ADJ
ejpam-4470	364	25	fractional	fractional	ADJ
ejpam-4470	364	26	order	order	NOUN
ejpam-4470	364	27	volterra	volterra	NOUN
ejpam-4470	364	28	-	-	PUNCT
ejpam-4470	364	29	fredholm	fredholm	NOUN
ejpam-4470	364	30	integro	integro	ADJ
ejpam-4470	364	31	-	-	PUNCT
ejpam-4470	364	32	differential	differential	NOUN
ejpam-4470	364	33	equation	equation	NOUN
ejpam-4470	364	34	,	,	PUNCT
ejpam-4470	364	35	alexandria	alexandria	PROPN
ejpam-4470	364	36	engineering	engineering	PROPN
ejpam-4470	364	37	journal	journal	PROPN
ejpam-4470	364	38	1827	1827	NUM
ejpam-4470	364	39	-	-	PUNCT
ejpam-4470	364	40	1838,60	1838,60	NUM
ejpam-4470	364	41	,	,	PUNCT
ejpam-4470	364	42	2021	2021	NUM
ejpam-4470	364	43	.	.	PUNCT
ejpam-4470	365	1	[	[	X
ejpam-4470	365	2	40	40	NUM
ejpam-4470	365	3	]	]	PUNCT
ejpam-4470	365	4	t.sitthiwirattham	t.sitthiwirattham	NUM
ejpam-4470	365	5	,	,	PUNCT
ejpam-4470	365	6	m.	m.	NOUN
ejpam-4470	365	7	arfan	arfan	PROPN
ejpam-4470	365	8	,	,	PUNCT
ejpam-4470	365	9	kamal	kamal	PROPN
ejpam-4470	365	10	shah	shah	PROPN
ejpam-4470	365	11	,	,	PUNCT
ejpam-4470	365	12	a.	a.	PROPN
ejpam-4470	365	13	zeb	zeb	PROPN
ejpam-4470	365	14	,	,	PUNCT
ejpam-4470	365	15	s.djilali	s.djilali	VERB
ejpam-4470	365	16	,	,	PUNCT
ejpam-4470	365	17	s.chasreechai	s.chasreechai	PROPN
ejpam-4470	365	18	semi	semi	ADV
ejpam-4470	365	19	analytical	analytical	ADJ
ejpam-4470	365	20	solutions	solution	NOUN
ejpam-4470	365	21	for	for	ADP
ejpam-4470	365	22	fuzzy	fuzzy	ADJ
ejpam-4470	365	23	caputo	caputo	PROPN
ejpam-4470	365	24	fabrizio	fabrizio	PROPN
ejpam-4470	365	25	fractional	fractional	PROPN
ejpam-4470	365	26	order	order	NOUN
ejpam-4470	365	27	two	two	NUM
ejpam-4470	365	28	-	-	PUNCT
ejpam-4470	365	29	dimensional	dimensional	ADJ
ejpam-4470	365	30	heat	heat	NOUN
ejpam-4470	365	31	equation	equation	NOUN
ejpam-4470	365	32	fractal	fractal	ADJ
ejpam-4470	365	33	fract	fract	NOUN
ejpam-4470	365	34	139	139	NUM
ejpam-4470	365	35	,	,	PUNCT
ejpam-4470	365	36	5,2021	5,2021	NUM
ejpam-4470	365	37	.	.	PUNCT
ejpam-4470	366	1	[	[	X
ejpam-4470	366	2	41	41	NUM
ejpam-4470	366	3	]	]	PUNCT
ejpam-4470	366	4	a.ullah	a.ullah	PROPN
ejpam-4470	366	5	,	,	PUNCT
ejpam-4470	366	6	z.	z.	PROPN
ejpam-4470	366	7	ullah	ullah	PROPN
ejpam-4470	366	8	,	,	PUNCT
ejpam-4470	366	9	t.abdeljawad	t.abdeljawad	NOUN
ejpam-4470	366	10	,	,	PUNCT
ejpam-4470	366	11	z.hammouch	z.hammouch	PROPN
ejpam-4470	366	12	,	,	PUNCT
ejpam-4470	366	13	k	k	PROPN
ejpam-4470	366	14	,	,	PUNCT
ejpam-4470	366	15	shah	shah	NOUN
ejpam-4470	366	16	a	a	DET
ejpam-4470	366	17	hybrid	hybrid	ADJ
ejpam-4470	366	18	method	method	NOUN
ejpam-4470	366	19	for	for	ADP
ejpam-4470	366	20	solving	solve	VERB
ejpam-4470	366	21	fuzzy	fuzzy	ADJ
ejpam-4470	366	22	volterra	volterra	PROPN
ejpam-4470	366	23	integral	integral	ADJ
ejpam-4470	366	24	equations	equation	NOUN
ejpam-4470	366	25	of	of	ADP
ejpam-4470	366	26	separable	separable	ADJ
ejpam-4470	366	27	type	type	NOUN
ejpam-4470	366	28	kernels	kernel	NOUN
ejpam-4470	366	29	journal	journal	NOUN
ejpam-4470	366	30	of	of	ADP
ejpam-4470	366	31	king	king	PROPN
ejpam-4470	366	32	saud	saud	PROPN
ejpam-4470	366	33	university	university	PROPN
ejpam-4470	366	34	science	science	NOUN
ejpam-4470	366	35	101246	101246	NUM
ejpam-4470	366	36	,	,	PUNCT
ejpam-4470	366	37	33,2021	33,2021	NUM
ejpam-4470	366	38	.	.	PUNCT