id	sid	tid	token	lemma	pos
ejpam-4299	1	1	european	european	PROPN
ejpam-4299	1	2	journal	journal	PROPN
ejpam-4299	1	3	of	of	ADP
ejpam-4299	1	4	pure	pure	ADJ
ejpam-4299	1	5	and	and	CCONJ
ejpam-4299	1	6	applied	apply	VERB
ejpam-4299	1	7	mathematics	mathematic	NOUN
ejpam-4299	1	8	vol	vol	NOUN
ejpam-4299	1	9	.	.	PROPN
ejpam-4299	2	1	15	15	NUM
ejpam-4299	2	2	,	,	PUNCT
ejpam-4299	2	3	no	no	INTJ
ejpam-4299	2	4	.	.	NOUN
ejpam-4299	2	5	2	2	NUM
ejpam-4299	2	6	,	,	PUNCT
ejpam-4299	2	7	2022	2022	NUM
ejpam-4299	2	8	,	,	PUNCT
ejpam-4299	2	9	557	557	NUM
ejpam-4299	2	10	-	-	SYM
ejpam-4299	2	11	571	571	NUM
ejpam-4299	2	12	issn	issn	PROPN
ejpam-4299	2	13	1307	1307	NUM
ejpam-4299	2	14	-	-	SYM
ejpam-4299	2	15	5543	5543	NUM
ejpam-4299	2	16	–	–	PUNCT
ejpam-4299	2	17	ejpam.com	ejpam.com	X
ejpam-4299	2	18	published	publish	VERB
ejpam-4299	2	19	by	by	ADP
ejpam-4299	2	20	new	new	PROPN
ejpam-4299	2	21	york	york	PROPN
ejpam-4299	2	22	business	business	PROPN
ejpam-4299	2	23	global	global	PROPN
ejpam-4299	2	24	the	the	DET
ejpam-4299	2	25	fractional	fractional	ADJ
ejpam-4299	2	26	differential	differential	ADJ
ejpam-4299	2	27	equations	equation	NOUN
ejpam-4299	2	28	with	with	ADP
ejpam-4299	2	29	uncertainty	uncertainty	NOUN
ejpam-4299	2	30	by	by	ADP
ejpam-4299	2	31	conformable	conformable	ADJ
ejpam-4299	2	32	derivative	derivative	ADJ
ejpam-4299	2	33	atimad	atimad	ADJ
ejpam-4299	2	34	harir1,∗	harir1,∗	NOUN
ejpam-4299	2	35	,	,	PUNCT
ejpam-4299	2	36	said	say	VERB
ejpam-4299	2	37	melliani1	melliani1	PROPN
ejpam-4299	2	38	,	,	PUNCT
ejpam-4299	2	39	lalla	lalla	PROPN
ejpam-4299	2	40	saadia	saadia	PROPN
ejpam-4299	2	41	chadli1	chadli1	PROPN
ejpam-4299	2	42	1	1	NUM
ejpam-4299	2	43	laboratory	laboratory	NOUN
ejpam-4299	2	44	of	of	ADP
ejpam-4299	2	45	applied	apply	VERB
ejpam-4299	2	46	mathematics	mathematic	NOUN
ejpam-4299	2	47	and	and	CCONJ
ejpam-4299	2	48	scientific	scientific	ADJ
ejpam-4299	2	49	computing	computing	NOUN
ejpam-4299	2	50	,	,	PUNCT
ejpam-4299	2	51	sultan	sultan	PROPN
ejpam-4299	2	52	moulay	moulay	PROPN
ejpam-4299	2	53	slimane	slimane	PROPN
ejpam-4299	2	54	university	university	PROPN
ejpam-4299	2	55	,	,	PUNCT
ejpam-4299	2	56	p.o	p.o	PROPN
ejpam-4299	2	57	.	.	PROPN
ejpam-4299	2	58	box	box	PROPN
ejpam-4299	2	59	523	523	NUM
ejpam-4299	2	60	,	,	PUNCT
ejpam-4299	2	61	beni	beni	ADJ
ejpam-4299	2	62	mellal	mellal	NOUN
ejpam-4299	2	63	,	,	PUNCT
ejpam-4299	2	64	23000	23000	NUM
ejpam-4299	2	65	,	,	PUNCT
ejpam-4299	2	66	morocco	morocco	PROPN
ejpam-4299	2	67	abstract	abstract	NOUN
ejpam-4299	2	68	.	.	PUNCT
ejpam-4299	3	1	we	we	PRON
ejpam-4299	3	2	provide	provide	VERB
ejpam-4299	3	3	a	a	DET
ejpam-4299	3	4	fractional	fractional	ADJ
ejpam-4299	3	5	order	order	NOUN
ejpam-4299	3	6	fuzzy	fuzzy	ADJ
ejpam-4299	3	7	fractional	fractional	ADJ
ejpam-4299	3	8	differential	differential	NOUN
ejpam-4299	3	9	equation	equation	NOUN
ejpam-4299	3	10	q	q	PROPN
ejpam-4299	3	11	∈	∈	PROPN
ejpam-4299	3	12	(	(	PUNCT
ejpam-4299	3	13	0	0	NUM
ejpam-4299	3	14	,	,	PUNCT
ejpam-4299	3	15	1	1	NUM
ejpam-4299	3	16	]	]	PUNCT
ejpam-4299	3	17	.	.	PUNCT
ejpam-4299	4	1	a	a	DET
ejpam-4299	4	2	fuzzy	fuzzy	ADJ
ejpam-4299	4	3	fractional	fractional	ADJ
ejpam-4299	4	4	integral	integral	ADJ
ejpam-4299	4	5	and	and	CCONJ
ejpam-4299	4	6	a	a	DET
ejpam-4299	4	7	fuzzy	fuzzy	ADJ
ejpam-4299	4	8	conformable	conformable	ADJ
ejpam-4299	4	9	derivative	derivative	NOUN
ejpam-4299	4	10	are	be	AUX
ejpam-4299	4	11	shown	show	VERB
ejpam-4299	4	12	and	and	CCONJ
ejpam-4299	4	13	proved	prove	VERB
ejpam-4299	4	14	.	.	PUNCT
ejpam-4299	5	1	to	to	PART
ejpam-4299	5	2	prove	prove	VERB
ejpam-4299	5	3	fuzzy	fuzzy	ADJ
ejpam-4299	5	4	solutions	solution	NOUN
ejpam-4299	5	5	for	for	ADP
ejpam-4299	5	6	fractional	fractional	ADJ
ejpam-4299	5	7	differential	differential	ADJ
ejpam-4299	5	8	equations	equation	NOUN
ejpam-4299	5	9	with	with	ADP
ejpam-4299	5	10	fuzzy	fuzzy	ADJ
ejpam-4299	5	11	beginning	beginning	NOUN
ejpam-4299	5	12	values	value	NOUN
ejpam-4299	5	13	and	and	CCONJ
ejpam-4299	5	14	deterministic	deterministic	ADJ
ejpam-4299	5	15	or	or	CCONJ
ejpam-4299	5	16	fuzzy	fuzzy	ADJ
ejpam-4299	5	17	functions	function	NOUN
ejpam-4299	5	18	,	,	PUNCT
ejpam-4299	5	19	two	two	NUM
ejpam-4299	5	20	alternative	alternative	ADJ
ejpam-4299	5	21	techniques	technique	NOUN
ejpam-4299	5	22	are	be	AUX
ejpam-4299	5	23	used	use	VERB
ejpam-4299	5	24	.	.	PUNCT
ejpam-4299	6	1	the	the	DET
ejpam-4299	6	2	application	application	NOUN
ejpam-4299	6	3	has	have	AUX
ejpam-4299	6	4	been	be	AUX
ejpam-4299	6	5	submitted	submit	VERB
ejpam-4299	6	6	.	.	PUNCT
ejpam-4299	7	1	2020	2020	NUM
ejpam-4299	7	2	mathematics	mathematic	NOUN
ejpam-4299	7	3	subject	subject	NOUN
ejpam-4299	7	4	classifications	classification	NOUN
ejpam-4299	7	5	:	:	PUNCT
ejpam-4299	7	6	34k36	34k36	NUM
ejpam-4299	7	7	,	,	PUNCT
ejpam-4299	7	8	34k37	34k37	NUM
ejpam-4299	7	9	,	,	PUNCT
ejpam-4299	7	10	46s40	46s40	NUM
ejpam-4299	7	11	key	key	ADJ
ejpam-4299	7	12	words	word	NOUN
ejpam-4299	7	13	and	and	CCONJ
ejpam-4299	7	14	phrases	phrase	NOUN
ejpam-4299	7	15	:	:	PUNCT
ejpam-4299	7	16	fuzzy	fuzzy	ADJ
ejpam-4299	7	17	fractional	fractional	ADJ
ejpam-4299	7	18	differential	differential	NOUN
ejpam-4299	7	19	equation	equation	NOUN
ejpam-4299	7	20	,	,	PUNCT
ejpam-4299	7	21	conformable	conformable	ADJ
ejpam-4299	7	22	derivative	derivative	ADJ
ejpam-4299	7	23	,	,	PUNCT
ejpam-4299	7	24	fuzzy	fuzzy	ADJ
ejpam-4299	7	25	number	number	NOUN
ejpam-4299	7	26	1	1	NUM
ejpam-4299	7	27	.	.	PUNCT
ejpam-4299	8	1	introduction	introduction	NOUN
ejpam-4299	8	2	in	in	ADP
ejpam-4299	8	3	this	this	DET
ejpam-4299	8	4	paper	paper	NOUN
ejpam-4299	8	5	we	we	PRON
ejpam-4299	8	6	will	will	AUX
ejpam-4299	8	7	consider	consider	VERB
ejpam-4299	8	8	the	the	DET
ejpam-4299	8	9	fractional	fractional	ADJ
ejpam-4299	8	10	differential	differential	ADJ
ejpam-4299	8	11	equation	equation	NOUN
ejpam-4299	8	12	y(q)(t	y(q)(t	NUM
ejpam-4299	8	13	)	)	PUNCT
ejpam-4299	8	14	=	=	SYM
ejpam-4299	8	15	f	f	PROPN
ejpam-4299	8	16	(	(	PUNCT
ejpam-4299	8	17	t	t	PROPN
ejpam-4299	8	18	,	,	PUNCT
ejpam-4299	8	19	y	y	PROPN
ejpam-4299	8	20	,	,	PUNCT
ejpam-4299	8	21	k	k	NOUN
ejpam-4299	8	22	)	)	PUNCT
ejpam-4299	8	23	,	,	PUNCT
ejpam-4299	8	24	q	q	PROPN
ejpam-4299	8	25	∈	∈	PROPN
ejpam-4299	8	26	(	(	PUNCT
ejpam-4299	8	27	0	0	NUM
ejpam-4299	8	28	,	,	PUNCT
ejpam-4299	8	29	1	1	NUM
ejpam-4299	8	30	]	]	PUNCT
ejpam-4299	8	31	(	(	PUNCT
ejpam-4299	8	32	1	1	X
ejpam-4299	8	33	)	)	PUNCT
ejpam-4299	8	34	y(0	y(0	PROPN
ejpam-4299	8	35	)	)	PUNCT
ejpam-4299	8	36	=	=	PUNCT
ejpam-4299	9	1	c	c	X
ejpam-4299	9	2	where	where	SCONJ
ejpam-4299	9	3	k	k	PROPN
ejpam-4299	9	4	=	=	PRON
ejpam-4299	9	5	(	(	PUNCT
ejpam-4299	9	6	k1	k1	PROPN
ejpam-4299	9	7	,	,	PUNCT
ejpam-4299	9	8	.	.	PUNCT
ejpam-4299	9	9	.	.	PUNCT
ejpam-4299	9	10	.	.	PUNCT
ejpam-4299	10	1	,	,	PUNCT
ejpam-4299	10	2	kn	kn	PROPN
ejpam-4299	10	3	)	)	PUNCT
ejpam-4299	10	4	is	be	AUX
ejpam-4299	10	5	a	a	DET
ejpam-4299	10	6	vector	vector	NOUN
ejpam-4299	10	7	of	of	ADP
ejpam-4299	10	8	constants	constant	NOUN
ejpam-4299	10	9	,	,	PUNCT
ejpam-4299	10	10	t	t	PROPN
ejpam-4299	10	11	∈	∈	PROPN
ejpam-4299	10	12	(	(	PUNCT
ejpam-4299	10	13	0	0	NUM
ejpam-4299	10	14	,	,	PUNCT
ejpam-4299	10	15	a	a	PRON
ejpam-4299	10	16	)	)	PUNCT
ejpam-4299	10	17	and	and	CCONJ
ejpam-4299	10	18	y(q	y(q	PROPN
ejpam-4299	10	19	)	)	PUNCT
ejpam-4299	10	20	is	be	AUX
ejpam-4299	10	21	the	the	DET
ejpam-4299	10	22	conformable	conformable	ADJ
ejpam-4299	10	23	derivative	derivative	NOUN
ejpam-4299	10	24	of	of	ADP
ejpam-4299	10	25	y	y	PRON
ejpam-4299	10	26	of	of	ADP
ejpam-4299	10	27	order	order	NOUN
ejpam-4299	10	28	q	q	X
ejpam-4299	10	29	∈	∈	NOUN
ejpam-4299	10	30	(	(	PUNCT
ejpam-4299	10	31	0	0	NUM
ejpam-4299	10	32	,	,	PUNCT
ejpam-4299	10	33	1	1	NUM
ejpam-4299	10	34	]	]	PUNCT
ejpam-4299	10	35	see	see	VERB
ejpam-4299	10	36	[	[	X
ejpam-4299	10	37	12	12	NUM
ejpam-4299	10	38	]	]	PUNCT
ejpam-4299	10	39	.	.	PUNCT
ejpam-4299	11	1	we	we	PRON
ejpam-4299	11	2	suppose	suppose	VERB
ejpam-4299	11	3	the	the	DET
ejpam-4299	11	4	existence	existence	NOUN
ejpam-4299	11	5	of	of	ADP
ejpam-4299	11	6	imprecise	imprecise	ADJ
ejpam-4299	11	7	parameters	parameter	NOUN
ejpam-4299	11	8	kj	kj	PROPN
ejpam-4299	11	9	and	and	CCONJ
ejpam-4299	11	10	c	c	PROPN
ejpam-4299	11	11	in	in	ADP
ejpam-4299	11	12	eq	eq	NOUN
ejpam-4299	11	13	(	(	PUNCT
ejpam-4299	11	14	1	1	NUM
ejpam-4299	11	15	)	)	PUNCT
ejpam-4299	11	16	.	.	PUNCT
ejpam-4299	12	1	because	because	SCONJ
ejpam-4299	12	2	fuzzy	fuzzy	ADJ
ejpam-4299	12	3	sets	set	NOUN
ejpam-4299	12	4	theory	theory	NOUN
ejpam-4299	12	5	is	be	AUX
ejpam-4299	12	6	a	a	DET
ejpam-4299	12	7	valuable	valuable	ADJ
ejpam-4299	12	8	tool	tool	NOUN
ejpam-4299	12	9	for	for	ADP
ejpam-4299	12	10	representing	represent	VERB
ejpam-4299	12	11	imprecision	imprecision	NOUN
ejpam-4299	12	12	and	and	CCONJ
ejpam-4299	12	13	processing	processing	NOUN
ejpam-4299	12	14	vagueness	vagueness	NOUN
ejpam-4299	12	15	in	in	ADP
ejpam-4299	12	16	mathematical	mathematical	ADJ
ejpam-4299	12	17	models	model	NOUN
ejpam-4299	12	18	[	[	X
ejpam-4299	12	19	10	10	NUM
ejpam-4299	12	20	,	,	PUNCT
ejpam-4299	12	21	12	12	NUM
ejpam-4299	12	22	]	]	PUNCT
ejpam-4299	12	23	,	,	PUNCT
ejpam-4299	12	24	the	the	DET
ejpam-4299	12	25	goal	goal	NOUN
ejpam-4299	12	26	of	of	ADP
ejpam-4299	12	27	this	this	DET
ejpam-4299	12	28	paper	paper	NOUN
ejpam-4299	12	29	is	be	AUX
ejpam-4299	12	30	to	to	PART
ejpam-4299	12	31	solve	solve	VERB
ejpam-4299	12	32	eq	eq	NOUN
ejpam-4299	12	33	(	(	PUNCT
ejpam-4299	12	34	1	1	NUM
ejpam-4299	12	35	)	)	PUNCT
ejpam-4299	12	36	with	with	ADP
ejpam-4299	12	37	fuzzy	fuzzy	ADJ
ejpam-4299	12	38	parameters	parameter	NOUN
ejpam-4299	12	39	using	use	VERB
ejpam-4299	12	40	fuzzy	fuzzy	ADJ
ejpam-4299	12	41	conformable	conformable	ADJ
ejpam-4299	12	42	derivative	derivative	NOUN
ejpam-4299	12	43	using	use	VERB
ejpam-4299	12	44	the	the	DET
ejpam-4299	12	45	same	same	ADJ
ejpam-4299	12	46	technique	technique	NOUN
ejpam-4299	12	47	as	as	ADP
ejpam-4299	12	48	buckley	buckley	NOUN
ejpam-4299	12	49	and	and	CCONJ
ejpam-4299	12	50	feuring	feure	VERB
ejpam-4299	12	51	[	[	X
ejpam-4299	12	52	10	10	NUM
ejpam-4299	12	53	]	]	PUNCT
ejpam-4299	12	54	.	.	PUNCT
ejpam-4299	13	1	as	as	ADP
ejpam-4299	13	2	a	a	DET
ejpam-4299	13	3	result	result	NOUN
ejpam-4299	13	4	,	,	PUNCT
ejpam-4299	13	5	the	the	DET
ejpam-4299	13	6	first	first	ADJ
ejpam-4299	13	7	part	part	NOUN
ejpam-4299	13	8	of	of	ADP
ejpam-4299	13	9	this	this	DET
ejpam-4299	13	10	work	work	NOUN
ejpam-4299	13	11	proposes	propose	VERB
ejpam-4299	13	12	a	a	DET
ejpam-4299	13	13	new	new	ADJ
ejpam-4299	13	14	solution	solution	NOUN
ejpam-4299	13	15	to	to	ADP
ejpam-4299	13	16	the	the	DET
ejpam-4299	13	17	q	q	X
ejpam-4299	13	18	∈	∈	PROPN
ejpam-4299	13	19	(	(	PUNCT
ejpam-4299	13	20	0	0	NUM
ejpam-4299	13	21	,	,	PUNCT
ejpam-4299	13	22	1	1	NUM
ejpam-4299	13	23	]	]	PUNCT
ejpam-4299	13	24	order	order	NOUN
ejpam-4299	13	25	fuzzy	fuzzy	ADJ
ejpam-4299	13	26	fractional	fractional	ADJ
ejpam-4299	13	27	initial	initial	ADJ
ejpam-4299	13	28	value	value	NOUN
ejpam-4299	13	29	problem	problem	NOUN
ejpam-4299	13	30	.	.	PUNCT
ejpam-4299	14	1	this	this	DET
ejpam-4299	14	2	new	new	ADJ
ejpam-4299	14	3	solution	solution	NOUN
ejpam-4299	14	4	’s	’s	PART
ejpam-4299	14	5	basic	basic	ADJ
ejpam-4299	14	6	attributes	attribute	NOUN
ejpam-4299	14	7	are	be	AUX
ejpam-4299	14	8	listed	list	VERB
ejpam-4299	14	9	.	.	PUNCT
ejpam-4299	15	1	[	[	X
ejpam-4299	15	2	8	8	NUM
ejpam-4299	15	3	]	]	PUNCT
ejpam-4299	15	4	developed	develop	VERB
ejpam-4299	15	5	the	the	DET
ejpam-4299	15	6	concept	concept	NOUN
ejpam-4299	15	7	of	of	ADP
ejpam-4299	15	8	the	the	DET
ejpam-4299	15	9	fuzzy	fuzzy	ADJ
ejpam-4299	15	10	conformable	conformable	ADJ
ejpam-4299	15	11	derivative	derivative	NOUN
ejpam-4299	15	12	,	,	PUNCT
ejpam-4299	15	13	which	which	PRON
ejpam-4299	15	14	is	be	AUX
ejpam-4299	15	15	the	the	DET
ejpam-4299	15	16	most	most	ADV
ejpam-4299	15	17	natural	natural	ADJ
ejpam-4299	15	18	and	and	CCONJ
ejpam-4299	15	19	efficient	efficient	ADJ
ejpam-4299	15	20	definition	definition	NOUN
ejpam-4299	15	21	of	of	ADP
ejpam-4299	15	22	the	the	DET
ejpam-4299	15	23	conformable	conformable	ADJ
ejpam-4299	15	24	derivative	derivative	NOUN
ejpam-4299	15	25	of	of	ADP
ejpam-4299	15	26	order	order	NOUN
ejpam-4299	15	27	q	q	X
ejpam-4299	15	28	∈	∈	PROPN
ejpam-4299	15	29	(	(	PUNCT
ejpam-4299	15	30	0	0	NUM
ejpam-4299	15	31	,	,	PUNCT
ejpam-4299	15	32	1	1	NUM
ejpam-4299	15	33	]	]	PUNCT
ejpam-4299	15	34	.	.	PUNCT
ejpam-4299	16	1	the	the	DET
ejpam-4299	16	2	following	follow	VERB
ejpam-4299	16	3	are	be	AUX
ejpam-4299	16	4	the	the	DET
ejpam-4299	16	5	key	key	ADJ
ejpam-4299	16	6	advantages	advantage	NOUN
ejpam-4299	16	7	of	of	ADP
ejpam-4299	16	8	this	this	DET
ejpam-4299	16	9	derivative	derivative	NOUN
ejpam-4299	16	10	:	:	PUNCT
ejpam-4299	16	11	∗corresponding	∗corresponde	VERB
ejpam-4299	16	12	author	author	NOUN
ejpam-4299	16	13	.	.	PUNCT
ejpam-4299	17	1	doi	doi	NOUN
ejpam-4299	17	2	:	:	PUNCT
ejpam-4299	17	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4299	https://doi.org/10.29020/nybg.ejpam.v15i2.4299	NOUN
ejpam-4299	17	4	email	email	NOUN
ejpam-4299	17	5	addresses	address	NOUN
ejpam-4299	17	6	:	:	PUNCT
ejpam-4299	17	7	atimad.harir@gmail.com	atimad.harir@gmail.com	X
ejpam-4299	17	8	(	(	PUNCT
ejpam-4299	17	9	a.	a.	NOUN
ejpam-4299	17	10	harir	harir	PROPN
ejpam-4299	17	11	)	)	PUNCT
ejpam-4299	17	12	,	,	PUNCT
ejpam-4299	17	13	s.melliani@usms.ma	s.melliani@usms.ma	X
ejpam-4299	17	14	(	(	PUNCT
ejpam-4299	17	15	s.	s.	PROPN
ejpam-4299	17	16	melliani	melliani	PROPN
ejpam-4299	17	17	)	)	PUNCT
ejpam-4299	17	18	,	,	PUNCT
ejpam-4299	17	19	sa.chadli@yahoo.fr	sa.chadli@yahoo.fr	PROPN
ejpam-4299	17	20	(	(	PUNCT
ejpam-4299	17	21	l.	l.	PROPN
ejpam-4299	17	22	s.	s.	PROPN
ejpam-4299	17	23	chadli	chadli	PROPN
ejpam-4299	17	24	)	)	PUNCT
ejpam-4299	17	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4299	18	1	557	557	NUM
ejpam-4299	19	1	©	©	PROPN
ejpam-4299	19	2	2022	2022	NUM
ejpam-4299	19	3	ejpam	ejpam	VERB
ejpam-4299	19	4	all	all	DET
ejpam-4299	19	5	rights	right	NOUN
ejpam-4299	19	6	reserved	reserve	VERB
ejpam-4299	19	7	.	.	PUNCT
ejpam-4299	20	1	a.	a.	NOUN
ejpam-4299	20	2	harir	harir	PROPN
ejpam-4299	20	3	,	,	PUNCT
ejpam-4299	20	4	s.	s.	PROPN
ejpam-4299	20	5	melliani	melliani	PROPN
ejpam-4299	20	6	,	,	PUNCT
ejpam-4299	20	7	l.	l.	PROPN
ejpam-4299	20	8	s.	s.	PROPN
ejpam-4299	20	9	chadli	chadli	PROPN
ejpam-4299	20	10	/	/	SYM
ejpam-4299	20	11	eur	eur	PROPN
ejpam-4299	20	12	.	.	PUNCT
ejpam-4299	21	1	j.	j.	PROPN
ejpam-4299	21	2	pure	pure	PROPN
ejpam-4299	21	3	appl	appl	PROPN
ejpam-4299	21	4	.	.	PROPN
ejpam-4299	21	5	math	math	PROPN
ejpam-4299	21	6	,	,	PUNCT
ejpam-4299	21	7	15	15	NUM
ejpam-4299	21	8	(	(	PUNCT
ejpam-4299	21	9	2	2	NUM
ejpam-4299	21	10	)	)	PUNCT
ejpam-4299	21	11	(	(	PUNCT
ejpam-4299	21	12	2022	2022	NUM
ejpam-4299	21	13	)	)	PUNCT
ejpam-4299	21	14	,	,	PUNCT
ejpam-4299	21	15	557	557	NUM
ejpam-4299	21	16	-	-	SYM
ejpam-4299	21	17	571	571	NUM
ejpam-4299	21	18	558	558	NUM
ejpam-4299	21	19	many	many	ADJ
ejpam-4299	21	20	applications	application	NOUN
ejpam-4299	21	21	and	and	CCONJ
ejpam-4299	21	22	phenomena	phenomenon	NOUN
ejpam-4299	21	23	can	can	AUX
ejpam-4299	21	24	be	be	AUX
ejpam-4299	21	25	modeled	model	VERB
ejpam-4299	21	26	using	use	VERB
ejpam-4299	21	27	conformable	conformable	ADJ
ejpam-4299	21	28	derivatives	derivative	NOUN
ejpam-4299	21	29	and	and	CCONJ
ejpam-4299	21	30	need	need	VERB
ejpam-4299	21	31	to	to	PART
ejpam-4299	21	32	be	be	AUX
ejpam-4299	21	33	solved	solve	VERB
ejpam-4299	21	34	(	(	PUNCT
ejpam-4299	21	35	physical	physical	ADJ
ejpam-4299	21	36	applications	application	NOUN
ejpam-4299	21	37	see[2	see[2	NOUN
ejpam-4299	21	38	,	,	PUNCT
ejpam-4299	21	39	4	4	NUM
ejpam-4299	21	40	,	,	PUNCT
ejpam-4299	21	41	5	5	NUM
ejpam-4299	21	42	,	,	PUNCT
ejpam-4299	21	43	13–17	13–17	NUM
ejpam-4299	21	44	]	]	PUNCT
ejpam-4299	21	45	.	.	PUNCT
ejpam-4299	21	46	)	)	PUNCT
ejpam-4299	22	1	it	it	PRON
ejpam-4299	22	2	can	can	AUX
ejpam-4299	22	3	be	be	AUX
ejpam-4299	22	4	extended	extend	VERB
ejpam-4299	22	5	to	to	PART
ejpam-4299	22	6	solve	solve	VERB
ejpam-4299	22	7	exactly	exactly	ADV
ejpam-4299	22	8	and	and	CCONJ
ejpam-4299	22	9	numerically	numerically	ADV
ejpam-4299	22	10	fractional	fractional	ADJ
ejpam-4299	22	11	differential	differential	ADJ
ejpam-4299	22	12	equations	equation	NOUN
ejpam-4299	22	13	and	and	CCONJ
ejpam-4299	22	14	systems	system	NOUN
ejpam-4299	22	15	easily	easily	ADV
ejpam-4299	22	16	and	and	CCONJ
ejpam-4299	22	17	efficiently	efficiently	ADV
ejpam-4299	22	18	.	.	PUNCT
ejpam-4299	23	1	it	it	PRON
ejpam-4299	23	2	creates	create	VERB
ejpam-4299	23	3	new	new	ADJ
ejpam-4299	23	4	comparisons	comparison	NOUN
ejpam-4299	23	5	of	of	ADP
ejpam-4299	23	6	conformable	conformable	ADJ
ejpam-4299	23	7	derivatives	derivative	NOUN
ejpam-4299	23	8	and	and	CCONJ
ejpam-4299	23	9	other	other	ADJ
ejpam-4299	23	10	previous	previous	ADJ
ejpam-4299	23	11	fractional	fractional	ADJ
ejpam-4299	23	12	definitions	definition	NOUN
ejpam-4299	23	13	in	in	ADP
ejpam-4299	23	14	many	many	ADJ
ejpam-4299	23	15	applications	application	NOUN
ejpam-4299	23	16	.	.	PUNCT
ejpam-4299	24	1	this	this	DET
ejpam-4299	24	2	paper	paper	NOUN
ejpam-4299	24	3	initially	initially	ADV
ejpam-4299	24	4	proposes	propose	VERB
ejpam-4299	24	5	a	a	DET
ejpam-4299	24	6	new	new	ADJ
ejpam-4299	24	7	solution	solution	NOUN
ejpam-4299	24	8	to	to	ADP
ejpam-4299	24	9	the	the	DET
ejpam-4299	24	10	q	q	X
ejpam-4299	24	11	∈	∈	PROPN
ejpam-4299	24	12	(	(	PUNCT
ejpam-4299	24	13	0	0	NUM
ejpam-4299	24	14	,	,	PUNCT
ejpam-4299	24	15	1	1	NUM
ejpam-4299	24	16	]	]	PUNCT
ejpam-4299	24	17	order	order	NOUN
ejpam-4299	24	18	fuzzy	fuzzy	ADJ
ejpam-4299	24	19	fractional	fractional	ADJ
ejpam-4299	24	20	initial	initial	ADJ
ejpam-4299	24	21	value	value	NOUN
ejpam-4299	24	22	problem	problem	NOUN
ejpam-4299	24	23	.	.	PUNCT
ejpam-4299	25	1	this	this	DET
ejpam-4299	25	2	new	new	ADJ
ejpam-4299	25	3	solution	solution	NOUN
ejpam-4299	25	4	’s	’s	PART
ejpam-4299	25	5	basic	basic	ADJ
ejpam-4299	25	6	qualities	quality	NOUN
ejpam-4299	25	7	are	be	AUX
ejpam-4299	25	8	listed	list	VERB
ejpam-4299	25	9	below	below	ADV
ejpam-4299	25	10	.	.	PUNCT
ejpam-4299	26	1	the	the	DET
ejpam-4299	26	2	following	follow	VERB
ejpam-4299	26	3	is	be	AUX
ejpam-4299	26	4	a	a	DET
ejpam-4299	26	5	breakdown	breakdown	NOUN
ejpam-4299	26	6	of	of	ADP
ejpam-4299	26	7	the	the	DET
ejpam-4299	26	8	paper	paper	NOUN
ejpam-4299	26	9	’s	’s	PART
ejpam-4299	26	10	sections	section	NOUN
ejpam-4299	26	11	:	:	PUNCT
ejpam-4299	26	12	section	section	NOUN
ejpam-4299	26	13	2	2	NUM
ejpam-4299	26	14	covers	cover	VERB
ejpam-4299	26	15	the	the	DET
ejpam-4299	26	16	fundamental	fundamental	ADJ
ejpam-4299	26	17	ideas	idea	NOUN
ejpam-4299	26	18	of	of	ADP
ejpam-4299	26	19	fuzzy	fuzzy	ADJ
ejpam-4299	26	20	numbers	number	NOUN
ejpam-4299	26	21	.	.	PUNCT
ejpam-4299	27	1	in	in	ADP
ejpam-4299	27	2	section	section	NOUN
ejpam-4299	27	3	3	3	NUM
ejpam-4299	27	4	,	,	PUNCT
ejpam-4299	27	5	we	we	PRON
ejpam-4299	27	6	prove	prove	VERB
ejpam-4299	27	7	certain	certain	ADJ
ejpam-4299	27	8	results	result	NOUN
ejpam-4299	27	9	on	on	ADP
ejpam-4299	27	10	a	a	DET
ejpam-4299	27	11	fuzzy	fuzzy	ADJ
ejpam-4299	27	12	fractional	fractional	ADJ
ejpam-4299	27	13	integral	integral	ADJ
ejpam-4299	27	14	and	and	CCONJ
ejpam-4299	27	15	a	a	DET
ejpam-4299	27	16	fuzzy	fuzzy	ADJ
ejpam-4299	27	17	conformable	conformable	ADJ
ejpam-4299	27	18	derivative	derivative	NOUN
ejpam-4299	27	19	.	.	PUNCT
ejpam-4299	28	1	the	the	DET
ejpam-4299	28	2	extension	extension	NOUN
ejpam-4299	28	3	principle	principle	NOUN
ejpam-4299	28	4	of	of	ADP
ejpam-4299	28	5	zadeh	zadeh	PROPN
ejpam-4299	28	6	and	and	CCONJ
ejpam-4299	28	7	the	the	DET
ejpam-4299	28	8	concept	concept	NOUN
ejpam-4299	28	9	of	of	ADP
ejpam-4299	28	10	fuzzy	fuzzy	ADJ
ejpam-4299	28	11	conformable	conformable	ADJ
ejpam-4299	28	12	derivatives	derivative	NOUN
ejpam-4299	28	13	are	be	AUX
ejpam-4299	28	14	applied	apply	VERB
ejpam-4299	28	15	in	in	ADP
ejpam-4299	28	16	section	section	NOUN
ejpam-4299	28	17	4	4	NUM
ejpam-4299	28	18	using	use	VERB
ejpam-4299	28	19	two	two	NUM
ejpam-4299	28	20	different	different	ADJ
ejpam-4299	28	21	ways	way	NOUN
ejpam-4299	28	22	.	.	PUNCT
ejpam-4299	29	1	the	the	DET
ejpam-4299	29	2	fuzzy	fuzzy	ADJ
ejpam-4299	29	3	fractional	fractional	ADJ
ejpam-4299	29	4	differential	differential	NOUN
ejpam-4299	29	5	equation	equation	NOUN
ejpam-4299	29	6	is	be	AUX
ejpam-4299	29	7	demonstrated	demonstrate	VERB
ejpam-4299	29	8	.	.	PUNCT
ejpam-4299	30	1	the	the	DET
ejpam-4299	30	2	applications	application	NOUN
ejpam-4299	30	3	are	be	AUX
ejpam-4299	30	4	in	in	ADP
ejpam-4299	30	5	section	section	NOUN
ejpam-4299	30	6	5	5	NUM
ejpam-4299	30	7	.	.	SYM
ejpam-4299	30	8	2	2	NUM
ejpam-4299	30	9	.	.	X
ejpam-4299	30	10	preliminaries	preliminary	NOUN
ejpam-4299	30	11	we	we	PRON
ejpam-4299	30	12	place	place	VERB
ejpam-4299	30	13	a	a	DET
ejpam-4299	30	14	bar	bar	NOUN
ejpam-4299	30	15	over	over	ADP
ejpam-4299	30	16	a	a	DET
ejpam-4299	30	17	letter	letter	NOUN
ejpam-4299	30	18	to	to	PART
ejpam-4299	30	19	denote	denote	VERB
ejpam-4299	30	20	a	a	DET
ejpam-4299	30	21	fuzzy	fuzzy	ADJ
ejpam-4299	30	22	number	number	NOUN
ejpam-4299	30	23	of	of	ADP
ejpam-4299	30	24	r.	r.	PROPN
ejpam-4299	30	25	so	so	ADV
ejpam-4299	30	26	,	,	PUNCT
ejpam-4299	30	27	ū	ū	NOUN
ejpam-4299	30	28	,	,	PUNCT
ejpam-4299	30	29	all	all	PRON
ejpam-4299	30	30	represent	represent	VERB
ejpam-4299	30	31	fuzzy	fuzzy	ADJ
ejpam-4299	30	32	numbers	number	NOUN
ejpam-4299	30	33	of	of	ADP
ejpam-4299	30	34	r.	r.	NOUN
ejpam-4299	30	35	we	we	PRON
ejpam-4299	30	36	write	write	VERB
ejpam-4299	30	37	µū(t	µū(t	PROPN
ejpam-4299	30	38	)	)	PUNCT
ejpam-4299	30	39	,	,	PUNCT
ejpam-4299	30	40	a	a	DET
ejpam-4299	30	41	number	number	NOUN
ejpam-4299	30	42	in	in	ADP
ejpam-4299	30	43	[	[	X
ejpam-4299	30	44	0	0	NUM
ejpam-4299	30	45	,	,	PUNCT
ejpam-4299	30	46	1	1	NUM
ejpam-4299	30	47	]	]	PUNCT
ejpam-4299	30	48	,	,	PUNCT
ejpam-4299	30	49	for	for	ADP
ejpam-4299	30	50	the	the	DET
ejpam-4299	30	51	membership	membership	NOUN
ejpam-4299	30	52	function	function	NOUN
ejpam-4299	30	53	of	of	ADP
ejpam-4299	30	54	ū	ū	NOUN
ejpam-4299	30	55	evaluated	evaluate	VERB
ejpam-4299	30	56	at	at	ADP
ejpam-4299	30	57	t	t	PROPN
ejpam-4299	30	58	∈	∈	PROPN
ejpam-4299	30	59	r.	r.	PROPN
ejpam-4299	30	60	let	let	VERB
ejpam-4299	30	61	us	we	PRON
ejpam-4299	30	62	denote	denote	VERB
ejpam-4299	30	63	by	by	ADP
ejpam-4299	30	64	rf	rf	ADJ
ejpam-4299	30	65	=	=	SYM
ejpam-4299	30	66	{	{	PUNCT
ejpam-4299	30	67	µū	µū	NOUN
ejpam-4299	30	68	:	:	PUNCT
ejpam-4299	30	69	r	r	NOUN
ejpam-4299	30	70	→	→	SYM
ejpam-4299	31	1	[	[	X
ejpam-4299	31	2	0	0	NUM
ejpam-4299	31	3	,	,	PUNCT
ejpam-4299	31	4	1	1	NUM
ejpam-4299	31	5	]	]	PUNCT
ejpam-4299	31	6	}	}	PUNCT
ejpam-4299	31	7	the	the	DET
ejpam-4299	31	8	class	class	NOUN
ejpam-4299	31	9	of	of	ADP
ejpam-4299	31	10	fuzzy	fuzzy	ADJ
ejpam-4299	31	11	subsets	subset	NOUN
ejpam-4299	31	12	of	of	ADP
ejpam-4299	31	13	the	the	DET
ejpam-4299	31	14	real	real	ADJ
ejpam-4299	31	15	axis	axis	NOUN
ejpam-4299	31	16	satisfying	satisfy	VERB
ejpam-4299	31	17	the	the	DET
ejpam-4299	31	18	following	follow	VERB
ejpam-4299	31	19	properties	property	NOUN
ejpam-4299	31	20	:	:	PUNCT
ejpam-4299	31	21	(	(	PUNCT
ejpam-4299	31	22	i	i	NOUN
ejpam-4299	31	23	)	)	PUNCT
ejpam-4299	31	24	ū	ū	NOUN
ejpam-4299	31	25	is	be	AUX
ejpam-4299	31	26	normal	normal	ADJ
ejpam-4299	31	27	i.e	i.e	NOUN
ejpam-4299	31	28	,	,	PUNCT
ejpam-4299	31	29	there	there	PRON
ejpam-4299	31	30	exists	exist	VERB
ejpam-4299	31	31	an	an	DET
ejpam-4299	31	32	x0	x0	PROPN
ejpam-4299	31	33	∈	∈	PROPN
ejpam-4299	31	34	r	r	NOUN
ejpam-4299	31	35	such	such	ADJ
ejpam-4299	31	36	that	that	DET
ejpam-4299	31	37	µū	µū	NOUN
ejpam-4299	31	38	(	(	PUNCT
ejpam-4299	31	39	x0	x0	PROPN
ejpam-4299	31	40	)	)	PUNCT
ejpam-4299	32	1	=	=	SYM
ejpam-4299	32	2	1	1	NUM
ejpam-4299	32	3	,	,	PUNCT
ejpam-4299	32	4	(	(	PUNCT
ejpam-4299	32	5	ii	ii	NOUN
ejpam-4299	32	6	)	)	PUNCT
ejpam-4299	32	7	ū	ū	NOUN
ejpam-4299	32	8	is	be	AUX
ejpam-4299	32	9	fuzzy	fuzzy	ADJ
ejpam-4299	32	10	convex	convex	NOUN
ejpam-4299	32	11	i.e	i.e	PRON
ejpam-4299	32	12	for	for	ADP
ejpam-4299	32	13	x	x	PROPN
ejpam-4299	32	14	,	,	PUNCT
ejpam-4299	32	15	y	y	PROPN
ejpam-4299	32	16	∈	∈	PROPN
ejpam-4299	32	17	r	r	NOUN
ejpam-4299	32	18	and	and	CCONJ
ejpam-4299	32	19	0	0	NUM
ejpam-4299	32	20	<	<	X
ejpam-4299	32	21	λ	λ	X
ejpam-4299	32	22	≤	≤	NUM
ejpam-4299	32	23	1	1	NUM
ejpam-4299	32	24	,	,	PUNCT
ejpam-4299	32	25	µū(λx+	µū(λx+	NUM
ejpam-4299	32	26	(	(	PUNCT
ejpam-4299	32	27	1−	1−	NUM
ejpam-4299	32	28	λ)y	λ)y	NOUN
ejpam-4299	32	29	)	)	PUNCT
ejpam-4299	32	30	≥	≥	NOUN
ejpam-4299	32	31	min	min	NOUN
ejpam-4299	33	1	[	[	X
ejpam-4299	33	2	µū(x	µū(x	PROPN
ejpam-4299	33	3	)	)	PUNCT
ejpam-4299	33	4	,	,	PUNCT
ejpam-4299	33	5	µū(y	µū(y	X
ejpam-4299	33	6	)	)	PUNCT
ejpam-4299	33	7	]	]	PUNCT
ejpam-4299	33	8	(	(	PUNCT
ejpam-4299	33	9	iii	iii	X
ejpam-4299	33	10	)	)	PUNCT
ejpam-4299	33	11	ū	ū	NOUN
ejpam-4299	33	12	is	be	AUX
ejpam-4299	33	13	upper	upper	ADJ
ejpam-4299	33	14	semicontinuous	semicontinuous	NOUN
ejpam-4299	33	15	,	,	PUNCT
ejpam-4299	33	16	(	(	PUNCT
ejpam-4299	33	17	iv	iv	X
ejpam-4299	33	18	)	)	PUNCT
ejpam-4299	34	1	[	[	X
ejpam-4299	34	2	ū]0	ū]0	NOUN
ejpam-4299	34	3	=	=	NOUN
ejpam-4299	34	4	cl	cl	NOUN
ejpam-4299	34	5	{	{	PUNCT
ejpam-4299	34	6	x	x	SYM
ejpam-4299	34	7	∈	∈	PROPN
ejpam-4299	34	8	r	r	NOUN
ejpam-4299	34	9	|	|	NOUN
ejpam-4299	34	10	µū(x	µū(x	PROPN
ejpam-4299	34	11	)	)	PUNCT
ejpam-4299	34	12	>	>	X
ejpam-4299	34	13	0	0	X
ejpam-4299	34	14	}	}	PUNCT
ejpam-4299	34	15	is	be	AUX
ejpam-4299	34	16	compact	compact	ADJ
ejpam-4299	34	17	.	.	PUNCT
ejpam-4299	35	1	then	then	ADV
ejpam-4299	35	2	rf	rf	PRON
ejpam-4299	35	3	is	be	AUX
ejpam-4299	35	4	called	call	VERB
ejpam-4299	35	5	the	the	DET
ejpam-4299	35	6	space	space	NOUN
ejpam-4299	35	7	of	of	ADP
ejpam-4299	35	8	fuzzy	fuzzy	ADJ
ejpam-4299	35	9	numbers	number	NOUN
ejpam-4299	35	10	.	.	PUNCT
ejpam-4299	36	1	obviously	obviously	ADV
ejpam-4299	36	2	,	,	PUNCT
ejpam-4299	36	3	r	r	NOUN
ejpam-4299	36	4	⊂	⊂	X
ejpam-4299	36	5	rf	rf	ADJ
ejpam-4299	36	6	.	.	PUNCT
ejpam-4299	37	1	for	for	ADP
ejpam-4299	37	2	0	0	NUM
ejpam-4299	37	3	<	<	X
ejpam-4299	37	4	α	α	PROPN
ejpam-4299	37	5	≤	≤	ADJ
ejpam-4299	37	6	1	1	NUM
ejpam-4299	37	7	denote	denote	NOUN
ejpam-4299	37	8	[	[	NOUN
ejpam-4299	37	9	ū]α	ū]α	ADV
ejpam-4299	37	10	=	=	PRON
ejpam-4299	37	11	{	{	PUNCT
ejpam-4299	37	12	x	x	SYM
ejpam-4299	37	13	∈	∈	PROPN
ejpam-4299	37	14	r	r	NOUN
ejpam-4299	37	15	|	|	NOUN
ejpam-4299	37	16	µū(x	µū(x	PROPN
ejpam-4299	37	17	)	)	PUNCT
ejpam-4299	37	18	≥	≥	NUM
ejpam-4299	37	19	α	α	NOUN
ejpam-4299	37	20	}	}	PUNCT
ejpam-4299	37	21	,	,	PUNCT
ejpam-4299	37	22	then	then	ADV
ejpam-4299	37	23	from	from	ADP
ejpam-4299	37	24	(	(	PUNCT
ejpam-4299	37	25	i	i	NOUN
ejpam-4299	37	26	)	)	PUNCT
ejpam-4299	37	27	to	to	PART
ejpam-4299	37	28	(	(	PUNCT
ejpam-4299	37	29	iv	iv	X
ejpam-4299	37	30	)	)	PUNCT
ejpam-4299	37	31	it	it	PRON
ejpam-4299	37	32	follows	follow	VERB
ejpam-4299	37	33	that	that	SCONJ
ejpam-4299	37	34	the	the	DET
ejpam-4299	37	35	α	α	NOUN
ejpam-4299	37	36	-	-	PUNCT
ejpam-4299	37	37	level	level	NOUN
ejpam-4299	37	38	sets	set	NOUN
ejpam-4299	37	39	[	[	X
ejpam-4299	37	40	ū]α	ū]α	PRON
ejpam-4299	37	41	∈	∈	NOUN
ejpam-4299	37	42	pk(r	pk(r	NOUN
ejpam-4299	37	43	)	)	PUNCT
ejpam-4299	37	44	for	for	ADP
ejpam-4299	37	45	all	all	PRON
ejpam-4299	37	46	0	0	NUM
ejpam-4299	37	47	≤	≤	NUM
ejpam-4299	37	48	α	α	PRON
ejpam-4299	37	49	≤	≤	NOUN
ejpam-4299	37	50	1	1	NUM
ejpam-4299	37	51	is	be	AUX
ejpam-4299	37	52	a	a	DET
ejpam-4299	37	53	closed	closed	ADJ
ejpam-4299	37	54	bounded	bound	VERB
ejpam-4299	37	55	interval	interval	NOUN
ejpam-4299	37	56	which	which	PRON
ejpam-4299	37	57	is	be	AUX
ejpam-4299	37	58	denoted	denote	VERB
ejpam-4299	37	59	by	by	ADP
ejpam-4299	37	60	[	[	NOUN
ejpam-4299	37	61	ū]α	ū]α	PRON
ejpam-4299	37	62	=	=	NOUN
ejpam-4299	38	1	[	[	X
ejpam-4299	38	2	uα1	uα1	NOUN
ejpam-4299	38	3	,	,	PUNCT
ejpam-4299	38	4	u	u	NOUN
ejpam-4299	38	5	α	α	NOUN
ejpam-4299	38	6	2	2	NUM
ejpam-4299	38	7	]	]	PUNCT
ejpam-4299	38	8	.	.	PUNCT
ejpam-4299	39	1	by	by	ADP
ejpam-4299	39	2	pk(r	pk(r	NOUN
ejpam-4299	39	3	)	)	PUNCT
ejpam-4299	39	4	we	we	PRON
ejpam-4299	39	5	denote	denote	VERB
ejpam-4299	39	6	the	the	DET
ejpam-4299	39	7	family	family	NOUN
ejpam-4299	39	8	of	of	ADP
ejpam-4299	39	9	all	all	DET
ejpam-4299	39	10	nonempty	nonempty	ADJ
ejpam-4299	39	11	compact	compact	ADJ
ejpam-4299	39	12	convex	convex	NOUN
ejpam-4299	39	13	subsets	subset	NOUN
ejpam-4299	39	14	of	of	ADP
ejpam-4299	39	15	r	r	NOUN
ejpam-4299	39	16	,	,	PUNCT
ejpam-4299	39	17	and	and	CCONJ
ejpam-4299	39	18	define	define	VERB
ejpam-4299	39	19	the	the	DET
ejpam-4299	39	20	addition	addition	NOUN
ejpam-4299	39	21	and	and	CCONJ
ejpam-4299	39	22	scalar	scalar	ADJ
ejpam-4299	39	23	multiplication	multiplication	NOUN
ejpam-4299	39	24	in	in	ADP
ejpam-4299	39	25	pk(r	pk(r	NOUN
ejpam-4299	39	26	)	)	PUNCT
ejpam-4299	39	27	as	as	ADP
ejpam-4299	39	28	usual	usual	ADJ
ejpam-4299	39	29	.	.	PUNCT
ejpam-4299	40	1	theorem	theorem	NOUN
ejpam-4299	40	2	1	1	NUM
ejpam-4299	40	3	.	.	PUNCT
ejpam-4299	41	1	see	see	VERB
ejpam-4299	41	2	[	[	X
ejpam-4299	41	3	1	1	X
ejpam-4299	41	4	]	]	PUNCT
ejpam-4299	41	5	if	if	SCONJ
ejpam-4299	41	6	ū	ū	NOUN
ejpam-4299	41	7	∈	∈	PROPN
ejpam-4299	41	8	rf	rf	NOUN
ejpam-4299	41	9	,	,	PUNCT
ejpam-4299	41	10	then	then	ADV
ejpam-4299	41	11	(	(	PUNCT
ejpam-4299	41	12	i	i	NOUN
ejpam-4299	41	13	)	)	PUNCT
ejpam-4299	42	1	[	[	X
ejpam-4299	42	2	ū]α	ū]α	DET
ejpam-4299	42	3	∈	∈	PROPN
ejpam-4299	42	4	pk(r	pk(r	NOUN
ejpam-4299	42	5	)	)	PUNCT
ejpam-4299	42	6	for	for	ADP
ejpam-4299	42	7	all	all	PRON
ejpam-4299	42	8	0	0	NUM
ejpam-4299	42	9	≤	≤	NUM
ejpam-4299	42	10	α	α	PRON
ejpam-4299	42	11	≤	≤	NUM
ejpam-4299	42	12	1	1	NUM
ejpam-4299	42	13	(	(	PUNCT
ejpam-4299	42	14	ii	ii	NOUN
ejpam-4299	42	15	)	)	PUNCT
ejpam-4299	43	1	[	[	X
ejpam-4299	43	2	ū]α2	ū]α2	X
ejpam-4299	43	3	⊂	⊂	X
ejpam-4299	43	4	[	[	X
ejpam-4299	43	5	ū]α1	ū]α1	ADJ
ejpam-4299	43	6	for	for	ADP
ejpam-4299	43	7	all	all	PRON
ejpam-4299	43	8	0	0	NUM
ejpam-4299	43	9	≤	≤	NUM
ejpam-4299	43	10	α1	α1	PROPN
ejpam-4299	43	11	≤	≤	ADV
ejpam-4299	43	12	α2	α2	ADJ
ejpam-4299	43	13	≤	≤	ADV
ejpam-4299	43	14	1	1	NUM
ejpam-4299	43	15	(	(	PUNCT
ejpam-4299	43	16	iii	iii	NOUN
ejpam-4299	43	17	)	)	PUNCT
ejpam-4299	43	18	{	{	PUNCT
ejpam-4299	43	19	αk	αk	NOUN
ejpam-4299	43	20	}	}	PUNCT
ejpam-4299	43	21	⊂	⊂	PROPN
ejpam-4299	44	1	[	[	X
ejpam-4299	44	2	0	0	NUM
ejpam-4299	44	3	,	,	PUNCT
ejpam-4299	44	4	1	1	NUM
ejpam-4299	44	5	]	]	PUNCT
ejpam-4299	44	6	is	be	AUX
ejpam-4299	44	7	a	a	DET
ejpam-4299	44	8	nondecreasing	nondecrease	VERB
ejpam-4299	44	9	sequence	sequence	NOUN
ejpam-4299	44	10	which	which	PRON
ejpam-4299	44	11	converges	converge	VERB
ejpam-4299	44	12	to	to	ADP
ejpam-4299	44	13	α	α	PRON
ejpam-4299	44	14	then	then	ADV
ejpam-4299	44	15	[	[	X
ejpam-4299	44	16	ū]α	ū]α	PRON
ejpam-4299	44	17	=	=	SYM
ejpam-4299	44	18	⋂	⋂	PROPN
ejpam-4299	44	19	k≥1	k≥1	NOUN
ejpam-4299	44	20	[	[	X
ejpam-4299	44	21	ū]αk	ū]αk	PRON
ejpam-4299	44	22	a.	a.	NOUN
ejpam-4299	44	23	harir	harir	NOUN
ejpam-4299	44	24	,	,	PUNCT
ejpam-4299	44	25	s.	s.	PROPN
ejpam-4299	44	26	melliani	melliani	PROPN
ejpam-4299	44	27	,	,	PUNCT
ejpam-4299	44	28	l.	l.	PROPN
ejpam-4299	44	29	s.	s.	PROPN
ejpam-4299	44	30	chadli	chadli	PROPN
ejpam-4299	44	31	/	/	SYM
ejpam-4299	44	32	eur	eur	PROPN
ejpam-4299	44	33	.	.	PUNCT
ejpam-4299	45	1	j.	j.	PROPN
ejpam-4299	45	2	pure	pure	PROPN
ejpam-4299	45	3	appl	appl	PROPN
ejpam-4299	45	4	.	.	PROPN
ejpam-4299	45	5	math	math	PROPN
ejpam-4299	45	6	,	,	PUNCT
ejpam-4299	45	7	15	15	NUM
ejpam-4299	45	8	(	(	PUNCT
ejpam-4299	45	9	2	2	NUM
ejpam-4299	45	10	)	)	PUNCT
ejpam-4299	45	11	(	(	PUNCT
ejpam-4299	45	12	2022	2022	NUM
ejpam-4299	45	13	)	)	PUNCT
ejpam-4299	45	14	,	,	PUNCT
ejpam-4299	45	15	557	557	NUM
ejpam-4299	45	16	-	-	SYM
ejpam-4299	45	17	571	571	NUM
ejpam-4299	45	18	559	559	NUM
ejpam-4299	45	19	conversely	conversely	ADV
ejpam-4299	45	20	,	,	PUNCT
ejpam-4299	45	21	if	if	SCONJ
ejpam-4299	45	22	aα	aα	NOUN
ejpam-4299	45	23	=	=	PRON
ejpam-4299	45	24	{	{	PUNCT
ejpam-4299	46	1	[	[	X
ejpam-4299	46	2	uα1	uα1	X
ejpam-4299	46	3	,	,	PUNCT
ejpam-4299	46	4	uα2	uα2	ADV
ejpam-4299	46	5	]	]	PUNCT
ejpam-4299	46	6	;	;	PUNCT
ejpam-4299	46	7	α	α	PROPN
ejpam-4299	46	8	∈	∈	PROPN
ejpam-4299	46	9	(	(	PUNCT
ejpam-4299	46	10	0	0	NUM
ejpam-4299	46	11	,	,	PUNCT
ejpam-4299	46	12	1	1	NUM
ejpam-4299	46	13	]	]	PUNCT
ejpam-4299	46	14	}	}	PUNCT
ejpam-4299	46	15	is	be	AUX
ejpam-4299	46	16	a	a	DET
ejpam-4299	46	17	family	family	NOUN
ejpam-4299	46	18	of	of	ADP
ejpam-4299	46	19	closed	closed	ADJ
ejpam-4299	46	20	real	real	ADJ
ejpam-4299	46	21	intervals	interval	NOUN
ejpam-4299	46	22	verifying	verify	VERB
ejpam-4299	46	23	(	(	PUNCT
ejpam-4299	46	24	i	i	NOUN
ejpam-4299	46	25	)	)	PUNCT
ejpam-4299	46	26	and	and	CCONJ
ejpam-4299	46	27	(	(	PUNCT
ejpam-4299	46	28	ii	ii	NOUN
ejpam-4299	46	29	)	)	PUNCT
ejpam-4299	46	30	,	,	PUNCT
ejpam-4299	46	31	then	then	ADV
ejpam-4299	46	32	{	{	PUNCT
ejpam-4299	46	33	aα	aα	NOUN
ejpam-4299	46	34	}	}	PUNCT
ejpam-4299	46	35	defined	define	VERB
ejpam-4299	46	36	a	a	DET
ejpam-4299	46	37	fuzzy	fuzzy	ADJ
ejpam-4299	46	38	number	number	NOUN
ejpam-4299	46	39	ū	ū	NOUN
ejpam-4299	46	40	∈	∈	PROPN
ejpam-4299	46	41	rf	rf	VERB
ejpam-4299	46	42	such	such	ADJ
ejpam-4299	46	43	that	that	SCONJ
ejpam-4299	47	1	[	[	NOUN
ejpam-4299	47	2	ū]α	ū]α	ADV
ejpam-4299	47	3	=	=	NUM
ejpam-4299	47	4	aα	aα	NOUN
ejpam-4299	47	5	for	for	ADP
ejpam-4299	47	6	0	0	NUM
ejpam-4299	47	7	<	<	X
ejpam-4299	47	8	α	α	PROPN
ejpam-4299	47	9	≤	≤	NUM
ejpam-4299	47	10	1	1	NUM
ejpam-4299	47	11	and	and	CCONJ
ejpam-4299	47	12	[	[	X
ejpam-4299	47	13	ū]0	ū]0	NOUN
ejpam-4299	47	14	=	=	SYM
ejpam-4299	47	15	∪0	∪0	PROPN
ejpam-4299	47	16	<	<	X
ejpam-4299	47	17	α≤1aα	α≤1aα	X
ejpam-4299	47	18	⊂	⊂	PROPN
ejpam-4299	47	19	a0	a0	PROPN
ejpam-4299	47	20	.	.	PUNCT
ejpam-4299	47	21	definition	definition	NOUN
ejpam-4299	47	22	1	1	NUM
ejpam-4299	47	23	.	.	PUNCT
ejpam-4299	48	1	[	[	X
ejpam-4299	48	2	7	7	NUM
ejpam-4299	48	3	,	,	PUNCT
ejpam-4299	48	4	9	9	NUM
ejpam-4299	48	5	,	,	PUNCT
ejpam-4299	48	6	11	11	NUM
ejpam-4299	48	7	]	]	PUNCT
ejpam-4299	48	8	we	we	PRON
ejpam-4299	48	9	represent	represent	VERB
ejpam-4299	48	10	an	an	DET
ejpam-4299	48	11	arbitrary	arbitrary	ADJ
ejpam-4299	48	12	fuzzy	fuzzy	ADJ
ejpam-4299	48	13	number	number	NOUN
ejpam-4299	48	14	by	by	ADP
ejpam-4299	48	15	an	an	DET
ejpam-4299	48	16	ordered	order	VERB
ejpam-4299	48	17	pair	pair	NOUN
ejpam-4299	48	18	of	of	ADP
ejpam-4299	48	19	functions	function	NOUN
ejpam-4299	48	20	[	[	X
ejpam-4299	48	21	ū]α	ū]α	PRON
ejpam-4299	48	22	=	=	NOUN
ejpam-4299	49	1	[	[	X
ejpam-4299	49	2	uα1	uα1	NOUN
ejpam-4299	49	3	,	,	PUNCT
ejpam-4299	49	4	u	u	NOUN
ejpam-4299	49	5	α	α	NOUN
ejpam-4299	49	6	2	2	NUM
ejpam-4299	49	7	]	]	PUNCT
ejpam-4299	49	8	,	,	PUNCT
ejpam-4299	49	9	α	α	PROPN
ejpam-4299	49	10	∈	∈	PROPN
ejpam-4299	50	1	[	[	X
ejpam-4299	50	2	0	0	NUM
ejpam-4299	50	3	,	,	PUNCT
ejpam-4299	50	4	1	1	NUM
ejpam-4299	50	5	]	]	PUNCT
ejpam-4299	50	6	,	,	PUNCT
ejpam-4299	50	7	which	which	PRON
ejpam-4299	50	8	satisfy	satisfy	VERB
ejpam-4299	50	9	the	the	DET
ejpam-4299	50	10	following	follow	VERB
ejpam-4299	50	11	requirements	requirement	NOUN
ejpam-4299	50	12	:	:	PUNCT
ejpam-4299	50	13	1	1	X
ejpam-4299	50	14	.	.	X
ejpam-4299	50	15	uα1	uα1	PROPN
ejpam-4299	50	16	is	be	AUX
ejpam-4299	50	17	an	an	DET
ejpam-4299	50	18	increasing	increase	VERB
ejpam-4299	50	19	function	function	NOUN
ejpam-4299	50	20	over	over	ADP
ejpam-4299	50	21	[	[	X
ejpam-4299	50	22	0	0	NUM
ejpam-4299	50	23	,	,	PUNCT
ejpam-4299	50	24	1	1	NUM
ejpam-4299	50	25	]	]	PUNCT
ejpam-4299	50	26	;	;	PUNCT
ejpam-4299	50	27	2	2	X
ejpam-4299	50	28	.	.	X
ejpam-4299	51	1	uα2	uα2	ADV
ejpam-4299	51	2	is	be	AUX
ejpam-4299	51	3	a	a	DET
ejpam-4299	51	4	decreasing	decrease	VERB
ejpam-4299	51	5	function	function	NOUN
ejpam-4299	51	6	on	on	ADP
ejpam-4299	51	7	[	[	X
ejpam-4299	51	8	0	0	NUM
ejpam-4299	51	9	,	,	PUNCT
ejpam-4299	51	10	1	1	NUM
ejpam-4299	51	11	]	]	PUNCT
ejpam-4299	51	12	;	;	PUNCT
ejpam-4299	51	13	3	3	X
ejpam-4299	51	14	.	.	X
ejpam-4299	51	15	uα1	uα1	PROPN
ejpam-4299	51	16	and	and	CCONJ
ejpam-4299	51	17	uα2	uα2	NOUN
ejpam-4299	51	18	are	be	AUX
ejpam-4299	51	19	bounded	bound	VERB
ejpam-4299	51	20	left	leave	VERB
ejpam-4299	51	21	continuous	continuous	ADJ
ejpam-4299	51	22	on	on	ADP
ejpam-4299	51	23	(	(	PUNCT
ejpam-4299	51	24	0	0	NUM
ejpam-4299	51	25	,	,	PUNCT
ejpam-4299	51	26	1	1	NUM
ejpam-4299	51	27	]	]	PUNCT
ejpam-4299	51	28	,	,	PUNCT
ejpam-4299	51	29	and	and	CCONJ
ejpam-4299	51	30	right	right	ADV
ejpam-4299	51	31	continuous	continuous	ADJ
ejpam-4299	51	32	at	at	ADP
ejpam-4299	51	33	α	α	NOUN
ejpam-4299	51	34	=	=	SYM
ejpam-4299	51	35	0	0	NUM
ejpam-4299	51	36	;	;	PUNCT
ejpam-4299	51	37	4	4	X
ejpam-4299	51	38	.	.	X
ejpam-4299	51	39	uα1	uα1	PROPN
ejpam-4299	51	40	≤	≤	ADV
ejpam-4299	51	41	uα2	uα2	ADV
ejpam-4299	51	42	,	,	PUNCT
ejpam-4299	51	43	for	for	ADP
ejpam-4299	51	44	0	0	NUM
ejpam-4299	51	45	≤	≤	NUM
ejpam-4299	51	46	α	α	NOUN
ejpam-4299	51	47	≤	≤	NUM
ejpam-4299	51	48	1	1	NUM
ejpam-4299	51	49	.	.	PUNCT
ejpam-4299	52	1	definition	definition	NOUN
ejpam-4299	52	2	2	2	NUM
ejpam-4299	52	3	.	.	PUNCT
ejpam-4299	53	1	for	for	ADP
ejpam-4299	53	2	a	a	DET
ejpam-4299	53	3	fuzzy	fuzzy	ADJ
ejpam-4299	53	4	set	set	VERB
ejpam-4299	53	5	ū	ū	NOUN
ejpam-4299	53	6	=	=	SYM
ejpam-4299	53	7	(	(	PUNCT
ejpam-4299	53	8	u1	u1	PROPN
ejpam-4299	53	9	,	,	PUNCT
ejpam-4299	53	10	u2	u2	NOUN
ejpam-4299	53	11	,	,	PUNCT
ejpam-4299	53	12	u3	u3	NOUN
ejpam-4299	53	13	)	)	PUNCT
ejpam-4299	53	14	,	,	PUNCT
ejpam-4299	53	15	(	(	PUNCT
ejpam-4299	53	16	u1	u1	VERB
ejpam-4299	53	17	<	<	X
ejpam-4299	53	18	u2	u2	PROPN
ejpam-4299	53	19	<	<	X
ejpam-4299	53	20	u3	u3	PROPN
ejpam-4299	53	21	)	)	PUNCT
ejpam-4299	53	22	,	,	PUNCT
ejpam-4299	53	23	ū	ū	PROPN
ejpam-4299	53	24	is	be	AUX
ejpam-4299	53	25	called	call	VERB
ejpam-4299	53	26	triangular	triangular	NOUN
ejpam-4299	53	27	fuzzy	fuzzy	ADJ
ejpam-4299	53	28	number	number	NOUN
ejpam-4299	53	29	with	with	ADP
ejpam-4299	53	30	peak	peak	NOUN
ejpam-4299	53	31	u2	u2	NOUN
ejpam-4299	53	32	,	,	PUNCT
ejpam-4299	53	33	left	leave	VERB
ejpam-4299	53	34	width	width	VERB
ejpam-4299	53	35	u2−u1	u2−u1	NUM
ejpam-4299	53	36	>	>	X
ejpam-4299	53	37	0	0	PUNCT
ejpam-4299	54	1	and	and	CCONJ
ejpam-4299	54	2	right	right	ADJ
ejpam-4299	54	3	width	width	NOUN
ejpam-4299	54	4	u3−u2	u3−u2	ADJ
ejpam-4299	54	5	>	>	X
ejpam-4299	54	6	0	0	NUM
ejpam-4299	54	7	,	,	PUNCT
ejpam-4299	54	8	if	if	SCONJ
ejpam-4299	54	9	its	its	PRON
ejpam-4299	54	10	membership	membership	NOUN
ejpam-4299	54	11	function	function	NOUN
ejpam-4299	54	12	has	have	VERB
ejpam-4299	54	13	the	the	DET
ejpam-4299	54	14	following	follow	VERB
ejpam-4299	54	15	form	form	NOUN
ejpam-4299	54	16	:	:	PUNCT
ejpam-4299	54	17	µū(t	µū(t	X
ejpam-4299	54	18	)	)	PUNCT
ejpam-4299	55	1	=	=	SYM
ejpam-4299	56	1			NUM
ejpam-4299	56	2	1−	1−	NUM
ejpam-4299	56	3	(	(	PUNCT
ejpam-4299	56	4	u2−t	u2−t	PROPN
ejpam-4299	56	5	)	)	PUNCT
ejpam-4299	56	6	u2−u1	u2−u1	NUM
ejpam-4299	56	7	,	,	PUNCT
ejpam-4299	56	8	u1	u1	PROPN
ejpam-4299	56	9	≤	≤	PROPN
ejpam-4299	56	10	t	t	PROPN
ejpam-4299	56	11	≤	≤	NOUN
ejpam-4299	56	12	u2	u2	NOUN
ejpam-4299	56	13	,	,	PUNCT
ejpam-4299	56	14	1−	1−	NUM
ejpam-4299	56	15	(	(	PUNCT
ejpam-4299	56	16	t−u2	t−u2	NOUN
ejpam-4299	56	17	)	)	PUNCT
ejpam-4299	56	18	u3−u2	u3−u2	NOUN
ejpam-4299	56	19	,	,	PUNCT
ejpam-4299	56	20	u2	u2	PROPN
ejpam-4299	56	21	≤	≤	PROPN
ejpam-4299	56	22	t	t	PROPN
ejpam-4299	56	23	≤	≤	NOUN
ejpam-4299	56	24	u3	u3	NOUN
ejpam-4299	56	25	,	,	PUNCT
ejpam-4299	56	26	0	0	NUM
ejpam-4299	56	27	,	,	PUNCT
ejpam-4299	56	28	otherwise	otherwise	ADV
ejpam-4299	56	29	.	.	PUNCT
ejpam-4299	57	1	lemma	lemma	PROPN
ejpam-4299	57	2	1	1	X
ejpam-4299	57	3	.	.	PUNCT
ejpam-4299	58	1	see	see	VERB
ejpam-4299	58	2	[	[	X
ejpam-4299	58	3	3	3	X
ejpam-4299	58	4	]	]	X
ejpam-4299	58	5	let	let	VERB
ejpam-4299	58	6	ū	ū	NOUN
ejpam-4299	58	7	,	,	PUNCT
ejpam-4299	58	8	v̄	v̄	NOUN
ejpam-4299	58	9	:	:	PUNCT
ejpam-4299	59	1	r	r	X
ejpam-4299	59	2	→	→	SYM
ejpam-4299	60	1	[	[	X
ejpam-4299	60	2	0	0	NUM
ejpam-4299	60	3	,	,	PUNCT
ejpam-4299	60	4	1	1	NUM
ejpam-4299	60	5	]	]	PUNCT
ejpam-4299	60	6	be	be	AUX
ejpam-4299	60	7	the	the	DET
ejpam-4299	60	8	fuzzy	fuzzy	ADJ
ejpam-4299	60	9	sets	set	NOUN
ejpam-4299	60	10	.	.	PUNCT
ejpam-4299	61	1	then	then	ADV
ejpam-4299	61	2	ū	ū	NOUN
ejpam-4299	61	3	=	=	PUNCT
ejpam-4299	61	4	v̄	v̄	NOUN
ejpam-4299	61	5	if	if	SCONJ
ejpam-4299	61	6	and	and	CCONJ
ejpam-4299	61	7	only	only	ADV
ejpam-4299	61	8	if	if	SCONJ
ejpam-4299	61	9	[	[	NOUN
ejpam-4299	61	10	ū]α	ū]α	PRON
ejpam-4299	61	11	=	=	NOUN
ejpam-4299	62	1	[	[	X
ejpam-4299	62	2	v̄]α	v̄]α	NOUN
ejpam-4299	62	3	for	for	ADP
ejpam-4299	62	4	all	all	DET
ejpam-4299	62	5	α	α	PRON
ejpam-4299	62	6	∈	∈	PROPN
ejpam-4299	63	1	[	[	X
ejpam-4299	63	2	0	0	NUM
ejpam-4299	63	3	,	,	PUNCT
ejpam-4299	63	4	1	1	NUM
ejpam-4299	63	5	]	]	PUNCT
ejpam-4299	63	6	.	.	PUNCT
ejpam-4299	64	1	the	the	DET
ejpam-4299	64	2	following	follow	VERB
ejpam-4299	64	3	arithmetic	arithmetic	ADJ
ejpam-4299	64	4	operations	operation	NOUN
ejpam-4299	64	5	on	on	ADP
ejpam-4299	64	6	fuzzy	fuzzy	ADJ
ejpam-4299	64	7	numbers	number	NOUN
ejpam-4299	64	8	are	be	AUX
ejpam-4299	64	9	well	well	ADV
ejpam-4299	64	10	known	know	VERB
ejpam-4299	64	11	and	and	CCONJ
ejpam-4299	64	12	frequently	frequently	ADV
ejpam-4299	64	13	used	use	VERB
ejpam-4299	64	14	below	below	ADV
ejpam-4299	64	15	.	.	PUNCT
ejpam-4299	65	1	if	if	SCONJ
ejpam-4299	65	2	ū	ū	NOUN
ejpam-4299	65	3	,	,	PUNCT
ejpam-4299	65	4	v̄	v̄	PROPN
ejpam-4299	65	5	∈	∈	PROPN
ejpam-4299	65	6	rf	rf	VERB
ejpam-4299	65	7	then	then	ADV
ejpam-4299	65	8	[	[	X
ejpam-4299	65	9	ū+	ū+	NUM
ejpam-4299	65	10	v̄]α	v̄]α	NOUN
ejpam-4299	65	11	=	=	PUNCT
ejpam-4299	66	1	[	[	X
ejpam-4299	66	2	uα1	uα1	X
ejpam-4299	66	3	+	+	X
ejpam-4299	66	4	vα1	vα1	NOUN
ejpam-4299	66	5	,	,	PUNCT
ejpam-4299	66	6	u	u	NOUN
ejpam-4299	66	7	α	α	NOUN
ejpam-4299	66	8	2	2	NUM
ejpam-4299	66	9	+	+	CCONJ
ejpam-4299	66	10	vα2	vα2	NOUN
ejpam-4299	66	11	]	]	PUNCT
ejpam-4299	67	1	[	[	X
ejpam-4299	67	2	λū]α	λū]α	X
ejpam-4299	67	3	=	=	SYM
ejpam-4299	67	4	λ[ū]α	λ[ū]α	NOUN
ejpam-4299	67	5	=	=	SYM
ejpam-4299	67	6	{	{	PUNCT
ejpam-4299	68	1	[	[	X
ejpam-4299	68	2	λuα1	λuα1	NOUN
ejpam-4299	68	3	,	,	PUNCT
ejpam-4299	68	4	λu	λu	X
ejpam-4299	68	5	α	α	NOUN
ejpam-4299	68	6	2	2	X
ejpam-4299	68	7	]	]	PUNCT
ejpam-4299	68	8	if	if	SCONJ
ejpam-4299	68	9	λ	λ	X
ejpam-4299	68	10	≥	≥	X
ejpam-4299	68	11	0	0	PUNCT
ejpam-4299	69	1	[	[	X
ejpam-4299	69	2	λuα2	λuα2	PROPN
ejpam-4299	69	3	,	,	PUNCT
ejpam-4299	69	4	λu	λu	X
ejpam-4299	69	5	α	α	NOUN
ejpam-4299	69	6	1	1	NUM
ejpam-4299	69	7	]	]	PUNCT
ejpam-4299	69	8	if	if	SCONJ
ejpam-4299	69	9	λ	λ	X
ejpam-4299	69	10	<	<	X
ejpam-4299	69	11	0	0	NUM
ejpam-4299	69	12	,	,	PUNCT
ejpam-4299	69	13	definition	definition	NOUN
ejpam-4299	69	14	3	3	NUM
ejpam-4299	69	15	.	.	PUNCT
ejpam-4299	70	1	let	let	VERB
ejpam-4299	70	2	ū	ū	NOUN
ejpam-4299	70	3	,	,	PUNCT
ejpam-4299	70	4	v̄	v̄	PROPN
ejpam-4299	70	5	∈	∈	PROPN
ejpam-4299	70	6	rf	rf	ADJ
ejpam-4299	70	7	.	.	PUNCT
ejpam-4299	71	1	if	if	SCONJ
ejpam-4299	71	2	there	there	PRON
ejpam-4299	71	3	exists	exist	VERB
ejpam-4299	71	4	w̄	w̄	NOUN
ejpam-4299	71	5	∈	∈	PROPN
ejpam-4299	71	6	rf	rf	VERB
ejpam-4299	71	7	such	such	ADJ
ejpam-4299	71	8	as	as	ADP
ejpam-4299	71	9	ū	ū	NOUN
ejpam-4299	71	10	=	=	SYM
ejpam-4299	71	11	v̄	v̄	NOUN
ejpam-4299	72	1	+	+	CCONJ
ejpam-4299	72	2	w̄	w̄	NOUN
ejpam-4299	72	3	then	then	ADV
ejpam-4299	72	4	w̄	w̄	NOUN
ejpam-4299	72	5	is	be	AUX
ejpam-4299	72	6	called	call	VERB
ejpam-4299	72	7	the	the	DET
ejpam-4299	72	8	h	h	NOUN
ejpam-4299	72	9	-	-	PUNCT
ejpam-4299	72	10	difference	difference	NOUN
ejpam-4299	72	11	of	of	ADP
ejpam-4299	72	12	ū	ū	NOUN
ejpam-4299	72	13	,	,	PUNCT
ejpam-4299	72	14	v̄	v̄	NOUN
ejpam-4299	72	15	and	and	CCONJ
ejpam-4299	72	16	it	it	PRON
ejpam-4299	72	17	is	be	AUX
ejpam-4299	72	18	denoted	denote	VERB
ejpam-4299	72	19	ū	ū	NOUN
ejpam-4299	72	20	v̄	v̄	NOUN
ejpam-4299	72	21	3	3	NUM
ejpam-4299	72	22	.	.	X
ejpam-4299	72	23	fuzzy	fuzzy	ADJ
ejpam-4299	72	24	conformable	conformable	ADJ
ejpam-4299	72	25	differentiability	differentiability	NOUN
ejpam-4299	72	26	and	and	CCONJ
ejpam-4299	72	27	fuzzy	fuzzy	ADJ
ejpam-4299	72	28	fractional	fractional	ADJ
ejpam-4299	72	29	integral	integral	ADJ
ejpam-4299	72	30	now	now	ADV
ejpam-4299	72	31	,	,	PUNCT
ejpam-4299	72	32	we	we	PRON
ejpam-4299	72	33	present	present	VERB
ejpam-4299	72	34	our	our	PRON
ejpam-4299	72	35	new	new	ADJ
ejpam-4299	72	36	definition	definition	NOUN
ejpam-4299	72	37	,	,	PUNCT
ejpam-4299	72	38	which	which	PRON
ejpam-4299	72	39	is	be	AUX
ejpam-4299	72	40	the	the	DET
ejpam-4299	72	41	simplest	simple	ADJ
ejpam-4299	72	42	and	and	CCONJ
ejpam-4299	72	43	most	most	ADV
ejpam-4299	72	44	natural	natural	ADJ
ejpam-4299	72	45	and	and	CCONJ
ejpam-4299	72	46	efficient	efficient	ADJ
ejpam-4299	72	47	definition	definition	NOUN
ejpam-4299	72	48	of	of	ADP
ejpam-4299	72	49	conformable	conformable	ADJ
ejpam-4299	72	50	derivative	derivative	NOUN
ejpam-4299	72	51	of	of	ADP
ejpam-4299	72	52	order	order	NOUN
ejpam-4299	72	53	q	q	X
ejpam-4299	72	54	∈	∈	PROPN
ejpam-4299	72	55	(	(	PUNCT
ejpam-4299	72	56	0	0	NUM
ejpam-4299	72	57	,	,	PUNCT
ejpam-4299	72	58	1	1	NUM
ejpam-4299	72	59	]	]	PUNCT
ejpam-4299	72	60	.	.	PUNCT
ejpam-4299	73	1	definition	definition	NOUN
ejpam-4299	73	2	4	4	NUM
ejpam-4299	73	3	.	.	PUNCT
ejpam-4299	74	1	[	[	X
ejpam-4299	74	2	8	8	NUM
ejpam-4299	74	3	]	]	PUNCT
ejpam-4299	74	4	let	let	VERB
ejpam-4299	74	5	f̄	f̄	NOUN
ejpam-4299	74	6	:	:	PUNCT
ejpam-4299	75	1	[	[	X
ejpam-4299	75	2	0	0	NUM
ejpam-4299	75	3	,	,	PUNCT
ejpam-4299	75	4	a	a	PRON
ejpam-4299	75	5	)	)	PUNCT
ejpam-4299	75	6	→	→	PUNCT
ejpam-4299	75	7	rf	rf	CCONJ
ejpam-4299	75	8	be	be	AUX
ejpam-4299	75	9	a	a	DET
ejpam-4299	75	10	fuzzy	fuzzy	ADJ
ejpam-4299	75	11	function	function	NOUN
ejpam-4299	75	12	.	.	PUNCT
ejpam-4299	76	1	qth	qth	NOUN
ejpam-4299	76	2	order	order	NOUN
ejpam-4299	76	3	fuzzy	fuzzy	ADJ
ejpam-4299	76	4	conformable	conformable	ADJ
ejpam-4299	76	5	derivative	derivative	NOUN
ejpam-4299	76	6	of	of	ADP
ejpam-4299	76	7	f̄	f̄	PROPN
ejpam-4299	76	8	is	be	AUX
ejpam-4299	76	9	defined	define	VERB
ejpam-4299	76	10	by	by	ADP
ejpam-4299	76	11	tq(f̄	tq(f̄	ADV
ejpam-4299	76	12	)	)	PUNCT
ejpam-4299	76	13	(	(	PUNCT
ejpam-4299	76	14	t	t	NOUN
ejpam-4299	76	15	)	)	PUNCT
ejpam-4299	77	1	=	=	PROPN
ejpam-4299	77	2	lim	lim	PROPN
ejpam-4299	77	3	ε→0	ε→0	NOUN
ejpam-4299	77	4	+	+	CCONJ
ejpam-4299	77	5	f̄	f̄	PROPN
ejpam-4299	77	6	(	(	PUNCT
ejpam-4299	77	7	t+	t+	NOUN
ejpam-4299	77	8	εt1−q	εt1−q	PROPN
ejpam-4299	77	9	)	)	PUNCT
ejpam-4299	77	10	f̄	f̄	PROPN
ejpam-4299	77	11	(	(	PUNCT
ejpam-4299	77	12	t	t	PROPN
ejpam-4299	77	13	)	)	PUNCT
ejpam-4299	77	14	ε	ε	PROPN
ejpam-4299	78	1	=	=	SYM
ejpam-4299	78	2	lim	lim	PROPN
ejpam-4299	78	3	ε→0	ε→0	NOUN
ejpam-4299	79	1	+	+	CCONJ
ejpam-4299	79	2	f̄	f̄	PROPN
ejpam-4299	79	3	(	(	PUNCT
ejpam-4299	79	4	t	t	PROPN
ejpam-4299	79	5	)	)	PUNCT
ejpam-4299	79	6	f̄	f̄	NOUN
ejpam-4299	79	7	(	(	PUNCT
ejpam-4299	79	8	t−	t−	PROPN
ejpam-4299	79	9	εt1−q	εt1−q	PROPN
ejpam-4299	79	10	)	)	PUNCT
ejpam-4299	79	11	ε	ε	PROPN
ejpam-4299	79	12	a.	a.	NOUN
ejpam-4299	79	13	harir	harir	PROPN
ejpam-4299	79	14	,	,	PUNCT
ejpam-4299	79	15	s.	s.	PROPN
ejpam-4299	79	16	melliani	melliani	PROPN
ejpam-4299	79	17	,	,	PUNCT
ejpam-4299	79	18	l.	l.	PROPN
ejpam-4299	79	19	s.	s.	PROPN
ejpam-4299	79	20	chadli	chadli	PROPN
ejpam-4299	79	21	/	/	SYM
ejpam-4299	79	22	eur	eur	PROPN
ejpam-4299	79	23	.	.	PUNCT
ejpam-4299	80	1	j.	j.	PROPN
ejpam-4299	80	2	pure	pure	PROPN
ejpam-4299	80	3	appl	appl	PROPN
ejpam-4299	80	4	.	.	PROPN
ejpam-4299	80	5	math	math	PROPN
ejpam-4299	80	6	,	,	PUNCT
ejpam-4299	80	7	15	15	NUM
ejpam-4299	80	8	(	(	PUNCT
ejpam-4299	80	9	2	2	NUM
ejpam-4299	80	10	)	)	PUNCT
ejpam-4299	80	11	(	(	PUNCT
ejpam-4299	80	12	2022	2022	NUM
ejpam-4299	80	13	)	)	PUNCT
ejpam-4299	80	14	,	,	PUNCT
ejpam-4299	80	15	557	557	NUM
ejpam-4299	80	16	-	-	SYM
ejpam-4299	80	17	571	571	NUM
ejpam-4299	80	18	560	560	NUM
ejpam-4299	80	19	for	for	ADP
ejpam-4299	80	20	all	all	DET
ejpam-4299	80	21	t	t	PROPN
ejpam-4299	80	22	>	>	X
ejpam-4299	80	23	0	0	NUM
ejpam-4299	80	24	,	,	PUNCT
ejpam-4299	80	25	q	q	PROPN
ejpam-4299	80	26	∈	∈	PROPN
ejpam-4299	80	27	(	(	PUNCT
ejpam-4299	80	28	0	0	NUM
ejpam-4299	80	29	,	,	PUNCT
ejpam-4299	80	30	1	1	NUM
ejpam-4299	80	31	)	)	PUNCT
ejpam-4299	80	32	.	.	PUNCT
ejpam-4299	81	1	let	let	VERB
ejpam-4299	81	2	f̄	f̄	PROPN
ejpam-4299	81	3	(	(	PUNCT
ejpam-4299	81	4	q)(t	q)(t	PROPN
ejpam-4299	81	5	)	)	PUNCT
ejpam-4299	81	6	stands	stand	VERB
ejpam-4299	81	7	for	for	ADP
ejpam-4299	81	8	tq(f̄	tq(f̄	ADV
ejpam-4299	81	9	)	)	PUNCT
ejpam-4299	81	10	(	(	PUNCT
ejpam-4299	81	11	t	t	PROPN
ejpam-4299	81	12	)	)	PUNCT
ejpam-4299	81	13	.	.	PUNCT
ejpam-4299	82	1	hence	hence	ADV
ejpam-4299	82	2	f̄	f̄	PROPN
ejpam-4299	82	3	(	(	PUNCT
ejpam-4299	82	4	q)(t	q)(t	PROPN
ejpam-4299	82	5	)	)	PUNCT
ejpam-4299	82	6	=	=	SYM
ejpam-4299	82	7	lim	lim	PROPN
ejpam-4299	82	8	ε→0	ε→0	NOUN
ejpam-4299	82	9	+	+	CCONJ
ejpam-4299	82	10	f̄	f̄	PROPN
ejpam-4299	82	11	(	(	PUNCT
ejpam-4299	82	12	t+	t+	NOUN
ejpam-4299	82	13	εt1−q	εt1−q	PROPN
ejpam-4299	82	14	)	)	PUNCT
ejpam-4299	82	15	f̄	f̄	PROPN
ejpam-4299	82	16	(	(	PUNCT
ejpam-4299	82	17	t	t	PROPN
ejpam-4299	82	18	)	)	PUNCT
ejpam-4299	82	19	ε	ε	PROPN
ejpam-4299	83	1	=	=	SYM
ejpam-4299	83	2	lim	lim	PROPN
ejpam-4299	83	3	ε→0	ε→0	NOUN
ejpam-4299	84	1	+	+	CCONJ
ejpam-4299	84	2	f̄	f̄	PROPN
ejpam-4299	84	3	(	(	PUNCT
ejpam-4299	84	4	t	t	PROPN
ejpam-4299	84	5	)	)	PUNCT
ejpam-4299	84	6	f̄	f̄	NOUN
ejpam-4299	84	7	(	(	PUNCT
ejpam-4299	84	8	t−	t−	PROPN
ejpam-4299	84	9	εt1−q	εt1−q	PROPN
ejpam-4299	84	10	)	)	PUNCT
ejpam-4299	84	11	ε	ε	PROPN
ejpam-4299	84	12	if	if	SCONJ
ejpam-4299	84	13	f̄	f̄	PROPN
ejpam-4299	84	14	is	be	AUX
ejpam-4299	84	15	q	q	NOUN
ejpam-4299	84	16	-	-	NOUN
ejpam-4299	84	17	differentiable	differentiable	ADJ
ejpam-4299	84	18	in	in	ADP
ejpam-4299	84	19	some	some	PRON
ejpam-4299	84	20	(	(	PUNCT
ejpam-4299	84	21	0	0	NUM
ejpam-4299	84	22	,	,	PUNCT
ejpam-4299	84	23	a	a	NOUN
ejpam-4299	84	24	)	)	PUNCT
ejpam-4299	84	25	,	,	PUNCT
ejpam-4299	84	26	and	and	CCONJ
ejpam-4299	85	1	limt→0	limt→0	PROPN
ejpam-4299	85	2	+	+	CCONJ
ejpam-4299	85	3	f̄	f̄	PROPN
ejpam-4299	85	4	(	(	PUNCT
ejpam-4299	85	5	q)(t	q)(t	PROPN
ejpam-4299	85	6	)	)	PUNCT
ejpam-4299	85	7	exists	exist	VERB
ejpam-4299	85	8	,	,	PUNCT
ejpam-4299	85	9	then	then	ADV
ejpam-4299	85	10	f̄	f̄	PROPN
ejpam-4299	85	11	(	(	PUNCT
ejpam-4299	85	12	q)(0	q)(0	PROPN
ejpam-4299	85	13	)	)	PUNCT
ejpam-4299	86	1	=	=	SYM
ejpam-4299	86	2	lim	lim	PROPN
ejpam-4299	86	3	t→0	t→0	PROPN
ejpam-4299	86	4	+	+	CCONJ
ejpam-4299	86	5	f̄	f̄	PROPN
ejpam-4299	86	6	(	(	PUNCT
ejpam-4299	86	7	q)(t	q)(t	PROPN
ejpam-4299	86	8	)	)	PUNCT
ejpam-4299	86	9	and	and	CCONJ
ejpam-4299	86	10	the	the	DET
ejpam-4299	86	11	limits	limit	NOUN
ejpam-4299	86	12	(	(	PUNCT
ejpam-4299	86	13	in	in	ADP
ejpam-4299	86	14	the	the	DET
ejpam-4299	86	15	metric	metric	PROPN
ejpam-4299	86	16	d.	d.	PROPN
ejpam-4299	86	17	)	)	PUNCT
ejpam-4299	86	18	remark	remark	VERB
ejpam-4299	86	19	1	1	NUM
ejpam-4299	86	20	.	.	PUNCT
ejpam-4299	86	21	from	from	ADP
ejpam-4299	86	22	the	the	DET
ejpam-4299	86	23	definition	definition	NOUN
ejpam-4299	86	24	,	,	PUNCT
ejpam-4299	86	25	it	it	PRON
ejpam-4299	86	26	directly	directly	ADV
ejpam-4299	86	27	follows	follow	VERB
ejpam-4299	86	28	that	that	SCONJ
ejpam-4299	86	29	if	if	SCONJ
ejpam-4299	86	30	f̄	f̄	PROPN
ejpam-4299	86	31	is	be	AUX
ejpam-4299	86	32	q	q	ADJ
ejpam-4299	86	33	-	-	ADJ
ejpam-4299	86	34	differentiable	differentiable	ADJ
ejpam-4299	86	35	then	then	ADV
ejpam-4299	86	36	the	the	DET
ejpam-4299	86	37	multi	multi	NOUN
ejpam-4299	86	38	valued	value	VERB
ejpam-4299	86	39	mapping	mapping	NOUN
ejpam-4299	86	40	f̄α	f̄α	PROPN
ejpam-4299	86	41	is	be	AUX
ejpam-4299	86	42	q	q	NOUN
ejpam-4299	86	43	-	-	NOUN
ejpam-4299	86	44	differentiable	differentiable	ADJ
ejpam-4299	86	45	for	for	ADP
ejpam-4299	86	46	all	all	DET
ejpam-4299	86	47	α	α	PRON
ejpam-4299	86	48	∈	∈	PROPN
ejpam-4299	87	1	[	[	X
ejpam-4299	87	2	0	0	NUM
ejpam-4299	87	3	,	,	PUNCT
ejpam-4299	87	4	1	1	NUM
ejpam-4299	87	5	]	]	PUNCT
ejpam-4299	87	6	and	and	CCONJ
ejpam-4299	87	7	tqf̄α	tqf̄α	NUM
ejpam-4299	87	8	=	=	SYM
ejpam-4299	87	9	[	[	PUNCT
ejpam-4299	87	10	f̄	f̄	NOUN
ejpam-4299	87	11	(	(	PUNCT
ejpam-4299	87	12	q)(t	q)(t	PROPN
ejpam-4299	87	13	)	)	PUNCT
ejpam-4299	88	1	]	]	X
ejpam-4299	88	2	α	α	X
ejpam-4299	88	3	(	(	PUNCT
ejpam-4299	88	4	2	2	NUM
ejpam-4299	88	5	)	)	PUNCT
ejpam-4299	88	6	here	here	ADV
ejpam-4299	88	7	tqf̄α	tqf̄α	PRON
ejpam-4299	88	8	is	be	AUX
ejpam-4299	88	9	denoted	denote	VERB
ejpam-4299	88	10	the	the	DET
ejpam-4299	88	11	conformable	conformable	ADJ
ejpam-4299	88	12	fractional	fractional	ADJ
ejpam-4299	88	13	derivative	derivative	NOUN
ejpam-4299	88	14	of	of	ADP
ejpam-4299	88	15	f̄α	f̄α	PROPN
ejpam-4299	88	16	of	of	ADP
ejpam-4299	88	17	order	order	NOUN
ejpam-4299	88	18	q.	q.	PROPN
ejpam-4299	88	19	theorem	theorem	NOUN
ejpam-4299	88	20	2	2	NUM
ejpam-4299	88	21	.	.	PUNCT
ejpam-4299	89	1	[	[	X
ejpam-4299	89	2	8	8	NUM
ejpam-4299	89	3	]	]	PUNCT
ejpam-4299	89	4	let	let	VERB
ejpam-4299	89	5	f̄	f̄	NOUN
ejpam-4299	89	6	:	:	PUNCT
ejpam-4299	90	1	[	[	X
ejpam-4299	90	2	0	0	NUM
ejpam-4299	90	3	,	,	PUNCT
ejpam-4299	90	4	a	a	PRON
ejpam-4299	90	5	)	)	PUNCT
ejpam-4299	90	6	→	→	SYM
ejpam-4299	90	7	rf	rf	NUM
ejpam-4299	90	8	be	be	AUX
ejpam-4299	90	9	q	q	ADJ
ejpam-4299	90	10	-	-	ADJ
ejpam-4299	90	11	differentiable	differentiable	ADJ
ejpam-4299	90	12	.	.	PUNCT
ejpam-4299	91	1	denote	denote	VERB
ejpam-4299	91	2	f̄α(t	f̄α(t	NOUN
ejpam-4299	91	3	)	)	PUNCT
ejpam-4299	91	4	=	=	PUNCT
ejpam-4299	92	1	[	[	X
ejpam-4299	92	2	fα	fα	ADP
ejpam-4299	92	3	1	1	NUM
ejpam-4299	92	4	(	(	PUNCT
ejpam-4299	92	5	t	t	PROPN
ejpam-4299	92	6	)	)	PUNCT
ejpam-4299	92	7	,	,	PUNCT
ejpam-4299	92	8	f	f	PROPN
ejpam-4299	92	9	α	α	PROPN
ejpam-4299	92	10	2	2	NUM
ejpam-4299	92	11	(	(	PUNCT
ejpam-4299	92	12	t	t	PROPN
ejpam-4299	92	13	)	)	PUNCT
ejpam-4299	92	14	]	]	PUNCT
ejpam-4299	92	15	,	,	PUNCT
ejpam-4299	92	16	α	α	PROPN
ejpam-4299	92	17	∈	∈	PROPN
ejpam-4299	93	1	[	[	X
ejpam-4299	93	2	0	0	NUM
ejpam-4299	93	3	,	,	PUNCT
ejpam-4299	93	4	1	1	NUM
ejpam-4299	93	5	]	]	PUNCT
ejpam-4299	93	6	.	.	PUNCT
ejpam-4299	94	1	then	then	ADV
ejpam-4299	94	2	fα	fα	ADV
ejpam-4299	94	3	1	1	NUM
ejpam-4299	94	4	(	(	PUNCT
ejpam-4299	94	5	t	t	NOUN
ejpam-4299	94	6	)	)	PUNCT
ejpam-4299	94	7	and	and	CCONJ
ejpam-4299	94	8	fα	fα	ADP
ejpam-4299	94	9	2	2	NUM
ejpam-4299	94	10	(	(	PUNCT
ejpam-4299	94	11	t	t	NOUN
ejpam-4299	94	12	)	)	PUNCT
ejpam-4299	94	13	are	be	AUX
ejpam-4299	94	14	q	q	ADJ
ejpam-4299	94	15	-	-	ADJ
ejpam-4299	94	16	differentiable	differentiable	ADJ
ejpam-4299	94	17	and	and	CCONJ
ejpam-4299	94	18	[	[	PUNCT
ejpam-4299	94	19	f̄	f̄	PROPN
ejpam-4299	94	20	(	(	PUNCT
ejpam-4299	94	21	q)(t	q)(t	PROPN
ejpam-4299	94	22	)	)	PUNCT
ejpam-4299	94	23	]	]	PUNCT
ejpam-4299	94	24	α	α	X
ejpam-4299	94	25	=	=	X
ejpam-4299	94	26	[	[	PUNCT
ejpam-4299	94	27	(	(	PUNCT
ejpam-4299	94	28	fα	fα	ADP
ejpam-4299	94	29	1	1	NUM
ejpam-4299	94	30	)	)	PUNCT
ejpam-4299	94	31	(	(	PUNCT
ejpam-4299	94	32	q	q	X
ejpam-4299	94	33	)	)	PUNCT
ejpam-4299	94	34	(	(	PUNCT
ejpam-4299	94	35	t	t	NOUN
ejpam-4299	94	36	)	)	PUNCT
ejpam-4299	94	37	,	,	PUNCT
ejpam-4299	94	38	(	(	PUNCT
ejpam-4299	94	39	fα	fα	ADP
ejpam-4299	94	40	2	2	NUM
ejpam-4299	94	41	)	)	PUNCT
ejpam-4299	94	42	(	(	PUNCT
ejpam-4299	94	43	q	q	X
ejpam-4299	94	44	)	)	PUNCT
ejpam-4299	94	45	(	(	PUNCT
ejpam-4299	94	46	t	t	PROPN
ejpam-4299	94	47	)	)	PUNCT
ejpam-4299	94	48	]	]	PUNCT
ejpam-4299	94	49	.	.	PUNCT
ejpam-4299	95	1	theorem	theorem	NOUN
ejpam-4299	95	2	3	3	X
ejpam-4299	95	3	.	.	PUNCT
ejpam-4299	96	1	if	if	SCONJ
ejpam-4299	96	2	a	a	DET
ejpam-4299	96	3	function	function	NOUN
ejpam-4299	96	4	f̄	f̄	NOUN
ejpam-4299	96	5	:	:	PUNCT
ejpam-4299	97	1	[	[	X
ejpam-4299	97	2	0	0	NUM
ejpam-4299	97	3	,	,	PUNCT
ejpam-4299	97	4	a	a	PRON
ejpam-4299	97	5	)	)	PUNCT
ejpam-4299	97	6	→	→	PUNCT
ejpam-4299	97	7	rf	rf	NUM
ejpam-4299	97	8	is	be	AUX
ejpam-4299	97	9	q	q	ADJ
ejpam-4299	97	10	-	-	NOUN
ejpam-4299	97	11	differentiable	differentiable	ADJ
ejpam-4299	97	12	at	at	ADP
ejpam-4299	97	13	t0	t0	PROPN
ejpam-4299	97	14	>	>	PUNCT
ejpam-4299	97	15	0	0	NUM
ejpam-4299	97	16	,	,	PUNCT
ejpam-4299	97	17	q	q	PROPN
ejpam-4299	97	18	∈	∈	PROPN
ejpam-4299	97	19	(	(	PUNCT
ejpam-4299	97	20	0	0	NUM
ejpam-4299	97	21	,	,	PUNCT
ejpam-4299	97	22	1	1	NUM
ejpam-4299	97	23	]	]	PUNCT
ejpam-4299	97	24	denote	denote	NOUN
ejpam-4299	97	25	f̄α(t	f̄α(t	NOUN
ejpam-4299	97	26	)	)	PUNCT
ejpam-4299	97	27	=	=	PUNCT
ejpam-4299	98	1	[	[	X
ejpam-4299	98	2	fα	fα	ADP
ejpam-4299	98	3	1	1	NUM
ejpam-4299	98	4	(	(	PUNCT
ejpam-4299	98	5	t	t	PROPN
ejpam-4299	98	6	)	)	PUNCT
ejpam-4299	98	7	,	,	PUNCT
ejpam-4299	98	8	f	f	PROPN
ejpam-4299	98	9	α	α	PROPN
ejpam-4299	98	10	2	2	NUM
ejpam-4299	98	11	(	(	PUNCT
ejpam-4299	98	12	t	t	PROPN
ejpam-4299	98	13	)	)	PUNCT
ejpam-4299	98	14	]	]	PUNCT
ejpam-4299	98	15	,	,	PUNCT
ejpam-4299	98	16	α	α	PROPN
ejpam-4299	98	17	∈	∈	PROPN
ejpam-4299	99	1	[	[	X
ejpam-4299	99	2	0	0	NUM
ejpam-4299	99	3	,	,	PUNCT
ejpam-4299	99	4	1	1	NUM
ejpam-4299	99	5	]	]	PUNCT
ejpam-4299	99	6	.	.	PUNCT
ejpam-4299	100	1	then	then	ADV
ejpam-4299	100	2	fα	fα	ADV
ejpam-4299	100	3	1	1	NUM
ejpam-4299	100	4	(	(	PUNCT
ejpam-4299	100	5	t	t	NOUN
ejpam-4299	100	6	)	)	PUNCT
ejpam-4299	100	7	and	and	CCONJ
ejpam-4299	100	8	fα	fα	ADP
ejpam-4299	100	9	2	2	NUM
ejpam-4299	100	10	(	(	PUNCT
ejpam-4299	100	11	t	t	NOUN
ejpam-4299	100	12	)	)	PUNCT
ejpam-4299	100	13	are	be	AUX
ejpam-4299	100	14	continuous	continuous	ADJ
ejpam-4299	100	15	at	at	ADP
ejpam-4299	100	16	t0	t0	PROPN
ejpam-4299	100	17	so	so	ADV
ejpam-4299	100	18	f̄	f̄	PROPN
ejpam-4299	100	19	is	be	AUX
ejpam-4299	100	20	continuous	continuous	ADJ
ejpam-4299	100	21	at	at	ADP
ejpam-4299	100	22	t0	t0	NOUN
ejpam-4299	100	23	.	.	PUNCT
ejpam-4299	101	1	proof	proof	NOUN
ejpam-4299	101	2	.	.	PUNCT
ejpam-4299	102	1	if	if	SCONJ
ejpam-4299	102	2	ε	ε	PROPN
ejpam-4299	102	3	>	>	X
ejpam-4299	102	4	0	0	PROPN
ejpam-4299	102	5	and	and	CCONJ
ejpam-4299	102	6	α	α	PRON
ejpam-4299	102	7	∈	∈	PROPN
ejpam-4299	103	1	[	[	X
ejpam-4299	103	2	0	0	NUM
ejpam-4299	103	3	,	,	PUNCT
ejpam-4299	103	4	1	1	NUM
ejpam-4299	103	5	]	]	PUNCT
ejpam-4299	103	6	,	,	PUNCT
ejpam-4299	103	7	we	we	PRON
ejpam-4299	103	8	have	have	VERB
ejpam-4299	103	9	:	:	PUNCT
ejpam-4299	103	10	[	[	PUNCT
ejpam-4299	103	11	f̄	f̄	PROPN
ejpam-4299	103	12	(	(	PUNCT
ejpam-4299	103	13	t0	t0	PROPN
ejpam-4299	103	14	+	+	CCONJ
ejpam-4299	103	15	εt1−q	εt1−q	PROPN
ejpam-4299	103	16	0	0	NUM
ejpam-4299	103	17	)	)	PUNCT
ejpam-4299	103	18	f̄	f̄	PROPN
ejpam-4299	103	19	(	(	PUNCT
ejpam-4299	103	20	t0	t0	PROPN
ejpam-4299	103	21	)	)	PUNCT
ejpam-4299	103	22	]	]	PUNCT
ejpam-4299	104	1	α	α	X
ejpam-4299	104	2	=	=	X
ejpam-4299	104	3	[	[	PUNCT
ejpam-4299	104	4	fα	fα	ADP
ejpam-4299	104	5	1	1	NUM
ejpam-4299	104	6	(	(	PUNCT
ejpam-4299	104	7	t0	t0	NOUN
ejpam-4299	104	8	+	+	CCONJ
ejpam-4299	104	9	εt1−q	εt1−q	PROPN
ejpam-4299	104	10	0	0	NUM
ejpam-4299	104	11	)	)	PUNCT
ejpam-4299	105	1	−	−	ADP
ejpam-4299	105	2	fα	fα	ADP
ejpam-4299	105	3	1	1	NUM
ejpam-4299	105	4	(	(	PUNCT
ejpam-4299	105	5	t0	t0	PROPN
ejpam-4299	105	6	)	)	PUNCT
ejpam-4299	105	7	,	,	PUNCT
ejpam-4299	105	8	f	f	PROPN
ejpam-4299	105	9	α	α	NOUN
ejpam-4299	105	10	2	2	NUM
ejpam-4299	105	11	(	(	PUNCT
ejpam-4299	105	12	t0	t0	NOUN
ejpam-4299	105	13	+	+	CCONJ
ejpam-4299	105	14	εt1−q	εt1−q	PROPN
ejpam-4299	105	15	0	0	NUM
ejpam-4299	105	16	)	)	PUNCT
ejpam-4299	106	1	−	−	ADP
ejpam-4299	106	2	fα	fα	ADP
ejpam-4299	106	3	2	2	NUM
ejpam-4299	106	4	(	(	PUNCT
ejpam-4299	106	5	t0	t0	PROPN
ejpam-4299	106	6	)	)	PUNCT
ejpam-4299	106	7	]	]	PUNCT
ejpam-4299	107	1	dividing	divide	VERB
ejpam-4299	107	2	and	and	CCONJ
ejpam-4299	107	3	multiplying	multiply	VERB
ejpam-4299	107	4	by	by	ADP
ejpam-4299	107	5	ε	ε	PROPN
ejpam-4299	107	6	,	,	PUNCT
ejpam-4299	107	7	we	we	PRON
ejpam-4299	107	8	have	have	VERB
ejpam-4299	107	9	:	:	PUNCT
ejpam-4299	107	10	[	[	PUNCT
ejpam-4299	107	11	f̄	f̄	PROPN
ejpam-4299	107	12	(	(	PUNCT
ejpam-4299	107	13	t0	t0	PROPN
ejpam-4299	107	14	+	+	CCONJ
ejpam-4299	107	15	εt1−q	εt1−q	PROPN
ejpam-4299	107	16	0	0	NUM
ejpam-4299	107	17	)	)	PUNCT
ejpam-4299	107	18	f̄	f̄	PROPN
ejpam-4299	107	19	(	(	PUNCT
ejpam-4299	107	20	t0	t0	PROPN
ejpam-4299	107	21	)	)	PUNCT
ejpam-4299	107	22	]	]	PUNCT
ejpam-4299	108	1	α	α	X
ejpam-4299	108	2	=	=	PUNCT
ejpam-4299	108	3	fα	fα	PROPN
ejpam-4299	108	4	1	1	NUM
ejpam-4299	108	5	(	(	PUNCT
ejpam-4299	108	6	t0	t0	NOUN
ejpam-4299	108	7	+	+	CCONJ
ejpam-4299	108	8	εt1−q	εt1−q	PROPN
ejpam-4299	108	9	0	0	NUM
ejpam-4299	108	10	)	)	PUNCT
ejpam-4299	108	11	−	−	ADP
ejpam-4299	108	12	fα	fα	ADP
ejpam-4299	108	13	1	1	NUM
ejpam-4299	108	14	(	(	PUNCT
ejpam-4299	108	15	t0	t0	PROPN
ejpam-4299	108	16	)	)	PUNCT
ejpam-4299	108	17	ε	ε	PROPN
ejpam-4299	108	18	·	·	PUNCT
ejpam-4299	108	19	ε	ε	PROPN
ejpam-4299	108	20	,	,	PUNCT
ejpam-4299	108	21	fα	fα	ADP
ejpam-4299	108	22	2	2	NUM
ejpam-4299	108	23	(	(	PUNCT
ejpam-4299	108	24	t0	t0	NOUN
ejpam-4299	108	25	+	+	CCONJ
ejpam-4299	108	26	εt1−q	εt1−q	PROPN
ejpam-4299	108	27	0	0	NUM
ejpam-4299	108	28	)	)	PUNCT
ejpam-4299	108	29	−	−	ADP
ejpam-4299	108	30	fα	fα	ADP
ejpam-4299	108	31	2	2	NUM
ejpam-4299	108	32	(	(	PUNCT
ejpam-4299	108	33	t0	t0	NOUN
ejpam-4299	108	34	)	)	PUNCT
ejpam-4299	108	35	ε	ε	PROPN
ejpam-4299	108	36	·	·	PUNCT
ejpam-4299	108	37	ε	ε	PROPN
ejpam-4299	108	38			NOUN
ejpam-4299	108	39	similarly	similarly	ADV
ejpam-4299	108	40	,	,	PUNCT
ejpam-4299	108	41	we	we	PRON
ejpam-4299	108	42	obtain	obtain	VERB
ejpam-4299	108	43	:	:	PUNCT
ejpam-4299	108	44	[	[	PUNCT
ejpam-4299	108	45	f̄	f̄	PROPN
ejpam-4299	108	46	(	(	PUNCT
ejpam-4299	108	47	t0	t0	PROPN
ejpam-4299	108	48	)	)	PUNCT
ejpam-4299	108	49	f̄	f̄	PROPN
ejpam-4299	108	50	(	(	PUNCT
ejpam-4299	108	51	t0	t0	PROPN
ejpam-4299	108	52	−	−	PROPN
ejpam-4299	108	53	εt1−q	εt1−q	PROPN
ejpam-4299	108	54	0	0	NUM
ejpam-4299	108	55	)	)	PUNCT
ejpam-4299	109	1	]	]	X
ejpam-4299	109	2	α	α	X
ejpam-4299	109	3	=	=	PUNCT
ejpam-4299	109	4	fα	fα	PROPN
ejpam-4299	109	5	1	1	NUM
ejpam-4299	109	6	(	(	PUNCT
ejpam-4299	109	7	t0)−	t0)−	ADV
ejpam-4299	109	8	fα	fα	ADP
ejpam-4299	109	9	1	1	NUM
ejpam-4299	109	10	(	(	PUNCT
ejpam-4299	109	11	t0	t0	NOUN
ejpam-4299	109	12	−	−	PROPN
ejpam-4299	109	13	εt1−q	εt1−q	PROPN
ejpam-4299	109	14	0	0	NUM
ejpam-4299	109	15	)	)	PUNCT
ejpam-4299	109	16	ε	ε	PROPN
ejpam-4299	109	17	·	·	PUNCT
ejpam-4299	109	18	ε	ε	PROPN
ejpam-4299	109	19	,	,	PUNCT
ejpam-4299	109	20	fα	fα	ADV
ejpam-4299	109	21	2	2	NUM
ejpam-4299	109	22	(	(	PUNCT
ejpam-4299	109	23	t0)−	t0)−	ADV
ejpam-4299	109	24	fα	fα	ADP
ejpam-4299	109	25	2	2	NUM
ejpam-4299	109	26	(	(	PUNCT
ejpam-4299	109	27	t0	t0	NOUN
ejpam-4299	109	28	−	−	PROPN
ejpam-4299	109	29	εt1−q	εt1−q	PROPN
ejpam-4299	109	30	0	0	NUM
ejpam-4299	109	31	)	)	PUNCT
ejpam-4299	109	32	ε	ε	PROPN
ejpam-4299	109	33	·	·	PUNCT
ejpam-4299	109	34	ε	ε	PROPN
ejpam-4299	109	35			NOUN
ejpam-4299	109	36	then	then	ADV
ejpam-4299	109	37	lim	lim	PROPN
ejpam-4299	109	38	ε→0	ε→0	VERB
ejpam-4299	109	39	+	+	CCONJ
ejpam-4299	109	40	[	[	PUNCT
ejpam-4299	109	41	f̄	f̄	PROPN
ejpam-4299	109	42	(	(	PUNCT
ejpam-4299	109	43	t0	t0	PROPN
ejpam-4299	109	44	+	+	CCONJ
ejpam-4299	109	45	εt1−q	εt1−q	PROPN
ejpam-4299	109	46	0	0	NUM
ejpam-4299	109	47	)	)	PUNCT
ejpam-4299	109	48	f̄	f̄	PROPN
ejpam-4299	109	49	(	(	PUNCT
ejpam-4299	109	50	t0	t0	PROPN
ejpam-4299	109	51	)	)	PUNCT
ejpam-4299	109	52	]	]	PUNCT
ejpam-4299	109	53	α	α	X
ejpam-4299	109	54	=	=	SYM
ejpam-4299	109	55			PROPN
ejpam-4299	109	56	lim	lim	NOUN
ejpam-4299	109	57	ε→0	ε→0	NOUN
ejpam-4299	109	58	+	+	CCONJ
ejpam-4299	109	59	fα	fα	SYM
ejpam-4299	109	60	1	1	NUM
ejpam-4299	109	61	(	(	PUNCT
ejpam-4299	109	62	t0	t0	NOUN
ejpam-4299	109	63	+	+	CCONJ
ejpam-4299	109	64	εt1−q	εt1−q	PROPN
ejpam-4299	109	65	0	0	NUM
ejpam-4299	109	66	)	)	PUNCT
ejpam-4299	110	1	−	−	ADP
ejpam-4299	110	2	fα	fα	ADP
ejpam-4299	110	3	1	1	NUM
ejpam-4299	110	4	(	(	PUNCT
ejpam-4299	110	5	t0	t0	PROPN
ejpam-4299	110	6	)	)	PUNCT
ejpam-4299	110	7	ε	ε	PROPN
ejpam-4299	110	8	·	·	PUNCT
ejpam-4299	110	9	lim	lim	PROPN
ejpam-4299	110	10	ε→0	ε→0	NOUN
ejpam-4299	110	11	+	+	CCONJ
ejpam-4299	110	12	ε	ε	PROPN
ejpam-4299	110	13	,	,	PUNCT
ejpam-4299	110	14	lim	lim	PROPN
ejpam-4299	110	15	ε→0	ε→0	NOUN
ejpam-4299	110	16	+	+	CCONJ
ejpam-4299	110	17	fα	fα	SYM
ejpam-4299	110	18	2	2	NUM
ejpam-4299	110	19	(	(	PUNCT
ejpam-4299	110	20	t0	t0	NOUN
ejpam-4299	110	21	+	+	CCONJ
ejpam-4299	110	22	εt1−q	εt1−q	PROPN
ejpam-4299	110	23	0	0	NUM
ejpam-4299	110	24	)	)	PUNCT
ejpam-4299	111	1	−	−	ADP
ejpam-4299	111	2	fα	fα	ADP
ejpam-4299	111	3	2	2	NUM
ejpam-4299	111	4	(	(	PUNCT
ejpam-4299	111	5	t0	t0	NOUN
ejpam-4299	111	6	)	)	PUNCT
ejpam-4299	111	7	ε	ε	PROPN
ejpam-4299	111	8	·	·	PUNCT
ejpam-4299	111	9	lim	lim	PROPN
ejpam-4299	111	10	ε→0	ε→0	NOUN
ejpam-4299	111	11	+	+	CCONJ
ejpam-4299	111	12	ε	ε	PROPN
ejpam-4299	111	13			NOUN
ejpam-4299	111	14	a.	a.	NOUN
ejpam-4299	111	15	harir	harir	NOUN
ejpam-4299	111	16	,	,	PUNCT
ejpam-4299	111	17	s.	s.	PROPN
ejpam-4299	111	18	melliani	melliani	PROPN
ejpam-4299	111	19	,	,	PUNCT
ejpam-4299	111	20	l.	l.	PROPN
ejpam-4299	111	21	s.	s.	PROPN
ejpam-4299	111	22	chadli	chadli	PROPN
ejpam-4299	111	23	/	/	SYM
ejpam-4299	111	24	eur	eur	PROPN
ejpam-4299	111	25	.	.	PUNCT
ejpam-4299	112	1	j.	j.	PROPN
ejpam-4299	112	2	pure	pure	PROPN
ejpam-4299	112	3	appl	appl	PROPN
ejpam-4299	112	4	.	.	PROPN
ejpam-4299	112	5	math	math	PROPN
ejpam-4299	112	6	,	,	PUNCT
ejpam-4299	112	7	15	15	NUM
ejpam-4299	112	8	(	(	PUNCT
ejpam-4299	112	9	2	2	NUM
ejpam-4299	112	10	)	)	PUNCT
ejpam-4299	112	11	(	(	PUNCT
ejpam-4299	112	12	2022	2022	NUM
ejpam-4299	112	13	)	)	PUNCT
ejpam-4299	112	14	,	,	PUNCT
ejpam-4299	112	15	557	557	NUM
ejpam-4299	112	16	-	-	SYM
ejpam-4299	112	17	571	571	NUM
ejpam-4299	112	18	561	561	NUM
ejpam-4299	112	19	similarly	similarly	ADV
ejpam-4299	112	20	,	,	PUNCT
ejpam-4299	112	21	we	we	PRON
ejpam-4299	112	22	obtain	obtain	VERB
ejpam-4299	112	23	:	:	PUNCT
ejpam-4299	112	24	lim	lim	NOUN
ejpam-4299	112	25	ε→0	ε→0	VERB
ejpam-4299	112	26	+	+	CCONJ
ejpam-4299	112	27	[	[	PUNCT
ejpam-4299	112	28	f̄	f̄	PROPN
ejpam-4299	112	29	(	(	PUNCT
ejpam-4299	112	30	t0	t0	PROPN
ejpam-4299	112	31	)	)	PUNCT
ejpam-4299	112	32	f̄	f̄	PROPN
ejpam-4299	113	1	(	(	PUNCT
ejpam-4299	113	2	t0	t0	PROPN
ejpam-4299	113	3	−	−	PROPN
ejpam-4299	113	4	εt1−q	εt1−q	PROPN
ejpam-4299	113	5	0	0	NUM
ejpam-4299	113	6	)	)	PUNCT
ejpam-4299	113	7	]	]	X
ejpam-4299	113	8	α	α	X
ejpam-4299	113	9	=	=	SYM
ejpam-4299	113	10			PROPN
ejpam-4299	113	11	lim	lim	NOUN
ejpam-4299	113	12	ε→0	ε→0	NOUN
ejpam-4299	113	13	+	+	CCONJ
ejpam-4299	113	14	fα	fα	SYM
ejpam-4299	113	15	1	1	NUM
ejpam-4299	113	16	(	(	PUNCT
ejpam-4299	113	17	t0)−	t0)−	ADV
ejpam-4299	113	18	fα	fα	ADP
ejpam-4299	113	19	1	1	NUM
ejpam-4299	113	20	(	(	PUNCT
ejpam-4299	113	21	t0	t0	NOUN
ejpam-4299	113	22	−	−	PROPN
ejpam-4299	113	23	εt1−q	εt1−q	PROPN
ejpam-4299	113	24	0	0	NUM
ejpam-4299	113	25	)	)	PUNCT
ejpam-4299	114	1	ε	ε	PROPN
ejpam-4299	114	2	·	·	PUNCT
ejpam-4299	114	3	lim	lim	PROPN
ejpam-4299	114	4	ε→0	ε→0	NOUN
ejpam-4299	114	5	+	+	CCONJ
ejpam-4299	114	6	ε	ε	PROPN
ejpam-4299	114	7	,	,	PUNCT
ejpam-4299	114	8	lim	lim	PROPN
ejpam-4299	114	9	ε→0	ε→0	NOUN
ejpam-4299	114	10	+	+	CCONJ
ejpam-4299	114	11	fα	fα	SYM
ejpam-4299	114	12	2	2	NUM
ejpam-4299	114	13	(	(	PUNCT
ejpam-4299	114	14	t0)−	t0)−	ADV
ejpam-4299	114	15	fα	fα	ADP
ejpam-4299	114	16	2	2	NUM
ejpam-4299	114	17	(	(	PUNCT
ejpam-4299	114	18	t0	t0	NOUN
ejpam-4299	114	19	−	−	PROPN
ejpam-4299	114	20	εt1−q	εt1−q	PROPN
ejpam-4299	114	21	0	0	NUM
ejpam-4299	114	22	)	)	PUNCT
ejpam-4299	115	1	ε	ε	PROPN
ejpam-4299	115	2	·	·	PUNCT
ejpam-4299	115	3	lim	lim	PROPN
ejpam-4299	115	4	ε→0	ε→0	NOUN
ejpam-4299	115	5	+	+	CCONJ
ejpam-4299	115	6	ε	ε	PROPN
ejpam-4299	115	7			NOUN
ejpam-4299	115	8	let	let	VERB
ejpam-4299	115	9	h	h	NOUN
ejpam-4299	115	10	=	=	PUNCT
ejpam-4299	115	11	εt1−q	εt1−q	PROPN
ejpam-4299	115	12	0	0	PROPN
ejpam-4299	115	13	.	.	PUNCT
ejpam-4299	116	1	then	then	ADV
ejpam-4299	116	2	lim	lim	PROPN
ejpam-4299	116	3	h→0	h→0	PROPN
ejpam-4299	117	1	+	+	CCONJ
ejpam-4299	117	2	[	[	PUNCT
ejpam-4299	117	3	f̄	f̄	PROPN
ejpam-4299	117	4	(	(	PUNCT
ejpam-4299	117	5	t0	t0	PROPN
ejpam-4299	117	6	+	+	CCONJ
ejpam-4299	117	7	h	h	X
ejpam-4299	117	8	)	)	PUNCT
ejpam-4299	117	9	f̄	f̄	PROPN
ejpam-4299	117	10	(	(	PUNCT
ejpam-4299	117	11	t0	t0	PROPN
ejpam-4299	117	12	)	)	PUNCT
ejpam-4299	118	1	]	]	PUNCT
ejpam-4299	118	2	α	α	X
ejpam-4299	118	3	=	=	X
ejpam-4299	118	4	[	[	PUNCT
ejpam-4299	118	5	(	(	PUNCT
ejpam-4299	118	6	fα	fα	ADP
ejpam-4299	118	7	1	1	NUM
ejpam-4299	118	8	)	)	PUNCT
ejpam-4299	118	9	(	(	PUNCT
ejpam-4299	118	10	q	q	X
ejpam-4299	118	11	)	)	PUNCT
ejpam-4299	118	12	(	(	PUNCT
ejpam-4299	118	13	t0	t0	PROPN
ejpam-4299	118	14	)	)	PUNCT
ejpam-4299	118	15	.0	.0	NUM
ejpam-4299	118	16	,	,	PUNCT
ejpam-4299	118	17	(	(	PUNCT
ejpam-4299	118	18	f	f	NOUN
ejpam-4299	118	19	α	α	PROPN
ejpam-4299	118	20	2	2	NUM
ejpam-4299	118	21	)	)	PUNCT
ejpam-4299	118	22	(	(	PUNCT
ejpam-4299	118	23	q	q	X
ejpam-4299	118	24	)	)	PUNCT
ejpam-4299	118	25	(	(	PUNCT
ejpam-4299	118	26	t0	t0	NOUN
ejpam-4299	118	27	)	)	PUNCT
ejpam-4299	118	28	.0	.0	NUM
ejpam-4299	118	29	]	]	PUNCT
ejpam-4299	119	1	similarly	similarly	ADV
ejpam-4299	119	2	,	,	PUNCT
ejpam-4299	119	3	we	we	PRON
ejpam-4299	119	4	obtain	obtain	VERB
ejpam-4299	119	5	:	:	PUNCT
ejpam-4299	119	6	lim	lim	PROPN
ejpam-4299	119	7	h→0	h→0	PROPN
ejpam-4299	120	1	+	+	CCONJ
ejpam-4299	120	2	[	[	PUNCT
ejpam-4299	120	3	f̄	f̄	PROPN
ejpam-4299	120	4	(	(	PUNCT
ejpam-4299	120	5	t0	t0	PROPN
ejpam-4299	120	6	)	)	PUNCT
ejpam-4299	120	7	f̄	f̄	PROPN
ejpam-4299	120	8	(	(	PUNCT
ejpam-4299	120	9	t0	t0	PROPN
ejpam-4299	120	10	−	−	PROPN
ejpam-4299	120	11	h	h	NOUN
ejpam-4299	120	12	)	)	PUNCT
ejpam-4299	120	13	]	]	PUNCT
ejpam-4299	120	14	α	α	X
ejpam-4299	120	15	=	=	X
ejpam-4299	120	16	[	[	PUNCT
ejpam-4299	120	17	(	(	PUNCT
ejpam-4299	120	18	fα	fα	ADP
ejpam-4299	120	19	1	1	NUM
ejpam-4299	120	20	)	)	PUNCT
ejpam-4299	120	21	(	(	PUNCT
ejpam-4299	120	22	q	q	X
ejpam-4299	120	23	)	)	PUNCT
ejpam-4299	120	24	(	(	PUNCT
ejpam-4299	120	25	t0	t0	PROPN
ejpam-4299	120	26	)	)	PUNCT
ejpam-4299	120	27	.0	.0	NUM
ejpam-4299	120	28	,	,	PUNCT
ejpam-4299	120	29	(	(	PUNCT
ejpam-4299	120	30	f	f	NOUN
ejpam-4299	120	31	α	α	PROPN
ejpam-4299	120	32	2	2	NUM
ejpam-4299	120	33	)	)	PUNCT
ejpam-4299	120	34	(	(	PUNCT
ejpam-4299	120	35	q	q	X
ejpam-4299	120	36	)	)	PUNCT
ejpam-4299	120	37	(	(	PUNCT
ejpam-4299	120	38	t0	t0	NOUN
ejpam-4299	120	39	)	)	PUNCT
ejpam-4299	120	40	.0	.0	NUM
ejpam-4299	120	41	]	]	PUNCT
ejpam-4299	120	42	which	which	PRON
ejpam-4299	120	43	implies	imply	VERB
ejpam-4299	120	44	that	that	SCONJ
ejpam-4299	120	45	lim	lim	PROPN
ejpam-4299	120	46	h→0	h→0	PROPN
ejpam-4299	120	47	+	+	CCONJ
ejpam-4299	120	48	[	[	PUNCT
ejpam-4299	120	49	f̄	f̄	PROPN
ejpam-4299	120	50	(	(	PUNCT
ejpam-4299	120	51	t0	t0	PROPN
ejpam-4299	120	52	+	+	CCONJ
ejpam-4299	120	53	h	h	NOUN
ejpam-4299	120	54	)	)	PUNCT
ejpam-4299	120	55	]	]	PUNCT
ejpam-4299	120	56	α	α	X
ejpam-4299	121	1	=	=	X
ejpam-4299	122	1	[	[	PUNCT
ejpam-4299	122	2	f̄	f̄	PROPN
ejpam-4299	122	3	(	(	PUNCT
ejpam-4299	122	4	t0	t0	PROPN
ejpam-4299	122	5	)	)	PUNCT
ejpam-4299	122	6	]	]	PUNCT
ejpam-4299	122	7	α	α	PRON
ejpam-4299	122	8	similarly	similarly	ADV
ejpam-4299	122	9	,	,	PUNCT
ejpam-4299	122	10	we	we	PRON
ejpam-4299	122	11	obtain	obtain	VERB
ejpam-4299	122	12	:	:	PUNCT
ejpam-4299	122	13	lim	lim	PROPN
ejpam-4299	122	14	h→0	h→0	PROPN
ejpam-4299	123	1	+	+	CCONJ
ejpam-4299	123	2	[	[	PUNCT
ejpam-4299	123	3	f̄	f̄	PROPN
ejpam-4299	123	4	(	(	PUNCT
ejpam-4299	123	5	t0	t0	PROPN
ejpam-4299	123	6	−	−	PROPN
ejpam-4299	123	7	h	h	NOUN
ejpam-4299	123	8	)	)	PUNCT
ejpam-4299	123	9	]	]	PUNCT
ejpam-4299	123	10	α	α	X
ejpam-4299	123	11	=	=	X
ejpam-4299	123	12	[	[	PUNCT
ejpam-4299	123	13	f̄	f̄	PROPN
ejpam-4299	123	14	(	(	PUNCT
ejpam-4299	123	15	t0	t0	PROPN
ejpam-4299	123	16	)	)	PUNCT
ejpam-4299	123	17	]	]	PUNCT
ejpam-4299	123	18	α	α	X
ejpam-4299	123	19	hence	hence	ADV
ejpam-4299	123	20	,	,	PUNCT
ejpam-4299	123	21	f̄	f̄	PROPN
ejpam-4299	123	22	is	be	AUX
ejpam-4299	123	23	continuous	continuous	ADJ
ejpam-4299	123	24	at	at	ADP
ejpam-4299	123	25	t0	t0	PROPN
ejpam-4299	123	26	.	.	PUNCT
ejpam-4299	124	1	theorem	theorem	ADJ
ejpam-4299	124	2	4	4	NUM
ejpam-4299	124	3	.	.	PUNCT
ejpam-4299	125	1	let	let	VERB
ejpam-4299	125	2	q	q	PROPN
ejpam-4299	125	3	∈	∈	PROPN
ejpam-4299	125	4	(	(	PUNCT
ejpam-4299	125	5	0	0	NUM
ejpam-4299	125	6	,	,	PUNCT
ejpam-4299	125	7	1	1	NUM
ejpam-4299	125	8	]	]	PUNCT
ejpam-4299	125	9	•	•	NOUN
ejpam-4299	125	10	if	if	SCONJ
ejpam-4299	125	11	f̄	f̄	PROPN
ejpam-4299	125	12	is	be	AUX
ejpam-4299	125	13	differentiable	differentiable	ADJ
ejpam-4299	125	14	and	and	CCONJ
ejpam-4299	125	15	f̄	f̄	PROPN
ejpam-4299	125	16	is	be	AUX
ejpam-4299	125	17	q	q	ADJ
ejpam-4299	125	18	-	-	ADV
ejpam-4299	125	19	differentiable	differentiable	ADJ
ejpam-4299	125	20	then	then	ADV
ejpam-4299	125	21	tqf̄	tqf̄	NUM
ejpam-4299	125	22	(	(	PUNCT
ejpam-4299	125	23	t	t	NOUN
ejpam-4299	125	24	)	)	PUNCT
ejpam-4299	125	25	=	=	PUNCT
ejpam-4299	125	26	t1−qf̄	t1−qf̄	ADP
ejpam-4299	125	27	′(t	′(t	NOUN
ejpam-4299	125	28	)	)	PUNCT
ejpam-4299	125	29	proof	proof	NOUN
ejpam-4299	125	30	.	.	PUNCT
ejpam-4299	126	1	let	let	VERB
ejpam-4299	126	2	h	h	NOUN
ejpam-4299	126	3	=	=	VERB
ejpam-4299	126	4	εt1−q	εt1−q	PROPN
ejpam-4299	126	5	in	in	ADP
ejpam-4299	126	6	definition	definition	NOUN
ejpam-4299	126	7	4	4	NUM
ejpam-4299	126	8	,	,	PUNCT
ejpam-4299	126	9	and	and	CCONJ
ejpam-4299	126	10	then	then	ADV
ejpam-4299	126	11	ε	ε	PROPN
ejpam-4299	126	12	=	=	SYM
ejpam-4299	126	13	tq−1h	tq−1h	PROPN
ejpam-4299	126	14	.	.	PUNCT
ejpam-4299	127	1	therefore	therefore	ADV
ejpam-4299	127	2	,	,	PUNCT
ejpam-4299	127	3	if	if	SCONJ
ejpam-4299	127	4	ε	ε	PROPN
ejpam-4299	127	5	>	>	X
ejpam-4299	127	6	0	0	PROPN
ejpam-4299	127	7	and	and	CCONJ
ejpam-4299	127	8	α	α	PRON
ejpam-4299	127	9	∈	∈	PROPN
ejpam-4299	127	10	[	[	X
ejpam-4299	127	11	0	0	NUM
ejpam-4299	127	12	,	,	PUNCT
ejpam-4299	127	13	1	1	NUM
ejpam-4299	127	14	]	]	PUNCT
ejpam-4299	127	15	,	,	PUNCT
ejpam-4299	127	16	we	we	PRON
ejpam-4299	127	17	have	have	VERB
ejpam-4299	127	18	[	[	PUNCT
ejpam-4299	127	19	f̄	f̄	PROPN
ejpam-4299	127	20	(	(	PUNCT
ejpam-4299	127	21	t+	t+	NOUN
ejpam-4299	127	22	εt1−q	εt1−q	PROPN
ejpam-4299	127	23	)	)	PUNCT
ejpam-4299	127	24	f̄	f̄	PROPN
ejpam-4299	127	25	(	(	PUNCT
ejpam-4299	127	26	t	t	PROPN
ejpam-4299	127	27	)	)	PUNCT
ejpam-4299	127	28	]	]	PUNCT
ejpam-4299	128	1	α	α	X
ejpam-4299	128	2	=	=	X
ejpam-4299	128	3	[	[	PUNCT
ejpam-4299	128	4	fα	fα	ADP
ejpam-4299	128	5	1	1	NUM
ejpam-4299	128	6	(	(	PUNCT
ejpam-4299	128	7	t+	t+	NOUN
ejpam-4299	128	8	εt1−q	εt1−q	NOUN
ejpam-4299	128	9	)	)	PUNCT
ejpam-4299	128	10	−	−	ADP
ejpam-4299	129	1	fα	fα	NOUN
ejpam-4299	129	2	1	1	NUM
ejpam-4299	129	3	(	(	PUNCT
ejpam-4299	129	4	t	t	PROPN
ejpam-4299	129	5	)	)	PUNCT
ejpam-4299	129	6	,	,	PUNCT
ejpam-4299	129	7	f	f	PROPN
ejpam-4299	129	8	α	α	PROPN
ejpam-4299	129	9	2	2	NUM
ejpam-4299	129	10	(	(	PUNCT
ejpam-4299	129	11	t+	t+	NOUN
ejpam-4299	129	12	εt1−q	εt1−q	NOUN
ejpam-4299	129	13	)	)	PUNCT
ejpam-4299	129	14	−	−	ADP
ejpam-4299	130	1	fα	fα	ADP
ejpam-4299	130	2	2	2	NUM
ejpam-4299	130	3	(	(	PUNCT
ejpam-4299	130	4	t	t	PROPN
ejpam-4299	130	5	)	)	PUNCT
ejpam-4299	130	6	]	]	PUNCT
ejpam-4299	130	7	.	.	PUNCT
ejpam-4299	131	1	dividing	divide	VERB
ejpam-4299	131	2	by	by	ADP
ejpam-4299	131	3	ε	ε	PROPN
ejpam-4299	131	4	,	,	PUNCT
ejpam-4299	131	5	we	we	PRON
ejpam-4299	131	6	have	have	VERB
ejpam-4299	131	7	[	[	PUNCT
ejpam-4299	131	8	f̄	f̄	PROPN
ejpam-4299	131	9	(	(	PUNCT
ejpam-4299	131	10	t+	t+	NOUN
ejpam-4299	131	11	εt1−q	εt1−q	PROPN
ejpam-4299	131	12	)	)	PUNCT
ejpam-4299	131	13	f̄	f̄	PROPN
ejpam-4299	131	14	(	(	PUNCT
ejpam-4299	131	15	t	t	PROPN
ejpam-4299	131	16	)	)	PUNCT
ejpam-4299	131	17	]	]	PUNCT
ejpam-4299	132	1	α	α	X
ejpam-4299	132	2	ε	ε	PROPN
ejpam-4299	132	3	=	=	PUNCT
ejpam-4299	132	4	[	[	PUNCT
ejpam-4299	132	5	fα	fα	ADP
ejpam-4299	132	6	1	1	NUM
ejpam-4299	132	7	(	(	PUNCT
ejpam-4299	132	8	t+	t+	NOUN
ejpam-4299	132	9	εt1−q	εt1−q	NOUN
ejpam-4299	132	10	)	)	PUNCT
ejpam-4299	132	11	−	−	ADP
ejpam-4299	132	12	fα	fα	NOUN
ejpam-4299	132	13	1	1	NUM
ejpam-4299	132	14	(	(	PUNCT
ejpam-4299	132	15	t	t	NOUN
ejpam-4299	132	16	)	)	PUNCT
ejpam-4299	132	17	ε	ε	PROPN
ejpam-4299	132	18	,	,	PUNCT
ejpam-4299	132	19	fα	fα	ADP
ejpam-4299	132	20	2	2	NUM
ejpam-4299	132	21	(	(	PUNCT
ejpam-4299	132	22	t+	t+	NOUN
ejpam-4299	132	23	εt1−q	εt1−q	NOUN
ejpam-4299	132	24	)	)	PUNCT
ejpam-4299	132	25	−	−	ADP
ejpam-4299	132	26	fα	fα	ADP
ejpam-4299	132	27	2	2	NUM
ejpam-4299	132	28	(	(	PUNCT
ejpam-4299	132	29	t	t	NOUN
ejpam-4299	132	30	)	)	PUNCT
ejpam-4299	132	31	ε	ε	PROPN
ejpam-4299	132	32	]	]	PUNCT
ejpam-4299	132	33	,	,	PUNCT
ejpam-4299	132	34	and	and	CCONJ
ejpam-4299	132	35	passing	pass	VERB
ejpam-4299	132	36	to	to	ADP
ejpam-4299	132	37	the	the	DET
ejpam-4299	132	38	limit	limit	NOUN
ejpam-4299	132	39	,	,	PUNCT
ejpam-4299	132	40	lim	lim	PROPN
ejpam-4299	132	41	ε−→0	ε−→0	PROPN
ejpam-4299	132	42	+	+	PROPN
ejpam-4299	132	43	[	[	PUNCT
ejpam-4299	132	44	f̄	f̄	NOUN
ejpam-4299	132	45	(	(	PUNCT
ejpam-4299	132	46	t+	t+	NOUN
ejpam-4299	132	47	εt1−q	εt1−q	PROPN
ejpam-4299	132	48	)	)	PUNCT
ejpam-4299	132	49	f̄	f̄	PROPN
ejpam-4299	132	50	(	(	PUNCT
ejpam-4299	132	51	t	t	PROPN
ejpam-4299	132	52	)	)	PUNCT
ejpam-4299	132	53	]	]	PUNCT
ejpam-4299	132	54	α	α	X
ejpam-4299	132	55	ε	ε	PROPN
ejpam-4299	132	56	=	=	SYM
ejpam-4299	132	57	lim	lim	PROPN
ejpam-4299	132	58	ε−→0	ε−→0	PROPN
ejpam-4299	132	59	+	+	X
ejpam-4299	132	60	[	[	PUNCT
ejpam-4299	132	61	fα	fα	ADP
ejpam-4299	132	62	1	1	NUM
ejpam-4299	132	63	(	(	PUNCT
ejpam-4299	132	64	t+	t+	NOUN
ejpam-4299	132	65	εt1−q	εt1−q	NOUN
ejpam-4299	132	66	)	)	PUNCT
ejpam-4299	133	1	−	−	ADP
ejpam-4299	133	2	fα	fα	NOUN
ejpam-4299	133	3	1	1	NUM
ejpam-4299	133	4	(	(	PUNCT
ejpam-4299	133	5	t	t	NOUN
ejpam-4299	133	6	)	)	PUNCT
ejpam-4299	133	7	ε	ε	PROPN
ejpam-4299	133	8	,	,	PUNCT
ejpam-4299	133	9	fα	fα	ADP
ejpam-4299	133	10	2	2	NUM
ejpam-4299	133	11	(	(	PUNCT
ejpam-4299	133	12	t+	t+	NOUN
ejpam-4299	133	13	εt1−q	εt1−q	NOUN
ejpam-4299	133	14	)	)	PUNCT
ejpam-4299	133	15	−	−	ADP
ejpam-4299	133	16	fα	fα	ADP
ejpam-4299	133	17	2	2	NUM
ejpam-4299	133	18	(	(	PUNCT
ejpam-4299	133	19	t	t	NOUN
ejpam-4299	133	20	)	)	PUNCT
ejpam-4299	133	21	ε	ε	PROPN
ejpam-4299	133	22	]	]	PUNCT
ejpam-4299	134	1	=	=	PROPN
ejpam-4299	134	2	lim	lim	PROPN
ejpam-4299	134	3	h−→0	h−→0	PROPN
ejpam-4299	134	4	+	+	PROPN
ejpam-4299	134	5	[	[	PUNCT
ejpam-4299	134	6	fα	fα	ADP
ejpam-4299	134	7	1	1	NUM
ejpam-4299	134	8	(	(	PUNCT
ejpam-4299	134	9	t+	t+	NOUN
ejpam-4299	134	10	h)−	h)−	PROPN
ejpam-4299	134	11	fα	fα	ADP
ejpam-4299	134	12	1	1	NUM
ejpam-4299	134	13	(	(	PUNCT
ejpam-4299	134	14	t	t	NOUN
ejpam-4299	134	15	)	)	PUNCT
ejpam-4299	134	16	tq−1h	tq−1h	NOUN
ejpam-4299	134	17	,	,	PUNCT
ejpam-4299	134	18	fα	fα	ADP
ejpam-4299	134	19	2	2	NUM
ejpam-4299	134	20	(	(	PUNCT
ejpam-4299	134	21	t+	t+	NOUN
ejpam-4299	134	22	h)−	h)−	PROPN
ejpam-4299	134	23	fα	fα	ADP
ejpam-4299	134	24	2	2	NUM
ejpam-4299	134	25	(	(	PUNCT
ejpam-4299	134	26	t	t	NOUN
ejpam-4299	134	27	)	)	PUNCT
ejpam-4299	134	28	tq−1h	tq−1h	NOUN
ejpam-4299	134	29	]	]	X
ejpam-4299	135	1	=	=	PUNCT
ejpam-4299	136	1	t1−q	t1−q	PROPN
ejpam-4299	136	2	lim	lim	PROPN
ejpam-4299	136	3	h−→0	h−→0	PROPN
ejpam-4299	136	4	+	+	PROPN
ejpam-4299	136	5	[	[	PUNCT
ejpam-4299	136	6	fα	fα	ADP
ejpam-4299	136	7	1	1	NUM
ejpam-4299	136	8	(	(	PUNCT
ejpam-4299	136	9	t+	t+	NOUN
ejpam-4299	136	10	h)−	h)−	PROPN
ejpam-4299	136	11	fα	fα	ADP
ejpam-4299	136	12	1	1	NUM
ejpam-4299	136	13	(	(	PUNCT
ejpam-4299	136	14	t	t	NOUN
ejpam-4299	136	15	)	)	PUNCT
ejpam-4299	136	16	h	h	NOUN
ejpam-4299	136	17	,	,	PUNCT
ejpam-4299	136	18	fα	fα	ADV
ejpam-4299	136	19	2	2	NUM
ejpam-4299	136	20	(	(	PUNCT
ejpam-4299	136	21	t+	t+	NOUN
ejpam-4299	136	22	h)−	h)−	PROPN
ejpam-4299	136	23	fα	fα	ADP
ejpam-4299	136	24	2	2	NUM
ejpam-4299	136	25	(	(	PUNCT
ejpam-4299	136	26	t	t	NOUN
ejpam-4299	136	27	)	)	PUNCT
ejpam-4299	136	28	h	h	NOUN
ejpam-4299	136	29	]	]	PUNCT
ejpam-4299	137	1	=	=	PUNCT
ejpam-4299	137	2	t1−q	t1−q	PROPN
ejpam-4299	137	3	[	[	PUNCT
ejpam-4299	137	4	(	(	PUNCT
ejpam-4299	137	5	fα	fα	ADP
ejpam-4299	137	6	1	1	NUM
ejpam-4299	137	7	)	)	PUNCT
ejpam-4299	137	8	′	′	NOUN
ejpam-4299	137	9	(	(	PUNCT
ejpam-4299	137	10	t	t	NOUN
ejpam-4299	137	11	)	)	PUNCT
ejpam-4299	137	12	,	,	PUNCT
ejpam-4299	137	13	(	(	PUNCT
ejpam-4299	137	14	fα	fα	ADP
ejpam-4299	137	15	2	2	NUM
ejpam-4299	137	16	)	)	PUNCT
ejpam-4299	137	17	′	′	NUM
ejpam-4299	137	18	(	(	PUNCT
ejpam-4299	137	19	t	t	PROPN
ejpam-4299	137	20	)	)	PUNCT
ejpam-4299	137	21	]	]	PUNCT
ejpam-4299	137	22	.	.	PUNCT
ejpam-4299	138	1	a.	a.	NOUN
ejpam-4299	138	2	harir	harir	PROPN
ejpam-4299	138	3	,	,	PUNCT
ejpam-4299	138	4	s.	s.	PROPN
ejpam-4299	138	5	melliani	melliani	PROPN
ejpam-4299	138	6	,	,	PUNCT
ejpam-4299	138	7	l.	l.	PROPN
ejpam-4299	138	8	s.	s.	PROPN
ejpam-4299	138	9	chadli	chadli	PROPN
ejpam-4299	138	10	/	/	SYM
ejpam-4299	138	11	eur	eur	PROPN
ejpam-4299	138	12	.	.	PUNCT
ejpam-4299	139	1	j.	j.	PROPN
ejpam-4299	139	2	pure	pure	PROPN
ejpam-4299	139	3	appl	appl	PROPN
ejpam-4299	139	4	.	.	PROPN
ejpam-4299	139	5	math	math	PROPN
ejpam-4299	139	6	,	,	PUNCT
ejpam-4299	139	7	15	15	NUM
ejpam-4299	139	8	(	(	PUNCT
ejpam-4299	139	9	2	2	NUM
ejpam-4299	139	10	)	)	PUNCT
ejpam-4299	139	11	(	(	PUNCT
ejpam-4299	139	12	2022	2022	NUM
ejpam-4299	139	13	)	)	PUNCT
ejpam-4299	139	14	,	,	PUNCT
ejpam-4299	139	15	557	557	NUM
ejpam-4299	139	16	-	-	SYM
ejpam-4299	139	17	571	571	NUM
ejpam-4299	139	18	562	562	NUM
ejpam-4299	139	19	similarly	similarly	ADV
ejpam-4299	139	20	,	,	PUNCT
ejpam-4299	139	21	we	we	PRON
ejpam-4299	139	22	obtain	obtain	VERB
ejpam-4299	139	23	[	[	PUNCT
ejpam-4299	139	24	f̄	f̄	PROPN
ejpam-4299	139	25	(	(	PUNCT
ejpam-4299	139	26	t	t	PROPN
ejpam-4299	139	27	)	)	PUNCT
ejpam-4299	139	28	f̄	f̄	NOUN
ejpam-4299	139	29	(	(	PUNCT
ejpam-4299	139	30	t−	t−	PROPN
ejpam-4299	139	31	εt1−q	εt1−q	PROPN
ejpam-4299	139	32	)	)	PUNCT
ejpam-4299	139	33	]	]	PUNCT
ejpam-4299	139	34	α	α	X
ejpam-4299	139	35	ε	ε	PROPN
ejpam-4299	139	36	=	=	PUNCT
ejpam-4299	139	37	[	[	PUNCT
ejpam-4299	139	38	fα	fα	ADP
ejpam-4299	139	39	1	1	NUM
ejpam-4299	139	40	(	(	PUNCT
ejpam-4299	139	41	t)−	t)−	PROPN
ejpam-4299	139	42	fα	fα	ADP
ejpam-4299	139	43	1	1	NUM
ejpam-4299	139	44	(	(	PUNCT
ejpam-4299	139	45	t−	t−	PROPN
ejpam-4299	139	46	εt1−q	εt1−q	PROPN
ejpam-4299	139	47	)	)	PUNCT
ejpam-4299	139	48	ε	ε	PROPN
ejpam-4299	139	49	,	,	PUNCT
ejpam-4299	139	50	fα	fα	ADP
ejpam-4299	139	51	2	2	NUM
ejpam-4299	139	52	(	(	PUNCT
ejpam-4299	139	53	t)−	t)−	PROPN
ejpam-4299	139	54	fα	fα	ADP
ejpam-4299	139	55	2	2	NUM
ejpam-4299	139	56	(	(	PUNCT
ejpam-4299	139	57	t−	t−	PROPN
ejpam-4299	139	58	εt1−q	εt1−q	PROPN
ejpam-4299	139	59	)	)	PUNCT
ejpam-4299	139	60	ε	ε	PROPN
ejpam-4299	139	61	]	]	PUNCT
ejpam-4299	139	62	,	,	PUNCT
ejpam-4299	139	63	and	and	CCONJ
ejpam-4299	139	64	passing	pass	VERB
ejpam-4299	139	65	to	to	ADP
ejpam-4299	139	66	the	the	DET
ejpam-4299	139	67	limit	limit	NOUN
ejpam-4299	139	68	and	and	CCONJ
ejpam-4299	139	69	ε	ε	PROPN
ejpam-4299	139	70	=	=	SYM
ejpam-4299	139	71	tq−1h	tq−1h	PROPN
ejpam-4299	139	72	gives	give	VERB
ejpam-4299	139	73	tqf̄	tqf̄	NUM
ejpam-4299	139	74	(	(	PUNCT
ejpam-4299	139	75	t	t	NOUN
ejpam-4299	139	76	)	)	PUNCT
ejpam-4299	139	77	=	=	PUNCT
ejpam-4299	140	1	t1−q	t1−q	PROPN
ejpam-4299	140	2	[	[	PUNCT
ejpam-4299	140	3	(	(	PUNCT
ejpam-4299	140	4	fα	fα	ADP
ejpam-4299	140	5	1	1	NUM
ejpam-4299	140	6	)	)	PUNCT
ejpam-4299	140	7	′	′	NOUN
ejpam-4299	140	8	(	(	PUNCT
ejpam-4299	140	9	t	t	NOUN
ejpam-4299	140	10	)	)	PUNCT
ejpam-4299	140	11	,	,	PUNCT
ejpam-4299	140	12	(	(	PUNCT
ejpam-4299	140	13	fα	fα	ADP
ejpam-4299	140	14	2	2	NUM
ejpam-4299	140	15	)	)	PUNCT
ejpam-4299	140	16	′	′	NUM
ejpam-4299	140	17	(	(	PUNCT
ejpam-4299	140	18	t	t	PROPN
ejpam-4299	140	19	)	)	PUNCT
ejpam-4299	140	20	]	]	PUNCT
ejpam-4299	140	21	.	.	PUNCT
ejpam-4299	141	1	let	let	VERB
ejpam-4299	141	2	q	q	PROPN
ejpam-4299	141	3	∈	∈	PROPN
ejpam-4299	141	4	(	(	PUNCT
ejpam-4299	141	5	0	0	NUM
ejpam-4299	141	6	,	,	PUNCT
ejpam-4299	141	7	1	1	NUM
ejpam-4299	141	8	]	]	PUNCT
ejpam-4299	141	9	and	and	CCONJ
ejpam-4299	141	10	f̄	f̄	NOUN
ejpam-4299	141	11	:	:	PUNCT
ejpam-4299	142	1	[	[	X
ejpam-4299	142	2	0	0	NUM
ejpam-4299	142	3	,	,	PUNCT
ejpam-4299	142	4	a	a	PRON
ejpam-4299	142	5	)	)	PUNCT
ejpam-4299	142	6	→	→	SYM
ejpam-4299	142	7	rf	rf	NUM
ejpam-4299	142	8	be	be	AUX
ejpam-4299	142	9	such	such	ADJ
ejpam-4299	142	10	that	that	SCONJ
ejpam-4299	143	1	[	[	X
ejpam-4299	143	2	f̄	f̄	NOUN
ejpam-4299	143	3	(	(	PUNCT
ejpam-4299	143	4	t)]α	t)]α	NOUN
ejpam-4299	143	5	=	=	PUNCT
ejpam-4299	144	1	[	[	X
ejpam-4299	144	2	fα	fα	ADP
ejpam-4299	144	3	1	1	NUM
ejpam-4299	144	4	(	(	PUNCT
ejpam-4299	144	5	t	t	PROPN
ejpam-4299	144	6	)	)	PUNCT
ejpam-4299	144	7	,	,	PUNCT
ejpam-4299	144	8	f	f	PROPN
ejpam-4299	144	9	α	α	PROPN
ejpam-4299	144	10	2	2	NUM
ejpam-4299	144	11	(	(	PUNCT
ejpam-4299	144	12	t	t	PROPN
ejpam-4299	144	13	)	)	PUNCT
ejpam-4299	144	14	]	]	PUNCT
ejpam-4299	144	15	for	for	ADP
ejpam-4299	144	16	all	all	DET
ejpam-4299	144	17	α	α	PRON
ejpam-4299	144	18	∈	∈	PROPN
ejpam-4299	145	1	[	[	X
ejpam-4299	145	2	0	0	NUM
ejpam-4299	145	3	,	,	PUNCT
ejpam-4299	145	4	1	1	NUM
ejpam-4299	145	5	]	]	PUNCT
ejpam-4299	145	6	.	.	PUNCT
ejpam-4299	146	1	suppose	suppose	VERB
ejpam-4299	146	2	that	that	SCONJ
ejpam-4299	146	3	fα	fα	ADP
ejpam-4299	146	4	1	1	NUM
ejpam-4299	146	5	,	,	PUNCT
ejpam-4299	146	6	f	f	PROPN
ejpam-4299	146	7	α	α	NOUN
ejpam-4299	146	8	2	2	NUM
ejpam-4299	146	9	∈	∈	NOUN
ejpam-4299	146	10	c	c	NOUN
ejpam-4299	146	11	(	(	PUNCT
ejpam-4299	146	12	[	[	X
ejpam-4299	146	13	0	0	NUM
ejpam-4299	146	14	,	,	PUNCT
ejpam-4299	146	15	a),r	a),r	ADJ
ejpam-4299	146	16	)	)	PUNCT
ejpam-4299	146	17	∩	∩	ADJ
ejpam-4299	146	18	l1	l1	PROPN
ejpam-4299	146	19	(	(	PUNCT
ejpam-4299	146	20	[	[	X
ejpam-4299	146	21	0	0	NUM
ejpam-4299	146	22	,	,	PUNCT
ejpam-4299	146	23	a),r	a),r	ADJ
ejpam-4299	146	24	)	)	PUNCT
ejpam-4299	146	25	for	for	ADP
ejpam-4299	146	26	all	all	DET
ejpam-4299	146	27	α	α	PRON
ejpam-4299	146	28	∈	∈	PROPN
ejpam-4299	147	1	[	[	X
ejpam-4299	147	2	0	0	NUM
ejpam-4299	147	3	,	,	PUNCT
ejpam-4299	147	4	1	1	NUM
ejpam-4299	147	5	]	]	PUNCT
ejpam-4299	147	6	and	and	CCONJ
ejpam-4299	147	7	let	let	VERB
ejpam-4299	147	8	aα	aα	NOUN
ejpam-4299	147	9	=	=	NOUN
ejpam-4299	147	10	:	:	PUNCT
ejpam-4299	148	1	[	[	X
ejpam-4299	148	2	∫	∫	X
ejpam-4299	148	3	t	t	NOUN
ejpam-4299	148	4	0	0	NUM
ejpam-4299	148	5	fα	fα	ADP
ejpam-4299	148	6	1	1	NUM
ejpam-4299	148	7	(	(	PUNCT
ejpam-4299	148	8	x	x	NOUN
ejpam-4299	148	9	)	)	PUNCT
ejpam-4299	148	10	x1−q	x1−q	PROPN
ejpam-4299	148	11	dx	dx	PROPN
ejpam-4299	148	12	,	,	PUNCT
ejpam-4299	148	13	∫	∫	PROPN
ejpam-4299	148	14	t	t	PROPN
ejpam-4299	148	15	0	0	NUM
ejpam-4299	148	16	fα	fα	ADP
ejpam-4299	148	17	2	2	NUM
ejpam-4299	148	18	(	(	PUNCT
ejpam-4299	148	19	x	x	NOUN
ejpam-4299	148	20	)	)	PUNCT
ejpam-4299	148	21	x1−q	x1−q	PROPN
ejpam-4299	148	22	dx	dx	PROPN
ejpam-4299	148	23	]	]	PUNCT
ejpam-4299	148	24	,	,	PUNCT
ejpam-4299	148	25	t	t	PROPN
ejpam-4299	148	26	∈	∈	PROPN
ejpam-4299	148	27	(	(	PUNCT
ejpam-4299	148	28	0	0	NUM
ejpam-4299	148	29	,	,	PUNCT
ejpam-4299	148	30	a	a	NOUN
ejpam-4299	148	31	)	)	PUNCT
ejpam-4299	148	32	(	(	PUNCT
ejpam-4299	148	33	3	3	X
ejpam-4299	148	34	)	)	PUNCT
ejpam-4299	148	35	lemma	lemma	PROPN
ejpam-4299	148	36	2	2	NUM
ejpam-4299	148	37	.	.	PUNCT
ejpam-4299	149	1	[	[	X
ejpam-4299	149	2	5	5	X
ejpam-4299	149	3	]	]	PUNCT
ejpam-4299	149	4	the	the	DET
ejpam-4299	149	5	family	family	NOUN
ejpam-4299	149	6	{	{	PUNCT
ejpam-4299	149	7	aα;α	aα;α	PROPN
ejpam-4299	149	8	∈	∈	PROPN
ejpam-4299	150	1	[	[	X
ejpam-4299	150	2	0	0	NUM
ejpam-4299	150	3	,	,	PUNCT
ejpam-4299	150	4	1	1	NUM
ejpam-4299	150	5	]	]	PUNCT
ejpam-4299	150	6	}	}	PUNCT
ejpam-4299	150	7	,	,	PUNCT
ejpam-4299	150	8	given	give	VERB
ejpam-4299	150	9	by	by	ADP
ejpam-4299	150	10	eq(3	eq(3	NOUN
ejpam-4299	150	11	)	)	PUNCT
ejpam-4299	150	12	,	,	PUNCT
ejpam-4299	150	13	defined	define	VERB
ejpam-4299	150	14	a	a	DET
ejpam-4299	150	15	fuzzy	fuzzy	ADJ
ejpam-4299	150	16	number	number	NOUN
ejpam-4299	150	17	f̄	f̄	PROPN
ejpam-4299	150	18	∈	∈	PROPN
ejpam-4299	150	19	rf	rf	VERB
ejpam-4299	151	1	such	such	ADJ
ejpam-4299	151	2	that	that	SCONJ
ejpam-4299	151	3	[	[	PUNCT
ejpam-4299	151	4	f̄	f̄	NOUN
ejpam-4299	151	5	]	]	X
ejpam-4299	151	6	α	α	X
ejpam-4299	151	7	=	=	SYM
ejpam-4299	151	8	aα	aα	NOUN
ejpam-4299	151	9	.	.	PUNCT
ejpam-4299	152	1	proof	proof	NOUN
ejpam-4299	152	2	.	.	PUNCT
ejpam-4299	153	1	for	for	ADP
ejpam-4299	153	2	α	α	PRON
ejpam-4299	153	3	<	<	X
ejpam-4299	153	4	β	β	X
ejpam-4299	153	5	we	we	PRON
ejpam-4299	153	6	have	have	VERB
ejpam-4299	153	7	that	that	DET
ejpam-4299	153	8	fα	fα	ADP
ejpam-4299	153	9	1	1	NUM
ejpam-4299	153	10	(	(	PUNCT
ejpam-4299	153	11	x	x	NOUN
ejpam-4299	153	12	)	)	PUNCT
ejpam-4299	153	13	≤	≤	NOUN
ejpam-4299	153	14	fβ	fβ	ADP
ejpam-4299	153	15	1	1	NUM
ejpam-4299	153	16	(	(	PUNCT
ejpam-4299	153	17	x	x	NOUN
ejpam-4299	153	18	)	)	PUNCT
ejpam-4299	153	19	and	and	CCONJ
ejpam-4299	153	20	fα	fα	ADP
ejpam-4299	153	21	2	2	NUM
ejpam-4299	153	22	(	(	PUNCT
ejpam-4299	153	23	x	x	NOUN
ejpam-4299	153	24	)	)	PUNCT
ejpam-4299	153	25	≥	≥	NOUN
ejpam-4299	153	26	fβ	fβ	ADP
ejpam-4299	153	27	2	2	NUM
ejpam-4299	153	28	(	(	PUNCT
ejpam-4299	153	29	x	x	NOUN
ejpam-4299	153	30	)	)	PUNCT
ejpam-4299	153	31	.	.	PUNCT
ejpam-4299	154	1	it	it	PRON
ejpam-4299	154	2	follows	follow	VERB
ejpam-4299	154	3	that	that	SCONJ
ejpam-4299	154	4	aα	aα	PROPN
ejpam-4299	154	5	⊇	⊇	PROPN
ejpam-4299	154	6	aβ	aβ	PROPN
ejpam-4299	154	7	.	.	PUNCT
ejpam-4299	155	1	since	since	SCONJ
ejpam-4299	155	2	f0	f0	PROPN
ejpam-4299	155	3	1	1	NUM
ejpam-4299	155	4	(	(	PUNCT
ejpam-4299	155	5	x	x	NOUN
ejpam-4299	155	6	)	)	PUNCT
ejpam-4299	155	7	≤	≤	NUM
ejpam-4299	155	8	fαn	fαn	NOUN
ejpam-4299	155	9	1	1	NUM
ejpam-4299	155	10	(	(	PUNCT
ejpam-4299	155	11	x	x	NOUN
ejpam-4299	155	12	)	)	PUNCT
ejpam-4299	155	13	≤	≤	NUM
ejpam-4299	155	14	f1	f1	NOUN
ejpam-4299	155	15	1	1	NUM
ejpam-4299	155	16	(	(	PUNCT
ejpam-4299	155	17	x	x	X
ejpam-4299	155	18	)	)	PUNCT
ejpam-4299	155	19	we	we	PRON
ejpam-4299	155	20	have∣∣xq−1fαn	have∣∣xq−1fαn	VERB
ejpam-4299	155	21	i	i	PRON
ejpam-4299	155	22	(	(	PUNCT
ejpam-4299	155	23	x	x	X
ejpam-4299	155	24	)	)	PUNCT
ejpam-4299	156	1	∣∣	∣∣	X
ejpam-4299	156	2	≤	≤	NUM
ejpam-4299	156	3	max	max	PROPN
ejpam-4299	156	4	{	{	PUNCT
ejpam-4299	156	5	aq−1	aq−1	NOUN
ejpam-4299	156	6	∣∣f0	∣∣f0	NOUN
ejpam-4299	156	7	i	i	PRON
ejpam-4299	156	8	(	(	PUNCT
ejpam-4299	156	9	x	x	X
ejpam-4299	156	10	)	)	PUNCT
ejpam-4299	156	11	∣∣	∣∣	NUM
ejpam-4299	156	12	,	,	PUNCT
ejpam-4299	156	13	aq−1	aq−1	NOUN
ejpam-4299	156	14	∣∣f1	∣∣f1	VERB
ejpam-4299	156	15	i	i	PRON
ejpam-4299	156	16	(	(	PUNCT
ejpam-4299	156	17	x	x	X
ejpam-4299	156	18	)	)	PUNCT
ejpam-4299	156	19	∣∣	∣∣	NUM
ejpam-4299	156	20	}	}	PUNCT
ejpam-4299	156	21	=	=	NOUN
ejpam-4299	156	22	:	:	PUNCT
ejpam-4299	156	23	gi(x	gi(x	X
ejpam-4299	156	24	)	)	PUNCT
ejpam-4299	156	25	for	for	ADP
ejpam-4299	156	26	αn	αn	NOUN
ejpam-4299	156	27	∈	∈	PROPN
ejpam-4299	157	1	[	[	X
ejpam-4299	157	2	0	0	NUM
ejpam-4299	157	3	,	,	PUNCT
ejpam-4299	157	4	1	1	NUM
ejpam-4299	157	5	]	]	PUNCT
ejpam-4299	157	6	and	and	CCONJ
ejpam-4299	157	7	i	i	NOUN
ejpam-4299	157	8	=	=	NOUN
ejpam-4299	157	9	1	1	NUM
ejpam-4299	157	10	,	,	PUNCT
ejpam-4299	157	11	2	2	NUM
ejpam-4299	157	12	.	.	PUNCT
ejpam-4299	158	1	obviously	obviously	ADV
ejpam-4299	158	2	,	,	PUNCT
ejpam-4299	158	3	gi	gi	PROPN
ejpam-4299	158	4	is	be	AUX
ejpam-4299	158	5	integrable	integrable	ADJ
ejpam-4299	158	6	on	on	ADP
ejpam-4299	158	7	[	[	X
ejpam-4299	158	8	0	0	NUM
ejpam-4299	158	9	,	,	PUNCT
ejpam-4299	158	10	a	a	PRON
ejpam-4299	158	11	)	)	PUNCT
ejpam-4299	158	12	.	.	PUNCT
ejpam-4299	159	1	therefore	therefore	ADV
ejpam-4299	159	2	,	,	PUNCT
ejpam-4299	159	3	if	if	SCONJ
ejpam-4299	159	4	αn	αn	NOUN
ejpam-4299	159	5	↑	↑	NOUN
ejpam-4299	159	6	α	α	NOUN
ejpam-4299	159	7	then	then	ADV
ejpam-4299	159	8	by	by	ADP
ejpam-4299	159	9	the	the	DET
ejpam-4299	159	10	lebesque	lebesque	NOUN
ejpam-4299	159	11	’s	’s	PART
ejpam-4299	159	12	dominated	dominate	VERB
ejpam-4299	159	13	convergence	convergence	NOUN
ejpam-4299	159	14	theorem	theorem	VERB
ejpam-4299	159	15	,	,	PUNCT
ejpam-4299	159	16	we	we	PRON
ejpam-4299	159	17	have	have	VERB
ejpam-4299	159	18	lim	lim	PROPN
ejpam-4299	159	19	n→∞	n→∞	NUM
ejpam-4299	160	1	∫	∫	PROPN
ejpam-4299	160	2	t	t	PROPN
ejpam-4299	160	3	0	0	NUM
ejpam-4299	160	4	fαn	fαn	NOUN
ejpam-4299	160	5	i	i	PRON
ejpam-4299	160	6	x1−q	x1−q	PROPN
ejpam-4299	160	7	(	(	PUNCT
ejpam-4299	161	1	x)dx	x)dx	PROPN
ejpam-4299	161	2	=	=	SYM
ejpam-4299	161	3	∫	∫	PROPN
ejpam-4299	161	4	t	t	PROPN
ejpam-4299	161	5	0	0	NUM
ejpam-4299	161	6	fα	fα	NOUN
ejpam-4299	161	7	i	i	PRON
ejpam-4299	161	8	x1−q	x1−q	PROPN
ejpam-4299	161	9	(	(	PUNCT
ejpam-4299	161	10	x)dx	x)dx	PROPN
ejpam-4299	161	11	,	,	PUNCT
ejpam-4299	161	12	i	i	NOUN
ejpam-4299	161	13	=	=	NOUN
ejpam-4299	161	14	1	1	NUM
ejpam-4299	161	15	,	,	PUNCT
ejpam-4299	161	16	2	2	NUM
ejpam-4299	161	17	from	from	ADP
ejpam-4299	161	18	theorem	theorem	NOUN
ejpam-4299	161	19	(	(	PUNCT
ejpam-4299	161	20	1	1	NUM
ejpam-4299	161	21	)	)	PUNCT
ejpam-4299	161	22	,	,	PUNCT
ejpam-4299	161	23	the	the	DET
ejpam-4299	161	24	proof	proof	NOUN
ejpam-4299	161	25	is	be	AUX
ejpam-4299	161	26	complete	complete	ADJ
ejpam-4299	161	27	.	.	PUNCT
ejpam-4299	162	1	remark	remark	NOUN
ejpam-4299	162	2	2	2	NUM
ejpam-4299	162	3	.	.	PUNCT
ejpam-4299	163	1	[	[	X
ejpam-4299	163	2	12	12	NUM
ejpam-4299	163	3	]	]	PUNCT
ejpam-4299	163	4	by	by	ADP
ejpam-4299	163	5	using	use	VERB
ejpam-4299	163	6	the	the	DET
ejpam-4299	163	7	weierstrass	weierstrass	NOUN
ejpam-4299	163	8	theorem	theorem	NOUN
ejpam-4299	163	9	,	,	PUNCT
ejpam-4299	163	10	it	it	PRON
ejpam-4299	163	11	is	be	AUX
ejpam-4299	163	12	enough	enough	ADJ
ejpam-4299	163	13	to	to	PART
ejpam-4299	163	14	define	define	VERB
ejpam-4299	163	15	the	the	DET
ejpam-4299	163	16	fractional	fractional	ADJ
ejpam-4299	163	17	integral	integral	ADJ
ejpam-4299	163	18	on	on	ADP
ejpam-4299	163	19	polynomials	polynomial	NOUN
ejpam-4299	163	20	.	.	PUNCT
ejpam-4299	164	1	this	this	PRON
ejpam-4299	164	2	suggests	suggest	VERB
ejpam-4299	164	3	the	the	DET
ejpam-4299	164	4	following	following	NOUN
ejpam-4299	164	5	.	.	PUNCT
ejpam-4299	165	1	let	let	VERB
ejpam-4299	165	2	q	q	PROPN
ejpam-4299	165	3	∈	∈	PROPN
ejpam-4299	165	4	(	(	PUNCT
ejpam-4299	165	5	0	0	NUM
ejpam-4299	165	6	,	,	PUNCT
ejpam-4299	165	7	1	1	NUM
ejpam-4299	165	8	]	]	PUNCT
ejpam-4299	165	9	.	.	PUNCT
ejpam-4299	166	1	define	define	VERB
ejpam-4299	166	2	iq	iq	NOUN
ejpam-4299	166	3	(	(	PUNCT
ejpam-4299	166	4	t	t	NOUN
ejpam-4299	166	5	p	p	X
ejpam-4299	166	6	)	)	PUNCT
ejpam-4299	166	7	=	=	PUNCT
ejpam-4299	166	8	tp+q	tp+q	PROPN
ejpam-4299	166	9	p+q	p+q	NOUN
ejpam-4299	166	10	for	for	ADP
ejpam-4299	166	11	any	any	DET
ejpam-4299	166	12	p	p	NOUN
ejpam-4299	166	13	∈	∈	PROPN
ejpam-4299	166	14	r	r	NOUN
ejpam-4299	166	15	,	,	PUNCT
ejpam-4299	166	16	and	and	CCONJ
ejpam-4299	166	17	q	q	X
ejpam-4299	167	1	6=	6=	ADP
ejpam-4299	167	2	−p	−p	ADJ
ejpam-4299	167	3	•	•	NOUN
ejpam-4299	167	4	if	if	SCONJ
ejpam-4299	167	5	f(t	f(t	NOUN
ejpam-4299	167	6	)	)	PUNCT
ejpam-4299	168	1	=	=	SYM
ejpam-4299	168	2	∑n	∑n	PROPN
ejpam-4299	168	3	k=0	k=0	PROPN
ejpam-4299	168	4	bkt	bkt	PROPN
ejpam-4299	168	5	k	k	PROPN
ejpam-4299	168	6	,	,	PUNCT
ejpam-4299	168	7	then	then	ADV
ejpam-4299	168	8	we	we	PRON
ejpam-4299	168	9	define	define	VERB
ejpam-4299	168	10	iq(f	iq(f	NOUN
ejpam-4299	168	11	)	)	PUNCT
ejpam-4299	168	12	=	=	SYM
ejpam-4299	169	1	∑n	∑n	PROPN
ejpam-4299	169	2	k=0	k=0	PROPN
ejpam-4299	169	3	bkiq	bkiq	PROPN
ejpam-4299	169	4	(	(	PUNCT
ejpam-4299	169	5	tk	tk	PROPN
ejpam-4299	169	6	)	)	PUNCT
ejpam-4299	169	7	=	=	SYM
ejpam-4299	170	1	∑n	∑n	PROPN
ejpam-4299	170	2	k=0	k=0	PROPN
ejpam-4299	170	3	bk	bk	ADP
ejpam-4299	170	4	tk+q	tk+q	PROPN
ejpam-4299	170	5	k+q	k+q	PROPN
ejpam-4299	170	6	•	•	NOUN
ejpam-4299	170	7	if	if	SCONJ
ejpam-4299	170	8	f(t	f(t	NOUN
ejpam-4299	170	9	)	)	PUNCT
ejpam-4299	170	10	=	=	SYM
ejpam-4299	170	11	∑∞	∑∞	NOUN
ejpam-4299	171	1	k=0	k=0	PROPN
ejpam-4299	171	2	bkt	bkt	PROPN
ejpam-4299	171	3	k	k	PROPN
ejpam-4299	171	4	,	,	PUNCT
ejpam-4299	171	5	where	where	SCONJ
ejpam-4299	171	6	the	the	DET
ejpam-4299	171	7	series	series	NOUN
ejpam-4299	171	8	is	be	AUX
ejpam-4299	171	9	uniformly	uniformly	ADV
ejpam-4299	171	10	convergent	convergent	NOUN
ejpam-4299	171	11	,	,	PUNCT
ejpam-4299	171	12	then	then	ADV
ejpam-4299	171	13	we	we	PRON
ejpam-4299	171	14	define	define	VERB
ejpam-4299	171	15	iq(f	iq(f	NOUN
ejpam-4299	171	16	)	)	PUNCT
ejpam-4299	171	17	=	=	NOUN
ejpam-4299	171	18	∑∞	∑∞	NOUN
ejpam-4299	171	19	k=0	k=0	PROPN
ejpam-4299	171	20	bk	bk	PROPN
ejpam-4299	171	21	tk+q	tk+q	PROPN
ejpam-4299	171	22	k+q	k+q	PUNCT
ejpam-4299	171	23	clearly	clearly	ADV
ejpam-4299	171	24	,	,	PUNCT
ejpam-4299	171	25	iq	iq	PROPN
ejpam-4299	171	26	is	be	AUX
ejpam-4299	171	27	linear	linear	ADJ
ejpam-4299	171	28	on	on	ADP
ejpam-4299	171	29	its	its	PRON
ejpam-4299	171	30	domain	domain	NOUN
ejpam-4299	171	31	.	.	PUNCT
ejpam-4299	172	1	further	far	ADV
ejpam-4299	172	2	,	,	PUNCT
ejpam-4299	172	3	if	if	SCONJ
ejpam-4299	172	4	q	q	NOUN
ejpam-4299	172	5	=	=	NOUN
ejpam-4299	172	6	1	1	NUM
ejpam-4299	172	7	,	,	PUNCT
ejpam-4299	172	8	then	then	ADV
ejpam-4299	172	9	iq	iq	PROPN
ejpam-4299	172	10	is	be	AUX
ejpam-4299	172	11	the	the	DET
ejpam-4299	172	12	usual	usual	ADJ
ejpam-4299	172	13	integral	integral	ADJ
ejpam-4299	172	14	.	.	PUNCT
ejpam-4299	173	1	definition	definition	NOUN
ejpam-4299	173	2	5	5	NUM
ejpam-4299	173	3	.	.	PUNCT
ejpam-4299	174	1	let	let	VERB
ejpam-4299	174	2	f̄	f̄	PROPN
ejpam-4299	174	3	∈	∈	PROPN
ejpam-4299	174	4	c	c	X
ejpam-4299	174	5	(	(	PUNCT
ejpam-4299	174	6	[	[	X
ejpam-4299	174	7	0	0	NUM
ejpam-4299	174	8	,	,	PUNCT
ejpam-4299	174	9	a),rf	a),rf	NUM
ejpam-4299	174	10	)	)	PUNCT
ejpam-4299	174	11	∩	∩	PROPN
ejpam-4299	174	12	l1	l1	PROPN
ejpam-4299	174	13	(	(	PUNCT
ejpam-4299	174	14	[	[	X
ejpam-4299	174	15	0	0	NUM
ejpam-4299	174	16	,	,	PUNCT
ejpam-4299	174	17	a),rf	a),rf	PROPN
ejpam-4299	174	18	)	)	PUNCT
ejpam-4299	174	19	,	,	PUNCT
ejpam-4299	174	20	define	define	VERB
ejpam-4299	174	21	the	the	DET
ejpam-4299	174	22	fuzzy	fuzzy	ADJ
ejpam-4299	174	23	fractional	fractional	ADJ
ejpam-4299	174	24	integral	integral	ADJ
ejpam-4299	174	25	for	for	ADP
ejpam-4299	174	26	a	a	DET
ejpam-4299	174	27	≥	≥	NOUN
ejpam-4299	174	28	0	0	NUM
ejpam-4299	174	29	and	and	CCONJ
ejpam-4299	174	30	q	q	ADJ
ejpam-4299	174	31	∈	∈	PROPN
ejpam-4299	174	32	(	(	PUNCT
ejpam-4299	174	33	0	0	NUM
ejpam-4299	174	34	,	,	PUNCT
ejpam-4299	174	35	1	1	NUM
ejpam-4299	174	36	)	)	PUNCT
ejpam-4299	174	37	iq(f̄	iq(f̄	ADV
ejpam-4299	174	38	)	)	PUNCT
ejpam-4299	174	39	(	(	PUNCT
ejpam-4299	174	40	t	t	NOUN
ejpam-4299	174	41	)	)	PUNCT
ejpam-4299	174	42	=	=	PROPN
ejpam-4299	174	43	i1	i1	PROPN
ejpam-4299	174	44	(	(	PUNCT
ejpam-4299	174	45	tq−1f̄	tq−1f̄	PROPN
ejpam-4299	174	46	)	)	PUNCT
ejpam-4299	174	47	(	(	PUNCT
ejpam-4299	174	48	t	t	NOUN
ejpam-4299	174	49	)	)	PUNCT
ejpam-4299	174	50	=	=	SYM
ejpam-4299	175	1	∫	∫	PROPN
ejpam-4299	175	2	t	t	PROPN
ejpam-4299	175	3	0	0	NUM
ejpam-4299	175	4	f̄	f̄	PROPN
ejpam-4299	175	5	(	(	PUNCT
ejpam-4299	175	6	x	x	NOUN
ejpam-4299	175	7	)	)	PUNCT
ejpam-4299	175	8	x1−q	x1−q	PROPN
ejpam-4299	175	9	dx	dx	PROPN
ejpam-4299	175	10	a.	a.	PROPN
ejpam-4299	175	11	harir	harir	PROPN
ejpam-4299	175	12	,	,	PUNCT
ejpam-4299	175	13	s.	s.	PROPN
ejpam-4299	175	14	melliani	melliani	PROPN
ejpam-4299	175	15	,	,	PUNCT
ejpam-4299	175	16	l.	l.	PROPN
ejpam-4299	175	17	s.	s.	PROPN
ejpam-4299	175	18	chadli	chadli	PROPN
ejpam-4299	175	19	/	/	SYM
ejpam-4299	175	20	eur	eur	PROPN
ejpam-4299	175	21	.	.	PUNCT
ejpam-4299	176	1	j.	j.	PROPN
ejpam-4299	176	2	pure	pure	PROPN
ejpam-4299	176	3	appl	appl	PROPN
ejpam-4299	176	4	.	.	PROPN
ejpam-4299	176	5	math	math	PROPN
ejpam-4299	176	6	,	,	PUNCT
ejpam-4299	176	7	15	15	NUM
ejpam-4299	176	8	(	(	PUNCT
ejpam-4299	176	9	2	2	NUM
ejpam-4299	176	10	)	)	PUNCT
ejpam-4299	176	11	(	(	PUNCT
ejpam-4299	176	12	2022	2022	NUM
ejpam-4299	176	13	)	)	PUNCT
ejpam-4299	176	14	,	,	PUNCT
ejpam-4299	176	15	557	557	NUM
ejpam-4299	176	16	-	-	SYM
ejpam-4299	176	17	571	571	NUM
ejpam-4299	176	18	563	563	NUM
ejpam-4299	176	19	by	by	ADP
ejpam-4299	176	20	[	[	PUNCT
ejpam-4299	176	21	iq(f̄	iq(f̄	NOUN
ejpam-4299	176	22	)	)	PUNCT
ejpam-4299	176	23	(	(	PUNCT
ejpam-4299	176	24	t	t	PROPN
ejpam-4299	176	25	)	)	PUNCT
ejpam-4299	176	26	]	]	PUNCT
ejpam-4299	177	1	α	α	X
ejpam-4299	177	2	=	=	X
ejpam-4299	177	3	[	[	PUNCT
ejpam-4299	177	4	i1	i1	PROPN
ejpam-4299	177	5	(	(	PUNCT
ejpam-4299	177	6	tq−1f̄	tq−1f̄	PROPN
ejpam-4299	177	7	)	)	PUNCT
ejpam-4299	177	8	(	(	PUNCT
ejpam-4299	177	9	t	t	PROPN
ejpam-4299	177	10	)	)	PUNCT
ejpam-4299	177	11	]	]	PUNCT
ejpam-4299	177	12	α	α	X
ejpam-4299	177	13	=	=	PUNCT
ejpam-4299	178	1	[	[	X
ejpam-4299	178	2	∫	∫	X
ejpam-4299	178	3	t	t	PROPN
ejpam-4299	178	4	0	0	NUM
ejpam-4299	178	5	f̄	f̄	PROPN
ejpam-4299	178	6	(	(	PUNCT
ejpam-4299	178	7	x	x	NOUN
ejpam-4299	178	8	)	)	PUNCT
ejpam-4299	178	9	x1−q	x1−q	PROPN
ejpam-4299	178	10	dx	dx	PROPN
ejpam-4299	178	11	]	]	X
ejpam-4299	178	12	α	α	X
ejpam-4299	178	13	=	=	PUNCT
ejpam-4299	179	1	[	[	X
ejpam-4299	179	2	∫	∫	X
ejpam-4299	179	3	t	t	PROPN
ejpam-4299	179	4	0	0	NUM
ejpam-4299	179	5	fα	fα	ADP
ejpam-4299	179	6	1	1	NUM
ejpam-4299	179	7	(	(	PUNCT
ejpam-4299	179	8	x	x	NOUN
ejpam-4299	179	9	)	)	PUNCT
ejpam-4299	179	10	x1−q	x1−q	PROPN
ejpam-4299	179	11	dx	dx	PROPN
ejpam-4299	179	12	,	,	PUNCT
ejpam-4299	179	13	∫	∫	PROPN
ejpam-4299	179	14	t	t	PROPN
ejpam-4299	179	15	0	0	NUM
ejpam-4299	179	16	fα	fα	ADP
ejpam-4299	179	17	2	2	NUM
ejpam-4299	179	18	(	(	PUNCT
ejpam-4299	179	19	x	x	NOUN
ejpam-4299	179	20	)	)	PUNCT
ejpam-4299	179	21	x1−q	x1−q	PROPN
ejpam-4299	179	22	dx	dx	PROPN
ejpam-4299	179	23	]	]	PUNCT
ejpam-4299	179	24	where	where	SCONJ
ejpam-4299	179	25	the	the	DET
ejpam-4299	179	26	integral	integral	ADJ
ejpam-4299	179	27	∫	∫	PROPN
ejpam-4299	179	28	t	t	PROPN
ejpam-4299	179	29	0	0	NUM
ejpam-4299	179	30	fα	fα	NOUN
ejpam-4299	179	31	i	i	PRON
ejpam-4299	179	32	x1−q	x1−q	PROPN
ejpam-4299	179	33	(	(	PUNCT
ejpam-4299	179	34	x)dx	x)dx	PROPN
ejpam-4299	179	35	,	,	PUNCT
ejpam-4299	179	36	for	for	ADP
ejpam-4299	179	37	i	i	PROPN
ejpam-4299	179	38	=	=	SYM
ejpam-4299	179	39	1	1	NUM
ejpam-4299	179	40	,	,	PUNCT
ejpam-4299	179	41	2	2	NUM
ejpam-4299	179	42	is	be	AUX
ejpam-4299	179	43	the	the	DET
ejpam-4299	179	44	usual	usual	ADJ
ejpam-4299	179	45	riemann	riemann	PROPN
ejpam-4299	179	46	improper	improper	PROPN
ejpam-4299	179	47	integral	integral	PROPN
ejpam-4299	179	48	.	.	PUNCT
ejpam-4299	180	1	also	also	ADV
ejpam-4299	180	2	,	,	PUNCT
ejpam-4299	180	3	the	the	DET
ejpam-4299	180	4	following	follow	VERB
ejpam-4299	180	5	properties	property	NOUN
ejpam-4299	180	6	are	be	AUX
ejpam-4299	180	7	obvious	obvious	ADJ
ejpam-4299	180	8	.	.	PUNCT
ejpam-4299	181	1	(	(	PUNCT
ejpam-4299	181	2	i	i	NOUN
ejpam-4299	181	3	)	)	PUNCT
ejpam-4299	181	4	iqλf̄	iqλf̄	PROPN
ejpam-4299	181	5	(	(	PUNCT
ejpam-4299	181	6	t	t	PROPN
ejpam-4299	181	7	)	)	PUNCT
ejpam-4299	181	8	=	=	PUNCT
ejpam-4299	182	1	λiqf̄	λiqf̄	X
ejpam-4299	182	2	(	(	PUNCT
ejpam-4299	182	3	t	t	NOUN
ejpam-4299	182	4	)	)	PUNCT
ejpam-4299	182	5	for	for	ADP
ejpam-4299	182	6	each	each	DET
ejpam-4299	182	7	λ	λ	PROPN
ejpam-4299	182	8	∈	∈	PROPN
ejpam-4299	182	9	r	r	NOUN
ejpam-4299	182	10	(	(	PUNCT
ejpam-4299	182	11	ii	ii	NOUN
ejpam-4299	182	12	)	)	PUNCT
ejpam-4299	182	13	iq(f̄	iq(f̄	PROPN
ejpam-4299	182	14	+	+	PUNCT
ejpam-4299	182	15	ḡ)(t	ḡ)(t	NOUN
ejpam-4299	182	16	)	)	PUNCT
ejpam-4299	182	17	=	=	SYM
ejpam-4299	182	18	iqf̄	iqf̄	NOUN
ejpam-4299	182	19	(	(	PUNCT
ejpam-4299	182	20	t	t	NOUN
ejpam-4299	182	21	)	)	PUNCT
ejpam-4299	182	22	+	+	CCONJ
ejpam-4299	182	23	iqḡ(t	iqḡ(t	ADJ
ejpam-4299	182	24	)	)	PUNCT
ejpam-4299	182	25	theorem	theorem	NOUN
ejpam-4299	182	26	5	5	NUM
ejpam-4299	182	27	.	.	PUNCT
ejpam-4299	183	1	tqiq(f̄	tqiq(f̄	ADV
ejpam-4299	183	2	)	)	PUNCT
ejpam-4299	183	3	(	(	PUNCT
ejpam-4299	183	4	t	t	NOUN
ejpam-4299	183	5	)	)	PUNCT
ejpam-4299	184	1	=	=	PRON
ejpam-4299	184	2	f̄	f̄	PROPN
ejpam-4299	184	3	(	(	PUNCT
ejpam-4299	184	4	t	t	PROPN
ejpam-4299	184	5	)	)	PUNCT
ejpam-4299	184	6	,	,	PUNCT
ejpam-4299	184	7	for	for	ADP
ejpam-4299	184	8	t	t	PROPN
ejpam-4299	184	9	≥	≥	NOUN
ejpam-4299	184	10	0	0	NUM
ejpam-4299	184	11	,	,	PUNCT
ejpam-4299	184	12	where	where	SCONJ
ejpam-4299	184	13	f̄	f̄	PROPN
ejpam-4299	184	14	is	be	AUX
ejpam-4299	184	15	any	any	DET
ejpam-4299	184	16	continuous	continuous	ADJ
ejpam-4299	184	17	function	function	NOUN
ejpam-4299	184	18	in	in	ADP
ejpam-4299	184	19	the	the	DET
ejpam-4299	184	20	domain	domain	NOUN
ejpam-4299	184	21	of	of	ADP
ejpam-4299	184	22	iq	iq	NOUN
ejpam-4299	184	23	.	.	PUNCT
ejpam-4299	185	1	proof	proof	NOUN
ejpam-4299	185	2	.	.	PUNCT
ejpam-4299	186	1	since	since	SCONJ
ejpam-4299	186	2	f̄	f̄	PROPN
ejpam-4299	186	3	is	be	AUX
ejpam-4299	186	4	continuous	continuous	ADJ
ejpam-4299	186	5	,	,	PUNCT
ejpam-4299	186	6	then	then	ADV
ejpam-4299	186	7	iq(f̄	iq(f̄	ADV
ejpam-4299	186	8	)	)	PUNCT
ejpam-4299	186	9	(	(	PUNCT
ejpam-4299	186	10	t	t	NOUN
ejpam-4299	186	11	)	)	PUNCT
ejpam-4299	186	12	is	be	AUX
ejpam-4299	186	13	clearly	clearly	ADV
ejpam-4299	186	14	differentiable	differentiable	ADJ
ejpam-4299	186	15	.	.	PUNCT
ejpam-4299	187	1	hence	hence	ADV
ejpam-4299	187	2	,	,	PUNCT
ejpam-4299	187	3	[	[	PUNCT
ejpam-4299	187	4	tqiq(f̄	tqiq(f̄	CCONJ
ejpam-4299	187	5	)	)	PUNCT
ejpam-4299	187	6	(	(	PUNCT
ejpam-4299	187	7	t	t	PROPN
ejpam-4299	187	8	)	)	PUNCT
ejpam-4299	187	9	]	]	PUNCT
ejpam-4299	187	10	α	α	X
ejpam-4299	187	11	=	=	X
ejpam-4299	188	1	[	[	PUNCT
ejpam-4299	188	2	t1−q	t1−q	PROPN
ejpam-4299	188	3	d	d	PROPN
ejpam-4299	188	4	dt	dt	X
ejpam-4299	188	5	iq(f̄	iq(f̄	PROPN
ejpam-4299	188	6	)	)	PUNCT
ejpam-4299	188	7	(	(	PUNCT
ejpam-4299	188	8	t	t	PROPN
ejpam-4299	188	9	)	)	PUNCT
ejpam-4299	188	10	]	]	PUNCT
ejpam-4299	188	11	α	α	X
ejpam-4299	188	12	=	=	X
ejpam-4299	189	1	[	[	PUNCT
ejpam-4299	189	2	t1−q	t1−q	PROPN
ejpam-4299	189	3	d	d	PROPN
ejpam-4299	189	4	dt	dt	X
ejpam-4299	189	5	∫	∫	PROPN
ejpam-4299	189	6	t	t	PROPN
ejpam-4299	189	7	0	0	NUM
ejpam-4299	189	8	fα	fα	ADP
ejpam-4299	189	9	1	1	NUM
ejpam-4299	189	10	(	(	PUNCT
ejpam-4299	189	11	x	x	NOUN
ejpam-4299	189	12	)	)	PUNCT
ejpam-4299	189	13	x1−q	x1−q	PROPN
ejpam-4299	189	14	dx	dx	PROPN
ejpam-4299	189	15	,	,	PUNCT
ejpam-4299	189	16	t1−q	t1−q	PROPN
ejpam-4299	189	17	d	d	PROPN
ejpam-4299	189	18	dt	dt	X
ejpam-4299	189	19	∫	∫	PROPN
ejpam-4299	189	20	t	t	PROPN
ejpam-4299	189	21	0	0	NUM
ejpam-4299	189	22	fα	fα	ADP
ejpam-4299	189	23	2	2	NUM
ejpam-4299	189	24	(	(	PUNCT
ejpam-4299	189	25	x	x	NOUN
ejpam-4299	189	26	)	)	PUNCT
ejpam-4299	189	27	x1−q	x1−q	PROPN
ejpam-4299	189	28	dx	dx	PROPN
ejpam-4299	189	29	]	]	PUNCT
ejpam-4299	190	1	=	=	PUNCT
ejpam-4299	190	2	[	[	PUNCT
ejpam-4299	190	3	t1−q	t1−q	PROPN
ejpam-4299	190	4	f	f	PROPN
ejpam-4299	190	5	α	α	PRON
ejpam-4299	190	6	1	1	NUM
ejpam-4299	190	7	(	(	PUNCT
ejpam-4299	190	8	t	t	NOUN
ejpam-4299	190	9	)	)	PUNCT
ejpam-4299	191	1	t1−q	t1−q	PROPN
ejpam-4299	191	2	,	,	PUNCT
ejpam-4299	191	3	t1−q	t1−q	PROPN
ejpam-4299	191	4	f	f	NOUN
ejpam-4299	191	5	α	α	PRON
ejpam-4299	191	6	2	2	NUM
ejpam-4299	191	7	(	(	PUNCT
ejpam-4299	191	8	t	t	NOUN
ejpam-4299	191	9	)	)	PUNCT
ejpam-4299	191	10	t1−q	t1−q	PROPN
ejpam-4299	191	11	]	]	PUNCT
ejpam-4299	192	1	=	=	PUNCT
ejpam-4299	193	1	[	[	X
ejpam-4299	193	2	f̄	f̄	PROPN
ejpam-4299	193	3	(	(	PUNCT
ejpam-4299	193	4	t)]α	t)]α	NOUN
ejpam-4299	193	5	4	4	NUM
ejpam-4299	193	6	.	.	X
ejpam-4299	193	7	fuzzy	fuzzy	ADJ
ejpam-4299	193	8	fractional	fractional	ADJ
ejpam-4299	193	9	differential	differential	ADJ
ejpam-4299	193	10	equation	equation	NOUN
ejpam-4299	193	11	in	in	ADP
ejpam-4299	193	12	this	this	DET
ejpam-4299	193	13	section	section	NOUN
ejpam-4299	193	14	,	,	PUNCT
ejpam-4299	193	15	we	we	PRON
ejpam-4299	193	16	consider	consider	VERB
ejpam-4299	193	17	eq	eq	NOUN
ejpam-4299	193	18	(	(	PUNCT
ejpam-4299	193	19	1	1	X
ejpam-4299	193	20	)	)	PUNCT
ejpam-4299	193	21	has	have	VERB
ejpam-4299	193	22	an	an	DET
ejpam-4299	193	23	unique	unique	ADJ
ejpam-4299	193	24	solution	solution	NOUN
ejpam-4299	193	25	y(t	y(t	NUM
ejpam-4299	193	26	)	)	PUNCT
ejpam-4299	194	1	=	=	PUNCT
ejpam-4299	194	2	g(t	g(t	PROPN
ejpam-4299	194	3	,	,	PUNCT
ejpam-4299	194	4	k	k	NOUN
ejpam-4299	194	5	,	,	PUNCT
ejpam-4299	194	6	c	c	NOUN
ejpam-4299	194	7	)	)	PUNCT
ejpam-4299	194	8	,	,	PUNCT
ejpam-4299	194	9	for	for	ADP
ejpam-4299	194	10	t	t	PROPN
ejpam-4299	194	11	∈	∈	PROPN
ejpam-4299	194	12	(	(	PUNCT
ejpam-4299	194	13	0	0	NUM
ejpam-4299	194	14	,	,	PUNCT
ejpam-4299	194	15	a	a	NOUN
ejpam-4299	194	16	)	)	PUNCT
ejpam-4299	194	17	,	,	PUNCT
ejpam-4299	194	18	k	k	PROPN
ejpam-4299	194	19	∈	∈	PROPN
ejpam-4299	194	20	rn	rn	PROPN
ejpam-4299	194	21	,	,	PUNCT
ejpam-4299	194	22	c	c	PROPN
ejpam-4299	194	23	∈	∈	PROPN
ejpam-4299	195	1	r	r	NOUN
ejpam-4299	195	2	i.e	i.e	NOUN
ejpam-4299	195	3	are	be	AUX
ejpam-4299	195	4	given	give	VERB
ejpam-4299	195	5	•	•	NUM
ejpam-4299	195	6	(	(	PUNCT
ejpam-4299	195	7	0	0	NUM
ejpam-4299	195	8	,	,	PUNCT
ejpam-4299	195	9	c	c	NOUN
ejpam-4299	195	10	)	)	PUNCT
ejpam-4299	195	11	is	be	AUX
ejpam-4299	195	12	in	in	ADP
ejpam-4299	195	13	(	(	PUNCT
ejpam-4299	195	14	0	0	NUM
ejpam-4299	195	15	,	,	PUNCT
ejpam-4299	195	16	a)×	a)×	PRON
ejpam-4299	195	17	i	i	PRON
ejpam-4299	195	18	where	where	SCONJ
ejpam-4299	195	19	i	i	PRON
ejpam-4299	195	20	be	be	VERB
ejpam-4299	195	21	an	an	DET
ejpam-4299	195	22	interval	interval	NOUN
ejpam-4299	195	23	for	for	ADP
ejpam-4299	195	24	the	the	DET
ejpam-4299	195	25	y	y	PROPN
ejpam-4299	195	26	-	-	PUNCT
ejpam-4299	195	27	values	value	NOUN
ejpam-4299	195	28	.	.	PUNCT
ejpam-4299	196	1	•	•	NUM
ejpam-4299	196	2	f	f	PROPN
ejpam-4299	196	3	is	be	AUX
ejpam-4299	196	4	continuous	continuous	ADJ
ejpam-4299	196	5	in	in	ADP
ejpam-4299	196	6	(	(	PUNCT
ejpam-4299	196	7	0	0	NUM
ejpam-4299	196	8	,	,	PUNCT
ejpam-4299	196	9	a)×	a)×	PRON
ejpam-4299	196	10	i(k	i(k	PROPN
ejpam-4299	196	11	is	be	AUX
ejpam-4299	196	12	fixed	fix	VERB
ejpam-4299	196	13	)	)	PUNCT
ejpam-4299	196	14	and	and	CCONJ
ejpam-4299	196	15	•	•	NOUN
ejpam-4299	196	16	∂f	∂f	PROPN
ejpam-4299	196	17	∂y	∂y	PRON
ejpam-4299	196	18	is	be	AUX
ejpam-4299	196	19	continuous	continuous	ADJ
ejpam-4299	196	20	in	in	ADP
ejpam-4299	196	21	(	(	PUNCT
ejpam-4299	196	22	0	0	NUM
ejpam-4299	196	23	,	,	PUNCT
ejpam-4299	196	24	a)×	a)×	PRON
ejpam-4299	196	25	i	i	PRON
ejpam-4299	196	26	let	let	VERB
ejpam-4299	196	27	k̄	k̄	VERB
ejpam-4299	196	28	=	=	SYM
ejpam-4299	196	29	(	(	PUNCT
ejpam-4299	196	30	k̄1	k̄1	NOUN
ejpam-4299	196	31	,	,	PUNCT
ejpam-4299	196	32	.	.	PUNCT
ejpam-4299	196	33	.	.	PUNCT
ejpam-4299	197	1	.	.	PUNCT
ejpam-4299	198	1	,	,	PUNCT
ejpam-4299	198	2	k̄n	k̄n	PROPN
ejpam-4299	198	3	)	)	PUNCT
ejpam-4299	198	4	be	be	AUX
ejpam-4299	198	5	a	a	DET
ejpam-4299	198	6	vector	vector	NOUN
ejpam-4299	198	7	of	of	ADP
ejpam-4299	198	8	triangular	triangular	NOUN
ejpam-4299	198	9	fuzzy	fuzzy	ADJ
ejpam-4299	198	10	numbers	number	NOUN
ejpam-4299	198	11	and	and	CCONJ
ejpam-4299	198	12	let	let	VERB
ejpam-4299	198	13	c̄	c̄	PROPN
ejpam-4299	198	14	be	be	AUX
ejpam-4299	198	15	another	another	DET
ejpam-4299	198	16	triangular	triangular	NOUN
ejpam-4299	198	17	fuzzy	fuzzy	ADJ
ejpam-4299	198	18	number	number	NOUN
ejpam-4299	198	19	.	.	PUNCT
ejpam-4299	199	1	substitute	substitute	NOUN
ejpam-4299	199	2	k̄	k̄	PROPN
ejpam-4299	199	3	for	for	ADP
ejpam-4299	199	4	k	k	PROPN
ejpam-4299	199	5	and	and	CCONJ
ejpam-4299	199	6	c̄	c̄	ADJ
ejpam-4299	199	7	for	for	ADP
ejpam-4299	199	8	c	c	PROPN
ejpam-4299	199	9	in	in	ADP
ejpam-4299	199	10	eq	eq	NOUN
ejpam-4299	199	11	(	(	PUNCT
ejpam-4299	199	12	1	1	NUM
ejpam-4299	199	13	)	)	PUNCT
ejpam-4299	199	14	and	and	CCONJ
ejpam-4299	199	15	we	we	PRON
ejpam-4299	199	16	get	get	VERB
ejpam-4299	199	17	the	the	DET
ejpam-4299	199	18	fuzzy	fuzzy	ADJ
ejpam-4299	199	19	fractional	fractional	ADJ
ejpam-4299	199	20	differential	differential	NOUN
ejpam-4299	199	21	equation	equation	NOUN
ejpam-4299	199	22	y	y	PROPN
ejpam-4299	199	23	q(t	q(t	PROPN
ejpam-4299	199	24	)	)	PUNCT
ejpam-4299	200	1	=	=	PRON
ejpam-4299	200	2	f̄	f̄	PROPN
ejpam-4299	200	3	(	(	PUNCT
ejpam-4299	200	4	t	t	PROPN
ejpam-4299	200	5	,	,	PUNCT
ejpam-4299	200	6	ȳ	ȳ	PROPN
ejpam-4299	200	7	,	,	PUNCT
ejpam-4299	200	8	k̄	k̄	PROPN
ejpam-4299	200	9	)	)	PUNCT
ejpam-4299	200	10	,	,	PUNCT
ejpam-4299	200	11	q	q	PROPN
ejpam-4299	200	12	∈	∈	PROPN
ejpam-4299	200	13	(	(	PUNCT
ejpam-4299	200	14	0	0	NUM
ejpam-4299	200	15	,	,	PUNCT
ejpam-4299	200	16	1	1	NUM
ejpam-4299	200	17	]	]	PUNCT
ejpam-4299	200	18	(	(	PUNCT
ejpam-4299	200	19	4	4	X
ejpam-4299	200	20	)	)	PUNCT
ejpam-4299	200	21	ȳ	ȳ	NOUN
ejpam-4299	200	22	(	(	PUNCT
ejpam-4299	200	23	0	0	NUM
ejpam-4299	200	24	)	)	PUNCT
ejpam-4299	200	25	=	=	SYM
ejpam-4299	200	26	c̄	c̄	ADJ
ejpam-4299	200	27	a.	a.	NOUN
ejpam-4299	200	28	harir	harir	NOUN
ejpam-4299	200	29	,	,	PUNCT
ejpam-4299	200	30	s.	s.	PROPN
ejpam-4299	200	31	melliani	melliani	PROPN
ejpam-4299	200	32	,	,	PUNCT
ejpam-4299	200	33	l.	l.	PROPN
ejpam-4299	200	34	s.	s.	PROPN
ejpam-4299	200	35	chadli	chadli	PROPN
ejpam-4299	200	36	/	/	SYM
ejpam-4299	200	37	eur	eur	PROPN
ejpam-4299	200	38	.	.	PUNCT
ejpam-4299	201	1	j.	j.	PROPN
ejpam-4299	201	2	pure	pure	PROPN
ejpam-4299	201	3	appl	appl	PROPN
ejpam-4299	201	4	.	.	PROPN
ejpam-4299	201	5	math	math	PROPN
ejpam-4299	201	6	,	,	PUNCT
ejpam-4299	201	7	15	15	NUM
ejpam-4299	201	8	(	(	PUNCT
ejpam-4299	201	9	2	2	NUM
ejpam-4299	201	10	)	)	PUNCT
ejpam-4299	201	11	(	(	PUNCT
ejpam-4299	201	12	2022	2022	NUM
ejpam-4299	201	13	)	)	PUNCT
ejpam-4299	201	14	,	,	PUNCT
ejpam-4299	201	15	557	557	NUM
ejpam-4299	201	16	-	-	SYM
ejpam-4299	201	17	571	571	NUM
ejpam-4299	201	18	564	564	NUM
ejpam-4299	201	19	4.1	4.1	NUM
ejpam-4299	201	20	.	.	PUNCT
ejpam-4299	202	1	buckley	buckley	NOUN
ejpam-4299	202	2	-	-	PUNCT
ejpam-4299	202	3	feuring	feuring	NOUN
ejpam-4299	202	4	solution	solution	NOUN
ejpam-4299	202	5	the	the	DET
ejpam-4299	202	6	buckley	buckley	NOUN
ejpam-4299	202	7	-	-	PUNCT
ejpam-4299	202	8	feuring	feure	VERB
ejpam-4299	202	9	solution	solution	NOUN
ejpam-4299	202	10	,	,	PUNCT
ejpam-4299	202	11	written	write	VERB
ejpam-4299	202	12	bf	bf	NOUN
ejpam-4299	202	13	-	-	PUNCT
ejpam-4299	202	14	solution	solution	NOUN
ejpam-4299	202	15	,	,	PUNCT
ejpam-4299	202	16	to	to	ADP
ejpam-4299	202	17	the	the	DET
ejpam-4299	202	18	fuzzy	fuzzy	ADJ
ejpam-4299	202	19	fractional	fractional	ADJ
ejpam-4299	202	20	differential	differential	NOUN
ejpam-4299	202	21	equation	equation	NOUN
ejpam-4299	202	22	[	[	X
ejpam-4299	202	23	?	?	PUNCT
ejpam-4299	203	1	]	]	X
ejpam-4299	203	2	,	,	PUNCT
ejpam-4299	203	3	we	we	PRON
ejpam-4299	203	4	first	first	ADV
ejpam-4299	203	5	fuzzify	fuzzify	VERB
ejpam-4299	203	6	the	the	DET
ejpam-4299	203	7	crisp	crisp	ADJ
ejpam-4299	203	8	solution	solution	NOUN
ejpam-4299	203	9	y(t	y(t	NUM
ejpam-4299	203	10	)	)	PUNCT
ejpam-4299	204	1	=	=	PUNCT
ejpam-4299	204	2	g(t	g(t	PROPN
ejpam-4299	204	3	,	,	PUNCT
ejpam-4299	204	4	k	k	NOUN
ejpam-4299	204	5	,	,	PUNCT
ejpam-4299	204	6	c	c	NOUN
ejpam-4299	204	7	)	)	PUNCT
ejpam-4299	204	8	to	to	PART
ejpam-4299	204	9	obtain	obtain	VERB
ejpam-4299	204	10	ȳ	ȳ	PROPN
ejpam-4299	204	11	(	(	PUNCT
ejpam-4299	204	12	t	t	NOUN
ejpam-4299	204	13	)	)	PUNCT
ejpam-4299	204	14	=	=	SYM
ejpam-4299	205	1	ḡ(t	ḡ(t	ADJ
ejpam-4299	205	2	,	,	PUNCT
ejpam-4299	205	3	k̄	k̄	X
ejpam-4299	205	4	,	,	PUNCT
ejpam-4299	205	5	c̄	c̄	PROPN
ejpam-4299	205	6	)	)	PUNCT
ejpam-4299	205	7	using	use	VERB
ejpam-4299	205	8	the	the	DET
ejpam-4299	205	9	extension	extension	NOUN
ejpam-4299	205	10	principle	principle	NOUN
ejpam-4299	205	11	.	.	PUNCT
ejpam-4299	206	1	alternatively	alternatively	ADV
ejpam-4299	206	2	,	,	PUNCT
ejpam-4299	206	3	we	we	PRON
ejpam-4299	206	4	get	get	VERB
ejpam-4299	206	5	α	α	NOUN
ejpam-4299	206	6	-	-	NOUN
ejpam-4299	206	7	cuts	cut	NOUN
ejpam-4299	206	8	as	as	SCONJ
ejpam-4299	206	9	follows	follow	VERB
ejpam-4299	206	10	:	:	PUNCT
ejpam-4299	207	1	[	[	X
ejpam-4299	207	2	ȳ	ȳ	INTJ
ejpam-4299	207	3	(	(	PUNCT
ejpam-4299	207	4	t)]α	t)]α	NOUN
ejpam-4299	207	5	=	=	PUNCT
ejpam-4299	207	6	[	[	X
ejpam-4299	207	7	yα1	yα1	NUM
ejpam-4299	207	8	(	(	PUNCT
ejpam-4299	207	9	t	t	PROPN
ejpam-4299	207	10	)	)	PUNCT
ejpam-4299	207	11	,	,	PUNCT
ejpam-4299	207	12	y	y	PROPN
ejpam-4299	207	13	α	α	PROPN
ejpam-4299	207	14	2	2	NUM
ejpam-4299	207	15	(	(	PUNCT
ejpam-4299	207	16	t	t	PROPN
ejpam-4299	207	17	)	)	PUNCT
ejpam-4299	207	18	]	]	PUNCT
ejpam-4299	207	19	,	,	PUNCT
ejpam-4299	207	20	(	(	PUNCT
ejpam-4299	207	21	5	5	X
ejpam-4299	207	22	)	)	PUNCT
ejpam-4299	207	23	[	[	X
ejpam-4299	207	24	f̄	f̄	PROPN
ejpam-4299	207	25	(	(	PUNCT
ejpam-4299	207	26	t	t	PROPN
ejpam-4299	207	27	,	,	PUNCT
ejpam-4299	207	28	ȳ	ȳ	PROPN
ejpam-4299	207	29	,	,	PUNCT
ejpam-4299	207	30	k̄)]α	k̄)]α	NOUN
ejpam-4299	207	31	=	=	PUNCT
ejpam-4299	208	1	[	[	X
ejpam-4299	208	2	fα	fα	ADP
ejpam-4299	208	3	1	1	NUM
ejpam-4299	208	4	(	(	PUNCT
ejpam-4299	208	5	t	t	PROPN
ejpam-4299	208	6	)	)	PUNCT
ejpam-4299	208	7	,	,	PUNCT
ejpam-4299	208	8	f	f	PROPN
ejpam-4299	208	9	α	α	PROPN
ejpam-4299	208	10	2	2	NUM
ejpam-4299	208	11	(	(	PUNCT
ejpam-4299	208	12	t	t	PROPN
ejpam-4299	208	13	)	)	PUNCT
ejpam-4299	208	14	]	]	PUNCT
ejpam-4299	208	15	,	,	PUNCT
ejpam-4299	208	16	(	(	PUNCT
ejpam-4299	208	17	6	6	X
ejpam-4299	208	18	)	)	PUNCT
ejpam-4299	208	19	let	let	VERB
ejpam-4299	208	20	w	w	NOUN
ejpam-4299	208	21	=	=	PUNCT
ejpam-4299	209	1	[	[	X
ejpam-4299	209	2	k̄]α	k̄]α	NOUN
ejpam-4299	209	3	×	×	NOUN
ejpam-4299	209	4	[	[	X
ejpam-4299	209	5	c̄]α	c̄]α	NUM
ejpam-4299	209	6	.	.	PUNCT
ejpam-4299	210	1	by	by	ADP
ejpam-4299	210	2	definition	definition	NOUN
ejpam-4299	210	3	yα1	yα1	NUM
ejpam-4299	210	4	(	(	PUNCT
ejpam-4299	210	5	t	t	NOUN
ejpam-4299	210	6	)	)	PUNCT
ejpam-4299	210	7	=	=	SYM
ejpam-4299	210	8	min{g(t	min{g(t	PROPN
ejpam-4299	210	9	,	,	PUNCT
ejpam-4299	210	10	k	k	NOUN
ejpam-4299	210	11	,	,	PUNCT
ejpam-4299	210	12	c	c	NOUN
ejpam-4299	210	13	)	)	PUNCT
ejpam-4299	210	14	:	:	PUNCT
ejpam-4299	210	15	(	(	PUNCT
ejpam-4299	210	16	k	k	X
ejpam-4299	210	17	,	,	PUNCT
ejpam-4299	210	18	c	c	NOUN
ejpam-4299	210	19	)	)	PUNCT
ejpam-4299	210	20	∈	∈	PROPN
ejpam-4299	210	21	w	w	PROPN
ejpam-4299	210	22	}	}	PUNCT
ejpam-4299	210	23	,	,	PUNCT
ejpam-4299	210	24	(	(	PUNCT
ejpam-4299	210	25	7	7	X
ejpam-4299	210	26	)	)	PUNCT
ejpam-4299	210	27	yα2	yα2	NOUN
ejpam-4299	210	28	(	(	PUNCT
ejpam-4299	210	29	t	t	PROPN
ejpam-4299	210	30	)	)	PUNCT
ejpam-4299	210	31	=	=	SYM
ejpam-4299	210	32	max{g(t	max{g(t	PROPN
ejpam-4299	210	33	,	,	PUNCT
ejpam-4299	210	34	k	k	PROPN
ejpam-4299	210	35	,	,	PUNCT
ejpam-4299	210	36	c	c	NOUN
ejpam-4299	210	37	)	)	PUNCT
ejpam-4299	210	38	:	:	PUNCT
ejpam-4299	210	39	(	(	PUNCT
ejpam-4299	210	40	k	k	X
ejpam-4299	210	41	,	,	PUNCT
ejpam-4299	210	42	c	c	NOUN
ejpam-4299	210	43	)	)	PUNCT
ejpam-4299	210	44	∈	∈	PROPN
ejpam-4299	210	45	w	w	PROPN
ejpam-4299	210	46	}	}	PUNCT
ejpam-4299	210	47	,	,	PUNCT
ejpam-4299	210	48	(	(	PUNCT
ejpam-4299	210	49	8)	8)	NUM
ejpam-4299	210	50	fα	fα	PART
ejpam-4299	210	51	1	1	NUM
ejpam-4299	210	52	(	(	PUNCT
ejpam-4299	210	53	t	t	NOUN
ejpam-4299	210	54	)	)	PUNCT
ejpam-4299	210	55	=	=	SYM
ejpam-4299	210	56	min	min	PROPN
ejpam-4299	210	57	{	{	PUNCT
ejpam-4299	210	58	f	f	PROPN
ejpam-4299	210	59	(	(	PUNCT
ejpam-4299	210	60	t	t	PROPN
ejpam-4299	210	61	,	,	PUNCT
ejpam-4299	210	62	y	y	PROPN
ejpam-4299	210	63	,	,	PUNCT
ejpam-4299	210	64	k	k	NOUN
ejpam-4299	210	65	)	)	PUNCT
ejpam-4299	210	66	:	:	PUNCT
ejpam-4299	210	67	y	y	PROPN
ejpam-4299	210	68	∈	∈	PROPN
ejpam-4299	211	1	[	[	X
ejpam-4299	211	2	ȳ	ȳ	PROPN
ejpam-4299	211	3	(	(	PUNCT
ejpam-4299	211	4	t)]α	t)]α	NOUN
ejpam-4299	211	5	,	,	PUNCT
ejpam-4299	211	6	k	k	PROPN
ejpam-4299	211	7	∈	∈	PROPN
ejpam-4299	211	8	[	[	X
ejpam-4299	211	9	k̄]α	k̄]α	NOUN
ejpam-4299	211	10	}	}	PUNCT
ejpam-4299	211	11	,	,	PUNCT
ejpam-4299	211	12	(	(	PUNCT
ejpam-4299	211	13	9	9	X
ejpam-4299	211	14	)	)	PUNCT
ejpam-4299	211	15	fα	fα	ADP
ejpam-4299	211	16	2	2	NUM
ejpam-4299	211	17	(	(	PUNCT
ejpam-4299	211	18	t	t	NOUN
ejpam-4299	211	19	)	)	PUNCT
ejpam-4299	211	20	=	=	SYM
ejpam-4299	211	21	max	max	PROPN
ejpam-4299	211	22	{	{	PUNCT
ejpam-4299	211	23	f	f	PROPN
ejpam-4299	211	24	(	(	PUNCT
ejpam-4299	211	25	t	t	PROPN
ejpam-4299	211	26	,	,	PUNCT
ejpam-4299	211	27	y	y	PROPN
ejpam-4299	211	28	,	,	PUNCT
ejpam-4299	211	29	k	k	NOUN
ejpam-4299	211	30	)	)	PUNCT
ejpam-4299	211	31	:	:	PUNCT
ejpam-4299	211	32	y	y	PROPN
ejpam-4299	211	33	∈	∈	PROPN
ejpam-4299	212	1	[	[	X
ejpam-4299	212	2	ȳ	ȳ	PROPN
ejpam-4299	212	3	(	(	PUNCT
ejpam-4299	212	4	t)]α	t)]α	NOUN
ejpam-4299	212	5	,	,	PUNCT
ejpam-4299	212	6	k	k	PROPN
ejpam-4299	212	7	∈	∈	PROPN
ejpam-4299	212	8	[	[	X
ejpam-4299	212	9	k̄]α	k̄]α	NOUN
ejpam-4299	212	10	}	}	PUNCT
ejpam-4299	212	11	,	,	PUNCT
ejpam-4299	212	12	(	(	PUNCT
ejpam-4299	212	13	10	10	NUM
ejpam-4299	212	14	)	)	PUNCT
ejpam-4299	212	15	for	for	ADP
ejpam-4299	212	16	t	t	PROPN
ejpam-4299	212	17	∈	∈	PROPN
ejpam-4299	212	18	(	(	PUNCT
ejpam-4299	212	19	0	0	NUM
ejpam-4299	212	20	,	,	PUNCT
ejpam-4299	212	21	a	a	PRON
ejpam-4299	212	22	)	)	PUNCT
ejpam-4299	212	23	and	and	CCONJ
ejpam-4299	212	24	α	α	PRON
ejpam-4299	212	25	∈	∈	PROPN
ejpam-4299	213	1	[	[	X
ejpam-4299	213	2	0	0	NUM
ejpam-4299	213	3	,	,	PUNCT
ejpam-4299	213	4	1	1	NUM
ejpam-4299	213	5	]	]	PUNCT
ejpam-4299	213	6	.	.	PUNCT
ejpam-4299	214	1	let	let	VERB
ejpam-4299	214	2	for	for	SCONJ
ejpam-4299	214	3	ȳ	ȳ	PROPN
ejpam-4299	214	4	(	(	PUNCT
ejpam-4299	214	5	t	t	PROPN
ejpam-4299	214	6	)	)	PUNCT
ejpam-4299	214	7	to	to	PART
ejpam-4299	214	8	be	be	AUX
ejpam-4299	214	9	a	a	DET
ejpam-4299	214	10	solution	solution	NOUN
ejpam-4299	214	11	to	to	ADP
ejpam-4299	214	12	the	the	DET
ejpam-4299	214	13	fuzzy	fuzzy	ADJ
ejpam-4299	214	14	fractional	fractional	ADJ
ejpam-4299	214	15	differential	differential	NOUN
ejpam-4299	214	16	equation	equation	NOUN
ejpam-4299	214	17	we	we	PRON
ejpam-4299	214	18	need	need	VERB
ejpam-4299	214	19	that	that	DET
ejpam-4299	214	20	ȳ	ȳ	PROPN
ejpam-4299	214	21	(	(	PUNCT
ejpam-4299	214	22	q)(t	q)(t	PROPN
ejpam-4299	214	23	)	)	PUNCT
ejpam-4299	214	24	exist	exist	VERB
ejpam-4299	214	25	but	but	CCONJ
ejpam-4299	214	26	also	also	ADV
ejpam-4299	214	27	(	(	PUNCT
ejpam-4299	214	28	4	4	X
ejpam-4299	214	29	)	)	PUNCT
ejpam-4299	214	30	must	must	AUX
ejpam-4299	214	31	hold	hold	VERB
ejpam-4299	214	32	.	.	PUNCT
ejpam-4299	215	1	assume	assume	VERB
ejpam-4299	215	2	that	that	SCONJ
ejpam-4299	215	3	(	(	PUNCT
ejpam-4299	215	4	y)αi	y)αi	PROPN
ejpam-4299	215	5	(	(	PUNCT
ejpam-4299	215	6	t	t	PROPN
ejpam-4299	215	7	)	)	PUNCT
ejpam-4299	215	8	for	for	ADP
ejpam-4299	215	9	all	all	DET
ejpam-4299	215	10	i	i	PRON
ejpam-4299	215	11	=	=	PUNCT
ejpam-4299	215	12	{	{	PUNCT
ejpam-4299	215	13	1	1	NUM
ejpam-4299	215	14	,	,	PUNCT
ejpam-4299	215	15	2	2	NUM
ejpam-4299	215	16	}	}	PUNCT
ejpam-4299	215	17	,	,	PUNCT
ejpam-4299	215	18	is	be	AUX
ejpam-4299	215	19	q	q	ADJ
ejpam-4299	215	20	-	-	ADJ
ejpam-4299	215	21	differentiable	differentiable	ADJ
ejpam-4299	215	22	(	(	PUNCT
ejpam-4299	215	23	conformable	conformable	ADJ
ejpam-4299	215	24	derivative	derivative	NOUN
ejpam-4299	215	25	)	)	PUNCT
ejpam-4299	215	26	with	with	ADP
ejpam-4299	215	27	respect	respect	NOUN
ejpam-4299	215	28	to	to	ADP
ejpam-4299	215	29	t	t	PROPN
ejpam-4299	215	30	∈	∈	PROPN
ejpam-4299	215	31	(	(	PUNCT
ejpam-4299	215	32	0	0	NUM
ejpam-4299	215	33	,	,	PUNCT
ejpam-4299	215	34	a	a	DET
ejpam-4299	215	35	)	)	PUNCT
ejpam-4299	215	36	for	for	ADP
ejpam-4299	215	37	each	each	DET
ejpam-4299	215	38	α	α	NOUN
ejpam-4299	215	39	∈	∈	PROPN
ejpam-4299	216	1	[	[	X
ejpam-4299	216	2	0	0	NUM
ejpam-4299	216	3	,	,	PUNCT
ejpam-4299	216	4	1	1	NUM
ejpam-4299	216	5	]	]	PUNCT
ejpam-4299	216	6	and	and	CCONJ
ejpam-4299	216	7	q	q	PROPN
ejpam-4299	216	8	∈	∈	PROPN
ejpam-4299	216	9	(	(	PUNCT
ejpam-4299	216	10	0	0	NUM
ejpam-4299	216	11	,	,	PUNCT
ejpam-4299	216	12	1	1	NUM
ejpam-4299	216	13	]	]	PUNCT
ejpam-4299	216	14	.	.	PUNCT
ejpam-4299	217	1	(	(	PUNCT
ejpam-4299	217	2	y(q	y(q	PROPN
ejpam-4299	217	3	)	)	PUNCT
ejpam-4299	217	4	)	)	PUNCT
ejpam-4299	218	1	α	α	PRON
ejpam-4299	218	2	i	i	PRON
ejpam-4299	218	3	(	(	PUNCT
ejpam-4299	218	4	t	t	PROPN
ejpam-4299	218	5	)	)	PUNCT
ejpam-4299	218	6	=	=	PUNCT
ejpam-4299	219	1	fα	fα	VERB
ejpam-4299	219	2	i	i	PRON
ejpam-4299	219	3	(	(	PUNCT
ejpam-4299	219	4	t	t	PROPN
ejpam-4299	219	5	)	)	PUNCT
ejpam-4299	219	6	(	(	PUNCT
ejpam-4299	219	7	11	11	NUM
ejpam-4299	219	8	)	)	PUNCT
ejpam-4299	219	9	or	or	CCONJ
ejpam-4299	219	10	(	(	PUNCT
ejpam-4299	219	11	y(q	y(q	PROPN
ejpam-4299	219	12	)	)	PUNCT
ejpam-4299	219	13	)	)	PUNCT
ejpam-4299	220	1	α	α	X
ejpam-4299	220	2	1	1	NUM
ejpam-4299	220	3	(	(	PUNCT
ejpam-4299	220	4	t	t	NOUN
ejpam-4299	220	5	)	)	PUNCT
ejpam-4299	220	6	=	=	NOUN
ejpam-4299	220	7	fα	fα	ADP
ejpam-4299	220	8	1	1	NUM
ejpam-4299	220	9	(	(	PUNCT
ejpam-4299	220	10	t	t	NOUN
ejpam-4299	220	11	)	)	PUNCT
ejpam-4299	220	12	(	(	PUNCT
ejpam-4299	220	13	12	12	NUM
ejpam-4299	220	14	)	)	PUNCT
ejpam-4299	220	15	(	(	PUNCT
ejpam-4299	220	16	y(q	y(q	PROPN
ejpam-4299	220	17	)	)	PUNCT
ejpam-4299	220	18	)	)	PUNCT
ejpam-4299	221	1	α	α	X
ejpam-4299	221	2	2	2	NUM
ejpam-4299	221	3	(	(	PUNCT
ejpam-4299	221	4	t	t	NOUN
ejpam-4299	221	5	)	)	PUNCT
ejpam-4299	221	6	=	=	NOUN
ejpam-4299	221	7	fα	fα	ADP
ejpam-4299	221	8	2	2	NUM
ejpam-4299	221	9	(	(	PUNCT
ejpam-4299	221	10	t	t	NOUN
ejpam-4299	221	11	)	)	PUNCT
ejpam-4299	221	12	(	(	PUNCT
ejpam-4299	221	13	13	13	NUM
ejpam-4299	221	14	)	)	PUNCT
ejpam-4299	221	15	yα1	yα1	NOUN
ejpam-4299	221	16	(	(	PUNCT
ejpam-4299	221	17	0	0	NUM
ejpam-4299	221	18	)	)	PUNCT
ejpam-4299	221	19	=	=	SYM
ejpam-4299	221	20	cα1	cα1	NOUN
ejpam-4299	221	21	(	(	PUNCT
ejpam-4299	221	22	14	14	NUM
ejpam-4299	221	23	)	)	PUNCT
ejpam-4299	221	24	yα2	yα2	NOUN
ejpam-4299	221	25	(	(	PUNCT
ejpam-4299	221	26	0	0	NUM
ejpam-4299	221	27	)	)	PUNCT
ejpam-4299	221	28	=	=	VERB
ejpam-4299	221	29	cα2	cα2	NOUN
ejpam-4299	221	30	(	(	PUNCT
ejpam-4299	221	31	15	15	NUM
ejpam-4299	221	32	)	)	PUNCT
ejpam-4299	222	1	where	where	SCONJ
ejpam-4299	222	2	[	[	X
ejpam-4299	222	3	c̄]α	c̄]α	NOUN
ejpam-4299	222	4	=	=	X
ejpam-4299	223	1	[	[	X
ejpam-4299	223	2	cα1	cα1	NOUN
ejpam-4299	223	3	,	,	PUNCT
ejpam-4299	223	4	c	c	NOUN
ejpam-4299	223	5	α	α	PRON
ejpam-4299	223	6	2	2	NUM
ejpam-4299	223	7	]	]	PUNCT
ejpam-4299	223	8	.	.	PUNCT
ejpam-4299	224	1	we	we	PRON
ejpam-4299	224	2	write	write	VERB
ejpam-4299	224	3	the	the	DET
ejpam-4299	224	4	partial	partial	NOUN
ejpam-4299	224	5	of	of	ADP
ejpam-4299	224	6	yαi	yαi	PROPN
ejpam-4299	224	7	(	(	PUNCT
ejpam-4299	224	8	t	t	PROPN
ejpam-4299	224	9	)	)	PUNCT
ejpam-4299	224	10	,	,	PUNCT
ejpam-4299	224	11	i	i	PRON
ejpam-4299	224	12	=	=	NOUN
ejpam-4299	224	13	1	1	NUM
ejpam-4299	224	14	,	,	PUNCT
ejpam-4299	224	15	2	2	NUM
ejpam-4299	224	16	with	with	ADP
ejpam-4299	224	17	respect	respect	NOUN
ejpam-4299	224	18	to	to	ADP
ejpam-4299	224	19	t	t	PROPN
ejpam-4299	224	20	as	as	ADP
ejpam-4299	224	21	(	(	PUNCT
ejpam-4299	224	22	y(q	y(q	PROPN
ejpam-4299	224	23	)	)	PUNCT
ejpam-4299	224	24	)	)	PUNCT
ejpam-4299	225	1	α	α	X
ejpam-4299	226	1	i	i	PRON
ejpam-4299	226	2	,	,	PUNCT
ejpam-4299	226	3	i	i	PRON
ejpam-4299	226	4	=	=	NOUN
ejpam-4299	226	5	1	1	NUM
ejpam-4299	226	6	,	,	PUNCT
ejpam-4299	226	7	2	2	NUM
ejpam-4299	226	8	and	and	CCONJ
ejpam-4299	226	9	q	q	ADJ
ejpam-4299	226	10	∈	∈	PROPN
ejpam-4299	226	11	(	(	PUNCT
ejpam-4299	226	12	0	0	NUM
ejpam-4299	226	13	,	,	PUNCT
ejpam-4299	226	14	1	1	NUM
ejpam-4299	226	15	]	]	PUNCT
ejpam-4299	226	16	.	.	PUNCT
ejpam-4299	227	1	let	let	VERB
ejpam-4299	227	2	γ(t	γ(t	NOUN
ejpam-4299	227	3	,	,	PUNCT
ejpam-4299	227	4	α	α	X
ejpam-4299	227	5	)	)	PUNCT
ejpam-4299	227	6	=	=	PUNCT
ejpam-4299	228	1	[	[	X
ejpam-4299	228	2	(	(	PUNCT
ejpam-4299	228	3	y(q	y(q	PROPN
ejpam-4299	228	4	)	)	PUNCT
ejpam-4299	228	5	)	)	PUNCT
ejpam-4299	229	1	α	α	X
ejpam-4299	229	2	1	1	NUM
ejpam-4299	229	3	(	(	PUNCT
ejpam-4299	229	4	t	t	PROPN
ejpam-4299	229	5	)	)	PUNCT
ejpam-4299	229	6	,	,	PUNCT
ejpam-4299	229	7	(	(	PUNCT
ejpam-4299	229	8	y(q	y(q	PROPN
ejpam-4299	229	9	)	)	PUNCT
ejpam-4299	229	10	)	)	PUNCT
ejpam-4299	230	1	α	α	X
ejpam-4299	230	2	2	2	NUM
ejpam-4299	230	3	(	(	PUNCT
ejpam-4299	230	4	t	t	PROPN
ejpam-4299	230	5	)	)	PUNCT
ejpam-4299	230	6	]	]	PUNCT
ejpam-4299	230	7	(	(	PUNCT
ejpam-4299	230	8	16	16	NUM
ejpam-4299	230	9	)	)	PUNCT
ejpam-4299	230	10	for	for	ADP
ejpam-4299	230	11	t	t	PROPN
ejpam-4299	230	12	∈	∈	PROPN
ejpam-4299	230	13	(	(	PUNCT
ejpam-4299	230	14	0	0	NUM
ejpam-4299	230	15	,	,	PUNCT
ejpam-4299	230	16	a	a	NOUN
ejpam-4299	230	17	)	)	PUNCT
ejpam-4299	230	18	,	,	PUNCT
ejpam-4299	230	19	α	α	PROPN
ejpam-4299	230	20	∈	∈	PROPN
ejpam-4299	231	1	[	[	X
ejpam-4299	231	2	0	0	NUM
ejpam-4299	231	3	,	,	PUNCT
ejpam-4299	231	4	1	1	NUM
ejpam-4299	231	5	]	]	PUNCT
ejpam-4299	231	6	and	and	CCONJ
ejpam-4299	231	7	for	for	ADP
ejpam-4299	231	8	q	q	PROPN
ejpam-4299	231	9	∈	∈	PROPN
ejpam-4299	231	10	(	(	PUNCT
ejpam-4299	231	11	0	0	NUM
ejpam-4299	231	12	,	,	PUNCT
ejpam-4299	231	13	1	1	NUM
ejpam-4299	231	14	]	]	PUNCT
ejpam-4299	231	15	.	.	PUNCT
ejpam-4299	232	1	if	if	SCONJ
ejpam-4299	232	2	γ(t	γ(t	NOUN
ejpam-4299	232	3	,	,	PUNCT
ejpam-4299	232	4	α	α	X
ejpam-4299	232	5	)	)	PUNCT
ejpam-4299	232	6	defines	define	VERB
ejpam-4299	232	7	the	the	DET
ejpam-4299	232	8	α	α	NOUN
ejpam-4299	232	9	-	-	PUNCT
ejpam-4299	232	10	cuts	cut	NOUN
ejpam-4299	232	11	of	of	ADP
ejpam-4299	232	12	a	a	DET
ejpam-4299	232	13	fuzzy	fuzzy	ADJ
ejpam-4299	232	14	number	number	NOUN
ejpam-4299	232	15	for	for	ADP
ejpam-4299	232	16	each	each	DET
ejpam-4299	232	17	t	t	NOUN
ejpam-4299	232	18	∈	∈	PROPN
ejpam-4299	232	19	(	(	PUNCT
ejpam-4299	232	20	0	0	NUM
ejpam-4299	232	21	,	,	PUNCT
ejpam-4299	232	22	a	a	X
ejpam-4299	232	23	)	)	PUNCT
ejpam-4299	232	24	we	we	PRON
ejpam-4299	232	25	will	will	AUX
ejpam-4299	232	26	say	say	VERB
ejpam-4299	232	27	that	that	SCONJ
ejpam-4299	232	28	ȳ	ȳ	PROPN
ejpam-4299	232	29	,	,	PUNCT
ejpam-4299	232	30	is	be	AUX
ejpam-4299	232	31	q	q	ADJ
ejpam-4299	232	32	-	-	ADV
ejpam-4299	232	33	differentiable	differentiable	ADJ
ejpam-4299	232	34	and	and	CCONJ
ejpam-4299	232	35	write	write	VERB
ejpam-4299	232	36	[	[	PUNCT
ejpam-4299	232	37	ȳ	ȳ	PROPN
ejpam-4299	232	38	(	(	PUNCT
ejpam-4299	232	39	q)(t	q)(t	PROPN
ejpam-4299	232	40	)	)	PUNCT
ejpam-4299	232	41	]	]	PUNCT
ejpam-4299	232	42	α	α	X
ejpam-4299	232	43	=	=	PUNCT
ejpam-4299	232	44	γ(t	γ(t	NOUN
ejpam-4299	232	45	,	,	PUNCT
ejpam-4299	232	46	α	α	X
ejpam-4299	232	47	)	)	PUNCT
ejpam-4299	232	48	=	=	PUNCT
ejpam-4299	233	1	[	[	X
ejpam-4299	233	2	(	(	PUNCT
ejpam-4299	233	3	y(q	y(q	PROPN
ejpam-4299	233	4	)	)	PUNCT
ejpam-4299	233	5	)	)	PUNCT
ejpam-4299	234	1	α	α	X
ejpam-4299	234	2	1	1	NUM
ejpam-4299	234	3	(	(	PUNCT
ejpam-4299	234	4	t	t	PROPN
ejpam-4299	234	5	)	)	PUNCT
ejpam-4299	234	6	,	,	PUNCT
ejpam-4299	234	7	(	(	PUNCT
ejpam-4299	234	8	y(q	y(q	PROPN
ejpam-4299	234	9	)	)	PUNCT
ejpam-4299	234	10	)	)	PUNCT
ejpam-4299	235	1	α	α	X
ejpam-4299	235	2	2	2	NUM
ejpam-4299	235	3	(	(	PUNCT
ejpam-4299	235	4	t	t	PROPN
ejpam-4299	235	5	)	)	PUNCT
ejpam-4299	235	6	]	]	PUNCT
ejpam-4299	235	7	(	(	PUNCT
ejpam-4299	235	8	17	17	NUM
ejpam-4299	235	9	)	)	PUNCT
ejpam-4299	235	10	for	for	ADP
ejpam-4299	235	11	all	all	DET
ejpam-4299	235	12	t	t	NOUN
ejpam-4299	235	13	∈	∈	PROPN
ejpam-4299	235	14	(	(	PUNCT
ejpam-4299	235	15	0	0	NUM
ejpam-4299	235	16	,	,	PUNCT
ejpam-4299	235	17	a	a	NOUN
ejpam-4299	235	18	)	)	PUNCT
ejpam-4299	235	19	,	,	PUNCT
ejpam-4299	235	20	α	α	PROPN
ejpam-4299	235	21	∈	∈	PROPN
ejpam-4299	236	1	[	[	X
ejpam-4299	236	2	0	0	NUM
ejpam-4299	236	3	,	,	PUNCT
ejpam-4299	236	4	1	1	NUM
ejpam-4299	236	5	]	]	PUNCT
ejpam-4299	236	6	and	and	CCONJ
ejpam-4299	236	7	for	for	ADP
ejpam-4299	236	8	q	q	PROPN
ejpam-4299	236	9	∈	∈	PROPN
ejpam-4299	236	10	(	(	PUNCT
ejpam-4299	236	11	0	0	NUM
ejpam-4299	236	12	,	,	PUNCT
ejpam-4299	236	13	1	1	NUM
ejpam-4299	236	14	]	]	PUNCT
ejpam-4299	236	15	.	.	PUNCT
ejpam-4299	237	1	notice	notice	NOUN
ejpam-4299	237	2	,	,	PUNCT
ejpam-4299	237	3	that	that	SCONJ
ejpam-4299	237	4	eq	eq	NOUN
ejpam-4299	237	5	(	(	PUNCT
ejpam-4299	237	6	17	17	NUM
ejpam-4299	237	7	)	)	PUNCT
ejpam-4299	237	8	is	be	AUX
ejpam-4299	237	9	just	just	ADV
ejpam-4299	237	10	the	the	DET
ejpam-4299	237	11	conformable	conformable	ADJ
ejpam-4299	237	12	derivative	derivative	NOUN
ejpam-4299	237	13	(	(	PUNCT
ejpam-4299	237	14	with	with	ADP
ejpam-4299	237	15	respect	respect	NOUN
ejpam-4299	237	16	to	to	ADP
ejpam-4299	237	17	t	t	PROPN
ejpam-4299	237	18	)	)	PUNCT
ejpam-4299	237	19	of	of	ADP
ejpam-4299	237	20	eq	eq	NOUN
ejpam-4299	237	21	(	(	PUNCT
ejpam-4299	237	22	6	6	NUM
ejpam-4299	237	23	)	)	PUNCT
ejpam-4299	237	24	.	.	PUNCT
ejpam-4299	238	1	so	so	ADV
ejpam-4299	238	2	,	,	PUNCT
ejpam-4299	238	3	eq	eq	X
ejpam-4299	238	4	(	(	PUNCT
ejpam-4299	238	5	17	17	NUM
ejpam-4299	238	6	)	)	PUNCT
ejpam-4299	238	7	could	could	AUX
ejpam-4299	238	8	be	be	AUX
ejpam-4299	238	9	written	write	VERB
ejpam-4299	238	10	[	[	PUNCT
ejpam-4299	238	11	ȳ	ȳ	PROPN
ejpam-4299	238	12	(	(	PUNCT
ejpam-4299	238	13	q)(t	q)(t	PROPN
ejpam-4299	238	14	)	)	PUNCT
ejpam-4299	238	15	]	]	X
ejpam-4299	238	16	α	α	X
ejpam-4299	238	17	.	.	PUNCT
ejpam-4299	239	1	sufficient	sufficient	ADJ
ejpam-4299	239	2	conditions	condition	NOUN
ejpam-4299	239	3	for	for	ADP
ejpam-4299	239	4	γ(t	γ(t	NOUN
ejpam-4299	239	5	,	,	PUNCT
ejpam-4299	239	6	α	α	NOUN
ejpam-4299	239	7	)	)	PUNCT
ejpam-4299	239	8	to	to	PART
ejpam-4299	239	9	define	define	VERB
ejpam-4299	239	10	the	the	DET
ejpam-4299	239	11	α	α	NOUN
ejpam-4299	239	12	-	-	PUNCT
ejpam-4299	239	13	cuts	cut	NOUN
ejpam-4299	239	14	of	of	ADP
ejpam-4299	239	15	a	a	DET
ejpam-4299	239	16	fuzzy	fuzzy	ADJ
ejpam-4299	239	17	number	number	NOUN
ejpam-4299	239	18	are	be	AUX
ejpam-4299	239	19	:	:	PUNCT
ejpam-4299	239	20	(	(	PUNCT
ejpam-4299	239	21	see	see	VERB
ejpam-4299	239	22	[	[	X
ejpam-4299	239	23	6	6	NUM
ejpam-4299	239	24	,	,	PUNCT
ejpam-4299	239	25	9	9	NUM
ejpam-4299	239	26	,	,	PUNCT
ejpam-4299	239	27	11	11	NUM
ejpam-4299	239	28	]	]	PUNCT
ejpam-4299	239	29	)	)	PUNCT
ejpam-4299	239	30	a.	a.	NOUN
ejpam-4299	239	31	harir	harir	PROPN
ejpam-4299	239	32	,	,	PUNCT
ejpam-4299	239	33	s.	s.	PROPN
ejpam-4299	239	34	melliani	melliani	PROPN
ejpam-4299	239	35	,	,	PUNCT
ejpam-4299	239	36	l.	l.	PROPN
ejpam-4299	239	37	s.	s.	PROPN
ejpam-4299	239	38	chadli	chadli	PROPN
ejpam-4299	239	39	/	/	SYM
ejpam-4299	239	40	eur	eur	PROPN
ejpam-4299	239	41	.	.	PUNCT
ejpam-4299	240	1	j.	j.	PROPN
ejpam-4299	240	2	pure	pure	PROPN
ejpam-4299	240	3	appl	appl	PROPN
ejpam-4299	240	4	.	.	PROPN
ejpam-4299	240	5	math	math	PROPN
ejpam-4299	240	6	,	,	PUNCT
ejpam-4299	240	7	15	15	NUM
ejpam-4299	240	8	(	(	PUNCT
ejpam-4299	240	9	2	2	NUM
ejpam-4299	240	10	)	)	PUNCT
ejpam-4299	240	11	(	(	PUNCT
ejpam-4299	240	12	2022	2022	NUM
ejpam-4299	240	13	)	)	PUNCT
ejpam-4299	240	14	,	,	PUNCT
ejpam-4299	240	15	557	557	NUM
ejpam-4299	240	16	-	-	SYM
ejpam-4299	240	17	571	571	NUM
ejpam-4299	240	18	565	565	NUM
ejpam-4299	240	19	(	(	PUNCT
ejpam-4299	240	20	i	i	NOUN
ejpam-4299	240	21	)	)	PUNCT
ejpam-4299	240	22	(	(	PUNCT
ejpam-4299	240	23	y(q	y(q	PROPN
ejpam-4299	240	24	)	)	PUNCT
ejpam-4299	240	25	)	)	PUNCT
ejpam-4299	241	1	α	α	PRON
ejpam-4299	241	2	1	1	NUM
ejpam-4299	241	3	and	and	CCONJ
ejpam-4299	241	4	(	(	PUNCT
ejpam-4299	241	5	y(q	y(q	PROPN
ejpam-4299	241	6	)	)	PUNCT
ejpam-4299	241	7	)	)	PUNCT
ejpam-4299	242	1	α	α	PROPN
ejpam-4299	242	2	2	2	NUM
ejpam-4299	242	3	are	be	AUX
ejpam-4299	242	4	continuous	continuous	ADJ
ejpam-4299	242	5	on	on	ADP
ejpam-4299	242	6	(	(	PUNCT
ejpam-4299	242	7	0	0	NUM
ejpam-4299	242	8	,	,	PUNCT
ejpam-4299	242	9	a)×	a)×	PRON
ejpam-4299	242	10	[	[	X
ejpam-4299	242	11	0	0	NUM
ejpam-4299	242	12	,	,	PUNCT
ejpam-4299	242	13	1	1	NUM
ejpam-4299	242	14	]	]	PUNCT
ejpam-4299	242	15	and	and	CCONJ
ejpam-4299	242	16	for	for	ADP
ejpam-4299	242	17	q	q	PROPN
ejpam-4299	242	18	∈	∈	PROPN
ejpam-4299	242	19	(	(	PUNCT
ejpam-4299	242	20	0	0	NUM
ejpam-4299	242	21	,	,	PUNCT
ejpam-4299	242	22	1	1	NUM
ejpam-4299	242	23	]	]	PUNCT
ejpam-4299	242	24	(	(	PUNCT
ejpam-4299	242	25	ii	ii	NOUN
ejpam-4299	242	26	)	)	PUNCT
ejpam-4299	242	27	(	(	PUNCT
ejpam-4299	242	28	y(q	y(q	PROPN
ejpam-4299	242	29	)	)	PUNCT
ejpam-4299	242	30	)	)	PUNCT
ejpam-4299	243	1	α	α	PROPN
ejpam-4299	243	2	1	1	NUM
ejpam-4299	243	3	is	be	AUX
ejpam-4299	243	4	an	an	DET
ejpam-4299	243	5	increasing	increase	VERB
ejpam-4299	243	6	function	function	NOUN
ejpam-4299	243	7	of	of	ADP
ejpam-4299	243	8	α	α	NOUN
ejpam-4299	243	9	for	for	ADP
ejpam-4299	243	10	each	each	DET
ejpam-4299	243	11	t	t	NOUN
ejpam-4299	243	12	∈	∈	PROPN
ejpam-4299	243	13	(	(	PUNCT
ejpam-4299	243	14	0	0	NUM
ejpam-4299	243	15	,	,	PUNCT
ejpam-4299	243	16	a	a	PRON
ejpam-4299	243	17	)	)	PUNCT
ejpam-4299	243	18	and	and	CCONJ
ejpam-4299	243	19	for	for	ADP
ejpam-4299	243	20	q	q	PROPN
ejpam-4299	243	21	∈	∈	PROPN
ejpam-4299	243	22	(	(	PUNCT
ejpam-4299	243	23	0	0	NUM
ejpam-4299	243	24	,	,	PUNCT
ejpam-4299	243	25	1	1	NUM
ejpam-4299	243	26	]	]	PUNCT
ejpam-4299	243	27	(	(	PUNCT
ejpam-4299	243	28	iii	iii	NOUN
ejpam-4299	243	29	)	)	PUNCT
ejpam-4299	243	30	(	(	PUNCT
ejpam-4299	243	31	y(q	y(q	PROPN
ejpam-4299	243	32	)	)	PUNCT
ejpam-4299	243	33	)	)	PUNCT
ejpam-4299	244	1	α	α	DET
ejpam-4299	244	2	2	2	NUM
ejpam-4299	244	3	is	be	AUX
ejpam-4299	244	4	a	a	DET
ejpam-4299	244	5	decreasing	decrease	VERB
ejpam-4299	244	6	function	function	NOUN
ejpam-4299	244	7	of	of	ADP
ejpam-4299	244	8	α	α	NOUN
ejpam-4299	244	9	for	for	ADP
ejpam-4299	244	10	each	each	DET
ejpam-4299	244	11	t	t	NOUN
ejpam-4299	244	12	∈	∈	PROPN
ejpam-4299	244	13	(	(	PUNCT
ejpam-4299	244	14	0	0	NUM
ejpam-4299	244	15	,	,	PUNCT
ejpam-4299	244	16	a	a	PRON
ejpam-4299	244	17	)	)	PUNCT
ejpam-4299	244	18	and	and	CCONJ
ejpam-4299	244	19	for	for	ADP
ejpam-4299	244	20	q	q	PROPN
ejpam-4299	244	21	∈	∈	PROPN
ejpam-4299	244	22	(	(	PUNCT
ejpam-4299	244	23	0	0	NUM
ejpam-4299	244	24	,	,	PUNCT
ejpam-4299	244	25	1	1	NUM
ejpam-4299	244	26	]	]	PUNCT
ejpam-4299	244	27	(	(	PUNCT
ejpam-4299	244	28	iv	iv	X
ejpam-4299	244	29	)	)	PUNCT
ejpam-4299	244	30	(	(	PUNCT
ejpam-4299	244	31	y(q	y(q	PROPN
ejpam-4299	244	32	)	)	PUNCT
ejpam-4299	244	33	)	)	PUNCT
ejpam-4299	244	34	α	α	PROPN
ejpam-4299	244	35	1	1	NUM
ejpam-4299	244	36	≤	≤	NOUN
ejpam-4299	244	37	(	(	PUNCT
ejpam-4299	244	38	y(q	y(q	PROPN
ejpam-4299	244	39	)	)	PUNCT
ejpam-4299	244	40	)	)	PUNCT
ejpam-4299	245	1	α	α	PRON
ejpam-4299	245	2	2	2	NUM
ejpam-4299	245	3	all	all	PRON
ejpam-4299	245	4	t	t	NOUN
ejpam-4299	245	5	∈	∈	PROPN
ejpam-4299	245	6	(	(	PUNCT
ejpam-4299	245	7	0	0	NUM
ejpam-4299	245	8	,	,	PUNCT
ejpam-4299	245	9	a	a	PRON
ejpam-4299	245	10	)	)	PUNCT
ejpam-4299	245	11	and	and	CCONJ
ejpam-4299	245	12	q	q	ADJ
ejpam-4299	245	13	∈	∈	PROPN
ejpam-4299	245	14	(	(	PUNCT
ejpam-4299	245	15	0	0	NUM
ejpam-4299	245	16	,	,	PUNCT
ejpam-4299	245	17	1	1	NUM
ejpam-4299	245	18	]	]	PUNCT
ejpam-4299	245	19	hence	hence	ADV
ejpam-4299	245	20	,	,	PUNCT
ejpam-4299	245	21	if	if	SCONJ
ejpam-4299	245	22	conditions	condition	NOUN
ejpam-4299	245	23	(	(	PUNCT
ejpam-4299	245	24	i)−	i)−	PROPN
ejpam-4299	245	25	(	(	PUNCT
ejpam-4299	245	26	iv	iv	NOUN
ejpam-4299	245	27	)	)	PUNCT
ejpam-4299	245	28	above	above	ADP
ejpam-4299	245	29	hold	hold	NOUN
ejpam-4299	245	30	,	,	PUNCT
ejpam-4299	245	31	ȳ	ȳ	PROPN
ejpam-4299	245	32	(	(	PUNCT
ejpam-4299	245	33	t	t	PROPN
ejpam-4299	245	34	)	)	PUNCT
ejpam-4299	245	35	is	be	AUX
ejpam-4299	245	36	q	q	ADJ
ejpam-4299	246	1	-	-	ADV
ejpam-4299	246	2	differentiable	differentiable	ADJ
ejpam-4299	246	3	.	.	PUNCT
ejpam-4299	247	1	ȳ	ȳ	PROPN
ejpam-4299	247	2	(	(	PUNCT
ejpam-4299	247	3	q)(t	q)(t	PROPN
ejpam-4299	247	4	)	)	PUNCT
ejpam-4299	247	5	,	,	PUNCT
ejpam-4299	247	6	∀q	∀q	PROPN
ejpam-4299	247	7	∈	∈	PROPN
ejpam-4299	247	8	(	(	PUNCT
ejpam-4299	247	9	0	0	NUM
ejpam-4299	247	10	,	,	PUNCT
ejpam-4299	247	11	1	1	NUM
ejpam-4299	247	12	]	]	PUNCT
ejpam-4299	247	13	will	will	AUX
ejpam-4299	247	14	be	be	AUX
ejpam-4299	247	15	a	a	DET
ejpam-4299	247	16	solution	solution	NOUN
ejpam-4299	247	17	to	to	ADP
ejpam-4299	247	18	eq	eq	NOUN
ejpam-4299	247	19	(	(	PUNCT
ejpam-4299	247	20	4	4	NUM
ejpam-4299	247	21	)	)	PUNCT
ejpam-4299	247	22	if	if	SCONJ
ejpam-4299	247	23	,	,	PUNCT
ejpam-4299	247	24	(	(	PUNCT
ejpam-4299	247	25	a	a	X
ejpam-4299	247	26	)	)	PUNCT
ejpam-4299	247	27	ȳ	ȳ	PROPN
ejpam-4299	247	28	(	(	PUNCT
ejpam-4299	247	29	q)(t	q)(t	PROPN
ejpam-4299	247	30	)	)	PUNCT
ejpam-4299	247	31	,	,	PUNCT
ejpam-4299	247	32	∀q	∀q	PROPN
ejpam-4299	247	33	∈	∈	PROPN
ejpam-4299	247	34	(	(	PUNCT
ejpam-4299	247	35	0	0	NUM
ejpam-4299	247	36	,	,	PUNCT
ejpam-4299	247	37	1	1	NUM
ejpam-4299	247	38	]	]	PUNCT
ejpam-4299	247	39	is	be	AUX
ejpam-4299	247	40	q	q	ADJ
ejpam-4299	247	41	-	-	ADJ
ejpam-4299	247	42	differentiable	differentiable	ADJ
ejpam-4299	247	43	;	;	PUNCT
ejpam-4299	247	44	(	(	PUNCT
ejpam-4299	247	45	b	b	X
ejpam-4299	247	46	)	)	PUNCT
ejpam-4299	247	47	(	(	PUNCT
ejpam-4299	247	48	4	4	X
ejpam-4299	247	49	)	)	PUNCT
ejpam-4299	247	50	holds	hold	VERB
ejpam-4299	247	51	for	for	ADP
ejpam-4299	247	52	ȳ	ȳ	PROPN
ejpam-4299	247	53	(	(	PUNCT
ejpam-4299	247	54	t	t	PROPN
ejpam-4299	247	55	)	)	PUNCT
ejpam-4299	247	56	=	=	SYM
ejpam-4299	248	1	ḡ(t	ḡ(t	ADJ
ejpam-4299	248	2	,	,	PUNCT
ejpam-4299	248	3	k̄	k̄	X
ejpam-4299	248	4	,	,	PUNCT
ejpam-4299	248	5	c̄	c̄	PROPN
ejpam-4299	248	6	)	)	PUNCT
ejpam-4299	248	7	;	;	PUNCT
ejpam-4299	248	8	(	(	PUNCT
ejpam-4299	248	9	c	c	X
ejpam-4299	248	10	)	)	PUNCT
ejpam-4299	248	11	ȳ	ȳ	PROPN
ejpam-4299	248	12	(	(	PUNCT
ejpam-4299	248	13	q)(t	q)(t	PROPN
ejpam-4299	248	14	)	)	PUNCT
ejpam-4299	248	15	,	,	PUNCT
ejpam-4299	248	16	∀q	∀q	PROPN
ejpam-4299	248	17	∈	∈	PROPN
ejpam-4299	248	18	(	(	PUNCT
ejpam-4299	248	19	0	0	NUM
ejpam-4299	248	20	,	,	PUNCT
ejpam-4299	248	21	1	1	NUM
ejpam-4299	248	22	]	]	PUNCT
ejpam-4299	248	23	satisfies	satisfy	VERB
ejpam-4299	248	24	the	the	DET
ejpam-4299	248	25	initial	initial	ADJ
ejpam-4299	248	26	and	and	CCONJ
ejpam-4299	248	27	boundary	boundary	ADJ
ejpam-4299	248	28	conditions	condition	NOUN
ejpam-4299	248	29	.	.	PUNCT
ejpam-4299	249	1	since	since	SCONJ
ejpam-4299	249	2	there	there	PRON
ejpam-4299	249	3	is	be	VERB
ejpam-4299	249	4	no	no	DET
ejpam-4299	249	5	specified	specify	VERB
ejpam-4299	249	6	particular	particular	ADJ
ejpam-4299	249	7	initial	initial	ADJ
ejpam-4299	249	8	and	and	CCONJ
ejpam-4299	249	9	boundary	boundary	ADJ
ejpam-4299	249	10	conditions	condition	NOUN
ejpam-4299	249	11	,	,	PUNCT
ejpam-4299	249	12	then	then	ADV
ejpam-4299	249	13	only	only	ADV
ejpam-4299	249	14	is	be	AUX
ejpam-4299	249	15	checked	check	VERB
ejpam-4299	249	16	if	if	SCONJ
ejpam-4299	249	17	(	(	PUNCT
ejpam-4299	249	18	4	4	X
ejpam-4299	249	19	)	)	PUNCT
ejpam-4299	249	20	holds	hold	VERB
ejpam-4299	249	21	.	.	PUNCT
ejpam-4299	250	1	we	we	PRON
ejpam-4299	250	2	will	will	AUX
ejpam-4299	250	3	say	say	VERB
ejpam-4299	250	4	that	that	SCONJ
ejpam-4299	250	5	ȳ	ȳ	PROPN
ejpam-4299	250	6	(	(	PUNCT
ejpam-4299	250	7	t	t	PROPN
ejpam-4299	250	8	)	)	PUNCT
ejpam-4299	250	9	is	be	AUX
ejpam-4299	250	10	a	a	DET
ejpam-4299	250	11	solution	solution	NOUN
ejpam-4299	250	12	(	(	PUNCT
ejpam-4299	250	13	without	without	ADP
ejpam-4299	250	14	the	the	DET
ejpam-4299	250	15	initial	initial	ADJ
ejpam-4299	250	16	and	and	CCONJ
ejpam-4299	250	17	boundary	boundary	ADJ
ejpam-4299	250	18	conditions	condition	NOUN
ejpam-4299	250	19	)	)	PUNCT
ejpam-4299	250	20	if	if	SCONJ
ejpam-4299	250	21	ȳ	ȳ	PROPN
ejpam-4299	250	22	(	(	PUNCT
ejpam-4299	250	23	q)(t	q)(t	PROPN
ejpam-4299	250	24	)	)	PUNCT
ejpam-4299	250	25	exists	exist	VERB
ejpam-4299	250	26	and	and	CCONJ
ejpam-4299	250	27	ȳ	ȳ	PROPN
ejpam-4299	250	28	(	(	PUNCT
ejpam-4299	250	29	q)(t	q)(t	PROPN
ejpam-4299	250	30	)	)	PUNCT
ejpam-4299	250	31	=	=	SYM
ejpam-4299	250	32	f̄	f̄	PROPN
ejpam-4299	250	33	(	(	PUNCT
ejpam-4299	250	34	t	t	PROPN
ejpam-4299	250	35	)	)	PUNCT
ejpam-4299	250	36	,	,	PUNCT
ejpam-4299	250	37	∀q	∀q	PROPN
ejpam-4299	250	38	∈	∈	PROPN
ejpam-4299	250	39	(	(	PUNCT
ejpam-4299	250	40	0	0	NUM
ejpam-4299	250	41	,	,	PUNCT
ejpam-4299	250	42	1	1	NUM
ejpam-4299	250	43	]	]	PUNCT
ejpam-4299	250	44	or	or	CCONJ
ejpam-4299	250	45	the	the	DET
ejpam-4299	250	46	following	follow	VERB
ejpam-4299	250	47	equations	equation	NOUN
ejpam-4299	250	48	must	must	AUX
ejpam-4299	250	49	hold	hold	VERB
ejpam-4299	250	50	(	(	PUNCT
ejpam-4299	250	51	y(q	y(q	PROPN
ejpam-4299	250	52	)	)	PUNCT
ejpam-4299	250	53	)	)	PUNCT
ejpam-4299	251	1	α	α	X
ejpam-4299	251	2	1	1	NUM
ejpam-4299	251	3	(	(	PUNCT
ejpam-4299	251	4	t	t	NOUN
ejpam-4299	251	5	)	)	PUNCT
ejpam-4299	251	6	=	=	NOUN
ejpam-4299	251	7	fα	fα	ADP
ejpam-4299	251	8	1	1	NUM
ejpam-4299	251	9	(	(	PUNCT
ejpam-4299	251	10	t	t	NOUN
ejpam-4299	251	11	)	)	PUNCT
ejpam-4299	251	12	,	,	PUNCT
ejpam-4299	251	13	(	(	PUNCT
ejpam-4299	251	14	18	18	NUM
ejpam-4299	251	15	)	)	PUNCT
ejpam-4299	251	16	(	(	PUNCT
ejpam-4299	251	17	y(q	y(q	PROPN
ejpam-4299	251	18	)	)	PUNCT
ejpam-4299	251	19	)	)	PUNCT
ejpam-4299	252	1	α	α	X
ejpam-4299	252	2	2	2	NUM
ejpam-4299	252	3	(	(	PUNCT
ejpam-4299	252	4	t	t	NOUN
ejpam-4299	252	5	)	)	PUNCT
ejpam-4299	252	6	=	=	NOUN
ejpam-4299	252	7	fα	fα	ADP
ejpam-4299	252	8	2	2	NUM
ejpam-4299	252	9	(	(	PUNCT
ejpam-4299	252	10	t	t	PROPN
ejpam-4299	252	11	)	)	PUNCT
ejpam-4299	252	12	,	,	PUNCT
ejpam-4299	252	13	(	(	PUNCT
ejpam-4299	252	14	19	19	NUM
ejpam-4299	252	15	)	)	PUNCT
ejpam-4299	252	16	for	for	ADP
ejpam-4299	252	17	all	all	DET
ejpam-4299	252	18	t	t	NOUN
ejpam-4299	252	19	∈	∈	PROPN
ejpam-4299	252	20	(	(	PUNCT
ejpam-4299	252	21	0	0	NUM
ejpam-4299	252	22	,	,	PUNCT
ejpam-4299	252	23	a	a	PRON
ejpam-4299	252	24	)	)	PUNCT
ejpam-4299	252	25	,	,	PUNCT
ejpam-4299	252	26	q	q	PROPN
ejpam-4299	252	27	∈	∈	PROPN
ejpam-4299	252	28	(	(	PUNCT
ejpam-4299	252	29	0	0	NUM
ejpam-4299	252	30	,	,	PUNCT
ejpam-4299	252	31	1	1	NUM
ejpam-4299	252	32	]	]	PUNCT
ejpam-4299	252	33	and	and	CCONJ
ejpam-4299	252	34	all	all	DET
ejpam-4299	252	35	α	α	NOUN
ejpam-4299	252	36	∈	∈	PROPN
ejpam-4299	253	1	[	[	X
ejpam-4299	253	2	0	0	NUM
ejpam-4299	253	3	,	,	PUNCT
ejpam-4299	253	4	1	1	NUM
ejpam-4299	253	5	]	]	PUNCT
ejpam-4299	253	6	.	.	PUNCT
ejpam-4299	254	1	we	we	PRON
ejpam-4299	254	2	have	have	VERB
ejpam-4299	254	3	the	the	DET
ejpam-4299	254	4	following	follow	VERB
ejpam-4299	254	5	results	result	NOUN
ejpam-4299	254	6	regarding	regard	VERB
ejpam-4299	254	7	bf	bf	NOUN
ejpam-4299	254	8	-	-	PUNCT
ejpam-4299	254	9	solution	solution	NOUN
ejpam-4299	254	10	=	=	SYM
ejpam-4299	254	11	ȳ	ȳ	PROPN
ejpam-4299	254	12	(	(	PUNCT
ejpam-4299	254	13	t	t	PROPN
ejpam-4299	254	14	)	)	PUNCT
ejpam-4299	254	15	.	.	PUNCT
ejpam-4299	255	1	theorem	theorem	ADJ
ejpam-4299	255	2	6	6	NUM
ejpam-4299	255	3	.	.	PUNCT
ejpam-4299	256	1	assume	assume	VERB
ejpam-4299	256	2	ȳ	ȳ	PROPN
ejpam-4299	256	3	(	(	PUNCT
ejpam-4299	256	4	q)(t	q)(t	PROPN
ejpam-4299	256	5	)	)	PUNCT
ejpam-4299	256	6	,	,	PUNCT
ejpam-4299	256	7	for	for	SCONJ
ejpam-4299	256	8	all	all	DET
ejpam-4299	256	9	q	q	PROPN
ejpam-4299	256	10	∈	∈	PROPN
ejpam-4299	256	11	(	(	PUNCT
ejpam-4299	256	12	0	0	NUM
ejpam-4299	256	13	,	,	PUNCT
ejpam-4299	256	14	1	1	NUM
ejpam-4299	256	15	]	]	PUNCT
ejpam-4299	256	16	is	be	AUX
ejpam-4299	256	17	q	q	NOUN
ejpam-4299	256	18	-	-	NOUN
ejpam-4299	256	19	differentiable	differentiable	ADJ
ejpam-4299	256	20	for	for	ADP
ejpam-4299	256	21	t	t	PROPN
ejpam-4299	256	22	∈	∈	PROPN
ejpam-4299	256	23	(	(	PUNCT
ejpam-4299	256	24	0	0	NUM
ejpam-4299	256	25	,	,	PUNCT
ejpam-4299	256	26	a	a	DET
ejpam-4299	256	27	)	)	PUNCT
ejpam-4299	256	28	.	.	PUNCT
ejpam-4299	257	1	then	then	ADV
ejpam-4299	257	2	if	if	SCONJ
ejpam-4299	257	3	(	(	PUNCT
ejpam-4299	257	4	a	a	X
ejpam-4299	257	5	)	)	PUNCT
ejpam-4299	257	6	∂f	∂f	PROPN
ejpam-4299	257	7	∂y	∂y	SYM
ejpam-4299	257	8	>	>	X
ejpam-4299	257	9	0	0	PROPN
ejpam-4299	257	10	,	,	PUNCT
ejpam-4299	257	11	∂g	∂g	PROPN
ejpam-4299	257	12	∂c	∂c	PROPN
ejpam-4299	257	13	>	>	X
ejpam-4299	257	14	0	0	PUNCT
ejpam-4299	258	1	(	(	PUNCT
ejpam-4299	258	2	20	20	NUM
ejpam-4299	258	3	)	)	PUNCT
ejpam-4299	258	4	and	and	CCONJ
ejpam-4299	258	5	(	(	PUNCT
ejpam-4299	258	6	∂f	∂f	PROPN
ejpam-4299	258	7	∂kj	∂kj	NOUN
ejpam-4299	258	8	)	)	PUNCT
ejpam-4299	258	9	(	(	PUNCT
ejpam-4299	258	10	∂g	∂g	PROPN
ejpam-4299	258	11	∂kj	∂kj	PROPN
ejpam-4299	258	12	)	)	PUNCT
ejpam-4299	258	13	>	>	X
ejpam-4299	259	1	0	0	NUM
ejpam-4299	259	2	,	,	PUNCT
ejpam-4299	259	3	j	j	PROPN
ejpam-4299	259	4	=	=	SYM
ejpam-4299	259	5	1	1	NUM
ejpam-4299	259	6	,	,	PUNCT
ejpam-4299	259	7	.	.	PUNCT
ejpam-4299	259	8	.	.	PUNCT
ejpam-4299	260	1	.	.	PUNCT
ejpam-4299	261	1	,	,	PUNCT
ejpam-4299	261	2	n	n	X
ejpam-4299	261	3	(	(	PUNCT
ejpam-4299	261	4	21	21	NUM
ejpam-4299	261	5	)	)	PUNCT
ejpam-4299	261	6	then	then	ADV
ejpam-4299	261	7	ȳ	ȳ	PROPN
ejpam-4299	261	8	(	(	PUNCT
ejpam-4299	261	9	t	t	PROPN
ejpam-4299	261	10	)	)	PUNCT
ejpam-4299	261	11	is	be	AUX
ejpam-4299	261	12	a	a	DET
ejpam-4299	261	13	bf	bf	NOUN
ejpam-4299	261	14	-	-	PUNCT
ejpam-4299	261	15	solution	solution	NOUN
ejpam-4299	261	16	.	.	PUNCT
ejpam-4299	262	1	(	(	PUNCT
ejpam-4299	262	2	b	b	X
ejpam-4299	262	3	)	)	PUNCT
ejpam-4299	262	4	if	if	SCONJ
ejpam-4299	262	5	eq	eq	NOUN
ejpam-4299	262	6	(	(	PUNCT
ejpam-4299	262	7	20	20	NUM
ejpam-4299	262	8	)	)	PUNCT
ejpam-4299	262	9	does	do	AUX
ejpam-4299	262	10	not	not	PART
ejpam-4299	262	11	hold	hold	VERB
ejpam-4299	262	12	or	or	CCONJ
ejpam-4299	262	13	eq	eq	NOUN
ejpam-4299	262	14	(	(	PUNCT
ejpam-4299	262	15	21	21	NUM
ejpam-4299	262	16	)	)	PUNCT
ejpam-4299	262	17	does	do	AUX
ejpam-4299	262	18	not	not	PART
ejpam-4299	262	19	hold	hold	VERB
ejpam-4299	262	20	for	for	ADP
ejpam-4299	262	21	some	some	DET
ejpam-4299	262	22	j	j	NOUN
ejpam-4299	262	23	,	,	PUNCT
ejpam-4299	262	24	then	then	ADV
ejpam-4299	262	25	ȳ	ȳ	PROPN
ejpam-4299	262	26	(	(	PUNCT
ejpam-4299	262	27	t	t	PROPN
ejpam-4299	262	28	)	)	PUNCT
ejpam-4299	262	29	does	do	VERB
ejpam-4299	262	30	not	not	PART
ejpam-4299	262	31	a	a	DET
ejpam-4299	262	32	bf	bf	NOUN
ejpam-4299	262	33	-	-	PUNCT
ejpam-4299	262	34	solution	solution	NOUN
ejpam-4299	262	35	.	.	PUNCT
ejpam-4299	263	1	a.	a.	NOUN
ejpam-4299	263	2	harir	harir	PROPN
ejpam-4299	263	3	,	,	PUNCT
ejpam-4299	263	4	s.	s.	PROPN
ejpam-4299	263	5	melliani	melliani	PROPN
ejpam-4299	263	6	,	,	PUNCT
ejpam-4299	263	7	l.	l.	PROPN
ejpam-4299	263	8	s.	s.	PROPN
ejpam-4299	263	9	chadli	chadli	PROPN
ejpam-4299	263	10	/	/	SYM
ejpam-4299	263	11	eur	eur	PROPN
ejpam-4299	263	12	.	.	PUNCT
ejpam-4299	264	1	j.	j.	PROPN
ejpam-4299	264	2	pure	pure	PROPN
ejpam-4299	264	3	appl	appl	PROPN
ejpam-4299	264	4	.	.	PROPN
ejpam-4299	264	5	math	math	PROPN
ejpam-4299	264	6	,	,	PUNCT
ejpam-4299	264	7	15	15	NUM
ejpam-4299	264	8	(	(	PUNCT
ejpam-4299	264	9	2	2	NUM
ejpam-4299	264	10	)	)	PUNCT
ejpam-4299	264	11	(	(	PUNCT
ejpam-4299	264	12	2022	2022	NUM
ejpam-4299	264	13	)	)	PUNCT
ejpam-4299	264	14	,	,	PUNCT
ejpam-4299	264	15	557	557	NUM
ejpam-4299	264	16	-	-	SYM
ejpam-4299	264	17	571	571	NUM
ejpam-4299	264	18	566	566	NUM
ejpam-4299	264	19	proof	proof	NOUN
ejpam-4299	264	20	.	.	PUNCT
ejpam-4299	265	1	let	let	VERB
ejpam-4299	265	2	us	we	PRON
ejpam-4299	265	3	assume	assume	VERB
ejpam-4299	265	4	there	there	PRON
ejpam-4299	265	5	is	be	VERB
ejpam-4299	265	6	only	only	ADV
ejpam-4299	265	7	one	one	NUM
ejpam-4299	265	8	ki	ki	PROPN
ejpam-4299	265	9	=	=	SYM
ejpam-4299	265	10	k	k	PROPN
ejpam-4299	265	11	and	and	CCONJ
ejpam-4299	265	12	that	that	SCONJ
ejpam-4299	265	13	∂g	∂g	PUNCT
ejpam-4299	266	1	∂k	∂k	ADJ
ejpam-4299	266	2	>	>	X
ejpam-4299	266	3	0	0	NUM
ejpam-4299	266	4	,	,	PUNCT
ejpam-4299	266	5	∂f	∂f	PROPN
ejpam-4299	267	1	∂k	∂k	INTJ
ejpam-4299	267	2	>	>	X
ejpam-4299	267	3	0	0	NUM
ejpam-4299	267	4	,	,	PUNCT
ejpam-4299	267	5	the	the	DET
ejpam-4299	267	6	proof	proof	NOUN
ejpam-4299	267	7	for	for	ADP
ejpam-4299	267	8	∂g	∂g	PROPN
ejpam-4299	267	9	∂k	∂k	NOUN
ejpam-4299	267	10	<	<	X
ejpam-4299	267	11	0	0	NUM
ejpam-4299	267	12	,	,	PUNCT
ejpam-4299	267	13	∂f	∂f	PROPN
ejpam-4299	268	1	∂k	∂k	ADP
ejpam-4299	268	2	<	<	X
ejpam-4299	268	3	0	0	X
ejpam-4299	268	4	is	be	AUX
ejpam-4299	268	5	similar	similar	ADJ
ejpam-4299	268	6	and	and	CCONJ
ejpam-4299	268	7	omitted	omit	VERB
ejpam-4299	268	8	.	.	PUNCT
ejpam-4299	269	1	since	since	SCONJ
ejpam-4299	269	2	∂g	∂g	PROPN
ejpam-4299	269	3	∂k	∂k	PROPN
ejpam-4299	269	4	>	>	SYM
ejpam-4299	269	5	0	0	PUNCT
ejpam-4299	269	6	and	and	CCONJ
ejpam-4299	269	7	∂g	∂g	PROPN
ejpam-4299	270	1	∂c	∂c	PROPN
ejpam-4299	271	1	>	>	X
ejpam-4299	271	2	0	0	PUNCT
ejpam-4299	272	1	we	we	PRON
ejpam-4299	272	2	have	have	VERB
ejpam-4299	272	3	yα1	yα1	NUM
ejpam-4299	272	4	(	(	PUNCT
ejpam-4299	272	5	t	t	NOUN
ejpam-4299	272	6	)	)	PUNCT
ejpam-4299	273	1	=	=	SYM
ejpam-4299	273	2	g	g	PROPN
ejpam-4299	273	3	(	(	PUNCT
ejpam-4299	273	4	t	t	PROPN
ejpam-4299	273	5	,	,	PUNCT
ejpam-4299	273	6	kα1	kα1	PROPN
ejpam-4299	273	7	,	,	PUNCT
ejpam-4299	273	8	c	c	NOUN
ejpam-4299	273	9	α	α	PRON
ejpam-4299	273	10	1	1	NUM
ejpam-4299	273	11	)	)	PUNCT
ejpam-4299	273	12	,	,	PUNCT
ejpam-4299	273	13	(	(	PUNCT
ejpam-4299	273	14	22	22	NUM
ejpam-4299	273	15	)	)	PUNCT
ejpam-4299	273	16	yα2	yα2	PROPN
ejpam-4299	273	17	(	(	PUNCT
ejpam-4299	273	18	t	t	PROPN
ejpam-4299	273	19	)	)	PUNCT
ejpam-4299	274	1	=	=	SYM
ejpam-4299	274	2	g	g	PROPN
ejpam-4299	274	3	(	(	PUNCT
ejpam-4299	274	4	t	t	PROPN
ejpam-4299	274	5	,	,	PUNCT
ejpam-4299	274	6	kα2	kα2	NOUN
ejpam-4299	274	7	,	,	PUNCT
ejpam-4299	274	8	c	c	NOUN
ejpam-4299	274	9	α	α	PRON
ejpam-4299	274	10	2	2	NUM
ejpam-4299	274	11	)	)	PUNCT
ejpam-4299	274	12	.	.	PUNCT
ejpam-4299	275	1	(	(	PUNCT
ejpam-4299	275	2	23	23	NUM
ejpam-4299	275	3	)	)	PUNCT
ejpam-4299	275	4	also	also	ADV
ejpam-4299	275	5	,	,	PUNCT
ejpam-4299	275	6	because	because	SCONJ
ejpam-4299	275	7	∂g	∂g	PROPN
ejpam-4299	275	8	∂y	∂y	X
ejpam-4299	275	9	>	>	X
ejpam-4299	275	10	0	0	PUNCT
ejpam-4299	276	1	and	and	CCONJ
ejpam-4299	276	2	∂f	∂f	PROPN
ejpam-4299	276	3	∂k	∂k	NOUN
ejpam-4299	276	4	>	>	X
ejpam-4299	276	5	0	0	NUM
ejpam-4299	277	1	we	we	PRON
ejpam-4299	277	2	see	see	VERB
ejpam-4299	277	3	that	that	SCONJ
ejpam-4299	277	4	fα	fα	ADP
ejpam-4299	277	5	1	1	NUM
ejpam-4299	277	6	(	(	PUNCT
ejpam-4299	277	7	t	t	NOUN
ejpam-4299	277	8	)	)	PUNCT
ejpam-4299	277	9	=	=	SYM
ejpam-4299	277	10	g	g	PROPN
ejpam-4299	277	11	(	(	PUNCT
ejpam-4299	277	12	t	t	PROPN
ejpam-4299	277	13	,	,	PUNCT
ejpam-4299	277	14	yα1	yα1	PROPN
ejpam-4299	277	15	(	(	PUNCT
ejpam-4299	277	16	t	t	PROPN
ejpam-4299	277	17	)	)	PUNCT
ejpam-4299	277	18	,	,	PUNCT
ejpam-4299	278	1	k	k	PROPN
ejpam-4299	278	2	α	α	PROPN
ejpam-4299	278	3	1	1	NUM
ejpam-4299	278	4	)	)	PUNCT
ejpam-4299	278	5	,	,	PUNCT
ejpam-4299	278	6	(	(	PUNCT
ejpam-4299	278	7	24	24	NUM
ejpam-4299	278	8	)	)	PUNCT
ejpam-4299	278	9	fα	fα	ADP
ejpam-4299	278	10	2	2	NUM
ejpam-4299	278	11	(	(	PUNCT
ejpam-4299	278	12	t	t	NOUN
ejpam-4299	278	13	)	)	PUNCT
ejpam-4299	279	1	=	=	SYM
ejpam-4299	279	2	g	g	PROPN
ejpam-4299	279	3	(	(	PUNCT
ejpam-4299	279	4	t	t	PROPN
ejpam-4299	279	5	,	,	PUNCT
ejpam-4299	279	6	yα2	yα2	PROPN
ejpam-4299	279	7	(	(	PUNCT
ejpam-4299	279	8	t	t	PROPN
ejpam-4299	279	9	)	)	PUNCT
ejpam-4299	279	10	,	,	PUNCT
ejpam-4299	280	1	k	k	PROPN
ejpam-4299	280	2	α	α	PROPN
ejpam-4299	280	3	2	2	NUM
ejpam-4299	280	4	)	)	PUNCT
ejpam-4299	280	5	.	.	PUNCT
ejpam-4299	281	1	(	(	PUNCT
ejpam-4299	281	2	25	25	NUM
ejpam-4299	281	3	)	)	PUNCT
ejpam-4299	281	4	now	now	ADV
ejpam-4299	281	5	,	,	PUNCT
ejpam-4299	281	6	y(t	y(t	PROPN
ejpam-4299	281	7	)	)	PUNCT
ejpam-4299	281	8	=	=	PUNCT
ejpam-4299	281	9	g(t	g(t	PROPN
ejpam-4299	281	10	,	,	PUNCT
ejpam-4299	281	11	k	k	NOUN
ejpam-4299	281	12	,	,	PUNCT
ejpam-4299	281	13	c	c	X
ejpam-4299	281	14	)	)	PUNCT
ejpam-4299	281	15	is	be	AUX
ejpam-4299	281	16	unique	unique	ADJ
ejpam-4299	281	17	solution	solution	NOUN
ejpam-4299	281	18	to	to	ADP
ejpam-4299	281	19	y(q)(t	y(q)(t	NOUN
ejpam-4299	281	20	)	)	PUNCT
ejpam-4299	281	21	=	=	SYM
ejpam-4299	281	22	f	f	PROPN
ejpam-4299	281	23	(	(	PUNCT
ejpam-4299	281	24	t	t	PROPN
ejpam-4299	281	25	,	,	PUNCT
ejpam-4299	281	26	y	y	PROPN
ejpam-4299	281	27	,	,	PUNCT
ejpam-4299	281	28	k	k	NOUN
ejpam-4299	281	29	)	)	PUNCT
ejpam-4299	281	30	,	,	PUNCT
ejpam-4299	281	31	for	for	ADP
ejpam-4299	281	32	all	all	DET
ejpam-4299	281	33	q	q	PROPN
ejpam-4299	281	34	∈	∈	PROPN
ejpam-4299	281	35	(	(	PUNCT
ejpam-4299	281	36	0	0	NUM
ejpam-4299	281	37	,	,	PUNCT
ejpam-4299	281	38	1	1	NUM
ejpam-4299	281	39	]	]	X
ejpam-4299	281	40	y(0	y(0	PROPN
ejpam-4299	281	41	)	)	PUNCT
ejpam-4299	281	42	=	=	PUNCT
ejpam-4299	281	43	c	c	NOUN
ejpam-4299	281	44	which	which	PRON
ejpam-4299	281	45	implies	imply	VERB
ejpam-4299	281	46	that	that	SCONJ
ejpam-4299	281	47	g(q)(t	g(q)(t	X
ejpam-4299	281	48	)	)	PUNCT
ejpam-4299	281	49	=	=	SYM
ejpam-4299	281	50	f	f	PROPN
ejpam-4299	281	51	(	(	PUNCT
ejpam-4299	281	52	t	t	PROPN
ejpam-4299	281	53	,	,	PUNCT
ejpam-4299	281	54	g(t	g(t	PROPN
ejpam-4299	281	55	,	,	PUNCT
ejpam-4299	281	56	k	k	PROPN
ejpam-4299	281	57	,	,	PUNCT
ejpam-4299	281	58	c	c	NOUN
ejpam-4299	281	59	)	)	PUNCT
ejpam-4299	281	60	,	,	PUNCT
ejpam-4299	281	61	k	k	NOUN
ejpam-4299	281	62	)	)	PUNCT
ejpam-4299	281	63	,	,	PUNCT
ejpam-4299	281	64	for	for	ADP
ejpam-4299	281	65	all	all	DET
ejpam-4299	281	66	q	q	PROPN
ejpam-4299	281	67	∈	∈	PROPN
ejpam-4299	281	68	(	(	PUNCT
ejpam-4299	281	69	0	0	NUM
ejpam-4299	281	70	,	,	PUNCT
ejpam-4299	281	71	1	1	NUM
ejpam-4299	281	72	]	]	PUNCT
ejpam-4299	281	73	(	(	PUNCT
ejpam-4299	281	74	26	26	NUM
ejpam-4299	281	75	)	)	PUNCT
ejpam-4299	281	76	and	and	CCONJ
ejpam-4299	281	77	g(0	g(0	PROPN
ejpam-4299	281	78	,	,	PUNCT
ejpam-4299	281	79	k	k	PROPN
ejpam-4299	281	80	,	,	PUNCT
ejpam-4299	281	81	c	c	NOUN
ejpam-4299	281	82	)	)	PUNCT
ejpam-4299	282	1	=	=	SYM
ejpam-4299	282	2	c	c	NOUN
ejpam-4299	282	3	(	(	PUNCT
ejpam-4299	282	4	27	27	NUM
ejpam-4299	282	5	)	)	PUNCT
ejpam-4299	282	6	assuming	assume	VERB
ejpam-4299	282	7	is	be	AUX
ejpam-4299	282	8	q	q	ADJ
ejpam-4299	282	9	-	-	ADV
ejpam-4299	282	10	differentiable	differentiable	ADJ
ejpam-4299	282	11	we	we	PRON
ejpam-4299	282	12	see	see	VERB
ejpam-4299	282	13	that	that	SCONJ
ejpam-4299	282	14	(	(	PUNCT
ejpam-4299	282	15	y(q	y(q	PROPN
ejpam-4299	282	16	)	)	PUNCT
ejpam-4299	282	17	)	)	PUNCT
ejpam-4299	283	1	α	α	X
ejpam-4299	283	2	1	1	NUM
ejpam-4299	283	3	(	(	PUNCT
ejpam-4299	283	4	t	t	NOUN
ejpam-4299	283	5	)	)	PUNCT
ejpam-4299	283	6	=	=	SYM
ejpam-4299	283	7	g(q	g(q	X
ejpam-4299	283	8	)	)	PUNCT
ejpam-4299	283	9	(	(	PUNCT
ejpam-4299	283	10	t	t	PROPN
ejpam-4299	283	11	,	,	PUNCT
ejpam-4299	283	12	kα1	kα1	PROPN
ejpam-4299	283	13	,	,	PUNCT
ejpam-4299	283	14	c	c	NOUN
ejpam-4299	283	15	α	α	PRON
ejpam-4299	283	16	1	1	NUM
ejpam-4299	283	17	)	)	PUNCT
ejpam-4299	283	18	,	,	PUNCT
ejpam-4299	283	19	q	q	PROPN
ejpam-4299	283	20	∈	∈	PROPN
ejpam-4299	283	21	(	(	PUNCT
ejpam-4299	283	22	0	0	NUM
ejpam-4299	283	23	,	,	PUNCT
ejpam-4299	283	24	1	1	NUM
ejpam-4299	283	25	]	]	PUNCT
ejpam-4299	283	26	=	=	SYM
ejpam-4299	283	27	f	f	X
ejpam-4299	283	28	(	(	PUNCT
ejpam-4299	283	29	t	t	PROPN
ejpam-4299	283	30	,	,	PUNCT
ejpam-4299	283	31	g	g	PROPN
ejpam-4299	283	32	(	(	PUNCT
ejpam-4299	283	33	t	t	PROPN
ejpam-4299	283	34	,	,	PUNCT
ejpam-4299	283	35	kα1	kα1	PROPN
ejpam-4299	283	36	,	,	PUNCT
ejpam-4299	283	37	c	c	NOUN
ejpam-4299	283	38	α	α	PRON
ejpam-4299	283	39	1	1	NUM
ejpam-4299	283	40	)	)	PUNCT
ejpam-4299	283	41	,	,	PUNCT
ejpam-4299	283	42	k	k	PROPN
ejpam-4299	283	43	α	α	PROPN
ejpam-4299	283	44	1	1	X
ejpam-4299	283	45	)	)	PUNCT
ejpam-4299	283	46	=	=	SYM
ejpam-4299	284	1	f	f	PROPN
ejpam-4299	284	2	(	(	PUNCT
ejpam-4299	284	3	t	t	PROPN
ejpam-4299	284	4	,	,	PUNCT
ejpam-4299	284	5	yα1	yα1	PROPN
ejpam-4299	284	6	(	(	PUNCT
ejpam-4299	284	7	t	t	PROPN
ejpam-4299	284	8	)	)	PUNCT
ejpam-4299	284	9	,	,	PUNCT
ejpam-4299	284	10	k	k	PROPN
ejpam-4299	284	11	α	α	PROPN
ejpam-4299	284	12	1	1	X
ejpam-4299	284	13	)	)	PUNCT
ejpam-4299	284	14	=	=	SYM
ejpam-4299	284	15	fα	fα	ADP
ejpam-4299	284	16	1	1	NUM
ejpam-4299	284	17	(	(	PUNCT
ejpam-4299	284	18	t	t	PROPN
ejpam-4299	284	19	)	)	PUNCT
ejpam-4299	284	20	and	and	CCONJ
ejpam-4299	284	21	yα1	yα1	NOUN
ejpam-4299	284	22	(	(	PUNCT
ejpam-4299	284	23	0	0	NUM
ejpam-4299	284	24	)	)	PUNCT
ejpam-4299	284	25	=	=	SYM
ejpam-4299	284	26	g	g	PROPN
ejpam-4299	284	27	(	(	PUNCT
ejpam-4299	284	28	0	0	NUM
ejpam-4299	284	29	,	,	PUNCT
ejpam-4299	284	30	kα1	kα1	PROPN
ejpam-4299	284	31	,	,	PUNCT
ejpam-4299	284	32	c	c	NOUN
ejpam-4299	284	33	α	α	PRON
ejpam-4299	284	34	1	1	X
ejpam-4299	284	35	)	)	PUNCT
ejpam-4299	284	36	=	=	SYM
ejpam-4299	285	1	cα1	cα1	NOUN
ejpam-4299	285	2	and	and	CCONJ
ejpam-4299	285	3	also	also	ADV
ejpam-4299	285	4	(	(	PUNCT
ejpam-4299	285	5	y(q	y(q	PROPN
ejpam-4299	285	6	)	)	PUNCT
ejpam-4299	285	7	)	)	PUNCT
ejpam-4299	286	1	α	α	X
ejpam-4299	286	2	2	2	NUM
ejpam-4299	286	3	(	(	PUNCT
ejpam-4299	286	4	t	t	NOUN
ejpam-4299	286	5	)	)	PUNCT
ejpam-4299	286	6	=	=	SYM
ejpam-4299	286	7	g(q	g(q	X
ejpam-4299	286	8	)	)	PUNCT
ejpam-4299	286	9	(	(	PUNCT
ejpam-4299	286	10	t	t	PROPN
ejpam-4299	286	11	,	,	PUNCT
ejpam-4299	286	12	kα2	kα2	NOUN
ejpam-4299	286	13	,	,	PUNCT
ejpam-4299	286	14	c	c	NOUN
ejpam-4299	286	15	α	α	PRON
ejpam-4299	286	16	2	2	NUM
ejpam-4299	286	17	)	)	PUNCT
ejpam-4299	286	18	,	,	PUNCT
ejpam-4299	286	19	q	q	PROPN
ejpam-4299	286	20	∈	∈	PROPN
ejpam-4299	286	21	(	(	PUNCT
ejpam-4299	286	22	0	0	NUM
ejpam-4299	286	23	,	,	PUNCT
ejpam-4299	286	24	1	1	NUM
ejpam-4299	286	25	]	]	PUNCT
ejpam-4299	286	26	=	=	SYM
ejpam-4299	286	27	f	f	X
ejpam-4299	286	28	(	(	PUNCT
ejpam-4299	286	29	t	t	PROPN
ejpam-4299	286	30	,	,	PUNCT
ejpam-4299	286	31	g	g	PROPN
ejpam-4299	286	32	(	(	PUNCT
ejpam-4299	286	33	t	t	PROPN
ejpam-4299	286	34	,	,	PUNCT
ejpam-4299	286	35	kα2	kα2	NOUN
ejpam-4299	286	36	,	,	PUNCT
ejpam-4299	286	37	c	c	NOUN
ejpam-4299	286	38	α	α	PRON
ejpam-4299	286	39	2	2	NUM
ejpam-4299	286	40	)	)	PUNCT
ejpam-4299	286	41	,	,	PUNCT
ejpam-4299	286	42	k	k	PROPN
ejpam-4299	286	43	α	α	PROPN
ejpam-4299	286	44	1	1	X
ejpam-4299	286	45	)	)	PUNCT
ejpam-4299	286	46	=	=	SYM
ejpam-4299	287	1	f	f	PROPN
ejpam-4299	287	2	(	(	PUNCT
ejpam-4299	287	3	t	t	PROPN
ejpam-4299	287	4	,	,	PUNCT
ejpam-4299	287	5	yα2	yα2	PROPN
ejpam-4299	287	6	(	(	PUNCT
ejpam-4299	287	7	t	t	PROPN
ejpam-4299	287	8	)	)	PUNCT
ejpam-4299	287	9	,	,	PUNCT
ejpam-4299	288	1	k	k	PROPN
ejpam-4299	288	2	α	α	PROPN
ejpam-4299	288	3	2	2	X
ejpam-4299	288	4	)	)	PUNCT
ejpam-4299	288	5	=	=	SYM
ejpam-4299	288	6	fα	fα	ADP
ejpam-4299	288	7	2	2	NUM
ejpam-4299	288	8	(	(	PUNCT
ejpam-4299	288	9	t	t	NOUN
ejpam-4299	288	10	)	)	PUNCT
ejpam-4299	288	11	a.	a.	NOUN
ejpam-4299	288	12	harir	harir	PROPN
ejpam-4299	288	13	,	,	PUNCT
ejpam-4299	288	14	s.	s.	PROPN
ejpam-4299	288	15	melliani	melliani	PROPN
ejpam-4299	288	16	,	,	PUNCT
ejpam-4299	288	17	l.	l.	PROPN
ejpam-4299	288	18	s.	s.	PROPN
ejpam-4299	288	19	chadli	chadli	PROPN
ejpam-4299	288	20	/	/	SYM
ejpam-4299	288	21	eur	eur	PROPN
ejpam-4299	288	22	.	.	PUNCT
ejpam-4299	289	1	j.	j.	PROPN
ejpam-4299	289	2	pure	pure	PROPN
ejpam-4299	289	3	appl	appl	PROPN
ejpam-4299	289	4	.	.	PROPN
ejpam-4299	289	5	math	math	PROPN
ejpam-4299	289	6	,	,	PUNCT
ejpam-4299	289	7	15	15	NUM
ejpam-4299	289	8	(	(	PUNCT
ejpam-4299	289	9	2	2	NUM
ejpam-4299	289	10	)	)	PUNCT
ejpam-4299	289	11	(	(	PUNCT
ejpam-4299	289	12	2022	2022	NUM
ejpam-4299	289	13	)	)	PUNCT
ejpam-4299	289	14	,	,	PUNCT
ejpam-4299	289	15	557	557	NUM
ejpam-4299	289	16	-	-	SYM
ejpam-4299	289	17	571	571	NUM
ejpam-4299	289	18	567	567	NUM
ejpam-4299	289	19	and	and	CCONJ
ejpam-4299	289	20	yα2	yα2	PROPN
ejpam-4299	289	21	(	(	PUNCT
ejpam-4299	289	22	0	0	NUM
ejpam-4299	289	23	)	)	PUNCT
ejpam-4299	289	24	=	=	SYM
ejpam-4299	289	25	g	g	PROPN
ejpam-4299	289	26	(	(	PUNCT
ejpam-4299	289	27	0	0	NUM
ejpam-4299	289	28	,	,	PUNCT
ejpam-4299	289	29	kα2	kα2	NOUN
ejpam-4299	289	30	,	,	PUNCT
ejpam-4299	289	31	c	c	NOUN
ejpam-4299	289	32	α	α	PRON
ejpam-4299	289	33	2	2	X
ejpam-4299	289	34	)	)	PUNCT
ejpam-4299	289	35	=	=	PUNCT
ejpam-4299	289	36	cα2	cα2	ADJ
ejpam-4299	289	37	for	for	ADP
ejpam-4299	289	38	all	all	DET
ejpam-4299	289	39	α	α	PRON
ejpam-4299	289	40	∈	∈	PROPN
ejpam-4299	290	1	[	[	X
ejpam-4299	290	2	0	0	NUM
ejpam-4299	290	3	,	,	PUNCT
ejpam-4299	290	4	1	1	NUM
ejpam-4299	290	5	]	]	PUNCT
ejpam-4299	290	6	and	and	CCONJ
ejpam-4299	290	7	t	t	PROPN
ejpam-4299	290	8	∈	∈	PROPN
ejpam-4299	290	9	(	(	PUNCT
ejpam-4299	290	10	0	0	NUM
ejpam-4299	290	11	,	,	PUNCT
ejpam-4299	290	12	a	a	PRON
ejpam-4299	290	13	)	)	PUNCT
ejpam-4299	290	14	.	.	PUNCT
ejpam-4299	291	1	hence	hence	ADV
ejpam-4299	291	2	eqs	eqs	X
ejpam-4299	291	3	(	(	PUNCT
ejpam-4299	291	4	12)-(15	12)-(15	X
ejpam-4299	291	5	)	)	PUNCT
ejpam-4299	291	6	hold	hold	NOUN
ejpam-4299	291	7	.	.	PUNCT
ejpam-4299	292	1	now	now	ADV
ejpam-4299	292	2	consider	consider	VERB
ejpam-4299	292	3	the	the	DET
ejpam-4299	292	4	situation	situation	NOUN
ejpam-4299	292	5	where	where	SCONJ
ejpam-4299	292	6	eq	eq	NOUN
ejpam-4299	292	7	(	(	PUNCT
ejpam-4299	292	8	20	20	NUM
ejpam-4299	292	9	)	)	PUNCT
ejpam-4299	292	10	or	or	CCONJ
ejpam-4299	292	11	(	(	PUNCT
ejpam-4299	292	12	21	21	NUM
ejpam-4299	292	13	)	)	PUNCT
ejpam-4299	292	14	does	do	AUX
ejpam-4299	292	15	not	not	PART
ejpam-4299	292	16	hold	hold	VERB
ejpam-4299	292	17	.	.	PUNCT
ejpam-4299	293	1	let	let	VERB
ejpam-4299	293	2	us	we	PRON
ejpam-4299	293	3	only	only	ADV
ejpam-4299	293	4	look	look	VERB
ejpam-4299	293	5	at	at	ADP
ejpam-4299	293	6	one	one	NUM
ejpam-4299	293	7	case	case	NOUN
ejpam-4299	293	8	where	where	SCONJ
ejpam-4299	293	9	∂g	∂g	PROPN
ejpam-4299	294	1	∂c	∂c	PROPN
ejpam-4299	295	1	<	<	X
ejpam-4299	295	2	0	0	PUNCT
ejpam-4299	295	3	(	(	PUNCT
ejpam-4299	295	4	assume	assume	VERB
ejpam-4299	295	5	∂g	∂g	ADP
ejpam-4299	296	1	∂k	∂k	X
ejpam-4299	296	2	<	<	X
ejpam-4299	296	3	0	0	NUM
ejpam-4299	296	4	,	,	PUNCT
ejpam-4299	296	5	∂f	∂f	PROPN
ejpam-4299	296	6	∂y	∂y	SYM
ejpam-4299	296	7	>	>	X
ejpam-4299	296	8	0	0	PUNCT
ejpam-4299	297	1	and	and	CCONJ
ejpam-4299	297	2	∂f	∂f	PROPN
ejpam-4299	298	1	∂k	∂k	NOUN
ejpam-4299	298	2	<	<	NOUN
ejpam-4299	298	3	0	0	NUM
ejpam-4299	298	4	)	)	PUNCT
ejpam-4299	298	5	.	.	PUNCT
ejpam-4299	299	1	then	then	ADV
ejpam-4299	299	2	we	we	PRON
ejpam-4299	299	3	have	have	VERB
ejpam-4299	299	4	fα	fα	ADP
ejpam-4299	299	5	1	1	NUM
ejpam-4299	299	6	(	(	PUNCT
ejpam-4299	299	7	t	t	NOUN
ejpam-4299	299	8	)	)	PUNCT
ejpam-4299	299	9	=	=	SYM
ejpam-4299	299	10	f	f	PROPN
ejpam-4299	299	11	(	(	PUNCT
ejpam-4299	299	12	t	t	PROPN
ejpam-4299	299	13	,	,	PUNCT
ejpam-4299	299	14	yα1	yα1	PROPN
ejpam-4299	299	15	(	(	PUNCT
ejpam-4299	299	16	t	t	PROPN
ejpam-4299	299	17	)	)	PUNCT
ejpam-4299	299	18	,	,	PUNCT
ejpam-4299	300	1	k	k	PROPN
ejpam-4299	300	2	α	α	PROPN
ejpam-4299	300	3	2	2	NUM
ejpam-4299	300	4	)	)	PUNCT
ejpam-4299	300	5	,	,	PUNCT
ejpam-4299	300	6	fα	fα	ADV
ejpam-4299	300	7	2	2	NUM
ejpam-4299	300	8	(	(	PUNCT
ejpam-4299	300	9	t	t	NOUN
ejpam-4299	300	10	)	)	PUNCT
ejpam-4299	300	11	=	=	SYM
ejpam-4299	301	1	f	f	PROPN
ejpam-4299	301	2	(	(	PUNCT
ejpam-4299	301	3	t	t	PROPN
ejpam-4299	301	4	,	,	PUNCT
ejpam-4299	301	5	yα2	yα2	PROPN
ejpam-4299	301	6	(	(	PUNCT
ejpam-4299	301	7	t	t	PROPN
ejpam-4299	301	8	)	)	PUNCT
ejpam-4299	301	9	,	,	PUNCT
ejpam-4299	301	10	k	k	PROPN
ejpam-4299	301	11	α	α	PROPN
ejpam-4299	301	12	1	1	NUM
ejpam-4299	301	13	)	)	PUNCT
ejpam-4299	301	14	,	,	PUNCT
ejpam-4299	301	15	yα1	yα1	PROPN
ejpam-4299	301	16	(	(	PUNCT
ejpam-4299	301	17	t	t	NOUN
ejpam-4299	301	18	)	)	PUNCT
ejpam-4299	302	1	=	=	SYM
ejpam-4299	302	2	g	g	PROPN
ejpam-4299	302	3	(	(	PUNCT
ejpam-4299	302	4	t	t	PROPN
ejpam-4299	302	5	,	,	PUNCT
ejpam-4299	302	6	kα2	kα2	NOUN
ejpam-4299	302	7	,	,	PUNCT
ejpam-4299	302	8	c	c	NOUN
ejpam-4299	302	9	α	α	PRON
ejpam-4299	302	10	2	2	NUM
ejpam-4299	302	11	)	)	PUNCT
ejpam-4299	302	12	and	and	CCONJ
ejpam-4299	302	13	yα2	yα2	PROPN
ejpam-4299	302	14	(	(	PUNCT
ejpam-4299	302	15	t	t	PROPN
ejpam-4299	302	16	)	)	PUNCT
ejpam-4299	302	17	=	=	SYM
ejpam-4299	303	1	g	g	PROPN
ejpam-4299	303	2	(	(	PUNCT
ejpam-4299	303	3	t	t	PROPN
ejpam-4299	303	4	,	,	PUNCT
ejpam-4299	303	5	kα1	kα1	PROPN
ejpam-4299	303	6	,	,	PUNCT
ejpam-4299	303	7	c	c	NOUN
ejpam-4299	303	8	α	α	DET
ejpam-4299	303	9	1	1	X
ejpam-4299	303	10	)	)	PUNCT
ejpam-4299	303	11	eqs	eqs	X
ejpam-4299	303	12	(	(	PUNCT
ejpam-4299	303	13	12)-(15	12)-(15	X
ejpam-4299	303	14	)	)	PUNCT
ejpam-4299	303	15	becames	became	NOUN
ejpam-4299	303	16	(	(	PUNCT
ejpam-4299	303	17	y(q	y(q	PROPN
ejpam-4299	303	18	)	)	PUNCT
ejpam-4299	303	19	)	)	PUNCT
ejpam-4299	304	1	α	α	X
ejpam-4299	304	2	1	1	NUM
ejpam-4299	304	3	(	(	PUNCT
ejpam-4299	304	4	t	t	NOUN
ejpam-4299	304	5	)	)	PUNCT
ejpam-4299	304	6	=	=	SYM
ejpam-4299	304	7	g(q	g(q	X
ejpam-4299	304	8	)	)	PUNCT
ejpam-4299	304	9	(	(	PUNCT
ejpam-4299	304	10	t	t	PROPN
ejpam-4299	304	11	,	,	PUNCT
ejpam-4299	304	12	kα2	kα2	NOUN
ejpam-4299	304	13	,	,	PUNCT
ejpam-4299	304	14	c	c	NOUN
ejpam-4299	304	15	α	α	PRON
ejpam-4299	304	16	2	2	NUM
ejpam-4299	304	17	)	)	PUNCT
ejpam-4299	304	18	,	,	PUNCT
ejpam-4299	304	19	q	q	PROPN
ejpam-4299	304	20	∈	∈	PROPN
ejpam-4299	304	21	(	(	PUNCT
ejpam-4299	304	22	0	0	NUM
ejpam-4299	304	23	,	,	PUNCT
ejpam-4299	304	24	1	1	NUM
ejpam-4299	304	25	]	]	PUNCT
ejpam-4299	304	26	=	=	SYM
ejpam-4299	304	27	f	f	X
ejpam-4299	304	28	(	(	PUNCT
ejpam-4299	304	29	t	t	PROPN
ejpam-4299	304	30	,	,	PUNCT
ejpam-4299	304	31	g	g	PROPN
ejpam-4299	304	32	(	(	PUNCT
ejpam-4299	304	33	t	t	PROPN
ejpam-4299	304	34	,	,	PUNCT
ejpam-4299	304	35	kα2	kα2	NOUN
ejpam-4299	304	36	,	,	PUNCT
ejpam-4299	304	37	c	c	NOUN
ejpam-4299	304	38	α	α	PRON
ejpam-4299	304	39	2	2	NUM
ejpam-4299	304	40	)	)	PUNCT
ejpam-4299	304	41	,	,	PUNCT
ejpam-4299	305	1	k	k	PROPN
ejpam-4299	305	2	α	α	NOUN
ejpam-4299	305	3	2	2	X
ejpam-4299	305	4	)	)	PUNCT
ejpam-4299	305	5	=	=	SYM
ejpam-4299	305	6	f	f	PROPN
ejpam-4299	305	7	(	(	PUNCT
ejpam-4299	305	8	t	t	PROPN
ejpam-4299	305	9	,	,	PUNCT
ejpam-4299	305	10	yα1	yα1	PROPN
ejpam-4299	305	11	(	(	PUNCT
ejpam-4299	305	12	t	t	PROPN
ejpam-4299	305	13	)	)	PUNCT
ejpam-4299	305	14	,	,	PUNCT
ejpam-4299	306	1	k	k	PROPN
ejpam-4299	306	2	α	α	PROPN
ejpam-4299	306	3	2	2	X
ejpam-4299	306	4	)	)	PUNCT
ejpam-4299	306	5	=	=	SYM
ejpam-4299	306	6	fα	fα	ADP
ejpam-4299	306	7	1	1	NUM
ejpam-4299	306	8	(	(	PUNCT
ejpam-4299	306	9	t	t	PROPN
ejpam-4299	306	10	)	)	PUNCT
ejpam-4299	306	11	and	and	CCONJ
ejpam-4299	306	12	yα1	yα1	NOUN
ejpam-4299	306	13	(	(	PUNCT
ejpam-4299	306	14	0	0	NUM
ejpam-4299	306	15	)	)	PUNCT
ejpam-4299	306	16	=	=	SYM
ejpam-4299	306	17	g	g	PROPN
ejpam-4299	306	18	(	(	PUNCT
ejpam-4299	306	19	0	0	NUM
ejpam-4299	306	20	,	,	PUNCT
ejpam-4299	306	21	kα2	kα2	NOUN
ejpam-4299	306	22	,	,	PUNCT
ejpam-4299	306	23	c	c	NOUN
ejpam-4299	306	24	α	α	PRON
ejpam-4299	306	25	2	2	X
ejpam-4299	306	26	)	)	PUNCT
ejpam-4299	306	27	=	=	SYM
ejpam-4299	306	28	cα2	cα2	NOUN
ejpam-4299	306	29	which	which	PRON
ejpam-4299	306	30	is	be	AUX
ejpam-4299	306	31	not	not	PART
ejpam-4299	306	32	true	true	ADJ
ejpam-4299	306	33	.	.	PUNCT
ejpam-4299	307	1	4.2	4.2	NUM
ejpam-4299	307	2	.	.	PUNCT
ejpam-4299	308	1	seikkala	seikkala	ADJ
ejpam-4299	308	2	solution	solution	NOUN
ejpam-4299	308	3	in	in	ADP
ejpam-4299	308	4	this	this	DET
ejpam-4299	308	5	section	section	NOUN
ejpam-4299	308	6	,	,	PUNCT
ejpam-4299	308	7	we	we	PRON
ejpam-4299	308	8	present	present	VERB
ejpam-4299	308	9	situations	situation	NOUN
ejpam-4299	308	10	where	where	SCONJ
ejpam-4299	308	11	the	the	DET
ejpam-4299	308	12	bf	bf	NOUN
ejpam-4299	308	13	-	-	PUNCT
ejpam-4299	308	14	solution	solution	NOUN
ejpam-4299	308	15	can	can	AUX
ejpam-4299	308	16	,	,	PUNCT
ejpam-4299	308	17	and	and	CCONJ
ejpam-4299	308	18	can	can	AUX
ejpam-4299	308	19	not	not	PART
ejpam-4299	308	20	exist	exist	VERB
ejpam-4299	308	21	,	,	PUNCT
ejpam-4299	308	22	with	with	ADP
ejpam-4299	308	23	these	these	DET
ejpam-4299	308	24	fuzzy	fuzzy	ADJ
ejpam-4299	308	25	fractional	fractional	ADJ
ejpam-4299	308	26	differential	differential	ADJ
ejpam-4299	308	27	equations	equation	NOUN
ejpam-4299	308	28	the	the	DET
ejpam-4299	308	29	main	main	ADJ
ejpam-4299	308	30	problem	problem	NOUN
ejpam-4299	308	31	is	be	AUX
ejpam-4299	308	32	determining	determine	VERB
ejpam-4299	308	33	where	where	SCONJ
ejpam-4299	308	34	the	the	DET
ejpam-4299	308	35	seikkala	seikkala	ADJ
ejpam-4299	308	36	solution	solution	NOUN
ejpam-4299	308	37	exists	exist	VERB
ejpam-4299	308	38	(	(	PUNCT
ejpam-4299	308	39	when	when	SCONJ
ejpam-4299	308	40	the	the	DET
ejpam-4299	308	41	bf	bf	NOUN
ejpam-4299	308	42	-	-	PUNCT
ejpam-4299	308	43	solution	solution	NOUN
ejpam-4299	308	44	does	do	AUX
ejpam-4299	308	45	not	not	PART
ejpam-4299	308	46	exist	exist	VERB
ejpam-4299	308	47	)	)	PUNCT
ejpam-4299	308	48	.	.	PUNCT
ejpam-4299	309	1	the	the	DET
ejpam-4299	309	2	seikkala	seikkala	ADJ
ejpam-4299	309	3	solution	solution	NOUN
ejpam-4299	309	4	,	,	PUNCT
ejpam-4299	309	5	written	write	VERB
ejpam-4299	309	6	ss	ss	NOUN
ejpam-4299	309	7	,	,	PUNCT
ejpam-4299	309	8	to	to	ADP
ejpam-4299	309	9	the	the	DET
ejpam-4299	309	10	fuzzy	fuzzy	ADJ
ejpam-4299	309	11	fractional	fractional	ADJ
ejpam-4299	309	12	differential	differential	ADJ
ejpam-4299	309	13	equations	equation	NOUN
ejpam-4299	309	14	xq(t	xq(t	NOUN
ejpam-4299	309	15	)	)	PUNCT
ejpam-4299	310	1	=	=	SYM
ejpam-4299	310	2	f̄	f̄	PROPN
ejpam-4299	310	3	(	(	PUNCT
ejpam-4299	310	4	t	t	PROPN
ejpam-4299	310	5	,	,	PUNCT
ejpam-4299	310	6	x̄	x̄	PROPN
ejpam-4299	310	7	,	,	PUNCT
ejpam-4299	310	8	k̄	k̄	PROPN
ejpam-4299	310	9	)	)	PUNCT
ejpam-4299	310	10	,	,	PUNCT
ejpam-4299	310	11	q	q	PROPN
ejpam-4299	310	12	∈	∈	PROPN
ejpam-4299	310	13	(	(	PUNCT
ejpam-4299	310	14	0	0	NUM
ejpam-4299	310	15	,	,	PUNCT
ejpam-4299	310	16	1	1	NUM
ejpam-4299	310	17	]	]	PUNCT
ejpam-4299	310	18	(	(	PUNCT
ejpam-4299	310	19	28	28	NUM
ejpam-4299	310	20	)	)	PUNCT
ejpam-4299	310	21	x̄(0	x̄(0	NUM
ejpam-4299	310	22	)	)	PUNCT
ejpam-4299	310	23	=	=	SYM
ejpam-4299	310	24	c̄	c̄	NUM
ejpam-4299	310	25	eq	eq	NOUN
ejpam-4299	310	26	(	(	PUNCT
ejpam-4299	310	27	28	28	NUM
ejpam-4299	310	28	)	)	PUNCT
ejpam-4299	310	29	is	be	AUX
ejpam-4299	310	30	equivalent	equivalent	ADJ
ejpam-4299	310	31	to	to	ADP
ejpam-4299	310	32	eq	eq	NOUN
ejpam-4299	310	33	(	(	PUNCT
ejpam-4299	310	34	4	4	X
ejpam-4299	310	35	)	)	PUNCT
ejpam-4299	310	36	substituting	substitute	VERB
ejpam-4299	310	37	xi	xi	NOUN
ejpam-4299	310	38	for	for	ADP
ejpam-4299	310	39	yi	yi	PROPN
ejpam-4299	310	40	,	,	PUNCT
ejpam-4299	310	41	for	for	SCONJ
ejpam-4299	310	42	x̄	x̄	SYM
ejpam-4299	310	43	∈	∈	PROPN
ejpam-4299	310	44	rf	rf	VERB
ejpam-4299	310	45	with	with	ADP
ejpam-4299	310	46	α	α	NOUN
ejpam-4299	310	47	-	-	NOUN
ejpam-4299	310	48	cut	cut	VERB
ejpam-4299	310	49	[	[	NOUN
ejpam-4299	310	50	x̄]α(t	x̄]α(t	NUM
ejpam-4299	310	51	)	)	PUNCT
ejpam-4299	310	52	=	=	PUNCT
ejpam-4299	311	1	[	[	X
ejpam-4299	311	2	xα1	xα1	X
ejpam-4299	311	3	(	(	PUNCT
ejpam-4299	311	4	t	t	NOUN
ejpam-4299	311	5	)	)	PUNCT
ejpam-4299	311	6	,	,	PUNCT
ejpam-4299	311	7	x	x	X
ejpam-4299	311	8	α	α	X
ejpam-4299	311	9	2	2	NUM
ejpam-4299	311	10	(	(	PUNCT
ejpam-4299	311	11	t	t	PROPN
ejpam-4299	311	12	)	)	PUNCT
ejpam-4299	311	13	]	]	PUNCT
ejpam-4299	311	14	,	,	PUNCT
ejpam-4299	311	15	α	α	PROPN
ejpam-4299	311	16	∈	∈	PROPN
ejpam-4299	312	1	[	[	X
ejpam-4299	312	2	0	0	NUM
ejpam-4299	312	3	,	,	PUNCT
ejpam-4299	312	4	1	1	NUM
ejpam-4299	312	5	]	]	PUNCT
ejpam-4299	312	6	.	.	PUNCT
ejpam-4299	313	1	since	since	SCONJ
ejpam-4299	313	2	the	the	DET
ejpam-4299	313	3	fuzzy	fuzzy	ADJ
ejpam-4299	313	4	conformable	conformable	ADJ
ejpam-4299	313	5	fractional	fractional	ADJ
ejpam-4299	313	6	derivative	derivative	NOUN
ejpam-4299	313	7	x̄(q	x̄(q	NOUN
ejpam-4299	313	8	)	)	PUNCT
ejpam-4299	313	9	,	,	PUNCT
ejpam-4299	313	10	q	q	PROPN
ejpam-4299	313	11	∈	∈	PROPN
ejpam-4299	313	12	(	(	PUNCT
ejpam-4299	313	13	0	0	NUM
ejpam-4299	313	14	,	,	PUNCT
ejpam-4299	313	15	1	1	NUM
ejpam-4299	313	16	]	]	PUNCT
ejpam-4299	313	17	of	of	ADP
ejpam-4299	313	18	fuzzy	fuzzy	ADJ
ejpam-4299	313	19	process	process	NOUN
ejpam-4299	313	20	x̄	x̄	NOUN
ejpam-4299	313	21	:	:	PUNCT
ejpam-4299	313	22	(	(	PUNCT
ejpam-4299	313	23	0	0	NUM
ejpam-4299	313	24	,	,	PUNCT
ejpam-4299	313	25	a	a	PRON
ejpam-4299	313	26	)	)	PUNCT
ejpam-4299	313	27	→	→	PUNCT
ejpam-4299	313	28	rf	rf	NUM
ejpam-4299	313	29	is	be	AUX
ejpam-4299	313	30	defined	define	VERB
ejpam-4299	313	31	by	by	ADP
ejpam-4299	313	32	[	[	PUNCT
ejpam-4299	313	33	x̄(q)(t	x̄(q)(t	PROPN
ejpam-4299	313	34	)	)	PUNCT
ejpam-4299	313	35	]	]	PUNCT
ejpam-4299	314	1	α	α	X
ejpam-4299	314	2	=	=	X
ejpam-4299	315	1	[	[	X
ejpam-4299	315	2	(	(	PUNCT
ejpam-4299	315	3	x(q	x(q	PROPN
ejpam-4299	315	4	)	)	PUNCT
ejpam-4299	315	5	)	)	PUNCT
ejpam-4299	316	1	α	α	X
ejpam-4299	316	2	1	1	NUM
ejpam-4299	316	3	(	(	PUNCT
ejpam-4299	316	4	t	t	PROPN
ejpam-4299	316	5	)	)	PUNCT
ejpam-4299	316	6	,	,	PUNCT
ejpam-4299	316	7	(	(	PUNCT
ejpam-4299	316	8	x(q	x(q	PROPN
ejpam-4299	316	9	)	)	PUNCT
ejpam-4299	316	10	)	)	PUNCT
ejpam-4299	317	1	α	α	X
ejpam-4299	317	2	2	2	NUM
ejpam-4299	317	3	(	(	PUNCT
ejpam-4299	317	4	t	t	PROPN
ejpam-4299	317	5	)	)	PUNCT
ejpam-4299	317	6	]	]	PUNCT
ejpam-4299	317	7	,	,	PUNCT
ejpam-4299	317	8	α	α	PROPN
ejpam-4299	317	9	∈	∈	PROPN
ejpam-4299	318	1	[	[	X
ejpam-4299	318	2	0	0	NUM
ejpam-4299	318	3	,	,	PUNCT
ejpam-4299	318	4	1	1	NUM
ejpam-4299	318	5	]	]	PUNCT
ejpam-4299	318	6	and	and	CCONJ
ejpam-4299	318	7	q	q	PROPN
ejpam-4299	318	8	∈	∈	PROPN
ejpam-4299	318	9	(	(	PUNCT
ejpam-4299	318	10	0	0	NUM
ejpam-4299	318	11	,	,	PUNCT
ejpam-4299	318	12	1	1	NUM
ejpam-4299	318	13	]	]	PUNCT
ejpam-4299	318	14	(	(	PUNCT
ejpam-4299	318	15	29	29	NUM
ejpam-4299	318	16	)	)	PUNCT
ejpam-4299	318	17	a.	a.	NOUN
ejpam-4299	318	18	harir	harir	PROPN
ejpam-4299	318	19	,	,	PUNCT
ejpam-4299	318	20	s.	s.	PROPN
ejpam-4299	318	21	melliani	melliani	PROPN
ejpam-4299	318	22	,	,	PUNCT
ejpam-4299	318	23	l.	l.	PROPN
ejpam-4299	318	24	s.	s.	PROPN
ejpam-4299	318	25	chadli	chadli	PROPN
ejpam-4299	318	26	/	/	SYM
ejpam-4299	318	27	eur	eur	PROPN
ejpam-4299	318	28	.	.	PUNCT
ejpam-4299	319	1	j.	j.	PROPN
ejpam-4299	319	2	pure	pure	PROPN
ejpam-4299	319	3	appl	appl	PROPN
ejpam-4299	319	4	.	.	PROPN
ejpam-4299	319	5	math	math	PROPN
ejpam-4299	319	6	,	,	PUNCT
ejpam-4299	319	7	15	15	NUM
ejpam-4299	319	8	(	(	PUNCT
ejpam-4299	319	9	2	2	NUM
ejpam-4299	319	10	)	)	PUNCT
ejpam-4299	319	11	(	(	PUNCT
ejpam-4299	319	12	2022	2022	NUM
ejpam-4299	319	13	)	)	PUNCT
ejpam-4299	319	14	,	,	PUNCT
ejpam-4299	319	15	557	557	NUM
ejpam-4299	319	16	-	-	SYM
ejpam-4299	319	17	571	571	NUM
ejpam-4299	319	18	568	568	NUM
ejpam-4299	319	19	we	we	PRON
ejpam-4299	319	20	call	call	VERB
ejpam-4299	319	21	x̄	x̄	NOUN
ejpam-4299	319	22	:	:	PUNCT
ejpam-4299	319	23	(	(	PUNCT
ejpam-4299	319	24	0	0	NUM
ejpam-4299	319	25	,	,	PUNCT
ejpam-4299	319	26	a	a	PRON
ejpam-4299	319	27	)	)	PUNCT
ejpam-4299	319	28	→	→	PUNCT
ejpam-4299	319	29	rf	rf	NUM
ejpam-4299	319	30	a	a	DET
ejpam-4299	319	31	fuzzy	fuzzy	ADJ
ejpam-4299	319	32	solution	solution	NOUN
ejpam-4299	319	33	of	of	ADP
ejpam-4299	319	34	(	(	PUNCT
ejpam-4299	319	35	28	28	NUM
ejpam-4299	319	36	)	)	PUNCT
ejpam-4299	319	37	on	on	ADP
ejpam-4299	319	38	(	(	PUNCT
ejpam-4299	319	39	0	0	NUM
ejpam-4299	319	40	,	,	PUNCT
ejpam-4299	319	41	a	a	NOUN
ejpam-4299	319	42	)	)	PUNCT
ejpam-4299	319	43	,	,	PUNCT
ejpam-4299	319	44	if	if	SCONJ
ejpam-4299	319	45	(	(	PUNCT
ejpam-4299	319	46	x(q	x(q	PROPN
ejpam-4299	319	47	)	)	PUNCT
ejpam-4299	319	48	)	)	PUNCT
ejpam-4299	320	1	α	α	X
ejpam-4299	320	2	1	1	NUM
ejpam-4299	320	3	(	(	PUNCT
ejpam-4299	320	4	t	t	NOUN
ejpam-4299	320	5	)	)	PUNCT
ejpam-4299	320	6	=	=	SYM
ejpam-4299	320	7	min	min	PROPN
ejpam-4299	320	8	{	{	PUNCT
ejpam-4299	320	9	f	f	PROPN
ejpam-4299	320	10	(	(	PUNCT
ejpam-4299	320	11	t	t	PROPN
ejpam-4299	320	12	,	,	PUNCT
ejpam-4299	320	13	y	y	PROPN
ejpam-4299	320	14	,	,	PUNCT
ejpam-4299	320	15	k	k	NOUN
ejpam-4299	320	16	)	)	PUNCT
ejpam-4299	320	17	:	:	PUNCT
ejpam-4299	320	18	y	y	PROPN
ejpam-4299	320	19	∈	∈	PROPN
ejpam-4299	321	1	[	[	X
ejpam-4299	321	2	x̄(t)]α	x̄(t)]α	PROPN
ejpam-4299	321	3	,	,	PUNCT
ejpam-4299	321	4	k	k	PROPN
ejpam-4299	321	5	∈	∈	PROPN
ejpam-4299	322	1	[	[	X
ejpam-4299	322	2	k̄]α	k̄]α	NOUN
ejpam-4299	322	3	}	}	PUNCT
ejpam-4299	322	4	(	(	PUNCT
ejpam-4299	322	5	30	30	NUM
ejpam-4299	322	6	)	)	PUNCT
ejpam-4299	322	7	xα1	xα1	NOUN
ejpam-4299	323	1	(	(	PUNCT
ejpam-4299	323	2	0	0	NUM
ejpam-4299	323	3	)	)	PUNCT
ejpam-4299	323	4	=	=	SYM
ejpam-4299	324	1	cα1	cα1	NOUN
ejpam-4299	324	2	(	(	PUNCT
ejpam-4299	324	3	31	31	NUM
ejpam-4299	324	4	)	)	PUNCT
ejpam-4299	324	5	(	(	PUNCT
ejpam-4299	324	6	x(q	x(q	PROPN
ejpam-4299	324	7	)	)	PUNCT
ejpam-4299	324	8	)	)	PUNCT
ejpam-4299	325	1	α	α	X
ejpam-4299	325	2	2	2	NUM
ejpam-4299	325	3	(	(	PUNCT
ejpam-4299	325	4	t	t	NOUN
ejpam-4299	325	5	)	)	PUNCT
ejpam-4299	325	6	=	=	SYM
ejpam-4299	325	7	max	max	PROPN
ejpam-4299	325	8	{	{	PUNCT
ejpam-4299	325	9	f	f	PROPN
ejpam-4299	325	10	(	(	PUNCT
ejpam-4299	325	11	t	t	PROPN
ejpam-4299	325	12	,	,	PUNCT
ejpam-4299	325	13	y	y	PROPN
ejpam-4299	325	14	,	,	PUNCT
ejpam-4299	325	15	k	k	NOUN
ejpam-4299	325	16	)	)	PUNCT
ejpam-4299	325	17	:	:	PUNCT
ejpam-4299	325	18	y	y	PROPN
ejpam-4299	325	19	∈	∈	PROPN
ejpam-4299	326	1	[	[	X
ejpam-4299	326	2	x̄(t)]α	x̄(t)]α	PROPN
ejpam-4299	326	3	,	,	PUNCT
ejpam-4299	326	4	k	k	PROPN
ejpam-4299	326	5	∈	∈	PROPN
ejpam-4299	327	1	[	[	X
ejpam-4299	327	2	k̄]α	k̄]α	NOUN
ejpam-4299	327	3	}	}	PUNCT
ejpam-4299	327	4	(	(	PUNCT
ejpam-4299	327	5	32	32	NUM
ejpam-4299	327	6	)	)	PUNCT
ejpam-4299	327	7	xα2	xα2	PUNCT
ejpam-4299	328	1	(	(	PUNCT
ejpam-4299	328	2	0	0	NUM
ejpam-4299	328	3	)	)	PUNCT
ejpam-4299	328	4	=	=	VERB
ejpam-4299	329	1	cα2	cα2	NOUN
ejpam-4299	329	2	(	(	PUNCT
ejpam-4299	329	3	33	33	NUM
ejpam-4299	329	4	)	)	PUNCT
ejpam-4299	329	5	for	for	ADP
ejpam-4299	329	6	t	t	PROPN
ejpam-4299	329	7	∈	∈	PROPN
ejpam-4299	329	8	(	(	PUNCT
ejpam-4299	329	9	0	0	NUM
ejpam-4299	329	10	,	,	PUNCT
ejpam-4299	329	11	a	a	PRON
ejpam-4299	329	12	)	)	PUNCT
ejpam-4299	329	13	,	,	PUNCT
ejpam-4299	329	14	for	for	ADP
ejpam-4299	329	15	all	all	DET
ejpam-4299	329	16	q	q	PROPN
ejpam-4299	329	17	∈	∈	PROPN
ejpam-4299	329	18	(	(	PUNCT
ejpam-4299	329	19	0	0	NUM
ejpam-4299	329	20	,	,	PUNCT
ejpam-4299	329	21	1	1	NUM
ejpam-4299	329	22	]	]	PUNCT
ejpam-4299	329	23	and	and	CCONJ
ejpam-4299	329	24	α	α	PRON
ejpam-4299	329	25	∈	∈	PROPN
ejpam-4299	330	1	[	[	X
ejpam-4299	330	2	0	0	NUM
ejpam-4299	330	3	,	,	PUNCT
ejpam-4299	330	4	1	1	NUM
ejpam-4299	330	5	]	]	PUNCT
ejpam-4299	330	6	.	.	PUNCT
ejpam-4299	331	1	thus	thus	ADV
ejpam-4299	331	2	for	for	ADP
ejpam-4299	331	3	fixed	fixed	ADJ
ejpam-4299	331	4	α	α	NOUN
ejpam-4299	331	5	,	,	PUNCT
ejpam-4299	331	6	we	we	PRON
ejpam-4299	331	7	have	have	VERB
ejpam-4299	331	8	an	an	DET
ejpam-4299	331	9	initial	initial	ADJ
ejpam-4299	331	10	value	value	NOUN
ejpam-4299	331	11	problem	problem	NOUN
ejpam-4299	331	12	in	in	ADP
ejpam-4299	331	13	r2	r2	PROPN
ejpam-4299	331	14	.	.	PUNCT
ejpam-4299	332	1	if	if	SCONJ
ejpam-4299	332	2	we	we	PRON
ejpam-4299	332	3	can	can	AUX
ejpam-4299	332	4	solve	solve	VERB
ejpam-4299	332	5	it	it	PRON
ejpam-4299	332	6	(	(	PUNCT
ejpam-4299	332	7	uniquely	uniquely	ADV
ejpam-4299	332	8	)	)	PUNCT
ejpam-4299	332	9	,	,	PUNCT
ejpam-4299	332	10	we	we	PRON
ejpam-4299	332	11	have	have	VERB
ejpam-4299	332	12	only	only	ADV
ejpam-4299	332	13	to	to	PART
ejpam-4299	332	14	verify	verify	VERB
ejpam-4299	332	15	that	that	SCONJ
ejpam-4299	332	16	the	the	DET
ejpam-4299	332	17	intervals	interval	NOUN
ejpam-4299	332	18	[	[	X
ejpam-4299	332	19	xα1	xα1	X
ejpam-4299	332	20	(	(	PUNCT
ejpam-4299	332	21	t	t	NOUN
ejpam-4299	332	22	)	)	PUNCT
ejpam-4299	332	23	,	,	PUNCT
ejpam-4299	332	24	xα2	xα2	PUNCT
ejpam-4299	332	25	(	(	PUNCT
ejpam-4299	332	26	t	t	PROPN
ejpam-4299	332	27	)	)	PUNCT
ejpam-4299	332	28	]	]	PUNCT
ejpam-4299	332	29	,	,	PUNCT
ejpam-4299	332	30	α	α	PROPN
ejpam-4299	332	31	∈	∈	PROPN
ejpam-4299	333	1	[	[	X
ejpam-4299	333	2	0	0	NUM
ejpam-4299	333	3	,	,	PUNCT
ejpam-4299	333	4	1	1	NUM
ejpam-4299	333	5	]	]	PUNCT
ejpam-4299	333	6	,	,	PUNCT
ejpam-4299	333	7	define	define	VERB
ejpam-4299	333	8	a	a	DET
ejpam-4299	333	9	fuzzy	fuzzy	ADJ
ejpam-4299	333	10	number	number	NOUN
ejpam-4299	333	11	x̄	x̄	PROPN
ejpam-4299	333	12	∈	∈	PROPN
ejpam-4299	333	13	rf	rf	NOUN
ejpam-4299	333	14	theorem	theorem	NOUN
ejpam-4299	333	15	7	7	X
ejpam-4299	333	16	.	.	PUNCT
ejpam-4299	334	1	let	let	VERB
ejpam-4299	334	2	f	f	PRON
ejpam-4299	334	3	satisfy	satisfy	VERB
ejpam-4299	334	4	|f	|f	PROPN
ejpam-4299	334	5	(	(	PUNCT
ejpam-4299	334	6	t	t	PROPN
ejpam-4299	334	7	,	,	PUNCT
ejpam-4299	334	8	x)−	x)−	PROPN
ejpam-4299	334	9	f	f	PROPN
ejpam-4299	334	10	(	(	PUNCT
ejpam-4299	334	11	t	t	PROPN
ejpam-4299	334	12	,	,	PUNCT
ejpam-4299	334	13	x̃)|	x̃)|	PROPN
ejpam-4299	334	14	≤	≤	ADV
ejpam-4299	334	15	h(t	h(t	PROPN
ejpam-4299	334	16	,	,	PUNCT
ejpam-4299	334	17	|x−	|x−	NOUN
ejpam-4299	334	18	x̃|	x̃|	NOUN
ejpam-4299	334	19	)	)	PUNCT
ejpam-4299	334	20	,	,	PUNCT
ejpam-4299	334	21	t	t	PROPN
ejpam-4299	334	22	≥	≥	NUM
ejpam-4299	334	23	0	0	NUM
ejpam-4299	334	24	,	,	PUNCT
ejpam-4299	334	25	x	x	PRON
ejpam-4299	334	26	,	,	PUNCT
ejpam-4299	334	27	x̃	x̃	PROPN
ejpam-4299	334	28	∈	∈	PROPN
ejpam-4299	334	29	r	r	NOUN
ejpam-4299	334	30	(	(	PUNCT
ejpam-4299	334	31	34	34	NUM
ejpam-4299	334	32	)	)	PUNCT
ejpam-4299	334	33	where	where	SCONJ
ejpam-4299	334	34	h	h	NOUN
ejpam-4299	334	35	:	:	PUNCT
ejpam-4299	334	36	r+	r+	NOUN
ejpam-4299	334	37	×r+	×r+	ADV
ejpam-4299	334	38	→	→	SYM
ejpam-4299	334	39	r+	r+	PRON
ejpam-4299	334	40	is	be	AUX
ejpam-4299	334	41	a	a	DET
ejpam-4299	334	42	continuous	continuous	ADJ
ejpam-4299	334	43	mapping	mapping	NOUN
ejpam-4299	334	44	such	such	ADJ
ejpam-4299	334	45	that	that	SCONJ
ejpam-4299	334	46	r	r	NOUN
ejpam-4299	334	47	→	→	SYM
ejpam-4299	334	48	h(t	h(t	PROPN
ejpam-4299	334	49	,	,	PUNCT
ejpam-4299	334	50	r	r	NOUN
ejpam-4299	334	51	)	)	PUNCT
ejpam-4299	334	52	is	be	AUX
ejpam-4299	334	53	nondecreasing	nondecrease	VERB
ejpam-4299	334	54	,	,	PUNCT
ejpam-4299	334	55	the	the	DET
ejpam-4299	334	56	initial	initial	ADJ
ejpam-4299	334	57	value	value	NOUN
ejpam-4299	334	58	problem	problem	NOUN
ejpam-4299	334	59	y(q)(t	y(q)(t	NOUN
ejpam-4299	334	60	)	)	PUNCT
ejpam-4299	334	61	=	=	SYM
ejpam-4299	334	62	h(t	h(t	PROPN
ejpam-4299	334	63	,	,	PUNCT
ejpam-4299	334	64	y(t	y(t	NOUN
ejpam-4299	334	65	)	)	PUNCT
ejpam-4299	334	66	)	)	PUNCT
ejpam-4299	334	67	,	,	PUNCT
ejpam-4299	334	68	y(0	y(0	PROPN
ejpam-4299	334	69	)	)	PUNCT
ejpam-4299	335	1	=	=	SYM
ejpam-4299	335	2	y0	y0	NOUN
ejpam-4299	335	3	(	(	PUNCT
ejpam-4299	335	4	35	35	NUM
ejpam-4299	335	5	)	)	PUNCT
ejpam-4299	335	6	has	have	VERB
ejpam-4299	335	7	a	a	DET
ejpam-4299	335	8	solution	solution	NOUN
ejpam-4299	335	9	on	on	ADP
ejpam-4299	335	10	r+	r+	NOUN
ejpam-4299	335	11	for	for	ADP
ejpam-4299	335	12	y0	y0	PROPN
ejpam-4299	335	13	>	>	X
ejpam-4299	335	14	0	0	PUNCT
ejpam-4299	335	15	and	and	CCONJ
ejpam-4299	335	16	that	that	PRON
ejpam-4299	335	17	y(t	y(t	PROPN
ejpam-4299	335	18	)	)	PUNCT
ejpam-4299	336	1	=	=	SYM
ejpam-4299	336	2	0	0	NUM
ejpam-4299	336	3	is	be	AUX
ejpam-4299	336	4	the	the	DET
ejpam-4299	336	5	only	only	ADJ
ejpam-4299	336	6	solution	solution	NOUN
ejpam-4299	336	7	of	of	ADP
ejpam-4299	336	8	(	(	PUNCT
ejpam-4299	336	9	35	35	NUM
ejpam-4299	336	10	)	)	PUNCT
ejpam-4299	336	11	for	for	ADP
ejpam-4299	336	12	y0	y0	PROPN
ejpam-4299	336	13	=	=	SYM
ejpam-4299	336	14	0	0	NUM
ejpam-4299	336	15	.	.	PUNCT
ejpam-4299	337	1	then	then	ADV
ejpam-4299	337	2	the	the	DET
ejpam-4299	337	3	initial	initial	ADJ
ejpam-4299	337	4	value	value	NOUN
ejpam-4299	337	5	problem	problem	NOUN
ejpam-4299	337	6	(	(	PUNCT
ejpam-4299	337	7	28	28	NUM
ejpam-4299	337	8	)	)	PUNCT
ejpam-4299	337	9	has	have	VERB
ejpam-4299	337	10	a	a	DET
ejpam-4299	337	11	unique	unique	ADJ
ejpam-4299	337	12	fuzzy	fuzzy	ADJ
ejpam-4299	337	13	solution	solution	NOUN
ejpam-4299	337	14	.	.	PUNCT
ejpam-4299	338	1	proof	proof	NOUN
ejpam-4299	338	2	.	.	PUNCT
ejpam-4299	339	1	denote	denote	VERB
ejpam-4299	339	2	f̃	f̃	PROPN
ejpam-4299	339	3	=	=	PUNCT
ejpam-4299	339	4	(	(	PUNCT
ejpam-4299	339	5	f1	f1	NOUN
ejpam-4299	339	6	,	,	PUNCT
ejpam-4299	339	7	f2	f2	PROPN
ejpam-4299	339	8	)	)	PUNCT
ejpam-4299	339	9	,	,	PUNCT
ejpam-4299	339	10	f1(t	f1(t	PROPN
ejpam-4299	339	11	,	,	PUNCT
ejpam-4299	339	12	x	x	NOUN
ejpam-4299	339	13	)	)	PUNCT
ejpam-4299	339	14	=	=	SYM
ejpam-4299	339	15	min	min	NOUN
ejpam-4299	339	16	{	{	PUNCT
ejpam-4299	339	17	f	f	PROPN
ejpam-4299	339	18	(	(	PUNCT
ejpam-4299	339	19	t	t	PROPN
ejpam-4299	339	20	,	,	PUNCT
ejpam-4299	339	21	y	y	PROPN
ejpam-4299	339	22	)	)	PUNCT
ejpam-4299	339	23	:	:	PUNCT
ejpam-4299	340	1	y	y	PROPN
ejpam-4299	340	2	∈	∈	PROPN
ejpam-4299	341	1	[	[	X
ejpam-4299	341	2	x1	x1	PROPN
ejpam-4299	341	3	,	,	PUNCT
ejpam-4299	341	4	x2	x2	PROPN
ejpam-4299	341	5	]	]	X
ejpam-4299	341	6	}	}	PUNCT
ejpam-4299	341	7	and	and	CCONJ
ejpam-4299	341	8	f2(t	f2(t	PROPN
ejpam-4299	341	9	,	,	PUNCT
ejpam-4299	341	10	x	x	NOUN
ejpam-4299	341	11	)	)	PUNCT
ejpam-4299	341	12	=	=	SYM
ejpam-4299	341	13	max	max	PROPN
ejpam-4299	341	14	{	{	PUNCT
ejpam-4299	341	15	f	f	PROPN
ejpam-4299	341	16	(	(	PUNCT
ejpam-4299	341	17	t	t	PROPN
ejpam-4299	341	18	,	,	PUNCT
ejpam-4299	341	19	y	y	PROPN
ejpam-4299	341	20	)	)	PUNCT
ejpam-4299	341	21	:	:	PUNCT
ejpam-4299	342	1	y	y	PROPN
ejpam-4299	342	2	∈	∈	PROPN
ejpam-4299	343	1	[	[	X
ejpam-4299	343	2	x1	x1	PROPN
ejpam-4299	343	3	,	,	PUNCT
ejpam-4299	343	4	x2	x2	PROPN
ejpam-4299	343	5	]	]	X
ejpam-4299	343	6	}	}	PUNCT
ejpam-4299	343	7	where	where	SCONJ
ejpam-4299	343	8	x	x	X
ejpam-4299	343	9	=	=	PRON
ejpam-4299	343	10	(	(	PUNCT
ejpam-4299	343	11	x1	x1	PROPN
ejpam-4299	343	12	,	,	PUNCT
ejpam-4299	343	13	x2	x2	ADJ
ejpam-4299	343	14	)	)	PUNCT
ejpam-4299	343	15	∈	∈	PROPN
ejpam-4299	343	16	r2	r2	NOUN
ejpam-4299	343	17	.	.	PUNCT
ejpam-4299	344	1	it	it	PRON
ejpam-4299	344	2	can	can	AUX
ejpam-4299	344	3	be	be	AUX
ejpam-4299	344	4	shown	show	VERB
ejpam-4299	344	5	that	that	SCONJ
ejpam-4299	344	6	(	(	PUNCT
ejpam-4299	344	7	26	26	NUM
ejpam-4299	344	8	)	)	PUNCT
ejpam-4299	344	9	implies	imply	VERB
ejpam-4299	344	10	‖f̃	‖f̃	PUNCT
ejpam-4299	344	11	(	(	PUNCT
ejpam-4299	344	12	t	t	PROPN
ejpam-4299	344	13	,	,	PUNCT
ejpam-4299	344	14	x)−	x)−	PROPN
ejpam-4299	344	15	f̃	f̃	PROPN
ejpam-4299	344	16	(	(	PUNCT
ejpam-4299	344	17	t	t	PROPN
ejpam-4299	344	18	,	,	PUNCT
ejpam-4299	344	19	x̃)‖	x̃)‖	PROPN
ejpam-4299	344	20	≤	≤	PROPN
ejpam-4299	344	21	h(t	h(t	PROPN
ejpam-4299	344	22	,	,	PUNCT
ejpam-4299	344	23	‖x−	‖x−	PROPN
ejpam-4299	344	24	x̃‖	x̃‖	NOUN
ejpam-4299	344	25	)	)	PUNCT
ejpam-4299	344	26	,	,	PUNCT
ejpam-4299	344	27	t	t	PROPN
ejpam-4299	344	28	≥	≥	NUM
ejpam-4299	344	29	0	0	NUM
ejpam-4299	344	30	,	,	PUNCT
ejpam-4299	344	31	x	x	PRON
ejpam-4299	344	32	,	,	PUNCT
ejpam-4299	344	33	x̃	x̃	PROPN
ejpam-4299	344	34	∈	∈	PROPN
ejpam-4299	344	35	r2	r2	PROPN
ejpam-4299	344	36	(	(	PUNCT
ejpam-4299	344	37	36	36	NUM
ejpam-4299	344	38	)	)	PUNCT
ejpam-4299	344	39	where	where	SCONJ
ejpam-4299	344	40	the	the	DET
ejpam-4299	344	41	norm	norm	NOUN
ejpam-4299	344	42	‖.‖	‖.‖	NOUN
ejpam-4299	344	43	is	be	AUX
ejpam-4299	344	44	defined	define	VERB
ejpam-4299	344	45	by	by	ADP
ejpam-4299	344	46	‖x‖	‖x‖	PROPN
ejpam-4299	344	47	=	=	SYM
ejpam-4299	344	48	max	max	PROPN
ejpam-4299	344	49	{	{	PUNCT
ejpam-4299	344	50	|x1|	|x1|	PROPN
ejpam-4299	344	51	,	,	PUNCT
ejpam-4299	344	52	|x2|	|x2|	PROPN
ejpam-4299	344	53	}	}	PUNCT
ejpam-4299	344	54	.	.	PUNCT
ejpam-4299	345	1	it	it	PRON
ejpam-4299	345	2	is	be	AUX
ejpam-4299	345	3	well	well	ADV
ejpam-4299	345	4	known	know	VERB
ejpam-4299	346	1	that	that	SCONJ
ejpam-4299	346	2	(	(	PUNCT
ejpam-4299	346	3	36	36	NUM
ejpam-4299	346	4	)	)	PUNCT
ejpam-4299	346	5	and	and	CCONJ
ejpam-4299	346	6	the	the	DET
ejpam-4299	346	7	assumptions	assumption	NOUN
ejpam-4299	346	8	on	on	ADP
ejpam-4299	346	9	h	h	PROPN
ejpam-4299	346	10	gurantee	gurantee	NOUN
ejpam-4299	346	11	tha	tha	NOUN
ejpam-4299	346	12	existence	existence	NOUN
ejpam-4299	346	13	,	,	PUNCT
ejpam-4299	346	14	uniqueness	uniqueness	NOUN
ejpam-4299	346	15	and	and	CCONJ
ejpam-4299	346	16	continuous	continuous	ADJ
ejpam-4299	346	17	dependence	dependence	NOUN
ejpam-4299	346	18	on	on	ADP
ejpam-4299	346	19	initial	initial	ADJ
ejpam-4299	346	20	value	value	NOUN
ejpam-4299	346	21	of	of	ADP
ejpam-4299	346	22	a	a	DET
ejpam-4299	346	23	solution	solution	NOUN
ejpam-4299	346	24	to	to	ADP
ejpam-4299	346	25	x(q)(t	x(q)(t	NUM
ejpam-4299	346	26	)	)	PUNCT
ejpam-4299	346	27	=	=	SYM
ejpam-4299	346	28	f̃	f̃	PROPN
ejpam-4299	346	29	(	(	PUNCT
ejpam-4299	346	30	t	t	PROPN
ejpam-4299	346	31	,	,	PUNCT
ejpam-4299	346	32	x(t	x(t	PROPN
ejpam-4299	346	33	)	)	PUNCT
ejpam-4299	346	34	)	)	PUNCT
ejpam-4299	346	35	,	,	PUNCT
ejpam-4299	346	36	x(0	x(0	PROPN
ejpam-4299	346	37	)	)	PUNCT
ejpam-4299	347	1	=	=	PUNCT
ejpam-4299	347	2	x0	x0	PROPN
ejpam-4299	347	3	∈	∈	PROPN
ejpam-4299	347	4	r2	r2	NOUN
ejpam-4299	347	5	(	(	PUNCT
ejpam-4299	347	6	37	37	NUM
ejpam-4299	347	7	)	)	PUNCT
ejpam-4299	347	8	and	and	CCONJ
ejpam-4299	347	9	that	that	SCONJ
ejpam-4299	347	10	for	for	ADP
ejpam-4299	347	11	any	any	DET
ejpam-4299	347	12	continuous	continuous	ADJ
ejpam-4299	347	13	function	function	NOUN
ejpam-4299	347	14	x1	x1	NOUN
ejpam-4299	347	15	:	:	PUNCT
ejpam-4299	347	16	r+	r+	VERB
ejpam-4299	347	17	−→	−→	ADJ
ejpam-4299	347	18	r2	r2	PROPN
ejpam-4299	347	19	the	the	DET
ejpam-4299	347	20	successive	successive	ADJ
ejpam-4299	347	21	approximations	approximation	NOUN
ejpam-4299	347	22	t	t	PROPN
ejpam-4299	347	23	≥	≥	NOUN
ejpam-4299	347	24	0	0	NUM
ejpam-4299	347	25	,	,	PUNCT
ejpam-4299	347	26	n	n	NOUN
ejpam-4299	347	27	=	=	SYM
ejpam-4299	347	28	1	1	NUM
ejpam-4299	347	29	,	,	PUNCT
ejpam-4299	347	30	2	2	NUM
ejpam-4299	347	31	,	,	PUNCT
ejpam-4299	347	32	.	.	PUNCT
ejpam-4299	347	33	.	.	PUNCT
ejpam-4299	347	34	.	.	PUNCT
ejpam-4299	348	1	xn+1(t	xn+1(t	PROPN
ejpam-4299	348	2	)	)	PUNCT
ejpam-4299	349	1	=	=	PUNCT
ejpam-4299	350	1	x0	x0	PROPN
ejpam-4299	350	2	+	+	CCONJ
ejpam-4299	350	3	iq(f̃	iq(f̃	NOUN
ejpam-4299	350	4	)	)	PUNCT
ejpam-4299	350	5	(	(	PUNCT
ejpam-4299	350	6	t	t	PROPN
ejpam-4299	350	7	,	,	PUNCT
ejpam-4299	350	8	xn(t	xn(t	NUM
ejpam-4299	350	9	)	)	PUNCT
ejpam-4299	350	10	)	)	PUNCT
ejpam-4299	351	1	=	=	SYM
ejpam-4299	352	1	x0	x0	PROPN
ejpam-4299	353	1	+	+	CCONJ
ejpam-4299	353	2	i	i	PRON
ejpam-4299	353	3	(	(	PUNCT
ejpam-4299	353	4	t1−qf̃	t1−qf̃	NUM
ejpam-4299	353	5	)	)	PUNCT
ejpam-4299	353	6	(	(	PUNCT
ejpam-4299	353	7	t	t	PROPN
ejpam-4299	353	8	,	,	PUNCT
ejpam-4299	353	9	xn(t	xn(t	NUM
ejpam-4299	353	10	)	)	PUNCT
ejpam-4299	353	11	)	)	PUNCT
ejpam-4299	354	1	=	=	SYM
ejpam-4299	355	1	x0	x0	PROPN
ejpam-4299	356	1	+	+	CCONJ
ejpam-4299	357	1	∫	∫	PROPN
ejpam-4299	357	2	t	t	PROPN
ejpam-4299	357	3	0	0	NUM
ejpam-4299	358	1	f̃	f̃	PROPN
ejpam-4299	358	2	x1−q	x1−q	PROPN
ejpam-4299	358	3	(	(	PUNCT
ejpam-4299	358	4	s	s	PROPN
ejpam-4299	358	5	,	,	PUNCT
ejpam-4299	358	6	xn(s	xn(s	NUM
ejpam-4299	358	7	)	)	PUNCT
ejpam-4299	358	8	)	)	PUNCT
ejpam-4299	359	1	ds	ds	INTJ
ejpam-4299	359	2	(	(	PUNCT
ejpam-4299	359	3	38	38	NUM
ejpam-4299	359	4	)	)	PUNCT
ejpam-4299	359	5	a.	a.	NOUN
ejpam-4299	359	6	harir	harir	PROPN
ejpam-4299	359	7	,	,	PUNCT
ejpam-4299	359	8	s.	s.	PROPN
ejpam-4299	359	9	melliani	melliani	PROPN
ejpam-4299	359	10	,	,	PUNCT
ejpam-4299	359	11	l.	l.	PROPN
ejpam-4299	359	12	s.	s.	PROPN
ejpam-4299	359	13	chadli	chadli	PROPN
ejpam-4299	359	14	/	/	SYM
ejpam-4299	359	15	eur	eur	PROPN
ejpam-4299	359	16	.	.	PUNCT
ejpam-4299	360	1	j.	j.	PROPN
ejpam-4299	360	2	pure	pure	PROPN
ejpam-4299	360	3	appl	appl	PROPN
ejpam-4299	360	4	.	.	PROPN
ejpam-4299	360	5	math	math	PROPN
ejpam-4299	360	6	,	,	PUNCT
ejpam-4299	360	7	15	15	NUM
ejpam-4299	360	8	(	(	PUNCT
ejpam-4299	360	9	2	2	NUM
ejpam-4299	360	10	)	)	PUNCT
ejpam-4299	360	11	(	(	PUNCT
ejpam-4299	360	12	2022	2022	NUM
ejpam-4299	360	13	)	)	PUNCT
ejpam-4299	360	14	,	,	PUNCT
ejpam-4299	360	15	557	557	NUM
ejpam-4299	360	16	-	-	SYM
ejpam-4299	360	17	571	571	NUM
ejpam-4299	360	18	569	569	NUM
ejpam-4299	360	19	converge	converge	VERB
ejpam-4299	360	20	uniformly	uniformly	ADV
ejpam-4299	360	21	on	on	ADP
ejpam-4299	360	22	closed	close	VERB
ejpam-4299	360	23	subintervals	subinterval	NOUN
ejpam-4299	360	24	of	of	ADP
ejpam-4299	360	25	r+	r+	NOUN
ejpam-4299	360	26	to	to	ADP
ejpam-4299	360	27	the	the	DET
ejpam-4299	360	28	solution	solution	NOUN
ejpam-4299	360	29	of	of	ADP
ejpam-4299	360	30	(	(	PUNCT
ejpam-4299	360	31	37	37	NUM
ejpam-4299	360	32	)	)	PUNCT
ejpam-4299	360	33	.	.	PUNCT
ejpam-4299	361	1	by	by	ADP
ejpam-4299	361	2	choosing	choose	VERB
ejpam-4299	361	3	x0	x0	PROPN
ejpam-4299	361	4	=	=	PRON
ejpam-4299	362	1	(	(	PUNCT
ejpam-4299	362	2	cα1	cα1	INTJ
ejpam-4299	362	3	,	,	PUNCT
ejpam-4299	362	4	c	c	NOUN
ejpam-4299	362	5	α	α	PRON
ejpam-4299	362	6	2	2	NUM
ejpam-4299	362	7	)	)	PUNCT
ejpam-4299	362	8	in	in	ADP
ejpam-4299	362	9	(	(	PUNCT
ejpam-4299	362	10	37	37	NUM
ejpam-4299	362	11	)	)	PUNCT
ejpam-4299	362	12	we	we	PRON
ejpam-4299	362	13	get	get	VERB
ejpam-4299	362	14	a	a	DET
ejpam-4299	362	15	unique	unique	ADJ
ejpam-4299	362	16	solution	solution	NOUN
ejpam-4299	362	17	xα(t	xα(t	NUM
ejpam-4299	362	18	)	)	PUNCT
ejpam-4299	362	19	=	=	SYM
ejpam-4299	362	20	(	(	PUNCT
ejpam-4299	362	21	xα1	xα1	X
ejpam-4299	362	22	(	(	PUNCT
ejpam-4299	362	23	t	t	PROPN
ejpam-4299	362	24	)	)	PUNCT
ejpam-4299	362	25	,	,	PUNCT
ejpam-4299	362	26	x	x	X
ejpam-4299	362	27	α	α	X
ejpam-4299	362	28	2	2	NUM
ejpam-4299	362	29	(	(	PUNCT
ejpam-4299	362	30	t	t	PROPN
ejpam-4299	362	31	)	)	PUNCT
ejpam-4299	362	32	)	)	PUNCT
ejpam-4299	362	33	to	to	ADP
ejpam-4299	362	34	(	(	PUNCT
ejpam-4299	362	35	30),(32	30),(32	NUM
ejpam-4299	362	36	)	)	PUNCT
ejpam-4299	362	37	for	for	ADP
ejpam-4299	362	38	each	each	DET
ejpam-4299	362	39	α	α	NOUN
ejpam-4299	362	40	∈	∈	PROPN
ejpam-4299	363	1	[	[	X
ejpam-4299	363	2	0	0	NUM
ejpam-4299	363	3	,	,	PUNCT
ejpam-4299	363	4	1	1	NUM
ejpam-4299	363	5	]	]	PUNCT
ejpam-4299	363	6	.	.	PUNCT
ejpam-4299	364	1	next	next	ADV
ejpam-4299	364	2	we	we	PRON
ejpam-4299	364	3	will	will	AUX
ejpam-4299	364	4	show	show	VERB
ejpam-4299	364	5	that	that	SCONJ
ejpam-4299	364	6	the	the	DET
ejpam-4299	364	7	intervals	interval	NOUN
ejpam-4299	364	8	[	[	X
ejpam-4299	364	9	xα1	xα1	X
ejpam-4299	364	10	(	(	PUNCT
ejpam-4299	364	11	t	t	NOUN
ejpam-4299	364	12	)	)	PUNCT
ejpam-4299	364	13	,	,	PUNCT
ejpam-4299	364	14	xα2	xα2	PUNCT
ejpam-4299	364	15	(	(	PUNCT
ejpam-4299	364	16	t	t	PROPN
ejpam-4299	364	17	)	)	PUNCT
ejpam-4299	364	18	]	]	PUNCT
ejpam-4299	364	19	,	,	PUNCT
ejpam-4299	364	20	α	α	PROPN
ejpam-4299	364	21	∈	∈	PROPN
ejpam-4299	365	1	[	[	X
ejpam-4299	365	2	0	0	NUM
ejpam-4299	365	3	,	,	PUNCT
ejpam-4299	365	4	1	1	NUM
ejpam-4299	365	5	]	]	PUNCT
ejpam-4299	365	6	,	,	PUNCT
ejpam-4299	365	7	define	define	VERB
ejpam-4299	365	8	a	a	DET
ejpam-4299	365	9	fuzzy	fuzzy	ADJ
ejpam-4299	365	10	number	number	NOUN
ejpam-4299	365	11	x̄	x̄	SYM
ejpam-4299	365	12	∈	∈	PROPN
ejpam-4299	365	13	rf	rf	VERB
ejpam-4299	365	14	for	for	ADP
ejpam-4299	365	15	eatch	eatch	PROPN
ejpam-4299	365	16	t	t	PROPN
ejpam-4299	365	17	≥	≥	PROPN
ejpam-4299	365	18	0	0	NUM
ejpam-4299	365	19	,	,	PUNCT
ejpam-4299	365	20	i.e	i.e	CCONJ
ejpam-4299	365	21	that	that	SCONJ
ejpam-4299	365	22	x̄	x̄	NOUN
ejpam-4299	365	23	is	be	AUX
ejpam-4299	365	24	a	a	DET
ejpam-4299	365	25	fuzzy	fuzzy	ADJ
ejpam-4299	365	26	solution	solution	NOUN
ejpam-4299	365	27	to	to	ADP
ejpam-4299	365	28	(	(	PUNCT
ejpam-4299	365	29	28	28	NUM
ejpam-4299	365	30	)	)	PUNCT
ejpam-4299	365	31	.	.	PUNCT
ejpam-4299	366	1	the	the	DET
ejpam-4299	366	2	successive	successive	ADJ
ejpam-4299	366	3	approximations	approximation	NOUN
ejpam-4299	366	4	x1(t	x1(t	PUNCT
ejpam-4299	366	5	)	)	PUNCT
ejpam-4299	366	6	=	=	SYM
ejpam-4299	366	7	x0	x0	PROPN
ejpam-4299	366	8	∈	∈	PROPN
ejpam-4299	366	9	rf	rf	NOUN
ejpam-4299	366	10	xn+1(t	xn+1(t	PROPN
ejpam-4299	366	11	)	)	PUNCT
ejpam-4299	367	1	=	=	PUNCT
ejpam-4299	368	1	x0	x0	PROPN
ejpam-4299	369	1	+	+	CCONJ
ejpam-4299	370	1	∫	∫	PROPN
ejpam-4299	370	2	t	t	PROPN
ejpam-4299	370	3	0	0	NUM
ejpam-4299	371	1	f	f	PROPN
ejpam-4299	371	2	x1−q	x1−q	PROPN
ejpam-4299	371	3	(	(	PUNCT
ejpam-4299	371	4	s	s	PROPN
ejpam-4299	371	5	,	,	PUNCT
ejpam-4299	371	6	xn(s	xn(s	NUM
ejpam-4299	371	7	)	)	PUNCT
ejpam-4299	371	8	)	)	PUNCT
ejpam-4299	371	9	ds	ds	PROPN
ejpam-4299	371	10	,	,	PUNCT
ejpam-4299	371	11	t	t	PROPN
ejpam-4299	371	12	≥	≥	NUM
ejpam-4299	371	13	0	0	NUM
ejpam-4299	371	14	,	,	PUNCT
ejpam-4299	371	15	n	n	NOUN
ejpam-4299	371	16	=	=	SYM
ejpam-4299	371	17	1	1	NUM
ejpam-4299	371	18	,	,	PUNCT
ejpam-4299	371	19	2	2	NUM
ejpam-4299	371	20	,	,	PUNCT
ejpam-4299	371	21	.	.	PUNCT
ejpam-4299	371	22	.	.	PUNCT
ejpam-4299	371	23	.	.	PUNCT
ejpam-4299	372	1	where	where	SCONJ
ejpam-4299	372	2	the	the	DET
ejpam-4299	372	3	integral	integral	ADJ
ejpam-4299	372	4	is	be	AUX
ejpam-4299	372	5	the	the	DET
ejpam-4299	372	6	fuzzy	fuzzy	ADJ
ejpam-4299	372	7	integral	integral	ADJ
ejpam-4299	372	8	,	,	PUNCT
ejpam-4299	372	9	define	define	VERB
ejpam-4299	372	10	a	a	DET
ejpam-4299	372	11	sequence	sequence	NOUN
ejpam-4299	372	12	of	of	ADP
ejpam-4299	372	13	fuzzy	fuzzy	ADJ
ejpam-4299	372	14	numbers	number	NOUN
ejpam-4299	372	15	xn(t	xn(t	PRON
ejpam-4299	372	16	)	)	PUNCT
ejpam-4299	372	17	∈	∈	PROPN
ejpam-4299	372	18	rf	rf	NOUN
ejpam-4299	372	19	,	,	PUNCT
ejpam-4299	372	20	∀t	∀t	PROPN
ejpam-4299	372	21	≥	≥	NOUN
ejpam-4299	372	22	0	0	PUNCT
ejpam-4299	372	23	hence	hence	ADV
ejpam-4299	372	24	[	[	X
ejpam-4299	372	25	xn(t	xn(t	NUM
ejpam-4299	372	26	)	)	PUNCT
ejpam-4299	372	27	]	]	PUNCT
ejpam-4299	373	1	α	α	PRON
ejpam-4299	373	2	⊃	⊃	PROPN
ejpam-4299	374	1	[	[	X
ejpam-4299	374	2	xn(t	xn(t	NUM
ejpam-4299	374	3	)	)	PUNCT
ejpam-4299	374	4	]	]	PUNCT
ejpam-4299	375	1	β	β	X
ejpam-4299	375	2	if	if	SCONJ
ejpam-4299	375	3	0	0	NUM
ejpam-4299	375	4	<	<	X
ejpam-4299	375	5	α	α	X
ejpam-4299	375	6	≤	≤	PUNCT
ejpam-4299	375	7	β	β	X
ejpam-4299	375	8	≤	≤	NUM
ejpam-4299	375	9	1	1	NUM
ejpam-4299	375	10	which	which	PRON
ejpam-4299	375	11	implies	imply	VERB
ejpam-4299	375	12	that	that	SCONJ
ejpam-4299	376	1	[	[	X
ejpam-4299	376	2	xα1	xα1	X
ejpam-4299	376	3	(	(	PUNCT
ejpam-4299	376	4	t	t	NOUN
ejpam-4299	376	5	)	)	PUNCT
ejpam-4299	376	6	,	,	PUNCT
ejpam-4299	376	7	x	x	X
ejpam-4299	376	8	α	α	X
ejpam-4299	376	9	2	2	NUM
ejpam-4299	376	10	(	(	PUNCT
ejpam-4299	376	11	t	t	PROPN
ejpam-4299	376	12	)	)	PUNCT
ejpam-4299	376	13	]	]	PUNCT
ejpam-4299	377	1	⊃	⊃	PROPN
ejpam-4299	377	2	[	[	PUNCT
ejpam-4299	377	3	xβ1	xβ1	PROPN
ejpam-4299	377	4	(	(	PUNCT
ejpam-4299	377	5	t	t	PROPN
ejpam-4299	377	6	)	)	PUNCT
ejpam-4299	377	7	,	,	PUNCT
ejpam-4299	377	8	x	x	X
ejpam-4299	377	9	β	β	X
ejpam-4299	377	10	2	2	NUM
ejpam-4299	377	11	(	(	PUNCT
ejpam-4299	377	12	t	t	PROPN
ejpam-4299	377	13	)	)	PUNCT
ejpam-4299	377	14	]	]	PUNCT
ejpam-4299	377	15	,	,	PUNCT
ejpam-4299	377	16	0	0	PUNCT
ejpam-4299	377	17	<	<	X
ejpam-4299	377	18	α	α	PROPN
ejpam-4299	377	19	≤	≤	PUNCT
ejpam-4299	377	20	β	β	X
ejpam-4299	377	21	≤	≤	NOUN
ejpam-4299	377	22	1	1	NUM
ejpam-4299	377	23	since	since	SCONJ
ejpam-4299	377	24	,	,	PUNCT
ejpam-4299	377	25	by	by	ADP
ejpam-4299	377	26	the	the	DET
ejpam-4299	377	27	convergence	convergence	NOUN
ejpam-4299	377	28	of	of	ADP
ejpam-4299	377	29	sequence	sequence	NOUN
ejpam-4299	377	30	(	(	PUNCT
ejpam-4299	377	31	38	38	NUM
ejpam-4299	377	32	)	)	PUNCT
ejpam-4299	377	33	,	,	PUNCT
ejpam-4299	377	34	the	the	DET
ejpam-4299	377	35	end	end	NOUN
ejpam-4299	377	36	points	point	NOUN
ejpam-4299	377	37	of	of	ADP
ejpam-4299	377	38	[	[	PUNCT
ejpam-4299	377	39	xn(t)]α	xn(t)]α	PROPN
ejpam-4299	377	40	converge	converge	VERB
ejpam-4299	377	41	to	to	ADP
ejpam-4299	377	42	xα1	xα1	PROPN
ejpam-4299	377	43	(	(	PUNCT
ejpam-4299	377	44	t	t	PROPN
ejpam-4299	377	45	)	)	PUNCT
ejpam-4299	377	46	and	and	CCONJ
ejpam-4299	377	47	xα2	xα2	PROPN
ejpam-4299	377	48	(	(	PUNCT
ejpam-4299	377	49	t	t	PROPN
ejpam-4299	377	50	)	)	PUNCT
ejpam-4299	377	51	respectively	respectively	ADV
ejpam-4299	377	52	.	.	PUNCT
ejpam-4299	378	1	thus	thus	ADV
ejpam-4299	378	2	the	the	DET
ejpam-4299	378	3	inclusion	inclusion	NOUN
ejpam-4299	378	4	(	(	PUNCT
ejpam-4299	378	5	ii	ii	NOUN
ejpam-4299	378	6	)	)	PUNCT
ejpam-4299	378	7	of	of	ADP
ejpam-4299	378	8	theorem	theorem	NOUN
ejpam-4299	378	9	(	(	PUNCT
ejpam-4299	378	10	1	1	NUM
ejpam-4299	378	11	)	)	PUNCT
ejpam-4299	378	12	holds	hold	VERB
ejpam-4299	378	13	for	for	ADP
ejpam-4299	378	14	the	the	DET
ejpam-4299	378	15	intervals	interval	NOUN
ejpam-4299	378	16	[	[	X
ejpam-4299	378	17	xα1	xα1	X
ejpam-4299	378	18	(	(	PUNCT
ejpam-4299	378	19	t	t	NOUN
ejpam-4299	378	20	)	)	PUNCT
ejpam-4299	378	21	,	,	PUNCT
ejpam-4299	378	22	x	x	X
ejpam-4299	378	23	α	α	X
ejpam-4299	378	24	2	2	NUM
ejpam-4299	378	25	(	(	PUNCT
ejpam-4299	378	26	t	t	PROPN
ejpam-4299	378	27	)	)	PUNCT
ejpam-4299	378	28	]	]	PUNCT
ejpam-4299	378	29	,	,	PUNCT
ejpam-4299	378	30	α	α	PROPN
ejpam-4299	378	31	∈	∈	PROPN
ejpam-4299	379	1	[	[	X
ejpam-4299	379	2	0	0	NUM
ejpam-4299	379	3	,	,	PUNCT
ejpam-4299	379	4	1	1	NUM
ejpam-4299	379	5	]	]	PUNCT
ejpam-4299	379	6	.	.	PUNCT
ejpam-4299	380	1	for	for	ADP
ejpam-4299	380	2	the	the	DET
ejpam-4299	380	3	proof	proof	NOUN
ejpam-4299	380	4	of	of	ADP
ejpam-4299	380	5	the	the	DET
ejpam-4299	380	6	continuity	continuity	NOUN
ejpam-4299	380	7	theorem	theorem	NOUN
ejpam-4299	380	8	(	(	PUNCT
ejpam-4299	380	9	1	1	NUM
ejpam-4299	380	10	)	)	PUNCT
ejpam-4299	380	11	by	by	ADP
ejpam-4299	380	12	(	(	PUNCT
ejpam-4299	380	13	iii	iii	NOUN
ejpam-4299	380	14	)	)	PUNCT
ejpam-4299	380	15	,	,	PUNCT
ejpam-4299	380	16	let	let	AUX
ejpam-4299	380	17	(	(	PUNCT
ejpam-4299	380	18	αk	αk	AUX
ejpam-4299	380	19	)	)	PUNCT
ejpam-4299	380	20	be	be	AUX
ejpam-4299	380	21	a	a	DET
ejpam-4299	380	22	increasing	increase	VERB
ejpam-4299	380	23	sequence	sequence	NOUN
ejpam-4299	380	24	in	in	ADP
ejpam-4299	380	25	[	[	X
ejpam-4299	380	26	0	0	NUM
ejpam-4299	380	27	,	,	PUNCT
ejpam-4299	380	28	1	1	NUM
ejpam-4299	380	29	]	]	PUNCT
ejpam-4299	380	30	converging	converge	VERB
ejpam-4299	380	31	to	to	ADP
ejpam-4299	380	32	α	α	PRON
ejpam-4299	380	33	.	.	PUNCT
ejpam-4299	381	1	then	then	ADV
ejpam-4299	381	2	cαk	cαk	NOUN
ejpam-4299	381	3	1	1	NUM
ejpam-4299	381	4	→	→	SYM
ejpam-4299	381	5	cα1	cα1	NOUN
ejpam-4299	381	6	and	and	CCONJ
ejpam-4299	381	7	cαk	cαk	NOUN
ejpam-4299	381	8	2	2	NUM
ejpam-4299	381	9	→	→	SYM
ejpam-4299	381	10	cα2	cα2	NOUN
ejpam-4299	381	11	because	because	SCONJ
ejpam-4299	381	12	x̄(0	x̄(0	NUM
ejpam-4299	381	13	)	)	PUNCT
ejpam-4299	381	14	∈	∈	PROPN
ejpam-4299	381	15	rf	rf	NOUN
ejpam-4299	381	16	.	.	PUNCT
ejpam-4299	382	1	but	but	CCONJ
ejpam-4299	382	2	then	then	ADV
ejpam-4299	382	3	,	,	PUNCT
ejpam-4299	382	4	by	by	ADP
ejpam-4299	382	5	the	the	DET
ejpam-4299	382	6	continous	continous	ADJ
ejpam-4299	382	7	dependence	dependence	NOUN
ejpam-4299	382	8	on	on	ADP
ejpam-4299	382	9	the	the	DET
ejpam-4299	382	10	initial	initial	ADJ
ejpam-4299	382	11	value	value	NOUN
ejpam-4299	382	12	of	of	ADP
ejpam-4299	382	13	the	the	DET
ejpam-4299	382	14	solution	solution	NOUN
ejpam-4299	382	15	of	of	ADP
ejpam-4299	382	16	(	(	PUNCT
ejpam-4299	382	17	37	37	NUM
ejpam-4299	382	18	)	)	PUNCT
ejpam-4299	382	19	,	,	PUNCT
ejpam-4299	382	20	xαk	xαk	NOUN
ejpam-4299	382	21	1	1	NUM
ejpam-4299	382	22	→	→	SYM
ejpam-4299	382	23	xα1	xα1	PROPN
ejpam-4299	382	24	and	and	CCONJ
ejpam-4299	382	25	xαk	xαk	NOUN
ejpam-4299	382	26	2	2	NUM
ejpam-4299	382	27	→	→	SYM
ejpam-4299	382	28	xα2	xα2	PROPN
ejpam-4299	383	1	i.e	i.e	PROPN
ejpam-4299	383	2	(	(	PUNCT
ejpam-4299	383	3	iii	iii	NOUN
ejpam-4299	383	4	)	)	PUNCT
ejpam-4299	383	5	holds	hold	VERB
ejpam-4299	383	6	for	for	ADP
ejpam-4299	383	7	the	the	DET
ejpam-4299	383	8	intervals	interval	NOUN
ejpam-4299	383	9	[	[	X
ejpam-4299	383	10	xα1	xα1	X
ejpam-4299	383	11	(	(	PUNCT
ejpam-4299	383	12	t	t	NOUN
ejpam-4299	383	13	)	)	PUNCT
ejpam-4299	383	14	,	,	PUNCT
ejpam-4299	383	15	x	x	X
ejpam-4299	383	16	α	α	X
ejpam-4299	383	17	2	2	NUM
ejpam-4299	383	18	(	(	PUNCT
ejpam-4299	383	19	t	t	PROPN
ejpam-4299	383	20	)	)	PUNCT
ejpam-4299	383	21	]	]	PUNCT
ejpam-4299	383	22	,	,	PUNCT
ejpam-4299	383	23	α	α	PROPN
ejpam-4299	383	24	∈	∈	PROPN
ejpam-4299	384	1	[	[	X
ejpam-4299	384	2	0	0	NUM
ejpam-4299	384	3	,	,	PUNCT
ejpam-4299	384	4	1	1	NUM
ejpam-4299	384	5	]	]	PUNCT
ejpam-4299	384	6	.	.	PUNCT
ejpam-4299	385	1	by	by	ADP
ejpam-4299	385	2	theorem	theorem	NOUN
ejpam-4299	385	3	(	(	PUNCT
ejpam-4299	385	4	1	1	NUM
ejpam-4299	385	5	)	)	PUNCT
ejpam-4299	385	6	,	,	PUNCT
ejpam-4299	385	7	x̄	x̄	PROPN
ejpam-4299	385	8	∈	∈	PROPN
ejpam-4299	385	9	rf	rf	X
ejpam-4299	385	10	,	,	PUNCT
ejpam-4299	385	11	so	so	ADV
ejpam-4299	385	12	x̄	x̄	PRON
ejpam-4299	385	13	is	be	AUX
ejpam-4299	385	14	a	a	DET
ejpam-4299	385	15	fuzzy	fuzzy	ADJ
ejpam-4299	385	16	solution	solution	NOUN
ejpam-4299	385	17	of	of	ADP
ejpam-4299	385	18	(	(	PUNCT
ejpam-4299	385	19	28	28	NUM
ejpam-4299	385	20	)	)	PUNCT
ejpam-4299	385	21	the	the	DET
ejpam-4299	385	22	uniqueness	uniqueness	NOUN
ejpam-4299	385	23	follows	follow	VERB
ejpam-4299	385	24	from	from	ADP
ejpam-4299	385	25	the	the	DET
ejpam-4299	385	26	uniqueness	uniqueness	NOUN
ejpam-4299	385	27	of	of	ADP
ejpam-4299	385	28	the	the	DET
ejpam-4299	385	29	solution	solution	NOUN
ejpam-4299	385	30	of	of	ADP
ejpam-4299	385	31	(	(	PUNCT
ejpam-4299	385	32	37	37	NUM
ejpam-4299	385	33	)	)	PUNCT
ejpam-4299	385	34	.	.	PUNCT
ejpam-4299	386	1	5	5	X
ejpam-4299	386	2	.	.	X
ejpam-4299	386	3	applications	application	NOUN
ejpam-4299	386	4	now	now	ADV
ejpam-4299	386	5	we	we	PRON
ejpam-4299	386	6	will	will	AUX
ejpam-4299	386	7	solve	solve	VERB
ejpam-4299	386	8	fuzzy	fuzzy	ADJ
ejpam-4299	386	9	fractional	fractional	ADJ
ejpam-4299	386	10	differential	differential	ADJ
ejpam-4299	386	11	equations	equation	NOUN
ejpam-4299	386	12	according	accord	VERB
ejpam-4299	386	13	to	to	ADP
ejpam-4299	386	14	our	our	PRON
ejpam-4299	386	15	theorems	theorem	NOUN
ejpam-4299	386	16	and	and	CCONJ
ejpam-4299	386	17	definitions	definition	NOUN
ejpam-4299	386	18	.	.	PUNCT
ejpam-4299	387	1	let	let	VERB
ejpam-4299	387	2	y(q)(t	y(q)(t	NOUN
ejpam-4299	387	3	)	)	PUNCT
ejpam-4299	387	4	=	=	SYM
ejpam-4299	387	5	ky(t	ky(t	NOUN
ejpam-4299	387	6	)	)	PUNCT
ejpam-4299	387	7	,	,	PUNCT
ejpam-4299	387	8	q	q	PROPN
ejpam-4299	387	9	∈	∈	PROPN
ejpam-4299	387	10	(	(	PUNCT
ejpam-4299	387	11	0	0	NUM
ejpam-4299	387	12	,	,	PUNCT
ejpam-4299	387	13	1	1	NUM
ejpam-4299	387	14	]	]	X
ejpam-4299	387	15	y(0	y(0	PROPN
ejpam-4299	387	16	)	)	PUNCT
ejpam-4299	387	17	=	=	PUNCT
ejpam-4299	388	1	c	c	NOUN
ejpam-4299	388	2	so	so	SCONJ
ejpam-4299	388	3	that	that	SCONJ
ejpam-4299	388	4	the	the	DET
ejpam-4299	388	5	solution	solution	NOUN
ejpam-4299	388	6	is	be	AUX
ejpam-4299	388	7	given	give	VERB
ejpam-4299	388	8	by	by	ADP
ejpam-4299	388	9	y(t	y(t	PROPN
ejpam-4299	388	10	)	)	PUNCT
ejpam-4299	389	1	=	=	SYM
ejpam-4299	389	2	cexp	cexp	NOUN
ejpam-4299	389	3	(	(	PUNCT
ejpam-4299	389	4	k	k	X
ejpam-4299	389	5	q	q	PROPN
ejpam-4299	389	6	t	t	PROPN
ejpam-4299	389	7	q	q	PROPN
ejpam-4299	389	8	)	)	PUNCT
ejpam-4299	389	9	.	.	PUNCT
ejpam-4299	390	1	now	now	ADV
ejpam-4299	390	2	we	we	PRON
ejpam-4299	390	3	fuzzify	fuzzify	VERB
ejpam-4299	390	4	f	f	X
ejpam-4299	390	5	(	(	PUNCT
ejpam-4299	390	6	t	t	PROPN
ejpam-4299	390	7	,	,	PUNCT
ejpam-4299	390	8	y	y	PROPN
ejpam-4299	390	9	,	,	PUNCT
ejpam-4299	390	10	k	k	NOUN
ejpam-4299	390	11	)	)	PUNCT
ejpam-4299	390	12	=	=	SYM
ejpam-4299	390	13	ky(t	ky(t	X
ejpam-4299	390	14	)	)	PUNCT
ejpam-4299	390	15	and	and	CCONJ
ejpam-4299	390	16	g(t	g(t	PROPN
ejpam-4299	390	17	,	,	PUNCT
ejpam-4299	390	18	k	k	PROPN
ejpam-4299	390	19	,	,	PUNCT
ejpam-4299	390	20	c	c	NOUN
ejpam-4299	390	21	)	)	PUNCT
ejpam-4299	390	22	=	=	SYM
ejpam-4299	391	1	cexp	cexp	NOUN
ejpam-4299	391	2	(	(	PUNCT
ejpam-4299	391	3	k	k	X
ejpam-4299	391	4	q	q	PROPN
ejpam-4299	391	5	t	t	PROPN
ejpam-4299	391	6	q	q	PROPN
ejpam-4299	391	7	)	)	PUNCT
ejpam-4299	391	8	.	.	PUNCT
ejpam-4299	392	1	clearly	clearly	ADV
ejpam-4299	392	2	let	let	VERB
ejpam-4299	392	3	f̄	f̄	PROPN
ejpam-4299	392	4	(	(	PUNCT
ejpam-4299	392	5	t	t	PROPN
ejpam-4299	392	6	,	,	PUNCT
ejpam-4299	392	7	ȳ	ȳ	PROPN
ejpam-4299	392	8	,	,	PUNCT
ejpam-4299	392	9	k̄	k̄	PROPN
ejpam-4299	392	10	)	)	PUNCT
ejpam-4299	393	1	=	=	SYM
ejpam-4299	393	2	ky	ky	PROPN
ejpam-4299	393	3	(	(	PUNCT
ejpam-4299	393	4	t	t	PROPN
ejpam-4299	393	5	)	)	PUNCT
ejpam-4299	393	6	,	,	PUNCT
ejpam-4299	393	7	q	q	PROPN
ejpam-4299	393	8	∈	∈	PROPN
ejpam-4299	393	9	(	(	PUNCT
ejpam-4299	393	10	0	0	NUM
ejpam-4299	393	11	,	,	PUNCT
ejpam-4299	393	12	1	1	NUM
ejpam-4299	393	13	]	]	SYM
ejpam-4299	393	14	ȳ	ȳ	PROPN
ejpam-4299	393	15	(	(	PUNCT
ejpam-4299	393	16	0	0	NUM
ejpam-4299	393	17	)	)	PUNCT
ejpam-4299	393	18	=	=	VERB
ejpam-4299	393	19	c̄	c̄	VERB
ejpam-4299	394	1	so	so	SCONJ
ejpam-4299	394	2	that	that	SCONJ
ejpam-4299	394	3	fα	fα	ADP
ejpam-4299	394	4	1	1	NUM
ejpam-4299	394	5	(	(	PUNCT
ejpam-4299	394	6	t	t	NOUN
ejpam-4299	394	7	)	)	PUNCT
ejpam-4299	394	8	=	=	VERB
ejpam-4299	395	1	kα1	kα1	PROPN
ejpam-4299	395	2	y	y	PROPN
ejpam-4299	395	3	α	α	NOUN
ejpam-4299	395	4	1	1	NUM
ejpam-4299	395	5	(	(	PUNCT
ejpam-4299	395	6	t	t	PROPN
ejpam-4299	395	7	)	)	PUNCT
ejpam-4299	395	8	,	,	PUNCT
ejpam-4299	395	9	fα	fα	ADP
ejpam-4299	395	10	2	2	NUM
ejpam-4299	395	11	(	(	PUNCT
ejpam-4299	395	12	t	t	NOUN
ejpam-4299	395	13	)	)	PUNCT
ejpam-4299	395	14	=	=	PUNCT
ejpam-4299	396	1	kα2	kα2	NOUN
ejpam-4299	397	1	y	y	PROPN
ejpam-4299	397	2	α	α	PROPN
ejpam-4299	397	3	2	2	NUM
ejpam-4299	397	4	(	(	PUNCT
ejpam-4299	397	5	t	t	PROPN
ejpam-4299	397	6	)	)	PUNCT
ejpam-4299	397	7	.	.	PUNCT
ejpam-4299	398	1	also	also	ADV
ejpam-4299	398	2	ḡ(t	ḡ(t	ADJ
ejpam-4299	398	3	,	,	PUNCT
ejpam-4299	398	4	ȳ	ȳ	PROPN
ejpam-4299	398	5	,	,	PUNCT
ejpam-4299	398	6	k̄	k̄	ADV
ejpam-4299	398	7	)	)	PUNCT
ejpam-4299	398	8	=	=	SYM
ejpam-4299	398	9	cexp	cexp	NOUN
ejpam-4299	398	10	(	(	PUNCT
ejpam-4299	398	11	k̄	k̄	VERB
ejpam-4299	398	12	q	q	PROPN
ejpam-4299	398	13	t	t	PROPN
ejpam-4299	398	14	q	q	PROPN
ejpam-4299	398	15	)	)	PUNCT
ejpam-4299	398	16	,	,	PUNCT
ejpam-4299	398	17	therefore	therefore	ADV
ejpam-4299	398	18	yαi	yαi	PROPN
ejpam-4299	398	19	(	(	PUNCT
ejpam-4299	398	20	t	t	PROPN
ejpam-4299	398	21	)	)	PUNCT
ejpam-4299	398	22	=	=	NOUN
ejpam-4299	398	23	cαi	cαi	NOUN
ejpam-4299	398	24	exp	exp	NOUN
ejpam-4299	398	25	(	(	PUNCT
ejpam-4299	398	26	kαi	kαi	NOUN
ejpam-4299	398	27	q	q	X
ejpam-4299	398	28	tq	tq	NOUN
ejpam-4299	398	29	)	)	PUNCT
ejpam-4299	398	30	references	reference	NOUN
ejpam-4299	398	31	570	570	NUM
ejpam-4299	398	32	for	for	ADP
ejpam-4299	398	33	i	i	PRON
ejpam-4299	398	34	=	=	NOUN
ejpam-4299	398	35	1	1	NUM
ejpam-4299	398	36	,	,	PUNCT
ejpam-4299	398	37	2	2	NUM
ejpam-4299	398	38	and	and	CCONJ
ejpam-4299	398	39	q	q	ADJ
ejpam-4299	398	40	∈	∈	PROPN
ejpam-4299	398	41	(	(	PUNCT
ejpam-4299	398	42	0	0	NUM
ejpam-4299	398	43	,	,	PUNCT
ejpam-4299	398	44	1	1	NUM
ejpam-4299	398	45	]	]	PUNCT
ejpam-4299	398	46	,	,	PUNCT
ejpam-4299	398	47	[	[	X
ejpam-4299	398	48	k̄]α	k̄]α	NOUN
ejpam-4299	398	49	=	=	PUNCT
ejpam-4299	399	1	[	[	X
ejpam-4299	399	2	kα1	kα1	INTJ
ejpam-4299	399	3	,	,	PUNCT
ejpam-4299	399	4	k	k	PROPN
ejpam-4299	399	5	α	α	PROPN
ejpam-4299	399	6	2	2	NUM
ejpam-4299	399	7	]	]	PUNCT
ejpam-4299	399	8	and	and	CCONJ
ejpam-4299	399	9	[	[	X
ejpam-4299	399	10	c̄]α	c̄]α	NOUN
ejpam-4299	399	11	=	=	X
ejpam-4299	400	1	[	[	X
ejpam-4299	400	2	cα1	cα1	NOUN
ejpam-4299	400	3	,	,	PUNCT
ejpam-4299	400	4	c	c	NOUN
ejpam-4299	400	5	α	α	PRON
ejpam-4299	400	6	2	2	NUM
ejpam-4299	400	7	]	]	PUNCT
ejpam-4299	400	8	,	,	PUNCT
ejpam-4299	400	9	ȳ	ȳ	PROPN
ejpam-4299	400	10	is	be	AUX
ejpam-4299	400	11	q	q	ADJ
ejpam-4299	400	12	-	-	ADV
ejpam-4299	400	13	differentiable	differentiable	ADJ
ejpam-4299	400	14	because	because	SCONJ
ejpam-4299	400	15	(	(	PUNCT
ejpam-4299	400	16	yαi	yαi	PROPN
ejpam-4299	400	17	)	)	PUNCT
ejpam-4299	400	18	(	(	PUNCT
ejpam-4299	400	19	q	q	X
ejpam-4299	400	20	)	)	PUNCT
ejpam-4299	400	21	(	(	PUNCT
ejpam-4299	400	22	t),∀q	t),∀q	PROPN
ejpam-4299	400	23	∈	∈	PROPN
ejpam-4299	400	24	(	(	PUNCT
ejpam-4299	400	25	0	0	NUM
ejpam-4299	400	26	,	,	PUNCT
ejpam-4299	400	27	1	1	NUM
ejpam-4299	400	28	]	]	PUNCT
ejpam-4299	400	29	,	,	PUNCT
ejpam-4299	400	30	for	for	ADP
ejpam-4299	400	31	i	i	PROPN
ejpam-4299	400	32	=	=	SYM
ejpam-4299	400	33	1	1	NUM
ejpam-4299	400	34	,	,	PUNCT
ejpam-4299	400	35	2	2	NUM
ejpam-4299	400	36	are	be	AUX
ejpam-4299	400	37	α	α	NOUN
ejpam-4299	400	38	-	-	PUNCT
ejpam-4299	400	39	cuts	cut	NOUN
ejpam-4299	400	40	of	of	ADP
ejpam-4299	400	41	ky	ky	PROPN
ejpam-4299	400	42	(	(	PUNCT
ejpam-4299	400	43	t	t	PROPN
ejpam-4299	400	44	)	)	PUNCT
ejpam-4299	400	45	i.e	i.e	PROPN
ejpam-4299	400	46	α	α	NOUN
ejpam-4299	400	47	-	-	PUNCT
ejpam-4299	400	48	cuts	cut	NOUN
ejpam-4299	400	49	of	of	ADP
ejpam-4299	400	50	a	a	DET
ejpam-4299	400	51	fuzzy	fuzzy	ADJ
ejpam-4299	400	52	number	number	NOUN
ejpam-4299	400	53	.	.	PUNCT
ejpam-4299	401	1	due	due	ADP
ejpam-4299	401	2	to	to	ADP
ejpam-4299	401	3	∂g	∂g	PROPN
ejpam-4299	401	4	∂k	∂k	PROPN
ejpam-4299	401	5	>	>	X
ejpam-4299	401	6	0	0	NUM
ejpam-4299	401	7	,	,	PUNCT
ejpam-4299	401	8	∂g∂c	∂g∂c	PROPN
ejpam-4299	401	9	>	>	X
ejpam-4299	401	10	0	0	NUM
ejpam-4299	401	11	,	,	PUNCT
ejpam-4299	401	12	∂f∂k	∂f∂k	PROPN
ejpam-4299	401	13	=	=	PUNCT
ejpam-4299	401	14	y	y	PROPN
ejpam-4299	401	15	>	>	X
ejpam-4299	401	16	0	0	PUNCT
ejpam-4299	401	17	for	for	ADP
ejpam-4299	401	18	all	all	DET
ejpam-4299	401	19	t	t	NOUN
ejpam-4299	401	20	,	,	PUNCT
ejpam-4299	401	21	∂f∂y	∂f∂y	X
ejpam-4299	401	22	=	=	PUNCT
ejpam-4299	401	23	k	k	X
ejpam-4299	401	24	>	>	X
ejpam-4299	401	25	0	0	X
ejpam-4299	401	26	.	.	PUNCT
ejpam-4299	402	1	so	so	ADV
ejpam-4299	402	2	theorem	theorem	ADJ
ejpam-4299	402	3	(	(	PUNCT
ejpam-4299	402	4	6	6	NUM
ejpam-4299	402	5	)	)	PUNCT
ejpam-4299	402	6	implies	imply	VERB
ejpam-4299	402	7	the	the	DET
ejpam-4299	402	8	result	result	NOUN
ejpam-4299	402	9	that	that	SCONJ
ejpam-4299	402	10	ȳ	ȳ	PROPN
ejpam-4299	402	11	(	(	PUNCT
ejpam-4299	402	12	t	t	PROPN
ejpam-4299	402	13	)	)	PUNCT
ejpam-4299	402	14	is	be	AUX
ejpam-4299	402	15	a	a	DET
ejpam-4299	402	16	bf	bf	NOUN
ejpam-4299	402	17	-	-	PUNCT
ejpam-4299	402	18	solution	solution	NOUN
ejpam-4299	402	19	.	.	PUNCT
ejpam-4299	403	1	we	we	PRON
ejpam-4299	403	2	easily	easily	ADV
ejpam-4299	403	3	see	see	VERB
ejpam-4299	403	4	that	that	DET
ejpam-4299	403	5	yαi	yαi	PROPN
ejpam-4299	403	6	(	(	PUNCT
ejpam-4299	403	7	0	0	NUM
ejpam-4299	403	8	)	)	PUNCT
ejpam-4299	403	9	=	=	NOUN
ejpam-4299	403	10	cαi	cαi	NOUN
ejpam-4299	403	11	for	for	ADP
ejpam-4299	403	12	i	i	PRON
ejpam-4299	403	13	=	=	NOUN
ejpam-4299	403	14	1	1	NUM
ejpam-4299	403	15	,	,	PUNCT
ejpam-4299	403	16	2	2	NUM
ejpam-4299	403	17	,	,	PUNCT
ejpam-4299	403	18	so	so	ADV
ejpam-4299	403	19	ȳ	ȳ	PROPN
ejpam-4299	403	20	(	(	PUNCT
ejpam-4299	403	21	t	t	PROPN
ejpam-4299	403	22	)	)	PUNCT
ejpam-4299	403	23	also	also	ADV
ejpam-4299	403	24	satisfies	satisfy	VERB
ejpam-4299	403	25	the	the	DET
ejpam-4299	403	26	initial	initial	ADJ
ejpam-4299	403	27	condition	condition	NOUN
ejpam-4299	403	28	.	.	PUNCT
ejpam-4299	404	1	the	the	DET
ejpam-4299	404	2	bf	bf	NOUN
ejpam-4299	404	3	-	-	PUNCT
ejpam-4299	404	4	solution	solution	NOUN
ejpam-4299	404	5	may	may	AUX
ejpam-4299	404	6	be	be	AUX
ejpam-4299	404	7	written	write	VERB
ejpam-4299	404	8	as	as	ADP
ejpam-4299	404	9	ȳ	ȳ	PROPN
ejpam-4299	404	10	(	(	PUNCT
ejpam-4299	404	11	t	t	NOUN
ejpam-4299	404	12	)	)	PUNCT
ejpam-4299	404	13	=	=	SYM
ejpam-4299	405	1	cexp	cexp	NOUN
ejpam-4299	405	2	(	(	PUNCT
ejpam-4299	405	3	k̄	k̄	ADV
ejpam-4299	405	4	q	q	X
ejpam-4299	405	5	tq	tq	INTJ
ejpam-4299	405	6	)	)	PUNCT
ejpam-4299	405	7	for	for	ADP
ejpam-4299	405	8	all	all	DET
ejpam-4299	405	9	t	t	NOUN
ejpam-4299	405	10	∈	∈	PROPN
ejpam-4299	405	11	(	(	PUNCT
ejpam-4299	405	12	0	0	NUM
ejpam-4299	405	13	,	,	PUNCT
ejpam-4299	405	14	a	a	DET
ejpam-4299	405	15	)	)	PUNCT
ejpam-4299	405	16	.	.	PUNCT
ejpam-4299	406	1	so	so	ADV
ejpam-4299	406	2	if	if	SCONJ
ejpam-4299	406	3	∂f	∂f	PROPN
ejpam-4299	406	4	∂y	∂y	PROPN
ejpam-4299	406	5	=	=	PUNCT
ejpam-4299	406	6	k	k	X
ejpam-4299	406	7	<	<	X
ejpam-4299	406	8	0	0	NUM
ejpam-4299	406	9	,	,	PUNCT
ejpam-4299	406	10	we	we	PRON
ejpam-4299	406	11	look	look	VERB
ejpam-4299	406	12	for	for	ADP
ejpam-4299	406	13	a	a	DET
ejpam-4299	406	14	ss	ss	NOUN
ejpam-4299	406	15	.	.	PUNCT
ejpam-4299	407	1	the	the	DET
ejpam-4299	407	2	function	function	NOUN
ejpam-4299	407	3	f	f	PROPN
ejpam-4299	407	4	(	(	PUNCT
ejpam-4299	407	5	t	t	PROPN
ejpam-4299	407	6	,	,	PUNCT
ejpam-4299	407	7	y	y	PROPN
ejpam-4299	407	8	,	,	PUNCT
ejpam-4299	407	9	k	k	NOUN
ejpam-4299	407	10	)	)	PUNCT
ejpam-4299	407	11	=	=	SYM
ejpam-4299	407	12	ky	ky	PROPN
ejpam-4299	407	13	and	and	CCONJ
ejpam-4299	407	14	k	k	X
ejpam-4299	407	15	<	<	X
ejpam-4299	407	16	0	0	NUM
ejpam-4299	407	17	satisfies	satisfy	VERB
ejpam-4299	407	18	the	the	DET
ejpam-4299	407	19	assumptions	assumption	NOUN
ejpam-4299	407	20	of	of	ADP
ejpam-4299	407	21	theorem	theorem	NOUN
ejpam-4299	407	22	(	(	PUNCT
ejpam-4299	407	23	7	7	NUM
ejpam-4299	407	24	)	)	PUNCT
ejpam-4299	407	25	with	with	ADP
ejpam-4299	407	26	h(t	h(t	PROPN
ejpam-4299	407	27	,	,	PUNCT
ejpam-4299	407	28	y	y	NOUN
ejpam-4299	407	29	)	)	PUNCT
ejpam-4299	407	30	=	=	SYM
ejpam-4299	407	31	y	y	PROPN
ejpam-4299	407	32	and	and	CCONJ
ejpam-4299	407	33	hance	hance	PROPN
ejpam-4299	407	34	the	the	DET
ejpam-4299	407	35	problem	problem	NOUN
ejpam-4299	407	36	x̄(q)(t	x̄(q)(t	PUNCT
ejpam-4299	407	37	)	)	PUNCT
ejpam-4299	408	1	=	=	SYM
ejpam-4299	408	2	kx̄(t	kx̄(t	PROPN
ejpam-4299	408	3	)	)	PUNCT
ejpam-4299	408	4	,	,	PUNCT
ejpam-4299	408	5	q	q	PROPN
ejpam-4299	408	6	∈	∈	PROPN
ejpam-4299	408	7	(	(	PUNCT
ejpam-4299	408	8	0	0	NUM
ejpam-4299	408	9	,	,	PUNCT
ejpam-4299	408	10	1	1	NUM
ejpam-4299	408	11	]	]	PUNCT
ejpam-4299	408	12	x̄(0	x̄(0	NUM
ejpam-4299	408	13	)	)	PUNCT
ejpam-4299	408	14	=	=	VERB
ejpam-4299	409	1	c̄	c̄	PROPN
ejpam-4299	409	2	i.e	i.e	INTJ
ejpam-4299	409	3	(	(	PUNCT
ejpam-4299	409	4	x(q	x(q	PROPN
ejpam-4299	409	5	)	)	PUNCT
ejpam-4299	409	6	)	)	PUNCT
ejpam-4299	410	1	α	α	X
ejpam-4299	410	2	1	1	NUM
ejpam-4299	410	3	(	(	PUNCT
ejpam-4299	410	4	t	t	NOUN
ejpam-4299	410	5	)	)	PUNCT
ejpam-4299	410	6	=	=	VERB
ejpam-4299	411	1	kα1	kα1	ADJ
ejpam-4299	411	2	x	x	SYM
ejpam-4299	411	3	α	α	PRON
ejpam-4299	411	4	2	2	NUM
ejpam-4299	411	5	(	(	PUNCT
ejpam-4299	411	6	t	t	NOUN
ejpam-4299	411	7	)	)	PUNCT
ejpam-4299	411	8	(	(	PUNCT
ejpam-4299	411	9	x(q	x(q	PROPN
ejpam-4299	411	10	)	)	PUNCT
ejpam-4299	411	11	)	)	PUNCT
ejpam-4299	412	1	α	α	X
ejpam-4299	412	2	2	2	NUM
ejpam-4299	412	3	(	(	PUNCT
ejpam-4299	412	4	t	t	NOUN
ejpam-4299	412	5	)	)	PUNCT
ejpam-4299	412	6	=	=	PUNCT
ejpam-4299	413	1	kα2	kα2	NOUN
ejpam-4299	413	2	x	x	SYM
ejpam-4299	414	1	α	α	NOUN
ejpam-4299	414	2	1	1	NUM
ejpam-4299	414	3	(	(	PUNCT
ejpam-4299	414	4	t	t	PROPN
ejpam-4299	414	5	)	)	PUNCT
ejpam-4299	414	6	xα1	xα1	NOUN
ejpam-4299	415	1	(	(	PUNCT
ejpam-4299	415	2	0	0	NUM
ejpam-4299	415	3	)	)	PUNCT
ejpam-4299	415	4	=	=	SYM
ejpam-4299	416	1	cα1	cα1	NOUN
ejpam-4299	416	2	xα2	xα2	PUNCT
ejpam-4299	416	3	(	(	PUNCT
ejpam-4299	416	4	0	0	NUM
ejpam-4299	416	5	)	)	PUNCT
ejpam-4299	417	1	=	=	VERB
ejpam-4299	417	2	cα2	cα2	PROPN
ejpam-4299	417	3	has	have	VERB
ejpam-4299	417	4	a	a	DET
ejpam-4299	417	5	unique	unique	ADJ
ejpam-4299	417	6	fuzzy	fuzzy	ADJ
ejpam-4299	417	7	solution	solution	NOUN
ejpam-4299	417	8	x	x	PUNCT
ejpam-4299	417	9	on	on	ADP
ejpam-4299	417	10	r+	r+	X
ejpam-4299	417	11	.	.	PUNCT
ejpam-4299	418	1	it	it	PRON
ejpam-4299	418	2	is	be	AUX
ejpam-4299	418	3	given	give	VERB
ejpam-4299	418	4	by	by	ADP
ejpam-4299	418	5	the	the	DET
ejpam-4299	418	6	α	α	NOUN
ejpam-4299	418	7	-	-	PUNCT
ejpam-4299	418	8	cuts	cut	NOUN
ejpam-4299	418	9	[	[	X
ejpam-4299	418	10	xα1	xα1	X
ejpam-4299	418	11	(	(	PUNCT
ejpam-4299	418	12	t	t	NOUN
ejpam-4299	418	13	)	)	PUNCT
ejpam-4299	418	14	,	,	PUNCT
ejpam-4299	418	15	xα2	xα2	PUNCT
ejpam-4299	418	16	(	(	PUNCT
ejpam-4299	418	17	t	t	PROPN
ejpam-4299	418	18	)	)	PUNCT
ejpam-4299	418	19	]	]	PUNCT
ejpam-4299	418	20	,	,	PUNCT
ejpam-4299	418	21	α	α	PROPN
ejpam-4299	418	22	∈	∈	PROPN
ejpam-4299	419	1	[	[	X
ejpam-4299	419	2	0	0	NUM
ejpam-4299	419	3	,	,	PUNCT
ejpam-4299	419	4	1	1	NUM
ejpam-4299	419	5	]	]	PUNCT
ejpam-4299	419	6	,	,	PUNCT
ejpam-4299	419	7	t	t	PROPN
ejpam-4299	419	8	∈	∈	PROPN
ejpam-4299	419	9	(	(	PUNCT
ejpam-4299	419	10	0	0	NUM
ejpam-4299	419	11	,	,	PUNCT
ejpam-4299	419	12	a	a	PRON
ejpam-4299	419	13	)	)	PUNCT
ejpam-4299	419	14	,	,	PUNCT
ejpam-4299	419	15	where	where	SCONJ
ejpam-4299	419	16	xα1	xα1	PROPN
ejpam-4299	419	17	(	(	PUNCT
ejpam-4299	419	18	t	t	NOUN
ejpam-4299	419	19	)	)	PUNCT
ejpam-4299	419	20	=	=	SYM
ejpam-4299	419	21	1	1	NUM
ejpam-4299	419	22	2	2	NUM
ejpam-4299	419	23	(	(	PUNCT
ejpam-4299	419	24	cα1	cα1	NOUN
ejpam-4299	420	1	+	+	CCONJ
ejpam-4299	420	2	√	√	ADJ
ejpam-4299	420	3	kα1	kα1	PRON
ejpam-4299	420	4	kα2	kα2	NOUN
ejpam-4299	420	5	cα2	cα2	NOUN
ejpam-4299	420	6	)	)	PUNCT
ejpam-4299	420	7	exp	exp	NOUN
ejpam-4299	420	8	(	(	PUNCT
ejpam-4299	420	9	√	√	INTJ
ejpam-4299	420	10	kα1	kα1	PROPN
ejpam-4299	420	11	k	k	PROPN
ejpam-4299	421	1	α	α	NOUN
ejpam-4299	421	2	2	2	NUM
ejpam-4299	421	3	tq	tq	NOUN
ejpam-4299	421	4	q	q	NOUN
ejpam-4299	421	5	)	)	PUNCT
ejpam-4299	422	1	+	+	CCONJ
ejpam-4299	422	2	1	1	NUM
ejpam-4299	422	3	2	2	NUM
ejpam-4299	422	4	(	(	PUNCT
ejpam-4299	422	5	cα1	cα1	NOUN
ejpam-4299	422	6	−	−	ADP
ejpam-4299	422	7	√	√	NOUN
ejpam-4299	423	1	kα1	kα1	PROPN
ejpam-4299	423	2	kα2	kα2	NOUN
ejpam-4299	423	3	cα2	cα2	NOUN
ejpam-4299	423	4	)	)	PUNCT
ejpam-4299	423	5	exp	exp	NOUN
ejpam-4299	423	6	(	(	PUNCT
ejpam-4299	423	7	−	−	PROPN
ejpam-4299	423	8	√	√	NOUN
ejpam-4299	424	1	kα1	kα1	PROPN
ejpam-4299	424	2	k	k	PROPN
ejpam-4299	425	1	α	α	PROPN
ejpam-4299	425	2	2	2	NUM
ejpam-4299	425	3	tq	tq	NOUN
ejpam-4299	425	4	q	q	NOUN
ejpam-4299	425	5	)	)	PUNCT
ejpam-4299	425	6	xα2	xα2	PUNCT
ejpam-4299	425	7	(	(	PUNCT
ejpam-4299	425	8	t	t	PROPN
ejpam-4299	425	9	)	)	PUNCT
ejpam-4299	425	10	=	=	SYM
ejpam-4299	425	11	1	1	NUM
ejpam-4299	425	12	2	2	NUM
ejpam-4299	425	13	(	(	PUNCT
ejpam-4299	425	14	cα1	cα1	NOUN
ejpam-4299	425	15	√	√	ADJ
ejpam-4299	425	16	kα2	kα2	NOUN
ejpam-4299	425	17	kα1	kα1	PROPN
ejpam-4299	425	18	+	+	CCONJ
ejpam-4299	425	19	cα2	cα2	NOUN
ejpam-4299	425	20	)	)	PUNCT
ejpam-4299	425	21	exp	exp	NOUN
ejpam-4299	425	22	(	(	PUNCT
ejpam-4299	425	23	√	√	INTJ
ejpam-4299	426	1	kα1	kα1	PROPN
ejpam-4299	426	2	k	k	PROPN
ejpam-4299	427	1	α	α	NOUN
ejpam-4299	427	2	2	2	NUM
ejpam-4299	427	3	tq	tq	NOUN
ejpam-4299	427	4	q	q	NOUN
ejpam-4299	427	5	)	)	PUNCT
ejpam-4299	427	6	−	−	NOUN
ejpam-4299	427	7	1	1	NUM
ejpam-4299	427	8	2	2	NUM
ejpam-4299	427	9	(	(	PUNCT
ejpam-4299	427	10	cα1	cα1	NOUN
ejpam-4299	427	11	√	√	ADJ
ejpam-4299	427	12	kα2	kα2	NOUN
ejpam-4299	428	1	kα1	kα1	PROPN
ejpam-4299	428	2	−	−	PUNCT
ejpam-4299	428	3	cα2	cα2	NOUN
ejpam-4299	428	4	)	)	PUNCT
ejpam-4299	428	5	exp	exp	NOUN
ejpam-4299	428	6	(	(	PUNCT
ejpam-4299	428	7	−	−	PROPN
ejpam-4299	428	8	√	√	NOUN
ejpam-4299	428	9	kα1	kα1	PROPN
ejpam-4299	428	10	k	k	PROPN
ejpam-4299	429	1	α	α	PROPN
ejpam-4299	429	2	2	2	NUM
ejpam-4299	429	3	tq	tq	NOUN
ejpam-4299	429	4	q	q	PROPN
ejpam-4299	429	5	)	)	PUNCT
ejpam-4299	429	6	then	then	ADV
ejpam-4299	429	7	ss	ss	INTJ
ejpam-4299	429	8	exist	exist	VERB
ejpam-4299	429	9	for	for	ADP
ejpam-4299	429	10	t	t	PROPN
ejpam-4299	429	11	∈	∈	PROPN
ejpam-4299	429	12	(	(	PUNCT
ejpam-4299	429	13	0	0	NUM
ejpam-4299	429	14	,	,	PUNCT
ejpam-4299	429	15	a	a	DET
ejpam-4299	429	16	)	)	PUNCT
ejpam-4299	429	17	.	.	PUNCT
ejpam-4299	430	1	references	reference	NOUN
ejpam-4299	430	2	[	[	X
ejpam-4299	431	1	1	1	X
ejpam-4299	431	2	]	]	PUNCT
ejpam-4299	431	3	s.	s.	PROPN
ejpam-4299	431	4	arshad	arshad	PROPN
ejpam-4299	431	5	and	and	CCONJ
ejpam-4299	431	6	v.	v.	ADP
ejpam-4299	431	7	lupulescu	lupulescu	NOUN
ejpam-4299	431	8	.	.	PUNCT
ejpam-4299	432	1	on	on	ADP
ejpam-4299	432	2	the	the	DET
ejpam-4299	432	3	fractional	fractional	ADJ
ejpam-4299	432	4	differential	differential	ADJ
ejpam-4299	432	5	equations	equation	NOUN
ejpam-4299	432	6	with	with	ADP
ejpam-4299	432	7	uncertainty	uncertainty	NOUN
ejpam-4299	432	8	.	.	PUNCT
ejpam-4299	433	1	nonliniear	nonliniear	ADJ
ejpam-4299	433	2	analysis	analysis	NOUN
ejpam-4299	433	3	,	,	PUNCT
ejpam-4299	433	4	74:3685–3693	74:3685–3693	NUM
ejpam-4299	433	5	,	,	PUNCT
ejpam-4299	433	6	2011	2011	NUM
ejpam-4299	433	7	.	.	PUNCT
ejpam-4299	434	1	[	[	X
ejpam-4299	434	2	2	2	NUM
ejpam-4299	434	3	]	]	X
ejpam-4299	434	4	f.	f.	PROPN
ejpam-4299	434	5	cooper	cooper	PROPN
ejpam-4299	434	6	,	,	PUNCT
ejpam-4299	434	7	a.	a.	PROPN
ejpam-4299	434	8	khare	khare	PROPN
ejpam-4299	434	9	a	a	PROPN
ejpam-4299	434	10	,	,	PUNCT
ejpam-4299	434	11	and	and	CCONJ
ejpam-4299	434	12	u.	u.	PROPN
ejpam-4299	434	13	sukhatme	sukhatme	PROPN
ejpam-4299	434	14	.	.	PUNCT
ejpam-4299	435	1	fuzzy	fuzzy	ADJ
ejpam-4299	435	2	differential	differential	ADJ
ejpam-4299	435	3	equations	equation	NOUN
ejpam-4299	435	4	.	.	PUNCT
ejpam-4299	436	1	supersymmetry	supersymmetry	NOUN
ejpam-4299	436	2	and	and	CCONJ
ejpam-4299	436	3	quantum	quantum	NOUN
ejpam-4299	436	4	mechanics	mechanic	NOUN
ejpam-4299	436	5	phys	phy	NOUN
ejpam-4299	436	6	.	.	PUNCT
ejpam-4299	437	1	rep	rep	PROPN
ejpam-4299	437	2	,	,	PUNCT
ejpam-4299	437	3	251:267–385	251:267–385	NUM
ejpam-4299	437	4	,	,	PUNCT
ejpam-4299	437	5	1995	1995	NUM
ejpam-4299	437	6	.	.	PUNCT
ejpam-4299	438	1	[	[	X
ejpam-4299	438	2	3	3	X
ejpam-4299	438	3	]	]	X
ejpam-4299	438	4	h.y	h.y	PROPN
ejpam-4299	438	5	.	.	PROPN
ejpam-4299	438	6	goo	goo	PROPN
ejpam-4299	438	7	and	and	CCONJ
ejpam-4299	438	8	j.s.park	j.s.park	NOUN
ejpam-4299	438	9	.	.	PUNCT
ejpam-4299	439	1	on	on	ADP
ejpam-4299	439	2	the	the	DET
ejpam-4299	439	3	continuity	continuity	NOUN
ejpam-4299	439	4	of	of	ADP
ejpam-4299	439	5	the	the	DET
ejpam-4299	439	6	zadeh	zadeh	PROPN
ejpam-4299	439	7	extensions	extension	NOUN
ejpam-4299	439	8	.	.	PUNCT
ejpam-4299	440	1	j.chungcheong	j.chungcheong	PROPN
ejpam-4299	440	2	math.soc	math.soc	PROPN
ejpam-4299	440	3	,	,	PUNCT
ejpam-4299	440	4	20(4):525–533	20(4):525–533	NUM
ejpam-4299	440	5	,	,	PUNCT
ejpam-4299	440	6	2007	2007	NUM
ejpam-4299	440	7	.	.	PUNCT
ejpam-4299	441	1	[	[	X
ejpam-4299	441	2	4	4	X
ejpam-4299	441	3	]	]	PUNCT
ejpam-4299	441	4	m.	m.	NOUN
ejpam-4299	441	5	paulo	paulo	PROPN
ejpam-4299	441	6	guzmán	guzmán	PROPN
ejpam-4299	441	7	,	,	PUNCT
ejpam-4299	441	8	g.	g.	PROPN
ejpam-4299	441	9	langton	langton	PROPN
ejpam-4299	441	10	,	,	PUNCT
ejpam-4299	441	11	m.	m.	PROPN
ejpam-4299	441	12	lugo	lugo	PROPN
ejpam-4299	441	13	luciano	luciano	PROPN
ejpam-4299	441	14	,	,	PUNCT
ejpam-4299	441	15	j.	j.	PROPN
ejpam-4299	441	16	medina	medina	PROPN
ejpam-4299	441	17	,	,	PUNCT
ejpam-4299	441	18	e	e	PROPN
ejpam-4299	441	19	.	.	PUNCT
ejpam-4299	442	1	juan	juan	PROPN
ejpam-4299	442	2	,	,	PUNCT
ejpam-4299	442	3	and	and	CCONJ
ejpam-4299	442	4	n.	n.	PROPN
ejpam-4299	442	5	valdes	valde	NOUN
ejpam-4299	442	6	.	.	PUNCT
ejpam-4299	443	1	a	a	DET
ejpam-4299	443	2	new	new	ADJ
ejpam-4299	443	3	definition	definition	NOUN
ejpam-4299	443	4	of	of	ADP
ejpam-4299	443	5	a	a	DET
ejpam-4299	443	6	fractional	fractional	ADJ
ejpam-4299	443	7	derivative	derivative	NOUN
ejpam-4299	443	8	of	of	ADP
ejpam-4299	443	9	local	local	ADJ
ejpam-4299	443	10	type	type	NOUN
ejpam-4299	443	11	,	,	PUNCT
ejpam-4299	443	12	journal	journal	NOUN
ejpam-4299	443	13	of	of	ADP
ejpam-4299	443	14	mathematical	mathematical	ADJ
ejpam-4299	443	15	analysis	analysis	NOUN
ejpam-4299	443	16	.	.	PUNCT
ejpam-4299	444	1	sigma	sigma	PROPN
ejpam-4299	444	2	j	j	PROPN
ejpam-4299	444	3	eng	eng	PROPN
ejpam-4299	444	4	nat	nat	PROPN
ejpam-4299	444	5	sci	sci	PROPN
ejpam-4299	444	6	,	,	PUNCT
ejpam-4299	444	7	9(2):88–98	9(2):88–98	NUM
ejpam-4299	444	8	,	,	PUNCT
ejpam-4299	444	9	2018	2018	NUM
ejpam-4299	444	10	.	.	PUNCT
ejpam-4299	445	1	references	reference	NOUN
ejpam-4299	445	2	571	571	NUM
ejpam-4299	445	3	[	[	X
ejpam-4299	445	4	5	5	NUM
ejpam-4299	445	5	]	]	PUNCT
ejpam-4299	445	6	a.	a.	NOUN
ejpam-4299	445	7	harir	harir	PROPN
ejpam-4299	445	8	,	,	PUNCT
ejpam-4299	445	9	h.	h.	PROPN
ejpam-4299	445	10	el	el	PROPN
ejpam-4299	445	11	harfi	harfi	PROPN
ejpam-4299	445	12	,	,	PUNCT
ejpam-4299	445	13	s.	s.	PROPN
ejpam-4299	445	14	melliani	melliani	PROPN
ejpam-4299	445	15	,	,	PUNCT
ejpam-4299	445	16	and	and	CCONJ
ejpam-4299	445	17	l.s	l.s	PROPN
ejpam-4299	445	18	.	.	PROPN
ejpam-4299	445	19	chadli	chadli	PROPN
ejpam-4299	445	20	.	.	PUNCT
ejpam-4299	446	1	fuzzy	fuzzy	ADJ
ejpam-4299	446	2	solutions	solution	NOUN
ejpam-4299	446	3	of	of	ADP
ejpam-4299	446	4	the	the	DET
ejpam-4299	446	5	sir	sir	NOUN
ejpam-4299	446	6	models	model	NOUN
ejpam-4299	446	7	using	use	VERB
ejpam-4299	446	8	vim	vim	PROPN
ejpam-4299	446	9	.	.	PUNCT
ejpam-4299	447	1	international	international	ADJ
ejpam-4299	447	2	journal	journal	NOUN
ejpam-4299	447	3	of	of	ADP
ejpam-4299	447	4	uncertainty	uncertainty	NOUN
ejpam-4299	447	5	,	,	PUNCT
ejpam-4299	447	6	fuzziness	fuzziness	NOUN
ejpam-4299	447	7	and	and	CCONJ
ejpam-4299	447	8	knowledgebased	knowledgebased	ADJ
ejpam-4299	447	9	systems	system	NOUN
ejpam-4299	447	10	,	,	PUNCT
ejpam-4299	447	11	30(1):43–61	30(1):43–61	NUM
ejpam-4299	447	12	,	,	PUNCT
ejpam-4299	447	13	2022	2022	NUM
ejpam-4299	447	14	.	.	PUNCT
ejpam-4299	448	1	[	[	X
ejpam-4299	448	2	6	6	NUM
ejpam-4299	448	3	]	]	PUNCT
ejpam-4299	448	4	a.	a.	NOUN
ejpam-4299	448	5	harir	harir	PROPN
ejpam-4299	448	6	,	,	PUNCT
ejpam-4299	448	7	s.	s.	PROPN
ejpam-4299	448	8	melliani	melliani	PROPN
ejpam-4299	448	9	,	,	PUNCT
ejpam-4299	448	10	and	and	CCONJ
ejpam-4299	448	11	l.s	l.s	PROPN
ejpam-4299	448	12	.	.	PROPN
ejpam-4299	448	13	chadli	chadli	PROPN
ejpam-4299	448	14	.	.	PUNCT
ejpam-4299	449	1	solutions	solution	NOUN
ejpam-4299	449	2	of	of	ADP
ejpam-4299	449	3	fuzzy	fuzzy	ADJ
ejpam-4299	449	4	wave	wave	NOUN
ejpam-4299	449	5	-	-	PUNCT
ejpam-4299	449	6	like	like	ADJ
ejpam-4299	449	7	equations	equation	NOUN
ejpam-4299	449	8	by	by	ADP
ejpam-4299	449	9	variational	variational	ADJ
ejpam-4299	449	10	iteration	iteration	NOUN
ejpam-4299	449	11	method	method	NOUN
ejpam-4299	449	12	.	.	PUNCT
ejpam-4299	450	1	international	international	ADJ
ejpam-4299	450	2	annals	annal	NOUN
ejpam-4299	450	3	of	of	ADP
ejpam-4299	450	4	fuzzy	fuzzy	ADJ
ejpam-4299	450	5	mathematics	mathematic	NOUN
ejpam-4299	450	6	and	and	CCONJ
ejpam-4299	450	7	informatics	informatic	NOUN
ejpam-4299	450	8	,	,	PUNCT
ejpam-4299	450	9	8(4):527–547	8(4):527–547	NUM
ejpam-4299	450	10	,	,	PUNCT
ejpam-4299	450	11	2014	2014	NUM
ejpam-4299	450	12	.	.	PUNCT
ejpam-4299	451	1	[	[	X
ejpam-4299	451	2	7	7	NUM
ejpam-4299	451	3	]	]	PUNCT
ejpam-4299	451	4	a.	a.	NOUN
ejpam-4299	451	5	harir	harir	PROPN
ejpam-4299	451	6	,	,	PUNCT
ejpam-4299	451	7	s.	s.	PROPN
ejpam-4299	451	8	melliani	melliani	PROPN
ejpam-4299	451	9	,	,	PUNCT
ejpam-4299	451	10	and	and	CCONJ
ejpam-4299	451	11	l.s	l.s	PROPN
ejpam-4299	451	12	.	.	PROPN
ejpam-4299	451	13	chadli	chadli	PROPN
ejpam-4299	451	14	.	.	PUNCT
ejpam-4299	452	1	solutions	solution	NOUN
ejpam-4299	452	2	of	of	ADP
ejpam-4299	452	3	fuzzy	fuzzy	ADJ
ejpam-4299	452	4	heat	heat	NOUN
ejpam-4299	452	5	-	-	PUNCT
ejpam-4299	452	6	like	like	ADJ
ejpam-4299	452	7	equations	equation	NOUN
ejpam-4299	452	8	by	by	ADP
ejpam-4299	452	9	variational	variational	ADJ
ejpam-4299	452	10	iterative	iterative	NOUN
ejpam-4299	452	11	method	method	NOUN
ejpam-4299	452	12	.	.	PUNCT
ejpam-4299	453	1	annals	annal	NOUN
ejpam-4299	453	2	of	of	ADP
ejpam-4299	453	3	fuzzy	fuzzy	ADJ
ejpam-4299	453	4	mathematics	mathematic	NOUN
ejpam-4299	453	5	and	and	CCONJ
ejpam-4299	453	6	informatics	informatic	NOUN
ejpam-4299	453	7	,	,	PUNCT
ejpam-4299	453	8	10(1):29–44	10(1):29–44	NUM
ejpam-4299	453	9	,	,	PUNCT
ejpam-4299	453	10	2015	2015	NUM
ejpam-4299	453	11	.	.	PUNCT
ejpam-4299	454	1	[	[	X
ejpam-4299	454	2	8	8	NUM
ejpam-4299	454	3	]	]	PUNCT
ejpam-4299	454	4	a.	a.	NOUN
ejpam-4299	454	5	harir	harir	PROPN
ejpam-4299	454	6	,	,	PUNCT
ejpam-4299	454	7	s.	s.	PROPN
ejpam-4299	454	8	melliani	melliani	PROPN
ejpam-4299	454	9	,	,	PUNCT
ejpam-4299	454	10	and	and	CCONJ
ejpam-4299	454	11	l.s	l.s	PROPN
ejpam-4299	454	12	.	.	PROPN
ejpam-4299	454	13	chadli	chadli	PROPN
ejpam-4299	454	14	.	.	PUNCT
ejpam-4299	455	1	fuzzy	fuzzy	ADJ
ejpam-4299	455	2	generalized	generalize	VERB
ejpam-4299	455	3	conformable	conformable	ADJ
ejpam-4299	455	4	fractional	fractional	ADJ
ejpam-4299	455	5	derivative	derivative	NOUN
ejpam-4299	455	6	.	.	PUNCT
ejpam-4299	456	1	advances	advance	NOUN
ejpam-4299	456	2	in	in	ADP
ejpam-4299	456	3	fuzzy	fuzzy	ADJ
ejpam-4299	456	4	systems	system	NOUN
ejpam-4299	456	5	,	,	PUNCT
ejpam-4299	456	6	2020(1):7	2020(1):7	PROPN
ejpam-4299	456	7	,	,	PUNCT
ejpam-4299	456	8	2020	2020	NUM
ejpam-4299	456	9	.	.	PUNCT
ejpam-4299	457	1	[	[	X
ejpam-4299	457	2	9	9	NUM
ejpam-4299	457	3	]	]	PUNCT
ejpam-4299	457	4	a.	a.	NOUN
ejpam-4299	457	5	harir	harir	PROPN
ejpam-4299	457	6	,	,	PUNCT
ejpam-4299	457	7	s.	s.	PROPN
ejpam-4299	457	8	melliani	melliani	PROPN
ejpam-4299	457	9	,	,	PUNCT
ejpam-4299	457	10	and	and	CCONJ
ejpam-4299	457	11	l.s	l.s	PROPN
ejpam-4299	457	12	.	.	PROPN
ejpam-4299	457	13	chadli	chadli	PROPN
ejpam-4299	457	14	.	.	PUNCT
ejpam-4299	458	1	solving	solve	VERB
ejpam-4299	458	2	fuzzy	fuzzy	ADJ
ejpam-4299	458	3	burgers	burger	NOUN
ejpam-4299	458	4	equation	equation	NOUN
ejpam-4299	458	5	by	by	ADP
ejpam-4299	458	6	variational	variational	ADJ
ejpam-4299	458	7	iteration	iteration	NOUN
ejpam-4299	458	8	method	method	NOUN
ejpam-4299	458	9	.	.	PUNCT
ejpam-4299	459	1	annals	annal	NOUN
ejpam-4299	459	2	of	of	ADP
ejpam-4299	459	3	fuzzy	fuzzy	ADJ
ejpam-4299	459	4	mathematics	mathematic	NOUN
ejpam-4299	459	5	and	and	CCONJ
ejpam-4299	459	6	informatics	informatic	NOUN
ejpam-4299	459	7	,	,	PUNCT
ejpam-4299	459	8	21(2):136–149	21(2):136–149	NUM
ejpam-4299	459	9	,	,	PUNCT
ejpam-4299	459	10	2020	2020	NUM
ejpam-4299	459	11	.	.	PUNCT
ejpam-4299	460	1	[	[	X
ejpam-4299	460	2	10	10	NUM
ejpam-4299	460	3	]	]	PUNCT
ejpam-4299	460	4	j.buckley	j.buckley	NOUN
ejpam-4299	460	5	and	and	CCONJ
ejpam-4299	460	6	t.feuring	t.feuring	NOUN
ejpam-4299	460	7	.	.	PUNCT
ejpam-4299	461	1	fuzzy	fuzzy	ADJ
ejpam-4299	461	2	differential	differential	ADJ
ejpam-4299	461	3	equations	equation	NOUN
ejpam-4299	461	4	.	.	PUNCT
ejpam-4299	462	1	fuzzy	fuzzy	ADJ
ejpam-4299	462	2	sets	set	NOUN
ejpam-4299	462	3	and	and	CCONJ
ejpam-4299	462	4	systems	system	NOUN
ejpam-4299	462	5	,	,	PUNCT
ejpam-4299	462	6	110:43–54	110:43–54	NUM
ejpam-4299	462	7	,	,	PUNCT
ejpam-4299	462	8	2000	2000	NUM
ejpam-4299	462	9	.	.	PUNCT
ejpam-4299	463	1	[	[	X
ejpam-4299	463	2	11	11	NUM
ejpam-4299	463	3	]	]	X
ejpam-4299	463	4	o.	o.	PROPN
ejpam-4299	463	5	kaleva	kaleva	PROPN
ejpam-4299	463	6	.	.	PUNCT
ejpam-4299	464	1	fuzzy	fuzzy	ADJ
ejpam-4299	464	2	fractional	fractional	ADJ
ejpam-4299	464	3	evolution	evolution	NOUN
ejpam-4299	464	4	equations	equation	NOUN
ejpam-4299	464	5	and	and	CCONJ
ejpam-4299	464	6	fuzzy	fuzzy	ADJ
ejpam-4299	464	7	solution	solution	NOUN
ejpam-4299	464	8	operators	operator	NOUN
ejpam-4299	464	9	.	.	PUNCT
ejpam-4299	465	1	fuzzy	fuzzy	ADJ
ejpam-4299	465	2	set	set	VERB
ejpam-4299	465	3	syst	syst	NOUN
ejpam-4299	465	4	,	,	PUNCT
ejpam-4299	465	5	24:301–17	24:301–17	NOUN
ejpam-4299	465	6	,	,	PUNCT
ejpam-4299	465	7	1987	1987	NUM
ejpam-4299	465	8	.	.	PUNCT
ejpam-4299	466	1	[	[	X
ejpam-4299	466	2	12	12	NUM
ejpam-4299	466	3	]	]	PUNCT
ejpam-4299	466	4	r.	r.	PROPN
ejpam-4299	466	5	khalil	khalil	PROPN
ejpam-4299	466	6	,	,	PUNCT
ejpam-4299	466	7	m.	m.	PROPN
ejpam-4299	466	8	al	al	PROPN
ejpam-4299	466	9	horani	horani	PROPN
ejpam-4299	466	10	,	,	PUNCT
ejpam-4299	466	11	a.	a.	NOUN
ejpam-4299	466	12	yousef	yousef	PROPN
ejpam-4299	466	13	,	,	PUNCT
ejpam-4299	466	14	and	and	CCONJ
ejpam-4299	466	15	m.	m.	NOUN
ejpam-4299	466	16	sababheh	sababheh	NOUN
ejpam-4299	466	17	.	.	PUNCT
ejpam-4299	467	1	a	a	DET
ejpam-4299	467	2	new	new	ADJ
ejpam-4299	467	3	definition	definition	NOUN
ejpam-4299	467	4	of	of	ADP
ejpam-4299	467	5	fractional	fractional	ADJ
ejpam-4299	467	6	derivative	derivative	NOUN
ejpam-4299	467	7	.	.	PUNCT
ejpam-4299	468	1	journal	journal	PROPN
ejpam-4299	468	2	of	of	ADP
ejpam-4299	468	3	computational	computational	ADJ
ejpam-4299	468	4	and	and	CCONJ
ejpam-4299	468	5	applied	applied	ADJ
ejpam-4299	468	6	mathematics	mathematic	NOUN
ejpam-4299	468	7	,	,	PUNCT
ejpam-4299	468	8	264:65–70	264:65–70	NUM
ejpam-4299	468	9	,	,	PUNCT
ejpam-4299	468	10	2014	2014	NUM
ejpam-4299	468	11	.	.	PUNCT
ejpam-4299	469	1	[	[	X
ejpam-4299	469	2	13	13	NUM
ejpam-4299	469	3	]	]	X
ejpam-4299	469	4	d.	d.	NOUN
ejpam-4299	469	5	r.anderson	r.anderson	NOUN
ejpam-4299	469	6	and	and	CCONJ
ejpam-4299	469	7	d.	d.	PROPN
ejpam-4299	469	8	j.	j.	PROPN
ejpam-4299	469	9	ulness	ulness	PROPN
ejpam-4299	469	10	.	.	PUNCT
ejpam-4299	470	1	properties	property	NOUN
ejpam-4299	470	2	of	of	ADP
ejpam-4299	470	3	the	the	DET
ejpam-4299	470	4	katugampola	katugampola	ADJ
ejpam-4299	470	5	fractional	fractional	PROPN
ejpam-4299	470	6	derivative	derivative	NOUN
ejpam-4299	470	7	with	with	ADP
ejpam-4299	470	8	potential	potential	ADJ
ejpam-4299	470	9	application	application	NOUN
ejpam-4299	470	10	in	in	ADP
ejpam-4299	470	11	quantum	quantum	ADJ
ejpam-4299	470	12	mechanics	mechanic	NOUN
ejpam-4299	470	13	.	.	PUNCT
ejpam-4299	471	1	j.	j.	PROPN
ejpam-4299	471	2	math	math	PROPN
ejpam-4299	471	3	.	.	PUNCT
ejpam-4299	472	1	phys	phy	NOUN
ejpam-4299	472	2	,	,	PUNCT
ejpam-4299	472	3	56(6):063502	56(6):063502	NUM
ejpam-4299	472	4	,	,	PUNCT
ejpam-4299	472	5	2015	2015	NUM
ejpam-4299	472	6	.	.	PUNCT
ejpam-4299	473	1	[	[	X
ejpam-4299	473	2	14	14	NUM
ejpam-4299	473	3	]	]	X
ejpam-4299	473	4	v.	v.	PROPN
ejpam-4299	473	5	tarasov	tarasov	NOUN
ejpam-4299	473	6	.	.	PUNCT
ejpam-4299	474	1	local	local	ADJ
ejpam-4299	474	2	fractional	fractional	ADJ
ejpam-4299	474	3	derivatives	derivative	NOUN
ejpam-4299	474	4	of	of	ADP
ejpam-4299	474	5	differentiable	differentiable	ADJ
ejpam-4299	474	6	functions	function	NOUN
ejpam-4299	474	7	are	be	AUX
ejpam-4299	474	8	integer	integer	NOUN
ejpam-4299	474	9	-	-	PUNCT
ejpam-4299	474	10	order	order	NOUN
ejpam-4299	474	11	derivatives	derivative	NOUN
ejpam-4299	474	12	or	or	CCONJ
ejpam-4299	474	13	zero	zero	NUM
ejpam-4299	474	14	.	.	PUNCT
ejpam-4299	475	1	int	int	NOUN
ejpam-4299	475	2	.	.	PUNCT
ejpam-4299	476	1	j.	j.	PROPN
ejpam-4299	476	2	appl	appl	PROPN
ejpam-4299	476	3	.	.	PUNCT
ejpam-4299	477	1	comput	comput	PROPN
ejpam-4299	477	2	.	.	PUNCT
ejpam-4299	478	1	math	math	NOUN
ejpam-4299	478	2	,	,	PUNCT
ejpam-4299	478	3	(	(	PUNCT
ejpam-4299	478	4	2	2	NUM
ejpam-4299	478	5	)	)	PUNCT
ejpam-4299	478	6	,	,	PUNCT
ejpam-4299	478	7	2016	2016	NUM
ejpam-4299	478	8	.	.	PUNCT
ejpam-4299	479	1	[	[	X
ejpam-4299	479	2	15	15	NUM
ejpam-4299	479	3	]	]	X
ejpam-4299	479	4	e.juan	e.juan	NOUN
ejpam-4299	479	5	nápoles	nápole	NOUN
ejpam-4299	479	6	valdes	valde	NOUN
ejpam-4299	479	7	,	,	PUNCT
ejpam-4299	479	8	m.	m.	NOUN
ejpam-4299	479	9	paulo	paulo	PROPN
ejpam-4299	479	10	guzmán	guzmán	PROPN
ejpam-4299	479	11	,	,	PUNCT
ejpam-4299	479	12	m.	m.	NOUN
ejpam-4299	479	13	lugo	lugo	PROPN
ejpam-4299	479	14	luciano	luciano	PROPN
ejpam-4299	479	15	,	,	PUNCT
ejpam-4299	479	16	and	and	CCONJ
ejpam-4299	479	17	a.	a.	NOUN
ejpam-4299	479	18	kashuri	kashuri	PROPN
ejpam-4299	479	19	.	.	PUNCT
ejpam-4299	480	1	the	the	DET
ejpam-4299	480	2	local	local	ADJ
ejpam-4299	480	3	generalized	generalized	ADJ
ejpam-4299	480	4	derivative	derivative	ADJ
ejpam-4299	480	5	and	and	CCONJ
ejpam-4299	480	6	mittag	mittag	ADJ
ejpam-4299	480	7	-	-	PUNCT
ejpam-4299	480	8	leffler	leffler	NOUN
ejpam-4299	480	9	function	function	NOUN
ejpam-4299	480	10	.	.	PUNCT
ejpam-4299	481	1	sigma	sigma	PROPN
ejpam-4299	481	2	j	j	PROPN
ejpam-4299	481	3	eng	eng	PROPN
ejpam-4299	481	4	nat	nat	PROPN
ejpam-4299	481	5	sci	sci	PROPN
ejpam-4299	481	6	,	,	PUNCT
ejpam-4299	481	7	38(2):1007–1017	38(2):1007–1017	NUM
ejpam-4299	481	8	,	,	PUNCT
ejpam-4299	481	9	2020	2020	NUM
ejpam-4299	481	10	.	.	PUNCT
ejpam-4299	482	1	[	[	X
ejpam-4299	482	2	16	16	NUM
ejpam-4299	482	3	]	]	X
ejpam-4299	482	4	j.	j.	PROPN
ejpam-4299	482	5	weberszpil	weberszpil	PROPN
ejpam-4299	482	6	and	and	CCONJ
ejpam-4299	482	7	j.	j.	PROPN
ejpam-4299	482	8	a.	a.	PROPN
ejpam-4299	482	9	helayel	helayel	PROPN
ejpam-4299	482	10	-	-	PUNCT
ejpam-4299	482	11	neto	neto	NOUN
ejpam-4299	482	12	.	.	PUNCT
ejpam-4299	483	1	variational	variational	ADJ
ejpam-4299	483	2	approach	approach	NOUN
ejpam-4299	483	3	and	and	CCONJ
ejpam-4299	483	4	deformed	deform	VERB
ejpam-4299	483	5	derivatives	derivative	NOUN
ejpam-4299	483	6	.	.	PUNCT
ejpam-4299	484	1	physica	physica	PROPN
ejpam-4299	484	2	a	a	PRON
ejpam-4299	484	3	,	,	PUNCT
ejpam-4299	484	4	450:217–227	450:217–227	NUM
ejpam-4299	484	5	,	,	PUNCT
ejpam-4299	484	6	2016	2016	NUM
ejpam-4299	484	7	.	.	PUNCT
ejpam-4299	485	1	[	[	X
ejpam-4299	485	2	17	17	NUM
ejpam-4299	485	3	]	]	X
ejpam-4299	485	4	h	h	PROPN
ejpam-4299	485	5	w.	w.	PROPN
ejpam-4299	485	6	zhou	zhou	PROPN
ejpam-4299	485	7	,	,	PUNCT
ejpam-4299	485	8	s.	s.	PROPN
ejpam-4299	485	9	yang	yang	PROPN
ejpam-4299	485	10	,	,	PUNCT
ejpam-4299	485	11	and	and	CCONJ
ejpam-4299	485	12	s	s	PROPN
ejpam-4299	485	13	q.	q.	PROPN
ejpam-4299	485	14	zhang	zhang	PROPN
ejpam-4299	485	15	.	.	PUNCT
ejpam-4299	485	16	conformable	conformable	VERB
ejpam-4299	485	17	derivative	derivative	ADJ
ejpam-4299	485	18	approach	approach	NOUN
ejpam-4299	485	19	to	to	ADP
ejpam-4299	485	20	anomalous	anomalous	ADJ
ejpam-4299	485	21	diffusion	diffusion	NOUN
ejpam-4299	485	22	.	.	PUNCT
ejpam-4299	486	1	physica	physica	PROPN
ejpam-4299	486	2	a	a	PRON
ejpam-4299	486	3	,	,	PUNCT
ejpam-4299	486	4	491:1001–1013	491:1001–1013	PROPN
ejpam-4299	486	5	,	,	PUNCT
ejpam-4299	486	6	2018	2018	NUM
ejpam-4299	486	7	.	.	PUNCT