id	sid	tid	token	lemma	pos
ejpam-5601	1	1	european	european	PROPN
ejpam-5601	1	2	journal	journal	PROPN
ejpam-5601	1	3	of	of	ADP
ejpam-5601	1	4	pure	pure	ADJ
ejpam-5601	1	5	and	and	CCONJ
ejpam-5601	1	6	applied	applied	ADJ
ejpam-5601	1	7	mathematics	mathematic	NOUN
ejpam-5601	1	8	2025	2025	NUM
ejpam-5601	1	9	,	,	PUNCT
ejpam-5601	1	10	vol	vol	NOUN
ejpam-5601	1	11	.	.	PROPN
ejpam-5601	1	12	18	18	NUM
ejpam-5601	1	13	,	,	PUNCT
ejpam-5601	1	14	issue	issue	NOUN
ejpam-5601	1	15	1	1	NUM
ejpam-5601	1	16	,	,	PUNCT
ejpam-5601	1	17	article	article	NOUN
ejpam-5601	1	18	number	number	NOUN
ejpam-5601	1	19	5601	5601	NUM
ejpam-5601	1	20	issn	issn	PROPN
ejpam-5601	1	21	1307	1307	NUM
ejpam-5601	1	22	-	-	SYM
ejpam-5601	1	23	5543	5543	NUM
ejpam-5601	1	24	–	–	PUNCT
ejpam-5601	1	25	ejpam.com	ejpam.com	X
ejpam-5601	1	26	published	publish	VERB
ejpam-5601	1	27	by	by	ADP
ejpam-5601	1	28	new	new	PROPN
ejpam-5601	1	29	york	york	PROPN
ejpam-5601	1	30	business	business	PROPN
ejpam-5601	1	31	global	global	ADJ
ejpam-5601	1	32	graphical	graphical	ADJ
ejpam-5601	1	33	representation	representation	NOUN
ejpam-5601	1	34	of	of	ADP
ejpam-5601	1	35	zadeh	zadeh	PROPN
ejpam-5601	1	36	’s	’s	PART
ejpam-5601	1	37	max	max	PROPN
ejpam-5601	1	38	-	-	PUNCT
ejpam-5601	1	39	min	min	NOUN
ejpam-5601	1	40	composition	composition	NOUN
ejpam-5601	1	41	operator	operator	NOUN
ejpam-5601	1	42	for	for	ADP
ejpam-5601	1	43	two	two	NUM
ejpam-5601	1	44	3	3	NUM
ejpam-5601	1	45	-	-	PUNCT
ejpam-5601	1	46	dimensional	dimensional	ADJ
ejpam-5601	1	47	quadratic	quadratic	ADJ
ejpam-5601	1	48	fuzzy	fuzzy	ADJ
ejpam-5601	1	49	numbers	number	NOUN
ejpam-5601	1	50	yong	yong	PROPN
ejpam-5601	1	51	sik	sik	PROPN
ejpam-5601	1	52	yun1	yun1	PROPN
ejpam-5601	1	53	,	,	PUNCT
ejpam-5601	1	54	bongju	bongju	NOUN
ejpam-5601	1	55	lee2,∗	lee2,∗	PROPN
ejpam-5601	1	56	1	1	NUM
ejpam-5601	1	57	department	department	NOUN
ejpam-5601	1	58	of	of	ADP
ejpam-5601	1	59	mathematics	mathematics	PROPN
ejpam-5601	1	60	.	.	PUNCT
ejpam-5601	2	1	jeju	jeju	PROPN
ejpam-5601	2	2	national	national	PROPN
ejpam-5601	2	3	university	university	PROPN
ejpam-5601	2	4	.	.	PUNCT
ejpam-5601	3	1	jeju	jeju	PROPN
ejpam-5601	3	2	63243	63243	NUM
ejpam-5601	3	3	,	,	PUNCT
ejpam-5601	3	4	republic	republic	NOUN
ejpam-5601	3	5	of	of	ADP
ejpam-5601	3	6	korea	korea	PROPN
ejpam-5601	3	7	2	2	PROPN
ejpam-5601	3	8	department	department	NOUN
ejpam-5601	3	9	of	of	ADP
ejpam-5601	3	10	mathematics	mathematics	PROPN
ejpam-5601	3	11	education	education	NOUN
ejpam-5601	3	12	.	.	PUNCT
ejpam-5601	4	1	kyungpook	kyungpook	PROPN
ejpam-5601	4	2	national	national	PROPN
ejpam-5601	4	3	university	university	PROPN
ejpam-5601	4	4	.	.	PUNCT
ejpam-5601	5	1	daegu	daegu	NOUN
ejpam-5601	5	2	41566	41566	NUM
ejpam-5601	5	3	,	,	PUNCT
ejpam-5601	5	4	republic	republic	NOUN
ejpam-5601	5	5	of	of	ADP
ejpam-5601	5	6	korea	korea	PROPN
ejpam-5601	5	7	abstract	abstract	PROPN
ejpam-5601	5	8	.	.	PUNCT
ejpam-5601	6	1	we	we	PRON
ejpam-5601	6	2	computed	compute	VERB
ejpam-5601	6	3	the	the	DET
ejpam-5601	6	4	extended	extended	ADJ
ejpam-5601	6	5	operations	operation	NOUN
ejpam-5601	6	6	for	for	ADP
ejpam-5601	6	7	generalized	generalized	ADJ
ejpam-5601	6	8	quadratic	quadratic	ADJ
ejpam-5601	6	9	fuzzy	fuzzy	ADJ
ejpam-5601	6	10	sets	set	NOUN
ejpam-5601	6	11	and	and	CCONJ
ejpam-5601	6	12	extended	extend	VERB
ejpam-5601	6	13	quadratic	quadratic	ADJ
ejpam-5601	6	14	fuzzy	fuzzy	ADJ
ejpam-5601	6	15	numbers	number	NOUN
ejpam-5601	6	16	from	from	ADP
ejpam-5601	6	17	r	r	NOUN
ejpam-5601	6	18	to	to	ADP
ejpam-5601	6	19	r2	r2	PROPN
ejpam-5601	6	20	.	.	PUNCT
ejpam-5601	7	1	by	by	ADP
ejpam-5601	7	2	defining	define	VERB
ejpam-5601	7	3	parametric	parametric	ADJ
ejpam-5601	7	4	operations	operation	NOUN
ejpam-5601	7	5	between	between	ADP
ejpam-5601	7	6	two	two	NUM
ejpam-5601	7	7	α	α	NOUN
ejpam-5601	7	8	-	-	PUNCT
ejpam-5601	7	9	cuts	cut	NOUN
ejpam-5601	7	10	,	,	PUNCT
ejpam-5601	7	11	which	which	PRON
ejpam-5601	7	12	are	be	AUX
ejpam-5601	7	13	regions	region	NOUN
ejpam-5601	7	14	,	,	PUNCT
ejpam-5601	7	15	we	we	PRON
ejpam-5601	7	16	derived	derive	VERB
ejpam-5601	7	17	the	the	DET
ejpam-5601	7	18	parametric	parametric	ADJ
ejpam-5601	7	19	operations	operation	NOUN
ejpam-5601	7	20	for	for	ADP
ejpam-5601	7	21	two	two	NUM
ejpam-5601	7	22	quadratic	quadratic	ADJ
ejpam-5601	7	23	fuzzy	fuzzy	ADJ
ejpam-5601	7	24	numbers	number	NOUN
ejpam-5601	7	25	defined	define	VERB
ejpam-5601	7	26	on	on	ADP
ejpam-5601	7	27	r2	r2	PROPN
ejpam-5601	7	28	.	.	PUNCT
ejpam-5601	8	1	the	the	DET
ejpam-5601	8	2	outcomes	outcome	NOUN
ejpam-5601	8	3	of	of	ADP
ejpam-5601	8	4	these	these	DET
ejpam-5601	8	5	parametric	parametric	ADJ
ejpam-5601	8	6	operations	operation	NOUN
ejpam-5601	8	7	serve	serve	VERB
ejpam-5601	8	8	as	as	ADP
ejpam-5601	8	9	a	a	DET
ejpam-5601	8	10	generalization	generalization	NOUN
ejpam-5601	8	11	of	of	ADP
ejpam-5601	8	12	zadeh	zadeh	PROPN
ejpam-5601	8	13	’s	’s	PART
ejpam-5601	8	14	extended	extend	VERB
ejpam-5601	8	15	algebraic	algebraic	ADJ
ejpam-5601	8	16	operations	operation	NOUN
ejpam-5601	8	17	.	.	PUNCT
ejpam-5601	9	1	we	we	PRON
ejpam-5601	9	2	demonstrated	demonstrate	VERB
ejpam-5601	9	3	that	that	SCONJ
ejpam-5601	9	4	the	the	DET
ejpam-5601	9	5	results	result	NOUN
ejpam-5601	9	6	obtained	obtain	VERB
ejpam-5601	9	7	from	from	ADP
ejpam-5601	9	8	the	the	DET
ejpam-5601	9	9	parametric	parametric	ADJ
ejpam-5601	9	10	operations	operation	NOUN
ejpam-5601	9	11	represent	represent	VERB
ejpam-5601	9	12	an	an	DET
ejpam-5601	9	13	extension	extension	NOUN
ejpam-5601	9	14	of	of	ADP
ejpam-5601	9	15	zadeh	zadeh	PROPN
ejpam-5601	9	16	’s	’s	PART
ejpam-5601	9	17	extended	extend	VERB
ejpam-5601	9	18	algebraic	algebraic	ADJ
ejpam-5601	9	19	operations	operation	NOUN
ejpam-5601	9	20	.	.	PUNCT
ejpam-5601	10	1	additionally	additionally	ADV
ejpam-5601	10	2	,	,	PUNCT
ejpam-5601	10	3	we	we	PRON
ejpam-5601	10	4	expanded	expand	VERB
ejpam-5601	10	5	quadratic	quadratic	ADJ
ejpam-5601	10	6	fuzzy	fuzzy	ADJ
ejpam-5601	10	7	numbers	number	NOUN
ejpam-5601	10	8	initially	initially	ADV
ejpam-5601	10	9	defined	define	VERB
ejpam-5601	10	10	in	in	ADP
ejpam-5601	10	11	two	two	NUM
ejpam-5601	10	12	dimensions	dimension	NOUN
ejpam-5601	10	13	to	to	ADP
ejpam-5601	10	14	three	three	NUM
ejpam-5601	10	15	dimensions	dimension	NOUN
ejpam-5601	10	16	and	and	CCONJ
ejpam-5601	10	17	calculated	calculate	VERB
ejpam-5601	10	18	zadeh	zadeh	PROPN
ejpam-5601	10	19	’s	’s	PART
ejpam-5601	10	20	max	max	PROPN
ejpam-5601	10	21	-	-	PUNCT
ejpam-5601	10	22	min	min	NOUN
ejpam-5601	10	23	composition	composition	NOUN
ejpam-5601	10	24	operator	operator	NOUN
ejpam-5601	10	25	for	for	ADP
ejpam-5601	10	26	two	two	NUM
ejpam-5601	10	27	extended	extended	ADJ
ejpam-5601	10	28	three	three	NUM
ejpam-5601	10	29	-	-	PUNCT
ejpam-5601	10	30	dimensional	dimensional	ADJ
ejpam-5601	10	31	quadratic	quadratic	ADJ
ejpam-5601	10	32	fuzzy	fuzzy	ADJ
ejpam-5601	10	33	numbers	number	NOUN
ejpam-5601	10	34	.	.	PUNCT
ejpam-5601	11	1	we	we	PRON
ejpam-5601	11	2	presented	present	VERB
ejpam-5601	11	3	an	an	DET
ejpam-5601	11	4	illustrative	illustrative	ADJ
ejpam-5601	11	5	example	example	NOUN
ejpam-5601	11	6	of	of	ADP
ejpam-5601	11	7	three	three	NUM
ejpam-5601	11	8	-	-	PUNCT
ejpam-5601	11	9	dimensional	dimensional	ADJ
ejpam-5601	11	10	results	result	NOUN
ejpam-5601	11	11	along	along	ADP
ejpam-5601	11	12	with	with	ADP
ejpam-5601	11	13	corresponding	correspond	VERB
ejpam-5601	11	14	graphs	graph	NOUN
ejpam-5601	11	15	.	.	PUNCT
ejpam-5601	12	1	2020	2020	NUM
ejpam-5601	12	2	mathematics	mathematic	NOUN
ejpam-5601	12	3	subject	subject	NOUN
ejpam-5601	12	4	classifications	classification	NOUN
ejpam-5601	12	5	:	:	PUNCT
ejpam-5601	12	6	47s40	47s40	NUM
ejpam-5601	12	7	,	,	PUNCT
ejpam-5601	12	8	03e72	03e72	X
ejpam-5601	12	9	key	key	ADJ
ejpam-5601	12	10	words	word	NOUN
ejpam-5601	12	11	and	and	CCONJ
ejpam-5601	12	12	phrases	phrase	NOUN
ejpam-5601	12	13	:	:	PUNCT
ejpam-5601	12	14	graphic	graphic	ADJ
ejpam-5601	12	15	representation	representation	NOUN
ejpam-5601	12	16	,	,	PUNCT
ejpam-5601	12	17	parametric	parametric	ADJ
ejpam-5601	12	18	operation	operation	NOUN
ejpam-5601	12	19	,	,	PUNCT
ejpam-5601	12	20	3	3	NUM
ejpam-5601	12	21	-	-	PUNCT
ejpam-5601	12	22	dimensional	dimensional	ADJ
ejpam-5601	12	23	quadraric	quadraric	ADJ
ejpam-5601	12	24	fuzzy	fuzzy	ADJ
ejpam-5601	12	25	number	number	NOUN
ejpam-5601	12	26	1	1	NUM
ejpam-5601	12	27	.	.	PUNCT
ejpam-5601	13	1	introduction	introduction	NOUN
ejpam-5601	13	2	a	a	DET
ejpam-5601	13	3	quadratic	quadratic	ADJ
ejpam-5601	13	4	fuzzy	fuzzy	ADJ
ejpam-5601	13	5	number	number	NOUN
ejpam-5601	13	6	expands	expand	VERB
ejpam-5601	13	7	upon	upon	SCONJ
ejpam-5601	13	8	the	the	DET
ejpam-5601	13	9	concept	concept	NOUN
ejpam-5601	13	10	of	of	ADP
ejpam-5601	13	11	traditional	traditional	ADJ
ejpam-5601	13	12	fuzzy	fuzzy	ADJ
ejpam-5601	13	13	numbers	number	NOUN
ejpam-5601	13	14	by	by	ADP
ejpam-5601	13	15	incorporating	incorporate	VERB
ejpam-5601	13	16	quadratic	quadratic	ADJ
ejpam-5601	13	17	functions	function	NOUN
ejpam-5601	13	18	to	to	PART
ejpam-5601	13	19	represent	represent	VERB
ejpam-5601	13	20	the	the	DET
ejpam-5601	13	21	degree	degree	NOUN
ejpam-5601	13	22	of	of	ADP
ejpam-5601	13	23	membership	membership	NOUN
ejpam-5601	13	24	of	of	ADP
ejpam-5601	13	25	an	an	DET
ejpam-5601	13	26	element	element	NOUN
ejpam-5601	13	27	in	in	ADP
ejpam-5601	13	28	a	a	DET
ejpam-5601	13	29	set	set	NOUN
ejpam-5601	13	30	.	.	PUNCT
ejpam-5601	14	1	fuzzy	fuzzy	ADJ
ejpam-5601	14	2	numbers	number	NOUN
ejpam-5601	14	3	are	be	AUX
ejpam-5601	14	4	utilized	utilize	VERB
ejpam-5601	14	5	to	to	PART
ejpam-5601	14	6	model	model	VERB
ejpam-5601	14	7	uncertainty	uncertainty	NOUN
ejpam-5601	14	8	and	and	CCONJ
ejpam-5601	14	9	imprecision	imprecision	NOUN
ejpam-5601	14	10	in	in	ADP
ejpam-5601	14	11	various	various	ADJ
ejpam-5601	14	12	applications	application	NOUN
ejpam-5601	14	13	,	,	PUNCT
ejpam-5601	14	14	and	and	CCONJ
ejpam-5601	14	15	quadratic	quadratic	ADJ
ejpam-5601	14	16	fuzzy	fuzzy	ADJ
ejpam-5601	14	17	numbers	number	NOUN
ejpam-5601	14	18	provide	provide	VERB
ejpam-5601	14	19	a	a	DET
ejpam-5601	14	20	more	more	ADV
ejpam-5601	14	21	flexible	flexible	ADJ
ejpam-5601	14	22	representation	representation	NOUN
ejpam-5601	14	23	through	through	ADP
ejpam-5601	14	24	the	the	DET
ejpam-5601	14	25	use	use	NOUN
ejpam-5601	14	26	of	of	ADP
ejpam-5601	14	27	quadratic	quadratic	ADJ
ejpam-5601	14	28	functions	function	NOUN
ejpam-5601	14	29	.	.	PUNCT
ejpam-5601	15	1	these	these	DET
ejpam-5601	15	2	numbers	number	NOUN
ejpam-5601	15	3	are	be	AUX
ejpam-5601	15	4	commonly	commonly	ADV
ejpam-5601	15	5	employed	employ	VERB
ejpam-5601	15	6	in	in	ADP
ejpam-5601	15	7	decision	decision	NOUN
ejpam-5601	15	8	-	-	PUNCT
ejpam-5601	15	9	making	make	VERB
ejpam-5601	15	10	processes	process	NOUN
ejpam-5601	15	11	,	,	PUNCT
ejpam-5601	15	12	especially	especially	ADV
ejpam-5601	15	13	in	in	ADP
ejpam-5601	15	14	scenarios	scenario	NOUN
ejpam-5601	15	15	where	where	SCONJ
ejpam-5601	15	16	there	there	PRON
ejpam-5601	15	17	is	be	VERB
ejpam-5601	15	18	a	a	DET
ejpam-5601	15	19	need	need	NOUN
ejpam-5601	15	20	to	to	PART
ejpam-5601	15	21	model	model	VERB
ejpam-5601	15	22	and	and	CCONJ
ejpam-5601	15	23	analyze	analyze	VERB
ejpam-5601	15	24	uncertain	uncertain	ADJ
ejpam-5601	15	25	or	or	CCONJ
ejpam-5601	15	26	imprecise	imprecise	ADJ
ejpam-5601	15	27	information	information	NOUN
ejpam-5601	15	28	.	.	PUNCT
ejpam-5601	16	1	they	they	PRON
ejpam-5601	16	2	find	find	VERB
ejpam-5601	16	3	applications	application	NOUN
ejpam-5601	16	4	in	in	ADP
ejpam-5601	16	5	diverse	diverse	ADJ
ejpam-5601	16	6	fields	field	NOUN
ejpam-5601	16	7	such	such	ADJ
ejpam-5601	16	8	as	as	ADP
ejpam-5601	16	9	optimization	optimization	NOUN
ejpam-5601	16	10	,	,	PUNCT
ejpam-5601	16	11	control	control	NOUN
ejpam-5601	16	12	systems	system	NOUN
ejpam-5601	16	13	,	,	PUNCT
ejpam-5601	16	14	and	and	CCONJ
ejpam-5601	16	15	decision	decision	NOUN
ejpam-5601	16	16	analysis	analysis	NOUN
ejpam-5601	16	17	[	[	X
ejpam-5601	16	18	4	4	NUM
ejpam-5601	16	19	,	,	PUNCT
ejpam-5601	16	20	7	7	NUM
ejpam-5601	16	21	]	]	PUNCT
ejpam-5601	16	22	.	.	PUNCT
ejpam-5601	17	1	it	it	PRON
ejpam-5601	17	2	’s	’	VERB
ejpam-5601	17	3	essential	essential	ADJ
ejpam-5601	17	4	to	to	PART
ejpam-5601	17	5	recognize	recognize	VERB
ejpam-5601	17	6	that	that	SCONJ
ejpam-5601	17	7	various	various	ADJ
ejpam-5601	17	8	researchers	researcher	NOUN
ejpam-5601	17	9	and	and	CCONJ
ejpam-5601	17	10	practitioners	practitioner	NOUN
ejpam-5601	17	11	may	may	AUX
ejpam-5601	17	12	employ	employ	VERB
ejpam-5601	17	13	slightly	slightly	ADV
ejpam-5601	17	14	different	different	ADJ
ejpam-5601	17	15	formulations	formulation	NOUN
ejpam-5601	17	16	and	and	CCONJ
ejpam-5601	17	17	definitions	definition	NOUN
ejpam-5601	17	18	for	for	ADP
ejpam-5601	17	19	quadratic	quadratic	ADJ
ejpam-5601	17	20	∗corresponding	∗corresponding	NOUN
ejpam-5601	17	21	author	author	NOUN
ejpam-5601	17	22	.	.	PUNCT
ejpam-5601	18	1	doi	doi	NOUN
ejpam-5601	18	2	:	:	PUNCT
ejpam-5601	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5601	https://doi.org/10.29020/nybg.ejpam.v18i1.5601	PROPN
ejpam-5601	18	4	email	email	NOUN
ejpam-5601	18	5	addresses	address	NOUN
ejpam-5601	18	6	:	:	PUNCT
ejpam-5601	18	7	yunys@jejunu.ac.kr	yunys@jejunu.ac.kr	PROPN
ejpam-5601	18	8	(	(	PUNCT
ejpam-5601	18	9	y.	y.	PROPN
ejpam-5601	18	10	s.	s.	PROPN
ejpam-5601	18	11	yun	yun	PROPN
ejpam-5601	18	12	)	)	PUNCT
ejpam-5601	18	13	,	,	PUNCT
ejpam-5601	18	14	leebj@knu.ac.kr	leebj@knu.ac.kr	X
ejpam-5601	18	15	(	(	PUNCT
ejpam-5601	18	16	b.	b.	PROPN
ejpam-5601	18	17	lee	lee	PROPN
ejpam-5601	18	18	)	)	PUNCT
ejpam-5601	18	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5601	19	1	1	1	NUM
ejpam-5601	19	2	copyright	copyright	NOUN
ejpam-5601	19	3	:	:	PUNCT
ejpam-5601	19	4	©	©	PROPN
ejpam-5601	19	5	2025	2025	NUM
ejpam-5601	19	6	the	the	DET
ejpam-5601	19	7	author(s	author(s	NOUN
ejpam-5601	19	8	)	)	PUNCT
ejpam-5601	19	9	.	.	PUNCT
ejpam-5601	20	1	(	(	PUNCT
ejpam-5601	20	2	cc	cc	NOUN
ejpam-5601	20	3	by	by	ADP
ejpam-5601	20	4	-	-	PUNCT
ejpam-5601	20	5	nc	nc	PROPN
ejpam-5601	20	6	4.0	4.0	NUM
ejpam-5601	20	7	)	)	PUNCT
ejpam-5601	20	8	y.	y.	PROPN
ejpam-5601	20	9	s.	s.	PROPN
ejpam-5601	20	10	yun	yun	PROPN
ejpam-5601	20	11	,	,	PUNCT
ejpam-5601	20	12	b.	b.	PROPN
ejpam-5601	20	13	lee	lee	PROPN
ejpam-5601	20	14	/	/	SYM
ejpam-5601	20	15	eur	eur	PROPN
ejpam-5601	20	16	.	.	PUNCT
ejpam-5601	21	1	j.	j.	PROPN
ejpam-5601	21	2	pure	pure	PROPN
ejpam-5601	21	3	appl	appl	PROPN
ejpam-5601	21	4	.	.	PROPN
ejpam-5601	21	5	math	math	PROPN
ejpam-5601	21	6	,	,	PUNCT
ejpam-5601	21	7	18	18	NUM
ejpam-5601	21	8	(	(	PUNCT
ejpam-5601	21	9	1	1	NUM
ejpam-5601	21	10	)	)	PUNCT
ejpam-5601	21	11	(	(	PUNCT
ejpam-5601	21	12	2025	2025	NUM
ejpam-5601	21	13	)	)	PUNCT
ejpam-5601	21	14	,	,	PUNCT
ejpam-5601	21	15	5601	5601	NUM
ejpam-5601	21	16	2	2	NUM
ejpam-5601	21	17	of	of	ADP
ejpam-5601	21	18	17	17	NUM
ejpam-5601	21	19	fuzzy	fuzzy	ADJ
ejpam-5601	21	20	numbers	number	NOUN
ejpam-5601	21	21	.	.	PUNCT
ejpam-5601	22	1	additionally	additionally	ADV
ejpam-5601	22	2	,	,	PUNCT
ejpam-5601	22	3	the	the	DET
ejpam-5601	22	4	specific	specific	ADJ
ejpam-5601	22	5	context	context	NOUN
ejpam-5601	22	6	of	of	ADP
ejpam-5601	22	7	their	their	PRON
ejpam-5601	22	8	application	application	NOUN
ejpam-5601	22	9	can	can	AUX
ejpam-5601	22	10	influence	influence	VERB
ejpam-5601	22	11	how	how	SCONJ
ejpam-5601	22	12	they	they	PRON
ejpam-5601	22	13	are	be	AUX
ejpam-5601	22	14	defined	define	VERB
ejpam-5601	22	15	and	and	CCONJ
ejpam-5601	22	16	utilized	utilize	VERB
ejpam-5601	22	17	.	.	PUNCT
ejpam-5601	23	1	the	the	DET
ejpam-5601	23	2	membership	membership	NOUN
ejpam-5601	23	3	function	function	NOUN
ejpam-5601	23	4	of	of	ADP
ejpam-5601	23	5	a	a	DET
ejpam-5601	23	6	quadratic	quadratic	ADJ
ejpam-5601	23	7	fuzzy	fuzzy	ADJ
ejpam-5601	23	8	number	number	NOUN
ejpam-5601	23	9	is	be	AUX
ejpam-5601	23	10	composed	compose	VERB
ejpam-5601	23	11	of	of	ADP
ejpam-5601	23	12	a	a	DET
ejpam-5601	23	13	quadratic	quadratic	ADJ
ejpam-5601	23	14	function	function	NOUN
ejpam-5601	23	15	with	with	ADP
ejpam-5601	23	16	the	the	DET
ejpam-5601	23	17	maximum	maximum	ADJ
ejpam-5601	23	18	value	value	NOUN
ejpam-5601	23	19	of	of	ADP
ejpam-5601	23	20	1	1	NUM
ejpam-5601	23	21	.	.	PUNCT
ejpam-5601	24	1	in	in	ADP
ejpam-5601	24	2	contrast	contrast	NOUN
ejpam-5601	24	3	,	,	PUNCT
ejpam-5601	24	4	a	a	DET
ejpam-5601	24	5	general	general	ADJ
ejpam-5601	24	6	quadratic	quadratic	ADJ
ejpam-5601	24	7	fuzzy	fuzzy	ADJ
ejpam-5601	24	8	set	set	NOUN
ejpam-5601	24	9	is	be	AUX
ejpam-5601	24	10	a	a	DET
ejpam-5601	24	11	quadratic	quadratic	ADJ
ejpam-5601	24	12	fuzzy	fuzzy	ADJ
ejpam-5601	24	13	set	set	NOUN
ejpam-5601	24	14	that	that	PRON
ejpam-5601	24	15	may	may	AUX
ejpam-5601	24	16	not	not	PART
ejpam-5601	24	17	have	have	VERB
ejpam-5601	24	18	a	a	DET
ejpam-5601	24	19	maximum	maximum	ADJ
ejpam-5601	24	20	value	value	NOUN
ejpam-5601	24	21	of	of	ADP
ejpam-5601	24	22	1	1	NUM
ejpam-5601	24	23	.	.	PUNCT
ejpam-5601	25	1	we	we	PRON
ejpam-5601	25	2	calculated	calculate	VERB
ejpam-5601	25	3	the	the	DET
ejpam-5601	25	4	extended	extended	ADJ
ejpam-5601	25	5	operations	operation	NOUN
ejpam-5601	25	6	for	for	ADP
ejpam-5601	25	7	generalized	generalized	ADJ
ejpam-5601	25	8	quadratic	quadratic	ADJ
ejpam-5601	25	9	fuzzy	fuzzy	ADJ
ejpam-5601	25	10	sets	set	NOUN
ejpam-5601	25	11	[	[	X
ejpam-5601	25	12	9	9	NUM
ejpam-5601	25	13	]	]	PUNCT
ejpam-5601	25	14	and	and	CCONJ
ejpam-5601	25	15	expanded	expand	VERB
ejpam-5601	25	16	the	the	DET
ejpam-5601	25	17	quadratic	quadratic	ADJ
ejpam-5601	25	18	fuzzy	fuzzy	ADJ
ejpam-5601	25	19	numbers	number	NOUN
ejpam-5601	25	20	from	from	ADP
ejpam-5601	25	21	r	r	NOUN
ejpam-5601	25	22	to	to	ADP
ejpam-5601	25	23	r2	r2	PROPN
ejpam-5601	25	24	[	[	X
ejpam-5601	25	25	2	2	NUM
ejpam-5601	25	26	]	]	PUNCT
ejpam-5601	25	27	.	.	PUNCT
ejpam-5601	26	1	by	by	ADP
ejpam-5601	26	2	defining	define	VERB
ejpam-5601	26	3	parametric	parametric	ADJ
ejpam-5601	26	4	operations	operation	NOUN
ejpam-5601	26	5	between	between	ADP
ejpam-5601	26	6	two	two	NUM
ejpam-5601	26	7	α	α	NOUN
ejpam-5601	26	8	-	-	PUNCT
ejpam-5601	26	9	cuts	cut	NOUN
ejpam-5601	26	10	,	,	PUNCT
ejpam-5601	26	11	which	which	PRON
ejpam-5601	26	12	are	be	AUX
ejpam-5601	26	13	regions	region	NOUN
ejpam-5601	26	14	,	,	PUNCT
ejpam-5601	26	15	we	we	PRON
ejpam-5601	26	16	derived	derive	VERB
ejpam-5601	26	17	the	the	DET
ejpam-5601	26	18	parametric	parametric	ADJ
ejpam-5601	26	19	operations	operation	NOUN
ejpam-5601	26	20	for	for	ADP
ejpam-5601	26	21	two	two	NUM
ejpam-5601	26	22	quadratic	quadratic	ADJ
ejpam-5601	26	23	fuzzy	fuzzy	ADJ
ejpam-5601	26	24	numbers	number	NOUN
ejpam-5601	26	25	defined	define	VERB
ejpam-5601	26	26	on	on	ADP
ejpam-5601	26	27	r2	r2	PROPN
ejpam-5601	26	28	.	.	PUNCT
ejpam-5601	27	1	the	the	DET
ejpam-5601	27	2	outcomes	outcome	NOUN
ejpam-5601	27	3	of	of	ADP
ejpam-5601	27	4	these	these	DET
ejpam-5601	27	5	parametric	parametric	ADJ
ejpam-5601	27	6	operations	operation	NOUN
ejpam-5601	27	7	serve	serve	VERB
ejpam-5601	27	8	as	as	ADP
ejpam-5601	27	9	a	a	DET
ejpam-5601	27	10	generalization	generalization	NOUN
ejpam-5601	27	11	of	of	ADP
ejpam-5601	27	12	zadeh	zadeh	PROPN
ejpam-5601	27	13	’s	’s	PART
ejpam-5601	27	14	extended	extend	VERB
ejpam-5601	27	15	algebraic	algebraic	ADJ
ejpam-5601	27	16	operations	operation	NOUN
ejpam-5601	27	17	.	.	PUNCT
ejpam-5601	28	1	we	we	PRON
ejpam-5601	28	2	have	have	AUX
ejpam-5601	28	3	shown	show	VERB
ejpam-5601	28	4	that	that	SCONJ
ejpam-5601	28	5	the	the	DET
ejpam-5601	28	6	results	result	NOUN
ejpam-5601	28	7	of	of	ADP
ejpam-5601	28	8	parametric	parametric	ADJ
ejpam-5601	28	9	operations	operation	NOUN
ejpam-5601	28	10	represent	represent	VERB
ejpam-5601	28	11	a	a	DET
ejpam-5601	28	12	generalization	generalization	NOUN
ejpam-5601	28	13	of	of	ADP
ejpam-5601	28	14	zadeh	zadeh	PROPN
ejpam-5601	28	15	’s	’s	PART
ejpam-5601	28	16	max	max	PROPN
ejpam-5601	28	17	-	-	PUNCT
ejpam-5601	28	18	min	min	PROPN
ejpam-5601	28	19	composition	composition	NOUN
ejpam-5601	28	20	operations	operation	NOUN
ejpam-5601	28	21	.	.	PUNCT
ejpam-5601	29	1	furthermore	furthermore	ADV
ejpam-5601	29	2	,	,	PUNCT
ejpam-5601	29	3	we	we	PRON
ejpam-5601	29	4	expanded	expand	VERB
ejpam-5601	29	5	the	the	DET
ejpam-5601	29	6	concept	concept	NOUN
ejpam-5601	29	7	of	of	ADP
ejpam-5601	29	8	general	general	ADJ
ejpam-5601	29	9	quadratic	quadratic	ADJ
ejpam-5601	29	10	fuzzy	fuzzy	ADJ
ejpam-5601	29	11	sets	set	NOUN
ejpam-5601	29	12	from	from	ADP
ejpam-5601	29	13	r	r	NOUN
ejpam-5601	29	14	to	to	ADP
ejpam-5601	29	15	r2	r2	PROPN
ejpam-5601	29	16	.	.	PUNCT
ejpam-5601	30	1	we	we	PRON
ejpam-5601	30	2	performed	perform	VERB
ejpam-5601	30	3	calculations	calculation	NOUN
ejpam-5601	30	4	for	for	ADP
ejpam-5601	30	5	the	the	DET
ejpam-5601	30	6	parametric	parametric	ADJ
ejpam-5601	30	7	operations	operation	NOUN
ejpam-5601	30	8	applied	apply	VERB
ejpam-5601	30	9	to	to	ADP
ejpam-5601	30	10	two	two	NUM
ejpam-5601	30	11	generalized	generalized	ADJ
ejpam-5601	30	12	2	2	NUM
ejpam-5601	30	13	-	-	PUNCT
ejpam-5601	30	14	dimensional	dimensional	ADJ
ejpam-5601	30	15	quadratic	quadratic	ADJ
ejpam-5601	30	16	fuzzy	fuzzy	ADJ
ejpam-5601	30	17	sets	set	NOUN
ejpam-5601	30	18	[	[	X
ejpam-5601	30	19	8	8	NUM
ejpam-5601	30	20	]	]	PUNCT
ejpam-5601	30	21	.	.	PUNCT
ejpam-5601	31	1	our	our	PRON
ejpam-5601	31	2	evidence	evidence	NOUN
ejpam-5601	31	3	demonstrates	demonstrate	VERB
ejpam-5601	31	4	that	that	SCONJ
ejpam-5601	31	5	the	the	DET
ejpam-5601	31	6	parametric	parametric	ADJ
ejpam-5601	31	7	operations	operation	NOUN
ejpam-5601	31	8	for	for	ADP
ejpam-5601	31	9	two	two	NUM
ejpam-5601	31	10	generalized	generalized	ADJ
ejpam-5601	31	11	quadratic	quadratic	ADJ
ejpam-5601	31	12	fuzzy	fuzzy	ADJ
ejpam-5601	31	13	sets	set	NOUN
ejpam-5601	31	14	defined	define	VERB
ejpam-5601	31	15	on	on	ADP
ejpam-5601	31	16	r2	r2	PROPN
ejpam-5601	31	17	constitute	constitute	VERB
ejpam-5601	31	18	a	a	DET
ejpam-5601	31	19	broader	broad	ADJ
ejpam-5601	31	20	generalization	generalization	NOUN
ejpam-5601	31	21	of	of	ADP
ejpam-5601	31	22	zadeh	zadeh	PROPN
ejpam-5601	31	23	’s	’s	PART
ejpam-5601	31	24	max	max	PROPN
ejpam-5601	31	25	-	-	PUNCT
ejpam-5601	31	26	min	min	NOUN
ejpam-5601	31	27	composition	composition	NOUN
ejpam-5601	31	28	operations	operation	NOUN
ejpam-5601	31	29	for	for	ADP
ejpam-5601	31	30	two	two	NUM
ejpam-5601	31	31	general	general	ADJ
ejpam-5601	31	32	quadratic	quadratic	ADJ
ejpam-5601	31	33	fuzzy	fuzzy	ADJ
ejpam-5601	31	34	sets	set	NOUN
ejpam-5601	31	35	defined	define	VERB
ejpam-5601	31	36	on	on	ADP
ejpam-5601	31	37	r	r	NOUN
ejpam-5601	31	38	[	[	X
ejpam-5601	31	39	6	6	NUM
ejpam-5601	31	40	]	]	PUNCT
ejpam-5601	31	41	.	.	PUNCT
ejpam-5601	32	1	in	in	ADP
ejpam-5601	32	2	this	this	DET
ejpam-5601	32	3	paper	paper	NOUN
ejpam-5601	32	4	,	,	PUNCT
ejpam-5601	32	5	we	we	PRON
ejpam-5601	32	6	extend	extend	VERB
ejpam-5601	32	7	quadratic	quadratic	ADJ
ejpam-5601	32	8	fuzzy	fuzzy	ADJ
ejpam-5601	32	9	numbers	number	NOUN
ejpam-5601	32	10	defined	define	VERB
ejpam-5601	32	11	in	in	ADP
ejpam-5601	32	12	two	two	NUM
ejpam-5601	32	13	dimensions	dimension	NOUN
ejpam-5601	32	14	to	to	ADP
ejpam-5601	32	15	three	three	NUM
ejpam-5601	32	16	dimensions	dimension	NOUN
ejpam-5601	32	17	and	and	CCONJ
ejpam-5601	32	18	calculate	calculate	VERB
ejpam-5601	32	19	zadeh	zadeh	PROPN
ejpam-5601	32	20	’s	’s	PART
ejpam-5601	32	21	max	max	PROPN
ejpam-5601	32	22	-	-	PUNCT
ejpam-5601	32	23	min	min	NOUN
ejpam-5601	32	24	composition	composition	NOUN
ejpam-5601	32	25	operator	operator	NOUN
ejpam-5601	32	26	for	for	ADP
ejpam-5601	32	27	two	two	NUM
ejpam-5601	32	28	extended	extended	ADJ
ejpam-5601	32	29	threedimensional	threedimensional	ADJ
ejpam-5601	32	30	quadratic	quadratic	ADJ
ejpam-5601	32	31	fuzzy	fuzzy	ADJ
ejpam-5601	32	32	numbers	number	NOUN
ejpam-5601	32	33	.	.	PUNCT
ejpam-5601	33	1	we	we	PRON
ejpam-5601	33	2	provide	provide	VERB
ejpam-5601	33	3	an	an	DET
ejpam-5601	33	4	illustrative	illustrative	ADJ
ejpam-5601	33	5	example	example	NOUN
ejpam-5601	33	6	showcasing	showcase	VERB
ejpam-5601	33	7	three	three	NUM
ejpam-5601	33	8	-	-	PUNCT
ejpam-5601	33	9	dimensional	dimensional	ADJ
ejpam-5601	33	10	results	result	NOUN
ejpam-5601	33	11	and	and	CCONJ
ejpam-5601	33	12	present	present	ADJ
ejpam-5601	33	13	graphs	graph	NOUN
ejpam-5601	33	14	depicting	depict	VERB
ejpam-5601	33	15	the	the	DET
ejpam-5601	33	16	example	example	NOUN
ejpam-5601	33	17	.	.	PUNCT
ejpam-5601	34	1	2	2	X
ejpam-5601	34	2	.	.	X
ejpam-5601	34	3	max	max	PROPN
ejpam-5601	34	4	-	-	PUNCT
ejpam-5601	34	5	min	min	PROPN
ejpam-5601	34	6	composition	composition	NOUN
ejpam-5601	34	7	operations	operation	NOUN
ejpam-5601	34	8	of	of	ADP
ejpam-5601	34	9	zadeh	zadeh	PROPN
ejpam-5601	34	10	for	for	ADP
ejpam-5601	34	11	generalized	generalized	ADJ
ejpam-5601	34	12	quadratic	quadratic	ADJ
ejpam-5601	34	13	fuzzy	fuzzy	ADJ
ejpam-5601	34	14	sets	set	NOUN
ejpam-5601	34	15	defined	define	VERB
ejpam-5601	34	16	on	on	ADP
ejpam-5601	34	17	r	r	NOUN
ejpam-5601	34	18	we	we	PRON
ejpam-5601	34	19	start	start	VERB
ejpam-5601	34	20	by	by	ADP
ejpam-5601	34	21	introducing	introduce	VERB
ejpam-5601	34	22	the	the	DET
ejpam-5601	34	23	α	α	NOUN
ejpam-5601	34	24	-	-	PUNCT
ejpam-5601	34	25	cut	cut	VERB
ejpam-5601	34	26	and	and	CCONJ
ejpam-5601	34	27	α	α	NOUN
ejpam-5601	34	28	-	-	PUNCT
ejpam-5601	34	29	set	set	NOUN
ejpam-5601	34	30	of	of	ADP
ejpam-5601	34	31	the	the	DET
ejpam-5601	34	32	fuzzy	fuzzy	ADJ
ejpam-5601	34	33	set	set	VERB
ejpam-5601	34	34	a	a	PRON
ejpam-5601	34	35	on	on	ADP
ejpam-5601	34	36	r	r	NOUN
ejpam-5601	34	37	with	with	ADP
ejpam-5601	34	38	the	the	DET
ejpam-5601	34	39	membership	membership	NOUN
ejpam-5601	34	40	function	function	NOUN
ejpam-5601	34	41	µa(x	µa(x	ADP
ejpam-5601	34	42	)	)	PUNCT
ejpam-5601	34	43	.	.	PUNCT
ejpam-5601	35	1	an	an	DET
ejpam-5601	35	2	α	α	NOUN
ejpam-5601	35	3	-	-	PUNCT
ejpam-5601	35	4	cut	cut	NOUN
ejpam-5601	35	5	of	of	ADP
ejpam-5601	35	6	the	the	DET
ejpam-5601	35	7	fuzzy	fuzzy	ADJ
ejpam-5601	35	8	number	number	NOUN
ejpam-5601	35	9	a	a	PRON
ejpam-5601	35	10	is	be	AUX
ejpam-5601	35	11	formally	formally	ADV
ejpam-5601	35	12	defined	define	VERB
ejpam-5601	35	13	as	as	ADP
ejpam-5601	35	14	aα	aα	NOUN
ejpam-5601	35	15	=	=	SYM
ejpam-5601	35	16	{	{	PUNCT
ejpam-5601	35	17	x	x	PUNCT
ejpam-5601	35	18	∈	∈	PROPN
ejpam-5601	35	19	r	r	NOUN
ejpam-5601	35	20	|	|	NOUN
ejpam-5601	35	21	µa(x	µa(x	PUNCT
ejpam-5601	35	22	)	)	PUNCT
ejpam-5601	35	23	≥	≥	NOUN
ejpam-5601	35	24	α	α	NOUN
ejpam-5601	35	25	}	}	PUNCT
ejpam-5601	35	26	when	when	SCONJ
ejpam-5601	35	27	α	α	X
ejpam-5601	35	28	∈	∈	PROPN
ejpam-5601	35	29	(	(	PUNCT
ejpam-5601	35	30	0	0	NUM
ejpam-5601	35	31	,	,	PUNCT
ejpam-5601	35	32	1	1	NUM
ejpam-5601	35	33	]	]	PUNCT
ejpam-5601	35	34	and	and	CCONJ
ejpam-5601	35	35	a0	a0	NOUN
ejpam-5601	35	36	is	be	AUX
ejpam-5601	35	37	determined	determine	VERB
ejpam-5601	35	38	as	as	ADP
ejpam-5601	35	39	the	the	DET
ejpam-5601	35	40	closure	closure	NOUN
ejpam-5601	35	41	of	of	ADP
ejpam-5601	35	42	{	{	PUNCT
ejpam-5601	35	43	x	x	SYM
ejpam-5601	35	44	∈	∈	PROPN
ejpam-5601	35	45	r	r	NOUN
ejpam-5601	35	46	|	|	NOUN
ejpam-5601	35	47	µa(x	µa(x	PUNCT
ejpam-5601	35	48	)	)	PUNCT
ejpam-5601	35	49	>	>	X
ejpam-5601	35	50	0	0	NUM
ejpam-5601	35	51	}	}	PUNCT
ejpam-5601	35	52	.	.	PUNCT
ejpam-5601	36	1	for	for	ADP
ejpam-5601	36	2	α	α	DET
ejpam-5601	36	3	∈	∈	PROPN
ejpam-5601	36	4	(	(	PUNCT
ejpam-5601	36	5	0	0	NUM
ejpam-5601	36	6	,	,	PUNCT
ejpam-5601	36	7	1	1	NUM
ejpam-5601	36	8	)	)	PUNCT
ejpam-5601	36	9	,	,	PUNCT
ejpam-5601	36	10	the	the	DET
ejpam-5601	36	11	set	set	NOUN
ejpam-5601	36	12	aα	aα	NOUN
ejpam-5601	36	13	=	=	SYM
ejpam-5601	36	14	{	{	PUNCT
ejpam-5601	36	15	x	x	PUNCT
ejpam-5601	36	16	∈	∈	PROPN
ejpam-5601	36	17	x	x	X
ejpam-5601	36	18	|	|	NOUN
ejpam-5601	36	19	µa(x	µa(x	PUNCT
ejpam-5601	36	20	)	)	PUNCT
ejpam-5601	36	21	=	=	SYM
ejpam-5601	36	22	α	α	X
ejpam-5601	36	23	}	}	PUNCT
ejpam-5601	36	24	is	be	AUX
ejpam-5601	36	25	referred	refer	VERB
ejpam-5601	36	26	to	to	ADP
ejpam-5601	36	27	as	as	ADP
ejpam-5601	36	28	the	the	DET
ejpam-5601	36	29	α	α	NOUN
ejpam-5601	36	30	-	-	PUNCT
ejpam-5601	36	31	set	set	NOUN
ejpam-5601	36	32	of	of	ADP
ejpam-5601	36	33	the	the	DET
ejpam-5601	36	34	fuzzy	fuzzy	ADJ
ejpam-5601	36	35	set	set	VERB
ejpam-5601	36	36	a	a	PRON
ejpam-5601	36	37	,	,	PUNCT
ejpam-5601	36	38	where	where	SCONJ
ejpam-5601	36	39	a0	a0	PROPN
ejpam-5601	36	40	represents	represent	VERB
ejpam-5601	36	41	the	the	DET
ejpam-5601	36	42	boundary	boundary	NOUN
ejpam-5601	36	43	of	of	ADP
ejpam-5601	36	44	{	{	PUNCT
ejpam-5601	36	45	x	x	SYM
ejpam-5601	36	46	∈	∈	PROPN
ejpam-5601	36	47	r	r	NOUN
ejpam-5601	36	48	|	|	NOUN
ejpam-5601	36	49	µa(x	µa(x	PUNCT
ejpam-5601	36	50	)	)	PUNCT
ejpam-5601	36	51	>	>	X
ejpam-5601	36	52	0	0	NUM
ejpam-5601	36	53	}	}	PUNCT
ejpam-5601	36	54	,	,	PUNCT
ejpam-5601	36	55	and	and	CCONJ
ejpam-5601	36	56	a1	a1	NOUN
ejpam-5601	36	57	is	be	AUX
ejpam-5601	36	58	equivalent	equivalent	ADJ
ejpam-5601	36	59	to	to	AUX
ejpam-5601	36	60	a1	a1	VERB
ejpam-5601	36	61	.	.	PUNCT
ejpam-5601	37	1	definition	definition	NOUN
ejpam-5601	37	2	1	1	NUM
ejpam-5601	37	3	.	.	PUNCT
ejpam-5601	38	1	[	[	X
ejpam-5601	38	2	12	12	NUM
ejpam-5601	38	3	]	]	PUNCT
ejpam-5601	38	4	the	the	DET
ejpam-5601	38	5	extended	extended	ADJ
ejpam-5601	38	6	addition	addition	NOUN
ejpam-5601	38	7	a(+)b	a(+)b	PROPN
ejpam-5601	38	8	,	,	PUNCT
ejpam-5601	38	9	extended	extend	VERB
ejpam-5601	38	10	subtraction	subtraction	NOUN
ejpam-5601	38	11	a(−)b	a(−)b	NOUN
ejpam-5601	38	12	,	,	PUNCT
ejpam-5601	38	13	extended	extended	ADJ
ejpam-5601	38	14	multiplication	multiplication	NOUN
ejpam-5601	38	15	a(·)b	a(·)b	NOUN
ejpam-5601	38	16	,	,	PUNCT
ejpam-5601	38	17	and	and	CCONJ
ejpam-5601	38	18	extended	extended	ADJ
ejpam-5601	38	19	division	division	NOUN
ejpam-5601	38	20	a(/)b	a(/)b	NOUN
ejpam-5601	38	21	are	be	AUX
ejpam-5601	38	22	fuzzy	fuzzy	ADJ
ejpam-5601	38	23	sets	set	NOUN
ejpam-5601	38	24	with	with	ADP
ejpam-5601	38	25	membership	membership	NOUN
ejpam-5601	38	26	functions	function	NOUN
ejpam-5601	38	27	as	as	SCONJ
ejpam-5601	38	28	follows	follow	VERB
ejpam-5601	38	29	.	.	PUNCT
ejpam-5601	39	1	for	for	ADP
ejpam-5601	39	2	all	all	DET
ejpam-5601	39	3	x	x	SYM
ejpam-5601	39	4	∈	∈	PROPN
ejpam-5601	39	5	a	a	PRON
ejpam-5601	39	6	and	and	CCONJ
ejpam-5601	39	7	y	y	PROPN
ejpam-5601	39	8	∈	∈	PROPN
ejpam-5601	39	9	b	b	PROPN
ejpam-5601	39	10	,	,	PUNCT
ejpam-5601	39	11	µa(∗)b(z	µa(∗)b(z	NOUN
ejpam-5601	39	12	)	)	PUNCT
ejpam-5601	39	13	=	=	PUNCT
ejpam-5601	39	14	sup	sup	NOUN
ejpam-5601	39	15	z	z	PROPN
ejpam-5601	39	16	=	=	X
ejpam-5601	39	17	x∗y	x∗y	X
ejpam-5601	39	18	min{µa(x	min{µa(x	NOUN
ejpam-5601	39	19	)	)	PUNCT
ejpam-5601	39	20	,	,	PUNCT
ejpam-5601	39	21	µb(y	µb(y	NUM
ejpam-5601	39	22	)	)	PUNCT
ejpam-5601	39	23	}	}	PUNCT
ejpam-5601	39	24	,	,	PUNCT
ejpam-5601	39	25	∗	∗	NOUN
ejpam-5601	39	26	=	=	PUNCT
ejpam-5601	39	27	+	+	ADJ
ejpam-5601	39	28	,	,	PUNCT
ejpam-5601	39	29	−	−	PROPN
ejpam-5601	39	30	,	,	PUNCT
ejpam-5601	39	31	·	·	PUNCT
ejpam-5601	39	32	,	,	PUNCT
ejpam-5601	39	33	/	/	PUNCT
ejpam-5601	39	34	now	now	ADV
ejpam-5601	39	35	,	,	PUNCT
ejpam-5601	39	36	we	we	PRON
ejpam-5601	39	37	extend	extend	VERB
ejpam-5601	39	38	the	the	DET
ejpam-5601	39	39	concept	concept	NOUN
ejpam-5601	39	40	to	to	PART
ejpam-5601	39	41	encompass	encompass	VERB
ejpam-5601	39	42	general	general	ADJ
ejpam-5601	39	43	quadratic	quadratic	ADJ
ejpam-5601	39	44	fuzzy	fuzzy	ADJ
ejpam-5601	39	45	sets	set	NOUN
ejpam-5601	39	46	.	.	PUNCT
ejpam-5601	40	1	a	a	DET
ejpam-5601	40	2	general	general	ADJ
ejpam-5601	40	3	quadratic	quadratic	ADJ
ejpam-5601	40	4	fuzzy	fuzzy	ADJ
ejpam-5601	40	5	set	set	NOUN
ejpam-5601	40	6	is	be	AUX
ejpam-5601	40	7	symmetric	symmetric	ADJ
ejpam-5601	40	8	and	and	CCONJ
ejpam-5601	40	9	may	may	AUX
ejpam-5601	40	10	not	not	PART
ejpam-5601	40	11	necessarily	necessarily	ADV
ejpam-5601	40	12	attain	attain	VERB
ejpam-5601	40	13	the	the	DET
ejpam-5601	40	14	maximum	maximum	ADJ
ejpam-5601	40	15	value	value	NOUN
ejpam-5601	40	16	of	of	ADP
ejpam-5601	40	17	1	1	NUM
ejpam-5601	40	18	.	.	PUNCT
ejpam-5601	41	1	the	the	DET
ejpam-5601	41	2	membership	membership	NOUN
ejpam-5601	41	3	function	function	NOUN
ejpam-5601	41	4	graph	graph	NOUN
ejpam-5601	41	5	of	of	ADP
ejpam-5601	41	6	a	a	DET
ejpam-5601	41	7	general	general	ADJ
ejpam-5601	41	8	quadratic	quadratic	ADJ
ejpam-5601	41	9	fuzzy	fuzzy	NOUN
ejpam-5601	41	10	set	set	VERB
ejpam-5601	41	11	exhibits	exhibit	NOUN
ejpam-5601	41	12	symmetry	symmetry	NOUN
ejpam-5601	41	13	with	with	ADP
ejpam-5601	41	14	respect	respect	NOUN
ejpam-5601	41	15	to	to	ADP
ejpam-5601	41	16	a	a	DET
ejpam-5601	41	17	certain	certain	ADJ
ejpam-5601	41	18	line	line	NOUN
ejpam-5601	41	19	defined	define	VERB
ejpam-5601	41	20	by	by	ADP
ejpam-5601	41	21	x	x	X
ejpam-5601	41	22	=	=	PUNCT
ejpam-5601	41	23	m.	m.	NOUN
ejpam-5601	41	24	definition	definition	NOUN
ejpam-5601	41	25	2	2	NUM
ejpam-5601	41	26	.	.	PUNCT
ejpam-5601	42	1	[	[	X
ejpam-5601	42	2	9	9	NUM
ejpam-5601	42	3	]	]	PUNCT
ejpam-5601	42	4	a	a	DET
ejpam-5601	42	5	fuzzy	fuzzy	ADJ
ejpam-5601	42	6	set	set	VERB
ejpam-5601	42	7	a	a	PRON
ejpam-5601	42	8	with	with	ADP
ejpam-5601	42	9	a	a	DET
ejpam-5601	42	10	membership	membership	NOUN
ejpam-5601	42	11	function	function	NOUN
ejpam-5601	42	12	y.	y.	PROPN
ejpam-5601	42	13	s.	s.	PROPN
ejpam-5601	42	14	yun	yun	PROPN
ejpam-5601	42	15	,	,	PUNCT
ejpam-5601	42	16	b.	b.	PROPN
ejpam-5601	42	17	lee	lee	PROPN
ejpam-5601	42	18	/	/	SYM
ejpam-5601	42	19	eur	eur	PROPN
ejpam-5601	42	20	.	.	PUNCT
ejpam-5601	43	1	j.	j.	PROPN
ejpam-5601	43	2	pure	pure	PROPN
ejpam-5601	43	3	appl	appl	PROPN
ejpam-5601	43	4	.	.	PROPN
ejpam-5601	43	5	math	math	PROPN
ejpam-5601	43	6	,	,	PUNCT
ejpam-5601	43	7	18	18	NUM
ejpam-5601	43	8	(	(	PUNCT
ejpam-5601	43	9	1	1	NUM
ejpam-5601	43	10	)	)	PUNCT
ejpam-5601	43	11	(	(	PUNCT
ejpam-5601	43	12	2025	2025	NUM
ejpam-5601	43	13	)	)	PUNCT
ejpam-5601	43	14	,	,	PUNCT
ejpam-5601	43	15	5601	5601	NUM
ejpam-5601	43	16	3	3	NUM
ejpam-5601	43	17	of	of	ADP
ejpam-5601	43	18	17	17	NUM
ejpam-5601	43	19	µa(x	µa(x	NOUN
ejpam-5601	43	20	)	)	PUNCT
ejpam-5601	43	21	=	=	SYM
ejpam-5601	43	22	{	{	PUNCT
ejpam-5601	43	23	0	0	NUM
ejpam-5601	43	24	,	,	PUNCT
ejpam-5601	43	25	x	x	X
ejpam-5601	43	26	<	<	X
ejpam-5601	43	27	x1	x1	PROPN
ejpam-5601	43	28	,	,	PUNCT
ejpam-5601	43	29	x2	x2	PROPN
ejpam-5601	43	30	≤	≤	NUM
ejpam-5601	43	31	x	x	X
ejpam-5601	43	32	,	,	PUNCT
ejpam-5601	43	33	−a(x−	−a(x−	X
ejpam-5601	43	34	x1)(x−	x1)(x−	PUNCT
ejpam-5601	44	1	x2	x2	PROPN
ejpam-5601	44	2	)	)	PUNCT
ejpam-5601	44	3	=	=	PUNCT
ejpam-5601	45	1	−a(x−m)2	−a(x−m)2	PUNCT
ejpam-5601	46	1	+	+	CCONJ
ejpam-5601	46	2	p	p	X
ejpam-5601	46	3	,	,	PUNCT
ejpam-5601	46	4	x1	x1	PROPN
ejpam-5601	46	5	≤	≤	NUM
ejpam-5601	46	6	x	x	PUNCT
ejpam-5601	46	7	<	<	X
ejpam-5601	46	8	x2	x2	PROPN
ejpam-5601	46	9	,	,	PUNCT
ejpam-5601	46	10	where	where	SCONJ
ejpam-5601	46	11	m	m	VERB
ejpam-5601	46	12	=	=	SYM
ejpam-5601	46	13	x1+x2	x1+x2	PROPN
ejpam-5601	46	14	2	2	NUM
ejpam-5601	46	15	,	,	PUNCT
ejpam-5601	46	16	0	0	PUNCT
ejpam-5601	46	17	<	<	X
ejpam-5601	46	18	a	a	X
ejpam-5601	46	19	,	,	PUNCT
ejpam-5601	46	20	0	0	PUNCT
ejpam-5601	46	21	<	<	X
ejpam-5601	46	22	p	p	X
ejpam-5601	46	23	≤	≤	NUM
ejpam-5601	46	24	1	1	NUM
ejpam-5601	46	25	,	,	PUNCT
ejpam-5601	46	26	is	be	AUX
ejpam-5601	46	27	called	call	VERB
ejpam-5601	46	28	a	a	DET
ejpam-5601	46	29	generalized	generalized	ADJ
ejpam-5601	46	30	quadratic	quadratic	ADJ
ejpam-5601	46	31	fuzzy	fuzzy	ADJ
ejpam-5601	46	32	set	set	NOUN
ejpam-5601	46	33	and	and	CCONJ
ejpam-5601	46	34	denoted	denote	VERB
ejpam-5601	46	35	by	by	ADP
ejpam-5601	46	36	[	[	X
ejpam-5601	46	37	[	[	X
ejpam-5601	46	38	x1	x1	ADJ
ejpam-5601	46	39	,	,	PUNCT
ejpam-5601	46	40	p	p	X
ejpam-5601	46	41	,	,	PUNCT
ejpam-5601	46	42	x2	x2	PROPN
ejpam-5601	46	43	]	]	X
ejpam-5601	46	44	]	]	PUNCT
ejpam-5601	46	45	or	or	CCONJ
ejpam-5601	46	46	[	[	X
ejpam-5601	46	47	[	[	X
ejpam-5601	46	48	a	a	X
ejpam-5601	46	49	,	,	PUNCT
ejpam-5601	46	50	m	m	NOUN
ejpam-5601	46	51	,	,	PUNCT
ejpam-5601	46	52	p]]+	p]]+	PROPN
ejpam-5601	46	53	.	.	PUNCT
ejpam-5601	47	1	theorem	theorem	NOUN
ejpam-5601	47	2	1	1	NUM
ejpam-5601	47	3	.	.	PUNCT
ejpam-5601	48	1	[	[	X
ejpam-5601	48	2	9	9	NUM
ejpam-5601	48	3	]	]	PUNCT
ejpam-5601	48	4	let	let	VERB
ejpam-5601	48	5	a	a	PRON
ejpam-5601	48	6	=	=	PUNCT
ejpam-5601	49	1	[	[	X
ejpam-5601	49	2	[	[	X
ejpam-5601	49	3	a	a	X
ejpam-5601	49	4	,	,	PUNCT
ejpam-5601	49	5	m	m	NOUN
ejpam-5601	49	6	,	,	PUNCT
ejpam-5601	49	7	p]]+	p]]+	PROPN
ejpam-5601	49	8	=	=	PUNCT
ejpam-5601	50	1	[	[	X
ejpam-5601	50	2	[	[	X
ejpam-5601	50	3	x1	x1	ADJ
ejpam-5601	50	4	,	,	PUNCT
ejpam-5601	50	5	p	p	X
ejpam-5601	50	6	,	,	PUNCT
ejpam-5601	50	7	x2	x2	PROPN
ejpam-5601	50	8	]	]	X
ejpam-5601	50	9	]	]	PUNCT
ejpam-5601	50	10	and	and	CCONJ
ejpam-5601	50	11	b	b	X
ejpam-5601	50	12	=	=	SYM
ejpam-5601	51	1	[	[	X
ejpam-5601	51	2	[	[	X
ejpam-5601	51	3	b	b	NOUN
ejpam-5601	51	4	,	,	PUNCT
ejpam-5601	51	5	n	n	CCONJ
ejpam-5601	51	6	,	,	PUNCT
ejpam-5601	51	7	q]]+	q]]+	NOUN
ejpam-5601	51	8	=	=	PUNCT
ejpam-5601	52	1	[	[	X
ejpam-5601	52	2	[	[	X
ejpam-5601	52	3	x3	x3	ADJ
ejpam-5601	52	4	,	,	PUNCT
ejpam-5601	52	5	q	q	X
ejpam-5601	52	6	,	,	PUNCT
ejpam-5601	52	7	x4	x4	PROPN
ejpam-5601	52	8	]	]	X
ejpam-5601	52	9	]	]	PUNCT
ejpam-5601	52	10	be	be	AUX
ejpam-5601	52	11	generalized	generalize	VERB
ejpam-5601	52	12	quadratic	quadratic	ADJ
ejpam-5601	52	13	fuzzy	fuzzy	ADJ
ejpam-5601	52	14	sets	set	NOUN
ejpam-5601	52	15	.	.	PUNCT
ejpam-5601	53	1	assume	assume	VERB
ejpam-5601	53	2	that	that	SCONJ
ejpam-5601	53	3	p	p	PROPN
ejpam-5601	53	4	≤	≤	X
ejpam-5601	53	5	q	q	PUNCT
ejpam-5601	53	6	and	and	CCONJ
ejpam-5601	53	7	µb(x	µb(x	NUM
ejpam-5601	53	8	)	)	PUNCT
ejpam-5601	53	9	≥	≥	NOUN
ejpam-5601	53	10	p	p	X
ejpam-5601	53	11	on	on	ADP
ejpam-5601	53	12	[	[	X
ejpam-5601	53	13	k1	k1	NOUN
ejpam-5601	53	14	,	,	PUNCT
ejpam-5601	53	15	k2	k2	NOUN
ejpam-5601	53	16	]	]	PUNCT
ejpam-5601	53	17	.	.	PUNCT
ejpam-5601	54	1	we	we	PRON
ejpam-5601	54	2	can	can	AUX
ejpam-5601	54	3	then	then	ADV
ejpam-5601	54	4	deduce	deduce	VERB
ejpam-5601	54	5	the	the	DET
ejpam-5601	54	6	followings	following	NOUN
ejpam-5601	54	7	:	:	PUNCT
ejpam-5601	54	8	(	(	PUNCT
ejpam-5601	54	9	1	1	X
ejpam-5601	54	10	)	)	PUNCT
ejpam-5601	54	11	a(+)b	a(+)b	PROPN
ejpam-5601	54	12	is	be	AUX
ejpam-5601	54	13	a	a	DET
ejpam-5601	54	14	fuzzy	fuzzy	ADJ
ejpam-5601	54	15	set	set	NOUN
ejpam-5601	54	16	with	with	ADP
ejpam-5601	54	17	a	a	DET
ejpam-5601	54	18	membership	membership	NOUN
ejpam-5601	54	19	function	function	NOUN
ejpam-5601	54	20	µa(+)b(x	µa(+)b(x	PUNCT
ejpam-5601	54	21	)	)	PUNCT
ejpam-5601	54	22	=	=	PUNCT
ejpam-5601	54	23			NOUN
ejpam-5601	54	24	0	0	PUNCT
ejpam-5601	55	1	(	(	PUNCT
ejpam-5601	55	2	x	x	X
ejpam-5601	55	3	<	<	X
ejpam-5601	55	4	x1	x1	PROPN
ejpam-5601	55	5	+	+	CCONJ
ejpam-5601	55	6	x3	x3	ADJ
ejpam-5601	55	7	,	,	PUNCT
ejpam-5601	55	8	x2	x2	PROPN
ejpam-5601	55	9	+	+	CCONJ
ejpam-5601	55	10	x4	x4	PROPN
ejpam-5601	55	11	≤	≤	ADJ
ejpam-5601	55	12	x	x	X
ejpam-5601	55	13	)	)	PUNCT
ejpam-5601	55	14	f1(x	f1(x	NUM
ejpam-5601	55	15	)	)	PUNCT
ejpam-5601	55	16	(	(	PUNCT
ejpam-5601	55	17	x1	x1	PROPN
ejpam-5601	56	1	+	+	CCONJ
ejpam-5601	56	2	x3	x3	ADJ
ejpam-5601	56	3	≤	≤	NUM
ejpam-5601	56	4	x	x	PUNCT
ejpam-5601	56	5	<	<	X
ejpam-5601	56	6	m+	m+	NUM
ejpam-5601	56	7	k1	k1	NOUN
ejpam-5601	56	8	)	)	PUNCT
ejpam-5601	56	9	p	p	X
ejpam-5601	56	10	(	(	PUNCT
ejpam-5601	56	11	m+	m+	NUM
ejpam-5601	56	12	k1	k1	PROPN
ejpam-5601	56	13	≤	≤	NUM
ejpam-5601	56	14	x	x	PUNCT
ejpam-5601	56	15	<	<	X
ejpam-5601	56	16	m+	m+	NUM
ejpam-5601	56	17	k2	k2	NOUN
ejpam-5601	56	18	)	)	PUNCT
ejpam-5601	56	19	f2(x	f2(x	PROPN
ejpam-5601	56	20	)	)	PUNCT
ejpam-5601	56	21	(	(	PUNCT
ejpam-5601	56	22	m+	m+	NUM
ejpam-5601	56	23	k2	k2	ADJ
ejpam-5601	56	24	≤	≤	PROPN
ejpam-5601	57	1	x	x	PUNCT
ejpam-5601	57	2	<	<	X
ejpam-5601	57	3	x2	x2	PROPN
ejpam-5601	57	4	+	+	CCONJ
ejpam-5601	57	5	x4	x4	PROPN
ejpam-5601	57	6	)	)	PUNCT
ejpam-5601	57	7	where	where	SCONJ
ejpam-5601	57	8	f1(x	f1(x	NOUN
ejpam-5601	57	9	)	)	PUNCT
ejpam-5601	57	10	=	=	SYM
ejpam-5601	57	11	1	1	NUM
ejpam-5601	57	12	a2	a2	PROPN
ejpam-5601	57	13	−	−	PROPN
ejpam-5601	57	14	2ab+	2ab+	PROPN
ejpam-5601	57	15	b2	b2	PROPN
ejpam-5601	57	16	(	(	PUNCT
ejpam-5601	57	17	−abm(a+	−abm(a+	PROPN
ejpam-5601	57	18	b+	b+	ADJ
ejpam-5601	57	19	an+	an+	NOUN
ejpam-5601	57	20	bn)−	bn)−	NOUN
ejpam-5601	57	21	abn(am+	abn(am+	PROPN
ejpam-5601	57	22	bm	bm	PROPN
ejpam-5601	57	23	+	+	CCONJ
ejpam-5601	57	24	an+	an+	PROPN
ejpam-5601	57	25	bn)−	bn)−	NOUN
ejpam-5601	57	26	ab(p+	ab(p+	PROPN
ejpam-5601	57	27	q	q	X
ejpam-5601	57	28	)	)	PUNCT
ejpam-5601	57	29	+	+	PUNCT
ejpam-5601	57	30	a2q	a2q	VERB
ejpam-5601	57	31	+	+	CCONJ
ejpam-5601	57	32	b2p+	b2p+	PROPN
ejpam-5601	57	33	2ab(am+	2ab(am+	PROPN
ejpam-5601	57	34	bm+	bm+	PROPN
ejpam-5601	57	35	an	an	DET
ejpam-5601	57	36	+	+	CCONJ
ejpam-5601	57	37	bn)x−	bn)x−	ADJ
ejpam-5601	57	38	ab(a+	ab(a+	PROPN
ejpam-5601	57	39	b)x2	b)x2	PROPN
ejpam-5601	57	40	+	+	CCONJ
ejpam-5601	57	41	2ab(m+	2ab(m+	NUM
ejpam-5601	57	42	n−	n−	PROPN
ejpam-5601	57	43	x	x	NOUN
ejpam-5601	57	44	)	)	PUNCT
ejpam-5601	57	45	·	·	PUNCT
ejpam-5601	57	46	√	√	NUM
ejpam-5601	57	47	g1(x	g1(x	NOUN
ejpam-5601	57	48	)	)	PUNCT
ejpam-5601	57	49	)	)	PUNCT
ejpam-5601	57	50	,	,	PUNCT
ejpam-5601	57	51	f2(x	f2(x	X
ejpam-5601	57	52	)	)	PUNCT
ejpam-5601	57	53	=	=	SYM
ejpam-5601	57	54	1	1	NUM
ejpam-5601	57	55	a2	a2	PROPN
ejpam-5601	57	56	−	−	PROPN
ejpam-5601	57	57	2ab+	2ab+	PROPN
ejpam-5601	57	58	b2	b2	PROPN
ejpam-5601	57	59	(	(	PUNCT
ejpam-5601	57	60	−abm(a+	−abm(a+	PROPN
ejpam-5601	57	61	b+	b+	ADJ
ejpam-5601	57	62	an+	an+	NOUN
ejpam-5601	57	63	bn)−	bn)−	NOUN
ejpam-5601	57	64	abn(am+	abn(am+	PROPN
ejpam-5601	57	65	bm	bm	PROPN
ejpam-5601	57	66	+	+	CCONJ
ejpam-5601	57	67	an+	an+	PROPN
ejpam-5601	57	68	bn)−	bn)−	NOUN
ejpam-5601	57	69	ab(p+	ab(p+	PROPN
ejpam-5601	57	70	q	q	X
ejpam-5601	57	71	)	)	PUNCT
ejpam-5601	58	1	+	+	PUNCT
ejpam-5601	58	2	a2q	a2q	VERB
ejpam-5601	58	3	+	+	CCONJ
ejpam-5601	58	4	b2p+	b2p+	PROPN
ejpam-5601	58	5	2ab(am+	2ab(am+	PROPN
ejpam-5601	58	6	bm+	bm+	PROPN
ejpam-5601	59	1	an	an	DET
ejpam-5601	59	2	+	+	CCONJ
ejpam-5601	59	3	bn)x−	bn)x−	ADJ
ejpam-5601	59	4	ab(a+	ab(a+	PROPN
ejpam-5601	59	5	b)x2	b)x2	PROPN
ejpam-5601	59	6	−	−	PROPN
ejpam-5601	59	7	2ab(m+	2ab(m+	NUM
ejpam-5601	59	8	n−	n−	PROPN
ejpam-5601	59	9	x	x	NOUN
ejpam-5601	59	10	)	)	PUNCT
ejpam-5601	59	11	·	·	PUNCT
ejpam-5601	59	12	√	√	NUM
ejpam-5601	60	1	g1(x	g1(x	NOUN
ejpam-5601	60	2	)	)	PUNCT
ejpam-5601	60	3	)	)	PUNCT
ejpam-5601	60	4	,	,	PUNCT
ejpam-5601	60	5	and	and	CCONJ
ejpam-5601	60	6	g1(x	g1(x	NOUN
ejpam-5601	60	7	)	)	PUNCT
ejpam-5601	60	8	=	=	SYM
ejpam-5601	60	9	ab(m+	ab(m+	PROPN
ejpam-5601	60	10	n)2	n)2	PROPN
ejpam-5601	60	11	+	+	CCONJ
ejpam-5601	60	12	(	(	PUNCT
ejpam-5601	60	13	a−	a−	PROPN
ejpam-5601	60	14	b)(p−	b)(p−	VERB
ejpam-5601	60	15	q)−	q)−	PROPN
ejpam-5601	60	16	2ab(m+	2ab(m+	NUM
ejpam-5601	60	17	n)x+	n)x+	NUM
ejpam-5601	60	18	abx2	abx2	NOUN
ejpam-5601	60	19	.	.	PUNCT
ejpam-5601	61	1	(	(	PUNCT
ejpam-5601	61	2	2	2	X
ejpam-5601	61	3	)	)	PUNCT
ejpam-5601	61	4	a(−)b	a(−)b	NOUN
ejpam-5601	61	5	is	be	AUX
ejpam-5601	61	6	a	a	DET
ejpam-5601	61	7	fuzzy	fuzzy	ADJ
ejpam-5601	61	8	set	set	NOUN
ejpam-5601	61	9	with	with	ADP
ejpam-5601	61	10	a	a	DET
ejpam-5601	61	11	membership	membership	NOUN
ejpam-5601	61	12	function	function	NOUN
ejpam-5601	61	13	µa(−)b(x	µa(−)b(x	NOUN
ejpam-5601	61	14	)	)	PUNCT
ejpam-5601	61	15	=	=	PUNCT
ejpam-5601	61	16			NOUN
ejpam-5601	61	17	0	0	PUNCT
ejpam-5601	62	1	(	(	PUNCT
ejpam-5601	62	2	x	x	X
ejpam-5601	62	3	<	<	X
ejpam-5601	62	4	x1	x1	PROPN
ejpam-5601	62	5	−	−	PROPN
ejpam-5601	62	6	x4	x4	PROPN
ejpam-5601	62	7	,	,	PUNCT
ejpam-5601	62	8	x2	x2	PROPN
ejpam-5601	62	9	−	−	PUNCT
ejpam-5601	62	10	x3	x3	ADJ
ejpam-5601	62	11	≤	≤	NUM
ejpam-5601	62	12	x	x	SYM
ejpam-5601	62	13	)	)	PUNCT
ejpam-5601	62	14	f3(x	f3(x	NUM
ejpam-5601	62	15	)	)	PUNCT
ejpam-5601	62	16	(	(	PUNCT
ejpam-5601	62	17	x1	x1	PROPN
ejpam-5601	62	18	−	−	PROPN
ejpam-5601	62	19	x4	x4	PROPN
ejpam-5601	62	20	≤	≤	PROPN
ejpam-5601	62	21	x	x	X
ejpam-5601	62	22	<	<	X
ejpam-5601	62	23	m−	m−	PROPN
ejpam-5601	62	24	k2	k2	PROPN
ejpam-5601	62	25	)	)	PUNCT
ejpam-5601	62	26	p	p	NOUN
ejpam-5601	62	27	(	(	PUNCT
ejpam-5601	62	28	m−	m−	PROPN
ejpam-5601	62	29	k2	k2	PROPN
ejpam-5601	62	30	≤	≤	PROPN
ejpam-5601	62	31	x	x	X
ejpam-5601	62	32	<	<	X
ejpam-5601	62	33	m−	m−	PROPN
ejpam-5601	62	34	k1	k1	PROPN
ejpam-5601	62	35	)	)	PUNCT
ejpam-5601	62	36	f4(x	f4(x	NUM
ejpam-5601	62	37	)	)	PUNCT
ejpam-5601	62	38	(	(	PUNCT
ejpam-5601	62	39	m−	m−	PROPN
ejpam-5601	62	40	k1	k1	PROPN
ejpam-5601	62	41	≤	≤	NUM
ejpam-5601	62	42	x	x	PUNCT
ejpam-5601	62	43	<	<	X
ejpam-5601	62	44	x2	x2	X
ejpam-5601	62	45	−	−	NOUN
ejpam-5601	62	46	x3	x3	PROPN
ejpam-5601	62	47	)	)	PUNCT
ejpam-5601	62	48	where	where	SCONJ
ejpam-5601	62	49	f3(x	f3(x	X
ejpam-5601	62	50	)	)	PUNCT
ejpam-5601	62	51	=	=	SYM
ejpam-5601	62	52	1	1	NUM
ejpam-5601	62	53	a2	a2	PROPN
ejpam-5601	62	54	−	−	PROPN
ejpam-5601	62	55	2ab+	2ab+	PROPN
ejpam-5601	62	56	b2	b2	PROPN
ejpam-5601	62	57	(	(	PUNCT
ejpam-5601	62	58	−abm(am+	−abm(am+	NOUN
ejpam-5601	62	59	bm−	bm−	PROPN
ejpam-5601	62	60	an−	an−	X
ejpam-5601	62	61	bn)−	bn)−	NOUN
ejpam-5601	62	62	abn(an+	abn(an+	PROPN
ejpam-5601	62	63	bn	bn	PROPN
ejpam-5601	62	64	−	−	PROPN
ejpam-5601	62	65	am−	am−	NUM
ejpam-5601	62	66	bm)−	bm)−	X
ejpam-5601	62	67	ab(p+	ab(p+	PROPN
ejpam-5601	62	68	q	q	X
ejpam-5601	62	69	)	)	PUNCT
ejpam-5601	62	70	+	+	PUNCT
ejpam-5601	62	71	a2q	a2q	VERB
ejpam-5601	62	72	+	+	CCONJ
ejpam-5601	62	73	b2p+	b2p+	NOUN
ejpam-5601	62	74	2ab(am+	2ab(am+	PROPN
ejpam-5601	62	75	bm−	bm−	PUNCT
ejpam-5601	62	76	an	an	DET
ejpam-5601	62	77	−	−	PROPN
ejpam-5601	62	78	bn)x−	bn)x−	ADJ
ejpam-5601	62	79	ab2x2	ab2x2	PROPN
ejpam-5601	62	80	+	+	CCONJ
ejpam-5601	62	81	2ab(m−	2ab(m−	NUM
ejpam-5601	62	82	n−	n−	PROPN
ejpam-5601	62	83	x	x	NOUN
ejpam-5601	62	84	)	)	PUNCT
ejpam-5601	62	85	·	·	PUNCT
ejpam-5601	62	86	√	√	NUM
ejpam-5601	62	87	g2(x	g2(x	NOUN
ejpam-5601	62	88	)	)	PUNCT
ejpam-5601	62	89	)	)	PUNCT
ejpam-5601	62	90	,	,	PUNCT
ejpam-5601	62	91	y.	y.	PROPN
ejpam-5601	62	92	s.	s.	PROPN
ejpam-5601	62	93	yun	yun	PROPN
ejpam-5601	62	94	,	,	PUNCT
ejpam-5601	62	95	b.	b.	PROPN
ejpam-5601	62	96	lee	lee	PROPN
ejpam-5601	62	97	/	/	SYM
ejpam-5601	62	98	eur	eur	PROPN
ejpam-5601	62	99	.	.	PUNCT
ejpam-5601	63	1	j.	j.	PROPN
ejpam-5601	63	2	pure	pure	PROPN
ejpam-5601	63	3	appl	appl	PROPN
ejpam-5601	63	4	.	.	PROPN
ejpam-5601	63	5	math	math	PROPN
ejpam-5601	63	6	,	,	PUNCT
ejpam-5601	63	7	18	18	NUM
ejpam-5601	63	8	(	(	PUNCT
ejpam-5601	63	9	1	1	NUM
ejpam-5601	63	10	)	)	PUNCT
ejpam-5601	63	11	(	(	PUNCT
ejpam-5601	63	12	2025	2025	NUM
ejpam-5601	63	13	)	)	PUNCT
ejpam-5601	63	14	,	,	PUNCT
ejpam-5601	63	15	5601	5601	NUM
ejpam-5601	63	16	4	4	NUM
ejpam-5601	63	17	of	of	ADP
ejpam-5601	63	18	17	17	NUM
ejpam-5601	63	19	f4(x	f4(x	NUM
ejpam-5601	63	20	)	)	PUNCT
ejpam-5601	63	21	=	=	SYM
ejpam-5601	63	22	1	1	NUM
ejpam-5601	63	23	a2	a2	PROPN
ejpam-5601	63	24	−	−	PROPN
ejpam-5601	63	25	2ab+	2ab+	PROPN
ejpam-5601	63	26	b2	b2	PROPN
ejpam-5601	63	27	(	(	PUNCT
ejpam-5601	63	28	−abm(am+	−abm(am+	NOUN
ejpam-5601	63	29	bm−	bm−	PROPN
ejpam-5601	63	30	an−	an−	X
ejpam-5601	63	31	bn)−	bn)−	NOUN
ejpam-5601	63	32	abn(an+	abn(an+	PROPN
ejpam-5601	63	33	bn	bn	PROPN
ejpam-5601	63	34	−	−	PROPN
ejpam-5601	63	35	am−	am−	NUM
ejpam-5601	63	36	bm)−	bm)−	X
ejpam-5601	63	37	ab(p+	ab(p+	PROPN
ejpam-5601	63	38	q	q	X
ejpam-5601	63	39	)	)	PUNCT
ejpam-5601	64	1	+	+	PUNCT
ejpam-5601	64	2	a2q	a2q	VERB
ejpam-5601	64	3	+	+	CCONJ
ejpam-5601	64	4	b2p+	b2p+	NOUN
ejpam-5601	64	5	2ab(am+	2ab(am+	PROPN
ejpam-5601	64	6	bm−	bm−	PUNCT
ejpam-5601	64	7	an	an	DET
ejpam-5601	64	8	−	−	PROPN
ejpam-5601	64	9	bn)x−	bn)x−	ADJ
ejpam-5601	64	10	ab2x2	ab2x2	PROPN
ejpam-5601	64	11	−	−	PROPN
ejpam-5601	64	12	2ab(m−	2ab(m−	NUM
ejpam-5601	64	13	n−	n−	PROPN
ejpam-5601	64	14	x	x	X
ejpam-5601	64	15	)	)	PUNCT
ejpam-5601	64	16	·	·	PUNCT
ejpam-5601	64	17	√	√	NUM
ejpam-5601	64	18	g2(x	g2(x	NOUN
ejpam-5601	64	19	)	)	PUNCT
ejpam-5601	64	20	)	)	PUNCT
ejpam-5601	64	21	,	,	PUNCT
ejpam-5601	64	22	and	and	CCONJ
ejpam-5601	64	23	g2(x	g2(x	PROPN
ejpam-5601	64	24	)	)	PUNCT
ejpam-5601	64	25	=	=	SYM
ejpam-5601	65	1	ab(m−	ab(m−	PROPN
ejpam-5601	65	2	n)2	n)2	PROPN
ejpam-5601	65	3	+	+	CCONJ
ejpam-5601	65	4	(	(	PUNCT
ejpam-5601	65	5	a−	a−	PROPN
ejpam-5601	65	6	b)(p−	b)(p−	VERB
ejpam-5601	65	7	q)−	q)−	PROPN
ejpam-5601	65	8	2ab(m−	2ab(m−	NUM
ejpam-5601	65	9	n)x+	n)x+	NUM
ejpam-5601	65	10	abx2	abx2	NOUN
ejpam-5601	65	11	.	.	PUNCT
ejpam-5601	66	1	(	(	PUNCT
ejpam-5601	66	2	3	3	X
ejpam-5601	66	3	)	)	PUNCT
ejpam-5601	66	4	if	if	SCONJ
ejpam-5601	66	5	p	p	NOUN
ejpam-5601	66	6	=	=	NOUN
ejpam-5601	66	7	q	q	NOUN
ejpam-5601	66	8	,	,	PUNCT
ejpam-5601	66	9	a(·)b	a(·)b	PROPN
ejpam-5601	66	10	is	be	AUX
ejpam-5601	66	11	a	a	DET
ejpam-5601	66	12	fuzzy	fuzzy	ADJ
ejpam-5601	66	13	set	set	NOUN
ejpam-5601	66	14	with	with	ADP
ejpam-5601	66	15	a	a	DET
ejpam-5601	66	16	membership	membership	NOUN
ejpam-5601	66	17	function	function	NOUN
ejpam-5601	66	18	µa(·)b(x	µa(·)b(x	PROPN
ejpam-5601	66	19	)	)	PUNCT
ejpam-5601	67	1	=	=	PRON
ejpam-5601	67	2	{	{	PUNCT
ejpam-5601	67	3	0	0	PUNCT
ejpam-5601	67	4	(	(	PUNCT
ejpam-5601	67	5	x	x	X
ejpam-5601	67	6	<	<	X
ejpam-5601	67	7	x1x3	x1x3	X
ejpam-5601	67	8	,	,	PUNCT
ejpam-5601	67	9	x2x4	x2x4	X
ejpam-5601	67	10	≤	≤	NUM
ejpam-5601	67	11	x	x	X
ejpam-5601	67	12	)	)	PUNCT
ejpam-5601	67	13	f5(x	f5(x	NOUN
ejpam-5601	67	14	)	)	PUNCT
ejpam-5601	67	15	(	(	PUNCT
ejpam-5601	67	16	x1x3	x1x3	X
ejpam-5601	67	17	≤	≤	NUM
ejpam-5601	67	18	x	x	PUNCT
ejpam-5601	67	19	<	<	X
ejpam-5601	67	20	x2x4	x2x4	X
ejpam-5601	67	21	)	)	PUNCT
ejpam-5601	67	22	where	where	SCONJ
ejpam-5601	67	23	f5(x	f5(x	NOUN
ejpam-5601	67	24	)	)	PUNCT
ejpam-5601	67	25	=	=	SYM
ejpam-5601	67	26	1	1	NUM
ejpam-5601	67	27	2	2	NUM
ejpam-5601	67	28	(	(	PUNCT
ejpam-5601	67	29	−am2	−am2	INTJ
ejpam-5601	67	30	−	−	NUM
ejpam-5601	67	31	bn2	bn2	NOUN
ejpam-5601	68	1	+	+	CCONJ
ejpam-5601	69	1	2p)−	2p)−	NUM
ejpam-5601	69	2	√	√	NUM
ejpam-5601	69	3	abx+	abx+	NOUN
ejpam-5601	69	4	1	1	NUM
ejpam-5601	69	5	2	2	NUM
ejpam-5601	69	6	√	√	NUM
ejpam-5601	69	7	g3(x	g3(x	NOUN
ejpam-5601	69	8	)	)	PUNCT
ejpam-5601	69	9	,	,	PUNCT
ejpam-5601	69	10	g3(x	g3(x	X
ejpam-5601	69	11	)	)	PUNCT
ejpam-5601	69	12	=	=	NOUN
ejpam-5601	69	13	−	−	NOUN
ejpam-5601	69	14	am2(am2	am2(am2	NOUN
ejpam-5601	69	15	+	+	CCONJ
ejpam-5601	69	16	3bn2)−	3bn2)−	NUM
ejpam-5601	69	17	bn2(bn2	bn2(bn2	NOUN
ejpam-5601	69	18	+	+	CCONJ
ejpam-5601	69	19	3am2	3am2	NUM
ejpam-5601	69	20	)	)	PUNCT
ejpam-5601	69	21	+	+	CCONJ
ejpam-5601	69	22	2(am2	2(am2	PROPN
ejpam-5601	70	1	+	+	NUM
ejpam-5601	70	2	bn2	bn2	NOUN
ejpam-5601	70	3	−	−	ADP
ejpam-5601	70	4	2p)2	2p)2	NUM
ejpam-5601	70	5	+	+	SYM
ejpam-5601	70	6	8p(am2	8p(am2	NOUN
ejpam-5601	70	7	+	+	CCONJ
ejpam-5601	70	8	bn2	bn2	NOUN
ejpam-5601	70	9	−	−	NOUN
ejpam-5601	70	10	p	p	X
ejpam-5601	70	11	)	)	PUNCT
ejpam-5601	71	1	+	+	CCONJ
ejpam-5601	71	2	8abmnx−	8abmnx−	NUM
ejpam-5601	71	3	1	1	NUM
ejpam-5601	71	4	8	8	NUM
ejpam-5601	71	5	√	√	NUM
ejpam-5601	71	6	abx	abx	NOUN
ejpam-5601	71	7	{	{	PUNCT
ejpam-5601	71	8	−8(am2	−8(am2	NOUN
ejpam-5601	71	9	+	+	X
ejpam-5601	71	10	bn2	bn2	NOUN
ejpam-5601	71	11	−	−	ADP
ejpam-5601	71	12	2p)3	2p)3	NUM
ejpam-5601	72	1	+	+	CCONJ
ejpam-5601	72	2	8(am2	8(am2	X
ejpam-5601	72	3	+	+	NUM
ejpam-5601	72	4	bn2	bn2	ADJ
ejpam-5601	72	5	−	−	PROPN
ejpam-5601	72	6	2p)h1(x)−	2p)h1(x)−	PROPN
ejpam-5601	72	7	16h2(x	16h2(x	NUM
ejpam-5601	72	8	)	)	PUNCT
ejpam-5601	72	9	}	}	PUNCT
ejpam-5601	72	10	,	,	PUNCT
ejpam-5601	72	11	h1(x	h1(x	X
ejpam-5601	72	12	)	)	PUNCT
ejpam-5601	72	13	=	=	NOUN
ejpam-5601	72	14	am2(am2	am2(am2	NOUN
ejpam-5601	72	15	+	+	CCONJ
ejpam-5601	72	16	2bn2	2bn2	NUM
ejpam-5601	72	17	)	)	PUNCT
ejpam-5601	72	18	+	+	CCONJ
ejpam-5601	72	19	bn2(bn2	bn2(bn2	NOUN
ejpam-5601	72	20	+	+	CCONJ
ejpam-5601	72	21	2am2)−	2am2)−	NUM
ejpam-5601	72	22	6p(am2	6p(am2	NUM
ejpam-5601	72	23	+	+	NUM
ejpam-5601	72	24	bn2	bn2	ADJ
ejpam-5601	72	25	−	−	ADP
ejpam-5601	72	26	p)−	p)−	NOUN
ejpam-5601	72	27	4abmnx−	4abmnx−	NUM
ejpam-5601	72	28	2abx2	2abx2	NUM
ejpam-5601	72	29	,	,	PUNCT
ejpam-5601	72	30	h2(x	h2(x	X
ejpam-5601	72	31	)	)	PUNCT
ejpam-5601	73	1	=	=	NOUN
ejpam-5601	73	2	abm2n2(am2	abm2n2(am2	NOUN
ejpam-5601	73	3	+	+	X
ejpam-5601	73	4	bn2	bn2	NOUN
ejpam-5601	73	5	−	−	NOUN
ejpam-5601	73	6	4p)−	4p)−	NUM
ejpam-5601	74	1	am2p(am2	am2p(am2	PRON
ejpam-5601	74	2	−	−	PROPN
ejpam-5601	74	3	3p)−	3p)−	NUM
ejpam-5601	74	4	bn2p(bn2	bn2p(bn2	PUNCT
ejpam-5601	75	1	−	−	NOUN
ejpam-5601	75	2	3p	3p	NUM
ejpam-5601	75	3	)	)	PUNCT
ejpam-5601	76	1	−	−	PROPN
ejpam-5601	76	2	2p3	2p3	NUM
ejpam-5601	77	1	−	−	NOUN
ejpam-5601	77	2	2abmn(am2	2abmn(am2	NUM
ejpam-5601	77	3	+	+	CCONJ
ejpam-5601	77	4	bn2	bn2	ADJ
ejpam-5601	77	5	−	−	NOUN
ejpam-5601	77	6	2p)x+	2p)x+	NUM
ejpam-5601	77	7	ab(am2	ab(am2	NOUN
ejpam-5601	77	8	+	+	NUM
ejpam-5601	77	9	bn2	bn2	ADJ
ejpam-5601	77	10	+	+	CCONJ
ejpam-5601	77	11	2p)x2	2p)x2	NUM
ejpam-5601	77	12	.	.	PUNCT
ejpam-5601	78	1	(	(	PUNCT
ejpam-5601	78	2	4	4	X
ejpam-5601	78	3	)	)	PUNCT
ejpam-5601	78	4	a(/)b	a(/)b	NOUN
ejpam-5601	78	5	is	be	AUX
ejpam-5601	78	6	a	a	DET
ejpam-5601	78	7	fuzzy	fuzzy	ADJ
ejpam-5601	78	8	set	set	NOUN
ejpam-5601	78	9	with	with	ADP
ejpam-5601	78	10	a	a	DET
ejpam-5601	78	11	membership	membership	NOUN
ejpam-5601	78	12	function	function	NOUN
ejpam-5601	78	13	µa(/)b(x	µa(/)b(x	PROPN
ejpam-5601	78	14	)	)	PUNCT
ejpam-5601	79	1	=	=	PUNCT
ejpam-5601	79	2			NOUN
ejpam-5601	79	3	0	0	PUNCT
ejpam-5601	80	1	(	(	PUNCT
ejpam-5601	80	2	x	x	PUNCT
ejpam-5601	80	3	<	<	X
ejpam-5601	80	4	x1	x1	PROPN
ejpam-5601	80	5	/	/	SYM
ejpam-5601	80	6	x4	x4	PROPN
ejpam-5601	80	7	,	,	PUNCT
ejpam-5601	80	8	x2	x2	PROPN
ejpam-5601	80	9	/	/	SYM
ejpam-5601	80	10	x3	x3	ADJ
ejpam-5601	80	11	≤	≤	NUM
ejpam-5601	80	12	x	x	SYM
ejpam-5601	80	13	)	)	PUNCT
ejpam-5601	80	14	f6(x	f6(x	PROPN
ejpam-5601	80	15	)	)	PUNCT
ejpam-5601	80	16	(	(	PUNCT
ejpam-5601	80	17	x1	x1	PROPN
ejpam-5601	80	18	/	/	SYM
ejpam-5601	80	19	x4	x4	PROPN
ejpam-5601	80	20	≤	≤	PROPN
ejpam-5601	80	21	x	x	PUNCT
ejpam-5601	80	22	<	<	X
ejpam-5601	80	23	m	m	PROPN
ejpam-5601	80	24	/	/	SYM
ejpam-5601	80	25	k2	k2	ADJ
ejpam-5601	80	26	)	)	PUNCT
ejpam-5601	80	27	p	p	NOUN
ejpam-5601	80	28	(	(	PUNCT
ejpam-5601	80	29	m	m	PROPN
ejpam-5601	80	30	/	/	SYM
ejpam-5601	80	31	k2	k2	ADJ
ejpam-5601	80	32	≤	≤	NUM
ejpam-5601	80	33	x	x	PUNCT
ejpam-5601	80	34	<	<	X
ejpam-5601	80	35	m	m	PROPN
ejpam-5601	80	36	/	/	SYM
ejpam-5601	80	37	k1	k1	NOUN
ejpam-5601	80	38	)	)	PUNCT
ejpam-5601	80	39	f7(x	f7(x	NOUN
ejpam-5601	80	40	)	)	PUNCT
ejpam-5601	80	41	(	(	PUNCT
ejpam-5601	80	42	m	m	NOUN
ejpam-5601	80	43	/	/	SYM
ejpam-5601	80	44	k1	k1	X
ejpam-5601	80	45	≤	≤	NUM
ejpam-5601	80	46	x	x	PUNCT
ejpam-5601	80	47	<	<	X
ejpam-5601	80	48	x2	x2	PROPN
ejpam-5601	80	49	/	/	SYM
ejpam-5601	80	50	x3	x3	PROPN
ejpam-5601	80	51	)	)	PUNCT
ejpam-5601	80	52	where	where	SCONJ
ejpam-5601	80	53	f6(x	f6(x	PROPN
ejpam-5601	80	54	)	)	PUNCT
ejpam-5601	80	55	=	=	SYM
ejpam-5601	80	56	1	1	NUM
ejpam-5601	80	57	b2	b2	NOUN
ejpam-5601	80	58	−	−	PROPN
ejpam-5601	80	59	2abx2	2abx2	NUM
ejpam-5601	81	1	+	+	CCONJ
ejpam-5601	81	2	a2x4	a2x4	X
ejpam-5601	81	3	(	(	PUNCT
ejpam-5601	81	4	−b2(am2	−b2(am2	PROPN
ejpam-5601	81	5	+	+	X
ejpam-5601	81	6	p	p	X
ejpam-5601	81	7	)	)	PUNCT
ejpam-5601	81	8	+	+	CCONJ
ejpam-5601	81	9	2ab2mnx−	2ab2mnx−	NUM
ejpam-5601	81	10	ab(am2	ab(am2	PART
ejpam-5601	82	1	+	+	NUM
ejpam-5601	82	2	bn2	bn2	ADJ
ejpam-5601	82	3	+	+	CCONJ
ejpam-5601	82	4	p	p	X
ejpam-5601	82	5	+	+	PROPN
ejpam-5601	82	6	q)x2	q)x2	NOUN
ejpam-5601	82	7	+	+	CCONJ
ejpam-5601	82	8	2a2bmnx3	2a2bmnx3	NUM
ejpam-5601	82	9	−	−	NOUN
ejpam-5601	82	10	a2(bn2	a2(bn2	NOUN
ejpam-5601	82	11	−	−	X
ejpam-5601	82	12	q)x4	q)x4	NOUN
ejpam-5601	82	13	+	+	NOUN
ejpam-5601	82	14	2abx(m−	2abx(m−	NUM
ejpam-5601	82	15	nx	nx	NOUN
ejpam-5601	82	16	)	)	PUNCT
ejpam-5601	82	17	·	·	PUNCT
ejpam-5601	82	18	√	√	NUM
ejpam-5601	82	19	g4(x	g4(x	NOUN
ejpam-5601	82	20	)	)	PUNCT
ejpam-5601	82	21	)	)	PUNCT
ejpam-5601	82	22	,	,	PUNCT
ejpam-5601	82	23	f7(x	f7(x	ADJ
ejpam-5601	82	24	)	)	PUNCT
ejpam-5601	82	25	=	=	SYM
ejpam-5601	82	26	1	1	NUM
ejpam-5601	82	27	b2	b2	NOUN
ejpam-5601	82	28	−	−	PROPN
ejpam-5601	82	29	2abx2	2abx2	NUM
ejpam-5601	82	30	+	+	CCONJ
ejpam-5601	82	31	a2x4	a2x4	X
ejpam-5601	82	32	(	(	PUNCT
ejpam-5601	82	33	−b2(am2	−b2(am2	PROPN
ejpam-5601	82	34	+	+	X
ejpam-5601	82	35	p	p	X
ejpam-5601	82	36	)	)	PUNCT
ejpam-5601	83	1	+	+	CCONJ
ejpam-5601	83	2	2ab2mnx−	2ab2mnx−	NUM
ejpam-5601	83	3	ab(am2	ab(am2	PART
ejpam-5601	84	1	+	+	NUM
ejpam-5601	84	2	bn2	bn2	ADJ
ejpam-5601	84	3	+	+	CCONJ
ejpam-5601	84	4	p	p	X
ejpam-5601	84	5	+	+	PROPN
ejpam-5601	84	6	q)x2	q)x2	NOUN
ejpam-5601	84	7	+	+	CCONJ
ejpam-5601	84	8	2a2bmnx3	2a2bmnx3	NUM
ejpam-5601	84	9	−	−	NOUN
ejpam-5601	84	10	a2(bn2	a2(bn2	NOUN
ejpam-5601	84	11	−	−	X
ejpam-5601	84	12	q)x4	q)x4	NOUN
ejpam-5601	84	13	−	−	PROPN
ejpam-5601	84	14	2abx(m−	2abx(m−	NUM
ejpam-5601	84	15	nx	nx	NOUN
ejpam-5601	84	16	)	)	PUNCT
ejpam-5601	84	17	·	·	PUNCT
ejpam-5601	84	18	√	√	NUM
ejpam-5601	84	19	g4(x	g4(x	NOUN
ejpam-5601	84	20	)	)	PUNCT
ejpam-5601	84	21	)	)	PUNCT
ejpam-5601	84	22	,	,	PUNCT
ejpam-5601	84	23	and	and	CCONJ
ejpam-5601	84	24	g4(x	g4(x	NOUN
ejpam-5601	84	25	)	)	PUNCT
ejpam-5601	84	26	=	=	SYM
ejpam-5601	85	1	b(am2	b(am2	ADP
ejpam-5601	85	2	−	−	PROPN
ejpam-5601	85	3	p+	p+	VERB
ejpam-5601	85	4	q)−	q)−	PROPN
ejpam-5601	85	5	2abmnx+	2abmnx+	NUM
ejpam-5601	85	6	a(bn2	a(bn2	NOUN
ejpam-5601	85	7	+	+	CCONJ
ejpam-5601	85	8	p−	p−	PROPN
ejpam-5601	85	9	q)x2	q)x2	NOUN
ejpam-5601	85	10	.	.	PUNCT
ejpam-5601	86	1	y.	y.	PROPN
ejpam-5601	86	2	s.	s.	PROPN
ejpam-5601	86	3	yun	yun	PROPN
ejpam-5601	86	4	,	,	PUNCT
ejpam-5601	86	5	b.	b.	PROPN
ejpam-5601	86	6	lee	lee	PROPN
ejpam-5601	86	7	/	/	SYM
ejpam-5601	86	8	eur	eur	PROPN
ejpam-5601	86	9	.	.	PUNCT
ejpam-5601	87	1	j.	j.	PROPN
ejpam-5601	87	2	pure	pure	PROPN
ejpam-5601	87	3	appl	appl	PROPN
ejpam-5601	87	4	.	.	PROPN
ejpam-5601	87	5	math	math	PROPN
ejpam-5601	87	6	,	,	PUNCT
ejpam-5601	87	7	18	18	NUM
ejpam-5601	87	8	(	(	PUNCT
ejpam-5601	87	9	1	1	NUM
ejpam-5601	87	10	)	)	PUNCT
ejpam-5601	87	11	(	(	PUNCT
ejpam-5601	87	12	2025	2025	NUM
ejpam-5601	87	13	)	)	PUNCT
ejpam-5601	87	14	,	,	PUNCT
ejpam-5601	87	15	5601	5601	NUM
ejpam-5601	87	16	5	5	NUM
ejpam-5601	87	17	of	of	ADP
ejpam-5601	87	18	17	17	NUM
ejpam-5601	87	19	3	3	NUM
ejpam-5601	87	20	.	.	PUNCT
ejpam-5601	87	21	max	max	PROPN
ejpam-5601	87	22	-	-	PUNCT
ejpam-5601	87	23	min	min	PROPN
ejpam-5601	87	24	composition	composition	NOUN
ejpam-5601	87	25	operations	operation	NOUN
ejpam-5601	87	26	of	of	ADP
ejpam-5601	87	27	zadeh	zadeh	PROPN
ejpam-5601	87	28	for	for	ADP
ejpam-5601	87	29	quadratic	quadratic	ADJ
ejpam-5601	87	30	fuzzy	fuzzy	ADJ
ejpam-5601	87	31	numbers	number	NOUN
ejpam-5601	87	32	defined	define	VERB
ejpam-5601	87	33	on	on	ADP
ejpam-5601	87	34	r2	r2	NOUN
ejpam-5601	87	35	we	we	PRON
ejpam-5601	87	36	extended	extend	VERB
ejpam-5601	87	37	the	the	DET
ejpam-5601	87	38	concept	concept	NOUN
ejpam-5601	87	39	of	of	ADP
ejpam-5601	87	40	quadratic	quadratic	ADJ
ejpam-5601	87	41	fuzzy	fuzzy	ADJ
ejpam-5601	87	42	numbers	number	NOUN
ejpam-5601	87	43	from	from	ADP
ejpam-5601	87	44	r	r	NOUN
ejpam-5601	87	45	to	to	ADP
ejpam-5601	87	46	r2	r2	PROPN
ejpam-5601	87	47	,	,	PUNCT
ejpam-5601	87	48	introducing	introduce	VERB
ejpam-5601	87	49	2dimensional	2dimensional	NUM
ejpam-5601	87	50	quadratic	quadratic	ADJ
ejpam-5601	87	51	fuzzy	fuzzy	ADJ
ejpam-5601	87	52	numbers	number	NOUN
ejpam-5601	87	53	.	.	PUNCT
ejpam-5601	88	1	additionally	additionally	ADV
ejpam-5601	88	2	,	,	PUNCT
ejpam-5601	88	3	we	we	PRON
ejpam-5601	88	4	formulated	formulate	VERB
ejpam-5601	88	5	parametric	parametric	ADJ
ejpam-5601	88	6	operations	operation	NOUN
ejpam-5601	88	7	for	for	ADP
ejpam-5601	88	8	two	two	NUM
ejpam-5601	88	9	such	such	ADJ
ejpam-5601	88	10	2	2	NUM
ejpam-5601	88	11	-	-	PUNCT
ejpam-5601	88	12	dimensional	dimensional	ADJ
ejpam-5601	88	13	quadratic	quadratic	ADJ
ejpam-5601	88	14	fuzzy	fuzzy	ADJ
ejpam-5601	88	15	numbers	number	NOUN
ejpam-5601	88	16	by	by	ADP
ejpam-5601	88	17	employing	employ	VERB
ejpam-5601	88	18	region	region	NOUN
ejpam-5601	88	19	-	-	PUNCT
ejpam-5601	88	20	valued	value	VERB
ejpam-5601	88	21	α	α	NOUN
ejpam-5601	88	22	-	-	PUNCT
ejpam-5601	88	23	cuts	cut	NOUN
ejpam-5601	88	24	in	in	ADP
ejpam-5601	88	25	r2	r2	PROPN
ejpam-5601	88	26	.	.	PUNCT
ejpam-5601	89	1	definition	definition	NOUN
ejpam-5601	89	2	3	3	NUM
ejpam-5601	89	3	.	.	PUNCT
ejpam-5601	90	1	[	[	X
ejpam-5601	90	2	2	2	X
ejpam-5601	90	3	]	]	PUNCT
ejpam-5601	90	4	a	a	DET
ejpam-5601	90	5	fuzzy	fuzzy	ADJ
ejpam-5601	90	6	set	set	VERB
ejpam-5601	90	7	a	a	PRON
ejpam-5601	90	8	with	with	ADP
ejpam-5601	90	9	a	a	DET
ejpam-5601	90	10	membership	membership	NOUN
ejpam-5601	90	11	function	function	NOUN
ejpam-5601	90	12	µa(x	µa(x	PROPN
ejpam-5601	90	13	,	,	PUNCT
ejpam-5601	90	14	y	y	NOUN
ejpam-5601	90	15	)	)	PUNCT
ejpam-5601	90	16	=	=	PRON
ejpam-5601	90	17	{	{	PUNCT
ejpam-5601	90	18	1−	1−	NUM
ejpam-5601	90	19	(	(	PUNCT
ejpam-5601	90	20	(	(	PUNCT
ejpam-5601	90	21	x−x1)2	x−x1)2	PROPN
ejpam-5601	90	22	a2	a2	PROPN
ejpam-5601	90	23	+	+	CCONJ
ejpam-5601	90	24	(	(	PUNCT
ejpam-5601	90	25	y−y1)2	y−y1)2	VERB
ejpam-5601	90	26	b2	b2	PROPN
ejpam-5601	90	27	)	)	PUNCT
ejpam-5601	90	28	,	,	PUNCT
ejpam-5601	90	29	b2(x−	b2(x−	VERB
ejpam-5601	90	30	x1	x1	NUM
ejpam-5601	90	31	)	)	PUNCT
ejpam-5601	90	32	2	2	NUM
ejpam-5601	91	1	+	+	CCONJ
ejpam-5601	91	2	a2(y	a2(y	CCONJ
ejpam-5601	91	3	−	−	PROPN
ejpam-5601	91	4	y1	y1	NOUN
ejpam-5601	91	5	)	)	PUNCT
ejpam-5601	91	6	2	2	NUM
ejpam-5601	91	7	≤	≤	NOUN
ejpam-5601	91	8	a2b2	a2b2	PUNCT
ejpam-5601	91	9	,	,	PUNCT
ejpam-5601	91	10	0	0	NUM
ejpam-5601	91	11	,	,	PUNCT
ejpam-5601	91	12	otherwise	otherwise	ADV
ejpam-5601	91	13	,	,	PUNCT
ejpam-5601	91	14	where	where	SCONJ
ejpam-5601	91	15	a	a	DET
ejpam-5601	91	16	,	,	PUNCT
ejpam-5601	91	17	b	b	X
ejpam-5601	91	18	>	>	X
ejpam-5601	91	19	0	0	NUM
ejpam-5601	91	20	is	be	AUX
ejpam-5601	91	21	reffered	reffere	VERB
ejpam-5601	91	22	to	to	ADP
ejpam-5601	91	23	as	as	ADP
ejpam-5601	91	24	a	a	DET
ejpam-5601	91	25	2	2	NUM
ejpam-5601	91	26	-	-	PUNCT
ejpam-5601	91	27	dimensional	dimensional	ADJ
ejpam-5601	91	28	quadratic	quadratic	ADJ
ejpam-5601	91	29	fuzzy	fuzzy	ADJ
ejpam-5601	91	30	number	number	NOUN
ejpam-5601	91	31	,	,	PUNCT
ejpam-5601	91	32	denoted	denote	VERB
ejpam-5601	91	33	by	by	ADP
ejpam-5601	91	34	[	[	X
ejpam-5601	91	35	a	a	X
ejpam-5601	91	36	,	,	PUNCT
ejpam-5601	91	37	x1	x1	PROPN
ejpam-5601	91	38	,	,	PUNCT
ejpam-5601	91	39	b	b	PROPN
ejpam-5601	91	40	,	,	PUNCT
ejpam-5601	91	41	y1	y1	X
ejpam-5601	91	42	]	]	PUNCT
ejpam-5601	91	43	2	2	NUM
ejpam-5601	91	44	.	.	PUNCT
ejpam-5601	92	1	the	the	DET
ejpam-5601	92	2	α	α	NOUN
ejpam-5601	92	3	-	-	PUNCT
ejpam-5601	92	4	cut	cut	VERB
ejpam-5601	92	5	aα	aα	NOUN
ejpam-5601	92	6	of	of	ADP
ejpam-5601	92	7	a	a	DET
ejpam-5601	92	8	2	2	NUM
ejpam-5601	92	9	-	-	PUNCT
ejpam-5601	92	10	dimensional	dimensional	ADJ
ejpam-5601	92	11	quadratic	quadratic	ADJ
ejpam-5601	92	12	fuzzy	fuzzy	ADJ
ejpam-5601	92	13	number	number	NOUN
ejpam-5601	92	14	a	a	NOUN
ejpam-5601	93	1	=	=	PUNCT
ejpam-5601	94	1	[	[	X
ejpam-5601	94	2	a	a	X
ejpam-5601	94	3	,	,	PUNCT
ejpam-5601	94	4	x1	x1	PROPN
ejpam-5601	94	5	,	,	PUNCT
ejpam-5601	94	6	b	b	PROPN
ejpam-5601	94	7	,	,	PUNCT
ejpam-5601	94	8	y1	y1	X
ejpam-5601	94	9	]	]	PUNCT
ejpam-5601	94	10	2	2	NUM
ejpam-5601	94	11	is	be	AUX
ejpam-5601	94	12	the	the	DET
ejpam-5601	94	13	interior	interior	NOUN
ejpam-5601	94	14	of	of	ADP
ejpam-5601	94	15	an	an	DET
ejpam-5601	94	16	ellipse	ellipse	NOUN
ejpam-5601	94	17	in	in	ADP
ejpam-5601	94	18	an	an	DET
ejpam-5601	94	19	xy	xy	NOUN
ejpam-5601	94	20	-	-	PUNCT
ejpam-5601	94	21	plane	plane	NOUN
ejpam-5601	94	22	,	,	PUNCT
ejpam-5601	94	23	including	include	VERB
ejpam-5601	94	24	the	the	DET
ejpam-5601	94	25	boundary	boundary	ADJ
ejpam-5601	94	26	aα	aα	NOUN
ejpam-5601	94	27	=	=	PRON
ejpam-5601	94	28	{	{	PUNCT
ejpam-5601	94	29	(	(	PUNCT
ejpam-5601	94	30	x	x	NOUN
ejpam-5601	94	31	,	,	PUNCT
ejpam-5601	94	32	y	y	NOUN
ejpam-5601	94	33	)	)	PUNCT
ejpam-5601	94	34	∈	∈	PROPN
ejpam-5601	94	35	r2	r2	PROPN
ejpam-5601	94	36	∣∣∣	∣∣∣	PROPN
ejpam-5601	94	37	b2(x−	b2(x−	X
ejpam-5601	94	38	x1	x1	PROPN
ejpam-5601	94	39	)	)	PUNCT
ejpam-5601	94	40	2	2	NUM
ejpam-5601	95	1	+	+	CCONJ
ejpam-5601	95	2	a2(y	a2(y	CCONJ
ejpam-5601	95	3	−	−	PROPN
ejpam-5601	95	4	y1	y1	NOUN
ejpam-5601	95	5	)	)	PUNCT
ejpam-5601	95	6	2	2	NUM
ejpam-5601	95	7	≤	≤	NOUN
ejpam-5601	96	1	a2b2(1−	a2b2(1−	PROPN
ejpam-5601	96	2	α	α	X
ejpam-5601	96	3	)	)	PUNCT
ejpam-5601	96	4	}	}	PUNCT
ejpam-5601	96	5	=	=	SYM
ejpam-5601	96	6	{	{	PUNCT
ejpam-5601	96	7	(	(	PUNCT
ejpam-5601	96	8	x	x	NOUN
ejpam-5601	96	9	,	,	PUNCT
ejpam-5601	96	10	y	y	NOUN
ejpam-5601	96	11	)	)	PUNCT
ejpam-5601	96	12	∈	∈	PROPN
ejpam-5601	96	13	r2	r2	NOUN
ejpam-5601	96	14	∣∣∣	∣∣∣	NOUN
ejpam-5601	96	15	(	(	PUNCT
ejpam-5601	96	16	x−	x−	PROPN
ejpam-5601	96	17	x1	x1	PROPN
ejpam-5601	96	18	)	)	PUNCT
ejpam-5601	96	19	2	2	NUM
ejpam-5601	96	20	a2(1−	a2(1−	NOUN
ejpam-5601	96	21	α	α	NOUN
ejpam-5601	96	22	)	)	PUNCT
ejpam-5601	96	23	+	+	CCONJ
ejpam-5601	96	24	(	(	PUNCT
ejpam-5601	96	25	y	y	PROPN
ejpam-5601	96	26	−	−	PROPN
ejpam-5601	96	27	y1	y1	PROPN
ejpam-5601	96	28	)	)	PUNCT
ejpam-5601	96	29	2	2	NUM
ejpam-5601	96	30	b2(1−	b2(1−	NOUN
ejpam-5601	96	31	α	α	NOUN
ejpam-5601	96	32	)	)	PUNCT
ejpam-5601	96	33	≤	≤	NOUN
ejpam-5601	96	34	1	1	NUM
ejpam-5601	96	35	}	}	PUNCT
ejpam-5601	96	36	.	.	PUNCT
ejpam-5601	97	1	theorem	theorem	NOUN
ejpam-5601	97	2	2	2	NUM
ejpam-5601	97	3	.	.	PUNCT
ejpam-5601	98	1	[	[	X
ejpam-5601	98	2	3	3	X
ejpam-5601	98	3	]	]	PUNCT
ejpam-5601	98	4	let	let	VERB
ejpam-5601	98	5	a	a	PRON
ejpam-5601	98	6	be	be	AUX
ejpam-5601	98	7	a	a	DET
ejpam-5601	98	8	continuous	continuous	ADJ
ejpam-5601	98	9	convex	convex	NOUN
ejpam-5601	98	10	fuzzy	fuzzy	ADJ
ejpam-5601	98	11	number	number	NOUN
ejpam-5601	98	12	defined	define	VERB
ejpam-5601	98	13	on	on	ADP
ejpam-5601	98	14	r2	r2	PROPN
ejpam-5601	98	15	and	and	CCONJ
ejpam-5601	98	16	aα	aα	NOUN
ejpam-5601	98	17	=	=	SYM
ejpam-5601	98	18	{	{	PUNCT
ejpam-5601	98	19	(	(	PUNCT
ejpam-5601	98	20	x	x	NOUN
ejpam-5601	98	21	,	,	PUNCT
ejpam-5601	98	22	y	y	NOUN
ejpam-5601	98	23	)	)	PUNCT
ejpam-5601	98	24	∈	∈	NOUN
ejpam-5601	98	25	r2|µa(x	r2|µa(x	NOUN
ejpam-5601	98	26	,	,	PUNCT
ejpam-5601	98	27	y	y	NOUN
ejpam-5601	98	28	)	)	PUNCT
ejpam-5601	98	29	=	=	SYM
ejpam-5601	99	1	α	α	X
ejpam-5601	99	2	}	}	PUNCT
ejpam-5601	99	3	be	be	VERB
ejpam-5601	99	4	the	the	DET
ejpam-5601	99	5	α	α	NOUN
ejpam-5601	99	6	-	-	PUNCT
ejpam-5601	99	7	set	set	NOUN
ejpam-5601	99	8	of	of	ADP
ejpam-5601	99	9	a.	a.	NOUN
ejpam-5601	99	10	then	then	ADV
ejpam-5601	99	11	for	for	ADP
ejpam-5601	99	12	all	all	DET
ejpam-5601	99	13	α	α	DET
ejpam-5601	99	14	∈	∈	NOUN
ejpam-5601	99	15	(	(	PUNCT
ejpam-5601	99	16	0	0	NUM
ejpam-5601	99	17	,	,	PUNCT
ejpam-5601	99	18	1	1	NUM
ejpam-5601	99	19	)	)	PUNCT
ejpam-5601	99	20	,	,	PUNCT
ejpam-5601	99	21	there	there	PRON
ejpam-5601	99	22	exist	exist	VERB
ejpam-5601	99	23	continuous	continuous	ADJ
ejpam-5601	99	24	functions	function	NOUN
ejpam-5601	99	25	fα	fα	ADP
ejpam-5601	99	26	1	1	NUM
ejpam-5601	99	27	(	(	PUNCT
ejpam-5601	99	28	t	t	NOUN
ejpam-5601	99	29	)	)	PUNCT
ejpam-5601	99	30	and	and	CCONJ
ejpam-5601	99	31	fα	fα	ADP
ejpam-5601	99	32	2	2	NUM
ejpam-5601	99	33	(	(	PUNCT
ejpam-5601	99	34	t	t	NOUN
ejpam-5601	99	35	)	)	PUNCT
ejpam-5601	99	36	defined	define	VERB
ejpam-5601	99	37	on	on	ADP
ejpam-5601	99	38	[	[	X
ejpam-5601	99	39	0	0	NUM
ejpam-5601	99	40	,	,	PUNCT
ejpam-5601	99	41	2π	2π	NOUN
ejpam-5601	99	42	]	]	PUNCT
ejpam-5601	99	43	such	such	ADJ
ejpam-5601	99	44	that	that	DET
ejpam-5601	99	45	aα	aα	NOUN
ejpam-5601	99	46	=	=	PRON
ejpam-5601	99	47	{	{	PUNCT
ejpam-5601	99	48	(	(	PUNCT
ejpam-5601	99	49	fα	fα	ADP
ejpam-5601	99	50	1	1	NUM
ejpam-5601	99	51	(	(	PUNCT
ejpam-5601	99	52	t	t	PROPN
ejpam-5601	99	53	)	)	PUNCT
ejpam-5601	99	54	,	,	PUNCT
ejpam-5601	100	1	f	f	PROPN
ejpam-5601	100	2	α	α	PROPN
ejpam-5601	100	3	2	2	NUM
ejpam-5601	100	4	(	(	PUNCT
ejpam-5601	100	5	t	t	NOUN
ejpam-5601	100	6	)	)	PUNCT
ejpam-5601	100	7	)	)	PUNCT
ejpam-5601	101	1	∈	∈	PROPN
ejpam-5601	101	2	r2|0	r2|0	NOUN
ejpam-5601	101	3	≤	≤	NOUN
ejpam-5601	101	4	t	t	PROPN
ejpam-5601	101	5	≤	≤	ADJ
ejpam-5601	101	6	2π	2π	NOUN
ejpam-5601	101	7	}	}	PUNCT
ejpam-5601	101	8	.	.	PUNCT
ejpam-5601	102	1	definition	definition	NOUN
ejpam-5601	102	2	4	4	NUM
ejpam-5601	102	3	.	.	PUNCT
ejpam-5601	103	1	[	[	X
ejpam-5601	103	2	3	3	X
ejpam-5601	103	3	]	]	PUNCT
ejpam-5601	103	4	let	let	VERB
ejpam-5601	103	5	a	a	PRON
ejpam-5601	103	6	and	and	CCONJ
ejpam-5601	103	7	b	b	NOUN
ejpam-5601	103	8	be	be	AUX
ejpam-5601	103	9	convex	convex	ADJ
ejpam-5601	103	10	fuzzy	fuzzy	ADJ
ejpam-5601	103	11	numbers	number	NOUN
ejpam-5601	103	12	defined	define	VERB
ejpam-5601	103	13	on	on	ADP
ejpam-5601	103	14	r2	r2	PROPN
ejpam-5601	103	15	and	and	CCONJ
ejpam-5601	103	16	aα	aα	NOUN
ejpam-5601	103	17	=	=	SYM
ejpam-5601	103	18	{	{	PUNCT
ejpam-5601	103	19	(	(	PUNCT
ejpam-5601	103	20	fα	fα	ADP
ejpam-5601	103	21	1	1	NUM
ejpam-5601	103	22	(	(	PUNCT
ejpam-5601	103	23	t	t	PROPN
ejpam-5601	103	24	)	)	PUNCT
ejpam-5601	103	25	,	,	PUNCT
ejpam-5601	103	26	f	f	PROPN
ejpam-5601	103	27	α	α	PROPN
ejpam-5601	103	28	2	2	NUM
ejpam-5601	103	29	(	(	PUNCT
ejpam-5601	103	30	t	t	NOUN
ejpam-5601	103	31	)	)	PUNCT
ejpam-5601	103	32	)	)	PUNCT
ejpam-5601	104	1	∈	∈	PROPN
ejpam-5601	104	2	r2|0	r2|0	NOUN
ejpam-5601	104	3	≤	≤	NOUN
ejpam-5601	104	4	t	t	PROPN
ejpam-5601	104	5	≤	≤	ADJ
ejpam-5601	104	6	2π	2π	NOUN
ejpam-5601	104	7	}	}	PUNCT
ejpam-5601	104	8	,	,	PUNCT
ejpam-5601	104	9	bα	bα	NOUN
ejpam-5601	104	10	=	=	PUNCT
ejpam-5601	104	11	{	{	PUNCT
ejpam-5601	104	12	(	(	PUNCT
ejpam-5601	104	13	gα1	gα1	X
ejpam-5601	104	14	(	(	PUNCT
ejpam-5601	104	15	t	t	PROPN
ejpam-5601	104	16	)	)	PUNCT
ejpam-5601	104	17	,	,	PUNCT
ejpam-5601	104	18	gα2	gα2	PROPN
ejpam-5601	104	19	(	(	PUNCT
ejpam-5601	104	20	t	t	PROPN
ejpam-5601	104	21	)	)	PUNCT
ejpam-5601	104	22	)	)	PUNCT
ejpam-5601	105	1	∈	∈	PROPN
ejpam-5601	105	2	r2|0	r2|0	NOUN
ejpam-5601	105	3	≤	≤	NOUN
ejpam-5601	105	4	t	t	PROPN
ejpam-5601	105	5	≤	≤	ADJ
ejpam-5601	105	6	2π	2π	NOUN
ejpam-5601	105	7	}	}	PUNCT
ejpam-5601	105	8	be	be	AUX
ejpam-5601	105	9	the	the	DET
ejpam-5601	105	10	α	α	NOUN
ejpam-5601	105	11	-	-	PUNCT
ejpam-5601	105	12	sets	set	NOUN
ejpam-5601	105	13	of	of	ADP
ejpam-5601	105	14	a	a	PRON
ejpam-5601	105	15	and	and	CCONJ
ejpam-5601	105	16	b	b	NOUN
ejpam-5601	105	17	,	,	PUNCT
ejpam-5601	105	18	respectively	respectively	ADV
ejpam-5601	105	19	.	.	PUNCT
ejpam-5601	106	1	for	for	ADP
ejpam-5601	106	2	α	α	PROPN
ejpam-5601	106	3	∈	∈	PROPN
ejpam-5601	106	4	(	(	PUNCT
ejpam-5601	106	5	0	0	NUM
ejpam-5601	106	6	,	,	PUNCT
ejpam-5601	106	7	1	1	NUM
ejpam-5601	106	8	)	)	PUNCT
ejpam-5601	106	9	,	,	PUNCT
ejpam-5601	106	10	the	the	DET
ejpam-5601	106	11	parametric	parametric	ADJ
ejpam-5601	106	12	addition	addition	NOUN
ejpam-5601	106	13	,	,	PUNCT
ejpam-5601	106	14	parametric	parametric	ADJ
ejpam-5601	106	15	subtraction	subtraction	NOUN
ejpam-5601	106	16	,	,	PUNCT
ejpam-5601	106	17	parametric	parametric	ADJ
ejpam-5601	106	18	multiplication	multiplication	NOUN
ejpam-5601	106	19	,	,	PUNCT
ejpam-5601	106	20	and	and	CCONJ
ejpam-5601	106	21	parametric	parametric	ADJ
ejpam-5601	106	22	division	division	NOUN
ejpam-5601	106	23	are	be	AUX
ejpam-5601	106	24	fuzzy	fuzzy	ADJ
ejpam-5601	106	25	numbers	number	NOUN
ejpam-5601	106	26	that	that	PRON
ejpam-5601	106	27	have	have	VERB
ejpam-5601	106	28	their	their	PRON
ejpam-5601	106	29	α	α	NOUN
ejpam-5601	106	30	-	-	PUNCT
ejpam-5601	106	31	sets	set	NOUN
ejpam-5601	106	32	as	as	SCONJ
ejpam-5601	106	33	follows	follow	VERB
ejpam-5601	106	34	:	:	PUNCT
ejpam-5601	106	35	(	(	PUNCT
ejpam-5601	106	36	1	1	X
ejpam-5601	106	37	)	)	PUNCT
ejpam-5601	106	38	parametric	parametric	ADJ
ejpam-5601	106	39	addition	addition	NOUN
ejpam-5601	106	40	a(+)pb	a(+)pb	PROPN
ejpam-5601	106	41	:	:	PUNCT
ejpam-5601	106	42	(	(	PUNCT
ejpam-5601	106	43	a(+)pb)α	a(+)pb)α	NOUN
ejpam-5601	106	44	=	=	SYM
ejpam-5601	106	45	{	{	PUNCT
ejpam-5601	106	46	(	(	PUNCT
ejpam-5601	106	47	fα	fα	ADP
ejpam-5601	106	48	1	1	NUM
ejpam-5601	106	49	(	(	PUNCT
ejpam-5601	106	50	t	t	NOUN
ejpam-5601	106	51	)	)	PUNCT
ejpam-5601	107	1	+	+	CCONJ
ejpam-5601	107	2	gα1	gα1	NOUN
ejpam-5601	107	3	(	(	PUNCT
ejpam-5601	107	4	t	t	PROPN
ejpam-5601	107	5	)	)	PUNCT
ejpam-5601	107	6	,	,	PUNCT
ejpam-5601	108	1	f	f	PROPN
ejpam-5601	108	2	α	α	PROPN
ejpam-5601	108	3	2	2	NUM
ejpam-5601	108	4	(	(	PUNCT
ejpam-5601	108	5	t	t	PROPN
ejpam-5601	108	6	)	)	PUNCT
ejpam-5601	109	1	+	+	NUM
ejpam-5601	109	2	gα2	gα2	PROPN
ejpam-5601	109	3	(	(	PUNCT
ejpam-5601	109	4	t	t	NOUN
ejpam-5601	109	5	)	)	PUNCT
ejpam-5601	109	6	)	)	PUNCT
ejpam-5601	110	1	∈	∈	PROPN
ejpam-5601	110	2	r2|0	r2|0	NOUN
ejpam-5601	110	3	≤	≤	NOUN
ejpam-5601	110	4	t	t	PROPN
ejpam-5601	110	5	≤	≤	ADJ
ejpam-5601	110	6	2π	2π	NOUN
ejpam-5601	110	7	}	}	PUNCT
ejpam-5601	110	8	(	(	PUNCT
ejpam-5601	110	9	2	2	X
ejpam-5601	110	10	)	)	PUNCT
ejpam-5601	110	11	parametric	parametric	ADJ
ejpam-5601	110	12	subtraction	subtraction	NOUN
ejpam-5601	110	13	a(−)pb	a(−)pb	PROPN
ejpam-5601	110	14	:	:	PUNCT
ejpam-5601	110	15	(	(	PUNCT
ejpam-5601	110	16	a(−)pb)α	a(−)pb)α	NOUN
ejpam-5601	110	17	=	=	SYM
ejpam-5601	110	18	{	{	PUNCT
ejpam-5601	110	19	(	(	PUNCT
ejpam-5601	110	20	xα(t	xα(t	NUM
ejpam-5601	110	21	)	)	PUNCT
ejpam-5601	110	22	,	,	PUNCT
ejpam-5601	110	23	yα(t	yα(t	NOUN
ejpam-5601	110	24	)	)	PUNCT
ejpam-5601	110	25	)	)	PUNCT
ejpam-5601	111	1	∈	∈	PROPN
ejpam-5601	111	2	r2|0	r2|0	NOUN
ejpam-5601	111	3	≤	≤	NOUN
ejpam-5601	111	4	t	t	PROPN
ejpam-5601	111	5	≤	≤	ADJ
ejpam-5601	111	6	2π	2π	NOUN
ejpam-5601	111	7	}	}	PUNCT
ejpam-5601	111	8	,	,	PUNCT
ejpam-5601	111	9	where	where	SCONJ
ejpam-5601	111	10	y.	y.	PROPN
ejpam-5601	111	11	s.	s.	PROPN
ejpam-5601	111	12	yun	yun	PROPN
ejpam-5601	111	13	,	,	PUNCT
ejpam-5601	111	14	b.	b.	PROPN
ejpam-5601	111	15	lee	lee	PROPN
ejpam-5601	111	16	/	/	SYM
ejpam-5601	111	17	eur	eur	PROPN
ejpam-5601	111	18	.	.	PUNCT
ejpam-5601	112	1	j.	j.	PROPN
ejpam-5601	112	2	pure	pure	PROPN
ejpam-5601	112	3	appl	appl	PROPN
ejpam-5601	112	4	.	.	PROPN
ejpam-5601	112	5	math	math	PROPN
ejpam-5601	112	6	,	,	PUNCT
ejpam-5601	112	7	18	18	NUM
ejpam-5601	112	8	(	(	PUNCT
ejpam-5601	112	9	1	1	NUM
ejpam-5601	112	10	)	)	PUNCT
ejpam-5601	112	11	(	(	PUNCT
ejpam-5601	112	12	2025	2025	NUM
ejpam-5601	112	13	)	)	PUNCT
ejpam-5601	112	14	,	,	PUNCT
ejpam-5601	112	15	5601	5601	NUM
ejpam-5601	112	16	6	6	NUM
ejpam-5601	112	17	of	of	ADP
ejpam-5601	112	18	17	17	NUM
ejpam-5601	112	19	xα(t	xα(t	NUM
ejpam-5601	112	20	)	)	PUNCT
ejpam-5601	113	1	=	=	PRON
ejpam-5601	113	2	{	{	PUNCT
ejpam-5601	113	3	fα	fα	ADP
ejpam-5601	113	4	1	1	NUM
ejpam-5601	113	5	(	(	PUNCT
ejpam-5601	113	6	t)−	t)−	PROPN
ejpam-5601	113	7	gα1	gα1	NOUN
ejpam-5601	113	8	(	(	PUNCT
ejpam-5601	113	9	t+	t+	NOUN
ejpam-5601	113	10	π	π	PROPN
ejpam-5601	113	11	)	)	PUNCT
ejpam-5601	113	12	,	,	PUNCT
ejpam-5601	113	13	if	if	SCONJ
ejpam-5601	113	14	0	0	NUM
ejpam-5601	113	15	≤	≤	NUM
ejpam-5601	113	16	t	t	NOUN
ejpam-5601	113	17	≤	≤	NUM
ejpam-5601	113	18	π	π	PROPN
ejpam-5601	113	19	fα	fα	ADP
ejpam-5601	113	20	1	1	NUM
ejpam-5601	113	21	(	(	PUNCT
ejpam-5601	113	22	t)−	t)−	PROPN
ejpam-5601	113	23	gα1	gα1	NOUN
ejpam-5601	113	24	(	(	PUNCT
ejpam-5601	113	25	t−	t−	PROPN
ejpam-5601	113	26	π	π	PROPN
ejpam-5601	113	27	)	)	PUNCT
ejpam-5601	113	28	,	,	PUNCT
ejpam-5601	113	29	if	if	SCONJ
ejpam-5601	113	30	π	π	PROPN
ejpam-5601	113	31	≤	≤	X
ejpam-5601	113	32	t	t	X
ejpam-5601	113	33	≤	≤	NOUN
ejpam-5601	113	34	2π	2π	NOUN
ejpam-5601	113	35	and	and	CCONJ
ejpam-5601	113	36	yα(t	yα(t	NOUN
ejpam-5601	113	37	)	)	PUNCT
ejpam-5601	113	38	=	=	PRON
ejpam-5601	113	39	{	{	PUNCT
ejpam-5601	113	40	fα	fα	ADP
ejpam-5601	113	41	2	2	NUM
ejpam-5601	113	42	(	(	PUNCT
ejpam-5601	113	43	t)−	t)−	PROPN
ejpam-5601	113	44	gα2	gα2	PROPN
ejpam-5601	113	45	(	(	PUNCT
ejpam-5601	113	46	t+	t+	NOUN
ejpam-5601	113	47	π	π	PROPN
ejpam-5601	113	48	)	)	PUNCT
ejpam-5601	113	49	,	,	PUNCT
ejpam-5601	113	50	if	if	SCONJ
ejpam-5601	113	51	0	0	NUM
ejpam-5601	113	52	≤	≤	NUM
ejpam-5601	113	53	t	t	NOUN
ejpam-5601	113	54	≤	≤	NUM
ejpam-5601	113	55	π	π	PROPN
ejpam-5601	113	56	fα	fα	ADP
ejpam-5601	113	57	2	2	NUM
ejpam-5601	113	58	(	(	PUNCT
ejpam-5601	113	59	t)−	t)−	PROPN
ejpam-5601	113	60	gα2	gα2	NOUN
ejpam-5601	113	61	(	(	PUNCT
ejpam-5601	113	62	t−	t−	PROPN
ejpam-5601	113	63	π	π	PROPN
ejpam-5601	113	64	)	)	PUNCT
ejpam-5601	113	65	,	,	PUNCT
ejpam-5601	113	66	if	if	SCONJ
ejpam-5601	113	67	π	π	PROPN
ejpam-5601	113	68	≤	≤	X
ejpam-5601	113	69	t	t	X
ejpam-5601	113	70	≤	≤	ADJ
ejpam-5601	113	71	2π	2π	NOUN
ejpam-5601	113	72	(	(	PUNCT
ejpam-5601	113	73	3	3	NUM
ejpam-5601	113	74	)	)	PUNCT
ejpam-5601	113	75	parametric	parametric	ADJ
ejpam-5601	113	76	multiplication	multiplication	NOUN
ejpam-5601	113	77	a(·)pb	a(·)pb	PROPN
ejpam-5601	113	78	:	:	PUNCT
ejpam-5601	113	79	(	(	PUNCT
ejpam-5601	113	80	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	113	81	=	=	SYM
ejpam-5601	113	82	{	{	PUNCT
ejpam-5601	113	83	(	(	PUNCT
ejpam-5601	113	84	fα	fα	ADP
ejpam-5601	113	85	1	1	NUM
ejpam-5601	113	86	(	(	PUNCT
ejpam-5601	113	87	t	t	PROPN
ejpam-5601	113	88	)	)	PUNCT
ejpam-5601	113	89	·	·	PUNCT
ejpam-5601	113	90	gα1	gα1	NOUN
ejpam-5601	113	91	(	(	PUNCT
ejpam-5601	113	92	t	t	PROPN
ejpam-5601	113	93	)	)	PUNCT
ejpam-5601	113	94	,	,	PUNCT
ejpam-5601	113	95	fα	fα	ADP
ejpam-5601	113	96	2	2	NUM
ejpam-5601	113	97	(	(	PUNCT
ejpam-5601	113	98	t	t	PROPN
ejpam-5601	113	99	)	)	PUNCT
ejpam-5601	113	100	·	·	PUNCT
ejpam-5601	114	1	gα2	gα2	NOUN
ejpam-5601	114	2	(	(	PUNCT
ejpam-5601	114	3	t	t	NOUN
ejpam-5601	114	4	)	)	PUNCT
ejpam-5601	114	5	)	)	PUNCT
ejpam-5601	115	1	∈	∈	PROPN
ejpam-5601	115	2	r2|0	r2|0	NOUN
ejpam-5601	115	3	≤	≤	NOUN
ejpam-5601	115	4	t	t	PROPN
ejpam-5601	115	5	≤	≤	ADJ
ejpam-5601	115	6	2π	2π	NOUN
ejpam-5601	115	7	}	}	PUNCT
ejpam-5601	115	8	(	(	PUNCT
ejpam-5601	115	9	4	4	X
ejpam-5601	115	10	)	)	PUNCT
ejpam-5601	115	11	parametric	parametric	ADJ
ejpam-5601	115	12	division	division	NOUN
ejpam-5601	115	13	a(/)pb	a(/)pb	PROPN
ejpam-5601	115	14	:	:	PUNCT
ejpam-5601	115	15	(	(	PUNCT
ejpam-5601	115	16	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	115	17	=	=	PRON
ejpam-5601	115	18	{	{	PUNCT
ejpam-5601	115	19	(	(	PUNCT
ejpam-5601	115	20	xα(t	xα(t	NUM
ejpam-5601	115	21	)	)	PUNCT
ejpam-5601	115	22	,	,	PUNCT
ejpam-5601	115	23	yα(t	yα(t	NOUN
ejpam-5601	115	24	)	)	PUNCT
ejpam-5601	115	25	)	)	PUNCT
ejpam-5601	116	1	∈	∈	PROPN
ejpam-5601	116	2	r2|0	r2|0	NOUN
ejpam-5601	116	3	≤	≤	NOUN
ejpam-5601	116	4	t	t	PROPN
ejpam-5601	116	5	≤	≤	ADJ
ejpam-5601	116	6	2π	2π	NOUN
ejpam-5601	116	7	}	}	PUNCT
ejpam-5601	116	8	,	,	PUNCT
ejpam-5601	116	9	where	where	SCONJ
ejpam-5601	116	10	xα(t	xα(t	NUM
ejpam-5601	116	11	)	)	PUNCT
ejpam-5601	116	12	=	=	SYM
ejpam-5601	116	13	fα	fα	ADP
ejpam-5601	116	14	1	1	NUM
ejpam-5601	116	15	(	(	PUNCT
ejpam-5601	116	16	t	t	NOUN
ejpam-5601	116	17	)	)	PUNCT
ejpam-5601	116	18	gα1	gα1	NOUN
ejpam-5601	116	19	(	(	PUNCT
ejpam-5601	116	20	t+	t+	NOUN
ejpam-5601	116	21	π	π	NOUN
ejpam-5601	116	22	)	)	PUNCT
ejpam-5601	116	23	(	(	PUNCT
ejpam-5601	116	24	0	0	NUM
ejpam-5601	116	25	≤	≤	NUM
ejpam-5601	116	26	t	t	PROPN
ejpam-5601	116	27	≤	≤	NUM
ejpam-5601	116	28	π	π	PROPN
ejpam-5601	116	29	)	)	PUNCT
ejpam-5601	116	30	,	,	PUNCT
ejpam-5601	116	31	xα(t	xα(t	NUM
ejpam-5601	116	32	)	)	PUNCT
ejpam-5601	116	33	=	=	SYM
ejpam-5601	116	34	fα	fα	ADP
ejpam-5601	116	35	1	1	NUM
ejpam-5601	116	36	(	(	PUNCT
ejpam-5601	116	37	t	t	NOUN
ejpam-5601	116	38	)	)	PUNCT
ejpam-5601	116	39	gα1	gα1	NOUN
ejpam-5601	116	40	(	(	PUNCT
ejpam-5601	116	41	t−	t−	PROPN
ejpam-5601	116	42	π	π	NOUN
ejpam-5601	116	43	)	)	PUNCT
ejpam-5601	116	44	(	(	PUNCT
ejpam-5601	116	45	π	π	PROPN
ejpam-5601	116	46	≤	≤	PROPN
ejpam-5601	116	47	t	t	X
ejpam-5601	116	48	≤	≤	ADJ
ejpam-5601	116	49	2π	2π	NOUN
ejpam-5601	116	50	)	)	PUNCT
ejpam-5601	116	51	and	and	CCONJ
ejpam-5601	116	52	yα(t	yα(t	NOUN
ejpam-5601	116	53	)	)	PUNCT
ejpam-5601	116	54	=	=	SYM
ejpam-5601	116	55	fα	fα	ADP
ejpam-5601	116	56	2	2	NUM
ejpam-5601	116	57	(	(	PUNCT
ejpam-5601	116	58	t	t	NOUN
ejpam-5601	116	59	)	)	PUNCT
ejpam-5601	116	60	gα2	gα2	NOUN
ejpam-5601	116	61	(	(	PUNCT
ejpam-5601	116	62	t+	t+	NOUN
ejpam-5601	116	63	π	π	NOUN
ejpam-5601	116	64	)	)	PUNCT
ejpam-5601	116	65	(	(	PUNCT
ejpam-5601	116	66	0	0	NUM
ejpam-5601	116	67	≤	≤	NUM
ejpam-5601	116	68	t	t	PROPN
ejpam-5601	116	69	≤	≤	NUM
ejpam-5601	116	70	π	π	PROPN
ejpam-5601	116	71	)	)	PUNCT
ejpam-5601	116	72	,	,	PUNCT
ejpam-5601	116	73	yα(t	yα(t	X
ejpam-5601	116	74	)	)	PUNCT
ejpam-5601	116	75	=	=	SYM
ejpam-5601	116	76	fα	fα	ADP
ejpam-5601	116	77	2	2	NUM
ejpam-5601	116	78	(	(	PUNCT
ejpam-5601	116	79	t	t	NOUN
ejpam-5601	116	80	)	)	PUNCT
ejpam-5601	116	81	gα2	gα2	NOUN
ejpam-5601	116	82	(	(	PUNCT
ejpam-5601	116	83	t−	t−	PROPN
ejpam-5601	116	84	π	π	PROPN
ejpam-5601	116	85	)	)	PUNCT
ejpam-5601	116	86	(	(	PUNCT
ejpam-5601	116	87	π	π	PROPN
ejpam-5601	116	88	≤	≤	PROPN
ejpam-5601	116	89	t	t	X
ejpam-5601	116	90	≤	≤	ADJ
ejpam-5601	116	91	2π	2π	NOUN
ejpam-5601	116	92	)	)	PUNCT
ejpam-5601	116	93	for	for	ADP
ejpam-5601	116	94	α	α	NOUN
ejpam-5601	116	95	=	=	SYM
ejpam-5601	116	96	0	0	PROPN
ejpam-5601	116	97	and	and	CCONJ
ejpam-5601	116	98	α	α	NOUN
ejpam-5601	116	99	=	=	SYM
ejpam-5601	116	100	1	1	NUM
ejpam-5601	116	101	,	,	PUNCT
ejpam-5601	116	102	(	(	PUNCT
ejpam-5601	116	103	a(∗)pb)0	a(∗)pb)0	PROPN
ejpam-5601	116	104	=	=	NOUN
ejpam-5601	116	105	limα→0+(a(∗)pb)α	limα→0+(a(∗)pb)α	NOUN
ejpam-5601	116	106	and	and	CCONJ
ejpam-5601	116	107	(	(	PUNCT
ejpam-5601	116	108	a(∗)pb)1	a(∗)pb)1	PROPN
ejpam-5601	116	109	=	=	SYM
ejpam-5601	116	110	limα→1−(a(∗)pb)α	limα→1−(a(∗)pb)α	PROPN
ejpam-5601	116	111	,	,	PUNCT
ejpam-5601	116	112	where	where	SCONJ
ejpam-5601	116	113	∗	∗	NOUN
ejpam-5601	116	114	=	=	PUNCT
ejpam-5601	117	1	+	+	ADJ
ejpam-5601	117	2	,	,	PUNCT
ejpam-5601	117	3	−	−	PROPN
ejpam-5601	117	4	,	,	PUNCT
ejpam-5601	117	5	·	·	PUNCT
ejpam-5601	117	6	,	,	PUNCT
ejpam-5601	117	7	/.	/.	PUNCT
ejpam-5601	118	1	theorem	theorem	NOUN
ejpam-5601	118	2	3	3	NUM
ejpam-5601	118	3	.	.	PUNCT
ejpam-5601	119	1	[	[	X
ejpam-5601	119	2	3	3	X
ejpam-5601	119	3	]	]	PUNCT
ejpam-5601	119	4	let	let	VERB
ejpam-5601	119	5	a	a	PRON
ejpam-5601	119	6	=	=	SYM
ejpam-5601	120	1	[	[	X
ejpam-5601	120	2	a1	a1	NOUN
ejpam-5601	120	3	,	,	PUNCT
ejpam-5601	120	4	x1	x1	PROPN
ejpam-5601	120	5	,	,	PUNCT
ejpam-5601	120	6	b1	b1	NOUN
ejpam-5601	120	7	,	,	PUNCT
ejpam-5601	120	8	y1	y1	NOUN
ejpam-5601	120	9	]	]	PUNCT
ejpam-5601	120	10	2	2	NUM
ejpam-5601	120	11	and	and	CCONJ
ejpam-5601	120	12	b	b	NOUN
ejpam-5601	120	13	=	=	SYM
ejpam-5601	121	1	[	[	X
ejpam-5601	121	2	a2	a2	PROPN
ejpam-5601	121	3	,	,	PUNCT
ejpam-5601	121	4	x2	x2	PROPN
ejpam-5601	121	5	,	,	PUNCT
ejpam-5601	121	6	b2	b2	NOUN
ejpam-5601	121	7	,	,	PUNCT
ejpam-5601	121	8	y2	y2	NOUN
ejpam-5601	121	9	]	]	PUNCT
ejpam-5601	121	10	2	2	NUM
ejpam-5601	121	11	be	be	VERB
ejpam-5601	121	12	two	two	NUM
ejpam-5601	121	13	2	2	NUM
ejpam-5601	121	14	-	-	PUNCT
ejpam-5601	121	15	dimensional	dimensional	ADJ
ejpam-5601	121	16	quadratic	quadratic	ADJ
ejpam-5601	121	17	fuzzy	fuzzy	ADJ
ejpam-5601	121	18	numbers	number	NOUN
ejpam-5601	121	19	.	.	PUNCT
ejpam-5601	122	1	subsequently	subsequently	ADV
ejpam-5601	122	2	,	,	PUNCT
ejpam-5601	122	3	the	the	DET
ejpam-5601	122	4	following	follow	VERB
ejpam-5601	122	5	results	result	NOUN
ejpam-5601	122	6	hold	hold	VERB
ejpam-5601	122	7	:	:	PUNCT
ejpam-5601	122	8	(	(	PUNCT
ejpam-5601	122	9	1	1	X
ejpam-5601	122	10	)	)	PUNCT
ejpam-5601	122	11	a(+)pb	a(+)pb	NOUN
ejpam-5601	122	12	=	=	PUNCT
ejpam-5601	123	1	[	[	PUNCT
ejpam-5601	123	2	a1	a1	NOUN
ejpam-5601	123	3	+	+	CCONJ
ejpam-5601	123	4	a2	a2	PROPN
ejpam-5601	123	5	,	,	PUNCT
ejpam-5601	123	6	x1	x1	PROPN
ejpam-5601	124	1	+	+	CCONJ
ejpam-5601	124	2	x2	x2	PROPN
ejpam-5601	124	3	,	,	PUNCT
ejpam-5601	124	4	b1	b1	NOUN
ejpam-5601	124	5	+	+	CCONJ
ejpam-5601	124	6	b2	b2	NOUN
ejpam-5601	124	7	,	,	PUNCT
ejpam-5601	124	8	y1	y1	NOUN
ejpam-5601	124	9	+	+	NOUN
ejpam-5601	124	10	y2	y2	NOUN
ejpam-5601	124	11	]	]	SYM
ejpam-5601	124	12	2	2	NUM
ejpam-5601	124	13	(	(	PUNCT
ejpam-5601	124	14	2	2	NUM
ejpam-5601	124	15	)	)	PUNCT
ejpam-5601	124	16	a(−)pb	a(−)pb	NOUN
ejpam-5601	124	17	=	=	PUNCT
ejpam-5601	125	1	[	[	PUNCT
ejpam-5601	125	2	a1	a1	NOUN
ejpam-5601	125	3	+	+	CCONJ
ejpam-5601	125	4	a2	a2	PROPN
ejpam-5601	125	5	,	,	PUNCT
ejpam-5601	125	6	x1	x1	PROPN
ejpam-5601	125	7	−	−	PROPN
ejpam-5601	125	8	x2	x2	PROPN
ejpam-5601	125	9	,	,	PUNCT
ejpam-5601	125	10	b1	b1	NOUN
ejpam-5601	125	11	+	+	CCONJ
ejpam-5601	125	12	b2	b2	NOUN
ejpam-5601	125	13	,	,	PUNCT
ejpam-5601	125	14	y1	y1	NOUN
ejpam-5601	125	15	−	−	PROPN
ejpam-5601	126	1	y2	y2	NOUN
ejpam-5601	126	2	]	]	SYM
ejpam-5601	126	3	2	2	NUM
ejpam-5601	126	4	(	(	PUNCT
ejpam-5601	126	5	3	3	NUM
ejpam-5601	126	6	)	)	PUNCT
ejpam-5601	126	7	(	(	PUNCT
ejpam-5601	126	8	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	126	9	=	=	SYM
ejpam-5601	126	10	{	{	PUNCT
ejpam-5601	126	11	(	(	PUNCT
ejpam-5601	126	12	xα(t	xα(t	NUM
ejpam-5601	126	13	)	)	PUNCT
ejpam-5601	126	14	,	,	PUNCT
ejpam-5601	126	15	yα(t	yα(t	NOUN
ejpam-5601	126	16	)	)	PUNCT
ejpam-5601	126	17	)	)	PUNCT
ejpam-5601	127	1	|	|	ADV
ejpam-5601	127	2	0	0	NUM
ejpam-5601	127	3	≤	≤	NOUN
ejpam-5601	127	4	t	t	X
ejpam-5601	127	5	≤	≤	ADJ
ejpam-5601	127	6	2π	2π	NOUN
ejpam-5601	127	7	}	}	PUNCT
ejpam-5601	127	8	,	,	PUNCT
ejpam-5601	127	9	where	where	SCONJ
ejpam-5601	127	10	xα(t	xα(t	NUM
ejpam-5601	127	11	)	)	PUNCT
ejpam-5601	127	12	=	=	PUNCT
ejpam-5601	128	1	x1x2	x1x2	PUNCT
ejpam-5601	129	1	+	+	CCONJ
ejpam-5601	129	2	(	(	PUNCT
ejpam-5601	129	3	x1a2	x1a2	X
ejpam-5601	129	4	+	+	X
ejpam-5601	129	5	x2a1	x2a1	X
ejpam-5601	129	6	)	)	PUNCT
ejpam-5601	129	7	√	√	ADP
ejpam-5601	129	8	1−	1−	NUM
ejpam-5601	129	9	α	α	PROPN
ejpam-5601	129	10	cos	cos	PROPN
ejpam-5601	129	11	t+	t+	PUNCT
ejpam-5601	129	12	a1a2(1−	a1a2(1−	PROPN
ejpam-5601	129	13	α	α	NUM
ejpam-5601	129	14	)	)	PUNCT
ejpam-5601	129	15	cos2	cos2	PROPN
ejpam-5601	129	16	t	t	PROPN
ejpam-5601	129	17	and	and	CCONJ
ejpam-5601	129	18	yα(t	yα(t	NOUN
ejpam-5601	129	19	)	)	PUNCT
ejpam-5601	129	20	=	=	SYM
ejpam-5601	130	1	y1y2	y1y2	PROPN
ejpam-5601	131	1	+	+	CCONJ
ejpam-5601	131	2	(	(	PUNCT
ejpam-5601	131	3	y1b2	y1b2	PROPN
ejpam-5601	131	4	+	+	NUM
ejpam-5601	131	5	y2b1	y2b1	NOUN
ejpam-5601	131	6	)	)	PUNCT
ejpam-5601	131	7	√	√	NOUN
ejpam-5601	131	8	1−	1−	NUM
ejpam-5601	131	9	α	α	PRON
ejpam-5601	131	10	sin	sin	NOUN
ejpam-5601	131	11	t+	t+	PUNCT
ejpam-5601	131	12	b1b2(1−	b1b2(1−	PROPN
ejpam-5601	131	13	α	α	NOUN
ejpam-5601	131	14	)	)	PUNCT
ejpam-5601	131	15	sin2	sin2	NOUN
ejpam-5601	131	16	t.	t.	NOUN
ejpam-5601	131	17	(	(	PUNCT
ejpam-5601	131	18	4	4	NUM
ejpam-5601	131	19	)	)	PUNCT
ejpam-5601	131	20	(	(	PUNCT
ejpam-5601	131	21	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	131	22	=	=	PRON
ejpam-5601	131	23	{	{	PUNCT
ejpam-5601	131	24	(	(	PUNCT
ejpam-5601	131	25	xα(t	xα(t	NUM
ejpam-5601	131	26	)	)	PUNCT
ejpam-5601	131	27	,	,	PUNCT
ejpam-5601	131	28	yα(t	yα(t	NOUN
ejpam-5601	131	29	)	)	PUNCT
ejpam-5601	131	30	)	)	PUNCT
ejpam-5601	132	1	|	|	ADV
ejpam-5601	132	2	0	0	NUM
ejpam-5601	132	3	≤	≤	NOUN
ejpam-5601	132	4	t	t	X
ejpam-5601	132	5	≤	≤	ADJ
ejpam-5601	132	6	2π	2π	NOUN
ejpam-5601	132	7	}	}	PUNCT
ejpam-5601	132	8	,	,	PUNCT
ejpam-5601	132	9	where	where	SCONJ
ejpam-5601	132	10	xα(t	xα(t	NUM
ejpam-5601	132	11	)	)	PUNCT
ejpam-5601	132	12	=	=	SYM
ejpam-5601	133	1	x1	x1	PROPN
ejpam-5601	134	1	+	+	CCONJ
ejpam-5601	134	2	a1	a1	NOUN
ejpam-5601	134	3	√	√	PROPN
ejpam-5601	134	4	1−	1−	NUM
ejpam-5601	134	5	α	α	PROPN
ejpam-5601	134	6	cos	cos	PROPN
ejpam-5601	134	7	t	t	PROPN
ejpam-5601	135	1	x2	x2	CCONJ
ejpam-5601	135	2	−	−	PROPN
ejpam-5601	135	3	a2	a2	PROPN
ejpam-5601	135	4	√	√	NOUN
ejpam-5601	135	5	1−	1−	NUM
ejpam-5601	135	6	α	α	PROPN
ejpam-5601	135	7	cos	cos	PROPN
ejpam-5601	135	8	t	t	PROPN
ejpam-5601	135	9	and	and	CCONJ
ejpam-5601	135	10	yα(t	yα(t	NOUN
ejpam-5601	135	11	)	)	PUNCT
ejpam-5601	135	12	=	=	SYM
ejpam-5601	135	13	y1	y1	NOUN
ejpam-5601	135	14	+	+	CCONJ
ejpam-5601	135	15	b1	b1	NOUN
ejpam-5601	135	16	√	√	NUM
ejpam-5601	135	17	1−	1−	NUM
ejpam-5601	136	1	α	α	PRON
ejpam-5601	136	2	sin	sin	NOUN
ejpam-5601	136	3	t	t	PROPN
ejpam-5601	136	4	y2	y2	NOUN
ejpam-5601	136	5	−	−	PROPN
ejpam-5601	136	6	b2	b2	NOUN
ejpam-5601	136	7	√	√	NOUN
ejpam-5601	136	8	1−	1−	NUM
ejpam-5601	136	9	α	α	PROPN
ejpam-5601	136	10	sin	sin	PROPN
ejpam-5601	136	11	t	t	PROPN
ejpam-5601	136	12	.	.	PUNCT
ejpam-5601	137	1	therefore	therefore	ADV
ejpam-5601	137	2	,	,	PUNCT
ejpam-5601	137	3	a(+)pb	a(+)pb	PROPN
ejpam-5601	137	4	and	and	CCONJ
ejpam-5601	137	5	a(−)pb	a(−)pb	PRON
ejpam-5601	137	6	become	become	VERB
ejpam-5601	137	7	2	2	NUM
ejpam-5601	137	8	-	-	PUNCT
ejpam-5601	137	9	dimensional	dimensional	ADJ
ejpam-5601	137	10	quadratic	quadratic	ADJ
ejpam-5601	137	11	fuzzy	fuzzy	ADJ
ejpam-5601	137	12	numbers	number	NOUN
ejpam-5601	137	13	,	,	PUNCT
ejpam-5601	137	14	whereas	whereas	SCONJ
ejpam-5601	137	15	a(·)pb	a(·)pb	ADJ
ejpam-5601	137	16	and	and	CCONJ
ejpam-5601	137	17	a(/)pb	a(/)pb	PROPN
ejpam-5601	137	18	do	do	AUX
ejpam-5601	137	19	not	not	PART
ejpam-5601	137	20	qualify	qualify	VERB
ejpam-5601	137	21	as	as	ADP
ejpam-5601	137	22	2	2	NUM
ejpam-5601	137	23	-	-	PUNCT
ejpam-5601	137	24	dimensional	dimensional	ADJ
ejpam-5601	137	25	quadratic	quadratic	ADJ
ejpam-5601	137	26	fuzzy	fuzzy	ADJ
ejpam-5601	137	27	numbers	number	NOUN
ejpam-5601	137	28	.	.	PUNCT
ejpam-5601	138	1	y.	y.	PROPN
ejpam-5601	138	2	s.	s.	PROPN
ejpam-5601	138	3	yun	yun	PROPN
ejpam-5601	138	4	,	,	PUNCT
ejpam-5601	138	5	b.	b.	PROPN
ejpam-5601	138	6	lee	lee	PROPN
ejpam-5601	138	7	/	/	SYM
ejpam-5601	138	8	eur	eur	PROPN
ejpam-5601	138	9	.	.	PUNCT
ejpam-5601	139	1	j.	j.	PROPN
ejpam-5601	139	2	pure	pure	PROPN
ejpam-5601	139	3	appl	appl	PROPN
ejpam-5601	139	4	.	.	PROPN
ejpam-5601	139	5	math	math	PROPN
ejpam-5601	139	6	,	,	PUNCT
ejpam-5601	139	7	18	18	NUM
ejpam-5601	139	8	(	(	PUNCT
ejpam-5601	139	9	1	1	NUM
ejpam-5601	139	10	)	)	PUNCT
ejpam-5601	139	11	(	(	PUNCT
ejpam-5601	139	12	2025	2025	NUM
ejpam-5601	139	13	)	)	PUNCT
ejpam-5601	139	14	,	,	PUNCT
ejpam-5601	139	15	5601	5601	NUM
ejpam-5601	139	16	7	7	NUM
ejpam-5601	139	17	of	of	ADP
ejpam-5601	139	18	17	17	NUM
ejpam-5601	139	19	example	example	NOUN
ejpam-5601	139	20	1	1	NUM
ejpam-5601	139	21	.	.	PUNCT
ejpam-5601	140	1	[	[	X
ejpam-5601	140	2	3	3	X
ejpam-5601	140	3	]	]	PUNCT
ejpam-5601	140	4	consider	consider	VERB
ejpam-5601	140	5	a	a	PRON
ejpam-5601	140	6	=	=	SYM
ejpam-5601	141	1	[	[	X
ejpam-5601	141	2	6	6	NUM
ejpam-5601	141	3	,	,	PUNCT
ejpam-5601	141	4	3	3	NUM
ejpam-5601	141	5	,	,	PUNCT
ejpam-5601	141	6	8	8	NUM
ejpam-5601	141	7	,	,	PUNCT
ejpam-5601	141	8	5]2	5]2	NUM
ejpam-5601	141	9	and	and	CCONJ
ejpam-5601	141	10	b	b	NOUN
ejpam-5601	142	1	=	=	SYM
ejpam-5601	143	1	[	[	X
ejpam-5601	143	2	4	4	NUM
ejpam-5601	143	3	,	,	PUNCT
ejpam-5601	143	4	2	2	NUM
ejpam-5601	143	5	,	,	PUNCT
ejpam-5601	143	6	5	5	NUM
ejpam-5601	143	7	,	,	PUNCT
ejpam-5601	143	8	3]2	3]2	NUM
ejpam-5601	143	9	.	.	PUNCT
ejpam-5601	144	1	subsequently	subsequently	ADV
ejpam-5601	144	2	,	,	PUNCT
ejpam-5601	144	3	the	the	DET
ejpam-5601	144	4	following	follow	VERB
ejpam-5601	144	5	observations	observation	NOUN
ejpam-5601	144	6	hold	hold	VERB
ejpam-5601	144	7	:	:	PUNCT
ejpam-5601	144	8	(	(	PUNCT
ejpam-5601	144	9	1	1	X
ejpam-5601	144	10	)	)	PUNCT
ejpam-5601	144	11	a(+)pb	a(+)pb	NOUN
ejpam-5601	145	1	=	=	PUNCT
ejpam-5601	146	1	[	[	X
ejpam-5601	146	2	10	10	NUM
ejpam-5601	146	3	,	,	PUNCT
ejpam-5601	146	4	5	5	NUM
ejpam-5601	146	5	,	,	PUNCT
ejpam-5601	146	6	13	13	NUM
ejpam-5601	146	7	,	,	PUNCT
ejpam-5601	146	8	8]2	8]2	X
ejpam-5601	146	9	(	(	PUNCT
ejpam-5601	146	10	2	2	NUM
ejpam-5601	146	11	)	)	PUNCT
ejpam-5601	146	12	a(−)pb	a(−)pb	NOUN
ejpam-5601	146	13	=	=	PUNCT
ejpam-5601	147	1	[	[	X
ejpam-5601	147	2	10	10	NUM
ejpam-5601	147	3	,	,	PUNCT
ejpam-5601	147	4	1	1	NUM
ejpam-5601	147	5	,	,	PUNCT
ejpam-5601	147	6	13	13	NUM
ejpam-5601	147	7	,	,	PUNCT
ejpam-5601	147	8	2]2	2]2	NUM
ejpam-5601	147	9	(	(	PUNCT
ejpam-5601	147	10	3	3	NUM
ejpam-5601	147	11	)	)	PUNCT
ejpam-5601	147	12	(	(	PUNCT
ejpam-5601	147	13	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	147	14	=	=	SYM
ejpam-5601	147	15	{	{	PUNCT
ejpam-5601	147	16	(	(	PUNCT
ejpam-5601	147	17	xα(t	xα(t	NUM
ejpam-5601	147	18	)	)	PUNCT
ejpam-5601	147	19	,	,	PUNCT
ejpam-5601	147	20	yα(t	yα(t	NOUN
ejpam-5601	147	21	)	)	PUNCT
ejpam-5601	147	22	)	)	PUNCT
ejpam-5601	147	23	|	|	ADV
ejpam-5601	147	24	0	0	NUM
ejpam-5601	147	25	≤	≤	NOUN
ejpam-5601	147	26	t	t	X
ejpam-5601	147	27	≤	≤	ADJ
ejpam-5601	147	28	2π	2π	NOUN
ejpam-5601	147	29	}	}	PUNCT
ejpam-5601	147	30	,	,	PUNCT
ejpam-5601	147	31	where	where	SCONJ
ejpam-5601	147	32	xα(t	xα(t	NUM
ejpam-5601	147	33	)	)	PUNCT
ejpam-5601	147	34	=	=	SYM
ejpam-5601	147	35	6	6	NUM
ejpam-5601	147	36	+	+	NUM
ejpam-5601	147	37	24	24	NUM
ejpam-5601	147	38	√	√	NUM
ejpam-5601	147	39	1−	1−	NUM
ejpam-5601	147	40	α	α	PROPN
ejpam-5601	147	41	cos	cos	PROPN
ejpam-5601	147	42	t+	t+	VERB
ejpam-5601	147	43	24(1−	24(1−	NUM
ejpam-5601	147	44	α	α	NOUN
ejpam-5601	147	45	)	)	PUNCT
ejpam-5601	147	46	cos2	cos2	PROPN
ejpam-5601	147	47	t	t	PROPN
ejpam-5601	147	48	and	and	CCONJ
ejpam-5601	147	49	yα(t	yα(t	NOUN
ejpam-5601	147	50	)	)	PUNCT
ejpam-5601	147	51	=	=	SYM
ejpam-5601	147	52	15	15	NUM
ejpam-5601	147	53	+	+	NUM
ejpam-5601	147	54	49	49	NUM
ejpam-5601	147	55	√	√	NUM
ejpam-5601	147	56	1−	1−	NUM
ejpam-5601	147	57	α	α	PRON
ejpam-5601	147	58	sin	sin	NOUN
ejpam-5601	147	59	t+	t+	PUNCT
ejpam-5601	147	60	40(1−	40(1−	NUM
ejpam-5601	147	61	α	α	NOUN
ejpam-5601	147	62	)	)	PUNCT
ejpam-5601	147	63	sin2	sin2	NOUN
ejpam-5601	147	64	t.	t.	NOUN
ejpam-5601	147	65	(	(	PUNCT
ejpam-5601	147	66	4	4	NUM
ejpam-5601	147	67	)	)	PUNCT
ejpam-5601	147	68	(	(	PUNCT
ejpam-5601	147	69	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	147	70	=	=	PRON
ejpam-5601	147	71	{	{	PUNCT
ejpam-5601	147	72	(	(	PUNCT
ejpam-5601	147	73	xα(t	xα(t	NUM
ejpam-5601	147	74	)	)	PUNCT
ejpam-5601	147	75	,	,	PUNCT
ejpam-5601	147	76	yα(t	yα(t	NOUN
ejpam-5601	147	77	)	)	PUNCT
ejpam-5601	147	78	)	)	PUNCT
ejpam-5601	148	1	|	|	ADV
ejpam-5601	148	2	0	0	NUM
ejpam-5601	148	3	≤	≤	NOUN
ejpam-5601	148	4	t	t	X
ejpam-5601	148	5	≤	≤	ADJ
ejpam-5601	148	6	2π	2π	NOUN
ejpam-5601	148	7	}	}	PUNCT
ejpam-5601	148	8	,	,	PUNCT
ejpam-5601	148	9	where	where	SCONJ
ejpam-5601	148	10	xα(t	xα(t	NUM
ejpam-5601	148	11	)	)	PUNCT
ejpam-5601	148	12	=	=	SYM
ejpam-5601	149	1	3	3	NUM
ejpam-5601	149	2	+	+	CCONJ
ejpam-5601	149	3	6	6	NUM
ejpam-5601	149	4	√	√	NUM
ejpam-5601	149	5	1−	1−	NUM
ejpam-5601	149	6	α	α	PROPN
ejpam-5601	149	7	cos	cos	PROPN
ejpam-5601	149	8	t	t	PROPN
ejpam-5601	149	9	2−	2−	NUM
ejpam-5601	149	10	4	4	NUM
ejpam-5601	149	11	√	√	PROPN
ejpam-5601	149	12	1−	1−	NUM
ejpam-5601	149	13	α	α	PROPN
ejpam-5601	149	14	cos	cos	PROPN
ejpam-5601	149	15	t	t	PROPN
ejpam-5601	149	16	and	and	CCONJ
ejpam-5601	149	17	yα(t	yα(t	NOUN
ejpam-5601	149	18	)	)	PUNCT
ejpam-5601	150	1	=	=	SYM
ejpam-5601	150	2	5	5	NUM
ejpam-5601	150	3	+	+	CCONJ
ejpam-5601	150	4	8	8	NUM
ejpam-5601	150	5	√	√	NUM
ejpam-5601	150	6	1−	1−	NUM
ejpam-5601	150	7	α	α	PRON
ejpam-5601	150	8	sin	sin	NOUN
ejpam-5601	150	9	t	t	PROPN
ejpam-5601	150	10	3−	3−	NUM
ejpam-5601	150	11	5	5	NUM
ejpam-5601	150	12	√	√	NUM
ejpam-5601	150	13	1−	1−	NUM
ejpam-5601	150	14	α	α	PRON
ejpam-5601	150	15	sin	sin	PROPN
ejpam-5601	150	16	t	t	NOUN
ejpam-5601	150	17	.	.	PUNCT
ejpam-5601	151	1	thus	thus	ADV
ejpam-5601	151	2	a(+)pb	a(+)pb	PROPN
ejpam-5601	151	3	and	and	CCONJ
ejpam-5601	151	4	a(−)pb	a(−)pb	PRON
ejpam-5601	151	5	become	become	VERB
ejpam-5601	151	6	2	2	NUM
ejpam-5601	151	7	-	-	PUNCT
ejpam-5601	151	8	dimensional	dimensional	ADJ
ejpam-5601	151	9	quadratic	quadratic	ADJ
ejpam-5601	151	10	fuzzy	fuzzy	ADJ
ejpam-5601	151	11	numbers	number	NOUN
ejpam-5601	151	12	,	,	PUNCT
ejpam-5601	151	13	but	but	CCONJ
ejpam-5601	151	14	a(·)pb	a(·)pb	NOUN
ejpam-5601	151	15	and	and	CCONJ
ejpam-5601	151	16	a(/)pb	a(/)pb	PROPN
ejpam-5601	151	17	are	be	AUX
ejpam-5601	151	18	not	not	PART
ejpam-5601	151	19	2	2	NUM
ejpam-5601	151	20	-	-	PUNCT
ejpam-5601	151	21	dimensional	dimensional	ADJ
ejpam-5601	151	22	quadratic	quadratic	ADJ
ejpam-5601	151	23	fuzzy	fuzzy	ADJ
ejpam-5601	151	24	numbers	number	NOUN
ejpam-5601	151	25	.	.	PUNCT
ejpam-5601	152	1	4	4	X
ejpam-5601	152	2	.	.	X
ejpam-5601	152	3	max	max	PROPN
ejpam-5601	152	4	-	-	PUNCT
ejpam-5601	152	5	min	min	PROPN
ejpam-5601	152	6	composition	composition	NOUN
ejpam-5601	152	7	operations	operation	NOUN
ejpam-5601	152	8	of	of	ADP
ejpam-5601	152	9	zadeh	zadeh	PROPN
ejpam-5601	152	10	for	for	ADP
ejpam-5601	152	11	quadratic	quadratic	ADJ
ejpam-5601	152	12	fuzzy	fuzzy	ADJ
ejpam-5601	152	13	numbers	number	NOUN
ejpam-5601	152	14	defined	define	VERB
ejpam-5601	152	15	on	on	ADP
ejpam-5601	152	16	r3	r3	PROPN
ejpam-5601	152	17	we	we	PRON
ejpam-5601	152	18	extended	extend	VERB
ejpam-5601	152	19	the	the	DET
ejpam-5601	152	20	concept	concept	NOUN
ejpam-5601	152	21	of	of	ADP
ejpam-5601	152	22	quadratic	quadratic	ADJ
ejpam-5601	152	23	fuzzy	fuzzy	ADJ
ejpam-5601	152	24	numbers	number	NOUN
ejpam-5601	152	25	from	from	ADP
ejpam-5601	152	26	r2	r2	PROPN
ejpam-5601	152	27	to	to	ADP
ejpam-5601	152	28	r3	r3	PROPN
ejpam-5601	152	29	,	,	PUNCT
ejpam-5601	152	30	thereby	thereby	ADV
ejpam-5601	152	31	introducing	introduce	VERB
ejpam-5601	152	32	3	3	NUM
ejpam-5601	152	33	-	-	PUNCT
ejpam-5601	152	34	dimensional	dimensional	ADJ
ejpam-5601	152	35	quadratic	quadratic	ADJ
ejpam-5601	152	36	fuzzy	fuzzy	ADJ
ejpam-5601	152	37	numbers	number	NOUN
ejpam-5601	152	38	.	.	PUNCT
ejpam-5601	153	1	our	our	PRON
ejpam-5601	153	2	objective	objective	NOUN
ejpam-5601	153	3	is	be	AUX
ejpam-5601	153	4	to	to	PART
ejpam-5601	153	5	formulate	formulate	VERB
ejpam-5601	153	6	parametric	parametric	ADJ
ejpam-5601	153	7	operations	operation	NOUN
ejpam-5601	153	8	between	between	ADP
ejpam-5601	153	9	two	two	NUM
ejpam-5601	153	10	such	such	ADJ
ejpam-5601	153	11	3	3	NUM
ejpam-5601	153	12	-	-	PUNCT
ejpam-5601	153	13	dimensional	dimensional	ADJ
ejpam-5601	153	14	quadratic	quadratic	ADJ
ejpam-5601	153	15	fuzzy	fuzzy	ADJ
ejpam-5601	153	16	numbers	number	NOUN
ejpam-5601	153	17	.	.	PUNCT
ejpam-5601	154	1	in	in	ADP
ejpam-5601	154	2	r3	r3	PROPN
ejpam-5601	154	3	,	,	PUNCT
ejpam-5601	154	4	α	α	NOUN
ejpam-5601	154	5	-	-	PUNCT
ejpam-5601	154	6	cuts	cut	NOUN
ejpam-5601	154	7	take	take	VERB
ejpam-5601	154	8	the	the	DET
ejpam-5601	154	9	form	form	NOUN
ejpam-5601	154	10	of	of	ADP
ejpam-5601	154	11	cubics	cubic	NOUN
ejpam-5601	154	12	,	,	PUNCT
ejpam-5601	154	13	which	which	PRON
ejpam-5601	154	14	makes	make	VERB
ejpam-5601	154	15	the	the	DET
ejpam-5601	154	16	traditional	traditional	ADJ
ejpam-5601	154	17	calculation	calculation	NOUN
ejpam-5601	154	18	methods	method	NOUN
ejpam-5601	154	19	between	between	ADP
ejpam-5601	154	20	α	α	NOUN
ejpam-5601	154	21	-	-	PUNCT
ejpam-5601	154	22	cuts	cut	NOUN
ejpam-5601	154	23	infeasible	infeasible	ADJ
ejpam-5601	154	24	.	.	PUNCT
ejpam-5601	155	1	therefore	therefore	ADV
ejpam-5601	155	2	,	,	PUNCT
ejpam-5601	155	3	we	we	PRON
ejpam-5601	155	4	adopted	adopt	VERB
ejpam-5601	155	5	a	a	DET
ejpam-5601	155	6	novel	novel	ADJ
ejpam-5601	155	7	approach	approach	NOUN
ejpam-5601	155	8	to	to	PART
ejpam-5601	155	9	reinterpret	reinterpret	VERB
ejpam-5601	155	10	the	the	DET
ejpam-5601	155	11	existing	exist	VERB
ejpam-5601	155	12	method	method	NOUN
ejpam-5601	155	13	and	and	CCONJ
ejpam-5601	155	14	apply	apply	VERB
ejpam-5601	155	15	it	it	PRON
ejpam-5601	155	16	to	to	ADP
ejpam-5601	155	17	cubic	cubic	ADV
ejpam-5601	155	18	-	-	PUNCT
ejpam-5601	155	19	valued	value	VERB
ejpam-5601	155	20	α	α	NOUN
ejpam-5601	155	21	-	-	PUNCT
ejpam-5601	155	22	cuts	cut	NOUN
ejpam-5601	155	23	in	in	ADP
ejpam-5601	155	24	r3	r3	PROPN
ejpam-5601	155	25	.	.	PUNCT
ejpam-5601	156	1	definition	definition	NOUN
ejpam-5601	156	2	5	5	NUM
ejpam-5601	156	3	.	.	PUNCT
ejpam-5601	157	1	a	a	DET
ejpam-5601	157	2	fuzzy	fuzzy	ADJ
ejpam-5601	157	3	set	set	VERB
ejpam-5601	157	4	a	a	PRON
ejpam-5601	157	5	with	with	ADP
ejpam-5601	157	6	a	a	DET
ejpam-5601	157	7	membership	membership	NOUN
ejpam-5601	157	8	function	function	NOUN
ejpam-5601	157	9	µa(x	µa(x	PROPN
ejpam-5601	157	10	,	,	PUNCT
ejpam-5601	157	11	y	y	PROPN
ejpam-5601	157	12	,	,	PUNCT
ejpam-5601	157	13	z	z	NOUN
ejpam-5601	157	14	)	)	PUNCT
ejpam-5601	157	15	=	=	SYM
ejpam-5601	158	1			NUM
ejpam-5601	158	2	1−	1−	NUM
ejpam-5601	159	1	(	(	PUNCT
ejpam-5601	159	2	(	(	PUNCT
ejpam-5601	159	3	x−x1)2	x−x1)2	PROPN
ejpam-5601	159	4	a2	a2	PROPN
ejpam-5601	159	5	+	+	CCONJ
ejpam-5601	159	6	(	(	PUNCT
ejpam-5601	159	7	y−y1)2	y−y1)2	VERB
ejpam-5601	159	8	b2	b2	PROPN
ejpam-5601	159	9	+	+	CCONJ
ejpam-5601	159	10	(	(	PUNCT
ejpam-5601	159	11	z−z1)2	z−z1)2	PROPN
ejpam-5601	159	12	c2	c2	PROPN
ejpam-5601	159	13	)	)	PUNCT
ejpam-5601	159	14	,	,	PUNCT
ejpam-5601	159	15	if	if	SCONJ
ejpam-5601	159	16	b2c2(x−	b2c2(x−	NOUN
ejpam-5601	159	17	x1	x1	NUM
ejpam-5601	159	18	)	)	PUNCT
ejpam-5601	159	19	2	2	NUM
ejpam-5601	160	1	+	+	CCONJ
ejpam-5601	160	2	c2a2(y	c2a2(y	ADP
ejpam-5601	160	3	−	−	PROPN
ejpam-5601	160	4	y1	y1	NOUN
ejpam-5601	160	5	)	)	PUNCT
ejpam-5601	160	6	2	2	NUM
ejpam-5601	161	1	+	+	NOUN
ejpam-5601	161	2	a2b2(z	a2b2(z	NOUN
ejpam-5601	161	3	−	−	NOUN
ejpam-5601	161	4	z1	z1	NUM
ejpam-5601	161	5	)	)	PUNCT
ejpam-5601	161	6	2	2	NUM
ejpam-5601	161	7	≤	≤	PROPN
ejpam-5601	161	8	a2b2c2	a2b2c2	PROPN
ejpam-5601	161	9	,	,	PUNCT
ejpam-5601	161	10	0	0	NUM
ejpam-5601	161	11	,	,	PUNCT
ejpam-5601	161	12	otherwise	otherwise	ADV
ejpam-5601	161	13	,	,	PUNCT
ejpam-5601	161	14	where	where	SCONJ
ejpam-5601	161	15	a	a	DET
ejpam-5601	161	16	,	,	PUNCT
ejpam-5601	161	17	b	b	NOUN
ejpam-5601	161	18	,	,	PUNCT
ejpam-5601	161	19	c	c	X
ejpam-5601	161	20	>	>	X
ejpam-5601	161	21	0	0	NUM
ejpam-5601	161	22	is	be	AUX
ejpam-5601	161	23	called	call	VERB
ejpam-5601	161	24	the	the	DET
ejpam-5601	161	25	3	3	NUM
ejpam-5601	161	26	-	-	PUNCT
ejpam-5601	161	27	dimensional	dimensional	ADJ
ejpam-5601	161	28	quadratic	quadratic	ADJ
ejpam-5601	161	29	fuzzy	fuzzy	ADJ
ejpam-5601	161	30	number	number	NOUN
ejpam-5601	161	31	and	and	CCONJ
ejpam-5601	161	32	denoted	denote	VERB
ejpam-5601	161	33	by	by	ADP
ejpam-5601	161	34	[	[	X
ejpam-5601	161	35	a	a	X
ejpam-5601	161	36	,	,	PUNCT
ejpam-5601	161	37	x1	x1	PROPN
ejpam-5601	161	38	,	,	PUNCT
ejpam-5601	161	39	b	b	PROPN
ejpam-5601	161	40	,	,	PUNCT
ejpam-5601	161	41	y1	y1	PROPN
ejpam-5601	161	42	,	,	PUNCT
ejpam-5601	161	43	c	c	X
ejpam-5601	161	44	,	,	PUNCT
ejpam-5601	161	45	z1	z1	NOUN
ejpam-5601	161	46	]	]	X
ejpam-5601	161	47	3	3	X
ejpam-5601	161	48	.	.	X
ejpam-5601	161	49	note	note	VERB
ejpam-5601	161	50	that	that	SCONJ
ejpam-5601	161	51	µa(x	µa(x	ADP
ejpam-5601	161	52	,	,	PUNCT
ejpam-5601	161	53	y	y	NOUN
ejpam-5601	161	54	)	)	PUNCT
ejpam-5601	161	55	forms	form	VERB
ejpam-5601	161	56	a	a	DET
ejpam-5601	161	57	cone	cone	NOUN
ejpam-5601	161	58	in	in	ADP
ejpam-5601	161	59	r2	r2	PROPN
ejpam-5601	161	60	,	,	PUNCT
ejpam-5601	161	61	but	but	CCONJ
ejpam-5601	161	62	we	we	PRON
ejpam-5601	161	63	can	can	AUX
ejpam-5601	161	64	not	not	PART
ejpam-5601	161	65	determine	determine	VERB
ejpam-5601	161	66	the	the	DET
ejpam-5601	161	67	shape	shape	NOUN
ejpam-5601	161	68	of	of	ADP
ejpam-5601	161	69	µa(x	µa(x	PROPN
ejpam-5601	161	70	,	,	PUNCT
ejpam-5601	161	71	y	y	PROPN
ejpam-5601	161	72	,	,	PUNCT
ejpam-5601	161	73	z	z	NOUN
ejpam-5601	161	74	)	)	PUNCT
ejpam-5601	161	75	in	in	ADP
ejpam-5601	161	76	r3	r3	PROPN
ejpam-5601	161	77	.	.	PUNCT
ejpam-5601	162	1	the	the	DET
ejpam-5601	162	2	α	α	NOUN
ejpam-5601	162	3	-	-	PUNCT
ejpam-5601	162	4	cut	cut	VERB
ejpam-5601	162	5	aα	aα	NOUN
ejpam-5601	162	6	of	of	ADP
ejpam-5601	162	7	a	a	DET
ejpam-5601	162	8	3	3	NUM
ejpam-5601	162	9	-	-	PUNCT
ejpam-5601	162	10	dimensional	dimensional	ADJ
ejpam-5601	162	11	quadratic	quadratic	ADJ
ejpam-5601	162	12	fuzzy	fuzzy	ADJ
ejpam-5601	162	13	number	number	NOUN
ejpam-5601	162	14	a	a	NOUN
ejpam-5601	163	1	=	=	PUNCT
ejpam-5601	164	1	[	[	X
ejpam-5601	164	2	a	a	X
ejpam-5601	164	3	,	,	PUNCT
ejpam-5601	164	4	x1	x1	PROPN
ejpam-5601	164	5	,	,	PUNCT
ejpam-5601	164	6	b	b	PROPN
ejpam-5601	164	7	,	,	PUNCT
ejpam-5601	164	8	y1	y1	PROPN
ejpam-5601	164	9	,	,	PUNCT
ejpam-5601	164	10	c	c	X
ejpam-5601	164	11	,	,	PUNCT
ejpam-5601	164	12	z1	z1	NOUN
ejpam-5601	164	13	]	]	X
ejpam-5601	164	14	3	3	NUM
ejpam-5601	164	15	is	be	AUX
ejpam-5601	164	16	defined	define	VERB
ejpam-5601	164	17	as	as	ADP
ejpam-5601	164	18	the	the	DET
ejpam-5601	164	19	following	following	NOUN
ejpam-5601	164	20	set	set	NOUN
ejpam-5601	164	21	aα	aα	NOUN
ejpam-5601	164	22	=	=	PRON
ejpam-5601	164	23	{	{	PUNCT
ejpam-5601	164	24	(	(	PUNCT
ejpam-5601	164	25	x	x	X
ejpam-5601	164	26	,	,	PUNCT
ejpam-5601	164	27	y	y	PROPN
ejpam-5601	164	28	,	,	PUNCT
ejpam-5601	164	29	z	z	NOUN
ejpam-5601	164	30	)	)	PUNCT
ejpam-5601	164	31	∈	∈	PROPN
ejpam-5601	164	32	r3	r3	PROPN
ejpam-5601	164	33	∣∣∣	∣∣∣	NOUN
ejpam-5601	164	34	(	(	PUNCT
ejpam-5601	164	35	x−	x−	PROPN
ejpam-5601	164	36	x1	x1	PROPN
ejpam-5601	164	37	)	)	PUNCT
ejpam-5601	164	38	2	2	NUM
ejpam-5601	164	39	a2	a2	PROPN
ejpam-5601	164	40	+	+	CCONJ
ejpam-5601	164	41	(	(	PUNCT
ejpam-5601	164	42	y	y	PROPN
ejpam-5601	164	43	−	−	PROPN
ejpam-5601	164	44	y1	y1	PROPN
ejpam-5601	164	45	)	)	PUNCT
ejpam-5601	164	46	2	2	NUM
ejpam-5601	164	47	b2	b2	NOUN
ejpam-5601	164	48	+	+	CCONJ
ejpam-5601	164	49	(	(	PUNCT
ejpam-5601	164	50	z	z	NOUN
ejpam-5601	164	51	−	−	PROPN
ejpam-5601	164	52	z1	z1	PROPN
ejpam-5601	164	53	)	)	PUNCT
ejpam-5601	164	54	2	2	NUM
ejpam-5601	164	55	c2	c2	PROPN
ejpam-5601	164	56	≤	≤	NUM
ejpam-5601	164	57	1−	1−	NUM
ejpam-5601	164	58	α	α	NOUN
ejpam-5601	164	59	}	}	PUNCT
ejpam-5601	164	60	=	=	SYM
ejpam-5601	164	61	{	{	PUNCT
ejpam-5601	164	62	(	(	PUNCT
ejpam-5601	164	63	x	x	X
ejpam-5601	164	64	,	,	PUNCT
ejpam-5601	164	65	y	y	PROPN
ejpam-5601	164	66	,	,	PUNCT
ejpam-5601	164	67	z	z	NOUN
ejpam-5601	164	68	)	)	PUNCT
ejpam-5601	164	69	∈	∈	PROPN
ejpam-5601	164	70	r3	r3	PROPN
ejpam-5601	164	71	∣∣∣	∣∣∣	NOUN
ejpam-5601	164	72	(	(	PUNCT
ejpam-5601	164	73	x−	x−	PROPN
ejpam-5601	164	74	x1	x1	PROPN
ejpam-5601	164	75	)	)	PUNCT
ejpam-5601	164	76	2	2	NUM
ejpam-5601	164	77	a2(1−	a2(1−	NOUN
ejpam-5601	164	78	α	α	NOUN
ejpam-5601	164	79	)	)	PUNCT
ejpam-5601	165	1	+	+	CCONJ
ejpam-5601	165	2	(	(	PUNCT
ejpam-5601	165	3	y	y	PROPN
ejpam-5601	165	4	−	−	PROPN
ejpam-5601	165	5	y1	y1	PROPN
ejpam-5601	165	6	)	)	PUNCT
ejpam-5601	165	7	2	2	NUM
ejpam-5601	165	8	b2(1−	b2(1−	NOUN
ejpam-5601	165	9	α	α	NOUN
ejpam-5601	165	10	)	)	PUNCT
ejpam-5601	165	11	+	+	CCONJ
ejpam-5601	165	12	(	(	PUNCT
ejpam-5601	165	13	z	z	NOUN
ejpam-5601	165	14	−	−	PROPN
ejpam-5601	165	15	z1	z1	NUM
ejpam-5601	165	16	)	)	PUNCT
ejpam-5601	165	17	2	2	NUM
ejpam-5601	165	18	c2(1−	c2(1−	PROPN
ejpam-5601	165	19	α	α	NOUN
ejpam-5601	165	20	)	)	PUNCT
ejpam-5601	165	21	≤	≤	NOUN
ejpam-5601	165	22	1	1	NUM
ejpam-5601	165	23	}	}	PUNCT
ejpam-5601	165	24	.	.	PUNCT
ejpam-5601	166	1	y.	y.	PROPN
ejpam-5601	166	2	s.	s.	PROPN
ejpam-5601	166	3	yun	yun	PROPN
ejpam-5601	166	4	,	,	PUNCT
ejpam-5601	166	5	b.	b.	PROPN
ejpam-5601	166	6	lee	lee	PROPN
ejpam-5601	166	7	/	/	SYM
ejpam-5601	166	8	eur	eur	PROPN
ejpam-5601	166	9	.	.	PUNCT
ejpam-5601	167	1	j.	j.	PROPN
ejpam-5601	167	2	pure	pure	PROPN
ejpam-5601	167	3	appl	appl	PROPN
ejpam-5601	167	4	.	.	PROPN
ejpam-5601	167	5	math	math	PROPN
ejpam-5601	167	6	,	,	PUNCT
ejpam-5601	167	7	18	18	NUM
ejpam-5601	167	8	(	(	PUNCT
ejpam-5601	167	9	1	1	NUM
ejpam-5601	167	10	)	)	PUNCT
ejpam-5601	167	11	(	(	PUNCT
ejpam-5601	167	12	2025	2025	NUM
ejpam-5601	167	13	)	)	PUNCT
ejpam-5601	167	14	,	,	PUNCT
ejpam-5601	167	15	5601	5601	NUM
ejpam-5601	167	16	8	8	NUM
ejpam-5601	167	17	of	of	ADP
ejpam-5601	167	18	17	17	NUM
ejpam-5601	167	19	definition	definition	NOUN
ejpam-5601	167	20	6	6	NUM
ejpam-5601	167	21	.	.	PUNCT
ejpam-5601	168	1	a	a	DET
ejpam-5601	168	2	3	3	NUM
ejpam-5601	168	3	-	-	PUNCT
ejpam-5601	168	4	dimensional	dimensional	ADJ
ejpam-5601	168	5	fuzzy	fuzzy	ADJ
ejpam-5601	168	6	number	number	NOUN
ejpam-5601	168	7	,	,	PUNCT
ejpam-5601	168	8	a	a	DET
ejpam-5601	168	9	defined	define	VERB
ejpam-5601	168	10	on	on	ADP
ejpam-5601	168	11	r3	r3	PROPN
ejpam-5601	168	12	,	,	PUNCT
ejpam-5601	168	13	is	be	AUX
ejpam-5601	168	14	termed	term	VERB
ejpam-5601	168	15	a	a	DET
ejpam-5601	168	16	convex	convex	ADJ
ejpam-5601	168	17	fuzzy	fuzzy	ADJ
ejpam-5601	168	18	number	number	NOUN
ejpam-5601	168	19	if	if	SCONJ
ejpam-5601	168	20	,	,	PUNCT
ejpam-5601	168	21	for	for	ADP
ejpam-5601	168	22	all	all	DET
ejpam-5601	168	23	α	α	DET
ejpam-5601	168	24	∈	∈	PROPN
ejpam-5601	168	25	(	(	PUNCT
ejpam-5601	168	26	0	0	NUM
ejpam-5601	168	27	,	,	PUNCT
ejpam-5601	168	28	1	1	NUM
ejpam-5601	168	29	)	)	PUNCT
ejpam-5601	168	30	,	,	PUNCT
ejpam-5601	168	31	the	the	DET
ejpam-5601	168	32	α	α	NOUN
ejpam-5601	168	33	-	-	PUNCT
ejpam-5601	168	34	cuts	cut	NOUN
ejpam-5601	168	35	aα	aα	NOUN
ejpam-5601	168	36	=	=	SYM
ejpam-5601	168	37	{	{	PUNCT
ejpam-5601	168	38	(	(	PUNCT
ejpam-5601	168	39	x	x	NOUN
ejpam-5601	168	40	,	,	PUNCT
ejpam-5601	168	41	y	y	PROPN
ejpam-5601	168	42	,	,	PUNCT
ejpam-5601	168	43	z	z	NOUN
ejpam-5601	168	44	)	)	PUNCT
ejpam-5601	168	45	∈	∈	PROPN
ejpam-5601	168	46	r3|µa(x	r3|µa(x	NOUN
ejpam-5601	168	47	,	,	PUNCT
ejpam-5601	168	48	y	y	PROPN
ejpam-5601	168	49	,	,	PUNCT
ejpam-5601	168	50	z	z	NOUN
ejpam-5601	168	51	)	)	PUNCT
ejpam-5601	168	52	≥	≥	NOUN
ejpam-5601	168	53	α	α	NOUN
ejpam-5601	168	54	}	}	PUNCT
ejpam-5601	168	55	represent	represent	VERB
ejpam-5601	168	56	convex	convex	NOUN
ejpam-5601	168	57	subsets	subset	NOUN
ejpam-5601	168	58	in	in	ADP
ejpam-5601	168	59	r3	r3	PROPN
ejpam-5601	168	60	.	.	PUNCT
ejpam-5601	169	1	theorem	theorem	VERB
ejpam-5601	169	2	4	4	NUM
ejpam-5601	169	3	.	.	PUNCT
ejpam-5601	170	1	[	[	X
ejpam-5601	170	2	10	10	NUM
ejpam-5601	170	3	]	]	PUNCT
ejpam-5601	170	4	let	let	VERB
ejpam-5601	170	5	a	a	PRON
ejpam-5601	170	6	be	be	AUX
ejpam-5601	170	7	a	a	DET
ejpam-5601	170	8	continuous	continuous	ADJ
ejpam-5601	170	9	convex	convex	NOUN
ejpam-5601	170	10	fuzzy	fuzzy	ADJ
ejpam-5601	170	11	number	number	NOUN
ejpam-5601	170	12	defined	define	VERB
ejpam-5601	170	13	on	on	ADP
ejpam-5601	170	14	r3	r3	PROPN
ejpam-5601	170	15	,	,	PUNCT
ejpam-5601	170	16	and	and	CCONJ
ejpam-5601	170	17	aα	aα	NOUN
ejpam-5601	170	18	=	=	SYM
ejpam-5601	170	19	{	{	PUNCT
ejpam-5601	170	20	(	(	PUNCT
ejpam-5601	170	21	x	x	NOUN
ejpam-5601	170	22	,	,	PUNCT
ejpam-5601	170	23	y	y	PROPN
ejpam-5601	170	24	,	,	PUNCT
ejpam-5601	170	25	z	z	NOUN
ejpam-5601	170	26	)	)	PUNCT
ejpam-5601	170	27	∈	∈	PROPN
ejpam-5601	170	28	r3|µa(x	r3|µa(x	NOUN
ejpam-5601	170	29	,	,	PUNCT
ejpam-5601	170	30	y	y	PROPN
ejpam-5601	170	31	,	,	PUNCT
ejpam-5601	170	32	z	z	NOUN
ejpam-5601	170	33	)	)	PUNCT
ejpam-5601	170	34	=	=	SYM
ejpam-5601	171	1	α	α	X
ejpam-5601	171	2	}	}	PUNCT
ejpam-5601	171	3	be	be	VERB
ejpam-5601	171	4	the	the	DET
ejpam-5601	171	5	α	α	NOUN
ejpam-5601	171	6	-	-	PUNCT
ejpam-5601	171	7	set	set	NOUN
ejpam-5601	171	8	of	of	ADP
ejpam-5601	171	9	a.	a.	NOUN
ejpam-5601	171	10	then	then	ADV
ejpam-5601	171	11	,	,	PUNCT
ejpam-5601	171	12	for	for	ADP
ejpam-5601	171	13	all	all	DET
ejpam-5601	171	14	α	α	DET
ejpam-5601	171	15	∈	∈	PROPN
ejpam-5601	171	16	(	(	PUNCT
ejpam-5601	171	17	0	0	NUM
ejpam-5601	171	18	,	,	PUNCT
ejpam-5601	171	19	1	1	NUM
ejpam-5601	171	20	)	)	PUNCT
ejpam-5601	171	21	,	,	PUNCT
ejpam-5601	171	22	there	there	PRON
ejpam-5601	171	23	exist	exist	VERB
ejpam-5601	171	24	continuous	continuous	ADJ
ejpam-5601	171	25	functions	function	NOUN
ejpam-5601	171	26	fα	fα	ADP
ejpam-5601	171	27	1	1	NUM
ejpam-5601	171	28	(	(	PUNCT
ejpam-5601	171	29	s	s	NOUN
ejpam-5601	171	30	)	)	PUNCT
ejpam-5601	171	31	,	,	PUNCT
ejpam-5601	172	1	f	f	PROPN
ejpam-5601	172	2	α	α	PROPN
ejpam-5601	172	3	2	2	NUM
ejpam-5601	172	4	(	(	PUNCT
ejpam-5601	172	5	s	s	PROPN
ejpam-5601	172	6	,	,	PUNCT
ejpam-5601	172	7	t	t	PROPN
ejpam-5601	172	8	)	)	PUNCT
ejpam-5601	172	9	,	,	PUNCT
ejpam-5601	172	10	and	and	CCONJ
ejpam-5601	172	11	fα	fα	ADP
ejpam-5601	172	12	3	3	NUM
ejpam-5601	172	13	(	(	PUNCT
ejpam-5601	172	14	s	s	PROPN
ejpam-5601	172	15	,	,	PUNCT
ejpam-5601	172	16	t)(0	t)(0	NUM
ejpam-5601	172	17	≤	≤	PROPN
ejpam-5601	172	18	s	s	VERB
ejpam-5601	172	19	≤	≤	NOUN
ejpam-5601	172	20	2π	2π	NOUN
ejpam-5601	172	21	,	,	PUNCT
ejpam-5601	172	22	0	0	NUM
ejpam-5601	172	23	≤	≤	NUM
ejpam-5601	172	24	t	t	PROPN
ejpam-5601	172	25	≤	≤	NUM
ejpam-5601	172	26	π	π	PROPN
ejpam-5601	172	27	2	2	X
ejpam-5601	172	28	)	)	PUNCT
ejpam-5601	172	29	such	such	ADJ
ejpam-5601	172	30	that	that	DET
ejpam-5601	172	31	aα	aα	NOUN
ejpam-5601	172	32	=	=	PRON
ejpam-5601	172	33	{	{	PUNCT
ejpam-5601	172	34	(	(	PUNCT
ejpam-5601	172	35	fα	fα	ADP
ejpam-5601	172	36	1	1	NUM
ejpam-5601	172	37	(	(	PUNCT
ejpam-5601	172	38	s	s	NOUN
ejpam-5601	172	39	)	)	PUNCT
ejpam-5601	172	40	,	,	PUNCT
ejpam-5601	172	41	f	f	PROPN
ejpam-5601	172	42	α	α	PROPN
ejpam-5601	172	43	2	2	NUM
ejpam-5601	172	44	(	(	PUNCT
ejpam-5601	172	45	s	s	PROPN
ejpam-5601	172	46	,	,	PUNCT
ejpam-5601	172	47	t	t	PROPN
ejpam-5601	172	48	)	)	PUNCT
ejpam-5601	172	49	,	,	PUNCT
ejpam-5601	172	50	f	f	PROPN
ejpam-5601	172	51	α	α	PROPN
ejpam-5601	172	52	3	3	NUM
ejpam-5601	172	53	(	(	PUNCT
ejpam-5601	172	54	s	s	PROPN
ejpam-5601	172	55	,	,	PUNCT
ejpam-5601	172	56	t	t	PROPN
ejpam-5601	172	57	)	)	PUNCT
ejpam-5601	172	58	)	)	PUNCT
ejpam-5601	173	1	∈	∈	PROPN
ejpam-5601	173	2	r3|0	r3|0	PROPN
ejpam-5601	173	3	≤	≤	PROPN
ejpam-5601	173	4	s	s	PART
ejpam-5601	173	5	≤	≤	NOUN
ejpam-5601	173	6	2π,−π	2π,−π	NUM
ejpam-5601	173	7	2	2	NUM
ejpam-5601	173	8	≤	≤	NOUN
ejpam-5601	173	9	t	t	PROPN
ejpam-5601	173	10	≤	≤	NUM
ejpam-5601	173	11	π	π	PROPN
ejpam-5601	173	12	2	2	NUM
ejpam-5601	173	13	}	}	PUNCT
ejpam-5601	173	14	.	.	PUNCT
ejpam-5601	174	1	definition	definition	NOUN
ejpam-5601	174	2	7	7	NUM
ejpam-5601	174	3	.	.	PUNCT
ejpam-5601	175	1	let	let	VERB
ejpam-5601	175	2	a	a	PRON
ejpam-5601	175	3	and	and	CCONJ
ejpam-5601	175	4	b	b	NOUN
ejpam-5601	175	5	are	be	AUX
ejpam-5601	175	6	two	two	NUM
ejpam-5601	175	7	continuous	continuous	ADJ
ejpam-5601	175	8	convex	convex	NOUN
ejpam-5601	175	9	fuzzy	fuzzy	ADJ
ejpam-5601	175	10	numbers	number	NOUN
ejpam-5601	175	11	defined	define	VERB
ejpam-5601	175	12	on	on	ADP
ejpam-5601	175	13	r3	r3	PROPN
ejpam-5601	175	14	and	and	CCONJ
ejpam-5601	175	15	aα	aα	NOUN
ejpam-5601	175	16	=	=	SYM
ejpam-5601	175	17	{	{	PUNCT
ejpam-5601	175	18	(	(	PUNCT
ejpam-5601	175	19	x	x	NOUN
ejpam-5601	175	20	,	,	PUNCT
ejpam-5601	175	21	y	y	PROPN
ejpam-5601	175	22	,	,	PUNCT
ejpam-5601	175	23	z	z	NOUN
ejpam-5601	175	24	)	)	PUNCT
ejpam-5601	175	25	∈	∈	PROPN
ejpam-5601	175	26	r3|µa(x	r3|µa(x	NOUN
ejpam-5601	175	27	,	,	PUNCT
ejpam-5601	175	28	y	y	PROPN
ejpam-5601	175	29	,	,	PUNCT
ejpam-5601	175	30	z	z	NOUN
ejpam-5601	175	31	)	)	PUNCT
ejpam-5601	176	1	=	=	SYM
ejpam-5601	176	2	α	α	X
ejpam-5601	176	3	}	}	PUNCT
ejpam-5601	176	4	=	=	PRON
ejpam-5601	176	5	{	{	PUNCT
ejpam-5601	176	6	(	(	PUNCT
ejpam-5601	176	7	fα	fα	ADP
ejpam-5601	176	8	1	1	NUM
ejpam-5601	176	9	(	(	PUNCT
ejpam-5601	176	10	s	s	NOUN
ejpam-5601	176	11	)	)	PUNCT
ejpam-5601	176	12	,	,	PUNCT
ejpam-5601	176	13	f	f	PROPN
ejpam-5601	176	14	α	α	PROPN
ejpam-5601	176	15	2	2	NUM
ejpam-5601	176	16	(	(	PUNCT
ejpam-5601	176	17	s	s	PROPN
ejpam-5601	176	18	,	,	PUNCT
ejpam-5601	176	19	t	t	PROPN
ejpam-5601	176	20	)	)	PUNCT
ejpam-5601	176	21	,	,	PUNCT
ejpam-5601	176	22	f	f	PROPN
ejpam-5601	176	23	α	α	PROPN
ejpam-5601	176	24	3	3	NUM
ejpam-5601	176	25	(	(	PUNCT
ejpam-5601	176	26	s	s	PROPN
ejpam-5601	176	27	,	,	PUNCT
ejpam-5601	176	28	t	t	PROPN
ejpam-5601	176	29	)	)	PUNCT
ejpam-5601	176	30	)	)	PUNCT
ejpam-5601	177	1	∈	∈	PROPN
ejpam-5601	177	2	r3|0	r3|0	PROPN
ejpam-5601	177	3	≤	≤	PROPN
ejpam-5601	177	4	s	s	PART
ejpam-5601	177	5	≤	≤	NOUN
ejpam-5601	177	6	2π,−π	2π,−π	NUM
ejpam-5601	177	7	2	2	NUM
ejpam-5601	177	8	≤	≤	NOUN
ejpam-5601	177	9	t	t	PROPN
ejpam-5601	177	10	≤	≤	NUM
ejpam-5601	177	11	π	π	PROPN
ejpam-5601	177	12	2	2	NUM
ejpam-5601	177	13	}	}	PUNCT
ejpam-5601	177	14	,	,	PUNCT
ejpam-5601	177	15	bα	bα	NOUN
ejpam-5601	177	16	=	=	SYM
ejpam-5601	177	17	{	{	PUNCT
ejpam-5601	177	18	(	(	PUNCT
ejpam-5601	177	19	x	x	NOUN
ejpam-5601	177	20	,	,	PUNCT
ejpam-5601	177	21	y	y	PROPN
ejpam-5601	177	22	,	,	PUNCT
ejpam-5601	177	23	z	z	NOUN
ejpam-5601	177	24	)	)	PUNCT
ejpam-5601	177	25	∈	∈	PROPN
ejpam-5601	178	1	r3|µb(x	r3|µb(x	NOUN
ejpam-5601	178	2	,	,	PUNCT
ejpam-5601	178	3	y	y	PROPN
ejpam-5601	178	4	,	,	PUNCT
ejpam-5601	178	5	z	z	NOUN
ejpam-5601	178	6	)	)	PUNCT
ejpam-5601	178	7	=	=	SYM
ejpam-5601	179	1	α	α	X
ejpam-5601	179	2	}	}	PUNCT
ejpam-5601	179	3	=	=	SYM
ejpam-5601	179	4	{	{	PUNCT
ejpam-5601	179	5	(	(	PUNCT
ejpam-5601	179	6	gα1	gα1	X
ejpam-5601	179	7	(	(	PUNCT
ejpam-5601	179	8	s	s	NOUN
ejpam-5601	179	9	)	)	PUNCT
ejpam-5601	179	10	,	,	PUNCT
ejpam-5601	179	11	gα2	gα2	PROPN
ejpam-5601	179	12	(	(	PUNCT
ejpam-5601	179	13	s	s	PROPN
ejpam-5601	179	14	,	,	PUNCT
ejpam-5601	179	15	t	t	PROPN
ejpam-5601	179	16	)	)	PUNCT
ejpam-5601	179	17	,	,	PUNCT
ejpam-5601	179	18	gα3	gα3	PROPN
ejpam-5601	179	19	(	(	PUNCT
ejpam-5601	179	20	s	s	PROPN
ejpam-5601	179	21	,	,	PUNCT
ejpam-5601	179	22	t	t	PROPN
ejpam-5601	179	23	)	)	PUNCT
ejpam-5601	179	24	)	)	PUNCT
ejpam-5601	180	1	∈	∈	PROPN
ejpam-5601	180	2	r3|0	r3|0	PROPN
ejpam-5601	180	3	≤	≤	PROPN
ejpam-5601	180	4	s	s	PART
ejpam-5601	180	5	≤	≤	NOUN
ejpam-5601	180	6	2π,−π	2π,−π	NUM
ejpam-5601	180	7	2	2	NUM
ejpam-5601	180	8	≤	≤	NOUN
ejpam-5601	180	9	t	t	PROPN
ejpam-5601	180	10	≤	≤	NUM
ejpam-5601	180	11	π	π	X
ejpam-5601	180	12	2	2	NUM
ejpam-5601	180	13	}	}	PUNCT
ejpam-5601	180	14	be	be	AUX
ejpam-5601	180	15	the	the	DET
ejpam-5601	180	16	α	α	NOUN
ejpam-5601	180	17	-	-	PUNCT
ejpam-5601	180	18	sets	set	NOUN
ejpam-5601	180	19	of	of	ADP
ejpam-5601	180	20	a	a	PRON
ejpam-5601	180	21	and	and	CCONJ
ejpam-5601	180	22	b	b	NOUN
ejpam-5601	180	23	,	,	PUNCT
ejpam-5601	180	24	respectively	respectively	ADV
ejpam-5601	180	25	.	.	PUNCT
ejpam-5601	181	1	for	for	ADP
ejpam-5601	181	2	α	α	PROPN
ejpam-5601	181	3	∈	∈	PROPN
ejpam-5601	181	4	(	(	PUNCT
ejpam-5601	181	5	0	0	NUM
ejpam-5601	181	6	,	,	PUNCT
ejpam-5601	181	7	1	1	NUM
ejpam-5601	181	8	)	)	PUNCT
ejpam-5601	181	9	,	,	PUNCT
ejpam-5601	181	10	we	we	PRON
ejpam-5601	181	11	define	define	VERB
ejpam-5601	181	12	the	the	DET
ejpam-5601	181	13	parametric	parametric	ADJ
ejpam-5601	181	14	addition	addition	NOUN
ejpam-5601	181	15	,	,	PUNCT
ejpam-5601	181	16	parametric	parametric	ADJ
ejpam-5601	181	17	subtraction	subtraction	NOUN
ejpam-5601	181	18	,	,	PUNCT
ejpam-5601	181	19	parametric	parametric	ADJ
ejpam-5601	181	20	multiplication	multiplication	NOUN
ejpam-5601	181	21	,	,	PUNCT
ejpam-5601	181	22	and	and	CCONJ
ejpam-5601	181	23	parametric	parametric	ADJ
ejpam-5601	181	24	division	division	NOUN
ejpam-5601	181	25	of	of	ADP
ejpam-5601	181	26	two	two	NUM
ejpam-5601	181	27	fuzzy	fuzzy	ADJ
ejpam-5601	181	28	numbers	number	NOUN
ejpam-5601	181	29	a	a	DET
ejpam-5601	181	30	and	and	CCONJ
ejpam-5601	181	31	b	b	NOUN
ejpam-5601	181	32	as	as	ADP
ejpam-5601	181	33	fuzzy	fuzzy	ADJ
ejpam-5601	181	34	numbers	number	NOUN
ejpam-5601	181	35	with	with	ADP
ejpam-5601	181	36	α	α	NOUN
ejpam-5601	181	37	-	-	PUNCT
ejpam-5601	181	38	sets	set	NOUN
ejpam-5601	181	39	as	as	SCONJ
ejpam-5601	181	40	follows	follow	VERB
ejpam-5601	181	41	:	:	PUNCT
ejpam-5601	181	42	(	(	PUNCT
ejpam-5601	181	43	1	1	X
ejpam-5601	181	44	)	)	PUNCT
ejpam-5601	181	45	parametric	parametric	ADJ
ejpam-5601	181	46	addition	addition	NOUN
ejpam-5601	181	47	a(+)pb	a(+)pb	PROPN
ejpam-5601	181	48	:	:	PUNCT
ejpam-5601	181	49	(	(	PUNCT
ejpam-5601	181	50	a(+)pb)α	a(+)pb)α	NOUN
ejpam-5601	181	51	=	=	SYM
ejpam-5601	181	52	{	{	PUNCT
ejpam-5601	181	53	(	(	PUNCT
ejpam-5601	181	54	fα	fα	ADP
ejpam-5601	181	55	1	1	NUM
ejpam-5601	181	56	(	(	PUNCT
ejpam-5601	181	57	s	s	X
ejpam-5601	181	58	)	)	PUNCT
ejpam-5601	181	59	+	+	CCONJ
ejpam-5601	181	60	gα1	gα1	NOUN
ejpam-5601	181	61	(	(	PUNCT
ejpam-5601	181	62	s	s	NOUN
ejpam-5601	181	63	)	)	PUNCT
ejpam-5601	181	64	,	,	PUNCT
ejpam-5601	181	65	f	f	PROPN
ejpam-5601	181	66	α	α	PROPN
ejpam-5601	181	67	2	2	NUM
ejpam-5601	181	68	(	(	PUNCT
ejpam-5601	181	69	s	s	PROPN
ejpam-5601	181	70	,	,	PUNCT
ejpam-5601	181	71	t	t	PROPN
ejpam-5601	181	72	)	)	PUNCT
ejpam-5601	182	1	+	+	NUM
ejpam-5601	182	2	gα2	gα2	NOUN
ejpam-5601	182	3	(	(	PUNCT
ejpam-5601	182	4	s	s	PROPN
ejpam-5601	182	5	,	,	PUNCT
ejpam-5601	182	6	t	t	PROPN
ejpam-5601	182	7	)	)	PUNCT
ejpam-5601	182	8	,	,	PUNCT
ejpam-5601	182	9	f	f	PROPN
ejpam-5601	182	10	α	α	PROPN
ejpam-5601	182	11	3	3	NUM
ejpam-5601	182	12	(	(	PUNCT
ejpam-5601	182	13	s	s	PROPN
ejpam-5601	182	14	,	,	PUNCT
ejpam-5601	182	15	t	t	PROPN
ejpam-5601	182	16	)	)	PUNCT
ejpam-5601	183	1	+	+	NUM
ejpam-5601	183	2	gα3	gα3	NOUN
ejpam-5601	183	3	(	(	PUNCT
ejpam-5601	183	4	s	s	PROPN
ejpam-5601	183	5	,	,	PUNCT
ejpam-5601	183	6	t	t	PROPN
ejpam-5601	183	7	)	)	PUNCT
ejpam-5601	183	8	)	)	PUNCT
ejpam-5601	184	1	∈	∈	PROPN
ejpam-5601	184	2	r3|	r3|	NOUN
ejpam-5601	184	3	0	0	X
ejpam-5601	184	4	≤	≤	NUM
ejpam-5601	184	5	s	s	PART
ejpam-5601	184	6	≤	≤	NOUN
ejpam-5601	184	7	2π,−π	2π,−π	NUM
ejpam-5601	184	8	2	2	NUM
ejpam-5601	184	9	≤	≤	NOUN
ejpam-5601	184	10	t	t	PROPN
ejpam-5601	184	11	≤	≤	NUM
ejpam-5601	184	12	π	π	PROPN
ejpam-5601	184	13	2	2	X
ejpam-5601	184	14	}	}	PUNCT
ejpam-5601	184	15	(	(	PUNCT
ejpam-5601	184	16	2	2	X
ejpam-5601	184	17	)	)	PUNCT
ejpam-5601	184	18	parametric	parametric	ADJ
ejpam-5601	184	19	subtraction	subtraction	NOUN
ejpam-5601	184	20	a(−)pb	a(−)pb	PROPN
ejpam-5601	184	21	:	:	PUNCT
ejpam-5601	184	22	(	(	PUNCT
ejpam-5601	184	23	a(−)pb)α	a(−)pb)α	NOUN
ejpam-5601	184	24	=	=	SYM
ejpam-5601	184	25	{	{	PUNCT
ejpam-5601	184	26	(	(	PUNCT
ejpam-5601	184	27	fα	fα	ADP
ejpam-5601	184	28	1	1	NUM
ejpam-5601	184	29	(	(	PUNCT
ejpam-5601	184	30	s)−	s)−	NOUN
ejpam-5601	184	31	gα1	gα1	NOUN
ejpam-5601	184	32	(	(	PUNCT
ejpam-5601	184	33	s+	s+	X
ejpam-5601	184	34	π	π	PROPN
ejpam-5601	184	35	)	)	PUNCT
ejpam-5601	184	36	,	,	PUNCT
ejpam-5601	184	37	fα	fα	ADP
ejpam-5601	184	38	2	2	NUM
ejpam-5601	184	39	(	(	PUNCT
ejpam-5601	184	40	s	s	X
ejpam-5601	184	41	,	,	PUNCT
ejpam-5601	184	42	t)−	t)−	PROPN
ejpam-5601	184	43	gα2	gα2	NOUN
ejpam-5601	184	44	(	(	PUNCT
ejpam-5601	184	45	s+	s+	X
ejpam-5601	184	46	π	π	PROPN
ejpam-5601	184	47	,	,	PUNCT
ejpam-5601	184	48	t	t	PROPN
ejpam-5601	184	49	)	)	PUNCT
ejpam-5601	184	50	,	,	PUNCT
ejpam-5601	184	51	fα	fα	ADP
ejpam-5601	184	52	3	3	NUM
ejpam-5601	184	53	(	(	PUNCT
ejpam-5601	184	54	s	s	X
ejpam-5601	184	55	,	,	PUNCT
ejpam-5601	184	56	t)−	t)−	PROPN
ejpam-5601	184	57	gα3	gα3	PROPN
ejpam-5601	184	58	(	(	PUNCT
ejpam-5601	184	59	s+	s+	X
ejpam-5601	184	60	π	π	PROPN
ejpam-5601	184	61	,	,	PUNCT
ejpam-5601	184	62	t	t	PROPN
ejpam-5601	184	63	)	)	PUNCT
ejpam-5601	184	64	)	)	PUNCT
ejpam-5601	185	1	∈	∈	PROPN
ejpam-5601	185	2	r3|0	r3|0	PROPN
ejpam-5601	185	3	≤	≤	PROPN
ejpam-5601	185	4	s	s	PART
ejpam-5601	185	5	≤	≤	NUM
ejpam-5601	185	6	π,−π	π,−π	NOUN
ejpam-5601	185	7	2	2	NUM
ejpam-5601	185	8	≤	≤	NOUN
ejpam-5601	185	9	t	t	PROPN
ejpam-5601	185	10	≤	≤	NUM
ejpam-5601	185	11	π	π	PROPN
ejpam-5601	185	12	2	2	NUM
ejpam-5601	185	13	}	}	PUNCT
ejpam-5601	185	14	,	,	PUNCT
ejpam-5601	185	15	(	(	PUNCT
ejpam-5601	185	16	a(−)pb)α	a(−)pb)α	NOUN
ejpam-5601	185	17	=	=	SYM
ejpam-5601	185	18	{	{	PUNCT
ejpam-5601	185	19	(	(	PUNCT
ejpam-5601	185	20	fα	fα	ADP
ejpam-5601	185	21	1	1	NUM
ejpam-5601	185	22	(	(	PUNCT
ejpam-5601	185	23	s)−	s)−	NOUN
ejpam-5601	185	24	gα1	gα1	NOUN
ejpam-5601	185	25	(	(	PUNCT
ejpam-5601	185	26	s−	s−	PROPN
ejpam-5601	185	27	π	π	PROPN
ejpam-5601	185	28	)	)	PUNCT
ejpam-5601	185	29	,	,	PUNCT
ejpam-5601	185	30	fα	fα	ADP
ejpam-5601	185	31	2	2	NUM
ejpam-5601	185	32	(	(	PUNCT
ejpam-5601	185	33	s	s	X
ejpam-5601	185	34	,	,	PUNCT
ejpam-5601	185	35	t)−	t)−	PROPN
ejpam-5601	185	36	gα2	gα2	NOUN
ejpam-5601	185	37	(	(	PUNCT
ejpam-5601	185	38	s−	s−	PROPN
ejpam-5601	185	39	π	π	PROPN
ejpam-5601	185	40	,	,	PUNCT
ejpam-5601	185	41	t	t	PROPN
ejpam-5601	185	42	)	)	PUNCT
ejpam-5601	185	43	,	,	PUNCT
ejpam-5601	185	44	fα	fα	ADP
ejpam-5601	185	45	3	3	NUM
ejpam-5601	185	46	(	(	PUNCT
ejpam-5601	185	47	s	s	X
ejpam-5601	185	48	,	,	PUNCT
ejpam-5601	185	49	t)−	t)−	PROPN
ejpam-5601	185	50	gα3	gα3	NOUN
ejpam-5601	185	51	(	(	PUNCT
ejpam-5601	185	52	s−	s−	PROPN
ejpam-5601	185	53	π	π	PROPN
ejpam-5601	185	54	,	,	PUNCT
ejpam-5601	185	55	t	t	PROPN
ejpam-5601	185	56	)	)	PUNCT
ejpam-5601	185	57	)	)	PUNCT
ejpam-5601	186	1	∈	∈	PROPN
ejpam-5601	186	2	r3|π	r3|π	NOUN
ejpam-5601	186	3	≤	≤	NOUN
ejpam-5601	186	4	s	s	PART
ejpam-5601	186	5	≤	≤	NOUN
ejpam-5601	186	6	2π,−π	2π,−π	NUM
ejpam-5601	186	7	2	2	NUM
ejpam-5601	186	8	≤	≤	NOUN
ejpam-5601	186	9	t	t	PROPN
ejpam-5601	186	10	≤	≤	NUM
ejpam-5601	186	11	π	π	PROPN
ejpam-5601	186	12	2	2	X
ejpam-5601	186	13	}	}	PUNCT
ejpam-5601	186	14	(	(	PUNCT
ejpam-5601	186	15	3	3	X
ejpam-5601	186	16	)	)	PUNCT
ejpam-5601	186	17	parametric	parametric	ADJ
ejpam-5601	186	18	multiplication	multiplication	NOUN
ejpam-5601	186	19	a(·)pb	a(·)pb	PROPN
ejpam-5601	186	20	:	:	PUNCT
ejpam-5601	186	21	(	(	PUNCT
ejpam-5601	186	22	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	186	23	=	=	SYM
ejpam-5601	186	24	{	{	PUNCT
ejpam-5601	186	25	(	(	PUNCT
ejpam-5601	186	26	fα	fα	ADP
ejpam-5601	186	27	1	1	NUM
ejpam-5601	186	28	(	(	PUNCT
ejpam-5601	186	29	s	s	NOUN
ejpam-5601	186	30	)	)	PUNCT
ejpam-5601	186	31	·	·	PUNCT
ejpam-5601	186	32	gα1	gα1	X
ejpam-5601	186	33	(	(	PUNCT
ejpam-5601	186	34	s	s	NOUN
ejpam-5601	186	35	)	)	PUNCT
ejpam-5601	186	36	,	,	PUNCT
ejpam-5601	186	37	fα	fα	ADP
ejpam-5601	186	38	2	2	NUM
ejpam-5601	186	39	(	(	PUNCT
ejpam-5601	186	40	s	s	PROPN
ejpam-5601	186	41	,	,	PUNCT
ejpam-5601	186	42	t	t	PROPN
ejpam-5601	186	43	)	)	PUNCT
ejpam-5601	186	44	·	·	PUNCT
ejpam-5601	187	1	gα2	gα2	NOUN
ejpam-5601	187	2	(	(	PUNCT
ejpam-5601	187	3	s	s	PROPN
ejpam-5601	187	4	,	,	PUNCT
ejpam-5601	187	5	t	t	PROPN
ejpam-5601	187	6	)	)	PUNCT
ejpam-5601	187	7	,	,	PUNCT
ejpam-5601	187	8	fα	fα	ADP
ejpam-5601	187	9	3	3	NUM
ejpam-5601	187	10	(	(	PUNCT
ejpam-5601	187	11	s	s	PROPN
ejpam-5601	187	12	,	,	PUNCT
ejpam-5601	187	13	t	t	PROPN
ejpam-5601	187	14	)	)	PUNCT
ejpam-5601	187	15	·	·	PUNCT
ejpam-5601	187	16	gα3	gα3	PROPN
ejpam-5601	187	17	(	(	PUNCT
ejpam-5601	187	18	s	s	PROPN
ejpam-5601	187	19	,	,	PUNCT
ejpam-5601	187	20	t	t	PROPN
ejpam-5601	187	21	)	)	PUNCT
ejpam-5601	187	22	)	)	PUNCT
ejpam-5601	188	1	∈	∈	PROPN
ejpam-5601	188	2	r3|	r3|	NOUN
ejpam-5601	188	3	0	0	X
ejpam-5601	188	4	≤	≤	NUM
ejpam-5601	188	5	s	s	PART
ejpam-5601	188	6	≤	≤	NOUN
ejpam-5601	188	7	2π,−π	2π,−π	NUM
ejpam-5601	188	8	2	2	NUM
ejpam-5601	188	9	≤	≤	NOUN
ejpam-5601	188	10	t	t	PROPN
ejpam-5601	188	11	≤	≤	NUM
ejpam-5601	188	12	π	π	PROPN
ejpam-5601	188	13	2	2	X
ejpam-5601	188	14	}	}	PUNCT
ejpam-5601	188	15	(	(	PUNCT
ejpam-5601	188	16	4	4	X
ejpam-5601	188	17	)	)	PUNCT
ejpam-5601	188	18	parametric	parametric	ADJ
ejpam-5601	188	19	division	division	NOUN
ejpam-5601	188	20	a(/)pb	a(/)pb	PROPN
ejpam-5601	188	21	:	:	PUNCT
ejpam-5601	188	22	y.	y.	PROPN
ejpam-5601	188	23	s.	s.	PROPN
ejpam-5601	188	24	yun	yun	PROPN
ejpam-5601	188	25	,	,	PUNCT
ejpam-5601	188	26	b.	b.	PROPN
ejpam-5601	188	27	lee	lee	PROPN
ejpam-5601	188	28	/	/	SYM
ejpam-5601	188	29	eur	eur	PROPN
ejpam-5601	188	30	.	.	PUNCT
ejpam-5601	189	1	j.	j.	PROPN
ejpam-5601	189	2	pure	pure	PROPN
ejpam-5601	189	3	appl	appl	PROPN
ejpam-5601	189	4	.	.	PROPN
ejpam-5601	189	5	math	math	PROPN
ejpam-5601	189	6	,	,	PUNCT
ejpam-5601	189	7	18	18	NUM
ejpam-5601	189	8	(	(	PUNCT
ejpam-5601	189	9	1	1	NUM
ejpam-5601	189	10	)	)	PUNCT
ejpam-5601	189	11	(	(	PUNCT
ejpam-5601	189	12	2025	2025	NUM
ejpam-5601	189	13	)	)	PUNCT
ejpam-5601	189	14	,	,	PUNCT
ejpam-5601	189	15	5601	5601	NUM
ejpam-5601	189	16	9	9	NUM
ejpam-5601	189	17	of	of	ADP
ejpam-5601	189	18	17	17	NUM
ejpam-5601	189	19	(	(	PUNCT
ejpam-5601	189	20	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	189	21	=	=	PRON
ejpam-5601	189	22	{	{	PUNCT
ejpam-5601	189	23	(	(	PUNCT
ejpam-5601	189	24	fα	fα	ADP
ejpam-5601	189	25	1	1	NUM
ejpam-5601	189	26	(	(	PUNCT
ejpam-5601	189	27	s	s	NOUN
ejpam-5601	189	28	)	)	PUNCT
ejpam-5601	189	29	gα1	gα1	NOUN
ejpam-5601	189	30	(	(	PUNCT
ejpam-5601	189	31	s+	s+	X
ejpam-5601	189	32	π	π	PROPN
ejpam-5601	189	33	)	)	PUNCT
ejpam-5601	189	34	,	,	PUNCT
ejpam-5601	189	35	fα	fα	ADP
ejpam-5601	189	36	2	2	NUM
ejpam-5601	189	37	(	(	PUNCT
ejpam-5601	189	38	s	s	PROPN
ejpam-5601	189	39	,	,	PUNCT
ejpam-5601	189	40	t	t	PROPN
ejpam-5601	189	41	)	)	PUNCT
ejpam-5601	189	42	gα2	gα2	NOUN
ejpam-5601	189	43	(	(	PUNCT
ejpam-5601	189	44	s+	s+	X
ejpam-5601	189	45	π	π	PROPN
ejpam-5601	189	46	,	,	PUNCT
ejpam-5601	189	47	t	t	PROPN
ejpam-5601	189	48	)	)	PUNCT
ejpam-5601	189	49	,	,	PUNCT
ejpam-5601	189	50	fα	fα	ADP
ejpam-5601	189	51	3	3	NUM
ejpam-5601	189	52	(	(	PUNCT
ejpam-5601	189	53	s	s	PROPN
ejpam-5601	189	54	,	,	PUNCT
ejpam-5601	189	55	t	t	PROPN
ejpam-5601	189	56	)	)	PUNCT
ejpam-5601	189	57	gα3	gα3	PROPN
ejpam-5601	189	58	(	(	PUNCT
ejpam-5601	189	59	s+	s+	PUNCT
ejpam-5601	189	60	π	π	PROPN
ejpam-5601	189	61	,	,	PUNCT
ejpam-5601	189	62	t	t	PROPN
ejpam-5601	189	63	)	)	PUNCT
ejpam-5601	189	64	)	)	PUNCT
ejpam-5601	190	1	∈	∈	PROPN
ejpam-5601	190	2	r3|	r3|	NOUN
ejpam-5601	190	3	0	0	NUM
ejpam-5601	190	4	≤	≤	NUM
ejpam-5601	190	5	s	s	PART
ejpam-5601	190	6	≤	≤	NUM
ejpam-5601	190	7	π,−π	π,−π	NOUN
ejpam-5601	190	8	2	2	NUM
ejpam-5601	190	9	≤	≤	NOUN
ejpam-5601	190	10	t	t	PROPN
ejpam-5601	190	11	≤	≤	NUM
ejpam-5601	190	12	π	π	PROPN
ejpam-5601	190	13	2	2	NUM
ejpam-5601	190	14	}	}	PUNCT
ejpam-5601	190	15	,	,	PUNCT
ejpam-5601	190	16	(	(	PUNCT
ejpam-5601	190	17	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	190	18	=	=	PRON
ejpam-5601	190	19	{	{	PUNCT
ejpam-5601	190	20	(	(	PUNCT
ejpam-5601	190	21	fα	fα	ADP
ejpam-5601	190	22	1	1	NUM
ejpam-5601	190	23	(	(	PUNCT
ejpam-5601	190	24	s	s	NOUN
ejpam-5601	190	25	)	)	PUNCT
ejpam-5601	190	26	gα1	gα1	NOUN
ejpam-5601	190	27	(	(	PUNCT
ejpam-5601	190	28	s−	s−	PROPN
ejpam-5601	190	29	π	π	PROPN
ejpam-5601	190	30	)	)	PUNCT
ejpam-5601	190	31	,	,	PUNCT
ejpam-5601	190	32	fα	fα	ADP
ejpam-5601	190	33	2	2	NUM
ejpam-5601	190	34	(	(	PUNCT
ejpam-5601	190	35	s	s	PROPN
ejpam-5601	190	36	,	,	PUNCT
ejpam-5601	190	37	t	t	PROPN
ejpam-5601	190	38	)	)	PUNCT
ejpam-5601	190	39	gα2	gα2	NOUN
ejpam-5601	190	40	(	(	PUNCT
ejpam-5601	190	41	s−	s−	PROPN
ejpam-5601	190	42	π	π	PROPN
ejpam-5601	190	43	,	,	PUNCT
ejpam-5601	190	44	t	t	PROPN
ejpam-5601	190	45	)	)	PUNCT
ejpam-5601	190	46	,	,	PUNCT
ejpam-5601	190	47	fα	fα	ADP
ejpam-5601	190	48	3	3	NUM
ejpam-5601	190	49	(	(	PUNCT
ejpam-5601	190	50	s	s	PROPN
ejpam-5601	190	51	,	,	PUNCT
ejpam-5601	190	52	t	t	PROPN
ejpam-5601	190	53	)	)	PUNCT
ejpam-5601	190	54	gα3	gα3	PROPN
ejpam-5601	190	55	(	(	PUNCT
ejpam-5601	190	56	s−	s−	PROPN
ejpam-5601	190	57	π	π	PROPN
ejpam-5601	190	58	,	,	PUNCT
ejpam-5601	190	59	t	t	PROPN
ejpam-5601	190	60	)	)	PUNCT
ejpam-5601	190	61	)	)	PUNCT
ejpam-5601	191	1	∈	∈	PROPN
ejpam-5601	191	2	r3|	r3|	NOUN
ejpam-5601	191	3	π	π	AUX
ejpam-5601	191	4	≤	≤	NUM
ejpam-5601	191	5	s	s	PART
ejpam-5601	191	6	≤	≤	NOUN
ejpam-5601	191	7	2π,−π	2π,−π	NUM
ejpam-5601	191	8	2	2	NUM
ejpam-5601	191	9	≤	≤	NOUN
ejpam-5601	191	10	t	t	PROPN
ejpam-5601	191	11	≤	≤	NUM
ejpam-5601	191	12	π	π	X
ejpam-5601	191	13	2	2	X
ejpam-5601	191	14	}	}	PUNCT
ejpam-5601	191	15	for	for	ADP
ejpam-5601	191	16	α	α	NOUN
ejpam-5601	191	17	=	=	SYM
ejpam-5601	191	18	0	0	PROPN
ejpam-5601	191	19	and	and	CCONJ
ejpam-5601	191	20	α	α	NOUN
ejpam-5601	191	21	=	=	SYM
ejpam-5601	191	22	1	1	NUM
ejpam-5601	191	23	,	,	PUNCT
ejpam-5601	191	24	(	(	PUNCT
ejpam-5601	191	25	a(∗)pb)0	a(∗)pb)0	PROPN
ejpam-5601	191	26	=	=	NOUN
ejpam-5601	191	27	limα→0+(a(∗)pb)α	limα→0+(a(∗)pb)α	NOUN
ejpam-5601	191	28	and	and	CCONJ
ejpam-5601	191	29	(	(	PUNCT
ejpam-5601	191	30	a(∗)pb)1	a(∗)pb)1	PROPN
ejpam-5601	191	31	=	=	SYM
ejpam-5601	191	32	limα→1−(a(∗)pb)α	limα→1−(a(∗)pb)α	PROPN
ejpam-5601	191	33	,	,	PUNCT
ejpam-5601	191	34	where	where	SCONJ
ejpam-5601	191	35	∗	∗	NOUN
ejpam-5601	191	36	=	=	PUNCT
ejpam-5601	192	1	+	+	ADJ
ejpam-5601	192	2	,	,	PUNCT
ejpam-5601	192	3	−	−	PROPN
ejpam-5601	192	4	,	,	PUNCT
ejpam-5601	192	5	·	·	PUNCT
ejpam-5601	192	6	,	,	PUNCT
ejpam-5601	192	7	/.	/.	PUNCT
ejpam-5601	193	1	theorem	theorem	NOUN
ejpam-5601	193	2	5	5	NUM
ejpam-5601	193	3	.	.	PUNCT
ejpam-5601	194	1	let	let	VERB
ejpam-5601	194	2	a	a	PRON
ejpam-5601	194	3	=	=	SYM
ejpam-5601	195	1	[	[	X
ejpam-5601	195	2	a1	a1	NOUN
ejpam-5601	195	3	,	,	PUNCT
ejpam-5601	195	4	x1	x1	PROPN
ejpam-5601	195	5	,	,	PUNCT
ejpam-5601	195	6	b1	b1	NOUN
ejpam-5601	195	7	,	,	PUNCT
ejpam-5601	195	8	y1	y1	PROPN
ejpam-5601	195	9	,	,	PUNCT
ejpam-5601	195	10	c1	c1	NOUN
ejpam-5601	195	11	,	,	PUNCT
ejpam-5601	195	12	z1	z1	PROPN
ejpam-5601	195	13	]	]	X
ejpam-5601	195	14	3	3	NUM
ejpam-5601	195	15	and	and	CCONJ
ejpam-5601	195	16	b	b	NOUN
ejpam-5601	195	17	=	=	SYM
ejpam-5601	196	1	[	[	X
ejpam-5601	196	2	a2	a2	PROPN
ejpam-5601	196	3	,	,	PUNCT
ejpam-5601	196	4	x2	x2	PROPN
ejpam-5601	196	5	,	,	PUNCT
ejpam-5601	196	6	b2	b2	NOUN
ejpam-5601	196	7	,	,	PUNCT
ejpam-5601	196	8	y2	y2	PROPN
ejpam-5601	196	9	,	,	PUNCT
ejpam-5601	196	10	c2	c2	PROPN
ejpam-5601	196	11	,	,	PUNCT
ejpam-5601	196	12	z2	z2	PROPN
ejpam-5601	196	13	]	]	X
ejpam-5601	196	14	3	3	NUM
ejpam-5601	196	15	be	be	VERB
ejpam-5601	196	16	two	two	NUM
ejpam-5601	196	17	3dimensional	3dimensional	ADJ
ejpam-5601	196	18	quadratic	quadratic	ADJ
ejpam-5601	196	19	fuzzy	fuzzy	ADJ
ejpam-5601	196	20	numbers	number	NOUN
ejpam-5601	196	21	.	.	PUNCT
ejpam-5601	197	1	subsequently	subsequently	ADV
ejpam-5601	197	2	,	,	PUNCT
ejpam-5601	197	3	the	the	DET
ejpam-5601	197	4	following	follow	VERB
ejpam-5601	197	5	results	result	NOUN
ejpam-5601	197	6	hold	hold	VERB
ejpam-5601	197	7	:	:	PUNCT
ejpam-5601	197	8	(	(	PUNCT
ejpam-5601	197	9	1	1	X
ejpam-5601	197	10	)	)	PUNCT
ejpam-5601	197	11	a(+)pb	a(+)pb	NOUN
ejpam-5601	197	12	=	=	PUNCT
ejpam-5601	198	1	[	[	PUNCT
ejpam-5601	198	2	a1	a1	NOUN
ejpam-5601	198	3	+	+	CCONJ
ejpam-5601	198	4	a2	a2	PROPN
ejpam-5601	198	5	,	,	PUNCT
ejpam-5601	198	6	x1	x1	PROPN
ejpam-5601	199	1	+	+	CCONJ
ejpam-5601	199	2	x2	x2	PROPN
ejpam-5601	199	3	,	,	PUNCT
ejpam-5601	199	4	b1	b1	NOUN
ejpam-5601	199	5	+	+	CCONJ
ejpam-5601	199	6	b2	b2	NOUN
ejpam-5601	199	7	,	,	PUNCT
ejpam-5601	199	8	y1	y1	NOUN
ejpam-5601	199	9	+	+	CCONJ
ejpam-5601	199	10	y2	y2	PROPN
ejpam-5601	199	11	,	,	PUNCT
ejpam-5601	199	12	c1	c1	PROPN
ejpam-5601	199	13	+	+	CCONJ
ejpam-5601	199	14	c2	c2	PROPN
ejpam-5601	199	15	,	,	PUNCT
ejpam-5601	199	16	z1	z1	PROPN
ejpam-5601	199	17	+	+	CCONJ
ejpam-5601	199	18	z2	z2	PROPN
ejpam-5601	199	19	]	]	SYM
ejpam-5601	199	20	3	3	NUM
ejpam-5601	199	21	(	(	PUNCT
ejpam-5601	199	22	2	2	NUM
ejpam-5601	199	23	)	)	PUNCT
ejpam-5601	199	24	a(−)pb	a(−)pb	NOUN
ejpam-5601	200	1	=	=	PUNCT
ejpam-5601	200	2	[	[	PUNCT
ejpam-5601	200	3	a1	a1	NOUN
ejpam-5601	200	4	+	+	CCONJ
ejpam-5601	200	5	a2	a2	PROPN
ejpam-5601	200	6	,	,	PUNCT
ejpam-5601	200	7	x1	x1	PROPN
ejpam-5601	200	8	−	−	PROPN
ejpam-5601	200	9	x2	x2	PROPN
ejpam-5601	200	10	,	,	PUNCT
ejpam-5601	200	11	b1	b1	NOUN
ejpam-5601	200	12	+	+	CCONJ
ejpam-5601	200	13	b2	b2	NOUN
ejpam-5601	200	14	,	,	PUNCT
ejpam-5601	200	15	y1	y1	NOUN
ejpam-5601	200	16	−	−	PROPN
ejpam-5601	200	17	y2	y2	PROPN
ejpam-5601	200	18	,	,	PUNCT
ejpam-5601	200	19	c1	c1	PROPN
ejpam-5601	200	20	+	+	CCONJ
ejpam-5601	200	21	c2	c2	PROPN
ejpam-5601	200	22	,	,	PUNCT
ejpam-5601	200	23	z1	z1	PROPN
ejpam-5601	200	24	−	−	PROPN
ejpam-5601	200	25	z2	z2	PROPN
ejpam-5601	200	26	]	]	SYM
ejpam-5601	200	27	3	3	NUM
ejpam-5601	200	28	(	(	PUNCT
ejpam-5601	200	29	3	3	NUM
ejpam-5601	200	30	)	)	PUNCT
ejpam-5601	200	31	(	(	PUNCT
ejpam-5601	200	32	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	200	33	=	=	SYM
ejpam-5601	200	34	{	{	PUNCT
ejpam-5601	200	35	(	(	PUNCT
ejpam-5601	200	36	xα(s	xα(s	NUM
ejpam-5601	200	37	)	)	PUNCT
ejpam-5601	200	38	,	,	PUNCT
ejpam-5601	200	39	yα(s	yα(s	PROPN
ejpam-5601	200	40	,	,	PUNCT
ejpam-5601	200	41	t	t	PROPN
ejpam-5601	200	42	)	)	PUNCT
ejpam-5601	200	43	,	,	PUNCT
ejpam-5601	200	44	zα(s	zα(s	NUM
ejpam-5601	200	45	,	,	PUNCT
ejpam-5601	200	46	t	t	PROPN
ejpam-5601	200	47	)	)	PUNCT
ejpam-5601	200	48	)	)	PUNCT
ejpam-5601	201	1	∈	∈	PROPN
ejpam-5601	201	2	r3	r3	PROPN
ejpam-5601	201	3	|	|	ADV
ejpam-5601	201	4	0	0	NUM
ejpam-5601	201	5	≤	≤	NUM
ejpam-5601	201	6	s	s	PART
ejpam-5601	201	7	≤	≤	NOUN
ejpam-5601	201	8	2π,−π	2π,−π	NUM
ejpam-5601	201	9	2	2	NUM
ejpam-5601	201	10	≤	≤	NOUN
ejpam-5601	201	11	t	t	PROPN
ejpam-5601	201	12	≤	≤	NUM
ejpam-5601	201	13	π	π	PROPN
ejpam-5601	201	14	2	2	NUM
ejpam-5601	201	15	}	}	PUNCT
ejpam-5601	201	16	,	,	PUNCT
ejpam-5601	201	17	where	where	SCONJ
ejpam-5601	201	18	xα(s	xα(s	X
ejpam-5601	201	19	)	)	PUNCT
ejpam-5601	201	20	=	=	PUNCT
ejpam-5601	202	1	x1x2	x1x2	PUNCT
ejpam-5601	203	1	+	+	CCONJ
ejpam-5601	203	2	(	(	PUNCT
ejpam-5601	203	3	x1a2	x1a2	X
ejpam-5601	203	4	+	+	X
ejpam-5601	203	5	x2a1	x2a1	X
ejpam-5601	203	6	)	)	PUNCT
ejpam-5601	203	7	√	√	ADP
ejpam-5601	203	8	1−	1−	NUM
ejpam-5601	203	9	α	α	PROPN
ejpam-5601	203	10	cos	cos	PROPN
ejpam-5601	203	11	s+	s+	PUNCT
ejpam-5601	203	12	a1a2(1−	a1a2(1−	PROPN
ejpam-5601	203	13	α	α	NUM
ejpam-5601	203	14	)	)	PUNCT
ejpam-5601	203	15	cos2	cos2	PROPN
ejpam-5601	203	16	s	s	PART
ejpam-5601	203	17	,	,	PUNCT
ejpam-5601	203	18	yα(s	yα(s	PROPN
ejpam-5601	203	19	,	,	PUNCT
ejpam-5601	203	20	t	t	PROPN
ejpam-5601	203	21	)	)	PUNCT
ejpam-5601	203	22	=	=	PUNCT
ejpam-5601	204	1	y1y2	y1y2	PROPN
ejpam-5601	204	2	+	+	CCONJ
ejpam-5601	204	3	(	(	PUNCT
ejpam-5601	204	4	y1b2	y1b2	PROPN
ejpam-5601	204	5	+	+	NUM
ejpam-5601	204	6	y2b1	y2b1	NOUN
ejpam-5601	204	7	)	)	PUNCT
ejpam-5601	204	8	√	√	NOUN
ejpam-5601	204	9	1−	1−	NUM
ejpam-5601	204	10	α	α	PRON
ejpam-5601	204	11	sin	sin	NOUN
ejpam-5601	204	12	s	s	PART
ejpam-5601	204	13	cos	cos	X
ejpam-5601	204	14	t+	t+	VERB
ejpam-5601	204	15	b1b2(1−	b1b2(1−	PROPN
ejpam-5601	204	16	α	α	NOUN
ejpam-5601	204	17	)	)	PUNCT
ejpam-5601	204	18	sin2	sin2	NOUN
ejpam-5601	204	19	s	s	PART
ejpam-5601	204	20	cos2	cos2	PROPN
ejpam-5601	204	21	t	t	PROPN
ejpam-5601	204	22	and	and	CCONJ
ejpam-5601	204	23	zα(s	zα(s	NUM
ejpam-5601	204	24	,	,	PUNCT
ejpam-5601	204	25	t	t	PROPN
ejpam-5601	204	26	)	)	PUNCT
ejpam-5601	204	27	=	=	PUNCT
ejpam-5601	205	1	z1z2	z1z2	PROPN
ejpam-5601	206	1	+	+	CCONJ
ejpam-5601	206	2	(	(	PUNCT
ejpam-5601	206	3	z1c2	z1c2	X
ejpam-5601	206	4	+	+	NUM
ejpam-5601	206	5	z2c1	z2c1	X
ejpam-5601	206	6	)	)	PUNCT
ejpam-5601	206	7	√	√	ADP
ejpam-5601	206	8	1−	1−	NUM
ejpam-5601	206	9	α	α	PRON
ejpam-5601	206	10	sin	sin	NOUN
ejpam-5601	206	11	s	s	PART
ejpam-5601	206	12	sin	sin	NOUN
ejpam-5601	206	13	t+	t+	PUNCT
ejpam-5601	206	14	c1c2(1−	c1c2(1−	PROPN
ejpam-5601	206	15	α	α	NOUN
ejpam-5601	206	16	)	)	PUNCT
ejpam-5601	206	17	sin2	sin2	NOUN
ejpam-5601	206	18	s	s	PART
ejpam-5601	206	19	sin2	sin2	NOUN
ejpam-5601	206	20	t.	t.	PROPN
ejpam-5601	206	21	(	(	PUNCT
ejpam-5601	206	22	4	4	NUM
ejpam-5601	206	23	)	)	PUNCT
ejpam-5601	206	24	(	(	PUNCT
ejpam-5601	206	25	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	206	26	=	=	PRON
ejpam-5601	206	27	{	{	PUNCT
ejpam-5601	206	28	(	(	PUNCT
ejpam-5601	206	29	xα(s	xα(s	NUM
ejpam-5601	206	30	)	)	PUNCT
ejpam-5601	206	31	,	,	PUNCT
ejpam-5601	206	32	yα(s	yα(s	PROPN
ejpam-5601	206	33	,	,	PUNCT
ejpam-5601	206	34	t	t	PROPN
ejpam-5601	206	35	)	)	PUNCT
ejpam-5601	206	36	,	,	PUNCT
ejpam-5601	206	37	zα(s	zα(s	NUM
ejpam-5601	206	38	,	,	PUNCT
ejpam-5601	206	39	t	t	PROPN
ejpam-5601	206	40	)	)	PUNCT
ejpam-5601	206	41	)	)	PUNCT
ejpam-5601	207	1	∈	∈	PROPN
ejpam-5601	207	2	r3	r3	PROPN
ejpam-5601	207	3	|	|	ADV
ejpam-5601	207	4	0	0	NUM
ejpam-5601	207	5	≤	≤	NUM
ejpam-5601	207	6	s	s	PART
ejpam-5601	207	7	≤	≤	NOUN
ejpam-5601	207	8	2π,−π	2π,−π	NUM
ejpam-5601	207	9	2	2	NUM
ejpam-5601	207	10	≤	≤	NOUN
ejpam-5601	207	11	t	t	PROPN
ejpam-5601	207	12	≤	≤	NUM
ejpam-5601	207	13	π	π	PROPN
ejpam-5601	207	14	2	2	NUM
ejpam-5601	207	15	}	}	PUNCT
ejpam-5601	207	16	,	,	PUNCT
ejpam-5601	207	17	where	where	SCONJ
ejpam-5601	207	18	xα(s	xα(s	X
ejpam-5601	207	19	)	)	PUNCT
ejpam-5601	208	1	=	=	SYM
ejpam-5601	209	1	x1	x1	PROPN
ejpam-5601	210	1	+	+	CCONJ
ejpam-5601	210	2	a1	a1	NOUN
ejpam-5601	210	3	√	√	PROPN
ejpam-5601	210	4	1−	1−	NUM
ejpam-5601	210	5	α	α	PROPN
ejpam-5601	210	6	cos	cos	PROPN
ejpam-5601	210	7	s	s	PROPN
ejpam-5601	210	8	x2	x2	PROPN
ejpam-5601	210	9	−	−	PROPN
ejpam-5601	210	10	a2	a2	PROPN
ejpam-5601	210	11	√	√	NOUN
ejpam-5601	210	12	1−	1−	NUM
ejpam-5601	210	13	α	α	PROPN
ejpam-5601	210	14	cos	cos	PROPN
ejpam-5601	210	15	s	s	PROPN
ejpam-5601	210	16	yα(s	yα(s	NUM
ejpam-5601	210	17	,	,	PUNCT
ejpam-5601	210	18	t	t	PROPN
ejpam-5601	210	19	)	)	PUNCT
ejpam-5601	210	20	=	=	PUNCT
ejpam-5601	210	21	y1	y1	NOUN
ejpam-5601	210	22	+	+	CCONJ
ejpam-5601	210	23	b1	b1	NOUN
ejpam-5601	210	24	√	√	NUM
ejpam-5601	210	25	1−	1−	NUM
ejpam-5601	211	1	α	α	PRON
ejpam-5601	211	2	sin	sin	NOUN
ejpam-5601	211	3	s	s	X
ejpam-5601	211	4	cos	cos	PROPN
ejpam-5601	211	5	t	t	NOUN
ejpam-5601	211	6	y2	y2	NOUN
ejpam-5601	211	7	−	−	PROPN
ejpam-5601	211	8	b2	b2	NOUN
ejpam-5601	211	9	√	√	NOUN
ejpam-5601	211	10	1−	1−	NUM
ejpam-5601	211	11	α	α	PRON
ejpam-5601	211	12	sin	sin	NOUN
ejpam-5601	211	13	s	s	X
ejpam-5601	211	14	cos	cos	PROPN
ejpam-5601	211	15	t	t	PROPN
ejpam-5601	211	16	and	and	CCONJ
ejpam-5601	211	17	zα(s	zα(s	NUM
ejpam-5601	211	18	,	,	PUNCT
ejpam-5601	211	19	t	t	PROPN
ejpam-5601	211	20	)	)	PUNCT
ejpam-5601	211	21	=	=	SYM
ejpam-5601	212	1	z1	z1	PROPN
ejpam-5601	212	2	+	+	CCONJ
ejpam-5601	212	3	c1	c1	PROPN
ejpam-5601	212	4	√	√	PROPN
ejpam-5601	212	5	1−	1−	NUM
ejpam-5601	212	6	α	α	PRON
ejpam-5601	212	7	sin	sin	NOUN
ejpam-5601	212	8	s	s	PART
ejpam-5601	212	9	sin	sin	NOUN
ejpam-5601	212	10	t	t	PROPN
ejpam-5601	212	11	z2	z2	PROPN
ejpam-5601	212	12	−	−	PROPN
ejpam-5601	212	13	c2	c2	PROPN
ejpam-5601	212	14	√	√	PROPN
ejpam-5601	212	15	1−	1−	NUM
ejpam-5601	213	1	α	α	PRON
ejpam-5601	213	2	sin	sin	NOUN
ejpam-5601	213	3	s	s	PART
ejpam-5601	213	4	sin	sin	NOUN
ejpam-5601	213	5	t	t	NOUN
ejpam-5601	213	6	.	.	PUNCT
ejpam-5601	214	1	therefore	therefore	ADV
ejpam-5601	214	2	,	,	PUNCT
ejpam-5601	214	3	a(+)pb	a(+)pb	PROPN
ejpam-5601	214	4	and	and	CCONJ
ejpam-5601	214	5	a(−)pb	a(−)pb	PRON
ejpam-5601	214	6	become	become	VERB
ejpam-5601	214	7	3	3	NUM
ejpam-5601	214	8	-	-	PUNCT
ejpam-5601	214	9	dimensional	dimensional	ADJ
ejpam-5601	214	10	quadratic	quadratic	ADJ
ejpam-5601	214	11	fuzzy	fuzzy	ADJ
ejpam-5601	214	12	numbers	number	NOUN
ejpam-5601	214	13	,	,	PUNCT
ejpam-5601	214	14	while	while	SCONJ
ejpam-5601	214	15	a(·)pb	a(·)pb	ADJ
ejpam-5601	214	16	and	and	CCONJ
ejpam-5601	214	17	a(/)pb	a(/)pb	PROPN
ejpam-5601	214	18	do	do	AUX
ejpam-5601	214	19	not	not	PART
ejpam-5601	214	20	qualify	qualify	VERB
ejpam-5601	214	21	as	as	ADP
ejpam-5601	214	22	3	3	NUM
ejpam-5601	214	23	-	-	PUNCT
ejpam-5601	214	24	dimensional	dimensional	ADJ
ejpam-5601	214	25	quadratic	quadratic	ADJ
ejpam-5601	214	26	fuzzy	fuzzy	ADJ
ejpam-5601	214	27	numbers	number	NOUN
ejpam-5601	214	28	.	.	PUNCT
ejpam-5601	215	1	proof	proof	NOUN
ejpam-5601	215	2	.	.	PUNCT
ejpam-5601	216	1	since	since	SCONJ
ejpam-5601	216	2	a	a	PRON
ejpam-5601	216	3	and	and	CCONJ
ejpam-5601	216	4	b	b	NOUN
ejpam-5601	216	5	are	be	AUX
ejpam-5601	216	6	continuous	continuous	ADJ
ejpam-5601	216	7	convex	convex	ADJ
ejpam-5601	216	8	fuzzy	fuzzy	ADJ
ejpam-5601	216	9	numbers	number	NOUN
ejpam-5601	216	10	defined	define	VERB
ejpam-5601	216	11	on	on	ADP
ejpam-5601	216	12	r3	r3	PROPN
ejpam-5601	216	13	,	,	PUNCT
ejpam-5601	216	14	by	by	ADP
ejpam-5601	216	15	theorem	theorem	NOUN
ejpam-5601	216	16	4	4	NUM
ejpam-5601	216	17	,	,	PUNCT
ejpam-5601	216	18	there	there	PRON
ejpam-5601	216	19	exists	exist	VERB
ejpam-5601	216	20	fα	fα	ADP
ejpam-5601	216	21	1	1	NUM
ejpam-5601	216	22	(	(	PUNCT
ejpam-5601	216	23	s	s	NOUN
ejpam-5601	216	24	)	)	PUNCT
ejpam-5601	216	25	,	,	PUNCT
ejpam-5601	216	26	g	g	PROPN
ejpam-5601	216	27	α	α	PROPN
ejpam-5601	216	28	1	1	NUM
ejpam-5601	216	29	(	(	PUNCT
ejpam-5601	216	30	s	s	NOUN
ejpam-5601	216	31	)	)	PUNCT
ejpam-5601	216	32	,	,	PUNCT
ejpam-5601	217	1	f	f	PROPN
ejpam-5601	217	2	α	α	INTJ
ejpam-5601	218	1	i	i	PRON
ejpam-5601	218	2	(	(	PUNCT
ejpam-5601	218	3	s	s	PROPN
ejpam-5601	218	4	,	,	PUNCT
ejpam-5601	218	5	t	t	PROPN
ejpam-5601	218	6	)	)	PUNCT
ejpam-5601	218	7	,	,	PUNCT
ejpam-5601	218	8	g	g	PROPN
ejpam-5601	218	9	α	α	INTJ
ejpam-5601	218	10	i	i	PRON
ejpam-5601	218	11	(	(	PUNCT
ejpam-5601	218	12	s	s	PROPN
ejpam-5601	218	13	,	,	PUNCT
ejpam-5601	218	14	t	t	PROPN
ejpam-5601	218	15	)	)	PUNCT
ejpam-5601	218	16	(	(	PUNCT
ejpam-5601	218	17	i	i	NOUN
ejpam-5601	218	18	=	=	NOUN
ejpam-5601	218	19	2	2	NUM
ejpam-5601	218	20	,	,	PUNCT
ejpam-5601	218	21	3	3	NUM
ejpam-5601	218	22	)	)	PUNCT
ejpam-5601	218	23	such	such	ADJ
ejpam-5601	218	24	that	that	DET
ejpam-5601	218	25	aα	aα	NOUN
ejpam-5601	218	26	=	=	PRON
ejpam-5601	218	27	{	{	PUNCT
ejpam-5601	218	28	(	(	PUNCT
ejpam-5601	218	29	fα	fα	ADP
ejpam-5601	218	30	1	1	NUM
ejpam-5601	218	31	(	(	PUNCT
ejpam-5601	218	32	s	s	NOUN
ejpam-5601	218	33	)	)	PUNCT
ejpam-5601	218	34	,	,	PUNCT
ejpam-5601	218	35	f	f	PROPN
ejpam-5601	218	36	α	α	PROPN
ejpam-5601	218	37	2	2	NUM
ejpam-5601	218	38	(	(	PUNCT
ejpam-5601	218	39	s	s	PROPN
ejpam-5601	218	40	,	,	PUNCT
ejpam-5601	218	41	t	t	PROPN
ejpam-5601	218	42	)	)	PUNCT
ejpam-5601	218	43	,	,	PUNCT
ejpam-5601	218	44	f	f	PROPN
ejpam-5601	218	45	α	α	PROPN
ejpam-5601	218	46	3	3	NUM
ejpam-5601	218	47	(	(	PUNCT
ejpam-5601	218	48	s	s	PROPN
ejpam-5601	218	49	,	,	PUNCT
ejpam-5601	218	50	t	t	PROPN
ejpam-5601	218	51	)	)	PUNCT
ejpam-5601	218	52	)	)	PUNCT
ejpam-5601	219	1	∈	∈	PROPN
ejpam-5601	219	2	r3|0	r3|0	PROPN
ejpam-5601	219	3	≤	≤	PROPN
ejpam-5601	219	4	s	s	PART
ejpam-5601	219	5	≤	≤	NOUN
ejpam-5601	219	6	2π,−π	2π,−π	NUM
ejpam-5601	219	7	2	2	NUM
ejpam-5601	219	8	≤	≤	NOUN
ejpam-5601	219	9	t	t	PROPN
ejpam-5601	219	10	≤	≤	NUM
ejpam-5601	219	11	π	π	PROPN
ejpam-5601	219	12	2	2	NUM
ejpam-5601	219	13	}	}	PUNCT
ejpam-5601	219	14	,	,	PUNCT
ejpam-5601	219	15	y.	y.	PROPN
ejpam-5601	219	16	s.	s.	PROPN
ejpam-5601	219	17	yun	yun	PROPN
ejpam-5601	219	18	,	,	PUNCT
ejpam-5601	219	19	b.	b.	PROPN
ejpam-5601	219	20	lee	lee	PROPN
ejpam-5601	219	21	/	/	SYM
ejpam-5601	219	22	eur	eur	PROPN
ejpam-5601	219	23	.	.	PUNCT
ejpam-5601	220	1	j.	j.	PROPN
ejpam-5601	220	2	pure	pure	PROPN
ejpam-5601	220	3	appl	appl	PROPN
ejpam-5601	220	4	.	.	PROPN
ejpam-5601	220	5	math	math	PROPN
ejpam-5601	220	6	,	,	PUNCT
ejpam-5601	220	7	18	18	NUM
ejpam-5601	220	8	(	(	PUNCT
ejpam-5601	220	9	1	1	NUM
ejpam-5601	220	10	)	)	PUNCT
ejpam-5601	220	11	(	(	PUNCT
ejpam-5601	220	12	2025	2025	NUM
ejpam-5601	220	13	)	)	PUNCT
ejpam-5601	220	14	,	,	PUNCT
ejpam-5601	220	15	5601	5601	NUM
ejpam-5601	220	16	10	10	NUM
ejpam-5601	220	17	of	of	ADP
ejpam-5601	220	18	17	17	NUM
ejpam-5601	220	19	and	and	CCONJ
ejpam-5601	220	20	bα	bα	NOUN
ejpam-5601	220	21	=	=	PUNCT
ejpam-5601	220	22	{	{	PUNCT
ejpam-5601	220	23	(	(	PUNCT
ejpam-5601	220	24	gα1	gα1	X
ejpam-5601	220	25	(	(	PUNCT
ejpam-5601	220	26	s	s	NOUN
ejpam-5601	220	27	)	)	PUNCT
ejpam-5601	220	28	,	,	PUNCT
ejpam-5601	220	29	gα2	gα2	PROPN
ejpam-5601	220	30	(	(	PUNCT
ejpam-5601	220	31	s	s	PROPN
ejpam-5601	220	32	,	,	PUNCT
ejpam-5601	220	33	t	t	PROPN
ejpam-5601	220	34	)	)	PUNCT
ejpam-5601	220	35	,	,	PUNCT
ejpam-5601	220	36	gα3	gα3	PROPN
ejpam-5601	220	37	(	(	PUNCT
ejpam-5601	220	38	s	s	PROPN
ejpam-5601	220	39	,	,	PUNCT
ejpam-5601	220	40	t	t	PROPN
ejpam-5601	220	41	)	)	PUNCT
ejpam-5601	220	42	)	)	PUNCT
ejpam-5601	221	1	∈	∈	PROPN
ejpam-5601	221	2	r3|0	r3|0	PROPN
ejpam-5601	221	3	≤	≤	PROPN
ejpam-5601	221	4	s	s	PART
ejpam-5601	221	5	≤	≤	NOUN
ejpam-5601	221	6	2π,−π	2π,−π	NUM
ejpam-5601	221	7	2	2	NUM
ejpam-5601	221	8	≤	≤	NOUN
ejpam-5601	221	9	t	t	PROPN
ejpam-5601	221	10	≤	≤	NUM
ejpam-5601	221	11	π	π	PROPN
ejpam-5601	221	12	2	2	NUM
ejpam-5601	221	13	}	}	PUNCT
ejpam-5601	221	14	.	.	PUNCT
ejpam-5601	222	1	since	since	SCONJ
ejpam-5601	222	2	a	a	DET
ejpam-5601	222	3	=	=	SYM
ejpam-5601	222	4	[	[	X
ejpam-5601	222	5	a1	a1	NOUN
ejpam-5601	222	6	,	,	PUNCT
ejpam-5601	222	7	x1	x1	PROPN
ejpam-5601	222	8	,	,	PUNCT
ejpam-5601	222	9	b1	b1	NOUN
ejpam-5601	222	10	,	,	PUNCT
ejpam-5601	222	11	y1	y1	PROPN
ejpam-5601	222	12	,	,	PUNCT
ejpam-5601	222	13	c1	c1	NOUN
ejpam-5601	222	14	,	,	PUNCT
ejpam-5601	222	15	z1	z1	PROPN
ejpam-5601	222	16	]	]	X
ejpam-5601	222	17	3	3	NUM
ejpam-5601	222	18	and	and	CCONJ
ejpam-5601	222	19	b	b	NOUN
ejpam-5601	222	20	=	=	SYM
ejpam-5601	222	21	[	[	X
ejpam-5601	222	22	a2	a2	PROPN
ejpam-5601	222	23	,	,	PUNCT
ejpam-5601	222	24	x2	x2	PROPN
ejpam-5601	222	25	,	,	PUNCT
ejpam-5601	222	26	b2	b2	NOUN
ejpam-5601	222	27	,	,	PUNCT
ejpam-5601	222	28	y2	y2	PROPN
ejpam-5601	222	29	,	,	PUNCT
ejpam-5601	222	30	c2	c2	PROPN
ejpam-5601	222	31	,	,	PUNCT
ejpam-5601	222	32	z2	z2	PROPN
ejpam-5601	222	33	]	]	X
ejpam-5601	222	34	3	3	NUM
ejpam-5601	222	35	,	,	PUNCT
ejpam-5601	222	36	we	we	PRON
ejpam-5601	222	37	have	have	VERB
ejpam-5601	222	38	fα	fα	ADP
ejpam-5601	222	39	1	1	NUM
ejpam-5601	222	40	(	(	PUNCT
ejpam-5601	222	41	s	s	NOUN
ejpam-5601	222	42	)	)	PUNCT
ejpam-5601	222	43	=	=	SYM
ejpam-5601	223	1	x1	x1	PROPN
ejpam-5601	224	1	+	+	CCONJ
ejpam-5601	224	2	a1	a1	NOUN
ejpam-5601	224	3	√	√	PROPN
ejpam-5601	224	4	1−	1−	NUM
ejpam-5601	224	5	α	α	PROPN
ejpam-5601	224	6	cos	cos	PROPN
ejpam-5601	224	7	s	s	PROPN
ejpam-5601	224	8	,	,	PUNCT
ejpam-5601	224	9	fα	fα	ADV
ejpam-5601	224	10	2	2	NUM
ejpam-5601	224	11	(	(	PUNCT
ejpam-5601	224	12	s	s	PROPN
ejpam-5601	224	13	,	,	PUNCT
ejpam-5601	224	14	t	t	PROPN
ejpam-5601	224	15	)	)	PUNCT
ejpam-5601	225	1	=	=	PUNCT
ejpam-5601	225	2	y1	y1	NOUN
ejpam-5601	225	3	+	+	CCONJ
ejpam-5601	225	4	b1	b1	NOUN
ejpam-5601	225	5	√	√	NUM
ejpam-5601	225	6	1−	1−	NUM
ejpam-5601	226	1	α	α	PRON
ejpam-5601	226	2	sin	sin	NOUN
ejpam-5601	226	3	s	s	X
ejpam-5601	226	4	cos	cos	PROPN
ejpam-5601	226	5	t	t	PROPN
ejpam-5601	226	6	fα	fα	ADP
ejpam-5601	226	7	3	3	NUM
ejpam-5601	226	8	(	(	PUNCT
ejpam-5601	226	9	s	s	PROPN
ejpam-5601	226	10	,	,	PUNCT
ejpam-5601	226	11	t	t	PROPN
ejpam-5601	226	12	)	)	PUNCT
ejpam-5601	226	13	=	=	SYM
ejpam-5601	227	1	z1	z1	PROPN
ejpam-5601	227	2	+	+	CCONJ
ejpam-5601	227	3	c1	c1	PROPN
ejpam-5601	227	4	√	√	PROPN
ejpam-5601	227	5	1−	1−	NUM
ejpam-5601	227	6	α	α	PRON
ejpam-5601	227	7	sin	sin	NOUN
ejpam-5601	227	8	s	s	PART
ejpam-5601	227	9	sin	sin	NOUN
ejpam-5601	227	10	t	t	NOUN
ejpam-5601	227	11	and	and	CCONJ
ejpam-5601	227	12	gα1	gα1	NOUN
ejpam-5601	227	13	(	(	PUNCT
ejpam-5601	227	14	s	s	X
ejpam-5601	227	15	)	)	PUNCT
ejpam-5601	227	16	=	=	SYM
ejpam-5601	228	1	x2	x2	PROPN
ejpam-5601	228	2	+	+	NUM
ejpam-5601	228	3	a2	a2	PROPN
ejpam-5601	228	4	√	√	NOUN
ejpam-5601	228	5	1−	1−	NUM
ejpam-5601	228	6	α	α	PROPN
ejpam-5601	228	7	cos	cos	PROPN
ejpam-5601	228	8	s	s	PROPN
ejpam-5601	228	9	,	,	PUNCT
ejpam-5601	228	10	gα2	gα2	PROPN
ejpam-5601	228	11	(	(	PUNCT
ejpam-5601	228	12	s	s	PROPN
ejpam-5601	228	13	,	,	PUNCT
ejpam-5601	228	14	t	t	PROPN
ejpam-5601	228	15	)	)	PUNCT
ejpam-5601	228	16	=	=	PUNCT
ejpam-5601	229	1	y2	y2	PROPN
ejpam-5601	229	2	+	+	CCONJ
ejpam-5601	229	3	b2	b2	NOUN
ejpam-5601	229	4	√	√	PROPN
ejpam-5601	229	5	1−	1−	NUM
ejpam-5601	229	6	α	α	PRON
ejpam-5601	229	7	sin	sin	NOUN
ejpam-5601	229	8	s	s	X
ejpam-5601	229	9	cos	cos	PROPN
ejpam-5601	229	10	t	t	PROPN
ejpam-5601	229	11	gα3	gα3	PROPN
ejpam-5601	229	12	(	(	PUNCT
ejpam-5601	229	13	s	s	PROPN
ejpam-5601	229	14	,	,	PUNCT
ejpam-5601	229	15	t	t	PROPN
ejpam-5601	229	16	)	)	PUNCT
ejpam-5601	230	1	=	=	SYM
ejpam-5601	230	2	z2	z2	PROPN
ejpam-5601	230	3	+	+	CCONJ
ejpam-5601	230	4	c2	c2	PROPN
ejpam-5601	230	5	√	√	NUM
ejpam-5601	230	6	1−	1−	NUM
ejpam-5601	230	7	α	α	PRON
ejpam-5601	230	8	sin	sin	NOUN
ejpam-5601	230	9	s	s	PART
ejpam-5601	230	10	sin	sin	NOUN
ejpam-5601	230	11	t.	t.	NOUN
ejpam-5601	230	12	(	(	PUNCT
ejpam-5601	230	13	1	1	NUM
ejpam-5601	230	14	)	)	PUNCT
ejpam-5601	230	15	since	since	SCONJ
ejpam-5601	230	16	fα	fα	ADV
ejpam-5601	230	17	1	1	NUM
ejpam-5601	230	18	(	(	PUNCT
ejpam-5601	230	19	s	s	X
ejpam-5601	230	20	)	)	PUNCT
ejpam-5601	230	21	+	+	CCONJ
ejpam-5601	230	22	gα1	gα1	NOUN
ejpam-5601	230	23	(	(	PUNCT
ejpam-5601	230	24	s	s	X
ejpam-5601	230	25	)	)	PUNCT
ejpam-5601	230	26	=	=	SYM
ejpam-5601	231	1	x1	x1	PROPN
ejpam-5601	232	1	+	+	NUM
ejpam-5601	232	2	x2	x2	PROPN
ejpam-5601	232	3	+	+	CCONJ
ejpam-5601	232	4	(	(	PUNCT
ejpam-5601	232	5	a1	a1	NOUN
ejpam-5601	232	6	+	+	SYM
ejpam-5601	232	7	a2	a2	PROPN
ejpam-5601	232	8	)	)	PUNCT
ejpam-5601	232	9	√	√	NOUN
ejpam-5601	232	10	1−	1−	NUM
ejpam-5601	232	11	α	α	PROPN
ejpam-5601	232	12	cos	cos	PROPN
ejpam-5601	232	13	s	s	NOUN
ejpam-5601	232	14	fα	fα	ADV
ejpam-5601	232	15	2	2	NUM
ejpam-5601	232	16	(	(	PUNCT
ejpam-5601	232	17	s	s	PROPN
ejpam-5601	232	18	,	,	PUNCT
ejpam-5601	232	19	t	t	PROPN
ejpam-5601	232	20	)	)	PUNCT
ejpam-5601	233	1	+	+	NUM
ejpam-5601	233	2	gα2	gα2	NOUN
ejpam-5601	233	3	(	(	PUNCT
ejpam-5601	233	4	s	s	PROPN
ejpam-5601	233	5	,	,	PUNCT
ejpam-5601	233	6	t	t	PROPN
ejpam-5601	233	7	)	)	PUNCT
ejpam-5601	233	8	=	=	SYM
ejpam-5601	233	9	y1	y1	INTJ
ejpam-5601	233	10	+	+	CCONJ
ejpam-5601	233	11	y2	y2	PROPN
ejpam-5601	233	12	+	+	CCONJ
ejpam-5601	233	13	(	(	PUNCT
ejpam-5601	233	14	b1	b1	NOUN
ejpam-5601	233	15	+	+	CCONJ
ejpam-5601	233	16	b2	b2	NOUN
ejpam-5601	233	17	)	)	PUNCT
ejpam-5601	233	18	√	√	NOUN
ejpam-5601	233	19	1−	1−	NUM
ejpam-5601	233	20	α	α	PRON
ejpam-5601	233	21	sin	sin	NOUN
ejpam-5601	233	22	s	s	X
ejpam-5601	233	23	cos	cos	PROPN
ejpam-5601	233	24	t	t	PROPN
ejpam-5601	233	25	and	and	CCONJ
ejpam-5601	233	26	fα	fα	ADP
ejpam-5601	233	27	3	3	NUM
ejpam-5601	233	28	(	(	PUNCT
ejpam-5601	233	29	s	s	PROPN
ejpam-5601	233	30	,	,	PUNCT
ejpam-5601	233	31	t	t	PROPN
ejpam-5601	233	32	)	)	PUNCT
ejpam-5601	234	1	+	+	NUM
ejpam-5601	234	2	gα3	gα3	NOUN
ejpam-5601	234	3	(	(	PUNCT
ejpam-5601	234	4	s	s	PROPN
ejpam-5601	234	5	,	,	PUNCT
ejpam-5601	234	6	t	t	PROPN
ejpam-5601	234	7	)	)	PUNCT
ejpam-5601	234	8	=	=	SYM
ejpam-5601	235	1	z1	z1	VERB
ejpam-5601	235	2	+	+	CCONJ
ejpam-5601	235	3	z2	z2	PROPN
ejpam-5601	235	4	+	+	CCONJ
ejpam-5601	235	5	(	(	PUNCT
ejpam-5601	235	6	c1	c1	PROPN
ejpam-5601	235	7	+	+	CCONJ
ejpam-5601	235	8	c2	c2	PROPN
ejpam-5601	235	9	)	)	PUNCT
ejpam-5601	235	10	√	√	PROPN
ejpam-5601	235	11	1−	1−	NUM
ejpam-5601	235	12	α	α	PRON
ejpam-5601	235	13	sin	sin	NOUN
ejpam-5601	235	14	s	s	PART
ejpam-5601	235	15	sin	sin	NOUN
ejpam-5601	235	16	t	t	PROPN
ejpam-5601	235	17	we	we	PRON
ejpam-5601	235	18	have	have	VERB
ejpam-5601	235	19	(	(	PUNCT
ejpam-5601	235	20	a(+)pb)α	a(+)pb)α	NOUN
ejpam-5601	235	21	=	=	PRON
ejpam-5601	235	22	{	{	PUNCT
ejpam-5601	235	23	(	(	PUNCT
ejpam-5601	235	24	x	x	X
ejpam-5601	235	25	,	,	PUNCT
ejpam-5601	235	26	y	y	PROPN
ejpam-5601	235	27	,	,	PUNCT
ejpam-5601	235	28	z	z	NOUN
ejpam-5601	235	29	)	)	PUNCT
ejpam-5601	235	30	∈	∈	PROPN
ejpam-5601	235	31	r3	r3	PROPN
ejpam-5601	235	32	∣∣∣	∣∣∣	NOUN
ejpam-5601	235	33	(	(	PUNCT
ejpam-5601	235	34	x−	x−	PROPN
ejpam-5601	235	35	x1	x1	PROPN
ejpam-5601	236	1	−	−	PROPN
ejpam-5601	236	2	x2	x2	PROPN
ejpam-5601	236	3	)	)	PUNCT
ejpam-5601	236	4	2	2	NUM
ejpam-5601	236	5	(	(	PUNCT
ejpam-5601	236	6	a1	a1	NOUN
ejpam-5601	236	7	+	+	CCONJ
ejpam-5601	236	8	a2)2(1−	a2)2(1−	ADJ
ejpam-5601	236	9	α	α	NUM
ejpam-5601	236	10	)	)	PUNCT
ejpam-5601	237	1	+	+	CCONJ
ejpam-5601	237	2	(	(	PUNCT
ejpam-5601	237	3	y	y	PROPN
ejpam-5601	237	4	−	−	PROPN
ejpam-5601	237	5	y1	y1	PROPN
ejpam-5601	237	6	−	−	PROPN
ejpam-5601	237	7	y2	y2	PROPN
ejpam-5601	237	8	)	)	PUNCT
ejpam-5601	237	9	2	2	NUM
ejpam-5601	237	10	(	(	PUNCT
ejpam-5601	237	11	b1	b1	NOUN
ejpam-5601	237	12	+	+	CCONJ
ejpam-5601	237	13	b2)2(1−	b2)2(1−	PROPN
ejpam-5601	237	14	α	α	NUM
ejpam-5601	237	15	)	)	PUNCT
ejpam-5601	238	1	+	+	CCONJ
ejpam-5601	238	2	(	(	PUNCT
ejpam-5601	238	3	z	z	NOUN
ejpam-5601	238	4	−	−	PROPN
ejpam-5601	238	5	z1	z1	PROPN
ejpam-5601	238	6	−	−	PROPN
ejpam-5601	238	7	z2	z2	PROPN
ejpam-5601	238	8	)	)	PUNCT
ejpam-5601	238	9	2	2	NUM
ejpam-5601	238	10	(	(	PUNCT
ejpam-5601	238	11	c1	c1	NOUN
ejpam-5601	238	12	+	+	CCONJ
ejpam-5601	238	13	c2)2(1−	c2)2(1−	PROPN
ejpam-5601	238	14	α	α	X
ejpam-5601	238	15	)	)	PUNCT
ejpam-5601	238	16	=	=	SYM
ejpam-5601	238	17	1	1	NUM
ejpam-5601	238	18	}	}	PUNCT
ejpam-5601	238	19	.	.	PUNCT
ejpam-5601	239	1	thus	thus	ADV
ejpam-5601	239	2	a(+)pb	a(+)pb	PROPN
ejpam-5601	239	3	=	=	PUNCT
ejpam-5601	239	4	[	[	PUNCT
ejpam-5601	239	5	a1	a1	NOUN
ejpam-5601	239	6	+	+	CCONJ
ejpam-5601	239	7	a2	a2	PROPN
ejpam-5601	239	8	,	,	PUNCT
ejpam-5601	239	9	x1	x1	PROPN
ejpam-5601	240	1	+	+	CCONJ
ejpam-5601	240	2	x2	x2	PROPN
ejpam-5601	240	3	,	,	PUNCT
ejpam-5601	240	4	b1	b1	NOUN
ejpam-5601	240	5	+	+	CCONJ
ejpam-5601	240	6	b2	b2	NOUN
ejpam-5601	240	7	,	,	PUNCT
ejpam-5601	240	8	y1	y1	NOUN
ejpam-5601	240	9	+	+	CCONJ
ejpam-5601	240	10	y2	y2	PROPN
ejpam-5601	240	11	,	,	PUNCT
ejpam-5601	240	12	c1	c1	PROPN
ejpam-5601	240	13	+	+	CCONJ
ejpam-5601	240	14	c2	c2	PROPN
ejpam-5601	240	15	,	,	PUNCT
ejpam-5601	240	16	z1	z1	PROPN
ejpam-5601	240	17	+	+	CCONJ
ejpam-5601	240	18	z2	z2	PROPN
ejpam-5601	240	19	]	]	SYM
ejpam-5601	240	20	3	3	NUM
ejpam-5601	240	21	.	.	PUNCT
ejpam-5601	241	1	(	(	PUNCT
ejpam-5601	241	2	2	2	X
ejpam-5601	241	3	)	)	PUNCT
ejpam-5601	241	4	if	if	SCONJ
ejpam-5601	241	5	0	0	NUM
ejpam-5601	241	6	≤	≤	NUM
ejpam-5601	241	7	s	s	PART
ejpam-5601	241	8	≤	≤	NUM
ejpam-5601	241	9	π	π	PROPN
ejpam-5601	241	10	,	,	PUNCT
ejpam-5601	241	11	fα	fα	ADV
ejpam-5601	241	12	1	1	NUM
ejpam-5601	241	13	(	(	PUNCT
ejpam-5601	241	14	s)−	s)−	NOUN
ejpam-5601	241	15	gα1	gα1	NOUN
ejpam-5601	241	16	(	(	PUNCT
ejpam-5601	241	17	s+	s+	X
ejpam-5601	241	18	π	π	X
ejpam-5601	241	19	)	)	PUNCT
ejpam-5601	242	1	=	=	SYM
ejpam-5601	242	2	x1	x1	NUM
ejpam-5601	242	3	−	−	PUNCT
ejpam-5601	243	1	x2	x2	INTJ
ejpam-5601	243	2	+	+	CCONJ
ejpam-5601	243	3	(	(	PUNCT
ejpam-5601	243	4	a1	a1	NOUN
ejpam-5601	243	5	+	+	SYM
ejpam-5601	243	6	a2	a2	PROPN
ejpam-5601	243	7	)	)	PUNCT
ejpam-5601	243	8	√	√	NOUN
ejpam-5601	243	9	1−	1−	NUM
ejpam-5601	243	10	α	α	PROPN
ejpam-5601	243	11	cos	cos	PROPN
ejpam-5601	243	12	s	s	NOUN
ejpam-5601	243	13	fα	fα	ADV
ejpam-5601	243	14	2	2	NUM
ejpam-5601	243	15	(	(	PUNCT
ejpam-5601	243	16	s	s	X
ejpam-5601	243	17	,	,	PUNCT
ejpam-5601	243	18	t)−	t)−	PROPN
ejpam-5601	243	19	gα2	gα2	NOUN
ejpam-5601	243	20	(	(	PUNCT
ejpam-5601	243	21	s+	s+	X
ejpam-5601	243	22	π	π	PROPN
ejpam-5601	243	23	,	,	PUNCT
ejpam-5601	243	24	t	t	PROPN
ejpam-5601	243	25	)	)	PUNCT
ejpam-5601	243	26	=	=	PUNCT
ejpam-5601	244	1	y1	y1	NOUN
ejpam-5601	244	2	−	−	PROPN
ejpam-5601	245	1	y2	y2	PROPN
ejpam-5601	245	2	+	+	CCONJ
ejpam-5601	245	3	(	(	PUNCT
ejpam-5601	245	4	b1	b1	NOUN
ejpam-5601	245	5	+	+	CCONJ
ejpam-5601	245	6	b2	b2	NOUN
ejpam-5601	245	7	)	)	PUNCT
ejpam-5601	245	8	√	√	NOUN
ejpam-5601	245	9	1−	1−	NUM
ejpam-5601	245	10	α	α	PRON
ejpam-5601	245	11	sin	sin	NOUN
ejpam-5601	245	12	s	s	X
ejpam-5601	245	13	cos	cos	PROPN
ejpam-5601	245	14	t	t	PROPN
ejpam-5601	245	15	and	and	CCONJ
ejpam-5601	245	16	fα	fα	ADP
ejpam-5601	245	17	3	3	NUM
ejpam-5601	245	18	(	(	PUNCT
ejpam-5601	245	19	s	s	X
ejpam-5601	245	20	,	,	PUNCT
ejpam-5601	245	21	t)−	t)−	PROPN
ejpam-5601	245	22	gα3	gα3	PROPN
ejpam-5601	245	23	(	(	PUNCT
ejpam-5601	245	24	s+	s+	X
ejpam-5601	245	25	π	π	PROPN
ejpam-5601	245	26	,	,	PUNCT
ejpam-5601	245	27	t	t	PROPN
ejpam-5601	245	28	)	)	PUNCT
ejpam-5601	245	29	=	=	SYM
ejpam-5601	246	1	z1	z1	VERB
ejpam-5601	246	2	−	−	PROPN
ejpam-5601	246	3	z2	z2	PROPN
ejpam-5601	246	4	+	+	CCONJ
ejpam-5601	246	5	(	(	PUNCT
ejpam-5601	246	6	c1	c1	PROPN
ejpam-5601	246	7	+	+	CCONJ
ejpam-5601	246	8	c2	c2	PROPN
ejpam-5601	246	9	)	)	PUNCT
ejpam-5601	246	10	√	√	PROPN
ejpam-5601	246	11	1−	1−	NUM
ejpam-5601	246	12	α	α	PRON
ejpam-5601	246	13	sin	sin	NOUN
ejpam-5601	246	14	s	s	PART
ejpam-5601	246	15	sin	sin	NOUN
ejpam-5601	246	16	t.	t.	NOUN
ejpam-5601	246	17	in	in	ADP
ejpam-5601	246	18	the	the	DET
ejpam-5601	246	19	case	case	NOUN
ejpam-5601	246	20	of	of	ADP
ejpam-5601	246	21	π	π	PROPN
ejpam-5601	246	22	≤	≤	PROPN
ejpam-5601	246	23	s	s	PART
ejpam-5601	246	24	≤	≤	NOUN
ejpam-5601	246	25	2π	2π	NOUN
ejpam-5601	246	26	,	,	PUNCT
ejpam-5601	246	27	we	we	PRON
ejpam-5601	246	28	have	have	VERB
ejpam-5601	246	29	fα	fα	ADP
ejpam-5601	246	30	1	1	NUM
ejpam-5601	246	31	(	(	PUNCT
ejpam-5601	246	32	s)−	s)−	NOUN
ejpam-5601	246	33	gα1	gα1	NOUN
ejpam-5601	246	34	(	(	PUNCT
ejpam-5601	246	35	s−	s−	PROPN
ejpam-5601	246	36	π	π	PROPN
ejpam-5601	246	37	)	)	PUNCT
ejpam-5601	246	38	=	=	NOUN
ejpam-5601	246	39	fα	fα	ADP
ejpam-5601	246	40	1	1	NUM
ejpam-5601	246	41	(	(	PUNCT
ejpam-5601	246	42	s)−	s)−	NOUN
ejpam-5601	246	43	gα1	gα1	NOUN
ejpam-5601	246	44	(	(	PUNCT
ejpam-5601	246	45	s+	s+	X
ejpam-5601	246	46	π	π	X
ejpam-5601	246	47	)	)	PUNCT
ejpam-5601	246	48	fα	fα	ADP
ejpam-5601	246	49	2	2	NUM
ejpam-5601	246	50	(	(	PUNCT
ejpam-5601	246	51	s	s	X
ejpam-5601	246	52	,	,	PUNCT
ejpam-5601	246	53	t)−	t)−	PROPN
ejpam-5601	246	54	gα2	gα2	NOUN
ejpam-5601	246	55	(	(	PUNCT
ejpam-5601	246	56	s−	s−	PROPN
ejpam-5601	246	57	π	π	PROPN
ejpam-5601	246	58	,	,	PUNCT
ejpam-5601	246	59	t	t	PROPN
ejpam-5601	246	60	)	)	PUNCT
ejpam-5601	246	61	=	=	SYM
ejpam-5601	246	62	fα	fα	ADP
ejpam-5601	246	63	2	2	NUM
ejpam-5601	246	64	(	(	PUNCT
ejpam-5601	246	65	s	s	X
ejpam-5601	246	66	,	,	PUNCT
ejpam-5601	246	67	t)−	t)−	PROPN
ejpam-5601	246	68	gα2	gα2	NOUN
ejpam-5601	246	69	(	(	PUNCT
ejpam-5601	246	70	s+	s+	X
ejpam-5601	246	71	π	π	PROPN
ejpam-5601	246	72	,	,	PUNCT
ejpam-5601	246	73	t	t	PROPN
ejpam-5601	246	74	)	)	PUNCT
ejpam-5601	246	75	y.	y.	PROPN
ejpam-5601	246	76	s.	s.	PROPN
ejpam-5601	246	77	yun	yun	PROPN
ejpam-5601	246	78	,	,	PUNCT
ejpam-5601	246	79	b.	b.	PROPN
ejpam-5601	246	80	lee	lee	PROPN
ejpam-5601	246	81	/	/	SYM
ejpam-5601	246	82	eur	eur	PROPN
ejpam-5601	246	83	.	.	PUNCT
ejpam-5601	247	1	j.	j.	PROPN
ejpam-5601	247	2	pure	pure	PROPN
ejpam-5601	247	3	appl	appl	PROPN
ejpam-5601	247	4	.	.	PROPN
ejpam-5601	247	5	math	math	PROPN
ejpam-5601	247	6	,	,	PUNCT
ejpam-5601	247	7	18	18	NUM
ejpam-5601	247	8	(	(	PUNCT
ejpam-5601	247	9	1	1	NUM
ejpam-5601	247	10	)	)	PUNCT
ejpam-5601	247	11	(	(	PUNCT
ejpam-5601	247	12	2025	2025	NUM
ejpam-5601	247	13	)	)	PUNCT
ejpam-5601	247	14	,	,	PUNCT
ejpam-5601	247	15	5601	5601	NUM
ejpam-5601	247	16	11	11	NUM
ejpam-5601	247	17	of	of	ADP
ejpam-5601	247	18	17	17	NUM
ejpam-5601	247	19	and	and	CCONJ
ejpam-5601	247	20	fα	fα	ADP
ejpam-5601	247	21	3	3	NUM
ejpam-5601	247	22	(	(	PUNCT
ejpam-5601	247	23	s	s	X
ejpam-5601	247	24	,	,	PUNCT
ejpam-5601	247	25	t)−	t)−	PROPN
ejpam-5601	247	26	gα3	gα3	NOUN
ejpam-5601	247	27	(	(	PUNCT
ejpam-5601	247	28	s−	s−	PROPN
ejpam-5601	247	29	π	π	PROPN
ejpam-5601	247	30	,	,	PUNCT
ejpam-5601	247	31	t	t	PROPN
ejpam-5601	247	32	)	)	PUNCT
ejpam-5601	247	33	=	=	PUNCT
ejpam-5601	247	34	fα	fα	ADP
ejpam-5601	247	35	3	3	NUM
ejpam-5601	247	36	(	(	PUNCT
ejpam-5601	247	37	s	s	X
ejpam-5601	247	38	,	,	PUNCT
ejpam-5601	247	39	t)−	t)−	PROPN
ejpam-5601	247	40	gα3	gα3	PROPN
ejpam-5601	247	41	(	(	PUNCT
ejpam-5601	247	42	s+	s+	X
ejpam-5601	247	43	π	π	PROPN
ejpam-5601	247	44	,	,	PUNCT
ejpam-5601	247	45	t	t	PROPN
ejpam-5601	247	46	)	)	PUNCT
ejpam-5601	247	47	.	.	PUNCT
ejpam-5601	248	1	thus	thus	ADV
ejpam-5601	248	2	(	(	PUNCT
ejpam-5601	248	3	a(−)pb)α	a(−)pb)α	NOUN
ejpam-5601	248	4	=	=	SYM
ejpam-5601	248	5	{	{	PUNCT
ejpam-5601	248	6	(	(	PUNCT
ejpam-5601	248	7	x	x	X
ejpam-5601	248	8	,	,	PUNCT
ejpam-5601	248	9	y	y	PROPN
ejpam-5601	248	10	,	,	PUNCT
ejpam-5601	248	11	z	z	NOUN
ejpam-5601	248	12	)	)	PUNCT
ejpam-5601	248	13	∈	∈	PROPN
ejpam-5601	248	14	r3	r3	PROPN
ejpam-5601	248	15	∣∣∣	∣∣∣	NOUN
ejpam-5601	248	16	(	(	PUNCT
ejpam-5601	248	17	x−	x−	PROPN
ejpam-5601	248	18	x1	x1	PROPN
ejpam-5601	249	1	+	+	CCONJ
ejpam-5601	249	2	x2	x2	ADJ
ejpam-5601	249	3	)	)	PUNCT
ejpam-5601	249	4	2	2	NUM
ejpam-5601	249	5	(	(	PUNCT
ejpam-5601	249	6	a1	a1	NOUN
ejpam-5601	249	7	+	+	CCONJ
ejpam-5601	249	8	a2)2(1−	a2)2(1−	ADJ
ejpam-5601	249	9	α	α	NUM
ejpam-5601	249	10	)	)	PUNCT
ejpam-5601	250	1	+	+	CCONJ
ejpam-5601	250	2	(	(	PUNCT
ejpam-5601	250	3	y	y	PROPN
ejpam-5601	250	4	−	−	PROPN
ejpam-5601	250	5	y1	y1	PROPN
ejpam-5601	250	6	+	+	CCONJ
ejpam-5601	250	7	y2	y2	NOUN
ejpam-5601	250	8	)	)	PUNCT
ejpam-5601	250	9	2	2	NUM
ejpam-5601	250	10	(	(	PUNCT
ejpam-5601	250	11	b1	b1	NOUN
ejpam-5601	250	12	+	+	CCONJ
ejpam-5601	250	13	b2)2(1−	b2)2(1−	PROPN
ejpam-5601	250	14	α	α	NUM
ejpam-5601	250	15	)	)	PUNCT
ejpam-5601	251	1	+	+	CCONJ
ejpam-5601	251	2	(	(	PUNCT
ejpam-5601	251	3	z	z	NOUN
ejpam-5601	251	4	−	−	PROPN
ejpam-5601	251	5	z1	z1	PROPN
ejpam-5601	251	6	+	+	CCONJ
ejpam-5601	251	7	z2	z2	NOUN
ejpam-5601	251	8	)	)	PUNCT
ejpam-5601	251	9	2	2	NUM
ejpam-5601	252	1	(	(	PUNCT
ejpam-5601	252	2	c1	c1	NOUN
ejpam-5601	252	3	+	+	CCONJ
ejpam-5601	252	4	c2)2(1−	c2)2(1−	PROPN
ejpam-5601	252	5	α	α	X
ejpam-5601	252	6	)	)	PUNCT
ejpam-5601	252	7	=	=	SYM
ejpam-5601	252	8	1	1	X
ejpam-5601	252	9	}	}	PUNCT
ejpam-5601	252	10	,	,	PUNCT
ejpam-5601	252	11	i.e.	i.e.	X
ejpam-5601	252	12	,	,	PUNCT
ejpam-5601	252	13	a(−)pb	a(−)pb	PROPN
ejpam-5601	252	14	=	=	X
ejpam-5601	252	15	[	[	PUNCT
ejpam-5601	252	16	a1	a1	NOUN
ejpam-5601	252	17	+	+	CCONJ
ejpam-5601	252	18	a2	a2	PROPN
ejpam-5601	252	19	,	,	PUNCT
ejpam-5601	252	20	x1	x1	PROPN
ejpam-5601	252	21	−	−	PROPN
ejpam-5601	252	22	x2	x2	PROPN
ejpam-5601	252	23	,	,	PUNCT
ejpam-5601	252	24	b1	b1	NOUN
ejpam-5601	252	25	+	+	CCONJ
ejpam-5601	252	26	b2	b2	NOUN
ejpam-5601	252	27	,	,	PUNCT
ejpam-5601	252	28	y1	y1	NOUN
ejpam-5601	252	29	−	−	PROPN
ejpam-5601	252	30	y2	y2	PROPN
ejpam-5601	252	31	,	,	PUNCT
ejpam-5601	252	32	c1	c1	PROPN
ejpam-5601	252	33	+	+	CCONJ
ejpam-5601	252	34	c2	c2	PROPN
ejpam-5601	252	35	,	,	PUNCT
ejpam-5601	252	36	z1	z1	PROPN
ejpam-5601	252	37	−	−	PROPN
ejpam-5601	252	38	z2	z2	PROPN
ejpam-5601	252	39	]	]	PUNCT
ejpam-5601	252	40	3	3	NUM
ejpam-5601	252	41	.	.	PUNCT
ejpam-5601	253	1	(	(	PUNCT
ejpam-5601	253	2	3	3	X
ejpam-5601	253	3	)	)	PUNCT
ejpam-5601	253	4	let	let	NOUN
ejpam-5601	253	5	(	(	PUNCT
ejpam-5601	253	6	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	253	7	=	=	SYM
ejpam-5601	253	8	{	{	PUNCT
ejpam-5601	253	9	(	(	PUNCT
ejpam-5601	253	10	xα(s	xα(s	NUM
ejpam-5601	253	11	)	)	PUNCT
ejpam-5601	253	12	,	,	PUNCT
ejpam-5601	253	13	yα(s	yα(s	PROPN
ejpam-5601	253	14	,	,	PUNCT
ejpam-5601	253	15	t	t	PROPN
ejpam-5601	253	16	)	)	PUNCT
ejpam-5601	253	17	,	,	PUNCT
ejpam-5601	253	18	zα(s	zα(s	NUM
ejpam-5601	253	19	,	,	PUNCT
ejpam-5601	253	20	t	t	PROPN
ejpam-5601	253	21	)	)	PUNCT
ejpam-5601	253	22	)	)	PUNCT
ejpam-5601	254	1	|	|	ADV
ejpam-5601	254	2	0	0	NUM
ejpam-5601	254	3	≤	≤	NUM
ejpam-5601	254	4	s	s	PART
ejpam-5601	254	5	≤	≤	NOUN
ejpam-5601	254	6	2π,−π	2π,−π	NUM
ejpam-5601	254	7	2	2	NUM
ejpam-5601	254	8	≤	≤	NOUN
ejpam-5601	254	9	t	t	PROPN
ejpam-5601	254	10	≤	≤	NUM
ejpam-5601	254	11	π	π	PROPN
ejpam-5601	254	12	2	2	NUM
ejpam-5601	254	13	}	}	PUNCT
ejpam-5601	254	14	.	.	PUNCT
ejpam-5601	255	1	since	since	SCONJ
ejpam-5601	255	2	fα	fα	ADV
ejpam-5601	255	3	1	1	NUM
ejpam-5601	255	4	(	(	PUNCT
ejpam-5601	255	5	s	s	NOUN
ejpam-5601	255	6	)	)	PUNCT
ejpam-5601	255	7	=	=	SYM
ejpam-5601	255	8	x1	x1	PROPN
ejpam-5601	256	1	+	+	CCONJ
ejpam-5601	256	2	a1	a1	NOUN
ejpam-5601	256	3	√	√	PROPN
ejpam-5601	256	4	1−	1−	NUM
ejpam-5601	256	5	α	α	PROPN
ejpam-5601	256	6	cos	cos	PROPN
ejpam-5601	256	7	s	s	PROPN
ejpam-5601	256	8	,	,	PUNCT
ejpam-5601	256	9	fα	fα	ADV
ejpam-5601	256	10	2	2	NUM
ejpam-5601	256	11	(	(	PUNCT
ejpam-5601	256	12	s	s	PROPN
ejpam-5601	256	13	,	,	PUNCT
ejpam-5601	256	14	t	t	PROPN
ejpam-5601	256	15	)	)	PUNCT
ejpam-5601	257	1	=	=	PUNCT
ejpam-5601	257	2	y1	y1	NOUN
ejpam-5601	257	3	+	+	CCONJ
ejpam-5601	257	4	b1	b1	NOUN
ejpam-5601	257	5	√	√	NUM
ejpam-5601	257	6	1−	1−	NUM
ejpam-5601	258	1	α	α	PRON
ejpam-5601	258	2	sin	sin	NOUN
ejpam-5601	258	3	s	s	PROPN
ejpam-5601	258	4	cos	cos	PROPN
ejpam-5601	258	5	t	t	PROPN
ejpam-5601	258	6	,	,	PUNCT
ejpam-5601	258	7	fα	fα	ADV
ejpam-5601	258	8	3	3	NUM
ejpam-5601	258	9	(	(	PUNCT
ejpam-5601	258	10	s	s	PROPN
ejpam-5601	258	11	,	,	PUNCT
ejpam-5601	258	12	t	t	PROPN
ejpam-5601	258	13	)	)	PUNCT
ejpam-5601	258	14	=	=	SYM
ejpam-5601	259	1	z1	z1	PROPN
ejpam-5601	259	2	+	+	CCONJ
ejpam-5601	259	3	c1	c1	PROPN
ejpam-5601	259	4	√	√	PROPN
ejpam-5601	259	5	1−	1−	NUM
ejpam-5601	259	6	α	α	PRON
ejpam-5601	259	7	sin	sin	NOUN
ejpam-5601	259	8	s	s	PART
ejpam-5601	259	9	sin	sin	NOUN
ejpam-5601	259	10	t	t	NOUN
ejpam-5601	259	11	and	and	CCONJ
ejpam-5601	259	12	gα1	gα1	NOUN
ejpam-5601	259	13	(	(	PUNCT
ejpam-5601	259	14	s	s	X
ejpam-5601	259	15	)	)	PUNCT
ejpam-5601	259	16	=	=	SYM
ejpam-5601	260	1	x2	x2	PROPN
ejpam-5601	260	2	+	+	NUM
ejpam-5601	260	3	a2	a2	PROPN
ejpam-5601	260	4	√	√	NOUN
ejpam-5601	260	5	1−	1−	NUM
ejpam-5601	260	6	α	α	PROPN
ejpam-5601	260	7	cos	cos	PROPN
ejpam-5601	260	8	s	s	PROPN
ejpam-5601	260	9	,	,	PUNCT
ejpam-5601	260	10	gα2	gα2	PROPN
ejpam-5601	260	11	(	(	PUNCT
ejpam-5601	260	12	s	s	PROPN
ejpam-5601	260	13	,	,	PUNCT
ejpam-5601	260	14	t	t	PROPN
ejpam-5601	260	15	)	)	PUNCT
ejpam-5601	260	16	=	=	PUNCT
ejpam-5601	261	1	y2	y2	PROPN
ejpam-5601	261	2	+	+	CCONJ
ejpam-5601	261	3	b2	b2	NOUN
ejpam-5601	261	4	√	√	PROPN
ejpam-5601	261	5	1−	1−	NUM
ejpam-5601	261	6	α	α	PRON
ejpam-5601	261	7	sin	sin	NOUN
ejpam-5601	261	8	s	s	PROPN
ejpam-5601	261	9	cos	cos	PROPN
ejpam-5601	261	10	t	t	PROPN
ejpam-5601	261	11	,	,	PUNCT
ejpam-5601	261	12	gα3	gα3	PROPN
ejpam-5601	261	13	(	(	PUNCT
ejpam-5601	261	14	s	s	PROPN
ejpam-5601	261	15	,	,	PUNCT
ejpam-5601	261	16	t	t	PROPN
ejpam-5601	261	17	)	)	PUNCT
ejpam-5601	262	1	=	=	SYM
ejpam-5601	262	2	z2	z2	PROPN
ejpam-5601	262	3	+	+	CCONJ
ejpam-5601	262	4	c2	c2	PROPN
ejpam-5601	262	5	√	√	NUM
ejpam-5601	262	6	1−	1−	NUM
ejpam-5601	262	7	α	α	PRON
ejpam-5601	262	8	sin	sin	NOUN
ejpam-5601	262	9	s	s	PART
ejpam-5601	262	10	sin	sin	PROPN
ejpam-5601	262	11	t	t	PROPN
ejpam-5601	262	12	,	,	PUNCT
ejpam-5601	262	13	we	we	PRON
ejpam-5601	262	14	have	have	VERB
ejpam-5601	262	15	xα(s	xα(s	NUM
ejpam-5601	262	16	)	)	PUNCT
ejpam-5601	263	1	=	=	SYM
ejpam-5601	263	2	fα	fα	ADP
ejpam-5601	263	3	1	1	NUM
ejpam-5601	263	4	(	(	PUNCT
ejpam-5601	263	5	s	s	NOUN
ejpam-5601	263	6	)	)	PUNCT
ejpam-5601	263	7	·	·	PUNCT
ejpam-5601	263	8	gα1	gα1	X
ejpam-5601	263	9	(	(	PUNCT
ejpam-5601	263	10	s	s	X
ejpam-5601	263	11	)	)	PUNCT
ejpam-5601	263	12	=	=	SYM
ejpam-5601	263	13	x1x2	x1x2	PUNCT
ejpam-5601	264	1	+	+	CCONJ
ejpam-5601	264	2	(	(	PUNCT
ejpam-5601	264	3	x1a2	x1a2	X
ejpam-5601	264	4	+	+	X
ejpam-5601	264	5	x2a1	x2a1	X
ejpam-5601	264	6	)	)	PUNCT
ejpam-5601	264	7	√	√	ADP
ejpam-5601	264	8	1−	1−	NUM
ejpam-5601	264	9	α	α	PROPN
ejpam-5601	264	10	cos	cos	PROPN
ejpam-5601	264	11	s	s	PROPN
ejpam-5601	264	12	+	+	CCONJ
ejpam-5601	264	13	a1a2(1−	a1a2(1−	PROPN
ejpam-5601	264	14	α	α	NUM
ejpam-5601	264	15	)	)	PUNCT
ejpam-5601	264	16	cos2	cos2	PROPN
ejpam-5601	264	17	s	s	PART
ejpam-5601	264	18	,	,	PUNCT
ejpam-5601	264	19	yα(s	yα(s	PROPN
ejpam-5601	264	20	,	,	PUNCT
ejpam-5601	264	21	t	t	PROPN
ejpam-5601	264	22	)	)	PUNCT
ejpam-5601	264	23	=	=	SYM
ejpam-5601	264	24	fα	fα	ADP
ejpam-5601	264	25	2	2	NUM
ejpam-5601	264	26	(	(	PUNCT
ejpam-5601	264	27	s	s	PROPN
ejpam-5601	264	28	,	,	PUNCT
ejpam-5601	264	29	t	t	PROPN
ejpam-5601	264	30	)	)	PUNCT
ejpam-5601	264	31	·	·	PUNCT
ejpam-5601	265	1	gα2	gα2	NOUN
ejpam-5601	265	2	(	(	PUNCT
ejpam-5601	265	3	s	s	PROPN
ejpam-5601	265	4	,	,	PUNCT
ejpam-5601	265	5	t	t	PROPN
ejpam-5601	265	6	)	)	PUNCT
ejpam-5601	265	7	=	=	PUNCT
ejpam-5601	266	1	y1y2	y1y2	PROPN
ejpam-5601	266	2	+	+	CCONJ
ejpam-5601	266	3	(	(	PUNCT
ejpam-5601	266	4	y1b2	y1b2	PROPN
ejpam-5601	266	5	+	+	NUM
ejpam-5601	266	6	y2b1	y2b1	NOUN
ejpam-5601	266	7	)	)	PUNCT
ejpam-5601	266	8	√	√	NOUN
ejpam-5601	266	9	1−	1−	NUM
ejpam-5601	266	10	α	α	PRON
ejpam-5601	266	11	sin	sin	NOUN
ejpam-5601	266	12	s	s	PART
ejpam-5601	266	13	cos	cos	PROPN
ejpam-5601	266	14	t	t	PROPN
ejpam-5601	266	15	+	+	CCONJ
ejpam-5601	266	16	b1b2(1−	b1b2(1−	PROPN
ejpam-5601	266	17	α	α	NOUN
ejpam-5601	266	18	)	)	PUNCT
ejpam-5601	266	19	sin2	sin2	NOUN
ejpam-5601	266	20	s	s	PART
ejpam-5601	266	21	cos2	cos2	PROPN
ejpam-5601	266	22	t	t	PROPN
ejpam-5601	266	23	,	,	PUNCT
ejpam-5601	266	24	zα(s	zα(s	NUM
ejpam-5601	266	25	,	,	PUNCT
ejpam-5601	266	26	t	t	PROPN
ejpam-5601	266	27	)	)	PUNCT
ejpam-5601	266	28	=	=	PUNCT
ejpam-5601	266	29	fα	fα	ADP
ejpam-5601	266	30	3	3	NUM
ejpam-5601	266	31	(	(	PUNCT
ejpam-5601	266	32	s	s	PROPN
ejpam-5601	266	33	,	,	PUNCT
ejpam-5601	266	34	t	t	PROPN
ejpam-5601	266	35	)	)	PUNCT
ejpam-5601	267	1	·	·	PUNCT
ejpam-5601	267	2	gα3	gα3	PROPN
ejpam-5601	267	3	(	(	PUNCT
ejpam-5601	267	4	s	s	PROPN
ejpam-5601	267	5	,	,	PUNCT
ejpam-5601	267	6	t	t	PROPN
ejpam-5601	267	7	)	)	PUNCT
ejpam-5601	267	8	=	=	PUNCT
ejpam-5601	268	1	z1z2	z1z2	PROPN
ejpam-5601	269	1	+	+	CCONJ
ejpam-5601	269	2	(	(	PUNCT
ejpam-5601	269	3	z1c2	z1c2	X
ejpam-5601	269	4	+	+	NUM
ejpam-5601	269	5	z2c1	z2c1	X
ejpam-5601	269	6	)	)	PUNCT
ejpam-5601	269	7	√	√	ADP
ejpam-5601	269	8	1−	1−	NUM
ejpam-5601	269	9	α	α	PRON
ejpam-5601	269	10	sin	sin	NOUN
ejpam-5601	269	11	s	s	PART
ejpam-5601	269	12	sin	sin	NOUN
ejpam-5601	269	13	t	t	NOUN
ejpam-5601	269	14	+	+	CCONJ
ejpam-5601	269	15	c1c2(1−	c1c2(1−	PROPN
ejpam-5601	269	16	α	α	NOUN
ejpam-5601	269	17	)	)	PUNCT
ejpam-5601	269	18	sin2	sin2	NOUN
ejpam-5601	269	19	s	s	PART
ejpam-5601	269	20	sin2	sin2	NOUN
ejpam-5601	269	21	t.	t.	PROPN
ejpam-5601	269	22	(	(	PUNCT
ejpam-5601	269	23	4	4	X
ejpam-5601	269	24	)	)	PUNCT
ejpam-5601	269	25	let	let	NOUN
ejpam-5601	269	26	(	(	PUNCT
ejpam-5601	269	27	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	269	28	=	=	PRON
ejpam-5601	269	29	{	{	PUNCT
ejpam-5601	269	30	(	(	PUNCT
ejpam-5601	269	31	xα(s	xα(s	NUM
ejpam-5601	269	32	)	)	PUNCT
ejpam-5601	269	33	,	,	PUNCT
ejpam-5601	269	34	yα(s	yα(s	PROPN
ejpam-5601	269	35	,	,	PUNCT
ejpam-5601	269	36	t	t	PROPN
ejpam-5601	269	37	)	)	PUNCT
ejpam-5601	269	38	,	,	PUNCT
ejpam-5601	269	39	zα(s	zα(s	NUM
ejpam-5601	269	40	,	,	PUNCT
ejpam-5601	269	41	t	t	PROPN
ejpam-5601	269	42	)	)	PUNCT
ejpam-5601	269	43	)	)	PUNCT
ejpam-5601	270	1	|	|	ADV
ejpam-5601	270	2	0	0	NUM
ejpam-5601	270	3	≤	≤	NUM
ejpam-5601	270	4	s	s	PART
ejpam-5601	270	5	≤	≤	NOUN
ejpam-5601	270	6	2π,−π	2π,−π	NUM
ejpam-5601	270	7	2	2	NUM
ejpam-5601	270	8	≤	≤	NOUN
ejpam-5601	270	9	t	t	PROPN
ejpam-5601	270	10	≤	≤	NUM
ejpam-5601	270	11	π	π	PROPN
ejpam-5601	270	12	2	2	NUM
ejpam-5601	270	13	}	}	PUNCT
ejpam-5601	270	14	.	.	PUNCT
ejpam-5601	271	1	similarly	similarly	ADV
ejpam-5601	271	2	,	,	PUNCT
ejpam-5601	271	3	we	we	PRON
ejpam-5601	271	4	have	have	VERB
ejpam-5601	271	5	xα(s	xα(s	NUM
ejpam-5601	271	6	)	)	PUNCT
ejpam-5601	272	1	=	=	SYM
ejpam-5601	272	2	x1	x1	PROPN
ejpam-5601	273	1	+	+	CCONJ
ejpam-5601	273	2	a1	a1	NOUN
ejpam-5601	273	3	√	√	PROPN
ejpam-5601	273	4	1−	1−	NUM
ejpam-5601	273	5	α	α	PROPN
ejpam-5601	273	6	cos	cos	PROPN
ejpam-5601	273	7	s	s	PROPN
ejpam-5601	273	8	x2	x2	PROPN
ejpam-5601	273	9	−	−	PROPN
ejpam-5601	273	10	a2	a2	PROPN
ejpam-5601	273	11	√	√	NOUN
ejpam-5601	273	12	1−	1−	NUM
ejpam-5601	273	13	α	α	PROPN
ejpam-5601	273	14	cos	cos	PROPN
ejpam-5601	273	15	s	s	PROPN
ejpam-5601	273	16	yα(s	yα(s	NUM
ejpam-5601	273	17	,	,	PUNCT
ejpam-5601	273	18	t	t	PROPN
ejpam-5601	273	19	)	)	PUNCT
ejpam-5601	273	20	=	=	PUNCT
ejpam-5601	273	21	y1	y1	NOUN
ejpam-5601	273	22	+	+	CCONJ
ejpam-5601	273	23	b1	b1	NOUN
ejpam-5601	273	24	√	√	NUM
ejpam-5601	273	25	1−	1−	NUM
ejpam-5601	274	1	α	α	PRON
ejpam-5601	274	2	sin	sin	NOUN
ejpam-5601	274	3	s	s	X
ejpam-5601	274	4	cos	cos	PROPN
ejpam-5601	274	5	t	t	NOUN
ejpam-5601	274	6	y2	y2	NOUN
ejpam-5601	274	7	−	−	PROPN
ejpam-5601	274	8	b2	b2	NOUN
ejpam-5601	274	9	√	√	NOUN
ejpam-5601	274	10	1−	1−	NUM
ejpam-5601	274	11	α	α	PRON
ejpam-5601	274	12	sin	sin	NOUN
ejpam-5601	274	13	s	s	X
ejpam-5601	274	14	cos	cos	PROPN
ejpam-5601	274	15	t	t	PROPN
ejpam-5601	274	16	,	,	PUNCT
ejpam-5601	274	17	zα(s	zα(s	NUM
ejpam-5601	274	18	,	,	PUNCT
ejpam-5601	274	19	t	t	PROPN
ejpam-5601	274	20	)	)	PUNCT
ejpam-5601	274	21	=	=	SYM
ejpam-5601	275	1	z1	z1	PROPN
ejpam-5601	275	2	+	+	CCONJ
ejpam-5601	275	3	c1	c1	PROPN
ejpam-5601	275	4	√	√	PROPN
ejpam-5601	275	5	1−	1−	NUM
ejpam-5601	275	6	α	α	PRON
ejpam-5601	275	7	sin	sin	NOUN
ejpam-5601	275	8	s	s	PART
ejpam-5601	275	9	sin	sin	NOUN
ejpam-5601	275	10	t	t	PROPN
ejpam-5601	275	11	z2	z2	PROPN
ejpam-5601	275	12	−	−	PROPN
ejpam-5601	275	13	c2	c2	PROPN
ejpam-5601	275	14	√	√	PROPN
ejpam-5601	275	15	1−	1−	NUM
ejpam-5601	276	1	α	α	PRON
ejpam-5601	276	2	sin	sin	NOUN
ejpam-5601	276	3	s	s	PART
ejpam-5601	276	4	sin	sin	NOUN
ejpam-5601	276	5	t	t	NOUN
ejpam-5601	276	6	.	.	PUNCT
ejpam-5601	277	1	the	the	DET
ejpam-5601	277	2	proof	proof	NOUN
ejpam-5601	277	3	is	be	AUX
ejpam-5601	277	4	complete	complete	ADJ
ejpam-5601	277	5	.	.	PUNCT
ejpam-5601	277	6	example	example	NOUN
ejpam-5601	278	1	2	2	NUM
ejpam-5601	278	2	.	.	X
ejpam-5601	278	3	consider	consider	VERB
ejpam-5601	278	4	a	a	PRON
ejpam-5601	278	5	=	=	SYM
ejpam-5601	279	1	[	[	X
ejpam-5601	279	2	6	6	NUM
ejpam-5601	279	3	,	,	PUNCT
ejpam-5601	279	4	3	3	NUM
ejpam-5601	279	5	,	,	PUNCT
ejpam-5601	279	6	8	8	NUM
ejpam-5601	279	7	,	,	PUNCT
ejpam-5601	279	8	5	5	NUM
ejpam-5601	279	9	,	,	PUNCT
ejpam-5601	279	10	4	4	NUM
ejpam-5601	279	11	,	,	PUNCT
ejpam-5601	279	12	7]3	7]3	NUM
ejpam-5601	279	13	and	and	CCONJ
ejpam-5601	279	14	b	b	NOUN
ejpam-5601	279	15	=	=	SYM
ejpam-5601	280	1	[	[	X
ejpam-5601	280	2	4	4	NUM
ejpam-5601	280	3	,	,	PUNCT
ejpam-5601	280	4	2	2	NUM
ejpam-5601	280	5	,	,	PUNCT
ejpam-5601	280	6	5	5	NUM
ejpam-5601	280	7	,	,	PUNCT
ejpam-5601	280	8	3	3	NUM
ejpam-5601	280	9	,	,	PUNCT
ejpam-5601	280	10	6	6	NUM
ejpam-5601	280	11	,	,	PUNCT
ejpam-5601	280	12	4]3	4]3	NUM
ejpam-5601	280	13	.	.	PUNCT
ejpam-5601	281	1	subsequently	subsequently	ADV
ejpam-5601	281	2	,	,	PUNCT
ejpam-5601	281	3	the	the	DET
ejpam-5601	281	4	following	follow	VERB
ejpam-5601	281	5	observations	observation	NOUN
ejpam-5601	281	6	hold	hold	VERB
ejpam-5601	281	7	:	:	PUNCT
ejpam-5601	281	8	(	(	PUNCT
ejpam-5601	281	9	1	1	X
ejpam-5601	281	10	)	)	PUNCT
ejpam-5601	281	11	a(+)pb	a(+)pb	NOUN
ejpam-5601	282	1	=	=	PUNCT
ejpam-5601	283	1	[	[	X
ejpam-5601	283	2	10	10	NUM
ejpam-5601	283	3	,	,	PUNCT
ejpam-5601	283	4	5	5	NUM
ejpam-5601	283	5	,	,	PUNCT
ejpam-5601	283	6	13	13	NUM
ejpam-5601	283	7	,	,	PUNCT
ejpam-5601	283	8	8	8	NUM
ejpam-5601	283	9	,	,	PUNCT
ejpam-5601	283	10	10	10	NUM
ejpam-5601	283	11	,	,	PUNCT
ejpam-5601	283	12	11]3	11]3	NUM
ejpam-5601	283	13	y.	y.	PROPN
ejpam-5601	283	14	s.	s.	PROPN
ejpam-5601	283	15	yun	yun	PROPN
ejpam-5601	283	16	,	,	PUNCT
ejpam-5601	283	17	b.	b.	PROPN
ejpam-5601	283	18	lee	lee	PROPN
ejpam-5601	283	19	/	/	SYM
ejpam-5601	283	20	eur	eur	PROPN
ejpam-5601	283	21	.	.	PUNCT
ejpam-5601	284	1	j.	j.	PROPN
ejpam-5601	284	2	pure	pure	PROPN
ejpam-5601	284	3	appl	appl	PROPN
ejpam-5601	284	4	.	.	PROPN
ejpam-5601	284	5	math	math	PROPN
ejpam-5601	284	6	,	,	PUNCT
ejpam-5601	284	7	18	18	NUM
ejpam-5601	284	8	(	(	PUNCT
ejpam-5601	284	9	1	1	NUM
ejpam-5601	284	10	)	)	PUNCT
ejpam-5601	284	11	(	(	PUNCT
ejpam-5601	284	12	2025	2025	NUM
ejpam-5601	284	13	)	)	PUNCT
ejpam-5601	284	14	,	,	PUNCT
ejpam-5601	284	15	5601	5601	NUM
ejpam-5601	284	16	12	12	NUM
ejpam-5601	284	17	of	of	ADP
ejpam-5601	284	18	17	17	NUM
ejpam-5601	284	19	(	(	PUNCT
ejpam-5601	284	20	2	2	NUM
ejpam-5601	284	21	)	)	PUNCT
ejpam-5601	284	22	a(−)pb	a(−)pb	NOUN
ejpam-5601	284	23	=	=	PUNCT
ejpam-5601	285	1	[	[	X
ejpam-5601	285	2	10	10	NUM
ejpam-5601	285	3	,	,	PUNCT
ejpam-5601	285	4	1	1	NUM
ejpam-5601	285	5	,	,	PUNCT
ejpam-5601	285	6	13	13	NUM
ejpam-5601	285	7	,	,	PUNCT
ejpam-5601	285	8	2	2	NUM
ejpam-5601	285	9	,	,	PUNCT
ejpam-5601	285	10	10	10	NUM
ejpam-5601	285	11	,	,	PUNCT
ejpam-5601	285	12	3]3	3]3	NUM
ejpam-5601	285	13	(	(	PUNCT
ejpam-5601	285	14	3	3	NUM
ejpam-5601	285	15	)	)	PUNCT
ejpam-5601	285	16	(	(	PUNCT
ejpam-5601	285	17	a(·)pb)α	a(·)pb)α	NOUN
ejpam-5601	285	18	=	=	SYM
ejpam-5601	285	19	{	{	PUNCT
ejpam-5601	285	20	(	(	PUNCT
ejpam-5601	285	21	xα(s	xα(s	NUM
ejpam-5601	285	22	)	)	PUNCT
ejpam-5601	285	23	,	,	PUNCT
ejpam-5601	285	24	yα(s	yα(s	PROPN
ejpam-5601	285	25	,	,	PUNCT
ejpam-5601	285	26	t	t	PROPN
ejpam-5601	285	27	)	)	PUNCT
ejpam-5601	285	28	,	,	PUNCT
ejpam-5601	285	29	zα(s	zα(s	NUM
ejpam-5601	285	30	,	,	PUNCT
ejpam-5601	285	31	t	t	PROPN
ejpam-5601	285	32	)	)	PUNCT
ejpam-5601	285	33	)	)	PUNCT
ejpam-5601	286	1	|	|	ADV
ejpam-5601	286	2	0	0	NUM
ejpam-5601	286	3	≤	≤	NUM
ejpam-5601	286	4	s	s	PART
ejpam-5601	286	5	≤	≤	NOUN
ejpam-5601	286	6	2π,−π	2π,−π	NUM
ejpam-5601	286	7	2	2	NUM
ejpam-5601	286	8	≤	≤	NOUN
ejpam-5601	286	9	t	t	PROPN
ejpam-5601	286	10	≤	≤	NUM
ejpam-5601	286	11	π	π	PROPN
ejpam-5601	286	12	2	2	NUM
ejpam-5601	286	13	}	}	PUNCT
ejpam-5601	286	14	,	,	PUNCT
ejpam-5601	286	15	where	where	SCONJ
ejpam-5601	286	16	xα(s	xα(s	X
ejpam-5601	286	17	)	)	PUNCT
ejpam-5601	286	18	=	=	PUNCT
ejpam-5601	287	1	6	6	NUM
ejpam-5601	287	2	+	+	NUM
ejpam-5601	287	3	24	24	NUM
ejpam-5601	287	4	√	√	NUM
ejpam-5601	287	5	1−	1−	NUM
ejpam-5601	287	6	α	α	PROPN
ejpam-5601	287	7	cos	cos	PROPN
ejpam-5601	287	8	s+	s+	PROPN
ejpam-5601	287	9	24(1−	24(1−	NUM
ejpam-5601	287	10	α	α	NOUN
ejpam-5601	287	11	)	)	PUNCT
ejpam-5601	287	12	cos2	cos2	PROPN
ejpam-5601	287	13	s	s	PART
ejpam-5601	287	14	,	,	PUNCT
ejpam-5601	287	15	yα(s	yα(s	PROPN
ejpam-5601	287	16	,	,	PUNCT
ejpam-5601	287	17	t	t	PROPN
ejpam-5601	287	18	)	)	PUNCT
ejpam-5601	287	19	=	=	SYM
ejpam-5601	288	1	15	15	NUM
ejpam-5601	289	1	+	+	NUM
ejpam-5601	289	2	49	49	NUM
ejpam-5601	289	3	√	√	NUM
ejpam-5601	289	4	1−	1−	NUM
ejpam-5601	289	5	α	α	PRON
ejpam-5601	289	6	sin	sin	NOUN
ejpam-5601	289	7	s	s	X
ejpam-5601	289	8	cos	cos	NOUN
ejpam-5601	289	9	t+	t+	VERB
ejpam-5601	289	10	40(1−	40(1−	NUM
ejpam-5601	289	11	α	α	NOUN
ejpam-5601	289	12	)	)	PUNCT
ejpam-5601	289	13	sin2	sin2	NOUN
ejpam-5601	289	14	s	s	PART
ejpam-5601	289	15	cos2	cos2	PROPN
ejpam-5601	289	16	t	t	PROPN
ejpam-5601	289	17	and	and	CCONJ
ejpam-5601	289	18	zα(s	zα(s	NUM
ejpam-5601	289	19	,	,	PUNCT
ejpam-5601	289	20	t	t	PROPN
ejpam-5601	289	21	)	)	PUNCT
ejpam-5601	289	22	=	=	PUNCT
ejpam-5601	290	1	28	28	NUM
ejpam-5601	291	1	+	+	CCONJ
ejpam-5601	292	1	58	58	NUM
ejpam-5601	292	2	√	√	NUM
ejpam-5601	292	3	1−	1−	NUM
ejpam-5601	292	4	α	α	DET
ejpam-5601	292	5	sin	sin	NOUN
ejpam-5601	292	6	s	s	PART
ejpam-5601	292	7	sin	sin	NOUN
ejpam-5601	292	8	t+	t+	PUNCT
ejpam-5601	292	9	24(1−	24(1−	NUM
ejpam-5601	292	10	α	α	X
ejpam-5601	292	11	)	)	PUNCT
ejpam-5601	292	12	sin2	sin2	NOUN
ejpam-5601	292	13	s	s	PART
ejpam-5601	292	14	sin2	sin2	NOUN
ejpam-5601	292	15	t.	t.	PROPN
ejpam-5601	292	16	(	(	PUNCT
ejpam-5601	292	17	4	4	NUM
ejpam-5601	292	18	)	)	PUNCT
ejpam-5601	292	19	(	(	PUNCT
ejpam-5601	292	20	a(/)pb)α	a(/)pb)α	PROPN
ejpam-5601	292	21	=	=	PRON
ejpam-5601	292	22	{	{	PUNCT
ejpam-5601	292	23	(	(	PUNCT
ejpam-5601	292	24	xα(s	xα(s	NUM
ejpam-5601	292	25	)	)	PUNCT
ejpam-5601	292	26	,	,	PUNCT
ejpam-5601	292	27	yα(s	yα(s	PROPN
ejpam-5601	292	28	,	,	PUNCT
ejpam-5601	292	29	t	t	PROPN
ejpam-5601	292	30	)	)	PUNCT
ejpam-5601	292	31	,	,	PUNCT
ejpam-5601	292	32	zα(s	zα(s	NUM
ejpam-5601	292	33	,	,	PUNCT
ejpam-5601	292	34	t	t	PROPN
ejpam-5601	292	35	)	)	PUNCT
ejpam-5601	292	36	)	)	PUNCT
ejpam-5601	293	1	|	|	ADV
ejpam-5601	293	2	0	0	NUM
ejpam-5601	293	3	≤	≤	NUM
ejpam-5601	293	4	s	s	PART
ejpam-5601	293	5	≤	≤	NOUN
ejpam-5601	293	6	2π,−π	2π,−π	NUM
ejpam-5601	293	7	2	2	NUM
ejpam-5601	293	8	≤	≤	NOUN
ejpam-5601	293	9	t	t	PROPN
ejpam-5601	293	10	≤	≤	NUM
ejpam-5601	293	11	π	π	PROPN
ejpam-5601	293	12	2	2	NUM
ejpam-5601	293	13	}	}	PUNCT
ejpam-5601	293	14	,	,	PUNCT
ejpam-5601	293	15	where	where	SCONJ
ejpam-5601	293	16	xα(s	xα(s	X
ejpam-5601	293	17	)	)	PUNCT
ejpam-5601	293	18	=	=	SYM
ejpam-5601	294	1	3	3	NUM
ejpam-5601	294	2	+	+	CCONJ
ejpam-5601	294	3	6	6	NUM
ejpam-5601	294	4	√	√	NUM
ejpam-5601	294	5	1−	1−	NUM
ejpam-5601	294	6	α	α	PROPN
ejpam-5601	294	7	cos	cos	PROPN
ejpam-5601	294	8	s	s	PROPN
ejpam-5601	294	9	2−	2−	NUM
ejpam-5601	294	10	4	4	NUM
ejpam-5601	294	11	√	√	PROPN
ejpam-5601	294	12	1−	1−	NUM
ejpam-5601	294	13	α	α	PROPN
ejpam-5601	294	14	cos	cos	PROPN
ejpam-5601	294	15	s	s	PROPN
ejpam-5601	294	16	yα(s	yα(s	NUM
ejpam-5601	294	17	,	,	PUNCT
ejpam-5601	294	18	t	t	PROPN
ejpam-5601	294	19	)	)	PUNCT
ejpam-5601	294	20	=	=	SYM
ejpam-5601	295	1	5	5	NUM
ejpam-5601	295	2	+	+	CCONJ
ejpam-5601	295	3	8	8	NUM
ejpam-5601	295	4	√	√	NUM
ejpam-5601	295	5	1−	1−	NUM
ejpam-5601	295	6	α	α	PRON
ejpam-5601	295	7	sin	sin	NOUN
ejpam-5601	295	8	s	s	X
ejpam-5601	295	9	cos	cos	PROPN
ejpam-5601	295	10	t	t	PROPN
ejpam-5601	295	11	3−	3−	NUM
ejpam-5601	295	12	5	5	NUM
ejpam-5601	295	13	√	√	NUM
ejpam-5601	295	14	1−	1−	NUM
ejpam-5601	295	15	α	α	PRON
ejpam-5601	295	16	sin	sin	NOUN
ejpam-5601	295	17	s	s	X
ejpam-5601	295	18	cos	cos	PROPN
ejpam-5601	295	19	t	t	PROPN
ejpam-5601	295	20	and	and	CCONJ
ejpam-5601	295	21	zα(s	zα(s	NUM
ejpam-5601	295	22	,	,	PUNCT
ejpam-5601	295	23	t	t	PROPN
ejpam-5601	295	24	)	)	PUNCT
ejpam-5601	296	1	=	=	PUNCT
ejpam-5601	296	2	7	7	NUM
ejpam-5601	297	1	+	+	CCONJ
ejpam-5601	297	2	4	4	NUM
ejpam-5601	297	3	√	√	NUM
ejpam-5601	297	4	1−	1−	NUM
ejpam-5601	297	5	α	α	PRON
ejpam-5601	297	6	sin	sin	NOUN
ejpam-5601	297	7	s	s	PART
ejpam-5601	297	8	sin	sin	NOUN
ejpam-5601	297	9	t	t	PROPN
ejpam-5601	297	10	4−	4−	NUM
ejpam-5601	297	11	6	6	NUM
ejpam-5601	297	12	√	√	NUM
ejpam-5601	297	13	1−	1−	NUM
ejpam-5601	297	14	α	α	PRON
ejpam-5601	297	15	sin	sin	NOUN
ejpam-5601	297	16	s	s	PART
ejpam-5601	297	17	sin	sin	NOUN
ejpam-5601	297	18	t	t	NOUN
ejpam-5601	297	19	.	.	PUNCT
ejpam-5601	298	1	thus	thus	ADV
ejpam-5601	298	2	a(+)pb	a(+)pb	PROPN
ejpam-5601	298	3	and	and	CCONJ
ejpam-5601	298	4	a(−)pb	a(−)pb	PRON
ejpam-5601	298	5	become	become	VERB
ejpam-5601	298	6	3	3	NUM
ejpam-5601	298	7	-	-	PUNCT
ejpam-5601	298	8	dimensional	dimensional	ADJ
ejpam-5601	298	9	quadratic	quadratic	ADJ
ejpam-5601	298	10	fuzzy	fuzzy	ADJ
ejpam-5601	298	11	numbers	number	NOUN
ejpam-5601	298	12	,	,	PUNCT
ejpam-5601	298	13	but	but	CCONJ
ejpam-5601	298	14	a(·)pb	a(·)pb	NOUN
ejpam-5601	298	15	and	and	CCONJ
ejpam-5601	298	16	a(/)pb	a(/)pb	PROPN
ejpam-5601	298	17	are	be	AUX
ejpam-5601	298	18	not	not	PART
ejpam-5601	298	19	3	3	NUM
ejpam-5601	298	20	-	-	PUNCT
ejpam-5601	298	21	dimensional	dimensional	ADJ
ejpam-5601	298	22	quadratic	quadratic	ADJ
ejpam-5601	298	23	fuzzy	fuzzy	ADJ
ejpam-5601	298	24	numbers	number	NOUN
ejpam-5601	298	25	.	.	PUNCT
ejpam-5601	299	1	the	the	DET
ejpam-5601	299	2	membership	membership	NOUN
ejpam-5601	299	3	function	function	NOUN
ejpam-5601	299	4	of	of	ADP
ejpam-5601	299	5	the	the	DET
ejpam-5601	299	6	3	3	NUM
ejpam-5601	299	7	-	-	PUNCT
ejpam-5601	299	8	dimensional	dimensional	ADJ
ejpam-5601	299	9	quadratic	quadratic	ADJ
ejpam-5601	299	10	fuzzy	fuzzy	ADJ
ejpam-5601	299	11	number	number	NOUN
ejpam-5601	299	12	is	be	AUX
ejpam-5601	299	13	a	a	DET
ejpam-5601	299	14	function	function	NOUN
ejpam-5601	299	15	defined	define	VERB
ejpam-5601	299	16	on	on	ADP
ejpam-5601	299	17	r3	r3	PROPN
ejpam-5601	299	18	with	with	ADP
ejpam-5601	299	19	values	value	NOUN
ejpam-5601	299	20	in	in	ADP
ejpam-5601	299	21	[	[	X
ejpam-5601	299	22	0	0	NUM
ejpam-5601	299	23	,	,	PUNCT
ejpam-5601	299	24	1	1	NUM
ejpam-5601	299	25	]	]	PUNCT
ejpam-5601	299	26	.	.	PUNCT
ejpam-5601	300	1	in	in	ADP
ejpam-5601	300	2	the	the	DET
ejpam-5601	300	3	case	case	NOUN
ejpam-5601	300	4	of	of	ADP
ejpam-5601	300	5	the	the	DET
ejpam-5601	300	6	3	3	NUM
ejpam-5601	300	7	-	-	PUNCT
ejpam-5601	300	8	dimensional	dimensional	ADJ
ejpam-5601	300	9	quadratic	quadratic	ADJ
ejpam-5601	300	10	fuzzy	fuzzy	ADJ
ejpam-5601	300	11	numbers	number	NOUN
ejpam-5601	300	12	a	a	PRON
ejpam-5601	300	13	=	=	SYM
ejpam-5601	301	1	[	[	X
ejpam-5601	301	2	6	6	NUM
ejpam-5601	301	3	,	,	PUNCT
ejpam-5601	301	4	3	3	NUM
ejpam-5601	301	5	,	,	PUNCT
ejpam-5601	301	6	8	8	NUM
ejpam-5601	301	7	,	,	PUNCT
ejpam-5601	301	8	5	5	NUM
ejpam-5601	301	9	,	,	PUNCT
ejpam-5601	301	10	4	4	NUM
ejpam-5601	301	11	,	,	PUNCT
ejpam-5601	301	12	7]3	7]3	NUM
ejpam-5601	301	13	and	and	CCONJ
ejpam-5601	301	14	b	b	NOUN
ejpam-5601	302	1	=	=	SYM
ejpam-5601	303	1	[	[	X
ejpam-5601	303	2	4	4	NUM
ejpam-5601	303	3	,	,	PUNCT
ejpam-5601	303	4	2	2	NUM
ejpam-5601	303	5	,	,	PUNCT
ejpam-5601	303	6	5	5	NUM
ejpam-5601	303	7	,	,	PUNCT
ejpam-5601	303	8	3	3	NUM
ejpam-5601	303	9	,	,	PUNCT
ejpam-5601	303	10	6	6	NUM
ejpam-5601	303	11	,	,	PUNCT
ejpam-5601	303	12	4]3	4]3	NUM
ejpam-5601	303	13	,	,	PUNCT
ejpam-5601	303	14	we	we	PRON
ejpam-5601	303	15	depict	depict	VERB
ejpam-5601	303	16	the	the	DET
ejpam-5601	303	17	values	value	NOUN
ejpam-5601	303	18	of	of	ADP
ejpam-5601	303	19	the	the	DET
ejpam-5601	303	20	membership	membership	NOUN
ejpam-5601	303	21	function	function	NOUN
ejpam-5601	303	22	using	use	VERB
ejpam-5601	303	23	colors	color	NOUN
ejpam-5601	303	24	,	,	PUNCT
ejpam-5601	303	25	as	as	ADP
ejpam-5601	303	26	illustrating	illustrate	VERB
ejpam-5601	303	27	in	in	ADP
ejpam-5601	303	28	figure	figure	NOUN
ejpam-5601	303	29	1	1	NUM
ejpam-5601	303	30	and	and	CCONJ
ejpam-5601	303	31	figure	figure	VERB
ejpam-5601	303	32	2	2	NUM
ejpam-5601	303	33	.	.	PUNCT
ejpam-5601	303	34	figure	figure	NOUN
ejpam-5601	303	35	1	1	NUM
ejpam-5601	303	36	:	:	PUNCT
ejpam-5601	303	37	a	a	DET
ejpam-5601	303	38	figure	figure	NOUN
ejpam-5601	303	39	2	2	NUM
ejpam-5601	303	40	:	:	PUNCT
ejpam-5601	303	41	b	b	X
ejpam-5601	303	42	figure	figure	NOUN
ejpam-5601	303	43	3	3	NUM
ejpam-5601	303	44	:	:	PUNCT
ejpam-5601	303	45	a(+)pb	a(+)pb	NOUN
ejpam-5601	303	46	figure	figure	VERB
ejpam-5601	303	47	4	4	NUM
ejpam-5601	303	48	:	:	PUNCT
ejpam-5601	303	49	a(−)pb	a(−)pb	PRON
ejpam-5601	303	50	figure	figure	NOUN
ejpam-5601	303	51	5	5	NUM
ejpam-5601	303	52	:	:	PUNCT
ejpam-5601	303	53	a(·)pb	a(·)pb	NUM
ejpam-5601	303	54	figure	figure	NOUN
ejpam-5601	303	55	6	6	NUM
ejpam-5601	303	56	:	:	PUNCT
ejpam-5601	303	57	a(/)pb	a(/)pb	VERB
ejpam-5601	303	58	the	the	DET
ejpam-5601	303	59	results	result	NOUN
ejpam-5601	303	60	of	of	ADP
ejpam-5601	303	61	the	the	DET
ejpam-5601	303	62	example	example	NOUN
ejpam-5601	303	63	are	be	AUX
ejpam-5601	303	64	depicted	depict	VERB
ejpam-5601	303	65	in	in	ADP
ejpam-5601	303	66	figures	figure	NOUN
ejpam-5601	303	67	3	3	NUM
ejpam-5601	303	68	to	to	PART
ejpam-5601	303	69	6	6	NUM
ejpam-5601	303	70	.	.	PUNCT
ejpam-5601	304	1	the	the	DET
ejpam-5601	304	2	membership	membership	NOUN
ejpam-5601	304	3	function	function	NOUN
ejpam-5601	304	4	values	value	NOUN
ejpam-5601	304	5	for	for	ADP
ejpam-5601	304	6	points	point	NOUN
ejpam-5601	304	7	within	within	ADP
ejpam-5601	304	8	a(+)pb	a(+)pb	PROPN
ejpam-5601	304	9	and	and	CCONJ
ejpam-5601	304	10	a(−)pb	a(−)pb	PROPN
ejpam-5601	304	11	,	,	PUNCT
ejpam-5601	304	12	when	when	SCONJ
ejpam-5601	304	13	intersected	intersect	VERB
ejpam-5601	304	14	by	by	ADP
ejpam-5601	304	15	a	a	DET
ejpam-5601	304	16	plane	plane	NOUN
ejpam-5601	304	17	,	,	PUNCT
ejpam-5601	304	18	are	be	AUX
ejpam-5601	304	19	demonstrated	demonstrate	VERB
ejpam-5601	304	20	in	in	ADP
ejpam-5601	304	21	figures	figure	NOUN
ejpam-5601	304	22	7	7	NUM
ejpam-5601	304	23	to	to	PART
ejpam-5601	304	24	12	12	NUM
ejpam-5601	304	25	and	and	CCONJ
ejpam-5601	304	26	figures	figure	NOUN
ejpam-5601	304	27	13	13	NUM
ejpam-5601	304	28	to	to	PART
ejpam-5601	304	29	21	21	NUM
ejpam-5601	304	30	,	,	PUNCT
ejpam-5601	304	31	respectively	respectively	ADV
ejpam-5601	304	32	.	.	PUNCT
ejpam-5601	305	1	although	although	SCONJ
ejpam-5601	305	2	all	all	DET
ejpam-5601	305	3	graphs	graph	NOUN
ejpam-5601	305	4	appear	appear	VERB
ejpam-5601	305	5	y.	y.	PROPN
ejpam-5601	305	6	s.	s.	PROPN
ejpam-5601	305	7	yun	yun	PROPN
ejpam-5601	305	8	,	,	PUNCT
ejpam-5601	305	9	b.	b.	PROPN
ejpam-5601	305	10	lee	lee	PROPN
ejpam-5601	305	11	/	/	SYM
ejpam-5601	305	12	eur	eur	PROPN
ejpam-5601	305	13	.	.	PUNCT
ejpam-5601	306	1	j.	j.	PROPN
ejpam-5601	306	2	pure	pure	PROPN
ejpam-5601	306	3	appl	appl	PROPN
ejpam-5601	306	4	.	.	PROPN
ejpam-5601	306	5	math	math	PROPN
ejpam-5601	306	6	,	,	PUNCT
ejpam-5601	306	7	18	18	NUM
ejpam-5601	306	8	(	(	PUNCT
ejpam-5601	306	9	1	1	NUM
ejpam-5601	306	10	)	)	PUNCT
ejpam-5601	306	11	(	(	PUNCT
ejpam-5601	306	12	2025	2025	NUM
ejpam-5601	306	13	)	)	PUNCT
ejpam-5601	306	14	,	,	PUNCT
ejpam-5601	306	15	5601	5601	NUM
ejpam-5601	306	16	13	13	NUM
ejpam-5601	306	17	of	of	ADP
ejpam-5601	306	18	17	17	NUM
ejpam-5601	306	19	similar	similar	ADJ
ejpam-5601	306	20	in	in	ADP
ejpam-5601	306	21	shape	shape	NOUN
ejpam-5601	306	22	,	,	PUNCT
ejpam-5601	306	23	a	a	DET
ejpam-5601	306	24	closer	close	ADJ
ejpam-5601	306	25	look	look	NOUN
ejpam-5601	306	26	at	at	ADP
ejpam-5601	306	27	the	the	DET
ejpam-5601	306	28	bar	bar	NOUN
ejpam-5601	306	29	graph	graph	NOUN
ejpam-5601	306	30	showing	show	VERB
ejpam-5601	306	31	the	the	DET
ejpam-5601	306	32	function	function	NOUN
ejpam-5601	306	33	values	value	NOUN
ejpam-5601	306	34	next	next	ADV
ejpam-5601	306	35	to	to	ADP
ejpam-5601	306	36	each	each	DET
ejpam-5601	306	37	figure	figure	NOUN
ejpam-5601	306	38	uncovers	uncover	NOUN
ejpam-5601	306	39	notable	notable	ADJ
ejpam-5601	306	40	differences	difference	NOUN
ejpam-5601	306	41	.	.	PUNCT
ejpam-5601	307	1	it	it	PRON
ejpam-5601	307	2	becomes	become	VERB
ejpam-5601	307	3	clear	clear	ADJ
ejpam-5601	307	4	that	that	SCONJ
ejpam-5601	307	5	the	the	DET
ejpam-5601	307	6	function	function	NOUN
ejpam-5601	307	7	values	value	NOUN
ejpam-5601	307	8	are	be	AUX
ejpam-5601	307	9	not	not	PART
ejpam-5601	307	10	consistent	consistent	ADJ
ejpam-5601	307	11	,	,	PUNCT
ejpam-5601	307	12	unlike	unlike	ADP
ejpam-5601	307	13	what	what	PRON
ejpam-5601	307	14	is	be	AUX
ejpam-5601	307	15	typically	typically	ADV
ejpam-5601	307	16	seen	see	VERB
ejpam-5601	307	17	in	in	ADP
ejpam-5601	307	18	one	one	NUM
ejpam-5601	307	19	or	or	CCONJ
ejpam-5601	307	20	two	two	NUM
ejpam-5601	307	21	dimensions	dimension	NOUN
ejpam-5601	307	22	.	.	PUNCT
ejpam-5601	308	1	fig	fig	NOUN
ejpam-5601	308	2	.	.	PUNCT
ejpam-5601	309	1	7	7	NUM
ejpam-5601	309	2	:	:	PUNCT
ejpam-5601	310	1	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	310	2	≤	≤	ADV
ejpam-5601	310	3	8	8	NUM
ejpam-5601	310	4	fig	fig	NOUN
ejpam-5601	310	5	.	.	PUNCT
ejpam-5601	311	1	8	8	NUM
ejpam-5601	311	2	:	:	PUNCT
ejpam-5601	312	1	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	312	2	≤	≤	ADV
ejpam-5601	312	3	9	9	NUM
ejpam-5601	312	4	fig	fig	NOUN
ejpam-5601	312	5	.	.	PUNCT
ejpam-5601	313	1	9	9	NUM
ejpam-5601	313	2	:	:	PUNCT
ejpam-5601	313	3	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	313	4	≤	≤	ADV
ejpam-5601	313	5	10	10	NUM
ejpam-5601	313	6	fig	fig	NOUN
ejpam-5601	313	7	.	.	PUNCT
ejpam-5601	314	1	10	10	NUM
ejpam-5601	314	2	:	:	PUNCT
ejpam-5601	314	3	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	314	4	≤	≤	ADV
ejpam-5601	314	5	11	11	NUM
ejpam-5601	314	6	fig	fig	NOUN
ejpam-5601	314	7	.	.	PUNCT
ejpam-5601	315	1	11	11	NUM
ejpam-5601	315	2	:	:	PUNCT
ejpam-5601	315	3	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	315	4	≤	≤	VERB
ejpam-5601	315	5	12	12	NUM
ejpam-5601	315	6	fig	fig	NOUN
ejpam-5601	315	7	.	.	PUNCT
ejpam-5601	316	1	12	12	NUM
ejpam-5601	316	2	:	:	PUNCT
ejpam-5601	317	1	a(+)pbz	a(+)pbz	PROPN
ejpam-5601	317	2	≤	≤	VERB
ejpam-5601	317	3	13	13	NUM
ejpam-5601	317	4	fig	fig	NOUN
ejpam-5601	317	5	.	.	PUNCT
ejpam-5601	318	1	13	13	NUM
ejpam-5601	318	2	:	:	PUNCT
ejpam-5601	318	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	318	4	≤	≤	X
ejpam-5601	318	5	−0.15	−0.15	ADP
ejpam-5601	318	6	fig	fig	NOUN
ejpam-5601	318	7	.	.	PUNCT
ejpam-5601	319	1	14	14	NUM
ejpam-5601	319	2	:	:	PUNCT
ejpam-5601	319	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	319	4	≤	≤	NUM
ejpam-5601	319	5	0.5	0.5	NUM
ejpam-5601	319	6	fig	fig	NOUN
ejpam-5601	319	7	.	.	PUNCT
ejpam-5601	320	1	15	15	NUM
ejpam-5601	320	2	:	:	PUNCT
ejpam-5601	320	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	320	4	≤	≤	NUM
ejpam-5601	320	5	1	1	NUM
ejpam-5601	320	6	5	5	NUM
ejpam-5601	320	7	.	.	PUNCT
ejpam-5601	321	1	conclusion	conclusion	NOUN
ejpam-5601	321	2	we	we	PRON
ejpam-5601	321	3	are	be	AUX
ejpam-5601	321	4	broadening	broaden	VERB
ejpam-5601	321	5	the	the	DET
ejpam-5601	321	6	scope	scope	NOUN
ejpam-5601	321	7	of	of	ADP
ejpam-5601	321	8	quadratic	quadratic	ADJ
ejpam-5601	321	9	fuzzy	fuzzy	ADJ
ejpam-5601	321	10	numbers	number	NOUN
ejpam-5601	321	11	from	from	ADP
ejpam-5601	321	12	a	a	DET
ejpam-5601	321	13	two	two	NUM
ejpam-5601	321	14	-	-	PUNCT
ejpam-5601	321	15	dimensional	dimensional	ADJ
ejpam-5601	321	16	space	space	NOUN
ejpam-5601	321	17	r2	r2	NOUN
ejpam-5601	321	18	to	to	ADP
ejpam-5601	321	19	a	a	DET
ejpam-5601	321	20	three	three	NUM
ejpam-5601	321	21	-	-	PUNCT
ejpam-5601	321	22	dimensional	dimensional	ADJ
ejpam-5601	321	23	space	space	NOUN
ejpam-5601	321	24	r3	r3	NOUN
ejpam-5601	321	25	.	.	PUNCT
ejpam-5601	322	1	by	by	ADP
ejpam-5601	322	2	establishing	establish	VERB
ejpam-5601	322	3	parametric	parametric	ADJ
ejpam-5601	322	4	operations	operation	NOUN
ejpam-5601	322	5	between	between	ADP
ejpam-5601	322	6	two	two	NUM
ejpam-5601	322	7	α	α	NOUN
ejpam-5601	322	8	-	-	PUNCT
ejpam-5601	322	9	cuts	cut	NOUN
ejpam-5601	322	10	,	,	PUNCT
ejpam-5601	322	11	which	which	PRON
ejpam-5601	322	12	are	be	AUX
ejpam-5601	322	13	subsets	subset	NOUN
ejpam-5601	322	14	of	of	ADP
ejpam-5601	322	15	r3	r3	PROPN
ejpam-5601	322	16	,	,	PUNCT
ejpam-5601	322	17	we	we	PRON
ejpam-5601	322	18	are	be	AUX
ejpam-5601	322	19	able	able	ADJ
ejpam-5601	322	20	to	to	PART
ejpam-5601	322	21	formulate	formulate	VERB
ejpam-5601	322	22	parametric	parametric	ADJ
ejpam-5601	322	23	operations	operation	NOUN
ejpam-5601	322	24	for	for	ADP
ejpam-5601	322	25	two	two	NUM
ejpam-5601	322	26	quadratic	quadratic	ADJ
ejpam-5601	322	27	fuzzy	fuzzy	ADJ
ejpam-5601	322	28	numbers	number	NOUN
ejpam-5601	322	29	within	within	ADP
ejpam-5601	322	30	the	the	DET
ejpam-5601	322	31	r3	r3	PROPN
ejpam-5601	322	32	space	space	NOUN
ejpam-5601	322	33	.	.	PUNCT
ejpam-5601	323	1	the	the	DET
ejpam-5601	323	2	significance	significance	NOUN
ejpam-5601	323	3	of	of	ADP
ejpam-5601	323	4	this	this	DET
ejpam-5601	323	5	dimensional	dimensional	ADJ
ejpam-5601	323	6	expansion	expansion	NOUN
ejpam-5601	323	7	lies	lie	VERB
ejpam-5601	323	8	in	in	ADP
ejpam-5601	323	9	its	its	PRON
ejpam-5601	323	10	incorporation	incorporation	NOUN
ejpam-5601	323	11	of	of	ADP
ejpam-5601	323	12	zadeh	zadeh	PROPN
ejpam-5601	323	13	’s	’s	PART
ejpam-5601	323	14	defined	define	VERB
ejpam-5601	323	15	max	max	PROPN
ejpam-5601	323	16	-	-	PUNCT
ejpam-5601	323	17	min	min	NOUN
ejpam-5601	323	18	operation	operation	NOUN
ejpam-5601	323	19	in	in	ADP
ejpam-5601	323	20	two	two	NUM
ejpam-5601	323	21	dimensions	dimension	NOUN
ejpam-5601	323	22	[	[	X
ejpam-5601	323	23	10	10	NUM
ejpam-5601	323	24	]	]	PUNCT
ejpam-5601	323	25	.	.	PUNCT
ejpam-5601	324	1	moreover	moreover	ADV
ejpam-5601	324	2	,	,	PUNCT
ejpam-5601	324	3	as	as	ADV
ejpam-5601	324	4	long	long	ADV
ejpam-5601	324	5	as	as	SCONJ
ejpam-5601	324	6	the	the	DET
ejpam-5601	324	7	computations	computation	NOUN
ejpam-5601	324	8	of	of	ADP
ejpam-5601	324	9	these	these	DET
ejpam-5601	324	10	operations	operation	NOUN
ejpam-5601	324	11	remain	remain	VERB
ejpam-5601	324	12	consistent	consistent	ADJ
ejpam-5601	324	13	,	,	PUNCT
ejpam-5601	324	14	this	this	DET
ejpam-5601	324	15	dimensional	dimensional	ADJ
ejpam-5601	324	16	expansion	expansion	NOUN
ejpam-5601	324	17	is	be	AUX
ejpam-5601	324	18	expected	expect	VERB
ejpam-5601	324	19	to	to	PART
ejpam-5601	324	20	further	further	VERB
ejpam-5601	324	21	the	the	DET
ejpam-5601	324	22	research	research	NOUN
ejpam-5601	324	23	in	in	ADP
ejpam-5601	324	24	fractional	fractional	ADJ
ejpam-5601	324	25	programming	programming	NOUN
ejpam-5601	324	26	in	in	ADP
ejpam-5601	324	27	the	the	DET
ejpam-5601	324	28	future	future	NOUN
ejpam-5601	324	29	[	[	X
ejpam-5601	324	30	1	1	NUM
ejpam-5601	324	31	]	]	PUNCT
ejpam-5601	324	32	.	.	PUNCT
ejpam-5601	325	1	y.	y.	PROPN
ejpam-5601	325	2	s.	s.	PROPN
ejpam-5601	325	3	yun	yun	PROPN
ejpam-5601	325	4	,	,	PUNCT
ejpam-5601	325	5	b.	b.	PROPN
ejpam-5601	325	6	lee	lee	PROPN
ejpam-5601	325	7	/	/	SYM
ejpam-5601	325	8	eur	eur	PROPN
ejpam-5601	325	9	.	.	PUNCT
ejpam-5601	326	1	j.	j.	PROPN
ejpam-5601	326	2	pure	pure	PROPN
ejpam-5601	326	3	appl	appl	PROPN
ejpam-5601	326	4	.	.	PROPN
ejpam-5601	326	5	math	math	PROPN
ejpam-5601	326	6	,	,	PUNCT
ejpam-5601	326	7	18	18	NUM
ejpam-5601	326	8	(	(	PUNCT
ejpam-5601	326	9	1	1	NUM
ejpam-5601	326	10	)	)	PUNCT
ejpam-5601	326	11	(	(	PUNCT
ejpam-5601	326	12	2025	2025	NUM
ejpam-5601	326	13	)	)	PUNCT
ejpam-5601	326	14	,	,	PUNCT
ejpam-5601	326	15	5601	5601	NUM
ejpam-5601	326	16	14	14	NUM
ejpam-5601	326	17	of	of	ADP
ejpam-5601	326	18	17	17	NUM
ejpam-5601	326	19	in	in	ADP
ejpam-5601	326	20	[	[	X
ejpam-5601	326	21	2	2	NUM
ejpam-5601	326	22	]	]	PUNCT
ejpam-5601	326	23	,	,	PUNCT
ejpam-5601	326	24	the	the	DET
ejpam-5601	326	25	results	result	NOUN
ejpam-5601	326	26	of	of	ADP
ejpam-5601	326	27	quadratic	quadratic	ADJ
ejpam-5601	326	28	fuzzy	fuzzy	ADJ
ejpam-5601	326	29	numbers	number	NOUN
ejpam-5601	326	30	in	in	ADP
ejpam-5601	326	31	two	two	NUM
ejpam-5601	326	32	dimensions	dimension	NOUN
ejpam-5601	326	33	have	have	AUX
ejpam-5601	326	34	been	be	AUX
ejpam-5601	326	35	detailed	detail	VERB
ejpam-5601	326	36	.	.	PUNCT
ejpam-5601	327	1	when	when	SCONJ
ejpam-5601	327	2	extended	extend	VERB
ejpam-5601	327	3	to	to	ADP
ejpam-5601	327	4	three	three	NUM
ejpam-5601	327	5	dimensions	dimension	NOUN
ejpam-5601	327	6	,	,	PUNCT
ejpam-5601	327	7	the	the	DET
ejpam-5601	327	8	operations	operation	NOUN
ejpam-5601	327	9	a(+)b	a(+)b	PROPN
ejpam-5601	327	10	and	and	CCONJ
ejpam-5601	327	11	a(−)b	a(−)b	NOUN
ejpam-5601	327	12	evolve	evolve	VERB
ejpam-5601	327	13	into	into	ADP
ejpam-5601	327	14	3dimensional	3dimensional	ADJ
ejpam-5601	327	15	quadratic	quadratic	ADJ
ejpam-5601	327	16	fuzzy	fuzzy	ADJ
ejpam-5601	327	17	numbers	number	NOUN
ejpam-5601	327	18	.	.	PUNCT
ejpam-5601	328	1	however	however	ADV
ejpam-5601	328	2	,	,	PUNCT
ejpam-5601	328	3	this	this	DET
ejpam-5601	328	4	transformation	transformation	NOUN
ejpam-5601	328	5	does	do	AUX
ejpam-5601	328	6	not	not	PART
ejpam-5601	328	7	apply	apply	VERB
ejpam-5601	328	8	to	to	ADP
ejpam-5601	328	9	a(·)b	a(·)b	NOUN
ejpam-5601	328	10	and	and	CCONJ
ejpam-5601	328	11	a(/)b	a(/)b	NOUN
ejpam-5601	328	12	.	.	PUNCT
ejpam-5601	329	1	the	the	DET
ejpam-5601	329	2	inherent	inherent	ADJ
ejpam-5601	329	3	well	well	ADV
ejpam-5601	329	4	-	-	PUNCT
ejpam-5601	329	5	structured	structure	VERB
ejpam-5601	329	6	nature	nature	NOUN
ejpam-5601	329	7	of	of	ADP
ejpam-5601	329	8	a(+)b	a(+)b	PROPN
ejpam-5601	329	9	and	and	CCONJ
ejpam-5601	329	10	a(−)b	a(−)b	PROPN
ejpam-5601	329	11	allows	allow	VERB
ejpam-5601	329	12	them	they	PRON
ejpam-5601	329	13	to	to	PART
ejpam-5601	329	14	be	be	AUX
ejpam-5601	329	15	utilized	utilize	VERB
ejpam-5601	329	16	in	in	ADP
ejpam-5601	329	17	a	a	DET
ejpam-5601	329	18	wide	wide	ADJ
ejpam-5601	329	19	range	range	NOUN
ejpam-5601	329	20	of	of	ADP
ejpam-5601	329	21	fields	field	NOUN
ejpam-5601	329	22	without	without	ADP
ejpam-5601	329	23	needing	need	VERB
ejpam-5601	329	24	any	any	DET
ejpam-5601	329	25	alterations	alteration	NOUN
ejpam-5601	329	26	.	.	PUNCT
ejpam-5601	330	1	conversely	conversely	ADV
ejpam-5601	330	2	,	,	PUNCT
ejpam-5601	330	3	by	by	ADP
ejpam-5601	330	4	modifying	modify	VERB
ejpam-5601	330	5	the	the	DET
ejpam-5601	330	6	forms	form	NOUN
ejpam-5601	330	7	of	of	ADP
ejpam-5601	330	8	a(·)b	a(·)b	NOUN
ejpam-5601	330	9	and	and	CCONJ
ejpam-5601	330	10	a(/)b	a(/)b	NUM
ejpam-5601	330	11	,	,	PUNCT
ejpam-5601	330	12	they	they	PRON
ejpam-5601	330	13	can	can	AUX
ejpam-5601	330	14	be	be	AUX
ejpam-5601	330	15	adapted	adapt	VERB
ejpam-5601	330	16	for	for	ADP
ejpam-5601	330	17	use	use	NOUN
ejpam-5601	330	18	in	in	ADP
ejpam-5601	330	19	various	various	ADJ
ejpam-5601	330	20	applications	application	NOUN
ejpam-5601	330	21	.	.	PUNCT
ejpam-5601	331	1	fig	fig	NOUN
ejpam-5601	331	2	.	.	PUNCT
ejpam-5601	332	1	16	16	NUM
ejpam-5601	332	2	:	:	PUNCT
ejpam-5601	332	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	332	4	≤	≤	ADJ
ejpam-5601	332	5	2	2	NUM
ejpam-5601	332	6	fig	fig	NOUN
ejpam-5601	332	7	.	.	PUNCT
ejpam-5601	333	1	17	17	NUM
ejpam-5601	333	2	:	:	PUNCT
ejpam-5601	333	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	333	4	≤	≤	ADJ
ejpam-5601	333	5	3	3	NUM
ejpam-5601	333	6	fig	fig	NOUN
ejpam-5601	333	7	.	.	PUNCT
ejpam-5601	334	1	18	18	NUM
ejpam-5601	334	2	:	:	PUNCT
ejpam-5601	334	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	334	4	≤	≤	NUM
ejpam-5601	334	5	4	4	NUM
ejpam-5601	334	6	fig	fig	NOUN
ejpam-5601	334	7	.	.	PUNCT
ejpam-5601	335	1	19	19	NUM
ejpam-5601	335	2	:	:	PUNCT
ejpam-5601	335	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	335	4	≤	≤	NUM
ejpam-5601	335	5	5	5	NUM
ejpam-5601	335	6	fig	fig	NOUN
ejpam-5601	335	7	.	.	PUNCT
ejpam-5601	336	1	20	20	NUM
ejpam-5601	336	2	:	:	PUNCT
ejpam-5601	336	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	336	4	≤	≤	NUM
ejpam-5601	336	5	5.5	5.5	NUM
ejpam-5601	336	6	fig	fig	NOUN
ejpam-5601	336	7	.	.	PUNCT
ejpam-5601	337	1	21	21	NUM
ejpam-5601	337	2	:	:	PUNCT
ejpam-5601	337	3	a(−)pbz	a(−)pbz	VERB
ejpam-5601	337	4	≤	≤	ADJ
ejpam-5601	337	5	6	6	NUM
ejpam-5601	337	6	this	this	DET
ejpam-5601	337	7	result	result	NOUN
ejpam-5601	337	8	can	can	AUX
ejpam-5601	337	9	be	be	AUX
ejpam-5601	337	10	applied	apply	VERB
ejpam-5601	337	11	to	to	PART
ejpam-5601	337	12	demonstrate	demonstrate	VERB
ejpam-5601	337	13	that	that	SCONJ
ejpam-5601	337	14	the	the	DET
ejpam-5601	337	15	3	3	NUM
ejpam-5601	337	16	-	-	PUNCT
ejpam-5601	337	17	dimensional	dimensional	ADJ
ejpam-5601	337	18	case	case	NOUN
ejpam-5601	337	19	is	be	AUX
ejpam-5601	337	20	a	a	DET
ejpam-5601	337	21	generalization	generalization	NOUN
ejpam-5601	337	22	of	of	ADP
ejpam-5601	337	23	the	the	DET
ejpam-5601	337	24	2	2	NUM
ejpam-5601	337	25	-	-	PUNCT
ejpam-5601	337	26	dimensional	dimensional	ADJ
ejpam-5601	337	27	case	case	NOUN
ejpam-5601	337	28	.	.	PUNCT
ejpam-5601	338	1	while	while	SCONJ
ejpam-5601	338	2	there	there	PRON
ejpam-5601	338	3	have	have	AUX
ejpam-5601	338	4	been	be	AUX
ejpam-5601	338	5	various	various	ADJ
ejpam-5601	338	6	attempts	attempt	NOUN
ejpam-5601	338	7	to	to	PART
ejpam-5601	338	8	expand	expand	VERB
ejpam-5601	338	9	the	the	DET
ejpam-5601	338	10	dimension	dimension	NOUN
ejpam-5601	338	11	,	,	PUNCT
ejpam-5601	338	12	no	no	DET
ejpam-5601	338	13	studies	study	NOUN
ejpam-5601	338	14	have	have	AUX
ejpam-5601	338	15	successfully	successfully	ADV
ejpam-5601	338	16	achieved	achieve	VERB
ejpam-5601	338	17	expansion	expansion	NOUN
ejpam-5601	338	18	while	while	SCONJ
ejpam-5601	338	19	preserving	preserve	VERB
ejpam-5601	338	20	zadeh	zadeh	PROPN
ejpam-5601	338	21	’s	’s	PART
ejpam-5601	338	22	results	result	NOUN
ejpam-5601	338	23	for	for	ADP
ejpam-5601	338	24	1	1	NUM
ejpam-5601	338	25	and	and	CCONJ
ejpam-5601	338	26	2	2	NUM
ejpam-5601	338	27	-	-	PUNCT
ejpam-5601	338	28	dimensional	dimensional	ADJ
ejpam-5601	338	29	quadratic	quadratic	ADJ
ejpam-5601	338	30	fuzzy	fuzzy	ADJ
ejpam-5601	338	31	numbers	number	NOUN
ejpam-5601	338	32	.	.	PUNCT
ejpam-5601	339	1	this	this	DET
ejpam-5601	339	2	paper	paper	NOUN
ejpam-5601	339	3	aims	aim	VERB
ejpam-5601	339	4	to	to	PART
ejpam-5601	339	5	contribute	contribute	VERB
ejpam-5601	339	6	to	to	ADP
ejpam-5601	339	7	the	the	DET
ejpam-5601	339	8	advancement	advancement	NOUN
ejpam-5601	339	9	of	of	ADP
ejpam-5601	339	10	applications	application	NOUN
ejpam-5601	339	11	of	of	ADP
ejpam-5601	339	12	quadratic	quadratic	ADJ
ejpam-5601	339	13	fuzzy	fuzzy	ADJ
ejpam-5601	339	14	numbers	number	NOUN
ejpam-5601	339	15	by	by	ADP
ejpam-5601	339	16	extending	extend	VERB
ejpam-5601	339	17	their	their	PRON
ejpam-5601	339	18	dimension	dimension	NOUN
ejpam-5601	339	19	.	.	PUNCT
ejpam-5601	340	1	the	the	DET
ejpam-5601	340	2	application	application	NOUN
ejpam-5601	340	3	scope	scope	NOUN
ejpam-5601	340	4	of	of	ADP
ejpam-5601	340	5	this	this	DET
ejpam-5601	340	6	paper	paper	NOUN
ejpam-5601	340	7	includes	include	VERB
ejpam-5601	340	8	solving	solve	VERB
ejpam-5601	340	9	the	the	DET
ejpam-5601	340	10	3	3	NUM
ejpam-5601	340	11	-	-	PUNCT
ejpam-5601	340	12	dimensional	dimensional	ADJ
ejpam-5601	340	13	flow	flow	NOUN
ejpam-5601	340	14	shop	shop	NOUN
ejpam-5601	340	15	scheduling	scheduling	NOUN
ejpam-5601	340	16	problem	problem	NOUN
ejpam-5601	340	17	and	and	CCONJ
ejpam-5601	340	18	quadratic	quadratic	ADJ
ejpam-5601	340	19	fuzzy	fuzzy	ADJ
ejpam-5601	340	20	equations	equation	NOUN
ejpam-5601	340	21	[	[	X
ejpam-5601	340	22	5	5	NUM
ejpam-5601	340	23	,	,	PUNCT
ejpam-5601	340	24	11	11	NUM
ejpam-5601	340	25	]	]	PUNCT
ejpam-5601	340	26	,	,	PUNCT
ejpam-5601	340	27	with	with	ADP
ejpam-5601	340	28	expectations	expectation	NOUN
ejpam-5601	340	29	of	of	ADP
ejpam-5601	340	30	further	further	ADJ
ejpam-5601	340	31	applications	application	NOUN
ejpam-5601	340	32	across	across	ADP
ejpam-5601	340	33	numerous	numerous	ADJ
ejpam-5601	340	34	fields	field	NOUN
ejpam-5601	340	35	.	.	PUNCT
ejpam-5601	341	1	conflicts	conflict	NOUN
ejpam-5601	341	2	of	of	ADP
ejpam-5601	341	3	interest	interest	NOUN
ejpam-5601	341	4	the	the	DET
ejpam-5601	341	5	authors	author	NOUN
ejpam-5601	341	6	declare	declare	VERB
ejpam-5601	341	7	that	that	SCONJ
ejpam-5601	341	8	there	there	PRON
ejpam-5601	341	9	are	be	VERB
ejpam-5601	341	10	no	no	DET
ejpam-5601	341	11	conflicts	conflict	NOUN
ejpam-5601	341	12	of	of	ADP
ejpam-5601	341	13	interest	interest	NOUN
ejpam-5601	341	14	regarding	regard	VERB
ejpam-5601	341	15	the	the	DET
ejpam-5601	341	16	publication	publication	NOUN
ejpam-5601	341	17	of	of	ADP
ejpam-5601	341	18	this	this	DET
ejpam-5601	341	19	article	article	NOUN
ejpam-5601	341	20	.	.	PUNCT
ejpam-5601	342	1	y.	y.	PROPN
ejpam-5601	342	2	s.	s.	PROPN
ejpam-5601	342	3	yun	yun	PROPN
ejpam-5601	342	4	,	,	PUNCT
ejpam-5601	342	5	b.	b.	PROPN
ejpam-5601	342	6	lee	lee	PROPN
ejpam-5601	342	7	/	/	SYM
ejpam-5601	342	8	eur	eur	PROPN
ejpam-5601	342	9	.	.	PUNCT
ejpam-5601	343	1	j.	j.	PROPN
ejpam-5601	343	2	pure	pure	PROPN
ejpam-5601	343	3	appl	appl	PROPN
ejpam-5601	343	4	.	.	PROPN
ejpam-5601	343	5	math	math	PROPN
ejpam-5601	343	6	,	,	PUNCT
ejpam-5601	343	7	18	18	NUM
ejpam-5601	343	8	(	(	PUNCT
ejpam-5601	343	9	1	1	NUM
ejpam-5601	343	10	)	)	PUNCT
ejpam-5601	343	11	(	(	PUNCT
ejpam-5601	343	12	2025	2025	NUM
ejpam-5601	343	13	)	)	PUNCT
ejpam-5601	343	14	,	,	PUNCT
ejpam-5601	343	15	5601	5601	NUM
ejpam-5601	343	16	15	15	NUM
ejpam-5601	343	17	of	of	ADP
ejpam-5601	343	18	17	17	NUM
ejpam-5601	343	19	references	reference	NOUN
ejpam-5601	343	20	[	[	X
ejpam-5601	343	21	1	1	NUM
ejpam-5601	343	22	]	]	PUNCT
ejpam-5601	343	23	s.	s.	PROPN
ejpam-5601	343	24	jain	jain	PROPN
ejpam-5601	343	25	.	.	PUNCT
ejpam-5601	344	1	close	close	ADJ
ejpam-5601	344	2	interval	interval	NOUN
ejpam-5601	344	3	approximation	approximation	NOUN
ejpam-5601	344	4	of	of	ADP
ejpam-5601	344	5	piecewise	piecewise	NOUN
ejpam-5601	344	6	quadratic	quadratic	ADJ
ejpam-5601	344	7	fuzzy	fuzzy	ADJ
ejpam-5601	344	8	numbers	number	NOUN
ejpam-5601	344	9	for	for	ADP
ejpam-5601	344	10	fuzzy	fuzzy	ADJ
ejpam-5601	344	11	fractional	fractional	ADJ
ejpam-5601	344	12	program	program	NOUN
ejpam-5601	344	13	.	.	PUNCT
ejpam-5601	345	1	iranian	iranian	ADJ
ejpam-5601	345	2	journal	journal	PROPN
ejpam-5601	345	3	of	of	ADP
ejpam-5601	345	4	operations	operation	NOUN
ejpam-5601	345	5	research	research	NOUN
ejpam-5601	345	6	,	,	PUNCT
ejpam-5601	345	7	2(1):77–88	2(1):77–88	NUM
ejpam-5601	345	8	,	,	PUNCT
ejpam-5601	345	9	2010	2010	NUM
ejpam-5601	345	10	.	.	PUNCT
ejpam-5601	346	1	[	[	X
ejpam-5601	346	2	2	2	NUM
ejpam-5601	346	3	]	]	PUNCT
ejpam-5601	346	4	c.	c.	PROPN
ejpam-5601	346	5	kang	kang	PROPN
ejpam-5601	346	6	and	and	CCONJ
ejpam-5601	346	7	y.s	y.s	PROPN
ejpam-5601	346	8	.	.	PROPN
ejpam-5601	346	9	yun	yun	PROPN
ejpam-5601	346	10	.	.	PUNCT
ejpam-5601	347	1	a	a	DET
ejpam-5601	347	2	zadeh‘s	zadeh‘s	NUM
ejpam-5601	347	3	max	max	PROPN
ejpam-5601	347	4	-	-	PUNCT
ejpam-5601	347	5	min	min	NOUN
ejpam-5601	347	6	composition	composition	NOUN
ejpam-5601	347	7	operator	operator	NOUN
ejpam-5601	347	8	for	for	ADP
ejpam-5601	347	9	two	two	NUM
ejpam-5601	347	10	2dimensional	2dimensional	NUM
ejpam-5601	347	11	quadratic	quadratic	ADJ
ejpam-5601	347	12	fuzzy	fuzzy	ADJ
ejpam-5601	347	13	numbers	number	NOUN
ejpam-5601	347	14	.	.	PUNCT
ejpam-5601	348	1	far	far	PROPN
ejpam-5601	348	2	east	east	PROPN
ejpam-5601	348	3	journal	journal	PROPN
ejpam-5601	348	4	of	of	ADP
ejpam-5601	348	5	mathematical	mathematical	ADJ
ejpam-5601	348	6	sciences	science	NOUN
ejpam-5601	348	7	,	,	PUNCT
ejpam-5601	348	8	101(10):2185–2193	101(10):2185–2193	NUM
ejpam-5601	348	9	,	,	PUNCT
ejpam-5601	348	10	2017	2017	NUM
ejpam-5601	348	11	.	.	PUNCT
ejpam-5601	349	1	[	[	X
ejpam-5601	349	2	3	3	X
ejpam-5601	349	3	]	]	X
ejpam-5601	349	4	c.	c.	PROPN
ejpam-5601	349	5	kim	kim	PROPN
ejpam-5601	349	6	and	and	CCONJ
ejpam-5601	349	7	y.s	y.s	PROPN
ejpam-5601	349	8	.	.	PROPN
ejpam-5601	349	9	yun	yun	PROPN
ejpam-5601	349	10	.	.	PUNCT
ejpam-5601	350	1	zadeh	zadeh	PROPN
ejpam-5601	350	2	’s	’s	PART
ejpam-5601	350	3	extension	extension	NOUN
ejpam-5601	350	4	principle	principle	NOUN
ejpam-5601	350	5	for	for	ADP
ejpam-5601	350	6	2	2	NUM
ejpam-5601	350	7	-	-	PUNCT
ejpam-5601	350	8	dimensional	dimensional	ADJ
ejpam-5601	350	9	triangular	triangular	NOUN
ejpam-5601	350	10	fuzzy	fuzzy	ADJ
ejpam-5601	350	11	numbers	number	NOUN
ejpam-5601	350	12	.	.	PUNCT
ejpam-5601	351	1	journal	journal	NOUN
ejpam-5601	351	2	of	of	ADP
ejpam-5601	351	3	fuzzy	fuzzy	ADJ
ejpam-5601	351	4	logic	logic	NOUN
ejpam-5601	351	5	and	and	CCONJ
ejpam-5601	351	6	intelligent	intelligent	ADJ
ejpam-5601	351	7	systems	system	NOUN
ejpam-5601	351	8	,	,	PUNCT
ejpam-5601	351	9	25(2):197–202	25(2):197–202	PROPN
ejpam-5601	351	10	,	,	PUNCT
ejpam-5601	351	11	2015	2015	NUM
ejpam-5601	351	12	.	.	PUNCT
ejpam-5601	352	1	[	[	X
ejpam-5601	352	2	4	4	X
ejpam-5601	352	3	]	]	X
ejpam-5601	352	4	w.	w.	PROPN
ejpam-5601	352	5	kumam	kumam	PROPN
ejpam-5601	352	6	and	and	CCONJ
ejpam-5601	352	7	a.	a.	NOUN
ejpam-5601	352	8	pongpullponsak	pongpullponsak	PROPN
ejpam-5601	352	9	.	.	PUNCT
ejpam-5601	353	1	optimization	optimization	NOUN
ejpam-5601	353	2	for	for	ADP
ejpam-5601	353	3	estimation	estimation	NOUN
ejpam-5601	353	4	to	to	ADP
ejpam-5601	353	5	medical	medical	ADJ
ejpam-5601	353	6	service	service	NOUN
ejpam-5601	353	7	value	value	NOUN
ejpam-5601	353	8	of	of	ADP
ejpam-5601	353	9	informal	informal	ADJ
ejpam-5601	353	10	workers	worker	NOUN
ejpam-5601	353	11	social	social	ADJ
ejpam-5601	353	12	security	security	NOUN
ejpam-5601	353	13	office	office	NOUN
ejpam-5601	353	14	in	in	ADP
ejpam-5601	353	15	thailand	thailand	PROPN
ejpam-5601	353	16	.	.	PUNCT
ejpam-5601	354	1	journal	journal	PROPN
ejpam-5601	354	2	of	of	ADP
ejpam-5601	354	3	information	information	NOUN
ejpam-5601	354	4	and	and	CCONJ
ejpam-5601	354	5	optimization	optimization	NOUN
ejpam-5601	354	6	sciences	science	NOUN
ejpam-5601	354	7	,	,	PUNCT
ejpam-5601	354	8	37(1):125–154	37(1):125–154	PROPN
ejpam-5601	354	9	,	,	PUNCT
ejpam-5601	354	10	2016	2016	NUM
ejpam-5601	354	11	.	.	PUNCT
ejpam-5601	355	1	[	[	X
ejpam-5601	355	2	5	5	NUM
ejpam-5601	355	3	]	]	PUNCT
ejpam-5601	355	4	m.	m.	NOUN
ejpam-5601	355	5	landowski	landowski	PROPN
ejpam-5601	355	6	.	.	PUNCT
ejpam-5601	356	1	horizontal	horizontal	ADJ
ejpam-5601	356	2	fuzzy	fuzzy	ADJ
ejpam-5601	356	3	numbers	number	NOUN
ejpam-5601	356	4	for	for	ADP
ejpam-5601	356	5	solving	solve	VERB
ejpam-5601	356	6	quadratic	quadratic	ADJ
ejpam-5601	356	7	fuzzy	fuzzy	ADJ
ejpam-5601	356	8	equation	equation	NOUN
ejpam-5601	356	9	.	.	PUNCT
ejpam-5601	357	1	springer	springer	NOUN
ejpam-5601	357	2	,	,	PUNCT
ejpam-5601	357	3	advances	advance	NOUN
ejpam-5601	357	4	in	in	ADP
ejpam-5601	357	5	soft	soft	ADJ
ejpam-5601	357	6	and	and	CCONJ
ejpam-5601	357	7	hard	hard	ADJ
ejpam-5601	357	8	computing	computing	NOUN
ejpam-5601	357	9	,	,	PUNCT
ejpam-5601	357	10	advances	advance	NOUN
ejpam-5601	357	11	in	in	ADP
ejpam-5601	357	12	intelligent	intelligent	ADJ
ejpam-5601	357	13	systems	system	NOUN
ejpam-5601	357	14	and	and	CCONJ
ejpam-5601	357	15	computing	computing	NOUN
ejpam-5601	357	16	889	889	NUM
ejpam-5601	357	17	,	,	PUNCT
ejpam-5601	357	18	2019	2019	NUM
ejpam-5601	357	19	.	.	PUNCT
ejpam-5601	358	1	[	[	X
ejpam-5601	358	2	6	6	NUM
ejpam-5601	358	3	]	]	X
ejpam-5601	358	4	j.w	j.w	PROPN
ejpam-5601	358	5	.	.	PROPN
ejpam-5601	358	6	park	park	PROPN
ejpam-5601	358	7	and	and	CCONJ
ejpam-5601	358	8	y.s	y.s	PROPN
ejpam-5601	358	9	.	.	PROPN
ejpam-5601	358	10	yun	yun	PROPN
ejpam-5601	358	11	.	.	PUNCT
ejpam-5601	359	1	the	the	DET
ejpam-5601	359	2	result	result	NOUN
ejpam-5601	359	3	of	of	ADP
ejpam-5601	359	4	arithmetic	arithmetic	ADJ
ejpam-5601	359	5	operations	operation	NOUN
ejpam-5601	359	6	applied	apply	VERB
ejpam-5601	359	7	on	on	ADP
ejpam-5601	359	8	general	general	ADJ
ejpam-5601	359	9	quadratic	quadratic	ADJ
ejpam-5601	359	10	fuzzy	fuzzy	ADJ
ejpam-5601	359	11	sets	set	NOUN
ejpam-5601	359	12	.	.	PUNCT
ejpam-5601	360	1	journal	journal	NOUN
ejpam-5601	360	2	of	of	ADP
ejpam-5601	360	3	analysis	analysis	NOUN
ejpam-5601	360	4	and	and	CCONJ
ejpam-5601	360	5	applications	application	NOUN
ejpam-5601	360	6	,	,	PUNCT
ejpam-5601	360	7	20(1):2459–2471	20(1):2459–2471	NUM
ejpam-5601	360	8	,	,	PUNCT
ejpam-5601	360	9	2022	2022	NUM
ejpam-5601	360	10	.	.	PUNCT
ejpam-5601	361	1	[	[	X
ejpam-5601	361	2	7	7	X
ejpam-5601	361	3	]	]	X
ejpam-5601	361	4	l.	l.	PROPN
ejpam-5601	361	5	platil	platil	PROPN
ejpam-5601	361	6	and	and	CCONJ
ejpam-5601	361	7	t.	t.	PROPN
ejpam-5601	361	8	tanaka	tanaka	PROPN
ejpam-5601	361	9	.	.	PUNCT
ejpam-5601	362	1	optimization	optimization	NOUN
ejpam-5601	362	2	for	for	ADP
ejpam-5601	362	3	estimation	estimation	NOUN
ejpam-5601	362	4	to	to	ADP
ejpam-5601	362	5	medical	medical	ADJ
ejpam-5601	362	6	office	office	NOUN
ejpam-5601	362	7	in	in	ADP
ejpam-5601	362	8	thailand	thailand	PROPN
ejpam-5601	362	9	.	.	PUNCT
ejpam-5601	363	1	multi	multi	ADJ
ejpam-5601	363	2	-	-	ADJ
ejpam-5601	363	3	criteria	criteria	ADJ
ejpam-5601	363	4	evaluation	evaluation	NOUN
ejpam-5601	363	5	for	for	ADP
ejpam-5601	363	6	intuitionistic	intuitionistic	ADJ
ejpam-5601	363	7	fuzzy	fuzzy	ADJ
ejpam-5601	363	8	sets	set	NOUN
ejpam-5601	363	9	based	base	VERB
ejpam-5601	363	10	on	on	ADP
ejpam-5601	363	11	set	set	NOUN
ejpam-5601	363	12	-	-	PUNCT
ejpam-5601	363	13	relations	relation	NOUN
ejpam-5601	363	14	,	,	PUNCT
ejpam-5601	363	15	34:1–18	34:1–18	NUM
ejpam-5601	363	16	,	,	PUNCT
ejpam-5601	363	17	2023	2023	NUM
ejpam-5601	363	18	.	.	PUNCT
ejpam-5601	364	1	[	[	X
ejpam-5601	364	2	8	8	NUM
ejpam-5601	364	3	]	]	X
ejpam-5601	364	4	y.s	y.s	PROPN
ejpam-5601	364	5	.	.	PROPN
ejpam-5601	364	6	yun	yun	PROPN
ejpam-5601	364	7	.	.	PUNCT
ejpam-5601	365	1	an	an	DET
ejpam-5601	365	2	algebraic	algebraic	ADJ
ejpam-5601	365	3	operations	operation	NOUN
ejpam-5601	365	4	for	for	ADP
ejpam-5601	365	5	two	two	NUM
ejpam-5601	365	6	generalized	generalized	ADJ
ejpam-5601	365	7	2	2	NUM
ejpam-5601	365	8	-	-	PUNCT
ejpam-5601	365	9	dimensional	dimensional	ADJ
ejpam-5601	365	10	quadratic	quadratic	ADJ
ejpam-5601	365	11	fuzzy	fuzzy	ADJ
ejpam-5601	365	12	sets	set	NOUN
ejpam-5601	365	13	.	.	PUNCT
ejpam-5601	366	1	journal	journal	NOUN
ejpam-5601	366	2	of	of	ADP
ejpam-5601	366	3	the	the	DET
ejpam-5601	366	4	chungcheong	chungcheong	PROPN
ejpam-5601	366	5	mathematical	mathematical	ADJ
ejpam-5601	366	6	society	society	NOUN
ejpam-5601	366	7	,	,	PUNCT
ejpam-5601	366	8	31(4):379–386	31(4):379–386	PROPN
ejpam-5601	366	9	,	,	PUNCT
ejpam-5601	366	10	2018	2018	NUM
ejpam-5601	366	11	.	.	PUNCT
ejpam-5601	367	1	[	[	X
ejpam-5601	367	2	9	9	NUM
ejpam-5601	367	3	]	]	X
ejpam-5601	367	4	y.s	y.s	PROPN
ejpam-5601	367	5	.	.	PROPN
ejpam-5601	367	6	yun	yun	PROPN
ejpam-5601	367	7	and	and	CCONJ
ejpam-5601	367	8	j.w	j.w	PROPN
ejpam-5601	367	9	.	.	PROPN
ejpam-5601	367	10	park	park	PROPN
ejpam-5601	367	11	.	.	PUNCT
ejpam-5601	368	1	the	the	DET
ejpam-5601	368	2	extended	extend	VERB
ejpam-5601	368	3	operations	operation	NOUN
ejpam-5601	368	4	for	for	ADP
ejpam-5601	368	5	generalized	generalized	ADJ
ejpam-5601	368	6	quadratic	quadratic	ADJ
ejpam-5601	368	7	fuzzy	fuzzy	ADJ
ejpam-5601	368	8	sets	set	NOUN
ejpam-5601	368	9	.	.	PUNCT
ejpam-5601	369	1	journal	journal	NOUN
ejpam-5601	369	2	of	of	ADP
ejpam-5601	369	3	the	the	DET
ejpam-5601	369	4	korean	korean	PROPN
ejpam-5601	369	5	institute	institute	PROPN
ejpam-5601	369	6	of	of	ADP
ejpam-5601	369	7	intelligent	intelligent	ADJ
ejpam-5601	369	8	systems	system	NOUN
ejpam-5601	369	9	,	,	PUNCT
ejpam-5601	369	10	20(4):592–595	20(4):592–595	PROPN
ejpam-5601	369	11	,	,	PUNCT
ejpam-5601	369	12	2010	2010	NUM
ejpam-5601	369	13	.	.	PUNCT
ejpam-5601	370	1	[	[	X
ejpam-5601	370	2	10	10	NUM
ejpam-5601	370	3	]	]	X
ejpam-5601	370	4	l.a	l.a	PROPN
ejpam-5601	370	5	.	.	PROPN
ejpam-5601	370	6	zadeh	zadeh	PROPN
ejpam-5601	370	7	.	.	PUNCT
ejpam-5601	371	1	the	the	DET
ejpam-5601	371	2	concept	concept	NOUN
ejpam-5601	371	3	of	of	ADP
ejpam-5601	371	4	a	a	DET
ejpam-5601	371	5	linguistic	linguistic	ADJ
ejpam-5601	371	6	variable	variable	NOUN
ejpam-5601	371	7	and	and	CCONJ
ejpam-5601	371	8	its	its	PRON
ejpam-5601	371	9	application	application	NOUN
ejpam-5601	371	10	to	to	PART
ejpam-5601	371	11	approximate	approximate	ADJ
ejpam-5601	371	12	reasoning	reasoning	NOUN
ejpam-5601	371	13	–	–	PUNCT
ejpam-5601	371	14	i.	i.	PROPN
ejpam-5601	371	15	information	information	PROPN
ejpam-5601	371	16	sciences	sciences	PROPN
ejpam-5601	371	17	,	,	PUNCT
ejpam-5601	371	18	8:199–249	8:199–249	NUM
ejpam-5601	371	19	,	,	PUNCT
ejpam-5601	371	20	1975	1975	NUM
ejpam-5601	371	21	.	.	PUNCT
ejpam-5601	372	1	[	[	X
ejpam-5601	372	2	11	11	NUM
ejpam-5601	372	3	]	]	PUNCT
ejpam-5601	372	4	t.	t.	PROPN
ejpam-5601	372	5	zhou	zhou	PROPN
ejpam-5601	372	6	,	,	PUNCT
ejpam-5601	372	7	h.e	h.e	PROPN
ejpam-5601	372	8	.	.	PROPN
ejpam-5601	372	9	khalifa	khalifa	PROPN
ejpam-5601	372	10	,	,	PUNCT
ejpam-5601	372	11	s.e	s.e	PROPN
ejpam-5601	372	12	.	.	PROPN
ejpam-5601	372	13	najafi	najafi	PROPN
ejpam-5601	372	14	,	,	PUNCT
ejpam-5601	372	15	and	and	CCONJ
ejpam-5601	372	16	s.a	s.a	PROPN
ejpam-5601	372	17	.	.	PROPN
ejpam-5601	372	18	edalatpanah	edalatpanah	PROPN
ejpam-5601	372	19	.	.	PUNCT
ejpam-5601	373	1	minimizing	minimize	VERB
ejpam-5601	373	2	the	the	DET
ejpam-5601	373	3	machine	machine	NOUN
ejpam-5601	373	4	processing	processing	NOUN
ejpam-5601	373	5	time	time	NOUN
ejpam-5601	373	6	in	in	ADP
ejpam-5601	373	7	a	a	DET
ejpam-5601	373	8	flow	flow	NOUN
ejpam-5601	373	9	shop	shop	NOUN
ejpam-5601	373	10	scheduling	scheduling	NOUN
ejpam-5601	373	11	problem	problem	NOUN
ejpam-5601	373	12	under	under	ADP
ejpam-5601	373	13	piecewise	piecewise	NOUN
ejpam-5601	373	14	quadratic	quadratic	ADJ
ejpam-5601	373	15	fuzzy	fuzzy	ADJ
ejpam-5601	373	16	numbers	number	NOUN
ejpam-5601	373	17	.	.	PUNCT
ejpam-5601	374	1	discrete	discrete	ADJ
ejpam-5601	374	2	dynamics	dynamic	NOUN
ejpam-5601	374	3	in	in	ADP
ejpam-5601	374	4	nature	nature	NOUN
ejpam-5601	374	5	and	and	CCONJ
ejpam-5601	374	6	society	society	NOUN
ejpam-5601	374	7	,	,	PUNCT
ejpam-5601	374	8	page	page	NOUN
ejpam-5601	374	9	article	article	NOUN
ejpam-5601	374	10	i	i	PROPN
ejpam-5601	374	11	d	d	PROPN
ejpam-5601	374	12	3990534	3990534	NUM
ejpam-5601	374	13	,	,	PUNCT
ejpam-5601	374	14	2022	2022	NUM
ejpam-5601	374	15	.	.	PUNCT
ejpam-5601	375	1	[	[	X
ejpam-5601	375	2	12	12	NUM
ejpam-5601	375	3	]	]	X
ejpam-5601	375	4	h.j	h.j	PROPN
ejpam-5601	375	5	.	.	PROPN
ejpam-5601	375	6	zimmermann	zimmermann	PROPN
ejpam-5601	375	7	.	.	PUNCT
ejpam-5601	375	8	fuzzy	fuzzy	ADJ
ejpam-5601	375	9	set	set	VERB
ejpam-5601	375	10	theory	theory	NOUN
ejpam-5601	375	11	and	and	CCONJ
ejpam-5601	375	12	its	its	PRON
ejpam-5601	375	13	applications	application	NOUN
ejpam-5601	375	14	.	.	PUNCT
ejpam-5601	376	1	kluwer	kluwer	NOUN
ejpam-5601	376	2	-	-	PUNCT
ejpam-5601	376	3	nijhoff	nijhoff	NOUN
ejpam-5601	376	4	publishing	publishing	NOUN
ejpam-5601	376	5	,	,	PUNCT
ejpam-5601	376	6	boston	boston	PROPN
ejpam-5601	376	7	-	-	PUNCT
ejpam-5601	376	8	dordrecht	dordrecht	PROPN
ejpam-5601	376	9	-	-	PUNCT
ejpam-5601	376	10	lancaster	lancaster	PROPN
ejpam-5601	376	11	,	,	PUNCT
ejpam-5601	376	12	1985	1985	NUM
ejpam-5601	376	13	.	.	PUNCT
ejpam-5601	377	1	appendix	appendix	VERB
ejpam-5601	377	2	the	the	DET
ejpam-5601	377	3	mathematica	mathematica	PROPN
ejpam-5601	377	4	commands	command	VERB
ejpam-5601	377	5	to	to	PART
ejpam-5601	377	6	obtain	obtain	VERB
ejpam-5601	377	7	the	the	DET
ejpam-5601	377	8	above	above	ADJ
ejpam-5601	377	9	graphs	graph	NOUN
ejpam-5601	377	10	are	be	AUX
ejpam-5601	377	11	as	as	SCONJ
ejpam-5601	377	12	follows	follow	VERB
ejpam-5601	377	13	.	.	PUNCT
ejpam-5601	378	1	(	(	PUNCT
ejpam-5601	378	2	figure	figure	NOUN
ejpam-5601	378	3	1	1	NUM
ejpam-5601	378	4	)	)	PUNCT
ejpam-5601	378	5	densityplot3d[1	densityplot3d[1	PROPN
ejpam-5601	378	6	(	(	PUNCT
ejpam-5601	378	7	(	(	PUNCT
ejpam-5601	378	8	x	x	SYM
ejpam-5601	378	9	3)^2/6	3)^2/6	NUM
ejpam-5601	378	10	+	+	CCONJ
ejpam-5601	378	11	(	(	PUNCT
ejpam-5601	378	12	y	y	PROPN
ejpam-5601	378	13	5)^2/8	5)^2/8	NUM
ejpam-5601	378	14	+	+	CCONJ
ejpam-5601	378	15	(	(	PUNCT
ejpam-5601	378	16	z	z	NOUN
ejpam-5601	378	17	7)^2/4	7)^2/4	NOUN
ejpam-5601	378	18	)	)	PUNCT
ejpam-5601	378	19	,	,	PUNCT
ejpam-5601	378	20	{	{	PUNCT
ejpam-5601	378	21	x	x	NOUN
ejpam-5601	378	22	,	,	PUNCT
ejpam-5601	378	23	y	y	PROPN
ejpam-5601	378	24	,	,	PUNCT
ejpam-5601	378	25	z	z	NOUN
ejpam-5601	378	26	}	}	PUNCT
ejpam-5601	378	27	in	in	ADP
ejpam-5601	378	28	ellipsoid[{3	ellipsoid[{3	NOUN
ejpam-5601	378	29	,	,	PUNCT
ejpam-5601	378	30	5	5	NUM
ejpam-5601	378	31	,	,	PUNCT
ejpam-5601	378	32	7	7	NUM
ejpam-5601	378	33	}	}	PUNCT
ejpam-5601	378	34	,	,	PUNCT
ejpam-5601	378	35	{	{	PUNCT
ejpam-5601	378	36	sqrt[6	sqrt[6	NOUN
ejpam-5601	378	37	]	]	PUNCT
ejpam-5601	378	38	,	,	PUNCT
ejpam-5601	378	39	sqrt[8	sqrt[8	ADP
ejpam-5601	378	40	]	]	PUNCT
ejpam-5601	378	41	,	,	PUNCT
ejpam-5601	378	42	2	2	NUM
ejpam-5601	378	43	}	}	PUNCT
ejpam-5601	378	44	]	]	PUNCT
ejpam-5601	378	45	,	,	PUNCT
ejpam-5601	378	46	plotpoints	plotpoint	NOUN
ejpam-5601	378	47	-	-	PUNCT
ejpam-5601	378	48	>	>	X
ejpam-5601	378	49	100	100	NUM
ejpam-5601	378	50	,	,	PUNCT
ejpam-5601	378	51	colorfunct	colorfunct	ADJ
ejpam-5601	378	52	ion	ion	NOUN
ejpam-5601	378	53	-	-	PUNCT
ejpam-5601	378	54	>	>	PUNCT
ejpam-5601	378	55	"	"	PUNCT
ejpam-5601	378	56	sunsetcolors	sunsetcolor	NOUN
ejpam-5601	378	57	"	"	PUNCT
ejpam-5601	378	58	,	,	PUNCT
ejpam-5601	378	59	opacityfunction	opacityfunction	NOUN
ejpam-5601	378	60	-	-	PUNCT
ejpam-5601	378	61	>	>	X
ejpam-5601	378	62	0.05	0.05	NUM
ejpam-5601	378	63	,	,	PUNCT
ejpam-5601	378	64	boxratios	boxratio	NOUN
ejpam-5601	378	65	-	-	PUNCT
ejpam-5601	378	66	>	>	X
ejpam-5601	378	67	{	{	PUNCT
ejpam-5601	378	68	sqrt[6	sqrt[6	NOUN
ejpam-5601	378	69	]	]	PUNCT
ejpam-5601	378	70	,	,	PUNCT
ejpam-5601	378	71	sqr	sqr	PROPN
ejpam-5601	378	72	t[8	t[8	NOUN
ejpam-5601	378	73	]	]	X
ejpam-5601	378	74	,	,	PUNCT
ejpam-5601	378	75	2	2	NUM
ejpam-5601	378	76	}	}	PUNCT
ejpam-5601	378	77	,	,	PUNCT
ejpam-5601	378	78	plotlegends	plotlegend	VERB
ejpam-5601	378	79	-	-	PUNCT
ejpam-5601	378	80	>	>	X
ejpam-5601	378	81	automatic	automatic	PROPN
ejpam-5601	378	82	]	]	X
ejpam-5601	378	83	y.	y.	PROPN
ejpam-5601	378	84	s.	s.	PROPN
ejpam-5601	378	85	yun	yun	PROPN
ejpam-5601	378	86	,	,	PUNCT
ejpam-5601	378	87	b.	b.	PROPN
ejpam-5601	378	88	lee	lee	PROPN
ejpam-5601	378	89	/	/	SYM
ejpam-5601	378	90	eur	eur	PROPN
ejpam-5601	378	91	.	.	PUNCT
ejpam-5601	379	1	j.	j.	PROPN
ejpam-5601	379	2	pure	pure	PROPN
ejpam-5601	379	3	appl	appl	PROPN
ejpam-5601	379	4	.	.	PROPN
ejpam-5601	379	5	math	math	PROPN
ejpam-5601	379	6	,	,	PUNCT
ejpam-5601	379	7	18	18	NUM
ejpam-5601	379	8	(	(	PUNCT
ejpam-5601	379	9	1	1	NUM
ejpam-5601	379	10	)	)	PUNCT
ejpam-5601	379	11	(	(	PUNCT
ejpam-5601	379	12	2025	2025	NUM
ejpam-5601	379	13	)	)	PUNCT
ejpam-5601	379	14	,	,	PUNCT
ejpam-5601	379	15	5601	5601	NUM
ejpam-5601	379	16	16	16	NUM
ejpam-5601	379	17	of	of	ADP
ejpam-5601	379	18	17	17	NUM
ejpam-5601	379	19	(	(	PUNCT
ejpam-5601	379	20	figure	figure	NOUN
ejpam-5601	379	21	3	3	NUM
ejpam-5601	379	22	)	)	PUNCT
ejpam-5601	379	23	densityplot3d[1	densityplot3d[1	PROPN
ejpam-5601	379	24	(	(	PUNCT
ejpam-5601	379	25	(	(	PUNCT
ejpam-5601	379	26	x	x	SYM
ejpam-5601	379	27	5)^2/10	5)^2/10	NUM
ejpam-5601	379	28	+	+	CCONJ
ejpam-5601	379	29	(	(	PUNCT
ejpam-5601	379	30	y	y	PROPN
ejpam-5601	379	31	8)^2/13	8)^2/13	PROPN
ejpam-5601	379	32	+	+	CCONJ
ejpam-5601	380	1	(	(	PUNCT
ejpam-5601	380	2	z	z	NOUN
ejpam-5601	380	3	11)^2/10	11)^2/10	PROPN
ejpam-5601	380	4	)	)	PUNCT
ejpam-5601	380	5	,	,	PUNCT
ejpam-5601	380	6	{	{	PUNCT
ejpam-5601	380	7	x	x	NOUN
ejpam-5601	380	8	,	,	PUNCT
ejpam-5601	380	9	y	y	PROPN
ejpam-5601	380	10	,	,	PUNCT
ejpam-5601	380	11	z	z	NOUN
ejpam-5601	380	12	}	}	PUNCT
ejpam-5601	380	13	in	in	ADP
ejpam-5601	380	14	ellipsoid[{5	ellipsoid[{5	ADP
ejpam-5601	380	15	,	,	PUNCT
ejpam-5601	380	16	8	8	NUM
ejpam-5601	380	17	,	,	PUNCT
ejpam-5601	380	18	11	11	NUM
ejpam-5601	380	19	}	}	PUNCT
ejpam-5601	380	20	,	,	PUNCT
ejpam-5601	380	21	{	{	PUNCT
ejpam-5601	380	22	sqrt[10	sqrt[10	NOUN
ejpam-5601	380	23	]	]	PUNCT
ejpam-5601	380	24	,	,	PUNCT
ejpam-5601	380	25	sqrt[13	sqrt[13	PROPN
ejpam-5601	380	26	]	]	PUNCT
ejpam-5601	380	27	,	,	PUNCT
ejpam-5601	380	28	sqrt[10	sqrt[10	PROPN
ejpam-5601	380	29	]	]	PUNCT
ejpam-5601	380	30	}	}	PUNCT
ejpam-5601	380	31	]	]	PUNCT
ejpam-5601	380	32	,	,	PUNCT
ejpam-5601	380	33	plotpoints	plotpoint	NOUN
ejpam-5601	380	34	-	-	PUNCT
ejpam-5601	380	35	>	>	X
ejpam-5601	380	36	10	10	NUM
ejpam-5601	380	37	0	0	NUM
ejpam-5601	380	38	,	,	PUNCT
ejpam-5601	380	39	colorfunction	colorfunction	NOUN
ejpam-5601	380	40	-	-	PUNCT
ejpam-5601	380	41	>	>	PUNCT
ejpam-5601	380	42	"	"	PUNCT
ejpam-5601	380	43	sunsetcolors	sunsetcolor	NOUN
ejpam-5601	380	44	"	"	PUNCT
ejpam-5601	380	45	,	,	PUNCT
ejpam-5601	380	46	opacityfunction	opacityfunction	NOUN
ejpam-5601	380	47	-	-	PUNCT
ejpam-5601	380	48	>	>	X
ejpam-5601	380	49	0.05	0.05	NUM
ejpam-5601	380	50	,	,	PUNCT
ejpam-5601	380	51	boxratios	boxratio	NOUN
ejpam-5601	380	52	-	-	PUNCT
ejpam-5601	380	53	>	>	X
ejpam-5601	380	54	{	{	PUNCT
ejpam-5601	380	55	sqrt[10	sqrt[10	NOUN
ejpam-5601	380	56	]	]	PUNCT
ejpam-5601	380	57	,	,	PUNCT
ejpam-5601	380	58	sqrt[13	sqrt[13	PROPN
ejpam-5601	380	59	]	]	PUNCT
ejpam-5601	380	60	,	,	PUNCT
ejpam-5601	380	61	sqrt[10	sqrt[10	PROPN
ejpam-5601	380	62	]	]	PUNCT
ejpam-5601	380	63	}	}	PUNCT
ejpam-5601	380	64	,	,	PUNCT
ejpam-5601	380	65	plotlegends	plotlegend	VERB
ejpam-5601	380	66	-	-	PUNCT
ejpam-5601	380	67	>	>	X
ejpam-5601	380	68	automatic	automatic	PROPN
ejpam-5601	380	69	]	]	X
ejpam-5601	380	70	(	(	PUNCT
ejpam-5601	380	71	figure	figure	NOUN
ejpam-5601	380	72	5	5	NUM
ejpam-5601	380	73	)	)	PUNCT
ejpam-5601	380	74	g[a	g[a	NOUN
ejpam-5601	380	75	_	_	X
ejpam-5601	380	76	]	]	PUNCT
ejpam-5601	380	77	:	:	PUNCT
ejpam-5601	380	78	=	=	SYM
ejpam-5601	380	79	parametricplot3d[{6	parametricplot3d[{6	PROPN
ejpam-5601	380	80	+	+	CCONJ
ejpam-5601	380	81	24	24	NUM
ejpam-5601	380	82	sqrt[1	sqrt[1	NOUN
ejpam-5601	380	83	a	a	DET
ejpam-5601	380	84	]	]	X
ejpam-5601	380	85	cos[s	cos[s	NOUN
ejpam-5601	380	86	]	]	X
ejpam-5601	381	1	+	+	CCONJ
ejpam-5601	381	2	24	24	NUM
ejpam-5601	381	3	(	(	PUNCT
ejpam-5601	381	4	1	1	NUM
ejpam-5601	381	5	a	a	NOUN
ejpam-5601	381	6	)	)	PUNCT
ejpam-5601	381	7	(	(	PUNCT
ejpam-5601	381	8	cos[s	cos[	VERB
ejpam-5601	381	9	]	]	PUNCT
ejpam-5601	381	10	)	)	PUNCT
ejpam-5601	381	11	^2	^2	PUNCT
ejpam-5601	381	12	,	,	PUNCT
ejpam-5601	381	13	15	15	NUM
ejpam-5601	381	14	+	+	SYM
ejpam-5601	381	15	49	49	NUM
ejpam-5601	381	16	sqrt[1	sqrt[1	NOUN
ejpam-5601	381	17	a	a	DET
ejpam-5601	381	18	]	]	PUNCT
ejpam-5601	381	19	sin[s	sin[	NOUN
ejpam-5601	381	20	]	]	PUNCT
ejpam-5601	381	21	cos[t	cos[t	PROPN
ejpam-5601	381	22	]	]	X
ejpam-5601	382	1	+	+	CCONJ
ejpam-5601	382	2	40	40	NUM
ejpam-5601	382	3	(	(	PUNCT
ejpam-5601	382	4	1	1	NUM
ejpam-5601	382	5	a	a	NOUN
ejpam-5601	382	6	)	)	PUNCT
ejpam-5601	382	7	(	(	PUNCT
ejpam-5601	382	8	sin[s])^2	sin[s])^2	X
ejpam-5601	382	9	(	(	PUNCT
ejpam-5601	382	10	cos[t])^2	cos[t])^2	PROPN
ejpam-5601	382	11	,	,	PUNCT
ejpam-5601	382	12	28	28	NUM
ejpam-5601	382	13	+	+	SYM
ejpam-5601	382	14	58	58	NUM
ejpam-5601	382	15	sqrt[1	sqrt[1	NOUN
ejpam-5601	382	16	a	a	DET
ejpam-5601	382	17	]	]	PUNCT
ejpam-5601	382	18	sin[s	sin[	NOUN
ejpam-5601	382	19	]	]	X
ejpam-5601	382	20	sin[t	sin[t	X
ejpam-5601	382	21	]	]	X
ejpam-5601	383	1	+	+	CCONJ
ejpam-5601	383	2	24(1	24(1	NUM
ejpam-5601	383	3	a	a	NOUN
ejpam-5601	383	4	)	)	PUNCT
ejpam-5601	383	5	(	(	PUNCT
ejpam-5601	383	6	sin[s])^2	sin[s])^2	X
ejpam-5601	383	7	(	(	PUNCT
ejpam-5601	383	8	sin[t])^2	sin[t])^2	PUNCT
ejpam-5601	383	9	}	}	PUNCT
ejpam-5601	383	10	,	,	PUNCT
ejpam-5601	383	11	{	{	PUNCT
ejpam-5601	383	12	s	s	X
ejpam-5601	383	13	,	,	PUNCT
ejpam-5601	383	14	0	0	NUM
ejpam-5601	383	15	,	,	PUNCT
ejpam-5601	383	16	2	2	NUM
ejpam-5601	383	17	pi	pi	NOUN
ejpam-5601	383	18	}	}	PUNCT
ejpam-5601	383	19	,	,	PUNCT
ejpam-5601	383	20	{	{	PUNCT
ejpam-5601	383	21	t	t	PROPN
ejpam-5601	383	22	,	,	PUNCT
ejpam-5601	383	23	-pi/2	-pi/2	NOUN
ejpam-5601	383	24	,	,	PUNCT
ejpam-5601	383	25	pi/2	pi/2	NOUN
ejpam-5601	383	26	}	}	PUNCT
ejpam-5601	383	27	,	,	PUNCT
ejpam-5601	383	28	plotstyle	plotstyle	NOUN
ejpam-5601	383	29	-	-	PUNCT
ejpam-5601	383	30	>	>	X
ejpam-5601	383	31	directive[rgbcolor[0.2	directive[rgbcolor[0.2	NOUN
ejpam-5601	383	32	,	,	PUNCT
ejpam-5601	383	33	0.5	0.5	NUM
ejpam-5601	383	34	+	+	CCONJ
ejpam-5601	383	35	a/2	a/2	NOUN
ejpam-5601	383	36	,	,	PUNCT
ejpam-5601	383	37	0.5	0.5	NUM
ejpam-5601	383	38	+	+	CCONJ
ejpam-5601	383	39	a/2	a/2	NOUN
ejpam-5601	383	40	]	]	PUNCT
ejpam-5601	383	41	,	,	PUNCT
ejpam-5601	383	42	opacity[0.3	opacity[0.3	X
ejpam-5601	383	43	]	]	X
ejpam-5601	383	44	]	]	X
ejpam-5601	383	45	,	,	PUNCT
ejpam-5601	383	46	boxratios	boxratio	NOUN
ejpam-5601	383	47	-	-	PUNCT
ejpam-5601	383	48	>	>	X
ejpam-5601	383	49	{	{	PUNCT
ejpam-5601	383	50	1	1	NUM
ejpam-5601	383	51	,	,	PUNCT
ejpam-5601	383	52	1	1	NUM
ejpam-5601	383	53	,	,	PUNCT
ejpam-5601	383	54	1	1	NUM
ejpam-5601	383	55	}	}	PUNCT
ejpam-5601	383	56	]	]	PUNCT
ejpam-5601	383	57	;	;	PUNCT
ejpam-5601	383	58	tg	tg	PROPN
ejpam-5601	383	59	=	=	PUNCT
ejpam-5601	383	60	table[g[i	table[g[i	PROPN
ejpam-5601	383	61	]	]	PUNCT
ejpam-5601	383	62	,	,	PUNCT
ejpam-5601	383	63	{	{	PUNCT
ejpam-5601	383	64	i	i	NOUN
ejpam-5601	383	65	,	,	PUNCT
ejpam-5601	383	66	0	0	NUM
ejpam-5601	383	67	,	,	PUNCT
ejpam-5601	383	68	1.0	1.0	NUM
ejpam-5601	383	69	,	,	PUNCT
ejpam-5601	383	70	0.01	0.01	NUM
ejpam-5601	383	71	}	}	PUNCT
ejpam-5601	383	72	]	]	PUNCT
ejpam-5601	383	73	;	;	PUNCT
ejpam-5601	383	74	show[tg	show[tg	PROPN
ejpam-5601	383	75	]	]	PUNCT
ejpam-5601	383	76	(	(	PUNCT
ejpam-5601	383	77	figure	figure	NOUN
ejpam-5601	383	78	7	7	NUM
ejpam-5601	383	79	)	)	PUNCT
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ejpam-5601	385	8	(	(	PUNCT
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ejpam-5601	386	10	)	)	PUNCT
ejpam-5601	386	11	(	(	PUNCT
ejpam-5601	386	12	2025	2025	NUM
ejpam-5601	386	13	)	)	PUNCT
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ejpam-5601	387	22	=	=	X
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ejpam-5601	387	25	{	{	PUNCT
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ejpam-5601	387	31	(	(	PUNCT
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ejpam-5601	387	77	]	]	PUNCT
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ejpam-5601	387	80	]	]	PUNCT
ejpam-5601	387	81	}	}	PUNCT
ejpam-5601	387	82	,	,	PUNCT
ejpam-5601	387	83	plotlegends	plotlegend	VERB
ejpam-5601	387	84	-	-	PUNCT
ejpam-5601	387	85	>	>	X
ejpam-5601	387	86	automatic	automatic	PROPN
ejpam-5601	387	87	]	]	X
ejpam-5601	387	88	(	(	PUNCT
ejpam-5601	387	89	figure	figure	NOUN
ejpam-5601	387	90	19	19	NUM
ejpam-5601	387	91	)	)	PUNCT
ejpam-5601	387	92	reg1	reg1	NOUN
ejpam-5601	387	93	=	=	PUNCT
ejpam-5601	388	1	implicitregion[0	implicitregion[0	PROPN
ejpam-5601	388	2	<	<	X
ejpam-5601	388	3	=	=	X
ejpam-5601	388	4	(	(	PUNCT
ejpam-5601	388	5	x	x	X
ejpam-5601	388	6	1)^2/10	1)^2/10	NUM
ejpam-5601	388	7	+	+	CCONJ
ejpam-5601	388	8	(	(	PUNCT
ejpam-5601	388	9	y	y	PROPN
ejpam-5601	388	10	2)^2/13	2)^2/13	PROPN
ejpam-5601	388	11	+	+	CCONJ
ejpam-5601	388	12	(	(	PUNCT
ejpam-5601	388	13	z	z	PROPN
ejpam-5601	388	14	3)^2/10	3)^2/10	NUM
ejpam-5601	388	15	<	<	X
ejpam-5601	388	16	=	=	SYM
ejpam-5601	388	17	1	1	NUM
ejpam-5601	388	18	&	&	CCONJ
ejpam-5601	388	19	&	&	CCONJ
ejpam-5601	388	20	z	z	PROPN
ejpam-5601	388	21	<	<	X
ejpam-5601	388	22	=	=	SYM
ejpam-5601	388	23	5	5	NUM
ejpam-5601	388	24	,	,	PUNCT
ejpam-5601	388	25	{	{	PUNCT
ejpam-5601	388	26	x	x	NOUN
ejpam-5601	388	27	,	,	PUNCT
ejpam-5601	388	28	y	y	PROPN
ejpam-5601	388	29	,	,	PUNCT
ejpam-5601	388	30	z}];densityplot3d[1	z}];densityplot3d[1	X
ejpam-5601	388	31	(	(	PUNCT
ejpam-5601	388	32	(	(	PUNCT
ejpam-5601	388	33	x	x	SYM
ejpam-5601	388	34	1)^2/10	1)^2/10	NUM
ejpam-5601	388	35	+	+	CCONJ
ejpam-5601	388	36	(	(	PUNCT
ejpam-5601	388	37	y	y	PROPN
ejpam-5601	388	38	2)^2/13	2)^2/13	PROPN
ejpam-5601	388	39	+	+	CCONJ
ejpam-5601	388	40	(	(	PUNCT
ejpam-5601	388	41	z	z	PROPN
ejpam-5601	388	42	3)^2/10),{x	3)^2/10),{x	NUM
ejpam-5601	388	43	,	,	PUNCT
ejpam-5601	388	44	y	y	PROPN
ejpam-5601	388	45	,	,	PUNCT
ejpam-5601	388	46	z	z	NOUN
ejpam-5601	388	47	}	}	PUNCT
ejpam-5601	388	48	in	in	ADP
ejpam-5601	388	49	reg1	reg1	PROPN
ejpam-5601	388	50	,	,	PUNCT
ejpam-5601	388	51	plotpoints	plotpoint	NOUN
ejpam-5601	388	52	-	-	PUNCT
ejpam-5601	388	53	>	>	X
ejpam-5601	388	54	100	100	NUM
ejpam-5601	388	55	,	,	PUNCT
ejpam-5601	388	56	colorfunction	colorfunction	NOUN
ejpam-5601	388	57	-	-	PUNCT
ejpam-5601	388	58	>	>	X
ejpam-5601	388	59	"	"	PUNCT
ejpam-5601	388	60	sunsetco	sunsetco	PROPN
ejpam-5601	388	61	lors	lor	NOUN
ejpam-5601	388	62	"	"	PUNCT
ejpam-5601	388	63	,	,	PUNCT
ejpam-5601	388	64	opacityfunction	opacityfunction	NOUN
ejpam-5601	388	65	-	-	PUNCT
ejpam-5601	388	66	>	>	X
ejpam-5601	388	67	1	1	NUM
ejpam-5601	388	68	,	,	PUNCT
ejpam-5601	388	69	boxratios	boxratio	NOUN
ejpam-5601	388	70	-	-	PUNCT
ejpam-5601	388	71	>	>	X
ejpam-5601	388	72	{	{	PUNCT
ejpam-5601	388	73	sqrt[10	sqrt[10	NOUN
ejpam-5601	388	74	]	]	PUNCT
ejpam-5601	388	75	,	,	PUNCT
ejpam-5601	388	76	sqrt[13	sqrt[13	PROPN
ejpam-5601	388	77	]	]	PUNCT
ejpam-5601	388	78	,	,	PUNCT
ejpam-5601	388	79	sqrt[10	sqrt[10	PROPN
ejpam-5601	388	80	]	]	PUNCT
ejpam-5601	388	81	}	}	PUNCT
ejpam-5601	388	82	,	,	PUNCT
ejpam-5601	388	83	plotlegends	plotlegend	VERB
ejpam-5601	388	84	-	-	PUNCT
ejpam-5601	388	85	>	>	X
ejpam-5601	388	86	automatic	automatic	ADJ
ejpam-5601	388	87	]	]	PUNCT