id	sid	tid	token	lemma	pos
ejpam-5832	1	1	european	european	PROPN
ejpam-5832	1	2	journal	journal	PROPN
ejpam-5832	1	3	of	of	ADP
ejpam-5832	1	4	pure	pure	ADJ
ejpam-5832	1	5	and	and	CCONJ
ejpam-5832	1	6	applied	applied	ADJ
ejpam-5832	1	7	mathematics	mathematic	NOUN
ejpam-5832	1	8	2025	2025	NUM
ejpam-5832	1	9	,	,	PUNCT
ejpam-5832	1	10	vol	vol	NOUN
ejpam-5832	1	11	.	.	PROPN
ejpam-5832	1	12	18	18	NUM
ejpam-5832	1	13	,	,	PUNCT
ejpam-5832	1	14	issue	issue	NOUN
ejpam-5832	1	15	3	3	NUM
ejpam-5832	1	16	,	,	PUNCT
ejpam-5832	1	17	article	article	NOUN
ejpam-5832	1	18	number	number	NOUN
ejpam-5832	1	19	5832	5832	NUM
ejpam-5832	1	20	issn	issn	PROPN
ejpam-5832	1	21	1307	1307	NUM
ejpam-5832	1	22	-	-	SYM
ejpam-5832	1	23	5543	5543	NUM
ejpam-5832	1	24	–	–	PUNCT
ejpam-5832	1	25	ejpam.com	ejpam.com	X
ejpam-5832	1	26	published	publish	VERB
ejpam-5832	1	27	by	by	ADP
ejpam-5832	1	28	new	new	PROPN
ejpam-5832	1	29	york	york	PROPN
ejpam-5832	1	30	business	business	PROPN
ejpam-5832	1	31	global	global	PROPN
ejpam-5832	1	32	an	an	DET
ejpam-5832	1	33	investigation	investigation	NOUN
ejpam-5832	1	34	of	of	ADP
ejpam-5832	1	35	q	q	ADJ
ejpam-5832	1	36	-	-	PUNCT
ejpam-5832	1	37	rung	rung	ADJ
ejpam-5832	1	38	orthopair	orthopair	ADJ
ejpam-5832	1	39	fuzzy	fuzzy	ADJ
ejpam-5832	1	40	subgroups	subgroup	NOUN
ejpam-5832	1	41	and	and	CCONJ
ejpam-5832	1	42	fundamental	fundamental	ADJ
ejpam-5832	1	43	isomorphism	isomorphism	NOUN
ejpam-5832	1	44	theorems	theorem	VERB
ejpam-5832	1	45	asima	asima	PROPN
ejpam-5832	1	46	razzaque1,2	razzaque1,2	PROPN
ejpam-5832	1	47	1	1	NUM
ejpam-5832	1	48	preparatory	preparatory	NOUN
ejpam-5832	1	49	year	year	NOUN
ejpam-5832	1	50	,	,	PUNCT
ejpam-5832	1	51	basic	basic	ADJ
ejpam-5832	1	52	science	science	NOUN
ejpam-5832	1	53	,	,	PUNCT
ejpam-5832	1	54	king	king	NOUN
ejpam-5832	1	55	faisal	faisal	PROPN
ejpam-5832	1	56	university	university	PROPN
ejpam-5832	1	57	,	,	PUNCT
ejpam-5832	1	58	al	al	PROPN
ejpam-5832	1	59	-	-	PUNCT
ejpam-5832	1	60	ahsa	ahsa	NOUN
ejpam-5832	1	61	31982	31982	NUM
ejpam-5832	1	62	,	,	PUNCT
ejpam-5832	1	63	saudi	saudi	PROPN
ejpam-5832	1	64	arabia	arabia	PROPN
ejpam-5832	1	65	2	2	NUM
ejpam-5832	1	66	department	department	NOUN
ejpam-5832	1	67	of	of	ADP
ejpam-5832	1	68	mathematics	mathematic	NOUN
ejpam-5832	1	69	,	,	PUNCT
ejpam-5832	1	70	college	college	NOUN
ejpam-5832	1	71	of	of	ADP
ejpam-5832	1	72	science	science	NOUN
ejpam-5832	1	73	,	,	PUNCT
ejpam-5832	1	74	king	king	NOUN
ejpam-5832	1	75	faisal	faisal	PROPN
ejpam-5832	1	76	university	university	PROPN
ejpam-5832	1	77	,	,	PUNCT
ejpam-5832	1	78	al	al	PROPN
ejpam-5832	1	79	-	-	PUNCT
ejpam-5832	1	80	ahsa	ahsa	NOUN
ejpam-5832	1	81	31982	31982	NUM
ejpam-5832	1	82	,	,	PUNCT
ejpam-5832	1	83	saudi	saudi	PROPN
ejpam-5832	1	84	arabia	arabia	PROPN
ejpam-5832	1	85	abstract	abstract	NOUN
ejpam-5832	1	86	.	.	PUNCT
ejpam-5832	2	1	abstract	abstract	ADJ
ejpam-5832	2	2	:	:	PUNCT
ejpam-5832	2	3	the	the	DET
ejpam-5832	2	4	q	q	ADJ
ejpam-5832	2	5	-	-	PUNCT
ejpam-5832	2	6	rung	rung	ADJ
ejpam-5832	2	7	orthopair	orthopair	ADJ
ejpam-5832	2	8	fuzzy	fuzzy	ADJ
ejpam-5832	2	9	set	set	NOUN
ejpam-5832	2	10	(	(	PUNCT
ejpam-5832	2	11	q	q	NOUN
ejpam-5832	2	12	-	-	PUNCT
ejpam-5832	2	13	rofs	rofs	NOUN
ejpam-5832	2	14	)	)	PUNCT
ejpam-5832	2	15	has	have	AUX
ejpam-5832	2	16	been	be	AUX
ejpam-5832	2	17	developed	develop	VERB
ejpam-5832	2	18	as	as	ADP
ejpam-5832	2	19	an	an	DET
ejpam-5832	2	20	extension	extension	NOUN
ejpam-5832	2	21	of	of	ADP
ejpam-5832	2	22	the	the	DET
ejpam-5832	2	23	pythagorean	pythagorean	PROPN
ejpam-5832	2	24	fuzzy	fuzzy	ADJ
ejpam-5832	2	25	set	set	NOUN
ejpam-5832	2	26	(	(	PUNCT
ejpam-5832	2	27	pfs	pfs	PROPN
ejpam-5832	2	28	)	)	PUNCT
ejpam-5832	2	29	to	to	PART
ejpam-5832	2	30	address	address	VERB
ejpam-5832	2	31	ambiguity	ambiguity	NOUN
ejpam-5832	2	32	in	in	ADP
ejpam-5832	2	33	various	various	ADJ
ejpam-5832	2	34	decision	decision	NOUN
ejpam-5832	2	35	-	-	PUNCT
ejpam-5832	2	36	making	make	VERB
ejpam-5832	2	37	contexts	contexts	NOUN
ejpam-5832	2	38	.	.	PUNCT
ejpam-5832	3	1	group	group	NOUN
ejpam-5832	3	2	theory	theory	NOUN
ejpam-5832	3	3	,	,	PUNCT
ejpam-5832	3	4	a	a	DET
ejpam-5832	3	5	significant	significant	ADJ
ejpam-5832	3	6	area	area	NOUN
ejpam-5832	3	7	of	of	ADP
ejpam-5832	3	8	mathematics	mathematic	NOUN
ejpam-5832	3	9	,	,	PUNCT
ejpam-5832	3	10	has	have	VERB
ejpam-5832	3	11	extensive	extensive	ADJ
ejpam-5832	3	12	applications	application	NOUN
ejpam-5832	3	13	across	across	ADP
ejpam-5832	3	14	diverse	diverse	ADJ
ejpam-5832	3	15	scientific	scientific	ADJ
ejpam-5832	3	16	fields	field	NOUN
ejpam-5832	3	17	,	,	PUNCT
ejpam-5832	3	18	including	include	VERB
ejpam-5832	3	19	cryptography	cryptography	NOUN
ejpam-5832	3	20	,	,	PUNCT
ejpam-5832	3	21	pattern	pattern	NOUN
ejpam-5832	3	22	recognition	recognition	NOUN
ejpam-5832	3	23	,	,	PUNCT
ejpam-5832	3	24	and	and	CCONJ
ejpam-5832	3	25	network	network	NOUN
ejpam-5832	3	26	analysis	analysis	NOUN
ejpam-5832	3	27	.	.	PUNCT
ejpam-5832	4	1	this	this	DET
ejpam-5832	4	2	paper	paper	NOUN
ejpam-5832	4	3	examines	examine	VERB
ejpam-5832	4	4	qrung	qrung	PROPN
ejpam-5832	4	5	orthopair	orthopair	PROPN
ejpam-5832	4	6	fuzzy	fuzzy	ADJ
ejpam-5832	4	7	group	group	NOUN
ejpam-5832	4	8	theory	theory	NOUN
ejpam-5832	4	9	,	,	PUNCT
ejpam-5832	4	10	emphasizing	emphasize	VERB
ejpam-5832	4	11	the	the	DET
ejpam-5832	4	12	importance	importance	NOUN
ejpam-5832	4	13	of	of	ADP
ejpam-5832	4	14	q	q	NOUN
ejpam-5832	4	15	-	-	PUNCT
ejpam-5832	4	16	rofs	rofs	ADJ
ejpam-5832	4	17	and	and	CCONJ
ejpam-5832	4	18	group	group	NOUN
ejpam-5832	4	19	theory	theory	NOUN
ejpam-5832	4	20	.	.	PUNCT
ejpam-5832	5	1	the	the	DET
ejpam-5832	5	2	concept	concept	NOUN
ejpam-5832	5	3	of	of	ADP
ejpam-5832	5	4	a	a	DET
ejpam-5832	5	5	q	q	ADJ
ejpam-5832	5	6	-	-	PUNCT
ejpam-5832	5	7	rung	rung	ADJ
ejpam-5832	5	8	orthopair	orthopair	ADJ
ejpam-5832	5	9	fuzzy	fuzzy	ADJ
ejpam-5832	5	10	subgroup	subgroup	NOUN
ejpam-5832	5	11	(	(	PUNCT
ejpam-5832	5	12	q	q	NOUN
ejpam-5832	5	13	-	-	PUNCT
ejpam-5832	5	14	rofsg	rofsg	NOUN
ejpam-5832	5	15	)	)	PUNCT
ejpam-5832	5	16	is	be	AUX
ejpam-5832	5	17	introduced	introduce	VERB
ejpam-5832	5	18	,	,	PUNCT
ejpam-5832	5	19	and	and	CCONJ
ejpam-5832	5	20	its	its	PRON
ejpam-5832	5	21	various	various	ADJ
ejpam-5832	5	22	algebraic	algebraic	ADJ
ejpam-5832	5	23	properties	property	NOUN
ejpam-5832	5	24	are	be	AUX
ejpam-5832	5	25	examined	examine	VERB
ejpam-5832	5	26	.	.	PUNCT
ejpam-5832	6	1	a	a	DET
ejpam-5832	6	2	comprehensive	comprehensive	ADJ
ejpam-5832	6	3	investigation	investigation	NOUN
ejpam-5832	6	4	into	into	ADP
ejpam-5832	6	5	q	q	ADJ
ejpam-5832	6	6	-	-	PUNCT
ejpam-5832	6	7	rung	rung	ADJ
ejpam-5832	6	8	orthopair	orthopair	ADJ
ejpam-5832	6	9	fuzzy	fuzzy	ADJ
ejpam-5832	6	10	cosets	coset	NOUN
ejpam-5832	6	11	(	(	PUNCT
ejpam-5832	6	12	qrofcs	qrofc	NOUN
ejpam-5832	6	13	)	)	PUNCT
ejpam-5832	6	14	and	and	CCONJ
ejpam-5832	6	15	q	q	ADJ
ejpam-5832	6	16	-	-	PUNCT
ejpam-5832	6	17	rung	rung	ADJ
ejpam-5832	6	18	orthopair	orthopair	NOUN
ejpam-5832	6	19	fuzzy	fuzzy	ADJ
ejpam-5832	6	20	normal	normal	ADJ
ejpam-5832	6	21	subgroups	subgroup	NOUN
ejpam-5832	6	22	(	(	PUNCT
ejpam-5832	6	23	q	q	NOUN
ejpam-5832	6	24	-	-	PUNCT
ejpam-5832	6	25	rofnsgs	rofnsg	NOUN
ejpam-5832	6	26	)	)	PUNCT
ejpam-5832	6	27	has	have	AUX
ejpam-5832	6	28	been	be	AUX
ejpam-5832	6	29	conducted	conduct	VERB
ejpam-5832	6	30	.	.	PUNCT
ejpam-5832	7	1	the	the	DET
ejpam-5832	7	2	definitions	definition	NOUN
ejpam-5832	7	3	of	of	ADP
ejpam-5832	7	4	q	q	NOUN
ejpam-5832	7	5	-	-	PUNCT
ejpam-5832	7	6	rung	rung	ADJ
ejpam-5832	7	7	orthopair	orthopair	ADJ
ejpam-5832	7	8	fuzzy	fuzzy	ADJ
ejpam-5832	7	9	homomorphism	homomorphism	PROPN
ejpam-5832	7	10	and	and	CCONJ
ejpam-5832	7	11	isomorphism	isomorphism	NOUN
ejpam-5832	7	12	are	be	AUX
ejpam-5832	7	13	presented	present	VERB
ejpam-5832	7	14	.	.	PUNCT
ejpam-5832	8	1	we	we	PRON
ejpam-5832	8	2	extend	extend	VERB
ejpam-5832	8	3	the	the	DET
ejpam-5832	8	4	concept	concept	NOUN
ejpam-5832	8	5	of	of	ADP
ejpam-5832	8	6	the	the	DET
ejpam-5832	8	7	quotient	quotient	NOUN
ejpam-5832	8	8	group	group	NOUN
ejpam-5832	8	9	of	of	ADP
ejpam-5832	8	10	a	a	DET
ejpam-5832	8	11	classical	classical	ADJ
ejpam-5832	8	12	group	group	NOUN
ejpam-5832	8	13	v	v	NOUN
ejpam-5832	8	14	in	in	ADP
ejpam-5832	8	15	relation	relation	NOUN
ejpam-5832	8	16	to	to	ADP
ejpam-5832	8	17	its	its	PRON
ejpam-5832	8	18	normal	normal	ADJ
ejpam-5832	8	19	subgroup	subgroup	NOUN
ejpam-5832	8	20	u	u	NOUN
ejpam-5832	8	21	by	by	ADP
ejpam-5832	8	22	introducing	introduce	VERB
ejpam-5832	8	23	a	a	DET
ejpam-5832	8	24	q	q	NOUN
ejpam-5832	8	25	-	-	PUNCT
ejpam-5832	8	26	rofsg	rofsg	NOUN
ejpam-5832	8	27	of	of	ADP
ejpam-5832	8	28	v	v	NOUN
ejpam-5832	8	29	/	/	SYM
ejpam-5832	8	30	u	u	NOUN
ejpam-5832	8	31	.	.	PUNCT
ejpam-5832	9	1	the	the	DET
ejpam-5832	9	2	q	q	ADJ
ejpam-5832	9	3	-	-	PUNCT
ejpam-5832	9	4	rung	rung	ADJ
ejpam-5832	9	5	orthopair	orthopair	ADJ
ejpam-5832	9	6	fuzzy	fuzzy	ADJ
ejpam-5832	9	7	variant	variant	NOUN
ejpam-5832	9	8	of	of	ADP
ejpam-5832	9	9	the	the	DET
ejpam-5832	9	10	three	three	NUM
ejpam-5832	9	11	fundamental	fundamental	ADJ
ejpam-5832	9	12	isomorphism	isomorphism	NOUN
ejpam-5832	9	13	theorems	theorem	NOUN
ejpam-5832	9	14	has	have	AUX
ejpam-5832	9	15	been	be	AUX
ejpam-5832	9	16	demonstrated	demonstrate	VERB
ejpam-5832	9	17	.	.	PUNCT
ejpam-5832	10	1	2020	2020	NUM
ejpam-5832	10	2	mathematics	mathematic	NOUN
ejpam-5832	10	3	subject	subject	NOUN
ejpam-5832	10	4	classifications	classification	NOUN
ejpam-5832	10	5	:	:	PUNCT
ejpam-5832	10	6	03e72	03e72	NUM
ejpam-5832	10	7	,	,	PUNCT
ejpam-5832	10	8	20n25	20n25	NOUN
ejpam-5832	10	9	key	key	ADJ
ejpam-5832	10	10	words	word	NOUN
ejpam-5832	10	11	and	and	CCONJ
ejpam-5832	10	12	phrases	phrase	NOUN
ejpam-5832	10	13	:	:	PUNCT
ejpam-5832	10	14	q	q	NOUN
ejpam-5832	10	15	-	-	PUNCT
ejpam-5832	10	16	rofs	rofs	ADJ
ejpam-5832	10	17	,	,	PUNCT
ejpam-5832	10	18	q	q	NOUN
ejpam-5832	10	19	-	-	PUNCT
ejpam-5832	10	20	rofsg	rofsg	ADJ
ejpam-5832	10	21	,	,	PUNCT
ejpam-5832	10	22	q	q	NOUN
ejpam-5832	10	23	-	-	PUNCT
ejpam-5832	10	24	rofcs	rofcs	ADJ
ejpam-5832	10	25	,	,	PUNCT
ejpam-5832	10	26	q	q	ADJ
ejpam-5832	10	27	-	-	PUNCT
ejpam-5832	10	28	rung	rung	ADJ
ejpam-5832	10	29	orthopair	orthopair	NOUN
ejpam-5832	10	30	fuzzy	fuzzy	ADJ
ejpam-5832	10	31	isomorphism	isomorphism	NOUN
ejpam-5832	10	32	1	1	NUM
ejpam-5832	10	33	.	.	PUNCT
ejpam-5832	10	34	introduction	introduction	NOUN
ejpam-5832	10	35	1.1	1.1	NUM
ejpam-5832	10	36	.	.	PUNCT
ejpam-5832	11	1	background	background	NOUN
ejpam-5832	11	2	zadeh	zadeh	PROPN
ejpam-5832	12	1	[	[	X
ejpam-5832	12	2	1	1	X
ejpam-5832	12	3	]	]	PUNCT
ejpam-5832	12	4	proposed	propose	VERB
ejpam-5832	12	5	the	the	DET
ejpam-5832	12	6	notion	notion	NOUN
ejpam-5832	12	7	of	of	ADP
ejpam-5832	12	8	a	a	DET
ejpam-5832	12	9	fuzzy	fuzzy	ADJ
ejpam-5832	12	10	set	set	NOUN
ejpam-5832	12	11	(	(	PUNCT
ejpam-5832	12	12	fs	fs	PROPN
ejpam-5832	12	13	)	)	PUNCT
ejpam-5832	12	14	which	which	PRON
ejpam-5832	12	15	has	have	VERB
ejpam-5832	12	16	many	many	ADJ
ejpam-5832	12	17	applications	application	NOUN
ejpam-5832	12	18	on	on	ADP
ejpam-5832	12	19	decision	decision	NOUN
ejpam-5832	12	20	making	making	NOUN
ejpam-5832	12	21	and	and	CCONJ
ejpam-5832	12	22	various	various	ADJ
ejpam-5832	12	23	other	other	ADJ
ejpam-5832	12	24	fields	field	NOUN
ejpam-5832	12	25	.	.	PUNCT
ejpam-5832	13	1	a	a	DET
ejpam-5832	13	2	fuzzy	fuzzy	ADJ
ejpam-5832	13	3	subset	subset	NOUN
ejpam-5832	13	4	q	q	NOUN
ejpam-5832	13	5	of	of	ADP
ejpam-5832	13	6	a	a	DET
ejpam-5832	13	7	conventional	conventional	ADJ
ejpam-5832	13	8	set	set	NOUN
ejpam-5832	13	9	v	v	NOUN
ejpam-5832	13	10	is	be	AUX
ejpam-5832	13	11	a	a	DET
ejpam-5832	13	12	function	function	NOUN
ejpam-5832	13	13	µq	µq	NOUN
ejpam-5832	13	14	from	from	ADP
ejpam-5832	13	15	v	v	NUM
ejpam-5832	13	16	to	to	ADP
ejpam-5832	13	17	a	a	DET
ejpam-5832	13	18	unit	unit	NOUN
ejpam-5832	13	19	interval	interval	NOUN
ejpam-5832	13	20	.	.	PUNCT
ejpam-5832	14	1	in	in	ADP
ejpam-5832	14	2	other	other	ADJ
ejpam-5832	14	3	words	word	NOUN
ejpam-5832	14	4	,	,	PUNCT
ejpam-5832	14	5	if	if	SCONJ
ejpam-5832	14	6	each	each	DET
ejpam-5832	14	7	element	element	NOUN
ejpam-5832	14	8	ϵ	ϵ	ADP
ejpam-5832	14	9	of	of	ADP
ejpam-5832	14	10	v	v	PROPN
ejpam-5832	14	11	is	be	AUX
ejpam-5832	14	12	associated	associate	VERB
ejpam-5832	14	13	with	with	ADP
ejpam-5832	14	14	a	a	DET
ejpam-5832	14	15	real	real	ADJ
ejpam-5832	14	16	number	number	NOUN
ejpam-5832	14	17	from	from	ADP
ejpam-5832	14	18	[	[	X
ejpam-5832	14	19	0	0	NUM
ejpam-5832	14	20	,	,	PUNCT
ejpam-5832	14	21	1	1	NUM
ejpam-5832	14	22	]	]	PUNCT
ejpam-5832	14	23	then	then	ADV
ejpam-5832	14	24	this	this	DET
ejpam-5832	14	25	setting	setting	NOUN
ejpam-5832	14	26	is	be	AUX
ejpam-5832	14	27	called	call	VERB
ejpam-5832	14	28	fuzzy	fuzzy	ADJ
ejpam-5832	14	29	subset	subset	NOUN
ejpam-5832	14	30	q	q	NOUN
ejpam-5832	14	31	of	of	ADP
ejpam-5832	14	32	v	v	NOUN
ejpam-5832	14	33	and	and	CCONJ
ejpam-5832	14	34	is	be	AUX
ejpam-5832	14	35	written	write	VERB
ejpam-5832	14	36	as	as	ADP
ejpam-5832	14	37	q	q	NOUN
ejpam-5832	14	38	=	=	SYM
ejpam-5832	14	39	ϵ	ϵ	NOUN
ejpam-5832	14	40	,	,	PUNCT
ejpam-5832	14	41	µq(ϵ	µq(ϵ	NUM
ejpam-5832	14	42	)	)	PUNCT
ejpam-5832	14	43	:	:	PUNCT
ejpam-5832	15	1	ϵ	ϵ	PROPN
ejpam-5832	15	2	∈	∈	PROPN
ejpam-5832	15	3	v	v	NOUN
ejpam-5832	15	4	.	.	PUNCT
ejpam-5832	16	1	in	in	ADP
ejpam-5832	16	2	this	this	DET
ejpam-5832	16	3	context	context	NOUN
ejpam-5832	16	4	,	,	PUNCT
ejpam-5832	16	5	µq	µq	PROPN
ejpam-5832	16	6	is	be	AUX
ejpam-5832	16	7	designated	designate	VERB
ejpam-5832	16	8	as	as	ADP
ejpam-5832	16	9	the	the	DET
ejpam-5832	16	10	membership	membership	NOUN
ejpam-5832	16	11	function	function	NOUN
ejpam-5832	16	12	,	,	PUNCT
ejpam-5832	16	13	whereas	whereas	SCONJ
ejpam-5832	16	14	µq	µq	PROPN
ejpam-5832	16	15	(	(	PUNCT
ejpam-5832	16	16	ϵ	ϵ	X
ejpam-5832	16	17	)	)	PUNCT
ejpam-5832	16	18	∈	∈	PROPN
ejpam-5832	17	1	[	[	X
ejpam-5832	17	2	0	0	NUM
ejpam-5832	17	3	,	,	PUNCT
ejpam-5832	17	4	1	1	NUM
ejpam-5832	17	5	]	]	PUNCT
ejpam-5832	17	6	represents	represent	VERB
ejpam-5832	17	7	the	the	DET
ejpam-5832	17	8	membership	membership	NOUN
ejpam-5832	17	9	degree	degree	NOUN
ejpam-5832	17	10	of	of	ADP
ejpam-5832	17	11	ϵ	ϵ	PROPN
ejpam-5832	17	12	∈	∈	PROPN
ejpam-5832	17	13	v	v	NOUN
ejpam-5832	17	14	with	with	ADP
ejpam-5832	17	15	regard	regard	NOUN
ejpam-5832	17	16	to	to	ADP
ejpam-5832	17	17	fs	fs	ADP
ejpam-5832	17	18	q.	q.	PROPN
ejpam-5832	17	19	the	the	DET
ejpam-5832	17	20	theory	theory	NOUN
ejpam-5832	17	21	of	of	ADP
ejpam-5832	17	22	fs	fs	PROPN
ejpam-5832	17	23	is	be	AUX
ejpam-5832	17	24	a	a	DET
ejpam-5832	17	25	potent	potent	ADJ
ejpam-5832	17	26	instrument	instrument	NOUN
ejpam-5832	17	27	that	that	PRON
ejpam-5832	17	28	organically	organically	ADV
ejpam-5832	17	29	extends	extend	VERB
ejpam-5832	17	30	the	the	DET
ejpam-5832	17	31	boundaries	boundary	NOUN
ejpam-5832	17	32	of	of	ADP
ejpam-5832	17	33	crisp	crisp	ADJ
ejpam-5832	17	34	set	set	NOUN
ejpam-5832	17	35	theory	theory	NOUN
ejpam-5832	17	36	.	.	PUNCT
ejpam-5832	18	1	the	the	DET
ejpam-5832	18	2	characteristic	characteristic	ADJ
ejpam-5832	18	3	function	function	NOUN
ejpam-5832	18	4	of	of	ADP
ejpam-5832	18	5	a	a	DET
ejpam-5832	18	6	crisp	crisp	ADJ
ejpam-5832	18	7	set	set	NOUN
ejpam-5832	18	8	,	,	PUNCT
ejpam-5832	18	9	which	which	PRON
ejpam-5832	18	10	assigns	assign	VERB
ejpam-5832	18	11	doi	doi	NOUN
ejpam-5832	18	12	:	:	PUNCT
ejpam-5832	18	13	https://doi.org/10.29020/nybg.ejpam.v18i3.5832	https://doi.org/10.29020/nybg.ejpam.v18i3.5832	X
ejpam-5832	18	14	email	email	NOUN
ejpam-5832	18	15	addresses	address	NOUN
ejpam-5832	18	16	:	:	PUNCT
ejpam-5832	18	17	asimarazzaque461@gmail.com	asimarazzaque461@gmail.com	PROPN
ejpam-5832	18	18	;	;	PUNCT
ejpam-5832	18	19	arazzaque@kfu.edu.sa	arazzaque@kfu.edu.sa	PROPN
ejpam-5832	18	20	(	(	PUNCT
ejpam-5832	18	21	a.	a.	NOUN
ejpam-5832	18	22	razzaque	razzaque	NOUN
ejpam-5832	18	23	)	)	PUNCT
ejpam-5832	18	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5832	18	25	1	1	NUM
ejpam-5832	18	26	copyright	copyright	NOUN
ejpam-5832	18	27	:	:	PUNCT
ejpam-5832	18	28	©	©	PROPN
ejpam-5832	18	29	2025	2025	NUM
ejpam-5832	18	30	the	the	DET
ejpam-5832	18	31	author(s	author(s	NOUN
ejpam-5832	18	32	)	)	PUNCT
ejpam-5832	18	33	.	.	PUNCT
ejpam-5832	19	1	(	(	PUNCT
ejpam-5832	19	2	cc	cc	NOUN
ejpam-5832	19	3	by	by	ADP
ejpam-5832	19	4	-	-	PUNCT
ejpam-5832	19	5	nc	nc	PROPN
ejpam-5832	19	6	4.0	4.0	NUM
ejpam-5832	19	7	)	)	PUNCT
ejpam-5832	19	8	a.	a.	NOUN
ejpam-5832	19	9	razzaque	razzaque	NOUN
ejpam-5832	19	10	/	/	SYM
ejpam-5832	19	11	eur	eur	NOUN
ejpam-5832	19	12	.	.	PUNCT
ejpam-5832	20	1	j.	j.	PROPN
ejpam-5832	20	2	pure	pure	PROPN
ejpam-5832	20	3	appl	appl	PROPN
ejpam-5832	20	4	.	.	PROPN
ejpam-5832	20	5	math	math	PROPN
ejpam-5832	20	6	,	,	PUNCT
ejpam-5832	20	7	18	18	NUM
ejpam-5832	20	8	(	(	PUNCT
ejpam-5832	20	9	3	3	NUM
ejpam-5832	20	10	)	)	PUNCT
ejpam-5832	20	11	(	(	PUNCT
ejpam-5832	20	12	2025	2025	NUM
ejpam-5832	20	13	)	)	PUNCT
ejpam-5832	20	14	,	,	PUNCT
ejpam-5832	20	15	5832	5832	NUM
ejpam-5832	20	16	2	2	NUM
ejpam-5832	20	17	of	of	ADP
ejpam-5832	20	18	21	21	NUM
ejpam-5832	20	19	a	a	DET
ejpam-5832	20	20	value	value	NOUN
ejpam-5832	20	21	of	of	ADP
ejpam-5832	20	22	1	1	NUM
ejpam-5832	20	23	if	if	SCONJ
ejpam-5832	20	24	ϵ	ϵ	PROPN
ejpam-5832	20	25	∈	∈	PROPN
ejpam-5832	20	26	v	v	NOUN
ejpam-5832	20	27	,	,	PUNCT
ejpam-5832	20	28	and	and	CCONJ
ejpam-5832	20	29	0	0	NUM
ejpam-5832	20	30	otherwise	otherwise	ADV
ejpam-5832	20	31	,	,	PUNCT
ejpam-5832	20	32	is	be	AUX
ejpam-5832	20	33	equivalent	equivalent	ADJ
ejpam-5832	20	34	with	with	ADP
ejpam-5832	20	35	the	the	DET
ejpam-5832	20	36	membership	membership	NOUN
ejpam-5832	20	37	function	function	NOUN
ejpam-5832	20	38	of	of	ADP
ejpam-5832	20	39	the	the	DET
ejpam-5832	20	40	set	set	NOUN
ejpam-5832	20	41	.	.	PUNCT
ejpam-5832	21	1	in	in	ADP
ejpam-5832	21	2	response	response	NOUN
ejpam-5832	21	3	to	to	ADP
ejpam-5832	21	4	the	the	DET
ejpam-5832	21	5	challenges	challenge	NOUN
ejpam-5832	21	6	posed	pose	VERB
ejpam-5832	21	7	by	by	ADP
ejpam-5832	21	8	ambiguity	ambiguity	NOUN
ejpam-5832	21	9	and	and	CCONJ
ejpam-5832	21	10	uncertainty	uncertainty	NOUN
ejpam-5832	21	11	,	,	PUNCT
ejpam-5832	21	12	a	a	DET
ejpam-5832	21	13	multitude	multitude	NOUN
ejpam-5832	21	14	of	of	ADP
ejpam-5832	21	15	innovative	innovative	ADJ
ejpam-5832	21	16	concepts	concept	NOUN
ejpam-5832	21	17	have	have	AUX
ejpam-5832	21	18	surfaced	surface	VERB
ejpam-5832	21	19	since	since	SCONJ
ejpam-5832	21	20	the	the	DET
ejpam-5832	21	21	inception	inception	NOUN
ejpam-5832	21	22	of	of	ADP
ejpam-5832	21	23	fuzzy	fuzzy	ADJ
ejpam-5832	21	24	sets	set	NOUN
ejpam-5832	21	25	.	.	PUNCT
ejpam-5832	22	1	to	to	PART
ejpam-5832	22	2	address	address	VERB
ejpam-5832	22	3	vagueness	vagueness	NOUN
ejpam-5832	22	4	and	and	CCONJ
ejpam-5832	22	5	ambiguity	ambiguity	NOUN
ejpam-5832	22	6	,	,	PUNCT
ejpam-5832	22	7	numerous	numerous	ADJ
ejpam-5832	22	8	theories	theory	NOUN
ejpam-5832	22	9	have	have	AUX
ejpam-5832	22	10	been	be	AUX
ejpam-5832	22	11	devised	devise	VERB
ejpam-5832	22	12	,	,	PUNCT
ejpam-5832	22	13	some	some	PRON
ejpam-5832	22	14	of	of	ADP
ejpam-5832	22	15	which	which	PRON
ejpam-5832	22	16	are	be	AUX
ejpam-5832	22	17	extensions	extension	NOUN
ejpam-5832	22	18	of	of	ADP
ejpam-5832	22	19	the	the	DET
ejpam-5832	22	20	fs	fs	PROPN
ejpam-5832	22	21	theory	theory	NOUN
ejpam-5832	22	22	.	.	PUNCT
ejpam-5832	23	1	certain	certain	ADJ
ejpam-5832	23	2	data	datum	NOUN
ejpam-5832	23	3	types	type	NOUN
ejpam-5832	23	4	might	might	AUX
ejpam-5832	23	5	not	not	PART
ejpam-5832	23	6	be	be	AUX
ejpam-5832	23	7	adequately	adequately	ADV
ejpam-5832	23	8	described	describe	VERB
ejpam-5832	23	9	by	by	ADP
ejpam-5832	23	10	membership	membership	NOUN
ejpam-5832	23	11	value	value	NOUN
ejpam-5832	23	12	alone	alone	ADV
ejpam-5832	23	13	.	.	PUNCT
ejpam-5832	24	1	as	as	ADP
ejpam-5832	24	2	a	a	DET
ejpam-5832	24	3	result	result	NOUN
ejpam-5832	24	4	,	,	PUNCT
ejpam-5832	24	5	the	the	DET
ejpam-5832	24	6	”	"	PUNCT
ejpam-5832	24	7	non	non	ADJ
ejpam-5832	24	8	-	-	ADJ
ejpam-5832	24	9	membership	membership	ADJ
ejpam-5832	24	10	value	value	NOUN
ejpam-5832	24	11	”	"	PUNCT
ejpam-5832	24	12	has	have	AUX
ejpam-5832	24	13	been	be	AUX
ejpam-5832	24	14	incorporated	incorporate	VERB
ejpam-5832	24	15	in	in	ADP
ejpam-5832	24	16	order	order	NOUN
ejpam-5832	24	17	to	to	PART
ejpam-5832	24	18	accurately	accurately	ADV
ejpam-5832	24	19	represent	represent	VERB
ejpam-5832	24	20	nuanced	nuanced	ADJ
ejpam-5832	24	21	information	information	NOUN
ejpam-5832	24	22	.	.	PUNCT
ejpam-5832	25	1	in	in	ADP
ejpam-5832	25	2	1986	1986	NUM
ejpam-5832	25	3	,	,	PUNCT
ejpam-5832	25	4	atanassov	atanassov	VERB
ejpam-5832	25	5	[	[	X
ejpam-5832	25	6	2	2	NUM
ejpam-5832	25	7	]	]	PUNCT
ejpam-5832	25	8	introduced	introduce	VERB
ejpam-5832	25	9	the	the	DET
ejpam-5832	25	10	notion	notion	NOUN
ejpam-5832	25	11	of	of	ADP
ejpam-5832	25	12	intuitionistic	intuitionistic	ADJ
ejpam-5832	25	13	fuzzy	fuzzy	ADJ
ejpam-5832	25	14	sets	set	NOUN
ejpam-5832	25	15	(	(	PUNCT
ejpam-5832	25	16	ifss	ifss	NOUN
ejpam-5832	25	17	)	)	PUNCT
ejpam-5832	25	18	and	and	CCONJ
ejpam-5832	25	19	presented	present	VERB
ejpam-5832	25	20	an	an	DET
ejpam-5832	25	21	extension	extension	NOUN
ejpam-5832	25	22	of	of	ADP
ejpam-5832	25	23	classical	classical	ADJ
ejpam-5832	25	24	fuzzy	fuzzy	ADJ
ejpam-5832	25	25	sets	set	NOUN
ejpam-5832	25	26	(	(	PUNCT
ejpam-5832	25	27	fss	fss	NOUN
ejpam-5832	25	28	)	)	PUNCT
ejpam-5832	25	29	.	.	PUNCT
ejpam-5832	26	1	an	an	DET
ejpam-5832	26	2	ifs	ifs	PROPN
ejpam-5832	26	3	q	q	PROPN
ejpam-5832	26	4	,	,	PUNCT
ejpam-5832	26	5	associated	associate	VERB
ejpam-5832	26	6	with	with	ADP
ejpam-5832	26	7	a	a	DET
ejpam-5832	26	8	crisp	crisp	ADJ
ejpam-5832	26	9	set	set	NOUN
ejpam-5832	26	10	v	v	NOUN
ejpam-5832	26	11	,	,	PUNCT
ejpam-5832	26	12	can	can	AUX
ejpam-5832	26	13	be	be	AUX
ejpam-5832	26	14	represented	represent	VERB
ejpam-5832	26	15	as	as	ADP
ejpam-5832	26	16	an	an	DET
ejpam-5832	26	17	entity	entity	NOUN
ejpam-5832	26	18	(	(	PUNCT
ejpam-5832	26	19	ϵ	ϵ	NOUN
ejpam-5832	26	20	,	,	PUNCT
ejpam-5832	26	21	µq(ϵ	µq(ϵ	NUM
ejpam-5832	26	22	)	)	PUNCT
ejpam-5832	26	23	,	,	PUNCT
ejpam-5832	26	24	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	26	25	)	)	PUNCT
ejpam-5832	26	26	)	)	PUNCT
ejpam-5832	26	27	:	:	PUNCT
ejpam-5832	27	1	ϵ	ϵ	X
ejpam-5832	27	2	∈	∈	PROPN
ejpam-5832	27	3	v	v	NOUN
ejpam-5832	27	4	,	,	PUNCT
ejpam-5832	27	5	where	where	SCONJ
ejpam-5832	27	6	µq	µq	PROPN
ejpam-5832	27	7	:	:	PUNCT
ejpam-5832	27	8	v	v	X
ejpam-5832	27	9	→	→	SYM
ejpam-5832	27	10	[	[	X
ejpam-5832	27	11	0	0	NUM
ejpam-5832	27	12	,	,	PUNCT
ejpam-5832	27	13	1	1	NUM
ejpam-5832	27	14	]	]	PUNCT
ejpam-5832	27	15	and	and	CCONJ
ejpam-5832	27	16	νq	νq	ADJ
ejpam-5832	27	17	:	:	PUNCT
ejpam-5832	27	18	v	v	X
ejpam-5832	27	19	→	→	SYM
ejpam-5832	27	20	[	[	X
ejpam-5832	27	21	0	0	NUM
ejpam-5832	27	22	,	,	PUNCT
ejpam-5832	27	23	1	1	NUM
ejpam-5832	27	24	]	]	PUNCT
ejpam-5832	27	25	,	,	PUNCT
ejpam-5832	27	26	are	be	AUX
ejpam-5832	27	27	membership	membership	NOUN
ejpam-5832	27	28	and	and	CCONJ
ejpam-5832	27	29	non	non	ADJ
ejpam-5832	27	30	-	-	ADJ
ejpam-5832	27	31	membership	membership	ADJ
ejpam-5832	27	32	functions	function	NOUN
ejpam-5832	27	33	satisfying	satisfy	VERB
ejpam-5832	27	34	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	27	35	)	)	PUNCT
ejpam-5832	27	36	+	+	NUM
ejpam-5832	27	37	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	27	38	)	)	PUNCT
ejpam-5832	27	39	≤	≤	NOUN
ejpam-5832	27	40	1	1	NUM
ejpam-5832	27	41	for	for	ADP
ejpam-5832	27	42	all	all	DET
ejpam-5832	27	43	s	s	PART
ejpam-5832	27	44	∈	∈	PROPN
ejpam-5832	27	45	v	v	NOUN
ejpam-5832	27	46	.	.	PUNCT
ejpam-5832	28	1	ifss	ifss	ADJ
ejpam-5832	28	2	,	,	PUNCT
ejpam-5832	28	3	contrary	contrary	ADV
ejpam-5832	28	4	to	to	ADP
ejpam-5832	28	5	classical	classical	ADJ
ejpam-5832	28	6	fss	fss	NOUN
ejpam-5832	28	7	,	,	PUNCT
ejpam-5832	28	8	integrate	integrate	VERB
ejpam-5832	28	9	membership	membership	NOUN
ejpam-5832	28	10	and	and	CCONJ
ejpam-5832	28	11	non	non	ADJ
ejpam-5832	28	12	-	-	ADJ
ejpam-5832	28	13	membership	membership	ADJ
ejpam-5832	28	14	functions	function	NOUN
ejpam-5832	28	15	in	in	ADP
ejpam-5832	28	16	order	order	NOUN
ejpam-5832	28	17	to	to	PART
ejpam-5832	28	18	more	more	ADV
ejpam-5832	28	19	effectively	effectively	ADV
ejpam-5832	28	20	manage	manage	VERB
ejpam-5832	28	21	ambiguity	ambiguity	NOUN
ejpam-5832	28	22	and	and	CCONJ
ejpam-5832	28	23	uncertainty	uncertainty	NOUN
ejpam-5832	28	24	in	in	ADP
ejpam-5832	28	25	practice	practice	NOUN
ejpam-5832	28	26	,	,	PUNCT
ejpam-5832	28	27	particularly	particularly	ADV
ejpam-5832	28	28	in	in	ADP
ejpam-5832	28	29	the	the	DET
ejpam-5832	28	30	context	context	NOUN
ejpam-5832	28	31	of	of	ADP
ejpam-5832	28	32	decision	decision	NOUN
ejpam-5832	28	33	-	-	PUNCT
ejpam-5832	28	34	making	making	NOUN
ejpam-5832	28	35	[	[	X
ejpam-5832	28	36	3–6	3–6	NUM
ejpam-5832	28	37	]	]	X
ejpam-5832	28	38	.	.	PUNCT
ejpam-5832	29	1	yager[7	yager[7	PROPN
ejpam-5832	29	2	]	]	X
ejpam-5832	29	3	generalized	generalize	VERB
ejpam-5832	29	4	ifss	ifss	NOUN
ejpam-5832	29	5	in	in	ADP
ejpam-5832	29	6	2013	2013	NUM
ejpam-5832	29	7	by	by	ADP
ejpam-5832	29	8	proposing	propose	VERB
ejpam-5832	29	9	the	the	DET
ejpam-5832	29	10	concept	concept	NOUN
ejpam-5832	29	11	of	of	ADP
ejpam-5832	29	12	a	a	DET
ejpam-5832	29	13	pythagorean	pythagorean	ADJ
ejpam-5832	29	14	fuzzy	fuzzy	ADJ
ejpam-5832	29	15	set	set	NOUN
ejpam-5832	29	16	(	(	PUNCT
ejpam-5832	29	17	pfs	pfs	PROPN
ejpam-5832	29	18	)	)	PUNCT
ejpam-5832	29	19	q	q	NOUN
ejpam-5832	30	1	=	=	PUNCT
ejpam-5832	30	2	(	(	PUNCT
ejpam-5832	30	3	ϵ	ϵ	NOUN
ejpam-5832	30	4	,	,	PUNCT
ejpam-5832	30	5	µq(ϵ	µq(ϵ	NUM
ejpam-5832	30	6	)	)	PUNCT
ejpam-5832	30	7	,	,	PUNCT
ejpam-5832	30	8	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	30	9	)	)	PUNCT
ejpam-5832	30	10	)	)	PUNCT
ejpam-5832	30	11	:	:	PUNCT
ejpam-5832	31	1	ϵ	ϵ	X
ejpam-5832	31	2	∈	∈	PROPN
ejpam-5832	31	3	v	v	NOUN
ejpam-5832	31	4	,	,	PUNCT
ejpam-5832	31	5	where	where	SCONJ
ejpam-5832	31	6	µq	µq	PROPN
ejpam-5832	31	7	:	:	PUNCT
ejpam-5832	31	8	v	v	X
ejpam-5832	31	9	→	→	SYM
ejpam-5832	31	10	[	[	X
ejpam-5832	31	11	0	0	NUM
ejpam-5832	31	12	,	,	PUNCT
ejpam-5832	31	13	1	1	NUM
ejpam-5832	31	14	]	]	PUNCT
ejpam-5832	31	15	and	and	CCONJ
ejpam-5832	31	16	νq	νq	ADJ
ejpam-5832	31	17	:	:	PUNCT
ejpam-5832	31	18	v	v	X
ejpam-5832	31	19	→	→	SYM
ejpam-5832	31	20	[	[	X
ejpam-5832	31	21	0	0	NUM
ejpam-5832	31	22	,	,	PUNCT
ejpam-5832	31	23	1	1	NUM
ejpam-5832	31	24	]	]	PUNCT
ejpam-5832	31	25	,	,	PUNCT
ejpam-5832	31	26	are	be	AUX
ejpam-5832	31	27	membership	membership	NOUN
ejpam-5832	31	28	and	and	CCONJ
ejpam-5832	31	29	non	non	ADJ
ejpam-5832	31	30	-	-	ADJ
ejpam-5832	31	31	membership	membership	ADJ
ejpam-5832	31	32	functions	function	NOUN
ejpam-5832	31	33	,	,	PUNCT
ejpam-5832	31	34	respectively	respectively	ADV
ejpam-5832	31	35	,	,	PUNCT
ejpam-5832	31	36	that	that	PRON
ejpam-5832	31	37	satisfy	satisfy	VERB
ejpam-5832	31	38	the	the	DET
ejpam-5832	31	39	condition	condition	NOUN
ejpam-5832	31	40	(	(	PUNCT
ejpam-5832	31	41	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	31	42	)	)	PUNCT
ejpam-5832	31	43	)	)	PUNCT
ejpam-5832	32	1	2	2	NUM
ejpam-5832	32	2	+	+	CCONJ
ejpam-5832	32	3	(	(	PUNCT
ejpam-5832	32	4	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	32	5	)	)	PUNCT
ejpam-5832	32	6	)	)	PUNCT
ejpam-5832	32	7	2	2	NUM
ejpam-5832	32	8	≤	≤	NUM
ejpam-5832	32	9	1	1	NUM
ejpam-5832	32	10	for	for	ADP
ejpam-5832	32	11	all	all	DET
ejpam-5832	32	12	s	s	PART
ejpam-5832	32	13	∈	∈	NOUN
ejpam-5832	32	14	v	v	NOUN
ejpam-5832	32	15	.	.	PUNCT
ejpam-5832	33	1	this	this	DET
ejpam-5832	33	2	conceptual	conceptual	ADJ
ejpam-5832	33	3	framework	framework	NOUN
ejpam-5832	33	4	aims	aim	VERB
ejpam-5832	33	5	to	to	PART
ejpam-5832	33	6	turn	turn	VERB
ejpam-5832	33	7	uncertainty	uncertainty	NOUN
ejpam-5832	33	8	and	and	CCONJ
ejpam-5832	33	9	ambiguity	ambiguity	NOUN
ejpam-5832	33	10	into	into	ADP
ejpam-5832	33	11	a	a	DET
ejpam-5832	33	12	mathematical	mathematical	ADJ
ejpam-5832	33	13	domain	domain	NOUN
ejpam-5832	33	14	to	to	PART
ejpam-5832	33	15	help	help	VERB
ejpam-5832	33	16	solve	solve	VERB
ejpam-5832	33	17	complicated	complicated	ADJ
ejpam-5832	33	18	physical	physical	ADJ
ejpam-5832	33	19	problems	problem	NOUN
ejpam-5832	33	20	[	[	X
ejpam-5832	33	21	8–11	8–11	X
ejpam-5832	33	22	]	]	PUNCT
ejpam-5832	33	23	.	.	PUNCT
ejpam-5832	34	1	pythagorean	pythagorean	PROPN
ejpam-5832	34	2	fuzzy	fuzzy	ADJ
ejpam-5832	34	3	subsets	subset	NOUN
ejpam-5832	34	4	(	(	PUNCT
ejpam-5832	34	5	pfss	pfss	NOUN
ejpam-5832	34	6	)	)	PUNCT
ejpam-5832	34	7	have	have	AUX
ejpam-5832	34	8	solved	solve	VERB
ejpam-5832	34	9	many	many	ADJ
ejpam-5832	34	10	real	real	ADJ
ejpam-5832	34	11	-	-	PUNCT
ejpam-5832	34	12	world	world	NOUN
ejpam-5832	34	13	issues	issue	NOUN
ejpam-5832	34	14	,	,	PUNCT
ejpam-5832	34	15	however	however	ADV
ejpam-5832	34	16	they	they	PRON
ejpam-5832	34	17	have	have	VERB
ejpam-5832	34	18	limits	limit	NOUN
ejpam-5832	34	19	that	that	PRON
ejpam-5832	34	20	require	require	VERB
ejpam-5832	34	21	further	further	ADJ
ejpam-5832	34	22	refining	refining	NOUN
ejpam-5832	34	23	.	.	PUNCT
ejpam-5832	35	1	pythagorean	pythagorean	PROPN
ejpam-5832	35	2	fuzzy	fuzzy	ADJ
ejpam-5832	35	3	subsets	subset	NOUN
ejpam-5832	35	4	can	can	AUX
ejpam-5832	35	5	not	not	PART
ejpam-5832	35	6	accommodate	accommodate	VERB
ejpam-5832	35	7	decision	decision	NOUN
ejpam-5832	35	8	-	-	PUNCT
ejpam-5832	35	9	makers	maker	NOUN
ejpam-5832	35	10	who	who	PRON
ejpam-5832	35	11	advocate	advocate	VERB
ejpam-5832	35	12	membership	membership	NOUN
ejpam-5832	35	13	and	and	CCONJ
ejpam-5832	35	14	non	non	ADJ
ejpam-5832	35	15	-	-	ADJ
ejpam-5832	35	16	membership	membership	ADJ
ejpam-5832	35	17	values	value	NOUN
ejpam-5832	35	18	like	like	ADP
ejpam-5832	35	19	0.85	0.85	NUM
ejpam-5832	35	20	and	and	CCONJ
ejpam-5832	35	21	0.65	0.65	NUM
ejpam-5832	35	22	.	.	PUNCT
ejpam-5832	36	1	this	this	DET
ejpam-5832	36	2	constraint	constraint	NOUN
ejpam-5832	36	3	arises	arise	VERB
ejpam-5832	36	4	from	from	ADP
ejpam-5832	36	5	the	the	DET
ejpam-5832	36	6	condition	condition	NOUN
ejpam-5832	36	7	(	(	PUNCT
ejpam-5832	36	8	0.85)2	0.85)2	NOUN
ejpam-5832	36	9	+	+	CCONJ
ejpam-5832	36	10	(	(	PUNCT
ejpam-5832	36	11	0.65)2	0.65)2	X
ejpam-5832	36	12	>	>	X
ejpam-5832	36	13	1	1	NUM
ejpam-5832	36	14	.	.	PUNCT
ejpam-5832	37	1	consequently	consequently	ADV
ejpam-5832	37	2	,	,	PUNCT
ejpam-5832	37	3	pythagorean	pythagorean	PROPN
ejpam-5832	37	4	fuzzy	fuzzy	ADJ
ejpam-5832	37	5	subsets	subset	NOUN
ejpam-5832	37	6	are	be	AUX
ejpam-5832	37	7	inadequate	inadequate	ADJ
ejpam-5832	37	8	for	for	ADP
ejpam-5832	37	9	addressing	address	VERB
ejpam-5832	37	10	such	such	ADJ
ejpam-5832	37	11	situations	situation	NOUN
ejpam-5832	37	12	.	.	PUNCT
ejpam-5832	38	1	in	in	ADP
ejpam-5832	38	2	response	response	NOUN
ejpam-5832	38	3	to	to	ADP
ejpam-5832	38	4	this	this	DET
ejpam-5832	38	5	limitation	limitation	NOUN
ejpam-5832	38	6	,	,	PUNCT
ejpam-5832	38	7	yager	yager	NOUN
ejpam-5832	39	1	[	[	X
ejpam-5832	39	2	12	12	NUM
ejpam-5832	39	3	]	]	PUNCT
ejpam-5832	39	4	introduces	introduce	VERB
ejpam-5832	39	5	the	the	DET
ejpam-5832	39	6	concept	concept	NOUN
ejpam-5832	39	7	of	of	ADP
ejpam-5832	39	8	the	the	DET
ejpam-5832	39	9	q	q	ADJ
ejpam-5832	39	10	-	-	PUNCT
ejpam-5832	39	11	rung	rung	ADJ
ejpam-5832	39	12	orthopair	orthopair	ADJ
ejpam-5832	39	13	fuzzy	fuzzy	ADJ
ejpam-5832	39	14	set	set	NOUN
ejpam-5832	39	15	(	(	PUNCT
ejpam-5832	39	16	q	q	NOUN
ejpam-5832	39	17	-	-	PUNCT
ejpam-5832	39	18	rofs	rofs	NOUN
ejpam-5832	39	19	)	)	PUNCT
ejpam-5832	39	20	,	,	PUNCT
ejpam-5832	39	21	wherein	wherein	SCONJ
ejpam-5832	39	22	q	q	NOUN
ejpam-5832	39	23	is	be	AUX
ejpam-5832	39	24	a	a	DET
ejpam-5832	39	25	natural	natural	ADJ
ejpam-5832	39	26	number	number	NOUN
ejpam-5832	39	27	.	.	PUNCT
ejpam-5832	40	1	this	this	DET
ejpam-5832	40	2	innovative	innovative	ADJ
ejpam-5832	40	3	concept	concept	NOUN
ejpam-5832	40	4	aims	aim	VERB
ejpam-5832	40	5	to	to	PART
ejpam-5832	40	6	provide	provide	VERB
ejpam-5832	40	7	a	a	DET
ejpam-5832	40	8	rational	rational	ADJ
ejpam-5832	40	9	solution	solution	NOUN
ejpam-5832	40	10	for	for	ADP
ejpam-5832	40	11	addressing	address	VERB
ejpam-5832	40	12	scenarios	scenario	NOUN
ejpam-5832	40	13	of	of	ADP
ejpam-5832	40	14	the	the	DET
ejpam-5832	40	15	aforementioned	aforementioned	ADJ
ejpam-5832	40	16	nature	nature	NOUN
ejpam-5832	40	17	.	.	PUNCT
ejpam-5832	41	1	the	the	DET
ejpam-5832	41	2	q	q	NOUN
ejpam-5832	41	3	-	-	PUNCT
ejpam-5832	41	4	rofs	rofs	ADJ
ejpam-5832	41	5	is	be	AUX
ejpam-5832	41	6	formally	formally	ADV
ejpam-5832	41	7	denoted	denote	VERB
ejpam-5832	41	8	as	as	ADP
ejpam-5832	41	9	q	q	NOUN
ejpam-5832	41	10	=	=	PUNCT
ejpam-5832	41	11	(	(	PUNCT
ejpam-5832	41	12	ϵ	ϵ	NOUN
ejpam-5832	41	13	,	,	PUNCT
ejpam-5832	41	14	µq(ϵ	µq(ϵ	NUM
ejpam-5832	41	15	)	)	PUNCT
ejpam-5832	41	16	,	,	PUNCT
ejpam-5832	41	17	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	41	18	)	)	PUNCT
ejpam-5832	41	19	)	)	PUNCT
ejpam-5832	41	20	:	:	PUNCT
ejpam-5832	42	1	ϵ	ϵ	X
ejpam-5832	42	2	∈	∈	PROPN
ejpam-5832	42	3	v	v	NOUN
ejpam-5832	42	4	,	,	PUNCT
ejpam-5832	42	5	where	where	SCONJ
ejpam-5832	42	6	µq	µq	PROPN
ejpam-5832	42	7	:	:	PUNCT
ejpam-5832	42	8	v	v	X
ejpam-5832	42	9	→	→	SYM
ejpam-5832	42	10	[	[	X
ejpam-5832	42	11	0	0	NUM
ejpam-5832	42	12	,	,	PUNCT
ejpam-5832	42	13	1	1	NUM
ejpam-5832	42	14	]	]	PUNCT
ejpam-5832	42	15	and	and	CCONJ
ejpam-5832	42	16	νq	νq	ADJ
ejpam-5832	42	17	:	:	PUNCT
ejpam-5832	42	18	v	v	X
ejpam-5832	42	19	→	→	SYM
ejpam-5832	42	20	[	[	X
ejpam-5832	42	21	0	0	NUM
ejpam-5832	42	22	,	,	PUNCT
ejpam-5832	42	23	1	1	NUM
ejpam-5832	42	24	]	]	PUNCT
ejpam-5832	42	25	,	,	PUNCT
ejpam-5832	42	26	are	be	AUX
ejpam-5832	42	27	membership	membership	NOUN
ejpam-5832	42	28	and	and	CCONJ
ejpam-5832	42	29	non	non	ADJ
ejpam-5832	42	30	-	-	ADJ
ejpam-5832	42	31	membership	membership	ADJ
ejpam-5832	42	32	functions	function	NOUN
ejpam-5832	42	33	,	,	PUNCT
ejpam-5832	42	34	respectively	respectively	ADV
ejpam-5832	42	35	,	,	PUNCT
ejpam-5832	42	36	that	that	PRON
ejpam-5832	42	37	ensure	ensure	VERB
ejpam-5832	42	38	the	the	DET
ejpam-5832	42	39	condition	condition	NOUN
ejpam-5832	42	40	that	that	SCONJ
ejpam-5832	42	41	(	(	PUNCT
ejpam-5832	42	42	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	42	43	)	)	PUNCT
ejpam-5832	42	44	)	)	PUNCT
ejpam-5832	43	1	q	q	NOUN
ejpam-5832	44	1	+	+	PUNCT
ejpam-5832	44	2	(	(	PUNCT
ejpam-5832	44	3	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	44	4	)	)	PUNCT
ejpam-5832	44	5	)	)	PUNCT
ejpam-5832	45	1	q	q	PROPN
ejpam-5832	45	2	≤	≤	NUM
ejpam-5832	45	3	1	1	NUM
ejpam-5832	45	4	for	for	ADP
ejpam-5832	45	5	all	all	DET
ejpam-5832	45	6	ϵ	ϵ	PART
ejpam-5832	45	7	∈	∈	PROPN
ejpam-5832	45	8	v	v	NOUN
ejpam-5832	45	9	.	.	PUNCT
ejpam-5832	46	1	for	for	ADP
ejpam-5832	46	2	further	further	ADJ
ejpam-5832	46	3	insights	insight	NOUN
ejpam-5832	46	4	into	into	ADP
ejpam-5832	46	5	the	the	DET
ejpam-5832	46	6	practical	practical	ADJ
ejpam-5832	46	7	uses	use	NOUN
ejpam-5832	46	8	of	of	ADP
ejpam-5832	46	9	q	q	NOUN
ejpam-5832	46	10	-	-	PUNCT
ejpam-5832	46	11	rofss	rofss	NOUN
ejpam-5832	46	12	,	,	PUNCT
ejpam-5832	46	13	we	we	PRON
ejpam-5832	46	14	suggest	suggest	AUX
ejpam-5832	46	15	referring	refer	VERB
ejpam-5832	46	16	to	to	ADP
ejpam-5832	46	17	the	the	DET
ejpam-5832	46	18	sources	source	NOUN
ejpam-5832	46	19	[	[	X
ejpam-5832	46	20	13–15	13–15	NUM
ejpam-5832	46	21	]	]	SYM
ejpam-5832	46	22	.	.	PUNCT
ejpam-5832	47	1	1.2	1.2	NUM
ejpam-5832	47	2	.	.	PUNCT
ejpam-5832	47	3	literature	literature	NOUN
ejpam-5832	47	4	review	review	PROPN
ejpam-5832	47	5	and	and	CCONJ
ejpam-5832	47	6	present	present	ADJ
ejpam-5832	47	7	study	study	NOUN
ejpam-5832	47	8	rosenfeld	rosenfeld	PROPN
ejpam-5832	48	1	[	[	X
ejpam-5832	48	2	16	16	NUM
ejpam-5832	48	3	]	]	PUNCT
ejpam-5832	48	4	introduced	introduce	VERB
ejpam-5832	48	5	the	the	DET
ejpam-5832	48	6	idea	idea	NOUN
ejpam-5832	48	7	of	of	ADP
ejpam-5832	48	8	fuzzy	fuzzy	ADJ
ejpam-5832	48	9	subgroups	subgroup	NOUN
ejpam-5832	48	10	(	(	PUNCT
ejpam-5832	48	11	fss	fss	NOUN
ejpam-5832	48	12	)	)	PUNCT
ejpam-5832	48	13	and	and	CCONJ
ejpam-5832	48	14	extended	extend	VERB
ejpam-5832	48	15	the	the	DET
ejpam-5832	48	16	idea	idea	NOUN
ejpam-5832	48	17	of	of	ADP
ejpam-5832	48	18	traditional	traditional	ADJ
ejpam-5832	48	19	subgroups	subgroup	NOUN
ejpam-5832	48	20	.	.	PUNCT
ejpam-5832	49	1	since	since	SCONJ
ejpam-5832	49	2	the	the	DET
ejpam-5832	49	3	advent	advent	NOUN
ejpam-5832	49	4	of	of	ADP
ejpam-5832	49	5	fss	fss	ADJ
ejpam-5832	49	6	,	,	PUNCT
ejpam-5832	49	7	multiple	multiple	ADJ
ejpam-5832	49	8	efforts	effort	NOUN
ejpam-5832	49	9	have	have	AUX
ejpam-5832	49	10	been	be	AUX
ejpam-5832	49	11	made	make	VERB
ejpam-5832	49	12	to	to	PART
ejpam-5832	49	13	extend	extend	VERB
ejpam-5832	49	14	the	the	DET
ejpam-5832	49	15	ideas	idea	NOUN
ejpam-5832	49	16	of	of	ADP
ejpam-5832	49	17	conventional	conventional	ADJ
ejpam-5832	49	18	groups	group	NOUN
ejpam-5832	49	19	in	in	ADP
ejpam-5832	49	20	a	a	DET
ejpam-5832	49	21	variety	variety	NOUN
ejpam-5832	49	22	of	of	ADP
ejpam-5832	49	23	fuzzy	fuzzy	ADJ
ejpam-5832	49	24	settings	setting	NOUN
ejpam-5832	49	25	.	.	PUNCT
ejpam-5832	50	1	the	the	DET
ejpam-5832	50	2	concept	concept	NOUN
ejpam-5832	50	3	of	of	ADP
ejpam-5832	50	4	a	a	DET
ejpam-5832	50	5	level	level	NOUN
ejpam-5832	50	6	subgroup	subgroup	NOUN
ejpam-5832	50	7	of	of	ADP
ejpam-5832	50	8	an	an	DET
ejpam-5832	50	9	fs	fs	PROPN
ejpam-5832	50	10	was	be	AUX
ejpam-5832	50	11	developed	develop	VERB
ejpam-5832	50	12	by	by	ADP
ejpam-5832	50	13	das	das	PROPN
ejpam-5832	50	14	in	in	ADP
ejpam-5832	50	15	[	[	X
ejpam-5832	50	16	17	17	NUM
ejpam-5832	50	17	]	]	PUNCT
ejpam-5832	50	18	.	.	PUNCT
ejpam-5832	51	1	the	the	DET
ejpam-5832	51	2	study	study	NOUN
ejpam-5832	51	3	investigated	investigate	VERB
ejpam-5832	51	4	several	several	ADJ
ejpam-5832	51	5	algebraic	algebraic	ADJ
ejpam-5832	51	6	implications	implication	NOUN
ejpam-5832	51	7	of	of	ADP
ejpam-5832	51	8	this	this	DET
ejpam-5832	51	9	topic	topic	NOUN
ejpam-5832	51	10	.	.	PUNCT
ejpam-5832	52	1	liu	liu	PROPN
ejpam-5832	53	1	[	[	X
ejpam-5832	53	2	18	18	NUM
ejpam-5832	53	3	]	]	PUNCT
ejpam-5832	53	4	,	,	PUNCT
ejpam-5832	53	5	presented	present	VERB
ejpam-5832	53	6	the	the	DET
ejpam-5832	53	7	idea	idea	NOUN
ejpam-5832	53	8	of	of	ADP
ejpam-5832	53	9	fuzzy	fuzzy	ADJ
ejpam-5832	53	10	invariant	invariant	ADJ
ejpam-5832	53	11	subgroups	subgroup	NOUN
ejpam-5832	53	12	and	and	CCONJ
ejpam-5832	53	13	established	establish	VERB
ejpam-5832	53	14	several	several	ADJ
ejpam-5832	53	15	key	key	ADJ
ejpam-5832	53	16	features	feature	NOUN
ejpam-5832	53	17	of	of	ADP
ejpam-5832	53	18	this	this	DET
ejpam-5832	53	19	term	term	NOUN
ejpam-5832	53	20	.	.	PUNCT
ejpam-5832	54	1	in	in	ADP
ejpam-5832	54	2	[	[	X
ejpam-5832	54	3	19	19	NUM
ejpam-5832	54	4	]	]	PUNCT
ejpam-5832	54	5	,	,	PUNCT
ejpam-5832	54	6	a	a	DET
ejpam-5832	54	7	proof	proof	NOUN
ejpam-5832	54	8	of	of	ADP
ejpam-5832	54	9	a	a	DET
ejpam-5832	54	10	fuzzy	fuzzy	ADJ
ejpam-5832	54	11	variant	variant	NOUN
ejpam-5832	54	12	of	of	ADP
ejpam-5832	54	13	lagrange	lagrange	PROPN
ejpam-5832	54	14	’s	’s	PART
ejpam-5832	54	15	theorem	theorem	NOUN
ejpam-5832	54	16	was	be	AUX
ejpam-5832	54	17	established	establish	VERB
ejpam-5832	54	18	by	by	ADP
ejpam-5832	54	19	mukherjee	mukherjee	NOUN
ejpam-5832	54	20	and	and	CCONJ
ejpam-5832	54	21	bhattacharya	bhattacharya	PROPN
ejpam-5832	54	22	.	.	PUNCT
ejpam-5832	55	1	the	the	DET
ejpam-5832	55	2	same	same	ADJ
ejpam-5832	55	3	authors	author	NOUN
ejpam-5832	55	4	established	establish	VERB
ejpam-5832	55	5	a	a	DET
ejpam-5832	55	6	variety	variety	NOUN
ejpam-5832	55	7	of	of	ADP
ejpam-5832	55	8	results	result	NOUN
ejpam-5832	55	9	that	that	PRON
ejpam-5832	55	10	are	be	AUX
ejpam-5832	55	11	analogues	analogue	NOUN
ejpam-5832	55	12	to	to	ADP
ejpam-5832	55	13	several	several	ADJ
ejpam-5832	55	14	fundamental	fundamental	ADJ
ejpam-5832	55	15	theorems	theorem	NOUN
ejpam-5832	55	16	of	of	ADP
ejpam-5832	55	17	traditional	traditional	ADJ
ejpam-5832	55	18	group	group	NOUN
ejpam-5832	55	19	theory	theory	NOUN
ejpam-5832	55	20	[	[	X
ejpam-5832	55	21	20	20	NUM
ejpam-5832	55	22	]	]	PUNCT
ejpam-5832	55	23	.	.	PUNCT
ejpam-5832	56	1	in	in	ADP
ejpam-5832	56	2	[	[	X
ejpam-5832	56	3	21	21	NUM
ejpam-5832	56	4	]	]	PUNCT
ejpam-5832	56	5	,	,	PUNCT
ejpam-5832	56	6	the	the	DET
ejpam-5832	56	7	idea	idea	NOUN
ejpam-5832	56	8	of	of	ADP
ejpam-5832	56	9	a	a	DET
ejpam-5832	56	10	semidirect	semidirect	NOUN
ejpam-5832	56	11	product	product	NOUN
ejpam-5832	56	12	of	of	ADP
ejpam-5832	56	13	fss	fss	NOUN
ejpam-5832	56	14	is	be	AUX
ejpam-5832	56	15	set	set	VERB
ejpam-5832	56	16	up	up	ADP
ejpam-5832	56	17	and	and	CCONJ
ejpam-5832	56	18	studied	study	VERB
ejpam-5832	56	19	,	,	PUNCT
ejpam-5832	56	20	along	along	ADP
ejpam-5832	56	21	with	with	ADP
ejpam-5832	56	22	a	a	DET
ejpam-5832	56	23	number	number	NOUN
ejpam-5832	56	24	of	of	ADP
ejpam-5832	56	25	findings	finding	NOUN
ejpam-5832	56	26	about	about	ADP
ejpam-5832	56	27	this	this	DET
ejpam-5832	56	28	topic	topic	NOUN
ejpam-5832	56	29	.	.	PUNCT
ejpam-5832	57	1	in	in	ADP
ejpam-5832	57	2	[	[	X
ejpam-5832	57	3	22–24	22–24	NUM
ejpam-5832	57	4	]	]	PUNCT
ejpam-5832	57	5	,	,	PUNCT
ejpam-5832	57	6	significant	significant	ADJ
ejpam-5832	57	7	research	research	NOUN
ejpam-5832	57	8	was	be	AUX
ejpam-5832	57	9	carried	carry	VERB
ejpam-5832	57	10	a.	a.	NOUN
ejpam-5832	57	11	razzaque	razzaque	NOUN
ejpam-5832	57	12	/	/	SYM
ejpam-5832	57	13	eur	eur	NOUN
ejpam-5832	57	14	.	.	PUNCT
ejpam-5832	58	1	j.	j.	PROPN
ejpam-5832	58	2	pure	pure	PROPN
ejpam-5832	58	3	appl	appl	PROPN
ejpam-5832	58	4	.	.	PROPN
ejpam-5832	58	5	math	math	PROPN
ejpam-5832	58	6	,	,	PUNCT
ejpam-5832	58	7	18	18	NUM
ejpam-5832	58	8	(	(	PUNCT
ejpam-5832	58	9	3	3	NUM
ejpam-5832	58	10	)	)	PUNCT
ejpam-5832	58	11	(	(	PUNCT
ejpam-5832	58	12	2025	2025	NUM
ejpam-5832	58	13	)	)	PUNCT
ejpam-5832	58	14	,	,	PUNCT
ejpam-5832	58	15	5832	5832	NUM
ejpam-5832	58	16	3	3	NUM
ejpam-5832	58	17	of	of	ADP
ejpam-5832	58	18	21	21	NUM
ejpam-5832	58	19	out	out	ADP
ejpam-5832	58	20	on	on	ADP
ejpam-5832	58	21	level	level	NOUN
ejpam-5832	58	22	fuzzy	fuzzy	ADJ
ejpam-5832	58	23	subgroups	subgroup	NOUN
ejpam-5832	58	24	and	and	CCONJ
ejpam-5832	58	25	normal	normal	ADJ
ejpam-5832	58	26	fss	fss	NOUN
ejpam-5832	58	27	.	.	PUNCT
ejpam-5832	59	1	biswas	biswas	PROPN
ejpam-5832	60	1	[	[	X
ejpam-5832	60	2	25	25	NUM
ejpam-5832	60	3	]	]	PUNCT
ejpam-5832	60	4	,	,	PUNCT
ejpam-5832	60	5	started	start	VERB
ejpam-5832	60	6	work	work	NOUN
ejpam-5832	60	7	on	on	ADP
ejpam-5832	60	8	intuitionistic	intuitionistic	ADJ
ejpam-5832	60	9	fuzzy	fuzzy	ADJ
ejpam-5832	60	10	subgroups	subgroup	NOUN
ejpam-5832	60	11	(	(	PUNCT
ejpam-5832	60	12	ifsgs	ifsgs	NOUN
ejpam-5832	60	13	)	)	PUNCT
ejpam-5832	60	14	.	.	PUNCT
ejpam-5832	61	1	in	in	ADP
ejpam-5832	61	2	[	[	X
ejpam-5832	61	3	26	26	NUM
ejpam-5832	61	4	]	]	PUNCT
ejpam-5832	61	5	,	,	PUNCT
ejpam-5832	61	6	several	several	ADJ
ejpam-5832	61	7	group	group	NOUN
ejpam-5832	61	8	theoretic	theoretic	NOUN
ejpam-5832	61	9	findings	finding	NOUN
ejpam-5832	61	10	pertaining	pertain	VERB
ejpam-5832	61	11	to	to	ADP
ejpam-5832	61	12	cosets	coset	NOUN
ejpam-5832	61	13	of	of	ADP
ejpam-5832	61	14	a	a	DET
ejpam-5832	61	15	subgroup	subgroup	NOUN
ejpam-5832	61	16	are	be	AUX
ejpam-5832	61	17	explored	explore	VERB
ejpam-5832	61	18	in	in	ADP
ejpam-5832	61	19	an	an	DET
ejpam-5832	61	20	ifs	ifs	NOUN
ejpam-5832	61	21	framework	framework	NOUN
ejpam-5832	61	22	.	.	PUNCT
ejpam-5832	62	1	in	in	ADP
ejpam-5832	62	2	[	[	X
ejpam-5832	62	3	27	27	NUM
ejpam-5832	62	4	]	]	PUNCT
ejpam-5832	62	5	,	,	PUNCT
ejpam-5832	62	6	the	the	DET
ejpam-5832	62	7	concept	concept	NOUN
ejpam-5832	62	8	of	of	ADP
ejpam-5832	62	9	the	the	DET
ejpam-5832	62	10	direct	direct	ADJ
ejpam-5832	62	11	product	product	NOUN
ejpam-5832	62	12	of	of	ADP
ejpam-5832	62	13	ifsgs	ifsgs	NOUN
ejpam-5832	62	14	is	be	AUX
ejpam-5832	62	15	established	establish	VERB
ejpam-5832	62	16	.	.	PUNCT
ejpam-5832	63	1	the	the	DET
ejpam-5832	63	2	concept	concept	NOUN
ejpam-5832	63	3	of	of	ADP
ejpam-5832	63	4	ω	ω	ADJ
ejpam-5832	63	5	-	-	ADJ
ejpam-5832	63	6	fuzzy	fuzzy	ADJ
ejpam-5832	63	7	subrings	subring	NOUN
ejpam-5832	63	8	was	be	AUX
ejpam-5832	63	9	first	first	ADV
ejpam-5832	63	10	explored	explore	VERB
ejpam-5832	63	11	by	by	ADP
ejpam-5832	63	12	altassan	altassan	ADJ
ejpam-5832	63	13	et	et	PROPN
ejpam-5832	63	14	al	al	PROPN
ejpam-5832	63	15	.	.	PUNCT
ejpam-5832	64	1	in	in	ADP
ejpam-5832	64	2	[	[	X
ejpam-5832	64	3	28	28	NUM
ejpam-5832	64	4	]	]	PUNCT
ejpam-5832	64	5	.	.	PUNCT
ejpam-5832	65	1	alharbi	alharbi	PROPN
ejpam-5832	65	2	and	and	CCONJ
ejpam-5832	65	3	alghazzawi	alghazzawi	NOUN
ejpam-5832	66	1	[	[	X
ejpam-5832	66	2	29	29	NUM
ejpam-5832	66	3	]	]	PUNCT
ejpam-5832	66	4	introduced	introduce	VERB
ejpam-5832	66	5	the	the	DET
ejpam-5832	66	6	notion	notion	NOUN
ejpam-5832	66	7	of	of	ADP
ejpam-5832	66	8	(	(	PUNCT
ejpam-5832	66	9	ρ	ρ	PROPN
ejpam-5832	66	10	,	,	PUNCT
ejpam-5832	66	11	η	η	NOUN
ejpam-5832	66	12	)	)	PUNCT
ejpam-5832	66	13	complex	complex	ADJ
ejpam-5832	66	14	fuzzy	fuzzy	ADJ
ejpam-5832	66	15	subgroups	subgroup	NOUN
ejpam-5832	66	16	.	.	PUNCT
ejpam-5832	67	1	for	for	ADP
ejpam-5832	67	2	more	more	ADJ
ejpam-5832	67	3	information	information	NOUN
ejpam-5832	67	4	on	on	ADP
ejpam-5832	67	5	ifsgs	ifsg	NOUN
ejpam-5832	67	6	,	,	PUNCT
ejpam-5832	67	7	the	the	DET
ejpam-5832	67	8	readers	reader	NOUN
ejpam-5832	67	9	should	should	AUX
ejpam-5832	67	10	consult	consult	VERB
ejpam-5832	67	11	[	[	X
ejpam-5832	67	12	30–32	30–32	NUM
ejpam-5832	67	13	]	]	PUNCT
ejpam-5832	67	14	.	.	PUNCT
ejpam-5832	68	1	bhunia	bhunia	PROPN
ejpam-5832	68	2	et	et	PROPN
ejpam-5832	68	3	al	al	PROPN
ejpam-5832	68	4	.	.	PUNCT
ejpam-5832	69	1	[	[	X
ejpam-5832	69	2	33	33	NUM
ejpam-5832	69	3	]	]	PUNCT
ejpam-5832	69	4	,	,	PUNCT
ejpam-5832	69	5	have	have	AUX
ejpam-5832	69	6	defined	define	VERB
ejpam-5832	69	7	the	the	DET
ejpam-5832	69	8	concept	concept	NOUN
ejpam-5832	69	9	of	of	ADP
ejpam-5832	69	10	pythagorean	pythagorean	PROPN
ejpam-5832	69	11	fuzzy	fuzzy	ADJ
ejpam-5832	69	12	subgroups	subgroup	NOUN
ejpam-5832	69	13	(	(	PUNCT
ejpam-5832	69	14	pfsg	pfsg	NOUN
ejpam-5832	69	15	)	)	PUNCT
ejpam-5832	69	16	.	.	PUNCT
ejpam-5832	70	1	the	the	DET
ejpam-5832	70	2	scholars	scholar	NOUN
ejpam-5832	70	3	provided	provide	VERB
ejpam-5832	70	4	some	some	PRON
ejpam-5832	70	5	of	of	ADP
ejpam-5832	70	6	the	the	DET
ejpam-5832	70	7	fundamental	fundamental	ADJ
ejpam-5832	70	8	characteristics	characteristic	NOUN
ejpam-5832	70	9	of	of	ADP
ejpam-5832	70	10	this	this	DET
ejpam-5832	70	11	idea	idea	NOUN
ejpam-5832	70	12	.	.	PUNCT
ejpam-5832	71	1	razaq	razaq	INTJ
ejpam-5832	71	2	et	et	PROPN
ejpam-5832	71	3	al	al	PROPN
ejpam-5832	71	4	.	.	PUNCT
ejpam-5832	72	1	[	[	X
ejpam-5832	72	2	34	34	NUM
ejpam-5832	72	3	]	]	PUNCT
ejpam-5832	72	4	proved	prove	VERB
ejpam-5832	72	5	many	many	ADJ
ejpam-5832	72	6	results	result	NOUN
ejpam-5832	72	7	related	relate	VERB
ejpam-5832	72	8	to	to	PART
ejpam-5832	72	9	pythagorean	pythagorean	VERB
ejpam-5832	72	10	normal	normal	ADJ
ejpam-5832	72	11	subgroup	subgroup	NOUN
ejpam-5832	72	12	and	and	CCONJ
ejpam-5832	72	13	pythagorean	pythagorean	PROPN
ejpam-5832	72	14	fuzzy	fuzzy	ADJ
ejpam-5832	72	15	quotient	quotient	NOUN
ejpam-5832	72	16	groups	group	NOUN
ejpam-5832	72	17	.	.	PUNCT
ejpam-5832	73	1	in	in	ADP
ejpam-5832	73	2	[	[	X
ejpam-5832	73	3	35	35	NUM
ejpam-5832	73	4	]	]	PUNCT
ejpam-5832	73	5	,	,	PUNCT
ejpam-5832	73	6	the	the	DET
ejpam-5832	73	7	notion	notion	NOUN
ejpam-5832	73	8	of	of	ADP
ejpam-5832	73	9	q	q	ADJ
ejpam-5832	73	10	-	-	PUNCT
ejpam-5832	73	11	rung	rung	ADJ
ejpam-5832	73	12	orthopair	orthopair	NOUN
ejpam-5832	73	13	fuzzy	fuzzy	ADJ
ejpam-5832	73	14	subgroups	subgroup	NOUN
ejpam-5832	73	15	is	be	AUX
ejpam-5832	73	16	introduced	introduce	VERB
ejpam-5832	73	17	.	.	PUNCT
ejpam-5832	74	1	addis	addis	PROPN
ejpam-5832	74	2	et	et	PROPN
ejpam-5832	74	3	al	al	PROPN
ejpam-5832	74	4	.	.	PUNCT
ejpam-5832	75	1	[	[	X
ejpam-5832	75	2	36	36	NUM
ejpam-5832	75	3	]	]	PUNCT
ejpam-5832	75	4	,	,	PUNCT
ejpam-5832	75	5	established	establish	VERB
ejpam-5832	75	6	fuzzy	fuzzy	ADJ
ejpam-5832	75	7	homomorphism	homomorphism	PROPN
ejpam-5832	75	8	theorems	theorem	NOUN
ejpam-5832	75	9	,	,	PUNCT
ejpam-5832	75	10	bridging	bridge	VERB
ejpam-5832	75	11	fuzzy	fuzzy	ADJ
ejpam-5832	75	12	kernels	kernel	NOUN
ejpam-5832	75	13	and	and	CCONJ
ejpam-5832	75	14	ideals	ideal	NOUN
ejpam-5832	75	15	.	.	PUNCT
ejpam-5832	76	1	the	the	DET
ejpam-5832	76	2	aforementioned	aforementioned	ADJ
ejpam-5832	76	3	summary	summary	NOUN
ejpam-5832	76	4	of	of	ADP
ejpam-5832	76	5	the	the	DET
ejpam-5832	76	6	literature	literature	NOUN
ejpam-5832	76	7	presents	present	VERB
ejpam-5832	76	8	a	a	DET
ejpam-5832	76	9	few	few	ADJ
ejpam-5832	76	10	of	of	ADP
ejpam-5832	76	11	the	the	DET
ejpam-5832	76	12	most	most	ADV
ejpam-5832	76	13	significant	significant	ADJ
ejpam-5832	76	14	findings	finding	NOUN
ejpam-5832	76	15	from	from	ADP
ejpam-5832	76	16	studies	study	NOUN
ejpam-5832	76	17	of	of	ADP
ejpam-5832	76	18	fsg	fsg	PROPN
ejpam-5832	76	19	,	,	PUNCT
ejpam-5832	76	20	ifsg	ifsg	NOUN
ejpam-5832	76	21	and	and	CCONJ
ejpam-5832	76	22	pfsg	pfsg	NOUN
ejpam-5832	76	23	.	.	PUNCT
ejpam-5832	77	1	in	in	ADP
ejpam-5832	77	2	addition	addition	NOUN
ejpam-5832	77	3	,	,	PUNCT
ejpam-5832	77	4	some	some	DET
ejpam-5832	77	5	results	result	NOUN
ejpam-5832	77	6	concerning	concern	VERB
ejpam-5832	77	7	q	q	ADJ
ejpam-5832	77	8	-	-	PUNCT
ejpam-5832	77	9	rung	rung	ADJ
ejpam-5832	77	10	orthopair	orthopair	ADJ
ejpam-5832	77	11	fuzzy	fuzzy	ADJ
ejpam-5832	77	12	cosets	coset	NOUN
ejpam-5832	77	13	,	,	PUNCT
ejpam-5832	77	14	q	q	ADJ
ejpam-5832	77	15	-	-	PUNCT
ejpam-5832	77	16	rung	rung	ADJ
ejpam-5832	77	17	orthopair	orthopair	NOUN
ejpam-5832	77	18	fuzzy	fuzzy	ADJ
ejpam-5832	77	19	normal	normal	ADJ
ejpam-5832	77	20	subgroups	subgroup	NOUN
ejpam-5832	77	21	,	,	PUNCT
ejpam-5832	77	22	and	and	CCONJ
ejpam-5832	77	23	q	q	X
ejpam-5832	77	24	-	-	PUNCT
ejpam-5832	77	25	rung	rung	ADJ
ejpam-5832	77	26	orthopair	orthopair	ADJ
ejpam-5832	77	27	fuzzy	fuzzy	ADJ
ejpam-5832	77	28	level	level	NOUN
ejpam-5832	77	29	subgroups	subgroup	NOUN
ejpam-5832	77	30	have	have	AUX
ejpam-5832	77	31	been	be	AUX
ejpam-5832	77	32	investigated	investigate	VERB
ejpam-5832	77	33	.	.	PUNCT
ejpam-5832	78	1	however	however	ADV
ejpam-5832	78	2	,	,	PUNCT
ejpam-5832	78	3	numerous	numerous	ADJ
ejpam-5832	78	4	unsolved	unsolved	ADJ
ejpam-5832	78	5	inquiries	inquiry	NOUN
ejpam-5832	78	6	remain	remain	VERB
ejpam-5832	78	7	.	.	PUNCT
ejpam-5832	79	1	keeping	keep	VERB
ejpam-5832	79	2	in	in	ADP
ejpam-5832	79	3	mind	mind	NOUN
ejpam-5832	79	4	a	a	DET
ejpam-5832	79	5	few	few	ADJ
ejpam-5832	79	6	of	of	ADP
ejpam-5832	79	7	those	those	DET
ejpam-5832	79	8	questions	question	NOUN
ejpam-5832	79	9	,	,	PUNCT
ejpam-5832	79	10	the	the	DET
ejpam-5832	79	11	present	present	ADJ
ejpam-5832	79	12	research	research	NOUN
ejpam-5832	79	13	has	have	AUX
ejpam-5832	79	14	been	be	AUX
ejpam-5832	79	15	carried	carry	VERB
ejpam-5832	79	16	out	out	ADP
ejpam-5832	79	17	.	.	PUNCT
ejpam-5832	80	1	our	our	PRON
ejpam-5832	80	2	main	main	ADJ
ejpam-5832	80	3	contributions	contribution	NOUN
ejpam-5832	80	4	are	be	AUX
ejpam-5832	80	5	as	as	SCONJ
ejpam-5832	80	6	follows	follow	VERB
ejpam-5832	80	7	;	;	PUNCT
ejpam-5832	80	8	(	(	PUNCT
ejpam-5832	80	9	i	i	NOUN
ejpam-5832	80	10	)	)	PUNCT
ejpam-5832	80	11	considering	consider	VERB
ejpam-5832	80	12	the	the	DET
ejpam-5832	80	13	importance	importance	NOUN
ejpam-5832	80	14	of	of	ADP
ejpam-5832	80	15	cosets	coset	NOUN
ejpam-5832	80	16	in	in	ADP
ejpam-5832	80	17	classical	classical	ADJ
ejpam-5832	80	18	group	group	NOUN
ejpam-5832	80	19	theory	theory	NOUN
ejpam-5832	80	20	,	,	PUNCT
ejpam-5832	80	21	we	we	PRON
ejpam-5832	80	22	have	have	AUX
ejpam-5832	80	23	proved	prove	VERB
ejpam-5832	80	24	many	many	ADJ
ejpam-5832	80	25	results	result	NOUN
ejpam-5832	80	26	related	relate	VERB
ejpam-5832	80	27	to	to	ADP
ejpam-5832	80	28	q	q	NOUN
ejpam-5832	80	29	-	-	PUNCT
ejpam-5832	80	30	rofcs	rofcs	NOUN
ejpam-5832	80	31	of	of	ADP
ejpam-5832	80	32	a	a	DET
ejpam-5832	80	33	q	q	NOUN
ejpam-5832	80	34	-	-	PUNCT
ejpam-5832	80	35	rofsg	rofsg	NOUN
ejpam-5832	80	36	.	.	PUNCT
ejpam-5832	81	1	(	(	PUNCT
ejpam-5832	81	2	ii	ii	NOUN
ejpam-5832	81	3	)	)	PUNCT
ejpam-5832	81	4	since	since	SCONJ
ejpam-5832	81	5	the	the	DET
ejpam-5832	81	6	normal	normal	ADJ
ejpam-5832	81	7	subgroups	subgroup	NOUN
ejpam-5832	81	8	and	and	CCONJ
ejpam-5832	81	9	quotient	quotient	NOUN
ejpam-5832	81	10	groups	group	NOUN
ejpam-5832	81	11	are	be	AUX
ejpam-5832	81	12	central	central	ADJ
ejpam-5832	81	13	notions	notion	NOUN
ejpam-5832	81	14	in	in	ADP
ejpam-5832	81	15	the	the	DET
ejpam-5832	81	16	theory	theory	NOUN
ejpam-5832	81	17	of	of	ADP
ejpam-5832	81	18	groups	group	NOUN
ejpam-5832	81	19	,	,	PUNCT
ejpam-5832	81	20	therefore	therefore	ADV
ejpam-5832	81	21	we	we	PRON
ejpam-5832	81	22	have	have	AUX
ejpam-5832	81	23	defined	define	VERB
ejpam-5832	81	24	pythagorean	pythagorean	PROPN
ejpam-5832	81	25	fuzzy	fuzzy	ADJ
ejpam-5832	81	26	normal	normal	ADJ
ejpam-5832	81	27	subgroup	subgroup	NOUN
ejpam-5832	81	28	of	of	ADP
ejpam-5832	81	29	a	a	DET
ejpam-5832	81	30	q	q	NOUN
ejpam-5832	81	31	-	-	PUNCT
ejpam-5832	81	32	rofsg	rofsg	NOUN
ejpam-5832	81	33	and	and	CCONJ
ejpam-5832	81	34	generalized	generalize	VERB
ejpam-5832	81	35	the	the	DET
ejpam-5832	81	36	notion	notion	NOUN
ejpam-5832	81	37	of	of	ADP
ejpam-5832	81	38	quotient	quotient	NOUN
ejpam-5832	81	39	group	group	NOUN
ejpam-5832	81	40	in	in	ADP
ejpam-5832	81	41	q	q	ADJ
ejpam-5832	81	42	-	-	PUNCT
ejpam-5832	81	43	rung	rung	ADJ
ejpam-5832	81	44	orthopair	orthopair	ADJ
ejpam-5832	81	45	fuzzy	fuzzy	ADJ
ejpam-5832	81	46	environment	environment	NOUN
ejpam-5832	81	47	.	.	PUNCT
ejpam-5832	82	1	furthermore	furthermore	ADV
ejpam-5832	82	2	,	,	PUNCT
ejpam-5832	82	3	several	several	ADJ
ejpam-5832	82	4	theorems	theorem	NOUN
ejpam-5832	82	5	associated	associate	VERB
ejpam-5832	82	6	with	with	ADP
ejpam-5832	82	7	these	these	DET
ejpam-5832	82	8	concepts	concept	NOUN
ejpam-5832	82	9	have	have	AUX
ejpam-5832	82	10	been	be	AUX
ejpam-5832	82	11	proved	prove	VERB
ejpam-5832	82	12	.	.	PUNCT
ejpam-5832	83	1	(	(	PUNCT
ejpam-5832	83	2	iii	iii	X
ejpam-5832	83	3	)	)	PUNCT
ejpam-5832	83	4	the	the	DET
ejpam-5832	83	5	concepts	concept	NOUN
ejpam-5832	83	6	of	of	ADP
ejpam-5832	83	7	q	q	ADJ
ejpam-5832	83	8	-	-	PUNCT
ejpam-5832	83	9	rung	rung	ADJ
ejpam-5832	83	10	orthopair	orthopair	ADJ
ejpam-5832	83	11	fuzzy	fuzzy	ADJ
ejpam-5832	83	12	homomorphism	homomorphism	PROPN
ejpam-5832	83	13	and	and	CCONJ
ejpam-5832	83	14	isomorphism	isomorphism	NOUN
ejpam-5832	83	15	have	have	AUX
ejpam-5832	83	16	been	be	AUX
ejpam-5832	83	17	defined	define	VERB
ejpam-5832	83	18	.	.	PUNCT
ejpam-5832	84	1	(	(	PUNCT
ejpam-5832	84	2	iv	iv	X
ejpam-5832	84	3	)	)	PUNCT
ejpam-5832	84	4	last	last	ADJ
ejpam-5832	84	5	but	but	CCONJ
ejpam-5832	84	6	not	not	PART
ejpam-5832	84	7	the	the	DET
ejpam-5832	84	8	least	least	ADJ
ejpam-5832	84	9	,	,	PUNCT
ejpam-5832	84	10	all	all	DET
ejpam-5832	84	11	three	three	NUM
ejpam-5832	84	12	fundamental	fundamental	ADJ
ejpam-5832	84	13	theorems	theorem	NOUN
ejpam-5832	84	14	of	of	ADP
ejpam-5832	84	15	group	group	NOUN
ejpam-5832	84	16	isomorphisms	isomorphism	NOUN
ejpam-5832	84	17	have	have	AUX
ejpam-5832	84	18	been	be	AUX
ejpam-5832	84	19	generalized	generalize	VERB
ejpam-5832	84	20	in	in	ADP
ejpam-5832	84	21	q	q	ADJ
ejpam-5832	84	22	-	-	PUNCT
ejpam-5832	84	23	rung	rung	ADJ
ejpam-5832	84	24	orthopair	orthopair	ADJ
ejpam-5832	84	25	fuzzy	fuzzy	ADJ
ejpam-5832	84	26	format	format	NOUN
ejpam-5832	84	27	.	.	PUNCT
ejpam-5832	85	1	the	the	DET
ejpam-5832	85	2	rest	rest	NOUN
ejpam-5832	85	3	of	of	ADP
ejpam-5832	85	4	the	the	DET
ejpam-5832	85	5	paper	paper	NOUN
ejpam-5832	85	6	is	be	AUX
ejpam-5832	85	7	structured	structure	VERB
ejpam-5832	85	8	as	as	SCONJ
ejpam-5832	85	9	follows	follow	VERB
ejpam-5832	85	10	:	:	PUNCT
ejpam-5832	85	11	the	the	DET
ejpam-5832	85	12	second	second	ADJ
ejpam-5832	85	13	section	section	NOUN
ejpam-5832	85	14	covers	cover	VERB
ejpam-5832	85	15	the	the	DET
ejpam-5832	85	16	basic	basic	ADJ
ejpam-5832	85	17	definitions	definition	NOUN
ejpam-5832	85	18	and	and	CCONJ
ejpam-5832	85	19	concepts	concept	NOUN
ejpam-5832	85	20	essential	essential	ADJ
ejpam-5832	85	21	to	to	PART
ejpam-5832	85	22	demonstrate	demonstrate	VERB
ejpam-5832	85	23	our	our	PRON
ejpam-5832	85	24	key	key	ADJ
ejpam-5832	85	25	findings	finding	NOUN
ejpam-5832	85	26	.	.	PUNCT
ejpam-5832	86	1	the	the	DET
ejpam-5832	86	2	qq	qq	NOUN
ejpam-5832	86	3	-	-	NOUN
ejpam-5832	86	4	rofcs	rofcs	NOUN
ejpam-5832	86	5	of	of	ADP
ejpam-5832	86	6	a	a	DET
ejpam-5832	86	7	q	q	NOUN
ejpam-5832	86	8	-	-	PUNCT
ejpam-5832	86	9	rofsg	rofsg	NOUN
ejpam-5832	86	10	and	and	CCONJ
ejpam-5832	86	11	q	q	NOUN
ejpam-5832	86	12	-	-	PUNCT
ejpam-5832	86	13	rofnsgs	rofnsg	NOUN
ejpam-5832	86	14	of	of	ADP
ejpam-5832	86	15	a	a	DET
ejpam-5832	86	16	group	group	NOUN
ejpam-5832	86	17	are	be	AUX
ejpam-5832	86	18	discussed	discuss	VERB
ejpam-5832	86	19	in	in	ADP
ejpam-5832	86	20	the	the	DET
ejpam-5832	86	21	third	third	ADJ
ejpam-5832	86	22	section	section	NOUN
ejpam-5832	86	23	.	.	PUNCT
ejpam-5832	87	1	we	we	PRON
ejpam-5832	87	2	also	also	ADV
ejpam-5832	87	3	demonstrate	demonstrate	VERB
ejpam-5832	87	4	many	many	ADJ
ejpam-5832	87	5	theorems	theorem	NOUN
ejpam-5832	87	6	relevant	relevant	ADJ
ejpam-5832	87	7	with	with	ADP
ejpam-5832	87	8	these	these	DET
ejpam-5832	87	9	concepts	concept	NOUN
ejpam-5832	87	10	.	.	PUNCT
ejpam-5832	88	1	in	in	ADP
ejpam-5832	88	2	section	section	NOUN
ejpam-5832	88	3	4	4	NUM
ejpam-5832	88	4	,	,	PUNCT
ejpam-5832	88	5	we	we	PRON
ejpam-5832	88	6	define	define	VERB
ejpam-5832	88	7	the	the	DET
ejpam-5832	88	8	q	q	ADJ
ejpam-5832	88	9	-	-	PUNCT
ejpam-5832	88	10	rung	rung	ADJ
ejpam-5832	88	11	orthopair	orthopair	NOUN
ejpam-5832	88	12	fuzzy	fuzzy	ADJ
ejpam-5832	88	13	normal	normal	ADJ
ejpam-5832	88	14	subgroup	subgroup	NOUN
ejpam-5832	88	15	of	of	ADP
ejpam-5832	88	16	a	a	DET
ejpam-5832	88	17	q	q	ADJ
ejpam-5832	88	18	-	-	PUNCT
ejpam-5832	88	19	rung	rung	ADJ
ejpam-5832	88	20	orthopair	orthopair	ADJ
ejpam-5832	88	21	fuzzy	fuzzy	ADJ
ejpam-5832	88	22	subgroup	subgroup	NOUN
ejpam-5832	88	23	and	and	CCONJ
ejpam-5832	88	24	examine	examine	VERB
ejpam-5832	88	25	this	this	DET
ejpam-5832	88	26	idea	idea	NOUN
ejpam-5832	88	27	in	in	ADP
ejpam-5832	88	28	detail	detail	NOUN
ejpam-5832	88	29	.	.	PUNCT
ejpam-5832	89	1	in	in	ADP
ejpam-5832	89	2	the	the	DET
ejpam-5832	89	3	fifth	fifth	ADJ
ejpam-5832	89	4	section	section	NOUN
ejpam-5832	89	5	,	,	PUNCT
ejpam-5832	89	6	the	the	DET
ejpam-5832	89	7	concepts	concept	NOUN
ejpam-5832	89	8	of	of	ADP
ejpam-5832	89	9	q	q	ADJ
ejpam-5832	89	10	-	-	PUNCT
ejpam-5832	89	11	rung	rung	ADJ
ejpam-5832	89	12	orthopair	orthopair	ADJ
ejpam-5832	89	13	fuzzy	fuzzy	ADJ
ejpam-5832	89	14	homomorphism	homomorphism	PROPN
ejpam-5832	89	15	and	and	CCONJ
ejpam-5832	89	16	isomorphism	isomorphism	NOUN
ejpam-5832	89	17	are	be	AUX
ejpam-5832	89	18	defined	define	VERB
ejpam-5832	89	19	.	.	PUNCT
ejpam-5832	90	1	by	by	ADP
ejpam-5832	90	2	introducing	introduce	VERB
ejpam-5832	90	3	a	a	DET
ejpam-5832	90	4	q	q	NOUN
ejpam-5832	90	5	-	-	PUNCT
ejpam-5832	90	6	rofsg	rofsg	NOUN
ejpam-5832	90	7	of	of	ADP
ejpam-5832	90	8	v	v	NOUN
ejpam-5832	90	9	/	/	SYM
ejpam-5832	90	10	u	u	NOUN
ejpam-5832	90	11	we	we	PRON
ejpam-5832	90	12	thus	thus	ADV
ejpam-5832	90	13	extend	extend	VERB
ejpam-5832	90	14	the	the	DET
ejpam-5832	90	15	idea	idea	NOUN
ejpam-5832	90	16	of	of	ADP
ejpam-5832	90	17	quotient	quotient	NOUN
ejpam-5832	90	18	group	group	NOUN
ejpam-5832	90	19	of	of	ADP
ejpam-5832	90	20	a	a	DET
ejpam-5832	90	21	classic	classic	ADJ
ejpam-5832	90	22	group	group	NOUN
ejpam-5832	90	23	v	v	NUM
ejpam-5832	90	24	related	relate	VERB
ejpam-5832	90	25	to	to	ADP
ejpam-5832	90	26	its	its	PRON
ejpam-5832	90	27	normal	normal	ADJ
ejpam-5832	90	28	subgroup	subgroup	NOUN
ejpam-5832	90	29	u	u	PROPN
ejpam-5832	90	30	.	.	PUNCT
ejpam-5832	91	1	in	in	ADP
ejpam-5832	91	2	addition	addition	NOUN
ejpam-5832	91	3	,	,	PUNCT
ejpam-5832	91	4	the	the	DET
ejpam-5832	91	5	q	q	ADJ
ejpam-5832	91	6	-	-	PUNCT
ejpam-5832	91	7	rung	rung	ADJ
ejpam-5832	91	8	orthopair	orthopair	ADJ
ejpam-5832	91	9	fuzzy	fuzzy	ADJ
ejpam-5832	91	10	formulation	formulation	NOUN
ejpam-5832	91	11	of	of	ADP
ejpam-5832	91	12	fundamental	fundamental	ADJ
ejpam-5832	91	13	isomorphism	isomorphism	NOUN
ejpam-5832	91	14	theorems	theorem	NOUN
ejpam-5832	91	15	have	have	AUX
ejpam-5832	91	16	also	also	ADV
ejpam-5832	91	17	been	be	AUX
ejpam-5832	91	18	demonstrated	demonstrate	VERB
ejpam-5832	91	19	.	.	PUNCT
ejpam-5832	92	1	2	2	X
ejpam-5832	92	2	.	.	X
ejpam-5832	92	3	preliminaries	preliminary	NOUN
ejpam-5832	92	4	definition	definition	NOUN
ejpam-5832	92	5	1	1	NUM
ejpam-5832	92	6	.	.	PUNCT
ejpam-5832	93	1	[	[	X
ejpam-5832	93	2	16	16	NUM
ejpam-5832	93	3	]	]	PUNCT
ejpam-5832	93	4	an	an	DET
ejpam-5832	93	5	fs	fs	INTJ
ejpam-5832	93	6	q	q	NOUN
ejpam-5832	94	1	=	=	PRON
ejpam-5832	95	1	{	{	PUNCT
ejpam-5832	96	1	(	(	PUNCT
ejpam-5832	96	2	ϵ	ϵ	NOUN
ejpam-5832	96	3	,	,	PUNCT
ejpam-5832	96	4	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	96	5	)	)	PUNCT
ejpam-5832	96	6	)	)	PUNCT
ejpam-5832	97	1	:	:	PUNCT
ejpam-5832	97	2	ϵ	ϵ	X
ejpam-5832	97	3	∈	∈	PROPN
ejpam-5832	97	4	v	v	NOUN
ejpam-5832	97	5	}	}	PUNCT
ejpam-5832	97	6	of	of	ADP
ejpam-5832	97	7	a	a	DET
ejpam-5832	97	8	conventional	conventional	ADJ
ejpam-5832	97	9	group	group	NOUN
ejpam-5832	97	10	v	v	NOUN
ejpam-5832	97	11	is	be	AUX
ejpam-5832	97	12	called	call	VERB
ejpam-5832	97	13	a	a	DET
ejpam-5832	97	14	a.	a.	NOUN
ejpam-5832	97	15	razzaque	razzaque	NOUN
ejpam-5832	97	16	/	/	SYM
ejpam-5832	97	17	eur	eur	NOUN
ejpam-5832	97	18	.	.	PUNCT
ejpam-5832	98	1	j.	j.	PROPN
ejpam-5832	98	2	pure	pure	PROPN
ejpam-5832	98	3	appl	appl	PROPN
ejpam-5832	98	4	.	.	PROPN
ejpam-5832	98	5	math	math	PROPN
ejpam-5832	98	6	,	,	PUNCT
ejpam-5832	98	7	18	18	NUM
ejpam-5832	98	8	(	(	PUNCT
ejpam-5832	98	9	3	3	NUM
ejpam-5832	98	10	)	)	PUNCT
ejpam-5832	98	11	(	(	PUNCT
ejpam-5832	98	12	2025	2025	NUM
ejpam-5832	98	13	)	)	PUNCT
ejpam-5832	98	14	,	,	PUNCT
ejpam-5832	98	15	5832	5832	NUM
ejpam-5832	98	16	4	4	NUM
ejpam-5832	98	17	of	of	ADP
ejpam-5832	98	18	21	21	NUM
ejpam-5832	98	19	fsg	fsg	NOUN
ejpam-5832	98	20	of	of	ADP
ejpam-5832	98	21	v	v	NOUN
ejpam-5832	98	22	if	if	SCONJ
ejpam-5832	98	23	the	the	DET
ejpam-5832	98	24	preceding	precede	VERB
ejpam-5832	98	25	conditions	condition	NOUN
ejpam-5832	98	26	are	be	AUX
ejpam-5832	98	27	satisfied	satisfied	ADJ
ejpam-5832	98	28	:	:	PUNCT
ejpam-5832	98	29	(	(	PUNCT
ejpam-5832	98	30	i	i	NOUN
ejpam-5832	98	31	)	)	PUNCT
ejpam-5832	98	32	µq(ϵ1ϵ2	µq(ϵ1ϵ2	PROPN
ejpam-5832	98	33	)	)	PUNCT
ejpam-5832	98	34	≥	≥	NOUN
ejpam-5832	98	35	min{µq(ϵ1	min{µq(ϵ1	PROPN
ejpam-5832	98	36	)	)	PUNCT
ejpam-5832	98	37	,	,	PUNCT
ejpam-5832	98	38	µq(ϵ2	µq(ϵ2	NOUN
ejpam-5832	98	39	)	)	PUNCT
ejpam-5832	98	40	}	}	PUNCT
ejpam-5832	98	41	for	for	ADP
ejpam-5832	98	42	all	all	DET
ejpam-5832	98	43	ϵ1	ϵ1	ADJ
ejpam-5832	98	44	,	,	PUNCT
ejpam-5832	98	45	ϵ2	ϵ2	PROPN
ejpam-5832	98	46	∈	∈	PROPN
ejpam-5832	98	47	v	v	NOUN
ejpam-5832	98	48	.	.	PUNCT
ejpam-5832	99	1	(	(	PUNCT
ejpam-5832	99	2	ii	ii	NOUN
ejpam-5832	99	3	)	)	PUNCT
ejpam-5832	99	4	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	99	5	−1	−1	NOUN
ejpam-5832	99	6	)	)	PUNCT
ejpam-5832	99	7	≥	≥	NOUN
ejpam-5832	99	8	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	99	9	)	)	PUNCT
ejpam-5832	99	10	for	for	ADP
ejpam-5832	99	11	all	all	DET
ejpam-5832	99	12	ϵ	ϵ	PROPN
ejpam-5832	99	13	∈	∈	PROPN
ejpam-5832	99	14	v	v	NOUN
ejpam-5832	99	15	.	.	PUNCT
ejpam-5832	100	1	definition	definition	NOUN
ejpam-5832	100	2	2	2	NUM
ejpam-5832	100	3	.	.	PUNCT
ejpam-5832	101	1	[	[	X
ejpam-5832	101	2	25	25	NUM
ejpam-5832	101	3	]	]	PUNCT
ejpam-5832	101	4	an	an	DET
ejpam-5832	101	5	ifs	ifs	PROPN
ejpam-5832	101	6	q	q	PROPN
ejpam-5832	101	7	=	=	PUNCT
ejpam-5832	101	8	{	{	PUNCT
ejpam-5832	101	9	(	(	PUNCT
ejpam-5832	101	10	ϵ	ϵ	NOUN
ejpam-5832	101	11	,	,	PUNCT
ejpam-5832	101	12	µq(ϵ	µq(ϵ	NUM
ejpam-5832	101	13	)	)	PUNCT
ejpam-5832	101	14	,	,	PUNCT
ejpam-5832	101	15	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	101	16	)	)	PUNCT
ejpam-5832	101	17	)	)	PUNCT
ejpam-5832	101	18	:	:	PUNCT
ejpam-5832	102	1	ϵ	ϵ	X
ejpam-5832	102	2	∈	∈	PROPN
ejpam-5832	102	3	v	v	NOUN
ejpam-5832	102	4	}	}	PUNCT
ejpam-5832	102	5	of	of	ADP
ejpam-5832	102	6	v	v	NUM
ejpam-5832	102	7	referred	refer	VERB
ejpam-5832	102	8	to	to	PART
ejpam-5832	102	9	be	be	AUX
ejpam-5832	102	10	an	an	DET
ejpam-5832	102	11	ifsg	ifsg	NOUN
ejpam-5832	102	12	of	of	ADP
ejpam-5832	102	13	v	v	NOUN
ejpam-5832	102	14	if	if	SCONJ
ejpam-5832	102	15	the	the	DET
ejpam-5832	102	16	following	follow	VERB
ejpam-5832	102	17	conditions	condition	NOUN
ejpam-5832	102	18	are	be	AUX
ejpam-5832	102	19	met	meet	VERB
ejpam-5832	102	20	:	:	PUNCT
ejpam-5832	102	21	(	(	PUNCT
ejpam-5832	102	22	i	i	NOUN
ejpam-5832	102	23	)	)	PUNCT
ejpam-5832	103	1	µq(ϵ1ϵ2	µq(ϵ1ϵ2	PROPN
ejpam-5832	103	2	)	)	PUNCT
ejpam-5832	103	3	≥	≥	NOUN
ejpam-5832	103	4	min{µq(ϵ1	min{µq(ϵ1	PROPN
ejpam-5832	103	5	)	)	PUNCT
ejpam-5832	103	6	,	,	PUNCT
ejpam-5832	103	7	µq(ϵ2	µq(ϵ2	NOUN
ejpam-5832	103	8	)	)	PUNCT
ejpam-5832	103	9	}	}	PUNCT
ejpam-5832	103	10	and	and	CCONJ
ejpam-5832	103	11	νq(ϵ1ϵ2	νq(ϵ1ϵ2	PROPN
ejpam-5832	103	12	)	)	PUNCT
ejpam-5832	103	13	≤	≤	NUM
ejpam-5832	103	14	max{νq(ϵ1	max{νq(ϵ1	PROPN
ejpam-5832	103	15	)	)	PUNCT
ejpam-5832	103	16	,	,	PUNCT
ejpam-5832	103	17	νq(ϵ2	νq(ϵ2	NOUN
ejpam-5832	103	18	)	)	PUNCT
ejpam-5832	103	19	}	}	PUNCT
ejpam-5832	103	20	for	for	ADP
ejpam-5832	103	21	all	all	DET
ejpam-5832	103	22	ϵ1	ϵ1	ADJ
ejpam-5832	103	23	,	,	PUNCT
ejpam-5832	103	24	ϵ2	ϵ2	PROPN
ejpam-5832	103	25	∈	∈	PROPN
ejpam-5832	103	26	v	v	NOUN
ejpam-5832	103	27	.	.	PUNCT
ejpam-5832	104	1	(	(	PUNCT
ejpam-5832	104	2	ii	ii	NOUN
ejpam-5832	104	3	)	)	PUNCT
ejpam-5832	104	4	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	104	5	−1	−1	NOUN
ejpam-5832	104	6	)	)	PUNCT
ejpam-5832	104	7	≥	≥	NOUN
ejpam-5832	104	8	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	104	9	)	)	PUNCT
ejpam-5832	104	10	and	and	CCONJ
ejpam-5832	104	11	νq(ϵ	νq(ϵ	NUM
ejpam-5832	104	12	−1	−1	NOUN
ejpam-5832	104	13	)	)	PUNCT
ejpam-5832	104	14	)	)	PUNCT
ejpam-5832	104	15	≤	≤	NUM
ejpam-5832	104	16	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	104	17	)	)	PUNCT
ejpam-5832	104	18	for	for	ADP
ejpam-5832	104	19	all	all	DET
ejpam-5832	104	20	ϵ	ϵ	PART
ejpam-5832	104	21	∈	∈	PROPN
ejpam-5832	104	22	v	v	NOUN
ejpam-5832	104	23	.	.	PUNCT
ejpam-5832	105	1	definition	definition	NOUN
ejpam-5832	105	2	3	3	NUM
ejpam-5832	105	3	.	.	PUNCT
ejpam-5832	106	1	[	[	X
ejpam-5832	106	2	33	33	NUM
ejpam-5832	106	3	]	]	PUNCT
ejpam-5832	106	4	a	a	DET
ejpam-5832	106	5	pfs	pfs	NOUN
ejpam-5832	106	6	q	q	PROPN
ejpam-5832	106	7	=	=	PRON
ejpam-5832	106	8	{	{	PUNCT
ejpam-5832	106	9	(	(	PUNCT
ejpam-5832	106	10	ϵ	ϵ	NOUN
ejpam-5832	106	11	,	,	PUNCT
ejpam-5832	106	12	µq(ϵ	µq(ϵ	NUM
ejpam-5832	106	13	)	)	PUNCT
ejpam-5832	106	14	,	,	PUNCT
ejpam-5832	106	15	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	106	16	)	)	PUNCT
ejpam-5832	106	17	)	)	PUNCT
ejpam-5832	106	18	:	:	PUNCT
ejpam-5832	107	1	ϵ	ϵ	X
ejpam-5832	107	2	∈	∈	PROPN
ejpam-5832	107	3	v	v	NOUN
ejpam-5832	107	4	}	}	PUNCT
ejpam-5832	107	5	of	of	ADP
ejpam-5832	107	6	v	v	NUM
ejpam-5832	107	7	referred	refer	VERB
ejpam-5832	107	8	to	to	PART
ejpam-5832	107	9	be	be	AUX
ejpam-5832	107	10	a	a	DET
ejpam-5832	107	11	pfsg	pfsg	NOUN
ejpam-5832	107	12	of	of	ADP
ejpam-5832	107	13	v	v	NOUN
ejpam-5832	107	14	if	if	SCONJ
ejpam-5832	107	15	the	the	DET
ejpam-5832	107	16	following	follow	VERB
ejpam-5832	107	17	conditions	condition	NOUN
ejpam-5832	107	18	are	be	AUX
ejpam-5832	107	19	met	meet	VERB
ejpam-5832	107	20	:	:	PUNCT
ejpam-5832	107	21	(	(	PUNCT
ejpam-5832	107	22	i	i	NOUN
ejpam-5832	107	23	)	)	PUNCT
ejpam-5832	107	24	(	(	PUNCT
ejpam-5832	107	25	µq(ϵ1ϵ2	µq(ϵ1ϵ2	PROPN
ejpam-5832	107	26	)	)	PUNCT
ejpam-5832	107	27	)	)	PUNCT
ejpam-5832	107	28	2	2	NUM
ejpam-5832	107	29	≥	≥	NOUN
ejpam-5832	107	30	min{(µq(ϵ1))2	min{(µq(ϵ1))2	NOUN
ejpam-5832	107	31	,	,	PUNCT
ejpam-5832	107	32	(	(	PUNCT
ejpam-5832	107	33	µq(ϵ2))2	µq(ϵ2))2	X
ejpam-5832	107	34	}	}	PUNCT
ejpam-5832	107	35	and	and	CCONJ
ejpam-5832	107	36	(	(	PUNCT
ejpam-5832	107	37	νq(ϵ1ϵ2	νq(ϵ1ϵ2	PROPN
ejpam-5832	107	38	)	)	PUNCT
ejpam-5832	107	39	)	)	PUNCT
ejpam-5832	107	40	2	2	NUM
ejpam-5832	107	41	≤	≤	NUM
ejpam-5832	107	42	max{(νq(ϵ1))2	max{(νq(ϵ1))2	NOUN
ejpam-5832	107	43	,	,	PUNCT
ejpam-5832	107	44	(	(	PUNCT
ejpam-5832	107	45	νq(ϵ2))2	νq(ϵ2))2	NOUN
ejpam-5832	107	46	}	}	PUNCT
ejpam-5832	107	47	for	for	ADP
ejpam-5832	107	48	all	all	DET
ejpam-5832	107	49	ϵ1	ϵ1	ADJ
ejpam-5832	107	50	,	,	PUNCT
ejpam-5832	107	51	ϵ2	ϵ2	PROPN
ejpam-5832	107	52	∈	∈	PROPN
ejpam-5832	107	53	v	v	NOUN
ejpam-5832	107	54	.	.	PUNCT
ejpam-5832	108	1	(	(	PUNCT
ejpam-5832	108	2	ii	ii	NOUN
ejpam-5832	108	3	)	)	PUNCT
ejpam-5832	108	4	(	(	PUNCT
ejpam-5832	108	5	µq(ϵ	µq(ϵ	NUM
ejpam-5832	108	6	−1))2	−1))2	X
ejpam-5832	108	7	≥	≥	X
ejpam-5832	108	8	(	(	PUNCT
ejpam-5832	108	9	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	108	10	)	)	PUNCT
ejpam-5832	108	11	)	)	PUNCT
ejpam-5832	108	12	2	2	NUM
ejpam-5832	108	13	and	and	CCONJ
ejpam-5832	108	14	(	(	PUNCT
ejpam-5832	108	15	νq(ϵ	νq(ϵ	X
ejpam-5832	108	16	−1))2	−1))2	X
ejpam-5832	108	17	≤	≤	NUM
ejpam-5832	108	18	(	(	PUNCT
ejpam-5832	108	19	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	108	20	)	)	PUNCT
ejpam-5832	108	21	)	)	PUNCT
ejpam-5832	108	22	2	2	NUM
ejpam-5832	108	23	for	for	ADP
ejpam-5832	108	24	all	all	DET
ejpam-5832	108	25	ϵ	ϵ	PART
ejpam-5832	108	26	∈	∈	PROPN
ejpam-5832	108	27	v	v	NOUN
ejpam-5832	108	28	.	.	PUNCT
ejpam-5832	109	1	definition	definition	NOUN
ejpam-5832	109	2	4	4	NUM
ejpam-5832	109	3	.	.	PUNCT
ejpam-5832	110	1	[	[	X
ejpam-5832	110	2	35	35	NUM
ejpam-5832	110	3	]	]	X
ejpam-5832	110	4	a	a	DET
ejpam-5832	110	5	q	q	NOUN
ejpam-5832	110	6	-	-	PUNCT
ejpam-5832	110	7	rofs	rofs	ADJ
ejpam-5832	110	8	q	q	NOUN
ejpam-5832	110	9	=	=	PUNCT
ejpam-5832	110	10	{	{	PUNCT
ejpam-5832	110	11	(	(	PUNCT
ejpam-5832	110	12	ϵ	ϵ	NOUN
ejpam-5832	110	13	,	,	PUNCT
ejpam-5832	110	14	µq(ϵ	µq(ϵ	NUM
ejpam-5832	110	15	)	)	PUNCT
ejpam-5832	110	16	,	,	PUNCT
ejpam-5832	110	17	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	110	18	)	)	PUNCT
ejpam-5832	110	19	)	)	PUNCT
ejpam-5832	110	20	:	:	PUNCT
ejpam-5832	110	21	ϵ	ϵ	X
ejpam-5832	110	22	∈	∈	PROPN
ejpam-5832	110	23	v	v	NOUN
ejpam-5832	110	24	}	}	PUNCT
ejpam-5832	110	25	of	of	ADP
ejpam-5832	110	26	v	v	NUM
ejpam-5832	110	27	referred	refer	VERB
ejpam-5832	110	28	to	to	PART
ejpam-5832	110	29	be	be	AUX
ejpam-5832	110	30	a	a	DET
ejpam-5832	110	31	q	q	NOUN
ejpam-5832	110	32	-	-	PUNCT
ejpam-5832	110	33	rofsg	rofsg	NOUN
ejpam-5832	110	34	of	of	ADP
ejpam-5832	110	35	v	v	NOUN
ejpam-5832	110	36	if	if	SCONJ
ejpam-5832	110	37	the	the	DET
ejpam-5832	110	38	following	follow	VERB
ejpam-5832	110	39	conditions	condition	NOUN
ejpam-5832	110	40	are	be	AUX
ejpam-5832	110	41	met	meet	VERB
ejpam-5832	110	42	:	:	PUNCT
ejpam-5832	110	43	.	.	PUNCT
ejpam-5832	111	1	(	(	PUNCT
ejpam-5832	111	2	i	i	NOUN
ejpam-5832	111	3	)	)	PUNCT
ejpam-5832	111	4	(	(	PUNCT
ejpam-5832	111	5	µq(ϵ1ϵ2	µq(ϵ1ϵ2	PROPN
ejpam-5832	111	6	)	)	PUNCT
ejpam-5832	111	7	)	)	PUNCT
ejpam-5832	112	1	q	q	PROPN
ejpam-5832	112	2	≥	≥	NUM
ejpam-5832	112	3	min{(µq(ϵ1))q	min{(µq(ϵ1))q	PROPN
ejpam-5832	112	4	,	,	PUNCT
ejpam-5832	112	5	(	(	PUNCT
ejpam-5832	112	6	µq(ϵ2))q	µq(ϵ2))q	NOUN
ejpam-5832	112	7	}	}	PUNCT
ejpam-5832	112	8	and	and	CCONJ
ejpam-5832	112	9	(	(	PUNCT
ejpam-5832	112	10	µq(ϵ1ϵ2	µq(ϵ1ϵ2	NOUN
ejpam-5832	112	11	)	)	PUNCT
ejpam-5832	112	12	)	)	PUNCT
ejpam-5832	112	13	q	q	PROPN
ejpam-5832	113	1	≤	≤	PROPN
ejpam-5832	113	2	max{(νq(ϵ1))q	max{(νq(ϵ1))q	PROPN
ejpam-5832	113	3	,	,	PUNCT
ejpam-5832	113	4	(	(	PUNCT
ejpam-5832	113	5	νq(ϵ2))q	νq(ϵ2))q	PROPN
ejpam-5832	113	6	}	}	PUNCT
ejpam-5832	113	7	for	for	ADP
ejpam-5832	113	8	all	all	DET
ejpam-5832	113	9	ϵ1	ϵ1	ADJ
ejpam-5832	113	10	,	,	PUNCT
ejpam-5832	113	11	ϵ2	ϵ2	PROPN
ejpam-5832	113	12	∈	∈	PROPN
ejpam-5832	113	13	v.	v.	PROPN
ejpam-5832	113	14	(	(	PUNCT
ejpam-5832	113	15	ii	ii	PROPN
ejpam-5832	113	16	)	)	PUNCT
ejpam-5832	113	17	(	(	PUNCT
ejpam-5832	113	18	µq(ϵ	µq(ϵ	NUM
ejpam-5832	113	19	−1))q	−1))q	PROPN
ejpam-5832	113	20	≥	≥	NUM
ejpam-5832	113	21	(	(	PUNCT
ejpam-5832	113	22	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	113	23	)	)	PUNCT
ejpam-5832	113	24	)	)	PUNCT
ejpam-5832	114	1	q	q	NOUN
ejpam-5832	114	2	and	and	CCONJ
ejpam-5832	114	3	(	(	PUNCT
ejpam-5832	114	4	νq(ϵ	νq(ϵ	NUM
ejpam-5832	114	5	−1))q	−1))q	NOUN
ejpam-5832	114	6	≤	≤	NUM
ejpam-5832	114	7	(	(	PUNCT
ejpam-5832	114	8	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	114	9	)	)	PUNCT
ejpam-5832	114	10	)	)	PUNCT
ejpam-5832	115	1	q	q	NOUN
ejpam-5832	115	2	for	for	ADP
ejpam-5832	115	3	all	all	DET
ejpam-5832	115	4	ϵ	ϵ	PART
ejpam-5832	115	5	∈	∈	PROPN
ejpam-5832	115	6	v	v	NOUN
ejpam-5832	115	7	.	.	PUNCT
ejpam-5832	116	1	theorem	theorem	NOUN
ejpam-5832	116	2	1	1	NUM
ejpam-5832	116	3	.	.	PUNCT
ejpam-5832	117	1	[	[	X
ejpam-5832	117	2	35	35	NUM
ejpam-5832	117	3	]	]	X
ejpam-5832	117	4	a	a	DET
ejpam-5832	117	5	q	q	NOUN
ejpam-5832	117	6	-	-	PUNCT
ejpam-5832	117	7	rofs	rofs	ADJ
ejpam-5832	117	8	q	q	NOUN
ejpam-5832	117	9	of	of	ADP
ejpam-5832	117	10	v	v	NOUN
ejpam-5832	117	11	is	be	AUX
ejpam-5832	117	12	a	a	DET
ejpam-5832	117	13	q	q	NOUN
ejpam-5832	117	14	-	-	PUNCT
ejpam-5832	117	15	rofsg	rofsg	NOUN
ejpam-5832	117	16	of	of	ADP
ejpam-5832	117	17	v	v	PROPN
ejpam-5832	117	18	⇔	⇔	X
ejpam-5832	117	19	(	(	PUNCT
ejpam-5832	117	20	µq(ϵ1ϵ	µq(ϵ1ϵ	PROPN
ejpam-5832	117	21	−1	−1	NOUN
ejpam-5832	117	22	2	2	NUM
ejpam-5832	117	23	)	)	PUNCT
ejpam-5832	117	24	)	)	PUNCT
ejpam-5832	118	1	q	q	PROPN
ejpam-5832	118	2	≥	≥	NUM
ejpam-5832	118	3	min{(µq(ϵ1))q	min{(µq(ϵ1))q	PROPN
ejpam-5832	118	4	,	,	PUNCT
ejpam-5832	118	5	(	(	PUNCT
ejpam-5832	118	6	µq(ϵ2))q	µq(ϵ2))q	NOUN
ejpam-5832	118	7	}	}	PUNCT
ejpam-5832	118	8	and	and	CCONJ
ejpam-5832	118	9	(	(	PUNCT
ejpam-5832	118	10	νq(ϵ1ϵ	νq(ϵ1ϵ	PROPN
ejpam-5832	118	11	−1	−1	NOUN
ejpam-5832	118	12	2	2	NUM
ejpam-5832	118	13	)	)	PUNCT
ejpam-5832	118	14	)	)	PUNCT
ejpam-5832	118	15	q	q	PROPN
ejpam-5832	119	1	≤	≤	PROPN
ejpam-5832	119	2	max{(νq(ϵ1))q	max{(νq(ϵ1))q	PROPN
ejpam-5832	119	3	,	,	PUNCT
ejpam-5832	119	4	(	(	PUNCT
ejpam-5832	119	5	νq(ϵ2))q	νq(ϵ2))q	PROPN
ejpam-5832	119	6	}	}	PUNCT
ejpam-5832	119	7	for	for	ADP
ejpam-5832	119	8	all	all	DET
ejpam-5832	119	9	ϵ1	ϵ1	ADJ
ejpam-5832	119	10	,	,	PUNCT
ejpam-5832	119	11	ϵ2	ϵ2	PROPN
ejpam-5832	119	12	∈	∈	PROPN
ejpam-5832	119	13	v	v	NOUN
ejpam-5832	119	14	.	.	PUNCT
ejpam-5832	119	15	theorem	theorem	NOUN
ejpam-5832	119	16	2	2	NUM
ejpam-5832	119	17	.	.	PUNCT
ejpam-5832	120	1	[	[	X
ejpam-5832	120	2	35	35	NUM
ejpam-5832	120	3	]	]	PUNCT
ejpam-5832	120	4	let	let	VERB
ejpam-5832	120	5	q	q	NOUN
ejpam-5832	120	6	and	and	CCONJ
ejpam-5832	120	7	k	k	PROPN
ejpam-5832	120	8	be	be	AUX
ejpam-5832	120	9	two	two	NUM
ejpam-5832	120	10	q	q	NOUN
ejpam-5832	120	11	-	-	PUNCT
ejpam-5832	120	12	rofsgs	rofsg	NOUN
ejpam-5832	120	13	of	of	ADP
ejpam-5832	120	14	v	v	NOUN
ejpam-5832	120	15	.	.	PUNCT
ejpam-5832	121	1	then	then	ADV
ejpam-5832	121	2	q	q	PROPN
ejpam-5832	121	3	∩k	∩k	PROPN
ejpam-5832	121	4	is	be	AUX
ejpam-5832	121	5	a	a	DET
ejpam-5832	121	6	q	q	NOUN
ejpam-5832	121	7	-	-	PUNCT
ejpam-5832	121	8	rofsg	rofsg	NOUN
ejpam-5832	121	9	of	of	ADP
ejpam-5832	121	10	v	v	NOUN
ejpam-5832	121	11	.	.	PUNCT
ejpam-5832	122	1	the	the	DET
ejpam-5832	122	2	notion	notion	NOUN
ejpam-5832	122	3	of	of	ADP
ejpam-5832	122	4	q	q	ADJ
ejpam-5832	122	5	-	-	PUNCT
ejpam-5832	122	6	rung	rung	ADJ
ejpam-5832	122	7	orthopair	orthopair	ADJ
ejpam-5832	122	8	fuzzy	fuzzy	ADJ
ejpam-5832	122	9	level	level	NOUN
ejpam-5832	122	10	subset	subset	NOUN
ejpam-5832	122	11	(	(	PUNCT
ejpam-5832	122	12	q	q	NOUN
ejpam-5832	122	13	-	-	PUNCT
ejpam-5832	122	14	rofls	rofls	ADJ
ejpam-5832	122	15	)	)	PUNCT
ejpam-5832	122	16	is	be	AUX
ejpam-5832	122	17	presented	present	VERB
ejpam-5832	122	18	in	in	ADP
ejpam-5832	122	19	[	[	X
ejpam-5832	122	20	35	35	NUM
ejpam-5832	122	21	]	]	SYM
ejpam-5832	122	22	.	.	PUNCT
ejpam-5832	123	1	herein	herein	NOUN
ejpam-5832	123	2	,	,	PUNCT
ejpam-5832	123	3	we	we	PRON
ejpam-5832	123	4	repeat	repeat	VERB
ejpam-5832	123	5	the	the	DET
ejpam-5832	123	6	definition	definition	NOUN
ejpam-5832	123	7	of	of	ADP
ejpam-5832	123	8	q	q	NOUN
ejpam-5832	123	9	-	-	PUNCT
ejpam-5832	123	10	rofls	rofls	ADJ
ejpam-5832	123	11	together	together	ADV
ejpam-5832	123	12	with	with	ADP
ejpam-5832	123	13	some	some	DET
ejpam-5832	123	14	associated	associated	ADJ
ejpam-5832	123	15	findings	finding	NOUN
ejpam-5832	123	16	.	.	PUNCT
ejpam-5832	124	1	definition	definition	NOUN
ejpam-5832	124	2	5	5	NUM
ejpam-5832	124	3	.	.	PUNCT
ejpam-5832	125	1	[	[	X
ejpam-5832	125	2	35	35	NUM
ejpam-5832	125	3	]	]	PUNCT
ejpam-5832	125	4	let	let	VERB
ejpam-5832	125	5	q	q	NOUN
ejpam-5832	125	6	=	=	PRON
ejpam-5832	125	7	{	{	PUNCT
ejpam-5832	125	8	(	(	PUNCT
ejpam-5832	125	9	ϵ	ϵ	NOUN
ejpam-5832	125	10	,	,	PUNCT
ejpam-5832	125	11	µq(ϵ	µq(ϵ	NUM
ejpam-5832	125	12	)	)	PUNCT
ejpam-5832	125	13	,	,	PUNCT
ejpam-5832	125	14	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	125	15	)	)	PUNCT
ejpam-5832	125	16	)	)	PUNCT
ejpam-5832	125	17	:	:	PUNCT
ejpam-5832	126	1	ϵ	ϵ	X
ejpam-5832	126	2	∈	∈	PROPN
ejpam-5832	126	3	v	v	PROPN
ejpam-5832	126	4	}	}	PUNCT
ejpam-5832	126	5	be	be	AUX
ejpam-5832	126	6	a	a	DET
ejpam-5832	126	7	q	q	NOUN
ejpam-5832	126	8	-	-	PUNCT
ejpam-5832	126	9	rofs	rofs	NOUN
ejpam-5832	126	10	of	of	ADP
ejpam-5832	126	11	v	v	NOUN
ejpam-5832	126	12	and	and	CCONJ
ejpam-5832	126	13	θ	θ	PROPN
ejpam-5832	126	14	,	,	PUNCT
ejpam-5832	126	15	τ	τ	PROPN
ejpam-5832	126	16	∈	∈	PROPN
ejpam-5832	127	1	[	[	X
ejpam-5832	127	2	0	0	NUM
ejpam-5832	127	3	,	,	PUNCT
ejpam-5832	127	4	1	1	NUM
ejpam-5832	127	5	]	]	PUNCT
ejpam-5832	127	6	satisfying	satisfy	VERB
ejpam-5832	127	7	θq	θq	ADP
ejpam-5832	127	8	+	+	NUM
ejpam-5832	127	9	τ	τ	PROPN
ejpam-5832	127	10	q	q	PROPN
ejpam-5832	127	11	≤	≤	PROPN
ejpam-5832	127	12	1	1	NUM
ejpam-5832	127	13	.	.	PUNCT
ejpam-5832	128	1	then	then	ADV
ejpam-5832	128	2	the	the	DET
ejpam-5832	128	3	set	set	NOUN
ejpam-5832	128	4	q(θ	q(θ	PROPN
ejpam-5832	128	5	,	,	PUNCT
ejpam-5832	128	6	τ	τ	X
ejpam-5832	128	7	)	)	PUNCT
ejpam-5832	128	8	=	=	PRON
ejpam-5832	128	9	{	{	PUNCT
ejpam-5832	128	10	ϵ	ϵ	PART
ejpam-5832	128	11	∈	∈	PROPN
ejpam-5832	128	12	v	v	NOUN
ejpam-5832	128	13	:	:	PUNCT
ejpam-5832	128	14	(	(	PUNCT
ejpam-5832	128	15	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	128	16	)	)	PUNCT
ejpam-5832	128	17	)	)	PUNCT
ejpam-5832	129	1	q	q	NOUN
ejpam-5832	129	2	≥	≥	NUM
ejpam-5832	129	3	θ	θ	NOUN
ejpam-5832	129	4	,	,	PUNCT
ejpam-5832	129	5	(	(	PUNCT
ejpam-5832	129	6	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	129	7	)	)	PUNCT
ejpam-5832	129	8	)	)	PUNCT
ejpam-5832	130	1	q	q	PROPN
ejpam-5832	130	2	≤	≤	NUM
ejpam-5832	130	3	τ	τ	X
ejpam-5832	130	4	}	}	PUNCT
ejpam-5832	130	5	is	be	AUX
ejpam-5832	130	6	known	know	VERB
ejpam-5832	130	7	as	as	ADP
ejpam-5832	130	8	q	q	NOUN
ejpam-5832	130	9	-	-	PUNCT
ejpam-5832	130	10	rofls	rofls	ADJ
ejpam-5832	130	11	of	of	ADP
ejpam-5832	130	12	q.	q.	PROPN
ejpam-5832	130	13	the	the	DET
ejpam-5832	130	14	succeeding	succeed	VERB
ejpam-5832	130	15	theorem	theorem	NOUN
ejpam-5832	130	16	presented	present	VERB
ejpam-5832	130	17	in	in	ADP
ejpam-5832	130	18	[	[	X
ejpam-5832	130	19	36	36	NUM
ejpam-5832	130	20	]	]	PUNCT
ejpam-5832	130	21	is	be	AUX
ejpam-5832	130	22	subsequently	subsequently	ADV
ejpam-5832	130	23	utilized	utilize	VERB
ejpam-5832	130	24	to	to	PART
ejpam-5832	130	25	demonstrate	demonstrate	VERB
ejpam-5832	130	26	our	our	PRON
ejpam-5832	130	27	findings	finding	NOUN
ejpam-5832	130	28	.	.	PUNCT
ejpam-5832	131	1	theorem	theorem	VERB
ejpam-5832	131	2	3	3	NUM
ejpam-5832	131	3	.	.	PUNCT
ejpam-5832	132	1	[	[	X
ejpam-5832	132	2	35	35	NUM
ejpam-5832	132	3	]	]	PUNCT
ejpam-5832	132	4	let	let	VERB
ejpam-5832	132	5	q	q	NOUN
ejpam-5832	132	6	and	and	CCONJ
ejpam-5832	132	7	k	k	PROPN
ejpam-5832	132	8	be	be	AUX
ejpam-5832	132	9	two	two	NUM
ejpam-5832	132	10	q	q	NOUN
ejpam-5832	132	11	-	-	PUNCT
ejpam-5832	132	12	rofss	rofss	NOUN
ejpam-5832	132	13	of	of	ADP
ejpam-5832	132	14	v	v	NOUN
ejpam-5832	132	15	and	and	CCONJ
ejpam-5832	133	1	q	q	NOUN
ejpam-5832	133	2	⊆	⊆	NUM
ejpam-5832	133	3	k	k	NOUN
ejpam-5832	133	4	,	,	PUNCT
ejpam-5832	133	5	then	then	ADV
ejpam-5832	133	6	q(θ	q(θ	PROPN
ejpam-5832	133	7	,	,	PUNCT
ejpam-5832	133	8	τ	τ	X
ejpam-5832	133	9	)	)	PUNCT
ejpam-5832	133	10	)	)	PUNCT
ejpam-5832	134	1	⊆	⊆	NUM
ejpam-5832	134	2	k(θ	k(θ	NOUN
ejpam-5832	134	3	,	,	PUNCT
ejpam-5832	134	4	τ	τ	X
ejpam-5832	134	5	)	)	PUNCT
ejpam-5832	134	6	for	for	ADP
ejpam-5832	134	7	all	all	DET
ejpam-5832	134	8	θ	θ	PROPN
ejpam-5832	134	9	,	,	PUNCT
ejpam-5832	134	10	τ	τ	PROPN
ejpam-5832	134	11	∈	∈	PROPN
ejpam-5832	135	1	[	[	X
ejpam-5832	135	2	0	0	NUM
ejpam-5832	135	3	,	,	PUNCT
ejpam-5832	135	4	1	1	NUM
ejpam-5832	135	5	]	]	PUNCT
ejpam-5832	135	6	satisfying	satisfy	VERB
ejpam-5832	135	7	θq	θq	ADP
ejpam-5832	135	8	+	+	NUM
ejpam-5832	135	9	τ	τ	PROPN
ejpam-5832	135	10	q	q	PROPN
ejpam-5832	135	11	≤	≤	PROPN
ejpam-5832	135	12	1	1	NUM
ejpam-5832	135	13	.	.	PUNCT
ejpam-5832	135	14	a.	a.	NOUN
ejpam-5832	135	15	razzaque	razzaque	PROPN
ejpam-5832	135	16	/	/	SYM
ejpam-5832	135	17	eur	eur	NOUN
ejpam-5832	135	18	.	.	PUNCT
ejpam-5832	136	1	j.	j.	PROPN
ejpam-5832	136	2	pure	pure	PROPN
ejpam-5832	136	3	appl	appl	PROPN
ejpam-5832	136	4	.	.	PROPN
ejpam-5832	136	5	math	math	PROPN
ejpam-5832	136	6	,	,	PUNCT
ejpam-5832	136	7	18	18	NUM
ejpam-5832	136	8	(	(	PUNCT
ejpam-5832	136	9	3	3	NUM
ejpam-5832	136	10	)	)	PUNCT
ejpam-5832	136	11	(	(	PUNCT
ejpam-5832	136	12	2025	2025	NUM
ejpam-5832	136	13	)	)	PUNCT
ejpam-5832	136	14	,	,	PUNCT
ejpam-5832	136	15	5832	5832	NUM
ejpam-5832	136	16	5	5	NUM
ejpam-5832	136	17	of	of	ADP
ejpam-5832	136	18	21	21	NUM
ejpam-5832	136	19	theorem	theorem	VERB
ejpam-5832	136	20	4	4	NUM
ejpam-5832	136	21	.	.	PUNCT
ejpam-5832	137	1	[	[	X
ejpam-5832	137	2	35	35	NUM
ejpam-5832	137	3	]	]	X
ejpam-5832	137	4	a	a	DET
ejpam-5832	137	5	q	q	NOUN
ejpam-5832	137	6	-	-	PUNCT
ejpam-5832	137	7	rofs	rofs	ADJ
ejpam-5832	137	8	q	q	NOUN
ejpam-5832	137	9	of	of	ADP
ejpam-5832	137	10	v	v	NOUN
ejpam-5832	137	11	is	be	AUX
ejpam-5832	137	12	a	a	DET
ejpam-5832	137	13	q	q	NOUN
ejpam-5832	137	14	-	-	PUNCT
ejpam-5832	137	15	rofsg	rofsg	NOUN
ejpam-5832	137	16	of	of	ADP
ejpam-5832	137	17	v	v	PROPN
ejpam-5832	137	18	⇔	⇔	PROPN
ejpam-5832	137	19	q(θ	q(θ	PROPN
ejpam-5832	137	20	,	,	PUNCT
ejpam-5832	137	21	τ	τ	X
ejpam-5832	137	22	)	)	PUNCT
ejpam-5832	137	23	is	be	AUX
ejpam-5832	137	24	a	a	DET
ejpam-5832	137	25	subgroup	subgroup	NOUN
ejpam-5832	137	26	of	of	ADP
ejpam-5832	137	27	v	v	NOUN
ejpam-5832	137	28	for	for	ADP
ejpam-5832	137	29	all	all	DET
ejpam-5832	137	30	θ	θ	PRON
ejpam-5832	137	31	∈	∈	PROPN
ejpam-5832	138	1	[	[	X
ejpam-5832	138	2	0	0	NUM
ejpam-5832	138	3	,	,	PUNCT
ejpam-5832	138	4	(	(	PUNCT
ejpam-5832	138	5	µq(e	µq(e	NUM
ejpam-5832	138	6	)	)	PUNCT
ejpam-5832	138	7	)	)	PUNCT
ejpam-5832	139	1	q	q	X
ejpam-5832	139	2	]	]	PUNCT
ejpam-5832	139	3	and	and	CCONJ
ejpam-5832	139	4	τ	τ	PROPN
ejpam-5832	139	5	∈	∈	PROPN
ejpam-5832	140	1	[	[	X
ejpam-5832	140	2	(	(	PUNCT
ejpam-5832	140	3	νq(e	νq(e	NUM
ejpam-5832	140	4	)	)	PUNCT
ejpam-5832	140	5	)	)	PUNCT
ejpam-5832	141	1	q	q	X
ejpam-5832	141	2	,	,	PUNCT
ejpam-5832	141	3	1	1	NUM
ejpam-5832	141	4	]	]	PUNCT
ejpam-5832	141	5	.	.	PUNCT
ejpam-5832	142	1	now	now	ADV
ejpam-5832	142	2	,	,	PUNCT
ejpam-5832	142	3	we	we	PRON
ejpam-5832	142	4	present	present	VERB
ejpam-5832	142	5	the	the	DET
ejpam-5832	142	6	concepts	concept	NOUN
ejpam-5832	142	7	of	of	ADP
ejpam-5832	142	8	q	q	ADJ
ejpam-5832	142	9	-	-	PUNCT
ejpam-5832	142	10	rung	rung	ADJ
ejpam-5832	142	11	orthopair	orthopair	NOUN
ejpam-5832	142	12	fuzzy	fuzzy	ADJ
ejpam-5832	142	13	left	left	ADJ
ejpam-5832	142	14	and	and	CCONJ
ejpam-5832	142	15	right	right	ADJ
ejpam-5832	142	16	cosets	coset	NOUN
ejpam-5832	142	17	of	of	ADP
ejpam-5832	142	18	a	a	DET
ejpam-5832	142	19	q	q	NOUN
ejpam-5832	142	20	-	-	PUNCT
ejpam-5832	142	21	rofsg	rofsg	NOUN
ejpam-5832	142	22	of	of	ADP
ejpam-5832	142	23	a	a	DET
ejpam-5832	142	24	group	group	NOUN
ejpam-5832	142	25	that	that	PRON
ejpam-5832	142	26	is	be	AUX
ejpam-5832	142	27	defined	define	VERB
ejpam-5832	142	28	in	in	ADP
ejpam-5832	142	29	[	[	X
ejpam-5832	142	30	36	36	NUM
ejpam-5832	142	31	]	]	PUNCT
ejpam-5832	142	32	.	.	PUNCT
ejpam-5832	143	1	definition	definition	NOUN
ejpam-5832	143	2	6	6	NUM
ejpam-5832	143	3	.	.	PUNCT
ejpam-5832	144	1	[	[	X
ejpam-5832	144	2	35	35	NUM
ejpam-5832	144	3	]	]	PUNCT
ejpam-5832	144	4	let	let	VERB
ejpam-5832	144	5	q	q	NOUN
ejpam-5832	144	6	=	=	PRON
ejpam-5832	144	7	{	{	PUNCT
ejpam-5832	144	8	(	(	PUNCT
ejpam-5832	144	9	ϵ	ϵ	NOUN
ejpam-5832	144	10	,	,	PUNCT
ejpam-5832	144	11	µq(ϵ	µq(ϵ	NUM
ejpam-5832	144	12	)	)	PUNCT
ejpam-5832	144	13	,	,	PUNCT
ejpam-5832	144	14	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	144	15	)	)	PUNCT
ejpam-5832	144	16	)	)	PUNCT
ejpam-5832	144	17	:	:	PUNCT
ejpam-5832	145	1	ϵ	ϵ	X
ejpam-5832	145	2	∈	∈	PROPN
ejpam-5832	145	3	v	v	PROPN
ejpam-5832	145	4	}	}	PUNCT
ejpam-5832	145	5	be	be	AUX
ejpam-5832	145	6	a	a	DET
ejpam-5832	145	7	q	q	NOUN
ejpam-5832	145	8	-	-	PUNCT
ejpam-5832	145	9	rofsg	rofsg	NOUN
ejpam-5832	145	10	of	of	ADP
ejpam-5832	145	11	v	v	NOUN
ejpam-5832	145	12	and	and	CCONJ
ejpam-5832	145	13	λ	λ	X
ejpam-5832	145	14	∈	∈	PROPN
ejpam-5832	145	15	v	v	NOUN
ejpam-5832	145	16	.	.	PUNCT
ejpam-5832	146	1	then	then	ADV
ejpam-5832	146	2	q	q	ADJ
ejpam-5832	146	3	-	-	PUNCT
ejpam-5832	146	4	rung	rung	ADJ
ejpam-5832	146	5	orthopair	orthopair	NOUN
ejpam-5832	146	6	fuzzy	fuzzy	ADJ
ejpam-5832	146	7	left	leave	VERB
ejpam-5832	146	8	coset	coset	NOUN
ejpam-5832	146	9	(	(	PUNCT
ejpam-5832	146	10	q	q	NOUN
ejpam-5832	146	11	-	-	PUNCT
ejpam-5832	146	12	roflc	roflc	VERB
ejpam-5832	146	13	)	)	PUNCT
ejpam-5832	146	14	of	of	ADP
ejpam-5832	146	15	q	q	PROPN
ejpam-5832	146	16	associated	associate	VERB
ejpam-5832	146	17	to	to	ADP
ejpam-5832	146	18	λ	λ	PROPN
ejpam-5832	146	19	is	be	AUX
ejpam-5832	146	20	denoted	denote	VERB
ejpam-5832	146	21	by	by	ADP
ejpam-5832	146	22	λq	λq	INTJ
ejpam-5832	146	23	such	such	ADJ
ejpam-5832	146	24	that	that	SCONJ
ejpam-5832	146	25	λq	λq	ADV
ejpam-5832	146	26	=	=	X
ejpam-5832	146	27	{	{	PUNCT
ejpam-5832	146	28	(	(	PUNCT
ejpam-5832	146	29	ϵ	ϵ	NOUN
ejpam-5832	146	30	,	,	PUNCT
ejpam-5832	146	31	µλq(ϵ	µλq(ϵ	PROPN
ejpam-5832	146	32	)	)	PUNCT
ejpam-5832	146	33	,	,	PUNCT
ejpam-5832	146	34	νλq(ϵ	νλq(ϵ	PROPN
ejpam-5832	146	35	)	)	PUNCT
ejpam-5832	146	36	)	)	PUNCT
ejpam-5832	146	37	:	:	PUNCT
ejpam-5832	147	1	ϵ	ϵ	X
ejpam-5832	147	2	∈	∈	PROPN
ejpam-5832	147	3	v	v	ADP
ejpam-5832	147	4	}	}	PUNCT
ejpam-5832	147	5	,	,	PUNCT
ejpam-5832	147	6	where	where	SCONJ
ejpam-5832	147	7	(	(	PUNCT
ejpam-5832	147	8	µλq(ϵ	µλq(ϵ	PROPN
ejpam-5832	147	9	)	)	PUNCT
ejpam-5832	147	10	)	)	PUNCT
ejpam-5832	147	11	q	q	NOUN
ejpam-5832	148	1	=	=	PUNCT
ejpam-5832	148	2	(	(	PUNCT
ejpam-5832	148	3	µq(λ	µq(λ	PUNCT
ejpam-5832	148	4	−1ϵ))q	−1ϵ))q	NOUN
ejpam-5832	148	5	and	and	CCONJ
ejpam-5832	148	6	(	(	PUNCT
ejpam-5832	148	7	νλq(ϵ	νλq(ϵ	PROPN
ejpam-5832	148	8	)	)	PUNCT
ejpam-5832	148	9	)	)	PUNCT
ejpam-5832	148	10	q	q	NOUN
ejpam-5832	149	1	=	=	PUNCT
ejpam-5832	149	2	(	(	PUNCT
ejpam-5832	149	3	νq(λ	νq(λ	NUM
ejpam-5832	149	4	−1ϵ))q	−1ϵ))q	NOUN
ejpam-5832	149	5	.	.	PUNCT
ejpam-5832	150	1	similarly	similarly	ADV
ejpam-5832	150	2	,	,	PUNCT
ejpam-5832	150	3	qλ	qλ	PROPN
ejpam-5832	150	4	=	=	PRON
ejpam-5832	150	5	{	{	PUNCT
ejpam-5832	150	6	(	(	PUNCT
ejpam-5832	150	7	ϵ	ϵ	NOUN
ejpam-5832	150	8	,	,	PUNCT
ejpam-5832	150	9	µqλ(ϵ	µqλ(ϵ	NOUN
ejpam-5832	150	10	)	)	PUNCT
ejpam-5832	150	11	,	,	PUNCT
ejpam-5832	150	12	νqλ(ϵ	νqλ(ϵ	PROPN
ejpam-5832	150	13	)	)	PUNCT
ejpam-5832	150	14	)	)	PUNCT
ejpam-5832	150	15	:	:	PUNCT
ejpam-5832	151	1	ϵ	ϵ	X
ejpam-5832	151	2	∈	∈	PROPN
ejpam-5832	151	3	v	v	ADP
ejpam-5832	151	4	}	}	PUNCT
ejpam-5832	151	5	,	,	PUNCT
ejpam-5832	151	6	where	where	SCONJ
ejpam-5832	151	7	(	(	PUNCT
ejpam-5832	151	8	µqλ(ϵ))q	µqλ(ϵ))q	PROPN
ejpam-5832	151	9	=	=	PUNCT
ejpam-5832	151	10	(	(	PUNCT
ejpam-5832	151	11	µq(ϵλ	µq(ϵλ	PROPN
ejpam-5832	151	12	−1))q	−1))q	PROPN
ejpam-5832	151	13	and	and	CCONJ
ejpam-5832	151	14	(	(	PUNCT
ejpam-5832	151	15	νqλ(ϵ	νqλ(ϵ	PROPN
ejpam-5832	151	16	)	)	PUNCT
ejpam-5832	151	17	)	)	PUNCT
ejpam-5832	151	18	q	q	NOUN
ejpam-5832	152	1	=	=	PUNCT
ejpam-5832	152	2	(	(	PUNCT
ejpam-5832	152	3	νq(ϵλ	νq(ϵλ	PROPN
ejpam-5832	152	4	−1))q	−1))q	NOUN
ejpam-5832	152	5	,	,	PUNCT
ejpam-5832	152	6	is	be	AUX
ejpam-5832	152	7	called	call	VERB
ejpam-5832	152	8	q	q	ADJ
ejpam-5832	152	9	-	-	PUNCT
ejpam-5832	152	10	rung	rung	ADJ
ejpam-5832	152	11	orthopair	orthopair	NOUN
ejpam-5832	152	12	fuzzy	fuzzy	ADJ
ejpam-5832	152	13	right	right	ADJ
ejpam-5832	152	14	coset	coset	NOUN
ejpam-5832	152	15	(	(	PUNCT
ejpam-5832	152	16	qrofrc	qrofrc	NOUN
ejpam-5832	152	17	)	)	PUNCT
ejpam-5832	152	18	of	of	ADP
ejpam-5832	152	19	q	q	PROPN
ejpam-5832	152	20	associated	associate	VERB
ejpam-5832	152	21	to	to	ADP
ejpam-5832	152	22	λ	λ	PROPN
ejpam-5832	152	23	.	.	PROPN
ejpam-5832	153	1	next	next	ADV
ejpam-5832	153	2	,	,	PUNCT
ejpam-5832	153	3	we	we	PRON
ejpam-5832	153	4	present	present	VERB
ejpam-5832	153	5	the	the	DET
ejpam-5832	153	6	definition	definition	NOUN
ejpam-5832	153	7	of	of	ADP
ejpam-5832	153	8	q	q	ADJ
ejpam-5832	153	9	-	-	PUNCT
ejpam-5832	153	10	rung	rung	ADJ
ejpam-5832	153	11	orthopair	orthopair	NOUN
ejpam-5832	153	12	fuzzy	fuzzy	ADJ
ejpam-5832	153	13	normal	normal	ADJ
ejpam-5832	153	14	subgroup	subgroup	NOUN
ejpam-5832	153	15	(	(	PUNCT
ejpam-5832	153	16	q	q	NOUN
ejpam-5832	153	17	-	-	PUNCT
ejpam-5832	153	18	rofnsg	rofnsg	NOUN
ejpam-5832	153	19	)	)	PUNCT
ejpam-5832	153	20	of	of	ADP
ejpam-5832	153	21	v	v	NOUN
ejpam-5832	153	22	that	that	PRON
ejpam-5832	153	23	is	be	AUX
ejpam-5832	153	24	demonstrated	demonstrate	VERB
ejpam-5832	153	25	in	in	ADP
ejpam-5832	153	26	[	[	X
ejpam-5832	153	27	35	35	NUM
ejpam-5832	153	28	]	]	PUNCT
ejpam-5832	153	29	.	.	PUNCT
ejpam-5832	154	1	definition	definition	NOUN
ejpam-5832	154	2	7	7	NUM
ejpam-5832	154	3	.	.	PUNCT
ejpam-5832	155	1	[	[	X
ejpam-5832	155	2	35	35	NUM
ejpam-5832	155	3	]	]	X
ejpam-5832	155	4	a	a	DET
ejpam-5832	155	5	q	q	ADJ
ejpam-5832	155	6	-	-	PUNCT
ejpam-5832	155	7	rofsg	rofsg	NOUN
ejpam-5832	155	8	q	q	NOUN
ejpam-5832	155	9	=	=	PUNCT
ejpam-5832	155	10	{	{	PUNCT
ejpam-5832	155	11	(	(	PUNCT
ejpam-5832	155	12	ϵ	ϵ	NOUN
ejpam-5832	155	13	,	,	PUNCT
ejpam-5832	155	14	µq(ϵ	µq(ϵ	NUM
ejpam-5832	155	15	)	)	PUNCT
ejpam-5832	155	16	,	,	PUNCT
ejpam-5832	155	17	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	155	18	)	)	PUNCT
ejpam-5832	155	19	)	)	PUNCT
ejpam-5832	155	20	:	:	PUNCT
ejpam-5832	156	1	ϵ	ϵ	X
ejpam-5832	156	2	∈	∈	PROPN
ejpam-5832	156	3	v	v	NOUN
ejpam-5832	156	4	}	}	PUNCT
ejpam-5832	156	5	of	of	ADP
ejpam-5832	156	6	v	v	NOUN
ejpam-5832	156	7	is	be	AUX
ejpam-5832	156	8	called	call	VERB
ejpam-5832	156	9	q	q	NOUN
ejpam-5832	156	10	-	-	PUNCT
ejpam-5832	156	11	rofnsg	rofnsg	NOUN
ejpam-5832	156	12	of	of	ADP
ejpam-5832	156	13	v	v	NOUN
ejpam-5832	156	14	if	if	SCONJ
ejpam-5832	156	15	λq	λq	ADV
ejpam-5832	156	16	=	=	SYM
ejpam-5832	156	17	qλ	qλ	PROPN
ejpam-5832	156	18	for	for	ADP
ejpam-5832	156	19	all	all	DET
ejpam-5832	156	20	λ	λ	PROPN
ejpam-5832	156	21	∈	∈	PROPN
ejpam-5832	156	22	v	v	NOUN
ejpam-5832	156	23	.	.	PUNCT
ejpam-5832	156	24	theorem	theorem	ADJ
ejpam-5832	156	25	5	5	NUM
ejpam-5832	156	26	.	.	PUNCT
ejpam-5832	157	1	[	[	X
ejpam-5832	157	2	35	35	NUM
ejpam-5832	157	3	]	]	PUNCT
ejpam-5832	157	4	let	let	VERB
ejpam-5832	157	5	q	q	NOUN
ejpam-5832	157	6	=	=	PRON
ejpam-5832	157	7	{	{	PUNCT
ejpam-5832	157	8	(	(	PUNCT
ejpam-5832	157	9	ϵ	ϵ	NOUN
ejpam-5832	157	10	,	,	PUNCT
ejpam-5832	157	11	µq(ϵ	µq(ϵ	NUM
ejpam-5832	157	12	)	)	PUNCT
ejpam-5832	157	13	,	,	PUNCT
ejpam-5832	157	14	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	157	15	)	)	PUNCT
ejpam-5832	157	16	)	)	PUNCT
ejpam-5832	157	17	:	:	PUNCT
ejpam-5832	158	1	ϵ	ϵ	X
ejpam-5832	158	2	∈	∈	PROPN
ejpam-5832	158	3	v	v	PROPN
ejpam-5832	158	4	}	}	PUNCT
ejpam-5832	158	5	be	be	AUX
ejpam-5832	158	6	a	a	DET
ejpam-5832	158	7	q	q	NOUN
ejpam-5832	158	8	-	-	PUNCT
ejpam-5832	158	9	rofsg	rofsg	NOUN
ejpam-5832	158	10	of	of	ADP
ejpam-5832	158	11	v	v	NOUN
ejpam-5832	158	12	.	.	PUNCT
ejpam-5832	159	1	then	then	ADV
ejpam-5832	159	2	q	q	PROPN
ejpam-5832	159	3	is	be	AUX
ejpam-5832	159	4	pfns	pfns	NOUN
ejpam-5832	159	5	of	of	ADP
ejpam-5832	159	6	v	v	NOUN
ejpam-5832	159	7	if	if	SCONJ
ejpam-5832	160	1	and	and	CCONJ
ejpam-5832	160	2	only	only	ADV
ejpam-5832	160	3	if	if	SCONJ
ejpam-5832	160	4	(	(	PUNCT
ejpam-5832	160	5	µq(ϵ1ϵ2	µq(ϵ1ϵ2	NOUN
ejpam-5832	160	6	)	)	PUNCT
ejpam-5832	160	7	)	)	PUNCT
ejpam-5832	161	1	q	q	NOUN
ejpam-5832	162	1	=	=	PUNCT
ejpam-5832	162	2	(	(	PUNCT
ejpam-5832	162	3	µq(ϵ2ϵ1	µq(ϵ2ϵ1	NOUN
ejpam-5832	162	4	)	)	PUNCT
ejpam-5832	162	5	)	)	PUNCT
ejpam-5832	162	6	q	q	NOUN
ejpam-5832	162	7	and	and	CCONJ
ejpam-5832	162	8	(	(	PUNCT
ejpam-5832	162	9	νq(ϵ1ϵ2	νq(ϵ1ϵ2	PROPN
ejpam-5832	162	10	)	)	PUNCT
ejpam-5832	162	11	)	)	PUNCT
ejpam-5832	163	1	q	q	NOUN
ejpam-5832	163	2	=	=	PUNCT
ejpam-5832	163	3	νq(ϵ2ϵ1	νq(ϵ2ϵ1	NUM
ejpam-5832	163	4	)	)	PUNCT
ejpam-5832	163	5	)	)	PUNCT
ejpam-5832	164	1	q	q	NOUN
ejpam-5832	164	2	for	for	ADP
ejpam-5832	164	3	all	all	DET
ejpam-5832	164	4	ϵ1	ϵ1	ADJ
ejpam-5832	164	5	,	,	PUNCT
ejpam-5832	164	6	ϵ2	ϵ2	PROPN
ejpam-5832	164	7	∈	∈	PROPN
ejpam-5832	164	8	v	v	NOUN
ejpam-5832	164	9	.	.	PUNCT
ejpam-5832	165	1	theorem	theorem	ADJ
ejpam-5832	165	2	6	6	NUM
ejpam-5832	165	3	.	.	PUNCT
ejpam-5832	166	1	[	[	X
ejpam-5832	166	2	35	35	NUM
ejpam-5832	166	3	]	]	PUNCT
ejpam-5832	166	4	let	let	VERB
ejpam-5832	166	5	q	q	NOUN
ejpam-5832	166	6	=	=	PRON
ejpam-5832	166	7	{	{	PUNCT
ejpam-5832	166	8	(	(	PUNCT
ejpam-5832	166	9	ϵ	ϵ	NOUN
ejpam-5832	166	10	,	,	PUNCT
ejpam-5832	166	11	µq(ϵ	µq(ϵ	NUM
ejpam-5832	166	12	)	)	PUNCT
ejpam-5832	166	13	,	,	PUNCT
ejpam-5832	166	14	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	166	15	)	)	PUNCT
ejpam-5832	166	16	)	)	PUNCT
ejpam-5832	166	17	:	:	PUNCT
ejpam-5832	167	1	ϵ	ϵ	X
ejpam-5832	167	2	∈	∈	PROPN
ejpam-5832	167	3	v	v	PROPN
ejpam-5832	167	4	}	}	PUNCT
ejpam-5832	167	5	be	be	AUX
ejpam-5832	167	6	a	a	DET
ejpam-5832	167	7	q	q	NOUN
ejpam-5832	167	8	-	-	PUNCT
ejpam-5832	167	9	rofsg	rofsg	NOUN
ejpam-5832	167	10	of	of	ADP
ejpam-5832	167	11	v	v	NOUN
ejpam-5832	167	12	.	.	PUNCT
ejpam-5832	168	1	then	then	ADV
ejpam-5832	168	2	q	q	PROPN
ejpam-5832	168	3	is	be	AUX
ejpam-5832	168	4	pfns	pfns	NOUN
ejpam-5832	168	5	of	of	ADP
ejpam-5832	168	6	v	v	NOUN
ejpam-5832	168	7	if	if	SCONJ
ejpam-5832	169	1	and	and	CCONJ
ejpam-5832	169	2	only	only	ADV
ejpam-5832	169	3	if	if	SCONJ
ejpam-5832	169	4	(	(	PUNCT
ejpam-5832	169	5	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	169	6	−1))q	−1))q	NOUN
ejpam-5832	169	7	=	=	SYM
ejpam-5832	169	8	(	(	PUNCT
ejpam-5832	169	9	µq(λ	µq(λ	NOUN
ejpam-5832	169	10	)	)	PUNCT
ejpam-5832	169	11	)	)	PUNCT
ejpam-5832	169	12	q	q	NOUN
ejpam-5832	170	1	and	and	CCONJ
ejpam-5832	170	2	(	(	PUNCT
ejpam-5832	170	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	170	4	−1))q	−1))q	NOUN
ejpam-5832	170	5	=	=	PUNCT
ejpam-5832	170	6	νq(λ	νq(λ	NUM
ejpam-5832	170	7	)	)	PUNCT
ejpam-5832	170	8	)	)	PUNCT
ejpam-5832	171	1	q	q	NOUN
ejpam-5832	171	2	for	for	ADP
ejpam-5832	171	3	all	all	DET
ejpam-5832	171	4	λ,∈	λ,∈	NUM
ejpam-5832	171	5	v	v	NOUN
ejpam-5832	171	6	.	.	PUNCT
ejpam-5832	172	1	3	3	X
ejpam-5832	172	2	.	.	X
ejpam-5832	172	3	more	more	ADJ
ejpam-5832	172	4	on	on	ADP
ejpam-5832	172	5	q	q	ADJ
ejpam-5832	172	6	-	-	PUNCT
ejpam-5832	172	7	rung	rung	ADJ
ejpam-5832	172	8	orthopair	orthopair	ADJ
ejpam-5832	172	9	fuzzy	fuzzy	ADJ
ejpam-5832	172	10	cosets	coset	NOUN
ejpam-5832	172	11	of	of	ADP
ejpam-5832	172	12	a	a	DET
ejpam-5832	172	13	q	q	ADJ
ejpam-5832	172	14	-	-	PUNCT
ejpam-5832	172	15	rung	rung	ADJ
ejpam-5832	172	16	orthopair	orthopair	ADJ
ejpam-5832	172	17	fuzzy	fuzzy	ADJ
ejpam-5832	172	18	subgroup	subgroup	NOUN
ejpam-5832	172	19	and	and	CCONJ
ejpam-5832	172	20	q	q	ADJ
ejpam-5832	172	21	-	-	PUNCT
ejpam-5832	172	22	rung	rung	ADJ
ejpam-5832	172	23	orthopair	orthopair	NOUN
ejpam-5832	172	24	fuzzy	fuzzy	ADJ
ejpam-5832	172	25	normal	normal	ADJ
ejpam-5832	172	26	subgroups	subgroup	NOUN
ejpam-5832	172	27	of	of	ADP
ejpam-5832	172	28	a	a	DET
ejpam-5832	172	29	group	group	NOUN
ejpam-5832	172	30	in	in	ADP
ejpam-5832	172	31	this	this	DET
ejpam-5832	172	32	section	section	NOUN
ejpam-5832	172	33	,	,	PUNCT
ejpam-5832	172	34	we	we	PRON
ejpam-5832	172	35	establish	establish	VERB
ejpam-5832	172	36	some	some	DET
ejpam-5832	172	37	fundamental	fundamental	ADJ
ejpam-5832	172	38	facts	fact	NOUN
ejpam-5832	172	39	about	about	ADP
ejpam-5832	172	40	q	q	NOUN
ejpam-5832	172	41	-	-	PUNCT
ejpam-5832	172	42	rofsg	rofsg	NOUN
ejpam-5832	172	43	that	that	PRON
ejpam-5832	172	44	serve	serve	VERB
ejpam-5832	172	45	as	as	ADP
ejpam-5832	172	46	the	the	DET
ejpam-5832	172	47	foundation	foundation	NOUN
ejpam-5832	172	48	for	for	ADP
ejpam-5832	172	49	proving	prove	VERB
ejpam-5832	172	50	the	the	DET
ejpam-5832	172	51	theorems	theorem	NOUN
ejpam-5832	172	52	discussed	discuss	VERB
ejpam-5832	172	53	in	in	ADP
ejpam-5832	172	54	sections	section	NOUN
ejpam-5832	172	55	4	4	NUM
ejpam-5832	172	56	and	and	CCONJ
ejpam-5832	172	57	5	5	NUM
ejpam-5832	172	58	.	.	PUNCT
ejpam-5832	173	1	this	this	DET
ejpam-5832	173	2	section	section	NOUN
ejpam-5832	173	3	is	be	AUX
ejpam-5832	173	4	dedicated	dedicate	VERB
ejpam-5832	173	5	to	to	ADP
ejpam-5832	173	6	expanding	expand	VERB
ejpam-5832	173	7	the	the	DET
ejpam-5832	173	8	ideas	idea	NOUN
ejpam-5832	173	9	of	of	ADP
ejpam-5832	173	10	q	q	NOUN
ejpam-5832	173	11	-	-	PUNCT
ejpam-5832	173	12	rung	rung	ADJ
ejpam-5832	173	13	orthopair	orthopair	ADJ
ejpam-5832	173	14	fuzzy	fuzzy	ADJ
ejpam-5832	173	15	cosets	coset	NOUN
ejpam-5832	173	16	of	of	ADP
ejpam-5832	173	17	a	a	DET
ejpam-5832	173	18	q	q	NOUN
ejpam-5832	173	19	-	-	PUNCT
ejpam-5832	173	20	rofsg	rofsg	NOUN
ejpam-5832	173	21	and	and	CCONJ
ejpam-5832	173	22	qrofnsgs	qrofnsg	NOUN
ejpam-5832	173	23	of	of	ADP
ejpam-5832	173	24	a	a	DET
ejpam-5832	173	25	crisp	crisp	ADJ
ejpam-5832	173	26	group	group	NOUN
ejpam-5832	173	27	by	by	ADP
ejpam-5832	173	28	establishing	establish	VERB
ejpam-5832	173	29	a	a	DET
ejpam-5832	173	30	number	number	NOUN
ejpam-5832	173	31	of	of	ADP
ejpam-5832	173	32	related	related	ADJ
ejpam-5832	173	33	theorems	theorem	NOUN
ejpam-5832	173	34	.	.	PUNCT
ejpam-5832	174	1	the	the	DET
ejpam-5832	174	2	example	example	NOUN
ejpam-5832	174	3	below	below	ADV
ejpam-5832	174	4	describes	describe	VERB
ejpam-5832	174	5	the	the	DET
ejpam-5832	174	6	notion	notion	NOUN
ejpam-5832	174	7	of	of	ADP
ejpam-5832	174	8	q	q	NOUN
ejpam-5832	174	9	-	-	PUNCT
ejpam-5832	174	10	roflcs	roflcs	NOUN
ejpam-5832	174	11	of	of	ADP
ejpam-5832	174	12	a	a	DET
ejpam-5832	174	13	q	q	NOUN
ejpam-5832	174	14	-	-	PUNCT
ejpam-5832	174	15	rofsg	rofsg	NOUN
ejpam-5832	174	16	of	of	ADP
ejpam-5832	174	17	a	a	DET
ejpam-5832	174	18	group	group	NOUN
ejpam-5832	174	19	.	.	PUNCT
ejpam-5832	174	20	example	example	NOUN
ejpam-5832	175	1	1	1	NUM
ejpam-5832	175	2	.	.	PUNCT
ejpam-5832	175	3	let	let	VERB
ejpam-5832	175	4	us	we	PRON
ejpam-5832	175	5	take	take	VERB
ejpam-5832	175	6	a	a	DET
ejpam-5832	175	7	finite	finite	ADJ
ejpam-5832	175	8	group	group	NOUN
ejpam-5832	175	9	v	v	NOUN
ejpam-5832	175	10	=	=	SYM
ejpam-5832	175	11	s3	s3	NOUN
ejpam-5832	175	12	=	=	SYM
ejpam-5832	175	13	⟨α	⟨α	PROPN
ejpam-5832	175	14	,	,	PUNCT
ejpam-5832	176	1	β	β	X
ejpam-5832	176	2	:	:	PUNCT
ejpam-5832	176	3	α2	α2	ADJ
ejpam-5832	176	4	=	=	SYM
ejpam-5832	176	5	β3	β3	PROPN
ejpam-5832	176	6	=	=	SYM
ejpam-5832	176	7	(	(	PUNCT
ejpam-5832	176	8	αβ)1	αβ)1	X
ejpam-5832	176	9	=	=	NOUN
ejpam-5832	176	10	1⟩	1⟩	NUM
ejpam-5832	176	11	=	=	SYM
ejpam-5832	176	12	{	{	PUNCT
ejpam-5832	176	13	e	e	NOUN
ejpam-5832	176	14	,	,	PUNCT
ejpam-5832	176	15	α	α	X
ejpam-5832	176	16	,	,	PUNCT
ejpam-5832	176	17	β	β	X
ejpam-5832	176	18	,	,	PUNCT
ejpam-5832	176	19	β2	β2	VERB
ejpam-5832	176	20	,	,	PUNCT
ejpam-5832	176	21	αβ	αβ	INTJ
ejpam-5832	176	22	,	,	PUNCT
ejpam-5832	176	23	αβ2	αβ2	NOUN
ejpam-5832	176	24	}	}	PUNCT
ejpam-5832	176	25	containing	contain	VERB
ejpam-5832	176	26	symmetries	symmetry	NOUN
ejpam-5832	176	27	of	of	ADP
ejpam-5832	176	28	equilateral	equilateral	ADJ
ejpam-5832	176	29	triangle	triangle	NOUN
ejpam-5832	176	30	.	.	PUNCT
ejpam-5832	177	1	the	the	DET
ejpam-5832	177	2	generators	generator	NOUN
ejpam-5832	177	3	α	α	PROPN
ejpam-5832	177	4	and	and	CCONJ
ejpam-5832	177	5	β	β	X
ejpam-5832	177	6	of	of	ADP
ejpam-5832	177	7	v	v	PROPN
ejpam-5832	177	8	represent	represent	VERB
ejpam-5832	177	9	diagonal	diagonal	ADJ
ejpam-5832	177	10	reflection	reflection	NOUN
ejpam-5832	177	11	and	and	CCONJ
ejpam-5832	177	12	rotation	rotation	NOUN
ejpam-5832	177	13	of	of	ADP
ejpam-5832	177	14	120	120	NUM
ejpam-5832	177	15	◦	◦	NOUN
ejpam-5832	177	16	anti	anti	ADJ
ejpam-5832	177	17	-	-	NOUN
ejpam-5832	177	18	clockwise	clockwise	NOUN
ejpam-5832	177	19	respectively	respectively	ADV
ejpam-5832	177	20	.	.	PUNCT
ejpam-5832	178	1	this	this	PRON
ejpam-5832	178	2	yields	yield	VERB
ejpam-5832	178	3	a	a	DET
ejpam-5832	178	4	total	total	NOUN
ejpam-5832	178	5	of	of	ADP
ejpam-5832	178	6	six	six	NUM
ejpam-5832	178	7	symmetries	symmetry	NOUN
ejpam-5832	178	8	e	e	NOUN
ejpam-5832	178	9	,	,	PUNCT
ejpam-5832	178	10	α	α	X
ejpam-5832	178	11	,	,	PUNCT
ejpam-5832	178	12	β	β	X
ejpam-5832	178	13	,	,	PUNCT
ejpam-5832	178	14	β2	β2	VERB
ejpam-5832	178	15	,	,	PUNCT
ejpam-5832	178	16	αβ	αβ	INTJ
ejpam-5832	178	17	,	,	PUNCT
ejpam-5832	178	18	α	α	PROPN
ejpam-5832	178	19	and	and	CCONJ
ejpam-5832	178	20	β2	β2	NOUN
ejpam-5832	178	21	of	of	ADP
ejpam-5832	178	22	equilateral	equilateral	ADJ
ejpam-5832	178	23	triangle	triangle	NOUN
ejpam-5832	178	24	.	.	PUNCT
ejpam-5832	179	1	next	next	ADV
ejpam-5832	179	2	,	,	PUNCT
ejpam-5832	179	3	we	we	PRON
ejpam-5832	179	4	design	design	VERB
ejpam-5832	179	5	a	a	DET
ejpam-5832	179	6	3	3	NUM
ejpam-5832	179	7	-	-	PUNCT
ejpam-5832	179	8	rofsg	rofsg	NOUN
ejpam-5832	179	9	of	of	ADP
ejpam-5832	179	10	v	v	NOUN
ejpam-5832	179	11	as	as	SCONJ
ejpam-5832	179	12	follows	follow	VERB
ejpam-5832	179	13	;	;	PUNCT
ejpam-5832	179	14	a.	a.	NOUN
ejpam-5832	179	15	razzaque	razzaque	NOUN
ejpam-5832	179	16	/	/	SYM
ejpam-5832	179	17	eur	eur	NOUN
ejpam-5832	179	18	.	.	PUNCT
ejpam-5832	180	1	j.	j.	PROPN
ejpam-5832	180	2	pure	pure	PROPN
ejpam-5832	180	3	appl	appl	PROPN
ejpam-5832	180	4	.	.	PROPN
ejpam-5832	180	5	math	math	PROPN
ejpam-5832	180	6	,	,	PUNCT
ejpam-5832	180	7	18	18	NUM
ejpam-5832	180	8	(	(	PUNCT
ejpam-5832	180	9	3	3	NUM
ejpam-5832	180	10	)	)	PUNCT
ejpam-5832	180	11	(	(	PUNCT
ejpam-5832	180	12	2025	2025	NUM
ejpam-5832	180	13	)	)	PUNCT
ejpam-5832	180	14	,	,	PUNCT
ejpam-5832	180	15	5832	5832	NUM
ejpam-5832	180	16	6	6	NUM
ejpam-5832	180	17	of	of	ADP
ejpam-5832	180	18	21	21	NUM
ejpam-5832	180	19	q	q	NOUN
ejpam-5832	180	20	=	=	PUNCT
ejpam-5832	180	21	{	{	PUNCT
ejpam-5832	180	22	(	(	PUNCT
ejpam-5832	180	23	e	e	NOUN
ejpam-5832	180	24	,	,	PUNCT
ejpam-5832	180	25	0.85	0.85	NUM
ejpam-5832	180	26	,	,	PUNCT
ejpam-5832	180	27	0.65	0.65	NUM
ejpam-5832	180	28	)	)	PUNCT
ejpam-5832	180	29	,	,	PUNCT
ejpam-5832	180	30	(	(	PUNCT
ejpam-5832	180	31	β	β	X
ejpam-5832	180	32	,	,	PUNCT
ejpam-5832	180	33	0.85	0.85	NUM
ejpam-5832	180	34	,	,	PUNCT
ejpam-5832	180	35	0.65	0.65	NUM
ejpam-5832	180	36	)	)	PUNCT
ejpam-5832	180	37	,	,	PUNCT
ejpam-5832	180	38	(	(	PUNCT
ejpam-5832	180	39	β2	β2	VERB
ejpam-5832	180	40	,	,	PUNCT
ejpam-5832	180	41	0.85	0.85	NUM
ejpam-5832	180	42	,	,	PUNCT
ejpam-5832	180	43	0.65	0.65	NUM
ejpam-5832	180	44	)	)	PUNCT
ejpam-5832	180	45	,	,	PUNCT
ejpam-5832	180	46	(	(	PUNCT
ejpam-5832	180	47	α	α	NOUN
ejpam-5832	180	48	,	,	PUNCT
ejpam-5832	180	49	0.80	0.80	NUM
ejpam-5832	180	50	,	,	PUNCT
ejpam-5832	180	51	0.75	0.75	NUM
ejpam-5832	180	52	)	)	PUNCT
ejpam-5832	180	53	,	,	PUNCT
ejpam-5832	180	54	(	(	PUNCT
ejpam-5832	180	55	αβ	αβ	INTJ
ejpam-5832	180	56	,	,	PUNCT
ejpam-5832	180	57	0.80	0.80	NUM
ejpam-5832	180	58	,	,	PUNCT
ejpam-5832	180	59	0.75	0.75	NUM
ejpam-5832	180	60	)	)	PUNCT
ejpam-5832	180	61	,	,	PUNCT
ejpam-5832	180	62	(	(	PUNCT
ejpam-5832	180	63	αβ2	αβ2	NOUN
ejpam-5832	180	64	,	,	PUNCT
ejpam-5832	180	65	0.80	0.80	NUM
ejpam-5832	180	66	,	,	PUNCT
ejpam-5832	180	67	0.75	0.75	NUM
ejpam-5832	180	68	)	)	PUNCT
ejpam-5832	180	69	}	}	PUNCT
ejpam-5832	181	1	then	then	ADV
ejpam-5832	181	2	,	,	PUNCT
ejpam-5832	181	3	we	we	PRON
ejpam-5832	181	4	compute	compute	VERB
ejpam-5832	181	5	the	the	DET
ejpam-5832	181	6	q	q	NOUN
ejpam-5832	181	7	-	-	NOUN
ejpam-5832	181	8	roflcs	roflcs	NOUN
ejpam-5832	181	9	of	of	ADP
ejpam-5832	181	10	q	q	NOUN
ejpam-5832	181	11	for	for	ADP
ejpam-5832	181	12	all	all	DET
ejpam-5832	181	13	ϵ	ϵ	PART
ejpam-5832	181	14	∈	∈	PROPN
ejpam-5832	181	15	v	v	NOUN
ejpam-5832	181	16	.	.	PUNCT
ejpam-5832	182	1	(	(	PUNCT
ejpam-5832	182	2	i	i	NOUN
ejpam-5832	182	3	)	)	PUNCT
ejpam-5832	182	4	the	the	DET
ejpam-5832	182	5	q	q	NOUN
ejpam-5832	182	6	-	-	PUNCT
ejpam-5832	182	7	roflc	roflc	NOUN
ejpam-5832	182	8	of	of	ADP
ejpam-5832	182	9	q	q	NOUN
ejpam-5832	182	10	for	for	ADP
ejpam-5832	182	11	e	e	PROPN
ejpam-5832	182	12	∈	∈	PROPN
ejpam-5832	182	13	v	v	NOUN
ejpam-5832	182	14	is	be	AUX
ejpam-5832	182	15	eq	eq	NOUN
ejpam-5832	182	16	=	=	PUNCT
ejpam-5832	182	17			PUNCT
ejpam-5832	182	18	(	(	PUNCT
ejpam-5832	182	19	e	e	NOUN
ejpam-5832	182	20	,	,	PUNCT
ejpam-5832	182	21	µq(e	µq(e	PUNCT
ejpam-5832	182	22	−1e	−1e	NOUN
ejpam-5832	182	23	)	)	PUNCT
ejpam-5832	182	24	,	,	PUNCT
ejpam-5832	182	25	νq(e	νq(e	PUNCT
ejpam-5832	182	26	−1e	−1e	NOUN
ejpam-5832	182	27	)	)	PUNCT
ejpam-5832	182	28	)	)	PUNCT
ejpam-5832	182	29	,	,	PUNCT
ejpam-5832	182	30	(	(	PUNCT
ejpam-5832	182	31	β	β	X
ejpam-5832	182	32	,	,	PUNCT
ejpam-5832	182	33	µq(e	µq(e	PUNCT
ejpam-5832	182	34	−1β	−1β	NUM
ejpam-5832	182	35	)	)	PUNCT
ejpam-5832	182	36	,	,	PUNCT
ejpam-5832	182	37	νq(e	νq(e	PUNCT
ejpam-5832	182	38	−1β	−1β	NUM
ejpam-5832	182	39	)	)	PUNCT
ejpam-5832	182	40	)	)	PUNCT
ejpam-5832	182	41	,	,	PUNCT
ejpam-5832	182	42	(	(	PUNCT
ejpam-5832	182	43	β2	β2	VERB
ejpam-5832	182	44	,	,	PUNCT
ejpam-5832	182	45	µq(e	µq(e	NUM
ejpam-5832	182	46	−1β2	−1β2	NUM
ejpam-5832	182	47	)	)	PUNCT
ejpam-5832	182	48	,	,	PUNCT
ejpam-5832	182	49	νq(e	νq(e	NUM
ejpam-5832	182	50	−1β2	−1β2	NUM
ejpam-5832	182	51	)	)	PUNCT
ejpam-5832	182	52	)	)	PUNCT
ejpam-5832	182	53	,	,	PUNCT
ejpam-5832	182	54	(	(	PUNCT
ejpam-5832	182	55	α	α	X
ejpam-5832	182	56	,	,	PUNCT
ejpam-5832	182	57	µq(e	µq(e	PROPN
ejpam-5832	182	58	−1α	−1α	PROPN
ejpam-5832	182	59	)	)	PUNCT
ejpam-5832	182	60	,	,	PUNCT
ejpam-5832	182	61	νq(e	νq(e	PROPN
ejpam-5832	182	62	−1α	−1α	PROPN
ejpam-5832	182	63	)	)	PUNCT
ejpam-5832	182	64	)	)	PUNCT
ejpam-5832	182	65	,	,	PUNCT
ejpam-5832	182	66	(	(	PUNCT
ejpam-5832	182	67	αβ	αβ	INTJ
ejpam-5832	182	68	,	,	PUNCT
ejpam-5832	182	69	µq(e	µq(e	PUNCT
ejpam-5832	182	70	−1αβ	−1αβ	NOUN
ejpam-5832	182	71	)	)	PUNCT
ejpam-5832	182	72	,	,	PUNCT
ejpam-5832	182	73	νq(e	νq(e	NUM
ejpam-5832	182	74	−1αβ	−1αβ	NOUN
ejpam-5832	182	75	)	)	PUNCT
ejpam-5832	182	76	)	)	PUNCT
ejpam-5832	182	77	,	,	PUNCT
ejpam-5832	182	78	(	(	PUNCT
ejpam-5832	182	79	αβ2	αβ2	INTJ
ejpam-5832	182	80	,	,	PUNCT
ejpam-5832	182	81	µq(e	µq(e	PUNCT
ejpam-5832	182	82	−1αβ2	−1αβ2	NOUN
ejpam-5832	182	83	)	)	PUNCT
ejpam-5832	182	84	,	,	PUNCT
ejpam-5832	182	85	νq(e	νq(e	X
ejpam-5832	182	86	−1αβ2	−1αβ2	PROPN
ejpam-5832	182	87	)	)	PUNCT
ejpam-5832	182	88	)	)	PUNCT
ejpam-5832	183	1			NOUN
ejpam-5832	183	2	=	=	PUNCT
ejpam-5832	183	3	{	{	PUNCT
ejpam-5832	183	4	(	(	PUNCT
ejpam-5832	183	5	e	e	NOUN
ejpam-5832	183	6	,	,	PUNCT
ejpam-5832	183	7	0.85	0.85	NUM
ejpam-5832	183	8	,	,	PUNCT
ejpam-5832	183	9	0.65	0.65	NUM
ejpam-5832	183	10	)	)	PUNCT
ejpam-5832	183	11	,	,	PUNCT
ejpam-5832	183	12	(	(	PUNCT
ejpam-5832	183	13	β	β	X
ejpam-5832	183	14	,	,	PUNCT
ejpam-5832	183	15	0.85	0.85	NUM
ejpam-5832	183	16	,	,	PUNCT
ejpam-5832	183	17	0.65	0.65	NUM
ejpam-5832	183	18	)	)	PUNCT
ejpam-5832	183	19	,	,	PUNCT
ejpam-5832	183	20	(	(	PUNCT
ejpam-5832	183	21	β2	β2	VERB
ejpam-5832	183	22	,	,	PUNCT
ejpam-5832	183	23	0.85	0.85	NUM
ejpam-5832	183	24	,	,	PUNCT
ejpam-5832	183	25	0.65	0.65	NUM
ejpam-5832	183	26	)	)	PUNCT
ejpam-5832	183	27	,	,	PUNCT
ejpam-5832	183	28	(	(	PUNCT
ejpam-5832	183	29	α	α	NOUN
ejpam-5832	183	30	,	,	PUNCT
ejpam-5832	183	31	0.80	0.80	NUM
ejpam-5832	183	32	,	,	PUNCT
ejpam-5832	183	33	0.75	0.75	NUM
ejpam-5832	183	34	)	)	PUNCT
ejpam-5832	183	35	,	,	PUNCT
ejpam-5832	183	36	(	(	PUNCT
ejpam-5832	183	37	αβ	αβ	INTJ
ejpam-5832	183	38	,	,	PUNCT
ejpam-5832	183	39	0.80	0.80	NUM
ejpam-5832	183	40	,	,	PUNCT
ejpam-5832	183	41	0.75	0.75	NUM
ejpam-5832	183	42	)	)	PUNCT
ejpam-5832	183	43	,	,	PUNCT
ejpam-5832	183	44	(	(	PUNCT
ejpam-5832	183	45	αβ2	αβ2	NOUN
ejpam-5832	183	46	,	,	PUNCT
ejpam-5832	183	47	0.80	0.80	NUM
ejpam-5832	183	48	,	,	PUNCT
ejpam-5832	183	49	0.75	0.75	NUM
ejpam-5832	183	50	)	)	PUNCT
ejpam-5832	183	51	}	}	PUNCT
ejpam-5832	183	52	(	(	PUNCT
ejpam-5832	183	53	ii	ii	NOUN
ejpam-5832	183	54	)	)	PUNCT
ejpam-5832	183	55	the	the	DET
ejpam-5832	183	56	q	q	NOUN
ejpam-5832	183	57	-	-	PUNCT
ejpam-5832	183	58	roflc	roflc	NOUN
ejpam-5832	183	59	of	of	ADP
ejpam-5832	183	60	q	q	NOUN
ejpam-5832	183	61	for	for	ADP
ejpam-5832	183	62	β	β	X
ejpam-5832	183	63	∈	∈	PROPN
ejpam-5832	183	64	v	v	NOUN
ejpam-5832	183	65	is	be	AUX
ejpam-5832	183	66	βq	βq	ADJ
ejpam-5832	183	67	=	=	PUNCT
ejpam-5832	183	68			PUNCT
ejpam-5832	183	69	(	(	PUNCT
ejpam-5832	183	70	e	e	NOUN
ejpam-5832	183	71	,	,	PUNCT
ejpam-5832	183	72	µq(β	µq(β	X
ejpam-5832	183	73	−1e	−1e	NOUN
ejpam-5832	183	74	)	)	PUNCT
ejpam-5832	183	75	,	,	PUNCT
ejpam-5832	183	76	νq(β	νq(β	X
ejpam-5832	183	77	−1e	−1e	NOUN
ejpam-5832	183	78	)	)	PUNCT
ejpam-5832	183	79	)	)	PUNCT
ejpam-5832	183	80	,	,	PUNCT
ejpam-5832	183	81	(	(	PUNCT
ejpam-5832	183	82	β	β	X
ejpam-5832	183	83	,	,	PUNCT
ejpam-5832	183	84	µq(β	µq(β	X
ejpam-5832	183	85	−1β	−1β	PROPN
ejpam-5832	183	86	)	)	PUNCT
ejpam-5832	183	87	,	,	PUNCT
ejpam-5832	183	88	νq(β	νq(β	X
ejpam-5832	183	89	−1β	−1β	NOUN
ejpam-5832	183	90	)	)	PUNCT
ejpam-5832	183	91	)	)	PUNCT
ejpam-5832	183	92	,	,	PUNCT
ejpam-5832	183	93	(	(	PUNCT
ejpam-5832	183	94	β2	β2	VERB
ejpam-5832	183	95	,	,	PUNCT
ejpam-5832	183	96	µq(β	µq(β	NUM
ejpam-5832	183	97	−1β2	−1β2	NUM
ejpam-5832	183	98	)	)	PUNCT
ejpam-5832	183	99	,	,	PUNCT
ejpam-5832	183	100	νq(β	νq(β	X
ejpam-5832	183	101	−1β2	−1β2	NUM
ejpam-5832	183	102	)	)	PUNCT
ejpam-5832	183	103	)	)	PUNCT
ejpam-5832	183	104	,	,	PUNCT
ejpam-5832	183	105	(	(	PUNCT
ejpam-5832	183	106	α	α	X
ejpam-5832	183	107	,	,	PUNCT
ejpam-5832	183	108	µq(β	µq(β	X
ejpam-5832	183	109	−1α	−1α	NOUN
ejpam-5832	183	110	)	)	PUNCT
ejpam-5832	183	111	,	,	PUNCT
ejpam-5832	183	112	νq(β	νq(β	X
ejpam-5832	183	113	−1α	−1α	NOUN
ejpam-5832	183	114	)	)	PUNCT
ejpam-5832	183	115	)	)	PUNCT
ejpam-5832	183	116	,	,	PUNCT
ejpam-5832	183	117	(	(	PUNCT
ejpam-5832	183	118	αβ	αβ	INTJ
ejpam-5832	183	119	,	,	PUNCT
ejpam-5832	183	120	µq(β	µq(β	X
ejpam-5832	183	121	−1αβ	−1αβ	NOUN
ejpam-5832	183	122	)	)	PUNCT
ejpam-5832	183	123	,	,	PUNCT
ejpam-5832	183	124	νq(β	νq(β	ADP
ejpam-5832	183	125	−1αβ	−1αβ	NOUN
ejpam-5832	183	126	)	)	PUNCT
ejpam-5832	183	127	)	)	PUNCT
ejpam-5832	183	128	,	,	PUNCT
ejpam-5832	183	129	(	(	PUNCT
ejpam-5832	183	130	αβ2	αβ2	NOUN
ejpam-5832	183	131	,	,	PUNCT
ejpam-5832	183	132	µq(β	µq(β	X
ejpam-5832	183	133	−1αβ2	−1αβ2	NOUN
ejpam-5832	183	134	)	)	PUNCT
ejpam-5832	183	135	,	,	PUNCT
ejpam-5832	183	136	νq(β	νq(β	X
ejpam-5832	183	137	−1αβ2	−1αβ2	PROPN
ejpam-5832	183	138	)	)	PUNCT
ejpam-5832	183	139	)	)	PUNCT
ejpam-5832	184	1			NOUN
ejpam-5832	184	2	=	=	PUNCT
ejpam-5832	184	3	{	{	PUNCT
ejpam-5832	184	4	(	(	PUNCT
ejpam-5832	184	5	e	e	NOUN
ejpam-5832	184	6	,	,	PUNCT
ejpam-5832	184	7	µq(β	µq(β	X
ejpam-5832	184	8	2	2	NUM
ejpam-5832	184	9	)	)	PUNCT
ejpam-5832	184	10	,	,	PUNCT
ejpam-5832	184	11	νq(β	νq(β	X
ejpam-5832	184	12	2	2	NUM
ejpam-5832	184	13	)	)	PUNCT
ejpam-5832	184	14	)	)	PUNCT
ejpam-5832	184	15	,	,	PUNCT
ejpam-5832	184	16	(	(	PUNCT
ejpam-5832	184	17	β	β	X
ejpam-5832	184	18	,	,	PUNCT
ejpam-5832	184	19	µq(e	µq(e	NUM
ejpam-5832	184	20	)	)	PUNCT
ejpam-5832	184	21	,	,	PUNCT
ejpam-5832	184	22	νq(e	νq(e	NUM
ejpam-5832	184	23	)	)	PUNCT
ejpam-5832	184	24	)	)	PUNCT
ejpam-5832	184	25	,	,	PUNCT
ejpam-5832	184	26	(	(	PUNCT
ejpam-5832	184	27	β2	β2	VERB
ejpam-5832	184	28	,	,	PUNCT
ejpam-5832	184	29	µq(β	µq(β	NOUN
ejpam-5832	184	30	)	)	PUNCT
ejpam-5832	184	31	,	,	PUNCT
ejpam-5832	184	32	νq(β	νq(β	NUM
ejpam-5832	184	33	)	)	PUNCT
ejpam-5832	184	34	)	)	PUNCT
ejpam-5832	184	35	,	,	PUNCT
ejpam-5832	184	36	(	(	PUNCT
ejpam-5832	184	37	α	α	NOUN
ejpam-5832	184	38	,	,	PUNCT
ejpam-5832	184	39	µq(αβ	µq(αβ	NOUN
ejpam-5832	184	40	)	)	PUNCT
ejpam-5832	184	41	,	,	PUNCT
ejpam-5832	184	42	νq(αβ	νq(αβ	NOUN
ejpam-5832	184	43	)	)	PUNCT
ejpam-5832	184	44	)	)	PUNCT
ejpam-5832	184	45	,	,	PUNCT
ejpam-5832	184	46	(	(	PUNCT
ejpam-5832	184	47	αβ	αβ	INTJ
ejpam-5832	184	48	,	,	PUNCT
ejpam-5832	184	49	µq(αβ	µq(αβ	NOUN
ejpam-5832	184	50	2	2	NUM
ejpam-5832	184	51	)	)	PUNCT
ejpam-5832	184	52	,	,	PUNCT
ejpam-5832	184	53	νq(αβ	νq(αβ	NOUN
ejpam-5832	184	54	2	2	NUM
ejpam-5832	184	55	)	)	PUNCT
ejpam-5832	184	56	)	)	PUNCT
ejpam-5832	184	57	,	,	PUNCT
ejpam-5832	184	58	(	(	PUNCT
ejpam-5832	184	59	αβ2	αβ2	INTJ
ejpam-5832	184	60	,	,	PUNCT
ejpam-5832	184	61	µq(α	µq(α	NUM
ejpam-5832	184	62	)	)	PUNCT
ejpam-5832	184	63	,	,	PUNCT
ejpam-5832	184	64	νq(α	νq(α	NOUN
ejpam-5832	184	65	)	)	PUNCT
ejpam-5832	184	66	)	)	PUNCT
ejpam-5832	184	67	}	}	PUNCT
ejpam-5832	184	68	=	=	PRON
ejpam-5832	184	69	{	{	PUNCT
ejpam-5832	184	70	(	(	PUNCT
ejpam-5832	184	71	e	e	NOUN
ejpam-5832	184	72	,	,	PUNCT
ejpam-5832	184	73	0.85	0.85	NUM
ejpam-5832	184	74	,	,	PUNCT
ejpam-5832	184	75	0.65	0.65	NUM
ejpam-5832	184	76	)	)	PUNCT
ejpam-5832	184	77	,	,	PUNCT
ejpam-5832	184	78	(	(	PUNCT
ejpam-5832	184	79	β	β	X
ejpam-5832	184	80	,	,	PUNCT
ejpam-5832	184	81	0.85	0.85	NUM
ejpam-5832	184	82	,	,	PUNCT
ejpam-5832	184	83	0.65	0.65	NUM
ejpam-5832	184	84	)	)	PUNCT
ejpam-5832	184	85	,	,	PUNCT
ejpam-5832	184	86	(	(	PUNCT
ejpam-5832	184	87	β2	β2	VERB
ejpam-5832	184	88	,	,	PUNCT
ejpam-5832	184	89	0.85	0.85	NUM
ejpam-5832	184	90	,	,	PUNCT
ejpam-5832	184	91	0.65	0.65	NUM
ejpam-5832	184	92	)	)	PUNCT
ejpam-5832	184	93	,	,	PUNCT
ejpam-5832	184	94	(	(	PUNCT
ejpam-5832	184	95	α	α	NOUN
ejpam-5832	184	96	,	,	PUNCT
ejpam-5832	184	97	0.80	0.80	NUM
ejpam-5832	184	98	,	,	PUNCT
ejpam-5832	184	99	0.75	0.75	NUM
ejpam-5832	184	100	)	)	PUNCT
ejpam-5832	184	101	,	,	PUNCT
ejpam-5832	184	102	(	(	PUNCT
ejpam-5832	184	103	αβ	αβ	INTJ
ejpam-5832	184	104	,	,	PUNCT
ejpam-5832	184	105	0.80	0.80	NUM
ejpam-5832	184	106	,	,	PUNCT
ejpam-5832	184	107	0.75	0.75	NUM
ejpam-5832	184	108	)	)	PUNCT
ejpam-5832	184	109	,	,	PUNCT
ejpam-5832	184	110	(	(	PUNCT
ejpam-5832	184	111	αβ2	αβ2	NOUN
ejpam-5832	184	112	,	,	PUNCT
ejpam-5832	184	113	0.80	0.80	NUM
ejpam-5832	184	114	,	,	PUNCT
ejpam-5832	184	115	0.75	0.75	NUM
ejpam-5832	184	116	)	)	PUNCT
ejpam-5832	184	117	}	}	PUNCT
ejpam-5832	184	118	(	(	PUNCT
ejpam-5832	184	119	iii	iii	X
ejpam-5832	184	120	)	)	PUNCT
ejpam-5832	184	121	the	the	DET
ejpam-5832	184	122	q	q	NOUN
ejpam-5832	184	123	-	-	PUNCT
ejpam-5832	184	124	roflc	roflc	NOUN
ejpam-5832	184	125	of	of	ADP
ejpam-5832	184	126	q	q	NOUN
ejpam-5832	184	127	for	for	ADP
ejpam-5832	184	128	β2	β2	PROPN
ejpam-5832	184	129	∈	∈	PROPN
ejpam-5832	184	130	v	v	NOUN
ejpam-5832	184	131	is	be	AUX
ejpam-5832	184	132	β2q	β2q	PUNCT
ejpam-5832	184	133	=	=	PUNCT
ejpam-5832	184	134			PUNCT
ejpam-5832	184	135	(	(	PUNCT
ejpam-5832	184	136	e	e	NOUN
ejpam-5832	184	137	,	,	PUNCT
ejpam-5832	184	138	µq((β	µq((β	NOUN
ejpam-5832	184	139	2)−1e	2)−1e	NUM
ejpam-5832	184	140	)	)	PUNCT
ejpam-5832	184	141	,	,	PUNCT
ejpam-5832	184	142	νq((β	νq((β	ADJ
ejpam-5832	184	143	2)−1e	2)−1e	NUM
ejpam-5832	184	144	)	)	PUNCT
ejpam-5832	184	145	)	)	PUNCT
ejpam-5832	184	146	,	,	PUNCT
ejpam-5832	184	147	(	(	PUNCT
ejpam-5832	184	148	β	β	X
ejpam-5832	184	149	,	,	PUNCT
ejpam-5832	184	150	µq((β	µq((β	NOUN
ejpam-5832	184	151	2)−1β	2)−1β	NUM
ejpam-5832	184	152	)	)	PUNCT
ejpam-5832	184	153	,	,	PUNCT
ejpam-5832	184	154	νq((β	νq((β	NOUN
ejpam-5832	184	155	2)−1β	2)−1β	NUM
ejpam-5832	184	156	)	)	PUNCT
ejpam-5832	184	157	)	)	PUNCT
ejpam-5832	184	158	,	,	PUNCT
ejpam-5832	184	159	(	(	PUNCT
ejpam-5832	184	160	β2	β2	VERB
ejpam-5832	184	161	,	,	PUNCT
ejpam-5832	184	162	µq((β	µq((β	NOUN
ejpam-5832	184	163	2)−1β2	2)−1β2	NUM
ejpam-5832	184	164	)	)	PUNCT
ejpam-5832	184	165	,	,	PUNCT
ejpam-5832	184	166	νq((β	νq((β	ADJ
ejpam-5832	184	167	2)−1β2	2)−1β2	NUM
ejpam-5832	184	168	)	)	PUNCT
ejpam-5832	184	169	)	)	PUNCT
ejpam-5832	184	170	,	,	PUNCT
ejpam-5832	184	171	(	(	PUNCT
ejpam-5832	184	172	α	α	NOUN
ejpam-5832	184	173	,	,	PUNCT
ejpam-5832	184	174	µq((β	µq((β	NOUN
ejpam-5832	184	175	2)−1α	2)−1α	NUM
ejpam-5832	184	176	)	)	PUNCT
ejpam-5832	184	177	,	,	PUNCT
ejpam-5832	184	178	νq((β	νq((β	ADJ
ejpam-5832	184	179	2)−1α	2)−1α	NUM
ejpam-5832	184	180	)	)	PUNCT
ejpam-5832	184	181	)	)	PUNCT
ejpam-5832	184	182	,	,	PUNCT
ejpam-5832	184	183	(	(	PUNCT
ejpam-5832	184	184	αβ	αβ	INTJ
ejpam-5832	184	185	,	,	PUNCT
ejpam-5832	184	186	µq((β	µq((β	NOUN
ejpam-5832	184	187	2)−1αβ	2)−1αβ	NUM
ejpam-5832	184	188	)	)	PUNCT
ejpam-5832	184	189	,	,	PUNCT
ejpam-5832	184	190	νq((β	νq((β	ADJ
ejpam-5832	184	191	2)−1αβ	2)−1αβ	NUM
ejpam-5832	184	192	)	)	PUNCT
ejpam-5832	184	193	)	)	PUNCT
ejpam-5832	184	194	,	,	PUNCT
ejpam-5832	184	195	(	(	PUNCT
ejpam-5832	184	196	αβ2	αβ2	ADV
ejpam-5832	184	197	,	,	PUNCT
ejpam-5832	184	198	µq((β	µq((β	NOUN
ejpam-5832	184	199	2)−1αβ2	2)−1αβ2	NUM
ejpam-5832	184	200	)	)	PUNCT
ejpam-5832	184	201	,	,	PUNCT
ejpam-5832	184	202	νq((β	νq((β	ADJ
ejpam-5832	184	203	2)−1αβ2	2)−1αβ2	NUM
ejpam-5832	184	204	)	)	PUNCT
ejpam-5832	184	205	)	)	PUNCT
ejpam-5832	185	1			NOUN
ejpam-5832	185	2	=	=	PUNCT
ejpam-5832	185	3	{	{	PUNCT
ejpam-5832	185	4	(	(	PUNCT
ejpam-5832	185	5	e	e	NOUN
ejpam-5832	185	6	,	,	PUNCT
ejpam-5832	185	7	µq(β	µq(β	NUM
ejpam-5832	185	8	)	)	PUNCT
ejpam-5832	185	9	,	,	PUNCT
ejpam-5832	185	10	νq(β	νq(β	NOUN
ejpam-5832	185	11	)	)	PUNCT
ejpam-5832	185	12	)	)	PUNCT
ejpam-5832	185	13	,	,	PUNCT
ejpam-5832	185	14	(	(	PUNCT
ejpam-5832	185	15	β	β	X
ejpam-5832	185	16	,	,	PUNCT
ejpam-5832	185	17	µq(β	µq(β	X
ejpam-5832	185	18	2	2	NUM
ejpam-5832	185	19	)	)	PUNCT
ejpam-5832	185	20	,	,	PUNCT
ejpam-5832	185	21	νq(β	νq(β	X
ejpam-5832	185	22	2	2	NUM
ejpam-5832	185	23	)	)	PUNCT
ejpam-5832	185	24	)	)	PUNCT
ejpam-5832	185	25	,	,	PUNCT
ejpam-5832	185	26	(	(	PUNCT
ejpam-5832	185	27	β2	β2	VERB
ejpam-5832	185	28	,	,	PUNCT
ejpam-5832	185	29	µq(e	µq(e	NUM
ejpam-5832	185	30	)	)	PUNCT
ejpam-5832	185	31	,	,	PUNCT
ejpam-5832	185	32	νq(e	νq(e	NUM
ejpam-5832	185	33	)	)	PUNCT
ejpam-5832	185	34	)	)	PUNCT
ejpam-5832	185	35	,	,	PUNCT
ejpam-5832	185	36	(	(	PUNCT
ejpam-5832	185	37	α	α	NOUN
ejpam-5832	185	38	,	,	PUNCT
ejpam-5832	185	39	µq(αβ	µq(αβ	NOUN
ejpam-5832	185	40	2	2	NUM
ejpam-5832	185	41	)	)	PUNCT
ejpam-5832	185	42	,	,	PUNCT
ejpam-5832	185	43	νq(αβ	νq(αβ	NOUN
ejpam-5832	185	44	2	2	NUM
ejpam-5832	185	45	)	)	PUNCT
ejpam-5832	185	46	)	)	PUNCT
ejpam-5832	185	47	,	,	PUNCT
ejpam-5832	185	48	(	(	PUNCT
ejpam-5832	185	49	αβ	αβ	INTJ
ejpam-5832	185	50	,	,	PUNCT
ejpam-5832	185	51	µq(α	µq(α	ADJ
ejpam-5832	185	52	)	)	PUNCT
ejpam-5832	185	53	,	,	PUNCT
ejpam-5832	185	54	νq(α	νq(α	NOUN
ejpam-5832	185	55	)	)	PUNCT
ejpam-5832	185	56	)	)	PUNCT
ejpam-5832	185	57	,	,	PUNCT
ejpam-5832	185	58	(	(	PUNCT
ejpam-5832	185	59	αβ2	αβ2	ADV
ejpam-5832	185	60	,	,	PUNCT
ejpam-5832	185	61	µq(αβ	µq(αβ	NOUN
ejpam-5832	185	62	)	)	PUNCT
ejpam-5832	185	63	,	,	PUNCT
ejpam-5832	185	64	νq(αβ	νq(αβ	NOUN
ejpam-5832	185	65	)	)	PUNCT
ejpam-5832	185	66	)	)	PUNCT
ejpam-5832	185	67	}	}	PUNCT
ejpam-5832	185	68	=	=	PRON
ejpam-5832	185	69	{	{	PUNCT
ejpam-5832	185	70	(	(	PUNCT
ejpam-5832	185	71	e	e	NOUN
ejpam-5832	185	72	,	,	PUNCT
ejpam-5832	185	73	0.85	0.85	NUM
ejpam-5832	185	74	,	,	PUNCT
ejpam-5832	185	75	0.65	0.65	NUM
ejpam-5832	185	76	)	)	PUNCT
ejpam-5832	185	77	,	,	PUNCT
ejpam-5832	185	78	(	(	PUNCT
ejpam-5832	185	79	β	β	X
ejpam-5832	185	80	,	,	PUNCT
ejpam-5832	185	81	0.85	0.85	NUM
ejpam-5832	185	82	,	,	PUNCT
ejpam-5832	185	83	0.65	0.65	NUM
ejpam-5832	185	84	)	)	PUNCT
ejpam-5832	185	85	,	,	PUNCT
ejpam-5832	185	86	(	(	PUNCT
ejpam-5832	185	87	β2	β2	VERB
ejpam-5832	185	88	,	,	PUNCT
ejpam-5832	185	89	0.85	0.85	NUM
ejpam-5832	185	90	,	,	PUNCT
ejpam-5832	185	91	0.65	0.65	NUM
ejpam-5832	185	92	)	)	PUNCT
ejpam-5832	185	93	,	,	PUNCT
ejpam-5832	185	94	(	(	PUNCT
ejpam-5832	185	95	α	α	NOUN
ejpam-5832	185	96	,	,	PUNCT
ejpam-5832	185	97	0.80	0.80	NUM
ejpam-5832	185	98	,	,	PUNCT
ejpam-5832	185	99	0.75	0.75	NUM
ejpam-5832	185	100	)	)	PUNCT
ejpam-5832	185	101	,	,	PUNCT
ejpam-5832	185	102	(	(	PUNCT
ejpam-5832	185	103	αβ	αβ	INTJ
ejpam-5832	185	104	,	,	PUNCT
ejpam-5832	185	105	0.80	0.80	NUM
ejpam-5832	185	106	,	,	PUNCT
ejpam-5832	185	107	0.75	0.75	NUM
ejpam-5832	185	108	)	)	PUNCT
ejpam-5832	185	109	,	,	PUNCT
ejpam-5832	185	110	(	(	PUNCT
ejpam-5832	185	111	αβ2	αβ2	NOUN
ejpam-5832	185	112	,	,	PUNCT
ejpam-5832	185	113	0.80	0.80	NUM
ejpam-5832	185	114	,	,	PUNCT
ejpam-5832	185	115	0.75	0.75	NUM
ejpam-5832	185	116	)	)	PUNCT
ejpam-5832	185	117	}	}	PUNCT
ejpam-5832	185	118	=	=	SYM
ejpam-5832	185	119	q	q	X
ejpam-5832	185	120	(	(	PUNCT
ejpam-5832	185	121	iv	iv	X
ejpam-5832	185	122	)	)	PUNCT
ejpam-5832	185	123	the	the	DET
ejpam-5832	185	124	q	q	NOUN
ejpam-5832	185	125	-	-	PUNCT
ejpam-5832	185	126	roflc	roflc	NOUN
ejpam-5832	185	127	of	of	ADP
ejpam-5832	185	128	q	q	NOUN
ejpam-5832	185	129	for	for	ADP
ejpam-5832	185	130	α	α	PROPN
ejpam-5832	185	131	∈	∈	PROPN
ejpam-5832	185	132	v	v	NOUN
ejpam-5832	185	133	is	be	AUX
ejpam-5832	185	134	αq	αq	ADP
ejpam-5832	185	135	=	=	PUNCT
ejpam-5832	185	136			PUNCT
ejpam-5832	185	137	(	(	PUNCT
ejpam-5832	185	138	e	e	NOUN
ejpam-5832	185	139	,	,	PUNCT
ejpam-5832	185	140	µq(α	µq(α	PRON
ejpam-5832	185	141	−1e	−1e	NOUN
ejpam-5832	185	142	)	)	PUNCT
ejpam-5832	185	143	,	,	PUNCT
ejpam-5832	185	144	νq(α	νq(α	X
ejpam-5832	185	145	−1e	−1e	NOUN
ejpam-5832	185	146	)	)	PUNCT
ejpam-5832	185	147	)	)	PUNCT
ejpam-5832	185	148	,	,	PUNCT
ejpam-5832	185	149	(	(	PUNCT
ejpam-5832	185	150	β	β	X
ejpam-5832	185	151	,	,	PUNCT
ejpam-5832	185	152	µq(α	µq(α	X
ejpam-5832	185	153	−1β	−1β	PROPN
ejpam-5832	185	154	)	)	PUNCT
ejpam-5832	185	155	,	,	PUNCT
ejpam-5832	185	156	νq(α	νq(α	X
ejpam-5832	185	157	−1β	−1β	NUM
ejpam-5832	185	158	)	)	PUNCT
ejpam-5832	185	159	)	)	PUNCT
ejpam-5832	185	160	,	,	PUNCT
ejpam-5832	185	161	(	(	PUNCT
ejpam-5832	185	162	β2	β2	PROPN
ejpam-5832	185	163	,	,	PUNCT
ejpam-5832	185	164	µq(α	µq(α	PRON
ejpam-5832	185	165	−1β2	−1β2	NUM
ejpam-5832	185	166	)	)	PUNCT
ejpam-5832	185	167	,	,	PUNCT
ejpam-5832	185	168	νq(α	νq(α	NUM
ejpam-5832	185	169	−1β2	−1β2	NUM
ejpam-5832	185	170	)	)	PUNCT
ejpam-5832	185	171	)	)	PUNCT
ejpam-5832	185	172	,	,	PUNCT
ejpam-5832	185	173	(	(	PUNCT
ejpam-5832	185	174	α	α	NOUN
ejpam-5832	185	175	,	,	PUNCT
ejpam-5832	185	176	µq(α	µq(α	PRON
ejpam-5832	185	177	−1α	−1α	PROPN
ejpam-5832	185	178	)	)	PUNCT
ejpam-5832	185	179	,	,	PUNCT
ejpam-5832	185	180	νq(α	νq(α	X
ejpam-5832	185	181	−1α	−1α	NOUN
ejpam-5832	185	182	)	)	PUNCT
ejpam-5832	185	183	)	)	PUNCT
ejpam-5832	185	184	,	,	PUNCT
ejpam-5832	185	185	(	(	PUNCT
ejpam-5832	185	186	αβ	αβ	INTJ
ejpam-5832	185	187	,	,	PUNCT
ejpam-5832	185	188	µq(α	µq(α	PRON
ejpam-5832	185	189	−1αβ	−1αβ	NOUN
ejpam-5832	185	190	)	)	PUNCT
ejpam-5832	185	191	,	,	PUNCT
ejpam-5832	185	192	νq(α	νq(α	NUM
ejpam-5832	185	193	−1αβ	−1αβ	NOUN
ejpam-5832	185	194	)	)	PUNCT
ejpam-5832	185	195	)	)	PUNCT
ejpam-5832	185	196	,	,	PUNCT
ejpam-5832	185	197	(	(	PUNCT
ejpam-5832	185	198	αβ2	αβ2	INTJ
ejpam-5832	185	199	,	,	PUNCT
ejpam-5832	185	200	µq(α	µq(α	X
ejpam-5832	185	201	−1αβ2	−1αβ2	NOUN
ejpam-5832	185	202	)	)	PUNCT
ejpam-5832	185	203	,	,	PUNCT
ejpam-5832	185	204	νq(α	νq(α	NOUN
ejpam-5832	185	205	−1αβ2	−1αβ2	NOUN
ejpam-5832	185	206	)	)	PUNCT
ejpam-5832	185	207	)	)	PUNCT
ejpam-5832	186	1			NOUN
ejpam-5832	186	2	=	=	PUNCT
ejpam-5832	186	3	{	{	PUNCT
ejpam-5832	186	4	(	(	PUNCT
ejpam-5832	186	5	e	e	NOUN
ejpam-5832	186	6	,	,	PUNCT
ejpam-5832	186	7	µq(α	µq(α	ADJ
ejpam-5832	186	8	)	)	PUNCT
ejpam-5832	186	9	,	,	PUNCT
ejpam-5832	186	10	νq(α	νq(α	NOUN
ejpam-5832	186	11	)	)	PUNCT
ejpam-5832	186	12	)	)	PUNCT
ejpam-5832	186	13	,	,	PUNCT
ejpam-5832	186	14	(	(	PUNCT
ejpam-5832	186	15	β	β	X
ejpam-5832	186	16	,	,	PUNCT
ejpam-5832	186	17	µq(αβ	µq(αβ	NOUN
ejpam-5832	186	18	)	)	PUNCT
ejpam-5832	186	19	,	,	PUNCT
ejpam-5832	186	20	νq(αβ	νq(αβ	NOUN
ejpam-5832	186	21	)	)	PUNCT
ejpam-5832	186	22	)	)	PUNCT
ejpam-5832	186	23	,	,	PUNCT
ejpam-5832	186	24	(	(	PUNCT
ejpam-5832	186	25	β2	β2	VERB
ejpam-5832	186	26	,	,	PUNCT
ejpam-5832	186	27	µq(αβ	µq(αβ	NOUN
ejpam-5832	186	28	2	2	NUM
ejpam-5832	186	29	)	)	PUNCT
ejpam-5832	186	30	,	,	PUNCT
ejpam-5832	186	31	νq(αβ	νq(αβ	NOUN
ejpam-5832	186	32	2	2	NUM
ejpam-5832	186	33	)	)	PUNCT
ejpam-5832	186	34	)	)	PUNCT
ejpam-5832	186	35	,	,	PUNCT
ejpam-5832	186	36	(	(	PUNCT
ejpam-5832	186	37	α	α	X
ejpam-5832	186	38	,	,	PUNCT
ejpam-5832	186	39	µq(e	µq(e	NUM
ejpam-5832	186	40	)	)	PUNCT
ejpam-5832	186	41	,	,	PUNCT
ejpam-5832	186	42	νq(e	νq(e	NUM
ejpam-5832	186	43	)	)	PUNCT
ejpam-5832	186	44	)	)	PUNCT
ejpam-5832	186	45	,	,	PUNCT
ejpam-5832	186	46	(	(	PUNCT
ejpam-5832	186	47	αβ	αβ	INTJ
ejpam-5832	186	48	,	,	PUNCT
ejpam-5832	186	49	µq(β	µq(β	NUM
ejpam-5832	186	50	)	)	PUNCT
ejpam-5832	186	51	,	,	PUNCT
ejpam-5832	186	52	νq(β	νq(β	NOUN
ejpam-5832	186	53	)	)	PUNCT
ejpam-5832	186	54	)	)	PUNCT
ejpam-5832	186	55	,	,	PUNCT
ejpam-5832	186	56	(	(	PUNCT
ejpam-5832	186	57	αβ2	αβ2	NOUN
ejpam-5832	186	58	,	,	PUNCT
ejpam-5832	186	59	µq(β	µq(β	X
ejpam-5832	186	60	2	2	NUM
ejpam-5832	186	61	)	)	PUNCT
ejpam-5832	186	62	,	,	PUNCT
ejpam-5832	186	63	νq(β	νq(β	X
ejpam-5832	186	64	2	2	NUM
ejpam-5832	186	65	)	)	PUNCT
ejpam-5832	186	66	)	)	PUNCT
ejpam-5832	186	67	}	}	PUNCT
ejpam-5832	186	68	=	=	PRON
ejpam-5832	186	69	{	{	PUNCT
ejpam-5832	186	70	(	(	PUNCT
ejpam-5832	186	71	e	e	NOUN
ejpam-5832	186	72	,	,	PUNCT
ejpam-5832	186	73	0.0.80	0.0.80	NUM
ejpam-5832	186	74	,	,	PUNCT
ejpam-5832	186	75	0.75	0.75	NUM
ejpam-5832	186	76	)	)	PUNCT
ejpam-5832	186	77	,	,	PUNCT
ejpam-5832	186	78	(	(	PUNCT
ejpam-5832	186	79	β	β	X
ejpam-5832	186	80	,	,	PUNCT
ejpam-5832	186	81	0.80	0.80	NUM
ejpam-5832	186	82	,	,	PUNCT
ejpam-5832	186	83	0.75	0.75	NUM
ejpam-5832	186	84	)	)	PUNCT
ejpam-5832	186	85	,	,	PUNCT
ejpam-5832	186	86	(	(	PUNCT
ejpam-5832	186	87	β2	β2	VERB
ejpam-5832	186	88	,	,	PUNCT
ejpam-5832	186	89	0.80	0.80	NUM
ejpam-5832	186	90	,	,	PUNCT
ejpam-5832	186	91	0.75	0.75	NUM
ejpam-5832	186	92	)	)	PUNCT
ejpam-5832	186	93	,	,	PUNCT
ejpam-5832	186	94	(	(	PUNCT
ejpam-5832	186	95	α	α	NOUN
ejpam-5832	186	96	,	,	PUNCT
ejpam-5832	186	97	0.85	0.85	NUM
ejpam-5832	186	98	,	,	PUNCT
ejpam-5832	186	99	0.65	0.65	NUM
ejpam-5832	186	100	)	)	PUNCT
ejpam-5832	186	101	,	,	PUNCT
ejpam-5832	186	102	(	(	PUNCT
ejpam-5832	186	103	αβ	αβ	INTJ
ejpam-5832	186	104	,	,	PUNCT
ejpam-5832	186	105	0.85	0.85	NUM
ejpam-5832	186	106	,	,	PUNCT
ejpam-5832	186	107	0.65	0.65	NUM
ejpam-5832	186	108	)	)	PUNCT
ejpam-5832	186	109	,	,	PUNCT
ejpam-5832	186	110	(	(	PUNCT
ejpam-5832	186	111	αβ2	αβ2	NOUN
ejpam-5832	186	112	,	,	PUNCT
ejpam-5832	186	113	0.85	0.85	NUM
ejpam-5832	186	114	,	,	PUNCT
ejpam-5832	186	115	0.65	0.65	NUM
ejpam-5832	186	116	)	)	PUNCT
ejpam-5832	186	117	}	}	PUNCT
ejpam-5832	186	118	a.	a.	NOUN
ejpam-5832	186	119	razzaque	razzaque	NOUN
ejpam-5832	186	120	/	/	SYM
ejpam-5832	186	121	eur	eur	NOUN
ejpam-5832	186	122	.	.	PUNCT
ejpam-5832	187	1	j.	j.	PROPN
ejpam-5832	187	2	pure	pure	PROPN
ejpam-5832	187	3	appl	appl	PROPN
ejpam-5832	187	4	.	.	PROPN
ejpam-5832	187	5	math	math	PROPN
ejpam-5832	187	6	,	,	PUNCT
ejpam-5832	187	7	18	18	NUM
ejpam-5832	187	8	(	(	PUNCT
ejpam-5832	187	9	3	3	NUM
ejpam-5832	187	10	)	)	PUNCT
ejpam-5832	187	11	(	(	PUNCT
ejpam-5832	187	12	2025	2025	NUM
ejpam-5832	187	13	)	)	PUNCT
ejpam-5832	187	14	,	,	PUNCT
ejpam-5832	187	15	5832	5832	NUM
ejpam-5832	187	16	7	7	NUM
ejpam-5832	187	17	of	of	ADP
ejpam-5832	187	18	21	21	NUM
ejpam-5832	187	19	(	(	PUNCT
ejpam-5832	187	20	v	v	NOUN
ejpam-5832	187	21	)	)	PUNCT
ejpam-5832	187	22	the	the	DET
ejpam-5832	187	23	q	q	NOUN
ejpam-5832	187	24	-	-	PUNCT
ejpam-5832	187	25	roflc	roflc	NOUN
ejpam-5832	187	26	of	of	ADP
ejpam-5832	187	27	q	q	NOUN
ejpam-5832	187	28	for	for	ADP
ejpam-5832	187	29	αβ	αβ	DET
ejpam-5832	187	30	∈	∈	PROPN
ejpam-5832	187	31	v	v	NOUN
ejpam-5832	187	32	is	be	AUX
ejpam-5832	187	33	αβq	αβq	NOUN
ejpam-5832	187	34	=	=	PUNCT
ejpam-5832	187	35			PUNCT
ejpam-5832	187	36	(	(	PUNCT
ejpam-5832	187	37	e	e	NOUN
ejpam-5832	187	38	,	,	PUNCT
ejpam-5832	187	39	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	40	)	)	PUNCT
ejpam-5832	187	41	−1e	−1e	NOUN
ejpam-5832	187	42	)	)	PUNCT
ejpam-5832	187	43	,	,	PUNCT
ejpam-5832	187	44	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	45	)	)	PUNCT
ejpam-5832	187	46	−1e	−1e	NOUN
ejpam-5832	187	47	)	)	PUNCT
ejpam-5832	187	48	)	)	PUNCT
ejpam-5832	187	49	,	,	PUNCT
ejpam-5832	187	50	(	(	PUNCT
ejpam-5832	187	51	β	β	X
ejpam-5832	187	52	,	,	PUNCT
ejpam-5832	187	53	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	54	)	)	PUNCT
ejpam-5832	187	55	−1β	−1β	NUM
ejpam-5832	187	56	)	)	PUNCT
ejpam-5832	187	57	,	,	PUNCT
ejpam-5832	187	58	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	59	)	)	PUNCT
ejpam-5832	187	60	−1β	−1β	PROPN
ejpam-5832	187	61	)	)	PUNCT
ejpam-5832	187	62	)	)	PUNCT
ejpam-5832	187	63	,	,	PUNCT
ejpam-5832	187	64	(	(	PUNCT
ejpam-5832	187	65	β2	β2	VERB
ejpam-5832	187	66	,	,	PUNCT
ejpam-5832	187	67	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	68	)	)	PUNCT
ejpam-5832	187	69	−1β2	−1β2	NUM
ejpam-5832	187	70	)	)	PUNCT
ejpam-5832	187	71	,	,	PUNCT
ejpam-5832	187	72	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	73	)	)	PUNCT
ejpam-5832	187	74	−1β2	−1β2	NUM
ejpam-5832	187	75	)	)	PUNCT
ejpam-5832	187	76	)	)	PUNCT
ejpam-5832	187	77	,	,	PUNCT
ejpam-5832	187	78	(	(	PUNCT
ejpam-5832	187	79	α	α	NOUN
ejpam-5832	187	80	,	,	PUNCT
ejpam-5832	187	81	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	82	)	)	PUNCT
ejpam-5832	187	83	−1α	−1α	PROPN
ejpam-5832	187	84	)	)	PUNCT
ejpam-5832	187	85	,	,	PUNCT
ejpam-5832	187	86	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	87	)	)	PUNCT
ejpam-5832	187	88	−1α	−1α	NOUN
ejpam-5832	187	89	)	)	PUNCT
ejpam-5832	187	90	)	)	PUNCT
ejpam-5832	187	91	,	,	PUNCT
ejpam-5832	187	92	(	(	PUNCT
ejpam-5832	187	93	αβ	αβ	INTJ
ejpam-5832	187	94	,	,	PUNCT
ejpam-5832	187	95	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	96	)	)	PUNCT
ejpam-5832	187	97	−1αβ	−1αβ	NOUN
ejpam-5832	187	98	)	)	PUNCT
ejpam-5832	187	99	,	,	PUNCT
ejpam-5832	187	100	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	101	)	)	PUNCT
ejpam-5832	187	102	−1αβ	−1αβ	NOUN
ejpam-5832	187	103	)	)	PUNCT
ejpam-5832	187	104	)	)	PUNCT
ejpam-5832	187	105	,	,	PUNCT
ejpam-5832	187	106	(	(	PUNCT
ejpam-5832	187	107	αβ2	αβ2	ADV
ejpam-5832	187	108	,	,	PUNCT
ejpam-5832	187	109	µq((αβ	µq((αβ	NOUN
ejpam-5832	187	110	)	)	PUNCT
ejpam-5832	187	111	−1αβ2	−1αβ2	NOUN
ejpam-5832	187	112	)	)	PUNCT
ejpam-5832	187	113	,	,	PUNCT
ejpam-5832	187	114	νq((αβ	νq((αβ	NOUN
ejpam-5832	187	115	)	)	PUNCT
ejpam-5832	187	116	−1αβ2	−1αβ2	NOUN
ejpam-5832	187	117	)	)	PUNCT
ejpam-5832	187	118	)	)	PUNCT
ejpam-5832	188	1			NOUN
ejpam-5832	188	2	=	=	PUNCT
ejpam-5832	188	3	{	{	PUNCT
ejpam-5832	188	4	(	(	PUNCT
ejpam-5832	188	5	e	e	NOUN
ejpam-5832	188	6	,	,	PUNCT
ejpam-5832	188	7	µq(αβ	µq(αβ	NOUN
ejpam-5832	188	8	)	)	PUNCT
ejpam-5832	188	9	,	,	PUNCT
ejpam-5832	188	10	νq(αβ	νq(αβ	NOUN
ejpam-5832	188	11	)	)	PUNCT
ejpam-5832	188	12	)	)	PUNCT
ejpam-5832	188	13	,	,	PUNCT
ejpam-5832	188	14	(	(	PUNCT
ejpam-5832	188	15	β	β	X
ejpam-5832	188	16	,	,	PUNCT
ejpam-5832	188	17	µq(αβ	µq(αβ	NOUN
ejpam-5832	188	18	2	2	NUM
ejpam-5832	188	19	)	)	PUNCT
ejpam-5832	188	20	,	,	PUNCT
ejpam-5832	188	21	νq(αβ	νq(αβ	NOUN
ejpam-5832	188	22	2	2	NUM
ejpam-5832	188	23	)	)	PUNCT
ejpam-5832	188	24	)	)	PUNCT
ejpam-5832	188	25	,	,	PUNCT
ejpam-5832	188	26	(	(	PUNCT
ejpam-5832	188	27	β2	β2	VERB
ejpam-5832	188	28	,	,	PUNCT
ejpam-5832	188	29	µq(α	µq(α	ADJ
ejpam-5832	188	30	)	)	PUNCT
ejpam-5832	188	31	,	,	PUNCT
ejpam-5832	188	32	νq(α	νq(α	NOUN
ejpam-5832	188	33	)	)	PUNCT
ejpam-5832	188	34	)	)	PUNCT
ejpam-5832	188	35	,	,	PUNCT
ejpam-5832	188	36	(	(	PUNCT
ejpam-5832	188	37	α	α	NOUN
ejpam-5832	188	38	,	,	PUNCT
ejpam-5832	188	39	µq(β	µq(β	X
ejpam-5832	188	40	2	2	NUM
ejpam-5832	188	41	)	)	PUNCT
ejpam-5832	188	42	,	,	PUNCT
ejpam-5832	188	43	νq(β	νq(β	X
ejpam-5832	188	44	2	2	NUM
ejpam-5832	188	45	)	)	PUNCT
ejpam-5832	188	46	)	)	PUNCT
ejpam-5832	188	47	,	,	PUNCT
ejpam-5832	188	48	(	(	PUNCT
ejpam-5832	188	49	αβ	αβ	INTJ
ejpam-5832	188	50	,	,	PUNCT
ejpam-5832	188	51	µq(e	µq(e	NUM
ejpam-5832	188	52	)	)	PUNCT
ejpam-5832	188	53	,	,	PUNCT
ejpam-5832	188	54	νq(e	νq(e	NUM
ejpam-5832	188	55	)	)	PUNCT
ejpam-5832	188	56	)	)	PUNCT
ejpam-5832	188	57	,	,	PUNCT
ejpam-5832	188	58	(	(	PUNCT
ejpam-5832	188	59	αβ2	αβ2	NOUN
ejpam-5832	188	60	,	,	PUNCT
ejpam-5832	188	61	µq(β	µq(β	NOUN
ejpam-5832	188	62	)	)	PUNCT
ejpam-5832	188	63	,	,	PUNCT
ejpam-5832	188	64	νq(β	νq(β	NUM
ejpam-5832	188	65	)	)	PUNCT
ejpam-5832	188	66	)	)	PUNCT
ejpam-5832	188	67	}	}	PUNCT
ejpam-5832	188	68	=	=	SYM
ejpam-5832	188	69	{	{	PUNCT
ejpam-5832	188	70	(	(	PUNCT
ejpam-5832	188	71	e	e	NOUN
ejpam-5832	188	72	,	,	PUNCT
ejpam-5832	188	73	0.0.80	0.0.80	NUM
ejpam-5832	188	74	,	,	PUNCT
ejpam-5832	188	75	0.75	0.75	NUM
ejpam-5832	188	76	)	)	PUNCT
ejpam-5832	188	77	,	,	PUNCT
ejpam-5832	188	78	(	(	PUNCT
ejpam-5832	188	79	β	β	X
ejpam-5832	188	80	,	,	PUNCT
ejpam-5832	188	81	0.80	0.80	NUM
ejpam-5832	188	82	,	,	PUNCT
ejpam-5832	188	83	0.75	0.75	NUM
ejpam-5832	188	84	)	)	PUNCT
ejpam-5832	188	85	,	,	PUNCT
ejpam-5832	188	86	(	(	PUNCT
ejpam-5832	188	87	β2	β2	VERB
ejpam-5832	188	88	,	,	PUNCT
ejpam-5832	188	89	0.80	0.80	NUM
ejpam-5832	188	90	,	,	PUNCT
ejpam-5832	188	91	0.75	0.75	NUM
ejpam-5832	188	92	)	)	PUNCT
ejpam-5832	188	93	,	,	PUNCT
ejpam-5832	188	94	(	(	PUNCT
ejpam-5832	188	95	α	α	NOUN
ejpam-5832	188	96	,	,	PUNCT
ejpam-5832	188	97	0.85	0.85	NUM
ejpam-5832	188	98	,	,	PUNCT
ejpam-5832	188	99	0.65	0.65	NUM
ejpam-5832	188	100	)	)	PUNCT
ejpam-5832	188	101	,	,	PUNCT
ejpam-5832	188	102	(	(	PUNCT
ejpam-5832	188	103	αβ	αβ	INTJ
ejpam-5832	188	104	,	,	PUNCT
ejpam-5832	188	105	0.85	0.85	NUM
ejpam-5832	188	106	,	,	PUNCT
ejpam-5832	188	107	0.65	0.65	NUM
ejpam-5832	188	108	)	)	PUNCT
ejpam-5832	188	109	,	,	PUNCT
ejpam-5832	188	110	(	(	PUNCT
ejpam-5832	188	111	αβ2	αβ2	NOUN
ejpam-5832	188	112	,	,	PUNCT
ejpam-5832	188	113	0.85	0.85	NUM
ejpam-5832	188	114	,	,	PUNCT
ejpam-5832	188	115	0.65	0.65	NUM
ejpam-5832	188	116	)	)	PUNCT
ejpam-5832	188	117	}	}	PUNCT
ejpam-5832	188	118	(	(	PUNCT
ejpam-5832	188	119	vi	vi	X
ejpam-5832	188	120	)	)	PUNCT
ejpam-5832	188	121	the	the	DET
ejpam-5832	188	122	q	q	NOUN
ejpam-5832	188	123	-	-	PUNCT
ejpam-5832	188	124	roflc	roflc	NOUN
ejpam-5832	188	125	of	of	ADP
ejpam-5832	188	126	q	q	NOUN
ejpam-5832	188	127	for	for	ADP
ejpam-5832	188	128	αβ2	αβ2	ADJ
ejpam-5832	188	129	∈	∈	PROPN
ejpam-5832	188	130	v	v	NOUN
ejpam-5832	188	131	is	be	AUX
ejpam-5832	188	132	αβ2q	αβ2q	NUM
ejpam-5832	188	133	=	=	SYM
ejpam-5832	188	134			X
ejpam-5832	188	135	(	(	PUNCT
ejpam-5832	188	136	e	e	NOUN
ejpam-5832	188	137	,	,	PUNCT
ejpam-5832	188	138	µq((αβ	µq((αβ	PROPN
ejpam-5832	188	139	2)−1e	2)−1e	NOUN
ejpam-5832	188	140	)	)	PUNCT
ejpam-5832	188	141	,	,	PUNCT
ejpam-5832	188	142	νq((αβ	νq((αβ	PROPN
ejpam-5832	188	143	2)−1e	2)−1e	PROPN
ejpam-5832	188	144	)	)	PUNCT
ejpam-5832	188	145	)	)	PUNCT
ejpam-5832	188	146	,	,	PUNCT
ejpam-5832	188	147	(	(	PUNCT
ejpam-5832	188	148	β	β	X
ejpam-5832	188	149	,	,	PUNCT
ejpam-5832	188	150	µq((αβ	µq((αβ	PROPN
ejpam-5832	188	151	2)−1β	2)−1β	NUM
ejpam-5832	188	152	)	)	PUNCT
ejpam-5832	188	153	,	,	PUNCT
ejpam-5832	188	154	νq((αβ	νq((αβ	PROPN
ejpam-5832	188	155	2)−1β	2)−1β	NUM
ejpam-5832	188	156	)	)	PUNCT
ejpam-5832	188	157	)	)	PUNCT
ejpam-5832	188	158	,	,	PUNCT
ejpam-5832	188	159	(	(	PUNCT
ejpam-5832	188	160	β2	β2	VERB
ejpam-5832	188	161	,	,	PUNCT
ejpam-5832	188	162	µq((αβ	µq((αβ	NOUN
ejpam-5832	188	163	2)−1β2	2)−1β2	NUM
ejpam-5832	188	164	)	)	PUNCT
ejpam-5832	188	165	,	,	PUNCT
ejpam-5832	188	166	νq((αβ	νq((αβ	PROPN
ejpam-5832	188	167	2)−1β2	2)−1β2	NUM
ejpam-5832	188	168	)	)	PUNCT
ejpam-5832	188	169	)	)	PUNCT
ejpam-5832	188	170	,	,	PUNCT
ejpam-5832	188	171	(	(	PUNCT
ejpam-5832	188	172	α	α	X
ejpam-5832	188	173	,	,	PUNCT
ejpam-5832	188	174	µq((αβ	µq((αβ	PROPN
ejpam-5832	188	175	2)−1α	2)−1α	NUM
ejpam-5832	188	176	)	)	PUNCT
ejpam-5832	188	177	,	,	PUNCT
ejpam-5832	188	178	νq((αβ	νq((αβ	PROPN
ejpam-5832	188	179	2)−1α	2)−1α	NUM
ejpam-5832	188	180	)	)	PUNCT
ejpam-5832	188	181	)	)	PUNCT
ejpam-5832	188	182	,	,	PUNCT
ejpam-5832	188	183	(	(	PUNCT
ejpam-5832	188	184	αβ	αβ	INTJ
ejpam-5832	188	185	,	,	PUNCT
ejpam-5832	188	186	µq((αβ	µq((αβ	PROPN
ejpam-5832	188	187	2)−1αβ	2)−1αβ	NUM
ejpam-5832	188	188	)	)	PUNCT
ejpam-5832	188	189	,	,	PUNCT
ejpam-5832	188	190	νq((αβ	νq((αβ	PROPN
ejpam-5832	188	191	2)−1αβ	2)−1αβ	NUM
ejpam-5832	188	192	)	)	PUNCT
ejpam-5832	188	193	)	)	PUNCT
ejpam-5832	188	194	,	,	PUNCT
ejpam-5832	188	195	(	(	PUNCT
ejpam-5832	188	196	αβ2	αβ2	ADV
ejpam-5832	188	197	,	,	PUNCT
ejpam-5832	188	198	µq((αβ	µq((αβ	NOUN
ejpam-5832	188	199	2)−1αβ2	2)−1αβ2	NUM
ejpam-5832	188	200	)	)	PUNCT
ejpam-5832	188	201	,	,	PUNCT
ejpam-5832	188	202	νq((αβ	νq((αβ	X
ejpam-5832	188	203	2)−1αβ2	2)−1αβ2	NUM
ejpam-5832	188	204	)	)	PUNCT
ejpam-5832	188	205	)	)	PUNCT
ejpam-5832	189	1			PROPN
ejpam-5832	189	2	=	=	SYM
ejpam-5832	189	3	{	{	PUNCT
ejpam-5832	189	4	(	(	PUNCT
ejpam-5832	189	5	e	e	NOUN
ejpam-5832	189	6	,	,	PUNCT
ejpam-5832	189	7	µq(αβ	µq(αβ	NOUN
ejpam-5832	189	8	2	2	NUM
ejpam-5832	189	9	)	)	PUNCT
ejpam-5832	189	10	,	,	PUNCT
ejpam-5832	189	11	νq(αβ	νq(αβ	NOUN
ejpam-5832	189	12	2	2	NUM
ejpam-5832	189	13	)	)	PUNCT
ejpam-5832	189	14	)	)	PUNCT
ejpam-5832	189	15	,	,	PUNCT
ejpam-5832	189	16	(	(	PUNCT
ejpam-5832	189	17	β	β	X
ejpam-5832	189	18	,	,	PUNCT
ejpam-5832	189	19	µq(α	µq(α	NUM
ejpam-5832	189	20	)	)	PUNCT
ejpam-5832	189	21	,	,	PUNCT
ejpam-5832	189	22	νq(α	νq(α	NOUN
ejpam-5832	189	23	)	)	PUNCT
ejpam-5832	189	24	)	)	PUNCT
ejpam-5832	189	25	,	,	PUNCT
ejpam-5832	189	26	(	(	PUNCT
ejpam-5832	189	27	β2	β2	VERB
ejpam-5832	189	28	,	,	PUNCT
ejpam-5832	189	29	µq(αβ	µq(αβ	NOUN
ejpam-5832	189	30	)	)	PUNCT
ejpam-5832	189	31	,	,	PUNCT
ejpam-5832	189	32	νq(αβ	νq(αβ	NOUN
ejpam-5832	189	33	)	)	PUNCT
ejpam-5832	189	34	)	)	PUNCT
ejpam-5832	189	35	,	,	PUNCT
ejpam-5832	189	36	(	(	PUNCT
ejpam-5832	189	37	α	α	X
ejpam-5832	189	38	,	,	PUNCT
ejpam-5832	189	39	µq(β	µq(β	NUM
ejpam-5832	189	40	)	)	PUNCT
ejpam-5832	189	41	,	,	PUNCT
ejpam-5832	189	42	νq(β	νq(β	NOUN
ejpam-5832	189	43	)	)	PUNCT
ejpam-5832	189	44	)	)	PUNCT
ejpam-5832	189	45	,	,	PUNCT
ejpam-5832	189	46	(	(	PUNCT
ejpam-5832	189	47	αβ	αβ	INTJ
ejpam-5832	189	48	,	,	PUNCT
ejpam-5832	189	49	µq(β	µq(β	NUM
ejpam-5832	189	50	)	)	PUNCT
ejpam-5832	189	51	,	,	PUNCT
ejpam-5832	189	52	νq(β	νq(β	NOUN
ejpam-5832	189	53	)	)	PUNCT
ejpam-5832	189	54	)	)	PUNCT
ejpam-5832	189	55	,	,	PUNCT
ejpam-5832	189	56	(	(	PUNCT
ejpam-5832	189	57	αβ2	αβ2	NOUN
ejpam-5832	189	58	,	,	PUNCT
ejpam-5832	189	59	µq(e	µq(e	NUM
ejpam-5832	189	60	)	)	PUNCT
ejpam-5832	189	61	,	,	PUNCT
ejpam-5832	189	62	νq(e	νq(e	NUM
ejpam-5832	189	63	)	)	PUNCT
ejpam-5832	189	64	)	)	PUNCT
ejpam-5832	189	65	}	}	PUNCT
ejpam-5832	190	1	=	=	SYM
ejpam-5832	190	2	{	{	PUNCT
ejpam-5832	190	3	(	(	PUNCT
ejpam-5832	190	4	e	e	NOUN
ejpam-5832	190	5	,	,	PUNCT
ejpam-5832	190	6	0.0.80	0.0.80	NUM
ejpam-5832	190	7	,	,	PUNCT
ejpam-5832	190	8	0.75	0.75	NUM
ejpam-5832	190	9	)	)	PUNCT
ejpam-5832	190	10	,	,	PUNCT
ejpam-5832	190	11	(	(	PUNCT
ejpam-5832	190	12	β	β	X
ejpam-5832	190	13	,	,	PUNCT
ejpam-5832	190	14	0.80	0.80	NUM
ejpam-5832	190	15	,	,	PUNCT
ejpam-5832	190	16	0.75	0.75	NUM
ejpam-5832	190	17	)	)	PUNCT
ejpam-5832	190	18	,	,	PUNCT
ejpam-5832	190	19	(	(	PUNCT
ejpam-5832	190	20	β2	β2	VERB
ejpam-5832	190	21	,	,	PUNCT
ejpam-5832	190	22	0.80	0.80	NUM
ejpam-5832	190	23	,	,	PUNCT
ejpam-5832	190	24	0.75	0.75	NUM
ejpam-5832	190	25	)	)	PUNCT
ejpam-5832	190	26	,	,	PUNCT
ejpam-5832	190	27	(	(	PUNCT
ejpam-5832	190	28	α	α	NOUN
ejpam-5832	190	29	,	,	PUNCT
ejpam-5832	190	30	0.85	0.85	NUM
ejpam-5832	190	31	,	,	PUNCT
ejpam-5832	190	32	0.65	0.65	NUM
ejpam-5832	190	33	)	)	PUNCT
ejpam-5832	190	34	,	,	PUNCT
ejpam-5832	190	35	(	(	PUNCT
ejpam-5832	190	36	αβ	αβ	INTJ
ejpam-5832	190	37	,	,	PUNCT
ejpam-5832	190	38	0.85	0.85	NUM
ejpam-5832	190	39	,	,	PUNCT
ejpam-5832	190	40	0.65	0.65	NUM
ejpam-5832	190	41	)	)	PUNCT
ejpam-5832	190	42	,	,	PUNCT
ejpam-5832	190	43	(	(	PUNCT
ejpam-5832	190	44	αβ2	αβ2	NOUN
ejpam-5832	190	45	,	,	PUNCT
ejpam-5832	190	46	0.85	0.85	NUM
ejpam-5832	190	47	,	,	PUNCT
ejpam-5832	190	48	0.65	0.65	NUM
ejpam-5832	190	49	)	)	PUNCT
ejpam-5832	190	50	}	}	PUNCT
ejpam-5832	190	51	as	as	ADP
ejpam-5832	190	52	a	a	DET
ejpam-5832	190	53	result	result	NOUN
ejpam-5832	190	54	,	,	PUNCT
ejpam-5832	190	55	q	q	PROPN
ejpam-5832	190	56	has	have	VERB
ejpam-5832	190	57	two	two	NUM
ejpam-5832	190	58	distinct	distinct	ADJ
ejpam-5832	190	59	q	q	NOUN
ejpam-5832	190	60	-	-	PUNCT
ejpam-5832	190	61	rofcs	rofcs	VERB
ejpam-5832	190	62	with	with	ADP
ejpam-5832	190	63	regard	regard	NOUN
ejpam-5832	190	64	to	to	ADP
ejpam-5832	190	65	all	all	DET
ejpam-5832	190	66	elements	element	NOUN
ejpam-5832	190	67	of	of	ADP
ejpam-5832	190	68	v	v	NOUN
ejpam-5832	190	69	,	,	PUNCT
ejpam-5832	190	70	namely	namely	ADV
ejpam-5832	190	71	,	,	PUNCT
ejpam-5832	190	72	eq	eq	NOUN
ejpam-5832	190	73	=	=	PRON
ejpam-5832	190	74	βq	βq	ADJ
ejpam-5832	190	75	=	=	ADJ
ejpam-5832	190	76	β2q	β2q	NOUN
ejpam-5832	190	77	and	and	CCONJ
ejpam-5832	190	78	αq	αq	ADP
ejpam-5832	190	79	=	=	PUNCT
ejpam-5832	190	80	αβq	αβq	NOUN
ejpam-5832	190	81	=	=	SYM
ejpam-5832	190	82	αβ2q	αβ2q	PROPN
ejpam-5832	190	83	.	.	PUNCT
ejpam-5832	191	1	definition	definition	NOUN
ejpam-5832	191	2	8	8	NUM
ejpam-5832	191	3	.	.	PUNCT
ejpam-5832	192	1	let	let	VERB
ejpam-5832	192	2	q	q	NOUN
ejpam-5832	193	1	=	=	PUNCT
ejpam-5832	193	2	(	(	PUNCT
ejpam-5832	193	3	ϵ	ϵ	NOUN
ejpam-5832	193	4	,	,	PUNCT
ejpam-5832	193	5	µq(ϵ	µq(ϵ	NUM
ejpam-5832	193	6	)	)	PUNCT
ejpam-5832	193	7	,	,	PUNCT
ejpam-5832	193	8	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	193	9	)	)	PUNCT
ejpam-5832	193	10	)	)	PUNCT
ejpam-5832	193	11	be	be	AUX
ejpam-5832	193	12	a	a	DET
ejpam-5832	193	13	q	q	NOUN
ejpam-5832	193	14	-	-	PUNCT
ejpam-5832	193	15	rofsg	rofsg	NOUN
ejpam-5832	193	16	of	of	ADP
ejpam-5832	193	17	v	v	NOUN
ejpam-5832	193	18	.	.	PUNCT
ejpam-5832	194	1	then	then	ADV
ejpam-5832	194	2	q∗	q∗	VERB
ejpam-5832	194	3	=	=	PUNCT
ejpam-5832	194	4	{	{	PUNCT
ejpam-5832	194	5	ϵ	ϵ	PART
ejpam-5832	194	6	∈	∈	PROPN
ejpam-5832	194	7	v	v	NOUN
ejpam-5832	194	8	:	:	PUNCT
ejpam-5832	194	9	(	(	PUNCT
ejpam-5832	194	10	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	194	11	)	)	PUNCT
ejpam-5832	194	12	)	)	PUNCT
ejpam-5832	195	1	2	2	NUM
ejpam-5832	195	2	=	=	SYM
ejpam-5832	195	3	(	(	PUNCT
ejpam-5832	195	4	µq(e	µq(e	NUM
ejpam-5832	195	5	)	)	PUNCT
ejpam-5832	195	6	)	)	PUNCT
ejpam-5832	195	7	2	2	NUM
ejpam-5832	195	8	and	and	CCONJ
ejpam-5832	195	9	(	(	PUNCT
ejpam-5832	195	10	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	195	11	)	)	PUNCT
ejpam-5832	195	12	)	)	PUNCT
ejpam-5832	196	1	2	2	NUM
ejpam-5832	196	2	=	=	SYM
ejpam-5832	196	3	(	(	PUNCT
ejpam-5832	196	4	νq(e	νq(e	NUM
ejpam-5832	196	5	)	)	PUNCT
ejpam-5832	196	6	)	)	PUNCT
ejpam-5832	196	7	2	2	X
ejpam-5832	196	8	}	}	PUNCT
ejpam-5832	196	9	definition	definition	NOUN
ejpam-5832	196	10	9	9	NUM
ejpam-5832	196	11	.	.	PUNCT
ejpam-5832	197	1	let	let	VERB
ejpam-5832	197	2	q	q	NOUN
ejpam-5832	197	3	=	=	PRON
ejpam-5832	197	4	{	{	PUNCT
ejpam-5832	197	5	(	(	PUNCT
ejpam-5832	197	6	ϵ	ϵ	NOUN
ejpam-5832	197	7	,	,	PUNCT
ejpam-5832	197	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	197	9	)	)	PUNCT
ejpam-5832	197	10	,	,	PUNCT
ejpam-5832	197	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	197	12	)	)	PUNCT
ejpam-5832	197	13	)	)	PUNCT
ejpam-5832	197	14	:	:	PUNCT
ejpam-5832	198	1	ϵ	ϵ	X
ejpam-5832	198	2	∈	∈	PROPN
ejpam-5832	198	3	v	v	PROPN
ejpam-5832	198	4	}	}	PUNCT
ejpam-5832	198	5	be	be	AUX
ejpam-5832	198	6	a	a	DET
ejpam-5832	198	7	q	q	NOUN
ejpam-5832	198	8	-	-	PUNCT
ejpam-5832	198	9	rofsg	rofsg	NOUN
ejpam-5832	198	10	of	of	ADP
ejpam-5832	198	11	v	v	NOUN
ejpam-5832	198	12	.	.	PUNCT
ejpam-5832	199	1	then	then	ADV
ejpam-5832	199	2	support	support	VERB
ejpam-5832	199	3	set	set	NOUN
ejpam-5832	199	4	of	of	ADP
ejpam-5832	199	5	q	q	PROPN
ejpam-5832	199	6	is	be	AUX
ejpam-5832	199	7	denoted	denote	VERB
ejpam-5832	199	8	by	by	ADP
ejpam-5832	199	9	q∗	q∗	NOUN
ejpam-5832	199	10	and	and	CCONJ
ejpam-5832	199	11	is	be	AUX
ejpam-5832	199	12	defined	define	VERB
ejpam-5832	199	13	as	as	ADP
ejpam-5832	199	14	;	;	PUNCT
ejpam-5832	199	15	q∗	q∗	NOUN
ejpam-5832	199	16	=	=	SYM
ejpam-5832	199	17	{	{	PUNCT
ejpam-5832	200	1	ϵ	ϵ	PART
ejpam-5832	200	2	∈	∈	PROPN
ejpam-5832	200	3	v	v	NOUN
ejpam-5832	200	4	:	:	PUNCT
ejpam-5832	200	5	(	(	PUNCT
ejpam-5832	200	6	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	200	7	)	)	PUNCT
ejpam-5832	200	8	)	)	PUNCT
ejpam-5832	201	1	2	2	NUM
ejpam-5832	201	2	>	>	SYM
ejpam-5832	201	3	0	0	PUNCT
ejpam-5832	202	1	and	and	CCONJ
ejpam-5832	202	2	(	(	PUNCT
ejpam-5832	202	3	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	202	4	)	)	PUNCT
ejpam-5832	202	5	)	)	PUNCT
ejpam-5832	203	1	2	2	NUM
ejpam-5832	203	2	<	<	SYM
ejpam-5832	203	3	1	1	NUM
ejpam-5832	203	4	}	}	PUNCT
ejpam-5832	203	5	the	the	DET
ejpam-5832	203	6	following	follow	VERB
ejpam-5832	203	7	theorem	theorem	ADJ
ejpam-5832	203	8	addresses	address	NOUN
ejpam-5832	203	9	the	the	DET
ejpam-5832	203	10	question	question	NOUN
ejpam-5832	203	11	:	:	PUNCT
ejpam-5832	203	12	what	what	DET
ejpam-5832	203	13	type	type	NOUN
ejpam-5832	203	14	of	of	ADP
ejpam-5832	203	15	elements	element	NOUN
ejpam-5832	203	16	of	of	ADP
ejpam-5832	203	17	v	v	NOUN
ejpam-5832	203	18	generates	generate	VERB
ejpam-5832	203	19	the	the	DET
ejpam-5832	203	20	same	same	ADJ
ejpam-5832	203	21	q	q	NOUN
ejpam-5832	203	22	-	-	PUNCT
ejpam-5832	203	23	rofcs	rofcs	NOUN
ejpam-5832	203	24	.	.	PUNCT
ejpam-5832	204	1	theorem	theorem	NOUN
ejpam-5832	204	2	7	7	NUM
ejpam-5832	204	3	.	.	PUNCT
ejpam-5832	205	1	let	let	VERB
ejpam-5832	205	2	q	q	NOUN
ejpam-5832	205	3	=	=	PRON
ejpam-5832	205	4	{	{	PUNCT
ejpam-5832	205	5	(	(	PUNCT
ejpam-5832	205	6	ϵ	ϵ	NOUN
ejpam-5832	205	7	,	,	PUNCT
ejpam-5832	205	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	205	9	)	)	PUNCT
ejpam-5832	205	10	,	,	PUNCT
ejpam-5832	205	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	205	12	)	)	PUNCT
ejpam-5832	205	13	)	)	PUNCT
ejpam-5832	205	14	:	:	PUNCT
ejpam-5832	206	1	ϵ	ϵ	X
ejpam-5832	206	2	∈	∈	PROPN
ejpam-5832	206	3	}	}	PUNCT
ejpam-5832	206	4	be	be	AUX
ejpam-5832	206	5	a	a	DET
ejpam-5832	206	6	q	q	NOUN
ejpam-5832	206	7	-	-	PUNCT
ejpam-5832	206	8	rofsg	rofsg	NOUN
ejpam-5832	206	9	of	of	ADP
ejpam-5832	206	10	v	v	NOUN
ejpam-5832	206	11	.	.	PUNCT
ejpam-5832	207	1	then	then	ADV
ejpam-5832	207	2	for	for	ADP
ejpam-5832	207	3	all	all	DET
ejpam-5832	207	4	λ	λ	PROPN
ejpam-5832	207	5	,	,	PUNCT
ejpam-5832	207	6	κ	κ	PROPN
ejpam-5832	207	7	∈	∈	PROPN
ejpam-5832	207	8	v	v	ADP
ejpam-5832	207	9	(	(	PUNCT
ejpam-5832	207	10	i	i	NOUN
ejpam-5832	207	11	)	)	PUNCT
ejpam-5832	207	12	λq	λq	PROPN
ejpam-5832	208	1	=	=	PUNCT
ejpam-5832	208	2	κq⇔	κq⇔	NOUN
ejpam-5832	208	3	λq∗	λq∗	NOUN
ejpam-5832	208	4	=	=	X
ejpam-5832	208	5	κq∗	κq∗	X
ejpam-5832	208	6	(	(	PUNCT
ejpam-5832	208	7	ii	ii	NOUN
ejpam-5832	208	8	)	)	PUNCT
ejpam-5832	208	9	qλ	qλ	PROPN
ejpam-5832	208	10	=	=	PUNCT
ejpam-5832	208	11	qκ⇔	qκ⇔	NOUN
ejpam-5832	208	12	q∗λ	q∗λ	PROPN
ejpam-5832	208	13	=	=	SYM
ejpam-5832	208	14	q∗κ	q∗κ	NUM
ejpam-5832	208	15	a.	a.	NOUN
ejpam-5832	208	16	razzaque	razzaque	NOUN
ejpam-5832	208	17	/	/	SYM
ejpam-5832	208	18	eur	eur	NOUN
ejpam-5832	208	19	.	.	PUNCT
ejpam-5832	209	1	j.	j.	PROPN
ejpam-5832	209	2	pure	pure	PROPN
ejpam-5832	209	3	appl	appl	PROPN
ejpam-5832	209	4	.	.	PROPN
ejpam-5832	209	5	math	math	PROPN
ejpam-5832	209	6	,	,	PUNCT
ejpam-5832	209	7	18	18	NUM
ejpam-5832	209	8	(	(	PUNCT
ejpam-5832	209	9	3	3	NUM
ejpam-5832	209	10	)	)	PUNCT
ejpam-5832	209	11	(	(	PUNCT
ejpam-5832	209	12	2025	2025	NUM
ejpam-5832	209	13	)	)	PUNCT
ejpam-5832	209	14	,	,	PUNCT
ejpam-5832	209	15	5832	5832	NUM
ejpam-5832	209	16	8	8	NUM
ejpam-5832	209	17	of	of	ADP
ejpam-5832	209	18	21	21	NUM
ejpam-5832	209	19	proof	proof	NOUN
ejpam-5832	209	20	.	.	PUNCT
ejpam-5832	210	1	due	due	ADP
ejpam-5832	210	2	to	to	ADP
ejpam-5832	210	3	the	the	DET
ejpam-5832	210	4	similarities	similarity	NOUN
ejpam-5832	210	5	of	of	ADP
ejpam-5832	210	6	the	the	DET
ejpam-5832	210	7	proofs	proof	NOUN
ejpam-5832	210	8	for	for	ADP
ejpam-5832	210	9	(	(	PUNCT
ejpam-5832	210	10	i	i	NOUN
ejpam-5832	210	11	)	)	PUNCT
ejpam-5832	210	12	and	and	CCONJ
ejpam-5832	210	13	(	(	PUNCT
ejpam-5832	210	14	ii	ii	NOUN
ejpam-5832	210	15	)	)	PUNCT
ejpam-5832	210	16	,	,	PUNCT
ejpam-5832	210	17	we	we	PRON
ejpam-5832	210	18	will	will	AUX
ejpam-5832	210	19	only	only	ADV
ejpam-5832	210	20	prove	prove	VERB
ejpam-5832	210	21	(	(	PUNCT
ejpam-5832	210	22	i	i	NOUN
ejpam-5832	210	23	)	)	PUNCT
ejpam-5832	210	24	here	here	ADV
ejpam-5832	210	25	.	.	PUNCT
ejpam-5832	211	1	assume	assume	VERB
ejpam-5832	211	2	that	that	SCONJ
ejpam-5832	211	3	λq	λq	ADV
ejpam-5832	211	4	=	=	SYM
ejpam-5832	211	5	κq	κq	NOUN
ejpam-5832	211	6	for	for	ADP
ejpam-5832	211	7	some	some	DET
ejpam-5832	211	8	λ	λ	NOUN
ejpam-5832	211	9	,	,	PUNCT
ejpam-5832	211	10	κ	κ	PROPN
ejpam-5832	211	11	∈	∈	PROPN
ejpam-5832	211	12	v	v	NOUN
ejpam-5832	211	13	.	.	PUNCT
ejpam-5832	212	1	then	then	ADV
ejpam-5832	212	2	µλq(ϵ	µλq(ϵ	PROPN
ejpam-5832	212	3	)	)	PUNCT
ejpam-5832	212	4	=	=	SYM
ejpam-5832	212	5	µκq(ϵ	µκq(ϵ	PROPN
ejpam-5832	212	6	)	)	PUNCT
ejpam-5832	212	7	and	and	CCONJ
ejpam-5832	212	8	νλq(ϵ	νλq(ϵ	NUM
ejpam-5832	212	9	)	)	PUNCT
ejpam-5832	212	10	=	=	SYM
ejpam-5832	212	11	νκq(ϵ	νκq(ϵ	PROPN
ejpam-5832	212	12	)	)	PUNCT
ejpam-5832	212	13	implies	imply	VERB
ejpam-5832	212	14	that	that	SCONJ
ejpam-5832	212	15	µq(λ	µq(λ	PUNCT
ejpam-5832	212	16	−1ϵ	−1ϵ	NOUN
ejpam-5832	212	17	)	)	PUNCT
ejpam-5832	212	18	=	=	SYM
ejpam-5832	212	19	µq(κ	µq(κ	NOUN
ejpam-5832	212	20	−1ϵ	−1ϵ	PROPN
ejpam-5832	212	21	)	)	PUNCT
ejpam-5832	212	22	and	and	CCONJ
ejpam-5832	212	23	νq(λ	νq(λ	NUM
ejpam-5832	212	24	−1ϵ	−1ϵ	NOUN
ejpam-5832	212	25	)	)	PUNCT
ejpam-5832	212	26	=	=	SYM
ejpam-5832	212	27	νq(κ	νq(κ	X
ejpam-5832	212	28	−1ϵ	−1ϵ	NOUN
ejpam-5832	212	29	)	)	PUNCT
ejpam-5832	212	30	for	for	ADP
ejpam-5832	212	31	all	all	DET
ejpam-5832	212	32	ϵ	ϵ	PART
ejpam-5832	212	33	∈	∈	PROPN
ejpam-5832	212	34	v	v	NOUN
ejpam-5832	212	35	.	.	PUNCT
ejpam-5832	213	1	let	let	VERB
ejpam-5832	213	2	us	we	PRON
ejpam-5832	213	3	take	take	VERB
ejpam-5832	213	4	ϵ	ϵ	PRON
ejpam-5832	213	5	=	=	SYM
ejpam-5832	213	6	κ	κ	NOUN
ejpam-5832	213	7	,	,	PUNCT
ejpam-5832	213	8	then	then	ADV
ejpam-5832	213	9	µq(λ	µq(λ	PUNCT
ejpam-5832	213	10	−1κ	−1κ	PROPN
ejpam-5832	213	11	)	)	PUNCT
ejpam-5832	213	12	=	=	PUNCT
ejpam-5832	213	13	µq(e	µq(e	PUNCT
ejpam-5832	213	14	)	)	PUNCT
ejpam-5832	213	15	and	and	CCONJ
ejpam-5832	213	16	νq(λ	νq(λ	NUM
ejpam-5832	213	17	−1κ	−1κ	PROPN
ejpam-5832	213	18	)	)	PUNCT
ejpam-5832	213	19	=	=	PUNCT
ejpam-5832	213	20	νq(e	νq(e	PROPN
ejpam-5832	213	21	)	)	PUNCT
ejpam-5832	213	22	.	.	PUNCT
ejpam-5832	214	1	so	so	ADV
ejpam-5832	214	2	,	,	PUNCT
ejpam-5832	214	3	λ−1κ	λ−1κ	PROPN
ejpam-5832	214	4	∈	∈	PROPN
ejpam-5832	214	5	q∗	q∗	NOUN
ejpam-5832	214	6	implying	imply	VERB
ejpam-5832	214	7	that	that	SCONJ
ejpam-5832	214	8	λ−1κq∗	λ−1κq∗	NOUN
ejpam-5832	214	9	=	=	PUNCT
ejpam-5832	214	10	q∗.	q∗.	ADP
ejpam-5832	214	11	consequently	consequently	ADV
ejpam-5832	214	12	,	,	PUNCT
ejpam-5832	214	13	κq∗	κq∗	X
ejpam-5832	214	14	=	=	PUNCT
ejpam-5832	214	15	λq∗.	λq∗.	ADV
ejpam-5832	214	16	conversely	conversely	ADV
ejpam-5832	214	17	,	,	PUNCT
ejpam-5832	214	18	suppose	suppose	VERB
ejpam-5832	214	19	that	that	SCONJ
ejpam-5832	214	20	κq∗	κq∗	PRON
ejpam-5832	214	21	=	=	SYM
ejpam-5832	214	22	λq∗	λq∗	PROPN
ejpam-5832	214	23	,	,	PUNCT
ejpam-5832	214	24	then	then	ADV
ejpam-5832	214	25	λ	λ	INTJ
ejpam-5832	214	26	−1κ	−1κ	PROPN
ejpam-5832	214	27	∈	∈	PROPN
ejpam-5832	214	28	q∗	q∗	NOUN
ejpam-5832	214	29	and	and	CCONJ
ejpam-5832	214	30	κ−1λ	κ−1λ	NOUN
ejpam-5832	214	31	∈	∈	PROPN
ejpam-5832	214	32	q∗.	q∗.	AUX
ejpam-5832	214	33	next	next	ADV
ejpam-5832	214	34	,	,	PUNCT
ejpam-5832	214	35	for	for	ADP
ejpam-5832	214	36	any	any	DET
ejpam-5832	214	37	ϵ	ϵ	PROPN
ejpam-5832	214	38	∈	∈	PROPN
ejpam-5832	214	39	v	v	NOUN
ejpam-5832	214	40	,	,	PUNCT
ejpam-5832	214	41	consider	consider	VERB
ejpam-5832	214	42	µq(λ	µq(λ	NOUN
ejpam-5832	214	43	−1ϵ	−1ϵ	NOUN
ejpam-5832	214	44	)	)	PUNCT
ejpam-5832	214	45	=	=	SYM
ejpam-5832	214	46	µq(λ	µq(λ	X
ejpam-5832	214	47	−1κκ−1ϵ	−1κκ−1ϵ	NUM
ejpam-5832	214	48	)	)	PUNCT
ejpam-5832	214	49	≥	≥	NOUN
ejpam-5832	214	50	min{µq(λ−1κ	min{µq(λ−1κ	NOUN
ejpam-5832	214	51	)	)	PUNCT
ejpam-5832	214	52	,	,	PUNCT
ejpam-5832	214	53	µq(κ	µq(κ	ADV
ejpam-5832	214	54	−1ϵ	−1ϵ	NOUN
ejpam-5832	214	55	)	)	PUNCT
ejpam-5832	214	56	}	}	PUNCT
ejpam-5832	214	57	=	=	SYM
ejpam-5832	214	58	minµq(e	minµq(e	PROPN
ejpam-5832	214	59	)	)	PUNCT
ejpam-5832	214	60	,	,	PUNCT
ejpam-5832	214	61	µq(κ	µq(κ	ADV
ejpam-5832	214	62	−1ϵ	−1ϵ	NOUN
ejpam-5832	214	63	)	)	PUNCT
ejpam-5832	214	64	=	=	SYM
ejpam-5832	214	65	µq(κ	µq(κ	NOUN
ejpam-5832	214	66	−1ϵ	−1ϵ	PROPN
ejpam-5832	214	67	)	)	PUNCT
ejpam-5832	214	68	in	in	ADP
ejpam-5832	214	69	a	a	DET
ejpam-5832	214	70	similar	similar	ADJ
ejpam-5832	214	71	manner	manner	NOUN
ejpam-5832	214	72	,	,	PUNCT
ejpam-5832	214	73	we	we	PRON
ejpam-5832	214	74	can	can	AUX
ejpam-5832	214	75	obtain	obtain	VERB
ejpam-5832	214	76	µq(κ	µq(κ	X
ejpam-5832	214	77	−1ϵ	−1ϵ	NOUN
ejpam-5832	214	78	)	)	PUNCT
ejpam-5832	214	79	≥	≥	NOUN
ejpam-5832	214	80	µq(λ	µq(λ	X
ejpam-5832	214	81	−1ϵ	−1ϵ	NOUN
ejpam-5832	214	82	)	)	PUNCT
ejpam-5832	214	83	.	.	PUNCT
ejpam-5832	215	1	therefore	therefore	ADV
ejpam-5832	215	2	,	,	PUNCT
ejpam-5832	215	3	µq(λ	µq(λ	PUNCT
ejpam-5832	215	4	−1ϵ	−1ϵ	NOUN
ejpam-5832	215	5	)	)	PUNCT
ejpam-5832	215	6	=	=	SYM
ejpam-5832	215	7	µq(κ	µq(κ	NOUN
ejpam-5832	215	8	−1ϵ	−1ϵ	PROPN
ejpam-5832	215	9	)	)	PUNCT
ejpam-5832	215	10	for	for	ADP
ejpam-5832	215	11	all	all	PRON
ejpam-5832	215	12	ϵ	ϵ	NOUN
ejpam-5832	215	13	∈	∈	PROPN
ejpam-5832	215	14	v.	v.	ADP
ejpam-5832	215	15	furthermore	furthermore	ADV
ejpam-5832	215	16	,	,	PUNCT
ejpam-5832	215	17	the	the	DET
ejpam-5832	215	18	same	same	ADJ
ejpam-5832	215	19	reasoning	reasoning	NOUN
ejpam-5832	215	20	leads	lead	VERB
ejpam-5832	215	21	to	to	ADP
ejpam-5832	215	22	νq(λ	νq(λ	X
ejpam-5832	215	23	−1ϵ	−1ϵ	PROPN
ejpam-5832	215	24	)	)	PUNCT
ejpam-5832	215	25	=	=	SYM
ejpam-5832	215	26	νq(κ	νq(κ	X
ejpam-5832	215	27	−1ϵ	−1ϵ	NOUN
ejpam-5832	215	28	)	)	PUNCT
ejpam-5832	215	29	which	which	PRON
ejpam-5832	215	30	implies	imply	VERB
ejpam-5832	215	31	that	that	PRON
ejpam-5832	215	32	µλq(ϵ	µλq(ϵ	PROPN
ejpam-5832	215	33	)	)	PUNCT
ejpam-5832	215	34	=	=	SYM
ejpam-5832	215	35	µκq(ϵ	µκq(ϵ	PROPN
ejpam-5832	215	36	)	)	PUNCT
ejpam-5832	215	37	and	and	CCONJ
ejpam-5832	215	38	νλq(ϵ	νλq(ϵ	NUM
ejpam-5832	215	39	)	)	PUNCT
ejpam-5832	215	40	=	=	SYM
ejpam-5832	215	41	νκq(ϵ	νκq(ϵ	PROPN
ejpam-5832	215	42	)	)	PUNCT
ejpam-5832	215	43	for	for	ADP
ejpam-5832	215	44	all	all	DET
ejpam-5832	215	45	ϵ	ϵ	PART
ejpam-5832	215	46	∈	∈	PROPN
ejpam-5832	215	47	v	v	NOUN
ejpam-5832	215	48	.	.	PUNCT
ejpam-5832	216	1	hence	hence	ADV
ejpam-5832	216	2	λq	λq	ADV
ejpam-5832	216	3	=	=	SYM
ejpam-5832	216	4	κq	κq	PROPN
ejpam-5832	216	5	.	.	PUNCT
ejpam-5832	217	1	lemma	lemma	PROPN
ejpam-5832	217	2	1	1	NUM
ejpam-5832	217	3	.	.	PUNCT
ejpam-5832	218	1	if	if	SCONJ
ejpam-5832	218	2	(	(	PUNCT
ejpam-5832	218	3	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	218	4	−1	−1	NOUN
ejpam-5832	218	5	)	)	PUNCT
ejpam-5832	218	6	)	)	PUNCT
ejpam-5832	219	1	q	q	NOUN
ejpam-5832	219	2	≥	≥	X
ejpam-5832	219	3	(	(	PUNCT
ejpam-5832	219	4	µq(λ	µq(λ	NOUN
ejpam-5832	219	5	)	)	PUNCT
ejpam-5832	219	6	)	)	PUNCT
ejpam-5832	219	7	q	q	NOUN
ejpam-5832	220	1	and	and	CCONJ
ejpam-5832	220	2	(	(	PUNCT
ejpam-5832	220	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	220	4	−1	−1	NOUN
ejpam-5832	220	5	)	)	PUNCT
ejpam-5832	220	6	)	)	PUNCT
ejpam-5832	221	1	q	q	PROPN
ejpam-5832	221	2	≤	≤	NUM
ejpam-5832	221	3	(	(	PUNCT
ejpam-5832	221	4	νq(λ	νq(λ	NUM
ejpam-5832	221	5	)	)	PUNCT
ejpam-5832	221	6	)	)	PUNCT
ejpam-5832	222	1	q	q	NOUN
ejpam-5832	222	2	for	for	ADP
ejpam-5832	222	3	all	all	DET
ejpam-5832	222	4	λ	λ	PROPN
ejpam-5832	222	5	,	,	PUNCT
ejpam-5832	222	6	ϵ	ϵ	PROPN
ejpam-5832	222	7	∈	∈	PROPN
ejpam-5832	222	8	v	v	NOUN
ejpam-5832	222	9	,	,	PUNCT
ejpam-5832	222	10	then	then	ADV
ejpam-5832	222	11	q	q	X
ejpam-5832	222	12	is	be	AUX
ejpam-5832	222	13	a	a	DET
ejpam-5832	222	14	q	q	NOUN
ejpam-5832	222	15	-	-	PUNCT
ejpam-5832	222	16	rofns	rofns	NOUN
ejpam-5832	222	17	of	of	ADP
ejpam-5832	222	18	v	v	NOUN
ejpam-5832	222	19	.	.	PUNCT
ejpam-5832	223	1	proof	proof	NOUN
ejpam-5832	223	2	.	.	PUNCT
ejpam-5832	224	1	let	let	VERB
ejpam-5832	224	2	(	(	PUNCT
ejpam-5832	224	3	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	224	4	−1	−1	NOUN
ejpam-5832	224	5	)	)	PUNCT
ejpam-5832	224	6	)	)	PUNCT
ejpam-5832	225	1	q	q	NOUN
ejpam-5832	225	2	≥	≥	X
ejpam-5832	225	3	(	(	PUNCT
ejpam-5832	225	4	µq(λ	µq(λ	NOUN
ejpam-5832	225	5	)	)	PUNCT
ejpam-5832	225	6	)	)	PUNCT
ejpam-5832	225	7	q	q	NOUN
ejpam-5832	226	1	and	and	CCONJ
ejpam-5832	226	2	(	(	PUNCT
ejpam-5832	226	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	226	4	−1	−1	NOUN
ejpam-5832	226	5	)	)	PUNCT
ejpam-5832	226	6	)	)	PUNCT
ejpam-5832	227	1	q	q	PROPN
ejpam-5832	227	2	≤	≤	NUM
ejpam-5832	227	3	(	(	PUNCT
ejpam-5832	227	4	νq(λ	νq(λ	NUM
ejpam-5832	227	5	)	)	PUNCT
ejpam-5832	227	6	)	)	PUNCT
ejpam-5832	228	1	q	q	NOUN
ejpam-5832	228	2	for	for	ADP
ejpam-5832	228	3	all	all	DET
ejpam-5832	228	4	λ	λ	PROPN
ejpam-5832	228	5	,	,	PUNCT
ejpam-5832	228	6	ϵ	ϵ	PROPN
ejpam-5832	228	7	∈	∈	PROPN
ejpam-5832	228	8	v	v	NOUN
ejpam-5832	228	9	.	.	PUNCT
ejpam-5832	229	1	since	since	SCONJ
ejpam-5832	229	2	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	229	3	,	,	PUNCT
ejpam-5832	229	4	ϵ−1	ϵ−1	PROPN
ejpam-5832	229	5	∈	∈	PROPN
ejpam-5832	229	6	v	v	NOUN
ejpam-5832	229	7	,	,	PUNCT
ejpam-5832	229	8	therefore	therefore	ADV
ejpam-5832	229	9	(	(	PUNCT
ejpam-5832	229	10	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	229	11	−1	−1	NOUN
ejpam-5832	229	12	)	)	PUNCT
ejpam-5832	229	13	)	)	PUNCT
ejpam-5832	230	1	q	q	PROPN
ejpam-5832	230	2	≤	≤	NUM
ejpam-5832	230	3	(	(	PUNCT
ejpam-5832	230	4	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	230	5	−1(ϵλϵ−1)(ϵ−1)−1	−1(ϵλϵ−1)(ϵ−1)−1	NUM
ejpam-5832	230	6	)	)	PUNCT
ejpam-5832	230	7	)	)	PUNCT
ejpam-5832	230	8	q	q	X
ejpam-5832	231	1	=	=	PUNCT
ejpam-5832	231	2	(	(	PUNCT
ejpam-5832	231	3	µq(λ	µq(λ	NOUN
ejpam-5832	231	4	)	)	PUNCT
ejpam-5832	231	5	)	)	PUNCT
ejpam-5832	231	6	q	q	PROPN
ejpam-5832	231	7	similarly	similarly	ADV
ejpam-5832	231	8	,	,	PUNCT
ejpam-5832	231	9	(	(	PUNCT
ejpam-5832	231	10	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	231	11	−1	−1	NOUN
ejpam-5832	231	12	)	)	PUNCT
ejpam-5832	231	13	)	)	PUNCT
ejpam-5832	231	14	q	q	NOUN
ejpam-5832	231	15	≥	≥	X
ejpam-5832	231	16	(	(	PUNCT
ejpam-5832	231	17	νq(λ	νq(λ	NUM
ejpam-5832	231	18	)	)	PUNCT
ejpam-5832	231	19	)	)	PUNCT
ejpam-5832	231	20	q.	q.	PROPN
ejpam-5832	231	21	therefore	therefore	ADV
ejpam-5832	231	22	,	,	PUNCT
ejpam-5832	231	23	(	(	PUNCT
ejpam-5832	231	24	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	231	25	−1	−1	NOUN
ejpam-5832	231	26	)	)	PUNCT
ejpam-5832	231	27	)	)	PUNCT
ejpam-5832	232	1	q	q	X
ejpam-5832	232	2	=	=	PUNCT
ejpam-5832	232	3	(	(	PUNCT
ejpam-5832	232	4	µq(λ	µq(λ	NOUN
ejpam-5832	232	5	)	)	PUNCT
ejpam-5832	232	6	)	)	PUNCT
ejpam-5832	233	1	q	q	NOUN
ejpam-5832	234	1	and	and	CCONJ
ejpam-5832	234	2	(	(	PUNCT
ejpam-5832	234	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	234	4	−1	−1	NOUN
ejpam-5832	234	5	)	)	PUNCT
ejpam-5832	234	6	)	)	PUNCT
ejpam-5832	235	1	q	q	X
ejpam-5832	235	2	=	=	PUNCT
ejpam-5832	235	3	(	(	PUNCT
ejpam-5832	235	4	νq(λ	νq(λ	NUM
ejpam-5832	235	5	)	)	PUNCT
ejpam-5832	235	6	)	)	PUNCT
ejpam-5832	236	1	q	q	PUNCT
ejpam-5832	236	2	then	then	ADV
ejpam-5832	236	3	,	,	PUNCT
ejpam-5832	236	4	theorem	theorem	VERB
ejpam-5832	236	5	6	6	NUM
ejpam-5832	236	6	reveals	reveal	VERB
ejpam-5832	236	7	that	that	SCONJ
ejpam-5832	236	8	q	q	NOUN
ejpam-5832	236	9	is	be	AUX
ejpam-5832	236	10	a	a	DET
ejpam-5832	236	11	q	q	NOUN
ejpam-5832	236	12	-	-	PUNCT
ejpam-5832	236	13	rofns	rofns	NOUN
ejpam-5832	236	14	of	of	ADP
ejpam-5832	236	15	v	v	NOUN
ejpam-5832	236	16	.	.	PUNCT
ejpam-5832	237	1	theorem	theorem	ADJ
ejpam-5832	237	2	8	8	NUM
ejpam-5832	237	3	.	.	PUNCT
ejpam-5832	238	1	let	let	VERB
ejpam-5832	238	2	q	q	NOUN
ejpam-5832	238	3	=	=	PRON
ejpam-5832	238	4	{	{	PUNCT
ejpam-5832	238	5	(	(	PUNCT
ejpam-5832	238	6	ϵ	ϵ	NOUN
ejpam-5832	238	7	,	,	PUNCT
ejpam-5832	238	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	238	9	)	)	PUNCT
ejpam-5832	238	10	,	,	PUNCT
ejpam-5832	238	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	238	12	)	)	PUNCT
ejpam-5832	238	13	)	)	PUNCT
ejpam-5832	238	14	:	:	PUNCT
ejpam-5832	239	1	ϵ	ϵ	X
ejpam-5832	239	2	∈	∈	PROPN
ejpam-5832	239	3	v	v	PROPN
ejpam-5832	239	4	}	}	PUNCT
ejpam-5832	239	5	be	be	AUX
ejpam-5832	239	6	a	a	DET
ejpam-5832	239	7	q	q	NOUN
ejpam-5832	239	8	-	-	PUNCT
ejpam-5832	239	9	rofsg	rofsg	NOUN
ejpam-5832	239	10	of	of	ADP
ejpam-5832	239	11	v	v	NOUN
ejpam-5832	239	12	.	.	PUNCT
ejpam-5832	240	1	then	then	ADV
ejpam-5832	240	2	q	q	X
ejpam-5832	240	3	is	be	AUX
ejpam-5832	240	4	a	a	DET
ejpam-5832	240	5	q	q	NOUN
ejpam-5832	240	6	-	-	PUNCT
ejpam-5832	240	7	rofnsg	rofnsg	NOUN
ejpam-5832	240	8	of	of	ADP
ejpam-5832	240	9	v	v	PROPN
ejpam-5832	240	10	⇔	⇔	PROPN
ejpam-5832	240	11	q(θ	q(θ	PROPN
ejpam-5832	240	12	,	,	PUNCT
ejpam-5832	240	13	τ	τ	X
ejpam-5832	240	14	)	)	PUNCT
ejpam-5832	240	15	⊴	⊴	ADP
ejpam-5832	240	16	v	v	NOUN
ejpam-5832	240	17	for	for	ADP
ejpam-5832	240	18	all	all	DET
ejpam-5832	240	19	θ	θ	PRON
ejpam-5832	240	20	∈	∈	PROPN
ejpam-5832	241	1	[	[	X
ejpam-5832	241	2	0	0	NUM
ejpam-5832	241	3	,	,	PUNCT
ejpam-5832	241	4	(	(	PUNCT
ejpam-5832	241	5	µq(e	µq(e	NUM
ejpam-5832	241	6	)	)	PUNCT
ejpam-5832	241	7	)	)	PUNCT
ejpam-5832	242	1	q	q	X
ejpam-5832	242	2	]	]	PUNCT
ejpam-5832	242	3	and	and	CCONJ
ejpam-5832	242	4	τ	τ	PROPN
ejpam-5832	242	5	∈	∈	PROPN
ejpam-5832	243	1	[	[	X
ejpam-5832	243	2	(	(	PUNCT
ejpam-5832	243	3	νq(e	νq(e	NUM
ejpam-5832	243	4	)	)	PUNCT
ejpam-5832	243	5	)	)	PUNCT
ejpam-5832	244	1	q	q	NOUN
ejpam-5832	244	2	,	,	PUNCT
ejpam-5832	244	3	1	1	NUM
ejpam-5832	244	4	]	]	PUNCT
ejpam-5832	244	5	.	.	PUNCT
ejpam-5832	245	1	a.	a.	NOUN
ejpam-5832	245	2	razzaque	razzaque	PROPN
ejpam-5832	245	3	/	/	SYM
ejpam-5832	245	4	eur	eur	NOUN
ejpam-5832	245	5	.	.	PUNCT
ejpam-5832	246	1	j.	j.	PROPN
ejpam-5832	246	2	pure	pure	PROPN
ejpam-5832	246	3	appl	appl	PROPN
ejpam-5832	246	4	.	.	PROPN
ejpam-5832	246	5	math	math	PROPN
ejpam-5832	246	6	,	,	PUNCT
ejpam-5832	246	7	18	18	NUM
ejpam-5832	246	8	(	(	PUNCT
ejpam-5832	246	9	3	3	NUM
ejpam-5832	246	10	)	)	PUNCT
ejpam-5832	246	11	(	(	PUNCT
ejpam-5832	246	12	2025	2025	NUM
ejpam-5832	246	13	)	)	PUNCT
ejpam-5832	246	14	,	,	PUNCT
ejpam-5832	246	15	5832	5832	NUM
ejpam-5832	246	16	9	9	NUM
ejpam-5832	246	17	of	of	ADP
ejpam-5832	246	18	21	21	NUM
ejpam-5832	246	19	proof	proof	NOUN
ejpam-5832	246	20	.	.	PUNCT
ejpam-5832	247	1	in	in	ADP
ejpam-5832	247	2	[	[	X
ejpam-5832	247	3	35	35	NUM
ejpam-5832	247	4	]	]	PUNCT
ejpam-5832	247	5	,	,	PUNCT
ejpam-5832	247	6	it	it	PRON
ejpam-5832	247	7	has	have	AUX
ejpam-5832	247	8	been	be	AUX
ejpam-5832	247	9	proved	prove	VERB
ejpam-5832	247	10	that	that	SCONJ
ejpam-5832	247	11	if	if	SCONJ
ejpam-5832	247	12	q	q	NOUN
ejpam-5832	247	13	is	be	AUX
ejpam-5832	247	14	a	a	DET
ejpam-5832	247	15	q	q	NOUN
ejpam-5832	247	16	-	-	PUNCT
ejpam-5832	247	17	rofns	rofns	NOUN
ejpam-5832	247	18	of	of	ADP
ejpam-5832	247	19	v	v	NOUN
ejpam-5832	247	20	,	,	PUNCT
ejpam-5832	247	21	then	then	ADV
ejpam-5832	247	22	q(θ	q(θ	PROPN
ejpam-5832	247	23	,	,	PUNCT
ejpam-5832	247	24	τ	τ	X
ejpam-5832	247	25	)	)	PUNCT
ejpam-5832	247	26	⊴	⊴	ADP
ejpam-5832	247	27	v	v	NOUN
ejpam-5832	247	28	for	for	ADP
ejpam-5832	247	29	all	all	DET
ejpam-5832	247	30	θ	θ	PRON
ejpam-5832	247	31	∈	∈	PROPN
ejpam-5832	248	1	[	[	X
ejpam-5832	248	2	0	0	NUM
ejpam-5832	248	3	,	,	PUNCT
ejpam-5832	248	4	(	(	PUNCT
ejpam-5832	248	5	µq(e	µq(e	NUM
ejpam-5832	248	6	)	)	PUNCT
ejpam-5832	248	7	)	)	PUNCT
ejpam-5832	249	1	q	q	X
ejpam-5832	249	2	]	]	PUNCT
ejpam-5832	249	3	and	and	CCONJ
ejpam-5832	249	4	τ	τ	PROPN
ejpam-5832	249	5	∈	∈	PROPN
ejpam-5832	250	1	[	[	X
ejpam-5832	250	2	(	(	PUNCT
ejpam-5832	250	3	νq(e	νq(e	NUM
ejpam-5832	250	4	)	)	PUNCT
ejpam-5832	250	5	)	)	PUNCT
ejpam-5832	251	1	q	q	NOUN
ejpam-5832	251	2	,	,	PUNCT
ejpam-5832	251	3	1	1	NUM
ejpam-5832	251	4	]	]	PUNCT
ejpam-5832	251	5	.	.	PUNCT
ejpam-5832	252	1	conversely	conversely	ADV
ejpam-5832	252	2	,	,	PUNCT
ejpam-5832	252	3	let	let	VERB
ejpam-5832	252	4	q(θ	q(θ	PROPN
ejpam-5832	252	5	,	,	PUNCT
ejpam-5832	252	6	τ	τ	X
ejpam-5832	252	7	)	)	PUNCT
ejpam-5832	252	8	⊴	⊴	ADP
ejpam-5832	252	9	v	v	NOUN
ejpam-5832	252	10	for	for	ADP
ejpam-5832	252	11	all	all	DET
ejpam-5832	252	12	θ	θ	PRON
ejpam-5832	252	13	∈	∈	PROPN
ejpam-5832	253	1	[	[	X
ejpam-5832	253	2	0	0	NUM
ejpam-5832	253	3	,	,	PUNCT
ejpam-5832	253	4	(	(	PUNCT
ejpam-5832	253	5	µq(e	µq(e	NUM
ejpam-5832	253	6	)	)	PUNCT
ejpam-5832	253	7	)	)	PUNCT
ejpam-5832	254	1	q	q	X
ejpam-5832	254	2	]	]	PUNCT
ejpam-5832	254	3	and	and	CCONJ
ejpam-5832	254	4	τ	τ	PROPN
ejpam-5832	254	5	∈	∈	PROPN
ejpam-5832	255	1	[	[	X
ejpam-5832	255	2	(	(	PUNCT
ejpam-5832	255	3	νq(e	νq(e	NUM
ejpam-5832	255	4	)	)	PUNCT
ejpam-5832	255	5	)	)	PUNCT
ejpam-5832	256	1	q	q	NOUN
ejpam-5832	256	2	,	,	PUNCT
ejpam-5832	256	3	1	1	NUM
ejpam-5832	256	4	]	]	PUNCT
ejpam-5832	256	5	.	.	PUNCT
ejpam-5832	257	1	according	accord	VERB
ejpam-5832	257	2	to	to	ADP
ejpam-5832	257	3	theorem	theorem	ADJ
ejpam-5832	257	4	4	4	NUM
ejpam-5832	257	5	,	,	PUNCT
ejpam-5832	257	6	q	q	PUNCT
ejpam-5832	257	7	is	be	AUX
ejpam-5832	257	8	a	a	DET
ejpam-5832	257	9	q	q	NOUN
ejpam-5832	257	10	-	-	PUNCT
ejpam-5832	257	11	rofsg	rofsg	NOUN
ejpam-5832	257	12	of	of	ADP
ejpam-5832	257	13	v	v	PROPN
ejpam-5832	257	14	.	.	PUNCT
ejpam-5832	258	1	assume	assume	VERB
ejpam-5832	258	2	that	that	SCONJ
ejpam-5832	258	3	λ	λ	PROPN
ejpam-5832	258	4	,	,	PUNCT
ejpam-5832	258	5	ϵ	ϵ	PROPN
ejpam-5832	258	6	∈	∈	PROPN
ejpam-5832	258	7	v	v	ADP
ejpam-5832	258	8	such	such	ADJ
ejpam-5832	258	9	that	that	SCONJ
ejpam-5832	258	10	(	(	PUNCT
ejpam-5832	258	11	µq(λ	µq(λ	NOUN
ejpam-5832	258	12	)	)	PUNCT
ejpam-5832	258	13	)	)	PUNCT
ejpam-5832	258	14	q	q	NOUN
ejpam-5832	259	1	=	=	PUNCT
ejpam-5832	259	2	a	a	PROPN
ejpam-5832	259	3	and	and	CCONJ
ejpam-5832	259	4	(	(	PUNCT
ejpam-5832	259	5	νq(λ	νq(λ	NUM
ejpam-5832	259	6	)	)	PUNCT
ejpam-5832	259	7	)	)	PUNCT
ejpam-5832	260	1	q	q	NOUN
ejpam-5832	260	2	=	=	PUNCT
ejpam-5832	260	3	b.	b.	PROPN
ejpam-5832	260	4	then	then	ADV
ejpam-5832	260	5	λ	λ	PROPN
ejpam-5832	260	6	∈	∈	PROPN
ejpam-5832	260	7	q(a	q(a	PROPN
ejpam-5832	260	8	,	,	PUNCT
ejpam-5832	260	9	b	b	NOUN
ejpam-5832	260	10	)	)	PUNCT
ejpam-5832	260	11	⇒	⇒	NOUN
ejpam-5832	260	12	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	260	13	∈	∈	PROPN
ejpam-5832	260	14	q(a	q(a	PROPN
ejpam-5832	260	15	,	,	PUNCT
ejpam-5832	260	16	b	b	NOUN
ejpam-5832	260	17	)	)	PUNCT
ejpam-5832	260	18	⇒	⇒	NOUN
ejpam-5832	260	19	(	(	PUNCT
ejpam-5832	260	20	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	260	21	−1	−1	NOUN
ejpam-5832	260	22	)	)	PUNCT
ejpam-5832	260	23	)	)	PUNCT
ejpam-5832	261	1	q	q	NOUN
ejpam-5832	261	2	≥	≥	NOUN
ejpam-5832	261	3	a	a	X
ejpam-5832	261	4	=	=	X
ejpam-5832	261	5	(	(	PUNCT
ejpam-5832	261	6	µq(λ	µq(λ	NOUN
ejpam-5832	261	7	)	)	PUNCT
ejpam-5832	261	8	)	)	PUNCT
ejpam-5832	261	9	q	q	NOUN
ejpam-5832	262	1	and	and	CCONJ
ejpam-5832	262	2	(	(	PUNCT
ejpam-5832	262	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	262	4	−1	−1	NOUN
ejpam-5832	262	5	)	)	PUNCT
ejpam-5832	262	6	)	)	PUNCT
ejpam-5832	263	1	q	q	PROPN
ejpam-5832	263	2	≤	≤	NUM
ejpam-5832	263	3	b	b	X
ejpam-5832	263	4	=	=	SYM
ejpam-5832	263	5	(	(	PUNCT
ejpam-5832	263	6	νq(λ	νq(λ	NUM
ejpam-5832	263	7	)	)	PUNCT
ejpam-5832	263	8	)	)	PUNCT
ejpam-5832	264	1	q	q	PUNCT
ejpam-5832	264	2	then	then	ADV
ejpam-5832	264	3	,	,	PUNCT
ejpam-5832	264	4	q	q	X
ejpam-5832	264	5	is	be	AUX
ejpam-5832	264	6	thus	thus	ADV
ejpam-5832	264	7	a	a	DET
ejpam-5832	264	8	q	q	NOUN
ejpam-5832	264	9	-	-	PUNCT
ejpam-5832	264	10	rofnsg	rofnsg	NOUN
ejpam-5832	264	11	of	of	ADP
ejpam-5832	264	12	v	v	NOUN
ejpam-5832	264	13	,	,	PUNCT
ejpam-5832	264	14	according	accord	VERB
ejpam-5832	264	15	to	to	ADP
ejpam-5832	264	16	lemma	lemma	PROPN
ejpam-5832	264	17	1	1	NUM
ejpam-5832	264	18	.	.	PUNCT
ejpam-5832	265	1	lemma	lemma	PROPN
ejpam-5832	265	2	2	2	X
ejpam-5832	265	3	.	.	PUNCT
ejpam-5832	266	1	if	if	SCONJ
ejpam-5832	266	2	q	q	PRON
ejpam-5832	266	3	=	=	PUNCT
ejpam-5832	266	4	{	{	PUNCT
ejpam-5832	266	5	(	(	PUNCT
ejpam-5832	266	6	ϵ	ϵ	NOUN
ejpam-5832	266	7	,	,	PUNCT
ejpam-5832	266	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	266	9	)	)	PUNCT
ejpam-5832	266	10	,	,	PUNCT
ejpam-5832	266	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	266	12	)	)	PUNCT
ejpam-5832	266	13	)	)	PUNCT
ejpam-5832	266	14	:	:	PUNCT
ejpam-5832	267	1	ϵ	ϵ	X
ejpam-5832	267	2	∈	∈	PROPN
ejpam-5832	267	3	v	v	PROPN
ejpam-5832	267	4	}	}	PUNCT
ejpam-5832	267	5	is	be	AUX
ejpam-5832	267	6	a	a	DET
ejpam-5832	267	7	q	q	NOUN
ejpam-5832	267	8	-	-	PUNCT
ejpam-5832	267	9	rofsg	rofsg	NOUN
ejpam-5832	267	10	of	of	ADP
ejpam-5832	267	11	v	v	NOUN
ejpam-5832	267	12	.	.	PUNCT
ejpam-5832	268	1	then	then	ADV
ejpam-5832	268	2	q∗	q∗	NOUN
ejpam-5832	268	3	and	and	CCONJ
ejpam-5832	268	4	q∗	q∗	NOUN
ejpam-5832	268	5	are	be	AUX
ejpam-5832	268	6	subgroups	subgroup	NOUN
ejpam-5832	268	7	of	of	ADP
ejpam-5832	268	8	v	v	NOUN
ejpam-5832	268	9	.	.	PUNCT
ejpam-5832	269	1	using	use	VERB
ejpam-5832	269	2	the	the	DET
ejpam-5832	269	3	preceding	precede	VERB
ejpam-5832	269	4	concepts	concept	NOUN
ejpam-5832	269	5	,	,	PUNCT
ejpam-5832	269	6	the	the	DET
ejpam-5832	269	7	proof	proof	NOUN
ejpam-5832	269	8	can	can	AUX
ejpam-5832	269	9	be	be	AUX
ejpam-5832	269	10	easily	easily	ADV
ejpam-5832	269	11	established	establish	VERB
ejpam-5832	269	12	.	.	PUNCT
ejpam-5832	270	1	theorem	theorem	VERB
ejpam-5832	270	2	9	9	NUM
ejpam-5832	270	3	.	.	PUNCT
ejpam-5832	271	1	if	if	SCONJ
ejpam-5832	271	2	q	q	PRON
ejpam-5832	271	3	=	=	PUNCT
ejpam-5832	271	4	{	{	PUNCT
ejpam-5832	271	5	(	(	PUNCT
ejpam-5832	271	6	ϵ	ϵ	NOUN
ejpam-5832	271	7	,	,	PUNCT
ejpam-5832	271	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	271	9	)	)	PUNCT
ejpam-5832	271	10	,	,	PUNCT
ejpam-5832	271	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	271	12	)	)	PUNCT
ejpam-5832	271	13	)	)	PUNCT
ejpam-5832	271	14	:	:	PUNCT
ejpam-5832	272	1	ϵ	ϵ	X
ejpam-5832	272	2	∈	∈	PROPN
ejpam-5832	272	3	v	v	PROPN
ejpam-5832	272	4	}	}	PUNCT
ejpam-5832	272	5	is	be	AUX
ejpam-5832	272	6	a	a	DET
ejpam-5832	272	7	q	q	NOUN
ejpam-5832	272	8	-	-	PUNCT
ejpam-5832	272	9	rofnsg	rofnsg	NOUN
ejpam-5832	272	10	of	of	ADP
ejpam-5832	272	11	v	v	NOUN
ejpam-5832	272	12	.	.	PUNCT
ejpam-5832	273	1	then	then	ADV
ejpam-5832	273	2	(	(	PUNCT
ejpam-5832	273	3	i	i	NOUN
ejpam-5832	273	4	)	)	PUNCT
ejpam-5832	273	5	q∗	q∗	PROPN
ejpam-5832	273	6	⊴	⊴	ADP
ejpam-5832	273	7	v	v	NOUN
ejpam-5832	273	8	.	.	PUNCT
ejpam-5832	274	1	(	(	PUNCT
ejpam-5832	274	2	ii	ii	NOUN
ejpam-5832	274	3	)	)	PUNCT
ejpam-5832	274	4	q∗	q∗	NOUN
ejpam-5832	274	5	⊴	⊴	ADP
ejpam-5832	274	6	v	v	NOUN
ejpam-5832	274	7	.	.	PUNCT
ejpam-5832	275	1	proof	proof	NOUN
ejpam-5832	275	2	.	.	PUNCT
ejpam-5832	276	1	let	let	VERB
ejpam-5832	276	2	q	q	NOUN
ejpam-5832	276	3	=	=	PRON
ejpam-5832	276	4	{	{	PUNCT
ejpam-5832	276	5	(	(	PUNCT
ejpam-5832	276	6	ϵ	ϵ	NOUN
ejpam-5832	276	7	,	,	PUNCT
ejpam-5832	276	8	µq(ϵ	µq(ϵ	NUM
ejpam-5832	276	9	)	)	PUNCT
ejpam-5832	276	10	,	,	PUNCT
ejpam-5832	276	11	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	276	12	)	)	PUNCT
ejpam-5832	276	13	)	)	PUNCT
ejpam-5832	276	14	:	:	PUNCT
ejpam-5832	277	1	ϵ	ϵ	X
ejpam-5832	277	2	∈	∈	PROPN
ejpam-5832	277	3	v	v	PROPN
ejpam-5832	277	4	}	}	PUNCT
ejpam-5832	277	5	be	be	AUX
ejpam-5832	277	6	a	a	DET
ejpam-5832	277	7	q	q	NOUN
ejpam-5832	277	8	-	-	PUNCT
ejpam-5832	277	9	rofnsg	rofnsg	NOUN
ejpam-5832	277	10	of	of	ADP
ejpam-5832	277	11	v	v	NOUN
ejpam-5832	277	12	.	.	PUNCT
ejpam-5832	278	1	then	then	ADV
ejpam-5832	278	2	(	(	PUNCT
ejpam-5832	278	3	µq(λ	µq(λ	NOUN
ejpam-5832	278	4	)	)	PUNCT
ejpam-5832	278	5	)	)	PUNCT
ejpam-5832	279	1	q	q	PUNCT
ejpam-5832	279	2	=(	=(	NOUN
ejpam-5832	279	3	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	279	4	−1	−1	NOUN
ejpam-5832	279	5	)	)	PUNCT
ejpam-5832	279	6	)	)	PUNCT
ejpam-5832	280	1	q	q	PROPN
ejpam-5832	280	2	and	and	CCONJ
ejpam-5832	280	3	(	(	PUNCT
ejpam-5832	280	4	νq(λ	νq(λ	NUM
ejpam-5832	280	5	)	)	PUNCT
ejpam-5832	280	6	)	)	PUNCT
ejpam-5832	281	1	q	q	NOUN
ejpam-5832	282	1	=	=	PUNCT
ejpam-5832	282	2	(	(	PUNCT
ejpam-5832	282	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	282	4	−1	−1	NOUN
ejpam-5832	282	5	)	)	PUNCT
ejpam-5832	282	6	)	)	PUNCT
ejpam-5832	282	7	q	q	PROPN
ejpam-5832	282	8	for	for	ADP
ejpam-5832	282	9	all	all	DET
ejpam-5832	282	10	λ	λ	PROPN
ejpam-5832	282	11	,	,	PUNCT
ejpam-5832	282	12	ϵ	ϵ	PROPN
ejpam-5832	282	13	∈	∈	PROPN
ejpam-5832	282	14	v	v	NOUN
ejpam-5832	282	15	.	.	PUNCT
ejpam-5832	283	1	(	(	PUNCT
ejpam-5832	283	2	i	i	NOUN
ejpam-5832	283	3	)	)	PUNCT
ejpam-5832	283	4	let	let	VERB
ejpam-5832	283	5	ϵ	ϵ	PROPN
ejpam-5832	283	6	∈	∈	PROPN
ejpam-5832	283	7	v	v	NOUN
ejpam-5832	283	8	and	and	CCONJ
ejpam-5832	283	9	λ	λ	PROPN
ejpam-5832	283	10	∈	∈	NOUN
ejpam-5832	283	11	q∗	q∗	NOUN
ejpam-5832	283	12	,	,	PUNCT
ejpam-5832	283	13	then	then	ADV
ejpam-5832	283	14	(	(	PUNCT
ejpam-5832	283	15	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	283	16	−1	−1	NOUN
ejpam-5832	283	17	)	)	PUNCT
ejpam-5832	283	18	)	)	PUNCT
ejpam-5832	284	1	q	q	X
ejpam-5832	284	2	=	=	PUNCT
ejpam-5832	284	3	(	(	PUNCT
ejpam-5832	284	4	µq(λ	µq(λ	NOUN
ejpam-5832	284	5	)	)	PUNCT
ejpam-5832	284	6	)	)	PUNCT
ejpam-5832	285	1	q	q	NOUN
ejpam-5832	285	2	(	(	PUNCT
ejpam-5832	285	3	sinceq	sinceq	NOUN
ejpam-5832	285	4	is	be	AUX
ejpam-5832	285	5	a	a	DET
ejpam-5832	285	6	q	q	NOUN
ejpam-5832	285	7	−rofnsgof	−rofnsgof	NOUN
ejpam-5832	285	8	v	v	NOUN
ejpam-5832	285	9	)	)	PUNCT
ejpam-5832	285	10	>	>	X
ejpam-5832	285	11	0	0	PUNCT
ejpam-5832	286	1	(	(	PUNCT
ejpam-5832	286	2	since	since	SCONJ
ejpam-5832	286	3	λ	λ	PROPN
ejpam-5832	286	4	∈	∈	PROPN
ejpam-5832	286	5	q∗	q∗	NOUN
ejpam-5832	286	6	)	)	PUNCT
ejpam-5832	286	7	similarly	similarly	ADV
ejpam-5832	286	8	,	,	PUNCT
ejpam-5832	286	9	it	it	PRON
ejpam-5832	286	10	can	can	AUX
ejpam-5832	286	11	be	be	AUX
ejpam-5832	286	12	derived	derive	VERB
ejpam-5832	286	13	,	,	PUNCT
ejpam-5832	286	14	(	(	PUNCT
ejpam-5832	286	15	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	286	16	−1	−1	NOUN
ejpam-5832	286	17	)	)	PUNCT
ejpam-5832	286	18	)	)	PUNCT
ejpam-5832	287	1	q	q	X
ejpam-5832	287	2	<	<	X
ejpam-5832	287	3	1	1	NUM
ejpam-5832	287	4	for	for	ADP
ejpam-5832	287	5	all	all	DET
ejpam-5832	287	6	ϵ	ϵ	PART
ejpam-5832	287	7	∈	∈	PROPN
ejpam-5832	287	8	v	v	NOUN
ejpam-5832	287	9	and	and	CCONJ
ejpam-5832	287	10	λ	λ	X
ejpam-5832	287	11	∈	∈	PROPN
ejpam-5832	287	12	q∗.	q∗.	NOUN
ejpam-5832	287	13	therefore	therefore	ADV
ejpam-5832	287	14	,	,	PUNCT
ejpam-5832	287	15	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	287	16	∈	∈	NOUN
ejpam-5832	287	17	q∗	q∗	NOUN
ejpam-5832	287	18	for	for	ADP
ejpam-5832	287	19	all	all	DET
ejpam-5832	287	20	ϵ	ϵ	PART
ejpam-5832	287	21	∈	∈	PROPN
ejpam-5832	287	22	v	v	NOUN
ejpam-5832	287	23	and	and	CCONJ
ejpam-5832	287	24	λ	λ	X
ejpam-5832	287	25	∈	∈	PROPN
ejpam-5832	287	26	q∗.	q∗.	NOUN
ejpam-5832	287	27	hence	hence	ADV
ejpam-5832	287	28	,	,	PUNCT
ejpam-5832	287	29	q∗	q∗	NOUN
ejpam-5832	287	30	⊴	⊴	ADP
ejpam-5832	287	31	v	v	NOUN
ejpam-5832	287	32	.	.	PUNCT
ejpam-5832	288	1	(	(	PUNCT
ejpam-5832	288	2	ii	ii	X
ejpam-5832	288	3	)	)	PUNCT
ejpam-5832	288	4	the	the	DET
ejpam-5832	288	5	proof	proof	NOUN
ejpam-5832	288	6	is	be	AUX
ejpam-5832	288	7	analogous	analogous	ADJ
ejpam-5832	288	8	to	to	ADP
ejpam-5832	288	9	(	(	PUNCT
ejpam-5832	288	10	i	i	NOUN
ejpam-5832	288	11	)	)	PUNCT
ejpam-5832	288	12	.	.	PUNCT
ejpam-5832	289	1	in	in	ADP
ejpam-5832	289	2	the	the	DET
ejpam-5832	289	3	following	follow	VERB
ejpam-5832	289	4	example	example	NOUN
ejpam-5832	289	5	,	,	PUNCT
ejpam-5832	289	6	the	the	DET
ejpam-5832	289	7	contrary	contrary	NOUN
ejpam-5832	289	8	of	of	ADP
ejpam-5832	289	9	theorem	theorem	ADJ
ejpam-5832	289	10	9	9	NUM
ejpam-5832	289	11	is	be	AUX
ejpam-5832	289	12	proved	prove	VERB
ejpam-5832	289	13	to	to	PART
ejpam-5832	289	14	be	be	AUX
ejpam-5832	289	15	false	false	ADJ
ejpam-5832	289	16	.	.	PUNCT
ejpam-5832	289	17	example	example	NOUN
ejpam-5832	290	1	2	2	NUM
ejpam-5832	290	2	.	.	PUNCT
ejpam-5832	290	3	let	let	VERB
ejpam-5832	290	4	us	we	PRON
ejpam-5832	290	5	design	design	VERB
ejpam-5832	290	6	a	a	DET
ejpam-5832	290	7	q	q	NOUN
ejpam-5832	290	8	-	-	PUNCT
ejpam-5832	290	9	rofsg	rofsg	VERB
ejpam-5832	290	10	q	q	NOUN
ejpam-5832	290	11	of	of	ADP
ejpam-5832	290	12	s3	s3	PROPN
ejpam-5832	290	13	=	=	SYM
ejpam-5832	290	14	{	{	PUNCT
ejpam-5832	290	15	e	e	NOUN
ejpam-5832	290	16	,	,	PUNCT
ejpam-5832	290	17	λ	λ	PROPN
ejpam-5832	290	18	,	,	PUNCT
ejpam-5832	290	19	κ	κ	PROPN
ejpam-5832	290	20	,	,	PUNCT
ejpam-5832	290	21	κ2	κ2	NOUN
ejpam-5832	290	22	,	,	PUNCT
ejpam-5832	290	23	λκ	λκ	PRON
ejpam-5832	290	24	,	,	PUNCT
ejpam-5832	290	25	λκ2	λκ2	PROPN
ejpam-5832	290	26	}	}	PUNCT
ejpam-5832	290	27	as	as	SCONJ
ejpam-5832	290	28	follows	follow	VERB
ejpam-5832	290	29	;	;	PUNCT
ejpam-5832	290	30	q	q	SYM
ejpam-5832	290	31	=	=	SYM
ejpam-5832	290	32	{	{	PUNCT
ejpam-5832	290	33	(	(	PUNCT
ejpam-5832	290	34	e	e	NOUN
ejpam-5832	290	35	,	,	PUNCT
ejpam-5832	290	36	1	1	NUM
ejpam-5832	290	37	,	,	PUNCT
ejpam-5832	290	38	0	0	NUM
ejpam-5832	290	39	)	)	PUNCT
ejpam-5832	290	40	,	,	PUNCT
ejpam-5832	290	41	(	(	PUNCT
ejpam-5832	290	42	λ	λ	NOUN
ejpam-5832	290	43	,	,	PUNCT
ejpam-5832	290	44	0.9	0.9	NUM
ejpam-5832	290	45	,	,	PUNCT
ejpam-5832	290	46	0.5)(κ	0.5)(κ	NOUN
ejpam-5832	290	47	,	,	PUNCT
ejpam-5832	290	48	0.7	0.7	NUM
ejpam-5832	290	49	,	,	PUNCT
ejpam-5832	290	50	0.8	0.8	NUM
ejpam-5832	290	51	)	)	PUNCT
ejpam-5832	290	52	,	,	PUNCT
ejpam-5832	290	53	(	(	PUNCT
ejpam-5832	290	54	κ2	κ2	NOUN
ejpam-5832	290	55	,	,	PUNCT
ejpam-5832	290	56	0.7	0.7	NUM
ejpam-5832	290	57	,	,	PUNCT
ejpam-5832	290	58	0.8	0.8	NUM
ejpam-5832	290	59	)	)	PUNCT
ejpam-5832	290	60	,	,	PUNCT
ejpam-5832	290	61	(	(	PUNCT
ejpam-5832	290	62	λκ	λκ	INTJ
ejpam-5832	290	63	,	,	PUNCT
ejpam-5832	290	64	0.7	0.7	NUM
ejpam-5832	290	65	,	,	PUNCT
ejpam-5832	290	66	0.8	0.8	NUM
ejpam-5832	290	67	)	)	PUNCT
ejpam-5832	290	68	,	,	PUNCT
ejpam-5832	290	69	(	(	PUNCT
ejpam-5832	290	70	λκ2	λκ2	X
ejpam-5832	290	71	,	,	PUNCT
ejpam-5832	290	72	0.7	0.7	NUM
ejpam-5832	290	73	,	,	PUNCT
ejpam-5832	290	74	0.8	0.8	NUM
ejpam-5832	290	75	)	)	PUNCT
ejpam-5832	290	76	}	}	PUNCT
ejpam-5832	290	77	.	.	PUNCT
ejpam-5832	291	1	then	then	ADV
ejpam-5832	291	2	q∗	q∗	NOUN
ejpam-5832	291	3	=	=	SYM
ejpam-5832	291	4	s3	s3	PROPN
ejpam-5832	291	5	and	and	CCONJ
ejpam-5832	291	6	q∗	q∗	NOUN
ejpam-5832	291	7	=	=	SYM
ejpam-5832	291	8	e	e	NOUN
ejpam-5832	291	9	are	be	AUX
ejpam-5832	291	10	normal	normal	ADJ
ejpam-5832	291	11	in	in	ADP
ejpam-5832	291	12	s3	s3	PROPN
ejpam-5832	291	13	but	but	CCONJ
ejpam-5832	291	14	q	q	NOUN
ejpam-5832	291	15	is	be	AUX
ejpam-5832	291	16	not	not	PART
ejpam-5832	291	17	a	a	DET
ejpam-5832	291	18	q	q	NOUN
ejpam-5832	291	19	-	-	PUNCT
ejpam-5832	291	20	rofnsg	rofnsg	NOUN
ejpam-5832	291	21	of	of	ADP
ejpam-5832	291	22	s3	s3	PROPN
ejpam-5832	291	23	because	because	SCONJ
ejpam-5832	291	24	µq	µq	PROPN
ejpam-5832	291	25	(	(	PUNCT
ejpam-5832	291	26	(	(	PUNCT
ejpam-5832	291	27	κ)(λκ2	κ)(λκ2	X
ejpam-5832	291	28	)	)	PUNCT
ejpam-5832	291	29	)	)	PUNCT
ejpam-5832	292	1	=	=	SYM
ejpam-5832	292	2	µq(λκ	µq(λκ	PROPN
ejpam-5832	292	3	)	)	PUNCT
ejpam-5832	292	4	=	=	PUNCT
ejpam-5832	293	1	0.7	0.7	NUM
ejpam-5832	293	2	̸=	̸=	PROPN
ejpam-5832	293	3	0.9	0.9	NUM
ejpam-5832	293	4	=	=	PUNCT
ejpam-5832	293	5	µq(λ	µq(λ	X
ejpam-5832	293	6	)	)	PUNCT
ejpam-5832	293	7	=	=	SYM
ejpam-5832	293	8	µq	µq	PROPN
ejpam-5832	293	9	(	(	PUNCT
ejpam-5832	293	10	(	(	PUNCT
ejpam-5832	293	11	λκ2)(κ	λκ2)(κ	PROPN
ejpam-5832	293	12	)	)	PUNCT
ejpam-5832	293	13	)	)	PUNCT
ejpam-5832	293	14	.	.	PUNCT
ejpam-5832	294	1	a.	a.	NOUN
ejpam-5832	294	2	razzaque	razzaque	PROPN
ejpam-5832	294	3	/	/	SYM
ejpam-5832	294	4	eur	eur	NOUN
ejpam-5832	294	5	.	.	PUNCT
ejpam-5832	295	1	j.	j.	PROPN
ejpam-5832	295	2	pure	pure	PROPN
ejpam-5832	295	3	appl	appl	PROPN
ejpam-5832	295	4	.	.	PROPN
ejpam-5832	295	5	math	math	PROPN
ejpam-5832	295	6	,	,	PUNCT
ejpam-5832	295	7	18	18	NUM
ejpam-5832	295	8	(	(	PUNCT
ejpam-5832	295	9	3	3	NUM
ejpam-5832	295	10	)	)	PUNCT
ejpam-5832	295	11	(	(	PUNCT
ejpam-5832	295	12	2025	2025	NUM
ejpam-5832	295	13	)	)	PUNCT
ejpam-5832	295	14	,	,	PUNCT
ejpam-5832	295	15	5832	5832	NUM
ejpam-5832	295	16	10	10	NUM
ejpam-5832	295	17	of	of	ADP
ejpam-5832	295	18	21	21	NUM
ejpam-5832	295	19	4	4	NUM
ejpam-5832	295	20	.	.	PUNCT
ejpam-5832	296	1	q	q	X
ejpam-5832	296	2	-	-	PUNCT
ejpam-5832	296	3	rung	rung	ADJ
ejpam-5832	296	4	orthopair	orthopair	NOUN
ejpam-5832	296	5	fuzzy	fuzzy	ADJ
ejpam-5832	296	6	normal	normal	ADJ
ejpam-5832	296	7	subgroup	subgroup	NOUN
ejpam-5832	296	8	of	of	ADP
ejpam-5832	296	9	a	a	DET
ejpam-5832	296	10	q	q	ADJ
ejpam-5832	296	11	-	-	PUNCT
ejpam-5832	296	12	rung	rung	ADJ
ejpam-5832	296	13	orthopair	orthopair	ADJ
ejpam-5832	296	14	fuzzy	fuzzy	ADJ
ejpam-5832	296	15	subgroup	subgroup	NOUN
ejpam-5832	296	16	this	this	DET
ejpam-5832	296	17	section	section	NOUN
ejpam-5832	296	18	introduces	introduce	VERB
ejpam-5832	296	19	the	the	DET
ejpam-5832	296	20	notion	notion	NOUN
ejpam-5832	296	21	of	of	ADP
ejpam-5832	296	22	q	q	NOUN
ejpam-5832	296	23	-	-	PUNCT
ejpam-5832	296	24	rofnsg	rofnsg	NOUN
ejpam-5832	296	25	of	of	ADP
ejpam-5832	296	26	a	a	DET
ejpam-5832	296	27	q	q	NOUN
ejpam-5832	296	28	-	-	PUNCT
ejpam-5832	296	29	rofsg	rofsg	NOUN
ejpam-5832	296	30	.	.	PUNCT
ejpam-5832	297	1	in	in	ADP
ejpam-5832	297	2	addition	addition	NOUN
ejpam-5832	297	3	,	,	PUNCT
ejpam-5832	297	4	an	an	DET
ejpam-5832	297	5	indepth	indepth	ADJ
ejpam-5832	297	6	study	study	NOUN
ejpam-5832	297	7	of	of	ADP
ejpam-5832	297	8	this	this	DET
ejpam-5832	297	9	concept	concept	NOUN
ejpam-5832	297	10	is	be	AUX
ejpam-5832	297	11	provided	provide	VERB
ejpam-5832	297	12	.	.	PUNCT
ejpam-5832	298	1	definition	definition	NOUN
ejpam-5832	298	2	10	10	NUM
ejpam-5832	298	3	.	.	PUNCT
ejpam-5832	299	1	let	let	VERB
ejpam-5832	299	2	q	q	NOUN
ejpam-5832	300	1	and	and	CCONJ
ejpam-5832	300	2	p	p	NOUN
ejpam-5832	300	3	be	be	AUX
ejpam-5832	300	4	two	two	NUM
ejpam-5832	300	5	q	q	NOUN
ejpam-5832	300	6	-	-	PUNCT
ejpam-5832	300	7	rofsgs	rofsg	NOUN
ejpam-5832	300	8	of	of	ADP
ejpam-5832	300	9	v	v	PRON
ejpam-5832	300	10	such	such	ADJ
ejpam-5832	300	11	that	that	DET
ejpam-5832	300	12	q	q	NOUN
ejpam-5832	300	13	⊆	⊆	NUM
ejpam-5832	300	14	p	p	NOUN
ejpam-5832	300	15	.	.	PUNCT
ejpam-5832	301	1	then	then	ADV
ejpam-5832	301	2	q	q	X
ejpam-5832	301	3	is	be	AUX
ejpam-5832	301	4	a	a	DET
ejpam-5832	301	5	q	q	NOUN
ejpam-5832	301	6	-	-	PUNCT
ejpam-5832	301	7	rofnsg	rofnsg	NOUN
ejpam-5832	301	8	of	of	ADP
ejpam-5832	301	9	p	p	PRON
ejpam-5832	301	10	if	if	SCONJ
ejpam-5832	301	11	(	(	PUNCT
ejpam-5832	301	12	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	301	13	−1	−1	NOUN
ejpam-5832	301	14	)	)	PUNCT
ejpam-5832	301	15	)	)	PUNCT
ejpam-5832	302	1	q	q	PROPN
ejpam-5832	302	2	≥	≥	PROPN
ejpam-5832	302	3	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	302	4	,	,	PUNCT
ejpam-5832	302	5	(	(	PUNCT
ejpam-5832	302	6	µp	µp	PROPN
ejpam-5832	302	7	(	(	PUNCT
ejpam-5832	302	8	ϵ))q	ϵ))q	NOUN
ejpam-5832	302	9	}	}	PUNCT
ejpam-5832	302	10	and	and	CCONJ
ejpam-5832	302	11	(	(	PUNCT
ejpam-5832	302	12	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	302	13	−1	−1	NOUN
ejpam-5832	302	14	)	)	PUNCT
ejpam-5832	302	15	)	)	PUNCT
ejpam-5832	303	1	q	q	PROPN
ejpam-5832	303	2	≤	≤	NUM
ejpam-5832	303	3	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	303	4	,	,	PUNCT
ejpam-5832	303	5	(	(	PUNCT
ejpam-5832	303	6	νp	νp	X
ejpam-5832	303	7	(	(	PUNCT
ejpam-5832	303	8	ϵ))q	ϵ))q	NOUN
ejpam-5832	303	9	}	}	PUNCT
ejpam-5832	303	10	for	for	ADP
ejpam-5832	303	11	all	all	DET
ejpam-5832	303	12	λ	λ	PROPN
ejpam-5832	303	13	,	,	PUNCT
ejpam-5832	303	14	ϵ	ϵ	PROPN
ejpam-5832	303	15	∈	∈	PROPN
ejpam-5832	303	16	v	v	NOUN
ejpam-5832	303	17	.	.	PUNCT
ejpam-5832	304	1	the	the	DET
ejpam-5832	304	2	result	result	NOUN
ejpam-5832	304	3	below	below	ADV
ejpam-5832	304	4	demonstrates	demonstrate	VERB
ejpam-5832	304	5	a	a	DET
ejpam-5832	304	6	necessary	necessary	ADJ
ejpam-5832	304	7	condition	condition	NOUN
ejpam-5832	304	8	for	for	ADP
ejpam-5832	304	9	a	a	DET
ejpam-5832	304	10	q	q	ADJ
ejpam-5832	304	11	-	-	PUNCT
ejpam-5832	304	12	rofsg	rofsg	NOUN
ejpam-5832	304	13	q	q	NOUN
ejpam-5832	304	14	that	that	PRON
ejpam-5832	304	15	is	be	AUX
ejpam-5832	304	16	a	a	DET
ejpam-5832	304	17	subset	subset	NOUN
ejpam-5832	304	18	of	of	ADP
ejpam-5832	304	19	a	a	DET
ejpam-5832	304	20	q	q	NOUN
ejpam-5832	304	21	-	-	PUNCT
ejpam-5832	304	22	rofsg	rofsg	VERB
ejpam-5832	304	23	p	p	NOUN
ejpam-5832	304	24	to	to	PART
ejpam-5832	304	25	be	be	AUX
ejpam-5832	304	26	a	a	DET
ejpam-5832	304	27	q	q	NOUN
ejpam-5832	304	28	-	-	PUNCT
ejpam-5832	304	29	rofnsg	rofnsg	NOUN
ejpam-5832	304	30	of	of	ADP
ejpam-5832	304	31	p	p	PROPN
ejpam-5832	304	32	.	.	PUNCT
ejpam-5832	305	1	theorem	theorem	ADJ
ejpam-5832	305	2	10	10	NUM
ejpam-5832	305	3	.	.	PUNCT
ejpam-5832	306	1	assume	assume	VERB
ejpam-5832	306	2	that	that	SCONJ
ejpam-5832	306	3	q	q	PROPN
ejpam-5832	307	1	and	and	CCONJ
ejpam-5832	307	2	p	p	NOUN
ejpam-5832	307	3	are	be	AUX
ejpam-5832	307	4	q	q	NOUN
ejpam-5832	307	5	-	-	PUNCT
ejpam-5832	307	6	rofsgs	rofsg	NOUN
ejpam-5832	307	7	of	of	ADP
ejpam-5832	307	8	v	v	PRON
ejpam-5832	307	9	such	such	DET
ejpam-5832	307	10	that	that	DET
ejpam-5832	307	11	q	q	NOUN
ejpam-5832	307	12	is	be	AUX
ejpam-5832	307	13	q	q	NOUN
ejpam-5832	307	14	-	-	PUNCT
ejpam-5832	307	15	rofnsg	rofnsg	NOUN
ejpam-5832	307	16	of	of	ADP
ejpam-5832	307	17	p	p	PROPN
ejpam-5832	307	18	.	.	PUNCT
ejpam-5832	308	1	then	then	ADV
ejpam-5832	308	2	q∗	q∗	VERB
ejpam-5832	308	3	⊴	⊴	ADP
ejpam-5832	308	4	p	p	X
ejpam-5832	308	5	∗.	∗.	ADJ
ejpam-5832	308	6	proof	proof	NOUN
ejpam-5832	308	7	.	.	PUNCT
ejpam-5832	309	1	let	let	VERB
ejpam-5832	309	2	λ	λ	X
ejpam-5832	309	3	∈	∈	NOUN
ejpam-5832	309	4	q∗	q∗	NOUN
ejpam-5832	309	5	and	and	CCONJ
ejpam-5832	309	6	ϵ	ϵ	ADP
ejpam-5832	309	7	∈	∈	PROPN
ejpam-5832	309	8	p	p	NOUN
ejpam-5832	309	9	∗	∗	NOUN
ejpam-5832	309	10	,	,	PUNCT
ejpam-5832	309	11	then	then	ADV
ejpam-5832	309	12	(	(	PUNCT
ejpam-5832	309	13	µq(λ	µq(λ	NOUN
ejpam-5832	309	14	)	)	PUNCT
ejpam-5832	309	15	)	)	PUNCT
ejpam-5832	310	1	q	q	NOUN
ejpam-5832	310	2	,	,	PUNCT
ejpam-5832	310	3	(	(	PUNCT
ejpam-5832	310	4	µp	µp	PROPN
ejpam-5832	310	5	(	(	PUNCT
ejpam-5832	310	6	ϵ	ϵ	NOUN
ejpam-5832	310	7	)	)	PUNCT
ejpam-5832	310	8	)	)	PUNCT
ejpam-5832	311	1	q	q	X
ejpam-5832	311	2	>	>	X
ejpam-5832	311	3	0	0	PUNCT
ejpam-5832	312	1	and	and	CCONJ
ejpam-5832	312	2	(	(	PUNCT
ejpam-5832	312	3	νq(λ	νq(λ	NUM
ejpam-5832	312	4	)	)	PUNCT
ejpam-5832	312	5	)	)	PUNCT
ejpam-5832	313	1	q	q	NOUN
ejpam-5832	313	2	,	,	PUNCT
ejpam-5832	313	3	(	(	PUNCT
ejpam-5832	313	4	νp	νp	X
ejpam-5832	313	5	(	(	PUNCT
ejpam-5832	313	6	ϵ	ϵ	NOUN
ejpam-5832	313	7	)	)	PUNCT
ejpam-5832	313	8	)	)	PUNCT
ejpam-5832	314	1	q	q	X
ejpam-5832	314	2	<	<	X
ejpam-5832	314	3	1	1	X
ejpam-5832	314	4	.	.	PUNCT
ejpam-5832	314	5	therefore	therefore	ADV
ejpam-5832	314	6	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	314	7	,	,	PUNCT
ejpam-5832	314	8	(	(	PUNCT
ejpam-5832	314	9	µp	µp	PROPN
ejpam-5832	314	10	(	(	PUNCT
ejpam-5832	314	11	ϵ))q	ϵ))q	NOUN
ejpam-5832	314	12	}	}	PUNCT
ejpam-5832	314	13	>	>	X
ejpam-5832	314	14	0	0	PUNCT
ejpam-5832	314	15	and	and	CCONJ
ejpam-5832	314	16	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	314	17	,	,	PUNCT
ejpam-5832	314	18	(	(	PUNCT
ejpam-5832	314	19	νp	νp	X
ejpam-5832	314	20	(	(	PUNCT
ejpam-5832	314	21	ϵ))q	ϵ))q	NOUN
ejpam-5832	314	22	}	}	PUNCT
ejpam-5832	314	23	<	<	X
ejpam-5832	314	24	1	1	X
ejpam-5832	314	25	.	.	PUNCT
ejpam-5832	315	1	consequently	consequently	ADV
ejpam-5832	315	2	,	,	PUNCT
ejpam-5832	315	3	we	we	PRON
ejpam-5832	315	4	yield	yield	VERB
ejpam-5832	315	5	(	(	PUNCT
ejpam-5832	315	6	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	315	7	−1	−1	NOUN
ejpam-5832	315	8	)	)	PUNCT
ejpam-5832	315	9	)	)	PUNCT
ejpam-5832	316	1	q	q	PROPN
ejpam-5832	317	1	≥	≥	PROPN
ejpam-5832	317	2	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	317	3	,	,	PUNCT
ejpam-5832	317	4	(	(	PUNCT
ejpam-5832	317	5	µp	µp	PROPN
ejpam-5832	317	6	(	(	PUNCT
ejpam-5832	317	7	ϵ))q	ϵ))q	NOUN
ejpam-5832	317	8	}	}	PUNCT
ejpam-5832	317	9	>	>	X
ejpam-5832	317	10	0	0	PUNCT
ejpam-5832	317	11	and	and	CCONJ
ejpam-5832	317	12	(	(	PUNCT
ejpam-5832	317	13	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	317	14	−1	−1	NOUN
ejpam-5832	317	15	)	)	PUNCT
ejpam-5832	317	16	)	)	PUNCT
ejpam-5832	317	17	q	q	PROPN
ejpam-5832	317	18	≤	≤	NUM
ejpam-5832	317	19	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	317	20	,	,	PUNCT
ejpam-5832	317	21	(	(	PUNCT
ejpam-5832	317	22	νp	νp	X
ejpam-5832	317	23	(	(	PUNCT
ejpam-5832	317	24	ϵ))q	ϵ))q	NOUN
ejpam-5832	317	25	}	}	PUNCT
ejpam-5832	317	26	<	<	X
ejpam-5832	317	27	1	1	NUM
ejpam-5832	317	28	,	,	PUNCT
ejpam-5832	317	29	both	both	PRON
ejpam-5832	317	30	of	of	ADP
ejpam-5832	317	31	which	which	PRON
ejpam-5832	317	32	indicate	indicate	VERB
ejpam-5832	317	33	that	that	SCONJ
ejpam-5832	317	34	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	317	35	∈	∈	PROPN
ejpam-5832	317	36	q∗.	q∗.	NOUN
ejpam-5832	317	37	hence	hence	ADV
ejpam-5832	317	38	,	,	PUNCT
ejpam-5832	317	39	q∗	q∗	PROPN
ejpam-5832	317	40	⊴	⊴	ADP
ejpam-5832	317	41	p	p	DET
ejpam-5832	317	42	∗.	∗.	PROPN
ejpam-5832	317	43	theorem	theorem	NOUN
ejpam-5832	317	44	11	11	NUM
ejpam-5832	317	45	.	.	PUNCT
ejpam-5832	317	46	suppose	suppose	VERB
ejpam-5832	317	47	that	that	SCONJ
ejpam-5832	317	48	q	q	PROPN
ejpam-5832	317	49	and	and	CCONJ
ejpam-5832	317	50	p	p	NOUN
ejpam-5832	317	51	are	be	AUX
ejpam-5832	317	52	q	q	NOUN
ejpam-5832	317	53	-	-	PUNCT
ejpam-5832	317	54	rofsgs	rofsg	NOUN
ejpam-5832	317	55	of	of	ADP
ejpam-5832	317	56	v	v	NOUN
ejpam-5832	317	57	and	and	CCONJ
ejpam-5832	317	58	q	q	NOUN
ejpam-5832	317	59	⊆	⊆	NUM
ejpam-5832	317	60	p	p	NOUN
ejpam-5832	317	61	.	.	PUNCT
ejpam-5832	318	1	then	then	ADV
ejpam-5832	318	2	q	q	X
ejpam-5832	318	3	is	be	AUX
ejpam-5832	318	4	a	a	DET
ejpam-5832	318	5	q	q	NOUN
ejpam-5832	318	6	-	-	PUNCT
ejpam-5832	318	7	rofnsg	rofnsg	NOUN
ejpam-5832	318	8	of	of	ADP
ejpam-5832	318	9	p	p	NOUN
ejpam-5832	318	10	if	if	SCONJ
ejpam-5832	319	1	and	and	CCONJ
ejpam-5832	319	2	only	only	ADV
ejpam-5832	319	3	if	if	SCONJ
ejpam-5832	319	4	(	(	PUNCT
ejpam-5832	319	5	µq(λϵ	µq(λϵ	PROPN
ejpam-5832	319	6	)	)	PUNCT
ejpam-5832	319	7	)	)	PUNCT
ejpam-5832	320	1	q	q	PROPN
ejpam-5832	320	2	≥	≥	PROPN
ejpam-5832	320	3	min{(µq(ϵλ))q	min{(µq(ϵλ))q	PROPN
ejpam-5832	320	4	,	,	PUNCT
ejpam-5832	320	5	(	(	PUNCT
ejpam-5832	320	6	µp	µp	PROPN
ejpam-5832	320	7	(	(	PUNCT
ejpam-5832	320	8	λ))q	λ))q	NOUN
ejpam-5832	320	9	}	}	PUNCT
ejpam-5832	320	10	and	and	CCONJ
ejpam-5832	320	11	(	(	PUNCT
ejpam-5832	320	12	νq(λϵ	νq(λϵ	PROPN
ejpam-5832	320	13	)	)	PUNCT
ejpam-5832	320	14	)	)	PUNCT
ejpam-5832	321	1	q	q	PROPN
ejpam-5832	321	2	≤	≤	ADJ
ejpam-5832	321	3	max{(νq(ϵλ))q	max{(νq(ϵλ))q	PROPN
ejpam-5832	321	4	,	,	PUNCT
ejpam-5832	321	5	(	(	PUNCT
ejpam-5832	321	6	νp	νp	X
ejpam-5832	321	7	(	(	PUNCT
ejpam-5832	321	8	λ))q	λ))q	NOUN
ejpam-5832	321	9	}	}	PUNCT
ejpam-5832	321	10	for	for	ADP
ejpam-5832	321	11	all	all	DET
ejpam-5832	321	12	ϵ	ϵ	NOUN
ejpam-5832	321	13	,	,	PUNCT
ejpam-5832	321	14	λ	λ	PROPN
ejpam-5832	321	15	∈	∈	NOUN
ejpam-5832	321	16	v	v	NOUN
ejpam-5832	321	17	.	.	PUNCT
ejpam-5832	322	1	proof	proof	NOUN
ejpam-5832	322	2	.	.	PUNCT
ejpam-5832	323	1	letq	letq	ADJ
ejpam-5832	323	2	be	be	VERB
ejpam-5832	323	3	a	a	DET
ejpam-5832	323	4	q	q	NOUN
ejpam-5832	323	5	-	-	PUNCT
ejpam-5832	323	6	rofnsg	rofnsg	NOUN
ejpam-5832	323	7	of	of	ADP
ejpam-5832	323	8	p	p	PROPN
ejpam-5832	323	9	,	,	PUNCT
ejpam-5832	323	10	then	then	ADV
ejpam-5832	323	11	(	(	PUNCT
ejpam-5832	323	12	µq(λϵ	µq(λϵ	PROPN
ejpam-5832	323	13	)	)	PUNCT
ejpam-5832	323	14	)	)	PUNCT
ejpam-5832	323	15	q	q	NOUN
ejpam-5832	324	1	=	=	PUNCT
ejpam-5832	324	2	(	(	PUNCT
ejpam-5832	324	3	µq(λϵλλ	µq(λϵλλ	NOUN
ejpam-5832	324	4	−1	−1	NOUN
ejpam-5832	324	5	)	)	PUNCT
ejpam-5832	324	6	)	)	PUNCT
ejpam-5832	325	1	q	q	PROPN
ejpam-5832	325	2	≥	≥	PROPN
ejpam-5832	325	3	min{(µq(ϵλ))q	min{(µq(ϵλ))q	PROPN
ejpam-5832	325	4	,	,	PUNCT
ejpam-5832	325	5	(	(	PUNCT
ejpam-5832	325	6	µp	µp	PROPN
ejpam-5832	325	7	(	(	PUNCT
ejpam-5832	325	8	λ))q	λ))q	NOUN
ejpam-5832	325	9	}	}	PUNCT
ejpam-5832	325	10	and	and	CCONJ
ejpam-5832	325	11	(	(	PUNCT
ejpam-5832	325	12	νq(λϵ	νq(λϵ	PROPN
ejpam-5832	325	13	)	)	PUNCT
ejpam-5832	325	14	)	)	PUNCT
ejpam-5832	326	1	q	q	NOUN
ejpam-5832	327	1	=	=	PUNCT
ejpam-5832	327	2	(	(	PUNCT
ejpam-5832	327	3	νq(λϵλλ	νq(λϵλλ	NOUN
ejpam-5832	327	4	−1	−1	NOUN
ejpam-5832	327	5	)	)	PUNCT
ejpam-5832	327	6	)	)	PUNCT
ejpam-5832	328	1	q	q	PROPN
ejpam-5832	328	2	≤	≤	PROPN
ejpam-5832	328	3	max{(νq(ϵλ))q	max{(νq(ϵλ))q	PROPN
ejpam-5832	328	4	,	,	PUNCT
ejpam-5832	328	5	(	(	PUNCT
ejpam-5832	328	6	νp	νp	X
ejpam-5832	328	7	(	(	PUNCT
ejpam-5832	328	8	λ))q	λ))q	NOUN
ejpam-5832	328	9	}	}	PUNCT
ejpam-5832	328	10	for	for	ADP
ejpam-5832	328	11	all	all	DET
ejpam-5832	328	12	ϵ	ϵ	NOUN
ejpam-5832	328	13	,	,	PUNCT
ejpam-5832	328	14	λ	λ	PROPN
ejpam-5832	328	15	∈	∈	NOUN
ejpam-5832	328	16	v	v	NOUN
ejpam-5832	328	17	.	.	PUNCT
ejpam-5832	329	1	conversely	conversely	ADV
ejpam-5832	329	2	,	,	PUNCT
ejpam-5832	329	3	consider	consider	VERB
ejpam-5832	329	4	(	(	PUNCT
ejpam-5832	329	5	µq(λϵ	µq(λϵ	PROPN
ejpam-5832	329	6	)	)	PUNCT
ejpam-5832	329	7	)	)	PUNCT
ejpam-5832	330	1	q	q	PROPN
ejpam-5832	330	2	≥	≥	PROPN
ejpam-5832	330	3	min{(µq(ϵλ))q	min{(µq(ϵλ))q	PROPN
ejpam-5832	330	4	,	,	PUNCT
ejpam-5832	330	5	(	(	PUNCT
ejpam-5832	330	6	µp	µp	PROPN
ejpam-5832	330	7	(	(	PUNCT
ejpam-5832	330	8	λ))q	λ))q	NOUN
ejpam-5832	330	9	}	}	PUNCT
ejpam-5832	330	10	and	and	CCONJ
ejpam-5832	330	11	(	(	PUNCT
ejpam-5832	330	12	νq(λϵ	νq(λϵ	PROPN
ejpam-5832	330	13	)	)	PUNCT
ejpam-5832	330	14	)	)	PUNCT
ejpam-5832	331	1	q	q	PROPN
ejpam-5832	331	2	≤	≤	ADJ
ejpam-5832	331	3	max{(νq(ϵλ))q	max{(νq(ϵλ))q	PROPN
ejpam-5832	331	4	,	,	PUNCT
ejpam-5832	331	5	(	(	PUNCT
ejpam-5832	331	6	νp	νp	X
ejpam-5832	331	7	(	(	PUNCT
ejpam-5832	331	8	λ))q	λ))q	NOUN
ejpam-5832	331	9	}	}	PUNCT
ejpam-5832	331	10	for	for	ADP
ejpam-5832	331	11	all	all	DET
ejpam-5832	331	12	ϵ	ϵ	NOUN
ejpam-5832	331	13	,	,	PUNCT
ejpam-5832	331	14	λ	λ	PROPN
ejpam-5832	331	15	∈	∈	NOUN
ejpam-5832	331	16	v	v	NOUN
ejpam-5832	331	17	.	.	PUNCT
ejpam-5832	332	1	then	then	ADV
ejpam-5832	332	2	(	(	PUNCT
ejpam-5832	332	3	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	332	4	−1	−1	NOUN
ejpam-5832	332	5	)	)	PUNCT
ejpam-5832	332	6	)	)	PUNCT
ejpam-5832	333	1	q	q	PROPN
ejpam-5832	333	2	≥	≥	NUM
ejpam-5832	333	3	min	min	PROPN
ejpam-5832	333	4	{	{	PUNCT
ejpam-5832	333	5	(	(	PUNCT
ejpam-5832	333	6	µq(λϵ	µq(λϵ	PROPN
ejpam-5832	333	7	−1ϵ	−1ϵ	PROPN
ejpam-5832	333	8	)	)	PUNCT
ejpam-5832	333	9	)	)	PUNCT
ejpam-5832	333	10	q	q	NOUN
ejpam-5832	333	11	,	,	PUNCT
ejpam-5832	333	12	(	(	PUNCT
ejpam-5832	333	13	µp	µp	PROPN
ejpam-5832	333	14	(	(	PUNCT
ejpam-5832	333	15	ϵ	ϵ	NOUN
ejpam-5832	333	16	)	)	PUNCT
ejpam-5832	333	17	)	)	PUNCT
ejpam-5832	334	1	q	q	X
ejpam-5832	334	2	}	}	PUNCT
ejpam-5832	334	3	=	=	SYM
ejpam-5832	334	4	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	334	5	,	,	PUNCT
ejpam-5832	334	6	(	(	PUNCT
ejpam-5832	334	7	µp	µp	PROPN
ejpam-5832	334	8	(	(	PUNCT
ejpam-5832	334	9	ϵ))q	ϵ))q	NOUN
ejpam-5832	334	10	}	}	PUNCT
ejpam-5832	334	11	and	and	CCONJ
ejpam-5832	334	12	(	(	PUNCT
ejpam-5832	334	13	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	334	14	−1	−1	NOUN
ejpam-5832	334	15	)	)	PUNCT
ejpam-5832	334	16	)	)	PUNCT
ejpam-5832	335	1	q	q	PROPN
ejpam-5832	335	2	≤	≤	NUM
ejpam-5832	335	3	max	max	PROPN
ejpam-5832	335	4	{	{	PUNCT
ejpam-5832	335	5	(	(	PUNCT
ejpam-5832	335	6	νq(λϵ	νq(λϵ	PROPN
ejpam-5832	335	7	−1ϵ	−1ϵ	PROPN
ejpam-5832	335	8	)	)	PUNCT
ejpam-5832	335	9	)	)	PUNCT
ejpam-5832	335	10	q	q	NOUN
ejpam-5832	335	11	,	,	PUNCT
ejpam-5832	335	12	(	(	PUNCT
ejpam-5832	335	13	νp	νp	X
ejpam-5832	335	14	(	(	PUNCT
ejpam-5832	335	15	ϵ	ϵ	NOUN
ejpam-5832	335	16	)	)	PUNCT
ejpam-5832	335	17	)	)	PUNCT
ejpam-5832	336	1	q	q	X
ejpam-5832	336	2	}	}	PUNCT
ejpam-5832	336	3	=	=	SYM
ejpam-5832	336	4	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	336	5	,	,	PUNCT
ejpam-5832	336	6	(	(	PUNCT
ejpam-5832	336	7	νp	νp	X
ejpam-5832	336	8	(	(	PUNCT
ejpam-5832	336	9	ϵ))q	ϵ))q	NOUN
ejpam-5832	336	10	}	}	PUNCT
ejpam-5832	336	11	forall	forall	NOUN
ejpam-5832	336	12	ϵ	ϵ	NOUN
ejpam-5832	336	13	,	,	PUNCT
ejpam-5832	336	14	λ	λ	PROPN
ejpam-5832	336	15	∈	∈	PROPN
ejpam-5832	336	16	v.	v.	CCONJ
ejpam-5832	336	17	thus	thus	ADV
ejpam-5832	336	18	,	,	PUNCT
ejpam-5832	336	19	q	q	PROPN
ejpam-5832	336	20	is	be	AUX
ejpam-5832	336	21	a	a	DET
ejpam-5832	336	22	q	q	NOUN
ejpam-5832	336	23	-	-	PUNCT
ejpam-5832	336	24	rofnsg	rofnsg	NOUN
ejpam-5832	336	25	of	of	ADP
ejpam-5832	336	26	p	p	PROPN
ejpam-5832	336	27	.	.	PUNCT
ejpam-5832	337	1	theorem	theorem	PROPN
ejpam-5832	337	2	12	12	NUM
ejpam-5832	337	3	.	.	PUNCT
ejpam-5832	338	1	suppose	suppose	VERB
ejpam-5832	338	2	that	that	SCONJ
ejpam-5832	338	3	q	q	PROPN
ejpam-5832	338	4	and	and	CCONJ
ejpam-5832	338	5	p	p	NOUN
ejpam-5832	338	6	are	be	AUX
ejpam-5832	338	7	q	q	NOUN
ejpam-5832	338	8	-	-	PUNCT
ejpam-5832	338	9	rofsgs	rofsg	NOUN
ejpam-5832	338	10	of	of	ADP
ejpam-5832	338	11	v	v	NOUN
ejpam-5832	338	12	.	.	PUNCT
ejpam-5832	339	1	then	then	ADV
ejpam-5832	339	2	q	q	X
ejpam-5832	339	3	is	be	AUX
ejpam-5832	339	4	a	a	DET
ejpam-5832	339	5	q	q	NOUN
ejpam-5832	339	6	-	-	PUNCT
ejpam-5832	339	7	rofnsg	rofnsg	NOUN
ejpam-5832	339	8	of	of	ADP
ejpam-5832	339	9	p	p	PROPN
ejpam-5832	339	10	⇔	⇔	PROPN
ejpam-5832	339	11	q(θ	q(θ	PROPN
ejpam-5832	339	12	,	,	PUNCT
ejpam-5832	339	13	τ	τ	X
ejpam-5832	339	14	)	)	PUNCT
ejpam-5832	339	15	⊴	⊴	ADP
ejpam-5832	339	16	p(θ	p(θ	PROPN
ejpam-5832	339	17	,	,	PUNCT
ejpam-5832	339	18	τ	τ	PROPN
ejpam-5832	339	19	)	)	PUNCT
ejpam-5832	339	20	,	,	PUNCT
ejpam-5832	339	21	for	for	ADP
ejpam-5832	339	22	all	all	DET
ejpam-5832	339	23	θ	θ	PRON
ejpam-5832	339	24	∈	∈	PROPN
ejpam-5832	340	1	[	[	X
ejpam-5832	340	2	0	0	NUM
ejpam-5832	340	3	,	,	PUNCT
ejpam-5832	340	4	(	(	PUNCT
ejpam-5832	340	5	µq(e	µq(e	NUM
ejpam-5832	340	6	)	)	PUNCT
ejpam-5832	340	7	)	)	PUNCT
ejpam-5832	341	1	q	q	X
ejpam-5832	341	2	]	]	PUNCT
ejpam-5832	341	3	and	and	CCONJ
ejpam-5832	341	4	τ	τ	PROPN
ejpam-5832	341	5	∈	∈	PROPN
ejpam-5832	342	1	[	[	X
ejpam-5832	342	2	(	(	PUNCT
ejpam-5832	342	3	νq(e	νq(e	NUM
ejpam-5832	342	4	)	)	PUNCT
ejpam-5832	342	5	)	)	PUNCT
ejpam-5832	343	1	q	q	NOUN
ejpam-5832	343	2	,	,	PUNCT
ejpam-5832	343	3	1	1	NUM
ejpam-5832	343	4	]	]	PUNCT
ejpam-5832	343	5	.	.	PUNCT
ejpam-5832	344	1	proof	proof	NOUN
ejpam-5832	344	2	.	.	PUNCT
ejpam-5832	345	1	let	let	VERB
ejpam-5832	345	2	q	q	PART
ejpam-5832	345	3	be	be	AUX
ejpam-5832	345	4	a	a	DET
ejpam-5832	345	5	q	q	NOUN
ejpam-5832	345	6	-	-	PUNCT
ejpam-5832	345	7	rofnsg	rofnsg	NOUN
ejpam-5832	345	8	of	of	ADP
ejpam-5832	345	9	q′	q′	NOUN
ejpam-5832	345	10	and	and	CCONJ
ejpam-5832	345	11	θ	θ	PROPN
ejpam-5832	345	12	∈	∈	PROPN
ejpam-5832	346	1	[	[	X
ejpam-5832	346	2	0	0	NUM
ejpam-5832	346	3	,	,	PUNCT
ejpam-5832	346	4	µq(e	µq(e	PUNCT
ejpam-5832	346	5	)	)	PUNCT
ejpam-5832	346	6	]	]	PUNCT
ejpam-5832	346	7	and	and	CCONJ
ejpam-5832	346	8	τ	τ	PROPN
ejpam-5832	346	9	∈	∈	PROPN
ejpam-5832	347	1	[	[	X
ejpam-5832	347	2	νq(e	νq(e	NUM
ejpam-5832	347	3	)	)	PUNCT
ejpam-5832	347	4	,	,	PUNCT
ejpam-5832	347	5	1	1	X
ejpam-5832	347	6	]	]	PUNCT
ejpam-5832	347	7	,	,	PUNCT
ejpam-5832	347	8	then	then	ADV
ejpam-5832	347	9	the	the	DET
ejpam-5832	347	10	combination	combination	NOUN
ejpam-5832	347	11	of	of	ADP
ejpam-5832	347	12	theorems	theorem	NOUN
ejpam-5832	347	13	3	3	NUM
ejpam-5832	347	14	and	and	CCONJ
ejpam-5832	347	15	4	4	NUM
ejpam-5832	347	16	reveals	reveal	VERB
ejpam-5832	347	17	that	that	SCONJ
ejpam-5832	347	18	q(θ	q(θ	PROPN
ejpam-5832	347	19	,	,	PUNCT
ejpam-5832	347	20	τ	τ	X
ejpam-5832	347	21	)	)	PUNCT
ejpam-5832	347	22	is	be	AUX
ejpam-5832	347	23	a	a	DET
ejpam-5832	347	24	subgroup	subgroup	NOUN
ejpam-5832	347	25	of	of	ADP
ejpam-5832	347	26	p(θ	p(θ	PROPN
ejpam-5832	347	27	,	,	PUNCT
ejpam-5832	347	28	τ	τ	PROPN
ejpam-5832	347	29	)	)	PUNCT
ejpam-5832	347	30	.	.	PUNCT
ejpam-5832	348	1	assume	assume	VERB
ejpam-5832	348	2	that	that	SCONJ
ejpam-5832	348	3	λ	λ	PROPN
ejpam-5832	348	4	∈	∈	PROPN
ejpam-5832	348	5	q(θ	q(θ	PROPN
ejpam-5832	348	6	,	,	PUNCT
ejpam-5832	348	7	τ	τ	X
ejpam-5832	348	8	)	)	PUNCT
ejpam-5832	348	9	and	and	CCONJ
ejpam-5832	348	10	ϵ	ϵ	PROPN
ejpam-5832	348	11	∈	∈	PROPN
ejpam-5832	348	12	p(θ	p(θ	PROPN
ejpam-5832	348	13	,	,	PUNCT
ejpam-5832	348	14	τ	τ	PROPN
ejpam-5832	348	15	)	)	PUNCT
ejpam-5832	348	16	,	,	PUNCT
ejpam-5832	348	17	then	then	ADV
ejpam-5832	348	18	(	(	PUNCT
ejpam-5832	348	19	µq(λ	µq(λ	NOUN
ejpam-5832	348	20	)	)	PUNCT
ejpam-5832	348	21	)	)	PUNCT
ejpam-5832	348	22	q	q	NOUN
ejpam-5832	348	23	,	,	PUNCT
ejpam-5832	348	24	(	(	PUNCT
ejpam-5832	348	25	µp	µp	PROPN
ejpam-5832	348	26	(	(	PUNCT
ejpam-5832	348	27	ϵ	ϵ	NOUN
ejpam-5832	348	28	)	)	PUNCT
ejpam-5832	348	29	)	)	PUNCT
ejpam-5832	349	1	q	q	NOUN
ejpam-5832	349	2	≥	≥	NUM
ejpam-5832	349	3	θ	θ	NOUN
ejpam-5832	349	4	and	and	CCONJ
ejpam-5832	349	5	(	(	PUNCT
ejpam-5832	349	6	νq(λ	νq(λ	NUM
ejpam-5832	349	7	)	)	PUNCT
ejpam-5832	349	8	)	)	PUNCT
ejpam-5832	350	1	q	q	NOUN
ejpam-5832	350	2	,	,	PUNCT
ejpam-5832	350	3	(	(	PUNCT
ejpam-5832	350	4	νp	νp	X
ejpam-5832	350	5	(	(	PUNCT
ejpam-5832	350	6	ϵ	ϵ	NOUN
ejpam-5832	350	7	)	)	PUNCT
ejpam-5832	350	8	)	)	PUNCT
ejpam-5832	351	1	q	q	PROPN
ejpam-5832	351	2	≤	≤	NUM
ejpam-5832	351	3	τ	τ	X
ejpam-5832	351	4	.	.	PUNCT
ejpam-5832	352	1	now	now	ADV
ejpam-5832	352	2	(	(	PUNCT
ejpam-5832	352	3	µq	µq	PROPN
ejpam-5832	352	4	(	(	PUNCT
ejpam-5832	352	5	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	352	6	)	)	PUNCT
ejpam-5832	352	7	)	)	PUNCT
ejpam-5832	352	8	q	q	PROPN
ejpam-5832	353	1	≥	≥	PROPN
ejpam-5832	353	2	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	353	3	,	,	PUNCT
ejpam-5832	353	4	(	(	PUNCT
ejpam-5832	353	5	µp	µp	PROPN
ejpam-5832	353	6	(	(	PUNCT
ejpam-5832	353	7	ϵ))q	ϵ))q	NOUN
ejpam-5832	353	8	}	}	PUNCT
ejpam-5832	353	9	≥	≥	NUM
ejpam-5832	353	10	θ	θ	NOUN
ejpam-5832	353	11	and	and	CCONJ
ejpam-5832	353	12	a.	a.	NOUN
ejpam-5832	353	13	razzaque	razzaque	NOUN
ejpam-5832	353	14	/	/	SYM
ejpam-5832	353	15	eur	eur	NOUN
ejpam-5832	353	16	.	.	PUNCT
ejpam-5832	354	1	j.	j.	PROPN
ejpam-5832	354	2	pure	pure	PROPN
ejpam-5832	354	3	appl	appl	PROPN
ejpam-5832	354	4	.	.	PROPN
ejpam-5832	354	5	math	math	PROPN
ejpam-5832	354	6	,	,	PUNCT
ejpam-5832	354	7	18	18	NUM
ejpam-5832	354	8	(	(	PUNCT
ejpam-5832	354	9	3	3	NUM
ejpam-5832	354	10	)	)	PUNCT
ejpam-5832	354	11	(	(	PUNCT
ejpam-5832	354	12	2025	2025	NUM
ejpam-5832	354	13	)	)	PUNCT
ejpam-5832	354	14	,	,	PUNCT
ejpam-5832	354	15	5832	5832	NUM
ejpam-5832	354	16	11	11	NUM
ejpam-5832	354	17	of	of	ADP
ejpam-5832	354	18	21	21	NUM
ejpam-5832	354	19	(	(	PUNCT
ejpam-5832	354	20	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	354	21	−1	−1	NOUN
ejpam-5832	354	22	)	)	PUNCT
ejpam-5832	354	23	)	)	PUNCT
ejpam-5832	355	1	q	q	PROPN
ejpam-5832	355	2	≤	≤	NUM
ejpam-5832	355	3	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	355	4	,	,	PUNCT
ejpam-5832	355	5	(	(	PUNCT
ejpam-5832	355	6	νp	νp	X
ejpam-5832	355	7	(	(	PUNCT
ejpam-5832	355	8	ϵ))q	ϵ))q	NOUN
ejpam-5832	355	9	}	}	PUNCT
ejpam-5832	355	10	≤	≤	NUM
ejpam-5832	355	11	τ	τ	X
ejpam-5832	355	12	.	.	PUNCT
ejpam-5832	356	1	therefore	therefore	ADV
ejpam-5832	356	2	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	356	3	∈	∈	PROPN
ejpam-5832	356	4	q(θ	q(θ	PROPN
ejpam-5832	356	5	,	,	PUNCT
ejpam-5832	356	6	τ	τ	X
ejpam-5832	356	7	)	)	PUNCT
ejpam-5832	356	8	which	which	PRON
ejpam-5832	356	9	further	far	ADV
ejpam-5832	356	10	gives	give	VERB
ejpam-5832	356	11	q(θ	q(θ	PROPN
ejpam-5832	356	12	,	,	PUNCT
ejpam-5832	356	13	τ	τ	X
ejpam-5832	356	14	)	)	PUNCT
ejpam-5832	356	15	⊴	⊴	ADP
ejpam-5832	356	16	p(θ	p(θ	PROPN
ejpam-5832	356	17	,	,	PUNCT
ejpam-5832	356	18	τ	τ	PROPN
ejpam-5832	356	19	)	)	PUNCT
ejpam-5832	356	20	.	.	PUNCT
ejpam-5832	357	1	conversely	conversely	ADV
ejpam-5832	357	2	,	,	PUNCT
ejpam-5832	357	3	let	let	VERB
ejpam-5832	357	4	q(θ	q(θ	PROPN
ejpam-5832	357	5	,	,	PUNCT
ejpam-5832	357	6	τ	τ	X
ejpam-5832	357	7	)	)	PUNCT
ejpam-5832	357	8	⊴	⊴	ADP
ejpam-5832	357	9	p(θ	p(θ	PROPN
ejpam-5832	357	10	,	,	PUNCT
ejpam-5832	357	11	τ	τ	PROPN
ejpam-5832	357	12	)	)	PUNCT
ejpam-5832	357	13	for	for	ADP
ejpam-5832	357	14	all	all	DET
ejpam-5832	357	15	θ	θ	PRON
ejpam-5832	357	16	∈	∈	PROPN
ejpam-5832	358	1	[	[	X
ejpam-5832	358	2	0	0	NUM
ejpam-5832	358	3	,	,	PUNCT
ejpam-5832	358	4	µq(e	µq(e	PUNCT
ejpam-5832	358	5	)	)	PUNCT
ejpam-5832	358	6	]	]	PUNCT
ejpam-5832	358	7	and	and	CCONJ
ejpam-5832	358	8	τ	τ	PROPN
ejpam-5832	358	9	∈	∈	PROPN
ejpam-5832	359	1	[	[	X
ejpam-5832	359	2	νq(e	νq(e	NUM
ejpam-5832	359	3	)	)	PUNCT
ejpam-5832	359	4	,	,	PUNCT
ejpam-5832	359	5	1	1	NUM
ejpam-5832	359	6	]	]	PUNCT
ejpam-5832	359	7	.	.	PUNCT
ejpam-5832	360	1	consider	consider	VERB
ejpam-5832	360	2	λ	λ	PROPN
ejpam-5832	360	3	,	,	PUNCT
ejpam-5832	360	4	ϵ	ϵ	PROPN
ejpam-5832	360	5	∈	∈	PROPN
ejpam-5832	360	6	v	v	ADP
ejpam-5832	360	7	such	such	ADJ
ejpam-5832	360	8	that	that	SCONJ
ejpam-5832	360	9	(	(	PUNCT
ejpam-5832	360	10	µq(λ	µq(λ	NOUN
ejpam-5832	360	11	)	)	PUNCT
ejpam-5832	360	12	)	)	PUNCT
ejpam-5832	361	1	q	q	NOUN
ejpam-5832	361	2	=	=	SYM
ejpam-5832	361	3	α	α	PROPN
ejpam-5832	361	4	,	,	PUNCT
ejpam-5832	361	5	(	(	PUNCT
ejpam-5832	361	6	νq(λ	νq(λ	NUM
ejpam-5832	361	7	)	)	PUNCT
ejpam-5832	361	8	)	)	PUNCT
ejpam-5832	361	9	q	q	NOUN
ejpam-5832	362	1	=	=	PUNCT
ejpam-5832	362	2	β	β	X
ejpam-5832	362	3	and	and	CCONJ
ejpam-5832	362	4	(	(	PUNCT
ejpam-5832	362	5	µp	µp	PROPN
ejpam-5832	362	6	(	(	PUNCT
ejpam-5832	362	7	ϵ	ϵ	NOUN
ejpam-5832	362	8	)	)	PUNCT
ejpam-5832	362	9	)	)	PUNCT
ejpam-5832	362	10	q	q	NOUN
ejpam-5832	363	1	=	=	PUNCT
ejpam-5832	363	2	γ	γ	X
ejpam-5832	363	3	,	,	PUNCT
ejpam-5832	363	4	(	(	PUNCT
ejpam-5832	363	5	νp	νp	X
ejpam-5832	363	6	(	(	PUNCT
ejpam-5832	363	7	ϵ	ϵ	NOUN
ejpam-5832	363	8	)	)	PUNCT
ejpam-5832	363	9	)	)	PUNCT
ejpam-5832	363	10	q	q	NOUN
ejpam-5832	364	1	=	=	PUNCT
ejpam-5832	364	2	δ	δ	PROPN
ejpam-5832	364	3	.	.	PUNCT
ejpam-5832	365	1	consequently	consequently	ADV
ejpam-5832	365	2	,	,	PUNCT
ejpam-5832	365	3	there	there	PRON
ejpam-5832	365	4	are	be	VERB
ejpam-5832	365	5	four	four	NUM
ejpam-5832	365	6	possibilities	possibility	NOUN
ejpam-5832	365	7	;	;	PUNCT
ejpam-5832	365	8	(	(	PUNCT
ejpam-5832	365	9	i	i	NOUN
ejpam-5832	365	10	)	)	PUNCT
ejpam-5832	365	11	γ	γ	PROPN
ejpam-5832	365	12	≥	≥	PROPN
ejpam-5832	365	13	α	α	PROPN
ejpam-5832	365	14	and	and	CCONJ
ejpam-5832	365	15	δ	δ	PROPN
ejpam-5832	365	16	≥	≥	NUM
ejpam-5832	365	17	β	β	X
ejpam-5832	365	18	(	(	PUNCT
ejpam-5832	365	19	ii	ii	NOUN
ejpam-5832	365	20	)	)	PUNCT
ejpam-5832	365	21	γ	γ	PROPN
ejpam-5832	365	22	≥	≥	PROPN
ejpam-5832	365	23	α	α	PROPN
ejpam-5832	365	24	and	and	CCONJ
ejpam-5832	365	25	δ	δ	PROPN
ejpam-5832	365	26	≤	≤	ADJ
ejpam-5832	365	27	β	β	X
ejpam-5832	365	28	(	(	PUNCT
ejpam-5832	365	29	iii	iii	X
ejpam-5832	365	30	)	)	PUNCT
ejpam-5832	365	31	γ	γ	NOUN
ejpam-5832	365	32	≤	≤	NUM
ejpam-5832	365	33	α	α	PROPN
ejpam-5832	365	34	and	and	CCONJ
ejpam-5832	365	35	δ	δ	PROPN
ejpam-5832	365	36	≥	≥	NUM
ejpam-5832	365	37	β	β	X
ejpam-5832	365	38	(	(	PUNCT
ejpam-5832	365	39	iv	iv	X
ejpam-5832	365	40	)	)	PUNCT
ejpam-5832	365	41	γ	γ	NOUN
ejpam-5832	365	42	≤	≤	NUM
ejpam-5832	365	43	α	α	PROPN
ejpam-5832	365	44	and	and	CCONJ
ejpam-5832	365	45	δ	δ	PROPN
ejpam-5832	365	46	≤	≤	ADJ
ejpam-5832	366	1	β	β	X
ejpam-5832	366	2	(	(	PUNCT
ejpam-5832	366	3	i	i	NOUN
ejpam-5832	366	4	)	)	PUNCT
ejpam-5832	366	5	γ	γ	PROPN
ejpam-5832	366	6	≥	≥	PROPN
ejpam-5832	366	7	α	α	PROPN
ejpam-5832	366	8	and	and	CCONJ
ejpam-5832	366	9	δ	δ	PROPN
ejpam-5832	366	10	≥	≥	X
ejpam-5832	366	11	β	β	X
ejpam-5832	366	12	then	then	ADV
ejpam-5832	366	13	ϵ	ϵ	PROPN
ejpam-5832	366	14	∈	∈	PROPN
ejpam-5832	366	15	p(α	p(α	PROPN
ejpam-5832	366	16	,	,	PUNCT
ejpam-5832	366	17	δ	δ	PROPN
ejpam-5832	366	18	)	)	PUNCT
ejpam-5832	366	19	and	and	CCONJ
ejpam-5832	366	20	λ	λ	PROPN
ejpam-5832	366	21	∈	∈	PROPN
ejpam-5832	366	22	q(α	q(α	PROPN
ejpam-5832	366	23	,	,	PUNCT
ejpam-5832	366	24	δ	δ	PROPN
ejpam-5832	366	25	)	)	PUNCT
ejpam-5832	366	26	.	.	PUNCT
ejpam-5832	367	1	then	then	ADV
ejpam-5832	367	2	by	by	ADP
ejpam-5832	367	3	assumption	assumption	NOUN
ejpam-5832	367	4	,	,	PUNCT
ejpam-5832	367	5	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	367	6	∈	∈	PROPN
ejpam-5832	367	7	q(α	q(α	PROPN
ejpam-5832	367	8	,	,	PUNCT
ejpam-5832	367	9	δ	δ	PROPN
ejpam-5832	367	10	)	)	PUNCT
ejpam-5832	367	11	which	which	PRON
ejpam-5832	367	12	gives	give	VERB
ejpam-5832	367	13	(	(	PUNCT
ejpam-5832	367	14	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	367	15	−1	−1	NOUN
ejpam-5832	367	16	)	)	PUNCT
ejpam-5832	367	17	)	)	PUNCT
ejpam-5832	368	1	q	q	NOUN
ejpam-5832	369	1	≥	≥	NOUN
ejpam-5832	369	2	α	α	NOUN
ejpam-5832	369	3	=	=	SYM
ejpam-5832	369	4	min(α	min(α	PROPN
ejpam-5832	369	5	,	,	PUNCT
ejpam-5832	369	6	γ	γ	NOUN
ejpam-5832	369	7	)	)	PUNCT
ejpam-5832	369	8	=	=	SYM
ejpam-5832	369	9	min((µq(λ	min((µq(λ	NOUN
ejpam-5832	369	10	)	)	PUNCT
ejpam-5832	369	11	)	)	PUNCT
ejpam-5832	370	1	q	q	X
ejpam-5832	370	2	,	,	PUNCT
ejpam-5832	370	3	(	(	PUNCT
ejpam-5832	370	4	µp	µp	PROPN
ejpam-5832	370	5	(	(	PUNCT
ejpam-5832	370	6	ϵ	ϵ	NOUN
ejpam-5832	370	7	)	)	PUNCT
ejpam-5832	370	8	)	)	PUNCT
ejpam-5832	370	9	q	q	X
ejpam-5832	370	10	)	)	PUNCT
ejpam-5832	370	11	and	and	CCONJ
ejpam-5832	370	12	(	(	PUNCT
ejpam-5832	370	13	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	370	14	−1	−1	NOUN
ejpam-5832	370	15	)	)	PUNCT
ejpam-5832	370	16	)	)	PUNCT
ejpam-5832	370	17	q	q	PROPN
ejpam-5832	370	18	≤	≤	NUM
ejpam-5832	370	19	δ	δ	X
ejpam-5832	370	20	=	=	SYM
ejpam-5832	370	21	max(β	max(β	PROPN
ejpam-5832	370	22	,	,	PUNCT
ejpam-5832	370	23	δ	δ	PROPN
ejpam-5832	370	24	)	)	PUNCT
ejpam-5832	370	25	=	=	SYM
ejpam-5832	370	26	max((νq(λ	max((νq(λ	NOUN
ejpam-5832	370	27	)	)	PUNCT
ejpam-5832	370	28	)	)	PUNCT
ejpam-5832	371	1	q	q	X
ejpam-5832	371	2	,	,	PUNCT
ejpam-5832	371	3	(	(	PUNCT
ejpam-5832	371	4	νp	νp	X
ejpam-5832	371	5	(	(	PUNCT
ejpam-5832	371	6	ϵ	ϵ	NOUN
ejpam-5832	371	7	)	)	PUNCT
ejpam-5832	371	8	)	)	PUNCT
ejpam-5832	371	9	q	q	X
ejpam-5832	371	10	)	)	PUNCT
ejpam-5832	371	11	(	(	PUNCT
ejpam-5832	371	12	ii	ii	NOUN
ejpam-5832	371	13	)	)	PUNCT
ejpam-5832	371	14	if	if	SCONJ
ejpam-5832	371	15	γ	γ	X
ejpam-5832	371	16	≥	≥	VERB
ejpam-5832	371	17	α	α	PROPN
ejpam-5832	371	18	and	and	CCONJ
ejpam-5832	371	19	δ	δ	PROPN
ejpam-5832	371	20	≤	≤	NOUN
ejpam-5832	371	21	β	β	X
ejpam-5832	371	22	then	then	ADV
ejpam-5832	371	23	ϵ	ϵ	PROPN
ejpam-5832	371	24	∈	∈	PROPN
ejpam-5832	371	25	p(α	p(α	PROPN
ejpam-5832	371	26	,	,	PUNCT
ejpam-5832	371	27	β	β	NOUN
ejpam-5832	371	28	)	)	PUNCT
ejpam-5832	371	29	and	and	CCONJ
ejpam-5832	371	30	λ	λ	PROPN
ejpam-5832	371	31	∈	∈	PROPN
ejpam-5832	371	32	q(α	q(α	PROPN
ejpam-5832	371	33	,	,	PUNCT
ejpam-5832	371	34	β	β	NOUN
ejpam-5832	371	35	)	)	PUNCT
ejpam-5832	371	36	.	.	PUNCT
ejpam-5832	372	1	then	then	ADV
ejpam-5832	372	2	by	by	ADP
ejpam-5832	372	3	assumption	assumption	NOUN
ejpam-5832	372	4	,	,	PUNCT
ejpam-5832	372	5	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	372	6	∈	∈	PROPN
ejpam-5832	372	7	q(α	q(α	PROPN
ejpam-5832	372	8	,	,	PUNCT
ejpam-5832	372	9	β	β	NOUN
ejpam-5832	372	10	)	)	PUNCT
ejpam-5832	372	11	which	which	PRON
ejpam-5832	372	12	gives	give	VERB
ejpam-5832	372	13	(	(	PUNCT
ejpam-5832	372	14	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	372	15	−1	−1	NOUN
ejpam-5832	372	16	)	)	PUNCT
ejpam-5832	372	17	)	)	PUNCT
ejpam-5832	373	1	q	q	NOUN
ejpam-5832	374	1	≥	≥	NOUN
ejpam-5832	374	2	α	α	NOUN
ejpam-5832	374	3	=	=	SYM
ejpam-5832	374	4	min(α	min(α	PROPN
ejpam-5832	374	5	,	,	PUNCT
ejpam-5832	374	6	γ	γ	NOUN
ejpam-5832	374	7	)	)	PUNCT
ejpam-5832	374	8	=	=	SYM
ejpam-5832	374	9	min((µq(λ	min((µq(λ	NOUN
ejpam-5832	374	10	)	)	PUNCT
ejpam-5832	374	11	)	)	PUNCT
ejpam-5832	375	1	q	q	X
ejpam-5832	375	2	,	,	PUNCT
ejpam-5832	375	3	(	(	PUNCT
ejpam-5832	375	4	µp	µp	PROPN
ejpam-5832	375	5	(	(	PUNCT
ejpam-5832	375	6	ϵ	ϵ	NOUN
ejpam-5832	375	7	)	)	PUNCT
ejpam-5832	375	8	)	)	PUNCT
ejpam-5832	375	9	q	q	X
ejpam-5832	375	10	)	)	PUNCT
ejpam-5832	375	11	and	and	CCONJ
ejpam-5832	375	12	(	(	PUNCT
ejpam-5832	375	13	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	375	14	−1	−1	NOUN
ejpam-5832	375	15	)	)	PUNCT
ejpam-5832	375	16	)	)	PUNCT
ejpam-5832	376	1	q	q	PROPN
ejpam-5832	376	2	≤	≤	NUM
ejpam-5832	376	3	β	β	X
ejpam-5832	376	4	=	=	SYM
ejpam-5832	376	5	max(β	max(β	PROPN
ejpam-5832	376	6	,	,	PUNCT
ejpam-5832	376	7	δ	δ	PROPN
ejpam-5832	376	8	)	)	PUNCT
ejpam-5832	376	9	=	=	SYM
ejpam-5832	376	10	max((νq(λ	max((νq(λ	NOUN
ejpam-5832	376	11	)	)	PUNCT
ejpam-5832	376	12	)	)	PUNCT
ejpam-5832	377	1	q	q	X
ejpam-5832	377	2	,	,	PUNCT
ejpam-5832	377	3	(	(	PUNCT
ejpam-5832	377	4	νp	νp	X
ejpam-5832	377	5	(	(	PUNCT
ejpam-5832	377	6	ϵ	ϵ	NOUN
ejpam-5832	377	7	)	)	PUNCT
ejpam-5832	377	8	)	)	PUNCT
ejpam-5832	377	9	q	q	X
ejpam-5832	377	10	)	)	PUNCT
ejpam-5832	377	11	likewise	likewise	ADV
ejpam-5832	377	12	,	,	PUNCT
ejpam-5832	377	13	for	for	ADP
ejpam-5832	377	14	(	(	PUNCT
ejpam-5832	377	15	iii	iii	NOUN
ejpam-5832	377	16	)	)	PUNCT
ejpam-5832	377	17	and	and	CCONJ
ejpam-5832	377	18	(	(	PUNCT
ejpam-5832	377	19	iv	iv	X
ejpam-5832	377	20	)	)	PUNCT
ejpam-5832	377	21	,	,	PUNCT
ejpam-5832	377	22	we	we	PRON
ejpam-5832	377	23	get	get	VERB
ejpam-5832	377	24	the	the	DET
ejpam-5832	377	25	same	same	ADJ
ejpam-5832	377	26	conclusion	conclusion	NOUN
ejpam-5832	377	27	.	.	PUNCT
ejpam-5832	378	1	consequently	consequently	ADV
ejpam-5832	378	2	,	,	PUNCT
ejpam-5832	378	3	q	q	X
ejpam-5832	378	4	is	be	AUX
ejpam-5832	378	5	a	a	DET
ejpam-5832	378	6	q	q	NOUN
ejpam-5832	378	7	-	-	PUNCT
ejpam-5832	378	8	rofnsg	rofnsg	NOUN
ejpam-5832	378	9	of	of	ADP
ejpam-5832	378	10	p	p	PROPN
ejpam-5832	378	11	.	.	PUNCT
ejpam-5832	379	1	theorem	theorem	ADJ
ejpam-5832	379	2	13	13	NUM
ejpam-5832	379	3	.	.	PUNCT
ejpam-5832	380	1	let	let	VERB
ejpam-5832	380	2	q	q	NOUN
ejpam-5832	381	1	and	and	CCONJ
ejpam-5832	381	2	p	p	NOUN
ejpam-5832	381	3	be	be	AUX
ejpam-5832	381	4	a	a	DET
ejpam-5832	381	5	q	q	NOUN
ejpam-5832	381	6	-	-	PUNCT
ejpam-5832	381	7	rofsgs	rofsg	NOUN
ejpam-5832	381	8	of	of	ADP
ejpam-5832	381	9	v	v	NOUN
ejpam-5832	381	10	.	.	PUNCT
ejpam-5832	382	1	then	then	ADV
ejpam-5832	382	2	q∗	q∗	VERB
ejpam-5832	382	3	⊴	⊴	ADP
ejpam-5832	382	4	p	p	NOUN
ejpam-5832	382	5	∗	∗	NOUN
ejpam-5832	382	6	and	and	CCONJ
ejpam-5832	382	7	q∗	q∗	NOUN
ejpam-5832	382	8	⊴	⊴	ADP
ejpam-5832	382	9	p∗	p∗	NOUN
ejpam-5832	382	10	if	if	SCONJ
ejpam-5832	382	11	q	q	NOUN
ejpam-5832	382	12	is	be	AUX
ejpam-5832	382	13	a	a	DET
ejpam-5832	382	14	q	q	NOUN
ejpam-5832	382	15	-	-	PUNCT
ejpam-5832	382	16	rofnsg	rofnsg	NOUN
ejpam-5832	382	17	of	of	ADP
ejpam-5832	382	18	p	p	PROPN
ejpam-5832	382	19	.	.	PUNCT
ejpam-5832	383	1	proof	proof	NOUN
ejpam-5832	383	2	.	.	PUNCT
ejpam-5832	384	1	assume	assume	VERB
ejpam-5832	384	2	that	that	SCONJ
ejpam-5832	384	3	q	q	NOUN
ejpam-5832	384	4	is	be	AUX
ejpam-5832	384	5	a	a	DET
ejpam-5832	384	6	q	q	NOUN
ejpam-5832	384	7	-	-	PUNCT
ejpam-5832	384	8	rofnsg	rofnsg	NOUN
ejpam-5832	384	9	of	of	ADP
ejpam-5832	384	10	p	p	PROPN
ejpam-5832	384	11	and	and	CCONJ
ejpam-5832	384	12	λ	λ	PROPN
ejpam-5832	384	13	∈	∈	NOUN
ejpam-5832	384	14	q∗	q∗	NOUN
ejpam-5832	384	15	and	and	CCONJ
ejpam-5832	384	16	ϵ	ϵ	ADP
ejpam-5832	384	17	∈	∈	PROPN
ejpam-5832	384	18	p	p	NOUN
ejpam-5832	384	19	∗	∗	NOUN
ejpam-5832	384	20	,	,	PUNCT
ejpam-5832	384	21	then	then	ADV
ejpam-5832	384	22	(	(	PUNCT
ejpam-5832	384	23	µq(ϵλϵ	µq(ϵλϵ	NUM
ejpam-5832	384	24	−1))q	−1))q	PROPN
ejpam-5832	384	25	≥	≥	NOUN
ejpam-5832	384	26	min((µ(λ	min((µ(λ	NOUN
ejpam-5832	384	27	)	)	PUNCT
ejpam-5832	384	28	)	)	PUNCT
ejpam-5832	385	1	q	q	NOUN
ejpam-5832	385	2	,	,	PUNCT
ejpam-5832	385	3	(	(	PUNCT
ejpam-5832	385	4	µp	µp	PROPN
ejpam-5832	385	5	(	(	PUNCT
ejpam-5832	385	6	ϵ	ϵ	NOUN
ejpam-5832	385	7	)	)	PUNCT
ejpam-5832	385	8	)	)	PUNCT
ejpam-5832	385	9	q	q	X
ejpam-5832	385	10	)	)	PUNCT
ejpam-5832	385	11	=	=	SYM
ejpam-5832	385	12	(	(	PUNCT
ejpam-5832	385	13	µq(e	µq(e	NUM
ejpam-5832	385	14	)	)	PUNCT
ejpam-5832	385	15	)	)	PUNCT
ejpam-5832	385	16	q	q	NOUN
ejpam-5832	386	1	and	and	CCONJ
ejpam-5832	386	2	(	(	PUNCT
ejpam-5832	386	3	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	386	4	−1))q	−1))q	NOUN
ejpam-5832	386	5	≤	≤	ADJ
ejpam-5832	386	6	max((νq(λ	max((νq(λ	NOUN
ejpam-5832	386	7	)	)	PUNCT
ejpam-5832	386	8	)	)	PUNCT
ejpam-5832	387	1	q	q	X
ejpam-5832	387	2	,	,	PUNCT
ejpam-5832	387	3	(	(	PUNCT
ejpam-5832	387	4	νp	νp	X
ejpam-5832	387	5	(	(	PUNCT
ejpam-5832	387	6	ϵ	ϵ	NOUN
ejpam-5832	387	7	)	)	PUNCT
ejpam-5832	387	8	)	)	PUNCT
ejpam-5832	387	9	q	q	X
ejpam-5832	387	10	)	)	PUNCT
ejpam-5832	387	11	=	=	SYM
ejpam-5832	387	12	(	(	PUNCT
ejpam-5832	387	13	νq(e	νq(e	NUM
ejpam-5832	387	14	)	)	PUNCT
ejpam-5832	387	15	)	)	PUNCT
ejpam-5832	388	1	q	q	PUNCT
ejpam-5832	388	2	consequently	consequently	ADV
ejpam-5832	388	3	,	,	PUNCT
ejpam-5832	388	4	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	388	5	∈	∈	PROPN
ejpam-5832	388	6	q∗	q∗	NOUN
ejpam-5832	388	7	implying	imply	VERB
ejpam-5832	388	8	that	that	DET
ejpam-5832	388	9	q∗	q∗	NOUN
ejpam-5832	388	10	⊴	⊴	ADP
ejpam-5832	388	11	p	p	X
ejpam-5832	388	12	∗.	∗.	PROPN
ejpam-5832	388	13	the	the	DET
ejpam-5832	388	14	similar	similar	ADJ
ejpam-5832	388	15	argument	argument	NOUN
ejpam-5832	388	16	indicates	indicate	VERB
ejpam-5832	388	17	that	that	SCONJ
ejpam-5832	388	18	q∗	q∗	NOUN
ejpam-5832	388	19	⊴	⊴	ADP
ejpam-5832	388	20	p∗.	p∗.	NOUN
ejpam-5832	388	21	a.	a.	NOUN
ejpam-5832	388	22	razzaque	razzaque	NOUN
ejpam-5832	388	23	/	/	SYM
ejpam-5832	388	24	eur	eur	NOUN
ejpam-5832	388	25	.	.	PUNCT
ejpam-5832	389	1	j.	j.	PROPN
ejpam-5832	389	2	pure	pure	PROPN
ejpam-5832	389	3	appl	appl	PROPN
ejpam-5832	389	4	.	.	PROPN
ejpam-5832	389	5	math	math	PROPN
ejpam-5832	389	6	,	,	PUNCT
ejpam-5832	389	7	18	18	NUM
ejpam-5832	389	8	(	(	PUNCT
ejpam-5832	389	9	3	3	NUM
ejpam-5832	389	10	)	)	PUNCT
ejpam-5832	389	11	(	(	PUNCT
ejpam-5832	389	12	2025	2025	NUM
ejpam-5832	389	13	)	)	PUNCT
ejpam-5832	389	14	,	,	PUNCT
ejpam-5832	389	15	5832	5832	NUM
ejpam-5832	389	16	12	12	NUM
ejpam-5832	389	17	of	of	ADP
ejpam-5832	389	18	21	21	NUM
ejpam-5832	389	19	theorem	theorem	VERB
ejpam-5832	389	20	14	14	NUM
ejpam-5832	389	21	.	.	PUNCT
ejpam-5832	390	1	assume	assume	VERB
ejpam-5832	390	2	that	that	SCONJ
ejpam-5832	390	3	q	q	NOUN
ejpam-5832	390	4	is	be	AUX
ejpam-5832	390	5	a	a	DET
ejpam-5832	390	6	q	q	NOUN
ejpam-5832	390	7	-	-	PUNCT
ejpam-5832	390	8	rofnsg	rofnsg	NOUN
ejpam-5832	390	9	and	and	CCONJ
ejpam-5832	390	10	p	p	NOUN
ejpam-5832	390	11	is	be	AUX
ejpam-5832	390	12	a	a	DET
ejpam-5832	390	13	q	q	NOUN
ejpam-5832	390	14	-	-	PUNCT
ejpam-5832	390	15	rofsg	rofsg	NOUN
ejpam-5832	390	16	of	of	ADP
ejpam-5832	390	17	v	v	NOUN
ejpam-5832	390	18	.	.	PUNCT
ejpam-5832	391	1	then	then	ADV
ejpam-5832	391	2	q	q	X
ejpam-5832	391	3	∩	∩	PROPN
ejpam-5832	391	4	p	p	NOUN
ejpam-5832	391	5	is	be	AUX
ejpam-5832	391	6	a	a	DET
ejpam-5832	391	7	q	q	NOUN
ejpam-5832	391	8	-	-	PUNCT
ejpam-5832	391	9	rofnsg	rofnsg	NOUN
ejpam-5832	391	10	of	of	ADP
ejpam-5832	391	11	p	p	PROPN
ejpam-5832	391	12	.	.	PUNCT
ejpam-5832	392	1	proof	proof	NOUN
ejpam-5832	392	2	.	.	PUNCT
ejpam-5832	393	1	in	in	ADP
ejpam-5832	393	2	accordance	accordance	NOUN
ejpam-5832	393	3	with	with	ADP
ejpam-5832	393	4	theorem	theorem	ADJ
ejpam-5832	393	5	2	2	NUM
ejpam-5832	393	6	,	,	PUNCT
ejpam-5832	393	7	q∩p	q∩p	PROPN
ejpam-5832	393	8	is	be	AUX
ejpam-5832	393	9	a	a	DET
ejpam-5832	393	10	q	q	NOUN
ejpam-5832	393	11	-	-	PUNCT
ejpam-5832	393	12	rofsg	rofsg	NOUN
ejpam-5832	393	13	of	of	ADP
ejpam-5832	393	14	v	v	NOUN
ejpam-5832	393	15	and	and	CCONJ
ejpam-5832	393	16	q∩p	q∩p	VERB
ejpam-5832	393	17	⊆	⊆	NUM
ejpam-5832	393	18	p	p	NOUN
ejpam-5832	393	19	.	.	PUNCT
ejpam-5832	394	1	let	let	VERB
ejpam-5832	394	2	λ	λ	PRON
ejpam-5832	394	3	,	,	PUNCT
ejpam-5832	394	4	ϵ	ϵ	PROPN
ejpam-5832	394	5	∈	∈	PROPN
ejpam-5832	394	6	v	v	NOUN
ejpam-5832	394	7	,	,	PUNCT
ejpam-5832	394	8	then	then	ADV
ejpam-5832	394	9	(	(	PUNCT
ejpam-5832	394	10	µq∩p	µq∩p	X
ejpam-5832	394	11	(	(	PUNCT
ejpam-5832	394	12	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	394	13	−1	−1	NOUN
ejpam-5832	394	14	)	)	PUNCT
ejpam-5832	394	15	)	)	PUNCT
ejpam-5832	395	1	q	q	NOUN
ejpam-5832	395	2	=	=	SYM
ejpam-5832	395	3	min	min	NOUN
ejpam-5832	395	4	{	{	PUNCT
ejpam-5832	395	5	(	(	PUNCT
ejpam-5832	395	6	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	395	7	−1	−1	NOUN
ejpam-5832	395	8	)	)	PUNCT
ejpam-5832	395	9	)	)	PUNCT
ejpam-5832	396	1	q	q	NOUN
ejpam-5832	396	2	,	,	PUNCT
ejpam-5832	396	3	(	(	PUNCT
ejpam-5832	396	4	µp	µp	PROPN
ejpam-5832	396	5	(	(	PUNCT
ejpam-5832	396	6	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	396	7	−1	−1	NOUN
ejpam-5832	396	8	)	)	PUNCT
ejpam-5832	396	9	)	)	PUNCT
ejpam-5832	396	10	q	q	X
ejpam-5832	396	11	}	}	PUNCT
ejpam-5832	396	12	≥	≥	PROPN
ejpam-5832	396	13	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	396	14	,	,	PUNCT
ejpam-5832	396	15	min{(µp	min{(µp	NOUN
ejpam-5832	396	16	(	(	PUNCT
ejpam-5832	396	17	ϵλ))q	ϵλ))q	PROPN
ejpam-5832	396	18	,	,	PUNCT
ejpam-5832	396	19	(	(	PUNCT
ejpam-5832	396	20	µp	µp	PROPN
ejpam-5832	396	21	(	(	PUNCT
ejpam-5832	396	22	ϵ	ϵ	NOUN
ejpam-5832	396	23	−1	−1	NOUN
ejpam-5832	396	24	)	)	PUNCT
ejpam-5832	396	25	)	)	PUNCT
ejpam-5832	396	26	q	q	X
ejpam-5832	396	27	}	}	PUNCT
ejpam-5832	396	28	}	}	PUNCT
ejpam-5832	396	29	≥	≥	PROPN
ejpam-5832	396	30	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	396	31	,	,	PUNCT
ejpam-5832	396	32	min{min{(µp	min{min{(µp	PROPN
ejpam-5832	396	33	(	(	PUNCT
ejpam-5832	396	34	ϵ))q	ϵ))q	NOUN
ejpam-5832	396	35	,	,	PUNCT
ejpam-5832	396	36	(	(	PUNCT
ejpam-5832	396	37	µp	µp	NOUN
ejpam-5832	396	38	(	(	PUNCT
ejpam-5832	396	39	λ))q	λ))q	PROPN
ejpam-5832	396	40	}	}	PUNCT
ejpam-5832	396	41	,	,	PUNCT
ejpam-5832	396	42	(	(	PUNCT
ejpam-5832	396	43	µp	µp	NOUN
ejpam-5832	396	44	(	(	PUNCT
ejpam-5832	396	45	ϵ))q	ϵ))q	NOUN
ejpam-5832	396	46	}	}	PUNCT
ejpam-5832	396	47	}	}	PUNCT
ejpam-5832	396	48	=	=	SYM
ejpam-5832	396	49	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	396	50	,	,	PUNCT
ejpam-5832	396	51	min{(µp	min{(µp	X
ejpam-5832	396	52	(	(	PUNCT
ejpam-5832	396	53	ϵ))q	ϵ))q	NOUN
ejpam-5832	396	54	,	,	PUNCT
ejpam-5832	396	55	(	(	PUNCT
ejpam-5832	396	56	µp	µp	PROPN
ejpam-5832	396	57	(	(	PUNCT
ejpam-5832	396	58	λ))q	λ))q	NOUN
ejpam-5832	396	59	}	}	PUNCT
ejpam-5832	396	60	}	}	PUNCT
ejpam-5832	396	61	=	=	SYM
ejpam-5832	396	62	min{min{(µq(λ))q	min{min{(µq(λ))q	PROPN
ejpam-5832	396	63	,	,	PUNCT
ejpam-5832	396	64	(	(	PUNCT
ejpam-5832	396	65	µp	µp	PROPN
ejpam-5832	396	66	(	(	PUNCT
ejpam-5832	396	67	λ))q	λ))q	PROPN
ejpam-5832	396	68	}	}	PUNCT
ejpam-5832	396	69	,	,	PUNCT
ejpam-5832	396	70	(	(	PUNCT
ejpam-5832	396	71	µp	µp	PROPN
ejpam-5832	396	72	(	(	PUNCT
ejpam-5832	396	73	ϵ))q	ϵ))q	NOUN
ejpam-5832	396	74	}	}	PUNCT
ejpam-5832	396	75	=	=	SYM
ejpam-5832	396	76	min{(µq∩p	min{(µq∩p	X
ejpam-5832	396	77	(	(	PUNCT
ejpam-5832	396	78	λ	λ	NOUN
ejpam-5832	396	79	)	)	PUNCT
ejpam-5832	396	80	)	)	PUNCT
ejpam-5832	396	81	q	q	NOUN
ejpam-5832	396	82	,	,	PUNCT
ejpam-5832	396	83	(	(	PUNCT
ejpam-5832	396	84	µp	µp	PROPN
ejpam-5832	396	85	(	(	PUNCT
ejpam-5832	396	86	ϵ	ϵ	NOUN
ejpam-5832	396	87	)	)	PUNCT
ejpam-5832	396	88	)	)	PUNCT
ejpam-5832	397	1	q	q	X
ejpam-5832	397	2	}	}	PUNCT
ejpam-5832	398	1	so	so	ADV
ejpam-5832	398	2	,	,	PUNCT
ejpam-5832	398	3	(	(	PUNCT
ejpam-5832	398	4	µq∩p	µq∩p	X
ejpam-5832	398	5	(	(	PUNCT
ejpam-5832	398	6	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	398	7	−1	−1	NOUN
ejpam-5832	398	8	)	)	PUNCT
ejpam-5832	398	9	)	)	PUNCT
ejpam-5832	398	10	q	q	NOUN
ejpam-5832	399	1	≥	≥	NOUN
ejpam-5832	399	2	min{(µq∩p	min{(µq∩p	NOUN
ejpam-5832	399	3	(	(	PUNCT
ejpam-5832	399	4	λ	λ	NOUN
ejpam-5832	399	5	)	)	PUNCT
ejpam-5832	399	6	)	)	PUNCT
ejpam-5832	399	7	q	q	NOUN
ejpam-5832	399	8	,	,	PUNCT
ejpam-5832	399	9	(	(	PUNCT
ejpam-5832	399	10	µp	µp	PROPN
ejpam-5832	399	11	(	(	PUNCT
ejpam-5832	399	12	ϵ	ϵ	NOUN
ejpam-5832	399	13	)	)	PUNCT
ejpam-5832	399	14	)	)	PUNCT
ejpam-5832	400	1	q	q	X
ejpam-5832	400	2	}	}	PUNCT
ejpam-5832	400	3	for	for	ADP
ejpam-5832	400	4	all	all	DET
ejpam-5832	400	5	λ	λ	PROPN
ejpam-5832	400	6	,	,	PUNCT
ejpam-5832	400	7	ϵ	ϵ	PROPN
ejpam-5832	400	8	∈	∈	PROPN
ejpam-5832	400	9	v	v	NOUN
ejpam-5832	400	10	.	.	PUNCT
ejpam-5832	401	1	in	in	ADP
ejpam-5832	401	2	a	a	DET
ejpam-5832	401	3	similar	similar	ADJ
ejpam-5832	401	4	vein	vein	NOUN
ejpam-5832	401	5	,	,	PUNCT
ejpam-5832	401	6	we	we	PRON
ejpam-5832	401	7	can	can	AUX
ejpam-5832	401	8	demonstrate	demonstrate	VERB
ejpam-5832	401	9	that	that	SCONJ
ejpam-5832	401	10	(	(	PUNCT
ejpam-5832	401	11	νq∩p	νq∩p	PROPN
ejpam-5832	401	12	(	(	PUNCT
ejpam-5832	401	13	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	401	14	−1	−1	NOUN
ejpam-5832	401	15	)	)	PUNCT
ejpam-5832	401	16	)	)	PUNCT
ejpam-5832	401	17	q	q	PROPN
ejpam-5832	402	1	≤	≤	NUM
ejpam-5832	402	2	max{(νq∩p	max{(νq∩p	X
ejpam-5832	402	3	(	(	PUNCT
ejpam-5832	402	4	λ	λ	NOUN
ejpam-5832	402	5	)	)	PUNCT
ejpam-5832	402	6	)	)	PUNCT
ejpam-5832	402	7	q	q	NOUN
ejpam-5832	402	8	,	,	PUNCT
ejpam-5832	402	9	(	(	PUNCT
ejpam-5832	402	10	νp	νp	X
ejpam-5832	402	11	(	(	PUNCT
ejpam-5832	402	12	ϵ	ϵ	NOUN
ejpam-5832	402	13	)	)	PUNCT
ejpam-5832	402	14	)	)	PUNCT
ejpam-5832	403	1	q	q	X
ejpam-5832	403	2	}	}	PUNCT
ejpam-5832	403	3	for	for	ADP
ejpam-5832	403	4	all	all	DET
ejpam-5832	403	5	λ	λ	PROPN
ejpam-5832	403	6	,	,	PUNCT
ejpam-5832	403	7	ϵ	ϵ	PROPN
ejpam-5832	403	8	∈	∈	PROPN
ejpam-5832	403	9	v	v	NOUN
ejpam-5832	403	10	.	.	PUNCT
ejpam-5832	404	1	thus	thus	ADV
ejpam-5832	404	2	,	,	PUNCT
ejpam-5832	404	3	q	q	SYM
ejpam-5832	404	4	∩	∩	NOUN
ejpam-5832	404	5	p	p	NOUN
ejpam-5832	404	6	is	be	AUX
ejpam-5832	404	7	a	a	DET
ejpam-5832	404	8	q	q	NOUN
ejpam-5832	404	9	-	-	PUNCT
ejpam-5832	404	10	rofnsg	rofnsg	NOUN
ejpam-5832	404	11	of	of	ADP
ejpam-5832	404	12	p	p	PROPN
ejpam-5832	404	13	.	.	PUNCT
ejpam-5832	405	1	theorem	theorem	ADJ
ejpam-5832	405	2	15	15	NUM
ejpam-5832	405	3	.	.	PUNCT
ejpam-5832	406	1	assume	assume	VERB
ejpam-5832	406	2	that	that	SCONJ
ejpam-5832	406	3	q	q	NOUN
ejpam-5832	406	4	,	,	PUNCT
ejpam-5832	406	5	p	p	NOUN
ejpam-5832	406	6	and	and	CCONJ
ejpam-5832	406	7	t	t	PROPN
ejpam-5832	406	8	are	be	AUX
ejpam-5832	406	9	q	q	NOUN
ejpam-5832	406	10	-	-	PUNCT
ejpam-5832	406	11	rofsgs	rofsg	NOUN
ejpam-5832	406	12	of	of	ADP
ejpam-5832	406	13	v	v	PRON
ejpam-5832	407	1	such	such	ADJ
ejpam-5832	407	2	that	that	DET
ejpam-5832	407	3	q	q	NOUN
ejpam-5832	408	1	and	and	CCONJ
ejpam-5832	408	2	p	p	NOUN
ejpam-5832	408	3	are	be	AUX
ejpam-5832	408	4	q	q	NOUN
ejpam-5832	408	5	-	-	PUNCT
ejpam-5832	408	6	rofnsgs	rofnsg	NOUN
ejpam-5832	408	7	of	of	ADP
ejpam-5832	408	8	t	t	PROPN
ejpam-5832	408	9	.	.	PUNCT
ejpam-5832	409	1	then	then	ADV
ejpam-5832	409	2	q	q	X
ejpam-5832	409	3	∩	∩	PROPN
ejpam-5832	409	4	p	p	NOUN
ejpam-5832	409	5	is	be	AUX
ejpam-5832	409	6	q	q	NOUN
ejpam-5832	409	7	-	-	PUNCT
ejpam-5832	409	8	rofsg	rofsg	NOUN
ejpam-5832	409	9	of	of	ADP
ejpam-5832	409	10	t	t	PROPN
ejpam-5832	409	11	.	.	PUNCT
ejpam-5832	410	1	proof	proof	NOUN
ejpam-5832	410	2	.	.	PUNCT
ejpam-5832	411	1	it	it	PRON
ejpam-5832	411	2	is	be	AUX
ejpam-5832	411	3	straightforward	straightforward	ADJ
ejpam-5832	411	4	to	to	PART
ejpam-5832	411	5	establish	establish	VERB
ejpam-5832	411	6	from	from	ADP
ejpam-5832	411	7	routine	routine	ADJ
ejpam-5832	411	8	calculation	calculation	NOUN
ejpam-5832	411	9	that	that	PRON
ejpam-5832	411	10	q	q	PROPN
ejpam-5832	411	11	∩	∩	NOUN
ejpam-5832	411	12	p	p	NOUN
ejpam-5832	411	13	is	be	AUX
ejpam-5832	411	14	a	a	DET
ejpam-5832	411	15	q	q	NOUN
ejpam-5832	411	16	-	-	PUNCT
ejpam-5832	411	17	rofsg	rofsg	NOUN
ejpam-5832	411	18	of	of	ADP
ejpam-5832	411	19	v	v	NOUN
ejpam-5832	411	20	and	and	CCONJ
ejpam-5832	411	21	q	q	NOUN
ejpam-5832	411	22	∩	∩	NOUN
ejpam-5832	411	23	p	p	ADP
ejpam-5832	411	24	⊆	⊆	NUM
ejpam-5832	411	25	t	t	NOUN
ejpam-5832	411	26	.	.	PUNCT
ejpam-5832	412	1	let	let	VERB
ejpam-5832	412	2	λ	λ	PRON
ejpam-5832	412	3	,	,	PUNCT
ejpam-5832	412	4	ϵ	ϵ	PROPN
ejpam-5832	412	5	∈	∈	PROPN
ejpam-5832	412	6	v	v	NOUN
ejpam-5832	412	7	,	,	PUNCT
ejpam-5832	412	8	then	then	ADV
ejpam-5832	412	9	(	(	PUNCT
ejpam-5832	412	10	µq∩p	µq∩p	X
ejpam-5832	412	11	(	(	PUNCT
ejpam-5832	412	12	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	412	13	−1	−1	NOUN
ejpam-5832	412	14	)	)	PUNCT
ejpam-5832	412	15	)	)	PUNCT
ejpam-5832	413	1	q	q	NOUN
ejpam-5832	413	2	=	=	SYM
ejpam-5832	413	3	min	min	NOUN
ejpam-5832	413	4	{	{	PUNCT
ejpam-5832	413	5	(	(	PUNCT
ejpam-5832	413	6	µ(q)(ϵλϵ−1	µ(q)(ϵλϵ−1	ADJ
ejpam-5832	413	7	)	)	PUNCT
ejpam-5832	413	8	)	)	PUNCT
ejpam-5832	414	1	q	q	NOUN
ejpam-5832	414	2	,	,	PUNCT
ejpam-5832	414	3	(	(	PUNCT
ejpam-5832	414	4	µp	µp	PROPN
ejpam-5832	414	5	(	(	PUNCT
ejpam-5832	414	6	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	414	7	−1	−1	NOUN
ejpam-5832	414	8	)	)	PUNCT
ejpam-5832	414	9	)	)	PUNCT
ejpam-5832	414	10	q	q	X
ejpam-5832	414	11	}	}	PUNCT
ejpam-5832	414	12	≥	≥	PROPN
ejpam-5832	414	13	min{min{(µq(λ))q	min{min{(µq(λ))q	PROPN
ejpam-5832	414	14	,	,	PUNCT
ejpam-5832	414	15	(	(	PUNCT
ejpam-5832	414	16	µt	µt	X
ejpam-5832	414	17	(	(	PUNCT
ejpam-5832	414	18	ϵ))q},min{(µp	ϵ))q},min{(µp	NUM
ejpam-5832	414	19	(	(	PUNCT
ejpam-5832	414	20	λ))q	λ))q	PROPN
ejpam-5832	414	21	,	,	PUNCT
ejpam-5832	414	22	(	(	PUNCT
ejpam-5832	414	23	µt	µt	INTJ
ejpam-5832	414	24	(	(	PUNCT
ejpam-5832	414	25	ϵ))q	ϵ))q	NOUN
ejpam-5832	414	26	}	}	PUNCT
ejpam-5832	414	27	}	}	PUNCT
ejpam-5832	414	28	=	=	SYM
ejpam-5832	414	29	min{min{(µq(λ))q	min{min{(µq(λ))q	PROPN
ejpam-5832	414	30	,	,	PUNCT
ejpam-5832	414	31	(	(	PUNCT
ejpam-5832	414	32	µp	µp	PROPN
ejpam-5832	414	33	(	(	PUNCT
ejpam-5832	414	34	λ))q	λ))q	PROPN
ejpam-5832	414	35	}	}	PUNCT
ejpam-5832	414	36	,	,	PUNCT
ejpam-5832	414	37	(	(	PUNCT
ejpam-5832	414	38	µt	µt	INTJ
ejpam-5832	414	39	(	(	PUNCT
ejpam-5832	414	40	ϵ))q	ϵ))q	NOUN
ejpam-5832	414	41	}	}	PUNCT
ejpam-5832	414	42	=	=	SYM
ejpam-5832	414	43	min{(µq∩p	min{(µq∩p	X
ejpam-5832	414	44	(	(	PUNCT
ejpam-5832	414	45	λ	λ	NOUN
ejpam-5832	414	46	)	)	PUNCT
ejpam-5832	414	47	)	)	PUNCT
ejpam-5832	414	48	q	q	NOUN
ejpam-5832	414	49	,	,	PUNCT
ejpam-5832	414	50	(	(	PUNCT
ejpam-5832	414	51	µt	µt	X
ejpam-5832	414	52	(	(	PUNCT
ejpam-5832	414	53	ϵ	ϵ	NOUN
ejpam-5832	414	54	)	)	PUNCT
ejpam-5832	414	55	)	)	PUNCT
ejpam-5832	415	1	q	q	X
ejpam-5832	415	2	}	}	PUNCT
ejpam-5832	415	3	similarly	similarly	ADV
ejpam-5832	415	4	,	,	PUNCT
ejpam-5832	415	5	(	(	PUNCT
ejpam-5832	415	6	νq∩p	νq∩p	PROPN
ejpam-5832	415	7	(	(	PUNCT
ejpam-5832	415	8	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	415	9	−1	−1	NOUN
ejpam-5832	415	10	)	)	PUNCT
ejpam-5832	415	11	)	)	PUNCT
ejpam-5832	415	12	q	q	NOUN
ejpam-5832	416	1	≥	≥	NOUN
ejpam-5832	416	2	max{(νq∩p	max{(νq∩p	NOUN
ejpam-5832	416	3	(	(	PUNCT
ejpam-5832	416	4	λ	λ	NOUN
ejpam-5832	416	5	)	)	PUNCT
ejpam-5832	416	6	)	)	PUNCT
ejpam-5832	417	1	q	q	NOUN
ejpam-5832	417	2	,	,	PUNCT
ejpam-5832	417	3	(	(	PUNCT
ejpam-5832	417	4	νt	νt	X
ejpam-5832	417	5	(	(	PUNCT
ejpam-5832	417	6	ϵ	ϵ	NOUN
ejpam-5832	417	7	)	)	PUNCT
ejpam-5832	417	8	)	)	PUNCT
ejpam-5832	417	9	q	q	X
ejpam-5832	417	10	}	}	PUNCT
ejpam-5832	417	11	theorem	theorem	VERB
ejpam-5832	417	12	16	16	NUM
ejpam-5832	417	13	.	.	PUNCT
ejpam-5832	418	1	suppose	suppose	VERB
ejpam-5832	418	2	that	that	SCONJ
ejpam-5832	418	3	q	q	PROPN
ejpam-5832	418	4	and	and	CCONJ
ejpam-5832	418	5	p	p	NOUN
ejpam-5832	418	6	are	be	AUX
ejpam-5832	418	7	q	q	NOUN
ejpam-5832	418	8	-	-	PUNCT
ejpam-5832	418	9	rofsgs	rofsg	NOUN
ejpam-5832	418	10	of	of	ADP
ejpam-5832	418	11	v	v	NUM
ejpam-5832	418	12	and	and	CCONJ
ejpam-5832	418	13	α	α	NOUN
ejpam-5832	418	14	is	be	AUX
ejpam-5832	418	15	a	a	DET
ejpam-5832	418	16	homomorphism	homomorphism	NOUN
ejpam-5832	418	17	from	from	ADP
ejpam-5832	418	18	v	v	NUM
ejpam-5832	418	19	to	to	ADP
ejpam-5832	418	20	w	w	PROPN
ejpam-5832	418	21	.	.	PUNCT
ejpam-5832	419	1	then	then	ADV
ejpam-5832	419	2	q	q	X
ejpam-5832	419	3	is	be	AUX
ejpam-5832	419	4	a	a	DET
ejpam-5832	419	5	q	q	NOUN
ejpam-5832	419	6	-	-	PUNCT
ejpam-5832	419	7	rofnsg	rofnsg	NOUN
ejpam-5832	419	8	of	of	ADP
ejpam-5832	419	9	p	p	PROPN
ejpam-5832	419	10	implies	imply	VERB
ejpam-5832	419	11	α(q	α(q	PROPN
ejpam-5832	419	12	)	)	PUNCT
ejpam-5832	419	13	is	be	AUX
ejpam-5832	419	14	a	a	DET
ejpam-5832	419	15	q	q	NOUN
ejpam-5832	419	16	-	-	PUNCT
ejpam-5832	419	17	rofnsg	rofnsg	NOUN
ejpam-5832	419	18	of	of	ADP
ejpam-5832	419	19	α(p	α(p	PROPN
ejpam-5832	419	20	)	)	PUNCT
ejpam-5832	419	21	.	.	PUNCT
ejpam-5832	420	1	proof	proof	NOUN
ejpam-5832	420	2	.	.	PUNCT
ejpam-5832	421	1	suppose	suppose	VERB
ejpam-5832	421	2	that	that	SCONJ
ejpam-5832	421	3	q	q	PROPN
ejpam-5832	421	4	and	and	CCONJ
ejpam-5832	421	5	p	p	NOUN
ejpam-5832	421	6	are	be	AUX
ejpam-5832	421	7	q	q	NOUN
ejpam-5832	421	8	-	-	PUNCT
ejpam-5832	421	9	rofsgs	rofsg	NOUN
ejpam-5832	421	10	of	of	ADP
ejpam-5832	421	11	v	v	NUM
ejpam-5832	421	12	and	and	CCONJ
ejpam-5832	421	13	α	α	NOUN
ejpam-5832	421	14	is	be	AUX
ejpam-5832	421	15	a	a	DET
ejpam-5832	421	16	homomorphism	homomorphism	NOUN
ejpam-5832	421	17	from	from	ADP
ejpam-5832	421	18	v	v	NUM
ejpam-5832	421	19	to	to	ADP
ejpam-5832	421	20	w	w	PROPN
ejpam-5832	421	21	.	.	PUNCT
ejpam-5832	422	1	then	then	ADV
ejpam-5832	422	2	q	q	X
ejpam-5832	422	3	is	be	AUX
ejpam-5832	422	4	a	a	DET
ejpam-5832	422	5	q	q	NOUN
ejpam-5832	422	6	-	-	PUNCT
ejpam-5832	422	7	rofnsg	rofnsg	NOUN
ejpam-5832	422	8	of	of	ADP
ejpam-5832	422	9	p	p	PROPN
ejpam-5832	422	10	implies	imply	VERB
ejpam-5832	422	11	α(q	α(q	PROPN
ejpam-5832	422	12	)	)	PUNCT
ejpam-5832	422	13	is	be	AUX
ejpam-5832	422	14	a	a	DET
ejpam-5832	422	15	q	q	NOUN
ejpam-5832	422	16	-	-	PUNCT
ejpam-5832	422	17	rofnsg	rofnsg	NOUN
ejpam-5832	422	18	of	of	ADP
ejpam-5832	422	19	α(p	α(p	PROPN
ejpam-5832	422	20	)	)	PUNCT
ejpam-5832	422	21	.	.	PUNCT
ejpam-5832	423	1	(	(	PUNCT
ejpam-5832	423	2	µα(q)(ϵλϵ	µα(q)(ϵλϵ	NUM
ejpam-5832	423	3	−1))q	−1))q	NOUN
ejpam-5832	423	4	=	=	SYM
ejpam-5832	423	5	max{(µq(z))q	max{(µq(z))q	NOUN
ejpam-5832	423	6	:	:	PUNCT
ejpam-5832	423	7	z	z	PROPN
ejpam-5832	423	8	∈	∈	PROPN
ejpam-5832	423	9	v	v	NOUN
ejpam-5832	423	10	,	,	PUNCT
ejpam-5832	423	11	α(z	α(z	NOUN
ejpam-5832	423	12	)	)	PUNCT
ejpam-5832	423	13	=	=	PUNCT
ejpam-5832	424	1	ϵλϵ−1	ϵλϵ−1	ADJ
ejpam-5832	424	2	}	}	PUNCT
ejpam-5832	424	3	=	=	SYM
ejpam-5832	424	4	max{(µq(kjk−1))q	max{(µq(kjk−1))q	NOUN
ejpam-5832	424	5	:	:	PUNCT
ejpam-5832	425	1	k	k	X
ejpam-5832	425	2	,	,	PUNCT
ejpam-5832	425	3	j	j	PROPN
ejpam-5832	425	4	∈	∈	PROPN
ejpam-5832	425	5	v	v	NOUN
ejpam-5832	425	6	,	,	PUNCT
ejpam-5832	425	7	α(k	α(k	NOUN
ejpam-5832	425	8	)	)	PUNCT
ejpam-5832	425	9	=	=	SYM
ejpam-5832	425	10	ϵ	ϵ	NOUN
ejpam-5832	425	11	,	,	PUNCT
ejpam-5832	425	12	α(j	α(j	NOUN
ejpam-5832	425	13	)	)	PUNCT
ejpam-5832	425	14	=	=	PUNCT
ejpam-5832	425	15	λ	λ	X
ejpam-5832	425	16	}	}	PUNCT
ejpam-5832	425	17	≥	≥	NOUN
ejpam-5832	425	18	max{min((µq(j	max{min((µq(j	NOUN
ejpam-5832	425	19	)	)	PUNCT
ejpam-5832	425	20	)	)	PUNCT
ejpam-5832	426	1	q	q	X
ejpam-5832	426	2	,	,	PUNCT
ejpam-5832	426	3	(	(	PUNCT
ejpam-5832	426	4	µp	µp	PROPN
ejpam-5832	426	5	(	(	PUNCT
ejpam-5832	426	6	k	k	NOUN
ejpam-5832	426	7	)	)	PUNCT
ejpam-5832	426	8	)	)	PUNCT
ejpam-5832	427	1	q	q	X
ejpam-5832	427	2	)	)	PUNCT
ejpam-5832	427	3	:	:	PUNCT
ejpam-5832	428	1	k	k	X
ejpam-5832	428	2	,	,	PUNCT
ejpam-5832	428	3	j	j	PROPN
ejpam-5832	428	4	∈	∈	PROPN
ejpam-5832	428	5	v	v	NOUN
ejpam-5832	428	6	,	,	PUNCT
ejpam-5832	428	7	α(k	α(k	NOUN
ejpam-5832	428	8	)	)	PUNCT
ejpam-5832	428	9	=	=	SYM
ejpam-5832	428	10	ϵ	ϵ	NOUN
ejpam-5832	428	11	,	,	PUNCT
ejpam-5832	428	12	α(j	α(j	NOUN
ejpam-5832	428	13	)	)	PUNCT
ejpam-5832	428	14	=	=	PUNCT
ejpam-5832	428	15	λ	λ	X
ejpam-5832	428	16	}	}	PUNCT
ejpam-5832	428	17	=	=	SYM
ejpam-5832	428	18	min	min	NOUN
ejpam-5832	428	19	(	(	PUNCT
ejpam-5832	428	20	max{(µq(j))q	max{(µq(j))q	NOUN
ejpam-5832	428	21	:	:	PUNCT
ejpam-5832	428	22	j	j	PROPN
ejpam-5832	428	23	∈	∈	PROPN
ejpam-5832	428	24	v	v	PROPN
ejpam-5832	428	25	,	,	PUNCT
ejpam-5832	428	26	α(j	α(j	NOUN
ejpam-5832	428	27	)	)	PUNCT
ejpam-5832	428	28	=	=	PUNCT
ejpam-5832	429	1	λ},max{(µp	λ},max{(µp	NOUN
ejpam-5832	429	2	(	(	PUNCT
ejpam-5832	429	3	k))q	k))q	NOUN
ejpam-5832	429	4	:	:	PUNCT
ejpam-5832	429	5	k	k	PROPN
ejpam-5832	429	6	∈	∈	PROPN
ejpam-5832	429	7	v	v	NOUN
ejpam-5832	429	8	,	,	PUNCT
ejpam-5832	429	9	α(k	α(k	NOUN
ejpam-5832	429	10	)	)	PUNCT
ejpam-5832	429	11	=	=	SYM
ejpam-5832	429	12	ϵ	ϵ	X
ejpam-5832	429	13	}	}	PUNCT
ejpam-5832	429	14	)	)	PUNCT
ejpam-5832	430	1	=	=	SYM
ejpam-5832	430	2	min	min	NOUN
ejpam-5832	430	3	(	(	PUNCT
ejpam-5832	430	4	(	(	PUNCT
ejpam-5832	430	5	µα(q)(λ	µα(q)(λ	NOUN
ejpam-5832	430	6	)	)	PUNCT
ejpam-5832	430	7	)	)	PUNCT
ejpam-5832	431	1	q	q	X
ejpam-5832	431	2	,	,	PUNCT
ejpam-5832	431	3	(	(	PUNCT
ejpam-5832	431	4	µα(p	µα(p	NUM
ejpam-5832	431	5	)	)	PUNCT
ejpam-5832	431	6	(	(	PUNCT
ejpam-5832	431	7	ϵ	ϵ	NOUN
ejpam-5832	431	8	)	)	PUNCT
ejpam-5832	431	9	)	)	PUNCT
ejpam-5832	431	10	q	q	X
ejpam-5832	431	11	)	)	PUNCT
ejpam-5832	431	12	a.	a.	NOUN
ejpam-5832	431	13	razzaque	razzaque	NOUN
ejpam-5832	431	14	/	/	SYM
ejpam-5832	431	15	eur	eur	NOUN
ejpam-5832	431	16	.	.	PUNCT
ejpam-5832	432	1	j.	j.	PROPN
ejpam-5832	432	2	pure	pure	PROPN
ejpam-5832	432	3	appl	appl	PROPN
ejpam-5832	432	4	.	.	PROPN
ejpam-5832	432	5	math	math	PROPN
ejpam-5832	432	6	,	,	PUNCT
ejpam-5832	432	7	18	18	NUM
ejpam-5832	432	8	(	(	PUNCT
ejpam-5832	432	9	3	3	NUM
ejpam-5832	432	10	)	)	PUNCT
ejpam-5832	432	11	(	(	PUNCT
ejpam-5832	432	12	2025	2025	NUM
ejpam-5832	432	13	)	)	PUNCT
ejpam-5832	432	14	,	,	PUNCT
ejpam-5832	432	15	5832	5832	NUM
ejpam-5832	432	16	13	13	NUM
ejpam-5832	432	17	of	of	ADP
ejpam-5832	432	18	21	21	NUM
ejpam-5832	432	19	similarly	similarly	ADV
ejpam-5832	432	20	,	,	PUNCT
ejpam-5832	432	21	we	we	PRON
ejpam-5832	432	22	can	can	AUX
ejpam-5832	432	23	acquire	acquire	VERB
ejpam-5832	432	24	(	(	PUNCT
ejpam-5832	432	25	να(q)(ϵλϵ	να(q)(ϵλϵ	NOUN
ejpam-5832	432	26	−1	−1	NOUN
ejpam-5832	432	27	)	)	PUNCT
ejpam-5832	432	28	)	)	PUNCT
ejpam-5832	433	1	q	q	PROPN
ejpam-5832	433	2	≤	≤	NUM
ejpam-5832	433	3	max	max	NOUN
ejpam-5832	433	4	(	(	PUNCT
ejpam-5832	433	5	(	(	PUNCT
ejpam-5832	433	6	να(q)(λ	να(q)(λ	NOUN
ejpam-5832	433	7	)	)	PUNCT
ejpam-5832	433	8	)	)	PUNCT
ejpam-5832	434	1	q	q	X
ejpam-5832	434	2	,	,	PUNCT
ejpam-5832	434	3	(	(	PUNCT
ejpam-5832	434	4	να(p	να(p	NUM
ejpam-5832	434	5	)	)	PUNCT
ejpam-5832	434	6	(	(	PUNCT
ejpam-5832	434	7	ϵ	ϵ	NOUN
ejpam-5832	434	8	)	)	PUNCT
ejpam-5832	434	9	)	)	PUNCT
ejpam-5832	434	10	q	q	X
ejpam-5832	434	11	)	)	PUNCT
ejpam-5832	434	12	thus	thus	ADV
ejpam-5832	434	13	,	,	PUNCT
ejpam-5832	434	14	α(q	α(q	NUM
ejpam-5832	434	15	)	)	PUNCT
ejpam-5832	434	16	is	be	AUX
ejpam-5832	434	17	a	a	DET
ejpam-5832	434	18	q	q	NOUN
ejpam-5832	434	19	-	-	PUNCT
ejpam-5832	434	20	rofnsg	rofnsg	NOUN
ejpam-5832	434	21	of	of	ADP
ejpam-5832	434	22	α(p	α(p	PROPN
ejpam-5832	434	23	)	)	PUNCT
ejpam-5832	434	24	.	.	PUNCT
ejpam-5832	435	1	theorem	theorem	NOUN
ejpam-5832	435	2	17	17	NUM
ejpam-5832	435	3	.	.	PUNCT
ejpam-5832	436	1	assume	assume	VERB
ejpam-5832	436	2	that	that	SCONJ
ejpam-5832	436	3	q	q	PROPN
ejpam-5832	437	1	and	and	CCONJ
ejpam-5832	437	2	p	p	NOUN
ejpam-5832	437	3	are	be	AUX
ejpam-5832	437	4	q	q	NOUN
ejpam-5832	437	5	-	-	PUNCT
ejpam-5832	437	6	rofsgs	rofsg	NOUN
ejpam-5832	437	7	of	of	ADP
ejpam-5832	437	8	w	w	PROPN
ejpam-5832	437	9	and	and	CCONJ
ejpam-5832	437	10	α	α	PROPN
ejpam-5832	437	11	is	be	AUX
ejpam-5832	437	12	a	a	DET
ejpam-5832	437	13	homomorphism	homomorphism	NOUN
ejpam-5832	437	14	from	from	ADP
ejpam-5832	437	15	v	v	NUM
ejpam-5832	437	16	to	to	ADP
ejpam-5832	437	17	w	w	PROPN
ejpam-5832	437	18	.	.	PUNCT
ejpam-5832	438	1	then	then	ADV
ejpam-5832	438	2	α−1(q	α−1(q	NUM
ejpam-5832	438	3	)	)	PUNCT
ejpam-5832	438	4	is	be	AUX
ejpam-5832	438	5	a	a	DET
ejpam-5832	438	6	q	q	NOUN
ejpam-5832	438	7	-	-	PUNCT
ejpam-5832	438	8	rofnsg	rofnsg	NOUN
ejpam-5832	438	9	of	of	ADP
ejpam-5832	438	10	α−1(p	α−1(p	PROPN
ejpam-5832	438	11	)	)	PUNCT
ejpam-5832	439	1	if	if	SCONJ
ejpam-5832	439	2	q	q	NOUN
ejpam-5832	439	3	is	be	AUX
ejpam-5832	439	4	a	a	DET
ejpam-5832	439	5	q	q	NOUN
ejpam-5832	439	6	-	-	PUNCT
ejpam-5832	439	7	rofnsg	rofnsg	NOUN
ejpam-5832	439	8	of	of	ADP
ejpam-5832	439	9	p	p	PROPN
ejpam-5832	439	10	.	.	PUNCT
ejpam-5832	440	1	proof	proof	NOUN
ejpam-5832	440	2	.	.	PUNCT
ejpam-5832	441	1	from	from	ADP
ejpam-5832	441	2	routine	routine	ADJ
ejpam-5832	441	3	computation	computation	NOUN
ejpam-5832	441	4	,	,	PUNCT
ejpam-5832	441	5	it	it	PRON
ejpam-5832	441	6	can	can	AUX
ejpam-5832	441	7	be	be	AUX
ejpam-5832	441	8	easily	easily	ADV
ejpam-5832	441	9	proved	prove	VERB
ejpam-5832	441	10	that	that	SCONJ
ejpam-5832	441	11	α−1(q	α−1(q	PROPN
ejpam-5832	441	12	)	)	PUNCT
ejpam-5832	441	13	and	and	CCONJ
ejpam-5832	441	14	α−1(p	α−1(p	PROPN
ejpam-5832	441	15	)	)	PUNCT
ejpam-5832	441	16	are	be	AUX
ejpam-5832	441	17	q	q	NOUN
ejpam-5832	441	18	-	-	PUNCT
ejpam-5832	441	19	rofnsgs	rofnsg	NOUN
ejpam-5832	441	20	of	of	ADP
ejpam-5832	441	21	v	v	NOUN
ejpam-5832	441	22	and	and	CCONJ
ejpam-5832	441	23	α−1(q	α−1(q	NUM
ejpam-5832	441	24	)	)	PUNCT
ejpam-5832	442	1	⊆	⊆	NUM
ejpam-5832	442	2	α−1(p	α−1(p	PROPN
ejpam-5832	442	3	)	)	PUNCT
ejpam-5832	442	4	.	.	PUNCT
ejpam-5832	443	1	now	now	ADV
ejpam-5832	443	2	(	(	PUNCT
ejpam-5832	443	3	µα−1(q)(ϵλϵ	µα−1(q)(ϵλϵ	ADJ
ejpam-5832	443	4	−1	−1	NOUN
ejpam-5832	443	5	)	)	PUNCT
ejpam-5832	443	6	)	)	PUNCT
ejpam-5832	444	1	q	q	X
ejpam-5832	445	1	=	=	PUNCT
ejpam-5832	445	2	(	(	PUNCT
ejpam-5832	445	3	µq(α(ϵλϵ	µq(α(ϵλϵ	NOUN
ejpam-5832	445	4	−1	−1	NOUN
ejpam-5832	445	5	)	)	PUNCT
ejpam-5832	445	6	)	)	PUNCT
ejpam-5832	445	7	)	)	PUNCT
ejpam-5832	446	1	q	q	X
ejpam-5832	446	2	=	=	PUNCT
ejpam-5832	446	3	(	(	PUNCT
ejpam-5832	446	4	µq(α(ϵ	µq(α(ϵ	NOUN
ejpam-5832	446	5	)	)	PUNCT
ejpam-5832	446	6	,	,	PUNCT
ejpam-5832	446	7	α(λ	α(λ	PROPN
ejpam-5832	446	8	)	)	PUNCT
ejpam-5832	446	9	,	,	PUNCT
ejpam-5832	446	10	(	(	PUNCT
ejpam-5832	446	11	α(ϵ	α(ϵ	PROPN
ejpam-5832	446	12	)	)	PUNCT
ejpam-5832	446	13	)	)	PUNCT
ejpam-5832	446	14	−1	−1	NOUN
ejpam-5832	446	15	)	)	PUNCT
ejpam-5832	446	16	)	)	PUNCT
ejpam-5832	447	1	q	q	PROPN
ejpam-5832	447	2	≥	≥	PROPN
ejpam-5832	447	3	min{(µq(α(λ)))q	min{(µq(α(λ)))q	NOUN
ejpam-5832	447	4	,	,	PUNCT
ejpam-5832	447	5	(	(	PUNCT
ejpam-5832	447	6	µp	µp	PROPN
ejpam-5832	447	7	(	(	PUNCT
ejpam-5832	447	8	α(ϵ)))q	α(ϵ)))q	NOUN
ejpam-5832	447	9	}	}	PUNCT
ejpam-5832	447	10	=	=	SYM
ejpam-5832	447	11	min{(µα−1(q)(λ	min{(µα−1(q)(λ	NOUN
ejpam-5832	447	12	)	)	PUNCT
ejpam-5832	447	13	)	)	PUNCT
ejpam-5832	448	1	q	q	X
ejpam-5832	448	2	,	,	PUNCT
ejpam-5832	448	3	(	(	PUNCT
ejpam-5832	448	4	µα−1(p	µα−1(p	PROPN
ejpam-5832	448	5	)	)	PUNCT
ejpam-5832	448	6	(	(	PUNCT
ejpam-5832	448	7	ϵ	ϵ	NOUN
ejpam-5832	448	8	)	)	PUNCT
ejpam-5832	448	9	)	)	PUNCT
ejpam-5832	448	10	q	q	X
ejpam-5832	448	11	}	}	PUNCT
ejpam-5832	448	12	similarly	similarly	ADV
ejpam-5832	448	13	(	(	PUNCT
ejpam-5832	448	14	να−1(q)(ϵλϵ	να−1(q)(ϵλϵ	PROPN
ejpam-5832	448	15	−1))q	−1))q	NOUN
ejpam-5832	448	16	≤	≤	ADJ
ejpam-5832	448	17	max{(να−1(q)(λ	max{(να−1(q)(λ	NOUN
ejpam-5832	448	18	)	)	PUNCT
ejpam-5832	448	19	)	)	PUNCT
ejpam-5832	449	1	q	q	X
ejpam-5832	449	2	,	,	PUNCT
ejpam-5832	449	3	(	(	PUNCT
ejpam-5832	449	4	να−1(p	να−1(p	NOUN
ejpam-5832	449	5	)	)	PUNCT
ejpam-5832	449	6	(	(	PUNCT
ejpam-5832	449	7	ϵ	ϵ	NOUN
ejpam-5832	449	8	)	)	PUNCT
ejpam-5832	449	9	)	)	PUNCT
ejpam-5832	450	1	q	q	X
ejpam-5832	450	2	}	}	PUNCT
ejpam-5832	450	3	therefore	therefore	ADV
ejpam-5832	450	4	,	,	PUNCT
ejpam-5832	450	5	α−1(q	α−1(q	PROPN
ejpam-5832	450	6	)	)	PUNCT
ejpam-5832	450	7	is	be	AUX
ejpam-5832	450	8	a	a	DET
ejpam-5832	450	9	q	q	NOUN
ejpam-5832	450	10	-	-	PUNCT
ejpam-5832	450	11	rofnsg	rofnsg	NOUN
ejpam-5832	450	12	of	of	ADP
ejpam-5832	450	13	α−1	α−1	PROPN
ejpam-5832	450	14	(	(	PUNCT
ejpam-5832	450	15	p	p	NOUN
ejpam-5832	450	16	)	)	PUNCT
ejpam-5832	450	17	.	.	PUNCT
ejpam-5832	451	1	5	5	X
ejpam-5832	451	2	.	.	X
ejpam-5832	451	3	fundamental	fundamental	ADJ
ejpam-5832	451	4	theorems	theorem	NOUN
ejpam-5832	451	5	of	of	ADP
ejpam-5832	451	6	q	q	NOUN
ejpam-5832	451	7	-	-	PUNCT
ejpam-5832	451	8	rung	rung	ADJ
ejpam-5832	451	9	orthopair	orthopair	NOUN
ejpam-5832	451	10	fuzzy	fuzzy	ADJ
ejpam-5832	451	11	isomorphisms	isomorphisms	PROPN
ejpam-5832	451	12	the	the	DET
ejpam-5832	451	13	present	present	ADJ
ejpam-5832	451	14	section	section	NOUN
ejpam-5832	451	15	introduces	introduce	VERB
ejpam-5832	451	16	the	the	DET
ejpam-5832	451	17	concepts	concept	NOUN
ejpam-5832	451	18	of	of	ADP
ejpam-5832	451	19	q	q	ADJ
ejpam-5832	451	20	-	-	PUNCT
ejpam-5832	451	21	rung	rung	ADJ
ejpam-5832	451	22	orthopair	orthopair	ADJ
ejpam-5832	451	23	fuzzy	fuzzy	ADJ
ejpam-5832	451	24	homomorphism	homomorphism	NOUN
ejpam-5832	451	25	(	(	PUNCT
ejpam-5832	451	26	q	q	NOUN
ejpam-5832	451	27	-	-	NOUN
ejpam-5832	451	28	rofhom	rofhom	NOUN
ejpam-5832	451	29	)	)	PUNCT
ejpam-5832	451	30	and	and	CCONJ
ejpam-5832	451	31	isomorphism	isomorphism	NOUN
ejpam-5832	451	32	(	(	PUNCT
ejpam-5832	451	33	q	q	NOUN
ejpam-5832	451	34	-	-	PUNCT
ejpam-5832	451	35	rofiso	rofiso	NOUN
ejpam-5832	451	36	)	)	PUNCT
ejpam-5832	451	37	.	.	PUNCT
ejpam-5832	452	1	to	to	PART
ejpam-5832	452	2	extend	extend	VERB
ejpam-5832	452	3	the	the	DET
ejpam-5832	452	4	concept	concept	NOUN
ejpam-5832	452	5	of	of	ADP
ejpam-5832	452	6	the	the	DET
ejpam-5832	452	7	quotient	quotient	NOUN
ejpam-5832	452	8	group	group	PROPN
ejpam-5832	452	9	v	v	PROPN
ejpam-5832	452	10	/	/	SYM
ejpam-5832	452	11	u	u	NOUN
ejpam-5832	452	12	of	of	ADP
ejpam-5832	452	13	v	v	NOUN
ejpam-5832	452	14	with	with	ADP
ejpam-5832	452	15	respect	respect	NOUN
ejpam-5832	452	16	to	to	ADP
ejpam-5832	452	17	its	its	PRON
ejpam-5832	452	18	normal	normal	ADJ
ejpam-5832	452	19	subgroup	subgroup	NOUN
ejpam-5832	452	20	u	u	NOUN
ejpam-5832	452	21	,	,	PUNCT
ejpam-5832	452	22	we	we	PRON
ejpam-5832	452	23	define	define	VERB
ejpam-5832	452	24	the	the	DET
ejpam-5832	452	25	q	q	NOUN
ejpam-5832	452	26	-	-	PUNCT
ejpam-5832	452	27	rofsg	rofsg	NOUN
ejpam-5832	452	28	of	of	ADP
ejpam-5832	452	29	v	v	NOUN
ejpam-5832	452	30	/	/	SYM
ejpam-5832	452	31	u	u	NOUN
ejpam-5832	452	32	.	.	PUNCT
ejpam-5832	453	1	in	in	ADP
ejpam-5832	453	2	addition	addition	NOUN
ejpam-5832	453	3	,	,	PUNCT
ejpam-5832	453	4	we	we	PRON
ejpam-5832	453	5	develop	develop	VERB
ejpam-5832	453	6	the	the	DET
ejpam-5832	453	7	q	q	ADJ
ejpam-5832	453	8	-	-	PUNCT
ejpam-5832	453	9	rung	rung	ADJ
ejpam-5832	453	10	orthopair	orthopair	ADJ
ejpam-5832	453	11	fuzzy	fuzzy	ADJ
ejpam-5832	453	12	counterpart	counterpart	NOUN
ejpam-5832	453	13	of	of	ADP
ejpam-5832	453	14	the	the	DET
ejpam-5832	453	15	fundamental	fundamental	ADJ
ejpam-5832	453	16	theorems	theorem	NOUN
ejpam-5832	453	17	of	of	ADP
ejpam-5832	453	18	isomorphisms	isomorphisms	PROPN
ejpam-5832	453	19	.	.	PUNCT
ejpam-5832	454	1	definition	definition	NOUN
ejpam-5832	454	2	11	11	NUM
ejpam-5832	454	3	.	.	PUNCT
ejpam-5832	455	1	assume	assume	VERB
ejpam-5832	455	2	that	that	SCONJ
ejpam-5832	455	3	q1	q1	PROPN
ejpam-5832	455	4	and	and	CCONJ
ejpam-5832	455	5	q2	q2	NOUN
ejpam-5832	455	6	are	be	AUX
ejpam-5832	455	7	q	q	NOUN
ejpam-5832	455	8	-	-	PUNCT
ejpam-5832	455	9	rofsgs	rofsg	NOUN
ejpam-5832	455	10	of	of	ADP
ejpam-5832	455	11	v	v	NOUN
ejpam-5832	455	12	and	and	CCONJ
ejpam-5832	455	13	w	w	NOUN
ejpam-5832	455	14	respectively	respectively	ADV
ejpam-5832	455	15	.	.	PUNCT
ejpam-5832	456	1	then	then	ADV
ejpam-5832	456	2	a	a	DET
ejpam-5832	456	3	homomorphism	homomorphism	PROPN
ejpam-5832	456	4	α	α	X
ejpam-5832	456	5	:	:	PUNCT
ejpam-5832	456	6	v	v	X
ejpam-5832	456	7	→	→	SYM
ejpam-5832	456	8	w	w	PROPN
ejpam-5832	456	9	is	be	AUX
ejpam-5832	456	10	called	call	VERB
ejpam-5832	456	11	q	q	NOUN
ejpam-5832	456	12	-	-	PUNCT
ejpam-5832	456	13	rofhom	rofhom	NOUN
ejpam-5832	456	14	from	from	ADP
ejpam-5832	456	15	q1	q1	PROPN
ejpam-5832	456	16	to	to	ADP
ejpam-5832	456	17	q2	q2	NOUN
ejpam-5832	456	18	if	if	SCONJ
ejpam-5832	456	19	α(q1	α(q1	ADV
ejpam-5832	456	20	)	)	PUNCT
ejpam-5832	456	21	=	=	SYM
ejpam-5832	456	22	q2	q2	NOUN
ejpam-5832	456	23	.	.	PUNCT
ejpam-5832	457	1	the	the	DET
ejpam-5832	457	2	existence	existence	NOUN
ejpam-5832	457	3	of	of	ADP
ejpam-5832	457	4	q	q	NOUN
ejpam-5832	457	5	-	-	PUNCT
ejpam-5832	457	6	rofhom	rofhom	NOUN
ejpam-5832	457	7	between	between	ADP
ejpam-5832	457	8	q1	q1	PROPN
ejpam-5832	457	9	and	and	CCONJ
ejpam-5832	457	10	q2	q2	NOUN
ejpam-5832	457	11	is	be	AUX
ejpam-5832	457	12	denoted	denote	VERB
ejpam-5832	457	13	by	by	ADP
ejpam-5832	457	14	q1	q1	PROPN
ejpam-5832	457	15	≈	≈	PROPN
ejpam-5832	457	16	q2	q2	PROPN
ejpam-5832	457	17	.	.	PUNCT
ejpam-5832	458	1	definition	definition	NOUN
ejpam-5832	458	2	12	12	NUM
ejpam-5832	458	3	.	.	PUNCT
ejpam-5832	459	1	assume	assume	VERB
ejpam-5832	459	2	that	that	SCONJ
ejpam-5832	459	3	q1	q1	PROPN
ejpam-5832	459	4	and	and	CCONJ
ejpam-5832	459	5	q2	q2	NOUN
ejpam-5832	459	6	are	be	AUX
ejpam-5832	459	7	q	q	NOUN
ejpam-5832	459	8	-	-	PUNCT
ejpam-5832	459	9	rofsgs	rofsg	NOUN
ejpam-5832	459	10	of	of	ADP
ejpam-5832	459	11	v	v	NOUN
ejpam-5832	459	12	and	and	CCONJ
ejpam-5832	459	13	w	w	NOUN
ejpam-5832	459	14	respectively	respectively	ADV
ejpam-5832	459	15	.	.	PUNCT
ejpam-5832	460	1	then	then	ADV
ejpam-5832	460	2	an	an	DET
ejpam-5832	460	3	isomorphism	isomorphism	NOUN
ejpam-5832	460	4	α	α	NOUN
ejpam-5832	460	5	:	:	PUNCT
ejpam-5832	460	6	v	v	ADP
ejpam-5832	460	7	→w	→w	NUM
ejpam-5832	460	8	is	be	AUX
ejpam-5832	460	9	called	call	VERB
ejpam-5832	460	10	q	q	NOUN
ejpam-5832	460	11	-	-	PUNCT
ejpam-5832	460	12	rofiso	rofiso	NOUN
ejpam-5832	460	13	from	from	ADP
ejpam-5832	460	14	q1	q1	PROPN
ejpam-5832	460	15	to	to	ADP
ejpam-5832	460	16	q2	q2	NOUN
ejpam-5832	460	17	if	if	SCONJ
ejpam-5832	460	18	α(q1	α(q1	ADV
ejpam-5832	460	19	)	)	PUNCT
ejpam-5832	460	20	=	=	SYM
ejpam-5832	460	21	q2	q2	NOUN
ejpam-5832	460	22	.	.	PUNCT
ejpam-5832	461	1	the	the	DET
ejpam-5832	461	2	existence	existence	NOUN
ejpam-5832	461	3	of	of	ADP
ejpam-5832	461	4	a	a	DET
ejpam-5832	461	5	q	q	NOUN
ejpam-5832	461	6	-	-	PUNCT
ejpam-5832	461	7	rofiso	rofiso	NOUN
ejpam-5832	461	8	between	between	ADP
ejpam-5832	461	9	q1	q1	PROPN
ejpam-5832	461	10	and	and	CCONJ
ejpam-5832	461	11	q2	q2	NOUN
ejpam-5832	461	12	is	be	AUX
ejpam-5832	461	13	denoted	denote	VERB
ejpam-5832	461	14	by	by	ADP
ejpam-5832	461	15	q1	q1	NOUN
ejpam-5832	461	16	∼=	∼=	PROPN
ejpam-5832	461	17	q2	q2	NOUN
ejpam-5832	461	18	.	.	PUNCT
ejpam-5832	462	1	definition	definition	NOUN
ejpam-5832	462	2	13	13	NUM
ejpam-5832	462	3	.	.	PUNCT
ejpam-5832	463	1	let	let	VERB
ejpam-5832	463	2	q	q	PART
ejpam-5832	463	3	be	be	AUX
ejpam-5832	463	4	a	a	DET
ejpam-5832	463	5	q	q	NOUN
ejpam-5832	463	6	-	-	PUNCT
ejpam-5832	463	7	rofsg	rofsg	NOUN
ejpam-5832	463	8	of	of	ADP
ejpam-5832	463	9	v	v	NOUN
ejpam-5832	463	10	and	and	CCONJ
ejpam-5832	463	11	u	u	NOUN
ejpam-5832	463	12	⊴	⊴	PROPN
ejpam-5832	463	13	v	v	NUM
ejpam-5832	463	14	.	.	PUNCT
ejpam-5832	464	1	then	then	ADV
ejpam-5832	464	2	q′	q′	PUNCT
ejpam-5832	464	3	=	=	SYM
ejpam-5832	464	4	{	{	PUNCT
ejpam-5832	464	5	(	(	PUNCT
ejpam-5832	464	6	ϵu	ϵu	PROPN
ejpam-5832	464	7	,	,	PUNCT
ejpam-5832	464	8	µq′(ϵu	µq′(ϵu	PROPN
ejpam-5832	464	9	)	)	PUNCT
ejpam-5832	464	10	,	,	PUNCT
ejpam-5832	464	11	νq′(ϵu	νq′(ϵu	PROPN
ejpam-5832	464	12	)	)	PUNCT
ejpam-5832	464	13	)	)	PUNCT
ejpam-5832	464	14	:	:	PUNCT
ejpam-5832	464	15	ϵu	ϵu	PROPN
ejpam-5832	464	16	∈	∈	PROPN
ejpam-5832	464	17	v	v	NOUN
ejpam-5832	464	18	/	/	SYM
ejpam-5832	464	19	u	u	NOUN
ejpam-5832	464	20	}	}	PUNCT
ejpam-5832	464	21	,	,	PUNCT
ejpam-5832	464	22	where	where	SCONJ
ejpam-5832	464	23	(	(	PUNCT
ejpam-5832	464	24	µq′(ϵu	µq′(ϵu	PROPN
ejpam-5832	464	25	)	)	PUNCT
ejpam-5832	464	26	)	)	PUNCT
ejpam-5832	464	27	q	q	NOUN
ejpam-5832	464	28	=	=	SYM
ejpam-5832	464	29	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	464	30	:	:	PUNCT
ejpam-5832	464	31	t	t	PROPN
ejpam-5832	464	32	∈	∈	PROPN
ejpam-5832	464	33	ϵu	ϵu	PRON
ejpam-5832	464	34	}	}	PUNCT
ejpam-5832	464	35	and	and	CCONJ
ejpam-5832	464	36	(	(	PUNCT
ejpam-5832	464	37	νq′(ϵu	νq′(ϵu	PROPN
ejpam-5832	464	38	)	)	PUNCT
ejpam-5832	464	39	)	)	PUNCT
ejpam-5832	465	1	q	q	NOUN
ejpam-5832	466	1	=	=	PUNCT
ejpam-5832	466	2	min{(νq(t))q	min{(νq(t))q	NOUN
ejpam-5832	466	3	:	:	PUNCT
ejpam-5832	466	4	t	t	PROPN
ejpam-5832	466	5	∈	∈	PROPN
ejpam-5832	466	6	ϵu	ϵu	X
ejpam-5832	466	7	}	}	PUNCT
ejpam-5832	466	8	,	,	PUNCT
ejpam-5832	466	9	forms	form	VERB
ejpam-5832	466	10	q	q	NOUN
ejpam-5832	466	11	-	-	PUNCT
ejpam-5832	466	12	rofs	rofs	NOUN
ejpam-5832	466	13	of	of	ADP
ejpam-5832	466	14	v	v	NOUN
ejpam-5832	466	15	/	/	SYM
ejpam-5832	466	16	u	u	NOUN
ejpam-5832	466	17	.	.	PUNCT
ejpam-5832	467	1	theorem	theorem	PROPN
ejpam-5832	467	2	18	18	NUM
ejpam-5832	467	3	.	.	PUNCT
ejpam-5832	467	4	q′	q′	NOUN
ejpam-5832	467	5	is	be	AUX
ejpam-5832	467	6	a	a	DET
ejpam-5832	467	7	q	q	NOUN
ejpam-5832	467	8	-	-	PUNCT
ejpam-5832	467	9	rofsg	rofsg	NOUN
ejpam-5832	467	10	of	of	ADP
ejpam-5832	467	11	v	v	NOUN
ejpam-5832	467	12	/	/	SYM
ejpam-5832	467	13	u	u	NOUN
ejpam-5832	467	14	.	.	PUNCT
ejpam-5832	468	1	a.	a.	NOUN
ejpam-5832	468	2	razzaque	razzaque	PROPN
ejpam-5832	468	3	/	/	SYM
ejpam-5832	468	4	eur	eur	NOUN
ejpam-5832	468	5	.	.	PUNCT
ejpam-5832	469	1	j.	j.	PROPN
ejpam-5832	469	2	pure	pure	PROPN
ejpam-5832	469	3	appl	appl	PROPN
ejpam-5832	469	4	.	.	PROPN
ejpam-5832	469	5	math	math	PROPN
ejpam-5832	469	6	,	,	PUNCT
ejpam-5832	469	7	18	18	NUM
ejpam-5832	469	8	(	(	PUNCT
ejpam-5832	469	9	3	3	NUM
ejpam-5832	469	10	)	)	PUNCT
ejpam-5832	469	11	(	(	PUNCT
ejpam-5832	469	12	2025	2025	NUM
ejpam-5832	469	13	)	)	PUNCT
ejpam-5832	469	14	,	,	PUNCT
ejpam-5832	469	15	5832	5832	NUM
ejpam-5832	469	16	14	14	NUM
ejpam-5832	469	17	of	of	ADP
ejpam-5832	469	18	21	21	NUM
ejpam-5832	469	19	proof	proof	NOUN
ejpam-5832	469	20	.	.	PUNCT
ejpam-5832	470	1	let	let	VERB
ejpam-5832	470	2	ϵu	ϵu	PRON
ejpam-5832	470	3	∈	∈	PROPN
ejpam-5832	470	4	v	v	NOUN
ejpam-5832	470	5	/	/	SYM
ejpam-5832	470	6	u	u	NOUN
ejpam-5832	470	7	,	,	PUNCT
ejpam-5832	470	8	then	then	ADV
ejpam-5832	470	9	(	(	PUNCT
ejpam-5832	470	10	µq′(ϵu)−1	µq′(ϵu)−1	NOUN
ejpam-5832	470	11	)	)	PUNCT
ejpam-5832	470	12	q	q	NOUN
ejpam-5832	471	1	=	=	PUNCT
ejpam-5832	471	2	(	(	PUNCT
ejpam-5832	471	3	µq′(ϵ−1u	µq′(ϵ−1u	PROPN
ejpam-5832	471	4	)	)	PUNCT
ejpam-5832	471	5	)	)	PUNCT
ejpam-5832	471	6	q	q	NOUN
ejpam-5832	472	1	=	=	SYM
ejpam-5832	472	2	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	472	3	:	:	PUNCT
ejpam-5832	472	4	t	t	PROPN
ejpam-5832	472	5	∈	∈	PROPN
ejpam-5832	472	6	ϵ−1u	ϵ−1u	NOUN
ejpam-5832	472	7	}	}	PUNCT
ejpam-5832	472	8	=	=	SYM
ejpam-5832	472	9	max{(µq(t−1))q	max{(µq(t−1))q	NOUN
ejpam-5832	472	10	:	:	PUNCT
ejpam-5832	472	11	t−1	t−1	PROPN
ejpam-5832	472	12	∈	∈	PROPN
ejpam-5832	473	1	ϵu	ϵu	NOUN
ejpam-5832	473	2	}	}	PUNCT
ejpam-5832	473	3	(	(	PUNCT
ejpam-5832	473	4	sinceu	sinceu	NOUN
ejpam-5832	473	5	is	be	AUX
ejpam-5832	473	6	normal	normal	ADJ
ejpam-5832	473	7	in	in	ADP
ejpam-5832	473	8	v	v	NOUN
ejpam-5832	473	9	)	)	PUNCT
ejpam-5832	473	10	=	=	SYM
ejpam-5832	473	11	(	(	PUNCT
ejpam-5832	473	12	µq′(ϵu	µq′(ϵu	PROPN
ejpam-5832	473	13	)	)	PUNCT
ejpam-5832	473	14	)	)	PUNCT
ejpam-5832	474	1	q	q	PROPN
ejpam-5832	474	2	similarly	similarly	ADV
ejpam-5832	474	3	,	,	PUNCT
ejpam-5832	474	4	(	(	PUNCT
ejpam-5832	474	5	νq′(ϵu)−1	νq′(ϵu)−1	NOUN
ejpam-5832	474	6	)	)	PUNCT
ejpam-5832	474	7	q	q	SYM
ejpam-5832	475	1	=	=	PUNCT
ejpam-5832	475	2	(	(	PUNCT
ejpam-5832	475	3	νq′(ϵu	νq′(ϵu	PROPN
ejpam-5832	475	4	)	)	PUNCT
ejpam-5832	475	5	)	)	PUNCT
ejpam-5832	476	1	q	q	PROPN
ejpam-5832	477	1	next	next	ADV
ejpam-5832	477	2	,	,	PUNCT
ejpam-5832	477	3	let	let	VERB
ejpam-5832	477	4	ϵ1u	ϵ1u	PRON
ejpam-5832	477	5	,	,	PUNCT
ejpam-5832	477	6	ϵ2u	ϵ2u	NOUN
ejpam-5832	477	7	∈	∈	PROPN
ejpam-5832	477	8	v	v	NOUN
ejpam-5832	477	9	/	/	SYM
ejpam-5832	477	10	u	u	NOUN
ejpam-5832	477	11	,	,	PUNCT
ejpam-5832	477	12	then	then	ADV
ejpam-5832	477	13	(	(	PUNCT
ejpam-5832	477	14	µq′(ϵ1uϵ̇2u	µq′(ϵ1uϵ̇2u	PROPN
ejpam-5832	477	15	)	)	PUNCT
ejpam-5832	477	16	)	)	PUNCT
ejpam-5832	477	17	q	q	X
ejpam-5832	478	1	=	=	PUNCT
ejpam-5832	478	2	(	(	PUNCT
ejpam-5832	478	3	µq′(ϵ1ϵ2u	µq′(ϵ1ϵ2u	ADV
ejpam-5832	478	4	)	)	PUNCT
ejpam-5832	478	5	)	)	PUNCT
ejpam-5832	478	6	q	q	NOUN
ejpam-5832	479	1	=	=	SYM
ejpam-5832	479	2	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	479	3	:	:	PUNCT
ejpam-5832	479	4	t	t	PROPN
ejpam-5832	479	5	∈	∈	PROPN
ejpam-5832	479	6	ϵ1ϵ2u	ϵ1ϵ2u	PUNCT
ejpam-5832	479	7	=	=	PUNCT
ejpam-5832	479	8	ϵ1ϵ̇2u	ϵ1ϵ̇2u	PROPN
ejpam-5832	479	9	}	}	PUNCT
ejpam-5832	480	1	=	=	SYM
ejpam-5832	480	2	max{(µq(λκ))q	max{(µq(λκ))q	PROPN
ejpam-5832	480	3	:	:	PUNCT
ejpam-5832	481	1	λ	λ	X
ejpam-5832	481	2	∈	∈	PROPN
ejpam-5832	481	3	ϵ1u	ϵ1u	NOUN
ejpam-5832	481	4	,	,	PUNCT
ejpam-5832	481	5	κ	κ	PROPN
ejpam-5832	481	6	∈	∈	PROPN
ejpam-5832	481	7	ϵ2u	ϵ2u	PRON
ejpam-5832	481	8	}	}	PUNCT
ejpam-5832	481	9	≥	≥	NOUN
ejpam-5832	481	10	max{min((µq(λ	max{min((µq(λ	NOUN
ejpam-5832	481	11	)	)	PUNCT
ejpam-5832	481	12	)	)	PUNCT
ejpam-5832	482	1	q	q	X
ejpam-5832	482	2	,	,	PUNCT
ejpam-5832	482	3	(	(	PUNCT
ejpam-5832	482	4	µq(κ	µq(κ	NUM
ejpam-5832	482	5	)	)	PUNCT
ejpam-5832	482	6	)	)	PUNCT
ejpam-5832	483	1	q	q	X
ejpam-5832	483	2	)	)	PUNCT
ejpam-5832	483	3	:	:	PUNCT
ejpam-5832	484	1	λ	λ	X
ejpam-5832	484	2	∈	∈	PROPN
ejpam-5832	484	3	ϵ1u	ϵ1u	NOUN
ejpam-5832	484	4	,	,	PUNCT
ejpam-5832	484	5	κ	κ	PROPN
ejpam-5832	484	6	∈	∈	PROPN
ejpam-5832	484	7	ϵ2u	ϵ2u	NOUN
ejpam-5832	484	8	}	}	PUNCT
ejpam-5832	484	9	=	=	SYM
ejpam-5832	484	10	min	min	PROPN
ejpam-5832	484	11	(	(	PUNCT
ejpam-5832	484	12	max{(µq(λ))q	max{(µq(λ))q	NOUN
ejpam-5832	484	13	:	:	PUNCT
ejpam-5832	484	14	λ	λ	X
ejpam-5832	484	15	∈	∈	PROPN
ejpam-5832	484	16	ϵ1u},max{(µq(κ))q	ϵ1u},max{(µq(κ))q	NOUN
ejpam-5832	484	17	:	:	PUNCT
ejpam-5832	484	18	κ	κ	X
ejpam-5832	484	19	∈	∈	PROPN
ejpam-5832	484	20	ϵ2u	ϵ2u	NUM
ejpam-5832	484	21	}	}	PUNCT
ejpam-5832	484	22	)	)	PUNCT
ejpam-5832	485	1	=	=	SYM
ejpam-5832	485	2	min	min	PROPN
ejpam-5832	485	3	(	(	PUNCT
ejpam-5832	485	4	(	(	PUNCT
ejpam-5832	485	5	µq′(ϵ1u))q	µq′(ϵ1u))q	NOUN
ejpam-5832	485	6	,	,	PUNCT
ejpam-5832	485	7	(	(	PUNCT
ejpam-5832	485	8	µq′(ϵ2u))q	µq′(ϵ2u))q	PROPN
ejpam-5832	485	9	)	)	PUNCT
ejpam-5832	485	10	likewise	likewise	ADV
ejpam-5832	485	11	,	,	PUNCT
ejpam-5832	485	12	it	it	PRON
ejpam-5832	485	13	can	can	AUX
ejpam-5832	485	14	be	be	AUX
ejpam-5832	485	15	demonstrated	demonstrate	VERB
ejpam-5832	485	16	that	that	SCONJ
ejpam-5832	485	17	(	(	PUNCT
ejpam-5832	485	18	νq′(ϵ1uϵ̇2u	νq′(ϵ1uϵ̇2u	PROPN
ejpam-5832	485	19	)	)	PUNCT
ejpam-5832	485	20	)	)	PUNCT
ejpam-5832	485	21	q	q	PROPN
ejpam-5832	485	22	≤	≤	NUM
ejpam-5832	485	23	max	max	NOUN
ejpam-5832	485	24	(	(	PUNCT
ejpam-5832	485	25	(	(	PUNCT
ejpam-5832	485	26	νq′(ϵ1u))q	νq′(ϵ1u))q	PROPN
ejpam-5832	485	27	,	,	PUNCT
ejpam-5832	485	28	(	(	PUNCT
ejpam-5832	485	29	νq′(ϵ2u))q	νq′(ϵ2u))q	NOUN
ejpam-5832	485	30	)	)	PUNCT
ejpam-5832	485	31	.	.	PUNCT
ejpam-5832	486	1	hence	hence	ADV
ejpam-5832	486	2	,	,	PUNCT
ejpam-5832	486	3	q′	q′	NOUN
ejpam-5832	486	4	is	be	AUX
ejpam-5832	486	5	a	a	DET
ejpam-5832	486	6	q	q	NOUN
ejpam-5832	486	7	-	-	PUNCT
ejpam-5832	486	8	rofsg	rofsg	NOUN
ejpam-5832	486	9	of	of	ADP
ejpam-5832	486	10	v	v	NOUN
ejpam-5832	486	11	/	/	SYM
ejpam-5832	486	12	u	u	NOUN
ejpam-5832	486	13	.	.	PUNCT
ejpam-5832	487	1	remark	remark	PROPN
ejpam-5832	487	2	1	1	NUM
ejpam-5832	487	3	.	.	PUNCT
ejpam-5832	488	1	the	the	DET
ejpam-5832	488	2	q	q	NOUN
ejpam-5832	488	3	-	-	PUNCT
ejpam-5832	488	4	rofsg	rofsg	NOUN
ejpam-5832	488	5	q′	q′	NOUN
ejpam-5832	488	6	is	be	AUX
ejpam-5832	488	7	called	call	VERB
ejpam-5832	488	8	q	q	ADJ
ejpam-5832	488	9	-	-	PUNCT
ejpam-5832	488	10	rung	rung	ADJ
ejpam-5832	488	11	orthopair	orthopair	ADJ
ejpam-5832	488	12	fuzzy	fuzzy	ADJ
ejpam-5832	488	13	quotient	quotient	NOUN
ejpam-5832	488	14	group	group	NOUN
ejpam-5832	488	15	(	(	PUNCT
ejpam-5832	488	16	q	q	NOUN
ejpam-5832	488	17	-	-	PUNCT
ejpam-5832	488	18	roffg	roffg	ADJ
ejpam-5832	488	19	)	)	PUNCT
ejpam-5832	488	20	of	of	ADP
ejpam-5832	488	21	q	q	NOUN
ejpam-5832	488	22	with	with	ADP
ejpam-5832	488	23	respect	respect	NOUN
ejpam-5832	488	24	to	to	ADP
ejpam-5832	488	25	u	u	PRON
ejpam-5832	488	26	.	.	PUNCT
ejpam-5832	489	1	consider	consider	VERB
ejpam-5832	489	2	two	two	NUM
ejpam-5832	489	3	q	q	NOUN
ejpam-5832	489	4	-	-	PUNCT
ejpam-5832	489	5	rofsgs	rofsgs	NOUN
ejpam-5832	489	6	q	q	NOUN
ejpam-5832	489	7	and	and	CCONJ
ejpam-5832	489	8	p	p	NOUN
ejpam-5832	489	9	of	of	ADP
ejpam-5832	489	10	v	v	NOUN
ejpam-5832	489	11	such	such	ADJ
ejpam-5832	489	12	that	that	SCONJ
ejpam-5832	489	13	p	p	NOUN
ejpam-5832	489	14	is	be	AUX
ejpam-5832	489	15	a	a	DET
ejpam-5832	489	16	q	q	NOUN
ejpam-5832	489	17	-	-	PUNCT
ejpam-5832	489	18	rofnsg	rofnsg	NOUN
ejpam-5832	489	19	of	of	ADP
ejpam-5832	489	20	q.	q.	PROPN
ejpam-5832	489	21	according	accord	VERB
ejpam-5832	489	22	to	to	ADP
ejpam-5832	489	23	theorem	theorem	ADJ
ejpam-5832	489	24	13	13	NUM
ejpam-5832	489	25	p	p	NOUN
ejpam-5832	489	26	∗	∗	NOUN
ejpam-5832	489	27	is	be	AUX
ejpam-5832	489	28	normal	normal	ADJ
ejpam-5832	489	29	in	in	ADP
ejpam-5832	489	30	q∗	q∗	NOUN
ejpam-5832	489	31	,	,	PUNCT
ejpam-5832	489	32	so	so	CCONJ
ejpam-5832	489	33	the	the	DET
ejpam-5832	489	34	quotient	quotient	NOUN
ejpam-5832	489	35	group	group	NOUN
ejpam-5832	489	36	q∗/p	q∗/p	PROPN
ejpam-5832	489	37	∗	∗	NOUN
ejpam-5832	489	38	can	can	AUX
ejpam-5832	489	39	be	be	AUX
ejpam-5832	489	40	formed	form	VERB
ejpam-5832	489	41	.	.	PUNCT
ejpam-5832	490	1	consider	consider	VERB
ejpam-5832	490	2	a	a	DET
ejpam-5832	490	3	q	q	NOUN
ejpam-5832	490	4	-	-	PUNCT
ejpam-5832	490	5	rofs	rofs	ADJ
ejpam-5832	490	6	q′′	q′′	NOUN
ejpam-5832	490	7	of	of	ADP
ejpam-5832	490	8	q∗	q∗	NOUN
ejpam-5832	490	9	as	as	SCONJ
ejpam-5832	490	10	follows	follow	VERB
ejpam-5832	490	11	;	;	PUNCT
ejpam-5832	490	12	(	(	PUNCT
ejpam-5832	490	13	i	i	NOUN
ejpam-5832	490	14	)	)	PUNCT
ejpam-5832	490	15	(	(	PUNCT
ejpam-5832	490	16	µq′′(ϵ	µq′′(ϵ	PROPN
ejpam-5832	490	17	)	)	PUNCT
ejpam-5832	490	18	)	)	PUNCT
ejpam-5832	490	19	q	q	X
ejpam-5832	491	1	=	=	SYM
ejpam-5832	491	2	(	(	PUNCT
ejpam-5832	491	3	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	491	4	)	)	PUNCT
ejpam-5832	491	5	)	)	PUNCT
ejpam-5832	491	6	q	q	PROPN
ejpam-5832	491	7	for	for	ADP
ejpam-5832	491	8	all	all	DET
ejpam-5832	491	9	ϵ	ϵ	PRON
ejpam-5832	491	10	∈	∈	PROPN
ejpam-5832	491	11	q∗	q∗	NOUN
ejpam-5832	491	12	(	(	PUNCT
ejpam-5832	491	13	ii	ii	NOUN
ejpam-5832	491	14	)	)	PUNCT
ejpam-5832	491	15	(	(	PUNCT
ejpam-5832	491	16	νq′′(ϵ	νq′′(ϵ	PROPN
ejpam-5832	491	17	)	)	PUNCT
ejpam-5832	491	18	)	)	PUNCT
ejpam-5832	491	19	q	q	X
ejpam-5832	492	1	=	=	PUNCT
ejpam-5832	492	2	(	(	PUNCT
ejpam-5832	492	3	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	492	4	)	)	PUNCT
ejpam-5832	492	5	)	)	PUNCT
ejpam-5832	492	6	q	q	NOUN
ejpam-5832	492	7	for	for	ADP
ejpam-5832	492	8	all	all	DET
ejpam-5832	492	9	ϵ	ϵ	PART
ejpam-5832	492	10	∈	∈	ADJ
ejpam-5832	492	11	q∗	q∗	NOUN
ejpam-5832	492	12	it	it	PRON
ejpam-5832	492	13	is	be	AUX
ejpam-5832	492	14	a	a	DET
ejpam-5832	492	15	matter	matter	NOUN
ejpam-5832	492	16	of	of	ADP
ejpam-5832	492	17	simple	simple	ADJ
ejpam-5832	492	18	calculations	calculation	NOUN
ejpam-5832	492	19	to	to	PART
ejpam-5832	492	20	verify	verify	VERB
ejpam-5832	492	21	that	that	SCONJ
ejpam-5832	492	22	q′′	q′′	SCONJ
ejpam-5832	492	23	is	be	AUX
ejpam-5832	492	24	a	a	DET
ejpam-5832	492	25	q	q	NOUN
ejpam-5832	492	26	-	-	PUNCT
ejpam-5832	492	27	rofsg	rofsg	NOUN
ejpam-5832	492	28	of	of	ADP
ejpam-5832	492	29	q∗.	q∗.	NOUN
ejpam-5832	492	30	according	accord	VERB
ejpam-5832	492	31	to	to	ADP
ejpam-5832	492	32	definition	definition	NOUN
ejpam-5832	492	33	13	13	NUM
ejpam-5832	492	34	and	and	CCONJ
ejpam-5832	492	35	theorem	theorem	VERB
ejpam-5832	492	36	18	18	NUM
ejpam-5832	492	37	,	,	PUNCT
ejpam-5832	492	38	q	q	NOUN
ejpam-5832	492	39	-	-	PUNCT
ejpam-5832	492	40	roffg	roffg	ADJ
ejpam-5832	492	41	of	of	ADP
ejpam-5832	492	42	q′′	q′′	NOUN
ejpam-5832	492	43	with	with	ADP
ejpam-5832	492	44	regard	regard	NOUN
ejpam-5832	492	45	to	to	ADP
ejpam-5832	492	46	p	p	NOUN
ejpam-5832	492	47	∗	∗	NOUN
ejpam-5832	492	48	exists	exist	VERB
ejpam-5832	492	49	.	.	PUNCT
ejpam-5832	493	1	we	we	PRON
ejpam-5832	493	2	refer	refer	VERB
ejpam-5832	493	3	to	to	ADP
ejpam-5832	493	4	it	it	PRON
ejpam-5832	493	5	as	as	ADP
ejpam-5832	493	6	q	q	PROPN
ejpam-5832	493	7	/	/	SYM
ejpam-5832	493	8	p	p	NOUN
ejpam-5832	493	9	for	for	ADP
ejpam-5832	493	10	the	the	DET
ejpam-5832	493	11	purpose	purpose	NOUN
ejpam-5832	493	12	of	of	ADP
ejpam-5832	493	13	convenience	convenience	NOUN
ejpam-5832	493	14	.	.	PUNCT
ejpam-5832	494	1	obviously	obviously	ADV
ejpam-5832	494	2	,	,	PUNCT
ejpam-5832	494	3	q	q	X
ejpam-5832	494	4	/	/	SYM
ejpam-5832	494	5	p	p	PRON
ejpam-5832	494	6	is	be	AUX
ejpam-5832	494	7	q	q	NOUN
ejpam-5832	494	8	-	-	PUNCT
ejpam-5832	494	9	rofsg	rofsg	NOUN
ejpam-5832	494	10	of	of	ADP
ejpam-5832	494	11	q∗/p	q∗/p	PROPN
ejpam-5832	494	12	∗	∗	NOUN
ejpam-5832	494	13	and	and	CCONJ
ejpam-5832	494	14	(	(	PUNCT
ejpam-5832	494	15	i	i	NOUN
ejpam-5832	494	16	)	)	PUNCT
ejpam-5832	494	17	(	(	PUNCT
ejpam-5832	494	18	µq	µq	PROPN
ejpam-5832	494	19	/	/	SYM
ejpam-5832	494	20	p	p	X
ejpam-5832	494	21	(	(	PUNCT
ejpam-5832	494	22	ϵp	ϵp	ADP
ejpam-5832	494	23	∗	∗	NOUN
ejpam-5832	494	24	)	)	PUNCT
ejpam-5832	494	25	)	)	PUNCT
ejpam-5832	495	1	q	q	X
ejpam-5832	496	1	=	=	SYM
ejpam-5832	496	2	max{(µq′′(t))q	max{(µq′′(t))q	NUM
ejpam-5832	496	3	:	:	PUNCT
ejpam-5832	496	4	t	t	PROPN
ejpam-5832	496	5	∈	∈	PROPN
ejpam-5832	496	6	ϵp	ϵp	ADP
ejpam-5832	496	7	∗	∗	PROPN
ejpam-5832	496	8	}	}	PUNCT
ejpam-5832	496	9	(	(	PUNCT
ejpam-5832	496	10	ii	ii	NOUN
ejpam-5832	496	11	)	)	PUNCT
ejpam-5832	496	12	(	(	PUNCT
ejpam-5832	496	13	νq	νq	PROPN
ejpam-5832	496	14	/	/	SYM
ejpam-5832	496	15	p	p	X
ejpam-5832	496	16	(	(	PUNCT
ejpam-5832	496	17	ϵp	ϵp	ADP
ejpam-5832	496	18	∗	∗	NOUN
ejpam-5832	496	19	)	)	PUNCT
ejpam-5832	496	20	)	)	PUNCT
ejpam-5832	496	21	q	q	PUNCT
ejpam-5832	497	1	=	=	PUNCT
ejpam-5832	497	2	min{(νq′′(t))q	min{(νq′′(t))q	NOUN
ejpam-5832	497	3	:	:	PUNCT
ejpam-5832	497	4	t	t	PROPN
ejpam-5832	497	5	∈	∈	PROPN
ejpam-5832	497	6	ϵp	ϵp	ADP
ejpam-5832	497	7	∗	∗	NOUN
ejpam-5832	497	8	}	}	PUNCT
ejpam-5832	497	9	a.	a.	NOUN
ejpam-5832	497	10	razzaque	razzaque	NOUN
ejpam-5832	497	11	/	/	SYM
ejpam-5832	497	12	eur	eur	NOUN
ejpam-5832	497	13	.	.	PUNCT
ejpam-5832	498	1	j.	j.	PROPN
ejpam-5832	498	2	pure	pure	PROPN
ejpam-5832	498	3	appl	appl	PROPN
ejpam-5832	498	4	.	.	PROPN
ejpam-5832	498	5	math	math	PROPN
ejpam-5832	498	6	,	,	PUNCT
ejpam-5832	498	7	18	18	NUM
ejpam-5832	498	8	(	(	PUNCT
ejpam-5832	498	9	3	3	NUM
ejpam-5832	498	10	)	)	PUNCT
ejpam-5832	498	11	(	(	PUNCT
ejpam-5832	498	12	2025	2025	NUM
ejpam-5832	498	13	)	)	PUNCT
ejpam-5832	498	14	,	,	PUNCT
ejpam-5832	498	15	5832	5832	NUM
ejpam-5832	498	16	15	15	NUM
ejpam-5832	498	17	of	of	ADP
ejpam-5832	498	18	21	21	NUM
ejpam-5832	498	19	theorem	theorem	NOUN
ejpam-5832	498	20	19	19	NUM
ejpam-5832	498	21	.	.	PUNCT
ejpam-5832	498	22	assume	assume	VERB
ejpam-5832	498	23	that	that	SCONJ
ejpam-5832	498	24	q	q	PROPN
ejpam-5832	499	1	and	and	CCONJ
ejpam-5832	499	2	p	p	NOUN
ejpam-5832	499	3	be	be	AUX
ejpam-5832	499	4	q	q	NOUN
ejpam-5832	499	5	-	-	PUNCT
ejpam-5832	499	6	rofsgs	rofsg	NOUN
ejpam-5832	499	7	of	of	ADP
ejpam-5832	499	8	v	v	NOUN
ejpam-5832	500	1	and	and	CCONJ
ejpam-5832	500	2	p	p	NOUN
ejpam-5832	500	3	be	be	AUX
ejpam-5832	500	4	a	a	DET
ejpam-5832	500	5	q	q	NOUN
ejpam-5832	500	6	-	-	PUNCT
ejpam-5832	500	7	rofnsg	rofnsg	NOUN
ejpam-5832	500	8	of	of	ADP
ejpam-5832	500	9	q.	q.	PROPN
ejpam-5832	500	10	then	then	ADV
ejpam-5832	500	11	q′′	q′′	ADP
ejpam-5832	500	12	≈	≈	PROPN
ejpam-5832	500	13	q	q	PROPN
ejpam-5832	500	14	/	/	SYM
ejpam-5832	500	15	p	p	NOUN
ejpam-5832	500	16	.	.	PUNCT
ejpam-5832	501	1	proof	proof	NOUN
ejpam-5832	501	2	.	.	PUNCT
ejpam-5832	502	1	we	we	PRON
ejpam-5832	502	2	know	know	VERB
ejpam-5832	502	3	q′′	q′′	ADV
ejpam-5832	502	4	is	be	AUX
ejpam-5832	502	5	q	q	NOUN
ejpam-5832	502	6	-	-	PUNCT
ejpam-5832	502	7	rofsg	rofsg	NOUN
ejpam-5832	502	8	of	of	ADP
ejpam-5832	502	9	q∗	q∗	NOUN
ejpam-5832	502	10	and	and	CCONJ
ejpam-5832	502	11	q	q	NOUN
ejpam-5832	502	12	/	/	SYM
ejpam-5832	502	13	p	p	PRON
ejpam-5832	502	14	is	be	AUX
ejpam-5832	502	15	a	a	DET
ejpam-5832	502	16	q	q	NOUN
ejpam-5832	502	17	-	-	PUNCT
ejpam-5832	502	18	rofsg	rofsg	NOUN
ejpam-5832	502	19	of	of	ADP
ejpam-5832	502	20	q∗/p	q∗/p	NOUN
ejpam-5832	502	21	∗.	∗.	PROPN
ejpam-5832	502	22	let	let	VERB
ejpam-5832	502	23	α	α	NOUN
ejpam-5832	502	24	:	:	PUNCT
ejpam-5832	502	25	q∗	q∗	PROPN
ejpam-5832	502	26	→	→	SYM
ejpam-5832	502	27	q∗/p	q∗/p	NOUN
ejpam-5832	502	28	∗	∗	NOUN
ejpam-5832	502	29	be	be	AUX
ejpam-5832	502	30	defined	define	VERB
ejpam-5832	502	31	by	by	ADP
ejpam-5832	502	32	α(ϵ	α(ϵ	PROPN
ejpam-5832	502	33	)	)	PUNCT
ejpam-5832	503	1	=	=	PUNCT
ejpam-5832	503	2	ϵp	ϵp	ADP
ejpam-5832	503	3	∗.	∗.	PROPN
ejpam-5832	503	4	then	then	ADV
ejpam-5832	503	5	obviously	obviously	ADV
ejpam-5832	503	6	α	α	PROPN
ejpam-5832	503	7	is	be	AUX
ejpam-5832	503	8	a	a	DET
ejpam-5832	503	9	homomorphism	homomorphism	NOUN
ejpam-5832	503	10	.	.	PUNCT
ejpam-5832	504	1	now	now	ADV
ejpam-5832	504	2	(	(	PUNCT
ejpam-5832	504	3	µα(q′′)(ϵp	µα(q′′)(ϵp	NUM
ejpam-5832	504	4	∗	∗	NOUN
ejpam-5832	504	5	)	)	PUNCT
ejpam-5832	504	6	)	)	PUNCT
ejpam-5832	505	1	q	q	X
ejpam-5832	506	1	=	=	SYM
ejpam-5832	506	2	max{(µq′′(t))q	max{(µq′′(t))q	NUM
ejpam-5832	506	3	:	:	PUNCT
ejpam-5832	506	4	t	t	PROPN
ejpam-5832	506	5	∈	∈	PROPN
ejpam-5832	506	6	q∗	q∗	PROPN
ejpam-5832	506	7	,	,	PUNCT
ejpam-5832	506	8	α(t	α(t	PROPN
ejpam-5832	506	9	)	)	PUNCT
ejpam-5832	506	10	=	=	PUNCT
ejpam-5832	506	11	ϵp	ϵp	ADP
ejpam-5832	506	12	∗	∗	NOUN
ejpam-5832	506	13	}	}	PUNCT
ejpam-5832	506	14	=	=	SYM
ejpam-5832	506	15	max{(µq(u))q	max{(µq(u))q	NOUN
ejpam-5832	506	16	:	:	PUNCT
ejpam-5832	506	17	u	u	NOUN
ejpam-5832	506	18	∈	∈	PROPN
ejpam-5832	506	19	ϵp	ϵp	ADP
ejpam-5832	506	20	∗	∗	NOUN
ejpam-5832	506	21	}	}	PUNCT
ejpam-5832	506	22	=	=	SYM
ejpam-5832	506	23	(	(	PUNCT
ejpam-5832	506	24	µq	µq	PROPN
ejpam-5832	506	25	/	/	SYM
ejpam-5832	506	26	p	p	X
ejpam-5832	506	27	(	(	PUNCT
ejpam-5832	506	28	ϵp	ϵp	ADP
ejpam-5832	506	29	∗	∗	NOUN
ejpam-5832	506	30	)	)	PUNCT
ejpam-5832	506	31	)	)	PUNCT
ejpam-5832	506	32	q	q	PUNCT
ejpam-5832	506	33	by	by	ADP
ejpam-5832	506	34	using	use	VERB
ejpam-5832	506	35	the	the	DET
ejpam-5832	506	36	same	same	ADJ
ejpam-5832	506	37	arguments	argument	NOUN
ejpam-5832	506	38	,	,	PUNCT
ejpam-5832	506	39	we	we	PRON
ejpam-5832	506	40	show	show	VERB
ejpam-5832	506	41	that	that	SCONJ
ejpam-5832	506	42	(	(	PUNCT
ejpam-5832	506	43	να(q′′)(ϵp	να(q′′)(ϵp	NUM
ejpam-5832	506	44	∗	∗	NOUN
ejpam-5832	506	45	)	)	PUNCT
ejpam-5832	506	46	)	)	PUNCT
ejpam-5832	506	47	q	q	X
ejpam-5832	507	1	=	=	PUNCT
ejpam-5832	507	2	(	(	PUNCT
ejpam-5832	507	3	νq	νq	PROPN
ejpam-5832	507	4	/	/	SYM
ejpam-5832	507	5	p	p	X
ejpam-5832	507	6	(	(	PUNCT
ejpam-5832	507	7	ϵp	ϵp	ADP
ejpam-5832	507	8	∗	∗	NOUN
ejpam-5832	507	9	)	)	PUNCT
ejpam-5832	507	10	)	)	PUNCT
ejpam-5832	507	11	q	q	PUNCT
ejpam-5832	507	12	therefore	therefore	ADV
ejpam-5832	507	13	,	,	PUNCT
ejpam-5832	507	14	α(q′′	α(q′′	NOUN
ejpam-5832	507	15	)	)	PUNCT
ejpam-5832	507	16	=	=	SYM
ejpam-5832	508	1	q	q	PUNCT
ejpam-5832	508	2	/	/	SYM
ejpam-5832	508	3	p	p	NOUN
ejpam-5832	508	4	.	.	PUNCT
ejpam-5832	509	1	finally	finally	ADV
ejpam-5832	509	2	,	,	PUNCT
ejpam-5832	509	3	definition	definition	NOUN
ejpam-5832	509	4	11	11	NUM
ejpam-5832	509	5	results	result	NOUN
ejpam-5832	509	6	in	in	ADP
ejpam-5832	509	7	q′′	q′′	ADP
ejpam-5832	509	8	≈	≈	PROPN
ejpam-5832	509	9	q	q	PROPN
ejpam-5832	509	10	/	/	SYM
ejpam-5832	509	11	p	p	NOUN
ejpam-5832	509	12	.	.	PUNCT
ejpam-5832	510	1	lemma	lemma	PROPN
ejpam-5832	510	2	3	3	X
ejpam-5832	510	3	.	.	PUNCT
ejpam-5832	510	4	suppose	suppose	VERB
ejpam-5832	510	5	that	that	SCONJ
ejpam-5832	510	6	q	q	NOUN
ejpam-5832	510	7	is	be	AUX
ejpam-5832	510	8	a	a	DET
ejpam-5832	510	9	q	q	NOUN
ejpam-5832	510	10	-	-	PUNCT
ejpam-5832	510	11	rofsg	rofsg	NOUN
ejpam-5832	510	12	of	of	ADP
ejpam-5832	510	13	v	v	NOUN
ejpam-5832	510	14	and	and	CCONJ
ejpam-5832	510	15	α	α	NOUN
ejpam-5832	510	16	:	:	PUNCT
ejpam-5832	510	17	v	v	NOUN
ejpam-5832	510	18	→	→	SYM
ejpam-5832	510	19	u	u	NOUN
ejpam-5832	510	20	is	be	AUX
ejpam-5832	510	21	a	a	DET
ejpam-5832	510	22	homomorphism	homomorphism	NOUN
ejpam-5832	510	23	from	from	ADP
ejpam-5832	510	24	v	v	NUM
ejpam-5832	510	25	to	to	ADP
ejpam-5832	510	26	u	u	PRON
ejpam-5832	510	27	.	.	PUNCT
ejpam-5832	511	1	then	then	ADV
ejpam-5832	511	2	(	(	PUNCT
ejpam-5832	511	3	α(q))∗	α(q))∗	NOUN
ejpam-5832	511	4	=	=	SYM
ejpam-5832	511	5	α(q∗	α(q∗	NUM
ejpam-5832	511	6	)	)	PUNCT
ejpam-5832	511	7	.	.	PUNCT
ejpam-5832	512	1	proof	proof	NOUN
ejpam-5832	512	2	.	.	PUNCT
ejpam-5832	513	1	consider	consider	VERB
ejpam-5832	513	2	λ	λ	X
ejpam-5832	513	3	∈	∈	NOUN
ejpam-5832	513	4	α(q∗	α(q∗	NOUN
ejpam-5832	513	5	)	)	PUNCT
ejpam-5832	513	6	,	,	PUNCT
ejpam-5832	513	7	then	then	ADV
ejpam-5832	513	8	there	there	PRON
ejpam-5832	513	9	exists	exist	VERB
ejpam-5832	513	10	ϵ	ϵ	X
ejpam-5832	513	11	∈	∈	PROPN
ejpam-5832	513	12	q∗	q∗	NOUN
ejpam-5832	513	13	for	for	ADP
ejpam-5832	513	14	which	which	PRON
ejpam-5832	513	15	α(ϵ	α(ϵ	PROPN
ejpam-5832	513	16	)	)	PUNCT
ejpam-5832	514	1	=	=	PUNCT
ejpam-5832	514	2	λ	λ	X
ejpam-5832	514	3	.	.	PUNCT
ejpam-5832	514	4	now	now	ADV
ejpam-5832	514	5	(	(	PUNCT
ejpam-5832	514	6	µα(q)(λ	µα(q)(λ	NOUN
ejpam-5832	514	7	)	)	PUNCT
ejpam-5832	514	8	)	)	PUNCT
ejpam-5832	514	9	q	q	NOUN
ejpam-5832	514	10	=	=	SYM
ejpam-5832	514	11	sup	sup	NOUN
ejpam-5832	514	12	{	{	PUNCT
ejpam-5832	514	13	(	(	PUNCT
ejpam-5832	514	14	µq(z	µq(z	NUM
ejpam-5832	514	15	)	)	PUNCT
ejpam-5832	514	16	:	:	PUNCT
ejpam-5832	514	17	z	z	PROPN
ejpam-5832	514	18	∈	∈	PROPN
ejpam-5832	514	19	α−1(λ	α−1(λ	PROPN
ejpam-5832	514	20	)	)	PUNCT
ejpam-5832	514	21	)	)	PUNCT
ejpam-5832	514	22	q	q	X
ejpam-5832	514	23	}	}	PUNCT
ejpam-5832	514	24	≥	≥	X
ejpam-5832	514	25	(	(	PUNCT
ejpam-5832	514	26	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	514	27	)	)	PUNCT
ejpam-5832	514	28	)	)	PUNCT
ejpam-5832	514	29	q	q	X
ejpam-5832	515	1	>	>	X
ejpam-5832	515	2	0	0	PUNCT
ejpam-5832	515	3	and	and	CCONJ
ejpam-5832	515	4	(	(	PUNCT
ejpam-5832	515	5	να(q)(λ	να(q)(λ	NOUN
ejpam-5832	515	6	)	)	PUNCT
ejpam-5832	515	7	)	)	PUNCT
ejpam-5832	516	1	q	q	X
ejpam-5832	516	2	=	=	SYM
ejpam-5832	516	3	inf	inf	NOUN
ejpam-5832	516	4	{	{	PUNCT
ejpam-5832	516	5	(	(	PUNCT
ejpam-5832	516	6	νq(z	νq(z	NUM
ejpam-5832	516	7	)	)	PUNCT
ejpam-5832	516	8	:	:	PUNCT
ejpam-5832	516	9	z	z	PROPN
ejpam-5832	516	10	∈	∈	PROPN
ejpam-5832	516	11	α−1(λ	α−1(λ	PROPN
ejpam-5832	516	12	)	)	PUNCT
ejpam-5832	516	13	)	)	PUNCT
ejpam-5832	516	14	q	q	X
ejpam-5832	516	15	}	}	PUNCT
ejpam-5832	516	16	≤	≤	NOUN
ejpam-5832	516	17	(	(	PUNCT
ejpam-5832	516	18	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	516	19	)	)	PUNCT
ejpam-5832	516	20	)	)	PUNCT
ejpam-5832	517	1	q	q	X
ejpam-5832	518	1	<	<	X
ejpam-5832	518	2	1	1	X
ejpam-5832	518	3	.	.	PUNCT
ejpam-5832	518	4	therefore	therefore	ADV
ejpam-5832	518	5	,	,	PUNCT
ejpam-5832	518	6	λ	λ	PROPN
ejpam-5832	518	7	∈	∈	PROPN
ejpam-5832	518	8	(	(	PUNCT
ejpam-5832	518	9	α(q))∗.	α(q))∗.	ADV
ejpam-5832	518	10	thus	thus	ADV
ejpam-5832	518	11	,	,	PUNCT
ejpam-5832	518	12	α(q∗	α(q∗	ADP
ejpam-5832	518	13	)	)	PUNCT
ejpam-5832	518	14	⊆	⊆	NUM
ejpam-5832	518	15	(	(	PUNCT
ejpam-5832	518	16	α(q))∗.	α(q))∗.	PROPN
ejpam-5832	518	17	on	on	ADP
ejpam-5832	518	18	the	the	DET
ejpam-5832	518	19	other	other	ADJ
ejpam-5832	518	20	hand	hand	NOUN
ejpam-5832	518	21	,	,	PUNCT
ejpam-5832	518	22	suppose	suppose	VERB
ejpam-5832	518	23	that	that	SCONJ
ejpam-5832	518	24	λ	λ	PROPN
ejpam-5832	518	25	∈	∈	PROPN
ejpam-5832	518	26	(	(	PUNCT
ejpam-5832	518	27	α(q))∗	α(q))∗	NUM
ejpam-5832	518	28	then	then	ADV
ejpam-5832	518	29	α(ϵ	α(ϵ	PROPN
ejpam-5832	518	30	)	)	PUNCT
ejpam-5832	519	1	=	=	SYM
ejpam-5832	519	2	λ	λ	NOUN
ejpam-5832	519	3	and	and	CCONJ
ejpam-5832	519	4	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	519	5	)	)	PUNCT
ejpam-5832	519	6	=	=	SYM
ejpam-5832	519	7	µα(q)(λ	µα(q)(λ	NOUN
ejpam-5832	519	8	)	)	PUNCT
ejpam-5832	519	9	for	for	ADP
ejpam-5832	519	10	some	some	DET
ejpam-5832	519	11	ϵ	ϵ	PROPN
ejpam-5832	519	12	∈	∈	PROPN
ejpam-5832	519	13	v	v	NOUN
ejpam-5832	519	14	.	.	PUNCT
ejpam-5832	520	1	since	since	SCONJ
ejpam-5832	520	2	(	(	PUNCT
ejpam-5832	520	3	µα(q)(λ	µα(q)(λ	NUM
ejpam-5832	520	4	)	)	PUNCT
ejpam-5832	520	5	)	)	PUNCT
ejpam-5832	520	6	q	q	X
ejpam-5832	520	7	>	>	X
ejpam-5832	520	8	0	0	NUM
ejpam-5832	520	9	,	,	PUNCT
ejpam-5832	520	10	therefore	therefore	ADV
ejpam-5832	520	11	(	(	PUNCT
ejpam-5832	520	12	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	520	13	)	)	PUNCT
ejpam-5832	520	14	)	)	PUNCT
ejpam-5832	520	15	q	q	X
ejpam-5832	520	16	>	>	X
ejpam-5832	520	17	0	0	NUM
ejpam-5832	520	18	,	,	PUNCT
ejpam-5832	520	19	which	which	PRON
ejpam-5832	520	20	further	far	ADV
ejpam-5832	520	21	reveals	reveal	VERB
ejpam-5832	520	22	that	that	SCONJ
ejpam-5832	520	23	(	(	PUNCT
ejpam-5832	520	24	νq(ϵ	νq(ϵ	NOUN
ejpam-5832	520	25	)	)	PUNCT
ejpam-5832	520	26	)	)	PUNCT
ejpam-5832	520	27	q	q	X
ejpam-5832	521	1	<	<	X
ejpam-5832	521	2	1	1	X
ejpam-5832	521	3	.	.	PUNCT
ejpam-5832	521	4	consequently	consequently	ADV
ejpam-5832	521	5	,	,	PUNCT
ejpam-5832	521	6	ϵ	ϵ	PROPN
ejpam-5832	521	7	∈	∈	PROPN
ejpam-5832	521	8	q∗	q∗	NOUN
ejpam-5832	521	9	implying	imply	VERB
ejpam-5832	521	10	that	that	SCONJ
ejpam-5832	521	11	λ	λ	PROPN
ejpam-5832	521	12	=	=	SYM
ejpam-5832	521	13	α(ϵ	α(ϵ	PROPN
ejpam-5832	521	14	)	)	PUNCT
ejpam-5832	521	15	∈	∈	PROPN
ejpam-5832	521	16	α(q∗	α(q∗	NOUN
ejpam-5832	521	17	)	)	PUNCT
ejpam-5832	521	18	.	.	PUNCT
ejpam-5832	522	1	thus	thus	ADV
ejpam-5832	522	2	,	,	PUNCT
ejpam-5832	522	3	(	(	PUNCT
ejpam-5832	522	4	α(q))∗	α(q))∗	NOUN
ejpam-5832	522	5	⊆	⊆	NUM
ejpam-5832	522	6	α(q∗	α(q∗	NUM
ejpam-5832	522	7	)	)	PUNCT
ejpam-5832	522	8	.	.	PUNCT
ejpam-5832	523	1	theorem	theorem	NOUN
ejpam-5832	523	2	20	20	NUM
ejpam-5832	523	3	.	.	PUNCT
ejpam-5832	524	1	(	(	PUNCT
ejpam-5832	524	2	first	first	ADV
ejpam-5832	524	3	isomorphism	isomorphism	NOUN
ejpam-5832	524	4	theorem	theorem	VERB
ejpam-5832	524	5	in	in	ADP
ejpam-5832	524	6	q	q	ADJ
ejpam-5832	524	7	-	-	PUNCT
ejpam-5832	524	8	rung	rung	ADJ
ejpam-5832	524	9	orthopair	orthopair	ADJ
ejpam-5832	524	10	fuzzy	fuzzy	ADJ
ejpam-5832	524	11	settings	setting	NOUN
ejpam-5832	524	12	)	)	PUNCT
ejpam-5832	524	13	suppose	suppose	VERB
ejpam-5832	524	14	q	q	NOUN
ejpam-5832	524	15	and	and	CCONJ
ejpam-5832	524	16	t	t	PROPN
ejpam-5832	524	17	are	be	AUX
ejpam-5832	524	18	q	q	NOUN
ejpam-5832	524	19	-	-	PUNCT
ejpam-5832	524	20	rofsgs	rofsg	NOUN
ejpam-5832	524	21	of	of	ADP
ejpam-5832	524	22	v	v	NOUN
ejpam-5832	524	23	and	and	CCONJ
ejpam-5832	524	24	u	u	NOUN
ejpam-5832	524	25	respectively	respectively	ADV
ejpam-5832	524	26	.	.	PUNCT
ejpam-5832	525	1	then	then	ADV
ejpam-5832	525	2	q	q	PROPN
ejpam-5832	525	3	∼=	∼=	PROPN
ejpam-5832	525	4	t	t	NOUN
ejpam-5832	525	5	implies	imply	VERB
ejpam-5832	525	6	q	q	X
ejpam-5832	525	7	/	/	SYM
ejpam-5832	525	8	p	p	NOUN
ejpam-5832	525	9	∼=	∼=	PROPN
ejpam-5832	525	10	t	t	NOUN
ejpam-5832	525	11	′′	′′	PROPN
ejpam-5832	525	12	for	for	ADP
ejpam-5832	525	13	some	some	DET
ejpam-5832	525	14	q	q	NOUN
ejpam-5832	525	15	-	-	PUNCT
ejpam-5832	525	16	rofnsg	rofnsg	ADJ
ejpam-5832	525	17	p	p	NOUN
ejpam-5832	525	18	of	of	ADP
ejpam-5832	525	19	q.	q.	PROPN
ejpam-5832	525	20	proof	proof	NOUN
ejpam-5832	525	21	.	.	PUNCT
ejpam-5832	526	1	obviously	obviously	ADV
ejpam-5832	526	2	,	,	PUNCT
ejpam-5832	526	3	q	q	PROPN
ejpam-5832	526	4	∼=	∼=	PROPN
ejpam-5832	526	5	t	t	NOUN
ejpam-5832	526	6	ensures	ensure	VERB
ejpam-5832	526	7	the	the	DET
ejpam-5832	526	8	existence	existence	NOUN
ejpam-5832	526	9	of	of	ADP
ejpam-5832	526	10	an	an	DET
ejpam-5832	526	11	epimorphism	epimorphism	NOUN
ejpam-5832	526	12	α	α	NOUN
ejpam-5832	526	13	:	:	PUNCT
ejpam-5832	526	14	v	v	X
ejpam-5832	526	15	→	→	SYM
ejpam-5832	526	16	u	u	NOUN
ejpam-5832	526	17	satisfying	satisfy	VERB
ejpam-5832	526	18	α(q	α(q	NUM
ejpam-5832	526	19	)	)	PUNCT
ejpam-5832	526	20	=	=	SYM
ejpam-5832	526	21	t	t	PROPN
ejpam-5832	526	22	.	.	PUNCT
ejpam-5832	527	1	design	design	VERB
ejpam-5832	527	2	a	a	DET
ejpam-5832	527	3	q	q	NOUN
ejpam-5832	527	4	-	-	PUNCT
ejpam-5832	527	5	rofsg	rofsg	NOUN
ejpam-5832	527	6	p	p	NOUN
ejpam-5832	527	7	of	of	ADP
ejpam-5832	527	8	v	v	NOUN
ejpam-5832	527	9	as	as	SCONJ
ejpam-5832	527	10	follows	follow	VERB
ejpam-5832	527	11	;	;	PUNCT
ejpam-5832	527	12	µp	µp	PROPN
ejpam-5832	527	13	(	(	PUNCT
ejpam-5832	527	14	ϵ	ϵ	NOUN
ejpam-5832	527	15	)	)	PUNCT
ejpam-5832	527	16	=	=	PRON
ejpam-5832	527	17	{	{	PUNCT
ejpam-5832	527	18	µq(ϵ	µq(ϵ	NOUN
ejpam-5832	527	19	)	)	PUNCT
ejpam-5832	527	20	,	,	PUNCT
ejpam-5832	527	21	if	if	SCONJ
ejpam-5832	527	22	ϵ	ϵ	PROPN
ejpam-5832	527	23	∈	∈	PROPN
ejpam-5832	527	24	kerα	kerα	NOUN
ejpam-5832	527	25	0	0	NUM
ejpam-5832	527	26	,	,	PUNCT
ejpam-5832	527	27	otherwise	otherwise	ADV
ejpam-5832	527	28	and	and	CCONJ
ejpam-5832	527	29	νp	νp	INTJ
ejpam-5832	527	30	(	(	PUNCT
ejpam-5832	527	31	ϵ	ϵ	X
ejpam-5832	527	32	)	)	PUNCT
ejpam-5832	527	33	=	=	NOUN
ejpam-5832	527	34	{	{	PUNCT
ejpam-5832	527	35	νq(ϵ	νq(ϵ	NUM
ejpam-5832	527	36	)	)	PUNCT
ejpam-5832	527	37	,	,	PUNCT
ejpam-5832	527	38	if	if	SCONJ
ejpam-5832	527	39	ϵ	ϵ	PROPN
ejpam-5832	527	40	∈	∈	PROPN
ejpam-5832	527	41	kerα	kerα	NOUN
ejpam-5832	527	42	1	1	NUM
ejpam-5832	527	43	,	,	PUNCT
ejpam-5832	527	44	otherwise	otherwise	ADV
ejpam-5832	527	45	clearly	clearly	ADV
ejpam-5832	527	46	,	,	PUNCT
ejpam-5832	527	47	p	p	PROPN
ejpam-5832	527	48	is	be	AUX
ejpam-5832	527	49	a	a	DET
ejpam-5832	527	50	q	q	NOUN
ejpam-5832	527	51	-	-	PUNCT
ejpam-5832	527	52	rofsg	rofsg	NOUN
ejpam-5832	527	53	of	of	ADP
ejpam-5832	527	54	v	v	NOUN
ejpam-5832	527	55	and	and	CCONJ
ejpam-5832	527	56	p	p	NOUN
ejpam-5832	527	57	⊆	⊆	NUM
ejpam-5832	527	58	q.	q.	NOUN
ejpam-5832	527	59	let	let	VERB
ejpam-5832	527	60	λ	λ	X
ejpam-5832	527	61	∈	∈	PROPN
ejpam-5832	527	62	v	v	NOUN
ejpam-5832	527	63	,	,	PUNCT
ejpam-5832	527	64	then	then	ADV
ejpam-5832	527	65	we	we	PRON
ejpam-5832	527	66	have	have	VERB
ejpam-5832	527	67	the	the	DET
ejpam-5832	527	68	two	two	NUM
ejpam-5832	527	69	following	follow	VERB
ejpam-5832	527	70	cases	case	NOUN
ejpam-5832	527	71	;	;	PUNCT
ejpam-5832	527	72	a.	a.	NOUN
ejpam-5832	527	73	razzaque	razzaque	NOUN
ejpam-5832	527	74	/	/	SYM
ejpam-5832	527	75	eur	eur	NOUN
ejpam-5832	527	76	.	.	PUNCT
ejpam-5832	528	1	j.	j.	PROPN
ejpam-5832	528	2	pure	pure	PROPN
ejpam-5832	528	3	appl	appl	PROPN
ejpam-5832	528	4	.	.	PROPN
ejpam-5832	528	5	math	math	PROPN
ejpam-5832	528	6	,	,	PUNCT
ejpam-5832	528	7	18	18	NUM
ejpam-5832	528	8	(	(	PUNCT
ejpam-5832	528	9	3	3	NUM
ejpam-5832	528	10	)	)	PUNCT
ejpam-5832	528	11	(	(	PUNCT
ejpam-5832	528	12	2025	2025	NUM
ejpam-5832	528	13	)	)	PUNCT
ejpam-5832	528	14	,	,	PUNCT
ejpam-5832	528	15	5832	5832	NUM
ejpam-5832	528	16	16	16	NUM
ejpam-5832	528	17	of	of	ADP
ejpam-5832	528	18	21	21	NUM
ejpam-5832	528	19	(	(	PUNCT
ejpam-5832	528	20	i	i	NOUN
ejpam-5832	528	21	)	)	PUNCT
ejpam-5832	528	22	if	if	SCONJ
ejpam-5832	528	23	λ	λ	PROPN
ejpam-5832	528	24	∈	∈	PROPN
ejpam-5832	528	25	kerα	kerα	NOUN
ejpam-5832	528	26	,	,	PUNCT
ejpam-5832	528	27	then	then	ADV
ejpam-5832	528	28	ϵλϵ−1	ϵλϵ−1	PROPN
ejpam-5832	528	29	∈	∈	PROPN
ejpam-5832	528	30	kerα	kerα	NOUN
ejpam-5832	528	31	for	for	ADP
ejpam-5832	528	32	all	all	DET
ejpam-5832	528	33	ϵ	ϵ	PART
ejpam-5832	528	34	∈	∈	PROPN
ejpam-5832	528	35	v	v	NOUN
ejpam-5832	528	36	.	.	PUNCT
ejpam-5832	529	1	(	(	PUNCT
ejpam-5832	529	2	µp	µp	PROPN
ejpam-5832	529	3	(	(	PUNCT
ejpam-5832	529	4	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	529	5	−1	−1	NOUN
ejpam-5832	529	6	)	)	PUNCT
ejpam-5832	529	7	)	)	PUNCT
ejpam-5832	529	8	q	q	X
ejpam-5832	530	1	=	=	PUNCT
ejpam-5832	530	2	(	(	PUNCT
ejpam-5832	530	3	µq(ϵλϵ	µq(ϵλϵ	NOUN
ejpam-5832	530	4	−1	−1	NOUN
ejpam-5832	530	5	)	)	PUNCT
ejpam-5832	530	6	)	)	PUNCT
ejpam-5832	531	1	q	q	PROPN
ejpam-5832	531	2	≥	≥	X
ejpam-5832	531	3	min{(µq(λ))q	min{(µq(λ))q	PROPN
ejpam-5832	531	4	,	,	PUNCT
ejpam-5832	531	5	(	(	PUNCT
ejpam-5832	531	6	µq(ϵ))q	µq(ϵ))q	NUM
ejpam-5832	531	7	}	}	PUNCT
ejpam-5832	531	8	=	=	SYM
ejpam-5832	531	9	min{(µp	min{(µp	NOUN
ejpam-5832	531	10	(	(	PUNCT
ejpam-5832	531	11	λ))q	λ))q	NOUN
ejpam-5832	531	12	,	,	PUNCT
ejpam-5832	531	13	(	(	PUNCT
ejpam-5832	531	14	µq(ϵ))q	µq(ϵ))q	NUM
ejpam-5832	531	15	}	}	PUNCT
ejpam-5832	531	16	and	and	CCONJ
ejpam-5832	531	17	(	(	PUNCT
ejpam-5832	531	18	νp	νp	INTJ
ejpam-5832	531	19	(	(	PUNCT
ejpam-5832	531	20	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	531	21	−1	−1	NOUN
ejpam-5832	531	22	)	)	PUNCT
ejpam-5832	531	23	)	)	PUNCT
ejpam-5832	532	1	q	q	X
ejpam-5832	532	2	=	=	PUNCT
ejpam-5832	532	3	(	(	PUNCT
ejpam-5832	532	4	νq(ϵλϵ	νq(ϵλϵ	PROPN
ejpam-5832	532	5	−1))q	−1))q	NOUN
ejpam-5832	532	6	≤	≤	NUM
ejpam-5832	532	7	max{(νq(λ))q	max{(νq(λ))q	NOUN
ejpam-5832	532	8	,	,	PUNCT
ejpam-5832	532	9	(	(	PUNCT
ejpam-5832	532	10	νq(ϵ))q	νq(ϵ))q	ADP
ejpam-5832	532	11	}	}	PUNCT
ejpam-5832	532	12	=	=	SYM
ejpam-5832	532	13	max{(νp	max{(νp	PROPN
ejpam-5832	532	14	(	(	PUNCT
ejpam-5832	532	15	λ))q	λ))q	NOUN
ejpam-5832	532	16	,	,	PUNCT
ejpam-5832	532	17	(	(	PUNCT
ejpam-5832	532	18	νq(ϵ))q	νq(ϵ))q	PUNCT
ejpam-5832	532	19	}	}	PUNCT
ejpam-5832	532	20	.	.	PUNCT
ejpam-5832	533	1	(	(	PUNCT
ejpam-5832	533	2	ii	ii	NOUN
ejpam-5832	533	3	)	)	PUNCT
ejpam-5832	533	4	if	if	SCONJ
ejpam-5832	533	5	λ	λ	PROPN
ejpam-5832	533	6	∈	∈	PROPN
ejpam-5832	533	7	v	v	NOUN
ejpam-5832	533	8	/	/	SYM
ejpam-5832	533	9	kerα	kerα	NOUN
ejpam-5832	533	10	,	,	PUNCT
ejpam-5832	533	11	then	then	ADV
ejpam-5832	533	12	µp	µp	PROPN
ejpam-5832	533	13	(	(	PUNCT
ejpam-5832	533	14	λ	λ	NOUN
ejpam-5832	533	15	)	)	PUNCT
ejpam-5832	533	16	=	=	SYM
ejpam-5832	533	17	0	0	NUM
ejpam-5832	533	18	and	and	CCONJ
ejpam-5832	533	19	νp	νp	INTJ
ejpam-5832	533	20	(	(	PUNCT
ejpam-5832	533	21	λ	λ	NOUN
ejpam-5832	533	22	)	)	PUNCT
ejpam-5832	533	23	=	=	SYM
ejpam-5832	533	24	1	1	X
ejpam-5832	533	25	.	.	PUNCT
ejpam-5832	534	1	now	now	ADV
ejpam-5832	534	2	(	(	PUNCT
ejpam-5832	534	3	µp	µp	PROPN
ejpam-5832	534	4	(	(	PUNCT
ejpam-5832	534	5	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	534	6	−1	−1	NOUN
ejpam-5832	534	7	)	)	PUNCT
ejpam-5832	534	8	)	)	PUNCT
ejpam-5832	534	9	q	q	PUNCT
ejpam-5832	534	10	≥	≥	NOUN
ejpam-5832	534	11	min{(µp	min{(µp	NOUN
ejpam-5832	534	12	(	(	PUNCT
ejpam-5832	534	13	λ))q	λ))q	PROPN
ejpam-5832	534	14	,	,	PUNCT
ejpam-5832	534	15	(	(	PUNCT
ejpam-5832	534	16	µq(ϵ))q	µq(ϵ))q	NUM
ejpam-5832	534	17	}	}	PUNCT
ejpam-5832	534	18	and	and	CCONJ
ejpam-5832	534	19	(	(	PUNCT
ejpam-5832	534	20	νp	νp	INTJ
ejpam-5832	534	21	(	(	PUNCT
ejpam-5832	534	22	ϵλϵ	ϵλϵ	PROPN
ejpam-5832	534	23	−1	−1	NOUN
ejpam-5832	534	24	)	)	PUNCT
ejpam-5832	534	25	)	)	PUNCT
ejpam-5832	534	26	q	q	PROPN
ejpam-5832	534	27	≤	≤	ADJ
ejpam-5832	534	28	max{(νp	max{(νp	NOUN
ejpam-5832	534	29	(	(	PUNCT
ejpam-5832	534	30	λ))q	λ))q	PROPN
ejpam-5832	534	31	,	,	PUNCT
ejpam-5832	534	32	(	(	PUNCT
ejpam-5832	534	33	νq(ϵ))q	νq(ϵ))q	X
ejpam-5832	534	34	}	}	PUNCT
ejpam-5832	534	35	thus	thus	ADV
ejpam-5832	534	36	,	,	PUNCT
ejpam-5832	534	37	p	p	PRON
ejpam-5832	534	38	is	be	AUX
ejpam-5832	534	39	a	a	DET
ejpam-5832	534	40	q	q	NOUN
ejpam-5832	534	41	-	-	PUNCT
ejpam-5832	534	42	rofnsg	rofnsg	NOUN
ejpam-5832	534	43	of	of	ADP
ejpam-5832	534	44	q	q	PROPN
ejpam-5832	534	45	in	in	ADP
ejpam-5832	534	46	both	both	DET
ejpam-5832	534	47	instances	instance	NOUN
ejpam-5832	534	48	.	.	PUNCT
ejpam-5832	535	1	also	also	ADV
ejpam-5832	535	2	q	q	X
ejpam-5832	535	3	∼=	∼=	PROPN
ejpam-5832	535	4	t	t	NOUN
ejpam-5832	535	5	gives	give	VERB
ejpam-5832	535	6	α(q	α(q	PROPN
ejpam-5832	535	7	)	)	PUNCT
ejpam-5832	535	8	=	=	SYM
ejpam-5832	535	9	t	t	PROPN
ejpam-5832	535	10	,	,	PUNCT
ejpam-5832	535	11	therefore	therefore	ADV
ejpam-5832	535	12	(	(	PUNCT
ejpam-5832	535	13	α(q))∗	α(q))∗	NUM
ejpam-5832	535	14	=	=	SYM
ejpam-5832	535	15	t	t	PROPN
ejpam-5832	535	16	∗.	∗.	PROPN
ejpam-5832	535	17	the	the	DET
ejpam-5832	535	18	use	use	NOUN
ejpam-5832	535	19	of	of	ADP
ejpam-5832	535	20	lemma	lemma	PROPN
ejpam-5832	535	21	3	3	NUM
ejpam-5832	535	22	yields	yield	NOUN
ejpam-5832	535	23	α(q∗	α(q∗	NUM
ejpam-5832	535	24	)	)	PUNCT
ejpam-5832	535	25	=	=	SYM
ejpam-5832	536	1	t	t	PROPN
ejpam-5832	536	2	∗.	∗.	PROPN
ejpam-5832	536	3	let	let	VERB
ejpam-5832	536	4	β	β	X
ejpam-5832	536	5	=	=	PUNCT
ejpam-5832	536	6	α|q∗	α|q∗	NUM
ejpam-5832	536	7	,	,	PUNCT
ejpam-5832	536	8	then	then	ADV
ejpam-5832	536	9	β	β	X
ejpam-5832	536	10	is	be	AUX
ejpam-5832	536	11	a	a	DET
ejpam-5832	536	12	homomophism	homomophism	NOUN
ejpam-5832	536	13	from	from	ADP
ejpam-5832	536	14	q∗	q∗	NOUN
ejpam-5832	536	15	to	to	ADP
ejpam-5832	536	16	t	t	PROPN
ejpam-5832	536	17	∗	∗	NOUN
ejpam-5832	536	18	such	such	ADJ
ejpam-5832	536	19	that	that	PRON
ejpam-5832	536	20	kerβ	kerβ	PROPN
ejpam-5832	537	1	=	=	PROPN
ejpam-5832	537	2	p	p	X
ejpam-5832	537	3	∗.	∗.	PROPN
ejpam-5832	537	4	the	the	DET
ejpam-5832	537	5	first	first	ADJ
ejpam-5832	537	6	isomorphism	isomorphism	NOUN
ejpam-5832	537	7	theorem	theorem	NOUN
ejpam-5832	537	8	of	of	ADP
ejpam-5832	537	9	conventional	conventional	ADJ
ejpam-5832	537	10	group	group	NOUN
ejpam-5832	537	11	theory	theory	NOUN
ejpam-5832	537	12	ensures	ensure	VERB
ejpam-5832	537	13	the	the	DET
ejpam-5832	537	14	existence	existence	NOUN
ejpam-5832	537	15	an	an	DET
ejpam-5832	537	16	isomorphism	isomorphism	NOUN
ejpam-5832	537	17	ψ	ψ	X
ejpam-5832	537	18	:	:	PUNCT
ejpam-5832	537	19	q∗/p	q∗/p	INTJ
ejpam-5832	537	20	∗	∗	NOUN
ejpam-5832	537	21	→	→	SYM
ejpam-5832	537	22	t	t	PROPN
ejpam-5832	537	23	∗	∗	NOUN
ejpam-5832	537	24	defined	define	VERB
ejpam-5832	537	25	by	by	ADP
ejpam-5832	537	26	ψ(ϵp	ψ(ϵp	ADP
ejpam-5832	537	27	∗	∗	NOUN
ejpam-5832	537	28	)	)	PUNCT
ejpam-5832	537	29	=	=	SYM
ejpam-5832	537	30	β(ϵ	β(ϵ	PROPN
ejpam-5832	537	31	)	)	PUNCT
ejpam-5832	537	32	=	=	SYM
ejpam-5832	537	33	α(ϵ	α(ϵ	PROPN
ejpam-5832	537	34	)	)	PUNCT
ejpam-5832	537	35	for	for	ADP
ejpam-5832	537	36	all	all	PRON
ejpam-5832	537	37	ϵp	ϵp	ADP
ejpam-5832	537	38	∗	∗	NOUN
ejpam-5832	537	39	∈	∈	PROPN
ejpam-5832	537	40	q∗/p	q∗/p	PUNCT
ejpam-5832	538	1	∗.	∗.	PROPN
ejpam-5832	538	2	suppose	suppose	VERB
ejpam-5832	538	3	that	that	SCONJ
ejpam-5832	538	4	k	k	PROPN
ejpam-5832	538	5	∈	∈	PROPN
ejpam-5832	538	6	t	t	PROPN
ejpam-5832	538	7	∗	∗	NOUN
ejpam-5832	538	8	,	,	PUNCT
ejpam-5832	538	9	then	then	ADV
ejpam-5832	538	10	(	(	PUNCT
ejpam-5832	538	11	µψ(q	µψ(q	PUNCT
ejpam-5832	538	12	/	/	SYM
ejpam-5832	538	13	p	p	NOUN
ejpam-5832	538	14	)	)	PUNCT
ejpam-5832	538	15	(	(	PUNCT
ejpam-5832	538	16	k	k	NOUN
ejpam-5832	538	17	)	)	PUNCT
ejpam-5832	538	18	)	)	PUNCT
ejpam-5832	538	19	q	q	NOUN
ejpam-5832	539	1	=	=	PUNCT
ejpam-5832	539	2	max{(µq	max{(µq	NOUN
ejpam-5832	539	3	/	/	SYM
ejpam-5832	539	4	p	p	X
ejpam-5832	539	5	(	(	PUNCT
ejpam-5832	539	6	ϵp	ϵp	ADP
ejpam-5832	539	7	∗))q	∗))q	NOUN
ejpam-5832	539	8	:	:	PUNCT
ejpam-5832	539	9	ϵ	ϵ	PROPN
ejpam-5832	539	10	∈	∈	PROPN
ejpam-5832	539	11	q∗	q∗	NOUN
ejpam-5832	539	12	,	,	PUNCT
ejpam-5832	539	13	ψ(ϵp	ψ(ϵp	ADP
ejpam-5832	539	14	∗	∗	NOUN
ejpam-5832	539	15	)	)	PUNCT
ejpam-5832	539	16	=	=	SYM
ejpam-5832	540	1	k	k	X
ejpam-5832	540	2	}	}	PUNCT
ejpam-5832	540	3	=	=	SYM
ejpam-5832	540	4	max{max{(µq(t))q	max{max{(µq(t))q	PROPN
ejpam-5832	540	5	:	:	PUNCT
ejpam-5832	540	6	t	t	PROPN
ejpam-5832	540	7	∈	∈	PROPN
ejpam-5832	540	8	ϵp	ϵp	ADP
ejpam-5832	540	9	∗	∗	NOUN
ejpam-5832	540	10	}	}	PUNCT
ejpam-5832	540	11	:	:	PUNCT
ejpam-5832	540	12	ϵ	ϵ	X
ejpam-5832	540	13	∈	∈	PROPN
ejpam-5832	540	14	q∗	q∗	PROPN
ejpam-5832	540	15	,	,	PUNCT
ejpam-5832	540	16	β(ϵ	β(ϵ	X
ejpam-5832	540	17	)	)	PUNCT
ejpam-5832	540	18	=	=	PUNCT
ejpam-5832	541	1	k	k	X
ejpam-5832	541	2	}	}	PUNCT
ejpam-5832	541	3	=	=	SYM
ejpam-5832	541	4	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	541	5	:	:	PUNCT
ejpam-5832	541	6	t	t	PROPN
ejpam-5832	541	7	∈	∈	PROPN
ejpam-5832	541	8	q∗	q∗	PROPN
ejpam-5832	541	9	,	,	PUNCT
ejpam-5832	541	10	β(t	β(t	NOUN
ejpam-5832	541	11	)	)	PUNCT
ejpam-5832	541	12	=	=	PUNCT
ejpam-5832	542	1	k	k	X
ejpam-5832	542	2	}	}	PUNCT
ejpam-5832	542	3	=	=	SYM
ejpam-5832	542	4	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	542	5	:	:	PUNCT
ejpam-5832	542	6	t	t	PROPN
ejpam-5832	542	7	∈	∈	PROPN
ejpam-5832	542	8	q∗	q∗	PROPN
ejpam-5832	542	9	,	,	PUNCT
ejpam-5832	542	10	β(t	β(t	NOUN
ejpam-5832	542	11	)	)	PUNCT
ejpam-5832	542	12	=	=	PUNCT
ejpam-5832	543	1	k	k	X
ejpam-5832	543	2	}	}	PUNCT
ejpam-5832	543	3	=	=	SYM
ejpam-5832	543	4	max{(µq(t))q	max{(µq(t))q	NOUN
ejpam-5832	543	5	:	:	PUNCT
ejpam-5832	543	6	t	t	PROPN
ejpam-5832	543	7	∈	∈	PROPN
ejpam-5832	543	8	v	v	PROPN
ejpam-5832	543	9	,	,	PUNCT
ejpam-5832	543	10	α(t	α(t	PROPN
ejpam-5832	543	11	)	)	PUNCT
ejpam-5832	543	12	=	=	SYM
ejpam-5832	544	1	k	k	NOUN
ejpam-5832	544	2	}	}	PUNCT
ejpam-5832	544	3	=	=	SYM
ejpam-5832	544	4	(	(	PUNCT
ejpam-5832	544	5	µα(q)(k	µα(q)(k	NOUN
ejpam-5832	544	6	)	)	PUNCT
ejpam-5832	544	7	)	)	PUNCT
ejpam-5832	545	1	q	q	NOUN
ejpam-5832	546	1	=	=	PUNCT
ejpam-5832	546	2	(	(	PUNCT
ejpam-5832	546	3	µt	µt	INTJ
ejpam-5832	546	4	(	(	PUNCT
ejpam-5832	546	5	k	k	NOUN
ejpam-5832	546	6	)	)	PUNCT
ejpam-5832	546	7	)	)	PUNCT
ejpam-5832	546	8	q	q	NOUN
ejpam-5832	547	1	=	=	PUNCT
ejpam-5832	547	2	(	(	PUNCT
ejpam-5832	547	3	µt	µt	PROPN
ejpam-5832	547	4	′′(k))q	′′(k))q	PROPN
ejpam-5832	547	5	(	(	PUNCT
ejpam-5832	547	6	since	since	SCONJ
ejpam-5832	547	7	k	k	PROPN
ejpam-5832	547	8	∈	∈	PROPN
ejpam-5832	547	9	t	t	PROPN
ejpam-5832	547	10	∗	∗	NOUN
ejpam-5832	547	11	)	)	PUNCT
ejpam-5832	547	12	similarly	similarly	ADV
ejpam-5832	547	13	,	,	PUNCT
ejpam-5832	547	14	(	(	PUNCT
ejpam-5832	547	15	νψ(q	νψ(q	X
ejpam-5832	547	16	/	/	SYM
ejpam-5832	547	17	p	p	NOUN
ejpam-5832	547	18	)	)	PUNCT
ejpam-5832	547	19	(	(	PUNCT
ejpam-5832	547	20	k	k	NOUN
ejpam-5832	547	21	)	)	PUNCT
ejpam-5832	547	22	)	)	PUNCT
ejpam-5832	547	23	q	q	X
ejpam-5832	547	24	=	=	PUNCT
ejpam-5832	547	25	(	(	PUNCT
ejpam-5832	547	26	νt	νt	PROPN
ejpam-5832	547	27	′′(k))q	′′(k))q	PROPN
ejpam-5832	547	28	thus	thus	ADV
ejpam-5832	547	29	,	,	PUNCT
ejpam-5832	547	30	q	q	X
ejpam-5832	547	31	/	/	SYM
ejpam-5832	547	32	p	p	NOUN
ejpam-5832	547	33	∼=	∼=	PROPN
ejpam-5832	547	34	t	t	NOUN
ejpam-5832	547	35	′′.	′′.	NOUN
ejpam-5832	547	36	a.	a.	NOUN
ejpam-5832	547	37	razzaque	razzaque	PROPN
ejpam-5832	547	38	/	/	SYM
ejpam-5832	547	39	eur	eur	NOUN
ejpam-5832	547	40	.	.	PUNCT
ejpam-5832	548	1	j.	j.	PROPN
ejpam-5832	548	2	pure	pure	PROPN
ejpam-5832	548	3	appl	appl	PROPN
ejpam-5832	548	4	.	.	PROPN
ejpam-5832	548	5	math	math	PROPN
ejpam-5832	548	6	,	,	PUNCT
ejpam-5832	548	7	18	18	NUM
ejpam-5832	548	8	(	(	PUNCT
ejpam-5832	548	9	3	3	NUM
ejpam-5832	548	10	)	)	PUNCT
ejpam-5832	548	11	(	(	PUNCT
ejpam-5832	548	12	2025	2025	NUM
ejpam-5832	548	13	)	)	PUNCT
ejpam-5832	548	14	,	,	PUNCT
ejpam-5832	548	15	5832	5832	NUM
ejpam-5832	548	16	17	17	NUM
ejpam-5832	548	17	of	of	ADP
ejpam-5832	548	18	21	21	NUM
ejpam-5832	548	19	definition	definition	NOUN
ejpam-5832	548	20	14	14	NUM
ejpam-5832	548	21	.	.	PUNCT
ejpam-5832	549	1	let	let	VERB
ejpam-5832	549	2	q	q	NOUN
ejpam-5832	550	1	and	and	CCONJ
ejpam-5832	550	2	p	p	NOUN
ejpam-5832	550	3	be	be	AUX
ejpam-5832	550	4	two	two	NUM
ejpam-5832	550	5	q	q	NOUN
ejpam-5832	550	6	-	-	PUNCT
ejpam-5832	550	7	rofsgs	rofsg	NOUN
ejpam-5832	550	8	of	of	ADP
ejpam-5832	550	9	v	v	NOUN
ejpam-5832	550	10	,	,	PUNCT
ejpam-5832	550	11	then	then	ADV
ejpam-5832	550	12	the	the	DET
ejpam-5832	550	13	product	product	NOUN
ejpam-5832	550	14	of	of	ADP
ejpam-5832	550	15	q	q	PROPN
ejpam-5832	551	1	and	and	CCONJ
ejpam-5832	551	2	p	p	NOUN
ejpam-5832	551	3	is	be	AUX
ejpam-5832	551	4	denoted	denote	VERB
ejpam-5832	551	5	by	by	ADP
ejpam-5832	551	6	q	q	PROPN
ejpam-5832	551	7	◦	◦	NOUN
ejpam-5832	551	8	p	p	NOUN
ejpam-5832	551	9	and	and	CCONJ
ejpam-5832	551	10	is	be	AUX
ejpam-5832	551	11	defined	define	VERB
ejpam-5832	551	12	as	as	ADP
ejpam-5832	551	13	;	;	PUNCT
ejpam-5832	551	14	(	(	PUNCT
ejpam-5832	551	15	i	i	NOUN
ejpam-5832	551	16	)	)	PUNCT
ejpam-5832	551	17	µq	µq	VERB
ejpam-5832	551	18	◦	◦	NOUN
ejpam-5832	551	19	p	p	NOUN
ejpam-5832	551	20	(	(	PUNCT
ejpam-5832	551	21	ϵ	ϵ	NOUN
ejpam-5832	551	22	)	)	PUNCT
ejpam-5832	551	23	=	=	SYM
ejpam-5832	551	24	max{min(µq(u	max{min(µq(u	NOUN
ejpam-5832	551	25	)	)	PUNCT
ejpam-5832	551	26	,	,	PUNCT
ejpam-5832	551	27	µp	µp	NOUN
ejpam-5832	551	28	(	(	PUNCT
ejpam-5832	551	29	v	v	NOUN
ejpam-5832	551	30	)	)	PUNCT
ejpam-5832	551	31	)	)	PUNCT
ejpam-5832	551	32	:	:	PUNCT
ejpam-5832	552	1	u	u	NOUN
ejpam-5832	552	2	,	,	PUNCT
ejpam-5832	552	3	v	v	PROPN
ejpam-5832	552	4	∈	∈	PROPN
ejpam-5832	552	5	v	v	NOUN
ejpam-5832	552	6	,	,	PUNCT
ejpam-5832	552	7	uv	uv	NOUN
ejpam-5832	552	8	=	=	SYM
ejpam-5832	552	9	ϵ	ϵ	NOUN
ejpam-5832	552	10	}	}	PUNCT
ejpam-5832	552	11	(	(	PUNCT
ejpam-5832	552	12	ii	ii	NOUN
ejpam-5832	552	13	)	)	PUNCT
ejpam-5832	552	14	νq	νq	PROPN
ejpam-5832	552	15	◦	◦	PROPN
ejpam-5832	552	16	p	p	X
ejpam-5832	552	17	(	(	PUNCT
ejpam-5832	552	18	ϵ	ϵ	NOUN
ejpam-5832	552	19	)	)	PUNCT
ejpam-5832	552	20	=	=	SYM
ejpam-5832	552	21	min{max(νq(u	min{max(νq(u	NOUN
ejpam-5832	552	22	)	)	PUNCT
ejpam-5832	552	23	,	,	PUNCT
ejpam-5832	552	24	νp	νp	X
ejpam-5832	552	25	(	(	PUNCT
ejpam-5832	552	26	v	v	NOUN
ejpam-5832	552	27	)	)	PUNCT
ejpam-5832	552	28	)	)	PUNCT
ejpam-5832	552	29	:	:	PUNCT
ejpam-5832	552	30	u	u	NOUN
ejpam-5832	552	31	,	,	PUNCT
ejpam-5832	552	32	v	v	PROPN
ejpam-5832	552	33	∈	∈	PROPN
ejpam-5832	552	34	v	v	NOUN
ejpam-5832	552	35	,	,	PUNCT
ejpam-5832	552	36	uv	uv	NOUN
ejpam-5832	552	37	=	=	SYM
ejpam-5832	552	38	ϵ	ϵ	NOUN
ejpam-5832	552	39	}	}	PUNCT
ejpam-5832	552	40	for	for	ADP
ejpam-5832	552	41	all	all	DET
ejpam-5832	552	42	ϵ	ϵ	PART
ejpam-5832	552	43	∈	∈	PROPN
ejpam-5832	552	44	v	v	NOUN
ejpam-5832	552	45	.	.	PUNCT
ejpam-5832	553	1	lemma	lemma	PROPN
ejpam-5832	553	2	4	4	X
ejpam-5832	553	3	.	.	PUNCT
ejpam-5832	554	1	let	let	VERB
ejpam-5832	554	2	q	q	NOUN
ejpam-5832	555	1	and	and	CCONJ
ejpam-5832	555	2	p	p	NOUN
ejpam-5832	555	3	be	be	AUX
ejpam-5832	555	4	two	two	NUM
ejpam-5832	555	5	q	q	NOUN
ejpam-5832	555	6	-	-	PUNCT
ejpam-5832	555	7	rofsgs	rofsg	NOUN
ejpam-5832	555	8	of	of	ADP
ejpam-5832	556	1	v.	v.	ADV
ejpam-5832	557	1	then	then	ADV
ejpam-5832	557	2	(	(	PUNCT
ejpam-5832	557	3	i	i	NOUN
ejpam-5832	557	4	)	)	PUNCT
ejpam-5832	557	5	(	(	PUNCT
ejpam-5832	557	6	q	q	X
ejpam-5832	557	7	∩	∩	PROPN
ejpam-5832	557	8	p	p	NOUN
ejpam-5832	557	9	)	)	PUNCT
ejpam-5832	557	10	∗	∗	NOUN
ejpam-5832	557	11	=	=	SYM
ejpam-5832	557	12	q∗	q∗	NOUN
ejpam-5832	557	13	∩	∩	NOUN
ejpam-5832	557	14	p	p	X
ejpam-5832	557	15	∗.	∗.	PROPN
ejpam-5832	557	16	(	(	PUNCT
ejpam-5832	557	17	ii	ii	NOUN
ejpam-5832	557	18	)	)	PUNCT
ejpam-5832	557	19	(	(	PUNCT
ejpam-5832	557	20	q	q	PUNCT
ejpam-5832	557	21	◦	◦	NOUN
ejpam-5832	557	22	p	p	NOUN
ejpam-5832	557	23	)	)	PUNCT
ejpam-5832	557	24	∗	∗	NOUN
ejpam-5832	557	25	=	=	SYM
ejpam-5832	557	26	q∗p	q∗p	ADJ
ejpam-5832	557	27	∗	∗	NOUN
ejpam-5832	557	28	proof	proof	NOUN
ejpam-5832	557	29	.	.	PUNCT
ejpam-5832	558	1	(	(	PUNCT
ejpam-5832	558	2	i	i	NOUN
ejpam-5832	558	3	)	)	PUNCT
ejpam-5832	558	4	suppose	suppose	VERB
ejpam-5832	558	5	that	that	SCONJ
ejpam-5832	558	6	ϵ	ϵ	PROPN
ejpam-5832	558	7	∈	∈	PROPN
ejpam-5832	558	8	v	v	NOUN
ejpam-5832	558	9	,	,	PUNCT
ejpam-5832	558	10	then	then	ADV
ejpam-5832	558	11	ϵ	ϵ	PROPN
ejpam-5832	558	12	∈	∈	PROPN
ejpam-5832	558	13	(	(	PUNCT
ejpam-5832	558	14	q1	q1	PROPN
ejpam-5832	558	15	∩q2	∩q2	NOUN
ejpam-5832	558	16	)	)	PUNCT
ejpam-5832	558	17	∗	∗	NOUN
ejpam-5832	558	18	⇔	⇔	X
ejpam-5832	558	19	(	(	PUNCT
ejpam-5832	558	20	µq1∩q2(ϵ	µq1∩q2(ϵ	NOUN
ejpam-5832	558	21	)	)	PUNCT
ejpam-5832	558	22	)	)	PUNCT
ejpam-5832	558	23	q	q	NOUN
ejpam-5832	559	1	>	>	X
ejpam-5832	559	2	0	0	PUNCT
ejpam-5832	560	1	and	and	CCONJ
ejpam-5832	560	2	(	(	PUNCT
ejpam-5832	560	3	νq1∩q2(ϵ	νq1∩q2(ϵ	NOUN
ejpam-5832	560	4	)	)	PUNCT
ejpam-5832	560	5	)	)	PUNCT
ejpam-5832	561	1	q	q	X
ejpam-5832	561	2	<	<	X
ejpam-5832	561	3	1	1	NUM
ejpam-5832	561	4	⇔	⇔	X
ejpam-5832	561	5	min	min	PROPN
ejpam-5832	561	6	(	(	PUNCT
ejpam-5832	561	7	(	(	PUNCT
ejpam-5832	561	8	µq1(ϵ	µq1(ϵ	NOUN
ejpam-5832	561	9	)	)	PUNCT
ejpam-5832	561	10	)	)	PUNCT
ejpam-5832	562	1	q	q	X
ejpam-5832	562	2	,	,	PUNCT
ejpam-5832	562	3	(	(	PUNCT
ejpam-5832	562	4	µ(q2)(ϵ	µ(q2)(ϵ	NOUN
ejpam-5832	562	5	)	)	PUNCT
ejpam-5832	562	6	)	)	PUNCT
ejpam-5832	563	1	q	q	X
ejpam-5832	563	2	)	)	PUNCT
ejpam-5832	563	3	>	>	SYM
ejpam-5832	563	4	0	0	PUNCT
ejpam-5832	563	5	and	and	CCONJ
ejpam-5832	563	6	min	min	NOUN
ejpam-5832	563	7	(	(	PUNCT
ejpam-5832	563	8	(	(	PUNCT
ejpam-5832	563	9	ν(q1)(ϵ	ν(q1)(ϵ	NOUN
ejpam-5832	563	10	)	)	PUNCT
ejpam-5832	563	11	)	)	PUNCT
ejpam-5832	564	1	q	q	X
ejpam-5832	564	2	,	,	PUNCT
ejpam-5832	564	3	(	(	PUNCT
ejpam-5832	564	4	ν(q2)(ϵ	ν(q2)(ϵ	NOUN
ejpam-5832	564	5	)	)	PUNCT
ejpam-5832	564	6	)	)	PUNCT
ejpam-5832	564	7	q	q	X
ejpam-5832	564	8	)	)	PUNCT
ejpam-5832	565	1	<	<	X
ejpam-5832	565	2	1	1	NUM
ejpam-5832	565	3	⇔	⇔	X
ejpam-5832	565	4	(	(	PUNCT
ejpam-5832	565	5	µ(q1)(ϵ	µ(q1)(ϵ	NOUN
ejpam-5832	565	6	)	)	PUNCT
ejpam-5832	565	7	)	)	PUNCT
ejpam-5832	565	8	q	q	NOUN
ejpam-5832	565	9	,	,	PUNCT
ejpam-5832	565	10	(	(	PUNCT
ejpam-5832	565	11	µ(q2)(ϵ	µ(q2)(ϵ	NOUN
ejpam-5832	565	12	)	)	PUNCT
ejpam-5832	565	13	)	)	PUNCT
ejpam-5832	566	1	q	q	X
ejpam-5832	566	2	>	>	X
ejpam-5832	566	3	0	0	PUNCT
ejpam-5832	567	1	and	and	CCONJ
ejpam-5832	567	2	(	(	PUNCT
ejpam-5832	567	3	ν(q1)(ϵ	ν(q1)(ϵ	NOUN
ejpam-5832	567	4	)	)	PUNCT
ejpam-5832	567	5	)	)	PUNCT
ejpam-5832	568	1	q	q	X
ejpam-5832	568	2	,	,	PUNCT
ejpam-5832	568	3	(	(	PUNCT
ejpam-5832	568	4	ν(q2)(ϵ	ν(q2)(ϵ	NOUN
ejpam-5832	568	5	)	)	PUNCT
ejpam-5832	568	6	)	)	PUNCT
ejpam-5832	569	1	q	q	X
ejpam-5832	569	2	<	<	X
ejpam-5832	569	3	1	1	NUM
ejpam-5832	569	4	⇔	⇔	X
ejpam-5832	569	5	ϵ	ϵ	X
ejpam-5832	569	6	∈	∈	PROPN
ejpam-5832	569	7	q∗	q∗	NOUN
ejpam-5832	569	8	1	1	NUM
ejpam-5832	569	9	,	,	PUNCT
ejpam-5832	569	10	q	q	NOUN
ejpam-5832	569	11	∗	∗	NOUN
ejpam-5832	569	12	2	2	NUM
ejpam-5832	569	13	⇔	⇔	X
ejpam-5832	569	14	ϵ	ϵ	X
ejpam-5832	569	15	∈	∈	PROPN
ejpam-5832	569	16	q∗	q∗	NOUN
ejpam-5832	569	17	1∩q∗	1∩q∗	PROPN
ejpam-5832	569	18	2	2	NUM
ejpam-5832	569	19	.	.	PUNCT
ejpam-5832	570	1	thus	thus	ADV
ejpam-5832	570	2	,	,	PUNCT
ejpam-5832	570	3	(	(	PUNCT
ejpam-5832	570	4	q1	q1	PROPN
ejpam-5832	570	5	∩q2	∩q2	NOUN
ejpam-5832	570	6	)	)	PUNCT
ejpam-5832	570	7	∗	∗	NOUN
ejpam-5832	570	8	=	=	SYM
ejpam-5832	570	9	q∗	q∗	PROPN
ejpam-5832	570	10	1	1	NUM
ejpam-5832	570	11	∩q∗	∩q∗	SYM
ejpam-5832	570	12	2	2	NUM
ejpam-5832	570	13	.	.	PUNCT
ejpam-5832	570	14	(	(	PUNCT
ejpam-5832	570	15	ii	ii	NOUN
ejpam-5832	570	16	)	)	PUNCT
ejpam-5832	570	17	suppose	suppose	VERB
ejpam-5832	570	18	that	that	SCONJ
ejpam-5832	570	19	ϵ	ϵ	PROPN
ejpam-5832	570	20	∈	∈	PROPN
ejpam-5832	570	21	v	v	NOUN
ejpam-5832	570	22	,	,	PUNCT
ejpam-5832	570	23	then	then	ADV
ejpam-5832	570	24	ϵ	ϵ	PROPN
ejpam-5832	570	25	∈	∈	PROPN
ejpam-5832	570	26	(	(	PUNCT
ejpam-5832	570	27	q	q	NOUN
ejpam-5832	570	28	◦	◦	NOUN
ejpam-5832	570	29	p	p	NOUN
ejpam-5832	570	30	)	)	PUNCT
ejpam-5832	570	31	∗	∗	NOUN
ejpam-5832	570	32	⇔	⇔	X
ejpam-5832	570	33	(	(	PUNCT
ejpam-5832	570	34	µq	µq	PROPN
ejpam-5832	570	35	◦	◦	NOUN
ejpam-5832	570	36	p	p	NOUN
ejpam-5832	570	37	(	(	PUNCT
ejpam-5832	570	38	ϵ	ϵ	NOUN
ejpam-5832	570	39	)	)	PUNCT
ejpam-5832	570	40	)	)	PUNCT
ejpam-5832	570	41	q	q	X
ejpam-5832	570	42	>	>	X
ejpam-5832	570	43	0	0	PUNCT
ejpam-5832	571	1	and	and	CCONJ
ejpam-5832	571	2	(	(	PUNCT
ejpam-5832	571	3	νq	νq	PROPN
ejpam-5832	571	4	◦	◦	PROPN
ejpam-5832	571	5	p	p	X
ejpam-5832	571	6	(	(	PUNCT
ejpam-5832	571	7	ϵ	ϵ	NOUN
ejpam-5832	571	8	)	)	PUNCT
ejpam-5832	571	9	)	)	PUNCT
ejpam-5832	572	1	q	q	X
ejpam-5832	572	2	<	<	X
ejpam-5832	572	3	1	1	NUM
ejpam-5832	572	4	⇔	⇔	X
ejpam-5832	572	5	max{min(µq(u	max{min(µq(u	PROPN
ejpam-5832	572	6	)	)	PUNCT
ejpam-5832	572	7	,	,	PUNCT
ejpam-5832	572	8	µp	µp	NOUN
ejpam-5832	572	9	(	(	PUNCT
ejpam-5832	572	10	v	v	NOUN
ejpam-5832	572	11	)	)	PUNCT
ejpam-5832	572	12	)	)	PUNCT
ejpam-5832	573	1	q	q	NOUN
ejpam-5832	573	2	:	:	PUNCT
ejpam-5832	573	3	u	u	NOUN
ejpam-5832	573	4	,	,	PUNCT
ejpam-5832	573	5	v	v	PROPN
ejpam-5832	573	6	∈	∈	PROPN
ejpam-5832	573	7	v	v	NOUN
ejpam-5832	573	8	,	,	PUNCT
ejpam-5832	573	9	uv	uv	NOUN
ejpam-5832	573	10	=	=	SYM
ejpam-5832	573	11	ϵ	ϵ	NOUN
ejpam-5832	573	12	}	}	PUNCT
ejpam-5832	573	13	>	>	X
ejpam-5832	573	14	0	0	PUNCT
ejpam-5832	573	15	and	and	CCONJ
ejpam-5832	573	16	νq	νq	PROPN
ejpam-5832	573	17	◦	◦	PROPN
ejpam-5832	573	18	p	p	X
ejpam-5832	573	19	(	(	PUNCT
ejpam-5832	573	20	ϵ	ϵ	NOUN
ejpam-5832	573	21	)	)	PUNCT
ejpam-5832	573	22	=	=	SYM
ejpam-5832	573	23	min{max(νq(u	min{max(νq(u	NOUN
ejpam-5832	573	24	)	)	PUNCT
ejpam-5832	573	25	,	,	PUNCT
ejpam-5832	573	26	νp	νp	X
ejpam-5832	573	27	(	(	PUNCT
ejpam-5832	573	28	v	v	NOUN
ejpam-5832	573	29	)	)	PUNCT
ejpam-5832	573	30	)	)	PUNCT
ejpam-5832	573	31	:	:	PUNCT
ejpam-5832	574	1	u	u	NOUN
ejpam-5832	574	2	,	,	PUNCT
ejpam-5832	574	3	v	v	PROPN
ejpam-5832	574	4	∈	∈	PROPN
ejpam-5832	574	5	v	v	NOUN
ejpam-5832	574	6	,	,	PUNCT
ejpam-5832	574	7	uv	uv	NOUN
ejpam-5832	574	8	=	=	SYM
ejpam-5832	574	9	ϵ	ϵ	NOUN
ejpam-5832	574	10	}	}	PUNCT
ejpam-5832	574	11	<	<	X
ejpam-5832	574	12	1	1	NUM
ejpam-5832	574	13	⇔	⇔	NUM
ejpam-5832	574	14	µq(u	µq(u	PUNCT
ejpam-5832	574	15	)	)	PUNCT
ejpam-5832	574	16	>	>	X
ejpam-5832	574	17	0	0	NUM
ejpam-5832	574	18	,	,	PUNCT
ejpam-5832	574	19	µp	µp	NOUN
ejpam-5832	574	20	(	(	PUNCT
ejpam-5832	574	21	v	v	NOUN
ejpam-5832	574	22	)	)	PUNCT
ejpam-5832	574	23	>	>	SYM
ejpam-5832	574	24	0	0	NUM
ejpam-5832	574	25	and	and	CCONJ
ejpam-5832	574	26	νq(u	νq(u	NUM
ejpam-5832	574	27	)	)	PUNCT
ejpam-5832	574	28	,	,	PUNCT
ejpam-5832	574	29	νp	νp	X
ejpam-5832	574	30	(	(	PUNCT
ejpam-5832	574	31	v	v	NOUN
ejpam-5832	574	32	)	)	PUNCT
ejpam-5832	574	33	<	<	X
ejpam-5832	574	34	1	1	NUM
ejpam-5832	574	35	,	,	PUNCT
ejpam-5832	574	36	where	where	SCONJ
ejpam-5832	574	37	u	u	NOUN
ejpam-5832	574	38	,	,	PUNCT
ejpam-5832	574	39	v	v	PROPN
ejpam-5832	574	40	∈	∈	NOUN
ejpam-5832	574	41	v	v	ADP
ejpam-5832	574	42	such	such	ADJ
ejpam-5832	574	43	that	that	DET
ejpam-5832	574	44	uv	uv	NOUN
ejpam-5832	574	45	=	=	SYM
ejpam-5832	574	46	ϵ	ϵ	X
ejpam-5832	574	47	⇔	⇔	PROPN
ejpam-5832	574	48	u	u	X
ejpam-5832	574	49	∈	∈	PROPN
ejpam-5832	574	50	q∗	q∗	NOUN
ejpam-5832	574	51	and	and	CCONJ
ejpam-5832	574	52	v	v	ADP
ejpam-5832	574	53	∈	∈	NOUN
ejpam-5832	574	54	p	p	NOUN
ejpam-5832	574	55	∗	∗	NOUN
ejpam-5832	574	56	,	,	PUNCT
ejpam-5832	574	57	where	where	SCONJ
ejpam-5832	574	58	u	u	NOUN
ejpam-5832	574	59	,	,	PUNCT
ejpam-5832	574	60	v	v	PROPN
ejpam-5832	574	61	∈	∈	NOUN
ejpam-5832	574	62	v	v	ADP
ejpam-5832	574	63	such	such	ADJ
ejpam-5832	574	64	that	that	DET
ejpam-5832	574	65	uv	uv	NOUN
ejpam-5832	574	66	=	=	SYM
ejpam-5832	574	67	ϵ⇔	ϵ⇔	NUM
ejpam-5832	574	68	ϵ	ϵ	X
ejpam-5832	574	69	=	=	PUNCT
ejpam-5832	574	70	uv	uv	NOUN
ejpam-5832	574	71	∈	∈	PROPN
ejpam-5832	574	72	q∗p	q∗p	NUM
ejpam-5832	574	73	∗.	∗.	PROPN
ejpam-5832	574	74	thus	thus	ADV
ejpam-5832	574	75	,	,	PUNCT
ejpam-5832	574	76	(	(	PUNCT
ejpam-5832	574	77	q	q	PUNCT
ejpam-5832	574	78	◦	◦	NOUN
ejpam-5832	574	79	p	p	NOUN
ejpam-5832	574	80	)	)	PUNCT
ejpam-5832	574	81	∗	∗	NOUN
ejpam-5832	574	82	=	=	SYM
ejpam-5832	574	83	q∗p	q∗p	NUM
ejpam-5832	574	84	∗.	∗.	PROPN
ejpam-5832	574	85	definition	definition	NOUN
ejpam-5832	574	86	15	15	NUM
ejpam-5832	574	87	.	.	PUNCT
ejpam-5832	574	88	assume	assume	VERB
ejpam-5832	574	89	that	that	SCONJ
ejpam-5832	574	90	q1	q1	PROPN
ejpam-5832	574	91	and	and	CCONJ
ejpam-5832	574	92	q2	q2	NOUN
ejpam-5832	574	93	are	be	AUX
ejpam-5832	574	94	q	q	NOUN
ejpam-5832	574	95	-	-	PUNCT
ejpam-5832	574	96	rofsgs	rofsg	NOUN
ejpam-5832	574	97	of	of	ADP
ejpam-5832	574	98	v	v	NOUN
ejpam-5832	574	99	and	and	CCONJ
ejpam-5832	574	100	w	w	NOUN
ejpam-5832	574	101	respectively	respectively	ADV
ejpam-5832	574	102	.	.	PUNCT
ejpam-5832	575	1	then	then	ADV
ejpam-5832	575	2	an	an	DET
ejpam-5832	575	3	isomorphism	isomorphism	NOUN
ejpam-5832	575	4	α	α	NOUN
ejpam-5832	575	5	:	:	PUNCT
ejpam-5832	575	6	v	v	X
ejpam-5832	575	7	→	→	SYM
ejpam-5832	575	8	w	w	PROPN
ejpam-5832	575	9	is	be	AUX
ejpam-5832	575	10	called	call	VERB
ejpam-5832	575	11	a	a	DET
ejpam-5832	575	12	weak	weak	ADJ
ejpam-5832	575	13	q	q	ADJ
ejpam-5832	575	14	-	-	PUNCT
ejpam-5832	575	15	rung	rung	ADJ
ejpam-5832	575	16	isomorphism	isomorphism	NOUN
ejpam-5832	575	17	(	(	PUNCT
ejpam-5832	575	18	wq	wq	NOUN
ejpam-5832	575	19	-	-	PUNCT
ejpam-5832	575	20	rofiso	rofiso	NOUN
ejpam-5832	575	21	)	)	PUNCT
ejpam-5832	575	22	from	from	ADP
ejpam-5832	575	23	q1	q1	PROPN
ejpam-5832	575	24	to	to	ADP
ejpam-5832	575	25	q2	q2	NOUN
ejpam-5832	575	26	if	if	SCONJ
ejpam-5832	575	27	α(q1	α(q1	PRON
ejpam-5832	575	28	)	)	PUNCT
ejpam-5832	575	29	⊆	⊆	NUM
ejpam-5832	575	30	q2	q2	NOUN
ejpam-5832	575	31	.	.	PUNCT
ejpam-5832	576	1	the	the	DET
ejpam-5832	576	2	existence	existence	NOUN
ejpam-5832	576	3	of	of	ADP
ejpam-5832	576	4	wq	wq	NOUN
ejpam-5832	576	5	-	-	PUNCT
ejpam-5832	576	6	rofiso	rofiso	NOUN
ejpam-5832	576	7	between	between	ADP
ejpam-5832	576	8	q1	q1	PROPN
ejpam-5832	576	9	and	and	CCONJ
ejpam-5832	576	10	q2	q2	NOUN
ejpam-5832	576	11	is	be	AUX
ejpam-5832	576	12	denoted	denote	VERB
ejpam-5832	576	13	by	by	ADP
ejpam-5832	576	14	q1	q1	PROPN
ejpam-5832	576	15	≃	≃	PROPN
ejpam-5832	576	16	q2	q2	PROPN
ejpam-5832	576	17	.	.	PUNCT
ejpam-5832	577	1	theorem	theorem	PROPN
ejpam-5832	577	2	21	21	NUM
ejpam-5832	577	3	.	.	PUNCT
ejpam-5832	578	1	(	(	PUNCT
ejpam-5832	578	2	second	second	ADJ
ejpam-5832	578	3	isomorphism	isomorphism	NOUN
ejpam-5832	578	4	theorem	theorem	VERB
ejpam-5832	578	5	in	in	ADP
ejpam-5832	578	6	q	q	ADJ
ejpam-5832	578	7	-	-	PUNCT
ejpam-5832	578	8	rung	rung	ADJ
ejpam-5832	578	9	orthopair	orthopair	ADJ
ejpam-5832	578	10	fuzzy	fuzzy	ADJ
ejpam-5832	578	11	settings	setting	NOUN
ejpam-5832	578	12	)	)	PUNCT
ejpam-5832	578	13	let	let	VERB
ejpam-5832	578	14	q	q	NOUN
ejpam-5832	578	15	be	be	AUX
ejpam-5832	578	16	a	a	DET
ejpam-5832	578	17	q	q	NOUN
ejpam-5832	578	18	-	-	PUNCT
ejpam-5832	578	19	rofnsg	rofnsg	NOUN
ejpam-5832	578	20	of	of	ADP
ejpam-5832	578	21	v	v	NOUN
ejpam-5832	578	22	and	and	CCONJ
ejpam-5832	578	23	p	p	NOUN
ejpam-5832	578	24	be	be	AUX
ejpam-5832	578	25	a	a	DET
ejpam-5832	578	26	q	q	NOUN
ejpam-5832	578	27	-	-	PUNCT
ejpam-5832	578	28	rofsg	rofsg	NOUN
ejpam-5832	578	29	of	of	ADP
ejpam-5832	578	30	v	v	NOUN
ejpam-5832	578	31	.	.	PUNCT
ejpam-5832	579	1	then	then	ADV
ejpam-5832	579	2	p	p	X
ejpam-5832	579	3	/	/	SYM
ejpam-5832	579	4	q	q	NOUN
ejpam-5832	579	5	∩	∩	NOUN
ejpam-5832	579	6	p	p	X
ejpam-5832	579	7	≃	≃	PROPN
ejpam-5832	579	8	(	(	PUNCT
ejpam-5832	579	9	q	q	PART
ejpam-5832	579	10	◦	◦	NOUN
ejpam-5832	579	11	p	p	NOUN
ejpam-5832	579	12	)	)	PUNCT
ejpam-5832	579	13	/q	/q	PUNCT
ejpam-5832	579	14	.	.	PUNCT
ejpam-5832	580	1	a.	a.	NOUN
ejpam-5832	580	2	razzaque	razzaque	PROPN
ejpam-5832	580	3	/	/	SYM
ejpam-5832	580	4	eur	eur	NOUN
ejpam-5832	580	5	.	.	PUNCT
ejpam-5832	581	1	j.	j.	PROPN
ejpam-5832	581	2	pure	pure	PROPN
ejpam-5832	581	3	appl	appl	PROPN
ejpam-5832	581	4	.	.	PROPN
ejpam-5832	581	5	math	math	PROPN
ejpam-5832	581	6	,	,	PUNCT
ejpam-5832	581	7	18	18	NUM
ejpam-5832	581	8	(	(	PUNCT
ejpam-5832	581	9	3	3	NUM
ejpam-5832	581	10	)	)	PUNCT
ejpam-5832	581	11	(	(	PUNCT
ejpam-5832	581	12	2025	2025	NUM
ejpam-5832	581	13	)	)	PUNCT
ejpam-5832	581	14	,	,	PUNCT
ejpam-5832	581	15	5832	5832	NUM
ejpam-5832	581	16	18	18	NUM
ejpam-5832	581	17	of	of	ADP
ejpam-5832	581	18	21	21	NUM
ejpam-5832	581	19	proof	proof	NOUN
ejpam-5832	581	20	.	.	PUNCT
ejpam-5832	582	1	by	by	ADP
ejpam-5832	582	2	theorem	theorem	NOUN
ejpam-5832	582	3	9	9	NUM
ejpam-5832	582	4	,	,	PUNCT
ejpam-5832	582	5	we	we	PRON
ejpam-5832	582	6	have	have	VERB
ejpam-5832	582	7	q∗	q∗	NOUN
ejpam-5832	582	8	⊴	⊴	ADP
ejpam-5832	582	9	v	v	NOUN
ejpam-5832	582	10	.	.	PUNCT
ejpam-5832	583	1	also	also	ADV
ejpam-5832	583	2	from	from	ADP
ejpam-5832	583	3	lemma	lemma	PROPN
ejpam-5832	583	4	2	2	NUM
ejpam-5832	583	5	,	,	PUNCT
ejpam-5832	583	6	we	we	PRON
ejpam-5832	583	7	obtain	obtain	VERB
ejpam-5832	583	8	p	p	NOUN
ejpam-5832	583	9	∗	∗	NOUN
ejpam-5832	583	10	is	be	AUX
ejpam-5832	583	11	a	a	DET
ejpam-5832	583	12	subgroup	subgroup	NOUN
ejpam-5832	583	13	of	of	ADP
ejpam-5832	583	14	v	v	NOUN
ejpam-5832	583	15	.	.	PUNCT
ejpam-5832	584	1	the	the	DET
ejpam-5832	584	2	second	second	ADJ
ejpam-5832	584	3	isomorphism	isomorphism	NOUN
ejpam-5832	584	4	theorem	theorem	NOUN
ejpam-5832	584	5	of	of	ADP
ejpam-5832	584	6	crisp	crisp	ADJ
ejpam-5832	584	7	groups	group	NOUN
ejpam-5832	584	8	shows	show	VERB
ejpam-5832	584	9	that	that	SCONJ
ejpam-5832	584	10	there	there	PRON
ejpam-5832	584	11	is	be	VERB
ejpam-5832	584	12	an	an	DET
ejpam-5832	584	13	isomorphism	isomorphism	NOUN
ejpam-5832	584	14	ψ	ψ	X
ejpam-5832	584	15	between	between	ADP
ejpam-5832	584	16	p	p	NOUN
ejpam-5832	584	17	∗/q∗∩p	∗/q∗∩p	NOUN
ejpam-5832	584	18	∗	∗	NOUN
ejpam-5832	584	19	and	and	CCONJ
ejpam-5832	584	20	q∗p	q∗p	NUM
ejpam-5832	584	21	∗/q∗	∗/q∗	PROPN
ejpam-5832	584	22	that	that	PRON
ejpam-5832	584	23	is	be	AUX
ejpam-5832	584	24	defined	define	VERB
ejpam-5832	584	25	by	by	ADP
ejpam-5832	584	26	ψ(k(q∗∩p	ψ(k(q∗∩p	NOUN
ejpam-5832	584	27	∗	∗	NOUN
ejpam-5832	584	28	)	)	PUNCT
ejpam-5832	584	29	)	)	PUNCT
ejpam-5832	585	1	=	=	SYM
ejpam-5832	585	2	kq∗	kq∗	ADJ
ejpam-5832	585	3	for	for	ADP
ejpam-5832	585	4	all	all	DET
ejpam-5832	585	5	k	k	PROPN
ejpam-5832	585	6	∈	∈	PROPN
ejpam-5832	585	7	p	p	NOUN
ejpam-5832	585	8	∗.	∗.	PROPN
ejpam-5832	585	9	by	by	ADP
ejpam-5832	585	10	lemma	lemma	PROPN
ejpam-5832	585	11	4	4	NUM
ejpam-5832	585	12	;	;	PUNCT
ejpam-5832	585	13	(	(	PUNCT
ejpam-5832	585	14	q∩p	q∩p	NOUN
ejpam-5832	585	15	)	)	PUNCT
ejpam-5832	585	16	∗	∗	NOUN
ejpam-5832	585	17	=	=	SYM
ejpam-5832	585	18	q∗∩p	q∗∩p	NOUN
ejpam-5832	585	19	∗	∗	NOUN
ejpam-5832	585	20	and	and	CCONJ
ejpam-5832	585	21	(	(	PUNCT
ejpam-5832	585	22	qp	qp	NOUN
ejpam-5832	585	23	)	)	PUNCT
ejpam-5832	585	24	∗	∗	NOUN
ejpam-5832	585	25	=	=	SYM
ejpam-5832	585	26	q∗p	q∗p	ADJ
ejpam-5832	585	27	∗	∗	NOUN
ejpam-5832	585	28	,	,	PUNCT
ejpam-5832	585	29	therefore	therefore	ADV
ejpam-5832	585	30	p	p	ADJ
ejpam-5832	585	31	∗/q∗∩p	∗/q∗∩p	PROPN
ejpam-5832	585	32	∗	∗	NOUN
ejpam-5832	585	33	is	be	AUX
ejpam-5832	585	34	isomorphic	isomorphic	ADJ
ejpam-5832	585	35	to	to	ADP
ejpam-5832	585	36	q∗p	q∗p	PROPN
ejpam-5832	585	37	∗/q∗.	∗/q∗.	NUM
ejpam-5832	585	38	now	now	ADV
ejpam-5832	585	39	(	(	PUNCT
ejpam-5832	585	40	µψ(p	µψ(p	NOUN
ejpam-5832	585	41	/	/	SYM
ejpam-5832	585	42	q∩p	q∩p	PROPN
ejpam-5832	585	43	)	)	PUNCT
ejpam-5832	585	44	(	(	PUNCT
ejpam-5832	585	45	kq	kq	PROPN
ejpam-5832	585	46	∗	∗	NOUN
ejpam-5832	585	47	)	)	PUNCT
ejpam-5832	585	48	)	)	PUNCT
ejpam-5832	586	1	q	q	X
ejpam-5832	587	1	=	=	PUNCT
ejpam-5832	587	2	(	(	PUNCT
ejpam-5832	587	3	µp	µp	PROPN
ejpam-5832	587	4	/	/	SYM
ejpam-5832	587	5	q∩p	q∩p	PROPN
ejpam-5832	587	6	(	(	PUNCT
ejpam-5832	587	7	k(q	k(q	PROPN
ejpam-5832	587	8	∩	∩	PROPN
ejpam-5832	587	9	p	p	NOUN
ejpam-5832	587	10	)	)	PUNCT
ejpam-5832	587	11	∗	∗	NOUN
ejpam-5832	587	12	)	)	PUNCT
ejpam-5832	587	13	)	)	PUNCT
ejpam-5832	587	14	q	q	NOUN
ejpam-5832	587	15	(	(	PUNCT
ejpam-5832	587	16	ψ	ψ	NOUN
ejpam-5832	587	17	is	be	AUX
ejpam-5832	587	18	one−	one−	PROPN
ejpam-5832	587	19	one	one	NUM
ejpam-5832	587	20	)	)	PUNCT
ejpam-5832	588	1	=	=	NOUN
ejpam-5832	588	2	max{(µp	max{(µp	NOUN
ejpam-5832	588	3	(	(	PUNCT
ejpam-5832	588	4	t))q	t))q	NOUN
ejpam-5832	588	5	:	:	PUNCT
ejpam-5832	588	6	t	t	PROPN
ejpam-5832	588	7	∈	∈	PROPN
ejpam-5832	588	8	k(q	k(q	PROPN
ejpam-5832	588	9	∩	∩	PROPN
ejpam-5832	588	10	p	p	NOUN
ejpam-5832	588	11	)	)	PUNCT
ejpam-5832	588	12	∗	∗	NOUN
ejpam-5832	588	13	}	}	PUNCT
ejpam-5832	588	14	≤	≤	X
ejpam-5832	588	15	max{((µq	max{((µq	AUX
ejpam-5832	588	16	◦	◦	VERB
ejpam-5832	588	17	µp	µp	NOUN
ejpam-5832	588	18	)	)	PUNCT
ejpam-5832	588	19	(	(	PUNCT
ejpam-5832	588	20	t))q	t))q	NOUN
ejpam-5832	588	21	:	:	PUNCT
ejpam-5832	588	22	t	t	PROPN
ejpam-5832	588	23	∈	∈	PROPN
ejpam-5832	588	24	k(q∗	k(q∗	NOUN
ejpam-5832	588	25	∩	∩	NOUN
ejpam-5832	588	26	p	p	NOUN
ejpam-5832	588	27	∗	∗	NOUN
ejpam-5832	588	28	)	)	PUNCT
ejpam-5832	588	29	}	}	PUNCT
ejpam-5832	588	30	≤	≤	NOUN
ejpam-5832	588	31	max{((µq	max{((µq	AUX
ejpam-5832	588	32	◦	◦	VERB
ejpam-5832	588	33	µp	µp	NOUN
ejpam-5832	588	34	)	)	PUNCT
ejpam-5832	588	35	(	(	PUNCT
ejpam-5832	588	36	t))q	t))q	NOUN
ejpam-5832	588	37	:	:	PUNCT
ejpam-5832	588	38	t	t	PROPN
ejpam-5832	588	39	∈	∈	PROPN
ejpam-5832	588	40	kq∗	kq∗	PROPN
ejpam-5832	588	41	}	}	PUNCT
ejpam-5832	588	42	=	=	SYM
ejpam-5832	588	43	(	(	PUNCT
ejpam-5832	588	44	(	(	PUNCT
ejpam-5832	588	45	(	(	PUNCT
ejpam-5832	588	46	µq	µq	PART
ejpam-5832	588	47	◦	◦	VERB
ejpam-5832	588	48	µp	µp	NOUN
ejpam-5832	588	49	)	)	PUNCT
ejpam-5832	588	50	/µq)(kq∗))q	/µq)(kq∗))q	PUNCT
ejpam-5832	589	1	the	the	DET
ejpam-5832	589	2	same	same	ADJ
ejpam-5832	589	3	reasoning	reasoning	NOUN
ejpam-5832	589	4	leads	lead	VERB
ejpam-5832	589	5	us	we	PRON
ejpam-5832	589	6	to	to	ADP
ejpam-5832	589	7	(	(	PUNCT
ejpam-5832	589	8	νψ(p	νψ(p	X
ejpam-5832	589	9	/	/	SYM
ejpam-5832	589	10	q∩p	q∩p	PROPN
ejpam-5832	589	11	)	)	PUNCT
ejpam-5832	589	12	(	(	PUNCT
ejpam-5832	589	13	kq	kq	PROPN
ejpam-5832	589	14	∗	∗	NOUN
ejpam-5832	589	15	)	)	PUNCT
ejpam-5832	589	16	)	)	PUNCT
ejpam-5832	590	1	q	q	NOUN
ejpam-5832	591	1	≥	≥	X
ejpam-5832	591	2	(	(	PUNCT
ejpam-5832	591	3	(	(	PUNCT
ejpam-5832	591	4	(	(	PUNCT
ejpam-5832	591	5	νq	νq	PROPN
ejpam-5832	591	6	◦	◦	NOUN
ejpam-5832	591	7	νp	νp	PUNCT
ejpam-5832	591	8	)	)	PUNCT
ejpam-5832	591	9	/νq)(kq∗))q	/νq)(kq∗))q	PROPN
ejpam-5832	591	10	.	.	PUNCT
ejpam-5832	592	1	therefore	therefore	ADV
ejpam-5832	592	2	,	,	PUNCT
ejpam-5832	592	3	ψ(p	ψ(p	NOUN
ejpam-5832	592	4	/	/	SYM
ejpam-5832	592	5	q	q	NOUN
ejpam-5832	592	6	∩	∩	NOUN
ejpam-5832	592	7	p	p	NOUN
ejpam-5832	592	8	)	)	PUNCT
ejpam-5832	592	9	⊆	⊆	NUM
ejpam-5832	592	10	(	(	PUNCT
ejpam-5832	592	11	q	q	NOUN
ejpam-5832	592	12	◦	◦	NOUN
ejpam-5832	592	13	p	p	NOUN
ejpam-5832	592	14	)	)	PUNCT
ejpam-5832	592	15	/q	/q	PUNCT
ejpam-5832	592	16	implying	imply	VERB
ejpam-5832	592	17	that	that	SCONJ
ejpam-5832	592	18	p	p	X
ejpam-5832	592	19	/	/	SYM
ejpam-5832	592	20	q	q	NOUN
ejpam-5832	592	21	∩	∩	NOUN
ejpam-5832	592	22	p	p	X
ejpam-5832	592	23	≃	≃	PROPN
ejpam-5832	592	24	(	(	PUNCT
ejpam-5832	592	25	q	q	PART
ejpam-5832	592	26	◦	◦	NOUN
ejpam-5832	592	27	p	p	NOUN
ejpam-5832	592	28	)	)	PUNCT
ejpam-5832	592	29	/q	/q	PUNCT
ejpam-5832	592	30	.	.	PUNCT
ejpam-5832	592	31	theorem	theorem	PROPN
ejpam-5832	592	32	22	22	NUM
ejpam-5832	592	33	.	.	PUNCT
ejpam-5832	593	1	(	(	PUNCT
ejpam-5832	593	2	third	third	ADJ
ejpam-5832	593	3	isomorphism	isomorphism	NOUN
ejpam-5832	593	4	theorem	theorem	VERB
ejpam-5832	593	5	in	in	ADP
ejpam-5832	593	6	q	q	ADJ
ejpam-5832	593	7	-	-	PUNCT
ejpam-5832	593	8	rung	rung	ADJ
ejpam-5832	593	9	orthopair	orthopair	ADJ
ejpam-5832	593	10	fuzzy	fuzzy	ADJ
ejpam-5832	593	11	settings	setting	NOUN
ejpam-5832	593	12	)	)	PUNCT
ejpam-5832	593	13	let	let	VERB
ejpam-5832	593	14	q	q	NOUN
ejpam-5832	593	15	,	,	PUNCT
ejpam-5832	593	16	p	p	NOUN
ejpam-5832	593	17	and	and	CCONJ
ejpam-5832	593	18	t	t	PROPN
ejpam-5832	593	19	be	be	AUX
ejpam-5832	593	20	q	q	NOUN
ejpam-5832	593	21	-	-	PUNCT
ejpam-5832	593	22	rofsg	rofsg	NOUN
ejpam-5832	593	23	of	of	ADP
ejpam-5832	593	24	v	v	NOUN
ejpam-5832	593	25	.	.	PUNCT
ejpam-5832	594	1	if	if	SCONJ
ejpam-5832	594	2	q	q	PROPN
ejpam-5832	594	3	and	and	CCONJ
ejpam-5832	594	4	p	p	NOUN
ejpam-5832	594	5	are	be	AUX
ejpam-5832	594	6	q	q	NOUN
ejpam-5832	594	7	-	-	PUNCT
ejpam-5832	594	8	rofnsgs	rofnsg	NOUN
ejpam-5832	594	9	of	of	ADP
ejpam-5832	594	10	t	t	PROPN
ejpam-5832	594	11	and	and	CCONJ
ejpam-5832	594	12	q	q	PRON
ejpam-5832	594	13	⊆	⊆	NUM
ejpam-5832	594	14	p	p	NOUN
ejpam-5832	594	15	.	.	PUNCT
ejpam-5832	595	1	then	then	ADV
ejpam-5832	595	2	(	(	PUNCT
ejpam-5832	595	3	t	t	PROPN
ejpam-5832	595	4	/	/	SYM
ejpam-5832	595	5	q)/(p	q)/(p	PROPN
ejpam-5832	595	6	/	/	SYM
ejpam-5832	595	7	q	q	NOUN
ejpam-5832	595	8	)	)	PUNCT
ejpam-5832	595	9	∼=	∼=	PROPN
ejpam-5832	595	10	t	t	PROPN
ejpam-5832	595	11	/	/	SYM
ejpam-5832	595	12	p	p	NOUN
ejpam-5832	595	13	.	.	PUNCT
ejpam-5832	596	1	proof	proof	NOUN
ejpam-5832	596	2	.	.	PUNCT
ejpam-5832	597	1	according	accord	VERB
ejpam-5832	597	2	to	to	ADP
ejpam-5832	597	3	theorem	theorem	ADJ
ejpam-5832	597	4	9	9	NUM
ejpam-5832	597	5	,	,	PUNCT
ejpam-5832	597	6	q∗	q∗	NOUN
ejpam-5832	597	7	⊴	⊴	ADP
ejpam-5832	597	8	t	t	NOUN
ejpam-5832	597	9	∗	∗	NOUN
ejpam-5832	597	10	and	and	CCONJ
ejpam-5832	597	11	p	p	NOUN
ejpam-5832	597	12	∗	∗	NOUN
ejpam-5832	597	13	⊴	⊴	ADP
ejpam-5832	597	14	t	t	PROPN
ejpam-5832	597	15	∗.	∗.	PUNCT
ejpam-5832	597	16	since	since	SCONJ
ejpam-5832	597	17	q	q	PROPN
ejpam-5832	597	18	⊆	⊆	NUM
ejpam-5832	597	19	p	p	NOUN
ejpam-5832	597	20	therefore	therefore	ADV
ejpam-5832	597	21	q∗	q∗	NOUN
ejpam-5832	597	22	⊴	⊴	ADP
ejpam-5832	597	23	p	p	X
ejpam-5832	597	24	∗.	∗.	PROPN
ejpam-5832	597	25	the	the	DET
ejpam-5832	597	26	third	third	ADJ
ejpam-5832	597	27	isomorphism	isomorphism	NOUN
ejpam-5832	597	28	theorem	theorem	NOUN
ejpam-5832	597	29	associated	associate	VERB
ejpam-5832	597	30	to	to	ADP
ejpam-5832	597	31	crisp	crisp	ADJ
ejpam-5832	597	32	groups	group	NOUN
ejpam-5832	597	33	theory	theory	NOUN
ejpam-5832	597	34	reveals	reveal	VERB
ejpam-5832	597	35	that	that	SCONJ
ejpam-5832	597	36	there	there	PRON
ejpam-5832	597	37	is	be	VERB
ejpam-5832	597	38	an	an	DET
ejpam-5832	597	39	isomorphism	isomorphism	NOUN
ejpam-5832	597	40	ψ	ψ	X
ejpam-5832	597	41	between	between	ADP
ejpam-5832	597	42	(	(	PUNCT
ejpam-5832	597	43	t	t	PROPN
ejpam-5832	597	44	∗/q∗)/(p	∗/q∗)/(p	PROPN
ejpam-5832	597	45	∗/q∗	∗/q∗	PROPN
ejpam-5832	597	46	)	)	PUNCT
ejpam-5832	597	47	and	and	CCONJ
ejpam-5832	597	48	t	t	PROPN
ejpam-5832	597	49	∗/p	∗/p	ADJ
ejpam-5832	597	50	∗	∗	NOUN
ejpam-5832	597	51	,	,	PUNCT
ejpam-5832	597	52	defined	define	VERB
ejpam-5832	597	53	by	by	ADP
ejpam-5832	597	54	ψ(lq∗(p	ψ(lq∗(p	SYM
ejpam-5832	597	55	∗/q∗	∗/q∗	PROPN
ejpam-5832	597	56	)	)	PUNCT
ejpam-5832	597	57	)	)	PUNCT
ejpam-5832	598	1	=	=	SYM
ejpam-5832	598	2	lp	lp	ADJ
ejpam-5832	598	3	∗	∗	NOUN
ejpam-5832	598	4	for	for	ADP
ejpam-5832	598	5	all	all	DET
ejpam-5832	598	6	l	l	NOUN
ejpam-5832	598	7	∈	∈	PROPN
ejpam-5832	598	8	t	t	NOUN
ejpam-5832	598	9	∗.	∗.	PROPN
ejpam-5832	598	10	(	(	PUNCT
ejpam-5832	598	11	µψ(((t	µψ(((t	PROPN
ejpam-5832	598	12	/	/	SYM
ejpam-5832	598	13	q))/((p	q))/((p	NOUN
ejpam-5832	598	14	/	/	SYM
ejpam-5832	598	15	q)))(lp	q)))(lp	PROPN
ejpam-5832	598	16	∗	∗	PROPN
ejpam-5832	598	17	)	)	PUNCT
ejpam-5832	598	18	)	)	PUNCT
ejpam-5832	599	1	q	q	X
ejpam-5832	599	2	=	=	PUNCT
ejpam-5832	599	3	(	(	PUNCT
ejpam-5832	599	4	µ(((t	µ(((t	PROPN
ejpam-5832	599	5	/	/	SYM
ejpam-5832	599	6	q))/((p	q))/((p	NOUN
ejpam-5832	599	7	/	/	SYM
ejpam-5832	599	8	q)))(lq∗(p	q)))(lq∗(p	NOUN
ejpam-5832	599	9	∗/q∗	∗/q∗	PROPN
ejpam-5832	599	10	)	)	PUNCT
ejpam-5832	599	11	)	)	PUNCT
ejpam-5832	599	12	)	)	PUNCT
ejpam-5832	600	1	q	q	X
ejpam-5832	601	1	=	=	PUNCT
ejpam-5832	601	2	max{(µt	max{(µt	ADJ
ejpam-5832	601	3	/	/	SYM
ejpam-5832	601	4	q(l′q∗))q	q(l′q∗))q	NOUN
ejpam-5832	601	5	:	:	PUNCT
ejpam-5832	601	6	l′	l′	PROPN
ejpam-5832	601	7	∈	∈	PROPN
ejpam-5832	601	8	t	t	PROPN
ejpam-5832	601	9	∗	∗	NOUN
ejpam-5832	601	10	,	,	PUNCT
ejpam-5832	601	11	l′q∗	l′q∗	PRON
ejpam-5832	601	12	∈	∈	PROPN
ejpam-5832	601	13	lq∗(p	lq∗(p	PROPN
ejpam-5832	601	14	∗/q∗	∗/q∗	PROPN
ejpam-5832	601	15	)	)	PUNCT
ejpam-5832	601	16	}	}	PUNCT
ejpam-5832	602	1	=	=	SYM
ejpam-5832	602	2	max{max{(µt	max{max{(µt	ADJ
ejpam-5832	602	3	(	(	PUNCT
ejpam-5832	602	4	t))q	t))q	NOUN
ejpam-5832	602	5	:	:	PUNCT
ejpam-5832	602	6	t	t	PROPN
ejpam-5832	602	7	∈	∈	PROPN
ejpam-5832	603	1	l′q∗	l′q∗	NOUN
ejpam-5832	603	2	}	}	PUNCT
ejpam-5832	603	3	:	:	PUNCT
ejpam-5832	603	4	l′	l′	PROPN
ejpam-5832	603	5	∈	∈	PROPN
ejpam-5832	603	6	t	t	PROPN
ejpam-5832	603	7	∗	∗	NOUN
ejpam-5832	603	8	,	,	PUNCT
ejpam-5832	603	9	l′q∗	l′q∗	PRON
ejpam-5832	603	10	∈	∈	PROPN
ejpam-5832	603	11	lq∗(p	lq∗(p	PROPN
ejpam-5832	603	12	∗/q∗	∗/q∗	PROPN
ejpam-5832	603	13	)	)	PUNCT
ejpam-5832	603	14	}	}	PUNCT
ejpam-5832	604	1	=	=	SYM
ejpam-5832	604	2	max{(µt	max{(µt	INTJ
ejpam-5832	604	3	(	(	PUNCT
ejpam-5832	604	4	z))q	z))q	NOUN
ejpam-5832	604	5	:	:	PUNCT
ejpam-5832	604	6	z	z	PROPN
ejpam-5832	604	7	∈	∈	PROPN
ejpam-5832	604	8	t	t	NOUN
ejpam-5832	604	9	∗	∗	NOUN
ejpam-5832	604	10	,	,	PUNCT
ejpam-5832	604	11	zq∗	zq∗	NOUN
ejpam-5832	604	12	∈	∈	PROPN
ejpam-5832	604	13	lq∗(p	lq∗(p	PROPN
ejpam-5832	604	14	∗/q∗	∗/q∗	PROPN
ejpam-5832	604	15	)	)	PUNCT
ejpam-5832	604	16	}	}	PUNCT
ejpam-5832	604	17	we	we	PRON
ejpam-5832	604	18	know	know	VERB
ejpam-5832	604	19	,	,	PUNCT
ejpam-5832	604	20	zq∗	zq∗	PUNCT
ejpam-5832	604	21	∈	∈	PROPN
ejpam-5832	604	22	lq∗(p	lq∗(p	PROPN
ejpam-5832	604	23	∗/q∗	∗/q∗	PROPN
ejpam-5832	604	24	)	)	PUNCT
ejpam-5832	604	25	,	,	PUNCT
ejpam-5832	604	26	then	then	ADV
ejpam-5832	604	27	lq∗(p	lq∗(p	PROPN
ejpam-5832	604	28	∗/q∗	∗/q∗	PROPN
ejpam-5832	604	29	)	)	PUNCT
ejpam-5832	605	1	=	=	SYM
ejpam-5832	605	2	zq∗(p	zq∗(p	NOUN
ejpam-5832	605	3	∗/q∗	∗/q∗	PROPN
ejpam-5832	605	4	)	)	PUNCT
ejpam-5832	605	5	(	(	PUNCT
ejpam-5832	605	6	since	since	SCONJ
ejpam-5832	605	7	λ	λ	PROPN
ejpam-5832	605	8	∈	∈	PROPN
ejpam-5832	605	9	gh	gh	PROPN
ejpam-5832	605	10	⇒	⇒	PROPN
ejpam-5832	605	11	gh	gh	PROPN
ejpam-5832	605	12	=	=	PROPN
ejpam-5832	605	13	λh	λh	PROPN
ejpam-5832	605	14	)	)	PUNCT
ejpam-5832	605	15	.	.	PUNCT
ejpam-5832	606	1	so	so	ADV
ejpam-5832	606	2	,	,	PUNCT
ejpam-5832	606	3	ψ(lq∗(p	ψ(lq∗(p	NUM
ejpam-5832	606	4	∗/q∗	∗/q∗	PROPN
ejpam-5832	606	5	)	)	PUNCT
ejpam-5832	606	6	)	)	PUNCT
ejpam-5832	607	1	=	=	SYM
ejpam-5832	607	2	ψ(zq∗(p	ψ(zq∗(p	NOUN
ejpam-5832	607	3	∗/q∗	∗/q∗	NOUN
ejpam-5832	607	4	)	)	PUNCT
ejpam-5832	607	5	)	)	PUNCT
ejpam-5832	608	1	implying	imply	VERB
ejpam-5832	608	2	that	that	SCONJ
ejpam-5832	608	3	lp	lp	ADJ
ejpam-5832	608	4	∗	∗	NOUN
ejpam-5832	608	5	=	=	PUNCT
ejpam-5832	608	6	zp	zp	NOUN
ejpam-5832	608	7	∗.	∗.	PUNCT
ejpam-5832	608	8	since	since	SCONJ
ejpam-5832	608	9	z	z	PROPN
ejpam-5832	608	10	∈	∈	PROPN
ejpam-5832	608	11	zp	zp	PROPN
ejpam-5832	608	12	∗	∗	NOUN
ejpam-5832	608	13	,	,	PUNCT
ejpam-5832	608	14	thus	thus	ADV
ejpam-5832	608	15	,	,	PUNCT
ejpam-5832	608	16	z	z	PROPN
ejpam-5832	608	17	∈	∈	PROPN
ejpam-5832	608	18	lp	lp	ADJ
ejpam-5832	608	19	∗.	∗.	PROPN
ejpam-5832	608	20	therefore	therefore	ADV
ejpam-5832	608	21	,	,	PUNCT
ejpam-5832	608	22	(	(	PUNCT
ejpam-5832	608	23	µψ(((t	µψ(((t	NOUN
ejpam-5832	608	24	/	/	SYM
ejpam-5832	608	25	q))/((p	q))/((p	NOUN
ejpam-5832	608	26	/	/	SYM
ejpam-5832	608	27	q)))(lp	q)))(lp	PROPN
ejpam-5832	608	28	∗))q	∗))q	NOUN
ejpam-5832	609	1	=	=	PUNCT
ejpam-5832	609	2	max{(µt	max{(µt	PROPN
ejpam-5832	609	3	(	(	PUNCT
ejpam-5832	609	4	z))q	z))q	NOUN
ejpam-5832	609	5	:	:	PUNCT
ejpam-5832	609	6	z	z	PROPN
ejpam-5832	609	7	∈	∈	PROPN
ejpam-5832	609	8	t	t	NOUN
ejpam-5832	609	9	∗	∗	NOUN
ejpam-5832	609	10	,	,	PUNCT
ejpam-5832	609	11	z	z	PROPN
ejpam-5832	609	12	∈	∈	PROPN
ejpam-5832	609	13	lp	lp	NOUN
ejpam-5832	609	14	∗	∗	NOUN
ejpam-5832	609	15	}	}	PUNCT
ejpam-5832	609	16	=	=	SYM
ejpam-5832	609	17	(	(	PUNCT
ejpam-5832	609	18	µt	µt	ADJ
ejpam-5832	609	19	/	/	SYM
ejpam-5832	609	20	p	p	X
ejpam-5832	609	21	(	(	PUNCT
ejpam-5832	609	22	lp	lp	ADJ
ejpam-5832	609	23	∗	∗	NOUN
ejpam-5832	609	24	)	)	PUNCT
ejpam-5832	609	25	)	)	PUNCT
ejpam-5832	609	26	q	q	PUNCT
ejpam-5832	610	1	by	by	ADP
ejpam-5832	610	2	the	the	DET
ejpam-5832	610	3	same	same	ADJ
ejpam-5832	610	4	method	method	NOUN
ejpam-5832	610	5	,	,	PUNCT
ejpam-5832	610	6	we	we	PRON
ejpam-5832	610	7	obtain	obtain	VERB
ejpam-5832	610	8	;	;	PUNCT
ejpam-5832	610	9	(	(	PUNCT
ejpam-5832	610	10	νψ(((t	νψ(((t	X
ejpam-5832	610	11	/	/	SYM
ejpam-5832	610	12	q))/((p	q))/((p	NOUN
ejpam-5832	610	13	/	/	SYM
ejpam-5832	610	14	q)))(lp	q)))(lp	PROPN
ejpam-5832	610	15	∗))q	∗))q	NOUN
ejpam-5832	610	16	=	=	SYM
ejpam-5832	610	17	(	(	PUNCT
ejpam-5832	610	18	ν(t	ν(t	NOUN
ejpam-5832	610	19	/	/	SYM
ejpam-5832	610	20	p	p	NOUN
ejpam-5832	610	21	)	)	PUNCT
ejpam-5832	610	22	(	(	PUNCT
ejpam-5832	610	23	lp	lp	PROPN
ejpam-5832	610	24	∗))q	∗))q	PROPN
ejpam-5832	610	25	therefore	therefore	ADV
ejpam-5832	610	26	,	,	PUNCT
ejpam-5832	610	27	ψ	ψ	X
ejpam-5832	610	28	(	(	PUNCT
ejpam-5832	610	29	(	(	PUNCT
ejpam-5832	610	30	(	(	PUNCT
ejpam-5832	610	31	t	t	NOUN
ejpam-5832	610	32	/	/	SYM
ejpam-5832	610	33	q))/((p	q))/((p	NOUN
ejpam-5832	610	34	/	/	SYM
ejpam-5832	610	35	q	q	NOUN
ejpam-5832	610	36	)	)	PUNCT
ejpam-5832	610	37	)	)	PUNCT
ejpam-5832	610	38	)	)	PUNCT
ejpam-5832	611	1	=	=	PUNCT
ejpam-5832	611	2	t	t	PROPN
ejpam-5832	611	3	/	/	SYM
ejpam-5832	611	4	p	p	NOUN
ejpam-5832	611	5	,	,	PUNCT
ejpam-5832	611	6	thus	thus	ADV
ejpam-5832	611	7	,	,	PUNCT
ejpam-5832	611	8	ψ	ψ	X
ejpam-5832	611	9	is	be	AUX
ejpam-5832	611	10	a	a	DET
ejpam-5832	611	11	q	q	NOUN
ejpam-5832	611	12	-	-	PUNCT
ejpam-5832	611	13	rofiso	rofiso	NOUN
ejpam-5832	611	14	from	from	ADP
ejpam-5832	611	15	(	(	PUNCT
ejpam-5832	611	16	t	t	PROPN
ejpam-5832	611	17	/	/	SYM
ejpam-5832	611	18	q)/(p	q)/(p	PROPN
ejpam-5832	611	19	/	/	SYM
ejpam-5832	611	20	q	q	NOUN
ejpam-5832	611	21	)	)	PUNCT
ejpam-5832	611	22	to	to	ADP
ejpam-5832	611	23	t	t	PROPN
ejpam-5832	611	24	/	/	SYM
ejpam-5832	611	25	p	p	NOUN
ejpam-5832	611	26	.	.	PUNCT
ejpam-5832	612	1	a.	a.	NOUN
ejpam-5832	612	2	razzaque	razzaque	PROPN
ejpam-5832	612	3	/	/	SYM
ejpam-5832	612	4	eur	eur	NOUN
ejpam-5832	612	5	.	.	PUNCT
ejpam-5832	613	1	j.	j.	PROPN
ejpam-5832	613	2	pure	pure	PROPN
ejpam-5832	613	3	appl	appl	PROPN
ejpam-5832	613	4	.	.	PROPN
ejpam-5832	613	5	math	math	PROPN
ejpam-5832	613	6	,	,	PUNCT
ejpam-5832	613	7	18	18	NUM
ejpam-5832	613	8	(	(	PUNCT
ejpam-5832	613	9	3	3	NUM
ejpam-5832	613	10	)	)	PUNCT
ejpam-5832	613	11	(	(	PUNCT
ejpam-5832	613	12	2025	2025	NUM
ejpam-5832	613	13	)	)	PUNCT
ejpam-5832	613	14	,	,	PUNCT
ejpam-5832	613	15	5832	5832	NUM
ejpam-5832	613	16	19	19	NUM
ejpam-5832	613	17	of	of	ADP
ejpam-5832	613	18	21	21	NUM
ejpam-5832	613	19	6	6	NUM
ejpam-5832	613	20	.	.	PUNCT
ejpam-5832	613	21	conclusion	conclusion	VERB
ejpam-5832	613	22	the	the	DET
ejpam-5832	613	23	primary	primary	ADJ
ejpam-5832	613	24	goal	goal	NOUN
ejpam-5832	613	25	of	of	ADP
ejpam-5832	613	26	this	this	DET
ejpam-5832	613	27	study	study	NOUN
ejpam-5832	613	28	is	be	AUX
ejpam-5832	613	29	to	to	PART
ejpam-5832	613	30	analyze	analyze	VERB
ejpam-5832	613	31	fundamental	fundamental	ADJ
ejpam-5832	613	32	isomorphism	isomorphism	NOUN
ejpam-5832	613	33	theorems	theorem	NOUN
ejpam-5832	613	34	in	in	ADP
ejpam-5832	613	35	the	the	DET
ejpam-5832	613	36	context	context	NOUN
ejpam-5832	613	37	of	of	ADP
ejpam-5832	613	38	q	q	NOUN
ejpam-5832	613	39	-	-	PUNCT
ejpam-5832	613	40	rofss	rofss	NOUN
ejpam-5832	613	41	.	.	PUNCT
ejpam-5832	614	1	many	many	ADJ
ejpam-5832	614	2	concepts	concept	NOUN
ejpam-5832	614	3	from	from	ADP
ejpam-5832	614	4	group	group	NOUN
ejpam-5832	614	5	theory	theory	NOUN
ejpam-5832	614	6	,	,	PUNCT
ejpam-5832	614	7	particularly	particularly	ADV
ejpam-5832	614	8	cosets	coset	NOUN
ejpam-5832	614	9	,	,	PUNCT
ejpam-5832	614	10	normal	normal	ADJ
ejpam-5832	614	11	subgroups	subgroup	NOUN
ejpam-5832	614	12	,	,	PUNCT
ejpam-5832	614	13	quotient	quotient	NOUN
ejpam-5832	614	14	groups	group	NOUN
ejpam-5832	614	15	,	,	PUNCT
ejpam-5832	614	16	homomorphisms	homomorphism	NOUN
ejpam-5832	614	17	and	and	CCONJ
ejpam-5832	614	18	isomorphisms	isomorphism	NOUN
ejpam-5832	614	19	are	be	AUX
ejpam-5832	614	20	translated	translate	VERB
ejpam-5832	614	21	into	into	ADP
ejpam-5832	614	22	the	the	DET
ejpam-5832	614	23	q	q	ADJ
ejpam-5832	614	24	-	-	PUNCT
ejpam-5832	614	25	rung	rung	ADJ
ejpam-5832	614	26	orthopair	orthopair	ADJ
ejpam-5832	614	27	fuzzy	fuzzy	ADJ
ejpam-5832	614	28	structure	structure	NOUN
ejpam-5832	614	29	and	and	CCONJ
ejpam-5832	614	30	various	various	ADJ
ejpam-5832	614	31	theorems	theorem	NOUN
ejpam-5832	614	32	are	be	AUX
ejpam-5832	614	33	proved	prove	VERB
ejpam-5832	614	34	in	in	ADP
ejpam-5832	614	35	this	this	DET
ejpam-5832	614	36	context	context	NOUN
ejpam-5832	614	37	.	.	PUNCT
ejpam-5832	615	1	as	as	ADP
ejpam-5832	615	2	a	a	DET
ejpam-5832	615	3	consequence	consequence	NOUN
ejpam-5832	615	4	of	of	ADP
ejpam-5832	615	5	this	this	DET
ejpam-5832	615	6	research	research	NOUN
ejpam-5832	615	7	,	,	PUNCT
ejpam-5832	615	8	we	we	PRON
ejpam-5832	615	9	want	want	VERB
ejpam-5832	615	10	to	to	PART
ejpam-5832	615	11	investigate	investigate	VERB
ejpam-5832	615	12	further	further	ADJ
ejpam-5832	615	13	topics	topic	NOUN
ejpam-5832	615	14	of	of	ADP
ejpam-5832	615	15	traditional	traditional	ADJ
ejpam-5832	615	16	group	group	NOUN
ejpam-5832	615	17	theory	theory	NOUN
ejpam-5832	615	18	such	such	ADJ
ejpam-5832	615	19	as	as	ADP
ejpam-5832	615	20	abelian	abelian	ADJ
ejpam-5832	615	21	groups	group	NOUN
ejpam-5832	615	22	,	,	PUNCT
ejpam-5832	615	23	commutator	commutator	NOUN
ejpam-5832	615	24	subgroups	subgroup	NOUN
ejpam-5832	615	25	,	,	PUNCT
ejpam-5832	615	26	lagrange	lagrange	NOUN
ejpam-5832	615	27	’s	’s	PART
ejpam-5832	615	28	and	and	CCONJ
ejpam-5832	615	29	caley	caley	PROPN
ejpam-5832	615	30	’s	’s	PART
ejpam-5832	615	31	theorems	theorem	NOUN
ejpam-5832	615	32	,	,	PUNCT
ejpam-5832	615	33	free	free	ADJ
ejpam-5832	615	34	group	group	NOUN
ejpam-5832	615	35	and	and	CCONJ
ejpam-5832	615	36	p	p	NOUN
ejpam-5832	615	37	-	-	PUNCT
ejpam-5832	615	38	groups	group	NOUN
ejpam-5832	615	39	etc	etc	X
ejpam-5832	615	40	in	in	ADP
ejpam-5832	615	41	q	q	ADJ
ejpam-5832	615	42	-	-	PUNCT
ejpam-5832	615	43	rung	rung	ADJ
ejpam-5832	615	44	orthopair	orthopair	ADJ
ejpam-5832	615	45	fuzzy	fuzzy	ADJ
ejpam-5832	615	46	environment	environment	NOUN
ejpam-5832	615	47	.	.	PUNCT
ejpam-5832	616	1	in	in	ADP
ejpam-5832	616	2	addition	addition	NOUN
ejpam-5832	616	3	,	,	PUNCT
ejpam-5832	616	4	we	we	PRON
ejpam-5832	616	5	will	will	AUX
ejpam-5832	616	6	extend	extend	VERB
ejpam-5832	616	7	these	these	DET
ejpam-5832	616	8	results	result	NOUN
ejpam-5832	616	9	to	to	ADP
ejpam-5832	616	10	other	other	ADJ
ejpam-5832	616	11	types	type	NOUN
ejpam-5832	616	12	(	(	PUNCT
ejpam-5832	616	13	rings	ring	NOUN
ejpam-5832	616	14	,	,	PUNCT
ejpam-5832	616	15	vector	vector	NOUN
ejpam-5832	616	16	spaces	space	NOUN
ejpam-5832	616	17	etc	etc	X
ejpam-5832	616	18	)	)	PUNCT
ejpam-5832	616	19	of	of	ADP
ejpam-5832	616	20	homomorphism	homomorphism	NOUN
ejpam-5832	616	21	and	and	CCONJ
ejpam-5832	616	22	under	under	ADP
ejpam-5832	616	23	different	different	ADJ
ejpam-5832	616	24	extensions	extension	NOUN
ejpam-5832	616	25	of	of	ADP
ejpam-5832	616	26	the	the	DET
ejpam-5832	616	27	fss	fss	NOUN
ejpam-5832	616	28	.	.	PUNCT
ejpam-5832	617	1	furthermore	furthermore	ADV
ejpam-5832	617	2	,	,	PUNCT
ejpam-5832	617	3	we	we	PRON
ejpam-5832	617	4	intend	intend	VERB
ejpam-5832	617	5	to	to	PART
ejpam-5832	617	6	employ	employ	VERB
ejpam-5832	617	7	the	the	DET
ejpam-5832	617	8	findings	finding	NOUN
ejpam-5832	617	9	from	from	ADP
ejpam-5832	617	10	this	this	DET
ejpam-5832	617	11	research	research	NOUN
ejpam-5832	617	12	in	in	ADP
ejpam-5832	617	13	a	a	DET
ejpam-5832	617	14	variety	variety	NOUN
ejpam-5832	617	15	of	of	ADP
ejpam-5832	617	16	practical	practical	ADJ
ejpam-5832	617	17	contexts	contexts	NOUN
ejpam-5832	617	18	,	,	PUNCT
ejpam-5832	617	19	including	include	VERB
ejpam-5832	617	20	cryptography	cryptography	NOUN
ejpam-5832	617	21	,	,	PUNCT
ejpam-5832	617	22	picture	picture	NOUN
ejpam-5832	617	23	encryption	encryption	NOUN
ejpam-5832	617	24	,	,	PUNCT
ejpam-5832	617	25	and	and	CCONJ
ejpam-5832	617	26	other	other	ADJ
ejpam-5832	617	27	related	related	ADJ
ejpam-5832	617	28	areas	area	NOUN
ejpam-5832	617	29	.	.	PUNCT
ejpam-5832	618	1	references	reference	NOUN
ejpam-5832	618	2	[	[	X
ejpam-5832	618	3	1	1	NUM
ejpam-5832	618	4	]	]	PUNCT
ejpam-5832	618	5	l	l	NOUN
ejpam-5832	618	6	a	a	DET
ejpam-5832	618	7	zadehi	zadehi	NOUN
ejpam-5832	618	8	.	.	PUNCT
ejpam-5832	619	1	fuzzy	fuzzy	ADJ
ejpam-5832	619	2	sets	set	NOUN
ejpam-5832	619	3	,	,	PUNCT
ejpam-5832	619	4	fuzzy	fuzzy	ADJ
ejpam-5832	619	5	logic	logic	NOUN
ejpam-5832	619	6	,	,	PUNCT
ejpam-5832	619	7	and	and	CCONJ
ejpam-5832	619	8	fuzzy	fuzzy	ADJ
ejpam-5832	619	9	systems	system	NOUN
ejpam-5832	619	10	.	.	PUNCT
ejpam-5832	620	1	pages	page	NOUN
ejpam-5832	620	2	394–432	394–432	NUM
ejpam-5832	620	3	,	,	PUNCT
ejpam-5832	620	4	1996	1996	NUM
ejpam-5832	620	5	.	.	PUNCT
ejpam-5832	621	1	[	[	X
ejpam-5832	621	2	2	2	NUM
ejpam-5832	621	3	]	]	PUNCT
ejpam-5832	621	4	kt	kt	PROPN
ejpam-5832	621	5	atanassov	atanassov	PROPN
ejpam-5832	621	6	.	.	PUNCT
ejpam-5832	622	1	intuitionistic	intuitionistic	ADJ
ejpam-5832	622	2	fuzzy	fuzzy	ADJ
ejpam-5832	622	3	sets	set	NOUN
ejpam-5832	622	4	.	.	PUNCT
ejpam-5832	623	1	fuzzy	fuzzy	ADJ
ejpam-5832	623	2	sets	set	NOUN
ejpam-5832	623	3	and	and	CCONJ
ejpam-5832	623	4	systems	system	NOUN
ejpam-5832	623	5	.	.	PUNCT
ejpam-5832	624	1	29:87–996	29:87–996	NUM
ejpam-5832	624	2	,	,	PUNCT
ejpam-5832	624	3	1986	1986	NUM
ejpam-5832	624	4	.	.	PUNCT
ejpam-5832	625	1	[	[	X
ejpam-5832	625	2	3	3	X
ejpam-5832	625	3	]	]	X
ejpam-5832	625	4	f	f	PROPN
ejpam-5832	625	5	xiao	xiao	PROPN
ejpam-5832	625	6	.	.	PUNCT
ejpam-5832	626	1	a	a	DET
ejpam-5832	626	2	distance	distance	NOUN
ejpam-5832	626	3	measure	measure	NOUN
ejpam-5832	626	4	for	for	ADP
ejpam-5832	626	5	intuitionistic	intuitionistic	ADJ
ejpam-5832	626	6	fuzzy	fuzzy	ADJ
ejpam-5832	626	7	sets	set	NOUN
ejpam-5832	626	8	and	and	CCONJ
ejpam-5832	626	9	its	its	PRON
ejpam-5832	626	10	application	application	NOUN
ejpam-5832	626	11	to	to	PART
ejpam-5832	626	12	pattern	pattern	VERB
ejpam-5832	626	13	classification	classification	NOUN
ejpam-5832	626	14	problems	problem	NOUN
ejpam-5832	626	15	.	.	PUNCT
ejpam-5832	627	1	ieee	ieee	NOUN
ejpam-5832	627	2	transactions	transaction	NOUN
ejpam-5832	627	3	on	on	ADP
ejpam-5832	627	4	systems	system	NOUN
ejpam-5832	627	5	,	,	PUNCT
ejpam-5832	627	6	man	man	NOUN
ejpam-5832	627	7	,	,	PUNCT
ejpam-5832	627	8	and	and	CCONJ
ejpam-5832	627	9	cybernetics	cybernetic	NOUN
ejpam-5832	627	10	:	:	PUNCT
ejpam-5832	627	11	systems	system	NOUN
ejpam-5832	627	12	,	,	PUNCT
ejpam-5832	627	13	51(6):3980–3992	51(6):3980–3992	NUM
ejpam-5832	627	14	,	,	PUNCT
ejpam-5832	627	15	2019	2019	NUM
ejpam-5832	627	16	.	.	PUNCT
ejpam-5832	628	1	[	[	X
ejpam-5832	628	2	4	4	NUM
ejpam-5832	628	3	]	]	X
ejpam-5832	628	4	h	h	NOUN
ejpam-5832	628	5	garg	garg	NOUN
ejpam-5832	628	6	and	and	CCONJ
ejpam-5832	628	7	k	k	PROPN
ejpam-5832	628	8	kumar	kumar	PROPN
ejpam-5832	628	9	.	.	PUNCT
ejpam-5832	629	1	linguistic	linguistic	ADJ
ejpam-5832	629	2	interval	interval	NOUN
ejpam-5832	629	3	-	-	PUNCT
ejpam-5832	629	4	valued	value	VERB
ejpam-5832	629	5	atanassov	atanassov	NOUN
ejpam-5832	629	6	intuitionistic	intuitionistic	ADJ
ejpam-5832	629	7	fuzzy	fuzzy	ADJ
ejpam-5832	629	8	sets	set	NOUN
ejpam-5832	629	9	and	and	CCONJ
ejpam-5832	629	10	their	their	PRON
ejpam-5832	629	11	applications	application	NOUN
ejpam-5832	629	12	to	to	ADP
ejpam-5832	629	13	group	group	NOUN
ejpam-5832	629	14	decision	decision	NOUN
ejpam-5832	629	15	making	make	VERB
ejpam-5832	629	16	problems	problem	NOUN
ejpam-5832	629	17	.	.	PUNCT
ejpam-5832	630	1	ieee	ieee	NOUN
ejpam-5832	630	2	transactions	transaction	NOUN
ejpam-5832	630	3	on	on	ADP
ejpam-5832	630	4	fuzzy	fuzzy	ADJ
ejpam-5832	630	5	systems	system	NOUN
ejpam-5832	630	6	,	,	PUNCT
ejpam-5832	630	7	27(12):2302–2311	27(12):2302–2311	NUM
ejpam-5832	630	8	,	,	PUNCT
ejpam-5832	630	9	2019	2019	NUM
ejpam-5832	630	10	.	.	PUNCT
ejpam-5832	631	1	[	[	X
ejpam-5832	631	2	5	5	NUM
ejpam-5832	631	3	]	]	PUNCT
ejpam-5832	631	4	y	y	PROPN
ejpam-5832	631	5	song	song	NOUN
ejpam-5832	631	6	,	,	PUNCT
ejpam-5832	631	7	q	q	PROPN
ejpam-5832	631	8	fu	fu	PROPN
ejpam-5832	631	9	,	,	PUNCT
ejpam-5832	631	10	y	y	PROPN
ejpam-5832	631	11	f	f	PROPN
ejpam-5832	631	12	wang	wang	PROPN
ejpam-5832	631	13	,	,	PUNCT
ejpam-5832	631	14	and	and	CCONJ
ejpam-5832	631	15	x	x	X
ejpam-5832	631	16	wang	wang	PROPN
ejpam-5832	631	17	.	.	PUNCT
ejpam-5832	632	1	divergence	divergence	NOUN
ejpam-5832	632	2	-	-	PUNCT
ejpam-5832	632	3	based	base	VERB
ejpam-5832	632	4	cross	cross	NOUN
ejpam-5832	632	5	entropy	entropy	NOUN
ejpam-5832	632	6	and	and	CCONJ
ejpam-5832	632	7	uncertainty	uncertainty	NOUN
ejpam-5832	632	8	measures	measure	NOUN
ejpam-5832	632	9	of	of	ADP
ejpam-5832	632	10	atanassov	atanassov	NOUN
ejpam-5832	632	11	’s	’s	PART
ejpam-5832	632	12	intuitionistic	intuitionistic	ADJ
ejpam-5832	632	13	fuzzy	fuzzy	ADJ
ejpam-5832	632	14	sets	set	NOUN
ejpam-5832	632	15	with	with	ADP
ejpam-5832	632	16	their	their	PRON
ejpam-5832	632	17	application	application	NOUN
ejpam-5832	632	18	in	in	ADP
ejpam-5832	632	19	decision	decision	NOUN
ejpam-5832	632	20	making	making	NOUN
ejpam-5832	632	21	.	.	PUNCT
ejpam-5832	633	1	applied	apply	VERB
ejpam-5832	633	2	soft	soft	ADJ
ejpam-5832	633	3	computing	computing	NOUN
ejpam-5832	633	4	,	,	PUNCT
ejpam-5832	633	5	84:105703	84:105703	NUM
ejpam-5832	633	6	,	,	PUNCT
ejpam-5832	633	7	2019	2019	NUM
ejpam-5832	633	8	.	.	PUNCT
ejpam-5832	634	1	[	[	X
ejpam-5832	634	2	6	6	NUM
ejpam-5832	634	3	]	]	PUNCT
ejpam-5832	634	4	h	h	NOUN
ejpam-5832	634	5	garg	garg	NOUN
ejpam-5832	634	6	and	and	CCONJ
ejpam-5832	634	7	k	k	PROPN
ejpam-5832	634	8	kumar	kumar	PROPN
ejpam-5832	634	9	.	.	PUNCT
ejpam-5832	635	1	an	an	DET
ejpam-5832	635	2	advanced	advanced	ADJ
ejpam-5832	635	3	study	study	NOUN
ejpam-5832	635	4	on	on	ADP
ejpam-5832	635	5	the	the	DET
ejpam-5832	635	6	similarity	similarity	NOUN
ejpam-5832	635	7	measures	measure	NOUN
ejpam-5832	635	8	of	of	ADP
ejpam-5832	635	9	intuitionistic	intuitionistic	ADJ
ejpam-5832	635	10	fuzzy	fuzzy	ADJ
ejpam-5832	635	11	sets	set	NOUN
ejpam-5832	635	12	based	base	VERB
ejpam-5832	635	13	on	on	ADP
ejpam-5832	635	14	the	the	DET
ejpam-5832	635	15	set	set	VERB
ejpam-5832	635	16	pair	pair	NOUN
ejpam-5832	635	17	analysis	analysis	NOUN
ejpam-5832	635	18	theory	theory	NOUN
ejpam-5832	635	19	and	and	CCONJ
ejpam-5832	635	20	their	their	PRON
ejpam-5832	635	21	application	application	NOUN
ejpam-5832	635	22	in	in	ADP
ejpam-5832	635	23	decision	decision	NOUN
ejpam-5832	635	24	making	making	NOUN
ejpam-5832	635	25	.	.	PUNCT
ejpam-5832	636	1	soft	soft	ADJ
ejpam-5832	636	2	computing	computing	NOUN
ejpam-5832	636	3	,	,	PUNCT
ejpam-5832	636	4	22	22	NUM
ejpam-5832	636	5	,	,	PUNCT
ejpam-5832	636	6	2018	2018	NUM
ejpam-5832	636	7	.	.	PUNCT
ejpam-5832	637	1	[	[	X
ejpam-5832	637	2	7	7	NUM
ejpam-5832	637	3	]	]	X
ejpam-5832	637	4	r	r	NOUN
ejpam-5832	637	5	r	r	NOUN
ejpam-5832	637	6	yager	yager	NOUN
ejpam-5832	637	7	.	.	PUNCT
ejpam-5832	638	1	pythagorean	pythagorean	PROPN
ejpam-5832	638	2	fuzzy	fuzzy	ADJ
ejpam-5832	638	3	subsets	subset	NOUN
ejpam-5832	638	4	.	.	PUNCT
ejpam-5832	639	1	joint	joint	ADJ
ejpam-5832	639	2	ifsa	ifsa	PROPN
ejpam-5832	639	3	world	world	PROPN
ejpam-5832	639	4	congress	congress	PROPN
ejpam-5832	639	5	and	and	CCONJ
ejpam-5832	639	6	nafips	nafip	NOUN
ejpam-5832	639	7	annual	annual	ADJ
ejpam-5832	639	8	meeting	meeting	NOUN
ejpam-5832	639	9	(	(	PUNCT
ejpam-5832	639	10	ifsa	ifsa	PROPN
ejpam-5832	639	11	/	/	SYM
ejpam-5832	639	12	nafips	nafip	NOUN
ejpam-5832	639	13	)	)	PUNCT
ejpam-5832	639	14	,	,	PUNCT
ejpam-5832	639	15	pages	page	NOUN
ejpam-5832	639	16	57–61	57–61	NUM
ejpam-5832	639	17	,	,	PUNCT
ejpam-5832	639	18	2013	2013	NUM
ejpam-5832	639	19	.	.	PUNCT
ejpam-5832	640	1	[	[	X
ejpam-5832	640	2	8	8	NUM
ejpam-5832	640	3	]	]	PUNCT
ejpam-5832	640	4	n	n	PRON
ejpam-5832	640	5	li	li	PROPN
ejpam-5832	640	6	,	,	PUNCT
ejpam-5832	640	7	h	h	NOUN
ejpam-5832	640	8	garg	garg	NOUN
ejpam-5832	640	9	,	,	PUNCT
ejpam-5832	640	10	and	and	CCONJ
ejpam-5832	640	11	l	l	PROPN
ejpam-5832	640	12	wang	wang	PROPN
ejpam-5832	640	13	.	.	PUNCT
ejpam-5832	641	1	some	some	DET
ejpam-5832	641	2	novel	novel	ADJ
ejpam-5832	641	3	interactive	interactive	ADJ
ejpam-5832	641	4	hybrid	hybrid	NOUN
ejpam-5832	641	5	weighted	weight	VERB
ejpam-5832	641	6	aggregation	aggregation	NOUN
ejpam-5832	641	7	operators	operator	NOUN
ejpam-5832	641	8	with	with	ADP
ejpam-5832	641	9	pythagorean	pythagorean	ADJ
ejpam-5832	641	10	fuzzy	fuzzy	ADJ
ejpam-5832	641	11	numbers	number	NOUN
ejpam-5832	641	12	and	and	CCONJ
ejpam-5832	641	13	their	their	PRON
ejpam-5832	641	14	applications	application	NOUN
ejpam-5832	641	15	to	to	PART
ejpam-5832	641	16	decision	decision	VERB
ejpam-5832	641	17	making	making	NOUN
ejpam-5832	641	18	.	.	PUNCT
ejpam-5832	642	1	mathematics	mathematic	NOUN
ejpam-5832	642	2	,	,	PUNCT
ejpam-5832	642	3	7(12):1150	7(12):1150	NOUN
ejpam-5832	642	4	,	,	PUNCT
ejpam-5832	642	5	2019	2019	NUM
ejpam-5832	642	6	.	.	PUNCT
ejpam-5832	643	1	[	[	X
ejpam-5832	643	2	9	9	NUM
ejpam-5832	643	3	]	]	X
ejpam-5832	643	4	q	q	X
ejpam-5832	643	5	zhou	zhou	PROPN
ejpam-5832	643	6	,	,	PUNCT
ejpam-5832	643	7	h	h	PROPN
ejpam-5832	643	8	mo	mo	PROPN
ejpam-5832	643	9	,	,	PUNCT
ejpam-5832	643	10	and	and	CCONJ
ejpam-5832	643	11	y	y	PROPN
ejpam-5832	643	12	deng	deng	PROPN
ejpam-5832	643	13	.	.	PUNCT
ejpam-5832	644	1	a	a	DET
ejpam-5832	644	2	new	new	ADJ
ejpam-5832	644	3	divergence	divergence	NOUN
ejpam-5832	644	4	measure	measure	NOUN
ejpam-5832	644	5	of	of	ADP
ejpam-5832	644	6	pythagorean	pythagorean	ADJ
ejpam-5832	644	7	fuzzy	fuzzy	ADJ
ejpam-5832	644	8	sets	set	NOUN
ejpam-5832	644	9	based	base	VERB
ejpam-5832	644	10	on	on	ADP
ejpam-5832	644	11	belief	belief	NOUN
ejpam-5832	644	12	function	function	NOUN
ejpam-5832	644	13	and	and	CCONJ
ejpam-5832	644	14	its	its	PRON
ejpam-5832	644	15	application	application	NOUN
ejpam-5832	644	16	in	in	ADP
ejpam-5832	644	17	medical	medical	ADJ
ejpam-5832	644	18	diagnosis	diagnosis	NOUN
ejpam-5832	644	19	.	.	PUNCT
ejpam-5832	645	1	mathematics	mathematic	NOUN
ejpam-5832	645	2	,	,	PUNCT
ejpam-5832	645	3	8(1):142	8(1):142	NUM
ejpam-5832	645	4	,	,	PUNCT
ejpam-5832	645	5	2020	2020	NUM
ejpam-5832	645	6	.	.	PUNCT
ejpam-5832	646	1	[	[	X
ejpam-5832	646	2	10	10	NUM
ejpam-5832	646	3	]	]	X
ejpam-5832	646	4	s	s	PART
ejpam-5832	646	5	naz	naz	PROPN
ejpam-5832	646	6	,	,	PUNCT
ejpam-5832	646	7	s	s	PART
ejpam-5832	646	8	ashraf	ashraf	NOUN
ejpam-5832	646	9	,	,	PUNCT
ejpam-5832	646	10	and	and	CCONJ
ejpam-5832	646	11	m	m	PROPN
ejpam-5832	646	12	akram	akram	PROPN
ejpam-5832	646	13	.	.	PUNCT
ejpam-5832	647	1	a	a	DET
ejpam-5832	647	2	novel	novel	ADJ
ejpam-5832	647	3	approach	approach	NOUN
ejpam-5832	647	4	to	to	ADP
ejpam-5832	647	5	decision	decision	NOUN
ejpam-5832	647	6	-	-	PUNCT
ejpam-5832	647	7	making	making	NOUN
ejpam-5832	647	8	with	with	ADP
ejpam-5832	647	9	pythagorean	pythagorean	PROPN
ejpam-5832	647	10	fuzzy	fuzzy	ADJ
ejpam-5832	647	11	information	information	NOUN
ejpam-5832	647	12	.	.	PUNCT
ejpam-5832	648	1	mathematics	mathematic	NOUN
ejpam-5832	648	2	,	,	PUNCT
ejpam-5832	648	3	6(6):95	6(6):95	NOUN
ejpam-5832	648	4	,	,	PUNCT
ejpam-5832	648	5	2018	2018	NUM
ejpam-5832	648	6	.	.	PUNCT
ejpam-5832	649	1	[	[	X
ejpam-5832	649	2	11	11	NUM
ejpam-5832	649	3	]	]	X
ejpam-5832	649	4	a	a	DET
ejpam-5832	649	5	hussain	hussain	NOUN
ejpam-5832	649	6	,	,	PUNCT
ejpam-5832	649	7	k	k	PROPN
ejpam-5832	649	8	ullah	ullah	PROPN
ejpam-5832	649	9	,	,	PUNCT
ejpam-5832	649	10	m	m	NOUN
ejpam-5832	649	11	n	n	PRON
ejpam-5832	649	12	alshahrani	alshahrani	NOUN
ejpam-5832	649	13	,	,	PUNCT
ejpam-5832	649	14	m	m	PROPN
ejpam-5832	649	15	s	s	PROPN
ejpam-5832	649	16	yang	yang	PROPN
ejpam-5832	649	17	,	,	PUNCT
ejpam-5832	649	18	and	and	CCONJ
ejpam-5832	649	19	d	d	ADP
ejpam-5832	649	20	pamucar	pamucar	NOUN
ejpam-5832	649	21	.	.	PUNCT
ejpam-5832	650	1	novel	novel	PROPN
ejpam-5832	650	2	aczel	aczel	PROPN
ejpam-5832	650	3	–	–	PUNCT
ejpam-5832	650	4	alsina	alsina	NOUN
ejpam-5832	650	5	operators	operator	NOUN
ejpam-5832	650	6	for	for	ADP
ejpam-5832	650	7	pythagorean	pythagorean	PROPN
ejpam-5832	650	8	fuzzy	fuzzy	ADJ
ejpam-5832	650	9	sets	set	NOUN
ejpam-5832	650	10	with	with	ADP
ejpam-5832	650	11	application	application	NOUN
ejpam-5832	650	12	in	in	ADP
ejpam-5832	650	13	multi	multi	ADJ
ejpam-5832	650	14	-	-	ADJ
ejpam-5832	650	15	attribute	attribute	NOUN
ejpam-5832	650	16	decision	decision	NOUN
ejpam-5832	650	17	making	making	NOUN
ejpam-5832	650	18	.	.	PUNCT
ejpam-5832	651	1	symmetry	symmetry	NOUN
ejpam-5832	651	2	,	,	PUNCT
ejpam-5832	651	3	14(5):940	14(5):940	NUM
ejpam-5832	651	4	,	,	PUNCT
ejpam-5832	651	5	2022	2022	NUM
ejpam-5832	651	6	.	.	PUNCT
ejpam-5832	652	1	a.	a.	NOUN
ejpam-5832	652	2	razzaque	razzaque	PROPN
ejpam-5832	652	3	/	/	SYM
ejpam-5832	652	4	eur	eur	NOUN
ejpam-5832	652	5	.	.	PUNCT
ejpam-5832	653	1	j.	j.	PROPN
ejpam-5832	653	2	pure	pure	PROPN
ejpam-5832	653	3	appl	appl	PROPN
ejpam-5832	653	4	.	.	PROPN
ejpam-5832	653	5	math	math	PROPN
ejpam-5832	653	6	,	,	PUNCT
ejpam-5832	653	7	18	18	NUM
ejpam-5832	653	8	(	(	PUNCT
ejpam-5832	653	9	3	3	NUM
ejpam-5832	653	10	)	)	PUNCT
ejpam-5832	653	11	(	(	PUNCT
ejpam-5832	653	12	2025	2025	NUM
ejpam-5832	653	13	)	)	PUNCT
ejpam-5832	653	14	,	,	PUNCT
ejpam-5832	653	15	5832	5832	NUM
ejpam-5832	653	16	20	20	NUM
ejpam-5832	653	17	of	of	ADP
ejpam-5832	653	18	21	21	NUM
ejpam-5832	653	19	[	[	X
ejpam-5832	653	20	12	12	NUM
ejpam-5832	653	21	]	]	X
ejpam-5832	653	22	r	r	NOUN
ejpam-5832	653	23	r	r	NOUN
ejpam-5832	653	24	yager	yager	NOUN
ejpam-5832	653	25	.	.	PUNCT
ejpam-5832	654	1	generalized	generalized	ADJ
ejpam-5832	654	2	orthopair	orthopair	ADJ
ejpam-5832	654	3	fuzzy	fuzzy	ADJ
ejpam-5832	654	4	sets	set	NOUN
ejpam-5832	654	5	.	.	PUNCT
ejpam-5832	655	1	ieee	ieee	NOUN
ejpam-5832	655	2	transactions	transaction	NOUN
ejpam-5832	655	3	on	on	ADP
ejpam-5832	655	4	fuzzy	fuzzy	ADJ
ejpam-5832	655	5	systems	system	NOUN
ejpam-5832	655	6	,	,	PUNCT
ejpam-5832	655	7	25(5):1222–1230	25(5):1222–1230	NUM
ejpam-5832	655	8	,	,	PUNCT
ejpam-5832	655	9	2016	2016	NUM
ejpam-5832	655	10	.	.	PUNCT
ejpam-5832	656	1	[	[	X
ejpam-5832	656	2	13	13	NUM
ejpam-5832	656	3	]	]	SYM
ejpam-5832	656	4	m	m	NOUN
ejpam-5832	656	5	palanikumar	palanikumar	NOUN
ejpam-5832	656	6	,	,	PUNCT
ejpam-5832	656	7	n	n	PRON
ejpam-5832	656	8	kausar	kausar	NOUN
ejpam-5832	656	9	,	,	PUNCT
ejpam-5832	656	10	p	p	PROPN
ejpam-5832	656	11	tharaniya	tharaniya	PROPN
ejpam-5832	656	12	,	,	PUNCT
ejpam-5832	656	13	z	z	NOUN
ejpam-5832	656	14	stevic	stevic	PROPN
ejpam-5832	656	15	,	,	PUNCT
ejpam-5832	656	16	and	and	CCONJ
ejpam-5832	656	17	f	f	PROPN
ejpam-5832	656	18	tesgera	tesgera	NOUN
ejpam-5832	656	19	tolasa	tolasa	PROPN
ejpam-5832	656	20	.	.	PUNCT
ejpam-5832	657	1	complex	complex	ADJ
ejpam-5832	657	2	diophantine	diophantine	NOUN
ejpam-5832	657	3	interval	interval	NOUN
ejpam-5832	657	4	-	-	PUNCT
ejpam-5832	657	5	valued	value	VERB
ejpam-5832	657	6	pythagorean	pythagorean	PROPN
ejpam-5832	657	7	normal	normal	ADJ
ejpam-5832	657	8	set	set	NOUN
ejpam-5832	657	9	for	for	ADP
ejpam-5832	657	10	decision	decision	NOUN
ejpam-5832	657	11	-	-	PUNCT
ejpam-5832	657	12	making	make	VERB
ejpam-5832	657	13	processes	process	NOUN
ejpam-5832	657	14	.	.	PUNCT
ejpam-5832	658	1	scientific	scientific	ADJ
ejpam-5832	658	2	reports	report	NOUN
ejpam-5832	658	3	,	,	PUNCT
ejpam-5832	658	4	15(1):783	15(1):783	NUM
ejpam-5832	658	5	,	,	PUNCT
ejpam-5832	658	6	2025	2025	NUM
ejpam-5832	658	7	.	.	PUNCT
ejpam-5832	659	1	[	[	X
ejpam-5832	659	2	14	14	NUM
ejpam-5832	659	3	]	]	X
ejpam-5832	659	4	s	s	PART
ejpam-5832	659	5	khan	khan	PROPN
ejpam-5832	659	6	,	,	PUNCT
ejpam-5832	659	7	m	m	PROPN
ejpam-5832	659	8	gulistan	gulistan	ADJ
ejpam-5832	659	9	,	,	PUNCT
ejpam-5832	659	10	n	n	PRON
ejpam-5832	659	11	kausar	kausar	NOUN
ejpam-5832	659	12	,	,	PUNCT
ejpam-5832	659	13	s	s	NOUN
ejpam-5832	659	14	kadry	kadry	NOUN
ejpam-5832	659	15	,	,	PUNCT
ejpam-5832	659	16	and	and	CCONJ
ejpam-5832	659	17	j	j	PROPN
ejpam-5832	659	18	kim	kim	PROPN
ejpam-5832	659	19	.	.	PUNCT
ejpam-5832	660	1	a	a	DET
ejpam-5832	660	2	novel	novel	ADJ
ejpam-5832	660	3	method	method	NOUN
ejpam-5832	660	4	for	for	ADP
ejpam-5832	660	5	determining	determine	VERB
ejpam-5832	660	6	tourism	tourism	NOUN
ejpam-5832	660	7	carrying	carry	VERB
ejpam-5832	660	8	capacity	capacity	NOUN
ejpam-5832	660	9	in	in	ADP
ejpam-5832	660	10	a	a	DET
ejpam-5832	660	11	decision	decision	NOUN
ejpam-5832	660	12	making	make	VERB
ejpam-5832	660	13	context	context	NOUN
ejpam-5832	660	14	using	use	VERB
ejpam-5832	660	15	q	q	PUNCT
ejpam-5832	660	16	rung	rung	PROPN
ejpam-5832	660	17	orthopair	orthopair	NOUN
ejpam-5832	660	18	fuzzy	fuzzy	ADJ
ejpam-5832	660	19	hypersoft	hypersoft	PROPN
ejpam-5832	660	20	environment	environment	NOUN
ejpam-5832	660	21	.	.	PUNCT
ejpam-5832	661	1	cmes	cme	VERB
ejpam-5832	661	2	computer	computer	NOUN
ejpam-5832	661	3	modeling	modeling	NOUN
ejpam-5832	661	4	in	in	ADP
ejpam-5832	661	5	engineering	engineering	NOUN
ejpam-5832	661	6	and	and	CCONJ
ejpam-5832	661	7	sciences	science	NOUN
ejpam-5832	661	8	,	,	PUNCT
ejpam-5832	661	9	138(2	138(2	NUM
ejpam-5832	661	10	)	)	PUNCT
ejpam-5832	661	11	,	,	PUNCT
ejpam-5832	661	12	2024	2024	NUM
ejpam-5832	661	13	.	.	PUNCT
ejpam-5832	662	1	[	[	X
ejpam-5832	662	2	15	15	NUM
ejpam-5832	662	3	]	]	X
ejpam-5832	662	4	m	m	NOUN
ejpam-5832	662	5	palanikumar	palanikumar	NOUN
ejpam-5832	662	6	,	,	PUNCT
ejpam-5832	662	7	n	n	PRON
ejpam-5832	662	8	kausar	kausar	NOUN
ejpam-5832	662	9	,	,	PUNCT
ejpam-5832	662	10	h	h	NOUN
ejpam-5832	662	11	garg	garg	NOUN
ejpam-5832	662	12	,	,	PUNCT
ejpam-5832	662	13	and	and	CCONJ
ejpam-5832	662	14	j	j	PROPN
ejpam-5832	662	15	kim	kim	PROPN
ejpam-5832	662	16	.	.	PUNCT
ejpam-5832	663	1	robotic	robotic	ADJ
ejpam-5832	663	2	sensor	sensor	NOUN
ejpam-5832	663	3	based	base	VERB
ejpam-5832	663	4	on	on	ADP
ejpam-5832	663	5	score	score	NOUN
ejpam-5832	663	6	and	and	CCONJ
ejpam-5832	663	7	accuracy	accuracy	NOUN
ejpam-5832	663	8	values	value	NOUN
ejpam-5832	663	9	in	in	ADP
ejpam-5832	663	10	q	q	ADJ
ejpam-5832	663	11	-	-	PUNCT
ejpam-5832	663	12	rung	rung	ADJ
ejpam-5832	663	13	complex	complex	ADJ
ejpam-5832	663	14	diophatine	diophatine	ADJ
ejpam-5832	663	15	neutrosophic	neutrosophic	ADJ
ejpam-5832	663	16	normal	normal	ADJ
ejpam-5832	663	17	set	set	NOUN
ejpam-5832	663	18	with	with	ADP
ejpam-5832	663	19	an	an	DET
ejpam-5832	663	20	aggregation	aggregation	NOUN
ejpam-5832	663	21	operation	operation	NOUN
ejpam-5832	663	22	.	.	PUNCT
ejpam-5832	664	1	alexandria	alexandria	PROPN
ejpam-5832	664	2	engineering	engineering	PROPN
ejpam-5832	664	3	journal	journal	PROPN
ejpam-5832	664	4	,	,	PUNCT
ejpam-5832	664	5	77:149–164	77:149–164	PROPN
ejpam-5832	664	6	,	,	PUNCT
ejpam-5832	664	7	2023	2023	NUM
ejpam-5832	664	8	.	.	PUNCT
ejpam-5832	665	1	[	[	X
ejpam-5832	665	2	16	16	NUM
ejpam-5832	665	3	]	]	PUNCT
ejpam-5832	665	4	a	a	DET
ejpam-5832	665	5	rosenfeld	rosenfeld	PROPN
ejpam-5832	665	6	.	.	PUNCT
ejpam-5832	666	1	fuzzy	fuzzy	ADJ
ejpam-5832	666	2	groups	group	NOUN
ejpam-5832	666	3	.	.	PUNCT
ejpam-5832	667	1	journal	journal	PROPN
ejpam-5832	667	2	of	of	ADP
ejpam-5832	667	3	mathematical	mathematical	ADJ
ejpam-5832	667	4	analysis	analysis	NOUN
ejpam-5832	667	5	and	and	CCONJ
ejpam-5832	667	6	applications	application	NOUN
ejpam-5832	667	7	,	,	PUNCT
ejpam-5832	667	8	35(3):512–517	35(3):512–517	PROPN
ejpam-5832	667	9	,	,	PUNCT
ejpam-5832	667	10	1971	1971	NUM
ejpam-5832	667	11	.	.	PUNCT
ejpam-5832	668	1	[	[	X
ejpam-5832	668	2	17	17	NUM
ejpam-5832	668	3	]	]	X
ejpam-5832	668	4	p	p	X
ejpam-5832	668	5	s	s	X
ejpam-5832	668	6	das	das	PROPN
ejpam-5832	668	7	.	.	PROPN
ejpam-5832	668	8	fuzzy	fuzzy	ADJ
ejpam-5832	668	9	groups	group	NOUN
ejpam-5832	668	10	and	and	CCONJ
ejpam-5832	668	11	level	level	NOUN
ejpam-5832	668	12	subgroups	subgroup	NOUN
ejpam-5832	668	13	.	.	PUNCT
ejpam-5832	669	1	journal	journal	PROPN
ejpam-5832	669	2	of	of	ADP
ejpam-5832	669	3	mathematical	mathematical	ADJ
ejpam-5832	669	4	analysis	analysis	NOUN
ejpam-5832	669	5	and	and	CCONJ
ejpam-5832	669	6	applications	application	NOUN
ejpam-5832	669	7	,	,	PUNCT
ejpam-5832	669	8	84(1):264–269	84(1):264–269	PROPN
ejpam-5832	669	9	,	,	PUNCT
ejpam-5832	669	10	1981	1981	NUM
ejpam-5832	669	11	.	.	PUNCT
ejpam-5832	670	1	[	[	X
ejpam-5832	670	2	18	18	NUM
ejpam-5832	670	3	]	]	X
ejpam-5832	670	4	w	w	PROPN
ejpam-5832	670	5	j	j	PROPN
ejpam-5832	670	6	liu	liu	PROPN
ejpam-5832	670	7	.	.	PROPN
ejpam-5832	671	1	fuzzy	fuzzy	ADJ
ejpam-5832	671	2	invariant	invariant	ADJ
ejpam-5832	671	3	subgroups	subgroup	NOUN
ejpam-5832	671	4	and	and	CCONJ
ejpam-5832	671	5	fuzzy	fuzzy	ADJ
ejpam-5832	671	6	ideals	ideal	NOUN
ejpam-5832	671	7	.	.	PUNCT
ejpam-5832	672	1	fuzzy	fuzzy	ADJ
ejpam-5832	672	2	sets	set	NOUN
ejpam-5832	672	3	and	and	CCONJ
ejpam-5832	672	4	systems	system	NOUN
ejpam-5832	672	5	,	,	PUNCT
ejpam-5832	672	6	8(2):133–139	8(2):133–139	NUM
ejpam-5832	672	7	,	,	PUNCT
ejpam-5832	672	8	1982	1982	NUM
ejpam-5832	672	9	.	.	PUNCT
ejpam-5832	673	1	[	[	X
ejpam-5832	673	2	19	19	NUM
ejpam-5832	673	3	]	]	PUNCT
ejpam-5832	673	4	n	n	PRON
ejpam-5832	673	5	p	p	NOUN
ejpam-5832	673	6	mukherjee	mukherjee	NOUN
ejpam-5832	673	7	and	and	CCONJ
ejpam-5832	673	8	p	p	PROPN
ejpam-5832	673	9	bhattacharya	bhattacharya	PROPN
ejpam-5832	673	10	.	.	PUNCT
ejpam-5832	674	1	fuzzy	fuzzy	ADJ
ejpam-5832	674	2	normal	normal	ADJ
ejpam-5832	674	3	subgroups	subgroup	NOUN
ejpam-5832	674	4	and	and	CCONJ
ejpam-5832	674	5	fuzzy	fuzzy	ADJ
ejpam-5832	674	6	cosets	coset	NOUN
ejpam-5832	674	7	.	.	PUNCT
ejpam-5832	675	1	information	information	NOUN
ejpam-5832	675	2	sciences	sciences	PROPN
ejpam-5832	675	3	,	,	PUNCT
ejpam-5832	675	4	34(3):225–239	34(3):225–239	PROPN
ejpam-5832	675	5	,	,	PUNCT
ejpam-5832	675	6	1984	1984	NUM
ejpam-5832	675	7	.	.	PUNCT
ejpam-5832	676	1	[	[	X
ejpam-5832	676	2	20	20	NUM
ejpam-5832	676	3	]	]	PUNCT
ejpam-5832	676	4	n	n	PRON
ejpam-5832	676	5	p	p	NOUN
ejpam-5832	676	6	mukherjee	mukherjee	NOUN
ejpam-5832	676	7	and	and	CCONJ
ejpam-5832	676	8	p	p	PROPN
ejpam-5832	676	9	bhattacharya	bhattacharya	PROPN
ejpam-5832	676	10	.	.	PUNCT
ejpam-5832	677	1	fuzzy	fuzzy	ADJ
ejpam-5832	677	2	groups	group	NOUN
ejpam-5832	677	3	:	:	PUNCT
ejpam-5832	677	4	some	some	DET
ejpam-5832	677	5	group	group	NOUN
ejpam-5832	677	6	-	-	PUNCT
ejpam-5832	677	7	theoretic	theoretic	NOUN
ejpam-5832	677	8	analogs	analog	NOUN
ejpam-5832	677	9	.	.	PUNCT
ejpam-5832	678	1	information	information	NOUN
ejpam-5832	678	2	sciences	sciences	PROPN
ejpam-5832	678	3	,	,	PUNCT
ejpam-5832	678	4	39(3):247–267	39(3):247–267	PROPN
ejpam-5832	678	5	,	,	PUNCT
ejpam-5832	678	6	1986	1986	NUM
ejpam-5832	678	7	.	.	PUNCT
ejpam-5832	679	1	[	[	X
ejpam-5832	679	2	21	21	NUM
ejpam-5832	679	3	]	]	SYM
ejpam-5832	679	4	b	b	PROPN
ejpam-5832	679	5	w	w	NOUN
ejpam-5832	679	6	wetherilt	wetherilt	NOUN
ejpam-5832	679	7	.	.	PUNCT
ejpam-5832	680	1	semidirect	semidirect	NOUN
ejpam-5832	680	2	products	product	NOUN
ejpam-5832	680	3	of	of	ADP
ejpam-5832	680	4	fuzzy	fuzzy	ADJ
ejpam-5832	680	5	subgroups	subgroup	NOUN
ejpam-5832	680	6	.	.	PUNCT
ejpam-5832	681	1	fuzzy	fuzzy	ADJ
ejpam-5832	681	2	sets	set	NOUN
ejpam-5832	681	3	and	and	CCONJ
ejpam-5832	681	4	systems	system	NOUN
ejpam-5832	681	5	,	,	PUNCT
ejpam-5832	681	6	16(3):237–242	16(3):237–242	PROPN
ejpam-5832	681	7	,	,	PUNCT
ejpam-5832	681	8	1985	1985	NUM
ejpam-5832	681	9	.	.	PUNCT
ejpam-5832	682	1	[	[	X
ejpam-5832	682	2	22	22	NUM
ejpam-5832	682	3	]	]	X
ejpam-5832	682	4	a	a	DET
ejpam-5832	682	5	s	s	X
ejpam-5832	682	6	mashour	mashour	NOUN
ejpam-5832	682	7	,	,	PUNCT
ejpam-5832	682	8	m	m	VERB
ejpam-5832	682	9	h	h	NOUN
ejpam-5832	682	10	ghanim	ghanim	NOUN
ejpam-5832	682	11	,	,	PUNCT
ejpam-5832	682	12	and	and	CCONJ
ejpam-5832	682	13	f	f	X
ejpam-5832	682	14	i	i	PROPN
ejpam-5832	682	15	sidky	sidky	VERB
ejpam-5832	682	16	.	.	PUNCT
ejpam-5832	683	1	normal	normal	ADJ
ejpam-5832	683	2	fuzzy	fuzzy	ADJ
ejpam-5832	683	3	subgroups	subgroup	NOUN
ejpam-5832	683	4	.	.	PUNCT
ejpam-5832	684	1	information	information	NOUN
ejpam-5832	684	2	sciences	sciences	PROPN
ejpam-5832	684	3	,	,	PUNCT
ejpam-5832	684	4	20:53–59	20:53–59	NUM
ejpam-5832	684	5	,	,	PUNCT
ejpam-5832	684	6	1990	1990	NUM
ejpam-5832	684	7	.	.	PUNCT
ejpam-5832	685	1	[	[	X
ejpam-5832	685	2	23	23	NUM
ejpam-5832	685	3	]	]	X
ejpam-5832	685	4	d	d	X
ejpam-5832	685	5	s	s	PROPN
ejpam-5832	685	6	malik	malik	PROPN
ejpam-5832	685	7	,	,	PUNCT
ejpam-5832	685	8	j	j	PROPN
ejpam-5832	685	9	n	n	PRON
ejpam-5832	685	10	mordeson	mordeson	NOUN
ejpam-5832	685	11	,	,	PUNCT
ejpam-5832	685	12	and	and	CCONJ
ejpam-5832	685	13	p	p	PRON
ejpam-5832	685	14	s	s	PROPN
ejpam-5832	685	15	nair	nair	NOUN
ejpam-5832	685	16	.	.	PUNCT
ejpam-5832	686	1	fuzzy	fuzzy	ADJ
ejpam-5832	686	2	normal	normal	ADJ
ejpam-5832	686	3	subgroups	subgroup	NOUN
ejpam-5832	686	4	in	in	ADP
ejpam-5832	686	5	fuzzy	fuzzy	ADJ
ejpam-5832	686	6	subgroups	subgroup	NOUN
ejpam-5832	686	7	.	.	PUNCT
ejpam-5832	687	1	journal	journal	NOUN
ejpam-5832	687	2	of	of	ADP
ejpam-5832	687	3	the	the	DET
ejpam-5832	687	4	korean	korean	PROPN
ejpam-5832	687	5	mathematical	mathematical	ADJ
ejpam-5832	687	6	society	society	NOUN
ejpam-5832	687	7	,	,	PUNCT
ejpam-5832	687	8	29(1):1–8	29(1):1–8	NUM
ejpam-5832	687	9	,	,	PUNCT
ejpam-5832	687	10	1992	1992	NUM
ejpam-5832	687	11	.	.	PUNCT
ejpam-5832	688	1	[	[	X
ejpam-5832	688	2	24	24	NUM
ejpam-5832	688	3	]	]	SYM
ejpam-5832	688	4	v	v	NOUN
ejpam-5832	688	5	n	n	X
ejpam-5832	688	6	dixit	dixit	PROPN
ejpam-5832	688	7	,	,	PUNCT
ejpam-5832	688	8	r	r	PROPN
ejpam-5832	688	9	kumar	kumar	PROPN
ejpam-5832	688	10	,	,	PUNCT
ejpam-5832	688	11	and	and	CCONJ
ejpam-5832	688	12	n	n	ADV
ejpam-5832	688	13	ajmal	ajmal	ADJ
ejpam-5832	688	14	.	.	PUNCT
ejpam-5832	689	1	level	level	NOUN
ejpam-5832	689	2	subgroups	subgroup	NOUN
ejpam-5832	689	3	and	and	CCONJ
ejpam-5832	689	4	union	union	NOUN
ejpam-5832	689	5	of	of	ADP
ejpam-5832	689	6	fuzzy	fuzzy	ADJ
ejpam-5832	689	7	subgroups	subgroup	NOUN
ejpam-5832	689	8	.	.	PUNCT
ejpam-5832	690	1	fuzzy	fuzzy	ADJ
ejpam-5832	690	2	sets	set	NOUN
ejpam-5832	690	3	and	and	CCONJ
ejpam-5832	690	4	systems	system	NOUN
ejpam-5832	690	5	,	,	PUNCT
ejpam-5832	690	6	37(3):359–371	37(3):359–371	NUM
ejpam-5832	690	7	,	,	PUNCT
ejpam-5832	690	8	1990	1990	NUM
ejpam-5832	690	9	.	.	PUNCT
ejpam-5832	691	1	[	[	X
ejpam-5832	691	2	25	25	NUM
ejpam-5832	691	3	]	]	X
ejpam-5832	691	4	r	r	NOUN
ejpam-5832	691	5	biswas	biswas	PROPN
ejpam-5832	691	6	.	.	PUNCT
ejpam-5832	692	1	intuitionistic	intuitionistic	ADJ
ejpam-5832	692	2	fuzzy	fuzzy	ADJ
ejpam-5832	692	3	subgroup	subgroup	NOUN
ejpam-5832	692	4	.	.	PUNCT
ejpam-5832	693	1	mathematical	mathematical	PROPN
ejpam-5832	693	2	forum	forum	PROPN
ejpam-5832	693	3	,	,	PUNCT
ejpam-5832	693	4	10:39–44	10:39–44	NUM
ejpam-5832	693	5	,	,	PUNCT
ejpam-5832	693	6	1989	1989	NUM
ejpam-5832	693	7	.	.	PUNCT
ejpam-5832	694	1	[	[	X
ejpam-5832	694	2	26	26	NUM
ejpam-5832	694	3	]	]	X
ejpam-5832	694	4	k	k	PROPN
ejpam-5832	694	5	hur	hur	PROPN
ejpam-5832	694	6	,	,	PUNCT
ejpam-5832	694	7	s	s	PROPN
ejpam-5832	694	8	y	y	PROPN
ejpam-5832	694	9	jang	jang	PROPN
ejpam-5832	694	10	,	,	PUNCT
ejpam-5832	694	11	and	and	CCONJ
ejpam-5832	694	12	h	h	PROPN
ejpam-5832	694	13	w	w	PROPN
ejpam-5832	694	14	kang	kang	PROPN
ejpam-5832	694	15	.	.	PUNCT
ejpam-5832	695	1	intuitionistic	intuitionistic	ADJ
ejpam-5832	695	2	fuzzy	fuzzy	ADJ
ejpam-5832	695	3	subgroups	subgroup	NOUN
ejpam-5832	695	4	and	and	CCONJ
ejpam-5832	695	5	cosets	coset	NOUN
ejpam-5832	695	6	.	.	PUNCT
ejpam-5832	696	1	honam	honam	PROPN
ejpam-5832	696	2	mathematical	mathematical	PROPN
ejpam-5832	696	3	journal	journal	PROPN
ejpam-5832	696	4	,	,	PUNCT
ejpam-5832	696	5	26(1):17–41	26(1):17–41	NUM
ejpam-5832	696	6	,	,	PUNCT
ejpam-5832	696	7	2004	2004	NUM
ejpam-5832	696	8	.	.	PUNCT
ejpam-5832	697	1	[	[	X
ejpam-5832	697	2	27	27	NUM
ejpam-5832	697	3	]	]	X
ejpam-5832	697	4	p	p	PROPN
ejpam-5832	697	5	k	k	PROPN
ejpam-5832	697	6	sharma	sharma	PROPN
ejpam-5832	697	7	.	.	PUNCT
ejpam-5832	698	1	on	on	ADP
ejpam-5832	698	2	the	the	DET
ejpam-5832	698	3	direct	direct	ADJ
ejpam-5832	698	4	product	product	NOUN
ejpam-5832	698	5	of	of	ADP
ejpam-5832	698	6	intuitionistic	intuitionistic	ADJ
ejpam-5832	698	7	fuzzy	fuzzy	ADJ
ejpam-5832	698	8	subgroups	subgroup	NOUN
ejpam-5832	698	9	.	.	PUNCT
ejpam-5832	699	1	int	int	NOUN
ejpam-5832	699	2	.	.	PUNCT
ejpam-5832	700	1	math	math	NOUN
ejpam-5832	700	2	.	.	PUNCT
ejpam-5832	701	1	forum	forum	PROPN
ejpam-5832	701	2	,	,	PUNCT
ejpam-5832	701	3	7(11):523–530	7(11):523–530	NUM
ejpam-5832	701	4	,	,	PUNCT
ejpam-5832	701	5	2012	2012	NUM
ejpam-5832	701	6	.	.	PUNCT
ejpam-5832	702	1	[	[	X
ejpam-5832	702	2	28	28	NUM
ejpam-5832	702	3	]	]	X
ejpam-5832	702	4	a	a	DET
ejpam-5832	702	5	altassan	altassan	ADJ
ejpam-5832	702	6	,	,	PUNCT
ejpam-5832	702	7	m	m	VERB
ejpam-5832	702	8	h	h	NOUN
ejpam-5832	702	9	mateen	mateen	PROPN
ejpam-5832	702	10	,	,	PUNCT
ejpam-5832	702	11	and	and	CCONJ
ejpam-5832	702	12	d	d	ADP
ejpam-5832	702	13	pamucar	pamucar	NOUN
ejpam-5832	702	14	.	.	PUNCT
ejpam-5832	703	1	on	on	ADP
ejpam-5832	703	2	fundamental	fundamental	ADJ
ejpam-5832	703	3	theorems	theorem	NOUN
ejpam-5832	703	4	of	of	ADP
ejpam-5832	703	5	fuzzy	fuzzy	ADJ
ejpam-5832	703	6	isomorphism	isomorphism	NOUN
ejpam-5832	703	7	of	of	ADP
ejpam-5832	703	8	fuzzy	fuzzy	ADJ
ejpam-5832	703	9	subrings	subring	NOUN
ejpam-5832	703	10	over	over	ADP
ejpam-5832	703	11	a	a	DET
ejpam-5832	703	12	certain	certain	ADJ
ejpam-5832	703	13	algebraic	algebraic	ADJ
ejpam-5832	703	14	product	product	NOUN
ejpam-5832	703	15	.	.	PUNCT
ejpam-5832	704	1	symmetry	symmetry	NOUN
ejpam-5832	704	2	,	,	PUNCT
ejpam-5832	704	3	13(6):998	13(6):998	NUM
ejpam-5832	704	4	,	,	PUNCT
ejpam-5832	704	5	2021	2021	NUM
ejpam-5832	704	6	.	.	PUNCT
ejpam-5832	705	1	[	[	X
ejpam-5832	705	2	29	29	NUM
ejpam-5832	705	3	]	]	X
ejpam-5832	705	4	a	a	DET
ejpam-5832	705	5	a	a	DET
ejpam-5832	705	6	alharbi	alharbi	NOUN
ejpam-5832	705	7	and	and	CCONJ
ejpam-5832	705	8	d	d	NOUN
ejpam-5832	705	9	alghazzawi	alghazzawi	NOUN
ejpam-5832	705	10	.	.	PUNCT
ejpam-5832	706	1	some	some	DET
ejpam-5832	706	2	characterizations	characterization	NOUN
ejpam-5832	706	3	of	of	ADP
ejpam-5832	706	4	certain	certain	ADJ
ejpam-5832	706	5	complex	complex	ADJ
ejpam-5832	706	6	fuzzy	fuzzy	ADJ
ejpam-5832	706	7	subgroups	subgroup	NOUN
ejpam-5832	706	8	.	.	PUNCT
ejpam-5832	707	1	symmetry	symmetry	NOUN
ejpam-5832	707	2	,	,	PUNCT
ejpam-5832	707	3	14(9):1812	14(9):1812	NUM
ejpam-5832	707	4	,	,	PUNCT
ejpam-5832	707	5	2002	2002	NUM
ejpam-5832	707	6	.	.	PUNCT
ejpam-5832	708	1	[	[	X
ejpam-5832	708	2	30	30	NUM
ejpam-5832	708	3	]	]	X
ejpam-5832	708	4	h	h	NOUN
ejpam-5832	708	5	alolaiyan	alolaiyan	ADJ
ejpam-5832	708	6	,	,	PUNCT
ejpam-5832	708	7	u	u	NOUN
ejpam-5832	708	8	shuaib	shuaib	NOUN
ejpam-5832	708	9	,	,	PUNCT
ejpam-5832	708	10	l	l	PROPN
ejpam-5832	708	11	latif	latif	PROPN
ejpam-5832	708	12	,	,	PUNCT
ejpam-5832	708	13	and	and	CCONJ
ejpam-5832	708	14	a	a	DET
ejpam-5832	708	15	razaq	razaq	NOUN
ejpam-5832	708	16	.	.	PUNCT
ejpam-5832	709	1	t	t	PROPN
ejpam-5832	709	2	intuitionistic	intuitionistic	ADJ
ejpam-5832	709	3	fuzzification	fuzzification	NOUN
ejpam-5832	709	4	of	of	ADP
ejpam-5832	709	5	lagrange	lagrange	PROPN
ejpam-5832	709	6	’s	’s	PART
ejpam-5832	709	7	theorem	theorem	NOUN
ejpam-5832	709	8	of	of	ADP
ejpam-5832	709	9	t	t	PROPN
ejpam-5832	709	10	intuitionistic	intuitionistic	ADJ
ejpam-5832	709	11	fuzzy	fuzzy	ADJ
ejpam-5832	709	12	subgroup	subgroup	NOUN
ejpam-5832	709	13	.	.	PUNCT
ejpam-5832	710	1	ieee	ieee	NOUN
ejpam-5832	710	2	access	access	NOUN
ejpam-5832	710	3	,	,	PUNCT
ejpam-5832	710	4	7:158419–158426	7:158419–158426	NUM
ejpam-5832	710	5	,	,	PUNCT
ejpam-5832	710	6	2019	2019	NUM
ejpam-5832	710	7	.	.	PUNCT
ejpam-5832	711	1	a.	a.	NOUN
ejpam-5832	711	2	razzaque	razzaque	PROPN
ejpam-5832	711	3	/	/	SYM
ejpam-5832	711	4	eur	eur	NOUN
ejpam-5832	711	5	.	.	PUNCT
ejpam-5832	712	1	j.	j.	PROPN
ejpam-5832	712	2	pure	pure	PROPN
ejpam-5832	712	3	appl	appl	PROPN
ejpam-5832	712	4	.	.	PROPN
ejpam-5832	712	5	math	math	PROPN
ejpam-5832	712	6	,	,	PUNCT
ejpam-5832	712	7	18	18	NUM
ejpam-5832	712	8	(	(	PUNCT
ejpam-5832	712	9	3	3	NUM
ejpam-5832	712	10	)	)	PUNCT
ejpam-5832	712	11	(	(	PUNCT
ejpam-5832	712	12	2025	2025	NUM
ejpam-5832	712	13	)	)	PUNCT
ejpam-5832	712	14	,	,	PUNCT
ejpam-5832	712	15	5832	5832	NUM
ejpam-5832	712	16	21	21	NUM
ejpam-5832	712	17	of	of	ADP
ejpam-5832	712	18	21	21	NUM
ejpam-5832	712	19	[	[	X
ejpam-5832	712	20	31	31	NUM
ejpam-5832	712	21	]	]	PUNCT
ejpam-5832	712	22	l	l	NOUN
ejpam-5832	712	23	xiaoping	xiaoping	PROPN
ejpam-5832	712	24	.	.	PUNCT
ejpam-5832	713	1	the	the	DET
ejpam-5832	713	2	intuitionistic	intuitionistic	ADJ
ejpam-5832	713	3	fuzzy	fuzzy	ADJ
ejpam-5832	713	4	normal	normal	ADJ
ejpam-5832	713	5	subgroup	subgroup	NOUN
ejpam-5832	713	6	and	and	CCONJ
ejpam-5832	713	7	its	its	PRON
ejpam-5832	713	8	some	some	DET
ejpam-5832	713	9	equivalent	equivalent	ADJ
ejpam-5832	713	10	propositions	proposition	NOUN
ejpam-5832	713	11	.	.	PUNCT
ejpam-5832	714	1	busefal	busefal	PROPN
ejpam-5832	714	2	,	,	PUNCT
ejpam-5832	714	3	82:40–44	82:40–44	NUM
ejpam-5832	714	4	,	,	PUNCT
ejpam-5832	714	5	2000	2000	NUM
ejpam-5832	714	6	.	.	PUNCT
ejpam-5832	715	1	[	[	X
ejpam-5832	715	2	32	32	NUM
ejpam-5832	715	3	]	]	X
ejpam-5832	715	4	r	r	NOUN
ejpam-5832	715	5	rasuli	rasuli	NOUN
ejpam-5832	715	6	.	.	PUNCT
ejpam-5832	716	1	intuitionistic	intuitionistic	ADJ
ejpam-5832	716	2	fuzzy	fuzzy	ADJ
ejpam-5832	716	3	subgroups	subgroup	NOUN
ejpam-5832	716	4	with	with	ADP
ejpam-5832	716	5	respect	respect	NOUN
ejpam-5832	716	6	to	to	ADP
ejpam-5832	716	7	norms	norm	NOUN
ejpam-5832	716	8	(	(	PUNCT
ejpam-5832	716	9	t	t	PROPN
ejpam-5832	716	10	,	,	PUNCT
ejpam-5832	716	11	s	s	PART
ejpam-5832	716	12	)	)	PUNCT
ejpam-5832	716	13	.	.	PUNCT
ejpam-5832	717	1	engineering	engineering	NOUN
ejpam-5832	717	2	and	and	CCONJ
ejpam-5832	717	3	applied	apply	VERB
ejpam-5832	717	4	science	science	NOUN
ejpam-5832	717	5	letters	letter	NOUN
ejpam-5832	717	6	(	(	PUNCT
ejpam-5832	717	7	easl	easl	NOUN
ejpam-5832	717	8	)	)	PUNCT
ejpam-5832	717	9	,	,	PUNCT
ejpam-5832	717	10	3:40–53	3:40–53	NUM
ejpam-5832	717	11	,	,	PUNCT
ejpam-5832	717	12	2020	2020	NUM
ejpam-5832	717	13	.	.	PUNCT
ejpam-5832	718	1	[	[	X
ejpam-5832	718	2	33	33	NUM
ejpam-5832	718	3	]	]	PUNCT
ejpam-5832	718	4	s	s	PART
ejpam-5832	718	5	bhunia	bhunia	NOUN
ejpam-5832	718	6	,	,	PUNCT
ejpam-5832	718	7	g	g	PROPN
ejpam-5832	718	8	ghorai	ghorai	PROPN
ejpam-5832	718	9	,	,	PUNCT
ejpam-5832	718	10	q	q	PROPN
ejpam-5832	718	11	xin	xin	PROPN
ejpam-5832	718	12	,	,	PUNCT
ejpam-5832	718	13	and	and	CCONJ
ejpam-5832	718	14	f	f	X
ejpam-5832	718	15	i	i	PRON
ejpam-5832	718	16	torshavn	torshavn	VERB
ejpam-5832	718	17	.	.	PUNCT
ejpam-5832	719	1	on	on	ADP
ejpam-5832	719	2	the	the	DET
ejpam-5832	719	3	characterization	characterization	NOUN
ejpam-5832	719	4	of	of	ADP
ejpam-5832	719	5	pythagorean	pythagorean	PROPN
ejpam-5832	719	6	fuzzy	fuzzy	ADJ
ejpam-5832	719	7	subgroups	subgroup	NOUN
ejpam-5832	719	8	.	.	PUNCT
ejpam-5832	720	1	aims	aim	VERB
ejpam-5832	720	2	mathematics	mathematic	NOUN
ejpam-5832	720	3	,	,	PUNCT
ejpam-5832	720	4	6(1):962–978	6(1):962–978	NOUN
ejpam-5832	720	5	,	,	PUNCT
ejpam-5832	720	6	2021	2021	NUM
ejpam-5832	720	7	.	.	PUNCT
ejpam-5832	721	1	[	[	X
ejpam-5832	721	2	34	34	NUM
ejpam-5832	721	3	]	]	X
ejpam-5832	721	4	a	a	DET
ejpam-5832	721	5	razaq	razaq	NOUN
ejpam-5832	721	6	,	,	PUNCT
ejpam-5832	721	7	g	g	PROPN
ejpam-5832	721	8	alhamzi	alhamzi	NOUN
ejpam-5832	721	9	,	,	PUNCT
ejpam-5832	721	10	a	a	DET
ejpam-5832	721	11	razzaque	razzaque	NOUN
ejpam-5832	721	12	,	,	PUNCT
ejpam-5832	721	13	and	and	CCONJ
ejpam-5832	721	14	h	h	PROPN
ejpam-5832	721	15	garg	garg	NOUN
ejpam-5832	721	16	.	.	PUNCT
ejpam-5832	722	1	a	a	DET
ejpam-5832	722	2	comprehensive	comprehensive	ADJ
ejpam-5832	722	3	study	study	NOUN
ejpam-5832	722	4	on	on	ADP
ejpam-5832	722	5	pythagorean	pythagorean	PROPN
ejpam-5832	722	6	fuzzy	fuzzy	ADJ
ejpam-5832	722	7	normal	normal	ADJ
ejpam-5832	722	8	subgroups	subgroup	NOUN
ejpam-5832	722	9	and	and	CCONJ
ejpam-5832	722	10	pythagorean	pythagorean	PROPN
ejpam-5832	722	11	fuzzy	fuzzy	PROPN
ejpam-5832	722	12	isomorphisms	isomorphisms	PROPN
ejpam-5832	722	13	.	.	PUNCT
ejpam-5832	723	1	symmetry	symmetry	PROPN
ejpam-5832	723	2	,	,	PUNCT
ejpam-5832	723	3	14(10):2084	14(10):2084	NUM
ejpam-5832	723	4	,	,	PUNCT
ejpam-5832	723	5	2022	2022	NUM
ejpam-5832	723	6	.	.	PUNCT
ejpam-5832	724	1	[	[	X
ejpam-5832	724	2	35	35	NUM
ejpam-5832	724	3	]	]	PUNCT
ejpam-5832	724	4	a	a	DET
ejpam-5832	724	5	razzaque	razzaque	NOUN
ejpam-5832	724	6	and	and	CCONJ
ejpam-5832	724	7	a	a	DET
ejpam-5832	724	8	razaq	razaq	NOUN
ejpam-5832	724	9	.	.	PUNCT
ejpam-5832	725	1	on	on	ADP
ejpam-5832	725	2	-	-	PUNCT
ejpam-5832	725	3	rung	rung	ADJ
ejpam-5832	725	4	orthopair	orthopair	ADJ
ejpam-5832	725	5	fuzzy	fuzzy	ADJ
ejpam-5832	725	6	subgroups	subgroup	NOUN
ejpam-5832	725	7	.	.	PUNCT
ejpam-5832	726	1	journal	journal	NOUN
ejpam-5832	726	2	of	of	ADP
ejpam-5832	726	3	function	function	NOUN
ejpam-5832	726	4	spaces	space	NOUN
ejpam-5832	726	5	,	,	PUNCT
ejpam-5832	726	6	2022	2022	NUM
ejpam-5832	726	7	.	.	PUNCT
ejpam-5832	727	1	[	[	X
ejpam-5832	727	2	36	36	NUM
ejpam-5832	727	3	]	]	X
ejpam-5832	727	4	g	g	PROPN
ejpam-5832	727	5	m	m	PROPN
ejpam-5832	727	6	addis	addis	PROPN
ejpam-5832	727	7	,	,	PUNCT
ejpam-5832	727	8	n	n	PRON
ejpam-5832	727	9	kausar	kausar	NOUN
ejpam-5832	727	10	,	,	PUNCT
ejpam-5832	727	11	and	and	CCONJ
ejpam-5832	727	12	m	m	PROPN
ejpam-5832	727	13	munir	munir	PROPN
ejpam-5832	727	14	.	.	PUNCT
ejpam-5832	728	1	gdsffjhdhsgcjd	gdsffjhdhsgcjd	PROPN
ejpam-5832	728	2	.	.	PUNCT
ejpam-5832	729	1	wjwgjdjhgcxjgdl	wjwgjdjhgcxjgdl	PROPN
ejpam-5832	729	2	,	,	PUNCT
ejpam-5832	729	3	25(6):1757	25(6):1757	NUM
ejpam-5832	729	4	–	–	PUNCT
ejpam-5832	729	5	1776	1776	NUM
ejpam-5832	729	6	,	,	PUNCT
ejpam-5832	729	7	2022	2022	NUM
ejpam-5832	729	8	.	.	PUNCT