id	sid	tid	token	lemma	pos
ejpam-6459	1	1	european	european	PROPN
ejpam-6459	1	2	journal	journal	PROPN
ejpam-6459	1	3	of	of	ADP
ejpam-6459	1	4	pure	pure	ADJ
ejpam-6459	1	5	and	and	CCONJ
ejpam-6459	1	6	applied	applied	ADJ
ejpam-6459	1	7	mathematics	mathematic	NOUN
ejpam-6459	1	8	2025	2025	NUM
ejpam-6459	1	9	,	,	PUNCT
ejpam-6459	1	10	vol	vol	NOUN
ejpam-6459	1	11	.	.	PROPN
ejpam-6459	1	12	18	18	NUM
ejpam-6459	1	13	,	,	PUNCT
ejpam-6459	1	14	issue	issue	NOUN
ejpam-6459	1	15	3	3	NUM
ejpam-6459	1	16	,	,	PUNCT
ejpam-6459	1	17	article	article	NOUN
ejpam-6459	1	18	number	number	NOUN
ejpam-6459	1	19	6459	6459	NUM
ejpam-6459	1	20	issn	issn	VERB
ejpam-6459	1	21	1307	1307	NUM
ejpam-6459	1	22	-	-	SYM
ejpam-6459	1	23	5543	5543	NUM
ejpam-6459	1	24	–	–	PUNCT
ejpam-6459	1	25	ejpam.com	ejpam.com	X
ejpam-6459	1	26	published	publish	VERB
ejpam-6459	1	27	by	by	ADP
ejpam-6459	1	28	new	new	PROPN
ejpam-6459	1	29	york	york	PROPN
ejpam-6459	1	30	business	business	PROPN
ejpam-6459	1	31	global	global	ADJ
ejpam-6459	1	32	algebraic	algebraic	ADJ
ejpam-6459	1	33	aspects	aspect	NOUN
ejpam-6459	1	34	of	of	ADP
ejpam-6459	1	35	bipolar	bipolar	ADJ
ejpam-6459	1	36	fuzzy	fuzzy	ADJ
ejpam-6459	1	37	soft	soft	ADJ
ejpam-6459	1	38	boolean	boolean	ADJ
ejpam-6459	1	39	rings	ring	NOUN
ejpam-6459	1	40	gadde	gadde	PROPN
ejpam-6459	1	41	sambasiva	sambasiva	PROPN
ejpam-6459	1	42	rao1	rao1	PROPN
ejpam-6459	1	43	,	,	PUNCT
ejpam-6459	1	44	velayutham	velayutham	NOUN
ejpam-6459	1	45	parthiban	parthiban	ADJ
ejpam-6459	1	46	kolanchinathan2	kolanchinathan2	PROPN
ejpam-6459	1	47	,	,	PUNCT
ejpam-6459	1	48	k.	k.	PROPN
ejpam-6459	1	49	jhansi	jhansi	PROPN
ejpam-6459	1	50	rani3	rani3	PROPN
ejpam-6459	1	51	,	,	PUNCT
ejpam-6459	1	52	aiyared	aiyare	VERB
ejpam-6459	1	53	iampan4,∗	iampan4,∗	ADJ
ejpam-6459	1	54	,	,	PUNCT
ejpam-6459	1	55	k.	k.	PROPN
ejpam-6459	1	56	hemabala5	hemabala5	PROPN
ejpam-6459	1	57	,	,	PUNCT
ejpam-6459	1	58	d.	d.	PROPN
ejpam-6459	1	59	ramesh6	ramesh6	PROPN
ejpam-6459	1	60	,	,	PUNCT
ejpam-6459	1	61	b.	b.	PROPN
ejpam-6459	1	62	satyanarayana7	satyanarayana7	PROPN
ejpam-6459	1	63	1	1	NUM
ejpam-6459	1	64	department	department	NOUN
ejpam-6459	1	65	of	of	ADP
ejpam-6459	1	66	mathematics	mathematics	PROPN
ejpam-6459	1	67	,	,	PUNCT
ejpam-6459	1	68	sree	sree	PROPN
ejpam-6459	1	69	dattha	dattha	PROPN
ejpam-6459	1	70	group	group	PROPN
ejpam-6459	1	71	of	of	ADP
ejpam-6459	1	72	institutions	institution	NOUN
ejpam-6459	1	73	,	,	PUNCT
ejpam-6459	1	74	sheriguda	sheriguda	NOUN
ejpam-6459	1	75	,	,	PUNCT
ejpam-6459	1	76	ibrahimpatnam	ibrahimpatnam	PROPN
ejpam-6459	1	77	,	,	PUNCT
ejpam-6459	1	78	ranga	ranga	PROPN
ejpam-6459	1	79	reddy	reddy	PROPN
ejpam-6459	1	80	,	,	PUNCT
ejpam-6459	1	81	telangana-501510	telangana-501510	ADJ
ejpam-6459	1	82	,	,	PUNCT
ejpam-6459	1	83	india	india	PROPN
ejpam-6459	1	84	2	2	NUM
ejpam-6459	1	85	department	department	NOUN
ejpam-6459	1	86	of	of	ADP
ejpam-6459	1	87	electronics	electronic	NOUN
ejpam-6459	1	88	and	and	CCONJ
ejpam-6459	1	89	communication	communication	NOUN
ejpam-6459	1	90	engineering	engineering	NOUN
ejpam-6459	1	91	,	,	PUNCT
ejpam-6459	1	92	vel	vel	ADJ
ejpam-6459	1	93	tech	tech	NOUN
ejpam-6459	1	94	high	high	ADJ
ejpam-6459	1	95	tech	tech	PROPN
ejpam-6459	1	96	dr	dr	PROPN
ejpam-6459	1	97	.	.	PROPN
ejpam-6459	1	98	rangarajan	rangarajan	PROPN
ejpam-6459	1	99	dr	dr	PROPN
ejpam-6459	1	100	.	.	PROPN
ejpam-6459	1	101	sakunthala	sakunthala	PROPN
ejpam-6459	1	102	engineering	engineering	PROPN
ejpam-6459	1	103	college	college	PROPN
ejpam-6459	1	104	,	,	PUNCT
ejpam-6459	1	105	anna	anna	PROPN
ejpam-6459	1	106	university	university	PROPN
ejpam-6459	1	107	,	,	PUNCT
ejpam-6459	1	108	chennai	chennai	PROPN
ejpam-6459	1	109	,	,	PUNCT
ejpam-6459	1	110	india	india	PROPN
ejpam-6459	1	111	3	3	NUM
ejpam-6459	1	112	department	department	PROPN
ejpam-6459	1	113	of	of	ADP
ejpam-6459	1	114	mathematics	mathematic	NOUN
ejpam-6459	1	115	,	,	PUNCT
ejpam-6459	1	116	lakireddy	lakireddy	PROPN
ejpam-6459	1	117	bali	bali	PROPN
ejpam-6459	1	118	reddy	reddy	PROPN
ejpam-6459	1	119	college	college	PROPN
ejpam-6459	1	120	of	of	ADP
ejpam-6459	1	121	engineering	engineering	PROPN
ejpam-6459	1	122	,	,	PUNCT
ejpam-6459	1	123	mylavaram	mylavaram	PROPN
ejpam-6459	1	124	,	,	PUNCT
ejpam-6459	1	125	andhra	andhra	PROPN
ejpam-6459	1	126	pradesh-521530	pradesh-521530	NOUN
ejpam-6459	1	127	,	,	PUNCT
ejpam-6459	1	128	india	india	PROPN
ejpam-6459	1	129	4	4	NUM
ejpam-6459	1	130	department	department	NOUN
ejpam-6459	1	131	of	of	ADP
ejpam-6459	1	132	mathematics	mathematic	NOUN
ejpam-6459	1	133	,	,	PUNCT
ejpam-6459	1	134	school	school	NOUN
ejpam-6459	1	135	of	of	ADP
ejpam-6459	1	136	science	science	NOUN
ejpam-6459	1	137	,	,	PUNCT
ejpam-6459	1	138	university	university	NOUN
ejpam-6459	1	139	of	of	ADP
ejpam-6459	1	140	phayao	phayao	NOUN
ejpam-6459	1	141	,	,	PUNCT
ejpam-6459	1	142	mae	mae	PROPN
ejpam-6459	1	143	ka	ka	PROPN
ejpam-6459	1	144	,	,	PUNCT
ejpam-6459	1	145	mueang	mueang	PROPN
ejpam-6459	1	146	,	,	PUNCT
ejpam-6459	1	147	phayao	phayao	NOUN
ejpam-6459	1	148	56000	56000	NUM
ejpam-6459	1	149	,	,	PUNCT
ejpam-6459	1	150	thailand	thailand	PROPN
ejpam-6459	1	151	5	5	NUM
ejpam-6459	1	152	department	department	NOUN
ejpam-6459	1	153	of	of	ADP
ejpam-6459	1	154	computer	computer	NOUN
ejpam-6459	1	155	science	science	NOUN
ejpam-6459	1	156	and	and	CCONJ
ejpam-6459	1	157	engineering	engineering	NOUN
ejpam-6459	1	158	,	,	PUNCT
ejpam-6459	1	159	siddharth	siddharth	PROPN
ejpam-6459	1	160	institute	institute	PROPN
ejpam-6459	1	161	of	of	ADP
ejpam-6459	1	162	engineering	engineering	NOUN
ejpam-6459	1	163	and	and	CCONJ
ejpam-6459	1	164	technology	technology	NOUN
ejpam-6459	1	165	(	(	PUNCT
ejpam-6459	1	166	autonomous	autonomous	ADJ
ejpam-6459	1	167	)	)	PUNCT
ejpam-6459	1	168	,	,	PUNCT
ejpam-6459	1	169	puttur-517583	puttur-517583	NOUN
ejpam-6459	1	170	,	,	PUNCT
ejpam-6459	1	171	india	india	PROPN
ejpam-6459	1	172	6	6	NUM
ejpam-6459	1	173	department	department	NOUN
ejpam-6459	1	174	of	of	ADP
ejpam-6459	1	175	engineering	engineering	NOUN
ejpam-6459	1	176	mathematics	mathematic	NOUN
ejpam-6459	1	177	,	,	PUNCT
ejpam-6459	1	178	college	college	NOUN
ejpam-6459	1	179	of	of	ADP
ejpam-6459	1	180	engineering	engineering	PROPN
ejpam-6459	1	181	,	,	PUNCT
ejpam-6459	1	182	koneru	koneru	PROPN
ejpam-6459	1	183	lakshmaiah	lakshmaiah	PROPN
ejpam-6459	1	184	educational	educational	ADJ
ejpam-6459	1	185	foundation	foundation	PROPN
ejpam-6459	1	186	,	,	PUNCT
ejpam-6459	1	187	vaddeswaram	vaddeswaram	PROPN
ejpam-6459	1	188	,	,	PUNCT
ejpam-6459	1	189	andhra	andhra	PROPN
ejpam-6459	1	190	pradesh-522302	pradesh-522302	NOUN
ejpam-6459	1	191	,	,	PUNCT
ejpam-6459	1	192	india	india	PROPN
ejpam-6459	1	193	7	7	NUM
ejpam-6459	1	194	department	department	NOUN
ejpam-6459	1	195	of	of	ADP
ejpam-6459	1	196	mathematics	mathematic	NOUN
ejpam-6459	1	197	,	,	PUNCT
ejpam-6459	1	198	acharya	acharya	PROPN
ejpam-6459	1	199	nagarjuna	nagarjuna	PROPN
ejpam-6459	1	200	university	university	PROPN
ejpam-6459	1	201	,	,	PUNCT
ejpam-6459	1	202	nagarjuna	nagarjuna	PROPN
ejpam-6459	1	203	nagar	nagar	PROPN
ejpam-6459	1	204	,	,	PUNCT
ejpam-6459	1	205	andhra	andhra	PROPN
ejpam-6459	1	206	pradesh-522510	pradesh-522510	PROPN
ejpam-6459	1	207	,	,	PUNCT
ejpam-6459	1	208	india	india	PROPN
ejpam-6459	1	209	abstract	abstract	NOUN
ejpam-6459	1	210	.	.	PUNCT
ejpam-6459	2	1	this	this	DET
ejpam-6459	2	2	work	work	NOUN
ejpam-6459	2	3	introduces	introduce	VERB
ejpam-6459	2	4	the	the	DET
ejpam-6459	2	5	concept	concept	NOUN
ejpam-6459	2	6	of	of	ADP
ejpam-6459	2	7	bipolar	bipolar	ADJ
ejpam-6459	2	8	fuzzy	fuzzy	ADJ
ejpam-6459	2	9	soft	soft	ADJ
ejpam-6459	2	10	boolean	boolean	ADJ
ejpam-6459	2	11	rings	ring	NOUN
ejpam-6459	2	12	(	(	PUNCT
ejpam-6459	2	13	bfsbrs	bfsbr	VERB
ejpam-6459	2	14	)	)	PUNCT
ejpam-6459	2	15	,	,	PUNCT
ejpam-6459	2	16	an	an	DET
ejpam-6459	2	17	algebraic	algebraic	ADJ
ejpam-6459	2	18	structure	structure	NOUN
ejpam-6459	2	19	that	that	PRON
ejpam-6459	2	20	unifies	unify	VERB
ejpam-6459	2	21	soft	soft	ADJ
ejpam-6459	2	22	sets	set	NOUN
ejpam-6459	2	23	(	(	PUNCT
ejpam-6459	2	24	sss	sss	NOUN
ejpam-6459	2	25	)	)	PUNCT
ejpam-6459	2	26	and	and	CCONJ
ejpam-6459	2	27	bipolar	bipolar	ADJ
ejpam-6459	2	28	fuzzy	fuzzy	ADJ
ejpam-6459	2	29	sets	set	NOUN
ejpam-6459	2	30	(	(	PUNCT
ejpam-6459	2	31	bfss	bfss	NOUN
ejpam-6459	2	32	)	)	PUNCT
ejpam-6459	2	33	within	within	ADP
ejpam-6459	2	34	boolean	boolean	ADJ
ejpam-6459	2	35	ring	ring	NOUN
ejpam-6459	2	36	(	(	PUNCT
ejpam-6459	2	37	br	br	NOUN
ejpam-6459	2	38	)	)	PUNCT
ejpam-6459	2	39	systems	system	NOUN
ejpam-6459	2	40	.	.	PUNCT
ejpam-6459	3	1	it	it	PRON
ejpam-6459	3	2	develops	develop	VERB
ejpam-6459	3	3	essential	essential	ADJ
ejpam-6459	3	4	definitions	definition	NOUN
ejpam-6459	3	5	,	,	PUNCT
ejpam-6459	3	6	operations	operation	NOUN
ejpam-6459	3	7	,	,	PUNCT
ejpam-6459	3	8	and	and	CCONJ
ejpam-6459	3	9	properties	property	NOUN
ejpam-6459	3	10	for	for	ADP
ejpam-6459	3	11	modeling	model	VERB
ejpam-6459	3	12	dual	dual	ADJ
ejpam-6459	3	13	-	-	PUNCT
ejpam-6459	3	14	sided	sided	ADJ
ejpam-6459	3	15	uncertainty	uncertainty	NOUN
ejpam-6459	3	16	in	in	ADP
ejpam-6459	3	17	decision	decision	NOUN
ejpam-6459	3	18	-	-	PUNCT
ejpam-6459	3	19	making	make	VERB
ejpam-6459	3	20	contexts	context	NOUN
ejpam-6459	3	21	.	.	PUNCT
ejpam-6459	4	1	beyond	beyond	ADP
ejpam-6459	4	2	its	its	PRON
ejpam-6459	4	3	theoretical	theoretical	ADJ
ejpam-6459	4	4	contributions	contribution	NOUN
ejpam-6459	4	5	,	,	PUNCT
ejpam-6459	4	6	the	the	DET
ejpam-6459	4	7	framework	framework	NOUN
ejpam-6459	4	8	is	be	AUX
ejpam-6459	4	9	designed	design	VERB
ejpam-6459	4	10	to	to	PART
ejpam-6459	4	11	support	support	VERB
ejpam-6459	4	12	early	early	ADJ
ejpam-6459	4	13	-	-	PUNCT
ejpam-6459	4	14	stage	stage	NOUN
ejpam-6459	4	15	mathematical	mathematical	ADJ
ejpam-6459	4	16	research	research	NOUN
ejpam-6459	4	17	by	by	ADP
ejpam-6459	4	18	science	science	NOUN
ejpam-6459	4	19	classroom	classroom	NOUN
ejpam-6459	4	20	students	student	NOUN
ejpam-6459	4	21	.	.	PUNCT
ejpam-6459	5	1	it	it	PRON
ejpam-6459	5	2	encourages	encourage	VERB
ejpam-6459	5	3	deeper	deep	ADJ
ejpam-6459	5	4	engagement	engagement	NOUN
ejpam-6459	5	5	with	with	ADP
ejpam-6459	5	6	abstract	abstract	ADJ
ejpam-6459	5	7	mathematical	mathematical	ADJ
ejpam-6459	5	8	thinking	thinking	NOUN
ejpam-6459	5	9	and	and	CCONJ
ejpam-6459	5	10	fosters	foster	VERB
ejpam-6459	5	11	collaboration	collaboration	NOUN
ejpam-6459	5	12	between	between	ADP
ejpam-6459	5	13	students	student	NOUN
ejpam-6459	5	14	,	,	PUNCT
ejpam-6459	5	15	teachers	teacher	NOUN
ejpam-6459	5	16	,	,	PUNCT
ejpam-6459	5	17	and	and	CCONJ
ejpam-6459	5	18	research	research	NOUN
ejpam-6459	5	19	mentors	mentor	NOUN
ejpam-6459	5	20	,	,	PUNCT
ejpam-6459	5	21	thus	thus	ADV
ejpam-6459	5	22	promoting	promote	VERB
ejpam-6459	5	23	a	a	DET
ejpam-6459	5	24	more	more	ADV
ejpam-6459	5	25	inclusive	inclusive	ADJ
ejpam-6459	5	26	and	and	CCONJ
ejpam-6459	5	27	research	research	NOUN
ejpam-6459	5	28	-	-	PUNCT
ejpam-6459	5	29	oriented	orient	VERB
ejpam-6459	5	30	learning	learning	NOUN
ejpam-6459	5	31	environment	environment	NOUN
ejpam-6459	5	32	.	.	PUNCT
ejpam-6459	6	1	2020	2020	NUM
ejpam-6459	6	2	mathematics	mathematic	NOUN
ejpam-6459	6	3	subject	subject	NOUN
ejpam-6459	6	4	classifications	classification	NOUN
ejpam-6459	6	5	:	:	PUNCT
ejpam-6459	6	6	16y30	16y30	NUM
ejpam-6459	6	7	,	,	PUNCT
ejpam-6459	6	8	08a72	08a72	NUM
ejpam-6459	6	9	,	,	PUNCT
ejpam-6459	6	10	06d72	06d72	VERB
ejpam-6459	6	11	key	key	ADJ
ejpam-6459	6	12	words	word	NOUN
ejpam-6459	6	13	and	and	CCONJ
ejpam-6459	6	14	phrases	phrase	NOUN
ejpam-6459	6	15	:	:	PUNCT
ejpam-6459	6	16	boolean	boolean	ADJ
ejpam-6459	6	17	ring	ring	NOUN
ejpam-6459	6	18	,	,	PUNCT
ejpam-6459	6	19	fuzzy	fuzzy	ADJ
ejpam-6459	6	20	set	set	NOUN
ejpam-6459	6	21	,	,	PUNCT
ejpam-6459	6	22	bipolar	bipolar	ADJ
ejpam-6459	6	23	fuzzy	fuzzy	ADJ
ejpam-6459	6	24	set	set	NOUN
ejpam-6459	6	25	,	,	PUNCT
ejpam-6459	6	26	fuzzy	fuzzy	ADJ
ejpam-6459	6	27	soft	soft	ADJ
ejpam-6459	6	28	set	set	NOUN
ejpam-6459	6	29	,	,	PUNCT
ejpam-6459	6	30	soft	soft	ADJ
ejpam-6459	6	31	set	set	NOUN
ejpam-6459	6	32	,	,	PUNCT
ejpam-6459	6	33	bipolar	bipolar	ADJ
ejpam-6459	6	34	fuzzy	fuzzy	ADJ
ejpam-6459	6	35	soft	soft	ADJ
ejpam-6459	6	36	boolean	boolean	ADJ
ejpam-6459	6	37	ring	ring	NOUN
ejpam-6459	6	38	,	,	PUNCT
ejpam-6459	6	39	bipolar	bipolar	ADJ
ejpam-6459	6	40	fuzzy	fuzzy	ADJ
ejpam-6459	6	41	soft	soft	ADJ
ejpam-6459	6	42	ideal	ideal	ADJ
ejpam-6459	6	43	∗corresponding	∗corresponde	VERB
ejpam-6459	6	44	author	author	NOUN
ejpam-6459	6	45	.	.	PUNCT
ejpam-6459	7	1	doi	doi	NOUN
ejpam-6459	7	2	:	:	PUNCT
ejpam-6459	8	1	https://doi.org/10.29020/nybg.ejpam.v18i3.6459	https://doi.org/10.29020/nybg.ejpam.v18i3.6459	NOUN
ejpam-6459	8	2	email	email	NOUN
ejpam-6459	8	3	addresses	address	VERB
ejpam-6459	8	4	:	:	PUNCT
ejpam-6459	8	5	gaddesambasivarao1@gmail.com	gaddesambasivarao1@gmail.com	X
ejpam-6459	8	6	(	(	PUNCT
ejpam-6459	8	7	g.	g.	PROPN
ejpam-6459	8	8	s.	s.	PROPN
ejpam-6459	8	9	rao	rao	PROPN
ejpam-6459	8	10	)	)	PUNCT
ejpam-6459	8	11	,	,	PUNCT
ejpam-6459	8	12	vpknathan@gmail.com	vpknathan@gmail.com	X
ejpam-6459	9	1	(	(	PUNCT
ejpam-6459	9	2	v.	v.	ADP
ejpam-6459	9	3	p.	p.	NOUN
ejpam-6459	9	4	kolanchinathan	kolanchinathan	PROPN
ejpam-6459	9	5	)	)	PUNCT
ejpam-6459	9	6	,	,	PUNCT
ejpam-6459	9	7	kjhansi83@gmail.com	kjhansi83@gmail.com	PROPN
ejpam-6459	9	8	(	(	PUNCT
ejpam-6459	9	9	k.	k.	PROPN
ejpam-6459	9	10	jhansi	jhansi	PROPN
ejpam-6459	9	11	rani	rani	PROPN
ejpam-6459	9	12	)	)	PUNCT
ejpam-6459	9	13	,	,	PUNCT
ejpam-6459	9	14	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6459	9	15	(	(	PUNCT
ejpam-6459	9	16	a.	a.	NOUN
ejpam-6459	9	17	iampan	iampan	PROPN
ejpam-6459	9	18	)	)	PUNCT
ejpam-6459	9	19	,	,	PUNCT
ejpam-6459	9	20	hemaram.magi@gmail.com	hemaram.magi@gmail.com	X
ejpam-6459	9	21	(	(	PUNCT
ejpam-6459	9	22	k.	k.	NOUN
ejpam-6459	9	23	hemabala	hemabala	PROPN
ejpam-6459	9	24	)	)	PUNCT
ejpam-6459	9	25	,	,	PUNCT
ejpam-6459	9	26	ram.fuzzy@gmail.com	ram.fuzzy@gmail.com	PROPN
ejpam-6459	9	27	(	(	PUNCT
ejpam-6459	9	28	d.	d.	PROPN
ejpam-6459	9	29	ramesh	ramesh	PROPN
ejpam-6459	9	30	)	)	PUNCT
ejpam-6459	9	31	,	,	PUNCT
ejpam-6459	9	32	drbsn63@yahoo.co.in	drbsn63@yahoo.co.in	NOUN
ejpam-6459	9	33	(	(	PUNCT
ejpam-6459	9	34	b.	b.	PROPN
ejpam-6459	9	35	satyanarayana	satyanarayana	PROPN
ejpam-6459	9	36	)	)	PUNCT
ejpam-6459	9	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6459	10	1	1	1	NUM
ejpam-6459	10	2	copyright	copyright	NOUN
ejpam-6459	10	3	:	:	PUNCT
ejpam-6459	10	4	©	©	PROPN
ejpam-6459	10	5	2025	2025	NUM
ejpam-6459	10	6	the	the	DET
ejpam-6459	10	7	author(s	author(s	NOUN
ejpam-6459	10	8	)	)	PUNCT
ejpam-6459	10	9	.	.	PUNCT
ejpam-6459	11	1	(	(	PUNCT
ejpam-6459	11	2	cc	cc	NOUN
ejpam-6459	11	3	by	by	ADP
ejpam-6459	11	4	-	-	PUNCT
ejpam-6459	11	5	nc	nc	PROPN
ejpam-6459	11	6	4.0	4.0	NUM
ejpam-6459	11	7	)	)	PUNCT
ejpam-6459	11	8	g.	g.	PROPN
ejpam-6459	11	9	s.	s.	PROPN
ejpam-6459	11	10	rao	rao	PROPN
ejpam-6459	11	11	et	et	PROPN
ejpam-6459	11	12	al	al	PROPN
ejpam-6459	11	13	.	.	PUNCT
ejpam-6459	11	14	/	/	SYM
ejpam-6459	11	15	eur	eur	PROPN
ejpam-6459	11	16	.	.	PUNCT
ejpam-6459	12	1	j.	j.	PROPN
ejpam-6459	12	2	pure	pure	PROPN
ejpam-6459	12	3	appl	appl	PROPN
ejpam-6459	12	4	.	.	PROPN
ejpam-6459	12	5	math	math	PROPN
ejpam-6459	12	6	,	,	PUNCT
ejpam-6459	12	7	18	18	NUM
ejpam-6459	12	8	(	(	PUNCT
ejpam-6459	12	9	3	3	NUM
ejpam-6459	12	10	)	)	PUNCT
ejpam-6459	12	11	(	(	PUNCT
ejpam-6459	12	12	2025	2025	NUM
ejpam-6459	12	13	)	)	PUNCT
ejpam-6459	12	14	,	,	PUNCT
ejpam-6459	12	15	6459	6459	NUM
ejpam-6459	12	16	2	2	NUM
ejpam-6459	12	17	of	of	ADP
ejpam-6459	12	18	16	16	NUM
ejpam-6459	12	19	1	1	NUM
ejpam-6459	12	20	.	.	PUNCT
ejpam-6459	13	1	introduction	introduction	NOUN
ejpam-6459	13	2	zadeh	zadeh	NOUN
ejpam-6459	13	3	[	[	X
ejpam-6459	13	4	1	1	X
ejpam-6459	13	5	]	]	PUNCT
ejpam-6459	13	6	proposed	propose	VERB
ejpam-6459	13	7	the	the	DET
ejpam-6459	13	8	theory	theory	NOUN
ejpam-6459	13	9	of	of	ADP
ejpam-6459	13	10	a	a	DET
ejpam-6459	13	11	fuzzy	fuzzy	ADJ
ejpam-6459	13	12	set	set	NOUN
ejpam-6459	13	13	(	(	PUNCT
ejpam-6459	13	14	fs	fs	PROPN
ejpam-6459	13	15	)	)	PUNCT
ejpam-6459	13	16	of	of	ADP
ejpam-6459	13	17	a	a	DET
ejpam-6459	13	18	set	set	NOUN
ejpam-6459	13	19	.	.	PUNCT
ejpam-6459	14	1	this	this	DET
ejpam-6459	14	2	concept	concept	NOUN
ejpam-6459	14	3	has	have	AUX
ejpam-6459	14	4	now	now	ADV
ejpam-6459	14	5	been	be	AUX
ejpam-6459	14	6	generalized	generalize	VERB
ejpam-6459	14	7	in	in	ADP
ejpam-6459	14	8	various	various	ADJ
ejpam-6459	14	9	ways	way	NOUN
ejpam-6459	14	10	.	.	PUNCT
ejpam-6459	15	1	lee	lee	PROPN
ejpam-6459	16	1	[	[	X
ejpam-6459	16	2	2	2	NUM
ejpam-6459	16	3	]	]	PUNCT
ejpam-6459	16	4	was	be	AUX
ejpam-6459	16	5	the	the	DET
ejpam-6459	16	6	first	first	ADJ
ejpam-6459	16	7	to	to	PART
ejpam-6459	16	8	suggest	suggest	VERB
ejpam-6459	16	9	the	the	DET
ejpam-6459	16	10	idea	idea	NOUN
ejpam-6459	16	11	of	of	ADP
ejpam-6459	16	12	bvfss	bvfss	PROPN
ejpam-6459	16	13	.	.	PUNCT
ejpam-6459	17	1	fuzzy	fuzzy	ADJ
ejpam-6459	17	2	sets	set	NOUN
ejpam-6459	17	3	with	with	ADP
ejpam-6459	17	4	membership	membership	NOUN
ejpam-6459	17	5	degrees	degree	NOUN
ejpam-6459	17	6	ranging	range	VERB
ejpam-6459	17	7	from	from	ADP
ejpam-6459	17	8	[	[	X
ejpam-6459	17	9	0	0	NUM
ejpam-6459	17	10	,	,	PUNCT
ejpam-6459	17	11	1	1	NUM
ejpam-6459	17	12	]	]	PUNCT
ejpam-6459	17	13	to	to	ADP
ejpam-6459	17	14	[	[	X
ejpam-6459	17	15	−1	−1	NOUN
ejpam-6459	17	16	,	,	PUNCT
ejpam-6459	17	17	1	1	NUM
ejpam-6459	17	18	]	]	PUNCT
ejpam-6459	17	19	are	be	AUX
ejpam-6459	17	20	known	know	VERB
ejpam-6459	17	21	as	as	ADP
ejpam-6459	17	22	bvfss	bvfss	PROPN
ejpam-6459	17	23	.	.	PUNCT
ejpam-6459	18	1	if	if	SCONJ
ejpam-6459	18	2	the	the	DET
ejpam-6459	18	3	membership	membership	NOUN
ejpam-6459	18	4	degree	degree	NOUN
ejpam-6459	18	5	is	be	AUX
ejpam-6459	18	6	zero	zero	NUM
ejpam-6459	18	7	,	,	PUNCT
ejpam-6459	18	8	the	the	DET
ejpam-6459	18	9	elements	element	NOUN
ejpam-6459	18	10	have	have	VERB
ejpam-6459	18	11	no	no	DET
ejpam-6459	18	12	relationship	relationship	NOUN
ejpam-6459	18	13	to	to	ADP
ejpam-6459	18	14	the	the	DET
ejpam-6459	18	15	associated	associated	ADJ
ejpam-6459	18	16	attribute	attribute	NOUN
ejpam-6459	18	17	.	.	PUNCT
ejpam-6459	19	1	elements	element	NOUN
ejpam-6459	19	2	with	with	ADP
ejpam-6459	19	3	a	a	DET
ejpam-6459	19	4	membership	membership	NOUN
ejpam-6459	19	5	degree	degree	NOUN
ejpam-6459	19	6	between	between	ADP
ejpam-6459	19	7	0	0	NUM
ejpam-6459	19	8	and	and	CCONJ
ejpam-6459	19	9	1	1	NUM
ejpam-6459	19	10	partially	partially	ADV
ejpam-6459	19	11	meet	meet	VERB
ejpam-6459	19	12	the	the	DET
ejpam-6459	19	13	requirement	requirement	NOUN
ejpam-6459	19	14	.	.	PUNCT
ejpam-6459	20	1	if	if	SCONJ
ejpam-6459	20	2	the	the	DET
ejpam-6459	20	3	membership	membership	NOUN
ejpam-6459	20	4	degree	degree	NOUN
ejpam-6459	20	5	is	be	AUX
ejpam-6459	20	6	[	[	X
ejpam-6459	20	7	−1	−1	NOUN
ejpam-6459	20	8	,	,	PUNCT
ejpam-6459	20	9	0	0	NUM
ejpam-6459	20	10	]	]	PUNCT
ejpam-6459	20	11	,	,	PUNCT
ejpam-6459	20	12	then	then	ADV
ejpam-6459	20	13	elements	element	NOUN
ejpam-6459	20	14	partially	partially	ADV
ejpam-6459	20	15	satisfy	satisfy	VERB
ejpam-6459	20	16	the	the	DET
ejpam-6459	20	17	implicit	implicit	ADJ
ejpam-6459	20	18	counter	counter	NOUN
ejpam-6459	20	19	attribute	attribute	NOUN
ejpam-6459	20	20	.	.	PUNCT
ejpam-6459	21	1	molodtsov	molodtsov	NOUN
ejpam-6459	22	1	[	[	X
ejpam-6459	22	2	3	3	X
ejpam-6459	22	3	]	]	PUNCT
ejpam-6459	22	4	was	be	AUX
ejpam-6459	22	5	the	the	DET
ejpam-6459	22	6	first	first	ADJ
ejpam-6459	22	7	to	to	PART
ejpam-6459	22	8	present	present	VERB
ejpam-6459	22	9	the	the	DET
ejpam-6459	22	10	idea	idea	NOUN
ejpam-6459	22	11	of	of	ADP
ejpam-6459	22	12	ss	ss	PROPN
ejpam-6459	22	13	theory	theory	NOUN
ejpam-6459	22	14	as	as	ADP
ejpam-6459	22	15	a	a	DET
ejpam-6459	22	16	new	new	ADJ
ejpam-6459	22	17	mathematical	mathematical	ADJ
ejpam-6459	22	18	tool	tool	NOUN
ejpam-6459	22	19	.	.	PUNCT
ejpam-6459	23	1	some	some	DET
ejpam-6459	23	2	scholars	scholar	NOUN
ejpam-6459	23	3	then	then	ADV
ejpam-6459	23	4	looked	look	VERB
ejpam-6459	23	5	at	at	ADP
ejpam-6459	23	6	the	the	DET
ejpam-6459	23	7	algebraic	algebraic	ADJ
ejpam-6459	23	8	aspects	aspect	NOUN
ejpam-6459	23	9	of	of	ADP
ejpam-6459	23	10	this	this	DET
ejpam-6459	23	11	idea	idea	NOUN
ejpam-6459	23	12	.	.	PUNCT
ejpam-6459	24	1	first	first	ADV
ejpam-6459	24	2	,	,	PUNCT
ejpam-6459	24	3	aktas	akta	NOUN
ejpam-6459	24	4	and	and	CCONJ
ejpam-6459	24	5	cagman	cagman	ADJ
ejpam-6459	24	6	[	[	X
ejpam-6459	24	7	4	4	NUM
ejpam-6459	24	8	]	]	PUNCT
ejpam-6459	24	9	employed	employ	VERB
ejpam-6459	24	10	ss	ss	NOUN
ejpam-6459	24	11	to	to	PART
ejpam-6459	24	12	define	define	VERB
ejpam-6459	24	13	the	the	DET
ejpam-6459	24	14	concept	concept	NOUN
ejpam-6459	24	15	of	of	ADP
ejpam-6459	24	16	soft	soft	ADJ
ejpam-6459	24	17	groups	group	NOUN
ejpam-6459	24	18	and	and	CCONJ
ejpam-6459	24	19	identify	identify	VERB
ejpam-6459	24	20	their	their	PRON
ejpam-6459	24	21	fundamental	fundamental	ADJ
ejpam-6459	24	22	characteristics	characteristic	NOUN
ejpam-6459	24	23	.	.	PUNCT
ejpam-6459	25	1	soft	soft	ADJ
ejpam-6459	25	2	rings	ring	NOUN
ejpam-6459	25	3	were	be	AUX
ejpam-6459	25	4	defined	define	VERB
ejpam-6459	25	5	and	and	CCONJ
ejpam-6459	25	6	their	their	PRON
ejpam-6459	25	7	basic	basic	ADJ
ejpam-6459	25	8	concepts	concept	NOUN
ejpam-6459	25	9	were	be	AUX
ejpam-6459	25	10	introduced	introduce	VERB
ejpam-6459	25	11	by	by	ADP
ejpam-6459	25	12	acar	acar	NOUN
ejpam-6459	25	13	et	et	PROPN
ejpam-6459	25	14	al	al	PROPN
ejpam-6459	25	15	.	.	PUNCT
ejpam-6459	26	1	[	[	X
ejpam-6459	26	2	5	5	NUM
ejpam-6459	26	3	]	]	PUNCT
ejpam-6459	26	4	.	.	PUNCT
ejpam-6459	27	1	çelik	çelik	PROPN
ejpam-6459	27	2	et	et	PROPN
ejpam-6459	27	3	al	al	PROPN
ejpam-6459	27	4	.	.	PUNCT
ejpam-6459	28	1	[	[	X
ejpam-6459	28	2	6	6	NUM
ejpam-6459	28	3	]	]	PUNCT
ejpam-6459	28	4	looked	look	VERB
ejpam-6459	28	5	at	at	ADP
ejpam-6459	28	6	some	some	DET
ejpam-6459	28	7	new	new	ADJ
ejpam-6459	28	8	characteristics	characteristic	NOUN
ejpam-6459	28	9	of	of	ADP
ejpam-6459	28	10	soft	soft	ADJ
ejpam-6459	28	11	rings	ring	NOUN
ejpam-6459	28	12	and	and	CCONJ
ejpam-6459	28	13	defined	define	VERB
ejpam-6459	28	14	some	some	DET
ejpam-6459	28	15	new	new	ADJ
ejpam-6459	28	16	binary	binary	ADJ
ejpam-6459	28	17	relations	relation	NOUN
ejpam-6459	28	18	on	on	ADP
ejpam-6459	28	19	sss	sss	PROPN
ejpam-6459	28	20	.	.	PUNCT
ejpam-6459	28	21	bipolar	bipolar	ADJ
ejpam-6459	28	22	fuzzy	fuzzy	ADJ
ejpam-6459	28	23	sets	set	NOUN
ejpam-6459	28	24	were	be	AUX
ejpam-6459	28	25	first	first	ADV
ejpam-6459	28	26	proposed	propose	VERB
ejpam-6459	28	27	by	by	ADP
ejpam-6459	28	28	zhang	zhang	PROPN
ejpam-6459	29	1	[	[	X
ejpam-6459	29	2	7	7	NUM
ejpam-6459	29	3	]	]	PUNCT
ejpam-6459	29	4	in	in	ADP
ejpam-6459	29	5	1994	1994	NUM
ejpam-6459	29	6	as	as	ADP
ejpam-6459	29	7	a	a	DET
ejpam-6459	29	8	generalization	generalization	NOUN
ejpam-6459	29	9	of	of	ADP
ejpam-6459	29	10	fuzzy	fuzzy	ADJ
ejpam-6459	29	11	sets	set	NOUN
ejpam-6459	29	12	[	[	X
ejpam-6459	29	13	1	1	NUM
ejpam-6459	29	14	]	]	PUNCT
ejpam-6459	29	15	.	.	PUNCT
ejpam-6459	30	1	naz	naz	PROPN
ejpam-6459	30	2	and	and	CCONJ
ejpam-6459	30	3	shabir	shabir	PROPN
ejpam-6459	31	1	[	[	X
ejpam-6459	31	2	8	8	NUM
ejpam-6459	31	3	]	]	PUNCT
ejpam-6459	31	4	developed	develop	VERB
ejpam-6459	31	5	the	the	DET
ejpam-6459	31	6	notions	notion	NOUN
ejpam-6459	31	7	of	of	ADP
ejpam-6459	31	8	fuzzy	fuzzy	ADJ
ejpam-6459	31	9	bipolar	bipolar	ADJ
ejpam-6459	31	10	soft	soft	ADJ
ejpam-6459	31	11	sets	set	NOUN
ejpam-6459	31	12	and	and	CCONJ
ejpam-6459	31	13	bipolar	bipolar	ADJ
ejpam-6459	31	14	fuzzy	fuzzy	ADJ
ejpam-6459	31	15	soft	soft	ADJ
ejpam-6459	31	16	sets	set	NOUN
ejpam-6459	31	17	(	(	PUNCT
ejpam-6459	31	18	bfsss	bfsss	NOUN
ejpam-6459	31	19	)	)	PUNCT
ejpam-6459	31	20	.	.	PUNCT
ejpam-6459	32	1	they	they	PRON
ejpam-6459	32	2	outlined	outline	VERB
ejpam-6459	32	3	the	the	DET
ejpam-6459	32	4	unique	unique	ADJ
ejpam-6459	32	5	intersection	intersection	NOUN
ejpam-6459	32	6	and	and	CCONJ
ejpam-6459	32	7	union	union	NOUN
ejpam-6459	32	8	of	of	ADP
ejpam-6459	32	9	the	the	DET
ejpam-6459	32	10	two	two	NUM
ejpam-6459	32	11	concepts	concept	NOUN
ejpam-6459	32	12	and	and	CCONJ
ejpam-6459	32	13	demonstrated	demonstrate	VERB
ejpam-6459	32	14	their	their	PRON
ejpam-6459	32	15	equivalency	equivalency	NOUN
ejpam-6459	32	16	.	.	PUNCT
ejpam-6459	33	1	bipolar	bipolar	ADJ
ejpam-6459	33	2	fuzzy	fuzzy	ADJ
ejpam-6459	33	3	soft	soft	ADJ
ejpam-6459	33	4	lie	lie	NOUN
ejpam-6459	33	5	subalgebras	subalgebra	NOUN
ejpam-6459	33	6	were	be	AUX
ejpam-6459	33	7	first	first	ADV
ejpam-6459	33	8	proposed	propose	VERB
ejpam-6459	33	9	by	by	ADP
ejpam-6459	33	10	akram	akram	PROPN
ejpam-6459	34	1	[	[	X
ejpam-6459	34	2	9	9	NUM
ejpam-6459	34	3	]	]	PUNCT
ejpam-6459	34	4	,	,	PUNCT
ejpam-6459	34	5	who	who	PRON
ejpam-6459	34	6	also	also	ADV
ejpam-6459	34	7	investigated	investigate	VERB
ejpam-6459	34	8	some	some	PRON
ejpam-6459	34	9	of	of	ADP
ejpam-6459	34	10	their	their	PRON
ejpam-6459	34	11	characteristics	characteristic	NOUN
ejpam-6459	34	12	.	.	PUNCT
ejpam-6459	35	1	the	the	DET
ejpam-6459	35	2	ideas	idea	NOUN
ejpam-6459	35	3	of	of	ADP
ejpam-6459	35	4	an	an	DET
ejpam-6459	35	5	ss	ss	NOUN
ejpam-6459	35	6	and	and	CCONJ
ejpam-6459	35	7	a	a	DET
ejpam-6459	35	8	bf	bf	NOUN
ejpam-6459	35	9	-	-	PUNCT
ejpam-6459	35	10	set	set	NOUN
ejpam-6459	35	11	were	be	AUX
ejpam-6459	35	12	blended	blend	VERB
ejpam-6459	35	13	by	by	ADP
ejpam-6459	35	14	abdullah	abdullah	PROPN
ejpam-6459	35	15	et	et	PROPN
ejpam-6459	35	16	al	al	PROPN
ejpam-6459	35	17	.	.	PUNCT
ejpam-6459	36	1	[	[	X
ejpam-6459	36	2	10	10	NUM
ejpam-6459	36	3	]	]	PUNCT
ejpam-6459	36	4	.	.	PUNCT
ejpam-6459	37	1	in	in	ADP
ejpam-6459	37	2	addition	addition	NOUN
ejpam-6459	37	3	,	,	PUNCT
ejpam-6459	37	4	they	they	PRON
ejpam-6459	37	5	presented	present	VERB
ejpam-6459	37	6	the	the	DET
ejpam-6459	37	7	concept	concept	NOUN
ejpam-6459	37	8	of	of	ADP
ejpam-6459	37	9	a	a	DET
ejpam-6459	37	10	bfss	bfss	NOUN
ejpam-6459	37	11	and	and	CCONJ
ejpam-6459	37	12	outlined	outline	VERB
ejpam-6459	37	13	some	some	PRON
ejpam-6459	37	14	of	of	ADP
ejpam-6459	37	15	its	its	PRON
ejpam-6459	37	16	key	key	ADJ
ejpam-6459	37	17	characteristics	characteristic	NOUN
ejpam-6459	37	18	.	.	PUNCT
ejpam-6459	38	1	bfsss	bfsss	NOUN
ejpam-6459	38	2	and	and	CCONJ
ejpam-6459	38	3	their	their	PRON
ejpam-6459	38	4	unique	unique	ADJ
ejpam-6459	38	5	union	union	NOUN
ejpam-6459	38	6	and	and	CCONJ
ejpam-6459	38	7	intersection	intersection	NOUN
ejpam-6459	38	8	were	be	AUX
ejpam-6459	38	9	also	also	ADV
ejpam-6459	38	10	studied	study	VERB
ejpam-6459	38	11	by	by	ADP
ejpam-6459	38	12	aslam	aslam	PROPN
ejpam-6459	38	13	et	et	PROPN
ejpam-6459	38	14	al	al	PROPN
ejpam-6459	38	15	.	.	PUNCT
ejpam-6459	39	1	[	[	X
ejpam-6459	39	2	11	11	NUM
ejpam-6459	39	3	]	]	PUNCT
ejpam-6459	39	4	.	.	PUNCT
ejpam-6459	40	1	the	the	DET
ejpam-6459	40	2	notion	notion	NOUN
ejpam-6459	40	3	of	of	ADP
ejpam-6459	40	4	bfs	bfs	PROPN
ejpam-6459	40	5	k	k	NOUN
ejpam-6459	40	6	-	-	PUNCT
ejpam-6459	40	7	algebras	algebras	PROPN
ejpam-6459	40	8	was	be	AUX
ejpam-6459	40	9	presented	present	VERB
ejpam-6459	40	10	by	by	ADP
ejpam-6459	40	11	akram	akram	PROPN
ejpam-6459	40	12	et	et	PROPN
ejpam-6459	40	13	al	al	PROPN
ejpam-6459	40	14	.	.	PUNCT
ejpam-6459	41	1	[	[	X
ejpam-6459	41	2	12	12	NUM
ejpam-6459	41	3	]	]	PUNCT
ejpam-6459	41	4	.	.	PUNCT
ejpam-6459	42	1	akram	akram	PROPN
ejpam-6459	42	2	et	et	PROPN
ejpam-6459	42	3	al	al	PROPN
ejpam-6459	42	4	.	.	PUNCT
ejpam-6459	43	1	[	[	X
ejpam-6459	43	2	13	13	NUM
ejpam-6459	43	3	]	]	PUNCT
ejpam-6459	43	4	introduced	introduce	VERB
ejpam-6459	43	5	the	the	DET
ejpam-6459	43	6	concept	concept	NOUN
ejpam-6459	43	7	of	of	ADP
ejpam-6459	43	8	bipolar	bipolar	ADJ
ejpam-6459	43	9	fuzzy	fuzzy	ADJ
ejpam-6459	43	10	soft	soft	ADJ
ejpam-6459	43	11	γ	γ	NOUN
ejpam-6459	43	12	-	-	PUNCT
ejpam-6459	43	13	semigroups	semigroup	NOUN
ejpam-6459	43	14	,	,	PUNCT
ejpam-6459	43	15	combining	combine	VERB
ejpam-6459	43	16	bfss	bfss	NOUN
ejpam-6459	43	17	and	and	CCONJ
ejpam-6459	43	18	sss	sss	VERB
ejpam-6459	43	19	within	within	ADP
ejpam-6459	43	20	γ	γ	PROPN
ejpam-6459	43	21	-	-	PUNCT
ejpam-6459	43	22	semigroup	semigroup	ADJ
ejpam-6459	43	23	structures	structure	NOUN
ejpam-6459	43	24	.	.	PUNCT
ejpam-6459	44	1	their	their	PRON
ejpam-6459	44	2	work	work	NOUN
ejpam-6459	44	3	laid	lay	VERB
ejpam-6459	44	4	foundational	foundational	ADJ
ejpam-6459	44	5	properties	property	NOUN
ejpam-6459	44	6	and	and	CCONJ
ejpam-6459	44	7	extended	extend	VERB
ejpam-6459	44	8	algebraic	algebraic	ADJ
ejpam-6459	44	9	models	model	NOUN
ejpam-6459	44	10	for	for	ADP
ejpam-6459	44	11	handling	handle	VERB
ejpam-6459	44	12	dual	dual	ADJ
ejpam-6459	44	13	-	-	PUNCT
ejpam-6459	44	14	sided	sided	ADJ
ejpam-6459	44	15	uncertainty	uncertainty	NOUN
ejpam-6459	44	16	in	in	ADP
ejpam-6459	44	17	structured	structured	ADJ
ejpam-6459	44	18	environments	environment	NOUN
ejpam-6459	44	19	.	.	PUNCT
ejpam-6459	45	1	yang	yang	PROPN
ejpam-6459	45	2	and	and	CCONJ
ejpam-6459	45	3	li	li	PROPN
ejpam-6459	46	1	[	[	X
ejpam-6459	46	2	14	14	NUM
ejpam-6459	46	3	]	]	PUNCT
ejpam-6459	46	4	introduced	introduce	VERB
ejpam-6459	46	5	bipolar	bipolar	ADJ
ejpam-6459	46	6	-	-	PUNCT
ejpam-6459	46	7	value	value	NOUN
ejpam-6459	46	8	fuzzy	fuzzy	ADJ
ejpam-6459	46	9	soft	soft	ADJ
ejpam-6459	46	10	sets	set	NOUN
ejpam-6459	46	11	as	as	ADP
ejpam-6459	46	12	a	a	DET
ejpam-6459	46	13	hybrid	hybrid	ADJ
ejpam-6459	46	14	model	model	NOUN
ejpam-6459	46	15	combining	combine	VERB
ejpam-6459	46	16	the	the	DET
ejpam-6459	46	17	strengths	strength	NOUN
ejpam-6459	46	18	of	of	ADP
ejpam-6459	46	19	bipolar	bipolar	ADJ
ejpam-6459	46	20	fuzzy	fuzzy	ADJ
ejpam-6459	46	21	logic	logic	NOUN
ejpam-6459	46	22	and	and	CCONJ
ejpam-6459	46	23	soft	soft	ADJ
ejpam-6459	46	24	set	set	NOUN
ejpam-6459	46	25	theory	theory	NOUN
ejpam-6459	46	26	.	.	PUNCT
ejpam-6459	47	1	some	some	DET
ejpam-6459	47	2	authors	author	NOUN
ejpam-6459	47	3	have	have	AUX
ejpam-6459	47	4	examined	examine	VERB
ejpam-6459	47	5	the	the	DET
ejpam-6459	47	6	algebraic	algebraic	ADJ
ejpam-6459	47	7	properties	property	NOUN
ejpam-6459	47	8	of	of	ADP
ejpam-6459	47	9	fuzzy	fuzzy	ADJ
ejpam-6459	47	10	soft	soft	ADJ
ejpam-6459	47	11	sets	set	NOUN
ejpam-6459	47	12	(	(	PUNCT
ejpam-6459	47	13	fsss	fsss	PROPN
ejpam-6459	47	14	)	)	PUNCT
ejpam-6459	47	15	.	.	PUNCT
ejpam-6459	48	1	first	first	ADV
ejpam-6459	48	2	,	,	PUNCT
ejpam-6459	48	3	fsss	fsss	PROPN
ejpam-6459	48	4	were	be	AUX
ejpam-6459	48	5	defined	define	VERB
ejpam-6459	48	6	,	,	PUNCT
ejpam-6459	48	7	and	and	CCONJ
ejpam-6459	48	8	some	some	DET
ejpam-6459	48	9	findings	finding	NOUN
ejpam-6459	48	10	were	be	AUX
ejpam-6459	48	11	established	establish	VERB
ejpam-6459	48	12	by	by	ADP
ejpam-6459	48	13	maji	maji	PROPN
ejpam-6459	48	14	et	et	PROPN
ejpam-6459	48	15	al	al	PROPN
ejpam-6459	48	16	.	.	PUNCT
ejpam-6459	49	1	[	[	X
ejpam-6459	49	2	15	15	NUM
ejpam-6459	49	3	]	]	PUNCT
ejpam-6459	49	4	.	.	PUNCT
ejpam-6459	50	1	fuzzy	fuzzy	ADJ
ejpam-6459	50	2	soft	soft	ADJ
ejpam-6459	50	3	groups	group	NOUN
ejpam-6459	50	4	were	be	AUX
ejpam-6459	50	5	determined	determine	VERB
ejpam-6459	50	6	by	by	ADP
ejpam-6459	50	7	liu	liu	PROPN
ejpam-6459	50	8	et	et	PROPN
ejpam-6459	50	9	al	al	PROPN
ejpam-6459	50	10	.	.	PUNCT
ejpam-6459	51	1	[	[	X
ejpam-6459	51	2	16	16	NUM
ejpam-6459	51	3	]	]	PUNCT
ejpam-6459	51	4	.	.	PUNCT
ejpam-6459	52	1	fuzzy	fuzzy	ADJ
ejpam-6459	52	2	soft	soft	ADJ
ejpam-6459	52	3	boolean	boolean	ADJ
ejpam-6459	52	4	rings	ring	NOUN
ejpam-6459	52	5	were	be	AUX
ejpam-6459	52	6	represented	represent	VERB
ejpam-6459	52	7	by	by	ADP
ejpam-6459	52	8	rao	rao	PROPN
ejpam-6459	52	9	et	et	PROPN
ejpam-6459	52	10	al	al	PROPN
ejpam-6459	52	11	.	.	PUNCT
ejpam-6459	53	1	[	[	X
ejpam-6459	53	2	17	17	NUM
ejpam-6459	53	3	]	]	PUNCT
ejpam-6459	53	4	.	.	PUNCT
ejpam-6459	54	1	rao	rao	PROPN
ejpam-6459	54	2	et	et	PROPN
ejpam-6459	54	3	al	al	PROPN
ejpam-6459	54	4	.	.	PUNCT
ejpam-6459	55	1	[	[	X
ejpam-6459	55	2	18	18	NUM
ejpam-6459	55	3	]	]	PUNCT
ejpam-6459	55	4	explored	explore	VERB
ejpam-6459	55	5	the	the	DET
ejpam-6459	55	6	structure	structure	NOUN
ejpam-6459	55	7	of	of	ADP
ejpam-6459	55	8	soft	soft	ADJ
ejpam-6459	55	9	boolean	boolean	ADJ
ejpam-6459	55	10	near	near	ADJ
ejpam-6459	55	11	-	-	PUNCT
ejpam-6459	55	12	rings	ring	NOUN
ejpam-6459	55	13	,	,	PUNCT
ejpam-6459	55	14	extending	extend	VERB
ejpam-6459	55	15	classical	classical	ADJ
ejpam-6459	55	16	near	near	ADJ
ejpam-6459	55	17	-	-	PUNCT
ejpam-6459	55	18	ring	ring	NOUN
ejpam-6459	55	19	theory	theory	NOUN
ejpam-6459	55	20	through	through	ADP
ejpam-6459	55	21	the	the	DET
ejpam-6459	55	22	lens	lens	NOUN
ejpam-6459	55	23	of	of	ADP
ejpam-6459	55	24	ss	ss	PRON
ejpam-6459	55	25	theory	theory	NOUN
ejpam-6459	55	26	.	.	PUNCT
ejpam-6459	56	1	aygünoǧlu	aygünoǧlu	X
ejpam-6459	56	2	and	and	CCONJ
ejpam-6459	56	3	aygün	aygün	NOUN
ejpam-6459	56	4	[	[	X
ejpam-6459	56	5	19	19	NUM
ejpam-6459	56	6	]	]	PUNCT
ejpam-6459	56	7	introduced	introduce	VERB
ejpam-6459	56	8	the	the	DET
ejpam-6459	56	9	concept	concept	NOUN
ejpam-6459	56	10	of	of	ADP
ejpam-6459	56	11	fuzzy	fuzzy	ADJ
ejpam-6459	56	12	soft	soft	ADJ
ejpam-6459	56	13	groups	group	NOUN
ejpam-6459	56	14	.	.	PUNCT
ejpam-6459	57	1	feng	feng	PROPN
ejpam-6459	57	2	et	et	PROPN
ejpam-6459	57	3	al	al	PROPN
ejpam-6459	57	4	.	.	PUNCT
ejpam-6459	58	1	[	[	X
ejpam-6459	58	2	20	20	NUM
ejpam-6459	58	3	]	]	PUNCT
ejpam-6459	58	4	introduced	introduce	VERB
ejpam-6459	58	5	the	the	DET
ejpam-6459	58	6	concept	concept	NOUN
ejpam-6459	58	7	of	of	ADP
ejpam-6459	58	8	soft	soft	ADJ
ejpam-6459	58	9	semirings	semiring	NOUN
ejpam-6459	58	10	.	.	PUNCT
ejpam-6459	59	1	i̇nan	i̇nan	PROPN
ejpam-6459	59	2	and	and	CCONJ
ejpam-6459	59	3	öztürk	öztürk	NOUN
ejpam-6459	60	1	[	[	X
ejpam-6459	60	2	21	21	NUM
ejpam-6459	60	3	]	]	PUNCT
ejpam-6459	60	4	introduced	introduce	VERB
ejpam-6459	60	5	the	the	DET
ejpam-6459	60	6	concepts	concept	NOUN
ejpam-6459	60	7	of	of	ADP
ejpam-6459	60	8	fuzzy	fuzzy	ADJ
ejpam-6459	60	9	soft	soft	ADJ
ejpam-6459	60	10	rings	ring	NOUN
ejpam-6459	60	11	and	and	CCONJ
ejpam-6459	60	12	(	(	PUNCT
ejpam-6459	60	13	∈,∈	∈,∈	X
ejpam-6459	60	14	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-6459	60	15	soft	soft	ADJ
ejpam-6459	60	16	subrings	subring	NOUN
ejpam-6459	60	17	.	.	PUNCT
ejpam-6459	61	1	jun	jun	PROPN
ejpam-6459	62	1	[	[	X
ejpam-6459	62	2	22	22	NUM
ejpam-6459	62	3	]	]	PUNCT
ejpam-6459	62	4	developed	develop	VERB
ejpam-6459	62	5	the	the	DET
ejpam-6459	62	6	theory	theory	NOUN
ejpam-6459	62	7	of	of	ADP
ejpam-6459	62	8	soft	soft	ADJ
ejpam-6459	62	9	bck	bck	NOUN
ejpam-6459	62	10	/	/	SYM
ejpam-6459	62	11	bci	bci	NOUN
ejpam-6459	62	12	-	-	PUNCT
ejpam-6459	62	13	algebras	algebras	X
ejpam-6459	62	14	.	.	PUNCT
ejpam-6459	63	1	kazancı	kazancı	PROPN
ejpam-6459	63	2	et	et	PROPN
ejpam-6459	63	3	al	al	PROPN
ejpam-6459	63	4	.	.	PUNCT
ejpam-6459	64	1	[	[	X
ejpam-6459	64	2	23	23	NUM
ejpam-6459	64	3	]	]	PUNCT
ejpam-6459	64	4	proposed	propose	VERB
ejpam-6459	64	5	the	the	DET
ejpam-6459	64	6	concept	concept	NOUN
ejpam-6459	64	7	of	of	ADP
ejpam-6459	64	8	soft	soft	ADJ
ejpam-6459	64	9	bch	bch	NOUN
ejpam-6459	64	10	-	-	PUNCT
ejpam-6459	64	11	algebras	algebras	PROPN
ejpam-6459	64	12	.	.	PUNCT
ejpam-6459	65	1	rao	rao	PROPN
ejpam-6459	65	2	et	et	PROPN
ejpam-6459	65	3	al	al	PROPN
ejpam-6459	65	4	.	.	PUNCT
ejpam-6459	66	1	[	[	X
ejpam-6459	66	2	24	24	NUM
ejpam-6459	66	3	]	]	PUNCT
ejpam-6459	66	4	introduced	introduce	VERB
ejpam-6459	66	5	the	the	DET
ejpam-6459	66	6	concept	concept	NOUN
ejpam-6459	66	7	of	of	ADP
ejpam-6459	66	8	soft	soft	ADJ
ejpam-6459	66	9	intersection	intersection	NOUN
ejpam-6459	66	10	boolean	boolean	ADJ
ejpam-6459	66	11	near	near	ADJ
ejpam-6459	66	12	-	-	PUNCT
ejpam-6459	66	13	rings	ring	NOUN
ejpam-6459	66	14	,	,	PUNCT
ejpam-6459	66	15	highlighting	highlight	VERB
ejpam-6459	66	16	their	their	PRON
ejpam-6459	66	17	structural	structural	ADJ
ejpam-6459	66	18	properties	property	NOUN
ejpam-6459	66	19	and	and	CCONJ
ejpam-6459	66	20	practical	practical	ADJ
ejpam-6459	66	21	relevance	relevance	NOUN
ejpam-6459	66	22	.	.	PUNCT
ejpam-6459	67	1	rao	rao	NOUN
ejpam-6459	67	2	et	et	PROPN
ejpam-6459	67	3	al	al	PROPN
ejpam-6459	67	4	.	.	PUNCT
ejpam-6459	68	1	[	[	X
ejpam-6459	68	2	25	25	NUM
ejpam-6459	68	3	]	]	PUNCT
ejpam-6459	68	4	proposed	propose	VERB
ejpam-6459	68	5	the	the	DET
ejpam-6459	68	6	(	(	PUNCT
ejpam-6459	68	7	∈,∈	∈,∈	X
ejpam-6459	68	8	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-6459	68	9	soft	soft	ADJ
ejpam-6459	68	10	boolean	boolean	ADJ
ejpam-6459	68	11	nearrings	nearring	NOUN
ejpam-6459	68	12	as	as	ADP
ejpam-6459	68	13	an	an	DET
ejpam-6459	68	14	extension	extension	NOUN
ejpam-6459	68	15	of	of	ADP
ejpam-6459	68	16	fuzzy	fuzzy	ADJ
ejpam-6459	68	17	soft	soft	ADJ
ejpam-6459	68	18	algebraic	algebraic	ADJ
ejpam-6459	68	19	structures	structure	NOUN
ejpam-6459	68	20	.	.	PUNCT
ejpam-6459	69	1	rao	rao	NOUN
ejpam-6459	69	2	et	et	PROPN
ejpam-6459	69	3	al	al	PROPN
ejpam-6459	69	4	.	.	PUNCT
ejpam-6459	70	1	[	[	X
ejpam-6459	70	2	26	26	NUM
ejpam-6459	70	3	]	]	PUNCT
ejpam-6459	70	4	developed	develop	VERB
ejpam-6459	70	5	fuzzy	fuzzy	ADJ
ejpam-6459	70	6	soft	soft	ADJ
ejpam-6459	70	7	boolean	boolean	ADJ
ejpam-6459	70	8	near	near	ADJ
ejpam-6459	70	9	-	-	PUNCT
ejpam-6459	70	10	rings	ring	NOUN
ejpam-6459	70	11	and	and	CCONJ
ejpam-6459	70	12	their	their	PRON
ejpam-6459	70	13	idealistic	idealistic	ADJ
ejpam-6459	70	14	variants	variant	NOUN
ejpam-6459	70	15	,	,	PUNCT
ejpam-6459	70	16	enriching	enrich	VERB
ejpam-6459	70	17	the	the	DET
ejpam-6459	70	18	algebraic	algebraic	ADJ
ejpam-6459	70	19	foundation	foundation	NOUN
ejpam-6459	70	20	for	for	ADP
ejpam-6459	70	21	soft	soft	ADJ
ejpam-6459	70	22	computing	computing	NOUN
ejpam-6459	70	23	by	by	ADP
ejpam-6459	70	24	formalizing	formalize	VERB
ejpam-6459	70	25	new	new	ADJ
ejpam-6459	70	26	structures	structure	NOUN
ejpam-6459	70	27	and	and	CCONJ
ejpam-6459	70	28	operations	operation	NOUN
ejpam-6459	70	29	under	under	ADP
ejpam-6459	70	30	fuzzy	fuzzy	ADJ
ejpam-6459	70	31	logic	logic	NOUN
ejpam-6459	70	32	.	.	PUNCT
ejpam-6459	71	1	rao	rao	PROPN
ejpam-6459	71	2	g.	g.	PROPN
ejpam-6459	71	3	s.	s.	PROPN
ejpam-6459	71	4	rao	rao	PROPN
ejpam-6459	71	5	et	et	PROPN
ejpam-6459	71	6	al	al	PROPN
ejpam-6459	71	7	.	.	PUNCT
ejpam-6459	71	8	/	/	SYM
ejpam-6459	71	9	eur	eur	PROPN
ejpam-6459	71	10	.	.	PUNCT
ejpam-6459	72	1	j.	j.	PROPN
ejpam-6459	72	2	pure	pure	PROPN
ejpam-6459	72	3	appl	appl	PROPN
ejpam-6459	72	4	.	.	PROPN
ejpam-6459	72	5	math	math	PROPN
ejpam-6459	72	6	,	,	PUNCT
ejpam-6459	72	7	18	18	NUM
ejpam-6459	72	8	(	(	PUNCT
ejpam-6459	72	9	3	3	NUM
ejpam-6459	72	10	)	)	PUNCT
ejpam-6459	72	11	(	(	PUNCT
ejpam-6459	72	12	2025	2025	NUM
ejpam-6459	72	13	)	)	PUNCT
ejpam-6459	72	14	,	,	PUNCT
ejpam-6459	72	15	6459	6459	NUM
ejpam-6459	72	16	3	3	NUM
ejpam-6459	72	17	of	of	ADP
ejpam-6459	72	18	16	16	NUM
ejpam-6459	72	19	et	et	NOUN
ejpam-6459	72	20	al	al	PROPN
ejpam-6459	72	21	.	.	PUNCT
ejpam-6459	73	1	[	[	X
ejpam-6459	73	2	27	27	NUM
ejpam-6459	73	3	]	]	PUNCT
ejpam-6459	73	4	presented	present	VERB
ejpam-6459	73	5	intuitionistic	intuitionistic	ADJ
ejpam-6459	73	6	fuzzy	fuzzy	ADJ
ejpam-6459	73	7	soft	soft	ADJ
ejpam-6459	73	8	boolean	boolean	ADJ
ejpam-6459	73	9	rings	ring	NOUN
ejpam-6459	73	10	,	,	PUNCT
ejpam-6459	73	11	combining	combine	VERB
ejpam-6459	73	12	intuitionistic	intuitionistic	ADJ
ejpam-6459	73	13	fuzzy	fuzzy	ADJ
ejpam-6459	73	14	logic	logic	NOUN
ejpam-6459	73	15	with	with	ADP
ejpam-6459	73	16	soft	soft	ADJ
ejpam-6459	73	17	ring	ring	NOUN
ejpam-6459	73	18	structures	structure	NOUN
ejpam-6459	73	19	to	to	PART
ejpam-6459	73	20	better	well	ADV
ejpam-6459	73	21	handle	handle	VERB
ejpam-6459	73	22	dual	dual	ADJ
ejpam-6459	73	23	uncertainty	uncertainty	NOUN
ejpam-6459	73	24	.	.	PUNCT
ejpam-6459	74	1	rao	rao	NOUN
ejpam-6459	74	2	et	et	PROPN
ejpam-6459	74	3	al	al	PROPN
ejpam-6459	74	4	.	.	PUNCT
ejpam-6459	75	1	[	[	X
ejpam-6459	75	2	28	28	NUM
ejpam-6459	75	3	]	]	PUNCT
ejpam-6459	75	4	introduced	introduce	VERB
ejpam-6459	75	5	(	(	PUNCT
ejpam-6459	75	6	∈,∈	∈,∈	X
ejpam-6459	75	7	∨qk)-intuitionistic	∨qk)-intuitionistic	ADJ
ejpam-6459	75	8	fuzzy	fuzzy	ADJ
ejpam-6459	75	9	soft	soft	ADJ
ejpam-6459	75	10	boolean	boolean	ADJ
ejpam-6459	75	11	near	near	ADJ
ejpam-6459	75	12	-	-	PUNCT
ejpam-6459	75	13	rings	ring	NOUN
ejpam-6459	75	14	,	,	PUNCT
ejpam-6459	75	15	enhancing	enhance	VERB
ejpam-6459	75	16	soft	soft	ADJ
ejpam-6459	75	17	algebraic	algebraic	ADJ
ejpam-6459	75	18	frameworks	framework	NOUN
ejpam-6459	75	19	by	by	ADP
ejpam-6459	75	20	integrating	integrate	VERB
ejpam-6459	75	21	intuitionistic	intuitionistic	ADJ
ejpam-6459	75	22	fuzzy	fuzzy	ADJ
ejpam-6459	75	23	logic	logic	NOUN
ejpam-6459	75	24	with	with	ADP
ejpam-6459	75	25	generalized	generalized	ADJ
ejpam-6459	75	26	membership	membership	NOUN
ejpam-6459	75	27	concepts	concept	NOUN
ejpam-6459	75	28	.	.	PUNCT
ejpam-6459	76	1	in	in	ADP
ejpam-6459	76	2	this	this	DET
ejpam-6459	76	3	work	work	NOUN
ejpam-6459	76	4	,	,	PUNCT
ejpam-6459	76	5	we	we	PRON
ejpam-6459	76	6	introduce	introduce	VERB
ejpam-6459	76	7	the	the	DET
ejpam-6459	76	8	notions	notion	NOUN
ejpam-6459	76	9	of	of	ADP
ejpam-6459	76	10	bfsbrs	bfsbrs	NOUN
ejpam-6459	76	11	and	and	CCONJ
ejpam-6459	76	12	bfsis	bfsis	NOUN
ejpam-6459	76	13	within	within	ADP
ejpam-6459	76	14	the	the	DET
ejpam-6459	76	15	framework	framework	NOUN
ejpam-6459	76	16	of	of	ADP
ejpam-6459	76	17	boolean	boolean	ADJ
ejpam-6459	76	18	rings	ring	NOUN
ejpam-6459	76	19	.	.	PUNCT
ejpam-6459	77	1	we	we	PRON
ejpam-6459	77	2	investigate	investigate	VERB
ejpam-6459	77	3	their	their	PRON
ejpam-6459	77	4	fundamental	fundamental	ADJ
ejpam-6459	77	5	algebraic	algebraic	ADJ
ejpam-6459	77	6	properties	property	NOUN
ejpam-6459	77	7	,	,	PUNCT
ejpam-6459	77	8	aiming	aim	VERB
ejpam-6459	77	9	to	to	PART
ejpam-6459	77	10	provide	provide	VERB
ejpam-6459	77	11	a	a	DET
ejpam-6459	77	12	theoretical	theoretical	ADJ
ejpam-6459	77	13	contribution	contribution	NOUN
ejpam-6459	77	14	to	to	ADP
ejpam-6459	77	15	soft	soft	ADJ
ejpam-6459	77	16	algebraic	algebraic	ADJ
ejpam-6459	77	17	structures	structure	NOUN
ejpam-6459	77	18	and	and	CCONJ
ejpam-6459	77	19	an	an	DET
ejpam-6459	77	20	accessible	accessible	ADJ
ejpam-6459	77	21	platform	platform	NOUN
ejpam-6459	77	22	for	for	ADP
ejpam-6459	77	23	students	student	NOUN
ejpam-6459	77	24	engaging	engage	VERB
ejpam-6459	77	25	in	in	ADP
ejpam-6459	77	26	early	early	ADJ
ejpam-6459	77	27	-	-	PUNCT
ejpam-6459	77	28	stage	stage	NOUN
ejpam-6459	77	29	mathematical	mathematical	ADJ
ejpam-6459	77	30	research	research	NOUN
ejpam-6459	77	31	.	.	PUNCT
ejpam-6459	78	1	2	2	X
ejpam-6459	78	2	.	.	X
ejpam-6459	78	3	preliminaries	preliminary	NOUN
ejpam-6459	78	4	this	this	DET
ejpam-6459	78	5	section	section	NOUN
ejpam-6459	78	6	outlines	outline	VERB
ejpam-6459	78	7	the	the	DET
ejpam-6459	78	8	fundamental	fundamental	ADJ
ejpam-6459	78	9	concepts	concept	NOUN
ejpam-6459	78	10	necessary	necessary	ADJ
ejpam-6459	78	11	for	for	ADP
ejpam-6459	78	12	developing	develop	VERB
ejpam-6459	78	13	bfsbrs	bfsbr	VERB
ejpam-6459	78	14	.	.	PUNCT
ejpam-6459	79	1	we	we	PRON
ejpam-6459	79	2	briefly	briefly	ADV
ejpam-6459	79	3	review	review	VERB
ejpam-6459	79	4	bfss	bfss	NUM
ejpam-6459	79	5	,	,	PUNCT
ejpam-6459	79	6	sss	sss	NOUN
ejpam-6459	79	7	,	,	PUNCT
ejpam-6459	79	8	and	and	CCONJ
ejpam-6459	79	9	their	their	PRON
ejpam-6459	79	10	integration	integration	NOUN
ejpam-6459	79	11	into	into	ADP
ejpam-6459	79	12	bfsss	bfsss	NOUN
ejpam-6459	79	13	,	,	PUNCT
ejpam-6459	79	14	along	along	ADP
ejpam-6459	79	15	with	with	ADP
ejpam-6459	79	16	basic	basic	ADJ
ejpam-6459	79	17	operations	operation	NOUN
ejpam-6459	79	18	.	.	PUNCT
ejpam-6459	80	1	these	these	DET
ejpam-6459	80	2	preliminaries	preliminary	NOUN
ejpam-6459	80	3	provide	provide	VERB
ejpam-6459	80	4	the	the	DET
ejpam-6459	80	5	algebraic	algebraic	ADJ
ejpam-6459	80	6	foundation	foundation	NOUN
ejpam-6459	80	7	for	for	ADP
ejpam-6459	80	8	the	the	DET
ejpam-6459	80	9	constructions	construction	NOUN
ejpam-6459	80	10	and	and	CCONJ
ejpam-6459	80	11	results	result	NOUN
ejpam-6459	80	12	that	that	PRON
ejpam-6459	80	13	follow	follow	VERB
ejpam-6459	80	14	.	.	PUNCT
ejpam-6459	81	1	definition	definition	NOUN
ejpam-6459	81	2	1	1	NUM
ejpam-6459	81	3	.	.	PUNCT
ejpam-6459	82	1	[	[	X
ejpam-6459	82	2	7	7	X
ejpam-6459	82	3	]	]	PUNCT
ejpam-6459	82	4	in	in	ADP
ejpam-6459	82	5	the	the	DET
ejpam-6459	82	6	universe	universe	NOUN
ejpam-6459	82	7	g	g	NOUN
ejpam-6459	82	8	,	,	PUNCT
ejpam-6459	82	9	a	a	DET
ejpam-6459	82	10	bipolar	bipolar	ADJ
ejpam-6459	82	11	fuzzy	fuzzy	ADJ
ejpam-6459	82	12	set	set	NOUN
ejpam-6459	82	13	(	(	PUNCT
ejpam-6459	82	14	bfs	bfs	NOUN
ejpam-6459	82	15	)	)	PUNCT
ejpam-6459	82	16	u	u	NOUN
ejpam-6459	82	17	is	be	AUX
ejpam-6459	82	18	an	an	DET
ejpam-6459	82	19	entity	entity	NOUN
ejpam-6459	82	20	with	with	ADP
ejpam-6459	82	21	the	the	DET
ejpam-6459	82	22	form	form	NOUN
ejpam-6459	82	23	u	u	NOUN
ejpam-6459	82	24	=	=	X
ejpam-6459	82	25	{	{	PUNCT
ejpam-6459	82	26	(	(	PUNCT
ejpam-6459	82	27	ρ	ρ	PROPN
ejpam-6459	82	28	,	,	PUNCT
ejpam-6459	82	29	j+	j+	NUM
ejpam-6459	82	30	u	u	PROPN
ejpam-6459	82	31	(	(	PUNCT
ejpam-6459	82	32	ρ	ρ	PROPN
ejpam-6459	82	33	)	)	PUNCT
ejpam-6459	82	34	,	,	PUNCT
ejpam-6459	82	35	j−	j−	PROPN
ejpam-6459	82	36	u	u	PROPN
ejpam-6459	82	37	(	(	PUNCT
ejpam-6459	82	38	ρ	ρ	NOUN
ejpam-6459	82	39	)	)	PUNCT
ejpam-6459	82	40	)	)	PUNCT
ejpam-6459	82	41	:	:	PUNCT
ejpam-6459	83	1	ρ	ρ	PROPN
ejpam-6459	83	2	∈	∈	PROPN
ejpam-6459	83	3	g	g	NOUN
ejpam-6459	83	4	}	}	PUNCT
ejpam-6459	83	5	.	.	PUNCT
ejpam-6459	84	1	in	in	ADP
ejpam-6459	84	2	this	this	DET
ejpam-6459	84	3	case	case	NOUN
ejpam-6459	84	4	,	,	PUNCT
ejpam-6459	84	5	j+	j+	NUM
ejpam-6459	84	6	u	u	PROPN
ejpam-6459	84	7	(	(	PUNCT
ejpam-6459	84	8	ρ	ρ	NOUN
ejpam-6459	84	9	)	)	PUNCT
ejpam-6459	84	10	denotes	denote	NOUN
ejpam-6459	84	11	how	how	SCONJ
ejpam-6459	84	12	satisfied	satisfied	ADJ
ejpam-6459	84	13	an	an	DET
ejpam-6459	84	14	element	element	NOUN
ejpam-6459	84	15	ρ	ρ	NOUN
ejpam-6459	84	16	is	be	AUX
ejpam-6459	84	17	with	with	ADP
ejpam-6459	84	18	the	the	DET
ejpam-6459	84	19	property	property	NOUN
ejpam-6459	84	20	that	that	PRON
ejpam-6459	84	21	corresponds	correspond	VERB
ejpam-6459	84	22	to	to	ADP
ejpam-6459	84	23	a	a	DET
ejpam-6459	84	24	bfs	bfs	NOUN
ejpam-6459	84	25	u	u	NOUN
ejpam-6459	84	26	=	=	PRON
ejpam-6459	84	27	{	{	PUNCT
ejpam-6459	84	28	(	(	PUNCT
ejpam-6459	84	29	ρ	ρ	PROPN
ejpam-6459	84	30	,	,	PUNCT
ejpam-6459	84	31	j+	j+	NUM
ejpam-6459	84	32	u	u	PROPN
ejpam-6459	84	33	(	(	PUNCT
ejpam-6459	84	34	ρ	ρ	PROPN
ejpam-6459	84	35	)	)	PUNCT
ejpam-6459	84	36	,	,	PUNCT
ejpam-6459	84	37	j−	j−	PROPN
ejpam-6459	84	38	u	u	PROPN
ejpam-6459	84	39	(	(	PUNCT
ejpam-6459	84	40	ρ	ρ	NOUN
ejpam-6459	84	41	)	)	PUNCT
ejpam-6459	84	42	)	)	PUNCT
ejpam-6459	84	43	:	:	PUNCT
ejpam-6459	85	1	ρ	ρ	PROPN
ejpam-6459	85	2	∈	∈	PROPN
ejpam-6459	85	3	g	g	NOUN
ejpam-6459	85	4	}	}	PUNCT
ejpam-6459	85	5	,	,	PUNCT
ejpam-6459	85	6	and	and	CCONJ
ejpam-6459	85	7	j−	j−	PROPN
ejpam-6459	85	8	u	u	PROPN
ejpam-6459	85	9	(	(	PUNCT
ejpam-6459	85	10	ρ	ρ	NOUN
ejpam-6459	85	11	)	)	PUNCT
ejpam-6459	85	12	denotes	denote	NOUN
ejpam-6459	85	13	how	how	SCONJ
ejpam-6459	85	14	satisfied	satisfied	ADJ
ejpam-6459	85	15	ρ	ρ	PROPN
ejpam-6459	85	16	is	be	AUX
ejpam-6459	85	17	with	with	ADP
ejpam-6459	85	18	an	an	DET
ejpam-6459	85	19	implicit	implicit	ADJ
ejpam-6459	85	20	counter	counter	NOUN
ejpam-6459	85	21	property	property	NOUN
ejpam-6459	85	22	of	of	ADP
ejpam-6459	85	23	u	u	NOUN
ejpam-6459	85	24	=	=	PUNCT
ejpam-6459	85	25	{	{	PUNCT
ejpam-6459	85	26	(	(	PUNCT
ejpam-6459	85	27	ρ	ρ	PROPN
ejpam-6459	85	28	,	,	PUNCT
ejpam-6459	85	29	j+	j+	NUM
ejpam-6459	85	30	u	u	PROPN
ejpam-6459	85	31	(	(	PUNCT
ejpam-6459	85	32	ρ	ρ	PROPN
ejpam-6459	85	33	)	)	PUNCT
ejpam-6459	85	34	,	,	PUNCT
ejpam-6459	85	35	j−	j−	PROPN
ejpam-6459	85	36	u	u	PROPN
ejpam-6459	85	37	(	(	PUNCT
ejpam-6459	85	38	ρ	ρ	NOUN
ejpam-6459	85	39	)	)	PUNCT
ejpam-6459	85	40	)	)	PUNCT
ejpam-6459	85	41	:	:	PUNCT
ejpam-6459	86	1	ρ	ρ	PROPN
ejpam-6459	86	2	∈	∈	PROPN
ejpam-6459	86	3	g	g	NOUN
ejpam-6459	86	4	}	}	PUNCT
ejpam-6459	86	5	.	.	PUNCT
ejpam-6459	87	1	the	the	DET
ejpam-6459	87	2	bfs	bfs	NOUN
ejpam-6459	87	3	u	u	NOUN
ejpam-6459	87	4	=	=	PRON
ejpam-6459	87	5	{	{	PUNCT
ejpam-6459	87	6	(	(	PUNCT
ejpam-6459	87	7	ρ	ρ	PROPN
ejpam-6459	87	8	,	,	PUNCT
ejpam-6459	87	9	j+	j+	NUM
ejpam-6459	87	10	u	u	PROPN
ejpam-6459	87	11	(	(	PUNCT
ejpam-6459	87	12	ρ	ρ	PROPN
ejpam-6459	87	13	)	)	PUNCT
ejpam-6459	87	14	,	,	PUNCT
ejpam-6459	87	15	j−	j−	PROPN
ejpam-6459	87	16	u	u	PROPN
ejpam-6459	87	17	(	(	PUNCT
ejpam-6459	87	18	ρ	ρ	NOUN
ejpam-6459	87	19	)	)	PUNCT
ejpam-6459	87	20	)	)	PUNCT
ejpam-6459	87	21	:	:	PUNCT
ejpam-6459	88	1	ρ	ρ	PROPN
ejpam-6459	88	2	∈	∈	PROPN
ejpam-6459	88	3	g	g	NOUN
ejpam-6459	88	4	}	}	PUNCT
ejpam-6459	88	5	has	have	AUX
ejpam-6459	88	6	been	be	AUX
ejpam-6459	88	7	denoted	denote	VERB
ejpam-6459	88	8	by	by	ADP
ejpam-6459	88	9	the	the	DET
ejpam-6459	88	10	symbol	symbol	NOUN
ejpam-6459	88	11	u	u	NOUN
ejpam-6459	88	12	=	=	PUNCT
ejpam-6459	88	13	(	(	PUNCT
ejpam-6459	88	14	j+	j+	NUM
ejpam-6459	88	15	u	u	PROPN
ejpam-6459	88	16	,	,	PUNCT
ejpam-6459	88	17	j−	j−	PROPN
ejpam-6459	88	18	u	u	NOUN
ejpam-6459	88	19	)	)	PUNCT
ejpam-6459	88	20	for	for	ADP
ejpam-6459	88	21	simplicity	simplicity	NOUN
ejpam-6459	88	22	’s	’s	PART
ejpam-6459	88	23	sake	sake	NOUN
ejpam-6459	88	24	.	.	PUNCT
ejpam-6459	89	1	definition	definition	NOUN
ejpam-6459	89	2	2	2	NUM
ejpam-6459	89	3	.	.	PUNCT
ejpam-6459	90	1	[	[	X
ejpam-6459	90	2	7	7	X
ejpam-6459	90	3	]	]	PUNCT
ejpam-6459	90	4	for	for	ADP
ejpam-6459	90	5	two	two	NUM
ejpam-6459	90	6	bfss	bfss	NOUN
ejpam-6459	90	7	u	u	NOUN
ejpam-6459	90	8	=	=	PUNCT
ejpam-6459	90	9	(	(	PUNCT
ejpam-6459	90	10	j+	j+	NUM
ejpam-6459	90	11	u	u	PROPN
ejpam-6459	90	12	,	,	PUNCT
ejpam-6459	90	13	j−	j−	PROPN
ejpam-6459	90	14	u	u	NOUN
ejpam-6459	90	15	)	)	PUNCT
ejpam-6459	90	16	and	and	CCONJ
ejpam-6459	90	17	v	v	X
ejpam-6459	90	18	=	=	SYM
ejpam-6459	90	19	(	(	PUNCT
ejpam-6459	90	20	j+	j+	PROPN
ejpam-6459	90	21	v	v	NOUN
ejpam-6459	90	22	,	,	PUNCT
ejpam-6459	90	23	j−	j−	PROPN
ejpam-6459	90	24	v	v	NOUN
ejpam-6459	90	25	)	)	PUNCT
ejpam-6459	90	26	in	in	ADP
ejpam-6459	90	27	the	the	DET
ejpam-6459	90	28	universe	universe	NOUN
ejpam-6459	90	29	g	g	NOUN
ejpam-6459	90	30	,	,	PUNCT
ejpam-6459	90	31	(	(	PUNCT
ejpam-6459	90	32	i	i	NOUN
ejpam-6459	90	33	)	)	PUNCT
ejpam-6459	90	34	u	u	NOUN
ejpam-6459	90	35	⊆	⊆	NUM
ejpam-6459	90	36	v	v	NOUN
ejpam-6459	90	37	indicates	indicate	VERB
ejpam-6459	90	38	that	that	SCONJ
ejpam-6459	90	39	j+	j+	PROPN
ejpam-6459	90	40	u	u	PROPN
ejpam-6459	90	41	(	(	PUNCT
ejpam-6459	90	42	ρ	ρ	PROPN
ejpam-6459	90	43	)	)	PUNCT
ejpam-6459	90	44	≥	≥	NOUN
ejpam-6459	90	45	j+	j+	NUM
ejpam-6459	90	46	v	v	PROPN
ejpam-6459	90	47	(	(	PUNCT
ejpam-6459	90	48	ρ	ρ	NOUN
ejpam-6459	90	49	)	)	PUNCT
ejpam-6459	90	50	and	and	CCONJ
ejpam-6459	90	51	j−	j−	PROPN
ejpam-6459	90	52	u	u	PROPN
ejpam-6459	90	53	(	(	PUNCT
ejpam-6459	90	54	ρ	ρ	NOUN
ejpam-6459	90	55	)	)	PUNCT
ejpam-6459	90	56	≤	≤	PUNCT
ejpam-6459	90	57	j−	j−	PROPN
ejpam-6459	90	58	v	v	PROPN
ejpam-6459	90	59	(	(	PUNCT
ejpam-6459	90	60	ρ	ρ	NOUN
ejpam-6459	90	61	)	)	PUNCT
ejpam-6459	90	62	for	for	ADP
ejpam-6459	90	63	all	all	PRON
ejpam-6459	90	64	ρ	ρ	NOUN
ejpam-6459	90	65	∈	∈	PROPN
ejpam-6459	90	66	g	g	PROPN
ejpam-6459	90	67	(	(	PUNCT
ejpam-6459	90	68	ii	ii	PROPN
ejpam-6459	90	69	)	)	PUNCT
ejpam-6459	90	70	u	u	NOUN
ejpam-6459	90	71	∪	∪	ADJ
ejpam-6459	90	72	v	v	NOUN
ejpam-6459	90	73	=	=	SYM
ejpam-6459	90	74	{	{	PUNCT
ejpam-6459	90	75	(	(	PUNCT
ejpam-6459	90	76	ρ	ρ	PROPN
ejpam-6459	90	77	,	,	PUNCT
ejpam-6459	90	78	max{j+	max{j+	ADJ
ejpam-6459	90	79	u	u	NOUN
ejpam-6459	90	80	(	(	PUNCT
ejpam-6459	90	81	ρ	ρ	PROPN
ejpam-6459	90	82	)	)	PUNCT
ejpam-6459	90	83	,	,	PUNCT
ejpam-6459	90	84	j+	j+	NUM
ejpam-6459	90	85	v	v	NOUN
ejpam-6459	90	86	(	(	PUNCT
ejpam-6459	90	87	ρ)},min{j−	ρ)},min{j−	NUM
ejpam-6459	90	88	u	u	NOUN
ejpam-6459	90	89	(	(	PUNCT
ejpam-6459	90	90	ρ	ρ	PROPN
ejpam-6459	90	91	)	)	PUNCT
ejpam-6459	90	92	,	,	PUNCT
ejpam-6459	90	93	j−	j−	PROPN
ejpam-6459	90	94	v	v	PROPN
ejpam-6459	90	95	(	(	PUNCT
ejpam-6459	90	96	ρ	ρ	NOUN
ejpam-6459	90	97	)	)	PUNCT
ejpam-6459	90	98	}	}	PUNCT
ejpam-6459	90	99	)	)	PUNCT
ejpam-6459	90	100	:	:	PUNCT
ejpam-6459	90	101	ρ	ρ	PROPN
ejpam-6459	90	102	∈	∈	PROPN
ejpam-6459	90	103	g	g	NOUN
ejpam-6459	90	104	}	}	PUNCT
ejpam-6459	90	105	=	=	SYM
ejpam-6459	90	106	(	(	PUNCT
ejpam-6459	90	107	j+	j+	NUM
ejpam-6459	90	108	u	u	PROPN
ejpam-6459	90	109	(	(	PUNCT
ejpam-6459	90	110	ρ	ρ	NOUN
ejpam-6459	90	111	)	)	PUNCT
ejpam-6459	90	112	∪	∪	NOUN
ejpam-6459	90	113	j+	j+	NUM
ejpam-6459	90	114	v	v	PROPN
ejpam-6459	90	115	(	(	PUNCT
ejpam-6459	90	116	ρ	ρ	PROPN
ejpam-6459	90	117	)	)	PUNCT
ejpam-6459	90	118	,	,	PUNCT
ejpam-6459	90	119	j−	j−	PROPN
ejpam-6459	90	120	u	u	PROPN
ejpam-6459	90	121	(	(	PUNCT
ejpam-6459	90	122	ρ	ρ	NOUN
ejpam-6459	90	123	)	)	PUNCT
ejpam-6459	90	124	∩	∩	NOUN
ejpam-6459	90	125	j−	j−	PROPN
ejpam-6459	90	126	v	v	PROPN
ejpam-6459	90	127	(	(	PUNCT
ejpam-6459	90	128	ρ	ρ	NOUN
ejpam-6459	90	129	)	)	PUNCT
ejpam-6459	90	130	)	)	PUNCT
ejpam-6459	90	131	(	(	PUNCT
ejpam-6459	90	132	iii	iii	X
ejpam-6459	90	133	)	)	PUNCT
ejpam-6459	90	134	u	u	NOUN
ejpam-6459	90	135	∩	∩	NOUN
ejpam-6459	90	136	v	v	NOUN
ejpam-6459	90	137	=	=	SYM
ejpam-6459	90	138	{	{	PUNCT
ejpam-6459	90	139	(	(	PUNCT
ejpam-6459	90	140	ρ	ρ	NOUN
ejpam-6459	90	141	,	,	PUNCT
ejpam-6459	90	142	min{j+	min{j+	ADJ
ejpam-6459	90	143	u	u	NOUN
ejpam-6459	90	144	(	(	PUNCT
ejpam-6459	90	145	ρ	ρ	PROPN
ejpam-6459	90	146	)	)	PUNCT
ejpam-6459	90	147	,	,	PUNCT
ejpam-6459	90	148	j+	j+	NUM
ejpam-6459	90	149	v	v	PROPN
ejpam-6459	90	150	(	(	PUNCT
ejpam-6459	90	151	ρ)},max{j−	ρ)},max{j−	PROPN
ejpam-6459	90	152	u	u	NOUN
ejpam-6459	90	153	(	(	PUNCT
ejpam-6459	90	154	ρ	ρ	PROPN
ejpam-6459	90	155	)	)	PUNCT
ejpam-6459	90	156	,	,	PUNCT
ejpam-6459	90	157	j−	j−	PROPN
ejpam-6459	90	158	v	v	PROPN
ejpam-6459	90	159	(	(	PUNCT
ejpam-6459	90	160	ρ	ρ	NOUN
ejpam-6459	90	161	)	)	PUNCT
ejpam-6459	90	162	}	}	PUNCT
ejpam-6459	90	163	)	)	PUNCT
ejpam-6459	90	164	:	:	PUNCT
ejpam-6459	91	1	ρ	ρ	PROPN
ejpam-6459	91	2	∈	∈	PROPN
ejpam-6459	91	3	g	g	NOUN
ejpam-6459	91	4	}	}	PUNCT
ejpam-6459	91	5	=	=	SYM
ejpam-6459	91	6	(	(	PUNCT
ejpam-6459	91	7	j+	j+	NUM
ejpam-6459	91	8	u	u	PROPN
ejpam-6459	91	9	(	(	PUNCT
ejpam-6459	91	10	ρ	ρ	NOUN
ejpam-6459	91	11	)	)	PUNCT
ejpam-6459	91	12	∩	∩	NOUN
ejpam-6459	91	13	j+	j+	NUM
ejpam-6459	91	14	v	v	PROPN
ejpam-6459	91	15	(	(	PUNCT
ejpam-6459	91	16	ρ	ρ	PROPN
ejpam-6459	91	17	)	)	PUNCT
ejpam-6459	91	18	,	,	PUNCT
ejpam-6459	91	19	j−	j−	PROPN
ejpam-6459	91	20	u	u	PROPN
ejpam-6459	91	21	(	(	PUNCT
ejpam-6459	91	22	ρ	ρ	NOUN
ejpam-6459	91	23	)	)	PUNCT
ejpam-6459	91	24	∪	∪	NOUN
ejpam-6459	91	25	j−	j−	PROPN
ejpam-6459	91	26	v	v	NOUN
ejpam-6459	91	27	(	(	PUNCT
ejpam-6459	91	28	ρ	ρ	NOUN
ejpam-6459	91	29	)	)	PUNCT
ejpam-6459	91	30	)	)	PUNCT
ejpam-6459	91	31	.	.	PUNCT
ejpam-6459	92	1	remark	remark	PROPN
ejpam-6459	92	2	1	1	NUM
ejpam-6459	92	3	.	.	PUNCT
ejpam-6459	93	1	[	[	X
ejpam-6459	93	2	7	7	X
ejpam-6459	93	3	]	]	PUNCT
ejpam-6459	93	4	for	for	ADP
ejpam-6459	93	5	the	the	DET
ejpam-6459	93	6	above	above	ADJ
ejpam-6459	93	7	definitions	definition	NOUN
ejpam-6459	93	8	,	,	PUNCT
ejpam-6459	93	9	we	we	PRON
ejpam-6459	93	10	can	can	AUX
ejpam-6459	93	11	verify	verify	VERB
ejpam-6459	93	12	that	that	SCONJ
ejpam-6459	93	13	(	(	PUNCT
ejpam-6459	93	14	i	i	NOUN
ejpam-6459	93	15	)	)	PUNCT
ejpam-6459	93	16	j+	j+	NUM
ejpam-6459	93	17	u∪v	u∪v	INTJ
ejpam-6459	93	18	(	(	PUNCT
ejpam-6459	93	19	ρ	ρ	NOUN
ejpam-6459	93	20	)	)	PUNCT
ejpam-6459	93	21	=	=	PUNCT
ejpam-6459	93	22	j+	j+	NUM
ejpam-6459	93	23	u	u	NOUN
ejpam-6459	93	24	(	(	PUNCT
ejpam-6459	93	25	ρ	ρ	NOUN
ejpam-6459	93	26	)	)	PUNCT
ejpam-6459	93	27	∪	∪	NOUN
ejpam-6459	93	28	j+	j+	NUM
ejpam-6459	93	29	v	v	PROPN
ejpam-6459	93	30	(	(	PUNCT
ejpam-6459	93	31	ρ	ρ	NOUN
ejpam-6459	93	32	)	)	PUNCT
ejpam-6459	93	33	(	(	PUNCT
ejpam-6459	93	34	ii	ii	NOUN
ejpam-6459	93	35	)	)	PUNCT
ejpam-6459	93	36	j−	j−	VERB
ejpam-6459	93	37	u∪v	u∪v	INTJ
ejpam-6459	93	38	(	(	PUNCT
ejpam-6459	93	39	ρ	ρ	NOUN
ejpam-6459	93	40	)	)	PUNCT
ejpam-6459	93	41	=	=	PUNCT
ejpam-6459	93	42	j−	j−	PROPN
ejpam-6459	93	43	u	u	PROPN
ejpam-6459	93	44	(	(	PUNCT
ejpam-6459	93	45	ρ	ρ	NOUN
ejpam-6459	93	46	)	)	PUNCT
ejpam-6459	93	47	∩	∩	NOUN
ejpam-6459	93	48	j−	j−	PROPN
ejpam-6459	93	49	v	v	PROPN
ejpam-6459	93	50	(	(	PUNCT
ejpam-6459	93	51	ρ	ρ	NOUN
ejpam-6459	93	52	)	)	PUNCT
ejpam-6459	93	53	(	(	PUNCT
ejpam-6459	93	54	iii	iii	NOUN
ejpam-6459	93	55	)	)	PUNCT
ejpam-6459	93	56	j+	j+	NUM
ejpam-6459	93	57	u∩v	u∩v	PROPN
ejpam-6459	93	58	(	(	PUNCT
ejpam-6459	93	59	ρ	ρ	NOUN
ejpam-6459	93	60	)	)	PUNCT
ejpam-6459	93	61	=	=	PUNCT
ejpam-6459	93	62	j+	j+	NUM
ejpam-6459	93	63	u	u	PROPN
ejpam-6459	93	64	(	(	PUNCT
ejpam-6459	93	65	ρ	ρ	NOUN
ejpam-6459	93	66	)	)	PUNCT
ejpam-6459	93	67	∩	∩	NOUN
ejpam-6459	93	68	j+	j+	NUM
ejpam-6459	93	69	v	v	PROPN
ejpam-6459	93	70	(	(	PUNCT
ejpam-6459	93	71	ρ	ρ	NOUN
ejpam-6459	93	72	)	)	PUNCT
ejpam-6459	93	73	(	(	PUNCT
ejpam-6459	93	74	iv	iv	X
ejpam-6459	93	75	)	)	PUNCT
ejpam-6459	93	76	j−	j−	PROPN
ejpam-6459	93	77	u∩v	u∩v	PROPN
ejpam-6459	93	78	(	(	PUNCT
ejpam-6459	93	79	ρ	ρ	NOUN
ejpam-6459	93	80	)	)	PUNCT
ejpam-6459	93	81	=	=	PUNCT
ejpam-6459	93	82	j−	j−	PROPN
ejpam-6459	93	83	u	u	PROPN
ejpam-6459	93	84	(	(	PUNCT
ejpam-6459	93	85	ρ	ρ	NOUN
ejpam-6459	93	86	)	)	PUNCT
ejpam-6459	93	87	∪	∪	NOUN
ejpam-6459	93	88	j−	j−	PROPN
ejpam-6459	93	89	v	v	NOUN
ejpam-6459	93	90	(	(	PUNCT
ejpam-6459	93	91	ρ	ρ	NOUN
ejpam-6459	93	92	)	)	PUNCT
ejpam-6459	93	93	.	.	PUNCT
ejpam-6459	94	1	definition	definition	NOUN
ejpam-6459	94	2	3	3	NUM
ejpam-6459	94	3	.	.	PUNCT
ejpam-6459	95	1	[	[	X
ejpam-6459	95	2	3	3	X
ejpam-6459	95	3	]	]	X
ejpam-6459	95	4	let	let	VERB
ejpam-6459	95	5	e	e	PRON
ejpam-6459	95	6	be	be	AUX
ejpam-6459	95	7	the	the	DET
ejpam-6459	95	8	collection	collection	NOUN
ejpam-6459	95	9	of	of	ADP
ejpam-6459	95	10	parameters	parameter	NOUN
ejpam-6459	95	11	and	and	CCONJ
ejpam-6459	95	12	g	g	NOUN
ejpam-6459	95	13	be	be	AUX
ejpam-6459	95	14	the	the	DET
ejpam-6459	95	15	initial	initial	ADJ
ejpam-6459	95	16	universe	universe	NOUN
ejpam-6459	95	17	.	.	PUNCT
ejpam-6459	96	1	the	the	DET
ejpam-6459	96	2	pair	pair	NOUN
ejpam-6459	96	3	(	(	PUNCT
ejpam-6459	96	4	j	j	NOUN
ejpam-6459	96	5	,	,	PUNCT
ejpam-6459	96	6	u	u	NOUN
ejpam-6459	96	7	)	)	PUNCT
ejpam-6459	96	8	is	be	AUX
ejpam-6459	96	9	called	call	VERB
ejpam-6459	96	10	a	a	DET
ejpam-6459	96	11	soft	soft	ADJ
ejpam-6459	96	12	set	set	NOUN
ejpam-6459	96	13	(	(	PUNCT
ejpam-6459	96	14	ss	ss	NOUN
ejpam-6459	96	15	)	)	PUNCT
ejpam-6459	96	16	over	over	ADP
ejpam-6459	96	17	g	g	PROPN
ejpam-6459	96	18	if	if	SCONJ
ejpam-6459	96	19	u	u	NOUN
ejpam-6459	96	20	is	be	AUX
ejpam-6459	96	21	a	a	DET
ejpam-6459	96	22	non	non	ADJ
ejpam-6459	96	23	-	-	ADJ
ejpam-6459	96	24	empty	empty	ADJ
ejpam-6459	96	25	subset	subset	NOUN
ejpam-6459	96	26	of	of	ADP
ejpam-6459	96	27	e.	e.	PROPN
ejpam-6459	97	1	the	the	DET
ejpam-6459	97	2	mapping	mapping	PROPN
ejpam-6459	97	3	j	j	PROPN
ejpam-6459	97	4	:	:	PUNCT
ejpam-6459	97	5	u	u	X
ejpam-6459	97	6	→	→	X
ejpam-6459	97	7	p	p	X
ejpam-6459	97	8	(	(	PUNCT
ejpam-6459	97	9	g	g	NOUN
ejpam-6459	97	10	)	)	PUNCT
ejpam-6459	97	11	is	be	AUX
ejpam-6459	97	12	used	use	VERB
ejpam-6459	97	13	to	to	PART
ejpam-6459	97	14	define	define	VERB
ejpam-6459	97	15	j	j	PROPN
ejpam-6459	97	16	.	.	PUNCT
ejpam-6459	98	1	definition	definition	NOUN
ejpam-6459	98	2	4	4	NUM
ejpam-6459	98	3	.	.	PUNCT
ejpam-6459	99	1	[	[	X
ejpam-6459	99	2	15	15	NUM
ejpam-6459	99	3	]	]	PUNCT
ejpam-6459	99	4	let	let	VERB
ejpam-6459	99	5	e	e	PRON
ejpam-6459	99	6	be	be	AUX
ejpam-6459	99	7	the	the	DET
ejpam-6459	99	8	collection	collection	NOUN
ejpam-6459	99	9	of	of	ADP
ejpam-6459	99	10	parameters	parameter	NOUN
ejpam-6459	99	11	and	and	CCONJ
ejpam-6459	99	12	g	g	NOUN
ejpam-6459	99	13	be	be	VERB
ejpam-6459	99	14	the	the	DET
ejpam-6459	99	15	initial	initial	ADJ
ejpam-6459	99	16	universe	universe	NOUN
ejpam-6459	99	17	set	set	NOUN
ejpam-6459	99	18	.	.	PUNCT
ejpam-6459	100	1	the	the	DET
ejpam-6459	100	2	pair	pair	NOUN
ejpam-6459	100	3	(	(	PUNCT
ejpam-6459	100	4	j	j	NOUN
ejpam-6459	100	5	,	,	PUNCT
ejpam-6459	100	6	u	u	NOUN
ejpam-6459	100	7	)	)	PUNCT
ejpam-6459	100	8	is	be	AUX
ejpam-6459	100	9	referred	refer	VERB
ejpam-6459	100	10	to	to	ADP
ejpam-6459	100	11	as	as	ADP
ejpam-6459	100	12	a	a	DET
ejpam-6459	100	13	fuzzy	fuzzy	ADJ
ejpam-6459	100	14	soft	soft	ADJ
ejpam-6459	100	15	set	set	NOUN
ejpam-6459	100	16	(	(	PUNCT
ejpam-6459	100	17	fss	fss	NOUN
ejpam-6459	100	18	)	)	PUNCT
ejpam-6459	100	19	over	over	ADP
ejpam-6459	100	20	g	g	PROPN
ejpam-6459	100	21	if	if	SCONJ
ejpam-6459	100	22	u	u	NOUN
ejpam-6459	100	23	is	be	AUX
ejpam-6459	100	24	a	a	DET
ejpam-6459	100	25	non	non	ADJ
ejpam-6459	100	26	-	-	ADJ
ejpam-6459	100	27	empty	empty	ADJ
ejpam-6459	100	28	subset	subset	NOUN
ejpam-6459	100	29	of	of	ADP
ejpam-6459	100	30	e	e	PROPN
ejpam-6459	100	31	and	and	CCONJ
ejpam-6459	100	32	p	p	X
ejpam-6459	100	33	(	(	PUNCT
ejpam-6459	100	34	fs(g	fs(g	NOUN
ejpam-6459	100	35	)	)	PUNCT
ejpam-6459	100	36	)	)	PUNCT
ejpam-6459	100	37	is	be	AUX
ejpam-6459	100	38	the	the	DET
ejpam-6459	100	39	collection	collection	NOUN
ejpam-6459	100	40	of	of	ADP
ejpam-6459	100	41	all	all	DET
ejpam-6459	100	42	fss	fss	NOUN
ejpam-6459	100	43	of	of	ADP
ejpam-6459	100	44	g.	g.	PROPN
ejpam-6459	100	45	j	j	PROPN
ejpam-6459	100	46	is	be	AUX
ejpam-6459	100	47	a	a	DET
ejpam-6459	100	48	mapping	mapping	NOUN
ejpam-6459	100	49	that	that	PRON
ejpam-6459	100	50	is	be	AUX
ejpam-6459	100	51	given	give	VERB
ejpam-6459	100	52	by	by	ADP
ejpam-6459	100	53	the	the	DET
ejpam-6459	100	54	expression	expression	NOUN
ejpam-6459	101	1	j	j	NOUN
ejpam-6459	101	2	:	:	PUNCT
ejpam-6459	101	3	u	u	X
ejpam-6459	101	4	→	→	X
ejpam-6459	101	5	p	p	X
ejpam-6459	101	6	(	(	PUNCT
ejpam-6459	101	7	fs(g	fs(g	NOUN
ejpam-6459	101	8	)	)	PUNCT
ejpam-6459	101	9	)	)	PUNCT
ejpam-6459	101	10	.	.	PUNCT
ejpam-6459	102	1	g.	g.	PROPN
ejpam-6459	102	2	s.	s.	PROPN
ejpam-6459	102	3	rao	rao	PROPN
ejpam-6459	102	4	et	et	PROPN
ejpam-6459	102	5	al	al	PROPN
ejpam-6459	102	6	.	.	PUNCT
ejpam-6459	102	7	/	/	SYM
ejpam-6459	102	8	eur	eur	PROPN
ejpam-6459	102	9	.	.	PUNCT
ejpam-6459	103	1	j.	j.	PROPN
ejpam-6459	103	2	pure	pure	PROPN
ejpam-6459	103	3	appl	appl	PROPN
ejpam-6459	103	4	.	.	PROPN
ejpam-6459	103	5	math	math	PROPN
ejpam-6459	103	6	,	,	PUNCT
ejpam-6459	103	7	18	18	NUM
ejpam-6459	103	8	(	(	PUNCT
ejpam-6459	103	9	3	3	NUM
ejpam-6459	103	10	)	)	PUNCT
ejpam-6459	103	11	(	(	PUNCT
ejpam-6459	103	12	2025	2025	NUM
ejpam-6459	103	13	)	)	PUNCT
ejpam-6459	103	14	,	,	PUNCT
ejpam-6459	103	15	6459	6459	NUM
ejpam-6459	103	16	4	4	NUM
ejpam-6459	103	17	of	of	ADP
ejpam-6459	103	18	16	16	NUM
ejpam-6459	103	19	definition	definition	NOUN
ejpam-6459	103	20	5	5	NUM
ejpam-6459	103	21	.	.	PUNCT
ejpam-6459	104	1	[	[	X
ejpam-6459	104	2	14	14	NUM
ejpam-6459	104	3	]	]	PUNCT
ejpam-6459	104	4	let	let	VERB
ejpam-6459	104	5	e	e	PRON
ejpam-6459	104	6	be	be	AUX
ejpam-6459	104	7	the	the	DET
ejpam-6459	104	8	collection	collection	NOUN
ejpam-6459	104	9	of	of	ADP
ejpam-6459	104	10	parameters	parameter	NOUN
ejpam-6459	104	11	and	and	CCONJ
ejpam-6459	104	12	g	g	NOUN
ejpam-6459	104	13	be	be	VERB
ejpam-6459	104	14	the	the	DET
ejpam-6459	104	15	initial	initial	ADJ
ejpam-6459	104	16	universe	universe	NOUN
ejpam-6459	104	17	set	set	NOUN
ejpam-6459	104	18	.	.	PUNCT
ejpam-6459	105	1	let	let	VERB
ejpam-6459	105	2	bf	bf	NOUN
ejpam-6459	105	3	(	(	PUNCT
ejpam-6459	105	4	g	g	NOUN
ejpam-6459	105	5	)	)	PUNCT
ejpam-6459	105	6	be	be	VERB
ejpam-6459	105	7	the	the	DET
ejpam-6459	105	8	set	set	NOUN
ejpam-6459	105	9	of	of	ADP
ejpam-6459	105	10	all	all	DET
ejpam-6459	105	11	bfss	bfss	NOUN
ejpam-6459	105	12	of	of	ADP
ejpam-6459	105	13	g	g	NOUN
ejpam-6459	105	14	and	and	CCONJ
ejpam-6459	105	15	u	u	NOUN
ejpam-6459	105	16	⊆	⊆	NUM
ejpam-6459	105	17	e.	e.	PROPN
ejpam-6459	105	18	when	when	SCONJ
ejpam-6459	105	19	j	j	PROPN
ejpam-6459	105	20	is	be	AUX
ejpam-6459	105	21	provided	provide	VERB
ejpam-6459	105	22	by	by	ADP
ejpam-6459	105	23	mapping	map	VERB
ejpam-6459	105	24	j	j	PROPN
ejpam-6459	105	25	:	:	PUNCT
ejpam-6459	105	26	u	u	PROPN
ejpam-6459	105	27	→	→	SYM
ejpam-6459	105	28	bf	bf	X
ejpam-6459	105	29	(	(	PUNCT
ejpam-6459	105	30	g	g	NOUN
ejpam-6459	105	31	)	)	PUNCT
ejpam-6459	105	32	,	,	PUNCT
ejpam-6459	105	33	then	then	ADV
ejpam-6459	105	34	a	a	DET
ejpam-6459	105	35	pair	pair	NOUN
ejpam-6459	105	36	(	(	PUNCT
ejpam-6459	105	37	j	j	NOUN
ejpam-6459	105	38	,	,	PUNCT
ejpam-6459	105	39	u	u	NOUN
ejpam-6459	105	40	)	)	PUNCT
ejpam-6459	105	41	is	be	AUX
ejpam-6459	105	42	referred	refer	VERB
ejpam-6459	105	43	to	to	ADP
ejpam-6459	105	44	as	as	ADP
ejpam-6459	105	45	a	a	DET
ejpam-6459	105	46	bipolar	bipolar	ADJ
ejpam-6459	105	47	fuzzy	fuzzy	ADJ
ejpam-6459	105	48	soft	soft	ADJ
ejpam-6459	105	49	set	set	NOUN
ejpam-6459	105	50	(	(	PUNCT
ejpam-6459	105	51	bfss	bfss	NOUN
ejpam-6459	105	52	)	)	PUNCT
ejpam-6459	105	53	over	over	ADP
ejpam-6459	105	54	g.	g.	PROPN
ejpam-6459	106	1	it	it	PRON
ejpam-6459	106	2	is	be	AUX
ejpam-6459	106	3	defined	define	VERB
ejpam-6459	106	4	as	as	ADP
ejpam-6459	106	5	(	(	PUNCT
ejpam-6459	106	6	j	j	PROPN
ejpam-6459	106	7	,	,	PUNCT
ejpam-6459	106	8	u	u	NOUN
ejpam-6459	106	9	)	)	PUNCT
ejpam-6459	106	10	=	=	SYM
ejpam-6459	106	11	{	{	PUNCT
ejpam-6459	106	12	(	(	PUNCT
ejpam-6459	106	13	ρ	ρ	PROPN
ejpam-6459	106	14	,	,	PUNCT
ejpam-6459	106	15	j+	j+	NUM
ejpam-6459	106	16	u	u	PROPN
ejpam-6459	106	17	(	(	PUNCT
ejpam-6459	106	18	ρ	ρ	PROPN
ejpam-6459	106	19	)	)	PUNCT
ejpam-6459	106	20	,	,	PUNCT
ejpam-6459	106	21	j−	j−	PROPN
ejpam-6459	106	22	u	u	PROPN
ejpam-6459	106	23	(	(	PUNCT
ejpam-6459	106	24	ρ	ρ	NOUN
ejpam-6459	106	25	)	)	PUNCT
ejpam-6459	106	26	)	)	PUNCT
ejpam-6459	106	27	:	:	PUNCT
ejpam-6459	107	1	ρ	ρ	PROPN
ejpam-6459	107	2	∈	∈	PROPN
ejpam-6459	107	3	g	g	PROPN
ejpam-6459	107	4	&	&	CCONJ
ejpam-6459	107	5	u	u	PROPN
ejpam-6459	107	6	∈	∈	PROPN
ejpam-6459	107	7	u	u	NOUN
ejpam-6459	107	8	}	}	PUNCT
ejpam-6459	107	9	.	.	PUNCT
ejpam-6459	108	1	for	for	ADP
ejpam-6459	108	2	any	any	DET
ejpam-6459	108	3	u	u	PROPN
ejpam-6459	108	4	∈	∈	PROPN
ejpam-6459	108	5	u	u	PROPN
ejpam-6459	108	6	,	,	PUNCT
ejpam-6459	108	7	j(u	j(u	PROPN
ejpam-6459	108	8	)	)	PUNCT
ejpam-6459	108	9	=	=	PRON
ejpam-6459	108	10	{	{	PUNCT
ejpam-6459	108	11	(	(	PUNCT
ejpam-6459	108	12	ρ	ρ	PROPN
ejpam-6459	108	13	,	,	PUNCT
ejpam-6459	108	14	j+	j+	NUM
ejpam-6459	108	15	u	u	PROPN
ejpam-6459	108	16	(	(	PUNCT
ejpam-6459	108	17	ρ	ρ	PROPN
ejpam-6459	108	18	)	)	PUNCT
ejpam-6459	108	19	,	,	PUNCT
ejpam-6459	108	20	j−	j−	PROPN
ejpam-6459	108	21	u	u	PROPN
ejpam-6459	108	22	(	(	PUNCT
ejpam-6459	108	23	ρ	ρ	NOUN
ejpam-6459	108	24	)	)	PUNCT
ejpam-6459	108	25	)	)	PUNCT
ejpam-6459	108	26	:	:	PUNCT
ejpam-6459	109	1	ρ	ρ	PROPN
ejpam-6459	109	2	∈	∈	PROPN
ejpam-6459	109	3	g	g	NOUN
ejpam-6459	109	4	}	}	PUNCT
ejpam-6459	109	5	=	=	SYM
ejpam-6459	109	6	{	{	PUNCT
ejpam-6459	109	7	j+	j+	NUM
ejpam-6459	109	8	u	u	PROPN
ejpam-6459	109	9	(	(	PUNCT
ejpam-6459	109	10	ρ	ρ	PROPN
ejpam-6459	109	11	)	)	PUNCT
ejpam-6459	109	12	,	,	PUNCT
ejpam-6459	109	13	j−	j−	PROPN
ejpam-6459	109	14	u	u	PROPN
ejpam-6459	109	15	(	(	PUNCT
ejpam-6459	109	16	ρ	ρ	NOUN
ejpam-6459	109	17	)	)	PUNCT
ejpam-6459	109	18	}	}	PUNCT
ejpam-6459	109	19	.	.	PUNCT
ejpam-6459	110	1	definition	definition	NOUN
ejpam-6459	110	2	6	6	NUM
ejpam-6459	110	3	.	.	PUNCT
ejpam-6459	111	1	[	[	X
ejpam-6459	111	2	14	14	NUM
ejpam-6459	111	3	]	]	PUNCT
ejpam-6459	111	4	the	the	DET
ejpam-6459	111	5	complement	complement	NOUN
ejpam-6459	111	6	of	of	ADP
ejpam-6459	111	7	a	a	DET
ejpam-6459	111	8	bfss	bfss	NOUN
ejpam-6459	111	9	(	(	PUNCT
ejpam-6459	111	10	j	j	NOUN
ejpam-6459	111	11	,	,	PUNCT
ejpam-6459	111	12	u	u	NOUN
ejpam-6459	111	13	)	)	PUNCT
ejpam-6459	111	14	is	be	AUX
ejpam-6459	111	15	symbolized	symbolize	VERB
ejpam-6459	111	16	by	by	ADP
ejpam-6459	111	17	(	(	PUNCT
ejpam-6459	111	18	j	j	NOUN
ejpam-6459	111	19	,	,	PUNCT
ejpam-6459	111	20	u)c	u)c	PUNCT
ejpam-6459	111	21	and	and	CCONJ
ejpam-6459	111	22	it	it	PRON
ejpam-6459	111	23	is	be	AUX
ejpam-6459	111	24	described	describe	VERB
ejpam-6459	111	25	as	as	ADP
ejpam-6459	111	26	(	(	PUNCT
ejpam-6459	111	27	j	j	NOUN
ejpam-6459	111	28	,	,	PUNCT
ejpam-6459	111	29	u)c	u)c	ADJ
ejpam-6459	111	30	=	=	SYM
ejpam-6459	111	31	{	{	PUNCT
ejpam-6459	111	32	(	(	PUNCT
ejpam-6459	111	33	ρ	ρ	PROPN
ejpam-6459	111	34	,	,	PUNCT
ejpam-6459	111	35	1−	1−	NUM
ejpam-6459	111	36	j+	j+	NUM
ejpam-6459	111	37	u	u	NOUN
ejpam-6459	111	38	(	(	PUNCT
ejpam-6459	111	39	ρ),−1−	ρ),−1−	ADJ
ejpam-6459	111	40	j−	j−	PROPN
ejpam-6459	111	41	u	u	PROPN
ejpam-6459	111	42	(	(	PUNCT
ejpam-6459	111	43	ρ	ρ	NOUN
ejpam-6459	111	44	)	)	PUNCT
ejpam-6459	111	45	)	)	PUNCT
ejpam-6459	111	46	:	:	PUNCT
ejpam-6459	112	1	ρ	ρ	PROPN
ejpam-6459	112	2	∈	∈	PROPN
ejpam-6459	112	3	g	g	NOUN
ejpam-6459	112	4	}	}	PUNCT
ejpam-6459	112	5	.	.	PUNCT
ejpam-6459	113	1	definition	definition	NOUN
ejpam-6459	113	2	7	7	NUM
ejpam-6459	113	3	.	.	PUNCT
ejpam-6459	114	1	[	[	X
ejpam-6459	114	2	14	14	NUM
ejpam-6459	114	3	]	]	PUNCT
ejpam-6459	114	4	for	for	ADP
ejpam-6459	114	5	any	any	DET
ejpam-6459	114	6	two	two	NUM
ejpam-6459	114	7	bfsss	bfsss	NOUN
ejpam-6459	114	8	(	(	PUNCT
ejpam-6459	114	9	j	j	PROPN
ejpam-6459	114	10	,	,	PUNCT
ejpam-6459	114	11	u	u	NOUN
ejpam-6459	114	12	)	)	PUNCT
ejpam-6459	114	13	and	and	CCONJ
ejpam-6459	114	14	(	(	PUNCT
ejpam-6459	114	15	k	k	X
ejpam-6459	114	16	,	,	PUNCT
ejpam-6459	114	17	v	v	NOUN
ejpam-6459	114	18	)	)	PUNCT
ejpam-6459	114	19	over	over	ADP
ejpam-6459	114	20	g	g	PROPN
ejpam-6459	114	21	,	,	PUNCT
ejpam-6459	114	22	then	then	ADV
ejpam-6459	114	23	we	we	PRON
ejpam-6459	114	24	say	say	VERB
ejpam-6459	114	25	that	that	SCONJ
ejpam-6459	114	26	(	(	PUNCT
ejpam-6459	114	27	j	j	NOUN
ejpam-6459	114	28	,	,	PUNCT
ejpam-6459	114	29	u	u	NOUN
ejpam-6459	114	30	)	)	PUNCT
ejpam-6459	114	31	is	be	AUX
ejpam-6459	114	32	a	a	DET
ejpam-6459	114	33	bfs	bfs	NOUN
ejpam-6459	114	34	subset	subset	NOUN
ejpam-6459	114	35	of	of	ADP
ejpam-6459	114	36	(	(	PUNCT
ejpam-6459	114	37	k	k	X
ejpam-6459	114	38	,	,	PUNCT
ejpam-6459	114	39	v	v	NOUN
ejpam-6459	114	40	)	)	PUNCT
ejpam-6459	114	41	if	if	SCONJ
ejpam-6459	114	42	u	u	PROPN
ejpam-6459	114	43	⊆	⊆	NUM
ejpam-6459	114	44	v	v	NOUN
ejpam-6459	114	45	and	and	CCONJ
ejpam-6459	114	46	j(u	j(u	PROPN
ejpam-6459	114	47	)	)	PUNCT
ejpam-6459	114	48	⊆	⊆	NUM
ejpam-6459	114	49	k(u	k(u	NOUN
ejpam-6459	114	50	)	)	PUNCT
ejpam-6459	114	51	,	,	PUNCT
ejpam-6459	114	52	∀u	∀u	NOUN
ejpam-6459	114	53	∈	∈	NOUN
ejpam-6459	114	54	u	u	NOUN
ejpam-6459	114	55	.	.	PUNCT
ejpam-6459	115	1	this	this	PRON
ejpam-6459	115	2	is	be	AUX
ejpam-6459	115	3	written	write	VERB
ejpam-6459	115	4	as	as	ADP
ejpam-6459	115	5	(	(	PUNCT
ejpam-6459	115	6	j	j	PROPN
ejpam-6459	115	7	,	,	PUNCT
ejpam-6459	115	8	u	u	NOUN
ejpam-6459	115	9	)	)	PUNCT
ejpam-6459	115	10	⊆	⊆	NUM
ejpam-6459	115	11	(	(	PUNCT
ejpam-6459	115	12	k	k	NOUN
ejpam-6459	115	13	,	,	PUNCT
ejpam-6459	115	14	v	v	NOUN
ejpam-6459	115	15	)	)	PUNCT
ejpam-6459	115	16	.	.	PUNCT
ejpam-6459	116	1	definition	definition	NOUN
ejpam-6459	116	2	8	8	NUM
ejpam-6459	116	3	.	.	PUNCT
ejpam-6459	117	1	[	[	X
ejpam-6459	117	2	8	8	NUM
ejpam-6459	117	3	,	,	PUNCT
ejpam-6459	117	4	14	14	NUM
ejpam-6459	117	5	]	]	PUNCT
ejpam-6459	117	6	let	let	VERB
ejpam-6459	117	7	(	(	PUNCT
ejpam-6459	117	8	j	j	NOUN
ejpam-6459	117	9	,	,	PUNCT
ejpam-6459	117	10	u	u	NOUN
ejpam-6459	117	11	)	)	PUNCT
ejpam-6459	117	12	and	and	CCONJ
ejpam-6459	117	13	(	(	PUNCT
ejpam-6459	117	14	k	k	X
ejpam-6459	117	15	,	,	PUNCT
ejpam-6459	117	16	v	v	NOUN
ejpam-6459	117	17	)	)	PUNCT
ejpam-6459	117	18	be	be	AUX
ejpam-6459	117	19	two	two	NUM
ejpam-6459	117	20	bfsss	bfsss	NOUN
ejpam-6459	117	21	over	over	ADP
ejpam-6459	117	22	g.	g.	PROPN
ejpam-6459	118	1	then	then	ADV
ejpam-6459	118	2	(	(	PUNCT
ejpam-6459	118	3	j	j	NOUN
ejpam-6459	118	4	,	,	PUNCT
ejpam-6459	118	5	u	u	NOUN
ejpam-6459	118	6	)	)	PUNCT
ejpam-6459	118	7	and	and	CCONJ
ejpam-6459	118	8	(	(	PUNCT
ejpam-6459	118	9	k	k	X
ejpam-6459	118	10	,	,	PUNCT
ejpam-6459	118	11	v	v	NOUN
ejpam-6459	118	12	)	)	PUNCT
ejpam-6459	118	13	,	,	PUNCT
ejpam-6459	118	14	indicated	indicate	VERB
ejpam-6459	118	15	by	by	ADP
ejpam-6459	118	16	(	(	PUNCT
ejpam-6459	118	17	j	j	PROPN
ejpam-6459	118	18	,	,	PUNCT
ejpam-6459	118	19	u	u	NOUN
ejpam-6459	118	20	)	)	PUNCT
ejpam-6459	118	21	∧	∧	PROPN
ejpam-6459	118	22	(	(	PUNCT
ejpam-6459	118	23	k	k	NOUN
ejpam-6459	118	24	,	,	PUNCT
ejpam-6459	118	25	v	v	NOUN
ejpam-6459	118	26	)	)	PUNCT
ejpam-6459	118	27	is	be	AUX
ejpam-6459	118	28	known	know	VERB
ejpam-6459	118	29	as	as	ADP
ejpam-6459	118	30	(	(	PUNCT
ejpam-6459	118	31	j	j	PROPN
ejpam-6459	118	32	,	,	PUNCT
ejpam-6459	118	33	u	u	NOUN
ejpam-6459	118	34	)	)	PUNCT
ejpam-6459	118	35	∧	∧	PROPN
ejpam-6459	118	36	(	(	PUNCT
ejpam-6459	118	37	k	k	NOUN
ejpam-6459	118	38	,	,	PUNCT
ejpam-6459	118	39	v	v	NOUN
ejpam-6459	118	40	)	)	PUNCT
ejpam-6459	118	41	=	=	SYM
ejpam-6459	119	1	(	(	PUNCT
ejpam-6459	119	2	l	l	NOUN
ejpam-6459	119	3	,	,	PUNCT
ejpam-6459	119	4	w	w	NOUN
ejpam-6459	119	5	)	)	PUNCT
ejpam-6459	119	6	where	where	SCONJ
ejpam-6459	119	7	w	w	NOUN
ejpam-6459	119	8	=	=	PUNCT
ejpam-6459	119	9	u	u	NOUN
ejpam-6459	119	10	×	×	NOUN
ejpam-6459	119	11	v	v	NOUN
ejpam-6459	119	12	and	and	CCONJ
ejpam-6459	119	13	l(ρ	l(ρ	PROPN
ejpam-6459	119	14	,	,	PUNCT
ejpam-6459	119	15	τ	τ	X
ejpam-6459	119	16	)	)	PUNCT
ejpam-6459	119	17	=	=	SYM
ejpam-6459	120	1	j(ρ	j(ρ	PROPN
ejpam-6459	120	2	)	)	PUNCT
ejpam-6459	120	3	∩k(τ	∩k(τ	PROPN
ejpam-6459	120	4	)	)	PUNCT
ejpam-6459	120	5	,	,	PUNCT
ejpam-6459	120	6	∀(ρ	∀(ρ	PROPN
ejpam-6459	120	7	,	,	PUNCT
ejpam-6459	120	8	τ	τ	NOUN
ejpam-6459	120	9	)	)	PUNCT
ejpam-6459	120	10	∈	∈	PROPN
ejpam-6459	120	11	w	w	NOUN
ejpam-6459	120	12	=	=	PUNCT
ejpam-6459	120	13	u	u	PROPN
ejpam-6459	120	14	×	×	NOUN
ejpam-6459	120	15	v	v	NOUN
ejpam-6459	120	16	.	.	PUNCT
ejpam-6459	121	1	definition	definition	NOUN
ejpam-6459	121	2	9	9	NUM
ejpam-6459	121	3	.	.	PUNCT
ejpam-6459	122	1	[	[	X
ejpam-6459	122	2	8	8	NUM
ejpam-6459	122	3	,	,	PUNCT
ejpam-6459	122	4	14	14	NUM
ejpam-6459	122	5	]	]	PUNCT
ejpam-6459	122	6	let	let	VERB
ejpam-6459	122	7	(	(	PUNCT
ejpam-6459	122	8	j	j	NOUN
ejpam-6459	122	9	,	,	PUNCT
ejpam-6459	122	10	u	u	NOUN
ejpam-6459	122	11	)	)	PUNCT
ejpam-6459	122	12	and	and	CCONJ
ejpam-6459	122	13	(	(	PUNCT
ejpam-6459	122	14	k	k	X
ejpam-6459	122	15	,	,	PUNCT
ejpam-6459	122	16	v	v	NOUN
ejpam-6459	122	17	)	)	PUNCT
ejpam-6459	122	18	be	be	AUX
ejpam-6459	122	19	two	two	NUM
ejpam-6459	122	20	bfsss	bfsss	NOUN
ejpam-6459	122	21	over	over	ADP
ejpam-6459	122	22	the	the	DET
ejpam-6459	122	23	universe	universe	NOUN
ejpam-6459	122	24	g.	g.	NOUN
ejpam-6459	123	1	then	then	ADV
ejpam-6459	123	2	(	(	PUNCT
ejpam-6459	123	3	j	j	NOUN
ejpam-6459	123	4	,	,	PUNCT
ejpam-6459	123	5	u	u	NOUN
ejpam-6459	123	6	)	)	PUNCT
ejpam-6459	123	7	or	or	CCONJ
ejpam-6459	123	8	(	(	PUNCT
ejpam-6459	123	9	k	k	NOUN
ejpam-6459	123	10	,	,	PUNCT
ejpam-6459	123	11	v	v	NOUN
ejpam-6459	123	12	)	)	PUNCT
ejpam-6459	123	13	,	,	PUNCT
ejpam-6459	123	14	indicated	indicate	VERB
ejpam-6459	123	15	by	by	ADP
ejpam-6459	123	16	(	(	PUNCT
ejpam-6459	123	17	j	j	NOUN
ejpam-6459	123	18	,	,	PUNCT
ejpam-6459	123	19	u)∨(k	u)∨(k	ADJ
ejpam-6459	123	20	,	,	PUNCT
ejpam-6459	123	21	v	v	NOUN
ejpam-6459	123	22	)	)	PUNCT
ejpam-6459	123	23	is	be	AUX
ejpam-6459	123	24	known	know	VERB
ejpam-6459	123	25	as	as	ADP
ejpam-6459	123	26	(	(	PUNCT
ejpam-6459	123	27	j	j	NOUN
ejpam-6459	123	28	,	,	PUNCT
ejpam-6459	123	29	u)∨(k	u)∨(k	ADJ
ejpam-6459	123	30	,	,	PUNCT
ejpam-6459	123	31	v	v	NOUN
ejpam-6459	123	32	)	)	PUNCT
ejpam-6459	123	33	=	=	SYM
ejpam-6459	124	1	(	(	PUNCT
ejpam-6459	124	2	l	l	NOUN
ejpam-6459	124	3	,	,	PUNCT
ejpam-6459	124	4	w	w	NOUN
ejpam-6459	124	5	)	)	PUNCT
ejpam-6459	124	6	where	where	SCONJ
ejpam-6459	124	7	w	w	NOUN
ejpam-6459	124	8	=	=	PUNCT
ejpam-6459	124	9	u	u	NOUN
ejpam-6459	124	10	×	×	NOUN
ejpam-6459	124	11	v	v	NOUN
ejpam-6459	124	12	and	and	CCONJ
ejpam-6459	124	13	l(ρ	l(ρ	PROPN
ejpam-6459	124	14	,	,	PUNCT
ejpam-6459	124	15	τ	τ	X
ejpam-6459	124	16	)	)	PUNCT
ejpam-6459	124	17	=	=	SYM
ejpam-6459	125	1	j(ρ	j(ρ	PROPN
ejpam-6459	125	2	)	)	PUNCT
ejpam-6459	125	3	∪k(τ	∪k(τ	PROPN
ejpam-6459	125	4	)	)	PUNCT
ejpam-6459	125	5	,	,	PUNCT
ejpam-6459	125	6	∀(ρ	∀(ρ	PROPN
ejpam-6459	125	7	,	,	PUNCT
ejpam-6459	125	8	τ	τ	NOUN
ejpam-6459	125	9	)	)	PUNCT
ejpam-6459	125	10	∈	∈	PROPN
ejpam-6459	125	11	w	w	NOUN
ejpam-6459	125	12	=	=	PUNCT
ejpam-6459	125	13	u	u	PROPN
ejpam-6459	125	14	×	×	NOUN
ejpam-6459	125	15	v	v	NOUN
ejpam-6459	125	16	.	.	PUNCT
ejpam-6459	126	1	definition	definition	NOUN
ejpam-6459	126	2	10	10	NUM
ejpam-6459	126	3	.	.	PUNCT
ejpam-6459	127	1	[	[	X
ejpam-6459	127	2	8	8	NUM
ejpam-6459	127	3	,	,	PUNCT
ejpam-6459	127	4	14	14	NUM
ejpam-6459	127	5	]	]	PUNCT
ejpam-6459	127	6	let	let	VERB
ejpam-6459	127	7	(	(	PUNCT
ejpam-6459	127	8	j	j	NOUN
ejpam-6459	127	9	,	,	PUNCT
ejpam-6459	127	10	u	u	NOUN
ejpam-6459	127	11	)	)	PUNCT
ejpam-6459	127	12	and	and	CCONJ
ejpam-6459	127	13	(	(	PUNCT
ejpam-6459	127	14	k	k	X
ejpam-6459	127	15	,	,	PUNCT
ejpam-6459	127	16	v	v	NOUN
ejpam-6459	127	17	)	)	PUNCT
ejpam-6459	127	18	be	be	AUX
ejpam-6459	127	19	two	two	NUM
ejpam-6459	127	20	bfsss	bfsss	NOUN
ejpam-6459	127	21	over	over	ADP
ejpam-6459	127	22	the	the	DET
ejpam-6459	127	23	universe	universe	NOUN
ejpam-6459	127	24	g.	g.	NOUN
ejpam-6459	128	1	then	then	ADV
ejpam-6459	128	2	their	their	PRON
ejpam-6459	128	3	extended	extended	ADJ
ejpam-6459	128	4	union	union	NOUN
ejpam-6459	128	5	is	be	AUX
ejpam-6459	128	6	a	a	DET
ejpam-6459	128	7	bfss	bfss	NOUN
ejpam-6459	128	8	over	over	ADP
ejpam-6459	128	9	g	g	NOUN
ejpam-6459	128	10	indicated	indicate	VERB
ejpam-6459	128	11	by	by	ADP
ejpam-6459	128	12	(	(	PUNCT
ejpam-6459	128	13	j	j	PROPN
ejpam-6459	128	14	,	,	PUNCT
ejpam-6459	128	15	u	u	NOUN
ejpam-6459	128	16	)	)	PUNCT
ejpam-6459	128	17	∪e	∪e	PUNCT
ejpam-6459	129	1	(	(	PUNCT
ejpam-6459	129	2	k	k	X
ejpam-6459	129	3	,	,	PUNCT
ejpam-6459	129	4	v	v	NOUN
ejpam-6459	129	5	)	)	PUNCT
ejpam-6459	129	6	and	and	CCONJ
ejpam-6459	129	7	is	be	AUX
ejpam-6459	129	8	known	know	VERB
ejpam-6459	129	9	as	as	ADP
ejpam-6459	129	10	(	(	PUNCT
ejpam-6459	129	11	j	j	PROPN
ejpam-6459	129	12	,	,	PUNCT
ejpam-6459	129	13	u	u	NOUN
ejpam-6459	129	14	)	)	PUNCT
ejpam-6459	129	15	∪e	∪e	PUNCT
ejpam-6459	129	16	(	(	PUNCT
ejpam-6459	129	17	k	k	X
ejpam-6459	129	18	,	,	PUNCT
ejpam-6459	129	19	v	v	NOUN
ejpam-6459	129	20	)	)	PUNCT
ejpam-6459	129	21	=	=	SYM
ejpam-6459	129	22	(	(	PUNCT
ejpam-6459	129	23	l	l	NOUN
ejpam-6459	129	24	,	,	PUNCT
ejpam-6459	129	25	w	w	NOUN
ejpam-6459	129	26	)	)	PUNCT
ejpam-6459	129	27	,	,	PUNCT
ejpam-6459	129	28	where	where	SCONJ
ejpam-6459	129	29	w	w	NOUN
ejpam-6459	129	30	=	=	SYM
ejpam-6459	129	31	u	u	NOUN
ejpam-6459	129	32	∪	∪	NOUN
ejpam-6459	129	33	v	v	NOUN
ejpam-6459	129	34	and	and	CCONJ
ejpam-6459	129	35	l	l	NOUN
ejpam-6459	129	36	:	:	PUNCT
ejpam-6459	129	37	w	w	X
ejpam-6459	129	38	→	→	SYM
ejpam-6459	129	39	bf	bf	NOUN
ejpam-6459	129	40	(	(	PUNCT
ejpam-6459	129	41	g	g	NOUN
ejpam-6459	129	42	)	)	PUNCT
ejpam-6459	129	43	is	be	AUX
ejpam-6459	129	44	provided	provide	VERB
ejpam-6459	129	45	as	as	ADP
ejpam-6459	129	46	,	,	PUNCT
ejpam-6459	129	47	l(ω	l(ω	PROPN
ejpam-6459	129	48	)	)	PUNCT
ejpam-6459	129	49	=	=	PUNCT
ejpam-6459	130	1			PROPN
ejpam-6459	130	2	j(ω	j(ω	PROPN
ejpam-6459	130	3	)	)	PUNCT
ejpam-6459	130	4	if	if	SCONJ
ejpam-6459	130	5	ω	ω	NUM
ejpam-6459	130	6	∈	∈	PROPN
ejpam-6459	130	7	u	u	NOUN
ejpam-6459	130	8	−	−	PROPN
ejpam-6459	130	9	v	v	ADP
ejpam-6459	130	10	k(ω	k(ω	PROPN
ejpam-6459	130	11	)	)	PUNCT
ejpam-6459	130	12	if	if	SCONJ
ejpam-6459	130	13	ω	ω	PROPN
ejpam-6459	130	14	∈	∈	PROPN
ejpam-6459	130	15	v	v	ADP
ejpam-6459	130	16	−	−	PROPN
ejpam-6459	130	17	u	u	NOUN
ejpam-6459	130	18	for	for	ADP
ejpam-6459	130	19	all	all	DET
ejpam-6459	130	20	ω	ω	NUM
ejpam-6459	130	21	∈	∈	PROPN
ejpam-6459	130	22	w.	w.	PROPN
ejpam-6459	130	23	max{j(ω),k(ω	max{j(ω),k(ω	PROPN
ejpam-6459	130	24	)	)	PUNCT
ejpam-6459	130	25	}	}	PUNCT
ejpam-6459	130	26	if	if	SCONJ
ejpam-6459	130	27	ω	ω	NUM
ejpam-6459	130	28	∈	∈	PROPN
ejpam-6459	130	29	u	u	NOUN
ejpam-6459	130	30	∩	∩	NOUN
ejpam-6459	130	31	v	v	ADP
ejpam-6459	130	32	definition	definition	NOUN
ejpam-6459	130	33	11	11	NUM
ejpam-6459	130	34	.	.	PUNCT
ejpam-6459	131	1	[	[	X
ejpam-6459	131	2	8	8	NUM
ejpam-6459	131	3	,	,	PUNCT
ejpam-6459	131	4	14	14	NUM
ejpam-6459	131	5	]	]	PUNCT
ejpam-6459	131	6	let	let	VERB
ejpam-6459	131	7	(	(	PUNCT
ejpam-6459	131	8	j	j	NOUN
ejpam-6459	131	9	,	,	PUNCT
ejpam-6459	131	10	u	u	NOUN
ejpam-6459	131	11	)	)	PUNCT
ejpam-6459	131	12	and	and	CCONJ
ejpam-6459	131	13	(	(	PUNCT
ejpam-6459	131	14	k	k	X
ejpam-6459	131	15	,	,	PUNCT
ejpam-6459	131	16	v	v	NOUN
ejpam-6459	131	17	)	)	PUNCT
ejpam-6459	131	18	be	be	AUX
ejpam-6459	131	19	two	two	NUM
ejpam-6459	131	20	bfsss	bfsss	NOUN
ejpam-6459	131	21	over	over	ADP
ejpam-6459	131	22	the	the	DET
ejpam-6459	131	23	universe	universe	NOUN
ejpam-6459	131	24	g.	g.	NOUN
ejpam-6459	132	1	then	then	ADV
ejpam-6459	132	2	their	their	PRON
ejpam-6459	132	3	extended	extended	ADJ
ejpam-6459	132	4	intersection	intersection	NOUN
ejpam-6459	132	5	is	be	AUX
ejpam-6459	132	6	a	a	DET
ejpam-6459	132	7	bfss	bfss	NOUN
ejpam-6459	132	8	over	over	ADP
ejpam-6459	132	9	g	g	NOUN
ejpam-6459	132	10	indicated	indicate	VERB
ejpam-6459	132	11	by	by	ADP
ejpam-6459	132	12	(	(	PUNCT
ejpam-6459	132	13	j	j	PROPN
ejpam-6459	132	14	,	,	PUNCT
ejpam-6459	132	15	u	u	NOUN
ejpam-6459	132	16	)	)	PUNCT
ejpam-6459	132	17	∩e	∩e	NOUN
ejpam-6459	132	18	(	(	PUNCT
ejpam-6459	132	19	k	k	X
ejpam-6459	132	20	,	,	PUNCT
ejpam-6459	132	21	v	v	NOUN
ejpam-6459	132	22	)	)	PUNCT
ejpam-6459	132	23	and	and	CCONJ
ejpam-6459	132	24	is	be	AUX
ejpam-6459	132	25	known	know	VERB
ejpam-6459	132	26	as	as	ADP
ejpam-6459	132	27	(	(	PUNCT
ejpam-6459	132	28	j	j	PROPN
ejpam-6459	132	29	,	,	PUNCT
ejpam-6459	132	30	u	u	NOUN
ejpam-6459	132	31	)	)	PUNCT
ejpam-6459	132	32	∩e	∩e	NOUN
ejpam-6459	132	33	(	(	PUNCT
ejpam-6459	132	34	k	k	X
ejpam-6459	132	35	,	,	PUNCT
ejpam-6459	132	36	v	v	NOUN
ejpam-6459	132	37	)	)	PUNCT
ejpam-6459	132	38	=	=	SYM
ejpam-6459	132	39	(	(	PUNCT
ejpam-6459	132	40	l	l	NOUN
ejpam-6459	132	41	,	,	PUNCT
ejpam-6459	132	42	w	w	NOUN
ejpam-6459	132	43	)	)	PUNCT
ejpam-6459	132	44	,	,	PUNCT
ejpam-6459	132	45	where	where	SCONJ
ejpam-6459	132	46	w	w	NOUN
ejpam-6459	132	47	=	=	SYM
ejpam-6459	132	48	u	u	NOUN
ejpam-6459	132	49	∪	∪	NOUN
ejpam-6459	132	50	v	v	NOUN
ejpam-6459	132	51	and	and	CCONJ
ejpam-6459	132	52	l	l	NOUN
ejpam-6459	132	53	:	:	PUNCT
ejpam-6459	132	54	w	w	X
ejpam-6459	132	55	→	→	SYM
ejpam-6459	132	56	bf	bf	NOUN
ejpam-6459	132	57	(	(	PUNCT
ejpam-6459	132	58	g	g	NOUN
ejpam-6459	132	59	)	)	PUNCT
ejpam-6459	132	60	is	be	AUX
ejpam-6459	132	61	provided	provide	VERB
ejpam-6459	132	62	as	as	ADP
ejpam-6459	132	63	,	,	PUNCT
ejpam-6459	132	64	l(ω	l(ω	PROPN
ejpam-6459	132	65	)	)	PUNCT
ejpam-6459	132	66	=	=	PUNCT
ejpam-6459	133	1			PROPN
ejpam-6459	133	2	j(ω	j(ω	PROPN
ejpam-6459	133	3	)	)	PUNCT
ejpam-6459	133	4	if	if	SCONJ
ejpam-6459	133	5	ω	ω	NUM
ejpam-6459	133	6	∈	∈	PROPN
ejpam-6459	133	7	u	u	NOUN
ejpam-6459	133	8	−	−	PROPN
ejpam-6459	133	9	v	v	ADP
ejpam-6459	133	10	k(ω	k(ω	PROPN
ejpam-6459	133	11	)	)	PUNCT
ejpam-6459	133	12	if	if	SCONJ
ejpam-6459	133	13	ω	ω	PROPN
ejpam-6459	133	14	∈	∈	PROPN
ejpam-6459	133	15	v	v	ADP
ejpam-6459	133	16	−	−	PROPN
ejpam-6459	133	17	u	u	NOUN
ejpam-6459	133	18	for	for	ADP
ejpam-6459	133	19	all	all	DET
ejpam-6459	133	20	ω	ω	NUM
ejpam-6459	133	21	∈	∈	PROPN
ejpam-6459	133	22	w.	w.	PROPN
ejpam-6459	133	23	min{j(ω),k(ω	min{j(ω),k(ω	PROPN
ejpam-6459	133	24	)	)	PUNCT
ejpam-6459	133	25	}	}	PUNCT
ejpam-6459	133	26	if	if	SCONJ
ejpam-6459	133	27	ω	ω	NUM
ejpam-6459	133	28	∈	∈	PROPN
ejpam-6459	133	29	u	u	NOUN
ejpam-6459	133	30	∩	∩	X
ejpam-6459	133	31	v	v	ADP
ejpam-6459	133	32	definition	definition	NOUN
ejpam-6459	133	33	12	12	NUM
ejpam-6459	133	34	.	.	PUNCT
ejpam-6459	134	1	[	[	X
ejpam-6459	134	2	14	14	NUM
ejpam-6459	134	3	]	]	X
ejpam-6459	134	4	let	let	NOUN
ejpam-6459	134	5	(	(	PUNCT
ejpam-6459	134	6	j	j	NOUN
ejpam-6459	134	7	,	,	PUNCT
ejpam-6459	134	8	u	u	NOUN
ejpam-6459	134	9	)	)	PUNCT
ejpam-6459	134	10	and	and	CCONJ
ejpam-6459	134	11	(	(	PUNCT
ejpam-6459	134	12	k	k	X
ejpam-6459	134	13	,	,	PUNCT
ejpam-6459	134	14	v	v	NOUN
ejpam-6459	134	15	)	)	PUNCT
ejpam-6459	134	16	be	be	AUX
ejpam-6459	134	17	two	two	NUM
ejpam-6459	134	18	bfsss	bfsss	NOUN
ejpam-6459	134	19	over	over	ADP
ejpam-6459	134	20	the	the	DET
ejpam-6459	134	21	universe	universe	NOUN
ejpam-6459	134	22	g	g	NOUN
ejpam-6459	134	23	such	such	ADJ
ejpam-6459	134	24	that	that	SCONJ
ejpam-6459	134	25	u	u	PROPN
ejpam-6459	134	26	∩	∩	NOUN
ejpam-6459	134	27	v	v	ADP
ejpam-6459	134	28	̸=	̸=	PROPN
ejpam-6459	134	29	∅.	∅.	ADP
ejpam-6459	134	30	the	the	DET
ejpam-6459	134	31	restricted	restricted	ADJ
ejpam-6459	134	32	union	union	NOUN
ejpam-6459	134	33	of	of	ADP
ejpam-6459	134	34	(	(	PUNCT
ejpam-6459	134	35	j	j	PROPN
ejpam-6459	134	36	,	,	PUNCT
ejpam-6459	134	37	u	u	NOUN
ejpam-6459	134	38	)	)	PUNCT
ejpam-6459	134	39	and	and	CCONJ
ejpam-6459	134	40	(	(	PUNCT
ejpam-6459	134	41	k	k	X
ejpam-6459	134	42	,	,	PUNCT
ejpam-6459	134	43	v	v	NOUN
ejpam-6459	134	44	)	)	PUNCT
ejpam-6459	134	45	is	be	AUX
ejpam-6459	134	46	described	describe	VERB
ejpam-6459	134	47	to	to	PART
ejpam-6459	134	48	be	be	AUX
ejpam-6459	134	49	a	a	DET
ejpam-6459	134	50	bfss	bfss	NOUN
ejpam-6459	134	51	(	(	PUNCT
ejpam-6459	134	52	l	l	NOUN
ejpam-6459	134	53	,	,	PUNCT
ejpam-6459	134	54	w	w	NOUN
ejpam-6459	134	55	)	)	PUNCT
ejpam-6459	134	56	over	over	ADP
ejpam-6459	134	57	g	g	PROPN
ejpam-6459	134	58	,	,	PUNCT
ejpam-6459	134	59	where	where	SCONJ
ejpam-6459	134	60	w	w	NOUN
ejpam-6459	134	61	=	=	SYM
ejpam-6459	134	62	u	u	NOUN
ejpam-6459	134	63	∩	∩	NOUN
ejpam-6459	134	64	v	v	NOUN
ejpam-6459	134	65	and	and	CCONJ
ejpam-6459	134	66	for	for	ADP
ejpam-6459	134	67	l(ω	l(ω	PROPN
ejpam-6459	134	68	)	)	PUNCT
ejpam-6459	134	69	=	=	SYM
ejpam-6459	134	70	j(ω	j(ω	PROPN
ejpam-6459	134	71	)	)	PUNCT
ejpam-6459	134	72	∪k(ω	∪k(ω	NOUN
ejpam-6459	134	73	)	)	PUNCT
ejpam-6459	134	74	,	,	PUNCT
ejpam-6459	134	75	∀	∀	X
ejpam-6459	134	76	ω	ω	NUM
ejpam-6459	134	77	∈	∈	PROPN
ejpam-6459	134	78	w	w	NOUN
ejpam-6459	134	79	.	.	PUNCT
ejpam-6459	135	1	this	this	PRON
ejpam-6459	135	2	is	be	AUX
ejpam-6459	135	3	indicated	indicate	VERB
ejpam-6459	135	4	by	by	ADP
ejpam-6459	135	5	(	(	PUNCT
ejpam-6459	135	6	l	l	NOUN
ejpam-6459	135	7	,	,	PUNCT
ejpam-6459	135	8	w	w	NOUN
ejpam-6459	135	9	)	)	PUNCT
ejpam-6459	135	10	=	=	SYM
ejpam-6459	135	11	(	(	PUNCT
ejpam-6459	135	12	j	j	PROPN
ejpam-6459	135	13	,	,	PUNCT
ejpam-6459	135	14	u	u	NOUN
ejpam-6459	135	15	)	)	PUNCT
ejpam-6459	135	16	∪r	∪r	PUNCT
ejpam-6459	135	17	(	(	PUNCT
ejpam-6459	135	18	k	k	X
ejpam-6459	135	19	,	,	PUNCT
ejpam-6459	135	20	v	v	NOUN
ejpam-6459	135	21	)	)	PUNCT
ejpam-6459	135	22	.	.	PUNCT
ejpam-6459	136	1	definition	definition	NOUN
ejpam-6459	136	2	13	13	NUM
ejpam-6459	136	3	.	.	PUNCT
ejpam-6459	137	1	[	[	X
ejpam-6459	137	2	14	14	NUM
ejpam-6459	137	3	]	]	X
ejpam-6459	137	4	let	let	NOUN
ejpam-6459	137	5	(	(	PUNCT
ejpam-6459	137	6	j	j	NOUN
ejpam-6459	137	7	,	,	PUNCT
ejpam-6459	137	8	u	u	NOUN
ejpam-6459	137	9	)	)	PUNCT
ejpam-6459	137	10	and	and	CCONJ
ejpam-6459	137	11	(	(	PUNCT
ejpam-6459	137	12	k	k	X
ejpam-6459	137	13	,	,	PUNCT
ejpam-6459	137	14	v	v	NOUN
ejpam-6459	137	15	)	)	PUNCT
ejpam-6459	137	16	be	be	AUX
ejpam-6459	137	17	two	two	NUM
ejpam-6459	137	18	bfsss	bfsss	NOUN
ejpam-6459	137	19	over	over	ADP
ejpam-6459	137	20	the	the	DET
ejpam-6459	137	21	universe	universe	NOUN
ejpam-6459	137	22	g	g	NOUN
ejpam-6459	137	23	such	such	ADJ
ejpam-6459	137	24	that	that	SCONJ
ejpam-6459	137	25	u	u	PROPN
ejpam-6459	137	26	∩	∩	NOUN
ejpam-6459	137	27	v	v	ADP
ejpam-6459	137	28	̸=	̸=	PROPN
ejpam-6459	137	29	∅.	∅.	ADP
ejpam-6459	137	30	the	the	DET
ejpam-6459	137	31	restricted	restricted	ADJ
ejpam-6459	137	32	intersection	intersection	NOUN
ejpam-6459	137	33	of	of	ADP
ejpam-6459	137	34	(	(	PUNCT
ejpam-6459	137	35	j	j	PROPN
ejpam-6459	137	36	,	,	PUNCT
ejpam-6459	137	37	u	u	NOUN
ejpam-6459	137	38	)	)	PUNCT
ejpam-6459	137	39	and	and	CCONJ
ejpam-6459	137	40	(	(	PUNCT
ejpam-6459	137	41	k	k	X
ejpam-6459	137	42	,	,	PUNCT
ejpam-6459	137	43	v	v	NOUN
ejpam-6459	137	44	)	)	PUNCT
ejpam-6459	137	45	is	be	AUX
ejpam-6459	137	46	described	describe	VERB
ejpam-6459	137	47	to	to	PART
ejpam-6459	137	48	be	be	AUX
ejpam-6459	137	49	a	a	DET
ejpam-6459	137	50	bfss	bfss	NOUN
ejpam-6459	137	51	(	(	PUNCT
ejpam-6459	137	52	l	l	NOUN
ejpam-6459	137	53	,	,	PUNCT
ejpam-6459	137	54	w	w	NOUN
ejpam-6459	137	55	)	)	PUNCT
ejpam-6459	137	56	over	over	ADP
ejpam-6459	137	57	g	g	PROPN
ejpam-6459	137	58	,	,	PUNCT
ejpam-6459	137	59	where	where	SCONJ
ejpam-6459	137	60	w	w	NOUN
ejpam-6459	137	61	=	=	SYM
ejpam-6459	137	62	u	u	NOUN
ejpam-6459	137	63	∩	∩	NOUN
ejpam-6459	137	64	v	v	NOUN
ejpam-6459	137	65	and	and	CCONJ
ejpam-6459	137	66	for	for	ADP
ejpam-6459	137	67	l(ω	l(ω	PROPN
ejpam-6459	137	68	)	)	PUNCT
ejpam-6459	137	69	=	=	SYM
ejpam-6459	137	70	j(ω	j(ω	PROPN
ejpam-6459	137	71	)	)	PUNCT
ejpam-6459	137	72	∪	∪	ADP
ejpam-6459	137	73	k(ω	k(ω	PROPN
ejpam-6459	137	74	)	)	PUNCT
ejpam-6459	137	75	,	,	PUNCT
ejpam-6459	137	76	∀	∀	X
ejpam-6459	137	77	ω	ω	NUM
ejpam-6459	137	78	∈	∈	PROPN
ejpam-6459	137	79	w	w	NOUN
ejpam-6459	137	80	.	.	PUNCT
ejpam-6459	138	1	this	this	PRON
ejpam-6459	138	2	is	be	AUX
ejpam-6459	138	3	indicated	indicate	VERB
ejpam-6459	138	4	by	by	ADP
ejpam-6459	138	5	(	(	PUNCT
ejpam-6459	138	6	l	l	NOUN
ejpam-6459	138	7	,	,	PUNCT
ejpam-6459	138	8	w	w	NOUN
ejpam-6459	138	9	)	)	PUNCT
ejpam-6459	138	10	=	=	SYM
ejpam-6459	138	11	(	(	PUNCT
ejpam-6459	138	12	j	j	PROPN
ejpam-6459	138	13	,	,	PUNCT
ejpam-6459	138	14	u	u	NOUN
ejpam-6459	138	15	)	)	PUNCT
ejpam-6459	138	16	∩r	∩r	PROPN
ejpam-6459	138	17	(	(	PUNCT
ejpam-6459	138	18	k	k	X
ejpam-6459	138	19	,	,	PUNCT
ejpam-6459	138	20	v	v	NOUN
ejpam-6459	138	21	)	)	PUNCT
ejpam-6459	138	22	.	.	PUNCT
ejpam-6459	139	1	g.	g.	PROPN
ejpam-6459	139	2	s.	s.	PROPN
ejpam-6459	139	3	rao	rao	PROPN
ejpam-6459	139	4	et	et	PROPN
ejpam-6459	139	5	al	al	PROPN
ejpam-6459	139	6	.	.	PUNCT
ejpam-6459	139	7	/	/	SYM
ejpam-6459	139	8	eur	eur	PROPN
ejpam-6459	139	9	.	.	PUNCT
ejpam-6459	140	1	j.	j.	PROPN
ejpam-6459	140	2	pure	pure	PROPN
ejpam-6459	140	3	appl	appl	PROPN
ejpam-6459	140	4	.	.	PROPN
ejpam-6459	140	5	math	math	PROPN
ejpam-6459	140	6	,	,	PUNCT
ejpam-6459	140	7	18	18	NUM
ejpam-6459	140	8	(	(	PUNCT
ejpam-6459	140	9	3	3	NUM
ejpam-6459	140	10	)	)	PUNCT
ejpam-6459	140	11	(	(	PUNCT
ejpam-6459	140	12	2025	2025	NUM
ejpam-6459	140	13	)	)	PUNCT
ejpam-6459	140	14	,	,	PUNCT
ejpam-6459	140	15	6459	6459	NUM
ejpam-6459	140	16	5	5	NUM
ejpam-6459	140	17	of	of	ADP
ejpam-6459	140	18	16	16	NUM
ejpam-6459	140	19	3	3	NUM
ejpam-6459	140	20	.	.	PUNCT
ejpam-6459	140	21	bipolar	bipolar	ADJ
ejpam-6459	140	22	fuzzy	fuzzy	ADJ
ejpam-6459	140	23	soft	soft	ADJ
ejpam-6459	140	24	boolean	boolean	ADJ
ejpam-6459	140	25	rings	ring	NOUN
ejpam-6459	140	26	in	in	ADP
ejpam-6459	140	27	this	this	DET
ejpam-6459	140	28	section	section	NOUN
ejpam-6459	140	29	,	,	PUNCT
ejpam-6459	140	30	we	we	PRON
ejpam-6459	140	31	introduce	introduce	VERB
ejpam-6459	140	32	the	the	DET
ejpam-6459	140	33	concept	concept	NOUN
ejpam-6459	140	34	of	of	ADP
ejpam-6459	140	35	bfsbrs	bfsbr	VERB
ejpam-6459	140	36	as	as	ADP
ejpam-6459	140	37	a	a	DET
ejpam-6459	140	38	natural	natural	ADJ
ejpam-6459	140	39	extension	extension	NOUN
ejpam-6459	140	40	of	of	ADP
ejpam-6459	140	41	ss	ss	NOUN
ejpam-6459	140	42	and	and	CCONJ
ejpam-6459	140	43	bfs	bfs	NOUN
ejpam-6459	140	44	theories	theory	NOUN
ejpam-6459	140	45	within	within	ADP
ejpam-6459	140	46	br	br	PROPN
ejpam-6459	140	47	structures	structure	NOUN
ejpam-6459	140	48	.	.	PUNCT
ejpam-6459	141	1	we	we	PRON
ejpam-6459	141	2	define	define	VERB
ejpam-6459	141	3	the	the	DET
ejpam-6459	141	4	core	core	NOUN
ejpam-6459	141	5	properties	property	NOUN
ejpam-6459	141	6	of	of	ADP
ejpam-6459	141	7	bfsbrs	bfsbr	VERB
ejpam-6459	141	8	and	and	CCONJ
ejpam-6459	141	9	demonstrate	demonstrate	VERB
ejpam-6459	141	10	how	how	SCONJ
ejpam-6459	141	11	they	they	PRON
ejpam-6459	141	12	preserve	preserve	VERB
ejpam-6459	141	13	algebraic	algebraic	ADJ
ejpam-6459	141	14	behavior	behavior	NOUN
ejpam-6459	141	15	under	under	ADP
ejpam-6459	141	16	fundamental	fundamental	ADJ
ejpam-6459	141	17	operations	operation	NOUN
ejpam-6459	141	18	.	.	PUNCT
ejpam-6459	142	1	in	in	ADP
ejpam-6459	142	2	this	this	DET
ejpam-6459	142	3	section	section	NOUN
ejpam-6459	142	4	,	,	PUNCT
ejpam-6459	142	5	ℜ	ℜ	PROPN
ejpam-6459	142	6	will	will	AUX
ejpam-6459	142	7	indicate	indicate	VERB
ejpam-6459	142	8	a	a	DET
ejpam-6459	142	9	br	br	NOUN
ejpam-6459	142	10	,	,	PUNCT
ejpam-6459	142	11	and	and	CCONJ
ejpam-6459	142	12	its	its	PRON
ejpam-6459	142	13	role	role	NOUN
ejpam-6459	142	14	within	within	ADP
ejpam-6459	142	15	the	the	DET
ejpam-6459	142	16	framework	framework	NOUN
ejpam-6459	142	17	will	will	AUX
ejpam-6459	142	18	be	be	AUX
ejpam-6459	142	19	made	make	VERB
ejpam-6459	142	20	explicit	explicit	ADJ
ejpam-6459	142	21	.	.	PUNCT
ejpam-6459	143	1	this	this	DET
ejpam-6459	143	2	approach	approach	NOUN
ejpam-6459	143	3	enables	enable	VERB
ejpam-6459	143	4	the	the	DET
ejpam-6459	143	5	modeling	modeling	NOUN
ejpam-6459	143	6	of	of	ADP
ejpam-6459	143	7	structured	structured	ADJ
ejpam-6459	143	8	uncertainty	uncertainty	NOUN
ejpam-6459	143	9	in	in	ADP
ejpam-6459	143	10	positive	positive	ADJ
ejpam-6459	143	11	and	and	CCONJ
ejpam-6459	143	12	negative	negative	ADJ
ejpam-6459	143	13	forms	form	NOUN
ejpam-6459	143	14	,	,	PUNCT
ejpam-6459	143	15	laying	lay	VERB
ejpam-6459	143	16	the	the	DET
ejpam-6459	143	17	groundwork	groundwork	NOUN
ejpam-6459	143	18	for	for	ADP
ejpam-6459	143	19	further	further	ADJ
ejpam-6459	143	20	theoretical	theoretical	ADJ
ejpam-6459	143	21	development	development	NOUN
ejpam-6459	143	22	.	.	PUNCT
ejpam-6459	144	1	definition	definition	NOUN
ejpam-6459	144	2	14	14	NUM
ejpam-6459	144	3	.	.	PUNCT
ejpam-6459	145	1	a	a	DET
ejpam-6459	145	2	bfss	bfss	NOUN
ejpam-6459	145	3	(	(	PUNCT
ejpam-6459	145	4	j	j	NOUN
ejpam-6459	145	5	,	,	PUNCT
ejpam-6459	145	6	u	u	NOUN
ejpam-6459	145	7	)	)	PUNCT
ejpam-6459	145	8	over	over	ADP
ejpam-6459	145	9	ℜ	ℜ	PROPN
ejpam-6459	145	10	is	be	AUX
ejpam-6459	145	11	called	call	VERB
ejpam-6459	145	12	a	a	DET
ejpam-6459	145	13	bipolar	bipolar	ADJ
ejpam-6459	145	14	fuzzy	fuzzy	ADJ
ejpam-6459	145	15	soft	soft	ADJ
ejpam-6459	145	16	boolean	boolean	ADJ
ejpam-6459	145	17	ring	ring	NOUN
ejpam-6459	145	18	(	(	PUNCT
ejpam-6459	145	19	bfsbr	bfsbr	NOUN
ejpam-6459	145	20	)	)	PUNCT
ejpam-6459	145	21	over	over	ADP
ejpam-6459	145	22	ℜ	ℜ	PROPN
ejpam-6459	145	23	if	if	SCONJ
ejpam-6459	145	24	(	(	PUNCT
ejpam-6459	145	25	i	i	NOUN
ejpam-6459	145	26	)	)	PUNCT
ejpam-6459	145	27	j+(κ+	j+(κ+	NOUN
ejpam-6459	145	28	ξ	ξ	SYM
ejpam-6459	145	29	)	)	PUNCT
ejpam-6459	145	30	≥	≥	NOUN
ejpam-6459	145	31	a{j+(κ	a{j+(κ	NUM
ejpam-6459	145	32	)	)	PUNCT
ejpam-6459	145	33	,	,	PUNCT
ejpam-6459	145	34	j+(ξ	j+(ξ	PROPN
ejpam-6459	145	35	)	)	PUNCT
ejpam-6459	145	36	}	}	PUNCT
ejpam-6459	145	37	(	(	PUNCT
ejpam-6459	145	38	a	a	PRON
ejpam-6459	145	39	indicates	indicate	VERB
ejpam-6459	145	40	min	min	NOUN
ejpam-6459	145	41	)	)	PUNCT
ejpam-6459	145	42	(	(	PUNCT
ejpam-6459	145	43	ii	ii	NOUN
ejpam-6459	145	44	)	)	PUNCT
ejpam-6459	145	45	j−(κ+	j−(κ+	NOUN
ejpam-6459	145	46	ξ	ξ	X
ejpam-6459	145	47	)	)	PUNCT
ejpam-6459	145	48	≤	≤	NUM
ejpam-6459	145	49	b{j−(κ	b{j−(κ	PROPN
ejpam-6459	145	50	)	)	PUNCT
ejpam-6459	145	51	,	,	PUNCT
ejpam-6459	145	52	j−(ξ	j−(ξ	PROPN
ejpam-6459	145	53	)	)	PUNCT
ejpam-6459	145	54	}	}	PUNCT
ejpam-6459	145	55	(	(	PUNCT
ejpam-6459	145	56	b	b	X
ejpam-6459	145	57	indicates	indicate	VERB
ejpam-6459	145	58	max	max	PROPN
ejpam-6459	145	59	)	)	PUNCT
ejpam-6459	145	60	(	(	PUNCT
ejpam-6459	145	61	iii	iii	NOUN
ejpam-6459	145	62	)	)	PUNCT
ejpam-6459	145	63	j+(κξ	j+(κξ	PROPN
ejpam-6459	145	64	)	)	PUNCT
ejpam-6459	145	65	≥	≥	NOUN
ejpam-6459	145	66	a{j+(κ	a{j+(κ	NUM
ejpam-6459	145	67	)	)	PUNCT
ejpam-6459	145	68	,	,	PUNCT
ejpam-6459	145	69	j+(ξ	j+(ξ	PROPN
ejpam-6459	145	70	)	)	PUNCT
ejpam-6459	145	71	}	}	PUNCT
ejpam-6459	145	72	(	(	PUNCT
ejpam-6459	145	73	iv	iv	X
ejpam-6459	145	74	)	)	PUNCT
ejpam-6459	145	75	j−(κξ	j−(κξ	NOUN
ejpam-6459	145	76	)	)	PUNCT
ejpam-6459	145	77	≤	≤	NUM
ejpam-6459	145	78	b{j−(κ	b{j−(κ	PROPN
ejpam-6459	145	79	)	)	PUNCT
ejpam-6459	145	80	,	,	PUNCT
ejpam-6459	145	81	j−(ξ	j−(ξ	PROPN
ejpam-6459	145	82	)	)	PUNCT
ejpam-6459	145	83	}	}	PUNCT
ejpam-6459	145	84	for	for	ADP
ejpam-6459	145	85	all	all	DET
ejpam-6459	145	86	κ	κ	NOUN
ejpam-6459	145	87	,	,	PUNCT
ejpam-6459	145	88	ξ	ξ	PROPN
ejpam-6459	145	89	∈	∈	PROPN
ejpam-6459	145	90	ℜ.	ℜ.	PROPN
ejpam-6459	145	91	example	example	NOUN
ejpam-6459	146	1	1	1	X
ejpam-6459	146	2	.	.	PUNCT
ejpam-6459	147	1	the	the	DET
ejpam-6459	147	2	binary	binary	PROPN
ejpam-6459	147	3	operations	operation	NOUN
ejpam-6459	147	4	+	+	CCONJ
ejpam-6459	147	5	and	and	CCONJ
ejpam-6459	147	6	∗	∗	NOUN
ejpam-6459	147	7	can	can	AUX
ejpam-6459	147	8	be	be	AUX
ejpam-6459	147	9	applied	apply	VERB
ejpam-6459	147	10	to	to	ADP
ejpam-6459	147	11	the	the	DET
ejpam-6459	147	12	non	non	ADJ
ejpam-6459	147	13	-	-	ADJ
ejpam-6459	147	14	empty	empty	ADJ
ejpam-6459	147	15	set	set	VERB
ejpam-6459	147	16	ℜ	ℜ	NOUN
ejpam-6459	147	17	=	=	SYM
ejpam-6459	147	18	{	{	PUNCT
ejpam-6459	147	19	0	0	NUM
ejpam-6459	147	20	,	,	PUNCT
ejpam-6459	147	21	κ	κ	NOUN
ejpam-6459	147	22	,	,	PUNCT
ejpam-6459	147	23	ξ	ξ	PROPN
ejpam-6459	147	24	,	,	PUNCT
ejpam-6459	147	25	τ	τ	X
ejpam-6459	147	26	}	}	PUNCT
ejpam-6459	147	27	in	in	ADP
ejpam-6459	147	28	the	the	DET
ejpam-6459	147	29	following	following	ADJ
ejpam-6459	147	30	ways	way	NOUN
ejpam-6459	147	31	:	:	PUNCT
ejpam-6459	147	32	let	let	VERB
ejpam-6459	147	33	u	u	PRON
ejpam-6459	147	34	=	=	PUNCT
ejpam-6459	147	35	{	{	PUNCT
ejpam-6459	147	36	e1	e1	PROPN
ejpam-6459	147	37	,	,	PUNCT
ejpam-6459	147	38	e2	e2	PROPN
ejpam-6459	147	39	,	,	PUNCT
ejpam-6459	147	40	e3	e3	PROPN
ejpam-6459	147	41	}	}	PUNCT
ejpam-6459	147	42	be	be	VERB
ejpam-6459	147	43	the	the	DET
ejpam-6459	147	44	parameters	parameter	NOUN
ejpam-6459	147	45	collection	collection	NOUN
ejpam-6459	147	46	.	.	PUNCT
ejpam-6459	148	1	then	then	ADV
ejpam-6459	148	2	,	,	PUNCT
ejpam-6459	148	3	+	+	PROPN
ejpam-6459	148	4	0	0	NUM
ejpam-6459	148	5	κ	κ	X
ejpam-6459	148	6	ξ	ξ	X
ejpam-6459	148	7	τ	τ	X
ejpam-6459	148	8	0	0	NUM
ejpam-6459	148	9	0	0	NUM
ejpam-6459	148	10	κ	κ	X
ejpam-6459	148	11	ξ	ξ	PROPN
ejpam-6459	148	12	τ	τ	X
ejpam-6459	148	13	κ	κ	PROPN
ejpam-6459	148	14	κ	κ	NOUN
ejpam-6459	148	15	0	0	NUM
ejpam-6459	148	16	τ	τ	PROPN
ejpam-6459	148	17	ξ	ξ	X
ejpam-6459	148	18	ξ	ξ	X
ejpam-6459	148	19	ξ	ξ	X
ejpam-6459	148	20	τ	τ	X
ejpam-6459	148	21	0	0	NUM
ejpam-6459	148	22	κ	κ	PROPN
ejpam-6459	148	23	τ	τ	PROPN
ejpam-6459	148	24	τ	τ	PROPN
ejpam-6459	148	25	ξ	ξ	PROPN
ejpam-6459	148	26	κ	κ	PROPN
ejpam-6459	148	27	0	0	NUM
ejpam-6459	148	28	∗	∗	NOUN
ejpam-6459	148	29	0	0	NUM
ejpam-6459	148	30	κ	κ	X
ejpam-6459	148	31	ξ	ξ	X
ejpam-6459	148	32	τ	τ	X
ejpam-6459	148	33	0	0	NUM
ejpam-6459	148	34	0	0	NUM
ejpam-6459	148	35	0	0	NUM
ejpam-6459	148	36	0	0	NUM
ejpam-6459	148	37	0	0	NUM
ejpam-6459	148	38	κ	κ	NOUN
ejpam-6459	148	39	0	0	NUM
ejpam-6459	148	40	κ	κ	NOUN
ejpam-6459	148	41	0	0	PROPN
ejpam-6459	148	42	κ	κ	PRON
ejpam-6459	148	43	ξ	ξ	PROPN
ejpam-6459	148	44	0	0	NUM
ejpam-6459	148	45	0	0	NUM
ejpam-6459	148	46	ξ	ξ	SYM
ejpam-6459	148	47	ξ	ξ	X
ejpam-6459	148	48	τ	τ	X
ejpam-6459	148	49	0	0	NUM
ejpam-6459	148	50	κ	κ	NOUN
ejpam-6459	148	51	ξ	ξ	PROPN
ejpam-6459	148	52	τ	τ	PROPN
ejpam-6459	148	53	specify	specify	VERB
ejpam-6459	148	54	a	a	DET
ejpam-6459	148	55	bfss	bfss	NOUN
ejpam-6459	148	56	(	(	PUNCT
ejpam-6459	148	57	j	j	NOUN
ejpam-6459	148	58	,	,	PUNCT
ejpam-6459	148	59	u	u	NOUN
ejpam-6459	148	60	)	)	PUNCT
ejpam-6459	148	61	on	on	ADP
ejpam-6459	148	62	a	a	DET
ejpam-6459	148	63	br	br	NOUN
ejpam-6459	148	64	ℜ.	ℜ.	PROPN
ejpam-6459	148	65	thus	thus	ADV
ejpam-6459	148	66	,	,	PUNCT
ejpam-6459	148	67	j(e1	j(e1	NOUN
ejpam-6459	148	68	)	)	PUNCT
ejpam-6459	149	1	=	=	PRON
ejpam-6459	149	2	{	{	PUNCT
ejpam-6459	149	3	(	(	PUNCT
ejpam-6459	149	4	0	0	NUM
ejpam-6459	149	5	,	,	PUNCT
ejpam-6459	149	6	0.7,−0.2	0.7,−0.2	NUM
ejpam-6459	149	7	)	)	PUNCT
ejpam-6459	149	8	,	,	PUNCT
ejpam-6459	149	9	(	(	PUNCT
ejpam-6459	149	10	κ	κ	NOUN
ejpam-6459	149	11	,	,	PUNCT
ejpam-6459	149	12	0.5,−0.3	0.5,−0.3	NUM
ejpam-6459	149	13	)	)	PUNCT
ejpam-6459	149	14	,	,	PUNCT
ejpam-6459	149	15	(	(	PUNCT
ejpam-6459	149	16	ξ	ξ	X
ejpam-6459	149	17	,	,	PUNCT
ejpam-6459	149	18	0.1,−0.4	0.1,−0.4	NUM
ejpam-6459	149	19	)	)	PUNCT
ejpam-6459	149	20	,	,	PUNCT
ejpam-6459	149	21	(	(	PUNCT
ejpam-6459	149	22	τ	τ	PROPN
ejpam-6459	149	23	,	,	PUNCT
ejpam-6459	149	24	0.1,−0.4	0.1,−0.4	NUM
ejpam-6459	149	25	)	)	PUNCT
ejpam-6459	149	26	}	}	PUNCT
ejpam-6459	149	27	j(e2	j(e2	NOUN
ejpam-6459	149	28	)	)	PUNCT
ejpam-6459	149	29	=	=	PRON
ejpam-6459	149	30	{	{	PUNCT
ejpam-6459	149	31	(	(	PUNCT
ejpam-6459	149	32	0	0	NUM
ejpam-6459	149	33	,	,	PUNCT
ejpam-6459	149	34	0.3,−0.3	0.3,−0.3	NUM
ejpam-6459	149	35	)	)	PUNCT
ejpam-6459	149	36	,	,	PUNCT
ejpam-6459	149	37	(	(	PUNCT
ejpam-6459	149	38	κ	κ	NOUN
ejpam-6459	149	39	,	,	PUNCT
ejpam-6459	149	40	0.3,−0.3	0.3,−0.3	NUM
ejpam-6459	149	41	)	)	PUNCT
ejpam-6459	149	42	,	,	PUNCT
ejpam-6459	149	43	(	(	PUNCT
ejpam-6459	149	44	ξ	ξ	X
ejpam-6459	149	45	,	,	PUNCT
ejpam-6459	149	46	0.7,−0.4	0.7,−0.4	NUM
ejpam-6459	149	47	)	)	PUNCT
ejpam-6459	149	48	,	,	PUNCT
ejpam-6459	149	49	(	(	PUNCT
ejpam-6459	149	50	τ	τ	X
ejpam-6459	149	51	,	,	PUNCT
ejpam-6459	149	52	0.9,−0.4	0.9,−0.4	NUM
ejpam-6459	149	53	)	)	PUNCT
ejpam-6459	149	54	}	}	PUNCT
ejpam-6459	149	55	j(e3	j(e3	VERB
ejpam-6459	149	56	)	)	PUNCT
ejpam-6459	149	57	=	=	PRON
ejpam-6459	149	58	{	{	PUNCT
ejpam-6459	149	59	(	(	PUNCT
ejpam-6459	149	60	0	0	NUM
ejpam-6459	149	61	,	,	PUNCT
ejpam-6459	149	62	0.9,−0.3	0.9,−0.3	NUM
ejpam-6459	149	63	)	)	PUNCT
ejpam-6459	149	64	,	,	PUNCT
ejpam-6459	149	65	(	(	PUNCT
ejpam-6459	149	66	κ	κ	NOUN
ejpam-6459	149	67	,	,	PUNCT
ejpam-6459	149	68	0.7,−0.3	0.7,−0.3	NUM
ejpam-6459	149	69	)	)	PUNCT
ejpam-6459	149	70	,	,	PUNCT
ejpam-6459	149	71	(	(	PUNCT
ejpam-6459	149	72	ξ	ξ	NOUN
ejpam-6459	149	73	,	,	PUNCT
ejpam-6459	149	74	0.4,−0.4	0.4,−0.4	NUM
ejpam-6459	149	75	)	)	PUNCT
ejpam-6459	149	76	,	,	PUNCT
ejpam-6459	149	77	(	(	PUNCT
ejpam-6459	149	78	τ	τ	PROPN
ejpam-6459	149	79	,	,	PUNCT
ejpam-6459	149	80	0.4,−0.4	0.4,−0.4	NUM
ejpam-6459	149	81	)	)	PUNCT
ejpam-6459	149	82	}	}	PUNCT
ejpam-6459	149	83	.	.	PUNCT
ejpam-6459	150	1	consequently	consequently	ADV
ejpam-6459	150	2	,	,	PUNCT
ejpam-6459	150	3	the	the	DET
ejpam-6459	150	4	bfss	bfss	NOUN
ejpam-6459	150	5	(	(	PUNCT
ejpam-6459	150	6	j	j	NOUN
ejpam-6459	150	7	,	,	PUNCT
ejpam-6459	150	8	u	u	NOUN
ejpam-6459	150	9	)	)	PUNCT
ejpam-6459	150	10	is	be	AUX
ejpam-6459	150	11	clearly	clearly	ADV
ejpam-6459	150	12	a	a	DET
ejpam-6459	150	13	bfsbr	bfsbr	NOUN
ejpam-6459	150	14	.	.	PUNCT
ejpam-6459	151	1	theorem	theorem	NOUN
ejpam-6459	151	2	1	1	NUM
ejpam-6459	151	3	.	.	PUNCT
ejpam-6459	152	1	if	if	SCONJ
ejpam-6459	152	2	(	(	PUNCT
ejpam-6459	152	3	j	j	NOUN
ejpam-6459	152	4	,	,	PUNCT
ejpam-6459	152	5	u	u	NOUN
ejpam-6459	152	6	)	)	PUNCT
ejpam-6459	152	7	and	and	CCONJ
ejpam-6459	152	8	(	(	PUNCT
ejpam-6459	152	9	k	k	X
ejpam-6459	152	10	,	,	PUNCT
ejpam-6459	152	11	v	v	NOUN
ejpam-6459	152	12	)	)	PUNCT
ejpam-6459	152	13	are	be	AUX
ejpam-6459	152	14	two	two	NUM
ejpam-6459	152	15	bfsbrs	bfsbr	VERB
ejpam-6459	152	16	over	over	ADP
ejpam-6459	152	17	ℜ	ℜ	PROPN
ejpam-6459	152	18	,	,	PUNCT
ejpam-6459	152	19	then	then	ADV
ejpam-6459	152	20	,	,	PUNCT
ejpam-6459	152	21	(	(	PUNCT
ejpam-6459	152	22	j	j	NOUN
ejpam-6459	152	23	,	,	PUNCT
ejpam-6459	152	24	u	u	NOUN
ejpam-6459	152	25	)	)	PUNCT
ejpam-6459	152	26	∧	∧	PROPN
ejpam-6459	152	27	(	(	PUNCT
ejpam-6459	152	28	k	k	NOUN
ejpam-6459	152	29	,	,	PUNCT
ejpam-6459	152	30	v	v	NOUN
ejpam-6459	152	31	)	)	PUNCT
ejpam-6459	152	32	is	be	AUX
ejpam-6459	152	33	also	also	ADV
ejpam-6459	152	34	a	a	DET
ejpam-6459	152	35	bfsbr	bfsbr	NOUN
ejpam-6459	152	36	over	over	ADP
ejpam-6459	152	37	ℜ.	ℜ.	PROPN
ejpam-6459	152	38	proof	proof	NOUN
ejpam-6459	152	39	.	.	PUNCT
ejpam-6459	153	1	let	let	VERB
ejpam-6459	153	2	(	(	PUNCT
ejpam-6459	153	3	j	j	NOUN
ejpam-6459	153	4	,	,	PUNCT
ejpam-6459	153	5	u	u	NOUN
ejpam-6459	153	6	)	)	PUNCT
ejpam-6459	153	7	and	and	CCONJ
ejpam-6459	153	8	(	(	PUNCT
ejpam-6459	153	9	k	k	X
ejpam-6459	153	10	,	,	PUNCT
ejpam-6459	153	11	v	v	NOUN
ejpam-6459	153	12	)	)	PUNCT
ejpam-6459	153	13	be	be	AUX
ejpam-6459	153	14	two	two	NUM
ejpam-6459	153	15	bfsbrs	bfsbr	VERB
ejpam-6459	153	16	over	over	ADP
ejpam-6459	153	17	ℜ.	ℜ.	PROPN
ejpam-6459	153	18	then	then	ADV
ejpam-6459	153	19	as	as	ADV
ejpam-6459	153	20	defined	define	VERB
ejpam-6459	153	21	(	(	PUNCT
ejpam-6459	153	22	j	j	NOUN
ejpam-6459	153	23	,	,	PUNCT
ejpam-6459	153	24	u)∧	u)∧	PROPN
ejpam-6459	153	25	(	(	PUNCT
ejpam-6459	153	26	k	k	X
ejpam-6459	153	27	,	,	PUNCT
ejpam-6459	153	28	v	v	NOUN
ejpam-6459	153	29	)	)	PUNCT
ejpam-6459	153	30	,	,	PUNCT
ejpam-6459	153	31	where	where	SCONJ
ejpam-6459	153	32	w	w	NOUN
ejpam-6459	153	33	=	=	PUNCT
ejpam-6459	153	34	u	u	NOUN
ejpam-6459	153	35	×v	×v	NOUN
ejpam-6459	153	36	and	and	CCONJ
ejpam-6459	153	37	l(ρ	l(ρ	PROPN
ejpam-6459	153	38	,	,	PUNCT
ejpam-6459	153	39	τ	τ	X
ejpam-6459	153	40	)	)	PUNCT
ejpam-6459	153	41	=	=	SYM
ejpam-6459	154	1	j(ρ)∩k(τ	j(ρ)∩k(τ	NOUN
ejpam-6459	154	2	)	)	PUNCT
ejpam-6459	154	3	,	,	PUNCT
ejpam-6459	154	4	∀(ρ	∀(ρ	PROPN
ejpam-6459	154	5	,	,	PUNCT
ejpam-6459	154	6	τ	τ	NOUN
ejpam-6459	154	7	)	)	PUNCT
ejpam-6459	154	8	∈	∈	PROPN
ejpam-6459	154	9	w	w	NOUN
ejpam-6459	154	10	=	=	PUNCT
ejpam-6459	154	11	u	u	NOUN
ejpam-6459	154	12	×v	×v	VERB
ejpam-6459	154	13	,	,	PUNCT
ejpam-6459	154	14	as	as	ADP
ejpam-6459	154	15	(	(	PUNCT
ejpam-6459	154	16	j	j	NOUN
ejpam-6459	154	17	,	,	PUNCT
ejpam-6459	154	18	u	u	NOUN
ejpam-6459	154	19	)	)	PUNCT
ejpam-6459	154	20	and	and	CCONJ
ejpam-6459	154	21	(	(	PUNCT
ejpam-6459	154	22	k	k	X
ejpam-6459	154	23	,	,	PUNCT
ejpam-6459	154	24	v	v	NOUN
ejpam-6459	154	25	)	)	PUNCT
ejpam-6459	154	26	are	be	AUX
ejpam-6459	154	27	bfsbrs	bfsbr	VERB
ejpam-6459	154	28	over	over	ADP
ejpam-6459	154	29	ℜ.	ℜ.	PROPN
ejpam-6459	154	30	thus	thus	ADV
ejpam-6459	154	31	,	,	PUNCT
ejpam-6459	154	32	for	for	ADP
ejpam-6459	154	33	κ	κ	PROPN
ejpam-6459	154	34	,	,	PUNCT
ejpam-6459	154	35	ξ	ξ	PROPN
ejpam-6459	154	36	∈	∈	PROPN
ejpam-6459	154	37	ℜ	ℜ	PROPN
ejpam-6459	154	38	,	,	PUNCT
ejpam-6459	154	39	l+	l+	X
ejpam-6459	154	40	(	(	PUNCT
ejpam-6459	154	41	ρ	ρ	NOUN
ejpam-6459	154	42	,	,	PUNCT
ejpam-6459	154	43	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	154	44	ξ	ξ	X
ejpam-6459	154	45	)	)	PUNCT
ejpam-6459	154	46	=	=	SYM
ejpam-6459	154	47	a{j+	a{j+	NOUN
ejpam-6459	154	48	ρ	ρ	PROPN
ejpam-6459	154	49	(	(	PUNCT
ejpam-6459	154	50	κ+	κ+	PROPN
ejpam-6459	154	51	ξ),k+	ξ),k+	PROPN
ejpam-6459	154	52	τ	τ	X
ejpam-6459	154	53	(	(	PUNCT
ejpam-6459	154	54	κ+	κ+	PROPN
ejpam-6459	154	55	ξ	ξ	NUM
ejpam-6459	154	56	)	)	PUNCT
ejpam-6459	154	57	}	}	PUNCT
ejpam-6459	154	58	≥	≥	NOUN
ejpam-6459	154	59	a{a{j+	a{a{j+	ADJ
ejpam-6459	154	60	ρ	ρ	PROPN
ejpam-6459	154	61	(	(	PUNCT
ejpam-6459	154	62	κ	κ	NOUN
ejpam-6459	154	63	)	)	PUNCT
ejpam-6459	154	64	,	,	PUNCT
ejpam-6459	154	65	j+	j+	NUM
ejpam-6459	154	66	ρ	ρ	PROPN
ejpam-6459	154	67	(	(	PUNCT
ejpam-6459	154	68	ξ	ξ	NOUN
ejpam-6459	154	69	)	)	PUNCT
ejpam-6459	154	70	}	}	PUNCT
ejpam-6459	154	71	,	,	PUNCT
ejpam-6459	154	72	a{k+	a{k+	ADP
ejpam-6459	154	73	τ	τ	X
ejpam-6459	154	74	(	(	PUNCT
ejpam-6459	154	75	κ),k+	κ),k+	PROPN
ejpam-6459	154	76	τ	τ	X
ejpam-6459	154	77	(	(	PUNCT
ejpam-6459	154	78	ξ	ξ	NOUN
ejpam-6459	154	79	)	)	PUNCT
ejpam-6459	154	80	}	}	PUNCT
ejpam-6459	154	81	}	}	PUNCT
ejpam-6459	154	82	=	=	SYM
ejpam-6459	154	83	a{a{j+	a{a{j+	ADJ
ejpam-6459	154	84	u	u	NOUN
ejpam-6459	154	85	(	(	PUNCT
ejpam-6459	154	86	κ),k+	κ),k+	PROPN
ejpam-6459	154	87	τ	τ	X
ejpam-6459	154	88	(	(	PUNCT
ejpam-6459	154	89	κ	κ	NOUN
ejpam-6459	154	90	)	)	PUNCT
ejpam-6459	154	91	}	}	PUNCT
ejpam-6459	154	92	,	,	PUNCT
ejpam-6459	154	93	a{j+	a{j+	NOUN
ejpam-6459	154	94	ρ	ρ	PROPN
ejpam-6459	154	95	(	(	PUNCT
ejpam-6459	154	96	ξ),k+	ξ),k+	PROPN
ejpam-6459	154	97	τ	τ	X
ejpam-6459	154	98	(	(	PUNCT
ejpam-6459	154	99	ξ	ξ	NOUN
ejpam-6459	154	100	)	)	PUNCT
ejpam-6459	154	101	}	}	PUNCT
ejpam-6459	154	102	}	}	PUNCT
ejpam-6459	154	103	=	=	SYM
ejpam-6459	154	104	a{l+	a{l+	NUM
ejpam-6459	154	105	(	(	PUNCT
ejpam-6459	154	106	ρ	ρ	NOUN
ejpam-6459	154	107	,	,	PUNCT
ejpam-6459	154	108	τ)(κ	τ)(κ	NOUN
ejpam-6459	154	109	)	)	PUNCT
ejpam-6459	154	110	,	,	PUNCT
ejpam-6459	154	111	l	l	PROPN
ejpam-6459	155	1	+	+	CCONJ
ejpam-6459	155	2	(	(	PUNCT
ejpam-6459	155	3	ρ	ρ	NOUN
ejpam-6459	155	4	,	,	PUNCT
ejpam-6459	155	5	τ)(ξ	τ)(ξ	NUM
ejpam-6459	155	6	)	)	PUNCT
ejpam-6459	155	7	}	}	PUNCT
ejpam-6459	155	8	,	,	PUNCT
ejpam-6459	155	9	g.	g.	PROPN
ejpam-6459	155	10	s.	s.	PROPN
ejpam-6459	155	11	rao	rao	PROPN
ejpam-6459	155	12	et	et	PROPN
ejpam-6459	155	13	al	al	PROPN
ejpam-6459	155	14	.	.	PUNCT
ejpam-6459	155	15	/	/	SYM
ejpam-6459	155	16	eur	eur	PROPN
ejpam-6459	155	17	.	.	PUNCT
ejpam-6459	156	1	j.	j.	PROPN
ejpam-6459	156	2	pure	pure	PROPN
ejpam-6459	156	3	appl	appl	PROPN
ejpam-6459	156	4	.	.	PROPN
ejpam-6459	156	5	math	math	PROPN
ejpam-6459	156	6	,	,	PUNCT
ejpam-6459	156	7	18	18	NUM
ejpam-6459	156	8	(	(	PUNCT
ejpam-6459	156	9	3	3	NUM
ejpam-6459	156	10	)	)	PUNCT
ejpam-6459	156	11	(	(	PUNCT
ejpam-6459	156	12	2025	2025	NUM
ejpam-6459	156	13	)	)	PUNCT
ejpam-6459	156	14	,	,	PUNCT
ejpam-6459	156	15	6459	6459	NUM
ejpam-6459	156	16	6	6	NUM
ejpam-6459	156	17	of	of	ADP
ejpam-6459	156	18	16	16	NUM
ejpam-6459	156	19	l−	l−	NOUN
ejpam-6459	156	20	(	(	PUNCT
ejpam-6459	156	21	ρ	ρ	NOUN
ejpam-6459	156	22	,	,	PUNCT
ejpam-6459	156	23	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	156	24	ξ	ξ	X
ejpam-6459	156	25	)	)	PUNCT
ejpam-6459	156	26	=	=	SYM
ejpam-6459	156	27	b{j−	b{j−	PROPN
ejpam-6459	156	28	ρ	ρ	NOUN
ejpam-6459	156	29	(	(	PUNCT
ejpam-6459	156	30	κ+	κ+	PROPN
ejpam-6459	156	31	ξ),k−	ξ),k−	PROPN
ejpam-6459	156	32	τ	τ	PROPN
ejpam-6459	156	33	(	(	PUNCT
ejpam-6459	156	34	κ+	κ+	PROPN
ejpam-6459	156	35	ξ	ξ	NUM
ejpam-6459	156	36	)	)	PUNCT
ejpam-6459	156	37	}	}	PUNCT
ejpam-6459	156	38	≤	≤	NUM
ejpam-6459	156	39	b{b{j−	b{b{j−	VERB
ejpam-6459	156	40	ρ	ρ	X
ejpam-6459	156	41	(	(	PUNCT
ejpam-6459	156	42	κ	κ	NOUN
ejpam-6459	156	43	)	)	PUNCT
ejpam-6459	156	44	,	,	PUNCT
ejpam-6459	156	45	j−	j−	PROPN
ejpam-6459	156	46	ρ	ρ	PROPN
ejpam-6459	156	47	(	(	PUNCT
ejpam-6459	156	48	ξ	ξ	NOUN
ejpam-6459	156	49	)	)	PUNCT
ejpam-6459	156	50	}	}	PUNCT
ejpam-6459	156	51	,	,	PUNCT
ejpam-6459	156	52	b{k−	b{k−	PROPN
ejpam-6459	156	53	τ	τ	X
ejpam-6459	156	54	(	(	PUNCT
ejpam-6459	156	55	κ),k−	κ),k−	PROPN
ejpam-6459	156	56	τ	τ	X
ejpam-6459	156	57	(	(	PUNCT
ejpam-6459	156	58	ξ	ξ	NOUN
ejpam-6459	156	59	)	)	PUNCT
ejpam-6459	156	60	}	}	PUNCT
ejpam-6459	156	61	}	}	PUNCT
ejpam-6459	156	62	=	=	SYM
ejpam-6459	156	63	b{b{j−	b{b{j−	NOUN
ejpam-6459	156	64	ρ	ρ	X
ejpam-6459	156	65	(	(	PUNCT
ejpam-6459	156	66	κ),k−	κ),k−	PROPN
ejpam-6459	156	67	τ	τ	X
ejpam-6459	156	68	(	(	PUNCT
ejpam-6459	156	69	κ	κ	NOUN
ejpam-6459	156	70	)	)	PUNCT
ejpam-6459	156	71	}	}	PUNCT
ejpam-6459	156	72	,	,	PUNCT
ejpam-6459	156	73	b{j−	b{j−	PROPN
ejpam-6459	156	74	ρ	ρ	NOUN
ejpam-6459	156	75	(	(	PUNCT
ejpam-6459	156	76	ξ),k−	ξ),k−	PROPN
ejpam-6459	156	77	τ	τ	PROPN
ejpam-6459	156	78	(	(	PUNCT
ejpam-6459	156	79	ξ	ξ	NOUN
ejpam-6459	156	80	)	)	PUNCT
ejpam-6459	156	81	}	}	PUNCT
ejpam-6459	156	82	}	}	PUNCT
ejpam-6459	156	83	=	=	PUNCT
ejpam-6459	156	84	b{l−	b{l−	NOUN
ejpam-6459	156	85	(	(	PUNCT
ejpam-6459	156	86	ρ	ρ	NOUN
ejpam-6459	156	87	,	,	PUNCT
ejpam-6459	156	88	τ)(κ	τ)(κ	NOUN
ejpam-6459	156	89	)	)	PUNCT
ejpam-6459	156	90	,	,	PUNCT
ejpam-6459	156	91	l	l	NOUN
ejpam-6459	156	92	−	−	PROPN
ejpam-6459	157	1	(	(	PUNCT
ejpam-6459	157	2	ρ	ρ	NOUN
ejpam-6459	157	3	,	,	PUNCT
ejpam-6459	157	4	τ)(ξ	τ)(ξ	NUM
ejpam-6459	157	5	)	)	PUNCT
ejpam-6459	157	6	}	}	PUNCT
ejpam-6459	157	7	,	,	PUNCT
ejpam-6459	157	8	l+	l+	X
ejpam-6459	157	9	(	(	PUNCT
ejpam-6459	157	10	ρ	ρ	NOUN
ejpam-6459	157	11	,	,	PUNCT
ejpam-6459	157	12	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	157	13	)	)	PUNCT
ejpam-6459	157	14	=	=	SYM
ejpam-6459	157	15	a{j+	a{j+	NOUN
ejpam-6459	157	16	ρ	ρ	PROPN
ejpam-6459	157	17	(	(	PUNCT
ejpam-6459	157	18	κξ),k+	κξ),k+	PROPN
ejpam-6459	157	19	τ	τ	X
ejpam-6459	157	20	(	(	PUNCT
ejpam-6459	157	21	κξ	κξ	NOUN
ejpam-6459	157	22	)	)	PUNCT
ejpam-6459	157	23	}	}	PUNCT
ejpam-6459	157	24	≥	≥	NOUN
ejpam-6459	157	25	a{a{j+	a{a{j+	ADJ
ejpam-6459	157	26	ρ	ρ	PROPN
ejpam-6459	157	27	(	(	PUNCT
ejpam-6459	157	28	κ	κ	NOUN
ejpam-6459	157	29	)	)	PUNCT
ejpam-6459	157	30	,	,	PUNCT
ejpam-6459	157	31	j+	j+	NUM
ejpam-6459	157	32	ρ	ρ	PROPN
ejpam-6459	157	33	(	(	PUNCT
ejpam-6459	157	34	ξ	ξ	NOUN
ejpam-6459	157	35	)	)	PUNCT
ejpam-6459	157	36	}	}	PUNCT
ejpam-6459	157	37	,	,	PUNCT
ejpam-6459	157	38	a{k+	a{k+	ADP
ejpam-6459	157	39	τ	τ	X
ejpam-6459	157	40	(	(	PUNCT
ejpam-6459	157	41	κ),k+	κ),k+	PROPN
ejpam-6459	157	42	τ	τ	X
ejpam-6459	157	43	(	(	PUNCT
ejpam-6459	157	44	ξ	ξ	NOUN
ejpam-6459	157	45	)	)	PUNCT
ejpam-6459	157	46	}	}	PUNCT
ejpam-6459	157	47	}	}	PUNCT
ejpam-6459	157	48	=	=	SYM
ejpam-6459	157	49	a{a{j+	a{a{j+	ADJ
ejpam-6459	157	50	u	u	NOUN
ejpam-6459	157	51	(	(	PUNCT
ejpam-6459	157	52	κ),k+	κ),k+	PROPN
ejpam-6459	157	53	τ	τ	X
ejpam-6459	157	54	(	(	PUNCT
ejpam-6459	157	55	κ	κ	NOUN
ejpam-6459	157	56	)	)	PUNCT
ejpam-6459	157	57	}	}	PUNCT
ejpam-6459	157	58	,	,	PUNCT
ejpam-6459	157	59	a{j+	a{j+	NOUN
ejpam-6459	157	60	ρ	ρ	PROPN
ejpam-6459	157	61	(	(	PUNCT
ejpam-6459	157	62	ξ),k+	ξ),k+	PROPN
ejpam-6459	157	63	τ	τ	X
ejpam-6459	157	64	(	(	PUNCT
ejpam-6459	157	65	ξ	ξ	NOUN
ejpam-6459	157	66	)	)	PUNCT
ejpam-6459	157	67	}	}	PUNCT
ejpam-6459	157	68	}	}	PUNCT
ejpam-6459	157	69	=	=	SYM
ejpam-6459	157	70	a{l+	a{l+	NUM
ejpam-6459	157	71	(	(	PUNCT
ejpam-6459	157	72	ρ	ρ	NOUN
ejpam-6459	157	73	,	,	PUNCT
ejpam-6459	157	74	τ)(κ	τ)(κ	NOUN
ejpam-6459	157	75	)	)	PUNCT
ejpam-6459	157	76	,	,	PUNCT
ejpam-6459	157	77	l	l	PROPN
ejpam-6459	158	1	+	+	CCONJ
ejpam-6459	158	2	(	(	PUNCT
ejpam-6459	158	3	ρ	ρ	NOUN
ejpam-6459	158	4	,	,	PUNCT
ejpam-6459	158	5	τ)(ξ	τ)(ξ	NUM
ejpam-6459	158	6	)	)	PUNCT
ejpam-6459	158	7	}	}	PUNCT
ejpam-6459	158	8	,	,	PUNCT
ejpam-6459	158	9	l−	l−	PROPN
ejpam-6459	158	10	(	(	PUNCT
ejpam-6459	158	11	ρ	ρ	NOUN
ejpam-6459	158	12	,	,	PUNCT
ejpam-6459	158	13	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	158	14	)	)	PUNCT
ejpam-6459	158	15	=	=	SYM
ejpam-6459	159	1	b{j−	b{j−	PUNCT
ejpam-6459	159	2	ρ	ρ	NOUN
ejpam-6459	159	3	(	(	PUNCT
ejpam-6459	159	4	κξ),k−	κξ),k−	PROPN
ejpam-6459	159	5	τ	τ	PROPN
ejpam-6459	159	6	(	(	PUNCT
ejpam-6459	159	7	κξ	κξ	NOUN
ejpam-6459	159	8	)	)	PUNCT
ejpam-6459	159	9	}	}	PUNCT
ejpam-6459	159	10	≤	≤	NUM
ejpam-6459	159	11	b{b{j−	b{b{j−	VERB
ejpam-6459	159	12	ρ	ρ	X
ejpam-6459	159	13	(	(	PUNCT
ejpam-6459	159	14	κ	κ	NOUN
ejpam-6459	159	15	)	)	PUNCT
ejpam-6459	159	16	,	,	PUNCT
ejpam-6459	159	17	j−	j−	PROPN
ejpam-6459	159	18	ρ	ρ	PROPN
ejpam-6459	159	19	(	(	PUNCT
ejpam-6459	159	20	ξ	ξ	NOUN
ejpam-6459	159	21	)	)	PUNCT
ejpam-6459	159	22	}	}	PUNCT
ejpam-6459	159	23	,	,	PUNCT
ejpam-6459	159	24	b{k−	b{k−	PROPN
ejpam-6459	159	25	τ	τ	X
ejpam-6459	159	26	(	(	PUNCT
ejpam-6459	159	27	κ),k−	κ),k−	PROPN
ejpam-6459	159	28	τ	τ	X
ejpam-6459	159	29	(	(	PUNCT
ejpam-6459	159	30	ξ	ξ	NOUN
ejpam-6459	159	31	)	)	PUNCT
ejpam-6459	159	32	}	}	PUNCT
ejpam-6459	159	33	}	}	PUNCT
ejpam-6459	159	34	=	=	SYM
ejpam-6459	159	35	b{b{j−	b{b{j−	NOUN
ejpam-6459	159	36	ρ	ρ	X
ejpam-6459	159	37	(	(	PUNCT
ejpam-6459	159	38	κ),k−	κ),k−	PROPN
ejpam-6459	159	39	τ	τ	X
ejpam-6459	159	40	(	(	PUNCT
ejpam-6459	159	41	κ	κ	NOUN
ejpam-6459	159	42	)	)	PUNCT
ejpam-6459	159	43	}	}	PUNCT
ejpam-6459	159	44	,	,	PUNCT
ejpam-6459	159	45	b{j−	b{j−	PROPN
ejpam-6459	159	46	ρ	ρ	NOUN
ejpam-6459	159	47	(	(	PUNCT
ejpam-6459	159	48	ξ),k−	ξ),k−	PROPN
ejpam-6459	159	49	τ	τ	PROPN
ejpam-6459	159	50	(	(	PUNCT
ejpam-6459	159	51	ξ	ξ	NOUN
ejpam-6459	159	52	)	)	PUNCT
ejpam-6459	159	53	}	}	PUNCT
ejpam-6459	159	54	}	}	PUNCT
ejpam-6459	159	55	=	=	PUNCT
ejpam-6459	159	56	b{l−	b{l−	NOUN
ejpam-6459	159	57	(	(	PUNCT
ejpam-6459	159	58	ρ	ρ	NOUN
ejpam-6459	159	59	,	,	PUNCT
ejpam-6459	159	60	τ)(κ	τ)(κ	NOUN
ejpam-6459	159	61	)	)	PUNCT
ejpam-6459	159	62	,	,	PUNCT
ejpam-6459	159	63	l	l	NOUN
ejpam-6459	159	64	−	−	PROPN
ejpam-6459	159	65	(	(	PUNCT
ejpam-6459	159	66	ρ	ρ	NOUN
ejpam-6459	159	67	,	,	PUNCT
ejpam-6459	159	68	τ)(ξ	τ)(ξ	NUM
ejpam-6459	159	69	)	)	PUNCT
ejpam-6459	159	70	}	}	PUNCT
ejpam-6459	159	71	.	.	PUNCT
ejpam-6459	160	1	therefore	therefore	ADV
ejpam-6459	160	2	,	,	PUNCT
ejpam-6459	160	3	(	(	PUNCT
ejpam-6459	160	4	l	l	NOUN
ejpam-6459	160	5	,	,	PUNCT
ejpam-6459	160	6	w	w	NOUN
ejpam-6459	160	7	)	)	PUNCT
ejpam-6459	160	8	=	=	SYM
ejpam-6459	160	9	(	(	PUNCT
ejpam-6459	160	10	j	j	PROPN
ejpam-6459	160	11	,	,	PUNCT
ejpam-6459	160	12	u	u	NOUN
ejpam-6459	160	13	)	)	PUNCT
ejpam-6459	160	14	∧	∧	PROPN
ejpam-6459	160	15	(	(	PUNCT
ejpam-6459	160	16	k	k	NOUN
ejpam-6459	160	17	,	,	PUNCT
ejpam-6459	160	18	v	v	NOUN
ejpam-6459	160	19	)	)	PUNCT
ejpam-6459	160	20	is	be	AUX
ejpam-6459	160	21	a	a	DET
ejpam-6459	160	22	bfsbr	bfsbr	NOUN
ejpam-6459	160	23	ℜ.	ℜ.	PROPN
ejpam-6459	160	24	theorem	theorem	NOUN
ejpam-6459	160	25	2	2	NUM
ejpam-6459	160	26	.	.	PUNCT
ejpam-6459	161	1	if	if	SCONJ
ejpam-6459	161	2	(	(	PUNCT
ejpam-6459	161	3	j	j	NOUN
ejpam-6459	161	4	,	,	PUNCT
ejpam-6459	161	5	u	u	NOUN
ejpam-6459	161	6	)	)	PUNCT
ejpam-6459	161	7	and	and	CCONJ
ejpam-6459	161	8	(	(	PUNCT
ejpam-6459	161	9	k	k	X
ejpam-6459	161	10	,	,	PUNCT
ejpam-6459	161	11	v	v	NOUN
ejpam-6459	161	12	)	)	PUNCT
ejpam-6459	161	13	are	be	AUX
ejpam-6459	161	14	two	two	NUM
ejpam-6459	161	15	bfsbrs	bfsbr	VERB
ejpam-6459	161	16	over	over	ADP
ejpam-6459	161	17	ℜ	ℜ	PROPN
ejpam-6459	161	18	,	,	PUNCT
ejpam-6459	161	19	then	then	ADV
ejpam-6459	161	20	(	(	PUNCT
ejpam-6459	161	21	j	j	NOUN
ejpam-6459	161	22	,	,	PUNCT
ejpam-6459	161	23	u	u	NOUN
ejpam-6459	161	24	)	)	PUNCT
ejpam-6459	161	25	∨	∨	PROPN
ejpam-6459	161	26	(	(	PUNCT
ejpam-6459	161	27	k	k	NOUN
ejpam-6459	161	28	,	,	PUNCT
ejpam-6459	161	29	v	v	NOUN
ejpam-6459	161	30	)	)	PUNCT
ejpam-6459	161	31	is	be	AUX
ejpam-6459	161	32	also	also	ADV
ejpam-6459	161	33	a	a	DET
ejpam-6459	161	34	bfsbr	bfsbr	NOUN
ejpam-6459	161	35	over	over	ADP
ejpam-6459	161	36	ℜ.	ℜ.	PROPN
ejpam-6459	161	37	proof	proof	NOUN
ejpam-6459	161	38	.	.	PUNCT
ejpam-6459	162	1	let	let	VERB
ejpam-6459	162	2	(	(	PUNCT
ejpam-6459	162	3	j	j	NOUN
ejpam-6459	162	4	,	,	PUNCT
ejpam-6459	162	5	u	u	NOUN
ejpam-6459	162	6	)	)	PUNCT
ejpam-6459	162	7	and	and	CCONJ
ejpam-6459	162	8	(	(	PUNCT
ejpam-6459	162	9	k	k	X
ejpam-6459	162	10	,	,	PUNCT
ejpam-6459	162	11	v	v	NOUN
ejpam-6459	162	12	)	)	PUNCT
ejpam-6459	162	13	be	be	AUX
ejpam-6459	162	14	two	two	NUM
ejpam-6459	162	15	bfsbrs	bfsbr	VERB
ejpam-6459	162	16	over	over	ADP
ejpam-6459	162	17	ℜ.	ℜ.	PROPN
ejpam-6459	162	18	then	then	ADV
ejpam-6459	162	19	as	as	ADV
ejpam-6459	162	20	defined	define	VERB
ejpam-6459	162	21	(	(	PUNCT
ejpam-6459	162	22	j	j	NOUN
ejpam-6459	162	23	,	,	PUNCT
ejpam-6459	162	24	u)∨(k	u)∨(k	ADJ
ejpam-6459	162	25	,	,	PUNCT
ejpam-6459	162	26	v	v	NOUN
ejpam-6459	162	27	)	)	PUNCT
ejpam-6459	162	28	=	=	SYM
ejpam-6459	163	1	(	(	PUNCT
ejpam-6459	163	2	l	l	NOUN
ejpam-6459	163	3	,	,	PUNCT
ejpam-6459	163	4	w	w	NOUN
ejpam-6459	163	5	)	)	PUNCT
ejpam-6459	163	6	,	,	PUNCT
ejpam-6459	163	7	where	where	SCONJ
ejpam-6459	163	8	w	w	NOUN
ejpam-6459	163	9	=	=	PUNCT
ejpam-6459	163	10	u	u	NOUN
ejpam-6459	163	11	×	×	NOUN
ejpam-6459	163	12	v	v	NOUN
ejpam-6459	163	13	and	and	CCONJ
ejpam-6459	163	14	l(ρ	l(ρ	PROPN
ejpam-6459	163	15	,	,	PUNCT
ejpam-6459	163	16	τ	τ	X
ejpam-6459	163	17	)	)	PUNCT
ejpam-6459	163	18	=	=	SYM
ejpam-6459	163	19	j(ρ	j(ρ	PROPN
ejpam-6459	163	20	)	)	PUNCT
ejpam-6459	163	21	∪	∪	ADP
ejpam-6459	163	22	k(τ	k(τ	PROPN
ejpam-6459	163	23	)	)	PUNCT
ejpam-6459	163	24	,	,	PUNCT
ejpam-6459	163	25	∀(ρ	∀(ρ	PROPN
ejpam-6459	163	26	,	,	PUNCT
ejpam-6459	163	27	τ	τ	NOUN
ejpam-6459	163	28	)	)	PUNCT
ejpam-6459	163	29	∈	∈	PROPN
ejpam-6459	163	30	w	w	NOUN
ejpam-6459	163	31	=	=	PUNCT
ejpam-6459	163	32	u	u	PROPN
ejpam-6459	163	33	×	×	NOUN
ejpam-6459	163	34	v	v	INTJ
ejpam-6459	163	35	,	,	PUNCT
ejpam-6459	163	36	as	as	ADP
ejpam-6459	163	37	(	(	PUNCT
ejpam-6459	163	38	j	j	NOUN
ejpam-6459	163	39	,	,	PUNCT
ejpam-6459	163	40	u	u	NOUN
ejpam-6459	163	41	)	)	PUNCT
ejpam-6459	163	42	and	and	CCONJ
ejpam-6459	163	43	(	(	PUNCT
ejpam-6459	163	44	k	k	X
ejpam-6459	163	45	,	,	PUNCT
ejpam-6459	163	46	v	v	NOUN
ejpam-6459	163	47	)	)	PUNCT
ejpam-6459	163	48	are	be	AUX
ejpam-6459	163	49	bfsbr	bfsbr	NOUN
ejpam-6459	163	50	over	over	ADP
ejpam-6459	163	51	ℜ.	ℜ.	PROPN
ejpam-6459	163	52	thus	thus	ADV
ejpam-6459	163	53	,	,	PUNCT
ejpam-6459	163	54	for	for	ADP
ejpam-6459	163	55	κ	κ	PROPN
ejpam-6459	163	56	,	,	PUNCT
ejpam-6459	163	57	ξ	ξ	PROPN
ejpam-6459	163	58	∈	∈	PROPN
ejpam-6459	163	59	ℜ	ℜ	PROPN
ejpam-6459	163	60	,	,	PUNCT
ejpam-6459	163	61	l+	l+	X
ejpam-6459	163	62	(	(	PUNCT
ejpam-6459	163	63	ρ	ρ	NOUN
ejpam-6459	163	64	,	,	PUNCT
ejpam-6459	163	65	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	163	66	ξ	ξ	X
ejpam-6459	163	67	)	)	PUNCT
ejpam-6459	164	1	=	=	SYM
ejpam-6459	164	2	b{j+	b{j+	ADJ
ejpam-6459	164	3	ρ	ρ	NOUN
ejpam-6459	164	4	(	(	PUNCT
ejpam-6459	164	5	κ+	κ+	PROPN
ejpam-6459	164	6	ξ),k+	ξ),k+	PROPN
ejpam-6459	164	7	τ	τ	X
ejpam-6459	164	8	(	(	PUNCT
ejpam-6459	164	9	κ+	κ+	PROPN
ejpam-6459	164	10	ξ	ξ	NUM
ejpam-6459	164	11	)	)	PUNCT
ejpam-6459	164	12	}	}	PUNCT
ejpam-6459	164	13	≥	≥	NOUN
ejpam-6459	164	14	b{a{j+	b{a{j+	NOUN
ejpam-6459	164	15	ρ	ρ	PROPN
ejpam-6459	164	16	(	(	PUNCT
ejpam-6459	164	17	κ	κ	NOUN
ejpam-6459	164	18	)	)	PUNCT
ejpam-6459	164	19	,	,	PUNCT
ejpam-6459	164	20	j+	j+	NUM
ejpam-6459	164	21	ρ	ρ	PROPN
ejpam-6459	164	22	(	(	PUNCT
ejpam-6459	164	23	ξ	ξ	NOUN
ejpam-6459	164	24	)	)	PUNCT
ejpam-6459	164	25	}	}	PUNCT
ejpam-6459	164	26	,	,	PUNCT
ejpam-6459	164	27	a{k+	a{k+	ADP
ejpam-6459	164	28	τ	τ	X
ejpam-6459	164	29	(	(	PUNCT
ejpam-6459	164	30	κ),k+	κ),k+	PROPN
ejpam-6459	164	31	τ	τ	X
ejpam-6459	164	32	(	(	PUNCT
ejpam-6459	164	33	ξ	ξ	NOUN
ejpam-6459	164	34	)	)	PUNCT
ejpam-6459	164	35	}	}	PUNCT
ejpam-6459	164	36	}	}	PUNCT
ejpam-6459	164	37	≥	≥	AUX
ejpam-6459	164	38	a{b{j+	a{b{j+	PROPN
ejpam-6459	164	39	ρ	ρ	PROPN
ejpam-6459	164	40	(	(	PUNCT
ejpam-6459	164	41	κ),k+	κ),k+	PROPN
ejpam-6459	164	42	τ	τ	X
ejpam-6459	164	43	(	(	PUNCT
ejpam-6459	164	44	κ	κ	NOUN
ejpam-6459	164	45	)	)	PUNCT
ejpam-6459	164	46	}	}	PUNCT
ejpam-6459	164	47	,	,	PUNCT
ejpam-6459	164	48	b{j+	b{j+	PROPN
ejpam-6459	164	49	ρ	ρ	PROPN
ejpam-6459	164	50	(	(	PUNCT
ejpam-6459	164	51	ξ),k+	ξ),k+	PROPN
ejpam-6459	164	52	τ	τ	X
ejpam-6459	164	53	(	(	PUNCT
ejpam-6459	164	54	ξ	ξ	NOUN
ejpam-6459	164	55	)	)	PUNCT
ejpam-6459	164	56	}	}	PUNCT
ejpam-6459	164	57	}	}	PUNCT
ejpam-6459	164	58	=	=	SYM
ejpam-6459	164	59	a{l+	a{l+	NUM
ejpam-6459	164	60	(	(	PUNCT
ejpam-6459	164	61	ρ	ρ	NOUN
ejpam-6459	164	62	,	,	PUNCT
ejpam-6459	164	63	τ)(κ	τ)(κ	NOUN
ejpam-6459	164	64	)	)	PUNCT
ejpam-6459	164	65	,	,	PUNCT
ejpam-6459	164	66	l	l	PROPN
ejpam-6459	164	67	+	+	CCONJ
ejpam-6459	164	68	(	(	PUNCT
ejpam-6459	164	69	ρ	ρ	NOUN
ejpam-6459	164	70	,	,	PUNCT
ejpam-6459	164	71	τ)(ξ	τ)(ξ	NUM
ejpam-6459	164	72	)	)	PUNCT
ejpam-6459	164	73	}	}	PUNCT
ejpam-6459	164	74	,	,	PUNCT
ejpam-6459	164	75	l−	l−	PROPN
ejpam-6459	164	76	(	(	PUNCT
ejpam-6459	164	77	ρ	ρ	NOUN
ejpam-6459	164	78	,	,	PUNCT
ejpam-6459	164	79	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	164	80	ξ	ξ	X
ejpam-6459	164	81	)	)	PUNCT
ejpam-6459	164	82	=	=	SYM
ejpam-6459	164	83	a{j−	a{j−	NUM
ejpam-6459	164	84	ρ	ρ	PROPN
ejpam-6459	164	85	(	(	PUNCT
ejpam-6459	164	86	κ+	κ+	PROPN
ejpam-6459	164	87	ξ),k−	ξ),k−	PROPN
ejpam-6459	164	88	τ	τ	PROPN
ejpam-6459	164	89	(	(	PUNCT
ejpam-6459	164	90	κ+	κ+	PROPN
ejpam-6459	164	91	ξ	ξ	NUM
ejpam-6459	164	92	)	)	PUNCT
ejpam-6459	164	93	}	}	PUNCT
ejpam-6459	164	94	≤	≤	NUM
ejpam-6459	164	95	a{b{j−	a{b{j−	VERB
ejpam-6459	164	96	ρ	ρ	X
ejpam-6459	164	97	(	(	PUNCT
ejpam-6459	164	98	κ	κ	NOUN
ejpam-6459	164	99	)	)	PUNCT
ejpam-6459	164	100	,	,	PUNCT
ejpam-6459	164	101	j−	j−	PROPN
ejpam-6459	164	102	ρ	ρ	PROPN
ejpam-6459	164	103	(	(	PUNCT
ejpam-6459	164	104	ξ	ξ	NOUN
ejpam-6459	164	105	)	)	PUNCT
ejpam-6459	164	106	}	}	PUNCT
ejpam-6459	164	107	,	,	PUNCT
ejpam-6459	164	108	b{k−	b{k−	PROPN
ejpam-6459	164	109	τ	τ	X
ejpam-6459	164	110	(	(	PUNCT
ejpam-6459	164	111	κ),k−	κ),k−	PROPN
ejpam-6459	164	112	τ	τ	X
ejpam-6459	164	113	(	(	PUNCT
ejpam-6459	164	114	ξ	ξ	NOUN
ejpam-6459	164	115	)	)	PUNCT
ejpam-6459	164	116	}	}	PUNCT
ejpam-6459	164	117	}	}	PUNCT
ejpam-6459	164	118	≤	≤	NUM
ejpam-6459	164	119	b{a{j−	b{a{j−	NOUN
ejpam-6459	164	120	ρ	ρ	NOUN
ejpam-6459	164	121	(	(	PUNCT
ejpam-6459	164	122	κ),k−	κ),k−	PROPN
ejpam-6459	164	123	τ	τ	X
ejpam-6459	164	124	(	(	PUNCT
ejpam-6459	164	125	κ	κ	NOUN
ejpam-6459	164	126	)	)	PUNCT
ejpam-6459	164	127	}	}	PUNCT
ejpam-6459	164	128	,	,	PUNCT
ejpam-6459	164	129	a{j−	a{j−	ADP
ejpam-6459	164	130	ρ	ρ	NOUN
ejpam-6459	164	131	(	(	PUNCT
ejpam-6459	164	132	ξ),k−	ξ),k−	PROPN
ejpam-6459	164	133	τ	τ	PROPN
ejpam-6459	164	134	(	(	PUNCT
ejpam-6459	164	135	ξ	ξ	NOUN
ejpam-6459	164	136	)	)	PUNCT
ejpam-6459	164	137	}	}	PUNCT
ejpam-6459	164	138	}	}	PUNCT
ejpam-6459	164	139	=	=	PUNCT
ejpam-6459	164	140	b{l−	b{l−	NOUN
ejpam-6459	164	141	(	(	PUNCT
ejpam-6459	164	142	ρ	ρ	NOUN
ejpam-6459	164	143	,	,	PUNCT
ejpam-6459	164	144	τ)(κ	τ)(κ	NOUN
ejpam-6459	164	145	)	)	PUNCT
ejpam-6459	164	146	,	,	PUNCT
ejpam-6459	164	147	l	l	NOUN
ejpam-6459	164	148	−	−	PROPN
ejpam-6459	164	149	(	(	PUNCT
ejpam-6459	164	150	ρ	ρ	NOUN
ejpam-6459	164	151	,	,	PUNCT
ejpam-6459	164	152	τ)(ξ	τ)(ξ	NUM
ejpam-6459	164	153	)	)	PUNCT
ejpam-6459	164	154	}	}	PUNCT
ejpam-6459	164	155	,	,	PUNCT
ejpam-6459	164	156	l+	l+	X
ejpam-6459	164	157	(	(	PUNCT
ejpam-6459	164	158	ρ	ρ	NOUN
ejpam-6459	164	159	,	,	PUNCT
ejpam-6459	164	160	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	164	161	)	)	PUNCT
ejpam-6459	164	162	=	=	SYM
ejpam-6459	164	163	b{j+	b{j+	ADJ
ejpam-6459	164	164	ρ	ρ	PROPN
ejpam-6459	164	165	(	(	PUNCT
ejpam-6459	164	166	κξ),k+	κξ),k+	PROPN
ejpam-6459	164	167	τ	τ	X
ejpam-6459	164	168	(	(	PUNCT
ejpam-6459	164	169	κξ	κξ	NOUN
ejpam-6459	164	170	)	)	PUNCT
ejpam-6459	164	171	}	}	PUNCT
ejpam-6459	164	172	≥	≥	NOUN
ejpam-6459	164	173	b{a{j+	b{a{j+	NOUN
ejpam-6459	164	174	ρ	ρ	PROPN
ejpam-6459	164	175	(	(	PUNCT
ejpam-6459	164	176	κ	κ	NOUN
ejpam-6459	164	177	)	)	PUNCT
ejpam-6459	164	178	,	,	PUNCT
ejpam-6459	164	179	j+	j+	NUM
ejpam-6459	164	180	ρ	ρ	PROPN
ejpam-6459	164	181	(	(	PUNCT
ejpam-6459	164	182	ξ	ξ	NOUN
ejpam-6459	164	183	)	)	PUNCT
ejpam-6459	164	184	}	}	PUNCT
ejpam-6459	164	185	,	,	PUNCT
ejpam-6459	164	186	a{k+	a{k+	ADP
ejpam-6459	164	187	τ	τ	X
ejpam-6459	164	188	(	(	PUNCT
ejpam-6459	164	189	κ),k+	κ),k+	PROPN
ejpam-6459	164	190	τ	τ	X
ejpam-6459	164	191	(	(	PUNCT
ejpam-6459	164	192	ξ	ξ	NOUN
ejpam-6459	164	193	)	)	PUNCT
ejpam-6459	164	194	}	}	PUNCT
ejpam-6459	164	195	}	}	PUNCT
ejpam-6459	164	196	≥	≥	AUX
ejpam-6459	164	197	a{b{j+	a{b{j+	PROPN
ejpam-6459	164	198	ρ	ρ	PROPN
ejpam-6459	164	199	(	(	PUNCT
ejpam-6459	164	200	κ),k+	κ),k+	PROPN
ejpam-6459	164	201	τ	τ	X
ejpam-6459	164	202	(	(	PUNCT
ejpam-6459	164	203	κ	κ	NOUN
ejpam-6459	164	204	)	)	PUNCT
ejpam-6459	164	205	}	}	PUNCT
ejpam-6459	164	206	,	,	PUNCT
ejpam-6459	164	207	b{j+	b{j+	PROPN
ejpam-6459	164	208	ρ	ρ	PROPN
ejpam-6459	164	209	(	(	PUNCT
ejpam-6459	164	210	ξ),k+	ξ),k+	PROPN
ejpam-6459	164	211	τ	τ	X
ejpam-6459	164	212	(	(	PUNCT
ejpam-6459	164	213	ξ	ξ	NOUN
ejpam-6459	164	214	)	)	PUNCT
ejpam-6459	164	215	}	}	PUNCT
ejpam-6459	164	216	}	}	PUNCT
ejpam-6459	164	217	=	=	SYM
ejpam-6459	164	218	a{l+	a{l+	NUM
ejpam-6459	164	219	(	(	PUNCT
ejpam-6459	164	220	ρ	ρ	NOUN
ejpam-6459	164	221	,	,	PUNCT
ejpam-6459	164	222	τ)(κ	τ)(κ	NOUN
ejpam-6459	164	223	)	)	PUNCT
ejpam-6459	164	224	,	,	PUNCT
ejpam-6459	164	225	l	l	PROPN
ejpam-6459	165	1	+	+	CCONJ
ejpam-6459	165	2	(	(	PUNCT
ejpam-6459	165	3	ρ	ρ	NOUN
ejpam-6459	165	4	,	,	PUNCT
ejpam-6459	165	5	τ)(ξ	τ)(ξ	NUM
ejpam-6459	165	6	)	)	PUNCT
ejpam-6459	165	7	}	}	PUNCT
ejpam-6459	165	8	,	,	PUNCT
ejpam-6459	165	9	l−	l−	PROPN
ejpam-6459	165	10	(	(	PUNCT
ejpam-6459	165	11	ρ	ρ	NOUN
ejpam-6459	165	12	,	,	PUNCT
ejpam-6459	165	13	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	165	14	)	)	PUNCT
ejpam-6459	165	15	=	=	SYM
ejpam-6459	165	16	a{j−	a{j−	NUM
ejpam-6459	165	17	ρ	ρ	PROPN
ejpam-6459	165	18	(	(	PUNCT
ejpam-6459	165	19	κξ),k−	κξ),k−	PROPN
ejpam-6459	165	20	τ	τ	PROPN
ejpam-6459	165	21	(	(	PUNCT
ejpam-6459	165	22	κξ	κξ	NOUN
ejpam-6459	165	23	)	)	PUNCT
ejpam-6459	165	24	}	}	PUNCT
ejpam-6459	165	25	g.	g.	PROPN
ejpam-6459	165	26	s.	s.	PROPN
ejpam-6459	165	27	rao	rao	PROPN
ejpam-6459	165	28	et	et	PROPN
ejpam-6459	165	29	al	al	PROPN
ejpam-6459	165	30	.	.	PUNCT
ejpam-6459	165	31	/	/	SYM
ejpam-6459	165	32	eur	eur	PROPN
ejpam-6459	165	33	.	.	PUNCT
ejpam-6459	166	1	j.	j.	PROPN
ejpam-6459	166	2	pure	pure	PROPN
ejpam-6459	166	3	appl	appl	PROPN
ejpam-6459	166	4	.	.	PROPN
ejpam-6459	166	5	math	math	PROPN
ejpam-6459	166	6	,	,	PUNCT
ejpam-6459	166	7	18	18	NUM
ejpam-6459	166	8	(	(	PUNCT
ejpam-6459	166	9	3	3	NUM
ejpam-6459	166	10	)	)	PUNCT
ejpam-6459	166	11	(	(	PUNCT
ejpam-6459	166	12	2025	2025	NUM
ejpam-6459	166	13	)	)	PUNCT
ejpam-6459	166	14	,	,	PUNCT
ejpam-6459	166	15	6459	6459	NUM
ejpam-6459	166	16	7	7	NUM
ejpam-6459	166	17	of	of	ADP
ejpam-6459	166	18	16	16	NUM
ejpam-6459	166	19	≤	≤	NUM
ejpam-6459	166	20	a{b{j−	a{b{j−	VERB
ejpam-6459	166	21	ρ	ρ	X
ejpam-6459	166	22	(	(	PUNCT
ejpam-6459	166	23	κ	κ	NOUN
ejpam-6459	166	24	)	)	PUNCT
ejpam-6459	166	25	,	,	PUNCT
ejpam-6459	166	26	j−	j−	PROPN
ejpam-6459	166	27	ρ	ρ	PROPN
ejpam-6459	166	28	(	(	PUNCT
ejpam-6459	166	29	ξ	ξ	NOUN
ejpam-6459	166	30	)	)	PUNCT
ejpam-6459	166	31	}	}	PUNCT
ejpam-6459	166	32	,	,	PUNCT
ejpam-6459	166	33	b{k−	b{k−	PROPN
ejpam-6459	166	34	τ	τ	X
ejpam-6459	166	35	(	(	PUNCT
ejpam-6459	166	36	κ),k−	κ),k−	PROPN
ejpam-6459	166	37	τ	τ	X
ejpam-6459	166	38	(	(	PUNCT
ejpam-6459	166	39	ξ	ξ	NOUN
ejpam-6459	166	40	)	)	PUNCT
ejpam-6459	166	41	}	}	PUNCT
ejpam-6459	166	42	}	}	PUNCT
ejpam-6459	166	43	≤	≤	NUM
ejpam-6459	166	44	b{a{j−	b{a{j−	NOUN
ejpam-6459	166	45	ρ	ρ	NOUN
ejpam-6459	166	46	(	(	PUNCT
ejpam-6459	166	47	κ),k−	κ),k−	PROPN
ejpam-6459	166	48	τ	τ	X
ejpam-6459	166	49	(	(	PUNCT
ejpam-6459	166	50	κ	κ	NOUN
ejpam-6459	166	51	)	)	PUNCT
ejpam-6459	166	52	}	}	PUNCT
ejpam-6459	166	53	,	,	PUNCT
ejpam-6459	166	54	a{j−	a{j−	ADP
ejpam-6459	166	55	ρ	ρ	NOUN
ejpam-6459	166	56	(	(	PUNCT
ejpam-6459	166	57	ξ),k−	ξ),k−	PROPN
ejpam-6459	166	58	τ	τ	PROPN
ejpam-6459	166	59	(	(	PUNCT
ejpam-6459	166	60	ξ	ξ	NOUN
ejpam-6459	166	61	)	)	PUNCT
ejpam-6459	166	62	}	}	PUNCT
ejpam-6459	166	63	}	}	PUNCT
ejpam-6459	166	64	=	=	PUNCT
ejpam-6459	166	65	b{l−	b{l−	NOUN
ejpam-6459	166	66	(	(	PUNCT
ejpam-6459	166	67	ρ	ρ	NOUN
ejpam-6459	166	68	,	,	PUNCT
ejpam-6459	166	69	τ)(κ	τ)(κ	NOUN
ejpam-6459	166	70	)	)	PUNCT
ejpam-6459	166	71	,	,	PUNCT
ejpam-6459	166	72	l	l	NOUN
ejpam-6459	167	1	−	−	PROPN
ejpam-6459	168	1	(	(	PUNCT
ejpam-6459	168	2	ρ	ρ	NOUN
ejpam-6459	168	3	,	,	PUNCT
ejpam-6459	168	4	τ)(ξ	τ)(ξ	NUM
ejpam-6459	168	5	)	)	PUNCT
ejpam-6459	168	6	}	}	PUNCT
ejpam-6459	168	7	.	.	PUNCT
ejpam-6459	169	1	therefore	therefore	ADV
ejpam-6459	169	2	,	,	PUNCT
ejpam-6459	169	3	(	(	PUNCT
ejpam-6459	169	4	l	l	NOUN
ejpam-6459	169	5	,	,	PUNCT
ejpam-6459	169	6	w	w	NOUN
ejpam-6459	169	7	)	)	PUNCT
ejpam-6459	169	8	=	=	SYM
ejpam-6459	169	9	(	(	PUNCT
ejpam-6459	169	10	j	j	PROPN
ejpam-6459	169	11	,	,	PUNCT
ejpam-6459	169	12	u	u	NOUN
ejpam-6459	169	13	)	)	PUNCT
ejpam-6459	169	14	∨	∨	PROPN
ejpam-6459	169	15	(	(	PUNCT
ejpam-6459	169	16	k	k	NOUN
ejpam-6459	169	17	,	,	PUNCT
ejpam-6459	169	18	v	v	NOUN
ejpam-6459	169	19	)	)	PUNCT
ejpam-6459	169	20	is	be	AUX
ejpam-6459	169	21	a	a	DET
ejpam-6459	169	22	bfsbr	bfsbr	NOUN
ejpam-6459	169	23	over	over	ADP
ejpam-6459	169	24	ℜ.	ℜ.	PROPN
ejpam-6459	169	25	example	example	NOUN
ejpam-6459	169	26	2	2	X
ejpam-6459	169	27	.	.	X
ejpam-6459	169	28	consider	consider	VERB
ejpam-6459	169	29	a	a	DET
ejpam-6459	169	30	decision	decision	NOUN
ejpam-6459	169	31	-	-	PUNCT
ejpam-6459	169	32	making	make	VERB
ejpam-6459	169	33	scenario	scenario	NOUN
ejpam-6459	169	34	where	where	SCONJ
ejpam-6459	169	35	two	two	NUM
ejpam-6459	169	36	decision	decision	NOUN
ejpam-6459	169	37	states	state	NOUN
ejpam-6459	169	38	,	,	PUNCT
ejpam-6459	169	39	0	0	NUM
ejpam-6459	169	40	and	and	CCONJ
ejpam-6459	169	41	1	1	NUM
ejpam-6459	169	42	,	,	PUNCT
ejpam-6459	169	43	represent	represent	VERB
ejpam-6459	169	44	binary	binary	ADJ
ejpam-6459	169	45	investment	investment	NOUN
ejpam-6459	169	46	options	option	NOUN
ejpam-6459	169	47	(	(	PUNCT
ejpam-6459	169	48	e.g.	e.g.	ADV
ejpam-6459	169	49	,	,	PUNCT
ejpam-6459	169	50	0	0	X
ejpam-6459	169	51	=	=	PUNCT
ejpam-6459	169	52	reject	reject	VERB
ejpam-6459	169	53	,	,	PUNCT
ejpam-6459	169	54	1	1	NUM
ejpam-6459	169	55	=	=	PUNCT
ejpam-6459	169	56	approve	approve	ADJ
ejpam-6459	169	57	)	)	PUNCT
ejpam-6459	169	58	.	.	PUNCT
ejpam-6459	170	1	let	let	VERB
ejpam-6459	170	2	ℜ	ℜ	PROPN
ejpam-6459	170	3	=	=	SYM
ejpam-6459	170	4	{	{	PUNCT
ejpam-6459	170	5	0	0	NUM
ejpam-6459	170	6	,	,	PUNCT
ejpam-6459	170	7	1	1	NUM
ejpam-6459	170	8	}	}	PUNCT
ejpam-6459	170	9	be	be	AUX
ejpam-6459	170	10	the	the	DET
ejpam-6459	170	11	br	br	NOUN
ejpam-6459	170	12	with	with	ADP
ejpam-6459	170	13	xor	xor	PROPN
ejpam-6459	170	14	and	and	CCONJ
ejpam-6459	170	15	and	and	CCONJ
ejpam-6459	170	16	as	as	ADP
ejpam-6459	170	17	addition	addition	NOUN
ejpam-6459	170	18	and	and	CCONJ
ejpam-6459	170	19	multiplication	multiplication	NOUN
ejpam-6459	170	20	,	,	PUNCT
ejpam-6459	170	21	respectively	respectively	ADV
ejpam-6459	170	22	.	.	PUNCT
ejpam-6459	171	1	define	define	VERB
ejpam-6459	171	2	two	two	NUM
ejpam-6459	171	3	bfsbrs	bfsbr	VERB
ejpam-6459	171	4	(	(	PUNCT
ejpam-6459	171	5	j	j	NOUN
ejpam-6459	171	6	,	,	PUNCT
ejpam-6459	171	7	{	{	PUNCT
ejpam-6459	171	8	p1	p1	NOUN
ejpam-6459	171	9	}	}	PUNCT
ejpam-6459	171	10	)	)	PUNCT
ejpam-6459	171	11	and	and	CCONJ
ejpam-6459	171	12	(	(	PUNCT
ejpam-6459	171	13	k	k	NOUN
ejpam-6459	171	14	,	,	PUNCT
ejpam-6459	171	15	{	{	PUNCT
ejpam-6459	171	16	p2	p2	X
ejpam-6459	171	17	}	}	PUNCT
ejpam-6459	171	18	)	)	PUNCT
ejpam-6459	171	19	over	over	ADP
ejpam-6459	171	20	the	the	DET
ejpam-6459	171	21	parameter	parameter	NOUN
ejpam-6459	171	22	set	set	NOUN
ejpam-6459	171	23	{	{	PUNCT
ejpam-6459	171	24	p1	p1	NOUN
ejpam-6459	171	25	,	,	PUNCT
ejpam-6459	171	26	p2	p2	PROPN
ejpam-6459	171	27	}	}	PUNCT
ejpam-6459	171	28	,	,	PUNCT
ejpam-6459	171	29	where	where	SCONJ
ejpam-6459	171	30	p1	p1	NOUN
ejpam-6459	171	31	represents	represent	VERB
ejpam-6459	171	32	risk	risk	NOUN
ejpam-6459	171	33	tolerance	tolerance	NOUN
ejpam-6459	171	34	and	and	CCONJ
ejpam-6459	171	35	p2	p2	PROPN
ejpam-6459	171	36	expected	expect	VERB
ejpam-6459	171	37	impact	impact	NOUN
ejpam-6459	171	38	.	.	PUNCT
ejpam-6459	172	1	assume	assume	VERB
ejpam-6459	172	2	the	the	DET
ejpam-6459	172	3	bipolar	bipolar	ADJ
ejpam-6459	172	4	fuzzy	fuzzy	ADJ
ejpam-6459	172	5	soft	soft	ADJ
ejpam-6459	172	6	membership	membership	NOUN
ejpam-6459	172	7	values	value	NOUN
ejpam-6459	172	8	are	be	AUX
ejpam-6459	172	9	:	:	PUNCT
ejpam-6459	172	10	j+	j+	PROPN
ejpam-6459	172	11	p1(0	p1(0	PROPN
ejpam-6459	172	12	)	)	PUNCT
ejpam-6459	172	13	=	=	SYM
ejpam-6459	172	14	0.9	0.9	NUM
ejpam-6459	172	15	,	,	PUNCT
ejpam-6459	172	16	j+	j+	NUM
ejpam-6459	172	17	p1(1	p1(1	PROPN
ejpam-6459	172	18	)	)	PUNCT
ejpam-6459	172	19	=	=	SYM
ejpam-6459	172	20	0.9	0.9	NUM
ejpam-6459	172	21	,	,	PUNCT
ejpam-6459	172	22	j−	j−	PROPN
ejpam-6459	172	23	p1(0	p1(0	PROPN
ejpam-6459	172	24	)	)	PUNCT
ejpam-6459	173	1	=	=	PUNCT
ejpam-6459	174	1	−0.1	−0.1	PROPN
ejpam-6459	174	2	,	,	PUNCT
ejpam-6459	174	3	j−	j−	PROPN
ejpam-6459	174	4	p1(1	p1(1	PROPN
ejpam-6459	174	5	)	)	PUNCT
ejpam-6459	174	6	=	=	SYM
ejpam-6459	175	1	−0.1	−0.1	PROPN
ejpam-6459	175	2	,	,	PUNCT
ejpam-6459	175	3	k+	k+	PROPN
ejpam-6459	175	4	p2(0	p2(0	NOUN
ejpam-6459	175	5	)	)	PUNCT
ejpam-6459	175	6	=	=	SYM
ejpam-6459	175	7	0.8	0.8	NUM
ejpam-6459	175	8	,	,	PUNCT
ejpam-6459	175	9	k+	k+	NOUN
ejpam-6459	175	10	p2(1	p2(1	NOUN
ejpam-6459	175	11	)	)	PUNCT
ejpam-6459	175	12	=	=	PUNCT
ejpam-6459	175	13	0.8	0.8	NUM
ejpam-6459	175	14	,	,	PUNCT
ejpam-6459	175	15	k−	k−	PROPN
ejpam-6459	175	16	p2(0	p2(0	NOUN
ejpam-6459	175	17	)	)	PUNCT
ejpam-6459	175	18	=	=	SYM
ejpam-6459	176	1	−0.3	−0.3	PROPN
ejpam-6459	176	2	,	,	PUNCT
ejpam-6459	176	3	k−	k−	PROPN
ejpam-6459	176	4	p2(1	p2(1	NOUN
ejpam-6459	176	5	)	)	PUNCT
ejpam-6459	176	6	=	=	PUNCT
ejpam-6459	177	1	−0.3	−0.3	PROPN
ejpam-6459	177	2	.	.	PUNCT
ejpam-6459	178	1	using	use	VERB
ejpam-6459	178	2	the	the	DET
ejpam-6459	178	3	join	join	NOUN
ejpam-6459	178	4	operation	operation	NOUN
ejpam-6459	178	5	(	(	PUNCT
ejpam-6459	178	6	l	l	NOUN
ejpam-6459	178	7	,	,	PUNCT
ejpam-6459	178	8	{	{	PUNCT
ejpam-6459	178	9	(	(	PUNCT
ejpam-6459	178	10	p1	p1	NOUN
ejpam-6459	178	11	,	,	PUNCT
ejpam-6459	178	12	p2	p2	NOUN
ejpam-6459	178	13	)	)	PUNCT
ejpam-6459	178	14	}	}	PUNCT
ejpam-6459	178	15	)	)	PUNCT
ejpam-6459	179	1	=	=	SYM
ejpam-6459	179	2	(	(	PUNCT
ejpam-6459	179	3	j	j	PROPN
ejpam-6459	179	4	,	,	PUNCT
ejpam-6459	179	5	{	{	PUNCT
ejpam-6459	179	6	p1	p1	NOUN
ejpam-6459	179	7	}	}	PUNCT
ejpam-6459	179	8	)	)	PUNCT
ejpam-6459	179	9	∨	∨	PROPN
ejpam-6459	179	10	(	(	PUNCT
ejpam-6459	179	11	k	k	NOUN
ejpam-6459	179	12	,	,	PUNCT
ejpam-6459	179	13	{	{	PUNCT
ejpam-6459	179	14	p2	p2	X
ejpam-6459	179	15	}	}	PUNCT
ejpam-6459	179	16	)	)	PUNCT
ejpam-6459	179	17	,	,	PUNCT
ejpam-6459	179	18	we	we	PRON
ejpam-6459	179	19	obtain	obtain	VERB
ejpam-6459	179	20	l+	l+	X
ejpam-6459	179	21	(	(	PUNCT
ejpam-6459	179	22	p1,p2	p1,p2	PROPN
ejpam-6459	179	23	)	)	PUNCT
ejpam-6459	179	24	(	(	PUNCT
ejpam-6459	179	25	0	0	NUM
ejpam-6459	179	26	)	)	PUNCT
ejpam-6459	179	27	=	=	SYM
ejpam-6459	179	28	max{0.9	max{0.9	PROPN
ejpam-6459	179	29	,	,	PUNCT
ejpam-6459	179	30	0.8	0.8	NUM
ejpam-6459	179	31	}	}	PUNCT
ejpam-6459	179	32	=	=	SYM
ejpam-6459	179	33	0.9	0.9	NUM
ejpam-6459	179	34	,	,	PUNCT
ejpam-6459	179	35	l−	l−	NOUN
ejpam-6459	179	36	(	(	PUNCT
ejpam-6459	179	37	p1,p2	p1,p2	PROPN
ejpam-6459	179	38	)	)	PUNCT
ejpam-6459	179	39	(	(	PUNCT
ejpam-6459	179	40	0	0	NUM
ejpam-6459	179	41	)	)	PUNCT
ejpam-6459	179	42	=	=	PUNCT
ejpam-6459	180	1	min{−0.1,−0.3	min{−0.1,−0.3	PROPN
ejpam-6459	180	2	}	}	PUNCT
ejpam-6459	180	3	=	=	SYM
ejpam-6459	180	4	−0.3	−0.3	PROPN
ejpam-6459	180	5	,	,	PUNCT
ejpam-6459	180	6	l+	l+	X
ejpam-6459	180	7	(	(	PUNCT
ejpam-6459	180	8	p1,p2	p1,p2	PROPN
ejpam-6459	180	9	)	)	PUNCT
ejpam-6459	180	10	(	(	PUNCT
ejpam-6459	180	11	1	1	X
ejpam-6459	180	12	)	)	PUNCT
ejpam-6459	180	13	=	=	SYM
ejpam-6459	180	14	max{0.9	max{0.9	PROPN
ejpam-6459	180	15	,	,	PUNCT
ejpam-6459	180	16	0.8	0.8	NUM
ejpam-6459	180	17	}	}	PUNCT
ejpam-6459	180	18	=	=	SYM
ejpam-6459	180	19	0.9	0.9	NUM
ejpam-6459	180	20	,	,	PUNCT
ejpam-6459	180	21	l−	l−	NOUN
ejpam-6459	180	22	(	(	PUNCT
ejpam-6459	180	23	p1,p2	p1,p2	PROPN
ejpam-6459	180	24	)	)	PUNCT
ejpam-6459	180	25	(	(	PUNCT
ejpam-6459	180	26	1	1	X
ejpam-6459	180	27	)	)	PUNCT
ejpam-6459	180	28	=	=	PUNCT
ejpam-6459	181	1	min{−0.1,−0.3	min{−0.1,−0.3	PROPN
ejpam-6459	181	2	}	}	PUNCT
ejpam-6459	181	3	=	=	SYM
ejpam-6459	181	4	−0.3	−0.3	PROPN
ejpam-6459	181	5	.	.	PUNCT
ejpam-6459	182	1	these	these	DET
ejpam-6459	182	2	values	value	NOUN
ejpam-6459	182	3	satisfy	satisfy	VERB
ejpam-6459	182	4	the	the	DET
ejpam-6459	182	5	axioms	axiom	NOUN
ejpam-6459	182	6	of	of	ADP
ejpam-6459	182	7	a	a	DET
ejpam-6459	182	8	bfsbr	bfsbr	NOUN
ejpam-6459	182	9	over	over	ADP
ejpam-6459	182	10	ℜ	ℜ	PROPN
ejpam-6459	182	11	,	,	PUNCT
ejpam-6459	182	12	and	and	CCONJ
ejpam-6459	182	13	thus	thus	ADV
ejpam-6459	182	14	,	,	PUNCT
ejpam-6459	182	15	under	under	ADP
ejpam-6459	182	16	this	this	DET
ejpam-6459	182	17	analysis	analysis	NOUN
ejpam-6459	182	18	,	,	PUNCT
ejpam-6459	182	19	both	both	DET
ejpam-6459	182	20	decision	decision	NOUN
ejpam-6459	182	21	states	state	NOUN
ejpam-6459	182	22	provide	provide	VERB
ejpam-6459	182	23	high	high	ADJ
ejpam-6459	182	24	positive	positive	ADJ
ejpam-6459	182	25	support	support	NOUN
ejpam-6459	182	26	with	with	ADP
ejpam-6459	182	27	equal	equal	ADJ
ejpam-6459	182	28	and	and	CCONJ
ejpam-6459	182	29	acceptable	acceptable	ADJ
ejpam-6459	182	30	negative	negative	ADJ
ejpam-6459	182	31	uncertainty	uncertainty	NOUN
ejpam-6459	182	32	,	,	PUNCT
ejpam-6459	182	33	highlighting	highlight	VERB
ejpam-6459	182	34	the	the	DET
ejpam-6459	182	35	model	model	NOUN
ejpam-6459	182	36	’s	’s	PART
ejpam-6459	182	37	capability	capability	NOUN
ejpam-6459	182	38	in	in	ADP
ejpam-6459	182	39	supporting	support	VERB
ejpam-6459	182	40	symmetric	symmetric	ADJ
ejpam-6459	182	41	decision	decision	NOUN
ejpam-6459	182	42	scenarios	scenario	NOUN
ejpam-6459	182	43	.	.	PUNCT
ejpam-6459	183	1	theorem	theorem	NOUN
ejpam-6459	183	2	3	3	NUM
ejpam-6459	183	3	.	.	PUNCT
ejpam-6459	184	1	if	if	SCONJ
ejpam-6459	184	2	(	(	PUNCT
ejpam-6459	184	3	j	j	NOUN
ejpam-6459	184	4	,	,	PUNCT
ejpam-6459	184	5	u	u	NOUN
ejpam-6459	184	6	)	)	PUNCT
ejpam-6459	184	7	and	and	CCONJ
ejpam-6459	184	8	(	(	PUNCT
ejpam-6459	184	9	k	k	X
ejpam-6459	184	10	,	,	PUNCT
ejpam-6459	184	11	v	v	NOUN
ejpam-6459	184	12	)	)	PUNCT
ejpam-6459	184	13	are	be	AUX
ejpam-6459	184	14	two	two	NUM
ejpam-6459	184	15	bfsbrs	bfsbr	VERB
ejpam-6459	184	16	over	over	ADP
ejpam-6459	184	17	ℜ	ℜ	PROPN
ejpam-6459	184	18	,	,	PUNCT
ejpam-6459	184	19	then	then	ADV
ejpam-6459	184	20	(	(	PUNCT
ejpam-6459	184	21	j	j	NOUN
ejpam-6459	184	22	,	,	PUNCT
ejpam-6459	184	23	u	u	NOUN
ejpam-6459	184	24	)	)	PUNCT
ejpam-6459	184	25	∩	∩	NOUN
ejpam-6459	184	26	(	(	PUNCT
ejpam-6459	184	27	k	k	X
ejpam-6459	184	28	,	,	PUNCT
ejpam-6459	184	29	v	v	NOUN
ejpam-6459	184	30	)	)	PUNCT
ejpam-6459	184	31	is	be	AUX
ejpam-6459	184	32	also	also	ADV
ejpam-6459	184	33	a	a	DET
ejpam-6459	184	34	bfsbr	bfsbr	NOUN
ejpam-6459	184	35	over	over	ADP
ejpam-6459	184	36	ℜ.	ℜ.	PROPN
ejpam-6459	184	37	proof	proof	NOUN
ejpam-6459	184	38	.	.	PUNCT
ejpam-6459	185	1	let	let	VERB
ejpam-6459	185	2	(	(	PUNCT
ejpam-6459	185	3	j	j	NOUN
ejpam-6459	185	4	,	,	PUNCT
ejpam-6459	185	5	u	u	NOUN
ejpam-6459	185	6	)	)	PUNCT
ejpam-6459	185	7	and	and	CCONJ
ejpam-6459	185	8	(	(	PUNCT
ejpam-6459	185	9	k	k	X
ejpam-6459	185	10	,	,	PUNCT
ejpam-6459	185	11	v	v	NOUN
ejpam-6459	185	12	)	)	PUNCT
ejpam-6459	185	13	be	be	AUX
ejpam-6459	185	14	two	two	NUM
ejpam-6459	185	15	bfsbrs	bfsbr	VERB
ejpam-6459	185	16	over	over	ADP
ejpam-6459	185	17	ℜ.	ℜ.	PROPN
ejpam-6459	185	18	then	then	ADV
ejpam-6459	185	19	(	(	PUNCT
ejpam-6459	185	20	j	j	NOUN
ejpam-6459	185	21	,	,	PUNCT
ejpam-6459	185	22	u)∩	u)∩	PROPN
ejpam-6459	185	23	(	(	PUNCT
ejpam-6459	185	24	k	k	X
ejpam-6459	185	25	,	,	PUNCT
ejpam-6459	185	26	v	v	NOUN
ejpam-6459	185	27	)	)	PUNCT
ejpam-6459	185	28	=	=	SYM
ejpam-6459	186	1	(	(	PUNCT
ejpam-6459	186	2	l	l	NOUN
ejpam-6459	186	3	,	,	PUNCT
ejpam-6459	186	4	w	w	NOUN
ejpam-6459	186	5	)	)	PUNCT
ejpam-6459	186	6	,	,	PUNCT
ejpam-6459	186	7	where	where	SCONJ
ejpam-6459	186	8	w	w	NOUN
ejpam-6459	186	9	=	=	SYM
ejpam-6459	186	10	u	u	NOUN
ejpam-6459	186	11	∩	∩	NOUN
ejpam-6459	186	12	v	v	NOUN
ejpam-6459	186	13	and	and	CCONJ
ejpam-6459	186	14	l(ω	l(ω	PROPN
ejpam-6459	186	15	)	)	PUNCT
ejpam-6459	186	16	=	=	SYM
ejpam-6459	186	17	j(ω	j(ω	PROPN
ejpam-6459	186	18	)	)	PUNCT
ejpam-6459	186	19	∩k(ω	∩k(ω	PROPN
ejpam-6459	186	20	)	)	PUNCT
ejpam-6459	186	21	,	,	PUNCT
ejpam-6459	186	22	∀	∀	X
ejpam-6459	186	23	ω	ω	NUM
ejpam-6459	186	24	∈	∈	PROPN
ejpam-6459	186	25	w	w	NOUN
ejpam-6459	186	26	.	.	PUNCT
ejpam-6459	187	1	now	now	ADV
ejpam-6459	187	2	,	,	PUNCT
ejpam-6459	187	3	l+	l+	X
ejpam-6459	187	4	ω	ω	X
ejpam-6459	187	5	(	(	PUNCT
ejpam-6459	187	6	κ+	κ+	PROPN
ejpam-6459	187	7	ξ	ξ	NUM
ejpam-6459	187	8	)	)	PUNCT
ejpam-6459	187	9	=	=	SYM
ejpam-6459	187	10	a{j+	a{j+	NOUN
ejpam-6459	187	11	ω	ω	PROPN
ejpam-6459	187	12	(	(	PUNCT
ejpam-6459	187	13	κ+	κ+	PROPN
ejpam-6459	187	14	ξ),k+	ξ),k+	PROPN
ejpam-6459	187	15	ω	ω	PROPN
ejpam-6459	187	16	(	(	PUNCT
ejpam-6459	187	17	κ+	κ+	PROPN
ejpam-6459	187	18	ξ	ξ	NUM
ejpam-6459	187	19	)	)	PUNCT
ejpam-6459	187	20	}	}	PUNCT
ejpam-6459	187	21	≥	≥	NOUN
ejpam-6459	187	22	a{a{j+	a{a{j+	NOUN
ejpam-6459	187	23	ω	ω	PROPN
ejpam-6459	187	24	(	(	PUNCT
ejpam-6459	187	25	κ	κ	NOUN
ejpam-6459	187	26	)	)	PUNCT
ejpam-6459	187	27	,	,	PUNCT
ejpam-6459	187	28	j+	j+	PROPN
ejpam-6459	187	29	ω	ω	PROPN
ejpam-6459	187	30	(	(	PUNCT
ejpam-6459	187	31	ξ	ξ	NOUN
ejpam-6459	187	32	)	)	PUNCT
ejpam-6459	187	33	}	}	PUNCT
ejpam-6459	187	34	,	,	PUNCT
ejpam-6459	187	35	a{k+	a{k+	ADP
ejpam-6459	187	36	ω	ω	X
ejpam-6459	187	37	(	(	PUNCT
ejpam-6459	187	38	κ),k+	κ),k+	PROPN
ejpam-6459	187	39	ω	ω	PROPN
ejpam-6459	187	40	(	(	PUNCT
ejpam-6459	187	41	ξ	ξ	NOUN
ejpam-6459	187	42	)	)	PUNCT
ejpam-6459	187	43	}	}	PUNCT
ejpam-6459	187	44	}	}	PUNCT
ejpam-6459	187	45	=	=	SYM
ejpam-6459	187	46	a{a{j+	a{a{j+	ADJ
ejpam-6459	187	47	ω	ω	PROPN
ejpam-6459	187	48	(	(	PUNCT
ejpam-6459	187	49	κ),k+	κ),k+	PROPN
ejpam-6459	187	50	ω	ω	PROPN
ejpam-6459	187	51	(	(	PUNCT
ejpam-6459	187	52	κ	κ	NOUN
ejpam-6459	187	53	)	)	PUNCT
ejpam-6459	187	54	}	}	PUNCT
ejpam-6459	187	55	,	,	PUNCT
ejpam-6459	187	56	a{j+	a{j+	PROPN
ejpam-6459	187	57	ω	ω	PROPN
ejpam-6459	187	58	(	(	PUNCT
ejpam-6459	187	59	ξ),k+	ξ),k+	PROPN
ejpam-6459	187	60	ω	ω	PROPN
ejpam-6459	187	61	(	(	PUNCT
ejpam-6459	187	62	ξ	ξ	NOUN
ejpam-6459	187	63	)	)	PUNCT
ejpam-6459	187	64	}	}	PUNCT
ejpam-6459	187	65	=	=	SYM
ejpam-6459	187	66	a{l+	a{l+	NUM
ejpam-6459	187	67	ω	ω	NUM
ejpam-6459	187	68	(	(	PUNCT
ejpam-6459	187	69	κ	κ	NOUN
ejpam-6459	187	70	)	)	PUNCT
ejpam-6459	187	71	,	,	PUNCT
ejpam-6459	187	72	l	l	PROPN
ejpam-6459	188	1	+	+	X
ejpam-6459	188	2	ω	ω	PROPN
ejpam-6459	188	3	(	(	PUNCT
ejpam-6459	188	4	ξ	ξ	NOUN
ejpam-6459	188	5	)	)	PUNCT
ejpam-6459	188	6	}	}	PUNCT
ejpam-6459	188	7	,	,	PUNCT
ejpam-6459	188	8	l−	l−	PROPN
ejpam-6459	188	9	ω	ω	PROPN
ejpam-6459	188	10	(	(	PUNCT
ejpam-6459	188	11	κ+	κ+	PROPN
ejpam-6459	188	12	ξ	ξ	X
ejpam-6459	188	13	)	)	PUNCT
ejpam-6459	188	14	=	=	SYM
ejpam-6459	188	15	b{j−	b{j−	PROPN
ejpam-6459	188	16	ω	ω	NOUN
ejpam-6459	188	17	(	(	PUNCT
ejpam-6459	188	18	κ+	κ+	PROPN
ejpam-6459	188	19	ξ),k−	ξ),k−	PROPN
ejpam-6459	188	20	ω	ω	PROPN
ejpam-6459	188	21	(	(	PUNCT
ejpam-6459	188	22	κ+	κ+	PROPN
ejpam-6459	188	23	ξ	ξ	NUM
ejpam-6459	188	24	)	)	PUNCT
ejpam-6459	188	25	}	}	PUNCT
ejpam-6459	188	26	≤	≤	NUM
ejpam-6459	188	27	b{b{j−	b{b{j−	VERB
ejpam-6459	188	28	ω	ω	X
ejpam-6459	188	29	(	(	PUNCT
ejpam-6459	188	30	κ	κ	NOUN
ejpam-6459	188	31	)	)	PUNCT
ejpam-6459	188	32	,	,	PUNCT
ejpam-6459	188	33	j−	j−	PROPN
ejpam-6459	188	34	ω	ω	PROPN
ejpam-6459	188	35	(	(	PUNCT
ejpam-6459	188	36	ξ	ξ	NOUN
ejpam-6459	188	37	)	)	PUNCT
ejpam-6459	188	38	}	}	PUNCT
ejpam-6459	188	39	,	,	PUNCT
ejpam-6459	188	40	b{k−	b{k−	PROPN
ejpam-6459	188	41	ω	ω	X
ejpam-6459	188	42	(	(	PUNCT
ejpam-6459	188	43	κ	κ	NOUN
ejpam-6459	188	44	)	)	PUNCT
ejpam-6459	188	45	,	,	PUNCT
ejpam-6459	188	46	ek−	ek−	NUM
ejpam-6459	188	47	ω	ω	X
ejpam-6459	188	48	(	(	PUNCT
ejpam-6459	188	49	ξ	ξ	NOUN
ejpam-6459	188	50	)	)	PUNCT
ejpam-6459	188	51	}	}	PUNCT
ejpam-6459	188	52	}	}	PUNCT
ejpam-6459	188	53	=	=	SYM
ejpam-6459	188	54	b{b{j−	b{b{j−	NOUN
ejpam-6459	188	55	ω	ω	X
ejpam-6459	188	56	(	(	PUNCT
ejpam-6459	188	57	κ),k−	κ),k−	PROPN
ejpam-6459	188	58	ω	ω	PROPN
ejpam-6459	188	59	(	(	PUNCT
ejpam-6459	188	60	κ	κ	NOUN
ejpam-6459	188	61	)	)	PUNCT
ejpam-6459	188	62	}	}	PUNCT
ejpam-6459	188	63	,	,	PUNCT
ejpam-6459	188	64	b{j−	b{j−	PROPN
ejpam-6459	188	65	ω	ω	NOUN
ejpam-6459	188	66	(	(	PUNCT
ejpam-6459	188	67	ξ),k−	ξ),k−	PROPN
ejpam-6459	188	68	ω	ω	PROPN
ejpam-6459	188	69	(	(	PUNCT
ejpam-6459	188	70	ξ	ξ	NOUN
ejpam-6459	188	71	)	)	PUNCT
ejpam-6459	188	72	}	}	PUNCT
ejpam-6459	188	73	}	}	PUNCT
ejpam-6459	188	74	=	=	PUNCT
ejpam-6459	189	1	b{l−	b{l−	PUNCT
ejpam-6459	189	2	ω	ω	NUM
ejpam-6459	189	3	(	(	PUNCT
ejpam-6459	189	4	κ	κ	NOUN
ejpam-6459	189	5	)	)	PUNCT
ejpam-6459	189	6	,	,	PUNCT
ejpam-6459	189	7	l	l	PROPN
ejpam-6459	189	8	−	−	PROPN
ejpam-6459	189	9	ω	ω	X
ejpam-6459	189	10	(	(	PUNCT
ejpam-6459	189	11	ξ	ξ	NOUN
ejpam-6459	189	12	)	)	PUNCT
ejpam-6459	189	13	}	}	PUNCT
ejpam-6459	189	14	,	,	PUNCT
ejpam-6459	189	15	l+	l+	X
ejpam-6459	189	16	ω	ω	X
ejpam-6459	189	17	(	(	PUNCT
ejpam-6459	189	18	κξ	κξ	NOUN
ejpam-6459	189	19	)	)	PUNCT
ejpam-6459	189	20	=	=	SYM
ejpam-6459	189	21	a{j+	a{j+	NOUN
ejpam-6459	189	22	ω	ω	PROPN
ejpam-6459	189	23	(	(	PUNCT
ejpam-6459	189	24	κξ),k+	κξ),k+	PROPN
ejpam-6459	189	25	ω	ω	PROPN
ejpam-6459	189	26	(	(	PUNCT
ejpam-6459	189	27	κξ	κξ	NOUN
ejpam-6459	189	28	)	)	PUNCT
ejpam-6459	189	29	}	}	PUNCT
ejpam-6459	189	30	≥	≥	PROPN
ejpam-6459	189	31	a{a{j+	a{a{j+	NOUN
ejpam-6459	189	32	ω	ω	PROPN
ejpam-6459	189	33	(	(	PUNCT
ejpam-6459	189	34	κ	κ	NOUN
ejpam-6459	189	35	)	)	PUNCT
ejpam-6459	189	36	,	,	PUNCT
ejpam-6459	189	37	j+	j+	PROPN
ejpam-6459	189	38	ω	ω	PROPN
ejpam-6459	189	39	(	(	PUNCT
ejpam-6459	189	40	ξ	ξ	NOUN
ejpam-6459	189	41	)	)	PUNCT
ejpam-6459	189	42	}	}	PUNCT
ejpam-6459	189	43	,	,	PUNCT
ejpam-6459	189	44	a{k+	a{k+	ADP
ejpam-6459	189	45	ω	ω	X
ejpam-6459	189	46	(	(	PUNCT
ejpam-6459	189	47	κ),k+	κ),k+	PROPN
ejpam-6459	189	48	ω	ω	PROPN
ejpam-6459	189	49	(	(	PUNCT
ejpam-6459	189	50	ξ	ξ	NOUN
ejpam-6459	189	51	)	)	PUNCT
ejpam-6459	189	52	}	}	PUNCT
ejpam-6459	189	53	}	}	PUNCT
ejpam-6459	189	54	=	=	SYM
ejpam-6459	189	55	a{a{j+	a{a{j+	ADJ
ejpam-6459	189	56	ω	ω	PROPN
ejpam-6459	189	57	(	(	PUNCT
ejpam-6459	189	58	κ),k+	κ),k+	PROPN
ejpam-6459	189	59	ω	ω	PROPN
ejpam-6459	189	60	(	(	PUNCT
ejpam-6459	189	61	κ	κ	NOUN
ejpam-6459	189	62	)	)	PUNCT
ejpam-6459	189	63	}	}	PUNCT
ejpam-6459	189	64	,	,	PUNCT
ejpam-6459	189	65	a{j+	a{j+	PROPN
ejpam-6459	189	66	ω	ω	PROPN
ejpam-6459	189	67	(	(	PUNCT
ejpam-6459	189	68	ξ),k+	ξ),k+	PROPN
ejpam-6459	189	69	ω	ω	PROPN
ejpam-6459	189	70	(	(	PUNCT
ejpam-6459	189	71	ξ	ξ	NOUN
ejpam-6459	189	72	)	)	PUNCT
ejpam-6459	189	73	}	}	PUNCT
ejpam-6459	189	74	g.	g.	PROPN
ejpam-6459	189	75	s.	s.	PROPN
ejpam-6459	189	76	rao	rao	PROPN
ejpam-6459	189	77	et	et	PROPN
ejpam-6459	189	78	al	al	PROPN
ejpam-6459	189	79	.	.	PUNCT
ejpam-6459	189	80	/	/	SYM
ejpam-6459	189	81	eur	eur	PROPN
ejpam-6459	189	82	.	.	PUNCT
ejpam-6459	190	1	j.	j.	PROPN
ejpam-6459	190	2	pure	pure	PROPN
ejpam-6459	190	3	appl	appl	PROPN
ejpam-6459	190	4	.	.	PROPN
ejpam-6459	190	5	math	math	PROPN
ejpam-6459	190	6	,	,	PUNCT
ejpam-6459	190	7	18	18	NUM
ejpam-6459	190	8	(	(	PUNCT
ejpam-6459	190	9	3	3	NUM
ejpam-6459	190	10	)	)	PUNCT
ejpam-6459	190	11	(	(	PUNCT
ejpam-6459	190	12	2025	2025	NUM
ejpam-6459	190	13	)	)	PUNCT
ejpam-6459	190	14	,	,	PUNCT
ejpam-6459	190	15	6459	6459	NUM
ejpam-6459	190	16	8	8	NUM
ejpam-6459	190	17	of	of	ADP
ejpam-6459	190	18	16	16	NUM
ejpam-6459	190	19	=	=	SYM
ejpam-6459	190	20	a{l+	a{l+	NUM
ejpam-6459	190	21	ω	ω	PROPN
ejpam-6459	190	22	(	(	PUNCT
ejpam-6459	190	23	κ	κ	NOUN
ejpam-6459	190	24	)	)	PUNCT
ejpam-6459	190	25	,	,	PUNCT
ejpam-6459	190	26	l	l	PROPN
ejpam-6459	191	1	+	+	X
ejpam-6459	191	2	ω	ω	PROPN
ejpam-6459	191	3	(	(	PUNCT
ejpam-6459	191	4	ξ	ξ	NOUN
ejpam-6459	191	5	)	)	PUNCT
ejpam-6459	191	6	}	}	PUNCT
ejpam-6459	191	7	,	,	PUNCT
ejpam-6459	191	8	l−	l−	PROPN
ejpam-6459	191	9	ω	ω	PROPN
ejpam-6459	191	10	(	(	PUNCT
ejpam-6459	191	11	κξ	κξ	NOUN
ejpam-6459	191	12	)	)	PUNCT
ejpam-6459	191	13	=	=	SYM
ejpam-6459	191	14	b{j−	b{j−	PROPN
ejpam-6459	191	15	ω	ω	NUM
ejpam-6459	191	16	(	(	PUNCT
ejpam-6459	191	17	κξ),k−	κξ),k−	PROPN
ejpam-6459	191	18	ω	ω	PROPN
ejpam-6459	191	19	(	(	PUNCT
ejpam-6459	191	20	κξ	κξ	NOUN
ejpam-6459	191	21	)	)	PUNCT
ejpam-6459	191	22	}	}	PUNCT
ejpam-6459	191	23	≤	≤	NUM
ejpam-6459	191	24	b{b{j−	b{b{j−	VERB
ejpam-6459	191	25	ω	ω	X
ejpam-6459	191	26	(	(	PUNCT
ejpam-6459	191	27	κ	κ	NOUN
ejpam-6459	191	28	)	)	PUNCT
ejpam-6459	191	29	,	,	PUNCT
ejpam-6459	191	30	j−	j−	PROPN
ejpam-6459	191	31	ω	ω	PROPN
ejpam-6459	191	32	(	(	PUNCT
ejpam-6459	191	33	ξ	ξ	NOUN
ejpam-6459	191	34	)	)	PUNCT
ejpam-6459	191	35	}	}	PUNCT
ejpam-6459	191	36	,	,	PUNCT
ejpam-6459	191	37	b{k−	b{k−	PROPN
ejpam-6459	191	38	ω	ω	X
ejpam-6459	191	39	(	(	PUNCT
ejpam-6459	191	40	κ	κ	NOUN
ejpam-6459	191	41	)	)	PUNCT
ejpam-6459	191	42	,	,	PUNCT
ejpam-6459	191	43	ek−	ek−	NUM
ejpam-6459	191	44	ω	ω	X
ejpam-6459	191	45	(	(	PUNCT
ejpam-6459	191	46	ξ	ξ	NOUN
ejpam-6459	191	47	)	)	PUNCT
ejpam-6459	191	48	}	}	PUNCT
ejpam-6459	191	49	}	}	PUNCT
ejpam-6459	191	50	=	=	SYM
ejpam-6459	191	51	b{b{j−	b{b{j−	NOUN
ejpam-6459	191	52	ω	ω	X
ejpam-6459	191	53	(	(	PUNCT
ejpam-6459	191	54	κ),k−	κ),k−	PROPN
ejpam-6459	191	55	ω	ω	PROPN
ejpam-6459	191	56	(	(	PUNCT
ejpam-6459	191	57	κ	κ	NOUN
ejpam-6459	191	58	)	)	PUNCT
ejpam-6459	191	59	}	}	PUNCT
ejpam-6459	191	60	,	,	PUNCT
ejpam-6459	191	61	b{j−	b{j−	PROPN
ejpam-6459	191	62	ω	ω	NOUN
ejpam-6459	191	63	(	(	PUNCT
ejpam-6459	191	64	ξ),k−	ξ),k−	PROPN
ejpam-6459	191	65	ω	ω	PROPN
ejpam-6459	191	66	(	(	PUNCT
ejpam-6459	191	67	ξ	ξ	NOUN
ejpam-6459	191	68	)	)	PUNCT
ejpam-6459	191	69	}	}	PUNCT
ejpam-6459	191	70	}	}	PUNCT
ejpam-6459	191	71	=	=	PUNCT
ejpam-6459	192	1	b{l−	b{l−	PUNCT
ejpam-6459	192	2	ω	ω	NUM
ejpam-6459	192	3	(	(	PUNCT
ejpam-6459	192	4	κ	κ	NOUN
ejpam-6459	192	5	)	)	PUNCT
ejpam-6459	192	6	,	,	PUNCT
ejpam-6459	192	7	l	l	PROPN
ejpam-6459	192	8	−	−	PROPN
ejpam-6459	192	9	ω	ω	X
ejpam-6459	192	10	(	(	PUNCT
ejpam-6459	192	11	ξ	ξ	NOUN
ejpam-6459	192	12	)	)	PUNCT
ejpam-6459	192	13	}	}	PUNCT
ejpam-6459	192	14	.	.	PUNCT
ejpam-6459	193	1	therefore	therefore	ADV
ejpam-6459	193	2	,	,	PUNCT
ejpam-6459	193	3	(	(	PUNCT
ejpam-6459	193	4	l	l	NOUN
ejpam-6459	193	5	,	,	PUNCT
ejpam-6459	193	6	w	w	NOUN
ejpam-6459	193	7	)	)	PUNCT
ejpam-6459	193	8	=	=	SYM
ejpam-6459	193	9	(	(	PUNCT
ejpam-6459	193	10	j	j	PROPN
ejpam-6459	193	11	,	,	PUNCT
ejpam-6459	193	12	u	u	NOUN
ejpam-6459	193	13	)	)	PUNCT
ejpam-6459	193	14	∩	∩	NOUN
ejpam-6459	193	15	(	(	PUNCT
ejpam-6459	193	16	k	k	X
ejpam-6459	193	17	,	,	PUNCT
ejpam-6459	193	18	v	v	NOUN
ejpam-6459	193	19	)	)	PUNCT
ejpam-6459	193	20	is	be	AUX
ejpam-6459	193	21	a	a	DET
ejpam-6459	193	22	bfsbr	bfsbr	NOUN
ejpam-6459	193	23	over	over	ADP
ejpam-6459	193	24	ℜ.	ℜ.	PROPN
ejpam-6459	193	25	theorem	theorem	NOUN
ejpam-6459	193	26	4	4	NUM
ejpam-6459	193	27	.	.	PUNCT
ejpam-6459	194	1	if	if	SCONJ
ejpam-6459	194	2	(	(	PUNCT
ejpam-6459	194	3	j	j	NOUN
ejpam-6459	194	4	,	,	PUNCT
ejpam-6459	194	5	u	u	NOUN
ejpam-6459	194	6	)	)	PUNCT
ejpam-6459	194	7	and	and	CCONJ
ejpam-6459	194	8	(	(	PUNCT
ejpam-6459	194	9	k	k	X
ejpam-6459	194	10	,	,	PUNCT
ejpam-6459	194	11	v	v	NOUN
ejpam-6459	194	12	)	)	PUNCT
ejpam-6459	194	13	are	be	AUX
ejpam-6459	194	14	two	two	NUM
ejpam-6459	194	15	bfsbrs	bfsbr	VERB
ejpam-6459	194	16	over	over	ADP
ejpam-6459	194	17	ℜ	ℜ	PROPN
ejpam-6459	194	18	,	,	PUNCT
ejpam-6459	194	19	then	then	ADV
ejpam-6459	194	20	(	(	PUNCT
ejpam-6459	194	21	j	j	NOUN
ejpam-6459	194	22	,	,	PUNCT
ejpam-6459	194	23	u	u	NOUN
ejpam-6459	194	24	)	)	PUNCT
ejpam-6459	194	25	∪	∪	ADV
ejpam-6459	194	26	(	(	PUNCT
ejpam-6459	194	27	k	k	NOUN
ejpam-6459	194	28	,	,	PUNCT
ejpam-6459	194	29	v	v	NOUN
ejpam-6459	194	30	)	)	PUNCT
ejpam-6459	194	31	is	be	AUX
ejpam-6459	194	32	also	also	ADV
ejpam-6459	194	33	a	a	DET
ejpam-6459	194	34	bfsbr	bfsbr	NOUN
ejpam-6459	194	35	over	over	ADP
ejpam-6459	194	36	ℜ.	ℜ.	PROPN
ejpam-6459	194	37	proof	proof	NOUN
ejpam-6459	194	38	.	.	PUNCT
ejpam-6459	195	1	let	let	VERB
ejpam-6459	195	2	(	(	PUNCT
ejpam-6459	195	3	j	j	NOUN
ejpam-6459	195	4	,	,	PUNCT
ejpam-6459	195	5	u	u	NOUN
ejpam-6459	195	6	)	)	PUNCT
ejpam-6459	195	7	and	and	CCONJ
ejpam-6459	195	8	(	(	PUNCT
ejpam-6459	195	9	k	k	X
ejpam-6459	195	10	,	,	PUNCT
ejpam-6459	195	11	v	v	NOUN
ejpam-6459	195	12	)	)	PUNCT
ejpam-6459	195	13	be	be	AUX
ejpam-6459	195	14	two	two	NUM
ejpam-6459	195	15	bfsbrs	bfsbr	VERB
ejpam-6459	195	16	over	over	ADP
ejpam-6459	195	17	ℜ.	ℜ.	PROPN
ejpam-6459	195	18	then	then	ADV
ejpam-6459	195	19	(	(	PUNCT
ejpam-6459	195	20	j	j	NOUN
ejpam-6459	195	21	,	,	PUNCT
ejpam-6459	195	22	u)∪	u)∪	PROPN
ejpam-6459	195	23	(	(	PUNCT
ejpam-6459	195	24	k	k	NOUN
ejpam-6459	195	25	,	,	PUNCT
ejpam-6459	195	26	v	v	NOUN
ejpam-6459	195	27	)	)	PUNCT
ejpam-6459	195	28	=	=	SYM
ejpam-6459	196	1	(	(	PUNCT
ejpam-6459	196	2	l	l	NOUN
ejpam-6459	196	3	,	,	PUNCT
ejpam-6459	196	4	w	w	NOUN
ejpam-6459	196	5	)	)	PUNCT
ejpam-6459	196	6	,	,	PUNCT
ejpam-6459	196	7	where	where	SCONJ
ejpam-6459	196	8	w	w	NOUN
ejpam-6459	196	9	=	=	SYM
ejpam-6459	196	10	u	u	NOUN
ejpam-6459	196	11	∪	∪	NOUN
ejpam-6459	196	12	v	v	NOUN
ejpam-6459	196	13	and	and	CCONJ
ejpam-6459	196	14	l(ω	l(ω	PROPN
ejpam-6459	196	15	)	)	PUNCT
ejpam-6459	196	16	=	=	PUNCT
ejpam-6459	197	1			PROPN
ejpam-6459	197	2	j(ω	j(ω	PROPN
ejpam-6459	197	3	)	)	PUNCT
ejpam-6459	197	4	if	if	SCONJ
ejpam-6459	197	5	ω	ω	NUM
ejpam-6459	197	6	∈	∈	PROPN
ejpam-6459	197	7	u	u	NOUN
ejpam-6459	197	8	−	−	PROPN
ejpam-6459	197	9	v	v	ADP
ejpam-6459	197	10	k(ω	k(ω	PROPN
ejpam-6459	197	11	)	)	PUNCT
ejpam-6459	197	12	if	if	SCONJ
ejpam-6459	197	13	ω	ω	PROPN
ejpam-6459	197	14	∈	∈	PROPN
ejpam-6459	197	15	v	v	ADP
ejpam-6459	197	16	−	−	PROPN
ejpam-6459	197	17	u	u	NOUN
ejpam-6459	197	18	for	for	ADP
ejpam-6459	197	19	all	all	DET
ejpam-6459	197	20	ω	ω	NUM
ejpam-6459	197	21	∈	∈	PROPN
ejpam-6459	197	22	w.	w.	PROPN
ejpam-6459	197	23	j(ω	j(ω	PROPN
ejpam-6459	197	24	)	)	PUNCT
ejpam-6459	197	25	∨k(ω	∨k(ω	NUM
ejpam-6459	197	26	)	)	PUNCT
ejpam-6459	197	27	if	if	SCONJ
ejpam-6459	197	28	ω	ω	NUM
ejpam-6459	197	29	∈	∈	PROPN
ejpam-6459	197	30	u	u	NOUN
ejpam-6459	197	31	∩	∩	X
ejpam-6459	197	32	v	v	X
ejpam-6459	197	33	then	then	ADV
ejpam-6459	197	34	we	we	PRON
ejpam-6459	197	35	have	have	VERB
ejpam-6459	197	36	the	the	DET
ejpam-6459	197	37	following	follow	VERB
ejpam-6459	197	38	cases	case	NOUN
ejpam-6459	197	39	:	:	PUNCT
ejpam-6459	197	40	case	case	NOUN
ejpam-6459	197	41	1	1	NUM
ejpam-6459	197	42	:	:	PUNCT
ejpam-6459	197	43	if	if	SCONJ
ejpam-6459	197	44	ω	ω	PROPN
ejpam-6459	197	45	∈	∈	PROPN
ejpam-6459	197	46	u	u	NOUN
ejpam-6459	197	47	−	−	PROPN
ejpam-6459	197	48	v	v	NOUN
ejpam-6459	197	49	,	,	PUNCT
ejpam-6459	197	50	then	then	ADV
ejpam-6459	197	51	l+	l+	X
ejpam-6459	197	52	ω	ω	PROPN
ejpam-6459	197	53	(	(	PUNCT
ejpam-6459	197	54	κ+	κ+	PROPN
ejpam-6459	197	55	ξ	ξ	NUM
ejpam-6459	197	56	)	)	PUNCT
ejpam-6459	197	57	=	=	SYM
ejpam-6459	198	1	j+	j+	NUM
ejpam-6459	198	2	ω	ω	PROPN
ejpam-6459	198	3	(	(	PUNCT
ejpam-6459	198	4	κ+	κ+	PROPN
ejpam-6459	198	5	ξ	ξ	PROPN
ejpam-6459	198	6	)	)	PUNCT
ejpam-6459	198	7	≥	≥	NOUN
ejpam-6459	198	8	a{j+	a{j+	PROPN
ejpam-6459	198	9	ω	ω	PROPN
ejpam-6459	198	10	(	(	PUNCT
ejpam-6459	198	11	κ	κ	NOUN
ejpam-6459	198	12	)	)	PUNCT
ejpam-6459	198	13	,	,	PUNCT
ejpam-6459	198	14	j+	j+	PROPN
ejpam-6459	198	15	ω	ω	PROPN
ejpam-6459	198	16	(	(	PUNCT
ejpam-6459	198	17	ξ	ξ	NOUN
ejpam-6459	198	18	)	)	PUNCT
ejpam-6459	198	19	}	}	PUNCT
ejpam-6459	198	20	=	=	SYM
ejpam-6459	198	21	a{l+	a{l+	NUM
ejpam-6459	198	22	ω	ω	NUM
ejpam-6459	198	23	(	(	PUNCT
ejpam-6459	198	24	κ	κ	NOUN
ejpam-6459	198	25	)	)	PUNCT
ejpam-6459	198	26	,	,	PUNCT
ejpam-6459	198	27	l	l	PROPN
ejpam-6459	199	1	+	+	X
ejpam-6459	199	2	ω	ω	PROPN
ejpam-6459	199	3	(	(	PUNCT
ejpam-6459	199	4	ξ	ξ	NOUN
ejpam-6459	199	5	)	)	PUNCT
ejpam-6459	199	6	}	}	PUNCT
ejpam-6459	199	7	,	,	PUNCT
ejpam-6459	199	8	l−	l−	PROPN
ejpam-6459	199	9	ω	ω	PROPN
ejpam-6459	199	10	(	(	PUNCT
ejpam-6459	199	11	κ+	κ+	PROPN
ejpam-6459	199	12	ξ	ξ	X
ejpam-6459	199	13	)	)	PUNCT
ejpam-6459	199	14	=	=	SYM
ejpam-6459	199	15	j−	j−	PROPN
ejpam-6459	199	16	ω	ω	PROPN
ejpam-6459	199	17	(	(	PUNCT
ejpam-6459	199	18	κ+	κ+	PROPN
ejpam-6459	199	19	ξ	ξ	PROPN
ejpam-6459	199	20	)	)	PUNCT
ejpam-6459	199	21	≤	≤	NOUN
ejpam-6459	199	22	b{j−	b{j−	PUNCT
ejpam-6459	199	23	ω	ω	NOUN
ejpam-6459	199	24	(	(	PUNCT
ejpam-6459	199	25	κ	κ	NOUN
ejpam-6459	199	26	)	)	PUNCT
ejpam-6459	199	27	,	,	PUNCT
ejpam-6459	199	28	j−	j−	PROPN
ejpam-6459	199	29	ω	ω	PROPN
ejpam-6459	199	30	(	(	PUNCT
ejpam-6459	199	31	ξ	ξ	NOUN
ejpam-6459	199	32	)	)	PUNCT
ejpam-6459	199	33	}	}	PUNCT
ejpam-6459	199	34	=	=	PUNCT
ejpam-6459	199	35	b{l−	b{l−	PUNCT
ejpam-6459	199	36	ω	ω	NUM
ejpam-6459	199	37	(	(	PUNCT
ejpam-6459	199	38	κ	κ	NOUN
ejpam-6459	199	39	)	)	PUNCT
ejpam-6459	199	40	,	,	PUNCT
ejpam-6459	199	41	l	l	PROPN
ejpam-6459	199	42	−	−	PROPN
ejpam-6459	199	43	ω	ω	X
ejpam-6459	199	44	(	(	PUNCT
ejpam-6459	199	45	ξ	ξ	NOUN
ejpam-6459	199	46	)	)	PUNCT
ejpam-6459	199	47	}	}	PUNCT
ejpam-6459	199	48	,	,	PUNCT
ejpam-6459	199	49	l+	l+	X
ejpam-6459	199	50	ω	ω	X
ejpam-6459	199	51	(	(	PUNCT
ejpam-6459	199	52	κξ	κξ	NOUN
ejpam-6459	199	53	)	)	PUNCT
ejpam-6459	199	54	=	=	PUNCT
ejpam-6459	200	1	j+	j+	NUM
ejpam-6459	200	2	ω	ω	PROPN
ejpam-6459	200	3	(	(	PUNCT
ejpam-6459	200	4	κξ	κξ	NOUN
ejpam-6459	200	5	)	)	PUNCT
ejpam-6459	200	6	≥	≥	NOUN
ejpam-6459	200	7	a{j+	a{j+	PROPN
ejpam-6459	200	8	ω	ω	PROPN
ejpam-6459	200	9	(	(	PUNCT
ejpam-6459	200	10	κ	κ	NOUN
ejpam-6459	200	11	)	)	PUNCT
ejpam-6459	200	12	,	,	PUNCT
ejpam-6459	200	13	j+	j+	PROPN
ejpam-6459	200	14	ω	ω	PROPN
ejpam-6459	200	15	(	(	PUNCT
ejpam-6459	200	16	ξ	ξ	NOUN
ejpam-6459	200	17	)	)	PUNCT
ejpam-6459	200	18	}	}	PUNCT
ejpam-6459	200	19	=	=	SYM
ejpam-6459	200	20	a{l+	a{l+	NUM
ejpam-6459	200	21	ω	ω	NUM
ejpam-6459	200	22	(	(	PUNCT
ejpam-6459	200	23	κ	κ	NOUN
ejpam-6459	200	24	)	)	PUNCT
ejpam-6459	200	25	,	,	PUNCT
ejpam-6459	200	26	l	l	PROPN
ejpam-6459	201	1	+	+	X
ejpam-6459	201	2	ω	ω	PROPN
ejpam-6459	201	3	(	(	PUNCT
ejpam-6459	201	4	ξ	ξ	NOUN
ejpam-6459	201	5	)	)	PUNCT
ejpam-6459	201	6	}	}	PUNCT
ejpam-6459	201	7	,	,	PUNCT
ejpam-6459	201	8	l−	l−	PROPN
ejpam-6459	201	9	ω	ω	PROPN
ejpam-6459	201	10	(	(	PUNCT
ejpam-6459	201	11	κξ	κξ	NOUN
ejpam-6459	201	12	)	)	PUNCT
ejpam-6459	201	13	=	=	PUNCT
ejpam-6459	201	14	j−	j−	PROPN
ejpam-6459	201	15	ω	ω	PROPN
ejpam-6459	201	16	(	(	PUNCT
ejpam-6459	201	17	κξ	κξ	NOUN
ejpam-6459	201	18	)	)	PUNCT
ejpam-6459	201	19	≤	≤	NOUN
ejpam-6459	201	20	b{j−	b{j−	PUNCT
ejpam-6459	201	21	ω	ω	NOUN
ejpam-6459	201	22	(	(	PUNCT
ejpam-6459	201	23	κ	κ	NOUN
ejpam-6459	201	24	)	)	PUNCT
ejpam-6459	201	25	,	,	PUNCT
ejpam-6459	201	26	j−	j−	PROPN
ejpam-6459	201	27	ω	ω	PROPN
ejpam-6459	201	28	(	(	PUNCT
ejpam-6459	201	29	ξ	ξ	NOUN
ejpam-6459	201	30	)	)	PUNCT
ejpam-6459	201	31	}	}	PUNCT
ejpam-6459	201	32	=	=	PUNCT
ejpam-6459	201	33	b{l−	b{l−	PUNCT
ejpam-6459	201	34	ω	ω	NUM
ejpam-6459	201	35	(	(	PUNCT
ejpam-6459	201	36	κ	κ	NOUN
ejpam-6459	201	37	)	)	PUNCT
ejpam-6459	201	38	,	,	PUNCT
ejpam-6459	201	39	l	l	PROPN
ejpam-6459	201	40	−	−	PROPN
ejpam-6459	201	41	ω	ω	X
ejpam-6459	201	42	(	(	PUNCT
ejpam-6459	201	43	ξ	ξ	NOUN
ejpam-6459	201	44	)	)	PUNCT
ejpam-6459	201	45	}	}	PUNCT
ejpam-6459	201	46	.	.	PUNCT
ejpam-6459	202	1	case	case	NOUN
ejpam-6459	202	2	2	2	NUM
ejpam-6459	202	3	:	:	PUNCT
ejpam-6459	203	1	if	if	SCONJ
ejpam-6459	203	2	ω	ω	PROPN
ejpam-6459	203	3	∈	∈	PROPN
ejpam-6459	203	4	v	v	ADP
ejpam-6459	203	5	−	−	PROPN
ejpam-6459	203	6	u	u	NOUN
ejpam-6459	203	7	,	,	PUNCT
ejpam-6459	203	8	then	then	ADV
ejpam-6459	203	9	l+	l+	X
ejpam-6459	203	10	ω	ω	PROPN
ejpam-6459	203	11	(	(	PUNCT
ejpam-6459	203	12	κ+	κ+	PROPN
ejpam-6459	203	13	ξ	ξ	PROPN
ejpam-6459	203	14	)	)	PUNCT
ejpam-6459	203	15	=	=	SYM
ejpam-6459	203	16	k+	k+	PROPN
ejpam-6459	203	17	ω	ω	PROPN
ejpam-6459	203	18	(	(	PUNCT
ejpam-6459	203	19	κ+	κ+	PROPN
ejpam-6459	203	20	ξ	ξ	PROPN
ejpam-6459	203	21	)	)	PUNCT
ejpam-6459	203	22	≥	≥	NOUN
ejpam-6459	203	23	a{k+	a{k+	ADP
ejpam-6459	203	24	ω	ω	X
ejpam-6459	203	25	(	(	PUNCT
ejpam-6459	203	26	κ),k+	κ),k+	PROPN
ejpam-6459	203	27	ω	ω	PROPN
ejpam-6459	203	28	(	(	PUNCT
ejpam-6459	203	29	ξ	ξ	NOUN
ejpam-6459	203	30	)	)	PUNCT
ejpam-6459	203	31	}	}	PUNCT
ejpam-6459	203	32	=	=	SYM
ejpam-6459	203	33	a{l+	a{l+	NUM
ejpam-6459	203	34	ω	ω	NUM
ejpam-6459	203	35	(	(	PUNCT
ejpam-6459	203	36	κ	κ	NOUN
ejpam-6459	203	37	)	)	PUNCT
ejpam-6459	203	38	,	,	PUNCT
ejpam-6459	203	39	l	l	PROPN
ejpam-6459	204	1	+	+	X
ejpam-6459	204	2	ω	ω	PROPN
ejpam-6459	204	3	(	(	PUNCT
ejpam-6459	204	4	ξ	ξ	NOUN
ejpam-6459	204	5	)	)	PUNCT
ejpam-6459	204	6	}	}	PUNCT
ejpam-6459	204	7	,	,	PUNCT
ejpam-6459	204	8	l−	l−	PROPN
ejpam-6459	204	9	ω	ω	PROPN
ejpam-6459	204	10	(	(	PUNCT
ejpam-6459	204	11	κ+	κ+	PROPN
ejpam-6459	204	12	ξ	ξ	PROPN
ejpam-6459	204	13	)	)	PUNCT
ejpam-6459	204	14	=	=	SYM
ejpam-6459	204	15	k−	k−	PROPN
ejpam-6459	204	16	ω	ω	PROPN
ejpam-6459	204	17	(	(	PUNCT
ejpam-6459	204	18	κ+	κ+	PROPN
ejpam-6459	204	19	ξ	ξ	PROPN
ejpam-6459	204	20	)	)	PUNCT
ejpam-6459	204	21	g.	g.	PROPN
ejpam-6459	204	22	s.	s.	PROPN
ejpam-6459	204	23	rao	rao	PROPN
ejpam-6459	204	24	et	et	PROPN
ejpam-6459	204	25	al	al	PROPN
ejpam-6459	204	26	.	.	PUNCT
ejpam-6459	204	27	/	/	SYM
ejpam-6459	204	28	eur	eur	PROPN
ejpam-6459	204	29	.	.	PUNCT
ejpam-6459	205	1	j.	j.	PROPN
ejpam-6459	205	2	pure	pure	PROPN
ejpam-6459	205	3	appl	appl	PROPN
ejpam-6459	205	4	.	.	PROPN
ejpam-6459	205	5	math	math	PROPN
ejpam-6459	205	6	,	,	PUNCT
ejpam-6459	205	7	18	18	NUM
ejpam-6459	205	8	(	(	PUNCT
ejpam-6459	205	9	3	3	NUM
ejpam-6459	205	10	)	)	PUNCT
ejpam-6459	205	11	(	(	PUNCT
ejpam-6459	205	12	2025	2025	NUM
ejpam-6459	205	13	)	)	PUNCT
ejpam-6459	205	14	,	,	PUNCT
ejpam-6459	205	15	6459	6459	NUM
ejpam-6459	205	16	9	9	NUM
ejpam-6459	205	17	of	of	ADP
ejpam-6459	205	18	16	16	NUM
ejpam-6459	205	19	≤	≤	NUM
ejpam-6459	205	20	b{k−	b{k−	PROPN
ejpam-6459	205	21	ω	ω	PROPN
ejpam-6459	205	22	(	(	PUNCT
ejpam-6459	205	23	κ),k−	κ),k−	PROPN
ejpam-6459	205	24	ω	ω	PROPN
ejpam-6459	205	25	(	(	PUNCT
ejpam-6459	205	26	ξ	ξ	NOUN
ejpam-6459	205	27	)	)	PUNCT
ejpam-6459	205	28	}	}	PUNCT
ejpam-6459	205	29	=	=	PUNCT
ejpam-6459	206	1	b{l−	b{l−	PUNCT
ejpam-6459	206	2	ω	ω	NUM
ejpam-6459	206	3	(	(	PUNCT
ejpam-6459	206	4	κ	κ	NOUN
ejpam-6459	206	5	)	)	PUNCT
ejpam-6459	206	6	,	,	PUNCT
ejpam-6459	206	7	l	l	PROPN
ejpam-6459	206	8	−	−	PROPN
ejpam-6459	206	9	ω	ω	X
ejpam-6459	206	10	(	(	PUNCT
ejpam-6459	206	11	ξ	ξ	NOUN
ejpam-6459	206	12	)	)	PUNCT
ejpam-6459	206	13	}	}	PUNCT
ejpam-6459	206	14	,	,	PUNCT
ejpam-6459	206	15	l+	l+	X
ejpam-6459	206	16	ω	ω	X
ejpam-6459	206	17	(	(	PUNCT
ejpam-6459	206	18	κξ	κξ	NOUN
ejpam-6459	206	19	)	)	PUNCT
ejpam-6459	206	20	=	=	PUNCT
ejpam-6459	206	21	k+	k+	PROPN
ejpam-6459	206	22	ω	ω	PROPN
ejpam-6459	206	23	(	(	PUNCT
ejpam-6459	206	24	κξ	κξ	NOUN
ejpam-6459	206	25	)	)	PUNCT
ejpam-6459	206	26	≥	≥	NOUN
ejpam-6459	206	27	a{k+	a{k+	X
ejpam-6459	206	28	ω	ω	X
ejpam-6459	206	29	(	(	PUNCT
ejpam-6459	206	30	κ),k+	κ),k+	PROPN
ejpam-6459	206	31	ω	ω	PROPN
ejpam-6459	206	32	(	(	PUNCT
ejpam-6459	206	33	ξ	ξ	NOUN
ejpam-6459	206	34	)	)	PUNCT
ejpam-6459	206	35	}	}	PUNCT
ejpam-6459	206	36	=	=	SYM
ejpam-6459	206	37	a{l+	a{l+	NUM
ejpam-6459	206	38	ω	ω	NUM
ejpam-6459	206	39	(	(	PUNCT
ejpam-6459	206	40	κ	κ	NOUN
ejpam-6459	206	41	)	)	PUNCT
ejpam-6459	206	42	,	,	PUNCT
ejpam-6459	206	43	l	l	PROPN
ejpam-6459	207	1	+	+	X
ejpam-6459	207	2	ω	ω	PROPN
ejpam-6459	207	3	(	(	PUNCT
ejpam-6459	207	4	ξ	ξ	NOUN
ejpam-6459	207	5	)	)	PUNCT
ejpam-6459	207	6	}	}	PUNCT
ejpam-6459	207	7	,	,	PUNCT
ejpam-6459	207	8	l−	l−	PROPN
ejpam-6459	207	9	ω	ω	PROPN
ejpam-6459	207	10	(	(	PUNCT
ejpam-6459	207	11	κξ	κξ	NOUN
ejpam-6459	207	12	)	)	PUNCT
ejpam-6459	207	13	=	=	SYM
ejpam-6459	207	14	k−	k−	PROPN
ejpam-6459	207	15	ω	ω	PROPN
ejpam-6459	207	16	(	(	PUNCT
ejpam-6459	207	17	κξ	κξ	NOUN
ejpam-6459	207	18	)	)	PUNCT
ejpam-6459	207	19	≤	≤	NOUN
ejpam-6459	207	20	b{k−	b{k−	PROPN
ejpam-6459	207	21	ω	ω	PROPN
ejpam-6459	207	22	(	(	PUNCT
ejpam-6459	207	23	κ),k−	κ),k−	PROPN
ejpam-6459	207	24	ω	ω	PROPN
ejpam-6459	207	25	(	(	PUNCT
ejpam-6459	207	26	ξ	ξ	NOUN
ejpam-6459	207	27	)	)	PUNCT
ejpam-6459	207	28	}	}	PUNCT
ejpam-6459	207	29	=	=	PUNCT
ejpam-6459	207	30	b{l−	b{l−	PUNCT
ejpam-6459	207	31	ω	ω	NUM
ejpam-6459	207	32	(	(	PUNCT
ejpam-6459	207	33	κ	κ	NOUN
ejpam-6459	207	34	)	)	PUNCT
ejpam-6459	207	35	,	,	PUNCT
ejpam-6459	207	36	l	l	PROPN
ejpam-6459	207	37	−	−	PROPN
ejpam-6459	207	38	ω	ω	X
ejpam-6459	207	39	(	(	PUNCT
ejpam-6459	207	40	ξ	ξ	NOUN
ejpam-6459	207	41	)	)	PUNCT
ejpam-6459	207	42	}	}	PUNCT
ejpam-6459	207	43	.	.	PUNCT
ejpam-6459	208	1	case	case	NOUN
ejpam-6459	208	2	3	3	NUM
ejpam-6459	208	3	:	:	PUNCT
ejpam-6459	208	4	if	if	SCONJ
ejpam-6459	208	5	ω	ω	PROPN
ejpam-6459	208	6	∈	∈	PROPN
ejpam-6459	208	7	u	u	NOUN
ejpam-6459	208	8	∩	∩	NOUN
ejpam-6459	208	9	v	v	NOUN
ejpam-6459	208	10	,	,	PUNCT
ejpam-6459	208	11	then	then	ADV
ejpam-6459	208	12	l+	l+	X
ejpam-6459	208	13	ω	ω	PROPN
ejpam-6459	208	14	(	(	PUNCT
ejpam-6459	208	15	κ+	κ+	PROPN
ejpam-6459	208	16	ξ	ξ	X
ejpam-6459	208	17	)	)	PUNCT
ejpam-6459	208	18	=	=	SYM
ejpam-6459	208	19	b{j+	b{j+	PROPN
ejpam-6459	208	20	ω	ω	NOUN
ejpam-6459	208	21	(	(	PUNCT
ejpam-6459	208	22	κ+	κ+	PROPN
ejpam-6459	208	23	ξ),k+	ξ),k+	PROPN
ejpam-6459	208	24	ω	ω	PROPN
ejpam-6459	208	25	(	(	PUNCT
ejpam-6459	208	26	κ+	κ+	PROPN
ejpam-6459	208	27	ξ	ξ	NUM
ejpam-6459	208	28	)	)	PUNCT
ejpam-6459	208	29	}	}	PUNCT
ejpam-6459	208	30	≥	≥	NOUN
ejpam-6459	208	31	b{a{j+	b{a{j+	NOUN
ejpam-6459	208	32	ω	ω	PROPN
ejpam-6459	208	33	(	(	PUNCT
ejpam-6459	208	34	κ	κ	NOUN
ejpam-6459	208	35	)	)	PUNCT
ejpam-6459	208	36	,	,	PUNCT
ejpam-6459	208	37	j+	j+	PROPN
ejpam-6459	208	38	ω	ω	PROPN
ejpam-6459	208	39	(	(	PUNCT
ejpam-6459	208	40	ξ	ξ	NOUN
ejpam-6459	208	41	)	)	PUNCT
ejpam-6459	208	42	}	}	PUNCT
ejpam-6459	208	43	,	,	PUNCT
ejpam-6459	208	44	a{k+	a{k+	ADP
ejpam-6459	208	45	ω	ω	X
ejpam-6459	208	46	(	(	PUNCT
ejpam-6459	208	47	κ),k+	κ),k+	PROPN
ejpam-6459	208	48	ω	ω	PROPN
ejpam-6459	208	49	(	(	PUNCT
ejpam-6459	208	50	ξ	ξ	NOUN
ejpam-6459	208	51	)	)	PUNCT
ejpam-6459	208	52	}	}	PUNCT
ejpam-6459	208	53	}	}	PUNCT
ejpam-6459	208	54	≥	≥	AUX
ejpam-6459	208	55	a{b{j+	a{b{j+	PROPN
ejpam-6459	208	56	ω	ω	PROPN
ejpam-6459	208	57	(	(	PUNCT
ejpam-6459	208	58	κ),k+	κ),k+	PROPN
ejpam-6459	208	59	ω	ω	PROPN
ejpam-6459	208	60	(	(	PUNCT
ejpam-6459	208	61	κ	κ	NOUN
ejpam-6459	208	62	)	)	PUNCT
ejpam-6459	208	63	}	}	PUNCT
ejpam-6459	208	64	,	,	PUNCT
ejpam-6459	208	65	b{j+	b{j+	PROPN
ejpam-6459	208	66	ω	ω	PROPN
ejpam-6459	208	67	(	(	PUNCT
ejpam-6459	208	68	ξ),k+	ξ),k+	PROPN
ejpam-6459	208	69	ω	ω	PROPN
ejpam-6459	208	70	(	(	PUNCT
ejpam-6459	208	71	ξ	ξ	NOUN
ejpam-6459	208	72	)	)	PUNCT
ejpam-6459	208	73	}	}	PUNCT
ejpam-6459	208	74	}	}	PUNCT
ejpam-6459	208	75	=	=	SYM
ejpam-6459	208	76	a{l+	a{l+	NUM
ejpam-6459	208	77	ω	ω	NUM
ejpam-6459	208	78	(	(	PUNCT
ejpam-6459	208	79	κ	κ	NOUN
ejpam-6459	208	80	)	)	PUNCT
ejpam-6459	208	81	,	,	PUNCT
ejpam-6459	208	82	l	l	PROPN
ejpam-6459	209	1	+	+	X
ejpam-6459	209	2	ω	ω	PROPN
ejpam-6459	209	3	(	(	PUNCT
ejpam-6459	209	4	ξ	ξ	NOUN
ejpam-6459	209	5	)	)	PUNCT
ejpam-6459	209	6	}	}	PUNCT
ejpam-6459	209	7	,	,	PUNCT
ejpam-6459	209	8	l−	l−	PROPN
ejpam-6459	209	9	ω	ω	PROPN
ejpam-6459	209	10	(	(	PUNCT
ejpam-6459	209	11	κ+	κ+	PROPN
ejpam-6459	209	12	ξ	ξ	NUM
ejpam-6459	209	13	)	)	PUNCT
ejpam-6459	209	14	=	=	SYM
ejpam-6459	209	15	a{j−	a{j−	NUM
ejpam-6459	209	16	ω	ω	PROPN
ejpam-6459	209	17	(	(	PUNCT
ejpam-6459	209	18	κ+	κ+	PROPN
ejpam-6459	209	19	ξ),k−	ξ),k−	PROPN
ejpam-6459	209	20	ω	ω	PROPN
ejpam-6459	209	21	(	(	PUNCT
ejpam-6459	209	22	κ+	κ+	PROPN
ejpam-6459	209	23	ξ	ξ	NUM
ejpam-6459	209	24	)	)	PUNCT
ejpam-6459	209	25	}	}	PUNCT
ejpam-6459	209	26	≤	≤	NUM
ejpam-6459	209	27	a{b{j−	a{b{j−	X
ejpam-6459	209	28	ω	ω	X
ejpam-6459	209	29	(	(	PUNCT
ejpam-6459	209	30	κ	κ	NOUN
ejpam-6459	209	31	)	)	PUNCT
ejpam-6459	209	32	,	,	PUNCT
ejpam-6459	209	33	j−	j−	PROPN
ejpam-6459	209	34	ω	ω	PROPN
ejpam-6459	209	35	(	(	PUNCT
ejpam-6459	209	36	ξ	ξ	NOUN
ejpam-6459	209	37	)	)	PUNCT
ejpam-6459	209	38	}	}	PUNCT
ejpam-6459	209	39	,	,	PUNCT
ejpam-6459	209	40	b{k−	b{k−	PROPN
ejpam-6459	209	41	ω	ω	PROPN
ejpam-6459	209	42	(	(	PUNCT
ejpam-6459	209	43	κ),k−	κ),k−	PROPN
ejpam-6459	209	44	ω	ω	PROPN
ejpam-6459	209	45	(	(	PUNCT
ejpam-6459	209	46	ξ	ξ	NOUN
ejpam-6459	209	47	)	)	PUNCT
ejpam-6459	209	48	}	}	PUNCT
ejpam-6459	209	49	}	}	PUNCT
ejpam-6459	209	50	≤	≤	NUM
ejpam-6459	209	51	b{a{j−	b{a{j−	NOUN
ejpam-6459	209	52	ω	ω	PROPN
ejpam-6459	209	53	(	(	PUNCT
ejpam-6459	209	54	κ),k−	κ),k−	PROPN
ejpam-6459	209	55	ω	ω	PROPN
ejpam-6459	209	56	(	(	PUNCT
ejpam-6459	209	57	κ	κ	NOUN
ejpam-6459	209	58	)	)	PUNCT
ejpam-6459	209	59	}	}	PUNCT
ejpam-6459	209	60	,	,	PUNCT
ejpam-6459	209	61	a{j−	a{j−	NUM
ejpam-6459	209	62	ω	ω	PROPN
ejpam-6459	209	63	(	(	PUNCT
ejpam-6459	209	64	ξ),k−	ξ),k−	PROPN
ejpam-6459	209	65	ω	ω	PROPN
ejpam-6459	209	66	(	(	PUNCT
ejpam-6459	209	67	ξ	ξ	NOUN
ejpam-6459	209	68	)	)	PUNCT
ejpam-6459	209	69	}	}	PUNCT
ejpam-6459	209	70	}	}	PUNCT
ejpam-6459	209	71	=	=	PUNCT
ejpam-6459	209	72	b{l−	b{l−	PUNCT
ejpam-6459	209	73	ω	ω	NUM
ejpam-6459	209	74	(	(	PUNCT
ejpam-6459	209	75	κ	κ	NOUN
ejpam-6459	209	76	)	)	PUNCT
ejpam-6459	209	77	,	,	PUNCT
ejpam-6459	209	78	l	l	PROPN
ejpam-6459	209	79	−	−	PROPN
ejpam-6459	209	80	ω	ω	X
ejpam-6459	209	81	(	(	PUNCT
ejpam-6459	209	82	ξ	ξ	NOUN
ejpam-6459	209	83	)	)	PUNCT
ejpam-6459	209	84	}	}	PUNCT
ejpam-6459	209	85	,	,	PUNCT
ejpam-6459	209	86	l+	l+	X
ejpam-6459	209	87	ω	ω	X
ejpam-6459	209	88	(	(	PUNCT
ejpam-6459	209	89	κξ	κξ	NOUN
ejpam-6459	209	90	)	)	PUNCT
ejpam-6459	209	91	=	=	NOUN
ejpam-6459	209	92	b{j+	b{j+	PROPN
ejpam-6459	209	93	ω	ω	PROPN
ejpam-6459	209	94	(	(	PUNCT
ejpam-6459	209	95	κξ),k+	κξ),k+	PROPN
ejpam-6459	209	96	ω	ω	PROPN
ejpam-6459	209	97	(	(	PUNCT
ejpam-6459	209	98	κξ	κξ	NOUN
ejpam-6459	209	99	)	)	PUNCT
ejpam-6459	209	100	}	}	PUNCT
ejpam-6459	209	101	≥	≥	AUX
ejpam-6459	209	102	b{a{j+	b{a{j+	NOUN
ejpam-6459	209	103	ω	ω	PROPN
ejpam-6459	209	104	(	(	PUNCT
ejpam-6459	209	105	κ	κ	NOUN
ejpam-6459	209	106	)	)	PUNCT
ejpam-6459	209	107	,	,	PUNCT
ejpam-6459	209	108	j+	j+	PROPN
ejpam-6459	209	109	ω	ω	PROPN
ejpam-6459	209	110	(	(	PUNCT
ejpam-6459	209	111	ξ	ξ	NOUN
ejpam-6459	209	112	)	)	PUNCT
ejpam-6459	209	113	}	}	PUNCT
ejpam-6459	209	114	,	,	PUNCT
ejpam-6459	209	115	a{k+	a{k+	ADP
ejpam-6459	209	116	ω	ω	X
ejpam-6459	209	117	(	(	PUNCT
ejpam-6459	209	118	κ),k+	κ),k+	PROPN
ejpam-6459	209	119	ω	ω	PROPN
ejpam-6459	209	120	(	(	PUNCT
ejpam-6459	209	121	ξ	ξ	NOUN
ejpam-6459	209	122	)	)	PUNCT
ejpam-6459	209	123	}	}	PUNCT
ejpam-6459	209	124	}	}	PUNCT
ejpam-6459	209	125	≥	≥	AUX
ejpam-6459	209	126	a{b{j+	a{b{j+	PROPN
ejpam-6459	209	127	ω	ω	PROPN
ejpam-6459	209	128	(	(	PUNCT
ejpam-6459	209	129	κ),k+	κ),k+	PROPN
ejpam-6459	209	130	ω	ω	PROPN
ejpam-6459	209	131	(	(	PUNCT
ejpam-6459	209	132	κ	κ	NOUN
ejpam-6459	209	133	)	)	PUNCT
ejpam-6459	209	134	}	}	PUNCT
ejpam-6459	209	135	,	,	PUNCT
ejpam-6459	209	136	b{j+	b{j+	PROPN
ejpam-6459	209	137	ω	ω	PROPN
ejpam-6459	209	138	(	(	PUNCT
ejpam-6459	209	139	ξ),k+	ξ),k+	PROPN
ejpam-6459	209	140	ω	ω	PROPN
ejpam-6459	209	141	(	(	PUNCT
ejpam-6459	209	142	ξ	ξ	NOUN
ejpam-6459	209	143	)	)	PUNCT
ejpam-6459	209	144	}	}	PUNCT
ejpam-6459	209	145	}	}	PUNCT
ejpam-6459	209	146	=	=	SYM
ejpam-6459	209	147	a{l+	a{l+	NUM
ejpam-6459	209	148	ω	ω	NUM
ejpam-6459	209	149	(	(	PUNCT
ejpam-6459	209	150	κ	κ	NOUN
ejpam-6459	209	151	)	)	PUNCT
ejpam-6459	209	152	,	,	PUNCT
ejpam-6459	209	153	l	l	PROPN
ejpam-6459	210	1	+	+	X
ejpam-6459	210	2	ω	ω	PROPN
ejpam-6459	210	3	(	(	PUNCT
ejpam-6459	210	4	ξ	ξ	NOUN
ejpam-6459	210	5	)	)	PUNCT
ejpam-6459	210	6	}	}	PUNCT
ejpam-6459	210	7	,	,	PUNCT
ejpam-6459	210	8	l−	l−	PROPN
ejpam-6459	210	9	ω	ω	PROPN
ejpam-6459	210	10	(	(	PUNCT
ejpam-6459	210	11	κξ	κξ	NOUN
ejpam-6459	210	12	)	)	PUNCT
ejpam-6459	210	13	=	=	PUNCT
ejpam-6459	210	14	a{j−	a{j−	NUM
ejpam-6459	210	15	ω	ω	PROPN
ejpam-6459	210	16	(	(	PUNCT
ejpam-6459	210	17	κξ),k−	κξ),k−	PROPN
ejpam-6459	210	18	ω	ω	PROPN
ejpam-6459	210	19	(	(	PUNCT
ejpam-6459	210	20	κξ	κξ	NOUN
ejpam-6459	210	21	)	)	PUNCT
ejpam-6459	210	22	}	}	PUNCT
ejpam-6459	210	23	≤	≤	NUM
ejpam-6459	210	24	a{b{j−	a{b{j−	X
ejpam-6459	210	25	ω	ω	X
ejpam-6459	210	26	(	(	PUNCT
ejpam-6459	210	27	κ	κ	NOUN
ejpam-6459	210	28	)	)	PUNCT
ejpam-6459	210	29	,	,	PUNCT
ejpam-6459	210	30	j−	j−	PROPN
ejpam-6459	210	31	ω	ω	PROPN
ejpam-6459	210	32	(	(	PUNCT
ejpam-6459	210	33	ξ	ξ	NOUN
ejpam-6459	210	34	)	)	PUNCT
ejpam-6459	210	35	}	}	PUNCT
ejpam-6459	210	36	,	,	PUNCT
ejpam-6459	210	37	b{k−	b{k−	PROPN
ejpam-6459	210	38	ω	ω	PROPN
ejpam-6459	210	39	(	(	PUNCT
ejpam-6459	210	40	κ),k−	κ),k−	PROPN
ejpam-6459	210	41	ω	ω	PROPN
ejpam-6459	210	42	(	(	PUNCT
ejpam-6459	210	43	ξ	ξ	NOUN
ejpam-6459	210	44	)	)	PUNCT
ejpam-6459	210	45	}	}	PUNCT
ejpam-6459	210	46	}	}	PUNCT
ejpam-6459	210	47	≤	≤	NUM
ejpam-6459	210	48	b{a{j−	b{a{j−	NOUN
ejpam-6459	210	49	ω	ω	PROPN
ejpam-6459	210	50	(	(	PUNCT
ejpam-6459	210	51	κ),k−	κ),k−	PROPN
ejpam-6459	210	52	ω	ω	PROPN
ejpam-6459	210	53	(	(	PUNCT
ejpam-6459	210	54	κ	κ	NOUN
ejpam-6459	210	55	)	)	PUNCT
ejpam-6459	210	56	}	}	PUNCT
ejpam-6459	210	57	,	,	PUNCT
ejpam-6459	210	58	a{j−	a{j−	NUM
ejpam-6459	210	59	ω	ω	PROPN
ejpam-6459	210	60	(	(	PUNCT
ejpam-6459	210	61	ξ),k−	ξ),k−	PROPN
ejpam-6459	210	62	ω	ω	PROPN
ejpam-6459	210	63	(	(	PUNCT
ejpam-6459	210	64	ξ	ξ	NOUN
ejpam-6459	210	65	)	)	PUNCT
ejpam-6459	210	66	}	}	PUNCT
ejpam-6459	210	67	}	}	PUNCT
ejpam-6459	210	68	=	=	PUNCT
ejpam-6459	210	69	b{l−	b{l−	PUNCT
ejpam-6459	210	70	ω	ω	NUM
ejpam-6459	210	71	(	(	PUNCT
ejpam-6459	210	72	κ	κ	NOUN
ejpam-6459	210	73	)	)	PUNCT
ejpam-6459	210	74	,	,	PUNCT
ejpam-6459	210	75	l	l	PROPN
ejpam-6459	210	76	−	−	PROPN
ejpam-6459	210	77	ω	ω	X
ejpam-6459	210	78	(	(	PUNCT
ejpam-6459	210	79	ξ	ξ	NOUN
ejpam-6459	210	80	)	)	PUNCT
ejpam-6459	210	81	}	}	PUNCT
ejpam-6459	210	82	.	.	PUNCT
ejpam-6459	211	1	therefore	therefore	ADV
ejpam-6459	211	2	,	,	PUNCT
ejpam-6459	211	3	(	(	PUNCT
ejpam-6459	211	4	l	l	NOUN
ejpam-6459	211	5	,	,	PUNCT
ejpam-6459	211	6	w	w	NOUN
ejpam-6459	211	7	)	)	PUNCT
ejpam-6459	211	8	=	=	SYM
ejpam-6459	211	9	(	(	PUNCT
ejpam-6459	211	10	j	j	PROPN
ejpam-6459	211	11	,	,	PUNCT
ejpam-6459	211	12	u	u	NOUN
ejpam-6459	211	13	)	)	PUNCT
ejpam-6459	211	14	∪	∪	ADV
ejpam-6459	211	15	(	(	PUNCT
ejpam-6459	211	16	k	k	NOUN
ejpam-6459	211	17	,	,	PUNCT
ejpam-6459	211	18	v	v	NOUN
ejpam-6459	211	19	)	)	PUNCT
ejpam-6459	211	20	is	be	AUX
ejpam-6459	211	21	a	a	DET
ejpam-6459	211	22	bfsbr	bfsbr	NOUN
ejpam-6459	211	23	over	over	ADP
ejpam-6459	211	24	ℜ.	ℜ.	PROPN
ejpam-6459	211	25	example	example	NOUN
ejpam-6459	211	26	3	3	X
ejpam-6459	211	27	.	.	PUNCT
ejpam-6459	211	28	let	let	VERB
ejpam-6459	211	29	the	the	DET
ejpam-6459	211	30	br	br	NOUN
ejpam-6459	211	31	be	be	AUX
ejpam-6459	211	32	ℜ	ℜ	ADV
ejpam-6459	211	33	=	=	SYM
ejpam-6459	211	34	{	{	PUNCT
ejpam-6459	211	35	0	0	NUM
ejpam-6459	211	36	,	,	PUNCT
ejpam-6459	211	37	κ	κ	NOUN
ejpam-6459	211	38	,	,	PUNCT
ejpam-6459	211	39	ξ	ξ	PROPN
ejpam-6459	211	40	,	,	PUNCT
ejpam-6459	211	41	τ	τ	X
ejpam-6459	211	42	}	}	PUNCT
ejpam-6459	211	43	,	,	PUNCT
ejpam-6459	211	44	and	and	CCONJ
ejpam-6459	211	45	the	the	DET
ejpam-6459	211	46	table	table	NOUN
ejpam-6459	211	47	is	be	AUX
ejpam-6459	211	48	provided	provide	VERB
ejpam-6459	211	49	in	in	ADP
ejpam-6459	211	50	example	example	NOUN
ejpam-6459	211	51	1	1	NUM
ejpam-6459	211	52	above	above	ADV
ejpam-6459	211	53	.	.	PUNCT
ejpam-6459	212	1	let	let	VERB
ejpam-6459	212	2	the	the	DET
ejpam-6459	212	3	parameters	parameter	NOUN
ejpam-6459	212	4	be	be	AUX
ejpam-6459	212	5	e	e	NOUN
ejpam-6459	212	6	=	=	PUNCT
ejpam-6459	212	7	{	{	PUNCT
ejpam-6459	212	8	e1	e1	PROPN
ejpam-6459	212	9	,	,	PUNCT
ejpam-6459	212	10	e2	e2	PROPN
ejpam-6459	212	11	,	,	PUNCT
ejpam-6459	212	12	e3	e3	NOUN
ejpam-6459	212	13	}	}	PUNCT
ejpam-6459	212	14	and	and	CCONJ
ejpam-6459	212	15	u	u	NOUN
ejpam-6459	212	16	=	=	PUNCT
ejpam-6459	212	17	{	{	PUNCT
ejpam-6459	212	18	e1	e1	PROPN
ejpam-6459	212	19	,	,	PUNCT
ejpam-6459	212	20	e2	e2	PROPN
ejpam-6459	212	21	}	}	PUNCT
ejpam-6459	212	22	⊆	⊆	NUM
ejpam-6459	212	23	e.	e.	PROPN
ejpam-6459	212	24	then	then	ADV
ejpam-6459	212	25	(	(	PUNCT
ejpam-6459	212	26	j	j	NOUN
ejpam-6459	212	27	,	,	PUNCT
ejpam-6459	212	28	u	u	NOUN
ejpam-6459	212	29	)	)	PUNCT
ejpam-6459	212	30	is	be	AUX
ejpam-6459	212	31	a	a	DET
ejpam-6459	212	32	bfss	bfss	ADV
ejpam-6459	212	33	defined	define	VERB
ejpam-6459	212	34	as	as	ADP
ejpam-6459	212	35	,	,	PUNCT
ejpam-6459	212	36	(	(	PUNCT
ejpam-6459	212	37	j	j	NOUN
ejpam-6459	212	38	,	,	PUNCT
ejpam-6459	212	39	u	u	NOUN
ejpam-6459	212	40	)	)	PUNCT
ejpam-6459	212	41	=	=	SYM
ejpam-6459	212	42	{	{	PUNCT
ejpam-6459	212	43	j(e1	j(e1	NOUN
ejpam-6459	212	44	)	)	PUNCT
ejpam-6459	212	45	,	,	PUNCT
ejpam-6459	212	46	j(e2	j(e2	NOUN
ejpam-6459	212	47	)	)	PUNCT
ejpam-6459	212	48	}	}	PUNCT
ejpam-6459	212	49	,	,	PUNCT
ejpam-6459	212	50	where	where	SCONJ
ejpam-6459	212	51	j(e1	j(e1	NOUN
ejpam-6459	212	52	)	)	PUNCT
ejpam-6459	213	1	=	=	PRON
ejpam-6459	213	2	{	{	PUNCT
ejpam-6459	213	3	(	(	PUNCT
ejpam-6459	213	4	0	0	NUM
ejpam-6459	213	5	,	,	PUNCT
ejpam-6459	213	6	0.9,−0.7	0.9,−0.7	NUM
ejpam-6459	213	7	)	)	PUNCT
ejpam-6459	213	8	,	,	PUNCT
ejpam-6459	213	9	(	(	PUNCT
ejpam-6459	213	10	κ	κ	NOUN
ejpam-6459	213	11	,	,	PUNCT
ejpam-6459	213	12	0.5,−0.3	0.5,−0.3	NUM
ejpam-6459	213	13	)	)	PUNCT
ejpam-6459	213	14	,	,	PUNCT
ejpam-6459	213	15	(	(	PUNCT
ejpam-6459	213	16	ξ	ξ	X
ejpam-6459	213	17	,	,	PUNCT
ejpam-6459	213	18	0.7,−0.2	0.7,−0.2	NUM
ejpam-6459	213	19	)	)	PUNCT
ejpam-6459	213	20	,	,	PUNCT
ejpam-6459	213	21	(	(	PUNCT
ejpam-6459	213	22	τ	τ	X
ejpam-6459	213	23	,	,	PUNCT
ejpam-6459	213	24	0.5,−0.2	0.5,−0.2	NUM
ejpam-6459	213	25	)	)	PUNCT
ejpam-6459	213	26	}	}	PUNCT
ejpam-6459	213	27	,	,	PUNCT
ejpam-6459	213	28	j(e2	j(e2	NOUN
ejpam-6459	213	29	)	)	PUNCT
ejpam-6459	213	30	=	=	PRON
ejpam-6459	213	31	{	{	PUNCT
ejpam-6459	213	32	(	(	PUNCT
ejpam-6459	213	33	0	0	NUM
ejpam-6459	213	34	,	,	PUNCT
ejpam-6459	213	35	0.8,−0.7	0.8,−0.7	NUM
ejpam-6459	213	36	)	)	PUNCT
ejpam-6459	213	37	,	,	PUNCT
ejpam-6459	213	38	(	(	PUNCT
ejpam-6459	213	39	κ	κ	NOUN
ejpam-6459	213	40	,	,	PUNCT
ejpam-6459	213	41	0.4,−0.1	0.4,−0.1	NOUN
ejpam-6459	213	42	)	)	PUNCT
ejpam-6459	213	43	,	,	PUNCT
ejpam-6459	213	44	(	(	PUNCT
ejpam-6459	213	45	ξ	ξ	X
ejpam-6459	213	46	,	,	PUNCT
ejpam-6459	213	47	0.2,−0.5	0.2,−0.5	NUM
ejpam-6459	213	48	)	)	PUNCT
ejpam-6459	213	49	,	,	PUNCT
ejpam-6459	213	50	(	(	PUNCT
ejpam-6459	213	51	τ	τ	X
ejpam-6459	213	52	,	,	PUNCT
ejpam-6459	213	53	0.2,−0.1	0.2,−0.1	NOUN
ejpam-6459	213	54	)	)	PUNCT
ejpam-6459	213	55	}	}	PUNCT
ejpam-6459	213	56	.	.	PUNCT
ejpam-6459	214	1	let	let	VERB
ejpam-6459	214	2	v	v	VERB
ejpam-6459	214	3	=	=	SYM
ejpam-6459	214	4	{	{	PUNCT
ejpam-6459	214	5	e2	e2	PROPN
ejpam-6459	214	6	,	,	PUNCT
ejpam-6459	214	7	e3	e3	PROPN
ejpam-6459	214	8	}	}	PUNCT
ejpam-6459	214	9	⊆	⊆	NUM
ejpam-6459	214	10	e.	e.	PROPN
ejpam-6459	214	11	then	then	ADV
ejpam-6459	214	12	(	(	PUNCT
ejpam-6459	214	13	k	k	X
ejpam-6459	214	14	,	,	PUNCT
ejpam-6459	214	15	v	v	NOUN
ejpam-6459	214	16	)	)	PUNCT
ejpam-6459	214	17	is	be	AUX
ejpam-6459	214	18	a	a	DET
ejpam-6459	214	19	bfss	bfss	ADV
ejpam-6459	214	20	defined	define	VERB
ejpam-6459	214	21	as	as	ADP
ejpam-6459	214	22	,	,	PUNCT
ejpam-6459	214	23	(	(	PUNCT
ejpam-6459	214	24	k	k	X
ejpam-6459	214	25	,	,	PUNCT
ejpam-6459	214	26	v	v	NOUN
ejpam-6459	214	27	)	)	PUNCT
ejpam-6459	214	28	=	=	SYM
ejpam-6459	214	29	{	{	PUNCT
ejpam-6459	214	30	k(e2),k(e3	k(e2),k(e3	PROPN
ejpam-6459	214	31	)	)	PUNCT
ejpam-6459	214	32	}	}	PUNCT
ejpam-6459	214	33	,	,	PUNCT
ejpam-6459	214	34	where	where	SCONJ
ejpam-6459	214	35	g.	g.	PROPN
ejpam-6459	214	36	s.	s.	PROPN
ejpam-6459	214	37	rao	rao	PROPN
ejpam-6459	214	38	et	et	PROPN
ejpam-6459	214	39	al	al	PROPN
ejpam-6459	214	40	.	.	PUNCT
ejpam-6459	214	41	/	/	SYM
ejpam-6459	214	42	eur	eur	PROPN
ejpam-6459	214	43	.	.	PUNCT
ejpam-6459	215	1	j.	j.	PROPN
ejpam-6459	215	2	pure	pure	PROPN
ejpam-6459	215	3	appl	appl	PROPN
ejpam-6459	215	4	.	.	PROPN
ejpam-6459	215	5	math	math	PROPN
ejpam-6459	215	6	,	,	PUNCT
ejpam-6459	215	7	18	18	NUM
ejpam-6459	215	8	(	(	PUNCT
ejpam-6459	215	9	3	3	NUM
ejpam-6459	215	10	)	)	PUNCT
ejpam-6459	215	11	(	(	PUNCT
ejpam-6459	215	12	2025	2025	NUM
ejpam-6459	215	13	)	)	PUNCT
ejpam-6459	215	14	,	,	PUNCT
ejpam-6459	215	15	6459	6459	NUM
ejpam-6459	215	16	10	10	NUM
ejpam-6459	215	17	of	of	ADP
ejpam-6459	215	18	16	16	NUM
ejpam-6459	215	19	k(e2	k(e2	NOUN
ejpam-6459	215	20	)	)	PUNCT
ejpam-6459	215	21	=	=	PRON
ejpam-6459	215	22	{	{	PUNCT
ejpam-6459	215	23	(	(	PUNCT
ejpam-6459	215	24	0	0	NUM
ejpam-6459	215	25	,	,	PUNCT
ejpam-6459	215	26	0.7,−0.6	0.7,−0.6	NOUN
ejpam-6459	215	27	)	)	PUNCT
ejpam-6459	215	28	,	,	PUNCT
ejpam-6459	215	29	(	(	PUNCT
ejpam-6459	215	30	κ	κ	NOUN
ejpam-6459	215	31	,	,	PUNCT
ejpam-6459	215	32	0.6,−0.4	0.6,−0.4	NUM
ejpam-6459	215	33	)	)	PUNCT
ejpam-6459	215	34	,	,	PUNCT
ejpam-6459	215	35	(	(	PUNCT
ejpam-6459	215	36	ξ	ξ	X
ejpam-6459	215	37	,	,	PUNCT
ejpam-6459	215	38	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	215	39	)	)	PUNCT
ejpam-6459	215	40	,	,	PUNCT
ejpam-6459	215	41	(	(	PUNCT
ejpam-6459	215	42	τ	τ	PROPN
ejpam-6459	215	43	,	,	PUNCT
ejpam-6459	215	44	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	215	45	)	)	PUNCT
ejpam-6459	215	46	}	}	PUNCT
ejpam-6459	215	47	,	,	PUNCT
ejpam-6459	215	48	k(e3	k(e3	PROPN
ejpam-6459	215	49	)	)	PUNCT
ejpam-6459	215	50	=	=	PRON
ejpam-6459	215	51	{	{	PUNCT
ejpam-6459	215	52	(	(	PUNCT
ejpam-6459	215	53	0	0	NUM
ejpam-6459	215	54	,	,	PUNCT
ejpam-6459	215	55	0.6,−0.9	0.6,−0.9	NUM
ejpam-6459	215	56	)	)	PUNCT
ejpam-6459	215	57	,	,	PUNCT
ejpam-6459	215	58	(	(	PUNCT
ejpam-6459	215	59	κ	κ	NOUN
ejpam-6459	215	60	,	,	PUNCT
ejpam-6459	215	61	0.4,−0.5	0.4,−0.5	NUM
ejpam-6459	215	62	)	)	PUNCT
ejpam-6459	215	63	,	,	PUNCT
ejpam-6459	215	64	(	(	PUNCT
ejpam-6459	215	65	ξ	ξ	X
ejpam-6459	215	66	,	,	PUNCT
ejpam-6459	215	67	0.3,−0.5	0.3,−0.5	NUM
ejpam-6459	215	68	)	)	PUNCT
ejpam-6459	215	69	,	,	PUNCT
ejpam-6459	215	70	(	(	PUNCT
ejpam-6459	215	71	τ	τ	PROPN
ejpam-6459	215	72	,	,	PUNCT
ejpam-6459	215	73	0.3,−0.5	0.3,−0.5	NUM
ejpam-6459	215	74	)	)	PUNCT
ejpam-6459	215	75	}	}	PUNCT
ejpam-6459	215	76	.	.	PUNCT
ejpam-6459	216	1	it	it	PRON
ejpam-6459	216	2	is	be	AUX
ejpam-6459	216	3	seen	see	VERB
ejpam-6459	216	4	that	that	SCONJ
ejpam-6459	216	5	(	(	PUNCT
ejpam-6459	216	6	j	j	NOUN
ejpam-6459	216	7	,	,	PUNCT
ejpam-6459	216	8	u	u	NOUN
ejpam-6459	216	9	)	)	PUNCT
ejpam-6459	216	10	and	and	CCONJ
ejpam-6459	216	11	(	(	PUNCT
ejpam-6459	216	12	k	k	X
ejpam-6459	216	13	,	,	PUNCT
ejpam-6459	216	14	v	v	NOUN
ejpam-6459	216	15	)	)	PUNCT
ejpam-6459	216	16	are	be	AUX
ejpam-6459	216	17	bfsbrs	bfsbr	VERB
ejpam-6459	216	18	of	of	ADP
ejpam-6459	216	19	ℜ.	ℜ.	PROPN
ejpam-6459	216	20	now	now	ADV
ejpam-6459	216	21	,	,	PUNCT
ejpam-6459	216	22	let	let	VERB
ejpam-6459	216	23	(	(	PUNCT
ejpam-6459	216	24	j	j	NOUN
ejpam-6459	216	25	,	,	PUNCT
ejpam-6459	216	26	u	u	NOUN
ejpam-6459	216	27	)	)	PUNCT
ejpam-6459	216	28	∧	∧	PROPN
ejpam-6459	216	29	(	(	PUNCT
ejpam-6459	216	30	k	k	NOUN
ejpam-6459	216	31	,	,	PUNCT
ejpam-6459	216	32	v	v	NOUN
ejpam-6459	216	33	)	)	PUNCT
ejpam-6459	216	34	=	=	SYM
ejpam-6459	216	35	(	(	PUNCT
ejpam-6459	216	36	l	l	NOUN
ejpam-6459	216	37	,	,	PUNCT
ejpam-6459	216	38	w	w	NOUN
ejpam-6459	216	39	)	)	PUNCT
ejpam-6459	216	40	,	,	PUNCT
ejpam-6459	216	41	where	where	SCONJ
ejpam-6459	216	42	w	w	NOUN
ejpam-6459	216	43	=	=	PUNCT
ejpam-6459	216	44	u	u	NOUN
ejpam-6459	216	45	×	×	NOUN
ejpam-6459	216	46	v	v	NOUN
ejpam-6459	216	47	=	=	SYM
ejpam-6459	216	48	{	{	PUNCT
ejpam-6459	216	49	(	(	PUNCT
ejpam-6459	216	50	e1	e1	PROPN
ejpam-6459	216	51	,	,	PUNCT
ejpam-6459	216	52	e2	e2	PROPN
ejpam-6459	216	53	)	)	PUNCT
ejpam-6459	216	54	,	,	PUNCT
ejpam-6459	216	55	(	(	PUNCT
ejpam-6459	216	56	e1	e1	NOUN
ejpam-6459	216	57	,	,	PUNCT
ejpam-6459	216	58	e3	e3	NOUN
ejpam-6459	216	59	)	)	PUNCT
ejpam-6459	216	60	,	,	PUNCT
ejpam-6459	216	61	(	(	PUNCT
ejpam-6459	216	62	e2	e2	PROPN
ejpam-6459	216	63	,	,	PUNCT
ejpam-6459	216	64	e2	e2	PROPN
ejpam-6459	216	65	)	)	PUNCT
ejpam-6459	216	66	,	,	PUNCT
ejpam-6459	216	67	(	(	PUNCT
ejpam-6459	216	68	e2	e2	PROPN
ejpam-6459	216	69	,	,	PUNCT
ejpam-6459	216	70	e3	e3	NOUN
ejpam-6459	216	71	)	)	PUNCT
ejpam-6459	216	72	}	}	PUNCT
ejpam-6459	216	73	.	.	PUNCT
ejpam-6459	217	1	then	then	ADV
ejpam-6459	217	2	(	(	PUNCT
ejpam-6459	217	3	j	j	PROPN
ejpam-6459	217	4	∧k	∧k	PROPN
ejpam-6459	217	5	,	,	PUNCT
ejpam-6459	217	6	w	w	NOUN
ejpam-6459	217	7	)	)	PUNCT
ejpam-6459	217	8	=	=	PRON
ejpam-6459	217	9	{	{	PUNCT
ejpam-6459	217	10	(	(	PUNCT
ejpam-6459	217	11	j	j	PROPN
ejpam-6459	217	12	∧k)(e1	∧k)(e1	PROPN
ejpam-6459	217	13	,	,	PUNCT
ejpam-6459	217	14	e2	e2	PROPN
ejpam-6459	217	15	)	)	PUNCT
ejpam-6459	217	16	,	,	PUNCT
ejpam-6459	217	17	(	(	PUNCT
ejpam-6459	217	18	j	j	PROPN
ejpam-6459	217	19	∧k)(e1	∧k)(e1	PROPN
ejpam-6459	217	20	,	,	PUNCT
ejpam-6459	217	21	e3	e3	NOUN
ejpam-6459	217	22	)	)	PUNCT
ejpam-6459	217	23	,	,	PUNCT
ejpam-6459	217	24	(	(	PUNCT
ejpam-6459	217	25	j	j	PROPN
ejpam-6459	217	26	∧k)(e2	∧k)(e2	PROPN
ejpam-6459	217	27	,	,	PUNCT
ejpam-6459	217	28	e2	e2	PROPN
ejpam-6459	217	29	)	)	PUNCT
ejpam-6459	217	30	,	,	PUNCT
ejpam-6459	217	31	(	(	PUNCT
ejpam-6459	217	32	j	j	PROPN
ejpam-6459	217	33	∧k)(e2	∧k)(e2	PROPN
ejpam-6459	217	34	,	,	PUNCT
ejpam-6459	217	35	e3	e3	NOUN
ejpam-6459	217	36	)	)	PUNCT
ejpam-6459	217	37	}	}	PUNCT
ejpam-6459	217	38	,	,	PUNCT
ejpam-6459	217	39	where	where	SCONJ
ejpam-6459	217	40	(	(	PUNCT
ejpam-6459	217	41	j	j	PROPN
ejpam-6459	217	42	∧k)(e1	∧k)(e1	PROPN
ejpam-6459	217	43	,	,	PUNCT
ejpam-6459	217	44	e2	e2	PROPN
ejpam-6459	217	45	)	)	PUNCT
ejpam-6459	217	46	=	=	PRON
ejpam-6459	217	47	{	{	PUNCT
ejpam-6459	217	48	(	(	PUNCT
ejpam-6459	217	49	0	0	NUM
ejpam-6459	217	50	,	,	PUNCT
ejpam-6459	217	51	0.7−	0.7−	NOUN
ejpam-6459	217	52	0.6	0.6	NUM
ejpam-6459	217	53	)	)	PUNCT
ejpam-6459	217	54	,	,	PUNCT
ejpam-6459	217	55	(	(	PUNCT
ejpam-6459	217	56	κ	κ	NOUN
ejpam-6459	217	57	,	,	PUNCT
ejpam-6459	217	58	0.5,−0.3	0.5,−0.3	NUM
ejpam-6459	217	59	)	)	PUNCT
ejpam-6459	217	60	,	,	PUNCT
ejpam-6459	217	61	(	(	PUNCT
ejpam-6459	217	62	ξ	ξ	X
ejpam-6459	217	63	,	,	PUNCT
ejpam-6459	217	64	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	217	65	)	)	PUNCT
ejpam-6459	217	66	,	,	PUNCT
ejpam-6459	217	67	(	(	PUNCT
ejpam-6459	217	68	τ	τ	PROPN
ejpam-6459	217	69	,	,	PUNCT
ejpam-6459	217	70	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	217	71	)	)	PUNCT
ejpam-6459	217	72	}	}	PUNCT
ejpam-6459	217	73	,	,	PUNCT
ejpam-6459	217	74	(	(	PUNCT
ejpam-6459	217	75	j	j	PROPN
ejpam-6459	217	76	∧k)(e1	∧k)(e1	PROPN
ejpam-6459	217	77	,	,	PUNCT
ejpam-6459	217	78	e3	e3	NOUN
ejpam-6459	217	79	)	)	PUNCT
ejpam-6459	217	80	=	=	PRON
ejpam-6459	217	81	{	{	PUNCT
ejpam-6459	217	82	(	(	PUNCT
ejpam-6459	217	83	0	0	NUM
ejpam-6459	217	84	,	,	PUNCT
ejpam-6459	217	85	0.6−	0.6−	NOUN
ejpam-6459	217	86	0.7	0.7	NUM
ejpam-6459	217	87	)	)	PUNCT
ejpam-6459	217	88	,	,	PUNCT
ejpam-6459	217	89	(	(	PUNCT
ejpam-6459	217	90	κ	κ	NOUN
ejpam-6459	217	91	,	,	PUNCT
ejpam-6459	217	92	0.4,−0.3	0.4,−0.3	NUM
ejpam-6459	217	93	)	)	PUNCT
ejpam-6459	217	94	,	,	PUNCT
ejpam-6459	217	95	(	(	PUNCT
ejpam-6459	217	96	ξ	ξ	X
ejpam-6459	217	97	,	,	PUNCT
ejpam-6459	217	98	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	217	99	)	)	PUNCT
ejpam-6459	217	100	,	,	PUNCT
ejpam-6459	217	101	(	(	PUNCT
ejpam-6459	217	102	τ	τ	PROPN
ejpam-6459	217	103	,	,	PUNCT
ejpam-6459	217	104	0.3,−0.2	0.3,−0.2	NUM
ejpam-6459	217	105	)	)	PUNCT
ejpam-6459	217	106	}	}	PUNCT
ejpam-6459	217	107	,	,	PUNCT
ejpam-6459	217	108	(	(	PUNCT
ejpam-6459	217	109	j	j	PROPN
ejpam-6459	217	110	∧k)(e2	∧k)(e2	PROPN
ejpam-6459	217	111	,	,	PUNCT
ejpam-6459	217	112	e2	e2	PROPN
ejpam-6459	217	113	)	)	PUNCT
ejpam-6459	217	114	=	=	PRON
ejpam-6459	217	115	{	{	PUNCT
ejpam-6459	217	116	(	(	PUNCT
ejpam-6459	217	117	0	0	NUM
ejpam-6459	217	118	,	,	PUNCT
ejpam-6459	217	119	0.7−	0.7−	NOUN
ejpam-6459	217	120	0.6	0.6	NUM
ejpam-6459	217	121	)	)	PUNCT
ejpam-6459	217	122	,	,	PUNCT
ejpam-6459	217	123	(	(	PUNCT
ejpam-6459	217	124	κ	κ	NOUN
ejpam-6459	217	125	,	,	PUNCT
ejpam-6459	217	126	0.4,−0.1	0.4,−0.1	NOUN
ejpam-6459	217	127	)	)	PUNCT
ejpam-6459	217	128	,	,	PUNCT
ejpam-6459	217	129	(	(	PUNCT
ejpam-6459	217	130	ξ	ξ	NOUN
ejpam-6459	217	131	,	,	PUNCT
ejpam-6459	217	132	0.2,−0.2	0.2,−0.2	NUM
ejpam-6459	217	133	)	)	PUNCT
ejpam-6459	217	134	,	,	PUNCT
ejpam-6459	217	135	(	(	PUNCT
ejpam-6459	217	136	τ	τ	X
ejpam-6459	217	137	,	,	PUNCT
ejpam-6459	217	138	0.2,−0.1	0.2,−0.1	NOUN
ejpam-6459	217	139	)	)	PUNCT
ejpam-6459	217	140	}	}	PUNCT
ejpam-6459	217	141	,	,	PUNCT
ejpam-6459	217	142	(	(	PUNCT
ejpam-6459	217	143	j	j	PROPN
ejpam-6459	217	144	∧k)(e2	∧k)(e2	PROPN
ejpam-6459	217	145	,	,	PUNCT
ejpam-6459	217	146	e3	e3	NOUN
ejpam-6459	217	147	)	)	PUNCT
ejpam-6459	217	148	=	=	PRON
ejpam-6459	217	149	{	{	PUNCT
ejpam-6459	217	150	(	(	PUNCT
ejpam-6459	217	151	0	0	NUM
ejpam-6459	217	152	,	,	PUNCT
ejpam-6459	217	153	0.6−	0.6−	NOUN
ejpam-6459	217	154	0.7	0.7	NUM
ejpam-6459	217	155	)	)	PUNCT
ejpam-6459	217	156	,	,	PUNCT
ejpam-6459	217	157	(	(	PUNCT
ejpam-6459	217	158	κ	κ	NOUN
ejpam-6459	217	159	,	,	PUNCT
ejpam-6459	217	160	0.4,−0.1	0.4,−0.1	NOUN
ejpam-6459	217	161	)	)	PUNCT
ejpam-6459	217	162	,	,	PUNCT
ejpam-6459	217	163	(	(	PUNCT
ejpam-6459	217	164	ξ	ξ	X
ejpam-6459	217	165	,	,	PUNCT
ejpam-6459	217	166	0.2,−0.5	0.2,−0.5	NUM
ejpam-6459	217	167	)	)	PUNCT
ejpam-6459	217	168	,	,	PUNCT
ejpam-6459	217	169	(	(	PUNCT
ejpam-6459	217	170	τ	τ	X
ejpam-6459	217	171	,	,	PUNCT
ejpam-6459	217	172	0.2,−0.1	0.2,−0.1	NOUN
ejpam-6459	217	173	)	)	PUNCT
ejpam-6459	217	174	}	}	PUNCT
ejpam-6459	217	175	.	.	PUNCT
ejpam-6459	218	1	obviously	obviously	ADV
ejpam-6459	218	2	,	,	PUNCT
ejpam-6459	218	3	for	for	ADP
ejpam-6459	218	4	all	all	DET
ejpam-6459	218	5	κ	κ	NOUN
ejpam-6459	218	6	,	,	PUNCT
ejpam-6459	218	7	ξ	ξ	PROPN
ejpam-6459	218	8	∈	∈	PROPN
ejpam-6459	218	9	ℜ	ℜ	PROPN
ejpam-6459	218	10	,	,	PUNCT
ejpam-6459	218	11	(	(	PUNCT
ejpam-6459	218	12	j	j	PROPN
ejpam-6459	218	13	∧k)+(κ+	∧k)+(κ+	PROPN
ejpam-6459	218	14	ξ	ξ	PROPN
ejpam-6459	218	15	)	)	PUNCT
ejpam-6459	218	16	≥	≥	NOUN
ejpam-6459	218	17	(	(	PUNCT
ejpam-6459	218	18	j	j	PROPN
ejpam-6459	218	19	∧k)+(κ	∧k)+(κ	ADJ
ejpam-6459	218	20	)	)	PUNCT
ejpam-6459	218	21	∧	∧	PROPN
ejpam-6459	218	22	(	(	PUNCT
ejpam-6459	218	23	j	j	PROPN
ejpam-6459	218	24	∧k)+(ξ	∧k)+(ξ	PROPN
ejpam-6459	218	25	)	)	PUNCT
ejpam-6459	218	26	,	,	PUNCT
ejpam-6459	218	27	(	(	PUNCT
ejpam-6459	218	28	j	j	PROPN
ejpam-6459	218	29	∧k)+(κξ	∧k)+(κξ	NOUN
ejpam-6459	218	30	)	)	PUNCT
ejpam-6459	218	31	≥	≥	PROPN
ejpam-6459	218	32	(	(	PUNCT
ejpam-6459	218	33	j	j	PROPN
ejpam-6459	218	34	∧k)+(κ	∧k)+(κ	ADJ
ejpam-6459	218	35	)	)	PUNCT
ejpam-6459	218	36	∧	∧	PROPN
ejpam-6459	218	37	(	(	PUNCT
ejpam-6459	218	38	j	j	PROPN
ejpam-6459	218	39	∧k)+(ξ	∧k)+(ξ	PROPN
ejpam-6459	218	40	)	)	PUNCT
ejpam-6459	218	41	,	,	PUNCT
ejpam-6459	218	42	(	(	PUNCT
ejpam-6459	218	43	j	j	PROPN
ejpam-6459	218	44	∧k)−(κ+	∧k)−(κ+	PROPN
ejpam-6459	218	45	ξ	ξ	PROPN
ejpam-6459	218	46	)	)	PUNCT
ejpam-6459	218	47	≤	≤	NOUN
ejpam-6459	218	48	(	(	PUNCT
ejpam-6459	218	49	j	j	PROPN
ejpam-6459	218	50	∧k)−(κ	∧k)−(κ	PROPN
ejpam-6459	218	51	)	)	PUNCT
ejpam-6459	218	52	∨	∨	PROPN
ejpam-6459	218	53	(	(	PUNCT
ejpam-6459	218	54	j	j	PROPN
ejpam-6459	218	55	∧k)−(ξ	∧k)−(ξ	PROPN
ejpam-6459	218	56	)	)	PUNCT
ejpam-6459	218	57	,	,	PUNCT
ejpam-6459	218	58	(	(	PUNCT
ejpam-6459	218	59	j	j	PROPN
ejpam-6459	218	60	∧k)−(κξ	∧k)−(κξ	NOUN
ejpam-6459	218	61	)	)	PUNCT
ejpam-6459	218	62	≤	≤	NOUN
ejpam-6459	218	63	(	(	PUNCT
ejpam-6459	218	64	j	j	PROPN
ejpam-6459	218	65	∧k)−(κ	∧k)−(κ	PROPN
ejpam-6459	218	66	)	)	PUNCT
ejpam-6459	218	67	∨	∨	PROPN
ejpam-6459	218	68	(	(	PUNCT
ejpam-6459	218	69	j	j	PROPN
ejpam-6459	218	70	∧k)−(ξ	∧k)−(ξ	PROPN
ejpam-6459	218	71	)	)	PUNCT
ejpam-6459	218	72	.	.	PUNCT
ejpam-6459	219	1	4	4	X
ejpam-6459	219	2	.	.	X
ejpam-6459	219	3	bipolar	bipolar	ADJ
ejpam-6459	219	4	fuzzy	fuzzy	ADJ
ejpam-6459	219	5	soft	soft	ADJ
ejpam-6459	219	6	ideals	ideal	NOUN
ejpam-6459	219	7	over	over	ADP
ejpam-6459	219	8	boolean	boolean	ADJ
ejpam-6459	219	9	rings	ring	NOUN
ejpam-6459	219	10	building	building	NOUN
ejpam-6459	219	11	upon	upon	SCONJ
ejpam-6459	219	12	the	the	DET
ejpam-6459	219	13	framework	framework	NOUN
ejpam-6459	219	14	of	of	ADP
ejpam-6459	219	15	bfsbrs	bfsbr	VERB
ejpam-6459	219	16	,	,	PUNCT
ejpam-6459	219	17	this	this	DET
ejpam-6459	219	18	section	section	NOUN
ejpam-6459	219	19	introduces	introduce	VERB
ejpam-6459	219	20	the	the	DET
ejpam-6459	219	21	notion	notion	NOUN
ejpam-6459	219	22	of	of	ADP
ejpam-6459	219	23	bfsis	bfsis	NOUN
ejpam-6459	219	24	.	.	PUNCT
ejpam-6459	220	1	these	these	DET
ejpam-6459	220	2	ideals	ideal	NOUN
ejpam-6459	220	3	adapt	adapt	VERB
ejpam-6459	220	4	classical	classical	ADJ
ejpam-6459	220	5	ring	ring	NOUN
ejpam-6459	220	6	-	-	PUNCT
ejpam-6459	220	7	theoretic	theoretic	NOUN
ejpam-6459	220	8	concepts	concept	NOUN
ejpam-6459	220	9	to	to	ADP
ejpam-6459	220	10	the	the	DET
ejpam-6459	220	11	bipolar	bipolar	ADJ
ejpam-6459	220	12	fuzzy	fuzzy	ADJ
ejpam-6459	220	13	soft	soft	ADJ
ejpam-6459	220	14	context	context	NOUN
ejpam-6459	220	15	,	,	PUNCT
ejpam-6459	220	16	allowing	allow	VERB
ejpam-6459	220	17	for	for	ADP
ejpam-6459	220	18	the	the	DET
ejpam-6459	220	19	representation	representation	NOUN
ejpam-6459	220	20	of	of	ADP
ejpam-6459	220	21	parameterized	parameterized	ADJ
ejpam-6459	220	22	uncertainty	uncertainty	NOUN
ejpam-6459	220	23	within	within	ADP
ejpam-6459	220	24	ideal	ideal	ADJ
ejpam-6459	220	25	structures	structure	NOUN
ejpam-6459	220	26	.	.	PUNCT
ejpam-6459	221	1	we	we	PRON
ejpam-6459	221	2	define	define	VERB
ejpam-6459	221	3	bfsis	bfsis	NOUN
ejpam-6459	221	4	over	over	ADP
ejpam-6459	221	5	brs	brs	NOUN
ejpam-6459	221	6	and	and	CCONJ
ejpam-6459	221	7	explore	explore	VERB
ejpam-6459	221	8	their	their	PRON
ejpam-6459	221	9	algebraic	algebraic	ADJ
ejpam-6459	221	10	properties	property	NOUN
ejpam-6459	221	11	,	,	PUNCT
ejpam-6459	221	12	focusing	focus	VERB
ejpam-6459	221	13	on	on	ADP
ejpam-6459	221	14	their	their	PRON
ejpam-6459	221	15	behavior	behavior	NOUN
ejpam-6459	221	16	under	under	ADP
ejpam-6459	221	17	binary	binary	ADJ
ejpam-6459	221	18	operations	operation	NOUN
ejpam-6459	221	19	and	and	CCONJ
ejpam-6459	221	20	their	their	PRON
ejpam-6459	221	21	role	role	NOUN
ejpam-6459	221	22	in	in	ADP
ejpam-6459	221	23	preserving	preserve	VERB
ejpam-6459	221	24	the	the	DET
ejpam-6459	221	25	integrity	integrity	NOUN
ejpam-6459	221	26	of	of	ADP
ejpam-6459	221	27	the	the	DET
ejpam-6459	221	28	extended	extended	ADJ
ejpam-6459	221	29	structure	structure	NOUN
ejpam-6459	221	30	.	.	PUNCT
ejpam-6459	222	1	definition	definition	NOUN
ejpam-6459	222	2	15	15	NUM
ejpam-6459	222	3	.	.	PUNCT
ejpam-6459	223	1	a	a	DET
ejpam-6459	223	2	bfss	bfss	NOUN
ejpam-6459	223	3	(	(	PUNCT
ejpam-6459	223	4	j	j	NOUN
ejpam-6459	223	5	,	,	PUNCT
ejpam-6459	223	6	u	u	NOUN
ejpam-6459	223	7	)	)	PUNCT
ejpam-6459	223	8	over	over	ADP
ejpam-6459	223	9	ℜ	ℜ	PROPN
ejpam-6459	223	10	is	be	AUX
ejpam-6459	223	11	called	call	VERB
ejpam-6459	223	12	a	a	DET
ejpam-6459	223	13	bipolar	bipolar	ADJ
ejpam-6459	223	14	fuzzy	fuzzy	ADJ
ejpam-6459	223	15	soft	soft	ADJ
ejpam-6459	223	16	ideal	ideal	NOUN
ejpam-6459	223	17	(	(	PUNCT
ejpam-6459	223	18	bfsi	bfsi	ADV
ejpam-6459	223	19	)	)	PUNCT
ejpam-6459	223	20	over	over	ADP
ejpam-6459	223	21	ℜ	ℜ	PROPN
ejpam-6459	223	22	if	if	SCONJ
ejpam-6459	223	23	(	(	PUNCT
ejpam-6459	223	24	i	i	NOUN
ejpam-6459	223	25	)	)	PUNCT
ejpam-6459	223	26	j+(κ+	j+(κ+	NOUN
ejpam-6459	223	27	ξ	ξ	SYM
ejpam-6459	223	28	)	)	PUNCT
ejpam-6459	223	29	≥	≥	NOUN
ejpam-6459	223	30	a{j+(κ	a{j+(κ	NUM
ejpam-6459	223	31	)	)	PUNCT
ejpam-6459	223	32	,	,	PUNCT
ejpam-6459	223	33	j+(ξ	j+(ξ	PROPN
ejpam-6459	223	34	)	)	PUNCT
ejpam-6459	223	35	}	}	PUNCT
ejpam-6459	223	36	(	(	PUNCT
ejpam-6459	223	37	ii	ii	NOUN
ejpam-6459	223	38	)	)	PUNCT
ejpam-6459	223	39	j−(κ+	j−(κ+	NOUN
ejpam-6459	223	40	ξ	ξ	X
ejpam-6459	223	41	)	)	PUNCT
ejpam-6459	223	42	≤	≤	NUM
ejpam-6459	223	43	b{j−(κ	b{j−(κ	PROPN
ejpam-6459	223	44	)	)	PUNCT
ejpam-6459	223	45	,	,	PUNCT
ejpam-6459	223	46	j−(ξ	j−(ξ	PROPN
ejpam-6459	223	47	)	)	PUNCT
ejpam-6459	223	48	}	}	PUNCT
ejpam-6459	223	49	(	(	PUNCT
ejpam-6459	223	50	iii	iii	X
ejpam-6459	223	51	)	)	PUNCT
ejpam-6459	223	52	j+(κξ	j+(κξ	PROPN
ejpam-6459	223	53	)	)	PUNCT
ejpam-6459	223	54	≥	≥	NOUN
ejpam-6459	223	55	j+(ξ	j+(ξ	X
ejpam-6459	223	56	)	)	PUNCT
ejpam-6459	223	57	(	(	PUNCT
ejpam-6459	223	58	iv	iv	X
ejpam-6459	223	59	)	)	PUNCT
ejpam-6459	223	60	j−(κξ	j−(κξ	NOUN
ejpam-6459	223	61	)	)	PUNCT
ejpam-6459	223	62	≤	≤	PUNCT
ejpam-6459	223	63	j−(ξ	j−(ξ	PROPN
ejpam-6459	223	64	)	)	PUNCT
ejpam-6459	223	65	for	for	ADP
ejpam-6459	223	66	all	all	DET
ejpam-6459	223	67	κ	κ	NOUN
ejpam-6459	223	68	,	,	PUNCT
ejpam-6459	223	69	ξ	ξ	PROPN
ejpam-6459	223	70	∈	∈	PROPN
ejpam-6459	223	71	ℜ.	ℜ.	PROPN
ejpam-6459	223	72	example	example	NOUN
ejpam-6459	223	73	4	4	NUM
ejpam-6459	223	74	.	.	PUNCT
ejpam-6459	224	1	the	the	DET
ejpam-6459	224	2	non	non	ADJ
ejpam-6459	224	3	-	-	ADJ
ejpam-6459	224	4	empty	empty	ADJ
ejpam-6459	224	5	set	set	NOUN
ejpam-6459	224	6	r	r	NOUN
ejpam-6459	224	7	=	=	PUNCT
ejpam-6459	224	8	{	{	PUNCT
ejpam-6459	224	9	0	0	NUM
ejpam-6459	224	10	,	,	PUNCT
ejpam-6459	224	11	κ	κ	NOUN
ejpam-6459	224	12	,	,	PUNCT
ejpam-6459	224	13	ξ	ξ	PROPN
ejpam-6459	224	14	,	,	PUNCT
ejpam-6459	224	15	τ	τ	X
ejpam-6459	224	16	}	}	PUNCT
ejpam-6459	224	17	can	can	AUX
ejpam-6459	224	18	be	be	AUX
ejpam-6459	224	19	subjected	subject	VERB
ejpam-6459	224	20	to	to	ADP
ejpam-6459	224	21	the	the	DET
ejpam-6459	224	22	binary	binary	ADJ
ejpam-6459	224	23	operations	operation	NOUN
ejpam-6459	224	24	in	in	ADP
ejpam-6459	224	25	the	the	DET
ejpam-6459	224	26	observing	observe	VERB
ejpam-6459	224	27	terms	term	NOUN
ejpam-6459	224	28	:	:	PUNCT
ejpam-6459	224	29	let	let	VERB
ejpam-6459	224	30	u	u	PRON
ejpam-6459	224	31	=	=	PUNCT
ejpam-6459	224	32	{	{	PUNCT
ejpam-6459	224	33	e1	e1	PROPN
ejpam-6459	224	34	,	,	PUNCT
ejpam-6459	224	35	e2	e2	PROPN
ejpam-6459	224	36	,	,	PUNCT
ejpam-6459	224	37	e3	e3	PROPN
ejpam-6459	224	38	}	}	PUNCT
ejpam-6459	224	39	be	be	VERB
ejpam-6459	224	40	the	the	DET
ejpam-6459	224	41	group	group	NOUN
ejpam-6459	224	42	of	of	ADP
ejpam-6459	224	43	parameters	parameter	NOUN
ejpam-6459	224	44	.	.	PUNCT
ejpam-6459	225	1	then	then	ADV
ejpam-6459	225	2	now	now	ADV
ejpam-6459	225	3	define	define	VERB
ejpam-6459	225	4	a	a	DET
ejpam-6459	225	5	bfss	bfss	NOUN
ejpam-6459	225	6	(	(	PUNCT
ejpam-6459	225	7	j	j	NOUN
ejpam-6459	225	8	,	,	PUNCT
ejpam-6459	225	9	u	u	NOUN
ejpam-6459	225	10	)	)	PUNCT
ejpam-6459	225	11	on	on	ADP
ejpam-6459	225	12	ℜ	ℜ	PROPN
ejpam-6459	225	13	as	as	SCONJ
ejpam-6459	225	14	follows	follow	VERB
ejpam-6459	225	15	:	:	PUNCT
ejpam-6459	225	16	j(e1	j(e1	NOUN
ejpam-6459	225	17	)	)	PUNCT
ejpam-6459	226	1	=	=	PRON
ejpam-6459	226	2	{	{	PUNCT
ejpam-6459	226	3	(	(	PUNCT
ejpam-6459	226	4	0	0	NUM
ejpam-6459	226	5	,	,	PUNCT
ejpam-6459	226	6	0.1,−0.2	0.1,−0.2	NOUN
ejpam-6459	226	7	)	)	PUNCT
ejpam-6459	226	8	,	,	PUNCT
ejpam-6459	226	9	(	(	PUNCT
ejpam-6459	226	10	κ	κ	NOUN
ejpam-6459	226	11	,	,	PUNCT
ejpam-6459	226	12	0.5,−0.3	0.5,−0.3	NUM
ejpam-6459	226	13	)	)	PUNCT
ejpam-6459	226	14	,	,	PUNCT
ejpam-6459	226	15	(	(	PUNCT
ejpam-6459	226	16	ξ	ξ	X
ejpam-6459	226	17	,	,	PUNCT
ejpam-6459	226	18	0.1,−0.4	0.1,−0.4	NUM
ejpam-6459	226	19	)	)	PUNCT
ejpam-6459	226	20	,	,	PUNCT
ejpam-6459	226	21	(	(	PUNCT
ejpam-6459	226	22	τ	τ	X
ejpam-6459	226	23	,	,	PUNCT
ejpam-6459	226	24	0.7,−0.4	0.7,−0.4	NUM
ejpam-6459	226	25	)	)	PUNCT
ejpam-6459	226	26	}	}	PUNCT
ejpam-6459	226	27	,	,	PUNCT
ejpam-6459	226	28	j(e2	j(e2	NOUN
ejpam-6459	226	29	)	)	PUNCT
ejpam-6459	226	30	=	=	PRON
ejpam-6459	226	31	{	{	PUNCT
ejpam-6459	226	32	(	(	PUNCT
ejpam-6459	226	33	0	0	NUM
ejpam-6459	226	34	,	,	PUNCT
ejpam-6459	226	35	0.3,−0.3	0.3,−0.3	NUM
ejpam-6459	226	36	)	)	PUNCT
ejpam-6459	226	37	,	,	PUNCT
ejpam-6459	226	38	(	(	PUNCT
ejpam-6459	226	39	κ	κ	NOUN
ejpam-6459	226	40	,	,	PUNCT
ejpam-6459	226	41	0.3,−0.3	0.3,−0.3	NUM
ejpam-6459	226	42	)	)	PUNCT
ejpam-6459	226	43	,	,	PUNCT
ejpam-6459	226	44	(	(	PUNCT
ejpam-6459	226	45	ξ	ξ	X
ejpam-6459	226	46	,	,	PUNCT
ejpam-6459	226	47	0.7,−0.4	0.7,−0.4	NUM
ejpam-6459	226	48	)	)	PUNCT
ejpam-6459	226	49	,	,	PUNCT
ejpam-6459	226	50	(	(	PUNCT
ejpam-6459	226	51	τ	τ	X
ejpam-6459	226	52	,	,	PUNCT
ejpam-6459	226	53	0.9,−0.4	0.9,−0.4	NUM
ejpam-6459	226	54	)	)	PUNCT
ejpam-6459	226	55	}	}	PUNCT
ejpam-6459	226	56	,	,	PUNCT
ejpam-6459	226	57	j(e3	j(e3	PROPN
ejpam-6459	226	58	)	)	PUNCT
ejpam-6459	227	1	=	=	PRON
ejpam-6459	227	2	{	{	PUNCT
ejpam-6459	227	3	(	(	PUNCT
ejpam-6459	227	4	0	0	NUM
ejpam-6459	227	5	,	,	PUNCT
ejpam-6459	227	6	0.9,−0.3	0.9,−0.3	NUM
ejpam-6459	227	7	)	)	PUNCT
ejpam-6459	227	8	,	,	PUNCT
ejpam-6459	227	9	(	(	PUNCT
ejpam-6459	227	10	κ	κ	NOUN
ejpam-6459	227	11	,	,	PUNCT
ejpam-6459	227	12	0.7,−0.3	0.7,−0.3	NUM
ejpam-6459	227	13	)	)	PUNCT
ejpam-6459	227	14	,	,	PUNCT
ejpam-6459	227	15	(	(	PUNCT
ejpam-6459	227	16	ξ	ξ	NOUN
ejpam-6459	227	17	,	,	PUNCT
ejpam-6459	227	18	0.4,−0.4	0.4,−0.4	NUM
ejpam-6459	227	19	)	)	PUNCT
ejpam-6459	227	20	,	,	PUNCT
ejpam-6459	227	21	(	(	PUNCT
ejpam-6459	227	22	τ	τ	PROPN
ejpam-6459	227	23	,	,	PUNCT
ejpam-6459	227	24	0.4,−0.4	0.4,−0.4	NUM
ejpam-6459	227	25	)	)	PUNCT
ejpam-6459	227	26	}	}	PUNCT
ejpam-6459	227	27	.	.	PUNCT
ejpam-6459	228	1	it	it	PRON
ejpam-6459	228	2	is	be	AUX
ejpam-6459	228	3	easy	easy	ADJ
ejpam-6459	228	4	to	to	PART
ejpam-6459	228	5	verify	verify	VERB
ejpam-6459	228	6	that	that	SCONJ
ejpam-6459	228	7	(	(	PUNCT
ejpam-6459	228	8	j	j	NOUN
ejpam-6459	228	9	,	,	PUNCT
ejpam-6459	228	10	u	u	NOUN
ejpam-6459	228	11	)	)	PUNCT
ejpam-6459	228	12	is	be	AUX
ejpam-6459	228	13	a	a	DET
ejpam-6459	228	14	bfsi	bfsi	ADV
ejpam-6459	228	15	over	over	ADP
ejpam-6459	228	16	ℜ.	ℜ.	PROPN
ejpam-6459	228	17	hence	hence	ADV
ejpam-6459	228	18	,	,	PUNCT
ejpam-6459	228	19	(	(	PUNCT
ejpam-6459	228	20	j	j	NOUN
ejpam-6459	228	21	,	,	PUNCT
ejpam-6459	228	22	u	u	NOUN
ejpam-6459	228	23	)	)	PUNCT
ejpam-6459	228	24	is	be	AUX
ejpam-6459	228	25	a	a	DET
ejpam-6459	228	26	bfsi	bfsi	ADV
ejpam-6459	228	27	over	over	ADP
ejpam-6459	228	28	ℜ.	ℜ.	PROPN
ejpam-6459	228	29	g.	g.	PROPN
ejpam-6459	228	30	s.	s.	PROPN
ejpam-6459	228	31	rao	rao	PROPN
ejpam-6459	229	1	et	et	PROPN
ejpam-6459	229	2	al	al	PROPN
ejpam-6459	229	3	.	.	PUNCT
ejpam-6459	229	4	/	/	SYM
ejpam-6459	229	5	eur	eur	PROPN
ejpam-6459	229	6	.	.	PUNCT
ejpam-6459	230	1	j.	j.	PROPN
ejpam-6459	230	2	pure	pure	PROPN
ejpam-6459	230	3	appl	appl	PROPN
ejpam-6459	230	4	.	.	PROPN
ejpam-6459	230	5	math	math	PROPN
ejpam-6459	230	6	,	,	PUNCT
ejpam-6459	230	7	18	18	NUM
ejpam-6459	230	8	(	(	PUNCT
ejpam-6459	230	9	3	3	NUM
ejpam-6459	230	10	)	)	PUNCT
ejpam-6459	230	11	(	(	PUNCT
ejpam-6459	230	12	2025	2025	NUM
ejpam-6459	230	13	)	)	PUNCT
ejpam-6459	230	14	,	,	PUNCT
ejpam-6459	230	15	6459	6459	NUM
ejpam-6459	230	16	11	11	NUM
ejpam-6459	230	17	of	of	ADP
ejpam-6459	230	18	16	16	NUM
ejpam-6459	230	19	+	+	CCONJ
ejpam-6459	230	20	0	0	NUM
ejpam-6459	230	21	κ	κ	X
ejpam-6459	230	22	ξ	ξ	X
ejpam-6459	230	23	τ	τ	X
ejpam-6459	230	24	0	0	NUM
ejpam-6459	230	25	0	0	NUM
ejpam-6459	230	26	κ	κ	X
ejpam-6459	230	27	ξ	ξ	PROPN
ejpam-6459	230	28	τ	τ	X
ejpam-6459	230	29	κ	κ	PROPN
ejpam-6459	230	30	κ	κ	NOUN
ejpam-6459	230	31	0	0	NUM
ejpam-6459	230	32	τ	τ	PROPN
ejpam-6459	230	33	ξ	ξ	X
ejpam-6459	230	34	ξ	ξ	X
ejpam-6459	230	35	ξ	ξ	X
ejpam-6459	230	36	τ	τ	X
ejpam-6459	230	37	0	0	NUM
ejpam-6459	230	38	κ	κ	PROPN
ejpam-6459	230	39	τ	τ	PROPN
ejpam-6459	230	40	τ	τ	PROPN
ejpam-6459	230	41	ξ	ξ	PROPN
ejpam-6459	230	42	κ	κ	PROPN
ejpam-6459	230	43	0	0	NUM
ejpam-6459	230	44	∗	∗	NOUN
ejpam-6459	230	45	0	0	NUM
ejpam-6459	230	46	κ	κ	X
ejpam-6459	230	47	ξ	ξ	X
ejpam-6459	230	48	τ	τ	X
ejpam-6459	230	49	0	0	NUM
ejpam-6459	230	50	0	0	NUM
ejpam-6459	230	51	0	0	NUM
ejpam-6459	230	52	0	0	NUM
ejpam-6459	230	53	0	0	NUM
ejpam-6459	230	54	κ	κ	NOUN
ejpam-6459	230	55	0	0	NUM
ejpam-6459	230	56	κ	κ	NOUN
ejpam-6459	230	57	0	0	PROPN
ejpam-6459	230	58	κ	κ	PRON
ejpam-6459	230	59	ξ	ξ	PROPN
ejpam-6459	230	60	0	0	NUM
ejpam-6459	230	61	0	0	NUM
ejpam-6459	230	62	ξ	ξ	SYM
ejpam-6459	230	63	ξ	ξ	X
ejpam-6459	230	64	τ	τ	X
ejpam-6459	230	65	0	0	NUM
ejpam-6459	230	66	κ	κ	PROPN
ejpam-6459	230	67	ξ	ξ	PROPN
ejpam-6459	230	68	τ	τ	X
ejpam-6459	230	69	theorem	theorem	VERB
ejpam-6459	230	70	5	5	NUM
ejpam-6459	230	71	.	.	PUNCT
ejpam-6459	231	1	if	if	SCONJ
ejpam-6459	231	2	(	(	PUNCT
ejpam-6459	231	3	j	j	NOUN
ejpam-6459	231	4	,	,	PUNCT
ejpam-6459	231	5	u	u	NOUN
ejpam-6459	231	6	)	)	PUNCT
ejpam-6459	231	7	and	and	CCONJ
ejpam-6459	231	8	(	(	PUNCT
ejpam-6459	231	9	k	k	X
ejpam-6459	231	10	,	,	PUNCT
ejpam-6459	231	11	v	v	NOUN
ejpam-6459	231	12	)	)	PUNCT
ejpam-6459	231	13	are	be	AUX
ejpam-6459	231	14	two	two	NUM
ejpam-6459	231	15	bfsis	bfsis	NOUN
ejpam-6459	231	16	over	over	ADP
ejpam-6459	231	17	ℜ	ℜ	PROPN
ejpam-6459	231	18	,	,	PUNCT
ejpam-6459	231	19	then	then	ADV
ejpam-6459	231	20	(	(	PUNCT
ejpam-6459	231	21	j	j	NOUN
ejpam-6459	231	22	,	,	PUNCT
ejpam-6459	231	23	u	u	NOUN
ejpam-6459	231	24	)	)	PUNCT
ejpam-6459	231	25	∧	∧	PROPN
ejpam-6459	231	26	(	(	PUNCT
ejpam-6459	231	27	k	k	NOUN
ejpam-6459	231	28	,	,	PUNCT
ejpam-6459	231	29	v	v	NOUN
ejpam-6459	231	30	)	)	PUNCT
ejpam-6459	231	31	is	be	AUX
ejpam-6459	231	32	also	also	ADV
ejpam-6459	231	33	a	a	DET
ejpam-6459	231	34	bfsi	bfsi	ADV
ejpam-6459	231	35	over	over	ADP
ejpam-6459	231	36	ℜ.	ℜ.	PROPN
ejpam-6459	231	37	proof	proof	NOUN
ejpam-6459	231	38	.	.	PUNCT
ejpam-6459	232	1	let	let	VERB
ejpam-6459	232	2	(	(	PUNCT
ejpam-6459	232	3	j	j	NOUN
ejpam-6459	232	4	,	,	PUNCT
ejpam-6459	232	5	u	u	NOUN
ejpam-6459	232	6	)	)	PUNCT
ejpam-6459	232	7	and	and	CCONJ
ejpam-6459	232	8	(	(	PUNCT
ejpam-6459	232	9	k	k	X
ejpam-6459	232	10	,	,	PUNCT
ejpam-6459	232	11	v	v	NOUN
ejpam-6459	232	12	)	)	PUNCT
ejpam-6459	232	13	be	be	AUX
ejpam-6459	232	14	two	two	NUM
ejpam-6459	232	15	bfsis	bfsis	NOUN
ejpam-6459	232	16	over	over	ADP
ejpam-6459	232	17	ℜ.	ℜ.	PROPN
ejpam-6459	232	18	then	then	ADV
ejpam-6459	232	19	as	as	ADV
ejpam-6459	232	20	defined	define	VERB
ejpam-6459	232	21	(	(	PUNCT
ejpam-6459	232	22	j	j	NOUN
ejpam-6459	232	23	,	,	PUNCT
ejpam-6459	232	24	u	u	NOUN
ejpam-6459	232	25	)	)	PUNCT
ejpam-6459	233	1	∧	∧	PROPN
ejpam-6459	233	2	(	(	PUNCT
ejpam-6459	233	3	k	k	NOUN
ejpam-6459	233	4	,	,	PUNCT
ejpam-6459	233	5	v	v	NOUN
ejpam-6459	233	6	)	)	PUNCT
ejpam-6459	233	7	,	,	PUNCT
ejpam-6459	233	8	where	where	SCONJ
ejpam-6459	233	9	w	w	NOUN
ejpam-6459	233	10	=	=	PUNCT
ejpam-6459	233	11	u	u	NOUN
ejpam-6459	233	12	×	×	NOUN
ejpam-6459	233	13	v	v	NOUN
ejpam-6459	233	14	and	and	CCONJ
ejpam-6459	233	15	l(ρ	l(ρ	PROPN
ejpam-6459	233	16	,	,	PUNCT
ejpam-6459	233	17	τ	τ	X
ejpam-6459	233	18	)	)	PUNCT
ejpam-6459	233	19	=	=	SYM
ejpam-6459	233	20	j(ρ	j(ρ	PROPN
ejpam-6459	233	21	)	)	PUNCT
ejpam-6459	233	22	∩k(τ	∩k(τ	PROPN
ejpam-6459	233	23	)	)	PUNCT
ejpam-6459	233	24	,	,	PUNCT
ejpam-6459	233	25	for	for	ADP
ejpam-6459	233	26	all	all	DET
ejpam-6459	233	27	(	(	PUNCT
ejpam-6459	233	28	ρ	ρ	PROPN
ejpam-6459	233	29	,	,	PUNCT
ejpam-6459	233	30	τ	τ	NOUN
ejpam-6459	233	31	)	)	PUNCT
ejpam-6459	233	32	∈	∈	PROPN
ejpam-6459	233	33	w	w	NOUN
ejpam-6459	233	34	=	=	PUNCT
ejpam-6459	233	35	u	u	PROPN
ejpam-6459	233	36	×	×	NOUN
ejpam-6459	233	37	v	v	INTJ
ejpam-6459	233	38	,	,	PUNCT
ejpam-6459	233	39	as	as	SCONJ
ejpam-6459	233	40	(	(	PUNCT
ejpam-6459	233	41	j	j	NOUN
ejpam-6459	233	42	,	,	PUNCT
ejpam-6459	233	43	u	u	NOUN
ejpam-6459	233	44	)	)	PUNCT
ejpam-6459	233	45	and	and	CCONJ
ejpam-6459	233	46	(	(	PUNCT
ejpam-6459	233	47	k	k	X
ejpam-6459	233	48	,	,	PUNCT
ejpam-6459	233	49	v	v	NOUN
ejpam-6459	233	50	)	)	PUNCT
ejpam-6459	233	51	are	be	AUX
ejpam-6459	233	52	bfsis	bfsis	NOUN
ejpam-6459	233	53	over	over	ADP
ejpam-6459	233	54	ℜ.	ℜ.	PROPN
ejpam-6459	233	55	thus	thus	ADV
ejpam-6459	233	56	,	,	PUNCT
ejpam-6459	233	57	for	for	ADP
ejpam-6459	233	58	κ	κ	PROPN
ejpam-6459	233	59	,	,	PUNCT
ejpam-6459	233	60	ξ	ξ	PROPN
ejpam-6459	233	61	∈	∈	PROPN
ejpam-6459	233	62	ℜ	ℜ	PROPN
ejpam-6459	233	63	,	,	PUNCT
ejpam-6459	233	64	l+	l+	X
ejpam-6459	233	65	(	(	PUNCT
ejpam-6459	233	66	ρ	ρ	NOUN
ejpam-6459	233	67	,	,	PUNCT
ejpam-6459	233	68	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	233	69	ξ	ξ	X
ejpam-6459	233	70	)	)	PUNCT
ejpam-6459	233	71	=	=	SYM
ejpam-6459	233	72	a{j+	a{j+	NOUN
ejpam-6459	233	73	ρ	ρ	PROPN
ejpam-6459	233	74	(	(	PUNCT
ejpam-6459	233	75	κ+	κ+	PROPN
ejpam-6459	233	76	ξ),k+	ξ),k+	PROPN
ejpam-6459	233	77	τ	τ	X
ejpam-6459	233	78	(	(	PUNCT
ejpam-6459	233	79	κ+	κ+	PROPN
ejpam-6459	233	80	ξ	ξ	NUM
ejpam-6459	233	81	)	)	PUNCT
ejpam-6459	233	82	}	}	PUNCT
ejpam-6459	233	83	≥	≥	NOUN
ejpam-6459	233	84	a{a{j+	a{a{j+	ADJ
ejpam-6459	233	85	ρ	ρ	PROPN
ejpam-6459	233	86	(	(	PUNCT
ejpam-6459	233	87	κ	κ	NOUN
ejpam-6459	233	88	)	)	PUNCT
ejpam-6459	233	89	,	,	PUNCT
ejpam-6459	233	90	j+	j+	NUM
ejpam-6459	233	91	ρ	ρ	PROPN
ejpam-6459	233	92	(	(	PUNCT
ejpam-6459	233	93	ξ	ξ	NOUN
ejpam-6459	233	94	)	)	PUNCT
ejpam-6459	233	95	}	}	PUNCT
ejpam-6459	233	96	,	,	PUNCT
ejpam-6459	233	97	a{k+	a{k+	ADP
ejpam-6459	233	98	τ	τ	X
ejpam-6459	233	99	(	(	PUNCT
ejpam-6459	233	100	κ),k+	κ),k+	PROPN
ejpam-6459	233	101	τ	τ	X
ejpam-6459	233	102	(	(	PUNCT
ejpam-6459	233	103	ξ	ξ	NOUN
ejpam-6459	233	104	)	)	PUNCT
ejpam-6459	233	105	}	}	PUNCT
ejpam-6459	233	106	}	}	PUNCT
ejpam-6459	233	107	=	=	SYM
ejpam-6459	233	108	a{a{j+	a{a{j+	ADJ
ejpam-6459	233	109	ρ	ρ	PROPN
ejpam-6459	233	110	(	(	PUNCT
ejpam-6459	233	111	κ),k+	κ),k+	PROPN
ejpam-6459	233	112	τ	τ	X
ejpam-6459	233	113	(	(	PUNCT
ejpam-6459	233	114	κ	κ	NOUN
ejpam-6459	233	115	)	)	PUNCT
ejpam-6459	233	116	}	}	PUNCT
ejpam-6459	233	117	,	,	PUNCT
ejpam-6459	233	118	a{j+	a{j+	NOUN
ejpam-6459	233	119	ρ	ρ	PROPN
ejpam-6459	233	120	(	(	PUNCT
ejpam-6459	233	121	ξ),k+	ξ),k+	PROPN
ejpam-6459	233	122	τ	τ	X
ejpam-6459	233	123	(	(	PUNCT
ejpam-6459	233	124	ξ	ξ	NOUN
ejpam-6459	233	125	)	)	PUNCT
ejpam-6459	233	126	}	}	PUNCT
ejpam-6459	233	127	}	}	PUNCT
ejpam-6459	233	128	=	=	SYM
ejpam-6459	233	129	a{l+	a{l+	NUM
ejpam-6459	233	130	(	(	PUNCT
ejpam-6459	233	131	ρ	ρ	NOUN
ejpam-6459	233	132	,	,	PUNCT
ejpam-6459	233	133	τ)(κ	τ)(κ	NOUN
ejpam-6459	233	134	)	)	PUNCT
ejpam-6459	233	135	,	,	PUNCT
ejpam-6459	233	136	l	l	PROPN
ejpam-6459	234	1	+	+	CCONJ
ejpam-6459	234	2	(	(	PUNCT
ejpam-6459	234	3	ρ	ρ	NOUN
ejpam-6459	234	4	,	,	PUNCT
ejpam-6459	234	5	τ)(ξ	τ)(ξ	NUM
ejpam-6459	234	6	)	)	PUNCT
ejpam-6459	234	7	}	}	PUNCT
ejpam-6459	234	8	,	,	PUNCT
ejpam-6459	234	9	l−	l−	PROPN
ejpam-6459	234	10	(	(	PUNCT
ejpam-6459	234	11	ρ	ρ	NOUN
ejpam-6459	234	12	,	,	PUNCT
ejpam-6459	234	13	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	234	14	ξ	ξ	X
ejpam-6459	234	15	)	)	PUNCT
ejpam-6459	234	16	=	=	SYM
ejpam-6459	234	17	b{j−	b{j−	PROPN
ejpam-6459	234	18	ρ	ρ	NOUN
ejpam-6459	234	19	(	(	PUNCT
ejpam-6459	234	20	κ+	κ+	PROPN
ejpam-6459	234	21	ξ),k−	ξ),k−	PROPN
ejpam-6459	234	22	τ	τ	PROPN
ejpam-6459	234	23	(	(	PUNCT
ejpam-6459	234	24	κ+	κ+	PROPN
ejpam-6459	234	25	ξ	ξ	NUM
ejpam-6459	234	26	)	)	PUNCT
ejpam-6459	234	27	}	}	PUNCT
ejpam-6459	234	28	≤	≤	NUM
ejpam-6459	234	29	b{b{j−	b{b{j−	VERB
ejpam-6459	234	30	ρ	ρ	X
ejpam-6459	234	31	(	(	PUNCT
ejpam-6459	234	32	κ	κ	NOUN
ejpam-6459	234	33	)	)	PUNCT
ejpam-6459	234	34	,	,	PUNCT
ejpam-6459	234	35	j−	j−	PROPN
ejpam-6459	234	36	ρ	ρ	PROPN
ejpam-6459	234	37	(	(	PUNCT
ejpam-6459	234	38	ξ	ξ	NOUN
ejpam-6459	234	39	)	)	PUNCT
ejpam-6459	234	40	}	}	PUNCT
ejpam-6459	234	41	,	,	PUNCT
ejpam-6459	234	42	b{k−	b{k−	PROPN
ejpam-6459	234	43	τ	τ	X
ejpam-6459	234	44	(	(	PUNCT
ejpam-6459	234	45	ξ),k−	ξ),k−	PROPN
ejpam-6459	234	46	τ	τ	PROPN
ejpam-6459	234	47	(	(	PUNCT
ejpam-6459	234	48	ξ	ξ	NOUN
ejpam-6459	234	49	)	)	PUNCT
ejpam-6459	234	50	}	}	PUNCT
ejpam-6459	234	51	}	}	PUNCT
ejpam-6459	234	52	=	=	SYM
ejpam-6459	234	53	b{b{j−	b{b{j−	NOUN
ejpam-6459	234	54	ρ	ρ	X
ejpam-6459	234	55	(	(	PUNCT
ejpam-6459	234	56	κ),k−	κ),k−	PROPN
ejpam-6459	234	57	τ	τ	X
ejpam-6459	234	58	(	(	PUNCT
ejpam-6459	234	59	κ	κ	NOUN
ejpam-6459	234	60	)	)	PUNCT
ejpam-6459	234	61	}	}	PUNCT
ejpam-6459	234	62	,	,	PUNCT
ejpam-6459	234	63	b{j−	b{j−	PROPN
ejpam-6459	234	64	ρ	ρ	NOUN
ejpam-6459	234	65	(	(	PUNCT
ejpam-6459	234	66	ξ),k−	ξ),k−	PROPN
ejpam-6459	234	67	τ	τ	PROPN
ejpam-6459	234	68	(	(	PUNCT
ejpam-6459	234	69	κ	κ	NOUN
ejpam-6459	234	70	)	)	PUNCT
ejpam-6459	234	71	}	}	PUNCT
ejpam-6459	234	72	}	}	PUNCT
ejpam-6459	234	73	=	=	PUNCT
ejpam-6459	234	74	b{l−	b{l−	NOUN
ejpam-6459	234	75	(	(	PUNCT
ejpam-6459	234	76	ρ	ρ	NOUN
ejpam-6459	234	77	,	,	PUNCT
ejpam-6459	234	78	τ)(κ	τ)(κ	NOUN
ejpam-6459	234	79	)	)	PUNCT
ejpam-6459	234	80	,	,	PUNCT
ejpam-6459	234	81	l	l	NOUN
ejpam-6459	234	82	−	−	PROPN
ejpam-6459	234	83	(	(	PUNCT
ejpam-6459	234	84	ρ	ρ	NOUN
ejpam-6459	234	85	,	,	PUNCT
ejpam-6459	234	86	τ)(ξ	τ)(ξ	NUM
ejpam-6459	234	87	)	)	PUNCT
ejpam-6459	234	88	}	}	PUNCT
ejpam-6459	234	89	,	,	PUNCT
ejpam-6459	234	90	l+	l+	X
ejpam-6459	234	91	(	(	PUNCT
ejpam-6459	234	92	ρ	ρ	NOUN
ejpam-6459	234	93	,	,	PUNCT
ejpam-6459	234	94	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	234	95	)	)	PUNCT
ejpam-6459	234	96	=	=	SYM
ejpam-6459	234	97	a{j+	a{j+	NOUN
ejpam-6459	234	98	ρ	ρ	PROPN
ejpam-6459	234	99	(	(	PUNCT
ejpam-6459	234	100	κξ),k+	κξ),k+	PROPN
ejpam-6459	234	101	τ	τ	X
ejpam-6459	234	102	(	(	PUNCT
ejpam-6459	234	103	κξ	κξ	NOUN
ejpam-6459	234	104	)	)	PUNCT
ejpam-6459	234	105	}	}	PUNCT
ejpam-6459	234	106	≥	≥	PROPN
ejpam-6459	234	107	a{j+	a{j+	PROPN
ejpam-6459	234	108	ρ	ρ	PROPN
ejpam-6459	234	109	(	(	PUNCT
ejpam-6459	234	110	ξ),k+	ξ),k+	PROPN
ejpam-6459	234	111	τ	τ	X
ejpam-6459	234	112	(	(	PUNCT
ejpam-6459	234	113	ξ	ξ	NOUN
ejpam-6459	234	114	)	)	PUNCT
ejpam-6459	234	115	}	}	PUNCT
ejpam-6459	234	116	=	=	SYM
ejpam-6459	234	117	l+	l+	X
ejpam-6459	234	118	(	(	PUNCT
ejpam-6459	234	119	ρ	ρ	NOUN
ejpam-6459	234	120	,	,	PUNCT
ejpam-6459	234	121	τ)(ξ	τ)(ξ	NUM
ejpam-6459	234	122	)	)	PUNCT
ejpam-6459	234	123	,	,	PUNCT
ejpam-6459	234	124	l−	l−	PROPN
ejpam-6459	234	125	(	(	PUNCT
ejpam-6459	234	126	ρ	ρ	NOUN
ejpam-6459	234	127	,	,	PUNCT
ejpam-6459	234	128	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	234	129	)	)	PUNCT
ejpam-6459	234	130	=	=	SYM
ejpam-6459	234	131	b{j−	b{j−	PUNCT
ejpam-6459	234	132	ρ	ρ	NOUN
ejpam-6459	234	133	(	(	PUNCT
ejpam-6459	234	134	κξ),k−	κξ),k−	PROPN
ejpam-6459	234	135	τ	τ	PROPN
ejpam-6459	234	136	(	(	PUNCT
ejpam-6459	234	137	κξ	κξ	NOUN
ejpam-6459	234	138	)	)	PUNCT
ejpam-6459	234	139	}	}	PUNCT
ejpam-6459	235	1	≤	≤	NOUN
ejpam-6459	235	2	b{j−	b{j−	PUNCT
ejpam-6459	235	3	ρ	ρ	NOUN
ejpam-6459	235	4	(	(	PUNCT
ejpam-6459	235	5	ξ),k−	ξ),k−	PROPN
ejpam-6459	235	6	τ	τ	PROPN
ejpam-6459	235	7	(	(	PUNCT
ejpam-6459	235	8	ξ	ξ	NOUN
ejpam-6459	235	9	)	)	PUNCT
ejpam-6459	235	10	}	}	PUNCT
ejpam-6459	235	11	=	=	SYM
ejpam-6459	235	12	l−	l−	NOUN
ejpam-6459	235	13	(	(	PUNCT
ejpam-6459	235	14	ρ	ρ	NOUN
ejpam-6459	235	15	,	,	PUNCT
ejpam-6459	235	16	τ)(ξ	τ)(ξ	NUM
ejpam-6459	235	17	)	)	PUNCT
ejpam-6459	235	18	.	.	PUNCT
ejpam-6459	236	1	therefore	therefore	ADV
ejpam-6459	236	2	,	,	PUNCT
ejpam-6459	236	3	(	(	PUNCT
ejpam-6459	236	4	l	l	NOUN
ejpam-6459	236	5	,	,	PUNCT
ejpam-6459	236	6	w	w	NOUN
ejpam-6459	236	7	)	)	PUNCT
ejpam-6459	236	8	=	=	SYM
ejpam-6459	236	9	(	(	PUNCT
ejpam-6459	236	10	j	j	PROPN
ejpam-6459	236	11	,	,	PUNCT
ejpam-6459	236	12	u	u	NOUN
ejpam-6459	236	13	)	)	PUNCT
ejpam-6459	236	14	∧	∧	PROPN
ejpam-6459	236	15	(	(	PUNCT
ejpam-6459	236	16	k	k	NOUN
ejpam-6459	236	17	,	,	PUNCT
ejpam-6459	236	18	v	v	NOUN
ejpam-6459	236	19	)	)	PUNCT
ejpam-6459	236	20	is	be	AUX
ejpam-6459	236	21	a	a	DET
ejpam-6459	236	22	bfsi	bfsi	ADV
ejpam-6459	236	23	over	over	ADP
ejpam-6459	236	24	ℜ.	ℜ.	PROPN
ejpam-6459	236	25	theorem	theorem	NOUN
ejpam-6459	236	26	6	6	NUM
ejpam-6459	236	27	.	.	PUNCT
ejpam-6459	237	1	if	if	SCONJ
ejpam-6459	237	2	(	(	PUNCT
ejpam-6459	237	3	j	j	NOUN
ejpam-6459	237	4	,	,	PUNCT
ejpam-6459	237	5	u	u	NOUN
ejpam-6459	237	6	)	)	PUNCT
ejpam-6459	237	7	and	and	CCONJ
ejpam-6459	237	8	(	(	PUNCT
ejpam-6459	237	9	k	k	X
ejpam-6459	237	10	,	,	PUNCT
ejpam-6459	237	11	v	v	NOUN
ejpam-6459	237	12	)	)	PUNCT
ejpam-6459	237	13	are	be	AUX
ejpam-6459	237	14	two	two	NUM
ejpam-6459	237	15	bfsis	bfsis	NOUN
ejpam-6459	237	16	over	over	ADP
ejpam-6459	237	17	ℜ	ℜ	PROPN
ejpam-6459	237	18	,	,	PUNCT
ejpam-6459	237	19	then	then	ADV
ejpam-6459	237	20	(	(	PUNCT
ejpam-6459	237	21	j	j	NOUN
ejpam-6459	237	22	,	,	PUNCT
ejpam-6459	237	23	u	u	NOUN
ejpam-6459	237	24	)	)	PUNCT
ejpam-6459	237	25	∨	∨	PROPN
ejpam-6459	237	26	(	(	PUNCT
ejpam-6459	237	27	k	k	NOUN
ejpam-6459	237	28	,	,	PUNCT
ejpam-6459	237	29	v	v	NOUN
ejpam-6459	237	30	)	)	PUNCT
ejpam-6459	237	31	is	be	AUX
ejpam-6459	237	32	also	also	ADV
ejpam-6459	237	33	a	a	DET
ejpam-6459	237	34	bfsi	bfsi	ADV
ejpam-6459	237	35	over	over	ADP
ejpam-6459	237	36	ℜ.	ℜ.	PROPN
ejpam-6459	237	37	proof	proof	NOUN
ejpam-6459	237	38	.	.	PUNCT
ejpam-6459	238	1	let	let	VERB
ejpam-6459	238	2	(	(	PUNCT
ejpam-6459	238	3	j	j	NOUN
ejpam-6459	238	4	,	,	PUNCT
ejpam-6459	238	5	u	u	NOUN
ejpam-6459	238	6	)	)	PUNCT
ejpam-6459	238	7	and	and	CCONJ
ejpam-6459	238	8	(	(	PUNCT
ejpam-6459	238	9	k	k	X
ejpam-6459	238	10	,	,	PUNCT
ejpam-6459	238	11	v	v	NOUN
ejpam-6459	238	12	)	)	PUNCT
ejpam-6459	238	13	be	be	AUX
ejpam-6459	238	14	two	two	NUM
ejpam-6459	238	15	bfsis	bfsis	NOUN
ejpam-6459	238	16	over	over	ADP
ejpam-6459	238	17	ℜ.	ℜ.	PROPN
ejpam-6459	238	18	then	then	ADV
ejpam-6459	238	19	as	as	ADV
ejpam-6459	238	20	defined	define	VERB
ejpam-6459	238	21	(	(	PUNCT
ejpam-6459	238	22	j	j	PROPN
ejpam-6459	238	23	,	,	PUNCT
ejpam-6459	238	24	u)∨	u)∨	PROPN
ejpam-6459	238	25	(	(	PUNCT
ejpam-6459	238	26	k	k	X
ejpam-6459	238	27	,	,	PUNCT
ejpam-6459	238	28	v	v	NOUN
ejpam-6459	238	29	)	)	PUNCT
ejpam-6459	238	30	=	=	SYM
ejpam-6459	238	31	(	(	PUNCT
ejpam-6459	238	32	l	l	NOUN
ejpam-6459	238	33	,	,	PUNCT
ejpam-6459	238	34	w	w	NOUN
ejpam-6459	238	35	)	)	PUNCT
ejpam-6459	238	36	,	,	PUNCT
ejpam-6459	238	37	where	where	SCONJ
ejpam-6459	238	38	w	w	NOUN
ejpam-6459	238	39	=	=	PUNCT
ejpam-6459	238	40	u	u	NOUN
ejpam-6459	238	41	×	×	NOUN
ejpam-6459	238	42	v	v	NOUN
ejpam-6459	238	43	and	and	CCONJ
ejpam-6459	238	44	l(ρ	l(ρ	PROPN
ejpam-6459	238	45	,	,	PUNCT
ejpam-6459	238	46	τ	τ	X
ejpam-6459	238	47	)	)	PUNCT
ejpam-6459	238	48	=	=	SYM
ejpam-6459	238	49	j(ρ	j(ρ	PROPN
ejpam-6459	238	50	)	)	PUNCT
ejpam-6459	238	51	∪	∪	ADP
ejpam-6459	238	52	k(τ	k(τ	PROPN
ejpam-6459	238	53	)	)	PUNCT
ejpam-6459	238	54	,	,	PUNCT
ejpam-6459	238	55	for	for	ADP
ejpam-6459	238	56	all	all	DET
ejpam-6459	238	57	(	(	PUNCT
ejpam-6459	238	58	ρ	ρ	PROPN
ejpam-6459	238	59	,	,	PUNCT
ejpam-6459	238	60	τ	τ	NOUN
ejpam-6459	238	61	)	)	PUNCT
ejpam-6459	238	62	∈	∈	PROPN
ejpam-6459	238	63	w	w	NOUN
ejpam-6459	238	64	=	=	PUNCT
ejpam-6459	238	65	u	u	PROPN
ejpam-6459	238	66	×	×	NOUN
ejpam-6459	238	67	v	v	INTJ
ejpam-6459	238	68	,	,	PUNCT
ejpam-6459	238	69	as	as	SCONJ
ejpam-6459	238	70	(	(	PUNCT
ejpam-6459	238	71	j	j	NOUN
ejpam-6459	238	72	,	,	PUNCT
ejpam-6459	238	73	u	u	NOUN
ejpam-6459	238	74	)	)	PUNCT
ejpam-6459	238	75	and	and	CCONJ
ejpam-6459	238	76	(	(	PUNCT
ejpam-6459	238	77	k	k	X
ejpam-6459	238	78	,	,	PUNCT
ejpam-6459	238	79	v	v	NOUN
ejpam-6459	238	80	)	)	PUNCT
ejpam-6459	238	81	are	be	AUX
ejpam-6459	238	82	bfsis	bfsis	NOUN
ejpam-6459	238	83	over	over	ADP
ejpam-6459	238	84	ℜ.	ℜ.	PROPN
ejpam-6459	238	85	thus	thus	ADV
ejpam-6459	238	86	,	,	PUNCT
ejpam-6459	238	87	for	for	ADP
ejpam-6459	238	88	κ	κ	PROPN
ejpam-6459	238	89	,	,	PUNCT
ejpam-6459	238	90	ξ	ξ	PROPN
ejpam-6459	238	91	∈	∈	PROPN
ejpam-6459	238	92	ℜ	ℜ	PROPN
ejpam-6459	238	93	,	,	PUNCT
ejpam-6459	238	94	l+	l+	X
ejpam-6459	238	95	(	(	PUNCT
ejpam-6459	238	96	ρ	ρ	NOUN
ejpam-6459	238	97	,	,	PUNCT
ejpam-6459	238	98	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	238	99	ξ	ξ	X
ejpam-6459	238	100	)	)	PUNCT
ejpam-6459	238	101	=	=	SYM
ejpam-6459	238	102	b{j+	b{j+	ADJ
ejpam-6459	238	103	ρ	ρ	NOUN
ejpam-6459	238	104	(	(	PUNCT
ejpam-6459	238	105	κ+	κ+	PROPN
ejpam-6459	238	106	ξ),k+	ξ),k+	PROPN
ejpam-6459	238	107	τ	τ	X
ejpam-6459	238	108	(	(	PUNCT
ejpam-6459	238	109	κ+	κ+	PROPN
ejpam-6459	238	110	ξ	ξ	NUM
ejpam-6459	238	111	)	)	PUNCT
ejpam-6459	238	112	}	}	PUNCT
ejpam-6459	238	113	≥	≥	NOUN
ejpam-6459	238	114	b{a{j+	b{a{j+	NOUN
ejpam-6459	238	115	ρ	ρ	PROPN
ejpam-6459	238	116	(	(	PUNCT
ejpam-6459	238	117	κ	κ	NOUN
ejpam-6459	238	118	)	)	PUNCT
ejpam-6459	238	119	,	,	PUNCT
ejpam-6459	238	120	j+	j+	NUM
ejpam-6459	238	121	ρ	ρ	PROPN
ejpam-6459	238	122	(	(	PUNCT
ejpam-6459	238	123	ξ	ξ	NOUN
ejpam-6459	238	124	)	)	PUNCT
ejpam-6459	238	125	}	}	PUNCT
ejpam-6459	238	126	,	,	PUNCT
ejpam-6459	238	127	a{k+	a{k+	ADP
ejpam-6459	238	128	τ	τ	X
ejpam-6459	238	129	(	(	PUNCT
ejpam-6459	238	130	κ),k+	κ),k+	PROPN
ejpam-6459	238	131	τ	τ	X
ejpam-6459	238	132	(	(	PUNCT
ejpam-6459	238	133	ξ	ξ	NOUN
ejpam-6459	238	134	)	)	PUNCT
ejpam-6459	238	135	}	}	PUNCT
ejpam-6459	238	136	}	}	PUNCT
ejpam-6459	238	137	g.	g.	PROPN
ejpam-6459	238	138	s.	s.	PROPN
ejpam-6459	238	139	rao	rao	PROPN
ejpam-6459	238	140	et	et	PROPN
ejpam-6459	238	141	al	al	PROPN
ejpam-6459	238	142	.	.	PUNCT
ejpam-6459	238	143	/	/	SYM
ejpam-6459	238	144	eur	eur	PROPN
ejpam-6459	238	145	.	.	PUNCT
ejpam-6459	239	1	j.	j.	PROPN
ejpam-6459	239	2	pure	pure	PROPN
ejpam-6459	239	3	appl	appl	PROPN
ejpam-6459	239	4	.	.	PROPN
ejpam-6459	239	5	math	math	PROPN
ejpam-6459	239	6	,	,	PUNCT
ejpam-6459	239	7	18	18	NUM
ejpam-6459	239	8	(	(	PUNCT
ejpam-6459	239	9	3	3	NUM
ejpam-6459	239	10	)	)	PUNCT
ejpam-6459	239	11	(	(	PUNCT
ejpam-6459	239	12	2025	2025	NUM
ejpam-6459	239	13	)	)	PUNCT
ejpam-6459	239	14	,	,	PUNCT
ejpam-6459	239	15	6459	6459	NUM
ejpam-6459	239	16	12	12	NUM
ejpam-6459	239	17	of	of	ADP
ejpam-6459	239	18	16	16	NUM
ejpam-6459	239	19	≥	≥	NUM
ejpam-6459	239	20	a{b{j+	a{b{j+	PROPN
ejpam-6459	239	21	ρ	ρ	PROPN
ejpam-6459	239	22	(	(	PUNCT
ejpam-6459	239	23	κ),k+	κ),k+	PROPN
ejpam-6459	239	24	τ	τ	X
ejpam-6459	239	25	(	(	PUNCT
ejpam-6459	239	26	κ	κ	NOUN
ejpam-6459	239	27	)	)	PUNCT
ejpam-6459	239	28	}	}	PUNCT
ejpam-6459	239	29	,	,	PUNCT
ejpam-6459	239	30	b{j+	b{j+	PROPN
ejpam-6459	239	31	ρ	ρ	PROPN
ejpam-6459	239	32	(	(	PUNCT
ejpam-6459	239	33	ξ),k+	ξ),k+	PROPN
ejpam-6459	239	34	τ	τ	X
ejpam-6459	239	35	(	(	PUNCT
ejpam-6459	239	36	ξ	ξ	NOUN
ejpam-6459	239	37	)	)	PUNCT
ejpam-6459	239	38	}	}	PUNCT
ejpam-6459	239	39	}	}	PUNCT
ejpam-6459	239	40	=	=	SYM
ejpam-6459	239	41	a{l+	a{l+	NUM
ejpam-6459	239	42	(	(	PUNCT
ejpam-6459	239	43	ρ	ρ	NOUN
ejpam-6459	239	44	,	,	PUNCT
ejpam-6459	239	45	τ)(κ	τ)(κ	NOUN
ejpam-6459	239	46	)	)	PUNCT
ejpam-6459	239	47	,	,	PUNCT
ejpam-6459	239	48	l	l	PROPN
ejpam-6459	240	1	+	+	CCONJ
ejpam-6459	240	2	(	(	PUNCT
ejpam-6459	240	3	ρ	ρ	NOUN
ejpam-6459	240	4	,	,	PUNCT
ejpam-6459	240	5	τ)(ξ	τ)(ξ	NUM
ejpam-6459	240	6	)	)	PUNCT
ejpam-6459	240	7	}	}	PUNCT
ejpam-6459	240	8	,	,	PUNCT
ejpam-6459	240	9	l−	l−	PROPN
ejpam-6459	240	10	(	(	PUNCT
ejpam-6459	240	11	ρ	ρ	NOUN
ejpam-6459	240	12	,	,	PUNCT
ejpam-6459	240	13	τ)(κ+	τ)(κ+	NOUN
ejpam-6459	240	14	ξ	ξ	X
ejpam-6459	240	15	)	)	PUNCT
ejpam-6459	240	16	=	=	SYM
ejpam-6459	240	17	a{j−	a{j−	NUM
ejpam-6459	240	18	ρ	ρ	PROPN
ejpam-6459	240	19	(	(	PUNCT
ejpam-6459	240	20	κ+	κ+	PROPN
ejpam-6459	240	21	ξ),k−	ξ),k−	PROPN
ejpam-6459	240	22	τ	τ	PROPN
ejpam-6459	240	23	(	(	PUNCT
ejpam-6459	240	24	κ+	κ+	PROPN
ejpam-6459	240	25	ξ	ξ	NUM
ejpam-6459	240	26	)	)	PUNCT
ejpam-6459	240	27	}	}	PUNCT
ejpam-6459	240	28	≤	≤	NUM
ejpam-6459	240	29	a{b{j−	a{b{j−	VERB
ejpam-6459	240	30	ρ	ρ	X
ejpam-6459	240	31	(	(	PUNCT
ejpam-6459	240	32	κ	κ	NOUN
ejpam-6459	240	33	)	)	PUNCT
ejpam-6459	240	34	,	,	PUNCT
ejpam-6459	240	35	j−	j−	PROPN
ejpam-6459	240	36	ρ	ρ	PROPN
ejpam-6459	240	37	(	(	PUNCT
ejpam-6459	240	38	ξ	ξ	NOUN
ejpam-6459	240	39	)	)	PUNCT
ejpam-6459	240	40	}	}	PUNCT
ejpam-6459	240	41	,	,	PUNCT
ejpam-6459	240	42	b{k−	b{k−	PROPN
ejpam-6459	240	43	τ	τ	X
ejpam-6459	240	44	(	(	PUNCT
ejpam-6459	240	45	κ),k−	κ),k−	PROPN
ejpam-6459	240	46	τ	τ	X
ejpam-6459	240	47	(	(	PUNCT
ejpam-6459	240	48	ξ	ξ	NOUN
ejpam-6459	240	49	)	)	PUNCT
ejpam-6459	240	50	}	}	PUNCT
ejpam-6459	240	51	}	}	PUNCT
ejpam-6459	240	52	≤	≤	NUM
ejpam-6459	240	53	b{a{j−	b{a{j−	NOUN
ejpam-6459	240	54	ρ	ρ	NOUN
ejpam-6459	240	55	(	(	PUNCT
ejpam-6459	240	56	κ),k−	κ),k−	PROPN
ejpam-6459	240	57	τ	τ	X
ejpam-6459	240	58	(	(	PUNCT
ejpam-6459	240	59	κ	κ	NOUN
ejpam-6459	240	60	)	)	PUNCT
ejpam-6459	240	61	}	}	PUNCT
ejpam-6459	240	62	,	,	PUNCT
ejpam-6459	240	63	a{j−	a{j−	ADP
ejpam-6459	240	64	ρ	ρ	NOUN
ejpam-6459	240	65	(	(	PUNCT
ejpam-6459	240	66	ξ),k−	ξ),k−	PROPN
ejpam-6459	240	67	τ	τ	PROPN
ejpam-6459	240	68	(	(	PUNCT
ejpam-6459	240	69	ξ	ξ	NOUN
ejpam-6459	240	70	)	)	PUNCT
ejpam-6459	240	71	}	}	PUNCT
ejpam-6459	240	72	}	}	PUNCT
ejpam-6459	240	73	=	=	PUNCT
ejpam-6459	240	74	b{l−	b{l−	NOUN
ejpam-6459	240	75	(	(	PUNCT
ejpam-6459	240	76	ρ	ρ	NOUN
ejpam-6459	240	77	,	,	PUNCT
ejpam-6459	240	78	τ)(κ	τ)(κ	NOUN
ejpam-6459	240	79	)	)	PUNCT
ejpam-6459	240	80	,	,	PUNCT
ejpam-6459	240	81	l	l	NOUN
ejpam-6459	240	82	−	−	PROPN
ejpam-6459	240	83	(	(	PUNCT
ejpam-6459	240	84	ρ	ρ	NOUN
ejpam-6459	240	85	,	,	PUNCT
ejpam-6459	240	86	τ)(ξ	τ)(ξ	NUM
ejpam-6459	240	87	)	)	PUNCT
ejpam-6459	240	88	}	}	PUNCT
ejpam-6459	240	89	,	,	PUNCT
ejpam-6459	240	90	l+	l+	X
ejpam-6459	240	91	(	(	PUNCT
ejpam-6459	240	92	ρ	ρ	NOUN
ejpam-6459	240	93	,	,	PUNCT
ejpam-6459	240	94	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	240	95	)	)	PUNCT
ejpam-6459	240	96	=	=	SYM
ejpam-6459	240	97	b{j+	b{j+	ADJ
ejpam-6459	240	98	ρ	ρ	PROPN
ejpam-6459	240	99	(	(	PUNCT
ejpam-6459	240	100	κξ),k+	κξ),k+	PROPN
ejpam-6459	240	101	τ	τ	X
ejpam-6459	240	102	(	(	PUNCT
ejpam-6459	240	103	κξ	κξ	NOUN
ejpam-6459	240	104	)	)	PUNCT
ejpam-6459	240	105	}	}	PUNCT
ejpam-6459	240	106	≥	≥	NOUN
ejpam-6459	240	107	b{j+	b{j+	PROPN
ejpam-6459	240	108	ρ	ρ	NOUN
ejpam-6459	240	109	(	(	PUNCT
ejpam-6459	240	110	ξ),k+	ξ),k+	PROPN
ejpam-6459	240	111	τ	τ	X
ejpam-6459	240	112	(	(	PUNCT
ejpam-6459	240	113	ξ	ξ	NOUN
ejpam-6459	240	114	)	)	PUNCT
ejpam-6459	240	115	}	}	PUNCT
ejpam-6459	240	116	=	=	SYM
ejpam-6459	240	117	l+	l+	X
ejpam-6459	240	118	(	(	PUNCT
ejpam-6459	240	119	ρ	ρ	NOUN
ejpam-6459	240	120	,	,	PUNCT
ejpam-6459	240	121	τ)(ξ	τ)(ξ	NUM
ejpam-6459	240	122	)	)	PUNCT
ejpam-6459	240	123	,	,	PUNCT
ejpam-6459	240	124	l−	l−	PROPN
ejpam-6459	240	125	(	(	PUNCT
ejpam-6459	240	126	ρ	ρ	NOUN
ejpam-6459	240	127	,	,	PUNCT
ejpam-6459	240	128	τ)(κξ	τ)(κξ	NOUN
ejpam-6459	240	129	)	)	PUNCT
ejpam-6459	240	130	=	=	SYM
ejpam-6459	240	131	a{j−	a{j−	NUM
ejpam-6459	240	132	ρ	ρ	PROPN
ejpam-6459	240	133	(	(	PUNCT
ejpam-6459	240	134	κξ),k−	κξ),k−	PROPN
ejpam-6459	240	135	τ	τ	PROPN
ejpam-6459	240	136	(	(	PUNCT
ejpam-6459	240	137	κξ	κξ	NOUN
ejpam-6459	240	138	)	)	PUNCT
ejpam-6459	240	139	}	}	PUNCT
ejpam-6459	240	140	≤	≤	PROPN
ejpam-6459	240	141	a{j−	a{j−	NUM
ejpam-6459	240	142	ρ	ρ	NOUN
ejpam-6459	240	143	(	(	PUNCT
ejpam-6459	240	144	ξ),k−	ξ),k−	PROPN
ejpam-6459	240	145	τ	τ	PROPN
ejpam-6459	240	146	(	(	PUNCT
ejpam-6459	240	147	ξ	ξ	NOUN
ejpam-6459	240	148	)	)	PUNCT
ejpam-6459	240	149	}	}	PUNCT
ejpam-6459	240	150	=	=	SYM
ejpam-6459	240	151	l−	l−	NOUN
ejpam-6459	240	152	(	(	PUNCT
ejpam-6459	240	153	ρ	ρ	NOUN
ejpam-6459	240	154	,	,	PUNCT
ejpam-6459	240	155	τ)(ξ	τ)(ξ	NUM
ejpam-6459	240	156	)	)	PUNCT
ejpam-6459	240	157	.	.	PUNCT
ejpam-6459	241	1	therefore	therefore	ADV
ejpam-6459	241	2	,	,	PUNCT
ejpam-6459	241	3	(	(	PUNCT
ejpam-6459	241	4	l	l	NOUN
ejpam-6459	241	5	,	,	PUNCT
ejpam-6459	241	6	w	w	NOUN
ejpam-6459	241	7	)	)	PUNCT
ejpam-6459	241	8	=	=	SYM
ejpam-6459	241	9	(	(	PUNCT
ejpam-6459	241	10	j	j	PROPN
ejpam-6459	241	11	,	,	PUNCT
ejpam-6459	241	12	u	u	NOUN
ejpam-6459	241	13	)	)	PUNCT
ejpam-6459	241	14	∨	∨	PROPN
ejpam-6459	241	15	(	(	PUNCT
ejpam-6459	241	16	k	k	NOUN
ejpam-6459	241	17	,	,	PUNCT
ejpam-6459	241	18	v	v	NOUN
ejpam-6459	241	19	)	)	PUNCT
ejpam-6459	241	20	is	be	AUX
ejpam-6459	241	21	a	a	PRON
ejpam-6459	241	22	bfsi	bfsi	ADV
ejpam-6459	241	23	over	over	ADP
ejpam-6459	241	24	ℜ.	ℜ.	PROPN
ejpam-6459	241	25	theorem	theorem	NOUN
ejpam-6459	241	26	7	7	NUM
ejpam-6459	241	27	.	.	PUNCT
ejpam-6459	242	1	if	if	SCONJ
ejpam-6459	242	2	(	(	PUNCT
ejpam-6459	242	3	j	j	NOUN
ejpam-6459	242	4	,	,	PUNCT
ejpam-6459	242	5	u	u	NOUN
ejpam-6459	242	6	)	)	PUNCT
ejpam-6459	242	7	and	and	CCONJ
ejpam-6459	242	8	(	(	PUNCT
ejpam-6459	242	9	k	k	X
ejpam-6459	242	10	,	,	PUNCT
ejpam-6459	242	11	v	v	NOUN
ejpam-6459	242	12	)	)	PUNCT
ejpam-6459	242	13	are	be	AUX
ejpam-6459	242	14	two	two	NUM
ejpam-6459	242	15	bfsis	bfsis	NOUN
ejpam-6459	242	16	over	over	ADP
ejpam-6459	242	17	ℜ	ℜ	PROPN
ejpam-6459	242	18	,	,	PUNCT
ejpam-6459	242	19	then	then	ADV
ejpam-6459	242	20	(	(	PUNCT
ejpam-6459	242	21	j	j	NOUN
ejpam-6459	242	22	,	,	PUNCT
ejpam-6459	242	23	u	u	NOUN
ejpam-6459	242	24	)	)	PUNCT
ejpam-6459	242	25	∩	∩	NOUN
ejpam-6459	242	26	(	(	PUNCT
ejpam-6459	242	27	k	k	X
ejpam-6459	242	28	,	,	PUNCT
ejpam-6459	242	29	v	v	NOUN
ejpam-6459	242	30	)	)	PUNCT
ejpam-6459	242	31	is	be	AUX
ejpam-6459	242	32	also	also	ADV
ejpam-6459	242	33	a	a	DET
ejpam-6459	242	34	bfsi	bfsi	ADV
ejpam-6459	242	35	over	over	ADP
ejpam-6459	242	36	ℜ.	ℜ.	PROPN
ejpam-6459	242	37	proof	proof	NOUN
ejpam-6459	242	38	.	.	PUNCT
ejpam-6459	243	1	let	let	VERB
ejpam-6459	243	2	(	(	PUNCT
ejpam-6459	243	3	j	j	NOUN
ejpam-6459	243	4	,	,	PUNCT
ejpam-6459	243	5	u	u	NOUN
ejpam-6459	243	6	)	)	PUNCT
ejpam-6459	243	7	and	and	CCONJ
ejpam-6459	243	8	(	(	PUNCT
ejpam-6459	243	9	k	k	X
ejpam-6459	243	10	,	,	PUNCT
ejpam-6459	243	11	v	v	NOUN
ejpam-6459	243	12	)	)	PUNCT
ejpam-6459	243	13	be	be	AUX
ejpam-6459	243	14	two	two	NUM
ejpam-6459	243	15	bfsis	bfsis	NOUN
ejpam-6459	243	16	over	over	ADP
ejpam-6459	243	17	ℜ.	ℜ.	PROPN
ejpam-6459	243	18	then	then	ADV
ejpam-6459	243	19	(	(	PUNCT
ejpam-6459	243	20	j	j	NOUN
ejpam-6459	243	21	,	,	PUNCT
ejpam-6459	243	22	u	u	NOUN
ejpam-6459	243	23	)	)	PUNCT
ejpam-6459	243	24	∩	∩	NOUN
ejpam-6459	243	25	(	(	PUNCT
ejpam-6459	243	26	k	k	X
ejpam-6459	243	27	,	,	PUNCT
ejpam-6459	243	28	v	v	NOUN
ejpam-6459	243	29	)	)	PUNCT
ejpam-6459	243	30	=	=	SYM
ejpam-6459	243	31	(	(	PUNCT
ejpam-6459	243	32	l	l	NOUN
ejpam-6459	243	33	,	,	PUNCT
ejpam-6459	243	34	w	w	NOUN
ejpam-6459	243	35	)	)	PUNCT
ejpam-6459	243	36	,	,	PUNCT
ejpam-6459	243	37	where	where	SCONJ
ejpam-6459	243	38	w	w	NOUN
ejpam-6459	243	39	=	=	SYM
ejpam-6459	243	40	u	u	NOUN
ejpam-6459	243	41	∩	∩	NOUN
ejpam-6459	243	42	v	v	NOUN
ejpam-6459	243	43	and	and	CCONJ
ejpam-6459	243	44	l(ω	l(ω	PROPN
ejpam-6459	243	45	)	)	PUNCT
ejpam-6459	243	46	=	=	SYM
ejpam-6459	243	47	j(ω	j(ω	PROPN
ejpam-6459	243	48	)	)	PUNCT
ejpam-6459	243	49	∩k(ω	∩k(ω	PROPN
ejpam-6459	243	50	)	)	PUNCT
ejpam-6459	243	51	,	,	PUNCT
ejpam-6459	243	52	for	for	ADP
ejpam-6459	243	53	all	all	DET
ejpam-6459	243	54	ω	ω	NUM
ejpam-6459	243	55	∈	∈	PROPN
ejpam-6459	243	56	w	w	NOUN
ejpam-6459	243	57	.	.	PUNCT
ejpam-6459	244	1	now	now	ADV
ejpam-6459	244	2	,	,	PUNCT
ejpam-6459	244	3	l+	l+	X
ejpam-6459	244	4	ω	ω	X
ejpam-6459	244	5	(	(	PUNCT
ejpam-6459	244	6	κ+	κ+	PROPN
ejpam-6459	244	7	ξ	ξ	NUM
ejpam-6459	244	8	)	)	PUNCT
ejpam-6459	244	9	=	=	SYM
ejpam-6459	244	10	a{j+	a{j+	NOUN
ejpam-6459	244	11	ω	ω	PROPN
ejpam-6459	244	12	(	(	PUNCT
ejpam-6459	244	13	κ+	κ+	PROPN
ejpam-6459	244	14	ξ),k+	ξ),k+	PROPN
ejpam-6459	244	15	ω	ω	PROPN
ejpam-6459	244	16	(	(	PUNCT
ejpam-6459	244	17	κ+	κ+	PROPN
ejpam-6459	244	18	ξ	ξ	NUM
ejpam-6459	244	19	)	)	PUNCT
ejpam-6459	244	20	}	}	PUNCT
ejpam-6459	244	21	≥	≥	NOUN
ejpam-6459	244	22	a{a{j+	a{a{j+	NOUN
ejpam-6459	244	23	ω	ω	PROPN
ejpam-6459	244	24	(	(	PUNCT
ejpam-6459	244	25	κ	κ	NOUN
ejpam-6459	244	26	)	)	PUNCT
ejpam-6459	244	27	,	,	PUNCT
ejpam-6459	244	28	j+	j+	PROPN
ejpam-6459	244	29	ω	ω	PROPN
ejpam-6459	244	30	(	(	PUNCT
ejpam-6459	244	31	ξ	ξ	NOUN
ejpam-6459	244	32	)	)	PUNCT
ejpam-6459	244	33	}	}	PUNCT
ejpam-6459	244	34	,	,	PUNCT
ejpam-6459	244	35	a{k+	a{k+	ADP
ejpam-6459	244	36	ω	ω	X
ejpam-6459	244	37	(	(	PUNCT
ejpam-6459	244	38	κ),k+	κ),k+	PROPN
ejpam-6459	244	39	ω	ω	PROPN
ejpam-6459	244	40	(	(	PUNCT
ejpam-6459	244	41	ξ	ξ	NOUN
ejpam-6459	244	42	)	)	PUNCT
ejpam-6459	244	43	}	}	PUNCT
ejpam-6459	244	44	}	}	PUNCT
ejpam-6459	244	45	=	=	SYM
ejpam-6459	244	46	a{j+	a{j+	NOUN
ejpam-6459	244	47	ω	ω	NOUN
ejpam-6459	244	48	(	(	PUNCT
ejpam-6459	244	49	κ),k+	κ),k+	PROPN
ejpam-6459	244	50	ω	ω	PROPN
ejpam-6459	244	51	(	(	PUNCT
ejpam-6459	244	52	κ	κ	NOUN
ejpam-6459	244	53	)	)	PUNCT
ejpam-6459	244	54	}	}	PUNCT
ejpam-6459	244	55	,	,	PUNCT
ejpam-6459	244	56	a{j+	a{j+	PROPN
ejpam-6459	244	57	ω	ω	PROPN
ejpam-6459	244	58	(	(	PUNCT
ejpam-6459	244	59	ξ),k+	ξ),k+	PROPN
ejpam-6459	244	60	ω	ω	PROPN
ejpam-6459	244	61	(	(	PUNCT
ejpam-6459	244	62	ξ	ξ	NOUN
ejpam-6459	244	63	)	)	PUNCT
ejpam-6459	244	64	}	}	PUNCT
ejpam-6459	244	65	}	}	PUNCT
ejpam-6459	244	66	=	=	SYM
ejpam-6459	244	67	a{l+	a{l+	NUM
ejpam-6459	244	68	ω	ω	NUM
ejpam-6459	244	69	(	(	PUNCT
ejpam-6459	244	70	κ	κ	NOUN
ejpam-6459	244	71	)	)	PUNCT
ejpam-6459	244	72	,	,	PUNCT
ejpam-6459	244	73	l	l	PROPN
ejpam-6459	245	1	+	+	X
ejpam-6459	245	2	ω	ω	PROPN
ejpam-6459	245	3	(	(	PUNCT
ejpam-6459	245	4	ξ	ξ	NOUN
ejpam-6459	245	5	)	)	PUNCT
ejpam-6459	245	6	}	}	PUNCT
ejpam-6459	245	7	,	,	PUNCT
ejpam-6459	245	8	l−	l−	PROPN
ejpam-6459	245	9	ω	ω	PROPN
ejpam-6459	245	10	(	(	PUNCT
ejpam-6459	245	11	κ+	κ+	PROPN
ejpam-6459	245	12	ξ	ξ	X
ejpam-6459	245	13	)	)	PUNCT
ejpam-6459	245	14	=	=	SYM
ejpam-6459	245	15	b{j−	b{j−	PROPN
ejpam-6459	245	16	ω	ω	NOUN
ejpam-6459	245	17	(	(	PUNCT
ejpam-6459	245	18	κ+	κ+	PROPN
ejpam-6459	245	19	ξ),k−	ξ),k−	PROPN
ejpam-6459	245	20	ω	ω	PROPN
ejpam-6459	245	21	(	(	PUNCT
ejpam-6459	245	22	κ+	κ+	PROPN
ejpam-6459	245	23	ξ	ξ	NUM
ejpam-6459	245	24	)	)	PUNCT
ejpam-6459	245	25	}	}	PUNCT
ejpam-6459	245	26	≤	≤	NUM
ejpam-6459	245	27	b{b{j−	b{b{j−	VERB
ejpam-6459	245	28	ω	ω	X
ejpam-6459	245	29	(	(	PUNCT
ejpam-6459	245	30	κ	κ	NOUN
ejpam-6459	245	31	)	)	PUNCT
ejpam-6459	245	32	,	,	PUNCT
ejpam-6459	245	33	j−	j−	PROPN
ejpam-6459	245	34	ω	ω	PROPN
ejpam-6459	245	35	(	(	PUNCT
ejpam-6459	245	36	ξ	ξ	NOUN
ejpam-6459	245	37	)	)	PUNCT
ejpam-6459	245	38	}	}	PUNCT
ejpam-6459	245	39	,	,	PUNCT
ejpam-6459	245	40	b{k−	b{k−	PROPN
ejpam-6459	245	41	ω	ω	PROPN
ejpam-6459	245	42	(	(	PUNCT
ejpam-6459	245	43	κ),k−	κ),k−	PROPN
ejpam-6459	245	44	ω	ω	PROPN
ejpam-6459	245	45	(	(	PUNCT
ejpam-6459	245	46	ξ	ξ	NOUN
ejpam-6459	245	47	)	)	PUNCT
ejpam-6459	245	48	}	}	PUNCT
ejpam-6459	245	49	}	}	PUNCT
ejpam-6459	245	50	=	=	SYM
ejpam-6459	245	51	b{b{j−	b{b{j−	NOUN
ejpam-6459	245	52	ω	ω	X
ejpam-6459	245	53	(	(	PUNCT
ejpam-6459	245	54	κ),k−	κ),k−	PROPN
ejpam-6459	245	55	ω	ω	PROPN
ejpam-6459	245	56	(	(	PUNCT
ejpam-6459	245	57	κ	κ	NOUN
ejpam-6459	245	58	)	)	PUNCT
ejpam-6459	245	59	}	}	PUNCT
ejpam-6459	245	60	,	,	PUNCT
ejpam-6459	245	61	b{j−	b{j−	PROPN
ejpam-6459	245	62	ω	ω	NOUN
ejpam-6459	245	63	(	(	PUNCT
ejpam-6459	245	64	ξ),k−	ξ),k−	PROPN
ejpam-6459	245	65	ω	ω	PROPN
ejpam-6459	245	66	(	(	PUNCT
ejpam-6459	245	67	ξ	ξ	NOUN
ejpam-6459	245	68	)	)	PUNCT
ejpam-6459	245	69	}	}	PUNCT
ejpam-6459	245	70	}	}	PUNCT
ejpam-6459	245	71	=	=	PUNCT
ejpam-6459	245	72	b{l−	b{l−	PUNCT
ejpam-6459	245	73	ω	ω	NUM
ejpam-6459	245	74	(	(	PUNCT
ejpam-6459	245	75	κ	κ	NOUN
ejpam-6459	245	76	)	)	PUNCT
ejpam-6459	245	77	,	,	PUNCT
ejpam-6459	246	1	l	l	PROPN
ejpam-6459	247	1	−	−	PROPN
ejpam-6459	248	1	ω	ω	X
ejpam-6459	248	2	(	(	PUNCT
ejpam-6459	248	3	ξ	ξ	NOUN
ejpam-6459	248	4	)	)	PUNCT
ejpam-6459	248	5	}	}	PUNCT
ejpam-6459	248	6	,	,	PUNCT
ejpam-6459	248	7	l+	l+	X
ejpam-6459	248	8	ω	ω	X
ejpam-6459	248	9	(	(	PUNCT
ejpam-6459	248	10	κξ	κξ	NOUN
ejpam-6459	248	11	)	)	PUNCT
ejpam-6459	248	12	=	=	SYM
ejpam-6459	248	13	a{j+	a{j+	NOUN
ejpam-6459	248	14	ω	ω	PROPN
ejpam-6459	248	15	(	(	PUNCT
ejpam-6459	248	16	κξ),k+	κξ),k+	PROPN
ejpam-6459	248	17	ω	ω	PROPN
ejpam-6459	248	18	(	(	PUNCT
ejpam-6459	248	19	κξ	κξ	NOUN
ejpam-6459	248	20	)	)	PUNCT
ejpam-6459	248	21	}	}	PUNCT
ejpam-6459	248	22	≥	≥	PROPN
ejpam-6459	248	23	a{j+	a{j+	PROPN
ejpam-6459	248	24	ω	ω	PROPN
ejpam-6459	248	25	(	(	PUNCT
ejpam-6459	248	26	ξ),k+	ξ),k+	PROPN
ejpam-6459	248	27	ω	ω	PROPN
ejpam-6459	248	28	(	(	PUNCT
ejpam-6459	248	29	ξ	ξ	NOUN
ejpam-6459	248	30	)	)	PUNCT
ejpam-6459	248	31	}	}	PUNCT
ejpam-6459	248	32	=	=	SYM
ejpam-6459	248	33	a{j+	a{j+	NOUN
ejpam-6459	248	34	ω	ω	NOUN
ejpam-6459	248	35	(	(	PUNCT
ejpam-6459	248	36	ξ),k+	ξ),k+	PROPN
ejpam-6459	248	37	ω	ω	PROPN
ejpam-6459	248	38	(	(	PUNCT
ejpam-6459	248	39	ξ	ξ	NOUN
ejpam-6459	248	40	)	)	PUNCT
ejpam-6459	248	41	}	}	PUNCT
ejpam-6459	248	42	=	=	SYM
ejpam-6459	248	43	l+	l+	X
ejpam-6459	248	44	ω	ω	X
ejpam-6459	248	45	(	(	PUNCT
ejpam-6459	248	46	ξ	ξ	NOUN
ejpam-6459	248	47	)	)	PUNCT
ejpam-6459	248	48	,	,	PUNCT
ejpam-6459	248	49	l−	l−	PROPN
ejpam-6459	248	50	ω	ω	PROPN
ejpam-6459	248	51	(	(	PUNCT
ejpam-6459	248	52	κξ	κξ	NOUN
ejpam-6459	248	53	)	)	PUNCT
ejpam-6459	248	54	=	=	SYM
ejpam-6459	248	55	b{j−	b{j−	PROPN
ejpam-6459	248	56	ω	ω	NOUN
ejpam-6459	248	57	(	(	PUNCT
ejpam-6459	248	58	κ+	κ+	PROPN
ejpam-6459	248	59	ξ),k−	ξ),k−	PROPN
ejpam-6459	248	60	ω	ω	PROPN
ejpam-6459	248	61	(	(	PUNCT
ejpam-6459	248	62	κ+	κ+	PROPN
ejpam-6459	248	63	ξ	ξ	NUM
ejpam-6459	248	64	)	)	PUNCT
ejpam-6459	248	65	}	}	PUNCT
ejpam-6459	248	66	≤	≤	PROPN
ejpam-6459	248	67	b{j−	b{j−	PUNCT
ejpam-6459	248	68	ω	ω	NOUN
ejpam-6459	248	69	(	(	PUNCT
ejpam-6459	248	70	ξ),k−	ξ),k−	PROPN
ejpam-6459	248	71	ω	ω	PROPN
ejpam-6459	248	72	(	(	PUNCT
ejpam-6459	248	73	ξ	ξ	NOUN
ejpam-6459	248	74	)	)	PUNCT
ejpam-6459	248	75	}	}	PUNCT
ejpam-6459	248	76	=	=	SYM
ejpam-6459	248	77	b{j−	b{j−	PROPN
ejpam-6459	248	78	ω	ω	NUM
ejpam-6459	248	79	(	(	PUNCT
ejpam-6459	248	80	ξ),k−	ξ),k−	PROPN
ejpam-6459	248	81	ω	ω	PROPN
ejpam-6459	248	82	(	(	PUNCT
ejpam-6459	248	83	ξ	ξ	NOUN
ejpam-6459	248	84	)	)	PUNCT
ejpam-6459	248	85	}	}	PUNCT
ejpam-6459	248	86	=	=	SYM
ejpam-6459	248	87	l−	l−	PROPN
ejpam-6459	248	88	ω	ω	PROPN
ejpam-6459	248	89	(	(	PUNCT
ejpam-6459	248	90	ξ	ξ	NOUN
ejpam-6459	248	91	)	)	PUNCT
ejpam-6459	248	92	.	.	PUNCT
ejpam-6459	249	1	g.	g.	PROPN
ejpam-6459	249	2	s.	s.	PROPN
ejpam-6459	249	3	rao	rao	PROPN
ejpam-6459	249	4	et	et	PROPN
ejpam-6459	249	5	al	al	PROPN
ejpam-6459	249	6	.	.	PUNCT
ejpam-6459	249	7	/	/	SYM
ejpam-6459	249	8	eur	eur	PROPN
ejpam-6459	249	9	.	.	PUNCT
ejpam-6459	250	1	j.	j.	PROPN
ejpam-6459	250	2	pure	pure	PROPN
ejpam-6459	250	3	appl	appl	PROPN
ejpam-6459	250	4	.	.	PROPN
ejpam-6459	250	5	math	math	PROPN
ejpam-6459	250	6	,	,	PUNCT
ejpam-6459	250	7	18	18	NUM
ejpam-6459	250	8	(	(	PUNCT
ejpam-6459	250	9	3	3	NUM
ejpam-6459	250	10	)	)	PUNCT
ejpam-6459	250	11	(	(	PUNCT
ejpam-6459	250	12	2025	2025	NUM
ejpam-6459	250	13	)	)	PUNCT
ejpam-6459	250	14	,	,	PUNCT
ejpam-6459	250	15	6459	6459	NUM
ejpam-6459	250	16	13	13	NUM
ejpam-6459	250	17	of	of	ADP
ejpam-6459	250	18	16	16	NUM
ejpam-6459	250	19	therefore	therefore	ADV
ejpam-6459	250	20	,	,	PUNCT
ejpam-6459	250	21	(	(	PUNCT
ejpam-6459	250	22	l	l	NOUN
ejpam-6459	250	23	,	,	PUNCT
ejpam-6459	250	24	w	w	NOUN
ejpam-6459	250	25	)	)	PUNCT
ejpam-6459	250	26	=	=	SYM
ejpam-6459	250	27	(	(	PUNCT
ejpam-6459	250	28	j	j	PROPN
ejpam-6459	250	29	,	,	PUNCT
ejpam-6459	250	30	u	u	NOUN
ejpam-6459	250	31	)	)	PUNCT
ejpam-6459	250	32	∩	∩	NOUN
ejpam-6459	250	33	(	(	PUNCT
ejpam-6459	250	34	k	k	X
ejpam-6459	250	35	,	,	PUNCT
ejpam-6459	250	36	v	v	NOUN
ejpam-6459	250	37	)	)	PUNCT
ejpam-6459	250	38	is	be	AUX
ejpam-6459	250	39	a	a	PRON
ejpam-6459	250	40	bfsi	bfsi	ADV
ejpam-6459	250	41	over	over	ADP
ejpam-6459	250	42	ℜ.	ℜ.	PROPN
ejpam-6459	250	43	theorem	theorem	NOUN
ejpam-6459	250	44	8	8	NUM
ejpam-6459	250	45	.	.	PUNCT
ejpam-6459	251	1	if	if	SCONJ
ejpam-6459	251	2	(	(	PUNCT
ejpam-6459	251	3	j	j	NOUN
ejpam-6459	251	4	,	,	PUNCT
ejpam-6459	251	5	u	u	NOUN
ejpam-6459	251	6	)	)	PUNCT
ejpam-6459	251	7	and	and	CCONJ
ejpam-6459	251	8	(	(	PUNCT
ejpam-6459	251	9	k	k	X
ejpam-6459	251	10	,	,	PUNCT
ejpam-6459	251	11	v	v	NOUN
ejpam-6459	251	12	)	)	PUNCT
ejpam-6459	251	13	are	be	AUX
ejpam-6459	251	14	two	two	NUM
ejpam-6459	251	15	bfsis	bfsis	NOUN
ejpam-6459	251	16	over	over	ADP
ejpam-6459	251	17	ℜ	ℜ	PROPN
ejpam-6459	251	18	,	,	PUNCT
ejpam-6459	251	19	then	then	ADV
ejpam-6459	251	20	(	(	PUNCT
ejpam-6459	251	21	j	j	NOUN
ejpam-6459	251	22	,	,	PUNCT
ejpam-6459	251	23	u	u	NOUN
ejpam-6459	251	24	)	)	PUNCT
ejpam-6459	251	25	∪	∪	ADV
ejpam-6459	251	26	(	(	PUNCT
ejpam-6459	251	27	k	k	NOUN
ejpam-6459	251	28	,	,	PUNCT
ejpam-6459	251	29	v	v	NOUN
ejpam-6459	251	30	)	)	PUNCT
ejpam-6459	251	31	is	be	AUX
ejpam-6459	251	32	also	also	ADV
ejpam-6459	251	33	a	a	DET
ejpam-6459	251	34	bfsi	bfsi	ADV
ejpam-6459	251	35	over	over	ADP
ejpam-6459	251	36	ℜ.	ℜ.	PROPN
ejpam-6459	251	37	proof	proof	NOUN
ejpam-6459	251	38	.	.	PUNCT
ejpam-6459	252	1	let	let	VERB
ejpam-6459	252	2	(	(	PUNCT
ejpam-6459	252	3	j	j	NOUN
ejpam-6459	252	4	,	,	PUNCT
ejpam-6459	252	5	u	u	NOUN
ejpam-6459	252	6	)	)	PUNCT
ejpam-6459	252	7	and	and	CCONJ
ejpam-6459	252	8	(	(	PUNCT
ejpam-6459	252	9	k	k	X
ejpam-6459	252	10	,	,	PUNCT
ejpam-6459	252	11	v	v	NOUN
ejpam-6459	252	12	)	)	PUNCT
ejpam-6459	252	13	be	be	AUX
ejpam-6459	252	14	two	two	NUM
ejpam-6459	252	15	bfsis	bfsis	NOUN
ejpam-6459	252	16	over	over	ADP
ejpam-6459	252	17	ℜ.	ℜ.	PROPN
ejpam-6459	252	18	then	then	ADV
ejpam-6459	252	19	(	(	PUNCT
ejpam-6459	252	20	j	j	NOUN
ejpam-6459	252	21	,	,	PUNCT
ejpam-6459	252	22	u	u	NOUN
ejpam-6459	252	23	)	)	PUNCT
ejpam-6459	252	24	∪	∪	ADV
ejpam-6459	252	25	(	(	PUNCT
ejpam-6459	252	26	k	k	NOUN
ejpam-6459	252	27	,	,	PUNCT
ejpam-6459	252	28	v	v	NOUN
ejpam-6459	252	29	)	)	PUNCT
ejpam-6459	252	30	=	=	SYM
ejpam-6459	252	31	(	(	PUNCT
ejpam-6459	252	32	l	l	NOUN
ejpam-6459	252	33	,	,	PUNCT
ejpam-6459	252	34	w	w	NOUN
ejpam-6459	252	35	)	)	PUNCT
ejpam-6459	252	36	,	,	PUNCT
ejpam-6459	252	37	where	where	SCONJ
ejpam-6459	252	38	w	w	NOUN
ejpam-6459	252	39	=	=	SYM
ejpam-6459	252	40	u	u	NOUN
ejpam-6459	252	41	∪	∪	NOUN
ejpam-6459	252	42	v	v	NOUN
ejpam-6459	252	43	and	and	CCONJ
ejpam-6459	252	44	l(ω	l(ω	PROPN
ejpam-6459	252	45	)	)	PUNCT
ejpam-6459	252	46	=	=	PUNCT
ejpam-6459	253	1			PROPN
ejpam-6459	253	2	j(ω	j(ω	PROPN
ejpam-6459	253	3	)	)	PUNCT
ejpam-6459	253	4	if	if	SCONJ
ejpam-6459	253	5	ω	ω	NUM
ejpam-6459	253	6	∈	∈	PROPN
ejpam-6459	253	7	u	u	NOUN
ejpam-6459	253	8	−	−	PROPN
ejpam-6459	253	9	v	v	ADP
ejpam-6459	253	10	k(ω	k(ω	PROPN
ejpam-6459	253	11	)	)	PUNCT
ejpam-6459	253	12	if	if	SCONJ
ejpam-6459	253	13	ω	ω	PROPN
ejpam-6459	253	14	∈	∈	PROPN
ejpam-6459	253	15	v	v	ADP
ejpam-6459	253	16	−	−	PROPN
ejpam-6459	253	17	u	u	NOUN
ejpam-6459	253	18	for	for	ADP
ejpam-6459	253	19	all	all	DET
ejpam-6459	253	20	ω	ω	NUM
ejpam-6459	253	21	∈	∈	PROPN
ejpam-6459	253	22	w.	w.	PROPN
ejpam-6459	253	23	j(ω	j(ω	PROPN
ejpam-6459	253	24	)	)	PUNCT
ejpam-6459	253	25	∨k(ω	∨k(ω	NUM
ejpam-6459	253	26	)	)	PUNCT
ejpam-6459	253	27	if	if	SCONJ
ejpam-6459	253	28	ω	ω	NUM
ejpam-6459	253	29	∈	∈	PROPN
ejpam-6459	253	30	u	u	NOUN
ejpam-6459	253	31	∩	∩	X
ejpam-6459	253	32	v	v	X
ejpam-6459	253	33	then	then	ADV
ejpam-6459	253	34	we	we	PRON
ejpam-6459	253	35	have	have	VERB
ejpam-6459	253	36	the	the	DET
ejpam-6459	253	37	following	follow	VERB
ejpam-6459	253	38	cases	case	NOUN
ejpam-6459	253	39	:	:	PUNCT
ejpam-6459	253	40	case	case	NOUN
ejpam-6459	253	41	1	1	NUM
ejpam-6459	253	42	:	:	PUNCT
ejpam-6459	253	43	if	if	SCONJ
ejpam-6459	253	44	ω	ω	PROPN
ejpam-6459	253	45	∈	∈	PROPN
ejpam-6459	253	46	u	u	NOUN
ejpam-6459	253	47	−	−	PROPN
ejpam-6459	253	48	v	v	NOUN
ejpam-6459	253	49	,	,	PUNCT
ejpam-6459	253	50	then	then	ADV
ejpam-6459	253	51	l+	l+	X
ejpam-6459	253	52	ω	ω	PROPN
ejpam-6459	253	53	(	(	PUNCT
ejpam-6459	253	54	κ+	κ+	PROPN
ejpam-6459	253	55	ξ	ξ	NUM
ejpam-6459	253	56	)	)	PUNCT
ejpam-6459	253	57	=	=	SYM
ejpam-6459	254	1	j+	j+	NUM
ejpam-6459	254	2	ω	ω	PROPN
ejpam-6459	254	3	(	(	PUNCT
ejpam-6459	254	4	κ+	κ+	PROPN
ejpam-6459	254	5	ξ	ξ	PROPN
ejpam-6459	254	6	)	)	PUNCT
ejpam-6459	254	7	≥	≥	NOUN
ejpam-6459	254	8	a{j+	a{j+	PROPN
ejpam-6459	254	9	ω	ω	PROPN
ejpam-6459	254	10	(	(	PUNCT
ejpam-6459	254	11	κ	κ	NOUN
ejpam-6459	254	12	)	)	PUNCT
ejpam-6459	254	13	,	,	PUNCT
ejpam-6459	254	14	j+	j+	PROPN
ejpam-6459	254	15	ω	ω	PROPN
ejpam-6459	254	16	(	(	PUNCT
ejpam-6459	254	17	ξ	ξ	NOUN
ejpam-6459	254	18	)	)	PUNCT
ejpam-6459	254	19	}	}	PUNCT
ejpam-6459	254	20	=	=	SYM
ejpam-6459	254	21	a{l+	a{l+	NUM
ejpam-6459	254	22	ω	ω	NUM
ejpam-6459	254	23	(	(	PUNCT
ejpam-6459	254	24	κ	κ	NOUN
ejpam-6459	254	25	)	)	PUNCT
ejpam-6459	254	26	,	,	PUNCT
ejpam-6459	254	27	l	l	PROPN
ejpam-6459	255	1	+	+	X
ejpam-6459	255	2	ω	ω	PROPN
ejpam-6459	255	3	(	(	PUNCT
ejpam-6459	255	4	ξ	ξ	NOUN
ejpam-6459	255	5	)	)	PUNCT
ejpam-6459	255	6	}	}	PUNCT
ejpam-6459	255	7	,	,	PUNCT
ejpam-6459	255	8	l−	l−	PROPN
ejpam-6459	255	9	ω	ω	PROPN
ejpam-6459	255	10	(	(	PUNCT
ejpam-6459	255	11	κ+	κ+	PROPN
ejpam-6459	255	12	ξ	ξ	X
ejpam-6459	255	13	)	)	PUNCT
ejpam-6459	255	14	=	=	SYM
ejpam-6459	255	15	j−	j−	PROPN
ejpam-6459	255	16	ω	ω	PROPN
ejpam-6459	255	17	(	(	PUNCT
ejpam-6459	255	18	κ+	κ+	PROPN
ejpam-6459	255	19	ξ	ξ	PROPN
ejpam-6459	255	20	)	)	PUNCT
ejpam-6459	255	21	≤	≤	NOUN
ejpam-6459	255	22	b{j−	b{j−	PUNCT
ejpam-6459	255	23	ω	ω	NOUN
ejpam-6459	255	24	(	(	PUNCT
ejpam-6459	255	25	κ	κ	NOUN
ejpam-6459	255	26	)	)	PUNCT
ejpam-6459	255	27	,	,	PUNCT
ejpam-6459	255	28	j−	j−	PROPN
ejpam-6459	255	29	ω	ω	PROPN
ejpam-6459	255	30	(	(	PUNCT
ejpam-6459	255	31	ξ	ξ	NOUN
ejpam-6459	255	32	)	)	PUNCT
ejpam-6459	255	33	}	}	PUNCT
ejpam-6459	255	34	=	=	PUNCT
ejpam-6459	255	35	b{l−	b{l−	PUNCT
ejpam-6459	255	36	ω	ω	NUM
ejpam-6459	255	37	(	(	PUNCT
ejpam-6459	255	38	κ	κ	NOUN
ejpam-6459	255	39	)	)	PUNCT
ejpam-6459	255	40	,	,	PUNCT
ejpam-6459	255	41	l	l	PROPN
ejpam-6459	255	42	−	−	PROPN
ejpam-6459	255	43	ω	ω	X
ejpam-6459	255	44	(	(	PUNCT
ejpam-6459	255	45	ξ	ξ	NOUN
ejpam-6459	255	46	)	)	PUNCT
ejpam-6459	255	47	}	}	PUNCT
ejpam-6459	255	48	,	,	PUNCT
ejpam-6459	255	49	l+	l+	X
ejpam-6459	255	50	ω	ω	X
ejpam-6459	255	51	(	(	PUNCT
ejpam-6459	255	52	κξ	κξ	NOUN
ejpam-6459	255	53	)	)	PUNCT
ejpam-6459	255	54	=	=	PUNCT
ejpam-6459	256	1	j+	j+	NUM
ejpam-6459	256	2	ω	ω	PROPN
ejpam-6459	256	3	(	(	PUNCT
ejpam-6459	256	4	κξ	κξ	NOUN
ejpam-6459	256	5	)	)	PUNCT
ejpam-6459	256	6	≥	≥	NOUN
ejpam-6459	256	7	j+	j+	NUM
ejpam-6459	256	8	ω	ω	PROPN
ejpam-6459	256	9	(	(	PUNCT
ejpam-6459	256	10	ξ	ξ	NOUN
ejpam-6459	256	11	)	)	PUNCT
ejpam-6459	256	12	=	=	SYM
ejpam-6459	256	13	l+	l+	X
ejpam-6459	256	14	ω	ω	X
ejpam-6459	256	15	(	(	PUNCT
ejpam-6459	256	16	ξ	ξ	NOUN
ejpam-6459	256	17	)	)	PUNCT
ejpam-6459	256	18	,	,	PUNCT
ejpam-6459	256	19	l−	l−	PROPN
ejpam-6459	256	20	ω	ω	PROPN
ejpam-6459	256	21	(	(	PUNCT
ejpam-6459	256	22	κξ	κξ	NOUN
ejpam-6459	256	23	)	)	PUNCT
ejpam-6459	256	24	=	=	PUNCT
ejpam-6459	256	25	j−	j−	PROPN
ejpam-6459	256	26	ω	ω	PROPN
ejpam-6459	256	27	(	(	PUNCT
ejpam-6459	256	28	κ+	κ+	PROPN
ejpam-6459	256	29	ξ	ξ	PROPN
ejpam-6459	256	30	)	)	PUNCT
ejpam-6459	256	31	≤	≤	PUNCT
ejpam-6459	256	32	j−	j−	PROPN
ejpam-6459	256	33	ω	ω	PROPN
ejpam-6459	256	34	(	(	PUNCT
ejpam-6459	256	35	ξ	ξ	NOUN
ejpam-6459	256	36	)	)	PUNCT
ejpam-6459	256	37	=	=	SYM
ejpam-6459	256	38	l−	l−	PROPN
ejpam-6459	256	39	ω	ω	PROPN
ejpam-6459	256	40	(	(	PUNCT
ejpam-6459	256	41	ξ	ξ	NOUN
ejpam-6459	256	42	)	)	PUNCT
ejpam-6459	256	43	.	.	PUNCT
ejpam-6459	257	1	case	case	NOUN
ejpam-6459	257	2	2	2	NUM
ejpam-6459	257	3	:	:	PUNCT
ejpam-6459	258	1	if	if	SCONJ
ejpam-6459	258	2	ω	ω	PROPN
ejpam-6459	258	3	∈	∈	PROPN
ejpam-6459	258	4	v	v	ADP
ejpam-6459	258	5	−	−	PROPN
ejpam-6459	258	6	u	u	NOUN
ejpam-6459	258	7	,	,	PUNCT
ejpam-6459	258	8	then	then	ADV
ejpam-6459	258	9	l+	l+	X
ejpam-6459	258	10	ω	ω	PROPN
ejpam-6459	258	11	(	(	PUNCT
ejpam-6459	258	12	κ+	κ+	PROPN
ejpam-6459	258	13	ξ	ξ	PROPN
ejpam-6459	258	14	)	)	PUNCT
ejpam-6459	258	15	=	=	SYM
ejpam-6459	258	16	k+	k+	PROPN
ejpam-6459	258	17	ω	ω	PROPN
ejpam-6459	258	18	(	(	PUNCT
ejpam-6459	258	19	κ+	κ+	PROPN
ejpam-6459	258	20	ξ	ξ	PROPN
ejpam-6459	258	21	)	)	PUNCT
ejpam-6459	258	22	≥	≥	NOUN
ejpam-6459	258	23	a{k+	a{k+	ADP
ejpam-6459	258	24	ω	ω	X
ejpam-6459	258	25	(	(	PUNCT
ejpam-6459	258	26	κ),k+	κ),k+	PROPN
ejpam-6459	258	27	ω	ω	PROPN
ejpam-6459	258	28	(	(	PUNCT
ejpam-6459	258	29	ξ	ξ	NOUN
ejpam-6459	258	30	)	)	PUNCT
ejpam-6459	258	31	}	}	PUNCT
ejpam-6459	258	32	=	=	SYM
ejpam-6459	258	33	a{l+	a{l+	NUM
ejpam-6459	258	34	ω	ω	NUM
ejpam-6459	258	35	(	(	PUNCT
ejpam-6459	258	36	κ	κ	NOUN
ejpam-6459	258	37	)	)	PUNCT
ejpam-6459	258	38	,	,	PUNCT
ejpam-6459	258	39	l	l	PROPN
ejpam-6459	259	1	+	+	X
ejpam-6459	259	2	ω	ω	PROPN
ejpam-6459	259	3	(	(	PUNCT
ejpam-6459	259	4	ξ	ξ	NOUN
ejpam-6459	259	5	)	)	PUNCT
ejpam-6459	259	6	}	}	PUNCT
ejpam-6459	259	7	,	,	PUNCT
ejpam-6459	259	8	l−	l−	PROPN
ejpam-6459	259	9	ω	ω	PROPN
ejpam-6459	259	10	(	(	PUNCT
ejpam-6459	259	11	κ+	κ+	PROPN
ejpam-6459	259	12	ξ	ξ	PROPN
ejpam-6459	259	13	)	)	PUNCT
ejpam-6459	259	14	=	=	SYM
ejpam-6459	259	15	k−	k−	PROPN
ejpam-6459	259	16	ω	ω	PROPN
ejpam-6459	259	17	(	(	PUNCT
ejpam-6459	259	18	κ+	κ+	PROPN
ejpam-6459	259	19	ξ	ξ	PROPN
ejpam-6459	259	20	)	)	PUNCT
ejpam-6459	259	21	≤	≤	PUNCT
ejpam-6459	259	22	b{k−	b{k−	PROPN
ejpam-6459	259	23	ω	ω	PROPN
ejpam-6459	259	24	(	(	PUNCT
ejpam-6459	259	25	κ),k−	κ),k−	PROPN
ejpam-6459	259	26	ω	ω	PROPN
ejpam-6459	259	27	(	(	PUNCT
ejpam-6459	259	28	ξ	ξ	NOUN
ejpam-6459	259	29	)	)	PUNCT
ejpam-6459	259	30	}	}	PUNCT
ejpam-6459	259	31	=	=	PUNCT
ejpam-6459	259	32	b{l−	b{l−	PUNCT
ejpam-6459	259	33	ω	ω	NUM
ejpam-6459	259	34	(	(	PUNCT
ejpam-6459	259	35	κ	κ	NOUN
ejpam-6459	259	36	)	)	PUNCT
ejpam-6459	259	37	,	,	PUNCT
ejpam-6459	259	38	l	l	PROPN
ejpam-6459	259	39	−	−	PROPN
ejpam-6459	259	40	ω	ω	X
ejpam-6459	259	41	(	(	PUNCT
ejpam-6459	259	42	ξ	ξ	NOUN
ejpam-6459	259	43	)	)	PUNCT
ejpam-6459	259	44	}	}	PUNCT
ejpam-6459	259	45	,	,	PUNCT
ejpam-6459	259	46	l+	l+	X
ejpam-6459	259	47	ω	ω	X
ejpam-6459	259	48	(	(	PUNCT
ejpam-6459	259	49	κξ	κξ	NOUN
ejpam-6459	259	50	)	)	PUNCT
ejpam-6459	259	51	=	=	PUNCT
ejpam-6459	259	52	k+	k+	PROPN
ejpam-6459	259	53	ω	ω	PROPN
ejpam-6459	259	54	(	(	PUNCT
ejpam-6459	259	55	κξ	κξ	NOUN
ejpam-6459	259	56	)	)	PUNCT
ejpam-6459	259	57	≥	≥	PROPN
ejpam-6459	259	58	k+	k+	PROPN
ejpam-6459	259	59	ω	ω	PROPN
ejpam-6459	259	60	(	(	PUNCT
ejpam-6459	259	61	ξ	ξ	NOUN
ejpam-6459	259	62	)	)	PUNCT
ejpam-6459	259	63	=	=	SYM
ejpam-6459	259	64	l+	l+	X
ejpam-6459	259	65	ω	ω	X
ejpam-6459	259	66	(	(	PUNCT
ejpam-6459	259	67	ξ	ξ	NOUN
ejpam-6459	259	68	)	)	PUNCT
ejpam-6459	259	69	,	,	PUNCT
ejpam-6459	259	70	l−	l−	PROPN
ejpam-6459	259	71	ω	ω	PROPN
ejpam-6459	259	72	(	(	PUNCT
ejpam-6459	259	73	κξ	κξ	NOUN
ejpam-6459	259	74	)	)	PUNCT
ejpam-6459	259	75	=	=	SYM
ejpam-6459	259	76	k−	k−	PROPN
ejpam-6459	259	77	ω	ω	PROPN
ejpam-6459	259	78	(	(	PUNCT
ejpam-6459	259	79	κ+	κ+	PROPN
ejpam-6459	259	80	ξ	ξ	PROPN
ejpam-6459	259	81	)	)	PUNCT
ejpam-6459	259	82	g.	g.	PROPN
ejpam-6459	259	83	s.	s.	PROPN
ejpam-6459	259	84	rao	rao	PROPN
ejpam-6459	259	85	et	et	PROPN
ejpam-6459	259	86	al	al	PROPN
ejpam-6459	259	87	.	.	PUNCT
ejpam-6459	259	88	/	/	SYM
ejpam-6459	259	89	eur	eur	PROPN
ejpam-6459	259	90	.	.	PUNCT
ejpam-6459	260	1	j.	j.	PROPN
ejpam-6459	260	2	pure	pure	PROPN
ejpam-6459	260	3	appl	appl	PROPN
ejpam-6459	260	4	.	.	PROPN
ejpam-6459	260	5	math	math	PROPN
ejpam-6459	260	6	,	,	PUNCT
ejpam-6459	260	7	18	18	NUM
ejpam-6459	260	8	(	(	PUNCT
ejpam-6459	260	9	3	3	NUM
ejpam-6459	260	10	)	)	PUNCT
ejpam-6459	260	11	(	(	PUNCT
ejpam-6459	260	12	2025	2025	NUM
ejpam-6459	260	13	)	)	PUNCT
ejpam-6459	260	14	,	,	PUNCT
ejpam-6459	260	15	6459	6459	NUM
ejpam-6459	260	16	14	14	NUM
ejpam-6459	260	17	of	of	ADP
ejpam-6459	260	18	16	16	NUM
ejpam-6459	260	19	≤	≤	NUM
ejpam-6459	260	20	k−	k−	PROPN
ejpam-6459	260	21	ω	ω	PROPN
ejpam-6459	260	22	(	(	PUNCT
ejpam-6459	260	23	ξ	ξ	NOUN
ejpam-6459	260	24	)	)	PUNCT
ejpam-6459	260	25	=	=	SYM
ejpam-6459	260	26	l−	l−	PROPN
ejpam-6459	260	27	ω	ω	PROPN
ejpam-6459	260	28	(	(	PUNCT
ejpam-6459	260	29	ξ	ξ	NOUN
ejpam-6459	260	30	)	)	PUNCT
ejpam-6459	260	31	.	.	PUNCT
ejpam-6459	261	1	case	case	NOUN
ejpam-6459	261	2	3	3	NUM
ejpam-6459	261	3	:	:	PUNCT
ejpam-6459	261	4	if	if	SCONJ
ejpam-6459	261	5	ω	ω	PROPN
ejpam-6459	261	6	∈	∈	PROPN
ejpam-6459	261	7	u	u	NOUN
ejpam-6459	261	8	∩	∩	NOUN
ejpam-6459	261	9	v	v	NOUN
ejpam-6459	261	10	,	,	PUNCT
ejpam-6459	261	11	then	then	ADV
ejpam-6459	261	12	l+	l+	X
ejpam-6459	261	13	ω	ω	PROPN
ejpam-6459	261	14	(	(	PUNCT
ejpam-6459	261	15	κ+	κ+	PROPN
ejpam-6459	261	16	ξ	ξ	X
ejpam-6459	261	17	)	)	PUNCT
ejpam-6459	261	18	=	=	SYM
ejpam-6459	261	19	b{j+	b{j+	PROPN
ejpam-6459	261	20	ω	ω	NOUN
ejpam-6459	261	21	(	(	PUNCT
ejpam-6459	261	22	κ+	κ+	PROPN
ejpam-6459	261	23	ξ),k+	ξ),k+	PROPN
ejpam-6459	261	24	ω	ω	PROPN
ejpam-6459	261	25	(	(	PUNCT
ejpam-6459	261	26	κ+	κ+	PROPN
ejpam-6459	261	27	ξ	ξ	NUM
ejpam-6459	261	28	)	)	PUNCT
ejpam-6459	261	29	}	}	PUNCT
ejpam-6459	261	30	≥	≥	NOUN
ejpam-6459	261	31	b{a{j+	b{a{j+	NOUN
ejpam-6459	261	32	ω	ω	PROPN
ejpam-6459	261	33	(	(	PUNCT
ejpam-6459	261	34	κ	κ	NOUN
ejpam-6459	261	35	)	)	PUNCT
ejpam-6459	261	36	,	,	PUNCT
ejpam-6459	261	37	j+	j+	PROPN
ejpam-6459	261	38	ω	ω	PROPN
ejpam-6459	261	39	(	(	PUNCT
ejpam-6459	261	40	ξ	ξ	NOUN
ejpam-6459	261	41	)	)	PUNCT
ejpam-6459	261	42	}	}	PUNCT
ejpam-6459	261	43	,	,	PUNCT
ejpam-6459	261	44	a{k+	a{k+	ADP
ejpam-6459	261	45	ω	ω	X
ejpam-6459	261	46	(	(	PUNCT
ejpam-6459	261	47	κ),k+	κ),k+	PROPN
ejpam-6459	261	48	ω	ω	PROPN
ejpam-6459	261	49	(	(	PUNCT
ejpam-6459	261	50	ξ	ξ	NOUN
ejpam-6459	261	51	)	)	PUNCT
ejpam-6459	261	52	}	}	PUNCT
ejpam-6459	261	53	}	}	PUNCT
ejpam-6459	261	54	≥	≥	AUX
ejpam-6459	261	55	a{b{j+	a{b{j+	PROPN
ejpam-6459	261	56	ω	ω	PROPN
ejpam-6459	261	57	(	(	PUNCT
ejpam-6459	261	58	κ),k+	κ),k+	PROPN
ejpam-6459	261	59	ω	ω	PROPN
ejpam-6459	261	60	(	(	PUNCT
ejpam-6459	261	61	κ	κ	NOUN
ejpam-6459	261	62	)	)	PUNCT
ejpam-6459	261	63	}	}	PUNCT
ejpam-6459	261	64	,	,	PUNCT
ejpam-6459	261	65	b{j+	b{j+	PROPN
ejpam-6459	261	66	ω	ω	PROPN
ejpam-6459	261	67	(	(	PUNCT
ejpam-6459	261	68	ξ),k+	ξ),k+	PROPN
ejpam-6459	261	69	ω	ω	PROPN
ejpam-6459	261	70	(	(	PUNCT
ejpam-6459	261	71	ξ	ξ	NOUN
ejpam-6459	261	72	)	)	PUNCT
ejpam-6459	261	73	}	}	PUNCT
ejpam-6459	261	74	}	}	PUNCT
ejpam-6459	261	75	=	=	SYM
ejpam-6459	261	76	a{l+	a{l+	NUM
ejpam-6459	261	77	ω	ω	NUM
ejpam-6459	261	78	(	(	PUNCT
ejpam-6459	261	79	κ	κ	NOUN
ejpam-6459	261	80	)	)	PUNCT
ejpam-6459	261	81	,	,	PUNCT
ejpam-6459	261	82	l	l	PROPN
ejpam-6459	262	1	+	+	X
ejpam-6459	262	2	ω	ω	PROPN
ejpam-6459	262	3	(	(	PUNCT
ejpam-6459	262	4	ξ	ξ	NOUN
ejpam-6459	262	5	)	)	PUNCT
ejpam-6459	262	6	}	}	PUNCT
ejpam-6459	262	7	,	,	PUNCT
ejpam-6459	262	8	l−	l−	PROPN
ejpam-6459	262	9	ω	ω	PROPN
ejpam-6459	262	10	(	(	PUNCT
ejpam-6459	262	11	κ+	κ+	PROPN
ejpam-6459	262	12	ξ	ξ	NUM
ejpam-6459	262	13	)	)	PUNCT
ejpam-6459	262	14	=	=	SYM
ejpam-6459	262	15	a{j−	a{j−	NUM
ejpam-6459	262	16	ω	ω	PROPN
ejpam-6459	262	17	(	(	PUNCT
ejpam-6459	262	18	κ+	κ+	PROPN
ejpam-6459	262	19	ξ),k−	ξ),k−	PROPN
ejpam-6459	262	20	ω	ω	PROPN
ejpam-6459	262	21	(	(	PUNCT
ejpam-6459	262	22	κ+	κ+	PROPN
ejpam-6459	262	23	ξ	ξ	NUM
ejpam-6459	262	24	)	)	PUNCT
ejpam-6459	262	25	}	}	PUNCT
ejpam-6459	262	26	≤	≤	NUM
ejpam-6459	262	27	a{b{j−	a{b{j−	X
ejpam-6459	262	28	ω	ω	X
ejpam-6459	262	29	(	(	PUNCT
ejpam-6459	262	30	κ	κ	NOUN
ejpam-6459	262	31	)	)	PUNCT
ejpam-6459	262	32	,	,	PUNCT
ejpam-6459	262	33	j−	j−	PROPN
ejpam-6459	262	34	ω	ω	PROPN
ejpam-6459	262	35	(	(	PUNCT
ejpam-6459	262	36	ξ	ξ	NOUN
ejpam-6459	262	37	)	)	PUNCT
ejpam-6459	262	38	}	}	PUNCT
ejpam-6459	262	39	,	,	PUNCT
ejpam-6459	262	40	b{k−	b{k−	PROPN
ejpam-6459	262	41	ω	ω	PROPN
ejpam-6459	262	42	(	(	PUNCT
ejpam-6459	262	43	κ),k−	κ),k−	PROPN
ejpam-6459	262	44	ω	ω	PROPN
ejpam-6459	262	45	(	(	PUNCT
ejpam-6459	262	46	ξ	ξ	NOUN
ejpam-6459	262	47	)	)	PUNCT
ejpam-6459	262	48	}	}	PUNCT
ejpam-6459	262	49	}	}	PUNCT
ejpam-6459	262	50	≤	≤	NUM
ejpam-6459	262	51	b{a{j−	b{a{j−	NOUN
ejpam-6459	262	52	ω	ω	PROPN
ejpam-6459	262	53	(	(	PUNCT
ejpam-6459	262	54	κ),k−	κ),k−	PROPN
ejpam-6459	262	55	ω	ω	PROPN
ejpam-6459	262	56	(	(	PUNCT
ejpam-6459	262	57	κ	κ	NOUN
ejpam-6459	262	58	)	)	PUNCT
ejpam-6459	262	59	}	}	PUNCT
ejpam-6459	262	60	,	,	PUNCT
ejpam-6459	262	61	a{j−	a{j−	NUM
ejpam-6459	262	62	ω	ω	PROPN
ejpam-6459	262	63	(	(	PUNCT
ejpam-6459	262	64	ξ),k−	ξ),k−	PROPN
ejpam-6459	262	65	ω	ω	PROPN
ejpam-6459	262	66	(	(	PUNCT
ejpam-6459	262	67	ξ	ξ	NOUN
ejpam-6459	262	68	)	)	PUNCT
ejpam-6459	262	69	}	}	PUNCT
ejpam-6459	262	70	}	}	PUNCT
ejpam-6459	262	71	=	=	PUNCT
ejpam-6459	262	72	b{l−	b{l−	PUNCT
ejpam-6459	262	73	ω	ω	NUM
ejpam-6459	262	74	(	(	PUNCT
ejpam-6459	262	75	κ	κ	NOUN
ejpam-6459	262	76	)	)	PUNCT
ejpam-6459	262	77	,	,	PUNCT
ejpam-6459	262	78	l	l	PROPN
ejpam-6459	262	79	−	−	PROPN
ejpam-6459	262	80	ω	ω	X
ejpam-6459	262	81	(	(	PUNCT
ejpam-6459	262	82	ξ	ξ	NOUN
ejpam-6459	262	83	)	)	PUNCT
ejpam-6459	262	84	}	}	PUNCT
ejpam-6459	262	85	,	,	PUNCT
ejpam-6459	262	86	l+	l+	X
ejpam-6459	262	87	ω	ω	X
ejpam-6459	262	88	(	(	PUNCT
ejpam-6459	262	89	κξ	κξ	NOUN
ejpam-6459	262	90	)	)	PUNCT
ejpam-6459	262	91	=	=	NOUN
ejpam-6459	262	92	b{j+	b{j+	PROPN
ejpam-6459	262	93	ω	ω	PROPN
ejpam-6459	262	94	(	(	PUNCT
ejpam-6459	262	95	κξ),k+	κξ),k+	PROPN
ejpam-6459	262	96	ω	ω	PROPN
ejpam-6459	262	97	(	(	PUNCT
ejpam-6459	262	98	κξ	κξ	NOUN
ejpam-6459	262	99	)	)	PUNCT
ejpam-6459	262	100	}	}	PUNCT
ejpam-6459	262	101	≥	≥	PROPN
ejpam-6459	262	102	b{j+	b{j+	PROPN
ejpam-6459	262	103	ω	ω	PROPN
ejpam-6459	262	104	(	(	PUNCT
ejpam-6459	262	105	ξ),k+	ξ),k+	PROPN
ejpam-6459	262	106	ω	ω	PROPN
ejpam-6459	262	107	(	(	PUNCT
ejpam-6459	262	108	ξ	ξ	NOUN
ejpam-6459	262	109	)	)	PUNCT
ejpam-6459	262	110	}	}	PUNCT
ejpam-6459	262	111	=	=	SYM
ejpam-6459	262	112	b{j+	b{j+	NOUN
ejpam-6459	262	113	ω	ω	NOUN
ejpam-6459	262	114	(	(	PUNCT
ejpam-6459	262	115	ξ),k+	ξ),k+	PROPN
ejpam-6459	262	116	ω	ω	PROPN
ejpam-6459	262	117	(	(	PUNCT
ejpam-6459	262	118	ξ	ξ	NOUN
ejpam-6459	262	119	)	)	PUNCT
ejpam-6459	262	120	}	}	PUNCT
ejpam-6459	262	121	=	=	SYM
ejpam-6459	262	122	l+	l+	X
ejpam-6459	262	123	ω	ω	X
ejpam-6459	262	124	(	(	PUNCT
ejpam-6459	262	125	ξ	ξ	NOUN
ejpam-6459	262	126	)	)	PUNCT
ejpam-6459	262	127	,	,	PUNCT
ejpam-6459	262	128	l−	l−	PROPN
ejpam-6459	262	129	ω	ω	PROPN
ejpam-6459	262	130	(	(	PUNCT
ejpam-6459	262	131	κξ	κξ	NOUN
ejpam-6459	262	132	)	)	PUNCT
ejpam-6459	262	133	=	=	PUNCT
ejpam-6459	262	134	a{j−	a{j−	NUM
ejpam-6459	262	135	ω	ω	PROPN
ejpam-6459	262	136	(	(	PUNCT
ejpam-6459	262	137	κξ),k−	κξ),k−	PROPN
ejpam-6459	262	138	ω	ω	PROPN
ejpam-6459	262	139	(	(	PUNCT
ejpam-6459	262	140	κξ	κξ	NOUN
ejpam-6459	262	141	)	)	PUNCT
ejpam-6459	262	142	}	}	PUNCT
ejpam-6459	262	143	≤	≤	PROPN
ejpam-6459	262	144	a{j−	a{j−	NUM
ejpam-6459	262	145	ω	ω	PROPN
ejpam-6459	262	146	(	(	PUNCT
ejpam-6459	262	147	ξ),k−	ξ),k−	PROPN
ejpam-6459	262	148	ω	ω	PROPN
ejpam-6459	262	149	(	(	PUNCT
ejpam-6459	262	150	ξ	ξ	NOUN
ejpam-6459	262	151	)	)	PUNCT
ejpam-6459	262	152	}	}	PUNCT
ejpam-6459	262	153	=	=	PUNCT
ejpam-6459	262	154	a{j−	a{j−	NUM
ejpam-6459	262	155	ω	ω	NOUN
ejpam-6459	262	156	(	(	PUNCT
ejpam-6459	262	157	ξ),k−	ξ),k−	PROPN
ejpam-6459	262	158	ω	ω	PROPN
ejpam-6459	262	159	(	(	PUNCT
ejpam-6459	262	160	ξ	ξ	NOUN
ejpam-6459	262	161	)	)	PUNCT
ejpam-6459	262	162	}	}	PUNCT
ejpam-6459	262	163	=	=	SYM
ejpam-6459	262	164	l−	l−	PROPN
ejpam-6459	262	165	ω	ω	PROPN
ejpam-6459	262	166	(	(	PUNCT
ejpam-6459	262	167	ξ	ξ	NOUN
ejpam-6459	262	168	)	)	PUNCT
ejpam-6459	262	169	.	.	PUNCT
ejpam-6459	263	1	therefore	therefore	ADV
ejpam-6459	263	2	,	,	PUNCT
ejpam-6459	263	3	(	(	PUNCT
ejpam-6459	263	4	l	l	NOUN
ejpam-6459	263	5	,	,	PUNCT
ejpam-6459	263	6	w	w	NOUN
ejpam-6459	263	7	)	)	PUNCT
ejpam-6459	263	8	=	=	SYM
ejpam-6459	263	9	(	(	PUNCT
ejpam-6459	263	10	j	j	PROPN
ejpam-6459	263	11	,	,	PUNCT
ejpam-6459	263	12	u	u	NOUN
ejpam-6459	263	13	)	)	PUNCT
ejpam-6459	263	14	∪	∪	ADV
ejpam-6459	263	15	(	(	PUNCT
ejpam-6459	263	16	k	k	NOUN
ejpam-6459	263	17	,	,	PUNCT
ejpam-6459	263	18	v	v	NOUN
ejpam-6459	263	19	)	)	PUNCT
ejpam-6459	263	20	is	be	AUX
ejpam-6459	263	21	a	a	DET
ejpam-6459	263	22	bfsi	bfsi	ADV
ejpam-6459	263	23	over	over	ADP
ejpam-6459	263	24	ℜ.	ℜ.	PROPN
ejpam-6459	263	25	5	5	NUM
ejpam-6459	263	26	.	.	PUNCT
ejpam-6459	263	27	conclusion	conclusion	NOUN
ejpam-6459	263	28	this	this	DET
ejpam-6459	263	29	study	study	NOUN
ejpam-6459	263	30	examined	examine	VERB
ejpam-6459	263	31	the	the	DET
ejpam-6459	263	32	integration	integration	NOUN
ejpam-6459	263	33	of	of	ADP
ejpam-6459	263	34	bfss	bfss	NOUN
ejpam-6459	263	35	and	and	CCONJ
ejpam-6459	263	36	sss	sss	VERB
ejpam-6459	263	37	within	within	ADP
ejpam-6459	263	38	boolean	boolean	ADJ
ejpam-6459	263	39	ring	ring	NOUN
ejpam-6459	263	40	structures	structure	NOUN
ejpam-6459	263	41	,	,	PUNCT
ejpam-6459	263	42	resulting	result	VERB
ejpam-6459	263	43	in	in	ADP
ejpam-6459	263	44	the	the	DET
ejpam-6459	263	45	development	development	NOUN
ejpam-6459	263	46	of	of	ADP
ejpam-6459	263	47	bfsbrs	bfsbr	VERB
ejpam-6459	263	48	and	and	CCONJ
ejpam-6459	263	49	their	their	PRON
ejpam-6459	263	50	corresponding	correspond	VERB
ejpam-6459	263	51	bfsis	bfsis	NOUN
ejpam-6459	263	52	.	.	PUNCT
ejpam-6459	264	1	the	the	DET
ejpam-6459	264	2	algebraic	algebraic	ADJ
ejpam-6459	264	3	properties	property	NOUN
ejpam-6459	264	4	and	and	CCONJ
ejpam-6459	264	5	structural	structural	ADJ
ejpam-6459	264	6	behaviors	behavior	NOUN
ejpam-6459	264	7	of	of	ADP
ejpam-6459	264	8	these	these	DET
ejpam-6459	264	9	models	model	NOUN
ejpam-6459	264	10	were	be	AUX
ejpam-6459	264	11	systematically	systematically	ADV
ejpam-6459	264	12	examined	examine	VERB
ejpam-6459	264	13	.	.	PUNCT
ejpam-6459	265	1	this	this	DET
ejpam-6459	265	2	framework	framework	NOUN
ejpam-6459	265	3	not	not	PART
ejpam-6459	265	4	only	only	ADV
ejpam-6459	265	5	advances	advance	VERB
ejpam-6459	265	6	mathematical	mathematical	ADJ
ejpam-6459	265	7	modeling	modeling	NOUN
ejpam-6459	265	8	under	under	ADP
ejpam-6459	265	9	uncertainty	uncertainty	NOUN
ejpam-6459	265	10	but	but	CCONJ
ejpam-6459	265	11	also	also	ADV
ejpam-6459	265	12	serves	serve	VERB
ejpam-6459	265	13	as	as	ADP
ejpam-6459	265	14	a	a	DET
ejpam-6459	265	15	valuable	valuable	ADJ
ejpam-6459	265	16	foundation	foundation	NOUN
ejpam-6459	265	17	for	for	ADP
ejpam-6459	265	18	students	student	NOUN
ejpam-6459	265	19	beginning	begin	VERB
ejpam-6459	265	20	research	research	NOUN
ejpam-6459	265	21	in	in	ADP
ejpam-6459	265	22	abstract	abstract	ADJ
ejpam-6459	265	23	algebra	algebra	NOUN
ejpam-6459	265	24	.	.	PUNCT
ejpam-6459	266	1	supporting	support	VERB
ejpam-6459	266	2	hands	hand	NOUN
ejpam-6459	266	3	-	-	PUNCT
ejpam-6459	266	4	on	on	ADP
ejpam-6459	266	5	exploration	exploration	NOUN
ejpam-6459	266	6	and	and	CCONJ
ejpam-6459	266	7	conceptual	conceptual	ADJ
ejpam-6459	266	8	learning	learning	NOUN
ejpam-6459	266	9	helps	helps	AUX
ejpam-6459	266	10	cultivate	cultivate	VERB
ejpam-6459	266	11	mathematical	mathematical	ADJ
ejpam-6459	266	12	intuition	intuition	NOUN
ejpam-6459	266	13	and	and	CCONJ
ejpam-6459	266	14	collaborative	collaborative	ADJ
ejpam-6459	266	15	research	research	NOUN
ejpam-6459	266	16	practices	practice	NOUN
ejpam-6459	266	17	in	in	ADP
ejpam-6459	266	18	educational	educational	ADJ
ejpam-6459	266	19	settings	setting	NOUN
ejpam-6459	266	20	.	.	PUNCT
ejpam-6459	267	1	acknowledgements	acknowledgement	NOUN
ejpam-6459	267	2	this	this	DET
ejpam-6459	267	3	research	research	NOUN
ejpam-6459	267	4	was	be	AUX
ejpam-6459	267	5	supported	support	VERB
ejpam-6459	267	6	by	by	ADP
ejpam-6459	267	7	university	university	NOUN
ejpam-6459	267	8	of	of	ADP
ejpam-6459	267	9	phayao	phayao	NOUN
ejpam-6459	267	10	and	and	CCONJ
ejpam-6459	267	11	thailand	thailand	PROPN
ejpam-6459	267	12	science	science	PROPN
ejpam-6459	267	13	research	research	PROPN
ejpam-6459	267	14	and	and	CCONJ
ejpam-6459	267	15	innovation	innovation	NOUN
ejpam-6459	267	16	fund	fund	NOUN
ejpam-6459	267	17	(	(	PUNCT
ejpam-6459	267	18	fundamental	fundamental	ADJ
ejpam-6459	267	19	fund	fund	NOUN
ejpam-6459	267	20	2025	2025	NUM
ejpam-6459	267	21	,	,	PUNCT
ejpam-6459	267	22	grant	grant	VERB
ejpam-6459	267	23	no	no	NOUN
ejpam-6459	267	24	.	.	PROPN
ejpam-6459	268	1	5027/2567	5027/2567	NUM
ejpam-6459	268	2	)	)	PUNCT
ejpam-6459	268	3	.	.	PUNCT
ejpam-6459	269	1	g.	g.	PROPN
ejpam-6459	269	2	s.	s.	PROPN
ejpam-6459	269	3	rao	rao	PROPN
ejpam-6459	269	4	et	et	PROPN
ejpam-6459	269	5	al	al	PROPN
ejpam-6459	269	6	.	.	PUNCT
ejpam-6459	269	7	/	/	SYM
ejpam-6459	269	8	eur	eur	PROPN
ejpam-6459	269	9	.	.	PUNCT
ejpam-6459	270	1	j.	j.	PROPN
ejpam-6459	270	2	pure	pure	PROPN
ejpam-6459	270	3	appl	appl	PROPN
ejpam-6459	270	4	.	.	PROPN
ejpam-6459	270	5	math	math	PROPN
ejpam-6459	270	6	,	,	PUNCT
ejpam-6459	270	7	18	18	NUM
ejpam-6459	270	8	(	(	PUNCT
ejpam-6459	270	9	3	3	NUM
ejpam-6459	270	10	)	)	PUNCT
ejpam-6459	270	11	(	(	PUNCT
ejpam-6459	270	12	2025	2025	NUM
ejpam-6459	270	13	)	)	PUNCT
ejpam-6459	270	14	,	,	PUNCT
ejpam-6459	270	15	6459	6459	NUM
ejpam-6459	270	16	15	15	NUM
ejpam-6459	270	17	of	of	ADP
ejpam-6459	270	18	16	16	NUM
ejpam-6459	270	19	references	reference	NOUN
ejpam-6459	270	20	[	[	X
ejpam-6459	270	21	1	1	NUM
ejpam-6459	270	22	]	]	PUNCT
ejpam-6459	270	23	l.	l.	PROPN
ejpam-6459	270	24	a.	a.	PROPN
ejpam-6459	270	25	zadeh	zadeh	PROPN
ejpam-6459	270	26	.	.	PUNCT
ejpam-6459	271	1	fuzzy	fuzzy	ADJ
ejpam-6459	271	2	sets	set	NOUN
ejpam-6459	271	3	.	.	PUNCT
ejpam-6459	272	1	information	information	NOUN
ejpam-6459	272	2	and	and	CCONJ
ejpam-6459	272	3	control	control	NOUN
ejpam-6459	272	4	,	,	PUNCT
ejpam-6459	272	5	8(3):338–353	8(3):338–353	NUM
ejpam-6459	272	6	,	,	PUNCT
ejpam-6459	272	7	1965	1965	NUM
ejpam-6459	272	8	.	.	PUNCT
ejpam-6459	273	1	[	[	X
ejpam-6459	273	2	2	2	NUM
ejpam-6459	273	3	]	]	PUNCT
ejpam-6459	273	4	k.	k.	PROPN
ejpam-6459	273	5	m.	m.	PROPN
ejpam-6459	273	6	lee	lee	PROPN
ejpam-6459	273	7	.	.	PUNCT
ejpam-6459	274	1	bipolar	bipolar	PROPN
ejpam-6459	274	2	valued	value	VERB
ejpam-6459	274	3	fuzzy	fuzzy	ADJ
ejpam-6459	274	4	sets	set	NOUN
ejpam-6459	274	5	and	and	CCONJ
ejpam-6459	274	6	their	their	PRON
ejpam-6459	274	7	applications	application	NOUN
ejpam-6459	274	8	.	.	PUNCT
ejpam-6459	275	1	in	in	ADP
ejpam-6459	275	2	proceedings	proceeding	NOUN
ejpam-6459	275	3	of	of	ADP
ejpam-6459	275	4	international	international	ADJ
ejpam-6459	275	5	conference	conference	NOUN
ejpam-6459	275	6	on	on	ADP
ejpam-6459	275	7	intelligent	intelligent	ADJ
ejpam-6459	275	8	technologies	technology	NOUN
ejpam-6459	275	9	,	,	PUNCT
ejpam-6459	275	10	pages	page	NOUN
ejpam-6459	275	11	307–312	307–312	NUM
ejpam-6459	275	12	,	,	PUNCT
ejpam-6459	275	13	bangkok	bangkok	PROPN
ejpam-6459	275	14	,	,	PUNCT
ejpam-6459	275	15	thailand	thailand	PROPN
ejpam-6459	275	16	,	,	PUNCT
ejpam-6459	275	17	2000	2000	NUM
ejpam-6459	275	18	.	.	PUNCT
ejpam-6459	276	1	ieee	ieee	NOUN
ejpam-6459	276	2	.	.	PUNCT
ejpam-6459	277	1	[	[	X
ejpam-6459	277	2	3	3	X
ejpam-6459	277	3	]	]	X
ejpam-6459	277	4	d.	d.	PROPN
ejpam-6459	277	5	molodtsov	molodtsov	PROPN
ejpam-6459	277	6	.	.	PUNCT
ejpam-6459	278	1	soft	soft	ADJ
ejpam-6459	278	2	set	set	ADJ
ejpam-6459	278	3	theory	theory	NOUN
ejpam-6459	278	4	first	first	ADJ
ejpam-6459	278	5	results	result	NOUN
ejpam-6459	278	6	.	.	PUNCT
ejpam-6459	279	1	computers	computer	NOUN
ejpam-6459	279	2	and	and	CCONJ
ejpam-6459	279	3	mathematics	mathematic	NOUN
ejpam-6459	279	4	with	with	ADP
ejpam-6459	279	5	applications	application	NOUN
ejpam-6459	279	6	,	,	PUNCT
ejpam-6459	279	7	37:19–31	37:19–31	NUM
ejpam-6459	279	8	,	,	PUNCT
ejpam-6459	279	9	1999	1999	NUM
ejpam-6459	279	10	.	.	PUNCT
ejpam-6459	280	1	[	[	X
ejpam-6459	280	2	4	4	X
ejpam-6459	280	3	]	]	PUNCT
ejpam-6459	280	4	h.	h.	PROPN
ejpam-6459	280	5	aktaş	aktaş	PROPN
ejpam-6459	280	6	and	and	CCONJ
ejpam-6459	280	7	n.	n.	PROPN
ejpam-6459	280	8	çağman	çağman	PROPN
ejpam-6459	280	9	.	.	PUNCT
ejpam-6459	280	10	soft	soft	ADJ
ejpam-6459	280	11	sets	set	NOUN
ejpam-6459	280	12	and	and	CCONJ
ejpam-6459	280	13	soft	soft	ADJ
ejpam-6459	280	14	groups	group	NOUN
ejpam-6459	280	15	.	.	PUNCT
ejpam-6459	281	1	information	information	NOUN
ejpam-6459	281	2	sciences	sciences	PROPN
ejpam-6459	281	3	,	,	PUNCT
ejpam-6459	281	4	177:2726	177:2726	NUM
ejpam-6459	281	5	–	–	PUNCT
ejpam-6459	281	6	2735	2735	NUM
ejpam-6459	281	7	,	,	PUNCT
ejpam-6459	281	8	2007	2007	NUM
ejpam-6459	281	9	.	.	PUNCT
ejpam-6459	282	1	[	[	X
ejpam-6459	282	2	5	5	X
ejpam-6459	282	3	]	]	X
ejpam-6459	282	4	u.	u.	NOUN
ejpam-6459	282	5	acar	acar	PROPN
ejpam-6459	282	6	,	,	PUNCT
ejpam-6459	282	7	f.	f.	PROPN
ejpam-6459	282	8	koyuncu	koyuncu	PROPN
ejpam-6459	282	9	,	,	PUNCT
ejpam-6459	282	10	and	and	CCONJ
ejpam-6459	282	11	b.	b.	PROPN
ejpam-6459	282	12	tanay	tanay	PROPN
ejpam-6459	282	13	.	.	PUNCT
ejpam-6459	283	1	soft	soft	ADJ
ejpam-6459	283	2	sets	set	NOUN
ejpam-6459	283	3	and	and	CCONJ
ejpam-6459	283	4	soft	soft	ADJ
ejpam-6459	283	5	rings	ring	NOUN
ejpam-6459	283	6	.	.	PUNCT
ejpam-6459	284	1	computers	computer	NOUN
ejpam-6459	284	2	and	and	CCONJ
ejpam-6459	284	3	mathematics	mathematic	NOUN
ejpam-6459	284	4	with	with	ADP
ejpam-6459	284	5	applications	application	NOUN
ejpam-6459	284	6	,	,	PUNCT
ejpam-6459	284	7	59:3458–3463	59:3458–3463	NUM
ejpam-6459	284	8	,	,	PUNCT
ejpam-6459	284	9	2010	2010	NUM
ejpam-6459	284	10	.	.	PUNCT
ejpam-6459	285	1	[	[	X
ejpam-6459	285	2	6	6	NUM
ejpam-6459	285	3	]	]	X
ejpam-6459	285	4	y.	y.	PROPN
ejpam-6459	285	5	çelik	çelik	PROPN
ejpam-6459	285	6	,	,	PUNCT
ejpam-6459	285	7	c.	c.	PROPN
ejpam-6459	285	8	ekiz	ekiz	NOUN
ejpam-6459	285	9	,	,	PUNCT
ejpam-6459	285	10	and	and	CCONJ
ejpam-6459	285	11	s.	s.	PROPN
ejpam-6459	285	12	yamak	yamak	PROPN
ejpam-6459	285	13	.	.	PUNCT
ejpam-6459	286	1	a	a	DET
ejpam-6459	286	2	new	new	ADJ
ejpam-6459	286	3	view	view	NOUN
ejpam-6459	286	4	on	on	ADP
ejpam-6459	286	5	soft	soft	ADJ
ejpam-6459	286	6	rings	ring	NOUN
ejpam-6459	286	7	.	.	PUNCT
ejpam-6459	287	1	hacettepe	hacettepe	PROPN
ejpam-6459	287	2	journal	journal	PROPN
ejpam-6459	287	3	of	of	ADP
ejpam-6459	287	4	mathematics	mathematic	NOUN
ejpam-6459	287	5	and	and	CCONJ
ejpam-6459	287	6	statistics	statistic	NOUN
ejpam-6459	287	7	,	,	PUNCT
ejpam-6459	287	8	40(2):273–286	40(2):273–286	ADJ
ejpam-6459	287	9	,	,	PUNCT
ejpam-6459	287	10	2011	2011	NUM
ejpam-6459	287	11	.	.	PUNCT
ejpam-6459	288	1	[	[	X
ejpam-6459	288	2	7	7	NUM
ejpam-6459	288	3	]	]	X
ejpam-6459	288	4	w.-r	w.-r	PROPN
ejpam-6459	288	5	.	.	PUNCT
ejpam-6459	289	1	zhang	zhang	PROPN
ejpam-6459	289	2	.	.	PUNCT
ejpam-6459	290	1	(	(	PUNCT
ejpam-6459	290	2	yin	yin	PROPN
ejpam-6459	290	3	)	)	PUNCT
ejpam-6459	290	4	(	(	PUNCT
ejpam-6459	290	5	yang	yang	NOUN
ejpam-6459	290	6	)	)	PUNCT
ejpam-6459	290	7	bipolar	bipolar	ADJ
ejpam-6459	290	8	fuzzy	fuzzy	ADJ
ejpam-6459	290	9	sets	set	NOUN
ejpam-6459	290	10	.	.	PUNCT
ejpam-6459	291	1	in	in	ADP
ejpam-6459	291	2	1998	1998	NUM
ejpam-6459	291	3	ieee	ieee	NOUN
ejpam-6459	291	4	international	international	ADJ
ejpam-6459	291	5	conference	conference	NOUN
ejpam-6459	291	6	on	on	ADP
ejpam-6459	291	7	fuzzy	fuzzy	ADJ
ejpam-6459	291	8	systems	system	NOUN
ejpam-6459	291	9	proceedings	proceeding	NOUN
ejpam-6459	291	10	,	,	PUNCT
ejpam-6459	291	11	pages	page	NOUN
ejpam-6459	291	12	835–840	835–840	NUM
ejpam-6459	291	13	,	,	PUNCT
ejpam-6459	291	14	anchorage	anchorage	PROPN
ejpam-6459	291	15	,	,	PUNCT
ejpam-6459	291	16	ak	ak	PROPN
ejpam-6459	291	17	,	,	PUNCT
ejpam-6459	291	18	usa	usa	PROPN
ejpam-6459	291	19	,	,	PUNCT
ejpam-6459	291	20	1998	1998	NUM
ejpam-6459	291	21	.	.	PUNCT
ejpam-6459	292	1	ieee	ieee	PROPN
ejpam-6459	292	2	world	world	PROPN
ejpam-6459	292	3	congress	congress	PROPN
ejpam-6459	292	4	on	on	ADP
ejpam-6459	292	5	computational	computational	ADJ
ejpam-6459	292	6	intelligence	intelligence	NOUN
ejpam-6459	292	7	(	(	PUNCT
ejpam-6459	292	8	cat	cat	NOUN
ejpam-6459	292	9	.	.	PUNCT
ejpam-6459	293	1	no	no	INTJ
ejpam-6459	293	2	.	.	PUNCT
ejpam-6459	294	1	98ch36228	98ch36228	NUM
ejpam-6459	294	2	)	)	PUNCT
ejpam-6459	294	3	.	.	PUNCT
ejpam-6459	295	1	[	[	X
ejpam-6459	295	2	8	8	NUM
ejpam-6459	295	3	]	]	PUNCT
ejpam-6459	295	4	m.	m.	NOUN
ejpam-6459	295	5	naz	naz	PROPN
ejpam-6459	295	6	and	and	CCONJ
ejpam-6459	295	7	m.	m.	NOUN
ejpam-6459	295	8	shabir	shabir	PROPN
ejpam-6459	295	9	.	.	PUNCT
ejpam-6459	296	1	on	on	ADP
ejpam-6459	296	2	fuzzy	fuzzy	ADJ
ejpam-6459	296	3	bipolar	bipolar	ADJ
ejpam-6459	296	4	soft	soft	ADJ
ejpam-6459	296	5	sets	set	NOUN
ejpam-6459	296	6	,	,	PUNCT
ejpam-6459	296	7	their	their	PRON
ejpam-6459	296	8	algebraic	algebraic	ADJ
ejpam-6459	296	9	structures	structure	NOUN
ejpam-6459	296	10	and	and	CCONJ
ejpam-6459	296	11	applications	application	NOUN
ejpam-6459	296	12	.	.	PUNCT
ejpam-6459	297	1	journal	journal	NOUN
ejpam-6459	297	2	of	of	ADP
ejpam-6459	297	3	intelligent	intelligent	ADJ
ejpam-6459	297	4	and	and	CCONJ
ejpam-6459	297	5	fuzzy	fuzzy	ADJ
ejpam-6459	297	6	systems	system	NOUN
ejpam-6459	297	7	,	,	PUNCT
ejpam-6459	297	8	26(4):1645–1656	26(4):1645–1656	NUM
ejpam-6459	297	9	,	,	PUNCT
ejpam-6459	297	10	2014	2014	NUM
ejpam-6459	297	11	.	.	PUNCT
ejpam-6459	298	1	[	[	X
ejpam-6459	298	2	9	9	NUM
ejpam-6459	298	3	]	]	PUNCT
ejpam-6459	298	4	m.	m.	NOUN
ejpam-6459	298	5	akram	akram	PROPN
ejpam-6459	298	6	.	.	PUNCT
ejpam-6459	299	1	bipolar	bipolar	ADJ
ejpam-6459	299	2	fuzzy	fuzzy	ADJ
ejpam-6459	299	3	soft	soft	ADJ
ejpam-6459	299	4	lie	lie	NOUN
ejpam-6459	299	5	algebras	algebra	NOUN
ejpam-6459	299	6	.	.	PUNCT
ejpam-6459	300	1	quasigroups	quasigroups	PROPN
ejpam-6459	300	2	and	and	CCONJ
ejpam-6459	300	3	related	related	ADJ
ejpam-6459	300	4	systems	system	NOUN
ejpam-6459	300	5	,	,	PUNCT
ejpam-6459	300	6	21:1–10	21:1–10	NUM
ejpam-6459	300	7	,	,	PUNCT
ejpam-6459	300	8	2013	2013	NUM
ejpam-6459	300	9	.	.	PUNCT
ejpam-6459	301	1	[	[	X
ejpam-6459	301	2	10	10	NUM
ejpam-6459	301	3	]	]	X
ejpam-6459	301	4	s.	s.	PROPN
ejpam-6459	301	5	abdullah	abdullah	PROPN
ejpam-6459	301	6	,	,	PUNCT
ejpam-6459	301	7	m.	m.	NOUN
ejpam-6459	301	8	aslam	aslam	PROPN
ejpam-6459	301	9	,	,	PUNCT
ejpam-6459	301	10	and	and	CCONJ
ejpam-6459	301	11	k.	k.	PROPN
ejpam-6459	301	12	ullah	ullah	PROPN
ejpam-6459	301	13	.	.	PUNCT
ejpam-6459	301	14	bipolar	bipolar	ADJ
ejpam-6459	301	15	fuzzy	fuzzy	ADJ
ejpam-6459	301	16	soft	soft	ADJ
ejpam-6459	301	17	sets	set	NOUN
ejpam-6459	301	18	and	and	CCONJ
ejpam-6459	301	19	its	its	PRON
ejpam-6459	301	20	applications	application	NOUN
ejpam-6459	301	21	in	in	ADP
ejpam-6459	301	22	decision	decision	NOUN
ejpam-6459	301	23	making	making	NOUN
ejpam-6459	301	24	problem	problem	NOUN
ejpam-6459	301	25	.	.	PUNCT
ejpam-6459	302	1	journal	journal	NOUN
ejpam-6459	302	2	of	of	ADP
ejpam-6459	302	3	intelligent	intelligent	ADJ
ejpam-6459	302	4	and	and	CCONJ
ejpam-6459	302	5	fuzzy	fuzzy	ADJ
ejpam-6459	302	6	systems	system	NOUN
ejpam-6459	302	7	,	,	PUNCT
ejpam-6459	302	8	27(2):729–742	27(2):729–742	NUM
ejpam-6459	302	9	,	,	PUNCT
ejpam-6459	302	10	2014	2014	NUM
ejpam-6459	302	11	.	.	PUNCT
ejpam-6459	303	1	[	[	X
ejpam-6459	303	2	11	11	NUM
ejpam-6459	303	3	]	]	PUNCT
ejpam-6459	303	4	m.	m.	NOUN
ejpam-6459	303	5	aslam	aslam	PROPN
ejpam-6459	303	6	,	,	PUNCT
ejpam-6459	303	7	s.	s.	PROPN
ejpam-6459	303	8	abdullah	abdullah	PROPN
ejpam-6459	303	9	,	,	PUNCT
ejpam-6459	303	10	and	and	CCONJ
ejpam-6459	303	11	k.	k.	PROPN
ejpam-6459	303	12	ullah	ullah	PROPN
ejpam-6459	303	13	.	.	PUNCT
ejpam-6459	304	1	bipolar	bipolar	ADJ
ejpam-6459	304	2	fuzzy	fuzzy	ADJ
ejpam-6459	304	3	soft	soft	ADJ
ejpam-6459	304	4	sets	set	NOUN
ejpam-6459	304	5	and	and	CCONJ
ejpam-6459	304	6	its	its	PRON
ejpam-6459	304	7	application	application	NOUN
ejpam-6459	304	8	in	in	ADP
ejpam-6459	304	9	decision	decision	NOUN
ejpam-6459	304	10	making	making	NOUN
ejpam-6459	304	11	problem	problem	NOUN
ejpam-6459	304	12	.	.	PUNCT
ejpam-6459	305	1	journal	journal	NOUN
ejpam-6459	305	2	of	of	ADP
ejpam-6459	305	3	intelligent	intelligent	ADJ
ejpam-6459	305	4	and	and	CCONJ
ejpam-6459	305	5	fuzzy	fuzzy	ADJ
ejpam-6459	305	6	systems	system	NOUN
ejpam-6459	305	7	,	,	PUNCT
ejpam-6459	305	8	27(2):729–742	27(2):729–742	NUM
ejpam-6459	305	9	,	,	PUNCT
ejpam-6459	305	10	2014	2014	NUM
ejpam-6459	305	11	.	.	PUNCT
ejpam-6459	306	1	[	[	X
ejpam-6459	306	2	12	12	NUM
ejpam-6459	306	3	]	]	PUNCT
ejpam-6459	306	4	m.	m.	NOUN
ejpam-6459	306	5	akram	akram	PROPN
ejpam-6459	306	6	,	,	PUNCT
ejpam-6459	306	7	n.	n.	NOUN
ejpam-6459	306	8	o.	o.	PROPN
ejpam-6459	306	9	alsherei	alsherei	PROPN
ejpam-6459	306	10	,	,	PUNCT
ejpam-6459	306	11	k.	k.	PROPN
ejpam-6459	306	12	p.	p.	PROPN
ejpam-6459	306	13	shum	shum	NOUN
ejpam-6459	306	14	,	,	PUNCT
ejpam-6459	306	15	and	and	CCONJ
ejpam-6459	306	16	a.	a.	PROPN
ejpam-6459	306	17	farooq	farooq	PROPN
ejpam-6459	306	18	.	.	PUNCT
ejpam-6459	307	1	application	application	NOUN
ejpam-6459	307	2	of	of	ADP
ejpam-6459	307	3	bipolar	bipolar	ADJ
ejpam-6459	307	4	fuzzy	fuzzy	ADJ
ejpam-6459	307	5	soft	soft	ADJ
ejpam-6459	307	6	sets	set	NOUN
ejpam-6459	307	7	in	in	ADP
ejpam-6459	307	8	k	k	NOUN
ejpam-6459	307	9	-	-	PUNCT
ejpam-6459	307	10	algebras	algebra	VERB
ejpam-6459	307	11	.	.	PUNCT
ejpam-6459	308	1	italian	italian	ADJ
ejpam-6459	308	2	journal	journal	NOUN
ejpam-6459	308	3	of	of	ADP
ejpam-6459	308	4	pure	pure	ADJ
ejpam-6459	308	5	and	and	CCONJ
ejpam-6459	308	6	applied	applied	ADJ
ejpam-6459	308	7	mathematics	mathematic	NOUN
ejpam-6459	308	8	,	,	PUNCT
ejpam-6459	308	9	32:533–546	32:533–546	NUM
ejpam-6459	308	10	,	,	PUNCT
ejpam-6459	308	11	2014	2014	NUM
ejpam-6459	308	12	.	.	PUNCT
ejpam-6459	309	1	[	[	X
ejpam-6459	309	2	13	13	NUM
ejpam-6459	309	3	]	]	PUNCT
ejpam-6459	309	4	m.	m.	NOUN
ejpam-6459	309	5	akram	akram	PROPN
ejpam-6459	309	6	,	,	PUNCT
ejpam-6459	309	7	j.	j.	PROPN
ejpam-6459	309	8	kavikumar	kavikumar	PROPN
ejpam-6459	309	9	,	,	PUNCT
ejpam-6459	309	10	and	and	CCONJ
ejpam-6459	309	11	a.	a.	PROPN
ejpam-6459	309	12	b.	b.	PROPN
ejpam-6459	309	13	khamis	khamis	PROPN
ejpam-6459	309	14	.	.	PUNCT
ejpam-6459	310	1	characterization	characterization	NOUN
ejpam-6459	310	2	of	of	ADP
ejpam-6459	310	3	bipolar	bipolar	ADJ
ejpam-6459	310	4	fuzzy	fuzzy	ADJ
ejpam-6459	310	5	soft	soft	ADJ
ejpam-6459	310	6	γ	γ	NOUN
ejpam-6459	310	7	-	-	PUNCT
ejpam-6459	310	8	semigroups	semigroup	NOUN
ejpam-6459	310	9	.	.	PUNCT
ejpam-6459	311	1	indian	indian	ADJ
ejpam-6459	311	2	journal	journal	PROPN
ejpam-6459	311	3	of	of	ADP
ejpam-6459	311	4	science	science	NOUN
ejpam-6459	311	5	and	and	CCONJ
ejpam-6459	311	6	technology	technology	NOUN
ejpam-6459	311	7	,	,	PUNCT
ejpam-6459	311	8	7(8):1211–1221	7(8):1211–1221	PROPN
ejpam-6459	311	9	,	,	PUNCT
ejpam-6459	311	10	2014	2014	NUM
ejpam-6459	311	11	.	.	PUNCT
ejpam-6459	312	1	[	[	X
ejpam-6459	312	2	14	14	NUM
ejpam-6459	312	3	]	]	X
ejpam-6459	312	4	w.	w.	PROPN
ejpam-6459	312	5	h.	h.	PROPN
ejpam-6459	312	6	yang	yang	PROPN
ejpam-6459	312	7	and	and	CCONJ
ejpam-6459	312	8	s.-g	s.-g	PROPN
ejpam-6459	312	9	.	.	PUNCT
ejpam-6459	313	1	li	li	PROPN
ejpam-6459	313	2	.	.	PUNCT
ejpam-6459	313	3	bipolar	bipolar	ADJ
ejpam-6459	313	4	-	-	PUNCT
ejpam-6459	313	5	value	value	NOUN
ejpam-6459	313	6	fuzzy	fuzzy	ADJ
ejpam-6459	313	7	soft	soft	ADJ
ejpam-6459	313	8	sets	set	NOUN
ejpam-6459	313	9	.	.	PUNCT
ejpam-6459	314	1	computer	computer	NOUN
ejpam-6459	314	2	engineering	engineering	NOUN
ejpam-6459	314	3	and	and	CCONJ
ejpam-6459	314	4	applications	application	NOUN
ejpam-6459	314	5	(	(	PUNCT
ejpam-6459	314	6	in	in	ADP
ejpam-6459	314	7	china	china	PROPN
ejpam-6459	314	8	)	)	PUNCT
ejpam-6459	314	9	,	,	PUNCT
ejpam-6459	314	10	48(35):15–18	48(35):15–18	NUM
ejpam-6459	314	11	,	,	PUNCT
ejpam-6459	314	12	2012	2012	NUM
ejpam-6459	314	13	.	.	PUNCT
ejpam-6459	315	1	[	[	X
ejpam-6459	315	2	15	15	NUM
ejpam-6459	315	3	]	]	X
ejpam-6459	315	4	p.	p.	PROPN
ejpam-6459	315	5	k.	k.	PROPN
ejpam-6459	316	1	maji	maji	PROPN
ejpam-6459	316	2	,	,	PUNCT
ejpam-6459	316	3	r.	r.	PROPN
ejpam-6459	316	4	biswas	biswas	PROPN
ejpam-6459	316	5	,	,	PUNCT
ejpam-6459	316	6	and	and	CCONJ
ejpam-6459	317	1	a.	a.	PROPN
ejpam-6459	317	2	r.	r.	PROPN
ejpam-6459	317	3	roy	roy	PROPN
ejpam-6459	317	4	.	.	PROPN
ejpam-6459	317	5	fuzzy	fuzzy	ADJ
ejpam-6459	317	6	soft	soft	ADJ
ejpam-6459	317	7	sets	set	NOUN
ejpam-6459	317	8	.	.	PUNCT
ejpam-6459	318	1	journal	journal	NOUN
ejpam-6459	318	2	of	of	ADP
ejpam-6459	318	3	fuzzy	fuzzy	ADJ
ejpam-6459	318	4	mathematics	mathematic	NOUN
ejpam-6459	318	5	,	,	PUNCT
ejpam-6459	318	6	9(3):589–602	9(3):589–602	NOUN
ejpam-6459	318	7	,	,	PUNCT
ejpam-6459	318	8	2001	2001	NUM
ejpam-6459	318	9	.	.	PUNCT
ejpam-6459	319	1	[	[	X
ejpam-6459	319	2	16	16	NUM
ejpam-6459	319	3	]	]	X
ejpam-6459	319	4	j.-h	j.-h	NOUN
ejpam-6459	319	5	.	.	PUNCT
ejpam-6459	320	1	liu	liu	PROPN
ejpam-6459	320	2	,	,	PUNCT
ejpam-6459	320	3	r.-x	r.-x	NOUN
ejpam-6459	320	4	.	.	PUNCT
ejpam-6459	320	5	yan	yan	PROPN
ejpam-6459	320	6	,	,	PUNCT
ejpam-6459	320	7	and	and	CCONJ
ejpam-6459	320	8	b.-x	b.-x	NOUN
ejpam-6459	320	9	.	.	PUNCT
ejpam-6459	321	1	yao	yao	PROPN
ejpam-6459	321	2	.	.	PUNCT
ejpam-6459	322	1	fuzzy	fuzzy	ADJ
ejpam-6459	322	2	soft	soft	ADJ
ejpam-6459	322	3	sets	set	NOUN
ejpam-6459	322	4	and	and	CCONJ
ejpam-6459	322	5	fuzzy	fuzzy	ADJ
ejpam-6459	322	6	soft	soft	ADJ
ejpam-6459	322	7	groups	group	NOUN
ejpam-6459	322	8	.	.	PUNCT
ejpam-6459	323	1	in	in	ADP
ejpam-6459	323	2	2008	2008	NUM
ejpam-6459	323	3	chinese	chinese	ADJ
ejpam-6459	323	4	control	control	NOUN
ejpam-6459	323	5	and	and	CCONJ
ejpam-6459	323	6	decision	decision	NOUN
ejpam-6459	323	7	conference	conference	NOUN
ejpam-6459	323	8	,	,	PUNCT
ejpam-6459	323	9	pages	page	NOUN
ejpam-6459	323	10	2626–2629	2626–2629	NUM
ejpam-6459	323	11	,	,	PUNCT
ejpam-6459	323	12	yantai	yantai	PROPN
ejpam-6459	323	13	,	,	PUNCT
ejpam-6459	323	14	china	china	PROPN
ejpam-6459	323	15	,	,	PUNCT
ejpam-6459	323	16	2008	2008	NUM
ejpam-6459	323	17	.	.	PUNCT
ejpam-6459	324	1	ieee	ieee	NOUN
ejpam-6459	324	2	.	.	PUNCT
ejpam-6459	325	1	[	[	X
ejpam-6459	325	2	17	17	NUM
ejpam-6459	325	3	]	]	X
ejpam-6459	325	4	g.	g.	PROPN
ejpam-6459	325	5	s.	s.	PROPN
ejpam-6459	325	6	rao	rao	PROPN
ejpam-6459	325	7	,	,	PUNCT
ejpam-6459	325	8	d.	d.	PROPN
ejpam-6459	325	9	ramesh	ramesh	PROPN
ejpam-6459	325	10	,	,	PUNCT
ejpam-6459	325	11	a.	a.	NOUN
ejpam-6459	325	12	iampan	iampan	PROPN
ejpam-6459	325	13	,	,	PUNCT
ejpam-6459	325	14	and	and	CCONJ
ejpam-6459	325	15	b.	b.	PROPN
ejpam-6459	325	16	satyanarayana	satyanarayana	PROPN
ejpam-6459	325	17	.	.	PUNCT
ejpam-6459	326	1	fuzzy	fuzzy	ADJ
ejpam-6459	326	2	soft	soft	ADJ
ejpam-6459	326	3	boolean	boolean	ADJ
ejpam-6459	326	4	rings	ring	NOUN
ejpam-6459	326	5	.	.	PUNCT
ejpam-6459	327	1	international	international	ADJ
ejpam-6459	327	2	journal	journal	NOUN
ejpam-6459	327	3	of	of	ADP
ejpam-6459	327	4	analysis	analysis	NOUN
ejpam-6459	327	5	and	and	CCONJ
ejpam-6459	327	6	applications	application	NOUN
ejpam-6459	327	7	,	,	PUNCT
ejpam-6459	327	8	21:60	21:60	NUM
ejpam-6459	327	9	,	,	PUNCT
ejpam-6459	327	10	2023	2023	NUM
ejpam-6459	327	11	.	.	PUNCT
ejpam-6459	328	1	[	[	X
ejpam-6459	328	2	18	18	NUM
ejpam-6459	328	3	]	]	X
ejpam-6459	328	4	g.	g.	PROPN
ejpam-6459	328	5	s.	s.	PROPN
ejpam-6459	328	6	rao	rao	PROPN
ejpam-6459	328	7	,	,	PUNCT
ejpam-6459	328	8	p.	p.	PROPN
ejpam-6459	328	9	kolluru	kolluru	PROPN
ejpam-6459	328	10	,	,	PUNCT
ejpam-6459	328	11	and	and	CCONJ
ejpam-6459	328	12	b.	b.	PROPN
ejpam-6459	328	13	p.	p.	NOUN
ejpam-6459	328	14	munagala	munagala	PROPN
ejpam-6459	328	15	.	.	PUNCT
ejpam-6459	329	1	a	a	DET
ejpam-6459	329	2	note	note	NOUN
ejpam-6459	329	3	on	on	ADP
ejpam-6459	329	4	soft	soft	ADJ
ejpam-6459	329	5	boolean	boolean	ADJ
ejpam-6459	329	6	near	near	ADJ
ejpam-6459	329	7	-	-	PUNCT
ejpam-6459	329	8	rings	ring	NOUN
ejpam-6459	329	9	.	.	PUNCT
ejpam-6459	330	1	aip	aip	PROPN
ejpam-6459	330	2	conference	conference	NOUN
ejpam-6459	330	3	proceedings	proceeding	NOUN
ejpam-6459	330	4	,	,	PUNCT
ejpam-6459	330	5	2707:020013	2707:020013	NUM
ejpam-6459	330	6	,	,	PUNCT
ejpam-6459	330	7	2023	2023	NUM
ejpam-6459	330	8	.	.	PUNCT
ejpam-6459	331	1	g.	g.	PROPN
ejpam-6459	331	2	s.	s.	PROPN
ejpam-6459	331	3	rao	rao	PROPN
ejpam-6459	331	4	et	et	PROPN
ejpam-6459	331	5	al	al	PROPN
ejpam-6459	331	6	.	.	PUNCT
ejpam-6459	331	7	/	/	SYM
ejpam-6459	331	8	eur	eur	PROPN
ejpam-6459	331	9	.	.	PUNCT
ejpam-6459	332	1	j.	j.	PROPN
ejpam-6459	332	2	pure	pure	PROPN
ejpam-6459	332	3	appl	appl	PROPN
ejpam-6459	332	4	.	.	PROPN
ejpam-6459	332	5	math	math	PROPN
ejpam-6459	332	6	,	,	PUNCT
ejpam-6459	332	7	18	18	NUM
ejpam-6459	332	8	(	(	PUNCT
ejpam-6459	332	9	3	3	NUM
ejpam-6459	332	10	)	)	PUNCT
ejpam-6459	332	11	(	(	PUNCT
ejpam-6459	332	12	2025	2025	NUM
ejpam-6459	332	13	)	)	PUNCT
ejpam-6459	332	14	,	,	PUNCT
ejpam-6459	332	15	6459	6459	NUM
ejpam-6459	332	16	16	16	NUM
ejpam-6459	332	17	of	of	ADP
ejpam-6459	332	18	16	16	NUM
ejpam-6459	332	19	[	[	X
ejpam-6459	332	20	19	19	NUM
ejpam-6459	332	21	]	]	PUNCT
ejpam-6459	332	22	a.	a.	NOUN
ejpam-6459	332	23	aygünoǧlu	aygünoǧlu	PROPN
ejpam-6459	332	24	and	and	CCONJ
ejpam-6459	332	25	h.	h.	PROPN
ejpam-6459	332	26	aygün	aygün	PROPN
ejpam-6459	332	27	.	.	PUNCT
ejpam-6459	333	1	introduction	introduction	NOUN
ejpam-6459	333	2	to	to	ADP
ejpam-6459	333	3	fuzzy	fuzzy	ADJ
ejpam-6459	333	4	soft	soft	ADJ
ejpam-6459	333	5	groups	group	NOUN
ejpam-6459	333	6	.	.	PUNCT
ejpam-6459	334	1	computers	computer	NOUN
ejpam-6459	334	2	and	and	CCONJ
ejpam-6459	334	3	mathematics	mathematic	NOUN
ejpam-6459	334	4	with	with	ADP
ejpam-6459	334	5	applications	application	NOUN
ejpam-6459	334	6	,	,	PUNCT
ejpam-6459	334	7	58:1279–1286	58:1279–1286	NUM
ejpam-6459	334	8	,	,	PUNCT
ejpam-6459	334	9	2009	2009	NUM
ejpam-6459	334	10	.	.	PUNCT
ejpam-6459	335	1	[	[	X
ejpam-6459	335	2	20	20	NUM
ejpam-6459	335	3	]	]	X
ejpam-6459	335	4	f.	f.	PROPN
ejpam-6459	335	5	feng	feng	PROPN
ejpam-6459	335	6	,	,	PUNCT
ejpam-6459	335	7	y.	y.	PROPN
ejpam-6459	335	8	b.	b.	PROPN
ejpam-6459	335	9	jun	jun	PROPN
ejpam-6459	335	10	,	,	PUNCT
ejpam-6459	335	11	and	and	CCONJ
ejpam-6459	335	12	x.	x.	PROPN
ejpam-6459	335	13	zhao	zhao	PROPN
ejpam-6459	335	14	.	.	PUNCT
ejpam-6459	335	15	soft	soft	ADJ
ejpam-6459	335	16	semirings	semiring	NOUN
ejpam-6459	335	17	.	.	PUNCT
ejpam-6459	336	1	computers	computer	NOUN
ejpam-6459	336	2	and	and	CCONJ
ejpam-6459	336	3	mathematics	mathematic	NOUN
ejpam-6459	336	4	with	with	ADP
ejpam-6459	336	5	applications	application	NOUN
ejpam-6459	336	6	,	,	PUNCT
ejpam-6459	336	7	56(10):2621–2628	56(10):2621–2628	NUM
ejpam-6459	336	8	,	,	PUNCT
ejpam-6459	336	9	2008	2008	NUM
ejpam-6459	336	10	.	.	PUNCT
ejpam-6459	337	1	[	[	X
ejpam-6459	337	2	21	21	NUM
ejpam-6459	337	3	]	]	X
ejpam-6459	337	4	e.	e.	PROPN
ejpam-6459	337	5	i̇nan	i̇nan	PROPN
ejpam-6459	337	6	and	and	CCONJ
ejpam-6459	337	7	m.	m.	NOUN
ejpam-6459	337	8	a.	a.	NOUN
ejpam-6459	337	9	öztürk	öztürk	PROPN
ejpam-6459	337	10	.	.	PUNCT
ejpam-6459	337	11	fuzzy	fuzzy	ADJ
ejpam-6459	337	12	soft	soft	ADJ
ejpam-6459	337	13	rings	ring	NOUN
ejpam-6459	337	14	and	and	CCONJ
ejpam-6459	337	15	fuzzy	fuzzy	ADJ
ejpam-6459	337	16	soft	soft	ADJ
ejpam-6459	337	17	ideals	ideal	NOUN
ejpam-6459	337	18	.	.	PUNCT
ejpam-6459	338	1	neural	neural	ADJ
ejpam-6459	338	2	computing	computing	NOUN
ejpam-6459	338	3	and	and	CCONJ
ejpam-6459	338	4	applications	application	NOUN
ejpam-6459	338	5	,	,	PUNCT
ejpam-6459	338	6	21(suppl	21(suppl	NUM
ejpam-6459	338	7	1):1–8	1):1–8	NUM
ejpam-6459	338	8	,	,	PUNCT
ejpam-6459	338	9	2011	2011	NUM
ejpam-6459	338	10	.	.	PUNCT
ejpam-6459	339	1	[	[	X
ejpam-6459	339	2	22	22	NUM
ejpam-6459	339	3	]	]	X
ejpam-6459	339	4	y.	y.	PROPN
ejpam-6459	339	5	b.	b.	PROPN
ejpam-6459	339	6	jun	jun	PROPN
ejpam-6459	339	7	.	.	PROPN
ejpam-6459	339	8	soft	soft	ADJ
ejpam-6459	339	9	bck	bck	PROPN
ejpam-6459	339	10	/	/	SYM
ejpam-6459	339	11	bci	bci	NOUN
ejpam-6459	339	12	-	-	PUNCT
ejpam-6459	339	13	algebras	algebra	NOUN
ejpam-6459	339	14	.	.	PUNCT
ejpam-6459	340	1	computers	computer	NOUN
ejpam-6459	340	2	and	and	CCONJ
ejpam-6459	340	3	mathematics	mathematic	NOUN
ejpam-6459	340	4	with	with	ADP
ejpam-6459	340	5	applications	application	NOUN
ejpam-6459	340	6	,	,	PUNCT
ejpam-6459	340	7	56:1408–1413	56:1408–1413	NUM
ejpam-6459	340	8	,	,	PUNCT
ejpam-6459	340	9	2008	2008	NUM
ejpam-6459	340	10	.	.	PUNCT
ejpam-6459	341	1	[	[	X
ejpam-6459	341	2	23	23	NUM
ejpam-6459	341	3	]	]	X
ejpam-6459	341	4	o.	o.	PROPN
ejpam-6459	341	5	kazancı	kazancı	PROPN
ejpam-6459	341	6	,	,	PUNCT
ejpam-6459	341	7	ş.	ş.	PROPN
ejpam-6459	341	8	yılmaz	yılmaz	PROPN
ejpam-6459	341	9	,	,	PUNCT
ejpam-6459	341	10	and	and	CCONJ
ejpam-6459	341	11	s.	s.	PROPN
ejpam-6459	341	12	yamak	yamak	PROPN
ejpam-6459	341	13	.	.	PUNCT
ejpam-6459	342	1	soft	soft	ADJ
ejpam-6459	342	2	sets	set	NOUN
ejpam-6459	342	3	and	and	CCONJ
ejpam-6459	342	4	soft	soft	ADJ
ejpam-6459	342	5	bch	bch	NOUN
ejpam-6459	342	6	-	-	PUNCT
ejpam-6459	342	7	algebras	algebras	PROPN
ejpam-6459	342	8	.	.	PUNCT
ejpam-6459	343	1	hacettepe	hacettepe	PROPN
ejpam-6459	343	2	journal	journal	PROPN
ejpam-6459	343	3	of	of	ADP
ejpam-6459	343	4	mathematics	mathematic	NOUN
ejpam-6459	343	5	and	and	CCONJ
ejpam-6459	343	6	statistics	statistic	NOUN
ejpam-6459	343	7	,	,	PUNCT
ejpam-6459	343	8	39(2):205–217	39(2):205–217	PROPN
ejpam-6459	343	9	,	,	PUNCT
ejpam-6459	343	10	2010	2010	NUM
ejpam-6459	343	11	.	.	PUNCT
ejpam-6459	344	1	[	[	X
ejpam-6459	344	2	24	24	NUM
ejpam-6459	344	3	]	]	X
ejpam-6459	344	4	g.	g.	PROPN
ejpam-6459	344	5	s.	s.	PROPN
ejpam-6459	344	6	rao	rao	PROPN
ejpam-6459	344	7	,	,	PUNCT
ejpam-6459	344	8	p.	p.	PROPN
ejpam-6459	344	9	kolluru	kolluru	PROPN
ejpam-6459	344	10	,	,	PUNCT
ejpam-6459	344	11	and	and	CCONJ
ejpam-6459	344	12	n.	n.	NOUN
ejpam-6459	344	13	thandu	thandu	NOUN
ejpam-6459	344	14	.	.	PUNCT
ejpam-6459	345	1	soft	soft	ADJ
ejpam-6459	345	2	intersection	intersection	NOUN
ejpam-6459	345	3	boolean	boolean	ADJ
ejpam-6459	345	4	near	near	ADP
ejpam-6459	345	5	-	-	PUNCT
ejpam-6459	345	6	rings	ring	NOUN
ejpam-6459	345	7	with	with	ADP
ejpam-6459	345	8	its	its	PRON
ejpam-6459	345	9	applications	application	NOUN
ejpam-6459	345	10	.	.	PUNCT
ejpam-6459	346	1	aip	aip	PROPN
ejpam-6459	346	2	conference	conference	NOUN
ejpam-6459	346	3	proceedings	proceeding	NOUN
ejpam-6459	346	4	,	,	PUNCT
ejpam-6459	346	5	2707:020012	2707:020012	NUM
ejpam-6459	346	6	,	,	PUNCT
ejpam-6459	346	7	2023	2023	NUM
ejpam-6459	346	8	.	.	PUNCT
ejpam-6459	347	1	[	[	X
ejpam-6459	347	2	25	25	NUM
ejpam-6459	347	3	]	]	X
ejpam-6459	347	4	g.	g.	PROPN
ejpam-6459	347	5	s.	s.	PROPN
ejpam-6459	347	6	rao	rao	PROPN
ejpam-6459	347	7	,	,	PUNCT
ejpam-6459	347	8	d.	d.	PROPN
ejpam-6459	347	9	ramesh	ramesh	PROPN
ejpam-6459	347	10	,	,	PUNCT
ejpam-6459	347	11	and	and	CCONJ
ejpam-6459	347	12	b.	b.	PROPN
ejpam-6459	347	13	satyanarayana	satyanarayana	PROPN
ejpam-6459	347	14	.	.	PUNCT
ejpam-6459	348	1	(	(	PUNCT
ejpam-6459	348	2	∈,∈	∈,∈	X
ejpam-6459	348	3	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-6459	348	4	soft	soft	ADJ
ejpam-6459	348	5	boolean	boolean	NOUN
ejpam-6459	348	6	near	near	ADP
ejpam-6459	348	7	rings	ring	NOUN
ejpam-6459	348	8	.	.	PUNCT
ejpam-6459	349	1	asia	asia	PROPN
ejpam-6459	349	2	pacific	pacific	PROPN
ejpam-6459	349	3	journal	journal	PROPN
ejpam-6459	349	4	of	of	ADP
ejpam-6459	349	5	mathematics	mathematic	NOUN
ejpam-6459	349	6	,	,	PUNCT
ejpam-6459	349	7	10:50	10:50	NUM
ejpam-6459	349	8	,	,	PUNCT
ejpam-6459	349	9	2023	2023	NUM
ejpam-6459	349	10	.	.	PUNCT
ejpam-6459	350	1	[	[	X
ejpam-6459	350	2	26	26	NUM
ejpam-6459	350	3	]	]	X
ejpam-6459	350	4	g.	g.	PROPN
ejpam-6459	350	5	s.	s.	PROPN
ejpam-6459	350	6	rao	rao	PROPN
ejpam-6459	350	7	,	,	PUNCT
ejpam-6459	350	8	d.	d.	PROPN
ejpam-6459	350	9	ramesh	ramesh	PROPN
ejpam-6459	350	10	,	,	PUNCT
ejpam-6459	350	11	a.	a.	NOUN
ejpam-6459	350	12	iampan	iampan	PROPN
ejpam-6459	350	13	,	,	PUNCT
ejpam-6459	350	14	and	and	CCONJ
ejpam-6459	350	15	b.	b.	PROPN
ejpam-6459	350	16	satyanarayana	satyanarayana	PROPN
ejpam-6459	350	17	.	.	PUNCT
ejpam-6459	351	1	fuzzy	fuzzy	ADJ
ejpam-6459	351	2	soft	soft	ADJ
ejpam-6459	351	3	boolean	boolean	ADJ
ejpam-6459	351	4	nearrings	nearring	NOUN
ejpam-6459	351	5	and	and	CCONJ
ejpam-6459	351	6	idealistic	idealistic	ADJ
ejpam-6459	351	7	fuzzy	fuzzy	ADJ
ejpam-6459	351	8	soft	soft	ADJ
ejpam-6459	351	9	boolean	boolean	ADJ
ejpam-6459	351	10	near	near	ADJ
ejpam-6459	351	11	-	-	PUNCT
ejpam-6459	351	12	rings	ring	NOUN
ejpam-6459	351	13	.	.	PUNCT
ejpam-6459	352	1	icic	icic	PROPN
ejpam-6459	352	2	express	express	PROPN
ejpam-6459	352	3	letters	letter	NOUN
ejpam-6459	352	4	,	,	PUNCT
ejpam-6459	352	5	18(7):677	18(7):677	NUM
ejpam-6459	352	6	–	–	PUNCT
ejpam-6459	352	7	684	684	NUM
ejpam-6459	352	8	,	,	PUNCT
ejpam-6459	352	9	2024	2024	NUM
ejpam-6459	352	10	.	.	PUNCT
ejpam-6459	353	1	[	[	X
ejpam-6459	353	2	27	27	NUM
ejpam-6459	353	3	]	]	X
ejpam-6459	353	4	g.	g.	PROPN
ejpam-6459	353	5	s.	s.	PROPN
ejpam-6459	353	6	rao	rao	PROPN
ejpam-6459	353	7	,	,	PUNCT
ejpam-6459	353	8	d.	d.	PROPN
ejpam-6459	353	9	ramesh	ramesh	PROPN
ejpam-6459	353	10	,	,	PUNCT
ejpam-6459	353	11	a.	a.	PROPN
ejpam-6459	353	12	iampan	iampan	PROPN
ejpam-6459	353	13	,	,	PUNCT
ejpam-6459	353	14	b.	b.	PROPN
ejpam-6459	353	15	satyanarayana	satyanarayana	PROPN
ejpam-6459	353	16	,	,	PUNCT
ejpam-6459	353	17	and	and	CCONJ
ejpam-6459	353	18	p.	p.	PROPN
ejpam-6459	353	19	rajani	rajani	PROPN
ejpam-6459	353	20	.	.	PUNCT
ejpam-6459	354	1	intuitionistic	intuitionistic	ADJ
ejpam-6459	354	2	fuzzy	fuzzy	ADJ
ejpam-6459	354	3	soft	soft	ADJ
ejpam-6459	354	4	boolean	boolean	ADJ
ejpam-6459	354	5	rings	ring	NOUN
ejpam-6459	354	6	.	.	PUNCT
ejpam-6459	355	1	international	international	ADJ
ejpam-6459	355	2	journal	journal	NOUN
ejpam-6459	355	3	of	of	ADP
ejpam-6459	355	4	analysis	analysis	NOUN
ejpam-6459	355	5	and	and	CCONJ
ejpam-6459	355	6	applications	application	NOUN
ejpam-6459	355	7	,	,	PUNCT
ejpam-6459	355	8	23:43	23:43	NUM
ejpam-6459	355	9	,	,	PUNCT
ejpam-6459	355	10	2025	2025	NUM
ejpam-6459	355	11	.	.	PUNCT
ejpam-6459	356	1	[	[	X
ejpam-6459	356	2	28	28	NUM
ejpam-6459	356	3	]	]	X
ejpam-6459	356	4	g.	g.	PROPN
ejpam-6459	356	5	s.	s.	PROPN
ejpam-6459	356	6	rao	rao	PROPN
ejpam-6459	356	7	,	,	PUNCT
ejpam-6459	356	8	d.	d.	PROPN
ejpam-6459	356	9	ramesh	ramesh	PROPN
ejpam-6459	356	10	,	,	PUNCT
ejpam-6459	356	11	a.	a.	PROPN
ejpam-6459	356	12	iampan	iampan	PROPN
ejpam-6459	356	13	,	,	PUNCT
ejpam-6459	356	14	g.	g.	PROPN
ejpam-6459	356	15	vijaya	vijaya	PROPN
ejpam-6459	356	16	lakshmi	lakshmi	PROPN
ejpam-6459	356	17	,	,	PUNCT
ejpam-6459	356	18	and	and	CCONJ
ejpam-6459	356	19	b.	b.	PROPN
ejpam-6459	356	20	satyanarayana	satyanarayana	PROPN
ejpam-6459	356	21	.	.	PUNCT
ejpam-6459	357	1	(	(	PUNCT
ejpam-6459	357	2	∈,∈	∈,∈	X
ejpam-6459	357	3	∨qk)-intuitionistic	∨qk)-intuitionistic	ADJ
ejpam-6459	357	4	fuzzy	fuzzy	ADJ
ejpam-6459	357	5	soft	soft	ADJ
ejpam-6459	357	6	boolean	boolean	ADJ
ejpam-6459	357	7	near	near	ADJ
ejpam-6459	357	8	-	-	PUNCT
ejpam-6459	357	9	rings	ring	NOUN
ejpam-6459	357	10	.	.	PUNCT
ejpam-6459	358	1	international	international	ADJ
ejpam-6459	358	2	journal	journal	NOUN
ejpam-6459	358	3	of	of	ADP
ejpam-6459	358	4	analysis	analysis	NOUN
ejpam-6459	358	5	and	and	CCONJ
ejpam-6459	358	6	applications	application	NOUN
ejpam-6459	358	7	,	,	PUNCT
ejpam-6459	358	8	23:91	23:91	NUM
ejpam-6459	358	9	,	,	PUNCT
ejpam-6459	358	10	2025	2025	NUM
ejpam-6459	358	11	.	.	PUNCT