id	sid	tid	token	lemma	pos
ejpam-6050	1	1	european	european	PROPN
ejpam-6050	1	2	journal	journal	PROPN
ejpam-6050	1	3	of	of	ADP
ejpam-6050	1	4	pure	pure	ADJ
ejpam-6050	1	5	and	and	CCONJ
ejpam-6050	1	6	applied	applied	ADJ
ejpam-6050	1	7	mathematics	mathematic	NOUN
ejpam-6050	1	8	2025	2025	NUM
ejpam-6050	1	9	,	,	PUNCT
ejpam-6050	1	10	vol	vol	NOUN
ejpam-6050	1	11	.	.	PROPN
ejpam-6050	1	12	18	18	NUM
ejpam-6050	1	13	,	,	PUNCT
ejpam-6050	1	14	issue	issue	NOUN
ejpam-6050	1	15	2	2	NUM
ejpam-6050	1	16	,	,	PUNCT
ejpam-6050	1	17	article	article	NOUN
ejpam-6050	1	18	number	number	NOUN
ejpam-6050	1	19	6050	6050	NUM
ejpam-6050	1	20	issn	issn	VERB
ejpam-6050	1	21	1307	1307	NUM
ejpam-6050	1	22	-	-	SYM
ejpam-6050	1	23	5543	5543	NUM
ejpam-6050	1	24	–	–	PUNCT
ejpam-6050	1	25	ejpam.com	ejpam.com	X
ejpam-6050	1	26	published	publish	VERB
ejpam-6050	1	27	by	by	ADP
ejpam-6050	1	28	new	new	PROPN
ejpam-6050	1	29	york	york	PROPN
ejpam-6050	1	30	business	business	PROPN
ejpam-6050	1	31	global	global	ADJ
ejpam-6050	1	32	exponential	exponential	ADJ
ejpam-6050	1	33	fuzzy	fuzzy	ADJ
ejpam-6050	1	34	sets	set	NOUN
ejpam-6050	1	35	and	and	CCONJ
ejpam-6050	1	36	applications	application	NOUN
ejpam-6050	1	37	of	of	ADP
ejpam-6050	1	38	ai	ai	ADJ
ejpam-6050	1	39	-	-	PUNCT
ejpam-6050	1	40	powered	power	VERB
ejpam-6050	1	41	investment	investment	NOUN
ejpam-6050	1	42	decision	decision	NOUN
ejpam-6050	1	43	-	-	PUNCT
ejpam-6050	1	44	making	making	NOUN
ejpam-6050	1	45	using	use	VERB
ejpam-6050	1	46	the	the	DET
ejpam-6050	1	47	weighted	weight	VERB
ejpam-6050	1	48	mean	mean	ADJ
ejpam-6050	1	49	method	method	NOUN
ejpam-6050	1	50	m.	m.	NOUN
ejpam-6050	1	51	kaviyarasu1,∗	kaviyarasu1,∗	PROPN
ejpam-6050	1	52	,	,	PUNCT
ejpam-6050	1	53	mohammed	mohammed	PROPN
ejpam-6050	1	54	alqahtani2	alqahtani2	PROPN
ejpam-6050	1	55	,	,	PUNCT
ejpam-6050	1	56	m.	m.	NOUN
ejpam-6050	1	57	rajeshwari3	rajeshwari3	NOUN
ejpam-6050	1	58	1	1	NUM
ejpam-6050	1	59	department	department	NOUN
ejpam-6050	1	60	of	of	ADP
ejpam-6050	1	61	mathematics	mathematic	NOUN
ejpam-6050	1	62	,	,	PUNCT
ejpam-6050	1	63	vel	vel	PROPN
ejpam-6050	1	64	tech	tech	PROPN
ejpam-6050	1	65	rangarajan	rangarajan	PROPN
ejpam-6050	1	66	dr	dr	PROPN
ejpam-6050	1	67	sagunthala	sagunthala	PROPN
ejpam-6050	1	68	r	r	PROPN
ejpam-6050	1	69	&	&	CCONJ
ejpam-6050	1	70	d	d	PROPN
ejpam-6050	1	71	institute	institute	PROPN
ejpam-6050	1	72	of	of	ADP
ejpam-6050	1	73	science	science	NOUN
ejpam-6050	1	74	and	and	CCONJ
ejpam-6050	1	75	technology	technology	NOUN
ejpam-6050	1	76	,	,	PUNCT
ejpam-6050	1	77	chennai	chennai	PROPN
ejpam-6050	1	78	,	,	PUNCT
ejpam-6050	1	79	tamilnadu-600062,india	tamilnadu-600062,india	PROPN
ejpam-6050	1	80	2	2	NUM
ejpam-6050	1	81	department	department	NOUN
ejpam-6050	1	82	of	of	ADP
ejpam-6050	1	83	basic	basic	ADJ
ejpam-6050	1	84	sciences	science	NOUN
ejpam-6050	1	85	,	,	PUNCT
ejpam-6050	1	86	college	college	NOUN
ejpam-6050	1	87	of	of	ADP
ejpam-6050	1	88	science	science	NOUN
ejpam-6050	1	89	and	and	CCONJ
ejpam-6050	1	90	theoretical	theoretical	ADJ
ejpam-6050	1	91	studies	study	NOUN
ejpam-6050	1	92	,	,	PUNCT
ejpam-6050	1	93	saudi	saudi	ADJ
ejpam-6050	1	94	electronic	electronic	ADJ
ejpam-6050	1	95	university	university	NOUN
ejpam-6050	1	96	,	,	PUNCT
ejpam-6050	1	97	p.o	p.o	PROPN
ejpam-6050	1	98	.	.	PROPN
ejpam-6050	1	99	box	box	PROPN
ejpam-6050	1	100	93499	93499	NUM
ejpam-6050	1	101	,	,	PUNCT
ejpam-6050	1	102	riyadh	riyadh	PROPN
ejpam-6050	1	103	11673	11673	NUM
ejpam-6050	1	104	,	,	PUNCT
ejpam-6050	1	105	saudi	saudi	PROPN
ejpam-6050	1	106	arabia	arabia	PROPN
ejpam-6050	1	107	3	3	NUM
ejpam-6050	1	108	department	department	NOUN
ejpam-6050	1	109	of	of	ADP
ejpam-6050	1	110	mathematics	mathematics	PROPN
ejpam-6050	1	111	,	,	PUNCT
ejpam-6050	1	112	presidency	presidency	NOUN
ejpam-6050	1	113	university	university	NOUN
ejpam-6050	1	114	,	,	PUNCT
ejpam-6050	1	115	bangalore	bangalore	PROPN
ejpam-6050	1	116	,	,	PUNCT
ejpam-6050	1	117	india	india	PROPN
ejpam-6050	1	118	abstract	abstract	NOUN
ejpam-6050	1	119	.	.	PUNCT
ejpam-6050	2	1	the	the	DET
ejpam-6050	2	2	exponential	exponential	ADJ
ejpam-6050	2	3	fuzzy	fuzzy	ADJ
ejpam-6050	2	4	set	set	NOUN
ejpam-6050	2	5	(	(	PUNCT
ejpam-6050	2	6	efs	ef	NOUN
ejpam-6050	2	7	)	)	PUNCT
ejpam-6050	2	8	is	be	AUX
ejpam-6050	2	9	a	a	DET
ejpam-6050	2	10	new	new	ADJ
ejpam-6050	2	11	modification	modification	NOUN
ejpam-6050	2	12	that	that	PRON
ejpam-6050	2	13	allows	allow	VERB
ejpam-6050	2	14	for	for	ADP
ejpam-6050	2	15	a	a	DET
ejpam-6050	2	16	more	more	ADV
ejpam-6050	2	17	flexible	flexible	ADJ
ejpam-6050	2	18	representation	representation	NOUN
ejpam-6050	2	19	of	of	ADP
ejpam-6050	2	20	uncertainty	uncertainty	NOUN
ejpam-6050	2	21	by	by	ADP
ejpam-6050	2	22	using	use	VERB
ejpam-6050	2	23	an	an	DET
ejpam-6050	2	24	exponential	exponential	ADJ
ejpam-6050	2	25	function	function	NOUN
ejpam-6050	2	26	to	to	PART
ejpam-6050	2	27	define	define	VERB
ejpam-6050	2	28	membership	membership	NOUN
ejpam-6050	2	29	degree	degree	NOUN
ejpam-6050	2	30	.	.	PUNCT
ejpam-6050	3	1	in	in	ADP
ejpam-6050	3	2	this	this	DET
ejpam-6050	3	3	work	work	NOUN
ejpam-6050	3	4	,	,	PUNCT
ejpam-6050	3	5	we	we	PRON
ejpam-6050	3	6	define	define	VERB
ejpam-6050	3	7	basic	basic	ADJ
ejpam-6050	3	8	operations	operation	NOUN
ejpam-6050	3	9	on	on	ADP
ejpam-6050	3	10	efs	ef	NOUN
ejpam-6050	3	11	,	,	PUNCT
ejpam-6050	3	12	such	such	ADJ
ejpam-6050	3	13	as	as	ADP
ejpam-6050	3	14	complement	complement	NOUN
ejpam-6050	3	15	,	,	PUNCT
ejpam-6050	3	16	union	union	NOUN
ejpam-6050	3	17	,	,	PUNCT
ejpam-6050	3	18	intersection	intersection	NOUN
ejpam-6050	3	19	,	,	PUNCT
ejpam-6050	3	20	simple	simple	ADJ
ejpam-6050	3	21	difference	difference	NOUN
ejpam-6050	3	22	,	,	PUNCT
ejpam-6050	3	23	and	and	CCONJ
ejpam-6050	3	24	limited	limited	ADJ
ejpam-6050	3	25	difference	difference	NOUN
ejpam-6050	3	26	functions	function	NOUN
ejpam-6050	3	27	.	.	PUNCT
ejpam-6050	4	1	the	the	DET
ejpam-6050	4	2	equivalency	equivalency	NOUN
ejpam-6050	4	3	formula	formula	NOUN
ejpam-6050	4	4	,	,	PUNCT
ejpam-6050	4	5	symmetrical	symmetrical	ADJ
ejpam-6050	4	6	difference	difference	NOUN
ejpam-6050	4	7	formula	formula	NOUN
ejpam-6050	4	8	,	,	PUNCT
ejpam-6050	4	9	disjoint	disjoint	NOUN
ejpam-6050	4	10	sets	set	NOUN
ejpam-6050	4	11	,	,	PUNCT
ejpam-6050	4	12	disjoint	disjoint	NOUN
ejpam-6050	4	13	sum	sum	NOUN
ejpam-6050	4	14	,	,	PUNCT
ejpam-6050	4	15	and	and	CCONJ
ejpam-6050	4	16	disjunctive	disjunctive	ADJ
ejpam-6050	4	17	sum	sum	NOUN
ejpam-6050	4	18	are	be	AUX
ejpam-6050	4	19	further	far	ADV
ejpam-6050	4	20	important	important	ADJ
ejpam-6050	4	21	qualities	quality	NOUN
ejpam-6050	4	22	that	that	PRON
ejpam-6050	4	23	we	we	PRON
ejpam-6050	4	24	examine	examine	VERB
ejpam-6050	4	25	.	.	PUNCT
ejpam-6050	5	1	we	we	PRON
ejpam-6050	5	2	analyse	analyse	VERB
ejpam-6050	5	3	essential	essential	ADJ
ejpam-6050	5	4	laws	law	NOUN
ejpam-6050	5	5	in	in	ADP
ejpam-6050	5	6	the	the	DET
ejpam-6050	5	7	exponential	exponential	ADJ
ejpam-6050	5	8	fuzzy	fuzzy	ADJ
ejpam-6050	5	9	framework	framework	NOUN
ejpam-6050	5	10	,	,	PUNCT
ejpam-6050	5	11	such	such	ADJ
ejpam-6050	5	12	as	as	ADP
ejpam-6050	5	13	the	the	DET
ejpam-6050	5	14	idempotent	idempotent	ADJ
ejpam-6050	5	15	law	law	NOUN
ejpam-6050	5	16	of	of	ADP
ejpam-6050	5	17	union	union	NOUN
ejpam-6050	5	18	.	.	PUNCT
ejpam-6050	6	1	in	in	ADP
ejpam-6050	6	2	addition	addition	NOUN
ejpam-6050	6	3	,	,	PUNCT
ejpam-6050	6	4	we	we	PRON
ejpam-6050	6	5	present	present	VERB
ejpam-6050	6	6	a	a	DET
ejpam-6050	6	7	few	few	ADJ
ejpam-6050	6	8	theorems	theorem	NOUN
ejpam-6050	6	9	that	that	PRON
ejpam-6050	6	10	govern	govern	VERB
ejpam-6050	6	11	the	the	DET
ejpam-6050	6	12	relational	relational	ADJ
ejpam-6050	6	13	and	and	CCONJ
ejpam-6050	6	14	algebraic	algebraic	ADJ
ejpam-6050	6	15	structures	structure	NOUN
ejpam-6050	6	16	of	of	ADP
ejpam-6050	6	17	efs	ef	NOUN
ejpam-6050	6	18	.	.	PUNCT
ejpam-6050	7	1	efs	ef	NOUN
ejpam-6050	7	2	has	have	AUX
ejpam-6050	7	3	been	be	AUX
ejpam-6050	7	4	compared	compare	VERB
ejpam-6050	7	5	against	against	ADP
ejpam-6050	7	6	traditional	traditional	ADJ
ejpam-6050	7	7	approaches	approach	NOUN
ejpam-6050	7	8	and	and	CCONJ
ejpam-6050	7	9	the	the	DET
ejpam-6050	7	10	resulting	result	VERB
ejpam-6050	7	11	studies	study	NOUN
ejpam-6050	7	12	showcase	showcase	VERB
ejpam-6050	7	13	its	its	PRON
ejpam-6050	7	14	advantages	advantage	NOUN
ejpam-6050	7	15	in	in	ADP
ejpam-6050	7	16	modeling	model	VERB
ejpam-6050	7	17	uncertainty	uncertainty	NOUN
ejpam-6050	7	18	,	,	PUNCT
ejpam-6050	7	19	artificial	artificial	ADJ
ejpam-6050	7	20	intelligence	intelligence	NOUN
ejpam-6050	7	21	,	,	PUNCT
ejpam-6050	7	22	and	and	CCONJ
ejpam-6050	7	23	decision	decision	NOUN
ejpam-6050	7	24	making	making	NOUN
ejpam-6050	7	25	.	.	PUNCT
ejpam-6050	8	1	this	this	DET
ejpam-6050	8	2	paper	paper	NOUN
ejpam-6050	8	3	studies	study	NOUN
ejpam-6050	8	4	the	the	DET
ejpam-6050	8	5	use	use	NOUN
ejpam-6050	8	6	of	of	ADP
ejpam-6050	8	7	exponential	exponential	ADJ
ejpam-6050	8	8	fuzzy	fuzzy	ADJ
ejpam-6050	8	9	sets	set	NOUN
ejpam-6050	8	10	in	in	ADP
ejpam-6050	8	11	ai	ai	PRON
ejpam-6050	8	12	driven	drive	VERB
ejpam-6050	8	13	investment	investment	NOUN
ejpam-6050	8	14	decision	decision	NOUN
ejpam-6050	8	15	processes	process	NOUN
ejpam-6050	8	16	using	use	VERB
ejpam-6050	8	17	the	the	DET
ejpam-6050	8	18	weighted	weight	VERB
ejpam-6050	8	19	mean	mean	ADJ
ejpam-6050	8	20	method	method	NOUN
ejpam-6050	8	21	of	of	ADP
ejpam-6050	8	22	multifactor	multifactor	NOUN
ejpam-6050	8	23	investment	investment	NOUN
ejpam-6050	8	24	analysis	analysis	NOUN
ejpam-6050	8	25	.	.	PUNCT
ejpam-6050	9	1	2020	2020	NUM
ejpam-6050	9	2	mathematics	mathematic	NOUN
ejpam-6050	9	3	subject	subject	NOUN
ejpam-6050	9	4	classifications	classification	NOUN
ejpam-6050	9	5	:	:	PUNCT
ejpam-6050	9	6	03e72	03e72	NUM
ejpam-6050	9	7	,	,	PUNCT
ejpam-6050	9	8	91b06	91b06	NUM
ejpam-6050	9	9	,	,	PUNCT
ejpam-6050	9	10	68t27	68t27	NOUN
ejpam-6050	9	11	,	,	PUNCT
ejpam-6050	9	12	91g10	91g10	NUM
ejpam-6050	9	13	key	key	ADJ
ejpam-6050	9	14	words	word	NOUN
ejpam-6050	9	15	and	and	CCONJ
ejpam-6050	9	16	phrases	phrase	NOUN
ejpam-6050	9	17	:	:	PUNCT
ejpam-6050	9	18	exponential	exponential	ADJ
ejpam-6050	9	19	fuzzy	fuzzy	ADJ
ejpam-6050	9	20	set	set	NOUN
ejpam-6050	9	21	,	,	PUNCT
ejpam-6050	9	22	operations	operation	NOUN
ejpam-6050	9	23	of	of	ADP
ejpam-6050	9	24	exponential	exponential	ADJ
ejpam-6050	9	25	fuzzy	fuzzy	ADJ
ejpam-6050	9	26	set	set	NOUN
ejpam-6050	9	27	,	,	PUNCT
ejpam-6050	9	28	decision	decision	NOUN
ejpam-6050	9	29	-	-	PUNCT
ejpam-6050	9	30	making	making	NOUN
ejpam-6050	9	31	,	,	PUNCT
ejpam-6050	9	32	weighted	weight	VERB
ejpam-6050	9	33	mean	mean	ADJ
ejpam-6050	9	34	method	method	NOUN
ejpam-6050	9	35	1	1	NUM
ejpam-6050	9	36	.	.	PUNCT
ejpam-6050	10	1	introduction	introduction	PROPN
ejpam-6050	10	2	zadeh	zadeh	PROPN
ejpam-6050	10	3	’s	’s	PART
ejpam-6050	10	4	[	[	X
ejpam-6050	10	5	1	1	NUM
ejpam-6050	10	6	]	]	X
ejpam-6050	10	7	fuzzy	fuzzy	ADJ
ejpam-6050	10	8	sets	set	NOUN
ejpam-6050	10	9	have	have	AUX
ejpam-6050	10	10	proved	prove	VERB
ejpam-6050	10	11	to	to	PART
ejpam-6050	10	12	be	be	AUX
ejpam-6050	10	13	beneficial	beneficial	ADJ
ejpam-6050	10	14	in	in	ADP
ejpam-6050	10	15	a	a	DET
ejpam-6050	10	16	number	number	NOUN
ejpam-6050	10	17	of	of	ADP
ejpam-6050	10	18	fields	field	NOUN
ejpam-6050	10	19	of	of	ADP
ejpam-6050	10	20	mathematical	mathematical	ADJ
ejpam-6050	10	21	modeling	modeling	NOUN
ejpam-6050	10	22	and	and	CCONJ
ejpam-6050	10	23	decision	decision	NOUN
ejpam-6050	10	24	making	making	NOUN
ejpam-6050	10	25	.	.	PUNCT
ejpam-6050	11	1	this	this	DET
ejpam-6050	11	2	concept	concept	NOUN
ejpam-6050	11	3	has	have	AUX
ejpam-6050	11	4	resulted	result	VERB
ejpam-6050	11	5	in	in	ADP
ejpam-6050	11	6	the	the	DET
ejpam-6050	11	7	creation	creation	NOUN
ejpam-6050	11	8	of	of	ADP
ejpam-6050	11	9	such	such	ADJ
ejpam-6050	11	10	sets	set	NOUN
ejpam-6050	11	11	as	as	ADP
ejpam-6050	11	12	the	the	DET
ejpam-6050	11	13	intuitionistic	intuitionistic	ADJ
ejpam-6050	11	14	fuzzy	fuzzy	ADJ
ejpam-6050	11	15	sets	set	NOUN
ejpam-6050	11	16	[	[	X
ejpam-6050	11	17	2	2	NUM
ejpam-6050	11	18	]	]	PUNCT
ejpam-6050	11	19	,	,	PUNCT
ejpam-6050	11	20	neutrosophic	neutrosophic	ADJ
ejpam-6050	11	21	fuzzy	fuzzy	ADJ
ejpam-6050	11	22	sets	set	NOUN
ejpam-6050	11	23	[	[	X
ejpam-6050	11	24	3	3	NUM
ejpam-6050	11	25	]	]	PUNCT
ejpam-6050	11	26	,	,	PUNCT
ejpam-6050	11	27	and	and	CCONJ
ejpam-6050	11	28	even	even	ADV
ejpam-6050	11	29	pythagorean	pythagorean	VERB
ejpam-6050	11	30	fuzzy	fuzzy	ADJ
ejpam-6050	11	31	sets	set	NOUN
ejpam-6050	11	32	(	(	PUNCT
ejpam-6050	11	33	yager	yager	NOUN
ejpam-6050	11	34	,	,	PUNCT
ejpam-6050	11	35	2013	2013	NUM
ejpam-6050	11	36	)	)	PUNCT
ejpam-6050	11	37	.	.	PUNCT
ejpam-6050	12	1	all	all	PRON
ejpam-6050	12	2	of	of	ADP
ejpam-6050	12	3	which	which	PRON
ejpam-6050	12	4	were	be	AUX
ejpam-6050	12	5	created	create	VERB
ejpam-6050	12	6	to	to	PART
ejpam-6050	12	7	solve	solve	VERB
ejpam-6050	12	8	some	some	DET
ejpam-6050	12	9	form	form	NOUN
ejpam-6050	12	10	of	of	ADP
ejpam-6050	12	11	ambiguity	ambiguity	NOUN
ejpam-6050	12	12	.	.	PUNCT
ejpam-6050	13	1	one	one	NUM
ejpam-6050	13	2	of	of	ADP
ejpam-6050	13	3	these	these	DET
ejpam-6050	13	4	extensions	extension	NOUN
ejpam-6050	13	5	is	be	AUX
ejpam-6050	13	6	the	the	DET
ejpam-6050	13	7	exponential	exponential	ADJ
ejpam-6050	13	8	fuzzy	fuzzy	ADJ
ejpam-6050	13	9	set	set	NOUN
ejpam-6050	13	10	,	,	PUNCT
ejpam-6050	13	11	which	which	PRON
ejpam-6050	13	12	enables	enable	VERB
ejpam-6050	13	13	the	the	DET
ejpam-6050	13	14	simulation	simulation	NOUN
ejpam-6050	13	15	of	of	ADP
ejpam-6050	13	16	∗corresponding	∗corresponde	VERB
ejpam-6050	13	17	author	author	NOUN
ejpam-6050	13	18	.	.	PUNCT
ejpam-6050	14	1	doi	doi	NOUN
ejpam-6050	14	2	:	:	PUNCT
ejpam-6050	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6050	https://doi.org/10.29020/nybg.ejpam.v18i2.6050	PROPN
ejpam-6050	14	4	email	email	NOUN
ejpam-6050	14	5	addresses	address	VERB
ejpam-6050	14	6	:	:	PUNCT
ejpam-6050	15	1	kavitamilm@gmail.com	kavitamilm@gmail.com	X
ejpam-6050	15	2	(	(	PUNCT
ejpam-6050	15	3	m.	m.	PROPN
ejpam-6050	15	4	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	15	5	)	)	PUNCT
ejpam-6050	15	6	,	,	PUNCT
ejpam-6050	15	7	,	,	PUNCT
ejpam-6050	15	8	m.alqahtani@seu.edu.sa	m.alqahtani@seu.edu.sa	PROPN
ejpam-6050	15	9	(	(	PUNCT
ejpam-6050	15	10	m.	m.	NOUN
ejpam-6050	15	11	alqahtani	alqahtani	PROPN
ejpam-6050	15	12	)	)	PUNCT
ejpam-6050	15	13	,	,	PUNCT
ejpam-6050	15	14	rajeakila@gmail.com	rajeakila@gmail.com	X
ejpam-6050	16	1	(	(	PUNCT
ejpam-6050	16	2	m.	m.	NOUN
ejpam-6050	16	3	rajeshwari	rajeshwari	PROPN
ejpam-6050	16	4	)	)	PUNCT
ejpam-6050	16	5	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6050	17	1	1	1	NUM
ejpam-6050	17	2	copyright	copyright	NOUN
ejpam-6050	17	3	:	:	PUNCT
ejpam-6050	17	4	©	©	PROPN
ejpam-6050	17	5	2025	2025	NUM
ejpam-6050	17	6	the	the	DET
ejpam-6050	17	7	author(s	author(s	NOUN
ejpam-6050	17	8	)	)	PUNCT
ejpam-6050	17	9	.	.	PUNCT
ejpam-6050	18	1	(	(	PUNCT
ejpam-6050	18	2	cc	cc	NOUN
ejpam-6050	18	3	by	by	ADP
ejpam-6050	18	4	-	-	PUNCT
ejpam-6050	18	5	nc	nc	PROPN
ejpam-6050	18	6	4.0	4.0	NUM
ejpam-6050	18	7	)	)	PUNCT
ejpam-6050	18	8	m.	m.	NOUN
ejpam-6050	18	9	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	18	10	,	,	PUNCT
ejpam-6050	18	11	m.	m.	NOUN
ejpam-6050	18	12	rajeshwari	rajeshwari	NOUN
ejpam-6050	18	13	,	,	PUNCT
ejpam-6050	18	14	m.	m.	NOUN
ejpam-6050	18	15	alqahtani	alqahtani	PROPN
ejpam-6050	18	16	/	/	SYM
ejpam-6050	18	17	eur	eur	PROPN
ejpam-6050	18	18	.	.	PUNCT
ejpam-6050	19	1	j.	j.	PROPN
ejpam-6050	19	2	pure	pure	PROPN
ejpam-6050	19	3	appl	appl	PROPN
ejpam-6050	19	4	.	.	PROPN
ejpam-6050	19	5	math	math	PROPN
ejpam-6050	19	6	,	,	PUNCT
ejpam-6050	19	7	18	18	NUM
ejpam-6050	19	8	(	(	PUNCT
ejpam-6050	19	9	2	2	NUM
ejpam-6050	19	10	)	)	PUNCT
ejpam-6050	19	11	(	(	PUNCT
ejpam-6050	19	12	2025	2025	NUM
ejpam-6050	19	13	)	)	PUNCT
ejpam-6050	19	14	,	,	PUNCT
ejpam-6050	19	15	6050	6050	NUM
ejpam-6050	19	16	2	2	NUM
ejpam-6050	19	17	of	of	ADP
ejpam-6050	19	18	29	29	NUM
ejpam-6050	19	19	systems	system	NOUN
ejpam-6050	19	20	where	where	SCONJ
ejpam-6050	19	21	there	there	PRON
ejpam-6050	19	22	is	be	VERB
ejpam-6050	19	23	a	a	DET
ejpam-6050	19	24	significant	significant	ADJ
ejpam-6050	19	25	level	level	NOUN
ejpam-6050	19	26	of	of	ADP
ejpam-6050	19	27	uncertainty	uncertainty	NOUN
ejpam-6050	19	28	and	and	CCONJ
ejpam-6050	19	29	provides	provide	VERB
ejpam-6050	19	30	robust	robust	ADJ
ejpam-6050	19	31	mathematical	mathematical	ADJ
ejpam-6050	19	32	support	support	NOUN
ejpam-6050	19	33	.	.	PUNCT
ejpam-6050	20	1	exponential	exponential	ADJ
ejpam-6050	20	2	fuzzy	fuzzy	ADJ
ejpam-6050	20	3	sets	set	NOUN
ejpam-6050	20	4	have	have	VERB
ejpam-6050	20	5	great	great	ADJ
ejpam-6050	20	6	potential	potential	NOUN
ejpam-6050	20	7	for	for	ADP
ejpam-6050	20	8	use	use	NOUN
ejpam-6050	20	9	in	in	ADP
ejpam-6050	20	10	optimization	optimization	NOUN
ejpam-6050	20	11	,	,	PUNCT
ejpam-6050	20	12	control	control	NOUN
ejpam-6050	20	13	systems	system	NOUN
ejpam-6050	20	14	,	,	PUNCT
ejpam-6050	20	15	as	as	ADV
ejpam-6050	20	16	well	well	ADV
ejpam-6050	20	17	as	as	ADP
ejpam-6050	20	18	decision	decision	NOUN
ejpam-6050	20	19	analysis	analysis	NOUN
ejpam-6050	20	20	.	.	PUNCT
ejpam-6050	21	1	the	the	DET
ejpam-6050	21	2	theoretical	theoretical	ADJ
ejpam-6050	21	3	basis	basis	NOUN
ejpam-6050	21	4	for	for	ADP
ejpam-6050	21	5	exponential	exponential	ADJ
ejpam-6050	21	6	fuzzy	fuzzy	ADJ
ejpam-6050	21	7	sets	set	NOUN
ejpam-6050	21	8	is	be	AUX
ejpam-6050	21	9	the	the	DET
ejpam-6050	21	10	need	need	NOUN
ejpam-6050	21	11	to	to	PART
ejpam-6050	21	12	define	define	VERB
ejpam-6050	21	13	uncertainty	uncertainty	NOUN
ejpam-6050	21	14	in	in	ADP
ejpam-6050	21	15	dynamic	dynamic	ADJ
ejpam-6050	21	16	environments	environment	NOUN
ejpam-6050	21	17	with	with	ADP
ejpam-6050	21	18	extreme	extreme	ADJ
ejpam-6050	21	19	rates	rate	NOUN
ejpam-6050	21	20	of	of	ADP
ejpam-6050	21	21	change	change	NOUN
ejpam-6050	21	22	.	.	PUNCT
ejpam-6050	22	1	for	for	ADP
ejpam-6050	22	2	example	example	NOUN
ejpam-6050	22	3	,	,	PUNCT
ejpam-6050	22	4	the	the	DET
ejpam-6050	22	5	effectiveness	effectiveness	NOUN
ejpam-6050	22	6	of	of	ADP
ejpam-6050	22	7	exponential	exponential	ADJ
ejpam-6050	22	8	membership	membership	NOUN
ejpam-6050	22	9	functions	function	NOUN
ejpam-6050	22	10	was	be	AUX
ejpam-6050	22	11	proved	prove	VERB
ejpam-6050	22	12	by	by	ADP
ejpam-6050	22	13	wu	wu	PROPN
ejpam-6050	22	14	et	et	PROPN
ejpam-6050	22	15	al	al	PROPN
ejpam-6050	22	16	.	.	PUNCT
ejpam-6050	23	1	[	[	X
ejpam-6050	23	2	4	4	NUM
ejpam-6050	23	3	]	]	PUNCT
ejpam-6050	23	4	,	,	PUNCT
ejpam-6050	23	5	who	who	PRON
ejpam-6050	23	6	employed	employ	VERB
ejpam-6050	23	7	them	they	PRON
ejpam-6050	23	8	in	in	ADP
ejpam-6050	23	9	a	a	DET
ejpam-6050	23	10	fuzzy	fuzzy	ADJ
ejpam-6050	23	11	control	control	NOUN
ejpam-6050	23	12	approach	approach	NOUN
ejpam-6050	23	13	to	to	PART
ejpam-6050	23	14	examine	examine	VERB
ejpam-6050	23	15	the	the	DET
ejpam-6050	23	16	stability	stability	NOUN
ejpam-6050	23	17	of	of	ADP
ejpam-6050	23	18	nonlinear	nonlinear	ADJ
ejpam-6050	23	19	parabolic	parabolic	PROPN
ejpam-6050	23	20	systems	system	NOUN
ejpam-6050	23	21	.	.	PUNCT
ejpam-6050	24	1	furthermore	furthermore	ADV
ejpam-6050	24	2	,	,	PUNCT
ejpam-6050	24	3	the	the	DET
ejpam-6050	24	4	predicted	predict	VERB
ejpam-6050	24	5	value	value	NOUN
ejpam-6050	24	6	of	of	ADP
ejpam-6050	24	7	exponential	exponential	ADJ
ejpam-6050	24	8	fuzzy	fuzzy	ADJ
ejpam-6050	24	9	numbers	number	NOUN
ejpam-6050	24	10	and	and	CCONJ
ejpam-6050	24	11	their	their	PRON
ejpam-6050	24	12	use	use	NOUN
ejpam-6050	24	13	in	in	ADP
ejpam-6050	24	14	inventory	inventory	NOUN
ejpam-6050	24	15	models	model	NOUN
ejpam-6050	24	16	for	for	ADP
ejpam-6050	24	17	degrading	degrade	VERB
ejpam-6050	24	18	objects	object	NOUN
ejpam-6050	24	19	were	be	AUX
ejpam-6050	24	20	investigated	investigate	VERB
ejpam-6050	24	21	by	by	ADP
ejpam-6050	24	22	garai	garai	PROPN
ejpam-6050	24	23	et	et	PROPN
ejpam-6050	24	24	al	al	PROPN
ejpam-6050	24	25	.	.	PUNCT
ejpam-6050	25	1	[	[	X
ejpam-6050	25	2	5	5	NUM
ejpam-6050	25	3	]	]	PUNCT
ejpam-6050	25	4	.	.	PUNCT
ejpam-6050	26	1	these	these	DET
ejpam-6050	26	2	works	work	NOUN
ejpam-6050	26	3	reflect	reflect	VERB
ejpam-6050	26	4	the	the	DET
ejpam-6050	26	5	practical	practical	ADJ
ejpam-6050	26	6	use	use	NOUN
ejpam-6050	26	7	of	of	ADP
ejpam-6050	26	8	fuzzy	fuzzy	ADJ
ejpam-6050	26	9	sets	set	NOUN
ejpam-6050	26	10	with	with	ADP
ejpam-6050	26	11	exponentialtype	exponentialtype	NOUN
ejpam-6050	26	12	membership	membership	NOUN
ejpam-6050	26	13	functions	function	NOUN
ejpam-6050	26	14	for	for	ADP
ejpam-6050	26	15	information	information	NOUN
ejpam-6050	26	16	systems	system	NOUN
ejpam-6050	26	17	that	that	PRON
ejpam-6050	26	18	are	be	AUX
ejpam-6050	26	19	rapidly	rapidly	ADV
ejpam-6050	26	20	evolving	evolve	VERB
ejpam-6050	26	21	and	and	CCONJ
ejpam-6050	26	22	have	have	VERB
ejpam-6050	26	23	a	a	DET
ejpam-6050	26	24	strong	strong	ADJ
ejpam-6050	26	25	time	time	NOUN
ejpam-6050	26	26	constraint	constraint	NOUN
ejpam-6050	26	27	.	.	PUNCT
ejpam-6050	27	1	one	one	NUM
ejpam-6050	27	2	of	of	ADP
ejpam-6050	27	3	the	the	DET
ejpam-6050	27	4	crucial	crucial	ADJ
ejpam-6050	27	5	advantages	advantage	NOUN
ejpam-6050	27	6	of	of	ADP
ejpam-6050	27	7	exponential	exponential	ADJ
ejpam-6050	27	8	fuzzy	fuzzy	ADJ
ejpam-6050	27	9	sets	set	NOUN
ejpam-6050	27	10	is	be	AUX
ejpam-6050	27	11	that	that	SCONJ
ejpam-6050	27	12	unlike	unlike	ADP
ejpam-6050	27	13	traditional	traditional	ADJ
ejpam-6050	27	14	fuzzy	fuzzy	ADJ
ejpam-6050	27	15	models	model	NOUN
ejpam-6050	27	16	,	,	PUNCT
ejpam-6050	27	17	they	they	PRON
ejpam-6050	27	18	can	can	AUX
ejpam-6050	27	19	represent	represent	VERB
ejpam-6050	27	20	abrupt	abrupt	ADJ
ejpam-6050	27	21	changes	change	NOUN
ejpam-6050	27	22	in	in	ADP
ejpam-6050	27	23	uncertainty	uncertainty	NOUN
ejpam-6050	27	24	more	more	ADV
ejpam-6050	27	25	effective	effective	ADJ
ejpam-6050	27	26	.	.	PUNCT
ejpam-6050	28	1	the	the	DET
ejpam-6050	28	2	quantitative	quantitative	ADJ
ejpam-6050	28	3	evaluation	evaluation	NOUN
ejpam-6050	28	4	of	of	ADP
ejpam-6050	28	5	differences	difference	NOUN
ejpam-6050	28	6	of	of	ADP
ejpam-6050	28	7	information	information	NOUN
ejpam-6050	28	8	in	in	ADP
ejpam-6050	28	9	uncertain	uncertain	ADJ
ejpam-6050	28	10	situations	situation	NOUN
ejpam-6050	28	11	has	have	AUX
ejpam-6050	28	12	been	be	AUX
ejpam-6050	28	13	enhanced	enhance	VERB
ejpam-6050	28	14	by	by	ADP
ejpam-6050	28	15	an	an	DET
ejpam-6050	28	16	extreme	extreme	ADJ
ejpam-6050	28	17	divergence	divergence	NOUN
ejpam-6050	28	18	measure	measure	NOUN
ejpam-6050	28	19	of	of	ADP
ejpam-6050	28	20	tomar	tomar	NOUN
ejpam-6050	28	21	and	and	CCONJ
ejpam-6050	28	22	ohlan	ohlan	ADJ
ejpam-6050	29	1	[	[	X
ejpam-6050	29	2	6	6	NUM
ejpam-6050	29	3	]	]	PUNCT
ejpam-6050	29	4	.	.	PUNCT
ejpam-6050	30	1	also	also	ADV
ejpam-6050	30	2	,	,	PUNCT
ejpam-6050	30	3	bustince	bustince	NOUN
ejpam-6050	30	4	et	et	NOUN
ejpam-6050	30	5	al	al	PROPN
ejpam-6050	30	6	.	.	PUNCT
ejpam-6050	31	1	[	[	X
ejpam-6050	31	2	7	7	X
ejpam-6050	31	3	]	]	PUNCT
ejpam-6050	31	4	provide	provide	VERB
ejpam-6050	31	5	an	an	DET
ejpam-6050	31	6	account	account	NOUN
ejpam-6050	31	7	of	of	ADP
ejpam-6050	31	8	the	the	DET
ejpam-6050	31	9	history	history	NOUN
ejpam-6050	31	10	of	of	ADP
ejpam-6050	31	11	all	all	DET
ejpam-6050	31	12	types	type	NOUN
ejpam-6050	31	13	of	of	ADP
ejpam-6050	31	14	fuzzy	fuzzy	ADJ
ejpam-6050	31	15	sets	set	NOUN
ejpam-6050	31	16	and	and	CCONJ
ejpam-6050	31	17	give	give	VERB
ejpam-6050	31	18	justification	justification	NOUN
ejpam-6050	31	19	for	for	ADP
ejpam-6050	31	20	the	the	DET
ejpam-6050	31	21	new	new	ADJ
ejpam-6050	31	22	novel	novel	ADJ
ejpam-6050	31	23	exponential	exponential	ADJ
ejpam-6050	31	24	fuzzy	fuzzy	ADJ
ejpam-6050	31	25	sets	set	NOUN
ejpam-6050	31	26	from	from	ADP
ejpam-6050	31	27	a	a	DET
ejpam-6050	31	28	research	research	NOUN
ejpam-6050	31	29	perspective	perspective	NOUN
ejpam-6050	31	30	.	.	PUNCT
ejpam-6050	32	1	in	in	ADP
ejpam-6050	32	2	the	the	DET
ejpam-6050	32	3	mathematical	mathematical	ADJ
ejpam-6050	32	4	formulation	formulation	NOUN
ejpam-6050	32	5	of	of	ADP
ejpam-6050	32	6	exponential	exponential	ADJ
ejpam-6050	32	7	fuzzy	fuzzy	ADJ
ejpam-6050	32	8	sets	set	NOUN
ejpam-6050	32	9	,	,	PUNCT
ejpam-6050	32	10	the	the	DET
ejpam-6050	32	11	degree	degree	NOUN
ejpam-6050	32	12	of	of	ADP
ejpam-6050	32	13	membership	membership	NOUN
ejpam-6050	32	14	is	be	AUX
ejpam-6050	32	15	implemented	implement	VERB
ejpam-6050	32	16	in	in	ADP
ejpam-6050	32	17	the	the	DET
ejpam-6050	32	18	form	form	NOUN
ejpam-6050	32	19	of	of	ADP
ejpam-6050	32	20	exponent	exponent	NOUN
ejpam-6050	32	21	,	,	PUNCT
ejpam-6050	32	22	which	which	PRON
ejpam-6050	32	23	is	be	AUX
ejpam-6050	32	24	the	the	DET
ejpam-6050	32	25	basic	basic	ADJ
ejpam-6050	32	26	parameter	parameter	NOUN
ejpam-6050	32	27	of	of	ADP
ejpam-6050	32	28	softening	soften	VERB
ejpam-6050	32	29	the	the	DET
ejpam-6050	32	30	set	set	NOUN
ejpam-6050	32	31	.	.	PUNCT
ejpam-6050	33	1	the	the	DET
ejpam-6050	33	2	use	use	NOUN
ejpam-6050	33	3	of	of	ADP
ejpam-6050	33	4	exponential	exponential	ADJ
ejpam-6050	33	5	functions	function	NOUN
ejpam-6050	33	6	in	in	ADP
ejpam-6050	33	7	fuzzy	fuzzy	ADJ
ejpam-6050	33	8	set	set	NOUN
ejpam-6050	33	9	theories	theory	NOUN
ejpam-6050	33	10	makes	make	VERB
ejpam-6050	33	11	it	it	PRON
ejpam-6050	33	12	possible	possible	ADJ
ejpam-6050	33	13	to	to	PART
ejpam-6050	33	14	more	more	ADV
ejpam-6050	33	15	accurately	accurately	ADV
ejpam-6050	33	16	model	model	VERB
ejpam-6050	33	17	a	a	DET
ejpam-6050	33	18	wide	wide	ADJ
ejpam-6050	33	19	range	range	NOUN
ejpam-6050	33	20	of	of	ADP
ejpam-6050	33	21	real	real	ADJ
ejpam-6050	33	22	life	life	NOUN
ejpam-6050	33	23	problems	problem	NOUN
ejpam-6050	33	24	such	such	ADJ
ejpam-6050	33	25	as	as	ADP
ejpam-6050	33	26	intelligent	intelligent	ADJ
ejpam-6050	33	27	decision	decision	NOUN
ejpam-6050	33	28	making	make	VERB
ejpam-6050	33	29	systems	system	NOUN
ejpam-6050	33	30	,	,	PUNCT
ejpam-6050	33	31	environmental	environmental	ADJ
ejpam-6050	33	32	,	,	PUNCT
ejpam-6050	33	33	economic	economic	ADJ
ejpam-6050	33	34	and	and	CCONJ
ejpam-6050	33	35	sociological	sociological	ADJ
ejpam-6050	33	36	forecasts	forecast	NOUN
ejpam-6050	33	37	(	(	PUNCT
ejpam-6050	33	38	hadi	hadi	NOUN
ejpam-6050	33	39	-	-	PUNCT
ejpam-6050	33	40	vencheh	vencheh	PROPN
ejpam-6050	33	41	&	&	CCONJ
ejpam-6050	33	42	mirjaberi	mirjaberi	PROPN
ejpam-6050	33	43	[	[	X
ejpam-6050	33	44	8	8	NUM
ejpam-6050	33	45	]	]	PUNCT
ejpam-6050	33	46	)	)	PUNCT
ejpam-6050	33	47	.	.	PUNCT
ejpam-6050	34	1	in	in	ADP
ejpam-6050	34	2	addition	addition	NOUN
ejpam-6050	34	3	liang	liang	PROPN
ejpam-6050	34	4	&	&	CCONJ
ejpam-6050	34	5	xu	xu	PROPN
ejpam-6050	35	1	[	[	X
ejpam-6050	35	2	9	9	NUM
ejpam-6050	35	3	]	]	PUNCT
ejpam-6050	35	4	,	,	PUNCT
ejpam-6050	35	5	the	the	DET
ejpam-6050	35	6	growing	grow	VERB
ejpam-6050	35	7	use	use	NOUN
ejpam-6050	35	8	of	of	ADP
ejpam-6050	35	9	fuzzy	fuzzy	ADJ
ejpam-6050	35	10	logic	logic	NOUN
ejpam-6050	35	11	in	in	ADP
ejpam-6050	35	12	practice	practice	NOUN
ejpam-6050	35	13	is	be	AUX
ejpam-6050	35	14	backed	back	VERB
ejpam-6050	35	15	by	by	ADP
ejpam-6050	35	16	new	new	ADJ
ejpam-6050	35	17	advances	advance	NOUN
ejpam-6050	35	18	in	in	ADP
ejpam-6050	35	19	multiple	multiple	ADJ
ejpam-6050	35	20	-	-	PUNCT
ejpam-6050	35	21	attribute	attribute	NOUN
ejpam-6050	35	22	decision	decision	NOUN
ejpam-6050	35	23	-	-	PUNCT
ejpam-6050	35	24	making	make	VERB
ejpam-6050	35	25	methods	method	NOUN
ejpam-6050	35	26	,	,	PUNCT
ejpam-6050	35	27	e.g.	e.g.	ADV
ejpam-6050	35	28	,	,	PUNCT
ejpam-6050	35	29	hesitant	hesitant	ADJ
ejpam-6050	35	30	pythagorean	pythagorean	PROPN
ejpam-6050	35	31	fuzzy	fuzzy	ADJ
ejpam-6050	35	32	sets	set	NOUN
ejpam-6050	35	33	and	and	CCONJ
ejpam-6050	35	34	exponential	exponential	ADJ
ejpam-6050	35	35	fuzzy	fuzzy	ADJ
ejpam-6050	35	36	topsis	topsis	NOUN
ejpam-6050	35	37	.	.	PUNCT
ejpam-6050	36	1	in	in	ADP
ejpam-6050	36	2	[	[	X
ejpam-6050	36	3	10	10	NUM
ejpam-6050	36	4	]	]	PUNCT
ejpam-6050	36	5	and	and	CCONJ
ejpam-6050	36	6	[	[	X
ejpam-6050	36	7	11	11	NUM
ejpam-6050	36	8	]	]	PUNCT
ejpam-6050	36	9	discussed	discuss	VERB
ejpam-6050	36	10	group	group	NOUN
ejpam-6050	36	11	decision	decision	NOUN
ejpam-6050	36	12	making	make	VERB
ejpam-6050	36	13	problems	problem	NOUN
ejpam-6050	36	14	.	.	PUNCT
ejpam-6050	37	1	the	the	DET
ejpam-6050	37	2	aim	aim	NOUN
ejpam-6050	37	3	of	of	ADP
ejpam-6050	37	4	this	this	DET
ejpam-6050	37	5	work	work	NOUN
ejpam-6050	37	6	is	be	AUX
ejpam-6050	37	7	to	to	PART
ejpam-6050	37	8	provide	provide	VERB
ejpam-6050	37	9	an	an	DET
ejpam-6050	37	10	extensive	extensive	ADJ
ejpam-6050	37	11	overview	overview	NOUN
ejpam-6050	37	12	of	of	ADP
ejpam-6050	37	13	exponential	exponential	ADJ
ejpam-6050	37	14	fuzzy	fuzzy	ADJ
ejpam-6050	37	15	sets	set	NOUN
ejpam-6050	37	16	,	,	PUNCT
ejpam-6050	37	17	such	such	ADJ
ejpam-6050	37	18	as	as	ADP
ejpam-6050	37	19	their	their	PRON
ejpam-6050	37	20	theory	theory	NOUN
ejpam-6050	37	21	and	and	CCONJ
ejpam-6050	37	22	numerous	numerous	ADJ
ejpam-6050	37	23	applications	application	NOUN
ejpam-6050	37	24	.	.	PUNCT
ejpam-6050	38	1	we	we	PRON
ejpam-6050	38	2	survey	survey	VERB
ejpam-6050	38	3	the	the	DET
ejpam-6050	38	4	existing	exist	VERB
ejpam-6050	38	5	material	material	NOUN
ejpam-6050	38	6	exponential	exponential	ADJ
ejpam-6050	38	7	membership	membership	NOUN
ejpam-6050	38	8	functions	function	NOUN
ejpam-6050	38	9	enhance	enhance	VERB
ejpam-6050	38	10	fuzzy	fuzzy	ADJ
ejpam-6050	38	11	modeling	modeling	NOUN
ejpam-6050	38	12	techniques	technique	NOUN
ejpam-6050	38	13	.	.	PUNCT
ejpam-6050	39	1	finally	finally	ADV
ejpam-6050	39	2	,	,	PUNCT
ejpam-6050	39	3	we	we	PRON
ejpam-6050	39	4	emphasize	emphasize	VERB
ejpam-6050	39	5	the	the	DET
ejpam-6050	39	6	advantages	advantage	NOUN
ejpam-6050	39	7	of	of	ADP
ejpam-6050	39	8	exponential	exponential	ADJ
ejpam-6050	39	9	fuzzy	fuzzy	ADJ
ejpam-6050	39	10	sets	set	NOUN
ejpam-6050	39	11	in	in	ADP
ejpam-6050	39	12	dealing	deal	VERB
ejpam-6050	39	13	with	with	ADP
ejpam-6050	39	14	dynamic	dynamic	ADJ
ejpam-6050	39	15	and	and	CCONJ
ejpam-6050	39	16	exponentially	exponentially	ADV
ejpam-6050	39	17	changing	change	VERB
ejpam-6050	39	18	uncertainty	uncertainty	NOUN
ejpam-6050	39	19	and	and	CCONJ
ejpam-6050	39	20	compare	compare	VERB
ejpam-6050	39	21	their	their	PRON
ejpam-6050	39	22	efficiencies	efficiency	NOUN
ejpam-6050	39	23	with	with	ADP
ejpam-6050	39	24	other	other	ADJ
ejpam-6050	39	25	fuzzy	fuzzy	ADJ
ejpam-6050	39	26	extensions	extension	NOUN
ejpam-6050	39	27	.	.	PUNCT
ejpam-6050	40	1	from	from	ADP
ejpam-6050	40	2	the	the	DET
ejpam-6050	40	3	above	above	ADJ
ejpam-6050	40	4	literature	literature	NOUN
ejpam-6050	40	5	we	we	PRON
ejpam-6050	40	6	found	find	VERB
ejpam-6050	40	7	the	the	DET
ejpam-6050	40	8	research	research	NOUN
ejpam-6050	40	9	gap	gap	NOUN
ejpam-6050	40	10	and	and	CCONJ
ejpam-6050	40	11	exponential	exponential	ADJ
ejpam-6050	40	12	fuzzy	fuzzy	ADJ
ejpam-6050	40	13	concept	concept	NOUN
ejpam-6050	40	14	we	we	PRON
ejpam-6050	40	15	introduced	introduce	VERB
ejpam-6050	40	16	.	.	PUNCT
ejpam-6050	41	1	this	this	DET
ejpam-6050	41	2	paper	paper	NOUN
ejpam-6050	41	3	is	be	AUX
ejpam-6050	41	4	organized	organize	VERB
ejpam-6050	41	5	as	as	ADP
ejpam-6050	41	6	:	:	PUNCT
ejpam-6050	41	7	the	the	DET
ejpam-6050	41	8	basic	basic	ADJ
ejpam-6050	41	9	definitions	definition	NOUN
ejpam-6050	41	10	in	in	ADP
ejpam-6050	41	11	section	section	NOUN
ejpam-6050	41	12	2	2	NUM
ejpam-6050	41	13	,	,	PUNCT
ejpam-6050	41	14	the	the	DET
ejpam-6050	41	15	basic	basic	ADJ
ejpam-6050	41	16	definitions	definition	NOUN
ejpam-6050	41	17	and	and	CCONJ
ejpam-6050	41	18	characteristics	characteristic	NOUN
ejpam-6050	41	19	of	of	ADP
ejpam-6050	41	20	exponential	exponential	ADJ
ejpam-6050	41	21	fuzzy	fuzzy	ADJ
ejpam-6050	41	22	sets	set	NOUN
ejpam-6050	41	23	are	be	AUX
ejpam-6050	41	24	covered	cover	VERB
ejpam-6050	41	25	in	in	ADP
ejpam-6050	41	26	section	section	NOUN
ejpam-6050	41	27	3	3	NUM
ejpam-6050	41	28	,	,	PUNCT
ejpam-6050	41	29	main	main	ADJ
ejpam-6050	41	30	results	result	NOUN
ejpam-6050	41	31	of	of	ADP
ejpam-6050	41	32	exponential	exponential	ADJ
ejpam-6050	41	33	fuzzy	fuzzy	ADJ
ejpam-6050	41	34	sets	set	NOUN
ejpam-6050	41	35	are	be	AUX
ejpam-6050	41	36	shown	show	VERB
ejpam-6050	41	37	in	in	ADP
ejpam-6050	41	38	section	section	NOUN
ejpam-6050	41	39	4	4	NUM
ejpam-6050	41	40	,	,	PUNCT
ejpam-6050	41	41	application	application	NOUN
ejpam-6050	41	42	in	in	ADP
ejpam-6050	41	43	section	section	NOUN
ejpam-6050	41	44	5	5	NUM
ejpam-6050	41	45	and	and	CCONJ
ejpam-6050	41	46	future	future	ADJ
ejpam-6050	41	47	research	research	NOUN
ejpam-6050	41	48	possibilities	possibility	NOUN
ejpam-6050	41	49	are	be	AUX
ejpam-6050	41	50	discussed	discuss	VERB
ejpam-6050	41	51	in	in	ADP
ejpam-6050	41	52	section	section	NOUN
ejpam-6050	41	53	6	6	NUM
ejpam-6050	41	54	.	.	NOUN
ejpam-6050	41	55	1.1	1.1	NUM
ejpam-6050	41	56	.	.	PUNCT
ejpam-6050	42	1	motivation	motivation	NOUN
ejpam-6050	42	2	•	•	NOUN
ejpam-6050	42	3	traditional	traditional	ADJ
ejpam-6050	42	4	f	f	NOUN
ejpam-6050	42	5	-	-	PUNCT
ejpam-6050	42	6	sets	set	NOUN
ejpam-6050	42	7	provide	provide	VERB
ejpam-6050	42	8	a	a	DET
ejpam-6050	42	9	foundation	foundation	NOUN
ejpam-6050	42	10	for	for	ADP
ejpam-6050	42	11	handling	handle	VERB
ejpam-6050	42	12	uncertainty	uncertainty	NOUN
ejpam-6050	42	13	,	,	PUNCT
ejpam-6050	42	14	but	but	CCONJ
ejpam-6050	42	15	they	they	PRON
ejpam-6050	42	16	have	have	VERB
ejpam-6050	42	17	limitations	limitation	NOUN
ejpam-6050	42	18	in	in	ADP
ejpam-6050	42	19	capturing	capture	VERB
ejpam-6050	42	20	rapid	rapid	ADJ
ejpam-6050	42	21	variations	variation	NOUN
ejpam-6050	42	22	in	in	ADP
ejpam-6050	42	23	membership	membership	NOUN
ejpam-6050	42	24	values	value	NOUN
ejpam-6050	42	25	.	.	PUNCT
ejpam-6050	43	1	•	•	NUM
ejpam-6050	43	2	efss	efss	NOUN
ejpam-6050	43	3	increase	increase	VERB
ejpam-6050	43	4	the	the	DET
ejpam-6050	43	5	flexibility	flexibility	NOUN
ejpam-6050	43	6	of	of	ADP
ejpam-6050	43	7	membership	membership	NOUN
ejpam-6050	43	8	functions	function	NOUN
ejpam-6050	43	9	by	by	ADP
ejpam-6050	43	10	introducing	introduce	VERB
ejpam-6050	43	11	a	a	DET
ejpam-6050	43	12	non	non	ADJ
ejpam-6050	43	13	-	-	ADJ
ejpam-6050	43	14	linear	linear	ADJ
ejpam-6050	43	15	transformation	transformation	NOUN
ejpam-6050	43	16	.	.	PUNCT
ejpam-6050	44	1	•	•	NUM
ejpam-6050	44	2	efs	ef	NOUN
ejpam-6050	44	3	increases	increase	VERB
ejpam-6050	44	4	decision	decision	NOUN
ejpam-6050	44	5	-	-	PUNCT
ejpam-6050	44	6	making	make	VERB
ejpam-6050	44	7	sensitivity	sensitivity	NOUN
ejpam-6050	44	8	,	,	PUNCT
ejpam-6050	44	9	especially	especially	ADV
ejpam-6050	44	10	in	in	ADP
ejpam-6050	44	11	situations	situation	NOUN
ejpam-6050	44	12	where	where	SCONJ
ejpam-6050	44	13	little	little	ADJ
ejpam-6050	44	14	m.	m.	NOUN
ejpam-6050	44	15	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	44	16	,	,	PUNCT
ejpam-6050	44	17	m.	m.	NOUN
ejpam-6050	44	18	rajeshwari	rajeshwari	NOUN
ejpam-6050	44	19	,	,	PUNCT
ejpam-6050	44	20	m.	m.	NOUN
ejpam-6050	44	21	alqahtani	alqahtani	PROPN
ejpam-6050	44	22	/	/	SYM
ejpam-6050	44	23	eur	eur	PROPN
ejpam-6050	44	24	.	.	PUNCT
ejpam-6050	45	1	j.	j.	PROPN
ejpam-6050	45	2	pure	pure	PROPN
ejpam-6050	45	3	appl	appl	PROPN
ejpam-6050	45	4	.	.	PROPN
ejpam-6050	45	5	math	math	PROPN
ejpam-6050	45	6	,	,	PUNCT
ejpam-6050	45	7	18	18	NUM
ejpam-6050	45	8	(	(	PUNCT
ejpam-6050	45	9	2	2	NUM
ejpam-6050	45	10	)	)	PUNCT
ejpam-6050	45	11	(	(	PUNCT
ejpam-6050	45	12	2025	2025	NUM
ejpam-6050	45	13	)	)	PUNCT
ejpam-6050	45	14	,	,	PUNCT
ejpam-6050	45	15	6050	6050	NUM
ejpam-6050	45	16	3	3	NUM
ejpam-6050	45	17	of	of	ADP
ejpam-6050	45	18	29	29	NUM
ejpam-6050	45	19	changes	change	NOUN
ejpam-6050	45	20	in	in	ADP
ejpam-6050	45	21	input	input	NOUN
ejpam-6050	45	22	have	have	VERB
ejpam-6050	45	23	a	a	DET
ejpam-6050	45	24	big	big	ADJ
ejpam-6050	45	25	influence	influence	NOUN
ejpam-6050	45	26	on	on	ADP
ejpam-6050	45	27	results	result	NOUN
ejpam-6050	45	28	.	.	PUNCT
ejpam-6050	46	1	•	•	NUM
ejpam-6050	46	2	by	by	ADP
ejpam-6050	46	3	adding	add	VERB
ejpam-6050	46	4	exponential	exponential	ADJ
ejpam-6050	46	5	functions	function	NOUN
ejpam-6050	46	6	,	,	PUNCT
ejpam-6050	46	7	it	it	PRON
ejpam-6050	46	8	expands	expand	VERB
ejpam-6050	46	9	on	on	ADP
ejpam-6050	46	10	traditional	traditional	ADJ
ejpam-6050	46	11	fuzzy	fuzzy	ADJ
ejpam-6050	46	12	logic	logic	NOUN
ejpam-6050	46	13	and	and	CCONJ
ejpam-6050	46	14	is	be	AUX
ejpam-6050	46	15	appropriate	appropriate	ADJ
ejpam-6050	46	16	for	for	ADP
ejpam-6050	46	17	more	more	ADJ
ejpam-6050	46	18	complex	complex	ADJ
ejpam-6050	46	19	uses	use	NOUN
ejpam-6050	46	20	like	like	ADP
ejpam-6050	46	21	pattern	pattern	NOUN
ejpam-6050	46	22	identification	identification	NOUN
ejpam-6050	46	23	and	and	CCONJ
ejpam-6050	46	24	risk	risk	NOUN
ejpam-6050	46	25	assessment	assessment	NOUN
ejpam-6050	46	26	.	.	PUNCT
ejpam-6050	47	1	•	•	NUM
ejpam-6050	47	2	efs	ef	NOUN
ejpam-6050	47	3	better	well	ADV
ejpam-6050	47	4	captures	capture	VERB
ejpam-6050	47	5	uncertainty	uncertainty	NOUN
ejpam-6050	47	6	and	and	CCONJ
ejpam-6050	47	7	hesitancy	hesitancy	NOUN
ejpam-6050	47	8	in	in	ADP
ejpam-6050	47	9	expert	expert	NOUN
ejpam-6050	47	10	opinions	opinion	NOUN
ejpam-6050	47	11	,	,	PUNCT
ejpam-6050	47	12	leading	lead	VERB
ejpam-6050	47	13	to	to	ADP
ejpam-6050	47	14	improved	improve	VERB
ejpam-6050	47	15	diagnostic	diagnostic	ADJ
ejpam-6050	47	16	accuracy	accuracy	NOUN
ejpam-6050	47	17	.	.	PUNCT
ejpam-6050	48	1	•	•	NUM
ejpam-6050	48	2	efs	ef	NOUN
ejpam-6050	48	3	improves	improve	VERB
ejpam-6050	48	4	edge	edge	NOUN
ejpam-6050	48	5	detection	detection	NOUN
ejpam-6050	48	6	and	and	CCONJ
ejpam-6050	48	7	noise	noise	NOUN
ejpam-6050	48	8	reduction	reduction	NOUN
ejpam-6050	48	9	in	in	ADP
ejpam-6050	48	10	image	image	NOUN
ejpam-6050	48	11	analysis	analysis	NOUN
ejpam-6050	48	12	,	,	PUNCT
ejpam-6050	48	13	leading	lead	VERB
ejpam-6050	48	14	to	to	ADP
ejpam-6050	48	15	clearer	clear	ADJ
ejpam-6050	48	16	and	and	CCONJ
ejpam-6050	48	17	more	more	ADV
ejpam-6050	48	18	accurate	accurate	ADJ
ejpam-6050	48	19	image	image	NOUN
ejpam-6050	48	20	segmentation	segmentation	NOUN
ejpam-6050	48	21	.	.	PUNCT
ejpam-6050	49	1	1.2	1.2	NUM
ejpam-6050	49	2	.	.	X
ejpam-6050	49	3	need	need	NOUN
ejpam-6050	49	4	of	of	ADP
ejpam-6050	49	5	efs	ef	NOUN
ejpam-6050	49	6	exponential	exponential	ADJ
ejpam-6050	49	7	fuzzy	fuzzy	ADJ
ejpam-6050	49	8	sets	set	NOUN
ejpam-6050	49	9	address	address	VERB
ejpam-6050	49	10	this	this	DET
ejpam-6050	49	11	issue	issue	NOUN
ejpam-6050	49	12	by	by	ADP
ejpam-6050	49	13	incorporating	incorporate	VERB
ejpam-6050	49	14	an	an	DET
ejpam-6050	49	15	exponential	exponential	ADJ
ejpam-6050	49	16	function	function	NOUN
ejpam-6050	49	17	into	into	ADP
ejpam-6050	49	18	the	the	DET
ejpam-6050	49	19	membership	membership	NOUN
ejpam-6050	49	20	structure	structure	NOUN
ejpam-6050	49	21	.	.	PUNCT
ejpam-6050	50	1	this	this	PRON
ejpam-6050	50	2	allows	allow	VERB
ejpam-6050	50	3	for	for	ADP
ejpam-6050	50	4	a	a	DET
ejpam-6050	50	5	more	more	ADV
ejpam-6050	50	6	flexible	flexible	ADJ
ejpam-6050	50	7	and	and	CCONJ
ejpam-6050	50	8	precise	precise	ADJ
ejpam-6050	50	9	representation	representation	NOUN
ejpam-6050	50	10	of	of	ADP
ejpam-6050	50	11	uncertainty	uncertainty	NOUN
ejpam-6050	50	12	,	,	PUNCT
ejpam-6050	50	13	especially	especially	ADV
ejpam-6050	50	14	in	in	ADP
ejpam-6050	50	15	situations	situation	NOUN
ejpam-6050	50	16	where	where	SCONJ
ejpam-6050	50	17	small	small	ADJ
ejpam-6050	50	18	changes	change	NOUN
ejpam-6050	50	19	in	in	ADP
ejpam-6050	50	20	input	input	NOUN
ejpam-6050	50	21	values	value	NOUN
ejpam-6050	50	22	lead	lead	VERB
ejpam-6050	50	23	to	to	ADP
ejpam-6050	50	24	significant	significant	ADJ
ejpam-6050	50	25	variations	variation	NOUN
ejpam-6050	50	26	in	in	ADP
ejpam-6050	50	27	membership	membership	NOUN
ejpam-6050	50	28	degrees	degree	NOUN
ejpam-6050	50	29	.	.	PUNCT
ejpam-6050	51	1	for	for	ADP
ejpam-6050	51	2	example	example	NOUN
ejpam-6050	51	3	,	,	PUNCT
ejpam-6050	51	4	in	in	ADP
ejpam-6050	51	5	medical	medical	ADJ
ejpam-6050	51	6	diagnosis	diagnosis	NOUN
ejpam-6050	51	7	,	,	PUNCT
ejpam-6050	51	8	financial	financial	ADJ
ejpam-6050	51	9	risk	risk	NOUN
ejpam-6050	51	10	assessment	assessment	NOUN
ejpam-6050	51	11	,	,	PUNCT
ejpam-6050	51	12	and	and	CCONJ
ejpam-6050	51	13	engineering	engineering	NOUN
ejpam-6050	51	14	problems	problem	NOUN
ejpam-6050	51	15	,	,	PUNCT
ejpam-6050	51	16	uncertainty	uncertainty	NOUN
ejpam-6050	51	17	often	often	ADV
ejpam-6050	51	18	behaves	behave	VERB
ejpam-6050	51	19	in	in	ADP
ejpam-6050	51	20	a	a	DET
ejpam-6050	51	21	nonlinear	nonlinear	ADJ
ejpam-6050	51	22	manner	manner	NOUN
ejpam-6050	51	23	,	,	PUNCT
ejpam-6050	51	24	making	make	VERB
ejpam-6050	51	25	exponential	exponential	ADJ
ejpam-6050	51	26	fuzzy	fuzzy	ADJ
ejpam-6050	51	27	sets	set	VERB
ejpam-6050	51	28	a	a	DET
ejpam-6050	51	29	better	well	ADJ
ejpam-6050	51	30	choice	choice	NOUN
ejpam-6050	51	31	.	.	PUNCT
ejpam-6050	52	1	1.3	1.3	NUM
ejpam-6050	52	2	.	.	PUNCT
ejpam-6050	52	3	advantages	advantage	NOUN
ejpam-6050	52	4	of	of	ADP
ejpam-6050	52	5	efs	ef	NOUN
ejpam-6050	52	6	•	•	NOUN
ejpam-6050	52	7	suitable	suitable	ADJ
ejpam-6050	52	8	for	for	ADP
ejpam-6050	52	9	situations	situation	NOUN
ejpam-6050	52	10	where	where	SCONJ
ejpam-6050	52	11	uncertainty	uncertainty	NOUN
ejpam-6050	52	12	follows	follow	VERB
ejpam-6050	52	13	an	an	DET
ejpam-6050	52	14	exponential	exponential	ADJ
ejpam-6050	52	15	pattern	pattern	NOUN
ejpam-6050	52	16	rather	rather	ADV
ejpam-6050	52	17	than	than	ADP
ejpam-6050	52	18	a	a	DET
ejpam-6050	52	19	linear	linear	ADJ
ejpam-6050	52	20	one	one	NUM
ejpam-6050	52	21	.	.	PUNCT
ejpam-6050	53	1	•	•	NOUN
ejpam-6050	53	2	ensures	ensure	VERB
ejpam-6050	53	3	gradual	gradual	ADJ
ejpam-6050	53	4	changes	change	NOUN
ejpam-6050	53	5	in	in	ADP
ejpam-6050	53	6	membership	membership	NOUN
ejpam-6050	53	7	values	value	NOUN
ejpam-6050	53	8	,	,	PUNCT
ejpam-6050	53	9	preventing	prevent	VERB
ejpam-6050	53	10	abrupt	abrupt	ADJ
ejpam-6050	53	11	shifts	shift	NOUN
ejpam-6050	53	12	.	.	PUNCT
ejpam-6050	54	1	•	•	NUM
ejpam-6050	54	2	more	more	ADV
ejpam-6050	54	3	responsive	responsive	ADJ
ejpam-6050	54	4	to	to	ADP
ejpam-6050	54	5	small	small	ADJ
ejpam-6050	54	6	variations	variation	NOUN
ejpam-6050	54	7	in	in	ADP
ejpam-6050	54	8	data	datum	NOUN
ejpam-6050	54	9	,	,	PUNCT
ejpam-6050	54	10	improving	improve	VERB
ejpam-6050	54	11	accuracy	accuracy	NOUN
ejpam-6050	54	12	in	in	ADP
ejpam-6050	54	13	decision	decision	NOUN
ejpam-6050	54	14	-	-	PUNCT
ejpam-6050	54	15	making	making	NOUN
ejpam-6050	54	16	.	.	PUNCT
ejpam-6050	55	1	•	•	NUM
ejpam-6050	55	2	enhances	enhance	NOUN
ejpam-6050	55	3	accuracy	accuracy	NOUN
ejpam-6050	55	4	and	and	CCONJ
ejpam-6050	55	5	robustness	robustness	NOUN
ejpam-6050	55	6	in	in	ADP
ejpam-6050	55	7	multi	multi	ADJ
ejpam-6050	55	8	-	-	ADJ
ejpam-6050	55	9	criteria	criterion	NOUN
ejpam-6050	55	10	decision	decision	NOUN
ejpam-6050	55	11	-	-	PUNCT
ejpam-6050	55	12	making	making	NOUN
ejpam-6050	55	13	(	(	PUNCT
ejpam-6050	55	14	mcdm	mcdm	ADJ
ejpam-6050	55	15	)	)	PUNCT
ejpam-6050	55	16	and	and	CCONJ
ejpam-6050	55	17	expert	expert	NOUN
ejpam-6050	55	18	systems	system	NOUN
ejpam-6050	55	19	.	.	PUNCT
ejpam-6050	56	1	1.4	1.4	NUM
ejpam-6050	56	2	.	.	PUNCT
ejpam-6050	56	3	novelty	novelty	NOUN
ejpam-6050	56	4	•	•	NOUN
ejpam-6050	56	5	describes	describe	VERB
ejpam-6050	56	6	a	a	DET
ejpam-6050	56	7	new	new	ADJ
ejpam-6050	56	8	membership	membership	NOUN
ejpam-6050	56	9	function	function	NOUN
ejpam-6050	56	10	transformation	transformation	NOUN
ejpam-6050	56	11	for	for	ADP
ejpam-6050	56	12	an	an	DET
ejpam-6050	56	13	efs	ef	NOUN
ejpam-6050	56	14	.	.	NOUN
ejpam-6050	56	15	•	•	NUM
ejpam-6050	56	16	incorporates	incorporate	VERB
ejpam-6050	56	17	exponential	exponential	ADJ
ejpam-6050	56	18	scaling	scaling	NOUN
ejpam-6050	56	19	to	to	PART
ejpam-6050	56	20	improve	improve	VERB
ejpam-6050	56	21	the	the	DET
ejpam-6050	56	22	representation	representation	NOUN
ejpam-6050	56	23	of	of	ADP
ejpam-6050	56	24	uncertainty	uncertainty	NOUN
ejpam-6050	56	25	in	in	ADP
ejpam-6050	56	26	conventional	conventional	ADJ
ejpam-6050	56	27	fuzzy	fuzzy	ADJ
ejpam-6050	56	28	set	set	NOUN
ejpam-6050	56	29	theory	theory	NOUN
ejpam-6050	56	30	.	.	PUNCT
ejpam-6050	57	1	•	•	NUM
ejpam-6050	57	2	enhances	enhance	VERB
ejpam-6050	57	3	similarity	similarity	NOUN
ejpam-6050	57	4	and	and	CCONJ
ejpam-6050	57	5	divergence	divergence	NOUN
ejpam-6050	57	6	metrics	metric	NOUN
ejpam-6050	57	7	to	to	PART
ejpam-6050	57	8	help	help	VERB
ejpam-6050	57	9	make	make	VERB
ejpam-6050	57	10	better	well	ADJ
ejpam-6050	57	11	decisions	decision	NOUN
ejpam-6050	57	12	.	.	PUNCT
ejpam-6050	58	1	2	2	X
ejpam-6050	58	2	.	.	X
ejpam-6050	58	3	preliminaries	preliminary	NOUN
ejpam-6050	58	4	definition	definition	NOUN
ejpam-6050	58	5	1	1	NUM
ejpam-6050	58	6	.	.	PUNCT
ejpam-6050	59	1	[	[	X
ejpam-6050	59	2	1	1	X
ejpam-6050	59	3	]	]	PUNCT
ejpam-6050	59	4	a	a	DET
ejpam-6050	59	5	fuzzy	fuzzy	ADJ
ejpam-6050	59	6	set	set	VERB
ejpam-6050	59	7	a	a	PRON
ejpam-6050	59	8	in	in	ADP
ejpam-6050	59	9	a	a	DET
ejpam-6050	59	10	universe	universe	NOUN
ejpam-6050	59	11	of	of	ADP
ejpam-6050	59	12	discourse	discourse	NOUN
ejpam-6050	59	13	z	z	PROPN
ejpam-6050	59	14	is	be	AUX
ejpam-6050	59	15	characterized	characterize	VERB
ejpam-6050	59	16	by	by	ADP
ejpam-6050	59	17	a	a	DET
ejpam-6050	59	18	membership	membership	NOUN
ejpam-6050	59	19	function	function	NOUN
ejpam-6050	59	20	ℵa	ℵa	NOUN
ejpam-6050	59	21	which	which	PRON
ejpam-6050	59	22	takes	take	VERB
ejpam-6050	59	23	the	the	DET
ejpam-6050	59	24	value	value	NOUN
ejpam-6050	59	25	in	in	ADP
ejpam-6050	59	26	the	the	DET
ejpam-6050	59	27	unit	unit	NOUN
ejpam-6050	59	28	interval	interval	NOUN
ejpam-6050	59	29	[	[	X
ejpam-6050	59	30	0	0	NUM
ejpam-6050	59	31	,	,	PUNCT
ejpam-6050	59	32	1	1	NUM
ejpam-6050	59	33	]	]	PUNCT
ejpam-6050	59	34	,	,	PUNCT
ejpam-6050	59	35	ℵa(s	ℵa(s	ADJ
ejpam-6050	59	36	)	)	PUNCT
ejpam-6050	60	1	=	=	SYM
ejpam-6050	60	2	z	z	X
ejpam-6050	60	3	→	→	PUNCT
ejpam-6050	61	1	[	[	X
ejpam-6050	61	2	0	0	NUM
ejpam-6050	61	3	,	,	PUNCT
ejpam-6050	61	4	1	1	NUM
ejpam-6050	61	5	]	]	PUNCT
ejpam-6050	61	6	.	.	PUNCT
ejpam-6050	62	1	the	the	DET
ejpam-6050	62	2	value	value	NOUN
ejpam-6050	62	3	of	of	ADP
ejpam-6050	62	4	ℵa(s	ℵa(s	NOUN
ejpam-6050	62	5	)	)	PUNCT
ejpam-6050	62	6	represents	represent	VERB
ejpam-6050	62	7	the	the	DET
ejpam-6050	62	8	grade	grade	NOUN
ejpam-6050	62	9	of	of	ADP
ejpam-6050	62	10	membership	membership	NOUN
ejpam-6050	62	11	of	of	ADP
ejpam-6050	62	12	z	z	PROPN
ejpam-6050	62	13	in	in	ADP
ejpam-6050	62	14	å	å	PROPN
ejpam-6050	62	15	and	and	CCONJ
ejpam-6050	62	16	is	be	AUX
ejpam-6050	62	17	a	a	DET
ejpam-6050	62	18	point	point	NOUN
ejpam-6050	62	19	in	in	ADP
ejpam-6050	62	20	[	[	X
ejpam-6050	62	21	0	0	NUM
ejpam-6050	62	22	,	,	PUNCT
ejpam-6050	62	23	1	1	NUM
ejpam-6050	62	24	]	]	PUNCT
ejpam-6050	62	25	.	.	PUNCT
ejpam-6050	63	1	m.	m.	PROPN
ejpam-6050	63	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	63	3	,	,	PUNCT
ejpam-6050	63	4	m.	m.	NOUN
ejpam-6050	63	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	63	6	,	,	PUNCT
ejpam-6050	63	7	m.	m.	NOUN
ejpam-6050	63	8	alqahtani	alqahtani	PROPN
ejpam-6050	63	9	/	/	SYM
ejpam-6050	63	10	eur	eur	PROPN
ejpam-6050	63	11	.	.	PUNCT
ejpam-6050	64	1	j.	j.	PROPN
ejpam-6050	64	2	pure	pure	PROPN
ejpam-6050	64	3	appl	appl	PROPN
ejpam-6050	64	4	.	.	PROPN
ejpam-6050	64	5	math	math	PROPN
ejpam-6050	64	6	,	,	PUNCT
ejpam-6050	64	7	18	18	NUM
ejpam-6050	64	8	(	(	PUNCT
ejpam-6050	64	9	2	2	NUM
ejpam-6050	64	10	)	)	PUNCT
ejpam-6050	64	11	(	(	PUNCT
ejpam-6050	64	12	2025	2025	NUM
ejpam-6050	64	13	)	)	PUNCT
ejpam-6050	64	14	,	,	PUNCT
ejpam-6050	64	15	6050	6050	NUM
ejpam-6050	64	16	4	4	NUM
ejpam-6050	64	17	of	of	ADP
ejpam-6050	64	18	29	29	NUM
ejpam-6050	64	19	definition	definition	NOUN
ejpam-6050	64	20	2	2	NUM
ejpam-6050	64	21	.	.	PUNCT
ejpam-6050	65	1	[	[	X
ejpam-6050	65	2	1	1	X
ejpam-6050	65	3	]	]	PUNCT
ejpam-6050	65	4	the	the	DET
ejpam-6050	65	5	complement	complement	NOUN
ejpam-6050	65	6	a′	a′	NOUN
ejpam-6050	65	7	is	be	AUX
ejpam-6050	65	8	defined	define	VERB
ejpam-6050	65	9	by	by	ADP
ejpam-6050	65	10	ℵa′	ℵa′	PROPN
ejpam-6050	65	11	(	(	PUNCT
ejpam-6050	65	12	s	s	X
ejpam-6050	65	13	)	)	PUNCT
ejpam-6050	65	14	=	=	SYM
ejpam-6050	65	15	1	1	NUM
ejpam-6050	65	16	−	−	NOUN
ejpam-6050	65	17	ℵa(s).where	ℵa(s).where	NOUN
ejpam-6050	65	18	a	a	PRON
ejpam-6050	65	19	is	be	AUX
ejpam-6050	65	20	a	a	DET
ejpam-6050	65	21	f	f	NOUN
ejpam-6050	65	22	-	-	PUNCT
ejpam-6050	65	23	set	set	VERB
ejpam-6050	65	24	in	in	ADP
ejpam-6050	65	25	z.	z.	PROPN
ejpam-6050	65	26	definition	definition	NOUN
ejpam-6050	65	27	3	3	NUM
ejpam-6050	65	28	.	.	PUNCT
ejpam-6050	66	1	[	[	X
ejpam-6050	66	2	12	12	NUM
ejpam-6050	66	3	]	]	X
ejpam-6050	66	4	if	if	SCONJ
ejpam-6050	66	5	ℵa	ℵa	NOUN
ejpam-6050	66	6	and	and	CCONJ
ejpam-6050	66	7	ℵb	ℵb	ADP
ejpam-6050	66	8	are	be	AUX
ejpam-6050	66	9	membership	membership	NOUN
ejpam-6050	66	10	functions	function	NOUN
ejpam-6050	66	11	of	of	ADP
ejpam-6050	66	12	f	f	NOUN
ejpam-6050	66	13	-	-	PUNCT
ejpam-6050	66	14	sets	set	VERB
ejpam-6050	66	15	a	a	PRON
ejpam-6050	66	16	and	and	CCONJ
ejpam-6050	66	17	b	b	NOUN
ejpam-6050	66	18	,	,	PUNCT
ejpam-6050	66	19	then	then	ADV
ejpam-6050	66	20	the	the	DET
ejpam-6050	66	21	union	union	NOUN
ejpam-6050	66	22	and	and	CCONJ
ejpam-6050	66	23	intersection	intersection	NOUN
ejpam-6050	66	24	of	of	ADP
ejpam-6050	66	25	two	two	NUM
ejpam-6050	66	26	f	f	NOUN
ejpam-6050	66	27	-	-	PUNCT
ejpam-6050	66	28	sets	set	NOUN
ejpam-6050	66	29	is	be	AUX
ejpam-6050	66	30	ℵa∪b(s	ℵa∪b(	NOUN
ejpam-6050	66	31	)	)	PUNCT
ejpam-6050	67	1	=	=	SYM
ejpam-6050	67	2	max	max	PROPN
ejpam-6050	67	3	{	{	PUNCT
ejpam-6050	67	4	ℵa(s),ℵb(s	ℵa(s),ℵb(	NOUN
ejpam-6050	67	5	)	)	PUNCT
ejpam-6050	67	6	}	}	PUNCT
ejpam-6050	67	7	,	,	PUNCT
ejpam-6050	67	8	∀s	∀s	PROPN
ejpam-6050	67	9	∈	∈	PROPN
ejpam-6050	67	10	z.	z.	PROPN
ejpam-6050	67	11	ℵa∩b(s	ℵa∩b(s	PROPN
ejpam-6050	67	12	)	)	PUNCT
ejpam-6050	68	1	=	=	SYM
ejpam-6050	68	2	min	min	NOUN
ejpam-6050	68	3	{	{	PUNCT
ejpam-6050	68	4	ℵa(s),ℵb(s	ℵa(s),ℵb(	NOUN
ejpam-6050	68	5	)	)	PUNCT
ejpam-6050	68	6	}	}	PUNCT
ejpam-6050	68	7	,	,	PUNCT
ejpam-6050	68	8	∀s	∀s	PROPN
ejpam-6050	68	9	∈	∈	PROPN
ejpam-6050	68	10	z.	z.	PROPN
ejpam-6050	68	11	definition	definition	NOUN
ejpam-6050	68	12	4	4	NUM
ejpam-6050	68	13	.	.	PUNCT
ejpam-6050	69	1	[	[	X
ejpam-6050	69	2	12	12	NUM
ejpam-6050	69	3	]	]	X
ejpam-6050	69	4	the	the	DET
ejpam-6050	69	5	difference	difference	NOUN
ejpam-6050	69	6	of	of	ADP
ejpam-6050	69	7	two	two	NUM
ejpam-6050	69	8	f	f	NOUN
ejpam-6050	69	9	-	-	PUNCT
ejpam-6050	69	10	sets	set	VERB
ejpam-6050	69	11	a	a	PRON
ejpam-6050	69	12	and	and	CCONJ
ejpam-6050	69	13	b	b	NOUN
ejpam-6050	69	14	is	be	AUX
ejpam-6050	69	15	given	give	VERB
ejpam-6050	69	16	by	by	ADP
ejpam-6050	69	17	a−	a−	PROPN
ejpam-6050	69	18	b	b	PROPN
ejpam-6050	69	19	=	=	PUNCT
ejpam-6050	69	20	a	a	DET
ejpam-6050	69	21	∩	∩	ADJ
ejpam-6050	69	22	bc	bc	PROPN
ejpam-6050	69	23	.	.	PROPN
ejpam-6050	69	24	definition	definition	NOUN
ejpam-6050	69	25	5	5	NUM
ejpam-6050	69	26	.	.	PUNCT
ejpam-6050	70	1	[	[	X
ejpam-6050	70	2	12	12	NUM
ejpam-6050	70	3	]	]	PUNCT
ejpam-6050	70	4	a	a	DET
ejpam-6050	70	5	bounded	bounded	ADJ
ejpam-6050	70	6	difference	difference	NOUN
ejpam-6050	70	7	of	of	ADP
ejpam-6050	70	8	two	two	NUM
ejpam-6050	70	9	f	f	NOUN
ejpam-6050	70	10	-	-	PUNCT
ejpam-6050	70	11	sets	set	VERB
ejpam-6050	70	12	a	a	PRON
ejpam-6050	70	13	and	and	CCONJ
ejpam-6050	70	14	b	b	NOUN
ejpam-6050	70	15	is	be	AUX
ejpam-6050	70	16	given	give	VERB
ejpam-6050	70	17	by	by	ADP
ejpam-6050	70	18	ℵaob(s	ℵaob(	NOUN
ejpam-6050	70	19	)	)	PUNCT
ejpam-6050	71	1	=	=	SYM
ejpam-6050	71	2	max	max	PROPN
ejpam-6050	72	1	[	[	X
ejpam-6050	72	2	o,ℵa(s),ℵb(s	o,ℵa(s),ℵb(	NOUN
ejpam-6050	72	3	)	)	PUNCT
ejpam-6050	72	4	]	]	PUNCT
ejpam-6050	72	5	definition	definition	NOUN
ejpam-6050	72	6	6	6	NUM
ejpam-6050	72	7	.	.	PUNCT
ejpam-6050	73	1	[	[	X
ejpam-6050	73	2	12	12	NUM
ejpam-6050	73	3	]	]	PUNCT
ejpam-6050	73	4	the	the	DET
ejpam-6050	73	5	disjoint	disjoint	ADJ
ejpam-6050	73	6	sum	sum	NOUN
ejpam-6050	73	7	of	of	ADP
ejpam-6050	73	8	two	two	NUM
ejpam-6050	73	9	f	f	NOUN
ejpam-6050	73	10	-	-	PUNCT
ejpam-6050	73	11	sets	set	NOUN
ejpam-6050	73	12	is	be	AUX
ejpam-6050	73	13	given	give	VERB
ejpam-6050	73	14	by	by	ADP
ejpam-6050	73	15	ℵa⊗b(s	ℵa⊗b(	NOUN
ejpam-6050	73	16	)	)	PUNCT
ejpam-6050	73	17	=	=	SYM
ejpam-6050	73	18	|⊗,ℵa(s),ℵb(s)|	|⊗,ℵa(s),ℵb(s)|	NOUN
ejpam-6050	73	19	where	where	SCONJ
ejpam-6050	73	20	ℵa(s	ℵa(s	ADJ
ejpam-6050	73	21	)	)	PUNCT
ejpam-6050	73	22	and	and	CCONJ
ejpam-6050	73	23	ℵb(s	ℵb(	NOUN
ejpam-6050	73	24	)	)	PUNCT
ejpam-6050	73	25	are	be	AUX
ejpam-6050	73	26	membership	membership	NOUN
ejpam-6050	73	27	function	function	NOUN
ejpam-6050	73	28	of	of	ADP
ejpam-6050	73	29	a	a	DET
ejpam-6050	73	30	and	and	CCONJ
ejpam-6050	73	31	b.	b.	PROPN
ejpam-6050	73	32	definition	definition	NOUN
ejpam-6050	73	33	7	7	NUM
ejpam-6050	73	34	.	.	PUNCT
ejpam-6050	74	1	let	let	VERB
ejpam-6050	74	2	a	a	PRON
ejpam-6050	74	3	and	and	CCONJ
ejpam-6050	74	4	b	b	NOUN
ejpam-6050	74	5	be	be	AUX
ejpam-6050	74	6	any	any	DET
ejpam-6050	74	7	two	two	NUM
ejpam-6050	74	8	f	f	NOUN
ejpam-6050	74	9	-	-	PUNCT
ejpam-6050	74	10	sets	set	NOUN
ejpam-6050	74	11	of	of	ADP
ejpam-6050	74	12	z	z	NOUN
ejpam-6050	74	13	then	then	ADV
ejpam-6050	74	14	the	the	DET
ejpam-6050	74	15	disjunctive	disjunctive	ADJ
ejpam-6050	74	16	sum	sum	NOUN
ejpam-6050	74	17	is	be	AUX
ejpam-6050	74	18	given	give	VERB
ejpam-6050	74	19	by	by	ADP
ejpam-6050	74	20	:	:	PUNCT
ejpam-6050	74	21	ℵa∆b(s	ℵa∆b(	NOUN
ejpam-6050	74	22	)	)	PUNCT
ejpam-6050	74	23	=	=	SYM
ejpam-6050	74	24	(	(	PUNCT
ejpam-6050	74	25	a	a	DET
ejpam-6050	74	26	∩	∩	ADJ
ejpam-6050	74	27	bc	bc	NOUN
ejpam-6050	74	28	)	)	PUNCT
ejpam-6050	74	29	∪	∪	NOUN
ejpam-6050	74	30	(	(	PUNCT
ejpam-6050	74	31	ac	ac	PROPN
ejpam-6050	74	32	∩	∩	ADJ
ejpam-6050	74	33	b	b	NOUN
ejpam-6050	74	34	)	)	PUNCT
ejpam-6050	75	1	=	=	SYM
ejpam-6050	75	2	(	(	PUNCT
ejpam-6050	75	3	a	a	DET
ejpam-6050	75	4	∗	∗	NOUN
ejpam-6050	75	5	bc)⊕	bc)⊕	NOUN
ejpam-6050	75	6	(	(	PUNCT
ejpam-6050	75	7	ac	ac	PROPN
ejpam-6050	75	8	∗	∗	PROPN
ejpam-6050	75	9	b	b	NOUN
ejpam-6050	75	10	)	)	PUNCT
ejpam-6050	75	11	.	.	PUNCT
ejpam-6050	76	1	definition	definition	NOUN
ejpam-6050	76	2	8	8	NUM
ejpam-6050	76	3	.	.	PUNCT
ejpam-6050	77	1	let	let	VERB
ejpam-6050	77	2	a	a	PRON
ejpam-6050	77	3	and	and	CCONJ
ejpam-6050	77	4	b	b	NOUN
ejpam-6050	77	5	be	be	AUX
ejpam-6050	77	6	any	any	DET
ejpam-6050	77	7	two	two	NUM
ejpam-6050	77	8	f	f	NOUN
ejpam-6050	77	9	-	-	PUNCT
ejpam-6050	77	10	sets	set	NOUN
ejpam-6050	77	11	of	of	ADP
ejpam-6050	77	12	z	z	NOUN
ejpam-6050	77	13	then	then	ADV
ejpam-6050	77	14	the	the	DET
ejpam-6050	77	15	equivalence	equivalence	NOUN
ejpam-6050	77	16	formula	formula	NOUN
ejpam-6050	77	17	is	be	AUX
ejpam-6050	77	18	(	(	PUNCT
ejpam-6050	77	19	ac	ac	PROPN
ejpam-6050	77	20	∪	∪	PROPN
ejpam-6050	77	21	b	b	NOUN
ejpam-6050	77	22	)	)	PUNCT
ejpam-6050	77	23	∩	∩	NOUN
ejpam-6050	77	24	(	(	PUNCT
ejpam-6050	77	25	a	a	DET
ejpam-6050	77	26	∪	∪	X
ejpam-6050	77	27	bc	bc	PROPN
ejpam-6050	77	28	)	)	PUNCT
ejpam-6050	78	1	=	=	PUNCT
ejpam-6050	78	2	(	(	PUNCT
ejpam-6050	78	3	ac	ac	PROPN
ejpam-6050	78	4	∩	∩	PROPN
ejpam-6050	78	5	bc	bc	PROPN
ejpam-6050	78	6	)	)	PUNCT
ejpam-6050	78	7	∪	∪	NOUN
ejpam-6050	78	8	(	(	PUNCT
ejpam-6050	78	9	a	a	DET
ejpam-6050	78	10	∩	∩	ADJ
ejpam-6050	78	11	b	b	NOUN
ejpam-6050	78	12	)	)	PUNCT
ejpam-6050	78	13	.	.	PUNCT
ejpam-6050	79	1	definition	definition	NOUN
ejpam-6050	79	2	9	9	NUM
ejpam-6050	79	3	.	.	NOUN
ejpam-6050	79	4	symmetrical	symmetrical	ADJ
ejpam-6050	79	5	difference	difference	NOUN
ejpam-6050	79	6	formula	formula	NOUN
ejpam-6050	79	7	for	for	ADP
ejpam-6050	79	8	two	two	NUM
ejpam-6050	79	9	fuzzy	fuzzy	ADJ
ejpam-6050	79	10	sets	set	NOUN
ejpam-6050	79	11	a	a	PRON
ejpam-6050	79	12	and	and	CCONJ
ejpam-6050	79	13	b	b	NOUN
ejpam-6050	79	14	is	be	AUX
ejpam-6050	79	15	given	give	VERB
ejpam-6050	79	16	by	by	ADP
ejpam-6050	79	17	(	(	PUNCT
ejpam-6050	79	18	ac	ac	PROPN
ejpam-6050	79	19	∩	∩	ADJ
ejpam-6050	79	20	b	b	X
ejpam-6050	79	21	)	)	PUNCT
ejpam-6050	79	22	∪	∪	NOUN
ejpam-6050	79	23	(	(	PUNCT
ejpam-6050	79	24	a	a	DET
ejpam-6050	79	25	∩	∩	ADJ
ejpam-6050	79	26	bc	bc	NOUN
ejpam-6050	79	27	)	)	PUNCT
ejpam-6050	79	28	=	=	SYM
ejpam-6050	79	29	(	(	PUNCT
ejpam-6050	79	30	ac	ac	PROPN
ejpam-6050	79	31	∪	∪	PROPN
ejpam-6050	79	32	bc	bc	PROPN
ejpam-6050	79	33	)	)	PUNCT
ejpam-6050	79	34	∩	∩	NOUN
ejpam-6050	79	35	(	(	PUNCT
ejpam-6050	79	36	a	a	DET
ejpam-6050	79	37	∪	∪	X
ejpam-6050	79	38	b	b	NOUN
ejpam-6050	79	39	)	)	PUNCT
ejpam-6050	79	40	.	.	PUNCT
ejpam-6050	80	1	3	3	X
ejpam-6050	80	2	.	.	X
ejpam-6050	80	3	exponential	exponential	ADJ
ejpam-6050	80	4	fuzzy	fuzzy	ADJ
ejpam-6050	80	5	sets	set	NOUN
ejpam-6050	80	6	definition	definition	NOUN
ejpam-6050	80	7	10	10	NUM
ejpam-6050	80	8	.	.	PUNCT
ejpam-6050	81	1	if	if	SCONJ
ejpam-6050	81	2	z	z	NOUN
ejpam-6050	81	3	is	be	AUX
ejpam-6050	81	4	a	a	DET
ejpam-6050	81	5	universe	universe	ADJ
ejpam-6050	81	6	discourse	discourse	NOUN
ejpam-6050	81	7	and	and	CCONJ
ejpam-6050	81	8	s	s	AUX
ejpam-6050	81	9	be	be	AUX
ejpam-6050	81	10	any	any	DET
ejpam-6050	81	11	particular	particular	ADJ
ejpam-6050	81	12	element	element	NOUN
ejpam-6050	81	13	of	of	ADP
ejpam-6050	81	14	z.	z.	PROPN
ejpam-6050	81	15	the	the	DET
ejpam-6050	81	16	efs	efs	PROPN
ejpam-6050	81	17	ea	ea	ADV
ejpam-6050	81	18	defined	define	VERB
ejpam-6050	81	19	on	on	ADP
ejpam-6050	81	20	z	z	PROPN
ejpam-6050	81	21	is	be	AUX
ejpam-6050	81	22	a	a	DET
ejpam-6050	81	23	collection	collection	NOUN
ejpam-6050	81	24	of	of	ADP
ejpam-6050	81	25	ordered	order	VERB
ejpam-6050	81	26	pairs	pair	NOUN
ejpam-6050	81	27	,	,	PUNCT
ejpam-6050	81	28	ea	ea	X
ejpam-6050	81	29	=	=	SYM
ejpam-6050	81	30	{	{	PUNCT
ejpam-6050	81	31	(	(	PUNCT
ejpam-6050	81	32	s,ℵa(s)e	s,ℵa(s)e	NOUN
ejpam-6050	81	33	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	81	34	)	)	PUNCT
ejpam-6050	81	35	)	)	PUNCT
ejpam-6050	82	1	|s	|s	PROPN
ejpam-6050	82	2	∈	∈	PROPN
ejpam-6050	82	3	z	z	PROPN
ejpam-6050	82	4	,	,	PUNCT
ejpam-6050	82	5	⊺	⊺	X
ejpam-6050	82	6	>	>	X
ejpam-6050	82	7	0	0	NUM
ejpam-6050	82	8	}	}	PUNCT
ejpam-6050	82	9	,	,	PUNCT
ejpam-6050	82	10	where	where	SCONJ
ejpam-6050	82	11	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	82	12	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	82	13	)	)	PUNCT
ejpam-6050	82	14	:	:	PUNCT
ejpam-6050	83	1	z	z	X
ejpam-6050	83	2	→	→	PUNCT
ejpam-6050	83	3	[	[	X
ejpam-6050	83	4	0	0	NUM
ejpam-6050	83	5	,	,	PUNCT
ejpam-6050	83	6	1	1	NUM
ejpam-6050	83	7	]	]	PUNCT
ejpam-6050	83	8	is	be	AUX
ejpam-6050	83	9	called	call	VERB
ejpam-6050	83	10	the	the	DET
ejpam-6050	83	11	membership	membership	NOUN
ejpam-6050	83	12	function	function	NOUN
ejpam-6050	83	13	.	.	PUNCT
ejpam-6050	84	1	the	the	DET
ejpam-6050	84	2	degree	degree	NOUN
ejpam-6050	84	3	of	of	ADP
ejpam-6050	84	4	membership	membership	NOUN
ejpam-6050	84	5	function	function	NOUN
ejpam-6050	84	6	0	0	NUM
ejpam-6050	84	7	≤	≤	NOUN
ejpam-6050	84	8	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	84	9	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	84	10	)	)	PUNCT
ejpam-6050	84	11	≤	≤	NUM
ejpam-6050	84	12	1	1	NUM
ejpam-6050	84	13	.	.	PUNCT
ejpam-6050	84	14	example	example	NOUN
ejpam-6050	85	1	1	1	NUM
ejpam-6050	85	2	.	.	PUNCT
ejpam-6050	86	1	let	let	VERB
ejpam-6050	86	2	z	z	NOUN
ejpam-6050	86	3	=	=	PUNCT
ejpam-6050	86	4	{	{	PUNCT
ejpam-6050	86	5	1	1	NUM
ejpam-6050	86	6	,	,	PUNCT
ejpam-6050	86	7	2	2	NUM
ejpam-6050	86	8	,	,	PUNCT
ejpam-6050	86	9	3	3	NUM
ejpam-6050	86	10	,	,	PUNCT
ejpam-6050	86	11	4	4	NUM
ejpam-6050	86	12	,	,	PUNCT
ejpam-6050	86	13	5	5	NUM
ejpam-6050	86	14	}	}	PUNCT
ejpam-6050	86	15	be	be	AUX
ejpam-6050	86	16	the	the	DET
ejpam-6050	86	17	universal	universal	ADJ
ejpam-6050	86	18	set	set	VERB
ejpam-6050	86	19	and	and	CCONJ
ejpam-6050	86	20	fuzzy	fuzzy	ADJ
ejpam-6050	86	21	membership	membership	NOUN
ejpam-6050	86	22	values	value	NOUN
ejpam-6050	86	23	of	of	ADP
ejpam-6050	86	24	z	z	PROPN
ejpam-6050	86	25	is	be	AUX
ejpam-6050	86	26	ℵa(s	ℵa(s	ADJ
ejpam-6050	86	27	)	)	PUNCT
ejpam-6050	87	1	=	=	PUNCT
ejpam-6050	87	2	{	{	PUNCT
ejpam-6050	87	3	0.9	0.9	NUM
ejpam-6050	87	4	,	,	PUNCT
ejpam-6050	87	5	0.7	0.7	NUM
ejpam-6050	87	6	,	,	PUNCT
ejpam-6050	87	7	0.5	0.5	NUM
ejpam-6050	87	8	,	,	PUNCT
ejpam-6050	87	9	0.4	0.4	NUM
ejpam-6050	87	10	,	,	PUNCT
ejpam-6050	87	11	0.3	0.3	NUM
ejpam-6050	87	12	}	}	PUNCT
ejpam-6050	87	13	,	,	PUNCT
ejpam-6050	87	14	the	the	DET
ejpam-6050	87	15	decay	decay	NOUN
ejpam-6050	87	16	parameter	parameter	NOUN
ejpam-6050	87	17	⊺	⊺	NOUN
ejpam-6050	87	18	=	=	NOUN
ejpam-6050	87	19	0.02	0.02	NUM
ejpam-6050	87	20	.	.	PUNCT
ejpam-6050	88	1	the	the	DET
ejpam-6050	88	2	exponential	exponential	ADJ
ejpam-6050	88	3	fuzzy	fuzzy	ADJ
ejpam-6050	88	4	membership	membership	NOUN
ejpam-6050	88	5	function	function	NOUN
ejpam-6050	88	6	is	be	AUX
ejpam-6050	88	7	given	give	VERB
ejpam-6050	88	8	by	by	ADP
ejpam-6050	88	9	:	:	PUNCT
ejpam-6050	88	10	ea(s	ea(s	NUM
ejpam-6050	88	11	)	)	PUNCT
ejpam-6050	88	12	=	=	SYM
ejpam-6050	88	13	ℵa(s)e	ℵa(s)e	X
ejpam-6050	88	14	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	88	15	)	)	PUNCT
ejpam-6050	88	16	.	.	PUNCT
ejpam-6050	89	1	the	the	DET
ejpam-6050	89	2	exponential	exponential	ADJ
ejpam-6050	89	3	fuzzy	fuzzy	ADJ
ejpam-6050	89	4	membership	membership	NOUN
ejpam-6050	89	5	values	value	NOUN
ejpam-6050	89	6	ea(s	ea(s	VERB
ejpam-6050	89	7	)	)	PUNCT
ejpam-6050	89	8	=	=	SYM
ejpam-6050	89	9	{	{	PUNCT
ejpam-6050	89	10	(	(	PUNCT
ejpam-6050	89	11	1	1	NUM
ejpam-6050	89	12	,	,	PUNCT
ejpam-6050	89	13	0.8839	0.8839	NUM
ejpam-6050	89	14	)	)	PUNCT
ejpam-6050	89	15	,	,	PUNCT
ejpam-6050	89	16	(	(	PUNCT
ejpam-6050	89	17	2	2	NUM
ejpam-6050	89	18	,	,	PUNCT
ejpam-6050	89	19	0.6903	0.6903	NUM
ejpam-6050	89	20	)	)	PUNCT
ejpam-6050	89	21	,	,	PUNCT
ejpam-6050	89	22	(	(	PUNCT
ejpam-6050	89	23	3	3	NUM
ejpam-6050	89	24	,	,	PUNCT
ejpam-6050	89	25	0.4950	0.4950	NUM
ejpam-6050	89	26	)	)	PUNCT
ejpam-6050	89	27	,	,	PUNCT
ejpam-6050	89	28	(	(	PUNCT
ejpam-6050	89	29	4	4	NUM
ejpam-6050	89	30	,	,	PUNCT
ejpam-6050	89	31	0.3968	0.3968	NUM
ejpam-6050	89	32	)	)	PUNCT
ejpam-6050	89	33	,	,	PUNCT
ejpam-6050	89	34	(	(	PUNCT
ejpam-6050	89	35	5	5	NUM
ejpam-6050	89	36	,	,	PUNCT
ejpam-6050	89	37	0.2982	0.2982	NUM
ejpam-6050	89	38	)	)	PUNCT
ejpam-6050	89	39	}	}	PUNCT
ejpam-6050	89	40	.	.	PUNCT
ejpam-6050	90	1	m.	m.	NOUN
ejpam-6050	90	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	90	3	,	,	PUNCT
ejpam-6050	90	4	m.	m.	NOUN
ejpam-6050	90	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	90	6	,	,	PUNCT
ejpam-6050	90	7	m.	m.	NOUN
ejpam-6050	90	8	alqahtani	alqahtani	PROPN
ejpam-6050	90	9	/	/	SYM
ejpam-6050	90	10	eur	eur	PROPN
ejpam-6050	90	11	.	.	PUNCT
ejpam-6050	91	1	j.	j.	PROPN
ejpam-6050	91	2	pure	pure	PROPN
ejpam-6050	91	3	appl	appl	PROPN
ejpam-6050	91	4	.	.	PROPN
ejpam-6050	91	5	math	math	PROPN
ejpam-6050	91	6	,	,	PUNCT
ejpam-6050	91	7	18	18	NUM
ejpam-6050	91	8	(	(	PUNCT
ejpam-6050	91	9	2	2	NUM
ejpam-6050	91	10	)	)	PUNCT
ejpam-6050	91	11	(	(	PUNCT
ejpam-6050	91	12	2025	2025	NUM
ejpam-6050	91	13	)	)	PUNCT
ejpam-6050	91	14	,	,	PUNCT
ejpam-6050	91	15	6050	6050	NUM
ejpam-6050	91	16	5	5	NUM
ejpam-6050	91	17	of	of	ADP
ejpam-6050	91	18	29	29	NUM
ejpam-6050	91	19	figure	figure	NOUN
ejpam-6050	91	20	1	1	NUM
ejpam-6050	91	21	:	:	PUNCT
ejpam-6050	91	22	exponential	exponential	ADJ
ejpam-6050	91	23	fuzzy	fuzzy	ADJ
ejpam-6050	91	24	set	set	VERB
ejpam-6050	91	25	definition	definition	NOUN
ejpam-6050	91	26	11	11	NUM
ejpam-6050	91	27	.	.	PUNCT
ejpam-6050	92	1	let	let	VERB
ejpam-6050	92	2	ea	ea	NOUN
ejpam-6050	92	3	and	and	CCONJ
ejpam-6050	92	4	eb	eb	PROPN
ejpam-6050	92	5	be	be	AUX
ejpam-6050	92	6	two	two	NUM
ejpam-6050	92	7	efss	efss	NOUN
ejpam-6050	92	8	on	on	ADP
ejpam-6050	92	9	z	z	NOUN
ejpam-6050	92	10	with	with	ADP
ejpam-6050	92	11	their	their	PRON
ejpam-6050	92	12	grade	grade	NOUN
ejpam-6050	92	13	values	value	NOUN
ejpam-6050	92	14	given	give	VERB
ejpam-6050	92	15	by	by	ADP
ejpam-6050	92	16	:	:	PUNCT
ejpam-6050	92	17	ℵea(s	ℵea(s	PROPN
ejpam-6050	92	18	)	)	PUNCT
ejpam-6050	92	19	=	=	PUNCT
ejpam-6050	93	1	ℵa(s)e	ℵa(s)e	X
ejpam-6050	93	2	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	93	3	)	)	PUNCT
ejpam-6050	93	4	ℵeb(s	ℵeb(s	PROPN
ejpam-6050	93	5	)	)	PUNCT
ejpam-6050	93	6	=	=	SYM
ejpam-6050	94	1	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	94	2	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	94	3	)	)	PUNCT
ejpam-6050	94	4	the	the	DET
ejpam-6050	94	5	exponential	exponential	ADJ
ejpam-6050	94	6	fuzzy	fuzzy	ADJ
ejpam-6050	94	7	intersection	intersection	NOUN
ejpam-6050	94	8	of	of	ADP
ejpam-6050	94	9	ea	ea	NOUN
ejpam-6050	94	10	and	and	CCONJ
ejpam-6050	94	11	eb	eb	PROPN
ejpam-6050	94	12	is	be	AUX
ejpam-6050	94	13	defined	define	VERB
ejpam-6050	94	14	as	as	ADP
ejpam-6050	94	15	:	:	PUNCT
ejpam-6050	94	16	ℵea∩eb(s	ℵea∩eb(s	PROPN
ejpam-6050	94	17	)	)	PUNCT
ejpam-6050	95	1	=	=	SYM
ejpam-6050	95	2	min	min	NOUN
ejpam-6050	95	3	{	{	PUNCT
ejpam-6050	95	4	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	95	5	)	)	PUNCT
ejpam-6050	95	6	}	}	PUNCT
ejpam-6050	95	7	=	=	SYM
ejpam-6050	95	8	min	min	NOUN
ejpam-6050	95	9	{	{	PUNCT
ejpam-6050	95	10	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	95	11	−⊺ℵa(s),ℵb(s)e	−⊺ℵa(s),ℵb(s)e	NOUN
ejpam-6050	95	12	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	95	13	)	)	PUNCT
ejpam-6050	95	14	}	}	PUNCT
ejpam-6050	95	15	(	(	PUNCT
ejpam-6050	95	16	3.1	3.1	NUM
ejpam-6050	95	17	)	)	PUNCT
ejpam-6050	95	18	similarly	similarly	ADV
ejpam-6050	95	19	,	,	PUNCT
ejpam-6050	95	20	the	the	DET
ejpam-6050	95	21	exponential	exponential	ADJ
ejpam-6050	95	22	fuzzy	fuzzy	ADJ
ejpam-6050	95	23	union	union	NOUN
ejpam-6050	95	24	of	of	ADP
ejpam-6050	95	25	ea	ea	PROPN
ejpam-6050	95	26	and	and	CCONJ
ejpam-6050	95	27	eb	eb	PROPN
ejpam-6050	95	28	is	be	AUX
ejpam-6050	95	29	defined	define	VERB
ejpam-6050	95	30	as	as	ADP
ejpam-6050	95	31	:	:	PUNCT
ejpam-6050	95	32	ℵea∪eb(s	ℵea∪eb(s	PROPN
ejpam-6050	95	33	)	)	PUNCT
ejpam-6050	96	1	=	=	SYM
ejpam-6050	96	2	max	max	PROPN
ejpam-6050	96	3	{	{	PUNCT
ejpam-6050	96	4	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	96	5	)	)	PUNCT
ejpam-6050	96	6	}	}	PUNCT
ejpam-6050	96	7	=	=	SYM
ejpam-6050	96	8	max	max	X
ejpam-6050	96	9	{	{	PUNCT
ejpam-6050	96	10	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	96	11	−⊺ℵa(s),ℵb(s)e	−⊺ℵa(s),ℵb(s)e	NOUN
ejpam-6050	96	12	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	96	13	)	)	PUNCT
ejpam-6050	96	14	}	}	PUNCT
ejpam-6050	96	15	(	(	PUNCT
ejpam-6050	96	16	3.2	3.2	NUM
ejpam-6050	96	17	)	)	PUNCT
ejpam-6050	96	18	example	example	NOUN
ejpam-6050	96	19	2	2	NUM
ejpam-6050	96	20	.	.	PUNCT
ejpam-6050	97	1	let	let	VERB
ejpam-6050	97	2	z	z	NOUN
ejpam-6050	97	3	=	=	PUNCT
ejpam-6050	97	4	{	{	PUNCT
ejpam-6050	97	5	s1	s1	NOUN
ejpam-6050	97	6	,	,	PUNCT
ejpam-6050	97	7	s2	s2	PROPN
ejpam-6050	97	8	,	,	PUNCT
ejpam-6050	97	9	s3	s3	PROPN
ejpam-6050	97	10	,	,	PUNCT
ejpam-6050	97	11	s4	s4	PROPN
ejpam-6050	97	12	,	,	PUNCT
ejpam-6050	97	13	s5	s5	PROPN
ejpam-6050	97	14	}	}	PUNCT
ejpam-6050	97	15	be	be	AUX
ejpam-6050	97	16	a	a	DET
ejpam-6050	97	17	finite	finite	ADJ
ejpam-6050	97	18	universe	universe	NOUN
ejpam-6050	97	19	,	,	PUNCT
ejpam-6050	97	20	and	and	CCONJ
ejpam-6050	97	21	the	the	DET
ejpam-6050	97	22	membership	membership	NOUN
ejpam-6050	97	23	functions	function	NOUN
ejpam-6050	97	24	of	of	ADP
ejpam-6050	97	25	two	two	NUM
ejpam-6050	97	26	exponential	exponential	ADJ
ejpam-6050	97	27	f	f	NOUN
ejpam-6050	97	28	-	-	PUNCT
ejpam-6050	97	29	sets	set	NOUN
ejpam-6050	97	30	ea	ea	NOUN
ejpam-6050	97	31	and	and	CCONJ
ejpam-6050	97	32	eb	eb	PROPN
ejpam-6050	97	33	are	be	AUX
ejpam-6050	97	34	ℵea(s	ℵea(s	PROPN
ejpam-6050	97	35	)	)	PUNCT
ejpam-6050	97	36	=	=	PUNCT
ejpam-6050	97	37	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	97	38	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	97	39	)	)	PUNCT
ejpam-6050	97	40	m.	m.	NOUN
ejpam-6050	97	41	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	97	42	,	,	PUNCT
ejpam-6050	97	43	m.	m.	NOUN
ejpam-6050	97	44	rajeshwari	rajeshwari	NOUN
ejpam-6050	97	45	,	,	PUNCT
ejpam-6050	97	46	m.	m.	NOUN
ejpam-6050	97	47	alqahtani	alqahtani	PROPN
ejpam-6050	97	48	/	/	SYM
ejpam-6050	97	49	eur	eur	PROPN
ejpam-6050	97	50	.	.	PUNCT
ejpam-6050	98	1	j.	j.	PROPN
ejpam-6050	98	2	pure	pure	PROPN
ejpam-6050	98	3	appl	appl	PROPN
ejpam-6050	98	4	.	.	PROPN
ejpam-6050	98	5	math	math	PROPN
ejpam-6050	98	6	,	,	PUNCT
ejpam-6050	98	7	18	18	NUM
ejpam-6050	98	8	(	(	PUNCT
ejpam-6050	98	9	2	2	NUM
ejpam-6050	98	10	)	)	PUNCT
ejpam-6050	98	11	(	(	PUNCT
ejpam-6050	98	12	2025	2025	NUM
ejpam-6050	98	13	)	)	PUNCT
ejpam-6050	98	14	,	,	PUNCT
ejpam-6050	98	15	6050	6050	NUM
ejpam-6050	98	16	6	6	NUM
ejpam-6050	98	17	of	of	ADP
ejpam-6050	98	18	29	29	NUM
ejpam-6050	98	19	ℵeb(s	ℵeb(	NOUN
ejpam-6050	98	20	)	)	PUNCT
ejpam-6050	99	1	=	=	SYM
ejpam-6050	99	2	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	99	3	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	99	4	)	)	PUNCT
ejpam-6050	99	5	now	now	ADV
ejpam-6050	99	6	,	,	PUNCT
ejpam-6050	99	7	we	we	PRON
ejpam-6050	99	8	compute	compute	VERB
ejpam-6050	99	9	the	the	DET
ejpam-6050	99	10	corresponding	correspond	VERB
ejpam-6050	99	11	ea	ea	PROPN
ejpam-6050	99	12	∩	∩	PROPN
ejpam-6050	99	13	eb	eb	PROPN
ejpam-6050	99	14	and	and	CCONJ
ejpam-6050	99	15	ea	ea	PROPN
ejpam-6050	99	16	∪	∪	PROPN
ejpam-6050	99	17	eb	eb	PROPN
ejpam-6050	99	18	membership	membership	NOUN
ejpam-6050	99	19	values	value	NOUN
ejpam-6050	99	20	:	:	PUNCT
ejpam-6050	99	21	s	s	VERB
ejpam-6050	99	22	ℵa(s	ℵa(s	NOUN
ejpam-6050	99	23	)	)	PUNCT
ejpam-6050	99	24	ea(s	ea(s	NUM
ejpam-6050	99	25	)	)	PUNCT
ejpam-6050	99	26	ℵb(s	ℵb(s	PUNCT
ejpam-6050	99	27	)	)	PUNCT
ejpam-6050	99	28	eb(s	eb(	NOUN
ejpam-6050	99	29	)	)	PUNCT
ejpam-6050	99	30	ea	ea	NOUN
ejpam-6050	99	31	∩	∩	PROPN
ejpam-6050	99	32	eb	eb	PROPN
ejpam-6050	99	33	ea	ea	PROPN
ejpam-6050	99	34	∪	∪	PROPN
ejpam-6050	99	35	eb	eb	PROPN
ejpam-6050	99	36	s1	s1	PROPN
ejpam-6050	99	37	0.8	0.8	NUM
ejpam-6050	99	38	0.7873	0.7873	NUM
ejpam-6050	99	39	0.7	0.7	NUM
ejpam-6050	99	40	0.6903	0.6903	NUM
ejpam-6050	99	41	0.6903	0.6903	NUM
ejpam-6050	99	42	0.7873	0.7873	NUM
ejpam-6050	99	43	s2	s2	NOUN
ejpam-6050	99	44	0.6	0.6	NUM
ejpam-6050	99	45	0.5928	0.5928	NUM
ejpam-6050	99	46	0.5	0.5	NUM
ejpam-6050	99	47	0.4950	0.4950	NUM
ejpam-6050	99	48	0.4950	0.4950	NUM
ejpam-6050	99	49	0.5928	0.5928	NUM
ejpam-6050	99	50	s3	s3	PROPN
ejpam-6050	99	51	0.4	0.4	NUM
ejpam-6050	99	52	0.3968	0.3968	NUM
ejpam-6050	99	53	0.3	0.3	NUM
ejpam-6050	99	54	0.2982	0.2982	NUM
ejpam-6050	99	55	0.2982	0.2982	NUM
ejpam-6050	99	56	0.3968	0.3968	NUM
ejpam-6050	99	57	s4	s4	PROPN
ejpam-6050	99	58	0.2	0.2	NUM
ejpam-6050	99	59	0.1992	0.1992	NUM
ejpam-6050	99	60	0.2	0.2	NUM
ejpam-6050	99	61	0.1992	0.1992	NUM
ejpam-6050	99	62	0.1992	0.1992	NUM
ejpam-6050	99	63	0.1992	0.1992	NUM
ejpam-6050	99	64	s5	s5	PROPN
ejpam-6050	99	65	0.1	0.1	NUM
ejpam-6050	99	66	0.0998	0.0998	NUM
ejpam-6050	99	67	0.1	0.1	NUM
ejpam-6050	99	68	0.0998	0.0998	NUM
ejpam-6050	99	69	0.0998	0.0998	NUM
ejpam-6050	99	70	0.0998	0.0998	NUM
ejpam-6050	99	71	definition	definition	NOUN
ejpam-6050	99	72	12	12	NUM
ejpam-6050	99	73	.	.	PUNCT
ejpam-6050	100	1	consider	consider	VERB
ejpam-6050	100	2	two	two	NUM
ejpam-6050	100	3	efss	efss	ADJ
ejpam-6050	100	4	ea	ea	NOUN
ejpam-6050	100	5	,	,	PUNCT
ejpam-6050	100	6	eb	eb	PROPN
ejpam-6050	100	7	,	,	PUNCT
ejpam-6050	100	8	and	and	CCONJ
ejpam-6050	100	9	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	100	10	−⊺ℵa(s),ℵb(s)e	−⊺ℵa(s),ℵb(s)e	NOUN
ejpam-6050	100	11	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	100	12	)	)	PUNCT
ejpam-6050	100	13	denotes	denote	VERB
ejpam-6050	100	14	the	the	DET
ejpam-6050	100	15	membership	membership	NOUN
ejpam-6050	100	16	functions	function	NOUN
ejpam-6050	100	17	ea	ea	PROPN
ejpam-6050	100	18	and	and	CCONJ
ejpam-6050	100	19	eb	eb	PROPN
ejpam-6050	100	20	.	.	PUNCT
ejpam-6050	101	1	the	the	DET
ejpam-6050	101	2	simple	simple	ADJ
ejpam-6050	101	3	difference	difference	NOUN
ejpam-6050	101	4	ea	ea	X
ejpam-6050	101	5	−eb	−eb	PROPN
ejpam-6050	101	6	of	of	ADP
ejpam-6050	101	7	these	these	DET
ejpam-6050	101	8	two	two	NUM
ejpam-6050	101	9	efss	efss	NOUN
ejpam-6050	101	10	ea	ea	PROPN
ejpam-6050	101	11	and	and	CCONJ
ejpam-6050	101	12	eb	eb	PROPN
ejpam-6050	101	13	is	be	AUX
ejpam-6050	101	14	given	give	VERB
ejpam-6050	101	15	by	by	ADP
ejpam-6050	101	16	ea	ea	PROPN
ejpam-6050	101	17	−	−	PROPN
ejpam-6050	101	18	eb	eb	PROPN
ejpam-6050	101	19	=	=	SYM
ejpam-6050	101	20	ea	ea	PROPN
ejpam-6050	101	21	∩	∩	PROPN
ejpam-6050	101	22	ebc	ebc	PROPN
ejpam-6050	101	23	=	=	PROPN
ejpam-6050	101	24	ℵea(s	ℵea(s	PROPN
ejpam-6050	101	25	)	)	PUNCT
ejpam-6050	101	26	∗	∗	NOUN
ejpam-6050	101	27	ℵ	ℵ	NOUN
ejpam-6050	101	28	c	c	NOUN
ejpam-6050	101	29	eb(s	eb(	NOUN
ejpam-6050	101	30	)	)	PUNCT
ejpam-6050	102	1	=	=	SYM
ejpam-6050	102	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	102	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	102	4	)	)	PUNCT
ejpam-6050	102	5	∗	∗	NOUN
ejpam-6050	102	6	ℵb(s	ℵb(s	NUM
ejpam-6050	102	7	)	)	PUNCT
ejpam-6050	102	8	ce−⊺ℵc	ce−⊺ℵc	PROPN
ejpam-6050	102	9	b(s	b(s	PROPN
ejpam-6050	102	10	)	)	PUNCT
ejpam-6050	102	11	example	example	NOUN
ejpam-6050	103	1	3	3	X
ejpam-6050	103	2	.	.	PUNCT
ejpam-6050	103	3	let	let	VERB
ejpam-6050	103	4	ea	ea	X
ejpam-6050	104	1	=	=	PUNCT
ejpam-6050	104	2	{	{	PUNCT
ejpam-6050	104	3	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	104	4	s1	s1	NOUN
ejpam-6050	104	5	+	+	CCONJ
ejpam-6050	104	6	0.5e−⊺0.5	0.5e−⊺0.5	ADJ
ejpam-6050	104	7	s2	s2	NOUN
ejpam-6050	104	8	+	+	CCONJ
ejpam-6050	104	9	0.6e−⊺0.6	0.6e−⊺0.6	PROPN
ejpam-6050	104	10	s3	s3	PROPN
ejpam-6050	104	11	}	}	PUNCT
ejpam-6050	104	12	and	and	CCONJ
ejpam-6050	104	13	eb	eb	PROPN
ejpam-6050	104	14	=	=	PUNCT
ejpam-6050	104	15	{	{	PUNCT
ejpam-6050	104	16	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	104	17	s1	s1	NOUN
ejpam-6050	104	18	+	+	CCONJ
ejpam-6050	104	19	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	104	20	s2	s2	NOUN
ejpam-6050	104	21	+	+	CCONJ
ejpam-6050	104	22	0.3e−⊺0.3	0.3e−⊺0.3	PROPN
ejpam-6050	104	23	s3	s3	PROPN
ejpam-6050	104	24	}	}	PUNCT
ejpam-6050	104	25	be	be	AUX
ejpam-6050	104	26	two	two	NUM
ejpam-6050	104	27	two	two	NUM
ejpam-6050	104	28	efss	efss	NOUN
ejpam-6050	104	29	.	.	PUNCT
ejpam-6050	105	1	the	the	DET
ejpam-6050	105	2	simple	simple	ADJ
ejpam-6050	105	3	difference	difference	NOUN
ejpam-6050	105	4	is	be	AUX
ejpam-6050	105	5	ea	ea	NUM
ejpam-6050	105	6	−	−	PROPN
ejpam-6050	105	7	eb	eb	PROPN
ejpam-6050	105	8	=	=	SYM
ejpam-6050	105	9	ea	ea	PROPN
ejpam-6050	105	10	∩	∩	PROPN
ejpam-6050	105	11	ebc	ebc	PROPN
ejpam-6050	105	12	=	=	PROPN
ejpam-6050	105	13	{	{	PUNCT
ejpam-6050	105	14	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	105	15	s1	s1	NOUN
ejpam-6050	105	16	+	+	CCONJ
ejpam-6050	105	17	0.5e−⊺0.5	0.5e−⊺0.5	ADJ
ejpam-6050	105	18	s2	s2	NOUN
ejpam-6050	105	19	+	+	CCONJ
ejpam-6050	105	20	0.6e−⊺0.6	0.6e−⊺0.6	PROPN
ejpam-6050	105	21	s3	s3	PROPN
ejpam-6050	105	22	}	}	PUNCT
ejpam-6050	105	23	∗	∗	X
ejpam-6050	105	24	{	{	PUNCT
ejpam-6050	105	25	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	105	26	s1	s1	NOUN
ejpam-6050	105	27	+	+	CCONJ
ejpam-6050	105	28	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	105	29	s2	s2	NOUN
ejpam-6050	105	30	+	+	CCONJ
ejpam-6050	105	31	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	105	32	s3	s3	PROPN
ejpam-6050	105	33	}	}	PUNCT
ejpam-6050	105	34	=	=	SYM
ejpam-6050	105	35	{	{	PUNCT
ejpam-6050	105	36	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	105	37	s1	s1	NOUN
ejpam-6050	105	38	+	+	CCONJ
ejpam-6050	105	39	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	105	40	s2	s2	NOUN
ejpam-6050	105	41	+	+	CCONJ
ejpam-6050	105	42	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	105	43	s3	s3	PROPN
ejpam-6050	105	44	}	}	PUNCT
ejpam-6050	105	45	.	.	PUNCT
ejpam-6050	106	1	definition	definition	NOUN
ejpam-6050	106	2	13	13	NUM
ejpam-6050	106	3	.	.	PUNCT
ejpam-6050	107	1	let	let	AUX
ejpam-6050	107	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	107	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	107	4	)	)	PUNCT
ejpam-6050	107	5	and	and	CCONJ
ejpam-6050	107	6	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	107	7	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	107	8	)	)	PUNCT
ejpam-6050	107	9	be	be	VERB
ejpam-6050	107	10	the	the	DET
ejpam-6050	107	11	membership	membership	NOUN
ejpam-6050	107	12	functions	function	NOUN
ejpam-6050	107	13	of	of	ADP
ejpam-6050	107	14	efs	ef	NOUN
ejpam-6050	107	15	ea	ea	PROPN
ejpam-6050	107	16	and	and	CCONJ
ejpam-6050	107	17	eb	eb	PROPN
ejpam-6050	107	18	.	.	PUNCT
ejpam-6050	108	1	the	the	DET
ejpam-6050	108	2	bounded	bounded	ADJ
ejpam-6050	108	3	difference	difference	NOUN
ejpam-6050	108	4	is	be	AUX
ejpam-6050	108	5	ea	ea	X
ejpam-6050	108	6	◦	◦	NOUN
ejpam-6050	108	7	eb(s	eb(	NOUN
ejpam-6050	108	8	)	)	PUNCT
ejpam-6050	109	1	=	=	SYM
ejpam-6050	109	2	max	max	PROPN
ejpam-6050	109	3	[	[	PUNCT
ejpam-6050	109	4	◦	◦	NOUN
ejpam-6050	109	5	,	,	PUNCT
ejpam-6050	109	6	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	109	7	−⊺ℵa(s),ℵb(s)e	−⊺ℵa(s),ℵb(s)e	NOUN
ejpam-6050	109	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	109	9	)	)	PUNCT
ejpam-6050	109	10	]	]	PUNCT
ejpam-6050	109	11	.	.	PUNCT
ejpam-6050	110	1	example	example	NOUN
ejpam-6050	111	1	4	4	X
ejpam-6050	111	2	.	.	PUNCT
ejpam-6050	111	3	let	let	VERB
ejpam-6050	111	4	ea	ea	X
ejpam-6050	112	1	=	=	PUNCT
ejpam-6050	113	1	(	(	PUNCT
ejpam-6050	113	2	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	113	3	s1	s1	NOUN
ejpam-6050	113	4	+	+	CCONJ
ejpam-6050	113	5	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	113	6	s2	s2	NOUN
ejpam-6050	113	7	+	+	CCONJ
ejpam-6050	113	8	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	113	9	s3	s3	PROPN
ejpam-6050	113	10	)	)	PUNCT
ejpam-6050	113	11	and	and	CCONJ
ejpam-6050	113	12	eb	eb	PROPN
ejpam-6050	113	13	=	=	SYM
ejpam-6050	113	14	(	(	PUNCT
ejpam-6050	113	15	0.1e−⊺0.1	0.1e−⊺0.1	NOUN
ejpam-6050	113	16	s1	s1	PROPN
ejpam-6050	113	17	+	+	CCONJ
ejpam-6050	113	18	0.4e−⊺0.4	0.4e−⊺0.4	PROPN
ejpam-6050	113	19	s2	s2	NOUN
ejpam-6050	113	20	+	+	CCONJ
ejpam-6050	113	21	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	113	22	s3	s3	PROPN
ejpam-6050	113	23	)	)	PUNCT
ejpam-6050	113	24	be	be	VERB
ejpam-6050	113	25	two	two	NUM
ejpam-6050	113	26	two	two	NUM
ejpam-6050	113	27	efss	efss	NOUN
ejpam-6050	113	28	.	.	PUNCT
ejpam-6050	114	1	the	the	DET
ejpam-6050	114	2	bounded	bounded	ADJ
ejpam-6050	114	3	difference	difference	NOUN
ejpam-6050	114	4	of	of	ADP
ejpam-6050	114	5	these	these	DET
ejpam-6050	114	6	two	two	NUM
ejpam-6050	114	7	efss	efss	NOUN
ejpam-6050	114	8	is	be	AUX
ejpam-6050	114	9	:	:	PUNCT
ejpam-6050	114	10	ea	ea	X
ejpam-6050	114	11	◦	◦	VERB
ejpam-6050	114	12	eb(s	eb(	NOUN
ejpam-6050	114	13	)	)	PUNCT
ejpam-6050	114	14	=	=	SYM
ejpam-6050	114	15	(	(	PUNCT
ejpam-6050	114	16	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	114	17	s1	s1	NOUN
ejpam-6050	114	18	+	+	CCONJ
ejpam-6050	114	19	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	114	20	s2	s2	NOUN
ejpam-6050	114	21	+	+	CCONJ
ejpam-6050	114	22	0.1e−⊺0.1	0.1e−⊺0.1	PROPN
ejpam-6050	114	23	s3	s3	PROPN
ejpam-6050	114	24	)	)	PUNCT
ejpam-6050	114	25	definition	definition	NOUN
ejpam-6050	114	26	14	14	NUM
ejpam-6050	114	27	.	.	PUNCT
ejpam-6050	115	1	a	a	DET
ejpam-6050	115	2	disjoint	disjoint	ADJ
ejpam-6050	115	3	sum	sum	NOUN
ejpam-6050	115	4	of	of	ADP
ejpam-6050	115	5	ea	ea	PROPN
ejpam-6050	115	6	and	and	CCONJ
ejpam-6050	115	7	eb	eb	PROPN
ejpam-6050	115	8	is	be	AUX
ejpam-6050	115	9	as	as	SCONJ
ejpam-6050	115	10	follows	follow	VERB
ejpam-6050	115	11	ea	ea	PROPN
ejpam-6050	115	12	⊗	⊗	NUM
ejpam-6050	115	13	eb(s	eb(	NOUN
ejpam-6050	115	14	)	)	PUNCT
ejpam-6050	116	1	=	=	SYM
ejpam-6050	116	2	∣∣∣∣∣ℵa(s)e	∣∣∣∣∣ℵa(s)e	NUM
ejpam-6050	116	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	116	4	)	)	PUNCT
ejpam-6050	116	5	−	−	NOUN
ejpam-6050	116	6	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	116	7	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	116	8	)	)	PUNCT
ejpam-6050	116	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6050	116	10	m.	m.	NOUN
ejpam-6050	116	11	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	116	12	,	,	PUNCT
ejpam-6050	116	13	m.	m.	NOUN
ejpam-6050	116	14	rajeshwari	rajeshwari	NOUN
ejpam-6050	116	15	,	,	PUNCT
ejpam-6050	116	16	m.	m.	NOUN
ejpam-6050	116	17	alqahtani	alqahtani	PROPN
ejpam-6050	116	18	/	/	SYM
ejpam-6050	116	19	eur	eur	PROPN
ejpam-6050	116	20	.	.	PUNCT
ejpam-6050	117	1	j.	j.	PROPN
ejpam-6050	117	2	pure	pure	PROPN
ejpam-6050	117	3	appl	appl	PROPN
ejpam-6050	117	4	.	.	PROPN
ejpam-6050	117	5	math	math	PROPN
ejpam-6050	117	6	,	,	PUNCT
ejpam-6050	117	7	18	18	NUM
ejpam-6050	117	8	(	(	PUNCT
ejpam-6050	117	9	2	2	NUM
ejpam-6050	117	10	)	)	PUNCT
ejpam-6050	117	11	(	(	PUNCT
ejpam-6050	117	12	2025	2025	NUM
ejpam-6050	117	13	)	)	PUNCT
ejpam-6050	117	14	,	,	PUNCT
ejpam-6050	117	15	6050	6050	NUM
ejpam-6050	117	16	7	7	NUM
ejpam-6050	117	17	of	of	ADP
ejpam-6050	117	18	29	29	NUM
ejpam-6050	117	19	example	example	NOUN
ejpam-6050	117	20	5	5	NUM
ejpam-6050	117	21	.	.	PUNCT
ejpam-6050	118	1	let	let	VERB
ejpam-6050	118	2	ea	ea	X
ejpam-6050	119	1	=	=	SYM
ejpam-6050	120	1	(	(	PUNCT
ejpam-6050	120	2	0.2e−⊺0.2	0.2e−⊺0.2	NOUN
ejpam-6050	120	3	s1	s1	NOUN
ejpam-6050	120	4	+	+	CCONJ
ejpam-6050	120	5	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	120	6	s2	s2	NOUN
ejpam-6050	120	7	+	+	CCONJ
ejpam-6050	120	8	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	120	9	s3	s3	PROPN
ejpam-6050	120	10	)	)	PUNCT
ejpam-6050	120	11	and	and	CCONJ
ejpam-6050	120	12	eb	eb	PROPN
ejpam-6050	120	13	=	=	SYM
ejpam-6050	120	14	(	(	PUNCT
ejpam-6050	120	15	0.15e−⊺0.15	0.15e−⊺0.15	NUM
ejpam-6050	120	16	s1	s1	NOUN
ejpam-6050	120	17	+	+	CCONJ
ejpam-6050	120	18	0.35e−⊺0.35	0.35e−⊺0.35	NOUN
ejpam-6050	120	19	s2	s2	NOUN
ejpam-6050	120	20	+	+	CCONJ
ejpam-6050	120	21	0.65e−⊺0.65	0.65e−⊺0.65	PROPN
ejpam-6050	120	22	s3	s3	PROPN
ejpam-6050	120	23	)	)	PUNCT
ejpam-6050	120	24	be	be	VERB
ejpam-6050	120	25	two	two	NUM
ejpam-6050	120	26	two	two	NUM
ejpam-6050	120	27	efss	efss	NOUN
ejpam-6050	120	28	.	.	PUNCT
ejpam-6050	121	1	using	use	VERB
ejpam-6050	121	2	the	the	DET
ejpam-6050	121	3	max	max	PROPN
ejpam-6050	121	4	function	function	NOUN
ejpam-6050	121	5	for	for	ADP
ejpam-6050	121	6	calculating	calculate	VERB
ejpam-6050	121	7	the	the	DET
ejpam-6050	121	8	phase	phase	NOUN
ejpam-6050	121	9	term	term	NOUN
ejpam-6050	121	10	,	,	PUNCT
ejpam-6050	121	11	the	the	DET
ejpam-6050	121	12	disjoint	disjoint	ADJ
ejpam-6050	121	13	sum	sum	NOUN
ejpam-6050	121	14	of	of	ADP
ejpam-6050	121	15	theses	theses	PROPN
ejpam-6050	121	16	two	two	NUM
ejpam-6050	121	17	two	two	NUM
ejpam-6050	121	18	efss	efss	NOUN
ejpam-6050	121	19	is	be	AUX
ejpam-6050	121	20	:	:	PUNCT
ejpam-6050	121	21	ea	ea	NOUN
ejpam-6050	121	22	⊗	⊗	NUM
ejpam-6050	121	23	eb(s	eb(	NOUN
ejpam-6050	121	24	)	)	PUNCT
ejpam-6050	121	25	=	=	PRON
ejpam-6050	121	26	(	(	PUNCT
ejpam-6050	121	27	0.05e−⊺0.05	0.05e−⊺0.05	NOUN
ejpam-6050	121	28	s1	s1	NOUN
ejpam-6050	121	29	+	+	CCONJ
ejpam-6050	121	30	0.05e−⊺0.05	0.05e−⊺0.05	NOUN
ejpam-6050	121	31	s2	s2	NOUN
ejpam-6050	121	32	+	+	CCONJ
ejpam-6050	121	33	0.05e−⊺0.05	0.05e−⊺0.05	NOUN
ejpam-6050	121	34	s3	s3	NOUN
ejpam-6050	121	35	)	)	PUNCT
ejpam-6050	121	36	definition	definition	NOUN
ejpam-6050	121	37	15	15	NUM
ejpam-6050	121	38	.	.	PUNCT
ejpam-6050	122	1	let	let	VERB
ejpam-6050	122	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	122	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	122	4	)	)	PUNCT
ejpam-6050	122	5	and	and	CCONJ
ejpam-6050	122	6	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	122	7	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	122	8	)	)	PUNCT
ejpam-6050	122	9	denotes	denotes	AUX
ejpam-6050	122	10	the	the	DET
ejpam-6050	122	11	membership	membership	NOUN
ejpam-6050	122	12	functions	function	NOUN
ejpam-6050	122	13	ea	ea	PROPN
ejpam-6050	122	14	and	and	CCONJ
ejpam-6050	122	15	eb	eb	PROPN
ejpam-6050	122	16	.	.	PUNCT
ejpam-6050	123	1	the	the	DET
ejpam-6050	123	2	disjunctive	disjunctive	ADJ
ejpam-6050	123	3	sum	sum	NOUN
ejpam-6050	123	4	is	be	AUX
ejpam-6050	123	5	ea∆eb(s	ea∆eb(s	PROPN
ejpam-6050	123	6	)	)	PUNCT
ejpam-6050	124	1	=	=	SYM
ejpam-6050	124	2	(	(	PUNCT
ejpam-6050	124	3	ea	ea	X
ejpam-6050	124	4	∩	∩	PROPN
ejpam-6050	124	5	ebc	ebc	PROPN
ejpam-6050	124	6	)	)	PUNCT
ejpam-6050	124	7	∪	∪	PROPN
ejpam-6050	124	8	(	(	PUNCT
ejpam-6050	124	9	eac	eac	PROPN
ejpam-6050	124	10	∩	∩	PROPN
ejpam-6050	124	11	eb	eb	PROPN
ejpam-6050	124	12	)	)	PUNCT
ejpam-6050	124	13	.	.	PUNCT
ejpam-6050	125	1	the	the	DET
ejpam-6050	125	2	membership	membership	NOUN
ejpam-6050	125	3	function	function	NOUN
ejpam-6050	125	4	of	of	ADP
ejpam-6050	125	5	ea∆eb(s	ea∆eb(s	PROPN
ejpam-6050	125	6	)	)	PUNCT
ejpam-6050	125	7	is	be	AUX
ejpam-6050	125	8	:	:	PUNCT
ejpam-6050	125	9	ℵea∆eb(s	ℵea∆eb(s	X
ejpam-6050	125	10	)	)	PUNCT
ejpam-6050	125	11	=	=	PUNCT
ejpam-6050	126	1	[	[	X
ejpam-6050	126	2	ℵea∩ebc(s)⊕	ℵea∩ebc(s)⊕	ADP
ejpam-6050	126	3	ℵeac∩eb(s	ℵeac∩eb(	NOUN
ejpam-6050	126	4	)	)	PUNCT
ejpam-6050	126	5	]	]	PUNCT
ejpam-6050	127	1	=	=	PUNCT
ejpam-6050	127	2	[	[	PUNCT
ejpam-6050	127	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	127	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	127	5	)	)	PUNCT
ejpam-6050	127	6	∗	∗	NOUN
ejpam-6050	127	7	ℵc	ℵc	NOUN
ejpam-6050	127	8	b(s)e	b(s)e	ADP
ejpam-6050	127	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	127	10	b(s	b(	NOUN
ejpam-6050	127	11	)	)	PUNCT
ejpam-6050	127	12	]	]	PUNCT
ejpam-6050	128	1	⊕	⊕	PROPN
ejpam-6050	128	2	[	[	PUNCT
ejpam-6050	128	3	ℵc	ℵc	NOUN
ejpam-6050	128	4	a(s)e	a(s)e	PROPN
ejpam-6050	128	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	128	6	a(s	a(s	PROPN
ejpam-6050	128	7	)	)	PUNCT
ejpam-6050	128	8	∗	∗	NOUN
ejpam-6050	128	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	128	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	128	11	)	)	PUNCT
ejpam-6050	128	12	]	]	PUNCT
ejpam-6050	128	13	.	.	PUNCT
ejpam-6050	129	1	example	example	NOUN
ejpam-6050	130	1	6	6	NUM
ejpam-6050	130	2	.	.	PUNCT
ejpam-6050	130	3	suppose	suppose	VERB
ejpam-6050	130	4	ea	ea	X
ejpam-6050	131	1	=	=	SYM
ejpam-6050	131	2	(	(	PUNCT
ejpam-6050	131	3	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	131	4	s1	s1	NOUN
ejpam-6050	131	5	+	+	CCONJ
ejpam-6050	131	6	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	131	7	s2	s2	NOUN
ejpam-6050	131	8	+	+	CCONJ
ejpam-6050	131	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	131	10	s3	s3	PROPN
ejpam-6050	131	11	)	)	PUNCT
ejpam-6050	131	12	and	and	CCONJ
ejpam-6050	131	13	eb	eb	PROPN
ejpam-6050	131	14	=	=	PUNCT
ejpam-6050	131	15	(	(	PUNCT
ejpam-6050	131	16	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	131	17	s1	s1	NOUN
ejpam-6050	131	18	+	+	CCONJ
ejpam-6050	131	19	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	131	20	s2	s2	NOUN
ejpam-6050	131	21	+	+	CCONJ
ejpam-6050	131	22	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	131	23	s3	s3	PROPN
ejpam-6050	131	24	)	)	PUNCT
ejpam-6050	131	25	.	.	PUNCT
ejpam-6050	132	1	then	then	ADV
ejpam-6050	132	2	the	the	DET
ejpam-6050	132	3	disjunctive	disjunctive	ADJ
ejpam-6050	132	4	sum	sum	NOUN
ejpam-6050	132	5	of	of	ADP
ejpam-6050	132	6	these	these	DET
ejpam-6050	132	7	two	two	NUM
ejpam-6050	132	8	efss	efss	NOUN
ejpam-6050	132	9	is	be	AUX
ejpam-6050	132	10	define	define	VERB
ejpam-6050	132	11	as	as	ADP
ejpam-6050	132	12	ℵea∆eb(s	ℵea∆eb(	NOUN
ejpam-6050	132	13	)	)	PUNCT
ejpam-6050	132	14	=	=	PUNCT
ejpam-6050	133	1	[	[	X
ejpam-6050	133	2	ℵea∩ebc(s)⊕	ℵea∩ebc(s)⊕	ADP
ejpam-6050	133	3	ℵeac∩eb(s	ℵeac∩eb(	NOUN
ejpam-6050	133	4	)	)	PUNCT
ejpam-6050	133	5	]	]	PUNCT
ejpam-6050	134	1	=	=	PUNCT
ejpam-6050	134	2	[	[	PUNCT
ejpam-6050	134	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	134	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	134	5	)	)	PUNCT
ejpam-6050	134	6	∗	∗	NOUN
ejpam-6050	134	7	ℵc	ℵc	NOUN
ejpam-6050	134	8	b(s)e	b(s)e	ADP
ejpam-6050	134	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	134	10	b(s	b(	NOUN
ejpam-6050	134	11	)	)	PUNCT
ejpam-6050	134	12	]	]	PUNCT
ejpam-6050	135	1	⊕	⊕	PROPN
ejpam-6050	135	2	[	[	PUNCT
ejpam-6050	135	3	ℵc	ℵc	NOUN
ejpam-6050	135	4	a(s)e	a(s)e	PROPN
ejpam-6050	135	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	135	6	a(s	a(s	PROPN
ejpam-6050	135	7	)	)	PUNCT
ejpam-6050	135	8	∗	∗	NOUN
ejpam-6050	135	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	135	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	135	11	)	)	PUNCT
ejpam-6050	135	12	]	]	PUNCT
ejpam-6050	135	13	.	.	PUNCT
ejpam-6050	136	1	ℵea∆eb(s	ℵea∆eb(	NOUN
ejpam-6050	136	2	)	)	PUNCT
ejpam-6050	136	3	=	=	SYM
ejpam-6050	136	4	(	(	PUNCT
ejpam-6050	136	5	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	136	6	s1	s1	NOUN
ejpam-6050	136	7	+	+	CCONJ
ejpam-6050	136	8	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	136	9	s2	s2	NOUN
ejpam-6050	136	10	+	+	CCONJ
ejpam-6050	136	11	0.3e−⊺0.3	0.3e−⊺0.3	PROPN
ejpam-6050	136	12	s3	s3	PROPN
ejpam-6050	136	13	)	)	PUNCT
ejpam-6050	136	14	⊕	⊕	PROPN
ejpam-6050	136	15	(	(	PUNCT
ejpam-6050	136	16	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	136	17	s1	s1	NOUN
ejpam-6050	136	18	+	+	CCONJ
ejpam-6050	136	19	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	136	20	s2	s2	NOUN
ejpam-6050	136	21	+	+	CCONJ
ejpam-6050	136	22	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	136	23	s3	s3	PROPN
ejpam-6050	136	24	)	)	PUNCT
ejpam-6050	136	25	.	.	PUNCT
ejpam-6050	137	1	ℵea∆eb(s	ℵea∆eb(	NOUN
ejpam-6050	137	2	)	)	PUNCT
ejpam-6050	137	3	=	=	SYM
ejpam-6050	137	4	(	(	PUNCT
ejpam-6050	137	5	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	137	6	s1	s1	NOUN
ejpam-6050	137	7	+	+	CCONJ
ejpam-6050	137	8	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	137	9	s2	s2	NOUN
ejpam-6050	137	10	+	+	CCONJ
ejpam-6050	137	11	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	137	12	s3	s3	PROPN
ejpam-6050	137	13	)	)	PUNCT
ejpam-6050	137	14	.	.	PUNCT
ejpam-6050	138	1	definition	definition	NOUN
ejpam-6050	138	2	16	16	NUM
ejpam-6050	138	3	.	.	PUNCT
ejpam-6050	139	1	for	for	ADP
ejpam-6050	139	2	any	any	DET
ejpam-6050	139	3	two	two	NUM
ejpam-6050	139	4	efss	efss	NOUN
ejpam-6050	139	5	ea	ea	PROPN
ejpam-6050	139	6	and	and	CCONJ
ejpam-6050	139	7	eb	eb	PROPN
ejpam-6050	139	8	,	,	PUNCT
ejpam-6050	139	9	the	the	DET
ejpam-6050	139	10	equivalence	equivalence	NOUN
ejpam-6050	139	11	formula	formula	NOUN
ejpam-6050	139	12	is	be	AUX
ejpam-6050	139	13	;	;	PUNCT
ejpam-6050	139	14	(	(	PUNCT
ejpam-6050	139	15	eac	eac	PROPN
ejpam-6050	139	16	∪	∪	PROPN
ejpam-6050	139	17	eb	eb	PROPN
ejpam-6050	139	18	)	)	PUNCT
ejpam-6050	139	19	∩	∩	NOUN
ejpam-6050	139	20	(	(	PUNCT
ejpam-6050	139	21	ea	ea	PROPN
ejpam-6050	139	22	∪	∪	PROPN
ejpam-6050	139	23	ebc	ebc	PROPN
ejpam-6050	139	24	)	)	PUNCT
ejpam-6050	139	25	=	=	PUNCT
ejpam-6050	140	1	(	(	PUNCT
ejpam-6050	140	2	eac	eac	PROPN
ejpam-6050	140	3	∩	∩	PROPN
ejpam-6050	140	4	ebc	ebc	PROPN
ejpam-6050	140	5	)	)	PUNCT
ejpam-6050	140	6	∪	∪	NOUN
ejpam-6050	140	7	(	(	PUNCT
ejpam-6050	140	8	ea	ea	X
ejpam-6050	140	9	∩	∩	PROPN
ejpam-6050	140	10	eb	eb	PROPN
ejpam-6050	140	11	)	)	PUNCT
ejpam-6050	140	12	.	.	PUNCT
ejpam-6050	141	1	the	the	DET
ejpam-6050	141	2	membership	membership	NOUN
ejpam-6050	141	3	function	function	NOUN
ejpam-6050	141	4	of	of	ADP
ejpam-6050	141	5	two	two	NUM
ejpam-6050	141	6	efss	efss	ADJ
ejpam-6050	141	7	ea	ea	PROPN
ejpam-6050	141	8	and	and	CCONJ
ejpam-6050	141	9	eb	eb	PROPN
ejpam-6050	141	10	are	be	AUX
ejpam-6050	141	11	given	give	VERB
ejpam-6050	141	12	below	below	ADP
ejpam-6050	141	13	[	[	NOUN
ejpam-6050	141	14	ℵeac∪eb(s	ℵeac∪eb(	NOUN
ejpam-6050	141	15	)	)	PUNCT
ejpam-6050	141	16	∩	∩	NOUN
ejpam-6050	141	17	ℵea∪ebc(s	ℵea∪ebc(s	NUM
ejpam-6050	141	18	)	)	PUNCT
ejpam-6050	141	19	]	]	PUNCT
ejpam-6050	142	1	=	=	PUNCT
ejpam-6050	142	2	[	[	PUNCT
ejpam-6050	142	3	ℵc	ℵc	NOUN
ejpam-6050	142	4	a(s)e	a(s)e	PROPN
ejpam-6050	142	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	142	6	a(s	a(s	PROPN
ejpam-6050	142	7	)	)	PUNCT
ejpam-6050	142	8	⊕	⊕	PROPN
ejpam-6050	142	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	143	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	143	2	)	)	PUNCT
ejpam-6050	143	3	]	]	PUNCT
ejpam-6050	144	1	∗	∗	NOUN
ejpam-6050	144	2	[	[	PUNCT
ejpam-6050	144	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	144	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	144	5	)	)	PUNCT
ejpam-6050	144	6	⊕	⊕	PROPN
ejpam-6050	144	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	144	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	144	9	)	)	PUNCT
ejpam-6050	144	10	]	]	PUNCT
ejpam-6050	145	1	[	[	X
ejpam-6050	145	2	ℵeac∩ebc(s	ℵeac∩ebc(s	X
ejpam-6050	145	3	)	)	PUNCT
ejpam-6050	145	4	∪	∪	ADP
ejpam-6050	145	5	ℵea∩eb(s	ℵea∩eb(	NOUN
ejpam-6050	145	6	)	)	PUNCT
ejpam-6050	145	7	]	]	PUNCT
ejpam-6050	146	1	=	=	PUNCT
ejpam-6050	146	2	[	[	PUNCT
ejpam-6050	146	3	ℵc	ℵc	NOUN
ejpam-6050	146	4	a(s)e	a(s)e	PROPN
ejpam-6050	146	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	146	6	a(s	a(s	PROPN
ejpam-6050	146	7	)	)	PUNCT
ejpam-6050	146	8	∗	∗	NOUN
ejpam-6050	146	9	ℵc	ℵc	NOUN
ejpam-6050	146	10	b(s)e	b(s)e	PROPN
ejpam-6050	146	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	146	12	b(s	b(	NOUN
ejpam-6050	146	13	)	)	PUNCT
ejpam-6050	146	14	]	]	PUNCT
ejpam-6050	147	1	⊕	⊕	PROPN
ejpam-6050	147	2	[	[	PUNCT
ejpam-6050	147	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	147	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	147	5	)	)	PUNCT
ejpam-6050	147	6	∗	∗	NOUN
ejpam-6050	147	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	147	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	147	9	)	)	PUNCT
ejpam-6050	147	10	]	]	PUNCT
ejpam-6050	147	11	example	example	NOUN
ejpam-6050	147	12	7	7	X
ejpam-6050	147	13	.	.	PUNCT
ejpam-6050	147	14	suppose	suppose	VERB
ejpam-6050	147	15	ea	ea	X
ejpam-6050	148	1	=	=	SYM
ejpam-6050	148	2	(	(	PUNCT
ejpam-6050	148	3	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	148	4	s1	s1	NOUN
ejpam-6050	148	5	+	+	CCONJ
ejpam-6050	148	6	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	148	7	s2	s2	NOUN
ejpam-6050	148	8	+	+	CCONJ
ejpam-6050	148	9	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	148	10	s3	s3	PROPN
ejpam-6050	148	11	)	)	PUNCT
ejpam-6050	148	12	and	and	CCONJ
ejpam-6050	148	13	eb	eb	PROPN
ejpam-6050	148	14	=	=	PUNCT
ejpam-6050	148	15	(	(	PUNCT
ejpam-6050	148	16	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	148	17	s1	s1	NOUN
ejpam-6050	148	18	+	+	CCONJ
ejpam-6050	148	19	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	148	20	s2	s2	NOUN
ejpam-6050	148	21	+	+	CCONJ
ejpam-6050	148	22	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	148	23	s3	s3	PROPN
ejpam-6050	148	24	)	)	PUNCT
ejpam-6050	148	25	.	.	PUNCT
ejpam-6050	149	1	the	the	DET
ejpam-6050	149	2	equivalence	equivalence	NOUN
ejpam-6050	149	3	formula	formula	NOUN
ejpam-6050	149	4	is	be	AUX
ejpam-6050	149	5	;	;	PUNCT
ejpam-6050	149	6	(	(	PUNCT
ejpam-6050	149	7	eac	eac	PROPN
ejpam-6050	149	8	∪	∪	PROPN
ejpam-6050	149	9	eb	eb	PROPN
ejpam-6050	149	10	)	)	PUNCT
ejpam-6050	149	11	∩	∩	NOUN
ejpam-6050	149	12	(	(	PUNCT
ejpam-6050	149	13	ea	ea	PROPN
ejpam-6050	149	14	∪	∪	PROPN
ejpam-6050	149	15	ebc	ebc	PROPN
ejpam-6050	149	16	)	)	PUNCT
ejpam-6050	149	17	=	=	PUNCT
ejpam-6050	150	1	(	(	PUNCT
ejpam-6050	150	2	eac	eac	PROPN
ejpam-6050	150	3	∩	∩	PROPN
ejpam-6050	150	4	ebc	ebc	PROPN
ejpam-6050	150	5	)	)	PUNCT
ejpam-6050	150	6	∪	∪	NOUN
ejpam-6050	150	7	(	(	PUNCT
ejpam-6050	150	8	ea	ea	X
ejpam-6050	150	9	∩	∩	PROPN
ejpam-6050	150	10	eb	eb	PROPN
ejpam-6050	150	11	)	)	PUNCT
ejpam-6050	150	12	.	.	PUNCT
ejpam-6050	151	1	(	(	PUNCT
ejpam-6050	151	2	eac	eac	PROPN
ejpam-6050	151	3	∪	∪	PROPN
ejpam-6050	151	4	eb	eb	PROPN
ejpam-6050	151	5	)	)	PUNCT
ejpam-6050	151	6	∩	∩	NOUN
ejpam-6050	151	7	(	(	PUNCT
ejpam-6050	151	8	ea	ea	PROPN
ejpam-6050	151	9	∪	∪	PROPN
ejpam-6050	151	10	ebc	ebc	PROPN
ejpam-6050	151	11	)	)	PUNCT
ejpam-6050	151	12	=	=	PUNCT
ejpam-6050	151	13	(	(	PUNCT
ejpam-6050	151	14	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	151	15	s1	s1	NOUN
ejpam-6050	151	16	+	+	CCONJ
ejpam-6050	151	17	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	151	18	s2	s2	NOUN
ejpam-6050	151	19	+	+	CCONJ
ejpam-6050	151	20	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	151	21	s3	s3	PROPN
ejpam-6050	151	22	)	)	PUNCT
ejpam-6050	151	23	∗	∗	NOUN
ejpam-6050	151	24	(	(	PUNCT
ejpam-6050	151	25	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	151	26	s1	s1	NOUN
ejpam-6050	151	27	+	+	CCONJ
ejpam-6050	151	28	0.8e−⊺0.8	0.8e−⊺0.8	NOUN
ejpam-6050	151	29	s2	s2	NOUN
ejpam-6050	151	30	+	+	CCONJ
ejpam-6050	151	31	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	151	32	s3	s3	PROPN
ejpam-6050	151	33	)	)	PUNCT
ejpam-6050	151	34	=	=	PUNCT
ejpam-6050	151	35	(	(	PUNCT
ejpam-6050	151	36	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	151	37	s1	s1	NOUN
ejpam-6050	151	38	+	+	CCONJ
ejpam-6050	151	39	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	151	40	s2	s2	NOUN
ejpam-6050	151	41	+	+	CCONJ
ejpam-6050	151	42	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	151	43	s3	s3	PROPN
ejpam-6050	151	44	)	)	PUNCT
ejpam-6050	151	45	(	(	PUNCT
ejpam-6050	151	46	3.3	3.3	NUM
ejpam-6050	151	47	)	)	PUNCT
ejpam-6050	151	48	m.	m.	NOUN
ejpam-6050	151	49	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	151	50	,	,	PUNCT
ejpam-6050	151	51	m.	m.	NOUN
ejpam-6050	151	52	rajeshwari	rajeshwari	NOUN
ejpam-6050	151	53	,	,	PUNCT
ejpam-6050	151	54	m.	m.	NOUN
ejpam-6050	151	55	alqahtani	alqahtani	PROPN
ejpam-6050	151	56	/	/	SYM
ejpam-6050	151	57	eur	eur	PROPN
ejpam-6050	151	58	.	.	PUNCT
ejpam-6050	152	1	j.	j.	PROPN
ejpam-6050	152	2	pure	pure	PROPN
ejpam-6050	152	3	appl	appl	PROPN
ejpam-6050	152	4	.	.	PROPN
ejpam-6050	152	5	math	math	PROPN
ejpam-6050	152	6	,	,	PUNCT
ejpam-6050	152	7	18	18	NUM
ejpam-6050	152	8	(	(	PUNCT
ejpam-6050	152	9	2	2	NUM
ejpam-6050	152	10	)	)	PUNCT
ejpam-6050	152	11	(	(	PUNCT
ejpam-6050	152	12	2025	2025	NUM
ejpam-6050	152	13	)	)	PUNCT
ejpam-6050	152	14	,	,	PUNCT
ejpam-6050	152	15	6050	6050	NUM
ejpam-6050	152	16	8	8	NUM
ejpam-6050	152	17	of	of	ADP
ejpam-6050	152	18	29	29	NUM
ejpam-6050	152	19	(	(	PUNCT
ejpam-6050	152	20	eac	eac	PROPN
ejpam-6050	152	21	∩	∩	PROPN
ejpam-6050	152	22	ebc	ebc	PROPN
ejpam-6050	152	23	)	)	PUNCT
ejpam-6050	152	24	∪	∪	NOUN
ejpam-6050	152	25	(	(	PUNCT
ejpam-6050	152	26	ea	ea	X
ejpam-6050	152	27	∩	∩	PROPN
ejpam-6050	152	28	eb	eb	PROPN
ejpam-6050	152	29	)	)	PUNCT
ejpam-6050	152	30	=	=	PRON
ejpam-6050	152	31	(	(	PUNCT
ejpam-6050	152	32	0.2e−⊺0.2	0.2e−⊺0.2	NOUN
ejpam-6050	152	33	s1	s1	PROPN
ejpam-6050	152	34	+	+	CCONJ
ejpam-6050	152	35	0.2e−⊺0.2	0.2e−⊺0.2	PROPN
ejpam-6050	152	36	s2	s2	NOUN
ejpam-6050	152	37	+	+	CCONJ
ejpam-6050	152	38	0.3e−⊺0.3	0.3e−⊺0.3	PROPN
ejpam-6050	152	39	s3	s3	PROPN
ejpam-6050	152	40	)	)	PUNCT
ejpam-6050	152	41	⊕	⊕	PROPN
ejpam-6050	152	42	(	(	PUNCT
ejpam-6050	152	43	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	152	44	s1	s1	NOUN
ejpam-6050	152	45	+	+	CCONJ
ejpam-6050	152	46	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	152	47	s2	s2	NOUN
ejpam-6050	152	48	+	+	CCONJ
ejpam-6050	152	49	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	152	50	s3	s3	PROPN
ejpam-6050	152	51	)	)	PUNCT
ejpam-6050	152	52	=	=	PUNCT
ejpam-6050	153	1	(	(	PUNCT
ejpam-6050	153	2	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	153	3	s1	s1	NOUN
ejpam-6050	153	4	+	+	CCONJ
ejpam-6050	153	5	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	153	6	s2	s2	NOUN
ejpam-6050	153	7	+	+	CCONJ
ejpam-6050	153	8	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	153	9	s3	s3	PROPN
ejpam-6050	153	10	)	)	PUNCT
ejpam-6050	153	11	(	(	PUNCT
ejpam-6050	153	12	3.4	3.4	NUM
ejpam-6050	153	13	)	)	PUNCT
ejpam-6050	153	14	from	from	ADP
ejpam-6050	153	15	equation	equation	NOUN
ejpam-6050	153	16	3.3	3.3	NUM
ejpam-6050	153	17	and	and	CCONJ
ejpam-6050	153	18	3.4	3.4	NUM
ejpam-6050	153	19	,	,	PUNCT
ejpam-6050	153	20	we	we	PRON
ejpam-6050	153	21	have	have	VERB
ejpam-6050	153	22	(	(	PUNCT
ejpam-6050	153	23	eac	eac	PROPN
ejpam-6050	153	24	∪	∪	PROPN
ejpam-6050	153	25	eb	eb	PROPN
ejpam-6050	153	26	)	)	PUNCT
ejpam-6050	153	27	∩	∩	NOUN
ejpam-6050	153	28	(	(	PUNCT
ejpam-6050	153	29	ea	ea	PROPN
ejpam-6050	153	30	∪	∪	PROPN
ejpam-6050	153	31	ebc	ebc	PROPN
ejpam-6050	153	32	)	)	PUNCT
ejpam-6050	153	33	=	=	PUNCT
ejpam-6050	154	1	(	(	PUNCT
ejpam-6050	154	2	eac	eac	PROPN
ejpam-6050	154	3	∩	∩	PROPN
ejpam-6050	154	4	ebc	ebc	PROPN
ejpam-6050	154	5	)	)	PUNCT
ejpam-6050	154	6	∪	∪	NOUN
ejpam-6050	154	7	(	(	PUNCT
ejpam-6050	154	8	ea	ea	X
ejpam-6050	154	9	∩	∩	PROPN
ejpam-6050	154	10	eb	eb	PROPN
ejpam-6050	154	11	)	)	PUNCT
ejpam-6050	154	12	.	.	PUNCT
ejpam-6050	155	1	definition	definition	NOUN
ejpam-6050	155	2	17	17	NUM
ejpam-6050	155	3	.	.	PUNCT
ejpam-6050	156	1	the	the	DET
ejpam-6050	156	2	symmetrical	symmetrical	ADJ
ejpam-6050	156	3	difference	difference	NOUN
ejpam-6050	156	4	formula	formula	NOUN
ejpam-6050	156	5	for	for	ADP
ejpam-6050	156	6	two	two	NUM
ejpam-6050	156	7	efss	efss	ADJ
ejpam-6050	156	8	ea	ea	PROPN
ejpam-6050	156	9	and	and	CCONJ
ejpam-6050	156	10	eb	eb	PROPN
ejpam-6050	156	11	are	be	AUX
ejpam-6050	156	12	denoted	denote	VERB
ejpam-6050	156	13	by	by	ADP
ejpam-6050	156	14	(	(	PUNCT
ejpam-6050	156	15	eac	eac	PROPN
ejpam-6050	156	16	∩	∩	PROPN
ejpam-6050	156	17	eb	eb	PROPN
ejpam-6050	156	18	)	)	PUNCT
ejpam-6050	156	19	∪	∪	NOUN
ejpam-6050	156	20	(	(	PUNCT
ejpam-6050	156	21	ea	ea	PROPN
ejpam-6050	156	22	∩	∩	PROPN
ejpam-6050	156	23	ebc	ebc	PROPN
ejpam-6050	156	24	)	)	PUNCT
ejpam-6050	157	1	=	=	PUNCT
ejpam-6050	157	2	(	(	PUNCT
ejpam-6050	157	3	eac	eac	PROPN
ejpam-6050	157	4	∪	∪	PROPN
ejpam-6050	157	5	ebc	ebc	PROPN
ejpam-6050	157	6	)	)	PUNCT
ejpam-6050	157	7	∩	∩	NOUN
ejpam-6050	157	8	(	(	PUNCT
ejpam-6050	157	9	ea	ea	PROPN
ejpam-6050	157	10	∩	∩	PROPN
ejpam-6050	157	11	eb	eb	PROPN
ejpam-6050	157	12	)	)	PUNCT
ejpam-6050	157	13	.	.	PUNCT
ejpam-6050	158	1	the	the	DET
ejpam-6050	158	2	symmetrical	symmetrical	ADJ
ejpam-6050	158	3	difference	difference	NOUN
ejpam-6050	158	4	formula	formula	NOUN
ejpam-6050	158	5	two	two	NUM
ejpam-6050	158	6	efss	efss	NOUN
ejpam-6050	158	7	ea	ea	PROPN
ejpam-6050	158	8	and	and	CCONJ
ejpam-6050	158	9	eb	eb	PROPN
ejpam-6050	158	10	are	be	AUX
ejpam-6050	158	11	given	give	VERB
ejpam-6050	158	12	below	below	ADP
ejpam-6050	158	13	[	[	PRON
ejpam-6050	158	14	ℵeac∩eb(s	ℵeac∩eb(	NOUN
ejpam-6050	158	15	)	)	PUNCT
ejpam-6050	158	16	∪	∪	ADP
ejpam-6050	158	17	ℵea∩ebc(s	ℵea∩ebc(s	NOUN
ejpam-6050	158	18	)	)	PUNCT
ejpam-6050	158	19	]	]	PUNCT
ejpam-6050	159	1	=	=	PUNCT
ejpam-6050	159	2	[	[	PUNCT
ejpam-6050	159	3	ℵc	ℵc	NOUN
ejpam-6050	159	4	a(s)e	a(s)e	PROPN
ejpam-6050	159	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	159	6	a(s	a(s	PROPN
ejpam-6050	159	7	)	)	PUNCT
ejpam-6050	159	8	∗	∗	NOUN
ejpam-6050	159	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	159	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	159	11	)	)	PUNCT
ejpam-6050	159	12	]	]	PUNCT
ejpam-6050	160	1	⊕	⊕	PROPN
ejpam-6050	160	2	[	[	PUNCT
ejpam-6050	160	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	160	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	160	5	)	)	PUNCT
ejpam-6050	160	6	∗	∗	NOUN
ejpam-6050	160	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	160	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	160	9	)	)	PUNCT
ejpam-6050	160	10	]	]	PUNCT
ejpam-6050	161	1	[	[	X
ejpam-6050	161	2	ℵeac∪ebc(s	ℵeac∪ebc(s	X
ejpam-6050	161	3	)	)	PUNCT
ejpam-6050	161	4	∩	∩	NOUN
ejpam-6050	161	5	ℵea∪eb(s	ℵea∪eb(	NOUN
ejpam-6050	161	6	)	)	PUNCT
ejpam-6050	161	7	]	]	PUNCT
ejpam-6050	162	1	=	=	PUNCT
ejpam-6050	162	2	[	[	PUNCT
ejpam-6050	162	3	ℵc	ℵc	NOUN
ejpam-6050	162	4	a(s)e	a(s)e	PROPN
ejpam-6050	162	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	162	6	a(s	a(s	PROPN
ejpam-6050	162	7	)	)	PUNCT
ejpam-6050	162	8	⊕	⊕	PROPN
ejpam-6050	162	9	ℵc	ℵc	VERB
ejpam-6050	162	10	b(s)e	b(s)e	ADP
ejpam-6050	162	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	162	12	b(s	b(	NOUN
ejpam-6050	162	13	)	)	PUNCT
ejpam-6050	162	14	]	]	PUNCT
ejpam-6050	163	1	∗	∗	NOUN
ejpam-6050	163	2	[	[	PUNCT
ejpam-6050	163	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	163	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	163	5	)	)	PUNCT
ejpam-6050	163	6	⊕	⊕	PROPN
ejpam-6050	163	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	163	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	163	9	)	)	PUNCT
ejpam-6050	163	10	]	]	PUNCT
ejpam-6050	163	11	example	example	NOUN
ejpam-6050	163	12	8	8	X
ejpam-6050	163	13	.	.	PUNCT
ejpam-6050	163	14	suppose	suppose	VERB
ejpam-6050	163	15	ea	ea	X
ejpam-6050	164	1	=	=	SYM
ejpam-6050	165	1	(	(	PUNCT
ejpam-6050	165	2	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	165	3	s1	s1	NOUN
ejpam-6050	165	4	+	+	CCONJ
ejpam-6050	165	5	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	165	6	s2	s2	NOUN
ejpam-6050	165	7	+	+	CCONJ
ejpam-6050	165	8	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	165	9	s3	s3	PROPN
ejpam-6050	165	10	)	)	PUNCT
ejpam-6050	165	11	and	and	CCONJ
ejpam-6050	165	12	eb	eb	PROPN
ejpam-6050	165	13	=	=	PUNCT
ejpam-6050	165	14	(	(	PUNCT
ejpam-6050	165	15	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	165	16	s1	s1	NOUN
ejpam-6050	165	17	+	+	CCONJ
ejpam-6050	165	18	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	165	19	s2	s2	NOUN
ejpam-6050	165	20	+	+	CCONJ
ejpam-6050	165	21	0.2e−⊺0.2	0.2e−⊺0.2	PROPN
ejpam-6050	165	22	s3	s3	PROPN
ejpam-6050	165	23	)	)	PUNCT
ejpam-6050	165	24	.	.	PUNCT
ejpam-6050	166	1	the	the	DET
ejpam-6050	166	2	symmetrical	symmetrical	ADJ
ejpam-6050	166	3	difference	difference	NOUN
ejpam-6050	166	4	formula	formula	NOUN
ejpam-6050	166	5	is	be	AUX
ejpam-6050	166	6	(	(	PUNCT
ejpam-6050	166	7	eac	eac	PROPN
ejpam-6050	166	8	∩	∩	PROPN
ejpam-6050	166	9	eb	eb	PROPN
ejpam-6050	166	10	)	)	PUNCT
ejpam-6050	166	11	∪	∪	NOUN
ejpam-6050	166	12	(	(	PUNCT
ejpam-6050	166	13	ea	ea	PROPN
ejpam-6050	166	14	∩	∩	PROPN
ejpam-6050	166	15	ebc	ebc	PROPN
ejpam-6050	166	16	)	)	PUNCT
ejpam-6050	166	17	=	=	PUNCT
ejpam-6050	167	1	(	(	PUNCT
ejpam-6050	167	2	eac	eac	PROPN
ejpam-6050	167	3	∪	∪	PROPN
ejpam-6050	167	4	ebc	ebc	PROPN
ejpam-6050	167	5	)	)	PUNCT
ejpam-6050	167	6	∩	∩	NOUN
ejpam-6050	167	7	(	(	PUNCT
ejpam-6050	167	8	ea	ea	PROPN
ejpam-6050	167	9	∩	∩	PROPN
ejpam-6050	167	10	eb	eb	PROPN
ejpam-6050	167	11	)	)	PUNCT
ejpam-6050	167	12	.	.	PUNCT
ejpam-6050	168	1	(	(	PUNCT
ejpam-6050	168	2	eac	eac	PROPN
ejpam-6050	168	3	∩	∩	PROPN
ejpam-6050	168	4	eb	eb	PROPN
ejpam-6050	168	5	)	)	PUNCT
ejpam-6050	168	6	∪	∪	NOUN
ejpam-6050	168	7	(	(	PUNCT
ejpam-6050	168	8	ea	ea	PROPN
ejpam-6050	168	9	∩	∩	PROPN
ejpam-6050	168	10	ebc	ebc	PROPN
ejpam-6050	168	11	)	)	PUNCT
ejpam-6050	168	12	=	=	PRON
ejpam-6050	168	13	(	(	PUNCT
ejpam-6050	168	14	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	168	15	s1	s1	NOUN
ejpam-6050	168	16	+	+	CCONJ
ejpam-6050	168	17	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	168	18	s2	s2	NOUN
ejpam-6050	168	19	+	+	CCONJ
ejpam-6050	168	20	0.2e−⊺0.2	0.2e−⊺0.2	PROPN
ejpam-6050	168	21	s3	s3	PROPN
ejpam-6050	168	22	)	)	PUNCT
ejpam-6050	168	23	⊕	⊕	PROPN
ejpam-6050	168	24	(	(	PUNCT
ejpam-6050	168	25	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	168	26	s1	s1	NOUN
ejpam-6050	168	27	+	+	CCONJ
ejpam-6050	168	28	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	168	29	s2	s2	NOUN
ejpam-6050	168	30	+	+	CCONJ
ejpam-6050	168	31	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	168	32	s3	s3	PROPN
ejpam-6050	168	33	)	)	PUNCT
ejpam-6050	168	34	=	=	PUNCT
ejpam-6050	169	1	(	(	PUNCT
ejpam-6050	169	2	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	169	3	s1	s1	NOUN
ejpam-6050	169	4	+	+	CCONJ
ejpam-6050	169	5	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	169	6	s2	s2	NOUN
ejpam-6050	169	7	+	+	CCONJ
ejpam-6050	169	8	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	169	9	s3	s3	PROPN
ejpam-6050	169	10	)	)	PUNCT
ejpam-6050	169	11	(	(	PUNCT
ejpam-6050	169	12	3.5	3.5	NUM
ejpam-6050	169	13	)	)	PUNCT
ejpam-6050	169	14	(	(	PUNCT
ejpam-6050	169	15	eac	eac	PROPN
ejpam-6050	169	16	∪	∪	PROPN
ejpam-6050	169	17	ebc	ebc	PROPN
ejpam-6050	169	18	)	)	PUNCT
ejpam-6050	169	19	∩	∩	NOUN
ejpam-6050	169	20	(	(	PUNCT
ejpam-6050	169	21	ea	ea	PROPN
ejpam-6050	169	22	∩	∩	PROPN
ejpam-6050	169	23	eb	eb	PROPN
ejpam-6050	169	24	)	)	PUNCT
ejpam-6050	169	25	=	=	PRON
ejpam-6050	169	26	(	(	PUNCT
ejpam-6050	169	27	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	169	28	s1	s1	NOUN
ejpam-6050	169	29	+	+	CCONJ
ejpam-6050	169	30	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	169	31	s2	s2	NOUN
ejpam-6050	169	32	+	+	CCONJ
ejpam-6050	169	33	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	169	34	s3	s3	PROPN
ejpam-6050	169	35	)	)	PUNCT
ejpam-6050	169	36	⊕	⊕	PROPN
ejpam-6050	169	37	(	(	PUNCT
ejpam-6050	169	38	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	169	39	s1	s1	NOUN
ejpam-6050	169	40	+	+	CCONJ
ejpam-6050	169	41	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	169	42	s2	s2	NOUN
ejpam-6050	169	43	+	+	CCONJ
ejpam-6050	169	44	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	169	45	s3	s3	PROPN
ejpam-6050	169	46	)	)	PUNCT
ejpam-6050	169	47	=	=	PUNCT
ejpam-6050	170	1	(	(	PUNCT
ejpam-6050	170	2	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	170	3	s1	s1	NOUN
ejpam-6050	170	4	+	+	CCONJ
ejpam-6050	170	5	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	170	6	s2	s2	NOUN
ejpam-6050	170	7	+	+	CCONJ
ejpam-6050	170	8	0.8e−⊺0.8	0.8e−⊺0.8	PROPN
ejpam-6050	170	9	s3	s3	PROPN
ejpam-6050	170	10	)	)	PUNCT
ejpam-6050	170	11	(	(	PUNCT
ejpam-6050	170	12	3.6	3.6	NUM
ejpam-6050	170	13	)	)	PUNCT
ejpam-6050	170	14	from	from	ADP
ejpam-6050	170	15	equation	equation	NOUN
ejpam-6050	170	16	3.5	3.5	NUM
ejpam-6050	170	17	and	and	CCONJ
ejpam-6050	170	18	3.6	3.6	NUM
ejpam-6050	170	19	,	,	PUNCT
ejpam-6050	170	20	we	we	PRON
ejpam-6050	170	21	have	have	VERB
ejpam-6050	170	22	(	(	PUNCT
ejpam-6050	170	23	eac	eac	PROPN
ejpam-6050	170	24	∩	∩	PROPN
ejpam-6050	170	25	eb	eb	PROPN
ejpam-6050	170	26	)	)	PUNCT
ejpam-6050	170	27	∪	∪	NOUN
ejpam-6050	170	28	(	(	PUNCT
ejpam-6050	170	29	ea	ea	PROPN
ejpam-6050	170	30	∩	∩	PROPN
ejpam-6050	170	31	ebc	ebc	PROPN
ejpam-6050	170	32	)	)	PUNCT
ejpam-6050	170	33	=	=	PUNCT
ejpam-6050	171	1	(	(	PUNCT
ejpam-6050	171	2	eac	eac	PROPN
ejpam-6050	171	3	∪	∪	PROPN
ejpam-6050	171	4	ebc	ebc	PROPN
ejpam-6050	171	5	)	)	PUNCT
ejpam-6050	171	6	∩	∩	NOUN
ejpam-6050	171	7	(	(	PUNCT
ejpam-6050	171	8	ea	ea	PROPN
ejpam-6050	171	9	∩	∩	PROPN
ejpam-6050	171	10	eb	eb	PROPN
ejpam-6050	171	11	)	)	PUNCT
ejpam-6050	171	12	.	.	PUNCT
ejpam-6050	172	1	definition	definition	NOUN
ejpam-6050	172	2	18	18	NUM
ejpam-6050	172	3	.	.	PUNCT
ejpam-6050	173	1	let	let	VERB
ejpam-6050	173	2	ea	ea	NOUN
ejpam-6050	173	3	and	and	CCONJ
ejpam-6050	173	4	eb	eb	PROPN
ejpam-6050	173	5	and	and	CCONJ
ejpam-6050	173	6	efss	efss	NOUN
ejpam-6050	173	7	be	be	AUX
ejpam-6050	173	8	three	three	NUM
ejpam-6050	173	9	efss	efss	NOUN
ejpam-6050	173	10	then	then	ADV
ejpam-6050	173	11	,	,	PUNCT
ejpam-6050	173	12	the	the	DET
ejpam-6050	173	13	distributive	distributive	ADJ
ejpam-6050	173	14	law	law	NOUN
ejpam-6050	173	15	are	be	AUX
ejpam-6050	173	16	ea	ea	NOUN
ejpam-6050	173	17	∪	∪	X
ejpam-6050	173	18	(	(	PUNCT
ejpam-6050	173	19	eb	eb	PROPN
ejpam-6050	173	20	∩	∩	PROPN
ejpam-6050	173	21	ec	ec	PROPN
ejpam-6050	173	22	)	)	PUNCT
ejpam-6050	174	1	=	=	PRON
ejpam-6050	174	2	(	(	PUNCT
ejpam-6050	174	3	ea	ea	PROPN
ejpam-6050	174	4	∪	∪	PROPN
ejpam-6050	174	5	eb	eb	PROPN
ejpam-6050	174	6	)	)	PUNCT
ejpam-6050	174	7	∩	∩	NOUN
ejpam-6050	174	8	(	(	PUNCT
ejpam-6050	174	9	ea	ea	X
ejpam-6050	174	10	∪	∪	ADP
ejpam-6050	174	11	ec	ec	PROPN
ejpam-6050	174	12	)	)	PUNCT
ejpam-6050	174	13	ea	ea	NOUN
ejpam-6050	174	14	∩	∩	NOUN
ejpam-6050	174	15	(	(	PUNCT
ejpam-6050	174	16	eb	eb	PROPN
ejpam-6050	174	17	∪	∪	PROPN
ejpam-6050	174	18	ec	ec	PROPN
ejpam-6050	174	19	)	)	PUNCT
ejpam-6050	174	20	=	=	SYM
ejpam-6050	174	21	(	(	PUNCT
ejpam-6050	174	22	ea	ea	X
ejpam-6050	174	23	∩	∩	PROPN
ejpam-6050	174	24	eb	eb	PROPN
ejpam-6050	174	25	)	)	PUNCT
ejpam-6050	174	26	∪	∪	NOUN
ejpam-6050	174	27	(	(	PUNCT
ejpam-6050	174	28	ea	ea	X
ejpam-6050	174	29	∩	∩	X
ejpam-6050	174	30	ec	ec	PROPN
ejpam-6050	174	31	)	)	PUNCT
ejpam-6050	174	32	.	.	PUNCT
ejpam-6050	175	1	theses	these	VERB
ejpam-6050	175	2	two	two	NUM
ejpam-6050	175	3	law	law	NOUN
ejpam-6050	175	4	are	be	AUX
ejpam-6050	175	5	said	say	VERB
ejpam-6050	175	6	to	to	PART
ejpam-6050	175	7	be	be	AUX
ejpam-6050	175	8	distributive	distributive	ADJ
ejpam-6050	175	9	law	law	NOUN
ejpam-6050	175	10	of	of	ADP
ejpam-6050	175	11	union	union	NOUN
ejpam-6050	175	12	over	over	ADP
ejpam-6050	175	13	intersection	intersection	NOUN
ejpam-6050	175	14	and	and	CCONJ
ejpam-6050	175	15	intersection	intersection	NOUN
ejpam-6050	175	16	over	over	ADP
ejpam-6050	175	17	union	union	NOUN
ejpam-6050	175	18	.	.	PUNCT
ejpam-6050	176	1	if	if	SCONJ
ejpam-6050	176	2	ea	ea	NUM
ejpam-6050	176	3	=	=	SYM
ejpam-6050	176	4	ℵea(s	ℵea(s	PROPN
ejpam-6050	176	5	)	)	PUNCT
ejpam-6050	176	6	=	=	PUNCT
ejpam-6050	176	7	ℵa(s)e	ℵa(s)e	X
ejpam-6050	176	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	176	9	)	)	PUNCT
ejpam-6050	176	10	,	,	PUNCT
ejpam-6050	176	11	eb	eb	PROPN
ejpam-6050	176	12	=	=	SYM
ejpam-6050	176	13	ℵeb(s	ℵeb(s	PROPN
ejpam-6050	176	14	)	)	PUNCT
ejpam-6050	176	15	=	=	SYM
ejpam-6050	176	16	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	176	17	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	176	18	)	)	PUNCT
ejpam-6050	176	19	and	and	CCONJ
ejpam-6050	176	20	ec	ec	PROPN
ejpam-6050	176	21	=	=	SYM
ejpam-6050	176	22	ℵec(s	ℵec(s	PROPN
ejpam-6050	176	23	)	)	PUNCT
ejpam-6050	176	24	=	=	PUNCT
ejpam-6050	176	25	ℵc(s)e	ℵc(s)e	SYM
ejpam-6050	176	26	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	176	27	)	)	PUNCT
ejpam-6050	176	28	,	,	PUNCT
ejpam-6050	176	29	the	the	DET
ejpam-6050	176	30	distributive	distributive	ADJ
ejpam-6050	176	31	law	law	NOUN
ejpam-6050	176	32	of	of	ADP
ejpam-6050	176	33	union	union	NOUN
ejpam-6050	176	34	intersection	intersection	NOUN
ejpam-6050	176	35	become	become	VERB
ejpam-6050	176	36	:	:	PUNCT
ejpam-6050	177	1	[	[	X
ejpam-6050	177	2	ℵea(s)⊕	ℵea(s)⊕	PROPN
ejpam-6050	177	3	(	(	PUNCT
ejpam-6050	177	4	ℵeb(s	ℵeb(	NOUN
ejpam-6050	177	5	)	)	PUNCT
ejpam-6050	177	6	∗	∗	NOUN
ejpam-6050	177	7	ℵec(s	ℵec(s	NUM
ejpam-6050	177	8	)	)	PUNCT
ejpam-6050	177	9	)	)	PUNCT
ejpam-6050	177	10	]	]	PUNCT
ejpam-6050	178	1	=	=	PUNCT
ejpam-6050	178	2	[	[	PUNCT
ejpam-6050	178	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	178	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	178	5	)	)	PUNCT
ejpam-6050	178	6	⊕	⊕	PROPN
ejpam-6050	178	7	[	[	PUNCT
ejpam-6050	178	8	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	178	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	178	10	)	)	PUNCT
ejpam-6050	178	11	∗	∗	NOUN
ejpam-6050	178	12	ℵc(s)e	ℵc(s)e	X
ejpam-6050	178	13	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	178	14	)	)	PUNCT
ejpam-6050	178	15	]	]	PUNCT
ejpam-6050	178	16	]	]	X
ejpam-6050	179	1	[	[	X
ejpam-6050	179	2	ℵea(s)⊕	ℵea(s)⊕	PROPN
ejpam-6050	179	3	ℵeb(s)]∗[ℵea(s)⊕	ℵeb(s)]∗[ℵea(s)⊕	ADV
ejpam-6050	179	4	ℵec(s	ℵec(s	NUM
ejpam-6050	179	5	)	)	PUNCT
ejpam-6050	179	6	]	]	PUNCT
ejpam-6050	180	1	=	=	PUNCT
ejpam-6050	180	2	[	[	PUNCT
ejpam-6050	180	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	180	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	180	5	)	)	PUNCT
ejpam-6050	180	6	⊕	⊕	PROPN
ejpam-6050	180	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	180	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	180	9	)	)	PUNCT
ejpam-6050	180	10	]	]	PUNCT
ejpam-6050	181	1	⊕	⊕	PROPN
ejpam-6050	181	2	[	[	PUNCT
ejpam-6050	181	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	181	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	181	5	)	)	PUNCT
ejpam-6050	181	6	⊕	⊕	PROPN
ejpam-6050	181	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	181	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	181	9	)	)	PUNCT
ejpam-6050	181	10	]	]	PUNCT
ejpam-6050	181	11	.	.	PUNCT
ejpam-6050	182	1	m.	m.	PROPN
ejpam-6050	182	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	182	3	,	,	PUNCT
ejpam-6050	182	4	m.	m.	NOUN
ejpam-6050	182	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	182	6	,	,	PUNCT
ejpam-6050	182	7	m.	m.	NOUN
ejpam-6050	182	8	alqahtani	alqahtani	PROPN
ejpam-6050	182	9	/	/	SYM
ejpam-6050	182	10	eur	eur	PROPN
ejpam-6050	182	11	.	.	PUNCT
ejpam-6050	183	1	j.	j.	PROPN
ejpam-6050	183	2	pure	pure	PROPN
ejpam-6050	183	3	appl	appl	PROPN
ejpam-6050	183	4	.	.	PROPN
ejpam-6050	183	5	math	math	PROPN
ejpam-6050	183	6	,	,	PUNCT
ejpam-6050	183	7	18	18	NUM
ejpam-6050	183	8	(	(	PUNCT
ejpam-6050	183	9	2	2	NUM
ejpam-6050	183	10	)	)	PUNCT
ejpam-6050	183	11	(	(	PUNCT
ejpam-6050	183	12	2025	2025	NUM
ejpam-6050	183	13	)	)	PUNCT
ejpam-6050	183	14	,	,	PUNCT
ejpam-6050	183	15	6050	6050	NUM
ejpam-6050	183	16	9	9	NUM
ejpam-6050	183	17	of	of	ADP
ejpam-6050	183	18	29	29	NUM
ejpam-6050	183	19	example	example	NOUN
ejpam-6050	183	20	9	9	NUM
ejpam-6050	183	21	.	.	PUNCT
ejpam-6050	183	22	ea	ea	NOUN
ejpam-6050	184	1	=	=	PUNCT
ejpam-6050	185	1	(	(	PUNCT
ejpam-6050	185	2	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	185	3	s1	s1	NOUN
ejpam-6050	185	4	+	+	CCONJ
ejpam-6050	185	5	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	185	6	s2	s2	NOUN
ejpam-6050	185	7	+	+	CCONJ
ejpam-6050	185	8	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	185	9	s3	s3	PROPN
ejpam-6050	185	10	)	)	PUNCT
ejpam-6050	185	11	,	,	PUNCT
ejpam-6050	185	12	eb	eb	PROPN
ejpam-6050	185	13	=	=	PUNCT
ejpam-6050	185	14	(	(	PUNCT
ejpam-6050	185	15	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	185	16	s1	s1	NOUN
ejpam-6050	185	17	+	+	CCONJ
ejpam-6050	185	18	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	185	19	s2	s2	NOUN
ejpam-6050	185	20	+	+	CCONJ
ejpam-6050	185	21	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	185	22	s3	s3	PROPN
ejpam-6050	185	23	)	)	PUNCT
ejpam-6050	185	24	and	and	CCONJ
ejpam-6050	185	25	ec	ec	PROPN
ejpam-6050	185	26	=	=	PUNCT
ejpam-6050	185	27	(	(	PUNCT
ejpam-6050	185	28	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	185	29	s1	s1	NOUN
ejpam-6050	185	30	+	+	CCONJ
ejpam-6050	185	31	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	185	32	s2	s2	NOUN
ejpam-6050	185	33	+	+	CCONJ
ejpam-6050	185	34	1e−⊺1	1e−⊺1	NUM
ejpam-6050	185	35	s3	s3	NOUN
ejpam-6050	185	36	)	)	PUNCT
ejpam-6050	185	37	be	be	AUX
ejpam-6050	185	38	the	the	DET
ejpam-6050	185	39	three	three	NUM
ejpam-6050	185	40	exponential	exponential	ADJ
ejpam-6050	185	41	fuzzysets	fuzzyset	NOUN
ejpam-6050	185	42	.	.	PUNCT
ejpam-6050	186	1	ea	ea	NOUN
ejpam-6050	186	2	∪	∪	X
ejpam-6050	186	3	(	(	PUNCT
ejpam-6050	186	4	eb	eb	PROPN
ejpam-6050	186	5	∩	∩	PROPN
ejpam-6050	186	6	ec	ec	PROPN
ejpam-6050	186	7	)	)	PUNCT
ejpam-6050	186	8	=	=	PUNCT
ejpam-6050	187	1	[	[	PUNCT
ejpam-6050	187	2	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	187	3	s1	s1	NOUN
ejpam-6050	187	4	+	+	CCONJ
ejpam-6050	187	5	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	187	6	s2	s2	NOUN
ejpam-6050	187	7	+	+	CCONJ
ejpam-6050	187	8	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	187	9	s3	s3	NOUN
ejpam-6050	187	10	]	]	PUNCT
ejpam-6050	187	11	⊕	⊕	PROPN
ejpam-6050	188	1	[	[	X
ejpam-6050	188	2	[	[	PUNCT
ejpam-6050	188	3	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	188	4	s1	s1	NOUN
ejpam-6050	188	5	+	+	CCONJ
ejpam-6050	188	6	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	188	7	s2	s2	NOUN
ejpam-6050	188	8	+	+	CCONJ
ejpam-6050	188	9	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	188	10	s3	s3	PROPN
ejpam-6050	188	11	]	]	PUNCT
ejpam-6050	188	12	∗	∗	NOUN
ejpam-6050	188	13	[	[	PUNCT
ejpam-6050	188	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	188	15	s1	s1	NOUN
ejpam-6050	188	16	+	+	CCONJ
ejpam-6050	188	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	188	18	s2	s2	NOUN
ejpam-6050	188	19	+	+	CCONJ
ejpam-6050	188	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	188	21	s3	s3	NOUN
ejpam-6050	188	22	]	]	X
ejpam-6050	188	23	]	]	X
ejpam-6050	189	1	=	=	PUNCT
ejpam-6050	189	2	[	[	PUNCT
ejpam-6050	189	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	189	4	s1	s1	NOUN
ejpam-6050	189	5	+	+	CCONJ
ejpam-6050	189	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	189	7	s2	s2	NOUN
ejpam-6050	189	8	+	+	CCONJ
ejpam-6050	189	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	189	10	s3	s3	NOUN
ejpam-6050	189	11	]	]	PUNCT
ejpam-6050	189	12	⊕	⊕	PROPN
ejpam-6050	189	13	[	[	PUNCT
ejpam-6050	189	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	189	15	s1	s1	NOUN
ejpam-6050	189	16	+	+	CCONJ
ejpam-6050	189	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	189	18	s2	s2	NOUN
ejpam-6050	189	19	+	+	CCONJ
ejpam-6050	189	20	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	189	21	s3	s3	PROPN
ejpam-6050	189	22	]	]	PUNCT
ejpam-6050	189	23	=	=	PUNCT
ejpam-6050	189	24	[	[	PUNCT
ejpam-6050	189	25	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	189	26	s1	s1	NOUN
ejpam-6050	189	27	+	+	CCONJ
ejpam-6050	189	28	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	189	29	s2	s2	NOUN
ejpam-6050	189	30	+	+	CCONJ
ejpam-6050	189	31	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	189	32	s3	s3	NOUN
ejpam-6050	189	33	]	]	X
ejpam-6050	189	34	(	(	PUNCT
ejpam-6050	189	35	3.7	3.7	NUM
ejpam-6050	189	36	)	)	PUNCT
ejpam-6050	189	37	(	(	PUNCT
ejpam-6050	189	38	ea	ea	PROPN
ejpam-6050	189	39	∪	∪	PROPN
ejpam-6050	189	40	eb	eb	PROPN
ejpam-6050	189	41	)	)	PUNCT
ejpam-6050	189	42	∩	∩	NOUN
ejpam-6050	189	43	(	(	PUNCT
ejpam-6050	189	44	ea	ea	X
ejpam-6050	189	45	∪	∪	X
ejpam-6050	189	46	ec	ec	PROPN
ejpam-6050	189	47	)	)	PUNCT
ejpam-6050	189	48	=	=	PUNCT
ejpam-6050	190	1	[	[	X
ejpam-6050	190	2	[	[	PUNCT
ejpam-6050	190	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	190	4	s1	s1	NOUN
ejpam-6050	190	5	+	+	CCONJ
ejpam-6050	190	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	190	7	s2	s2	NOUN
ejpam-6050	190	8	+	+	CCONJ
ejpam-6050	190	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	190	10	s3	s3	NOUN
ejpam-6050	190	11	]	]	PUNCT
ejpam-6050	190	12	⊕	⊕	PROPN
ejpam-6050	190	13	[	[	PUNCT
ejpam-6050	190	14	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	190	15	s1	s1	NOUN
ejpam-6050	190	16	+	+	CCONJ
ejpam-6050	190	17	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	190	18	s2	s2	NOUN
ejpam-6050	190	19	+	+	CCONJ
ejpam-6050	190	20	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	190	21	s3	s3	PROPN
ejpam-6050	190	22	]	]	X
ejpam-6050	190	23	]	]	X
ejpam-6050	190	24	∗	∗	NOUN
ejpam-6050	191	1	[	[	X
ejpam-6050	191	2	[	[	PUNCT
ejpam-6050	191	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	191	4	s1	s1	NOUN
ejpam-6050	191	5	+	+	CCONJ
ejpam-6050	191	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	191	7	s2	s2	NOUN
ejpam-6050	191	8	+	+	CCONJ
ejpam-6050	191	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	191	10	s3	s3	NOUN
ejpam-6050	191	11	]	]	PUNCT
ejpam-6050	191	12	⊕	⊕	PROPN
ejpam-6050	191	13	[	[	PUNCT
ejpam-6050	191	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	191	15	s1	s1	NOUN
ejpam-6050	191	16	+	+	CCONJ
ejpam-6050	191	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	191	18	s2	s2	NOUN
ejpam-6050	191	19	+	+	CCONJ
ejpam-6050	191	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	191	21	s3	s3	NOUN
ejpam-6050	191	22	]	]	X
ejpam-6050	191	23	]	]	X
ejpam-6050	192	1	=	=	PUNCT
ejpam-6050	193	1	[	[	X
ejpam-6050	193	2	[	[	PUNCT
ejpam-6050	193	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	193	4	s1	s1	NOUN
ejpam-6050	193	5	+	+	CCONJ
ejpam-6050	193	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	193	7	s2	s2	NOUN
ejpam-6050	193	8	+	+	CCONJ
ejpam-6050	193	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	193	10	s3	s3	NOUN
ejpam-6050	193	11	]	]	PUNCT
ejpam-6050	193	12	∗	∗	NOUN
ejpam-6050	193	13	[	[	PUNCT
ejpam-6050	193	14	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	193	15	s1	s1	NOUN
ejpam-6050	193	16	+	+	CCONJ
ejpam-6050	193	17	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	193	18	s2	s2	NOUN
ejpam-6050	193	19	+	+	CCONJ
ejpam-6050	193	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	193	21	s3	s3	NOUN
ejpam-6050	193	22	]	]	X
ejpam-6050	193	23	]	]	X
ejpam-6050	194	1	=	=	PUNCT
ejpam-6050	194	2	[	[	PUNCT
ejpam-6050	194	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	194	4	s1	s1	NOUN
ejpam-6050	194	5	+	+	CCONJ
ejpam-6050	194	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	194	7	s2	s2	NOUN
ejpam-6050	194	8	+	+	CCONJ
ejpam-6050	194	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	194	10	s3	s3	NOUN
ejpam-6050	194	11	]	]	X
ejpam-6050	194	12	(	(	PUNCT
ejpam-6050	194	13	3.8	3.8	NUM
ejpam-6050	194	14	)	)	PUNCT
ejpam-6050	194	15	from	from	ADP
ejpam-6050	194	16	equation	equation	NOUN
ejpam-6050	194	17	3.7	3.7	NUM
ejpam-6050	194	18	and	and	CCONJ
ejpam-6050	194	19	3.8	3.8	NUM
ejpam-6050	194	20	we	we	PRON
ejpam-6050	194	21	have	have	VERB
ejpam-6050	194	22	ea	ea	NOUN
ejpam-6050	194	23	∪	∪	X
ejpam-6050	194	24	(	(	PUNCT
ejpam-6050	194	25	eb	eb	PROPN
ejpam-6050	194	26	∩	∩	PROPN
ejpam-6050	194	27	ec	ec	PROPN
ejpam-6050	194	28	)	)	PUNCT
ejpam-6050	194	29	=	=	PRON
ejpam-6050	195	1	(	(	PUNCT
ejpam-6050	195	2	ea	ea	PROPN
ejpam-6050	195	3	∪	∪	PROPN
ejpam-6050	195	4	eb	eb	PROPN
ejpam-6050	195	5	)	)	PUNCT
ejpam-6050	195	6	∩	∩	NOUN
ejpam-6050	195	7	(	(	PUNCT
ejpam-6050	195	8	ea	ea	X
ejpam-6050	195	9	∪	∪	PROPN
ejpam-6050	195	10	ec	ec	PROPN
ejpam-6050	195	11	)	)	PUNCT
ejpam-6050	195	12	.	.	PUNCT
ejpam-6050	196	1	next	next	ADV
ejpam-6050	196	2	,	,	PUNCT
ejpam-6050	196	3	we	we	PRON
ejpam-6050	196	4	see	see	VERB
ejpam-6050	196	5	the	the	DET
ejpam-6050	196	6	distributive	distributive	ADJ
ejpam-6050	196	7	condition	condition	NOUN
ejpam-6050	196	8	of	of	ADP
ejpam-6050	196	9	intersection	intersection	NOUN
ejpam-6050	196	10	over	over	ADP
ejpam-6050	196	11	union	union	NOUN
ejpam-6050	196	12	is	be	AUX
ejpam-6050	196	13	ea	ea	X
ejpam-6050	196	14	∩	∩	NOUN
ejpam-6050	196	15	(	(	PUNCT
ejpam-6050	196	16	eb	eb	PROPN
ejpam-6050	196	17	∪	∪	PROPN
ejpam-6050	196	18	ec	ec	PROPN
ejpam-6050	196	19	)	)	PUNCT
ejpam-6050	196	20	=	=	PUNCT
ejpam-6050	197	1	[	[	PUNCT
ejpam-6050	197	2	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	197	3	s1	s1	NOUN
ejpam-6050	197	4	+	+	CCONJ
ejpam-6050	197	5	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	197	6	s2	s2	NOUN
ejpam-6050	197	7	+	+	CCONJ
ejpam-6050	197	8	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	197	9	s3	s3	NOUN
ejpam-6050	197	10	]	]	PUNCT
ejpam-6050	197	11	∗	∗	NOUN
ejpam-6050	198	1	[	[	X
ejpam-6050	198	2	[	[	PUNCT
ejpam-6050	198	3	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	198	4	s1	s1	NOUN
ejpam-6050	198	5	+	+	CCONJ
ejpam-6050	198	6	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	198	7	s2	s2	NOUN
ejpam-6050	198	8	+	+	CCONJ
ejpam-6050	198	9	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	198	10	s3	s3	PROPN
ejpam-6050	198	11	]	]	PUNCT
ejpam-6050	198	12	⊕	⊕	PROPN
ejpam-6050	198	13	[	[	PUNCT
ejpam-6050	198	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	198	15	s1	s1	NOUN
ejpam-6050	198	16	+	+	CCONJ
ejpam-6050	198	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	198	18	s2	s2	NOUN
ejpam-6050	198	19	+	+	CCONJ
ejpam-6050	198	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	198	21	s3	s3	NOUN
ejpam-6050	198	22	]	]	X
ejpam-6050	198	23	]	]	X
ejpam-6050	199	1	=	=	PUNCT
ejpam-6050	199	2	[	[	PUNCT
ejpam-6050	199	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	199	4	s1	s1	NOUN
ejpam-6050	199	5	+	+	CCONJ
ejpam-6050	199	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	199	7	s2	s2	NOUN
ejpam-6050	199	8	+	+	CCONJ
ejpam-6050	199	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	199	10	s3	s3	NOUN
ejpam-6050	199	11	]	]	PUNCT
ejpam-6050	199	12	∗	∗	NOUN
ejpam-6050	199	13	[	[	PUNCT
ejpam-6050	199	14	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	199	15	s1	s1	NOUN
ejpam-6050	199	16	+	+	CCONJ
ejpam-6050	199	17	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	199	18	s2	s2	NOUN
ejpam-6050	199	19	+	+	CCONJ
ejpam-6050	199	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	199	21	s3	s3	NOUN
ejpam-6050	199	22	]	]	X
ejpam-6050	199	23	=	=	PUNCT
ejpam-6050	200	1	[	[	PUNCT
ejpam-6050	200	2	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	200	3	s1	s1	NOUN
ejpam-6050	200	4	+	+	CCONJ
ejpam-6050	200	5	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	200	6	s2	s2	NOUN
ejpam-6050	200	7	+	+	CCONJ
ejpam-6050	200	8	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	200	9	s3	s3	NOUN
ejpam-6050	200	10	]	]	PUNCT
ejpam-6050	200	11	(	(	PUNCT
ejpam-6050	200	12	3.9	3.9	NUM
ejpam-6050	200	13	)	)	PUNCT
ejpam-6050	200	14	(	(	PUNCT
ejpam-6050	200	15	ea	ea	X
ejpam-6050	200	16	∩	∩	PROPN
ejpam-6050	200	17	eb	eb	PROPN
ejpam-6050	200	18	)	)	PUNCT
ejpam-6050	200	19	∪	∪	NOUN
ejpam-6050	200	20	(	(	PUNCT
ejpam-6050	200	21	ea	ea	X
ejpam-6050	200	22	∩	∩	X
ejpam-6050	200	23	ec	ec	PROPN
ejpam-6050	200	24	)	)	PUNCT
ejpam-6050	200	25	=	=	PUNCT
ejpam-6050	201	1	[	[	X
ejpam-6050	201	2	[	[	PUNCT
ejpam-6050	201	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	201	4	s1	s1	NOUN
ejpam-6050	201	5	+	+	CCONJ
ejpam-6050	201	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	201	7	s2	s2	NOUN
ejpam-6050	201	8	+	+	CCONJ
ejpam-6050	201	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	201	10	s3	s3	NOUN
ejpam-6050	201	11	]	]	PUNCT
ejpam-6050	201	12	∗	∗	NOUN
ejpam-6050	201	13	[	[	PUNCT
ejpam-6050	201	14	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	201	15	s1	s1	NOUN
ejpam-6050	201	16	+	+	CCONJ
ejpam-6050	201	17	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	201	18	s2	s2	NOUN
ejpam-6050	201	19	+	+	CCONJ
ejpam-6050	201	20	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	201	21	s3	s3	PROPN
ejpam-6050	201	22	]	]	X
ejpam-6050	201	23	]	]	X
ejpam-6050	201	24	⊕	⊕	PROPN
ejpam-6050	202	1	[	[	X
ejpam-6050	202	2	[	[	PUNCT
ejpam-6050	202	3	0.9e−⊺0.9	0.9e−⊺0.9	NOUN
ejpam-6050	202	4	s1	s1	NOUN
ejpam-6050	202	5	+	+	CCONJ
ejpam-6050	202	6	0.6e−⊺0.6	0.6e−⊺0.6	ADJ
ejpam-6050	202	7	s2	s2	NOUN
ejpam-6050	202	8	+	+	CCONJ
ejpam-6050	202	9	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	202	10	s3	s3	NOUN
ejpam-6050	202	11	]	]	PUNCT
ejpam-6050	202	12	∗	∗	NOUN
ejpam-6050	202	13	[	[	PUNCT
ejpam-6050	202	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	202	15	s1	s1	NOUN
ejpam-6050	202	16	+	+	CCONJ
ejpam-6050	202	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	202	18	s2	s2	NOUN
ejpam-6050	202	19	+	+	CCONJ
ejpam-6050	202	20	1e−⊺1	1e−⊺1	NUM
ejpam-6050	202	21	s3	s3	NOUN
ejpam-6050	202	22	]	]	X
ejpam-6050	202	23	]	]	X
ejpam-6050	203	1	=	=	PUNCT
ejpam-6050	204	1	[	[	X
ejpam-6050	204	2	[	[	PUNCT
ejpam-6050	204	3	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	204	4	s1	s1	NOUN
ejpam-6050	204	5	+	+	CCONJ
ejpam-6050	204	6	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	204	7	s2	s2	NOUN
ejpam-6050	204	8	+	+	CCONJ
ejpam-6050	204	9	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	204	10	s3	s3	PROPN
ejpam-6050	204	11	]	]	PUNCT
ejpam-6050	204	12	⊕	⊕	PROPN
ejpam-6050	204	13	[	[	PUNCT
ejpam-6050	204	14	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	204	15	s1	s1	NOUN
ejpam-6050	204	16	+	+	CCONJ
ejpam-6050	204	17	0.3e−⊺0.3	0.3e−⊺0.3	NOUN
ejpam-6050	204	18	s2	s2	NOUN
ejpam-6050	204	19	+	+	CCONJ
ejpam-6050	204	20	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	204	21	s3	s3	NOUN
ejpam-6050	204	22	]	]	X
ejpam-6050	204	23	]	]	X
ejpam-6050	204	24	m.	m.	PROPN
ejpam-6050	204	25	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	204	26	,	,	PUNCT
ejpam-6050	204	27	m.	m.	NOUN
ejpam-6050	204	28	rajeshwari	rajeshwari	NOUN
ejpam-6050	204	29	,	,	PUNCT
ejpam-6050	204	30	m.	m.	NOUN
ejpam-6050	204	31	alqahtani	alqahtani	PROPN
ejpam-6050	204	32	/	/	SYM
ejpam-6050	204	33	eur	eur	PROPN
ejpam-6050	204	34	.	.	PUNCT
ejpam-6050	205	1	j.	j.	PROPN
ejpam-6050	205	2	pure	pure	PROPN
ejpam-6050	205	3	appl	appl	PROPN
ejpam-6050	205	4	.	.	PROPN
ejpam-6050	205	5	math	math	PROPN
ejpam-6050	205	6	,	,	PUNCT
ejpam-6050	205	7	18	18	NUM
ejpam-6050	205	8	(	(	PUNCT
ejpam-6050	205	9	2	2	NUM
ejpam-6050	205	10	)	)	PUNCT
ejpam-6050	205	11	(	(	PUNCT
ejpam-6050	205	12	2025	2025	NUM
ejpam-6050	205	13	)	)	PUNCT
ejpam-6050	205	14	,	,	PUNCT
ejpam-6050	205	15	6050	6050	NUM
ejpam-6050	205	16	10	10	NUM
ejpam-6050	205	17	of	of	ADP
ejpam-6050	205	18	29	29	NUM
ejpam-6050	205	19	=	=	SYM
ejpam-6050	205	20	[	[	PUNCT
ejpam-6050	205	21	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	205	22	s1	s1	NOUN
ejpam-6050	205	23	+	+	CCONJ
ejpam-6050	205	24	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	205	25	s2	s2	NOUN
ejpam-6050	205	26	+	+	CCONJ
ejpam-6050	205	27	0.5e−⊺0.5	0.5e−⊺0.5	NOUN
ejpam-6050	205	28	s3	s3	NOUN
ejpam-6050	205	29	]	]	X
ejpam-6050	205	30	(	(	PUNCT
ejpam-6050	205	31	3.10	3.10	NUM
ejpam-6050	205	32	)	)	PUNCT
ejpam-6050	205	33	from	from	ADP
ejpam-6050	205	34	equation	equation	NOUN
ejpam-6050	205	35	3.9	3.9	NUM
ejpam-6050	205	36	and	and	CCONJ
ejpam-6050	205	37	3.10	3.10	NUM
ejpam-6050	205	38	we	we	PRON
ejpam-6050	205	39	have	have	VERB
ejpam-6050	205	40	ea	ea	NOUN
ejpam-6050	205	41	∩	∩	NOUN
ejpam-6050	205	42	(	(	PUNCT
ejpam-6050	205	43	eb	eb	PROPN
ejpam-6050	205	44	∪	∪	PROPN
ejpam-6050	205	45	ec	ec	PROPN
ejpam-6050	205	46	)	)	PUNCT
ejpam-6050	205	47	=	=	SYM
ejpam-6050	205	48	(	(	PUNCT
ejpam-6050	205	49	ea	ea	X
ejpam-6050	205	50	∩	∩	PROPN
ejpam-6050	205	51	eb	eb	PROPN
ejpam-6050	205	52	)	)	PUNCT
ejpam-6050	205	53	∪	∪	NOUN
ejpam-6050	205	54	(	(	PUNCT
ejpam-6050	205	55	ea	ea	X
ejpam-6050	205	56	∩	∩	X
ejpam-6050	205	57	ec	ec	PROPN
ejpam-6050	205	58	)	)	PUNCT
ejpam-6050	205	59	.	.	PUNCT
ejpam-6050	206	1	definition	definition	NOUN
ejpam-6050	206	2	19	19	NUM
ejpam-6050	206	3	.	.	PUNCT
ejpam-6050	207	1	the	the	DET
ejpam-6050	207	2	union	union	NOUN
ejpam-6050	207	3	of	of	ADP
ejpam-6050	207	4	idempotent	idempotent	ADJ
ejpam-6050	207	5	law	law	NOUN
ejpam-6050	207	6	in	in	ADP
ejpam-6050	207	7	a	a	DET
ejpam-6050	207	8	efss	efss	NOUN
ejpam-6050	207	9	ea	ea	NOUN
ejpam-6050	207	10	is	be	AUX
ejpam-6050	207	11	ea	ea	NOUN
ejpam-6050	207	12	∪	∪	X
ejpam-6050	207	13	ea	ea	X
ejpam-6050	207	14	=	=	SYM
ejpam-6050	207	15	ea	ea	PROPN
ejpam-6050	207	16	and	and	CCONJ
ejpam-6050	207	17	the	the	DET
ejpam-6050	207	18	idempotent	idempotent	ADJ
ejpam-6050	207	19	law	law	NOUN
ejpam-6050	207	20	of	of	ADP
ejpam-6050	207	21	intersection	intersection	NOUN
ejpam-6050	207	22	is	be	AUX
ejpam-6050	207	23	ea	ea	NOUN
ejpam-6050	207	24	∩	∩	X
ejpam-6050	207	25	ea	ea	X
ejpam-6050	207	26	=	=	SYM
ejpam-6050	207	27	ea	ea	PROPN
ejpam-6050	207	28	.	.	PUNCT
ejpam-6050	208	1	if	if	SCONJ
ejpam-6050	208	2	a	a	DET
ejpam-6050	208	3	membership	membership	NOUN
ejpam-6050	208	4	value	value	NOUN
ejpam-6050	208	5	of	of	ADP
ejpam-6050	208	6	ea	ea	PROPN
ejpam-6050	208	7	is	be	AUX
ejpam-6050	208	8	ℵea(s	ℵea(s	PROPN
ejpam-6050	208	9	)	)	PUNCT
ejpam-6050	208	10	=	=	PUNCT
ejpam-6050	208	11	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	208	12	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	208	13	)	)	PUNCT
ejpam-6050	208	14	the	the	DET
ejpam-6050	208	15	idempotent	idempotent	ADJ
ejpam-6050	208	16	law	law	NOUN
ejpam-6050	208	17	of	of	ADP
ejpam-6050	208	18	union	union	NOUN
ejpam-6050	208	19	becomes	become	VERB
ejpam-6050	208	20	ℵea(s	ℵea(s	NOUN
ejpam-6050	208	21	)	)	PUNCT
ejpam-6050	208	22	=	=	PUNCT
ejpam-6050	208	23	ℵea∪ea(s	ℵea∪ea(s	PROPN
ejpam-6050	208	24	)	)	PUNCT
ejpam-6050	208	25	.	.	PUNCT
ejpam-6050	209	1	this	this	PRON
ejpam-6050	209	2	prove	prove	VERB
ejpam-6050	209	3	this	this	PRON
ejpam-6050	209	4	,	,	PUNCT
ejpam-6050	209	5	we	we	PRON
ejpam-6050	209	6	have	have	VERB
ejpam-6050	209	7	ℵea∪ea(s	ℵea∪ea(	NOUN
ejpam-6050	209	8	)	)	PUNCT
ejpam-6050	209	9	=	=	PUNCT
ejpam-6050	210	1	[	[	PUNCT
ejpam-6050	210	2	ℵea(s)⊕	ℵea(s)⊕	PROPN
ejpam-6050	210	3	ℵea(s	ℵea(s	PROPN
ejpam-6050	210	4	)	)	PUNCT
ejpam-6050	210	5	]	]	PUNCT
ejpam-6050	211	1	=	=	PUNCT
ejpam-6050	211	2	[	[	PUNCT
ejpam-6050	211	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	211	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	211	5	)	)	PUNCT
ejpam-6050	211	6	⊕	⊕	PROPN
ejpam-6050	211	7	ℵa(s)e	ℵa(s)e	PROPN
ejpam-6050	211	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	211	9	)	)	PUNCT
ejpam-6050	211	10	]	]	PUNCT
ejpam-6050	212	1	=	=	SYM
ejpam-6050	212	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	212	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	212	4	)	)	PUNCT
ejpam-6050	212	5	=	=	SYM
ejpam-6050	212	6	ℵea(s	ℵea(s	PROPN
ejpam-6050	212	7	)	)	PUNCT
ejpam-6050	212	8	.	.	PUNCT
ejpam-6050	213	1	similarly	similarly	ADV
ejpam-6050	213	2	ℵea∪ea(s	ℵea∪ea(s	NUM
ejpam-6050	213	3	)	)	PUNCT
ejpam-6050	213	4	=	=	SYM
ejpam-6050	213	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	213	6	)	)	PUNCT
ejpam-6050	213	7	.	.	PUNCT
ejpam-6050	214	1	example	example	NOUN
ejpam-6050	215	1	10	10	NUM
ejpam-6050	215	2	.	.	PUNCT
ejpam-6050	216	1	let	let	VERB
ejpam-6050	216	2	ea	ea	X
ejpam-6050	217	1	=	=	SYM
ejpam-6050	218	1	(	(	PUNCT
ejpam-6050	218	2	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	218	3	s1	s1	PROPN
ejpam-6050	218	4	+	+	CCONJ
ejpam-6050	218	5	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	218	6	s2	s2	NOUN
ejpam-6050	218	7	+	+	CCONJ
ejpam-6050	218	8	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	218	9	s3	s3	PROPN
ejpam-6050	218	10	)	)	PUNCT
ejpam-6050	218	11	,	,	PUNCT
ejpam-6050	218	12	be	be	AUX
ejpam-6050	218	13	a	a	DET
ejpam-6050	218	14	efs	ef	NOUN
ejpam-6050	218	15	,	,	PUNCT
ejpam-6050	218	16	the	the	DET
ejpam-6050	218	17	idempotent	idempotent	ADJ
ejpam-6050	218	18	law	law	NOUN
ejpam-6050	218	19	of	of	ADP
ejpam-6050	218	20	union	union	NOUN
ejpam-6050	218	21	is	be	AUX
ejpam-6050	218	22	,	,	PUNCT
ejpam-6050	218	23	ℵea∪ea(s	ℵea∪ea(s	PROPN
ejpam-6050	218	24	)	)	PUNCT
ejpam-6050	218	25	=	=	NOUN
ejpam-6050	219	1	(	(	PUNCT
ejpam-6050	219	2	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	219	3	s1	s1	PROPN
ejpam-6050	219	4	+	+	CCONJ
ejpam-6050	219	5	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	219	6	s2	s2	NOUN
ejpam-6050	219	7	+	+	CCONJ
ejpam-6050	219	8	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	219	9	s3	s3	PROPN
ejpam-6050	219	10	)	)	PUNCT
ejpam-6050	219	11	⊕	⊕	PROPN
ejpam-6050	219	12	(	(	PUNCT
ejpam-6050	219	13	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	219	14	s1	s1	PROPN
ejpam-6050	219	15	+	+	CCONJ
ejpam-6050	219	16	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	219	17	s2	s2	NOUN
ejpam-6050	219	18	+	+	CCONJ
ejpam-6050	219	19	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	219	20	s3	s3	PROPN
ejpam-6050	219	21	)	)	PUNCT
ejpam-6050	220	1	=	=	PRON
ejpam-6050	221	1	(	(	PUNCT
ejpam-6050	221	2	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	221	3	s1	s1	PROPN
ejpam-6050	221	4	+	+	CCONJ
ejpam-6050	221	5	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	221	6	s2	s2	NOUN
ejpam-6050	221	7	+	+	CCONJ
ejpam-6050	221	8	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	221	9	s3	s3	PROPN
ejpam-6050	221	10	)	)	PUNCT
ejpam-6050	221	11	=	=	SYM
ejpam-6050	221	12	ℵea(s	ℵea(s	PROPN
ejpam-6050	221	13	)	)	PUNCT
ejpam-6050	221	14	.	.	PUNCT
ejpam-6050	222	1	the	the	DET
ejpam-6050	222	2	idempotent	idempotent	ADJ
ejpam-6050	222	3	law	law	NOUN
ejpam-6050	222	4	of	of	ADP
ejpam-6050	222	5	intersection	intersection	NOUN
ejpam-6050	222	6	is	be	AUX
ejpam-6050	222	7	,	,	PUNCT
ejpam-6050	222	8	ℵea∩ea(s	ℵea∩ea(s	NUM
ejpam-6050	222	9	)	)	PUNCT
ejpam-6050	222	10	=	=	NOUN
ejpam-6050	222	11	(	(	PUNCT
ejpam-6050	222	12	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	222	13	s1	s1	PROPN
ejpam-6050	222	14	+	+	CCONJ
ejpam-6050	222	15	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	222	16	s2	s2	NOUN
ejpam-6050	222	17	+	+	CCONJ
ejpam-6050	222	18	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	222	19	s3	s3	PROPN
ejpam-6050	222	20	)	)	PUNCT
ejpam-6050	223	1	∗	∗	NOUN
ejpam-6050	223	2	(	(	PUNCT
ejpam-6050	223	3	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	223	4	s1	s1	PROPN
ejpam-6050	223	5	+	+	CCONJ
ejpam-6050	223	6	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	223	7	s2	s2	NOUN
ejpam-6050	223	8	+	+	CCONJ
ejpam-6050	223	9	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	223	10	s3	s3	PROPN
ejpam-6050	223	11	)	)	PUNCT
ejpam-6050	223	12	=	=	PRON
ejpam-6050	224	1	(	(	PUNCT
ejpam-6050	224	2	0.8e−⊺08	0.8e−⊺08	PROPN
ejpam-6050	224	3	s1	s1	PROPN
ejpam-6050	224	4	+	+	CCONJ
ejpam-6050	224	5	0.9e−⊺0.9	0.9e−⊺0.9	PROPN
ejpam-6050	224	6	s2	s2	NOUN
ejpam-6050	224	7	+	+	CCONJ
ejpam-6050	224	8	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	224	9	s3	s3	PROPN
ejpam-6050	224	10	)	)	PUNCT
ejpam-6050	224	11	=	=	SYM
ejpam-6050	224	12	ℵea(s	ℵea(s	PROPN
ejpam-6050	224	13	)	)	PUNCT
ejpam-6050	224	14	.	.	PUNCT
ejpam-6050	225	1	the	the	DET
ejpam-6050	225	2	union	union	NOUN
ejpam-6050	225	3	and	and	CCONJ
ejpam-6050	225	4	intersection	intersection	NOUN
ejpam-6050	225	5	law	law	NOUN
ejpam-6050	225	6	of	of	ADP
ejpam-6050	225	7	idempotent	idempotent	ADJ
ejpam-6050	225	8	laws	law	NOUN
ejpam-6050	225	9	are	be	AUX
ejpam-6050	225	10	hold	hold	NOUN
ejpam-6050	225	11	.	.	PUNCT
ejpam-6050	226	1	definition	definition	NOUN
ejpam-6050	226	2	20	20	NUM
ejpam-6050	226	3	.	.	PUNCT
ejpam-6050	227	1	efs	ef	NOUN
ejpam-6050	227	2	satisfied	satisfy	VERB
ejpam-6050	227	3	the	the	DET
ejpam-6050	227	4	involution	involution	NOUN
ejpam-6050	227	5	law	law	NOUN
ejpam-6050	227	6	using	use	VERB
ejpam-6050	227	7	standard	standard	ADJ
ejpam-6050	227	8	complement	complement	NOUN
ejpam-6050	227	9	function	function	NOUN
ejpam-6050	227	10	.	.	PUNCT
ejpam-6050	228	1	the	the	DET
ejpam-6050	228	2	involution	involution	NOUN
ejpam-6050	228	3	law	law	NOUN
ejpam-6050	228	4	for	for	ADP
ejpam-6050	228	5	a	a	DET
ejpam-6050	228	6	efs	ef	NOUN
ejpam-6050	228	7	ea	ea	X
ejpam-6050	228	8	is	be	AUX
ejpam-6050	228	9	(	(	PUNCT
ejpam-6050	228	10	eac)c	eac)c	X
ejpam-6050	228	11	=	=	SYM
ejpam-6050	228	12	ea	ea	NOUN
ejpam-6050	228	13	.	.	PUNCT
ejpam-6050	229	1	if	if	SCONJ
ejpam-6050	229	2	a	a	DET
ejpam-6050	229	3	membership	membership	NOUN
ejpam-6050	229	4	value	value	NOUN
ejpam-6050	229	5	of	of	ADP
ejpam-6050	229	6	ea	ea	PROPN
ejpam-6050	229	7	is	be	AUX
ejpam-6050	229	8	ℵea(s	ℵea(s	PROPN
ejpam-6050	229	9	)	)	PUNCT
ejpam-6050	229	10	=	=	PUNCT
ejpam-6050	229	11	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	229	12	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	229	13	)	)	PUNCT
ejpam-6050	229	14	the	the	DET
ejpam-6050	229	15	involution	involution	NOUN
ejpam-6050	229	16	law	law	NOUN
ejpam-6050	229	17	is	be	AUX
ejpam-6050	229	18	ℵa(s)e	ℵa(s)e	ADJ
ejpam-6050	229	19	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	229	20	)	)	PUNCT
ejpam-6050	229	21	=	=	PUNCT
ejpam-6050	229	22	(	(	PUNCT
ejpam-6050	229	23	ℵc	ℵc	PROPN
ejpam-6050	229	24	a(s	a(s	PROPN
ejpam-6050	229	25	)	)	PUNCT
ejpam-6050	229	26	)	)	PUNCT
ejpam-6050	230	1	ce−⊺(ℵc	ce−⊺(ℵc	NUM
ejpam-6050	231	1	a(s))c	a(s))c	PROPN
ejpam-6050	231	2	.	.	PUNCT
ejpam-6050	232	1	m.	m.	PROPN
ejpam-6050	232	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	232	3	,	,	PUNCT
ejpam-6050	232	4	m.	m.	NOUN
ejpam-6050	232	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	232	6	,	,	PUNCT
ejpam-6050	232	7	m.	m.	NOUN
ejpam-6050	232	8	alqahtani	alqahtani	PROPN
ejpam-6050	232	9	/	/	SYM
ejpam-6050	232	10	eur	eur	PROPN
ejpam-6050	232	11	.	.	PUNCT
ejpam-6050	233	1	j.	j.	PROPN
ejpam-6050	233	2	pure	pure	PROPN
ejpam-6050	233	3	appl	appl	PROPN
ejpam-6050	233	4	.	.	PROPN
ejpam-6050	233	5	math	math	PROPN
ejpam-6050	233	6	,	,	PUNCT
ejpam-6050	233	7	18	18	NUM
ejpam-6050	233	8	(	(	PUNCT
ejpam-6050	233	9	2	2	NUM
ejpam-6050	233	10	)	)	PUNCT
ejpam-6050	233	11	(	(	PUNCT
ejpam-6050	233	12	2025	2025	NUM
ejpam-6050	233	13	)	)	PUNCT
ejpam-6050	233	14	,	,	PUNCT
ejpam-6050	233	15	6050	6050	NUM
ejpam-6050	233	16	11	11	NUM
ejpam-6050	233	17	of	of	ADP
ejpam-6050	233	18	29	29	NUM
ejpam-6050	233	19	example	example	NOUN
ejpam-6050	233	20	11	11	NUM
ejpam-6050	233	21	.	.	PUNCT
ejpam-6050	234	1	let	let	VERB
ejpam-6050	234	2	ea	ea	X
ejpam-6050	235	1	=	=	PUNCT
ejpam-6050	236	1	(	(	PUNCT
ejpam-6050	236	2	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	236	3	s1	s1	NOUN
ejpam-6050	236	4	+	+	CCONJ
ejpam-6050	236	5	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	236	6	s2	s2	NOUN
ejpam-6050	236	7	+	+	CCONJ
ejpam-6050	236	8	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	236	9	s3	s3	PROPN
ejpam-6050	236	10	)	)	PUNCT
ejpam-6050	236	11	,	,	PUNCT
ejpam-6050	236	12	be	be	AUX
ejpam-6050	236	13	a	a	DET
ejpam-6050	236	14	efs	ef	NOUN
ejpam-6050	236	15	.	.	PUNCT
ejpam-6050	237	1	by	by	ADP
ejpam-6050	237	2	using	use	VERB
ejpam-6050	237	3	standard	standard	ADJ
ejpam-6050	237	4	complement	complement	NOUN
ejpam-6050	237	5	function	function	NOUN
ejpam-6050	237	6	,	,	PUNCT
ejpam-6050	237	7	the	the	DET
ejpam-6050	237	8	involution	involution	NOUN
ejpam-6050	237	9	law	law	NOUN
ejpam-6050	237	10	valid	valid	NOUN
ejpam-6050	237	11	.	.	PUNCT
ejpam-6050	238	1	eac	eac	PROPN
ejpam-6050	238	2	=	=	SYM
ejpam-6050	238	3	0.3e−⊺0.3	0.3e−⊺0.3	PROPN
ejpam-6050	238	4	s1	s1	NOUN
ejpam-6050	238	5	+	+	CCONJ
ejpam-6050	238	6	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	238	7	s2	s2	NOUN
ejpam-6050	238	8	+	+	CCONJ
ejpam-6050	238	9	0.6e−⊺0.6	0.6e−⊺0.6	PROPN
ejpam-6050	238	10	s3	s3	PROPN
ejpam-6050	238	11	eacc	eacc	PROPN
ejpam-6050	238	12	=	=	PROPN
ejpam-6050	238	13	0.7e−⊺0.7	0.7e−⊺0.7	NOUN
ejpam-6050	238	14	s1	s1	NOUN
ejpam-6050	238	15	+	+	CCONJ
ejpam-6050	238	16	0.6e−⊺0.6	0.6e−⊺0.6	NOUN
ejpam-6050	238	17	s2	s2	NOUN
ejpam-6050	238	18	+	+	CCONJ
ejpam-6050	238	19	0.4e−⊺0.4	0.4e−⊺0.4	NOUN
ejpam-6050	238	20	s3	s3	PROPN
ejpam-6050	238	21	=	=	SYM
ejpam-6050	238	22	ea	ea	PROPN
ejpam-6050	238	23	.	.	PROPN
ejpam-6050	238	24	4	4	NUM
ejpam-6050	238	25	.	.	X
ejpam-6050	238	26	main	main	ADJ
ejpam-6050	238	27	results	result	NOUN
ejpam-6050	238	28	of	of	ADP
ejpam-6050	238	29	exponential	exponential	ADJ
ejpam-6050	238	30	fuzzy	fuzzy	ADJ
ejpam-6050	238	31	sets	set	NOUN
ejpam-6050	238	32	theorem	theorem	VERB
ejpam-6050	238	33	1	1	X
ejpam-6050	238	34	.	.	PUNCT
ejpam-6050	239	1	let	let	VERB
ejpam-6050	239	2	ea	ea	NOUN
ejpam-6050	239	3	and	and	CCONJ
ejpam-6050	239	4	eb	eb	PROPN
ejpam-6050	239	5	be	be	AUX
ejpam-6050	239	6	efss	efss	ADJ
ejpam-6050	239	7	over	over	ADP
ejpam-6050	239	8	the	the	DET
ejpam-6050	239	9	classical	classical	ADJ
ejpam-6050	239	10	set	set	NOUN
ejpam-6050	239	11	z	z	PROPN
ejpam-6050	239	12	,	,	PUNCT
ejpam-6050	239	13	the	the	DET
ejpam-6050	239	14	symmetrical	symmetrical	ADJ
ejpam-6050	239	15	difference	difference	NOUN
ejpam-6050	239	16	condition	condition	NOUN
ejpam-6050	239	17	is	be	AUX
ejpam-6050	239	18	satisfied	satisfied	ADJ
ejpam-6050	239	19	for	for	ADP
ejpam-6050	239	20	union	union	NOUN
ejpam-6050	239	21	,	,	PUNCT
ejpam-6050	239	22	intersection	intersection	NOUN
ejpam-6050	239	23	and	and	CCONJ
ejpam-6050	239	24	their	their	PRON
ejpam-6050	239	25	complement	complement	NOUN
ejpam-6050	239	26	functions	function	NOUN
ejpam-6050	239	27	of	of	ADP
ejpam-6050	239	28	phase	phase	NOUN
ejpam-6050	239	29	term	term	NOUN
ejpam-6050	239	30	.	.	PUNCT
ejpam-6050	240	1	proof	proof	NOUN
ejpam-6050	240	2	.	.	PUNCT
ejpam-6050	241	1	ea	ea	NOUN
ejpam-6050	241	2	and	and	CCONJ
ejpam-6050	241	3	eb	eb	PROPN
ejpam-6050	241	4	be	be	AUX
ejpam-6050	241	5	two	two	NUM
ejpam-6050	241	6	efss	efss	NOUN
ejpam-6050	241	7	.	.	PUNCT
ejpam-6050	242	1	to	to	PART
ejpam-6050	242	2	demonstrate	demonstrate	VERB
ejpam-6050	242	3	the	the	DET
ejpam-6050	242	4	formula	formula	NOUN
ejpam-6050	242	5	for	for	ADP
ejpam-6050	242	6	symmetrical	symmetrical	ADJ
ejpam-6050	242	7	difference	difference	NOUN
ejpam-6050	242	8	(	(	PUNCT
ejpam-6050	242	9	eac	eac	PROPN
ejpam-6050	242	10	∩	∩	PROPN
ejpam-6050	242	11	eb	eb	PROPN
ejpam-6050	242	12	)	)	PUNCT
ejpam-6050	242	13	∪	∪	NOUN
ejpam-6050	242	14	(	(	PUNCT
ejpam-6050	242	15	ea	ea	PROPN
ejpam-6050	242	16	∩	∩	PROPN
ejpam-6050	242	17	ebc	ebc	PROPN
ejpam-6050	242	18	)	)	PUNCT
ejpam-6050	243	1	=	=	PUNCT
ejpam-6050	243	2	(	(	PUNCT
ejpam-6050	243	3	eac	eac	PROPN
ejpam-6050	243	4	∪	∪	PROPN
ejpam-6050	243	5	ebc	ebc	PROPN
ejpam-6050	243	6	)	)	PUNCT
ejpam-6050	243	7	∩	∩	NOUN
ejpam-6050	243	8	(	(	PUNCT
ejpam-6050	243	9	ea	ea	PROPN
ejpam-6050	243	10	∪	∪	PROPN
ejpam-6050	243	11	eb	eb	PROPN
ejpam-6050	243	12	)	)	PUNCT
ejpam-6050	243	13	,	,	PUNCT
ejpam-6050	243	14	to	to	PART
ejpam-6050	243	15	determine	determine	VERB
ejpam-6050	243	16	the	the	DET
ejpam-6050	243	17	phase	phase	NOUN
ejpam-6050	243	18	term	term	NOUN
ejpam-6050	243	19	,	,	PUNCT
ejpam-6050	243	20	the	the	DET
ejpam-6050	243	21	max	max	PROPN
ejpam-6050	243	22	function	function	NOUN
ejpam-6050	243	23	.	.	PUNCT
ejpam-6050	244	1	case	case	NOUN
ejpam-6050	244	2	1	1	NUM
ejpam-6050	244	3	.	.	PUNCT
ejpam-6050	244	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	244	5	)	)	PUNCT
ejpam-6050	244	6	≤	≤	PUNCT
ejpam-6050	245	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	245	2	ea(s	ea(	NOUN
ejpam-6050	245	3	)	)	PUNCT
ejpam-6050	245	4	≤	≤	NOUN
ejpam-6050	246	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	246	2	eb(s	eb(	NOUN
ejpam-6050	246	3	)	)	PUNCT
ejpam-6050	246	4	≤	≤	NUM
ejpam-6050	246	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	246	6	)	)	PUNCT
ejpam-6050	246	7	and	and	CCONJ
ejpam-6050	246	8	ℵc	ℵc	ADJ
ejpam-6050	246	9	eb(s	eb(	NOUN
ejpam-6050	246	10	)	)	PUNCT
ejpam-6050	246	11	≤	≤	NUM
ejpam-6050	246	12	ℵc	ℵc	ADP
ejpam-6050	246	13	ea(s	ea(s	NUM
ejpam-6050	246	14	)	)	PUNCT
ejpam-6050	246	15	.	.	PUNCT
ejpam-6050	247	1	(	(	PUNCT
ejpam-6050	247	2	eac	eac	PROPN
ejpam-6050	247	3	∩	∩	PROPN
ejpam-6050	247	4	eb	eb	PROPN
ejpam-6050	247	5	)	)	PUNCT
ejpam-6050	247	6	∪	∪	NOUN
ejpam-6050	247	7	(	(	PUNCT
ejpam-6050	247	8	ea	ea	PROPN
ejpam-6050	247	9	∩	∩	PROPN
ejpam-6050	247	10	ebc	ebc	PROPN
ejpam-6050	247	11	)	)	PUNCT
ejpam-6050	247	12	=	=	PUNCT
ejpam-6050	248	1	[	[	PUNCT
ejpam-6050	248	2	ℵc	ℵc	NOUN
ejpam-6050	248	3	a(s)e	a(s)e	PROPN
ejpam-6050	248	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	248	5	a(s	a(s	PROPN
ejpam-6050	248	6	)	)	PUNCT
ejpam-6050	248	7	∗	∗	NOUN
ejpam-6050	248	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	248	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	248	10	)	)	PUNCT
ejpam-6050	248	11	]	]	PUNCT
ejpam-6050	249	1	⊕	⊕	PROPN
ejpam-6050	249	2	[	[	PUNCT
ejpam-6050	249	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	249	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	249	5	)	)	PUNCT
ejpam-6050	249	6	∗	∗	NOUN
ejpam-6050	249	7	ℵc	ℵc	NOUN
ejpam-6050	249	8	b(s)e	b(s)e	ADP
ejpam-6050	249	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	249	10	b(s	b(	NOUN
ejpam-6050	249	11	)	)	PUNCT
ejpam-6050	249	12	]	]	PUNCT
ejpam-6050	250	1	=	=	PUNCT
ejpam-6050	250	2	[	[	PUNCT
ejpam-6050	250	3	ℵc	ℵc	NOUN
ejpam-6050	250	4	a(s)e	a(s)e	PROPN
ejpam-6050	250	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	250	6	a(s	a(s	PROPN
ejpam-6050	250	7	)	)	PUNCT
ejpam-6050	250	8	⊕	⊕	PROPN
ejpam-6050	250	9	ℵc	ℵc	VERB
ejpam-6050	250	10	b(s)e	b(s)e	ADP
ejpam-6050	250	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	250	12	b(s	b(	NOUN
ejpam-6050	250	13	)	)	PUNCT
ejpam-6050	250	14	]	]	PUNCT
ejpam-6050	251	1	=	=	PUNCT
ejpam-6050	251	2	[	[	PUNCT
ejpam-6050	251	3	ℵc	ℵc	NOUN
ejpam-6050	251	4	a(s)e	a(s)e	PROPN
ejpam-6050	251	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	251	6	a(s	a(s	PROPN
ejpam-6050	251	7	)	)	PUNCT
ejpam-6050	251	8	]	]	PUNCT
ejpam-6050	251	9	(	(	PUNCT
ejpam-6050	251	10	4.1	4.1	NUM
ejpam-6050	251	11	)	)	PUNCT
ejpam-6050	251	12	(	(	PUNCT
ejpam-6050	251	13	eac	eac	PROPN
ejpam-6050	251	14	∪	∪	PROPN
ejpam-6050	251	15	ebc	ebc	PROPN
ejpam-6050	251	16	)	)	PUNCT
ejpam-6050	251	17	∩	∩	NOUN
ejpam-6050	251	18	(	(	PUNCT
ejpam-6050	251	19	ea	ea	PROPN
ejpam-6050	251	20	∪	∪	PROPN
ejpam-6050	251	21	eb	eb	PROPN
ejpam-6050	251	22	)	)	PUNCT
ejpam-6050	251	23	=	=	PUNCT
ejpam-6050	252	1	[	[	PUNCT
ejpam-6050	252	2	ℵc	ℵc	NOUN
ejpam-6050	252	3	a(s)e	a(s)e	PROPN
ejpam-6050	252	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	252	5	a(s	a(s	PROPN
ejpam-6050	252	6	)	)	PUNCT
ejpam-6050	252	7	⊕	⊕	PROPN
ejpam-6050	252	8	ℵc	ℵc	VERB
ejpam-6050	252	9	b(s)e	b(s)e	ADP
ejpam-6050	252	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	252	11	b(s	b(	NOUN
ejpam-6050	252	12	)	)	PUNCT
ejpam-6050	252	13	]	]	PUNCT
ejpam-6050	253	1	∗	∗	NOUN
ejpam-6050	253	2	[	[	PUNCT
ejpam-6050	253	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	253	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	253	5	)	)	PUNCT
ejpam-6050	253	6	⊕	⊕	PROPN
ejpam-6050	253	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	253	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	253	9	)	)	PUNCT
ejpam-6050	253	10	]	]	PUNCT
ejpam-6050	254	1	=	=	PUNCT
ejpam-6050	254	2	[	[	PUNCT
ejpam-6050	254	3	ℵc	ℵc	NOUN
ejpam-6050	254	4	a(s)e	a(s)e	PROPN
ejpam-6050	254	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	254	6	a(s	a(s	PROPN
ejpam-6050	254	7	)	)	PUNCT
ejpam-6050	254	8	∗	∗	NOUN
ejpam-6050	254	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	254	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	254	11	)	)	PUNCT
ejpam-6050	254	12	]	]	PUNCT
ejpam-6050	255	1	=	=	PUNCT
ejpam-6050	255	2	[	[	PUNCT
ejpam-6050	255	3	ℵc	ℵc	NOUN
ejpam-6050	255	4	a(s)e	a(s)e	PROPN
ejpam-6050	255	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	255	6	a(s	a(s	PROPN
ejpam-6050	255	7	)	)	PUNCT
ejpam-6050	255	8	]	]	PUNCT
ejpam-6050	255	9	(	(	PUNCT
ejpam-6050	255	10	4.2	4.2	NUM
ejpam-6050	255	11	)	)	PUNCT
ejpam-6050	255	12	from	from	ADP
ejpam-6050	255	13	equation	equation	NOUN
ejpam-6050	255	14	4.1	4.1	NUM
ejpam-6050	255	15	and	and	CCONJ
ejpam-6050	255	16	4.2	4.2	NUM
ejpam-6050	255	17	(	(	PUNCT
ejpam-6050	255	18	eac	eac	PROPN
ejpam-6050	255	19	∩	∩	PROPN
ejpam-6050	255	20	eb	eb	PROPN
ejpam-6050	255	21	)	)	PUNCT
ejpam-6050	255	22	∪	∪	NOUN
ejpam-6050	255	23	(	(	PUNCT
ejpam-6050	255	24	ea	ea	PROPN
ejpam-6050	255	25	∩	∩	PROPN
ejpam-6050	255	26	ebc	ebc	PROPN
ejpam-6050	255	27	)	)	PUNCT
ejpam-6050	255	28	=	=	PUNCT
ejpam-6050	256	1	(	(	PUNCT
ejpam-6050	256	2	eac	eac	PROPN
ejpam-6050	256	3	∪	∪	PROPN
ejpam-6050	256	4	ebc	ebc	PROPN
ejpam-6050	256	5	)	)	PUNCT
ejpam-6050	256	6	∩	∩	NOUN
ejpam-6050	256	7	(	(	PUNCT
ejpam-6050	256	8	ea	ea	PROPN
ejpam-6050	256	9	∪	∪	PROPN
ejpam-6050	256	10	eb	eb	PROPN
ejpam-6050	256	11	)	)	PUNCT
ejpam-6050	256	12	.	.	PUNCT
ejpam-6050	257	1	case	case	NOUN
ejpam-6050	257	2	2	2	NUM
ejpam-6050	257	3	.	.	PUNCT
ejpam-6050	257	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	257	5	)	)	PUNCT
ejpam-6050	257	6	≤	≤	NUM
ejpam-6050	257	7	ℵeb(s),ℵeb(s	ℵeb(s),ℵeb(	NOUN
ejpam-6050	257	8	)	)	PUNCT
ejpam-6050	257	9	≤	≤	NUM
ejpam-6050	257	10	ℵc	ℵc	ADP
ejpam-6050	257	11	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	257	12	)	)	PUNCT
ejpam-6050	257	13	≤	≤	NUM
ejpam-6050	257	14	ℵc	ℵc	ADP
ejpam-6050	257	15	eb(s	eb(	NOUN
ejpam-6050	257	16	)	)	PUNCT
ejpam-6050	257	17	and	and	CCONJ
ejpam-6050	257	18	ℵc	ℵc	ADJ
ejpam-6050	257	19	eb(s	eb(	NOUN
ejpam-6050	257	20	)	)	PUNCT
ejpam-6050	257	21	≤	≤	NUM
ejpam-6050	257	22	ℵc	ℵc	ADP
ejpam-6050	257	23	ea(s	ea(s	NUM
ejpam-6050	257	24	)	)	PUNCT
ejpam-6050	257	25	.	.	PUNCT
ejpam-6050	258	1	(	(	PUNCT
ejpam-6050	258	2	eac	eac	PROPN
ejpam-6050	258	3	∩	∩	PROPN
ejpam-6050	258	4	eb	eb	PROPN
ejpam-6050	258	5	)	)	PUNCT
ejpam-6050	258	6	∪	∪	NOUN
ejpam-6050	258	7	(	(	PUNCT
ejpam-6050	258	8	ea	ea	PROPN
ejpam-6050	258	9	∩	∩	PROPN
ejpam-6050	258	10	ebc	ebc	PROPN
ejpam-6050	258	11	)	)	PUNCT
ejpam-6050	258	12	=	=	PUNCT
ejpam-6050	259	1	[	[	PUNCT
ejpam-6050	259	2	ℵc	ℵc	NOUN
ejpam-6050	259	3	a(s)e	a(s)e	PROPN
ejpam-6050	259	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	259	5	a(s	a(s	PROPN
ejpam-6050	259	6	)	)	PUNCT
ejpam-6050	259	7	∗	∗	NOUN
ejpam-6050	259	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	259	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	259	10	)	)	PUNCT
ejpam-6050	259	11	]	]	PUNCT
ejpam-6050	260	1	⊕	⊕	PROPN
ejpam-6050	260	2	[	[	PUNCT
ejpam-6050	260	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	260	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	260	5	)	)	PUNCT
ejpam-6050	260	6	∗	∗	NOUN
ejpam-6050	260	7	ℵc	ℵc	NOUN
ejpam-6050	260	8	b(s)e	b(s)e	ADP
ejpam-6050	260	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	260	10	b(s	b(	NOUN
ejpam-6050	260	11	)	)	PUNCT
ejpam-6050	260	12	]	]	PUNCT
ejpam-6050	261	1	=	=	PUNCT
ejpam-6050	261	2	[	[	PUNCT
ejpam-6050	261	3	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	261	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	261	5	)	)	PUNCT
ejpam-6050	261	6	⊕	⊕	PROPN
ejpam-6050	261	7	ℵa(s)e	ℵa(s)e	PUNCT
ejpam-6050	261	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	261	9	)	)	PUNCT
ejpam-6050	261	10	]	]	PUNCT
ejpam-6050	262	1	=	=	PUNCT
ejpam-6050	262	2	[	[	PUNCT
ejpam-6050	262	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	262	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	262	5	)	)	PUNCT
ejpam-6050	262	6	]	]	PUNCT
ejpam-6050	262	7	(	(	PUNCT
ejpam-6050	262	8	4.3	4.3	NUM
ejpam-6050	262	9	)	)	PUNCT
ejpam-6050	262	10	m.	m.	NOUN
ejpam-6050	262	11	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	262	12	,	,	PUNCT
ejpam-6050	262	13	m.	m.	NOUN
ejpam-6050	262	14	rajeshwari	rajeshwari	NOUN
ejpam-6050	262	15	,	,	PUNCT
ejpam-6050	262	16	m.	m.	NOUN
ejpam-6050	262	17	alqahtani	alqahtani	PROPN
ejpam-6050	262	18	/	/	SYM
ejpam-6050	262	19	eur	eur	PROPN
ejpam-6050	262	20	.	.	PUNCT
ejpam-6050	263	1	j.	j.	PROPN
ejpam-6050	263	2	pure	pure	PROPN
ejpam-6050	263	3	appl	appl	PROPN
ejpam-6050	263	4	.	.	PROPN
ejpam-6050	263	5	math	math	PROPN
ejpam-6050	263	6	,	,	PUNCT
ejpam-6050	263	7	18	18	NUM
ejpam-6050	263	8	(	(	PUNCT
ejpam-6050	263	9	2	2	NUM
ejpam-6050	263	10	)	)	PUNCT
ejpam-6050	263	11	(	(	PUNCT
ejpam-6050	263	12	2025	2025	NUM
ejpam-6050	263	13	)	)	PUNCT
ejpam-6050	263	14	,	,	PUNCT
ejpam-6050	263	15	6050	6050	NUM
ejpam-6050	263	16	12	12	NUM
ejpam-6050	263	17	of	of	ADP
ejpam-6050	263	18	29	29	NUM
ejpam-6050	263	19	(	(	PUNCT
ejpam-6050	263	20	eac	eac	PROPN
ejpam-6050	263	21	∪	∪	PROPN
ejpam-6050	263	22	ebc	ebc	PROPN
ejpam-6050	263	23	)	)	PUNCT
ejpam-6050	263	24	∩	∩	NOUN
ejpam-6050	263	25	(	(	PUNCT
ejpam-6050	263	26	ea	ea	PROPN
ejpam-6050	263	27	∪	∪	PROPN
ejpam-6050	263	28	eb	eb	PROPN
ejpam-6050	263	29	)	)	PUNCT
ejpam-6050	263	30	=	=	PUNCT
ejpam-6050	264	1	[	[	PUNCT
ejpam-6050	264	2	ℵc	ℵc	NOUN
ejpam-6050	264	3	a(s)e	a(s)e	PROPN
ejpam-6050	264	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	264	5	a(s	a(s	PROPN
ejpam-6050	264	6	)	)	PUNCT
ejpam-6050	264	7	⊕	⊕	PROPN
ejpam-6050	264	8	ℵc	ℵc	VERB
ejpam-6050	264	9	b(s)e	b(s)e	ADP
ejpam-6050	264	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	264	11	b(s	b(	NOUN
ejpam-6050	264	12	)	)	PUNCT
ejpam-6050	264	13	]	]	PUNCT
ejpam-6050	265	1	∗	∗	NOUN
ejpam-6050	265	2	[	[	PUNCT
ejpam-6050	265	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	265	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	265	5	)	)	PUNCT
ejpam-6050	265	6	⊕	⊕	PROPN
ejpam-6050	265	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	265	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	265	9	)	)	PUNCT
ejpam-6050	265	10	]	]	PUNCT
ejpam-6050	266	1	=	=	PUNCT
ejpam-6050	266	2	[	[	PUNCT
ejpam-6050	266	3	ℵc	ℵc	NOUN
ejpam-6050	266	4	a(s)e	a(s)e	PROPN
ejpam-6050	266	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	266	6	a(s	a(s	PROPN
ejpam-6050	266	7	)	)	PUNCT
ejpam-6050	266	8	∗	∗	NOUN
ejpam-6050	266	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	266	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	266	11	)	)	PUNCT
ejpam-6050	266	12	]	]	PUNCT
ejpam-6050	267	1	=	=	PUNCT
ejpam-6050	267	2	[	[	PUNCT
ejpam-6050	267	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	267	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	267	5	)	)	PUNCT
ejpam-6050	267	6	]	]	PUNCT
ejpam-6050	267	7	(	(	PUNCT
ejpam-6050	267	8	4.4	4.4	NUM
ejpam-6050	267	9	)	)	PUNCT
ejpam-6050	267	10	from	from	ADP
ejpam-6050	267	11	equation	equation	NOUN
ejpam-6050	267	12	4.3	4.3	NUM
ejpam-6050	267	13	and	and	CCONJ
ejpam-6050	267	14	4.4	4.4	NUM
ejpam-6050	267	15	(	(	PUNCT
ejpam-6050	267	16	eac	eac	PROPN
ejpam-6050	267	17	∩	∩	PROPN
ejpam-6050	267	18	eb	eb	PROPN
ejpam-6050	267	19	)	)	PUNCT
ejpam-6050	267	20	∪	∪	NOUN
ejpam-6050	267	21	(	(	PUNCT
ejpam-6050	267	22	ea	ea	PROPN
ejpam-6050	267	23	∩	∩	PROPN
ejpam-6050	267	24	ebc	ebc	PROPN
ejpam-6050	267	25	)	)	PUNCT
ejpam-6050	267	26	=	=	PUNCT
ejpam-6050	267	27	(	(	PUNCT
ejpam-6050	267	28	eac	eac	PROPN
ejpam-6050	267	29	∪	∪	PROPN
ejpam-6050	267	30	ebc	ebc	PROPN
ejpam-6050	267	31	)	)	PUNCT
ejpam-6050	267	32	∩	∩	NOUN
ejpam-6050	267	33	(	(	PUNCT
ejpam-6050	267	34	ea	ea	PROPN
ejpam-6050	267	35	∪	∪	PROPN
ejpam-6050	267	36	eb	eb	PROPN
ejpam-6050	267	37	)	)	PUNCT
ejpam-6050	267	38	.	.	PUNCT
ejpam-6050	268	1	case	case	NOUN
ejpam-6050	268	2	3	3	NUM
ejpam-6050	268	3	.	.	PUNCT
ejpam-6050	268	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	268	5	)	)	PUNCT
ejpam-6050	268	6	≤	≤	PUNCT
ejpam-6050	269	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	269	2	ea(s	ea(	NOUN
ejpam-6050	269	3	)	)	PUNCT
ejpam-6050	269	4	≤	≤	NOUN
ejpam-6050	270	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	270	2	eb(s	eb(	NOUN
ejpam-6050	270	3	)	)	PUNCT
ejpam-6050	270	4	≤	≤	NUM
ejpam-6050	270	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	270	6	)	)	PUNCT
ejpam-6050	270	7	and	and	CCONJ
ejpam-6050	270	8	ℵc	ℵc	ADJ
ejpam-6050	270	9	eb(s	eb(	NOUN
ejpam-6050	270	10	)	)	PUNCT
ejpam-6050	270	11	≤	≤	NUM
ejpam-6050	270	12	ℵc	ℵc	ADP
ejpam-6050	270	13	ea(s	ea(s	NUM
ejpam-6050	270	14	)	)	PUNCT
ejpam-6050	270	15	.	.	PUNCT
ejpam-6050	271	1	(	(	PUNCT
ejpam-6050	271	2	eac	eac	PROPN
ejpam-6050	271	3	∩	∩	PROPN
ejpam-6050	271	4	eb	eb	PROPN
ejpam-6050	271	5	)	)	PUNCT
ejpam-6050	271	6	∪	∪	NOUN
ejpam-6050	271	7	(	(	PUNCT
ejpam-6050	271	8	ea	ea	PROPN
ejpam-6050	271	9	∩	∩	PROPN
ejpam-6050	271	10	ebc	ebc	PROPN
ejpam-6050	271	11	)	)	PUNCT
ejpam-6050	271	12	=	=	PUNCT
ejpam-6050	272	1	[	[	PUNCT
ejpam-6050	272	2	ℵc	ℵc	NOUN
ejpam-6050	272	3	a(s)e	a(s)e	PROPN
ejpam-6050	272	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	272	5	a(s	a(s	PROPN
ejpam-6050	272	6	)	)	PUNCT
ejpam-6050	272	7	∗	∗	NOUN
ejpam-6050	272	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	272	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	272	10	)	)	PUNCT
ejpam-6050	272	11	]	]	PUNCT
ejpam-6050	273	1	⊕	⊕	PROPN
ejpam-6050	273	2	[	[	PUNCT
ejpam-6050	273	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	273	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	273	5	)	)	PUNCT
ejpam-6050	273	6	∗	∗	NOUN
ejpam-6050	273	7	ℵc	ℵc	NOUN
ejpam-6050	273	8	b(s)e	b(s)e	ADP
ejpam-6050	273	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	273	10	b(s	b(	NOUN
ejpam-6050	273	11	)	)	PUNCT
ejpam-6050	273	12	]	]	PUNCT
ejpam-6050	274	1	=	=	PUNCT
ejpam-6050	274	2	[	[	PUNCT
ejpam-6050	274	3	ℵc	ℵc	NOUN
ejpam-6050	274	4	b(s)e	b(s)e	ADP
ejpam-6050	274	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	274	6	b(s	b(	NOUN
ejpam-6050	274	7	)	)	PUNCT
ejpam-6050	274	8	⊕	⊕	PROPN
ejpam-6050	274	9	ℵc	ℵc	NOUN
ejpam-6050	275	1	a(s)e	a(s)e	PROPN
ejpam-6050	275	2	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	275	3	a(s	a(s	PROPN
ejpam-6050	275	4	)	)	PUNCT
ejpam-6050	275	5	]	]	PUNCT
ejpam-6050	276	1	=	=	PUNCT
ejpam-6050	276	2	[	[	PUNCT
ejpam-6050	276	3	ℵc	ℵc	NOUN
ejpam-6050	276	4	b(s)e	b(s)e	PROPN
ejpam-6050	276	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	276	6	b(s	b(	NOUN
ejpam-6050	276	7	)	)	PUNCT
ejpam-6050	276	8	]	]	PUNCT
ejpam-6050	276	9	(	(	PUNCT
ejpam-6050	276	10	4.5	4.5	NUM
ejpam-6050	276	11	)	)	PUNCT
ejpam-6050	276	12	(	(	PUNCT
ejpam-6050	276	13	eac	eac	PROPN
ejpam-6050	276	14	∪	∪	PROPN
ejpam-6050	276	15	ebc	ebc	PROPN
ejpam-6050	276	16	)	)	PUNCT
ejpam-6050	276	17	∩	∩	NOUN
ejpam-6050	276	18	(	(	PUNCT
ejpam-6050	276	19	ea	ea	PROPN
ejpam-6050	276	20	∪	∪	PROPN
ejpam-6050	276	21	eb	eb	PROPN
ejpam-6050	276	22	)	)	PUNCT
ejpam-6050	276	23	=	=	PUNCT
ejpam-6050	277	1	[	[	PUNCT
ejpam-6050	277	2	ℵc	ℵc	NOUN
ejpam-6050	277	3	a(s)e	a(s)e	PROPN
ejpam-6050	277	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	277	5	a(s	a(s	PROPN
ejpam-6050	277	6	)	)	PUNCT
ejpam-6050	277	7	⊕	⊕	PROPN
ejpam-6050	277	8	ℵc	ℵc	VERB
ejpam-6050	277	9	b(s)e	b(s)e	ADP
ejpam-6050	277	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	277	11	b(s	b(	NOUN
ejpam-6050	277	12	)	)	PUNCT
ejpam-6050	277	13	]	]	PUNCT
ejpam-6050	278	1	∗	∗	NOUN
ejpam-6050	278	2	[	[	PUNCT
ejpam-6050	278	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	278	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	278	5	)	)	PUNCT
ejpam-6050	278	6	⊕	⊕	PROPN
ejpam-6050	278	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	278	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	278	9	)	)	PUNCT
ejpam-6050	278	10	]	]	PUNCT
ejpam-6050	279	1	=	=	PUNCT
ejpam-6050	279	2	[	[	PUNCT
ejpam-6050	279	3	ℵc	ℵc	NOUN
ejpam-6050	279	4	a(s)e	a(s)e	PROPN
ejpam-6050	279	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	279	6	a(s	a(s	PROPN
ejpam-6050	279	7	)	)	PUNCT
ejpam-6050	279	8	∗	∗	NOUN
ejpam-6050	279	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	279	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	279	11	)	)	PUNCT
ejpam-6050	279	12	]	]	PUNCT
ejpam-6050	280	1	=	=	PUNCT
ejpam-6050	280	2	[	[	PUNCT
ejpam-6050	280	3	ℵc	ℵc	NOUN
ejpam-6050	280	4	b(s)e	b(s)e	PROPN
ejpam-6050	280	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	280	6	b(s	b(	NOUN
ejpam-6050	280	7	)	)	PUNCT
ejpam-6050	280	8	]	]	PUNCT
ejpam-6050	280	9	(	(	PUNCT
ejpam-6050	280	10	4.6	4.6	NUM
ejpam-6050	280	11	)	)	PUNCT
ejpam-6050	280	12	from	from	ADP
ejpam-6050	280	13	equation	equation	NOUN
ejpam-6050	280	14	4.5	4.5	NUM
ejpam-6050	280	15	and	and	CCONJ
ejpam-6050	280	16	4.6	4.6	NUM
ejpam-6050	280	17	(	(	PUNCT
ejpam-6050	280	18	eac	eac	PROPN
ejpam-6050	280	19	∩	∩	PROPN
ejpam-6050	280	20	eb	eb	PROPN
ejpam-6050	280	21	)	)	PUNCT
ejpam-6050	280	22	∪	∪	NOUN
ejpam-6050	280	23	(	(	PUNCT
ejpam-6050	280	24	ea	ea	PROPN
ejpam-6050	280	25	∩	∩	PROPN
ejpam-6050	280	26	ebc	ebc	PROPN
ejpam-6050	280	27	)	)	PUNCT
ejpam-6050	280	28	=	=	PUNCT
ejpam-6050	281	1	(	(	PUNCT
ejpam-6050	281	2	eac	eac	PROPN
ejpam-6050	281	3	∪	∪	PROPN
ejpam-6050	281	4	ebc	ebc	PROPN
ejpam-6050	281	5	)	)	PUNCT
ejpam-6050	281	6	∩	∩	NOUN
ejpam-6050	281	7	(	(	PUNCT
ejpam-6050	281	8	ea	ea	PROPN
ejpam-6050	281	9	∪	∪	PROPN
ejpam-6050	281	10	eb	eb	PROPN
ejpam-6050	281	11	)	)	PUNCT
ejpam-6050	281	12	.	.	PUNCT
ejpam-6050	282	1	case	case	NOUN
ejpam-6050	282	2	4	4	NUM
ejpam-6050	282	3	.	.	PUNCT
ejpam-6050	282	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	282	5	)	)	PUNCT
ejpam-6050	282	6	≤	≤	NUM
ejpam-6050	282	7	ℵeb(s),ℵeb(s	ℵeb(s),ℵeb(	NOUN
ejpam-6050	282	8	)	)	PUNCT
ejpam-6050	282	9	≤	≤	NUM
ejpam-6050	282	10	ℵc	ℵc	ADP
ejpam-6050	282	11	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	282	12	)	)	PUNCT
ejpam-6050	282	13	≤	≤	NUM
ejpam-6050	282	14	ℵc	ℵc	ADP
ejpam-6050	282	15	eb(s	eb(	NOUN
ejpam-6050	282	16	)	)	PUNCT
ejpam-6050	282	17	and	and	CCONJ
ejpam-6050	282	18	ℵc	ℵc	ADJ
ejpam-6050	282	19	eb(s	eb(	NOUN
ejpam-6050	282	20	)	)	PUNCT
ejpam-6050	282	21	≤	≤	NUM
ejpam-6050	282	22	ℵc	ℵc	ADP
ejpam-6050	282	23	ea(s	ea(s	NUM
ejpam-6050	282	24	)	)	PUNCT
ejpam-6050	282	25	.	.	PUNCT
ejpam-6050	283	1	(	(	PUNCT
ejpam-6050	283	2	eac	eac	PROPN
ejpam-6050	283	3	∩	∩	PROPN
ejpam-6050	283	4	eb	eb	PROPN
ejpam-6050	283	5	)	)	PUNCT
ejpam-6050	283	6	∪	∪	NOUN
ejpam-6050	283	7	(	(	PUNCT
ejpam-6050	283	8	ea	ea	PROPN
ejpam-6050	283	9	∩	∩	PROPN
ejpam-6050	283	10	ebc	ebc	PROPN
ejpam-6050	283	11	)	)	PUNCT
ejpam-6050	283	12	=	=	PUNCT
ejpam-6050	284	1	[	[	PUNCT
ejpam-6050	284	2	ℵc	ℵc	NOUN
ejpam-6050	284	3	a(s)e	a(s)e	PROPN
ejpam-6050	284	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	284	5	a(s	a(s	PROPN
ejpam-6050	284	6	)	)	PUNCT
ejpam-6050	284	7	∗	∗	NOUN
ejpam-6050	284	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	284	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	284	10	)	)	PUNCT
ejpam-6050	284	11	]	]	PUNCT
ejpam-6050	285	1	⊕	⊕	PROPN
ejpam-6050	285	2	[	[	PUNCT
ejpam-6050	285	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	285	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	285	5	)	)	PUNCT
ejpam-6050	285	6	∗	∗	NOUN
ejpam-6050	285	7	ℵc	ℵc	NOUN
ejpam-6050	285	8	b(s)e	b(s)e	ADP
ejpam-6050	285	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	285	10	b(s	b(	NOUN
ejpam-6050	285	11	)	)	PUNCT
ejpam-6050	285	12	]	]	PUNCT
ejpam-6050	286	1	=	=	PUNCT
ejpam-6050	286	2	[	[	PUNCT
ejpam-6050	286	3	ℵc	ℵc	NOUN
ejpam-6050	286	4	b(s)e	b(s)e	ADP
ejpam-6050	286	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	286	6	b(s	b(	NOUN
ejpam-6050	286	7	)	)	PUNCT
ejpam-6050	286	8	⊕	⊕	PROPN
ejpam-6050	286	9	ℵa(s)e	ℵa(s)e	PUNCT
ejpam-6050	286	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	286	11	)	)	PUNCT
ejpam-6050	286	12	]	]	PUNCT
ejpam-6050	287	1	=	=	PUNCT
ejpam-6050	287	2	[	[	PUNCT
ejpam-6050	287	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	287	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	287	5	)	)	PUNCT
ejpam-6050	287	6	]	]	PUNCT
ejpam-6050	287	7	(	(	PUNCT
ejpam-6050	287	8	4.7	4.7	NUM
ejpam-6050	287	9	)	)	PUNCT
ejpam-6050	287	10	(	(	PUNCT
ejpam-6050	287	11	eac	eac	PROPN
ejpam-6050	287	12	∪	∪	PROPN
ejpam-6050	287	13	ebc	ebc	PROPN
ejpam-6050	287	14	)	)	PUNCT
ejpam-6050	287	15	∩	∩	NOUN
ejpam-6050	287	16	(	(	PUNCT
ejpam-6050	287	17	ea	ea	PROPN
ejpam-6050	287	18	∪	∪	PROPN
ejpam-6050	287	19	eb	eb	PROPN
ejpam-6050	287	20	)	)	PUNCT
ejpam-6050	287	21	=	=	PUNCT
ejpam-6050	288	1	[	[	PUNCT
ejpam-6050	288	2	ℵc	ℵc	NOUN
ejpam-6050	288	3	a(s)e	a(s)e	PROPN
ejpam-6050	288	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	288	5	a(s	a(s	PROPN
ejpam-6050	288	6	)	)	PUNCT
ejpam-6050	288	7	⊕	⊕	PROPN
ejpam-6050	288	8	ℵc	ℵc	VERB
ejpam-6050	288	9	b(s)e	b(s)e	ADP
ejpam-6050	288	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	288	11	b(s	b(	NOUN
ejpam-6050	288	12	)	)	PUNCT
ejpam-6050	288	13	]	]	PUNCT
ejpam-6050	289	1	∗	∗	NOUN
ejpam-6050	289	2	[	[	PUNCT
ejpam-6050	289	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	289	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	289	5	)	)	PUNCT
ejpam-6050	289	6	⊕	⊕	PROPN
ejpam-6050	289	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	289	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	289	9	)	)	PUNCT
ejpam-6050	289	10	]	]	PUNCT
ejpam-6050	290	1	=	=	PUNCT
ejpam-6050	290	2	[	[	PUNCT
ejpam-6050	290	3	ℵc	ℵc	NOUN
ejpam-6050	290	4	a(s)e	a(s)e	PROPN
ejpam-6050	290	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	290	6	a(s	a(s	PROPN
ejpam-6050	290	7	)	)	PUNCT
ejpam-6050	290	8	∗	∗	NOUN
ejpam-6050	290	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	290	10	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	290	11	)	)	PUNCT
ejpam-6050	290	12	]	]	PUNCT
ejpam-6050	291	1	=	=	PUNCT
ejpam-6050	291	2	[	[	PUNCT
ejpam-6050	291	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	291	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	291	5	)	)	PUNCT
ejpam-6050	291	6	]	]	PUNCT
ejpam-6050	291	7	(	(	PUNCT
ejpam-6050	291	8	4.8	4.8	NUM
ejpam-6050	291	9	)	)	PUNCT
ejpam-6050	291	10	from	from	ADP
ejpam-6050	291	11	equation	equation	NOUN
ejpam-6050	291	12	4.7	4.7	NUM
ejpam-6050	291	13	and	and	CCONJ
ejpam-6050	291	14	4.8	4.8	NUM
ejpam-6050	291	15	(	(	PUNCT
ejpam-6050	291	16	eac	eac	PROPN
ejpam-6050	291	17	∩	∩	PROPN
ejpam-6050	291	18	eb	eb	PROPN
ejpam-6050	291	19	)	)	PUNCT
ejpam-6050	291	20	∪	∪	NOUN
ejpam-6050	291	21	(	(	PUNCT
ejpam-6050	291	22	ea	ea	PROPN
ejpam-6050	291	23	∩	∩	PROPN
ejpam-6050	291	24	ebc	ebc	PROPN
ejpam-6050	291	25	)	)	PUNCT
ejpam-6050	291	26	=	=	PUNCT
ejpam-6050	291	27	(	(	PUNCT
ejpam-6050	291	28	eac	eac	PROPN
ejpam-6050	291	29	∪	∪	PROPN
ejpam-6050	291	30	ebc	ebc	PROPN
ejpam-6050	291	31	)	)	PUNCT
ejpam-6050	291	32	∩	∩	NOUN
ejpam-6050	291	33	(	(	PUNCT
ejpam-6050	291	34	ea	ea	PROPN
ejpam-6050	291	35	∪	∪	PROPN
ejpam-6050	291	36	eb	eb	PROPN
ejpam-6050	291	37	)	)	PUNCT
ejpam-6050	291	38	.	.	PUNCT
ejpam-6050	292	1	m.	m.	PROPN
ejpam-6050	292	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	292	3	,	,	PUNCT
ejpam-6050	292	4	m.	m.	NOUN
ejpam-6050	292	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	292	6	,	,	PUNCT
ejpam-6050	292	7	m.	m.	NOUN
ejpam-6050	292	8	alqahtani	alqahtani	PROPN
ejpam-6050	292	9	/	/	SYM
ejpam-6050	292	10	eur	eur	PROPN
ejpam-6050	292	11	.	.	PUNCT
ejpam-6050	293	1	j.	j.	PROPN
ejpam-6050	293	2	pure	pure	PROPN
ejpam-6050	293	3	appl	appl	PROPN
ejpam-6050	293	4	.	.	PROPN
ejpam-6050	293	5	math	math	PROPN
ejpam-6050	293	6	,	,	PUNCT
ejpam-6050	293	7	18	18	NUM
ejpam-6050	293	8	(	(	PUNCT
ejpam-6050	293	9	2	2	NUM
ejpam-6050	293	10	)	)	PUNCT
ejpam-6050	293	11	(	(	PUNCT
ejpam-6050	293	12	2025	2025	NUM
ejpam-6050	293	13	)	)	PUNCT
ejpam-6050	293	14	,	,	PUNCT
ejpam-6050	293	15	6050	6050	NUM
ejpam-6050	293	16	13	13	NUM
ejpam-6050	293	17	of	of	ADP
ejpam-6050	293	18	29	29	NUM
ejpam-6050	293	19	case	case	NOUN
ejpam-6050	293	20	5	5	NUM
ejpam-6050	293	21	.	.	PUNCT
ejpam-6050	294	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	294	2	)	)	PUNCT
ejpam-6050	294	3	≤	≤	NOUN
ejpam-6050	294	4	ℵea(s),ℵc	ℵea(s),ℵc	NUM
ejpam-6050	294	5	ea(s	ea(	NOUN
ejpam-6050	294	6	)	)	PUNCT
ejpam-6050	294	7	≤	≤	NOUN
ejpam-6050	295	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	295	2	eb(s	eb(	NOUN
ejpam-6050	295	3	)	)	PUNCT
ejpam-6050	295	4	≤	≤	NUM
ejpam-6050	295	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	295	6	)	)	PUNCT
ejpam-6050	295	7	and	and	CCONJ
ejpam-6050	295	8	ℵc	ℵc	NOUN
ejpam-6050	295	9	ea(s	ea(	NOUN
ejpam-6050	295	10	)	)	PUNCT
ejpam-6050	295	11	≤	≤	NUM
ejpam-6050	295	12	ℵc	ℵc	ADP
ejpam-6050	295	13	eb(s	eb(	NOUN
ejpam-6050	295	14	)	)	PUNCT
ejpam-6050	295	15	.	.	PUNCT
ejpam-6050	296	1	(	(	PUNCT
ejpam-6050	296	2	eac	eac	PROPN
ejpam-6050	296	3	∩	∩	PROPN
ejpam-6050	296	4	eb	eb	PROPN
ejpam-6050	296	5	)	)	PUNCT
ejpam-6050	296	6	∪	∪	NOUN
ejpam-6050	296	7	(	(	PUNCT
ejpam-6050	296	8	ea	ea	PROPN
ejpam-6050	296	9	∩	∩	PROPN
ejpam-6050	296	10	ebc	ebc	PROPN
ejpam-6050	296	11	)	)	PUNCT
ejpam-6050	296	12	=	=	PUNCT
ejpam-6050	297	1	[	[	PUNCT
ejpam-6050	297	2	ℵc	ℵc	NOUN
ejpam-6050	297	3	a(s)e	a(s)e	PROPN
ejpam-6050	297	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	297	5	a(s	a(s	PROPN
ejpam-6050	297	6	)	)	PUNCT
ejpam-6050	297	7	∗	∗	NOUN
ejpam-6050	297	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	297	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	297	10	)	)	PUNCT
ejpam-6050	297	11	]	]	PUNCT
ejpam-6050	298	1	⊕	⊕	PROPN
ejpam-6050	298	2	[	[	PUNCT
ejpam-6050	298	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	298	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	298	5	)	)	PUNCT
ejpam-6050	298	6	∗	∗	NOUN
ejpam-6050	298	7	ℵc	ℵc	NOUN
ejpam-6050	298	8	b(s)e	b(s)e	ADP
ejpam-6050	298	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	298	10	b(s	b(	NOUN
ejpam-6050	298	11	)	)	PUNCT
ejpam-6050	298	12	]	]	PUNCT
ejpam-6050	299	1	=	=	PUNCT
ejpam-6050	299	2	[	[	PUNCT
ejpam-6050	299	3	ℵc	ℵc	NOUN
ejpam-6050	299	4	a(s)e	a(s)e	PROPN
ejpam-6050	299	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	299	6	a(s	a(s	PROPN
ejpam-6050	299	7	)	)	PUNCT
ejpam-6050	299	8	⊕	⊕	PROPN
ejpam-6050	299	9	ℵc	ℵc	VERB
ejpam-6050	299	10	b(s)e	b(s)e	ADP
ejpam-6050	299	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	299	12	b(s	b(	NOUN
ejpam-6050	299	13	)	)	PUNCT
ejpam-6050	299	14	]	]	PUNCT
ejpam-6050	300	1	=	=	PUNCT
ejpam-6050	300	2	[	[	PUNCT
ejpam-6050	300	3	ℵc	ℵc	NOUN
ejpam-6050	300	4	b(s)e	b(s)e	PROPN
ejpam-6050	300	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	300	6	b(s	b(	NOUN
ejpam-6050	300	7	)	)	PUNCT
ejpam-6050	300	8	]	]	PUNCT
ejpam-6050	300	9	(	(	PUNCT
ejpam-6050	300	10	4.9	4.9	NUM
ejpam-6050	300	11	)	)	PUNCT
ejpam-6050	300	12	(	(	PUNCT
ejpam-6050	300	13	eac	eac	PROPN
ejpam-6050	300	14	∪	∪	PROPN
ejpam-6050	300	15	ebc	ebc	PROPN
ejpam-6050	300	16	)	)	PUNCT
ejpam-6050	300	17	∩	∩	NOUN
ejpam-6050	300	18	(	(	PUNCT
ejpam-6050	300	19	ea	ea	PROPN
ejpam-6050	300	20	∪	∪	PROPN
ejpam-6050	300	21	eb	eb	PROPN
ejpam-6050	300	22	)	)	PUNCT
ejpam-6050	300	23	=	=	PUNCT
ejpam-6050	301	1	[	[	PUNCT
ejpam-6050	301	2	ℵc	ℵc	NOUN
ejpam-6050	301	3	a(s)e	a(s)e	PROPN
ejpam-6050	301	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	301	5	a(s	a(s	PROPN
ejpam-6050	301	6	)	)	PUNCT
ejpam-6050	301	7	⊕	⊕	PROPN
ejpam-6050	301	8	ℵc	ℵc	VERB
ejpam-6050	301	9	b(s)e	b(s)e	ADP
ejpam-6050	301	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	301	11	b(s	b(	NOUN
ejpam-6050	301	12	)	)	PUNCT
ejpam-6050	301	13	]	]	PUNCT
ejpam-6050	302	1	∗	∗	NOUN
ejpam-6050	302	2	[	[	PUNCT
ejpam-6050	302	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	302	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	302	5	)	)	PUNCT
ejpam-6050	302	6	⊕	⊕	PROPN
ejpam-6050	302	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	302	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	302	9	)	)	PUNCT
ejpam-6050	302	10	]	]	PUNCT
ejpam-6050	303	1	=	=	PUNCT
ejpam-6050	303	2	[	[	PUNCT
ejpam-6050	303	3	ℵc	ℵc	NOUN
ejpam-6050	303	4	b(s)e	b(s)e	ADP
ejpam-6050	303	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	303	6	b(s	b(	NOUN
ejpam-6050	303	7	)	)	PUNCT
ejpam-6050	303	8	∗	∗	NOUN
ejpam-6050	303	9	ℵa(s)e	ℵa(s)e	X
ejpam-6050	303	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	303	11	)	)	PUNCT
ejpam-6050	303	12	]	]	PUNCT
ejpam-6050	304	1	=	=	PUNCT
ejpam-6050	304	2	[	[	PUNCT
ejpam-6050	304	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	304	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	304	5	)	)	PUNCT
ejpam-6050	304	6	]	]	PUNCT
ejpam-6050	304	7	(	(	PUNCT
ejpam-6050	304	8	4.10	4.10	NUM
ejpam-6050	304	9	)	)	PUNCT
ejpam-6050	304	10	from	from	ADP
ejpam-6050	304	11	equation	equation	NOUN
ejpam-6050	304	12	4.9	4.9	NUM
ejpam-6050	304	13	and	and	CCONJ
ejpam-6050	304	14	4.10	4.10	NUM
ejpam-6050	304	15	(	(	PUNCT
ejpam-6050	304	16	eac	eac	PROPN
ejpam-6050	304	17	∩	∩	PROPN
ejpam-6050	304	18	eb	eb	PROPN
ejpam-6050	304	19	)	)	PUNCT
ejpam-6050	304	20	∪	∪	NOUN
ejpam-6050	304	21	(	(	PUNCT
ejpam-6050	304	22	ea	ea	PROPN
ejpam-6050	304	23	∩	∩	PROPN
ejpam-6050	304	24	ebc	ebc	PROPN
ejpam-6050	304	25	)	)	PUNCT
ejpam-6050	304	26	=	=	PUNCT
ejpam-6050	304	27	(	(	PUNCT
ejpam-6050	304	28	eac	eac	PROPN
ejpam-6050	304	29	∪	∪	PROPN
ejpam-6050	304	30	ebc	ebc	PROPN
ejpam-6050	304	31	)	)	PUNCT
ejpam-6050	304	32	∩	∩	NOUN
ejpam-6050	304	33	(	(	PUNCT
ejpam-6050	304	34	ea	ea	PROPN
ejpam-6050	304	35	∪	∪	PROPN
ejpam-6050	304	36	eb	eb	PROPN
ejpam-6050	304	37	)	)	PUNCT
ejpam-6050	304	38	.	.	PUNCT
ejpam-6050	305	1	case	case	NOUN
ejpam-6050	305	2	6	6	NUM
ejpam-6050	305	3	.	.	PUNCT
ejpam-6050	306	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	306	2	)	)	PUNCT
ejpam-6050	306	3	≤	≤	NUM
ejpam-6050	306	4	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	306	5	)	)	PUNCT
ejpam-6050	306	6	≤	≤	NUM
ejpam-6050	306	7	ℵc	ℵc	ADP
ejpam-6050	306	8	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	306	9	)	)	PUNCT
ejpam-6050	306	10	≤	≤	NUM
ejpam-6050	306	11	ℵc	ℵc	ADP
ejpam-6050	306	12	eb(s	eb(	NOUN
ejpam-6050	306	13	)	)	PUNCT
ejpam-6050	306	14	and	and	CCONJ
ejpam-6050	306	15	ℵc	ℵc	NOUN
ejpam-6050	306	16	ea(s	ea(	NOUN
ejpam-6050	306	17	)	)	PUNCT
ejpam-6050	306	18	≤	≤	NUM
ejpam-6050	306	19	ℵc	ℵc	ADP
ejpam-6050	306	20	eb(s	eb(	NOUN
ejpam-6050	306	21	)	)	PUNCT
ejpam-6050	306	22	.	.	PUNCT
ejpam-6050	307	1	(	(	PUNCT
ejpam-6050	307	2	eac	eac	PROPN
ejpam-6050	307	3	∩	∩	PROPN
ejpam-6050	307	4	eb	eb	PROPN
ejpam-6050	307	5	)	)	PUNCT
ejpam-6050	307	6	∪	∪	NOUN
ejpam-6050	307	7	(	(	PUNCT
ejpam-6050	307	8	ea	ea	PROPN
ejpam-6050	307	9	∩	∩	PROPN
ejpam-6050	307	10	ebc	ebc	PROPN
ejpam-6050	307	11	)	)	PUNCT
ejpam-6050	307	12	=	=	PUNCT
ejpam-6050	308	1	[	[	PUNCT
ejpam-6050	308	2	ℵc	ℵc	NOUN
ejpam-6050	308	3	a(s)e	a(s)e	PROPN
ejpam-6050	308	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	308	5	a(s	a(s	PROPN
ejpam-6050	308	6	)	)	PUNCT
ejpam-6050	308	7	∗	∗	NOUN
ejpam-6050	308	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	308	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	308	10	)	)	PUNCT
ejpam-6050	308	11	]	]	PUNCT
ejpam-6050	309	1	⊕	⊕	PROPN
ejpam-6050	309	2	[	[	PUNCT
ejpam-6050	309	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	309	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	309	5	)	)	PUNCT
ejpam-6050	309	6	∗	∗	NOUN
ejpam-6050	309	7	ℵc	ℵc	NOUN
ejpam-6050	309	8	b(s)e	b(s)e	ADP
ejpam-6050	309	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	309	10	b(s	b(	NOUN
ejpam-6050	309	11	)	)	PUNCT
ejpam-6050	309	12	]	]	PUNCT
ejpam-6050	310	1	=	=	PUNCT
ejpam-6050	310	2	[	[	PUNCT
ejpam-6050	310	3	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	310	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	310	5	)	)	PUNCT
ejpam-6050	310	6	⊕	⊕	PROPN
ejpam-6050	310	7	ℵa(s)e	ℵa(s)e	PUNCT
ejpam-6050	310	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	310	9	)	)	PUNCT
ejpam-6050	310	10	]	]	PUNCT
ejpam-6050	311	1	=	=	PUNCT
ejpam-6050	311	2	[	[	PUNCT
ejpam-6050	311	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	311	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	311	5	)	)	PUNCT
ejpam-6050	311	6	]	]	PUNCT
ejpam-6050	311	7	(	(	PUNCT
ejpam-6050	311	8	4.11	4.11	NUM
ejpam-6050	311	9	)	)	PUNCT
ejpam-6050	311	10	(	(	PUNCT
ejpam-6050	311	11	eac	eac	PROPN
ejpam-6050	311	12	∪	∪	PROPN
ejpam-6050	311	13	ebc	ebc	PROPN
ejpam-6050	311	14	)	)	PUNCT
ejpam-6050	311	15	∩	∩	NOUN
ejpam-6050	311	16	(	(	PUNCT
ejpam-6050	311	17	ea	ea	PROPN
ejpam-6050	311	18	∪	∪	PROPN
ejpam-6050	311	19	eb	eb	PROPN
ejpam-6050	311	20	)	)	PUNCT
ejpam-6050	311	21	=	=	PUNCT
ejpam-6050	312	1	[	[	PUNCT
ejpam-6050	312	2	ℵc	ℵc	NOUN
ejpam-6050	312	3	a(s)e	a(s)e	PROPN
ejpam-6050	312	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	312	5	a(s	a(s	PROPN
ejpam-6050	312	6	)	)	PUNCT
ejpam-6050	312	7	⊕	⊕	PROPN
ejpam-6050	312	8	ℵc	ℵc	VERB
ejpam-6050	312	9	b(s)e	b(s)e	ADP
ejpam-6050	312	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	312	11	b(s	b(	NOUN
ejpam-6050	312	12	)	)	PUNCT
ejpam-6050	312	13	]	]	PUNCT
ejpam-6050	313	1	∗	∗	NOUN
ejpam-6050	313	2	[	[	PUNCT
ejpam-6050	313	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	313	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	313	5	)	)	PUNCT
ejpam-6050	313	6	⊕	⊕	PROPN
ejpam-6050	313	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	313	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	313	9	)	)	PUNCT
ejpam-6050	313	10	]	]	PUNCT
ejpam-6050	314	1	=	=	PUNCT
ejpam-6050	314	2	[	[	PUNCT
ejpam-6050	314	3	ℵc	ℵc	NOUN
ejpam-6050	314	4	b(s)e	b(s)e	ADP
ejpam-6050	314	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	314	6	b(s	b(	NOUN
ejpam-6050	314	7	)	)	PUNCT
ejpam-6050	314	8	∗	∗	NOUN
ejpam-6050	314	9	ℵa(s)e	ℵa(s)e	X
ejpam-6050	314	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	314	11	)	)	PUNCT
ejpam-6050	314	12	]	]	PUNCT
ejpam-6050	315	1	=	=	PUNCT
ejpam-6050	315	2	[	[	PUNCT
ejpam-6050	315	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	315	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	315	5	)	)	PUNCT
ejpam-6050	315	6	]	]	PUNCT
ejpam-6050	315	7	(	(	PUNCT
ejpam-6050	315	8	4.12	4.12	NUM
ejpam-6050	315	9	)	)	PUNCT
ejpam-6050	315	10	from	from	ADP
ejpam-6050	315	11	equation	equation	NOUN
ejpam-6050	315	12	4.11	4.11	NUM
ejpam-6050	315	13	and	and	CCONJ
ejpam-6050	315	14	4.12	4.12	NUM
ejpam-6050	315	15	(	(	PUNCT
ejpam-6050	315	16	eac	eac	PROPN
ejpam-6050	315	17	∩	∩	PROPN
ejpam-6050	315	18	eb	eb	PROPN
ejpam-6050	315	19	)	)	PUNCT
ejpam-6050	315	20	∪	∪	NOUN
ejpam-6050	315	21	(	(	PUNCT
ejpam-6050	315	22	ea	ea	PROPN
ejpam-6050	315	23	∩	∩	PROPN
ejpam-6050	315	24	ebc	ebc	PROPN
ejpam-6050	315	25	)	)	PUNCT
ejpam-6050	315	26	=	=	PUNCT
ejpam-6050	316	1	(	(	PUNCT
ejpam-6050	316	2	eac	eac	PROPN
ejpam-6050	316	3	∪	∪	PROPN
ejpam-6050	316	4	ebc	ebc	PROPN
ejpam-6050	316	5	)	)	PUNCT
ejpam-6050	316	6	∩	∩	NOUN
ejpam-6050	316	7	(	(	PUNCT
ejpam-6050	316	8	ea	ea	PROPN
ejpam-6050	316	9	∪	∪	PROPN
ejpam-6050	316	10	eb	eb	PROPN
ejpam-6050	316	11	)	)	PUNCT
ejpam-6050	316	12	.	.	PUNCT
ejpam-6050	317	1	case	case	NOUN
ejpam-6050	317	2	7	7	NUM
ejpam-6050	317	3	.	.	PUNCT
ejpam-6050	318	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	318	2	)	)	PUNCT
ejpam-6050	318	3	≤	≤	NOUN
ejpam-6050	318	4	ℵea(s),ℵc	ℵea(s),ℵc	NUM
ejpam-6050	318	5	ea(s	ea(	NOUN
ejpam-6050	318	6	)	)	PUNCT
ejpam-6050	318	7	≤	≤	NOUN
ejpam-6050	319	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	319	2	eb(s	eb(	NOUN
ejpam-6050	319	3	)	)	PUNCT
ejpam-6050	319	4	≤	≤	NUM
ejpam-6050	319	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	319	6	)	)	PUNCT
ejpam-6050	319	7	and	and	CCONJ
ejpam-6050	319	8	ℵc	ℵc	NOUN
ejpam-6050	319	9	ea(s	ea(	NOUN
ejpam-6050	319	10	)	)	PUNCT
ejpam-6050	319	11	≤	≤	NUM
ejpam-6050	319	12	ℵc	ℵc	ADP
ejpam-6050	319	13	eb(s	eb(	NOUN
ejpam-6050	319	14	)	)	PUNCT
ejpam-6050	319	15	.	.	PUNCT
ejpam-6050	320	1	(	(	PUNCT
ejpam-6050	320	2	eac	eac	PROPN
ejpam-6050	320	3	∩	∩	PROPN
ejpam-6050	320	4	eb	eb	PROPN
ejpam-6050	320	5	)	)	PUNCT
ejpam-6050	320	6	∪	∪	NOUN
ejpam-6050	320	7	(	(	PUNCT
ejpam-6050	320	8	ea	ea	PROPN
ejpam-6050	320	9	∩	∩	PROPN
ejpam-6050	320	10	ebc	ebc	PROPN
ejpam-6050	320	11	)	)	PUNCT
ejpam-6050	320	12	=	=	PUNCT
ejpam-6050	321	1	[	[	PUNCT
ejpam-6050	321	2	ℵc	ℵc	NOUN
ejpam-6050	321	3	a(s)e	a(s)e	PROPN
ejpam-6050	321	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	321	5	a(s	a(s	PROPN
ejpam-6050	321	6	)	)	PUNCT
ejpam-6050	321	7	∗	∗	NOUN
ejpam-6050	321	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	321	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	321	10	)	)	PUNCT
ejpam-6050	321	11	]	]	PUNCT
ejpam-6050	322	1	⊕	⊕	PROPN
ejpam-6050	322	2	[	[	PUNCT
ejpam-6050	322	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	322	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	322	5	)	)	PUNCT
ejpam-6050	322	6	∗	∗	NOUN
ejpam-6050	322	7	ℵc	ℵc	NOUN
ejpam-6050	322	8	b(s)e	b(s)e	ADP
ejpam-6050	322	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	322	10	b(s	b(	NOUN
ejpam-6050	322	11	)	)	PUNCT
ejpam-6050	322	12	]	]	PUNCT
ejpam-6050	323	1	=	=	PUNCT
ejpam-6050	323	2	[	[	PUNCT
ejpam-6050	323	3	ℵc	ℵc	NOUN
ejpam-6050	323	4	a(s)e	a(s)e	PROPN
ejpam-6050	323	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	323	6	b(s	b(	NOUN
ejpam-6050	323	7	)	)	PUNCT
ejpam-6050	324	1	⊕	⊕	PROPN
ejpam-6050	324	2	ℵc	ℵc	VERB
ejpam-6050	324	3	b(s)e	b(s)e	ADP
ejpam-6050	324	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	324	5	b(s	b(	NOUN
ejpam-6050	324	6	)	)	PUNCT
ejpam-6050	324	7	]	]	PUNCT
ejpam-6050	325	1	=	=	PUNCT
ejpam-6050	325	2	[	[	PUNCT
ejpam-6050	325	3	ℵc	ℵc	NOUN
ejpam-6050	325	4	b(s)e	b(s)e	PROPN
ejpam-6050	325	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	325	6	b(s	b(	NOUN
ejpam-6050	325	7	)	)	PUNCT
ejpam-6050	325	8	]	]	PUNCT
ejpam-6050	325	9	(	(	PUNCT
ejpam-6050	325	10	4.13	4.13	NUM
ejpam-6050	325	11	)	)	PUNCT
ejpam-6050	325	12	(	(	PUNCT
ejpam-6050	325	13	eac	eac	PROPN
ejpam-6050	325	14	∪	∪	PROPN
ejpam-6050	325	15	ebc	ebc	PROPN
ejpam-6050	325	16	)	)	PUNCT
ejpam-6050	325	17	∩	∩	NOUN
ejpam-6050	325	18	(	(	PUNCT
ejpam-6050	325	19	ea	ea	PROPN
ejpam-6050	325	20	∪	∪	PROPN
ejpam-6050	325	21	eb	eb	PROPN
ejpam-6050	325	22	)	)	PUNCT
ejpam-6050	325	23	=	=	PUNCT
ejpam-6050	326	1	[	[	PUNCT
ejpam-6050	326	2	ℵc	ℵc	NOUN
ejpam-6050	326	3	a(s)e	a(s)e	PROPN
ejpam-6050	326	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	326	5	a(s	a(s	PROPN
ejpam-6050	326	6	)	)	PUNCT
ejpam-6050	326	7	⊕	⊕	PROPN
ejpam-6050	326	8	ℵc	ℵc	VERB
ejpam-6050	326	9	b(s)e	b(s)e	ADP
ejpam-6050	326	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	326	11	b(s	b(	NOUN
ejpam-6050	326	12	)	)	PUNCT
ejpam-6050	326	13	]	]	PUNCT
ejpam-6050	327	1	∗	∗	NOUN
ejpam-6050	327	2	[	[	PUNCT
ejpam-6050	327	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	327	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	327	5	)	)	PUNCT
ejpam-6050	327	6	⊕	⊕	PROPN
ejpam-6050	327	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	327	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	327	9	)	)	PUNCT
ejpam-6050	327	10	]	]	PUNCT
ejpam-6050	328	1	=	=	PUNCT
ejpam-6050	328	2	[	[	PUNCT
ejpam-6050	328	3	ℵc	ℵc	NOUN
ejpam-6050	328	4	b(s)e	b(s)e	ADP
ejpam-6050	328	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	328	6	b(s	b(	NOUN
ejpam-6050	328	7	)	)	PUNCT
ejpam-6050	328	8	∗	∗	NOUN
ejpam-6050	328	9	ℵa(s)e	ℵa(s)e	X
ejpam-6050	328	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	328	11	)	)	PUNCT
ejpam-6050	328	12	]	]	PUNCT
ejpam-6050	328	13	m.	m.	NOUN
ejpam-6050	328	14	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	328	15	,	,	PUNCT
ejpam-6050	328	16	m.	m.	NOUN
ejpam-6050	328	17	rajeshwari	rajeshwari	NOUN
ejpam-6050	328	18	,	,	PUNCT
ejpam-6050	328	19	m.	m.	NOUN
ejpam-6050	328	20	alqahtani	alqahtani	PROPN
ejpam-6050	328	21	/	/	SYM
ejpam-6050	328	22	eur	eur	PROPN
ejpam-6050	328	23	.	.	PUNCT
ejpam-6050	329	1	j.	j.	PROPN
ejpam-6050	329	2	pure	pure	PROPN
ejpam-6050	329	3	appl	appl	PROPN
ejpam-6050	329	4	.	.	PROPN
ejpam-6050	329	5	math	math	PROPN
ejpam-6050	329	6	,	,	PUNCT
ejpam-6050	329	7	18	18	NUM
ejpam-6050	329	8	(	(	PUNCT
ejpam-6050	329	9	2	2	NUM
ejpam-6050	329	10	)	)	PUNCT
ejpam-6050	329	11	(	(	PUNCT
ejpam-6050	329	12	2025	2025	NUM
ejpam-6050	329	13	)	)	PUNCT
ejpam-6050	329	14	,	,	PUNCT
ejpam-6050	329	15	6050	6050	NUM
ejpam-6050	329	16	14	14	NUM
ejpam-6050	329	17	of	of	ADP
ejpam-6050	329	18	29	29	NUM
ejpam-6050	329	19	=	=	SYM
ejpam-6050	329	20	[	[	PUNCT
ejpam-6050	329	21	ℵc	ℵc	NOUN
ejpam-6050	329	22	b(s)e	b(s)e	PROPN
ejpam-6050	329	23	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	329	24	b(s	b(	NOUN
ejpam-6050	329	25	)	)	PUNCT
ejpam-6050	329	26	]	]	PUNCT
ejpam-6050	329	27	(	(	PUNCT
ejpam-6050	329	28	4.14	4.14	NUM
ejpam-6050	329	29	)	)	PUNCT
ejpam-6050	329	30	from	from	ADP
ejpam-6050	329	31	equation	equation	NOUN
ejpam-6050	329	32	4.13	4.13	NUM
ejpam-6050	329	33	and	and	CCONJ
ejpam-6050	329	34	4.14	4.14	NUM
ejpam-6050	329	35	(	(	PUNCT
ejpam-6050	329	36	eac	eac	PROPN
ejpam-6050	329	37	∩	∩	PROPN
ejpam-6050	329	38	eb	eb	PROPN
ejpam-6050	329	39	)	)	PUNCT
ejpam-6050	329	40	∪	∪	NOUN
ejpam-6050	329	41	(	(	PUNCT
ejpam-6050	329	42	ea	ea	PROPN
ejpam-6050	329	43	∩	∩	PROPN
ejpam-6050	329	44	ebc	ebc	PROPN
ejpam-6050	329	45	)	)	PUNCT
ejpam-6050	329	46	=	=	PUNCT
ejpam-6050	329	47	(	(	PUNCT
ejpam-6050	329	48	eac	eac	PROPN
ejpam-6050	329	49	∪	∪	PROPN
ejpam-6050	329	50	ebc	ebc	PROPN
ejpam-6050	329	51	)	)	PUNCT
ejpam-6050	329	52	∩	∩	NOUN
ejpam-6050	329	53	(	(	PUNCT
ejpam-6050	329	54	ea	ea	PROPN
ejpam-6050	329	55	∪	∪	PROPN
ejpam-6050	329	56	eb	eb	PROPN
ejpam-6050	329	57	)	)	PUNCT
ejpam-6050	329	58	.	.	PUNCT
ejpam-6050	330	1	case	case	NOUN
ejpam-6050	330	2	8	8	NUM
ejpam-6050	330	3	.	.	PUNCT
ejpam-6050	331	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	331	2	)	)	PUNCT
ejpam-6050	331	3	≤	≤	NUM
ejpam-6050	331	4	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	331	5	)	)	PUNCT
ejpam-6050	331	6	≤	≤	NUM
ejpam-6050	331	7	ℵc	ℵc	ADP
ejpam-6050	331	8	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	331	9	)	)	PUNCT
ejpam-6050	331	10	≤	≤	NUM
ejpam-6050	331	11	ℵc	ℵc	ADP
ejpam-6050	331	12	eb(s	eb(	NOUN
ejpam-6050	331	13	)	)	PUNCT
ejpam-6050	331	14	and	and	CCONJ
ejpam-6050	331	15	ℵc	ℵc	NOUN
ejpam-6050	331	16	ea(s	ea(	NOUN
ejpam-6050	331	17	)	)	PUNCT
ejpam-6050	331	18	≤	≤	NUM
ejpam-6050	331	19	ℵc	ℵc	ADP
ejpam-6050	331	20	eb(s	eb(	NOUN
ejpam-6050	331	21	)	)	PUNCT
ejpam-6050	331	22	.	.	PUNCT
ejpam-6050	332	1	(	(	PUNCT
ejpam-6050	332	2	eac	eac	PROPN
ejpam-6050	332	3	∩	∩	PROPN
ejpam-6050	332	4	eb	eb	PROPN
ejpam-6050	332	5	)	)	PUNCT
ejpam-6050	332	6	∪	∪	NOUN
ejpam-6050	332	7	(	(	PUNCT
ejpam-6050	332	8	ea	ea	PROPN
ejpam-6050	332	9	∩	∩	PROPN
ejpam-6050	332	10	ebc	ebc	PROPN
ejpam-6050	332	11	)	)	PUNCT
ejpam-6050	332	12	=	=	PUNCT
ejpam-6050	333	1	[	[	PUNCT
ejpam-6050	333	2	ℵc	ℵc	NOUN
ejpam-6050	333	3	a(s)e	a(s)e	PROPN
ejpam-6050	333	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	333	5	a(s	a(s	PROPN
ejpam-6050	333	6	)	)	PUNCT
ejpam-6050	333	7	∗	∗	NOUN
ejpam-6050	333	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	333	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	333	10	)	)	PUNCT
ejpam-6050	333	11	]	]	PUNCT
ejpam-6050	334	1	⊕	⊕	PROPN
ejpam-6050	334	2	[	[	PUNCT
ejpam-6050	334	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	334	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	334	5	)	)	PUNCT
ejpam-6050	334	6	∗	∗	NOUN
ejpam-6050	334	7	ℵc	ℵc	NOUN
ejpam-6050	334	8	b(s)e	b(s)e	ADP
ejpam-6050	334	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	334	10	b(s	b(	NOUN
ejpam-6050	334	11	)	)	PUNCT
ejpam-6050	334	12	]	]	PUNCT
ejpam-6050	335	1	=	=	PUNCT
ejpam-6050	335	2	[	[	PUNCT
ejpam-6050	335	3	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	335	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	335	5	)	)	PUNCT
ejpam-6050	335	6	⊕	⊕	PROPN
ejpam-6050	335	7	ℵa(s)e	ℵa(s)e	PUNCT
ejpam-6050	335	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	335	9	)	)	PUNCT
ejpam-6050	335	10	]	]	PUNCT
ejpam-6050	336	1	=	=	PUNCT
ejpam-6050	336	2	[	[	PUNCT
ejpam-6050	336	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	336	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	336	5	)	)	PUNCT
ejpam-6050	336	6	]	]	PUNCT
ejpam-6050	336	7	(	(	PUNCT
ejpam-6050	336	8	4.15	4.15	NUM
ejpam-6050	336	9	)	)	PUNCT
ejpam-6050	336	10	(	(	PUNCT
ejpam-6050	336	11	eac	eac	PROPN
ejpam-6050	336	12	∪	∪	PROPN
ejpam-6050	336	13	ebc	ebc	PROPN
ejpam-6050	336	14	)	)	PUNCT
ejpam-6050	336	15	∩	∩	NOUN
ejpam-6050	336	16	(	(	PUNCT
ejpam-6050	336	17	ea	ea	PROPN
ejpam-6050	336	18	∪	∪	PROPN
ejpam-6050	336	19	eb	eb	PROPN
ejpam-6050	336	20	)	)	PUNCT
ejpam-6050	336	21	=	=	PUNCT
ejpam-6050	337	1	[	[	PUNCT
ejpam-6050	337	2	ℵc	ℵc	NOUN
ejpam-6050	337	3	a(s)e	a(s)e	PROPN
ejpam-6050	337	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	337	5	a(s	a(s	PROPN
ejpam-6050	337	6	)	)	PUNCT
ejpam-6050	337	7	⊕	⊕	PROPN
ejpam-6050	337	8	ℵc	ℵc	VERB
ejpam-6050	337	9	b(s)e	b(s)e	ADP
ejpam-6050	337	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	337	11	b(s	b(	NOUN
ejpam-6050	337	12	)	)	PUNCT
ejpam-6050	337	13	]	]	PUNCT
ejpam-6050	338	1	∗	∗	NOUN
ejpam-6050	338	2	[	[	PUNCT
ejpam-6050	338	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	338	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	338	5	)	)	PUNCT
ejpam-6050	338	6	⊕	⊕	PROPN
ejpam-6050	338	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	338	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	338	9	)	)	PUNCT
ejpam-6050	338	10	]	]	PUNCT
ejpam-6050	339	1	=	=	PUNCT
ejpam-6050	339	2	[	[	PUNCT
ejpam-6050	339	3	ℵc	ℵc	NOUN
ejpam-6050	339	4	b(s)e	b(s)e	ADP
ejpam-6050	339	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	339	6	b(s	b(	NOUN
ejpam-6050	339	7	)	)	PUNCT
ejpam-6050	339	8	∗	∗	NOUN
ejpam-6050	339	9	ℵa(s)e	ℵa(s)e	X
ejpam-6050	339	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	339	11	)	)	PUNCT
ejpam-6050	339	12	]	]	PUNCT
ejpam-6050	340	1	=	=	PUNCT
ejpam-6050	340	2	[	[	PUNCT
ejpam-6050	340	3	ℵc	ℵc	NOUN
ejpam-6050	340	4	b(s)e	b(s)e	PROPN
ejpam-6050	340	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	340	6	b(s	b(	NOUN
ejpam-6050	340	7	)	)	PUNCT
ejpam-6050	340	8	]	]	PUNCT
ejpam-6050	341	1	(	(	PUNCT
ejpam-6050	341	2	4.16	4.16	NUM
ejpam-6050	341	3	)	)	PUNCT
ejpam-6050	341	4	from	from	ADP
ejpam-6050	341	5	equation	equation	NOUN
ejpam-6050	341	6	4.15	4.15	NUM
ejpam-6050	341	7	and	and	CCONJ
ejpam-6050	341	8	4.16	4.16	NUM
ejpam-6050	341	9	(	(	PUNCT
ejpam-6050	341	10	eac	eac	PROPN
ejpam-6050	341	11	∩	∩	PROPN
ejpam-6050	341	12	eb	eb	PROPN
ejpam-6050	341	13	)	)	PUNCT
ejpam-6050	341	14	∪	∪	NOUN
ejpam-6050	341	15	(	(	PUNCT
ejpam-6050	341	16	ea	ea	PROPN
ejpam-6050	341	17	∩	∩	PROPN
ejpam-6050	341	18	ebc	ebc	PROPN
ejpam-6050	341	19	)	)	PUNCT
ejpam-6050	341	20	=	=	PUNCT
ejpam-6050	342	1	(	(	PUNCT
ejpam-6050	342	2	eac	eac	PROPN
ejpam-6050	342	3	∪	∪	PROPN
ejpam-6050	342	4	ebc	ebc	PROPN
ejpam-6050	342	5	)	)	PUNCT
ejpam-6050	342	6	∩	∩	NOUN
ejpam-6050	342	7	(	(	PUNCT
ejpam-6050	342	8	ea	ea	PROPN
ejpam-6050	342	9	∪	∪	PROPN
ejpam-6050	342	10	eb	eb	PROPN
ejpam-6050	342	11	)	)	PUNCT
ejpam-6050	342	12	.	.	PUNCT
ejpam-6050	343	1	therefore	therefore	ADV
ejpam-6050	343	2	,	,	PUNCT
ejpam-6050	343	3	the	the	DET
ejpam-6050	343	4	formula	formula	NOUN
ejpam-6050	343	5	for	for	ADP
ejpam-6050	343	6	symmetrical	symmetrical	ADJ
ejpam-6050	343	7	difference	difference	NOUN
ejpam-6050	343	8	is	be	AUX
ejpam-6050	343	9	valid	valid	ADJ
ejpam-6050	343	10	for	for	ADP
ejpam-6050	343	11	all	all	DET
ejpam-6050	343	12	cases	case	NOUN
ejpam-6050	343	13	.	.	PUNCT
ejpam-6050	344	1	theorem	theorem	NOUN
ejpam-6050	344	2	2	2	NUM
ejpam-6050	344	3	.	.	PUNCT
ejpam-6050	345	1	the	the	DET
ejpam-6050	345	2	union	union	NOUN
ejpam-6050	345	3	,	,	PUNCT
ejpam-6050	345	4	intersection	intersection	NOUN
ejpam-6050	345	5	and	and	CCONJ
ejpam-6050	345	6	complement	complement	NOUN
ejpam-6050	345	7	function	function	NOUN
ejpam-6050	345	8	of	of	ADP
ejpam-6050	345	9	exponential	exponential	ADJ
ejpam-6050	345	10	efss	efss	NOUN
ejpam-6050	345	11	ea	ea	PROPN
ejpam-6050	345	12	and	and	CCONJ
ejpam-6050	345	13	eb	eb	PROPN
ejpam-6050	345	14	is	be	AUX
ejpam-6050	345	15	an	an	DET
ejpam-6050	345	16	equivalence	equivalence	NOUN
ejpam-6050	345	17	relation	relation	NOUN
ejpam-6050	345	18	.	.	PUNCT
ejpam-6050	346	1	proof	proof	NOUN
ejpam-6050	346	2	.	.	PUNCT
ejpam-6050	347	1	ea	ea	NOUN
ejpam-6050	347	2	and	and	CCONJ
ejpam-6050	347	3	eb	eb	PROPN
ejpam-6050	347	4	be	be	AUX
ejpam-6050	347	5	two	two	NUM
ejpam-6050	347	6	efss	efss	NOUN
ejpam-6050	347	7	.	.	PUNCT
ejpam-6050	348	1	to	to	PART
ejpam-6050	348	2	demonstrate	demonstrate	VERB
ejpam-6050	348	3	the	the	DET
ejpam-6050	348	4	equivalence	equivalence	NOUN
ejpam-6050	348	5	relation	relation	NOUN
ejpam-6050	348	6	.	.	PUNCT
ejpam-6050	349	1	(	(	PUNCT
ejpam-6050	349	2	eac	eac	PROPN
ejpam-6050	349	3	∪	∪	PROPN
ejpam-6050	349	4	eb	eb	PROPN
ejpam-6050	349	5	)	)	PUNCT
ejpam-6050	349	6	∩	∩	NOUN
ejpam-6050	349	7	(	(	PUNCT
ejpam-6050	349	8	ea	ea	PROPN
ejpam-6050	349	9	∪	∪	PROPN
ejpam-6050	349	10	ebc	ebc	PROPN
ejpam-6050	349	11	)	)	PUNCT
ejpam-6050	349	12	=	=	PUNCT
ejpam-6050	349	13	(	(	PUNCT
ejpam-6050	349	14	eac	eac	PROPN
ejpam-6050	349	15	∩	∩	PROPN
ejpam-6050	349	16	ebc	ebc	PROPN
ejpam-6050	349	17	)	)	PUNCT
ejpam-6050	349	18	∪	∪	NOUN
ejpam-6050	349	19	(	(	PUNCT
ejpam-6050	349	20	ea	ea	X
ejpam-6050	349	21	∩	∩	PROPN
ejpam-6050	349	22	eb	eb	PROPN
ejpam-6050	349	23	)	)	PUNCT
ejpam-6050	349	24	.	.	PUNCT
ejpam-6050	350	1	case	case	NOUN
ejpam-6050	350	2	1	1	NUM
ejpam-6050	350	3	.	.	PUNCT
ejpam-6050	350	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	350	5	)	)	PUNCT
ejpam-6050	350	6	≤	≤	PUNCT
ejpam-6050	351	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	351	2	ea(s	ea(	NOUN
ejpam-6050	351	3	)	)	PUNCT
ejpam-6050	351	4	≤	≤	NOUN
ejpam-6050	352	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	352	2	eb(s	eb(	NOUN
ejpam-6050	352	3	)	)	PUNCT
ejpam-6050	352	4	≤	≤	NUM
ejpam-6050	352	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	352	6	)	)	PUNCT
ejpam-6050	352	7	and	and	CCONJ
ejpam-6050	352	8	ℵc	ℵc	ADJ
ejpam-6050	352	9	eb(s	eb(	NOUN
ejpam-6050	352	10	)	)	PUNCT
ejpam-6050	352	11	≤	≤	NUM
ejpam-6050	352	12	ℵc	ℵc	ADP
ejpam-6050	352	13	ea(s	ea(s	NUM
ejpam-6050	352	14	)	)	PUNCT
ejpam-6050	352	15	.	.	PUNCT
ejpam-6050	353	1	(	(	PUNCT
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ejpam-6050	353	7	(	(	PUNCT
ejpam-6050	353	8	ea	ea	PROPN
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ejpam-6050	363	8	4.18	4.18	NUM
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ejpam-6050	363	10	from	from	ADP
ejpam-6050	363	11	equation	equation	NOUN
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ejpam-6050	363	17	∪	∪	PROPN
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ejpam-6050	363	34	ea	ea	X
ejpam-6050	363	35	∩	∩	PROPN
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ejpam-6050	365	12	2025	2025	NUM
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ejpam-6050	365	20	2	2	NUM
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ejpam-6050	374	5	a(s	a(s	PROPN
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ejpam-6050	376	11	)	)	PUNCT
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ejpam-6050	377	13	equation	equation	NOUN
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ejpam-6050	377	15	and	and	CCONJ
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ejpam-6050	377	19	∪	∪	PROPN
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ejpam-6050	377	36	ea	ea	X
ejpam-6050	377	37	∩	∩	PROPN
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ejpam-6050	378	3	.	.	PUNCT
ejpam-6050	378	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	378	5	)	)	PUNCT
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ejpam-6050	379	3	)	)	PUNCT
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ejpam-6050	380	2	eb(s	eb(	NOUN
ejpam-6050	380	3	)	)	PUNCT
ejpam-6050	380	4	≤	≤	NUM
ejpam-6050	380	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	380	6	)	)	PUNCT
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ejpam-6050	380	10	)	)	PUNCT
ejpam-6050	380	11	≤	≤	NUM
ejpam-6050	380	12	ℵc	ℵc	ADP
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ejpam-6050	380	14	)	)	PUNCT
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ejpam-6050	381	2	eac	eac	PROPN
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ejpam-6050	381	6	∩	∩	NOUN
ejpam-6050	381	7	(	(	PUNCT
ejpam-6050	381	8	ea	ea	PROPN
ejpam-6050	381	9	∪	∪	PROPN
ejpam-6050	381	10	ebc	ebc	PROPN
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ejpam-6050	381	12	=	=	PUNCT
ejpam-6050	382	1	[	[	PUNCT
ejpam-6050	382	2	ℵc	ℵc	NOUN
ejpam-6050	382	3	a(s)e	a(s)e	PROPN
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ejpam-6050	382	5	a(s	a(s	PROPN
ejpam-6050	382	6	)	)	PUNCT
ejpam-6050	382	7	⊕	⊕	PROPN
ejpam-6050	382	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	383	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	383	2	)	)	PUNCT
ejpam-6050	383	3	]	]	PUNCT
ejpam-6050	384	1	∗	∗	NOUN
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ejpam-6050	384	5	)	)	PUNCT
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ejpam-6050	385	3	b(s	b(	NOUN
ejpam-6050	385	4	)	)	PUNCT
ejpam-6050	385	5	]	]	PUNCT
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ejpam-6050	386	5	)	)	PUNCT
ejpam-6050	386	6	∗	∗	NOUN
ejpam-6050	386	7	ℵa(s)e	ℵa(s)e	X
ejpam-6050	386	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	386	9	)	)	PUNCT
ejpam-6050	386	10	]	]	PUNCT
ejpam-6050	387	1	=	=	PUNCT
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ejpam-6050	387	5	)	)	PUNCT
ejpam-6050	387	6	]	]	PUNCT
ejpam-6050	387	7	(	(	PUNCT
ejpam-6050	387	8	4.21	4.21	NUM
ejpam-6050	387	9	)	)	PUNCT
ejpam-6050	387	10	(	(	PUNCT
ejpam-6050	387	11	eac	eac	PROPN
ejpam-6050	387	12	∩	∩	PROPN
ejpam-6050	387	13	ebc	ebc	PROPN
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ejpam-6050	387	16	(	(	PUNCT
ejpam-6050	387	17	ea	ea	X
ejpam-6050	387	18	∩	∩	PROPN
ejpam-6050	387	19	eb	eb	PROPN
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ejpam-6050	388	1	=	=	PUNCT
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ejpam-6050	389	3	a(s)e	a(s)e	PROPN
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ejpam-6050	389	5	a(s	a(s	PROPN
ejpam-6050	389	6	)	)	PUNCT
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ejpam-6050	389	9	b(s)e	b(s)e	PROPN
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ejpam-6050	389	12	)	)	PUNCT
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ejpam-6050	390	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	390	5	)	)	PUNCT
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ejpam-6050	390	7	ℵb(s)e	ℵb(s)e	NUM
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ejpam-6050	390	9	)	)	PUNCT
ejpam-6050	390	10	]	]	PUNCT
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ejpam-6050	391	4	b(s)e	b(s)e	ADP
ejpam-6050	391	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	391	6	b(s	b(	NOUN
ejpam-6050	391	7	)	)	PUNCT
ejpam-6050	391	8	⊕	⊕	PROPN
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ejpam-6050	391	10	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	391	11	)	)	PUNCT
ejpam-6050	391	12	]	]	PUNCT
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ejpam-6050	392	5	)	)	PUNCT
ejpam-6050	392	6	]	]	PUNCT
ejpam-6050	392	7	(	(	PUNCT
ejpam-6050	392	8	4.22	4.22	NUM
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ejpam-6050	392	10	from	from	ADP
ejpam-6050	392	11	equation	equation	NOUN
ejpam-6050	392	12	4.21	4.21	NUM
ejpam-6050	392	13	and	and	CCONJ
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ejpam-6050	392	16	eac	eac	PROPN
ejpam-6050	392	17	∪	∪	PROPN
ejpam-6050	392	18	eb	eb	PROPN
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ejpam-6050	392	21	(	(	PUNCT
ejpam-6050	392	22	ea	ea	PROPN
ejpam-6050	392	23	∪	∪	PROPN
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ejpam-6050	393	2	eac	eac	PROPN
ejpam-6050	393	3	∩	∩	PROPN
ejpam-6050	393	4	ebc	ebc	PROPN
ejpam-6050	393	5	)	)	PUNCT
ejpam-6050	393	6	∪	∪	NOUN
ejpam-6050	393	7	(	(	PUNCT
ejpam-6050	393	8	ea	ea	X
ejpam-6050	393	9	∩	∩	PROPN
ejpam-6050	393	10	eb	eb	PROPN
ejpam-6050	393	11	)	)	PUNCT
ejpam-6050	393	12	.	.	PUNCT
ejpam-6050	394	1	case	case	NOUN
ejpam-6050	394	2	4	4	NUM
ejpam-6050	394	3	.	.	PUNCT
ejpam-6050	394	4	ℵea(s	ℵea(s	NOUN
ejpam-6050	394	5	)	)	PUNCT
ejpam-6050	394	6	≤	≤	NUM
ejpam-6050	394	7	ℵeb(s),ℵeb(s	ℵeb(s),ℵeb(	NOUN
ejpam-6050	394	8	)	)	PUNCT
ejpam-6050	394	9	≤	≤	NUM
ejpam-6050	394	10	ℵc	ℵc	ADP
ejpam-6050	394	11	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	394	12	)	)	PUNCT
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ejpam-6050	394	15	eb(s	eb(	NOUN
ejpam-6050	394	16	)	)	PUNCT
ejpam-6050	394	17	and	and	CCONJ
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ejpam-6050	394	19	eb(s	eb(	NOUN
ejpam-6050	394	20	)	)	PUNCT
ejpam-6050	394	21	≤	≤	NUM
ejpam-6050	394	22	ℵc	ℵc	ADP
ejpam-6050	394	23	ea(s	ea(s	NUM
ejpam-6050	394	24	)	)	PUNCT
ejpam-6050	394	25	.	.	PUNCT
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ejpam-6050	395	4	eb	eb	PROPN
ejpam-6050	395	5	)	)	PUNCT
ejpam-6050	395	6	∩	∩	NOUN
ejpam-6050	395	7	(	(	PUNCT
ejpam-6050	395	8	ea	ea	PROPN
ejpam-6050	395	9	∪	∪	PROPN
ejpam-6050	395	10	ebc	ebc	PROPN
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ejpam-6050	395	12	=	=	PUNCT
ejpam-6050	396	1	[	[	PUNCT
ejpam-6050	396	2	ℵc	ℵc	NOUN
ejpam-6050	396	3	a(s)e	a(s)e	PROPN
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ejpam-6050	396	5	a(s	a(s	PROPN
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ejpam-6050	397	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	397	2	)	)	PUNCT
ejpam-6050	397	3	]	]	PUNCT
ejpam-6050	398	1	∗	∗	NOUN
ejpam-6050	398	2	[	[	PUNCT
ejpam-6050	398	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	398	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	398	5	)	)	PUNCT
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ejpam-6050	399	3	b(s	b(	NOUN
ejpam-6050	399	4	)	)	PUNCT
ejpam-6050	399	5	]	]	PUNCT
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ejpam-6050	400	7	)	)	PUNCT
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ejpam-6050	400	10	b(s)e	b(s)e	PROPN
ejpam-6050	400	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	400	12	b(s	b(	NOUN
ejpam-6050	400	13	)	)	PUNCT
ejpam-6050	400	14	]	]	PUNCT
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ejpam-6050	401	2	[	[	PUNCT
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ejpam-6050	401	4	b(s)e	b(s)e	PROPN
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ejpam-6050	401	6	b(s	b(	NOUN
ejpam-6050	401	7	)	)	PUNCT
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ejpam-6050	401	12	(	(	PUNCT
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ejpam-6050	401	20	∩	∩	PROPN
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ejpam-6050	402	3	a(s)e	a(s)e	PROPN
ejpam-6050	402	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	402	5	a(s	a(s	PROPN
ejpam-6050	402	6	)	)	PUNCT
ejpam-6050	402	7	∗	∗	NOUN
ejpam-6050	402	8	ℵc	ℵc	NOUN
ejpam-6050	402	9	b(s)e	b(s)e	PROPN
ejpam-6050	402	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	402	11	b(s	b(	NOUN
ejpam-6050	402	12	)	)	PUNCT
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ejpam-6050	403	2	[	[	PUNCT
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ejpam-6050	403	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	403	5	)	)	PUNCT
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ejpam-6050	403	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	403	9	)	)	PUNCT
ejpam-6050	403	10	]	]	PUNCT
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ejpam-6050	404	2	[	[	PUNCT
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ejpam-6050	404	4	b(s)e	b(s)e	ADP
ejpam-6050	404	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	404	6	b(s	b(	NOUN
ejpam-6050	404	7	)	)	PUNCT
ejpam-6050	405	1	⊕	⊕	PROPN
ejpam-6050	405	2	ℵa(s)e	ℵa(s)e	PUNCT
ejpam-6050	405	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	405	4	)	)	PUNCT
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ejpam-6050	405	11	,	,	PUNCT
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ejpam-6050	405	15	eur	eur	PROPN
ejpam-6050	405	16	.	.	PUNCT
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ejpam-6050	406	2	pure	pure	PROPN
ejpam-6050	406	3	appl	appl	PROPN
ejpam-6050	406	4	.	.	PROPN
ejpam-6050	406	5	math	math	PROPN
ejpam-6050	406	6	,	,	PUNCT
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ejpam-6050	406	9	2	2	NUM
ejpam-6050	406	10	)	)	PUNCT
ejpam-6050	406	11	(	(	PUNCT
ejpam-6050	406	12	2025	2025	NUM
ejpam-6050	406	13	)	)	PUNCT
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ejpam-6050	406	15	6050	6050	NUM
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ejpam-6050	406	18	29	29	NUM
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ejpam-6050	406	21	ℵc	ℵc	NOUN
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ejpam-6050	406	24	b(s	b(	NOUN
ejpam-6050	406	25	)	)	PUNCT
ejpam-6050	406	26	]	]	PUNCT
ejpam-6050	406	27	(	(	PUNCT
ejpam-6050	406	28	4.24	4.24	NUM
ejpam-6050	406	29	)	)	PUNCT
ejpam-6050	406	30	from	from	ADP
ejpam-6050	406	31	equation	equation	NOUN
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ejpam-6050	406	33	and	and	CCONJ
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ejpam-6050	406	36	eac	eac	PROPN
ejpam-6050	406	37	∪	∪	PROPN
ejpam-6050	406	38	eb	eb	PROPN
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ejpam-6050	406	40	∩	∩	NOUN
ejpam-6050	406	41	(	(	PUNCT
ejpam-6050	406	42	ea	ea	PROPN
ejpam-6050	406	43	∪	∪	PROPN
ejpam-6050	406	44	ebc	ebc	PROPN
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ejpam-6050	406	46	=	=	PUNCT
ejpam-6050	406	47	(	(	PUNCT
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ejpam-6050	406	49	∩	∩	PROPN
ejpam-6050	406	50	ebc	ebc	PROPN
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ejpam-6050	406	52	∪	∪	NOUN
ejpam-6050	406	53	(	(	PUNCT
ejpam-6050	406	54	ea	ea	X
ejpam-6050	406	55	∩	∩	PROPN
ejpam-6050	406	56	eb	eb	PROPN
ejpam-6050	406	57	)	)	PUNCT
ejpam-6050	406	58	.	.	PUNCT
ejpam-6050	407	1	case	case	NOUN
ejpam-6050	407	2	5	5	NUM
ejpam-6050	407	3	.	.	PUNCT
ejpam-6050	408	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	408	2	)	)	PUNCT
ejpam-6050	408	3	≤	≤	NOUN
ejpam-6050	408	4	ℵea(s),ℵc	ℵea(s),ℵc	NUM
ejpam-6050	408	5	ea(s	ea(	NOUN
ejpam-6050	408	6	)	)	PUNCT
ejpam-6050	408	7	≤	≤	NOUN
ejpam-6050	409	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	409	2	eb(s	eb(	NOUN
ejpam-6050	409	3	)	)	PUNCT
ejpam-6050	409	4	≤	≤	NUM
ejpam-6050	409	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	409	6	)	)	PUNCT
ejpam-6050	409	7	and	and	CCONJ
ejpam-6050	409	8	ℵc	ℵc	NOUN
ejpam-6050	409	9	ea(s	ea(	NOUN
ejpam-6050	409	10	)	)	PUNCT
ejpam-6050	409	11	≤	≤	NUM
ejpam-6050	409	12	ℵc	ℵc	ADP
ejpam-6050	409	13	eb(s	eb(	NOUN
ejpam-6050	409	14	)	)	PUNCT
ejpam-6050	409	15	.	.	PUNCT
ejpam-6050	410	1	(	(	PUNCT
ejpam-6050	410	2	eac	eac	PROPN
ejpam-6050	410	3	∪	∪	PROPN
ejpam-6050	410	4	eb	eb	PROPN
ejpam-6050	410	5	)	)	PUNCT
ejpam-6050	410	6	∩	∩	NOUN
ejpam-6050	410	7	(	(	PUNCT
ejpam-6050	410	8	ea	ea	PROPN
ejpam-6050	410	9	∪	∪	PROPN
ejpam-6050	410	10	ebc	ebc	PROPN
ejpam-6050	410	11	)	)	PUNCT
ejpam-6050	410	12	=	=	PUNCT
ejpam-6050	411	1	[	[	PUNCT
ejpam-6050	411	2	ℵc	ℵc	NOUN
ejpam-6050	411	3	a(s)e	a(s)e	PROPN
ejpam-6050	411	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	411	5	a(s	a(s	PROPN
ejpam-6050	411	6	)	)	PUNCT
ejpam-6050	411	7	⊕	⊕	PROPN
ejpam-6050	411	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	412	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	412	2	)	)	PUNCT
ejpam-6050	412	3	]	]	PUNCT
ejpam-6050	413	1	∗	∗	NOUN
ejpam-6050	413	2	[	[	PUNCT
ejpam-6050	413	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	413	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	413	5	)	)	PUNCT
ejpam-6050	413	6	⊕	⊕	PROPN
ejpam-6050	413	7	ℵc	ℵc	NOUN
ejpam-6050	414	1	b(s)e	b(s)e	ADP
ejpam-6050	414	2	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	414	3	b(s	b(	NOUN
ejpam-6050	414	4	)	)	PUNCT
ejpam-6050	414	5	]	]	PUNCT
ejpam-6050	415	1	=	=	PUNCT
ejpam-6050	415	2	[	[	PUNCT
ejpam-6050	415	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	415	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	415	5	)	)	PUNCT
ejpam-6050	415	6	∗	∗	NOUN
ejpam-6050	415	7	ℵa(s)e	ℵa(s)e	X
ejpam-6050	415	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	415	9	)	)	PUNCT
ejpam-6050	415	10	]	]	PUNCT
ejpam-6050	416	1	=	=	PUNCT
ejpam-6050	417	1	[	[	PUNCT
ejpam-6050	417	2	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	417	3	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	417	4	)	)	PUNCT
ejpam-6050	417	5	]	]	PUNCT
ejpam-6050	417	6	(	(	PUNCT
ejpam-6050	417	7	4.25	4.25	NUM
ejpam-6050	417	8	)	)	PUNCT
ejpam-6050	417	9	(	(	PUNCT
ejpam-6050	417	10	eac	eac	PROPN
ejpam-6050	417	11	∩	∩	PROPN
ejpam-6050	417	12	ebc	ebc	PROPN
ejpam-6050	417	13	)	)	PUNCT
ejpam-6050	417	14	∪	∪	NOUN
ejpam-6050	417	15	(	(	PUNCT
ejpam-6050	417	16	ea	ea	X
ejpam-6050	417	17	∩	∩	PROPN
ejpam-6050	417	18	eb	eb	PROPN
ejpam-6050	417	19	)	)	PUNCT
ejpam-6050	417	20	=	=	PUNCT
ejpam-6050	418	1	[	[	PUNCT
ejpam-6050	418	2	ℵc	ℵc	NOUN
ejpam-6050	418	3	a(s)e	a(s)e	PROPN
ejpam-6050	418	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	418	5	a(s	a(s	PROPN
ejpam-6050	418	6	)	)	PUNCT
ejpam-6050	418	7	∗	∗	NOUN
ejpam-6050	418	8	ℵc	ℵc	NOUN
ejpam-6050	418	9	b(s)e	b(s)e	PROPN
ejpam-6050	418	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	418	11	b(s	b(	NOUN
ejpam-6050	418	12	)	)	PUNCT
ejpam-6050	418	13	]	]	PUNCT
ejpam-6050	419	1	⊕	⊕	PROPN
ejpam-6050	419	2	[	[	PUNCT
ejpam-6050	419	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	419	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	419	5	)	)	PUNCT
ejpam-6050	419	6	∗	∗	NOUN
ejpam-6050	419	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	419	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	419	9	)	)	PUNCT
ejpam-6050	419	10	]	]	PUNCT
ejpam-6050	420	1	=	=	PUNCT
ejpam-6050	420	2	[	[	PUNCT
ejpam-6050	420	3	ℵc	ℵc	NOUN
ejpam-6050	420	4	a(s)e	a(s)e	PROPN
ejpam-6050	420	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	420	6	a(s	a(s	PROPN
ejpam-6050	420	7	)	)	PUNCT
ejpam-6050	420	8	⊕	⊕	PROPN
ejpam-6050	420	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	420	10	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	420	11	)	)	PUNCT
ejpam-6050	420	12	]	]	PUNCT
ejpam-6050	421	1	=	=	PUNCT
ejpam-6050	421	2	[	[	PUNCT
ejpam-6050	421	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	421	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	421	5	)	)	PUNCT
ejpam-6050	421	6	]	]	PUNCT
ejpam-6050	421	7	(	(	PUNCT
ejpam-6050	421	8	4.26	4.26	NUM
ejpam-6050	421	9	)	)	PUNCT
ejpam-6050	421	10	from	from	ADP
ejpam-6050	421	11	equation	equation	NOUN
ejpam-6050	421	12	4.25	4.25	NUM
ejpam-6050	421	13	and	and	CCONJ
ejpam-6050	421	14	4.26	4.26	NUM
ejpam-6050	421	15	(	(	PUNCT
ejpam-6050	421	16	eac	eac	PROPN
ejpam-6050	421	17	∪	∪	PROPN
ejpam-6050	421	18	eb	eb	PROPN
ejpam-6050	421	19	)	)	PUNCT
ejpam-6050	421	20	∩	∩	NOUN
ejpam-6050	421	21	(	(	PUNCT
ejpam-6050	421	22	ea	ea	PROPN
ejpam-6050	421	23	∪	∪	PROPN
ejpam-6050	421	24	ebc	ebc	PROPN
ejpam-6050	421	25	)	)	PUNCT
ejpam-6050	421	26	=	=	PUNCT
ejpam-6050	421	27	(	(	PUNCT
ejpam-6050	421	28	eac	eac	PROPN
ejpam-6050	421	29	∩	∩	PROPN
ejpam-6050	421	30	ebc	ebc	PROPN
ejpam-6050	421	31	)	)	PUNCT
ejpam-6050	421	32	∪	∪	NOUN
ejpam-6050	421	33	(	(	PUNCT
ejpam-6050	421	34	ea	ea	X
ejpam-6050	421	35	∩	∩	PROPN
ejpam-6050	421	36	eb	eb	PROPN
ejpam-6050	421	37	)	)	PUNCT
ejpam-6050	421	38	.	.	PUNCT
ejpam-6050	422	1	case	case	NOUN
ejpam-6050	422	2	6	6	NUM
ejpam-6050	422	3	.	.	PUNCT
ejpam-6050	423	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	423	2	)	)	PUNCT
ejpam-6050	423	3	≤	≤	NUM
ejpam-6050	423	4	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	423	5	)	)	PUNCT
ejpam-6050	423	6	≤	≤	NUM
ejpam-6050	423	7	ℵc	ℵc	ADP
ejpam-6050	423	8	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	423	9	)	)	PUNCT
ejpam-6050	423	10	≤	≤	NUM
ejpam-6050	423	11	ℵc	ℵc	ADP
ejpam-6050	423	12	eb(s	eb(	NOUN
ejpam-6050	423	13	)	)	PUNCT
ejpam-6050	423	14	and	and	CCONJ
ejpam-6050	423	15	ℵc	ℵc	NOUN
ejpam-6050	423	16	ea(s	ea(	NOUN
ejpam-6050	423	17	)	)	PUNCT
ejpam-6050	423	18	≤	≤	NUM
ejpam-6050	423	19	ℵc	ℵc	ADP
ejpam-6050	423	20	eb(s	eb(	NOUN
ejpam-6050	423	21	)	)	PUNCT
ejpam-6050	423	22	.	.	PUNCT
ejpam-6050	424	1	(	(	PUNCT
ejpam-6050	424	2	eac	eac	PROPN
ejpam-6050	424	3	∪	∪	PROPN
ejpam-6050	424	4	eb	eb	PROPN
ejpam-6050	424	5	)	)	PUNCT
ejpam-6050	424	6	∩	∩	NOUN
ejpam-6050	424	7	(	(	PUNCT
ejpam-6050	424	8	ea	ea	PROPN
ejpam-6050	424	9	∪	∪	PROPN
ejpam-6050	424	10	ebc	ebc	PROPN
ejpam-6050	424	11	)	)	PUNCT
ejpam-6050	424	12	=	=	PUNCT
ejpam-6050	425	1	[	[	PUNCT
ejpam-6050	425	2	ℵc	ℵc	NOUN
ejpam-6050	425	3	a(s)e	a(s)e	PROPN
ejpam-6050	425	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	425	5	a(s	a(s	PROPN
ejpam-6050	425	6	)	)	PUNCT
ejpam-6050	425	7	⊕	⊕	PROPN
ejpam-6050	425	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	426	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	426	2	)	)	PUNCT
ejpam-6050	426	3	]	]	PUNCT
ejpam-6050	427	1	∗	∗	NOUN
ejpam-6050	427	2	[	[	PUNCT
ejpam-6050	427	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	427	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	427	5	)	)	PUNCT
ejpam-6050	427	6	⊕	⊕	PROPN
ejpam-6050	427	7	ℵc	ℵc	NOUN
ejpam-6050	428	1	b(s)e	b(s)e	ADP
ejpam-6050	428	2	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	428	3	b(s	b(	NOUN
ejpam-6050	428	4	)	)	PUNCT
ejpam-6050	428	5	]	]	PUNCT
ejpam-6050	429	1	=	=	PUNCT
ejpam-6050	429	2	[	[	PUNCT
ejpam-6050	429	3	ℵc	ℵc	NOUN
ejpam-6050	429	4	a(s)e	a(s)e	PROPN
ejpam-6050	429	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	429	6	a(s	a(s	PROPN
ejpam-6050	429	7	)	)	PUNCT
ejpam-6050	429	8	∗	∗	NOUN
ejpam-6050	429	9	ℵc	ℵc	NOUN
ejpam-6050	429	10	b(s)e	b(s)e	PROPN
ejpam-6050	429	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	429	12	b(s	b(	NOUN
ejpam-6050	429	13	)	)	PUNCT
ejpam-6050	429	14	]	]	PUNCT
ejpam-6050	430	1	=	=	PUNCT
ejpam-6050	430	2	ℵc	ℵc	PROPN
ejpam-6050	430	3	a(s)e	a(s)e	PROPN
ejpam-6050	430	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	430	5	a(s	a(s	PROPN
ejpam-6050	430	6	)	)	PUNCT
ejpam-6050	430	7	(	(	PUNCT
ejpam-6050	430	8	4.27	4.27	NUM
ejpam-6050	430	9	)	)	PUNCT
ejpam-6050	430	10	(	(	PUNCT
ejpam-6050	430	11	eac	eac	PROPN
ejpam-6050	430	12	∩	∩	PROPN
ejpam-6050	430	13	ebc	ebc	PROPN
ejpam-6050	430	14	)	)	PUNCT
ejpam-6050	430	15	∪	∪	NOUN
ejpam-6050	430	16	(	(	PUNCT
ejpam-6050	430	17	ea	ea	X
ejpam-6050	430	18	∩	∩	PROPN
ejpam-6050	430	19	eb	eb	PROPN
ejpam-6050	430	20	)	)	PUNCT
ejpam-6050	431	1	=	=	PUNCT
ejpam-6050	432	1	[	[	PUNCT
ejpam-6050	432	2	ℵc	ℵc	NOUN
ejpam-6050	432	3	a(s)e	a(s)e	PROPN
ejpam-6050	432	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	432	5	a(s	a(s	PROPN
ejpam-6050	432	6	)	)	PUNCT
ejpam-6050	432	7	∗	∗	NOUN
ejpam-6050	432	8	ℵc	ℵc	NOUN
ejpam-6050	432	9	b(s)e	b(s)e	PROPN
ejpam-6050	432	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	432	11	b(s	b(	NOUN
ejpam-6050	432	12	)	)	PUNCT
ejpam-6050	432	13	]	]	PUNCT
ejpam-6050	433	1	⊕	⊕	PROPN
ejpam-6050	433	2	[	[	PUNCT
ejpam-6050	433	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	433	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	433	5	)	)	PUNCT
ejpam-6050	433	6	∗	∗	NOUN
ejpam-6050	433	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	433	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	433	9	)	)	PUNCT
ejpam-6050	433	10	]	]	PUNCT
ejpam-6050	434	1	=	=	PUNCT
ejpam-6050	434	2	[	[	PUNCT
ejpam-6050	434	3	ℵc	ℵc	NOUN
ejpam-6050	434	4	a(s)e	a(s)e	PROPN
ejpam-6050	434	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	434	6	a(s	a(s	PROPN
ejpam-6050	434	7	)	)	PUNCT
ejpam-6050	434	8	⊕	⊕	PROPN
ejpam-6050	434	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	434	10	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	434	11	)	)	PUNCT
ejpam-6050	434	12	]	]	PUNCT
ejpam-6050	435	1	=	=	PUNCT
ejpam-6050	435	2	[	[	PUNCT
ejpam-6050	435	3	ℵc	ℵc	NOUN
ejpam-6050	435	4	a(s)e	a(s)e	PROPN
ejpam-6050	435	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	435	6	a(s	a(s	PROPN
ejpam-6050	435	7	)	)	PUNCT
ejpam-6050	435	8	]	]	PUNCT
ejpam-6050	435	9	(	(	PUNCT
ejpam-6050	435	10	4.28	4.28	NUM
ejpam-6050	435	11	)	)	PUNCT
ejpam-6050	435	12	from	from	ADP
ejpam-6050	435	13	equation	equation	NOUN
ejpam-6050	435	14	4.27	4.27	NUM
ejpam-6050	435	15	and	and	CCONJ
ejpam-6050	435	16	4.28	4.28	NUM
ejpam-6050	435	17	(	(	PUNCT
ejpam-6050	435	18	eac	eac	PROPN
ejpam-6050	435	19	∪	∪	PROPN
ejpam-6050	435	20	eb	eb	PROPN
ejpam-6050	435	21	)	)	PUNCT
ejpam-6050	435	22	∩	∩	NOUN
ejpam-6050	435	23	(	(	PUNCT
ejpam-6050	435	24	ea	ea	PROPN
ejpam-6050	435	25	∪	∪	PROPN
ejpam-6050	435	26	ebc	ebc	PROPN
ejpam-6050	435	27	)	)	PUNCT
ejpam-6050	435	28	=	=	PUNCT
ejpam-6050	435	29	(	(	PUNCT
ejpam-6050	435	30	eac	eac	PROPN
ejpam-6050	435	31	∩	∩	PROPN
ejpam-6050	435	32	ebc	ebc	PROPN
ejpam-6050	435	33	)	)	PUNCT
ejpam-6050	435	34	∪	∪	NOUN
ejpam-6050	435	35	(	(	PUNCT
ejpam-6050	435	36	ea	ea	X
ejpam-6050	435	37	∩	∩	PROPN
ejpam-6050	435	38	eb	eb	PROPN
ejpam-6050	435	39	)	)	PUNCT
ejpam-6050	435	40	.	.	PUNCT
ejpam-6050	436	1	case	case	NOUN
ejpam-6050	436	2	7	7	NUM
ejpam-6050	436	3	.	.	PUNCT
ejpam-6050	437	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	437	2	)	)	PUNCT
ejpam-6050	437	3	≤	≤	NOUN
ejpam-6050	437	4	ℵea(s),ℵc	ℵea(s),ℵc	NUM
ejpam-6050	437	5	ea(s	ea(	NOUN
ejpam-6050	437	6	)	)	PUNCT
ejpam-6050	437	7	≤	≤	NOUN
ejpam-6050	438	1	ℵeb(s),ℵc	ℵeb(s),ℵc	PROPN
ejpam-6050	438	2	eb(s	eb(	NOUN
ejpam-6050	438	3	)	)	PUNCT
ejpam-6050	438	4	≤	≤	NUM
ejpam-6050	438	5	ℵea(s	ℵea(s	PROPN
ejpam-6050	438	6	)	)	PUNCT
ejpam-6050	438	7	and	and	CCONJ
ejpam-6050	438	8	ℵc	ℵc	NOUN
ejpam-6050	438	9	ea(s	ea(	NOUN
ejpam-6050	438	10	)	)	PUNCT
ejpam-6050	438	11	≤	≤	NUM
ejpam-6050	438	12	ℵc	ℵc	ADP
ejpam-6050	438	13	eb(s	eb(	NOUN
ejpam-6050	438	14	)	)	PUNCT
ejpam-6050	438	15	.	.	PUNCT
ejpam-6050	439	1	(	(	PUNCT
ejpam-6050	439	2	eac	eac	PROPN
ejpam-6050	439	3	∪	∪	PROPN
ejpam-6050	439	4	eb	eb	PROPN
ejpam-6050	439	5	)	)	PUNCT
ejpam-6050	439	6	∩	∩	NOUN
ejpam-6050	439	7	(	(	PUNCT
ejpam-6050	439	8	ea	ea	PROPN
ejpam-6050	439	9	∪	∪	PROPN
ejpam-6050	439	10	ebc	ebc	PROPN
ejpam-6050	439	11	)	)	PUNCT
ejpam-6050	439	12	=	=	PUNCT
ejpam-6050	440	1	[	[	PUNCT
ejpam-6050	440	2	ℵc	ℵc	NOUN
ejpam-6050	440	3	a(s)e	a(s)e	PROPN
ejpam-6050	440	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	440	5	a(s	a(s	PROPN
ejpam-6050	440	6	)	)	PUNCT
ejpam-6050	440	7	⊕	⊕	PROPN
ejpam-6050	440	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	441	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	441	2	)	)	PUNCT
ejpam-6050	441	3	]	]	PUNCT
ejpam-6050	442	1	∗	∗	NOUN
ejpam-6050	442	2	[	[	PUNCT
ejpam-6050	442	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	442	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	442	5	)	)	PUNCT
ejpam-6050	442	6	⊕	⊕	PROPN
ejpam-6050	442	7	ℵc	ℵc	NOUN
ejpam-6050	443	1	b(s)e	b(s)e	ADP
ejpam-6050	443	2	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	443	3	b(s	b(	NOUN
ejpam-6050	443	4	)	)	PUNCT
ejpam-6050	443	5	]	]	PUNCT
ejpam-6050	444	1	=	=	PUNCT
ejpam-6050	444	2	[	[	PUNCT
ejpam-6050	444	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	444	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	444	5	)	)	PUNCT
ejpam-6050	444	6	∗	∗	NOUN
ejpam-6050	444	7	ℵa(s)e	ℵa(s)e	X
ejpam-6050	444	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	444	9	)	)	PUNCT
ejpam-6050	444	10	]	]	PUNCT
ejpam-6050	444	11	m.	m.	NOUN
ejpam-6050	444	12	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	444	13	,	,	PUNCT
ejpam-6050	444	14	m.	m.	NOUN
ejpam-6050	444	15	rajeshwari	rajeshwari	NOUN
ejpam-6050	444	16	,	,	PUNCT
ejpam-6050	444	17	m.	m.	NOUN
ejpam-6050	444	18	alqahtani	alqahtani	PROPN
ejpam-6050	444	19	/	/	SYM
ejpam-6050	444	20	eur	eur	PROPN
ejpam-6050	444	21	.	.	PUNCT
ejpam-6050	445	1	j.	j.	PROPN
ejpam-6050	445	2	pure	pure	PROPN
ejpam-6050	445	3	appl	appl	PROPN
ejpam-6050	445	4	.	.	PROPN
ejpam-6050	445	5	math	math	PROPN
ejpam-6050	445	6	,	,	PUNCT
ejpam-6050	445	7	18	18	NUM
ejpam-6050	445	8	(	(	PUNCT
ejpam-6050	445	9	2	2	NUM
ejpam-6050	445	10	)	)	PUNCT
ejpam-6050	445	11	(	(	PUNCT
ejpam-6050	445	12	2025	2025	NUM
ejpam-6050	445	13	)	)	PUNCT
ejpam-6050	445	14	,	,	PUNCT
ejpam-6050	445	15	6050	6050	NUM
ejpam-6050	445	16	17	17	NUM
ejpam-6050	445	17	of	of	ADP
ejpam-6050	445	18	29	29	NUM
ejpam-6050	445	19	=	=	SYM
ejpam-6050	445	20	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	445	21	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	445	22	)	)	PUNCT
ejpam-6050	445	23	(	(	PUNCT
ejpam-6050	445	24	4.29	4.29	NUM
ejpam-6050	445	25	)	)	PUNCT
ejpam-6050	445	26	(	(	PUNCT
ejpam-6050	445	27	eac	eac	PROPN
ejpam-6050	445	28	∩	∩	PROPN
ejpam-6050	445	29	ebc	ebc	PROPN
ejpam-6050	445	30	)	)	PUNCT
ejpam-6050	445	31	∪	∪	NOUN
ejpam-6050	445	32	(	(	PUNCT
ejpam-6050	445	33	ea	ea	X
ejpam-6050	445	34	∩	∩	PROPN
ejpam-6050	445	35	eb	eb	PROPN
ejpam-6050	445	36	)	)	PUNCT
ejpam-6050	445	37	=	=	PUNCT
ejpam-6050	446	1	[	[	PUNCT
ejpam-6050	446	2	ℵc	ℵc	NOUN
ejpam-6050	446	3	a(s)e	a(s)e	PROPN
ejpam-6050	446	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	446	5	a(s	a(s	PROPN
ejpam-6050	446	6	)	)	PUNCT
ejpam-6050	446	7	∗	∗	NOUN
ejpam-6050	446	8	ℵc	ℵc	NOUN
ejpam-6050	446	9	b(s)e	b(s)e	PROPN
ejpam-6050	446	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	446	11	b(s	b(	NOUN
ejpam-6050	446	12	)	)	PUNCT
ejpam-6050	446	13	]	]	PUNCT
ejpam-6050	447	1	⊕	⊕	PROPN
ejpam-6050	447	2	[	[	PUNCT
ejpam-6050	447	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	447	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	447	5	)	)	PUNCT
ejpam-6050	447	6	∗	∗	NOUN
ejpam-6050	447	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	447	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	447	9	)	)	PUNCT
ejpam-6050	447	10	]	]	PUNCT
ejpam-6050	448	1	=	=	PUNCT
ejpam-6050	448	2	[	[	PUNCT
ejpam-6050	448	3	ℵc	ℵc	NOUN
ejpam-6050	448	4	a(s)e	a(s)e	PROPN
ejpam-6050	448	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	448	6	a(s	a(s	PROPN
ejpam-6050	448	7	)	)	PUNCT
ejpam-6050	448	8	⊕	⊕	PROPN
ejpam-6050	448	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	448	10	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	448	11	)	)	PUNCT
ejpam-6050	448	12	]	]	PUNCT
ejpam-6050	449	1	=	=	PUNCT
ejpam-6050	449	2	[	[	PUNCT
ejpam-6050	449	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	449	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	449	5	)	)	PUNCT
ejpam-6050	449	6	]	]	PUNCT
ejpam-6050	449	7	(	(	PUNCT
ejpam-6050	449	8	4.30	4.30	NUM
ejpam-6050	449	9	)	)	PUNCT
ejpam-6050	449	10	from	from	ADP
ejpam-6050	449	11	equation	equation	NOUN
ejpam-6050	449	12	4.29	4.29	NUM
ejpam-6050	449	13	and	and	CCONJ
ejpam-6050	449	14	4.30	4.30	NUM
ejpam-6050	449	15	(	(	PUNCT
ejpam-6050	449	16	eac	eac	PROPN
ejpam-6050	449	17	∪	∪	PROPN
ejpam-6050	449	18	eb	eb	PROPN
ejpam-6050	449	19	)	)	PUNCT
ejpam-6050	449	20	∩	∩	NOUN
ejpam-6050	449	21	(	(	PUNCT
ejpam-6050	449	22	ea	ea	PROPN
ejpam-6050	449	23	∪	∪	PROPN
ejpam-6050	449	24	ebc	ebc	PROPN
ejpam-6050	449	25	)	)	PUNCT
ejpam-6050	449	26	=	=	PUNCT
ejpam-6050	449	27	(	(	PUNCT
ejpam-6050	449	28	eac	eac	PROPN
ejpam-6050	449	29	∩	∩	PROPN
ejpam-6050	449	30	ebc	ebc	PROPN
ejpam-6050	449	31	)	)	PUNCT
ejpam-6050	449	32	∪	∪	NOUN
ejpam-6050	449	33	(	(	PUNCT
ejpam-6050	449	34	ea	ea	X
ejpam-6050	449	35	∩	∩	PROPN
ejpam-6050	449	36	eb	eb	PROPN
ejpam-6050	449	37	)	)	PUNCT
ejpam-6050	449	38	.	.	PUNCT
ejpam-6050	450	1	case	case	NOUN
ejpam-6050	450	2	8	8	NUM
ejpam-6050	450	3	.	.	PUNCT
ejpam-6050	451	1	ℵeb(s	ℵeb(	VERB
ejpam-6050	451	2	)	)	PUNCT
ejpam-6050	451	3	≤	≤	NUM
ejpam-6050	451	4	ℵeb(s),ℵeb(s	ℵeb(s),ℵeb(	NOUN
ejpam-6050	451	5	)	)	PUNCT
ejpam-6050	451	6	≤	≤	NUM
ejpam-6050	451	7	ℵc	ℵc	ADP
ejpam-6050	451	8	ea(s),ℵea(s	ea(s),ℵea(	NOUN
ejpam-6050	451	9	)	)	PUNCT
ejpam-6050	451	10	≤	≤	NUM
ejpam-6050	451	11	ℵc	ℵc	ADP
ejpam-6050	451	12	eb(s	eb(	NOUN
ejpam-6050	451	13	)	)	PUNCT
ejpam-6050	451	14	and	and	CCONJ
ejpam-6050	451	15	ℵc	ℵc	NOUN
ejpam-6050	451	16	ea(s	ea(	NOUN
ejpam-6050	451	17	)	)	PUNCT
ejpam-6050	451	18	≤	≤	NUM
ejpam-6050	451	19	ℵc	ℵc	ADP
ejpam-6050	451	20	eb(s	eb(	NOUN
ejpam-6050	451	21	)	)	PUNCT
ejpam-6050	451	22	.	.	PUNCT
ejpam-6050	452	1	(	(	PUNCT
ejpam-6050	452	2	eac	eac	PROPN
ejpam-6050	452	3	∪	∪	PROPN
ejpam-6050	452	4	eb	eb	PROPN
ejpam-6050	452	5	)	)	PUNCT
ejpam-6050	452	6	∩	∩	NOUN
ejpam-6050	452	7	(	(	PUNCT
ejpam-6050	452	8	ea	ea	PROPN
ejpam-6050	452	9	∪	∪	PROPN
ejpam-6050	452	10	ebc	ebc	PROPN
ejpam-6050	452	11	)	)	PUNCT
ejpam-6050	452	12	=	=	PUNCT
ejpam-6050	453	1	[	[	PUNCT
ejpam-6050	453	2	ℵc	ℵc	NOUN
ejpam-6050	453	3	a(s)e	a(s)e	PROPN
ejpam-6050	453	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	453	5	a(s	a(s	PROPN
ejpam-6050	453	6	)	)	PUNCT
ejpam-6050	453	7	⊕	⊕	PROPN
ejpam-6050	453	8	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	454	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	454	2	)	)	PUNCT
ejpam-6050	454	3	]	]	PUNCT
ejpam-6050	455	1	∗	∗	NOUN
ejpam-6050	455	2	[	[	PUNCT
ejpam-6050	455	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	455	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	455	5	)	)	PUNCT
ejpam-6050	455	6	⊕	⊕	PROPN
ejpam-6050	455	7	ℵc	ℵc	NOUN
ejpam-6050	456	1	b(s)e	b(s)e	ADP
ejpam-6050	456	2	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	456	3	b(s	b(	NOUN
ejpam-6050	456	4	)	)	PUNCT
ejpam-6050	456	5	]	]	PUNCT
ejpam-6050	457	1	=	=	PUNCT
ejpam-6050	457	2	[	[	PUNCT
ejpam-6050	457	3	ℵc	ℵc	NOUN
ejpam-6050	457	4	a(s)e	a(s)e	PROPN
ejpam-6050	457	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	457	6	a(s	a(s	PROPN
ejpam-6050	457	7	)	)	PUNCT
ejpam-6050	457	8	∗	∗	NOUN
ejpam-6050	457	9	ℵc	ℵc	NOUN
ejpam-6050	457	10	b(s)e	b(s)e	PROPN
ejpam-6050	457	11	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	457	12	b(s	b(	NOUN
ejpam-6050	457	13	)	)	PUNCT
ejpam-6050	457	14	]	]	PUNCT
ejpam-6050	458	1	=	=	PUNCT
ejpam-6050	458	2	ℵc	ℵc	PROPN
ejpam-6050	458	3	a(s)e	a(s)e	PROPN
ejpam-6050	458	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	458	5	a(s	a(s	PROPN
ejpam-6050	458	6	)	)	PUNCT
ejpam-6050	458	7	(	(	PUNCT
ejpam-6050	458	8	4.31	4.31	NUM
ejpam-6050	458	9	)	)	PUNCT
ejpam-6050	458	10	(	(	PUNCT
ejpam-6050	458	11	eac	eac	PROPN
ejpam-6050	458	12	∩	∩	PROPN
ejpam-6050	458	13	ebc	ebc	PROPN
ejpam-6050	458	14	)	)	PUNCT
ejpam-6050	458	15	∪	∪	NOUN
ejpam-6050	458	16	(	(	PUNCT
ejpam-6050	458	17	ea	ea	X
ejpam-6050	458	18	∩	∩	PROPN
ejpam-6050	458	19	eb	eb	PROPN
ejpam-6050	458	20	)	)	PUNCT
ejpam-6050	459	1	=	=	PUNCT
ejpam-6050	460	1	[	[	PUNCT
ejpam-6050	460	2	ℵc	ℵc	NOUN
ejpam-6050	460	3	a(s)e	a(s)e	PROPN
ejpam-6050	460	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	460	5	a(s	a(s	PROPN
ejpam-6050	460	6	)	)	PUNCT
ejpam-6050	460	7	∗	∗	NOUN
ejpam-6050	460	8	ℵc	ℵc	NOUN
ejpam-6050	460	9	b(s)e	b(s)e	PROPN
ejpam-6050	460	10	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	460	11	b(s	b(	NOUN
ejpam-6050	460	12	)	)	PUNCT
ejpam-6050	460	13	]	]	PUNCT
ejpam-6050	461	1	⊕	⊕	PROPN
ejpam-6050	461	2	[	[	PUNCT
ejpam-6050	461	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	461	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	461	5	)	)	PUNCT
ejpam-6050	461	6	∗	∗	NOUN
ejpam-6050	461	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	461	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	461	9	)	)	PUNCT
ejpam-6050	461	10	]	]	PUNCT
ejpam-6050	462	1	=	=	PUNCT
ejpam-6050	462	2	[	[	PUNCT
ejpam-6050	462	3	ℵc	ℵc	NOUN
ejpam-6050	462	4	a(s)e	a(s)e	PROPN
ejpam-6050	462	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	462	6	a(s	a(s	PROPN
ejpam-6050	462	7	)	)	PUNCT
ejpam-6050	462	8	⊕	⊕	PROPN
ejpam-6050	462	9	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	462	10	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	462	11	)	)	PUNCT
ejpam-6050	462	12	]	]	PUNCT
ejpam-6050	463	1	=	=	PUNCT
ejpam-6050	463	2	[	[	PUNCT
ejpam-6050	463	3	ℵc	ℵc	NOUN
ejpam-6050	463	4	a(s)e	a(s)e	PROPN
ejpam-6050	463	5	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	463	6	a(s	a(s	PROPN
ejpam-6050	463	7	)	)	PUNCT
ejpam-6050	463	8	]	]	PUNCT
ejpam-6050	463	9	(	(	PUNCT
ejpam-6050	463	10	4.32	4.32	NUM
ejpam-6050	463	11	)	)	PUNCT
ejpam-6050	463	12	from	from	ADP
ejpam-6050	463	13	equation	equation	NOUN
ejpam-6050	463	14	4.31	4.31	NUM
ejpam-6050	463	15	and	and	CCONJ
ejpam-6050	463	16	4.32	4.32	NUM
ejpam-6050	463	17	(	(	PUNCT
ejpam-6050	463	18	eac	eac	PROPN
ejpam-6050	463	19	∪	∪	PROPN
ejpam-6050	463	20	eb	eb	PROPN
ejpam-6050	463	21	)	)	PUNCT
ejpam-6050	463	22	∩	∩	NOUN
ejpam-6050	463	23	(	(	PUNCT
ejpam-6050	463	24	ea	ea	PROPN
ejpam-6050	463	25	∪	∪	PROPN
ejpam-6050	463	26	ebc	ebc	PROPN
ejpam-6050	463	27	)	)	PUNCT
ejpam-6050	463	28	=	=	PUNCT
ejpam-6050	463	29	(	(	PUNCT
ejpam-6050	463	30	eac	eac	PROPN
ejpam-6050	463	31	∩	∩	PROPN
ejpam-6050	463	32	ebc	ebc	PROPN
ejpam-6050	463	33	)	)	PUNCT
ejpam-6050	463	34	∪	∪	NOUN
ejpam-6050	463	35	(	(	PUNCT
ejpam-6050	463	36	ea	ea	X
ejpam-6050	463	37	∩	∩	PROPN
ejpam-6050	463	38	eb	eb	PROPN
ejpam-6050	463	39	)	)	PUNCT
ejpam-6050	463	40	.	.	PUNCT
ejpam-6050	464	1	from	from	ADP
ejpam-6050	464	2	the	the	DET
ejpam-6050	464	3	all	all	DET
ejpam-6050	464	4	cases	case	NOUN
ejpam-6050	464	5	ea	ea	NOUN
ejpam-6050	464	6	and	and	CCONJ
ejpam-6050	464	7	eb	eb	PROPN
ejpam-6050	464	8	is	be	AUX
ejpam-6050	464	9	equivalence	equivalence	NOUN
ejpam-6050	464	10	relation	relation	NOUN
ejpam-6050	464	11	.	.	PUNCT
ejpam-6050	465	1	theorem	theorem	NOUN
ejpam-6050	465	2	3	3	NUM
ejpam-6050	465	3	.	.	PUNCT
ejpam-6050	466	1	any	any	DET
ejpam-6050	466	2	finite	finite	ADJ
ejpam-6050	466	3	collection	collection	NOUN
ejpam-6050	466	4	of	of	ADP
ejpam-6050	466	5	efss	efss	NOUN
ejpam-6050	466	6	is	be	AUX
ejpam-6050	466	7	always	always	ADV
ejpam-6050	466	8	an	an	DET
ejpam-6050	466	9	efss	efss	NOUN
ejpam-6050	466	10	for	for	ADP
ejpam-6050	466	11	union	union	NOUN
ejpam-6050	466	12	and	and	CCONJ
ejpam-6050	466	13	intersection	intersection	NOUN
ejpam-6050	466	14	.	.	PUNCT
ejpam-6050	467	1	proof	proof	NOUN
ejpam-6050	467	2	.	.	PUNCT
ejpam-6050	468	1	case	case	NOUN
ejpam-6050	469	1	i	i	PRON
ejpam-6050	469	2	.	.	PUNCT
ejpam-6050	470	1	let	let	VERB
ejpam-6050	470	2	ea1	ea1	VERB
ejpam-6050	470	3	,	,	PUNCT
ejpam-6050	470	4	ea2	ea2	PROPN
ejpam-6050	470	5	,	,	PUNCT
ejpam-6050	470	6	ea3	ea3	PROPN
ejpam-6050	470	7	,	,	PUNCT
ejpam-6050	470	8	.....	.....	PUNCT
ejpam-6050	471	1	eam	eam	PROPN
ejpam-6050	471	2	be	be	AUX
ejpam-6050	471	3	efss	efss	ADJ
ejpam-6050	471	4	and	and	CCONJ
ejpam-6050	471	5	its	its	PRON
ejpam-6050	471	6	membership	membership	NOUN
ejpam-6050	471	7	functions	function	NOUN
ejpam-6050	471	8	is	be	AUX
ejpam-6050	471	9	ℵea1	ℵea1	NOUN
ejpam-6050	471	10	,	,	PUNCT
ejpam-6050	471	11	ℵea2	ℵea2	NOUN
ejpam-6050	471	12	,	,	PUNCT
ejpam-6050	471	13	ℵea3	ℵea3	PROPN
ejpam-6050	471	14	,	,	PUNCT
ejpam-6050	471	15	......	......	PUNCT
ejpam-6050	471	16	,	,	PUNCT
ejpam-6050	471	17	ℵeam	ℵeam	NOUN
ejpam-6050	471	18	.	.	PUNCT
ejpam-6050	472	1	ℵ′	ℵ′	ADV
ejpam-6050	472	2	ea(s	ea(	NOUN
ejpam-6050	472	3	)	)	PUNCT
ejpam-6050	472	4	=	=	SYM
ejpam-6050	472	5	max	max	PROPN
ejpam-6050	472	6	[	[	PUNCT
ejpam-6050	472	7	ℵea1	ℵea1	NOUN
ejpam-6050	472	8	,	,	PUNCT
ejpam-6050	472	9	ℵea2	ℵea2	NOUN
ejpam-6050	472	10	,	,	PUNCT
ejpam-6050	472	11	ℵea3	ℵea3	PROPN
ejpam-6050	472	12	,	,	PUNCT
ejpam-6050	472	13	......	......	PUNCT
ejpam-6050	472	14	,	,	PUNCT
ejpam-6050	472	15	ℵeam	ℵeam	NOUN
ejpam-6050	472	16	]	]	PUNCT
ejpam-6050	472	17	.	.	PUNCT
ejpam-6050	473	1	now	now	ADV
ejpam-6050	473	2	,	,	PUNCT
ejpam-6050	473	3	ea1	ea1	NOUN
ejpam-6050	473	4	∪	∪	VERB
ejpam-6050	473	5	ea2	ea2	VERB
ejpam-6050	473	6	∪	∪	ADV
ejpam-6050	473	7	......	......	PUNCT
ejpam-6050	473	8	∪	∪	PROPN
ejpam-6050	473	9	eam	eam	NOUN
ejpam-6050	473	10	=	=	PUNCT
ejpam-6050	473	11	[	[	PUNCT
ejpam-6050	473	12	ℵa1(s)e	ℵa1(s)e	NOUN
ejpam-6050	473	13	−⊺ℵa1	−⊺ℵa1	NOUN
ejpam-6050	473	14	(	(	PUNCT
ejpam-6050	473	15	s	s	NOUN
ejpam-6050	473	16	)	)	PUNCT
ejpam-6050	473	17	⊕	⊕	PROPN
ejpam-6050	473	18	ℵa2(s)e	ℵa2(s)e	PROPN
ejpam-6050	473	19	−⊺ℵa2	−⊺ℵa2	PROPN
ejpam-6050	473	20	(	(	PUNCT
ejpam-6050	473	21	s	s	NOUN
ejpam-6050	473	22	)	)	PUNCT
ejpam-6050	473	23	⊕	⊕	PROPN
ejpam-6050	473	24	.....	.....	PUNCT
ejpam-6050	473	25	⊕	⊕	PROPN
ejpam-6050	473	26	ℵam(s)e	ℵam(s)e	ADV
ejpam-6050	474	1	−⊺ℵam	−⊺ℵam	PROPN
ejpam-6050	474	2	(	(	PUNCT
ejpam-6050	474	3	s	s	NOUN
ejpam-6050	474	4	)	)	PUNCT
ejpam-6050	474	5	]	]	PUNCT
ejpam-6050	474	6	=	=	PUNCT
ejpam-6050	475	1	ℵ′	ℵ′	CCONJ
ejpam-6050	475	2	a1	a1	NOUN
ejpam-6050	475	3	(	(	PUNCT
ejpam-6050	475	4	s)e	s)e	NOUN
ejpam-6050	475	5	−⊺ℵ′	−⊺ℵ′	PROPN
ejpam-6050	475	6	a1	a1	NOUN
ejpam-6050	475	7	(	(	PUNCT
ejpam-6050	475	8	s	s	NOUN
ejpam-6050	475	9	)	)	PUNCT
ejpam-6050	475	10	=	=	SYM
ejpam-6050	475	11	e	e	NOUN
ejpam-6050	475	12	′	′	NUM
ejpam-6050	475	13	a1	a1	NOUN
ejpam-6050	475	14	.	.	PUNCT
ejpam-6050	476	1	m.	m.	NOUN
ejpam-6050	476	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	476	3	,	,	PUNCT
ejpam-6050	476	4	m.	m.	NOUN
ejpam-6050	476	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	476	6	,	,	PUNCT
ejpam-6050	476	7	m.	m.	NOUN
ejpam-6050	476	8	alqahtani	alqahtani	PROPN
ejpam-6050	476	9	/	/	SYM
ejpam-6050	476	10	eur	eur	PROPN
ejpam-6050	476	11	.	.	PUNCT
ejpam-6050	477	1	j.	j.	PROPN
ejpam-6050	477	2	pure	pure	PROPN
ejpam-6050	477	3	appl	appl	PROPN
ejpam-6050	477	4	.	.	PROPN
ejpam-6050	477	5	math	math	PROPN
ejpam-6050	477	6	,	,	PUNCT
ejpam-6050	477	7	18	18	NUM
ejpam-6050	477	8	(	(	PUNCT
ejpam-6050	477	9	2	2	NUM
ejpam-6050	477	10	)	)	PUNCT
ejpam-6050	477	11	(	(	PUNCT
ejpam-6050	477	12	2025	2025	NUM
ejpam-6050	477	13	)	)	PUNCT
ejpam-6050	477	14	,	,	PUNCT
ejpam-6050	477	15	6050	6050	NUM
ejpam-6050	477	16	18	18	NUM
ejpam-6050	477	17	of	of	ADP
ejpam-6050	477	18	29	29	NUM
ejpam-6050	477	19	case	case	NOUN
ejpam-6050	477	20	ii	ii	NOUN
ejpam-6050	477	21	.	.	PUNCT
ejpam-6050	478	1	ea1	ea1	PROPN
ejpam-6050	478	2	,	,	PUNCT
ejpam-6050	478	3	ea2	ea2	PROPN
ejpam-6050	478	4	,	,	PUNCT
ejpam-6050	478	5	ea3	ea3	PROPN
ejpam-6050	478	6	,	,	PUNCT
ejpam-6050	478	7	.....	.....	PUNCT
ejpam-6050	478	8	eam	eam	PROPN
ejpam-6050	478	9	be	be	AUX
ejpam-6050	478	10	anym	anym	NOUN
ejpam-6050	478	11	efss	efss	NOUN
ejpam-6050	478	12	and	and	CCONJ
ejpam-6050	478	13	ℵa1(s)e	ℵa1(s)e	PROPN
ejpam-6050	478	14	−⊺ℵa1	−⊺ℵa1	NOUN
ejpam-6050	478	15	(	(	PUNCT
ejpam-6050	478	16	s),ℵa2(s)e	s),ℵa2(s)e	PROPN
ejpam-6050	478	17	−⊺ℵa2	−⊺ℵa2	PROPN
ejpam-6050	478	18	(	(	PUNCT
ejpam-6050	478	19	s	s	PROPN
ejpam-6050	478	20	)	)	PUNCT
ejpam-6050	478	21	,	,	PUNCT
ejpam-6050	478	22	.....	.....	PUNCT
ejpam-6050	479	1	ℵam(s)e	ℵam(s)e	ADV
ejpam-6050	479	2	−⊺ℵam	−⊺ℵam	PROPN
ejpam-6050	479	3	(	(	PUNCT
ejpam-6050	479	4	s	s	X
ejpam-6050	479	5	)	)	PUNCT
ejpam-6050	479	6	denotes	denote	VERB
ejpam-6050	479	7	the	the	DET
ejpam-6050	479	8	membership	membership	NOUN
ejpam-6050	479	9	functions	function	NOUN
ejpam-6050	479	10	of	of	ADP
ejpam-6050	479	11	these	these	DET
ejpam-6050	479	12	efss	efss	NOUN
ejpam-6050	479	13	.	.	PUNCT
ejpam-6050	480	1	ℵ′	ℵ′	PART
ejpam-6050	480	2	ea(s	ea(s	NUM
ejpam-6050	480	3	)	)	PUNCT
ejpam-6050	480	4	=	=	SYM
ejpam-6050	480	5	min	min	PROPN
ejpam-6050	480	6	[	[	PUNCT
ejpam-6050	480	7	ℵea1	ℵea1	NOUN
ejpam-6050	480	8	,	,	PUNCT
ejpam-6050	480	9	ℵea2	ℵea2	NOUN
ejpam-6050	480	10	,	,	PUNCT
ejpam-6050	480	11	ℵea3	ℵea3	PROPN
ejpam-6050	480	12	,	,	PUNCT
ejpam-6050	480	13	......	......	PUNCT
ejpam-6050	480	14	,	,	PUNCT
ejpam-6050	480	15	ℵeam	ℵeam	NOUN
ejpam-6050	480	16	]	]	PUNCT
ejpam-6050	480	17	.	.	PUNCT
ejpam-6050	481	1	now	now	ADV
ejpam-6050	481	2	,	,	PUNCT
ejpam-6050	481	3	ea1	ea1	PROPN
ejpam-6050	481	4	∩	∩	NOUN
ejpam-6050	481	5	ea2	ea2	VERB
ejpam-6050	481	6	∩	∩	NOUN
ejpam-6050	481	7	......	......	PUNCT
ejpam-6050	481	8	∩	∩	ADJ
ejpam-6050	481	9	eam	eam	NOUN
ejpam-6050	481	10	=	=	PUNCT
ejpam-6050	481	11	[	[	PUNCT
ejpam-6050	481	12	ℵa1(s)e	ℵa1(s)e	NOUN
ejpam-6050	481	13	−⊺ℵa1	−⊺ℵa1	NOUN
ejpam-6050	481	14	(	(	PUNCT
ejpam-6050	481	15	s	s	NOUN
ejpam-6050	481	16	)	)	PUNCT
ejpam-6050	481	17	∗	∗	NOUN
ejpam-6050	481	18	ℵa2(s)e	ℵa2(s)e	PROPN
ejpam-6050	481	19	−⊺ℵa2	−⊺ℵa2	PROPN
ejpam-6050	481	20	(	(	PUNCT
ejpam-6050	481	21	s	s	NOUN
ejpam-6050	481	22	)	)	PUNCT
ejpam-6050	481	23	∗	∗	NOUN
ejpam-6050	481	24	.....	.....	PUNCT
ejpam-6050	481	25	∗	∗	NOUN
ejpam-6050	481	26	ℵam(s)e	ℵam(s)e	ADV
ejpam-6050	481	27	−⊺ℵam	−⊺ℵam	PROPN
ejpam-6050	481	28	(	(	PUNCT
ejpam-6050	481	29	s	s	NOUN
ejpam-6050	481	30	)	)	PUNCT
ejpam-6050	481	31	]	]	PUNCT
ejpam-6050	482	1	=	=	PUNCT
ejpam-6050	483	1	ℵ′	ℵ′	CCONJ
ejpam-6050	483	2	a1	a1	NOUN
ejpam-6050	483	3	(	(	PUNCT
ejpam-6050	483	4	s)e	s)e	NOUN
ejpam-6050	483	5	−⊺ℵ′	−⊺ℵ′	PROPN
ejpam-6050	483	6	a1	a1	NOUN
ejpam-6050	483	7	(	(	PUNCT
ejpam-6050	483	8	s	s	NOUN
ejpam-6050	483	9	)	)	PUNCT
ejpam-6050	483	10	=	=	SYM
ejpam-6050	483	11	e	e	NOUN
ejpam-6050	483	12	′	′	NUM
ejpam-6050	483	13	a1	a1	NOUN
ejpam-6050	483	14	.	.	PUNCT
ejpam-6050	484	1	which	which	PRON
ejpam-6050	484	2	is	be	AUX
ejpam-6050	484	3	also	also	ADV
ejpam-6050	484	4	a	a	DET
ejpam-6050	484	5	efs	ef	NOUN
ejpam-6050	484	6	.	.	PUNCT
ejpam-6050	485	1	theorem	theorem	VERB
ejpam-6050	485	2	4	4	NUM
ejpam-6050	485	3	.	.	X
ejpam-6050	486	1	for	for	ADP
ejpam-6050	486	2	any	any	DET
ejpam-6050	486	3	two	two	NUM
ejpam-6050	486	4	efs	ef	NOUN
ejpam-6050	486	5	ea	ea	NOUN
ejpam-6050	486	6	and	and	CCONJ
ejpam-6050	486	7	eb	eb	PROPN
ejpam-6050	486	8	,	,	PUNCT
ejpam-6050	486	9	the	the	DET
ejpam-6050	486	10	union	union	NOUN
ejpam-6050	486	11	and	and	CCONJ
ejpam-6050	486	12	intersection	intersection	NOUN
ejpam-6050	486	13	function	function	NOUN
ejpam-6050	486	14	with	with	ADP
ejpam-6050	486	15	the	the	DET
ejpam-6050	486	16	same	same	ADJ
ejpam-6050	486	17	function	function	NOUN
ejpam-6050	486	18	for	for	ADP
ejpam-6050	486	19	determining	determine	VERB
ejpam-6050	486	20	the	the	DET
ejpam-6050	486	21	phase	phase	NOUN
ejpam-6050	486	22	term	term	NOUN
ejpam-6050	486	23	satisfy	satisfy	NOUN
ejpam-6050	486	24	:	:	PUNCT
ejpam-6050	486	25	m∑	m∑	ADV
ejpam-6050	486	26	j=1,sj∈z	j=1,sj∈z	PROPN
ejpam-6050	486	27	|ℵea∩eb(si)|	|ℵea∩eb(si)|	PUNCT
ejpam-6050	486	28	≤	≤	NUM
ejpam-6050	486	29	m∑	m∑	NOUN
ejpam-6050	486	30	j=1,sj∈z	j=1,sj∈z	NOUN
ejpam-6050	486	31	|ℵea∪eb(si)|	|ℵea∪eb(si)|	X
ejpam-6050	486	32	.	.	PUNCT
ejpam-6050	487	1	proof	proof	NOUN
ejpam-6050	487	2	.	.	PUNCT
ejpam-6050	488	1	the	the	DET
ejpam-6050	488	2	expression	expression	NOUN
ejpam-6050	488	3	function	function	NOUN
ejpam-6050	488	4	of	of	ADP
ejpam-6050	488	5	union	union	NOUN
ejpam-6050	488	6	and	and	CCONJ
ejpam-6050	488	7	intersection	intersection	NOUN
ejpam-6050	488	8	are	be	AUX
ejpam-6050	488	9	define	define	VERB
ejpam-6050	488	10	by	by	ADP
ejpam-6050	488	11	ℵea∪eb(s	ℵea∪eb(	NOUN
ejpam-6050	488	12	)	)	PUNCT
ejpam-6050	489	1	=	=	SYM
ejpam-6050	489	2	max	max	PROPN
ejpam-6050	490	1	[	[	X
ejpam-6050	490	2	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	490	3	)	)	PUNCT
ejpam-6050	490	4	]	]	PUNCT
ejpam-6050	490	5	and	and	CCONJ
ejpam-6050	490	6	ℵea∩eb(s	ℵea∩eb(s	PROPN
ejpam-6050	490	7	)	)	PUNCT
ejpam-6050	490	8	=	=	SYM
ejpam-6050	490	9	min	min	NOUN
ejpam-6050	491	1	[	[	X
ejpam-6050	491	2	ℵea(s),ℵeb(s	ℵea(s),ℵeb(	NOUN
ejpam-6050	491	3	)	)	PUNCT
ejpam-6050	491	4	]	]	PUNCT
ejpam-6050	491	5	.	.	PUNCT
ejpam-6050	492	1	as	as	SCONJ
ejpam-6050	492	2	|ℵea∩eb(u)|	|ℵea∩eb(u)|	PROPN
ejpam-6050	492	3	≤	≤	NUM
ejpam-6050	492	4	|ℵea∪eb(u)|	|ℵea∪eb(u)|	NOUN
ejpam-6050	492	5	|ℵea∩eb(v)|	|ℵea∩eb(v)|	PROPN
ejpam-6050	492	6	≤	≤	NOUN
ejpam-6050	492	7	|ℵea∪eb(v)|	|ℵea∪eb(v)|	NOUN
ejpam-6050	492	8	...	...	PUNCT
ejpam-6050	492	9	...	...	PUNCT
ejpam-6050	492	10	...	...	PUNCT
ejpam-6050	493	1	|ℵea∩eb(sm)|	|ℵea∩eb(sm)|	X
ejpam-6050	493	2	≤	≤	X
ejpam-6050	493	3	|ℵea∪eb(sm)|	|ℵea∪eb(sm)|	PUNCT
ejpam-6050	493	4	.	.	PUNCT
ejpam-6050	494	1	sum	sum	NOUN
ejpam-6050	494	2	of	of	ADP
ejpam-6050	494	3	all	all	DET
ejpam-6050	494	4	above	above	ADJ
ejpam-6050	494	5	inequalities	inequality	NOUN
ejpam-6050	494	6	we	we	PRON
ejpam-6050	494	7	obtained	obtain	VERB
ejpam-6050	494	8	m∑	m∑	VERB
ejpam-6050	494	9	i=1,si∈z	i=1,si∈z	PROPN
ejpam-6050	494	10	|ℵea∩eb(si)|	|ℵea∩eb(si)|	NUM
ejpam-6050	494	11	≤	≤	NUM
ejpam-6050	494	12	m∑	m∑	VERB
ejpam-6050	494	13	i=1,si∈z	i=1,si∈z	X
ejpam-6050	494	14	|ℵea∪eb(si)|	|ℵea∪eb(si)|	X
ejpam-6050	494	15	.	.	PUNCT
ejpam-6050	495	1	theorem	theorem	NOUN
ejpam-6050	495	2	5	5	NUM
ejpam-6050	495	3	.	.	X
ejpam-6050	495	4	for	for	ADP
ejpam-6050	495	5	any	any	DET
ejpam-6050	495	6	efss	efss	NOUN
ejpam-6050	495	7	ea	ea	NOUN
ejpam-6050	495	8	,	,	PUNCT
ejpam-6050	495	9	eb	eb	PROPN
ejpam-6050	495	10	and	and	CCONJ
ejpam-6050	495	11	ec	ec	PROPN
ejpam-6050	495	12	,	,	PUNCT
ejpam-6050	495	13	the	the	DET
ejpam-6050	495	14	intersection	intersection	NOUN
ejpam-6050	495	15	union	union	NOUN
ejpam-6050	495	16	functions	function	NOUN
ejpam-6050	495	17	with	with	ADP
ejpam-6050	495	18	the	the	DET
ejpam-6050	495	19	same	same	ADJ
ejpam-6050	495	20	function	function	NOUN
ejpam-6050	495	21	for	for	ADP
ejpam-6050	495	22	determining	determine	VERB
ejpam-6050	495	23	the	the	DET
ejpam-6050	495	24	phase	phase	NOUN
ejpam-6050	495	25	term	term	NOUN
ejpam-6050	495	26	stratify	stratify	VERB
ejpam-6050	495	27	the	the	DET
ejpam-6050	495	28	distributive	distributive	ADJ
ejpam-6050	495	29	law	law	NOUN
ejpam-6050	495	30	.	.	PUNCT
ejpam-6050	496	1	proof	proof	NOUN
ejpam-6050	496	2	.	.	PUNCT
ejpam-6050	497	1	first	first	ADV
ejpam-6050	497	2	,	,	PUNCT
ejpam-6050	497	3	we	we	PRON
ejpam-6050	497	4	prove	prove	VERB
ejpam-6050	497	5	the	the	DET
ejpam-6050	497	6	distributive	distributive	ADJ
ejpam-6050	497	7	law	law	NOUN
ejpam-6050	497	8	for	for	ADP
ejpam-6050	497	9	any	any	DET
ejpam-6050	497	10	efss	efss	NOUN
ejpam-6050	497	11	ea	ea	NOUN
ejpam-6050	497	12	,	,	PUNCT
ejpam-6050	497	13	eb	eb	PROPN
ejpam-6050	497	14	and	and	CCONJ
ejpam-6050	497	15	ec	ec	PROPN
ejpam-6050	497	16	,	,	PUNCT
ejpam-6050	497	17	six	six	NUM
ejpam-6050	497	18	cases	case	NOUN
ejpam-6050	497	19	arise	arise	VERB
ejpam-6050	497	20	here	here	ADV
ejpam-6050	497	21	.	.	PUNCT
ejpam-6050	498	1	we	we	PRON
ejpam-6050	498	2	prove	prove	VERB
ejpam-6050	498	3	distributive	distributive	ADJ
ejpam-6050	498	4	law	law	NOUN
ejpam-6050	498	5	of	of	ADP
ejpam-6050	498	6	union	union	NOUN
ejpam-6050	498	7	over	over	ADP
ejpam-6050	498	8	intersection	intersection	NOUN
ejpam-6050	498	9	.	.	PUNCT
ejpam-6050	499	1	m.	m.	NOUN
ejpam-6050	499	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	499	3	,	,	PUNCT
ejpam-6050	499	4	m.	m.	NOUN
ejpam-6050	499	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	499	6	,	,	PUNCT
ejpam-6050	499	7	m.	m.	NOUN
ejpam-6050	499	8	alqahtani	alqahtani	PROPN
ejpam-6050	499	9	/	/	SYM
ejpam-6050	499	10	eur	eur	PROPN
ejpam-6050	499	11	.	.	PUNCT
ejpam-6050	500	1	j.	j.	PROPN
ejpam-6050	500	2	pure	pure	PROPN
ejpam-6050	500	3	appl	appl	PROPN
ejpam-6050	500	4	.	.	PROPN
ejpam-6050	500	5	math	math	PROPN
ejpam-6050	500	6	,	,	PUNCT
ejpam-6050	500	7	18	18	NUM
ejpam-6050	500	8	(	(	PUNCT
ejpam-6050	500	9	2	2	NUM
ejpam-6050	500	10	)	)	PUNCT
ejpam-6050	500	11	(	(	PUNCT
ejpam-6050	500	12	2025	2025	NUM
ejpam-6050	500	13	)	)	PUNCT
ejpam-6050	500	14	,	,	PUNCT
ejpam-6050	500	15	6050	6050	NUM
ejpam-6050	500	16	19	19	NUM
ejpam-6050	500	17	of	of	ADP
ejpam-6050	500	18	29	29	NUM
ejpam-6050	500	19	case	case	NOUN
ejpam-6050	500	20	1	1	NUM
ejpam-6050	500	21	ℵea(s	ℵea(s	PROPN
ejpam-6050	500	22	)	)	PUNCT
ejpam-6050	500	23	≤	≤	PUNCT
ejpam-6050	500	24	ℵeb(s	ℵeb(	VERB
ejpam-6050	500	25	)	)	PUNCT
ejpam-6050	500	26	≤	≤	NUM
ejpam-6050	500	27	ℵec(s	ℵec(s	NUM
ejpam-6050	500	28	)	)	PUNCT
ejpam-6050	500	29	ea	ea	NOUN
ejpam-6050	500	30	∪	∪	X
ejpam-6050	500	31	(	(	PUNCT
ejpam-6050	500	32	eb	eb	PROPN
ejpam-6050	500	33	∩	∩	PROPN
ejpam-6050	500	34	ec	ec	PROPN
ejpam-6050	500	35	)	)	PUNCT
ejpam-6050	501	1	=	=	PUNCT
ejpam-6050	501	2	[	[	PUNCT
ejpam-6050	501	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	501	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	501	5	)	)	PUNCT
ejpam-6050	501	6	⊕	⊕	PROPN
ejpam-6050	501	7	(	(	PUNCT
ejpam-6050	501	8	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	501	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	501	10	)	)	PUNCT
ejpam-6050	501	11	∗	∗	NOUN
ejpam-6050	501	12	ℵc(s)e	ℵc(s)e	X
ejpam-6050	501	13	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	501	14	)	)	PUNCT
ejpam-6050	501	15	)	)	PUNCT
ejpam-6050	501	16	]	]	PUNCT
ejpam-6050	502	1	=	=	PUNCT
ejpam-6050	502	2	[	[	PUNCT
ejpam-6050	502	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	502	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	502	5	)	)	PUNCT
ejpam-6050	502	6	⊕	⊕	PROPN
ejpam-6050	502	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	502	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	502	9	)	)	PUNCT
ejpam-6050	502	10	]	]	PUNCT
ejpam-6050	502	11	ea	ea	X
ejpam-6050	502	12	∪	∪	X
ejpam-6050	502	13	(	(	PUNCT
ejpam-6050	502	14	eb	eb	PROPN
ejpam-6050	502	15	∩	∩	PROPN
ejpam-6050	502	16	ec	ec	PROPN
ejpam-6050	502	17	)	)	PUNCT
ejpam-6050	502	18	=	=	SYM
ejpam-6050	502	19	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	502	20	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	502	21	)	)	PUNCT
ejpam-6050	502	22	.	.	PUNCT
ejpam-6050	503	1	(	(	PUNCT
ejpam-6050	503	2	4.33	4.33	NUM
ejpam-6050	503	3	)	)	PUNCT
ejpam-6050	503	4	(	(	PUNCT
ejpam-6050	503	5	ea	ea	PROPN
ejpam-6050	503	6	∪	∪	PROPN
ejpam-6050	503	7	eb	eb	PROPN
ejpam-6050	503	8	)	)	PUNCT
ejpam-6050	503	9	∩	∩	NOUN
ejpam-6050	503	10	(	(	PUNCT
ejpam-6050	503	11	ea	ea	X
ejpam-6050	503	12	∪	∪	X
ejpam-6050	503	13	ec	ec	PROPN
ejpam-6050	503	14	)	)	PUNCT
ejpam-6050	503	15	=	=	PUNCT
ejpam-6050	503	16	[	[	PUNCT
ejpam-6050	503	17	ℵa(s)e	ℵa(s)e	X
ejpam-6050	503	18	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	503	19	)	)	PUNCT
ejpam-6050	503	20	⊕	⊕	PROPN
ejpam-6050	503	21	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	503	22	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	503	23	)	)	PUNCT
ejpam-6050	503	24	]	]	PUNCT
ejpam-6050	503	25	∗	∗	NOUN
ejpam-6050	503	26	[	[	PUNCT
ejpam-6050	503	27	ℵa(s)e	ℵa(s)e	X
ejpam-6050	503	28	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	503	29	)	)	PUNCT
ejpam-6050	503	30	⊕	⊕	PROPN
ejpam-6050	503	31	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	503	32	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	503	33	)	)	PUNCT
ejpam-6050	503	34	]	]	PUNCT
ejpam-6050	504	1	=	=	PUNCT
ejpam-6050	504	2	[	[	PUNCT
ejpam-6050	504	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	504	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	504	5	)	)	PUNCT
ejpam-6050	504	6	∗	∗	NOUN
ejpam-6050	504	7	ℵc(s)e	ℵc(s)e	X
ejpam-6050	504	8	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	504	9	)	)	PUNCT
ejpam-6050	504	10	]	]	PUNCT
ejpam-6050	504	11	(	(	PUNCT
ejpam-6050	504	12	ea	ea	PROPN
ejpam-6050	504	13	∪	∪	ADP
ejpam-6050	504	14	eb	eb	PROPN
ejpam-6050	504	15	)	)	PUNCT
ejpam-6050	504	16	∩	∩	NOUN
ejpam-6050	504	17	(	(	PUNCT
ejpam-6050	504	18	ea	ea	X
ejpam-6050	504	19	∪	∪	X
ejpam-6050	504	20	ec	ec	PROPN
ejpam-6050	504	21	)	)	PUNCT
ejpam-6050	504	22	=	=	SYM
ejpam-6050	505	1	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	505	2	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	505	3	)	)	PUNCT
ejpam-6050	505	4	(	(	PUNCT
ejpam-6050	505	5	4.34	4.34	NUM
ejpam-6050	505	6	)	)	PUNCT
ejpam-6050	505	7	from	from	ADP
ejpam-6050	505	8	equation	equation	NOUN
ejpam-6050	505	9	(	(	PUNCT
ejpam-6050	505	10	4.33	4.33	NUM
ejpam-6050	505	11	)	)	PUNCT
ejpam-6050	505	12	and	and	CCONJ
ejpam-6050	505	13	(	(	PUNCT
ejpam-6050	505	14	4.34	4.34	NUM
ejpam-6050	505	15	)	)	PUNCT
ejpam-6050	505	16	,	,	PUNCT
ejpam-6050	505	17	we	we	PRON
ejpam-6050	505	18	have	have	VERB
ejpam-6050	505	19	ea	ea	NOUN
ejpam-6050	505	20	∪	∪	X
ejpam-6050	505	21	(	(	PUNCT
ejpam-6050	505	22	eb	eb	PROPN
ejpam-6050	505	23	∩	∩	PROPN
ejpam-6050	505	24	ec	ec	PROPN
ejpam-6050	505	25	)	)	PUNCT
ejpam-6050	505	26	=	=	PRON
ejpam-6050	505	27	(	(	PUNCT
ejpam-6050	505	28	ea	ea	PROPN
ejpam-6050	505	29	∪	∪	PROPN
ejpam-6050	505	30	eb	eb	PROPN
ejpam-6050	505	31	)	)	PUNCT
ejpam-6050	505	32	∩	∩	NOUN
ejpam-6050	505	33	(	(	PUNCT
ejpam-6050	505	34	ea	ea	X
ejpam-6050	505	35	∪	∪	ADP
ejpam-6050	505	36	ec	ec	PROPN
ejpam-6050	505	37	)	)	PUNCT
ejpam-6050	505	38	case	case	NOUN
ejpam-6050	505	39	2	2	NUM
ejpam-6050	505	40	ℵeb(s	ℵeb(	NOUN
ejpam-6050	505	41	)	)	PUNCT
ejpam-6050	505	42	≤	≤	NUM
ejpam-6050	505	43	ℵec(s	ℵec(s	NUM
ejpam-6050	505	44	)	)	PUNCT
ejpam-6050	505	45	≤	≤	NUM
ejpam-6050	505	46	ℵea(s	ℵea(s	PROPN
ejpam-6050	505	47	)	)	PUNCT
ejpam-6050	505	48	ea	ea	NOUN
ejpam-6050	505	49	∪	∪	X
ejpam-6050	505	50	(	(	PUNCT
ejpam-6050	505	51	eb	eb	PROPN
ejpam-6050	505	52	∩	∩	PROPN
ejpam-6050	505	53	ec	ec	PROPN
ejpam-6050	505	54	)	)	PUNCT
ejpam-6050	505	55	=	=	PUNCT
ejpam-6050	505	56	[	[	PUNCT
ejpam-6050	505	57	ℵa(s)e	ℵa(s)e	X
ejpam-6050	505	58	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	505	59	)	)	PUNCT
ejpam-6050	505	60	⊕	⊕	PROPN
ejpam-6050	505	61	(	(	PUNCT
ejpam-6050	505	62	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	505	63	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	505	64	)	)	PUNCT
ejpam-6050	505	65	∗	∗	NOUN
ejpam-6050	505	66	ℵc(s)e	ℵc(s)e	X
ejpam-6050	505	67	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	505	68	)	)	PUNCT
ejpam-6050	505	69	)	)	PUNCT
ejpam-6050	505	70	]	]	PUNCT
ejpam-6050	506	1	=	=	PUNCT
ejpam-6050	506	2	[	[	PUNCT
ejpam-6050	506	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	506	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	506	5	)	)	PUNCT
ejpam-6050	506	6	⊕	⊕	PROPN
ejpam-6050	506	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	506	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	506	9	)	)	PUNCT
ejpam-6050	506	10	]	]	PUNCT
ejpam-6050	506	11	ea	ea	X
ejpam-6050	506	12	∪	∪	X
ejpam-6050	506	13	(	(	PUNCT
ejpam-6050	506	14	eb	eb	PROPN
ejpam-6050	506	15	∩	∩	PROPN
ejpam-6050	506	16	ec	ec	PROPN
ejpam-6050	506	17	)	)	PUNCT
ejpam-6050	506	18	=	=	PUNCT
ejpam-6050	506	19	ℵa(s)e	ℵa(s)e	X
ejpam-6050	506	20	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	506	21	)	)	PUNCT
ejpam-6050	506	22	.	.	PUNCT
ejpam-6050	507	1	(	(	PUNCT
ejpam-6050	507	2	4.35	4.35	NUM
ejpam-6050	507	3	)	)	PUNCT
ejpam-6050	507	4	(	(	PUNCT
ejpam-6050	507	5	ea	ea	PROPN
ejpam-6050	507	6	∪	∪	PROPN
ejpam-6050	507	7	eb	eb	PROPN
ejpam-6050	507	8	)	)	PUNCT
ejpam-6050	507	9	∩	∩	NOUN
ejpam-6050	507	10	(	(	PUNCT
ejpam-6050	507	11	ea	ea	X
ejpam-6050	507	12	∪	∪	X
ejpam-6050	507	13	ec	ec	PROPN
ejpam-6050	507	14	)	)	PUNCT
ejpam-6050	507	15	=	=	PUNCT
ejpam-6050	507	16	[	[	PUNCT
ejpam-6050	507	17	ℵa(s)e	ℵa(s)e	X
ejpam-6050	507	18	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	507	19	)	)	PUNCT
ejpam-6050	507	20	⊕	⊕	PROPN
ejpam-6050	507	21	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	508	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	508	2	)	)	PUNCT
ejpam-6050	508	3	]	]	PUNCT
ejpam-6050	509	1	∗	∗	NOUN
ejpam-6050	509	2	[	[	PUNCT
ejpam-6050	509	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	509	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	509	5	)	)	PUNCT
ejpam-6050	509	6	⊕	⊕	PROPN
ejpam-6050	509	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	509	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	509	9	)	)	PUNCT
ejpam-6050	509	10	]	]	PUNCT
ejpam-6050	510	1	=	=	PUNCT
ejpam-6050	510	2	[	[	PUNCT
ejpam-6050	510	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	510	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	510	5	)	)	PUNCT
ejpam-6050	510	6	∗	∗	NOUN
ejpam-6050	510	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	510	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	510	9	)	)	PUNCT
ejpam-6050	510	10	]	]	PUNCT
ejpam-6050	510	11	(	(	PUNCT
ejpam-6050	510	12	ea	ea	PROPN
ejpam-6050	510	13	∪	∪	ADP
ejpam-6050	510	14	eb	eb	PROPN
ejpam-6050	510	15	)	)	PUNCT
ejpam-6050	510	16	∩	∩	NOUN
ejpam-6050	510	17	(	(	PUNCT
ejpam-6050	510	18	ea	ea	X
ejpam-6050	510	19	∪	∪	X
ejpam-6050	510	20	ec	ec	PROPN
ejpam-6050	510	21	)	)	PUNCT
ejpam-6050	510	22	=	=	PUNCT
ejpam-6050	510	23	ℵa(s)e	ℵa(s)e	X
ejpam-6050	510	24	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	510	25	)	)	PUNCT
ejpam-6050	510	26	(	(	PUNCT
ejpam-6050	510	27	4.36	4.36	NUM
ejpam-6050	510	28	)	)	PUNCT
ejpam-6050	510	29	from	from	ADP
ejpam-6050	510	30	equation	equation	NOUN
ejpam-6050	510	31	(	(	PUNCT
ejpam-6050	510	32	4.35	4.35	NUM
ejpam-6050	510	33	)	)	PUNCT
ejpam-6050	510	34	and	and	CCONJ
ejpam-6050	510	35	(	(	PUNCT
ejpam-6050	510	36	4.36	4.36	NUM
ejpam-6050	510	37	)	)	PUNCT
ejpam-6050	510	38	ea	ea	X
ejpam-6050	510	39	∪	∪	X
ejpam-6050	510	40	(	(	PUNCT
ejpam-6050	510	41	eb	eb	PROPN
ejpam-6050	510	42	∩	∩	PROPN
ejpam-6050	510	43	ec	ec	PROPN
ejpam-6050	510	44	)	)	PUNCT
ejpam-6050	510	45	=	=	PRON
ejpam-6050	510	46	(	(	PUNCT
ejpam-6050	510	47	ea	ea	PROPN
ejpam-6050	510	48	∪	∪	PROPN
ejpam-6050	510	49	eb	eb	PROPN
ejpam-6050	510	50	)	)	PUNCT
ejpam-6050	510	51	∩	∩	NOUN
ejpam-6050	510	52	(	(	PUNCT
ejpam-6050	510	53	ea	ea	X
ejpam-6050	510	54	∪	∪	ADP
ejpam-6050	510	55	ec	ec	PROPN
ejpam-6050	510	56	)	)	PUNCT
ejpam-6050	510	57	case	case	NOUN
ejpam-6050	510	58	3	3	NUM
ejpam-6050	510	59	ℵea(s	ℵea(s	PROPN
ejpam-6050	510	60	)	)	PUNCT
ejpam-6050	510	61	≤	≤	NOUN
ejpam-6050	510	62	ℵec(s	ℵec(s	NUM
ejpam-6050	510	63	)	)	PUNCT
ejpam-6050	510	64	≤	≤	NUM
ejpam-6050	510	65	ℵeb(s	ℵeb(s	PUNCT
ejpam-6050	510	66	)	)	PUNCT
ejpam-6050	510	67	ea	ea	NOUN
ejpam-6050	510	68	∪	∪	X
ejpam-6050	510	69	(	(	PUNCT
ejpam-6050	510	70	eb	eb	PROPN
ejpam-6050	510	71	∩	∩	PROPN
ejpam-6050	510	72	ec	ec	PROPN
ejpam-6050	510	73	)	)	PUNCT
ejpam-6050	511	1	=	=	PUNCT
ejpam-6050	511	2	[	[	PUNCT
ejpam-6050	511	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	511	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	511	5	)	)	PUNCT
ejpam-6050	511	6	⊕	⊕	PROPN
ejpam-6050	511	7	(	(	PUNCT
ejpam-6050	511	8	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	511	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	511	10	)	)	PUNCT
ejpam-6050	511	11	∗	∗	NOUN
ejpam-6050	511	12	ℵc(s)e	ℵc(s)e	X
ejpam-6050	511	13	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	511	14	)	)	PUNCT
ejpam-6050	511	15	)	)	PUNCT
ejpam-6050	511	16	]	]	PUNCT
ejpam-6050	512	1	=	=	PUNCT
ejpam-6050	512	2	[	[	PUNCT
ejpam-6050	512	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	512	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	512	5	)	)	PUNCT
ejpam-6050	512	6	⊕	⊕	PROPN
ejpam-6050	512	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	512	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	512	9	)	)	PUNCT
ejpam-6050	512	10	]	]	PUNCT
ejpam-6050	512	11	ea	ea	ADP
ejpam-6050	512	12	∪	∪	X
ejpam-6050	512	13	(	(	PUNCT
ejpam-6050	512	14	eb	eb	PROPN
ejpam-6050	512	15	∩	∩	PROPN
ejpam-6050	512	16	ec	ec	PROPN
ejpam-6050	512	17	)	)	PUNCT
ejpam-6050	512	18	=	=	PUNCT
ejpam-6050	513	1	ℵc(s)e	ℵc(s)e	SYM
ejpam-6050	513	2	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	513	3	)	)	PUNCT
ejpam-6050	513	4	.	.	PUNCT
ejpam-6050	514	1	(	(	PUNCT
ejpam-6050	514	2	4.37	4.37	NUM
ejpam-6050	514	3	)	)	PUNCT
ejpam-6050	514	4	(	(	PUNCT
ejpam-6050	514	5	ea	ea	PROPN
ejpam-6050	514	6	∪	∪	PROPN
ejpam-6050	514	7	eb	eb	PROPN
ejpam-6050	514	8	)	)	PUNCT
ejpam-6050	514	9	∩	∩	NOUN
ejpam-6050	514	10	(	(	PUNCT
ejpam-6050	514	11	ea	ea	X
ejpam-6050	514	12	∪	∪	X
ejpam-6050	514	13	ec	ec	PROPN
ejpam-6050	514	14	)	)	PUNCT
ejpam-6050	514	15	=	=	PUNCT
ejpam-6050	514	16	[	[	PUNCT
ejpam-6050	514	17	ℵa(s)e	ℵa(s)e	X
ejpam-6050	514	18	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	514	19	)	)	PUNCT
ejpam-6050	514	20	⊕	⊕	PROPN
ejpam-6050	514	21	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	514	22	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	514	23	)	)	PUNCT
ejpam-6050	514	24	]	]	PUNCT
ejpam-6050	514	25	∗	∗	NOUN
ejpam-6050	514	26	[	[	PUNCT
ejpam-6050	514	27	ℵa(s)e	ℵa(s)e	X
ejpam-6050	514	28	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	514	29	)	)	PUNCT
ejpam-6050	514	30	⊕	⊕	PROPN
ejpam-6050	514	31	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	514	32	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	514	33	)	)	PUNCT
ejpam-6050	514	34	]	]	PUNCT
ejpam-6050	515	1	=	=	PUNCT
ejpam-6050	515	2	[	[	PUNCT
ejpam-6050	515	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	515	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	515	5	)	)	PUNCT
ejpam-6050	515	6	∗	∗	NOUN
ejpam-6050	515	7	ℵc(s)e	ℵc(s)e	X
ejpam-6050	515	8	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	515	9	)	)	PUNCT
ejpam-6050	515	10	]	]	PUNCT
ejpam-6050	515	11	(	(	PUNCT
ejpam-6050	515	12	ea	ea	PROPN
ejpam-6050	515	13	∪	∪	ADP
ejpam-6050	515	14	eb	eb	PROPN
ejpam-6050	515	15	)	)	PUNCT
ejpam-6050	515	16	∩	∩	NOUN
ejpam-6050	515	17	(	(	PUNCT
ejpam-6050	515	18	ea	ea	X
ejpam-6050	515	19	∪	∪	X
ejpam-6050	515	20	ec	ec	PROPN
ejpam-6050	515	21	)	)	PUNCT
ejpam-6050	515	22	=	=	PUNCT
ejpam-6050	516	1	ℵc(s)e	ℵc(s)e	SYM
ejpam-6050	516	2	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	516	3	)	)	PUNCT
ejpam-6050	516	4	(	(	PUNCT
ejpam-6050	516	5	4.38	4.38	NUM
ejpam-6050	516	6	)	)	PUNCT
ejpam-6050	516	7	from	from	ADP
ejpam-6050	516	8	equation	equation	NOUN
ejpam-6050	516	9	(	(	PUNCT
ejpam-6050	516	10	4.37	4.37	NUM
ejpam-6050	516	11	)	)	PUNCT
ejpam-6050	516	12	and	and	CCONJ
ejpam-6050	516	13	(	(	PUNCT
ejpam-6050	516	14	4.38	4.38	NUM
ejpam-6050	516	15	)	)	PUNCT
ejpam-6050	516	16	ea	ea	NOUN
ejpam-6050	516	17	∪	∪	X
ejpam-6050	516	18	(	(	PUNCT
ejpam-6050	516	19	eb	eb	PROPN
ejpam-6050	516	20	∩	∩	PROPN
ejpam-6050	516	21	ec	ec	PROPN
ejpam-6050	516	22	)	)	PUNCT
ejpam-6050	516	23	=	=	PRON
ejpam-6050	517	1	(	(	PUNCT
ejpam-6050	517	2	ea	ea	PROPN
ejpam-6050	517	3	∪	∪	PROPN
ejpam-6050	517	4	eb	eb	PROPN
ejpam-6050	517	5	)	)	PUNCT
ejpam-6050	517	6	∩	∩	NOUN
ejpam-6050	517	7	(	(	PUNCT
ejpam-6050	517	8	ea	ea	X
ejpam-6050	517	9	∪	∪	PROPN
ejpam-6050	517	10	ec	ec	PROPN
ejpam-6050	517	11	)	)	PUNCT
ejpam-6050	517	12	.	.	PUNCT
ejpam-6050	518	1	m.	m.	PROPN
ejpam-6050	518	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	518	3	,	,	PUNCT
ejpam-6050	518	4	m.	m.	NOUN
ejpam-6050	518	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	518	6	,	,	PUNCT
ejpam-6050	518	7	m.	m.	NOUN
ejpam-6050	518	8	alqahtani	alqahtani	PROPN
ejpam-6050	518	9	/	/	SYM
ejpam-6050	518	10	eur	eur	PROPN
ejpam-6050	518	11	.	.	PUNCT
ejpam-6050	519	1	j.	j.	PROPN
ejpam-6050	519	2	pure	pure	PROPN
ejpam-6050	519	3	appl	appl	PROPN
ejpam-6050	519	4	.	.	PROPN
ejpam-6050	519	5	math	math	PROPN
ejpam-6050	519	6	,	,	PUNCT
ejpam-6050	519	7	18	18	NUM
ejpam-6050	519	8	(	(	PUNCT
ejpam-6050	519	9	2	2	NUM
ejpam-6050	519	10	)	)	PUNCT
ejpam-6050	519	11	(	(	PUNCT
ejpam-6050	519	12	2025	2025	NUM
ejpam-6050	519	13	)	)	PUNCT
ejpam-6050	519	14	,	,	PUNCT
ejpam-6050	519	15	6050	6050	NUM
ejpam-6050	519	16	20	20	NUM
ejpam-6050	519	17	of	of	ADP
ejpam-6050	519	18	29	29	NUM
ejpam-6050	519	19	case	case	NOUN
ejpam-6050	519	20	4	4	NUM
ejpam-6050	519	21	ℵec(s	ℵec(s	NUM
ejpam-6050	519	22	)	)	PUNCT
ejpam-6050	519	23	≤	≤	NUM
ejpam-6050	519	24	ℵeb(s	ℵeb(	VERB
ejpam-6050	519	25	)	)	PUNCT
ejpam-6050	519	26	≤	≤	NUM
ejpam-6050	519	27	ℵea(s	ℵea(s	PROPN
ejpam-6050	519	28	)	)	PUNCT
ejpam-6050	519	29	ea	ea	NOUN
ejpam-6050	519	30	∪	∪	X
ejpam-6050	519	31	(	(	PUNCT
ejpam-6050	519	32	eb	eb	PROPN
ejpam-6050	519	33	∩	∩	PROPN
ejpam-6050	519	34	ec	ec	PROPN
ejpam-6050	519	35	)	)	PUNCT
ejpam-6050	520	1	=	=	PUNCT
ejpam-6050	520	2	[	[	PUNCT
ejpam-6050	520	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	520	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	520	5	)	)	PUNCT
ejpam-6050	520	6	⊕	⊕	PROPN
ejpam-6050	520	7	(	(	PUNCT
ejpam-6050	520	8	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	520	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	520	10	)	)	PUNCT
ejpam-6050	520	11	∗	∗	NOUN
ejpam-6050	520	12	ℵc(s)e	ℵc(s)e	X
ejpam-6050	520	13	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	520	14	)	)	PUNCT
ejpam-6050	520	15	)	)	PUNCT
ejpam-6050	520	16	]	]	PUNCT
ejpam-6050	521	1	=	=	PUNCT
ejpam-6050	521	2	[	[	PUNCT
ejpam-6050	521	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	521	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	521	5	)	)	PUNCT
ejpam-6050	521	6	⊕	⊕	PROPN
ejpam-6050	521	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	521	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	521	9	)	)	PUNCT
ejpam-6050	521	10	]	]	PUNCT
ejpam-6050	521	11	ea	ea	ADP
ejpam-6050	521	12	∪	∪	X
ejpam-6050	521	13	(	(	PUNCT
ejpam-6050	521	14	eb	eb	PROPN
ejpam-6050	521	15	∩	∩	PROPN
ejpam-6050	521	16	ec	ec	PROPN
ejpam-6050	521	17	)	)	PUNCT
ejpam-6050	521	18	=	=	PUNCT
ejpam-6050	521	19	ℵa(s)e	ℵa(s)e	X
ejpam-6050	521	20	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	521	21	)	)	PUNCT
ejpam-6050	521	22	.	.	PUNCT
ejpam-6050	522	1	(	(	PUNCT
ejpam-6050	522	2	4.39	4.39	NUM
ejpam-6050	522	3	)	)	PUNCT
ejpam-6050	522	4	(	(	PUNCT
ejpam-6050	522	5	ea	ea	PROPN
ejpam-6050	522	6	∪	∪	PROPN
ejpam-6050	522	7	eb	eb	PROPN
ejpam-6050	522	8	)	)	PUNCT
ejpam-6050	522	9	∩	∩	NOUN
ejpam-6050	522	10	(	(	PUNCT
ejpam-6050	522	11	ea	ea	X
ejpam-6050	522	12	∪	∪	X
ejpam-6050	522	13	ec	ec	PROPN
ejpam-6050	522	14	)	)	PUNCT
ejpam-6050	522	15	=	=	PUNCT
ejpam-6050	522	16	[	[	PUNCT
ejpam-6050	522	17	ℵa(s)e	ℵa(s)e	X
ejpam-6050	522	18	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	522	19	)	)	PUNCT
ejpam-6050	522	20	⊕	⊕	PROPN
ejpam-6050	522	21	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	522	22	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	522	23	)	)	PUNCT
ejpam-6050	522	24	]	]	PUNCT
ejpam-6050	522	25	∗	∗	NOUN
ejpam-6050	522	26	[	[	PUNCT
ejpam-6050	522	27	ℵa(s)e	ℵa(s)e	X
ejpam-6050	522	28	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	522	29	)	)	PUNCT
ejpam-6050	522	30	⊕	⊕	PROPN
ejpam-6050	522	31	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	522	32	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	522	33	)	)	PUNCT
ejpam-6050	522	34	]	]	PUNCT
ejpam-6050	523	1	=	=	PUNCT
ejpam-6050	523	2	[	[	PUNCT
ejpam-6050	523	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	523	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	523	5	)	)	PUNCT
ejpam-6050	523	6	∗	∗	NOUN
ejpam-6050	523	7	ℵa(s)e	ℵa(s)e	X
ejpam-6050	523	8	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	523	9	)	)	PUNCT
ejpam-6050	523	10	]	]	PUNCT
ejpam-6050	523	11	(	(	PUNCT
ejpam-6050	523	12	ea	ea	PROPN
ejpam-6050	523	13	∪	∪	ADP
ejpam-6050	523	14	eb	eb	PROPN
ejpam-6050	523	15	)	)	PUNCT
ejpam-6050	523	16	∩	∩	NOUN
ejpam-6050	523	17	(	(	PUNCT
ejpam-6050	523	18	ea	ea	X
ejpam-6050	523	19	∪	∪	X
ejpam-6050	523	20	ec	ec	PROPN
ejpam-6050	523	21	)	)	PUNCT
ejpam-6050	523	22	=	=	PUNCT
ejpam-6050	523	23	ℵa(s)e	ℵa(s)e	X
ejpam-6050	523	24	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	523	25	)	)	PUNCT
ejpam-6050	523	26	(	(	PUNCT
ejpam-6050	523	27	4.40	4.40	NUM
ejpam-6050	523	28	)	)	PUNCT
ejpam-6050	523	29	from	from	ADP
ejpam-6050	523	30	equation	equation	NOUN
ejpam-6050	523	31	(	(	PUNCT
ejpam-6050	523	32	4.39	4.39	NUM
ejpam-6050	523	33	)	)	PUNCT
ejpam-6050	523	34	and	and	CCONJ
ejpam-6050	523	35	(	(	PUNCT
ejpam-6050	523	36	4.40	4.40	NUM
ejpam-6050	523	37	)	)	PUNCT
ejpam-6050	523	38	,	,	PUNCT
ejpam-6050	523	39	ea	ea	X
ejpam-6050	523	40	∪	∪	X
ejpam-6050	523	41	(	(	PUNCT
ejpam-6050	523	42	eb	eb	PROPN
ejpam-6050	523	43	∩	∩	PROPN
ejpam-6050	523	44	ec	ec	PROPN
ejpam-6050	523	45	)	)	PUNCT
ejpam-6050	523	46	=	=	PRON
ejpam-6050	524	1	(	(	PUNCT
ejpam-6050	524	2	ea	ea	PROPN
ejpam-6050	524	3	∪	∪	PROPN
ejpam-6050	524	4	eb	eb	PROPN
ejpam-6050	524	5	)	)	PUNCT
ejpam-6050	524	6	∩	∩	NOUN
ejpam-6050	524	7	(	(	PUNCT
ejpam-6050	524	8	ea	ea	X
ejpam-6050	524	9	∪	∪	ADP
ejpam-6050	524	10	ec	ec	PROPN
ejpam-6050	524	11	)	)	PUNCT
ejpam-6050	524	12	case	case	NOUN
ejpam-6050	524	13	5	5	NUM
ejpam-6050	524	14	ℵeb(s	ℵeb(	NOUN
ejpam-6050	524	15	)	)	PUNCT
ejpam-6050	524	16	≤	≤	NUM
ejpam-6050	524	17	ℵea(s	ℵea(s	PROPN
ejpam-6050	524	18	)	)	PUNCT
ejpam-6050	524	19	≤	≤	NOUN
ejpam-6050	524	20	ℵec(s	ℵec(s	NUM
ejpam-6050	524	21	)	)	PUNCT
ejpam-6050	524	22	ea	ea	NOUN
ejpam-6050	524	23	∪	∪	X
ejpam-6050	524	24	(	(	PUNCT
ejpam-6050	524	25	eb	eb	PROPN
ejpam-6050	524	26	∩	∩	PROPN
ejpam-6050	524	27	ec	ec	PROPN
ejpam-6050	524	28	)	)	PUNCT
ejpam-6050	524	29	=	=	PUNCT
ejpam-6050	524	30	[	[	PUNCT
ejpam-6050	524	31	ℵa(s)e	ℵa(s)e	X
ejpam-6050	524	32	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	524	33	)	)	PUNCT
ejpam-6050	524	34	⊕	⊕	PROPN
ejpam-6050	524	35	(	(	PUNCT
ejpam-6050	524	36	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	524	37	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	524	38	)	)	PUNCT
ejpam-6050	524	39	∗	∗	NOUN
ejpam-6050	524	40	ℵc(s)e	ℵc(s)e	X
ejpam-6050	524	41	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	524	42	)	)	PUNCT
ejpam-6050	524	43	)	)	PUNCT
ejpam-6050	524	44	]	]	PUNCT
ejpam-6050	525	1	=	=	PUNCT
ejpam-6050	525	2	[	[	PUNCT
ejpam-6050	525	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	525	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	525	5	)	)	PUNCT
ejpam-6050	525	6	⊕	⊕	PROPN
ejpam-6050	525	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	525	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	525	9	)	)	PUNCT
ejpam-6050	525	10	]	]	PUNCT
ejpam-6050	525	11	ea	ea	X
ejpam-6050	525	12	∪	∪	X
ejpam-6050	525	13	(	(	PUNCT
ejpam-6050	525	14	eb	eb	PROPN
ejpam-6050	525	15	∩	∩	PROPN
ejpam-6050	525	16	ec	ec	PROPN
ejpam-6050	525	17	)	)	PUNCT
ejpam-6050	525	18	=	=	PUNCT
ejpam-6050	525	19	ℵa(s)e	ℵa(s)e	X
ejpam-6050	525	20	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	525	21	)	)	PUNCT
ejpam-6050	525	22	.	.	PUNCT
ejpam-6050	526	1	(	(	PUNCT
ejpam-6050	526	2	4.41	4.41	NUM
ejpam-6050	526	3	)	)	PUNCT
ejpam-6050	526	4	(	(	PUNCT
ejpam-6050	526	5	ea	ea	PROPN
ejpam-6050	526	6	∪	∪	PROPN
ejpam-6050	526	7	eb	eb	PROPN
ejpam-6050	526	8	)	)	PUNCT
ejpam-6050	526	9	∩	∩	NOUN
ejpam-6050	526	10	(	(	PUNCT
ejpam-6050	526	11	ea	ea	X
ejpam-6050	526	12	∪	∪	X
ejpam-6050	526	13	ec	ec	PROPN
ejpam-6050	526	14	)	)	PUNCT
ejpam-6050	526	15	=	=	PUNCT
ejpam-6050	526	16	[	[	PUNCT
ejpam-6050	526	17	ℵa(s)e	ℵa(s)e	X
ejpam-6050	526	18	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	526	19	)	)	PUNCT
ejpam-6050	526	20	⊕	⊕	PROPN
ejpam-6050	526	21	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	527	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	527	2	)	)	PUNCT
ejpam-6050	527	3	]	]	PUNCT
ejpam-6050	528	1	∗	∗	NOUN
ejpam-6050	528	2	[	[	PUNCT
ejpam-6050	528	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	528	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	528	5	)	)	PUNCT
ejpam-6050	528	6	⊕	⊕	PROPN
ejpam-6050	528	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	528	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	528	9	)	)	PUNCT
ejpam-6050	528	10	]	]	PUNCT
ejpam-6050	529	1	=	=	PUNCT
ejpam-6050	529	2	[	[	PUNCT
ejpam-6050	529	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	529	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	529	5	)	)	PUNCT
ejpam-6050	529	6	∗	∗	NOUN
ejpam-6050	529	7	ℵc(s)e	ℵc(s)e	NOUN
ejpam-6050	529	8	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	529	9	)	)	PUNCT
ejpam-6050	529	10	]	]	PUNCT
ejpam-6050	529	11	(	(	PUNCT
ejpam-6050	529	12	ea	ea	PROPN
ejpam-6050	529	13	∪	∪	ADP
ejpam-6050	529	14	eb	eb	PROPN
ejpam-6050	529	15	)	)	PUNCT
ejpam-6050	529	16	∩	∩	NOUN
ejpam-6050	529	17	(	(	PUNCT
ejpam-6050	529	18	ea	ea	X
ejpam-6050	529	19	∪	∪	X
ejpam-6050	529	20	ec	ec	PROPN
ejpam-6050	529	21	)	)	PUNCT
ejpam-6050	529	22	=	=	PUNCT
ejpam-6050	529	23	ℵa(s)e	ℵa(s)e	X
ejpam-6050	529	24	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	529	25	)	)	PUNCT
ejpam-6050	529	26	(	(	PUNCT
ejpam-6050	529	27	4.42	4.42	NUM
ejpam-6050	529	28	)	)	PUNCT
ejpam-6050	529	29	from	from	ADP
ejpam-6050	529	30	equation	equation	NOUN
ejpam-6050	529	31	(	(	PUNCT
ejpam-6050	529	32	4.41	4.41	NUM
ejpam-6050	529	33	)	)	PUNCT
ejpam-6050	529	34	and	and	CCONJ
ejpam-6050	529	35	(	(	PUNCT
ejpam-6050	529	36	4.42	4.42	NUM
ejpam-6050	529	37	)	)	PUNCT
ejpam-6050	529	38	ea	ea	NOUN
ejpam-6050	529	39	∪	∪	X
ejpam-6050	529	40	(	(	PUNCT
ejpam-6050	529	41	eb	eb	PROPN
ejpam-6050	529	42	∩	∩	PROPN
ejpam-6050	529	43	ec	ec	PROPN
ejpam-6050	529	44	)	)	PUNCT
ejpam-6050	529	45	=	=	PRON
ejpam-6050	530	1	(	(	PUNCT
ejpam-6050	530	2	ea	ea	PROPN
ejpam-6050	530	3	∪	∪	PROPN
ejpam-6050	530	4	eb	eb	PROPN
ejpam-6050	530	5	)	)	PUNCT
ejpam-6050	530	6	∩	∩	NOUN
ejpam-6050	530	7	(	(	PUNCT
ejpam-6050	530	8	ea	ea	X
ejpam-6050	530	9	∪	∪	ADP
ejpam-6050	530	10	ec	ec	PROPN
ejpam-6050	530	11	)	)	PUNCT
ejpam-6050	530	12	case	case	NOUN
ejpam-6050	530	13	6	6	NUM
ejpam-6050	530	14	ℵec(s	ℵec(s	NUM
ejpam-6050	530	15	)	)	PUNCT
ejpam-6050	530	16	≤	≤	NUM
ejpam-6050	530	17	ℵea(s	ℵea(s	PROPN
ejpam-6050	530	18	)	)	PUNCT
ejpam-6050	530	19	≤	≤	NOUN
ejpam-6050	530	20	ℵeb(s	ℵeb(s	PUNCT
ejpam-6050	530	21	)	)	PUNCT
ejpam-6050	530	22	ea	ea	NOUN
ejpam-6050	530	23	∪	∪	X
ejpam-6050	530	24	(	(	PUNCT
ejpam-6050	530	25	eb	eb	PROPN
ejpam-6050	530	26	∩	∩	PROPN
ejpam-6050	530	27	ec	ec	PROPN
ejpam-6050	530	28	)	)	PUNCT
ejpam-6050	530	29	=	=	PUNCT
ejpam-6050	530	30	[	[	PUNCT
ejpam-6050	530	31	ℵa(s)e	ℵa(s)e	X
ejpam-6050	530	32	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	530	33	)	)	PUNCT
ejpam-6050	530	34	⊕	⊕	PROPN
ejpam-6050	530	35	(	(	PUNCT
ejpam-6050	530	36	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	530	37	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	530	38	)	)	PUNCT
ejpam-6050	530	39	∗	∗	NOUN
ejpam-6050	530	40	ℵc(s)e	ℵc(s)e	X
ejpam-6050	530	41	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	530	42	)	)	PUNCT
ejpam-6050	530	43	)	)	PUNCT
ejpam-6050	530	44	]	]	PUNCT
ejpam-6050	531	1	=	=	PUNCT
ejpam-6050	531	2	[	[	PUNCT
ejpam-6050	531	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	531	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	531	5	)	)	PUNCT
ejpam-6050	531	6	⊕	⊕	PROPN
ejpam-6050	531	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	531	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	531	9	)	)	PUNCT
ejpam-6050	531	10	]	]	PUNCT
ejpam-6050	531	11	ea	ea	ADP
ejpam-6050	531	12	∪	∪	X
ejpam-6050	531	13	(	(	PUNCT
ejpam-6050	531	14	eb	eb	PROPN
ejpam-6050	531	15	∩	∩	PROPN
ejpam-6050	531	16	ec	ec	PROPN
ejpam-6050	531	17	)	)	PUNCT
ejpam-6050	531	18	=	=	PUNCT
ejpam-6050	531	19	ℵa(s)e	ℵa(s)e	X
ejpam-6050	531	20	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	531	21	)	)	PUNCT
ejpam-6050	531	22	.	.	PUNCT
ejpam-6050	532	1	(	(	PUNCT
ejpam-6050	532	2	4.43	4.43	NUM
ejpam-6050	532	3	)	)	PUNCT
ejpam-6050	532	4	(	(	PUNCT
ejpam-6050	532	5	ea	ea	PROPN
ejpam-6050	532	6	∪	∪	PROPN
ejpam-6050	532	7	eb	eb	PROPN
ejpam-6050	532	8	)	)	PUNCT
ejpam-6050	532	9	∩	∩	NOUN
ejpam-6050	532	10	(	(	PUNCT
ejpam-6050	532	11	ea	ea	X
ejpam-6050	532	12	∪	∪	X
ejpam-6050	532	13	ec	ec	PROPN
ejpam-6050	532	14	)	)	PUNCT
ejpam-6050	533	1	=	=	PUNCT
ejpam-6050	533	2	[	[	PUNCT
ejpam-6050	533	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	533	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	533	5	)	)	PUNCT
ejpam-6050	533	6	⊕	⊕	PROPN
ejpam-6050	533	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	533	8	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	533	9	)	)	PUNCT
ejpam-6050	533	10	]	]	PUNCT
ejpam-6050	534	1	∗	∗	NOUN
ejpam-6050	534	2	[	[	PUNCT
ejpam-6050	534	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	534	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	534	5	)	)	PUNCT
ejpam-6050	534	6	⊕	⊕	PROPN
ejpam-6050	534	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	534	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	534	9	)	)	PUNCT
ejpam-6050	534	10	]	]	PUNCT
ejpam-6050	535	1	=	=	PUNCT
ejpam-6050	535	2	[	[	PUNCT
ejpam-6050	535	3	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	535	4	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	535	5	)	)	PUNCT
ejpam-6050	535	6	∗	∗	NOUN
ejpam-6050	535	7	ℵr(s)e	ℵr(s)e	NOUN
ejpam-6050	535	8	−⊺ℵr(s	−⊺ℵr(s	NOUN
ejpam-6050	535	9	)	)	PUNCT
ejpam-6050	535	10	]	]	PUNCT
ejpam-6050	536	1	(	(	PUNCT
ejpam-6050	536	2	ea	ea	PROPN
ejpam-6050	536	3	∪	∪	ADP
ejpam-6050	536	4	eb	eb	PROPN
ejpam-6050	536	5	)	)	PUNCT
ejpam-6050	536	6	∩	∩	NOUN
ejpam-6050	536	7	(	(	PUNCT
ejpam-6050	536	8	ea	ea	X
ejpam-6050	536	9	∪	∪	X
ejpam-6050	536	10	ec	ec	PROPN
ejpam-6050	536	11	)	)	PUNCT
ejpam-6050	536	12	=	=	PUNCT
ejpam-6050	536	13	ℵa(s)e	ℵa(s)e	X
ejpam-6050	536	14	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	536	15	)	)	PUNCT
ejpam-6050	536	16	(	(	PUNCT
ejpam-6050	536	17	4.44	4.44	NUM
ejpam-6050	536	18	)	)	PUNCT
ejpam-6050	536	19	m.	m.	NOUN
ejpam-6050	536	20	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	536	21	,	,	PUNCT
ejpam-6050	536	22	m.	m.	NOUN
ejpam-6050	536	23	rajeshwari	rajeshwari	NOUN
ejpam-6050	536	24	,	,	PUNCT
ejpam-6050	536	25	m.	m.	NOUN
ejpam-6050	536	26	alqahtani	alqahtani	PROPN
ejpam-6050	536	27	/	/	SYM
ejpam-6050	536	28	eur	eur	PROPN
ejpam-6050	536	29	.	.	PUNCT
ejpam-6050	537	1	j.	j.	PROPN
ejpam-6050	537	2	pure	pure	PROPN
ejpam-6050	537	3	appl	appl	PROPN
ejpam-6050	537	4	.	.	PROPN
ejpam-6050	537	5	math	math	PROPN
ejpam-6050	537	6	,	,	PUNCT
ejpam-6050	537	7	18	18	NUM
ejpam-6050	537	8	(	(	PUNCT
ejpam-6050	537	9	2	2	NUM
ejpam-6050	537	10	)	)	PUNCT
ejpam-6050	537	11	(	(	PUNCT
ejpam-6050	537	12	2025	2025	NUM
ejpam-6050	537	13	)	)	PUNCT
ejpam-6050	537	14	,	,	PUNCT
ejpam-6050	537	15	6050	6050	NUM
ejpam-6050	537	16	21	21	NUM
ejpam-6050	537	17	of	of	ADP
ejpam-6050	537	18	29	29	NUM
ejpam-6050	537	19	from	from	ADP
ejpam-6050	537	20	equation	equation	NOUN
ejpam-6050	537	21	(	(	PUNCT
ejpam-6050	537	22	4.43	4.43	NUM
ejpam-6050	537	23	)	)	PUNCT
ejpam-6050	537	24	and	and	CCONJ
ejpam-6050	537	25	(	(	PUNCT
ejpam-6050	537	26	4.44	4.44	NUM
ejpam-6050	537	27	)	)	PUNCT
ejpam-6050	538	1	,	,	PUNCT
ejpam-6050	538	2	we	we	PRON
ejpam-6050	538	3	have	have	VERB
ejpam-6050	538	4	ea	ea	NOUN
ejpam-6050	538	5	∪	∪	X
ejpam-6050	538	6	(	(	PUNCT
ejpam-6050	538	7	eb	eb	PROPN
ejpam-6050	538	8	∩	∩	PROPN
ejpam-6050	538	9	ec	ec	PROPN
ejpam-6050	538	10	)	)	PUNCT
ejpam-6050	538	11	=	=	PRON
ejpam-6050	538	12	(	(	PUNCT
ejpam-6050	538	13	ea	ea	PROPN
ejpam-6050	538	14	∪	∪	PROPN
ejpam-6050	538	15	eb	eb	PROPN
ejpam-6050	538	16	)	)	PUNCT
ejpam-6050	538	17	∩	∩	NOUN
ejpam-6050	538	18	(	(	PUNCT
ejpam-6050	538	19	ea	ea	X
ejpam-6050	538	20	∪	∪	PROPN
ejpam-6050	538	21	ec	ec	PROPN
ejpam-6050	538	22	)	)	PUNCT
ejpam-6050	538	23	the	the	DET
ejpam-6050	538	24	law	law	NOUN
ejpam-6050	538	25	is	be	AUX
ejpam-6050	538	26	valid	valid	ADJ
ejpam-6050	538	27	for	for	ADP
ejpam-6050	538	28	all	all	PRON
ejpam-6050	538	29	above	above	ADP
ejpam-6050	538	30	cases	case	NOUN
ejpam-6050	538	31	.	.	PUNCT
ejpam-6050	539	1	similar	similar	ADJ
ejpam-6050	539	2	way	way	NOUN
ejpam-6050	539	3	the	the	DET
ejpam-6050	539	4	distributive	distributive	ADJ
ejpam-6050	539	5	law	law	NOUN
ejpam-6050	539	6	of	of	ADP
ejpam-6050	539	7	intersection	intersection	NOUN
ejpam-6050	539	8	over	over	ADP
ejpam-6050	539	9	union	union	NOUN
ejpam-6050	539	10	is	be	AUX
ejpam-6050	539	11	prove	prove	ADJ
ejpam-6050	539	12	.	.	PUNCT
ejpam-6050	540	1	ea	ea	NOUN
ejpam-6050	540	2	∩	∩	NOUN
ejpam-6050	540	3	(	(	PUNCT
ejpam-6050	540	4	eb	eb	PROPN
ejpam-6050	540	5	∪	∪	PROPN
ejpam-6050	540	6	ec	ec	PROPN
ejpam-6050	540	7	)	)	PUNCT
ejpam-6050	540	8	=	=	SYM
ejpam-6050	540	9	(	(	PUNCT
ejpam-6050	540	10	ea	ea	X
ejpam-6050	540	11	∩	∩	PROPN
ejpam-6050	540	12	eb	eb	PROPN
ejpam-6050	540	13	)	)	PUNCT
ejpam-6050	540	14	∪	∪	NOUN
ejpam-6050	540	15	(	(	PUNCT
ejpam-6050	540	16	ea	ea	X
ejpam-6050	540	17	∩	∩	ADJ
ejpam-6050	540	18	ec	ec	PROPN
ejpam-6050	540	19	)	)	PUNCT
ejpam-6050	540	20	theorem	theorem	VERB
ejpam-6050	540	21	6	6	NUM
ejpam-6050	540	22	.	.	PUNCT
ejpam-6050	540	23	for	for	ADP
ejpam-6050	540	24	any	any	DET
ejpam-6050	540	25	efs	ef	NOUN
ejpam-6050	540	26	ea	ea	ADP
ejpam-6050	540	27	,	,	PUNCT
ejpam-6050	540	28	the	the	DET
ejpam-6050	540	29	union	union	NOUN
ejpam-6050	540	30	,	,	PUNCT
ejpam-6050	540	31	intersection	intersection	NOUN
ejpam-6050	540	32	,	,	PUNCT
ejpam-6050	540	33	complement	complement	NOUN
ejpam-6050	540	34	function	function	NOUN
ejpam-6050	540	35	with	with	ADP
ejpam-6050	540	36	the	the	DET
ejpam-6050	540	37	same	same	ADJ
ejpam-6050	540	38	function	function	NOUN
ejpam-6050	540	39	for	for	ADP
ejpam-6050	540	40	determining	determine	VERB
ejpam-6050	540	41	the	the	DET
ejpam-6050	540	42	phase	phase	NOUN
ejpam-6050	540	43	term	term	NOUN
ejpam-6050	540	44	satisfy	satisfy	VERB
ejpam-6050	540	45	the	the	DET
ejpam-6050	540	46	following	following	NOUN
ejpam-6050	540	47	:	:	PUNCT
ejpam-6050	541	1	i	i	PRON
ejpam-6050	541	2	.	.	PUNCT
ejpam-6050	542	1	ea	ea	PROPN
ejpam-6050	542	2	∪	∪	PROPN
ejpam-6050	542	3	eac	eac	PROPN
ejpam-6050	542	4	=	=	SYM
ejpam-6050	542	5	ea	ea	PROPN
ejpam-6050	542	6	or	or	CCONJ
ejpam-6050	542	7	ea	ea	X
ejpam-6050	542	8	∪	∪	PROPN
ejpam-6050	542	9	eac	eac	PROPN
ejpam-6050	542	10	=	=	PROPN
ejpam-6050	542	11	eac	eac	PROPN
ejpam-6050	542	12	.	.	PUNCT
ejpam-6050	543	1	ii	ii	PROPN
ejpam-6050	543	2	.	.	PUNCT
ejpam-6050	544	1	ea	ea	NOUN
ejpam-6050	544	2	∩	∩	PROPN
ejpam-6050	544	3	eac	eac	NOUN
ejpam-6050	544	4	=	=	SYM
ejpam-6050	544	5	ea	ea	PROPN
ejpam-6050	544	6	or	or	CCONJ
ejpam-6050	544	7	ea	ea	PROPN
ejpam-6050	544	8	∩	∩	PROPN
ejpam-6050	544	9	eac	eac	PROPN
ejpam-6050	544	10	=	=	PROPN
ejpam-6050	544	11	eac	eac	PROPN
ejpam-6050	544	12	.	.	PUNCT
ejpam-6050	545	1	proof	proof	NOUN
ejpam-6050	545	2	.	.	PUNCT
ejpam-6050	546	1	to	to	PART
ejpam-6050	546	2	prove	prove	VERB
ejpam-6050	546	3	(	(	PUNCT
ejpam-6050	546	4	i	i	NOUN
ejpam-6050	546	5	)	)	PUNCT
ejpam-6050	546	6	and	and	CCONJ
ejpam-6050	546	7	(	(	PUNCT
ejpam-6050	546	8	ii	ii	NOUN
ejpam-6050	546	9	)	)	PUNCT
ejpam-6050	546	10	,	,	PUNCT
ejpam-6050	546	11	two	two	NUM
ejpam-6050	546	12	cases	case	NOUN
ejpam-6050	546	13	arise	arise	VERB
ejpam-6050	546	14	here	here	ADV
ejpam-6050	546	15	.	.	PUNCT
ejpam-6050	547	1	i	i	PRON
ejpam-6050	547	2	.	.	PUNCT
ejpam-6050	548	1	ea	ea	PROPN
ejpam-6050	548	2	∪	∪	PROPN
ejpam-6050	548	3	eac	eac	PROPN
ejpam-6050	548	4	=	=	SYM
ejpam-6050	548	5	ea	ea	PROPN
ejpam-6050	548	6	or	or	CCONJ
ejpam-6050	548	7	ea	ea	X
ejpam-6050	548	8	∪	∪	PROPN
ejpam-6050	548	9	eac	eac	PROPN
ejpam-6050	548	10	=	=	PROPN
ejpam-6050	548	11	eac	eac	PROPN
ejpam-6050	548	12	.	.	PUNCT
ejpam-6050	549	1	case	case	NOUN
ejpam-6050	549	2	1	1	NUM
ejpam-6050	549	3	.	.	PUNCT
ejpam-6050	550	1	ℵc	ℵc	PROPN
ejpam-6050	550	2	a(s	a(s	PROPN
ejpam-6050	550	3	)	)	PUNCT
ejpam-6050	550	4	≤	≤	NOUN
ejpam-6050	550	5	ℵa(s	ℵa(s	ADJ
ejpam-6050	550	6	)	)	PUNCT
ejpam-6050	551	1	ea	ea	X
ejpam-6050	551	2	∪	∪	ADP
ejpam-6050	551	3	eac	eac	NOUN
ejpam-6050	551	4	=	=	PUNCT
ejpam-6050	551	5	[	[	PUNCT
ejpam-6050	551	6	ℵa(s)e	ℵa(s)e	X
ejpam-6050	551	7	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	551	8	)	)	PUNCT
ejpam-6050	551	9	⊕	⊕	PROPN
ejpam-6050	551	10	ℵc	ℵc	NOUN
ejpam-6050	551	11	a(s)e	a(s)e	PROPN
ejpam-6050	551	12	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	551	13	a(s	a(s	PROPN
ejpam-6050	551	14	)	)	PUNCT
ejpam-6050	551	15	]	]	PUNCT
ejpam-6050	552	1	=	=	PUNCT
ejpam-6050	552	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	552	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	552	4	)	)	PUNCT
ejpam-6050	552	5	=	=	SYM
ejpam-6050	552	6	ea	ea	NOUN
ejpam-6050	552	7	.	.	PUNCT
ejpam-6050	552	8	case	case	NOUN
ejpam-6050	552	9	2	2	NUM
ejpam-6050	552	10	.	.	PUNCT
ejpam-6050	553	1	ℵa(s	ℵa(s	ADJ
ejpam-6050	553	2	)	)	PUNCT
ejpam-6050	553	3	≤	≤	NOUN
ejpam-6050	553	4	ℵc	ℵc	ADP
ejpam-6050	553	5	a(s	a(s	PROPN
ejpam-6050	553	6	)	)	PUNCT
ejpam-6050	553	7	ea	ea	X
ejpam-6050	553	8	∪	∪	NOUN
ejpam-6050	553	9	eac	eac	NOUN
ejpam-6050	553	10	=	=	PUNCT
ejpam-6050	553	11	[	[	PUNCT
ejpam-6050	553	12	ℵa(s)e	ℵa(s)e	X
ejpam-6050	553	13	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	553	14	)	)	PUNCT
ejpam-6050	553	15	⊕	⊕	PROPN
ejpam-6050	553	16	ℵc	ℵc	NOUN
ejpam-6050	553	17	a(s)e	a(s)e	PROPN
ejpam-6050	553	18	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	553	19	a(s	a(s	PROPN
ejpam-6050	553	20	)	)	PUNCT
ejpam-6050	553	21	]	]	PUNCT
ejpam-6050	553	22	=	=	PUNCT
ejpam-6050	553	23	ℵc	ℵc	PROPN
ejpam-6050	553	24	a(s)e	a(s)e	PROPN
ejpam-6050	553	25	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	553	26	a(s	a(s	PROPN
ejpam-6050	553	27	)	)	PUNCT
ejpam-6050	553	28	=	=	SYM
ejpam-6050	553	29	eac	eac	PROPN
ejpam-6050	553	30	.	.	PUNCT
ejpam-6050	553	31	ii	ii	PROPN
ejpam-6050	553	32	.ea	.ea	PUNCT
ejpam-6050	554	1	∩	∩	PROPN
ejpam-6050	554	2	eac	eac	PROPN
ejpam-6050	554	3	=	=	SYM
ejpam-6050	554	4	ea	ea	PROPN
ejpam-6050	554	5	or	or	CCONJ
ejpam-6050	554	6	ea	ea	PROPN
ejpam-6050	554	7	∩	∩	PROPN
ejpam-6050	554	8	eac	eac	PROPN
ejpam-6050	554	9	=	=	PROPN
ejpam-6050	554	10	eac	eac	PROPN
ejpam-6050	554	11	.	.	PUNCT
ejpam-6050	555	1	case	case	NOUN
ejpam-6050	555	2	1	1	NUM
ejpam-6050	555	3	.	.	PUNCT
ejpam-6050	556	1	ℵc	ℵc	PROPN
ejpam-6050	556	2	a(s	a(s	PROPN
ejpam-6050	556	3	)	)	PUNCT
ejpam-6050	556	4	≤	≤	NOUN
ejpam-6050	556	5	ℵa(s	ℵa(s	NOUN
ejpam-6050	556	6	)	)	PUNCT
ejpam-6050	556	7	ea	ea	NOUN
ejpam-6050	556	8	∩	∩	PROPN
ejpam-6050	556	9	eac	eac	NOUN
ejpam-6050	556	10	=	=	PUNCT
ejpam-6050	556	11	[	[	PUNCT
ejpam-6050	556	12	ℵa(s)e	ℵa(s)e	X
ejpam-6050	556	13	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	556	14	)	)	PUNCT
ejpam-6050	556	15	∗	∗	NOUN
ejpam-6050	556	16	ℵc	ℵc	NOUN
ejpam-6050	556	17	a(s)e	a(s)e	PROPN
ejpam-6050	556	18	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	556	19	a(s	a(s	PROPN
ejpam-6050	556	20	)	)	PUNCT
ejpam-6050	556	21	]	]	PUNCT
ejpam-6050	557	1	=	=	PUNCT
ejpam-6050	557	2	ℵc	ℵc	PROPN
ejpam-6050	557	3	a(s)e	a(s)e	PROPN
ejpam-6050	557	4	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	557	5	a(s	a(s	PROPN
ejpam-6050	557	6	)	)	PUNCT
ejpam-6050	557	7	=	=	SYM
ejpam-6050	557	8	eac	eac	PROPN
ejpam-6050	557	9	.	.	PUNCT
ejpam-6050	557	10	m.	m.	PROPN
ejpam-6050	557	11	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	557	12	,	,	PUNCT
ejpam-6050	557	13	m.	m.	NOUN
ejpam-6050	557	14	rajeshwari	rajeshwari	NOUN
ejpam-6050	557	15	,	,	PUNCT
ejpam-6050	557	16	m.	m.	NOUN
ejpam-6050	557	17	alqahtani	alqahtani	PROPN
ejpam-6050	557	18	/	/	SYM
ejpam-6050	557	19	eur	eur	PROPN
ejpam-6050	557	20	.	.	PUNCT
ejpam-6050	558	1	j.	j.	PROPN
ejpam-6050	558	2	pure	pure	PROPN
ejpam-6050	558	3	appl	appl	PROPN
ejpam-6050	558	4	.	.	PROPN
ejpam-6050	558	5	math	math	PROPN
ejpam-6050	558	6	,	,	PUNCT
ejpam-6050	558	7	18	18	NUM
ejpam-6050	558	8	(	(	PUNCT
ejpam-6050	558	9	2	2	NUM
ejpam-6050	558	10	)	)	PUNCT
ejpam-6050	558	11	(	(	PUNCT
ejpam-6050	558	12	2025	2025	NUM
ejpam-6050	558	13	)	)	PUNCT
ejpam-6050	558	14	,	,	PUNCT
ejpam-6050	558	15	6050	6050	NUM
ejpam-6050	558	16	22	22	NUM
ejpam-6050	558	17	of	of	ADP
ejpam-6050	558	18	29	29	NUM
ejpam-6050	558	19	case	case	NOUN
ejpam-6050	558	20	2	2	NUM
ejpam-6050	558	21	.	.	PUNCT
ejpam-6050	559	1	ℵa(s	ℵa(s	ADJ
ejpam-6050	559	2	)	)	PUNCT
ejpam-6050	559	3	≤	≤	NOUN
ejpam-6050	559	4	ℵc	ℵc	ADP
ejpam-6050	559	5	a(s	a(s	PROPN
ejpam-6050	559	6	)	)	PUNCT
ejpam-6050	559	7	ea	ea	PROPN
ejpam-6050	559	8	∩	∩	PROPN
ejpam-6050	559	9	eac	eac	NOUN
ejpam-6050	560	1	=	=	PUNCT
ejpam-6050	560	2	[	[	PUNCT
ejpam-6050	560	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	560	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	560	5	)	)	PUNCT
ejpam-6050	560	6	∗	∗	NOUN
ejpam-6050	560	7	ℵc	ℵc	NOUN
ejpam-6050	560	8	a(s)e	a(s)e	PROPN
ejpam-6050	560	9	−⊺ℵc	−⊺ℵc	PROPN
ejpam-6050	560	10	a(s	a(s	PROPN
ejpam-6050	560	11	)	)	PUNCT
ejpam-6050	560	12	]	]	PUNCT
ejpam-6050	561	1	=	=	PUNCT
ejpam-6050	561	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	561	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	561	4	)	)	PUNCT
ejpam-6050	561	5	=	=	SYM
ejpam-6050	561	6	ea	ea	X
ejpam-6050	561	7	.	.	PUNCT
ejpam-6050	561	8	theorem	theorem	VERB
ejpam-6050	561	9	7	7	NUM
ejpam-6050	561	10	.	.	X
ejpam-6050	561	11	for	for	ADP
ejpam-6050	561	12	any	any	DET
ejpam-6050	561	13	efss	efss	NOUN
ejpam-6050	561	14	ea	ea	PROPN
ejpam-6050	561	15	and	and	CCONJ
ejpam-6050	561	16	eb	eb	PROPN
ejpam-6050	561	17	over	over	ADP
ejpam-6050	561	18	a	a	DET
ejpam-6050	561	19	crisp	crisp	ADJ
ejpam-6050	561	20	set	set	NOUN
ejpam-6050	561	21	z	z	NOUN
ejpam-6050	561	22	,	,	PUNCT
ejpam-6050	561	23	union	union	NOUN
ejpam-6050	561	24	and	and	CCONJ
ejpam-6050	561	25	intersection	intersection	NOUN
ejpam-6050	561	26	function	function	NOUN
ejpam-6050	561	27	with	with	ADP
ejpam-6050	561	28	the	the	DET
ejpam-6050	561	29	max	max	PROPN
ejpam-6050	561	30	function	function	NOUN
ejpam-6050	561	31	for	for	ADP
ejpam-6050	561	32	determining	determine	VERB
ejpam-6050	561	33	the	the	DET
ejpam-6050	561	34	phase	phase	NOUN
ejpam-6050	561	35	term	term	NOUN
ejpam-6050	561	36	does	do	AUX
ejpam-6050	561	37	not	not	PART
ejpam-6050	561	38	satisfy	satisfy	VERB
ejpam-6050	561	39	the	the	DET
ejpam-6050	561	40	absorption	absorption	NOUN
ejpam-6050	561	41	law	law	NOUN
ejpam-6050	561	42	.	.	PUNCT
ejpam-6050	562	1	proof	proof	NOUN
ejpam-6050	562	2	.	.	PUNCT
ejpam-6050	563	1	the	the	DET
ejpam-6050	563	2	absorption	absorption	NOUN
ejpam-6050	563	3	laws	law	NOUN
ejpam-6050	563	4	for	for	ADP
ejpam-6050	563	5	crisp	crisp	ADJ
ejpam-6050	563	6	set	set	NOUN
ejpam-6050	563	7	are	be	AUX
ejpam-6050	563	8	efss	efss	PROPN
ejpam-6050	563	9	ea	ea	PROPN
ejpam-6050	563	10	and	and	CCONJ
ejpam-6050	563	11	eb	eb	PROPN
ejpam-6050	563	12	,	,	PUNCT
ejpam-6050	563	13	the	the	DET
ejpam-6050	563	14	absorption	absorption	NOUN
ejpam-6050	563	15	laws	law	NOUN
ejpam-6050	563	16	do	do	AUX
ejpam-6050	563	17	not	not	PART
ejpam-6050	563	18	hold	hold	VERB
ejpam-6050	563	19	.	.	PUNCT
ejpam-6050	564	1	if	if	SCONJ
ejpam-6050	564	2	ℵa(s	ℵa(s	ADJ
ejpam-6050	564	3	)	)	PUNCT
ejpam-6050	564	4	≤	≤	NOUN
ejpam-6050	564	5	ℵb(s	ℵb(s	NUM
ejpam-6050	564	6	)	)	PUNCT
ejpam-6050	564	7	.	.	PUNCT
ejpam-6050	565	1	ea	ea	NOUN
ejpam-6050	565	2	∩	∩	NOUN
ejpam-6050	565	3	(	(	PUNCT
ejpam-6050	565	4	ea	ea	PROPN
ejpam-6050	565	5	∪	∪	PROPN
ejpam-6050	565	6	eb	eb	PROPN
ejpam-6050	565	7	)	)	PUNCT
ejpam-6050	565	8	=	=	PUNCT
ejpam-6050	565	9	[	[	PUNCT
ejpam-6050	565	10	ℵa(s)e	ℵa(s)e	X
ejpam-6050	565	11	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	565	12	)	)	PUNCT
ejpam-6050	565	13	∗	∗	NOUN
ejpam-6050	565	14	(	(	PUNCT
ejpam-6050	565	15	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	565	16	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	565	17	)	)	PUNCT
ejpam-6050	565	18	⊕	⊕	PROPN
ejpam-6050	565	19	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	565	20	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	565	21	)	)	PUNCT
ejpam-6050	565	22	)	)	PUNCT
ejpam-6050	565	23	]	]	PUNCT
ejpam-6050	566	1	=	=	SYM
ejpam-6050	566	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	566	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	566	4	)	)	PUNCT
ejpam-6050	566	5	∗	∗	NOUN
ejpam-6050	566	6	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	566	7	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	566	8	)	)	PUNCT
ejpam-6050	566	9	=	=	PUNCT
ejpam-6050	566	10	ℵa(s)e	ℵa(s)e	NUM
ejpam-6050	566	11	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	566	12	)	)	PUNCT
ejpam-6050	566	13	̸=	̸=	PROPN
ejpam-6050	566	14	ea	ea	NOUN
ejpam-6050	566	15	.	.	PUNCT
ejpam-6050	567	1	ea	ea	NOUN
ejpam-6050	567	2	∪	∪	X
ejpam-6050	567	3	(	(	PUNCT
ejpam-6050	567	4	ea	ea	X
ejpam-6050	567	5	∩	∩	PROPN
ejpam-6050	567	6	eb	eb	PROPN
ejpam-6050	567	7	)	)	PUNCT
ejpam-6050	568	1	=	=	PUNCT
ejpam-6050	568	2	[	[	PUNCT
ejpam-6050	568	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	568	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	568	5	)	)	PUNCT
ejpam-6050	568	6	⊕	⊕	PROPN
ejpam-6050	568	7	(	(	PUNCT
ejpam-6050	568	8	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	568	9	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	568	10	)	)	PUNCT
ejpam-6050	568	11	∗	∗	NOUN
ejpam-6050	568	12	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	568	13	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	568	14	)	)	PUNCT
ejpam-6050	568	15	)	)	PUNCT
ejpam-6050	568	16	]	]	PUNCT
ejpam-6050	569	1	=	=	SYM
ejpam-6050	569	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	569	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	569	4	)	)	PUNCT
ejpam-6050	569	5	⊕	⊕	PROPN
ejpam-6050	569	6	ℵa(s)e	ℵa(s)e	PROPN
ejpam-6050	569	7	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	569	8	)	)	PUNCT
ejpam-6050	569	9	=	=	PUNCT
ejpam-6050	569	10	ℵa(s)e	ℵa(s)e	NUM
ejpam-6050	569	11	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	569	12	)	)	PUNCT
ejpam-6050	569	13	̸=	̸=	PROPN
ejpam-6050	569	14	ea	ea	NUM
ejpam-6050	569	15	.	.	PUNCT
ejpam-6050	570	1	also	also	ADV
ejpam-6050	570	2	if	if	SCONJ
ejpam-6050	570	3	ℵb(s	ℵb(	NOUN
ejpam-6050	570	4	)	)	PUNCT
ejpam-6050	570	5	≤	≤	NOUN
ejpam-6050	570	6	ℵa(s	ℵa(s	ADJ
ejpam-6050	570	7	)	)	PUNCT
ejpam-6050	570	8	.	.	PUNCT
ejpam-6050	571	1	ea	ea	NOUN
ejpam-6050	571	2	∪	∪	X
ejpam-6050	571	3	(	(	PUNCT
ejpam-6050	571	4	ea	ea	X
ejpam-6050	571	5	∩	∩	PROPN
ejpam-6050	571	6	eb	eb	PROPN
ejpam-6050	571	7	)	)	PUNCT
ejpam-6050	571	8	=	=	PUNCT
ejpam-6050	571	9	[	[	PUNCT
ejpam-6050	571	10	ℵa(s)e	ℵa(s)e	X
ejpam-6050	571	11	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	571	12	)	)	PUNCT
ejpam-6050	571	13	∗	∗	NOUN
ejpam-6050	571	14	(	(	PUNCT
ejpam-6050	571	15	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	571	16	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	571	17	)	)	PUNCT
ejpam-6050	571	18	⊕	⊕	PROPN
ejpam-6050	571	19	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	571	20	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	571	21	)	)	PUNCT
ejpam-6050	571	22	)	)	PUNCT
ejpam-6050	571	23	]	]	PUNCT
ejpam-6050	572	1	=	=	SYM
ejpam-6050	572	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	572	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	572	4	)	)	PUNCT
ejpam-6050	572	5	∗	∗	NOUN
ejpam-6050	572	6	ℵa(s)e	ℵa(s)e	X
ejpam-6050	572	7	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	572	8	)	)	PUNCT
ejpam-6050	572	9	=	=	PUNCT
ejpam-6050	572	10	ℵa(s)e	ℵa(s)e	NUM
ejpam-6050	572	11	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	572	12	)	)	PUNCT
ejpam-6050	572	13	̸=	̸=	PROPN
ejpam-6050	572	14	ea	ea	NOUN
ejpam-6050	572	15	.	.	PUNCT
ejpam-6050	573	1	ea	ea	NOUN
ejpam-6050	573	2	∪	∪	X
ejpam-6050	573	3	(	(	PUNCT
ejpam-6050	573	4	ea	ea	X
ejpam-6050	573	5	∩	∩	PROPN
ejpam-6050	573	6	eb	eb	PROPN
ejpam-6050	573	7	)	)	PUNCT
ejpam-6050	574	1	=	=	PUNCT
ejpam-6050	574	2	[	[	PUNCT
ejpam-6050	574	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	574	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	574	5	)	)	PUNCT
ejpam-6050	574	6	⊕	⊕	PROPN
ejpam-6050	574	7	(	(	PUNCT
ejpam-6050	574	8	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	574	9	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	574	10	)	)	PUNCT
ejpam-6050	574	11	∗	∗	NOUN
ejpam-6050	574	12	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	574	13	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	574	14	)	)	PUNCT
ejpam-6050	574	15	)	)	PUNCT
ejpam-6050	574	16	]	]	PUNCT
ejpam-6050	575	1	=	=	SYM
ejpam-6050	575	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	575	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	575	4	)	)	PUNCT
ejpam-6050	575	5	⊕	⊕	PROPN
ejpam-6050	575	6	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	575	7	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	575	8	)	)	PUNCT
ejpam-6050	575	9	=	=	PUNCT
ejpam-6050	575	10	ℵa(s)e	ℵa(s)e	NUM
ejpam-6050	575	11	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	575	12	)	)	PUNCT
ejpam-6050	575	13	̸=	̸=	PROPN
ejpam-6050	575	14	ea	ea	NOUN
ejpam-6050	575	15	.	.	PUNCT
ejpam-6050	576	1	hence	hence	ADV
ejpam-6050	576	2	,	,	PUNCT
ejpam-6050	576	3	the	the	DET
ejpam-6050	576	4	absorption	absorption	NOUN
ejpam-6050	576	5	law	law	NOUN
ejpam-6050	576	6	does	do	AUX
ejpam-6050	576	7	not	not	PART
ejpam-6050	576	8	hold	hold	VERB
ejpam-6050	576	9	for	for	ADP
ejpam-6050	576	10	any	any	DET
ejpam-6050	576	11	efss	efss	NOUN
ejpam-6050	576	12	.	.	PUNCT
ejpam-6050	577	1	theorem	theorem	ADJ
ejpam-6050	577	2	8	8	NUM
ejpam-6050	577	3	.	.	PUNCT
ejpam-6050	578	1	for	for	ADP
ejpam-6050	578	2	any	any	DET
ejpam-6050	578	3	efss	efss	NOUN
ejpam-6050	578	4	ea	ea	NOUN
ejpam-6050	578	5	,	,	PUNCT
ejpam-6050	578	6	eb	eb	PROPN
ejpam-6050	578	7	and	and	CCONJ
ejpam-6050	578	8	ec	ec	PROPN
ejpam-6050	578	9	,	,	PUNCT
ejpam-6050	578	10	the	the	DET
ejpam-6050	578	11	complement	complement	NOUN
ejpam-6050	578	12	,	,	PUNCT
ejpam-6050	578	13	intersection	intersection	NOUN
ejpam-6050	578	14	,	,	PUNCT
ejpam-6050	578	15	union	union	NOUN
ejpam-6050	578	16	function	function	NOUN
ejpam-6050	578	17	for	for	ADP
ejpam-6050	578	18	determining	determine	VERB
ejpam-6050	578	19	the	the	DET
ejpam-6050	578	20	phase	phase	NOUN
ejpam-6050	578	21	term	term	NOUN
ejpam-6050	578	22	does	do	AUX
ejpam-6050	578	23	not	not	PART
ejpam-6050	578	24	satisfy	satisfy	VERB
ejpam-6050	578	25	the	the	DET
ejpam-6050	578	26	distributive	distributive	ADJ
ejpam-6050	578	27	laws	law	NOUN
ejpam-6050	578	28	.	.	PUNCT
ejpam-6050	579	1	proof	proof	NOUN
ejpam-6050	579	2	.	.	PUNCT
ejpam-6050	580	1	the	the	DET
ejpam-6050	580	2	distributive	distributive	ADJ
ejpam-6050	580	3	law	law	NOUN
ejpam-6050	580	4	of	of	ADP
ejpam-6050	580	5	union	union	NOUN
ejpam-6050	580	6	over	over	ADP
ejpam-6050	580	7	intersection	intersection	NOUN
ejpam-6050	580	8	is	be	AUX
ejpam-6050	580	9	ea∪(eb	ea∪(eb	PROPN
ejpam-6050	580	10	∩	∩	ADJ
ejpam-6050	580	11	ec	ec	PROPN
ejpam-6050	580	12	)	)	PUNCT
ejpam-6050	580	13	=	=	PRON
ejpam-6050	581	1	(	(	PUNCT
ejpam-6050	581	2	ea	ea	X
ejpam-6050	581	3	∪	∪	ADP
ejpam-6050	581	4	eb)∩	eb)∩	PROPN
ejpam-6050	581	5	(	(	PUNCT
ejpam-6050	581	6	ea	ea	X
ejpam-6050	581	7	∪	∪	PROPN
ejpam-6050	581	8	ec	ec	PROPN
ejpam-6050	581	9	)	)	PUNCT
ejpam-6050	581	10	.	.	PUNCT
ejpam-6050	582	1	if	if	SCONJ
ejpam-6050	582	2	ℵea(s	ℵea(s	PROPN
ejpam-6050	582	3	)	)	PUNCT
ejpam-6050	582	4	≤	≤	NOUN
ejpam-6050	582	5	ℵeb(s	ℵeb(	VERB
ejpam-6050	582	6	)	)	PUNCT
ejpam-6050	582	7	≤	≤	NOUN
ejpam-6050	582	8	ℵec(s	ℵec(s	NUM
ejpam-6050	582	9	)	)	PUNCT
ejpam-6050	582	10	.	.	PUNCT
ejpam-6050	583	1	ea	ea	NOUN
ejpam-6050	583	2	∪	∪	X
ejpam-6050	583	3	(	(	PUNCT
ejpam-6050	583	4	eb	eb	PROPN
ejpam-6050	583	5	∩	∩	PROPN
ejpam-6050	583	6	ec	ec	PROPN
ejpam-6050	583	7	)	)	PUNCT
ejpam-6050	583	8	=	=	PUNCT
ejpam-6050	583	9	[	[	PUNCT
ejpam-6050	583	10	ℵa(s)e	ℵa(s)e	X
ejpam-6050	583	11	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	583	12	)	)	PUNCT
ejpam-6050	583	13	⊕	⊕	PROPN
ejpam-6050	583	14	(	(	PUNCT
ejpam-6050	583	15	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	583	16	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	583	17	)	)	PUNCT
ejpam-6050	583	18	∗	∗	NOUN
ejpam-6050	583	19	ℵc(s)e	ℵc(s)e	X
ejpam-6050	583	20	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	583	21	)	)	PUNCT
ejpam-6050	583	22	)	)	PUNCT
ejpam-6050	583	23	]	]	PUNCT
ejpam-6050	583	24	m.	m.	NOUN
ejpam-6050	583	25	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	583	26	,	,	PUNCT
ejpam-6050	583	27	m.	m.	NOUN
ejpam-6050	583	28	rajeshwari	rajeshwari	NOUN
ejpam-6050	583	29	,	,	PUNCT
ejpam-6050	583	30	m.	m.	NOUN
ejpam-6050	583	31	alqahtani	alqahtani	PROPN
ejpam-6050	583	32	/	/	SYM
ejpam-6050	583	33	eur	eur	PROPN
ejpam-6050	583	34	.	.	PUNCT
ejpam-6050	584	1	j.	j.	PROPN
ejpam-6050	584	2	pure	pure	PROPN
ejpam-6050	584	3	appl	appl	PROPN
ejpam-6050	584	4	.	.	PROPN
ejpam-6050	584	5	math	math	PROPN
ejpam-6050	584	6	,	,	PUNCT
ejpam-6050	584	7	18	18	NUM
ejpam-6050	584	8	(	(	PUNCT
ejpam-6050	584	9	2	2	NUM
ejpam-6050	584	10	)	)	PUNCT
ejpam-6050	584	11	(	(	PUNCT
ejpam-6050	584	12	2025	2025	NUM
ejpam-6050	584	13	)	)	PUNCT
ejpam-6050	584	14	,	,	PUNCT
ejpam-6050	584	15	6050	6050	NUM
ejpam-6050	584	16	23	23	NUM
ejpam-6050	584	17	of	of	ADP
ejpam-6050	584	18	29	29	NUM
ejpam-6050	584	19	=	=	SYM
ejpam-6050	584	20	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	584	21	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	584	22	)	)	PUNCT
ejpam-6050	584	23	⊕	⊕	PROPN
ejpam-6050	584	24	ℵb(s)e	ℵb(s)e	PUNCT
ejpam-6050	584	25	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	584	26	)	)	PUNCT
ejpam-6050	584	27	=	=	SYM
ejpam-6050	584	28	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	585	1	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	585	2	)	)	PUNCT
ejpam-6050	585	3	(	(	PUNCT
ejpam-6050	585	4	4.45	4.45	NUM
ejpam-6050	585	5	)	)	PUNCT
ejpam-6050	585	6	(	(	PUNCT
ejpam-6050	585	7	ea	ea	PROPN
ejpam-6050	585	8	∪	∪	PROPN
ejpam-6050	585	9	eb	eb	PROPN
ejpam-6050	585	10	)	)	PUNCT
ejpam-6050	585	11	∩	∩	NOUN
ejpam-6050	585	12	(	(	PUNCT
ejpam-6050	585	13	ea	ea	X
ejpam-6050	585	14	∪	∪	X
ejpam-6050	585	15	ec	ec	PROPN
ejpam-6050	585	16	)	)	PUNCT
ejpam-6050	585	17	=	=	PUNCT
ejpam-6050	585	18	[	[	PUNCT
ejpam-6050	585	19	ℵa(s)e	ℵa(s)e	X
ejpam-6050	585	20	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	585	21	)	)	PUNCT
ejpam-6050	585	22	⊕	⊕	PROPN
ejpam-6050	585	23	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	586	1	−⊺ℵb(s	−⊺ℵb(s	PROPN
ejpam-6050	586	2	)	)	PUNCT
ejpam-6050	586	3	]	]	PUNCT
ejpam-6050	587	1	∗	∗	NOUN
ejpam-6050	587	2	[	[	PUNCT
ejpam-6050	587	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	587	4	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	587	5	)	)	PUNCT
ejpam-6050	587	6	⊕	⊕	PROPN
ejpam-6050	587	7	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	587	8	−⊺ℵc(s	−⊺ℵc(s	X
ejpam-6050	587	9	)	)	PUNCT
ejpam-6050	587	10	]	]	PUNCT
ejpam-6050	588	1	=	=	SYM
ejpam-6050	588	2	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	588	3	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	588	4	)	)	PUNCT
ejpam-6050	588	5	∗	∗	NOUN
ejpam-6050	588	6	ℵc(s)e	ℵc(s)e	X
ejpam-6050	588	7	−⊺ℵc(s	−⊺ℵc(s	ADJ
ejpam-6050	588	8	)	)	PUNCT
ejpam-6050	588	9	=	=	SYM
ejpam-6050	588	10	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	588	11	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	588	12	)	)	PUNCT
ejpam-6050	588	13	.	.	PUNCT
ejpam-6050	589	1	(	(	PUNCT
ejpam-6050	589	2	4.46	4.46	NUM
ejpam-6050	589	3	)	)	PUNCT
ejpam-6050	589	4	from	from	ADP
ejpam-6050	589	5	equation	equation	NOUN
ejpam-6050	589	6	4.45	4.45	NUM
ejpam-6050	589	7	and	and	CCONJ
ejpam-6050	589	8	4.46	4.46	NUM
ejpam-6050	589	9	,	,	PUNCT
ejpam-6050	589	10	we	we	PRON
ejpam-6050	589	11	have	have	VERB
ejpam-6050	589	12	ea	ea	NOUN
ejpam-6050	589	13	∪	∪	X
ejpam-6050	589	14	(	(	PUNCT
ejpam-6050	589	15	eb	eb	PROPN
ejpam-6050	589	16	∩	∩	PROPN
ejpam-6050	589	17	ec	ec	PROPN
ejpam-6050	589	18	)	)	PUNCT
ejpam-6050	589	19	̸=	̸=	PROPN
ejpam-6050	589	20	(	(	PUNCT
ejpam-6050	589	21	ea	ea	PROPN
ejpam-6050	589	22	∪	∪	PROPN
ejpam-6050	589	23	eb	eb	PROPN
ejpam-6050	589	24	)	)	PUNCT
ejpam-6050	589	25	∩	∩	NOUN
ejpam-6050	589	26	(	(	PUNCT
ejpam-6050	589	27	ea	ea	X
ejpam-6050	589	28	∪	∪	PROPN
ejpam-6050	589	29	ec	ec	PROPN
ejpam-6050	589	30	)	)	PUNCT
ejpam-6050	589	31	now	now	ADV
ejpam-6050	589	32	distributive	distributive	ADJ
ejpam-6050	589	33	law	law	NOUN
ejpam-6050	589	34	of	of	ADP
ejpam-6050	589	35	intersection	intersection	NOUN
ejpam-6050	589	36	over	over	ADP
ejpam-6050	589	37	union	union	NOUN
ejpam-6050	589	38	ea	ea	X
ejpam-6050	589	39	∩	∩	X
ejpam-6050	589	40	(	(	PUNCT
ejpam-6050	589	41	eb	eb	PROPN
ejpam-6050	589	42	∪	∪	PROPN
ejpam-6050	589	43	ec	ec	PROPN
ejpam-6050	589	44	)	)	PUNCT
ejpam-6050	590	1	=	=	PUNCT
ejpam-6050	590	2	[	[	PUNCT
ejpam-6050	590	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	590	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	590	5	)	)	PUNCT
ejpam-6050	590	6	∗	∗	NOUN
ejpam-6050	590	7	(	(	PUNCT
ejpam-6050	590	8	ℵb(s)e	ℵb(s)e	NOUN
ejpam-6050	590	9	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	590	10	)	)	PUNCT
ejpam-6050	590	11	⊕	⊕	PROPN
ejpam-6050	590	12	ℵc(s)e	ℵc(s)e	PUNCT
ejpam-6050	591	1	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	591	2	)	)	PUNCT
ejpam-6050	591	3	)	)	PUNCT
ejpam-6050	591	4	]	]	PUNCT
ejpam-6050	592	1	=	=	SYM
ejpam-6050	592	2	ℵa(s)e	ℵa(s)e	X
ejpam-6050	592	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	592	4	)	)	PUNCT
ejpam-6050	592	5	∗	∗	NOUN
ejpam-6050	592	6	ℵc(s)e	ℵc(s)e	NOUN
ejpam-6050	592	7	−⊺ℵc(s	−⊺ℵc(s	ADJ
ejpam-6050	592	8	)	)	PUNCT
ejpam-6050	592	9	=	=	PUNCT
ejpam-6050	592	10	ℵa(s)e	ℵa(s)e	NUM
ejpam-6050	592	11	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	592	12	)	)	PUNCT
ejpam-6050	592	13	(	(	PUNCT
ejpam-6050	592	14	4.47	4.47	NUM
ejpam-6050	592	15	)	)	PUNCT
ejpam-6050	592	16	(	(	PUNCT
ejpam-6050	592	17	ea	ea	X
ejpam-6050	592	18	∩	∩	PROPN
ejpam-6050	592	19	eb	eb	PROPN
ejpam-6050	592	20	)	)	PUNCT
ejpam-6050	592	21	∪	∪	NOUN
ejpam-6050	592	22	(	(	PUNCT
ejpam-6050	592	23	ea	ea	X
ejpam-6050	592	24	∩	∩	X
ejpam-6050	592	25	ec	ec	PROPN
ejpam-6050	592	26	)	)	PUNCT
ejpam-6050	593	1	=	=	PUNCT
ejpam-6050	593	2	[	[	PUNCT
ejpam-6050	593	3	ℵa(s)e	ℵa(s)e	X
ejpam-6050	593	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	593	5	)	)	PUNCT
ejpam-6050	593	6	∗	∗	NOUN
ejpam-6050	593	7	ℵb(s)e	ℵb(s)e	NUM
ejpam-6050	593	8	−⊺ℵb(s	−⊺ℵb(	NOUN
ejpam-6050	593	9	)	)	PUNCT
ejpam-6050	593	10	]	]	PUNCT
ejpam-6050	594	1	⊕	⊕	PROPN
ejpam-6050	594	2	[	[	PUNCT
ejpam-6050	594	3	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	594	4	−⊺ℵa(s	−⊺ℵa(	NOUN
ejpam-6050	594	5	)	)	PUNCT
ejpam-6050	594	6	∗	∗	NOUN
ejpam-6050	594	7	ℵc(s)e	ℵc(s)e	NOUN
ejpam-6050	594	8	−⊺ℵc(s	−⊺ℵc(	NOUN
ejpam-6050	594	9	)	)	PUNCT
ejpam-6050	594	10	]	]	PUNCT
ejpam-6050	595	1	=	=	SYM
ejpam-6050	595	2	ℵa(s)e	ℵa(s)e	ADP
ejpam-6050	595	3	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	595	4	)	)	PUNCT
ejpam-6050	595	5	⊕	⊕	PROPN
ejpam-6050	595	6	ℵa(s)e	ℵa(s)e	PROPN
ejpam-6050	595	7	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	595	8	)	)	PUNCT
ejpam-6050	595	9	=	=	SYM
ejpam-6050	595	10	ℵa(s)e	ℵa(s)e	X
ejpam-6050	595	11	−⊺ℵa(s	−⊺ℵa(s	PROPN
ejpam-6050	595	12	)	)	PUNCT
ejpam-6050	595	13	(	(	PUNCT
ejpam-6050	595	14	4.48	4.48	NUM
ejpam-6050	595	15	)	)	PUNCT
ejpam-6050	595	16	from	from	ADP
ejpam-6050	595	17	equation	equation	NOUN
ejpam-6050	595	18	4.47	4.47	NUM
ejpam-6050	595	19	and	and	CCONJ
ejpam-6050	595	20	4.48	4.48	NUM
ejpam-6050	595	21	,	,	PUNCT
ejpam-6050	595	22	we	we	PRON
ejpam-6050	595	23	have	have	VERB
ejpam-6050	595	24	ea	ea	NOUN
ejpam-6050	595	25	∩	∩	NOUN
ejpam-6050	595	26	(	(	PUNCT
ejpam-6050	595	27	eb	eb	PROPN
ejpam-6050	595	28	∪	∪	PROPN
ejpam-6050	595	29	ec	ec	PROPN
ejpam-6050	595	30	)	)	PUNCT
ejpam-6050	595	31	̸=	̸=	PROPN
ejpam-6050	595	32	(	(	PUNCT
ejpam-6050	595	33	ea	ea	PROPN
ejpam-6050	595	34	∩	∩	PROPN
ejpam-6050	595	35	eb	eb	PROPN
ejpam-6050	595	36	)	)	PUNCT
ejpam-6050	595	37	∪	∪	NOUN
ejpam-6050	595	38	(	(	PUNCT
ejpam-6050	595	39	ea	ea	X
ejpam-6050	595	40	∩	∩	X
ejpam-6050	595	41	ec	ec	PROPN
ejpam-6050	595	42	)	)	PUNCT
ejpam-6050	595	43	.	.	PUNCT
ejpam-6050	596	1	hence	hence	ADV
ejpam-6050	596	2	,	,	PUNCT
ejpam-6050	596	3	the	the	DET
ejpam-6050	596	4	absorption	absorption	NOUN
ejpam-6050	596	5	law	law	NOUN
ejpam-6050	596	6	does	do	AUX
ejpam-6050	596	7	not	not	PART
ejpam-6050	596	8	hold	hold	VERB
ejpam-6050	596	9	for	for	ADP
ejpam-6050	596	10	any	any	DET
ejpam-6050	596	11	efss	efss	NOUN
ejpam-6050	596	12	.	.	PUNCT
ejpam-6050	597	1	5	5	X
ejpam-6050	597	2	.	.	X
ejpam-6050	597	3	application	application	NOUN
ejpam-6050	597	4	:	:	PUNCT
ejpam-6050	597	5	ai	ai	VERB
ejpam-6050	597	6	-	-	PUNCT
ejpam-6050	597	7	powered	power	VERB
ejpam-6050	597	8	investment	investment	NOUN
ejpam-6050	597	9	decision	decision	NOUN
ejpam-6050	597	10	-	-	PUNCT
ejpam-6050	597	11	making	making	NOUN
ejpam-6050	597	12	using	use	VERB
ejpam-6050	597	13	the	the	DET
ejpam-6050	597	14	weighted	weight	VERB
ejpam-6050	597	15	mean	mean	ADJ
ejpam-6050	597	16	method	method	NOUN
ejpam-6050	597	17	investments	investment	NOUN
ejpam-6050	597	18	are	be	AUX
ejpam-6050	597	19	essential	essential	ADJ
ejpam-6050	597	20	for	for	ADP
ejpam-6050	597	21	people	people	NOUN
ejpam-6050	597	22	because	because	SCONJ
ejpam-6050	597	23	they	they	PRON
ejpam-6050	597	24	help	help	VERB
ejpam-6050	597	25	grow	grow	VERB
ejpam-6050	597	26	wealth	wealth	NOUN
ejpam-6050	597	27	,	,	PUNCT
ejpam-6050	597	28	provide	provide	VERB
ejpam-6050	597	29	financial	financial	ADJ
ejpam-6050	597	30	security	security	NOUN
ejpam-6050	597	31	,	,	PUNCT
ejpam-6050	597	32	and	and	CCONJ
ejpam-6050	597	33	ensure	ensure	VERB
ejpam-6050	597	34	a	a	DET
ejpam-6050	597	35	stable	stable	ADJ
ejpam-6050	597	36	future	future	NOUN
ejpam-6050	597	37	.	.	PUNCT
ejpam-6050	598	1	by	by	ADP
ejpam-6050	598	2	investing	investing	NOUN
ejpam-6050	598	3	,	,	PUNCT
ejpam-6050	598	4	individuals	individual	NOUN
ejpam-6050	598	5	can	can	AUX
ejpam-6050	598	6	increase	increase	VERB
ejpam-6050	598	7	their	their	PRON
ejpam-6050	598	8	money	money	NOUN
ejpam-6050	598	9	over	over	ADP
ejpam-6050	598	10	time	time	NOUN
ejpam-6050	598	11	through	through	ADP
ejpam-6050	598	12	interest	interest	NOUN
ejpam-6050	598	13	,	,	PUNCT
ejpam-6050	598	14	dividends	dividend	NOUN
ejpam-6050	598	15	,	,	PUNCT
ejpam-6050	598	16	or	or	CCONJ
ejpam-6050	598	17	asset	asset	NOUN
ejpam-6050	598	18	appreciation	appreciation	NOUN
ejpam-6050	598	19	,	,	PUNCT
ejpam-6050	598	20	rather	rather	ADV
ejpam-6050	598	21	than	than	ADP
ejpam-6050	598	22	relying	rely	VERB
ejpam-6050	598	23	solely	solely	ADV
ejpam-6050	598	24	on	on	ADP
ejpam-6050	598	25	savings	saving	NOUN
ejpam-6050	598	26	.	.	PUNCT
ejpam-6050	599	1	investments	investment	NOUN
ejpam-6050	599	2	also	also	ADV
ejpam-6050	599	3	protect	protect	VERB
ejpam-6050	599	4	against	against	ADP
ejpam-6050	599	5	inflation	inflation	NOUN
ejpam-6050	599	6	,	,	PUNCT
ejpam-6050	599	7	which	which	PRON
ejpam-6050	599	8	reduces	reduce	VERB
ejpam-6050	599	9	the	the	DET
ejpam-6050	599	10	value	value	NOUN
ejpam-6050	599	11	of	of	ADP
ejpam-6050	599	12	money	money	NOUN
ejpam-6050	599	13	,	,	PUNCT
ejpam-6050	599	14	ensuring	ensure	VERB
ejpam-6050	599	15	that	that	SCONJ
ejpam-6050	599	16	purchasing	purchase	VERB
ejpam-6050	599	17	power	power	NOUN
ejpam-6050	599	18	remains	remain	VERB
ejpam-6050	599	19	strong	strong	ADJ
ejpam-6050	599	20	.	.	PUNCT
ejpam-6050	600	1	they	they	PRON
ejpam-6050	600	2	also	also	ADV
ejpam-6050	600	3	act	act	VERB
ejpam-6050	600	4	as	as	ADP
ejpam-6050	600	5	a	a	DET
ejpam-6050	600	6	source	source	NOUN
ejpam-6050	600	7	of	of	ADP
ejpam-6050	600	8	financial	financial	ADJ
ejpam-6050	600	9	relief	relief	NOUN
ejpam-6050	600	10	in	in	ADP
ejpam-6050	600	11	cases	case	NOUN
ejpam-6050	600	12	of	of	ADP
ejpam-6050	600	13	emergencies	emergency	NOUN
ejpam-6050	600	14	and	and	CCONJ
ejpam-6050	600	15	enable	enable	VERB
ejpam-6050	600	16	individuals	individual	NOUN
ejpam-6050	600	17	to	to	PART
ejpam-6050	600	18	fulfill	fulfill	VERB
ejpam-6050	600	19	long	long	ADJ
ejpam-6050	600	20	-	-	PUNCT
ejpam-6050	600	21	term	term	NOUN
ejpam-6050	600	22	objectives	objective	NOUN
ejpam-6050	600	23	like	like	ADP
ejpam-6050	600	24	purchasing	purchase	VERB
ejpam-6050	600	25	a	a	DET
ejpam-6050	600	26	house	house	NOUN
ejpam-6050	600	27	,	,	PUNCT
ejpam-6050	600	28	covering	cover	VERB
ejpam-6050	600	29	education	education	NOUN
ejpam-6050	600	30	expenses	expense	NOUN
ejpam-6050	600	31	,	,	PUNCT
ejpam-6050	600	32	or	or	CCONJ
ejpam-6050	600	33	saving	save	VERB
ejpam-6050	600	34	for	for	ADP
ejpam-6050	600	35	retirement	retirement	NOUN
ejpam-6050	600	36	.	.	PUNCT
ejpam-6050	601	1	investments	investment	NOUN
ejpam-6050	601	2	are	be	AUX
ejpam-6050	601	3	also	also	ADV
ejpam-6050	601	4	capable	capable	ADJ
ejpam-6050	601	5	of	of	ADP
ejpam-6050	601	6	creating	create	VERB
ejpam-6050	601	7	passive	passive	ADJ
ejpam-6050	601	8	income	income	NOUN
ejpam-6050	601	9	from	from	ADP
ejpam-6050	601	10	dividends	dividend	NOUN
ejpam-6050	601	11	,	,	PUNCT
ejpam-6050	601	12	rental	rental	ADJ
ejpam-6050	601	13	properties	property	NOUN
ejpam-6050	601	14	,	,	PUNCT
ejpam-6050	601	15	or	or	CCONJ
ejpam-6050	601	16	bonds	bond	NOUN
ejpam-6050	601	17	,	,	PUNCT
ejpam-6050	601	18	giving	give	VERB
ejpam-6050	601	19	financial	financial	ADJ
ejpam-6050	601	20	security	security	NOUN
ejpam-6050	601	21	without	without	ADP
ejpam-6050	601	22	hard	hard	ADJ
ejpam-6050	601	23	labor	labor	NOUN
ejpam-6050	601	24	.	.	PUNCT
ejpam-6050	602	1	investment	investment	NOUN
ejpam-6050	602	2	diversification	diversification	NOUN
ejpam-6050	602	3	among	among	ADP
ejpam-6050	602	4	various	various	ADJ
ejpam-6050	602	5	assets	asset	NOUN
ejpam-6050	602	6	minimizes	minimize	VERB
ejpam-6050	602	7	risk	risk	NOUN
ejpam-6050	602	8	even	even	ADV
ejpam-6050	602	9	more	more	ADV
ejpam-6050	602	10	,	,	PUNCT
ejpam-6050	602	11	providing	provide	VERB
ejpam-6050	602	12	financial	financial	ADJ
ejpam-6050	602	13	security	security	NOUN
ejpam-6050	602	14	and	and	CCONJ
ejpam-6050	602	15	a	a	DET
ejpam-6050	602	16	balanced	balanced	ADJ
ejpam-6050	602	17	future	future	NOUN
ejpam-6050	602	18	.	.	PUNCT
ejpam-6050	603	1	finally	finally	ADV
ejpam-6050	603	2	,	,	PUNCT
ejpam-6050	603	3	achieving	achieve	VERB
ejpam-6050	603	4	long	long	ADJ
ejpam-6050	603	5	-	-	PUNCT
ejpam-6050	603	6	term	term	NOUN
ejpam-6050	603	7	wealth	wealth	NOUN
ejpam-6050	603	8	and	and	CCONJ
ejpam-6050	603	9	financial	financial	ADJ
ejpam-6050	603	10	freedom	freedom	NOUN
ejpam-6050	603	11	requires	require	VERB
ejpam-6050	603	12	investment	investment	NOUN
ejpam-6050	603	13	.	.	PUNCT
ejpam-6050	604	1	nowadays	nowadays	ADV
ejpam-6050	604	2	,	,	PUNCT
ejpam-6050	604	3	investing	invest	VERB
ejpam-6050	604	4	money	money	NOUN
ejpam-6050	604	5	poses	pose	VERB
ejpam-6050	604	6	a	a	DET
ejpam-6050	604	7	variety	variety	NOUN
ejpam-6050	604	8	of	of	ADP
ejpam-6050	604	9	m.	m.	PROPN
ejpam-6050	604	10	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	604	11	,	,	PUNCT
ejpam-6050	604	12	m.	m.	NOUN
ejpam-6050	604	13	rajeshwari	rajeshwari	NOUN
ejpam-6050	604	14	,	,	PUNCT
ejpam-6050	604	15	m.	m.	NOUN
ejpam-6050	604	16	alqahtani	alqahtani	PROPN
ejpam-6050	604	17	/	/	SYM
ejpam-6050	604	18	eur	eur	PROPN
ejpam-6050	604	19	.	.	PUNCT
ejpam-6050	605	1	j.	j.	PROPN
ejpam-6050	605	2	pure	pure	PROPN
ejpam-6050	605	3	appl	appl	PROPN
ejpam-6050	605	4	.	.	PROPN
ejpam-6050	605	5	math	math	PROPN
ejpam-6050	605	6	,	,	PUNCT
ejpam-6050	605	7	18	18	NUM
ejpam-6050	605	8	(	(	PUNCT
ejpam-6050	605	9	2	2	NUM
ejpam-6050	605	10	)	)	PUNCT
ejpam-6050	605	11	(	(	PUNCT
ejpam-6050	605	12	2025	2025	NUM
ejpam-6050	605	13	)	)	PUNCT
ejpam-6050	605	14	,	,	PUNCT
ejpam-6050	605	15	6050	6050	NUM
ejpam-6050	605	16	24	24	NUM
ejpam-6050	605	17	of	of	ADP
ejpam-6050	605	18	29	29	NUM
ejpam-6050	605	19	difficulties	difficulty	NOUN
ejpam-6050	605	20	for	for	ADP
ejpam-6050	605	21	individuals	individual	NOUN
ejpam-6050	605	22	,	,	PUNCT
ejpam-6050	605	23	making	make	VERB
ejpam-6050	605	24	it	it	PRON
ejpam-6050	605	25	difficult	difficult	ADJ
ejpam-6050	605	26	to	to	PART
ejpam-6050	605	27	increase	increase	VERB
ejpam-6050	605	28	wealth	wealth	NOUN
ejpam-6050	605	29	and	and	CCONJ
ejpam-6050	605	30	safeguard	safeguard	VERB
ejpam-6050	605	31	one?s	one?s	NOUN
ejpam-6050	605	32	financial	financial	ADJ
ejpam-6050	605	33	future	future	NOUN
ejpam-6050	605	34	.	.	PUNCT
ejpam-6050	606	1	a	a	DET
ejpam-6050	606	2	significant	significant	ADJ
ejpam-6050	606	3	obstacle	obstacle	NOUN
ejpam-6050	606	4	is	be	AUX
ejpam-6050	606	5	a	a	DET
ejpam-6050	606	6	lack	lack	NOUN
ejpam-6050	606	7	of	of	ADP
ejpam-6050	606	8	financial	financial	ADJ
ejpam-6050	606	9	literacy	literacy	NOUN
ejpam-6050	606	10	,	,	PUNCT
ejpam-6050	606	11	since	since	SCONJ
ejpam-6050	606	12	most	most	ADJ
ejpam-6050	606	13	individuals	individual	NOUN
ejpam-6050	606	14	do	do	AUX
ejpam-6050	606	15	not	not	PART
ejpam-6050	606	16	know	know	VERB
ejpam-6050	606	17	where	where	SCONJ
ejpam-6050	606	18	or	or	CCONJ
ejpam-6050	606	19	how	how	SCONJ
ejpam-6050	606	20	to	to	PART
ejpam-6050	606	21	start	start	VERB
ejpam-6050	606	22	or	or	CCONJ
ejpam-6050	606	23	how	how	SCONJ
ejpam-6050	606	24	investments	investment	NOUN
ejpam-6050	606	25	work	work	VERB
ejpam-6050	606	26	.	.	PUNCT
ejpam-6050	607	1	limited	limited	ADJ
ejpam-6050	607	2	capital	capital	NOUN
ejpam-6050	607	3	is	be	AUX
ejpam-6050	607	4	another	another	DET
ejpam-6050	607	5	problem	problem	NOUN
ejpam-6050	607	6	;	;	PUNCT
ejpam-6050	607	7	some	some	DET
ejpam-6050	607	8	individuals	individual	NOUN
ejpam-6050	607	9	believe	believe	VERB
ejpam-6050	607	10	that	that	SCONJ
ejpam-6050	607	11	only	only	ADJ
ejpam-6050	607	12	rich	rich	ADJ
ejpam-6050	607	13	people	people	NOUN
ejpam-6050	607	14	can	can	AUX
ejpam-6050	607	15	invest	invest	VERB
ejpam-6050	607	16	since	since	SCONJ
ejpam-6050	607	17	they	they	PRON
ejpam-6050	607	18	lack	lack	VERB
ejpam-6050	607	19	sufficient	sufficient	ADJ
ejpam-6050	607	20	funds	fund	NOUN
ejpam-6050	607	21	.	.	PUNCT
ejpam-6050	608	1	making	make	VERB
ejpam-6050	608	2	the	the	DET
ejpam-6050	608	3	right	right	ADJ
ejpam-6050	608	4	investment	investment	NOUN
ejpam-6050	608	5	decision	decision	NOUN
ejpam-6050	608	6	can	can	AUX
ejpam-6050	608	7	be	be	AUX
ejpam-6050	608	8	complex	complex	ADJ
ejpam-6050	608	9	due	due	ADP
ejpam-6050	608	10	to	to	ADP
ejpam-6050	608	11	uncertainty	uncertainty	NOUN
ejpam-6050	608	12	,	,	PUNCT
ejpam-6050	608	13	market	market	NOUN
ejpam-6050	608	14	fluctuations	fluctuation	NOUN
ejpam-6050	608	15	,	,	PUNCT
ejpam-6050	608	16	and	and	CCONJ
ejpam-6050	608	17	multiple	multiple	ADJ
ejpam-6050	608	18	investment	investment	NOUN
ejpam-6050	608	19	options	option	NOUN
ejpam-6050	608	20	.	.	PUNCT
ejpam-6050	609	1	our	our	PRON
ejpam-6050	609	2	exponential	exponential	ADJ
ejpam-6050	609	3	fuzzy	fuzzy	ADJ
ejpam-6050	609	4	investment	investment	NOUN
ejpam-6050	609	5	decision	decision	NOUN
ejpam-6050	609	6	system	system	NOUN
ejpam-6050	609	7	is	be	AUX
ejpam-6050	609	8	designed	design	VERB
ejpam-6050	609	9	to	to	PART
ejpam-6050	609	10	assist	assist	VERB
ejpam-6050	609	11	investors	investor	NOUN
ejpam-6050	609	12	in	in	ADP
ejpam-6050	609	13	choosing	choose	VERB
ejpam-6050	609	14	the	the	DET
ejpam-6050	609	15	most	most	ADV
ejpam-6050	609	16	suitable	suitable	ADJ
ejpam-6050	609	17	investment	investment	NOUN
ejpam-6050	609	18	scheme	scheme	NOUN
ejpam-6050	609	19	based	base	VERB
ejpam-6050	609	20	on	on	ADP
ejpam-6050	609	21	a	a	DET
ejpam-6050	609	22	exponential	exponential	ADJ
ejpam-6050	609	23	fuzzy	fuzzy	ADJ
ejpam-6050	609	24	set	set	NOUN
ejpam-6050	609	25	approach	approach	NOUN
ejpam-6050	609	26	.	.	PUNCT
ejpam-6050	610	1	this	this	DET
ejpam-6050	610	2	application	application	NOUN
ejpam-6050	610	3	evaluates	evaluate	VERB
ejpam-6050	610	4	investment	investment	NOUN
ejpam-6050	610	5	opportunities	opportunity	NOUN
ejpam-6050	610	6	by	by	ADP
ejpam-6050	610	7	considering	consider	VERB
ejpam-6050	610	8	multiple	multiple	ADJ
ejpam-6050	610	9	factors	factor	NOUN
ejpam-6050	610	10	,	,	PUNCT
ejpam-6050	610	11	such	such	ADJ
ejpam-6050	610	12	as	as	ADP
ejpam-6050	610	13	risk	risk	NOUN
ejpam-6050	610	14	level	level	NOUN
ejpam-6050	610	15	,	,	PUNCT
ejpam-6050	610	16	expected	expect	VERB
ejpam-6050	610	17	return	return	NOUN
ejpam-6050	610	18	,	,	PUNCT
ejpam-6050	610	19	investment	investment	NOUN
ejpam-6050	610	20	horizon	horizon	NOUN
ejpam-6050	610	21	,	,	PUNCT
ejpam-6050	610	22	and	and	CCONJ
ejpam-6050	610	23	financial	financial	ADJ
ejpam-6050	610	24	goals	goal	NOUN
ejpam-6050	610	25	.	.	PUNCT
ejpam-6050	611	1	unlike	unlike	ADP
ejpam-6050	611	2	fuzzy	fuzzy	ADJ
ejpam-6050	611	3	logic	logic	NOUN
ejpam-6050	611	4	decision	decision	NOUN
ejpam-6050	611	5	-	-	PUNCT
ejpam-6050	611	6	making	make	VERB
ejpam-6050	611	7	models	model	NOUN
ejpam-6050	611	8	,	,	PUNCT
ejpam-6050	611	9	exponential	exponential	ADJ
ejpam-6050	611	10	fuzzy	fuzzy	ADJ
ejpam-6050	611	11	logic	logic	NOUN
ejpam-6050	611	12	enables	enable	VERB
ejpam-6050	611	13	a	a	DET
ejpam-6050	611	14	more	more	ADV
ejpam-6050	611	15	flexible	flexible	ADJ
ejpam-6050	611	16	and	and	CCONJ
ejpam-6050	611	17	human	human	ADJ
ejpam-6050	611	18	-	-	PUNCT
ejpam-6050	611	19	like	like	ADJ
ejpam-6050	611	20	reasoning	reasoning	NOUN
ejpam-6050	611	21	process	process	NOUN
ejpam-6050	611	22	,	,	PUNCT
ejpam-6050	611	23	allowing	allow	VERB
ejpam-6050	611	24	for	for	ADP
ejpam-6050	611	25	better	well	ADJ
ejpam-6050	611	26	handling	handling	NOUN
ejpam-6050	611	27	of	of	ADP
ejpam-6050	611	28	imprecise	imprecise	ADJ
ejpam-6050	611	29	and	and	CCONJ
ejpam-6050	611	30	uncertain	uncertain	ADJ
ejpam-6050	611	31	data	datum	NOUN
ejpam-6050	611	32	this	this	DET
ejpam-6050	611	33	application	application	NOUN
ejpam-6050	611	34	helps	help	VERB
ejpam-6050	611	35	you	you	PRON
ejpam-6050	611	36	make	make	VERB
ejpam-6050	611	37	data	data	NOUN
ejpam-6050	611	38	-	-	PUNCT
ejpam-6050	611	39	driven	drive	VERB
ejpam-6050	611	40	investment	investment	NOUN
ejpam-6050	611	41	decisions	decision	NOUN
ejpam-6050	611	42	with	with	ADP
ejpam-6050	611	43	confidence	confidence	NOUN
ejpam-6050	611	44	.	.	PUNCT
ejpam-6050	612	1	in	in	ADP
ejpam-6050	612	2	this	this	DET
ejpam-6050	612	3	section	section	NOUN
ejpam-6050	612	4	,	,	PUNCT
ejpam-6050	612	5	we	we	PRON
ejpam-6050	612	6	use	use	VERB
ejpam-6050	612	7	the	the	DET
ejpam-6050	612	8	weighted	weight	VERB
ejpam-6050	612	9	mean	mean	ADJ
ejpam-6050	612	10	method	method	NOUN
ejpam-6050	612	11	for	for	ADP
ejpam-6050	612	12	ai	ai	ADJ
ejpam-6050	612	13	-	-	PUNCT
ejpam-6050	612	14	powered	power	VERB
ejpam-6050	612	15	investment	investment	NOUN
ejpam-6050	612	16	decisionmaking	decisionmaking	NOUN
ejpam-6050	612	17	,	,	PUNCT
ejpam-6050	612	18	where	where	SCONJ
ejpam-6050	612	19	financial	financial	ADJ
ejpam-6050	612	20	experts	expert	NOUN
ejpam-6050	612	21	(	(	PUNCT
ejpam-6050	612	22	with	with	ADP
ejpam-6050	612	23	different	different	ADJ
ejpam-6050	612	24	importance	importance	NOUN
ejpam-6050	612	25	weights	weight	NOUN
ejpam-6050	612	26	)	)	PUNCT
ejpam-6050	612	27	assess	assess	NOUN
ejpam-6050	612	28	stocks	stock	NOUN
ejpam-6050	612	29	,	,	PUNCT
ejpam-6050	612	30	and	and	CCONJ
ejpam-6050	612	31	their	their	PRON
ejpam-6050	612	32	opinions	opinion	NOUN
ejpam-6050	612	33	are	be	AUX
ejpam-6050	612	34	aggregated	aggregate	VERB
ejpam-6050	612	35	using	use	VERB
ejpam-6050	612	36	efss	efss	NOUN
ejpam-6050	612	37	.	.	PUNCT
ejpam-6050	613	1	let	let	VERB
ejpam-6050	613	2	s	s	VERB
ejpam-6050	613	3	=	=	NOUN
ejpam-6050	613	4	{	{	PUNCT
ejpam-6050	613	5	s1	s1	NOUN
ejpam-6050	613	6	,	,	PUNCT
ejpam-6050	613	7	s2	s2	PROPN
ejpam-6050	613	8	,	,	PUNCT
ejpam-6050	613	9	s3	s3	PROPN
ejpam-6050	613	10	,	,	PUNCT
ejpam-6050	613	11	s4	s4	PROPN
ejpam-6050	613	12	,	,	PUNCT
ejpam-6050	613	13	s5	s5	PROPN
ejpam-6050	613	14	,	,	PUNCT
ejpam-6050	613	15	s6	s6	PROPN
ejpam-6050	613	16	,	,	PUNCT
ejpam-6050	613	17	s7	s7	NOUN
ejpam-6050	613	18	,	,	PUNCT
ejpam-6050	613	19	s8	s8	NOUN
ejpam-6050	613	20	,	,	PUNCT
ejpam-6050	613	21	s9	s9	NOUN
ejpam-6050	613	22	,	,	PUNCT
ejpam-6050	613	23	s10	s10	PROPN
ejpam-6050	613	24	}	}	PUNCT
ejpam-6050	613	25	be	be	VERB
ejpam-6050	613	26	the	the	DET
ejpam-6050	613	27	set	set	NOUN
ejpam-6050	613	28	of	of	ADP
ejpam-6050	613	29	investments	investment	NOUN
ejpam-6050	613	30	where	where	SCONJ
ejpam-6050	613	31	s1	s1	PROPN
ejpam-6050	613	32	(	(	PUNCT
ejpam-6050	613	33	bonds	bond	NOUN
ejpam-6050	613	34	)	)	PUNCT
ejpam-6050	613	35	,	,	PUNCT
ejpam-6050	613	36	s2	s2	PROPN
ejpam-6050	613	37	(	(	PUNCT
ejpam-6050	613	38	public	public	ADJ
ejpam-6050	613	39	provident	provident	ADJ
ejpam-6050	613	40	fund	fund	PROPN
ejpam-6050	613	41	)	)	PUNCT
ejpam-6050	613	42	,	,	PUNCT
ejpam-6050	613	43	s3	s3	PROPN
ejpam-6050	613	44	(	(	PUNCT
ejpam-6050	613	45	stocks	stock	NOUN
ejpam-6050	613	46	)	)	PUNCT
ejpam-6050	613	47	,	,	PUNCT
ejpam-6050	613	48	s4	s4	PROPN
ejpam-6050	613	49	(	(	PUNCT
ejpam-6050	613	50	real	real	ADJ
ejpam-6050	613	51	estate	estate	NOUN
ejpam-6050	613	52	)	)	PUNCT
ejpam-6050	613	53	,	,	PUNCT
ejpam-6050	613	54	s5	s5	X
ejpam-6050	613	55	(	(	PUNCT
ejpam-6050	613	56	treasurys	treasury	NOUN
ejpam-6050	613	57	)	)	PUNCT
ejpam-6050	613	58	,	,	PUNCT
ejpam-6050	613	59	s6	s6	PROPN
ejpam-6050	613	60	(	(	PUNCT
ejpam-6050	613	61	cryptocurrencies	cryptocurrencie	NOUN
ejpam-6050	613	62	)	)	PUNCT
ejpam-6050	613	63	,	,	PUNCT
ejpam-6050	613	64	s7	s7	NOUN
ejpam-6050	613	65	(	(	PUNCT
ejpam-6050	613	66	mutual	mutual	ADJ
ejpam-6050	613	67	funds	fund	NOUN
ejpam-6050	613	68	)	)	PUNCT
ejpam-6050	613	69	,	,	PUNCT
ejpam-6050	613	70	s8	s8	NOUN
ejpam-6050	613	71	(	(	PUNCT
ejpam-6050	613	72	fixed	fix	VERB
ejpam-6050	613	73	deposits	deposit	NOUN
ejpam-6050	613	74	)	)	PUNCT
ejpam-6050	613	75	,	,	PUNCT
ejpam-6050	613	76	s9	s9	NOUN
ejpam-6050	613	77	(	(	PUNCT
ejpam-6050	613	78	gold	gold	NOUN
ejpam-6050	613	79	)	)	PUNCT
ejpam-6050	613	80	,	,	PUNCT
ejpam-6050	613	81	s10	s10	PROPN
ejpam-6050	613	82	(	(	PUNCT
ejpam-6050	613	83	national	national	ADJ
ejpam-6050	613	84	pension	pension	NOUN
ejpam-6050	613	85	scheme	scheme	NOUN
ejpam-6050	613	86	)	)	PUNCT
ejpam-6050	613	87	.	.	PUNCT
ejpam-6050	614	1	the	the	DET
ejpam-6050	614	2	decision	decision	NOUN
ejpam-6050	614	3	-	-	PUNCT
ejpam-6050	614	4	makers	maker	NOUN
ejpam-6050	614	5	are	be	AUX
ejpam-6050	614	6	:	:	PUNCT
ejpam-6050	614	7	•	•	NUM
ejpam-6050	614	8	e1	e1	NOUN
ejpam-6050	614	9	:	:	PUNCT
ejpam-6050	614	10	junior	junior	ADJ
ejpam-6050	614	11	analyst	analyst	NOUN
ejpam-6050	614	12	(	(	PUNCT
ejpam-6050	614	13	weight	weight	NOUN
ejpam-6050	614	14	=	=	SYM
ejpam-6050	614	15	w1	w1	NOUN
ejpam-6050	614	16	=	=	NOUN
ejpam-6050	614	17	0.2	0.2	NUM
ejpam-6050	614	18	)	)	PUNCT
ejpam-6050	614	19	•	•	NUM
ejpam-6050	614	20	e2	e2	PROPN
ejpam-6050	614	21	:	:	PUNCT
ejpam-6050	614	22	senior	senior	ADJ
ejpam-6050	614	23	analyst	analyst	NOUN
ejpam-6050	614	24	(	(	PUNCT
ejpam-6050	614	25	weight	weight	NOUN
ejpam-6050	614	26	=	=	SYM
ejpam-6050	614	27	w2	w2	NOUN
ejpam-6050	614	28	=	=	NOUN
ejpam-6050	614	29	0.3	0.3	NUM
ejpam-6050	614	30	)	)	PUNCT
ejpam-6050	614	31	•	•	ADP
ejpam-6050	614	32	e3	e3	NOUN
ejpam-6050	614	33	:	:	PUNCT
ejpam-6050	614	34	ai	ai	AUX
ejpam-6050	614	35	model	model	NOUN
ejpam-6050	614	36	(	(	PUNCT
ejpam-6050	614	37	weight	weight	NOUN
ejpam-6050	614	38	=	=	SYM
ejpam-6050	614	39	w3	w3	PROPN
ejpam-6050	614	40	=	=	NOUN
ejpam-6050	614	41	0.5	0.5	NUM
ejpam-6050	614	42	)	)	PUNCT
ejpam-6050	615	1	where	where	SCONJ
ejpam-6050	615	2	∑3	∑3	PROPN
ejpam-6050	615	3	j=1wj	j=1wj	PART
ejpam-6050	615	4	=	=	SYM
ejpam-6050	615	5	1	1	NUM
ejpam-6050	615	6	and	and	CCONJ
ejpam-6050	615	7	⊺	⊺	NUM
ejpam-6050	615	8	=	=	SYM
ejpam-6050	615	9	2	2	X
ejpam-6050	615	10	.	.	X
ejpam-6050	615	11	experts	expert	NOUN
ejpam-6050	615	12	assign	assign	VERB
ejpam-6050	615	13	fuzzy	fuzzy	ADJ
ejpam-6050	615	14	membership	membership	NOUN
ejpam-6050	615	15	values	value	NOUN
ejpam-6050	615	16	ℵaj	ℵaj	NOUN
ejpam-6050	615	17	(	(	PUNCT
ejpam-6050	615	18	s	s	X
ejpam-6050	615	19	)	)	PUNCT
ejpam-6050	615	20	to	to	ADP
ejpam-6050	615	21	each	each	DET
ejpam-6050	615	22	stock	stock	NOUN
ejpam-6050	615	23	:	:	PUNCT
ejpam-6050	615	24	investments	investments	PROPN
ejpam-6050	615	25	ℵa1(s	ℵa1(s	PROPN
ejpam-6050	615	26	)	)	PUNCT
ejpam-6050	615	27	ℵa2(s	ℵa2(s	PROPN
ejpam-6050	615	28	)	)	PUNCT
ejpam-6050	615	29	ℵa3(s	ℵa3(s	PROPN
ejpam-6050	615	30	)	)	PUNCT
ejpam-6050	615	31	s1	s1	NOUN
ejpam-6050	615	32	0.3	0.3	NUM
ejpam-6050	615	33	0.4	0.4	NUM
ejpam-6050	615	34	0.5	0.5	NUM
ejpam-6050	615	35	s2	s2	NOUN
ejpam-6050	615	36	0.6	0.6	NUM
ejpam-6050	615	37	0.7	0.7	NUM
ejpam-6050	615	38	0.8	0.8	NUM
ejpam-6050	615	39	s3	s3	PROPN
ejpam-6050	615	40	0.8	0.8	NUM
ejpam-6050	615	41	0.9	0.9	NUM
ejpam-6050	615	42	1.0	1.0	NUM
ejpam-6050	615	43	s4	s4	PROPN
ejpam-6050	615	44	0.5	0.5	NUM
ejpam-6050	615	45	0.6	0.6	NUM
ejpam-6050	615	46	0.7	0.7	NUM
ejpam-6050	615	47	s5	s5	NOUN
ejpam-6050	615	48	0.9	0.9	NUM
ejpam-6050	615	49	1.0	1.0	NUM
ejpam-6050	615	50	0.9	0.9	NUM
ejpam-6050	615	51	s6	s6	PROPN
ejpam-6050	615	52	0.7	0.7	NUM
ejpam-6050	615	53	0.4	0.4	NUM
ejpam-6050	615	54	0.8	0.8	NUM
ejpam-6050	615	55	s7	s7	NOUN
ejpam-6050	615	56	0.5	0.5	NUM
ejpam-6050	615	57	1.0	1.0	NUM
ejpam-6050	615	58	0.3	0.3	NUM
ejpam-6050	615	59	s8	s8	NOUN
ejpam-6050	615	60	1.0	1.0	NUM
ejpam-6050	615	61	0.3	0.3	NUM
ejpam-6050	615	62	0.2	0.2	NUM
ejpam-6050	615	63	s9	s9	NOUN
ejpam-6050	615	64	0.1	0.1	NUM
ejpam-6050	615	65	0.5	0.5	NUM
ejpam-6050	615	66	0.9	0.9	NUM
ejpam-6050	615	67	s10	s10	NOUN
ejpam-6050	615	68	0.7	0.7	NUM
ejpam-6050	615	69	1.0	1.0	NUM
ejpam-6050	615	70	0.4	0.4	NUM
ejpam-6050	615	71	table	table	NOUN
ejpam-6050	615	72	1	1	NUM
ejpam-6050	615	73	:	:	PUNCT
ejpam-6050	615	74	fuzzy	fuzzy	ADJ
ejpam-6050	615	75	membership	membership	NOUN
ejpam-6050	615	76	values	value	NOUN
ejpam-6050	615	77	for	for	ADP
ejpam-6050	615	78	each	each	DET
ejpam-6050	615	79	stock	stock	NOUN
ejpam-6050	615	80	the	the	DET
ejpam-6050	615	81	exponential	exponential	ADJ
ejpam-6050	615	82	fuzzy	fuzzy	ADJ
ejpam-6050	615	83	membership	membership	NOUN
ejpam-6050	615	84	formula	formula	NOUN
ejpam-6050	616	1	is	be	AUX
ejpam-6050	616	2	ℵeaj	ℵeaj	PROPN
ejpam-6050	616	3	(	(	PUNCT
ejpam-6050	616	4	s	s	X
ejpam-6050	616	5	)	)	PUNCT
ejpam-6050	616	6	=	=	SYM
ejpam-6050	616	7	ℵaj	ℵaj	NOUN
ejpam-6050	616	8	(	(	PUNCT
ejpam-6050	616	9	s)e	s)e	X
ejpam-6050	616	10	−2ℵaj	−2ℵaj	PROPN
ejpam-6050	616	11	(	(	PUNCT
ejpam-6050	616	12	s	s	NOUN
ejpam-6050	616	13	)	)	PUNCT
ejpam-6050	616	14	(	(	PUNCT
ejpam-6050	616	15	5.1	5.1	NUM
ejpam-6050	616	16	)	)	PUNCT
ejpam-6050	616	17	m.	m.	NOUN
ejpam-6050	616	18	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	616	19	,	,	PUNCT
ejpam-6050	616	20	m.	m.	NOUN
ejpam-6050	616	21	rajeshwari	rajeshwari	NOUN
ejpam-6050	616	22	,	,	PUNCT
ejpam-6050	616	23	m.	m.	NOUN
ejpam-6050	616	24	alqahtani	alqahtani	PROPN
ejpam-6050	616	25	/	/	SYM
ejpam-6050	616	26	eur	eur	PROPN
ejpam-6050	616	27	.	.	PUNCT
ejpam-6050	617	1	j.	j.	PROPN
ejpam-6050	617	2	pure	pure	PROPN
ejpam-6050	617	3	appl	appl	PROPN
ejpam-6050	617	4	.	.	PROPN
ejpam-6050	617	5	math	math	PROPN
ejpam-6050	617	6	,	,	PUNCT
ejpam-6050	617	7	18	18	NUM
ejpam-6050	617	8	(	(	PUNCT
ejpam-6050	617	9	2	2	NUM
ejpam-6050	617	10	)	)	PUNCT
ejpam-6050	617	11	(	(	PUNCT
ejpam-6050	617	12	2025	2025	NUM
ejpam-6050	617	13	)	)	PUNCT
ejpam-6050	617	14	,	,	PUNCT
ejpam-6050	617	15	6050	6050	NUM
ejpam-6050	617	16	25	25	NUM
ejpam-6050	617	17	of	of	ADP
ejpam-6050	617	18	29	29	NUM
ejpam-6050	617	19	investment	investment	NOUN
ejpam-6050	617	20	ℵea1	ℵea1	NOUN
ejpam-6050	617	21	(	(	PUNCT
ejpam-6050	617	22	s	s	X
ejpam-6050	617	23	)	)	PUNCT
ejpam-6050	617	24	ℵea2	ℵea2	NOUN
ejpam-6050	617	25	(	(	PUNCT
ejpam-6050	617	26	s	s	NOUN
ejpam-6050	617	27	)	)	PUNCT
ejpam-6050	617	28	ℵea3	ℵea3	PROPN
ejpam-6050	617	29	(	(	PUNCT
ejpam-6050	617	30	s	s	NOUN
ejpam-6050	617	31	)	)	PUNCT
ejpam-6050	617	32	s1	s1	NOUN
ejpam-6050	617	33	0.1646	0.1646	NUM
ejpam-6050	617	34	0.1797	0.1797	NUM
ejpam-6050	617	35	0.1839	0.1839	NUM
ejpam-6050	617	36	s2	s2	NOUN
ejpam-6050	617	37	0.1807	0.1807	NUM
ejpam-6050	617	38	0.1726	0.1726	NUM
ejpam-6050	617	39	0.1615	0.1615	NUM
ejpam-6050	617	40	s3	s3	PROPN
ejpam-6050	617	41	0.1615	0.1615	NUM
ejpam-6050	617	42	0.1487	0.1487	NUM
ejpam-6050	617	43	0.1353	0.1353	NUM
ejpam-6050	617	44	s4	s4	VERB
ejpam-6050	617	45	0.1839	0.1839	NUM
ejpam-6050	617	46	0.1807	0.1807	NUM
ejpam-6050	617	47	0.1726	0.1726	NUM
ejpam-6050	617	48	s5	s5	NOUN
ejpam-6050	617	49	0.1487	0.1487	NUM
ejpam-6050	617	50	0.1353	0.1353	NUM
ejpam-6050	617	51	0.1487	0.1487	NUM
ejpam-6050	617	52	s6	s6	PROPN
ejpam-6050	617	53	0.1726	0.1726	NUM
ejpam-6050	617	54	0.1797	0.1797	NUM
ejpam-6050	617	55	0.1615	0.1615	NUM
ejpam-6050	617	56	s7	s7	VERB
ejpam-6050	617	57	0.1839	0.1839	NUM
ejpam-6050	617	58	0.1353	0.1353	NUM
ejpam-6050	617	59	0.1646	0.1646	NUM
ejpam-6050	617	60	s8	s8	VERB
ejpam-6050	617	61	0.1353	0.1353	NUM
ejpam-6050	617	62	0.1646	0.1646	NUM
ejpam-6050	617	63	0.1340	0.1340	NUM
ejpam-6050	617	64	s9	s9	NOUN
ejpam-6050	617	65	0.0818	0.0818	NUM
ejpam-6050	617	66	0.1839	0.1839	NUM
ejpam-6050	617	67	0.1487	0.1487	NUM
ejpam-6050	617	68	s10	s10	NOUN
ejpam-6050	617	69	0.1726	0.1726	NUM
ejpam-6050	617	70	0.1353	0.1353	NUM
ejpam-6050	617	71	0.1737	0.1737	NUM
ejpam-6050	617	72	table	table	NOUN
ejpam-6050	617	73	2	2	NUM
ejpam-6050	617	74	:	:	PUNCT
ejpam-6050	617	75	exponential	exponential	ADJ
ejpam-6050	617	76	fuzzy	fuzzy	ADJ
ejpam-6050	617	77	membership	membership	NOUN
ejpam-6050	617	78	values	value	NOUN
ejpam-6050	617	79	for	for	ADP
ejpam-6050	617	80	each	each	DET
ejpam-6050	617	81	stock	stock	NOUN
ejpam-6050	617	82	weighted	weight	VERB
ejpam-6050	617	83	mean	mean	ADJ
ejpam-6050	617	84	aggregation	aggregation	NOUN
ejpam-6050	617	85	using	use	VERB
ejpam-6050	617	86	the	the	DET
ejpam-6050	617	87	formula	formula	NOUN
ejpam-6050	617	88	:	:	PUNCT
ejpam-6050	617	89	ℵeg(s	ℵeg(s	X
ejpam-6050	617	90	)	)	PUNCT
ejpam-6050	617	91	=	=	SYM
ejpam-6050	618	1	3∑	3∑	NUM
ejpam-6050	618	2	j=1	j=1	NOUN
ejpam-6050	618	3	wjℵeaj	wjℵeaj	VERB
ejpam-6050	618	4	(	(	PUNCT
ejpam-6050	618	5	s	s	NOUN
ejpam-6050	618	6	)	)	PUNCT
ejpam-6050	618	7	(	(	PUNCT
ejpam-6050	618	8	5.2	5.2	NUM
ejpam-6050	618	9	)	)	PUNCT
ejpam-6050	618	10	we	we	PRON
ejpam-6050	618	11	compute	compute	VERB
ejpam-6050	618	12	the	the	DET
ejpam-6050	618	13	aggregated	aggregate	VERB
ejpam-6050	618	14	fuzzy	fuzzy	ADJ
ejpam-6050	618	15	values	value	NOUN
ejpam-6050	618	16	:	:	PUNCT
ejpam-6050	618	17	investment	investment	NOUN
ejpam-6050	618	18	ℵe(s	ℵe(s	PUNCT
ejpam-6050	618	19	)	)	PUNCT
ejpam-6050	618	20	s1	s1	NOUN
ejpam-6050	618	21	0.1787	0.1787	NUM
ejpam-6050	618	22	s2	s2	PROPN
ejpam-6050	618	23	0.1686	0.1686	NUM
ejpam-6050	618	24	s3	s3	PROPN
ejpam-6050	618	25	0.1445	0.1445	PROPN
ejpam-6050	618	26	s4	s4	PROPN
ejpam-6050	618	27	0.1772	0.1772	NUM
ejpam-6050	618	28	s5	s5	PROPN
ejpam-6050	618	29	0.1446	0.1446	NUM
ejpam-6050	618	30	s6	s6	PROPN
ejpam-6050	618	31	0.1691	0.1691	NUM
ejpam-6050	618	32	s7	s7	PROPN
ejpam-6050	618	33	0.1596	0.1596	NUM
ejpam-6050	618	34	s8	s8	VERB
ejpam-6050	618	35	0.1434	0.1434	NUM
ejpam-6050	618	36	s9	s9	NOUN
ejpam-6050	618	37	0.1458	0.1458	NUM
ejpam-6050	618	38	s10	s10	NOUN
ejpam-6050	618	39	0.1619	0.1619	NUM
ejpam-6050	618	40	table	table	NOUN
ejpam-6050	618	41	3	3	NUM
ejpam-6050	618	42	:	:	PUNCT
ejpam-6050	618	43	aggregated	aggregate	VERB
ejpam-6050	618	44	membership	membership	NOUN
ejpam-6050	618	45	values	value	NOUN
ejpam-6050	618	46	of	of	ADP
ejpam-6050	618	47	efs	ef	NOUN
ejpam-6050	618	48	the	the	DET
ejpam-6050	618	49	stock	stock	NOUN
ejpam-6050	618	50	with	with	ADP
ejpam-6050	618	51	the	the	DET
ejpam-6050	618	52	highest	high	ADJ
ejpam-6050	618	53	aggregated	aggregate	VERB
ejpam-6050	618	54	value	value	NOUN
ejpam-6050	618	55	in	in	ADP
ejpam-6050	618	56	table	table	NOUN
ejpam-6050	618	57	3	3	NUM
ejpam-6050	618	58	:	:	PUNCT
ejpam-6050	618	59	max	max	PROPN
ejpam-6050	618	60	s∈z	s∈z	NOUN
ejpam-6050	618	61	ℵe(s	ℵe(s	PUNCT
ejpam-6050	618	62	)	)	PUNCT
ejpam-6050	618	63	=	=	SYM
ejpam-6050	618	64	ℵe(s1	ℵe(s1	X
ejpam-6050	618	65	)	)	PUNCT
ejpam-6050	618	66	=	=	SYM
ejpam-6050	618	67	0.1784	0.1784	NUM
ejpam-6050	618	68	(	(	PUNCT
ejpam-6050	618	69	5.3	5.3	NUM
ejpam-6050	618	70	)	)	PUNCT
ejpam-6050	618	71	thus	thus	ADV
ejpam-6050	618	72	,	,	PUNCT
ejpam-6050	618	73	the	the	DET
ejpam-6050	618	74	best	good	ADJ
ejpam-6050	618	75	investment	investment	NOUN
ejpam-6050	618	76	decision	decision	NOUN
ejpam-6050	618	77	is	be	AUX
ejpam-6050	618	78	bonds	bond	NOUN
ejpam-6050	618	79	.	.	PUNCT
ejpam-6050	619	1	5.1	5.1	NUM
ejpam-6050	619	2	.	.	PUNCT
ejpam-6050	620	1	sensitivity	sensitivity	NOUN
ejpam-6050	620	2	analysis	analysis	NOUN
ejpam-6050	620	3	sensitivity	sensitivity	NOUN
ejpam-6050	620	4	analysis	analysis	NOUN
ejpam-6050	620	5	sensitivity	sensitivity	NOUN
ejpam-6050	620	6	analysis	analysis	NOUN
ejpam-6050	620	7	assists	assist	NOUN
ejpam-6050	620	8	in	in	ADP
ejpam-6050	620	9	assessing	assess	VERB
ejpam-6050	620	10	the	the	DET
ejpam-6050	620	11	effect	effect	NOUN
ejpam-6050	620	12	of	of	ADP
ejpam-6050	620	13	changes	change	NOUN
ejpam-6050	620	14	in	in	ADP
ejpam-6050	620	15	input	input	NOUN
ejpam-6050	620	16	parameters	parameter	NOUN
ejpam-6050	620	17	on	on	ADP
ejpam-6050	620	18	the	the	DET
ejpam-6050	620	19	investment	investment	NOUN
ejpam-6050	620	20	decision	decision	NOUN
ejpam-6050	620	21	.	.	PUNCT
ejpam-6050	621	1	by	by	ADP
ejpam-6050	621	2	varying	vary	VERB
ejpam-6050	621	3	expert	expert	NOUN
ejpam-6050	621	4	-	-	PUNCT
ejpam-6050	621	5	specified	specify	VERB
ejpam-6050	621	6	weights	weight	NOUN
ejpam-6050	621	7	or	or	CCONJ
ejpam-6050	621	8	m.	m.	NOUN
ejpam-6050	621	9	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	621	10	,	,	PUNCT
ejpam-6050	621	11	m.	m.	NOUN
ejpam-6050	621	12	rajeshwari	rajeshwari	NOUN
ejpam-6050	621	13	,	,	PUNCT
ejpam-6050	621	14	m.	m.	NOUN
ejpam-6050	621	15	alqahtani	alqahtani	PROPN
ejpam-6050	621	16	/	/	SYM
ejpam-6050	621	17	eur	eur	PROPN
ejpam-6050	621	18	.	.	PUNCT
ejpam-6050	622	1	j.	j.	PROPN
ejpam-6050	622	2	pure	pure	PROPN
ejpam-6050	622	3	appl	appl	PROPN
ejpam-6050	622	4	.	.	PROPN
ejpam-6050	622	5	math	math	PROPN
ejpam-6050	622	6	,	,	PUNCT
ejpam-6050	622	7	18	18	NUM
ejpam-6050	622	8	(	(	PUNCT
ejpam-6050	622	9	2	2	NUM
ejpam-6050	622	10	)	)	PUNCT
ejpam-6050	622	11	(	(	PUNCT
ejpam-6050	622	12	2025	2025	NUM
ejpam-6050	622	13	)	)	PUNCT
ejpam-6050	622	14	,	,	PUNCT
ejpam-6050	622	15	6050	6050	NUM
ejpam-6050	622	16	26	26	NUM
ejpam-6050	622	17	of	of	ADP
ejpam-6050	622	18	29	29	NUM
ejpam-6050	622	19	membership	membership	NOUN
ejpam-6050	622	20	values	value	NOUN
ejpam-6050	622	21	,	,	PUNCT
ejpam-6050	622	22	we	we	PRON
ejpam-6050	622	23	can	can	AUX
ejpam-6050	622	24	find	find	VERB
ejpam-6050	622	25	the	the	DET
ejpam-6050	622	26	stability	stability	NOUN
ejpam-6050	622	27	of	of	ADP
ejpam-6050	622	28	the	the	DET
ejpam-6050	622	29	exponential	exponential	ADJ
ejpam-6050	622	30	fuzzy	fuzzy	ADJ
ejpam-6050	622	31	investment	investment	NOUN
ejpam-6050	622	32	decision	decision	NOUN
ejpam-6050	622	33	system	system	NOUN
ejpam-6050	622	34	.	.	PUNCT
ejpam-6050	623	1	sensitivity	sensitivity	NOUN
ejpam-6050	623	2	analysis	analysis	NOUN
ejpam-6050	623	3	investigates	investigate	VERB
ejpam-6050	623	4	the	the	DET
ejpam-6050	623	5	effect	effect	NOUN
ejpam-6050	623	6	of	of	ADP
ejpam-6050	623	7	membership	membership	NOUN
ejpam-6050	623	8	value	value	NOUN
ejpam-6050	623	9	changes	change	NOUN
ejpam-6050	623	10	on	on	ADP
ejpam-6050	623	11	the	the	DET
ejpam-6050	623	12	investment	investment	NOUN
ejpam-6050	623	13	ranking	ranking	NOUN
ejpam-6050	623	14	.	.	PUNCT
ejpam-6050	624	1	5.1.1	5.1.1	X
ejpam-6050	624	2	.	.	PUNCT
ejpam-6050	624	3	initial	initial	ADJ
ejpam-6050	624	4	aggregation	aggregation	NOUN
ejpam-6050	624	5	analysis	analysis	NOUN
ejpam-6050	624	6	with	with	ADP
ejpam-6050	624	7	the	the	DET
ejpam-6050	624	8	fuzzy	fuzzy	ADJ
ejpam-6050	624	9	membership	membership	NOUN
ejpam-6050	624	10	values	value	NOUN
ejpam-6050	624	11	for	for	ADP
ejpam-6050	624	12	each	each	DET
ejpam-6050	624	13	stock	stock	NOUN
ejpam-6050	624	14	from	from	ADP
ejpam-6050	624	15	table	table	NOUN
ejpam-6050	624	16	2	2	NUM
ejpam-6050	624	17	,	,	PUNCT
ejpam-6050	624	18	the	the	DET
ejpam-6050	624	19	fuzzy	fuzzy	ADJ
ejpam-6050	624	20	aggregated	aggregate	VERB
ejpam-6050	624	21	value	value	NOUN
ejpam-6050	624	22	for	for	ADP
ejpam-6050	624	23	investment	investment	NOUN
ejpam-6050	624	24	decision	decision	NOUN
ejpam-6050	624	25	is	be	AUX
ejpam-6050	624	26	:	:	PUNCT
ejpam-6050	624	27	max	max	PROPN
ejpam-6050	624	28	s∈z	s∈z	NOUN
ejpam-6050	624	29	ℵe(s	ℵe(s	PUNCT
ejpam-6050	624	30	)	)	PUNCT
ejpam-6050	624	31	=	=	SYM
ejpam-6050	624	32	ℵe(s1	ℵe(s1	X
ejpam-6050	624	33	)	)	PUNCT
ejpam-6050	624	34	=	=	PUNCT
ejpam-6050	625	1	0.1784	0.1784	NUM
ejpam-6050	625	2	therefore	therefore	ADV
ejpam-6050	625	3	,	,	PUNCT
ejpam-6050	625	4	the	the	DET
ejpam-6050	625	5	optimal	optimal	ADJ
ejpam-6050	625	6	investment	investment	NOUN
ejpam-6050	625	7	choice	choice	NOUN
ejpam-6050	625	8	is	be	AUX
ejpam-6050	625	9	bonds	bond	NOUN
ejpam-6050	625	10	(	(	PUNCT
ejpam-6050	625	11	s1	s1	NOUN
ejpam-6050	625	12	)	)	PUNCT
ejpam-6050	625	13	.	.	PUNCT
ejpam-6050	626	1	5.1.2	5.1.2	X
ejpam-6050	626	2	.	.	PUNCT
ejpam-6050	626	3	scenario	scenario	NOUN
ejpam-6050	626	4	1	1	NUM
ejpam-6050	626	5	:	:	PUNCT
ejpam-6050	626	6	membership	membership	NOUN
ejpam-6050	626	7	value	value	NOUN
ejpam-6050	626	8	changes	change	NOUN
ejpam-6050	626	9	scenario	scenario	NOUN
ejpam-6050	626	10	1	1	NUM
ejpam-6050	626	11	:	:	PUNCT
ejpam-6050	626	12	membership	membership	NOUN
ejpam-6050	626	13	value	value	NOUN
ejpam-6050	626	14	changes	change	NOUN
ejpam-6050	626	15	to	to	PART
ejpam-6050	626	16	measure	measure	VERB
ejpam-6050	626	17	stability	stability	NOUN
ejpam-6050	626	18	,	,	PUNCT
ejpam-6050	626	19	we	we	PRON
ejpam-6050	626	20	adjust	adjust	VERB
ejpam-6050	626	21	the	the	DET
ejpam-6050	626	22	membership	membership	NOUN
ejpam-6050	626	23	values	value	NOUN
ejpam-6050	626	24	by	by	ADP
ejpam-6050	626	25	raising	raise	VERB
ejpam-6050	626	26	and	and	CCONJ
ejpam-6050	626	27	lowering	lower	VERB
ejpam-6050	626	28	each	each	DET
ejpam-6050	626	29	entry	entry	NOUN
ejpam-6050	626	30	by	by	ADP
ejpam-6050	626	31	5	5	NUM
ejpam-6050	626	32	%	%	NOUN
ejpam-6050	626	33	and	and	CCONJ
ejpam-6050	626	34	recompute	recompute	VERB
ejpam-6050	626	35	the	the	DET
ejpam-6050	626	36	aggregated	aggregate	VERB
ejpam-6050	626	37	values	value	NOUN
ejpam-6050	626	38	.	.	PUNCT
ejpam-6050	627	1	case	case	NOUN
ejpam-6050	627	2	1.1	1.1	NUM
ejpam-6050	627	3	:	:	PUNCT
ejpam-6050	627	4	raise	raise	VERB
ejpam-6050	627	5	membership	membership	NOUN
ejpam-6050	627	6	values	value	NOUN
ejpam-6050	627	7	by	by	ADP
ejpam-6050	627	8	5	5	NUM
ejpam-6050	627	9	%	%	NOUN
ejpam-6050	627	10	if	if	SCONJ
ejpam-6050	627	11	membership	membership	NOUN
ejpam-6050	627	12	values	value	NOUN
ejpam-6050	627	13	are	be	AUX
ejpam-6050	627	14	raised	raise	VERB
ejpam-6050	627	15	by	by	ADP
ejpam-6050	627	16	5	5	NUM
ejpam-6050	627	17	%	%	NOUN
ejpam-6050	627	18	,	,	PUNCT
ejpam-6050	627	19	new	new	ADJ
ejpam-6050	627	20	fuzzy	fuzzy	ADJ
ejpam-6050	627	21	values	value	NOUN
ejpam-6050	627	22	are	be	AUX
ejpam-6050	627	23	recomputed	recompute	VERB
ejpam-6050	627	24	,	,	PUNCT
ejpam-6050	627	25	and	and	CCONJ
ejpam-6050	627	26	the	the	DET
ejpam-6050	627	27	new	new	ADJ
ejpam-6050	627	28	maximum	maximum	ADJ
ejpam-6050	627	29	aggregated	aggregate	VERB
ejpam-6050	627	30	value	value	NOUN
ejpam-6050	627	31	is	be	AUX
ejpam-6050	627	32	:	:	PUNCT
ejpam-6050	627	33	max	max	PROPN
ejpam-6050	627	34	s∈z	s∈z	NOUN
ejpam-6050	627	35	ℵe(s	ℵe(s	PUNCT
ejpam-6050	627	36	)	)	PUNCT
ejpam-6050	627	37	=	=	PUNCT
ejpam-6050	627	38	ℵe(s1	ℵe(s1	NOUN
ejpam-6050	627	39	′	′	NUM
ejpam-6050	627	40	)	)	PUNCT
ejpam-6050	628	1	=	=	PUNCT
ejpam-6050	628	2	0.1832	0.1832	NUM
ejpam-6050	628	3	the	the	DET
ejpam-6050	628	4	best	good	ADJ
ejpam-6050	628	5	investment	investment	NOUN
ejpam-6050	628	6	choice	choice	NOUN
ejpam-6050	628	7	does	do	AUX
ejpam-6050	628	8	not	not	PART
ejpam-6050	628	9	change	change	VERB
ejpam-6050	628	10	bonds	bond	NOUN
ejpam-6050	628	11	(	(	PUNCT
ejpam-6050	628	12	s1	s1	NOUN
ejpam-6050	628	13	)	)	PUNCT
ejpam-6050	628	14	.	.	PUNCT
ejpam-6050	629	1	case	case	NOUN
ejpam-6050	629	2	1.2	1.2	NUM
ejpam-6050	629	3	:	:	PUNCT
ejpam-6050	629	4	lower	low	ADJ
ejpam-6050	629	5	membership	membership	NOUN
ejpam-6050	629	6	values	value	NOUN
ejpam-6050	629	7	by	by	ADP
ejpam-6050	629	8	5	5	NUM
ejpam-6050	629	9	%	%	NOUN
ejpam-6050	629	10	if	if	SCONJ
ejpam-6050	629	11	all	all	DET
ejpam-6050	629	12	membership	membership	NOUN
ejpam-6050	629	13	values	value	NOUN
ejpam-6050	629	14	are	be	AUX
ejpam-6050	629	15	reduced	reduce	VERB
ejpam-6050	629	16	by	by	ADP
ejpam-6050	629	17	5	5	NUM
ejpam-6050	629	18	%	%	NOUN
ejpam-6050	629	19	,	,	PUNCT
ejpam-6050	629	20	the	the	DET
ejpam-6050	629	21	new	new	ADJ
ejpam-6050	629	22	maximum	maximum	ADJ
ejpam-6050	629	23	aggregated	aggregate	VERB
ejpam-6050	629	24	value	value	NOUN
ejpam-6050	629	25	is	be	AUX
ejpam-6050	629	26	:	:	PUNCT
ejpam-6050	629	27	max	max	PROPN
ejpam-6050	629	28	s∈z	s∈z	NOUN
ejpam-6050	629	29	ℵe(s	ℵe(s	PUNCT
ejpam-6050	629	30	)	)	PUNCT
ejpam-6050	629	31	=	=	PUNCT
ejpam-6050	629	32	ℵe(s1	ℵe(s1	NUM
ejpam-6050	629	33	′′	′′	PROPN
ejpam-6050	629	34	)	)	PUNCT
ejpam-6050	630	1	=	=	PUNCT
ejpam-6050	631	1	0.1741	0.1741	NUM
ejpam-6050	631	2	once	once	ADV
ejpam-6050	631	3	again	again	ADV
ejpam-6050	631	4	,	,	PUNCT
ejpam-6050	631	5	bonds	bond	NOUN
ejpam-6050	631	6	(	(	PUNCT
ejpam-6050	631	7	s1	s1	NOUN
ejpam-6050	631	8	)	)	PUNCT
ejpam-6050	631	9	is	be	AUX
ejpam-6050	631	10	the	the	DET
ejpam-6050	631	11	best	good	ADJ
ejpam-6050	631	12	choice	choice	NOUN
ejpam-6050	631	13	.	.	PUNCT
ejpam-6050	632	1	scenario	scenario	NOUN
ejpam-6050	632	2	2	2	NUM
ejpam-6050	632	3	:	:	PUNCT
ejpam-6050	632	4	varying	vary	VERB
ejpam-6050	632	5	expert	expert	NOUN
ejpam-6050	632	6	weights	weight	NOUN
ejpam-6050	632	7	final	final	ADJ
ejpam-6050	632	8	ranking	ranking	NOUN
ejpam-6050	632	9	is	be	AUX
ejpam-6050	632	10	determined	determine	VERB
ejpam-6050	632	11	by	by	ADP
ejpam-6050	632	12	weights	weight	NOUN
ejpam-6050	632	13	allocated	allocate	VERB
ejpam-6050	632	14	to	to	ADP
ejpam-6050	632	15	investment	investment	NOUN
ejpam-6050	632	16	criteria	criterion	NOUN
ejpam-6050	632	17	.	.	PUNCT
ejpam-6050	633	1	let	let	VERB
ejpam-6050	633	2	’s	’s	PRON
ejpam-6050	633	3	assume	assume	VERB
ejpam-6050	633	4	two	two	NUM
ejpam-6050	633	5	varied	varied	ADJ
ejpam-6050	633	6	weight	weight	NOUN
ejpam-6050	633	7	scenarios	scenario	NOUN
ejpam-6050	633	8	case	case	NOUN
ejpam-6050	633	9	2.1	2.1	NUM
ejpam-6050	633	10	:	:	PUNCT
ejpam-6050	633	11	same	same	ADJ
ejpam-6050	633	12	weights	weight	NOUN
ejpam-6050	633	13	for	for	ADP
ejpam-6050	633	14	all	all	DET
ejpam-6050	633	15	factors	factor	NOUN
ejpam-6050	633	16	allocating	allocate	VERB
ejpam-6050	633	17	same	same	ADJ
ejpam-6050	633	18	weights	weight	NOUN
ejpam-6050	633	19	to	to	ADP
ejpam-6050	633	20	all	all	DET
ejpam-6050	633	21	three	three	NUM
ejpam-6050	633	22	fuzzy	fuzzy	ADJ
ejpam-6050	633	23	membership	membership	NOUN
ejpam-6050	633	24	values	value	NOUN
ejpam-6050	633	25	:	:	PUNCT
ejpam-6050	633	26	w1	w1	NOUN
ejpam-6050	633	27	=	=	PROPN
ejpam-6050	633	28	w2	w2	NOUN
ejpam-6050	633	29	=	=	PROPN
ejpam-6050	633	30	w3	w3	PROPN
ejpam-6050	633	31	=	=	PROPN
ejpam-6050	634	1	0.33	0.33	NUM
ejpam-6050	634	2	recalculating	recalculating	NOUN
ejpam-6050	634	3	aggregated	aggregate	VERB
ejpam-6050	634	4	values	value	NOUN
ejpam-6050	634	5	,	,	PUNCT
ejpam-6050	634	6	we	we	PRON
ejpam-6050	634	7	observe	observe	VERB
ejpam-6050	634	8	s1	s1	NOUN
ejpam-6050	634	9	continues	continue	VERB
ejpam-6050	634	10	to	to	PART
ejpam-6050	634	11	have	have	VERB
ejpam-6050	634	12	the	the	DET
ejpam-6050	634	13	maximum	maximum	ADJ
ejpam-6050	634	14	value	value	NOUN
ejpam-6050	634	15	,	,	PUNCT
ejpam-6050	634	16	verifying	verify	VERB
ejpam-6050	634	17	the	the	DET
ejpam-6050	634	18	consistency	consistency	NOUN
ejpam-6050	634	19	of	of	ADP
ejpam-6050	634	20	the	the	DET
ejpam-6050	634	21	decision	decision	NOUN
ejpam-6050	634	22	.	.	PUNCT
ejpam-6050	635	1	case	case	NOUN
ejpam-6050	635	2	2.2	2.2	NUM
ejpam-6050	635	3	:	:	PUNCT
ejpam-6050	635	4	increased	increase	VERB
ejpam-6050	635	5	weight	weight	NOUN
ejpam-6050	635	6	on	on	ADP
ejpam-6050	635	7	risk	risk	NOUN
ejpam-6050	635	8	factor	factor	NOUN
ejpam-6050	635	9	if	if	SCONJ
ejpam-6050	635	10	the	the	DET
ejpam-6050	635	11	expert	expert	NOUN
ejpam-6050	635	12	gives	give	VERB
ejpam-6050	635	13	greater	great	ADJ
ejpam-6050	635	14	weight	weight	NOUN
ejpam-6050	635	15	(	(	PUNCT
ejpam-6050	635	16	0.5	0.5	NUM
ejpam-6050	635	17	)	)	PUNCT
ejpam-6050	635	18	to	to	ADP
ejpam-6050	635	19	the	the	DET
ejpam-6050	635	20	risk	risk	NOUN
ejpam-6050	635	21	factor	factor	NOUN
ejpam-6050	635	22	but	but	CCONJ
ejpam-6050	635	23	leaves	leave	VERB
ejpam-6050	635	24	the	the	DET
ejpam-6050	635	25	others	other	NOUN
ejpam-6050	635	26	unchanged	unchanged	ADJ
ejpam-6050	635	27	at	at	ADP
ejpam-6050	635	28	0.25	0.25	NUM
ejpam-6050	635	29	,	,	PUNCT
ejpam-6050	635	30	the	the	DET
ejpam-6050	635	31	ranking	ranking	NOUN
ejpam-6050	635	32	is	be	AUX
ejpam-6050	635	33	slightly	slightly	ADV
ejpam-6050	635	34	different	different	ADJ
ejpam-6050	635	35	.	.	PUNCT
ejpam-6050	636	1	but	but	CCONJ
ejpam-6050	636	2	bonds	bond	NOUN
ejpam-6050	636	3	(	(	PUNCT
ejpam-6050	636	4	s1	s1	NOUN
ejpam-6050	636	5	)	)	PUNCT
ejpam-6050	636	6	is	be	AUX
ejpam-6050	636	7	still	still	ADV
ejpam-6050	636	8	among	among	ADP
ejpam-6050	636	9	the	the	DET
ejpam-6050	636	10	best	good	ADJ
ejpam-6050	636	11	investment	investment	NOUN
ejpam-6050	636	12	options	option	NOUN
ejpam-6050	636	13	.	.	PUNCT
ejpam-6050	637	1	m.	m.	NOUN
ejpam-6050	637	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	637	3	,	,	PUNCT
ejpam-6050	637	4	m.	m.	NOUN
ejpam-6050	637	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	637	6	,	,	PUNCT
ejpam-6050	637	7	m.	m.	NOUN
ejpam-6050	637	8	alqahtani	alqahtani	PROPN
ejpam-6050	637	9	/	/	SYM
ejpam-6050	637	10	eur	eur	PROPN
ejpam-6050	637	11	.	.	PUNCT
ejpam-6050	638	1	j.	j.	PROPN
ejpam-6050	638	2	pure	pure	PROPN
ejpam-6050	638	3	appl	appl	PROPN
ejpam-6050	638	4	.	.	PROPN
ejpam-6050	638	5	math	math	PROPN
ejpam-6050	638	6	,	,	PUNCT
ejpam-6050	638	7	18	18	NUM
ejpam-6050	638	8	(	(	PUNCT
ejpam-6050	638	9	2	2	NUM
ejpam-6050	638	10	)	)	PUNCT
ejpam-6050	638	11	(	(	PUNCT
ejpam-6050	638	12	2025	2025	NUM
ejpam-6050	638	13	)	)	PUNCT
ejpam-6050	638	14	,	,	PUNCT
ejpam-6050	638	15	6050	6050	NUM
ejpam-6050	638	16	27	27	NUM
ejpam-6050	638	17	of	of	ADP
ejpam-6050	638	18	29	29	NUM
ejpam-6050	638	19	figure	figure	NOUN
ejpam-6050	638	20	2	2	NUM
ejpam-6050	638	21	:	:	PUNCT
ejpam-6050	638	22	investment	investment	NOUN
ejpam-6050	638	23	:	:	PUNCT
ejpam-6050	638	24	stocks	stock	VERB
ejpam-6050	638	25	5.2	5.2	NUM
ejpam-6050	638	26	.	.	PUNCT
ejpam-6050	639	1	comparison	comparison	NOUN
ejpam-6050	639	2	analysis	analysis	NOUN
ejpam-6050	639	3	of	of	ADP
ejpam-6050	639	4	exponential	exponential	ADJ
ejpam-6050	639	5	fuzzy	fuzzy	ADJ
ejpam-6050	639	6	sets	set	NOUN
ejpam-6050	639	7	efs	ef	NOUN
ejpam-6050	639	8	with	with	ADP
ejpam-6050	639	9	traditional	traditional	ADJ
ejpam-6050	639	10	fuzzy	fuzzy	ADJ
ejpam-6050	639	11	models	model	NOUN
ejpam-6050	639	12	one	one	NUM
ejpam-6050	639	13	of	of	ADP
ejpam-6050	639	14	the	the	DET
ejpam-6050	639	15	key	key	ADJ
ejpam-6050	639	16	advantages	advantage	NOUN
ejpam-6050	639	17	of	of	ADP
ejpam-6050	639	18	efs	ef	NOUN
ejpam-6050	639	19	over	over	ADP
ejpam-6050	639	20	traditional	traditional	ADJ
ejpam-6050	639	21	fuzzy	fuzzy	ADJ
ejpam-6050	639	22	models	model	NOUN
ejpam-6050	639	23	is	be	AUX
ejpam-6050	639	24	their	their	PRON
ejpam-6050	639	25	ability	ability	NOUN
ejpam-6050	639	26	to	to	PART
ejpam-6050	639	27	handle	handle	VERB
ejpam-6050	639	28	uncertainty	uncertainty	NOUN
ejpam-6050	639	29	more	more	ADV
ejpam-6050	639	30	effectively	effectively	ADV
ejpam-6050	639	31	.	.	PUNCT
ejpam-6050	640	1	traditional	traditional	ADJ
ejpam-6050	640	2	fuzzy	fuzzy	ADJ
ejpam-6050	640	3	models	model	NOUN
ejpam-6050	640	4	assign	assign	VERB
ejpam-6050	640	5	a	a	DET
ejpam-6050	640	6	direct	direct	ADJ
ejpam-6050	640	7	membership	membership	NOUN
ejpam-6050	640	8	degree	degree	NOUN
ejpam-6050	640	9	to	to	ADP
ejpam-6050	640	10	an	an	DET
ejpam-6050	640	11	investment	investment	NOUN
ejpam-6050	640	12	option	option	NOUN
ejpam-6050	640	13	,	,	PUNCT
ejpam-6050	640	14	which	which	PRON
ejpam-6050	640	15	may	may	AUX
ejpam-6050	640	16	not	not	PART
ejpam-6050	640	17	fully	fully	ADV
ejpam-6050	640	18	capture	capture	VERB
ejpam-6050	640	19	the	the	DET
ejpam-6050	640	20	gradual	gradual	ADJ
ejpam-6050	640	21	decline	decline	NOUN
ejpam-6050	640	22	in	in	ADP
ejpam-6050	640	23	confidence	confidence	NOUN
ejpam-6050	640	24	as	as	SCONJ
ejpam-6050	640	25	uncertainty	uncertainty	NOUN
ejpam-6050	640	26	increases	increase	VERB
ejpam-6050	640	27	.	.	PUNCT
ejpam-6050	641	1	in	in	ADP
ejpam-6050	641	2	contrast	contrast	NOUN
ejpam-6050	641	3	,	,	PUNCT
ejpam-6050	641	4	efs	ef	NOUN
ejpam-6050	641	5	introduces	introduce	VERB
ejpam-6050	641	6	an	an	DET
ejpam-6050	641	7	exponential	exponential	ADJ
ejpam-6050	641	8	decay	decay	NOUN
ejpam-6050	641	9	function	function	NOUN
ejpam-6050	641	10	,	,	PUNCT
ejpam-6050	641	11	which	which	PRON
ejpam-6050	641	12	provides	provide	VERB
ejpam-6050	641	13	a	a	DET
ejpam-6050	641	14	more	more	ADV
ejpam-6050	641	15	refined	refined	ADJ
ejpam-6050	641	16	approach	approach	NOUN
ejpam-6050	641	17	to	to	ADP
ejpam-6050	641	18	uncertainty	uncertainty	NOUN
ejpam-6050	641	19	modeling	modeling	NOUN
ejpam-6050	641	20	.	.	PUNCT
ejpam-6050	642	1	this	this	PRON
ejpam-6050	642	2	is	be	AUX
ejpam-6050	642	3	particularly	particularly	ADV
ejpam-6050	642	4	beneficial	beneficial	ADJ
ejpam-6050	642	5	in	in	ADP
ejpam-6050	642	6	investment	investment	NOUN
ejpam-6050	642	7	decision	decision	NOUN
ejpam-6050	642	8	-	-	PUNCT
ejpam-6050	642	9	making	making	NOUN
ejpam-6050	642	10	,	,	PUNCT
ejpam-6050	642	11	where	where	SCONJ
ejpam-6050	642	12	risk	risk	NOUN
ejpam-6050	642	13	levels	level	NOUN
ejpam-6050	642	14	vary	vary	VERB
ejpam-6050	642	15	significantly	significantly	ADV
ejpam-6050	642	16	,	,	PUNCT
ejpam-6050	642	17	and	and	CCONJ
ejpam-6050	642	18	a	a	DET
ejpam-6050	642	19	more	more	ADV
ejpam-6050	642	20	nuanced	nuanced	ADJ
ejpam-6050	642	21	representation	representation	NOUN
ejpam-6050	642	22	of	of	ADP
ejpam-6050	642	23	uncertainty	uncertainty	NOUN
ejpam-6050	642	24	leads	lead	VERB
ejpam-6050	642	25	to	to	ADP
ejpam-6050	642	26	better	well	ADJ
ejpam-6050	642	27	investment	investment	NOUN
ejpam-6050	642	28	choices	choice	NOUN
ejpam-6050	642	29	.	.	PUNCT
ejpam-6050	643	1	flexibility	flexibility	NOUN
ejpam-6050	643	2	in	in	ADP
ejpam-6050	643	3	decision	decision	NOUN
ejpam-6050	643	4	-	-	PUNCT
ejpam-6050	643	5	making	making	NOUN
ejpam-6050	643	6	is	be	AUX
ejpam-6050	643	7	another	another	DET
ejpam-6050	643	8	critical	critical	ADJ
ejpam-6050	643	9	factor	factor	NOUN
ejpam-6050	643	10	where	where	SCONJ
ejpam-6050	643	11	efs	ef	VERB
ejpam-6050	643	12	outperforms	outperform	VERB
ejpam-6050	643	13	traditional	traditional	ADJ
ejpam-6050	643	14	fuzzy	fuzzy	ADJ
ejpam-6050	643	15	models	model	NOUN
ejpam-6050	643	16	.	.	PUNCT
ejpam-6050	644	1	traditional	traditional	ADJ
ejpam-6050	644	2	fuzzy	fuzzy	ADJ
ejpam-6050	644	3	logic	logic	NOUN
ejpam-6050	644	4	uses	use	VERB
ejpam-6050	644	5	a	a	DET
ejpam-6050	644	6	linear	linear	ADJ
ejpam-6050	644	7	membership	membership	NOUN
ejpam-6050	644	8	assignment	assignment	NOUN
ejpam-6050	644	9	,	,	PUNCT
ejpam-6050	644	10	making	make	VERB
ejpam-6050	644	11	it	it	PRON
ejpam-6050	644	12	less	less	ADV
ejpam-6050	644	13	adaptable	adaptable	ADJ
ejpam-6050	644	14	in	in	ADP
ejpam-6050	644	15	differentiating	differentiate	VERB
ejpam-6050	644	16	between	between	ADP
ejpam-6050	644	17	investments	investment	NOUN
ejpam-6050	644	18	with	with	ADP
ejpam-6050	644	19	similar	similar	ADJ
ejpam-6050	644	20	membership	membership	NOUN
ejpam-6050	644	21	values	value	NOUN
ejpam-6050	644	22	.	.	PUNCT
ejpam-6050	645	1	efs	ef	NOUN
ejpam-6050	645	2	,	,	PUNCT
ejpam-6050	645	3	however	however	ADV
ejpam-6050	645	4	,	,	PUNCT
ejpam-6050	645	5	applies	apply	VERB
ejpam-6050	645	6	an	an	DET
ejpam-6050	645	7	exponential	exponential	ADJ
ejpam-6050	645	8	transformation	transformation	NOUN
ejpam-6050	645	9	,	,	PUNCT
ejpam-6050	645	10	ensuring	ensure	VERB
ejpam-6050	645	11	a	a	DET
ejpam-6050	645	12	smoother	smooth	ADJ
ejpam-6050	645	13	transition	transition	NOUN
ejpam-6050	645	14	between	between	ADP
ejpam-6050	645	15	choices	choice	NOUN
ejpam-6050	645	16	.	.	PUNCT
ejpam-6050	646	1	this	this	PRON
ejpam-6050	646	2	allows	allow	VERB
ejpam-6050	646	3	for	for	ADP
ejpam-6050	646	4	a	a	DET
ejpam-6050	646	5	more	more	ADV
ejpam-6050	646	6	sensitive	sensitive	ADJ
ejpam-6050	646	7	response	response	NOUN
ejpam-6050	646	8	to	to	ADP
ejpam-6050	646	9	small	small	ADJ
ejpam-6050	646	10	variations	variation	NOUN
ejpam-6050	646	11	in	in	ADP
ejpam-6050	646	12	investment	investment	NOUN
ejpam-6050	646	13	attributes	attribute	NOUN
ejpam-6050	646	14	,	,	PUNCT
ejpam-6050	646	15	improving	improve	VERB
ejpam-6050	646	16	the	the	DET
ejpam-6050	646	17	accuracy	accuracy	NOUN
ejpam-6050	646	18	of	of	ADP
ejpam-6050	646	19	financial	financial	ADJ
ejpam-6050	646	20	assessments	assessment	NOUN
ejpam-6050	646	21	.	.	PUNCT
ejpam-6050	647	1	numerical	numerical	ADJ
ejpam-6050	647	2	stability	stability	NOUN
ejpam-6050	647	3	and	and	CCONJ
ejpam-6050	647	4	sensitivity	sensitivity	NOUN
ejpam-6050	647	5	analysis	analysis	NOUN
ejpam-6050	647	6	further	far	ADV
ejpam-6050	647	7	highlight	highlight	VERB
ejpam-6050	647	8	the	the	DET
ejpam-6050	647	9	advantages	advantage	NOUN
ejpam-6050	647	10	of	of	ADP
ejpam-6050	647	11	efs	ef	NOUN
ejpam-6050	647	12	.	.	PUNCT
ejpam-6050	648	1	traditional	traditional	ADJ
ejpam-6050	648	2	fuzzy	fuzzy	ADJ
ejpam-6050	648	3	models	model	NOUN
ejpam-6050	648	4	often	often	ADV
ejpam-6050	648	5	experience	experience	VERB
ejpam-6050	648	6	abrupt	abrupt	ADJ
ejpam-6050	648	7	shifts	shift	NOUN
ejpam-6050	648	8	in	in	ADP
ejpam-6050	648	9	decision	decision	NOUN
ejpam-6050	648	10	outcomes	outcome	NOUN
ejpam-6050	648	11	when	when	SCONJ
ejpam-6050	648	12	input	input	NOUN
ejpam-6050	648	13	data	data	NOUN
ejpam-6050	648	14	changes	change	NOUN
ejpam-6050	648	15	.	.	PUNCT
ejpam-6050	649	1	in	in	ADP
ejpam-6050	649	2	contrast	contrast	NOUN
ejpam-6050	649	3	,	,	PUNCT
ejpam-6050	649	4	efs	ef	NOUN
ejpam-6050	649	5	incorporates	incorporate	VERB
ejpam-6050	649	6	a	a	DET
ejpam-6050	649	7	sensitivity	sensitivity	NOUN
ejpam-6050	649	8	mechanism	mechanism	NOUN
ejpam-6050	649	9	that	that	PRON
ejpam-6050	649	10	stabilizes	stabilize	VERB
ejpam-6050	649	11	rankings	ranking	NOUN
ejpam-6050	649	12	even	even	ADV
ejpam-6050	649	13	with	with	ADP
ejpam-6050	649	14	small	small	ADJ
ejpam-6050	649	15	fluctuations	fluctuation	NOUN
ejpam-6050	649	16	in	in	ADP
ejpam-6050	649	17	the	the	DET
ejpam-6050	649	18	membership	membership	NOUN
ejpam-6050	649	19	values	value	NOUN
ejpam-6050	649	20	.	.	PUNCT
ejpam-6050	650	1	as	as	SCONJ
ejpam-6050	650	2	demonstrated	demonstrate	VERB
ejpam-6050	650	3	in	in	ADP
ejpam-6050	650	4	the	the	DET
ejpam-6050	650	5	sensitivity	sensitivity	NOUN
ejpam-6050	650	6	analysis	analysis	NOUN
ejpam-6050	650	7	,	,	PUNCT
ejpam-6050	650	8	adjusting	adjust	VERB
ejpam-6050	650	9	membership	membership	NOUN
ejpam-6050	650	10	values	value	NOUN
ejpam-6050	650	11	by	by	ADP
ejpam-6050	650	12	5	5	NUM
ejpam-6050	650	13	%	%	NOUN
ejpam-6050	650	14	does	do	AUX
ejpam-6050	650	15	not	not	PART
ejpam-6050	650	16	significantly	significantly	ADV
ejpam-6050	650	17	alter	alter	VERB
ejpam-6050	650	18	the	the	DET
ejpam-6050	650	19	ranking	ranking	NOUN
ejpam-6050	650	20	of	of	ADP
ejpam-6050	650	21	the	the	DET
ejpam-6050	650	22	best	good	ADJ
ejpam-6050	650	23	investment	investment	NOUN
ejpam-6050	650	24	choice	choice	NOUN
ejpam-6050	650	25	in	in	ADP
ejpam-6050	650	26	the	the	DET
ejpam-6050	650	27	efs	ef	NOUN
ejpam-6050	650	28	model	model	NOUN
ejpam-6050	650	29	,	,	PUNCT
ejpam-6050	650	30	confirming	confirm	VERB
ejpam-6050	650	31	its	its	PRON
ejpam-6050	650	32	robustness	robustness	NOUN
ejpam-6050	650	33	in	in	ADP
ejpam-6050	650	34	real	real	ADJ
ejpam-6050	650	35	-	-	PUNCT
ejpam-6050	650	36	world	world	NOUN
ejpam-6050	650	37	applications	application	NOUN
ejpam-6050	650	38	.	.	PUNCT
ejpam-6050	651	1	a	a	DET
ejpam-6050	651	2	graphical	graphical	ADJ
ejpam-6050	651	3	comparison	comparison	NOUN
ejpam-6050	651	4	further	far	ADV
ejpam-6050	651	5	strengthens	strengthen	VERB
ejpam-6050	651	6	the	the	DET
ejpam-6050	651	7	argument	argument	NOUN
ejpam-6050	651	8	for	for	ADP
ejpam-6050	651	9	efs	ef	NOUN
ejpam-6050	651	10	.	.	PUNCT
ejpam-6050	652	1	in	in	ADP
ejpam-6050	652	2	a	a	DET
ejpam-6050	652	3	traditional	traditional	ADJ
ejpam-6050	652	4	fuzzy	fuzzy	ADJ
ejpam-6050	652	5	model	model	NOUN
ejpam-6050	652	6	,	,	PUNCT
ejpam-6050	652	7	membership	membership	NOUN
ejpam-6050	652	8	values	value	NOUN
ejpam-6050	652	9	are	be	AUX
ejpam-6050	652	10	assigned	assign	VERB
ejpam-6050	652	11	directly	directly	ADV
ejpam-6050	652	12	,	,	PUNCT
ejpam-6050	652	13	leading	lead	VERB
ejpam-6050	652	14	to	to	ADP
ejpam-6050	652	15	a	a	DET
ejpam-6050	652	16	more	more	ADV
ejpam-6050	652	17	rigid	rigid	ADJ
ejpam-6050	652	18	classification	classification	NOUN
ejpam-6050	652	19	of	of	ADP
ejpam-6050	652	20	investment	investment	NOUN
ejpam-6050	652	21	options	option	NOUN
ejpam-6050	652	22	.	.	PUNCT
ejpam-6050	653	1	the	the	DET
ejpam-6050	653	2	efs	efs	PROPN
ejpam-6050	653	3	model	model	NOUN
ejpam-6050	653	4	,	,	PUNCT
ejpam-6050	653	5	however	however	ADV
ejpam-6050	653	6	,	,	PUNCT
ejpam-6050	653	7	applies	apply	VERB
ejpam-6050	653	8	an	an	DET
ejpam-6050	653	9	exponential	exponential	ADJ
ejpam-6050	653	10	transm	transm	PROPN
ejpam-6050	653	11	.	.	PUNCT
ejpam-6050	654	1	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	654	2	,	,	PUNCT
ejpam-6050	654	3	m.	m.	NOUN
ejpam-6050	654	4	rajeshwari	rajeshwari	NOUN
ejpam-6050	654	5	,	,	PUNCT
ejpam-6050	654	6	m.	m.	NOUN
ejpam-6050	654	7	alqahtani	alqahtani	PROPN
ejpam-6050	654	8	/	/	SYM
ejpam-6050	654	9	eur	eur	PROPN
ejpam-6050	654	10	.	.	PUNCT
ejpam-6050	655	1	j.	j.	PROPN
ejpam-6050	655	2	pure	pure	PROPN
ejpam-6050	655	3	appl	appl	PROPN
ejpam-6050	655	4	.	.	PROPN
ejpam-6050	655	5	math	math	PROPN
ejpam-6050	655	6	,	,	PUNCT
ejpam-6050	655	7	18	18	NUM
ejpam-6050	655	8	(	(	PUNCT
ejpam-6050	655	9	2	2	NUM
ejpam-6050	655	10	)	)	PUNCT
ejpam-6050	655	11	(	(	PUNCT
ejpam-6050	655	12	2025	2025	NUM
ejpam-6050	655	13	)	)	PUNCT
ejpam-6050	655	14	,	,	PUNCT
ejpam-6050	655	15	6050	6050	NUM
ejpam-6050	655	16	28	28	NUM
ejpam-6050	655	17	of	of	ADP
ejpam-6050	655	18	29	29	NUM
ejpam-6050	655	19	formation	formation	NOUN
ejpam-6050	655	20	that	that	PRON
ejpam-6050	655	21	results	result	VERB
ejpam-6050	655	22	in	in	ADP
ejpam-6050	655	23	a	a	DET
ejpam-6050	655	24	sharper	sharp	ADJ
ejpam-6050	655	25	differentiation	differentiation	NOUN
ejpam-6050	655	26	of	of	ADP
ejpam-6050	655	27	choices	choice	NOUN
ejpam-6050	655	28	.	.	PUNCT
ejpam-6050	656	1	this	this	PRON
ejpam-6050	656	2	means	mean	VERB
ejpam-6050	656	3	that	that	SCONJ
ejpam-6050	656	4	efs	ef	NOUN
ejpam-6050	656	5	can	can	AUX
ejpam-6050	656	6	more	more	ADV
ejpam-6050	656	7	effectively	effectively	ADV
ejpam-6050	656	8	distinguish	distinguish	VERB
ejpam-6050	656	9	between	between	ADP
ejpam-6050	656	10	investments	investment	NOUN
ejpam-6050	656	11	with	with	ADP
ejpam-6050	656	12	slight	slight	ADJ
ejpam-6050	656	13	variations	variation	NOUN
ejpam-6050	656	14	in	in	ADP
ejpam-6050	656	15	risk	risk	NOUN
ejpam-6050	656	16	and	and	CCONJ
ejpam-6050	656	17	return	return	NOUN
ejpam-6050	656	18	,	,	PUNCT
ejpam-6050	656	19	leading	lead	VERB
ejpam-6050	656	20	to	to	ADP
ejpam-6050	656	21	more	more	ADV
ejpam-6050	656	22	precise	precise	ADJ
ejpam-6050	656	23	decision	decision	NOUN
ejpam-6050	656	24	-	-	PUNCT
ejpam-6050	656	25	making	making	NOUN
ejpam-6050	656	26	.	.	PUNCT
ejpam-6050	657	1	finally	finally	ADV
ejpam-6050	657	2	,	,	PUNCT
ejpam-6050	657	3	in	in	ADP
ejpam-6050	657	4	practical	practical	ADJ
ejpam-6050	657	5	applications	application	NOUN
ejpam-6050	657	6	,	,	PUNCT
ejpam-6050	657	7	efs	ef	NOUN
ejpam-6050	657	8	proves	prove	VERB
ejpam-6050	657	9	to	to	PART
ejpam-6050	657	10	be	be	AUX
ejpam-6050	657	11	a	a	DET
ejpam-6050	657	12	more	more	ADV
ejpam-6050	657	13	effective	effective	ADJ
ejpam-6050	657	14	tool	tool	NOUN
ejpam-6050	657	15	for	for	ADP
ejpam-6050	657	16	investment	investment	NOUN
ejpam-6050	657	17	decision	decision	NOUN
ejpam-6050	657	18	-	-	PUNCT
ejpam-6050	657	19	making	making	NOUN
ejpam-6050	657	20	.	.	PUNCT
ejpam-6050	658	1	traditional	traditional	ADJ
ejpam-6050	658	2	fuzzy	fuzzy	ADJ
ejpam-6050	658	3	models	model	NOUN
ejpam-6050	658	4	rely	rely	VERB
ejpam-6050	658	5	on	on	ADP
ejpam-6050	658	6	fixed	fix	VERB
ejpam-6050	658	7	weight	weight	NOUN
ejpam-6050	658	8	allocations	allocation	NOUN
ejpam-6050	658	9	and	and	CCONJ
ejpam-6050	658	10	may	may	AUX
ejpam-6050	658	11	struggle	struggle	VERB
ejpam-6050	658	12	in	in	ADP
ejpam-6050	658	13	highly	highly	ADV
ejpam-6050	658	14	uncertain	uncertain	ADJ
ejpam-6050	658	15	investment	investment	NOUN
ejpam-6050	658	16	environments	environment	NOUN
ejpam-6050	658	17	.	.	PUNCT
ejpam-6050	659	1	efs	ef	NOUN
ejpam-6050	659	2	,	,	PUNCT
ejpam-6050	659	3	by	by	ADP
ejpam-6050	659	4	incorporating	incorporate	VERB
ejpam-6050	659	5	an	an	DET
ejpam-6050	659	6	exponential	exponential	ADJ
ejpam-6050	659	7	factor	factor	NOUN
ejpam-6050	659	8	,	,	PUNCT
ejpam-6050	659	9	ensures	ensure	VERB
ejpam-6050	659	10	a	a	DET
ejpam-6050	659	11	more	more	ADV
ejpam-6050	659	12	dynamic	dynamic	ADJ
ejpam-6050	659	13	and	and	CCONJ
ejpam-6050	659	14	realistic	realistic	ADJ
ejpam-6050	659	15	risk	risk	NOUN
ejpam-6050	659	16	assessment	assessment	NOUN
ejpam-6050	659	17	.	.	PUNCT
ejpam-6050	660	1	this	this	DET
ejpam-6050	660	2	feature	feature	NOUN
ejpam-6050	660	3	makes	make	VERB
ejpam-6050	660	4	it	it	PRON
ejpam-6050	660	5	particularly	particularly	ADV
ejpam-6050	660	6	useful	useful	ADJ
ejpam-6050	660	7	for	for	ADP
ejpam-6050	660	8	financial	financial	ADJ
ejpam-6050	660	9	forecasting	forecasting	NOUN
ejpam-6050	660	10	,	,	PUNCT
ejpam-6050	660	11	portfolio	portfolio	NOUN
ejpam-6050	660	12	optimization	optimization	NOUN
ejpam-6050	660	13	,	,	PUNCT
ejpam-6050	660	14	and	and	CCONJ
ejpam-6050	660	15	strategic	strategic	ADJ
ejpam-6050	660	16	investment	investment	NOUN
ejpam-6050	660	17	planning	planning	NOUN
ejpam-6050	660	18	.	.	PUNCT
ejpam-6050	661	1	by	by	ADP
ejpam-6050	661	2	improving	improve	VERB
ejpam-6050	661	3	uncertainty	uncertainty	NOUN
ejpam-6050	661	4	management	management	NOUN
ejpam-6050	661	5	and	and	CCONJ
ejpam-6050	661	6	decision	decision	NOUN
ejpam-6050	661	7	flexibility	flexibility	NOUN
ejpam-6050	661	8	,	,	PUNCT
ejpam-6050	661	9	efs	ef	NOUN
ejpam-6050	661	10	provides	provide	VERB
ejpam-6050	661	11	investors	investor	NOUN
ejpam-6050	661	12	with	with	ADP
ejpam-6050	661	13	a	a	DET
ejpam-6050	661	14	more	more	ADV
ejpam-6050	661	15	reliable	reliable	ADJ
ejpam-6050	661	16	approach	approach	NOUN
ejpam-6050	661	17	to	to	ADP
ejpam-6050	661	18	selecting	select	VERB
ejpam-6050	661	19	optimal	optimal	ADJ
ejpam-6050	661	20	investment	investment	NOUN
ejpam-6050	661	21	schemes	scheme	NOUN
ejpam-6050	661	22	.	.	PUNCT
ejpam-6050	662	1	6	6	X
ejpam-6050	662	2	.	.	X
ejpam-6050	662	3	conclusion	conclusion	NOUN
ejpam-6050	662	4	the	the	DET
ejpam-6050	662	5	efs	ef	NOUN
ejpam-6050	662	6	offers	offer	VERB
ejpam-6050	662	7	a	a	DET
ejpam-6050	662	8	strong	strong	ADJ
ejpam-6050	662	9	tool	tool	NOUN
ejpam-6050	662	10	for	for	ADP
ejpam-6050	662	11	managing	manage	VERB
ejpam-6050	662	12	uncertainty	uncertainty	NOUN
ejpam-6050	662	13	in	in	ADP
ejpam-6050	662	14	mathematical	mathematical	ADJ
ejpam-6050	662	15	modeling	modeling	NOUN
ejpam-6050	662	16	and	and	CCONJ
ejpam-6050	662	17	decision	decision	NOUN
ejpam-6050	662	18	-	-	PUNCT
ejpam-6050	662	19	making	making	NOUN
ejpam-6050	662	20	.	.	PUNCT
ejpam-6050	663	1	with	with	ADP
ejpam-6050	663	2	the	the	DET
ejpam-6050	663	3	use	use	NOUN
ejpam-6050	663	4	of	of	ADP
ejpam-6050	663	5	an	an	DET
ejpam-6050	663	6	exponential	exponential	ADJ
ejpam-6050	663	7	membership	membership	NOUN
ejpam-6050	663	8	function	function	NOUN
ejpam-6050	663	9	,	,	PUNCT
ejpam-6050	663	10	efs	ef	NOUN
ejpam-6050	663	11	successfully	successfully	ADV
ejpam-6050	663	12	describes	describe	VERB
ejpam-6050	663	13	systems	system	NOUN
ejpam-6050	663	14	with	with	ADP
ejpam-6050	663	15	high	high	ADJ
ejpam-6050	663	16	uncertainty	uncertainty	NOUN
ejpam-6050	663	17	rates	rate	NOUN
ejpam-6050	663	18	of	of	ADP
ejpam-6050	663	19	change	change	NOUN
ejpam-6050	663	20	.	.	PUNCT
ejpam-6050	664	1	this	this	DET
ejpam-6050	664	2	paper	paper	NOUN
ejpam-6050	664	3	has	have	AUX
ejpam-6050	664	4	discussed	discuss	VERB
ejpam-6050	664	5	the	the	DET
ejpam-6050	664	6	basic	basic	ADJ
ejpam-6050	664	7	properties	property	NOUN
ejpam-6050	664	8	and	and	CCONJ
ejpam-6050	664	9	operations	operation	NOUN
ejpam-6050	664	10	of	of	ADP
ejpam-6050	664	11	efs	ef	NOUN
ejpam-6050	664	12	,	,	PUNCT
ejpam-6050	664	13	as	as	ADV
ejpam-6050	664	14	well	well	ADV
ejpam-6050	664	15	as	as	ADP
ejpam-6050	664	16	its	its	PRON
ejpam-6050	664	17	uses	use	NOUN
ejpam-6050	664	18	in	in	ADP
ejpam-6050	664	19	ai	ai	ADV
ejpam-6050	664	20	-	-	PUNCT
ejpam-6050	664	21	based	base	VERB
ejpam-6050	664	22	investment	investment	NOUN
ejpam-6050	664	23	decisions	decision	NOUN
ejpam-6050	664	24	.	.	PUNCT
ejpam-6050	665	1	our	our	PRON
ejpam-6050	665	2	exponential	exponential	ADJ
ejpam-6050	665	3	fuzzy	fuzzy	ADJ
ejpam-6050	665	4	investment	investment	NOUN
ejpam-6050	665	5	decision	decision	NOUN
ejpam-6050	665	6	system	system	NOUN
ejpam-6050	665	7	showcases	showcase	VERB
ejpam-6050	665	8	the	the	DET
ejpam-6050	665	9	strengths	strength	NOUN
ejpam-6050	665	10	of	of	ADP
ejpam-6050	665	11	efs	ef	NOUN
ejpam-6050	665	12	in	in	ADP
ejpam-6050	665	13	making	make	VERB
ejpam-6050	665	14	optimal	optimal	ADJ
ejpam-6050	665	15	investment	investment	NOUN
ejpam-6050	665	16	decisions	decision	NOUN
ejpam-6050	665	17	.	.	PUNCT
ejpam-6050	666	1	compared	compare	VERB
ejpam-6050	666	2	to	to	ADP
ejpam-6050	666	3	conventional	conventional	ADJ
ejpam-6050	666	4	fuzzy	fuzzy	ADJ
ejpam-6050	666	5	models	model	NOUN
ejpam-6050	666	6	,	,	PUNCT
ejpam-6050	666	7	efs	ef	NOUN
ejpam-6050	666	8	supports	support	VERB
ejpam-6050	666	9	more	more	ADV
ejpam-6050	666	10	accurate	accurate	ADJ
ejpam-6050	666	11	and	and	CCONJ
ejpam-6050	666	12	dynamic	dynamic	ADJ
ejpam-6050	666	13	decision	decision	NOUN
ejpam-6050	666	14	-	-	PUNCT
ejpam-6050	666	15	making	making	NOUN
ejpam-6050	666	16	,	,	PUNCT
ejpam-6050	666	17	especially	especially	ADV
ejpam-6050	666	18	in	in	ADP
ejpam-6050	666	19	unstable	unstable	ADJ
ejpam-6050	666	20	financial	financial	ADJ
ejpam-6050	666	21	markets	market	NOUN
ejpam-6050	666	22	.	.	PUNCT
ejpam-6050	667	1	the	the	DET
ejpam-6050	667	2	integration	integration	NOUN
ejpam-6050	667	3	of	of	ADP
ejpam-6050	667	4	the	the	DET
ejpam-6050	667	5	weighted	weight	VERB
ejpam-6050	667	6	mean	mean	NOUN
ejpam-6050	667	7	method	method	NOUN
ejpam-6050	667	8	within	within	ADP
ejpam-6050	667	9	the	the	DET
ejpam-6050	667	10	efs	ef	NOUN
ejpam-6050	667	11	system	system	NOUN
ejpam-6050	667	12	maximizes	maximize	VERB
ejpam-6050	667	13	investment	investment	NOUN
ejpam-6050	667	14	analysis	analysis	NOUN
ejpam-6050	667	15	by	by	ADP
ejpam-6050	667	16	combining	combine	VERB
ejpam-6050	667	17	expert	expert	ADJ
ejpam-6050	667	18	opinions	opinion	NOUN
ejpam-6050	667	19	efficiently	efficiently	ADV
ejpam-6050	667	20	.	.	PUNCT
ejpam-6050	668	1	6.1	6.1	NUM
ejpam-6050	668	2	.	.	PUNCT
ejpam-6050	669	1	future	future	ADJ
ejpam-6050	669	2	research	research	NOUN
ejpam-6050	669	3	directions	direction	NOUN
ejpam-6050	669	4	the	the	DET
ejpam-6050	669	5	efs	ef	NOUN
ejpam-6050	669	6	concept	concept	NOUN
ejpam-6050	669	7	we	we	PRON
ejpam-6050	669	8	can	can	AUX
ejpam-6050	669	9	extend	extend	VERB
ejpam-6050	669	10	in	in	ADP
ejpam-6050	669	11	intuitionistic	intuitionistic	ADJ
ejpam-6050	669	12	fuzzy	fuzzy	ADJ
ejpam-6050	669	13	set	set	NOUN
ejpam-6050	669	14	,	,	PUNCT
ejpam-6050	669	15	neutrosophic	neutrosophic	ADJ
ejpam-6050	669	16	fuzzy	fuzzy	NOUN
ejpam-6050	669	17	set	set	VERB
ejpam-6050	669	18	all	all	DET
ejpam-6050	669	19	areas	area	NOUN
ejpam-6050	669	20	like	like	ADP
ejpam-6050	669	21	graph	graph	NOUN
ejpam-6050	669	22	theory	theory	NOUN
ejpam-6050	669	23	,	,	PUNCT
ejpam-6050	669	24	bci	bci	PROPN
ejpam-6050	669	25	algebra	algebra	NOUN
ejpam-6050	669	26	and	and	CCONJ
ejpam-6050	669	27	different	different	ADJ
ejpam-6050	669	28	type	type	NOUN
ejpam-6050	669	29	of	of	ADP
ejpam-6050	669	30	algebras	algebras	PROPN
ejpam-6050	669	31	.	.	PUNCT
ejpam-6050	670	1	then	then	ADV
ejpam-6050	670	2	decision	decision	VERB
ejpam-6050	670	3	making	make	VERB
ejpam-6050	670	4	problems	problem	NOUN
ejpam-6050	670	5	.	.	PUNCT
ejpam-6050	671	1	references	reference	NOUN
ejpam-6050	671	2	[	[	X
ejpam-6050	671	3	1	1	NUM
ejpam-6050	671	4	]	]	PUNCT
ejpam-6050	671	5	l.	l.	PROPN
ejpam-6050	671	6	a.	a.	PROPN
ejpam-6050	671	7	zadeh	zadeh	PROPN
ejpam-6050	671	8	.	.	PUNCT
ejpam-6050	672	1	fuzzy	fuzzy	ADJ
ejpam-6050	672	2	sets	set	NOUN
ejpam-6050	672	3	.	.	PUNCT
ejpam-6050	673	1	information	information	NOUN
ejpam-6050	673	2	and	and	CCONJ
ejpam-6050	673	3	control	control	NOUN
ejpam-6050	673	4	,	,	PUNCT
ejpam-6050	673	5	8(3):338–353	8(3):338–353	NUM
ejpam-6050	673	6	,	,	PUNCT
ejpam-6050	673	7	1985	1985	NUM
ejpam-6050	673	8	.	.	PUNCT
ejpam-6050	674	1	[	[	X
ejpam-6050	674	2	2	2	X
ejpam-6050	674	3	]	]	PUNCT
ejpam-6050	674	4	k.	k.	PROPN
ejpam-6050	674	5	t.	t.	PROPN
ejpam-6050	674	6	atanassov	atanassov	PROPN
ejpam-6050	674	7	.	.	PUNCT
ejpam-6050	675	1	intuitionistic	intuitionistic	ADJ
ejpam-6050	675	2	fuzzy	fuzzy	ADJ
ejpam-6050	675	3	sets	set	NOUN
ejpam-6050	675	4	.	.	PUNCT
ejpam-6050	676	1	fuzzy	fuzzy	ADJ
ejpam-6050	676	2	sets	set	NOUN
ejpam-6050	676	3	and	and	CCONJ
ejpam-6050	676	4	systems	system	NOUN
ejpam-6050	676	5	,	,	PUNCT
ejpam-6050	676	6	20:87–96	20:87–96	NUM
ejpam-6050	676	7	,	,	PUNCT
ejpam-6050	676	8	1986	1986	NUM
ejpam-6050	676	9	.	.	PUNCT
ejpam-6050	677	1	[	[	X
ejpam-6050	677	2	3	3	X
ejpam-6050	677	3	]	]	X
ejpam-6050	677	4	m.	m.	NOUN
ejpam-6050	677	5	abdel	abdel	PROPN
ejpam-6050	677	6	-	-	PUNCT
ejpam-6050	677	7	basset	basset	PROPN
ejpam-6050	677	8	,	,	PUNCT
ejpam-6050	677	9	m.	m.	NOUN
ejpam-6050	677	10	mohamed	mohamed	PROPN
ejpam-6050	677	11	,	,	PUNCT
ejpam-6050	677	12	and	and	CCONJ
ejpam-6050	677	13	a.	a.	PROPN
ejpam-6050	677	14	k.	k.	PROPN
ejpam-6050	677	15	sangaiah	sangaiah	PROPN
ejpam-6050	677	16	.	.	PUNCT
ejpam-6050	678	1	neutrosophic	neutrosophic	PROPN
ejpam-6050	678	2	ahp	ahp	PROPN
ejpam-6050	678	3	-	-	PUNCT
ejpam-6050	678	4	delphi	delphi	NOUN
ejpam-6050	678	5	group	group	NOUN
ejpam-6050	678	6	decision	decision	NOUN
ejpam-6050	678	7	-	-	PUNCT
ejpam-6050	678	8	making	make	VERB
ejpam-6050	678	9	model	model	NOUN
ejpam-6050	678	10	based	base	VERB
ejpam-6050	678	11	on	on	ADP
ejpam-6050	678	12	trapezoidal	trapezoidal	ADJ
ejpam-6050	678	13	neutrosophic	neutrosophic	ADJ
ejpam-6050	678	14	numbers	number	NOUN
ejpam-6050	678	15	.	.	PUNCT
ejpam-6050	679	1	journal	journal	PROPN
ejpam-6050	679	2	of	of	ADP
ejpam-6050	679	3	ambient	ambient	ADJ
ejpam-6050	679	4	intelligence	intelligence	NOUN
ejpam-6050	679	5	and	and	CCONJ
ejpam-6050	679	6	humanized	humanize	VERB
ejpam-6050	679	7	computing	computing	NOUN
ejpam-6050	679	8	,	,	PUNCT
ejpam-6050	679	9	9:1427–1443	9:1427–1443	NUM
ejpam-6050	679	10	,	,	PUNCT
ejpam-6050	679	11	2018	2018	NUM
ejpam-6050	679	12	.	.	PUNCT
ejpam-6050	680	1	[	[	X
ejpam-6050	680	2	4	4	X
ejpam-6050	680	3	]	]	PUNCT
ejpam-6050	680	4	k.	k.	PROPN
ejpam-6050	680	5	t.	t.	PROPN
ejpam-6050	680	6	atanassov	atanassov	PROPN
ejpam-6050	680	7	.	.	PUNCT
ejpam-6050	681	1	on	on	ADP
ejpam-6050	681	2	intuitionistic	intuitionistic	ADJ
ejpam-6050	681	3	fuzzy	fuzzy	ADJ
ejpam-6050	681	4	sets	set	NOUN
ejpam-6050	681	5	theory	theory	NOUN
ejpam-6050	681	6	.	.	PUNCT
ejpam-6050	682	1	springer	springer	PROPN
ejpam-6050	682	2	berlin	berlin	PROPN
ejpam-6050	682	3	,	,	PUNCT
ejpam-6050	682	4	heidelberg	heidelberg	PROPN
ejpam-6050	682	5	,	,	PUNCT
ejpam-6050	682	6	2012	2012	NUM
ejpam-6050	682	7	.	.	PUNCT
ejpam-6050	683	1	[	[	X
ejpam-6050	683	2	5	5	X
ejpam-6050	683	3	]	]	PUNCT
ejpam-6050	683	4	t.	t.	PROPN
ejpam-6050	683	5	garai	garai	PROPN
ejpam-6050	683	6	,	,	PUNCT
ejpam-6050	683	7	d.	d.	PROPN
ejpam-6050	683	8	chakraborty	chakraborty	PROPN
ejpam-6050	683	9	,	,	PUNCT
ejpam-6050	683	10	and	and	CCONJ
ejpam-6050	683	11	t.	t.	PROPN
ejpam-6050	683	12	k.	k.	PROPN
ejpam-6050	683	13	roy	roy	PROPN
ejpam-6050	683	14	.	.	PROPN
ejpam-6050	683	15	expected	expect	VERB
ejpam-6050	683	16	value	value	NOUN
ejpam-6050	683	17	of	of	ADP
ejpam-6050	683	18	exponential	exponential	ADJ
ejpam-6050	683	19	fuzzy	fuzzy	ADJ
ejpam-6050	683	20	number	number	NOUN
ejpam-6050	683	21	and	and	CCONJ
ejpam-6050	683	22	its	its	PRON
ejpam-6050	683	23	application	application	NOUN
ejpam-6050	683	24	to	to	ADP
ejpam-6050	683	25	multi	multi	ADJ
ejpam-6050	683	26	-	-	ADJ
ejpam-6050	683	27	item	item	ADJ
ejpam-6050	683	28	deterministic	deterministic	ADJ
ejpam-6050	683	29	inventory	inventory	NOUN
ejpam-6050	683	30	model	model	NOUN
ejpam-6050	683	31	for	for	ADP
ejpam-6050	683	32	deteriorating	deteriorate	VERB
ejpam-6050	683	33	items	item	NOUN
ejpam-6050	683	34	.	.	PUNCT
ejpam-6050	684	1	journal	journal	NOUN
ejpam-6050	684	2	of	of	ADP
ejpam-6050	684	3	uncertainty	uncertainty	NOUN
ejpam-6050	684	4	analysis	analysis	NOUN
ejpam-6050	684	5	and	and	CCONJ
ejpam-6050	684	6	applications	application	NOUN
ejpam-6050	684	7	,	,	PUNCT
ejpam-6050	684	8	5:1–20	5:1–20	NUM
ejpam-6050	684	9	,	,	PUNCT
ejpam-6050	684	10	2017	2017	NUM
ejpam-6050	684	11	.	.	PUNCT
ejpam-6050	685	1	[	[	X
ejpam-6050	685	2	6	6	X
ejpam-6050	685	3	]	]	PUNCT
ejpam-6050	685	4	v.	v.	ADP
ejpam-6050	685	5	p.	p.	PROPN
ejpam-6050	685	6	tomar	tomar	PROPN
ejpam-6050	685	7	and	and	CCONJ
ejpam-6050	685	8	a.	a.	NOUN
ejpam-6050	685	9	ohlan	ohlan	PROPN
ejpam-6050	685	10	.	.	PUNCT
ejpam-6050	686	1	new	new	ADJ
ejpam-6050	686	2	parametric	parametric	ADJ
ejpam-6050	686	3	generalized	generalize	VERB
ejpam-6050	686	4	exponential	exponential	ADJ
ejpam-6050	686	5	fuzzy	fuzzy	ADJ
ejpam-6050	686	6	divergence	divergence	NOUN
ejpam-6050	686	7	measure	measure	NOUN
ejpam-6050	686	8	.	.	PUNCT
ejpam-6050	687	1	journal	journal	NOUN
ejpam-6050	687	2	of	of	ADP
ejpam-6050	687	3	uncertainty	uncertainty	NOUN
ejpam-6050	687	4	analysis	analysis	NOUN
ejpam-6050	687	5	and	and	CCONJ
ejpam-6050	687	6	applications	application	NOUN
ejpam-6050	687	7	,	,	PUNCT
ejpam-6050	687	8	2:1–14	2:1–14	NUM
ejpam-6050	687	9	,	,	PUNCT
ejpam-6050	687	10	2014	2014	NUM
ejpam-6050	687	11	.	.	PUNCT
ejpam-6050	688	1	m.	m.	NOUN
ejpam-6050	688	2	kaviyarasu	kaviyarasu	PROPN
ejpam-6050	688	3	,	,	PUNCT
ejpam-6050	688	4	m.	m.	NOUN
ejpam-6050	688	5	rajeshwari	rajeshwari	NOUN
ejpam-6050	688	6	,	,	PUNCT
ejpam-6050	688	7	m.	m.	NOUN
ejpam-6050	688	8	alqahtani	alqahtani	PROPN
ejpam-6050	688	9	/	/	SYM
ejpam-6050	688	10	eur	eur	PROPN
ejpam-6050	688	11	.	.	PUNCT
ejpam-6050	689	1	j.	j.	PROPN
ejpam-6050	689	2	pure	pure	PROPN
ejpam-6050	689	3	appl	appl	PROPN
ejpam-6050	689	4	.	.	PROPN
ejpam-6050	689	5	math	math	PROPN
ejpam-6050	689	6	,	,	PUNCT
ejpam-6050	689	7	18	18	NUM
ejpam-6050	689	8	(	(	PUNCT
ejpam-6050	689	9	2	2	NUM
ejpam-6050	689	10	)	)	PUNCT
ejpam-6050	689	11	(	(	PUNCT
ejpam-6050	689	12	2025	2025	NUM
ejpam-6050	689	13	)	)	PUNCT
ejpam-6050	689	14	,	,	PUNCT
ejpam-6050	689	15	6050	6050	NUM
ejpam-6050	689	16	29	29	NUM
ejpam-6050	689	17	of	of	ADP
ejpam-6050	689	18	29	29	NUM
ejpam-6050	689	19	[	[	SYM
ejpam-6050	689	20	7	7	NUM
ejpam-6050	689	21	]	]	X
ejpam-6050	689	22	h.	h.	NOUN
ejpam-6050	689	23	bustince	bustince	PROPN
ejpam-6050	689	24	,	,	PUNCT
ejpam-6050	689	25	j.	j.	PROPN
ejpam-6050	689	26	kacprzyk	kacprzyk	PROPN
ejpam-6050	689	27	,	,	PUNCT
ejpam-6050	689	28	and	and	CCONJ
ejpam-6050	690	1	v.	v.	ADP
ejpam-6050	690	2	mohedano	mohedano	PROPN
ejpam-6050	690	3	.	.	PUNCT
ejpam-6050	691	1	a	a	DET
ejpam-6050	691	2	historical	historical	ADJ
ejpam-6050	691	3	account	account	NOUN
ejpam-6050	691	4	of	of	ADP
ejpam-6050	691	5	types	type	NOUN
ejpam-6050	691	6	of	of	ADP
ejpam-6050	691	7	fuzzy	fuzzy	ADJ
ejpam-6050	691	8	sets	set	NOUN
ejpam-6050	691	9	and	and	CCONJ
ejpam-6050	691	10	their	their	PRON
ejpam-6050	691	11	relationships	relationship	NOUN
ejpam-6050	691	12	.	.	PUNCT
ejpam-6050	692	1	ieee	ieee	NOUN
ejpam-6050	692	2	transactions	transaction	NOUN
ejpam-6050	692	3	on	on	ADP
ejpam-6050	692	4	fuzzy	fuzzy	ADJ
ejpam-6050	692	5	systems	system	NOUN
ejpam-6050	692	6	,	,	PUNCT
ejpam-6050	692	7	24:179–194	24:179–194	PROPN
ejpam-6050	692	8	,	,	PUNCT
ejpam-6050	692	9	2016	2016	NUM
ejpam-6050	692	10	.	.	PUNCT
ejpam-6050	693	1	[	[	X
ejpam-6050	693	2	8	8	NUM
ejpam-6050	693	3	]	]	PUNCT
ejpam-6050	693	4	a.	a.	NOUN
ejpam-6050	693	5	hadi	hadi	PROPN
ejpam-6050	693	6	-	-	PUNCT
ejpam-6050	693	7	vencheh	vencheh	PROPN
ejpam-6050	693	8	and	and	CCONJ
ejpam-6050	693	9	m.	m.	NOUN
ejpam-6050	693	10	mirjaberi	mirjaberi	PROPN
ejpam-6050	693	11	.	.	PUNCT
ejpam-6050	694	1	fuzzy	fuzzy	ADJ
ejpam-6050	694	2	inferior	inferior	ADJ
ejpam-6050	694	3	ratio	ratio	NOUN
ejpam-6050	694	4	method	method	NOUN
ejpam-6050	694	5	for	for	ADP
ejpam-6050	694	6	multiple	multiple	ADJ
ejpam-6050	694	7	attribute	attribute	NOUN
ejpam-6050	694	8	decision	decision	NOUN
ejpam-6050	694	9	making	make	VERB
ejpam-6050	694	10	problems	problem	NOUN
ejpam-6050	694	11	.	.	PUNCT
ejpam-6050	695	1	information	information	NOUN
ejpam-6050	695	2	sciences	sciences	PROPN
ejpam-6050	695	3	,	,	PUNCT
ejpam-6050	695	4	277:263–272	277:263–272	NUM
ejpam-6050	695	5	,	,	PUNCT
ejpam-6050	695	6	2014	2014	NUM
ejpam-6050	695	7	.	.	PUNCT
ejpam-6050	696	1	[	[	X
ejpam-6050	696	2	9	9	NUM
ejpam-6050	696	3	]	]	PUNCT
ejpam-6050	696	4	decui	decui	NOUN
ejpam-6050	696	5	liang	liang	PROPN
ejpam-6050	696	6	and	and	CCONJ
ejpam-6050	696	7	zeshui	zeshui	PROPN
ejpam-6050	696	8	xu	xu	PROPN
ejpam-6050	696	9	.	.	PUNCT
ejpam-6050	697	1	the	the	DET
ejpam-6050	697	2	new	new	ADJ
ejpam-6050	697	3	extension	extension	NOUN
ejpam-6050	697	4	of	of	ADP
ejpam-6050	697	5	topsis	topsis	NOUN
ejpam-6050	697	6	method	method	NOUN
ejpam-6050	697	7	for	for	ADP
ejpam-6050	697	8	multiple	multiple	ADJ
ejpam-6050	697	9	criteria	criterion	NOUN
ejpam-6050	697	10	decision	decision	NOUN
ejpam-6050	697	11	making	make	VERB
ejpam-6050	697	12	with	with	ADP
ejpam-6050	697	13	hesitant	hesitant	ADJ
ejpam-6050	697	14	pythagorean	pythagorean	PROPN
ejpam-6050	697	15	fuzzy	fuzzy	ADJ
ejpam-6050	697	16	sets	set	NOUN
ejpam-6050	697	17	.	.	PUNCT
ejpam-6050	697	18	applied	apply	VERB
ejpam-6050	697	19	soft	soft	ADJ
ejpam-6050	697	20	computing	computing	NOUN
ejpam-6050	697	21	,	,	PUNCT
ejpam-6050	697	22	60:167–179	60:167–179	PROPN
ejpam-6050	697	23	,	,	PUNCT
ejpam-6050	697	24	2017	2017	NUM
ejpam-6050	697	25	.	.	PUNCT
ejpam-6050	698	1	[	[	X
ejpam-6050	698	2	10	10	NUM
ejpam-6050	698	3	]	]	PUNCT
ejpam-6050	698	4	j.	j.	PROPN
ejpam-6050	698	5	kannan	kannan	PROPN
ejpam-6050	698	6	and	and	CCONJ
ejpam-6050	698	7	v.	v.	ADP
ejpam-6050	698	8	jayakumar	jayakumar	NOUN
ejpam-6050	698	9	.	.	PUNCT
ejpam-6050	699	1	advanced	advanced	ADJ
ejpam-6050	699	2	fuzzy	fuzzy	ADV
ejpam-6050	699	3	-	-	PUNCT
ejpam-6050	699	4	based	base	VERB
ejpam-6050	699	5	decision	decision	NOUN
ejpam-6050	699	6	-	-	PUNCT
ejpam-6050	699	7	making	making	NOUN
ejpam-6050	699	8	:	:	PUNCT
ejpam-6050	699	9	the	the	DET
ejpam-6050	699	10	linear	linear	ADJ
ejpam-6050	699	11	diophantine	diophantine	VERB
ejpam-6050	699	12	fuzzy	fuzzy	ADJ
ejpam-6050	699	13	codas	codas	ADJ
ejpam-6050	699	14	method	method	NOUN
ejpam-6050	699	15	for	for	ADP
ejpam-6050	699	16	logistic	logistic	ADJ
ejpam-6050	699	17	specialist	specialist	NOUN
ejpam-6050	699	18	selection	selection	NOUN
ejpam-6050	699	19	.	.	PUNCT
ejpam-6050	700	1	spectr	spectr	PROPN
ejpam-6050	700	2	oper	oper	PROPN
ejpam-6050	700	3	res	re	NOUN
ejpam-6050	700	4	,	,	PUNCT
ejpam-6050	700	5	2(1):41–60	2(1):41–60	NUM
ejpam-6050	700	6	,	,	PUNCT
ejpam-6050	700	7	2025	2025	NUM
ejpam-6050	700	8	.	.	PUNCT
ejpam-6050	701	1	[	[	X
ejpam-6050	701	2	11	11	NUM
ejpam-6050	701	3	]	]	X
ejpam-6050	701	4	n.	n.	PROPN
ejpam-6050	701	5	liao	liao	PROPN
ejpam-6050	701	6	,	,	PUNCT
ejpam-6050	701	7	h.	h.	PROPN
ejpam-6050	701	8	gao	gao	PROPN
ejpam-6050	701	9	,	,	PUNCT
ejpam-6050	701	10	r.	r.	PROPN
ejpam-6050	701	11	lin	lin	PROPN
ejpam-6050	701	12	,	,	PUNCT
ejpam-6050	701	13	g.	g.	PROPN
ejpam-6050	701	14	wei	wei	PROPN
ejpam-6050	701	15	,	,	PUNCT
ejpam-6050	701	16	and	and	CCONJ
ejpam-6050	701	17	x.	x.	PROPN
ejpam-6050	701	18	chen	chen	PROPN
ejpam-6050	701	19	.	.	PUNCT
ejpam-6050	702	1	an	an	DET
ejpam-6050	702	2	extended	extend	VERB
ejpam-6050	702	3	edas	eda	NOUN
ejpam-6050	702	4	approach	approach	NOUN
ejpam-6050	702	5	based	base	VERB
ejpam-6050	702	6	on	on	ADP
ejpam-6050	702	7	cumulative	cumulative	ADJ
ejpam-6050	702	8	prospect	prospect	NOUN
ejpam-6050	702	9	theory	theory	NOUN
ejpam-6050	702	10	for	for	ADP
ejpam-6050	702	11	multiple	multiple	ADJ
ejpam-6050	702	12	attributes	attribute	NOUN
ejpam-6050	702	13	group	group	NOUN
ejpam-6050	702	14	decision	decision	NOUN
ejpam-6050	702	15	making	make	VERB
ejpam-6050	702	16	with	with	ADP
ejpam-6050	702	17	probabilistic	probabilistic	ADJ
ejpam-6050	702	18	hesitant	hesitant	ADJ
ejpam-6050	702	19	fuzzy	fuzzy	ADJ
ejpam-6050	702	20	information	information	NOUN
ejpam-6050	702	21	.	.	PUNCT
ejpam-6050	703	1	artif	artif	PROPN
ejpam-6050	703	2	intell	intell	PROPN
ejpam-6050	703	3	rev	rev	VERB
ejpam-6050	703	4	,	,	PUNCT
ejpam-6050	703	5	56(4):2971–3003	56(4):2971–3003	NUM
ejpam-6050	703	6	,	,	PUNCT
ejpam-6050	703	7	2023	2023	NUM
ejpam-6050	703	8	.	.	PUNCT
ejpam-6050	704	1	[	[	X
ejpam-6050	704	2	12	12	NUM
ejpam-6050	704	3	]	]	PUNCT
ejpam-6050	704	4	a.	a.	NOUN
ejpam-6050	704	5	garrido	garrido	PROPN
ejpam-6050	704	6	.	.	PUNCT
ejpam-6050	705	1	fuzzy	fuzzy	ADJ
ejpam-6050	705	2	mathematical	mathematical	ADJ
ejpam-6050	705	3	analysis	analysis	NOUN
ejpam-6050	705	4	.	.	PUNCT
ejpam-6050	706	1	in	in	ADP
ejpam-6050	706	2	conference	conference	NOUN
ejpam-6050	706	3	paper	paper	NOUN
ejpam-6050	706	4	,	,	PUNCT
ejpam-6050	706	5	september	september	PROPN
ejpam-6050	706	6	2007	2007	NUM
ejpam-6050	706	7	.	.	PUNCT