id	sid	tid	token	lemma	pos
ejpam-6489	1	1	european	european	PROPN
ejpam-6489	1	2	journal	journal	PROPN
ejpam-6489	1	3	of	of	ADP
ejpam-6489	1	4	pure	pure	ADJ
ejpam-6489	1	5	and	and	CCONJ
ejpam-6489	1	6	applied	applied	ADJ
ejpam-6489	1	7	mathematics	mathematic	NOUN
ejpam-6489	1	8	2025	2025	NUM
ejpam-6489	1	9	,	,	PUNCT
ejpam-6489	1	10	vol	vol	NOUN
ejpam-6489	1	11	.	.	PROPN
ejpam-6489	1	12	18	18	NUM
ejpam-6489	1	13	,	,	PUNCT
ejpam-6489	1	14	issue	issue	NOUN
ejpam-6489	1	15	3	3	NUM
ejpam-6489	1	16	,	,	PUNCT
ejpam-6489	1	17	article	article	NOUN
ejpam-6489	1	18	number	number	NOUN
ejpam-6489	1	19	6489	6489	NUM
ejpam-6489	1	20	issn	issn	PROPN
ejpam-6489	1	21	1307	1307	NUM
ejpam-6489	1	22	-	-	SYM
ejpam-6489	1	23	5543	5543	NUM
ejpam-6489	1	24	–	–	PUNCT
ejpam-6489	1	25	ejpam.com	ejpam.com	X
ejpam-6489	1	26	published	publish	VERB
ejpam-6489	1	27	by	by	ADP
ejpam-6489	1	28	new	new	PROPN
ejpam-6489	1	29	york	york	PROPN
ejpam-6489	1	30	business	business	PROPN
ejpam-6489	1	31	global	global	ADJ
ejpam-6489	1	32	tripolar	tripolar	ADJ
ejpam-6489	1	33	complex	complex	ADJ
ejpam-6489	1	34	fuzzy	fuzzy	ADJ
ejpam-6489	1	35	lie	lie	NOUN
ejpam-6489	1	36	subalgebras	subalgebra	NOUN
ejpam-6489	1	37	of	of	ADP
ejpam-6489	1	38	lie	lie	NOUN
ejpam-6489	1	39	algebras	algebras	PROPN
ejpam-6489	1	40	m.	m.	PROPN
ejpam-6489	1	41	balamurugan1	balamurugan1	PROPN
ejpam-6489	1	42	,	,	PUNCT
ejpam-6489	1	43	g.	g.	PROPN
ejpam-6489	1	44	ellammal1	ellammal1	PROPN
ejpam-6489	1	45	,	,	PUNCT
ejpam-6489	1	46	aiyared	aiyare	VERB
ejpam-6489	1	47	iampan2,∗	iampan2,∗	VERB
ejpam-6489	1	48	1	1	NUM
ejpam-6489	1	49	department	department	NOUN
ejpam-6489	1	50	of	of	ADP
ejpam-6489	1	51	mathematics	mathematic	NOUN
ejpam-6489	1	52	,	,	PUNCT
ejpam-6489	1	53	vel	vel	PROPN
ejpam-6489	1	54	tech	tech	PROPN
ejpam-6489	1	55	rangarajan	rangarajan	PROPN
ejpam-6489	1	56	dr	dr	PROPN
ejpam-6489	1	57	.	.	PROPN
ejpam-6489	1	58	sagunthala	sagunthala	PROPN
ejpam-6489	1	59	r&d	r&d	PROPN
ejpam-6489	1	60	institute	institute	PROPN
ejpam-6489	1	61	of	of	ADP
ejpam-6489	1	62	science	science	NOUN
ejpam-6489	1	63	and	and	CCONJ
ejpam-6489	1	64	technology	technology	NOUN
ejpam-6489	1	65	,	,	PUNCT
ejpam-6489	1	66	chennai	chennai	NOUN
ejpam-6489	1	67	600062	600062	NUM
ejpam-6489	1	68	,	,	PUNCT
ejpam-6489	1	69	tamil	tamil	PROPN
ejpam-6489	1	70	nadu	nadu	PROPN
ejpam-6489	1	71	,	,	PUNCT
ejpam-6489	1	72	india	india	PROPN
ejpam-6489	1	73	2	2	NUM
ejpam-6489	1	74	department	department	NOUN
ejpam-6489	1	75	of	of	ADP
ejpam-6489	1	76	mathematics	mathematic	NOUN
ejpam-6489	1	77	,	,	PUNCT
ejpam-6489	1	78	school	school	NOUN
ejpam-6489	1	79	of	of	ADP
ejpam-6489	1	80	science	science	NOUN
ejpam-6489	1	81	,	,	PUNCT
ejpam-6489	1	82	university	university	NOUN
ejpam-6489	1	83	of	of	ADP
ejpam-6489	1	84	phayao	phayao	NOUN
ejpam-6489	1	85	,	,	PUNCT
ejpam-6489	1	86	mae	mae	PROPN
ejpam-6489	1	87	ka	ka	PROPN
ejpam-6489	1	88	,	,	PUNCT
ejpam-6489	1	89	mueang	mueang	PROPN
ejpam-6489	1	90	,	,	PUNCT
ejpam-6489	1	91	phayao	phayao	NOUN
ejpam-6489	1	92	56000	56000	NUM
ejpam-6489	1	93	,	,	PUNCT
ejpam-6489	1	94	thailand	thailand	PROPN
ejpam-6489	1	95	abstract	abstract	NOUN
ejpam-6489	1	96	.	.	PUNCT
ejpam-6489	2	1	the	the	DET
ejpam-6489	2	2	tripolar	tripolar	ADJ
ejpam-6489	2	3	complex	complex	ADJ
ejpam-6489	2	4	fuzzy	fuzzy	ADJ
ejpam-6489	2	5	set	set	NOUN
ejpam-6489	2	6	(	(	PUNCT
ejpam-6489	2	7	t	t	PROPN
ejpam-6489	2	8	cfs	cfs	PROPN
ejpam-6489	2	9	)	)	PUNCT
ejpam-6489	2	10	is	be	AUX
ejpam-6489	2	11	an	an	DET
ejpam-6489	2	12	extension	extension	NOUN
ejpam-6489	2	13	of	of	ADP
ejpam-6489	2	14	the	the	DET
ejpam-6489	2	15	bipolar	bipolar	ADJ
ejpam-6489	2	16	complex	complex	ADJ
ejpam-6489	2	17	fuzzy	fuzzy	ADJ
ejpam-6489	2	18	set	set	NOUN
ejpam-6489	2	19	(	(	PUNCT
ejpam-6489	2	20	bcfs	bcfs	PROPN
ejpam-6489	2	21	)	)	PUNCT
ejpam-6489	2	22	,	,	PUNCT
ejpam-6489	2	23	which	which	PRON
ejpam-6489	2	24	itself	itself	PRON
ejpam-6489	2	25	generalizes	generalize	VERB
ejpam-6489	2	26	traditional	traditional	ADJ
ejpam-6489	2	27	fuzzy	fuzzy	ADJ
ejpam-6489	2	28	sets	set	NOUN
ejpam-6489	2	29	and	and	CCONJ
ejpam-6489	2	30	bipolar	bipolar	ADJ
ejpam-6489	2	31	fuzzy	fuzzy	ADJ
ejpam-6489	2	32	sets	set	NOUN
ejpam-6489	2	33	.	.	PUNCT
ejpam-6489	3	1	in	in	ADP
ejpam-6489	3	2	this	this	DET
ejpam-6489	3	3	paper	paper	NOUN
ejpam-6489	3	4	,	,	PUNCT
ejpam-6489	3	5	we	we	PRON
ejpam-6489	3	6	further	far	ADV
ejpam-6489	3	7	develop	develop	VERB
ejpam-6489	3	8	this	this	DET
ejpam-6489	3	9	framework	framework	NOUN
ejpam-6489	3	10	by	by	ADP
ejpam-6489	3	11	introducing	introduce	VERB
ejpam-6489	3	12	the	the	DET
ejpam-6489	3	13	concept	concept	NOUN
ejpam-6489	3	14	of	of	ADP
ejpam-6489	3	15	tripolar	tripolar	ADJ
ejpam-6489	3	16	complex	complex	ADJ
ejpam-6489	3	17	fuzzy	fuzzy	ADJ
ejpam-6489	3	18	lie	lie	NOUN
ejpam-6489	3	19	brackets	bracket	NOUN
ejpam-6489	3	20	and	and	CCONJ
ejpam-6489	3	21	investigating	investigate	VERB
ejpam-6489	3	22	their	their	PRON
ejpam-6489	3	23	algebraic	algebraic	ADJ
ejpam-6489	3	24	properties	property	NOUN
ejpam-6489	3	25	.	.	PUNCT
ejpam-6489	4	1	additionally	additionally	ADV
ejpam-6489	4	2	,	,	PUNCT
ejpam-6489	4	3	we	we	PRON
ejpam-6489	4	4	demonstrate	demonstrate	VERB
ejpam-6489	4	5	that	that	SCONJ
ejpam-6489	4	6	the	the	DET
ejpam-6489	4	7	scalar	scalar	ADJ
ejpam-6489	4	8	multiplication	multiplication	NOUN
ejpam-6489	4	9	and	and	CCONJ
ejpam-6489	4	10	addition	addition	NOUN
ejpam-6489	4	11	of	of	ADP
ejpam-6489	4	12	tripolar	tripolar	ADJ
ejpam-6489	4	13	complex	complex	ADJ
ejpam-6489	4	14	fuzzy	fuzzy	ADJ
ejpam-6489	4	15	lie	lie	NOUN
ejpam-6489	4	16	subalgebras	subalgebras	PROPN
ejpam-6489	4	17	yield	yield	VERB
ejpam-6489	4	18	another	another	DET
ejpam-6489	4	19	tripolar	tripolar	ADJ
ejpam-6489	4	20	complex	complex	ADJ
ejpam-6489	4	21	fuzzy	fuzzy	ADJ
ejpam-6489	4	22	lie	lie	NOUN
ejpam-6489	4	23	subalgebra	subalgebra	NOUN
ejpam-6489	4	24	.	.	PUNCT
ejpam-6489	5	1	moreover	moreover	ADV
ejpam-6489	5	2	,	,	PUNCT
ejpam-6489	5	3	we	we	PRON
ejpam-6489	5	4	establish	establish	VERB
ejpam-6489	5	5	that	that	SCONJ
ejpam-6489	5	6	the	the	DET
ejpam-6489	5	7	homomorphic	homomorphic	ADJ
ejpam-6489	5	8	image	image	NOUN
ejpam-6489	5	9	of	of	ADP
ejpam-6489	5	10	a	a	DET
ejpam-6489	5	11	nilpotent	nilpotent	NOUN
ejpam-6489	5	12	(	(	PUNCT
ejpam-6489	5	13	or	or	CCONJ
ejpam-6489	5	14	solvable	solvable	ADJ
ejpam-6489	5	15	)	)	PUNCT
ejpam-6489	5	16	tripolar	tripolar	ADJ
ejpam-6489	5	17	complex	complex	ADJ
ejpam-6489	5	18	fuzzy	fuzzy	ADJ
ejpam-6489	5	19	lie	lie	NOUN
ejpam-6489	5	20	ideal	ideal	NOUN
ejpam-6489	5	21	remains	remain	VERB
ejpam-6489	5	22	a	a	DET
ejpam-6489	5	23	nilpotent	nilpotent	NOUN
ejpam-6489	5	24	(	(	PUNCT
ejpam-6489	5	25	or	or	CCONJ
ejpam-6489	5	26	solvable	solvable	ADJ
ejpam-6489	5	27	)	)	PUNCT
ejpam-6489	5	28	tripolar	tripolar	ADJ
ejpam-6489	5	29	complex	complex	ADJ
ejpam-6489	5	30	fuzzy	fuzzy	ADJ
ejpam-6489	5	31	lie	lie	NOUN
ejpam-6489	5	32	ideal	ideal	ADJ
ejpam-6489	5	33	.	.	PUNCT
ejpam-6489	6	1	finally	finally	ADV
ejpam-6489	6	2	,	,	PUNCT
ejpam-6489	6	3	we	we	PRON
ejpam-6489	6	4	establish	establish	VERB
ejpam-6489	6	5	that	that	SCONJ
ejpam-6489	6	6	every	every	DET
ejpam-6489	6	7	nilpotent	nilpotent	ADJ
ejpam-6489	6	8	tripolar	tripolar	ADJ
ejpam-6489	6	9	complex	complex	ADJ
ejpam-6489	6	10	fuzzy	fuzzy	ADJ
ejpam-6489	6	11	lie	lie	NOUN
ejpam-6489	6	12	ideal	ideal	NOUN
ejpam-6489	6	13	is	be	AUX
ejpam-6489	6	14	solvable	solvable	ADJ
ejpam-6489	6	15	.	.	PUNCT
ejpam-6489	7	1	2020	2020	NUM
ejpam-6489	7	2	mathematics	mathematic	NOUN
ejpam-6489	7	3	subject	subject	NOUN
ejpam-6489	7	4	classifications	classification	NOUN
ejpam-6489	7	5	:	:	PUNCT
ejpam-6489	7	6	17b99	17b99	NUM
ejpam-6489	7	7	,	,	PUNCT
ejpam-6489	7	8	22e60	22e60	NUM
ejpam-6489	7	9	,	,	PUNCT
ejpam-6489	7	10	08a72	08a72	NUM
ejpam-6489	7	11	,	,	PUNCT
ejpam-6489	7	12	03e72	03e72	NUM
ejpam-6489	7	13	,	,	PUNCT
ejpam-6489	7	14	20n25	20n25	NOUN
ejpam-6489	7	15	key	key	ADJ
ejpam-6489	7	16	words	word	NOUN
ejpam-6489	7	17	and	and	CCONJ
ejpam-6489	7	18	phrases	phrase	NOUN
ejpam-6489	7	19	:	:	PUNCT
ejpam-6489	7	20	lie	lie	NOUN
ejpam-6489	7	21	algebra	algebra	NOUN
ejpam-6489	7	22	,	,	PUNCT
ejpam-6489	7	23	tripolar	tripolar	ADJ
ejpam-6489	7	24	complex	complex	ADJ
ejpam-6489	7	25	fuzzy	fuzzy	ADJ
ejpam-6489	7	26	set	set	NOUN
ejpam-6489	7	27	,	,	PUNCT
ejpam-6489	7	28	tripolar	tripolar	ADJ
ejpam-6489	7	29	complex	complex	ADJ
ejpam-6489	7	30	fuzzy	fuzzy	ADJ
ejpam-6489	7	31	lie	lie	NOUN
ejpam-6489	7	32	subalgebra	subalgebra	NOUN
ejpam-6489	7	33	,	,	PUNCT
ejpam-6489	7	34	tripolar	tripolar	ADJ
ejpam-6489	7	35	complex	complex	ADJ
ejpam-6489	7	36	fuzzy	fuzzy	ADJ
ejpam-6489	7	37	lie	lie	NOUN
ejpam-6489	7	38	ideal	ideal	ADJ
ejpam-6489	7	39	,	,	PUNCT
ejpam-6489	7	40	nilpotent	nilpotent	ADJ
ejpam-6489	7	41	,	,	PUNCT
ejpam-6489	7	42	solvable	solvable	ADJ
ejpam-6489	7	43	1	1	NUM
ejpam-6489	7	44	.	.	PUNCT
ejpam-6489	7	45	introduction	introduction	NOUN
ejpam-6489	7	46	a	a	DET
ejpam-6489	7	47	lie	lie	NOUN
ejpam-6489	7	48	algebra	algebra	NOUN
ejpam-6489	7	49	is	be	AUX
ejpam-6489	7	50	a	a	DET
ejpam-6489	7	51	fundamental	fundamental	ADJ
ejpam-6489	7	52	mathematical	mathematical	ADJ
ejpam-6489	7	53	framework	framework	NOUN
ejpam-6489	7	54	in	in	ADP
ejpam-6489	7	55	algebra	algebra	NOUN
ejpam-6489	7	56	that	that	PRON
ejpam-6489	7	57	has	have	VERB
ejpam-6489	7	58	important	important	ADJ
ejpam-6489	7	59	applications	application	NOUN
ejpam-6489	7	60	in	in	ADP
ejpam-6489	7	61	many	many	ADJ
ejpam-6489	7	62	domains	domain	NOUN
ejpam-6489	7	63	,	,	PUNCT
ejpam-6489	7	64	including	include	VERB
ejpam-6489	7	65	theoretical	theoretical	ADJ
ejpam-6489	7	66	physics	physics	NOUN
ejpam-6489	7	67	and	and	CCONJ
ejpam-6489	7	68	mathematics	mathematic	NOUN
ejpam-6489	7	69	.	.	PUNCT
ejpam-6489	8	1	lie	lie	PROPN
ejpam-6489	8	2	algebras	algebra	NOUN
ejpam-6489	8	3	,	,	PUNCT
ejpam-6489	8	4	named	name	VERB
ejpam-6489	8	5	after	after	SCONJ
ejpam-6489	8	6	norwegian	norwegian	ADJ
ejpam-6489	8	7	mathematician	mathematician	ADJ
ejpam-6489	8	8	sophus	sophus	PROPN
ejpam-6489	8	9	lie	lie	VERB
ejpam-6489	8	10	[	[	X
ejpam-6489	8	11	1	1	NUM
ejpam-6489	8	12	]	]	PUNCT
ejpam-6489	8	13	,	,	PUNCT
ejpam-6489	8	14	provide	provide	VERB
ejpam-6489	8	15	a	a	DET
ejpam-6489	8	16	robust	robust	ADJ
ejpam-6489	8	17	framework	framework	NOUN
ejpam-6489	8	18	for	for	ADP
ejpam-6489	8	19	examining	examine	VERB
ejpam-6489	8	20	the	the	DET
ejpam-6489	8	21	algebraic	algebraic	ADJ
ejpam-6489	8	22	properties	property	NOUN
ejpam-6489	8	23	of	of	ADP
ejpam-6489	8	24	symmetries	symmetry	NOUN
ejpam-6489	8	25	,	,	PUNCT
ejpam-6489	8	26	vector	vector	NOUN
ejpam-6489	8	27	fields	field	NOUN
ejpam-6489	8	28	,	,	PUNCT
ejpam-6489	8	29	and	and	CCONJ
ejpam-6489	8	30	transformations	transformation	NOUN
ejpam-6489	8	31	.	.	PUNCT
ejpam-6489	9	1	over	over	ADP
ejpam-6489	9	2	time	time	NOUN
ejpam-6489	9	3	,	,	PUNCT
ejpam-6489	9	4	academics	academic	NOUN
ejpam-6489	9	5	have	have	AUX
ejpam-6489	9	6	thoroughly	thoroughly	ADV
ejpam-6489	9	7	investigated	investigate	VERB
ejpam-6489	9	8	lie	lie	NOUN
ejpam-6489	9	9	algebras	algebra	NOUN
ejpam-6489	9	10	,	,	PUNCT
ejpam-6489	9	11	revealing	reveal	VERB
ejpam-6489	9	12	a	a	DET
ejpam-6489	9	13	variety	variety	NOUN
ejpam-6489	9	14	of	of	ADP
ejpam-6489	9	15	structural	structural	ADJ
ejpam-6489	9	16	themes	theme	NOUN
ejpam-6489	9	17	that	that	PRON
ejpam-6489	9	18	apply	apply	VERB
ejpam-6489	9	19	to	to	ADP
ejpam-6489	9	20	groups	group	NOUN
ejpam-6489	9	21	,	,	PUNCT
ejpam-6489	9	22	rings	ring	NOUN
ejpam-6489	9	23	,	,	PUNCT
ejpam-6489	9	24	fields	field	NOUN
ejpam-6489	9	25	,	,	PUNCT
ejpam-6489	9	26	and	and	CCONJ
ejpam-6489	9	27	other	other	ADJ
ejpam-6489	9	28	algebraic	algebraic	ADJ
ejpam-6489	9	29	systems	system	NOUN
ejpam-6489	9	30	.	.	PUNCT
ejpam-6489	10	1	lie	lie	PROPN
ejpam-6489	10	2	algebras	algebra	NOUN
ejpam-6489	10	3	have	have	VERB
ejpam-6489	10	4	applications	application	NOUN
ejpam-6489	10	5	in	in	ADP
ejpam-6489	10	6	domains	domain	NOUN
ejpam-6489	10	7	such	such	ADJ
ejpam-6489	10	8	as	as	ADP
ejpam-6489	10	9	computer	computer	NOUN
ejpam-6489	10	10	science	science	NOUN
ejpam-6489	10	11	[	[	X
ejpam-6489	10	12	2	2	NUM
ejpam-6489	10	13	]	]	PUNCT
ejpam-6489	10	14	and	and	CCONJ
ejpam-6489	10	15	coding	code	VERB
ejpam-6489	10	16	theory	theory	NOUN
ejpam-6489	10	17	[	[	X
ejpam-6489	10	18	3	3	NUM
ejpam-6489	10	19	]	]	PUNCT
ejpam-6489	10	20	.	.	PUNCT
ejpam-6489	11	1	zadeh	zadeh	PROPN
ejpam-6489	11	2	’s	’s	PART
ejpam-6489	11	3	introduction	introduction	NOUN
ejpam-6489	11	4	of	of	ADP
ejpam-6489	11	5	fuzzy	fuzzy	ADJ
ejpam-6489	11	6	set	set	NOUN
ejpam-6489	11	7	theory	theory	NOUN
ejpam-6489	11	8	(	(	PUNCT
ejpam-6489	11	9	fs	fs	PROPN
ejpam-6489	11	10	)	)	PUNCT
ejpam-6489	11	11	in	in	ADP
ejpam-6489	11	12	1965	1965	NUM
ejpam-6489	11	13	[	[	X
ejpam-6489	11	14	4	4	X
ejpam-6489	11	15	]	]	PUNCT
ejpam-6489	11	16	transformed	transform	VERB
ejpam-6489	11	17	the	the	DET
ejpam-6489	11	18	mathematical	mathematical	ADJ
ejpam-6489	11	19	representation	representation	NOUN
ejpam-6489	11	20	of	of	ADP
ejpam-6489	11	21	uncertainty	uncertainty	NOUN
ejpam-6489	11	22	.	.	PUNCT
ejpam-6489	12	1	zhang	zhang	PROPN
ejpam-6489	12	2	introduced	introduce	VERB
ejpam-6489	12	3	bipolar	bipolar	ADJ
ejpam-6489	12	4	fuzzy	fuzzy	ADJ
ejpam-6489	12	5	sets	set	NOUN
ejpam-6489	12	6	(	(	PUNCT
ejpam-6489	12	7	bfs	bfs	NOUN
ejpam-6489	12	8	)	)	PUNCT
ejpam-6489	12	9	in	in	ADP
ejpam-6489	12	10	1998	1998	NUM
ejpam-6489	12	11	[	[	X
ejpam-6489	12	12	5	5	NUM
ejpam-6489	12	13	]	]	PUNCT
ejpam-6489	12	14	,	,	PUNCT
ejpam-6489	12	15	and	and	CCONJ
ejpam-6489	12	16	lee	lee	PROPN
ejpam-6489	13	1	[	[	X
ejpam-6489	13	2	6	6	NUM
ejpam-6489	13	3	]	]	PUNCT
ejpam-6489	13	4	expanded	expand	VERB
ejpam-6489	13	5	on	on	ADP
ejpam-6489	13	6	this	this	PRON
ejpam-6489	13	7	by	by	ADP
ejpam-6489	13	8	introducing	introduce	VERB
ejpam-6489	13	9	the	the	DET
ejpam-6489	13	10	notion	notion	NOUN
ejpam-6489	13	11	of	of	ADP
ejpam-6489	13	12	bipolar	bipolar	ADV
ejpam-6489	13	13	-	-	PUNCT
ejpam-6489	13	14	valued	value	VERB
ejpam-6489	13	15	fuzzy	fuzzy	ADJ
ejpam-6489	13	16	sets	set	NOUN
ejpam-6489	13	17	with	with	ADP
ejpam-6489	13	18	membership	membership	NOUN
ejpam-6489	13	19	functions	function	NOUN
ejpam-6489	13	20	ξpb̃	ξpb̃	VERB
ejpam-6489	13	21	:	:	PUNCT
ejpam-6489	14	1	l̃	l̃	PROPN
ejpam-6489	14	2	→	→	PUNCT
ejpam-6489	14	3	[	[	X
ejpam-6489	14	4	0	0	NUM
ejpam-6489	14	5	,	,	PUNCT
ejpam-6489	14	6	1	1	NUM
ejpam-6489	14	7	]	]	PUNCT
ejpam-6489	14	8	and	and	CCONJ
ejpam-6489	14	9	ξnb̃	ξnb̃	ADP
ejpam-6489	14	10	:	:	PUNCT
ejpam-6489	14	11	l̃	l̃	PROPN
ejpam-6489	14	12	→	→	PUNCT
ejpam-6489	14	13	[	[	X
ejpam-6489	14	14	−1	−1	NOUN
ejpam-6489	14	15	,	,	PUNCT
ejpam-6489	14	16	0	0	NUM
ejpam-6489	14	17	]	]	PUNCT
ejpam-6489	14	18	.	.	PUNCT
ejpam-6489	15	1	∗corresponding	∗corresponde	VERB
ejpam-6489	15	2	author	author	NOUN
ejpam-6489	15	3	.	.	PUNCT
ejpam-6489	16	1	doi	doi	NOUN
ejpam-6489	16	2	:	:	PUNCT
ejpam-6489	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6489	https://doi.org/10.29020/nybg.ejpam.v18i3.6489	NUM
ejpam-6489	16	4	email	email	NOUN
ejpam-6489	16	5	addresses	address	VERB
ejpam-6489	16	6	:	:	PUNCT
ejpam-6489	16	7	balamurugansvm@gmail.com	balamurugansvm@gmail.com	X
ejpam-6489	16	8	(	(	PUNCT
ejpam-6489	16	9	m.	m.	NOUN
ejpam-6489	16	10	balamurugan	balamurugan	PROPN
ejpam-6489	16	11	)	)	PUNCT
ejpam-6489	16	12	,	,	PUNCT
ejpam-6489	16	13	vinoellu@gmail.com	vinoellu@gmail.com	X
ejpam-6489	16	14	(	(	PUNCT
ejpam-6489	16	15	g.	g.	PROPN
ejpam-6489	16	16	ellammal	ellammal	PROPN
ejpam-6489	16	17	)	)	PUNCT
ejpam-6489	16	18	,	,	PUNCT
ejpam-6489	16	19	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6489	16	20	(	(	PUNCT
ejpam-6489	16	21	a.	a.	NOUN
ejpam-6489	16	22	iampan	iampan	PROPN
ejpam-6489	16	23	)	)	PUNCT
ejpam-6489	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6489	17	1	1	1	NUM
ejpam-6489	17	2	copyright	copyright	NOUN
ejpam-6489	17	3	:	:	PUNCT
ejpam-6489	17	4	©	©	PROPN
ejpam-6489	17	5	2025	2025	NUM
ejpam-6489	17	6	the	the	DET
ejpam-6489	17	7	author(s	author(s	NOUN
ejpam-6489	17	8	)	)	PUNCT
ejpam-6489	17	9	.	.	PUNCT
ejpam-6489	18	1	(	(	PUNCT
ejpam-6489	18	2	cc	cc	NOUN
ejpam-6489	18	3	by	by	ADP
ejpam-6489	18	4	-	-	PUNCT
ejpam-6489	18	5	nc	nc	PROPN
ejpam-6489	18	6	4.0	4.0	NUM
ejpam-6489	18	7	)	)	PUNCT
ejpam-6489	18	8	m.	m.	NOUN
ejpam-6489	18	9	balamurugan	balamurugan	NOUN
ejpam-6489	18	10	,	,	PUNCT
ejpam-6489	18	11	g.	g.	PROPN
ejpam-6489	18	12	ellammal	ellammal	PROPN
ejpam-6489	18	13	,	,	PUNCT
ejpam-6489	18	14	a.	a.	NOUN
ejpam-6489	18	15	iampan	iampan	PROPN
ejpam-6489	18	16	/	/	SYM
ejpam-6489	18	17	eur	eur	PROPN
ejpam-6489	18	18	.	.	PUNCT
ejpam-6489	19	1	j.	j.	PROPN
ejpam-6489	19	2	pure	pure	PROPN
ejpam-6489	19	3	appl	appl	PROPN
ejpam-6489	19	4	.	.	PROPN
ejpam-6489	19	5	math	math	PROPN
ejpam-6489	19	6	,	,	PUNCT
ejpam-6489	19	7	18	18	NUM
ejpam-6489	19	8	(	(	PUNCT
ejpam-6489	19	9	3	3	NUM
ejpam-6489	19	10	)	)	PUNCT
ejpam-6489	19	11	(	(	PUNCT
ejpam-6489	19	12	2025	2025	NUM
ejpam-6489	19	13	)	)	PUNCT
ejpam-6489	19	14	,	,	PUNCT
ejpam-6489	19	15	6489	6489	NUM
ejpam-6489	19	16	2	2	NUM
ejpam-6489	19	17	of	of	ADP
ejpam-6489	19	18	26	26	NUM
ejpam-6489	19	19	in	in	ADP
ejpam-6489	19	20	the	the	DET
ejpam-6489	19	21	complex	complex	ADJ
ejpam-6489	19	22	plane	plane	NOUN
ejpam-6489	19	23	,	,	PUNCT
ejpam-6489	19	24	ramot	ramot	NOUN
ejpam-6489	19	25	et	et	PROPN
ejpam-6489	19	26	al	al	PROPN
ejpam-6489	19	27	.	.	PUNCT
ejpam-6489	20	1	[	[	X
ejpam-6489	20	2	7	7	NUM
ejpam-6489	20	3	]	]	PUNCT
ejpam-6489	20	4	developed	develop	VERB
ejpam-6489	20	5	the	the	DET
ejpam-6489	20	6	concept	concept	NOUN
ejpam-6489	20	7	of	of	ADP
ejpam-6489	20	8	complex	complex	ADJ
ejpam-6489	20	9	fuzzy	fuzzy	ADJ
ejpam-6489	20	10	sets	set	NOUN
ejpam-6489	20	11	(	(	PUNCT
ejpam-6489	20	12	cfs	cfs	PROPN
ejpam-6489	20	13	)	)	PUNCT
ejpam-6489	20	14	,	,	PUNCT
ejpam-6489	20	15	expanding	expand	VERB
ejpam-6489	20	16	the	the	DET
ejpam-6489	20	17	range	range	NOUN
ejpam-6489	20	18	[	[	X
ejpam-6489	20	19	0	0	NUM
ejpam-6489	20	20	,	,	PUNCT
ejpam-6489	20	21	1	1	NUM
ejpam-6489	20	22	]	]	PUNCT
ejpam-6489	20	23	to	to	ADP
ejpam-6489	20	24	the	the	DET
ejpam-6489	20	25	unit	unit	NOUN
ejpam-6489	20	26	disk	disk	NOUN
ejpam-6489	20	27	.	.	PUNCT
ejpam-6489	21	1	tamir	tamir	PROPN
ejpam-6489	21	2	et	et	PROPN
ejpam-6489	21	3	al	al	PROPN
ejpam-6489	21	4	.	.	PUNCT
ejpam-6489	22	1	[	[	X
ejpam-6489	22	2	8	8	NUM
ejpam-6489	22	3	]	]	PUNCT
ejpam-6489	22	4	expanded	expand	VERB
ejpam-6489	22	5	on	on	ADP
ejpam-6489	22	6	this	this	DET
ejpam-6489	22	7	notion	notion	NOUN
ejpam-6489	22	8	by	by	ADP
ejpam-6489	22	9	mapping	map	VERB
ejpam-6489	22	10	the	the	DET
ejpam-6489	22	11	range	range	NOUN
ejpam-6489	22	12	to	to	ADP
ejpam-6489	22	13	[	[	X
ejpam-6489	22	14	0	0	NUM
ejpam-6489	22	15	,	,	PUNCT
ejpam-6489	22	16	1	1	NUM
ejpam-6489	22	17	]	]	PUNCT
ejpam-6489	22	18	+	+	NUM
ejpam-6489	22	19	i[0	i[0	PROPN
ejpam-6489	22	20	,	,	PUNCT
ejpam-6489	22	21	1	1	NUM
ejpam-6489	22	22	]	]	PUNCT
ejpam-6489	22	23	.	.	PUNCT
ejpam-6489	23	1	mahmood	mahmood	PROPN
ejpam-6489	23	2	et	et	PROPN
ejpam-6489	23	3	al	al	PROPN
ejpam-6489	23	4	.	.	PUNCT
ejpam-6489	24	1	[	[	X
ejpam-6489	24	2	9	9	NUM
ejpam-6489	24	3	]	]	PUNCT
ejpam-6489	24	4	proposed	propose	VERB
ejpam-6489	24	5	bipolar	bipolar	ADJ
ejpam-6489	24	6	complex	complex	ADJ
ejpam-6489	24	7	fuzzy	fuzzy	ADJ
ejpam-6489	24	8	sets	set	NOUN
ejpam-6489	24	9	(	(	PUNCT
ejpam-6489	24	10	bcfs	bcfs	NOUN
ejpam-6489	24	11	)	)	PUNCT
ejpam-6489	24	12	,	,	PUNCT
ejpam-6489	24	13	which	which	PRON
ejpam-6489	24	14	combine	combine	VERB
ejpam-6489	24	15	bfs	bfs	PROPN
ejpam-6489	24	16	and	and	CCONJ
ejpam-6489	24	17	cfs	cfs	PROPN
ejpam-6489	24	18	concepts	concept	NOUN
ejpam-6489	24	19	.	.	PUNCT
ejpam-6489	25	1	rosenfeld	rosenfeld	PROPN
ejpam-6489	26	1	[	[	X
ejpam-6489	26	2	10	10	NUM
ejpam-6489	26	3	]	]	PUNCT
ejpam-6489	26	4	was	be	AUX
ejpam-6489	26	5	the	the	DET
ejpam-6489	26	6	first	first	ADJ
ejpam-6489	26	7	to	to	PART
ejpam-6489	26	8	connect	connect	VERB
ejpam-6489	26	9	fuzzy	fuzzy	ADJ
ejpam-6489	26	10	set	set	NOUN
ejpam-6489	26	11	theory	theory	NOUN
ejpam-6489	26	12	(	(	PUNCT
ejpam-6489	26	13	fs	f	NOUN
ejpam-6489	26	14	)	)	PUNCT
ejpam-6489	26	15	to	to	ADP
ejpam-6489	26	16	group	group	NOUN
ejpam-6489	26	17	theory	theory	NOUN
ejpam-6489	26	18	.	.	PUNCT
ejpam-6489	27	1	he	he	PRON
ejpam-6489	27	2	invented	invent	VERB
ejpam-6489	27	3	the	the	DET
ejpam-6489	27	4	concept	concept	NOUN
ejpam-6489	27	5	of	of	ADP
ejpam-6489	27	6	fuzzy	fuzzy	ADJ
ejpam-6489	27	7	subgroups	subgroup	NOUN
ejpam-6489	27	8	and	and	CCONJ
ejpam-6489	27	9	investigated	investigate	VERB
ejpam-6489	27	10	its	its	PRON
ejpam-6489	27	11	fundamental	fundamental	ADJ
ejpam-6489	27	12	features	feature	NOUN
ejpam-6489	27	13	.	.	PUNCT
ejpam-6489	28	1	following	follow	VERB
ejpam-6489	28	2	this	this	PRON
ejpam-6489	28	3	,	,	PUNCT
ejpam-6489	28	4	other	other	ADJ
ejpam-6489	28	5	scholars	scholar	NOUN
ejpam-6489	28	6	expanded	expand	VERB
ejpam-6489	28	7	these	these	DET
ejpam-6489	28	8	ideas	idea	NOUN
ejpam-6489	28	9	to	to	ADP
ejpam-6489	28	10	various	various	ADJ
ejpam-6489	28	11	algebraic	algebraic	ADJ
ejpam-6489	28	12	structures	structure	NOUN
ejpam-6489	28	13	,	,	PUNCT
ejpam-6489	28	14	including	include	VERB
ejpam-6489	28	15	hx	hx	PROPN
ejpam-6489	28	16	-	-	PUNCT
ejpam-6489	28	17	subgroups	subgroup	NOUN
ejpam-6489	28	18	,	,	PUNCT
ejpam-6489	28	19	ordered	order	VERB
ejpam-6489	28	20	semigroups	semigroup	NOUN
ejpam-6489	28	21	,	,	PUNCT
ejpam-6489	28	22	and	and	CCONJ
ejpam-6489	28	23	bck	bck	PROPN
ejpam-6489	28	24	/	/	SYM
ejpam-6489	28	25	bci	bci	NOUN
ejpam-6489	28	26	-	-	PUNCT
ejpam-6489	28	27	algebras	algebra	NOUN
ejpam-6489	28	28	,	,	PUNCT
ejpam-6489	28	29	in	in	ADP
ejpam-6489	28	30	the	the	DET
ejpam-6489	28	31	setting	setting	NOUN
ejpam-6489	28	32	of	of	ADP
ejpam-6489	28	33	uncertainty	uncertainty	NOUN
ejpam-6489	28	34	(	(	PUNCT
ejpam-6489	28	35	see	see	VERB
ejpam-6489	28	36	[	[	X
ejpam-6489	28	37	11–16	11–16	NUM
ejpam-6489	28	38	]	]	NUM
ejpam-6489	28	39	)	)	PUNCT
ejpam-6489	28	40	.	.	PUNCT
ejpam-6489	29	1	yehia	yehia	PROPN
ejpam-6489	29	2	[	[	X
ejpam-6489	29	3	17	17	NUM
ejpam-6489	29	4	]	]	PUNCT
ejpam-6489	29	5	introduced	introduce	VERB
ejpam-6489	29	6	the	the	DET
ejpam-6489	29	7	concept	concept	NOUN
ejpam-6489	29	8	of	of	ADP
ejpam-6489	29	9	fuzzy	fuzzy	ADJ
ejpam-6489	29	10	lie	lie	NOUN
ejpam-6489	29	11	algebras	algebra	NOUN
ejpam-6489	29	12	by	by	ADP
ejpam-6489	29	13	incorporating	incorporate	VERB
ejpam-6489	29	14	fs	fs	ADP
ejpam-6489	29	15	theory	theory	NOUN
ejpam-6489	29	16	into	into	ADP
ejpam-6489	29	17	the	the	DET
ejpam-6489	29	18	study	study	NOUN
ejpam-6489	29	19	of	of	ADP
ejpam-6489	29	20	lie	lie	NOUN
ejpam-6489	29	21	algebraic	algebraic	ADJ
ejpam-6489	29	22	ambiguity	ambiguity	NOUN
ejpam-6489	29	23	.	.	PUNCT
ejpam-6489	30	1	subsequent	subsequent	ADJ
ejpam-6489	30	2	studies	study	NOUN
ejpam-6489	30	3	investigated	investigate	VERB
ejpam-6489	30	4	lie	lie	NOUN
ejpam-6489	30	5	algebras	algebra	NOUN
ejpam-6489	30	6	in	in	ADP
ejpam-6489	30	7	the	the	DET
ejpam-6489	30	8	context	context	NOUN
ejpam-6489	30	9	of	of	ADP
ejpam-6489	30	10	fss	fss	PROPN
ejpam-6489	30	11	(	(	PUNCT
ejpam-6489	30	12	see	see	VERB
ejpam-6489	30	13	[	[	X
ejpam-6489	30	14	18	18	NUM
ejpam-6489	30	15	,	,	PUNCT
ejpam-6489	30	16	19	19	NUM
ejpam-6489	30	17	]	]	NUM
ejpam-6489	30	18	)	)	PUNCT
ejpam-6489	30	19	.	.	PUNCT
ejpam-6489	31	1	atanassov	atanassov	PROPN
ejpam-6489	32	1	[	[	X
ejpam-6489	32	2	20	20	NUM
ejpam-6489	32	3	]	]	PUNCT
ejpam-6489	32	4	generalized	generalize	VERB
ejpam-6489	32	5	fuzzy	fuzzy	ADJ
ejpam-6489	32	6	sets	set	NOUN
ejpam-6489	32	7	by	by	ADP
ejpam-6489	32	8	introducing	introduce	VERB
ejpam-6489	32	9	intuitionistic	intuitionistic	ADJ
ejpam-6489	32	10	fuzzy	fuzzy	ADJ
ejpam-6489	32	11	sets	set	NOUN
ejpam-6489	32	12	(	(	PUNCT
ejpam-6489	32	13	ifss	ifss	NOUN
ejpam-6489	32	14	)	)	PUNCT
ejpam-6489	32	15	,	,	PUNCT
ejpam-6489	32	16	which	which	PRON
ejpam-6489	32	17	incorporate	incorporate	VERB
ejpam-6489	32	18	degrees	degree	NOUN
ejpam-6489	32	19	of	of	ADP
ejpam-6489	32	20	membership	membership	NOUN
ejpam-6489	32	21	,	,	PUNCT
ejpam-6489	32	22	non	non	ADJ
ejpam-6489	32	23	-	-	NOUN
ejpam-6489	32	24	membership	membership	NOUN
ejpam-6489	32	25	,	,	PUNCT
ejpam-6489	32	26	and	and	CCONJ
ejpam-6489	32	27	hesitation	hesitation	NOUN
ejpam-6489	32	28	to	to	PART
ejpam-6489	32	29	model	model	VERB
ejpam-6489	32	30	uncertainty	uncertainty	NOUN
ejpam-6489	32	31	more	more	ADV
ejpam-6489	32	32	robustly	robustly	ADV
ejpam-6489	32	33	.	.	PUNCT
ejpam-6489	33	1	akram	akram	NOUN
ejpam-6489	33	2	and	and	CCONJ
ejpam-6489	33	3	shum	shum	NOUN
ejpam-6489	34	1	[	[	X
ejpam-6489	34	2	21	21	NUM
ejpam-6489	34	3	]	]	PUNCT
ejpam-6489	34	4	studied	study	VERB
ejpam-6489	34	5	intuitionistic	intuitionistic	ADJ
ejpam-6489	34	6	fuzzy	fuzzy	ADJ
ejpam-6489	34	7	lie	lie	NOUN
ejpam-6489	34	8	subalgebras	subalgebras	PROPN
ejpam-6489	34	9	and	and	CCONJ
ejpam-6489	34	10	their	their	PRON
ejpam-6489	34	11	properties	property	NOUN
ejpam-6489	34	12	.	.	PUNCT
ejpam-6489	35	1	akram	akram	PROPN
ejpam-6489	36	1	[	[	X
ejpam-6489	36	2	22	22	NUM
ejpam-6489	36	3	]	]	PUNCT
ejpam-6489	36	4	studied	study	VERB
ejpam-6489	36	5	fuzzy	fuzzy	ADJ
ejpam-6489	36	6	lie	lie	NOUN
ejpam-6489	36	7	ideals	ideal	NOUN
ejpam-6489	36	8	with	with	ADP
ejpam-6489	36	9	interval	interval	NOUN
ejpam-6489	36	10	-	-	PUNCT
ejpam-6489	36	11	valued	value	VERB
ejpam-6489	36	12	membership	membership	NOUN
ejpam-6489	36	13	functions	function	NOUN
ejpam-6489	36	14	,	,	PUNCT
ejpam-6489	36	15	as	as	ADV
ejpam-6489	36	16	well	well	ADV
ejpam-6489	36	17	as	as	ADP
ejpam-6489	36	18	solvable	solvable	ADJ
ejpam-6489	36	19	and	and	CCONJ
ejpam-6489	36	20	nilpotent	nilpotent	ADJ
ejpam-6489	36	21	lie	lie	NOUN
ejpam-6489	36	22	l	l	NOUN
ejpam-6489	36	23	-	-	PUNCT
ejpam-6489	36	24	algebras	algebras	ADV
ejpam-6489	36	25	utilizing	utilize	VERB
ejpam-6489	36	26	bipolar	bipolar	ADJ
ejpam-6489	36	27	fuzzy	fuzzy	ADJ
ejpam-6489	36	28	sets	set	NOUN
ejpam-6489	36	29	(	(	PUNCT
ejpam-6489	36	30	bfs	bfs	NOUN
ejpam-6489	36	31	)	)	PUNCT
ejpam-6489	37	1	[	[	X
ejpam-6489	37	2	23	23	NUM
ejpam-6489	37	3	]	]	PUNCT
ejpam-6489	37	4	.	.	PUNCT
ejpam-6489	38	1	shaqaqha	shaqaqha	PROPN
ejpam-6489	39	1	[	[	X
ejpam-6489	39	2	24	24	NUM
ejpam-6489	39	3	]	]	PUNCT
ejpam-6489	39	4	introduced	introduce	VERB
ejpam-6489	39	5	the	the	DET
ejpam-6489	39	6	concept	concept	NOUN
ejpam-6489	39	7	of	of	ADP
ejpam-6489	39	8	complex	complex	ADJ
ejpam-6489	39	9	fuzzy	fuzzy	ADJ
ejpam-6489	39	10	lie	lie	NOUN
ejpam-6489	39	11	subalgebras	subalgebras	PROPN
ejpam-6489	39	12	,	,	PUNCT
ejpam-6489	39	13	examining	examine	VERB
ejpam-6489	39	14	their	their	PRON
ejpam-6489	39	15	key	key	ADJ
ejpam-6489	39	16	properties	property	NOUN
ejpam-6489	39	17	.	.	PUNCT
ejpam-6489	40	1	kousar	kousar	VERB
ejpam-6489	40	2	et	et	PROPN
ejpam-6489	40	3	al	al	PROPN
ejpam-6489	40	4	.	.	PUNCT
ejpam-6489	41	1	[	[	X
ejpam-6489	41	2	25	25	NUM
ejpam-6489	41	3	]	]	PUNCT
ejpam-6489	41	4	studied	study	VERB
ejpam-6489	41	5	nilpotent	nilpotent	NOUN
ejpam-6489	41	6	and	and	CCONJ
ejpam-6489	41	7	solvable	solvable	ADJ
ejpam-6489	41	8	lie	lie	NOUN
ejpam-6489	41	9	algebras	algebra	NOUN
ejpam-6489	41	10	in	in	ADP
ejpam-6489	41	11	an	an	DET
ejpam-6489	41	12	image	image	NOUN
ejpam-6489	41	13	fuzzy	fuzzy	ADJ
ejpam-6489	41	14	environment	environment	NOUN
ejpam-6489	41	15	.	.	PUNCT
ejpam-6489	42	1	al	al	PROPN
ejpam-6489	42	2	-	-	PROPN
ejpam-6489	42	3	masarwah	masarwah	PROPN
ejpam-6489	42	4	et	et	PROPN
ejpam-6489	42	5	al	al	PROPN
ejpam-6489	42	6	.	.	PUNCT
ejpam-6489	43	1	[	[	X
ejpam-6489	43	2	26	26	NUM
ejpam-6489	43	3	]	]	PUNCT
ejpam-6489	43	4	established	establish	VERB
ejpam-6489	43	5	the	the	DET
ejpam-6489	43	6	notion	notion	NOUN
ejpam-6489	43	7	of	of	ADP
ejpam-6489	43	8	crossing	cross	VERB
ejpam-6489	43	9	cubic	cubic	ADJ
ejpam-6489	43	10	lie	lie	NOUN
ejpam-6489	43	11	algebras	algebra	NOUN
ejpam-6489	43	12	,	,	PUNCT
ejpam-6489	43	13	researching	research	VERB
ejpam-6489	43	14	homomorphisms	homomorphism	NOUN
ejpam-6489	43	15	,	,	PUNCT
ejpam-6489	43	16	isomorphism	isomorphism	NOUN
ejpam-6489	43	17	theorems	theorem	NOUN
ejpam-6489	43	18	,	,	PUNCT
ejpam-6489	43	19	cartesian	cartesian	ADJ
ejpam-6489	43	20	products	product	NOUN
ejpam-6489	43	21	,	,	PUNCT
ejpam-6489	43	22	and	and	CCONJ
ejpam-6489	43	23	quotients	quotient	VERB
ejpam-6489	43	24	within	within	ADP
ejpam-6489	43	25	this	this	DET
ejpam-6489	43	26	framework	framework	NOUN
ejpam-6489	43	27	.	.	PUNCT
ejpam-6489	44	1	jaleel	jaleel	PROPN
ejpam-6489	44	2	et	et	PROPN
ejpam-6489	44	3	al	al	PROPN
ejpam-6489	44	4	.	.	PUNCT
ejpam-6489	45	1	[	[	X
ejpam-6489	45	2	27	27	NUM
ejpam-6489	45	3	]	]	PUNCT
ejpam-6489	45	4	proposed	propose	VERB
ejpam-6489	45	5	interval	interval	NOUN
ejpam-6489	45	6	-	-	PUNCT
ejpam-6489	45	7	valued	value	VERB
ejpam-6489	45	8	bipolar	bipolar	ADJ
ejpam-6489	45	9	complex	complex	ADJ
ejpam-6489	45	10	fuzzy	fuzzy	ADJ
ejpam-6489	45	11	sets	set	NOUN
ejpam-6489	45	12	(	(	PUNCT
ejpam-6489	45	13	ivbcfs	ivbcfs	ADJ
ejpam-6489	45	14	)	)	PUNCT
ejpam-6489	45	15	,	,	PUNCT
ejpam-6489	45	16	whereas	whereas	SCONJ
ejpam-6489	45	17	qiyasi	qiyasi	PROPN
ejpam-6489	45	18	et	et	PROPN
ejpam-6489	45	19	al	al	PROPN
ejpam-6489	45	20	.	.	PUNCT
ejpam-6489	46	1	[	[	X
ejpam-6489	46	2	28	28	NUM
ejpam-6489	46	3	]	]	PUNCT
ejpam-6489	46	4	created	create	VERB
ejpam-6489	46	5	the	the	DET
ejpam-6489	46	6	underlying	underlying	ADJ
ejpam-6489	46	7	theory	theory	NOUN
ejpam-6489	46	8	of	of	ADP
ejpam-6489	46	9	confidence	confidence	NOUN
ejpam-6489	46	10	-	-	PUNCT
ejpam-6489	46	11	level	level	NOUN
ejpam-6489	46	12	-	-	PUNCT
ejpam-6489	46	13	based	base	VERB
ejpam-6489	46	14	bipolar	bipolar	ADJ
ejpam-6489	46	15	complex	complex	ADJ
ejpam-6489	46	16	fuzzy	fuzzy	ADJ
ejpam-6489	46	17	sets	set	NOUN
ejpam-6489	46	18	.	.	PUNCT
ejpam-6489	47	1	prommai	prommai	PROPN
ejpam-6489	47	2	et	et	PROPN
ejpam-6489	47	3	al	al	PROPN
ejpam-6489	47	4	.	.	PUNCT
ejpam-6489	48	1	[	[	X
ejpam-6489	48	2	29	29	NUM
ejpam-6489	48	3	]	]	PUNCT
ejpam-6489	48	4	presented	present	VERB
ejpam-6489	48	5	tripolar	tripolar	ADJ
ejpam-6489	48	6	fuzzy	fuzzy	ADJ
ejpam-6489	48	7	ideals	ideal	NOUN
ejpam-6489	48	8	in	in	ADP
ejpam-6489	48	9	semigroups	semigroup	NOUN
ejpam-6489	48	10	.	.	PUNCT
ejpam-6489	49	1	wattanasiripong	wattanasiripong	PROPN
ejpam-6489	49	2	et	et	PROPN
ejpam-6489	49	3	al	al	PROPN
ejpam-6489	49	4	.	.	PUNCT
ejpam-6489	50	1	[	[	X
ejpam-6489	50	2	30	30	NUM
ejpam-6489	50	3	]	]	PUNCT
ejpam-6489	50	4	introduced	introduce	VERB
ejpam-6489	50	5	tripolar	tripolar	ADJ
ejpam-6489	50	6	fuzzy	fuzzy	ADJ
ejpam-6489	50	7	pure	pure	ADJ
ejpam-6489	50	8	ideals	ideal	NOUN
ejpam-6489	50	9	in	in	ADP
ejpam-6489	50	10	ordered	order	VERB
ejpam-6489	50	11	semigroups	semigroup	NOUN
ejpam-6489	50	12	.	.	PUNCT
ejpam-6489	51	1	muhiuddin	muhiuddin	VERB
ejpam-6489	51	2	et	et	PROPN
ejpam-6489	51	3	al	al	PROPN
ejpam-6489	51	4	.	.	PUNCT
ejpam-6489	52	1	[	[	X
ejpam-6489	52	2	14	14	NUM
ejpam-6489	52	3	]	]	PUNCT
ejpam-6489	52	4	developed	develop	VERB
ejpam-6489	52	5	tripolar	tripolar	ADJ
ejpam-6489	52	6	picture	picture	NOUN
ejpam-6489	52	7	fuzzy	fuzzy	ADJ
ejpam-6489	52	8	ideals	ideal	NOUN
ejpam-6489	52	9	of	of	ADP
ejpam-6489	52	10	bck	bck	NOUN
ejpam-6489	52	11	-	-	PUNCT
ejpam-6489	52	12	algebras	algebras	PROPN
ejpam-6489	52	13	.	.	PUNCT
ejpam-6489	53	1	balamurugan	balamurugan	PROPN
ejpam-6489	53	2	et	et	PROPN
ejpam-6489	53	3	al	al	PROPN
ejpam-6489	53	4	.	.	PUNCT
ejpam-6489	54	1	[	[	X
ejpam-6489	54	2	31	31	NUM
ejpam-6489	54	3	]	]	PUNCT
ejpam-6489	54	4	introduced	introduce	VERB
ejpam-6489	54	5	complex	complex	ADJ
ejpam-6489	54	6	fuzzy	fuzzy	ADJ
ejpam-6489	54	7	subalgebras	subalgebra	NOUN
ejpam-6489	54	8	and	and	CCONJ
ejpam-6489	54	9	investigated	investigate	VERB
ejpam-6489	54	10	their	their	PRON
ejpam-6489	54	11	properties	property	NOUN
ejpam-6489	54	12	.	.	PUNCT
ejpam-6489	55	1	al	al	PROPN
ejpam-6489	55	2	-	-	PROPN
ejpam-6489	55	3	masarwah	masarwah	PROPN
ejpam-6489	55	4	et	et	PROPN
ejpam-6489	55	5	al	al	PROPN
ejpam-6489	55	6	.	.	PUNCT
ejpam-6489	56	1	[	[	X
ejpam-6489	56	2	32	32	NUM
ejpam-6489	56	3	]	]	PUNCT
ejpam-6489	56	4	investigated	investigate	VERB
ejpam-6489	56	5	complex	complex	ADJ
ejpam-6489	56	6	linear	linear	ADJ
ejpam-6489	56	7	diophantine	diophantine	VERB
ejpam-6489	56	8	fuzzy	fuzzy	ADJ
ejpam-6489	56	9	ideals	ideal	NOUN
ejpam-6489	56	10	in	in	ADP
ejpam-6489	56	11	bckalgebras	bckalgebra	NOUN
ejpam-6489	56	12	.	.	PUNCT
ejpam-6489	57	1	the	the	DET
ejpam-6489	57	2	aim	aim	NOUN
ejpam-6489	57	3	of	of	ADP
ejpam-6489	57	4	a	a	DET
ejpam-6489	57	5	tripolar	tripolar	ADJ
ejpam-6489	57	6	complex	complex	ADJ
ejpam-6489	57	7	fuzzy	fuzzy	ADJ
ejpam-6489	57	8	set	set	NOUN
ejpam-6489	57	9	(	(	PUNCT
ejpam-6489	57	10	t	t	NOUN
ejpam-6489	57	11	cfs	cfs	PROPN
ejpam-6489	57	12	)	)	PUNCT
ejpam-6489	57	13	is	be	AUX
ejpam-6489	57	14	to	to	PART
ejpam-6489	57	15	extend	extend	VERB
ejpam-6489	57	16	the	the	DET
ejpam-6489	57	17	capabilities	capability	NOUN
ejpam-6489	57	18	of	of	ADP
ejpam-6489	57	19	traditional	traditional	ADJ
ejpam-6489	57	20	fuzzy	fuzzy	ADJ
ejpam-6489	57	21	sets	set	NOUN
ejpam-6489	57	22	,	,	PUNCT
ejpam-6489	57	23	bipolar	bipolar	ADJ
ejpam-6489	57	24	fuzzy	fuzzy	ADJ
ejpam-6489	57	25	sets	set	NOUN
ejpam-6489	57	26	,	,	PUNCT
ejpam-6489	57	27	and	and	CCONJ
ejpam-6489	57	28	complex	complex	ADJ
ejpam-6489	57	29	fuzzy	fuzzy	ADJ
ejpam-6489	57	30	sets	set	NOUN
ejpam-6489	57	31	by	by	ADP
ejpam-6489	57	32	incorporating	incorporate	VERB
ejpam-6489	57	33	three	three	NUM
ejpam-6489	57	34	independent	independent	ADJ
ejpam-6489	57	35	dimensions	dimension	NOUN
ejpam-6489	57	36	of	of	ADP
ejpam-6489	57	37	information	information	NOUN
ejpam-6489	57	38	to	to	PART
ejpam-6489	57	39	model	model	VERB
ejpam-6489	57	40	more	more	ADV
ejpam-6489	57	41	complex	complex	ADJ
ejpam-6489	57	42	and	and	CCONJ
ejpam-6489	57	43	nuanced	nuanced	ADJ
ejpam-6489	57	44	real	real	ADJ
ejpam-6489	57	45	-	-	PUNCT
ejpam-6489	57	46	world	world	NOUN
ejpam-6489	57	47	scenarios	scenario	NOUN
ejpam-6489	57	48	.	.	PUNCT
ejpam-6489	58	1	from	from	ADP
ejpam-6489	58	2	the	the	DET
ejpam-6489	58	3	above	above	ADJ
ejpam-6489	58	4	literature	literature	NOUN
ejpam-6489	58	5	we	we	PRON
ejpam-6489	58	6	found	find	VERB
ejpam-6489	58	7	the	the	DET
ejpam-6489	58	8	research	research	NOUN
ejpam-6489	58	9	gap	gap	NOUN
ejpam-6489	58	10	and	and	CCONJ
ejpam-6489	58	11	tripolar	tripolar	ADJ
ejpam-6489	58	12	complex	complex	ADJ
ejpam-6489	58	13	fuzzy	fuzzy	ADJ
ejpam-6489	58	14	set	set	NOUN
ejpam-6489	58	15	is	be	AUX
ejpam-6489	58	16	introduced	introduce	VERB
ejpam-6489	58	17	.	.	PUNCT
ejpam-6489	59	1	the	the	DET
ejpam-6489	59	2	paper	paper	NOUN
ejpam-6489	59	3	is	be	AUX
ejpam-6489	59	4	organized	organize	VERB
ejpam-6489	59	5	as	as	SCONJ
ejpam-6489	59	6	follows	follow	VERB
ejpam-6489	59	7	:	:	PUNCT
ejpam-6489	59	8	section	section	NOUN
ejpam-6489	59	9	2	2	NUM
ejpam-6489	59	10	provides	provide	VERB
ejpam-6489	59	11	a	a	DET
ejpam-6489	59	12	concise	concise	ADJ
ejpam-6489	59	13	set	set	NOUN
ejpam-6489	59	14	of	of	ADP
ejpam-6489	59	15	basic	basic	ADJ
ejpam-6489	59	16	definitions	definition	NOUN
ejpam-6489	59	17	.	.	PUNCT
ejpam-6489	60	1	section	section	NOUN
ejpam-6489	60	2	3	3	NUM
ejpam-6489	60	3	introduces	introduce	VERB
ejpam-6489	60	4	the	the	DET
ejpam-6489	60	5	novel	novel	ADJ
ejpam-6489	60	6	concept	concept	NOUN
ejpam-6489	60	7	of	of	ADP
ejpam-6489	60	8	tripolar	tripolar	ADJ
ejpam-6489	60	9	complex	complex	ADJ
ejpam-6489	60	10	fuzzy	fuzzy	ADJ
ejpam-6489	60	11	lie	lie	NOUN
ejpam-6489	60	12	bracket	bracket	NOUN
ejpam-6489	60	13	and	and	CCONJ
ejpam-6489	60	14	examines	examine	VERB
ejpam-6489	60	15	its	its	PRON
ejpam-6489	60	16	key	key	ADJ
ejpam-6489	60	17	properties	property	NOUN
ejpam-6489	60	18	.	.	PUNCT
ejpam-6489	61	1	section	section	NOUN
ejpam-6489	61	2	4	4	NUM
ejpam-6489	61	3	develops	develop	VERB
ejpam-6489	61	4	the	the	DET
ejpam-6489	61	5	concept	concept	NOUN
ejpam-6489	61	6	of	of	ADP
ejpam-6489	61	7	tripolar	tripolar	ADJ
ejpam-6489	61	8	complex	complex	ADJ
ejpam-6489	61	9	fuzzy	fuzzy	ADJ
ejpam-6489	61	10	lie	lie	NOUN
ejpam-6489	61	11	subalgebras	subalgebras	PROPN
ejpam-6489	61	12	.	.	PUNCT
ejpam-6489	62	1	section	section	NOUN
ejpam-6489	62	2	5	5	NUM
ejpam-6489	62	3	investigates	investigate	VERB
ejpam-6489	62	4	nilpotent	nilpotent	ADJ
ejpam-6489	62	5	and	and	CCONJ
ejpam-6489	62	6	solvable	solvable	ADJ
ejpam-6489	62	7	tripolar	tripolar	ADJ
ejpam-6489	62	8	complex	complex	ADJ
ejpam-6489	62	9	fuzzy	fuzzy	ADJ
ejpam-6489	62	10	lie	lie	NOUN
ejpam-6489	62	11	ideals	ideal	NOUN
ejpam-6489	62	12	.	.	PUNCT
ejpam-6489	63	1	section	section	NOUN
ejpam-6489	63	2	6	6	NUM
ejpam-6489	63	3	concludes	conclude	VERB
ejpam-6489	63	4	the	the	DET
ejpam-6489	63	5	study	study	NOUN
ejpam-6489	63	6	and	and	CCONJ
ejpam-6489	63	7	suggests	suggest	VERB
ejpam-6489	63	8	promising	promise	VERB
ejpam-6489	63	9	directions	direction	NOUN
ejpam-6489	63	10	for	for	ADP
ejpam-6489	63	11	future	future	ADJ
ejpam-6489	63	12	research	research	NOUN
ejpam-6489	63	13	.	.	PUNCT
ejpam-6489	64	1	to	to	PART
ejpam-6489	64	2	ensure	ensure	VERB
ejpam-6489	64	3	clarity	clarity	NOUN
ejpam-6489	64	4	,	,	PUNCT
ejpam-6489	64	5	table	table	NOUN
ejpam-6489	64	6	1	1	NUM
ejpam-6489	64	7	summarizes	summarize	NOUN
ejpam-6489	64	8	all	all	DET
ejpam-6489	64	9	mathematical	mathematical	ADJ
ejpam-6489	64	10	notation	notation	NOUN
ejpam-6489	64	11	and	and	CCONJ
ejpam-6489	64	12	terminology	terminology	NOUN
ejpam-6489	64	13	used	use	VERB
ejpam-6489	64	14	throughout	throughout	ADP
ejpam-6489	64	15	the	the	DET
ejpam-6489	64	16	paper	paper	NOUN
ejpam-6489	64	17	.	.	PUNCT
ejpam-6489	65	1	m.	m.	NOUN
ejpam-6489	65	2	balamurugan	balamurugan	PROPN
ejpam-6489	65	3	,	,	PUNCT
ejpam-6489	65	4	g.	g.	PROPN
ejpam-6489	65	5	ellammal	ellammal	PROPN
ejpam-6489	65	6	,	,	PUNCT
ejpam-6489	65	7	a.	a.	NOUN
ejpam-6489	65	8	iampan	iampan	PROPN
ejpam-6489	65	9	/	/	SYM
ejpam-6489	65	10	eur	eur	PROPN
ejpam-6489	65	11	.	.	PUNCT
ejpam-6489	66	1	j.	j.	PROPN
ejpam-6489	66	2	pure	pure	PROPN
ejpam-6489	66	3	appl	appl	PROPN
ejpam-6489	66	4	.	.	PROPN
ejpam-6489	66	5	math	math	PROPN
ejpam-6489	66	6	,	,	PUNCT
ejpam-6489	66	7	18	18	NUM
ejpam-6489	66	8	(	(	PUNCT
ejpam-6489	66	9	3	3	NUM
ejpam-6489	66	10	)	)	PUNCT
ejpam-6489	66	11	(	(	PUNCT
ejpam-6489	66	12	2025	2025	NUM
ejpam-6489	66	13	)	)	PUNCT
ejpam-6489	66	14	,	,	PUNCT
ejpam-6489	66	15	6489	6489	NUM
ejpam-6489	66	16	3	3	NUM
ejpam-6489	66	17	of	of	ADP
ejpam-6489	66	18	26	26	NUM
ejpam-6489	66	19	table	table	NOUN
ejpam-6489	66	20	1	1	NUM
ejpam-6489	66	21	:	:	PUNCT
ejpam-6489	66	22	acronyms	acronym	NOUN
ejpam-6489	66	23	list	list	NOUN
ejpam-6489	66	24	.	.	PUNCT
ejpam-6489	67	1	acronyms	acronym	NOUN
ejpam-6489	67	2	representations	representation	NOUN
ejpam-6489	67	3	l	l	NOUN
ejpam-6489	67	4	lie	lie	NOUN
ejpam-6489	67	5	algebra	algebra	NOUN
ejpam-6489	67	6	fs(s	fs(s	PUNCT
ejpam-6489	67	7	)	)	PUNCT
ejpam-6489	67	8	fuzzy	fuzzy	ADJ
ejpam-6489	67	9	set(s	set(s	PROPN
ejpam-6489	67	10	)	)	PUNCT
ejpam-6489	67	11	cfs(s	cfs(s	NOUN
ejpam-6489	67	12	)	)	PUNCT
ejpam-6489	67	13	complex	complex	ADJ
ejpam-6489	67	14	fuzzy	fuzzy	ADJ
ejpam-6489	67	15	set(s	set(s	SYM
ejpam-6489	67	16	)	)	PUNCT
ejpam-6489	67	17	ifs(s	ifs(s	PROPN
ejpam-6489	67	18	)	)	PUNCT
ejpam-6489	67	19	complex	complex	ADJ
ejpam-6489	67	20	intuitionistic	intuitionistic	ADJ
ejpam-6489	67	21	fuzzy	fuzzy	ADJ
ejpam-6489	67	22	set(s	set(s	NOUN
ejpam-6489	67	23	)	)	PUNCT
ejpam-6489	67	24	bfs(s	bfs(s	NOUN
ejpam-6489	67	25	)	)	PUNCT
ejpam-6489	67	26	bipolar	bipolar	ADJ
ejpam-6489	67	27	fuzzy	fuzzy	ADJ
ejpam-6489	67	28	set(s	set(s	PROPN
ejpam-6489	67	29	)	)	PUNCT
ejpam-6489	67	30	bcfs(s	bcfs(s	NOUN
ejpam-6489	67	31	)	)	PUNCT
ejpam-6489	67	32	bipolar	bipolar	ADJ
ejpam-6489	67	33	complex	complex	ADJ
ejpam-6489	67	34	fuzzy	fuzzy	ADJ
ejpam-6489	67	35	set(s	set(s	PROPN
ejpam-6489	67	36	)	)	PUNCT
ejpam-6489	67	37	t	t	NOUN
ejpam-6489	67	38	fs(s	fs(s	PUNCT
ejpam-6489	67	39	)	)	PUNCT
ejpam-6489	67	40	tripolar	tripolar	ADJ
ejpam-6489	67	41	fuzzy	fuzzy	ADJ
ejpam-6489	67	42	set(s	set(s	PROPN
ejpam-6489	67	43	)	)	PUNCT
ejpam-6489	67	44	t	t	PROPN
ejpam-6489	67	45	cfs(s	cfs(s	PROPN
ejpam-6489	67	46	)	)	PUNCT
ejpam-6489	67	47	tripolar	tripolar	ADJ
ejpam-6489	67	48	complex	complex	ADJ
ejpam-6489	67	49	fuzzy	fuzzy	ADJ
ejpam-6489	67	50	set(s	set(s	PROPN
ejpam-6489	67	51	)	)	PUNCT
ejpam-6489	67	52	t	t	PROPN
ejpam-6489	67	53	cfls(s	cfls(s	PROPN
ejpam-6489	67	54	)	)	PUNCT
ejpam-6489	67	55	tripolar	tripolar	ADJ
ejpam-6489	67	56	complex	complex	ADJ
ejpam-6489	67	57	fuzzy	fuzzy	ADJ
ejpam-6489	67	58	lie	lie	NOUN
ejpam-6489	67	59	subalgebra(s	subalgebra(s	PROPN
ejpam-6489	67	60	)	)	PUNCT
ejpam-6489	67	61	t	t	PROPN
ejpam-6489	67	62	cfli(s	cfli(s	NUM
ejpam-6489	67	63	)	)	PUNCT
ejpam-6489	67	64	tripolar	tripolar	ADJ
ejpam-6489	67	65	complex	complex	ADJ
ejpam-6489	67	66	fuzzy	fuzzy	ADJ
ejpam-6489	67	67	lie	lie	NOUN
ejpam-6489	67	68	ideal(s	ideal(s	PROPN
ejpam-6489	67	69	)	)	PUNCT
ejpam-6489	67	70	nt	not	PART
ejpam-6489	67	71	cfli(s	cfli(s	NOUN
ejpam-6489	67	72	)	)	PUNCT
ejpam-6489	67	73	nilpotent	nilpotent	ADJ
ejpam-6489	67	74	tripolar	tripolar	ADJ
ejpam-6489	67	75	complex	complex	ADJ
ejpam-6489	67	76	fuzzy	fuzzy	ADJ
ejpam-6489	67	77	lie	lie	NOUN
ejpam-6489	67	78	ideal(s	ideal(s	PROPN
ejpam-6489	67	79	)	)	PUNCT
ejpam-6489	67	80	st	st	PROPN
ejpam-6489	67	81	cfli(s	cfli(s	NOUN
ejpam-6489	67	82	)	)	PUNCT
ejpam-6489	67	83	solvable	solvable	ADJ
ejpam-6489	67	84	tripolar	tripolar	ADJ
ejpam-6489	67	85	complex	complex	ADJ
ejpam-6489	67	86	fuzzy	fuzzy	ADJ
ejpam-6489	67	87	lie	lie	NOUN
ejpam-6489	67	88	ideal(s	ideal(s	PROPN
ejpam-6489	67	89	)	)	PUNCT
ejpam-6489	67	90	2	2	NUM
ejpam-6489	67	91	.	.	PUNCT
ejpam-6489	67	92	preliminaries	preliminary	NOUN
ejpam-6489	67	93	definition	definition	NOUN
ejpam-6489	67	94	1	1	NUM
ejpam-6489	67	95	.	.	PUNCT
ejpam-6489	68	1	[	[	X
ejpam-6489	68	2	21	21	NUM
ejpam-6489	68	3	]	]	PUNCT
ejpam-6489	68	4	a	a	DET
ejpam-6489	68	5	lie	lie	NOUN
ejpam-6489	68	6	algebra	algebra	NOUN
ejpam-6489	68	7	l̃	l̃	PROPN
ejpam-6489	68	8	defined	define	VERB
ejpam-6489	68	9	over	over	ADP
ejpam-6489	68	10	a	a	DET
ejpam-6489	68	11	field	field	NOUN
ejpam-6489	68	12	f	f	X
ejpam-6489	68	13	is	be	AUX
ejpam-6489	68	14	a	a	DET
ejpam-6489	68	15	vector	vector	NOUN
ejpam-6489	68	16	space	space	NOUN
ejpam-6489	68	17	together	together	ADV
ejpam-6489	68	18	with	with	ADP
ejpam-6489	68	19	a	a	DET
ejpam-6489	68	20	bilinear	bilinear	NOUN
ejpam-6489	68	21	operation	operation	NOUN
ejpam-6489	68	22	,	,	PUNCT
ejpam-6489	68	23	called	call	VERB
ejpam-6489	68	24	the	the	DET
ejpam-6489	68	25	lie	lie	NOUN
ejpam-6489	68	26	bracket	bracket	NOUN
ejpam-6489	68	27	,	,	PUNCT
ejpam-6489	68	28	which	which	PRON
ejpam-6489	68	29	adheres	adhere	VERB
ejpam-6489	68	30	to	to	ADP
ejpam-6489	68	31	certain	certain	ADJ
ejpam-6489	68	32	key	key	ADJ
ejpam-6489	68	33	properties	property	NOUN
ejpam-6489	68	34	:	:	PUNCT
ejpam-6489	68	35	(	(	PUNCT
ejpam-6489	68	36	i	i	NOUN
ejpam-6489	68	37	)	)	PUNCT
ejpam-6489	68	38	bilinear	bilinear	NOUN
ejpam-6489	68	39	:	:	PUNCT
ejpam-6489	68	40	the	the	DET
ejpam-6489	68	41	lie	lie	NOUN
ejpam-6489	68	42	bracket	bracket	NOUN
ejpam-6489	68	43	[	[	X
ejpam-6489	68	44	,	,	PUNCT
ejpam-6489	68	45	]	]	X
ejpam-6489	68	46	:	:	PUNCT
ejpam-6489	68	47	l̃	l̃	PROPN
ejpam-6489	68	48	×	×	NOUN
ejpam-6489	68	49	l̃	l̃	PROPN
ejpam-6489	68	50	→	→	PUNCT
ejpam-6489	68	51	l̃	l̃	PROPN
ejpam-6489	68	52	is	be	AUX
ejpam-6489	68	53	a	a	DET
ejpam-6489	68	54	bilinear	bilinear	NOUN
ejpam-6489	68	55	.	.	PUNCT
ejpam-6489	69	1	(	(	PUNCT
ejpam-6489	69	2	ii	ii	NOUN
ejpam-6489	69	3	)	)	PUNCT
ejpam-6489	69	4	skew	skew	NOUN
ejpam-6489	69	5	-	-	PUNCT
ejpam-6489	69	6	symmetry	symmetry	NOUN
ejpam-6489	69	7	:	:	PUNCT
ejpam-6489	69	8	for	for	ADP
ejpam-6489	69	9	any	any	DET
ejpam-6489	69	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	69	11	,	,	PUNCT
ejpam-6489	69	12	η̃	η̃	PROPN
ejpam-6489	69	13	∈	∈	PROPN
ejpam-6489	69	14	l̃	l̃	PROPN
ejpam-6489	69	15	,	,	PUNCT
ejpam-6489	70	1	[	[	X
ejpam-6489	70	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	70	3	,	,	PUNCT
ejpam-6489	70	4	η̃	η̃	PROPN
ejpam-6489	70	5	]	]	PUNCT
ejpam-6489	70	6	=	=	SYM
ejpam-6489	70	7	−[η̃	−[η̃	PROPN
ejpam-6489	70	8	,	,	PUNCT
ejpam-6489	70	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	70	10	]	]	X
ejpam-6489	70	11	.	.	PUNCT
ejpam-6489	71	1	(	(	PUNCT
ejpam-6489	71	2	iii	iii	X
ejpam-6489	71	3	)	)	PUNCT
ejpam-6489	71	4	jacobi	jacobi	NOUN
ejpam-6489	71	5	identity	identity	NOUN
ejpam-6489	71	6	:	:	PUNCT
ejpam-6489	71	7	for	for	ADP
ejpam-6489	71	8	any	any	DET
ejpam-6489	71	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	71	10	,	,	PUNCT
ejpam-6489	71	11	η̃	η̃	PROPN
ejpam-6489	71	12	,	,	PUNCT
ejpam-6489	71	13	ρ̃	ρ̃	PROPN
ejpam-6489	71	14	∈	∈	PROPN
ejpam-6489	71	15	l	l	NOUN
ejpam-6489	71	16	,	,	PUNCT
ejpam-6489	71	17	[	[	X
ejpam-6489	71	18	ϕ̃	ϕ̃	X
ejpam-6489	71	19	,	,	PUNCT
ejpam-6489	71	20	[	[	X
ejpam-6489	71	21	η̃	η̃	PROPN
ejpam-6489	71	22	,	,	PUNCT
ejpam-6489	71	23	ρ̃	ρ̃	PROPN
ejpam-6489	71	24	]	]	X
ejpam-6489	71	25	]	]	PUNCT
ejpam-6489	72	1	+	+	CCONJ
ejpam-6489	72	2	[	[	X
ejpam-6489	72	3	η̃	η̃	PROPN
ejpam-6489	72	4	,	,	PUNCT
ejpam-6489	72	5	[	[	X
ejpam-6489	72	6	ρ̃	ρ̃	PROPN
ejpam-6489	72	7	,	,	PUNCT
ejpam-6489	72	8	ϕ̃	ϕ̃	PROPN
ejpam-6489	72	9	]	]	X
ejpam-6489	72	10	]	]	PUNCT
ejpam-6489	73	1	+	+	CCONJ
ejpam-6489	73	2	[	[	X
ejpam-6489	73	3	ρ̃	ρ̃	PROPN
ejpam-6489	73	4	,	,	PUNCT
ejpam-6489	73	5	[	[	X
ejpam-6489	73	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	73	7	,	,	PUNCT
ejpam-6489	73	8	η̃	η̃	PROPN
ejpam-6489	73	9	]	]	PUNCT
ejpam-6489	73	10	]	]	X
ejpam-6489	73	11	=	=	PUNCT
ejpam-6489	73	12	0	0	X
ejpam-6489	73	13	.	.	PUNCT
ejpam-6489	73	14	definition	definition	NOUN
ejpam-6489	73	15	2	2	NUM
ejpam-6489	73	16	.	.	PUNCT
ejpam-6489	74	1	[	[	X
ejpam-6489	74	2	4	4	X
ejpam-6489	74	3	]	]	PUNCT
ejpam-6489	74	4	a	a	DET
ejpam-6489	74	5	fs	fs	ADP
ejpam-6489	74	6	f̃	f̃	PROPN
ejpam-6489	74	7	=	=	SYM
ejpam-6489	74	8	{	{	PUNCT
ejpam-6489	74	9	(	(	PUNCT
ejpam-6489	74	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	74	11	,	,	PUNCT
ejpam-6489	74	12	ξf̃	ξf̃	PROPN
ejpam-6489	74	13	(	(	PUNCT
ejpam-6489	74	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	74	15	)	)	PUNCT
ejpam-6489	74	16	)	)	PUNCT
ejpam-6489	75	1	|	|	ADV
ejpam-6489	75	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	75	3	∈	∈	PROPN
ejpam-6489	75	4	l̃	l̃	PROPN
ejpam-6489	75	5	}	}	PUNCT
ejpam-6489	75	6	,	,	PUNCT
ejpam-6489	75	7	where	where	SCONJ
ejpam-6489	75	8	ξf̃	ξf̃	PROPN
ejpam-6489	75	9	(	(	PUNCT
ejpam-6489	75	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	75	11	)	)	PUNCT
ejpam-6489	75	12	:	:	PUNCT
ejpam-6489	76	1	l̃	l̃	PROPN
ejpam-6489	76	2	→	→	PUNCT
ejpam-6489	76	3	[	[	X
ejpam-6489	76	4	0	0	NUM
ejpam-6489	76	5	,	,	PUNCT
ejpam-6489	76	6	1	1	NUM
ejpam-6489	76	7	]	]	PUNCT
ejpam-6489	76	8	is	be	AUX
ejpam-6489	76	9	the	the	DET
ejpam-6489	76	10	md	md	PROPN
ejpam-6489	76	11	of	of	ADP
ejpam-6489	76	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	76	13	to	to	PART
ejpam-6489	76	14	fs	fs	ADP
ejpam-6489	76	15	f̃	f̃	PROPN
ejpam-6489	76	16	.	.	PUNCT
ejpam-6489	77	1	definition	definition	NOUN
ejpam-6489	77	2	3	3	NUM
ejpam-6489	77	3	.	.	PUNCT
ejpam-6489	78	1	[	[	X
ejpam-6489	78	2	7	7	X
ejpam-6489	78	3	]	]	X
ejpam-6489	78	4	a	a	DET
ejpam-6489	78	5	cfs	cfs	NOUN
ejpam-6489	78	6	c̃	c̃	PROPN
ejpam-6489	78	7	in	in	ADP
ejpam-6489	78	8	l̃	l̃	PROPN
ejpam-6489	78	9	is	be	AUX
ejpam-6489	78	10	the	the	DET
ejpam-6489	78	11	structure	structure	NOUN
ejpam-6489	78	12	c̃	c̃	PROPN
ejpam-6489	78	13	=	=	PRON
ejpam-6489	78	14	{	{	PUNCT
ejpam-6489	78	15	(	(	PUNCT
ejpam-6489	78	16	ϕ̃	ϕ̃	PROPN
ejpam-6489	78	17	,	,	PUNCT
ejpam-6489	78	18	ξc̃(ϕ̃	ξc̃(ϕ̃	PROPN
ejpam-6489	78	19	)	)	PUNCT
ejpam-6489	78	20	=	=	SYM
ejpam-6489	78	21	r̃c̃(ϕ̃)e	r̃c̃(ϕ̃)e	PROPN
ejpam-6489	78	22	i2πω̃c̃(ϕ̃	i2πω̃c̃(ϕ̃	PRON
ejpam-6489	78	23	)	)	PUNCT
ejpam-6489	78	24	)	)	PUNCT
ejpam-6489	79	1	|	|	ADV
ejpam-6489	79	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	79	3	∈	∈	PROPN
ejpam-6489	79	4	l̃	l̃	PROPN
ejpam-6489	79	5	}	}	PUNCT
ejpam-6489	79	6	,	,	PUNCT
ejpam-6489	79	7	where	where	SCONJ
ejpam-6489	79	8	r̃c̃(ϕ̃	r̃c̃(ϕ̃	VERB
ejpam-6489	79	9	)	)	PUNCT
ejpam-6489	79	10	∈	∈	PROPN
ejpam-6489	80	1	[	[	X
ejpam-6489	80	2	0	0	NUM
ejpam-6489	80	3	,	,	PUNCT
ejpam-6489	80	4	1	1	NUM
ejpam-6489	80	5	]	]	PUNCT
ejpam-6489	80	6	,	,	PUNCT
ejpam-6489	80	7	ω̃c̃(ϕ̃	ω̃c̃(ϕ̃	NUM
ejpam-6489	80	8	)	)	PUNCT
ejpam-6489	80	9	∈	∈	PROPN
ejpam-6489	81	1	[	[	X
ejpam-6489	81	2	0	0	NUM
ejpam-6489	81	3	,	,	PUNCT
ejpam-6489	81	4	2π	2π	NOUN
ejpam-6489	81	5	]	]	PUNCT
ejpam-6489	81	6	.	.	PUNCT
ejpam-6489	82	1	definition	definition	NOUN
ejpam-6489	82	2	4	4	NUM
ejpam-6489	82	3	.	.	PUNCT
ejpam-6489	83	1	[	[	X
ejpam-6489	83	2	20	20	NUM
ejpam-6489	83	3	]	]	PUNCT
ejpam-6489	83	4	an	an	DET
ejpam-6489	83	5	ifs	ifs	PROPN
ejpam-6489	83	6	ĩ	ĩ	PROPN
ejpam-6489	83	7	in	in	ADP
ejpam-6489	83	8	l̃	l̃	PROPN
ejpam-6489	83	9	is	be	AUX
ejpam-6489	83	10	the	the	DET
ejpam-6489	83	11	collection	collection	NOUN
ejpam-6489	83	12	ĩ	ĩ	PROPN
ejpam-6489	83	13	=	=	SYM
ejpam-6489	83	14	{	{	PUNCT
ejpam-6489	83	15	(	(	PUNCT
ejpam-6489	83	16	ϕ̃	ϕ̃	PROPN
ejpam-6489	83	17	,	,	PUNCT
ejpam-6489	83	18	ξĩ(ϕ̃	ξĩ(ϕ̃	PROPN
ejpam-6489	83	19	)	)	PUNCT
ejpam-6489	83	20	,	,	PUNCT
ejpam-6489	83	21	ηĩ(ϕ̃	ηĩ(ϕ̃	PROPN
ejpam-6489	83	22	)	)	PUNCT
ejpam-6489	83	23	)	)	PUNCT
ejpam-6489	84	1	|	|	ADV
ejpam-6489	84	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	84	3	∈	∈	PROPN
ejpam-6489	84	4	l̃	l̃	PROPN
ejpam-6489	84	5	}	}	PUNCT
ejpam-6489	84	6	,	,	PUNCT
ejpam-6489	84	7	where	where	SCONJ
ejpam-6489	84	8	ξĩ(ϕ̃	ξĩ(ϕ̃	NOUN
ejpam-6489	84	9	)	)	PUNCT
ejpam-6489	84	10	:	:	PUNCT
ejpam-6489	85	1	l̃	l̃	PROPN
ejpam-6489	85	2	→	→	PUNCT
ejpam-6489	86	1	[	[	X
ejpam-6489	86	2	0	0	NUM
ejpam-6489	86	3	,	,	PUNCT
ejpam-6489	86	4	1	1	NUM
ejpam-6489	86	5	]	]	PUNCT
ejpam-6489	86	6	and	and	CCONJ
ejpam-6489	86	7	ηĩ(ϕ̃	ηĩ(ϕ̃	PROPN
ejpam-6489	86	8	)	)	PUNCT
ejpam-6489	86	9	:	:	PUNCT
ejpam-6489	87	1	l̃	l̃	PROPN
ejpam-6489	87	2	→	→	PUNCT
ejpam-6489	87	3	[	[	X
ejpam-6489	87	4	0	0	NUM
ejpam-6489	87	5	,	,	PUNCT
ejpam-6489	87	6	1	1	NUM
ejpam-6489	87	7	]	]	PUNCT
ejpam-6489	87	8	denotes	denote	VERB
ejpam-6489	87	9	the	the	DET
ejpam-6489	87	10	md	md	PROPN
ejpam-6489	87	11	and	and	CCONJ
ejpam-6489	87	12	nmd	nmd	PROPN
ejpam-6489	87	13	degree	degree	NOUN
ejpam-6489	87	14	of	of	ADP
ejpam-6489	87	15	ϕ̃	ϕ̃	PROPN
ejpam-6489	87	16	,	,	PUNCT
ejpam-6489	87	17	respectively	respectively	ADV
ejpam-6489	87	18	with	with	ADP
ejpam-6489	87	19	0	0	NUM
ejpam-6489	87	20	≤	≤	NUM
ejpam-6489	87	21	ξĩ(ϕ̃	ξĩ(ϕ̃	PROPN
ejpam-6489	87	22	)	)	PUNCT
ejpam-6489	87	23	+	+	CCONJ
ejpam-6489	87	24	ηĩ(ϕ̃	ηĩ(ϕ̃	PROPN
ejpam-6489	87	25	)	)	PUNCT
ejpam-6489	87	26	≤	≤	NOUN
ejpam-6489	87	27	1	1	NUM
ejpam-6489	87	28	for	for	ADP
ejpam-6489	87	29	all	all	DET
ejpam-6489	87	30	ϕ̃	ϕ̃	PROPN
ejpam-6489	87	31	∈	∈	PROPN
ejpam-6489	87	32	l̃.	l̃.	ADJ
ejpam-6489	87	33	definition	definition	NOUN
ejpam-6489	87	34	5	5	NUM
ejpam-6489	87	35	.	.	PUNCT
ejpam-6489	88	1	[	[	X
ejpam-6489	88	2	5	5	NUM
ejpam-6489	88	3	]	]	PUNCT
ejpam-6489	88	4	a	a	DET
ejpam-6489	88	5	bfs	bfs	NOUN
ejpam-6489	88	6	b̃	b̃	PROPN
ejpam-6489	88	7	=	=	PROPN
ejpam-6489	88	8	{	{	PUNCT
ejpam-6489	88	9	(	(	PUNCT
ejpam-6489	88	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	88	11	,	,	PUNCT
ejpam-6489	88	12	ξpb̃	ξpb̃	X
ejpam-6489	88	13	(	(	PUNCT
ejpam-6489	88	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	88	15	)	)	PUNCT
ejpam-6489	88	16	,	,	PUNCT
ejpam-6489	88	17	ξ	ξ	PROPN
ejpam-6489	88	18	n	n	X
ejpam-6489	88	19	b̃	b̃	PROPN
ejpam-6489	88	20	(	(	PUNCT
ejpam-6489	88	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	88	22	)	)	PUNCT
ejpam-6489	88	23	)	)	PUNCT
ejpam-6489	89	1	|	|	ADV
ejpam-6489	89	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	89	3	∈	∈	PROPN
ejpam-6489	89	4	l̃	l̃	PROPN
ejpam-6489	89	5	}	}	PUNCT
ejpam-6489	89	6	,	,	PUNCT
ejpam-6489	89	7	where	where	SCONJ
ejpam-6489	89	8	ξpb̃	ξpb̃	PROPN
ejpam-6489	89	9	(	(	PUNCT
ejpam-6489	89	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	89	11	)	)	PUNCT
ejpam-6489	89	12	:	:	PUNCT
ejpam-6489	90	1	l̃	l̃	PROPN
ejpam-6489	90	2	→	→	PUNCT
ejpam-6489	91	1	[	[	X
ejpam-6489	91	2	0	0	NUM
ejpam-6489	91	3	,	,	PUNCT
ejpam-6489	91	4	1	1	NUM
ejpam-6489	91	5	]	]	PUNCT
ejpam-6489	91	6	and	and	CCONJ
ejpam-6489	91	7	ξnb̃	ξnb̃	PROPN
ejpam-6489	91	8	(	(	PUNCT
ejpam-6489	91	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	91	10	)	)	PUNCT
ejpam-6489	91	11	:	:	PUNCT
ejpam-6489	92	1	l̃	l̃	PROPN
ejpam-6489	92	2	→	→	PUNCT
ejpam-6489	92	3	[	[	X
ejpam-6489	92	4	-1	-1	X
ejpam-6489	92	5	,	,	PUNCT
ejpam-6489	92	6	0	0	NUM
ejpam-6489	92	7	]	]	PUNCT
ejpam-6489	92	8	are	be	AUX
ejpam-6489	92	9	+	+	ADP
ejpam-6489	92	10	md	md	PROPN
ejpam-6489	92	11	and	and	CCONJ
ejpam-6489	92	12	−md	−md	PROPN
ejpam-6489	92	13	of	of	ADP
ejpam-6489	92	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	92	15	,	,	PUNCT
ejpam-6489	92	16	respectively	respectively	ADV
ejpam-6489	92	17	,	,	PUNCT
ejpam-6489	92	18	with	with	ADP
ejpam-6489	92	19	−1	−1	NOUN
ejpam-6489	92	20	≤	≤	NUM
ejpam-6489	92	21	ξpb̃	ξpb̃	X
ejpam-6489	92	22	(	(	PUNCT
ejpam-6489	92	23	ϕ̃)+ξnb̃	ϕ̃)+ξnb̃	X
ejpam-6489	92	24	(	(	PUNCT
ejpam-6489	92	25	ϕ̃	ϕ̃	PROPN
ejpam-6489	92	26	)	)	PUNCT
ejpam-6489	92	27	≤	≤	NOUN
ejpam-6489	92	28	1	1	NUM
ejpam-6489	92	29	.	.	PUNCT
ejpam-6489	93	1	the	the	DET
ejpam-6489	93	2	pair	pair	NOUN
ejpam-6489	93	3	(	(	PUNCT
ejpam-6489	93	4	µp	µp	PROPN
ejpam-6489	93	5	b̃	b̃	PROPN
ejpam-6489	93	6	,	,	PUNCT
ejpam-6489	93	7	ξnb̃	ξnb̃	PROPN
ejpam-6489	93	8	)	)	PUNCT
ejpam-6489	93	9	denotes	denote	VERB
ejpam-6489	93	10	the	the	DET
ejpam-6489	93	11	bfn	bfn	PROPN
ejpam-6489	93	12	.	.	PUNCT
ejpam-6489	94	1	the	the	DET
ejpam-6489	94	2	+	+	PROPN
ejpam-6489	94	3	md	md	PROPN
ejpam-6489	94	4	is	be	AUX
ejpam-6489	94	5	the	the	DET
ejpam-6489	94	6	degree	degree	NOUN
ejpam-6489	94	7	of	of	ADP
ejpam-6489	94	8	conformity	conformity	NOUN
ejpam-6489	94	9	of	of	ADP
ejpam-6489	94	10	any	any	DET
ejpam-6489	94	11	property	property	NOUN
ejpam-6489	94	12	for	for	ADP
ejpam-6489	94	13	an	an	DET
ejpam-6489	94	14	entity	entity	NOUN
ejpam-6489	94	15	,	,	PUNCT
ejpam-6489	94	16	while	while	SCONJ
ejpam-6489	94	17	−md	−md	PRON
ejpam-6489	94	18	shows	show	VERB
ejpam-6489	94	19	the	the	DET
ejpam-6489	94	20	satisfaction	satisfaction	NOUN
ejpam-6489	94	21	degree	degree	NOUN
ejpam-6489	94	22	of	of	ADP
ejpam-6489	94	23	the	the	DET
ejpam-6489	94	24	inherent	inherent	ADJ
ejpam-6489	94	25	opposing	opposing	ADJ
ejpam-6489	94	26	characteristic	characteristic	NOUN
ejpam-6489	94	27	.	.	PUNCT
ejpam-6489	95	1	m.	m.	NOUN
ejpam-6489	95	2	balamurugan	balamurugan	PROPN
ejpam-6489	95	3	,	,	PUNCT
ejpam-6489	95	4	g.	g.	PROPN
ejpam-6489	95	5	ellammal	ellammal	PROPN
ejpam-6489	95	6	,	,	PUNCT
ejpam-6489	95	7	a.	a.	NOUN
ejpam-6489	95	8	iampan	iampan	PROPN
ejpam-6489	95	9	/	/	SYM
ejpam-6489	95	10	eur	eur	PROPN
ejpam-6489	95	11	.	.	PUNCT
ejpam-6489	96	1	j.	j.	PROPN
ejpam-6489	96	2	pure	pure	PROPN
ejpam-6489	96	3	appl	appl	PROPN
ejpam-6489	96	4	.	.	PROPN
ejpam-6489	96	5	math	math	PROPN
ejpam-6489	96	6	,	,	PUNCT
ejpam-6489	96	7	18	18	NUM
ejpam-6489	96	8	(	(	PUNCT
ejpam-6489	96	9	3	3	NUM
ejpam-6489	96	10	)	)	PUNCT
ejpam-6489	96	11	(	(	PUNCT
ejpam-6489	96	12	2025	2025	NUM
ejpam-6489	96	13	)	)	PUNCT
ejpam-6489	96	14	,	,	PUNCT
ejpam-6489	96	15	6489	6489	NUM
ejpam-6489	96	16	4	4	NUM
ejpam-6489	96	17	of	of	ADP
ejpam-6489	96	18	26	26	NUM
ejpam-6489	96	19	definition	definition	NOUN
ejpam-6489	96	20	6	6	NUM
ejpam-6489	96	21	.	.	PUNCT
ejpam-6489	97	1	[	[	X
ejpam-6489	97	2	9	9	NUM
ejpam-6489	97	3	]	]	PUNCT
ejpam-6489	97	4	a	a	DET
ejpam-6489	97	5	bcfs	bcfs	NOUN
ejpam-6489	97	6	b̃	b̃	PROPN
ejpam-6489	97	7	in	in	ADP
ejpam-6489	97	8	l̃	l̃	PROPN
ejpam-6489	97	9	is	be	AUX
ejpam-6489	97	10	the	the	DET
ejpam-6489	97	11	structure	structure	NOUN
ejpam-6489	97	12	b̃	b̃	PROPN
ejpam-6489	97	13	=	=	PRON
ejpam-6489	97	14	{	{	PUNCT
ejpam-6489	97	15	(	(	PUNCT
ejpam-6489	97	16	ϕ̃	ϕ̃	PROPN
ejpam-6489	97	17	,	,	PUNCT
ejpam-6489	97	18	ξpb̃	ξpb̃	X
ejpam-6489	97	19	(	(	PUNCT
ejpam-6489	97	20	ϕ̃	ϕ̃	PROPN
ejpam-6489	97	21	)	)	PUNCT
ejpam-6489	97	22	=	=	SYM
ejpam-6489	97	23	r̃pb̃	r̃pb̃	PROPN
ejpam-6489	97	24	(	(	PUNCT
ejpam-6489	97	25	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	97	26	i2πω̃p	i2πω̃p	X
ejpam-6489	97	27	b̃	b̃	PROPN
ejpam-6489	97	28	(	(	PUNCT
ejpam-6489	97	29	ϕ̃	ϕ̃	PROPN
ejpam-6489	97	30	)	)	PUNCT
ejpam-6489	97	31	,	,	PUNCT
ejpam-6489	97	32	ξnb̃	ξnb̃	X
ejpam-6489	97	33	(	(	PUNCT
ejpam-6489	97	34	ϕ̃	ϕ̃	PROPN
ejpam-6489	97	35	)	)	PUNCT
ejpam-6489	97	36	=	=	SYM
ejpam-6489	98	1	r̃nb̃	r̃nb̃	X
ejpam-6489	98	2	(	(	PUNCT
ejpam-6489	98	3	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	98	4	n	n	CCONJ
ejpam-6489	98	5	b̃	b̃	PROPN
ejpam-6489	98	6	(	(	PUNCT
ejpam-6489	98	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	98	8	)	)	PUNCT
ejpam-6489	98	9	)	)	PUNCT
ejpam-6489	99	1	|	|	ADV
ejpam-6489	99	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	99	3	∈	∈	PROPN
ejpam-6489	99	4	l̃	l̃	PROPN
ejpam-6489	99	5	}	}	PUNCT
ejpam-6489	99	6	,	,	PUNCT
ejpam-6489	99	7	where	where	SCONJ
ejpam-6489	99	8	ξpb̃	ξpb̃	PROPN
ejpam-6489	99	9	(	(	PUNCT
ejpam-6489	99	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	99	11	)	)	PUNCT
ejpam-6489	99	12	:	:	PUNCT
ejpam-6489	100	1	l̃	l̃	PROPN
ejpam-6489	100	2	→	→	PUNCT
ejpam-6489	101	1	[	[	X
ejpam-6489	101	2	0	0	NUM
ejpam-6489	101	3	,	,	PUNCT
ejpam-6489	101	4	1	1	NUM
ejpam-6489	101	5	]	]	PUNCT
ejpam-6489	101	6	,	,	PUNCT
ejpam-6489	101	7	ξnb̃	ξnb̃	X
ejpam-6489	101	8	(	(	PUNCT
ejpam-6489	101	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	101	10	)	)	PUNCT
ejpam-6489	101	11	:	:	PUNCT
ejpam-6489	102	1	l̃	l̃	PROPN
ejpam-6489	102	2	→	→	PUNCT
ejpam-6489	102	3	[	[	X
ejpam-6489	102	4	−1	−1	NOUN
ejpam-6489	102	5	,	,	PUNCT
ejpam-6489	102	6	0	0	NUM
ejpam-6489	102	7	]	]	PUNCT
ejpam-6489	102	8	.	.	PUNCT
ejpam-6489	103	1	definition	definition	NOUN
ejpam-6489	103	2	7	7	NUM
ejpam-6489	103	3	.	.	PUNCT
ejpam-6489	104	1	[	[	X
ejpam-6489	104	2	29	29	NUM
ejpam-6489	104	3	]	]	PUNCT
ejpam-6489	104	4	a	a	DET
ejpam-6489	104	5	t	t	NOUN
ejpam-6489	104	6	fs	fs	ADP
ejpam-6489	104	7	̃ג	̃ג	NOUN
ejpam-6489	104	8	=	=	PUNCT
ejpam-6489	104	9	{	{	PUNCT
ejpam-6489	104	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	104	11	,	,	PUNCT
ejpam-6489	104	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	104	13	(	(	PUNCT
ejpam-6489	104	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	104	15	)	)	PUNCT
ejpam-6489	104	16	,	,	PUNCT
ejpam-6489	104	17	ξ	ξ	PROPN
ejpam-6489	104	18	n	n	PRON
ejpam-6489	104	19	̃ג	̃ג	PROPN
ejpam-6489	104	20	(	(	PUNCT
ejpam-6489	104	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	104	22	)	)	PUNCT
ejpam-6489	104	23	,	,	PUNCT
ejpam-6489	104	24	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	104	25	)	)	PUNCT
ejpam-6489	104	26	}	}	PUNCT
ejpam-6489	104	27	with	with	ADP
ejpam-6489	104	28	ϕ̃	ϕ̃	PROPN
ejpam-6489	104	29	∈	∈	PROPN
ejpam-6489	104	30	l̃	l̃	PROPN
ejpam-6489	104	31	,	,	PUNCT
ejpam-6489	104	32	where	where	SCONJ
ejpam-6489	104	33	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	104	34	(	(	PUNCT
ejpam-6489	104	35	ϕ̃	ϕ̃	PROPN
ejpam-6489	104	36	)	)	PUNCT
ejpam-6489	104	37	:	:	PUNCT
ejpam-6489	105	1	l̃	l̃	PROPN
ejpam-6489	105	2	→	→	PUNCT
ejpam-6489	105	3	[	[	X
ejpam-6489	105	4	0	0	NUM
ejpam-6489	105	5	,	,	PUNCT
ejpam-6489	105	6	1	1	NUM
ejpam-6489	105	7	]	]	PUNCT
ejpam-6489	105	8	is	be	AUX
ejpam-6489	105	9	the	the	DET
ejpam-6489	105	10	+	+	PROPN
ejpam-6489	105	11	md	md	PROPN
ejpam-6489	105	12	,	,	PUNCT
ejpam-6489	105	13	ξñג	ξñג	PROPN
ejpam-6489	105	14	(	(	PUNCT
ejpam-6489	105	15	ϕ̃	ϕ̃	PROPN
ejpam-6489	105	16	)	)	PUNCT
ejpam-6489	105	17	:	:	PUNCT
ejpam-6489	106	1	l̃	l̃	PROPN
ejpam-6489	106	2	→	→	PUNCT
ejpam-6489	106	3	[	[	X
ejpam-6489	106	4	−1	−1	NOUN
ejpam-6489	106	5	,	,	PUNCT
ejpam-6489	106	6	0	0	NUM
ejpam-6489	106	7	]	]	PUNCT
ejpam-6489	106	8	is	be	AUX
ejpam-6489	106	9	the	the	DET
ejpam-6489	106	10	−md	−md	PROPN
ejpam-6489	106	11	and	and	CCONJ
ejpam-6489	106	12	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	106	13	)	)	PUNCT
ejpam-6489	106	14	:	:	PUNCT
ejpam-6489	107	1	l̃	l̃	PROPN
ejpam-6489	107	2	→	→	PUNCT
ejpam-6489	107	3	[	[	X
ejpam-6489	107	4	0	0	NUM
ejpam-6489	107	5	,	,	PUNCT
ejpam-6489	107	6	1	1	NUM
ejpam-6489	107	7	]	]	PUNCT
ejpam-6489	107	8	is	be	AUX
ejpam-6489	107	9	the	the	DET
ejpam-6489	107	10	nm	nm	ADJ
ejpam-6489	107	11	degree	degree	NOUN
ejpam-6489	107	12	with	with	ADP
ejpam-6489	107	13	−1	−1	NOUN
ejpam-6489	107	14	≤	≤	NUM
ejpam-6489	107	15	ξñג	ξñג	PROPN
ejpam-6489	107	16	(	(	PUNCT
ejpam-6489	107	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	107	18	)	)	PUNCT
ejpam-6489	108	1	+	+	CCONJ
ejpam-6489	109	1	η̃ג(ϕ̃	η̃ג(ϕ̃	NOUN
ejpam-6489	109	2	)	)	PUNCT
ejpam-6489	109	3	≤	≤	NOUN
ejpam-6489	109	4	1	1	NUM
ejpam-6489	109	5	and	and	CCONJ
ejpam-6489	109	6	0	0	NUM
ejpam-6489	109	7	≤	≤	NOUN
ejpam-6489	110	1	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	110	2	(	(	PUNCT
ejpam-6489	110	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	110	4	)	)	PUNCT
ejpam-6489	110	5	+	+	CCONJ
ejpam-6489	110	6	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	110	7	)	)	PUNCT
ejpam-6489	110	8	≤	≤	NUM
ejpam-6489	110	9	1	1	NUM
ejpam-6489	110	10	.	.	PUNCT
ejpam-6489	110	11	remark	remark	NOUN
ejpam-6489	110	12	1	1	NUM
ejpam-6489	110	13	.	.	PUNCT
ejpam-6489	111	1	a	a	DET
ejpam-6489	111	2	t	t	NOUN
ejpam-6489	111	3	fs	fs	X
ejpam-6489	111	4	consists	consist	NOUN
ejpam-6489	111	5	of	of	ADP
ejpam-6489	111	6	the	the	DET
ejpam-6489	111	7	md(also	md(also	PROPN
ejpam-6489	111	8	called	call	VERB
ejpam-6489	111	9	+	+	PROPN
ejpam-6489	111	10	md	md	PROPN
ejpam-6489	111	11	)	)	PUNCT
ejpam-6489	111	12	,	,	PUNCT
ejpam-6489	111	13	−md	−md	PROPN
ejpam-6489	111	14	,	,	PUNCT
ejpam-6489	111	15	and	and	CCONJ
ejpam-6489	111	16	nmd	nmd	PROPN
ejpam-6489	111	17	all	all	ADV
ejpam-6489	111	18	together	together	ADV
ejpam-6489	111	19	.	.	PUNCT
ejpam-6489	112	1	the	the	DET
ejpam-6489	112	2	+	+	ADJ
ejpam-6489	112	3	md(md	md(md	ADJ
ejpam-6489	112	4	)	)	PUNCT
ejpam-6489	112	5	denotes	denote	VERB
ejpam-6489	112	6	the	the	DET
ejpam-6489	112	7	somewhat	somewhat	ADV
ejpam-6489	112	8	satisfied	satisfied	ADJ
ejpam-6489	112	9	property	property	NOUN
ejpam-6489	112	10	,	,	PUNCT
ejpam-6489	112	11	nmd	nmd	PROPN
ejpam-6489	112	12	denotes	denote	VERB
ejpam-6489	112	13	the	the	DET
ejpam-6489	112	14	property	property	NOUN
ejpam-6489	112	15	that	that	PRON
ejpam-6489	112	16	is	be	AUX
ejpam-6489	112	17	not	not	PART
ejpam-6489	112	18	fulfilled	fulfil	VERB
ejpam-6489	112	19	,	,	PUNCT
ejpam-6489	112	20	and	and	CCONJ
ejpam-6489	112	21	−md	−md	PRON
ejpam-6489	112	22	denotes	denote	VERB
ejpam-6489	112	23	some	some	DET
ejpam-6489	112	24	implicit	implicit	ADJ
ejpam-6489	112	25	-	-	PUNCT
ejpam-6489	112	26	counter	counter	NOUN
ejpam-6489	112	27	property	property	NOUN
ejpam-6489	112	28	(	(	PUNCT
ejpam-6489	112	29	opposite	opposite	ADJ
ejpam-6489	112	30	to	to	ADP
ejpam-6489	112	31	md	md	PROPN
ejpam-6489	112	32	)	)	PUNCT
ejpam-6489	112	33	.	.	PUNCT
ejpam-6489	113	1	3	3	X
ejpam-6489	113	2	.	.	X
ejpam-6489	113	3	tripolar	tripolar	ADJ
ejpam-6489	113	4	complex	complex	ADJ
ejpam-6489	113	5	fuzzy	fuzzy	ADJ
ejpam-6489	113	6	bracket	bracket	NOUN
ejpam-6489	113	7	product	product	NOUN
ejpam-6489	113	8	definition	definition	NOUN
ejpam-6489	113	9	8	8	NUM
ejpam-6489	113	10	.	.	PUNCT
ejpam-6489	114	1	a	a	DET
ejpam-6489	114	2	t	t	NOUN
ejpam-6489	114	3	cfs	cfs	PROPN
ejpam-6489	114	4	̃ג	̃ג	PROPN
ejpam-6489	114	5	in	in	ADP
ejpam-6489	114	6	l̃	l̃	PROPN
ejpam-6489	114	7	is	be	AUX
ejpam-6489	114	8	the	the	DET
ejpam-6489	114	9	structure	structure	NOUN
ejpam-6489	114	10	̃ג	̃ג	NOUN
ejpam-6489	114	11	=	=	PUNCT
ejpam-6489	114	12	{	{	PUNCT
ejpam-6489	114	13	(	(	PUNCT
ejpam-6489	114	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	114	15	,	,	PUNCT
ejpam-6489	114	16	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	114	17	(	(	PUNCT
ejpam-6489	114	18	ϕ̃	ϕ̃	PROPN
ejpam-6489	114	19	)	)	PUNCT
ejpam-6489	114	20	=	=	SYM
ejpam-6489	115	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	115	2	(	(	PUNCT
ejpam-6489	115	3	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	115	4	i2πω̃p	i2πω̃p	X
ejpam-6489	115	5	̃ג	̃ג	NOUN
ejpam-6489	115	6	(	(	PUNCT
ejpam-6489	115	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	115	8	)	)	PUNCT
ejpam-6489	115	9	,	,	PUNCT
ejpam-6489	115	10	ξñג	ξñג	PROPN
ejpam-6489	115	11	(	(	PUNCT
ejpam-6489	115	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	115	13	)	)	PUNCT
ejpam-6489	115	14	=	=	SYM
ejpam-6489	115	15	r̃ñג	r̃ñג	PROPN
ejpam-6489	115	16	(	(	PUNCT
ejpam-6489	115	17	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	115	18	n	n	PRON
ejpam-6489	115	19	̃ג	̃ג	PROPN
ejpam-6489	115	20	(	(	PUNCT
ejpam-6489	115	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	115	22	)	)	PUNCT
ejpam-6489	115	23	,	,	PUNCT
ejpam-6489	115	24	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	115	25	)	)	PUNCT
ejpam-6489	115	26	=	=	PUNCT
ejpam-6489	115	27	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	X
ejpam-6489	115	28	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	115	29	)	)	PUNCT
ejpam-6489	115	30	)	)	PUNCT
ejpam-6489	116	1	|	|	ADV
ejpam-6489	116	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	116	3	∈	∈	PROPN
ejpam-6489	116	4	l̃	l̃	PROPN
ejpam-6489	116	5	}	}	PUNCT
ejpam-6489	116	6	,	,	PUNCT
ejpam-6489	116	7	where	where	SCONJ
ejpam-6489	116	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	116	9	(	(	PUNCT
ejpam-6489	116	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	116	11	)	)	PUNCT
ejpam-6489	116	12	:	:	PUNCT
ejpam-6489	117	1	l̃	l̃	PROPN
ejpam-6489	117	2	→	→	PUNCT
ejpam-6489	118	1	[	[	X
ejpam-6489	118	2	0	0	NUM
ejpam-6489	118	3	,	,	PUNCT
ejpam-6489	118	4	1	1	NUM
ejpam-6489	118	5	]	]	PUNCT
ejpam-6489	118	6	,	,	PUNCT
ejpam-6489	118	7	ξñג	ξñג	PROPN
ejpam-6489	118	8	(	(	PUNCT
ejpam-6489	118	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	118	10	)	)	PUNCT
ejpam-6489	118	11	:	:	PUNCT
ejpam-6489	119	1	l̃	l̃	PROPN
ejpam-6489	119	2	→	→	PUNCT
ejpam-6489	119	3	[	[	X
ejpam-6489	119	4	−1	−1	NOUN
ejpam-6489	119	5	,	,	PUNCT
ejpam-6489	119	6	0	0	NUM
ejpam-6489	119	7	]	]	PUNCT
ejpam-6489	119	8	,	,	PUNCT
ejpam-6489	119	9	ζ̃ג	ζ̃ג	PROPN
ejpam-6489	119	10	:	:	PUNCT
ejpam-6489	120	1	l̃	l̃	PROPN
ejpam-6489	120	2	→	→	PUNCT
ejpam-6489	121	1	[	[	X
ejpam-6489	121	2	0	0	NUM
ejpam-6489	121	3	,	,	PUNCT
ejpam-6489	121	4	1	1	NUM
ejpam-6489	121	5	]	]	PUNCT
ejpam-6489	121	6	.	.	PUNCT
ejpam-6489	121	7	example	example	NOUN
ejpam-6489	122	1	1	1	NUM
ejpam-6489	122	2	.	.	PUNCT
ejpam-6489	122	3	let	let	VERB
ejpam-6489	122	4	l̃	l̃	PROPN
ejpam-6489	122	5	=	=	PUNCT
ejpam-6489	122	6	{	{	PUNCT
ejpam-6489	122	7	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	122	8	,	,	PUNCT
ejpam-6489	122	9	ϕ̃2	ϕ̃2	PROPN
ejpam-6489	122	10	,	,	PUNCT
ejpam-6489	122	11	ϕ̃3	ϕ̃3	PROPN
ejpam-6489	122	12	}	}	PUNCT
ejpam-6489	122	13	be	be	VERB
ejpam-6489	122	14	a	a	DET
ejpam-6489	122	15	universe	universe	NOUN
ejpam-6489	122	16	of	of	ADP
ejpam-6489	122	17	discourse	discourse	NOUN
ejpam-6489	122	18	.	.	PUNCT
ejpam-6489	123	1	a	a	DET
ejpam-6489	123	2	t	t	NOUN
ejpam-6489	123	3	cfs	cfs	PROPN
ejpam-6489	123	4	̃ג	̃ג	PROPN
ejpam-6489	123	5	in	in	ADP
ejpam-6489	123	6	l̃	l̃	PROPN
ejpam-6489	123	7	is	be	AUX
ejpam-6489	123	8	defined	define	VERB
ejpam-6489	123	9	as	as	ADP
ejpam-6489	123	10	:	:	PUNCT
ejpam-6489	123	11	̃ג	̃ג	NOUN
ejpam-6489	123	12	=	=	NOUN
ejpam-6489	123	13			NOUN
ejpam-6489	123	14	(	(	PUNCT
ejpam-6489	123	15	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	123	16	,	,	PUNCT
ejpam-6489	123	17	0.8e	0.8e	NUM
ejpam-6489	123	18	i2π(0.7),−0.5ei2π(0.3	i2π(0.7),−0.5ei2π(0.3	PROPN
ejpam-6489	123	19	)	)	PUNCT
ejpam-6489	123	20	,	,	PUNCT
ejpam-6489	123	21	0.4ei2π(0.5	0.4ei2π(0.5	NUM
ejpam-6489	123	22	)	)	PUNCT
ejpam-6489	123	23	)	)	PUNCT
ejpam-6489	124	1	,	,	PUNCT
ejpam-6489	124	2	(	(	PUNCT
ejpam-6489	124	3	ϕ̃2	ϕ̃2	PROPN
ejpam-6489	124	4	,	,	PUNCT
ejpam-6489	124	5	0.6e	0.6e	PROPN
ejpam-6489	124	6	i2π(0.6),−0.4ei2π(0.4	i2π(0.6),−0.4ei2π(0.4	NUM
ejpam-6489	124	7	)	)	PUNCT
ejpam-6489	124	8	,	,	PUNCT
ejpam-6489	124	9	0.3ei2π(0.4	0.3ei2π(0.4	NUM
ejpam-6489	124	10	)	)	PUNCT
ejpam-6489	124	11	)	)	PUNCT
ejpam-6489	124	12	,	,	PUNCT
ejpam-6489	124	13	(	(	PUNCT
ejpam-6489	124	14	ϕ̃3	ϕ̃3	PROPN
ejpam-6489	124	15	,	,	PUNCT
ejpam-6489	124	16	0.9e	0.9e	PROPN
ejpam-6489	124	17	i2π(0.8),−0.7ei2π(0.2	i2π(0.8),−0.7ei2π(0.2	NOUN
ejpam-6489	124	18	)	)	PUNCT
ejpam-6489	124	19	,	,	PUNCT
ejpam-6489	124	20	0.2ei2π(0.3	0.2ei2π(0.3	PROPN
ejpam-6489	124	21	)	)	PUNCT
ejpam-6489	124	22	)	)	PUNCT
ejpam-6489	124	23			ADP
ejpam-6489	124	24	here	here	ADV
ejpam-6489	124	25	:	:	PUNCT
ejpam-6489	124	26	•	•	NUM
ejpam-6489	124	27	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	124	28	(	(	PUNCT
ejpam-6489	124	29	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	124	30	)	)	PUNCT
ejpam-6489	124	31	=	=	SYM
ejpam-6489	124	32	0.8ei2π(0.7	0.8ei2π(0.7	PROPN
ejpam-6489	124	33	)	)	PUNCT
ejpam-6489	124	34	is	be	AUX
ejpam-6489	124	35	the	the	DET
ejpam-6489	124	36	+	+	PROPN
ejpam-6489	124	37	md	md	NOUN
ejpam-6489	124	38	of	of	ADP
ejpam-6489	124	39	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	124	40	with	with	ADP
ejpam-6489	124	41	amplitude	amplitude	NOUN
ejpam-6489	124	42	0.8	0.8	NUM
ejpam-6489	124	43	and	and	CCONJ
ejpam-6489	124	44	phase	phase	NOUN
ejpam-6489	124	45	0.7	0.7	NUM
ejpam-6489	124	46	,	,	PUNCT
ejpam-6489	124	47	•	•	NUM
ejpam-6489	124	48	ξñג	ξñג	NOUN
ejpam-6489	124	49	(	(	PUNCT
ejpam-6489	124	50	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	124	51	)	)	PUNCT
ejpam-6489	124	52	=	=	SYM
ejpam-6489	124	53	−0.5ei2π(0.3	−0.5ei2π(0.3	PROPN
ejpam-6489	124	54	)	)	PUNCT
ejpam-6489	124	55	is	be	AUX
ejpam-6489	124	56	the	the	DET
ejpam-6489	124	57	−md	−md	X
ejpam-6489	124	58	of	of	ADP
ejpam-6489	124	59	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	124	60	with	with	ADP
ejpam-6489	124	61	amplitude	amplitude	NOUN
ejpam-6489	124	62	0.5	0.5	NUM
ejpam-6489	124	63	(	(	PUNCT
ejpam-6489	124	64	but	but	CCONJ
ejpam-6489	124	65	sign	sign	VERB
ejpam-6489	124	66	−1	−1	NOUN
ejpam-6489	124	67	)	)	PUNCT
ejpam-6489	124	68	and	and	CCONJ
ejpam-6489	124	69	phase	phase	NOUN
ejpam-6489	124	70	0.3	0.3	NUM
ejpam-6489	124	71	,	,	PUNCT
ejpam-6489	124	72	•	•	DET
ejpam-6489	124	73	ζ̃ג(ϕ̃1	ζ̃ג(ϕ̃1	NOUN
ejpam-6489	124	74	)	)	PUNCT
ejpam-6489	124	75	=	=	SYM
ejpam-6489	124	76	0.4ei2π(0.5	0.4ei2π(0.5	X
ejpam-6489	124	77	)	)	PUNCT
ejpam-6489	124	78	is	be	AUX
ejpam-6489	124	79	the	the	DET
ejpam-6489	124	80	nmd	nmd	NOUN
ejpam-6489	124	81	of	of	ADP
ejpam-6489	124	82	ϕ̃1	ϕ̃1	PROPN
ejpam-6489	124	83	with	with	ADP
ejpam-6489	124	84	amplitude	amplitude	NOUN
ejpam-6489	124	85	0.4	0.4	NUM
ejpam-6489	124	86	and	and	CCONJ
ejpam-6489	124	87	phase	phase	NOUN
ejpam-6489	124	88	0.5	0.5	NUM
ejpam-6489	124	89	.	.	PUNCT
ejpam-6489	124	90	definition	definition	NOUN
ejpam-6489	124	91	9	9	NUM
ejpam-6489	124	92	.	.	PUNCT
ejpam-6489	125	1	for	for	ADP
ejpam-6489	125	2	any	any	DET
ejpam-6489	125	3	t	t	PROPN
ejpam-6489	125	4	cfss	cfss	ADJ
ejpam-6489	125	5	̃ג	̃ג	NOUN
ejpam-6489	125	6	=	=	SYM
ejpam-6489	125	7	(	(	PUNCT
ejpam-6489	125	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	125	9	(	(	PUNCT
ejpam-6489	125	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	125	11	)	)	PUNCT
ejpam-6489	125	12	,	,	PUNCT
ejpam-6489	125	13	ξ	ξ	PROPN
ejpam-6489	125	14	n	n	PRON
ejpam-6489	125	15	̃ג	̃ג	PROPN
ejpam-6489	125	16	(	(	PUNCT
ejpam-6489	125	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	125	18	)	)	PUNCT
ejpam-6489	125	19	,	,	PUNCT
ejpam-6489	125	20	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	125	21	)	)	PUNCT
ejpam-6489	125	22	)	)	PUNCT
ejpam-6489	125	23	and	and	CCONJ
ejpam-6489	125	24	ℸ̃	ℸ̃	PROPN
ejpam-6489	125	25	=	=	SYM
ejpam-6489	125	26	(	(	PUNCT
ejpam-6489	125	27	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	125	28	(	(	PUNCT
ejpam-6489	125	29	ϕ̃	ϕ̃	PROPN
ejpam-6489	125	30	)	)	PUNCT
ejpam-6489	125	31	,	,	PUNCT
ejpam-6489	125	32	ξ	ξ	PROPN
ejpam-6489	125	33	n	n	PRON
ejpam-6489	125	34	ℸ̃	ℸ̃	PROPN
ejpam-6489	125	35	(	(	PUNCT
ejpam-6489	125	36	ϕ̃	ϕ̃	PROPN
ejpam-6489	125	37	)	)	PUNCT
ejpam-6489	125	38	,	,	PUNCT
ejpam-6489	125	39	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	125	40	)	)	PUNCT
ejpam-6489	125	41	)	)	PUNCT
ejpam-6489	125	42	of	of	ADP
ejpam-6489	125	43	l̃.	l̃.	ADJ
ejpam-6489	125	44	then	then	ADV
ejpam-6489	125	45	,	,	PUNCT
ejpam-6489	125	46	̃ג	̃ג	NOUN
ejpam-6489	125	47	]	]	PUNCT
ejpam-6489	125	48	ℸ̃	ℸ̃	PROPN
ejpam-6489	125	49	]	]	X
ejpam-6489	125	50	=	=	SYM
ejpam-6489	125	51	(	(	PUNCT
ejpam-6489	125	52	ξp	ξp	NOUN
ejpam-6489	125	53	,	,	PUNCT
ejpam-6489	125	54	(	(	PUNCT
ejpam-6489	125	55	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	125	56	]	]	X
ejpam-6489	125	57	ξ	ξ	PROPN
ejpam-6489	125	58	n	n	PROPN
ejpam-6489	125	59	,	,	PUNCT
ejpam-6489	125	60	(	(	PUNCT
ejpam-6489	125	61	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	125	62	]	]	X
ejpam-6489	125	63	ζ[̃ג,ℸ̃](ϕ̃	ζ[̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	125	64	)	)	PUNCT
ejpam-6489	125	65	)	)	PUNCT
ejpam-6489	125	66	,	,	PUNCT
ejpam-6489	125	67	where	where	SCONJ
ejpam-6489	125	68	(	(	PUNCT
ejpam-6489	125	69	i	i	NOUN
ejpam-6489	125	70	)	)	PUNCT
ejpam-6489	125	71	if	if	SCONJ
ejpam-6489	125	72	β̃j	β̃j	PROPN
ejpam-6489	125	73	∈	∈	PROPN
ejpam-6489	125	74	f	f	PROPN
ejpam-6489	125	75	,	,	PUNCT
ejpam-6489	125	76	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	125	77	,	,	PUNCT
ejpam-6489	125	78	η̃j	η̃j	PROPN
ejpam-6489	125	79	∈	∈	PROPN
ejpam-6489	125	80	l̃	l̃	PROPN
ejpam-6489	125	81	,	,	PUNCT
ejpam-6489	125	82	then	then	ADV
ejpam-6489	125	83	ξp	ξp	X
ejpam-6489	125	84	(	(	PUNCT
ejpam-6489	125	85	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	125	86	]	]	X
ejpam-6489	125	87	=	=	PUNCT
ejpam-6489	125	88	supϕ̃=	supϕ̃=	ADV
ejpam-6489	125	89	∑	∑	PART
ejpam-6489	125	90	j∈n	j∈n	NOUN
ejpam-6489	125	91	βj	βj	PRON
ejpam-6489	126	1	[	[	X
ejpam-6489	126	2	ϕ̃j	ϕ̃j	X
ejpam-6489	126	3	,	,	PUNCT
ejpam-6489	126	4	η̃j	η̃j	PROPN
ejpam-6489	126	5	]	]	PUNCT
ejpam-6489	126	6	{	{	PUNCT
ejpam-6489	126	7	minj∈n	minj∈n	INTJ
ejpam-6489	126	8	{	{	PUNCT
ejpam-6489	126	9	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	126	10	(	(	PUNCT
ejpam-6489	126	11	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	126	12	)	)	PUNCT
ejpam-6489	127	1	∧	∧	PROPN
ejpam-6489	127	2	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	127	3	(	(	PUNCT
ejpam-6489	127	4	η̃j)}e	η̃j)}e	PRON
ejpam-6489	127	5	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	127	6	{	{	PUNCT
ejpam-6489	127	7	ω̃p	ω̃p	PROPN
ejpam-6489	127	8	̃ג	̃ג	PROPN
ejpam-6489	127	9	(	(	PUNCT
ejpam-6489	127	10	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	127	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	127	12	(	(	PUNCT
ejpam-6489	127	13	η̃j	η̃j	NOUN
ejpam-6489	127	14	)	)	PUNCT
ejpam-6489	127	15	}	}	PUNCT
ejpam-6489	127	16	m.	m.	NOUN
ejpam-6489	127	17	balamurugan	balamurugan	NOUN
ejpam-6489	127	18	,	,	PUNCT
ejpam-6489	127	19	g.	g.	PROPN
ejpam-6489	127	20	ellammal	ellammal	PROPN
ejpam-6489	127	21	,	,	PUNCT
ejpam-6489	127	22	a.	a.	NOUN
ejpam-6489	127	23	iampan	iampan	PROPN
ejpam-6489	127	24	/	/	SYM
ejpam-6489	127	25	eur	eur	PROPN
ejpam-6489	127	26	.	.	PUNCT
ejpam-6489	128	1	j.	j.	PROPN
ejpam-6489	128	2	pure	pure	PROPN
ejpam-6489	128	3	appl	appl	PROPN
ejpam-6489	128	4	.	.	PROPN
ejpam-6489	128	5	math	math	PROPN
ejpam-6489	128	6	,	,	PUNCT
ejpam-6489	128	7	18	18	NUM
ejpam-6489	128	8	(	(	PUNCT
ejpam-6489	128	9	3	3	NUM
ejpam-6489	128	10	)	)	PUNCT
ejpam-6489	128	11	(	(	PUNCT
ejpam-6489	128	12	2025	2025	NUM
ejpam-6489	128	13	)	)	PUNCT
ejpam-6489	128	14	,	,	PUNCT
ejpam-6489	128	15	6489	6489	NUM
ejpam-6489	128	16	5	5	NUM
ejpam-6489	128	17	of	of	ADP
ejpam-6489	128	18	26	26	NUM
ejpam-6489	128	19	and	and	CCONJ
ejpam-6489	128	20	if	if	SCONJ
ejpam-6489	128	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	128	22	̸=	̸=	PROPN
ejpam-6489	128	23	∑	∑	ADP
ejpam-6489	128	24	j∈n	j∈n	PROPN
ejpam-6489	128	25	βi[ϕ̃i	βi[ϕ̃i	PROPN
ejpam-6489	128	26	,	,	PUNCT
ejpam-6489	128	27	η̃j	η̃j	PROPN
ejpam-6489	128	28	]	]	PUNCT
ejpam-6489	128	29	,	,	PUNCT
ejpam-6489	128	30	then	then	ADV
ejpam-6489	128	31	ξp	ξp	X
ejpam-6489	128	32	(	(	PUNCT
ejpam-6489	128	33	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	128	34	]	]	X
ejpam-6489	128	35	=	=	SYM
ejpam-6489	128	36	0	0	NUM
ejpam-6489	128	37	,	,	PUNCT
ejpam-6489	128	38	(	(	PUNCT
ejpam-6489	128	39	ii	ii	NOUN
ejpam-6489	128	40	)	)	PUNCT
ejpam-6489	128	41	if	if	SCONJ
ejpam-6489	128	42	β̃j	β̃j	PROPN
ejpam-6489	128	43	∈	∈	PROPN
ejpam-6489	128	44	f	f	PROPN
ejpam-6489	128	45	,	,	PUNCT
ejpam-6489	128	46	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	128	47	,	,	PUNCT
ejpam-6489	128	48	η̃j	η̃j	PROPN
ejpam-6489	128	49	∈	∈	PROPN
ejpam-6489	128	50	l̃	l̃	PROPN
ejpam-6489	128	51	,	,	PUNCT
ejpam-6489	128	52	then	then	ADV
ejpam-6489	128	53	ξn	ξn	X
ejpam-6489	128	54	(	(	PUNCT
ejpam-6489	128	55	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	128	56	]	]	X
ejpam-6489	128	57	=	=	SYM
ejpam-6489	128	58	inf	inf	PROPN
ejpam-6489	128	59	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	128	60	∑	∑	PROPN
ejpam-6489	128	61	j∈n	j∈n	NOUN
ejpam-6489	128	62	βj	βj	NOUN
ejpam-6489	129	1	[	[	X
ejpam-6489	129	2	ϕ̃j	ϕ̃j	X
ejpam-6489	129	3	,	,	PUNCT
ejpam-6489	129	4	η̃j	η̃j	PROPN
ejpam-6489	129	5	]	]	PUNCT
ejpam-6489	129	6	{	{	PUNCT
ejpam-6489	129	7	maxj∈n	maxj∈n	NOUN
ejpam-6489	129	8	{	{	PUNCT
ejpam-6489	129	9	r̃ñג	r̃ñג	PROPN
ejpam-6489	129	10	(	(	PUNCT
ejpam-6489	129	11	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	129	12	)	)	PUNCT
ejpam-6489	130	1	∨	∨	PROPN
ejpam-6489	130	2	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	130	3	(	(	PUNCT
ejpam-6489	130	4	η̃j)}ei2πmaxj∈n	η̃j)}ei2πmaxj∈n	PROPN
ejpam-6489	130	5	{	{	PUNCT
ejpam-6489	130	6	ω̃n	ω̃n	PROPN
ejpam-6489	130	7	̃ג	̃ג	PROPN
ejpam-6489	130	8	(	(	PUNCT
ejpam-6489	130	9	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	NUM
ejpam-6489	130	10	ℸ̃	ℸ̃	PROPN
ejpam-6489	130	11	(	(	PUNCT
ejpam-6489	130	12	η̃j	η̃j	NOUN
ejpam-6489	130	13	)	)	PUNCT
ejpam-6489	130	14	}	}	PUNCT
ejpam-6489	130	15	and	and	CCONJ
ejpam-6489	130	16	if	if	SCONJ
ejpam-6489	130	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	130	18	̸=	̸=	PROPN
ejpam-6489	130	19	∑	∑	ADP
ejpam-6489	130	20	j∈n	j∈n	PROPN
ejpam-6489	130	21	βi[ϕ̃i	βi[ϕ̃i	PROPN
ejpam-6489	130	22	,	,	PUNCT
ejpam-6489	130	23	η̃j	η̃j	PROPN
ejpam-6489	130	24	]	]	PUNCT
ejpam-6489	130	25	,	,	PUNCT
ejpam-6489	130	26	then	then	ADV
ejpam-6489	130	27	ξn	ξn	X
ejpam-6489	130	28	(	(	PUNCT
ejpam-6489	130	29	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	130	30	]	]	X
ejpam-6489	130	31	=	=	SYM
ejpam-6489	130	32	0	0	NUM
ejpam-6489	130	33	,	,	PUNCT
ejpam-6489	130	34	(	(	PUNCT
ejpam-6489	130	35	iii	iii	X
ejpam-6489	130	36	)	)	PUNCT
ejpam-6489	130	37	if	if	SCONJ
ejpam-6489	130	38	β̃j	β̃j	PROPN
ejpam-6489	130	39	∈	∈	PROPN
ejpam-6489	130	40	f	f	PROPN
ejpam-6489	130	41	,	,	PUNCT
ejpam-6489	130	42	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	130	43	,	,	PUNCT
ejpam-6489	130	44	η̃j	η̃j	PROPN
ejpam-6489	130	45	∈	∈	PROPN
ejpam-6489	130	46	l̃	l̃	PROPN
ejpam-6489	130	47	,	,	PUNCT
ejpam-6489	130	48	then	then	ADV
ejpam-6489	130	49	ζ[̃ג,ℸ̃](ϕ̃	ζ[̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	130	50	)	)	PUNCT
ejpam-6489	130	51	=	=	SYM
ejpam-6489	130	52	inf	inf	NOUN
ejpam-6489	130	53	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	130	54	∑	∑	PROPN
ejpam-6489	130	55	j∈n	j∈n	NOUN
ejpam-6489	130	56	βj	βj	NOUN
ejpam-6489	131	1	[	[	X
ejpam-6489	131	2	ϕ̃j	ϕ̃j	X
ejpam-6489	131	3	,	,	PUNCT
ejpam-6489	131	4	η̃j	η̃j	PROPN
ejpam-6489	131	5	]	]	PUNCT
ejpam-6489	131	6	{	{	PUNCT
ejpam-6489	131	7	maxj∈n	maxj∈n	NOUN
ejpam-6489	131	8	{	{	PUNCT
ejpam-6489	131	9	r̃̃ג(ϕ̃j	r̃̃ג(ϕ̃j	PROPN
ejpam-6489	131	10	)	)	PUNCT
ejpam-6489	131	11	∨	∨	NOUN
ejpam-6489	131	12	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	131	13	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	131	14	{	{	PUNCT
ejpam-6489	131	15	ω̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	ω̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	131	16	)	)	PUNCT
ejpam-6489	131	17	}	}	PUNCT
ejpam-6489	131	18	and	and	CCONJ
ejpam-6489	131	19	if	if	SCONJ
ejpam-6489	131	20	ϕ̃	ϕ̃	PROPN
ejpam-6489	131	21	̸=	̸=	PROPN
ejpam-6489	131	22	∑	∑	ADP
ejpam-6489	131	23	j∈n	j∈n	PROPN
ejpam-6489	131	24	βi[ϕ̃i	βi[ϕ̃i	PROPN
ejpam-6489	131	25	,	,	PUNCT
ejpam-6489	131	26	η̃j	η̃j	PROPN
ejpam-6489	131	27	]	]	PUNCT
ejpam-6489	131	28	,	,	PUNCT
ejpam-6489	131	29	then	then	ADV
ejpam-6489	131	30	ζ[̃ג,ℸ̃](ϕ̃	ζ[̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	131	31	)	)	PUNCT
ejpam-6489	132	1	=	=	SYM
ejpam-6489	132	2	0	0	X
ejpam-6489	132	3	.	.	PUNCT
ejpam-6489	132	4	remark	remark	NOUN
ejpam-6489	132	5	2	2	NUM
ejpam-6489	132	6	.	.	PUNCT
ejpam-6489	133	1	if	if	SCONJ
ejpam-6489	133	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	133	3	,	,	PUNCT
ejpam-6489	133	4	η̃	η̃	PROPN
ejpam-6489	133	5	∈	∈	PROPN
ejpam-6489	133	6	l̃	l̃	PROPN
ejpam-6489	133	7	,	,	PUNCT
ejpam-6489	133	8	then	then	ADV
ejpam-6489	133	9	(	(	PUNCT
ejpam-6489	133	10	1	1	X
ejpam-6489	133	11	)	)	PUNCT
ejpam-6489	133	12	ξp	ξp	NOUN
ejpam-6489	133	13	,	,	PUNCT
ejpam-6489	133	14	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	133	15	]	]	X
ejpam-6489	133	16	η̃	η̃	PROPN
ejpam-6489	133	17	]	]	PUNCT
ejpam-6489	133	18	)	)	PUNCT
ejpam-6489	134	1	=	=	SYM
ejpam-6489	134	2	r̃p	r̃p	NOUN
ejpam-6489	134	3	,	,	PUNCT
ejpam-6489	134	4	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	134	5	]	]	X
ejpam-6489	134	6	η̃])e	η̃])e	PROPN
ejpam-6489	134	7	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	135	1	[	[	X
ejpam-6489	135	2	ℸ̃,̃ג	ℸ̃,̃ג	X
ejpam-6489	135	3	]	]	X
ejpam-6489	135	4	(	(	PUNCT
ejpam-6489	135	5	[	[	X
ejpam-6489	135	6	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	135	7	]	]	X
ejpam-6489	135	8	)	)	PUNCT
ejpam-6489	135	9	,	,	PUNCT
ejpam-6489	135	10	r̃p	r̃p	NOUN
ejpam-6489	135	11	,	,	PUNCT
ejpam-6489	135	12	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	135	13	]	]	X
ejpam-6489	135	14	η̃	η̃	PROPN
ejpam-6489	135	15	]	]	PUNCT
ejpam-6489	135	16	)	)	PUNCT
ejpam-6489	135	17	≥	≥	AUX
ejpam-6489	135	18	r̃p	r̃p	VERB
ejpam-6489	135	19	r̃∧(ϕ̃)[ℸ̃,̃ג	r̃∧(ϕ̃)[ℸ̃,̃ג	NUM
ejpam-6489	135	20	]	]	X
ejpam-6489	135	21	p	p	X
ejpam-6489	135	22	,	,	PUNCT
ejpam-6489	135	23	(	(	PUNCT
ejpam-6489	135	24	η̃)[ℸ̃,̃ג	η̃)[ℸ̃,̃ג	X
ejpam-6489	135	25	]	]	PUNCT
ejpam-6489	135	26	and	and	CCONJ
ejpam-6489	135	27	ω̃p	ω̃p	NUM
ejpam-6489	135	28	,	,	PUNCT
ejpam-6489	135	29	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	PROPN
ejpam-6489	135	30	]	]	X
ejpam-6489	135	31	η̃	η̃	PROPN
ejpam-6489	135	32	]	]	PUNCT
ejpam-6489	135	33	)	)	PUNCT
ejpam-6489	135	34	≥	≥	NOUN
ejpam-6489	135	35	ω̃p	ω̃p	PROPN
ejpam-6489	135	36	(	(	PUNCT
ejpam-6489	135	37	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	135	38	]	]	X
ejpam-6489	135	39	∧	∧	PROPN
ejpam-6489	135	40	ω̃p	ω̃p	INTJ
ejpam-6489	135	41	,	,	PUNCT
ejpam-6489	135	42	(	(	PUNCT
ejpam-6489	135	43	η̃)[ℸ̃,̃ג	η̃)[ℸ̃,̃ג	X
ejpam-6489	135	44	]	]	X
ejpam-6489	135	45	(	(	PUNCT
ejpam-6489	135	46	2	2	X
ejpam-6489	135	47	)	)	PUNCT
ejpam-6489	135	48	ξn	ξn	NOUN
ejpam-6489	135	49	,	,	PUNCT
ejpam-6489	135	50	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	135	51	]	]	X
ejpam-6489	135	52	η̃	η̃	PROPN
ejpam-6489	135	53	]	]	PUNCT
ejpam-6489	135	54	)	)	PUNCT
ejpam-6489	136	1	=	=	SYM
ejpam-6489	136	2	r̃n	r̃n	PROPN
ejpam-6489	136	3	,	,	PUNCT
ejpam-6489	136	4	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	PROPN
ejpam-6489	136	5	]	]	X
ejpam-6489	136	6	η̃])e	η̃])e	PROPN
ejpam-6489	137	1	i2πω̃n	i2πω̃n	X
ejpam-6489	137	2	[	[	X
ejpam-6489	137	3	ℸ̃,̃ג	ℸ̃,̃ג	X
ejpam-6489	137	4	]	]	X
ejpam-6489	137	5	(	(	PUNCT
ejpam-6489	137	6	[	[	X
ejpam-6489	137	7	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	137	8	]	]	X
ejpam-6489	137	9	)	)	PUNCT
ejpam-6489	137	10	,	,	PUNCT
ejpam-6489	137	11	r̃n	r̃n	PROPN
ejpam-6489	137	12	,	,	PUNCT
ejpam-6489	137	13	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	137	14	]	]	X
ejpam-6489	137	15	η̃	η̃	PROPN
ejpam-6489	137	16	]	]	PUNCT
ejpam-6489	137	17	)	)	PUNCT
ejpam-6489	137	18	≤	≤	NOUN
ejpam-6489	138	1	r̃n	r̃n	PROPN
ejpam-6489	138	2	r̃∨(ϕ̃)[ℸ̃,̃ג	r̃∨(ϕ̃)[ℸ̃,̃ג	NOUN
ejpam-6489	138	3	]	]	X
ejpam-6489	138	4	n	n	CCONJ
ejpam-6489	138	5	,	,	PUNCT
ejpam-6489	138	6	(	(	PUNCT
ejpam-6489	138	7	η̃)[ℸ̃,̃ג	η̃)[ℸ̃,̃ג	X
ejpam-6489	138	8	]	]	X
ejpam-6489	138	9	and	and	CCONJ
ejpam-6489	138	10	ω̃n	ω̃n	PRON
ejpam-6489	138	11	,	,	PUNCT
ejpam-6489	138	12	ϕ̃])[ℸ̃,̃ג	ϕ̃])[ℸ̃,̃ג	NOUN
ejpam-6489	138	13	]	]	X
ejpam-6489	138	14	η̃	η̃	PROPN
ejpam-6489	138	15	]	]	PUNCT
ejpam-6489	138	16	)	)	PUNCT
ejpam-6489	138	17	≤	≤	ADV
ejpam-6489	138	18	ω̃n	ω̃n	PUNCT
ejpam-6489	138	19	(	(	PUNCT
ejpam-6489	138	20	ϕ̃)[ℸ̃,̃ג	ϕ̃)[ℸ̃,̃ג	X
ejpam-6489	138	21	]	]	X
ejpam-6489	138	22	∨	∨	NUM
ejpam-6489	138	23	ω̃n	ω̃n	X
ejpam-6489	138	24	,	,	PUNCT
ejpam-6489	138	25	(	(	PUNCT
ejpam-6489	138	26	η̃)[ℸ̃,̃ג	η̃)[ℸ̃,̃ג	X
ejpam-6489	138	27	]	]	X
ejpam-6489	138	28	(	(	PUNCT
ejpam-6489	138	29	3	3	X
ejpam-6489	138	30	)	)	PUNCT
ejpam-6489	138	31	ζ[̃ג,ℸ̃]([ϕ̃	ζ[̃ג,ℸ̃]([ϕ̃	PROPN
ejpam-6489	138	32	,	,	PUNCT
ejpam-6489	138	33	η̃	η̃	PROPN
ejpam-6489	138	34	]	]	PUNCT
ejpam-6489	138	35	)	)	PUNCT
ejpam-6489	138	36	=	=	SYM
ejpam-6489	138	37	r̃[̃ג,ℸ̃]([ϕ̃	r̃[̃ג,ℸ̃]([ϕ̃	NOUN
ejpam-6489	138	38	,	,	PUNCT
ejpam-6489	138	39	η̃])e	η̃])e	PROPN
ejpam-6489	138	40	i2πω̃[̃ג,ℸ̃]([ϕ̃,η̃	i2πω̃[̃ג,ℸ̃]([ϕ̃,η̃	PROPN
ejpam-6489	138	41	]	]	X
ejpam-6489	138	42	)	)	PUNCT
ejpam-6489	138	43	,	,	PUNCT
ejpam-6489	138	44	r̃[̃ג,ℸ̃]([ϕ̃	r̃[̃ג,ℸ̃]([ϕ̃	PROPN
ejpam-6489	138	45	,	,	PUNCT
ejpam-6489	138	46	η̃	η̃	PROPN
ejpam-6489	138	47	]	]	PUNCT
ejpam-6489	138	48	)	)	PUNCT
ejpam-6489	138	49	≤	≤	NUM
ejpam-6489	138	50	r̃[̃ג,ℸ̃](ϕ̃)∨r̃[̃ג,ℸ̃](η̃	r̃[̃ג,ℸ̃](ϕ̃)∨r̃[̃ג,ℸ̃](η̃	NOUN
ejpam-6489	138	51	)	)	PUNCT
ejpam-6489	138	52	,	,	PUNCT
ejpam-6489	138	53	and	and	CCONJ
ejpam-6489	138	54	ω̃[̃ג,ℸ̃]([ϕ̃	ω̃[̃ג,ℸ̃]([ϕ̃	NUM
ejpam-6489	138	55	,	,	PUNCT
ejpam-6489	138	56	η̃	η̃	PROPN
ejpam-6489	138	57	]	]	PUNCT
ejpam-6489	138	58	)	)	PUNCT
ejpam-6489	138	59	≤	≤	NUM
ejpam-6489	138	60	ω̃[̃ג,ℸ̃](ϕ̃	ω̃[̃ג,ℸ̃](ϕ̃	NUM
ejpam-6489	138	61	)	)	PUNCT
ejpam-6489	138	62	∨	∨	NUM
ejpam-6489	138	63	ω̃n	ω̃n	NUM
ejpam-6489	138	64	.(η̃)[ℸ̃,̃ג	.(η̃)[ℸ̃,̃ג	PROPN
ejpam-6489	138	65	]	]	PUNCT
ejpam-6489	138	66	theorem	theorem	VERB
ejpam-6489	138	67	1	1	X
ejpam-6489	138	68	.	.	PUNCT
ejpam-6489	139	1	let	let	VERB
ejpam-6489	139	2	̃ג	̃ג	NOUN
ejpam-6489	139	3	=	=	SYM
ejpam-6489	139	4	(	(	PUNCT
ejpam-6489	139	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	139	6	(	(	PUNCT
ejpam-6489	139	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	8	)	)	PUNCT
ejpam-6489	139	9	,	,	PUNCT
ejpam-6489	139	10	ξ	ξ	PROPN
ejpam-6489	139	11	n	n	PRON
ejpam-6489	139	12	̃ג	̃ג	PROPN
ejpam-6489	139	13	(	(	PUNCT
ejpam-6489	139	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	15	)	)	PUNCT
ejpam-6489	139	16	,	,	PUNCT
ejpam-6489	139	17	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	139	18	)	)	PUNCT
ejpam-6489	139	19	)	)	PUNCT
ejpam-6489	139	20	,	,	PUNCT
ejpam-6489	139	21	ℸ̃	ℸ̃	PROPN
ejpam-6489	139	22	=	=	SYM
ejpam-6489	139	23	(	(	PUNCT
ejpam-6489	139	24	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	139	25	(	(	PUNCT
ejpam-6489	139	26	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	27	)	)	PUNCT
ejpam-6489	139	28	,	,	PUNCT
ejpam-6489	139	29	ξ	ξ	PROPN
ejpam-6489	139	30	n	n	PRON
ejpam-6489	139	31	ℸ̃	ℸ̃	PROPN
ejpam-6489	139	32	(	(	PUNCT
ejpam-6489	139	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	34	)	)	PUNCT
ejpam-6489	139	35	,	,	PUNCT
ejpam-6489	139	36	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	139	37	)	)	PUNCT
ejpam-6489	139	38	)	)	PUNCT
ejpam-6489	139	39	,	,	PUNCT
ejpam-6489	139	40	and	and	CCONJ
ejpam-6489	139	41	ℵ̃	ℵ̃	PROPN
ejpam-6489	139	42	=	=	SYM
ejpam-6489	139	43	(	(	PUNCT
ejpam-6489	139	44	ξpℵ̃	ξpℵ̃	X
ejpam-6489	139	45	(	(	PUNCT
ejpam-6489	139	46	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	47	)	)	PUNCT
ejpam-6489	139	48	,	,	PUNCT
ejpam-6489	139	49	ξ	ξ	PROPN
ejpam-6489	139	50	n	n	PRON
ejpam-6489	139	51	ℵ̃	ℵ̃	PROPN
ejpam-6489	139	52	(	(	PUNCT
ejpam-6489	139	53	ϕ̃	ϕ̃	PROPN
ejpam-6489	139	54	)	)	PUNCT
ejpam-6489	139	55	,	,	PUNCT
ejpam-6489	139	56	ζℵ̃(ϕ̃	ζℵ̃(ϕ̃	PROPN
ejpam-6489	139	57	)	)	PUNCT
ejpam-6489	139	58	)	)	PUNCT
ejpam-6489	139	59	be	be	VERB
ejpam-6489	139	60	t	t	PROPN
ejpam-6489	139	61	cfss	cfss	NOUN
ejpam-6489	139	62	of	of	ADP
ejpam-6489	139	63	l̃	l̃	PROPN
ejpam-6489	139	64	such	such	ADJ
ejpam-6489	139	65	that	that	DET
ejpam-6489	139	66	̃ג	̃ג	NOUN
ejpam-6489	139	67	⊆	⊆	NUM
ejpam-6489	139	68	ℵ̃	ℵ̃	PROPN
ejpam-6489	139	69	and	and	CCONJ
ejpam-6489	139	70	ℵ̃	ℵ̃	PROPN
ejpam-6489	139	71	⊆	⊆	NUM
ejpam-6489	139	72	ℵ̃.	ℵ̃.	PROPN
ejpam-6489	139	73	then	then	ADV
ejpam-6489	139	74	+	+	PROPN
ejpam-6489	139	75	̃ג	̃ג	ADJ
ejpam-6489	139	76	ℵ̃	ℵ̃	NOUN
ejpam-6489	139	77	⊆	⊆	NUM
ejpam-6489	139	78	ℵ̃.	ℵ̃.	NOUN
ejpam-6489	139	79	proof	proof	NOUN
ejpam-6489	139	80	.	.	PUNCT
ejpam-6489	140	1	let	let	VERB
ejpam-6489	140	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	140	3	∈	∈	PROPN
ejpam-6489	140	4	l̃.	l̃.	PROPN
ejpam-6489	140	5	then	then	ADV
ejpam-6489	140	6	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	140	7	)	)	PUNCT
ejpam-6489	141	1	=	=	NOUN
ejpam-6489	141	2	r̃p̃ג+ℸ̃(ϕ̃)e	r̃p̃ג+ℸ̃(ϕ̃)e	NOUN
ejpam-6489	141	3	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	141	4	ℸ̃+̃ג	ℸ̃+̃ג	X
ejpam-6489	141	5	(	(	PUNCT
ejpam-6489	141	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	141	7	)	)	PUNCT
ejpam-6489	141	8	≥	≥	NOUN
ejpam-6489	141	9	sup	sup	NOUN
ejpam-6489	141	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	142	1	=	=	SYM
ejpam-6489	142	2	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	142	3	{	{	PUNCT
ejpam-6489	142	4	(	(	PUNCT
ejpam-6489	142	5	r̃p̃ג	r̃p̃ג	X
ejpam-6489	142	6	(	(	PUNCT
ejpam-6489	142	7	ϱ̃	ϱ̃	PROPN
ejpam-6489	142	8	)	)	PUNCT
ejpam-6489	142	9	∧	∧	PROPN
ejpam-6489	142	10	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	142	11	(	(	PUNCT
ejpam-6489	142	12	ϑ̃))e	ϑ̃))e	X
ejpam-6489	142	13	i2π(ω̃p	i2π(ω̃p	X
ejpam-6489	142	14	̃ג	̃ג	NOUN
ejpam-6489	142	15	(	(	PUNCT
ejpam-6489	142	16	ϱ̃)∧ϑ̃p	ϱ̃)∧ϑ̃p	PROPN
ejpam-6489	142	17	ℸ̃	ℸ̃	PROPN
ejpam-6489	142	18	(	(	PUNCT
ejpam-6489	142	19	ϑ̃	ϑ̃	PROPN
ejpam-6489	142	20	)	)	PUNCT
ejpam-6489	142	21	)	)	PUNCT
ejpam-6489	142	22	}	}	PUNCT
ejpam-6489	142	23	≥	≥	PROPN
ejpam-6489	142	24	sup	sup	NOUN
ejpam-6489	142	25	ϕ̃	ϕ̃	PROPN
ejpam-6489	143	1	=	=	SYM
ejpam-6489	143	2	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	143	3	{	{	PUNCT
ejpam-6489	143	4	(	(	PUNCT
ejpam-6489	143	5	r̃pℵ̃	r̃pℵ̃	X
ejpam-6489	143	6	(	(	PUNCT
ejpam-6489	143	7	ϱ̃	ϱ̃	PROPN
ejpam-6489	143	8	)	)	PUNCT
ejpam-6489	143	9	∧	∧	NOUN
ejpam-6489	143	10	r̃pℵ̃	r̃pℵ̃	NOUN
ejpam-6489	143	11	(	(	PUNCT
ejpam-6489	143	12	ϑ̃))e	ϑ̃))e	X
ejpam-6489	143	13	i2π(ω̃p	i2π(ω̃p	PROPN
ejpam-6489	143	14	ℵ̃	ℵ̃	PROPN
ejpam-6489	143	15	(	(	PUNCT
ejpam-6489	143	16	ϱ̃)∧ω̃p	ϱ̃)∧ω̃p	PROPN
ejpam-6489	143	17	ℵ̃	ℵ̃	PROPN
ejpam-6489	143	18	(	(	PUNCT
ejpam-6489	143	19	ϑ̃	ϑ̃	PROPN
ejpam-6489	143	20	)	)	PUNCT
ejpam-6489	143	21	)	)	PUNCT
ejpam-6489	143	22	}	}	PUNCT
ejpam-6489	143	23	≥	≥	PROPN
ejpam-6489	143	24	sup	sup	NOUN
ejpam-6489	143	25	ϕ̃	ϕ̃	PROPN
ejpam-6489	144	1	=	=	SYM
ejpam-6489	144	2	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	144	3	{	{	PUNCT
ejpam-6489	144	4	r̃pℵ̃	r̃pℵ̃	X
ejpam-6489	144	5	(	(	PUNCT
ejpam-6489	144	6	ϱ̃+	ϱ̃+	PROPN
ejpam-6489	144	7	ϑ̃)ei2πω̃	ϑ̃)ei2πω̃	PROPN
ejpam-6489	144	8	p	p	PROPN
ejpam-6489	144	9	ℵ̃	ℵ̃	PROPN
ejpam-6489	144	10	(	(	PUNCT
ejpam-6489	144	11	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	144	12	)	)	PUNCT
ejpam-6489	144	13	}	}	PUNCT
ejpam-6489	144	14	=	=	SYM
ejpam-6489	144	15	r̃pℵ̃	r̃pℵ̃	NOUN
ejpam-6489	144	16	(	(	PUNCT
ejpam-6489	144	17	ϕ̃)e	ϕ̃)e	NOUN
ejpam-6489	144	18	i2πω̃p	i2πω̃p	X
ejpam-6489	144	19	ℵ̃	ℵ̃	PROPN
ejpam-6489	144	20	(	(	PUNCT
ejpam-6489	144	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	144	22	)	)	PUNCT
ejpam-6489	144	23	=	=	SYM
ejpam-6489	145	1	ξpℵ̃	ξpℵ̃	X
ejpam-6489	145	2	(	(	PUNCT
ejpam-6489	145	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	145	4	)	)	PUNCT
ejpam-6489	145	5	,	,	PUNCT
ejpam-6489	145	6	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	145	7	)	)	PUNCT
ejpam-6489	145	8	=	=	PRON
ejpam-6489	145	9	r̃ñג+ℸ̃(ϕ̃)e	r̃ñג+ℸ̃(ϕ̃)e	VERB
ejpam-6489	145	10	i2πω̃n	i2πω̃n	PROPN
ejpam-6489	145	11	ℸ̃+̃ג	ℸ̃+̃ג	X
ejpam-6489	145	12	(	(	PUNCT
ejpam-6489	145	13	ϕ̃	ϕ̃	PROPN
ejpam-6489	145	14	)	)	PUNCT
ejpam-6489	145	15	≤	≤	NUM
ejpam-6489	145	16	inf	inf	NOUN
ejpam-6489	145	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	146	1	=	=	PROPN
ejpam-6489	147	1	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	147	2	{	{	PUNCT
ejpam-6489	147	3	(	(	PUNCT
ejpam-6489	147	4	r̃ñג	r̃ñג	PROPN
ejpam-6489	147	5	(	(	PUNCT
ejpam-6489	147	6	ϱ̃	ϱ̃	PROPN
ejpam-6489	147	7	)	)	PUNCT
ejpam-6489	147	8	∨	∨	NUM
ejpam-6489	147	9	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	147	10	(	(	PUNCT
ejpam-6489	147	11	ϑ̃))ei2π(ω̃	ϑ̃))ei2π(ω̃	PROPN
ejpam-6489	147	12	n	n	PRON
ejpam-6489	147	13	̃ג	̃ג	NOUN
ejpam-6489	147	14	(	(	PUNCT
ejpam-6489	147	15	ϱ̃)∨ω̃n	ϱ̃)∨ω̃n	NOUN
ejpam-6489	147	16	ℸ̃	ℸ̃	PROPN
ejpam-6489	147	17	(	(	PUNCT
ejpam-6489	147	18	ϑ̃	ϑ̃	PROPN
ejpam-6489	147	19	)	)	PUNCT
ejpam-6489	147	20	)	)	PUNCT
ejpam-6489	147	21	}	}	PUNCT
ejpam-6489	147	22	m.	m.	NOUN
ejpam-6489	147	23	balamurugan	balamurugan	NOUN
ejpam-6489	147	24	,	,	PUNCT
ejpam-6489	147	25	g.	g.	PROPN
ejpam-6489	147	26	ellammal	ellammal	PROPN
ejpam-6489	147	27	,	,	PUNCT
ejpam-6489	147	28	a.	a.	NOUN
ejpam-6489	147	29	iampan	iampan	PROPN
ejpam-6489	147	30	/	/	SYM
ejpam-6489	147	31	eur	eur	PROPN
ejpam-6489	147	32	.	.	PUNCT
ejpam-6489	148	1	j.	j.	PROPN
ejpam-6489	148	2	pure	pure	PROPN
ejpam-6489	148	3	appl	appl	PROPN
ejpam-6489	148	4	.	.	PROPN
ejpam-6489	148	5	math	math	PROPN
ejpam-6489	148	6	,	,	PUNCT
ejpam-6489	148	7	18	18	NUM
ejpam-6489	148	8	(	(	PUNCT
ejpam-6489	148	9	3	3	NUM
ejpam-6489	148	10	)	)	PUNCT
ejpam-6489	148	11	(	(	PUNCT
ejpam-6489	148	12	2025	2025	NUM
ejpam-6489	148	13	)	)	PUNCT
ejpam-6489	148	14	,	,	PUNCT
ejpam-6489	148	15	6489	6489	NUM
ejpam-6489	148	16	6	6	NUM
ejpam-6489	148	17	of	of	ADP
ejpam-6489	148	18	26	26	NUM
ejpam-6489	148	19	≤	≤	NUM
ejpam-6489	148	20	inf	inf	NOUN
ejpam-6489	148	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	148	22	=	=	PROPN
ejpam-6489	148	23	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	148	24	{	{	PUNCT
ejpam-6489	148	25	(	(	PUNCT
ejpam-6489	148	26	r̃nℵ̃	r̃nℵ̃	X
ejpam-6489	148	27	(	(	PUNCT
ejpam-6489	148	28	ϱ̃	ϱ̃	PROPN
ejpam-6489	148	29	)	)	PUNCT
ejpam-6489	148	30	∨	∨	NOUN
ejpam-6489	148	31	r̃nℵ̃	r̃nℵ̃	PROPN
ejpam-6489	148	32	(	(	PUNCT
ejpam-6489	148	33	ϑ̃))ei2π(ω̃	ϑ̃))ei2π(ω̃	PROPN
ejpam-6489	148	34	n	n	X
ejpam-6489	148	35	ℵ̃	ℵ̃	PROPN
ejpam-6489	148	36	(	(	PUNCT
ejpam-6489	148	37	ϱ̃)∨ω̃n	ϱ̃)∨ω̃n	PROPN
ejpam-6489	148	38	ℵ̃	ℵ̃	PROPN
ejpam-6489	148	39	(	(	PUNCT
ejpam-6489	148	40	ϑ̃	ϑ̃	PROPN
ejpam-6489	148	41	)	)	PUNCT
ejpam-6489	148	42	)	)	PUNCT
ejpam-6489	148	43	}	}	PUNCT
ejpam-6489	148	44	≤	≤	NUM
ejpam-6489	148	45	inf	inf	NOUN
ejpam-6489	148	46	ϕ̃	ϕ̃	PROPN
ejpam-6489	149	1	=	=	PROPN
ejpam-6489	149	2	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	149	3	{	{	PUNCT
ejpam-6489	149	4	r̃nℵ̃	r̃nℵ̃	PROPN
ejpam-6489	149	5	(	(	PUNCT
ejpam-6489	149	6	ϱ̃+	ϱ̃+	PROPN
ejpam-6489	149	7	ϑ̃)ei2πω̃	ϑ̃)ei2πω̃	PROPN
ejpam-6489	149	8	n	n	PRON
ejpam-6489	149	9	ℵ̃	ℵ̃	PROPN
ejpam-6489	149	10	(	(	PUNCT
ejpam-6489	149	11	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	149	12	)	)	PUNCT
ejpam-6489	149	13	}	}	PUNCT
ejpam-6489	149	14	=	=	SYM
ejpam-6489	150	1	r̃nℵ̃	r̃nℵ̃	PROPN
ejpam-6489	150	2	(	(	PUNCT
ejpam-6489	150	3	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	150	4	n	n	CCONJ
ejpam-6489	150	5	ℵ̃	ℵ̃	PROPN
ejpam-6489	150	6	(	(	PUNCT
ejpam-6489	150	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	150	8	)	)	PUNCT
ejpam-6489	150	9	=	=	SYM
ejpam-6489	150	10	ξnℵ̃	ξnℵ̃	NOUN
ejpam-6489	150	11	(	(	PUNCT
ejpam-6489	150	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	150	13	)	)	PUNCT
ejpam-6489	150	14	,	,	PUNCT
ejpam-6489	150	15	and	and	CCONJ
ejpam-6489	150	16	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	150	17	)	)	PUNCT
ejpam-6489	150	18	=	=	NOUN
ejpam-6489	150	19	r̃̃ג+ℸ̃(ϕ̃)e	r̃̃ג+ℸ̃(ϕ̃)e	VERB
ejpam-6489	150	20	i2πω̃̃ג+ℸ̃(ϕ̃	i2πω̃̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	150	21	)	)	PUNCT
ejpam-6489	150	22	≤	≤	NOUN
ejpam-6489	150	23	inf	inf	NOUN
ejpam-6489	150	24	ϕ̃	ϕ̃	PROPN
ejpam-6489	150	25	=	=	PROPN
ejpam-6489	150	26	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	150	27	{	{	PUNCT
ejpam-6489	150	28	(	(	PUNCT
ejpam-6489	150	29	r̃̃ג(ϱ̃	r̃̃ג(ϱ̃	NOUN
ejpam-6489	150	30	)	)	PUNCT
ejpam-6489	150	31	∨	∨	NUM
ejpam-6489	150	32	r̃ℸ̃(ϑ̃))e	r̃ℸ̃(ϑ̃))e	PROPN
ejpam-6489	150	33	i2π(ω̃̃ג(ϱ̃)∨ω̃ℸ̃(ϑ̃	i2π(ω̃̃ג(ϱ̃)∨ω̃ℸ̃(ϑ̃	PROPN
ejpam-6489	150	34	)	)	PUNCT
ejpam-6489	150	35	)	)	PUNCT
ejpam-6489	150	36	}	}	PUNCT
ejpam-6489	150	37	≤	≤	NUM
ejpam-6489	150	38	inf	inf	NOUN
ejpam-6489	150	39	ϕ̃	ϕ̃	PROPN
ejpam-6489	151	1	=	=	PROPN
ejpam-6489	152	1	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	152	2	{	{	PUNCT
ejpam-6489	152	3	(	(	PUNCT
ejpam-6489	152	4	r̃ℵ̃(ϱ̃	r̃ℵ̃(ϱ̃	X
ejpam-6489	152	5	)	)	PUNCT
ejpam-6489	152	6	∨	∨	NUM
ejpam-6489	152	7	r̃ℵ̃(ϑ̃))e	r̃ℵ̃(ϑ̃))e	PROPN
ejpam-6489	152	8	i2π(ω̃ℵ̃(ϱ̃)∨ω̃ℵ̃(ϑ̃	i2π(ω̃ℵ̃(ϱ̃)∨ω̃ℵ̃(ϑ̃	PROPN
ejpam-6489	152	9	)	)	PUNCT
ejpam-6489	152	10	)	)	PUNCT
ejpam-6489	152	11	}	}	PUNCT
ejpam-6489	152	12	≤	≤	NUM
ejpam-6489	152	13	inf	inf	NOUN
ejpam-6489	152	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	153	1	=	=	PROPN
ejpam-6489	153	2	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	153	3	{	{	PUNCT
ejpam-6489	153	4	r̃ℵ̃(ϱ̃+	r̃ℵ̃(ϱ̃+	PROPN
ejpam-6489	153	5	ϑ̃)ei2πω̃ℵ̃(ϱ̃+ϑ̃	ϑ̃)ei2πω̃ℵ̃(ϱ̃+ϑ̃	PROPN
ejpam-6489	153	6	)	)	PUNCT
ejpam-6489	153	7	}	}	PUNCT
ejpam-6489	153	8	=	=	PUNCT
ejpam-6489	153	9	r̃ℵ̃(ϕ̃)e	r̃ℵ̃(ϕ̃)e	PROPN
ejpam-6489	153	10	i2πω̃ℵ̃(ϕ̃	i2πω̃ℵ̃(ϕ̃	PROPN
ejpam-6489	153	11	)	)	PUNCT
ejpam-6489	153	12	=	=	SYM
ejpam-6489	153	13	ζℵ̃(ϕ̃	ζℵ̃(ϕ̃	PROPN
ejpam-6489	153	14	)	)	PUNCT
ejpam-6489	153	15	.	.	PUNCT
ejpam-6489	154	1	hence	hence	ADV
ejpam-6489	154	2	,	,	PUNCT
ejpam-6489	154	3	+	+	ADJ
ejpam-6489	154	4	̃ג	̃ג	ADJ
ejpam-6489	154	5	ℸ̃	ℸ̃	PROPN
ejpam-6489	154	6	⊆	⊆	NUM
ejpam-6489	154	7	ℵ̃.	ℵ̃.	NOUN
ejpam-6489	154	8	theorem	theorem	NOUN
ejpam-6489	154	9	2	2	X
ejpam-6489	154	10	.	.	PUNCT
ejpam-6489	155	1	let	let	VERB
ejpam-6489	155	2	1̃ג	1̃ג	NUM
ejpam-6489	155	3	=	=	SYM
ejpam-6489	155	4	(	(	PUNCT
ejpam-6489	155	5	ξp1̃ג	ξp1̃ג	PROPN
ejpam-6489	155	6	(	(	PUNCT
ejpam-6489	155	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	155	8	)	)	PUNCT
ejpam-6489	155	9	,	,	PUNCT
ejpam-6489	155	10	ξn1̃ג	ξn1̃ג	X
ejpam-6489	155	11	(	(	PUNCT
ejpam-6489	155	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	155	13	)	)	PUNCT
ejpam-6489	155	14	,	,	PUNCT
ejpam-6489	155	15	ζ1̃ג(ϕ̃	ζ1̃ג(ϕ̃	PROPN
ejpam-6489	155	16	)	)	PUNCT
ejpam-6489	155	17	)	)	PUNCT
ejpam-6489	155	18	,	,	PUNCT
ejpam-6489	156	1	2̃ג	2̃ג	X
ejpam-6489	156	2	=	=	SYM
ejpam-6489	156	3	(	(	PUNCT
ejpam-6489	156	4	ξp2̃ג	ξp2̃ג	PROPN
ejpam-6489	156	5	(	(	PUNCT
ejpam-6489	156	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	7	)	)	PUNCT
ejpam-6489	156	8	,	,	PUNCT
ejpam-6489	156	9	ξn2̃ג	ξn2̃ג	PROPN
ejpam-6489	156	10	(	(	PUNCT
ejpam-6489	156	11	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	12	)	)	PUNCT
ejpam-6489	156	13	,	,	PUNCT
ejpam-6489	156	14	ζ2̃ג(ϕ̃	ζ2̃ג(ϕ̃	PROPN
ejpam-6489	156	15	)	)	PUNCT
ejpam-6489	156	16	)	)	PUNCT
ejpam-6489	156	17	and	and	CCONJ
ejpam-6489	156	18	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	156	19	=	=	SYM
ejpam-6489	156	20	(	(	PUNCT
ejpam-6489	156	21	ξpℸ̃1	ξpℸ̃1	PRON
ejpam-6489	156	22	(	(	PUNCT
ejpam-6489	156	23	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	24	)	)	PUNCT
ejpam-6489	156	25	,	,	PUNCT
ejpam-6489	156	26	ξnℸ̃1	ξnℸ̃1	NOUN
ejpam-6489	156	27	(	(	PUNCT
ejpam-6489	156	28	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	29	)	)	PUNCT
ejpam-6489	156	30	,	,	PUNCT
ejpam-6489	156	31	ζℸ̃1	ζℸ̃1	NOUN
ejpam-6489	156	32	(	(	PUNCT
ejpam-6489	156	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	34	)	)	PUNCT
ejpam-6489	156	35	)	)	PUNCT
ejpam-6489	156	36	,	,	PUNCT
ejpam-6489	156	37	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	156	38	=	=	PUNCT
ejpam-6489	156	39	(	(	PUNCT
ejpam-6489	156	40	ξpℸ̃2	ξpℸ̃2	NOUN
ejpam-6489	156	41	(	(	PUNCT
ejpam-6489	156	42	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	43	)	)	PUNCT
ejpam-6489	156	44	,	,	PUNCT
ejpam-6489	156	45	ξnℸ̃2	ξnℸ̃2	NOUN
ejpam-6489	156	46	(	(	PUNCT
ejpam-6489	156	47	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	48	)	)	PUNCT
ejpam-6489	156	49	,	,	PUNCT
ejpam-6489	156	50	ζℸ̃2	ζℸ̃2	NOUN
ejpam-6489	156	51	(	(	PUNCT
ejpam-6489	156	52	ϕ̃	ϕ̃	PROPN
ejpam-6489	156	53	)	)	PUNCT
ejpam-6489	156	54	)	)	PUNCT
ejpam-6489	156	55	be	be	AUX
ejpam-6489	156	56	t	t	PROPN
ejpam-6489	156	57	cfss	cfss	NOUN
ejpam-6489	156	58	of	of	ADP
ejpam-6489	156	59	l̃	l̃	PROPN
ejpam-6489	156	60	such	such	ADJ
ejpam-6489	156	61	that	that	SCONJ
ejpam-6489	156	62	1̃ג	1̃ג	NUM
ejpam-6489	156	63	⊆	⊆	NUM
ejpam-6489	156	64	,	,	PUNCT
ejpam-6489	156	65	2̃ג	2̃ג	NUM
ejpam-6489	156	66	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	156	67	⊆	⊆	NUM
ejpam-6489	156	68	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	156	69	.	.	PUNCT
ejpam-6489	157	1	then	then	ADV
ejpam-6489	157	2	,	,	PUNCT
ejpam-6489	157	3	1̃ג	1̃ג	X
ejpam-6489	157	4	]	]	PUNCT
ejpam-6489	157	5	ℸ̃	ℸ̃	PROPN
ejpam-6489	157	6	]	]	X
ejpam-6489	157	7	⊆	⊆	NUM
ejpam-6489	157	8	,	,	PUNCT
ejpam-6489	157	9	2̃ג	2̃ג	NUM
ejpam-6489	157	10	]	]	PUNCT
ejpam-6489	157	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	157	12	]	]	PUNCT
ejpam-6489	157	13	and	and	CCONJ
ejpam-6489	157	14	,	,	PUNCT
ejpam-6489	157	15	̃ג	̃ג	NOUN
ejpam-6489	157	16	]	]	PUNCT
ejpam-6489	157	17	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	157	18	]	]	X
ejpam-6489	157	19	⊆	⊆	NUM
ejpam-6489	157	20	,	,	PUNCT
ejpam-6489	157	21	̃ג	̃ג	NOUN
ejpam-6489	157	22	]	]	PUNCT
ejpam-6489	157	23	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	157	24	]	]	PUNCT
ejpam-6489	157	25	.	.	PUNCT
ejpam-6489	158	1	proof	proof	NOUN
ejpam-6489	158	2	.	.	PUNCT
ejpam-6489	159	1	let	let	VERB
ejpam-6489	160	1	ϕ̃	ϕ̃	PROPN
ejpam-6489	160	2	∈	∈	PROPN
ejpam-6489	160	3	l̃.	l̃.	NOUN
ejpam-6489	160	4	then	then	ADV
ejpam-6489	160	5	ξp	ξp	ADP
ejpam-6489	160	6	[	[	X
ejpam-6489	160	7	ℸ̃1,1̃ג	ℸ̃1,1̃ג	X
ejpam-6489	160	8	]	]	X
ejpam-6489	160	9	(	(	PUNCT
ejpam-6489	160	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	160	11	)	)	PUNCT
ejpam-6489	160	12	=	=	SYM
ejpam-6489	160	13	sup	sup	NOUN
ejpam-6489	160	14	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	160	15	∑	∑	PUNCT
ejpam-6489	160	16	j∈n	j∈n	NOUN
ejpam-6489	161	1	βj	βj	NOUN
ejpam-6489	162	1	[	[	X
ejpam-6489	162	2	ϕ̃j	ϕ̃j	X
ejpam-6489	162	3	,	,	PUNCT
ejpam-6489	162	4	η̃j	η̃j	PROPN
ejpam-6489	162	5	]	]	PUNCT
ejpam-6489	162	6	{	{	PUNCT
ejpam-6489	162	7	min	min	NOUN
ejpam-6489	162	8	j∈n	j∈n	NOUN
ejpam-6489	162	9	{	{	PUNCT
ejpam-6489	162	10	r̃p1̃ג(ϕ̃j	r̃p1̃ג(ϕ̃j	NOUN
ejpam-6489	162	11	)	)	PUNCT
ejpam-6489	162	12	∧	∧	PROPN
ejpam-6489	162	13	r̃pℸ̃1	r̃pℸ̃1	PROPN
ejpam-6489	162	14	(	(	PUNCT
ejpam-6489	162	15	η̃j)}e	η̃j)}e	PRON
ejpam-6489	162	16	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	162	17	{	{	PUNCT
ejpam-6489	162	18	ω̃p	ω̃p	PROPN
ejpam-6489	162	19	1̃ג	1̃ג	PROPN
ejpam-6489	162	20	(	(	PUNCT
ejpam-6489	162	21	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	162	22	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	162	23	(	(	PUNCT
ejpam-6489	162	24	η̃j	η̃j	NOUN
ejpam-6489	162	25	)	)	PUNCT
ejpam-6489	162	26	}	}	PUNCT
ejpam-6489	162	27	}	}	PUNCT
ejpam-6489	162	28	≥	≥	X
ejpam-6489	162	29	sup	sup	NUM
ejpam-6489	162	30	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	162	31	∑	∑	PUNCT
ejpam-6489	162	32	j∈n	j∈n	NOUN
ejpam-6489	162	33	βj	βj	NOUN
ejpam-6489	163	1	[	[	X
ejpam-6489	163	2	ϕ̃j	ϕ̃j	X
ejpam-6489	163	3	,	,	PUNCT
ejpam-6489	163	4	η̃j	η̃j	PROPN
ejpam-6489	163	5	]	]	PUNCT
ejpam-6489	163	6	{	{	PUNCT
ejpam-6489	163	7	min	min	NOUN
ejpam-6489	163	8	j∈n	j∈n	NOUN
ejpam-6489	163	9	{	{	PUNCT
ejpam-6489	163	10	r̃p2̃ג(ϕ̃j	r̃p2̃ג(ϕ̃j	NOUN
ejpam-6489	163	11	)	)	PUNCT
ejpam-6489	163	12	∧	∧	PROPN
ejpam-6489	163	13	r̃pℸ̃2	r̃pℸ̃2	NOUN
ejpam-6489	163	14	(	(	PUNCT
ejpam-6489	163	15	η̃j)}e	η̃j)}e	PRON
ejpam-6489	163	16	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	163	17	{	{	PUNCT
ejpam-6489	163	18	ω̃p	ω̃p	PROPN
ejpam-6489	163	19	2̃ג	2̃ג	PROPN
ejpam-6489	163	20	(	(	PUNCT
ejpam-6489	163	21	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	163	22	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	163	23	(	(	PUNCT
ejpam-6489	163	24	η̃j	η̃j	PROPN
ejpam-6489	163	25	)	)	PUNCT
ejpam-6489	163	26	}	}	PUNCT
ejpam-6489	163	27	}	}	PUNCT
ejpam-6489	163	28	=	=	SYM
ejpam-6489	163	29	ξp	ξp	AUX
ejpam-6489	163	30	[	[	X
ejpam-6489	163	31	ℸ̃2,2̃ג	ℸ̃2,2̃ג	X
ejpam-6489	163	32	]	]	X
ejpam-6489	163	33	(	(	PUNCT
ejpam-6489	163	34	ϕ̃	ϕ̃	PROPN
ejpam-6489	163	35	)	)	PUNCT
ejpam-6489	163	36	,	,	PUNCT
ejpam-6489	163	37	ξn	ξn	X
ejpam-6489	164	1	[	[	X
ejpam-6489	164	2	ℸ̃1,1̃ג	ℸ̃1,1̃ג	PROPN
ejpam-6489	164	3	]	]	X
ejpam-6489	164	4	(	(	PUNCT
ejpam-6489	164	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	164	6	)	)	PUNCT
ejpam-6489	164	7	=	=	SYM
ejpam-6489	164	8	inf	inf	NOUN
ejpam-6489	164	9	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	164	10	∑	∑	PROPN
ejpam-6489	164	11	j∈n	j∈n	NOUN
ejpam-6489	164	12	βj	βj	NOUN
ejpam-6489	165	1	[	[	X
ejpam-6489	165	2	ϕ̃j	ϕ̃j	X
ejpam-6489	165	3	,	,	PUNCT
ejpam-6489	165	4	η̃j	η̃j	PROPN
ejpam-6489	165	5	]	]	PUNCT
ejpam-6489	166	1	{	{	PUNCT
ejpam-6489	166	2	max	max	PROPN
ejpam-6489	166	3	j∈n	j∈n	PROPN
ejpam-6489	166	4	{	{	PUNCT
ejpam-6489	166	5	r̃n1̃ג	r̃n1̃ג	PROPN
ejpam-6489	166	6	(	(	PUNCT
ejpam-6489	166	7	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	166	8	)	)	PUNCT
ejpam-6489	166	9	∨	∨	PROPN
ejpam-6489	166	10	r̃nℸ̃1	r̃nℸ̃1	NOUN
ejpam-6489	166	11	(	(	PUNCT
ejpam-6489	166	12	η̃j)}e	η̃j)}e	PRON
ejpam-6489	166	13	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	166	14	{	{	PUNCT
ejpam-6489	166	15	ω̃n	ω̃n	PROPN
ejpam-6489	166	16	1̃ג	1̃ג	PROPN
ejpam-6489	166	17	(	(	PUNCT
ejpam-6489	166	18	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	PUNCT
ejpam-6489	166	19	ℸ̃1	ℸ̃1	PROPN
ejpam-6489	166	20	(	(	PUNCT
ejpam-6489	166	21	η̃j	η̃j	NOUN
ejpam-6489	166	22	)	)	PUNCT
ejpam-6489	166	23	}	}	PUNCT
ejpam-6489	166	24	}	}	PUNCT
ejpam-6489	166	25	≤	≤	NUM
ejpam-6489	166	26	inf	inf	PROPN
ejpam-6489	166	27	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	166	28	∑	∑	PROPN
ejpam-6489	166	29	j∈n	j∈n	NOUN
ejpam-6489	166	30	βj	βj	NOUN
ejpam-6489	167	1	[	[	X
ejpam-6489	167	2	ϕ̃j	ϕ̃j	X
ejpam-6489	167	3	,	,	PUNCT
ejpam-6489	167	4	η̃j	η̃j	PROPN
ejpam-6489	167	5	]	]	PUNCT
ejpam-6489	168	1	{	{	PUNCT
ejpam-6489	168	2	max	max	PROPN
ejpam-6489	168	3	j∈n	j∈n	PROPN
ejpam-6489	168	4	{	{	PUNCT
ejpam-6489	168	5	r̃n2̃ג	r̃n2̃ג	PROPN
ejpam-6489	168	6	(	(	PUNCT
ejpam-6489	168	7	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	168	8	)	)	PUNCT
ejpam-6489	168	9	∨	∨	NUM
ejpam-6489	168	10	r̃nℸ̃2	r̃nℸ̃2	PROPN
ejpam-6489	168	11	(	(	PUNCT
ejpam-6489	168	12	η̃j)}e	η̃j)}e	PRON
ejpam-6489	168	13	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	168	14	{	{	PUNCT
ejpam-6489	168	15	ω̃n	ω̃n	PROPN
ejpam-6489	168	16	2̃ג	2̃ג	PROPN
ejpam-6489	168	17	(	(	PUNCT
ejpam-6489	168	18	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	X
ejpam-6489	168	19	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	168	20	(	(	PUNCT
ejpam-6489	168	21	η̃j	η̃j	PROPN
ejpam-6489	168	22	)	)	PUNCT
ejpam-6489	168	23	}	}	PUNCT
ejpam-6489	168	24	}	}	PUNCT
ejpam-6489	168	25	=	=	SYM
ejpam-6489	168	26	ξn	ξn	PROPN
ejpam-6489	168	27	[	[	X
ejpam-6489	168	28	ℸ̃2,2̃ג	ℸ̃2,2̃ג	X
ejpam-6489	168	29	]	]	X
ejpam-6489	168	30	(	(	PUNCT
ejpam-6489	168	31	ϕ̃	ϕ̃	PROPN
ejpam-6489	168	32	)	)	PUNCT
ejpam-6489	168	33	,	,	PUNCT
ejpam-6489	168	34	m.	m.	NOUN
ejpam-6489	168	35	balamurugan	balamurugan	VERB
ejpam-6489	168	36	,	,	PUNCT
ejpam-6489	168	37	g.	g.	PROPN
ejpam-6489	168	38	ellammal	ellammal	PROPN
ejpam-6489	168	39	,	,	PUNCT
ejpam-6489	168	40	a.	a.	NOUN
ejpam-6489	168	41	iampan	iampan	PROPN
ejpam-6489	168	42	/	/	SYM
ejpam-6489	168	43	eur	eur	PROPN
ejpam-6489	168	44	.	.	PUNCT
ejpam-6489	169	1	j.	j.	PROPN
ejpam-6489	169	2	pure	pure	PROPN
ejpam-6489	169	3	appl	appl	PROPN
ejpam-6489	169	4	.	.	PROPN
ejpam-6489	169	5	math	math	PROPN
ejpam-6489	169	6	,	,	PUNCT
ejpam-6489	169	7	18	18	NUM
ejpam-6489	169	8	(	(	PUNCT
ejpam-6489	169	9	3	3	NUM
ejpam-6489	169	10	)	)	PUNCT
ejpam-6489	169	11	(	(	PUNCT
ejpam-6489	169	12	2025	2025	NUM
ejpam-6489	169	13	)	)	PUNCT
ejpam-6489	169	14	,	,	PUNCT
ejpam-6489	169	15	6489	6489	NUM
ejpam-6489	169	16	7	7	NUM
ejpam-6489	169	17	of	of	ADP
ejpam-6489	169	18	26	26	NUM
ejpam-6489	169	19	and	and	CCONJ
ejpam-6489	169	20	ζ[1̃ג,ℸ̃1	ζ[1̃ג,ℸ̃1	NOUN
ejpam-6489	169	21	]	]	PUNCT
ejpam-6489	169	22	(	(	PUNCT
ejpam-6489	169	23	ϕ̃	ϕ̃	PROPN
ejpam-6489	169	24	)	)	PUNCT
ejpam-6489	169	25	=	=	SYM
ejpam-6489	169	26	inf	inf	NOUN
ejpam-6489	169	27	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	169	28	∑	∑	PROPN
ejpam-6489	169	29	j∈n	j∈n	NOUN
ejpam-6489	170	1	βj	βj	NOUN
ejpam-6489	171	1	[	[	X
ejpam-6489	171	2	ϕ̃j	ϕ̃j	X
ejpam-6489	171	3	,	,	PUNCT
ejpam-6489	171	4	η̃j	η̃j	PROPN
ejpam-6489	171	5	]	]	PUNCT
ejpam-6489	172	1	{	{	PUNCT
ejpam-6489	172	2	max	max	PROPN
ejpam-6489	172	3	j∈n	j∈n	PROPN
ejpam-6489	172	4	{	{	PUNCT
ejpam-6489	172	5	r̃1̃ג(ϕ̃j	r̃1̃ג(ϕ̃j	PROPN
ejpam-6489	172	6	)	)	PUNCT
ejpam-6489	172	7	∨	∨	NUM
ejpam-6489	172	8	r̃ℸ̃1	r̃ℸ̃1	NOUN
ejpam-6489	172	9	(	(	PUNCT
ejpam-6489	172	10	η̃j)}ei2πmaxj∈n	η̃j)}ei2πmaxj∈n	PROPN
ejpam-6489	172	11	{	{	PUNCT
ejpam-6489	172	12	ω̃1̃ג	ω̃1̃ג	NUM
ejpam-6489	172	13	(	(	PUNCT
ejpam-6489	172	14	ϕ̃j)∨ω̃ℸ̃1	ϕ̃j)∨ω̃ℸ̃1	X
ejpam-6489	172	15	(	(	PUNCT
ejpam-6489	172	16	η̃j	η̃j	NOUN
ejpam-6489	172	17	)	)	PUNCT
ejpam-6489	172	18	}	}	PUNCT
ejpam-6489	172	19	}	}	PUNCT
ejpam-6489	172	20	≤	≤	NUM
ejpam-6489	172	21	inf	inf	PROPN
ejpam-6489	172	22	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	172	23	∑	∑	PROPN
ejpam-6489	172	24	j∈n	j∈n	NOUN
ejpam-6489	172	25	βj	βj	NOUN
ejpam-6489	173	1	[	[	X
ejpam-6489	173	2	ϕ̃j	ϕ̃j	X
ejpam-6489	173	3	,	,	PUNCT
ejpam-6489	173	4	η̃j	η̃j	PROPN
ejpam-6489	173	5	]	]	PUNCT
ejpam-6489	174	1	{	{	PUNCT
ejpam-6489	174	2	max	max	PROPN
ejpam-6489	174	3	j∈n	j∈n	PROPN
ejpam-6489	174	4	{	{	PUNCT
ejpam-6489	174	5	r̃2̃ג(ϕ̃j	r̃2̃ג(ϕ̃j	PROPN
ejpam-6489	174	6	)	)	PUNCT
ejpam-6489	174	7	∨	∨	NUM
ejpam-6489	174	8	r̃ℸ̃2	r̃ℸ̃2	NOUN
ejpam-6489	174	9	(	(	PUNCT
ejpam-6489	174	10	η̃j)}ei2πmaxj∈n	η̃j)}ei2πmaxj∈n	PROPN
ejpam-6489	174	11	{	{	PUNCT
ejpam-6489	174	12	ω̃2̃ג	ω̃2̃ג	NUM
ejpam-6489	174	13	(	(	PUNCT
ejpam-6489	174	14	ϕ̃j)∨ω̃ℸ̃2	ϕ̃j)∨ω̃ℸ̃2	NOUN
ejpam-6489	174	15	(	(	PUNCT
ejpam-6489	174	16	η̃j	η̃j	PROPN
ejpam-6489	174	17	)	)	PUNCT
ejpam-6489	174	18	}	}	PUNCT
ejpam-6489	174	19	}	}	PUNCT
ejpam-6489	174	20	=	=	SYM
ejpam-6489	174	21	ζ[2̃ג,ℸ̃2	ζ[2̃ג,ℸ̃2	NOUN
ejpam-6489	174	22	]	]	PUNCT
ejpam-6489	174	23	(	(	PUNCT
ejpam-6489	174	24	ϕ̃	ϕ̃	PROPN
ejpam-6489	174	25	)	)	PUNCT
ejpam-6489	174	26	.	.	PUNCT
ejpam-6489	175	1	theorem	theorem	NOUN
ejpam-6489	175	2	3	3	X
ejpam-6489	175	3	.	.	PUNCT
ejpam-6489	176	1	let	let	VERB
ejpam-6489	176	2	1̃ג	1̃ג	NUM
ejpam-6489	176	3	=	=	SYM
ejpam-6489	176	4	(	(	PUNCT
ejpam-6489	176	5	ξp1̃ג	ξp1̃ג	PROPN
ejpam-6489	176	6	(	(	PUNCT
ejpam-6489	176	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	176	8	)	)	PUNCT
ejpam-6489	176	9	,	,	PUNCT
ejpam-6489	176	10	ξn1̃ג	ξn1̃ג	X
ejpam-6489	176	11	(	(	PUNCT
ejpam-6489	176	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	176	13	)	)	PUNCT
ejpam-6489	176	14	,	,	PUNCT
ejpam-6489	176	15	ζ1̃ג(ϕ̃	ζ1̃ג(ϕ̃	PROPN
ejpam-6489	176	16	)	)	PUNCT
ejpam-6489	176	17	)	)	PUNCT
ejpam-6489	176	18	,	,	PUNCT
ejpam-6489	177	1	2̃ג	2̃ג	X
ejpam-6489	177	2	=	=	SYM
ejpam-6489	177	3	(	(	PUNCT
ejpam-6489	177	4	ξp2̃ג	ξp2̃ג	PROPN
ejpam-6489	177	5	(	(	PUNCT
ejpam-6489	177	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	7	)	)	PUNCT
ejpam-6489	177	8	,	,	PUNCT
ejpam-6489	177	9	ξn2̃ג	ξn2̃ג	PROPN
ejpam-6489	177	10	(	(	PUNCT
ejpam-6489	177	11	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	12	)	)	PUNCT
ejpam-6489	177	13	,	,	PUNCT
ejpam-6489	177	14	ζ2̃ג(ϕ̃	ζ2̃ג(ϕ̃	PROPN
ejpam-6489	177	15	)	)	PUNCT
ejpam-6489	177	16	)	)	PUNCT
ejpam-6489	177	17	and	and	CCONJ
ejpam-6489	177	18	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	177	19	=	=	SYM
ejpam-6489	177	20	(	(	PUNCT
ejpam-6489	177	21	ξpℸ̃1	ξpℸ̃1	PRON
ejpam-6489	177	22	(	(	PUNCT
ejpam-6489	177	23	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	24	)	)	PUNCT
ejpam-6489	177	25	,	,	PUNCT
ejpam-6489	177	26	ξnℸ̃1	ξnℸ̃1	NOUN
ejpam-6489	177	27	(	(	PUNCT
ejpam-6489	177	28	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	29	)	)	PUNCT
ejpam-6489	177	30	,	,	PUNCT
ejpam-6489	177	31	ζℸ̃1	ζℸ̃1	NOUN
ejpam-6489	177	32	(	(	PUNCT
ejpam-6489	177	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	34	)	)	PUNCT
ejpam-6489	177	35	)	)	PUNCT
ejpam-6489	177	36	,	,	PUNCT
ejpam-6489	177	37	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	177	38	=	=	PUNCT
ejpam-6489	177	39	(	(	PUNCT
ejpam-6489	177	40	ξpℸ̃2	ξpℸ̃2	NOUN
ejpam-6489	177	41	(	(	PUNCT
ejpam-6489	177	42	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	43	)	)	PUNCT
ejpam-6489	177	44	,	,	PUNCT
ejpam-6489	177	45	ξnℸ̃2	ξnℸ̃2	NOUN
ejpam-6489	177	46	(	(	PUNCT
ejpam-6489	177	47	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	48	)	)	PUNCT
ejpam-6489	177	49	,	,	PUNCT
ejpam-6489	177	50	ζℸ̃2	ζℸ̃2	NOUN
ejpam-6489	177	51	(	(	PUNCT
ejpam-6489	177	52	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	53	)	)	PUNCT
ejpam-6489	177	54	)	)	PUNCT
ejpam-6489	177	55	and	and	CCONJ
ejpam-6489	177	56	̃ג	̃ג	NOUN
ejpam-6489	177	57	=	=	SYM
ejpam-6489	177	58	(	(	PUNCT
ejpam-6489	177	59	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	177	60	(	(	PUNCT
ejpam-6489	177	61	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	62	)	)	PUNCT
ejpam-6489	177	63	,	,	PUNCT
ejpam-6489	177	64	ξ	ξ	PROPN
ejpam-6489	177	65	n	n	PRON
ejpam-6489	177	66	̃ג	̃ג	PROPN
ejpam-6489	177	67	(	(	PUNCT
ejpam-6489	177	68	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	69	)	)	PUNCT
ejpam-6489	177	70	,	,	PUNCT
ejpam-6489	177	71	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	177	72	)	)	PUNCT
ejpam-6489	177	73	)	)	PUNCT
ejpam-6489	177	74	,	,	PUNCT
ejpam-6489	177	75	ℸ̃	ℸ̃	PROPN
ejpam-6489	177	76	=	=	SYM
ejpam-6489	177	77	(	(	PUNCT
ejpam-6489	177	78	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	177	79	(	(	PUNCT
ejpam-6489	177	80	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	81	)	)	PUNCT
ejpam-6489	177	82	,	,	PUNCT
ejpam-6489	177	83	ξ	ξ	PROPN
ejpam-6489	177	84	n	n	PRON
ejpam-6489	177	85	ℸ̃	ℸ̃	PROPN
ejpam-6489	177	86	(	(	PUNCT
ejpam-6489	177	87	ϕ̃	ϕ̃	PROPN
ejpam-6489	177	88	)	)	PUNCT
ejpam-6489	177	89	,	,	PUNCT
ejpam-6489	177	90	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	177	91	)	)	PUNCT
ejpam-6489	177	92	)	)	PUNCT
ejpam-6489	177	93	be	be	VERB
ejpam-6489	177	94	t	t	PROPN
ejpam-6489	177	95	cfss	cfss	ADV
ejpam-6489	177	96	of	of	ADP
ejpam-6489	177	97	l̃.	l̃.	ADJ
ejpam-6489	177	98	then	then	ADV
ejpam-6489	177	99	+1̃ג	+1̃ג	PROPN
ejpam-6489	177	100	]	]	PUNCT
ejpam-6489	177	101	,	,	PUNCT
ejpam-6489	177	102	2̃ג	2̃ג	NUM
ejpam-6489	177	103	ℸ̃	ℸ̃	NOUN
ejpam-6489	177	104	]	]	X
ejpam-6489	177	105	=	=	SYM
ejpam-6489	177	106	,	,	PUNCT
ejpam-6489	177	107	1̃ג	1̃ג	PROPN
ejpam-6489	177	108	]	]	X
ejpam-6489	177	109	ℸ̃]+[2̃ג	ℸ̃]+[2̃ג	NOUN
ejpam-6489	177	110	,	,	PUNCT
ejpam-6489	177	111	ℸ̃	ℸ̃	PROPN
ejpam-6489	177	112	]	]	PUNCT
ejpam-6489	177	113	and	and	CCONJ
ejpam-6489	177	114	,	,	PUNCT
ejpam-6489	177	115	̃ג	̃ג	PROPN
ejpam-6489	177	116	]	]	PUNCT
ejpam-6489	177	117	ℸ̃1+ℸ̃2	ℸ̃1+ℸ̃2	NOUN
ejpam-6489	177	118	]	]	X
ejpam-6489	177	119	=	=	SYM
ejpam-6489	177	120	,	,	PUNCT
ejpam-6489	177	121	̃ג	̃ג	NOUN
ejpam-6489	177	122	]	]	PUNCT
ejpam-6489	177	123	ℸ̃1	ℸ̃1	NOUN
ejpam-6489	177	124	]	]	X
ejpam-6489	177	125	+	+	CCONJ
ejpam-6489	177	126	,	,	PUNCT
ejpam-6489	177	127	̃ג	̃ג	PROPN
ejpam-6489	177	128	]	]	PUNCT
ejpam-6489	177	129	ℸ̃2	ℸ̃2	PROPN
ejpam-6489	177	130	]	]	PUNCT
ejpam-6489	177	131	.	.	PUNCT
ejpam-6489	178	1	proof	proof	NOUN
ejpam-6489	178	2	.	.	PUNCT
ejpam-6489	179	1	let	let	VERB
ejpam-6489	179	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	179	3	∈	∈	PROPN
ejpam-6489	179	4	l̃	l̃	PROPN
ejpam-6489	179	5	and	and	CCONJ
ejpam-6489	179	6	sup	sup	NOUN
ejpam-6489	179	7	=	=	PUNCT
ejpam-6489	180	1	supϕ̃=	supϕ̃=	ADV
ejpam-6489	180	2	∑	∑	PUNCT
ejpam-6489	180	3	j∈n	j∈n	NOUN
ejpam-6489	180	4	βj	βj	PRON
ejpam-6489	181	1	[	[	X
ejpam-6489	181	2	ϕ̃j	ϕ̃j	X
ejpam-6489	181	3	,	,	PUNCT
ejpam-6489	181	4	η̃j	η̃j	PROPN
ejpam-6489	181	5	]	]	PUNCT
ejpam-6489	181	6	.	.	PUNCT
ejpam-6489	182	1	then	then	ADV
ejpam-6489	182	2	ξp	ξp	ADP
ejpam-6489	182	3	[	[	X
ejpam-6489	182	4	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	182	5	]	]	X
ejpam-6489	182	6	(	(	PUNCT
ejpam-6489	182	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	182	8	)	)	PUNCT
ejpam-6489	182	9	=	=	VERB
ejpam-6489	183	1	supϕ̃=	supϕ̃=	ADV
ejpam-6489	183	2	∑	∑	PART
ejpam-6489	183	3	j∈n	j∈n	NOUN
ejpam-6489	183	4	βj	βj	PRON
ejpam-6489	184	1	[	[	X
ejpam-6489	184	2	ϕ̃j	ϕ̃j	X
ejpam-6489	184	3	,	,	PUNCT
ejpam-6489	184	4	η̃j	η̃j	PROPN
ejpam-6489	184	5	]	]	PUNCT
ejpam-6489	184	6	{	{	PUNCT
ejpam-6489	184	7	minj∈n	minj∈n	INTJ
ejpam-6489	184	8	{	{	PUNCT
ejpam-6489	184	9	r̃p2̃ג+1̃ג	r̃p2̃ג+1̃ג	X
ejpam-6489	184	10	(	(	PUNCT
ejpam-6489	184	11	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	184	12	)	)	PUNCT
ejpam-6489	185	1	∧	∧	PROPN
ejpam-6489	185	2	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	185	3	(	(	PUNCT
ejpam-6489	185	4	η̃j)}e	η̃j)}e	PRON
ejpam-6489	185	5	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	185	6	{	{	PUNCT
ejpam-6489	185	7	ω̃p	ω̃p	PROPN
ejpam-6489	185	8	2̃ג+1̃ג	2̃ג+1̃ג	NUM
ejpam-6489	185	9	(	(	PUNCT
ejpam-6489	185	10	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	185	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	185	12	(	(	PUNCT
ejpam-6489	185	13	η̃j	η̃j	NOUN
ejpam-6489	185	14	)	)	PUNCT
ejpam-6489	185	15	}	}	PUNCT
ejpam-6489	185	16	}	}	PUNCT
ejpam-6489	185	17	=	=	SYM
ejpam-6489	185	18	sup{minj∈n	sup{minj∈n	PRON
ejpam-6489	185	19	{	{	PUNCT
ejpam-6489	185	20	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	21	{	{	PUNCT
ejpam-6489	185	22	r̃p1̃ג(ϱ̃j)∧r̃	r̃p1̃ג(ϱ̃j)∧r̃	PROPN
ejpam-6489	185	23	p	p	X
ejpam-6489	185	24	2̃ג	2̃ג	NUM
ejpam-6489	185	25	(	(	PUNCT
ejpam-6489	185	26	ϑ̃j)}∧r̃pℸ̃	ϑ̃j)}∧r̃pℸ̃	X
ejpam-6489	185	27	(	(	PUNCT
ejpam-6489	185	28	η̃j)}e	η̃j)}e	NUM
ejpam-6489	185	29	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	185	30	{	{	PUNCT
ejpam-6489	185	31	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	32	{	{	PUNCT
ejpam-6489	185	33	ω̃p	ω̃p	PROPN
ejpam-6489	185	34	1̃ג	1̃ג	PROPN
ejpam-6489	185	35	(	(	PUNCT
ejpam-6489	185	36	ϱ̃j)∧ω̃p	ϱ̃j)∧ω̃p	NUM
ejpam-6489	185	37	2̃ג	2̃ג	NUM
ejpam-6489	185	38	(	(	PUNCT
ejpam-6489	185	39	ϑ̃j)}∧ω̃p	ϑ̃j)}∧ω̃p	PROPN
ejpam-6489	185	40	ℸ̃	ℸ̃	PROPN
ejpam-6489	185	41	(	(	PUNCT
ejpam-6489	185	42	η̃j	η̃j	NOUN
ejpam-6489	185	43	)	)	PUNCT
ejpam-6489	185	44	}	}	PUNCT
ejpam-6489	185	45	}	}	PUNCT
ejpam-6489	185	46	=	=	SYM
ejpam-6489	185	47	sup{minj∈n	sup{minj∈n	PRON
ejpam-6489	185	48	{	{	PUNCT
ejpam-6489	185	49	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	50	{	{	PUNCT
ejpam-6489	185	51	r̃p1̃ג(ϱ̃j)∧r̃	r̃p1̃ג(ϱ̃j)∧r̃	PROPN
ejpam-6489	185	52	p	p	X
ejpam-6489	185	53	2̃ג	2̃ג	NUM
ejpam-6489	185	54	(	(	PUNCT
ejpam-6489	185	55	ϑ̃j)∧r̃pℸ̃	ϑ̃j)∧r̃pℸ̃	PROPN
ejpam-6489	185	56	(	(	PUNCT
ejpam-6489	185	57	η̃j)}}e	η̃j)}}e	PROPN
ejpam-6489	185	58	i2πminj∈n	i2πminj∈n	PROPN
ejpam-6489	185	59	{	{	PUNCT
ejpam-6489	185	60	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	61	{	{	PUNCT
ejpam-6489	185	62	ω̃p	ω̃p	PROPN
ejpam-6489	185	63	1̃ג	1̃ג	PROPN
ejpam-6489	185	64	(	(	PUNCT
ejpam-6489	185	65	ϱ̃j)∧ω̃p	ϱ̃j)∧ω̃p	PROPN
ejpam-6489	185	66	2̃ג	2̃ג	NUM
ejpam-6489	185	67	(	(	PUNCT
ejpam-6489	185	68	ϑ̃j)∧ω̃p	ϑ̃j)∧ω̃p	X
ejpam-6489	185	69	ℸ̃	ℸ̃	PROPN
ejpam-6489	185	70	(	(	PUNCT
ejpam-6489	185	71	η̃j	η̃j	NOUN
ejpam-6489	185	72	)	)	PUNCT
ejpam-6489	185	73	}	}	PUNCT
ejpam-6489	185	74	}	}	PUNCT
ejpam-6489	185	75	}	}	PUNCT
ejpam-6489	185	76	=	=	SYM
ejpam-6489	185	77	sup{minj∈n	sup{minj∈n	PRON
ejpam-6489	185	78	{	{	PUNCT
ejpam-6489	185	79	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	80	{	{	PUNCT
ejpam-6489	185	81	r̃p1̃ג(ϱ̃j)∧r̃	r̃p1̃ג(ϱ̃j)∧r̃	PROPN
ejpam-6489	185	82	p	p	X
ejpam-6489	185	83	2̃ג	2̃ג	NUM
ejpam-6489	185	84	(	(	PUNCT
ejpam-6489	185	85	ϑ̃j)∧r̃pℸ̃	ϑ̃j)∧r̃pℸ̃	PROPN
ejpam-6489	185	86	(	(	PUNCT
ejpam-6489	185	87	η̃j)}}}e	η̃j)}}}e	PROPN
ejpam-6489	185	88	i2πsup{minj∈n	i2πsup{minj∈n	PROPN
ejpam-6489	185	89	{	{	PUNCT
ejpam-6489	185	90	supϕ̃j=ϱ̃j+ϑ̃j	supϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	185	91	{	{	PUNCT
ejpam-6489	185	92	ω̃p	ω̃p	PROPN
ejpam-6489	185	93	1̃ג	1̃ג	PROPN
ejpam-6489	185	94	(	(	PUNCT
ejpam-6489	185	95	ϱ̃j)∧ω̃p	ϱ̃j)∧ω̃p	PROPN
ejpam-6489	185	96	2̃ג	2̃ג	NUM
ejpam-6489	185	97	(	(	PUNCT
ejpam-6489	185	98	ϑ̃j)∧ω̃p	ϑ̃j)∧ω̃p	X
ejpam-6489	185	99	ℸ̃	ℸ̃	PROPN
ejpam-6489	185	100	(	(	PUNCT
ejpam-6489	185	101	η̃j	η̃j	NOUN
ejpam-6489	185	102	)	)	PUNCT
ejpam-6489	185	103	}	}	PUNCT
ejpam-6489	185	104	}	}	PUNCT
ejpam-6489	185	105	}	}	PUNCT
ejpam-6489	185	106	=	=	SYM
ejpam-6489	185	107	r̃p	r̃p	NOUN
ejpam-6489	185	108	[	[	X
ejpam-6489	185	109	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	185	110	]	]	X
ejpam-6489	185	111	(	(	PUNCT
ejpam-6489	185	112	ϕ̃)e	ϕ̃)e	X
ejpam-6489	185	113	i2πω̃p	i2πω̃p	X
ejpam-6489	186	1	[	[	X
ejpam-6489	186	2	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	186	3	]	]	X
ejpam-6489	186	4	(	(	PUNCT
ejpam-6489	186	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	186	6	)	)	PUNCT
ejpam-6489	186	7	≥	≥	NOUN
ejpam-6489	186	8	r̃p	r̃p	NOUN
ejpam-6489	186	9	[	[	X
ejpam-6489	186	10	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	186	11	]	]	X
ejpam-6489	186	12	(	(	PUNCT
ejpam-6489	186	13	ϕ̃)e	ϕ̃)e	X
ejpam-6489	186	14	i2πω̃p	i2πω̃p	X
ejpam-6489	187	1	[	[	X
ejpam-6489	187	2	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	187	3	]	]	X
ejpam-6489	187	4	(	(	PUNCT
ejpam-6489	187	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	187	6	)	)	PUNCT
ejpam-6489	187	7	≥	≥	NOUN
ejpam-6489	187	8	ξp	ξp	ADP
ejpam-6489	188	1	[	[	X
ejpam-6489	188	2	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	188	3	]	]	X
ejpam-6489	188	4	(	(	PUNCT
ejpam-6489	188	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	188	6	)	)	PUNCT
ejpam-6489	188	7	,	,	PUNCT
ejpam-6489	188	8	ξn	ξn	X
ejpam-6489	189	1	[	[	X
ejpam-6489	189	2	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	189	3	]	]	X
ejpam-6489	189	4	(	(	PUNCT
ejpam-6489	189	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	189	6	)	)	PUNCT
ejpam-6489	189	7	=	=	SYM
ejpam-6489	189	8	inf	inf	NOUN
ejpam-6489	189	9	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	189	10	∑	∑	PROPN
ejpam-6489	189	11	j∈n	j∈n	NOUN
ejpam-6489	190	1	βj	βj	NOUN
ejpam-6489	191	1	[	[	X
ejpam-6489	191	2	ϕ̃j	ϕ̃j	X
ejpam-6489	191	3	,	,	PUNCT
ejpam-6489	191	4	η̃j	η̃j	PROPN
ejpam-6489	191	5	]	]	PUNCT
ejpam-6489	191	6	{	{	PUNCT
ejpam-6489	191	7	maxj∈n	maxj∈n	NOUN
ejpam-6489	191	8	{	{	PUNCT
ejpam-6489	191	9	r̃n2̃ג+1̃ג	r̃n2̃ג+1̃ג	X
ejpam-6489	191	10	(	(	PUNCT
ejpam-6489	191	11	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	191	12	)	)	PUNCT
ejpam-6489	191	13	∨	∨	PROPN
ejpam-6489	191	14	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	191	15	(	(	PUNCT
ejpam-6489	191	16	η̃j)}e	η̃j)}e	NUM
ejpam-6489	191	17	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	191	18	{	{	PUNCT
ejpam-6489	191	19	ω̃n	ω̃n	PROPN
ejpam-6489	191	20	2̃ג+1̃ג	2̃ג+1̃ג	NUM
ejpam-6489	191	21	(	(	PUNCT
ejpam-6489	191	22	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	NUM
ejpam-6489	191	23	ℸ̃	ℸ̃	PROPN
ejpam-6489	191	24	(	(	PUNCT
ejpam-6489	191	25	η̃j	η̃j	NOUN
ejpam-6489	191	26	)	)	PUNCT
ejpam-6489	191	27	}	}	PUNCT
ejpam-6489	191	28	}	}	PUNCT
ejpam-6489	191	29	=	=	SYM
ejpam-6489	191	30	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	191	31	{	{	PUNCT
ejpam-6489	191	32	inf	inf	PROPN
ejpam-6489	191	33	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	191	34	{	{	PUNCT
ejpam-6489	191	35	r̃n1̃ג	r̃n1̃ג	PROPN
ejpam-6489	191	36	(	(	PUNCT
ejpam-6489	191	37	ϱ̃j)∨r̃	ϱ̃j)∨r̃	NOUN
ejpam-6489	191	38	n	n	PROPN
ejpam-6489	191	39	2̃ג	2̃ג	NUM
ejpam-6489	191	40	(	(	PUNCT
ejpam-6489	191	41	ϑ̃j)}∨r̃nℸ̃	ϑ̃j)}∨r̃nℸ̃	PROPN
ejpam-6489	191	42	(	(	PUNCT
ejpam-6489	191	43	η̃j)}e	η̃j)}e	NOUN
ejpam-6489	191	44	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	191	45	{	{	PUNCT
ejpam-6489	191	46	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	191	47	{	{	PUNCT
ejpam-6489	191	48	ω̃n	ω̃n	PROPN
ejpam-6489	191	49	1̃ג	1̃ג	PROPN
ejpam-6489	191	50	(	(	PUNCT
ejpam-6489	191	51	ϱ̃j)∨ω̃n	ϱ̃j)∨ω̃n	PROPN
ejpam-6489	191	52	2̃ג	2̃ג	NUM
ejpam-6489	191	53	(	(	PUNCT
ejpam-6489	191	54	ϑ̃j)}∨ω̃n	ϑ̃j)}∨ω̃n	PROPN
ejpam-6489	191	55	ℸ̃	ℸ̃	PROPN
ejpam-6489	191	56	(	(	PUNCT
ejpam-6489	191	57	η̃j	η̃j	NOUN
ejpam-6489	191	58	)	)	PUNCT
ejpam-6489	191	59	}	}	PUNCT
ejpam-6489	191	60	}	}	PUNCT
ejpam-6489	191	61	=	=	SYM
ejpam-6489	191	62	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	191	63	{	{	PUNCT
ejpam-6489	191	64	inf	inf	PROPN
ejpam-6489	191	65	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	191	66	{	{	PUNCT
ejpam-6489	191	67	r̃n1̃ג	r̃n1̃ג	PROPN
ejpam-6489	191	68	(	(	PUNCT
ejpam-6489	191	69	ϱ̃j)∨r̃	ϱ̃j)∨r̃	NOUN
ejpam-6489	191	70	n	n	PROPN
ejpam-6489	191	71	2̃ג	2̃ג	NUM
ejpam-6489	191	72	(	(	PUNCT
ejpam-6489	191	73	ϑ̃j)∨r̃nℸ̃	ϑ̃j)∨r̃nℸ̃	X
ejpam-6489	191	74	(	(	PUNCT
ejpam-6489	191	75	η̃j)}}e	η̃j)}}e	NOUN
ejpam-6489	191	76	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	191	77	{	{	PUNCT
ejpam-6489	191	78	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	191	79	{	{	PUNCT
ejpam-6489	191	80	ω̃n	ω̃n	PROPN
ejpam-6489	191	81	1̃ג	1̃ג	PROPN
ejpam-6489	191	82	(	(	PUNCT
ejpam-6489	191	83	ϱ̃j)∨ω̃n	ϱ̃j)∨ω̃n	PROPN
ejpam-6489	191	84	2̃ג	2̃ג	NUM
ejpam-6489	191	85	(	(	PUNCT
ejpam-6489	191	86	ϑ̃j)∨ω̃n	ϑ̃j)∨ω̃n	PUNCT
ejpam-6489	191	87	ℸ̃	ℸ̃	PROPN
ejpam-6489	191	88	(	(	PUNCT
ejpam-6489	191	89	η̃j	η̃j	NOUN
ejpam-6489	191	90	)	)	PUNCT
ejpam-6489	191	91	}	}	PUNCT
ejpam-6489	191	92	}	}	PUNCT
ejpam-6489	191	93	}	}	PUNCT
ejpam-6489	191	94	=	=	SYM
ejpam-6489	191	95	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	191	96	{	{	PUNCT
ejpam-6489	191	97	inf	inf	PROPN
ejpam-6489	191	98	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	191	99	{	{	PUNCT
ejpam-6489	191	100	r̃n1̃ג	r̃n1̃ג	PROPN
ejpam-6489	191	101	(	(	PUNCT
ejpam-6489	191	102	ϱ̃j)∨r̃	ϱ̃j)∨r̃	NOUN
ejpam-6489	191	103	n	n	PROPN
ejpam-6489	191	104	2̃ג	2̃ג	NUM
ejpam-6489	191	105	(	(	PUNCT
ejpam-6489	191	106	ϑ̃j)∨r̃nℸ̃	ϑ̃j)∨r̃nℸ̃	X
ejpam-6489	191	107	(	(	PUNCT
ejpam-6489	191	108	η̃j)}}}e	η̃j)}}}e	ADJ
ejpam-6489	191	109	i2πinf{maxj∈n	i2πinf{maxj∈n	PROPN
ejpam-6489	191	110	{	{	PUNCT
ejpam-6489	191	111	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	191	112	{	{	PUNCT
ejpam-6489	191	113	ω̃n	ω̃n	PROPN
ejpam-6489	191	114	1̃ג	1̃ג	PROPN
ejpam-6489	191	115	(	(	PUNCT
ejpam-6489	191	116	ϱ̃j)∨ω̃n	ϱ̃j)∨ω̃n	PROPN
ejpam-6489	191	117	2̃ג	2̃ג	NUM
ejpam-6489	191	118	(	(	PUNCT
ejpam-6489	191	119	ϑ̃j)∨ω̃n	ϑ̃j)∨ω̃n	PUNCT
ejpam-6489	191	120	ℸ̃	ℸ̃	PROPN
ejpam-6489	191	121	(	(	PUNCT
ejpam-6489	191	122	η̃j	η̃j	NOUN
ejpam-6489	191	123	)	)	PUNCT
ejpam-6489	191	124	}	}	PUNCT
ejpam-6489	191	125	}	}	PUNCT
ejpam-6489	191	126	}	}	PUNCT
ejpam-6489	191	127	=	=	SYM
ejpam-6489	192	1	r̃n	r̃n	PROPN
ejpam-6489	193	1	[	[	X
ejpam-6489	193	2	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	193	3	]	]	X
ejpam-6489	193	4	(	(	PUNCT
ejpam-6489	193	5	ϕ̃)e	ϕ̃)e	X
ejpam-6489	193	6	i2πω̃n	i2πω̃n	X
ejpam-6489	193	7	[	[	X
ejpam-6489	193	8	ℸ̃,2̃ג+1̃ג	ℸ̃,2̃ג+1̃ג	X
ejpam-6489	193	9	]	]	X
ejpam-6489	193	10	(	(	PUNCT
ejpam-6489	193	11	ϕ̃	ϕ̃	PROPN
ejpam-6489	193	12	)	)	PUNCT
ejpam-6489	193	13	≤	≤	NOUN
ejpam-6489	194	1	r̃n	r̃n	PROPN
ejpam-6489	194	2	[	[	X
ejpam-6489	194	3	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	194	4	]	]	X
ejpam-6489	194	5	(	(	PUNCT
ejpam-6489	194	6	ϕ̃)e	ϕ̃)e	X
ejpam-6489	194	7	i2πω̃n	i2πω̃n	X
ejpam-6489	194	8	[	[	X
ejpam-6489	194	9	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	194	10	]	]	X
ejpam-6489	194	11	(	(	PUNCT
ejpam-6489	194	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	194	13	)	)	PUNCT
ejpam-6489	194	14	≤	≤	NOUN
ejpam-6489	194	15	ξn	ξn	PROPN
ejpam-6489	194	16	[	[	X
ejpam-6489	194	17	ℸ̃,2̃ג]+[ℸ̃,1̃ג	ℸ̃,2̃ג]+[ℸ̃,1̃ג	X
ejpam-6489	194	18	]	]	X
ejpam-6489	194	19	(	(	PUNCT
ejpam-6489	194	20	ϕ̃	ϕ̃	PROPN
ejpam-6489	194	21	)	)	PUNCT
ejpam-6489	194	22	,	,	PUNCT
ejpam-6489	194	23	and	and	CCONJ
ejpam-6489	194	24	ζ[2̃ג+1̃ג,ℸ̃](ϕ̃	ζ[2̃ג+1̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	194	25	)	)	PUNCT
ejpam-6489	194	26	m.	m.	NOUN
ejpam-6489	194	27	balamurugan	balamurugan	VERB
ejpam-6489	194	28	,	,	PUNCT
ejpam-6489	194	29	g.	g.	PROPN
ejpam-6489	194	30	ellammal	ellammal	PROPN
ejpam-6489	194	31	,	,	PUNCT
ejpam-6489	194	32	a.	a.	NOUN
ejpam-6489	194	33	iampan	iampan	PROPN
ejpam-6489	194	34	/	/	SYM
ejpam-6489	194	35	eur	eur	PROPN
ejpam-6489	194	36	.	.	PUNCT
ejpam-6489	195	1	j.	j.	PROPN
ejpam-6489	195	2	pure	pure	PROPN
ejpam-6489	195	3	appl	appl	PROPN
ejpam-6489	195	4	.	.	PROPN
ejpam-6489	195	5	math	math	PROPN
ejpam-6489	195	6	,	,	PUNCT
ejpam-6489	195	7	18	18	NUM
ejpam-6489	195	8	(	(	PUNCT
ejpam-6489	195	9	3	3	NUM
ejpam-6489	195	10	)	)	PUNCT
ejpam-6489	195	11	(	(	PUNCT
ejpam-6489	195	12	2025	2025	NUM
ejpam-6489	195	13	)	)	PUNCT
ejpam-6489	195	14	,	,	PUNCT
ejpam-6489	195	15	6489	6489	NUM
ejpam-6489	195	16	8	8	NUM
ejpam-6489	195	17	of	of	ADP
ejpam-6489	195	18	26	26	NUM
ejpam-6489	195	19	=	=	SYM
ejpam-6489	195	20	inf	inf	NOUN
ejpam-6489	195	21	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	195	22	∑	∑	PROPN
ejpam-6489	195	23	j∈n	j∈n	NOUN
ejpam-6489	195	24	βj	βj	NOUN
ejpam-6489	196	1	[	[	X
ejpam-6489	196	2	ϕ̃j	ϕ̃j	X
ejpam-6489	196	3	,	,	PUNCT
ejpam-6489	196	4	η̃j	η̃j	PROPN
ejpam-6489	196	5	]	]	PUNCT
ejpam-6489	196	6	{	{	PUNCT
ejpam-6489	196	7	maxj∈n	maxj∈n	NOUN
ejpam-6489	196	8	{	{	PUNCT
ejpam-6489	196	9	r̃2̃ג+1̃ג(ϕ̃j	r̃2̃ג+1̃ג(ϕ̃j	NOUN
ejpam-6489	196	10	)	)	PUNCT
ejpam-6489	196	11	∨	∨	NOUN
ejpam-6489	196	12	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	196	13	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	196	14	{	{	PUNCT
ejpam-6489	196	15	ω̃2̃ג+1̃ג	ω̃2̃ג+1̃ג	PROPN
ejpam-6489	196	16	(	(	PUNCT
ejpam-6489	196	17	ϕ̃j)∨ω̃ℸ̃(η̃j	ϕ̃j)∨ω̃ℸ̃(η̃j	NOUN
ejpam-6489	196	18	)	)	PUNCT
ejpam-6489	196	19	}	}	PUNCT
ejpam-6489	196	20	}	}	PUNCT
ejpam-6489	196	21	=	=	SYM
ejpam-6489	196	22	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	196	23	{	{	PUNCT
ejpam-6489	196	24	inf	inf	PROPN
ejpam-6489	196	25	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	196	26	{	{	PUNCT
ejpam-6489	196	27	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)}∨r̃ℸ̃(η̃j)}e	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)}∨r̃ℸ̃(η̃j)}e	PROPN
ejpam-6489	196	28	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	196	29	{	{	PUNCT
ejpam-6489	196	30	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	196	31	{	{	PUNCT
ejpam-6489	196	32	ω̃n	ω̃n	PROPN
ejpam-6489	196	33	1̃ג	1̃ג	PROPN
ejpam-6489	196	34	(	(	PUNCT
ejpam-6489	196	35	ϱ̃j)∨ω̃2̃ג	ϱ̃j)∨ω̃2̃ג	X
ejpam-6489	196	36	(	(	PUNCT
ejpam-6489	196	37	ϑ̃j)}∨ω̃ℸ̃(η̃j	ϑ̃j)}∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	196	38	)	)	PUNCT
ejpam-6489	196	39	}	}	PUNCT
ejpam-6489	196	40	}	}	PUNCT
ejpam-6489	197	1	=	=	SYM
ejpam-6489	197	2	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	197	3	{	{	PUNCT
ejpam-6489	197	4	inf	inf	NOUN
ejpam-6489	197	5	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	197	6	{	{	PUNCT
ejpam-6489	197	7	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)∨r̃ℸ̃(η̃j)}}e	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)∨r̃ℸ̃(η̃j)}}e	NOUN
ejpam-6489	197	8	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	197	9	{	{	PUNCT
ejpam-6489	197	10	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	INTJ
ejpam-6489	197	11	{	{	PUNCT
ejpam-6489	197	12	ω̃n	ω̃n	PROPN
ejpam-6489	197	13	1̃ג	1̃ג	PROPN
ejpam-6489	197	14	(	(	PUNCT
ejpam-6489	197	15	ϱ̃j)∨ω̃2̃ג	ϱ̃j)∨ω̃2̃ג	X
ejpam-6489	197	16	(	(	PUNCT
ejpam-6489	197	17	ϑ̃j)∨ω̃ℸ̃(η̃j	ϑ̃j)∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	197	18	)	)	PUNCT
ejpam-6489	197	19	}	}	PUNCT
ejpam-6489	197	20	}	}	PUNCT
ejpam-6489	197	21	}	}	PUNCT
ejpam-6489	197	22	=	=	SYM
ejpam-6489	197	23	inf{maxj∈n	inf{maxj∈n	PRON
ejpam-6489	197	24	{	{	PUNCT
ejpam-6489	197	25	inf	inf	PROPN
ejpam-6489	197	26	ϕ̃j=ϱ̃j+ϑ̃j	ϕ̃j=ϱ̃j+ϑ̃j	PROPN
ejpam-6489	197	27	{	{	PUNCT
ejpam-6489	197	28	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)∨r̃ℸ̃(η̃j)}}}e	r̃1̃ג(ϱ̃j)∨r̃2̃ג(ϑ̃j)∨r̃ℸ̃(η̃j)}}}e	PROPN
ejpam-6489	197	29	i2πinf{maxj∈n	i2πinf{maxj∈n	PROPN
ejpam-6489	197	30	{	{	PUNCT
ejpam-6489	197	31	infϕ̃j=ϱ̃j+ϑ̃j	infϕ̃j=ϱ̃j+ϑ̃j	X
ejpam-6489	197	32	{	{	PUNCT
ejpam-6489	197	33	ω̃1̃ג	ω̃1̃ג	NUM
ejpam-6489	197	34	(	(	PUNCT
ejpam-6489	197	35	ϱ̃j)∨ω̃2̃ג	ϱ̃j)∨ω̃2̃ג	X
ejpam-6489	197	36	(	(	PUNCT
ejpam-6489	197	37	ϑ̃j)∨ω̃ℸ̃(η̃j	ϑ̃j)∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	197	38	)	)	PUNCT
ejpam-6489	197	39	}	}	PUNCT
ejpam-6489	197	40	}	}	PUNCT
ejpam-6489	197	41	}	}	PUNCT
ejpam-6489	197	42	=	=	PUNCT
ejpam-6489	197	43	r̃[2̃ג+1̃ג,ℸ̃](ϕ̃)e	r̃[2̃ג+1̃ג,ℸ̃](ϕ̃)e	PROPN
ejpam-6489	197	44	i2πω̃[2̃ג+1̃ג,ℸ̃](ϕ̃	i2πω̃[2̃ג+1̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	197	45	)	)	PUNCT
ejpam-6489	197	46	≤	≤	NUM
ejpam-6489	197	47	r̃[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃)e	r̃[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃)e	VERB
ejpam-6489	197	48	i2πω̃[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃	i2πω̃[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	197	49	)	)	PUNCT
ejpam-6489	197	50	≤	≤	NOUN
ejpam-6489	197	51	ζ[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃	ζ[1̃ג,ℸ̃]+[2̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	197	52	)	)	PUNCT
ejpam-6489	197	53	.	.	PUNCT
ejpam-6489	198	1	this	this	PRON
ejpam-6489	198	2	shows	show	VERB
ejpam-6489	198	3	that	that	SCONJ
ejpam-6489	198	4	1̃ג	1̃ג	X
ejpam-6489	198	5	]	]	X
ejpam-6489	199	1	+	+	CCONJ
ejpam-6489	199	2	,	,	PUNCT
ejpam-6489	199	3	2̃ג	2̃ג	NUM
ejpam-6489	199	4	ℸ̃	ℸ̃	NOUN
ejpam-6489	199	5	]	]	X
ejpam-6489	199	6	⊆	⊆	NUM
ejpam-6489	199	7	,	,	PUNCT
ejpam-6489	199	8	1̃ג	1̃ג	PROPN
ejpam-6489	199	9	]	]	PUNCT
ejpam-6489	199	10	ℸ̃	ℸ̃	PROPN
ejpam-6489	199	11	]	]	X
ejpam-6489	199	12	+	+	CCONJ
ejpam-6489	199	13	,	,	PUNCT
ejpam-6489	199	14	2̃ג	2̃ג	NUM
ejpam-6489	199	15	]	]	PUNCT
ejpam-6489	199	16	ℸ̃	ℸ̃	PROPN
ejpam-6489	199	17	]	]	PUNCT
ejpam-6489	199	18	.	.	PUNCT
ejpam-6489	200	1	let	let	VERB
ejpam-6489	201	1	ϕ̃	ϕ̃	PROPN
ejpam-6489	201	2	∈	∈	PROPN
ejpam-6489	201	3	l̃.	l̃.	PROPN
ejpam-6489	201	4	then	then	ADV
ejpam-6489	201	5	ξp2̃ג+1̃ג	ξp2̃ג+1̃ג	NUM
ejpam-6489	201	6	(	(	PUNCT
ejpam-6489	201	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	201	8	)	)	PUNCT
ejpam-6489	201	9	=	=	PRON
ejpam-6489	201	10	r̃p2̃ג+1̃ג	r̃p2̃ג+1̃ג	X
ejpam-6489	201	11	(	(	PUNCT
ejpam-6489	201	12	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	201	13	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	201	14	2̃ג+1̃ג	2̃ג+1̃ג	NUM
ejpam-6489	201	15	(	(	PUNCT
ejpam-6489	201	16	ϕ̃	ϕ̃	PROPN
ejpam-6489	201	17	)	)	PUNCT
ejpam-6489	201	18	=	=	SYM
ejpam-6489	202	1	sup	sup	NOUN
ejpam-6489	202	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	202	3	=	=	SYM
ejpam-6489	202	4	ϱ̃+ϑ̃	ϱ̃+ϑ̃	NOUN
ejpam-6489	202	5	{	{	PUNCT
ejpam-6489	202	6	(	(	PUNCT
ejpam-6489	202	7	r̃p1̃ג(ϱ̃	r̃p1̃ג(ϱ̃	NOUN
ejpam-6489	202	8	)	)	PUNCT
ejpam-6489	202	9	∧	∧	PROPN
ejpam-6489	202	10	r̃p2̃ג	r̃p2̃ג	PROPN
ejpam-6489	202	11	(	(	PUNCT
ejpam-6489	202	12	ϑ̃))e	ϑ̃))e	X
ejpam-6489	202	13	i2π(ω̃p	i2π(ω̃p	X
ejpam-6489	202	14	1̃ג	1̃ג	PROPN
ejpam-6489	202	15	(	(	PUNCT
ejpam-6489	202	16	ϱ̃)∧ω̃p	ϱ̃)∧ω̃p	PROPN
ejpam-6489	202	17	2̃ג	2̃ג	NUM
ejpam-6489	202	18	(	(	PUNCT
ejpam-6489	202	19	ϑ̃	ϑ̃	PROPN
ejpam-6489	202	20	)	)	PUNCT
ejpam-6489	202	21	)	)	PUNCT
ejpam-6489	202	22	}	}	PUNCT
ejpam-6489	202	23	≥	≥	X
ejpam-6489	202	24	(	(	PUNCT
ejpam-6489	202	25	r̃p1̃ג	r̃p1̃ג	PROPN
ejpam-6489	202	26	(	(	PUNCT
ejpam-6489	202	27	ϕ̃	ϕ̃	PROPN
ejpam-6489	202	28	)	)	PUNCT
ejpam-6489	202	29	∧	∧	PROPN
ejpam-6489	202	30	r̃p2̃ג	r̃p2̃ג	PROPN
ejpam-6489	202	31	(	(	PUNCT
ejpam-6489	202	32	0))e	0))e	PROPN
ejpam-6489	202	33	i2π(ω̃p	i2π(ω̃p	PROPN
ejpam-6489	202	34	1̃ג	1̃ג	PROPN
ejpam-6489	202	35	(	(	PUNCT
ejpam-6489	202	36	ϕ̃)∧ω̃p	ϕ̃)∧ω̃p	PROPN
ejpam-6489	202	37	2̃ג	2̃ג	PROPN
ejpam-6489	202	38	(	(	PUNCT
ejpam-6489	202	39	0	0	NUM
ejpam-6489	202	40	)	)	PUNCT
ejpam-6489	202	41	)	)	PUNCT
ejpam-6489	203	1	=	=	PUNCT
ejpam-6489	203	2	r̃p1̃ג	r̃p1̃ג	X
ejpam-6489	203	3	(	(	PUNCT
ejpam-6489	203	4	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	203	5	i2πω̃p	i2πω̃p	X
ejpam-6489	203	6	1̃ג	1̃ג	PROPN
ejpam-6489	203	7	(	(	PUNCT
ejpam-6489	203	8	ϕ̃	ϕ̃	PROPN
ejpam-6489	203	9	)	)	PUNCT
ejpam-6489	203	10	,	,	PUNCT
ejpam-6489	203	11	ξn2̃ג+1̃ג	ξn2̃ג+1̃ג	PRON
ejpam-6489	203	12	(	(	PUNCT
ejpam-6489	203	13	ϕ̃	ϕ̃	PROPN
ejpam-6489	203	14	)	)	PUNCT
ejpam-6489	203	15	=	=	PRON
ejpam-6489	203	16	r̃n2̃ג+1̃ג	r̃n2̃ג+1̃ג	X
ejpam-6489	203	17	(	(	PUNCT
ejpam-6489	203	18	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	203	19	i2πω̃n	i2πω̃n	PRON
ejpam-6489	203	20	2̃ג+1̃ג	2̃ג+1̃ג	NUM
ejpam-6489	203	21	(	(	PUNCT
ejpam-6489	203	22	ϕ̃	ϕ̃	PROPN
ejpam-6489	203	23	)	)	PUNCT
ejpam-6489	203	24	=	=	SYM
ejpam-6489	203	25	inf	inf	NOUN
ejpam-6489	203	26	ϕ̃	ϕ̃	PROPN
ejpam-6489	203	27	=	=	SYM
ejpam-6489	203	28	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	203	29	{	{	PUNCT
ejpam-6489	203	30	(	(	PUNCT
ejpam-6489	203	31	r̃n1̃ג	r̃n1̃ג	X
ejpam-6489	203	32	(	(	PUNCT
ejpam-6489	203	33	ϱ̃	ϱ̃	PROPN
ejpam-6489	203	34	)	)	PUNCT
ejpam-6489	203	35	∨	∨	NOUN
ejpam-6489	203	36	r̃n2̃ג	r̃n2̃ג	NOUN
ejpam-6489	203	37	(	(	PUNCT
ejpam-6489	203	38	ϑ̃))e	ϑ̃))e	X
ejpam-6489	203	39	i2π(ω̃n	i2π(ω̃n	ADJ
ejpam-6489	203	40	1̃ג	1̃ג	PROPN
ejpam-6489	203	41	(	(	PUNCT
ejpam-6489	203	42	ϱ̃)∨ω̃n	ϱ̃)∨ω̃n	PROPN
ejpam-6489	203	43	2̃ג	2̃ג	PROPN
ejpam-6489	203	44	(	(	PUNCT
ejpam-6489	203	45	ϑ̃	ϑ̃	PROPN
ejpam-6489	203	46	)	)	PUNCT
ejpam-6489	203	47	)	)	PUNCT
ejpam-6489	203	48	}	}	PUNCT
ejpam-6489	203	49	≤	≤	NOUN
ejpam-6489	203	50	(	(	PUNCT
ejpam-6489	203	51	r̃n1̃ג	r̃n1̃ג	PROPN
ejpam-6489	203	52	(	(	PUNCT
ejpam-6489	203	53	ϕ̃	ϕ̃	PROPN
ejpam-6489	203	54	)	)	PUNCT
ejpam-6489	203	55	∨	∨	NOUN
ejpam-6489	203	56	r̃n2̃ג	r̃n2̃ג	NOUN
ejpam-6489	203	57	(	(	PUNCT
ejpam-6489	203	58	0))e	0))e	NOUN
ejpam-6489	203	59	i2π(ω̃n	i2π(ω̃n	PROPN
ejpam-6489	203	60	1̃ג	1̃ג	PROPN
ejpam-6489	203	61	(	(	PUNCT
ejpam-6489	203	62	ϕ̃)∨ω̃n	ϕ̃)∨ω̃n	PROPN
ejpam-6489	203	63	2̃ג	2̃ג	NUM
ejpam-6489	203	64	(	(	PUNCT
ejpam-6489	203	65	0	0	NUM
ejpam-6489	203	66	)	)	PUNCT
ejpam-6489	203	67	)	)	PUNCT
ejpam-6489	204	1	=	=	SYM
ejpam-6489	204	2	r̃n1̃ג	r̃n1̃ג	X
ejpam-6489	204	3	(	(	PUNCT
ejpam-6489	204	4	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	204	5	i2πω̃n	i2πω̃n	PRON
ejpam-6489	204	6	1̃ג	1̃ג	PROPN
ejpam-6489	204	7	(	(	PUNCT
ejpam-6489	204	8	ϕ̃	ϕ̃	PROPN
ejpam-6489	204	9	)	)	PUNCT
ejpam-6489	204	10	,	,	PUNCT
ejpam-6489	204	11	and	and	CCONJ
ejpam-6489	204	12	ζ	ζ	NOUN
ejpam-6489	204	13	(	(	PUNCT
ejpam-6489	204	14	ϕ̃)2̃ג+1̃ג	ϕ̃)2̃ג+1̃ג	X
ejpam-6489	204	15	=	=	NOUN
ejpam-6489	204	16	r̃2̃ג+1̃ג(ϕ̃)e	r̃2̃ג+1̃ג(ϕ̃)e	VERB
ejpam-6489	204	17	i2πω̃2̃ג+1̃ג	i2πω̃2̃ג+1̃ג	X
ejpam-6489	204	18	(	(	PUNCT
ejpam-6489	204	19	ϕ̃	ϕ̃	PROPN
ejpam-6489	204	20	)	)	PUNCT
ejpam-6489	204	21	=	=	SYM
ejpam-6489	204	22	inf	inf	NOUN
ejpam-6489	204	23	ϕ̃	ϕ̃	PROPN
ejpam-6489	204	24	=	=	SYM
ejpam-6489	204	25	ϱ̃+ϑ̃	ϱ̃+ϑ̃	PROPN
ejpam-6489	204	26	{	{	PUNCT
ejpam-6489	204	27	(	(	PUNCT
ejpam-6489	204	28	r̃1̃ג(ϱ̃	r̃1̃ג(ϱ̃	NOUN
ejpam-6489	204	29	)	)	PUNCT
ejpam-6489	204	30	∨	∨	NUM
ejpam-6489	204	31	r̃2̃ג(ϑ̃))e	r̃2̃ג(ϑ̃))e	PROPN
ejpam-6489	204	32	i2π(ω̃1̃ג	i2π(ω̃1̃ג	NOUN
ejpam-6489	204	33	(	(	PUNCT
ejpam-6489	204	34	ϱ̃)∨ω̃2̃ג	ϱ̃)∨ω̃2̃ג	NOUN
ejpam-6489	204	35	(	(	PUNCT
ejpam-6489	204	36	ϑ̃	ϑ̃	PROPN
ejpam-6489	204	37	)	)	PUNCT
ejpam-6489	204	38	)	)	PUNCT
ejpam-6489	204	39	}	}	PUNCT
ejpam-6489	204	40	≤	≤	NUM
ejpam-6489	204	41	(	(	PUNCT
ejpam-6489	204	42	r̃1̃ג(ϕ̃	r̃1̃ג(ϕ̃	PROPN
ejpam-6489	204	43	)	)	PUNCT
ejpam-6489	204	44	∨	∨	NUM
ejpam-6489	204	45	r̃(0)2̃ג)e	r̃(0)2̃ג)e	NOUN
ejpam-6489	204	46	i2π(ω̃1̃ג	i2π(ω̃1̃ג	NOUN
ejpam-6489	204	47	(	(	PUNCT
ejpam-6489	204	48	ϕ̃)∨ω̃2̃ג	ϕ̃)∨ω̃2̃ג	NOUN
ejpam-6489	204	49	(	(	PUNCT
ejpam-6489	204	50	0	0	NUM
ejpam-6489	204	51	)	)	PUNCT
ejpam-6489	204	52	)	)	PUNCT
ejpam-6489	205	1	=	=	PUNCT
ejpam-6489	205	2	r̃1̃ג(ϕ̃)e	r̃1̃ג(ϕ̃)e	VERB
ejpam-6489	205	3	i2πω̃1̃ג	i2πω̃1̃ג	X
ejpam-6489	205	4	(	(	PUNCT
ejpam-6489	205	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	205	6	)	)	PUNCT
ejpam-6489	205	7	.	.	PUNCT
ejpam-6489	206	1	therefore	therefore	ADV
ejpam-6489	206	2	,	,	PUNCT
ejpam-6489	206	3	1̃ג	1̃ג	PROPN
ejpam-6489	206	4	⊆	⊆	NUM
ejpam-6489	206	5	.2̃ג+1̃ג	.2̃ג+1̃ג	ADP
ejpam-6489	206	6	similarly	similarly	ADV
ejpam-6489	206	7	,	,	PUNCT
ejpam-6489	206	8	2̃ג	2̃ג	NUM
ejpam-6489	206	9	⊆	⊆	NUM
ejpam-6489	206	10	.2̃ג+1̃ג	.2̃ג+1̃ג	NUM
ejpam-6489	206	11	by	by	ADP
ejpam-6489	206	12	theorem	theorem	NOUN
ejpam-6489	206	13	2	2	NUM
ejpam-6489	206	14	,	,	PUNCT
ejpam-6489	206	15	we	we	PRON
ejpam-6489	206	16	have	have	VERB
ejpam-6489	206	17	,	,	PUNCT
ejpam-6489	206	18	1̃ג	1̃ג	PROPN
ejpam-6489	206	19	]	]	PUNCT
ejpam-6489	206	20	ℸ̃	ℸ̃	NOUN
ejpam-6489	206	21	]	]	X
ejpam-6489	206	22	⊆	⊆	NUM
ejpam-6489	206	23	,	,	PUNCT
ejpam-6489	206	24	2̃ג+1̃ג	2̃ג+1̃ג	NUM
ejpam-6489	206	25	]	]	PUNCT
ejpam-6489	206	26	ℸ̃	ℸ̃	PROPN
ejpam-6489	206	27	]	]	PUNCT
ejpam-6489	206	28	,	,	PUNCT
ejpam-6489	206	29	,	,	PUNCT
ejpam-6489	206	30	1̃ג	1̃ג	PROPN
ejpam-6489	206	31	]	]	PUNCT
ejpam-6489	206	32	ℸ̃	ℸ̃	PROPN
ejpam-6489	206	33	]	]	X
ejpam-6489	206	34	⊆	⊆	NUM
ejpam-6489	206	35	+1̃ג	+1̃ג	PROPN
ejpam-6489	206	36	]	]	X
ejpam-6489	206	37	,	,	PUNCT
ejpam-6489	206	38	2̃ג	2̃ג	NUM
ejpam-6489	206	39	ℸ̃	ℸ̃	NOUN
ejpam-6489	206	40	]	]	PUNCT
ejpam-6489	206	41	.	.	PUNCT
ejpam-6489	207	1	so	so	ADV
ejpam-6489	207	2	,	,	PUNCT
ejpam-6489	207	3	by	by	ADP
ejpam-6489	207	4	theorem	theorem	NOUN
ejpam-6489	207	5	1	1	NUM
ejpam-6489	207	6	,	,	PUNCT
ejpam-6489	207	7	,	,	PUNCT
ejpam-6489	207	8	1̃ג	1̃ג	X
ejpam-6489	207	9	]	]	PUNCT
ejpam-6489	207	10	ℸ̃	ℸ̃	PROPN
ejpam-6489	207	11	]	]	X
ejpam-6489	207	12	+	+	CCONJ
ejpam-6489	207	13	,	,	PUNCT
ejpam-6489	207	14	2̃ג	2̃ג	NUM
ejpam-6489	207	15	]	]	PUNCT
ejpam-6489	207	16	ℸ̃	ℸ̃	PROPN
ejpam-6489	207	17	]	]	X
ejpam-6489	207	18	⊆	⊆	NUM
ejpam-6489	207	19	+1̃ג	+1̃ג	PROPN
ejpam-6489	207	20	]	]	X
ejpam-6489	207	21	,	,	PUNCT
ejpam-6489	207	22	2̃ג	2̃ג	NUM
ejpam-6489	207	23	ℸ̃	ℸ̃	NOUN
ejpam-6489	207	24	]	]	PUNCT
ejpam-6489	207	25	.	.	PUNCT
ejpam-6489	208	1	hence	hence	ADV
ejpam-6489	208	2	,	,	PUNCT
ejpam-6489	208	3	+1̃ג	+1̃ג	PROPN
ejpam-6489	208	4	]	]	PUNCT
ejpam-6489	208	5	,	,	PUNCT
ejpam-6489	208	6	2̃ג	2̃ג	NUM
ejpam-6489	208	7	ℸ̃	ℸ̃	NOUN
ejpam-6489	208	8	]	]	X
ejpam-6489	208	9	=	=	SYM
ejpam-6489	208	10	,	,	PUNCT
ejpam-6489	208	11	1̃ג	1̃ג	PROPN
ejpam-6489	208	12	]	]	PUNCT
ejpam-6489	208	13	ℸ̃	ℸ̃	PROPN
ejpam-6489	208	14	]	]	X
ejpam-6489	208	15	+	+	CCONJ
ejpam-6489	208	16	,	,	PUNCT
ejpam-6489	208	17	2̃ג	2̃ג	NUM
ejpam-6489	208	18	]	]	PUNCT
ejpam-6489	208	19	ℸ̃	ℸ̃	PROPN
ejpam-6489	208	20	]	]	PUNCT
ejpam-6489	208	21	.	.	PUNCT
ejpam-6489	209	1	m.	m.	NOUN
ejpam-6489	209	2	balamurugan	balamurugan	PROPN
ejpam-6489	209	3	,	,	PUNCT
ejpam-6489	209	4	g.	g.	PROPN
ejpam-6489	209	5	ellammal	ellammal	PROPN
ejpam-6489	209	6	,	,	PUNCT
ejpam-6489	209	7	a.	a.	NOUN
ejpam-6489	209	8	iampan	iampan	PROPN
ejpam-6489	209	9	/	/	SYM
ejpam-6489	209	10	eur	eur	PROPN
ejpam-6489	209	11	.	.	PUNCT
ejpam-6489	210	1	j.	j.	PROPN
ejpam-6489	210	2	pure	pure	PROPN
ejpam-6489	210	3	appl	appl	PROPN
ejpam-6489	210	4	.	.	PROPN
ejpam-6489	210	5	math	math	PROPN
ejpam-6489	210	6	,	,	PUNCT
ejpam-6489	210	7	18	18	NUM
ejpam-6489	210	8	(	(	PUNCT
ejpam-6489	210	9	3	3	NUM
ejpam-6489	210	10	)	)	PUNCT
ejpam-6489	210	11	(	(	PUNCT
ejpam-6489	210	12	2025	2025	NUM
ejpam-6489	210	13	)	)	PUNCT
ejpam-6489	210	14	,	,	PUNCT
ejpam-6489	210	15	6489	6489	NUM
ejpam-6489	210	16	9	9	NUM
ejpam-6489	210	17	of	of	ADP
ejpam-6489	210	18	26	26	NUM
ejpam-6489	210	19	theorem	theorem	NOUN
ejpam-6489	210	20	4	4	NUM
ejpam-6489	210	21	.	.	PUNCT
ejpam-6489	211	1	let	let	VERB
ejpam-6489	211	2	̃ג	̃ג	NOUN
ejpam-6489	211	3	=	=	SYM
ejpam-6489	211	4	(	(	PUNCT
ejpam-6489	211	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	211	6	(	(	PUNCT
ejpam-6489	211	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	211	8	)	)	PUNCT
ejpam-6489	211	9	,	,	PUNCT
ejpam-6489	211	10	ξ	ξ	PROPN
ejpam-6489	211	11	n	n	PRON
ejpam-6489	211	12	̃ג	̃ג	PROPN
ejpam-6489	211	13	(	(	PUNCT
ejpam-6489	211	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	211	15	)	)	PUNCT
ejpam-6489	211	16	,	,	PUNCT
ejpam-6489	211	17	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	211	18	)	)	PUNCT
ejpam-6489	211	19	)	)	PUNCT
ejpam-6489	211	20	,	,	PUNCT
ejpam-6489	211	21	ℸ̃	ℸ̃	PROPN
ejpam-6489	211	22	=	=	SYM
ejpam-6489	211	23	(	(	PUNCT
ejpam-6489	211	24	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	211	25	(	(	PUNCT
ejpam-6489	211	26	ϕ̃	ϕ̃	PROPN
ejpam-6489	211	27	)	)	PUNCT
ejpam-6489	211	28	,	,	PUNCT
ejpam-6489	211	29	ξ	ξ	PROPN
ejpam-6489	211	30	n	n	PRON
ejpam-6489	211	31	ℸ̃	ℸ̃	PROPN
ejpam-6489	211	32	(	(	PUNCT
ejpam-6489	211	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	211	34	)	)	PUNCT
ejpam-6489	211	35	,	,	PUNCT
ejpam-6489	211	36	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	211	37	)	)	PUNCT
ejpam-6489	211	38	)	)	PUNCT
ejpam-6489	211	39	be	be	VERB
ejpam-6489	211	40	t	t	PROPN
ejpam-6489	211	41	cfss	cfss	ADV
ejpam-6489	211	42	of	of	ADP
ejpam-6489	211	43	l̃.	l̃.	ADJ
ejpam-6489	211	44	then	then	ADV
ejpam-6489	211	45	[	[	X
ejpam-6489	211	46	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	211	47	,	,	PUNCT
ejpam-6489	211	48	ℸ̃	ℸ̃	PROPN
ejpam-6489	211	49	]	]	X
ejpam-6489	211	50	=	=	SYM
ejpam-6489	211	51	β̃[̃ג	β̃[̃ג	NOUN
ejpam-6489	211	52	,	,	PUNCT
ejpam-6489	211	53	ℸ̃	ℸ̃	PROPN
ejpam-6489	211	54	]	]	PUNCT
ejpam-6489	211	55	and	and	CCONJ
ejpam-6489	211	56	,	,	PUNCT
ejpam-6489	211	57	̃ג	̃ג	NOUN
ejpam-6489	211	58	]	]	PUNCT
ejpam-6489	211	59	β̃ℸ̃	β̃ℸ̃	X
ejpam-6489	211	60	]	]	X
ejpam-6489	211	61	=	=	SYM
ejpam-6489	211	62	β̃[̃ג	β̃[̃ג	NOUN
ejpam-6489	211	63	,	,	PUNCT
ejpam-6489	211	64	ℸ̃	ℸ̃	PROPN
ejpam-6489	211	65	]	]	PUNCT
ejpam-6489	211	66	,	,	PUNCT
ejpam-6489	211	67	for	for	ADP
ejpam-6489	211	68	every	every	DET
ejpam-6489	211	69	β̃	β̃	PROPN
ejpam-6489	211	70	∈	∈	PROPN
ejpam-6489	211	71	f	f	X
ejpam-6489	211	72	.	.	PUNCT
ejpam-6489	212	1	proof	proof	NOUN
ejpam-6489	212	2	.	.	PUNCT
ejpam-6489	213	1	let	let	VERB
ejpam-6489	213	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	213	3	∈	∈	PROPN
ejpam-6489	213	4	l̃.	l̃.	NOUN
ejpam-6489	213	5	then	then	ADV
ejpam-6489	213	6	ξp	ξp	ADP
ejpam-6489	213	7	[	[	X
ejpam-6489	213	8	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	X
ejpam-6489	213	9	)	)	PUNCT
ejpam-6489	213	10	=	=	SYM
ejpam-6489	214	1	sup	sup	NOUN
ejpam-6489	214	2	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	214	3	∑	∑	PROPN
ejpam-6489	214	4	j∈n	j∈n	NOUN
ejpam-6489	214	5	β̃j	β̃j	PROPN
ejpam-6489	215	1	[	[	X
ejpam-6489	215	2	ϕ̃j	ϕ̃j	X
ejpam-6489	215	3	,	,	PUNCT
ejpam-6489	215	4	η̃j	η̃j	PROPN
ejpam-6489	215	5	]	]	PUNCT
ejpam-6489	215	6	{	{	PUNCT
ejpam-6489	215	7	min	min	NOUN
ejpam-6489	215	8	j∈n	j∈n	NOUN
ejpam-6489	215	9	{	{	PUNCT
ejpam-6489	215	10	r̃p	r̃p	NOUN
ejpam-6489	215	11	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	ADV
ejpam-6489	215	12	)	)	PUNCT
ejpam-6489	215	13	∧	∧	PROPN
ejpam-6489	215	14	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	215	15	(	(	PUNCT
ejpam-6489	215	16	η̃j)}e	η̃j)}e	PRON
ejpam-6489	215	17	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	215	18	{	{	PUNCT
ejpam-6489	215	19	ω̃p	ω̃p	PROPN
ejpam-6489	215	20	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	215	21	(	(	PUNCT
ejpam-6489	215	22	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	215	23	ℸ̃	ℸ̃	PROPN
ejpam-6489	215	24	(	(	PUNCT
ejpam-6489	215	25	η̃j	η̃j	NOUN
ejpam-6489	215	26	)	)	PUNCT
ejpam-6489	215	27	}	}	PUNCT
ejpam-6489	215	28	}	}	PUNCT
ejpam-6489	215	29	=	=	SYM
ejpam-6489	216	1	sup	sup	NOUN
ejpam-6489	216	2	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	216	3	∑	∑	PROPN
ejpam-6489	216	4	j∈n	j∈n	NOUN
ejpam-6489	216	5	β̃j	β̃j	PROPN
ejpam-6489	217	1	[	[	X
ejpam-6489	217	2	ϕ̃j	ϕ̃j	X
ejpam-6489	217	3	,	,	PUNCT
ejpam-6489	217	4	η̃j	η̃j	PROPN
ejpam-6489	217	5	]	]	PUNCT
ejpam-6489	217	6	{	{	PUNCT
ejpam-6489	217	7	min	min	NOUN
ejpam-6489	217	8	j∈n	j∈n	NOUN
ejpam-6489	217	9	{	{	PUNCT
ejpam-6489	217	10	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	217	11	(	(	PUNCT
ejpam-6489	217	12	β̃	β̃	PROPN
ejpam-6489	217	13	−1ϕ̃j	−1ϕ̃j	NOUN
ejpam-6489	217	14	)	)	PUNCT
ejpam-6489	218	1	∧	∧	PROPN
ejpam-6489	218	2	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	218	3	(	(	PUNCT
ejpam-6489	218	4	η̃j)}e	η̃j)}e	PRON
ejpam-6489	218	5	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	218	6	{	{	PUNCT
ejpam-6489	218	7	ω̃p	ω̃p	PROPN
ejpam-6489	218	8	̃ג	̃ג	PROPN
ejpam-6489	218	9	(	(	PUNCT
ejpam-6489	218	10	β̃−1ϕ̃j)∧ω̃p	β̃−1ϕ̃j)∧ω̃p	NUM
ejpam-6489	218	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	218	12	(	(	PUNCT
ejpam-6489	218	13	η̃j	η̃j	NOUN
ejpam-6489	218	14	)	)	PUNCT
ejpam-6489	218	15	}	}	PUNCT
ejpam-6489	218	16	}	}	PUNCT
ejpam-6489	218	17	=	=	SYM
ejpam-6489	218	18	sup	sup	NOUN
ejpam-6489	218	19	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	218	20	∑	∑	NOUN
ejpam-6489	218	21	j∈n	j∈n	NOUN
ejpam-6489	219	1	β̃β̃j	β̃β̃j	NOUN
ejpam-6489	220	1	[	[	X
ejpam-6489	220	2	β̃−1ϕ̃j	β̃−1ϕ̃j	ADV
ejpam-6489	220	3	,	,	PUNCT
ejpam-6489	220	4	η̃j	η̃j	PROPN
ejpam-6489	220	5	]	]	PUNCT
ejpam-6489	220	6	{	{	PUNCT
ejpam-6489	220	7	min	min	NOUN
ejpam-6489	220	8	j∈n	j∈n	NOUN
ejpam-6489	220	9	{	{	PUNCT
ejpam-6489	220	10	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	220	11	(	(	PUNCT
ejpam-6489	220	12	β̃	β̃	PROPN
ejpam-6489	220	13	−1ϕ̃j	−1ϕ̃j	NOUN
ejpam-6489	220	14	)	)	PUNCT
ejpam-6489	221	1	∧	∧	PROPN
ejpam-6489	221	2	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	221	3	(	(	PUNCT
ejpam-6489	221	4	η̃j)}e	η̃j)}e	PRON
ejpam-6489	221	5	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	221	6	{	{	PUNCT
ejpam-6489	221	7	ω̃p	ω̃p	PROPN
ejpam-6489	221	8	̃ג	̃ג	PROPN
ejpam-6489	221	9	(	(	PUNCT
ejpam-6489	221	10	β̃−1ϕ̃j)∧ω̃p	β̃−1ϕ̃j)∧ω̃p	NUM
ejpam-6489	221	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	221	12	(	(	PUNCT
ejpam-6489	221	13	η̃j	η̃j	NOUN
ejpam-6489	221	14	)	)	PUNCT
ejpam-6489	221	15	}	}	PUNCT
ejpam-6489	221	16	}	}	PUNCT
ejpam-6489	221	17	=	=	SYM
ejpam-6489	221	18	ξp	ξp	ADP
ejpam-6489	221	19	β̃)[ℸ̃,̃ג	β̃)[ℸ̃,̃ג	X
ejpam-6489	221	20	]	]	X
ejpam-6489	221	21	−1ϕ̃	−1ϕ̃	X
ejpam-6489	221	22	)	)	PUNCT
ejpam-6489	221	23	=	=	PRON
ejpam-6489	221	24	ξp	ξp	ADP
ejpam-6489	221	25	β̃[̃ג,ℸ̃](ϕ̃	β̃[̃ג,ℸ̃](ϕ̃	PUNCT
ejpam-6489	221	26	)	)	PUNCT
ejpam-6489	221	27	,	,	PUNCT
ejpam-6489	221	28	ξn	ξn	X
ejpam-6489	221	29	[	[	X
ejpam-6489	221	30	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	221	31	)	)	PUNCT
ejpam-6489	221	32	=	=	SYM
ejpam-6489	221	33	inf	inf	NOUN
ejpam-6489	221	34	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	221	35	∑	∑	PROPN
ejpam-6489	221	36	j∈n	j∈n	NOUN
ejpam-6489	221	37	β̃j	β̃j	PROPN
ejpam-6489	222	1	[	[	X
ejpam-6489	222	2	ϕ̃j	ϕ̃j	X
ejpam-6489	222	3	,	,	PUNCT
ejpam-6489	222	4	η̃j	η̃j	PROPN
ejpam-6489	222	5	]	]	PUNCT
ejpam-6489	223	1	{	{	PUNCT
ejpam-6489	223	2	max	max	PROPN
ejpam-6489	223	3	j∈n	j∈n	PROPN
ejpam-6489	223	4	{	{	PUNCT
ejpam-6489	223	5	r̃n	r̃n	NOUN
ejpam-6489	223	6	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	NUM
ejpam-6489	223	7	)	)	PUNCT
ejpam-6489	223	8	∨	∨	NOUN
ejpam-6489	223	9	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	223	10	(	(	PUNCT
ejpam-6489	223	11	η̃j)}e	η̃j)}e	NUM
ejpam-6489	223	12	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	223	13	{	{	PUNCT
ejpam-6489	223	14	ω̃n	ω̃n	PROPN
ejpam-6489	223	15	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	223	16	(	(	PUNCT
ejpam-6489	223	17	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	NUM
ejpam-6489	223	18	ℸ̃	ℸ̃	PROPN
ejpam-6489	223	19	(	(	PUNCT
ejpam-6489	223	20	η̃j	η̃j	NOUN
ejpam-6489	223	21	)	)	PUNCT
ejpam-6489	223	22	}	}	PUNCT
ejpam-6489	223	23	}	}	PUNCT
ejpam-6489	223	24	=	=	SYM
ejpam-6489	223	25	inf	inf	ADJ
ejpam-6489	223	26	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	223	27	∑	∑	PROPN
ejpam-6489	223	28	j∈n	j∈n	NOUN
ejpam-6489	223	29	β̃j	β̃j	PROPN
ejpam-6489	224	1	[	[	X
ejpam-6489	224	2	ϕ̃j	ϕ̃j	X
ejpam-6489	224	3	,	,	PUNCT
ejpam-6489	224	4	η̃j	η̃j	PROPN
ejpam-6489	224	5	]	]	PUNCT
ejpam-6489	225	1	{	{	PUNCT
ejpam-6489	225	2	max	max	PROPN
ejpam-6489	225	3	j∈n	j∈n	PROPN
ejpam-6489	225	4	{	{	PUNCT
ejpam-6489	225	5	r̃ñג	r̃ñג	NOUN
ejpam-6489	225	6	(	(	PUNCT
ejpam-6489	225	7	β̃−1ϕ̃j	β̃−1ϕ̃j	ADJ
ejpam-6489	225	8	)	)	PUNCT
ejpam-6489	225	9	∨	∨	NUM
ejpam-6489	225	10	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	225	11	(	(	PUNCT
ejpam-6489	225	12	η̃j)}ei2πmaxj∈n	η̃j)}ei2πmaxj∈n	PROPN
ejpam-6489	225	13	{	{	PUNCT
ejpam-6489	225	14	ω̃n	ω̃n	PROPN
ejpam-6489	225	15	̃ג	̃ג	PROPN
ejpam-6489	225	16	(	(	PUNCT
ejpam-6489	225	17	β̃−1ϕ̃j)∨ω̃n	β̃−1ϕ̃j)∨ω̃n	NUM
ejpam-6489	225	18	ℸ̃	ℸ̃	PROPN
ejpam-6489	225	19	(	(	PUNCT
ejpam-6489	225	20	η̃j	η̃j	NOUN
ejpam-6489	225	21	)	)	PUNCT
ejpam-6489	225	22	}	}	PUNCT
ejpam-6489	225	23	}	}	PUNCT
ejpam-6489	225	24	=	=	SYM
ejpam-6489	225	25	inf	inf	ADJ
ejpam-6489	225	26	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	225	27	∑	∑	PROPN
ejpam-6489	225	28	j∈n	j∈n	NOUN
ejpam-6489	225	29	β̃β̃j	β̃β̃j	NOUN
ejpam-6489	226	1	[	[	X
ejpam-6489	226	2	β̃−1ϕ̃j	β̃−1ϕ̃j	ADV
ejpam-6489	226	3	,	,	PUNCT
ejpam-6489	226	4	η̃j	η̃j	PROPN
ejpam-6489	226	5	]	]	PUNCT
ejpam-6489	226	6	{	{	PUNCT
ejpam-6489	226	7	max	max	PROPN
ejpam-6489	226	8	j∈n	j∈n	PROPN
ejpam-6489	226	9	{	{	PUNCT
ejpam-6489	226	10	r̃ñג	r̃ñג	NOUN
ejpam-6489	226	11	(	(	PUNCT
ejpam-6489	226	12	β̃−1ϕ̃j	β̃−1ϕ̃j	ADJ
ejpam-6489	226	13	)	)	PUNCT
ejpam-6489	226	14	∨	∨	NUM
ejpam-6489	226	15	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	226	16	(	(	PUNCT
ejpam-6489	226	17	η̃j)}ei2πmaxj∈n	η̃j)}ei2πmaxj∈n	PROPN
ejpam-6489	226	18	{	{	PUNCT
ejpam-6489	226	19	ω̃n	ω̃n	PROPN
ejpam-6489	226	20	̃ג	̃ג	PROPN
ejpam-6489	226	21	(	(	PUNCT
ejpam-6489	226	22	β̃−1ϕ̃j)∨ω̃n	β̃−1ϕ̃j)∨ω̃n	NUM
ejpam-6489	226	23	ℸ̃	ℸ̃	PROPN
ejpam-6489	226	24	(	(	PUNCT
ejpam-6489	226	25	η̃j	η̃j	NOUN
ejpam-6489	226	26	)	)	PUNCT
ejpam-6489	226	27	}	}	PUNCT
ejpam-6489	226	28	}	}	PUNCT
ejpam-6489	226	29	=	=	SYM
ejpam-6489	226	30	ξn	ξn	PROPN
ejpam-6489	226	31	β̃)[ℸ̃,̃ג	β̃)[ℸ̃,̃ג	X
ejpam-6489	226	32	]	]	X
ejpam-6489	226	33	−1ϕ̃	−1ϕ̃	X
ejpam-6489	226	34	)	)	PUNCT
ejpam-6489	226	35	=	=	SYM
ejpam-6489	226	36	ξn	ξn	NOUN
ejpam-6489	226	37	β̃[̃ג,ℸ̃](ϕ̃	β̃[̃ג,ℸ̃](ϕ̃	PUNCT
ejpam-6489	226	38	)	)	PUNCT
ejpam-6489	226	39	,	,	PUNCT
ejpam-6489	226	40	and	and	CCONJ
ejpam-6489	226	41	ζ[β̃̃ג,ℸ̃](ϕ̃	ζ[β̃̃ג,ℸ̃](ϕ̃	X
ejpam-6489	226	42	)	)	PUNCT
ejpam-6489	226	43	=	=	SYM
ejpam-6489	226	44	inf	inf	NOUN
ejpam-6489	226	45	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	226	46	∑	∑	PROPN
ejpam-6489	226	47	j∈n	j∈n	NOUN
ejpam-6489	226	48	β̃j	β̃j	PROPN
ejpam-6489	227	1	[	[	X
ejpam-6489	227	2	ϕ̃j	ϕ̃j	X
ejpam-6489	227	3	,	,	PUNCT
ejpam-6489	227	4	η̃j	η̃j	PROPN
ejpam-6489	227	5	]	]	PUNCT
ejpam-6489	228	1	{	{	PUNCT
ejpam-6489	228	2	max	max	PROPN
ejpam-6489	228	3	j∈n	j∈n	PROPN
ejpam-6489	228	4	{	{	PUNCT
ejpam-6489	228	5	r̃β̃̃ג(ϕ̃j	r̃β̃̃ג(ϕ̃j	PROPN
ejpam-6489	228	6	)	)	PUNCT
ejpam-6489	228	7	∨	∨	NUM
ejpam-6489	228	8	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	228	9	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	228	10	{	{	PUNCT
ejpam-6489	228	11	ω̃β̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	ω̃β̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	228	12	)	)	PUNCT
ejpam-6489	228	13	}	}	PUNCT
ejpam-6489	228	14	}	}	PUNCT
ejpam-6489	228	15	=	=	SYM
ejpam-6489	228	16	inf	inf	ADJ
ejpam-6489	228	17	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	228	18	∑	∑	PROPN
ejpam-6489	228	19	j∈n	j∈n	NOUN
ejpam-6489	228	20	β̃j	β̃j	PROPN
ejpam-6489	229	1	[	[	X
ejpam-6489	229	2	ϕ̃j	ϕ̃j	X
ejpam-6489	229	3	,	,	PUNCT
ejpam-6489	229	4	η̃j	η̃j	PROPN
ejpam-6489	229	5	]	]	PUNCT
ejpam-6489	230	1	{	{	PUNCT
ejpam-6489	230	2	max	max	PROPN
ejpam-6489	230	3	j∈n	j∈n	PROPN
ejpam-6489	230	4	{	{	PUNCT
ejpam-6489	230	5	r̃̃ג(β̃	r̃̃ג(β̃	PROPN
ejpam-6489	230	6	−1ϕ̃j	−1ϕ̃j	PROPN
ejpam-6489	230	7	)	)	PUNCT
ejpam-6489	230	8	∨	∨	NUM
ejpam-6489	230	9	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	230	10	i2πmaxj∈n	i2πmaxj∈n	NOUN
ejpam-6489	230	11	{	{	PUNCT
ejpam-6489	230	12	ω̃̃ג(β̃	ω̃̃ג(β̃	PROPN
ejpam-6489	230	13	−1ϕ̃j)∨ω̃ℸ̃(η̃j	−1ϕ̃j)∨ω̃ℸ̃(η̃j	NUM
ejpam-6489	230	14	)	)	PUNCT
ejpam-6489	230	15	}	}	PUNCT
ejpam-6489	230	16	}	}	PUNCT
ejpam-6489	230	17	=	=	SYM
ejpam-6489	230	18	inf	inf	ADJ
ejpam-6489	230	19	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	230	20	∑	∑	PROPN
ejpam-6489	230	21	j∈n	j∈n	NOUN
ejpam-6489	230	22	β̃β̃j	β̃β̃j	NOUN
ejpam-6489	231	1	[	[	X
ejpam-6489	231	2	β̃−1ϕ̃j	β̃−1ϕ̃j	ADV
ejpam-6489	231	3	,	,	PUNCT
ejpam-6489	231	4	η̃j	η̃j	PROPN
ejpam-6489	231	5	]	]	PUNCT
ejpam-6489	231	6	{	{	PUNCT
ejpam-6489	231	7	max	max	PROPN
ejpam-6489	231	8	j∈n	j∈n	PROPN
ejpam-6489	231	9	{	{	PUNCT
ejpam-6489	231	10	r̃̃ג(β̃	r̃̃ג(β̃	PROPN
ejpam-6489	231	11	−1ϕ̃j	−1ϕ̃j	PROPN
ejpam-6489	231	12	)	)	PUNCT
ejpam-6489	231	13	∨	∨	NUM
ejpam-6489	231	14	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	231	15	i2πmaxj∈n	i2πmaxj∈n	NOUN
ejpam-6489	231	16	{	{	PUNCT
ejpam-6489	231	17	ω̃̃ג(β̃	ω̃̃ג(β̃	PROPN
ejpam-6489	231	18	−1ϕ̃j)∨ω̃ℸ̃(η̃j	−1ϕ̃j)∨ω̃ℸ̃(η̃j	NUM
ejpam-6489	231	19	)	)	PUNCT
ejpam-6489	231	20	}	}	PUNCT
ejpam-6489	231	21	}	}	PUNCT
ejpam-6489	231	22	=	=	SYM
ejpam-6489	231	23	ξ[̃ג,ℸ̃](β̃	ξ[̃ג,ℸ̃](β̃	PROPN
ejpam-6489	231	24	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	231	25	)	)	PUNCT
ejpam-6489	231	26	=	=	SYM
ejpam-6489	231	27	ξβ̃[̃ג,ℸ̃](ϕ̃	ξβ̃[̃ג,ℸ̃](ϕ̃	PROPN
ejpam-6489	231	28	)	)	PUNCT
ejpam-6489	231	29	.	.	PUNCT
ejpam-6489	232	1	if	if	SCONJ
ejpam-6489	232	2	β̃	β̃	PROPN
ejpam-6489	232	3	=	=	SYM
ejpam-6489	232	4	0	0	NUM
ejpam-6489	232	5	,	,	PUNCT
ejpam-6489	232	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	232	7	̸=	̸=	PROPN
ejpam-6489	232	8	0	0	NUM
ejpam-6489	232	9	,	,	PUNCT
ejpam-6489	232	10	then	then	ADV
ejpam-6489	232	11	ξp	ξp	ADP
ejpam-6489	232	12	[	[	X
ejpam-6489	232	13	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	X
ejpam-6489	232	14	)	)	PUNCT
ejpam-6489	232	15	=	=	SYM
ejpam-6489	232	16	sup	sup	NOUN
ejpam-6489	232	17	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	232	18	∑	∑	PROPN
ejpam-6489	232	19	j∈n	j∈n	NOUN
ejpam-6489	232	20	β̃j	β̃j	PROPN
ejpam-6489	233	1	[	[	X
ejpam-6489	233	2	ϕ̃j	ϕ̃j	X
ejpam-6489	233	3	,	,	PUNCT
ejpam-6489	233	4	η̃j	η̃j	PROPN
ejpam-6489	233	5	]	]	PUNCT
ejpam-6489	233	6	{	{	PUNCT
ejpam-6489	233	7	min	min	NOUN
ejpam-6489	233	8	j∈n	j∈n	NOUN
ejpam-6489	233	9	{	{	PUNCT
ejpam-6489	233	10	r̃p	r̃p	NOUN
ejpam-6489	233	11	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	ADV
ejpam-6489	233	12	)	)	PUNCT
ejpam-6489	233	13	∧	∧	PROPN
ejpam-6489	233	14	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	233	15	(	(	PUNCT
ejpam-6489	233	16	η̃j)}e	η̃j)}e	PRON
ejpam-6489	233	17	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	233	18	{	{	PUNCT
ejpam-6489	233	19	ω̃p	ω̃p	PROPN
ejpam-6489	233	20	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	233	21	(	(	PUNCT
ejpam-6489	233	22	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	233	23	ℸ̃	ℸ̃	PROPN
ejpam-6489	233	24	(	(	PUNCT
ejpam-6489	233	25	η̃j	η̃j	NOUN
ejpam-6489	233	26	)	)	PUNCT
ejpam-6489	233	27	}	}	PUNCT
ejpam-6489	233	28	}	}	PUNCT
ejpam-6489	233	29	,	,	PUNCT
ejpam-6489	233	30	m.	m.	NOUN
ejpam-6489	233	31	balamurugan	balamurugan	NOUN
ejpam-6489	233	32	,	,	PUNCT
ejpam-6489	233	33	g.	g.	PROPN
ejpam-6489	233	34	ellammal	ellammal	PROPN
ejpam-6489	233	35	,	,	PUNCT
ejpam-6489	233	36	a.	a.	NOUN
ejpam-6489	233	37	iampan	iampan	PROPN
ejpam-6489	233	38	/	/	SYM
ejpam-6489	233	39	eur	eur	PROPN
ejpam-6489	233	40	.	.	PUNCT
ejpam-6489	234	1	j.	j.	PROPN
ejpam-6489	234	2	pure	pure	PROPN
ejpam-6489	234	3	appl	appl	PROPN
ejpam-6489	234	4	.	.	PROPN
ejpam-6489	234	5	math	math	PROPN
ejpam-6489	234	6	,	,	PUNCT
ejpam-6489	234	7	18	18	NUM
ejpam-6489	234	8	(	(	PUNCT
ejpam-6489	234	9	3	3	NUM
ejpam-6489	234	10	)	)	PUNCT
ejpam-6489	234	11	(	(	PUNCT
ejpam-6489	234	12	2025	2025	NUM
ejpam-6489	234	13	)	)	PUNCT
ejpam-6489	234	14	,	,	PUNCT
ejpam-6489	234	15	6489	6489	NUM
ejpam-6489	234	16	10	10	NUM
ejpam-6489	234	17	of	of	ADP
ejpam-6489	234	18	26	26	NUM
ejpam-6489	234	19	ξn	ξn	NOUN
ejpam-6489	234	20	[	[	X
ejpam-6489	234	21	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	234	22	)	)	PUNCT
ejpam-6489	234	23	=	=	SYM
ejpam-6489	234	24	inf	inf	NOUN
ejpam-6489	234	25	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	234	26	∑	∑	PROPN
ejpam-6489	234	27	j∈n	j∈n	NOUN
ejpam-6489	234	28	β̃j	β̃j	PROPN
ejpam-6489	235	1	[	[	X
ejpam-6489	235	2	ϕ̃j	ϕ̃j	X
ejpam-6489	235	3	,	,	PUNCT
ejpam-6489	235	4	η̃j	η̃j	PROPN
ejpam-6489	235	5	]	]	PUNCT
ejpam-6489	236	1	{	{	PUNCT
ejpam-6489	236	2	max	max	PROPN
ejpam-6489	236	3	j∈n	j∈n	PROPN
ejpam-6489	236	4	{	{	PUNCT
ejpam-6489	236	5	r̃n	r̃n	NOUN
ejpam-6489	236	6	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	NUM
ejpam-6489	236	7	)	)	PUNCT
ejpam-6489	236	8	∨	∨	NOUN
ejpam-6489	236	9	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	236	10	(	(	PUNCT
ejpam-6489	236	11	η̃j)}e	η̃j)}e	NUM
ejpam-6489	236	12	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	236	13	{	{	PUNCT
ejpam-6489	236	14	ω̃n	ω̃n	PROPN
ejpam-6489	236	15	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	236	16	(	(	PUNCT
ejpam-6489	236	17	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	NUM
ejpam-6489	236	18	ℸ̃	ℸ̃	PROPN
ejpam-6489	236	19	(	(	PUNCT
ejpam-6489	236	20	η̃j	η̃j	NOUN
ejpam-6489	236	21	)	)	PUNCT
ejpam-6489	236	22	}	}	PUNCT
ejpam-6489	236	23	}	}	PUNCT
ejpam-6489	236	24	,	,	PUNCT
ejpam-6489	236	25	and	and	CCONJ
ejpam-6489	236	26	ζ[β̃̃ג,ℸ̃](ϕ̃	ζ[β̃̃ג,ℸ̃](ϕ̃	X
ejpam-6489	236	27	)	)	PUNCT
ejpam-6489	236	28	=	=	SYM
ejpam-6489	236	29	inf	inf	NOUN
ejpam-6489	236	30	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	236	31	∑	∑	PROPN
ejpam-6489	236	32	j∈n	j∈n	NOUN
ejpam-6489	236	33	β̃j	β̃j	PROPN
ejpam-6489	237	1	[	[	X
ejpam-6489	237	2	ϕ̃j	ϕ̃j	X
ejpam-6489	237	3	,	,	PUNCT
ejpam-6489	237	4	η̃j	η̃j	PROPN
ejpam-6489	237	5	]	]	PUNCT
ejpam-6489	238	1	{	{	PUNCT
ejpam-6489	238	2	max	max	PROPN
ejpam-6489	238	3	j∈n	j∈n	PROPN
ejpam-6489	238	4	{	{	PUNCT
ejpam-6489	238	5	r̃β̃̃ג(ϕ̃j	r̃β̃̃ג(ϕ̃j	PROPN
ejpam-6489	238	6	)	)	PUNCT
ejpam-6489	238	7	∨	∨	NUM
ejpam-6489	238	8	r̃ℸ̃(η̃j)}e	r̃ℸ̃(η̃j)}e	NOUN
ejpam-6489	238	9	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	238	10	{	{	PUNCT
ejpam-6489	238	11	ω̃β̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	ω̃β̃̃ג(ϕ̃j)∨ω̃ℸ̃(η̃j	PROPN
ejpam-6489	238	12	)	)	PUNCT
ejpam-6489	238	13	}	}	PUNCT
ejpam-6489	238	14	}	}	PUNCT
ejpam-6489	238	15	,	,	PUNCT
ejpam-6489	238	16	there	there	PRON
ejpam-6489	238	17	exists	exist	VERB
ejpam-6489	238	18	ϕ̃	ϕ̃	PROPN
ejpam-6489	238	19	̸=	̸=	PROPN
ejpam-6489	238	20	0	0	NUM
ejpam-6489	238	21	,	,	PUNCT
ejpam-6489	238	22	which	which	PRON
ejpam-6489	238	23	implies	imply	VERB
ejpam-6489	238	24	that	that	DET
ejpam-6489	238	25	r̃p	r̃p	NOUN
ejpam-6489	238	26	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	ADV
ejpam-6489	238	27	)	)	PUNCT
ejpam-6489	238	28	=	=	SYM
ejpam-6489	239	1	0	0	NUM
ejpam-6489	239	2	,	,	PUNCT
ejpam-6489	239	3	ω̃p	ω̃p	NOUN
ejpam-6489	239	4	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	NUM
ejpam-6489	239	5	)	)	PUNCT
ejpam-6489	239	6	=	=	SYM
ejpam-6489	239	7	0	0	NUM
ejpam-6489	239	8	,	,	PUNCT
ejpam-6489	239	9	r̃n	r̃n	NOUN
ejpam-6489	239	10	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	X
ejpam-6489	239	11	)	)	PUNCT
ejpam-6489	239	12	=	=	SYM
ejpam-6489	239	13	1	1	NUM
ejpam-6489	239	14	,	,	PUNCT
ejpam-6489	239	15	ω̃n	ω̃n	NOUN
ejpam-6489	239	16	β̃̃ג(ϕ̃j	β̃̃ג(ϕ̃j	NOUN
ejpam-6489	239	17	)	)	PUNCT
ejpam-6489	239	18	=	=	SYM
ejpam-6489	239	19	1	1	NUM
ejpam-6489	239	20	,	,	PUNCT
ejpam-6489	239	21	and	and	CCONJ
ejpam-6489	239	22	r̃β̃̃ג(ϕ̃j	r̃β̃̃ג(ϕ̃j	VERB
ejpam-6489	239	23	)	)	PUNCT
ejpam-6489	239	24	=	=	SYM
ejpam-6489	239	25	1	1	NUM
ejpam-6489	239	26	,	,	PUNCT
ejpam-6489	239	27	ω̃β̃̃ג(ϕ̃j	ω̃β̃̃ג(ϕ̃j	NUM
ejpam-6489	239	28	)	)	PUNCT
ejpam-6489	239	29	=	=	SYM
ejpam-6489	240	1	1	1	X
ejpam-6489	240	2	.	.	PUNCT
ejpam-6489	241	1	so	so	ADV
ejpam-6489	241	2	,	,	PUNCT
ejpam-6489	241	3	ξp	ξp	ADP
ejpam-6489	241	4	[	[	X
ejpam-6489	241	5	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	X
ejpam-6489	241	6	)	)	PUNCT
ejpam-6489	241	7	=	=	SYM
ejpam-6489	242	1	0	0	NUM
ejpam-6489	242	2	,	,	PUNCT
ejpam-6489	242	3	ξn	ξn	X
ejpam-6489	243	1	[	[	X
ejpam-6489	243	2	β̃̃ג,ℸ̃](ϕ̃	β̃̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	243	3	)	)	PUNCT
ejpam-6489	243	4	=	=	SYM
ejpam-6489	243	5	1	1	NUM
ejpam-6489	243	6	and	and	CCONJ
ejpam-6489	243	7	ζ[β̃̃ג,ℸ̃](ϕ̃	ζ[β̃̃ג,ℸ̃](ϕ̃	NOUN
ejpam-6489	243	8	)	)	PUNCT
ejpam-6489	243	9	=	=	SYM
ejpam-6489	244	1	1	1	X
ejpam-6489	244	2	.	.	PUNCT
ejpam-6489	245	1	if	if	SCONJ
ejpam-6489	245	2	β̃	β̃	PROPN
ejpam-6489	245	3	=	=	SYM
ejpam-6489	245	4	0	0	NUM
ejpam-6489	245	5	and	and	CCONJ
ejpam-6489	245	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	245	7	=	=	NOUN
ejpam-6489	245	8	0	0	PROPN
ejpam-6489	245	9	,	,	PUNCT
ejpam-6489	245	10	then	then	ADV
ejpam-6489	245	11	it	it	PRON
ejpam-6489	245	12	is	be	AUX
ejpam-6489	245	13	obvious	obvious	ADJ
ejpam-6489	245	14	.	.	PUNCT
ejpam-6489	246	1	the	the	DET
ejpam-6489	246	2	second	second	ADJ
ejpam-6489	246	3	one	one	NOUN
ejpam-6489	246	4	can	can	AUX
ejpam-6489	246	5	be	be	AUX
ejpam-6489	246	6	obtained	obtain	VERB
ejpam-6489	246	7	in	in	ADP
ejpam-6489	246	8	the	the	DET
ejpam-6489	246	9	same	same	ADJ
ejpam-6489	246	10	way	way	NOUN
ejpam-6489	246	11	.	.	PUNCT
ejpam-6489	247	1	4	4	X
ejpam-6489	247	2	.	.	X
ejpam-6489	247	3	tripolar	tripolar	ADJ
ejpam-6489	247	4	complex	complex	ADJ
ejpam-6489	247	5	fuzzy	fuzzy	ADJ
ejpam-6489	247	6	lie	lie	NOUN
ejpam-6489	247	7	subalgebras	subalgebras	PROPN
ejpam-6489	247	8	definition	definition	NOUN
ejpam-6489	247	9	10	10	NUM
ejpam-6489	247	10	.	.	PUNCT
ejpam-6489	248	1	a	a	DET
ejpam-6489	248	2	t	t	NOUN
ejpam-6489	248	3	cfs	cfs	PROPN
ejpam-6489	248	4	̃ג	̃ג	NOUN
ejpam-6489	248	5	=	=	PUNCT
ejpam-6489	248	6	{	{	PUNCT
ejpam-6489	248	7	(	(	PUNCT
ejpam-6489	248	8	ϕ̃	ϕ̃	PROPN
ejpam-6489	248	9	,	,	PUNCT
ejpam-6489	248	10	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	248	11	(	(	PUNCT
ejpam-6489	248	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	248	13	)	)	PUNCT
ejpam-6489	248	14	=	=	SYM
ejpam-6489	249	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	249	2	(	(	PUNCT
ejpam-6489	249	3	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	249	4	i2πω̃p	i2πω̃p	X
ejpam-6489	249	5	̃ג	̃ג	NOUN
ejpam-6489	249	6	(	(	PUNCT
ejpam-6489	249	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	249	8	)	)	PUNCT
ejpam-6489	249	9	,	,	PUNCT
ejpam-6489	249	10	ξñג	ξñג	PROPN
ejpam-6489	249	11	(	(	PUNCT
ejpam-6489	249	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	249	13	)	)	PUNCT
ejpam-6489	249	14	=	=	SYM
ejpam-6489	249	15	r̃ñג	r̃ñג	PROPN
ejpam-6489	249	16	(	(	PUNCT
ejpam-6489	249	17	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	249	18	p	p	X
ejpam-6489	249	19	̃ג	̃ג	PROPN
ejpam-6489	249	20	(	(	PUNCT
ejpam-6489	249	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	249	22	)	)	PUNCT
ejpam-6489	249	23	,	,	PUNCT
ejpam-6489	249	24	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	249	25	)	)	PUNCT
ejpam-6489	249	26	=	=	PUNCT
ejpam-6489	249	27	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	X
ejpam-6489	249	28	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	249	29	)	)	PUNCT
ejpam-6489	249	30	)	)	PUNCT
ejpam-6489	250	1	|	|	ADV
ejpam-6489	250	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	250	3	∈	∈	PROPN
ejpam-6489	250	4	l̃	l̃	PROPN
ejpam-6489	250	5	}	}	PUNCT
ejpam-6489	250	6	on	on	ADP
ejpam-6489	250	7	l̃	l̃	PROPN
ejpam-6489	250	8	is	be	AUX
ejpam-6489	250	9	termed	term	VERB
ejpam-6489	250	10	as	as	ADP
ejpam-6489	250	11	a	a	DET
ejpam-6489	250	12	t	t	NOUN
ejpam-6489	250	13	cfls	cfls	NOUN
ejpam-6489	250	14	on	on	ADP
ejpam-6489	250	15	l̃	l̃	PROPN
ejpam-6489	250	16	if	if	SCONJ
ejpam-6489	250	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	250	18	,	,	PUNCT
ejpam-6489	250	19	η̃	η̃	PROPN
ejpam-6489	250	20	∈	∈	PROPN
ejpam-6489	250	21	l̃	l̃	PROPN
ejpam-6489	250	22	,	,	PUNCT
ejpam-6489	250	23	β̃	β̃	PROPN
ejpam-6489	250	24	∈	∈	PROPN
ejpam-6489	250	25	f	f	PROPN
ejpam-6489	250	26	,	,	PUNCT
ejpam-6489	250	27	the	the	DET
ejpam-6489	250	28	underneath	underneath	NOUN
ejpam-6489	250	29	holds	hold	VERB
ejpam-6489	250	30	:	:	PUNCT
ejpam-6489	250	31	(	(	PUNCT
ejpam-6489	250	32	i	i	NOUN
ejpam-6489	250	33	)	)	PUNCT
ejpam-6489	250	34	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	251	1	(	(	PUNCT
ejpam-6489	251	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	251	3	+	+	NUM
ejpam-6489	251	4	η̃	η̃	PROPN
ejpam-6489	251	5	)	)	PUNCT
ejpam-6489	251	6	≥	≥	X
ejpam-6489	251	7	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	251	8	(	(	PUNCT
ejpam-6489	251	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	251	10	)	)	PUNCT
ejpam-6489	251	11	∧	∧	PROPN
ejpam-6489	251	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	251	13	(	(	PUNCT
ejpam-6489	251	14	η̃	η̃	PROPN
ejpam-6489	251	15	)	)	PUNCT
ejpam-6489	251	16	⇒	⇒	VERB
ejpam-6489	251	17	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	251	18	(	(	PUNCT
ejpam-6489	251	19	ϕ̃	ϕ̃	PROPN
ejpam-6489	252	1	+	+	X
ejpam-6489	252	2	η̃)ei2πω̃	η̃)ei2πω̃	PRON
ejpam-6489	252	3	p	p	PRON
ejpam-6489	252	4	̃ג	̃ג	PROPN
ejpam-6489	252	5	(	(	PUNCT
ejpam-6489	252	6	ϕ̃+η̃	ϕ̃+η̃	PROPN
ejpam-6489	252	7	)	)	PUNCT
ejpam-6489	252	8	≥	≥	NOUN
ejpam-6489	253	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	253	2	(	(	PUNCT
ejpam-6489	253	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	253	4	+	+	X
ejpam-6489	253	5	η̃)ei2πω̃	η̃)ei2πω̃	PRON
ejpam-6489	253	6	p	p	PRON
ejpam-6489	253	7	̃ג	̃ג	PROPN
ejpam-6489	253	8	(	(	PUNCT
ejpam-6489	253	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	253	10	)	)	PUNCT
ejpam-6489	253	11	∧	∧	NOUN
ejpam-6489	253	12	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	253	13	(	(	PUNCT
ejpam-6489	253	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	253	15	+	+	X
ejpam-6489	253	16	η̃)ei2πω̃	η̃)ei2πω̃	PRON
ejpam-6489	253	17	p	p	PRON
ejpam-6489	253	18	̃ג	̃ג	PROPN
ejpam-6489	253	19	(	(	PUNCT
ejpam-6489	253	20	η̃	η̃	PROPN
ejpam-6489	253	21	)	)	PUNCT
ejpam-6489	253	22	,	,	PUNCT
ejpam-6489	253	23	(	(	PUNCT
ejpam-6489	253	24	ii	ii	NOUN
ejpam-6489	253	25	)	)	PUNCT
ejpam-6489	253	26	ξñג	ξñג	PROPN
ejpam-6489	253	27	(	(	PUNCT
ejpam-6489	253	28	ϕ̃+	ϕ̃+	PROPN
ejpam-6489	253	29	η̃	η̃	PROPN
ejpam-6489	253	30	)	)	PUNCT
ejpam-6489	253	31	≤	≤	NUM
ejpam-6489	254	1	ξñג	ξñג	NOUN
ejpam-6489	254	2	(	(	PUNCT
ejpam-6489	254	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	254	4	)	)	PUNCT
ejpam-6489	254	5	∨	∨	NUM
ejpam-6489	254	6	ξñג	ξñג	PROPN
ejpam-6489	254	7	(	(	PUNCT
ejpam-6489	254	8	η̃	η̃	PROPN
ejpam-6489	254	9	)	)	PUNCT
ejpam-6489	254	10	⇒	⇒	PROPN
ejpam-6489	254	11	r̃ñג	r̃ñג	PROPN
ejpam-6489	254	12	(	(	PUNCT
ejpam-6489	254	13	ϕ̃+	ϕ̃+	PROPN
ejpam-6489	254	14	η̃)ei2πω̃	η̃)ei2πω̃	PROPN
ejpam-6489	254	15	n	n	PRON
ejpam-6489	254	16	̃ג	̃ג	PROPN
ejpam-6489	254	17	(	(	PUNCT
ejpam-6489	254	18	ϕ̃+η̃	ϕ̃+η̃	NOUN
ejpam-6489	254	19	)	)	PUNCT
ejpam-6489	254	20	≤	≤	NUM
ejpam-6489	254	21	r̃ñג	r̃ñג	NOUN
ejpam-6489	254	22	(	(	PUNCT
ejpam-6489	254	23	ϕ̃+	ϕ̃+	PROPN
ejpam-6489	254	24	η̃)ei2πω̃	η̃)ei2πω̃	PROPN
ejpam-6489	254	25	n	n	PRON
ejpam-6489	254	26	̃ג	̃ג	PROPN
ejpam-6489	254	27	(	(	PUNCT
ejpam-6489	254	28	ϕ̃	ϕ̃	PROPN
ejpam-6489	254	29	)	)	PUNCT
ejpam-6489	254	30	∨	∨	NUM
ejpam-6489	254	31	r̃ñג	r̃ñג	NOUN
ejpam-6489	254	32	(	(	PUNCT
ejpam-6489	254	33	ϕ̃+	ϕ̃+	PROPN
ejpam-6489	254	34	η̃)ei2πω̃	η̃)ei2πω̃	PROPN
ejpam-6489	254	35	n	n	PRON
ejpam-6489	254	36	̃ג	̃ג	PROPN
ejpam-6489	254	37	(	(	PUNCT
ejpam-6489	254	38	η̃	η̃	PROPN
ejpam-6489	254	39	)	)	PUNCT
ejpam-6489	254	40	,	,	PUNCT
ejpam-6489	254	41	(	(	PUNCT
ejpam-6489	254	42	iii	iii	X
ejpam-6489	254	43	)	)	PUNCT
ejpam-6489	254	44	ζ̃ג(ϕ̃+	ζ̃ג(ϕ̃+	PROPN
ejpam-6489	254	45	η̃	η̃	PROPN
ejpam-6489	254	46	)	)	PUNCT
ejpam-6489	254	47	≤	≤	NUM
ejpam-6489	254	48	ζ̃ג(ϕ̃)∨ζ̃ג(η̃	ζ̃ג(ϕ̃)∨ζ̃ג(η̃	NOUN
ejpam-6489	254	49	)	)	PUNCT
ejpam-6489	254	50	⇒	⇒	PROPN
ejpam-6489	254	51	r̃̃ג(ϕ̃+	r̃̃ג(ϕ̃+	PROPN
ejpam-6489	254	52	η̃)ei2πω̃̃ג(ϕ̃+η̃	η̃)ei2πω̃̃ג(ϕ̃+η̃	NOUN
ejpam-6489	254	53	)	)	PUNCT
ejpam-6489	255	1	≤	≤	NOUN
ejpam-6489	256	1	r̃̃ג(ϕ̃+	r̃̃ג(ϕ̃+	NOUN
ejpam-6489	256	2	η̃)ei2πω̃̃ג(ϕ̃)∨	η̃)ei2πω̃̃ג(ϕ̃)∨	NOUN
ejpam-6489	256	3	r̃̃ג(ϕ̃+	r̃̃ג(ϕ̃+	PROPN
ejpam-6489	256	4	η̃)ei2πω̃̃ג(η̃	η̃)ei2πω̃̃ג(η̃	PROPN
ejpam-6489	256	5	)	)	PUNCT
ejpam-6489	256	6	,	,	PUNCT
ejpam-6489	256	7	(	(	PUNCT
ejpam-6489	256	8	iv	iv	X
ejpam-6489	256	9	)	)	PUNCT
ejpam-6489	256	10	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	256	11	(	(	PUNCT
ejpam-6489	256	12	β̃ϕ̃	β̃ϕ̃	NOUN
ejpam-6489	256	13	)	)	PUNCT
ejpam-6489	256	14	≥	≥	NOUN
ejpam-6489	256	15	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	256	16	(	(	PUNCT
ejpam-6489	256	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	256	18	)	)	PUNCT
ejpam-6489	256	19	⇒	⇒	NOUN
ejpam-6489	256	20	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	256	21	(	(	PUNCT
ejpam-6489	256	22	β̃ϕ̃)e	β̃ϕ̃)e	X
ejpam-6489	256	23	i2πω̃p	i2πω̃p	X
ejpam-6489	256	24	̃ג	̃ג	NOUN
ejpam-6489	256	25	(	(	PUNCT
ejpam-6489	256	26	β̃ϕ̃	β̃ϕ̃	NOUN
ejpam-6489	256	27	)	)	PUNCT
ejpam-6489	256	28	≥	≥	NOUN
ejpam-6489	257	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	257	2	(	(	PUNCT
ejpam-6489	257	3	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	257	4	i2πω̃p	i2πω̃p	X
ejpam-6489	257	5	̃ג	̃ג	NOUN
ejpam-6489	257	6	(	(	PUNCT
ejpam-6489	257	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	257	8	)	)	PUNCT
ejpam-6489	257	9	,	,	PUNCT
ejpam-6489	257	10	(	(	PUNCT
ejpam-6489	257	11	ϑ̃	ϑ̃	PROPN
ejpam-6489	257	12	)	)	PUNCT
ejpam-6489	257	13	ξñג	ξñג	NOUN
ejpam-6489	257	14	(	(	PUNCT
ejpam-6489	257	15	β̃ϕ̃	β̃ϕ̃	NOUN
ejpam-6489	257	16	)	)	PUNCT
ejpam-6489	257	17	≤	≤	NUM
ejpam-6489	258	1	ξñג	ξñג	INTJ
ejpam-6489	258	2	(	(	PUNCT
ejpam-6489	258	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	258	4	)	)	PUNCT
ejpam-6489	258	5	⇒	⇒	NOUN
ejpam-6489	258	6	r̃ñג	r̃ñג	PROPN
ejpam-6489	258	7	(	(	PUNCT
ejpam-6489	258	8	β̃ϕ̃)ei2πω̃	β̃ϕ̃)ei2πω̃	X
ejpam-6489	258	9	n	n	PRON
ejpam-6489	258	10	̃ג	̃ג	NOUN
ejpam-6489	258	11	(	(	PUNCT
ejpam-6489	258	12	β̃ϕ̃	β̃ϕ̃	NOUN
ejpam-6489	258	13	)	)	PUNCT
ejpam-6489	258	14	≤	≤	NOUN
ejpam-6489	259	1	r̃ñג	r̃ñג	NOUN
ejpam-6489	259	2	(	(	PUNCT
ejpam-6489	259	3	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	259	4	n	n	PRON
ejpam-6489	259	5	̃ג	̃ג	PROPN
ejpam-6489	259	6	(	(	PUNCT
ejpam-6489	259	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	259	8	)	)	PUNCT
ejpam-6489	259	9	,	,	PUNCT
ejpam-6489	259	10	(	(	PUNCT
ejpam-6489	259	11	vi	vi	NOUN
ejpam-6489	259	12	)	)	PUNCT
ejpam-6489	259	13	ζ̃ג(β̃ϕ̃	ζ̃ג(β̃ϕ̃	PROPN
ejpam-6489	259	14	)	)	PUNCT
ejpam-6489	259	15	≤	≤	NUM
ejpam-6489	260	1	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	260	2	)	)	PUNCT
ejpam-6489	260	3	⇒	⇒	PROPN
ejpam-6489	260	4	r̃̃ג(β̃ϕ̃)e	r̃̃ג(β̃ϕ̃)e	VERB
ejpam-6489	260	5	i2πω̃̃ג(β̃ϕ̃	i2πω̃̃ג(β̃ϕ̃	PART
ejpam-6489	260	6	)	)	PUNCT
ejpam-6489	260	7	≤	≤	NOUN
ejpam-6489	260	8	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	VERB
ejpam-6489	260	9	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	260	10	)	)	PUNCT
ejpam-6489	260	11	,	,	PUNCT
ejpam-6489	260	12	(	(	PUNCT
ejpam-6489	260	13	vii	vii	PROPN
ejpam-6489	260	14	)	)	PUNCT
ejpam-6489	260	15	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	261	1	(	(	PUNCT
ejpam-6489	261	2	[	[	X
ejpam-6489	261	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	261	4	,	,	PUNCT
ejpam-6489	261	5	η̃	η̃	PROPN
ejpam-6489	261	6	]	]	PUNCT
ejpam-6489	261	7	)	)	PUNCT
ejpam-6489	261	8	≥	≥	X
ejpam-6489	261	9	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	261	10	(	(	PUNCT
ejpam-6489	261	11	ϕ̃)∧	ϕ̃)∧	X
ejpam-6489	261	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	261	13	(	(	PUNCT
ejpam-6489	261	14	η̃	η̃	PROPN
ejpam-6489	261	15	)	)	PUNCT
ejpam-6489	261	16	⇒	⇒	VERB
ejpam-6489	261	17	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	261	18	(	(	PUNCT
ejpam-6489	261	19	[	[	X
ejpam-6489	261	20	ϕ̃	ϕ̃	PROPN
ejpam-6489	261	21	,	,	PUNCT
ejpam-6489	261	22	η̃])e	η̃])e	PROPN
ejpam-6489	261	23	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	261	24	̃ג	̃ג	NOUN
ejpam-6489	261	25	(	(	PUNCT
ejpam-6489	261	26	[	[	X
ejpam-6489	261	27	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	261	28	]	]	X
ejpam-6489	261	29	)	)	PUNCT
ejpam-6489	261	30	≥	≥	NOUN
ejpam-6489	261	31	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	261	32	(	(	PUNCT
ejpam-6489	261	33	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	261	34	i2πω̃p	i2πω̃p	X
ejpam-6489	261	35	̃ג	̃ג	NOUN
ejpam-6489	261	36	(	(	PUNCT
ejpam-6489	261	37	ϕ̃	ϕ̃	PROPN
ejpam-6489	261	38	)	)	PUNCT
ejpam-6489	261	39	∧	∧	NOUN
ejpam-6489	261	40	r̃̃ג(η̃)e	r̃̃ג(η̃)e	VERB
ejpam-6489	261	41	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	261	42	̃ג	̃ג	NOUN
ejpam-6489	261	43	(	(	PUNCT
ejpam-6489	261	44	η̃	η̃	PROPN
ejpam-6489	261	45	)	)	PUNCT
ejpam-6489	261	46	,	,	PUNCT
ejpam-6489	261	47	(	(	PUNCT
ejpam-6489	261	48	viii	viii	NOUN
ejpam-6489	261	49	)	)	PUNCT
ejpam-6489	261	50	ξñג	ξñג	NOUN
ejpam-6489	262	1	(	(	PUNCT
ejpam-6489	262	2	[	[	X
ejpam-6489	262	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	262	4	,	,	PUNCT
ejpam-6489	262	5	η̃	η̃	PROPN
ejpam-6489	262	6	]	]	PUNCT
ejpam-6489	262	7	)	)	PUNCT
ejpam-6489	262	8	≤	≤	NUM
ejpam-6489	263	1	ξñג	ξñג	NOUN
ejpam-6489	263	2	(	(	PUNCT
ejpam-6489	263	3	ϕ̃)∨ξñג	ϕ̃)∨ξñג	PROPN
ejpam-6489	263	4	(	(	PUNCT
ejpam-6489	263	5	η̃	η̃	PROPN
ejpam-6489	263	6	)	)	PUNCT
ejpam-6489	263	7	⇒	⇒	PROPN
ejpam-6489	263	8	r̃ñג	r̃ñג	PROPN
ejpam-6489	263	9	(	(	PUNCT
ejpam-6489	263	10	[	[	X
ejpam-6489	263	11	ϕ̃	ϕ̃	PROPN
ejpam-6489	263	12	,	,	PUNCT
ejpam-6489	263	13	η̃])ei2πω̃	η̃])ei2πω̃	PROPN
ejpam-6489	263	14	n	n	PRON
ejpam-6489	263	15	̃ג	̃ג	NOUN
ejpam-6489	263	16	(	(	PUNCT
ejpam-6489	263	17	[	[	X
ejpam-6489	263	18	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	263	19	]	]	X
ejpam-6489	263	20	)	)	PUNCT
ejpam-6489	263	21	≥	≥	NOUN
ejpam-6489	263	22	r̃ñג	r̃ñג	PROPN
ejpam-6489	263	23	(	(	PUNCT
ejpam-6489	263	24	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	263	25	n	n	PRON
ejpam-6489	263	26	̃ג	̃ג	PROPN
ejpam-6489	263	27	(	(	PUNCT
ejpam-6489	263	28	ϕ̃)∨r̃ñג	ϕ̃)∨r̃ñג	PROPN
ejpam-6489	263	29	(	(	PUNCT
ejpam-6489	263	30	η̃)ei2πω̃	η̃)ei2πω̃	PROPN
ejpam-6489	263	31	n	n	PRON
ejpam-6489	263	32	̃ג	̃ג	PROPN
ejpam-6489	263	33	(	(	PUNCT
ejpam-6489	263	34	η̃	η̃	PROPN
ejpam-6489	263	35	)	)	PUNCT
ejpam-6489	263	36	,	,	PUNCT
ejpam-6489	263	37	(	(	PUNCT
ejpam-6489	263	38	ix	ix	ADV
ejpam-6489	263	39	)	)	PUNCT
ejpam-6489	263	40	ζ̃ג([ϕ̃	ζ̃ג([ϕ̃	PROPN
ejpam-6489	263	41	,	,	PUNCT
ejpam-6489	263	42	η̃	η̃	PROPN
ejpam-6489	263	43	]	]	PUNCT
ejpam-6489	263	44	)	)	PUNCT
ejpam-6489	263	45	≤	≤	NUM
ejpam-6489	264	1	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	264	2	)	)	PUNCT
ejpam-6489	264	3	∨	∨	NUM
ejpam-6489	264	4	ζ̃ג(η̃	ζ̃ג(η̃	NOUN
ejpam-6489	264	5	)	)	PUNCT
ejpam-6489	264	6	⇒	⇒	NOUN
ejpam-6489	264	7	r̃̃ג([ϕ̃	r̃̃ג([ϕ̃	VERB
ejpam-6489	264	8	,	,	PUNCT
ejpam-6489	264	9	η̃])e	η̃])e	PROPN
ejpam-6489	264	10	i2πω̃̃ג([ϕ̃,η̃	i2πω̃̃ג([ϕ̃,η̃	X
ejpam-6489	264	11	]	]	X
ejpam-6489	264	12	)	)	PUNCT
ejpam-6489	264	13	≥	≥	NOUN
ejpam-6489	264	14	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	VERB
ejpam-6489	264	15	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	264	16	)	)	PUNCT
ejpam-6489	264	17	∨	∨	NUM
ejpam-6489	264	18	r̃̃ג(η̃)e	r̃̃ג(η̃)e	VERB
ejpam-6489	264	19	i2πω̃̃ג(η̃	i2πω̃̃ג(η̃	NOUN
ejpam-6489	264	20	)	)	PUNCT
ejpam-6489	264	21	.	.	PUNCT
ejpam-6489	265	1	when	when	SCONJ
ejpam-6489	265	2	the	the	DET
ejpam-6489	265	3	conditions	condition	NOUN
ejpam-6489	265	4	(	(	PUNCT
ejpam-6489	265	5	vii	vii	PROPN
ejpam-6489	265	6	)	)	PUNCT
ejpam-6489	265	7	,	,	PUNCT
ejpam-6489	265	8	(	(	PUNCT
ejpam-6489	265	9	viii	viii	NOUN
ejpam-6489	265	10	)	)	PUNCT
ejpam-6489	265	11	and	and	CCONJ
ejpam-6489	265	12	(	(	PUNCT
ejpam-6489	265	13	ix	ix	X
ejpam-6489	265	14	)	)	PUNCT
ejpam-6489	265	15	are	be	AUX
ejpam-6489	265	16	modified	modify	VERB
ejpam-6489	265	17	to	to	ADP
ejpam-6489	265	18	(	(	PUNCT
ejpam-6489	265	19	x	x	X
ejpam-6489	265	20	)	)	PUNCT
ejpam-6489	265	21	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	266	1	(	(	PUNCT
ejpam-6489	266	2	[	[	X
ejpam-6489	266	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	266	4	,	,	PUNCT
ejpam-6489	266	5	η̃	η̃	PROPN
ejpam-6489	266	6	]	]	PUNCT
ejpam-6489	266	7	)	)	PUNCT
ejpam-6489	266	8	≥	≥	X
ejpam-6489	266	9	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	266	10	(	(	PUNCT
ejpam-6489	266	11	ϕ̃	ϕ̃	PROPN
ejpam-6489	266	12	)	)	PUNCT
ejpam-6489	266	13	∨	∨	NUM
ejpam-6489	266	14	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	266	15	(	(	PUNCT
ejpam-6489	266	16	η̃	η̃	PROPN
ejpam-6489	266	17	)	)	PUNCT
ejpam-6489	266	18	⇒	⇒	VERB
ejpam-6489	266	19	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	266	20	(	(	PUNCT
ejpam-6489	267	1	[	[	X
ejpam-6489	267	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	267	3	,	,	PUNCT
ejpam-6489	267	4	η̃])e	η̃])e	PROPN
ejpam-6489	267	5	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	267	6	̃ג	̃ג	NOUN
ejpam-6489	267	7	(	(	PUNCT
ejpam-6489	267	8	[	[	X
ejpam-6489	267	9	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	267	10	]	]	X
ejpam-6489	267	11	)	)	PUNCT
ejpam-6489	267	12	≥	≥	NOUN
ejpam-6489	267	13	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	267	14	(	(	PUNCT
ejpam-6489	267	15	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	267	16	i2πω̃p	i2πω̃p	X
ejpam-6489	267	17	̃ג	̃ג	NOUN
ejpam-6489	267	18	(	(	PUNCT
ejpam-6489	267	19	ϕ̃	ϕ̃	PROPN
ejpam-6489	267	20	)	)	PUNCT
ejpam-6489	267	21	∨	∨	NOUN
ejpam-6489	267	22	r̃̃ג(η̃)e	r̃̃ג(η̃)e	VERB
ejpam-6489	267	23	i2πω̃p	i2πω̃p	PROPN
ejpam-6489	267	24	̃ג	̃ג	NOUN
ejpam-6489	267	25	(	(	PUNCT
ejpam-6489	267	26	η̃	η̃	PROPN
ejpam-6489	267	27	)	)	PUNCT
ejpam-6489	267	28	,	,	PUNCT
ejpam-6489	267	29	(	(	PUNCT
ejpam-6489	267	30	xi	xi	NOUN
ejpam-6489	267	31	)	)	PUNCT
ejpam-6489	267	32	ξñג	ξñג	NOUN
ejpam-6489	268	1	(	(	PUNCT
ejpam-6489	268	2	[	[	X
ejpam-6489	268	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	268	4	,	,	PUNCT
ejpam-6489	268	5	η̃	η̃	PROPN
ejpam-6489	268	6	]	]	PUNCT
ejpam-6489	268	7	)	)	PUNCT
ejpam-6489	268	8	≤	≤	NUM
ejpam-6489	268	9	ξñג	ξñג	NOUN
ejpam-6489	268	10	(	(	PUNCT
ejpam-6489	268	11	ϕ̃)∧ξñג	ϕ̃)∧ξñג	PROPN
ejpam-6489	268	12	(	(	PUNCT
ejpam-6489	268	13	η̃	η̃	PROPN
ejpam-6489	268	14	)	)	PUNCT
ejpam-6489	269	1	⇒	⇒	PROPN
ejpam-6489	269	2	r̃ñג	r̃ñג	PROPN
ejpam-6489	269	3	(	(	PUNCT
ejpam-6489	269	4	[	[	X
ejpam-6489	269	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	269	6	,	,	PUNCT
ejpam-6489	269	7	η̃])ei2πω̃	η̃])ei2πω̃	PROPN
ejpam-6489	269	8	n	n	PRON
ejpam-6489	269	9	̃ג	̃ג	NOUN
ejpam-6489	269	10	(	(	PUNCT
ejpam-6489	269	11	[	[	X
ejpam-6489	269	12	ϕ̃,η̃	ϕ̃,η̃	X
ejpam-6489	269	13	]	]	X
ejpam-6489	269	14	)	)	PUNCT
ejpam-6489	269	15	≥	≥	NOUN
ejpam-6489	269	16	r̃ñג	r̃ñג	PROPN
ejpam-6489	269	17	(	(	PUNCT
ejpam-6489	269	18	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	269	19	n	n	PRON
ejpam-6489	269	20	̃ג	̃ג	PROPN
ejpam-6489	269	21	(	(	PUNCT
ejpam-6489	269	22	ϕ̃)∧r̃ñג	ϕ̃)∧r̃ñג	PROPN
ejpam-6489	269	23	(	(	PUNCT
ejpam-6489	269	24	η̃)ei2πω̃	η̃)ei2πω̃	X
ejpam-6489	269	25	n	n	PRON
ejpam-6489	269	26	̃ג	̃ג	PROPN
ejpam-6489	269	27	(	(	PUNCT
ejpam-6489	269	28	η̃	η̃	PROPN
ejpam-6489	269	29	)	)	PUNCT
ejpam-6489	269	30	,	,	PUNCT
ejpam-6489	269	31	(	(	PUNCT
ejpam-6489	269	32	xii	xii	NOUN
ejpam-6489	269	33	)	)	PUNCT
ejpam-6489	269	34	ζ̃ג([ϕ̃	ζ̃ג([ϕ̃	PROPN
ejpam-6489	269	35	,	,	PUNCT
ejpam-6489	269	36	η̃	η̃	PROPN
ejpam-6489	269	37	]	]	PUNCT
ejpam-6489	269	38	)	)	PUNCT
ejpam-6489	269	39	≤	≤	NUM
ejpam-6489	270	1	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	NOUN
ejpam-6489	270	2	)	)	PUNCT
ejpam-6489	270	3	∧	∧	PROPN
ejpam-6489	270	4	ζ̃ג(η̃	ζ̃ג(η̃	NOUN
ejpam-6489	270	5	)	)	PUNCT
ejpam-6489	270	6	⇒	⇒	NOUN
ejpam-6489	270	7	r̃̃ג([ϕ̃	r̃̃ג([ϕ̃	VERB
ejpam-6489	270	8	,	,	PUNCT
ejpam-6489	270	9	η̃])e	η̃])e	PROPN
ejpam-6489	270	10	i2πω̃̃ג([ϕ̃,η̃	i2πω̃̃ג([ϕ̃,η̃	X
ejpam-6489	270	11	]	]	X
ejpam-6489	270	12	)	)	PUNCT
ejpam-6489	270	13	≥	≥	NOUN
ejpam-6489	270	14	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	VERB
ejpam-6489	270	15	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	270	16	)	)	PUNCT
ejpam-6489	270	17	∧	∧	PROPN
ejpam-6489	270	18	r̃̃ג(η̃)e	r̃̃ג(η̃)e	VERB
ejpam-6489	270	19	i2πω̃̃ג(η̃	i2πω̃̃ג(η̃	NOUN
ejpam-6489	270	20	)	)	PUNCT
ejpam-6489	270	21	,	,	PUNCT
ejpam-6489	270	22	the	the	DET
ejpam-6489	270	23	t	t	PROPN
ejpam-6489	270	24	cfs	cfs	PROPN
ejpam-6489	270	25	̃ג	̃ג	PROPN
ejpam-6489	270	26	is	be	AUX
ejpam-6489	270	27	a	a	DET
ejpam-6489	270	28	tripolar	tripolar	ADJ
ejpam-6489	270	29	complex	complex	ADJ
ejpam-6489	270	30	fuzzy	fuzzy	ADJ
ejpam-6489	270	31	lie	lie	NOUN
ejpam-6489	270	32	ideal	ideal	NOUN
ejpam-6489	270	33	(	(	PUNCT
ejpam-6489	270	34	shortly	shortly	ADV
ejpam-6489	270	35	,	,	PUNCT
ejpam-6489	270	36	t	t	PROPN
ejpam-6489	270	37	cfli	cfli	PROPN
ejpam-6489	270	38	)	)	PUNCT
ejpam-6489	270	39	on	on	ADP
ejpam-6489	270	40	l̃.	l̃.	ADJ
ejpam-6489	270	41	definition	definition	NOUN
ejpam-6489	270	42	11	11	NUM
ejpam-6489	270	43	.	.	PUNCT
ejpam-6489	271	1	let	let	VERB
ejpam-6489	271	2	̃ג	̃ג	NOUN
ejpam-6489	271	3	=	=	PRON
ejpam-6489	271	4	{	{	PUNCT
ejpam-6489	271	5	(	(	PUNCT
ejpam-6489	271	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	271	7	,	,	PUNCT
ejpam-6489	271	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	271	9	(	(	PUNCT
ejpam-6489	271	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	271	11	)	)	PUNCT
ejpam-6489	271	12	=	=	SYM
ejpam-6489	272	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	272	2	(	(	PUNCT
ejpam-6489	272	3	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	272	4	i2πω̃p	i2πω̃p	X
ejpam-6489	272	5	̃ג	̃ג	NOUN
ejpam-6489	272	6	(	(	PUNCT
ejpam-6489	272	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	272	8	)	)	PUNCT
ejpam-6489	272	9	,	,	PUNCT
ejpam-6489	272	10	ξñג	ξñג	PROPN
ejpam-6489	272	11	(	(	PUNCT
ejpam-6489	272	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	272	13	)	)	PUNCT
ejpam-6489	272	14	=	=	SYM
ejpam-6489	272	15	r̃ñג	r̃ñג	PROPN
ejpam-6489	272	16	(	(	PUNCT
ejpam-6489	272	17	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	272	18	p	p	X
ejpam-6489	272	19	̃ג	̃ג	PROPN
ejpam-6489	272	20	(	(	PUNCT
ejpam-6489	272	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	272	22	)	)	PUNCT
ejpam-6489	272	23	,	,	PUNCT
ejpam-6489	272	24	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	272	25	)	)	PUNCT
ejpam-6489	272	26	=	=	PUNCT
ejpam-6489	272	27	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	X
ejpam-6489	272	28	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	272	29	)	)	PUNCT
ejpam-6489	272	30	)	)	PUNCT
ejpam-6489	273	1	|	|	ADV
ejpam-6489	273	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	273	3	∈	∈	PROPN
ejpam-6489	273	4	l̃	l̃	PROPN
ejpam-6489	273	5	}	}	PUNCT
ejpam-6489	273	6	be	be	AUX
ejpam-6489	273	7	a	a	DET
ejpam-6489	273	8	t	t	NOUN
ejpam-6489	273	9	cfs	cfs	NOUN
ejpam-6489	273	10	on	on	ADP
ejpam-6489	273	11	l̃.	l̃.	NOUN
ejpam-6489	273	12	for	for	ADP
ejpam-6489	273	13	β̃	β̃	PROPN
ejpam-6489	273	14	∈	∈	PROPN
ejpam-6489	273	15	f	f	PROPN
ejpam-6489	273	16	and	and	CCONJ
ejpam-6489	273	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	273	18	∈	∈	PROPN
ejpam-6489	273	19	l̃	l̃	PROPN
ejpam-6489	273	20	,	,	PUNCT
ejpam-6489	273	21	define	define	VERB
ejpam-6489	273	22	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	273	23	=	=	PRON
ejpam-6489	273	24	{	{	PUNCT
ejpam-6489	273	25	(	(	PUNCT
ejpam-6489	273	26	ϕ̃	ϕ̃	PROPN
ejpam-6489	273	27	,	,	PUNCT
ejpam-6489	273	28	ξp	ξp	AUX
ejpam-6489	273	29	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	273	30	)	)	PUNCT
ejpam-6489	273	31	,	,	PUNCT
ejpam-6489	273	32	ξ	ξ	PROPN
ejpam-6489	273	33	n	n	PRON
ejpam-6489	273	34	β̃ñ	β̃ñ	PROPN
ejpam-6489	273	35	(	(	PUNCT
ejpam-6489	273	36	ϕ̃	ϕ̃	PROPN
ejpam-6489	273	37	)	)	PUNCT
ejpam-6489	273	38	,	,	PUNCT
ejpam-6489	273	39	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	273	40	)	)	PUNCT
ejpam-6489	273	41	)	)	PUNCT
ejpam-6489	274	1	|	|	ADV
ejpam-6489	274	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	274	3	∈	∈	PROPN
ejpam-6489	274	4	l̃	l̃	PROPN
ejpam-6489	274	5	}	}	PUNCT
ejpam-6489	274	6	,	,	PUNCT
ejpam-6489	274	7	where	where	SCONJ
ejpam-6489	274	8	m.	m.	NOUN
ejpam-6489	274	9	balamurugan	balamurugan	VERB
ejpam-6489	274	10	,	,	PUNCT
ejpam-6489	274	11	g.	g.	PROPN
ejpam-6489	274	12	ellammal	ellammal	PROPN
ejpam-6489	274	13	,	,	PUNCT
ejpam-6489	274	14	a.	a.	NOUN
ejpam-6489	274	15	iampan	iampan	PROPN
ejpam-6489	274	16	/	/	SYM
ejpam-6489	274	17	eur	eur	PROPN
ejpam-6489	274	18	.	.	PUNCT
ejpam-6489	275	1	j.	j.	PROPN
ejpam-6489	275	2	pure	pure	PROPN
ejpam-6489	275	3	appl	appl	PROPN
ejpam-6489	275	4	.	.	PROPN
ejpam-6489	275	5	math	math	PROPN
ejpam-6489	275	6	,	,	PUNCT
ejpam-6489	275	7	18	18	NUM
ejpam-6489	275	8	(	(	PUNCT
ejpam-6489	275	9	3	3	NUM
ejpam-6489	275	10	)	)	PUNCT
ejpam-6489	275	11	(	(	PUNCT
ejpam-6489	275	12	2025	2025	NUM
ejpam-6489	275	13	)	)	PUNCT
ejpam-6489	275	14	,	,	PUNCT
ejpam-6489	275	15	6489	6489	NUM
ejpam-6489	275	16	11	11	NUM
ejpam-6489	275	17	of	of	ADP
ejpam-6489	275	18	26	26	NUM
ejpam-6489	275	19	ξp	ξp	NUM
ejpam-6489	275	20	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	VERB
ejpam-6489	275	21	)	)	PUNCT
ejpam-6489	276	1	=	=	SYM
ejpam-6489	277	1			NOUN
ejpam-6489	277	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	277	3	(	(	PUNCT
ejpam-6489	277	4	β̃	β̃	PROPN
ejpam-6489	277	5	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	277	6	)	)	PUNCT
ejpam-6489	277	7	if	if	SCONJ
ejpam-6489	277	8	β̃	β̃	PROPN
ejpam-6489	277	9	̸=	̸=	PROPN
ejpam-6489	277	10	0	0	NUM
ejpam-6489	277	11	1	1	NUM
ejpam-6489	277	12	if	if	SCONJ
ejpam-6489	277	13	β̃	β̃	PROPN
ejpam-6489	277	14	=	=	SYM
ejpam-6489	277	15	0	0	NUM
ejpam-6489	277	16	,	,	PUNCT
ejpam-6489	277	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	278	1	=	=	NOUN
ejpam-6489	278	2	0	0	NUM
ejpam-6489	278	3	0	0	NUM
ejpam-6489	279	1	if	if	SCONJ
ejpam-6489	279	2	β̃	β̃	PROPN
ejpam-6489	279	3	=	=	SYM
ejpam-6489	279	4	0	0	NUM
ejpam-6489	279	5	,	,	PUNCT
ejpam-6489	279	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	279	7	̸=	̸=	PROPN
ejpam-6489	279	8	0	0	NUM
ejpam-6489	279	9	,	,	PUNCT
ejpam-6489	279	10	ξn	ξn	NOUN
ejpam-6489	279	11	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	NOUN
ejpam-6489	279	12	)	)	PUNCT
ejpam-6489	279	13	=	=	PUNCT
ejpam-6489	280	1			PRON
ejpam-6489	280	2	ξñג	ξñג	NOUN
ejpam-6489	280	3	(	(	PUNCT
ejpam-6489	280	4	β̃−1ϕ̃	β̃−1ϕ̃	NOUN
ejpam-6489	280	5	)	)	PUNCT
ejpam-6489	280	6	if	if	SCONJ
ejpam-6489	280	7	β̃	β̃	PROPN
ejpam-6489	280	8	̸=	̸=	PROPN
ejpam-6489	280	9	0	0	NUM
ejpam-6489	280	10	0	0	NUM
ejpam-6489	281	1	if	if	SCONJ
ejpam-6489	281	2	β̃	β̃	PROPN
ejpam-6489	281	3	=	=	SYM
ejpam-6489	281	4	0	0	NUM
ejpam-6489	281	5	,	,	PUNCT
ejpam-6489	281	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	281	7	=	=	NOUN
ejpam-6489	281	8	0	0	NUM
ejpam-6489	281	9	1	1	NUM
ejpam-6489	281	10	if	if	SCONJ
ejpam-6489	281	11	β̃	β̃	PROPN
ejpam-6489	281	12	=	=	SYM
ejpam-6489	281	13	0	0	NUM
ejpam-6489	281	14	,	,	PUNCT
ejpam-6489	281	15	ϕ̃	ϕ̃	PROPN
ejpam-6489	281	16	̸=	̸=	PROPN
ejpam-6489	281	17	0	0	NUM
ejpam-6489	281	18	,	,	PUNCT
ejpam-6489	281	19	and	and	CCONJ
ejpam-6489	281	20	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	281	21	)	)	PUNCT
ejpam-6489	281	22	=	=	PUNCT
ejpam-6489	282	1			PUNCT
ejpam-6489	282	2	ζ̃ג(β̃	ζ̃ג(β̃	PROPN
ejpam-6489	282	3	−1ϕ̃	−1ϕ̃	PRON
ejpam-6489	282	4	)	)	PUNCT
ejpam-6489	282	5	if	if	SCONJ
ejpam-6489	282	6	β̃	β̃	PROPN
ejpam-6489	282	7	̸=	̸=	PROPN
ejpam-6489	282	8	0	0	NUM
ejpam-6489	282	9	0	0	NUM
ejpam-6489	283	1	if	if	SCONJ
ejpam-6489	283	2	β̃	β̃	PROPN
ejpam-6489	283	3	=	=	SYM
ejpam-6489	283	4	0	0	NUM
ejpam-6489	283	5	,	,	PUNCT
ejpam-6489	283	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	283	7	=	=	NOUN
ejpam-6489	283	8	0	0	NUM
ejpam-6489	283	9	1	1	NUM
ejpam-6489	283	10	if	if	SCONJ
ejpam-6489	283	11	β̃	β̃	PROPN
ejpam-6489	283	12	=	=	SYM
ejpam-6489	283	13	0	0	NUM
ejpam-6489	283	14	,	,	PUNCT
ejpam-6489	283	15	ϕ̃	ϕ̃	PROPN
ejpam-6489	283	16	̸=	̸=	PROPN
ejpam-6489	283	17	0	0	NUM
ejpam-6489	283	18	.	.	PUNCT
ejpam-6489	283	19	example	example	NOUN
ejpam-6489	284	1	2	2	NUM
ejpam-6489	284	2	.	.	PUNCT
ejpam-6489	284	3	let	let	VERB
ejpam-6489	284	4	l̃	l̃	PROPN
ejpam-6489	284	5	=	=	PUNCT
ejpam-6489	284	6	{	{	PUNCT
ejpam-6489	284	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	284	8	,	,	PUNCT
ejpam-6489	284	9	η̃	η̃	PROPN
ejpam-6489	284	10	,	,	PUNCT
ejpam-6489	284	11	ρ̃	ρ̃	PROPN
ejpam-6489	284	12	}	}	PUNCT
ejpam-6489	284	13	and	and	CCONJ
ejpam-6489	284	14	define	define	VERB
ejpam-6489	284	15	the	the	DET
ejpam-6489	284	16	t	t	NOUN
ejpam-6489	284	17	cfs	cfs	PROPN
ejpam-6489	284	18	̃ג	̃ג	PROPN
ejpam-6489	284	19	on	on	ADP
ejpam-6489	284	20	l̃	l̃	PROPN
ejpam-6489	284	21	as	as	ADP
ejpam-6489	284	22	:	:	PUNCT
ejpam-6489	284	23	̃ג	̃ג	NOUN
ejpam-6489	284	24	=	=	SYM
ejpam-6489	284	25			PUNCT
ejpam-6489	284	26	(	(	PUNCT
ejpam-6489	284	27	ϕ̃	ϕ̃	PROPN
ejpam-6489	284	28	,	,	PUNCT
ejpam-6489	284	29	0.5ei2π(0.2	0.5ei2π(0.2	PROPN
ejpam-6489	284	30	)	)	PUNCT
ejpam-6489	284	31	,	,	PUNCT
ejpam-6489	284	32	0.4ei2π(0.2	0.4ei2π(0.2	NOUN
ejpam-6489	284	33	)	)	PUNCT
ejpam-6489	284	34	,	,	PUNCT
ejpam-6489	284	35	0.6ei2π(0.3	0.6ei2π(0.3	PROPN
ejpam-6489	284	36	)	)	PUNCT
ejpam-6489	284	37	)	)	PUNCT
ejpam-6489	284	38	,	,	PUNCT
ejpam-6489	284	39	(	(	PUNCT
ejpam-6489	284	40	η̃	η̃	PROPN
ejpam-6489	284	41	,	,	PUNCT
ejpam-6489	284	42	1ei2π(0	1ei2π(0	NUM
ejpam-6489	284	43	)	)	PUNCT
ejpam-6489	284	44	,	,	PUNCT
ejpam-6489	284	45	0ei2π(0	0ei2π(0	NUM
ejpam-6489	284	46	)	)	PUNCT
ejpam-6489	284	47	,	,	PUNCT
ejpam-6489	284	48	0ei2π(0	0ei2π(0	NUM
ejpam-6489	284	49	)	)	PUNCT
ejpam-6489	284	50	)	)	PUNCT
ejpam-6489	284	51	,	,	PUNCT
ejpam-6489	284	52	(	(	PUNCT
ejpam-6489	284	53	ρ̃	ρ̃	PROPN
ejpam-6489	284	54	,	,	PUNCT
ejpam-6489	284	55	0.8ei2π(0.1	0.8ei2π(0.1	PROPN
ejpam-6489	284	56	)	)	PUNCT
ejpam-6489	284	57	,	,	PUNCT
ejpam-6489	284	58	0.2ei2π(0.1	0.2ei2π(0.1	PROPN
ejpam-6489	284	59	)	)	PUNCT
ejpam-6489	284	60	,	,	PUNCT
ejpam-6489	284	61	0.7ei2π(0.25	0.7ei2π(0.25	NUM
ejpam-6489	284	62	)	)	PUNCT
ejpam-6489	284	63	)	)	PUNCT
ejpam-6489	285	1			NOUN
ejpam-6489	285	2	let	let	VERB
ejpam-6489	285	3	β̃	β̃	PROPN
ejpam-6489	285	4	=	=	SYM
ejpam-6489	285	5	1	1	X
ejpam-6489	285	6	.	.	PUNCT
ejpam-6489	285	7	then	then	ADV
ejpam-6489	285	8	ξp	ξp	ADP
ejpam-6489	285	9	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	VERB
ejpam-6489	285	10	)	)	PUNCT
ejpam-6489	285	11	=	=	SYM
ejpam-6489	286	1	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	286	2	(	(	PUNCT
ejpam-6489	286	3	β̃	β̃	PROPN
ejpam-6489	286	4	−1ϕ̃	−1ϕ̃	X
ejpam-6489	286	5	)	)	PUNCT
ejpam-6489	286	6	=	=	SYM
ejpam-6489	286	7	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	286	8	(	(	PUNCT
ejpam-6489	286	9	ϕ̃	ϕ̃	PROPN
ejpam-6489	286	10	)	)	PUNCT
ejpam-6489	286	11	and	and	CCONJ
ejpam-6489	286	12	similarly	similarly	ADV
ejpam-6489	286	13	for	for	ADP
ejpam-6489	286	14	ξn	ξn	NOUN
ejpam-6489	286	15	and	and	CCONJ
ejpam-6489	286	16	ζ	ζ	NOUN
ejpam-6489	286	17	.	.	PUNCT
ejpam-6489	287	1	therefore	therefore	ADV
ejpam-6489	287	2	,	,	PUNCT
ejpam-6489	287	3	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	287	4	=	=	SYM
ejpam-6489	287	5	̃ג	̃ג	PROPN
ejpam-6489	287	6	(	(	PUNCT
ejpam-6489	287	7	since	since	SCONJ
ejpam-6489	287	8	β̃	β̃	PROPN
ejpam-6489	287	9	=	=	SYM
ejpam-6489	287	10	1	1	X
ejpam-6489	287	11	)	)	PUNCT
ejpam-6489	287	12	now	now	ADV
ejpam-6489	287	13	consider	consider	VERB
ejpam-6489	287	14	β̃	β̃	PROPN
ejpam-6489	287	15	=	=	SYM
ejpam-6489	288	1	0	0	X
ejpam-6489	288	2	.	.	PUNCT
ejpam-6489	289	1	then	then	ADV
ejpam-6489	289	2	for	for	ADP
ejpam-6489	289	3	each	each	DET
ejpam-6489	289	4	ϕ̃	ϕ̃	PROPN
ejpam-6489	289	5	∈	∈	PROPN
ejpam-6489	289	6	l̃	l̃	PROPN
ejpam-6489	289	7	,	,	PUNCT
ejpam-6489	289	8	ξp	ξp	ADP
ejpam-6489	289	9	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	VERB
ejpam-6489	289	10	)	)	PUNCT
ejpam-6489	290	1	=	=	PRON
ejpam-6489	290	2	{	{	PUNCT
ejpam-6489	290	3	1	1	NUM
ejpam-6489	290	4	if	if	SCONJ
ejpam-6489	290	5	ϕ̃	ϕ̃	PROPN
ejpam-6489	290	6	=	=	NOUN
ejpam-6489	291	1	0	0	NUM
ejpam-6489	291	2	0	0	NUM
ejpam-6489	292	1	if	if	SCONJ
ejpam-6489	292	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	292	3	̸=	̸=	PROPN
ejpam-6489	292	4	0	0	NUM
ejpam-6489	292	5	,	,	PUNCT
ejpam-6489	292	6	ξn	ξn	PROPN
ejpam-6489	292	7	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	292	8	)	)	PUNCT
ejpam-6489	292	9	=	=	PRON
ejpam-6489	292	10	{	{	PUNCT
ejpam-6489	292	11	0	0	NUM
ejpam-6489	292	12	if	if	SCONJ
ejpam-6489	292	13	ϕ̃	ϕ̃	PROPN
ejpam-6489	292	14	=	=	NOUN
ejpam-6489	292	15	0	0	NUM
ejpam-6489	292	16	1	1	NUM
ejpam-6489	292	17	if	if	SCONJ
ejpam-6489	292	18	ϕ̃	ϕ̃	PROPN
ejpam-6489	292	19	̸=	̸=	PROPN
ejpam-6489	292	20	0	0	NUM
ejpam-6489	292	21	,	,	PUNCT
ejpam-6489	292	22	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	292	23	)	)	PUNCT
ejpam-6489	292	24	=	=	PRON
ejpam-6489	292	25	{	{	PUNCT
ejpam-6489	292	26	0	0	NUM
ejpam-6489	292	27	if	if	SCONJ
ejpam-6489	292	28	ϕ̃	ϕ̃	PROPN
ejpam-6489	292	29	=	=	NOUN
ejpam-6489	292	30	0	0	NUM
ejpam-6489	292	31	1	1	NUM
ejpam-6489	293	1	if	if	SCONJ
ejpam-6489	293	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	293	3	̸=	̸=	PROPN
ejpam-6489	293	4	0	0	PUNCT
ejpam-6489	294	1	so	so	ADV
ejpam-6489	294	2	,	,	PUNCT
ejpam-6489	294	3	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	294	4	=	=	PUNCT
ejpam-6489	294	5			PUNCT
ejpam-6489	294	6	(	(	PUNCT
ejpam-6489	294	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	294	8	,	,	PUNCT
ejpam-6489	294	9	0	0	NUM
ejpam-6489	294	10	,	,	PUNCT
ejpam-6489	294	11	1	1	NUM
ejpam-6489	294	12	,	,	PUNCT
ejpam-6489	294	13	1	1	NUM
ejpam-6489	294	14	)	)	PUNCT
ejpam-6489	294	15	,	,	PUNCT
ejpam-6489	294	16	(	(	PUNCT
ejpam-6489	294	17	η̃	η̃	PROPN
ejpam-6489	294	18	,	,	PUNCT
ejpam-6489	294	19	1	1	NUM
ejpam-6489	294	20	,	,	PUNCT
ejpam-6489	294	21	0	0	NUM
ejpam-6489	294	22	,	,	PUNCT
ejpam-6489	294	23	0	0	NUM
ejpam-6489	294	24	)	)	PUNCT
ejpam-6489	294	25	,	,	PUNCT
ejpam-6489	294	26	(	(	PUNCT
ejpam-6489	294	27	ρ̃	ρ̃	PROPN
ejpam-6489	294	28	,	,	PUNCT
ejpam-6489	294	29	0	0	NUM
ejpam-6489	294	30	,	,	PUNCT
ejpam-6489	294	31	1	1	NUM
ejpam-6489	294	32	,	,	PUNCT
ejpam-6489	294	33	1	1	X
ejpam-6489	294	34	)	)	PUNCT
ejpam-6489	294	35			NOUN
ejpam-6489	294	36	theorem	theorem	VERB
ejpam-6489	294	37	5	5	NUM
ejpam-6489	294	38	.	.	PUNCT
ejpam-6489	295	1	let	let	VERB
ejpam-6489	295	2	̃ג	̃ג	NOUN
ejpam-6489	295	3	be	be	AUX
ejpam-6489	295	4	a	a	DET
ejpam-6489	295	5	t	t	NOUN
ejpam-6489	295	6	cfls	cfls	NOUN
ejpam-6489	295	7	on	on	ADP
ejpam-6489	295	8	.̃ג	.̃ג	NUM
ejpam-6489	295	9	then	then	ADV
ejpam-6489	295	10	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	295	11	is	be	AUX
ejpam-6489	295	12	also	also	ADV
ejpam-6489	295	13	a	a	DET
ejpam-6489	295	14	t	t	NOUN
ejpam-6489	295	15	cfls	cfls	NOUN
ejpam-6489	295	16	for	for	ADP
ejpam-6489	295	17	any	any	DET
ejpam-6489	295	18	β̃	β̃	PROPN
ejpam-6489	295	19	∈	∈	PROPN
ejpam-6489	295	20	f	f	X
ejpam-6489	295	21	.	.	PUNCT
ejpam-6489	296	1	proof	proof	NOUN
ejpam-6489	296	2	.	.	PUNCT
ejpam-6489	297	1	let	let	VERB
ejpam-6489	297	2	̃ג	̃ג	NOUN
ejpam-6489	297	3	=	=	PRON
ejpam-6489	297	4	{	{	PUNCT
ejpam-6489	297	5	(	(	PUNCT
ejpam-6489	297	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	297	7	,	,	PUNCT
ejpam-6489	297	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	297	9	(	(	PUNCT
ejpam-6489	297	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	297	11	)	)	PUNCT
ejpam-6489	297	12	=	=	SYM
ejpam-6489	298	1	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	298	2	(	(	PUNCT
ejpam-6489	298	3	ϕ̃)e	ϕ̃)e	PROPN
ejpam-6489	298	4	i2πω̃p	i2πω̃p	X
ejpam-6489	298	5	̃ג	̃ג	NOUN
ejpam-6489	298	6	(	(	PUNCT
ejpam-6489	298	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	298	8	)	)	PUNCT
ejpam-6489	298	9	,	,	PUNCT
ejpam-6489	298	10	ξñג	ξñג	PROPN
ejpam-6489	298	11	(	(	PUNCT
ejpam-6489	298	12	ϕ̃	ϕ̃	PROPN
ejpam-6489	298	13	)	)	PUNCT
ejpam-6489	298	14	=	=	SYM
ejpam-6489	298	15	r̃ñג	r̃ñג	PROPN
ejpam-6489	298	16	(	(	PUNCT
ejpam-6489	298	17	ϕ̃)ei2πω̃	ϕ̃)ei2πω̃	PROPN
ejpam-6489	298	18	p	p	X
ejpam-6489	298	19	̃ג	̃ג	PROPN
ejpam-6489	298	20	(	(	PUNCT
ejpam-6489	298	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	298	22	)	)	PUNCT
ejpam-6489	298	23	,	,	PUNCT
ejpam-6489	298	24	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	298	25	)	)	PUNCT
ejpam-6489	298	26	=	=	PUNCT
ejpam-6489	298	27	r̃̃ג(ϕ̃)e	r̃̃ג(ϕ̃)e	X
ejpam-6489	298	28	i2πω̃̃ג(ϕ̃	i2πω̃̃ג(ϕ̃	NOUN
ejpam-6489	298	29	)	)	PUNCT
ejpam-6489	298	30	)	)	PUNCT
ejpam-6489	299	1	|	|	ADV
ejpam-6489	299	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	299	3	∈	∈	PROPN
ejpam-6489	299	4	l̃	l̃	PROPN
ejpam-6489	299	5	}	}	PUNCT
ejpam-6489	299	6	be	be	AUX
ejpam-6489	299	7	a	a	DET
ejpam-6489	299	8	t	t	NOUN
ejpam-6489	299	9	cfls	cfls	NOUN
ejpam-6489	299	10	on	on	ADP
ejpam-6489	299	11	l̃.	l̃.	ADJ
ejpam-6489	299	12	define	define	VERB
ejpam-6489	299	13	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	299	14	=	=	PRON
ejpam-6489	299	15	{	{	PUNCT
ejpam-6489	299	16	(	(	PUNCT
ejpam-6489	299	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	299	18	,	,	PUNCT
ejpam-6489	299	19	ξp	ξp	ADP
ejpam-6489	299	20	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	299	21	)	)	PUNCT
ejpam-6489	299	22	,	,	PUNCT
ejpam-6489	299	23	ξ	ξ	PROPN
ejpam-6489	299	24	n	n	PRON
ejpam-6489	299	25	β̃ñ	β̃ñ	PROPN
ejpam-6489	299	26	(	(	PUNCT
ejpam-6489	299	27	ϕ̃	ϕ̃	PROPN
ejpam-6489	299	28	)	)	PUNCT
ejpam-6489	299	29	,	,	PUNCT
ejpam-6489	299	30	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	299	31	)	)	PUNCT
ejpam-6489	299	32	)	)	PUNCT
ejpam-6489	300	1	|	|	ADV
ejpam-6489	300	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	300	3	∈	∈	PROPN
ejpam-6489	300	4	l̃	l̃	PROPN
ejpam-6489	300	5	}	}	PUNCT
ejpam-6489	300	6	,	,	PUNCT
ejpam-6489	300	7	where	where	SCONJ
ejpam-6489	300	8	ξp	ξp	PART
ejpam-6489	300	9	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	VERB
ejpam-6489	300	10	)	)	PUNCT
ejpam-6489	300	11	=	=	SYM
ejpam-6489	301	1	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	301	2	(	(	PUNCT
ejpam-6489	301	3	β̃	β̃	PROPN
ejpam-6489	301	4	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	301	5	)	)	PUNCT
ejpam-6489	301	6	,	,	PUNCT
ejpam-6489	301	7	m.	m.	NOUN
ejpam-6489	301	8	balamurugan	balamurugan	VERB
ejpam-6489	301	9	,	,	PUNCT
ejpam-6489	301	10	g.	g.	PROPN
ejpam-6489	301	11	ellammal	ellammal	PROPN
ejpam-6489	301	12	,	,	PUNCT
ejpam-6489	301	13	a.	a.	NOUN
ejpam-6489	301	14	iampan	iampan	PROPN
ejpam-6489	301	15	/	/	SYM
ejpam-6489	301	16	eur	eur	PROPN
ejpam-6489	301	17	.	.	PUNCT
ejpam-6489	302	1	j.	j.	PROPN
ejpam-6489	302	2	pure	pure	PROPN
ejpam-6489	302	3	appl	appl	PROPN
ejpam-6489	302	4	.	.	PROPN
ejpam-6489	302	5	math	math	PROPN
ejpam-6489	302	6	,	,	PUNCT
ejpam-6489	302	7	18	18	NUM
ejpam-6489	302	8	(	(	PUNCT
ejpam-6489	302	9	3	3	NUM
ejpam-6489	302	10	)	)	PUNCT
ejpam-6489	302	11	(	(	PUNCT
ejpam-6489	302	12	2025	2025	NUM
ejpam-6489	302	13	)	)	PUNCT
ejpam-6489	302	14	,	,	PUNCT
ejpam-6489	302	15	6489	6489	NUM
ejpam-6489	302	16	12	12	NUM
ejpam-6489	302	17	of	of	ADP
ejpam-6489	302	18	26	26	NUM
ejpam-6489	302	19	ξn	ξn	NOUN
ejpam-6489	302	20	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	302	21	)	)	PUNCT
ejpam-6489	302	22	=	=	SYM
ejpam-6489	302	23	ξñג	ξñג	NOUN
ejpam-6489	302	24	(	(	PUNCT
ejpam-6489	302	25	β̃−1ϕ̃	β̃−1ϕ̃	NOUN
ejpam-6489	302	26	)	)	PUNCT
ejpam-6489	302	27	,	,	PUNCT
ejpam-6489	302	28	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	302	29	)	)	PUNCT
ejpam-6489	302	30	=	=	PUNCT
ejpam-6489	302	31	ζ̃ג(β̃	ζ̃ג(β̃	PROPN
ejpam-6489	302	32	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	302	33	)	)	PUNCT
ejpam-6489	302	34	.	.	PUNCT
ejpam-6489	303	1	we	we	PRON
ejpam-6489	303	2	need	need	VERB
ejpam-6489	303	3	to	to	PART
ejpam-6489	303	4	verify	verify	VERB
ejpam-6489	303	5	that	that	SCONJ
ejpam-6489	303	6	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	303	7	is	be	AUX
ejpam-6489	303	8	also	also	ADV
ejpam-6489	303	9	a	a	DET
ejpam-6489	303	10	t	t	NOUN
ejpam-6489	303	11	cfls	cfls	NOUN
ejpam-6489	303	12	for	for	ADP
ejpam-6489	303	13	any	any	DET
ejpam-6489	303	14	β̃	β̃	PROPN
ejpam-6489	303	15	∈	∈	PROPN
ejpam-6489	303	16	f	f	X
ejpam-6489	303	17	.	.	PUNCT
ejpam-6489	304	1	let	let	VERB
ejpam-6489	304	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	304	3	,	,	PUNCT
ejpam-6489	304	4	η̃	η̃	PROPN
ejpam-6489	304	5	∈	∈	PROPN
ejpam-6489	304	6	l̃.	l̃.	ADJ
ejpam-6489	304	7	case	case	NOUN
ejpam-6489	304	8	1	1	X
ejpam-6489	304	9	.	.	X
ejpam-6489	304	10	ξp	ξp	ADP
ejpam-6489	304	11	β̃̃ג(ϕ̃+	β̃̃ג(ϕ̃+	PROPN
ejpam-6489	304	12	η̃	η̃	PROPN
ejpam-6489	304	13	)	)	PUNCT
ejpam-6489	305	1	=	=	SYM
ejpam-6489	305	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	305	3	(	(	PUNCT
ejpam-6489	305	4	β̃	β̃	PROPN
ejpam-6489	305	5	−1(ϕ̃+	−1(ϕ̃+	PROPN
ejpam-6489	305	6	η̃	η̃	PROPN
ejpam-6489	305	7	)	)	PUNCT
ejpam-6489	305	8	)	)	PUNCT
ejpam-6489	306	1	=	=	SYM
ejpam-6489	307	1	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	307	2	(	(	PUNCT
ejpam-6489	307	3	β̃	β̃	PROPN
ejpam-6489	307	4	−1ϕ̃+	−1ϕ̃+	PROPN
ejpam-6489	307	5	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	307	6	)	)	PUNCT
ejpam-6489	307	7	≥	≥	X
ejpam-6489	307	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	307	9	(	(	PUNCT
ejpam-6489	307	10	β̃	β̃	PROPN
ejpam-6489	307	11	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	307	12	)	)	PUNCT
ejpam-6489	307	13	∧	∧	PROPN
ejpam-6489	307	14	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	307	15	(	(	PUNCT
ejpam-6489	307	16	β̃	β̃	PROPN
ejpam-6489	307	17	−1η̃	−1η̃	NOUN
ejpam-6489	307	18	)	)	PUNCT
ejpam-6489	307	19	=	=	PRON
ejpam-6489	307	20	ξp	ξp	PART
ejpam-6489	307	21	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	ADJ
ejpam-6489	307	22	)	)	PUNCT
ejpam-6489	307	23	∧	∧	NOUN
ejpam-6489	307	24	ξp	ξp	NOUN
ejpam-6489	307	25	β̃̃ג(η̃	β̃̃ג(η̃	NUM
ejpam-6489	307	26	)	)	PUNCT
ejpam-6489	307	27	.	.	PUNCT
ejpam-6489	308	1	case	case	NOUN
ejpam-6489	308	2	2	2	X
ejpam-6489	308	3	.	.	X
ejpam-6489	308	4	ξn	ξn	PROPN
ejpam-6489	308	5	β̃̃ג(ϕ̃+	β̃̃ג(ϕ̃+	PROPN
ejpam-6489	308	6	η̃	η̃	PROPN
ejpam-6489	308	7	)	)	PUNCT
ejpam-6489	309	1	=	=	SYM
ejpam-6489	309	2	ξñג	ξñג	PROPN
ejpam-6489	309	3	(	(	PUNCT
ejpam-6489	309	4	β̃−1(ϕ̃+	β̃−1(ϕ̃+	PROPN
ejpam-6489	309	5	η̃	η̃	PROPN
ejpam-6489	309	6	)	)	PUNCT
ejpam-6489	309	7	)	)	PUNCT
ejpam-6489	310	1	=	=	PUNCT
ejpam-6489	310	2	ξñג	ξñג	NOUN
ejpam-6489	310	3	(	(	PUNCT
ejpam-6489	310	4	β̃−1ϕ̃+	β̃−1ϕ̃+	NOUN
ejpam-6489	310	5	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	310	6	)	)	PUNCT
ejpam-6489	310	7	≤	≤	NUM
ejpam-6489	311	1	ξñג	ξñג	NOUN
ejpam-6489	311	2	(	(	PUNCT
ejpam-6489	311	3	β̃−1ϕ̃	β̃−1ϕ̃	NOUN
ejpam-6489	311	4	)	)	PUNCT
ejpam-6489	311	5	∨	∨	NUM
ejpam-6489	311	6	ξñג	ξñג	PROPN
ejpam-6489	311	7	(	(	PUNCT
ejpam-6489	311	8	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	311	9	)	)	PUNCT
ejpam-6489	311	10	=	=	SYM
ejpam-6489	311	11	ξn	ξn	PROPN
ejpam-6489	311	12	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	311	13	)	)	PUNCT
ejpam-6489	311	14	∨	∨	NOUN
ejpam-6489	311	15	ξn	ξn	PROPN
ejpam-6489	311	16	β̃̃ג(η̃	β̃̃ג(η̃	PROPN
ejpam-6489	311	17	)	)	PUNCT
ejpam-6489	311	18	.	.	PUNCT
ejpam-6489	312	1	case	case	NOUN
ejpam-6489	312	2	3	3	X
ejpam-6489	312	3	.	.	PUNCT
ejpam-6489	313	1	ζβ̃̃ג(ϕ̃+	ζβ̃̃ג(ϕ̃+	PROPN
ejpam-6489	313	2	η̃	η̃	PROPN
ejpam-6489	313	3	)	)	PUNCT
ejpam-6489	314	1	=	=	PUNCT
ejpam-6489	314	2	ζ̃ג(β̃	ζ̃ג(β̃	PROPN
ejpam-6489	314	3	−1(ϕ̃+	−1(ϕ̃+	NUM
ejpam-6489	314	4	η̃	η̃	PROPN
ejpam-6489	314	5	)	)	PUNCT
ejpam-6489	314	6	)	)	PUNCT
ejpam-6489	315	1	=	=	PUNCT
ejpam-6489	315	2	ζ̃ג(β̃	ζ̃ג(β̃	VERB
ejpam-6489	315	3	−1ϕ̃+	−1ϕ̃+	PROPN
ejpam-6489	315	4	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	315	5	)	)	PUNCT
ejpam-6489	315	6	≤	≤	NOUN
ejpam-6489	316	1	ζ̃ג(β̃	ζ̃ג(β̃	PROPN
ejpam-6489	316	2	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	316	3	)	)	PUNCT
ejpam-6489	316	4	∨	∨	NOUN
ejpam-6489	316	5	ζ̃ג(β̃	ζ̃ג(β̃	PROPN
ejpam-6489	316	6	−1η̃	−1η̃	NOUN
ejpam-6489	316	7	)	)	PUNCT
ejpam-6489	317	1	=	=	SYM
ejpam-6489	317	2	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	317	3	)	)	PUNCT
ejpam-6489	317	4	∨	∨	NOUN
ejpam-6489	317	5	ζβ̃̃ג(η̃	ζβ̃̃ג(η̃	NOUN
ejpam-6489	317	6	)	)	PUNCT
ejpam-6489	317	7	.	.	PUNCT
ejpam-6489	318	1	case	case	NOUN
ejpam-6489	318	2	4	4	NUM
ejpam-6489	318	3	.	.	PUNCT
ejpam-6489	318	4	ξp	ξp	ADP
ejpam-6489	318	5	β̃̃ג(β̃ϕ̃	β̃̃ג(β̃ϕ̃	ADV
ejpam-6489	318	6	)	)	PUNCT
ejpam-6489	319	1	=	=	SYM
ejpam-6489	319	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	319	3	(	(	PUNCT
ejpam-6489	319	4	β̃	β̃	PROPN
ejpam-6489	319	5	−1β̃ϕ̃	−1β̃ϕ̃	PROPN
ejpam-6489	319	6	)	)	PUNCT
ejpam-6489	320	1	=	=	SYM
ejpam-6489	320	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	320	3	(	(	PUNCT
ejpam-6489	320	4	β̃(β̃	β̃(β̃	NUM
ejpam-6489	320	5	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	320	6	)	)	PUNCT
ejpam-6489	320	7	)	)	PUNCT
ejpam-6489	320	8	≥	≥	X
ejpam-6489	320	9	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	320	10	(	(	PUNCT
ejpam-6489	320	11	β̃	β̃	PROPN
ejpam-6489	320	12	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	320	13	)	)	PUNCT
ejpam-6489	320	14	=	=	PRON
ejpam-6489	320	15	ξp	ξp	PROPN
ejpam-6489	320	16	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	ADJ
ejpam-6489	320	17	)	)	PUNCT
ejpam-6489	320	18	.	.	PUNCT
ejpam-6489	321	1	case	case	NOUN
ejpam-6489	321	2	5	5	NUM
ejpam-6489	321	3	.	.	PUNCT
ejpam-6489	321	4	ξn	ξn	PROPN
ejpam-6489	321	5	β̃̃ג(β̃ϕ̃	β̃̃ג(β̃ϕ̃	NOUN
ejpam-6489	321	6	)	)	PUNCT
ejpam-6489	322	1	=	=	SYM
ejpam-6489	322	2	ξñג	ξñג	PROPN
ejpam-6489	322	3	(	(	PUNCT
ejpam-6489	322	4	β̃−1β̃ϕ̃	β̃−1β̃ϕ̃	ADJ
ejpam-6489	322	5	)	)	PUNCT
ejpam-6489	322	6	=	=	SYM
ejpam-6489	322	7	ξñג	ξñג	NOUN
ejpam-6489	322	8	(	(	PUNCT
ejpam-6489	322	9	β̃(β̃−1ϕ̃	β̃(β̃−1ϕ̃	ADJ
ejpam-6489	322	10	)	)	PUNCT
ejpam-6489	322	11	)	)	PUNCT
ejpam-6489	323	1	≤	≤	NUM
ejpam-6489	323	2	ξñג	ξñג	NOUN
ejpam-6489	323	3	(	(	PUNCT
ejpam-6489	323	4	β̃−1ϕ̃	β̃−1ϕ̃	NOUN
ejpam-6489	323	5	)	)	PUNCT
ejpam-6489	323	6	=	=	SYM
ejpam-6489	323	7	ξn	ξn	PROPN
ejpam-6489	323	8	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	323	9	)	)	PUNCT
ejpam-6489	323	10	.	.	PUNCT
ejpam-6489	324	1	m.	m.	NOUN
ejpam-6489	324	2	balamurugan	balamurugan	PROPN
ejpam-6489	324	3	,	,	PUNCT
ejpam-6489	324	4	g.	g.	PROPN
ejpam-6489	324	5	ellammal	ellammal	PROPN
ejpam-6489	324	6	,	,	PUNCT
ejpam-6489	324	7	a.	a.	NOUN
ejpam-6489	324	8	iampan	iampan	PROPN
ejpam-6489	324	9	/	/	SYM
ejpam-6489	324	10	eur	eur	PROPN
ejpam-6489	324	11	.	.	PUNCT
ejpam-6489	325	1	j.	j.	PROPN
ejpam-6489	325	2	pure	pure	PROPN
ejpam-6489	325	3	appl	appl	PROPN
ejpam-6489	325	4	.	.	PROPN
ejpam-6489	325	5	math	math	PROPN
ejpam-6489	325	6	,	,	PUNCT
ejpam-6489	325	7	18	18	NUM
ejpam-6489	325	8	(	(	PUNCT
ejpam-6489	325	9	3	3	NUM
ejpam-6489	325	10	)	)	PUNCT
ejpam-6489	325	11	(	(	PUNCT
ejpam-6489	325	12	2025	2025	NUM
ejpam-6489	325	13	)	)	PUNCT
ejpam-6489	325	14	,	,	PUNCT
ejpam-6489	325	15	6489	6489	NUM
ejpam-6489	325	16	13	13	NUM
ejpam-6489	325	17	of	of	ADP
ejpam-6489	325	18	26	26	NUM
ejpam-6489	325	19	case	case	NOUN
ejpam-6489	325	20	6	6	NUM
ejpam-6489	325	21	.	.	PUNCT
ejpam-6489	325	22	ζβ̃̃ג(β̃ϕ̃	ζβ̃̃ג(β̃ϕ̃	NUM
ejpam-6489	325	23	)	)	PUNCT
ejpam-6489	326	1	=	=	PRON
ejpam-6489	326	2	ζ̃ג(β̃	ζ̃ג(β̃	VERB
ejpam-6489	326	3	−1β̃ϕ̃	−1β̃ϕ̃	NOUN
ejpam-6489	326	4	)	)	PUNCT
ejpam-6489	326	5	=	=	X
ejpam-6489	326	6	ζ̃ג(β̃(β̃	ζ̃ג(β̃(β̃	NOUN
ejpam-6489	326	7	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	326	8	)	)	PUNCT
ejpam-6489	326	9	)	)	PUNCT
ejpam-6489	326	10	≤	≤	NOUN
ejpam-6489	327	1	ζ̃ג(β̃	ζ̃ג(β̃	VERB
ejpam-6489	327	2	−1ϕ̃	−1ϕ̃	PRON
ejpam-6489	327	3	)	)	PUNCT
ejpam-6489	327	4	=	=	SYM
ejpam-6489	327	5	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	327	6	)	)	PUNCT
ejpam-6489	327	7	.	.	PUNCT
ejpam-6489	328	1	case	case	NOUN
ejpam-6489	328	2	7	7	NUM
ejpam-6489	328	3	.	.	X
ejpam-6489	328	4	ξp	ξp	ADP
ejpam-6489	328	5	β̃̃ג([ϕ̃	β̃̃ג([ϕ̃	PROPN
ejpam-6489	328	6	,	,	PUNCT
ejpam-6489	328	7	η̃	η̃	PROPN
ejpam-6489	328	8	]	]	PUNCT
ejpam-6489	328	9	)	)	PUNCT
ejpam-6489	329	1	=	=	SYM
ejpam-6489	329	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	329	3	(	(	PUNCT
ejpam-6489	329	4	β̃	β̃	PROPN
ejpam-6489	329	5	−1[ϕ̃	−1[ϕ̃	PROPN
ejpam-6489	329	6	,	,	PUNCT
ejpam-6489	329	7	η̃	η̃	PROPN
ejpam-6489	329	8	]	]	PUNCT
ejpam-6489	329	9	)	)	PUNCT
ejpam-6489	330	1	=	=	SYM
ejpam-6489	330	2	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	330	3	(	(	PUNCT
ejpam-6489	330	4	[	[	X
ejpam-6489	330	5	β̃	β̃	PROPN
ejpam-6489	330	6	−1ϕ̃	−1ϕ̃	X
ejpam-6489	330	7	,	,	PUNCT
ejpam-6489	330	8	β̃−1η̃	β̃−1η̃	PRON
ejpam-6489	330	9	]	]	PUNCT
ejpam-6489	330	10	)	)	PUNCT
ejpam-6489	330	11	≥	≥	X
ejpam-6489	330	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	330	13	(	(	PUNCT
ejpam-6489	330	14	β̃	β̃	PROPN
ejpam-6489	330	15	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	330	16	)	)	PUNCT
ejpam-6489	330	17	∧	∧	PROPN
ejpam-6489	330	18	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	330	19	(	(	PUNCT
ejpam-6489	330	20	β̃	β̃	PROPN
ejpam-6489	330	21	−1η̃	−1η̃	NOUN
ejpam-6489	330	22	)	)	PUNCT
ejpam-6489	330	23	=	=	PRON
ejpam-6489	330	24	ξp	ξp	PART
ejpam-6489	330	25	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	ADJ
ejpam-6489	330	26	)	)	PUNCT
ejpam-6489	330	27	∧	∧	NOUN
ejpam-6489	330	28	ξp	ξp	NOUN
ejpam-6489	330	29	β̃̃ג(η̃	β̃̃ג(η̃	NUM
ejpam-6489	330	30	)	)	PUNCT
ejpam-6489	330	31	.	.	PUNCT
ejpam-6489	331	1	case	case	NOUN
ejpam-6489	331	2	8	8	NUM
ejpam-6489	331	3	.	.	PUNCT
ejpam-6489	332	1	ξn	ξn	PROPN
ejpam-6489	332	2	β̃̃ג([ϕ̃	β̃̃ג([ϕ̃	PROPN
ejpam-6489	332	3	,	,	PUNCT
ejpam-6489	332	4	η̃	η̃	PROPN
ejpam-6489	332	5	]	]	PUNCT
ejpam-6489	332	6	)	)	PUNCT
ejpam-6489	333	1	=	=	SYM
ejpam-6489	333	2	ξñג	ξñג	NOUN
ejpam-6489	333	3	(	(	PUNCT
ejpam-6489	333	4	β̃−1[ϕ̃	β̃−1[ϕ̃	NOUN
ejpam-6489	333	5	,	,	PUNCT
ejpam-6489	333	6	η̃	η̃	PROPN
ejpam-6489	333	7	]	]	PUNCT
ejpam-6489	333	8	)	)	PUNCT
ejpam-6489	334	1	=	=	SYM
ejpam-6489	334	2	ξñג	ξñג	NOUN
ejpam-6489	334	3	(	(	PUNCT
ejpam-6489	334	4	[	[	X
ejpam-6489	334	5	β̃−1ϕ̃	β̃−1ϕ̃	X
ejpam-6489	334	6	,	,	PUNCT
ejpam-6489	334	7	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	334	8	]	]	X
ejpam-6489	334	9	)	)	PUNCT
ejpam-6489	334	10	≤	≤	NUM
ejpam-6489	335	1	ξñג	ξñג	NOUN
ejpam-6489	335	2	(	(	PUNCT
ejpam-6489	335	3	β̃−1ϕ̃	β̃−1ϕ̃	NOUN
ejpam-6489	335	4	)	)	PUNCT
ejpam-6489	335	5	∨	∨	NUM
ejpam-6489	335	6	ξñג	ξñג	PROPN
ejpam-6489	335	7	(	(	PUNCT
ejpam-6489	335	8	β̃−1η̃	β̃−1η̃	NOUN
ejpam-6489	335	9	)	)	PUNCT
ejpam-6489	335	10	=	=	SYM
ejpam-6489	335	11	ξn	ξn	PROPN
ejpam-6489	335	12	β̃̃ג(ϕ̃	β̃̃ג(ϕ̃	PROPN
ejpam-6489	335	13	)	)	PUNCT
ejpam-6489	335	14	∨	∨	NOUN
ejpam-6489	335	15	ξn	ξn	PROPN
ejpam-6489	335	16	β̃̃ג(η̃	β̃̃ג(η̃	PROPN
ejpam-6489	335	17	)	)	PUNCT
ejpam-6489	335	18	.	.	PUNCT
ejpam-6489	336	1	case	case	NOUN
ejpam-6489	336	2	9	9	NUM
ejpam-6489	336	3	.	.	PUNCT
ejpam-6489	337	1	ζβ̃̃ג([ϕ̃	ζβ̃̃ג([ϕ̃	NOUN
ejpam-6489	337	2	,	,	PUNCT
ejpam-6489	337	3	η̃	η̃	PROPN
ejpam-6489	337	4	]	]	PUNCT
ejpam-6489	337	5	)	)	PUNCT
ejpam-6489	338	1	=	=	SYM
ejpam-6489	338	2	ζ̃ג(β̃	ζ̃ג(β̃	VERB
ejpam-6489	338	3	−1[ϕ̃	−1[ϕ̃	NOUN
ejpam-6489	338	4	,	,	PUNCT
ejpam-6489	338	5	η̃	η̃	PROPN
ejpam-6489	338	6	]	]	PUNCT
ejpam-6489	338	7	)	)	PUNCT
ejpam-6489	339	1	=	=	SYM
ejpam-6489	339	2	ζ̃ג([β̃	ζ̃ג([β̃	PROPN
ejpam-6489	339	3	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	339	4	,	,	PUNCT
ejpam-6489	339	5	β̃−1η̃	β̃−1η̃	PRON
ejpam-6489	339	6	]	]	X
ejpam-6489	339	7	)	)	PUNCT
ejpam-6489	339	8	≤	≤	NOUN
ejpam-6489	339	9	ζ̃ג(β̃	ζ̃ג(β̃	VERB
ejpam-6489	339	10	−1ϕ̃	−1ϕ̃	NUM
ejpam-6489	339	11	)	)	PUNCT
ejpam-6489	339	12	∨	∨	NUM
ejpam-6489	339	13	ξñג	ξñג	PROPN
ejpam-6489	339	14	(	(	PUNCT
ejpam-6489	339	15	β̃−1η̃	β̃−1η̃	NUM
ejpam-6489	339	16	)	)	PUNCT
ejpam-6489	339	17	=	=	SYM
ejpam-6489	339	18	ζβ̃̃ג(ϕ̃	ζβ̃̃ג(ϕ̃	PROPN
ejpam-6489	339	19	)	)	PUNCT
ejpam-6489	339	20	∨	∨	NOUN
ejpam-6489	339	21	ζβ̃̃ג(η̃	ζβ̃̃ג(η̃	NOUN
ejpam-6489	339	22	)	)	PUNCT
ejpam-6489	339	23	.	.	PUNCT
ejpam-6489	340	1	hence	hence	ADV
ejpam-6489	340	2	,	,	PUNCT
ejpam-6489	340	3	β̃̃ג	β̃̃ג	PROPN
ejpam-6489	340	4	is	be	AUX
ejpam-6489	340	5	indeed	indeed	ADV
ejpam-6489	340	6	a	a	DET
ejpam-6489	340	7	t	t	NOUN
ejpam-6489	340	8	cfls	cfls	NOUN
ejpam-6489	340	9	on	on	ADP
ejpam-6489	340	10	l̃.	l̃.	ADJ
ejpam-6489	340	11	definition	definition	NOUN
ejpam-6489	340	12	12	12	NUM
ejpam-6489	340	13	.	.	PUNCT
ejpam-6489	341	1	let	let	VERB
ejpam-6489	341	2	̃ג	̃ג	NOUN
ejpam-6489	341	3	=	=	PRON
ejpam-6489	341	4	{	{	PUNCT
ejpam-6489	341	5	(	(	PUNCT
ejpam-6489	341	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	7	,	,	PUNCT
ejpam-6489	341	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	341	9	(	(	PUNCT
ejpam-6489	341	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	11	)	)	PUNCT
ejpam-6489	341	12	,	,	PUNCT
ejpam-6489	341	13	ξ	ξ	PROPN
ejpam-6489	341	14	n	n	PRON
ejpam-6489	341	15	̃ג	̃ג	PROPN
ejpam-6489	341	16	(	(	PUNCT
ejpam-6489	341	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	18	)	)	PUNCT
ejpam-6489	341	19	,	,	PUNCT
ejpam-6489	341	20	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	341	21	)	)	PUNCT
ejpam-6489	341	22	)	)	PUNCT
ejpam-6489	341	23	}	}	PUNCT
ejpam-6489	341	24	and	and	CCONJ
ejpam-6489	341	25	ℸ̃	ℸ̃	PROPN
ejpam-6489	341	26	=	=	SYM
ejpam-6489	341	27	{	{	PUNCT
ejpam-6489	341	28	(	(	PUNCT
ejpam-6489	341	29	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	30	,	,	PUNCT
ejpam-6489	341	31	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	341	32	(	(	PUNCT
ejpam-6489	341	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	34	)	)	PUNCT
ejpam-6489	341	35	,	,	PUNCT
ejpam-6489	341	36	ξ	ξ	PROPN
ejpam-6489	341	37	n	n	PRON
ejpam-6489	341	38	ℸ̃	ℸ̃	PROPN
ejpam-6489	341	39	(	(	PUNCT
ejpam-6489	341	40	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	41	)	)	PUNCT
ejpam-6489	341	42	,	,	PUNCT
ejpam-6489	341	43	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	341	44	)	)	PUNCT
ejpam-6489	341	45	)	)	PUNCT
ejpam-6489	341	46	}	}	PUNCT
ejpam-6489	341	47	be	be	AUX
ejpam-6489	341	48	two	two	NUM
ejpam-6489	341	49	t	t	NOUN
ejpam-6489	341	50	cfls	cfls	NOUN
ejpam-6489	341	51	on	on	ADP
ejpam-6489	341	52	l̃.	l̃.	ADJ
ejpam-6489	341	53	then	then	ADV
ejpam-6489	341	54	+	+	PROPN
ejpam-6489	341	55	̃ג	̃ג	ADJ
ejpam-6489	341	56	ℸ̃	ℸ̃	PROPN
ejpam-6489	341	57	=	=	SYM
ejpam-6489	341	58	{	{	PUNCT
ejpam-6489	341	59	(	(	PUNCT
ejpam-6489	341	60	ϕ̃	ϕ̃	PROPN
ejpam-6489	341	61	,	,	PUNCT
ejpam-6489	341	62	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	341	63	)	)	PUNCT
ejpam-6489	341	64	,	,	PUNCT
ejpam-6489	341	65	ξ	ξ	PROPN
ejpam-6489	341	66	n	n	NUM
ejpam-6489	341	67	,	,	PUNCT
ejpam-6489	341	68	ℸ̃(ϕ̃)+̃ג	ℸ̃(ϕ̃)+̃ג	PROPN
ejpam-6489	341	69	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	341	70	)	)	PUNCT
ejpam-6489	341	71	)	)	PUNCT
ejpam-6489	341	72	}	}	PUNCT
ejpam-6489	341	73	be	be	AUX
ejpam-6489	341	74	t	t	PROPN
ejpam-6489	341	75	cfs	cfs	NOUN
ejpam-6489	341	76	on	on	ADP
ejpam-6489	341	77	l̃	l̃	PROPN
ejpam-6489	341	78	given	give	VERB
ejpam-6489	341	79	by	by	ADP
ejpam-6489	341	80	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	341	81	)	)	PUNCT
ejpam-6489	342	1	=	=	PRON
ejpam-6489	342	2	{	{	PUNCT
ejpam-6489	342	3	supϕ̃=ε̃+ς̃	supϕ̃=ε̃+ς̃	X
ejpam-6489	342	4	{	{	PUNCT
ejpam-6489	342	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	342	6	(	(	PUNCT
ejpam-6489	342	7	ε̃	ε̃	PROPN
ejpam-6489	342	8	)	)	PUNCT
ejpam-6489	342	9	∧	∧	PROPN
ejpam-6489	342	10	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	342	11	(	(	PUNCT
ejpam-6489	342	12	ς̃	ς̃	PROPN
ejpam-6489	342	13	)	)	PUNCT
ejpam-6489	342	14	}	}	PUNCT
ejpam-6489	343	1	if	if	SCONJ
ejpam-6489	343	2	ϕ̃	ϕ̃	PROPN
ejpam-6489	343	3	=	=	SYM
ejpam-6489	343	4	ε̃+	ε̃+	VERB
ejpam-6489	343	5	ς̃	ς̃	PROPN
ejpam-6489	343	6	0	0	NUM
ejpam-6489	344	1	otherwise	otherwise	ADV
ejpam-6489	344	2	,	,	PUNCT
ejpam-6489	344	3	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	344	4	)	)	PUNCT
ejpam-6489	344	5	=	=	PRON
ejpam-6489	344	6	{	{	PUNCT
ejpam-6489	344	7	inf	inf	PROPN
ejpam-6489	344	8	ϕ̃=ε̃+ς̃	ϕ̃=ε̃+ς̃	PROPN
ejpam-6489	344	9	{	{	PUNCT
ejpam-6489	344	10	ξñג	ξñג	NOUN
ejpam-6489	344	11	(	(	PUNCT
ejpam-6489	344	12	ε̃	ε̃	PROPN
ejpam-6489	344	13	)	)	PUNCT
ejpam-6489	344	14	∨	∨	NUM
ejpam-6489	344	15	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	344	16	(	(	PUNCT
ejpam-6489	344	17	ς̃	ς̃	PROPN
ejpam-6489	344	18	)	)	PUNCT
ejpam-6489	344	19	}	}	PUNCT
ejpam-6489	344	20	if	if	SCONJ
ejpam-6489	344	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	344	22	=	=	PUNCT
ejpam-6489	344	23	ε̃+	ε̃+	VERB
ejpam-6489	344	24	ς̃	ς̃	PROPN
ejpam-6489	344	25	1	1	NUM
ejpam-6489	344	26	otherwise	otherwise	ADV
ejpam-6489	344	27	,	,	PUNCT
ejpam-6489	344	28	and	and	CCONJ
ejpam-6489	344	29	m.	m.	NOUN
ejpam-6489	344	30	balamurugan	balamurugan	VERB
ejpam-6489	344	31	,	,	PUNCT
ejpam-6489	344	32	g.	g.	PROPN
ejpam-6489	344	33	ellammal	ellammal	PROPN
ejpam-6489	344	34	,	,	PUNCT
ejpam-6489	344	35	a.	a.	NOUN
ejpam-6489	344	36	iampan	iampan	PROPN
ejpam-6489	344	37	/	/	SYM
ejpam-6489	344	38	eur	eur	PROPN
ejpam-6489	344	39	.	.	PUNCT
ejpam-6489	345	1	j.	j.	PROPN
ejpam-6489	345	2	pure	pure	PROPN
ejpam-6489	345	3	appl	appl	PROPN
ejpam-6489	345	4	.	.	PROPN
ejpam-6489	345	5	math	math	PROPN
ejpam-6489	345	6	,	,	PUNCT
ejpam-6489	345	7	18	18	NUM
ejpam-6489	345	8	(	(	PUNCT
ejpam-6489	345	9	3	3	NUM
ejpam-6489	345	10	)	)	PUNCT
ejpam-6489	345	11	(	(	PUNCT
ejpam-6489	345	12	2025	2025	NUM
ejpam-6489	345	13	)	)	PUNCT
ejpam-6489	345	14	,	,	PUNCT
ejpam-6489	345	15	6489	6489	NUM
ejpam-6489	345	16	14	14	NUM
ejpam-6489	345	17	of	of	ADP
ejpam-6489	345	18	26	26	NUM
ejpam-6489	345	19	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	345	20	)	)	PUNCT
ejpam-6489	346	1	=	=	PRON
ejpam-6489	346	2	{	{	PUNCT
ejpam-6489	346	3	inf	inf	PROPN
ejpam-6489	346	4	ϕ̃=ε̃+ς̃	ϕ̃=ε̃+ς̃	PROPN
ejpam-6489	346	5	{	{	PUNCT
ejpam-6489	346	6	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	346	7	)	)	PUNCT
ejpam-6489	346	8	∨	∨	NUM
ejpam-6489	346	9	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	346	10	)	)	PUNCT
ejpam-6489	346	11	}	}	PUNCT
ejpam-6489	346	12	if	if	SCONJ
ejpam-6489	346	13	ϕ̃	ϕ̃	PROPN
ejpam-6489	346	14	=	=	PUNCT
ejpam-6489	346	15	ε̃+	ε̃+	VERB
ejpam-6489	346	16	ς̃	ς̃	PROPN
ejpam-6489	346	17	1	1	NUM
ejpam-6489	346	18	otherwise	otherwise	ADV
ejpam-6489	346	19	.	.	PUNCT
ejpam-6489	347	1	theorem	theorem	VERB
ejpam-6489	347	2	6	6	NUM
ejpam-6489	347	3	.	.	PUNCT
ejpam-6489	348	1	let	let	VERB
ejpam-6489	348	2	̃ג	̃ג	NOUN
ejpam-6489	348	3	and	and	CCONJ
ejpam-6489	348	4	ℸ̃	ℸ̃	PROPN
ejpam-6489	348	5	be	be	VERB
ejpam-6489	348	6	a	a	DET
ejpam-6489	348	7	t	t	NOUN
ejpam-6489	348	8	cfls	cfls	NOUN
ejpam-6489	348	9	of	of	ADP
ejpam-6489	348	10	l̃.	l̃.	ADJ
ejpam-6489	348	11	then	then	ADV
ejpam-6489	348	12	+	+	ADJ
ejpam-6489	348	13	̃ג	̃ג	ADJ
ejpam-6489	348	14	ℸ̃	ℸ̃	PROPN
ejpam-6489	348	15	is	be	AUX
ejpam-6489	348	16	a	a	DET
ejpam-6489	348	17	t	t	NOUN
ejpam-6489	348	18	cfls	cfls	NOUN
ejpam-6489	348	19	of	of	ADP
ejpam-6489	348	20	l̃.	l̃.	ADJ
ejpam-6489	348	21	proof	proof	NOUN
ejpam-6489	348	22	.	.	PUNCT
ejpam-6489	349	1	let	let	VERB
ejpam-6489	349	2	̃ג	̃ג	NOUN
ejpam-6489	349	3	=	=	PRON
ejpam-6489	349	4	{	{	PUNCT
ejpam-6489	349	5	(	(	PUNCT
ejpam-6489	349	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	7	,	,	PUNCT
ejpam-6489	349	8	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	349	9	(	(	PUNCT
ejpam-6489	349	10	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	11	)	)	PUNCT
ejpam-6489	349	12	,	,	PUNCT
ejpam-6489	349	13	ξ	ξ	PROPN
ejpam-6489	349	14	n	n	PRON
ejpam-6489	349	15	̃ג	̃ג	PROPN
ejpam-6489	349	16	(	(	PUNCT
ejpam-6489	349	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	18	)	)	PUNCT
ejpam-6489	349	19	,	,	PUNCT
ejpam-6489	349	20	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	349	21	)	)	PUNCT
ejpam-6489	349	22	)	)	PUNCT
ejpam-6489	349	23	}	}	PUNCT
ejpam-6489	349	24	and	and	CCONJ
ejpam-6489	349	25	ℸ̃	ℸ̃	PROPN
ejpam-6489	349	26	=	=	SYM
ejpam-6489	349	27	{	{	PUNCT
ejpam-6489	349	28	(	(	PUNCT
ejpam-6489	349	29	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	30	,	,	PUNCT
ejpam-6489	349	31	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	349	32	(	(	PUNCT
ejpam-6489	349	33	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	34	)	)	PUNCT
ejpam-6489	349	35	,	,	PUNCT
ejpam-6489	349	36	ξ	ξ	PROPN
ejpam-6489	349	37	n	n	PRON
ejpam-6489	349	38	ℸ̃	ℸ̃	PROPN
ejpam-6489	349	39	(	(	PUNCT
ejpam-6489	349	40	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	41	)	)	PUNCT
ejpam-6489	349	42	,	,	PUNCT
ejpam-6489	349	43	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	349	44	)	)	PUNCT
ejpam-6489	349	45	)	)	PUNCT
ejpam-6489	349	46	}	}	PUNCT
ejpam-6489	349	47	be	be	AUX
ejpam-6489	349	48	two	two	NUM
ejpam-6489	349	49	t	t	NOUN
ejpam-6489	349	50	cfls	cfls	NOUN
ejpam-6489	349	51	on	on	ADP
ejpam-6489	349	52	l̃.	l̃.	ADV
ejpam-6489	349	53	define	define	VERB
ejpam-6489	349	54	their	their	PRON
ejpam-6489	349	55	sum	sum	NOUN
ejpam-6489	349	56	as	as	ADP
ejpam-6489	349	57	:	:	PUNCT
ejpam-6489	349	58	+	+	ADJ
ejpam-6489	349	59	̃ג	̃ג	ADJ
ejpam-6489	349	60	ℸ̃	ℸ̃	PROPN
ejpam-6489	349	61	=	=	SYM
ejpam-6489	349	62	{	{	PUNCT
ejpam-6489	349	63	(	(	PUNCT
ejpam-6489	349	64	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	65	,	,	PUNCT
ejpam-6489	349	66	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	349	67	)	)	PUNCT
ejpam-6489	349	68	,	,	PUNCT
ejpam-6489	349	69	ξ	ξ	PROPN
ejpam-6489	349	70	n	n	NUM
ejpam-6489	349	71	,	,	PUNCT
ejpam-6489	349	72	ℸ̃(ϕ̃)+̃ג	ℸ̃(ϕ̃)+̃ג	PROPN
ejpam-6489	349	73	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	349	74	)	)	PUNCT
ejpam-6489	349	75	)	)	PUNCT
ejpam-6489	349	76	}	}	PUNCT
ejpam-6489	349	77	,	,	PUNCT
ejpam-6489	349	78	where	where	SCONJ
ejpam-6489	349	79	for	for	ADP
ejpam-6489	349	80	each	each	DET
ejpam-6489	349	81	ϕ̃	ϕ̃	PROPN
ejpam-6489	349	82	∈	∈	PROPN
ejpam-6489	349	83	l̃	l̃	PROPN
ejpam-6489	349	84	,	,	PUNCT
ejpam-6489	349	85	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	PROPN
ejpam-6489	349	86	)	)	PUNCT
ejpam-6489	350	1	=	=	SYM
ejpam-6489	350	2	sup	sup	PROPN
ejpam-6489	350	3	ϕ̃=ε̃+ς̃	ϕ̃=ε̃+ς̃	PROPN
ejpam-6489	350	4	{	{	PUNCT
ejpam-6489	350	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	350	6	(	(	PUNCT
ejpam-6489	350	7	ε̃	ε̃	PROPN
ejpam-6489	350	8	)	)	PUNCT
ejpam-6489	350	9	∧	∧	PROPN
ejpam-6489	350	10	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	350	11	(	(	PUNCT
ejpam-6489	350	12	ς̃	ς̃	PROPN
ejpam-6489	350	13	)	)	PUNCT
ejpam-6489	350	14	}	}	PUNCT
ejpam-6489	350	15	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	350	16	)	)	PUNCT
ejpam-6489	350	17	=	=	VERB
ejpam-6489	350	18	inf	inf	PROPN
ejpam-6489	350	19	ϕ̃=ε̃+ς̃	ϕ̃=ε̃+ς̃	PROPN
ejpam-6489	350	20	{	{	PUNCT
ejpam-6489	350	21	ξñג	ξñג	NOUN
ejpam-6489	350	22	(	(	PUNCT
ejpam-6489	350	23	ε̃	ε̃	PROPN
ejpam-6489	350	24	)	)	PUNCT
ejpam-6489	350	25	∨	∨	NUM
ejpam-6489	350	26	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	350	27	(	(	PUNCT
ejpam-6489	350	28	ς̃	ς̃	PROPN
ejpam-6489	350	29	)	)	PUNCT
ejpam-6489	350	30	}	}	PUNCT
ejpam-6489	350	31	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	350	32	)	)	PUNCT
ejpam-6489	350	33	=	=	VERB
ejpam-6489	350	34	inf	inf	PROPN
ejpam-6489	350	35	ϕ̃=ε̃+ς̃	ϕ̃=ε̃+ς̃	PROPN
ejpam-6489	350	36	{	{	PUNCT
ejpam-6489	350	37	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	350	38	)	)	PUNCT
ejpam-6489	350	39	∨	∨	NUM
ejpam-6489	350	40	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	350	41	)	)	PUNCT
ejpam-6489	350	42	}	}	PUNCT
ejpam-6489	350	43	to	to	PART
ejpam-6489	350	44	verify	verify	VERB
ejpam-6489	350	45	that	that	SCONJ
ejpam-6489	350	46	+	+	ADJ
ejpam-6489	350	47	̃ג	̃ג	ADJ
ejpam-6489	350	48	ℸ̃	ℸ̃	PROPN
ejpam-6489	350	49	is	be	AUX
ejpam-6489	350	50	a	a	DET
ejpam-6489	350	51	t	t	NOUN
ejpam-6489	350	52	cfls	cfls	NOUN
ejpam-6489	350	53	of	of	ADP
ejpam-6489	350	54	l̃.	l̃.	ADJ
ejpam-6489	350	55	let	let	VERB
ejpam-6489	350	56	ϕ̃	ϕ̃	PROPN
ejpam-6489	350	57	,	,	PUNCT
ejpam-6489	350	58	η̃	η̃	PROPN
ejpam-6489	350	59	∈	∈	PROPN
ejpam-6489	350	60	l̃.	l̃.	ADJ
ejpam-6489	350	61	case	case	NOUN
ejpam-6489	350	62	1	1	NUM
ejpam-6489	350	63	.	.	PUNCT
ejpam-6489	351	1	ξp̃ג+ℸ̃(ϕ̃+	ξp̃ג+ℸ̃(ϕ̃+	PROPN
ejpam-6489	351	2	η̃	η̃	PROPN
ejpam-6489	351	3	)	)	PUNCT
ejpam-6489	352	1	=	=	SYM
ejpam-6489	352	2	sup	sup	NOUN
ejpam-6489	352	3	(	(	PUNCT
ejpam-6489	352	4	ϕ̃+η̃)=ε̃+ς̃	ϕ̃+η̃)=ε̃+ς̃	PRON
ejpam-6489	352	5	{	{	PUNCT
ejpam-6489	352	6	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	352	7	(	(	PUNCT
ejpam-6489	352	8	ε̃	ε̃	PROPN
ejpam-6489	352	9	)	)	PUNCT
ejpam-6489	352	10	∧	∧	PROPN
ejpam-6489	352	11	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	352	12	(	(	PUNCT
ejpam-6489	352	13	ς̃	ς̃	PROPN
ejpam-6489	352	14	)	)	PUNCT
ejpam-6489	352	15	}	}	PUNCT
ejpam-6489	352	16	≥	≥	AUX
ejpam-6489	352	17	sup	sup	NOUN
ejpam-6489	352	18	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	INTJ
ejpam-6489	352	19	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	352	20	{	{	PUNCT
ejpam-6489	352	21	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	352	22	(	(	PUNCT
ejpam-6489	352	23	ε̃1	ε̃1	PROPN
ejpam-6489	352	24	+	+	CCONJ
ejpam-6489	352	25	ε̃2	ε̃2	PROPN
ejpam-6489	352	26	)	)	PUNCT
ejpam-6489	352	27	∧	∧	PROPN
ejpam-6489	352	28	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	352	29	(	(	PUNCT
ejpam-6489	352	30	ς̃1	ς̃1	PROPN
ejpam-6489	352	31	+	+	CCONJ
ejpam-6489	352	32	ς̃2	ς̃2	NOUN
ejpam-6489	352	33	)	)	PUNCT
ejpam-6489	352	34	}	}	PUNCT
ejpam-6489	352	35	≥	≥	AUX
ejpam-6489	352	36	sup	sup	NOUN
ejpam-6489	352	37	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	INTJ
ejpam-6489	352	38	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	352	39	{	{	PUNCT
ejpam-6489	352	40	(	(	PUNCT
ejpam-6489	352	41	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	352	42	(	(	PUNCT
ejpam-6489	352	43	ε̃1	ε̃1	PROPN
ejpam-6489	352	44	)	)	PUNCT
ejpam-6489	352	45	∧	∧	PROPN
ejpam-6489	352	46	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	352	47	(	(	PUNCT
ejpam-6489	352	48	ε̃2	ε̃2	NOUN
ejpam-6489	352	49	)	)	PUNCT
ejpam-6489	352	50	)	)	PUNCT
ejpam-6489	353	1	∧	∧	NOUN
ejpam-6489	353	2	(	(	PUNCT
ejpam-6489	353	3	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	353	4	(	(	PUNCT
ejpam-6489	353	5	ς̃1	ς̃1	NOUN
ejpam-6489	353	6	)	)	PUNCT
ejpam-6489	353	7	∧	∧	PROPN
ejpam-6489	353	8	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	353	9	(	(	PUNCT
ejpam-6489	353	10	ς̃2	ς̃2	NOUN
ejpam-6489	353	11	)	)	PUNCT
ejpam-6489	353	12	)	)	PUNCT
ejpam-6489	353	13	}	}	PUNCT
ejpam-6489	354	1	=	=	PUNCT
ejpam-6489	354	2	(	(	PUNCT
ejpam-6489	354	3	sup	sup	NOUN
ejpam-6489	354	4	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	PROPN
ejpam-6489	354	5	{	{	PUNCT
ejpam-6489	354	6	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	354	7	(	(	PUNCT
ejpam-6489	354	8	ε̃1	ε̃1	PROPN
ejpam-6489	354	9	)	)	PUNCT
ejpam-6489	354	10	∧	∧	PROPN
ejpam-6489	354	11	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	354	12	(	(	PUNCT
ejpam-6489	354	13	ς̃1	ς̃1	PROPN
ejpam-6489	354	14	)	)	PUNCT
ejpam-6489	354	15	}	}	PUNCT
ejpam-6489	354	16	)	)	PUNCT
ejpam-6489	355	1	∧	∧	NOUN
ejpam-6489	355	2	(	(	PUNCT
ejpam-6489	355	3	sup	sup	NUM
ejpam-6489	355	4	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	355	5	{	{	PUNCT
ejpam-6489	355	6	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	355	7	(	(	PUNCT
ejpam-6489	355	8	ε̃2	ε̃2	PROPN
ejpam-6489	355	9	)	)	PUNCT
ejpam-6489	355	10	∧	∧	PROPN
ejpam-6489	355	11	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	355	12	(	(	PUNCT
ejpam-6489	355	13	ς̃2	ς̃2	NOUN
ejpam-6489	355	14	)	)	PUNCT
ejpam-6489	355	15	}	}	PUNCT
ejpam-6489	355	16	)	)	PUNCT
ejpam-6489	355	17	=	=	SYM
ejpam-6489	355	18	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	X
ejpam-6489	355	19	)	)	PUNCT
ejpam-6489	355	20	∧	∧	PROPN
ejpam-6489	355	21	ξp̃ג+ℸ̃(η̃	ξp̃ג+ℸ̃(η̃	NOUN
ejpam-6489	355	22	)	)	PUNCT
ejpam-6489	355	23	.	.	PUNCT
ejpam-6489	356	1	case	case	NOUN
ejpam-6489	356	2	2	2	NUM
ejpam-6489	356	3	.	.	PUNCT
ejpam-6489	356	4	ξñג+ℸ̃(ϕ̃+	ξñג+ℸ̃(ϕ̃+	PROPN
ejpam-6489	356	5	η̃	η̃	PROPN
ejpam-6489	356	6	)	)	PUNCT
ejpam-6489	357	1	=	=	PROPN
ejpam-6489	357	2	inf	inf	PROPN
ejpam-6489	357	3	(	(	PUNCT
ejpam-6489	357	4	ϕ̃+η̃)=ε̃+ς̃	ϕ̃+η̃)=ε̃+ς̃	X
ejpam-6489	357	5	{	{	PUNCT
ejpam-6489	357	6	ξñג	ξñג	NOUN
ejpam-6489	357	7	(	(	PUNCT
ejpam-6489	357	8	ε̃	ε̃	PROPN
ejpam-6489	357	9	)	)	PUNCT
ejpam-6489	357	10	∨	∨	NUM
ejpam-6489	357	11	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	357	12	(	(	PUNCT
ejpam-6489	357	13	ς̃	ς̃	PROPN
ejpam-6489	357	14	)	)	PUNCT
ejpam-6489	357	15	}	}	PUNCT
ejpam-6489	357	16	≤	≤	NUM
ejpam-6489	357	17	inf	inf	PROPN
ejpam-6489	357	18	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	357	19	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	357	20	{	{	PUNCT
ejpam-6489	357	21	ξñג	ξñג	NOUN
ejpam-6489	357	22	(	(	PUNCT
ejpam-6489	357	23	ε̃1	ε̃1	PROPN
ejpam-6489	357	24	+	+	NUM
ejpam-6489	357	25	ε̃2	ε̃2	PROPN
ejpam-6489	357	26	)	)	PUNCT
ejpam-6489	357	27	∨	∨	NUM
ejpam-6489	357	28	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	357	29	(	(	PUNCT
ejpam-6489	357	30	ς̃1	ς̃1	PROPN
ejpam-6489	357	31	+	+	CCONJ
ejpam-6489	357	32	ς̃2	ς̃2	NOUN
ejpam-6489	357	33	)	)	PUNCT
ejpam-6489	357	34	}	}	PUNCT
ejpam-6489	357	35	≤	≤	NUM
ejpam-6489	357	36	inf	inf	PROPN
ejpam-6489	357	37	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	357	38	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	357	39	{	{	PUNCT
ejpam-6489	357	40	(	(	PUNCT
ejpam-6489	357	41	ξñג	ξñג	PROPN
ejpam-6489	357	42	(	(	PUNCT
ejpam-6489	357	43	ε̃1	ε̃1	PROPN
ejpam-6489	357	44	)	)	PUNCT
ejpam-6489	357	45	∨	∨	NUM
ejpam-6489	357	46	ξñג	ξñג	PROPN
ejpam-6489	357	47	(	(	PUNCT
ejpam-6489	357	48	ε̃2	ε̃2	NOUN
ejpam-6489	357	49	)	)	PUNCT
ejpam-6489	357	50	)	)	PUNCT
ejpam-6489	357	51	∨	∨	NUM
ejpam-6489	357	52	(	(	PUNCT
ejpam-6489	357	53	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	357	54	(	(	PUNCT
ejpam-6489	357	55	ς̃1	ς̃1	PROPN
ejpam-6489	357	56	)	)	PUNCT
ejpam-6489	357	57	∨	∨	NUM
ejpam-6489	357	58	ξnℸ̃	ξnℸ̃	X
ejpam-6489	357	59	(	(	PUNCT
ejpam-6489	357	60	ς̃2	ς̃2	NOUN
ejpam-6489	357	61	)	)	PUNCT
ejpam-6489	357	62	)	)	PUNCT
ejpam-6489	357	63	}	}	PUNCT
ejpam-6489	358	1	=	=	SYM
ejpam-6489	358	2	(	(	PUNCT
ejpam-6489	358	3	inf	inf	NOUN
ejpam-6489	358	4	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	PROPN
ejpam-6489	358	5	{	{	PUNCT
ejpam-6489	358	6	ξñג	ξñג	PROPN
ejpam-6489	358	7	(	(	PUNCT
ejpam-6489	358	8	ε̃1	ε̃1	PROPN
ejpam-6489	358	9	)	)	PUNCT
ejpam-6489	358	10	∨	∨	NUM
ejpam-6489	358	11	ξnℸ̃	ξnℸ̃	X
ejpam-6489	358	12	(	(	PUNCT
ejpam-6489	358	13	ς̃1	ς̃1	NOUN
ejpam-6489	358	14	)	)	PUNCT
ejpam-6489	358	15	}	}	PUNCT
ejpam-6489	358	16	)	)	PUNCT
ejpam-6489	358	17	∨	∨	PROPN
ejpam-6489	358	18	(	(	PUNCT
ejpam-6489	358	19	inf	inf	PROPN
ejpam-6489	358	20	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	358	21	{	{	PUNCT
ejpam-6489	358	22	ξñג	ξñג	NOUN
ejpam-6489	358	23	(	(	PUNCT
ejpam-6489	358	24	ε̃2	ε̃2	NOUN
ejpam-6489	358	25	)	)	PUNCT
ejpam-6489	358	26	∨	∨	NUM
ejpam-6489	358	27	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	358	28	(	(	PUNCT
ejpam-6489	358	29	ς̃2	ς̃2	NOUN
ejpam-6489	358	30	)	)	PUNCT
ejpam-6489	358	31	}	}	PUNCT
ejpam-6489	358	32	)	)	PUNCT
ejpam-6489	358	33	m.	m.	NOUN
ejpam-6489	358	34	balamurugan	balamurugan	NOUN
ejpam-6489	358	35	,	,	PUNCT
ejpam-6489	358	36	g.	g.	PROPN
ejpam-6489	358	37	ellammal	ellammal	PROPN
ejpam-6489	358	38	,	,	PUNCT
ejpam-6489	358	39	a.	a.	NOUN
ejpam-6489	358	40	iampan	iampan	PROPN
ejpam-6489	358	41	/	/	SYM
ejpam-6489	358	42	eur	eur	PROPN
ejpam-6489	358	43	.	.	PUNCT
ejpam-6489	359	1	j.	j.	PROPN
ejpam-6489	359	2	pure	pure	PROPN
ejpam-6489	359	3	appl	appl	PROPN
ejpam-6489	359	4	.	.	PROPN
ejpam-6489	359	5	math	math	PROPN
ejpam-6489	359	6	,	,	PUNCT
ejpam-6489	359	7	18	18	NUM
ejpam-6489	359	8	(	(	PUNCT
ejpam-6489	359	9	3	3	NUM
ejpam-6489	359	10	)	)	PUNCT
ejpam-6489	359	11	(	(	PUNCT
ejpam-6489	359	12	2025	2025	NUM
ejpam-6489	359	13	)	)	PUNCT
ejpam-6489	359	14	,	,	PUNCT
ejpam-6489	359	15	6489	6489	NUM
ejpam-6489	359	16	15	15	NUM
ejpam-6489	359	17	of	of	ADP
ejpam-6489	359	18	26	26	NUM
ejpam-6489	359	19	=	=	SYM
ejpam-6489	359	20	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	359	21	)	)	PUNCT
ejpam-6489	359	22	∨	∨	NUM
ejpam-6489	359	23	ξñג+ℸ̃(η̃	ξñג+ℸ̃(η̃	NOUN
ejpam-6489	359	24	)	)	PUNCT
ejpam-6489	359	25	.	.	PUNCT
ejpam-6489	360	1	case	case	NOUN
ejpam-6489	360	2	3	3	NUM
ejpam-6489	360	3	.	.	PUNCT
ejpam-6489	361	1	ζ̃ג+ℸ̃(ϕ̃+	ζ̃ג+ℸ̃(ϕ̃+	PROPN
ejpam-6489	361	2	η̃	η̃	PROPN
ejpam-6489	361	3	)	)	PUNCT
ejpam-6489	362	1	=	=	PROPN
ejpam-6489	362	2	inf	inf	NOUN
ejpam-6489	362	3	(	(	PUNCT
ejpam-6489	362	4	ϕ̃+η̃)=ε̃+ς̃	ϕ̃+η̃)=ε̃+ς̃	X
ejpam-6489	362	5	{	{	PUNCT
ejpam-6489	362	6	ζ̃ג(ε̃	ζ̃ג(ε̃	NOUN
ejpam-6489	362	7	)	)	PUNCT
ejpam-6489	362	8	∨	∨	NUM
ejpam-6489	362	9	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	362	10	)	)	PUNCT
ejpam-6489	362	11	}	}	PUNCT
ejpam-6489	362	12	≤	≤	NUM
ejpam-6489	362	13	inf	inf	PROPN
ejpam-6489	362	14	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	PROPN
ejpam-6489	362	15	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	362	16	{	{	PUNCT
ejpam-6489	362	17	ζ̃ג(ε̃1	ζ̃ג(ε̃1	NOUN
ejpam-6489	362	18	+	+	NUM
ejpam-6489	362	19	ε̃2	ε̃2	PROPN
ejpam-6489	362	20	)	)	PUNCT
ejpam-6489	362	21	∨	∨	NUM
ejpam-6489	362	22	ζℸ̃(ς̃1	ζℸ̃(ς̃1	NOUN
ejpam-6489	362	23	+	+	CCONJ
ejpam-6489	362	24	ς̃2	ς̃2	NOUN
ejpam-6489	362	25	)	)	PUNCT
ejpam-6489	362	26	}	}	PUNCT
ejpam-6489	362	27	≤	≤	NUM
ejpam-6489	362	28	inf	inf	PROPN
ejpam-6489	362	29	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	362	30	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	362	31	{	{	PUNCT
ejpam-6489	362	32	(	(	PUNCT
ejpam-6489	362	33	ζ̃ג(ε̃1	ζ̃ג(ε̃1	NOUN
ejpam-6489	362	34	)	)	PUNCT
ejpam-6489	362	35	∨	∨	NUM
ejpam-6489	362	36	ζ̃ג(ε̃2	ζ̃ג(ε̃2	NOUN
ejpam-6489	362	37	)	)	PUNCT
ejpam-6489	362	38	)	)	PUNCT
ejpam-6489	362	39	∨	∨	NOUN
ejpam-6489	362	40	(	(	PUNCT
ejpam-6489	362	41	ζℸ̃(ς̃1	ζℸ̃(ς̃1	PROPN
ejpam-6489	362	42	)	)	PUNCT
ejpam-6489	362	43	∨	∨	NUM
ejpam-6489	362	44	ζℸ̃(ς̃2	ζℸ̃(ς̃2	NOUN
ejpam-6489	362	45	)	)	PUNCT
ejpam-6489	362	46	)	)	PUNCT
ejpam-6489	362	47	}	}	PUNCT
ejpam-6489	363	1	=	=	SYM
ejpam-6489	363	2	(	(	PUNCT
ejpam-6489	363	3	inf	inf	PROPN
ejpam-6489	363	4	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	PROPN
ejpam-6489	363	5	{	{	PUNCT
ejpam-6489	363	6	ζ̃ג(ε̃1	ζ̃ג(ε̃1	NOUN
ejpam-6489	363	7	)	)	PUNCT
ejpam-6489	363	8	∨	∨	NUM
ejpam-6489	363	9	ζℸ̃(ς̃1	ζℸ̃(ς̃1	NOUN
ejpam-6489	363	10	)	)	PUNCT
ejpam-6489	363	11	}	}	PUNCT
ejpam-6489	363	12	)	)	PUNCT
ejpam-6489	363	13	∨	∨	PROPN
ejpam-6489	363	14	(	(	PUNCT
ejpam-6489	363	15	inf	inf	PROPN
ejpam-6489	363	16	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	363	17	{	{	PUNCT
ejpam-6489	363	18	ζ̃ג(ε̃2	ζ̃ג(ε̃2	NOUN
ejpam-6489	363	19	)	)	PUNCT
ejpam-6489	363	20	∨	∨	NOUN
ejpam-6489	363	21	ζℸ̃(ς̃2	ζℸ̃(ς̃2	NOUN
ejpam-6489	363	22	)	)	PUNCT
ejpam-6489	363	23	}	}	PUNCT
ejpam-6489	363	24	)	)	PUNCT
ejpam-6489	363	25	=	=	SYM
ejpam-6489	363	26	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	363	27	)	)	PUNCT
ejpam-6489	363	28	∨	∨	NOUN
ejpam-6489	363	29	ζ̃ג+ℸ̃(η̃	ζ̃ג+ℸ̃(η̃	NUM
ejpam-6489	363	30	)	)	PUNCT
ejpam-6489	363	31	.	.	PUNCT
ejpam-6489	364	1	case	case	NOUN
ejpam-6489	364	2	4	4	NUM
ejpam-6489	364	3	.	.	X
ejpam-6489	364	4	ξp̃ג+ℸ̃(β̃ϕ̃	ξp̃ג+ℸ̃(β̃ϕ̃	NUM
ejpam-6489	364	5	)	)	PUNCT
ejpam-6489	364	6	=	=	SYM
ejpam-6489	364	7	sup	sup	NOUN
ejpam-6489	364	8	β̃ϕ̃=ε̃+ς̃	β̃ϕ̃=ε̃+ς̃	X
ejpam-6489	364	9	{	{	PUNCT
ejpam-6489	364	10	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	364	11	(	(	PUNCT
ejpam-6489	364	12	ε̃	ε̃	PROPN
ejpam-6489	364	13	)	)	PUNCT
ejpam-6489	364	14	∧	∧	PROPN
ejpam-6489	364	15	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	364	16	(	(	PUNCT
ejpam-6489	364	17	ς̃	ς̃	PROPN
ejpam-6489	364	18	)	)	PUNCT
ejpam-6489	364	19	}	}	PUNCT
ejpam-6489	365	1	=	=	PUNCT
ejpam-6489	365	2	sup	sup	X
ejpam-6489	365	3	ϕ̃=ε̃/β̃+ς̃/β̃	ϕ̃=ε̃/β̃+ς̃/β̃	NOUN
ejpam-6489	365	4	{	{	PUNCT
ejpam-6489	365	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	365	6	(	(	PUNCT
ejpam-6489	365	7	β̃(ε̃/β̃	β̃(ε̃/β̃	ADJ
ejpam-6489	365	8	)	)	PUNCT
ejpam-6489	365	9	)	)	PUNCT
ejpam-6489	366	1	∧	∧	PROPN
ejpam-6489	366	2	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	366	3	(	(	PUNCT
ejpam-6489	366	4	β̃(ς̃/β̃	β̃(ς̃/β̃	NOUN
ejpam-6489	366	5	)	)	PUNCT
ejpam-6489	366	6	)	)	PUNCT
ejpam-6489	366	7	}	}	PUNCT
ejpam-6489	366	8	≥	≥	PROPN
ejpam-6489	366	9	sup	sup	PROPN
ejpam-6489	366	10	ϕ̃=ε̃′+ς̃′	ϕ̃=ε̃′+ς̃′	PROPN
ejpam-6489	366	11	{	{	PUNCT
ejpam-6489	366	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	366	13	(	(	PUNCT
ejpam-6489	366	14	ε̃	ε̃	PROPN
ejpam-6489	366	15	′	′	NOUN
ejpam-6489	366	16	)	)	PUNCT
ejpam-6489	366	17	∧	∧	PROPN
ejpam-6489	366	18	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	366	19	(	(	PUNCT
ejpam-6489	366	20	ς̃	ς̃	PROPN
ejpam-6489	366	21	′	′	NUM
ejpam-6489	366	22	)	)	PUNCT
ejpam-6489	366	23	}	}	PUNCT
ejpam-6489	366	24	=	=	SYM
ejpam-6489	366	25	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	NOUN
ejpam-6489	366	26	)	)	PUNCT
ejpam-6489	366	27	.	.	PUNCT
ejpam-6489	367	1	case	case	NOUN
ejpam-6489	367	2	5	5	NUM
ejpam-6489	367	3	.	.	PUNCT
ejpam-6489	367	4	ξñג+ℸ̃(β̃ϕ̃	ξñג+ℸ̃(β̃ϕ̃	NUM
ejpam-6489	367	5	)	)	PUNCT
ejpam-6489	367	6	=	=	NOUN
ejpam-6489	367	7	inf	inf	PROPN
ejpam-6489	367	8	β̃ϕ̃=ε̃+ς̃	β̃ϕ̃=ε̃+ς̃	PRON
ejpam-6489	367	9	{	{	PUNCT
ejpam-6489	367	10	ξñג	ξñג	NOUN
ejpam-6489	367	11	(	(	PUNCT
ejpam-6489	367	12	ε̃	ε̃	PROPN
ejpam-6489	367	13	)	)	PUNCT
ejpam-6489	367	14	∨	∨	NUM
ejpam-6489	367	15	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	367	16	(	(	PUNCT
ejpam-6489	367	17	ς̃	ς̃	PROPN
ejpam-6489	367	18	)	)	PUNCT
ejpam-6489	367	19	}	}	PUNCT
ejpam-6489	367	20	=	=	SYM
ejpam-6489	368	1	inf	inf	ADJ
ejpam-6489	368	2	ϕ̃=ε̃/β̃+ς̃/β̃	ϕ̃=ε̃/β̃+ς̃/β̃	NOUN
ejpam-6489	368	3	{	{	PUNCT
ejpam-6489	368	4	ξñג	ξñג	INTJ
ejpam-6489	368	5	(	(	PUNCT
ejpam-6489	368	6	β̃(ε̃/β̃	β̃(ε̃/β̃	ADJ
ejpam-6489	368	7	)	)	PUNCT
ejpam-6489	368	8	)	)	PUNCT
ejpam-6489	369	1	∨	∨	NUM
ejpam-6489	369	2	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	369	3	(	(	PUNCT
ejpam-6489	369	4	β̃(ς̃/β̃	β̃(ς̃/β̃	NOUN
ejpam-6489	369	5	)	)	PUNCT
ejpam-6489	369	6	)	)	PUNCT
ejpam-6489	369	7	}	}	PUNCT
ejpam-6489	369	8	≤	≤	NUM
ejpam-6489	369	9	inf	inf	PROPN
ejpam-6489	369	10	ϕ̃=ε̃′+ς̃′	ϕ̃=ε̃′+ς̃′	PROPN
ejpam-6489	369	11	{	{	PUNCT
ejpam-6489	369	12	ξñג	ξñג	PROPN
ejpam-6489	369	13	(	(	PUNCT
ejpam-6489	369	14	ε̃′	ε̃′	PROPN
ejpam-6489	369	15	)	)	PUNCT
ejpam-6489	369	16	∨	∨	NUM
ejpam-6489	369	17	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	369	18	(	(	PUNCT
ejpam-6489	369	19	ς̃	ς̃	PROPN
ejpam-6489	369	20	′	′	NUM
ejpam-6489	369	21	)	)	PUNCT
ejpam-6489	369	22	}	}	PUNCT
ejpam-6489	369	23	=	=	SYM
ejpam-6489	369	24	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	369	25	)	)	PUNCT
ejpam-6489	369	26	case	case	NOUN
ejpam-6489	369	27	6	6	NUM
ejpam-6489	369	28	.	.	PUNCT
ejpam-6489	369	29	ζ̃ג+ℸ̃(β̃ϕ̃	ζ̃ג+ℸ̃(β̃ϕ̃	VERB
ejpam-6489	369	30	)	)	PUNCT
ejpam-6489	369	31	=	=	SYM
ejpam-6489	369	32	inf	inf	PROPN
ejpam-6489	369	33	β̃ϕ̃=ε̃+ς̃	β̃ϕ̃=ε̃+ς̃	PRON
ejpam-6489	369	34	{	{	PUNCT
ejpam-6489	369	35	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	369	36	)	)	PUNCT
ejpam-6489	369	37	∨	∨	NUM
ejpam-6489	369	38	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	369	39	)	)	PUNCT
ejpam-6489	369	40	}	}	PUNCT
ejpam-6489	370	1	=	=	SYM
ejpam-6489	370	2	inf	inf	ADJ
ejpam-6489	370	3	ϕ̃=ε̃/β̃+ς̃/β̃	ϕ̃=ε̃/β̃+ς̃/β̃	X
ejpam-6489	370	4	{	{	PUNCT
ejpam-6489	370	5	ζ̃ג(β̃(ε̃/β̃	ζ̃ג(β̃(ε̃/β̃	NOUN
ejpam-6489	370	6	)	)	PUNCT
ejpam-6489	370	7	)	)	PUNCT
ejpam-6489	370	8	∨	∨	NUM
ejpam-6489	370	9	ζℸ̃(β̃(ς̃/β̃	ζℸ̃(β̃(ς̃/β̃	NOUN
ejpam-6489	370	10	)	)	PUNCT
ejpam-6489	370	11	)	)	PUNCT
ejpam-6489	370	12	}	}	PUNCT
ejpam-6489	370	13	≤	≤	NUM
ejpam-6489	370	14	inf	inf	PROPN
ejpam-6489	370	15	ϕ̃=ε̃′+ς̃′	ϕ̃=ε̃′+ς̃′	PROPN
ejpam-6489	370	16	{	{	PUNCT
ejpam-6489	370	17	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	370	18	′	′	NUM
ejpam-6489	370	19	)	)	PUNCT
ejpam-6489	371	1	∨	∨	PROPN
ejpam-6489	371	2	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	371	3	′	′	NOUN
ejpam-6489	371	4	)	)	PUNCT
ejpam-6489	371	5	}	}	PUNCT
ejpam-6489	372	1	=	=	SYM
ejpam-6489	372	2	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	372	3	)	)	PUNCT
ejpam-6489	372	4	.	.	PUNCT
ejpam-6489	373	1	m.	m.	NOUN
ejpam-6489	373	2	balamurugan	balamurugan	PROPN
ejpam-6489	373	3	,	,	PUNCT
ejpam-6489	373	4	g.	g.	PROPN
ejpam-6489	373	5	ellammal	ellammal	PROPN
ejpam-6489	373	6	,	,	PUNCT
ejpam-6489	373	7	a.	a.	NOUN
ejpam-6489	373	8	iampan	iampan	PROPN
ejpam-6489	373	9	/	/	SYM
ejpam-6489	373	10	eur	eur	PROPN
ejpam-6489	373	11	.	.	PUNCT
ejpam-6489	374	1	j.	j.	PROPN
ejpam-6489	374	2	pure	pure	PROPN
ejpam-6489	374	3	appl	appl	PROPN
ejpam-6489	374	4	.	.	PROPN
ejpam-6489	374	5	math	math	PROPN
ejpam-6489	374	6	,	,	PUNCT
ejpam-6489	374	7	18	18	NUM
ejpam-6489	374	8	(	(	PUNCT
ejpam-6489	374	9	3	3	NUM
ejpam-6489	374	10	)	)	PUNCT
ejpam-6489	374	11	(	(	PUNCT
ejpam-6489	374	12	2025	2025	NUM
ejpam-6489	374	13	)	)	PUNCT
ejpam-6489	374	14	,	,	PUNCT
ejpam-6489	374	15	6489	6489	NUM
ejpam-6489	374	16	16	16	NUM
ejpam-6489	374	17	of	of	ADP
ejpam-6489	374	18	26	26	NUM
ejpam-6489	374	19	case	case	NOUN
ejpam-6489	374	20	7	7	NUM
ejpam-6489	374	21	.	.	X
ejpam-6489	374	22	ξp̃ג+ℸ̃([ϕ̃	ξp̃ג+ℸ̃([ϕ̃	PROPN
ejpam-6489	374	23	,	,	PUNCT
ejpam-6489	374	24	η̃	η̃	PROPN
ejpam-6489	374	25	]	]	PUNCT
ejpam-6489	374	26	)	)	PUNCT
ejpam-6489	375	1	=	=	SYM
ejpam-6489	375	2	sup	sup	NUM
ejpam-6489	376	1	[	[	X
ejpam-6489	376	2	ϕ̃,η̃]=ε̃+ς̃	ϕ̃,η̃]=ε̃+ς̃	PUNCT
ejpam-6489	376	3	{	{	PUNCT
ejpam-6489	376	4	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	376	5	(	(	PUNCT
ejpam-6489	376	6	ε̃	ε̃	PROPN
ejpam-6489	376	7	)	)	PUNCT
ejpam-6489	376	8	∧	∧	PROPN
ejpam-6489	376	9	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	376	10	(	(	PUNCT
ejpam-6489	376	11	ς̃	ς̃	PROPN
ejpam-6489	376	12	)	)	PUNCT
ejpam-6489	376	13	}	}	PUNCT
ejpam-6489	376	14	≥	≥	AUX
ejpam-6489	376	15	sup	sup	NOUN
ejpam-6489	376	16	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	INTJ
ejpam-6489	376	17	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	376	18	{	{	PUNCT
ejpam-6489	376	19	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	376	20	(	(	PUNCT
ejpam-6489	376	21	[	[	X
ejpam-6489	376	22	ε̃1	ε̃1	PROPN
ejpam-6489	376	23	,	,	PUNCT
ejpam-6489	376	24	ε̃2	ε̃2	PROPN
ejpam-6489	376	25	]	]	SYM
ejpam-6489	376	26	)	)	PUNCT
ejpam-6489	376	27	∧	∧	PROPN
ejpam-6489	376	28	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	376	29	(	(	PUNCT
ejpam-6489	376	30	[	[	X
ejpam-6489	376	31	ς̃1	ς̃1	PROPN
ejpam-6489	376	32	,	,	PUNCT
ejpam-6489	376	33	ς̃2	ς̃2	PROPN
ejpam-6489	376	34	]	]	X
ejpam-6489	376	35	)	)	PUNCT
ejpam-6489	376	36	}	}	PUNCT
ejpam-6489	376	37	≥	≥	NUM
ejpam-6489	376	38	sup	sup	NOUN
ejpam-6489	376	39	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	INTJ
ejpam-6489	376	40	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	NOUN
ejpam-6489	376	41	{	{	PUNCT
ejpam-6489	376	42	(	(	PUNCT
ejpam-6489	376	43	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	376	44	(	(	PUNCT
ejpam-6489	376	45	ε̃1	ε̃1	PROPN
ejpam-6489	376	46	)	)	PUNCT
ejpam-6489	376	47	∧	∧	PROPN
ejpam-6489	376	48	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	376	49	(	(	PUNCT
ejpam-6489	376	50	ε̃2	ε̃2	NOUN
ejpam-6489	376	51	)	)	PUNCT
ejpam-6489	376	52	)	)	PUNCT
ejpam-6489	377	1	∧	∧	NOUN
ejpam-6489	377	2	(	(	PUNCT
ejpam-6489	377	3	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	377	4	(	(	PUNCT
ejpam-6489	377	5	ς̃1	ς̃1	NOUN
ejpam-6489	377	6	)	)	PUNCT
ejpam-6489	377	7	∧	∧	PROPN
ejpam-6489	377	8	ξpℸ̃	ξpℸ̃	PROPN
ejpam-6489	377	9	(	(	PUNCT
ejpam-6489	377	10	ς̃2	ς̃2	NOUN
ejpam-6489	377	11	)	)	PUNCT
ejpam-6489	377	12	)	)	PUNCT
ejpam-6489	377	13	}	}	PUNCT
ejpam-6489	377	14	=	=	SYM
ejpam-6489	377	15	ξp̃ג+ℸ̃(ϕ̃	ξp̃ג+ℸ̃(ϕ̃	X
ejpam-6489	377	16	)	)	PUNCT
ejpam-6489	377	17	∧	∧	PROPN
ejpam-6489	377	18	ξp̃ג+ℸ̃(η̃	ξp̃ג+ℸ̃(η̃	NOUN
ejpam-6489	377	19	)	)	PUNCT
ejpam-6489	377	20	.	.	PUNCT
ejpam-6489	378	1	case	case	NOUN
ejpam-6489	378	2	8	8	NUM
ejpam-6489	378	3	.	.	PUNCT
ejpam-6489	378	4	ξñג+ℸ̃([ϕ̃	ξñג+ℸ̃([ϕ̃	NOUN
ejpam-6489	378	5	,	,	PUNCT
ejpam-6489	378	6	η̃	η̃	PROPN
ejpam-6489	378	7	]	]	PUNCT
ejpam-6489	378	8	)	)	PUNCT
ejpam-6489	379	1	=	=	SYM
ejpam-6489	379	2	inf	inf	PROPN
ejpam-6489	380	1	[	[	X
ejpam-6489	380	2	ϕ̃,η̃]=ε̃+ς̃	ϕ̃,η̃]=ε̃+ς̃	X
ejpam-6489	380	3	{	{	PUNCT
ejpam-6489	380	4	ξñג	ξñג	NOUN
ejpam-6489	380	5	(	(	PUNCT
ejpam-6489	380	6	ε̃	ε̃	PROPN
ejpam-6489	380	7	)	)	PUNCT
ejpam-6489	380	8	∨	∨	NUM
ejpam-6489	380	9	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	380	10	(	(	PUNCT
ejpam-6489	380	11	ς̃	ς̃	PROPN
ejpam-6489	380	12	)	)	PUNCT
ejpam-6489	380	13	}	}	PUNCT
ejpam-6489	380	14	≤	≤	NUM
ejpam-6489	380	15	inf	inf	PROPN
ejpam-6489	380	16	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	380	17	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	380	18	{	{	PUNCT
ejpam-6489	380	19	ξñג	ξñג	NOUN
ejpam-6489	380	20	(	(	PUNCT
ejpam-6489	380	21	[	[	X
ejpam-6489	380	22	ε̃1	ε̃1	PROPN
ejpam-6489	380	23	,	,	PUNCT
ejpam-6489	380	24	ε̃2	ε̃2	PROPN
ejpam-6489	380	25	]	]	PUNCT
ejpam-6489	380	26	)	)	PUNCT
ejpam-6489	380	27	∨	∨	NUM
ejpam-6489	380	28	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	380	29	(	(	PUNCT
ejpam-6489	380	30	[	[	X
ejpam-6489	380	31	ς̃1	ς̃1	PROPN
ejpam-6489	380	32	,	,	PUNCT
ejpam-6489	380	33	ς̃2	ς̃2	PROPN
ejpam-6489	380	34	]	]	X
ejpam-6489	380	35	)	)	PUNCT
ejpam-6489	380	36	}	}	PUNCT
ejpam-6489	380	37	≤	≤	NUM
ejpam-6489	380	38	inf	inf	PROPN
ejpam-6489	380	39	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	380	40	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	380	41	{	{	PUNCT
ejpam-6489	380	42	(	(	PUNCT
ejpam-6489	380	43	ξñג	ξñג	PROPN
ejpam-6489	380	44	(	(	PUNCT
ejpam-6489	380	45	ε̃1	ε̃1	PROPN
ejpam-6489	380	46	)	)	PUNCT
ejpam-6489	380	47	∨	∨	NUM
ejpam-6489	380	48	ξñג	ξñג	PROPN
ejpam-6489	380	49	(	(	PUNCT
ejpam-6489	380	50	ε̃2	ε̃2	NOUN
ejpam-6489	380	51	)	)	PUNCT
ejpam-6489	380	52	)	)	PUNCT
ejpam-6489	380	53	∨	∨	NUM
ejpam-6489	380	54	(	(	PUNCT
ejpam-6489	380	55	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	380	56	(	(	PUNCT
ejpam-6489	380	57	ς̃1	ς̃1	PROPN
ejpam-6489	380	58	)	)	PUNCT
ejpam-6489	380	59	∨	∨	NUM
ejpam-6489	380	60	ξnℸ̃	ξnℸ̃	X
ejpam-6489	380	61	(	(	PUNCT
ejpam-6489	380	62	ς̃2	ς̃2	NOUN
ejpam-6489	380	63	)	)	PUNCT
ejpam-6489	380	64	)	)	PUNCT
ejpam-6489	380	65	}	}	PUNCT
ejpam-6489	380	66	=	=	SYM
ejpam-6489	380	67	ξñג+ℸ̃(ϕ̃	ξñג+ℸ̃(ϕ̃	PROPN
ejpam-6489	380	68	)	)	PUNCT
ejpam-6489	380	69	∨	∨	NUM
ejpam-6489	380	70	ξñג+ℸ̃(η̃	ξñג+ℸ̃(η̃	NOUN
ejpam-6489	380	71	)	)	PUNCT
ejpam-6489	380	72	.	.	PUNCT
ejpam-6489	381	1	case	case	NOUN
ejpam-6489	381	2	9	9	NUM
ejpam-6489	381	3	.	.	X
ejpam-6489	381	4	ζ̃ג+ℸ̃([ϕ̃	ζ̃ג+ℸ̃([ϕ̃	PROPN
ejpam-6489	381	5	,	,	PUNCT
ejpam-6489	381	6	η̃	η̃	PROPN
ejpam-6489	381	7	]	]	PUNCT
ejpam-6489	381	8	)	)	PUNCT
ejpam-6489	382	1	=	=	SYM
ejpam-6489	382	2	inf	inf	NOUN
ejpam-6489	383	1	[	[	X
ejpam-6489	383	2	ϕ̃,η̃]=ε̃+ς̃	ϕ̃,η̃]=ε̃+ς̃	X
ejpam-6489	383	3	{	{	PUNCT
ejpam-6489	383	4	ζ̃ג(ε̃	ζ̃ג(ε̃	NOUN
ejpam-6489	383	5	)	)	PUNCT
ejpam-6489	383	6	∨	∨	NUM
ejpam-6489	383	7	ζℸ̃(ς̃	ζℸ̃(ς̃	PROPN
ejpam-6489	383	8	)	)	PUNCT
ejpam-6489	383	9	}	}	PUNCT
ejpam-6489	383	10	≤	≤	NUM
ejpam-6489	383	11	inf	inf	PROPN
ejpam-6489	383	12	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	PROPN
ejpam-6489	383	13	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	383	14	{	{	PUNCT
ejpam-6489	383	15	ζ̃ג([ε̃1	ζ̃ג([ε̃1	PROPN
ejpam-6489	383	16	,	,	PUNCT
ejpam-6489	383	17	ε̃2	ε̃2	PROPN
ejpam-6489	383	18	]	]	PUNCT
ejpam-6489	383	19	)	)	PUNCT
ejpam-6489	383	20	∨	∨	NUM
ejpam-6489	383	21	ζℸ̃([ς̃1	ζℸ̃([ς̃1	PROPN
ejpam-6489	383	22	,	,	PUNCT
ejpam-6489	383	23	ς̃2	ς̃2	PROPN
ejpam-6489	383	24	]	]	X
ejpam-6489	383	25	)	)	PUNCT
ejpam-6489	383	26	}	}	PUNCT
ejpam-6489	383	27	≤	≤	NUM
ejpam-6489	383	28	inf	inf	PROPN
ejpam-6489	384	1	ϕ̃=ε̃1+ς̃1	ϕ̃=ε̃1+ς̃1	ADP
ejpam-6489	384	2	η̃=ε̃2+ς̃2	η̃=ε̃2+ς̃2	PROPN
ejpam-6489	384	3	{	{	PUNCT
ejpam-6489	384	4	(	(	PUNCT
ejpam-6489	384	5	ζ̃ג(ε̃1	ζ̃ג(ε̃1	NOUN
ejpam-6489	384	6	)	)	PUNCT
ejpam-6489	384	7	∨	∨	NUM
ejpam-6489	384	8	ζ̃ג(ε̃2	ζ̃ג(ε̃2	NOUN
ejpam-6489	384	9	)	)	PUNCT
ejpam-6489	384	10	)	)	PUNCT
ejpam-6489	385	1	∨	∨	NOUN
ejpam-6489	385	2	(	(	PUNCT
ejpam-6489	385	3	ζℸ̃(ς̃1	ζℸ̃(ς̃1	PROPN
ejpam-6489	385	4	)	)	PUNCT
ejpam-6489	385	5	∨	∨	NUM
ejpam-6489	385	6	ζℸ̃(ς̃2	ζℸ̃(ς̃2	NOUN
ejpam-6489	385	7	)	)	PUNCT
ejpam-6489	385	8	)	)	PUNCT
ejpam-6489	385	9	}	}	PUNCT
ejpam-6489	385	10	=	=	SYM
ejpam-6489	385	11	ζ̃ג+ℸ̃(ϕ̃	ζ̃ג+ℸ̃(ϕ̃	NUM
ejpam-6489	385	12	)	)	PUNCT
ejpam-6489	385	13	∨	∨	NOUN
ejpam-6489	385	14	ζ̃ג+ℸ̃(η̃	ζ̃ג+ℸ̃(η̃	NUM
ejpam-6489	385	15	)	)	PUNCT
ejpam-6489	385	16	.	.	PUNCT
ejpam-6489	386	1	hence	hence	ADV
ejpam-6489	386	2	,	,	PUNCT
ejpam-6489	386	3	+	+	ADJ
ejpam-6489	386	4	̃ג	̃ג	ADJ
ejpam-6489	386	5	ℸ̃	ℸ̃	PROPN
ejpam-6489	386	6	is	be	AUX
ejpam-6489	386	7	indeed	indeed	ADV
ejpam-6489	386	8	a	a	DET
ejpam-6489	386	9	+	+	ADJ
ejpam-6489	386	10	̃ג	̃ג	ADJ
ejpam-6489	386	11	ℸ̃	ℸ̃	PROPN
ejpam-6489	386	12	is	be	AUX
ejpam-6489	386	13	a	a	DET
ejpam-6489	386	14	t	t	NOUN
ejpam-6489	386	15	cfls	cfls	NOUN
ejpam-6489	386	16	of	of	ADP
ejpam-6489	386	17	l̃.	l̃.	ADJ
ejpam-6489	386	18	5	5	NUM
ejpam-6489	386	19	.	.	NOUN
ejpam-6489	386	20	nilpotent	nilpotent	ADJ
ejpam-6489	386	21	and	and	CCONJ
ejpam-6489	386	22	solvable	solvable	ADJ
ejpam-6489	386	23	tripolar	tripolar	ADJ
ejpam-6489	386	24	complex	complex	ADJ
ejpam-6489	386	25	fuzzy	fuzzy	ADJ
ejpam-6489	386	26	lie	lie	NOUN
ejpam-6489	386	27	ideals	ideal	NOUN
ejpam-6489	386	28	definition	definition	NOUN
ejpam-6489	386	29	13	13	NUM
ejpam-6489	386	30	.	.	PUNCT
ejpam-6489	387	1	a	a	DET
ejpam-6489	387	2	t	t	NOUN
ejpam-6489	387	3	cfli	cfli	PROPN
ejpam-6489	387	4	̃ג	̃ג	PROPN
ejpam-6489	387	5	=	=	PUNCT
ejpam-6489	387	6	(	(	PUNCT
ejpam-6489	387	7	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	387	8	,	,	PUNCT
ejpam-6489	387	9	ξ	ξ	PROPN
ejpam-6489	387	10	n	n	PRON
ejpam-6489	387	11	̃ג	̃ג	NOUN
ejpam-6489	387	12	,	,	PUNCT
ejpam-6489	387	13	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	387	14	)	)	PUNCT
ejpam-6489	387	15	is	be	AUX
ejpam-6489	387	16	called	call	VERB
ejpam-6489	387	17	nilpotent	nilpotent	ADJ
ejpam-6489	387	18	if	if	SCONJ
ejpam-6489	387	19	there	there	PRON
ejpam-6489	387	20	exists	exist	VERB
ejpam-6489	387	21	a	a	DET
ejpam-6489	387	22	positive	positive	ADJ
ejpam-6489	387	23	integer	integer	NOUN
ejpam-6489	387	24	n	n	CCONJ
ejpam-6489	387	25	such	such	ADJ
ejpam-6489	387	26	that	that	SCONJ
ejpam-6489	387	27	ñג	ñג	ADJ
ejpam-6489	387	28	=	=	ADJ
ejpam-6489	387	29	0	0	PROPN
ejpam-6489	387	30	.	.	PUNCT
ejpam-6489	387	31	theorem	theorem	VERB
ejpam-6489	387	32	7	7	NUM
ejpam-6489	387	33	.	.	PUNCT
ejpam-6489	388	1	a	a	DET
ejpam-6489	388	2	homomorphic	homomorphic	ADJ
ejpam-6489	388	3	image	image	NOUN
ejpam-6489	388	4	of	of	ADP
ejpam-6489	388	5	an	an	DET
ejpam-6489	388	6	nt	not	PART
ejpam-6489	388	7	cfli	cfli	NOUN
ejpam-6489	388	8	is	be	AUX
ejpam-6489	388	9	an	an	DET
ejpam-6489	388	10	nt	not	PART
ejpam-6489	388	11	cfli	cfli	NOUN
ejpam-6489	388	12	.	.	PUNCT
ejpam-6489	389	1	proof	proof	NOUN
ejpam-6489	389	2	.	.	PUNCT
ejpam-6489	390	1	let	let	VERB
ejpam-6489	390	2	f	f	NOUN
ejpam-6489	390	3	:	:	PUNCT
ejpam-6489	390	4	l̃1	l̃1	PROPN
ejpam-6489	390	5	→	→	PUNCT
ejpam-6489	390	6	l̃2	l̃2	PROPN
ejpam-6489	390	7	be	be	AUX
ejpam-6489	390	8	a	a	DET
ejpam-6489	390	9	homomorphism	homomorphism	NOUN
ejpam-6489	390	10	of	of	ADP
ejpam-6489	390	11	l̃	l̃	PROPN
ejpam-6489	390	12	,	,	PUNCT
ejpam-6489	390	13	and	and	CCONJ
ejpam-6489	390	14	let	let	VERB
ejpam-6489	390	15	̃ג	̃ג	NOUN
ejpam-6489	390	16	=	=	PUNCT
ejpam-6489	390	17	(	(	PUNCT
ejpam-6489	390	18	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	390	19	,	,	PUNCT
ejpam-6489	390	20	ξ	ξ	PROPN
ejpam-6489	390	21	n	n	PRON
ejpam-6489	390	22	̃ג	̃ג	NOUN
ejpam-6489	390	23	,	,	PUNCT
ejpam-6489	390	24	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	390	25	)	)	PUNCT
ejpam-6489	390	26	be	be	VERB
ejpam-6489	390	27	an	an	DET
ejpam-6489	390	28	nt	not	PART
ejpam-6489	390	29	cfli	cfli	NOUN
ejpam-6489	390	30	in	in	ADP
ejpam-6489	390	31	l̃1	l̃1	PROPN
ejpam-6489	390	32	.	.	PUNCT
ejpam-6489	391	1	assume	assume	VERB
ejpam-6489	391	2	f(̃ג	f(̃ג	PROPN
ejpam-6489	391	3	)	)	PUNCT
ejpam-6489	391	4	=	=	PROPN
ejpam-6489	391	5	ℸ̃.	ℸ̃.	PROPN
ejpam-6489	391	6	we	we	PRON
ejpam-6489	391	7	proceed	proceed	VERB
ejpam-6489	391	8	by	by	ADP
ejpam-6489	391	9	induction	induction	NOUN
ejpam-6489	391	10	to	to	PART
ejpam-6489	391	11	establish	establish	VERB
ejpam-6489	391	12	that	that	SCONJ
ejpam-6489	391	13	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	391	14	)	)	PUNCT
ejpam-6489	391	15	)	)	PUNCT
ejpam-6489	391	16	⊇	⊇	PROPN
ejpam-6489	391	17	m.	m.	NOUN
ejpam-6489	391	18	balamurugan	balamurugan	VERB
ejpam-6489	391	19	,	,	PUNCT
ejpam-6489	391	20	g.	g.	PROPN
ejpam-6489	391	21	ellammal	ellammal	PROPN
ejpam-6489	391	22	,	,	PUNCT
ejpam-6489	391	23	a.	a.	NOUN
ejpam-6489	391	24	iampan	iampan	PROPN
ejpam-6489	391	25	/	/	SYM
ejpam-6489	391	26	eur	eur	PROPN
ejpam-6489	391	27	.	.	PUNCT
ejpam-6489	392	1	j.	j.	PROPN
ejpam-6489	392	2	pure	pure	PROPN
ejpam-6489	392	3	appl	appl	PROPN
ejpam-6489	392	4	.	.	PROPN
ejpam-6489	392	5	math	math	PROPN
ejpam-6489	392	6	,	,	PUNCT
ejpam-6489	392	7	18	18	NUM
ejpam-6489	392	8	(	(	PUNCT
ejpam-6489	392	9	3	3	NUM
ejpam-6489	392	10	)	)	PUNCT
ejpam-6489	392	11	(	(	PUNCT
ejpam-6489	392	12	2025	2025	NUM
ejpam-6489	392	13	)	)	PUNCT
ejpam-6489	392	14	,	,	PUNCT
ejpam-6489	392	15	6489	6489	NUM
ejpam-6489	392	16	17	17	NUM
ejpam-6489	392	17	of	of	ADP
ejpam-6489	392	18	26	26	NUM
ejpam-6489	392	19	ℸ̃(n	ℸ̃(n	PROPN
ejpam-6489	392	20	)	)	PUNCT
ejpam-6489	392	21	for	for	ADP
ejpam-6489	392	22	n	n	DET
ejpam-6489	392	23	∈	∈	PROPN
ejpam-6489	392	24	ñ	ñ	PROPN
ejpam-6489	392	25	.	.	PUNCT
ejpam-6489	393	1	as	as	ADP
ejpam-6489	393	2	a	a	DET
ejpam-6489	393	3	base	base	NOUN
ejpam-6489	393	4	case	case	NOUN
ejpam-6489	393	5	,	,	PUNCT
ejpam-6489	393	6	we	we	PRON
ejpam-6489	393	7	first	first	ADV
ejpam-6489	393	8	demonstrate	demonstrate	VERB
ejpam-6489	393	9	that	that	SCONJ
ejpam-6489	393	10	f([̃ג	f([̃ג	NOUN
ejpam-6489	393	11	,	,	PUNCT
ejpam-6489	393	12	(	(	PUNCT
ejpam-6489	393	13	[	[	X
ejpam-6489	393	14	̃ג	̃ג	X
ejpam-6489	393	15	⊇	⊇	NOUN
ejpam-6489	393	16	[	[	X
ejpam-6489	393	17	f(̃ג	f(̃ג	PROPN
ejpam-6489	393	18	)	)	PUNCT
ejpam-6489	393	19	,	,	PUNCT
ejpam-6489	393	20	f(̃ג	f(̃ג	PROPN
ejpam-6489	393	21	)	)	PUNCT
ejpam-6489	393	22	]	]	PUNCT
ejpam-6489	393	23	=	=	PUNCT
ejpam-6489	394	1	[	[	X
ejpam-6489	394	2	ℸ̃	ℸ̃	PROPN
ejpam-6489	394	3	,	,	PUNCT
ejpam-6489	394	4	ℸ̃	ℸ̃	PROPN
ejpam-6489	394	5	]	]	PUNCT
ejpam-6489	394	6	.	.	PUNCT
ejpam-6489	395	1	let	let	VERB
ejpam-6489	395	2	η̃	η̃	PROPN
ejpam-6489	395	3	∈	∈	PROPN
ejpam-6489	395	4	l̃2	l̃2	PROPN
ejpam-6489	395	5	.	.	PUNCT
ejpam-6489	396	1	then	then	ADV
ejpam-6489	396	2	f	f	PROPN
ejpam-6489	396	3	(	(	PUNCT
ejpam-6489	396	4	⟨⟨ξp̃ג	⟨⟨ξp̃ג	X
ejpam-6489	396	5	,	,	PUNCT
ejpam-6489	396	6	ξ	ξ	X
ejpam-6489	396	7	p	p	X
ejpam-6489	396	8	̃ג	̃ג	NOUN
ejpam-6489	396	9	⟩⟩	⟩⟩	PUNCT
ejpam-6489	396	10	)	)	PUNCT
ejpam-6489	396	11	(	(	PUNCT
ejpam-6489	396	12	η̃	η̃	PROPN
ejpam-6489	396	13	)	)	PUNCT
ejpam-6489	397	1	=	=	SYM
ejpam-6489	397	2	sup	sup	NOUN
ejpam-6489	397	3	{	{	PUNCT
ejpam-6489	397	4	⟨⟨ξp̃ג	⟨⟨ξp̃ג	PROPN
ejpam-6489	397	5	,	,	PUNCT
ejpam-6489	397	6	ξ	ξ	X
ejpam-6489	397	7	p	p	X
ejpam-6489	397	8	̃ג	̃ג	NOUN
ejpam-6489	397	9	⟩⟩(ϕ̃	⟩⟩(ϕ̃	PROPN
ejpam-6489	397	10	)	)	PUNCT
ejpam-6489	397	11	|	|	ADV
ejpam-6489	397	12	f(ϕ̃	f(ϕ̃	ADJ
ejpam-6489	397	13	)	)	PUNCT
ejpam-6489	397	14	=	=	SYM
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ejpam-6489	397	20	sup	sup	PROPN
ejpam-6489	397	21	{	{	PUNCT
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ejpam-6489	397	23	{	{	PUNCT
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ejpam-6489	397	26	ε̃	ε̃	PROPN
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ejpam-6489	397	32	(	(	PUNCT
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ejpam-6489	398	9	ε̃	ε̃	PROPN
ejpam-6489	398	10	,	,	PUNCT
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ejpam-6489	398	17	)	)	PUNCT
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ejpam-6489	398	26	{	{	PUNCT
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ejpam-6489	398	29	ε̃	ε̃	PROPN
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ejpam-6489	398	35	(	(	PUNCT
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ejpam-6489	400	2	ε̃	ε̃	PROPN
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ejpam-6489	400	4	ς̃	ς̃	PROPN
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ejpam-6489	400	8	,	,	PUNCT
ejpam-6489	400	9	f(ϕ̃	f(ϕ̃	PROPN
ejpam-6489	400	10	)	)	PUNCT
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ejpam-6489	400	18	{	{	PUNCT
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ejpam-6489	400	21	ε̃	ε̃	PROPN
ejpam-6489	400	22	)	)	PUNCT
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ejpam-6489	400	25	p	p	X
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ejpam-6489	400	28	ς̃	ς̃	PROPN
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ejpam-6489	401	3	,	,	PUNCT
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ejpam-6489	401	7	,	,	PUNCT
ejpam-6489	401	8	[	[	X
ejpam-6489	401	9	f(ε̃	f(ε̃	NOUN
ejpam-6489	401	10	)	)	PUNCT
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ejpam-6489	401	12	f(ς̃	f(ς̃	PROPN
ejpam-6489	401	13	)	)	PUNCT
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ejpam-6489	402	6	{	{	PUNCT
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ejpam-6489	402	8	{	{	PUNCT
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ejpam-6489	402	10	(	(	PUNCT
ejpam-6489	402	11	ε̃	ε̃	PROPN
ejpam-6489	402	12	)	)	PUNCT
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ejpam-6489	402	15	p	p	X
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ejpam-6489	402	17	(	(	PUNCT
ejpam-6489	402	18	ς̃	ς̃	PROPN
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ejpam-6489	402	21	|	|	ADV
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ejpam-6489	402	23	,	,	PUNCT
ejpam-6489	402	24	ς̃	ς̃	PROPN
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ejpam-6489	402	28	f(ε̃	f(ε̃	NOUN
ejpam-6489	402	29	)	)	PUNCT
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ejpam-6489	402	33	f(ς̃	f(ς̃	PROPN
ejpam-6489	402	34	)	)	PUNCT
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ejpam-6489	402	37	,	,	PUNCT
ejpam-6489	402	38	[	[	X
ejpam-6489	402	39	ϖ̃	ϖ̃	PROPN
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ejpam-6489	402	48	{	{	PUNCT
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ejpam-6489	402	50	{	{	PUNCT
ejpam-6489	402	51	sup	sup	NOUN
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ejpam-6489	402	53	)	)	PUNCT
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ejpam-6489	402	59	sup	sup	NOUN
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ejpam-6489	402	61	)	)	PUNCT
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ejpam-6489	403	1	|	|	CCONJ
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ejpam-6489	403	3	ϖ̃	ϖ̃	PROPN
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ejpam-6489	403	5	ϑ̃	ϑ̃	PROPN
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ejpam-6489	403	14	{	{	PUNCT
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ejpam-6489	403	16	(	(	PUNCT
ejpam-6489	403	17	ϖ̃	ϖ̃	PROPN
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ejpam-6489	403	22	(	(	PUNCT
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ejpam-6489	404	3	ϖ̃	ϖ̃	PROPN
ejpam-6489	404	4	,	,	PUNCT
ejpam-6489	404	5	ϑ̃	ϑ̃	PROPN
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ejpam-6489	404	12	)	)	PUNCT
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ejpam-6489	404	15	p	p	X
ejpam-6489	404	16	̃ג	̃ג	NOUN
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ejpam-6489	404	19	)	)	PUNCT
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ejpam-6489	404	25	ξñג	ξñג	NOUN
ejpam-6489	404	26	⟩⟩	⟩⟩	PROPN
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ejpam-6489	404	29	η̃	η̃	PROPN
ejpam-6489	404	30	)	)	PUNCT
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ejpam-6489	404	33	{	{	PUNCT
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ejpam-6489	404	35	,	,	PUNCT
ejpam-6489	404	36	ξñג	ξñג	NOUN
ejpam-6489	404	37	⟩⟩(ϕ̃	⟩⟩(ϕ̃	PROPN
ejpam-6489	404	38	)	)	PUNCT
ejpam-6489	404	39	|	|	ADV
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ejpam-6489	404	41	)	)	PUNCT
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ejpam-6489	404	47	{	{	PUNCT
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ejpam-6489	404	51	{	{	PUNCT
ejpam-6489	404	52	ξñג	ξñג	PROPN
ejpam-6489	404	53	(	(	PUNCT
ejpam-6489	404	54	ε̃	ε̃	PROPN
ejpam-6489	404	55	)	)	PUNCT
ejpam-6489	404	56	,	,	PUNCT
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ejpam-6489	404	58	(	(	PUNCT
ejpam-6489	404	59	ς̃	ς̃	PROPN
ejpam-6489	404	60	)	)	PUNCT
ejpam-6489	404	61	}	}	PUNCT
ejpam-6489	404	62	|	|	ADV
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ejpam-6489	404	64	,	,	PUNCT
ejpam-6489	404	65	ς̃	ς̃	PROPN
ejpam-6489	404	66	∈	∈	PROPN
ejpam-6489	404	67	l̃1	l̃1	NOUN
ejpam-6489	404	68	,	,	PUNCT
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ejpam-6489	405	2	ε̃	ε̃	PROPN
ejpam-6489	405	3	,	,	PUNCT
ejpam-6489	405	4	ς̃	ς̃	PROPN
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ejpam-6489	405	6	=	=	SYM
ejpam-6489	405	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	405	8	,	,	PUNCT
ejpam-6489	405	9	f(ϕ̃	f(ϕ̃	PROPN
ejpam-6489	405	10	)	)	PUNCT
ejpam-6489	405	11	=	=	SYM
ejpam-6489	405	12	η̃	η̃	PROPN
ejpam-6489	405	13	}	}	PUNCT
ejpam-6489	405	14	}	}	PUNCT
ejpam-6489	405	15	=	=	SYM
ejpam-6489	405	16	inf	inf	PROPN
ejpam-6489	405	17	{	{	PUNCT
ejpam-6489	405	18	max	max	PROPN
ejpam-6489	405	19	{	{	PUNCT
ejpam-6489	405	20	ξñג	ξñג	PROPN
ejpam-6489	405	21	(	(	PUNCT
ejpam-6489	405	22	ε̃	ε̃	PROPN
ejpam-6489	405	23	)	)	PUNCT
ejpam-6489	405	24	,	,	PUNCT
ejpam-6489	405	25	ξñג	ξñג	PROPN
ejpam-6489	405	26	(	(	PUNCT
ejpam-6489	405	27	ς̃	ς̃	PROPN
ejpam-6489	405	28	)	)	PUNCT
ejpam-6489	405	29	}	}	PUNCT
ejpam-6489	406	1	|	|	ADV
ejpam-6489	406	2	ε̃	ε̃	PROPN
ejpam-6489	406	3	,	,	PUNCT
ejpam-6489	406	4	ς̃	ς̃	PROPN
ejpam-6489	406	5	∈	∈	PROPN
ejpam-6489	406	6	l̃1	l̃1	NOUN
ejpam-6489	406	7	,	,	PUNCT
ejpam-6489	406	8	[	[	X
ejpam-6489	406	9	ε̃	ε̃	PROPN
ejpam-6489	406	10	,	,	PUNCT
ejpam-6489	406	11	ς̃	ς̃	PROPN
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ejpam-6489	406	13	=	=	SYM
ejpam-6489	406	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	406	15	,	,	PUNCT
ejpam-6489	406	16	f(ϕ̃	f(ϕ̃	PROPN
ejpam-6489	406	17	)	)	PUNCT
ejpam-6489	406	18	=	=	SYM
ejpam-6489	406	19	η̃	η̃	PROPN
ejpam-6489	406	20	}	}	PUNCT
ejpam-6489	406	21	=	=	SYM
ejpam-6489	406	22	inf	inf	PROPN
ejpam-6489	406	23	{	{	PUNCT
ejpam-6489	406	24	max	max	PROPN
ejpam-6489	406	25	{	{	PUNCT
ejpam-6489	406	26	ξñג	ξñג	PROPN
ejpam-6489	406	27	(	(	PUNCT
ejpam-6489	406	28	ε̃	ε̃	PROPN
ejpam-6489	406	29	)	)	PUNCT
ejpam-6489	406	30	,	,	PUNCT
ejpam-6489	406	31	ξñג	ξñג	PROPN
ejpam-6489	406	32	(	(	PUNCT
ejpam-6489	406	33	ς̃	ς̃	PROPN
ejpam-6489	406	34	)	)	PUNCT
ejpam-6489	406	35	}	}	PUNCT
ejpam-6489	407	1	|	|	ADV
ejpam-6489	407	2	ε̃	ε̃	PROPN
ejpam-6489	407	3	,	,	PUNCT
ejpam-6489	407	4	ς̃	ς̃	PROPN
ejpam-6489	407	5	∈	∈	PROPN
ejpam-6489	407	6	l̃1	l̃1	PROPN
ejpam-6489	407	7	,	,	PUNCT
ejpam-6489	407	8	[	[	X
ejpam-6489	407	9	f(ε̃	f(ε̃	NOUN
ejpam-6489	407	10	)	)	PUNCT
ejpam-6489	407	11	,	,	PUNCT
ejpam-6489	407	12	f(ς̃	f(ς̃	PROPN
ejpam-6489	407	13	)	)	PUNCT
ejpam-6489	407	14	]	]	PUNCT
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ejpam-6489	408	2	η̃	η̃	PROPN
ejpam-6489	408	3	}	}	PUNCT
ejpam-6489	408	4	=	=	SYM
ejpam-6489	408	5	inf	inf	PROPN
ejpam-6489	408	6	{	{	PUNCT
ejpam-6489	408	7	max	max	PROPN
ejpam-6489	408	8	{	{	PUNCT
ejpam-6489	408	9	ξñג	ξñג	PROPN
ejpam-6489	408	10	(	(	PUNCT
ejpam-6489	408	11	ε̃	ε̃	PROPN
ejpam-6489	408	12	)	)	PUNCT
ejpam-6489	408	13	,	,	PUNCT
ejpam-6489	408	14	ξñג	ξñג	PROPN
ejpam-6489	408	15	(	(	PUNCT
ejpam-6489	408	16	ς̃	ς̃	PROPN
ejpam-6489	408	17	)	)	PUNCT
ejpam-6489	408	18	}	}	PUNCT
ejpam-6489	408	19	|	|	ADV
ejpam-6489	408	20	f(ε̃	f(ε̃	NOUN
ejpam-6489	408	21	)	)	PUNCT
ejpam-6489	408	22	=	=	SYM
ejpam-6489	408	23	ϖ̃	ϖ̃	PROPN
ejpam-6489	408	24	,	,	PUNCT
ejpam-6489	408	25	f(ς̃	f(ς̃	PROPN
ejpam-6489	408	26	)	)	PUNCT
ejpam-6489	408	27	=	=	SYM
ejpam-6489	408	28	ϑ̃	ϑ̃	PROPN
ejpam-6489	408	29	,	,	PUNCT
ejpam-6489	408	30	[	[	X
ejpam-6489	408	31	ϖ̃	ϖ̃	PROPN
ejpam-6489	408	32	,	,	PUNCT
ejpam-6489	408	33	ϑ̃	ϑ̃	PROPN
ejpam-6489	408	34	]	]	X
ejpam-6489	408	35	=	=	SYM
ejpam-6489	408	36	η̃	η̃	PROPN
ejpam-6489	408	37	}	}	PUNCT
ejpam-6489	408	38	≤	≤	PROPN
ejpam-6489	408	39	inf	inf	PROPN
ejpam-6489	408	40	{	{	PUNCT
ejpam-6489	408	41	max	max	PROPN
ejpam-6489	408	42	{	{	PUNCT
ejpam-6489	408	43	inf	inf	PROPN
ejpam-6489	408	44	ε̃∈f−1(ϖ̃	ε̃∈f−1(ϖ̃	PROPN
ejpam-6489	408	45	)	)	PUNCT
ejpam-6489	408	46	ξñג	ξñג	NOUN
ejpam-6489	408	47	(	(	PUNCT
ejpam-6489	408	48	ε̃	ε̃	PROPN
ejpam-6489	408	49	)	)	PUNCT
ejpam-6489	408	50	,	,	PUNCT
ejpam-6489	408	51	inf	inf	PROPN
ejpam-6489	408	52	ς̃∈f−1(ϑ̃	ς̃∈f−1(ϑ̃	NOUN
ejpam-6489	408	53	)	)	PUNCT
ejpam-6489	408	54	ξñג	ξñג	NOUN
ejpam-6489	408	55	(	(	PUNCT
ejpam-6489	408	56	ς̃	ς̃	PROPN
ejpam-6489	408	57	)	)	PUNCT
ejpam-6489	408	58	}	}	PUNCT
ejpam-6489	409	1	|	|	CCONJ
ejpam-6489	409	2	[	[	X
ejpam-6489	409	3	ϖ̃	ϖ̃	PROPN
ejpam-6489	409	4	,	,	PUNCT
ejpam-6489	409	5	ϑ̃	ϑ̃	PROPN
ejpam-6489	409	6	]	]	X
ejpam-6489	409	7	=	=	SYM
ejpam-6489	409	8	η̃	η̃	PROPN
ejpam-6489	409	9	}	}	PUNCT
ejpam-6489	409	10	=	=	SYM
ejpam-6489	409	11	inf	inf	PROPN
ejpam-6489	409	12	{	{	PUNCT
ejpam-6489	409	13	max	max	PROPN
ejpam-6489	409	14	{	{	PUNCT
ejpam-6489	409	15	f(ξñג	f(ξñג	PROPN
ejpam-6489	409	16	(	(	PUNCT
ejpam-6489	409	17	ϖ̃	ϖ̃	PROPN
ejpam-6489	409	18	)	)	PUNCT
ejpam-6489	409	19	)	)	PUNCT
ejpam-6489	409	20	,	,	PUNCT
ejpam-6489	409	21	f(ξñג	f(ξñג	PROPN
ejpam-6489	409	22	(	(	PUNCT
ejpam-6489	409	23	ϑ̃	ϑ̃	PROPN
ejpam-6489	409	24	)	)	PUNCT
ejpam-6489	409	25	)	)	PUNCT
ejpam-6489	409	26	}	}	PUNCT
ejpam-6489	410	1	|	|	CCONJ
ejpam-6489	410	2	[	[	X
ejpam-6489	410	3	ϖ̃	ϖ̃	PROPN
ejpam-6489	410	4	,	,	PUNCT
ejpam-6489	410	5	ϑ̃	ϑ̃	PROPN
ejpam-6489	410	6	]	]	X
ejpam-6489	410	7	=	=	SYM
ejpam-6489	410	8	η̃	η̃	PROPN
ejpam-6489	410	9	}	}	PUNCT
ejpam-6489	410	10	=	=	SYM
ejpam-6489	410	11	⟨⟨f(ξñג	⟨⟨f(ξñג	PROPN
ejpam-6489	410	12	)	)	PUNCT
ejpam-6489	410	13	,	,	PUNCT
ejpam-6489	410	14	f(ξñג	f(ξñג	NOUN
ejpam-6489	410	15	)	)	PUNCT
ejpam-6489	410	16	⟩⟩(η̃	⟩⟩(η̃	NOUN
ejpam-6489	410	17	)	)	PUNCT
ejpam-6489	410	18	.	.	PUNCT
ejpam-6489	411	1	also	also	ADV
ejpam-6489	411	2	,	,	PUNCT
ejpam-6489	411	3	f	f	PROPN
ejpam-6489	411	4	(	(	PUNCT
ejpam-6489	411	5	⟨⟨ζ̃ג	⟨⟨ζ̃ג	PROPN
ejpam-6489	411	6	,	,	PUNCT
ejpam-6489	411	7	ζ̃ג⟩⟩	ζ̃ג⟩⟩	PROPN
ejpam-6489	411	8	)	)	PUNCT
ejpam-6489	411	9	(	(	PUNCT
ejpam-6489	411	10	η̃	η̃	PROPN
ejpam-6489	411	11	)	)	PUNCT
ejpam-6489	411	12	=	=	PROPN
ejpam-6489	411	13	inf	inf	NOUN
ejpam-6489	411	14	{	{	PUNCT
ejpam-6489	411	15	⟨⟨ζ̃ג	⟨⟨ζ̃ג	PROPN
ejpam-6489	411	16	,	,	PUNCT
ejpam-6489	411	17	ζ̃ג⟩⟩(ϕ̃	ζ̃ג⟩⟩(ϕ̃	NUM
ejpam-6489	411	18	)	)	PUNCT
ejpam-6489	411	19	|	|	ADV
ejpam-6489	411	20	f(ϕ̃	f(ϕ̃	ADJ
ejpam-6489	411	21	)	)	PUNCT
ejpam-6489	411	22	=	=	SYM
ejpam-6489	411	23	η̃	η̃	PROPN
ejpam-6489	411	24	}	}	PUNCT
ejpam-6489	411	25	=	=	SYM
ejpam-6489	411	26	inf	inf	PROPN
ejpam-6489	411	27	{	{	PUNCT
ejpam-6489	411	28	inf	inf	PROPN
ejpam-6489	411	29	{	{	PUNCT
ejpam-6489	411	30	max	max	PROPN
ejpam-6489	411	31	{	{	PUNCT
ejpam-6489	411	32	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	411	33	)	)	PUNCT
ejpam-6489	411	34	,	,	PUNCT
ejpam-6489	411	35	ζ̃ג(ς̃	ζ̃ג(ς̃	PROPN
ejpam-6489	411	36	)	)	PUNCT
ejpam-6489	411	37	}	}	PUNCT
ejpam-6489	411	38	|	|	ADV
ejpam-6489	411	39	ε̃	ε̃	PROPN
ejpam-6489	411	40	,	,	PUNCT
ejpam-6489	411	41	ς̃	ς̃	PROPN
ejpam-6489	411	42	∈	∈	PROPN
ejpam-6489	411	43	l̃1	l̃1	NOUN
ejpam-6489	411	44	,	,	PUNCT
ejpam-6489	412	1	[	[	X
ejpam-6489	412	2	ε̃	ε̃	PROPN
ejpam-6489	412	3	,	,	PUNCT
ejpam-6489	412	4	ς̃	ς̃	PROPN
ejpam-6489	412	5	]	]	X
ejpam-6489	412	6	=	=	SYM
ejpam-6489	412	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	412	8	,	,	PUNCT
ejpam-6489	412	9	f(ϕ̃	f(ϕ̃	PROPN
ejpam-6489	412	10	)	)	PUNCT
ejpam-6489	412	11	=	=	SYM
ejpam-6489	412	12	η̃	η̃	PROPN
ejpam-6489	412	13	}	}	PUNCT
ejpam-6489	412	14	}	}	PUNCT
ejpam-6489	412	15	=	=	SYM
ejpam-6489	412	16	inf	inf	PROPN
ejpam-6489	412	17	{	{	PUNCT
ejpam-6489	412	18	max	max	PROPN
ejpam-6489	412	19	{	{	PUNCT
ejpam-6489	412	20	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	412	21	)	)	PUNCT
ejpam-6489	412	22	,	,	PUNCT
ejpam-6489	412	23	ζ̃ג(ς̃	ζ̃ג(ς̃	PROPN
ejpam-6489	412	24	)	)	PUNCT
ejpam-6489	412	25	}	}	PUNCT
ejpam-6489	413	1	|	|	ADV
ejpam-6489	413	2	ε̃	ε̃	PROPN
ejpam-6489	413	3	,	,	PUNCT
ejpam-6489	413	4	ς̃	ς̃	PROPN
ejpam-6489	413	5	∈	∈	PROPN
ejpam-6489	413	6	l̃1	l̃1	NOUN
ejpam-6489	413	7	,	,	PUNCT
ejpam-6489	413	8	[	[	X
ejpam-6489	413	9	ε̃	ε̃	PROPN
ejpam-6489	413	10	,	,	PUNCT
ejpam-6489	413	11	ς̃	ς̃	PROPN
ejpam-6489	413	12	]	]	X
ejpam-6489	413	13	=	=	SYM
ejpam-6489	413	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	413	15	,	,	PUNCT
ejpam-6489	413	16	f(ϕ̃	f(ϕ̃	PROPN
ejpam-6489	413	17	)	)	PUNCT
ejpam-6489	413	18	=	=	SYM
ejpam-6489	413	19	η̃	η̃	PROPN
ejpam-6489	413	20	}	}	PUNCT
ejpam-6489	413	21	=	=	SYM
ejpam-6489	413	22	inf	inf	PROPN
ejpam-6489	413	23	{	{	PUNCT
ejpam-6489	413	24	max	max	PROPN
ejpam-6489	413	25	{	{	PUNCT
ejpam-6489	413	26	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	413	27	)	)	PUNCT
ejpam-6489	413	28	,	,	PUNCT
ejpam-6489	413	29	ζ̃ג(ς̃	ζ̃ג(ς̃	PROPN
ejpam-6489	413	30	)	)	PUNCT
ejpam-6489	413	31	}	}	PUNCT
ejpam-6489	413	32	|	|	ADV
ejpam-6489	413	33	ε̃	ε̃	PROPN
ejpam-6489	413	34	,	,	PUNCT
ejpam-6489	413	35	ς̃	ς̃	PROPN
ejpam-6489	413	36	∈	∈	PROPN
ejpam-6489	413	37	l̃1	l̃1	PROPN
ejpam-6489	413	38	,	,	PUNCT
ejpam-6489	413	39	[	[	X
ejpam-6489	413	40	f(ε̃	f(ε̃	NOUN
ejpam-6489	413	41	)	)	PUNCT
ejpam-6489	413	42	,	,	PUNCT
ejpam-6489	413	43	f(ς̃	f(ς̃	PROPN
ejpam-6489	413	44	)	)	PUNCT
ejpam-6489	413	45	]	]	PUNCT
ejpam-6489	414	1	=	=	PUNCT
ejpam-6489	414	2	η̃	η̃	PROPN
ejpam-6489	414	3	}	}	PUNCT
ejpam-6489	414	4	m.	m.	NOUN
ejpam-6489	414	5	balamurugan	balamurugan	PROPN
ejpam-6489	414	6	,	,	PUNCT
ejpam-6489	414	7	g.	g.	PROPN
ejpam-6489	414	8	ellammal	ellammal	PROPN
ejpam-6489	414	9	,	,	PUNCT
ejpam-6489	414	10	a.	a.	NOUN
ejpam-6489	414	11	iampan	iampan	PROPN
ejpam-6489	414	12	/	/	SYM
ejpam-6489	414	13	eur	eur	PROPN
ejpam-6489	414	14	.	.	PUNCT
ejpam-6489	415	1	j.	j.	PROPN
ejpam-6489	415	2	pure	pure	PROPN
ejpam-6489	415	3	appl	appl	PROPN
ejpam-6489	415	4	.	.	PROPN
ejpam-6489	415	5	math	math	PROPN
ejpam-6489	415	6	,	,	PUNCT
ejpam-6489	415	7	18	18	NUM
ejpam-6489	415	8	(	(	PUNCT
ejpam-6489	415	9	3	3	NUM
ejpam-6489	415	10	)	)	PUNCT
ejpam-6489	415	11	(	(	PUNCT
ejpam-6489	415	12	2025	2025	NUM
ejpam-6489	415	13	)	)	PUNCT
ejpam-6489	415	14	,	,	PUNCT
ejpam-6489	415	15	6489	6489	NUM
ejpam-6489	415	16	18	18	NUM
ejpam-6489	415	17	of	of	ADP
ejpam-6489	415	18	26	26	NUM
ejpam-6489	415	19	=	=	SYM
ejpam-6489	415	20	inf	inf	PROPN
ejpam-6489	415	21	{	{	PUNCT
ejpam-6489	415	22	max	max	PROPN
ejpam-6489	415	23	{	{	PUNCT
ejpam-6489	415	24	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	415	25	)	)	PUNCT
ejpam-6489	415	26	,	,	PUNCT
ejpam-6489	415	27	ζ̃ג(ς̃	ζ̃ג(ς̃	PROPN
ejpam-6489	415	28	)	)	PUNCT
ejpam-6489	415	29	}	}	PUNCT
ejpam-6489	416	1	|	|	ADV
ejpam-6489	416	2	f(ε̃	f(ε̃	NOUN
ejpam-6489	416	3	)	)	PUNCT
ejpam-6489	417	1	=	=	SYM
ejpam-6489	417	2	ϖ̃	ϖ̃	PROPN
ejpam-6489	417	3	,	,	PUNCT
ejpam-6489	417	4	f(ς̃	f(ς̃	PROPN
ejpam-6489	417	5	)	)	PUNCT
ejpam-6489	417	6	=	=	SYM
ejpam-6489	417	7	ϑ̃	ϑ̃	PROPN
ejpam-6489	417	8	,	,	PUNCT
ejpam-6489	417	9	[	[	X
ejpam-6489	417	10	ϖ̃	ϖ̃	PROPN
ejpam-6489	417	11	,	,	PUNCT
ejpam-6489	417	12	ϑ̃	ϑ̃	PROPN
ejpam-6489	417	13	]	]	X
ejpam-6489	417	14	=	=	SYM
ejpam-6489	417	15	η̃	η̃	PROPN
ejpam-6489	417	16	}	}	PUNCT
ejpam-6489	417	17	≤	≤	PROPN
ejpam-6489	417	18	inf	inf	PROPN
ejpam-6489	417	19	{	{	PUNCT
ejpam-6489	417	20	max	max	PROPN
ejpam-6489	417	21	{	{	PUNCT
ejpam-6489	417	22	inf	inf	PROPN
ejpam-6489	417	23	ε̃∈f−1(ϖ̃	ε̃∈f−1(ϖ̃	PROPN
ejpam-6489	417	24	)	)	PUNCT
ejpam-6489	417	25	ζ̃ג(ε̃	ζ̃ג(ε̃	NOUN
ejpam-6489	417	26	)	)	PUNCT
ejpam-6489	417	27	,	,	PUNCT
ejpam-6489	417	28	inf	inf	NOUN
ejpam-6489	417	29	ς̃∈f−1(ϑ̃	ς̃∈f−1(ϑ̃	NOUN
ejpam-6489	417	30	)	)	PUNCT
ejpam-6489	417	31	ζ̃ג(ς̃	ζ̃ג(ς̃	PROPN
ejpam-6489	417	32	)	)	PUNCT
ejpam-6489	417	33	}	}	PUNCT
ejpam-6489	418	1	|	|	CCONJ
ejpam-6489	419	1	[	[	X
ejpam-6489	419	2	ϖ̃	ϖ̃	PROPN
ejpam-6489	419	3	,	,	PUNCT
ejpam-6489	419	4	ϑ̃	ϑ̃	PROPN
ejpam-6489	419	5	]	]	X
ejpam-6489	419	6	=	=	SYM
ejpam-6489	419	7	η̃	η̃	PROPN
ejpam-6489	419	8	}	}	PUNCT
ejpam-6489	419	9	=	=	SYM
ejpam-6489	419	10	inf	inf	PROPN
ejpam-6489	419	11	{	{	PUNCT
ejpam-6489	419	12	max	max	PROPN
ejpam-6489	419	13	{	{	PUNCT
ejpam-6489	419	14	f(ζ̃ג(ϖ̃	f(ζ̃ג(ϖ̃	PROPN
ejpam-6489	419	15	)	)	PUNCT
ejpam-6489	419	16	)	)	PUNCT
ejpam-6489	419	17	,	,	PUNCT
ejpam-6489	419	18	f(ζ̃ג(ϑ̃	f(ζ̃ג(ϑ̃	NOUN
ejpam-6489	419	19	)	)	PUNCT
ejpam-6489	419	20	)	)	PUNCT
ejpam-6489	419	21	}	}	PUNCT
ejpam-6489	420	1	|	|	CCONJ
ejpam-6489	420	2	[	[	X
ejpam-6489	420	3	ϖ̃	ϖ̃	PROPN
ejpam-6489	420	4	,	,	PUNCT
ejpam-6489	420	5	ϑ̃	ϑ̃	PROPN
ejpam-6489	420	6	]	]	X
ejpam-6489	420	7	=	=	SYM
ejpam-6489	420	8	η̃	η̃	PROPN
ejpam-6489	420	9	}	}	PUNCT
ejpam-6489	420	10	=	=	SYM
ejpam-6489	420	11	⟨⟨f(ζ̃ג	⟨⟨f(ζ̃ג	NUM
ejpam-6489	420	12	)	)	PUNCT
ejpam-6489	420	13	,	,	PUNCT
ejpam-6489	420	14	f(ζ̃ג)⟩⟩(η̃	f(ζ̃ג)⟩⟩(η̃	NOUN
ejpam-6489	420	15	)	)	PUNCT
ejpam-6489	420	16	.	.	PUNCT
ejpam-6489	421	1	thus	thus	ADV
ejpam-6489	421	2	,	,	PUNCT
ejpam-6489	421	3	f([̃ג	f([̃ג	NOUN
ejpam-6489	421	4	,	,	PUNCT
ejpam-6489	421	5	(	(	PUNCT
ejpam-6489	421	6	[	[	X
ejpam-6489	421	7	̃ג	̃ג	X
ejpam-6489	421	8	⊇	⊇	NOUN
ejpam-6489	421	9	f(⟨⟨̃ג	f(⟨⟨̃ג	NOUN
ejpam-6489	421	10	,	,	PUNCT
ejpam-6489	421	11	(	(	PUNCT
ejpam-6489	421	12	⟨⟨̃ג	⟨⟨̃ג	PROPN
ejpam-6489	421	13	⊇	⊇	X
ejpam-6489	421	14	⟨⟨f(̃ג	⟨⟨f(̃ג	PROPN
ejpam-6489	421	15	)	)	PUNCT
ejpam-6489	421	16	,	,	PUNCT
ejpam-6489	421	17	f(̃ג)⟩⟩	f(̃ג)⟩⟩	PROPN
ejpam-6489	421	18	=	=	SYM
ejpam-6489	421	19	[	[	X
ejpam-6489	421	20	f(̃ג	f(̃ג	PROPN
ejpam-6489	421	21	)	)	PUNCT
ejpam-6489	421	22	,	,	PUNCT
ejpam-6489	421	23	f(̃ג	f(̃ג	PROPN
ejpam-6489	421	24	)	)	PUNCT
ejpam-6489	421	25	]	]	PUNCT
ejpam-6489	421	26	.	.	PUNCT
ejpam-6489	422	1	for	for	ADP
ejpam-6489	422	2	n	n	PROPN
ejpam-6489	422	3	>	>	X
ejpam-6489	422	4	1	1	NUM
ejpam-6489	422	5	,	,	PUNCT
ejpam-6489	422	6	we	we	PRON
ejpam-6489	422	7	get	get	VERB
ejpam-6489	422	8	f(̃גn	f(̃גn	NOUN
ejpam-6489	422	9	)	)	PUNCT
ejpam-6489	423	1	=	=	SYM
ejpam-6489	423	2	f(̃ג	f(̃ג	PROPN
ejpam-6489	423	3	·	·	PUNCT
ejpam-6489	423	4	(	(	PUNCT
ejpam-6489	423	5	n−1̃ג	n−1̃ג	ADV
ejpam-6489	423	6	⊇	⊇	X
ejpam-6489	423	7	[	[	X
ejpam-6489	423	8	f(̃ג	f(̃ג	PROPN
ejpam-6489	423	9	)	)	PUNCT
ejpam-6489	423	10	,	,	PUNCT
ejpam-6489	423	11	f(̃גn−1	f(̃גn−1	NUM
ejpam-6489	423	12	)	)	PUNCT
ejpam-6489	423	13	]	]	PUNCT
ejpam-6489	423	14	⊇	⊇	NOUN
ejpam-6489	423	15	[	[	X
ejpam-6489	423	16	ℸ̃	ℸ̃	PROPN
ejpam-6489	423	17	,	,	PUNCT
ejpam-6489	423	18	ℸ̃n−1	ℸ̃n−1	PROPN
ejpam-6489	423	19	]	]	X
ejpam-6489	423	20	=	=	SYM
ejpam-6489	423	21	ℸ̃n	ℸ̃n	NOUN
ejpam-6489	423	22	.	.	PUNCT
ejpam-6489	424	1	let	let	VERB
ejpam-6489	424	2	m	m	PRON
ejpam-6489	424	3	be	be	AUX
ejpam-6489	424	4	a	a	DET
ejpam-6489	424	5	positive	positive	ADJ
ejpam-6489	424	6	integer	integer	NOUN
ejpam-6489	424	7	such	such	DET
ejpam-6489	424	8	that	that	SCONJ
ejpam-6489	424	9	m̃ג	m̃ג	PROPN
ejpam-6489	425	1	=	=	PROPN
ejpam-6489	425	2	0	0	PROPN
ejpam-6489	425	3	.	.	PUNCT
ejpam-6489	426	1	then	then	ADV
ejpam-6489	426	2	,	,	PUNCT
ejpam-6489	426	3	for	for	ADP
ejpam-6489	426	4	0	0	NUM
ejpam-6489	426	5	̸=	̸=	PROPN
ejpam-6489	426	6	η̃	η̃	PROPN
ejpam-6489	426	7	∈	∈	PROPN
ejpam-6489	426	8	l̃2	l̃2	PROPN
ejpam-6489	426	9	,	,	PUNCT
ejpam-6489	426	10	ξpℸ̃(m)(η̃	ξpℸ̃(m)(η̃	NOUN
ejpam-6489	426	11	)	)	PUNCT
ejpam-6489	426	12	≤	≤	NUM
ejpam-6489	426	13	f(ξp̃גn)(η̃	f(ξp̃גn)(η̃	NOUN
ejpam-6489	426	14	)	)	PUNCT
ejpam-6489	426	15	=	=	SYM
ejpam-6489	426	16	f(0)η̃	f(0)η̃	NOUN
ejpam-6489	426	17	=	=	SYM
ejpam-6489	426	18	sup	sup	NOUN
ejpam-6489	426	19	{	{	PUNCT
ejpam-6489	426	20	0(ε̃	0(ε̃	NOUN
ejpam-6489	426	21	)	)	PUNCT
ejpam-6489	426	22	|	|	ADV
ejpam-6489	426	23	f(ε̃	f(ε̃	NOUN
ejpam-6489	426	24	)	)	PUNCT
ejpam-6489	426	25	=	=	SYM
ejpam-6489	426	26	η̃	η̃	PROPN
ejpam-6489	426	27	}	}	PUNCT
ejpam-6489	426	28	=	=	SYM
ejpam-6489	426	29	0	0	NUM
ejpam-6489	426	30	,	,	PUNCT
ejpam-6489	426	31	ξnℸ̃m(η	ξnℸ̃m(η	NOUN
ejpam-6489	426	32	)	)	PUNCT
ejpam-6489	426	33	≤	≤	NUM
ejpam-6489	426	34	f(ξñגn)(η̃	f(ξñגn)(η̃	NOUN
ejpam-6489	426	35	)	)	PUNCT
ejpam-6489	426	36	=	=	SYM
ejpam-6489	426	37	f(0)η̃	f(0)η̃	NOUN
ejpam-6489	427	1	=	=	PROPN
ejpam-6489	427	2	inf	inf	PROPN
ejpam-6489	427	3	{	{	PUNCT
ejpam-6489	427	4	1(ε̃	1(ε̃	NUM
ejpam-6489	427	5	)	)	PUNCT
ejpam-6489	427	6	|	|	ADV
ejpam-6489	427	7	f(ε̃	f(ε̃	NOUN
ejpam-6489	427	8	)	)	PUNCT
ejpam-6489	427	9	=	=	SYM
ejpam-6489	427	10	η̃	η̃	PROPN
ejpam-6489	427	11	}	}	PUNCT
ejpam-6489	427	12	=	=	PUNCT
ejpam-6489	427	13	0	0	X
ejpam-6489	427	14	.	.	PUNCT
ejpam-6489	428	1	also	also	ADV
ejpam-6489	428	2	,	,	PUNCT
ejpam-6489	428	3	ζ̃ℸ̃m(η̃	ζ̃ℸ̃m(η̃	NOUN
ejpam-6489	428	4	)	)	PUNCT
ejpam-6489	428	5	≥	≥	PROPN
ejpam-6489	428	6	f(ζ̃̃גn)(η̃	f(ζ̃̃גn)(η̃	PROPN
ejpam-6489	428	7	)	)	PUNCT
ejpam-6489	428	8	=	=	PROPN
ejpam-6489	428	9	inf	inf	NOUN
ejpam-6489	428	10	{	{	PUNCT
ejpam-6489	428	11	1(ε̃	1(ε̃	NUM
ejpam-6489	428	12	)	)	PUNCT
ejpam-6489	428	13	|	|	ADV
ejpam-6489	428	14	f(ε̃	f(ε̃	NOUN
ejpam-6489	428	15	)	)	PUNCT
ejpam-6489	428	16	=	=	SYM
ejpam-6489	428	17	η̃	η̃	PROPN
ejpam-6489	428	18	}	}	PUNCT
ejpam-6489	428	19	=	=	PUNCT
ejpam-6489	428	20	0	0	X
ejpam-6489	428	21	.	.	PUNCT
ejpam-6489	429	1	thus	thus	ADV
ejpam-6489	429	2	,	,	PUNCT
ejpam-6489	429	3	ℸ̃m	ℸ̃m	ADJ
ejpam-6489	429	4	=	=	SYM
ejpam-6489	429	5	0	0	X
ejpam-6489	429	6	.	.	PUNCT
ejpam-6489	430	1	definition	definition	NOUN
ejpam-6489	430	2	14	14	NUM
ejpam-6489	430	3	.	.	PUNCT
ejpam-6489	431	1	let	let	VERB
ejpam-6489	431	2	̃ג	̃ג	NOUN
ejpam-6489	431	3	=	=	PUNCT
ejpam-6489	431	4	(	(	PUNCT
ejpam-6489	431	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	431	6	,	,	PUNCT
ejpam-6489	431	7	ξ	ξ	PROPN
ejpam-6489	431	8	n	n	PRON
ejpam-6489	431	9	̃ג	̃ג	NOUN
ejpam-6489	431	10	,	,	PUNCT
ejpam-6489	431	11	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	431	12	)	)	PUNCT
ejpam-6489	431	13	and	and	CCONJ
ejpam-6489	431	14	ℸ̃	ℸ̃	PROPN
ejpam-6489	431	15	=	=	SYM
ejpam-6489	431	16	(	(	PUNCT
ejpam-6489	431	17	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	431	18	,	,	PUNCT
ejpam-6489	431	19	ξ	ξ	PROPN
ejpam-6489	431	20	n	n	PRON
ejpam-6489	431	21	ℸ̃	ℸ̃	PROPN
ejpam-6489	431	22	,	,	PUNCT
ejpam-6489	431	23	ζ̃ℸ̃	ζ̃ℸ̃	NOUN
ejpam-6489	431	24	)	)	PUNCT
ejpam-6489	431	25	be	be	VERB
ejpam-6489	431	26	two	two	NUM
ejpam-6489	431	27	t	t	NOUN
ejpam-6489	431	28	cfli	cfli	NOUN
ejpam-6489	431	29	of	of	ADP
ejpam-6489	431	30	l̃.	l̃.	ADJ
ejpam-6489	431	31	the	the	DET
ejpam-6489	431	32	sum	sum	NOUN
ejpam-6489	431	33	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	431	34	ℸ̃	ℸ̃	PROPN
ejpam-6489	431	35	is	be	AUX
ejpam-6489	431	36	called	call	VERB
ejpam-6489	431	37	a	a	DET
ejpam-6489	431	38	direct	direct	ADJ
ejpam-6489	431	39	sum	sum	NOUN
ejpam-6489	431	40	if	if	SCONJ
ejpam-6489	431	41	̃ג	̃ג	NOUN
ejpam-6489	431	42	∩	∩	NOUN
ejpam-6489	431	43	ℸ̃	ℸ̃	PROPN
ejpam-6489	431	44	=	=	SYM
ejpam-6489	431	45	0	0	X
ejpam-6489	431	46	.	.	PUNCT
ejpam-6489	432	1	theorem	theorem	VERB
ejpam-6489	432	2	8	8	NUM
ejpam-6489	432	3	.	.	PUNCT
ejpam-6489	433	1	the	the	DET
ejpam-6489	433	2	direct	direct	ADJ
ejpam-6489	433	3	sum	sum	NOUN
ejpam-6489	433	4	of	of	ADP
ejpam-6489	433	5	two	two	NUM
ejpam-6489	433	6	nt	not	PART
ejpam-6489	433	7	cflis	cflis	PROPN
ejpam-6489	433	8	is	be	AUX
ejpam-6489	433	9	also	also	ADV
ejpam-6489	433	10	an	an	DET
ejpam-6489	433	11	nt	not	PART
ejpam-6489	433	12	cfli	cfli	NOUN
ejpam-6489	433	13	.	.	PUNCT
ejpam-6489	434	1	proof	proof	NOUN
ejpam-6489	434	2	.	.	PUNCT
ejpam-6489	435	1	suppose	suppose	VERB
ejpam-6489	435	2	that	that	SCONJ
ejpam-6489	435	3	̃ג	̃ג	NOUN
ejpam-6489	435	4	=	=	SYM
ejpam-6489	435	5	(	(	PUNCT
ejpam-6489	435	6	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	435	7	,	,	PUNCT
ejpam-6489	435	8	ξ	ξ	PROPN
ejpam-6489	435	9	n	n	PRON
ejpam-6489	435	10	̃ג	̃ג	NOUN
ejpam-6489	435	11	,	,	PUNCT
ejpam-6489	435	12	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	435	13	)	)	PUNCT
ejpam-6489	435	14	and	and	CCONJ
ejpam-6489	435	15	ℸ̃	ℸ̃	PROPN
ejpam-6489	435	16	=	=	SYM
ejpam-6489	435	17	(	(	PUNCT
ejpam-6489	435	18	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	435	19	,	,	PUNCT
ejpam-6489	435	20	ξ	ξ	PROPN
ejpam-6489	435	21	n	n	PRON
ejpam-6489	435	22	ℸ̃	ℸ̃	PROPN
ejpam-6489	435	23	,	,	PUNCT
ejpam-6489	435	24	ζ̃ℸ̃	ζ̃ℸ̃	NOUN
ejpam-6489	435	25	)	)	PUNCT
ejpam-6489	435	26	are	be	AUX
ejpam-6489	435	27	two	two	NUM
ejpam-6489	435	28	t	t	NOUN
ejpam-6489	435	29	cflis	cfli	VERB
ejpam-6489	435	30	such	such	ADJ
ejpam-6489	435	31	that	that	DET
ejpam-6489	435	32	̃ג	̃ג	NOUN
ejpam-6489	435	33	∩	∩	NOUN
ejpam-6489	435	34	ℸ̃	ℸ̃	PROPN
ejpam-6489	435	35	=	=	SYM
ejpam-6489	435	36	0	0	X
ejpam-6489	435	37	.	.	PUNCT
ejpam-6489	436	1	we	we	PRON
ejpam-6489	436	2	prove	prove	VERB
ejpam-6489	436	3	that	that	SCONJ
ejpam-6489	436	4	̃ג	̃ג	NOUN
ejpam-6489	436	5	∩	∩	NOUN
ejpam-6489	436	6	ℸ̃	ℸ̃	PROPN
ejpam-6489	436	7	=	=	SYM
ejpam-6489	436	8	0	0	X
ejpam-6489	436	9	.	.	PUNCT
ejpam-6489	437	1	let	let	VERB
ejpam-6489	437	2	ϕ̃(̸=	ϕ̃(̸=	ADJ
ejpam-6489	437	3	0	0	NUM
ejpam-6489	437	4	)	)	PUNCT
ejpam-6489	437	5	∈	∈	PROPN
ejpam-6489	438	1	l̃.	l̃.	ADV
ejpam-6489	438	2	then	then	ADV
ejpam-6489	438	3	⟨⟨ξp̃ג	⟨⟨ξp̃ג	PROPN
ejpam-6489	438	4	,	,	PUNCT
ejpam-6489	438	5	ξ	ξ	X
ejpam-6489	438	6	p	p	X
ejpam-6489	438	7	ℸ̃	ℸ̃	PROPN
ejpam-6489	438	8	⟩⟩(ϕ̃	⟩⟩(ϕ̃	NUM
ejpam-6489	438	9	)	)	PUNCT
ejpam-6489	438	10	=	=	SYM
ejpam-6489	438	11	sup	sup	NOUN
ejpam-6489	438	12	{	{	PUNCT
ejpam-6489	438	13	min	min	NOUN
ejpam-6489	438	14	{	{	PUNCT
ejpam-6489	438	15	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	438	16	(	(	PUNCT
ejpam-6489	438	17	ε̃	ε̃	PROPN
ejpam-6489	438	18	)	)	PUNCT
ejpam-6489	438	19	,	,	PUNCT
ejpam-6489	439	1	ξ	ξ	PROPN
ejpam-6489	439	2	p	p	X
ejpam-6489	439	3	ℸ̃	ℸ̃	PROPN
ejpam-6489	439	4	(	(	PUNCT
ejpam-6489	439	5	ϑ̃	ϑ̃	PROPN
ejpam-6489	439	6	)	)	PUNCT
ejpam-6489	439	7	}	}	PUNCT
ejpam-6489	440	1	|	|	CCONJ
ejpam-6489	441	1	[	[	X
ejpam-6489	441	2	ε̃	ε̃	PROPN
ejpam-6489	441	3	,	,	PUNCT
ejpam-6489	441	4	ς̃	ς̃	PROPN
ejpam-6489	441	5	]	]	X
ejpam-6489	441	6	=	=	PUNCT
ejpam-6489	441	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	441	8	}	}	PUNCT
ejpam-6489	441	9	≤	≤	NUM
ejpam-6489	441	10	min	min	NOUN
ejpam-6489	441	11	{	{	PUNCT
ejpam-6489	441	12	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	441	13	(	(	PUNCT
ejpam-6489	441	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	441	15	)	)	PUNCT
ejpam-6489	441	16	,	,	PUNCT
ejpam-6489	441	17	ξ	ξ	PROPN
ejpam-6489	441	18	p	p	X
ejpam-6489	441	19	ℸ̃	ℸ̃	PROPN
ejpam-6489	441	20	(	(	PUNCT
ejpam-6489	441	21	ϕ̃	ϕ̃	PROPN
ejpam-6489	441	22	)	)	PUNCT
ejpam-6489	441	23	}	}	PUNCT
ejpam-6489	441	24	=	=	SYM
ejpam-6489	441	25	0	0	NUM
ejpam-6489	441	26	and	and	CCONJ
ejpam-6489	441	27	⟨⟨ξñג	⟨⟨ξñג	PRON
ejpam-6489	441	28	,	,	PUNCT
ejpam-6489	441	29	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	441	30	⟩⟩(ϕ	⟩⟩(ϕ	NOUN
ejpam-6489	441	31	)	)	PUNCT
ejpam-6489	441	32	=	=	SYM
ejpam-6489	441	33	inf	inf	NOUN
ejpam-6489	441	34	{	{	PUNCT
ejpam-6489	441	35	max	max	PROPN
ejpam-6489	441	36	{	{	PUNCT
ejpam-6489	441	37	ξñג	ξñג	PROPN
ejpam-6489	441	38	(	(	PUNCT
ejpam-6489	441	39	ε̃	ε̃	PROPN
ejpam-6489	441	40	)	)	PUNCT
ejpam-6489	441	41	,	,	PUNCT
ejpam-6489	441	42	ξnℸ̃	ξnℸ̃	X
ejpam-6489	441	43	(	(	PUNCT
ejpam-6489	441	44	ϑ̃	ϑ̃	PROPN
ejpam-6489	441	45	)	)	PUNCT
ejpam-6489	441	46	}	}	PUNCT
ejpam-6489	441	47	|	|	CCONJ
ejpam-6489	442	1	[	[	X
ejpam-6489	442	2	ε̃	ε̃	PROPN
ejpam-6489	442	3	,	,	PUNCT
ejpam-6489	442	4	ς̃	ς̃	PROPN
ejpam-6489	442	5	]	]	X
ejpam-6489	442	6	=	=	SYM
ejpam-6489	442	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	442	8	}	}	PUNCT
ejpam-6489	442	9	≥	≥	NOUN
ejpam-6489	442	10	max	max	PROPN
ejpam-6489	442	11	{	{	PUNCT
ejpam-6489	442	12	ξñג	ξñג	PROPN
ejpam-6489	442	13	(	(	PUNCT
ejpam-6489	442	14	ϕ̃	ϕ̃	PROPN
ejpam-6489	442	15	)	)	PUNCT
ejpam-6489	442	16	,	,	PUNCT
ejpam-6489	442	17	ξnℸ̃	ξnℸ̃	X
ejpam-6489	442	18	(	(	PUNCT
ejpam-6489	442	19	ϕ̃	ϕ̃	PROPN
ejpam-6489	442	20	)	)	PUNCT
ejpam-6489	442	21	}	}	PUNCT
ejpam-6489	442	22	m.	m.	NOUN
ejpam-6489	442	23	balamurugan	balamurugan	NOUN
ejpam-6489	442	24	,	,	PUNCT
ejpam-6489	442	25	g.	g.	PROPN
ejpam-6489	442	26	ellammal	ellammal	PROPN
ejpam-6489	442	27	,	,	PUNCT
ejpam-6489	442	28	a.	a.	NOUN
ejpam-6489	442	29	iampan	iampan	PROPN
ejpam-6489	442	30	/	/	SYM
ejpam-6489	442	31	eur	eur	PROPN
ejpam-6489	442	32	.	.	PUNCT
ejpam-6489	443	1	j.	j.	PROPN
ejpam-6489	443	2	pure	pure	PROPN
ejpam-6489	443	3	appl	appl	PROPN
ejpam-6489	443	4	.	.	PROPN
ejpam-6489	443	5	math	math	PROPN
ejpam-6489	443	6	,	,	PUNCT
ejpam-6489	443	7	18	18	NUM
ejpam-6489	443	8	(	(	PUNCT
ejpam-6489	443	9	3	3	NUM
ejpam-6489	443	10	)	)	PUNCT
ejpam-6489	443	11	(	(	PUNCT
ejpam-6489	443	12	2025	2025	NUM
ejpam-6489	443	13	)	)	PUNCT
ejpam-6489	443	14	,	,	PUNCT
ejpam-6489	443	15	6489	6489	NUM
ejpam-6489	443	16	19	19	NUM
ejpam-6489	443	17	of	of	ADP
ejpam-6489	443	18	26	26	NUM
ejpam-6489	443	19	=	=	SYM
ejpam-6489	443	20	0	0	NUM
ejpam-6489	443	21	.	.	PUNCT
ejpam-6489	444	1	also	also	ADV
ejpam-6489	444	2	,	,	PUNCT
ejpam-6489	444	3	⟨⟨ζ̃ג	⟨⟨ζ̃ג	PROPN
ejpam-6489	444	4	,	,	PUNCT
ejpam-6489	444	5	ζℸ̃⟩⟩(ϕ	ζℸ̃⟩⟩(ϕ	NOUN
ejpam-6489	444	6	)	)	PUNCT
ejpam-6489	444	7	=	=	SYM
ejpam-6489	444	8	inf	inf	PROPN
ejpam-6489	444	9	{	{	PUNCT
ejpam-6489	444	10	max	max	PROPN
ejpam-6489	444	11	{	{	PUNCT
ejpam-6489	444	12	ζ̃ג(ε̃	ζ̃ג(ε̃	PROPN
ejpam-6489	444	13	)	)	PUNCT
ejpam-6489	444	14	,	,	PUNCT
ejpam-6489	444	15	ζℸ̃(ϑ̃	ζℸ̃(ϑ̃	PROPN
ejpam-6489	444	16	)	)	PUNCT
ejpam-6489	444	17	}	}	PUNCT
ejpam-6489	445	1	|	|	CCONJ
ejpam-6489	446	1	[	[	X
ejpam-6489	446	2	ε̃	ε̃	PROPN
ejpam-6489	446	3	,	,	PUNCT
ejpam-6489	446	4	ς̃	ς̃	PROPN
ejpam-6489	446	5	]	]	X
ejpam-6489	446	6	=	=	SYM
ejpam-6489	446	7	ϕ̃	ϕ̃	PROPN
ejpam-6489	446	8	}	}	PUNCT
ejpam-6489	446	9	≥	≥	NOUN
ejpam-6489	446	10	max	max	PROPN
ejpam-6489	446	11	{	{	PUNCT
ejpam-6489	446	12	ζ̃ג(ϕ̃	ζ̃ג(ϕ̃	PROPN
ejpam-6489	446	13	)	)	PUNCT
ejpam-6489	446	14	,	,	PUNCT
ejpam-6489	446	15	ζℸ̃(ϕ̃	ζℸ̃(ϕ̃	PROPN
ejpam-6489	446	16	)	)	PUNCT
ejpam-6489	446	17	}	}	PUNCT
ejpam-6489	446	18	=	=	PUNCT
ejpam-6489	446	19	0	0	X
ejpam-6489	446	20	.	.	PUNCT
ejpam-6489	447	1	therefore	therefore	ADV
ejpam-6489	447	2	,	,	PUNCT
ejpam-6489	447	3	̃ג	̃ג	NOUN
ejpam-6489	447	4	∩	∩	NOUN
ejpam-6489	447	5	ℸ̃	ℸ̃	PROPN
ejpam-6489	447	6	=	=	SYM
ejpam-6489	447	7	0	0	NUM
ejpam-6489	447	8	⇒	⇒	NOUN
ejpam-6489	447	9	,	,	PUNCT
ejpam-6489	447	10	m̃ג	m̃ג	PROPN
ejpam-6489	447	11	]	]	PUNCT
ejpam-6489	447	12	ℸ̃n	ℸ̃n	PROPN
ejpam-6489	447	13	]	]	X
ejpam-6489	447	14	=	=	PUNCT
ejpam-6489	447	15	0	0	NUM
ejpam-6489	447	16	,	,	PUNCT
ejpam-6489	447	17	for	for	ADP
ejpam-6489	447	18	all	all	DET
ejpam-6489	447	19	positive	positive	ADJ
ejpam-6489	447	20	integers	integer	NOUN
ejpam-6489	447	21	m	m	VERB
ejpam-6489	447	22	,	,	PUNCT
ejpam-6489	447	23	n.	n.	PROPN
ejpam-6489	447	24	also	also	ADV
ejpam-6489	447	25	,	,	PUNCT
ejpam-6489	447	26	we	we	PRON
ejpam-6489	447	27	claim	claim	VERB
ejpam-6489	447	28	that	that	SCONJ
ejpam-6489	447	29	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	447	30	)	)	PUNCT
ejpam-6489	448	1	ℸ̃)n	ℸ̃)n	X
ejpam-6489	448	2	⊆	⊆	NUM
ejpam-6489	448	3	ñג	ñג	PROPN
ejpam-6489	448	4	⊕	⊕	PROPN
ejpam-6489	448	5	ℸ̃n	ℸ̃n	PROPN
ejpam-6489	448	6	for	for	ADP
ejpam-6489	448	7	n	n	DET
ejpam-6489	448	8	∈	∈	PROPN
ejpam-6489	448	9	ñ	ñ	PROPN
ejpam-6489	448	10	.	.	PUNCT
ejpam-6489	449	1	we	we	PRON
ejpam-6489	449	2	proceed	proceed	VERB
ejpam-6489	449	3	by	by	ADP
ejpam-6489	449	4	induction	induction	NOUN
ejpam-6489	449	5	on	on	ADP
ejpam-6489	449	6	n.	n.	NOUN
ejpam-6489	449	7	for	for	ADP
ejpam-6489	449	8	n	n	NOUN
ejpam-6489	449	9	=	=	SYM
ejpam-6489	449	10	1	1	NUM
ejpam-6489	449	11	,	,	PUNCT
ejpam-6489	449	12	⊕̃ג	⊕̃ג	PROPN
ejpam-6489	449	13	)	)	PUNCT
ejpam-6489	449	14	ℸ̃)1	ℸ̃)1	NOUN
ejpam-6489	450	1	=	=	SYM
ejpam-6489	450	2	⊕̃ג	⊕̃ג	PROPN
ejpam-6489	450	3	]	]	PUNCT
ejpam-6489	450	4	ℸ̃	ℸ̃	PROPN
ejpam-6489	450	5	,	,	PUNCT
ejpam-6489	450	6	⊕̃ג	⊕̃ג	PROPN
ejpam-6489	450	7	ℸ̃	ℸ̃	PROPN
ejpam-6489	450	8	]	]	X
ejpam-6489	450	9	⊆	⊆	NUM
ejpam-6489	450	10	,	,	PUNCT
ejpam-6489	450	11	̃ג	̃ג	NOUN
ejpam-6489	450	12	]	]	PUNCT
ejpam-6489	450	13	⊕[̃ג	⊕[̃ג	ADP
ejpam-6489	450	14	,	,	PUNCT
ejpam-6489	450	15	̃ג	̃ג	PROPN
ejpam-6489	450	16	]	]	PUNCT
ejpam-6489	450	17	ℸ̃]⊕	ℸ̃]⊕	PROPN
ejpam-6489	450	18	[	[	X
ejpam-6489	450	19	ℸ̃	ℸ̃	PROPN
ejpam-6489	450	20	,	,	PUNCT
ejpam-6489	450	21	⊕[̃ג	⊕[̃ג	ADP
ejpam-6489	450	22	[	[	X
ejpam-6489	450	23	ℸ̃	ℸ̃	NOUN
ejpam-6489	450	24	,	,	PUNCT
ejpam-6489	450	25	ℸ̃	ℸ̃	PROPN
ejpam-6489	450	26	]	]	X
ejpam-6489	450	27	=	=	SYM
ejpam-6489	450	28	1̃ג	1̃ג	NUM
ejpam-6489	450	29	+	+	NUM
ejpam-6489	450	30	ℸ̃1	ℸ̃1	PROPN
ejpam-6489	450	31	.	.	PUNCT
ejpam-6489	451	1	now	now	ADV
ejpam-6489	451	2	,	,	PUNCT
ejpam-6489	451	3	for	for	ADP
ejpam-6489	451	4	n	n	PROPN
ejpam-6489	451	5	>	>	X
ejpam-6489	451	6	1	1	NUM
ejpam-6489	451	7	,	,	PUNCT
ejpam-6489	451	8	⊕̃ג	⊕̃ג	PROPN
ejpam-6489	451	9	)	)	PUNCT
ejpam-6489	451	10	ℸ̃)n	ℸ̃)n	NOUN
ejpam-6489	452	1	=	=	PUNCT
ejpam-6489	452	2	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	452	3	]	]	PUNCT
ejpam-6489	452	4	ℸ̃	ℸ̃	PROPN
ejpam-6489	452	5	,	,	PUNCT
ejpam-6489	452	6	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	452	7	)	)	PUNCT
ejpam-6489	452	8	ℸ̃)n−1	ℸ̃)n−1	PROPN
ejpam-6489	452	9	]	]	X
ejpam-6489	452	10	⊆	⊆	NUM
ejpam-6489	452	11	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	452	12	]	]	PUNCT
ejpam-6489	452	13	ℸ̃	ℸ̃	PROPN
ejpam-6489	452	14	,	,	PUNCT
ejpam-6489	452	15	n−1̃ג	n−1̃ג	ADV
ejpam-6489	452	16	⊕	⊕	PROPN
ejpam-6489	452	17	ℸ̃n−1	ℸ̃n−1	PROPN
ejpam-6489	452	18	]	]	X
ejpam-6489	452	19	⊆	⊆	NUM
ejpam-6489	452	20	,	,	PUNCT
ejpam-6489	452	21	̃ג	̃ג	NOUN
ejpam-6489	452	22	]	]	X
ejpam-6489	452	23	⊕[n−1̃ג	⊕[n−1̃ג	ADJ
ejpam-6489	452	24	,	,	PUNCT
ejpam-6489	452	25	̃ג	̃ג	X
ejpam-6489	452	26	]	]	PUNCT
ejpam-6489	453	1	ℸ̃n−1]⊕	ℸ̃n−1]⊕	PROPN
ejpam-6489	454	1	[	[	X
ejpam-6489	454	2	ℸ̃	ℸ̃	NOUN
ejpam-6489	454	3	,	,	PUNCT
ejpam-6489	454	4	⊕[n−1̃ג	⊕[n−1̃ג	ADJ
ejpam-6489	454	5	[	[	X
ejpam-6489	454	6	ℸ̃	ℸ̃	NOUN
ejpam-6489	454	7	,	,	PUNCT
ejpam-6489	454	8	ℸ̃n−1	ℸ̃n−1	PROPN
ejpam-6489	454	9	]	]	X
ejpam-6489	454	10	=	=	SYM
ejpam-6489	454	11	ñג	ñג	PROPN
ejpam-6489	454	12	⊕	⊕	PROPN
ejpam-6489	454	13	ℸ̃n	ℸ̃n	PROPN
ejpam-6489	454	14	.	.	PUNCT
ejpam-6489	455	1	since	since	SCONJ
ejpam-6489	455	2	,	,	PUNCT
ejpam-6489	455	3	there	there	PRON
ejpam-6489	455	4	are	be	VERB
ejpam-6489	455	5	two	two	NUM
ejpam-6489	455	6	positive	positive	ADJ
ejpam-6489	455	7	integers	integer	NOUN
ejpam-6489	455	8	r&t	r&t	NOUN
ejpam-6489	455	9	such	such	ADJ
ejpam-6489	455	10	that	that	DET
ejpam-6489	455	11	r̃ג	r̃ג	NOUN
ejpam-6489	455	12	=	=	PUNCT
ejpam-6489	455	13	ℸ̃t	ℸ̃t	PROPN
ejpam-6489	455	14	=	=	SYM
ejpam-6489	455	15	0	0	PROPN
ejpam-6489	455	16	,	,	PUNCT
ejpam-6489	455	17	we	we	PRON
ejpam-6489	455	18	have	have	VERB
ejpam-6489	455	19	⊕̃ג	⊕̃ג	NOUN
ejpam-6489	455	20	)	)	PUNCT
ejpam-6489	455	21	ℸ̃)r+t	ℸ̃)r+t	PROPN
ejpam-6489	456	1	⊆	⊆	NUM
ejpam-6489	456	2	r+t̃ג	r+t̃ג	PROPN
ejpam-6489	456	3	⊕	⊕	NOUN
ejpam-6489	456	4	ℸ̃r+t	ℸ̃r+t	PROPN
ejpam-6489	457	1	=	=	PUNCT
ejpam-6489	457	2	0	0	X
ejpam-6489	457	3	.	.	PUNCT
ejpam-6489	458	1	definition	definition	NOUN
ejpam-6489	458	2	15	15	NUM
ejpam-6489	458	3	.	.	PUNCT
ejpam-6489	459	1	a	a	DET
ejpam-6489	459	2	t	t	NOUN
ejpam-6489	459	3	cfli	cfli	PROPN
ejpam-6489	459	4	̃ג	̃ג	PROPN
ejpam-6489	459	5	=	=	PUNCT
ejpam-6489	459	6	(	(	PUNCT
ejpam-6489	459	7	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	459	8	,	,	PUNCT
ejpam-6489	459	9	ξ	ξ	PROPN
ejpam-6489	459	10	n	n	PRON
ejpam-6489	459	11	̃ג	̃ג	NOUN
ejpam-6489	459	12	,	,	PUNCT
ejpam-6489	459	13	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	459	14	)	)	PUNCT
ejpam-6489	459	15	is	be	AUX
ejpam-6489	459	16	called	call	VERB
ejpam-6489	459	17	solvable	solvable	ADJ
ejpam-6489	459	18	if	if	SCONJ
ejpam-6489	459	19	there	there	PRON
ejpam-6489	459	20	exists	exist	VERB
ejpam-6489	459	21	a	a	DET
ejpam-6489	459	22	positive	positive	ADJ
ejpam-6489	459	23	integer	integer	NOUN
ejpam-6489	459	24	n	n	CCONJ
ejpam-6489	459	25	such	such	ADJ
ejpam-6489	459	26	that	that	DET
ejpam-6489	459	27	ℸ̃(n	ℸ̃(n	PROPN
ejpam-6489	459	28	)	)	PUNCT
ejpam-6489	460	1	=	=	SYM
ejpam-6489	460	2	0	0	X
ejpam-6489	460	3	.	.	PUNCT
ejpam-6489	460	4	theorem	theorem	VERB
ejpam-6489	460	5	9	9	NUM
ejpam-6489	460	6	.	.	PUNCT
ejpam-6489	461	1	an	an	DET
ejpam-6489	461	2	nt	not	PART
ejpam-6489	461	3	cfli	cfli	NOUN
ejpam-6489	461	4	is	be	AUX
ejpam-6489	461	5	solvable	solvable	ADJ
ejpam-6489	461	6	.	.	PUNCT
ejpam-6489	462	1	proof	proof	NOUN
ejpam-6489	462	2	.	.	PUNCT
ejpam-6489	463	1	to	to	PART
ejpam-6489	463	2	establish	establish	VERB
ejpam-6489	463	3	the	the	DET
ejpam-6489	463	4	desired	desire	VERB
ejpam-6489	463	5	result	result	NOUN
ejpam-6489	463	6	,	,	PUNCT
ejpam-6489	463	7	it	it	PRON
ejpam-6489	463	8	suffices	suffice	VERB
ejpam-6489	463	9	to	to	PART
ejpam-6489	463	10	show	show	VERB
ejpam-6489	463	11	that	that	SCONJ
ejpam-6489	463	12	(	(	PUNCT
ejpam-6489	463	13	n)̃ג	n)̃ג	PROPN
ejpam-6489	463	14	⊆	⊆	NUM
ejpam-6489	463	15	,	,	PUNCT
ejpam-6489	463	16	ñג	ñג	ADJ
ejpam-6489	463	17	for	for	ADP
ejpam-6489	463	18	all	all	DET
ejpam-6489	463	19	positive	positive	ADJ
ejpam-6489	463	20	integer	integer	NOUN
ejpam-6489	463	21	n.	n.	NOUN
ejpam-6489	463	22	we	we	PRON
ejpam-6489	463	23	will	will	AUX
ejpam-6489	463	24	prove	prove	VERB
ejpam-6489	463	25	this	this	DET
ejpam-6489	463	26	statement	statement	NOUN
ejpam-6489	463	27	by	by	ADP
ejpam-6489	463	28	induction	induction	NOUN
ejpam-6489	463	29	on	on	ADP
ejpam-6489	463	30	n	n	CCONJ
ejpam-6489	463	31	,	,	PUNCT
ejpam-6489	463	32	making	make	VERB
ejpam-6489	463	33	use	use	NOUN
ejpam-6489	463	34	of	of	ADP
ejpam-6489	463	35	theorem	theorem	NOUN
ejpam-6489	463	36	2	2	NUM
ejpam-6489	463	37	,	,	PUNCT
ejpam-6489	463	38	(	(	PUNCT
ejpam-6489	463	39	1)̃ג	1)̃ג	NUM
ejpam-6489	463	40	=	=	SYM
ejpam-6489	463	41	,	,	PUNCT
ejpam-6489	463	42	̃ג	̃ג	X
ejpam-6489	463	43	]	]	PUNCT
ejpam-6489	464	1	[	[	X
ejpam-6489	464	2	̃ג	̃ג	NOUN
ejpam-6489	464	3	=	=	SYM
ejpam-6489	464	4	(	(	PUNCT
ejpam-6489	464	5	1)̃ג	1)̃ג	NUM
ejpam-6489	464	6	(	(	PUNCT
ejpam-6489	464	7	2)̃ג	2)̃ג	NUM
ejpam-6489	464	8	=	=	SYM
ejpam-6489	464	9	,	,	PUNCT
ejpam-6489	464	10	(	(	PUNCT
ejpam-6489	464	11	1)̃ג	1)̃ג	NUM
ejpam-6489	464	12	]	]	PUNCT
ejpam-6489	465	1	[	[	X
ejpam-6489	465	2	(	(	PUNCT
ejpam-6489	465	3	1)̃ג	1)̃ג	NUM
ejpam-6489	465	4	⊆	⊆	NUM
ejpam-6489	465	5	,	,	PUNCT
ejpam-6489	465	6	̃ג	̃ג	X
ejpam-6489	465	7	]	]	PUNCT
ejpam-6489	466	1	[	[	X
ejpam-6489	466	2	(	(	PUNCT
ejpam-6489	466	3	1)̃ג	1)̃ג	NUM
ejpam-6489	466	4	=	=	SYM
ejpam-6489	466	5	2̃ג	2̃ג	NUM
ejpam-6489	466	6	(	(	PUNCT
ejpam-6489	466	7	3)̃ג	3)̃ג	NUM
ejpam-6489	466	8	=	=	SYM
ejpam-6489	466	9	,	,	PUNCT
ejpam-6489	466	10	(	(	PUNCT
ejpam-6489	466	11	2)̃ג	2)̃ג	NUM
ejpam-6489	466	12	]	]	X
ejpam-6489	467	1	[	[	X
ejpam-6489	467	2	(	(	PUNCT
ejpam-6489	467	3	2)̃ג	2)̃ג	NUM
ejpam-6489	467	4	⊆	⊆	NUM
ejpam-6489	467	5	,	,	PUNCT
ejpam-6489	467	6	̃ג	̃ג	X
ejpam-6489	467	7	]	]	PUNCT
ejpam-6489	467	8	[	[	X
ejpam-6489	467	9	(	(	PUNCT
ejpam-6489	467	10	2)̃ג	2)̃ג	NUM
ejpam-6489	467	11	=	=	SYM
ejpam-6489	467	12	3̃ג	3̃ג	NUM
ejpam-6489	467	13	...	...	PUNCT
ejpam-6489	467	14	(	(	PUNCT
ejpam-6489	467	15	n)̃ג	n)̃ג	PROPN
ejpam-6489	467	16	=	=	SYM
ejpam-6489	467	17	,	,	PUNCT
ejpam-6489	467	18	(	(	PUNCT
ejpam-6489	467	19	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	467	20	]	]	X
ejpam-6489	468	1	[	[	X
ejpam-6489	468	2	(	(	PUNCT
ejpam-6489	468	3	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	468	4	⊆	⊆	NUM
ejpam-6489	468	5	,	,	PUNCT
ejpam-6489	468	6	̃ג	̃ג	X
ejpam-6489	468	7	]	]	PUNCT
ejpam-6489	469	1	[	[	X
ejpam-6489	469	2	(	(	PUNCT
ejpam-6489	469	3	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	469	4	⊆	⊆	NUM
ejpam-6489	469	5	,	,	PUNCT
ejpam-6489	469	6	̃ג	̃ג	X
ejpam-6489	469	7	]	]	PUNCT
ejpam-6489	470	1	[	[	X
ejpam-6489	470	2	(	(	PUNCT
ejpam-6489	470	3	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	470	4	=	=	SYM
ejpam-6489	470	5	.ñג	.ñג	PROPN
ejpam-6489	470	6	definition	definition	NOUN
ejpam-6489	470	7	16	16	NUM
ejpam-6489	470	8	.	.	PUNCT
ejpam-6489	471	1	let	let	VERB
ejpam-6489	471	2	̃ג	̃ג	NOUN
ejpam-6489	471	3	=	=	PUNCT
ejpam-6489	471	4	(	(	PUNCT
ejpam-6489	471	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	471	6	,	,	PUNCT
ejpam-6489	471	7	ξ	ξ	PROPN
ejpam-6489	471	8	n	n	PRON
ejpam-6489	471	9	̃ג	̃ג	PROPN
ejpam-6489	471	10	,	,	PUNCT
ejpam-6489	471	11	ζ̃ג	ζ̃ג	PROPN
ejpam-6489	471	12	)	)	PUNCT
ejpam-6489	471	13	be	be	VERB
ejpam-6489	471	14	a	a	DET
ejpam-6489	471	15	t	t	NOUN
ejpam-6489	471	16	cfli	cfli	NOUN
ejpam-6489	471	17	of	of	ADP
ejpam-6489	471	18	l̃.	l̃.	ADV
ejpam-6489	471	19	construct	construct	VERB
ejpam-6489	471	20	a	a	DET
ejpam-6489	471	21	sequence	sequence	NOUN
ejpam-6489	471	22	of	of	ADP
ejpam-6489	471	23	t	t	NOUN
ejpam-6489	471	24	cflis	cfli	NOUN
ejpam-6489	471	25	of	of	ADP
ejpam-6489	471	26	l̃	l̃	PROPN
ejpam-6489	471	27	by	by	ADP
ejpam-6489	471	28	m.	m.	NOUN
ejpam-6489	471	29	balamurugan	balamurugan	PROPN
ejpam-6489	471	30	,	,	PUNCT
ejpam-6489	471	31	g.	g.	PROPN
ejpam-6489	471	32	ellammal	ellammal	PROPN
ejpam-6489	471	33	,	,	PUNCT
ejpam-6489	471	34	a.	a.	NOUN
ejpam-6489	471	35	iampan	iampan	PROPN
ejpam-6489	471	36	/	/	SYM
ejpam-6489	471	37	eur	eur	PROPN
ejpam-6489	471	38	.	.	PUNCT
ejpam-6489	472	1	j.	j.	PROPN
ejpam-6489	472	2	pure	pure	PROPN
ejpam-6489	472	3	appl	appl	PROPN
ejpam-6489	472	4	.	.	PROPN
ejpam-6489	472	5	math	math	PROPN
ejpam-6489	472	6	,	,	PUNCT
ejpam-6489	472	7	18	18	NUM
ejpam-6489	472	8	(	(	PUNCT
ejpam-6489	472	9	3	3	NUM
ejpam-6489	472	10	)	)	PUNCT
ejpam-6489	472	11	(	(	PUNCT
ejpam-6489	472	12	2025	2025	NUM
ejpam-6489	472	13	)	)	PUNCT
ejpam-6489	472	14	,	,	PUNCT
ejpam-6489	472	15	6489	6489	NUM
ejpam-6489	472	16	20	20	NUM
ejpam-6489	472	17	of	of	ADP
ejpam-6489	472	18	26	26	NUM
ejpam-6489	472	19	(	(	PUNCT
ejpam-6489	472	20	0)̃ג	0)̃ג	NUM
ejpam-6489	472	21	=	=	SYM
ejpam-6489	472	22	,	,	PUNCT
ejpam-6489	472	23	̃ג	̃ג	NOUN
ejpam-6489	472	24	(	(	PUNCT
ejpam-6489	472	25	1)̃ג	1)̃ג	NUM
ejpam-6489	472	26	=	=	SYM
ejpam-6489	472	27	,	,	PUNCT
ejpam-6489	472	28	(	(	PUNCT
ejpam-6489	472	29	0)̃ג	0)̃ג	NUM
ejpam-6489	472	30	]	]	PUNCT
ejpam-6489	472	31	,	,	PUNCT
ejpam-6489	472	32	[	[	X
ejpam-6489	472	33	(	(	PUNCT
ejpam-6489	472	34	0)̃ג	0)̃ג	NUM
ejpam-6489	472	35	(	(	PUNCT
ejpam-6489	472	36	2)̃ג	2)̃ג	NUM
ejpam-6489	472	37	=	=	SYM
ejpam-6489	472	38	,	,	PUNCT
ejpam-6489	472	39	(	(	PUNCT
ejpam-6489	472	40	1)̃ג	1)̃ג	NUM
ejpam-6489	472	41	]	]	PUNCT
ejpam-6489	472	42	,	,	PUNCT
ejpam-6489	472	43	[	[	X
ejpam-6489	472	44	(	(	PUNCT
ejpam-6489	472	45	1)̃ג	1)̃ג	NUM
ejpam-6489	472	46	...	...	PUNCT
ejpam-6489	472	47	,	,	PUNCT
ejpam-6489	472	48	(	(	PUNCT
ejpam-6489	472	49	n)̃ג	n)̃ג	PROPN
ejpam-6489	472	50	=	=	SYM
ejpam-6489	472	51	,	,	PUNCT
ejpam-6489	472	52	(	(	PUNCT
ejpam-6489	472	53	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	472	54	]	]	PUNCT
ejpam-6489	472	55	,	,	PUNCT
ejpam-6489	472	56	[	[	X
ejpam-6489	472	57	(	(	PUNCT
ejpam-6489	472	58	n−1)̃ג	n−1)̃ג	NOUN
ejpam-6489	472	59	then	then	ADV
ejpam-6489	472	60	(	(	PUNCT
ejpam-6489	472	61	n)̃ג	n)̃ג	PROPN
ejpam-6489	472	62	is	be	AUX
ejpam-6489	472	63	called	call	VERB
ejpam-6489	472	64	the	the	DET
ejpam-6489	472	65	nth	nth	NOUN
ejpam-6489	472	66	derived	derive	VERB
ejpam-6489	472	67	tcfli	tcfli	NOUN
ejpam-6489	472	68	of	of	ADP
ejpam-6489	472	69	l̃.	l̃.	NOUN
ejpam-6489	472	70	in	in	ADP
ejpam-6489	472	71	which	which	PRON
ejpam-6489	472	72	,	,	PUNCT
ejpam-6489	472	73	(	(	PUNCT
ejpam-6489	472	74	i+1)̃ג	i+1)̃ג	PROPN
ejpam-6489	472	75	=	=	SYM
ejpam-6489	472	76	(	(	PUNCT
ejpam-6489	472	77	ξp̃ג(i+1	ξp̃ג(i+1	ADV
ejpam-6489	472	78	)	)	PUNCT
ejpam-6489	472	79	,	,	PUNCT
ejpam-6489	472	80	ξ	ξ	PROPN
ejpam-6489	472	81	n	n	X
ejpam-6489	472	82	(	(	PUNCT
ejpam-6489	472	83	i+1)̃ג	i+1)̃ג	PROPN
ejpam-6489	472	84	,	,	PUNCT
ejpam-6489	472	85	ζ̃ג(i+1	ζ̃ג(i+1	PROPN
ejpam-6489	472	86	)	)	PUNCT
ejpam-6489	472	87	)	)	PUNCT
ejpam-6489	472	88	,	,	PUNCT
ejpam-6489	472	89	where	where	SCONJ
ejpam-6489	472	90	(	(	PUNCT
ejpam-6489	472	91	i	i	NOUN
ejpam-6489	472	92	)	)	PUNCT
ejpam-6489	472	93	if	if	SCONJ
ejpam-6489	472	94	β̃j	β̃j	PROPN
ejpam-6489	472	95	∈	∈	PROPN
ejpam-6489	472	96	f	f	PROPN
ejpam-6489	472	97	,	,	PUNCT
ejpam-6489	472	98	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	472	99	,	,	PUNCT
ejpam-6489	472	100	η̃j	η̃j	PROPN
ejpam-6489	472	101	∈	∈	PROPN
ejpam-6489	472	102	l̃	l̃	PROPN
ejpam-6489	472	103	,	,	PUNCT
ejpam-6489	472	104	then	then	ADV
ejpam-6489	472	105	ξp̃ג(i+1)(ϕ̃	ξp̃ג(i+1)(ϕ̃	NUM
ejpam-6489	472	106	)	)	PUNCT
ejpam-6489	472	107	=	=	VERB
ejpam-6489	473	1	supϕ̃=	supϕ̃=	ADV
ejpam-6489	473	2	∑	∑	PUNCT
ejpam-6489	473	3	j∈n	j∈n	NOUN
ejpam-6489	473	4	β̃j	β̃j	PROPN
ejpam-6489	474	1	[	[	X
ejpam-6489	474	2	ϕ̃j	ϕ̃j	X
ejpam-6489	474	3	,	,	PUNCT
ejpam-6489	474	4	η̃j	η̃j	PROPN
ejpam-6489	474	5	]	]	PUNCT
ejpam-6489	474	6	{	{	PUNCT
ejpam-6489	474	7	minj∈n	minj∈n	PROPN
ejpam-6489	474	8	{	{	PUNCT
ejpam-6489	474	9	r̃p̃ג(i)(ϕ̃j	r̃p̃ג(i)(ϕ̃j	PROPN
ejpam-6489	474	10	)	)	PUNCT
ejpam-6489	474	11	∧	∧	PROPN
ejpam-6489	474	12	r̃p̃ג(i)(η̃j)}e	r̃p̃ג(i)(η̃j)}e	NOUN
ejpam-6489	475	1	i2πminj∈n	i2πminj∈n	INTJ
ejpam-6489	475	2	{	{	PUNCT
ejpam-6489	475	3	ω̃p	ω̃p	PROPN
ejpam-6489	475	4	(	(	PUNCT
ejpam-6489	475	5	i)̃ג	i)̃ג	PROPN
ejpam-6489	475	6	(	(	PUNCT
ejpam-6489	475	7	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	475	8	(	(	PUNCT
ejpam-6489	475	9	i)̃ג	i)̃ג	PROPN
ejpam-6489	475	10	(	(	PUNCT
ejpam-6489	475	11	η̃j	η̃j	NOUN
ejpam-6489	475	12	)	)	PUNCT
ejpam-6489	475	13	}	}	PUNCT
ejpam-6489	475	14	}	}	PUNCT
ejpam-6489	475	15	and	and	CCONJ
ejpam-6489	475	16	if	if	SCONJ
ejpam-6489	475	17	ϕ̃	ϕ̃	PROPN
ejpam-6489	475	18	̸=	̸=	PROPN
ejpam-6489	475	19	∑	∑	ADP
ejpam-6489	475	20	j∈n	j∈n	NOUN
ejpam-6489	475	21	β̃i[ϕ̃i	β̃i[ϕ̃i	PROPN
ejpam-6489	475	22	,	,	PUNCT
ejpam-6489	475	23	η̃j	η̃j	PROPN
ejpam-6489	475	24	]	]	PUNCT
ejpam-6489	475	25	,	,	PUNCT
ejpam-6489	475	26	then	then	ADV
ejpam-6489	475	27	ξp̃ג(i+1)(ϕ̃	ξp̃ג(i+1)(ϕ̃	ADP
ejpam-6489	475	28	)	)	PUNCT
ejpam-6489	475	29	=	=	SYM
ejpam-6489	475	30	0	0	NUM
ejpam-6489	475	31	,	,	PUNCT
ejpam-6489	475	32	(	(	PUNCT
ejpam-6489	475	33	ii	ii	NOUN
ejpam-6489	475	34	)	)	PUNCT
ejpam-6489	475	35	if	if	SCONJ
ejpam-6489	475	36	β̃j	β̃j	PROPN
ejpam-6489	475	37	∈	∈	PROPN
ejpam-6489	475	38	f	f	PROPN
ejpam-6489	475	39	,	,	PUNCT
ejpam-6489	475	40	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	475	41	,	,	PUNCT
ejpam-6489	475	42	η̃j	η̃j	PROPN
ejpam-6489	475	43	∈	∈	PROPN
ejpam-6489	475	44	l̃	l̃	PROPN
ejpam-6489	475	45	,	,	PUNCT
ejpam-6489	475	46	then	then	ADV
ejpam-6489	475	47	ξñג(i+1)(ϕ̃	ξñג(i+1)(ϕ̃	PROPN
ejpam-6489	475	48	)	)	PUNCT
ejpam-6489	475	49	=	=	SYM
ejpam-6489	475	50	inf	inf	ADJ
ejpam-6489	475	51	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	475	52	∑	∑	PROPN
ejpam-6489	475	53	j∈n	j∈n	NOUN
ejpam-6489	475	54	β̃j	β̃j	PROPN
ejpam-6489	476	1	[	[	X
ejpam-6489	476	2	ϕ̃j	ϕ̃j	X
ejpam-6489	476	3	,	,	PUNCT
ejpam-6489	476	4	η̃j	η̃j	PROPN
ejpam-6489	476	5	]	]	PUNCT
ejpam-6489	476	6	{	{	PUNCT
ejpam-6489	476	7	maxj∈n	maxj∈n	NOUN
ejpam-6489	476	8	{	{	PUNCT
ejpam-6489	476	9	r̃ñג(i)(ϕ̃j	r̃ñג(i)(ϕ̃j	PROPN
ejpam-6489	476	10	)	)	PUNCT
ejpam-6489	476	11	∨	∨	NUM
ejpam-6489	476	12	r̃ñג(i)(η̃j)}e	r̃ñג(i)(η̃j)}e	PROPN
ejpam-6489	476	13	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	476	14	{	{	PUNCT
ejpam-6489	476	15	ω̃n	ω̃n	X
ejpam-6489	476	16	(	(	PUNCT
ejpam-6489	476	17	i)̃ג	i)̃ג	PROPN
ejpam-6489	476	18	(	(	PUNCT
ejpam-6489	476	19	ϕ̃j)∨ω̃n	ϕ̃j)∨ω̃n	X
ejpam-6489	476	20	(	(	PUNCT
ejpam-6489	476	21	i)̃ג	i)̃ג	PROPN
ejpam-6489	476	22	(	(	PUNCT
ejpam-6489	476	23	η̃j	η̃j	NOUN
ejpam-6489	476	24	)	)	PUNCT
ejpam-6489	476	25	}	}	PUNCT
ejpam-6489	476	26	}	}	PUNCT
ejpam-6489	476	27	and	and	CCONJ
ejpam-6489	476	28	if	if	SCONJ
ejpam-6489	476	29	ϕ̃	ϕ̃	PROPN
ejpam-6489	476	30	̸=	̸=	PROPN
ejpam-6489	476	31	∑	∑	ADP
ejpam-6489	476	32	j∈n	j∈n	NOUN
ejpam-6489	476	33	β̃i[ϕ̃i	β̃i[ϕ̃i	PROPN
ejpam-6489	476	34	,	,	PUNCT
ejpam-6489	476	35	η̃j	η̃j	NOUN
ejpam-6489	476	36	]	]	PUNCT
ejpam-6489	476	37	,	,	PUNCT
ejpam-6489	476	38	then	then	ADV
ejpam-6489	476	39	ξñג(i+1)(ϕ̃	ξñג(i+1)(ϕ̃	PROPN
ejpam-6489	476	40	)	)	PUNCT
ejpam-6489	476	41	=	=	SYM
ejpam-6489	476	42	0	0	NUM
ejpam-6489	476	43	,	,	PUNCT
ejpam-6489	476	44	(	(	PUNCT
ejpam-6489	476	45	iii	iii	X
ejpam-6489	476	46	)	)	PUNCT
ejpam-6489	476	47	if	if	SCONJ
ejpam-6489	476	48	β̃j	β̃j	PROPN
ejpam-6489	476	49	∈	∈	PROPN
ejpam-6489	476	50	f	f	PROPN
ejpam-6489	476	51	,	,	PUNCT
ejpam-6489	476	52	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	476	53	,	,	PUNCT
ejpam-6489	476	54	η̃j	η̃j	PROPN
ejpam-6489	476	55	∈	∈	PROPN
ejpam-6489	476	56	l̃	l̃	PROPN
ejpam-6489	476	57	,	,	PUNCT
ejpam-6489	476	58	then	then	ADV
ejpam-6489	476	59	ζ̃ג(i+1)(ϕ̃	ζ̃ג(i+1)(ϕ̃	PROPN
ejpam-6489	476	60	)	)	PUNCT
ejpam-6489	476	61	=	=	SYM
ejpam-6489	476	62	inf	inf	ADJ
ejpam-6489	476	63	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	476	64	∑	∑	PROPN
ejpam-6489	476	65	j∈n	j∈n	NOUN
ejpam-6489	476	66	β̃j	β̃j	PROPN
ejpam-6489	477	1	[	[	X
ejpam-6489	477	2	ϕ̃j	ϕ̃j	X
ejpam-6489	477	3	,	,	PUNCT
ejpam-6489	477	4	η̃j	η̃j	PROPN
ejpam-6489	477	5	]	]	PUNCT
ejpam-6489	478	1	{	{	PUNCT
ejpam-6489	478	2	maxj∈n	maxj∈n	NOUN
ejpam-6489	478	3	{	{	PUNCT
ejpam-6489	478	4	r̃̃ג(i)(ϕ̃j	r̃̃ג(i)(ϕ̃j	NOUN
ejpam-6489	478	5	)	)	PUNCT
ejpam-6489	478	6	∨	∨	PROPN
ejpam-6489	478	7	r̃̃ג(i)(η̃j)}e	r̃̃ג(i)(η̃j)}e	PROPN
ejpam-6489	478	8	i2πmaxj∈n	i2πmaxj∈n	PROPN
ejpam-6489	478	9	{	{	PUNCT
ejpam-6489	478	10	ω̃̃ג(i	ω̃̃ג(i	NUM
ejpam-6489	478	11	)	)	PUNCT
ejpam-6489	478	12	(	(	PUNCT
ejpam-6489	478	13	ϕ̃j)∨ω̃̃ג(i	ϕ̃j)∨ω̃̃ג(i	NOUN
ejpam-6489	478	14	)	)	PUNCT
ejpam-6489	478	15	(	(	PUNCT
ejpam-6489	478	16	η̃j	η̃j	NOUN
ejpam-6489	478	17	)	)	PUNCT
ejpam-6489	478	18	}	}	PUNCT
ejpam-6489	478	19	}	}	PUNCT
ejpam-6489	478	20	and	and	CCONJ
ejpam-6489	478	21	if	if	SCONJ
ejpam-6489	478	22	ϕ̃	ϕ̃	PROPN
ejpam-6489	478	23	̸=	̸=	PROPN
ejpam-6489	478	24	∑	∑	ADP
ejpam-6489	478	25	j∈n	j∈n	NOUN
ejpam-6489	478	26	β̃i[ϕ̃i	β̃i[ϕ̃i	PROPN
ejpam-6489	478	27	,	,	PUNCT
ejpam-6489	478	28	η̃j	η̃j	NOUN
ejpam-6489	478	29	]	]	PUNCT
ejpam-6489	478	30	,	,	PUNCT
ejpam-6489	478	31	then	then	ADV
ejpam-6489	478	32	ζ̃ג(i+1)(ϕ̃	ζ̃ג(i+1)(ϕ̃	PROPN
ejpam-6489	478	33	)	)	PUNCT
ejpam-6489	478	34	=	=	SYM
ejpam-6489	479	1	0	0	X
ejpam-6489	479	2	.	.	PUNCT
ejpam-6489	479	3	remark	remark	PROPN
ejpam-6489	479	4	3	3	NUM
ejpam-6489	479	5	.	.	PROPN
ejpam-6489	479	6	from	from	ADP
ejpam-6489	479	7	the	the	DET
ejpam-6489	479	8	definition	definition	NOUN
ejpam-6489	479	9	13	13	NUM
ejpam-6489	479	10	,	,	PUNCT
ejpam-6489	479	11	we	we	PRON
ejpam-6489	479	12	can	can	AUX
ejpam-6489	479	13	get	get	VERB
ejpam-6489	479	14	ξp(0)̃ג	ξp(0)̃ג	PUNCT
ejpam-6489	479	15	⊇	⊇	PROPN
ejpam-6489	479	16	ξp(1)̃ג	ξp(1)̃ג	PROPN
ejpam-6489	479	17	⊇	⊇	PROPN
ejpam-6489	479	18	ξp(2)̃ג	ξp(2)̃ג	PUNCT
ejpam-6489	479	19	⊇	⊇	X
ejpam-6489	479	20	...	...	PUNCT
ejpam-6489	479	21	⊇	⊇	PROPN
ejpam-6489	479	22	ξp̃ג(n	ξp̃ג(n	NOUN
ejpam-6489	479	23	)	)	PUNCT
ejpam-6489	479	24	⊇	⊇	NOUN
ejpam-6489	479	25	...	...	PUNCT
ejpam-6489	479	26	,	,	PUNCT
ejpam-6489	479	27	ξn(0)̃ג	ξn(0)̃ג	PROPN
ejpam-6489	480	1	⊆	⊆	NUM
ejpam-6489	480	2	ξn(1)̃ג	ξn(1)̃ג	NUM
ejpam-6489	480	3	⊆	⊆	NUM
ejpam-6489	480	4	ξn(2)̃ג	ξn(2)̃ג	NUM
ejpam-6489	480	5	⊆	⊆	NUM
ejpam-6489	480	6	...	...	PUNCT
ejpam-6489	480	7	⊆	⊆	NUM
ejpam-6489	480	8	ξñג(n	ξñג(n	NUM
ejpam-6489	480	9	)	)	PUNCT
ejpam-6489	480	10	⊆	⊆	NUM
ejpam-6489	480	11	...	...	PUNCT
ejpam-6489	480	12	,	,	PUNCT
ejpam-6489	480	13	and	and	CCONJ
ejpam-6489	480	14	ζ	ζ	NOUN
ejpam-6489	480	15	(	(	PUNCT
ejpam-6489	480	16	0)̃ג	0)̃ג	NOUN
ejpam-6489	480	17	⊆	⊆	NUM
ejpam-6489	480	18	ζ	ζ	NOUN
ejpam-6489	480	19	(	(	PUNCT
ejpam-6489	480	20	1)̃ג	1)̃ג	NUM
ejpam-6489	480	21	⊆	⊆	NUM
ejpam-6489	480	22	ζ	ζ	NOUN
ejpam-6489	480	23	(	(	PUNCT
ejpam-6489	480	24	2)̃ג	2)̃ג	NUM
ejpam-6489	480	25	⊆	⊆	NUM
ejpam-6489	480	26	...	...	PUNCT
ejpam-6489	480	27	⊆	⊆	NUM
ejpam-6489	480	28	ζ	ζ	NOUN
ejpam-6489	480	29	(	(	PUNCT
ejpam-6489	480	30	n)̃ג	n)̃ג	PROPN
ejpam-6489	480	31	⊆	⊆	NUM
ejpam-6489	480	32	....	....	PUNCT
ejpam-6489	480	33	definition	definition	NOUN
ejpam-6489	480	34	17	17	NUM
ejpam-6489	480	35	.	.	PUNCT
ejpam-6489	481	1	a	a	DET
ejpam-6489	481	2	̃ג	̃ג	NOUN
ejpam-6489	481	3	=	=	SYM
ejpam-6489	481	4	(	(	PUNCT
ejpam-6489	481	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	481	6	,	,	PUNCT
ejpam-6489	481	7	ξ	ξ	PROPN
ejpam-6489	481	8	n	n	PRON
ejpam-6489	481	9	̃ג	̃ג	PROPN
ejpam-6489	481	10	,	,	PUNCT
ejpam-6489	481	11	ζ̃ג	ζ̃ג	PROPN
ejpam-6489	481	12	)	)	PUNCT
ejpam-6489	481	13	be	be	VERB
ejpam-6489	481	14	a	a	DET
ejpam-6489	481	15	t	t	NOUN
ejpam-6489	481	16	cfli	cfli	NOUN
ejpam-6489	481	17	of	of	ADP
ejpam-6489	481	18	l̃.	l̃.	ADJ
ejpam-6489	481	19	then	then	ADV
ejpam-6489	481	20	̃ג	̃ג	NOUN
ejpam-6489	481	21	=	=	SYM
ejpam-6489	481	22	(	(	PUNCT
ejpam-6489	481	23	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	481	24	,	,	PUNCT
ejpam-6489	481	25	ξ	ξ	PROPN
ejpam-6489	481	26	n	n	PRON
ejpam-6489	481	27	̃ג	̃ג	PROPN
ejpam-6489	481	28	,	,	PUNCT
ejpam-6489	481	29	ζ̃ג	ζ̃ג	PROPN
ejpam-6489	481	30	)	)	PUNCT
ejpam-6489	481	31	is	be	AUX
ejpam-6489	481	32	st	st	PROPN
ejpam-6489	481	33	cfli	cfli	PROPN
ejpam-6489	482	1	if	if	SCONJ
ejpam-6489	482	2	and	and	CCONJ
ejpam-6489	482	3	if	if	SCONJ
ejpam-6489	482	4	there	there	PRON
ejpam-6489	482	5	exists	exist	VERB
ejpam-6489	482	6	a	a	DET
ejpam-6489	482	7	positive	positive	ADJ
ejpam-6489	482	8	integer	integer	NOUN
ejpam-6489	482	9	n	n	CCONJ
ejpam-6489	482	10	such	such	ADJ
ejpam-6489	482	11	that	that	DET
ejpam-6489	482	12	ξp̃ג(m)(n	ξp̃ג(m)(n	NOUN
ejpam-6489	482	13	)	)	PUNCT
ejpam-6489	482	14	=	=	SYM
ejpam-6489	482	15	10	10	NUM
ejpam-6489	482	16	,	,	PUNCT
ejpam-6489	482	17	ξñגm(n	ξñגm(n	PROPN
ejpam-6489	482	18	)	)	PUNCT
ejpam-6489	482	19	=	=	PUNCT
ejpam-6489	482	20	(	(	PUNCT
ejpam-6489	482	21	−1)0	−1)0	NOUN
ejpam-6489	482	22	and	and	CCONJ
ejpam-6489	482	23	ζ̃גm(n	ζ̃גm(n	X
ejpam-6489	482	24	)	)	PUNCT
ejpam-6489	482	25	=	=	SYM
ejpam-6489	482	26	00	00	NUM
ejpam-6489	482	27	,	,	PUNCT
ejpam-6489	482	28	for	for	ADP
ejpam-6489	482	29	all	all	DET
ejpam-6489	482	30	positive	positive	ADJ
ejpam-6489	482	31	integer	integer	NOUN
ejpam-6489	482	32	m	m	PROPN
ejpam-6489	482	33	≥	≥	PROPN
ejpam-6489	482	34	n.	n.	NOUN
ejpam-6489	482	35	theorem	theorem	VERB
ejpam-6489	482	36	10	10	NUM
ejpam-6489	482	37	.	.	PUNCT
ejpam-6489	483	1	a	a	DET
ejpam-6489	483	2	homomorphic	homomorphic	ADJ
ejpam-6489	483	3	images	image	NOUN
ejpam-6489	483	4	of	of	ADP
ejpam-6489	483	5	st	st	PROPN
ejpam-6489	483	6	cflis	cflis	PROPN
ejpam-6489	483	7	are	be	AUX
ejpam-6489	483	8	st	st	PROPN
ejpam-6489	483	9	cflis	cflis	PROPN
ejpam-6489	483	10	.	.	PUNCT
ejpam-6489	484	1	proof	proof	NOUN
ejpam-6489	484	2	.	.	PUNCT
ejpam-6489	485	1	consider	consider	VERB
ejpam-6489	485	2	f	f	NOUN
ejpam-6489	485	3	:	:	PUNCT
ejpam-6489	485	4	l̃	l̃	PROPN
ejpam-6489	485	5	→	→	PUNCT
ejpam-6489	485	6	l̃′	l̃′	PROPN
ejpam-6489	485	7	be	be	AUX
ejpam-6489	485	8	a	a	DET
ejpam-6489	485	9	homomorphism	homomorphism	NOUN
ejpam-6489	485	10	of	of	ADP
ejpam-6489	485	11	l̃	l̃	PROPN
ejpam-6489	485	12	,	,	PUNCT
ejpam-6489	485	13	and	and	CCONJ
ejpam-6489	485	14	assume	assume	VERB
ejpam-6489	485	15	that	that	SCONJ
ejpam-6489	485	16	̃ג	̃ג	NOUN
ejpam-6489	485	17	=	=	SYM
ejpam-6489	485	18	(	(	PUNCT
ejpam-6489	485	19	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	485	20	,	,	PUNCT
ejpam-6489	485	21	ξ	ξ	PROPN
ejpam-6489	485	22	n	n	PRON
ejpam-6489	485	23	̃ג	̃ג	PROPN
ejpam-6489	485	24	,	,	PUNCT
ejpam-6489	485	25	ζ̃ג	ζ̃ג	PROPN
ejpam-6489	485	26	)	)	PUNCT
ejpam-6489	485	27	is	be	AUX
ejpam-6489	485	28	a	a	DET
ejpam-6489	485	29	t	t	NOUN
ejpam-6489	485	30	cfli	cfli	NOUN
ejpam-6489	485	31	l̃.	l̃.	ADV
ejpam-6489	485	32	let	let	VERB
ejpam-6489	485	33	f(̃ג	f(̃ג	PROPN
ejpam-6489	485	34	)	)	PUNCT
ejpam-6489	485	35	=	=	PUNCT
ejpam-6489	486	1	ℸ̃	ℸ̃	PROPN
ejpam-6489	486	2	,	,	PUNCT
ejpam-6489	486	3	i.e.	i.e.	X
ejpam-6489	486	4	,	,	PUNCT
ejpam-6489	486	5	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	486	6	=	=	SYM
ejpam-6489	486	7	ξp	ξp	PROPN
ejpam-6489	486	8	f(̃ג	f(̃ג	PROPN
ejpam-6489	486	9	)	)	PUNCT
ejpam-6489	486	10	,	,	PUNCT
ejpam-6489	486	11	ξnℸ̃	ξnℸ̃	NOUN
ejpam-6489	486	12	=	=	PUNCT
ejpam-6489	486	13	ξn	ξn	PROPN
ejpam-6489	486	14	f(̃ג	f(̃ג	PROPN
ejpam-6489	486	15	)	)	PUNCT
ejpam-6489	486	16	.	.	PUNCT
ejpam-6489	487	1	we	we	PRON
ejpam-6489	487	2	aim	aim	VERB
ejpam-6489	487	3	to	to	PART
ejpam-6489	487	4	prove	prove	VERB
ejpam-6489	487	5	,	,	PUNCT
ejpam-6489	487	6	by	by	ADP
ejpam-6489	487	7	induction	induction	NOUN
ejpam-6489	487	8	on	on	ADP
ejpam-6489	487	9	n	n	CCONJ
ejpam-6489	487	10	,	,	PUNCT
ejpam-6489	487	11	that	that	PRON
ejpam-6489	487	12	ξp	ξp	ADP
ejpam-6489	487	13	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	487	14	)	)	PUNCT
ejpam-6489	487	15	)	)	PUNCT
ejpam-6489	488	1	=	=	SYM
ejpam-6489	488	2	ξpℸ̃(n	ξpℸ̃(n	PROPN
ejpam-6489	488	3	)	)	PUNCT
ejpam-6489	488	4	and	and	CCONJ
ejpam-6489	488	5	ξn	ξn	PROPN
ejpam-6489	488	6	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	488	7	)	)	PUNCT
ejpam-6489	488	8	)	)	PUNCT
ejpam-6489	489	1	=	=	SYM
ejpam-6489	489	2	ξnℸ̃(n	ξnℸ̃(n	PROPN
ejpam-6489	489	3	)	)	PUNCT
ejpam-6489	489	4	,	,	PUNCT
ejpam-6489	489	5	for	for	ADP
ejpam-6489	489	6	all	all	DET
ejpam-6489	489	7	positive	positive	ADJ
ejpam-6489	489	8	integer	integer	NOUN
ejpam-6489	489	9	n.	n.	NOUN
ejpam-6489	489	10	as	as	ADP
ejpam-6489	489	11	the	the	DET
ejpam-6489	489	12	base	base	NOUN
ejpam-6489	489	13	case	case	NOUN
ejpam-6489	489	14	,	,	PUNCT
ejpam-6489	489	15	consider	consider	VERB
ejpam-6489	489	16	n	n	NOUN
ejpam-6489	489	17	=	=	SYM
ejpam-6489	489	18	1	1	X
ejpam-6489	489	19	.	.	PUNCT
ejpam-6489	490	1	let	let	VERB
ejpam-6489	490	2	η̃	η̃	PROPN
ejpam-6489	490	3	∈	∈	PROPN
ejpam-6489	490	4	l̃′	l̃′	PROPN
ejpam-6489	490	5	.	.	PUNCT
ejpam-6489	491	1	then	then	ADV
ejpam-6489	491	2	ξp	ξp	ADP
ejpam-6489	491	3	f((1)̃ג)(η̃	f((1)̃ג)(η̃	NOUN
ejpam-6489	491	4	)	)	PUNCT
ejpam-6489	491	5	=	=	SYM
ejpam-6489	491	6	ξp	ξp	PROPN
ejpam-6489	491	7	f([t̃	f([t̃	PROPN
ejpam-6489	491	8	,	,	PUNCT
ejpam-6489	491	9	t̃	t̃	PROPN
ejpam-6489	491	10	]	]	PUNCT
ejpam-6489	491	11	)	)	PUNCT
ejpam-6489	491	12	(	(	PUNCT
ejpam-6489	491	13	η̃	η̃	PROPN
ejpam-6489	491	14	)	)	PUNCT
ejpam-6489	491	15	=	=	SYM
ejpam-6489	491	16	sup	sup	NOUN
ejpam-6489	491	17	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	491	18	)	)	PUNCT
ejpam-6489	491	19	{	{	PUNCT
ejpam-6489	491	20	ξp	ξp	X
ejpam-6489	491	21	[	[	X
ejpam-6489	491	22	t̃	t̃	PROPN
ejpam-6489	491	23	,	,	PUNCT
ejpam-6489	491	24	t̃	t̃	PROPN
ejpam-6489	491	25	]	]	PUNCT
ejpam-6489	491	26	(	(	PUNCT
ejpam-6489	491	27	η̃	η̃	PROPN
ejpam-6489	491	28	)	)	PUNCT
ejpam-6489	491	29	}	}	PUNCT
ejpam-6489	492	1	=	=	SYM
ejpam-6489	492	2	sup	sup	NOUN
ejpam-6489	492	3	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	492	4	)	)	PUNCT
ejpam-6489	492	5			PRON
ejpam-6489	492	6	sup	sup	NOUN
ejpam-6489	492	7	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	492	8	∑	∑	PROPN
ejpam-6489	492	9	j∈n	j∈n	NOUN
ejpam-6489	492	10	β̃j	β̃j	PROPN
ejpam-6489	493	1	[	[	X
ejpam-6489	493	2	ϕ̃j	ϕ̃j	X
ejpam-6489	493	3	,	,	PUNCT
ejpam-6489	493	4	η̃j	η̃j	PROPN
ejpam-6489	493	5	]	]	PUNCT
ejpam-6489	493	6	{	{	PUNCT
ejpam-6489	493	7	min	min	PROPN
ejpam-6489	493	8	j∈n	j∈n	NOUN
ejpam-6489	493	9	{	{	PUNCT
ejpam-6489	493	10	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	493	11	(	(	PUNCT
ejpam-6489	493	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	493	13	)	)	PUNCT
ejpam-6489	494	1	∧	∧	NOUN
ejpam-6489	494	2	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	494	3	(	(	PUNCT
ejpam-6489	494	4	η̃j	η̃j	NOUN
ejpam-6489	494	5	)	)	PUNCT
ejpam-6489	494	6	}	}	PUNCT
ejpam-6489	494	7	ei2πminj∈n	ei2πminj∈n	PROPN
ejpam-6489	494	8	{	{	PUNCT
ejpam-6489	494	9	ω̃p	ω̃p	PROPN
ejpam-6489	494	10	̃ג	̃ג	PROPN
ejpam-6489	494	11	(	(	PUNCT
ejpam-6489	494	12	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	494	13	̃ג	̃ג	NOUN
ejpam-6489	494	14	(	(	PUNCT
ejpam-6489	494	15	η̃j	η̃j	NOUN
ejpam-6489	494	16	)	)	PUNCT
ejpam-6489	494	17	}	}	PUNCT
ejpam-6489	494	18	}	}	PUNCT
ejpam-6489	494	19			X
ejpam-6489	494	20	=	=	SYM
ejpam-6489	494	21	sup	sup	NOUN
ejpam-6489	494	22	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	494	23	∑	∑	PROPN
ejpam-6489	494	24	j∈n	j∈n	NOUN
ejpam-6489	494	25	β̃j	β̃j	PROPN
ejpam-6489	495	1	[	[	X
ejpam-6489	495	2	ϕ̃j	ϕ̃j	X
ejpam-6489	495	3	,	,	PUNCT
ejpam-6489	495	4	η̃j	η̃j	PROPN
ejpam-6489	495	5	]	]	PUNCT
ejpam-6489	495	6	{	{	PUNCT
ejpam-6489	495	7	min	min	PROPN
ejpam-6489	495	8	j∈n	j∈n	NOUN
ejpam-6489	495	9	{	{	PUNCT
ejpam-6489	495	10	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	495	11	(	(	PUNCT
ejpam-6489	495	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	495	13	)	)	PUNCT
ejpam-6489	496	1	∧	∧	NOUN
ejpam-6489	496	2	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	496	3	(	(	PUNCT
ejpam-6489	496	4	η̃j	η̃j	NOUN
ejpam-6489	496	5	)	)	PUNCT
ejpam-6489	496	6	}	}	PUNCT
ejpam-6489	496	7	ei2πminj∈n	ei2πminj∈n	PROPN
ejpam-6489	496	8	{	{	PUNCT
ejpam-6489	496	9	ω̃p	ω̃p	PROPN
ejpam-6489	496	10	̃ג	̃ג	PROPN
ejpam-6489	496	11	(	(	PUNCT
ejpam-6489	496	12	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	496	13	̃ג	̃ג	NOUN
ejpam-6489	496	14	(	(	PUNCT
ejpam-6489	496	15	η̃j	η̃j	NOUN
ejpam-6489	496	16	)	)	PUNCT
ejpam-6489	496	17	}	}	PUNCT
ejpam-6489	496	18	}	}	PUNCT
ejpam-6489	496	19	=	=	PUNCT
ejpam-6489	496	20	sup	sup	NOUN
ejpam-6489	496	21	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	496	22	∑	∑	PROPN
ejpam-6489	496	23	j∈n	j∈n	NOUN
ejpam-6489	496	24	β̃j	β̃j	PROPN
ejpam-6489	497	1	[	[	X
ejpam-6489	497	2	ε̃j	ε̃j	NOUN
ejpam-6489	497	3	,	,	PUNCT
ejpam-6489	497	4	ς̃j	ς̃j	PROPN
ejpam-6489	497	5	]	]	PUNCT
ejpam-6489	497	6	{	{	PUNCT
ejpam-6489	497	7	min	min	PROPN
ejpam-6489	497	8	j∈n	j∈n	NOUN
ejpam-6489	497	9	{	{	PUNCT
ejpam-6489	497	10	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	497	11	(	(	PUNCT
ejpam-6489	497	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	497	13	)	)	PUNCT
ejpam-6489	498	1	∧	∧	NOUN
ejpam-6489	498	2	r̃p̃ג	r̃p̃ג	NOUN
ejpam-6489	498	3	(	(	PUNCT
ejpam-6489	498	4	η̃j	η̃j	NOUN
ejpam-6489	498	5	)	)	PUNCT
ejpam-6489	498	6	}	}	PUNCT
ejpam-6489	498	7	ei2πminj∈n	ei2πminj∈n	PROPN
ejpam-6489	498	8	{	{	PUNCT
ejpam-6489	498	9	ω̃p	ω̃p	PROPN
ejpam-6489	498	10	̃ג	̃ג	PROPN
ejpam-6489	498	11	(	(	PUNCT
ejpam-6489	498	12	ϕ̃j)∧ω̃p	ϕ̃j)∧ω̃p	NUM
ejpam-6489	498	13	̃ג	̃ג	NOUN
ejpam-6489	498	14	(	(	PUNCT
ejpam-6489	498	15	η̃j	η̃j	NOUN
ejpam-6489	498	16	)	)	PUNCT
ejpam-6489	498	17	}	}	PUNCT
ejpam-6489	498	18	|	|	ADV
ejpam-6489	498	19	f(ϕ̃j	f(ϕ̃j	VERB
ejpam-6489	498	20	)	)	PUNCT
ejpam-6489	499	1	=	=	PRON
ejpam-6489	499	2	ε̃j	ε̃j	NOUN
ejpam-6489	499	3	,	,	PUNCT
ejpam-6489	499	4	f(η̃j	f(η̃j	PROPN
ejpam-6489	499	5	)	)	PUNCT
ejpam-6489	499	6	=	=	SYM
ejpam-6489	499	7	ς̃j	ς̃j	PROPN
ejpam-6489	499	8	}	}	PUNCT
ejpam-6489	499	9	m.	m.	NOUN
ejpam-6489	499	10	balamurugan	balamurugan	NOUN
ejpam-6489	499	11	,	,	PUNCT
ejpam-6489	499	12	g.	g.	PROPN
ejpam-6489	499	13	ellammal	ellammal	PROPN
ejpam-6489	499	14	,	,	PUNCT
ejpam-6489	499	15	a.	a.	NOUN
ejpam-6489	499	16	iampan	iampan	PROPN
ejpam-6489	499	17	/	/	SYM
ejpam-6489	499	18	eur	eur	PROPN
ejpam-6489	499	19	.	.	PUNCT
ejpam-6489	500	1	j.	j.	PROPN
ejpam-6489	500	2	pure	pure	PROPN
ejpam-6489	500	3	appl	appl	PROPN
ejpam-6489	500	4	.	.	PROPN
ejpam-6489	500	5	math	math	PROPN
ejpam-6489	500	6	,	,	PUNCT
ejpam-6489	500	7	18	18	NUM
ejpam-6489	500	8	(	(	PUNCT
ejpam-6489	500	9	3	3	NUM
ejpam-6489	500	10	)	)	PUNCT
ejpam-6489	500	11	(	(	PUNCT
ejpam-6489	500	12	2025	2025	NUM
ejpam-6489	500	13	)	)	PUNCT
ejpam-6489	500	14	,	,	PUNCT
ejpam-6489	500	15	6489	6489	NUM
ejpam-6489	500	16	21	21	NUM
ejpam-6489	500	17	of	of	ADP
ejpam-6489	500	18	26	26	NUM
ejpam-6489	500	19	=	=	SYM
ejpam-6489	500	20	sup∑	sup∑	PROPN
ejpam-6489	500	21	j∈n	j∈n	NOUN
ejpam-6489	500	22	β̃j	β̃j	PROPN
ejpam-6489	501	1	[	[	X
ejpam-6489	501	2	ε̃j	ε̃j	NOUN
ejpam-6489	501	3	,	,	PUNCT
ejpam-6489	501	4	ς̃j	ς̃j	PROPN
ejpam-6489	501	5	]=	]=	NOUN
ejpam-6489	501	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	501	7	{	{	PUNCT
ejpam-6489	501	8	min	min	NOUN
ejpam-6489	501	9	j∈n	j∈n	NOUN
ejpam-6489	501	10	{	{	PUNCT
ejpam-6489	501	11	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	501	12	(	(	PUNCT
ejpam-6489	501	13	ε̃j	ε̃j	NOUN
ejpam-6489	501	14	)	)	PUNCT
ejpam-6489	501	15	∧	∧	PROPN
ejpam-6489	501	16	r̃pℸ̃	r̃pℸ̃	ADJ
ejpam-6489	501	17	(	(	PUNCT
ejpam-6489	501	18	ς̃j	ς̃j	NOUN
ejpam-6489	501	19	)	)	PUNCT
ejpam-6489	501	20	}	}	PUNCT
ejpam-6489	501	21	ei2πminj∈n	ei2πminj∈n	PROPN
ejpam-6489	501	22	{	{	PUNCT
ejpam-6489	501	23	ω̃p	ω̃p	PROPN
ejpam-6489	501	24	ℸ̃	ℸ̃	PROPN
ejpam-6489	501	25	(	(	PUNCT
ejpam-6489	501	26	ε̃j)∧ω̃p	ε̃j)∧ω̃p	PROPN
ejpam-6489	501	27	ℸ̃	ℸ̃	PROPN
ejpam-6489	501	28	(	(	PUNCT
ejpam-6489	501	29	ς̃j	ς̃j	NOUN
ejpam-6489	501	30	)	)	PUNCT
ejpam-6489	501	31	}	}	PUNCT
ejpam-6489	501	32	}	}	PUNCT
ejpam-6489	501	33	=	=	PUNCT
ejpam-6489	501	34	ξp	ξp	ADP
ejpam-6489	501	35	[	[	X
ejpam-6489	501	36	ℸ̃,ℸ̃](η̃	ℸ̃,ℸ̃](η̃	ADJ
ejpam-6489	501	37	)	)	PUNCT
ejpam-6489	501	38	=	=	SYM
ejpam-6489	501	39	ξpℸ̃(1)(η̃	ξpℸ̃(1)(η̃	NOUN
ejpam-6489	501	40	)	)	PUNCT
ejpam-6489	501	41	and	and	CCONJ
ejpam-6489	501	42	ξn	ξn	PROPN
ejpam-6489	501	43	f((1)̃ג)(η̃	f((1)̃ג)(η̃	NOUN
ejpam-6489	501	44	)	)	PUNCT
ejpam-6489	501	45	=	=	SYM
ejpam-6489	501	46	ξn	ξn	PROPN
ejpam-6489	501	47	f([t̃	f([t̃	PROPN
ejpam-6489	501	48	,	,	PUNCT
ejpam-6489	501	49	t̃	t̃	PROPN
ejpam-6489	501	50	]	]	PUNCT
ejpam-6489	501	51	)	)	PUNCT
ejpam-6489	501	52	(	(	PUNCT
ejpam-6489	501	53	η̃	η̃	PROPN
ejpam-6489	501	54	)	)	PUNCT
ejpam-6489	501	55	=	=	PROPN
ejpam-6489	501	56	inf	inf	PROPN
ejpam-6489	501	57	η̃=f(ϕ̃	η̃=f(ϕ̃	PROPN
ejpam-6489	501	58	)	)	PUNCT
ejpam-6489	501	59	{	{	PUNCT
ejpam-6489	501	60	ξn	ξn	X
ejpam-6489	501	61	[	[	X
ejpam-6489	501	62	t̃	t̃	PROPN
ejpam-6489	501	63	,	,	PUNCT
ejpam-6489	501	64	t̃	t̃	PROPN
ejpam-6489	501	65	]	]	PUNCT
ejpam-6489	501	66	(	(	PUNCT
ejpam-6489	501	67	η̃	η̃	PROPN
ejpam-6489	501	68	)	)	PUNCT
ejpam-6489	501	69	}	}	PUNCT
ejpam-6489	501	70	=	=	SYM
ejpam-6489	501	71	inf	inf	PROPN
ejpam-6489	501	72	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	501	73	)	)	PUNCT
ejpam-6489	501	74			PROPN
ejpam-6489	501	75	inf	inf	VERB
ejpam-6489	501	76	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	501	77	∑	∑	PROPN
ejpam-6489	501	78	j∈n	j∈n	NOUN
ejpam-6489	501	79	β̃j	β̃j	PROPN
ejpam-6489	502	1	[	[	X
ejpam-6489	502	2	ϕ̃j	ϕ̃j	X
ejpam-6489	502	3	,	,	PUNCT
ejpam-6489	502	4	η̃j	η̃j	PROPN
ejpam-6489	502	5	]	]	PUNCT
ejpam-6489	502	6	{	{	PUNCT
ejpam-6489	502	7	max	max	PROPN
ejpam-6489	502	8	j∈n	j∈n	PROPN
ejpam-6489	502	9	{	{	PUNCT
ejpam-6489	502	10	r̃ñג	r̃ñג	PROPN
ejpam-6489	502	11	(	(	PUNCT
ejpam-6489	502	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	502	13	)	)	PUNCT
ejpam-6489	503	1	∧	∧	NOUN
ejpam-6489	503	2	r̃ñג	r̃ñג	NOUN
ejpam-6489	503	3	(	(	PUNCT
ejpam-6489	503	4	η̃j	η̃j	NOUN
ejpam-6489	503	5	)	)	PUNCT
ejpam-6489	503	6	}	}	PUNCT
ejpam-6489	503	7	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	503	8	{	{	PUNCT
ejpam-6489	503	9	ω̃n	ω̃n	PROPN
ejpam-6489	503	10	̃ג	̃ג	PROPN
ejpam-6489	503	11	(	(	PUNCT
ejpam-6489	503	12	ϕ̃j)∧ω̃n	ϕ̃j)∧ω̃n	PROPN
ejpam-6489	503	13	̃ג	̃ג	PROPN
ejpam-6489	503	14	(	(	PUNCT
ejpam-6489	503	15	η̃j	η̃j	NOUN
ejpam-6489	503	16	)	)	PUNCT
ejpam-6489	503	17	}	}	PUNCT
ejpam-6489	503	18	}	}	PUNCT
ejpam-6489	503	19			X
ejpam-6489	503	20	=	=	SYM
ejpam-6489	503	21	inf	inf	PROPN
ejpam-6489	503	22	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	503	23	∑	∑	PROPN
ejpam-6489	503	24	j∈n	j∈n	NOUN
ejpam-6489	503	25	β̃j	β̃j	PROPN
ejpam-6489	504	1	[	[	X
ejpam-6489	504	2	ϕ̃j	ϕ̃j	X
ejpam-6489	504	3	,	,	PUNCT
ejpam-6489	504	4	η̃j	η̃j	PROPN
ejpam-6489	504	5	]	]	PUNCT
ejpam-6489	504	6	{	{	PUNCT
ejpam-6489	504	7	max	max	PROPN
ejpam-6489	504	8	j∈n	j∈n	PROPN
ejpam-6489	504	9	{	{	PUNCT
ejpam-6489	504	10	r̃ñג	r̃ñג	PROPN
ejpam-6489	504	11	(	(	PUNCT
ejpam-6489	504	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	504	13	)	)	PUNCT
ejpam-6489	505	1	∧	∧	NOUN
ejpam-6489	505	2	r̃ñג	r̃ñג	NOUN
ejpam-6489	505	3	(	(	PUNCT
ejpam-6489	505	4	η̃j	η̃j	NOUN
ejpam-6489	505	5	)	)	PUNCT
ejpam-6489	505	6	}	}	PUNCT
ejpam-6489	505	7	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	505	8	{	{	PUNCT
ejpam-6489	505	9	ω̃n	ω̃n	PROPN
ejpam-6489	505	10	̃ג	̃ג	PROPN
ejpam-6489	505	11	(	(	PUNCT
ejpam-6489	505	12	ϕ̃j)∧ω̃n	ϕ̃j)∧ω̃n	PROPN
ejpam-6489	505	13	̃ג	̃ג	PROPN
ejpam-6489	505	14	(	(	PUNCT
ejpam-6489	505	15	η̃j	η̃j	NOUN
ejpam-6489	505	16	)	)	PUNCT
ejpam-6489	505	17	}	}	PUNCT
ejpam-6489	505	18	}	}	PUNCT
ejpam-6489	505	19	=	=	SYM
ejpam-6489	505	20	inf	inf	ADJ
ejpam-6489	505	21	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	505	22	∑	∑	PROPN
ejpam-6489	505	23	j∈n	j∈n	NOUN
ejpam-6489	505	24	β̃j	β̃j	PROPN
ejpam-6489	506	1	[	[	X
ejpam-6489	506	2	ε̃j	ε̃j	NOUN
ejpam-6489	506	3	,	,	PUNCT
ejpam-6489	506	4	ς̃j	ς̃j	PROPN
ejpam-6489	506	5	]	]	PUNCT
ejpam-6489	506	6	{	{	PUNCT
ejpam-6489	506	7	max	max	PROPN
ejpam-6489	506	8	j∈n	j∈n	PROPN
ejpam-6489	506	9	{	{	PUNCT
ejpam-6489	506	10	r̃ñג	r̃ñג	PROPN
ejpam-6489	506	11	(	(	PUNCT
ejpam-6489	506	12	ϕ̃j	ϕ̃j	PROPN
ejpam-6489	506	13	)	)	PUNCT
ejpam-6489	507	1	∧	∧	NOUN
ejpam-6489	507	2	r̃ñג	r̃ñג	NOUN
ejpam-6489	507	3	(	(	PUNCT
ejpam-6489	507	4	η̃j	η̃j	NOUN
ejpam-6489	507	5	)	)	PUNCT
ejpam-6489	507	6	}	}	PUNCT
ejpam-6489	507	7	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	507	8	{	{	PUNCT
ejpam-6489	507	9	ω̃n	ω̃n	PROPN
ejpam-6489	507	10	̃ג	̃ג	PROPN
ejpam-6489	507	11	(	(	PUNCT
ejpam-6489	507	12	ϕ̃j)∧ω̃n	ϕ̃j)∧ω̃n	PROPN
ejpam-6489	507	13	̃ג	̃ג	PROPN
ejpam-6489	507	14	(	(	PUNCT
ejpam-6489	507	15	η̃j	η̃j	NOUN
ejpam-6489	507	16	)	)	PUNCT
ejpam-6489	507	17	}	}	PUNCT
ejpam-6489	508	1	|	|	ADV
ejpam-6489	508	2	f(ϕ̃j	f(ϕ̃j	VERB
ejpam-6489	508	3	)	)	PUNCT
ejpam-6489	508	4	=	=	PRON
ejpam-6489	508	5	ε̃j	ε̃j	NOUN
ejpam-6489	508	6	,	,	PUNCT
ejpam-6489	508	7	f(η̃j	f(η̃j	PROPN
ejpam-6489	508	8	)	)	PUNCT
ejpam-6489	509	1	=	=	SYM
ejpam-6489	509	2	ς̃j	ς̃j	PROPN
ejpam-6489	509	3	}	}	PUNCT
ejpam-6489	509	4	=	=	SYM
ejpam-6489	509	5	inf∑	inf∑	PROPN
ejpam-6489	509	6	j∈n	j∈n	NOUN
ejpam-6489	509	7	β̃j	β̃j	PROPN
ejpam-6489	510	1	[	[	X
ejpam-6489	510	2	ε̃j	ε̃j	NOUN
ejpam-6489	510	3	,	,	PUNCT
ejpam-6489	510	4	ς̃j	ς̃j	PROPN
ejpam-6489	510	5	]=	]=	NOUN
ejpam-6489	510	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	510	7	{	{	PUNCT
ejpam-6489	510	8	max	max	PROPN
ejpam-6489	510	9	j∈n	j∈n	PROPN
ejpam-6489	510	10	{	{	PUNCT
ejpam-6489	510	11	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	510	12	(	(	PUNCT
ejpam-6489	510	13	ε̃j	ε̃j	NOUN
ejpam-6489	510	14	)	)	PUNCT
ejpam-6489	510	15	∧	∧	PROPN
ejpam-6489	510	16	r̃nℸ̃	r̃nℸ̃	NOUN
ejpam-6489	510	17	(	(	PUNCT
ejpam-6489	510	18	ς̃j	ς̃j	NOUN
ejpam-6489	510	19	)	)	PUNCT
ejpam-6489	510	20	}	}	PUNCT
ejpam-6489	510	21	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	510	22	{	{	PUNCT
ejpam-6489	510	23	ω̃n	ω̃n	X
ejpam-6489	510	24	ℸ̃	ℸ̃	PROPN
ejpam-6489	510	25	(	(	PUNCT
ejpam-6489	510	26	ε̃j)∧ω̃n	ε̃j)∧ω̃n	PROPN
ejpam-6489	510	27	ℸ̃	ℸ̃	PROPN
ejpam-6489	510	28	(	(	PUNCT
ejpam-6489	510	29	ς̃j	ς̃j	NOUN
ejpam-6489	510	30	)	)	PUNCT
ejpam-6489	510	31	}	}	PUNCT
ejpam-6489	510	32	}	}	PUNCT
ejpam-6489	510	33	=	=	PUNCT
ejpam-6489	510	34	ξn	ξn	X
ejpam-6489	510	35	[	[	X
ejpam-6489	510	36	ℸ̃,ℸ̃](η̃	ℸ̃,ℸ̃](η̃	ADJ
ejpam-6489	510	37	)	)	PUNCT
ejpam-6489	510	38	=	=	SYM
ejpam-6489	510	39	ξnℸ̃(1)(η̃	ξnℸ̃(1)(η̃	NOUN
ejpam-6489	510	40	)	)	PUNCT
ejpam-6489	510	41	.	.	PUNCT
ejpam-6489	511	1	also	also	ADV
ejpam-6489	511	2	,	,	PUNCT
ejpam-6489	511	3	ζf((1)̃ג)(η̃	ζf((1)̃ג)(η̃	NOUN
ejpam-6489	511	4	)	)	PUNCT
ejpam-6489	511	5	=	=	SYM
ejpam-6489	512	1	ζf([t̃	ζf([t̃	PROPN
ejpam-6489	512	2	,	,	PUNCT
ejpam-6489	512	3	t̃	t̃	PROPN
ejpam-6489	512	4	]	]	PUNCT
ejpam-6489	512	5	)	)	PUNCT
ejpam-6489	512	6	(	(	PUNCT
ejpam-6489	512	7	η̃	η̃	PROPN
ejpam-6489	512	8	)	)	PUNCT
ejpam-6489	512	9	=	=	PROPN
ejpam-6489	512	10	inf	inf	PROPN
ejpam-6489	512	11	η̃=f(ϕ̃	η̃=f(ϕ̃	PROPN
ejpam-6489	512	12	)	)	PUNCT
ejpam-6489	512	13	{	{	PUNCT
ejpam-6489	512	14	ζn	ζn	X
ejpam-6489	512	15	[	[	X
ejpam-6489	512	16	t̃	t̃	PROPN
ejpam-6489	512	17	,	,	PUNCT
ejpam-6489	512	18	t̃	t̃	PROPN
ejpam-6489	512	19	]	]	PUNCT
ejpam-6489	512	20	(	(	PUNCT
ejpam-6489	512	21	η̃	η̃	PROPN
ejpam-6489	512	22	)	)	PUNCT
ejpam-6489	512	23	}	}	PUNCT
ejpam-6489	513	1	=	=	SYM
ejpam-6489	513	2	inf	inf	PROPN
ejpam-6489	513	3	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	513	4	)	)	PUNCT
ejpam-6489	513	5			PROPN
ejpam-6489	513	6	inf	inf	VERB
ejpam-6489	513	7	ϕ̃=	ϕ̃=	ADJ
ejpam-6489	513	8	∑	∑	PROPN
ejpam-6489	513	9	j∈n	j∈n	NOUN
ejpam-6489	513	10	β̃j	β̃j	PROPN
ejpam-6489	514	1	[	[	X
ejpam-6489	514	2	ϕ̃j	ϕ̃j	X
ejpam-6489	514	3	,	,	PUNCT
ejpam-6489	514	4	η̃j	η̃j	PROPN
ejpam-6489	514	5	]	]	PUNCT
ejpam-6489	514	6	{	{	PUNCT
ejpam-6489	514	7	max	max	PROPN
ejpam-6489	514	8	j∈n	j∈n	PROPN
ejpam-6489	514	9	{	{	PUNCT
ejpam-6489	514	10	r̃̃ג(ϕ̃j	r̃̃ג(ϕ̃j	PROPN
ejpam-6489	514	11	)	)	PUNCT
ejpam-6489	514	12	∧	∧	NOUN
ejpam-6489	514	13	r̃̃ג(η̃j	r̃̃ג(η̃j	NOUN
ejpam-6489	514	14	)	)	PUNCT
ejpam-6489	514	15	}	}	PUNCT
ejpam-6489	514	16	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	514	17	{	{	PUNCT
ejpam-6489	514	18	ω̃̃ג	ω̃̃ג	PROPN
ejpam-6489	514	19	(	(	PUNCT
ejpam-6489	514	20	ϕ̃j)∧ω̃̃ג	ϕ̃j)∧ω̃̃ג	NOUN
ejpam-6489	514	21	(	(	PUNCT
ejpam-6489	514	22	η̃j	η̃j	NOUN
ejpam-6489	514	23	)	)	PUNCT
ejpam-6489	514	24	}	}	PUNCT
ejpam-6489	514	25	}	}	PUNCT
ejpam-6489	514	26			X
ejpam-6489	514	27	=	=	SYM
ejpam-6489	514	28	inf	inf	PROPN
ejpam-6489	514	29	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	514	30	∑	∑	PROPN
ejpam-6489	514	31	j∈n	j∈n	NOUN
ejpam-6489	514	32	β̃j	β̃j	PROPN
ejpam-6489	515	1	[	[	X
ejpam-6489	515	2	ϕ̃j	ϕ̃j	X
ejpam-6489	515	3	,	,	PUNCT
ejpam-6489	515	4	η̃j	η̃j	PROPN
ejpam-6489	515	5	]	]	PUNCT
ejpam-6489	515	6	{	{	PUNCT
ejpam-6489	515	7	max	max	PROPN
ejpam-6489	515	8	j∈n	j∈n	PROPN
ejpam-6489	515	9	{	{	PUNCT
ejpam-6489	515	10	r̃̃ג(ϕ̃j	r̃̃ג(ϕ̃j	PROPN
ejpam-6489	515	11	)	)	PUNCT
ejpam-6489	515	12	∧	∧	NOUN
ejpam-6489	515	13	r̃̃ג(η̃j	r̃̃ג(η̃j	NOUN
ejpam-6489	515	14	)	)	PUNCT
ejpam-6489	515	15	}	}	PUNCT
ejpam-6489	515	16	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	515	17	{	{	PUNCT
ejpam-6489	515	18	ω̃̃ג	ω̃̃ג	PROPN
ejpam-6489	515	19	(	(	PUNCT
ejpam-6489	515	20	ϕ̃j)∧ω̃̃ג	ϕ̃j)∧ω̃̃ג	NOUN
ejpam-6489	515	21	(	(	PUNCT
ejpam-6489	515	22	η̃j	η̃j	NOUN
ejpam-6489	515	23	)	)	PUNCT
ejpam-6489	515	24	}	}	PUNCT
ejpam-6489	515	25	}	}	PUNCT
ejpam-6489	515	26	m.	m.	NOUN
ejpam-6489	515	27	balamurugan	balamurugan	NOUN
ejpam-6489	515	28	,	,	PUNCT
ejpam-6489	515	29	g.	g.	PROPN
ejpam-6489	515	30	ellammal	ellammal	PROPN
ejpam-6489	515	31	,	,	PUNCT
ejpam-6489	515	32	a.	a.	NOUN
ejpam-6489	515	33	iampan	iampan	PROPN
ejpam-6489	515	34	/	/	SYM
ejpam-6489	515	35	eur	eur	PROPN
ejpam-6489	515	36	.	.	PUNCT
ejpam-6489	516	1	j.	j.	PROPN
ejpam-6489	516	2	pure	pure	PROPN
ejpam-6489	516	3	appl	appl	PROPN
ejpam-6489	516	4	.	.	PROPN
ejpam-6489	516	5	math	math	PROPN
ejpam-6489	516	6	,	,	PUNCT
ejpam-6489	516	7	18	18	NUM
ejpam-6489	516	8	(	(	PUNCT
ejpam-6489	516	9	3	3	NUM
ejpam-6489	516	10	)	)	PUNCT
ejpam-6489	516	11	(	(	PUNCT
ejpam-6489	516	12	2025	2025	NUM
ejpam-6489	516	13	)	)	PUNCT
ejpam-6489	516	14	,	,	PUNCT
ejpam-6489	516	15	6489	6489	NUM
ejpam-6489	516	16	22	22	NUM
ejpam-6489	516	17	of	of	ADP
ejpam-6489	516	18	26	26	NUM
ejpam-6489	516	19	=	=	SYM
ejpam-6489	516	20	inf	inf	NOUN
ejpam-6489	516	21	ϕ̃=	ϕ̃=	NOUN
ejpam-6489	516	22	∑	∑	PROPN
ejpam-6489	516	23	j∈n	j∈n	NOUN
ejpam-6489	516	24	β̃j	β̃j	PROPN
ejpam-6489	517	1	[	[	X
ejpam-6489	517	2	ε̃j	ε̃j	NOUN
ejpam-6489	517	3	,	,	PUNCT
ejpam-6489	517	4	ς̃j	ς̃j	PROPN
ejpam-6489	517	5	]	]	PUNCT
ejpam-6489	517	6	{	{	PUNCT
ejpam-6489	517	7	max	max	PROPN
ejpam-6489	517	8	j∈n	j∈n	PROPN
ejpam-6489	517	9	{	{	PUNCT
ejpam-6489	517	10	r̃̃ג(ϕ̃j	r̃̃ג(ϕ̃j	PROPN
ejpam-6489	517	11	)	)	PUNCT
ejpam-6489	517	12	∧	∧	NOUN
ejpam-6489	517	13	r̃̃ג(η̃j	r̃̃ג(η̃j	NOUN
ejpam-6489	517	14	)	)	PUNCT
ejpam-6489	517	15	}	}	PUNCT
ejpam-6489	517	16	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	517	17	{	{	PUNCT
ejpam-6489	517	18	ω̃̃ג	ω̃̃ג	PROPN
ejpam-6489	517	19	(	(	PUNCT
ejpam-6489	517	20	ϕ̃j)∧ω̃̃ג	ϕ̃j)∧ω̃̃ג	NOUN
ejpam-6489	517	21	(	(	PUNCT
ejpam-6489	517	22	η̃j	η̃j	NOUN
ejpam-6489	517	23	)	)	PUNCT
ejpam-6489	517	24	}	}	PUNCT
ejpam-6489	517	25	|	|	ADV
ejpam-6489	517	26	f(ϕ̃j	f(ϕ̃j	VERB
ejpam-6489	517	27	)	)	PUNCT
ejpam-6489	518	1	=	=	PRON
ejpam-6489	518	2	ε̃j	ε̃j	NOUN
ejpam-6489	518	3	,	,	PUNCT
ejpam-6489	518	4	f(η̃j	f(η̃j	PROPN
ejpam-6489	518	5	)	)	PUNCT
ejpam-6489	519	1	=	=	SYM
ejpam-6489	519	2	ς̃j	ς̃j	PROPN
ejpam-6489	519	3	}	}	PUNCT
ejpam-6489	519	4	=	=	SYM
ejpam-6489	519	5	inf∑	inf∑	PROPN
ejpam-6489	519	6	j∈n	j∈n	NOUN
ejpam-6489	519	7	β̃j	β̃j	PROPN
ejpam-6489	520	1	[	[	X
ejpam-6489	520	2	ε̃j	ε̃j	NOUN
ejpam-6489	520	3	,	,	PUNCT
ejpam-6489	520	4	ς̃j	ς̃j	PROPN
ejpam-6489	520	5	]=	]=	NOUN
ejpam-6489	520	6	ϕ̃	ϕ̃	PROPN
ejpam-6489	520	7	{	{	PUNCT
ejpam-6489	520	8	max	max	PROPN
ejpam-6489	520	9	j∈n	j∈n	PROPN
ejpam-6489	520	10	{	{	PUNCT
ejpam-6489	520	11	r̃ℸ̃(ε̃j	r̃ℸ̃(ε̃j	PROPN
ejpam-6489	520	12	)	)	PUNCT
ejpam-6489	520	13	∧	∧	PROPN
ejpam-6489	520	14	r̃ℸ̃(ς̃j	r̃ℸ̃(ς̃j	PROPN
ejpam-6489	520	15	)	)	PUNCT
ejpam-6489	520	16	}	}	PUNCT
ejpam-6489	520	17	ei2πmaxj∈n	ei2πmaxj∈n	NOUN
ejpam-6489	520	18	{	{	PUNCT
ejpam-6489	520	19	ω̃ℸ̃	ω̃ℸ̃	NOUN
ejpam-6489	520	20	(	(	PUNCT
ejpam-6489	520	21	ε̃j)∧ω̃ℸ̃	ε̃j)∧ω̃ℸ̃	X
ejpam-6489	520	22	(	(	PUNCT
ejpam-6489	520	23	ς̃j	ς̃j	NOUN
ejpam-6489	520	24	)	)	PUNCT
ejpam-6489	520	25	}	}	PUNCT
ejpam-6489	520	26	}	}	PUNCT
ejpam-6489	520	27	=	=	SYM
ejpam-6489	520	28	ζ[ℸ̃,ℸ̃](η̃	ζ[ℸ̃,ℸ̃](η̃	NOUN
ejpam-6489	520	29	)	)	PUNCT
ejpam-6489	520	30	=	=	SYM
ejpam-6489	520	31	ζℸ̃(1)(η̃	ζℸ̃(1)(η̃	NOUN
ejpam-6489	520	32	)	)	PUNCT
ejpam-6489	520	33	.	.	PUNCT
ejpam-6489	521	1	the	the	DET
ejpam-6489	521	2	statement	statement	NOUN
ejpam-6489	521	3	holds	hold	VERB
ejpam-6489	521	4	for	for	ADP
ejpam-6489	521	5	the	the	DET
ejpam-6489	521	6	base	base	NOUN
ejpam-6489	521	7	case	case	NOUN
ejpam-6489	521	8	n	n	X
ejpam-6489	521	9	=	=	SYM
ejpam-6489	521	10	1	1	X
ejpam-6489	521	11	.	.	PUNCT
ejpam-6489	522	1	now	now	ADV
ejpam-6489	522	2	,	,	PUNCT
ejpam-6489	522	3	assume	assume	VERB
ejpam-6489	522	4	that	that	SCONJ
ejpam-6489	522	5	it	it	PRON
ejpam-6489	522	6	is	be	AUX
ejpam-6489	522	7	true	true	ADJ
ejpam-6489	522	8	for	for	ADP
ejpam-6489	522	9	some	some	DET
ejpam-6489	522	10	positive	positive	ADJ
ejpam-6489	522	11	integer	integer	NOUN
ejpam-6489	522	12	n−	n−	NOUN
ejpam-6489	522	13	1	1	NUM
ejpam-6489	522	14	;	;	PUNCT
ejpam-6489	522	15	that	that	PRON
ejpam-6489	522	16	is	is	ADV
ejpam-6489	522	17	,	,	PUNCT
ejpam-6489	522	18	we	we	PRON
ejpam-6489	522	19	assume	assume	VERB
ejpam-6489	522	20	the	the	DET
ejpam-6489	522	21	induction	induction	NOUN
ejpam-6489	522	22	hypothesis	hypothesis	NOUN
ejpam-6489	522	23	holds	hold	VERB
ejpam-6489	522	24	for	for	ADP
ejpam-6489	522	25	n−	n−	NOUN
ejpam-6489	522	26	1	1	NUM
ejpam-6489	522	27	.	.	PUNCT
ejpam-6489	523	1	then	then	ADV
ejpam-6489	523	2	ξp	ξp	ADP
ejpam-6489	523	3	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	523	4	)	)	PUNCT
ejpam-6489	523	5	)	)	PUNCT
ejpam-6489	524	1	=	=	PRON
ejpam-6489	524	2	ξp	ξp	AUX
ejpam-6489	524	3	f([̃ג(n−1),̃ג(n−1	f([̃ג(n−1),̃ג(n−1	PROPN
ejpam-6489	524	4	)	)	PUNCT
ejpam-6489	524	5	]	]	PUNCT
ejpam-6489	524	6	)	)	PUNCT
ejpam-6489	524	7	=	=	SYM
ejpam-6489	524	8	ξp	ξp	ADP
ejpam-6489	525	1	[	[	X
ejpam-6489	525	2	f(̃ג(n−1)),f(̃ג(n−1	f(̃ג(n−1)),f(̃ג(n−1	PROPN
ejpam-6489	525	3	)	)	PUNCT
ejpam-6489	525	4	)	)	PUNCT
ejpam-6489	525	5	]	]	PUNCT
ejpam-6489	526	1	=	=	PUNCT
ejpam-6489	526	2	ξp	ξp	NUM
ejpam-6489	526	3	[	[	X
ejpam-6489	526	4	ℸ̃(n−1),ℸ̃(n−1	ℸ̃(n−1),ℸ̃(n−1	NOUN
ejpam-6489	526	5	)	)	PUNCT
ejpam-6489	526	6	]	]	PUNCT
ejpam-6489	527	1	=	=	PUNCT
ejpam-6489	527	2	ξpℸ̃(n	ξpℸ̃(n	PROPN
ejpam-6489	527	3	)	)	PUNCT
ejpam-6489	527	4	,	,	PUNCT
ejpam-6489	527	5	ξn	ξn	PROPN
ejpam-6489	527	6	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	527	7	)	)	PUNCT
ejpam-6489	527	8	)	)	PUNCT
ejpam-6489	528	1	=	=	SYM
ejpam-6489	528	2	ξn	ξn	PROPN
ejpam-6489	528	3	f([̃ג(n−1),̃ג(n−1	f([̃ג(n−1),̃ג(n−1	PROPN
ejpam-6489	528	4	)	)	PUNCT
ejpam-6489	528	5	]	]	PUNCT
ejpam-6489	528	6	)	)	PUNCT
ejpam-6489	529	1	=	=	SYM
ejpam-6489	529	2	ξn	ξn	X
ejpam-6489	530	1	[	[	X
ejpam-6489	530	2	f(̃ג(n−1)),f(̃ג(n−1	f(̃ג(n−1)),f(̃ג(n−1	PROPN
ejpam-6489	530	3	)	)	PUNCT
ejpam-6489	530	4	)	)	PUNCT
ejpam-6489	530	5	]	]	PUNCT
ejpam-6489	531	1	=	=	PUNCT
ejpam-6489	531	2	ξn	ξn	PROPN
ejpam-6489	532	1	[	[	X
ejpam-6489	532	2	ℸ̃(n−1),ℸ̃(n−1	ℸ̃(n−1),ℸ̃(n−1	NOUN
ejpam-6489	532	3	)	)	PUNCT
ejpam-6489	532	4	]	]	PUNCT
ejpam-6489	533	1	=	=	PUNCT
ejpam-6489	533	2	ξnℸ̃(n	ξnℸ̃(n	PROPN
ejpam-6489	533	3	)	)	PUNCT
ejpam-6489	533	4	and	and	CCONJ
ejpam-6489	533	5	ζf(̃ג(n	ζf(̃ג(n	PROPN
ejpam-6489	533	6	)	)	PUNCT
ejpam-6489	533	7	)	)	PUNCT
ejpam-6489	534	1	=	=	SYM
ejpam-6489	534	2	ζf([̃ג(n−1),̃ג(n−1	ζf([̃ג(n−1),̃ג(n−1	PROPN
ejpam-6489	534	3	)	)	PUNCT
ejpam-6489	534	4	]	]	PUNCT
ejpam-6489	534	5	)	)	PUNCT
ejpam-6489	535	1	=	=	SYM
ejpam-6489	535	2	ζ[f(̃ג(n−1)),f(̃ג(n−1	ζ[f(̃ג(n−1)),f(̃ג(n−1	NOUN
ejpam-6489	535	3	)	)	PUNCT
ejpam-6489	535	4	)	)	PUNCT
ejpam-6489	535	5	]	]	PUNCT
ejpam-6489	536	1	=	=	PUNCT
ejpam-6489	536	2	ζ[ℸ̃(n−1),ℸ̃(n−1	ζ[ℸ̃(n−1),ℸ̃(n−1	X
ejpam-6489	536	3	)	)	PUNCT
ejpam-6489	536	4	]	]	PUNCT
ejpam-6489	536	5	=	=	SYM
ejpam-6489	536	6	ζℸ̃(n	ζℸ̃(n	NOUN
ejpam-6489	536	7	)	)	PUNCT
ejpam-6489	536	8	.	.	PUNCT
ejpam-6489	537	1	let	let	VERB
ejpam-6489	537	2	ξp̃ג(m	ξp̃ג(m	NUM
ejpam-6489	537	3	)	)	PUNCT
ejpam-6489	537	4	=	=	SYM
ejpam-6489	538	1	10	10	NUM
ejpam-6489	538	2	,	,	PUNCT
ejpam-6489	538	3	ξ	ξ	PROPN
ejpam-6489	538	4	n	n	PRON
ejpam-6489	538	5	(	(	PUNCT
ejpam-6489	538	6	m)̃ג	m)̃ג	PROPN
ejpam-6489	538	7	=	=	SYM
ejpam-6489	538	8	(	(	PUNCT
ejpam-6489	538	9	−1)0	−1)0	NOUN
ejpam-6489	538	10	,	,	PUNCT
ejpam-6489	538	11	and	and	CCONJ
ejpam-6489	538	12	ζ̃ג(m	ζ̃ג(m	NUM
ejpam-6489	538	13	)	)	PUNCT
ejpam-6489	538	14	=	=	PUNCT
ejpam-6489	538	15	00	00	PUNCT
ejpam-6489	538	16	.	.	PUNCT
ejpam-6489	539	1	then	then	ADV
ejpam-6489	539	2	ξpℸ̃(m)(η̃	ξpℸ̃(m)(η̃	NOUN
ejpam-6489	539	3	)	)	PUNCT
ejpam-6489	539	4	=	=	PRON
ejpam-6489	539	5	ξp	ξp	NUM
ejpam-6489	539	6	f(̃גm	f(̃גm	X
ejpam-6489	539	7	)	)	PUNCT
ejpam-6489	539	8	(	(	PUNCT
ejpam-6489	539	9	η̃	η̃	PROPN
ejpam-6489	539	10	)	)	PUNCT
ejpam-6489	539	11	=	=	SYM
ejpam-6489	539	12	sup	sup	NOUN
ejpam-6489	539	13	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	539	14	)	)	PUNCT
ejpam-6489	539	15	{	{	PUNCT
ejpam-6489	539	16	10(ϕ̃	10(ϕ̃	NUM
ejpam-6489	539	17	)	)	PUNCT
ejpam-6489	539	18	}	}	PUNCT
ejpam-6489	540	1	=	=	SYM
ejpam-6489	540	2	0	0	NUM
ejpam-6489	540	3	,	,	PUNCT
ejpam-6489	540	4	ξnℸ̃(m)(η̃	ξnℸ̃(m)(η̃	NOUN
ejpam-6489	540	5	)	)	PUNCT
ejpam-6489	540	6	=	=	SYM
ejpam-6489	540	7	ξn	ξn	PROPN
ejpam-6489	540	8	f(̃גm	f(̃גm	NUM
ejpam-6489	540	9	)	)	PUNCT
ejpam-6489	540	10	(	(	PUNCT
ejpam-6489	540	11	η̃	η̃	PROPN
ejpam-6489	540	12	)	)	PUNCT
ejpam-6489	540	13	=	=	PROPN
ejpam-6489	541	1	inf	inf	PROPN
ejpam-6489	541	2	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	541	3	)	)	PUNCT
ejpam-6489	541	4	{	{	PUNCT
ejpam-6489	541	5	(	(	PUNCT
ejpam-6489	541	6	−1)0(ϕ̃	−1)0(ϕ̃	X
ejpam-6489	541	7	)	)	PUNCT
ejpam-6489	541	8	}	}	PUNCT
ejpam-6489	542	1	=	=	SYM
ejpam-6489	542	2	0	0	NUM
ejpam-6489	542	3	,	,	PUNCT
ejpam-6489	542	4	and	and	CCONJ
ejpam-6489	542	5	ζℸ̃(m)(η̃	ζℸ̃(m)(η̃	NOUN
ejpam-6489	542	6	)	)	PUNCT
ejpam-6489	542	7	=	=	SYM
ejpam-6489	542	8	ζf(̃גm)(η̃	ζf(̃גm)(η̃	NOUN
ejpam-6489	542	9	)	)	PUNCT
ejpam-6489	542	10	=	=	SYM
ejpam-6489	542	11	inf	inf	PROPN
ejpam-6489	542	12	η̃=f(ϕ̃	η̃=f(ϕ̃	NOUN
ejpam-6489	542	13	)	)	PUNCT
ejpam-6489	542	14	{	{	PUNCT
ejpam-6489	542	15	00(ϕ̃	00(ϕ̃	NOUN
ejpam-6489	542	16	)	)	PUNCT
ejpam-6489	542	17	}	}	PUNCT
ejpam-6489	543	1	=	=	PUNCT
ejpam-6489	543	2	0	0	NUM
ejpam-6489	543	3	,	,	PUNCT
ejpam-6489	543	4	for	for	ADP
ejpam-6489	543	5	every	every	DET
ejpam-6489	543	6	0	0	NUM
ejpam-6489	543	7	̸=	̸=	PROPN
ejpam-6489	543	8	η̃	η̃	PROPN
ejpam-6489	543	9	∈	∈	PROPN
ejpam-6489	543	10	l̃′	l̃′	PROPN
ejpam-6489	543	11	.	.	PUNCT
ejpam-6489	544	1	so	so	ADV
ejpam-6489	544	2	ξpℸ̃(m	ξpℸ̃(m	NOUN
ejpam-6489	544	3	)	)	PUNCT
ejpam-6489	544	4	=	=	SYM
ejpam-6489	544	5	10	10	NUM
ejpam-6489	544	6	,	,	PUNCT
ejpam-6489	544	7	ξ	ξ	PROPN
ejpam-6489	544	8	n	n	X
ejpam-6489	544	9	ℸ̃(m	ℸ̃(m	NOUN
ejpam-6489	544	10	)	)	PUNCT
ejpam-6489	544	11	=	=	PUNCT
ejpam-6489	544	12	(	(	PUNCT
ejpam-6489	544	13	−1)0	−1)0	NOUN
ejpam-6489	544	14	and	and	CCONJ
ejpam-6489	544	15	ζℸ̃(m	ζℸ̃(m	NOUN
ejpam-6489	544	16	)	)	PUNCT
ejpam-6489	544	17	=	=	SYM
ejpam-6489	544	18	00	00	X
ejpam-6489	544	19	.	.	PUNCT
ejpam-6489	545	1	theorem	theorem	VERB
ejpam-6489	545	2	11	11	NUM
ejpam-6489	545	3	.	.	PUNCT
ejpam-6489	546	1	let	let	VERB
ejpam-6489	546	2	̃ג	̃ג	NOUN
ejpam-6489	546	3	=	=	PUNCT
ejpam-6489	546	4	(	(	PUNCT
ejpam-6489	546	5	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	546	6	,	,	PUNCT
ejpam-6489	546	7	ξ	ξ	PROPN
ejpam-6489	546	8	n	n	PRON
ejpam-6489	546	9	̃ג	̃ג	NOUN
ejpam-6489	546	10	,	,	PUNCT
ejpam-6489	546	11	ζ̃	ζ̃	PROPN
ejpam-6489	546	12	)	)	PUNCT
ejpam-6489	546	13	be	be	VERB
ejpam-6489	546	14	a	a	DET
ejpam-6489	546	15	t	t	NOUN
ejpam-6489	546	16	cfli	cfli	NOUN
ejpam-6489	546	17	of	of	ADP
ejpam-6489	546	18	l̃	l̃	PROPN
ejpam-6489	546	19	and	and	CCONJ
ejpam-6489	546	20	suppose	suppose	VERB
ejpam-6489	546	21	that	that	SCONJ
ejpam-6489	546	22	the	the	DET
ejpam-6489	546	23	quotient	quotient	NOUN
ejpam-6489	546	24	̃ג	̃ג	X
ejpam-6489	546	25	j̃	j̃	PROPN
ejpam-6489	546	26	forms	form	VERB
ejpam-6489	546	27	a	a	DET
ejpam-6489	546	28	st	st	PROPN
ejpam-6489	546	29	cfli	cfli	PROPN
ejpam-6489	546	30	in	in	ADP
ejpam-6489	546	31	the	the	DET
ejpam-6489	546	32	quotient	quotient	NOUN
ejpam-6489	546	33	algebra	algebra	NOUN
ejpam-6489	546	34	l̃	l̃	PROPN
ejpam-6489	546	35	j̃	j̃	PROPN
ejpam-6489	546	36	.	.	PUNCT
ejpam-6489	547	1	assume	assume	VERB
ejpam-6489	547	2	that	that	SCONJ
ejpam-6489	547	3	ℸ̃	ℸ̃	PROPN
ejpam-6489	547	4	=	=	SYM
ejpam-6489	547	5	(	(	PUNCT
ejpam-6489	547	6	ξpℸ̃	ξpℸ̃	NOUN
ejpam-6489	547	7	,	,	PUNCT
ejpam-6489	547	8	ξ	ξ	PROPN
ejpam-6489	547	9	n	n	PRON
ejpam-6489	547	10	ℸ̃	ℸ̃	PROPN
ejpam-6489	547	11	,	,	PUNCT
ejpam-6489	547	12	ζ̃ℸ̃	ζ̃ℸ̃	NOUN
ejpam-6489	547	13	)	)	PUNCT
ejpam-6489	547	14	is	be	AUX
ejpam-6489	547	15	a	a	DET
ejpam-6489	547	16	st	st	PROPN
ejpam-6489	547	17	cfli	cfli	NOUN
ejpam-6489	547	18	of	of	ADP
ejpam-6489	547	19	l̃	l̃	PROPN
ejpam-6489	547	20	,	,	PUNCT
ejpam-6489	547	21	and	and	CCONJ
ejpam-6489	547	22	also	also	ADV
ejpam-6489	547	23	serves	serve	VERB
ejpam-6489	547	24	as	as	ADP
ejpam-6489	547	25	a	a	DET
ejpam-6489	547	26	t	t	NOUN
ejpam-6489	547	27	cfli	cfli	NOUN
ejpam-6489	547	28	of	of	ADP
ejpam-6489	547	29	̃ג	̃ג	NOUN
ejpam-6489	547	30	=	=	SYM
ejpam-6489	547	31	(	(	PUNCT
ejpam-6489	547	32	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	547	33	,	,	PUNCT
ejpam-6489	547	34	ξ	ξ	PROPN
ejpam-6489	547	35	n	n	PRON
ejpam-6489	547	36	̃ג	̃ג	NOUN
ejpam-6489	547	37	,	,	PUNCT
ejpam-6489	547	38	ζ̃	ζ̃	PROPN
ejpam-6489	547	39	)	)	PUNCT
ejpam-6489	547	40	.	.	PUNCT
ejpam-6489	548	1	if	if	SCONJ
ejpam-6489	548	2	,	,	PUNCT
ejpam-6489	548	3	in	in	ADP
ejpam-6489	548	4	addition	addition	NOUN
ejpam-6489	548	5	,	,	PUNCT
ejpam-6489	548	6	ℸ̃(j̃	ℸ̃(j̃	X
ejpam-6489	548	7	)	)	PUNCT
ejpam-6489	548	8	=	=	PUNCT
ejpam-6489	548	9	j̃)̃ג	j̃)̃ג	PROPN
ejpam-6489	548	10	)	)	PUNCT
ejpam-6489	548	11	,	,	PUNCT
ejpam-6489	548	12	then	then	ADV
ejpam-6489	548	13	̃ג	̃ג	NOUN
ejpam-6489	548	14	=	=	SYM
ejpam-6489	548	15	(	(	PUNCT
ejpam-6489	548	16	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	548	17	,	,	PUNCT
ejpam-6489	548	18	ξ	ξ	PROPN
ejpam-6489	548	19	n	n	PRON
ejpam-6489	548	20	̃ג	̃ג	NOUN
ejpam-6489	548	21	,	,	PUNCT
ejpam-6489	548	22	ζ̃̃ג	ζ̃̃ג	PROPN
ejpam-6489	548	23	)	)	PUNCT
ejpam-6489	548	24	is	be	AUX
ejpam-6489	548	25	solvable	solvable	ADJ
ejpam-6489	548	26	.	.	PUNCT
ejpam-6489	549	1	proof	proof	NOUN
ejpam-6489	549	2	.	.	PUNCT
ejpam-6489	550	1	let	let	VERB
ejpam-6489	550	2	f	f	NOUN
ejpam-6489	550	3	:	:	PUNCT
ejpam-6489	550	4	l̃	l̃	PROPN
ejpam-6489	550	5	→	→	PUNCT
ejpam-6489	550	6	l̃	l̃	PROPN
ejpam-6489	550	7	j̃	j̃	PROPN
ejpam-6489	550	8	be	be	AUX
ejpam-6489	550	9	the	the	DET
ejpam-6489	550	10	canonical	canonical	ADJ
ejpam-6489	550	11	map	map	NOUN
ejpam-6489	550	12	.	.	PUNCT
ejpam-6489	551	1	according	accord	VERB
ejpam-6489	551	2	to	to	ADP
ejpam-6489	551	3	the	the	DET
ejpam-6489	551	4	argument	argument	NOUN
ejpam-6489	551	5	presented	present	VERB
ejpam-6489	551	6	in	in	ADP
ejpam-6489	551	7	the	the	DET
ejpam-6489	551	8	proof	proof	NOUN
ejpam-6489	551	9	of	of	ADP
ejpam-6489	551	10	theorem	theorem	NOUN
ejpam-6489	551	11	7	7	NUM
ejpam-6489	551	12	,	,	PUNCT
ejpam-6489	551	13	ξp	ξp	ADP
ejpam-6489	551	14	ϕ(̃ג(n	ϕ(̃ג(n	PROPN
ejpam-6489	551	15	)	)	PUNCT
ejpam-6489	551	16	)	)	PUNCT
ejpam-6489	552	1	=	=	PRON
ejpam-6489	552	2	ξp	ξp	X
ejpam-6489	552	3	(	(	PUNCT
ejpam-6489	552	4	̃ג	̃ג	NOUN
ejpam-6489	552	5	j	j	PROPN
ejpam-6489	552	6	)	)	PUNCT
ejpam-6489	552	7	(	(	PUNCT
ejpam-6489	552	8	n	n	CCONJ
ejpam-6489	552	9	)	)	PUNCT
ejpam-6489	552	10	,	,	PUNCT
ejpam-6489	552	11	ξn	ξn	PROPN
ejpam-6489	552	12	ϕ(̃ג(n	ϕ(̃ג(n	PROPN
ejpam-6489	552	13	)	)	PUNCT
ejpam-6489	552	14	)	)	PUNCT
ejpam-6489	553	1	=	=	PRON
ejpam-6489	553	2	ξp	ξp	X
ejpam-6489	553	3	(	(	PUNCT
ejpam-6489	553	4	̃ג	̃ג	NOUN
ejpam-6489	553	5	j	j	PROPN
ejpam-6489	553	6	)	)	PUNCT
ejpam-6489	553	7	(	(	PUNCT
ejpam-6489	553	8	n	n	CCONJ
ejpam-6489	553	9	)	)	PUNCT
ejpam-6489	553	10	and	and	CCONJ
ejpam-6489	553	11	ζϕ(̃ג(n	ζϕ(̃ג(n	PROPN
ejpam-6489	553	12	)	)	PUNCT
ejpam-6489	553	13	)	)	PUNCT
ejpam-6489	554	1	=	=	SYM
ejpam-6489	554	2	ζ	ζ	NOUN
ejpam-6489	554	3	(	(	PUNCT
ejpam-6489	554	4	̃ג	̃ג	NOUN
ejpam-6489	554	5	j	j	PROPN
ejpam-6489	554	6	)	)	PUNCT
ejpam-6489	554	7	(	(	PUNCT
ejpam-6489	554	8	n	n	CCONJ
ejpam-6489	554	9	)	)	PUNCT
ejpam-6489	554	10	.	.	PUNCT
ejpam-6489	555	1	m.	m.	NOUN
ejpam-6489	555	2	balamurugan	balamurugan	PROPN
ejpam-6489	555	3	,	,	PUNCT
ejpam-6489	555	4	g.	g.	PROPN
ejpam-6489	555	5	ellammal	ellammal	PROPN
ejpam-6489	555	6	,	,	PUNCT
ejpam-6489	555	7	a.	a.	NOUN
ejpam-6489	555	8	iampan	iampan	PROPN
ejpam-6489	555	9	/	/	SYM
ejpam-6489	555	10	eur	eur	PROPN
ejpam-6489	555	11	.	.	PUNCT
ejpam-6489	556	1	j.	j.	PROPN
ejpam-6489	556	2	pure	pure	PROPN
ejpam-6489	556	3	appl	appl	PROPN
ejpam-6489	556	4	.	.	PROPN
ejpam-6489	556	5	math	math	PROPN
ejpam-6489	556	6	,	,	PUNCT
ejpam-6489	556	7	18	18	NUM
ejpam-6489	556	8	(	(	PUNCT
ejpam-6489	556	9	3	3	NUM
ejpam-6489	556	10	)	)	PUNCT
ejpam-6489	556	11	(	(	PUNCT
ejpam-6489	556	12	2025	2025	NUM
ejpam-6489	556	13	)	)	PUNCT
ejpam-6489	556	14	,	,	PUNCT
ejpam-6489	556	15	6489	6489	NUM
ejpam-6489	556	16	23	23	NUM
ejpam-6489	556	17	of	of	ADP
ejpam-6489	556	18	26	26	NUM
ejpam-6489	556	19	since	since	SCONJ
ejpam-6489	556	20	̃ג	̃ג	ADJ
ejpam-6489	556	21	j	j	PROPN
ejpam-6489	556	22	is	be	AUX
ejpam-6489	556	23	solvable	solvable	ADJ
ejpam-6489	556	24	,	,	PUNCT
ejpam-6489	556	25	there	there	PRON
ejpam-6489	556	26	exists	exist	VERB
ejpam-6489	556	27	a	a	DET
ejpam-6489	556	28	positive	positive	ADJ
ejpam-6489	556	29	integer	integer	NOUN
ejpam-6489	556	30	n	n	CCONJ
ejpam-6489	557	1	such	such	ADJ
ejpam-6489	557	2	that	that	PRON
ejpam-6489	557	3	ξp	ξp	ADP
ejpam-6489	557	4	(	(	PUNCT
ejpam-6489	557	5	̃ג	̃ג	NOUN
ejpam-6489	557	6	j̃	j̃	PROPN
ejpam-6489	557	7	)	)	PUNCT
ejpam-6489	557	8	(	(	PUNCT
ejpam-6489	557	9	n	n	CCONJ
ejpam-6489	557	10	)	)	PUNCT
ejpam-6489	557	11	=	=	SYM
ejpam-6489	557	12	10	10	NUM
ejpam-6489	557	13	,	,	PUNCT
ejpam-6489	557	14	ξ	ξ	PROPN
ejpam-6489	557	15	n	n	CCONJ
ejpam-6489	557	16	(	(	PUNCT
ejpam-6489	557	17	̃ג	̃ג	NOUN
ejpam-6489	557	18	j̃	j̃	PROPN
ejpam-6489	557	19	)	)	PUNCT
ejpam-6489	557	20	(	(	PUNCT
ejpam-6489	557	21	n	n	CCONJ
ejpam-6489	557	22	)	)	PUNCT
ejpam-6489	557	23	=	=	SYM
ejpam-6489	557	24	(	(	PUNCT
ejpam-6489	557	25	−1)0	−1)0	NOUN
ejpam-6489	557	26	and	and	CCONJ
ejpam-6489	557	27	ζ	ζ	NOUN
ejpam-6489	557	28	(	(	PUNCT
ejpam-6489	557	29	̃ג	̃ג	NOUN
ejpam-6489	557	30	j̃	j̃	PROPN
ejpam-6489	557	31	)	)	PUNCT
ejpam-6489	557	32	(	(	PUNCT
ejpam-6489	557	33	n	n	CCONJ
ejpam-6489	557	34	)	)	PUNCT
ejpam-6489	557	35	=	=	SYM
ejpam-6489	557	36	00	00	PROPN
ejpam-6489	557	37	.	.	PUNCT
ejpam-6489	558	1	for	for	ADP
ejpam-6489	558	2	0	0	NUM
ejpam-6489	558	3	̸=	̸=	PROPN
ejpam-6489	558	4	η̃	η̃	PROPN
ejpam-6489	558	5	∈	∈	PROPN
ejpam-6489	558	6	l̃	l̃	PROPN
ejpam-6489	558	7	j̃	j̃	PROPN
ejpam-6489	558	8	,	,	PUNCT
ejpam-6489	558	9	we	we	PRON
ejpam-6489	558	10	have	have	VERB
ejpam-6489	558	11	sup	sup	NOUN
ejpam-6489	558	12	m∈f−1(η̃	m∈f−1(η̃	NOUN
ejpam-6489	558	13	)	)	PUNCT
ejpam-6489	558	14	{	{	PUNCT
ejpam-6489	558	15	ξp̃ג(n)(m	ξp̃ג(n)(m	NUM
ejpam-6489	558	16	)	)	PUNCT
ejpam-6489	558	17	}	}	PUNCT
ejpam-6489	558	18	=	=	PUNCT
ejpam-6489	558	19	ξp	ξp	ADP
ejpam-6489	558	20	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	558	21	)	)	PUNCT
ejpam-6489	558	22	)	)	PUNCT
ejpam-6489	559	1	(	(	PUNCT
ejpam-6489	559	2	η̃	η̃	PROPN
ejpam-6489	559	3	)	)	PUNCT
ejpam-6489	559	4	=	=	PRON
ejpam-6489	560	1	ξp	ξp	X
ejpam-6489	560	2	(	(	PUNCT
ejpam-6489	560	3	̃ג	̃ג	NOUN
ejpam-6489	560	4	j̃	j̃	PROPN
ejpam-6489	560	5	)	)	PUNCT
ejpam-6489	560	6	(	(	PUNCT
ejpam-6489	560	7	n	n	CCONJ
ejpam-6489	560	8	)	)	PUNCT
ejpam-6489	560	9	(	(	PUNCT
ejpam-6489	560	10	η̃	η̃	PROPN
ejpam-6489	560	11	)	)	PUNCT
ejpam-6489	560	12	=	=	SYM
ejpam-6489	560	13	0	0	NUM
ejpam-6489	560	14	,	,	PUNCT
ejpam-6489	560	15	inf	inf	ADJ
ejpam-6489	560	16	m∈f−1(η̃	m∈f−1(η̃	NOUN
ejpam-6489	560	17	)	)	PUNCT
ejpam-6489	560	18	{	{	PUNCT
ejpam-6489	560	19	ξñג(n)(m	ξñג(n)(m	NUM
ejpam-6489	560	20	)	)	PUNCT
ejpam-6489	560	21	}	}	PUNCT
ejpam-6489	560	22	=	=	PUNCT
ejpam-6489	560	23	ξn	ξn	PROPN
ejpam-6489	560	24	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	560	25	)	)	PUNCT
ejpam-6489	560	26	)	)	PUNCT
ejpam-6489	561	1	(	(	PUNCT
ejpam-6489	561	2	η̃	η̃	PROPN
ejpam-6489	561	3	)	)	PUNCT
ejpam-6489	562	1	=	=	SYM
ejpam-6489	562	2	ξn	ξn	PROPN
ejpam-6489	562	3	(	(	PUNCT
ejpam-6489	562	4	̃ג	̃ג	NOUN
ejpam-6489	562	5	j̃	j̃	PROPN
ejpam-6489	562	6	)	)	PUNCT
ejpam-6489	562	7	(	(	PUNCT
ejpam-6489	562	8	n	n	CCONJ
ejpam-6489	562	9	)	)	PUNCT
ejpam-6489	562	10	(	(	PUNCT
ejpam-6489	562	11	η̃	η̃	PROPN
ejpam-6489	562	12	)	)	PUNCT
ejpam-6489	562	13	=	=	SYM
ejpam-6489	562	14	0	0	NUM
ejpam-6489	562	15	,	,	PUNCT
ejpam-6489	562	16	and	and	CCONJ
ejpam-6489	562	17	inf	inf	PROPN
ejpam-6489	562	18	m∈f−1(η̃	m∈f−1(η̃	NOUN
ejpam-6489	562	19	)	)	PUNCT
ejpam-6489	562	20	{	{	PUNCT
ejpam-6489	562	21	ζ̃ג(n)(m	ζ̃ג(n)(m	PROPN
ejpam-6489	562	22	)	)	PUNCT
ejpam-6489	562	23	}	}	PUNCT
ejpam-6489	562	24	=	=	SYM
ejpam-6489	562	25	ζf(̃ג(n))(η̃	ζf(̃ג(n))(η̃	NOUN
ejpam-6489	562	26	)	)	PUNCT
ejpam-6489	562	27	=	=	SYM
ejpam-6489	562	28	ζ	ζ	NOUN
ejpam-6489	562	29	(	(	PUNCT
ejpam-6489	562	30	̃ג	̃ג	NOUN
ejpam-6489	562	31	j̃	j̃	PROPN
ejpam-6489	562	32	)	)	PUNCT
ejpam-6489	562	33	(	(	PUNCT
ejpam-6489	562	34	n)(η̃	n)(η̃	NOUN
ejpam-6489	562	35	)	)	PUNCT
ejpam-6489	562	36	=	=	SYM
ejpam-6489	562	37	0	0	X
ejpam-6489	562	38	.	.	X
ejpam-6489	562	39	note	note	VERB
ejpam-6489	562	40	that	that	SCONJ
ejpam-6489	562	41	m	m	VERB
ejpam-6489	562	42	̸=	̸=	NOUN
ejpam-6489	562	43	0	0	NUM
ejpam-6489	562	44	and	and	CCONJ
ejpam-6489	562	45	m	m	PROPN
ejpam-6489	562	46	∈	∈	PROPN
ejpam-6489	562	47	l̃.	l̃.	PROPN
ejpam-6489	562	48	then	then	ADV
ejpam-6489	562	49	ξp̃ג(n)(m	ξp̃ג(n)(m	NUM
ejpam-6489	562	50	)	)	PUNCT
ejpam-6489	562	51	=	=	SYM
ejpam-6489	562	52	0	0	NUM
ejpam-6489	562	53	,	,	PUNCT
ejpam-6489	562	54	ξñג(n)(m	ξñג(n)(m	NUM
ejpam-6489	562	55	)	)	PUNCT
ejpam-6489	562	56	=	=	SYM
ejpam-6489	562	57	0	0	NUM
ejpam-6489	562	58	and	and	CCONJ
ejpam-6489	562	59	ζ̃ג(n)(m	ζ̃ג(n)(m	VERB
ejpam-6489	562	60	)	)	PUNCT
ejpam-6489	562	61	=	=	SYM
ejpam-6489	562	62	0	0	X
ejpam-6489	562	63	.	.	X
ejpam-6489	562	64	for	for	ADP
ejpam-6489	562	65	η̃	η̃	PROPN
ejpam-6489	562	66	=	=	SYM
ejpam-6489	562	67	0	0	PROPN
ejpam-6489	562	68	,	,	PUNCT
ejpam-6489	562	69	we	we	PRON
ejpam-6489	562	70	have	have	VERB
ejpam-6489	562	71	sup	sup	PROPN
ejpam-6489	562	72	m∈f−1(0	m∈f−1(0	PROPN
ejpam-6489	562	73	)	)	PUNCT
ejpam-6489	562	74	{	{	PUNCT
ejpam-6489	562	75	ξp	ξp	X
ejpam-6489	562	76	(	(	PUNCT
ejpam-6489	562	77	(	(	PUNCT
ejpam-6489	562	78	n)̃ג	n)̃ג	PROPN
ejpam-6489	562	79	)	)	PUNCT
ejpam-6489	562	80	(	(	PUNCT
ejpam-6489	562	81	m	m	NOUN
ejpam-6489	562	82	)	)	PUNCT
ejpam-6489	562	83	}	}	PUNCT
ejpam-6489	562	84	=	=	PUNCT
ejpam-6489	562	85	ξp	ξp	ADP
ejpam-6489	562	86	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	562	87	)	)	PUNCT
ejpam-6489	562	88	)	)	PUNCT
ejpam-6489	562	89	(	(	PUNCT
ejpam-6489	562	90	0	0	X
ejpam-6489	562	91	)	)	PUNCT
ejpam-6489	562	92	=	=	SYM
ejpam-6489	562	93	1	1	X
ejpam-6489	562	94	,	,	PUNCT
ejpam-6489	562	95	inf	inf	PROPN
ejpam-6489	562	96	m∈f−1(0	m∈f−1(0	PROPN
ejpam-6489	562	97	)	)	PUNCT
ejpam-6489	562	98	{	{	PUNCT
ejpam-6489	562	99	ξn	ξn	PROPN
ejpam-6489	562	100	(	(	PUNCT
ejpam-6489	562	101	(	(	PUNCT
ejpam-6489	562	102	n)̃ג	n)̃ג	PROPN
ejpam-6489	562	103	)	)	PUNCT
ejpam-6489	562	104	(	(	PUNCT
ejpam-6489	562	105	m	m	NOUN
ejpam-6489	562	106	)	)	PUNCT
ejpam-6489	562	107	}	}	PUNCT
ejpam-6489	562	108	=	=	PUNCT
ejpam-6489	562	109	ξn	ξn	PROPN
ejpam-6489	562	110	f(̃ג(n	f(̃ג(n	PROPN
ejpam-6489	562	111	)	)	PUNCT
ejpam-6489	562	112	)	)	PUNCT
ejpam-6489	562	113	(	(	PUNCT
ejpam-6489	562	114	0	0	X
ejpam-6489	562	115	)	)	PUNCT
ejpam-6489	562	116	=	=	SYM
ejpam-6489	562	117	−1	−1	NOUN
ejpam-6489	562	118	and	and	CCONJ
ejpam-6489	562	119	inf	inf	PROPN
ejpam-6489	562	120	m∈f−1(0	m∈f−1(0	PROPN
ejpam-6489	562	121	)	)	PUNCT
ejpam-6489	562	122	{	{	PUNCT
ejpam-6489	562	123	ζ(̃ג(n))(m	ζ(̃ג(n))(m	NOUN
ejpam-6489	562	124	)	)	PUNCT
ejpam-6489	562	125	}	}	PUNCT
ejpam-6489	562	126	=	=	PUNCT
ejpam-6489	562	127	ζf(̃ג(n))(0	ζf(̃ג(n))(0	NUM
ejpam-6489	562	128	)	)	PUNCT
ejpam-6489	562	129	=	=	SYM
ejpam-6489	563	1	0	0	X
ejpam-6489	563	2	.	.	PUNCT
ejpam-6489	563	3	since	since	SCONJ
ejpam-6489	563	4	f−1(0	f−1(0	PROPN
ejpam-6489	563	5	)	)	PUNCT
ejpam-6489	563	6	=	=	PUNCT
ejpam-6489	564	1	j̃	j̃	PROPN
ejpam-6489	564	2	and	and	CCONJ
ejpam-6489	564	3	ℸ̃(j̃	ℸ̃(j̃	PUNCT
ejpam-6489	564	4	)	)	PUNCT
ejpam-6489	565	1	=	=	PUNCT
ejpam-6489	565	2	j̃)̃ג	j̃)̃ג	PROPN
ejpam-6489	565	3	)	)	PUNCT
ejpam-6489	565	4	,	,	PUNCT
ejpam-6489	565	5	we	we	PRON
ejpam-6489	565	6	have	have	VERB
ejpam-6489	565	7	ξpℸ̃(n)(j̃	ξpℸ̃(n)(j̃	NOUN
ejpam-6489	565	8	)	)	PUNCT
ejpam-6489	565	9	=	=	SYM
ejpam-6489	565	10	ξp̃ג(n)(j̃	ξp̃ג(n)(j̃	PUNCT
ejpam-6489	565	11	)	)	PUNCT
ejpam-6489	565	12	,	,	PUNCT
ejpam-6489	565	13	ξnℸ̃(n)(j̃	ξnℸ̃(n)(j̃	NOUN
ejpam-6489	565	14	)	)	PUNCT
ejpam-6489	566	1	=	=	SYM
ejpam-6489	566	2	ξñג(n)(j̃	ξñג(n)(j̃	NOUN
ejpam-6489	566	3	)	)	PUNCT
ejpam-6489	566	4	and	and	CCONJ
ejpam-6489	566	5	ζℸ̃(n)(j̃	ζℸ̃(n)(j̃	NOUN
ejpam-6489	566	6	)	)	PUNCT
ejpam-6489	567	1	=	=	SYM
ejpam-6489	567	2	ζ̃ג(n)(j̃	ζ̃ג(n)(j̃	NOUN
ejpam-6489	567	3	)	)	PUNCT
ejpam-6489	567	4	.	.	PUNCT
ejpam-6489	568	1	for	for	ADP
ejpam-6489	568	2	any	any	DET
ejpam-6489	568	3	ϕ̃	ϕ̃	PROPN
ejpam-6489	568	4	∈	∈	PROPN
ejpam-6489	568	5	j̃	j̃	PROPN
ejpam-6489	568	6	,	,	PUNCT
ejpam-6489	568	7	ℸ̃	ℸ̃	PROPN
ejpam-6489	568	8	is	be	AUX
ejpam-6489	568	9	solvable	solvable	ADJ
ejpam-6489	568	10	,	,	PUNCT
ejpam-6489	568	11	then	then	ADV
ejpam-6489	568	12	there	there	PRON
ejpam-6489	568	13	exists	exist	VERB
ejpam-6489	568	14	a	a	DET
ejpam-6489	568	15	positive	positive	ADJ
ejpam-6489	568	16	integer	integer	NOUN
ejpam-6489	568	17	n	n	CCONJ
ejpam-6489	569	1	such	such	ADJ
ejpam-6489	569	2	that	that	PRON
ejpam-6489	569	3	ξp	ξp	ADP
ejpam-6489	569	4	s̃(n	s̃(n	ADJ
ejpam-6489	569	5	)	)	PUNCT
ejpam-6489	569	6	=	=	SYM
ejpam-6489	569	7	10	10	NUM
ejpam-6489	569	8	and	and	CCONJ
ejpam-6489	569	9	ξn	ξn	PRON
ejpam-6489	569	10	s̃(n	s̃(n	NOUN
ejpam-6489	569	11	)	)	PUNCT
ejpam-6489	569	12	=	=	SYM
ejpam-6489	569	13	(	(	PUNCT
ejpam-6489	569	14	−1)0	−1)0	NOUN
ejpam-6489	569	15	,	,	PUNCT
ejpam-6489	569	16	ξpℸ̃(n	ξpℸ̃(n	PROPN
ejpam-6489	569	17	)	)	PUNCT
ejpam-6489	569	18	=	=	SYM
ejpam-6489	569	19	10	10	NUM
ejpam-6489	569	20	,	,	PUNCT
ejpam-6489	569	21	ξ	ξ	PROPN
ejpam-6489	569	22	n	n	X
ejpam-6489	569	23	(	(	PUNCT
ejpam-6489	569	24	n)̃ג	n)̃ג	PROPN
ejpam-6489	569	25	=	=	SYM
ejpam-6489	569	26	(	(	PUNCT
ejpam-6489	569	27	−1)0	−1)0	NOUN
ejpam-6489	569	28	and	and	CCONJ
ejpam-6489	569	29	ζ̃ג(n	ζ̃ג(n	NOUN
ejpam-6489	569	30	)	)	PUNCT
ejpam-6489	569	31	=	=	SYM
ejpam-6489	569	32	00	00	PUNCT
ejpam-6489	569	33	.	.	PUNCT
ejpam-6489	570	1	hence	hence	ADV
ejpam-6489	570	2	,	,	PUNCT
ejpam-6489	570	3	ξp̃ג(n	ξp̃ג(n	NOUN
ejpam-6489	570	4	)	)	PUNCT
ejpam-6489	570	5	=	=	SYM
ejpam-6489	570	6	10	10	NUM
ejpam-6489	570	7	,	,	PUNCT
ejpam-6489	570	8	ξñג(n	ξñג(n	NUM
ejpam-6489	570	9	)	)	PUNCT
ejpam-6489	570	10	=	=	PRON
ejpam-6489	570	11	(	(	PUNCT
ejpam-6489	570	12	−1)0	−1)0	NOUN
ejpam-6489	570	13	and	and	CCONJ
ejpam-6489	570	14	ζ̃ג(n	ζ̃ג(n	NOUN
ejpam-6489	570	15	)	)	PUNCT
ejpam-6489	570	16	=	=	SYM
ejpam-6489	570	17	00	00	PUNCT
ejpam-6489	570	18	,	,	PUNCT
ejpam-6489	570	19	which	which	PRON
ejpam-6489	570	20	implies	imply	VERB
ejpam-6489	570	21	that	that	PRON
ejpam-6489	570	22	̃ג	̃ג	NOUN
ejpam-6489	570	23	=	=	SYM
ejpam-6489	570	24	(	(	PUNCT
ejpam-6489	570	25	ξp̃ג	ξp̃ג	PROPN
ejpam-6489	570	26	,	,	PUNCT
ejpam-6489	570	27	ξ	ξ	PROPN
ejpam-6489	570	28	n	n	PRON
ejpam-6489	570	29	̃ג	̃ג	NOUN
ejpam-6489	570	30	,	,	PUNCT
ejpam-6489	570	31	ζ̃	ζ̃	PROPN
ejpam-6489	570	32	)	)	PUNCT
ejpam-6489	570	33	is	be	AUX
ejpam-6489	570	34	solvable	solvable	ADJ
ejpam-6489	570	35	.	.	PUNCT
ejpam-6489	571	1	6	6	X
ejpam-6489	571	2	.	.	X
ejpam-6489	571	3	conclusion	conclusion	NOUN
ejpam-6489	571	4	in	in	ADP
ejpam-6489	571	5	this	this	DET
ejpam-6489	571	6	paper	paper	NOUN
ejpam-6489	571	7	,	,	PUNCT
ejpam-6489	571	8	we	we	PRON
ejpam-6489	571	9	extended	extend	VERB
ejpam-6489	571	10	the	the	DET
ejpam-6489	571	11	framework	framework	NOUN
ejpam-6489	571	12	of	of	ADP
ejpam-6489	571	13	tripolar	tripolar	ADJ
ejpam-6489	571	14	complex	complex	ADJ
ejpam-6489	571	15	fuzzy	fuzzy	ADJ
ejpam-6489	571	16	sets	set	NOUN
ejpam-6489	571	17	(	(	PUNCT
ejpam-6489	571	18	t	t	NOUN
ejpam-6489	571	19	cfs	cfs	PROPN
ejpam-6489	571	20	by	by	ADP
ejpam-6489	571	21	introducing	introduce	VERB
ejpam-6489	571	22	the	the	DET
ejpam-6489	571	23	concept	concept	NOUN
ejpam-6489	571	24	of	of	ADP
ejpam-6489	571	25	tripolar	tripolar	ADJ
ejpam-6489	571	26	complex	complex	ADJ
ejpam-6489	571	27	fuzzy	fuzzy	ADJ
ejpam-6489	571	28	lie	lie	NOUN
ejpam-6489	571	29	brackets	bracket	NOUN
ejpam-6489	571	30	and	and	CCONJ
ejpam-6489	571	31	investigating	investigate	VERB
ejpam-6489	571	32	their	their	PRON
ejpam-6489	571	33	fundamental	fundamental	ADJ
ejpam-6489	571	34	algebraic	algebraic	ADJ
ejpam-6489	571	35	properties	property	NOUN
ejpam-6489	571	36	.	.	PUNCT
ejpam-6489	572	1	we	we	PRON
ejpam-6489	572	2	demonstrated	demonstrate	VERB
ejpam-6489	572	3	that	that	SCONJ
ejpam-6489	572	4	the	the	DET
ejpam-6489	572	5	scalar	scalar	ADJ
ejpam-6489	572	6	multiplication	multiplication	NOUN
ejpam-6489	572	7	and	and	CCONJ
ejpam-6489	572	8	addition	addition	NOUN
ejpam-6489	572	9	of	of	ADP
ejpam-6489	572	10	tripolar	tripolar	ADJ
ejpam-6489	572	11	complex	complex	ADJ
ejpam-6489	572	12	fuzzy	fuzzy	ADJ
ejpam-6489	572	13	lie	lie	NOUN
ejpam-6489	572	14	subalgebras	subalgebras	PROPN
ejpam-6489	572	15	yield	yield	VERB
ejpam-6489	572	16	a	a	DET
ejpam-6489	572	17	tripolar	tripolar	ADJ
ejpam-6489	572	18	complex	complex	ADJ
ejpam-6489	572	19	fuzzy	fuzzy	ADJ
ejpam-6489	572	20	lie	lie	NOUN
ejpam-6489	572	21	subalgebra	subalgebra	NOUN
ejpam-6489	572	22	,	,	PUNCT
ejpam-6489	572	23	m.	m.	NOUN
ejpam-6489	572	24	balamurugan	balamurugan	NOUN
ejpam-6489	572	25	,	,	PUNCT
ejpam-6489	572	26	g.	g.	PROPN
ejpam-6489	572	27	ellammal	ellammal	PROPN
ejpam-6489	572	28	,	,	PUNCT
ejpam-6489	572	29	a.	a.	NOUN
ejpam-6489	572	30	iampan	iampan	PROPN
ejpam-6489	572	31	/	/	SYM
ejpam-6489	572	32	eur	eur	PROPN
ejpam-6489	572	33	.	.	PUNCT
ejpam-6489	573	1	j.	j.	PROPN
ejpam-6489	573	2	pure	pure	PROPN
ejpam-6489	573	3	appl	appl	PROPN
ejpam-6489	573	4	.	.	PROPN
ejpam-6489	573	5	math	math	PROPN
ejpam-6489	573	6	,	,	PUNCT
ejpam-6489	573	7	18	18	NUM
ejpam-6489	573	8	(	(	PUNCT
ejpam-6489	573	9	3	3	NUM
ejpam-6489	573	10	)	)	PUNCT
ejpam-6489	573	11	(	(	PUNCT
ejpam-6489	573	12	2025	2025	NUM
ejpam-6489	573	13	)	)	PUNCT
ejpam-6489	573	14	,	,	PUNCT
ejpam-6489	573	15	6489	6489	NUM
ejpam-6489	573	16	24	24	NUM
ejpam-6489	573	17	of	of	ADP
ejpam-6489	573	18	26	26	NUM
ejpam-6489	573	19	reinforcing	reinforce	VERB
ejpam-6489	573	20	their	their	PRON
ejpam-6489	573	21	algebraic	algebraic	ADJ
ejpam-6489	573	22	closure	closure	NOUN
ejpam-6489	573	23	properties	property	NOUN
ejpam-6489	573	24	.	.	PUNCT
ejpam-6489	574	1	also	also	ADV
ejpam-6489	574	2	,	,	PUNCT
ejpam-6489	574	3	we	we	PRON
ejpam-6489	574	4	established	establish	VERB
ejpam-6489	574	5	that	that	SCONJ
ejpam-6489	574	6	the	the	DET
ejpam-6489	574	7	homomorphic	homomorphic	ADJ
ejpam-6489	574	8	image	image	NOUN
ejpam-6489	574	9	of	of	ADP
ejpam-6489	574	10	a	a	DET
ejpam-6489	574	11	nilpotent	nilpotent	NOUN
ejpam-6489	574	12	(	(	PUNCT
ejpam-6489	574	13	or	or	CCONJ
ejpam-6489	574	14	solvable	solvable	ADJ
ejpam-6489	574	15	)	)	PUNCT
ejpam-6489	574	16	tripolar	tripolar	ADJ
ejpam-6489	574	17	complex	complex	ADJ
ejpam-6489	574	18	fuzzy	fuzzy	ADJ
ejpam-6489	574	19	lie	lie	NOUN
ejpam-6489	574	20	ideal	ideal	NOUN
ejpam-6489	574	21	remains	remain	VERB
ejpam-6489	574	22	nilpotent	nilpotent	ADJ
ejpam-6489	574	23	(	(	PUNCT
ejpam-6489	574	24	or	or	CCONJ
ejpam-6489	574	25	solvable	solvable	ADJ
ejpam-6489	574	26	)	)	PUNCT
ejpam-6489	574	27	,	,	PUNCT
ejpam-6489	574	28	highlighting	highlight	VERB
ejpam-6489	574	29	the	the	DET
ejpam-6489	574	30	structural	structural	ADJ
ejpam-6489	574	31	preservation	preservation	NOUN
ejpam-6489	574	32	under	under	ADP
ejpam-6489	574	33	homomorphisms	homomorphism	NOUN
ejpam-6489	574	34	.	.	PUNCT
ejpam-6489	575	1	finally	finally	ADV
ejpam-6489	575	2	,	,	PUNCT
ejpam-6489	575	3	we	we	PRON
ejpam-6489	575	4	proved	prove	VERB
ejpam-6489	575	5	that	that	SCONJ
ejpam-6489	575	6	every	every	DET
ejpam-6489	575	7	nilpotent	nilpotent	ADJ
ejpam-6489	575	8	tripolar	tripolar	ADJ
ejpam-6489	575	9	complex	complex	ADJ
ejpam-6489	575	10	fuzzy	fuzzy	ADJ
ejpam-6489	575	11	lie	lie	NOUN
ejpam-6489	575	12	ideal	ideal	NOUN
ejpam-6489	575	13	is	be	AUX
ejpam-6489	575	14	solvable	solvable	ADJ
ejpam-6489	575	15	,	,	PUNCT
ejpam-6489	575	16	extending	extend	VERB
ejpam-6489	575	17	a	a	DET
ejpam-6489	575	18	fundamental	fundamental	ADJ
ejpam-6489	575	19	result	result	NOUN
ejpam-6489	575	20	from	from	ADP
ejpam-6489	575	21	classical	classical	ADJ
ejpam-6489	575	22	lie	lie	NOUN
ejpam-6489	575	23	theory	theory	NOUN
ejpam-6489	575	24	to	to	ADP
ejpam-6489	575	25	the	the	DET
ejpam-6489	575	26	tripolar	tripolar	ADJ
ejpam-6489	575	27	complex	complex	ADJ
ejpam-6489	575	28	fuzzy	fuzzy	ADJ
ejpam-6489	575	29	setting	setting	NOUN
ejpam-6489	575	30	.	.	PUNCT
ejpam-6489	576	1	these	these	DET
ejpam-6489	576	2	results	result	NOUN
ejpam-6489	576	3	contribute	contribute	VERB
ejpam-6489	576	4	to	to	ADP
ejpam-6489	576	5	the	the	DET
ejpam-6489	576	6	growing	grow	VERB
ejpam-6489	576	7	body	body	NOUN
ejpam-6489	576	8	of	of	ADP
ejpam-6489	576	9	research	research	NOUN
ejpam-6489	576	10	on	on	ADP
ejpam-6489	576	11	fuzzy	fuzzy	ADJ
ejpam-6489	576	12	algebraic	algebraic	ADJ
ejpam-6489	576	13	structures	structure	NOUN
ejpam-6489	576	14	,	,	PUNCT
ejpam-6489	576	15	particularly	particularly	ADV
ejpam-6489	576	16	in	in	ADP
ejpam-6489	576	17	the	the	DET
ejpam-6489	576	18	context	context	NOUN
ejpam-6489	576	19	of	of	ADP
ejpam-6489	576	20	multipolar	multipolar	ADJ
ejpam-6489	576	21	and	and	CCONJ
ejpam-6489	576	22	complex	complex	ADV
ejpam-6489	576	23	-	-	PUNCT
ejpam-6489	576	24	valued	value	VERB
ejpam-6489	576	25	fuzzy	fuzzy	ADJ
ejpam-6489	576	26	systems	system	NOUN
ejpam-6489	576	27	.	.	PUNCT
ejpam-6489	577	1	in	in	ADP
ejpam-6489	577	2	future	future	ADJ
ejpam-6489	577	3	work	work	NOUN
ejpam-6489	577	4	,	,	PUNCT
ejpam-6489	577	5	we	we	PRON
ejpam-6489	577	6	will	will	AUX
ejpam-6489	577	7	extend	extend	VERB
ejpam-6489	577	8	the	the	DET
ejpam-6489	577	9	framework	framework	NOUN
ejpam-6489	577	10	to	to	ADP
ejpam-6489	577	11	n	n	CCONJ
ejpam-6489	577	12	-	-	PUNCT
ejpam-6489	577	13	polar	polar	ADJ
ejpam-6489	577	14	complex	complex	ADJ
ejpam-6489	577	15	pythagorean	pythagorean	NOUN
ejpam-6489	577	16	fuzzy	fuzzy	ADJ
ejpam-6489	577	17	lie	lie	NOUN
ejpam-6489	577	18	algebras	algebra	NOUN
ejpam-6489	577	19	to	to	PART
ejpam-6489	577	20	explore	explore	VERB
ejpam-6489	577	21	higher	high	ADJ
ejpam-6489	577	22	-	-	PUNCT
ejpam-6489	577	23	dimensional	dimensional	ADJ
ejpam-6489	577	24	algebraic	algebraic	ADJ
ejpam-6489	577	25	properties	property	NOUN
ejpam-6489	577	26	.	.	PUNCT
ejpam-6489	578	1	acknowledgements	acknowledgement	NOUN
ejpam-6489	578	2	this	this	DET
ejpam-6489	578	3	research	research	NOUN
ejpam-6489	578	4	was	be	AUX
ejpam-6489	578	5	supported	support	VERB
ejpam-6489	578	6	by	by	ADP
ejpam-6489	578	7	university	university	NOUN
ejpam-6489	578	8	of	of	ADP
ejpam-6489	578	9	phayao	phayao	NOUN
ejpam-6489	578	10	and	and	CCONJ
ejpam-6489	578	11	thailand	thailand	PROPN
ejpam-6489	578	12	science	science	PROPN
ejpam-6489	578	13	research	research	PROPN
ejpam-6489	578	14	and	and	CCONJ
ejpam-6489	578	15	innovation	innovation	NOUN
ejpam-6489	578	16	fund	fund	NOUN
ejpam-6489	578	17	(	(	PUNCT
ejpam-6489	578	18	fundamental	fundamental	ADJ
ejpam-6489	578	19	fund	fund	NOUN
ejpam-6489	578	20	2025	2025	NUM
ejpam-6489	578	21	,	,	PUNCT
ejpam-6489	578	22	grant	grant	VERB
ejpam-6489	578	23	no	no	NOUN
ejpam-6489	578	24	.	.	PROPN
ejpam-6489	579	1	5027/2567	5027/2567	NUM
ejpam-6489	579	2	)	)	PUNCT
ejpam-6489	579	3	.	.	PUNCT
ejpam-6489	580	1	references	reference	NOUN
ejpam-6489	580	2	[	[	X
ejpam-6489	580	3	1	1	X
ejpam-6489	580	4	]	]	PUNCT
ejpam-6489	580	5	j.	j.	PROPN
ejpam-6489	580	6	e.	e.	PROPN
ejpam-6489	580	7	humphreys	humphreys	PROPN
ejpam-6489	580	8	.	.	PUNCT
ejpam-6489	581	1	introduction	introduction	NOUN
ejpam-6489	581	2	to	to	PART
ejpam-6489	581	3	lie	lie	VERB
ejpam-6489	581	4	algebras	algebra	NOUN
ejpam-6489	581	5	and	and	CCONJ
ejpam-6489	581	6	representation	representation	NOUN
ejpam-6489	581	7	theory	theory	NOUN
ejpam-6489	581	8	,	,	PUNCT
ejpam-6489	581	9	volume	volume	NOUN
ejpam-6489	581	10	9	9	NUM
ejpam-6489	581	11	of	of	ADP
ejpam-6489	581	12	graduate	graduate	NOUN
ejpam-6489	581	13	texts	text	NOUN
ejpam-6489	581	14	in	in	ADP
ejpam-6489	581	15	mathematics	mathematic	NOUN
ejpam-6489	581	16	.	.	PUNCT
ejpam-6489	582	1	springer	springer	NOUN
ejpam-6489	582	2	-	-	PUNCT
ejpam-6489	582	3	verlag	verlag	PROPN
ejpam-6489	582	4	,	,	PUNCT
ejpam-6489	582	5	new	new	PROPN
ejpam-6489	582	6	york	york	PROPN
ejpam-6489	582	7	,	,	PUNCT
ejpam-6489	582	8	1972	1972	NUM
ejpam-6489	582	9	.	.	PUNCT
ejpam-6489	583	1	[	[	X
ejpam-6489	583	2	2	2	X
ejpam-6489	583	3	]	]	PUNCT
ejpam-6489	583	4	w.	w.	NOUN
ejpam-6489	583	5	wechler	wechler	NOUN
ejpam-6489	583	6	.	.	PUNCT
ejpam-6489	584	1	universal	universal	ADJ
ejpam-6489	584	2	algebra	algebra	PROPN
ejpam-6489	584	3	for	for	ADP
ejpam-6489	584	4	computer	computer	NOUN
ejpam-6489	584	5	scientists	scientist	NOUN
ejpam-6489	584	6	.	.	PUNCT
ejpam-6489	585	1	springer	springer	NOUN
ejpam-6489	585	2	science	science	PROPN
ejpam-6489	585	3	&	&	CCONJ
ejpam-6489	585	4	business	business	NOUN
ejpam-6489	585	5	media	medium	NOUN
ejpam-6489	585	6	,	,	PUNCT
ejpam-6489	585	7	berlin	berlin	PROPN
ejpam-6489	585	8	/	/	SYM
ejpam-6489	585	9	heidelberg	heidelberg	PROPN
ejpam-6489	585	10	,	,	PUNCT
ejpam-6489	585	11	germany	germany	PROPN
ejpam-6489	585	12	,	,	PUNCT
ejpam-6489	585	13	2012	2012	NUM
ejpam-6489	585	14	.	.	PUNCT
ejpam-6489	586	1	[	[	X
ejpam-6489	586	2	3	3	X
ejpam-6489	586	3	]	]	PUNCT
ejpam-6489	586	4	m.	m.	NOUN
ejpam-6489	586	5	guerreiro	guerreiro	PROPN
ejpam-6489	586	6	.	.	PUNCT
ejpam-6489	587	1	group	group	PROPN
ejpam-6489	587	2	algebras	algebra	NOUN
ejpam-6489	587	3	and	and	CCONJ
ejpam-6489	587	4	coding	code	VERB
ejpam-6489	587	5	theory	theory	NOUN
ejpam-6489	587	6	.	.	PUNCT
ejpam-6489	588	1	são	são	PROPN
ejpam-6489	588	2	paulo	paulo	PROPN
ejpam-6489	588	3	journal	journal	PROPN
ejpam-6489	588	4	of	of	ADP
ejpam-6489	588	5	mathematical	mathematical	ADJ
ejpam-6489	588	6	sciences	science	NOUN
ejpam-6489	588	7	,	,	PUNCT
ejpam-6489	588	8	10(2):346–371	10(2):346–371	PROPN
ejpam-6489	588	9	,	,	PUNCT
ejpam-6489	588	10	2016	2016	NUM
ejpam-6489	588	11	.	.	PUNCT
ejpam-6489	589	1	[	[	X
ejpam-6489	589	2	4	4	X
ejpam-6489	589	3	]	]	PUNCT
ejpam-6489	589	4	l.	l.	PROPN
ejpam-6489	589	5	a.	a.	PROPN
ejpam-6489	589	6	zadeh	zadeh	PROPN
ejpam-6489	589	7	.	.	PUNCT
ejpam-6489	589	8	fuzzy	fuzzy	ADJ
ejpam-6489	589	9	sets	set	NOUN
ejpam-6489	589	10	.	.	PUNCT
ejpam-6489	590	1	information	information	NOUN
ejpam-6489	590	2	and	and	CCONJ
ejpam-6489	590	3	control	control	NOUN
ejpam-6489	590	4	,	,	PUNCT
ejpam-6489	590	5	8(3):338–353	8(3):338–353	NUM
ejpam-6489	590	6	,	,	PUNCT
ejpam-6489	590	7	1965	1965	NUM
ejpam-6489	590	8	.	.	PUNCT
ejpam-6489	591	1	[	[	X
ejpam-6489	591	2	5	5	X
ejpam-6489	591	3	]	]	PUNCT
ejpam-6489	591	4	w.	w.	PROPN
ejpam-6489	591	5	r.	r.	PROPN
ejpam-6489	591	6	zhang	zhang	PROPN
ejpam-6489	591	7	.	.	PUNCT
ejpam-6489	592	1	bipolar	bipolar	ADJ
ejpam-6489	592	2	fuzzy	fuzzy	ADJ
ejpam-6489	592	3	sets	set	NOUN
ejpam-6489	592	4	and	and	CCONJ
ejpam-6489	592	5	relations	relation	NOUN
ejpam-6489	592	6	:	:	PUNCT
ejpam-6489	592	7	a	a	DET
ejpam-6489	592	8	computational	computational	ADJ
ejpam-6489	592	9	framework	framework	NOUN
ejpam-6489	592	10	for	for	ADP
ejpam-6489	592	11	cognitive	cognitive	ADJ
ejpam-6489	592	12	modeling	modeling	NOUN
ejpam-6489	592	13	and	and	CCONJ
ejpam-6489	592	14	multiagent	multiagent	ADJ
ejpam-6489	592	15	decision	decision	NOUN
ejpam-6489	592	16	analysis	analysis	NOUN
ejpam-6489	592	17	.	.	PUNCT
ejpam-6489	593	1	in	in	ADP
ejpam-6489	593	2	proceedings	proceeding	NOUN
ejpam-6489	593	3	of	of	ADP
ejpam-6489	593	4	ieee	ieee	NOUN
ejpam-6489	593	5	conference	conference	NOUN
ejpam-6489	593	6	,	,	PUNCT
ejpam-6489	593	7	pages	page	NOUN
ejpam-6489	593	8	305–309	305–309	NUM
ejpam-6489	593	9	,	,	PUNCT
ejpam-6489	593	10	1994	1994	NUM
ejpam-6489	593	11	.	.	PUNCT
ejpam-6489	594	1	[	[	X
ejpam-6489	594	2	6	6	NUM
ejpam-6489	594	3	]	]	PUNCT
ejpam-6489	594	4	k.	k.	PROPN
ejpam-6489	594	5	m.	m.	PROPN
ejpam-6489	594	6	lee	lee	PROPN
ejpam-6489	594	7	.	.	PUNCT
ejpam-6489	595	1	bipolar	bipolar	ADJ
ejpam-6489	595	2	-	-	PUNCT
ejpam-6489	595	3	valued	value	VERB
ejpam-6489	595	4	fuzzy	fuzzy	ADJ
ejpam-6489	595	5	sets	set	NOUN
ejpam-6489	595	6	and	and	CCONJ
ejpam-6489	595	7	their	their	PRON
ejpam-6489	595	8	operations	operation	NOUN
ejpam-6489	595	9	.	.	PUNCT
ejpam-6489	596	1	in	in	ADP
ejpam-6489	596	2	proceedings	proceeding	NOUN
ejpam-6489	596	3	of	of	ADP
ejpam-6489	596	4	international	international	ADJ
ejpam-6489	596	5	conference	conference	NOUN
ejpam-6489	596	6	on	on	ADP
ejpam-6489	596	7	intelligent	intelligent	ADJ
ejpam-6489	596	8	technologies	technology	NOUN
ejpam-6489	596	9	,	,	PUNCT
ejpam-6489	596	10	pages	page	NOUN
ejpam-6489	596	11	307–312	307–312	NUM
ejpam-6489	596	12	,	,	PUNCT
ejpam-6489	596	13	bangkok	bangkok	PROPN
ejpam-6489	596	14	,	,	PUNCT
ejpam-6489	596	15	2000	2000	NUM
ejpam-6489	596	16	.	.	PUNCT
ejpam-6489	597	1	[	[	X
ejpam-6489	597	2	7	7	X
ejpam-6489	597	3	]	]	X
ejpam-6489	597	4	d.	d.	PROPN
ejpam-6489	597	5	ramot	ramot	PROPN
ejpam-6489	597	6	,	,	PUNCT
ejpam-6489	597	7	r.	r.	PROPN
ejpam-6489	597	8	milo	milo	PROPN
ejpam-6489	597	9	,	,	PUNCT
ejpam-6489	597	10	m.	m.	NOUN
ejpam-6489	597	11	friedman	friedman	PROPN
ejpam-6489	597	12	,	,	PUNCT
ejpam-6489	597	13	and	and	CCONJ
ejpam-6489	597	14	a.	a.	NOUN
ejpam-6489	597	15	kandel	kandel	PROPN
ejpam-6489	597	16	.	.	PUNCT
ejpam-6489	598	1	complex	complex	ADJ
ejpam-6489	598	2	fuzzy	fuzzy	ADJ
ejpam-6489	598	3	sets	set	NOUN
ejpam-6489	598	4	.	.	PUNCT
ejpam-6489	599	1	ieee	ieee	NOUN
ejpam-6489	599	2	transactions	transaction	NOUN
ejpam-6489	599	3	on	on	ADP
ejpam-6489	599	4	fuzzy	fuzzy	ADJ
ejpam-6489	599	5	systems	system	NOUN
ejpam-6489	599	6	,	,	PUNCT
ejpam-6489	599	7	10(2):171–186	10(2):171–186	NUM
ejpam-6489	599	8	,	,	PUNCT
ejpam-6489	599	9	2002	2002	NUM
ejpam-6489	599	10	.	.	PUNCT
ejpam-6489	600	1	[	[	X
ejpam-6489	600	2	8	8	NUM
ejpam-6489	600	3	]	]	X
ejpam-6489	600	4	d.	d.	PROPN
ejpam-6489	600	5	e.	e.	PROPN
ejpam-6489	600	6	tamir	tamir	PROPN
ejpam-6489	600	7	,	,	PUNCT
ejpam-6489	600	8	l.	l.	PROPN
ejpam-6489	600	9	jin	jin	PROPN
ejpam-6489	600	10	,	,	PUNCT
ejpam-6489	600	11	and	and	CCONJ
ejpam-6489	600	12	a.	a.	NOUN
ejpam-6489	600	13	kandel	kandel	PROPN
ejpam-6489	600	14	.	.	PUNCT
ejpam-6489	601	1	a	a	DET
ejpam-6489	601	2	new	new	ADJ
ejpam-6489	601	3	interpretation	interpretation	NOUN
ejpam-6489	601	4	of	of	ADP
ejpam-6489	601	5	complex	complex	ADJ
ejpam-6489	601	6	membership	membership	NOUN
ejpam-6489	601	7	grade	grade	NOUN
ejpam-6489	601	8	.	.	PUNCT
ejpam-6489	602	1	international	international	ADJ
ejpam-6489	602	2	journal	journal	NOUN
ejpam-6489	602	3	of	of	ADP
ejpam-6489	602	4	intelligent	intelligent	ADJ
ejpam-6489	602	5	systems	system	NOUN
ejpam-6489	602	6	,	,	PUNCT
ejpam-6489	602	7	26(4):285–312	26(4):285–312	PROPN
ejpam-6489	602	8	,	,	PUNCT
ejpam-6489	602	9	2011	2011	NUM
ejpam-6489	602	10	.	.	PUNCT
ejpam-6489	603	1	[	[	X
ejpam-6489	603	2	9	9	NUM
ejpam-6489	603	3	]	]	PUNCT
ejpam-6489	603	4	t.	t.	PROPN
ejpam-6489	603	5	mahmood	mahmood	PROPN
ejpam-6489	603	6	and	and	CCONJ
ejpam-6489	603	7	u.	u.	PROPN
ejpam-6489	603	8	ur	ur	PROPN
ejpam-6489	603	9	rehman	rehman	PROPN
ejpam-6489	603	10	.	.	PUNCT
ejpam-6489	604	1	a	a	DET
ejpam-6489	604	2	novel	novel	ADJ
ejpam-6489	604	3	approach	approach	NOUN
ejpam-6489	604	4	towards	towards	ADP
ejpam-6489	604	5	bipolar	bipolar	ADJ
ejpam-6489	604	6	complex	complex	ADJ
ejpam-6489	604	7	fuzzy	fuzzy	ADJ
ejpam-6489	604	8	sets	set	NOUN
ejpam-6489	604	9	and	and	CCONJ
ejpam-6489	604	10	their	their	PRON
ejpam-6489	604	11	applications	application	NOUN
ejpam-6489	604	12	in	in	ADP
ejpam-6489	604	13	generalized	generalized	ADJ
ejpam-6489	604	14	similarity	similarity	NOUN
ejpam-6489	604	15	measures	measure	NOUN
ejpam-6489	604	16	.	.	PUNCT
ejpam-6489	605	1	international	international	ADJ
ejpam-6489	605	2	journal	journal	NOUN
ejpam-6489	605	3	of	of	ADP
ejpam-6489	605	4	intelligent	intelligent	ADJ
ejpam-6489	605	5	systems	system	NOUN
ejpam-6489	605	6	,	,	PUNCT
ejpam-6489	605	7	37:1–33	37:1–33	NUM
ejpam-6489	605	8	,	,	PUNCT
ejpam-6489	605	9	2021	2021	NUM
ejpam-6489	605	10	.	.	PUNCT
ejpam-6489	606	1	[	[	X
ejpam-6489	606	2	10	10	NUM
ejpam-6489	606	3	]	]	PUNCT
ejpam-6489	606	4	a.	a.	NOUN
ejpam-6489	606	5	rosenfeld	rosenfeld	PROPN
ejpam-6489	606	6	.	.	PUNCT
ejpam-6489	607	1	fuzzy	fuzzy	ADJ
ejpam-6489	607	2	groups	group	NOUN
ejpam-6489	607	3	.	.	PUNCT
ejpam-6489	608	1	journal	journal	PROPN
ejpam-6489	608	2	of	of	ADP
ejpam-6489	608	3	mathematical	mathematical	ADJ
ejpam-6489	608	4	analysis	analysis	NOUN
ejpam-6489	608	5	and	and	CCONJ
ejpam-6489	608	6	applications	application	NOUN
ejpam-6489	608	7	,	,	PUNCT
ejpam-6489	608	8	35:512–517	35:512–517	PROPN
ejpam-6489	608	9	,	,	PUNCT
ejpam-6489	608	10	1971	1971	NUM
ejpam-6489	608	11	.	.	PUNCT
ejpam-6489	609	1	[	[	X
ejpam-6489	609	2	11	11	NUM
ejpam-6489	609	3	]	]	PUNCT
ejpam-6489	609	4	a.	a.	NOUN
ejpam-6489	609	5	fallatah	fallatah	PROPN
ejpam-6489	609	6	,	,	PUNCT
ejpam-6489	609	7	m.	m.	NOUN
ejpam-6489	609	8	o.	o.	PROPN
ejpam-6489	609	9	massa’deh	massa’deh	PROPN
ejpam-6489	609	10	,	,	PUNCT
ejpam-6489	609	11	and	and	CCONJ
ejpam-6489	609	12	a.	a.	PROPN
ejpam-6489	609	13	u.	u.	PROPN
ejpam-6489	609	14	alkouri	alkouri	PROPN
ejpam-6489	609	15	.	.	PUNCT
ejpam-6489	610	1	normal	normal	ADJ
ejpam-6489	610	2	and	and	CCONJ
ejpam-6489	610	3	cosets	coset	NOUN
ejpam-6489	610	4	of	of	ADP
ejpam-6489	610	5	(	(	PUNCT
ejpam-6489	610	6	γ	γ	PROPN
ejpam-6489	610	7	,	,	PUNCT
ejpam-6489	610	8	δ)-fuzzy	δ)-fuzzy	ADJ
ejpam-6489	610	9	hx	hx	PROPN
ejpam-6489	610	10	-	-	PUNCT
ejpam-6489	610	11	subgroups	subgroup	NOUN
ejpam-6489	610	12	.	.	PUNCT
ejpam-6489	611	1	journal	journal	NOUN
ejpam-6489	611	2	of	of	ADP
ejpam-6489	611	3	applied	apply	VERB
ejpam-6489	611	4	mathematics	mathematic	NOUN
ejpam-6489	611	5	and	and	CCONJ
ejpam-6489	611	6	informatics	informatic	NOUN
ejpam-6489	611	7	,	,	PUNCT
ejpam-6489	611	8	40(3	40(3	NOUN
ejpam-6489	611	9	-	-	SYM
ejpam-6489	611	10	4):719–729	4):719–729	NUM
ejpam-6489	611	11	,	,	PUNCT
ejpam-6489	611	12	2022	2022	NUM
ejpam-6489	611	13	.	.	PUNCT
ejpam-6489	612	1	[	[	X
ejpam-6489	612	2	12	12	NUM
ejpam-6489	612	3	]	]	X
ejpam-6489	612	4	y.	y.	PROPN
ejpam-6489	612	5	b.	b.	PROPN
ejpam-6489	612	6	jun	jun	PROPN
ejpam-6489	612	7	,	,	PUNCT
ejpam-6489	612	8	k.	k.	PROPN
ejpam-6489	612	9	j.	j.	PROPN
ejpam-6489	612	10	lee	lee	PROPN
ejpam-6489	612	11	,	,	PUNCT
ejpam-6489	612	12	and	and	CCONJ
ejpam-6489	612	13	s.	s.	PROPN
ejpam-6489	612	14	z.	z.	PROPN
ejpam-6489	612	15	song	song	PROPN
ejpam-6489	612	16	.	.	PUNCT
ejpam-6489	613	1	n	n	PRON
ejpam-6489	613	2	-ideals	-ideal	NOUN
ejpam-6489	613	3	of	of	ADP
ejpam-6489	613	4	bck	bck	PROPN
ejpam-6489	613	5	/	/	SYM
ejpam-6489	613	6	bci	bci	NOUN
ejpam-6489	613	7	-	-	PUNCT
ejpam-6489	613	8	algebras	algebras	PROPN
ejpam-6489	613	9	.	.	PUNCT
ejpam-6489	614	1	journal	journal	PROPN
ejpam-6489	614	2	of	of	ADP
ejpam-6489	614	3	the	the	DET
ejpam-6489	614	4	chungcheong	chungcheong	PROPN
ejpam-6489	614	5	mathematical	mathematical	ADJ
ejpam-6489	614	6	society	society	NOUN
ejpam-6489	614	7	,	,	PUNCT
ejpam-6489	614	8	22(3):417–437	22(3):417–437	NUM
ejpam-6489	614	9	,	,	PUNCT
ejpam-6489	614	10	2009	2009	NUM
ejpam-6489	614	11	.	.	PUNCT
ejpam-6489	615	1	m.	m.	NOUN
ejpam-6489	615	2	balamurugan	balamurugan	PROPN
ejpam-6489	615	3	,	,	PUNCT
ejpam-6489	615	4	g.	g.	PROPN
ejpam-6489	615	5	ellammal	ellammal	PROPN
ejpam-6489	615	6	,	,	PUNCT
ejpam-6489	615	7	a.	a.	NOUN
ejpam-6489	615	8	iampan	iampan	PROPN
ejpam-6489	615	9	/	/	SYM
ejpam-6489	615	10	eur	eur	PROPN
ejpam-6489	615	11	.	.	PUNCT
ejpam-6489	616	1	j.	j.	PROPN
ejpam-6489	616	2	pure	pure	PROPN
ejpam-6489	616	3	appl	appl	PROPN
ejpam-6489	616	4	.	.	PROPN
ejpam-6489	616	5	math	math	PROPN
ejpam-6489	616	6	,	,	PUNCT
ejpam-6489	616	7	18	18	NUM
ejpam-6489	616	8	(	(	PUNCT
ejpam-6489	616	9	3	3	NUM
ejpam-6489	616	10	)	)	PUNCT
ejpam-6489	616	11	(	(	PUNCT
ejpam-6489	616	12	2025	2025	NUM
ejpam-6489	616	13	)	)	PUNCT
ejpam-6489	616	14	,	,	PUNCT
ejpam-6489	616	15	6489	6489	NUM
ejpam-6489	616	16	25	25	NUM
ejpam-6489	616	17	of	of	ADP
ejpam-6489	616	18	26	26	NUM
ejpam-6489	616	19	[	[	SYM
ejpam-6489	616	20	13	13	NUM
ejpam-6489	616	21	]	]	PUNCT
ejpam-6489	616	22	a.	a.	PROPN
ejpam-6489	616	23	al	al	PROPN
ejpam-6489	616	24	-	-	PROPN
ejpam-6489	616	25	masarwah	masarwah	PROPN
ejpam-6489	616	26	and	and	CCONJ
ejpam-6489	616	27	a.	a.	NOUN
ejpam-6489	616	28	g.	g.	PROPN
ejpam-6489	616	29	ahmad	ahmad	PROPN
ejpam-6489	616	30	.	.	PUNCT
ejpam-6489	617	1	m	m	ADJ
ejpam-6489	617	2	-	-	ADJ
ejpam-6489	617	3	polar	polar	ADJ
ejpam-6489	617	4	fuzzy	fuzzy	ADJ
ejpam-6489	617	5	ideals	ideal	NOUN
ejpam-6489	617	6	of	of	ADP
ejpam-6489	617	7	bck	bck	PROPN
ejpam-6489	617	8	/	/	SYM
ejpam-6489	617	9	bci	bci	NOUN
ejpam-6489	617	10	-	-	PUNCT
ejpam-6489	617	11	algebras	algebras	PROPN
ejpam-6489	617	12	.	.	PUNCT
ejpam-6489	618	1	journal	journal	PROPN
ejpam-6489	618	2	of	of	ADP
ejpam-6489	618	3	king	king	PROPN
ejpam-6489	618	4	saud	saud	PROPN
ejpam-6489	618	5	university	university	PROPN
ejpam-6489	618	6	science	science	NOUN
ejpam-6489	618	7	,	,	PUNCT
ejpam-6489	618	8	31(4):1220–1226	31(4):1220–1226	NUM
ejpam-6489	618	9	,	,	PUNCT
ejpam-6489	618	10	2019	2019	NUM
ejpam-6489	618	11	.	.	PUNCT
ejpam-6489	619	1	[	[	X
ejpam-6489	619	2	14	14	NUM
ejpam-6489	619	3	]	]	X
ejpam-6489	619	4	g.	g.	PROPN
ejpam-6489	619	5	muhiuddin	muhiuddin	PROPN
ejpam-6489	619	6	,	,	PUNCT
ejpam-6489	619	7	n.	n.	PROPN
ejpam-6489	619	8	abughazalah	abughazalah	NOUN
ejpam-6489	619	9	,	,	PUNCT
ejpam-6489	619	10	a.	a.	NOUN
ejpam-6489	619	11	aljuhani	aljuhani	PROPN
ejpam-6489	619	12	,	,	PUNCT
ejpam-6489	619	13	and	and	CCONJ
ejpam-6489	619	14	m.	m.	NOUN
ejpam-6489	619	15	balamurugan	balamurugan	VERB
ejpam-6489	619	16	.	.	PUNCT
ejpam-6489	620	1	tripolar	tripolar	ADJ
ejpam-6489	620	2	picture	picture	NOUN
ejpam-6489	620	3	fuzzy	fuzzy	ADJ
ejpam-6489	620	4	ideals	ideal	NOUN
ejpam-6489	620	5	of	of	ADP
ejpam-6489	620	6	bck	bck	NOUN
ejpam-6489	620	7	-	-	PUNCT
ejpam-6489	620	8	algebras	algebras	PROPN
ejpam-6489	620	9	.	.	PUNCT
ejpam-6489	620	10	symmetry	symmetry	PROPN
ejpam-6489	620	11	,	,	PUNCT
ejpam-6489	620	12	14:1562	14:1562	NUM
ejpam-6489	620	13	,	,	PUNCT
ejpam-6489	620	14	2022	2022	NUM
ejpam-6489	620	15	.	.	PUNCT
ejpam-6489	621	1	[	[	X
ejpam-6489	621	2	15	15	NUM
ejpam-6489	621	3	]	]	X
ejpam-6489	621	4	g.	g.	PROPN
ejpam-6489	621	5	muhiuddin	muhiuddin	PROPN
ejpam-6489	621	6	,	,	PUNCT
ejpam-6489	621	7	k.	k.	PROPN
ejpam-6489	621	8	porselvi	porselvi	PROPN
ejpam-6489	621	9	,	,	PUNCT
ejpam-6489	621	10	b.	b.	PROPN
ejpam-6489	621	11	elavarasan	elavarasan	PROPN
ejpam-6489	621	12	,	,	PUNCT
ejpam-6489	621	13	and	and	CCONJ
ejpam-6489	621	14	d.	d.	PROPN
ejpam-6489	621	15	al	al	PROPN
ejpam-6489	621	16	-	-	PUNCT
ejpam-6489	621	17	kadi	kadi	PROPN
ejpam-6489	621	18	.	.	PUNCT
ejpam-6489	622	1	neutrosophic	neutrosophic	ADJ
ejpam-6489	622	2	kstructures	kstructure	NOUN
ejpam-6489	622	3	in	in	ADP
ejpam-6489	622	4	ordered	order	VERB
ejpam-6489	622	5	semigroups	semigroup	NOUN
ejpam-6489	622	6	.	.	PUNCT
ejpam-6489	623	1	computer	computer	NOUN
ejpam-6489	623	2	modeling	modeling	NOUN
ejpam-6489	623	3	in	in	ADP
ejpam-6489	623	4	engineering	engineering	NOUN
ejpam-6489	623	5	and	and	CCONJ
ejpam-6489	623	6	sciences	science	NOUN
ejpam-6489	623	7	,	,	PUNCT
ejpam-6489	623	8	131(2):1–21	131(2):1–21	NUM
ejpam-6489	623	9	,	,	PUNCT
ejpam-6489	623	10	2022	2022	NUM
ejpam-6489	623	11	.	.	PUNCT
ejpam-6489	624	1	[	[	X
ejpam-6489	624	2	16	16	NUM
ejpam-6489	624	3	]	]	PUNCT
ejpam-6489	624	4	t.	t.	PROPN
ejpam-6489	624	5	mahmood	mahmood	PROPN
ejpam-6489	624	6	and	and	CCONJ
ejpam-6489	624	7	m.	m.	PROPN
ejpam-6489	624	8	munir	munir	PROPN
ejpam-6489	624	9	.	.	PUNCT
ejpam-6489	625	1	on	on	ADP
ejpam-6489	625	2	bipolar	bipolar	ADJ
ejpam-6489	625	3	fuzzy	fuzzy	ADJ
ejpam-6489	625	4	subgroups	subgroup	NOUN
ejpam-6489	625	5	.	.	PUNCT
ejpam-6489	626	1	world	world	NOUN
ejpam-6489	626	2	applied	apply	VERB
ejpam-6489	626	3	sciences	science	NOUN
ejpam-6489	626	4	journal	journal	NOUN
ejpam-6489	626	5	,	,	PUNCT
ejpam-6489	626	6	27(12):1806–1811	27(12):1806–1811	NUM
ejpam-6489	626	7	,	,	PUNCT
ejpam-6489	626	8	2013	2013	NUM
ejpam-6489	626	9	.	.	PUNCT
ejpam-6489	627	1	[	[	X
ejpam-6489	627	2	17	17	NUM
ejpam-6489	627	3	]	]	PUNCT
ejpam-6489	627	4	s.	s.	PROPN
ejpam-6489	627	5	e.	e.	PROPN
ejpam-6489	627	6	yehia	yehia	PROPN
ejpam-6489	627	7	.	.	PUNCT
ejpam-6489	627	8	fuzzy	fuzzy	ADJ
ejpam-6489	627	9	ideals	ideal	NOUN
ejpam-6489	627	10	and	and	CCONJ
ejpam-6489	627	11	fuzzy	fuzzy	ADJ
ejpam-6489	627	12	subalgebras	subalgebra	NOUN
ejpam-6489	627	13	of	of	ADP
ejpam-6489	627	14	lie	lie	NOUN
ejpam-6489	627	15	algebras	algebra	NOUN
ejpam-6489	627	16	.	.	PUNCT
ejpam-6489	627	17	fuzzy	fuzzy	ADJ
ejpam-6489	627	18	sets	set	NOUN
ejpam-6489	627	19	and	and	CCONJ
ejpam-6489	627	20	systems	system	NOUN
ejpam-6489	627	21	,	,	PUNCT
ejpam-6489	627	22	80(2):237–244	80(2):237–244	NOUN
ejpam-6489	627	23	,	,	PUNCT
ejpam-6489	627	24	1996	1996	NUM
ejpam-6489	627	25	.	.	PUNCT
ejpam-6489	628	1	[	[	X
ejpam-6489	628	2	18	18	NUM
ejpam-6489	628	3	]	]	PUNCT
ejpam-6489	628	4	m.	m.	NOUN
ejpam-6489	628	5	akram	akram	PROPN
ejpam-6489	628	6	.	.	PUNCT
ejpam-6489	629	1	generalized	generalize	VERB
ejpam-6489	629	2	fuzzy	fuzzy	ADJ
ejpam-6489	629	3	lie	lie	NOUN
ejpam-6489	629	4	subalgebras	subalgebras	PROPN
ejpam-6489	629	5	.	.	PUNCT
ejpam-6489	630	1	journal	journal	PROPN
ejpam-6489	630	2	of	of	ADP
ejpam-6489	630	3	generalized	generalized	ADJ
ejpam-6489	630	4	lie	lie	NOUN
ejpam-6489	630	5	theory	theory	NOUN
ejpam-6489	630	6	and	and	CCONJ
ejpam-6489	630	7	applications	application	NOUN
ejpam-6489	630	8	,	,	PUNCT
ejpam-6489	630	9	4(2):261–268	4(2):261–268	NOUN
ejpam-6489	630	10	,	,	PUNCT
ejpam-6489	630	11	2008	2008	NUM
ejpam-6489	630	12	.	.	PUNCT
ejpam-6489	631	1	[	[	X
ejpam-6489	631	2	19	19	NUM
ejpam-6489	631	3	]	]	PUNCT
ejpam-6489	631	4	m.	m.	NOUN
ejpam-6489	631	5	akram	akram	PROPN
ejpam-6489	631	6	and	and	CCONJ
ejpam-6489	631	7	k.	k.	PROPN
ejpam-6489	631	8	p.	p.	PROPN
ejpam-6489	631	9	shum	shum	PROPN
ejpam-6489	631	10	.	.	PUNCT
ejpam-6489	632	1	fuzzy	fuzzy	ADJ
ejpam-6489	632	2	lie	lie	NOUN
ejpam-6489	632	3	ideals	ideal	NOUN
ejpam-6489	632	4	over	over	ADP
ejpam-6489	632	5	a	a	DET
ejpam-6489	632	6	fuzzy	fuzzy	ADJ
ejpam-6489	632	7	field	field	NOUN
ejpam-6489	632	8	.	.	PUNCT
ejpam-6489	633	1	italian	italian	ADJ
ejpam-6489	633	2	journal	journal	NOUN
ejpam-6489	633	3	of	of	ADP
ejpam-6489	633	4	pure	pure	ADJ
ejpam-6489	633	5	and	and	CCONJ
ejpam-6489	633	6	applied	applied	ADJ
ejpam-6489	633	7	mathematics	mathematic	NOUN
ejpam-6489	633	8	,	,	PUNCT
ejpam-6489	633	9	27:281–292	27:281–292	PROPN
ejpam-6489	633	10	,	,	PUNCT
ejpam-6489	633	11	2010	2010	NUM
ejpam-6489	633	12	.	.	PUNCT
ejpam-6489	634	1	[	[	X
ejpam-6489	634	2	20	20	NUM
ejpam-6489	634	3	]	]	PUNCT
ejpam-6489	634	4	k.	k.	PROPN
ejpam-6489	634	5	t.	t.	PROPN
ejpam-6489	634	6	atanassov	atanassov	PROPN
ejpam-6489	634	7	.	.	PUNCT
ejpam-6489	635	1	intuitionistic	intuitionistic	ADJ
ejpam-6489	635	2	fuzzy	fuzzy	ADJ
ejpam-6489	635	3	sets	set	NOUN
ejpam-6489	635	4	.	.	PUNCT
ejpam-6489	636	1	fuzzy	fuzzy	ADJ
ejpam-6489	636	2	sets	set	NOUN
ejpam-6489	636	3	and	and	CCONJ
ejpam-6489	636	4	systems	system	NOUN
ejpam-6489	636	5	,	,	PUNCT
ejpam-6489	636	6	20:87–96	20:87–96	NUM
ejpam-6489	636	7	,	,	PUNCT
ejpam-6489	636	8	1986	1986	NUM
ejpam-6489	636	9	.	.	PUNCT
ejpam-6489	637	1	[	[	X
ejpam-6489	637	2	21	21	NUM
ejpam-6489	637	3	]	]	PUNCT
ejpam-6489	637	4	m.	m.	NOUN
ejpam-6489	637	5	akram	akram	PROPN
ejpam-6489	637	6	and	and	CCONJ
ejpam-6489	637	7	k.	k.	PROPN
ejpam-6489	637	8	p.	p.	PROPN
ejpam-6489	637	9	shum	shum	PROPN
ejpam-6489	637	10	.	.	PUNCT
ejpam-6489	638	1	intuitionistic	intuitionistic	ADJ
ejpam-6489	638	2	fuzzy	fuzzy	ADJ
ejpam-6489	638	3	lie	lie	NOUN
ejpam-6489	638	4	algebras	algebra	NOUN
ejpam-6489	638	5	.	.	PUNCT
ejpam-6489	639	1	southeast	southeast	ADJ
ejpam-6489	639	2	asian	asian	ADJ
ejpam-6489	639	3	bulletin	bulletin	NOUN
ejpam-6489	639	4	of	of	ADP
ejpam-6489	639	5	mathematics	mathematic	NOUN
ejpam-6489	639	6	,	,	PUNCT
ejpam-6489	639	7	31(5):843–855	31(5):843–855	PROPN
ejpam-6489	639	8	,	,	PUNCT
ejpam-6489	639	9	2007	2007	NUM
ejpam-6489	639	10	.	.	PUNCT
ejpam-6489	640	1	[	[	X
ejpam-6489	640	2	22	22	NUM
ejpam-6489	640	3	]	]	PUNCT
ejpam-6489	640	4	m.	m.	NOUN
ejpam-6489	640	5	akram	akram	PROPN
ejpam-6489	640	6	.	.	PUNCT
ejpam-6489	641	1	fuzzy	fuzzy	ADJ
ejpam-6489	641	2	lie	lie	NOUN
ejpam-6489	641	3	ideals	ideal	NOUN
ejpam-6489	641	4	of	of	ADP
ejpam-6489	641	5	lie	lie	NOUN
ejpam-6489	641	6	algebras	algebra	NOUN
ejpam-6489	641	7	with	with	ADP
ejpam-6489	641	8	interval	interval	NOUN
ejpam-6489	641	9	-	-	PUNCT
ejpam-6489	641	10	valued	value	VERB
ejpam-6489	641	11	membership	membership	NOUN
ejpam-6489	641	12	functions	function	NOUN
ejpam-6489	641	13	.	.	PUNCT
ejpam-6489	642	1	quasigroups	quasigroup	NOUN
ejpam-6489	642	2	and	and	CCONJ
ejpam-6489	642	3	related	related	ADJ
ejpam-6489	642	4	systems	system	NOUN
ejpam-6489	642	5	,	,	PUNCT
ejpam-6489	642	6	16:1–12	16:1–12	NUM
ejpam-6489	642	7	,	,	PUNCT
ejpam-6489	642	8	2008	2008	NUM
ejpam-6489	642	9	.	.	PUNCT
ejpam-6489	643	1	[	[	X
ejpam-6489	643	2	23	23	NUM
ejpam-6489	643	3	]	]	PUNCT
ejpam-6489	643	4	m.	m.	NOUN
ejpam-6489	643	5	akram	akram	PROPN
ejpam-6489	643	6	.	.	PUNCT
ejpam-6489	644	1	bipolar	bipolar	ADJ
ejpam-6489	644	2	fuzzy	fuzzy	ADJ
ejpam-6489	644	3	lie	lie	NOUN
ejpam-6489	644	4	l	l	NOUN
ejpam-6489	644	5	-	-	NOUN
ejpam-6489	644	6	algebra	algebra	NOUN
ejpam-6489	644	7	.	.	PUNCT
ejpam-6489	645	1	world	world	NOUN
ejpam-6489	645	2	applied	apply	VERB
ejpam-6489	645	3	sciences	science	NOUN
ejpam-6489	645	4	journal	journal	NOUN
ejpam-6489	645	5	,	,	PUNCT
ejpam-6489	645	6	14(2):1908	14(2):1908	NUM
ejpam-6489	645	7	–	–	PUNCT
ejpam-6489	645	8	1913	1913	NUM
ejpam-6489	645	9	,	,	PUNCT
ejpam-6489	645	10	2011	2011	NUM
ejpam-6489	645	11	.	.	PUNCT
ejpam-6489	646	1	[	[	X
ejpam-6489	646	2	24	24	NUM
ejpam-6489	646	3	]	]	PUNCT
ejpam-6489	646	4	s.	s.	PROPN
ejpam-6489	646	5	shaqaqha	shaqaqha	PROPN
ejpam-6489	646	6	.	.	PUNCT
ejpam-6489	647	1	complex	complex	ADJ
ejpam-6489	647	2	fuzzy	fuzzy	ADJ
ejpam-6489	647	3	lie	lie	NOUN
ejpam-6489	647	4	algebras	algebras	PROPN
ejpam-6489	647	5	.	.	PUNCT
ejpam-6489	648	1	jordan	jordan	PROPN
ejpam-6489	648	2	journal	journal	PROPN
ejpam-6489	648	3	of	of	ADP
ejpam-6489	648	4	mathematics	mathematics	PROPN
ejpam-6489	648	5	and	and	CCONJ
ejpam-6489	648	6	statistics	statistic	NOUN
ejpam-6489	648	7	,	,	PUNCT
ejpam-6489	648	8	13(2):231–247	13(2):231–247	PROPN
ejpam-6489	648	9	,	,	PUNCT
ejpam-6489	648	10	2020	2020	NUM
ejpam-6489	648	11	.	.	PUNCT
ejpam-6489	649	1	[	[	X
ejpam-6489	649	2	25	25	NUM
ejpam-6489	649	3	]	]	X
ejpam-6489	649	4	s.	s.	PROPN
ejpam-6489	649	5	kousar	kousar	PROPN
ejpam-6489	649	6	,	,	PUNCT
ejpam-6489	649	7	s.	s.	PROPN
ejpam-6489	649	8	arshad	arshad	PROPN
ejpam-6489	649	9	,	,	PUNCT
ejpam-6489	649	10	n.	n.	PROPN
ejpam-6489	649	11	kausar	kausar	PROPN
ejpam-6489	649	12	,	,	PUNCT
ejpam-6489	649	13	and	and	CCONJ
ejpam-6489	649	14	t.	t.	PROPN
ejpam-6489	649	15	p.	p.	PROPN
ejpam-6489	649	16	hong	hong	PROPN
ejpam-6489	649	17	.	.	PUNCT
ejpam-6489	650	1	construction	construction	NOUN
ejpam-6489	650	2	of	of	ADP
ejpam-6489	650	3	nilpotent	nilpotent	ADJ
ejpam-6489	650	4	and	and	CCONJ
ejpam-6489	650	5	solvable	solvable	ADJ
ejpam-6489	650	6	lie	lie	NOUN
ejpam-6489	650	7	algebra	algebra	NOUN
ejpam-6489	650	8	in	in	ADP
ejpam-6489	650	9	picture	picture	NOUN
ejpam-6489	650	10	fuzzy	fuzzy	ADJ
ejpam-6489	650	11	environment	environment	NOUN
ejpam-6489	650	12	.	.	PUNCT
ejpam-6489	651	1	international	international	ADJ
ejpam-6489	651	2	journal	journal	PROPN
ejpam-6489	651	3	of	of	ADP
ejpam-6489	651	4	computational	computational	ADJ
ejpam-6489	651	5	intelligence	intelligence	NOUN
ejpam-6489	651	6	systems	system	NOUN
ejpam-6489	651	7	,	,	PUNCT
ejpam-6489	651	8	16:37	16:37	NUM
ejpam-6489	651	9	,	,	PUNCT
ejpam-6489	651	10	2023	2023	NUM
ejpam-6489	651	11	.	.	PUNCT
ejpam-6489	652	1	[	[	X
ejpam-6489	652	2	26	26	NUM
ejpam-6489	652	3	]	]	PUNCT
ejpam-6489	652	4	a.	a.	PROPN
ejpam-6489	652	5	al	al	PROPN
ejpam-6489	652	6	-	-	PROPN
ejpam-6489	652	7	masarwah	masarwah	PROPN
ejpam-6489	652	8	,	,	PUNCT
ejpam-6489	652	9	n.	n.	PROPN
ejpam-6489	652	10	kdaisat	kdaisat	PROPN
ejpam-6489	652	11	,	,	PUNCT
ejpam-6489	652	12	m.	m.	NOUN
ejpam-6489	652	13	abuqamar	abuqamar	PROPN
ejpam-6489	652	14	,	,	PUNCT
ejpam-6489	652	15	and	and	CCONJ
ejpam-6489	652	16	k.	k.	PROPN
ejpam-6489	652	17	alsager	alsager	PROPN
ejpam-6489	652	18	.	.	PUNCT
ejpam-6489	653	1	crossing	cross	VERB
ejpam-6489	653	2	cubic	cubic	ADJ
ejpam-6489	653	3	lie	lie	NOUN
ejpam-6489	653	4	algebras	algebra	NOUN
ejpam-6489	653	5	.	.	PUNCT
ejpam-6489	654	1	aims	aim	VERB
ejpam-6489	654	2	mathematics	mathematic	NOUN
ejpam-6489	654	3	,	,	PUNCT
ejpam-6489	654	4	9(8):22112–22129	9(8):22112–22129	NUM
ejpam-6489	654	5	,	,	PUNCT
ejpam-6489	654	6	2024	2024	NUM
ejpam-6489	654	7	.	.	PUNCT
ejpam-6489	655	1	[	[	X
ejpam-6489	655	2	27	27	NUM
ejpam-6489	655	3	]	]	PUNCT
ejpam-6489	655	4	a.	a.	NOUN
ejpam-6489	655	5	jaleel	jaleel	PROPN
ejpam-6489	655	6	,	,	PUNCT
ejpam-6489	655	7	t.	t.	PROPN
ejpam-6489	655	8	mahmood	mahmood	PROPN
ejpam-6489	655	9	,	,	PUNCT
ejpam-6489	655	10	w.	w.	PROPN
ejpam-6489	655	11	emam	emam	PROPN
ejpam-6489	655	12	,	,	PUNCT
ejpam-6489	655	13	and	and	CCONJ
ejpam-6489	655	14	s.	s.	PROPN
ejpam-6489	655	15	yin	yin	PROPN
ejpam-6489	655	16	.	.	PUNCT
ejpam-6489	656	1	interval	interval	NOUN
ejpam-6489	656	2	-	-	PUNCT
ejpam-6489	656	3	valued	value	VERB
ejpam-6489	656	4	bipolar	bipolar	ADJ
ejpam-6489	656	5	complex	complex	ADJ
ejpam-6489	656	6	fuzzy	fuzzy	ADJ
ejpam-6489	656	7	soft	soft	ADJ
ejpam-6489	656	8	sets	set	NOUN
ejpam-6489	656	9	and	and	CCONJ
ejpam-6489	656	10	their	their	PRON
ejpam-6489	656	11	applications	application	NOUN
ejpam-6489	656	12	in	in	ADP
ejpam-6489	656	13	decision	decision	NOUN
ejpam-6489	656	14	making	making	NOUN
ejpam-6489	656	15	.	.	PUNCT
ejpam-6489	657	1	scientific	scientific	ADJ
ejpam-6489	657	2	reports	report	NOUN
ejpam-6489	657	3	,	,	PUNCT
ejpam-6489	657	4	14(1):1	14(1):1	NUM
ejpam-6489	657	5	–	–	PUNCT
ejpam-6489	657	6	29	29	NUM
ejpam-6489	657	7	,	,	PUNCT
ejpam-6489	657	8	2024	2024	NUM
ejpam-6489	657	9	.	.	PUNCT
ejpam-6489	658	1	[	[	X
ejpam-6489	658	2	28	28	NUM
ejpam-6489	658	3	]	]	X
ejpam-6489	658	4	m.	m.	NOUN
ejpam-6489	658	5	qiyasi	qiyasi	PROPN
ejpam-6489	658	6	,	,	PUNCT
ejpam-6489	658	7	m.	m.	NOUN
ejpam-6489	658	8	naeem	naeem	PROPN
ejpam-6489	658	9	,	,	PUNCT
ejpam-6489	658	10	n.	n.	PROPN
ejpam-6489	658	11	khan	khan	PROPN
ejpam-6489	658	12	,	,	PUNCT
ejpam-6489	658	13	s.	s.	PROPN
ejpam-6489	658	14	khan	khan	PROPN
ejpam-6489	658	15	,	,	PUNCT
ejpam-6489	658	16	and	and	CCONJ
ejpam-6489	658	17	f.	f.	PROPN
ejpam-6489	658	18	khan	khan	PROPN
ejpam-6489	658	19	.	.	PUNCT
ejpam-6489	659	1	confidence	confidence	NOUN
ejpam-6489	659	2	levels	level	VERB
ejpam-6489	659	3	bipolar	bipolar	ADJ
ejpam-6489	659	4	complex	complex	ADJ
ejpam-6489	659	5	fuzzy	fuzzy	ADJ
ejpam-6489	659	6	aggregation	aggregation	NOUN
ejpam-6489	659	7	operators	operator	NOUN
ejpam-6489	659	8	and	and	CCONJ
ejpam-6489	659	9	their	their	PRON
ejpam-6489	659	10	application	application	NOUN
ejpam-6489	659	11	in	in	ADP
ejpam-6489	659	12	decision	decision	NOUN
ejpam-6489	659	13	making	making	NOUN
ejpam-6489	659	14	problem	problem	NOUN
ejpam-6489	659	15	.	.	PUNCT
ejpam-6489	660	1	ieee	ieee	NOUN
ejpam-6489	660	2	access	access	NOUN
ejpam-6489	660	3	,	,	PUNCT
ejpam-6489	660	4	12:6204–6214	12:6204–6214	NUM
ejpam-6489	660	5	,	,	PUNCT
ejpam-6489	660	6	2024	2024	NUM
ejpam-6489	660	7	.	.	PUNCT
ejpam-6489	661	1	[	[	X
ejpam-6489	661	2	29	29	NUM
ejpam-6489	661	3	]	]	PUNCT
ejpam-6489	661	4	t.	t.	PROPN
ejpam-6489	661	5	prommai	prommai	PROPN
ejpam-6489	661	6	,	,	PUNCT
ejpam-6489	661	7	a.	a.	NOUN
ejpam-6489	661	8	iampan	iampan	PROPN
ejpam-6489	661	9	,	,	PUNCT
ejpam-6489	661	10	and	and	CCONJ
ejpam-6489	661	11	t.	t.	PROPN
ejpam-6489	661	12	gaketem	gaketem	PROPN
ejpam-6489	661	13	.	.	PUNCT
ejpam-6489	662	1	tripolar	tripolar	ADJ
ejpam-6489	662	2	fuzzy	fuzzy	ADJ
ejpam-6489	662	3	ideals	ideal	NOUN
ejpam-6489	662	4	in	in	ADP
ejpam-6489	662	5	semigroups	semigroup	NOUN
ejpam-6489	662	6	.	.	PUNCT
ejpam-6489	663	1	iaeng	iaeng	PROPN
ejpam-6489	663	2	international	international	PROPN
ejpam-6489	663	3	journal	journal	PROPN
ejpam-6489	663	4	of	of	ADP
ejpam-6489	663	5	applied	apply	VERB
ejpam-6489	663	6	mathematics	mathematic	NOUN
ejpam-6489	663	7	,	,	PUNCT
ejpam-6489	663	8	54(2):2775–2782	54(2):2775–2782	NUM
ejpam-6489	663	9	,	,	PUNCT
ejpam-6489	663	10	2024	2024	NUM
ejpam-6489	663	11	.	.	PUNCT
ejpam-6489	664	1	[	[	X
ejpam-6489	664	2	30	30	NUM
ejpam-6489	664	3	]	]	X
ejpam-6489	664	4	n.	n.	NOUN
ejpam-6489	664	5	wattanasiripong	wattanasiripong	PROPN
ejpam-6489	664	6	,	,	PUNCT
ejpam-6489	664	7	j.	j.	PROPN
ejpam-6489	664	8	mekwian	mekwian	PROPN
ejpam-6489	664	9	,	,	PUNCT
ejpam-6489	664	10	h.	h.	PROPN
ejpam-6489	664	11	sanpan	sanpan	PROPN
ejpam-6489	664	12	,	,	PUNCT
ejpam-6489	664	13	and	and	CCONJ
ejpam-6489	664	14	s.	s.	PROPN
ejpam-6489	664	15	lekkoksung	lekkoksung	PROPN
ejpam-6489	664	16	.	.	PUNCT
ejpam-6489	665	1	on	on	ADP
ejpam-6489	665	2	tripolar	tripolar	ADJ
ejpam-6489	665	3	fuzzy	fuzzy	ADJ
ejpam-6489	665	4	pure	pure	ADJ
ejpam-6489	665	5	ideals	ideal	NOUN
ejpam-6489	665	6	in	in	ADP
ejpam-6489	665	7	ordered	order	VERB
ejpam-6489	665	8	semigroups	semigroup	NOUN
ejpam-6489	665	9	.	.	PUNCT
ejpam-6489	666	1	international	international	ADJ
ejpam-6489	666	2	journal	journal	NOUN
ejpam-6489	666	3	of	of	ADP
ejpam-6489	666	4	analysis	analysis	NOUN
ejpam-6489	666	5	and	and	CCONJ
ejpam-6489	666	6	applications	application	NOUN
ejpam-6489	666	7	,	,	PUNCT
ejpam-6489	666	8	20:49	20:49	NUM
ejpam-6489	666	9	,	,	PUNCT
ejpam-6489	666	10	2022	2022	NUM
ejpam-6489	666	11	.	.	PUNCT
ejpam-6489	667	1	[	[	X
ejpam-6489	667	2	31	31	NUM
ejpam-6489	667	3	]	]	PUNCT
ejpam-6489	667	4	m.	m.	NOUN
ejpam-6489	667	5	balamurugan	balamurugan	NOUN
ejpam-6489	667	6	,	,	PUNCT
ejpam-6489	667	7	t.	t.	PROPN
ejpam-6489	667	8	ramesh	ramesh	PROPN
ejpam-6489	667	9	,	,	PUNCT
ejpam-6489	667	10	a.	a.	PROPN
ejpam-6489	667	11	al	al	PROPN
ejpam-6489	667	12	-	-	PROPN
ejpam-6489	667	13	masarwah	masarwah	PROPN
ejpam-6489	667	14	,	,	PUNCT
ejpam-6489	667	15	and	and	CCONJ
ejpam-6489	667	16	k.	k.	PROPN
ejpam-6489	667	17	a.	a.	PROPN
ejpam-6489	667	18	alsager	alsager	PROPN
ejpam-6489	667	19	.	.	PUNCT
ejpam-6489	668	1	a	a	DET
ejpam-6489	668	2	new	new	ADJ
ejpam-6489	668	3	approach	approach	NOUN
ejpam-6489	668	4	of	of	ADP
ejpam-6489	668	5	complex	complex	ADJ
ejpam-6489	668	6	fuzzy	fuzzy	ADJ
ejpam-6489	668	7	ideals	ideal	NOUN
ejpam-6489	668	8	in	in	ADP
ejpam-6489	668	9	bck	bck	PROPN
ejpam-6489	668	10	/	/	SYM
ejpam-6489	668	11	bci	bci	NOUN
ejpam-6489	668	12	-	-	PUNCT
ejpam-6489	668	13	algebras	algebra	NOUN
ejpam-6489	668	14	.	.	PUNCT
ejpam-6489	669	1	mathematics	mathematic	NOUN
ejpam-6489	669	2	,	,	PUNCT
ejpam-6489	669	3	12(10):1583	12(10):1583	NUM
ejpam-6489	669	4	,	,	PUNCT
ejpam-6489	669	5	2024	2024	NUM
ejpam-6489	669	6	.	.	PUNCT
ejpam-6489	670	1	[	[	X
ejpam-6489	670	2	32	32	NUM
ejpam-6489	670	3	]	]	PUNCT
ejpam-6489	670	4	a.	a.	PROPN
ejpam-6489	670	5	al	al	PROPN
ejpam-6489	670	6	-	-	PUNCT
ejpam-6489	670	7	masarwah	masarwah	PROPN
ejpam-6489	670	8	,	,	PUNCT
ejpam-6489	670	9	m.	m.	NOUN
ejpam-6489	670	10	balamurugan	balamurugan	NOUN
ejpam-6489	670	11	,	,	PUNCT
ejpam-6489	670	12	t.	t.	PROPN
ejpam-6489	670	13	ramesh	ramesh	PROPN
ejpam-6489	670	14	,	,	PUNCT
ejpam-6489	670	15	m.	m.	NOUN
ejpam-6489	670	16	abuqamar	abuqamar	PROPN
ejpam-6489	670	17	,	,	PUNCT
ejpam-6489	670	18	and	and	CCONJ
ejpam-6489	670	19	m.	m.	NOUN
ejpam-6489	670	20	a.	a.	NOUN
ejpam-6489	670	21	alshayea	alshayea	PROPN
ejpam-6489	670	22	.	.	PUNCT
ejpam-6489	671	1	m.	m.	NOUN
ejpam-6489	671	2	balamurugan	balamurugan	PROPN
ejpam-6489	671	3	,	,	PUNCT
ejpam-6489	671	4	g.	g.	PROPN
ejpam-6489	671	5	ellammal	ellammal	PROPN
ejpam-6489	671	6	,	,	PUNCT
ejpam-6489	671	7	a.	a.	NOUN
ejpam-6489	671	8	iampan	iampan	PROPN
ejpam-6489	671	9	/	/	SYM
ejpam-6489	671	10	eur	eur	PROPN
ejpam-6489	671	11	.	.	PUNCT
ejpam-6489	672	1	j.	j.	PROPN
ejpam-6489	672	2	pure	pure	PROPN
ejpam-6489	672	3	appl	appl	PROPN
ejpam-6489	672	4	.	.	PROPN
ejpam-6489	672	5	math	math	PROPN
ejpam-6489	672	6	,	,	PUNCT
ejpam-6489	672	7	18	18	NUM
ejpam-6489	672	8	(	(	PUNCT
ejpam-6489	672	9	3	3	NUM
ejpam-6489	672	10	)	)	PUNCT
ejpam-6489	672	11	(	(	PUNCT
ejpam-6489	672	12	2025	2025	NUM
ejpam-6489	672	13	)	)	PUNCT
ejpam-6489	672	14	,	,	PUNCT
ejpam-6489	672	15	6489	6489	NUM
ejpam-6489	672	16	26	26	NUM
ejpam-6489	672	17	of	of	ADP
ejpam-6489	672	18	26	26	NUM
ejpam-6489	672	19	an	an	DET
ejpam-6489	672	20	investigation	investigation	NOUN
ejpam-6489	672	21	of	of	ADP
ejpam-6489	672	22	complex	complex	ADJ
ejpam-6489	672	23	linear	linear	ADJ
ejpam-6489	672	24	diophantine	diophantine	VERB
ejpam-6489	672	25	fuzzy	fuzzy	ADJ
ejpam-6489	672	26	ideals	ideal	NOUN
ejpam-6489	672	27	in	in	ADP
ejpam-6489	672	28	bck	bck	NOUN
ejpam-6489	672	29	-	-	PUNCT
ejpam-6489	672	30	algebras	algebras	PROPN
ejpam-6489	672	31	.	.	PUNCT
ejpam-6489	673	1	international	international	ADJ
ejpam-6489	673	2	journal	journal	PROPN
ejpam-6489	673	3	of	of	ADP
ejpam-6489	673	4	neutrosophic	neutrosophic	ADJ
ejpam-6489	673	5	science	science	NOUN
ejpam-6489	673	6	,	,	PUNCT
ejpam-6489	673	7	26(3):26–48	26(3):26–48	NUM
ejpam-6489	673	8	,	,	PUNCT
ejpam-6489	673	9	2025	2025	NUM
ejpam-6489	673	10	.	.	PUNCT